From ad8a49371ad75edb3078615a4fb2f23adf030ef5 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 8 Jun 2024 20:53:24 +0000 Subject: [PATCH] build based on ccaa3ac --- dev/404.html | 10 ++-- dev/api.html | 28 ++++----- dev/article01.html | 20 +++---- dev/assets/api.md.BiqC9tVJ.js | 58 +++++++++++++++++++ dev/assets/api.md.BiqC9tVJ.lean.js | 1 + dev/assets/api.md.CM80ZGQK.js | 58 ------------------- dev/assets/api.md.CM80ZGQK.lean.js | 1 - dev/assets/app.DJvmlMci.js | 1 + dev/assets/app.s0WURkb8.js | 1 - dev/assets/article01.md.BL6r3tif.lean.js | 1 - ...d.BL6r3tif.js => article01.md.BrGXw77Y.js} | 6 +- dev/assets/article01.md.BrGXw77Y.lean.js | 1 + ...aXJV.js => biomarkovchains.md.0rg0z1ev.js} | 2 +- ...js => biomarkovchains.md.0rg0z1ev.lean.js} | 2 +- .../chunks/@localSearchIndexroot.Bh2pKAzu.js | 1 - .../chunks/@localSearchIndexroot.Bj-EWWk0.js | 1 + .../chunks/VPLocalSearchBox.CaalGK9M.js | 7 --- .../chunks/VPLocalSearchBox.DqWxI-Ji.js | 7 +++ dev/assets/chunks/framework.Cvv1S4VC.js | 17 ++++++ dev/assets/chunks/framework.D1rHXXmm.js | 17 ------ dev/assets/chunks/theme.BWgOxzZE.js | 7 --- dev/assets/chunks/theme.CNBIs78H.js | 2 + ....BxUYlh-U.js => getstarted.md.EJuNxDSJ.js} | 8 +-- ...lean.js => getstarted.md.EJuNxDSJ.lean.js} | 2 +- ...ome.md.nGdy1Xvl.js => home.md.DYCAAGxb.js} | 2 +- ...y1Xvl.lean.js => home.md.DYCAAGxb.lean.js} | 2 +- dev/assets/index.md.Ba-cgBKx.js | 1 + ...IapY.lean.js => index.md.Ba-cgBKx.lean.js} | 2 +- dev/assets/index.md.mmk1IapY.js | 1 - dev/assets/style.BSicJgYg.css | 1 + dev/assets/style.COODeMdn.css | 1 - dev/biomarkovchains.html | 16 ++--- dev/getstarted.html | 22 +++---- dev/hashmap.json | 2 +- dev/home.html | 16 ++--- dev/index.html | 16 ++--- 36 files changed, 168 insertions(+), 173 deletions(-) create mode 100644 dev/assets/api.md.BiqC9tVJ.js create mode 100644 dev/assets/api.md.BiqC9tVJ.lean.js delete mode 100644 dev/assets/api.md.CM80ZGQK.js delete mode 100644 dev/assets/api.md.CM80ZGQK.lean.js create mode 100644 dev/assets/app.DJvmlMci.js delete mode 100644 dev/assets/app.s0WURkb8.js delete mode 100644 dev/assets/article01.md.BL6r3tif.lean.js rename dev/assets/{article01.md.BL6r3tif.js => article01.md.BrGXw77Y.js} (79%) create mode 100644 dev/assets/article01.md.BrGXw77Y.lean.js rename dev/assets/{biomarkovchains.md.DhkAaXJV.js => biomarkovchains.md.0rg0z1ev.js} (99%) rename dev/assets/{biomarkovchains.md.DhkAaXJV.lean.js => biomarkovchains.md.0rg0z1ev.lean.js} (99%) delete mode 100644 dev/assets/chunks/@localSearchIndexroot.Bh2pKAzu.js create mode 100644 dev/assets/chunks/@localSearchIndexroot.Bj-EWWk0.js delete mode 100644 dev/assets/chunks/VPLocalSearchBox.CaalGK9M.js create mode 100644 dev/assets/chunks/VPLocalSearchBox.DqWxI-Ji.js create mode 100644 dev/assets/chunks/framework.Cvv1S4VC.js delete mode 100644 dev/assets/chunks/framework.D1rHXXmm.js delete mode 100644 dev/assets/chunks/theme.BWgOxzZE.js create mode 100644 dev/assets/chunks/theme.CNBIs78H.js rename dev/assets/{getstarted.md.BxUYlh-U.js => getstarted.md.EJuNxDSJ.js} (88%) rename dev/assets/{getstarted.md.BxUYlh-U.lean.js => getstarted.md.EJuNxDSJ.lean.js} (95%) rename dev/assets/{home.md.nGdy1Xvl.js => home.md.DYCAAGxb.js} (85%) rename dev/assets/{home.md.nGdy1Xvl.lean.js => home.md.DYCAAGxb.lean.js} (85%) create mode 100644 dev/assets/index.md.Ba-cgBKx.js rename dev/assets/{index.md.mmk1IapY.lean.js => index.md.Ba-cgBKx.lean.js} (60%) delete mode 100644 dev/assets/index.md.mmk1IapY.js create mode 100644 dev/assets/style.BSicJgYg.css delete mode 100644 dev/assets/style.COODeMdn.css diff --git a/dev/404.html b/dev/404.html index c370f1a..5bfc900 100644 --- a/dev/404.html +++ b/dev/404.html @@ -5,17 +5,17 @@ 404 | BioMarkovChains.jl - - + + - + -
BioMarkovChains.jl

Appearance

404

PAGE NOT FOUND

But if you don't change your direction, and if you keep looking, you may end up where you are heading.
Take me home
- +
+ \ No newline at end of file diff --git a/dev/api.html b/dev/api.html index 9cc57eb..f8753b1 100644 --- a/dev/api.html +++ b/dev/api.html @@ -5,19 +5,19 @@ BioMarkovChains.jl - - + + - + - - - + + + -
BioMarkovChains.jl

Appearance

# BioMarkovChains.BMC — Type.
julia
BMC

Alias for the type BioMarkovChain.

source


# BioMarkovChains.BioMarkovChain — Type.
julia
struct BioMarkovChain{S<:DataType, M<:AbstractMatrix, I<:AbstractVector, N<:Integer} <: AbstractBioMarkovChain

A BioMarkovChain represents a Markov chain used in biological sequence analysis. It contains a transition probability matrix (tpm) and an initial distribution of probabilities (inits) and also the order of the Markov chain.

Fields

  • alphabet::A: Is the state space of the sequence whether DNA, RNA AminoAcid DataTypes.

  • tpm::M: The transition probability matrix.

  • inits::I: The initial distribution of probabilities.

  • n::N: The order of the Markov chain.

Constructors

  • BioMarkovChain(tpm::M, inits::I, n::N=1) where {M<:AbstractMatrix, I<:AbstractVector, N<:Integer}: Constructs a BioMarkovChain object with the provided transition probability matrix, initial distribution, and order.

  • BioMarkovChain(sequence::LongNucOrView{4}, n::Int64=1): Constructs a BioMarkovChain object based on the DNA sequence and transition order.

Example

julia
sequence = LongDNA{4}("ACTACATCTA")
+    
BioMarkovChains.jl
Appearance
# BioMarkovChains.BMC — Type. 
julia
BMC
Alias for the type BioMarkovChain.
source

# BioMarkovChains.BioMarkovChain — Type. 
julia
struct BioMarkovChain{S<:DataType, M<:AbstractMatrix, I<:AbstractVector, N<:Integer} <: AbstractBioMarkovChain
A BioMarkovChain represents a Markov chain used in biological sequence analysis. It contains a transition probability matrix (tpm) and an initial distribution of probabilities (inits) and also the order of the Markov chain.
Fields
  • alphabet::A: Is the state space of the sequence whether DNA, RNA AminoAcid DataTypes.
  • tpm::M: The transition probability matrix.
  • inits::I: The initial distribution of probabilities.
  • n::N: The order of the Markov chain.
Constructors
  • BioMarkovChain(tpm::M, inits::I, n::N=1) where {M<:AbstractMatrix, I<:AbstractVector, N<:Integer}: Constructs a BioMarkovChain object with the provided transition probability matrix, initial distribution, and order.
  • BioMarkovChain(sequence::LongNucOrView{4}, n::Int64=1): Constructs a BioMarkovChain object based on the DNA sequence and transition order.
Example
julia
sequence = LongDNA{4}("ACTACATCTA")
 
 model = BioMarkovChain(sequence, 2)
 BioMarkovChain of DNAAlphabet{4}() and order 1:
@@ -30,7 +30,7 @@
    0.3333
    0.3333
    0.0
-   0.3333
source

# BioMarkovChains.dnaseqprobability — Method. 
julia
dnaseqprobability(sequence::LongNucOrView{4}, model::BioMarkovChain)
Compute the probability of a given sequence using a transition probability matrix and the initial probabilities distributions of a BioMarkovModel.
P(X1=i1,…,XT=iT)=πi1T−1∏t=1T−1ait,it+1
Arguments
  • sequence::LongNucOrView{4}: The input sequence of nucleotides.
  • model::BioMarkovChain: A given BioMarkovChain.
Returns
  • probability::Float64: The probability of the input sequence given the model.
Example
julia
mainseq = LongDNA{4}("CCTCCCGGACCCTGGGCTCGGGAC")
+   0.3333
source

# BioMarkovChains.dnaseqprobability — Method. 
julia
dnaseqprobability(sequence::LongNucOrView{4}, model::BioMarkovChain)
Compute the probability of a given sequence using a transition probability matrix and the initial probabilities distributions of a BioMarkovModel.
P(X1=i1,…,XT=iT)=πi1T−1∏t=1T−1ait,it+1
Arguments
  • sequence::LongNucOrView{4}: The input sequence of nucleotides.
  • model::BioMarkovChain: A given BioMarkovChain.
Returns
  • probability::Float64: The probability of the input sequence given the model.
Example
julia
mainseq = LongDNA{4}("CCTCCCGGACCCTGGGCTCGGGAC")
    
 bmc = BioMarkovChain(mainseq)
 
@@ -54,11 +54,11 @@
 
 dnaseqprobability(newseq, bmc)
     
-    0.021739130434782608
source

# BioMarkovChains.initials — Method. 
julia
initials(sequence::SeqOrView{A}) where A
Calculate the estimated initial probabilities for a Markov chain based on a given sequence.
This function takes a sequence of states and calculates the estimated initial probabilities of each state in the sequence for a Markov chain. The initial probabilities are estimated by counting the occurrences of each state at the beginning of the sequence and normalizing the counts to sum up to 1.
πi=P(Xi=i),i∈T∑i=1Nπi=1
Now using the dinucleotides counts estimating the initials would follow:
πi^=ci∑kck
Arguments
  • sequence::SeqOrView{A}: The sequence of states representing the Markov chain.
Returns
An Vector{Flot64} of estimated initial probabilities for each state in the sequence.
source

# BioMarkovChains.log_odds_ratio_matrix — Method. 
julia
log_odds_ratio_matrix(model1::BioMarkovChain, model2::BioMarkovChain)
Calculates the log-odds ratio between the transition probability matrices of two BioMarkovChain models.
β=log⁡P(x|m1)P(x|m2)
Where m1 and m2 are the two models transition probability matrices.
Arguments
  • model1::BioMarkovChain: The first BioMarkovChain model.
  • model2::BioMarkovChain: The second BioMarkovChain model.
source

# BioMarkovChains.log_odds_ratio_matrix — Method. 
julia
log_odds_ratio_matrix(sequence::NucleicSeqOrView{A}, model::BioMarkovChain) where A
Calculates the log-odds ratio between the transition probability matrix of a given DNA sequence and a reference model.
Arguments
  • sequence::NucleicSeqOrView{A}: A DNA, RNA sequence or view with a length of 4 nucleotides.
  • model::BioMarkovChain: A reference BioMarkovChain model.
Examples
julia
sequence = LongNucOrView{4}("ACGT")
+    0.021739130434782608
source

# BioMarkovChains.initials — Method. 
julia
initials(sequence::SeqOrView{A}) where A
Calculate the estimated initial probabilities for a Markov chain based on a given sequence.
This function takes a sequence of states and calculates the estimated initial probabilities of each state in the sequence for a Markov chain. The initial probabilities are estimated by counting the occurrences of each state at the beginning of the sequence and normalizing the counts to sum up to 1.
πi=P(Xi=i),i∈T∑i=1Nπi=1
Now using the dinucleotides counts estimating the initials would follow:
πi^=ci∑kck
Arguments
  • sequence::SeqOrView{A}: The sequence of states representing the Markov chain.
Returns
An Vector{Flot64} of estimated initial probabilities for each state in the sequence.
source

# BioMarkovChains.log_odds_ratio_matrix — Method. 
julia
log_odds_ratio_matrix(model1::BioMarkovChain, model2::BioMarkovChain)
Calculates the log-odds ratio between the transition probability matrices of two BioMarkovChain models.
β=log⁡P(x|m1)P(x|m2)
Where m1 and m2 are the two models transition probability matrices.
Arguments
  • model1::BioMarkovChain: The first BioMarkovChain model.
  • model2::BioMarkovChain: The second BioMarkovChain model.
source

# BioMarkovChains.log_odds_ratio_matrix — Method. 
julia
log_odds_ratio_matrix(sequence::NucleicSeqOrView{A}, model::BioMarkovChain) where A
Calculates the log-odds ratio between the transition probability matrix of a given DNA sequence and a reference model.
Arguments
  • sequence::NucleicSeqOrView{A}: A DNA, RNA sequence or view with a length of 4 nucleotides.
  • model::BioMarkovChain: A reference BioMarkovChain model.
Examples
julia
sequence = LongNucOrView{4}("ACGT")
 model = BioMarkovChain(sequence)  # Provide appropriate initialization for BioMarkovChain
-result = log_odds_ratio_matrix(sequence, model)
source

# BioMarkovChains.log_odds_ratio_score — Method. 
julia
log_odds_ratio_score(sequence::SeqOrView{A}, model::BioMarkovChain; b::Number = ℯ)
Compute the log odds ratio score between a given sequence and a BioMarkovChain model.
S(x)=∑i=1Lβxix=∑i=1log⁡ai−1m1xiai−1m2xi
Arguments
  • sequence::SeqOrView{A}: A sequence of elements of type A.
  • model::BioMarkovChain: A BioMarkovChain model.
  • b::Number = ℯ: The base of the logarithm used to compute the log odds ratio.
Returns
The log odds ratio score between the sequence and the model.
Example
source

# BioMarkovChains.perronfrobenius — Method. 
julia
perronfrobenius(sequence::SeqOrView{A}, n::Int64=1) where A
Compute the Perron-Frobenius matrix, a column-stochastic version of the transition probability matrix (TPM), for a given nucleotide sequence.
The Perron-Frobenius matrix captures the asymptotic probabilities of transitioning between nucleotides in the sequence over a specified number of steps n. It provides insight into the long-term behavior of a Markov chain or a dynamical system associated with the sequence.
Arguments
  • sequence::SeqOrView{A}: A nucleotide sequence represented as a NucleicSeqOrView{A} object.
  • n::Int64=1: The number of steps to consider for the transition probability matrix. Default is 1.
Returns
A copy of the Perron-Frobenius matrix. Each column of this matrix corresponds to the probabilities of transitioning from the current nucleotide state to all possible nucleotide states after n steps.
Example
julia
sequence = LongSequence{DNAAlphabet{4}}("ACGTCGTCCACTACGACATCAGC")  # Replace with an actual nucleotide sequence
+result = log_odds_ratio_matrix(sequence, model)
source

# BioMarkovChains.log_odds_ratio_score — Method. 
julia
log_odds_ratio_score(sequence::SeqOrView{A}, model::BioMarkovChain; b::Number = ℯ)
Compute the log odds ratio score between a given sequence and a BioMarkovChain model.
S(x)=∑i=1Lβxix=∑i=1log⁡ai−1m1xiai−1m2xi
Arguments
  • sequence::SeqOrView{A}: A sequence of elements of type A.
  • model::BioMarkovChain: A BioMarkovChain model.
  • b::Number = ℯ: The base of the logarithm used to compute the log odds ratio.
Returns
The log odds ratio score between the sequence and the model.
Example
source

# BioMarkovChains.perronfrobenius — Method. 
julia
perronfrobenius(sequence::SeqOrView{A}, n::Int64=1) where A
Compute the Perron-Frobenius matrix, a column-stochastic version of the transition probability matrix (TPM), for a given nucleotide sequence.
The Perron-Frobenius matrix captures the asymptotic probabilities of transitioning between nucleotides in the sequence over a specified number of steps n. It provides insight into the long-term behavior of a Markov chain or a dynamical system associated with the sequence.
Arguments
  • sequence::SeqOrView{A}: A nucleotide sequence represented as a NucleicSeqOrView{A} object.
  • n::Int64=1: The number of steps to consider for the transition probability matrix. Default is 1.
Returns
A copy of the Perron-Frobenius matrix. Each column of this matrix corresponds to the probabilities of transitioning from the current nucleotide state to all possible nucleotide states after n steps.
Example
julia
sequence = LongSequence{DNAAlphabet{4}}("ACGTCGTCCACTACGACATCAGC")  # Replace with an actual nucleotide sequence
 n = 2
-pf = perronfrobenius(sequence, n)
source

# BioMarkovChains.transition_count_matrix — Method. 
julia
transition_count_matrix(sequence::LongSequence{DNAAlphabet{4}})
Compute the transition count matrix (TCM) of a given DNA sequence.
Arguments
  • sequence::LongSequence{DNAAlphabet{4}}: a LongSequence{DNAAlphabet{4}} object representing the DNA sequence.
Returns
A Matrix object representing the transition count matrix of the sequence.
Example
seq = LongDNA{4}("AGCTAGCTAGCT")
+pf = perronfrobenius(sequence, n)
source

# BioMarkovChains.transition_count_matrix — Method. 
julia
transition_count_matrix(sequence::LongSequence{DNAAlphabet{4}})
Compute the transition count matrix (TCM) of a given DNA sequence.
Arguments
  • sequence::LongSequence{DNAAlphabet{4}}: a LongSequence{DNAAlphabet{4}} object representing the DNA sequence.
Returns
A Matrix object representing the transition count matrix of the sequence.
Example
seq = LongDNA{4}("AGCTAGCTAGCT")
 
 tcm = transition_count_matrix(seq)
 
@@ -66,7 +66,7 @@
  0  0  3  0
  0  0  0  3
  0  3  0  0
- 2  0  0  0
source

# BioMarkovChains.transition_probability_matrix — Method. 
julia
transition_probability_matrix(sequence::LongSequence{DNAAlphabet{4}}, n::Int64=1)
Compute the transition probability matrix (TPM) of a given DNA sequence. Formally it construct M^ where:
mij=P(Xt=j∣Xt−1=i)=P(Xt−1=i,Xt=j)P(Xt−1=i)
The transition matrices of DNA and Amino-Acids are arranged sorted and in row-wise matrices:
First the DNA matrix:
MDNA=[AAACAGATCACCCGCTGAGCGGGTTATCTGTT]
And then, the Aminoacids:
MAA=[AAACAD…AWCACCCD…CWDADCDD…DW⋮⋮⋮⋱⋮WAWCWD…WW]
Arguments
  • sequence::LongNucOrView{4}: a LongNucOrView{4} object representing the DNA sequence.
  • n::Int64=1: The order of the Markov model. That is the M^n
Keywords
  • extended_alphabet::Bool=false: If true will pass the extended alphabet of DNA to search
Returns
A Matrix object representing the transition probability matrix of the sequence.
Example
julia
seq = dna"AGCTAGCTAGCT"
+ 2  0  0  0
source

# BioMarkovChains.transition_probability_matrix — Method. 
julia
transition_probability_matrix(sequence::LongSequence{DNAAlphabet{4}}, n::Int64=1)
Compute the transition probability matrix (TPM) of a given DNA sequence. Formally it construct M^ where:
mij=P(Xt=j∣Xt−1=i)=P(Xt−1=i,Xt=j)P(Xt−1=i)
The transition matrices of DNA and Amino-Acids are arranged sorted and in row-wise matrices:
First the DNA matrix:
MDNA=[AAACAGATCACCCGCTGAGCGGGTTATCTGTT]
And then, the Aminoacids:
MAA=[AAACAD…AWCACCCD…CWDADCDD…DW⋮⋮⋮⋱⋮WAWCWD…WW]
Arguments
  • sequence::LongNucOrView{4}: a LongNucOrView{4} object representing the DNA sequence.
  • n::Int64=1: The order of the Markov model. That is the M^n
Keywords
  • extended_alphabet::Bool=false: If true will pass the extended alphabet of DNA to search
Returns
A Matrix object representing the transition probability matrix of the sequence.
Example
julia
seq = dna"AGCTAGCTAGCT"
 
 tpm = transition_probability_matrix(seq)
 
@@ -74,8 +74,8 @@
  0.0  0.0  1.0  0.0
  0.0  0.0  0.0  1.0
  0.0  1.0  0.0  0.0
- 1.0  0.0  0.0  0.0
source


-    
+ 1.0  0.0  0.0  0.0

source


+ \ No newline at end of file diff --git a/dev/article01.html b/dev/article01.html index f0f4fc7..29ce82c 100644 --- a/dev/article01.html +++ b/dev/article01.html @@ -5,19 +5,19 @@ From BMC to sequence probabilties | BioMarkovChains.jl - - + + - + - - - + + + -
BioMarkovChains.jl

Appearance

From BMC to sequence probabilties ​

We can now calculate a transition probability matrix from a LongDNA sequence using the transition_probability_matrix and initials methods:

julia
using BioSequences
+    
BioMarkovChains.jl
Appearance
From BMC to sequence probabilties ​
We can now calculate a transition probability matrix from a LongDNA sequence using the transition_probability_matrix and initials methods:
julia
using BioSequences
 
 sequence = dna"CCTCCCGGACCCTGGGCTCGGGAC"
 
@@ -25,7 +25,7 @@
 initials = initials(sequence)
 
 println(tpm)
-println(initials)
4×4 Matrix{Float64}:
+println(initials)
4×4 Matrix{Float64}:
  0.0   1.0       0.0       0.0
  0.0   0.5       0.2       0.3
  0.25  0.125     0.625     0.0
@@ -35,8 +35,8 @@
  0.08695652173913043
  0.43478260869565216
  0.34782608695652173
- 0.13043478260869565

-    
+ 0.13043478260869565
+ \ No newline at end of file diff --git a/dev/assets/api.md.BiqC9tVJ.js b/dev/assets/api.md.BiqC9tVJ.js new file mode 100644 index 0000000..941a69f --- /dev/null +++ b/dev/assets/api.md.BiqC9tVJ.js @@ -0,0 +1,58 @@ +import{_ as T,c as s,j as a,a as t,a6 as Q,o as e}from"./chunks/framework.Cvv1S4VC.js";const c6=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),l={name:"api.md"},n=Q(`
# BioMarkovChains.BMC — Type.
julia
BMC

Alias for the type BioMarkovChain.

source


# BioMarkovChains.BioMarkovChain — Type.
julia
struct BioMarkovChain{S<:DataType, M<:AbstractMatrix, I<:AbstractVector, N<:Integer} <: AbstractBioMarkovChain

A BioMarkovChain represents a Markov chain used in biological sequence analysis. It contains a transition probability matrix (tpm) and an initial distribution of probabilities (inits) and also the order of the Markov chain.

Fields

Constructors

Example

julia
sequence = LongDNA{4}("ACTACATCTA")
+
+model = BioMarkovChain(sequence, 2)
+BioMarkovChain of DNAAlphabet{4}() and order 1:
+  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
+   0.0     0.6667  0.0     0.3333
+   0.3333  0.0     0.0     0.6667
+   0.0     0.0     0.0     0.0
+   0.6667  0.3333  0.0     0.0
+  - Initial Probabilities -> Vector{Float64}(4 × 1):
+   0.3333
+   0.3333
+   0.0
+   0.3333

source


`,4),i={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},d=a("a",{id:"BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet",href:"#BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet"},"#",-1),o=a("b",null,[a("u",null,"BioMarkovChains.dnaseqprobability")],-1),m=a("i",null,"Method",-1),r=Q('
julia
dnaseqprobability(sequence::LongNucOrView{4}, model::BioMarkovChain)

Compute the probability of a given sequence using a transition probability matrix and the initial probabilities distributions of a BioMarkovModel.

',2),h={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},p={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.819ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.497ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1728.7 18341.5 2974.6","aria-hidden":"true"},g=Q('',1),c=[g],k=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mn",null,"1")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mn",null,"1")]),a("mo",null,","),a("mo",null,"…"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"T")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mi",null,"T")]),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("msubsup",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mn",null,"1")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∏"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("msub",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mi",null,"t")]),a("mo",null,","),a("msub",null,[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])])])])])],-1),u=Q(`

Arguments

Returns

Example

julia
mainseq = LongDNA{4}("CCTCCCGGACCCTGGGCTCGGGAC")
+   
+bmc = BioMarkovChain(mainseq)
+
+    BioMarkovChain of DNAAlphabet{4}() and order 1:
+      - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
+       0.0     1.0     0.0     0.0
+       0.0     0.5     0.2     0.3
+       0.25    0.125   0.625   0.0
+       0.0     0.6667  0.3333  0.0
+      - Initial Probabilities -> Vector{Float64}(4 × 1):
+       0.087
+       0.4348
+       0.3478
+       0.1304
+
+newseq = LongDNA{4}("CCTG")
+
+    4nt DNA Sequence:
+    CCTG
+
+
+dnaseqprobability(newseq, bmc)
+    
+    0.021739130434782608

source

`,7),H=a("br",null,null,-1),x={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},y=a("a",{id:"BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet"},"#",-1),L=a("b",null,[a("u",null,"BioMarkovChains.initials")],-1),w=a("i",null,"Method",-1),b=Q('
julia
initials(sequence::SeqOrView{A}) where A

Calculate the estimated initial probabilities for a Markov chain based on a given sequence.

This function takes a sequence of states and calculates the estimated initial probabilities of each state in the sequence for a Markov chain. The initial probabilities are estimated by counting the occurrences of each state at the beginning of the sequence and normalizing the counts to sum up to 1.

',3),_={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-4.275ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.706ex",height:"9.681ex",role:"img",focusable:"false",viewBox:"0 -2389.4 10919.9 4278.9","aria-hidden":"true"},f=Q('',1),C=[f],D=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mtable",{displaystyle:"true",columnalign:"right left",columnspacing:"0em",rowspacing:"3pt"},[a("mtr",null,[a("mtd",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,","),a("mi",null,"i"),a("mo",null,"∈"),a("mi",null,"T")])]),a("mtr",null,[a("mtd",null,[a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"N")])]),a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mn",null,"1")])])])])],-1),A=a("p",null,"Now using the dinucleotides counts estimating the initials would follow:",-1),E={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.75ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.788ex",height:"4.899ex",role:"img",focusable:"false",viewBox:"0 -950 5652.2 2165.5","aria-hidden":"true"},v=Q('',1),F=[v],B=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",{stretchy:"false"},"^")])]),a("mo",null,"="),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])]),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])])])],-1),V=a("p",null,[a("strong",null,"Arguments")],-1),j=a("ul",null,[a("li",null,[a("code",null,"sequence::SeqOrView{A}"),t(": The sequence of states representing the Markov chain.")])],-1),R=a("p",null,[a("strong",null,"Returns")],-1),O=a("p",null,[t("An "),a("code",null,"Vector{Flot64}"),t(" of estimated initial probabilities for each state in the sequence.")],-1),S=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),q=a("br",null,null,-1),X={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},N=a("a",{id:"BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}",href:"#BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}"},"#",-1),P=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_matrix")],-1),I=a("i",null,"Method",-1),G=Q('
julia
log_odds_ratio_matrix(model1::BioMarkovChain, model2::BioMarkovChain)

Calculates the log-odds ratio between the transition probability matrices of two BioMarkovChain models.

',2),U={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"16.289ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 7199.8 2420","aria-hidden":"true"},J=Q('𝓂𝓂',1),W=[J],$=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"β"),a("mo",null,"="),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])]),a("mo",{stretchy:"false"},")")]),a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])]),a("mo",{stretchy:"false"},")")])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},a2=Q('𝓂',1),t2=[a2],Q2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])],-1),s2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},T2=Q('𝓂',1),l2=[T2],n2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])],-1),i2=a("p",null,[a("strong",null,"Arguments")],-1),d2=a("ul",null,[a("li",null,[a("p",null,[a("code",null,"model1::BioMarkovChain"),t(": The first BioMarkovChain model.")])]),a("li",null,[a("p",null,[a("code",null,"model2::BioMarkovChain"),t(": The second BioMarkovChain model.")])])],-1),o2=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),m2=Q(`
# BioMarkovChains.log_odds_ratio_matrix — Method.
julia
log_odds_ratio_matrix(sequence::NucleicSeqOrView{A}, model::BioMarkovChain) where A

Calculates the log-odds ratio between the transition probability matrix of a given DNA sequence and a reference model.

Arguments

Examples

julia
sequence = LongNucOrView{4}("ACGT")
+model = BioMarkovChain(sequence)  # Provide appropriate initialization for BioMarkovChain
+result = log_odds_ratio_matrix(sequence, model)

source


`,3),r2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},h2=a("a",{id:"BioMarkovChains.log_odds_ratio_score-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.log_odds_ratio_score-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet"},"#",-1),p2=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_score")],-1),g2=a("i",null,"Method",-1),c2=Q('
julia
log_odds_ratio_score(sequence::SeqOrView{A}, model::BioMarkovChain; b::Number = ℯ)

Compute the log odds ratio score between a given sequence and a BioMarkovChain model.

',2),k2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.936ex",height:"7.198ex",role:"img",focusable:"false",viewBox:"0 -1840.7 14115.8 3181.3","aria-hidden":"true"},H2=Q('𝓂𝓂',1),x2=[H2],y2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"S"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"L")])]),a("msub",null,[a("mi",null,"β"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"x"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mi",null,"x")])]),a("mo",null,"="),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")])]),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])]),a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])])])])],-1),L2=Q('

Arguments

Returns

The log odds ratio score between the sequence and the model.

Example

source

',6),w2=Q(`
# BioMarkovChains.perronfrobenius — Method.
julia
perronfrobenius(sequence::SeqOrView{A}, n::Int64=1) where A

Compute the Perron-Frobenius matrix, a column-stochastic version of the transition probability matrix (TPM), for a given nucleotide sequence.

The Perron-Frobenius matrix captures the asymptotic probabilities of transitioning between nucleotides in the sequence over a specified number of steps n. It provides insight into the long-term behavior of a Markov chain or a dynamical system associated with the sequence.

Arguments

Returns

A copy of the Perron-Frobenius matrix. Each column of this matrix corresponds to the probabilities of transitioning from the current nucleotide state to all possible nucleotide states after n steps.

Example

julia
sequence = LongSequence{DNAAlphabet{4}}("ACGTCGTCCACTACGACATCAGC")  # Replace with an actual nucleotide sequence
+n = 2
+pf = perronfrobenius(sequence, n)

source


# BioMarkovChains.transition_count_matrix — Method.
julia
transition_count_matrix(sequence::LongSequence{DNAAlphabet{4}})

Compute the transition count matrix (TCM) of a given DNA sequence.

Arguments

Returns

A Matrix object representing the transition count matrix of the sequence.

Example

seq = LongDNA{4}("AGCTAGCTAGCT")
+
+tcm = transition_count_matrix(seq)
+
+4×4 Matrix{Int64}:
+ 0  0  3  0
+ 0  0  0  3
+ 0  3  0  0
+ 2  0  0  0

source


`,5),b2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},_2=a("a",{id:"BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet"},"#",-1),M2=a("b",null,[a("u",null,"BioMarkovChains.transition_probability_matrix")],-1),f2=a("i",null,"Method",-1),C2=Q('
julia
transition_probability_matrix(sequence::LongSequence{DNAAlphabet{4}}, n::Int64=1)
',1),D2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.577ex",role:"img",focusable:"false",viewBox:"0 -1089 1216 1139","aria-hidden":"true"},E2=Q('',1),Z2=[E2],v2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mo",{stretchy:"false"},"^")])])])],-1),F2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},B2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.734ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 21982.3 2420","aria-hidden":"true"},V2=Q('𝓂',1),j2=[V2],R2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",null,"∣"),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("mfrac",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",{stretchy:"false"},")")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")")])])])],-1),O2=a("p",null,"The transition matrices of DNA and Amino-Acids are arranged sorted and in row-wise matrices:",-1),S2=a("p",null,"First the DNA matrix:",-1),q2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},X2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-5.317ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.979ex",height:"11.765ex",role:"img",focusable:"false",viewBox:"0 -2850 13250.7 5200","aria-hidden":"true"},N2=Q('',1),P2=[N2],I2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"N"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"T")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),G2=a("p",null,"And then, the Aminoacids:",-1),U2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-7.771ex"},xmlns:"http://www.w3.org/2000/svg",width:"35.891ex",height:"16.674ex",role:"img",focusable:"false",viewBox:"0 -3935 15863.7 7370","aria-hidden":"true"},J2=Q('',1),W2=[J2],$2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mo",null,"⋱")]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"W")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),K2=a("p",null,[a("strong",null,"Arguments")],-1),Y2=a("li",null,[a("p",null,[a("code",null,"sequence::LongNucOrView{4}"),t(": a "),a("code",null,"LongNucOrView{4}"),t(" object representing the DNA sequence.")])],-1),a6=a("code",null,"n::Int64=1",-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"3.648ex",height:"2.378ex",role:"img",focusable:"false",viewBox:"0 -1051 1612.3 1051","aria-hidden":"true"},s6=Q('',1),e6=[s6],T6=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",null,"M"),a("mo",{stretchy:"false"},"^")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])])])],-1),l6=Q(`

Keywords

Returns

A Matrix object representing the transition probability matrix of the sequence.

Example

julia
seq = dna"AGCTAGCTAGCT"
+
+tpm = transition_probability_matrix(seq)
+
+4×4 Matrix{Float64}:
+ 0.0  0.0  1.0  0.0
+ 0.0  0.0  0.0  1.0
+ 0.0  1.0  0.0  0.0
+ 1.0  0.0  0.0  0.0

source

`,7),n6=a("br",null,null,-1);function i6(d6,o6,m6,r6,h6,p6){return e(),s("div",null,[n,a("div",i,[d,t(" "),o,t(" — "),m,t(". "),r,a("mjx-container",h,[(e(),s("svg",p,c)),k]),u]),H,a("div",x,[y,t(" "),L,t(" — "),w,t(". "),b,a("mjx-container",_,[(e(),s("svg",M,C)),D]),A,a("mjx-container",E,[(e(),s("svg",Z,F)),B]),V,j,R,O,S]),q,a("div",X,[N,t(" "),P,t(" — "),I,t(". "),G,a("mjx-container",U,[(e(),s("svg",z,W)),$]),a("p",null,[t("Where "),a("mjx-container",K,[(e(),s("svg",Y,t2)),Q2]),t(" and "),a("mjx-container",s2,[(e(),s("svg",e2,l2)),n2]),t(" are the two models transition probability matrices.")]),i2,d2,o2]),m2,a("div",r2,[h2,t(" "),p2,t(" — "),g2,t(". "),c2,a("mjx-container",k2,[(e(),s("svg",u2,x2)),y2]),L2]),w2,a("div",b2,[_2,t(" "),M2,t(" — "),f2,t(". "),C2,a("p",null,[t("Compute the transition probability matrix (TPM) of a given DNA sequence. Formally it construct "),a("mjx-container",D2,[(e(),s("svg",A2,Z2)),v2]),t(" where:")]),a("mjx-container",F2,[(e(),s("svg",B2,j2)),R2]),O2,S2,a("mjx-container",q2,[(e(),s("svg",X2,P2)),I2]),G2,a("mjx-container",U2,[(e(),s("svg",z2,W2)),$2]),K2,a("ul",null,[Y2,a("li",null,[a("p",null,[a6,t(": The order of the Markov model. That is the "),a("mjx-container",t6,[(e(),s("svg",Q6,e6)),T6])])])]),l6]),n6])}const k6=T(l,[["render",i6]]);export{c6 as __pageData,k6 as default}; diff --git a/dev/assets/api.md.BiqC9tVJ.lean.js b/dev/assets/api.md.BiqC9tVJ.lean.js new file mode 100644 index 0000000..9488df2 --- /dev/null +++ b/dev/assets/api.md.BiqC9tVJ.lean.js @@ -0,0 +1 @@ +import{_ as T,c as s,j as a,a as t,a6 as Q,o as e}from"./chunks/framework.Cvv1S4VC.js";const c6=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),l={name:"api.md"},n=Q("",4),i={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},d=a("a",{id:"BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet",href:"#BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet"},"#",-1),o=a("b",null,[a("u",null,"BioMarkovChains.dnaseqprobability")],-1),m=a("i",null,"Method",-1),r=Q("",2),h={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},p={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.819ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.497ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1728.7 18341.5 2974.6","aria-hidden":"true"},g=Q("",1),c=[g],k=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mn",null,"1")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mn",null,"1")]),a("mo",null,","),a("mo",null,"…"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"T")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mi",null,"T")]),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("msubsup",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mn",null,"1")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∏"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("msub",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mi",null,"t")]),a("mo",null,","),a("msub",null,[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])])])])])],-1),u=Q("",7),H=a("br",null,null,-1),x={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},y=a("a",{id:"BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet"},"#",-1),L=a("b",null,[a("u",null,"BioMarkovChains.initials")],-1),w=a("i",null,"Method",-1),b=Q("",3),_={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-4.275ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.706ex",height:"9.681ex",role:"img",focusable:"false",viewBox:"0 -2389.4 10919.9 4278.9","aria-hidden":"true"},f=Q("",1),C=[f],D=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mtable",{displaystyle:"true",columnalign:"right left",columnspacing:"0em",rowspacing:"3pt"},[a("mtr",null,[a("mtd",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,","),a("mi",null,"i"),a("mo",null,"∈"),a("mi",null,"T")])]),a("mtr",null,[a("mtd",null,[a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"N")])]),a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mn",null,"1")])])])])],-1),A=a("p",null,"Now using the dinucleotides counts estimating the initials would follow:",-1),E={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.75ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.788ex",height:"4.899ex",role:"img",focusable:"false",viewBox:"0 -950 5652.2 2165.5","aria-hidden":"true"},v=Q("",1),F=[v],B=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",{stretchy:"false"},"^")])]),a("mo",null,"="),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])]),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])])])],-1),V=a("p",null,[a("strong",null,"Arguments")],-1),j=a("ul",null,[a("li",null,[a("code",null,"sequence::SeqOrView{A}"),t(": The sequence of states representing the Markov chain.")])],-1),R=a("p",null,[a("strong",null,"Returns")],-1),O=a("p",null,[t("An "),a("code",null,"Vector{Flot64}"),t(" of estimated initial probabilities for each state in the sequence.")],-1),S=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),q=a("br",null,null,-1),X={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},N=a("a",{id:"BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}",href:"#BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}"},"#",-1),P=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_matrix")],-1),I=a("i",null,"Method",-1),G=Q("",2),U={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"16.289ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 7199.8 2420","aria-hidden":"true"},J=Q("",1),W=[J],$=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"β"),a("mo",null,"="),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])]),a("mo",{stretchy:"false"},")")]),a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])]),a("mo",{stretchy:"false"},")")])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},a2=Q("",1),t2=[a2],Q2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])],-1),s2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},T2=Q("",1),l2=[T2],n2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])],-1),i2=a("p",null,[a("strong",null,"Arguments")],-1),d2=a("ul",null,[a("li",null,[a("p",null,[a("code",null,"model1::BioMarkovChain"),t(": The first BioMarkovChain model.")])]),a("li",null,[a("p",null,[a("code",null,"model2::BioMarkovChain"),t(": The second BioMarkovChain model.")])])],-1),o2=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),m2=Q("",3),r2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},h2=a("a",{id:"BioMarkovChains.log_odds_ratio_score-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.log_odds_ratio_score-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet"},"#",-1),p2=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_score")],-1),g2=a("i",null,"Method",-1),c2=Q("",2),k2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.936ex",height:"7.198ex",role:"img",focusable:"false",viewBox:"0 -1840.7 14115.8 3181.3","aria-hidden":"true"},H2=Q("",1),x2=[H2],y2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"S"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"L")])]),a("msub",null,[a("mi",null,"β"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"x"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mi",null,"x")])]),a("mo",null,"="),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")])]),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])]),a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])])])])],-1),L2=Q("",6),w2=Q("",5),b2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},_2=a("a",{id:"BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet"},"#",-1),M2=a("b",null,[a("u",null,"BioMarkovChains.transition_probability_matrix")],-1),f2=a("i",null,"Method",-1),C2=Q("",1),D2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.577ex",role:"img",focusable:"false",viewBox:"0 -1089 1216 1139","aria-hidden":"true"},E2=Q("",1),Z2=[E2],v2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mo",{stretchy:"false"},"^")])])])],-1),F2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},B2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.734ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 21982.3 2420","aria-hidden":"true"},V2=Q("",1),j2=[V2],R2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",null,"∣"),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("mfrac",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",{stretchy:"false"},")")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")")])])])],-1),O2=a("p",null,"The transition matrices of DNA and Amino-Acids are arranged sorted and in row-wise matrices:",-1),S2=a("p",null,"First the DNA matrix:",-1),q2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},X2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-5.317ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.979ex",height:"11.765ex",role:"img",focusable:"false",viewBox:"0 -2850 13250.7 5200","aria-hidden":"true"},N2=Q("",1),P2=[N2],I2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"N"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"T")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),G2=a("p",null,"And then, the Aminoacids:",-1),U2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-7.771ex"},xmlns:"http://www.w3.org/2000/svg",width:"35.891ex",height:"16.674ex",role:"img",focusable:"false",viewBox:"0 -3935 15863.7 7370","aria-hidden":"true"},J2=Q("",1),W2=[J2],$2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mo",null,"⋱")]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"W")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),K2=a("p",null,[a("strong",null,"Arguments")],-1),Y2=a("li",null,[a("p",null,[a("code",null,"sequence::LongNucOrView{4}"),t(": a "),a("code",null,"LongNucOrView{4}"),t(" object representing the DNA sequence.")])],-1),a6=a("code",null,"n::Int64=1",-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"3.648ex",height:"2.378ex",role:"img",focusable:"false",viewBox:"0 -1051 1612.3 1051","aria-hidden":"true"},s6=Q("",1),e6=[s6],T6=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",null,"M"),a("mo",{stretchy:"false"},"^")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])])])],-1),l6=Q("",7),n6=a("br",null,null,-1);function i6(d6,o6,m6,r6,h6,p6){return e(),s("div",null,[n,a("div",i,[d,t(" "),o,t(" — "),m,t(". "),r,a("mjx-container",h,[(e(),s("svg",p,c)),k]),u]),H,a("div",x,[y,t(" "),L,t(" — "),w,t(". "),b,a("mjx-container",_,[(e(),s("svg",M,C)),D]),A,a("mjx-container",E,[(e(),s("svg",Z,F)),B]),V,j,R,O,S]),q,a("div",X,[N,t(" "),P,t(" — "),I,t(". "),G,a("mjx-container",U,[(e(),s("svg",z,W)),$]),a("p",null,[t("Where "),a("mjx-container",K,[(e(),s("svg",Y,t2)),Q2]),t(" and "),a("mjx-container",s2,[(e(),s("svg",e2,l2)),n2]),t(" are the two models transition probability matrices.")]),i2,d2,o2]),m2,a("div",r2,[h2,t(" "),p2,t(" — "),g2,t(". "),c2,a("mjx-container",k2,[(e(),s("svg",u2,x2)),y2]),L2]),w2,a("div",b2,[_2,t(" "),M2,t(" — "),f2,t(". "),C2,a("p",null,[t("Compute the transition probability matrix (TPM) of a given DNA sequence. Formally it construct "),a("mjx-container",D2,[(e(),s("svg",A2,Z2)),v2]),t(" where:")]),a("mjx-container",F2,[(e(),s("svg",B2,j2)),R2]),O2,S2,a("mjx-container",q2,[(e(),s("svg",X2,P2)),I2]),G2,a("mjx-container",U2,[(e(),s("svg",z2,W2)),$2]),K2,a("ul",null,[Y2,a("li",null,[a("p",null,[a6,t(": The order of the Markov model. That is the "),a("mjx-container",t6,[(e(),s("svg",Q6,e6)),T6])])])]),l6]),n6])}const k6=T(l,[["render",i6]]);export{c6 as __pageData,k6 as default}; diff --git a/dev/assets/api.md.CM80ZGQK.js b/dev/assets/api.md.CM80ZGQK.js deleted file mode 100644 index 8d58152..0000000 --- a/dev/assets/api.md.CM80ZGQK.js +++ /dev/null @@ -1,58 +0,0 @@ -import{_ as T,c as s,l as a,a as t,a7 as Q,o as e}from"./chunks/framework.D1rHXXmm.js";const c6=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),l={name:"api.md"},n=Q(`
# BioMarkovChains.BMC — Type.
julia
BMC

Alias for the type BioMarkovChain.

source


# BioMarkovChains.BioMarkovChain — Type.
julia
struct BioMarkovChain{S<:DataType, M<:AbstractMatrix, I<:AbstractVector, N<:Integer} <: AbstractBioMarkovChain

A BioMarkovChain represents a Markov chain used in biological sequence analysis. It contains a transition probability matrix (tpm) and an initial distribution of probabilities (inits) and also the order of the Markov chain.

Fields

Constructors

Example

julia
sequence = LongDNA{4}("ACTACATCTA")
-
-model = BioMarkovChain(sequence, 2)
-BioMarkovChain of DNAAlphabet{4}() and order 1:
-  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
-   0.0     0.6667  0.0     0.3333
-   0.3333  0.0     0.0     0.6667
-   0.0     0.0     0.0     0.0
-   0.6667  0.3333  0.0     0.0
-  - Initial Probabilities -> Vector{Float64}(4 × 1):
-   0.3333
-   0.3333
-   0.0
-   0.3333

source


`,4),i={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},d=a("a",{id:"BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet",href:"#BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet"},"#",-1),o=a("b",null,[a("u",null,"BioMarkovChains.dnaseqprobability")],-1),m=a("i",null,"Method",-1),r=Q('
julia
dnaseqprobability(sequence::LongNucOrView{4}, model::BioMarkovChain)

Compute the probability of a given sequence using a transition probability matrix and the initial probabilities distributions of a BioMarkovModel.

',2),h={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},p={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.819ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.497ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1728.7 18341.5 2974.6","aria-hidden":"true"},g=Q('',1),c=[g],k=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mn",null,"1")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mn",null,"1")]),a("mo",null,","),a("mo",null,"…"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"T")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mi",null,"T")]),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("msubsup",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mn",null,"1")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∏"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("msub",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mi",null,"t")]),a("mo",null,","),a("msub",null,[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])])])])])],-1),u=Q(`

Arguments

Returns

Example

julia
mainseq = LongDNA{4}("CCTCCCGGACCCTGGGCTCGGGAC")
-   
-bmc = BioMarkovChain(mainseq)
-
-    BioMarkovChain of DNAAlphabet{4}() and order 1:
-      - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
-       0.0     1.0     0.0     0.0
-       0.0     0.5     0.2     0.3
-       0.25    0.125   0.625   0.0
-       0.0     0.6667  0.3333  0.0
-      - Initial Probabilities -> Vector{Float64}(4 × 1):
-       0.087
-       0.4348
-       0.3478
-       0.1304
-
-newseq = LongDNA{4}("CCTG")
-
-    4nt DNA Sequence:
-    CCTG
-
-
-dnaseqprobability(newseq, bmc)
-    
-    0.021739130434782608

source

`,7),H=a("br",null,null,-1),x={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},y=a("a",{id:"BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet"},"#",-1),L=a("b",null,[a("u",null,"BioMarkovChains.initials")],-1),w=a("i",null,"Method",-1),b=Q('
julia
initials(sequence::SeqOrView{A}) where A

Calculate the estimated initial probabilities for a Markov chain based on a given sequence.

This function takes a sequence of states and calculates the estimated initial probabilities of each state in the sequence for a Markov chain. The initial probabilities are estimated by counting the occurrences of each state at the beginning of the sequence and normalizing the counts to sum up to 1.

',3),_={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-4.275ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.706ex",height:"9.681ex",role:"img",focusable:"false",viewBox:"0 -2389.4 10919.9 4278.9","aria-hidden":"true"},f=Q('',1),C=[f],D=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mtable",{displaystyle:"true",columnalign:"right left",columnspacing:"0em",rowspacing:"3pt"},[a("mtr",null,[a("mtd",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,","),a("mi",null,"i"),a("mo",null,"∈"),a("mi",null,"T")])]),a("mtr",null,[a("mtd",null,[a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"N")])]),a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mn",null,"1")])])])])],-1),A=a("p",null,"Now using the dinucleotides counts estimating the initials would follow:",-1),E={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.75ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.788ex",height:"4.899ex",role:"img",focusable:"false",viewBox:"0 -950 5652.2 2165.5","aria-hidden":"true"},v=Q('',1),F=[v],B=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",{stretchy:"false"},"^")])]),a("mo",null,"="),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])]),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])])])],-1),V=a("p",null,[a("strong",null,"Arguments")],-1),j=a("ul",null,[a("li",null,[a("code",null,"sequence::SeqOrView{A}"),t(": The sequence of states representing the Markov chain.")])],-1),R=a("p",null,[a("strong",null,"Returns")],-1),O=a("p",null,[t("An "),a("code",null,"Vector{Flot64}"),t(" of estimated initial probabilities for each state in the sequence.")],-1),S=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),q=a("br",null,null,-1),X={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},N=a("a",{id:"BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}",href:"#BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}"},"#",-1),P=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_matrix")],-1),I=a("i",null,"Method",-1),G=Q('
julia
log_odds_ratio_matrix(model1::BioMarkovChain, model2::BioMarkovChain)

Calculates the log-odds ratio between the transition probability matrices of two BioMarkovChain models.

',2),U={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"16.289ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 7199.8 2420","aria-hidden":"true"},J=Q('𝓂𝓂',1),W=[J],$=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"β"),a("mo",null,"="),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])]),a("mo",{stretchy:"false"},")")]),a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])]),a("mo",{stretchy:"false"},")")])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},a2=Q('𝓂',1),t2=[a2],Q2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])],-1),s2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},T2=Q('𝓂',1),l2=[T2],n2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])],-1),i2=a("p",null,[a("strong",null,"Arguments")],-1),d2=a("ul",null,[a("li",null,[a("p",null,[a("code",null,"model1::BioMarkovChain"),t(": The first BioMarkovChain model.")])]),a("li",null,[a("p",null,[a("code",null,"model2::BioMarkovChain"),t(": The second BioMarkovChain model.")])])],-1),o2=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),m2=Q(`
# BioMarkovChains.log_odds_ratio_matrix — Method.
julia
log_odds_ratio_matrix(sequence::NucleicSeqOrView{A}, model::BioMarkovChain) where A

Calculates the log-odds ratio between the transition probability matrix of a given DNA sequence and a reference model.

Arguments

Examples

julia
sequence = LongNucOrView{4}("ACGT")
-model = BioMarkovChain(sequence)  # Provide appropriate initialization for BioMarkovChain
-result = log_odds_ratio_matrix(sequence, model)

source


`,3),r2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},h2=a("a",{id:"BioMarkovChains.log_odds_ratio_score-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.log_odds_ratio_score-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.Alphabet"},"#",-1),p2=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_score")],-1),g2=a("i",null,"Method",-1),c2=Q('
julia
log_odds_ratio_score(sequence::SeqOrView{A}, model::BioMarkovChain; b::Number = ℯ)

Compute the log odds ratio score between a given sequence and a BioMarkovChain model.

',2),k2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.936ex",height:"7.198ex",role:"img",focusable:"false",viewBox:"0 -1840.7 14115.8 3181.3","aria-hidden":"true"},H2=Q('𝓂𝓂',1),x2=[H2],y2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"S"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"L")])]),a("msub",null,[a("mi",null,"β"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"x"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mi",null,"x")])]),a("mo",null,"="),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")])]),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])]),a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])])])])],-1),L2=Q('

Arguments

Returns

The log odds ratio score between the sequence and the model.

Example

source

',6),w2=Q(`
# BioMarkovChains.perronfrobenius — Method.
julia
perronfrobenius(sequence::SeqOrView{A}, n::Int64=1) where A

Compute the Perron-Frobenius matrix, a column-stochastic version of the transition probability matrix (TPM), for a given nucleotide sequence.

The Perron-Frobenius matrix captures the asymptotic probabilities of transitioning between nucleotides in the sequence over a specified number of steps n. It provides insight into the long-term behavior of a Markov chain or a dynamical system associated with the sequence.

Arguments

Returns

A copy of the Perron-Frobenius matrix. Each column of this matrix corresponds to the probabilities of transitioning from the current nucleotide state to all possible nucleotide states after n steps.

Example

julia
sequence = LongSequence{DNAAlphabet{4}}("ACGTCGTCCACTACGACATCAGC")  # Replace with an actual nucleotide sequence
-n = 2
-pf = perronfrobenius(sequence, n)

source


# BioMarkovChains.transition_count_matrix — Method.
julia
transition_count_matrix(sequence::LongSequence{DNAAlphabet{4}})

Compute the transition count matrix (TCM) of a given DNA sequence.

Arguments

Returns

A Matrix object representing the transition count matrix of the sequence.

Example

seq = LongDNA{4}("AGCTAGCTAGCT")
-
-tcm = transition_count_matrix(seq)
-
-4×4 Matrix{Int64}:
- 0  0  3  0
- 0  0  0  3
- 0  3  0  0
- 2  0  0  0

source


`,5),b2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},_2=a("a",{id:"BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet"},"#",-1),M2=a("b",null,[a("u",null,"BioMarkovChains.transition_probability_matrix")],-1),f2=a("i",null,"Method",-1),C2=Q('
julia
transition_probability_matrix(sequence::LongSequence{DNAAlphabet{4}}, n::Int64=1)
',1),D2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.577ex",role:"img",focusable:"false",viewBox:"0 -1089 1216 1139","aria-hidden":"true"},E2=Q('',1),Z2=[E2],v2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mo",{stretchy:"false"},"^")])])])],-1),F2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},B2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.734ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 21982.3 2420","aria-hidden":"true"},V2=Q('𝓂',1),j2=[V2],R2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",null,"∣"),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("mfrac",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",{stretchy:"false"},")")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")")])])])],-1),O2=a("p",null,"The transition matrices of DNA and Amino-Acids are arranged sorted and in row-wise matrices:",-1),S2=a("p",null,"First the DNA matrix:",-1),q2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},X2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-5.317ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.979ex",height:"11.765ex",role:"img",focusable:"false",viewBox:"0 -2850 13250.7 5200","aria-hidden":"true"},N2=Q('',1),P2=[N2],I2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"N"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"T")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),G2=a("p",null,"And then, the Aminoacids:",-1),U2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-7.771ex"},xmlns:"http://www.w3.org/2000/svg",width:"35.891ex",height:"16.674ex",role:"img",focusable:"false",viewBox:"0 -3935 15863.7 7370","aria-hidden":"true"},J2=Q('',1),W2=[J2],$2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mo",null,"⋱")]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"W")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),K2=a("p",null,[a("strong",null,"Arguments")],-1),Y2=a("li",null,[a("p",null,[a("code",null,"sequence::LongNucOrView{4}"),t(": a "),a("code",null,"LongNucOrView{4}"),t(" object representing the DNA sequence.")])],-1),a6=a("code",null,"n::Int64=1",-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"3.648ex",height:"2.378ex",role:"img",focusable:"false",viewBox:"0 -1051 1612.3 1051","aria-hidden":"true"},s6=Q('',1),e6=[s6],T6=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",null,"M"),a("mo",{stretchy:"false"},"^")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])])])],-1),l6=Q(`

Keywords

Returns

A Matrix object representing the transition probability matrix of the sequence.

Example

julia
seq = dna"AGCTAGCTAGCT"
-
-tpm = transition_probability_matrix(seq)
-
-4×4 Matrix{Float64}:
- 0.0  0.0  1.0  0.0
- 0.0  0.0  0.0  1.0
- 0.0  1.0  0.0  0.0
- 1.0  0.0  0.0  0.0

source

`,7),n6=a("br",null,null,-1);function i6(d6,o6,m6,r6,h6,p6){return e(),s("div",null,[n,a("div",i,[d,t(" "),o,t(" — "),m,t(". "),r,a("mjx-container",h,[(e(),s("svg",p,c)),k]),u]),H,a("div",x,[y,t(" "),L,t(" — "),w,t(". "),b,a("mjx-container",_,[(e(),s("svg",M,C)),D]),A,a("mjx-container",E,[(e(),s("svg",Z,F)),B]),V,j,R,O,S]),q,a("div",X,[N,t(" "),P,t(" — "),I,t(". "),G,a("mjx-container",U,[(e(),s("svg",z,W)),$]),a("p",null,[t("Where "),a("mjx-container",K,[(e(),s("svg",Y,t2)),Q2]),t(" and "),a("mjx-container",s2,[(e(),s("svg",e2,l2)),n2]),t(" are the two models transition probability matrices.")]),i2,d2,o2]),m2,a("div",r2,[h2,t(" "),p2,t(" — "),g2,t(". "),c2,a("mjx-container",k2,[(e(),s("svg",u2,x2)),y2]),L2]),w2,a("div",b2,[_2,t(" "),M2,t(" — "),f2,t(". "),C2,a("p",null,[t("Compute the transition probability matrix (TPM) of a given DNA sequence. Formally it construct "),a("mjx-container",D2,[(e(),s("svg",A2,Z2)),v2]),t(" where:")]),a("mjx-container",F2,[(e(),s("svg",B2,j2)),R2]),O2,S2,a("mjx-container",q2,[(e(),s("svg",X2,P2)),I2]),G2,a("mjx-container",U2,[(e(),s("svg",z2,W2)),$2]),K2,a("ul",null,[Y2,a("li",null,[a("p",null,[a6,t(": The order of the Markov model. That is the "),a("mjx-container",t6,[(e(),s("svg",Q6,e6)),T6])])])]),l6]),n6])}const k6=T(l,[["render",i6]]);export{c6 as __pageData,k6 as default}; diff --git a/dev/assets/api.md.CM80ZGQK.lean.js b/dev/assets/api.md.CM80ZGQK.lean.js deleted file mode 100644 index e557643..0000000 --- a/dev/assets/api.md.CM80ZGQK.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as T,c as s,l as a,a as t,a7 as Q,o as e}from"./chunks/framework.D1rHXXmm.js";const c6=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),l={name:"api.md"},n=Q("",4),i={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},d=a("a",{id:"BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet",href:"#BioMarkovChains.dnaseqprobability-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.NucleicAcidAlphabet"},"#",-1),o=a("b",null,[a("u",null,"BioMarkovChains.dnaseqprobability")],-1),m=a("i",null,"Method",-1),r=Q("",2),h={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},p={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.819ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.497ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1728.7 18341.5 2974.6","aria-hidden":"true"},g=Q("",1),c=[g],k=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mn",null,"1")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mn",null,"1")]),a("mo",null,","),a("mo",null,"…"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"T")]),a("mo",null,"="),a("msub",null,[a("mi",null,"i"),a("mi",null,"T")]),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("msubsup",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mn",null,"1")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∏"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mo",null,"−"),a("mn",null,"1")])]),a("msub",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"i"),a("mi",null,"t")]),a("mo",null,","),a("msub",null,[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])])])])])],-1),u=Q("",7),H=a("br",null,null,-1),x={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},y=a("a",{id:"BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.initials-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}} where A<:BioSequences.Alphabet"},"#",-1),L=a("b",null,[a("u",null,"BioMarkovChains.initials")],-1),w=a("i",null,"Method",-1),b=Q("",3),_={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-4.275ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.706ex",height:"9.681ex",role:"img",focusable:"false",viewBox:"0 -2389.4 10919.9 4278.9","aria-hidden":"true"},f=Q("",1),C=[f],D=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mtable",{displaystyle:"true",columnalign:"right left",columnspacing:"0em",rowspacing:"3pt"},[a("mtr",null,[a("mtd",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,","),a("mi",null,"i"),a("mo",null,"∈"),a("mi",null,"T")])]),a("mtr",null,[a("mtd",null,[a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"N")])]),a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])])]),a("mtd",null,[a("mi"),a("mo",null,"="),a("mn",null,"1")])])])])],-1),A=a("p",null,"Now using the dinucleotides counts estimating the initials would follow:",-1),E={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.75ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.788ex",height:"4.899ex",role:"img",focusable:"false",viewBox:"0 -950 5652.2 2165.5","aria-hidden":"true"},v=Q("",1),F=[v],B=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("msub",null,[a("mi",null,"π"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mo",{stretchy:"false"},"^")])]),a("mo",null,"="),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])]),a("msub",null,[a("mi",null,"c"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k")])])])],-1),V=a("p",null,[a("strong",null,"Arguments")],-1),j=a("ul",null,[a("li",null,[a("code",null,"sequence::SeqOrView{A}"),t(": The sequence of states representing the Markov chain.")])],-1),R=a("p",null,[a("strong",null,"Returns")],-1),O=a("p",null,[t("An "),a("code",null,"Vector{Flot64}"),t(" of estimated initial probabilities for each state in the sequence.")],-1),S=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),q=a("br",null,null,-1),X={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},N=a("a",{id:"BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}",href:"#BioMarkovChains.log_odds_ratio_matrix-Tuple{BioMarkovChain, BioMarkovChain}"},"#",-1),P=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_matrix")],-1),I=a("i",null,"Method",-1),G=Q("",2),U={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"16.289ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 7199.8 2420","aria-hidden":"true"},J=Q("",1),W=[J],$=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"β"),a("mo",null,"="),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])]),a("mo",{stretchy:"false"},")")]),a("mrow",null,[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])]),a("mo",{stretchy:"false"},")")])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},a2=Q("",1),t2=[a2],Q2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])],-1),s2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.452ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.345ex",height:"2.149ex",role:"img",focusable:"false",viewBox:"0 -750 1036.6 950","aria-hidden":"true"},T2=Q("",1),l2=[T2],n2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])],-1),i2=a("p",null,[a("strong",null,"Arguments")],-1),d2=a("ul",null,[a("li",null,[a("p",null,[a("code",null,"model1::BioMarkovChain"),t(": The first BioMarkovChain model.")])]),a("li",null,[a("p",null,[a("code",null,"model2::BioMarkovChain"),t(": The second BioMarkovChain model.")])])],-1),o2=a("p",null,[a("a",{href:"https://github.com/camilogarciabotero/BioMarkovChains.jl/",target:"_blank",rel:"noreferrer"},"source")],-1),m2=Q("",3),r2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},h2=a("a",{id:"BioMarkovChains.log_odds_ratio_score-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.log_odds_ratio_score-Union{Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, BioMarkovChain}} where A<:BioSequences.Alphabet"},"#",-1),p2=a("b",null,[a("u",null,"BioMarkovChains.log_odds_ratio_score")],-1),g2=a("i",null,"Method",-1),c2=Q("",2),k2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.936ex",height:"7.198ex",role:"img",focusable:"false",viewBox:"0 -1840.7 14115.8 3181.3","aria-hidden":"true"},H2=Q("",1),x2=[H2],y2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mi",null,"S"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"L")])]),a("msub",null,[a("mi",null,"β"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mi",null,"x"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i")])]),a("mi",null,"x")])]),a("mo",null,"="),a("munder",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1")])]),a("mi",null,"log"),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("mfrac",null,[a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])]),a("mrow",null,[a("msubsup",null,[a("mi",null,"a"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mo",null,"−"),a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])])])]),a("msub",null,[a("mi",null,"x"),a("mi",null,"i")])])])])],-1),L2=Q("",6),w2=Q("",5),b2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},_2=a("a",{id:"BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet",href:"#BioMarkovChains.transition_probability_matrix-Union{Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}}, Tuple{A}, Tuple{Union{BioSequences.LongSequence{A}, BioSequences.LongSubSeq{A}}, Int64}} where A<:BioSequences.Alphabet"},"#",-1),M2=a("b",null,[a("u",null,"BioMarkovChains.transition_probability_matrix")],-1),f2=a("i",null,"Method",-1),C2=Q("",1),D2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.577ex",role:"img",focusable:"false",viewBox:"0 -1089 1216 1139","aria-hidden":"true"},E2=Q("",1),Z2=[E2],v2=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mo",{stretchy:"false"},"^")])])])],-1),F2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},B2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.734ex",height:"5.475ex",role:"img",focusable:"false",viewBox:"0 -1460 21982.3 2420","aria-hidden":"true"},V2=Q("",1),j2=[V2],R2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",null,"="),a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",null,"∣"),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("mfrac",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",null,","),a("msub",null,[a("mi",null,"X"),a("mi",null,"t")]),a("mo",null,"="),a("mi",null,"j"),a("mo",{stretchy:"false"},")")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"P"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"X"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",null,"="),a("mi",null,"i"),a("mo",{stretchy:"false"},")")])])])],-1),O2=a("p",null,"The transition matrices of DNA and Amino-Acids are arranged sorted and in row-wise matrices:",-1),S2=a("p",null,"First the DNA matrix:",-1),q2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},X2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-5.317ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.979ex",height:"11.765ex",role:"img",focusable:"false",viewBox:"0 -2850 13250.7 5200","aria-hidden":"true"},N2=Q("",1),P2=[N2],I2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"N"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"G"),a("mi",null,"T")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"G")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"T"),a("mi",null,"T")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),G2=a("p",null,"And then, the Aminoacids:",-1),U2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-7.771ex"},xmlns:"http://www.w3.org/2000/svg",width:"35.891ex",height:"16.674ex",role:"img",focusable:"false",viewBox:"0 -3935 15863.7 7370","aria-hidden":"true"},J2=Q("",1),W2=[J2],$2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])]),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"["),a("mtable",{columnspacing:"1em",rowspacing:"4pt"},[a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"A"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"C"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"D"),a("mi",null,"W")])])])]),a("mtr",null,[a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])]),a("mtd",null,[a("mo",null,"⋱")]),a("mtd",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null,"⋮")])])]),a("mtr",null,[a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"A")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"C")])])]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"D")])])]),a("mtd",null,[a("mo",null,"…")]),a("mtd",null,[a("msub",null,[a("mi"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"W"),a("mi",null,"W")])])])])]),a("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),K2=a("p",null,[a("strong",null,"Arguments")],-1),Y2=a("li",null,[a("p",null,[a("code",null,"sequence::LongNucOrView{4}"),t(": a "),a("code",null,"LongNucOrView{4}"),t(" object representing the DNA sequence.")])],-1),a6=a("code",null,"n::Int64=1",-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"3.648ex",height:"2.378ex",role:"img",focusable:"false",viewBox:"0 -1051 1612.3 1051","aria-hidden":"true"},s6=Q("",1),e6=[s6],T6=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",null,"M"),a("mo",{stretchy:"false"},"^")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])])])],-1),l6=Q("",7),n6=a("br",null,null,-1);function i6(d6,o6,m6,r6,h6,p6){return e(),s("div",null,[n,a("div",i,[d,t(" "),o,t(" — "),m,t(". "),r,a("mjx-container",h,[(e(),s("svg",p,c)),k]),u]),H,a("div",x,[y,t(" "),L,t(" — "),w,t(". "),b,a("mjx-container",_,[(e(),s("svg",M,C)),D]),A,a("mjx-container",E,[(e(),s("svg",Z,F)),B]),V,j,R,O,S]),q,a("div",X,[N,t(" "),P,t(" — "),I,t(". "),G,a("mjx-container",U,[(e(),s("svg",z,W)),$]),a("p",null,[t("Where "),a("mjx-container",K,[(e(),s("svg",Y,t2)),Q2]),t(" and "),a("mjx-container",s2,[(e(),s("svg",e2,l2)),n2]),t(" are the two models transition probability matrices.")]),i2,d2,o2]),m2,a("div",r2,[h2,t(" "),p2,t(" — "),g2,t(". "),c2,a("mjx-container",k2,[(e(),s("svg",u2,x2)),y2]),L2]),w2,a("div",b2,[_2,t(" "),M2,t(" — "),f2,t(". "),C2,a("p",null,[t("Compute the transition probability matrix (TPM) of a given DNA sequence. Formally it construct "),a("mjx-container",D2,[(e(),s("svg",A2,Z2)),v2]),t(" where:")]),a("mjx-container",F2,[(e(),s("svg",B2,j2)),R2]),O2,S2,a("mjx-container",q2,[(e(),s("svg",X2,P2)),I2]),G2,a("mjx-container",U2,[(e(),s("svg",z2,W2)),$2]),K2,a("ul",null,[Y2,a("li",null,[a("p",null,[a6,t(": The order of the Markov model. That is the "),a("mjx-container",t6,[(e(),s("svg",Q6,e6)),T6])])])]),l6]),n6])}const k6=T(l,[["render",i6]]);export{c6 as __pageData,k6 as default}; diff --git a/dev/assets/app.DJvmlMci.js b/dev/assets/app.DJvmlMci.js new file mode 100644 index 0000000..d29cb2a --- /dev/null +++ b/dev/assets/app.DJvmlMci.js @@ -0,0 +1 @@ +import{U as o,a8 as p,a9 as u,aa as l,ab as c,ac as f,ad as d,ae as m,af as h,ag as g,ah as A,d as P,u as v,y,x as w,ai as C,aj as R,ak as b,a5 as E}from"./chunks/framework.Cvv1S4VC.js";import{R as S}from"./chunks/theme.CNBIs78H.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(S),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return y(()=>{w(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),R(),b(),s.setup&&s.setup(),()=>E(s.Layout)}});async function _(){globalThis.__VITEPRESS__=!0;const e=x(),a=j();a.provide(u,e);const t=l(e.route);return a.provide(c,t),a.component("Content",f),a.component("ClientOnly",d),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:m}),{app:a,router:e,data:t}}function j(){return h(T)}function x(){let e=o,a;return g(t=>{let n=A(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&_().then(({app:e,router:a,data:t})=>{a.go().then(()=>{p(a.route,t.site),e.mount("#app")})});export{_ as createApp}; diff --git a/dev/assets/app.s0WURkb8.js b/dev/assets/app.s0WURkb8.js deleted file mode 100644 index 295239b..0000000 --- a/dev/assets/app.s0WURkb8.js +++ /dev/null @@ -1 +0,0 @@ -import{V as o,a9 as p,aa as u,ab as l,ac as c,ad as f,ae as d,af as m,ag as h,ah as g,ai as A,Y as P,d as _,u as v,k as y,y as R,aj as w,ak as C,al as E,a6 as b}from"./chunks/framework.D1rHXXmm.js";import{R as T}from"./chunks/theme.BWgOxzZE.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(T),S=_({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return y(()=>{R(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&w(),C(),E(),s.setup&&s.setup(),()=>b(s.Layout)}});async function D(){globalThis.__VITEPRESS__=!0;const e=j(),a=V();a.provide(u,e);const t=l(e.route);return a.provide(c,t),a.component("Content",f),a.component("ClientOnly",d),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:m}),{app:a,router:e,data:t}}function V(){return h(S)}function j(){let e=o,a;return g(t=>{let n=A(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=P(()=>import(n),[])),o&&(e=!1),r},s.NotFound)}o&&D().then(({app:e,router:a,data:t})=>{a.go().then(()=>{p(a.route,t.site),e.mount("#app")})});export{D as createApp}; diff --git a/dev/assets/article01.md.BL6r3tif.lean.js b/dev/assets/article01.md.BL6r3tif.lean.js deleted file mode 100644 index eee1cec..0000000 --- a/dev/assets/article01.md.BL6r3tif.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as a,o as n,a7 as i}from"./chunks/framework.D1rHXXmm.js";const g=JSON.parse('{"title":"From BMC to sequence probabilties","description":"","frontmatter":{},"headers":[],"relativePath":"article01.md","filePath":"article01.md","lastUpdated":null}'),e={name:"article01.md"},p=i("",5),t=[p];function l(c,o,h,r,d,k){return n(),a("div",null,t)}const C=s(e,[["render",l]]);export{g as __pageData,C as default}; diff --git a/dev/assets/article01.md.BL6r3tif.js b/dev/assets/article01.md.BrGXw77Y.js similarity index 79% rename from dev/assets/article01.md.BL6r3tif.js rename to dev/assets/article01.md.BrGXw77Y.js index c5c5dcd..f1fdc95 100644 --- a/dev/assets/article01.md.BL6r3tif.js +++ b/dev/assets/article01.md.BrGXw77Y.js @@ -1,4 +1,4 @@ -import{_ as s,c as a,o as n,a7 as i}from"./chunks/framework.D1rHXXmm.js";const g=JSON.parse('{"title":"From BMC to sequence probabilties","description":"","frontmatter":{},"headers":[],"relativePath":"article01.md","filePath":"article01.md","lastUpdated":null}'),e={name:"article01.md"},p=i(`

From BMC to sequence probabilties ​

We can now calculate a transition probability matrix from a LongDNA sequence using the transition_probability_matrix and initials methods:

julia
using BioSequences
+import{_ as s,c as a,o as n,a6 as i}from"./chunks/framework.Cvv1S4VC.js";const g=JSON.parse('{"title":"From BMC to sequence probabilties","description":"","frontmatter":{},"headers":[],"relativePath":"article01.md","filePath":"article01.md","lastUpdated":null}'),e={name:"article01.md"},t=i(`
From BMC to sequence probabilties ​
We can now calculate a transition probability matrix from a LongDNA sequence using the transition_probability_matrix and initials methods:
julia
using BioSequences
 
 sequence = dna"CCTCCCGGACCCTGGGCTCGGGAC"
 
@@ -6,7 +6,7 @@ import{_ as s,c as a,o as n,a7 as i}from"./chunks/framework.D1rHXXmm.js";const g
 initials = initials(sequence)
 
 println(tpm)
-println(initials)
4×4 Matrix{Float64}:
+println(initials)
4×4 Matrix{Float64}:
  0.0   1.0       0.0       0.0
  0.0   0.5       0.2       0.3
  0.25  0.125     0.625     0.0
@@ -16,4 +16,4 @@ import{_ as s,c as a,o as n,a7 as i}from"./chunks/framework.D1rHXXmm.js";const g
  0.08695652173913043
  0.43478260869565216
  0.34782608695652173
- 0.13043478260869565
`,5),t=[p];function l(c,o,h,r,d,k){return n(),a("div",null,t)}const C=s(e,[["render",l]]);export{g as __pageData,C as default};
+ 0.13043478260869565
`,5),p=[t];function l(c,o,h,r,d,k){return n(),a("div",null,p)}const C=s(e,[["render",l]]);export{g as __pageData,C as default}; diff --git a/dev/assets/article01.md.BrGXw77Y.lean.js b/dev/assets/article01.md.BrGXw77Y.lean.js new file mode 100644 index 0000000..0987431 --- /dev/null +++ b/dev/assets/article01.md.BrGXw77Y.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as n,a6 as i}from"./chunks/framework.Cvv1S4VC.js";const g=JSON.parse('{"title":"From BMC to sequence probabilties","description":"","frontmatter":{},"headers":[],"relativePath":"article01.md","filePath":"article01.md","lastUpdated":null}'),e={name:"article01.md"},t=i("",5),p=[t];function l(c,o,h,r,d,k){return n(),a("div",null,p)}const C=s(e,[["render",l]]);export{g as __pageData,C as default}; diff --git a/dev/assets/biomarkovchains.md.DhkAaXJV.js b/dev/assets/biomarkovchains.md.0rg0z1ev.js similarity index 99% rename from dev/assets/biomarkovchains.md.DhkAaXJV.js rename to dev/assets/biomarkovchains.md.0rg0z1ev.js index 47dea7b..07d72f8 100644 --- a/dev/assets/biomarkovchains.md.DhkAaXJV.js +++ b/dev/assets/biomarkovchains.md.0rg0z1ev.js @@ -1 +1 @@ -import{_ as s,c as a,l as t,a as Q,a7 as e,o as T}from"./chunks/framework.D1rHXXmm.js";const g6=JSON.parse('{"title":"Towards Markov Chains","description":"","frontmatter":{},"headers":[],"relativePath":"biomarkovchains.md","filePath":"biomarkovchains.md","lastUpdated":null}'),l={name:"biomarkovchains.md"},o=e('

Towards Markov Chains ​

DNA as a Markov chain ​

Several packages (e.g. MarkovChainsHammer.jl, DiscreteMarkovChains.jl, etc.) in the Julia ecosystem have been implemented to work with Markov chains with a state space of integers, those could be efficient in many ways, but they are clumsy to work with a specialized biological types as in the BioJulia ecosystem. Therefore, in the GeneFinder package we dedicated some implementations to work with BioSequence types so that we can expand the functionality in an efficient way (see complete API).

',3),n={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"20.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8850.6 1000","aria-hidden":"true"},m=e('',1),r=[m],i=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{fence:"false",stretchy:"false"},"{"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T"),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),h={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p=e('',1),g=[p],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w=t("em",null,"state (vertex)",-1),u=t("em",null,"transitions",-1),H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.316ex",height:"1.645ex",role:"img",focusable:"false",viewBox:"0 -716 3675.6 727","aria-hidden":"true"},L=e('',1),f=[L],M=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"→"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},Z=e('',1),b=[Z],V=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),v={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.639ex",height:"1.902ex",role:"img",focusable:"false",viewBox:"0 -683 1166.3 840.8","aria-hidden":"true"},j=e('',1),A=[j],C=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])])])],-1),R={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.175ex",height:"1.622ex",role:"img",focusable:"false",viewBox:"0 -677 2287.6 717","aria-hidden":"true"},O=e('',1),P=[O],X=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"∈"),t("mi",null,"T")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},B=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),G=[B],N=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),z=t("em",null,"only dependent of the current state",-1),J=t("em",null,"Markov property",-1),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.157ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8467.3 1000","aria-hidden":"true"},$=e('',1),U=[$],W=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("mi",null,"j"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("mi",null,"i"),t("mo",{stretchy:"false"},")")])])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.668ex",height:"2.084ex",role:"img",focusable:"false",viewBox:"0 -717 4273.2 921","aria-hidden":"true"},t1=e('',1),Q1=[t1],a1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"j"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"∈"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),T1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},s1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),l1=[s1],o1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),n1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.827ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4785.4 1000","aria-hidden":"true"},m1=e('',1),r1=[m1],i1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")")])],-1),h1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p1=e('',1),g1=[p1],x1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w1={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.799ex"},xmlns:"http://www.w3.org/2000/svg",width:"64.783ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1737.3 28634.2 2974.6","aria-hidden":"true"},H1=e('',1),_1=[H1],L1=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,","),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,","),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")"),t("munderover",null,[t("mo",{"data-mjx-texclass":"OP"},"∏"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])])])])],-1),f1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.106ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4908.7 1000","aria-hidden":"true"},k1=e('',1),y1=[k1],Z1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])],-1),b1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.965ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2194.6 748","aria-hidden":"true"},v1=e('',1),D1=[v1],j1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")])],-1),A1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},C1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},R1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),S1=[R1],O1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),P1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},X1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.676ex",role:"img",focusable:"false",viewBox:"0 -1133 1216 1183","aria-hidden":"true"},E1=e('',1),I1=[E1],B1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")]),t("mo",null,"^")])])])],-1),G1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},N1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"2.119ex",height:"1.887ex",role:"img",focusable:"false",viewBox:"0 -833.9 936.6 833.9","aria-hidden":"true"},z1=e('',1),J1=[z1],q1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msup",null,[t("mn",null,"4"),t("mn",null,"2")])])],-1),F1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},$1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.078ex",height:"2.059ex",role:"img",focusable:"false",viewBox:"0 -716 7548.3 910","aria-hidden":"true"},U1=e('',1),W1=[U1],K1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"."),t("mo",null,"."),t("mo",null,".")])],-1),Y1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},t2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.557ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -677 1572 688","aria-hidden":"true"},Q2=e('',1),a2=[Q2],T2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mn",null,"4"),t("mi",null,"x"),t("mn",null,"4")])],-1),e2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},s2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},l2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),o2=[l2],n2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),d2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},m2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.312ex",height:"1.67ex",role:"img",focusable:"false",viewBox:"0 -716 18260 738","aria-hidden":"true"},r2=e('',1),i2=[r2],h2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C")])],-1),c2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},p2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.08ex",height:"2.98ex",role:"img",focusable:"false",viewBox:"0 -860.6 4013.2 1317.2","aria-hidden":"true"},g2=e('',1),x2=[g2],w2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"m"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])])],-1),u2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},H2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},_2=e('',1),L2=[_2],f2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),M2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.719ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 760 599.8","aria-hidden":"true"},y2=e('',1),Z2=[y2],b2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])],-1),V2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.781ex",height:"1.52ex",role:"img",focusable:"false",viewBox:"0 -661 345 672","aria-hidden":"true"},D2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D456",d:"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),j2=[D2],A2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i")])],-1),C2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},R2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-6.9ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.934ex",height:"14.932ex",role:"img",focusable:"false",viewBox:"0 -3550 13231 6600","aria-hidden":"true"},S2=e('',1),O2=[S2],P2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"["),t("mtable",{columnspacing:"1em",rowspacing:"4pt"},[t("mtr",null,[t("mtd"),t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mtext",null,"T")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"1.00")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.56")]),t("mtd",null,[t("mn",null,"0.22")]),t("mtd",null,[t("mn",null,"0.30")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mn",null,"0.25")]),t("mtd",null,[t("mn",null,"0.12")]),t("mtd",null,[t("mn",null,"0.62")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"T")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.67")]),t("mtd",null,[t("mn",null,"0.33")]),t("mtd",null,[t("mn",null,"0.00")])])]),t("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),X2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},I2=e('',1),B2=[I2],G2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),N2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.001ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 884.4 599.8","aria-hidden":"true"},J2=e('',1),q2=[J2],F2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])],-1),$2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.834ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.83ex",height:"4.799ex",role:"img",focusable:"false",viewBox:"0 -1310.6 5229 2121.1","aria-hidden":"true"},W2=e('',1),K2=[W2],Y2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mrow",null,[t("munder",null,[t("mo",{"data-mjx-texclass":"OP"},"∑"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])])])])])])],-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"26.682ex",height:"2.466ex",role:"img",focusable:"false",viewBox:"0 -840 11793.6 1090","aria-hidden":"true"},a6=e('',1),T6=[a6],e6=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"("),t("mn",null,"0.08"),t("mo",null,","),t("mn",null,"0.43"),t("mo",null,","),t("mn",null,"0.34"),t("mo",null,","),t("mn",null,"0.13"),t("mo",{stretchy:"false"},")")])],-1),s6=t("em",null,"transition model",-1),l6=t("h2",{id:"References",tabindex:"-1"},[Q("References "),t("a",{class:"header-anchor",href:"#References","aria-label":'Permalink to "References {#References}"'},"​")],-1),o6=t("p",null,[Q("Axelson-Fisk, Marina. 2015. "),t("em",null,"Comparative Gene Finding"),Q(". Vol. 20. Computational Biology. London: Springer London. "),t("a",{href:"http://link.springer.com/10.1007/978-1-4471-6693-1",target:"_blank",rel:"noreferrer"},"http://link.springer.com/10.1007/978-1-4471-6693-1"),Q(".")],-1);function n6(d6,m6,r6,i6,h6,c6){return T(),a("div",null,[o,t("p",null,[Q("One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet "),t("mjx-container",n,[(T(),a("svg",d,r)),i]),Q(" is draw as a four-vertex graph, where each letter of "),t("mjx-container",h,[(T(),a("svg",c,g)),x]),Q(" is a "),w,Q(" and the edges of the graph represent "),u,Q(" from one nucleotide to another in a sequence (e.g. "),t("mjx-container",H,[(T(),a("svg",_,f)),M]),Q(" represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet "),t("mjx-container",k,[(T(),a("svg",y,b)),V]),Q(".")]),t("p",null,[Q("More formally a Markov chain is a random process where each state is a random variable "),t("mjx-container",v,[(T(),a("svg",D,A)),C]),Q(" where "),t("mjx-container",R,[(T(),a("svg",S,P)),X]),Q(" is a discrete time in a finite sequence "),t("mjx-container",E,[(T(),a("svg",I,G)),N]),Q(" and the probability to jump from one state into another is "),z,Q(". Therefore a definition of this "),J,Q(" is given by:")]),t("mjx-container",q,[(T(),a("svg",F,U)),W]),t("p",null,[Q("where "),t("mjx-container",K,[(T(),a("svg",Y,Q1)),a1]),Q(" . This property led us to generalize a way to calculate the probability of a sequence "),t("mjx-container",T1,[(T(),a("svg",e1,l1)),o1]),Q(" from a process "),t("mjx-container",n1,[(T(),a("svg",d1,r1)),i1]),Q(" where each random variable is a nucleotide from "),t("mjx-container",h1,[(T(),a("svg",c1,g1)),x1]),Q(" so that:")]),t("mjx-container",w1,[(T(),a("svg",u1,_1)),L1]),t("p",null,[Q("Note that previous equations has two terms, a initial probability "),t("mjx-container",f1,[(T(),a("svg",M1,y1)),Z1]),Q(" and the the product of all transitions beginning at "),t("mjx-container",b1,[(T(),a("svg",V1,D1)),j1]),Q(". So, to calculate the initial probability distribution of each of the nucleotides of a string "),t("mjx-container",A1,[(T(),a("svg",C1,S1)),O1]),Q(" with the alphabet 𝒜 we can first calculate the transition probability matrix "),t("mjx-container",P1,[(T(),a("svg",X1,I1)),B1]),Q(" out of the frequency count of the transitions. In an alphabet 𝒜 we got "),t("mjx-container",G1,[(T(),a("svg",N1,J1)),q1]),Q(" transitions of one order, that is the "),t("mjx-container",F1,[(T(),a("svg",$1,W1)),K1]),Q(" which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a "),t("mjx-container",Y1,[(T(),a("svg",t2,a2)),T2]),Q(" matrix representing all the transitions. For instance in a DNA sequence "),t("mjx-container",e2,[(T(),a("svg",s2,o2)),n2]),Q(" of 24 nucleotides:")]),t("mjx-container",d2,[(T(),a("svg",m2,i2)),h2]),t("p",null,[Q("We can calculate each frequency nucleotide to any other nucleotide "),t("mjx-container",c2,[(T(),a("svg",p2,x2)),w2]),Q(" where "),t("mjx-container",u2,[(T(),a("svg",H2,L2)),f2]),Q(" is the actual count of the dinucleotide, and therefore "),t("mjx-container",M2,[(T(),a("svg",k2,Z2)),b2]),Q(" is the counts of the nucleotide "),t("mjx-container",V2,[(T(),a("svg",v2,j2)),A2]),Q(" to any other nucleotide and build the transition probability matrix:")]),t("mjx-container",C2,[(T(),a("svg",R2,O2)),P2]),t("p",null,[Q("It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions "),t("mjx-container",X2,[(T(),a("svg",E2,B2)),G2]),Q(" over the total sum of the dinucleotide counts "),t("mjx-container",N2,[(T(),a("svg",z2,q2)),F2]),Q(":")]),t("mjx-container",$2,[(T(),a("svg",U2,K2)),Y2]),t("p",null,[Q("That way for the previous example example we can can calculate the initial probabilities "),t("mjx-container",t6,[(T(),a("svg",Q6,T6)),e6]),Q(". Both set of probabilities composed a "),s6,Q(" that can be used to predict the probability of any DNA sequence using equation (2).")]),l6,o6])}const x6=s(l,[["render",n6]]);export{g6 as __pageData,x6 as default}; +import{_ as s,c as a,j as t,a as Q,a6 as e,o as T}from"./chunks/framework.Cvv1S4VC.js";const g6=JSON.parse('{"title":"Towards Markov Chains","description":"","frontmatter":{},"headers":[],"relativePath":"biomarkovchains.md","filePath":"biomarkovchains.md","lastUpdated":null}'),l={name:"biomarkovchains.md"},o=e('

Towards Markov Chains ​

DNA as a Markov chain ​

Several packages (e.g. MarkovChainsHammer.jl, DiscreteMarkovChains.jl, etc.) in the Julia ecosystem have been implemented to work with Markov chains with a state space of integers, those could be efficient in many ways, but they are clumsy to work with a specialized biological types as in the BioJulia ecosystem. Therefore, in the GeneFinder package we dedicated some implementations to work with BioSequence types so that we can expand the functionality in an efficient way (see complete API).

',3),n={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"20.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8850.6 1000","aria-hidden":"true"},m=e('',1),r=[m],i=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{fence:"false",stretchy:"false"},"{"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T"),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),h={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p=e('',1),g=[p],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w=t("em",null,"state (vertex)",-1),u=t("em",null,"transitions",-1),H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.316ex",height:"1.645ex",role:"img",focusable:"false",viewBox:"0 -716 3675.6 727","aria-hidden":"true"},L=e('',1),f=[L],M=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"→"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},Z=e('',1),b=[Z],V=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),v={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.639ex",height:"1.902ex",role:"img",focusable:"false",viewBox:"0 -683 1166.3 840.8","aria-hidden":"true"},j=e('',1),A=[j],C=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])])])],-1),R={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.175ex",height:"1.622ex",role:"img",focusable:"false",viewBox:"0 -677 2287.6 717","aria-hidden":"true"},O=e('',1),P=[O],X=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"∈"),t("mi",null,"T")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},B=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),G=[B],N=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),z=t("em",null,"only dependent of the current state",-1),J=t("em",null,"Markov property",-1),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.157ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8467.3 1000","aria-hidden":"true"},$=e('',1),U=[$],W=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("mi",null,"j"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("mi",null,"i"),t("mo",{stretchy:"false"},")")])])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.668ex",height:"2.084ex",role:"img",focusable:"false",viewBox:"0 -717 4273.2 921","aria-hidden":"true"},t1=e('',1),Q1=[t1],a1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"j"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"∈"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),T1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},s1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),l1=[s1],o1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),n1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.827ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4785.4 1000","aria-hidden":"true"},m1=e('',1),r1=[m1],i1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")")])],-1),h1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p1=e('',1),g1=[p1],x1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w1={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.799ex"},xmlns:"http://www.w3.org/2000/svg",width:"64.783ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1737.3 28634.2 2974.6","aria-hidden":"true"},H1=e('',1),_1=[H1],L1=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,","),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,","),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")"),t("munderover",null,[t("mo",{"data-mjx-texclass":"OP"},"∏"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])])])])],-1),f1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.106ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4908.7 1000","aria-hidden":"true"},k1=e('',1),y1=[k1],Z1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])],-1),b1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.965ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2194.6 748","aria-hidden":"true"},v1=e('',1),D1=[v1],j1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")])],-1),A1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},C1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},R1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),S1=[R1],O1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),P1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},X1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.676ex",role:"img",focusable:"false",viewBox:"0 -1133 1216 1183","aria-hidden":"true"},E1=e('',1),I1=[E1],B1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")]),t("mo",null,"^")])])])],-1),G1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},N1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"2.119ex",height:"1.887ex",role:"img",focusable:"false",viewBox:"0 -833.9 936.6 833.9","aria-hidden":"true"},z1=e('',1),J1=[z1],q1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msup",null,[t("mn",null,"4"),t("mn",null,"2")])])],-1),F1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},$1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.078ex",height:"2.059ex",role:"img",focusable:"false",viewBox:"0 -716 7548.3 910","aria-hidden":"true"},U1=e('',1),W1=[U1],K1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"."),t("mo",null,"."),t("mo",null,".")])],-1),Y1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},t2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.557ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -677 1572 688","aria-hidden":"true"},Q2=e('',1),a2=[Q2],T2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mn",null,"4"),t("mi",null,"x"),t("mn",null,"4")])],-1),e2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},s2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},l2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),o2=[l2],n2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),d2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},m2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.312ex",height:"1.67ex",role:"img",focusable:"false",viewBox:"0 -716 18260 738","aria-hidden":"true"},r2=e('',1),i2=[r2],h2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C")])],-1),c2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},p2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.08ex",height:"2.98ex",role:"img",focusable:"false",viewBox:"0 -860.6 4013.2 1317.2","aria-hidden":"true"},g2=e('',1),x2=[g2],w2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"m"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])])],-1),u2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},H2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},_2=e('',1),L2=[_2],f2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),M2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.719ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 760 599.8","aria-hidden":"true"},y2=e('',1),Z2=[y2],b2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])],-1),V2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.781ex",height:"1.52ex",role:"img",focusable:"false",viewBox:"0 -661 345 672","aria-hidden":"true"},D2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D456",d:"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),j2=[D2],A2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i")])],-1),C2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},R2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-6.9ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.934ex",height:"14.932ex",role:"img",focusable:"false",viewBox:"0 -3550 13231 6600","aria-hidden":"true"},S2=e('',1),O2=[S2],P2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"["),t("mtable",{columnspacing:"1em",rowspacing:"4pt"},[t("mtr",null,[t("mtd"),t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mtext",null,"T")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"1.00")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.56")]),t("mtd",null,[t("mn",null,"0.22")]),t("mtd",null,[t("mn",null,"0.30")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mn",null,"0.25")]),t("mtd",null,[t("mn",null,"0.12")]),t("mtd",null,[t("mn",null,"0.62")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"T")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.67")]),t("mtd",null,[t("mn",null,"0.33")]),t("mtd",null,[t("mn",null,"0.00")])])]),t("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),X2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},I2=e('',1),B2=[I2],G2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),N2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.001ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 884.4 599.8","aria-hidden":"true"},J2=e('',1),q2=[J2],F2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])],-1),$2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.834ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.83ex",height:"4.799ex",role:"img",focusable:"false",viewBox:"0 -1310.6 5229 2121.1","aria-hidden":"true"},W2=e('',1),K2=[W2],Y2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mrow",null,[t("munder",null,[t("mo",{"data-mjx-texclass":"OP"},"∑"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])])])])])])],-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"26.682ex",height:"2.466ex",role:"img",focusable:"false",viewBox:"0 -840 11793.6 1090","aria-hidden":"true"},a6=e('',1),T6=[a6],e6=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"("),t("mn",null,"0.08"),t("mo",null,","),t("mn",null,"0.43"),t("mo",null,","),t("mn",null,"0.34"),t("mo",null,","),t("mn",null,"0.13"),t("mo",{stretchy:"false"},")")])],-1),s6=t("em",null,"transition model",-1),l6=t("h2",{id:"References",tabindex:"-1"},[Q("References "),t("a",{class:"header-anchor",href:"#References","aria-label":'Permalink to "References {#References}"'},"​")],-1),o6=t("p",null,[Q("Axelson-Fisk, Marina. 2015. "),t("em",null,"Comparative Gene Finding"),Q(". Vol. 20. Computational Biology. London: Springer London. "),t("a",{href:"http://link.springer.com/10.1007/978-1-4471-6693-1",target:"_blank",rel:"noreferrer"},"http://link.springer.com/10.1007/978-1-4471-6693-1"),Q(".")],-1);function n6(d6,m6,r6,i6,h6,c6){return T(),a("div",null,[o,t("p",null,[Q("One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet "),t("mjx-container",n,[(T(),a("svg",d,r)),i]),Q(" is draw as a four-vertex graph, where each letter of "),t("mjx-container",h,[(T(),a("svg",c,g)),x]),Q(" is a "),w,Q(" and the edges of the graph represent "),u,Q(" from one nucleotide to another in a sequence (e.g. "),t("mjx-container",H,[(T(),a("svg",_,f)),M]),Q(" represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet "),t("mjx-container",k,[(T(),a("svg",y,b)),V]),Q(".")]),t("p",null,[Q("More formally a Markov chain is a random process where each state is a random variable "),t("mjx-container",v,[(T(),a("svg",D,A)),C]),Q(" where "),t("mjx-container",R,[(T(),a("svg",S,P)),X]),Q(" is a discrete time in a finite sequence "),t("mjx-container",E,[(T(),a("svg",I,G)),N]),Q(" and the probability to jump from one state into another is "),z,Q(". Therefore a definition of this "),J,Q(" is given by:")]),t("mjx-container",q,[(T(),a("svg",F,U)),W]),t("p",null,[Q("where "),t("mjx-container",K,[(T(),a("svg",Y,Q1)),a1]),Q(" . This property led us to generalize a way to calculate the probability of a sequence "),t("mjx-container",T1,[(T(),a("svg",e1,l1)),o1]),Q(" from a process "),t("mjx-container",n1,[(T(),a("svg",d1,r1)),i1]),Q(" where each random variable is a nucleotide from "),t("mjx-container",h1,[(T(),a("svg",c1,g1)),x1]),Q(" so that:")]),t("mjx-container",w1,[(T(),a("svg",u1,_1)),L1]),t("p",null,[Q("Note that previous equations has two terms, a initial probability "),t("mjx-container",f1,[(T(),a("svg",M1,y1)),Z1]),Q(" and the the product of all transitions beginning at "),t("mjx-container",b1,[(T(),a("svg",V1,D1)),j1]),Q(". So, to calculate the initial probability distribution of each of the nucleotides of a string "),t("mjx-container",A1,[(T(),a("svg",C1,S1)),O1]),Q(" with the alphabet 𝒜 we can first calculate the transition probability matrix "),t("mjx-container",P1,[(T(),a("svg",X1,I1)),B1]),Q(" out of the frequency count of the transitions. In an alphabet 𝒜 we got "),t("mjx-container",G1,[(T(),a("svg",N1,J1)),q1]),Q(" transitions of one order, that is the "),t("mjx-container",F1,[(T(),a("svg",$1,W1)),K1]),Q(" which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a "),t("mjx-container",Y1,[(T(),a("svg",t2,a2)),T2]),Q(" matrix representing all the transitions. For instance in a DNA sequence "),t("mjx-container",e2,[(T(),a("svg",s2,o2)),n2]),Q(" of 24 nucleotides:")]),t("mjx-container",d2,[(T(),a("svg",m2,i2)),h2]),t("p",null,[Q("We can calculate each frequency nucleotide to any other nucleotide "),t("mjx-container",c2,[(T(),a("svg",p2,x2)),w2]),Q(" where "),t("mjx-container",u2,[(T(),a("svg",H2,L2)),f2]),Q(" is the actual count of the dinucleotide, and therefore "),t("mjx-container",M2,[(T(),a("svg",k2,Z2)),b2]),Q(" is the counts of the nucleotide "),t("mjx-container",V2,[(T(),a("svg",v2,j2)),A2]),Q(" to any other nucleotide and build the transition probability matrix:")]),t("mjx-container",C2,[(T(),a("svg",R2,O2)),P2]),t("p",null,[Q("It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions "),t("mjx-container",X2,[(T(),a("svg",E2,B2)),G2]),Q(" over the total sum of the dinucleotide counts "),t("mjx-container",N2,[(T(),a("svg",z2,q2)),F2]),Q(":")]),t("mjx-container",$2,[(T(),a("svg",U2,K2)),Y2]),t("p",null,[Q("That way for the previous example example we can can calculate the initial probabilities "),t("mjx-container",t6,[(T(),a("svg",Q6,T6)),e6]),Q(". Both set of probabilities composed a "),s6,Q(" that can be used to predict the probability of any DNA sequence using equation (2).")]),l6,o6])}const x6=s(l,[["render",n6]]);export{g6 as __pageData,x6 as default}; diff --git a/dev/assets/biomarkovchains.md.DhkAaXJV.lean.js b/dev/assets/biomarkovchains.md.0rg0z1ev.lean.js similarity index 99% rename from dev/assets/biomarkovchains.md.DhkAaXJV.lean.js rename to dev/assets/biomarkovchains.md.0rg0z1ev.lean.js index ebe5f0b..2b57b56 100644 --- a/dev/assets/biomarkovchains.md.DhkAaXJV.lean.js +++ b/dev/assets/biomarkovchains.md.0rg0z1ev.lean.js @@ -1 +1 @@ -import{_ as s,c as a,l as t,a as Q,a7 as e,o as T}from"./chunks/framework.D1rHXXmm.js";const g6=JSON.parse('{"title":"Towards Markov Chains","description":"","frontmatter":{},"headers":[],"relativePath":"biomarkovchains.md","filePath":"biomarkovchains.md","lastUpdated":null}'),l={name:"biomarkovchains.md"},o=e("",3),n={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"20.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8850.6 1000","aria-hidden":"true"},m=e("",1),r=[m],i=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{fence:"false",stretchy:"false"},"{"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T"),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),h={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p=e("",1),g=[p],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w=t("em",null,"state (vertex)",-1),u=t("em",null,"transitions",-1),H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.316ex",height:"1.645ex",role:"img",focusable:"false",viewBox:"0 -716 3675.6 727","aria-hidden":"true"},L=e("",1),f=[L],M=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"→"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},Z=e("",1),b=[Z],V=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),v={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.639ex",height:"1.902ex",role:"img",focusable:"false",viewBox:"0 -683 1166.3 840.8","aria-hidden":"true"},j=e("",1),A=[j],C=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])])])],-1),R={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.175ex",height:"1.622ex",role:"img",focusable:"false",viewBox:"0 -677 2287.6 717","aria-hidden":"true"},O=e("",1),P=[O],X=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"∈"),t("mi",null,"T")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},B=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),G=[B],N=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),z=t("em",null,"only dependent of the current state",-1),J=t("em",null,"Markov property",-1),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.157ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8467.3 1000","aria-hidden":"true"},$=e("",1),U=[$],W=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("mi",null,"j"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("mi",null,"i"),t("mo",{stretchy:"false"},")")])])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.668ex",height:"2.084ex",role:"img",focusable:"false",viewBox:"0 -717 4273.2 921","aria-hidden":"true"},t1=e("",1),Q1=[t1],a1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"j"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"∈"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),T1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},s1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),l1=[s1],o1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),n1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.827ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4785.4 1000","aria-hidden":"true"},m1=e("",1),r1=[m1],i1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")")])],-1),h1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p1=e("",1),g1=[p1],x1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w1={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.799ex"},xmlns:"http://www.w3.org/2000/svg",width:"64.783ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1737.3 28634.2 2974.6","aria-hidden":"true"},H1=e("",1),_1=[H1],L1=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,","),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,","),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")"),t("munderover",null,[t("mo",{"data-mjx-texclass":"OP"},"∏"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])])])])],-1),f1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.106ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4908.7 1000","aria-hidden":"true"},k1=e("",1),y1=[k1],Z1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])],-1),b1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.965ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2194.6 748","aria-hidden":"true"},v1=e("",1),D1=[v1],j1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")])],-1),A1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},C1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},R1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),S1=[R1],O1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),P1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},X1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.676ex",role:"img",focusable:"false",viewBox:"0 -1133 1216 1183","aria-hidden":"true"},E1=e("",1),I1=[E1],B1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")]),t("mo",null,"^")])])])],-1),G1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},N1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"2.119ex",height:"1.887ex",role:"img",focusable:"false",viewBox:"0 -833.9 936.6 833.9","aria-hidden":"true"},z1=e("",1),J1=[z1],q1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msup",null,[t("mn",null,"4"),t("mn",null,"2")])])],-1),F1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},$1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.078ex",height:"2.059ex",role:"img",focusable:"false",viewBox:"0 -716 7548.3 910","aria-hidden":"true"},U1=e("",1),W1=[U1],K1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"."),t("mo",null,"."),t("mo",null,".")])],-1),Y1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},t2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.557ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -677 1572 688","aria-hidden":"true"},Q2=e("",1),a2=[Q2],T2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mn",null,"4"),t("mi",null,"x"),t("mn",null,"4")])],-1),e2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},s2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},l2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),o2=[l2],n2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),d2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},m2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.312ex",height:"1.67ex",role:"img",focusable:"false",viewBox:"0 -716 18260 738","aria-hidden":"true"},r2=e("",1),i2=[r2],h2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C")])],-1),c2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},p2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.08ex",height:"2.98ex",role:"img",focusable:"false",viewBox:"0 -860.6 4013.2 1317.2","aria-hidden":"true"},g2=e("",1),x2=[g2],w2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"m"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])])],-1),u2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},H2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},_2=e("",1),L2=[_2],f2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),M2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.719ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 760 599.8","aria-hidden":"true"},y2=e("",1),Z2=[y2],b2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])],-1),V2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.781ex",height:"1.52ex",role:"img",focusable:"false",viewBox:"0 -661 345 672","aria-hidden":"true"},D2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D456",d:"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),j2=[D2],A2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i")])],-1),C2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},R2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-6.9ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.934ex",height:"14.932ex",role:"img",focusable:"false",viewBox:"0 -3550 13231 6600","aria-hidden":"true"},S2=e("",1),O2=[S2],P2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"["),t("mtable",{columnspacing:"1em",rowspacing:"4pt"},[t("mtr",null,[t("mtd"),t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mtext",null,"T")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"1.00")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.56")]),t("mtd",null,[t("mn",null,"0.22")]),t("mtd",null,[t("mn",null,"0.30")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mn",null,"0.25")]),t("mtd",null,[t("mn",null,"0.12")]),t("mtd",null,[t("mn",null,"0.62")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"T")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.67")]),t("mtd",null,[t("mn",null,"0.33")]),t("mtd",null,[t("mn",null,"0.00")])])]),t("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),X2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},I2=e("",1),B2=[I2],G2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),N2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.001ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 884.4 599.8","aria-hidden":"true"},J2=e("",1),q2=[J2],F2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])],-1),$2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.834ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.83ex",height:"4.799ex",role:"img",focusable:"false",viewBox:"0 -1310.6 5229 2121.1","aria-hidden":"true"},W2=e("",1),K2=[W2],Y2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mrow",null,[t("munder",null,[t("mo",{"data-mjx-texclass":"OP"},"∑"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])])])])])])],-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"26.682ex",height:"2.466ex",role:"img",focusable:"false",viewBox:"0 -840 11793.6 1090","aria-hidden":"true"},a6=e("",1),T6=[a6],e6=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"("),t("mn",null,"0.08"),t("mo",null,","),t("mn",null,"0.43"),t("mo",null,","),t("mn",null,"0.34"),t("mo",null,","),t("mn",null,"0.13"),t("mo",{stretchy:"false"},")")])],-1),s6=t("em",null,"transition model",-1),l6=t("h2",{id:"References",tabindex:"-1"},[Q("References "),t("a",{class:"header-anchor",href:"#References","aria-label":'Permalink to "References {#References}"'},"​")],-1),o6=t("p",null,[Q("Axelson-Fisk, Marina. 2015. "),t("em",null,"Comparative Gene Finding"),Q(". Vol. 20. Computational Biology. London: Springer London. "),t("a",{href:"http://link.springer.com/10.1007/978-1-4471-6693-1",target:"_blank",rel:"noreferrer"},"http://link.springer.com/10.1007/978-1-4471-6693-1"),Q(".")],-1);function n6(d6,m6,r6,i6,h6,c6){return T(),a("div",null,[o,t("p",null,[Q("One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet "),t("mjx-container",n,[(T(),a("svg",d,r)),i]),Q(" is draw as a four-vertex graph, where each letter of "),t("mjx-container",h,[(T(),a("svg",c,g)),x]),Q(" is a "),w,Q(" and the edges of the graph represent "),u,Q(" from one nucleotide to another in a sequence (e.g. "),t("mjx-container",H,[(T(),a("svg",_,f)),M]),Q(" represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet "),t("mjx-container",k,[(T(),a("svg",y,b)),V]),Q(".")]),t("p",null,[Q("More formally a Markov chain is a random process where each state is a random variable "),t("mjx-container",v,[(T(),a("svg",D,A)),C]),Q(" where "),t("mjx-container",R,[(T(),a("svg",S,P)),X]),Q(" is a discrete time in a finite sequence "),t("mjx-container",E,[(T(),a("svg",I,G)),N]),Q(" and the probability to jump from one state into another is "),z,Q(". Therefore a definition of this "),J,Q(" is given by:")]),t("mjx-container",q,[(T(),a("svg",F,U)),W]),t("p",null,[Q("where "),t("mjx-container",K,[(T(),a("svg",Y,Q1)),a1]),Q(" . This property led us to generalize a way to calculate the probability of a sequence "),t("mjx-container",T1,[(T(),a("svg",e1,l1)),o1]),Q(" from a process "),t("mjx-container",n1,[(T(),a("svg",d1,r1)),i1]),Q(" where each random variable is a nucleotide from "),t("mjx-container",h1,[(T(),a("svg",c1,g1)),x1]),Q(" so that:")]),t("mjx-container",w1,[(T(),a("svg",u1,_1)),L1]),t("p",null,[Q("Note that previous equations has two terms, a initial probability "),t("mjx-container",f1,[(T(),a("svg",M1,y1)),Z1]),Q(" and the the product of all transitions beginning at "),t("mjx-container",b1,[(T(),a("svg",V1,D1)),j1]),Q(". So, to calculate the initial probability distribution of each of the nucleotides of a string "),t("mjx-container",A1,[(T(),a("svg",C1,S1)),O1]),Q(" with the alphabet 𝒜 we can first calculate the transition probability matrix "),t("mjx-container",P1,[(T(),a("svg",X1,I1)),B1]),Q(" out of the frequency count of the transitions. In an alphabet 𝒜 we got "),t("mjx-container",G1,[(T(),a("svg",N1,J1)),q1]),Q(" transitions of one order, that is the "),t("mjx-container",F1,[(T(),a("svg",$1,W1)),K1]),Q(" which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a "),t("mjx-container",Y1,[(T(),a("svg",t2,a2)),T2]),Q(" matrix representing all the transitions. For instance in a DNA sequence "),t("mjx-container",e2,[(T(),a("svg",s2,o2)),n2]),Q(" of 24 nucleotides:")]),t("mjx-container",d2,[(T(),a("svg",m2,i2)),h2]),t("p",null,[Q("We can calculate each frequency nucleotide to any other nucleotide "),t("mjx-container",c2,[(T(),a("svg",p2,x2)),w2]),Q(" where "),t("mjx-container",u2,[(T(),a("svg",H2,L2)),f2]),Q(" is the actual count of the dinucleotide, and therefore "),t("mjx-container",M2,[(T(),a("svg",k2,Z2)),b2]),Q(" is the counts of the nucleotide "),t("mjx-container",V2,[(T(),a("svg",v2,j2)),A2]),Q(" to any other nucleotide and build the transition probability matrix:")]),t("mjx-container",C2,[(T(),a("svg",R2,O2)),P2]),t("p",null,[Q("It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions "),t("mjx-container",X2,[(T(),a("svg",E2,B2)),G2]),Q(" over the total sum of the dinucleotide counts "),t("mjx-container",N2,[(T(),a("svg",z2,q2)),F2]),Q(":")]),t("mjx-container",$2,[(T(),a("svg",U2,K2)),Y2]),t("p",null,[Q("That way for the previous example example we can can calculate the initial probabilities "),t("mjx-container",t6,[(T(),a("svg",Q6,T6)),e6]),Q(". Both set of probabilities composed a "),s6,Q(" that can be used to predict the probability of any DNA sequence using equation (2).")]),l6,o6])}const x6=s(l,[["render",n6]]);export{g6 as __pageData,x6 as default}; +import{_ as s,c as a,j as t,a as Q,a6 as e,o as T}from"./chunks/framework.Cvv1S4VC.js";const g6=JSON.parse('{"title":"Towards Markov Chains","description":"","frontmatter":{},"headers":[],"relativePath":"biomarkovchains.md","filePath":"biomarkovchains.md","lastUpdated":null}'),l={name:"biomarkovchains.md"},o=e("",3),n={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"20.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8850.6 1000","aria-hidden":"true"},m=e("",1),r=[m],i=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{fence:"false",stretchy:"false"},"{"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T"),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),h={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p=e("",1),g=[p],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w=t("em",null,"state (vertex)",-1),u=t("em",null,"transitions",-1),H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.316ex",height:"1.645ex",role:"img",focusable:"false",viewBox:"0 -716 3675.6 727","aria-hidden":"true"},L=e("",1),f=[L],M=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"→"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"T")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},Z=e("",1),b=[Z],V=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),v={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.639ex",height:"1.902ex",role:"img",focusable:"false",viewBox:"0 -683 1166.3 840.8","aria-hidden":"true"},j=e("",1),A=[j],C=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])])])],-1),R={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.175ex",height:"1.622ex",role:"img",focusable:"false",viewBox:"0 -677 2287.6 717","aria-hidden":"true"},O=e("",1),P=[O],X=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"∈"),t("mi",null,"T")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},B=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),G=[B],N=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),z=t("em",null,"only dependent of the current state",-1),J=t("em",null,"Markov property",-1),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.157ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8467.3 1000","aria-hidden":"true"},$=e("",1),U=[$],W=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("mi",null,"j"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("mi",null,"i"),t("mo",{stretchy:"false"},")")])])])])],-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.668ex",height:"2.084ex",role:"img",focusable:"false",viewBox:"0 -717 4273.2 921","aria-hidden":"true"},t1=e("",1),Q1=[t1],a1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"j"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"∈"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),T1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},e1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},s1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),l1=[s1],o1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),n1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.827ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4785.4 1000","aria-hidden":"true"},m1=e("",1),r1=[m1],i1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")")])],-1),h1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.018ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.299ex",height:"1.64ex",role:"img",focusable:"false",viewBox:"0 -717 1016 725","aria-hidden":"true"},p1=e("",1),g1=[p1],x1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"A")])])],-1),w1={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.799ex"},xmlns:"http://www.w3.org/2000/svg",width:"64.783ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1737.3 28634.2 2974.6","aria-hidden":"true"},H1=e("",1),_1=[H1],L1=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,","),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,","),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")"),t("munderover",null,[t("mo",{"data-mjx-texclass":"OP"},"∏"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"T")])]),t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t")])]),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])])])])],-1),f1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.106ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4908.7 1000","aria-hidden":"true"},k1=e("",1),y1=[k1],Z1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"P"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"X"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",null,"="),t("msub",null,[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1")])]),t("mo",{stretchy:"false"},")")])],-1),b1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.965ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2194.6 748","aria-hidden":"true"},v1=e("",1),D1=[v1],j1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"t"),t("mo",null,"="),t("mn",null,"2")])],-1),A1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},C1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},R1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),S1=[R1],O1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),P1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},X1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"2.676ex",role:"img",focusable:"false",viewBox:"0 -1133 1216 1183","aria-hidden":"true"},E1=e("",1),I1=[E1],B1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")]),t("mo",null,"^")])])])],-1),G1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},N1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"2.119ex",height:"1.887ex",role:"img",focusable:"false",viewBox:"0 -833.9 936.6 833.9","aria-hidden":"true"},z1=e("",1),J1=[z1],q1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msup",null,[t("mn",null,"4"),t("mn",null,"2")])])],-1),F1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},$1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.078ex",height:"2.059ex",role:"img",focusable:"false",viewBox:"0 -716 7548.3 910","aria-hidden":"true"},U1=e("",1),W1=[U1],K1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"A"),t("mi",null,"A"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"C"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mi",null,"A"),t("mi",null,"G"),t("mo",null,","),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"."),t("mo",null,"."),t("mo",null,".")])],-1),Y1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},t2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.557ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -677 1572 688","aria-hidden":"true"},Q2=e("",1),a2=[Q2],T2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mn",null,"4"),t("mi",null,"x"),t("mn",null,"4")])],-1),e2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},s2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.593ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 704 677","aria-hidden":"true"},l2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D447",d:"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",style:{"stroke-width":"3"}})])])],-1),o2=[l2],n2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"T")])],-1),d2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},m2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"41.312ex",height:"1.67ex",role:"img",focusable:"false",viewBox:"0 -716 18260 738","aria-hidden":"true"},r2=e("",1),i2=[r2],h2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"C"),t("mi",null,"T"),t("mi",null,"C"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"G"),t("mi",null,"A"),t("mi",null,"C")])],-1),c2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},p2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.033ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.08ex",height:"2.98ex",role:"img",focusable:"false",viewBox:"0 -860.6 4013.2 1317.2","aria-hidden":"true"},g2=e("",1),x2=[g2],w2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"m"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])])],-1),u2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},H2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},_2=e("",1),L2=[_2],f2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),M2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.719ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 760 599.8","aria-hidden":"true"},y2=e("",1),Z2=[y2],b2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])])])],-1),V2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.781ex",height:"1.52ex",role:"img",focusable:"false",viewBox:"0 -661 345 672","aria-hidden":"true"},D2=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D456",d:"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),j2=[D2],A2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i")])],-1),C2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},R2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-6.9ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.934ex",height:"14.932ex",role:"img",focusable:"false",viewBox:"0 -3550 13231 6600","aria-hidden":"true"},S2=e("",1),O2=[S2],P2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"["),t("mtable",{columnspacing:"1em",rowspacing:"4pt"},[t("mtr",null,[t("mtd"),t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mtext",null,"T")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"A")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"1.00")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"C")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.56")]),t("mtd",null,[t("mn",null,"0.22")]),t("mtd",null,[t("mn",null,"0.30")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"G")]),t("mtd",null,[t("mn",null,"0.25")]),t("mtd",null,[t("mn",null,"0.12")]),t("mtd",null,[t("mn",null,"0.62")]),t("mtd",null,[t("mn",null,"0.00")])]),t("mtr",null,[t("mtd",null,[t("mtext",null,"T")]),t("mtd",null,[t("mn",null,"0.00")]),t("mtd",null,[t("mn",null,"0.67")]),t("mtd",null,[t("mn",null,"0.33")]),t("mtd",null,[t("mn",null,"0.00")])])]),t("mo",{"data-mjx-texclass":"CLOSE"},"]")])])],-1),X2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.378ex",height:"1.666ex",role:"img",focusable:"false",viewBox:"0 -442 1051.3 736.2","aria-hidden":"true"},I2=e("",1),B2=[I2],G2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])])])],-1),N2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.001ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 884.4 599.8","aria-hidden":"true"},J2=e("",1),q2=[J2],F2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])],-1),$2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.834ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.83ex",height:"4.799ex",role:"img",focusable:"false",viewBox:"0 -1310.6 5229 2121.1","aria-hidden":"true"},W2=e("",1),K2=[W2],Y2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right",columnspacing:"",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mo",null,"="),t("mfrac",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mrow",null,[t("munder",null,[t("mo",{"data-mjx-texclass":"OP"},"∑"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])]),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k")])])])])])])])])],-1),t6={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q6={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"26.682ex",height:"2.466ex",role:"img",focusable:"false",viewBox:"0 -840 11793.6 1090","aria-hidden":"true"},a6=e("",1),T6=[a6],e6=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",null,"π"),t("mo",null,"^")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"("),t("mn",null,"0.08"),t("mo",null,","),t("mn",null,"0.43"),t("mo",null,","),t("mn",null,"0.34"),t("mo",null,","),t("mn",null,"0.13"),t("mo",{stretchy:"false"},")")])],-1),s6=t("em",null,"transition model",-1),l6=t("h2",{id:"References",tabindex:"-1"},[Q("References "),t("a",{class:"header-anchor",href:"#References","aria-label":'Permalink to "References {#References}"'},"​")],-1),o6=t("p",null,[Q("Axelson-Fisk, Marina. 2015. "),t("em",null,"Comparative Gene Finding"),Q(". Vol. 20. Computational Biology. London: Springer London. "),t("a",{href:"http://link.springer.com/10.1007/978-1-4471-6693-1",target:"_blank",rel:"noreferrer"},"http://link.springer.com/10.1007/978-1-4471-6693-1"),Q(".")],-1);function n6(d6,m6,r6,i6,h6,c6){return T(),a("div",null,[o,t("p",null,[Q("One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet "),t("mjx-container",n,[(T(),a("svg",d,r)),i]),Q(" is draw as a four-vertex graph, where each letter of "),t("mjx-container",h,[(T(),a("svg",c,g)),x]),Q(" is a "),w,Q(" and the edges of the graph represent "),u,Q(" from one nucleotide to another in a sequence (e.g. "),t("mjx-container",H,[(T(),a("svg",_,f)),M]),Q(" represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet "),t("mjx-container",k,[(T(),a("svg",y,b)),V]),Q(".")]),t("p",null,[Q("More formally a Markov chain is a random process where each state is a random variable "),t("mjx-container",v,[(T(),a("svg",D,A)),C]),Q(" where "),t("mjx-container",R,[(T(),a("svg",S,P)),X]),Q(" is a discrete time in a finite sequence "),t("mjx-container",E,[(T(),a("svg",I,G)),N]),Q(" and the probability to jump from one state into another is "),z,Q(". Therefore a definition of this "),J,Q(" is given by:")]),t("mjx-container",q,[(T(),a("svg",F,U)),W]),t("p",null,[Q("where "),t("mjx-container",K,[(T(),a("svg",Y,Q1)),a1]),Q(" . This property led us to generalize a way to calculate the probability of a sequence "),t("mjx-container",T1,[(T(),a("svg",e1,l1)),o1]),Q(" from a process "),t("mjx-container",n1,[(T(),a("svg",d1,r1)),i1]),Q(" where each random variable is a nucleotide from "),t("mjx-container",h1,[(T(),a("svg",c1,g1)),x1]),Q(" so that:")]),t("mjx-container",w1,[(T(),a("svg",u1,_1)),L1]),t("p",null,[Q("Note that previous equations has two terms, a initial probability "),t("mjx-container",f1,[(T(),a("svg",M1,y1)),Z1]),Q(" and the the product of all transitions beginning at "),t("mjx-container",b1,[(T(),a("svg",V1,D1)),j1]),Q(". So, to calculate the initial probability distribution of each of the nucleotides of a string "),t("mjx-container",A1,[(T(),a("svg",C1,S1)),O1]),Q(" with the alphabet 𝒜 we can first calculate the transition probability matrix "),t("mjx-container",P1,[(T(),a("svg",X1,I1)),B1]),Q(" out of the frequency count of the transitions. In an alphabet 𝒜 we got "),t("mjx-container",G1,[(T(),a("svg",N1,J1)),q1]),Q(" transitions of one order, that is the "),t("mjx-container",F1,[(T(),a("svg",$1,W1)),K1]),Q(" which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a "),t("mjx-container",Y1,[(T(),a("svg",t2,a2)),T2]),Q(" matrix representing all the transitions. For instance in a DNA sequence "),t("mjx-container",e2,[(T(),a("svg",s2,o2)),n2]),Q(" of 24 nucleotides:")]),t("mjx-container",d2,[(T(),a("svg",m2,i2)),h2]),t("p",null,[Q("We can calculate each frequency nucleotide to any other nucleotide "),t("mjx-container",c2,[(T(),a("svg",p2,x2)),w2]),Q(" where "),t("mjx-container",u2,[(T(),a("svg",H2,L2)),f2]),Q(" is the actual count of the dinucleotide, and therefore "),t("mjx-container",M2,[(T(),a("svg",k2,Z2)),b2]),Q(" is the counts of the nucleotide "),t("mjx-container",V2,[(T(),a("svg",v2,j2)),A2]),Q(" to any other nucleotide and build the transition probability matrix:")]),t("mjx-container",C2,[(T(),a("svg",R2,O2)),P2]),t("p",null,[Q("It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions "),t("mjx-container",X2,[(T(),a("svg",E2,B2)),G2]),Q(" over the total sum of the dinucleotide counts "),t("mjx-container",N2,[(T(),a("svg",z2,q2)),F2]),Q(":")]),t("mjx-container",$2,[(T(),a("svg",U2,K2)),Y2]),t("p",null,[Q("That way for the previous example example we can can calculate the initial probabilities "),t("mjx-container",t6,[(T(),a("svg",Q6,T6)),e6]),Q(". Both set of probabilities composed a "),s6,Q(" that can be used to predict the probability of any DNA sequence using equation (2).")]),l6,o6])}const x6=s(l,[["render",n6]]);export{g6 as __pageData,x6 as default}; diff --git a/dev/assets/chunks/@localSearchIndexroot.Bh2pKAzu.js b/dev/assets/chunks/@localSearchIndexroot.Bh2pKAzu.js deleted file mode 100644 index b218c89..0000000 --- a/dev/assets/chunks/@localSearchIndexroot.Bh2pKAzu.js +++ /dev/null @@ -1 +0,0 @@ -const e='{"documentCount":8,"nextId":8,"documentIds":{"0":"/BioMarkovChains.jl/dev/article01#From-BMC-to-sequence-probabilties","1":"/BioMarkovChains.jl/dev/getstarted#Get-started","2":"/BioMarkovChains.jl/dev/getstarted#Installation","3":"/BioMarkovChains.jl/dev/getstarted#Create-a-BioMarkovChain-of-DNA","4":"/BioMarkovChains.jl/dev/biomarkovchains#Towards-Markov-Chains","5":"/BioMarkovChains.jl/dev/biomarkovchains#DNA-as-a-Markov-chain","6":"/BioMarkovChains.jl/dev/biomarkovchains#References","7":"/BioMarkovChains.jl/dev/home#Overview"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[5,1,44],"1":[2,1,1],"2":[1,2,36],"3":[5,2,110],"4":[3,1,1],"5":[5,3,235],"6":[1,3,24],"7":[1,1,16]},"averageFieldLength":[2.875,1.75,58.375],"storedFields":{"0":{"title":"From BMC to sequence probabilties","titles":[]},"1":{"title":"Get started","titles":[]},"2":{"title":"Installation","titles":["Get started"]},"3":{"title":"Create a BioMarkovChain of DNA","titles":["Get started"]},"4":{"title":"Towards Markov Chains","titles":[]},"5":{"title":"DNA as a Markov chain","titles":["Towards Markov Chains"]},"6":{"title":"References","titles":["Towards Markov Chains"]},"7":{"title":"Overview","titles":[]}},"dirtCount":0,"index":[["978",{"2":{"6":1}}],["π^",{"2":{"5":1}}],["π^i=ci∑kckthat",{"2":{"5":1}}],["𝒜",{"2":{"5":2}}],["𝓂mn=",{"2":{"3":1}}],["∏t=2tp",{"2":{"5":1}}],["x1=i1",{"2":{"5":3}}],["x1",{"2":{"5":1}}],["xt=it|xt−1=it−1",{"2":{"5":1}}],["xt=it",{"2":{"5":1}}],["xt=j|xt−1=i",{"2":{"5":1}}],["xt",{"2":{"5":2}}],["∈",{"2":{"5":1}}],["vol",{"2":{"6":1}}],["variable",{"2":{"5":2}}],["vertex",{"2":{"5":2}}],["very",{"2":{"3":1}}],["vector",{"2":{"0":1,"3":2}}],["random",{"2":{"5":3}}],["references",{"0":{"6":1}}],["reduced",{"2":{"5":1}}],["representing",{"2":{"5":1}}],["representation",{"2":{"5":1}}],["represent",{"2":{"5":3,"7":1}}],["represents",{"2":{"3":2}}],["repl",{"2":{"2":1}}],["release",{"2":{"2":1}}],["→",{"2":{"5":1}}],["→j",{"2":{"3":1}}],["link",{"2":{"6":1}}],["london",{"2":{"6":2}}],["longdna",{"2":{"0":1}}],["later",{"2":{"5":1}}],["led",{"2":{"5":1}}],["letter",{"2":{"5":1}}],["j",{"2":{"5":1}}],["jump",{"2":{"5":1}}],["juliabiomarkovchain",{"2":{"3":1}}],["julia",{"2":{"2":2,"5":1}}],["juliausing",{"2":{"0":1,"3":1}}],["jl",{"2":{"5":2}}],["got",{"2":{"5":1}}],["given",{"2":{"5":1}}],["graph",{"2":{"5":2}}],["generalize",{"2":{"5":1}}],["gene",{"2":{"5":1,"6":1}}],["genefinder",{"2":{"5":1}}],["get",{"0":{"1":1},"1":{"2":1,"3":1}}],["g",{"2":{"5":3}}],["http",{"2":{"6":1}}],["higher",{"2":{"3":1}}],["has",{"2":{"5":1}}],["have",{"2":{"3":1,"5":1}}],["harbor",{"2":{"3":1}}],["used",{"2":{"5":1}}],["us",{"2":{"5":1}}],["usually",{"2":{"3":1}}],["using",{"2":{"0":1,"5":1}}],["which",{"2":{"5":1}}],["where",{"2":{"5":6}}],["whereas",{"2":{"3":1}}],["way",{"2":{"5":3}}],["ways",{"2":{"5":1}}],["want",{"2":{"3":1}}],["with",{"2":{"5":6}}],["work",{"2":{"5":3}}],["we",{"2":{"0":1,"3":2,"5":6}}],["×",{"2":{"3":4}}],[">",{"2":{"3":4}}],["nucleotides",{"2":{"5":2}}],["nucleotide",{"2":{"5":9}}],["nth",{"2":{"3":1}}],["n",{"2":{"3":3}}],["nice",{"2":{"3":2}}],["not",{"2":{"3":1}}],["noteworthy",{"2":{"5":1}}],["note",{"2":{"3":1,"5":1}}],["now",{"2":{"0":1}}],["new",{"2":{"2":1}}],["operations",{"2":{"7":1}}],["overview",{"0":{"7":1}}],["over",{"2":{"5":1}}],["obtained",{"2":{"5":1}}],["other",{"2":{"5":2}}],["only",{"2":{"5":1}}],["one",{"2":{"5":4}}],["or",{"2":{"3":1}}],["order",{"2":{"3":4,"5":1}}],["out",{"2":{"2":1,"5":1}}],["of",{"0":{"3":1},"2":{"2":1,"3":6,"5":25}}],["draw",{"2":{"5":1}}],["definition",{"2":{"5":1}}],["dependent",{"2":{"5":1}}],["dedicated",{"2":{"5":1}}],["development",{"2":{"2":1}}],["different",{"2":{"7":1}}],["dinucleotide",{"2":{"5":2}}],["dinucleotides",{"2":{"3":1,"5":1}}],["distribution",{"2":{"5":1}}],["discrete",{"2":{"5":2}}],["discretemarkovchains",{"2":{"5":1}}],["do",{"2":{"3":1}}],["dnaalphabet",{"2":{"3":2}}],["dna",{"0":{"3":1,"5":1},"2":{"0":1,"3":1,"5":5}}],["it",{"2":{"5":1}}],["implementations",{"2":{"5":1}}],["implemented",{"2":{"5":1}}],["important",{"2":{"3":1,"5":1}}],["i",{"2":{"3":1,"5":2}}],["is",{"2":{"3":3,"5":14}}],["if",{"2":{"2":1}}],["instance",{"2":{"5":1}}],["install",{"2":{"2":1}}],["installation",{"0":{"2":1}}],["into",{"2":{"5":1}}],["integers",{"2":{"5":1}}],["interested",{"2":{"2":1}}],["initial",{"2":{"3":2,"5":4}}],["initials",{"2":{"0":4}}],["in",{"2":{"2":1,"3":2,"5":12}}],["perform",{"2":{"7":1}}],["p",{"2":{"5":3}}],["package",{"2":{"5":1,"7":1}}],["packages",{"2":{"5":1}}],["power",{"2":{"3":1}}],["possible",{"2":{"3":1}}],["please",{"2":{"2":1}}],["pkg",{"2":{"2":1}}],["predictions",{"2":{"7":1}}],["predict",{"2":{"5":1}}],["previous",{"2":{"5":2}}],["press",{"2":{"2":1}}],["product",{"2":{"5":1}}],["process",{"2":{"5":2}}],["property",{"2":{"3":1,"5":2}}],["proteins",{"2":{"3":1}}],["probabilities",{"2":{"3":2,"5":3}}],["probability",{"2":{"0":3,"3":4,"5":7}}],["probabilties",{"0":{"0":1}}],["println",{"2":{"0":2}}],["equation",{"2":{"5":1}}],["equations",{"2":{"5":1}}],["example",{"2":{"5":2}}],["expand",{"2":{"5":1}}],["each",{"2":{"5":6}}],["efficient",{"2":{"5":2}}],["ecosystem",{"2":{"5":2}}],["etc",{"2":{"5":1}}],["e",{"2":{"5":2}}],["edges",{"2":{"5":1}}],["edge",{"2":{"2":1}}],["enter",{"2":{"2":2}}],["element",{"2":{"0":1}}],["you",{"2":{"2":2}}],["sum",{"2":{"5":1}}],["single",{"2":{"5":1}}],["so",{"2":{"5":4}}],["some",{"2":{"5":1}}],["sometimes",{"2":{"3":2}}],["springer",{"2":{"6":2}}],["specifically",{"2":{"5":1}}],["specialized",{"2":{"5":1}}],["space",{"2":{"5":1}}],["string",{"2":{"5":1}}],["states",{"2":{"5":1}}],["state",{"2":{"5":5}}],["started",{"0":{"1":1},"1":{"2":1,"3":1}}],["steps",{"2":{"3":1}}],["step",{"2":{"3":1,"5":1}}],["set",{"2":{"5":2}}],["see",{"2":{"5":1}}],["several",{"2":{"5":1}}],["second",{"2":{"3":1}}],["sequence",{"0":{"0":1},"2":{"0":4,"3":3,"5":9}}],["4471",{"2":{"6":1}}],["43",{"2":{"5":1}}],["4348",{"2":{"3":2}}],["43478260869565216",{"2":{"0":1}}],["4x4",{"2":{"5":1}}],["42",{"2":{"5":1}}],["4156",{"2":{"3":1}}],["475",{"2":{"3":1}}],["4",{"2":{"0":1,"3":8}}],["4×4",{"2":{"0":1}}],["6693",{"2":{"6":1}}],["6667",{"2":{"3":1}}],["666667",{"2":{"0":1}}],["670",{"2":{"5":1}}],["620",{"2":{"5":1}}],["625",{"2":{"0":1,"3":1}}],["330",{"2":{"5":1}}],["3333",{"2":{"3":1}}],["333333",{"2":{"0":1}}],["30g0",{"2":{"5":1}}],["34",{"2":{"5":1}}],["3417",{"2":{"3":1}}],["3478",{"2":{"3":2}}],["34782608695652173",{"2":{"0":1}}],["375",{"2":{"3":1}}],["3906",{"2":{"3":1}}],["325",{"2":{"3":1}}],["3",{"2":{"0":1,"3":2}}],["20",{"2":{"6":1}}],["2015",{"2":{"5":1,"6":1}}],["220",{"2":{"5":1}}],["24",{"2":{"5":1}}],["250",{"2":{"5":1}}],["25",{"2":{"0":1,"3":1}}],["2",{"2":{"0":1,"3":5,"5":1}}],["560",{"2":{"5":1}}],["5",{"2":{"0":1,"3":2}}],["1007",{"2":{"6":1}}],["10",{"2":{"6":1}}],["13",{"2":{"5":1}}],["1304",{"2":{"3":2}}],["13043478260869565",{"2":{"0":1}}],["120",{"2":{"5":1}}],["125",{"2":{"0":1,"3":1}}],["1562",{"2":{"3":1}}],["15",{"2":{"3":1}}],["1",{"2":{"0":1,"3":4,"6":2}}],["00",{"2":{"5":1}}],["00t0",{"2":{"5":1}}],["00c0",{"2":{"5":1}}],["000",{"2":{"5":4}}],["001",{"2":{"5":1}}],["0375",{"2":{"3":1}}],["05",{"2":{"3":1}}],["08",{"2":{"5":1}}],["0833",{"2":{"3":1}}],["087",{"2":{"3":2}}],["08695652173913043",{"2":{"0":1}}],["0",{"2":{"0":27,"3":48,"5":4}}],["frequency",{"2":{"5":3}}],["from",{"0":{"0":1},"2":{"0":1,"2":1,"5":5}}],["first",{"2":{"5":1}}],["finite",{"2":{"5":1}}],["finding",{"2":{"5":1,"6":1}}],["fisk",{"2":{"5":1,"6":1}}],["for",{"2":{"5":2}}],["formally",{"2":{"5":1}}],["four",{"2":{"5":1}}],["following",{"2":{"2":1}}],["functionality",{"2":{"5":1}}],["fact",{"2":{"3":1,"5":1}}],["features",{"2":{"2":1}}],["float64",{"2":{"0":2,"3":4}}],["ck",{"2":{"5":1}}],["ci",{"2":{"5":1}}],["cij",{"2":{"5":2}}],["current",{"2":{"5":1}}],["cutting",{"2":{"2":1}}],["c",{"2":{"5":1}}],["clumsy",{"2":{"5":1}}],["com",{"2":{"6":1}}],["computational",{"2":{"6":1}}],["comparative",{"2":{"6":1}}],["composed",{"2":{"5":1}}],["complete",{"2":{"5":2}}],["coincides",{"2":{"5":1}}],["counts",{"2":{"5":3}}],["count",{"2":{"5":2}}],["could",{"2":{"5":1}}],["considered",{"2":{"5":1}}],["codons",{"2":{"3":1}}],["chains",{"0":{"4":1},"1":{"5":1,"6":1},"2":{"5":1,"7":1}}],["chain",{"0":{"5":1},"2":{"3":1,"5":3}}],["check",{"2":{"2":1}}],["create",{"0":{"3":1}}],["cctcccggaccctgggctcgggacwe",{"2":{"5":1}}],["cctcccggaccctgggctcgggac",{"2":{"0":1,"3":1}}],["calculate",{"2":{"0":1,"5":5}}],["can",{"2":{"0":1,"2":1,"3":1,"5":8}}],["=p",{"2":{"5":1}}],["=",{"2":{"0":3,"3":1,"5":2}}],["both",{"2":{"5":1}}],["by",{"2":{"5":1}}],["but",{"2":{"5":1}}],["build",{"2":{"3":1,"5":2}}],["building",{"2":{"3":1}}],["beginning",{"2":{"5":1}}],["be",{"2":{"5":3}}],["been",{"2":{"5":1}}],["before",{"2":{"2":1}}],["block",{"2":{"3":1}}],["branch",{"2":{"2":1}}],["biology",{"2":{"6":1}}],["biological",{"2":{"3":1,"5":1}}],["biosequence",{"2":{"5":1}}],["biosequences",{"2":{"0":1,"3":1,"7":1}}],["biojulia",{"2":{"5":1}}],["biomarkovchain",{"0":{"3":1},"2":{"3":3}}],["biomarkovchains",{"2":{"2":2,"3":1}}],["bmc",{"0":{"0":1}}],["m^ij=cijci",{"2":{"5":1}}],["m^",{"2":{"5":1}}],["more",{"2":{"5":2}}],["models",{"2":{"3":1}}],["model",{"2":{"3":1,"5":1}}],["mode",{"2":{"2":1}}],["m",{"2":{"3":1}}],["mij",{"2":{"3":1}}],["meaning",{"2":{"3":1}}],["methods",{"2":{"0":1}}],["marina",{"2":{"6":1}}],["markovchainshammer",{"2":{"5":1}}],["markov",{"0":{"4":1,"5":1},"1":{"5":1,"6":1},"2":{"3":1,"5":5,"7":1}}],["many",{"2":{"5":2}}],["main",{"2":{"2":1}}],["matrix",{"2":{"0":4,"3":6,"5":3}}],["t=2",{"2":{"5":1}}],["terms",{"2":{"5":1}}],["two",{"2":{"5":1}}],["time",{"2":{"5":1}}],["t∈t",{"2":{"5":1}}],["t",{"2":{"5":6}}],["types",{"2":{"5":2,"7":1}}],["this",{"2":{"5":4,"7":1}}],["those",{"2":{"5":1}}],["that",{"2":{"3":4,"5":6}}],["they",{"2":{"5":1}}],["therefore",{"2":{"3":1,"5":3}}],["the",{"2":{"0":1,"2":5,"3":7,"5":34}}],["trinucleotide",{"2":{"3":1}}],["trinucleotides",{"2":{"3":1}}],["try",{"2":{"2":1}}],["transitions",{"2":{"3":2,"5":7}}],["transition",{"2":{"0":3,"3":7,"5":4}}],["tpm",{"2":{"0":2}}],["total",{"2":{"5":1}}],["towards",{"0":{"4":1},"1":{"5":1,"6":1},"2":{"5":1}}],["to",{"0":{"0":1},"2":{"2":2,"3":1,"5":13,"7":2}}],["aim",{"2":{"7":1}}],["ag",{"2":{"5":1}}],["acgta0",{"2":{"5":1}}],["actual",{"2":{"5":1}}],["ac",{"2":{"5":1}}],["aa",{"2":{"5":1}}],["at",{"2":{"5":1}}],["axelson",{"2":{"5":1,"6":1}}],["all",{"2":{"5":2}}],["alphabet",{"2":{"5":4}}],["algorithms",{"2":{"5":1}}],["also",{"2":{"3":1,"5":2}}],["api",{"2":{"5":1}}],["any",{"2":{"5":3}}],["another",{"2":{"5":2}}],["an",{"2":{"5":2}}],["and",{"2":{"0":1,"2":1,"3":2,"5":6,"7":1}}],["as",{"0":{"5":1},"2":{"3":1,"5":4,"7":1}}],["are",{"2":{"2":1,"3":1,"5":1}}],["add",{"2":{"2":1}}],["a",{"0":{"3":1,"5":1},"2":{"0":2,"3":3,"5":34}}]],"serializationVersion":2}';export{e as default}; diff --git a/dev/assets/chunks/@localSearchIndexroot.Bj-EWWk0.js b/dev/assets/chunks/@localSearchIndexroot.Bj-EWWk0.js new file mode 100644 index 0000000..bdbbcef --- /dev/null +++ b/dev/assets/chunks/@localSearchIndexroot.Bj-EWWk0.js @@ -0,0 +1 @@ +const e='{"documentCount":8,"nextId":8,"documentIds":{"0":"/BioMarkovChains.jl/dev/article01#From-BMC-to-sequence-probabilties","1":"/BioMarkovChains.jl/dev/biomarkovchains#Towards-Markov-Chains","2":"/BioMarkovChains.jl/dev/biomarkovchains#DNA-as-a-Markov-chain","3":"/BioMarkovChains.jl/dev/biomarkovchains#References","4":"/BioMarkovChains.jl/dev/getstarted#Get-started","5":"/BioMarkovChains.jl/dev/getstarted#Installation","6":"/BioMarkovChains.jl/dev/getstarted#Create-a-BioMarkovChain-of-DNA","7":"/BioMarkovChains.jl/dev/home#Overview"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[5,1,44],"1":[3,1,1],"2":[5,3,235],"3":[1,3,24],"4":[2,1,1],"5":[1,2,36],"6":[5,2,110],"7":[1,1,16]},"averageFieldLength":[2.875,1.75,58.375],"storedFields":{"0":{"title":"From BMC to sequence probabilties","titles":[]},"1":{"title":"Towards Markov Chains","titles":[]},"2":{"title":"DNA as a Markov chain","titles":["Towards Markov Chains"]},"3":{"title":"References","titles":["Towards Markov Chains"]},"4":{"title":"Get started","titles":[]},"5":{"title":"Installation","titles":["Get started"]},"6":{"title":"Create a BioMarkovChain of DNA","titles":["Get started"]},"7":{"title":"Overview","titles":[]}},"dirtCount":0,"index":[["𝓂mn=",{"2":{"6":1}}],["𝒜",{"2":{"2":2}}],["×",{"2":{"6":4}}],[">",{"2":{"6":4}}],["you",{"2":{"5":2}}],["978",{"2":{"3":1}}],["higher",{"2":{"6":1}}],["http",{"2":{"3":1}}],["harbor",{"2":{"6":1}}],["has",{"2":{"2":1}}],["have",{"2":{"2":1,"6":1}}],["π^",{"2":{"2":1}}],["π^i=ci∑kckthat",{"2":{"2":1}}],["∏t=2tp",{"2":{"2":1}}],["x1=i1",{"2":{"2":3}}],["x1",{"2":{"2":1}}],["xt=it|xt−1=it−1",{"2":{"2":1}}],["xt=it",{"2":{"2":1}}],["xt=j|xt−1=i",{"2":{"2":1}}],["xt",{"2":{"2":2}}],["usually",{"2":{"6":1}}],["used",{"2":{"2":1}}],["us",{"2":{"2":1}}],["using",{"2":{"0":1,"2":1}}],["∈",{"2":{"2":1}}],["vol",{"2":{"3":1}}],["variable",{"2":{"2":2}}],["very",{"2":{"6":1}}],["vertex",{"2":{"2":2}}],["vector",{"2":{"0":1,"6":2}}],["random",{"2":{"2":3}}],["release",{"2":{"5":1}}],["repl",{"2":{"5":1}}],["represents",{"2":{"6":2}}],["representing",{"2":{"2":1}}],["representation",{"2":{"2":1}}],["represent",{"2":{"2":3,"7":1}}],["references",{"0":{"3":1}}],["reduced",{"2":{"2":1}}],["→j",{"2":{"6":1}}],["→",{"2":{"2":1}}],["nth",{"2":{"6":1}}],["n",{"2":{"6":3}}],["nice",{"2":{"6":2}}],["new",{"2":{"5":1}}],["not",{"2":{"6":1}}],["noteworthy",{"2":{"2":1}}],["note",{"2":{"2":1,"6":1}}],["now",{"2":{"0":1}}],["nucleotides",{"2":{"2":2}}],["nucleotide",{"2":{"2":9}}],["link",{"2":{"3":1}}],["london",{"2":{"3":2}}],["longdna",{"2":{"0":1}}],["later",{"2":{"2":1}}],["led",{"2":{"2":1}}],["letter",{"2":{"2":1}}],["operations",{"2":{"7":1}}],["or",{"2":{"6":1}}],["order",{"2":{"2":1,"6":4}}],["overview",{"0":{"7":1}}],["over",{"2":{"2":1}}],["obtained",{"2":{"2":1}}],["other",{"2":{"2":2}}],["out",{"2":{"2":1,"5":1}}],["only",{"2":{"2":1}}],["one",{"2":{"2":4}}],["of",{"0":{"6":1},"2":{"2":25,"5":1,"6":6}}],["sum",{"2":{"2":1}}],["single",{"2":{"2":1}}],["started",{"0":{"4":1},"1":{"5":1,"6":1}}],["states",{"2":{"2":1}}],["state",{"2":{"2":5}}],["string",{"2":{"2":1}}],["steps",{"2":{"6":1}}],["step",{"2":{"2":1,"6":1}}],["so",{"2":{"2":4}}],["sometimes",{"2":{"6":2}}],["some",{"2":{"2":1}}],["springer",{"2":{"3":2}}],["specifically",{"2":{"2":1}}],["specialized",{"2":{"2":1}}],["space",{"2":{"2":1}}],["second",{"2":{"6":1}}],["set",{"2":{"2":2}}],["see",{"2":{"2":1}}],["several",{"2":{"2":1}}],["sequence",{"0":{"0":1},"2":{"0":4,"2":9,"6":3}}],["want",{"2":{"6":1}}],["way",{"2":{"2":3}}],["ways",{"2":{"2":1}}],["which",{"2":{"2":1}}],["whereas",{"2":{"6":1}}],["where",{"2":{"2":6}}],["with",{"2":{"2":6}}],["work",{"2":{"2":3}}],["we",{"2":{"0":1,"2":6,"6":2}}],["if",{"2":{"5":1}}],["it",{"2":{"2":1}}],["i",{"2":{"2":2,"6":1}}],["is",{"2":{"2":14,"6":3}}],["important",{"2":{"2":1,"6":1}}],["implementations",{"2":{"2":1}}],["implemented",{"2":{"2":1}}],["install",{"2":{"5":1}}],["installation",{"0":{"5":1}}],["instance",{"2":{"2":1}}],["initial",{"2":{"2":4,"6":2}}],["initials",{"2":{"0":4}}],["interested",{"2":{"5":1}}],["integers",{"2":{"2":1}}],["into",{"2":{"2":1}}],["in",{"2":{"2":12,"5":1,"6":2}}],["do",{"2":{"6":1}}],["different",{"2":{"7":1}}],["dinucleotide",{"2":{"2":2}}],["dinucleotides",{"2":{"2":1,"6":1}}],["distribution",{"2":{"2":1}}],["discrete",{"2":{"2":2}}],["discretemarkovchains",{"2":{"2":1}}],["development",{"2":{"5":1}}],["definition",{"2":{"2":1}}],["dependent",{"2":{"2":1}}],["dedicated",{"2":{"2":1}}],["draw",{"2":{"2":1}}],["dnaalphabet",{"2":{"6":2}}],["dna",{"0":{"2":1,"6":1},"2":{"0":1,"2":5,"6":1}}],["j",{"2":{"2":1}}],["jump",{"2":{"2":1}}],["juliabiomarkovchain",{"2":{"6":1}}],["julia",{"2":{"2":1,"5":2}}],["juliausing",{"2":{"0":1,"6":1}}],["jl",{"2":{"2":2}}],["get",{"0":{"4":1},"1":{"5":1,"6":1}}],["generalize",{"2":{"2":1}}],["gene",{"2":{"2":1,"3":1}}],["genefinder",{"2":{"2":1}}],["got",{"2":{"2":1}}],["given",{"2":{"2":1}}],["graph",{"2":{"2":2}}],["g",{"2":{"2":3}}],["edge",{"2":{"5":1}}],["edges",{"2":{"2":1}}],["enter",{"2":{"5":2}}],["equation",{"2":{"2":1}}],["equations",{"2":{"2":1}}],["example",{"2":{"2":2}}],["expand",{"2":{"2":1}}],["each",{"2":{"2":6}}],["efficient",{"2":{"2":2}}],["ecosystem",{"2":{"2":2}}],["etc",{"2":{"2":1}}],["e",{"2":{"2":2}}],["element",{"2":{"0":1}}],["perform",{"2":{"7":1}}],["power",{"2":{"6":1}}],["possible",{"2":{"6":1}}],["please",{"2":{"5":1}}],["pkg",{"2":{"5":1}}],["p",{"2":{"2":3}}],["package",{"2":{"2":1,"7":1}}],["packages",{"2":{"2":1}}],["press",{"2":{"5":1}}],["predictions",{"2":{"7":1}}],["predict",{"2":{"2":1}}],["previous",{"2":{"2":2}}],["proteins",{"2":{"6":1}}],["product",{"2":{"2":1}}],["property",{"2":{"2":2,"6":1}}],["process",{"2":{"2":2}}],["probabilities",{"2":{"2":3,"6":2}}],["probability",{"2":{"0":3,"2":7,"6":4}}],["probabilties",{"0":{"0":1}}],["println",{"2":{"0":2}}],["4156",{"2":{"6":1}}],["475",{"2":{"6":1}}],["4471",{"2":{"3":1}}],["4348",{"2":{"6":2}}],["43478260869565216",{"2":{"0":1}}],["43",{"2":{"2":1}}],["4x4",{"2":{"2":1}}],["42",{"2":{"2":1}}],["4",{"2":{"0":1,"6":8}}],["4×4",{"2":{"0":1}}],["6667",{"2":{"6":1}}],["666667",{"2":{"0":1}}],["6693",{"2":{"3":1}}],["670",{"2":{"2":1}}],["620",{"2":{"2":1}}],["625",{"2":{"0":1,"6":1}}],["375",{"2":{"6":1}}],["3906",{"2":{"6":1}}],["325",{"2":{"6":1}}],["3417",{"2":{"6":1}}],["3478",{"2":{"6":2}}],["34782608695652173",{"2":{"0":1}}],["34",{"2":{"2":1}}],["3333",{"2":{"6":1}}],["333333",{"2":{"0":1}}],["330",{"2":{"2":1}}],["30g0",{"2":{"2":1}}],["3",{"2":{"0":1,"6":2}}],["20",{"2":{"3":1}}],["2015",{"2":{"2":1,"3":1}}],["220",{"2":{"2":1}}],["24",{"2":{"2":1}}],["250",{"2":{"2":1}}],["25",{"2":{"0":1,"6":1}}],["2",{"2":{"0":1,"2":1,"6":5}}],["560",{"2":{"2":1}}],["5",{"2":{"0":1,"6":2}}],["1562",{"2":{"6":1}}],["15",{"2":{"6":1}}],["1007",{"2":{"3":1}}],["10",{"2":{"3":1}}],["1304",{"2":{"6":2}}],["13043478260869565",{"2":{"0":1}}],["13",{"2":{"2":1}}],["120",{"2":{"2":1}}],["125",{"2":{"0":1,"6":1}}],["1",{"2":{"0":1,"3":2,"6":4}}],["0375",{"2":{"6":1}}],["05",{"2":{"6":1}}],["0833",{"2":{"6":1}}],["087",{"2":{"6":2}}],["08",{"2":{"2":1}}],["08695652173913043",{"2":{"0":1}}],["00",{"2":{"2":1}}],["00t0",{"2":{"2":1}}],["00c0",{"2":{"2":1}}],["000",{"2":{"2":4}}],["001",{"2":{"2":1}}],["0",{"2":{"0":27,"2":4,"6":48}}],["features",{"2":{"5":1}}],["fact",{"2":{"2":1,"6":1}}],["frequency",{"2":{"2":3}}],["from",{"0":{"0":1},"2":{"0":1,"2":5,"5":1}}],["following",{"2":{"5":1}}],["for",{"2":{"2":2}}],["formally",{"2":{"2":1}}],["four",{"2":{"2":1}}],["first",{"2":{"2":1}}],["finite",{"2":{"2":1}}],["finding",{"2":{"2":1,"3":1}}],["fisk",{"2":{"2":1,"3":1}}],["functionality",{"2":{"2":1}}],["float64",{"2":{"0":2,"6":4}}],["create",{"0":{"6":1}}],["check",{"2":{"5":1}}],["chain",{"0":{"2":1},"2":{"2":3,"6":1}}],["chains",{"0":{"1":1},"1":{"2":1,"3":1},"2":{"2":1,"7":1}}],["cutting",{"2":{"5":1}}],["current",{"2":{"2":1}}],["ck",{"2":{"2":1}}],["ci",{"2":{"2":1}}],["cij",{"2":{"2":2}}],["c",{"2":{"2":1}}],["codons",{"2":{"6":1}}],["com",{"2":{"3":1}}],["computational",{"2":{"3":1}}],["comparative",{"2":{"3":1}}],["composed",{"2":{"2":1}}],["complete",{"2":{"2":2}}],["coincides",{"2":{"2":1}}],["counts",{"2":{"2":3}}],["count",{"2":{"2":2}}],["could",{"2":{"2":1}}],["considered",{"2":{"2":1}}],["clumsy",{"2":{"2":1}}],["cctcccggaccctgggctcgggacwe",{"2":{"2":1}}],["cctcccggaccctgggctcgggac",{"2":{"0":1,"6":1}}],["calculate",{"2":{"0":1,"2":5}}],["can",{"2":{"0":1,"2":8,"5":1,"6":1}}],["=p",{"2":{"2":1}}],["=",{"2":{"0":3,"2":2,"6":1}}],["block",{"2":{"6":1}}],["branch",{"2":{"5":1}}],["both",{"2":{"2":1}}],["building",{"2":{"6":1}}],["build",{"2":{"2":2,"6":1}}],["but",{"2":{"2":1}}],["by",{"2":{"2":1}}],["biomarkovchain",{"0":{"6":1},"2":{"6":3}}],["biomarkovchains",{"2":{"5":2,"6":1}}],["biology",{"2":{"3":1}}],["biological",{"2":{"2":1,"6":1}}],["biosequence",{"2":{"2":1}}],["biosequences",{"2":{"0":1,"6":1,"7":1}}],["biojulia",{"2":{"2":1}}],["before",{"2":{"5":1}}],["beginning",{"2":{"2":1}}],["be",{"2":{"2":3}}],["been",{"2":{"2":1}}],["bmc",{"0":{"0":1}}],["m",{"2":{"6":1}}],["mij",{"2":{"6":1}}],["meaning",{"2":{"6":1}}],["methods",{"2":{"0":1}}],["mode",{"2":{"5":1}}],["models",{"2":{"6":1}}],["model",{"2":{"2":1,"6":1}}],["more",{"2":{"2":2}}],["m^ij=cijci",{"2":{"2":1}}],["m^",{"2":{"2":1}}],["main",{"2":{"5":1}}],["marina",{"2":{"3":1}}],["markovchainshammer",{"2":{"2":1}}],["markov",{"0":{"1":1,"2":1},"1":{"2":1,"3":1},"2":{"2":5,"6":1,"7":1}}],["many",{"2":{"2":2}}],["matrix",{"2":{"0":4,"2":3,"6":6}}],["trinucleotide",{"2":{"6":1}}],["trinucleotides",{"2":{"6":1}}],["try",{"2":{"5":1}}],["transitions",{"2":{"2":7,"6":2}}],["transition",{"2":{"0":3,"2":4,"6":7}}],["t=2",{"2":{"2":1}}],["terms",{"2":{"2":1}}],["two",{"2":{"2":1}}],["time",{"2":{"2":1}}],["t∈t",{"2":{"2":1}}],["t",{"2":{"2":6}}],["types",{"2":{"2":2,"7":1}}],["this",{"2":{"2":4,"7":1}}],["that",{"2":{"2":6,"6":4}}],["those",{"2":{"2":1}}],["therefore",{"2":{"2":3,"6":1}}],["they",{"2":{"2":1}}],["the",{"2":{"0":1,"2":34,"5":5,"6":7}}],["tpm",{"2":{"0":2}}],["total",{"2":{"2":1}}],["towards",{"0":{"1":1},"1":{"2":1,"3":1},"2":{"2":1}}],["to",{"0":{"0":1},"2":{"2":13,"5":2,"6":1,"7":2}}],["aim",{"2":{"7":1}}],["add",{"2":{"5":1}}],["ag",{"2":{"2":1}}],["acgta0",{"2":{"2":1}}],["actual",{"2":{"2":1}}],["ac",{"2":{"2":1}}],["aa",{"2":{"2":1}}],["at",{"2":{"2":1}}],["axelson",{"2":{"2":1,"3":1}}],["all",{"2":{"2":2}}],["also",{"2":{"2":2,"6":1}}],["alphabet",{"2":{"2":4}}],["algorithms",{"2":{"2":1}}],["api",{"2":{"2":1}}],["any",{"2":{"2":3}}],["another",{"2":{"2":2}}],["an",{"2":{"2":2}}],["and",{"2":{"0":1,"2":6,"5":1,"6":2,"7":1}}],["are",{"2":{"2":1,"5":1,"6":1}}],["as",{"0":{"2":1},"2":{"2":4,"6":1,"7":1}}],["a",{"0":{"2":1,"6":1},"2":{"0":2,"2":34,"6":3}}]],"serializationVersion":2}';export{e as default}; diff --git a/dev/assets/chunks/VPLocalSearchBox.CaalGK9M.js b/dev/assets/chunks/VPLocalSearchBox.CaalGK9M.js deleted file mode 100644 index eb48203..0000000 --- a/dev/assets/chunks/VPLocalSearchBox.CaalGK9M.js +++ /dev/null @@ -1,7 +0,0 @@ -var It=Object.defineProperty;var Dt=(o,e,t)=>e in o?It(o,e,{enumerable:!0,configurable:!0,writable:!0,value:t}):o[e]=t;var Oe=(o,e,t)=>(Dt(o,typeof e!="symbol"?e+"":e,t),t);import{Y as yt,j as oe,x as $e,am as kt,an as Ot,d as Rt,G as xe,ao as tt,h as Fe,ap as _t,aq as Mt,y as Lt,ar as Pt,k as Re,S as de,R as Ee,as as zt,at as Vt,Z as Bt,V as $t,au as Wt,o as ee,b as Kt,l as k,a2 as Jt,m as j,av as Ut,aw as jt,ax as Gt,c as re,n as rt,e as Se,E as at,F as nt,a as ve,t as pe,ay as qt,p as Ht,q as Qt,az as it,aA as Yt,ac as Zt,ai as Xt,aB as er,_ as tr}from"./framework.D1rHXXmm.js";import{u as rr,c as ar}from"./theme.BWgOxzZE.js";const nr={root:()=>yt(()=>import("./@localSearchIndexroot.Bh2pKAzu.js"),[])};/*! -* tabbable 6.2.0 -* @license MIT, https://github.com/focus-trap/tabbable/blob/master/LICENSE -*/var mt=["input:not([inert])","select:not([inert])","textarea:not([inert])","a[href]:not([inert])","button:not([inert])","[tabindex]:not(slot):not([inert])","audio[controls]:not([inert])","video[controls]:not([inert])",'[contenteditable]:not([contenteditable="false"]):not([inert])',"details>summary:first-of-type:not([inert])","details:not([inert])"],Ne=mt.join(","),gt=typeof Element>"u",ue=gt?function(){}:Element.prototype.matches||Element.prototype.msMatchesSelector||Element.prototype.webkitMatchesSelector,Ce=!gt&&Element.prototype.getRootNode?function(o){var e;return o==null||(e=o.getRootNode)===null||e===void 0?void 0:e.call(o)}:function(o){return o==null?void 0:o.ownerDocument},Ie=function o(e,t){var r;t===void 0&&(t=!0);var n=e==null||(r=e.getAttribute)===null||r===void 0?void 0:r.call(e,"inert"),a=n===""||n==="true",i=a||t&&e&&o(e.parentNode);return i},ir=function(e){var t,r=e==null||(t=e.getAttribute)===null||t===void 0?void 0:t.call(e,"contenteditable");return r===""||r==="true"},bt=function(e,t,r){if(Ie(e))return[];var n=Array.prototype.slice.apply(e.querySelectorAll(Ne));return t&&ue.call(e,Ne)&&n.unshift(e),n=n.filter(r),n},wt=function o(e,t,r){for(var n=[],a=Array.from(e);a.length;){var i=a.shift();if(!Ie(i,!1))if(i.tagName==="SLOT"){var s=i.assignedElements(),u=s.length?s:i.children,l=o(u,!0,r);r.flatten?n.push.apply(n,l):n.push({scopeParent:i,candidates:l})}else{var h=ue.call(i,Ne);h&&r.filter(i)&&(t||!e.includes(i))&&n.push(i);var d=i.shadowRoot||typeof r.getShadowRoot=="function"&&r.getShadowRoot(i),v=!Ie(d,!1)&&(!r.shadowRootFilter||r.shadowRootFilter(i));if(d&&v){var y=o(d===!0?i.children:d.children,!0,r);r.flatten?n.push.apply(n,y):n.push({scopeParent:i,candidates:y})}else a.unshift.apply(a,i.children)}}return n},xt=function(e){return!isNaN(parseInt(e.getAttribute("tabindex"),10))},se=function(e){if(!e)throw new Error("No node provided");return e.tabIndex<0&&(/^(AUDIO|VIDEO|DETAILS)$/.test(e.tagName)||ir(e))&&!xt(e)?0:e.tabIndex},or=function(e,t){var r=se(e);return r<0&&t&&!xt(e)?0:r},sr=function(e,t){return e.tabIndex===t.tabIndex?e.documentOrder-t.documentOrder:e.tabIndex-t.tabIndex},Ft=function(e){return e.tagName==="INPUT"},ur=function(e){return Ft(e)&&e.type==="hidden"},lr=function(e){var t=e.tagName==="DETAILS"&&Array.prototype.slice.apply(e.children).some(function(r){return r.tagName==="SUMMARY"});return t},cr=function(e,t){for(var r=0;rsummary:first-of-type"),i=a?e.parentElement:e;if(ue.call(i,"details:not([open]) *"))return!0;if(!r||r==="full"||r==="legacy-full"){if(typeof n=="function"){for(var s=e;e;){var u=e.parentElement,l=Ce(e);if(u&&!u.shadowRoot&&n(u)===!0)return ot(e);e.assignedSlot?e=e.assignedSlot:!u&&l!==e.ownerDocument?e=l.host:e=u}e=s}if(vr(e))return!e.getClientRects().length;if(r!=="legacy-full")return!0}else if(r==="non-zero-area")return ot(e);return!1},yr=function(e){if(/^(INPUT|BUTTON|SELECT|TEXTAREA)$/.test(e.tagName))for(var t=e.parentElement;t;){if(t.tagName==="FIELDSET"&&t.disabled){for(var r=0;r=0)},gr=function o(e){var t=[],r=[];return e.forEach(function(n,a){var i=!!n.scopeParent,s=i?n.scopeParent:n,u=or(s,i),l=i?o(n.candidates):s;u===0?i?t.push.apply(t,l):t.push(s):r.push({documentOrder:a,tabIndex:u,item:n,isScope:i,content:l})}),r.sort(sr).reduce(function(n,a){return a.isScope?n.push.apply(n,a.content):n.push(a.content),n},[]).concat(t)},br=function(e,t){t=t||{};var r;return t.getShadowRoot?r=wt([e],t.includeContainer,{filter:We.bind(null,t),flatten:!1,getShadowRoot:t.getShadowRoot,shadowRootFilter:mr}):r=bt(e,t.includeContainer,We.bind(null,t)),gr(r)},wr=function(e,t){t=t||{};var r;return t.getShadowRoot?r=wt([e],t.includeContainer,{filter:De.bind(null,t),flatten:!0,getShadowRoot:t.getShadowRoot}):r=bt(e,t.includeContainer,De.bind(null,t)),r},le=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ue.call(e,Ne)===!1?!1:We(t,e)},xr=mt.concat("iframe").join(","),_e=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ue.call(e,xr)===!1?!1:De(t,e)};/*! -* focus-trap 7.5.4 -* @license MIT, https://github.com/focus-trap/focus-trap/blob/master/LICENSE -*/function st(o,e){var t=Object.keys(o);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(o);e&&(r=r.filter(function(n){return Object.getOwnPropertyDescriptor(o,n).enumerable})),t.push.apply(t,r)}return t}function ut(o){for(var e=1;e0){var r=e[e.length-1];r!==t&&r.pause()}var n=e.indexOf(t);n===-1||e.splice(n,1),e.push(t)},deactivateTrap:function(e,t){var r=e.indexOf(t);r!==-1&&e.splice(r,1),e.length>0&&e[e.length-1].unpause()}},Ar=function(e){return e.tagName&&e.tagName.toLowerCase()==="input"&&typeof e.select=="function"},Tr=function(e){return(e==null?void 0:e.key)==="Escape"||(e==null?void 0:e.key)==="Esc"||(e==null?void 0:e.keyCode)===27},ge=function(e){return(e==null?void 0:e.key)==="Tab"||(e==null?void 0:e.keyCode)===9},Nr=function(e){return ge(e)&&!e.shiftKey},Cr=function(e){return ge(e)&&e.shiftKey},ct=function(e){return setTimeout(e,0)},ft=function(e,t){var r=-1;return e.every(function(n,a){return t(n)?(r=a,!1):!0}),r},ye=function(e){for(var t=arguments.length,r=new Array(t>1?t-1:0),n=1;n1?p-1:0),I=1;I=0)c=r.activeElement;else{var f=i.tabbableGroups[0],p=f&&f.firstTabbableNode;c=p||h("fallbackFocus")}if(!c)throw new Error("Your focus-trap needs to have at least one focusable element");return c},v=function(){if(i.containerGroups=i.containers.map(function(c){var f=br(c,a.tabbableOptions),p=wr(c,a.tabbableOptions),C=f.length>0?f[0]:void 0,I=f.length>0?f[f.length-1]:void 0,M=p.find(function(m){return le(m)}),P=p.slice().reverse().find(function(m){return le(m)}),z=!!f.find(function(m){return se(m)>0});return{container:c,tabbableNodes:f,focusableNodes:p,posTabIndexesFound:z,firstTabbableNode:C,lastTabbableNode:I,firstDomTabbableNode:M,lastDomTabbableNode:P,nextTabbableNode:function(x){var $=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!0,K=f.indexOf(x);return K<0?$?p.slice(p.indexOf(x)+1).find(function(q){return le(q)}):p.slice(0,p.indexOf(x)).reverse().find(function(q){return le(q)}):f[K+($?1:-1)]}}}),i.tabbableGroups=i.containerGroups.filter(function(c){return c.tabbableNodes.length>0}),i.tabbableGroups.length<=0&&!h("fallbackFocus"))throw new Error("Your focus-trap must have at least one container with at least one tabbable node in it at all times");if(i.containerGroups.find(function(c){return c.posTabIndexesFound})&&i.containerGroups.length>1)throw new Error("At least one node with a positive tabindex was found in one of your focus-trap's multiple containers. Positive tabindexes are only supported in single-container focus-traps.")},y=function w(c){var f=c.activeElement;if(f)return f.shadowRoot&&f.shadowRoot.activeElement!==null?w(f.shadowRoot):f},b=function w(c){if(c!==!1&&c!==y(document)){if(!c||!c.focus){w(d());return}c.focus({preventScroll:!!a.preventScroll}),i.mostRecentlyFocusedNode=c,Ar(c)&&c.select()}},E=function(c){var f=h("setReturnFocus",c);return f||(f===!1?!1:c)},g=function(c){var f=c.target,p=c.event,C=c.isBackward,I=C===void 0?!1:C;f=f||Ae(p),v();var M=null;if(i.tabbableGroups.length>0){var P=l(f,p),z=P>=0?i.containerGroups[P]:void 0;if(P<0)I?M=i.tabbableGroups[i.tabbableGroups.length-1].lastTabbableNode:M=i.tabbableGroups[0].firstTabbableNode;else if(I){var m=ft(i.tabbableGroups,function(V){var U=V.firstTabbableNode;return f===U});if(m<0&&(z.container===f||_e(f,a.tabbableOptions)&&!le(f,a.tabbableOptions)&&!z.nextTabbableNode(f,!1))&&(m=P),m>=0){var x=m===0?i.tabbableGroups.length-1:m-1,$=i.tabbableGroups[x];M=se(f)>=0?$.lastTabbableNode:$.lastDomTabbableNode}else ge(p)||(M=z.nextTabbableNode(f,!1))}else{var K=ft(i.tabbableGroups,function(V){var U=V.lastTabbableNode;return f===U});if(K<0&&(z.container===f||_e(f,a.tabbableOptions)&&!le(f,a.tabbableOptions)&&!z.nextTabbableNode(f))&&(K=P),K>=0){var q=K===i.tabbableGroups.length-1?0:K+1,H=i.tabbableGroups[q];M=se(f)>=0?H.firstTabbableNode:H.firstDomTabbableNode}else ge(p)||(M=z.nextTabbableNode(f))}}else M=h("fallbackFocus");return M},S=function(c){var f=Ae(c);if(!(l(f,c)>=0)){if(ye(a.clickOutsideDeactivates,c)){s.deactivate({returnFocus:a.returnFocusOnDeactivate});return}ye(a.allowOutsideClick,c)||c.preventDefault()}},T=function(c){var f=Ae(c),p=l(f,c)>=0;if(p||f instanceof Document)p&&(i.mostRecentlyFocusedNode=f);else{c.stopImmediatePropagation();var C,I=!0;if(i.mostRecentlyFocusedNode)if(se(i.mostRecentlyFocusedNode)>0){var M=l(i.mostRecentlyFocusedNode),P=i.containerGroups[M].tabbableNodes;if(P.length>0){var z=P.findIndex(function(m){return m===i.mostRecentlyFocusedNode});z>=0&&(a.isKeyForward(i.recentNavEvent)?z+1=0&&(C=P[z-1],I=!1))}}else i.containerGroups.some(function(m){return m.tabbableNodes.some(function(x){return se(x)>0})})||(I=!1);else I=!1;I&&(C=g({target:i.mostRecentlyFocusedNode,isBackward:a.isKeyBackward(i.recentNavEvent)})),b(C||i.mostRecentlyFocusedNode||d())}i.recentNavEvent=void 0},F=function(c){var f=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!1;i.recentNavEvent=c;var p=g({event:c,isBackward:f});p&&(ge(c)&&c.preventDefault(),b(p))},L=function(c){if(Tr(c)&&ye(a.escapeDeactivates,c)!==!1){c.preventDefault(),s.deactivate();return}(a.isKeyForward(c)||a.isKeyBackward(c))&&F(c,a.isKeyBackward(c))},_=function(c){var f=Ae(c);l(f,c)>=0||ye(a.clickOutsideDeactivates,c)||ye(a.allowOutsideClick,c)||(c.preventDefault(),c.stopImmediatePropagation())},B=function(){if(i.active)return lt.activateTrap(n,s),i.delayInitialFocusTimer=a.delayInitialFocus?ct(function(){b(d())}):b(d()),r.addEventListener("focusin",T,!0),r.addEventListener("mousedown",S,{capture:!0,passive:!1}),r.addEventListener("touchstart",S,{capture:!0,passive:!1}),r.addEventListener("click",_,{capture:!0,passive:!1}),r.addEventListener("keydown",L,{capture:!0,passive:!1}),s},N=function(){if(i.active)return r.removeEventListener("focusin",T,!0),r.removeEventListener("mousedown",S,!0),r.removeEventListener("touchstart",S,!0),r.removeEventListener("click",_,!0),r.removeEventListener("keydown",L,!0),s},R=function(c){var f=c.some(function(p){var C=Array.from(p.removedNodes);return C.some(function(I){return I===i.mostRecentlyFocusedNode})});f&&b(d())},A=typeof window<"u"&&"MutationObserver"in window?new MutationObserver(R):void 0,O=function(){A&&(A.disconnect(),i.active&&!i.paused&&i.containers.map(function(c){A.observe(c,{subtree:!0,childList:!0})}))};return s={get active(){return i.active},get paused(){return i.paused},activate:function(c){if(i.active)return this;var f=u(c,"onActivate"),p=u(c,"onPostActivate"),C=u(c,"checkCanFocusTrap");C||v(),i.active=!0,i.paused=!1,i.nodeFocusedBeforeActivation=r.activeElement,f==null||f();var I=function(){C&&v(),B(),O(),p==null||p()};return C?(C(i.containers.concat()).then(I,I),this):(I(),this)},deactivate:function(c){if(!i.active)return this;var f=ut({onDeactivate:a.onDeactivate,onPostDeactivate:a.onPostDeactivate,checkCanReturnFocus:a.checkCanReturnFocus},c);clearTimeout(i.delayInitialFocusTimer),i.delayInitialFocusTimer=void 0,N(),i.active=!1,i.paused=!1,O(),lt.deactivateTrap(n,s);var p=u(f,"onDeactivate"),C=u(f,"onPostDeactivate"),I=u(f,"checkCanReturnFocus"),M=u(f,"returnFocus","returnFocusOnDeactivate");p==null||p();var P=function(){ct(function(){M&&b(E(i.nodeFocusedBeforeActivation)),C==null||C()})};return M&&I?(I(E(i.nodeFocusedBeforeActivation)).then(P,P),this):(P(),this)},pause:function(c){if(i.paused||!i.active)return this;var f=u(c,"onPause"),p=u(c,"onPostPause");return i.paused=!0,f==null||f(),N(),O(),p==null||p(),this},unpause:function(c){if(!i.paused||!i.active)return this;var f=u(c,"onUnpause"),p=u(c,"onPostUnpause");return i.paused=!1,f==null||f(),v(),B(),O(),p==null||p(),this},updateContainerElements:function(c){var f=[].concat(c).filter(Boolean);return i.containers=f.map(function(p){return typeof p=="string"?r.querySelector(p):p}),i.active&&v(),O(),this}},s.updateContainerElements(e),s};function kr(o,e={}){let t;const{immediate:r,...n}=e,a=oe(!1),i=oe(!1),s=d=>t&&t.activate(d),u=d=>t&&t.deactivate(d),l=()=>{t&&(t.pause(),i.value=!0)},h=()=>{t&&(t.unpause(),i.value=!1)};return $e(()=>kt(o),d=>{d&&(t=Dr(d,{...n,onActivate(){a.value=!0,e.onActivate&&e.onActivate()},onDeactivate(){a.value=!1,e.onDeactivate&&e.onDeactivate()}}),r&&s())},{flush:"post"}),Ot(()=>u()),{hasFocus:a,isPaused:i,activate:s,deactivate:u,pause:l,unpause:h}}class fe{constructor(e,t=!0,r=[],n=5e3){this.ctx=e,this.iframes=t,this.exclude=r,this.iframesTimeout=n}static matches(e,t){const r=typeof t=="string"?[t]:t,n=e.matches||e.matchesSelector||e.msMatchesSelector||e.mozMatchesSelector||e.oMatchesSelector||e.webkitMatchesSelector;if(n){let a=!1;return r.every(i=>n.call(e,i)?(a=!0,!1):!0),a}else return!1}getContexts(){let e,t=[];return typeof this.ctx>"u"||!this.ctx?e=[]:NodeList.prototype.isPrototypeOf(this.ctx)?e=Array.prototype.slice.call(this.ctx):Array.isArray(this.ctx)?e=this.ctx:typeof this.ctx=="string"?e=Array.prototype.slice.call(document.querySelectorAll(this.ctx)):e=[this.ctx],e.forEach(r=>{const n=t.filter(a=>a.contains(r)).length>0;t.indexOf(r)===-1&&!n&&t.push(r)}),t}getIframeContents(e,t,r=()=>{}){let n;try{const a=e.contentWindow;if(n=a.document,!a||!n)throw new Error("iframe inaccessible")}catch{r()}n&&t(n)}isIframeBlank(e){const t="about:blank",r=e.getAttribute("src").trim();return e.contentWindow.location.href===t&&r!==t&&r}observeIframeLoad(e,t,r){let n=!1,a=null;const i=()=>{if(!n){n=!0,clearTimeout(a);try{this.isIframeBlank(e)||(e.removeEventListener("load",i),this.getIframeContents(e,t,r))}catch{r()}}};e.addEventListener("load",i),a=setTimeout(i,this.iframesTimeout)}onIframeReady(e,t,r){try{e.contentWindow.document.readyState==="complete"?this.isIframeBlank(e)?this.observeIframeLoad(e,t,r):this.getIframeContents(e,t,r):this.observeIframeLoad(e,t,r)}catch{r()}}waitForIframes(e,t){let r=0;this.forEachIframe(e,()=>!0,n=>{r++,this.waitForIframes(n.querySelector("html"),()=>{--r||t()})},n=>{n||t()})}forEachIframe(e,t,r,n=()=>{}){let a=e.querySelectorAll("iframe"),i=a.length,s=0;a=Array.prototype.slice.call(a);const u=()=>{--i<=0&&n(s)};i||u(),a.forEach(l=>{fe.matches(l,this.exclude)?u():this.onIframeReady(l,h=>{t(l)&&(s++,r(h)),u()},u)})}createIterator(e,t,r){return document.createNodeIterator(e,t,r,!1)}createInstanceOnIframe(e){return new fe(e.querySelector("html"),this.iframes)}compareNodeIframe(e,t,r){const n=e.compareDocumentPosition(r),a=Node.DOCUMENT_POSITION_PRECEDING;if(n&a)if(t!==null){const i=t.compareDocumentPosition(r),s=Node.DOCUMENT_POSITION_FOLLOWING;if(i&s)return!0}else return!0;return!1}getIteratorNode(e){const t=e.previousNode();let r;return t===null?r=e.nextNode():r=e.nextNode()&&e.nextNode(),{prevNode:t,node:r}}checkIframeFilter(e,t,r,n){let a=!1,i=!1;return n.forEach((s,u)=>{s.val===r&&(a=u,i=s.handled)}),this.compareNodeIframe(e,t,r)?(a===!1&&!i?n.push({val:r,handled:!0}):a!==!1&&!i&&(n[a].handled=!0),!0):(a===!1&&n.push({val:r,handled:!1}),!1)}handleOpenIframes(e,t,r,n){e.forEach(a=>{a.handled||this.getIframeContents(a.val,i=>{this.createInstanceOnIframe(i).forEachNode(t,r,n)})})}iterateThroughNodes(e,t,r,n,a){const i=this.createIterator(t,e,n);let s=[],u=[],l,h,d=()=>({prevNode:h,node:l}=this.getIteratorNode(i),l);for(;d();)this.iframes&&this.forEachIframe(t,v=>this.checkIframeFilter(l,h,v,s),v=>{this.createInstanceOnIframe(v).forEachNode(e,y=>u.push(y),n)}),u.push(l);u.forEach(v=>{r(v)}),this.iframes&&this.handleOpenIframes(s,e,r,n),a()}forEachNode(e,t,r,n=()=>{}){const a=this.getContexts();let i=a.length;i||n(),a.forEach(s=>{const u=()=>{this.iterateThroughNodes(e,s,t,r,()=>{--i<=0&&n()})};this.iframes?this.waitForIframes(s,u):u()})}}let Or=class{constructor(e){this.ctx=e,this.ie=!1;const t=window.navigator.userAgent;(t.indexOf("MSIE")>-1||t.indexOf("Trident")>-1)&&(this.ie=!0)}set opt(e){this._opt=Object.assign({},{element:"",className:"",exclude:[],iframes:!1,iframesTimeout:5e3,separateWordSearch:!0,diacritics:!0,synonyms:{},accuracy:"partially",acrossElements:!1,caseSensitive:!1,ignoreJoiners:!1,ignoreGroups:0,ignorePunctuation:[],wildcards:"disabled",each:()=>{},noMatch:()=>{},filter:()=>!0,done:()=>{},debug:!1,log:window.console},e)}get opt(){return this._opt}get iterator(){return new fe(this.ctx,this.opt.iframes,this.opt.exclude,this.opt.iframesTimeout)}log(e,t="debug"){const r=this.opt.log;this.opt.debug&&typeof r=="object"&&typeof r[t]=="function"&&r[t](`mark.js: ${e}`)}escapeStr(e){return e.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")}createRegExp(e){return this.opt.wildcards!=="disabled"&&(e=this.setupWildcardsRegExp(e)),e=this.escapeStr(e),Object.keys(this.opt.synonyms).length&&(e=this.createSynonymsRegExp(e)),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),this.opt.diacritics&&(e=this.createDiacriticsRegExp(e)),e=this.createMergedBlanksRegExp(e),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.createJoinersRegExp(e)),this.opt.wildcards!=="disabled"&&(e=this.createWildcardsRegExp(e)),e=this.createAccuracyRegExp(e),e}createSynonymsRegExp(e){const t=this.opt.synonyms,r=this.opt.caseSensitive?"":"i",n=this.opt.ignoreJoiners||this.opt.ignorePunctuation.length?"\0":"";for(let a in t)if(t.hasOwnProperty(a)){const i=t[a],s=this.opt.wildcards!=="disabled"?this.setupWildcardsRegExp(a):this.escapeStr(a),u=this.opt.wildcards!=="disabled"?this.setupWildcardsRegExp(i):this.escapeStr(i);s!==""&&u!==""&&(e=e.replace(new RegExp(`(${this.escapeStr(s)}|${this.escapeStr(u)})`,`gm${r}`),n+`(${this.processSynomyms(s)}|${this.processSynomyms(u)})`+n))}return e}processSynomyms(e){return(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),e}setupWildcardsRegExp(e){return e=e.replace(/(?:\\)*\?/g,t=>t.charAt(0)==="\\"?"?":""),e.replace(/(?:\\)*\*/g,t=>t.charAt(0)==="\\"?"*":"")}createWildcardsRegExp(e){let t=this.opt.wildcards==="withSpaces";return e.replace(/\u0001/g,t?"[\\S\\s]?":"\\S?").replace(/\u0002/g,t?"[\\S\\s]*?":"\\S*")}setupIgnoreJoinersRegExp(e){return e.replace(/[^(|)\\]/g,(t,r,n)=>{let a=n.charAt(r+1);return/[(|)\\]/.test(a)||a===""?t:t+"\0"})}createJoinersRegExp(e){let t=[];const r=this.opt.ignorePunctuation;return Array.isArray(r)&&r.length&&t.push(this.escapeStr(r.join(""))),this.opt.ignoreJoiners&&t.push("\\u00ad\\u200b\\u200c\\u200d"),t.length?e.split(/\u0000+/).join(`[${t.join("")}]*`):e}createDiacriticsRegExp(e){const t=this.opt.caseSensitive?"":"i",r=this.opt.caseSensitive?["aàáảãạăằắẳẵặâầấẩẫậäåāą","AÀÁẢÃẠĂẰẮẲẴẶÂẦẤẨẪẬÄÅĀĄ","cçćč","CÇĆČ","dđď","DĐĎ","eèéẻẽẹêềếểễệëěēę","EÈÉẺẼẸÊỀẾỂỄỆËĚĒĘ","iìíỉĩịîïī","IÌÍỈĨỊÎÏĪ","lł","LŁ","nñňń","NÑŇŃ","oòóỏõọôồốổỗộơởỡớờợöøō","OÒÓỎÕỌÔỒỐỔỖỘƠỞỠỚỜỢÖØŌ","rř","RŘ","sšśșş","SŠŚȘŞ","tťțţ","TŤȚŢ","uùúủũụưừứửữựûüůū","UÙÚỦŨỤƯỪỨỬỮỰÛÜŮŪ","yýỳỷỹỵÿ","YÝỲỶỸỴŸ","zžżź","ZŽŻŹ"]:["aàáảãạăằắẳẵặâầấẩẫậäåāąAÀÁẢÃẠĂẰẮẲẴẶÂẦẤẨẪẬÄÅĀĄ","cçćčCÇĆČ","dđďDĐĎ","eèéẻẽẹêềếểễệëěēęEÈÉẺẼẸÊỀẾỂỄỆËĚĒĘ","iìíỉĩịîïīIÌÍỈĨỊÎÏĪ","lłLŁ","nñňńNÑŇŃ","oòóỏõọôồốổỗộơởỡớờợöøōOÒÓỎÕỌÔỒỐỔỖỘƠỞỠỚỜỢÖØŌ","rřRŘ","sšśșşSŠŚȘŞ","tťțţTŤȚŢ","uùúủũụưừứửữựûüůūUÙÚỦŨỤƯỪỨỬỮỰÛÜŮŪ","yýỳỷỹỵÿYÝỲỶỸỴŸ","zžżźZŽŻŹ"];let n=[];return e.split("").forEach(a=>{r.every(i=>{if(i.indexOf(a)!==-1){if(n.indexOf(i)>-1)return!1;e=e.replace(new RegExp(`[${i}]`,`gm${t}`),`[${i}]`),n.push(i)}return!0})}),e}createMergedBlanksRegExp(e){return e.replace(/[\s]+/gmi,"[\\s]+")}createAccuracyRegExp(e){const t="!\"#$%&'()*+,-./:;<=>?@[\\]^_`{|}~¡¿";let r=this.opt.accuracy,n=typeof r=="string"?r:r.value,a=typeof r=="string"?[]:r.limiters,i="";switch(a.forEach(s=>{i+=`|${this.escapeStr(s)}`}),n){case"partially":default:return`()(${e})`;case"complementary":return i="\\s"+(i||this.escapeStr(t)),`()([^${i}]*${e}[^${i}]*)`;case"exactly":return`(^|\\s${i})(${e})(?=$|\\s${i})`}}getSeparatedKeywords(e){let t=[];return e.forEach(r=>{this.opt.separateWordSearch?r.split(" ").forEach(n=>{n.trim()&&t.indexOf(n)===-1&&t.push(n)}):r.trim()&&t.indexOf(r)===-1&&t.push(r)}),{keywords:t.sort((r,n)=>n.length-r.length),length:t.length}}isNumeric(e){return Number(parseFloat(e))==e}checkRanges(e){if(!Array.isArray(e)||Object.prototype.toString.call(e[0])!=="[object Object]")return this.log("markRanges() will only accept an array of objects"),this.opt.noMatch(e),[];const t=[];let r=0;return e.sort((n,a)=>n.start-a.start).forEach(n=>{let{start:a,end:i,valid:s}=this.callNoMatchOnInvalidRanges(n,r);s&&(n.start=a,n.length=i-a,t.push(n),r=i)}),t}callNoMatchOnInvalidRanges(e,t){let r,n,a=!1;return e&&typeof e.start<"u"?(r=parseInt(e.start,10),n=r+parseInt(e.length,10),this.isNumeric(e.start)&&this.isNumeric(e.length)&&n-t>0&&n-r>0?a=!0:(this.log(`Ignoring invalid or overlapping range: ${JSON.stringify(e)}`),this.opt.noMatch(e))):(this.log(`Ignoring invalid range: ${JSON.stringify(e)}`),this.opt.noMatch(e)),{start:r,end:n,valid:a}}checkWhitespaceRanges(e,t,r){let n,a=!0,i=r.length,s=t-i,u=parseInt(e.start,10)-s;return u=u>i?i:u,n=u+parseInt(e.length,10),n>i&&(n=i,this.log(`End range automatically set to the max value of ${i}`)),u<0||n-u<0||u>i||n>i?(a=!1,this.log(`Invalid range: ${JSON.stringify(e)}`),this.opt.noMatch(e)):r.substring(u,n).replace(/\s+/g,"")===""&&(a=!1,this.log("Skipping whitespace only range: "+JSON.stringify(e)),this.opt.noMatch(e)),{start:u,end:n,valid:a}}getTextNodes(e){let t="",r=[];this.iterator.forEachNode(NodeFilter.SHOW_TEXT,n=>{r.push({start:t.length,end:(t+=n.textContent).length,node:n})},n=>this.matchesExclude(n.parentNode)?NodeFilter.FILTER_REJECT:NodeFilter.FILTER_ACCEPT,()=>{e({value:t,nodes:r})})}matchesExclude(e){return fe.matches(e,this.opt.exclude.concat(["script","style","title","head","html"]))}wrapRangeInTextNode(e,t,r){const n=this.opt.element?this.opt.element:"mark",a=e.splitText(t),i=a.splitText(r-t);let s=document.createElement(n);return s.setAttribute("data-markjs","true"),this.opt.className&&s.setAttribute("class",this.opt.className),s.textContent=a.textContent,a.parentNode.replaceChild(s,a),i}wrapRangeInMappedTextNode(e,t,r,n,a){e.nodes.every((i,s)=>{const u=e.nodes[s+1];if(typeof u>"u"||u.start>t){if(!n(i.node))return!1;const l=t-i.start,h=(r>i.end?i.end:r)-i.start,d=e.value.substr(0,i.start),v=e.value.substr(h+i.start);if(i.node=this.wrapRangeInTextNode(i.node,l,h),e.value=d+v,e.nodes.forEach((y,b)=>{b>=s&&(e.nodes[b].start>0&&b!==s&&(e.nodes[b].start-=h),e.nodes[b].end-=h)}),r-=h,a(i.node.previousSibling,i.start),r>i.end)t=i.end;else return!1}return!0})}wrapMatches(e,t,r,n,a){const i=t===0?0:t+1;this.getTextNodes(s=>{s.nodes.forEach(u=>{u=u.node;let l;for(;(l=e.exec(u.textContent))!==null&&l[i]!=="";){if(!r(l[i],u))continue;let h=l.index;if(i!==0)for(let d=1;d{let u;for(;(u=e.exec(s.value))!==null&&u[i]!=="";){let l=u.index;if(i!==0)for(let d=1;dr(u[i],d),(d,v)=>{e.lastIndex=v,n(d)})}a()})}wrapRangeFromIndex(e,t,r,n){this.getTextNodes(a=>{const i=a.value.length;e.forEach((s,u)=>{let{start:l,end:h,valid:d}=this.checkWhitespaceRanges(s,i,a.value);d&&this.wrapRangeInMappedTextNode(a,l,h,v=>t(v,s,a.value.substring(l,h),u),v=>{r(v,s)})}),n()})}unwrapMatches(e){const t=e.parentNode;let r=document.createDocumentFragment();for(;e.firstChild;)r.appendChild(e.removeChild(e.firstChild));t.replaceChild(r,e),this.ie?this.normalizeTextNode(t):t.normalize()}normalizeTextNode(e){if(e){if(e.nodeType===3)for(;e.nextSibling&&e.nextSibling.nodeType===3;)e.nodeValue+=e.nextSibling.nodeValue,e.parentNode.removeChild(e.nextSibling);else this.normalizeTextNode(e.firstChild);this.normalizeTextNode(e.nextSibling)}}markRegExp(e,t){this.opt=t,this.log(`Searching with expression "${e}"`);let r=0,n="wrapMatches";const a=i=>{r++,this.opt.each(i)};this.opt.acrossElements&&(n="wrapMatchesAcrossElements"),this[n](e,this.opt.ignoreGroups,(i,s)=>this.opt.filter(s,i,r),a,()=>{r===0&&this.opt.noMatch(e),this.opt.done(r)})}mark(e,t){this.opt=t;let r=0,n="wrapMatches";const{keywords:a,length:i}=this.getSeparatedKeywords(typeof e=="string"?[e]:e),s=this.opt.caseSensitive?"":"i",u=l=>{let h=new RegExp(this.createRegExp(l),`gm${s}`),d=0;this.log(`Searching with expression "${h}"`),this[n](h,1,(v,y)=>this.opt.filter(y,l,r,d),v=>{d++,r++,this.opt.each(v)},()=>{d===0&&this.opt.noMatch(l),a[i-1]===l?this.opt.done(r):u(a[a.indexOf(l)+1])})};this.opt.acrossElements&&(n="wrapMatchesAcrossElements"),i===0?this.opt.done(r):u(a[0])}markRanges(e,t){this.opt=t;let r=0,n=this.checkRanges(e);n&&n.length?(this.log("Starting to mark with the following ranges: "+JSON.stringify(n)),this.wrapRangeFromIndex(n,(a,i,s,u)=>this.opt.filter(a,i,s,u),(a,i)=>{r++,this.opt.each(a,i)},()=>{this.opt.done(r)})):this.opt.done(r)}unmark(e){this.opt=e;let t=this.opt.element?this.opt.element:"*";t+="[data-markjs]",this.opt.className&&(t+=`.${this.opt.className}`),this.log(`Removal selector "${t}"`),this.iterator.forEachNode(NodeFilter.SHOW_ELEMENT,r=>{this.unwrapMatches(r)},r=>{const n=fe.matches(r,t),a=this.matchesExclude(r);return!n||a?NodeFilter.FILTER_REJECT:NodeFilter.FILTER_ACCEPT},this.opt.done)}};function Rr(o){const e=new Or(o);return this.mark=(t,r)=>(e.mark(t,r),this),this.markRegExp=(t,r)=>(e.markRegExp(t,r),this),this.markRanges=(t,r)=>(e.markRanges(t,r),this),this.unmark=t=>(e.unmark(t),this),this}var W=function(){return W=Object.assign||function(e){for(var t,r=1,n=arguments.length;r0&&a[a.length-1])&&(l[0]===6||l[0]===2)){t=0;continue}if(l[0]===3&&(!a||l[1]>a[0]&&l[1]=o.length&&(o=void 0),{value:o&&o[r++],done:!o}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")}function J(o,e){var t=typeof Symbol=="function"&&o[Symbol.iterator];if(!t)return o;var r=t.call(o),n,a=[],i;try{for(;(e===void 0||e-- >0)&&!(n=r.next()).done;)a.push(n.value)}catch(s){i={error:s}}finally{try{n&&!n.done&&(t=r.return)&&t.call(r)}finally{if(i)throw i.error}}return a}var Lr="ENTRIES",Et="KEYS",St="VALUES",G="",Me=function(){function o(e,t){var r=e._tree,n=Array.from(r.keys());this.set=e,this._type=t,this._path=n.length>0?[{node:r,keys:n}]:[]}return o.prototype.next=function(){var e=this.dive();return this.backtrack(),e},o.prototype.dive=function(){if(this._path.length===0)return{done:!0,value:void 0};var e=ce(this._path),t=e.node,r=e.keys;if(ce(r)===G)return{done:!1,value:this.result()};var n=t.get(ce(r));return this._path.push({node:n,keys:Array.from(n.keys())}),this.dive()},o.prototype.backtrack=function(){if(this._path.length!==0){var e=ce(this._path).keys;e.pop(),!(e.length>0)&&(this._path.pop(),this.backtrack())}},o.prototype.key=function(){return this.set._prefix+this._path.map(function(e){var t=e.keys;return ce(t)}).filter(function(e){return e!==G}).join("")},o.prototype.value=function(){return ce(this._path).node.get(G)},o.prototype.result=function(){switch(this._type){case St:return this.value();case Et:return this.key();default:return[this.key(),this.value()]}},o.prototype[Symbol.iterator]=function(){return this},o}(),ce=function(o){return o[o.length-1]},Pr=function(o,e,t){var r=new Map;if(e===void 0)return r;for(var n=e.length+1,a=n+t,i=new Uint8Array(a*n).fill(t+1),s=0;st)continue e}At(o.get(y),e,t,r,n,E,i,s+y)}}}catch(f){u={error:f}}finally{try{v&&!v.done&&(l=d.return)&&l.call(d)}finally{if(u)throw u.error}}},Le=function(){function o(e,t){e===void 0&&(e=new Map),t===void 0&&(t=""),this._size=void 0,this._tree=e,this._prefix=t}return o.prototype.atPrefix=function(e){var t,r;if(!e.startsWith(this._prefix))throw new Error("Mismatched prefix");var n=J(ke(this._tree,e.slice(this._prefix.length)),2),a=n[0],i=n[1];if(a===void 0){var s=J(je(i),2),u=s[0],l=s[1];try{for(var h=D(u.keys()),d=h.next();!d.done;d=h.next()){var v=d.value;if(v!==G&&v.startsWith(l)){var y=new Map;return y.set(v.slice(l.length),u.get(v)),new o(y,e)}}}catch(b){t={error:b}}finally{try{d&&!d.done&&(r=h.return)&&r.call(h)}finally{if(t)throw t.error}}}return new o(a,e)},o.prototype.clear=function(){this._size=void 0,this._tree.clear()},o.prototype.delete=function(e){return this._size=void 0,zr(this._tree,e)},o.prototype.entries=function(){return new Me(this,Lr)},o.prototype.forEach=function(e){var t,r;try{for(var n=D(this),a=n.next();!a.done;a=n.next()){var i=J(a.value,2),s=i[0],u=i[1];e(s,u,this)}}catch(l){t={error:l}}finally{try{a&&!a.done&&(r=n.return)&&r.call(n)}finally{if(t)throw t.error}}},o.prototype.fuzzyGet=function(e,t){return Pr(this._tree,e,t)},o.prototype.get=function(e){var t=Ke(this._tree,e);return t!==void 0?t.get(G):void 0},o.prototype.has=function(e){var t=Ke(this._tree,e);return t!==void 0&&t.has(G)},o.prototype.keys=function(){return new Me(this,Et)},o.prototype.set=function(e,t){if(typeof e!="string")throw new Error("key must be a string");this._size=void 0;var r=Pe(this._tree,e);return r.set(G,t),this},Object.defineProperty(o.prototype,"size",{get:function(){if(this._size)return this._size;this._size=0;for(var e=this.entries();!e.next().done;)this._size+=1;return this._size},enumerable:!1,configurable:!0}),o.prototype.update=function(e,t){if(typeof e!="string")throw new Error("key must be a string");this._size=void 0;var r=Pe(this._tree,e);return r.set(G,t(r.get(G))),this},o.prototype.fetch=function(e,t){if(typeof e!="string")throw new Error("key must be a string");this._size=void 0;var r=Pe(this._tree,e),n=r.get(G);return n===void 0&&r.set(G,n=t()),n},o.prototype.values=function(){return new Me(this,St)},o.prototype[Symbol.iterator]=function(){return this.entries()},o.from=function(e){var t,r,n=new o;try{for(var a=D(e),i=a.next();!i.done;i=a.next()){var s=J(i.value,2),u=s[0],l=s[1];n.set(u,l)}}catch(h){t={error:h}}finally{try{i&&!i.done&&(r=a.return)&&r.call(a)}finally{if(t)throw t.error}}return n},o.fromObject=function(e){return o.from(Object.entries(e))},o}(),ke=function(o,e,t){var r,n;if(t===void 0&&(t=[]),e.length===0||o==null)return[o,t];try{for(var a=D(o.keys()),i=a.next();!i.done;i=a.next()){var s=i.value;if(s!==G&&e.startsWith(s))return t.push([o,s]),ke(o.get(s),e.slice(s.length),t)}}catch(u){r={error:u}}finally{try{i&&!i.done&&(n=a.return)&&n.call(a)}finally{if(r)throw r.error}}return t.push([o,e]),ke(void 0,"",t)},Ke=function(o,e){var t,r;if(e.length===0||o==null)return o;try{for(var n=D(o.keys()),a=n.next();!a.done;a=n.next()){var i=a.value;if(i!==G&&e.startsWith(i))return Ke(o.get(i),e.slice(i.length))}}catch(s){t={error:s}}finally{try{a&&!a.done&&(r=n.return)&&r.call(n)}finally{if(t)throw t.error}}},Pe=function(o,e){var t,r,n=e.length;e:for(var a=0;o&&a0)throw new Error("Expected documents to be present. Omit the argument to remove all documents.");this._index=new Le,this._documentCount=0,this._documentIds=new Map,this._idToShortId=new Map,this._fieldLength=new Map,this._avgFieldLength=[],this._storedFields=new Map,this._nextId=0}},o.prototype.discard=function(e){var t=this,r=this._idToShortId.get(e);if(r==null)throw new Error("MiniSearch: cannot discard document with ID ".concat(e,": it is not in the index"));this._idToShortId.delete(e),this._documentIds.delete(r),this._storedFields.delete(r),(this._fieldLength.get(r)||[]).forEach(function(n,a){t.removeFieldLength(r,a,t._documentCount,n)}),this._fieldLength.delete(r),this._documentCount-=1,this._dirtCount+=1,this.maybeAutoVacuum()},o.prototype.maybeAutoVacuum=function(){if(this._options.autoVacuum!==!1){var e=this._options.autoVacuum,t=e.minDirtFactor,r=e.minDirtCount,n=e.batchSize,a=e.batchWait;this.conditionalVacuum({batchSize:n,batchWait:a},{minDirtCount:r,minDirtFactor:t})}},o.prototype.discardAll=function(e){var t,r,n=this._options.autoVacuum;try{this._options.autoVacuum=!1;try{for(var a=D(e),i=a.next();!i.done;i=a.next()){var s=i.value;this.discard(s)}}catch(u){t={error:u}}finally{try{i&&!i.done&&(r=a.return)&&r.call(a)}finally{if(t)throw t.error}}}finally{this._options.autoVacuum=n}this.maybeAutoVacuum()},o.prototype.replace=function(e){var t=this._options,r=t.idField,n=t.extractField,a=n(e,r);this.discard(a),this.add(e)},o.prototype.vacuum=function(e){return e===void 0&&(e={}),this.conditionalVacuum(e)},o.prototype.conditionalVacuum=function(e,t){var r=this;return this._currentVacuum?(this._enqueuedVacuumConditions=this._enqueuedVacuumConditions&&t,this._enqueuedVacuum!=null?this._enqueuedVacuum:(this._enqueuedVacuum=this._currentVacuum.then(function(){var n=r._enqueuedVacuumConditions;return r._enqueuedVacuumConditions=Ue,r.performVacuuming(e,n)}),this._enqueuedVacuum)):this.vacuumConditionsMet(t)===!1?Promise.resolve():(this._currentVacuum=this.performVacuuming(e),this._currentVacuum)},o.prototype.performVacuuming=function(e,t){return _r(this,void 0,void 0,function(){var r,n,a,i,s,u,l,h,d,v,y,b,E,g,S,T,F,L,_,B,N,R,A,O,w;return Mr(this,function(c){switch(c.label){case 0:if(r=this._dirtCount,!this.vacuumConditionsMet(t))return[3,10];n=e.batchSize||Je.batchSize,a=e.batchWait||Je.batchWait,i=1,c.label=1;case 1:c.trys.push([1,7,8,9]),s=D(this._index),u=s.next(),c.label=2;case 2:if(u.done)return[3,6];l=J(u.value,2),h=l[0],d=l[1];try{for(v=(R=void 0,D(d)),y=v.next();!y.done;y=v.next()){b=J(y.value,2),E=b[0],g=b[1];try{for(S=(O=void 0,D(g)),T=S.next();!T.done;T=S.next())F=J(T.value,1),L=F[0],!this._documentIds.has(L)&&(g.size<=1?d.delete(E):g.delete(L))}catch(f){O={error:f}}finally{try{T&&!T.done&&(w=S.return)&&w.call(S)}finally{if(O)throw O.error}}}}catch(f){R={error:f}}finally{try{y&&!y.done&&(A=v.return)&&A.call(v)}finally{if(R)throw R.error}}return this._index.get(h).size===0&&this._index.delete(h),i%n!==0?[3,4]:[4,new Promise(function(f){return setTimeout(f,a)})];case 3:c.sent(),c.label=4;case 4:i+=1,c.label=5;case 5:return u=s.next(),[3,2];case 6:return[3,9];case 7:return _=c.sent(),B={error:_},[3,9];case 8:try{u&&!u.done&&(N=s.return)&&N.call(s)}finally{if(B)throw B.error}return[7];case 9:this._dirtCount-=r,c.label=10;case 10:return[4,null];case 11:return c.sent(),this._currentVacuum=this._enqueuedVacuum,this._enqueuedVacuum=null,[2]}})})},o.prototype.vacuumConditionsMet=function(e){if(e==null)return!0;var t=e.minDirtCount,r=e.minDirtFactor;return t=t||Be.minDirtCount,r=r||Be.minDirtFactor,this.dirtCount>=t&&this.dirtFactor>=r},Object.defineProperty(o.prototype,"isVacuuming",{get:function(){return this._currentVacuum!=null},enumerable:!1,configurable:!0}),Object.defineProperty(o.prototype,"dirtCount",{get:function(){return this._dirtCount},enumerable:!1,configurable:!0}),Object.defineProperty(o.prototype,"dirtFactor",{get:function(){return this._dirtCount/(1+this._documentCount+this._dirtCount)},enumerable:!1,configurable:!0}),o.prototype.has=function(e){return this._idToShortId.has(e)},o.prototype.getStoredFields=function(e){var t=this._idToShortId.get(e);if(t!=null)return this._storedFields.get(t)},o.prototype.search=function(e,t){var r,n;t===void 0&&(t={});var a=this.executeQuery(e,t),i=[];try{for(var s=D(a),u=s.next();!u.done;u=s.next()){var l=J(u.value,2),h=l[0],d=l[1],v=d.score,y=d.terms,b=d.match,E=y.length||1,g={id:this._documentIds.get(h),score:v*E,terms:Object.keys(b),queryTerms:y,match:b};Object.assign(g,this._storedFields.get(h)),(t.filter==null||t.filter(g))&&i.push(g)}}catch(S){r={error:S}}finally{try{u&&!u.done&&(n=s.return)&&n.call(s)}finally{if(r)throw r.error}}return e===o.wildcard&&t.boostDocument==null&&this._options.searchOptions.boostDocument==null||i.sort(vt),i},o.prototype.autoSuggest=function(e,t){var r,n,a,i;t===void 0&&(t={}),t=W(W({},this._options.autoSuggestOptions),t);var s=new Map;try{for(var u=D(this.search(e,t)),l=u.next();!l.done;l=u.next()){var h=l.value,d=h.score,v=h.terms,y=v.join(" "),b=s.get(y);b!=null?(b.score+=d,b.count+=1):s.set(y,{score:d,terms:v,count:1})}}catch(_){r={error:_}}finally{try{l&&!l.done&&(n=u.return)&&n.call(u)}finally{if(r)throw r.error}}var E=[];try{for(var g=D(s),S=g.next();!S.done;S=g.next()){var T=J(S.value,2),b=T[0],F=T[1],d=F.score,v=F.terms,L=F.count;E.push({suggestion:b,terms:v,score:d/L})}}catch(_){a={error:_}}finally{try{S&&!S.done&&(i=g.return)&&i.call(g)}finally{if(a)throw a.error}}return E.sort(vt),E},Object.defineProperty(o.prototype,"documentCount",{get:function(){return this._documentCount},enumerable:!1,configurable:!0}),Object.defineProperty(o.prototype,"termCount",{get:function(){return this._index.size},enumerable:!1,configurable:!0}),o.loadJSON=function(e,t){if(t==null)throw new Error("MiniSearch: loadJSON should be given the same options used when serializing the index");return this.loadJS(JSON.parse(e),t)},o.getDefault=function(e){if(Ve.hasOwnProperty(e))return ze(Ve,e);throw new Error('MiniSearch: unknown option "'.concat(e,'"'))},o.loadJS=function(e,t){var r,n,a,i,s,u,l=e.index,h=e.documentCount,d=e.nextId,v=e.documentIds,y=e.fieldIds,b=e.fieldLength,E=e.averageFieldLength,g=e.storedFields,S=e.dirtCount,T=e.serializationVersion;if(T!==1&&T!==2)throw new Error("MiniSearch: cannot deserialize an index created with an incompatible version");var F=new o(t);F._documentCount=h,F._nextId=d,F._documentIds=Te(v),F._idToShortId=new Map,F._fieldIds=y,F._fieldLength=Te(b),F._avgFieldLength=E,F._storedFields=Te(g),F._dirtCount=S||0,F._index=new Le;try{for(var L=D(F._documentIds),_=L.next();!_.done;_=L.next()){var B=J(_.value,2),N=B[0],R=B[1];F._idToShortId.set(R,N)}}catch(z){r={error:z}}finally{try{_&&!_.done&&(n=L.return)&&n.call(L)}finally{if(r)throw r.error}}try{for(var A=D(l),O=A.next();!O.done;O=A.next()){var w=J(O.value,2),c=w[0],f=w[1],p=new Map;try{for(var C=(s=void 0,D(Object.keys(f))),I=C.next();!I.done;I=C.next()){var M=I.value,P=f[M];T===1&&(P=P.ds),p.set(parseInt(M,10),Te(P))}}catch(z){s={error:z}}finally{try{I&&!I.done&&(u=C.return)&&u.call(C)}finally{if(s)throw s.error}}F._index.set(c,p)}}catch(z){a={error:z}}finally{try{O&&!O.done&&(i=A.return)&&i.call(A)}finally{if(a)throw a.error}}return F},o.prototype.executeQuery=function(e,t){var r=this;if(t===void 0&&(t={}),e===o.wildcard)return this.executeWildcardQuery(t);if(typeof e!="string"){var n=W(W(W({},t),e),{queries:void 0}),a=e.queries.map(function(g){return r.executeQuery(g,n)});return this.combineResults(a,n.combineWith)}var i=this._options,s=i.tokenize,u=i.processTerm,l=i.searchOptions,h=W(W({tokenize:s,processTerm:u},l),t),d=h.tokenize,v=h.processTerm,y=d(e).flatMap(function(g){return v(g)}).filter(function(g){return!!g}),b=y.map(Jr(h)),E=b.map(function(g){return r.executeQuerySpec(g,h)});return this.combineResults(E,h.combineWith)},o.prototype.executeQuerySpec=function(e,t){var r,n,a,i,s=W(W({},this._options.searchOptions),t),u=(s.fields||this._options.fields).reduce(function(M,P){var z;return W(W({},M),(z={},z[P]=ze(s.boost,P)||1,z))},{}),l=s.boostDocument,h=s.weights,d=s.maxFuzzy,v=s.bm25,y=W(W({},ht.weights),h),b=y.fuzzy,E=y.prefix,g=this._index.get(e.term),S=this.termResults(e.term,e.term,1,g,u,l,v),T,F;if(e.prefix&&(T=this._index.atPrefix(e.term)),e.fuzzy){var L=e.fuzzy===!0?.2:e.fuzzy,_=L<1?Math.min(d,Math.round(e.term.length*L)):L;_&&(F=this._index.fuzzyGet(e.term,_))}if(T)try{for(var B=D(T),N=B.next();!N.done;N=B.next()){var R=J(N.value,2),A=R[0],O=R[1],w=A.length-e.term.length;if(w){F==null||F.delete(A);var c=E*A.length/(A.length+.3*w);this.termResults(e.term,A,c,O,u,l,v,S)}}}catch(M){r={error:M}}finally{try{N&&!N.done&&(n=B.return)&&n.call(B)}finally{if(r)throw r.error}}if(F)try{for(var f=D(F.keys()),p=f.next();!p.done;p=f.next()){var A=p.value,C=J(F.get(A),2),I=C[0],w=C[1];if(w){var c=b*A.length/(A.length+w);this.termResults(e.term,A,c,I,u,l,v,S)}}}catch(M){a={error:M}}finally{try{p&&!p.done&&(i=f.return)&&i.call(f)}finally{if(a)throw a.error}}return S},o.prototype.executeWildcardQuery=function(e){var t,r,n=new Map,a=W(W({},this._options.searchOptions),e);try{for(var i=D(this._documentIds),s=i.next();!s.done;s=i.next()){var u=J(s.value,2),l=u[0],h=u[1],d=a.boostDocument?a.boostDocument(h,"",this._storedFields.get(l)):1;n.set(l,{score:d,terms:[],match:{}})}}catch(v){t={error:v}}finally{try{s&&!s.done&&(r=i.return)&&r.call(i)}finally{if(t)throw t.error}}return n},o.prototype.combineResults=function(e,t){if(t===void 0&&(t=Ge),e.length===0)return new Map;var r=t.toLowerCase();return e.reduce($r[r])||new Map},o.prototype.toJSON=function(){var e,t,r,n,a=[];try{for(var i=D(this._index),s=i.next();!s.done;s=i.next()){var u=J(s.value,2),l=u[0],h=u[1],d={};try{for(var v=(r=void 0,D(h)),y=v.next();!y.done;y=v.next()){var b=J(y.value,2),E=b[0],g=b[1];d[E]=Object.fromEntries(g)}}catch(S){r={error:S}}finally{try{y&&!y.done&&(n=v.return)&&n.call(v)}finally{if(r)throw r.error}}a.push([l,d])}}catch(S){e={error:S}}finally{try{s&&!s.done&&(t=i.return)&&t.call(i)}finally{if(e)throw e.error}}return{documentCount:this._documentCount,nextId:this._nextId,documentIds:Object.fromEntries(this._documentIds),fieldIds:this._fieldIds,fieldLength:Object.fromEntries(this._fieldLength),averageFieldLength:this._avgFieldLength,storedFields:Object.fromEntries(this._storedFields),dirtCount:this._dirtCount,index:a,serializationVersion:2}},o.prototype.termResults=function(e,t,r,n,a,i,s,u){var l,h,d,v,y;if(u===void 0&&(u=new Map),n==null)return u;try{for(var b=D(Object.keys(a)),E=b.next();!E.done;E=b.next()){var g=E.value,S=a[g],T=this._fieldIds[g],F=n.get(T);if(F!=null){var L=F.size,_=this._avgFieldLength[T];try{for(var B=(d=void 0,D(F.keys())),N=B.next();!N.done;N=B.next()){var R=N.value;if(!this._documentIds.has(R)){this.removeTerm(T,R,t),L-=1;continue}var A=i?i(this._documentIds.get(R),t,this._storedFields.get(R)):1;if(A){var O=F.get(R),w=this._fieldLength.get(R)[T],c=Kr(O,L,this._documentCount,w,_,s),f=r*S*A*c,p=u.get(R);if(p){p.score+=f,jr(p.terms,e);var C=ze(p.match,t);C?C.push(g):p.match[t]=[g]}else u.set(R,{score:f,terms:[e],match:(y={},y[t]=[g],y)})}}}catch(I){d={error:I}}finally{try{N&&!N.done&&(v=B.return)&&v.call(B)}finally{if(d)throw d.error}}}}}catch(I){l={error:I}}finally{try{E&&!E.done&&(h=b.return)&&h.call(b)}finally{if(l)throw l.error}}return u},o.prototype.addTerm=function(e,t,r){var n=this._index.fetch(r,pt),a=n.get(e);if(a==null)a=new Map,a.set(t,1),n.set(e,a);else{var i=a.get(t);a.set(t,(i||0)+1)}},o.prototype.removeTerm=function(e,t,r){if(!this._index.has(r)){this.warnDocumentChanged(t,e,r);return}var n=this._index.fetch(r,pt),a=n.get(e);a==null||a.get(t)==null?this.warnDocumentChanged(t,e,r):a.get(t)<=1?a.size<=1?n.delete(e):a.delete(t):a.set(t,a.get(t)-1),this._index.get(r).size===0&&this._index.delete(r)},o.prototype.warnDocumentChanged=function(e,t,r){var n,a;try{for(var i=D(Object.keys(this._fieldIds)),s=i.next();!s.done;s=i.next()){var u=s.value;if(this._fieldIds[u]===t){this._options.logger("warn","MiniSearch: document with ID ".concat(this._documentIds.get(e),' has changed before removal: term "').concat(r,'" was not present in field "').concat(u,'". Removing a document after it has changed can corrupt the index!'),"version_conflict");return}}}catch(l){n={error:l}}finally{try{s&&!s.done&&(a=i.return)&&a.call(i)}finally{if(n)throw n.error}}},o.prototype.addDocumentId=function(e){var t=this._nextId;return this._idToShortId.set(e,t),this._documentIds.set(t,e),this._documentCount+=1,this._nextId+=1,t},o.prototype.addFields=function(e){for(var t=0;t(Ht("data-v-f5c68218"),o=o(),Qt(),o),Hr=["aria-owns"],Qr={class:"shell"},Yr=["title"],Zr=Y(()=>k("span",{"aria-hidden":"true",class:"vpi-search search-icon local-search-icon"},null,-1)),Xr=[Zr],ea={class:"search-actions before"},ta=["title"],ra=Y(()=>k("span",{class:"vpi-arrow-left local-search-icon"},null,-1)),aa=[ra],na=["placeholder"],ia={class:"search-actions"},oa=["title"],sa=Y(()=>k("span",{class:"vpi-layout-list local-search-icon"},null,-1)),ua=[sa],la=["disabled","title"],ca=Y(()=>k("span",{class:"vpi-delete local-search-icon"},null,-1)),fa=[ca],ha=["id","role","aria-labelledby"],da=["aria-selected"],va=["href","aria-label","onMouseenter","onFocusin"],pa={class:"titles"},ya=Y(()=>k("span",{class:"title-icon"},"#",-1)),ma=["innerHTML"],ga=Y(()=>k("span",{class:"vpi-chevron-right local-search-icon"},null,-1)),ba={class:"title main"},wa=["innerHTML"],xa={key:0,class:"excerpt-wrapper"},Fa={key:0,class:"excerpt",inert:""},Ea=["innerHTML"],Sa=Y(()=>k("div",{class:"excerpt-gradient-bottom"},null,-1)),Aa=Y(()=>k("div",{class:"excerpt-gradient-top"},null,-1)),Ta={key:0,class:"no-results"},Na={class:"search-keyboard-shortcuts"},Ca=["aria-label"],Ia=Y(()=>k("span",{class:"vpi-arrow-up navigate-icon"},null,-1)),Da=[Ia],ka=["aria-label"],Oa=Y(()=>k("span",{class:"vpi-arrow-down navigate-icon"},null,-1)),Ra=[Oa],_a=["aria-label"],Ma=Y(()=>k("span",{class:"vpi-corner-down-left navigate-icon"},null,-1)),La=[Ma],Pa=["aria-label"],za=Rt({__name:"VPLocalSearchBox",emits:["close"],setup(o,{emit:e}){var P,z;const t=e,r=xe(),n=xe(),a=xe(nr),i=rr(),{activate:s}=kr(r,{immediate:!0,allowOutsideClick:!0,clickOutsideDeactivates:!0,escapeDeactivates:!0}),{localeIndex:u,theme:l}=i,h=tt(async()=>{var m,x,$,K,q,H,V,U,Z;return it(Br.loadJSON(($=await((x=(m=a.value)[u.value])==null?void 0:x.call(m)))==null?void 0:$.default,{fields:["title","titles","text"],storeFields:["title","titles"],searchOptions:{fuzzy:.2,prefix:!0,boost:{title:4,text:2,titles:1},...((K=l.value.search)==null?void 0:K.provider)==="local"&&((H=(q=l.value.search.options)==null?void 0:q.miniSearch)==null?void 0:H.searchOptions)},...((V=l.value.search)==null?void 0:V.provider)==="local"&&((Z=(U=l.value.search.options)==null?void 0:U.miniSearch)==null?void 0:Z.options)}))}),v=Fe(()=>{var m,x;return((m=l.value.search)==null?void 0:m.provider)==="local"&&((x=l.value.search.options)==null?void 0:x.disableQueryPersistence)===!0}).value?oe(""):_t("vitepress:local-search-filter",""),y=Mt("vitepress:local-search-detailed-list",((P=l.value.search)==null?void 0:P.provider)==="local"&&((z=l.value.search.options)==null?void 0:z.detailedView)===!0),b=Fe(()=>{var m,x,$;return((m=l.value.search)==null?void 0:m.provider)==="local"&&(((x=l.value.search.options)==null?void 0:x.disableDetailedView)===!0||(($=l.value.search.options)==null?void 0:$.detailedView)===!1)}),E=Fe(()=>{var x,$,K,q,H,V,U;const m=((x=l.value.search)==null?void 0:x.options)??l.value.algolia;return((H=(q=(K=($=m==null?void 0:m.locales)==null?void 0:$[u.value])==null?void 0:K.translations)==null?void 0:q.button)==null?void 0:H.buttonText)||((U=(V=m==null?void 0:m.translations)==null?void 0:V.button)==null?void 0:U.buttonText)||"Search"});Lt(()=>{b.value&&(y.value=!1)});const g=xe([]),S=oe(!1);$e(v,()=>{S.value=!1});const T=tt(async()=>{if(n.value)return it(new Rr(n.value))},null),F=new qr(16);Pt(()=>[h.value,v.value,y.value],async([m,x,$],K,q)=>{var be,qe,He,Qe;(K==null?void 0:K[0])!==m&&F.clear();let H=!1;if(q(()=>{H=!0}),!m)return;g.value=m.search(x).slice(0,16),S.value=!0;const V=$?await Promise.all(g.value.map(Q=>L(Q.id))):[];if(H)return;for(const{id:Q,mod:ae}of V){const ne=Q.slice(0,Q.indexOf("#"));let te=F.get(ne);if(te)continue;te=new Map,F.set(ne,te);const X=ae.default??ae;if(X!=null&&X.render||X!=null&&X.setup){const ie=Yt(X);ie.config.warnHandler=()=>{},ie.provide(Zt,i),Object.defineProperties(ie.config.globalProperties,{$frontmatter:{get(){return i.frontmatter.value}},$params:{get(){return i.page.value.params}}});const Ye=document.createElement("div");ie.mount(Ye),Ye.querySelectorAll("h1, h2, h3, h4, h5, h6").forEach(he=>{var et;const we=(et=he.querySelector("a"))==null?void 0:et.getAttribute("href"),Ze=(we==null?void 0:we.startsWith("#"))&&we.slice(1);if(!Ze)return;let Xe="";for(;(he=he.nextElementSibling)&&!/^h[1-6]$/i.test(he.tagName);)Xe+=he.outerHTML;te.set(Ze,Xe)}),ie.unmount()}if(H)return}const U=new Set;if(g.value=g.value.map(Q=>{const[ae,ne]=Q.id.split("#"),te=F.get(ae),X=(te==null?void 0:te.get(ne))??"";for(const ie in Q.match)U.add(ie);return{...Q,text:X}}),await de(),H)return;await new Promise(Q=>{var ae;(ae=T.value)==null||ae.unmark({done:()=>{var ne;(ne=T.value)==null||ne.markRegExp(M(U),{done:Q})}})});const Z=((be=r.value)==null?void 0:be.querySelectorAll(".result .excerpt"))??[];for(const Q of Z)(qe=Q.querySelector('mark[data-markjs="true"]'))==null||qe.scrollIntoView({block:"center"});(Qe=(He=n.value)==null?void 0:He.firstElementChild)==null||Qe.scrollIntoView({block:"start"})},{debounce:200,immediate:!0});async function L(m){const x=Xt(m.slice(0,m.indexOf("#")));try{if(!x)throw new Error(`Cannot find file for id: ${m}`);return{id:m,mod:await yt(()=>import(x),[])}}catch($){return console.error($),{id:m,mod:{}}}}const _=oe(),B=Fe(()=>{var m;return((m=v.value)==null?void 0:m.length)<=0});function N(m=!0){var x,$;(x=_.value)==null||x.focus(),m&&(($=_.value)==null||$.select())}Re(()=>{N()});function R(m){m.pointerType==="mouse"&&N()}const A=oe(-1),O=oe(!1);$e(g,m=>{A.value=m.length?0:-1,w()});function w(){de(()=>{const m=document.querySelector(".result.selected");m&&m.scrollIntoView({block:"nearest"})})}Ee("ArrowUp",m=>{m.preventDefault(),A.value--,A.value<0&&(A.value=g.value.length-1),O.value=!0,w()}),Ee("ArrowDown",m=>{m.preventDefault(),A.value++,A.value>=g.value.length&&(A.value=0),O.value=!0,w()});const c=zt();Ee("Enter",m=>{if(m.isComposing||m.target instanceof HTMLButtonElement&&m.target.type!=="submit")return;const x=g.value[A.value];if(m.target instanceof HTMLInputElement&&!x){m.preventDefault();return}x&&(c.go(x.id),t("close"))}),Ee("Escape",()=>{t("close")});const p=ar({modal:{displayDetails:"Display detailed list",resetButtonTitle:"Reset search",backButtonTitle:"Close search",noResultsText:"No results for",footer:{selectText:"to select",selectKeyAriaLabel:"enter",navigateText:"to navigate",navigateUpKeyAriaLabel:"up arrow",navigateDownKeyAriaLabel:"down arrow",closeText:"to close",closeKeyAriaLabel:"escape"}}});Re(()=>{window.history.pushState(null,"",null)}),Vt("popstate",m=>{m.preventDefault(),t("close")});const C=Bt($t?document.body:null);Re(()=>{de(()=>{C.value=!0,de().then(()=>s())})}),Wt(()=>{C.value=!1});function I(){v.value="",de().then(()=>N(!1))}function M(m){return new RegExp([...m].sort((x,$)=>$.length-x.length).map(x=>`(${er(x)})`).join("|"),"gi")}return(m,x)=>{var $,K,q,H;return ee(),Kt(qt,{to:"body"},[k("div",{ref_key:"el",ref:r,role:"button","aria-owns":($=g.value)!=null&&$.length?"localsearch-list":void 0,"aria-expanded":"true","aria-haspopup":"listbox","aria-labelledby":"localsearch-label",class:"VPLocalSearchBox"},[k("div",{class:"backdrop",onClick:x[0]||(x[0]=V=>m.$emit("close"))}),k("div",Qr,[k("form",{class:"search-bar",onPointerup:x[4]||(x[4]=V=>R(V)),onSubmit:x[5]||(x[5]=Jt(()=>{},["prevent"]))},[k("label",{title:E.value,id:"localsearch-label",for:"localsearch-input"},Xr,8,Yr),k("div",ea,[k("button",{class:"back-button",title:j(p)("modal.backButtonTitle"),onClick:x[1]||(x[1]=V=>m.$emit("close"))},aa,8,ta)]),Ut(k("input",{ref_key:"searchInput",ref:_,"onUpdate:modelValue":x[2]||(x[2]=V=>Gt(v)?v.value=V:null),placeholder:E.value,id:"localsearch-input","aria-labelledby":"localsearch-label",class:"search-input"},null,8,na),[[jt,j(v)]]),k("div",ia,[b.value?Se("",!0):(ee(),re("button",{key:0,class:rt(["toggle-layout-button",{"detailed-list":j(y)}]),type:"button",title:j(p)("modal.displayDetails"),onClick:x[3]||(x[3]=V=>A.value>-1&&(y.value=!j(y)))},ua,10,oa)),k("button",{class:"clear-button",type:"reset",disabled:B.value,title:j(p)("modal.resetButtonTitle"),onClick:I},fa,8,la)])],32),k("ul",{ref_key:"resultsEl",ref:n,id:(K=g.value)!=null&&K.length?"localsearch-list":void 0,role:(q=g.value)!=null&&q.length?"listbox":void 0,"aria-labelledby":(H=g.value)!=null&&H.length?"localsearch-label":void 0,class:"results",onMousemove:x[7]||(x[7]=V=>O.value=!1)},[(ee(!0),re(nt,null,at(g.value,(V,U)=>(ee(),re("li",{key:V.id,role:"option","aria-selected":A.value===U?"true":"false"},[k("a",{href:V.id,class:rt(["result",{selected:A.value===U}]),"aria-label":[...V.titles,V.title].join(" > "),onMouseenter:Z=>!O.value&&(A.value=U),onFocusin:Z=>A.value=U,onClick:x[6]||(x[6]=Z=>m.$emit("close"))},[k("div",null,[k("div",pa,[ya,(ee(!0),re(nt,null,at(V.titles,(Z,be)=>(ee(),re("span",{key:be,class:"title"},[k("span",{class:"text",innerHTML:Z},null,8,ma),ga]))),128)),k("span",ba,[k("span",{class:"text",innerHTML:V.title},null,8,wa)])]),j(y)?(ee(),re("div",xa,[V.text?(ee(),re("div",Fa,[k("div",{class:"vp-doc",innerHTML:V.text},null,8,Ea)])):Se("",!0),Sa,Aa])):Se("",!0)])],42,va)],8,da))),128)),j(v)&&!g.value.length&&S.value?(ee(),re("li",Ta,[ve(pe(j(p)("modal.noResultsText"))+' "',1),k("strong",null,pe(j(v)),1),ve('" ')])):Se("",!0)],40,ha),k("div",Na,[k("span",null,[k("kbd",{"aria-label":j(p)("modal.footer.navigateUpKeyAriaLabel")},Da,8,Ca),k("kbd",{"aria-label":j(p)("modal.footer.navigateDownKeyAriaLabel")},Ra,8,ka),ve(" "+pe(j(p)("modal.footer.navigateText")),1)]),k("span",null,[k("kbd",{"aria-label":j(p)("modal.footer.selectKeyAriaLabel")},La,8,_a),ve(" "+pe(j(p)("modal.footer.selectText")),1)]),k("span",null,[k("kbd",{"aria-label":j(p)("modal.footer.closeKeyAriaLabel")},"esc",8,Pa),ve(" "+pe(j(p)("modal.footer.closeText")),1)])])])],8,Hr)])}}}),Ja=tr(za,[["__scopeId","data-v-f5c68218"]]);export{Ja as default}; diff --git a/dev/assets/chunks/VPLocalSearchBox.DqWxI-Ji.js b/dev/assets/chunks/VPLocalSearchBox.DqWxI-Ji.js new file mode 100644 index 0000000..ae9f4a4 --- /dev/null +++ b/dev/assets/chunks/VPLocalSearchBox.DqWxI-Ji.js @@ -0,0 +1,7 @@ +var Ct=Object.defineProperty;var It=(o,e,t)=>e in o?Ct(o,e,{enumerable:!0,configurable:!0,writable:!0,value:t}):o[e]=t;var Oe=(o,e,t)=>(It(o,typeof e!="symbol"?e+"":e,t),t);import{X as Dt,s as oe,v as $e,al as kt,am as Ot,d as Rt,G as xe,an as tt,h as Fe,ao as _t,ap as Mt,x as Lt,aq as zt,y as Re,R as de,Q as Ee,ar as Pt,as as Bt,Y as Vt,U as $t,at as Wt,o as ee,b as Kt,j as k,a1 as Jt,k as j,au as Ut,av as jt,aw as Gt,c as re,n as rt,e as Se,E as at,F as nt,a as ve,t as pe,ax as Qt,p as qt,l as Ht,ay as it,az as Yt,ab as Zt,ah as Xt,aA as er,_ as tr}from"./framework.Cvv1S4VC.js";import{u as rr,c as ar}from"./theme.CNBIs78H.js";const nr={root:()=>Dt(()=>import("./@localSearchIndexroot.Bj-EWWk0.js"),[])};/*! +* tabbable 6.2.0 +* @license MIT, https://github.com/focus-trap/tabbable/blob/master/LICENSE +*/var yt=["input:not([inert])","select:not([inert])","textarea:not([inert])","a[href]:not([inert])","button:not([inert])","[tabindex]:not(slot):not([inert])","audio[controls]:not([inert])","video[controls]:not([inert])",'[contenteditable]:not([contenteditable="false"]):not([inert])',"details>summary:first-of-type:not([inert])","details:not([inert])"],Ne=yt.join(","),mt=typeof Element>"u",ue=mt?function(){}:Element.prototype.matches||Element.prototype.msMatchesSelector||Element.prototype.webkitMatchesSelector,Ce=!mt&&Element.prototype.getRootNode?function(o){var e;return o==null||(e=o.getRootNode)===null||e===void 0?void 0:e.call(o)}:function(o){return o==null?void 0:o.ownerDocument},Ie=function o(e,t){var r;t===void 0&&(t=!0);var n=e==null||(r=e.getAttribute)===null||r===void 0?void 0:r.call(e,"inert"),a=n===""||n==="true",i=a||t&&e&&o(e.parentNode);return i},ir=function(e){var t,r=e==null||(t=e.getAttribute)===null||t===void 0?void 0:t.call(e,"contenteditable");return r===""||r==="true"},gt=function(e,t,r){if(Ie(e))return[];var n=Array.prototype.slice.apply(e.querySelectorAll(Ne));return t&&ue.call(e,Ne)&&n.unshift(e),n=n.filter(r),n},bt=function o(e,t,r){for(var n=[],a=Array.from(e);a.length;){var i=a.shift();if(!Ie(i,!1))if(i.tagName==="SLOT"){var s=i.assignedElements(),u=s.length?s:i.children,l=o(u,!0,r);r.flatten?n.push.apply(n,l):n.push({scopeParent:i,candidates:l})}else{var h=ue.call(i,Ne);h&&r.filter(i)&&(t||!e.includes(i))&&n.push(i);var d=i.shadowRoot||typeof r.getShadowRoot=="function"&&r.getShadowRoot(i),v=!Ie(d,!1)&&(!r.shadowRootFilter||r.shadowRootFilter(i));if(d&&v){var y=o(d===!0?i.children:d.children,!0,r);r.flatten?n.push.apply(n,y):n.push({scopeParent:i,candidates:y})}else a.unshift.apply(a,i.children)}}return n},wt=function(e){return!isNaN(parseInt(e.getAttribute("tabindex"),10))},se=function(e){if(!e)throw new Error("No node provided");return e.tabIndex<0&&(/^(AUDIO|VIDEO|DETAILS)$/.test(e.tagName)||ir(e))&&!wt(e)?0:e.tabIndex},or=function(e,t){var r=se(e);return r<0&&t&&!wt(e)?0:r},sr=function(e,t){return e.tabIndex===t.tabIndex?e.documentOrder-t.documentOrder:e.tabIndex-t.tabIndex},xt=function(e){return e.tagName==="INPUT"},ur=function(e){return xt(e)&&e.type==="hidden"},lr=function(e){var t=e.tagName==="DETAILS"&&Array.prototype.slice.apply(e.children).some(function(r){return r.tagName==="SUMMARY"});return t},cr=function(e,t){for(var r=0;rsummary:first-of-type"),i=a?e.parentElement:e;if(ue.call(i,"details:not([open]) *"))return!0;if(!r||r==="full"||r==="legacy-full"){if(typeof n=="function"){for(var s=e;e;){var u=e.parentElement,l=Ce(e);if(u&&!u.shadowRoot&&n(u)===!0)return ot(e);e.assignedSlot?e=e.assignedSlot:!u&&l!==e.ownerDocument?e=l.host:e=u}e=s}if(vr(e))return!e.getClientRects().length;if(r!=="legacy-full")return!0}else if(r==="non-zero-area")return ot(e);return!1},yr=function(e){if(/^(INPUT|BUTTON|SELECT|TEXTAREA)$/.test(e.tagName))for(var t=e.parentElement;t;){if(t.tagName==="FIELDSET"&&t.disabled){for(var r=0;r=0)},gr=function o(e){var t=[],r=[];return e.forEach(function(n,a){var i=!!n.scopeParent,s=i?n.scopeParent:n,u=or(s,i),l=i?o(n.candidates):s;u===0?i?t.push.apply(t,l):t.push(s):r.push({documentOrder:a,tabIndex:u,item:n,isScope:i,content:l})}),r.sort(sr).reduce(function(n,a){return a.isScope?n.push.apply(n,a.content):n.push(a.content),n},[]).concat(t)},br=function(e,t){t=t||{};var r;return t.getShadowRoot?r=bt([e],t.includeContainer,{filter:We.bind(null,t),flatten:!1,getShadowRoot:t.getShadowRoot,shadowRootFilter:mr}):r=gt(e,t.includeContainer,We.bind(null,t)),gr(r)},wr=function(e,t){t=t||{};var r;return t.getShadowRoot?r=bt([e],t.includeContainer,{filter:De.bind(null,t),flatten:!0,getShadowRoot:t.getShadowRoot}):r=gt(e,t.includeContainer,De.bind(null,t)),r},le=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ue.call(e,Ne)===!1?!1:We(t,e)},xr=yt.concat("iframe").join(","),_e=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ue.call(e,xr)===!1?!1:De(t,e)};/*! +* focus-trap 7.5.4 +* @license MIT, https://github.com/focus-trap/focus-trap/blob/master/LICENSE +*/function st(o,e){var t=Object.keys(o);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(o);e&&(r=r.filter(function(n){return Object.getOwnPropertyDescriptor(o,n).enumerable})),t.push.apply(t,r)}return t}function ut(o){for(var e=1;e0){var r=e[e.length-1];r!==t&&r.pause()}var n=e.indexOf(t);n===-1||e.splice(n,1),e.push(t)},deactivateTrap:function(e,t){var r=e.indexOf(t);r!==-1&&e.splice(r,1),e.length>0&&e[e.length-1].unpause()}},Ar=function(e){return e.tagName&&e.tagName.toLowerCase()==="input"&&typeof e.select=="function"},Tr=function(e){return(e==null?void 0:e.key)==="Escape"||(e==null?void 0:e.key)==="Esc"||(e==null?void 0:e.keyCode)===27},ge=function(e){return(e==null?void 0:e.key)==="Tab"||(e==null?void 0:e.keyCode)===9},Nr=function(e){return ge(e)&&!e.shiftKey},Cr=function(e){return ge(e)&&e.shiftKey},ct=function(e){return setTimeout(e,0)},ft=function(e,t){var r=-1;return e.every(function(n,a){return t(n)?(r=a,!1):!0}),r},ye=function(e){for(var t=arguments.length,r=new Array(t>1?t-1:0),n=1;n1?p-1:0),I=1;I=0)c=r.activeElement;else{var f=i.tabbableGroups[0],p=f&&f.firstTabbableNode;c=p||h("fallbackFocus")}if(!c)throw new Error("Your focus-trap needs to have at least one focusable element");return c},v=function(){if(i.containerGroups=i.containers.map(function(c){var f=br(c,a.tabbableOptions),p=wr(c,a.tabbableOptions),C=f.length>0?f[0]:void 0,I=f.length>0?f[f.length-1]:void 0,M=p.find(function(m){return le(m)}),z=p.slice().reverse().find(function(m){return le(m)}),P=!!f.find(function(m){return se(m)>0});return{container:c,tabbableNodes:f,focusableNodes:p,posTabIndexesFound:P,firstTabbableNode:C,lastTabbableNode:I,firstDomTabbableNode:M,lastDomTabbableNode:z,nextTabbableNode:function(x){var $=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!0,K=f.indexOf(x);return K<0?$?p.slice(p.indexOf(x)+1).find(function(Q){return le(Q)}):p.slice(0,p.indexOf(x)).reverse().find(function(Q){return le(Q)}):f[K+($?1:-1)]}}}),i.tabbableGroups=i.containerGroups.filter(function(c){return c.tabbableNodes.length>0}),i.tabbableGroups.length<=0&&!h("fallbackFocus"))throw new Error("Your focus-trap must have at least one container with at least one tabbable node in it at all times");if(i.containerGroups.find(function(c){return c.posTabIndexesFound})&&i.containerGroups.length>1)throw new Error("At least one node with a positive tabindex was found in one of your focus-trap's multiple containers. Positive tabindexes are only supported in single-container focus-traps.")},y=function w(c){var f=c.activeElement;if(f)return f.shadowRoot&&f.shadowRoot.activeElement!==null?w(f.shadowRoot):f},b=function w(c){if(c!==!1&&c!==y(document)){if(!c||!c.focus){w(d());return}c.focus({preventScroll:!!a.preventScroll}),i.mostRecentlyFocusedNode=c,Ar(c)&&c.select()}},E=function(c){var f=h("setReturnFocus",c);return f||(f===!1?!1:c)},g=function(c){var f=c.target,p=c.event,C=c.isBackward,I=C===void 0?!1:C;f=f||Ae(p),v();var M=null;if(i.tabbableGroups.length>0){var z=l(f,p),P=z>=0?i.containerGroups[z]:void 0;if(z<0)I?M=i.tabbableGroups[i.tabbableGroups.length-1].lastTabbableNode:M=i.tabbableGroups[0].firstTabbableNode;else if(I){var m=ft(i.tabbableGroups,function(B){var U=B.firstTabbableNode;return f===U});if(m<0&&(P.container===f||_e(f,a.tabbableOptions)&&!le(f,a.tabbableOptions)&&!P.nextTabbableNode(f,!1))&&(m=z),m>=0){var x=m===0?i.tabbableGroups.length-1:m-1,$=i.tabbableGroups[x];M=se(f)>=0?$.lastTabbableNode:$.lastDomTabbableNode}else ge(p)||(M=P.nextTabbableNode(f,!1))}else{var K=ft(i.tabbableGroups,function(B){var U=B.lastTabbableNode;return f===U});if(K<0&&(P.container===f||_e(f,a.tabbableOptions)&&!le(f,a.tabbableOptions)&&!P.nextTabbableNode(f))&&(K=z),K>=0){var Q=K===i.tabbableGroups.length-1?0:K+1,q=i.tabbableGroups[Q];M=se(f)>=0?q.firstTabbableNode:q.firstDomTabbableNode}else ge(p)||(M=P.nextTabbableNode(f))}}else M=h("fallbackFocus");return M},S=function(c){var f=Ae(c);if(!(l(f,c)>=0)){if(ye(a.clickOutsideDeactivates,c)){s.deactivate({returnFocus:a.returnFocusOnDeactivate});return}ye(a.allowOutsideClick,c)||c.preventDefault()}},T=function(c){var f=Ae(c),p=l(f,c)>=0;if(p||f instanceof Document)p&&(i.mostRecentlyFocusedNode=f);else{c.stopImmediatePropagation();var C,I=!0;if(i.mostRecentlyFocusedNode)if(se(i.mostRecentlyFocusedNode)>0){var M=l(i.mostRecentlyFocusedNode),z=i.containerGroups[M].tabbableNodes;if(z.length>0){var P=z.findIndex(function(m){return m===i.mostRecentlyFocusedNode});P>=0&&(a.isKeyForward(i.recentNavEvent)?P+1=0&&(C=z[P-1],I=!1))}}else i.containerGroups.some(function(m){return m.tabbableNodes.some(function(x){return se(x)>0})})||(I=!1);else I=!1;I&&(C=g({target:i.mostRecentlyFocusedNode,isBackward:a.isKeyBackward(i.recentNavEvent)})),b(C||i.mostRecentlyFocusedNode||d())}i.recentNavEvent=void 0},F=function(c){var f=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!1;i.recentNavEvent=c;var p=g({event:c,isBackward:f});p&&(ge(c)&&c.preventDefault(),b(p))},L=function(c){if(Tr(c)&&ye(a.escapeDeactivates,c)!==!1){c.preventDefault(),s.deactivate();return}(a.isKeyForward(c)||a.isKeyBackward(c))&&F(c,a.isKeyBackward(c))},_=function(c){var f=Ae(c);l(f,c)>=0||ye(a.clickOutsideDeactivates,c)||ye(a.allowOutsideClick,c)||(c.preventDefault(),c.stopImmediatePropagation())},V=function(){if(i.active)return lt.activateTrap(n,s),i.delayInitialFocusTimer=a.delayInitialFocus?ct(function(){b(d())}):b(d()),r.addEventListener("focusin",T,!0),r.addEventListener("mousedown",S,{capture:!0,passive:!1}),r.addEventListener("touchstart",S,{capture:!0,passive:!1}),r.addEventListener("click",_,{capture:!0,passive:!1}),r.addEventListener("keydown",L,{capture:!0,passive:!1}),s},N=function(){if(i.active)return r.removeEventListener("focusin",T,!0),r.removeEventListener("mousedown",S,!0),r.removeEventListener("touchstart",S,!0),r.removeEventListener("click",_,!0),r.removeEventListener("keydown",L,!0),s},R=function(c){var f=c.some(function(p){var C=Array.from(p.removedNodes);return C.some(function(I){return I===i.mostRecentlyFocusedNode})});f&&b(d())},A=typeof window<"u"&&"MutationObserver"in window?new MutationObserver(R):void 0,O=function(){A&&(A.disconnect(),i.active&&!i.paused&&i.containers.map(function(c){A.observe(c,{subtree:!0,childList:!0})}))};return s={get active(){return i.active},get paused(){return i.paused},activate:function(c){if(i.active)return this;var f=u(c,"onActivate"),p=u(c,"onPostActivate"),C=u(c,"checkCanFocusTrap");C||v(),i.active=!0,i.paused=!1,i.nodeFocusedBeforeActivation=r.activeElement,f==null||f();var I=function(){C&&v(),V(),O(),p==null||p()};return C?(C(i.containers.concat()).then(I,I),this):(I(),this)},deactivate:function(c){if(!i.active)return this;var f=ut({onDeactivate:a.onDeactivate,onPostDeactivate:a.onPostDeactivate,checkCanReturnFocus:a.checkCanReturnFocus},c);clearTimeout(i.delayInitialFocusTimer),i.delayInitialFocusTimer=void 0,N(),i.active=!1,i.paused=!1,O(),lt.deactivateTrap(n,s);var p=u(f,"onDeactivate"),C=u(f,"onPostDeactivate"),I=u(f,"checkCanReturnFocus"),M=u(f,"returnFocus","returnFocusOnDeactivate");p==null||p();var z=function(){ct(function(){M&&b(E(i.nodeFocusedBeforeActivation)),C==null||C()})};return M&&I?(I(E(i.nodeFocusedBeforeActivation)).then(z,z),this):(z(),this)},pause:function(c){if(i.paused||!i.active)return this;var f=u(c,"onPause"),p=u(c,"onPostPause");return i.paused=!0,f==null||f(),N(),O(),p==null||p(),this},unpause:function(c){if(!i.paused||!i.active)return this;var f=u(c,"onUnpause"),p=u(c,"onPostUnpause");return i.paused=!1,f==null||f(),v(),V(),O(),p==null||p(),this},updateContainerElements:function(c){var f=[].concat(c).filter(Boolean);return i.containers=f.map(function(p){return typeof p=="string"?r.querySelector(p):p}),i.active&&v(),O(),this}},s.updateContainerElements(e),s};function kr(o,e={}){let t;const{immediate:r,...n}=e,a=oe(!1),i=oe(!1),s=d=>t&&t.activate(d),u=d=>t&&t.deactivate(d),l=()=>{t&&(t.pause(),i.value=!0)},h=()=>{t&&(t.unpause(),i.value=!1)};return $e(()=>kt(o),d=>{d&&(t=Dr(d,{...n,onActivate(){a.value=!0,e.onActivate&&e.onActivate()},onDeactivate(){a.value=!1,e.onDeactivate&&e.onDeactivate()}}),r&&s())},{flush:"post"}),Ot(()=>u()),{hasFocus:a,isPaused:i,activate:s,deactivate:u,pause:l,unpause:h}}class fe{constructor(e,t=!0,r=[],n=5e3){this.ctx=e,this.iframes=t,this.exclude=r,this.iframesTimeout=n}static matches(e,t){const r=typeof t=="string"?[t]:t,n=e.matches||e.matchesSelector||e.msMatchesSelector||e.mozMatchesSelector||e.oMatchesSelector||e.webkitMatchesSelector;if(n){let a=!1;return r.every(i=>n.call(e,i)?(a=!0,!1):!0),a}else return!1}getContexts(){let e,t=[];return typeof this.ctx>"u"||!this.ctx?e=[]:NodeList.prototype.isPrototypeOf(this.ctx)?e=Array.prototype.slice.call(this.ctx):Array.isArray(this.ctx)?e=this.ctx:typeof this.ctx=="string"?e=Array.prototype.slice.call(document.querySelectorAll(this.ctx)):e=[this.ctx],e.forEach(r=>{const n=t.filter(a=>a.contains(r)).length>0;t.indexOf(r)===-1&&!n&&t.push(r)}),t}getIframeContents(e,t,r=()=>{}){let n;try{const a=e.contentWindow;if(n=a.document,!a||!n)throw new Error("iframe inaccessible")}catch{r()}n&&t(n)}isIframeBlank(e){const t="about:blank",r=e.getAttribute("src").trim();return e.contentWindow.location.href===t&&r!==t&&r}observeIframeLoad(e,t,r){let n=!1,a=null;const i=()=>{if(!n){n=!0,clearTimeout(a);try{this.isIframeBlank(e)||(e.removeEventListener("load",i),this.getIframeContents(e,t,r))}catch{r()}}};e.addEventListener("load",i),a=setTimeout(i,this.iframesTimeout)}onIframeReady(e,t,r){try{e.contentWindow.document.readyState==="complete"?this.isIframeBlank(e)?this.observeIframeLoad(e,t,r):this.getIframeContents(e,t,r):this.observeIframeLoad(e,t,r)}catch{r()}}waitForIframes(e,t){let r=0;this.forEachIframe(e,()=>!0,n=>{r++,this.waitForIframes(n.querySelector("html"),()=>{--r||t()})},n=>{n||t()})}forEachIframe(e,t,r,n=()=>{}){let a=e.querySelectorAll("iframe"),i=a.length,s=0;a=Array.prototype.slice.call(a);const u=()=>{--i<=0&&n(s)};i||u(),a.forEach(l=>{fe.matches(l,this.exclude)?u():this.onIframeReady(l,h=>{t(l)&&(s++,r(h)),u()},u)})}createIterator(e,t,r){return document.createNodeIterator(e,t,r,!1)}createInstanceOnIframe(e){return new fe(e.querySelector("html"),this.iframes)}compareNodeIframe(e,t,r){const n=e.compareDocumentPosition(r),a=Node.DOCUMENT_POSITION_PRECEDING;if(n&a)if(t!==null){const i=t.compareDocumentPosition(r),s=Node.DOCUMENT_POSITION_FOLLOWING;if(i&s)return!0}else return!0;return!1}getIteratorNode(e){const t=e.previousNode();let r;return t===null?r=e.nextNode():r=e.nextNode()&&e.nextNode(),{prevNode:t,node:r}}checkIframeFilter(e,t,r,n){let a=!1,i=!1;return n.forEach((s,u)=>{s.val===r&&(a=u,i=s.handled)}),this.compareNodeIframe(e,t,r)?(a===!1&&!i?n.push({val:r,handled:!0}):a!==!1&&!i&&(n[a].handled=!0),!0):(a===!1&&n.push({val:r,handled:!1}),!1)}handleOpenIframes(e,t,r,n){e.forEach(a=>{a.handled||this.getIframeContents(a.val,i=>{this.createInstanceOnIframe(i).forEachNode(t,r,n)})})}iterateThroughNodes(e,t,r,n,a){const i=this.createIterator(t,e,n);let s=[],u=[],l,h,d=()=>({prevNode:h,node:l}=this.getIteratorNode(i),l);for(;d();)this.iframes&&this.forEachIframe(t,v=>this.checkIframeFilter(l,h,v,s),v=>{this.createInstanceOnIframe(v).forEachNode(e,y=>u.push(y),n)}),u.push(l);u.forEach(v=>{r(v)}),this.iframes&&this.handleOpenIframes(s,e,r,n),a()}forEachNode(e,t,r,n=()=>{}){const a=this.getContexts();let i=a.length;i||n(),a.forEach(s=>{const u=()=>{this.iterateThroughNodes(e,s,t,r,()=>{--i<=0&&n()})};this.iframes?this.waitForIframes(s,u):u()})}}let Or=class{constructor(e){this.ctx=e,this.ie=!1;const t=window.navigator.userAgent;(t.indexOf("MSIE")>-1||t.indexOf("Trident")>-1)&&(this.ie=!0)}set opt(e){this._opt=Object.assign({},{element:"",className:"",exclude:[],iframes:!1,iframesTimeout:5e3,separateWordSearch:!0,diacritics:!0,synonyms:{},accuracy:"partially",acrossElements:!1,caseSensitive:!1,ignoreJoiners:!1,ignoreGroups:0,ignorePunctuation:[],wildcards:"disabled",each:()=>{},noMatch:()=>{},filter:()=>!0,done:()=>{},debug:!1,log:window.console},e)}get opt(){return this._opt}get iterator(){return new fe(this.ctx,this.opt.iframes,this.opt.exclude,this.opt.iframesTimeout)}log(e,t="debug"){const r=this.opt.log;this.opt.debug&&typeof r=="object"&&typeof r[t]=="function"&&r[t](`mark.js: ${e}`)}escapeStr(e){return e.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")}createRegExp(e){return this.opt.wildcards!=="disabled"&&(e=this.setupWildcardsRegExp(e)),e=this.escapeStr(e),Object.keys(this.opt.synonyms).length&&(e=this.createSynonymsRegExp(e)),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),this.opt.diacritics&&(e=this.createDiacriticsRegExp(e)),e=this.createMergedBlanksRegExp(e),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.createJoinersRegExp(e)),this.opt.wildcards!=="disabled"&&(e=this.createWildcardsRegExp(e)),e=this.createAccuracyRegExp(e),e}createSynonymsRegExp(e){const t=this.opt.synonyms,r=this.opt.caseSensitive?"":"i",n=this.opt.ignoreJoiners||this.opt.ignorePunctuation.length?"\0":"";for(let a in t)if(t.hasOwnProperty(a)){const i=t[a],s=this.opt.wildcards!=="disabled"?this.setupWildcardsRegExp(a):this.escapeStr(a),u=this.opt.wildcards!=="disabled"?this.setupWildcardsRegExp(i):this.escapeStr(i);s!==""&&u!==""&&(e=e.replace(new RegExp(`(${this.escapeStr(s)}|${this.escapeStr(u)})`,`gm${r}`),n+`(${this.processSynomyms(s)}|${this.processSynomyms(u)})`+n))}return e}processSynomyms(e){return(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),e}setupWildcardsRegExp(e){return e=e.replace(/(?:\\)*\?/g,t=>t.charAt(0)==="\\"?"?":""),e.replace(/(?:\\)*\*/g,t=>t.charAt(0)==="\\"?"*":"")}createWildcardsRegExp(e){let t=this.opt.wildcards==="withSpaces";return e.replace(/\u0001/g,t?"[\\S\\s]?":"\\S?").replace(/\u0002/g,t?"[\\S\\s]*?":"\\S*")}setupIgnoreJoinersRegExp(e){return e.replace(/[^(|)\\]/g,(t,r,n)=>{let a=n.charAt(r+1);return/[(|)\\]/.test(a)||a===""?t:t+"\0"})}createJoinersRegExp(e){let t=[];const r=this.opt.ignorePunctuation;return Array.isArray(r)&&r.length&&t.push(this.escapeStr(r.join(""))),this.opt.ignoreJoiners&&t.push("\\u00ad\\u200b\\u200c\\u200d"),t.length?e.split(/\u0000+/).join(`[${t.join("")}]*`):e}createDiacriticsRegExp(e){const t=this.opt.caseSensitive?"":"i",r=this.opt.caseSensitive?["aàáảãạăằắẳẵặâầấẩẫậäåāą","AÀÁẢÃẠĂẰẮẲẴẶÂẦẤẨẪẬÄÅĀĄ","cçćč","CÇĆČ","dđď","DĐĎ","eèéẻẽẹêềếểễệëěēę","EÈÉẺẼẸÊỀẾỂỄỆËĚĒĘ","iìíỉĩịîïī","IÌÍỈĨỊÎÏĪ","lł","LŁ","nñňń","NÑŇŃ","oòóỏõọôồốổỗộơởỡớờợöøō","OÒÓỎÕỌÔỒỐỔỖỘƠỞỠỚỜỢÖØŌ","rř","RŘ","sšśșş","SŠŚȘŞ","tťțţ","TŤȚŢ","uùúủũụưừứửữựûüůū","UÙÚỦŨỤƯỪỨỬỮỰÛÜŮŪ","yýỳỷỹỵÿ","YÝỲỶỸỴŸ","zžżź","ZŽŻŹ"]:["aàáảãạăằắẳẵặâầấẩẫậäåāąAÀÁẢÃẠĂẰẮẲẴẶÂẦẤẨẪẬÄÅĀĄ","cçćčCÇĆČ","dđďDĐĎ","eèéẻẽẹêềếểễệëěēęEÈÉẺẼẸÊỀẾỂỄỆËĚĒĘ","iìíỉĩịîïīIÌÍỈĨỊÎÏĪ","lłLŁ","nñňńNÑŇŃ","oòóỏõọôồốổỗộơởỡớờợöøōOÒÓỎÕỌÔỒỐỔỖỘƠỞỠỚỜỢÖØŌ","rřRŘ","sšśșşSŠŚȘŞ","tťțţTŤȚŢ","uùúủũụưừứửữựûüůūUÙÚỦŨỤƯỪỨỬỮỰÛÜŮŪ","yýỳỷỹỵÿYÝỲỶỸỴŸ","zžżźZŽŻŹ"];let n=[];return e.split("").forEach(a=>{r.every(i=>{if(i.indexOf(a)!==-1){if(n.indexOf(i)>-1)return!1;e=e.replace(new RegExp(`[${i}]`,`gm${t}`),`[${i}]`),n.push(i)}return!0})}),e}createMergedBlanksRegExp(e){return e.replace(/[\s]+/gmi,"[\\s]+")}createAccuracyRegExp(e){const t="!\"#$%&'()*+,-./:;<=>?@[\\]^_`{|}~¡¿";let r=this.opt.accuracy,n=typeof r=="string"?r:r.value,a=typeof r=="string"?[]:r.limiters,i="";switch(a.forEach(s=>{i+=`|${this.escapeStr(s)}`}),n){case"partially":default:return`()(${e})`;case"complementary":return i="\\s"+(i||this.escapeStr(t)),`()([^${i}]*${e}[^${i}]*)`;case"exactly":return`(^|\\s${i})(${e})(?=$|\\s${i})`}}getSeparatedKeywords(e){let t=[];return e.forEach(r=>{this.opt.separateWordSearch?r.split(" ").forEach(n=>{n.trim()&&t.indexOf(n)===-1&&t.push(n)}):r.trim()&&t.indexOf(r)===-1&&t.push(r)}),{keywords:t.sort((r,n)=>n.length-r.length),length:t.length}}isNumeric(e){return Number(parseFloat(e))==e}checkRanges(e){if(!Array.isArray(e)||Object.prototype.toString.call(e[0])!=="[object Object]")return this.log("markRanges() will only accept an array of objects"),this.opt.noMatch(e),[];const t=[];let r=0;return e.sort((n,a)=>n.start-a.start).forEach(n=>{let{start:a,end:i,valid:s}=this.callNoMatchOnInvalidRanges(n,r);s&&(n.start=a,n.length=i-a,t.push(n),r=i)}),t}callNoMatchOnInvalidRanges(e,t){let r,n,a=!1;return e&&typeof e.start<"u"?(r=parseInt(e.start,10),n=r+parseInt(e.length,10),this.isNumeric(e.start)&&this.isNumeric(e.length)&&n-t>0&&n-r>0?a=!0:(this.log(`Ignoring invalid or overlapping range: ${JSON.stringify(e)}`),this.opt.noMatch(e))):(this.log(`Ignoring invalid range: ${JSON.stringify(e)}`),this.opt.noMatch(e)),{start:r,end:n,valid:a}}checkWhitespaceRanges(e,t,r){let n,a=!0,i=r.length,s=t-i,u=parseInt(e.start,10)-s;return u=u>i?i:u,n=u+parseInt(e.length,10),n>i&&(n=i,this.log(`End range automatically set to the max value of ${i}`)),u<0||n-u<0||u>i||n>i?(a=!1,this.log(`Invalid range: ${JSON.stringify(e)}`),this.opt.noMatch(e)):r.substring(u,n).replace(/\s+/g,"")===""&&(a=!1,this.log("Skipping whitespace only range: "+JSON.stringify(e)),this.opt.noMatch(e)),{start:u,end:n,valid:a}}getTextNodes(e){let t="",r=[];this.iterator.forEachNode(NodeFilter.SHOW_TEXT,n=>{r.push({start:t.length,end:(t+=n.textContent).length,node:n})},n=>this.matchesExclude(n.parentNode)?NodeFilter.FILTER_REJECT:NodeFilter.FILTER_ACCEPT,()=>{e({value:t,nodes:r})})}matchesExclude(e){return fe.matches(e,this.opt.exclude.concat(["script","style","title","head","html"]))}wrapRangeInTextNode(e,t,r){const n=this.opt.element?this.opt.element:"mark",a=e.splitText(t),i=a.splitText(r-t);let s=document.createElement(n);return s.setAttribute("data-markjs","true"),this.opt.className&&s.setAttribute("class",this.opt.className),s.textContent=a.textContent,a.parentNode.replaceChild(s,a),i}wrapRangeInMappedTextNode(e,t,r,n,a){e.nodes.every((i,s)=>{const u=e.nodes[s+1];if(typeof u>"u"||u.start>t){if(!n(i.node))return!1;const l=t-i.start,h=(r>i.end?i.end:r)-i.start,d=e.value.substr(0,i.start),v=e.value.substr(h+i.start);if(i.node=this.wrapRangeInTextNode(i.node,l,h),e.value=d+v,e.nodes.forEach((y,b)=>{b>=s&&(e.nodes[b].start>0&&b!==s&&(e.nodes[b].start-=h),e.nodes[b].end-=h)}),r-=h,a(i.node.previousSibling,i.start),r>i.end)t=i.end;else return!1}return!0})}wrapMatches(e,t,r,n,a){const i=t===0?0:t+1;this.getTextNodes(s=>{s.nodes.forEach(u=>{u=u.node;let l;for(;(l=e.exec(u.textContent))!==null&&l[i]!=="";){if(!r(l[i],u))continue;let h=l.index;if(i!==0)for(let d=1;d{let u;for(;(u=e.exec(s.value))!==null&&u[i]!=="";){let l=u.index;if(i!==0)for(let d=1;dr(u[i],d),(d,v)=>{e.lastIndex=v,n(d)})}a()})}wrapRangeFromIndex(e,t,r,n){this.getTextNodes(a=>{const i=a.value.length;e.forEach((s,u)=>{let{start:l,end:h,valid:d}=this.checkWhitespaceRanges(s,i,a.value);d&&this.wrapRangeInMappedTextNode(a,l,h,v=>t(v,s,a.value.substring(l,h),u),v=>{r(v,s)})}),n()})}unwrapMatches(e){const t=e.parentNode;let r=document.createDocumentFragment();for(;e.firstChild;)r.appendChild(e.removeChild(e.firstChild));t.replaceChild(r,e),this.ie?this.normalizeTextNode(t):t.normalize()}normalizeTextNode(e){if(e){if(e.nodeType===3)for(;e.nextSibling&&e.nextSibling.nodeType===3;)e.nodeValue+=e.nextSibling.nodeValue,e.parentNode.removeChild(e.nextSibling);else this.normalizeTextNode(e.firstChild);this.normalizeTextNode(e.nextSibling)}}markRegExp(e,t){this.opt=t,this.log(`Searching with expression "${e}"`);let r=0,n="wrapMatches";const a=i=>{r++,this.opt.each(i)};this.opt.acrossElements&&(n="wrapMatchesAcrossElements"),this[n](e,this.opt.ignoreGroups,(i,s)=>this.opt.filter(s,i,r),a,()=>{r===0&&this.opt.noMatch(e),this.opt.done(r)})}mark(e,t){this.opt=t;let r=0,n="wrapMatches";const{keywords:a,length:i}=this.getSeparatedKeywords(typeof e=="string"?[e]:e),s=this.opt.caseSensitive?"":"i",u=l=>{let h=new RegExp(this.createRegExp(l),`gm${s}`),d=0;this.log(`Searching with expression "${h}"`),this[n](h,1,(v,y)=>this.opt.filter(y,l,r,d),v=>{d++,r++,this.opt.each(v)},()=>{d===0&&this.opt.noMatch(l),a[i-1]===l?this.opt.done(r):u(a[a.indexOf(l)+1])})};this.opt.acrossElements&&(n="wrapMatchesAcrossElements"),i===0?this.opt.done(r):u(a[0])}markRanges(e,t){this.opt=t;let r=0,n=this.checkRanges(e);n&&n.length?(this.log("Starting to mark with the following ranges: "+JSON.stringify(n)),this.wrapRangeFromIndex(n,(a,i,s,u)=>this.opt.filter(a,i,s,u),(a,i)=>{r++,this.opt.each(a,i)},()=>{this.opt.done(r)})):this.opt.done(r)}unmark(e){this.opt=e;let t=this.opt.element?this.opt.element:"*";t+="[data-markjs]",this.opt.className&&(t+=`.${this.opt.className}`),this.log(`Removal selector "${t}"`),this.iterator.forEachNode(NodeFilter.SHOW_ELEMENT,r=>{this.unwrapMatches(r)},r=>{const n=fe.matches(r,t),a=this.matchesExclude(r);return!n||a?NodeFilter.FILTER_REJECT:NodeFilter.FILTER_ACCEPT},this.opt.done)}};function Rr(o){const e=new Or(o);return this.mark=(t,r)=>(e.mark(t,r),this),this.markRegExp=(t,r)=>(e.markRegExp(t,r),this),this.markRanges=(t,r)=>(e.markRanges(t,r),this),this.unmark=t=>(e.unmark(t),this),this}var W=function(){return W=Object.assign||function(e){for(var t,r=1,n=arguments.length;r0&&a[a.length-1])&&(l[0]===6||l[0]===2)){t=0;continue}if(l[0]===3&&(!a||l[1]>a[0]&&l[1]=o.length&&(o=void 0),{value:o&&o[r++],done:!o}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")}function J(o,e){var t=typeof Symbol=="function"&&o[Symbol.iterator];if(!t)return o;var r=t.call(o),n,a=[],i;try{for(;(e===void 0||e-- >0)&&!(n=r.next()).done;)a.push(n.value)}catch(s){i={error:s}}finally{try{n&&!n.done&&(t=r.return)&&t.call(r)}finally{if(i)throw i.error}}return a}var Lr="ENTRIES",Ft="KEYS",Et="VALUES",G="",Me=function(){function o(e,t){var r=e._tree,n=Array.from(r.keys());this.set=e,this._type=t,this._path=n.length>0?[{node:r,keys:n}]:[]}return o.prototype.next=function(){var e=this.dive();return this.backtrack(),e},o.prototype.dive=function(){if(this._path.length===0)return{done:!0,value:void 0};var e=ce(this._path),t=e.node,r=e.keys;if(ce(r)===G)return{done:!1,value:this.result()};var n=t.get(ce(r));return this._path.push({node:n,keys:Array.from(n.keys())}),this.dive()},o.prototype.backtrack=function(){if(this._path.length!==0){var e=ce(this._path).keys;e.pop(),!(e.length>0)&&(this._path.pop(),this.backtrack())}},o.prototype.key=function(){return this.set._prefix+this._path.map(function(e){var t=e.keys;return ce(t)}).filter(function(e){return e!==G}).join("")},o.prototype.value=function(){return ce(this._path).node.get(G)},o.prototype.result=function(){switch(this._type){case Et:return this.value();case Ft:return this.key();default:return[this.key(),this.value()]}},o.prototype[Symbol.iterator]=function(){return this},o}(),ce=function(o){return o[o.length-1]},zr=function(o,e,t){var r=new Map;if(e===void 0)return r;for(var n=e.length+1,a=n+t,i=new Uint8Array(a*n).fill(t+1),s=0;st)continue e}St(o.get(y),e,t,r,n,E,i,s+y)}}}catch(f){u={error:f}}finally{try{v&&!v.done&&(l=d.return)&&l.call(d)}finally{if(u)throw u.error}}},Le=function(){function o(e,t){e===void 0&&(e=new Map),t===void 0&&(t=""),this._size=void 0,this._tree=e,this._prefix=t}return o.prototype.atPrefix=function(e){var t,r;if(!e.startsWith(this._prefix))throw new Error("Mismatched prefix");var n=J(ke(this._tree,e.slice(this._prefix.length)),2),a=n[0],i=n[1];if(a===void 0){var s=J(je(i),2),u=s[0],l=s[1];try{for(var h=D(u.keys()),d=h.next();!d.done;d=h.next()){var v=d.value;if(v!==G&&v.startsWith(l)){var y=new Map;return y.set(v.slice(l.length),u.get(v)),new o(y,e)}}}catch(b){t={error:b}}finally{try{d&&!d.done&&(r=h.return)&&r.call(h)}finally{if(t)throw t.error}}}return new o(a,e)},o.prototype.clear=function(){this._size=void 0,this._tree.clear()},o.prototype.delete=function(e){return this._size=void 0,Pr(this._tree,e)},o.prototype.entries=function(){return new Me(this,Lr)},o.prototype.forEach=function(e){var t,r;try{for(var n=D(this),a=n.next();!a.done;a=n.next()){var i=J(a.value,2),s=i[0],u=i[1];e(s,u,this)}}catch(l){t={error:l}}finally{try{a&&!a.done&&(r=n.return)&&r.call(n)}finally{if(t)throw t.error}}},o.prototype.fuzzyGet=function(e,t){return zr(this._tree,e,t)},o.prototype.get=function(e){var t=Ke(this._tree,e);return t!==void 0?t.get(G):void 0},o.prototype.has=function(e){var t=Ke(this._tree,e);return t!==void 0&&t.has(G)},o.prototype.keys=function(){return new Me(this,Ft)},o.prototype.set=function(e,t){if(typeof e!="string")throw new Error("key must be a string");this._size=void 0;var r=ze(this._tree,e);return r.set(G,t),this},Object.defineProperty(o.prototype,"size",{get:function(){if(this._size)return this._size;this._size=0;for(var e=this.entries();!e.next().done;)this._size+=1;return this._size},enumerable:!1,configurable:!0}),o.prototype.update=function(e,t){if(typeof e!="string")throw new Error("key must be a string");this._size=void 0;var r=ze(this._tree,e);return r.set(G,t(r.get(G))),this},o.prototype.fetch=function(e,t){if(typeof e!="string")throw new Error("key must be a string");this._size=void 0;var r=ze(this._tree,e),n=r.get(G);return n===void 0&&r.set(G,n=t()),n},o.prototype.values=function(){return new Me(this,Et)},o.prototype[Symbol.iterator]=function(){return this.entries()},o.from=function(e){var t,r,n=new o;try{for(var a=D(e),i=a.next();!i.done;i=a.next()){var s=J(i.value,2),u=s[0],l=s[1];n.set(u,l)}}catch(h){t={error:h}}finally{try{i&&!i.done&&(r=a.return)&&r.call(a)}finally{if(t)throw t.error}}return n},o.fromObject=function(e){return o.from(Object.entries(e))},o}(),ke=function(o,e,t){var r,n;if(t===void 0&&(t=[]),e.length===0||o==null)return[o,t];try{for(var a=D(o.keys()),i=a.next();!i.done;i=a.next()){var s=i.value;if(s!==G&&e.startsWith(s))return t.push([o,s]),ke(o.get(s),e.slice(s.length),t)}}catch(u){r={error:u}}finally{try{i&&!i.done&&(n=a.return)&&n.call(a)}finally{if(r)throw r.error}}return t.push([o,e]),ke(void 0,"",t)},Ke=function(o,e){var t,r;if(e.length===0||o==null)return o;try{for(var n=D(o.keys()),a=n.next();!a.done;a=n.next()){var i=a.value;if(i!==G&&e.startsWith(i))return Ke(o.get(i),e.slice(i.length))}}catch(s){t={error:s}}finally{try{a&&!a.done&&(r=n.return)&&r.call(n)}finally{if(t)throw t.error}}},ze=function(o,e){var t,r,n=e.length;e:for(var a=0;o&&a0)throw new Error("Expected documents to be present. Omit the argument to remove all documents.");this._index=new Le,this._documentCount=0,this._documentIds=new Map,this._idToShortId=new Map,this._fieldLength=new Map,this._avgFieldLength=[],this._storedFields=new Map,this._nextId=0}},o.prototype.discard=function(e){var t=this,r=this._idToShortId.get(e);if(r==null)throw new Error("MiniSearch: cannot discard document with ID ".concat(e,": it is not in the index"));this._idToShortId.delete(e),this._documentIds.delete(r),this._storedFields.delete(r),(this._fieldLength.get(r)||[]).forEach(function(n,a){t.removeFieldLength(r,a,t._documentCount,n)}),this._fieldLength.delete(r),this._documentCount-=1,this._dirtCount+=1,this.maybeAutoVacuum()},o.prototype.maybeAutoVacuum=function(){if(this._options.autoVacuum!==!1){var e=this._options.autoVacuum,t=e.minDirtFactor,r=e.minDirtCount,n=e.batchSize,a=e.batchWait;this.conditionalVacuum({batchSize:n,batchWait:a},{minDirtCount:r,minDirtFactor:t})}},o.prototype.discardAll=function(e){var t,r,n=this._options.autoVacuum;try{this._options.autoVacuum=!1;try{for(var a=D(e),i=a.next();!i.done;i=a.next()){var s=i.value;this.discard(s)}}catch(u){t={error:u}}finally{try{i&&!i.done&&(r=a.return)&&r.call(a)}finally{if(t)throw t.error}}}finally{this._options.autoVacuum=n}this.maybeAutoVacuum()},o.prototype.replace=function(e){var t=this._options,r=t.idField,n=t.extractField,a=n(e,r);this.discard(a),this.add(e)},o.prototype.vacuum=function(e){return e===void 0&&(e={}),this.conditionalVacuum(e)},o.prototype.conditionalVacuum=function(e,t){var r=this;return this._currentVacuum?(this._enqueuedVacuumConditions=this._enqueuedVacuumConditions&&t,this._enqueuedVacuum!=null?this._enqueuedVacuum:(this._enqueuedVacuum=this._currentVacuum.then(function(){var n=r._enqueuedVacuumConditions;return r._enqueuedVacuumConditions=Ue,r.performVacuuming(e,n)}),this._enqueuedVacuum)):this.vacuumConditionsMet(t)===!1?Promise.resolve():(this._currentVacuum=this.performVacuuming(e),this._currentVacuum)},o.prototype.performVacuuming=function(e,t){return _r(this,void 0,void 0,function(){var r,n,a,i,s,u,l,h,d,v,y,b,E,g,S,T,F,L,_,V,N,R,A,O,w;return Mr(this,function(c){switch(c.label){case 0:if(r=this._dirtCount,!this.vacuumConditionsMet(t))return[3,10];n=e.batchSize||Je.batchSize,a=e.batchWait||Je.batchWait,i=1,c.label=1;case 1:c.trys.push([1,7,8,9]),s=D(this._index),u=s.next(),c.label=2;case 2:if(u.done)return[3,6];l=J(u.value,2),h=l[0],d=l[1];try{for(v=(R=void 0,D(d)),y=v.next();!y.done;y=v.next()){b=J(y.value,2),E=b[0],g=b[1];try{for(S=(O=void 0,D(g)),T=S.next();!T.done;T=S.next())F=J(T.value,1),L=F[0],!this._documentIds.has(L)&&(g.size<=1?d.delete(E):g.delete(L))}catch(f){O={error:f}}finally{try{T&&!T.done&&(w=S.return)&&w.call(S)}finally{if(O)throw O.error}}}}catch(f){R={error:f}}finally{try{y&&!y.done&&(A=v.return)&&A.call(v)}finally{if(R)throw R.error}}return this._index.get(h).size===0&&this._index.delete(h),i%n!==0?[3,4]:[4,new Promise(function(f){return setTimeout(f,a)})];case 3:c.sent(),c.label=4;case 4:i+=1,c.label=5;case 5:return u=s.next(),[3,2];case 6:return[3,9];case 7:return _=c.sent(),V={error:_},[3,9];case 8:try{u&&!u.done&&(N=s.return)&&N.call(s)}finally{if(V)throw V.error}return[7];case 9:this._dirtCount-=r,c.label=10;case 10:return[4,null];case 11:return c.sent(),this._currentVacuum=this._enqueuedVacuum,this._enqueuedVacuum=null,[2]}})})},o.prototype.vacuumConditionsMet=function(e){if(e==null)return!0;var t=e.minDirtCount,r=e.minDirtFactor;return t=t||Ve.minDirtCount,r=r||Ve.minDirtFactor,this.dirtCount>=t&&this.dirtFactor>=r},Object.defineProperty(o.prototype,"isVacuuming",{get:function(){return this._currentVacuum!=null},enumerable:!1,configurable:!0}),Object.defineProperty(o.prototype,"dirtCount",{get:function(){return this._dirtCount},enumerable:!1,configurable:!0}),Object.defineProperty(o.prototype,"dirtFactor",{get:function(){return this._dirtCount/(1+this._documentCount+this._dirtCount)},enumerable:!1,configurable:!0}),o.prototype.has=function(e){return this._idToShortId.has(e)},o.prototype.getStoredFields=function(e){var t=this._idToShortId.get(e);if(t!=null)return this._storedFields.get(t)},o.prototype.search=function(e,t){var r,n;t===void 0&&(t={});var a=this.executeQuery(e,t),i=[];try{for(var s=D(a),u=s.next();!u.done;u=s.next()){var l=J(u.value,2),h=l[0],d=l[1],v=d.score,y=d.terms,b=d.match,E=y.length||1,g={id:this._documentIds.get(h),score:v*E,terms:Object.keys(b),queryTerms:y,match:b};Object.assign(g,this._storedFields.get(h)),(t.filter==null||t.filter(g))&&i.push(g)}}catch(S){r={error:S}}finally{try{u&&!u.done&&(n=s.return)&&n.call(s)}finally{if(r)throw r.error}}return e===o.wildcard&&t.boostDocument==null&&this._options.searchOptions.boostDocument==null||i.sort(vt),i},o.prototype.autoSuggest=function(e,t){var r,n,a,i;t===void 0&&(t={}),t=W(W({},this._options.autoSuggestOptions),t);var s=new Map;try{for(var u=D(this.search(e,t)),l=u.next();!l.done;l=u.next()){var h=l.value,d=h.score,v=h.terms,y=v.join(" "),b=s.get(y);b!=null?(b.score+=d,b.count+=1):s.set(y,{score:d,terms:v,count:1})}}catch(_){r={error:_}}finally{try{l&&!l.done&&(n=u.return)&&n.call(u)}finally{if(r)throw r.error}}var E=[];try{for(var g=D(s),S=g.next();!S.done;S=g.next()){var T=J(S.value,2),b=T[0],F=T[1],d=F.score,v=F.terms,L=F.count;E.push({suggestion:b,terms:v,score:d/L})}}catch(_){a={error:_}}finally{try{S&&!S.done&&(i=g.return)&&i.call(g)}finally{if(a)throw a.error}}return E.sort(vt),E},Object.defineProperty(o.prototype,"documentCount",{get:function(){return this._documentCount},enumerable:!1,configurable:!0}),Object.defineProperty(o.prototype,"termCount",{get:function(){return this._index.size},enumerable:!1,configurable:!0}),o.loadJSON=function(e,t){if(t==null)throw new Error("MiniSearch: loadJSON should be given the same options used when serializing the index");return this.loadJS(JSON.parse(e),t)},o.getDefault=function(e){if(Be.hasOwnProperty(e))return Pe(Be,e);throw new Error('MiniSearch: unknown option "'.concat(e,'"'))},o.loadJS=function(e,t){var r,n,a,i,s,u,l=e.index,h=e.documentCount,d=e.nextId,v=e.documentIds,y=e.fieldIds,b=e.fieldLength,E=e.averageFieldLength,g=e.storedFields,S=e.dirtCount,T=e.serializationVersion;if(T!==1&&T!==2)throw new Error("MiniSearch: cannot deserialize an index created with an incompatible version");var F=new o(t);F._documentCount=h,F._nextId=d,F._documentIds=Te(v),F._idToShortId=new Map,F._fieldIds=y,F._fieldLength=Te(b),F._avgFieldLength=E,F._storedFields=Te(g),F._dirtCount=S||0,F._index=new Le;try{for(var L=D(F._documentIds),_=L.next();!_.done;_=L.next()){var V=J(_.value,2),N=V[0],R=V[1];F._idToShortId.set(R,N)}}catch(P){r={error:P}}finally{try{_&&!_.done&&(n=L.return)&&n.call(L)}finally{if(r)throw r.error}}try{for(var A=D(l),O=A.next();!O.done;O=A.next()){var w=J(O.value,2),c=w[0],f=w[1],p=new Map;try{for(var C=(s=void 0,D(Object.keys(f))),I=C.next();!I.done;I=C.next()){var M=I.value,z=f[M];T===1&&(z=z.ds),p.set(parseInt(M,10),Te(z))}}catch(P){s={error:P}}finally{try{I&&!I.done&&(u=C.return)&&u.call(C)}finally{if(s)throw s.error}}F._index.set(c,p)}}catch(P){a={error:P}}finally{try{O&&!O.done&&(i=A.return)&&i.call(A)}finally{if(a)throw a.error}}return F},o.prototype.executeQuery=function(e,t){var r=this;if(t===void 0&&(t={}),e===o.wildcard)return this.executeWildcardQuery(t);if(typeof e!="string"){var n=W(W(W({},t),e),{queries:void 0}),a=e.queries.map(function(g){return r.executeQuery(g,n)});return this.combineResults(a,n.combineWith)}var i=this._options,s=i.tokenize,u=i.processTerm,l=i.searchOptions,h=W(W({tokenize:s,processTerm:u},l),t),d=h.tokenize,v=h.processTerm,y=d(e).flatMap(function(g){return v(g)}).filter(function(g){return!!g}),b=y.map(Jr(h)),E=b.map(function(g){return r.executeQuerySpec(g,h)});return this.combineResults(E,h.combineWith)},o.prototype.executeQuerySpec=function(e,t){var r,n,a,i,s=W(W({},this._options.searchOptions),t),u=(s.fields||this._options.fields).reduce(function(M,z){var P;return W(W({},M),(P={},P[z]=Pe(s.boost,z)||1,P))},{}),l=s.boostDocument,h=s.weights,d=s.maxFuzzy,v=s.bm25,y=W(W({},ht.weights),h),b=y.fuzzy,E=y.prefix,g=this._index.get(e.term),S=this.termResults(e.term,e.term,1,g,u,l,v),T,F;if(e.prefix&&(T=this._index.atPrefix(e.term)),e.fuzzy){var L=e.fuzzy===!0?.2:e.fuzzy,_=L<1?Math.min(d,Math.round(e.term.length*L)):L;_&&(F=this._index.fuzzyGet(e.term,_))}if(T)try{for(var V=D(T),N=V.next();!N.done;N=V.next()){var R=J(N.value,2),A=R[0],O=R[1],w=A.length-e.term.length;if(w){F==null||F.delete(A);var c=E*A.length/(A.length+.3*w);this.termResults(e.term,A,c,O,u,l,v,S)}}}catch(M){r={error:M}}finally{try{N&&!N.done&&(n=V.return)&&n.call(V)}finally{if(r)throw r.error}}if(F)try{for(var f=D(F.keys()),p=f.next();!p.done;p=f.next()){var A=p.value,C=J(F.get(A),2),I=C[0],w=C[1];if(w){var c=b*A.length/(A.length+w);this.termResults(e.term,A,c,I,u,l,v,S)}}}catch(M){a={error:M}}finally{try{p&&!p.done&&(i=f.return)&&i.call(f)}finally{if(a)throw a.error}}return S},o.prototype.executeWildcardQuery=function(e){var t,r,n=new Map,a=W(W({},this._options.searchOptions),e);try{for(var i=D(this._documentIds),s=i.next();!s.done;s=i.next()){var u=J(s.value,2),l=u[0],h=u[1],d=a.boostDocument?a.boostDocument(h,"",this._storedFields.get(l)):1;n.set(l,{score:d,terms:[],match:{}})}}catch(v){t={error:v}}finally{try{s&&!s.done&&(r=i.return)&&r.call(i)}finally{if(t)throw t.error}}return n},o.prototype.combineResults=function(e,t){if(t===void 0&&(t=Ge),e.length===0)return new Map;var r=t.toLowerCase();return e.reduce($r[r])||new Map},o.prototype.toJSON=function(){var e,t,r,n,a=[];try{for(var i=D(this._index),s=i.next();!s.done;s=i.next()){var u=J(s.value,2),l=u[0],h=u[1],d={};try{for(var v=(r=void 0,D(h)),y=v.next();!y.done;y=v.next()){var b=J(y.value,2),E=b[0],g=b[1];d[E]=Object.fromEntries(g)}}catch(S){r={error:S}}finally{try{y&&!y.done&&(n=v.return)&&n.call(v)}finally{if(r)throw r.error}}a.push([l,d])}}catch(S){e={error:S}}finally{try{s&&!s.done&&(t=i.return)&&t.call(i)}finally{if(e)throw e.error}}return{documentCount:this._documentCount,nextId:this._nextId,documentIds:Object.fromEntries(this._documentIds),fieldIds:this._fieldIds,fieldLength:Object.fromEntries(this._fieldLength),averageFieldLength:this._avgFieldLength,storedFields:Object.fromEntries(this._storedFields),dirtCount:this._dirtCount,index:a,serializationVersion:2}},o.prototype.termResults=function(e,t,r,n,a,i,s,u){var l,h,d,v,y;if(u===void 0&&(u=new Map),n==null)return u;try{for(var b=D(Object.keys(a)),E=b.next();!E.done;E=b.next()){var g=E.value,S=a[g],T=this._fieldIds[g],F=n.get(T);if(F!=null){var L=F.size,_=this._avgFieldLength[T];try{for(var V=(d=void 0,D(F.keys())),N=V.next();!N.done;N=V.next()){var R=N.value;if(!this._documentIds.has(R)){this.removeTerm(T,R,t),L-=1;continue}var A=i?i(this._documentIds.get(R),t,this._storedFields.get(R)):1;if(A){var O=F.get(R),w=this._fieldLength.get(R)[T],c=Kr(O,L,this._documentCount,w,_,s),f=r*S*A*c,p=u.get(R);if(p){p.score+=f,jr(p.terms,e);var C=Pe(p.match,t);C?C.push(g):p.match[t]=[g]}else u.set(R,{score:f,terms:[e],match:(y={},y[t]=[g],y)})}}}catch(I){d={error:I}}finally{try{N&&!N.done&&(v=V.return)&&v.call(V)}finally{if(d)throw d.error}}}}}catch(I){l={error:I}}finally{try{E&&!E.done&&(h=b.return)&&h.call(b)}finally{if(l)throw l.error}}return u},o.prototype.addTerm=function(e,t,r){var n=this._index.fetch(r,pt),a=n.get(e);if(a==null)a=new Map,a.set(t,1),n.set(e,a);else{var i=a.get(t);a.set(t,(i||0)+1)}},o.prototype.removeTerm=function(e,t,r){if(!this._index.has(r)){this.warnDocumentChanged(t,e,r);return}var n=this._index.fetch(r,pt),a=n.get(e);a==null||a.get(t)==null?this.warnDocumentChanged(t,e,r):a.get(t)<=1?a.size<=1?n.delete(e):a.delete(t):a.set(t,a.get(t)-1),this._index.get(r).size===0&&this._index.delete(r)},o.prototype.warnDocumentChanged=function(e,t,r){var n,a;try{for(var i=D(Object.keys(this._fieldIds)),s=i.next();!s.done;s=i.next()){var u=s.value;if(this._fieldIds[u]===t){this._options.logger("warn","MiniSearch: document with ID ".concat(this._documentIds.get(e),' has changed before removal: term "').concat(r,'" was not present in field "').concat(u,'". Removing a document after it has changed can corrupt the index!'),"version_conflict");return}}}catch(l){n={error:l}}finally{try{s&&!s.done&&(a=i.return)&&a.call(i)}finally{if(n)throw n.error}}},o.prototype.addDocumentId=function(e){var t=this._nextId;return this._idToShortId.set(e,t),this._documentIds.set(t,e),this._documentCount+=1,this._nextId+=1,t},o.prototype.addFields=function(e){for(var t=0;t(qt("data-v-f4c4f812"),o=o(),Ht(),o),qr=["aria-owns"],Hr={class:"shell"},Yr=["title"],Zr=Y(()=>k("span",{"aria-hidden":"true",class:"vpi-search search-icon local-search-icon"},null,-1)),Xr=[Zr],ea={class:"search-actions before"},ta=["title"],ra=Y(()=>k("span",{class:"vpi-arrow-left local-search-icon"},null,-1)),aa=[ra],na=["placeholder"],ia={class:"search-actions"},oa=["title"],sa=Y(()=>k("span",{class:"vpi-layout-list local-search-icon"},null,-1)),ua=[sa],la=["disabled","title"],ca=Y(()=>k("span",{class:"vpi-delete local-search-icon"},null,-1)),fa=[ca],ha=["id","role","aria-labelledby"],da=["aria-selected"],va=["href","aria-label","onMouseenter","onFocusin"],pa={class:"titles"},ya=Y(()=>k("span",{class:"title-icon"},"#",-1)),ma=["innerHTML"],ga=Y(()=>k("span",{class:"vpi-chevron-right local-search-icon"},null,-1)),ba={class:"title main"},wa=["innerHTML"],xa={key:0,class:"excerpt-wrapper"},Fa={key:0,class:"excerpt",inert:""},Ea=["innerHTML"],Sa=Y(()=>k("div",{class:"excerpt-gradient-bottom"},null,-1)),Aa=Y(()=>k("div",{class:"excerpt-gradient-top"},null,-1)),Ta={key:0,class:"no-results"},Na={class:"search-keyboard-shortcuts"},Ca=["aria-label"],Ia=Y(()=>k("span",{class:"vpi-arrow-up navigate-icon"},null,-1)),Da=[Ia],ka=["aria-label"],Oa=Y(()=>k("span",{class:"vpi-arrow-down navigate-icon"},null,-1)),Ra=[Oa],_a=["aria-label"],Ma=Y(()=>k("span",{class:"vpi-corner-down-left navigate-icon"},null,-1)),La=[Ma],za=["aria-label"],Pa=Rt({__name:"VPLocalSearchBox",emits:["close"],setup(o,{emit:e}){var z,P;const t=e,r=xe(),n=xe(),a=xe(nr),i=rr(),{activate:s}=kr(r,{immediate:!0,allowOutsideClick:!0,clickOutsideDeactivates:!0,escapeDeactivates:!0}),{localeIndex:u,theme:l}=i,h=tt(async()=>{var m,x,$,K,Q,q,B,U,Z;return it(Vr.loadJSON(($=await((x=(m=a.value)[u.value])==null?void 0:x.call(m)))==null?void 0:$.default,{fields:["title","titles","text"],storeFields:["title","titles"],searchOptions:{fuzzy:.2,prefix:!0,boost:{title:4,text:2,titles:1},...((K=l.value.search)==null?void 0:K.provider)==="local"&&((q=(Q=l.value.search.options)==null?void 0:Q.miniSearch)==null?void 0:q.searchOptions)},...((B=l.value.search)==null?void 0:B.provider)==="local"&&((Z=(U=l.value.search.options)==null?void 0:U.miniSearch)==null?void 0:Z.options)}))}),v=Fe(()=>{var m,x;return((m=l.value.search)==null?void 0:m.provider)==="local"&&((x=l.value.search.options)==null?void 0:x.disableQueryPersistence)===!0}).value?oe(""):_t("vitepress:local-search-filter",""),y=Mt("vitepress:local-search-detailed-list",((z=l.value.search)==null?void 0:z.provider)==="local"&&((P=l.value.search.options)==null?void 0:P.detailedView)===!0),b=Fe(()=>{var m,x,$;return((m=l.value.search)==null?void 0:m.provider)==="local"&&(((x=l.value.search.options)==null?void 0:x.disableDetailedView)===!0||(($=l.value.search.options)==null?void 0:$.detailedView)===!1)}),E=Fe(()=>{var x,$,K,Q,q,B,U;const m=((x=l.value.search)==null?void 0:x.options)??l.value.algolia;return((q=(Q=(K=($=m==null?void 0:m.locales)==null?void 0:$[u.value])==null?void 0:K.translations)==null?void 0:Q.button)==null?void 0:q.buttonText)||((U=(B=m==null?void 0:m.translations)==null?void 0:B.button)==null?void 0:U.buttonText)||"Search"});Lt(()=>{b.value&&(y.value=!1)});const g=xe([]),S=oe(!1);$e(v,()=>{S.value=!1});const T=tt(async()=>{if(n.value)return it(new Rr(n.value))},null),F=new Qr(16);zt(()=>[h.value,v.value,y.value],async([m,x,$],K,Q)=>{var be,Qe,qe,He;(K==null?void 0:K[0])!==m&&F.clear();let q=!1;if(Q(()=>{q=!0}),!m)return;g.value=m.search(x).slice(0,16),S.value=!0;const B=$?await Promise.all(g.value.map(H=>L(H.id))):[];if(q)return;for(const{id:H,mod:ae}of B){const ne=H.slice(0,H.indexOf("#"));let te=F.get(ne);if(te)continue;te=new Map,F.set(ne,te);const X=ae.default??ae;if(X!=null&&X.render||X!=null&&X.setup){const ie=Yt(X);ie.config.warnHandler=()=>{},ie.provide(Zt,i),Object.defineProperties(ie.config.globalProperties,{$frontmatter:{get(){return i.frontmatter.value}},$params:{get(){return i.page.value.params}}});const Ye=document.createElement("div");ie.mount(Ye),Ye.querySelectorAll("h1, h2, h3, h4, h5, h6").forEach(he=>{var et;const we=(et=he.querySelector("a"))==null?void 0:et.getAttribute("href"),Ze=(we==null?void 0:we.startsWith("#"))&&we.slice(1);if(!Ze)return;let Xe="";for(;(he=he.nextElementSibling)&&!/^h[1-6]$/i.test(he.tagName);)Xe+=he.outerHTML;te.set(Ze,Xe)}),ie.unmount()}if(q)return}const U=new Set;if(g.value=g.value.map(H=>{const[ae,ne]=H.id.split("#"),te=F.get(ae),X=(te==null?void 0:te.get(ne))??"";for(const ie in H.match)U.add(ie);return{...H,text:X}}),await de(),q)return;await new Promise(H=>{var ae;(ae=T.value)==null||ae.unmark({done:()=>{var ne;(ne=T.value)==null||ne.markRegExp(M(U),{done:H})}})});const Z=((be=r.value)==null?void 0:be.querySelectorAll(".result .excerpt"))??[];for(const H of Z)(Qe=H.querySelector('mark[data-markjs="true"]'))==null||Qe.scrollIntoView({block:"center"});(He=(qe=n.value)==null?void 0:qe.firstElementChild)==null||He.scrollIntoView({block:"start"})},{debounce:200,immediate:!0});async function L(m){const x=Xt(m.slice(0,m.indexOf("#")));try{if(!x)throw new Error(`Cannot find file for id: ${m}`);return{id:m,mod:await import(x)}}catch($){return console.error($),{id:m,mod:{}}}}const _=oe(),V=Fe(()=>{var m;return((m=v.value)==null?void 0:m.length)<=0});function N(m=!0){var x,$;(x=_.value)==null||x.focus(),m&&(($=_.value)==null||$.select())}Re(()=>{N()});function R(m){m.pointerType==="mouse"&&N()}const A=oe(-1),O=oe(!1);$e(g,m=>{A.value=m.length?0:-1,w()});function w(){de(()=>{const m=document.querySelector(".result.selected");m==null||m.scrollIntoView({block:"nearest"})})}Ee("ArrowUp",m=>{m.preventDefault(),A.value--,A.value<0&&(A.value=g.value.length-1),O.value=!0,w()}),Ee("ArrowDown",m=>{m.preventDefault(),A.value++,A.value>=g.value.length&&(A.value=0),O.value=!0,w()});const c=Pt();Ee("Enter",m=>{if(m.isComposing||m.target instanceof HTMLButtonElement&&m.target.type!=="submit")return;const x=g.value[A.value];if(m.target instanceof HTMLInputElement&&!x){m.preventDefault();return}x&&(c.go(x.id),t("close"))}),Ee("Escape",()=>{t("close")});const p=ar({modal:{displayDetails:"Display detailed list",resetButtonTitle:"Reset search",backButtonTitle:"Close search",noResultsText:"No results for",footer:{selectText:"to select",selectKeyAriaLabel:"enter",navigateText:"to navigate",navigateUpKeyAriaLabel:"up arrow",navigateDownKeyAriaLabel:"down arrow",closeText:"to close",closeKeyAriaLabel:"escape"}}});Re(()=>{window.history.pushState(null,"",null)}),Bt("popstate",m=>{m.preventDefault(),t("close")});const C=Vt($t?document.body:null);Re(()=>{de(()=>{C.value=!0,de().then(()=>s())})}),Wt(()=>{C.value=!1});function I(){v.value="",de().then(()=>N(!1))}function M(m){return new RegExp([...m].sort((x,$)=>$.length-x.length).map(x=>`(${er(x)})`).join("|"),"gi")}return(m,x)=>{var $,K,Q,q;return ee(),Kt(Qt,{to:"body"},[k("div",{ref_key:"el",ref:r,role:"button","aria-owns":($=g.value)!=null&&$.length?"localsearch-list":void 0,"aria-expanded":"true","aria-haspopup":"listbox","aria-labelledby":"localsearch-label",class:"VPLocalSearchBox"},[k("div",{class:"backdrop",onClick:x[0]||(x[0]=B=>m.$emit("close"))}),k("div",Hr,[k("form",{class:"search-bar",onPointerup:x[4]||(x[4]=B=>R(B)),onSubmit:x[5]||(x[5]=Jt(()=>{},["prevent"]))},[k("label",{title:E.value,id:"localsearch-label",for:"localsearch-input"},Xr,8,Yr),k("div",ea,[k("button",{class:"back-button",title:j(p)("modal.backButtonTitle"),onClick:x[1]||(x[1]=B=>m.$emit("close"))},aa,8,ta)]),Ut(k("input",{ref_key:"searchInput",ref:_,"onUpdate:modelValue":x[2]||(x[2]=B=>Gt(v)?v.value=B:null),placeholder:E.value,id:"localsearch-input","aria-labelledby":"localsearch-label",class:"search-input"},null,8,na),[[jt,j(v)]]),k("div",ia,[b.value?Se("",!0):(ee(),re("button",{key:0,class:rt(["toggle-layout-button",{"detailed-list":j(y)}]),type:"button",title:j(p)("modal.displayDetails"),onClick:x[3]||(x[3]=B=>A.value>-1&&(y.value=!j(y)))},ua,10,oa)),k("button",{class:"clear-button",type:"reset",disabled:V.value,title:j(p)("modal.resetButtonTitle"),onClick:I},fa,8,la)])],32),k("ul",{ref_key:"resultsEl",ref:n,id:(K=g.value)!=null&&K.length?"localsearch-list":void 0,role:(Q=g.value)!=null&&Q.length?"listbox":void 0,"aria-labelledby":(q=g.value)!=null&&q.length?"localsearch-label":void 0,class:"results",onMousemove:x[7]||(x[7]=B=>O.value=!1)},[(ee(!0),re(nt,null,at(g.value,(B,U)=>(ee(),re("li",{key:B.id,role:"option","aria-selected":A.value===U?"true":"false"},[k("a",{href:B.id,class:rt(["result",{selected:A.value===U}]),"aria-label":[...B.titles,B.title].join(" > "),onMouseenter:Z=>!O.value&&(A.value=U),onFocusin:Z=>A.value=U,onClick:x[6]||(x[6]=Z=>m.$emit("close"))},[k("div",null,[k("div",pa,[ya,(ee(!0),re(nt,null,at(B.titles,(Z,be)=>(ee(),re("span",{key:be,class:"title"},[k("span",{class:"text",innerHTML:Z},null,8,ma),ga]))),128)),k("span",ba,[k("span",{class:"text",innerHTML:B.title},null,8,wa)])]),j(y)?(ee(),re("div",xa,[B.text?(ee(),re("div",Fa,[k("div",{class:"vp-doc",innerHTML:B.text},null,8,Ea)])):Se("",!0),Sa,Aa])):Se("",!0)])],42,va)],8,da))),128)),j(v)&&!g.value.length&&S.value?(ee(),re("li",Ta,[ve(pe(j(p)("modal.noResultsText"))+' "',1),k("strong",null,pe(j(v)),1),ve('" ')])):Se("",!0)],40,ha),k("div",Na,[k("span",null,[k("kbd",{"aria-label":j(p)("modal.footer.navigateUpKeyAriaLabel")},Da,8,Ca),k("kbd",{"aria-label":j(p)("modal.footer.navigateDownKeyAriaLabel")},Ra,8,ka),ve(" "+pe(j(p)("modal.footer.navigateText")),1)]),k("span",null,[k("kbd",{"aria-label":j(p)("modal.footer.selectKeyAriaLabel")},La,8,_a),ve(" "+pe(j(p)("modal.footer.selectText")),1)]),k("span",null,[k("kbd",{"aria-label":j(p)("modal.footer.closeKeyAriaLabel")},"esc",8,za),ve(" "+pe(j(p)("modal.footer.closeText")),1)])])])],8,qr)])}}}),Ja=tr(Pa,[["__scopeId","data-v-f4c4f812"]]);export{Ja as default}; diff --git a/dev/assets/chunks/framework.Cvv1S4VC.js b/dev/assets/chunks/framework.Cvv1S4VC.js new file mode 100644 index 0000000..ad2d66b --- /dev/null +++ b/dev/assets/chunks/framework.Cvv1S4VC.js @@ -0,0 +1,17 @@ +/** +* @vue/shared v3.4.27 +* (c) 2018-present Yuxi (Evan) You and Vue contributors +* @license MIT +**//*! #__NO_SIDE_EFFECTS__ */function wr(e,t){const n=new Set(e.split(","));return r=>n.has(r)}const ee={},mt=[],xe=()=>{},Ti=()=>!1,kt=e=>e.charCodeAt(0)===111&&e.charCodeAt(1)===110&&(e.charCodeAt(2)>122||e.charCodeAt(2)<97),Er=e=>e.startsWith("onUpdate:"),ie=Object.assign,Cr=(e,t)=>{const n=e.indexOf(t);n>-1&&e.splice(n,1)},Ai=Object.prototype.hasOwnProperty,Y=(e,t)=>Ai.call(e,t),k=Array.isArray,yt=e=>xn(e)==="[object Map]",Gs=e=>xn(e)==="[object Set]",K=e=>typeof e=="function",se=e=>typeof e=="string",ft=e=>typeof e=="symbol",Z=e=>e!==null&&typeof e=="object",zs=e=>(Z(e)||K(e))&&K(e.then)&&K(e.catch),Xs=Object.prototype.toString,xn=e=>Xs.call(e),Ri=e=>xn(e).slice(8,-1),Ys=e=>xn(e)==="[object Object]",xr=e=>se(e)&&e!=="NaN"&&e[0]!=="-"&&""+parseInt(e,10)===e,_t=wr(",key,ref,ref_for,ref_key,onVnodeBeforeMount,onVnodeMounted,onVnodeBeforeUpdate,onVnodeUpdated,onVnodeBeforeUnmount,onVnodeUnmounted"),Sn=e=>{const t=Object.create(null);return n=>t[n]||(t[n]=e(n))},Oi=/-(\w)/g,$e=Sn(e=>e.replace(Oi,(t,n)=>n?n.toUpperCase():"")),Li=/\B([A-Z])/g,dt=Sn(e=>e.replace(Li,"-$1").toLowerCase()),Tn=Sn(e=>e.charAt(0).toUpperCase()+e.slice(1)),un=Sn(e=>e?`on${Tn(e)}`:""),Je=(e,t)=>!Object.is(e,t),fn=(e,t)=>{for(let n=0;n{Object.defineProperty(e,t,{configurable:!0,enumerable:!1,writable:r,value:n})},lr=e=>{const t=parseFloat(e);return isNaN(t)?e:t},Ii=e=>{const t=se(e)?Number(e):NaN;return isNaN(t)?e:t};let Jr;const Qs=()=>Jr||(Jr=typeof globalThis<"u"?globalThis:typeof self<"u"?self:typeof window<"u"?window:typeof global<"u"?global:{});function Sr(e){if(k(e)){const t={};for(let n=0;n{if(n){const r=n.split(Pi);r.length>1&&(t[r[0].trim()]=r[1].trim())}}),t}function Tr(e){let t="";if(se(e))t=e;else if(k(e))for(let n=0;nse(e)?e:e==null?"":k(e)||Z(e)&&(e.toString===Xs||!K(e.toString))?JSON.stringify(e,eo,2):String(e),eo=(e,t)=>t&&t.__v_isRef?eo(e,t.value):yt(t)?{[`Map(${t.size})`]:[...t.entries()].reduce((n,[r,s],o)=>(n[Bn(r,o)+" =>"]=s,n),{})}:Gs(t)?{[`Set(${t.size})`]:[...t.values()].map(n=>Bn(n))}:ft(t)?Bn(t):Z(t)&&!k(t)&&!Ys(t)?String(t):t,Bn=(e,t="")=>{var n;return ft(e)?`Symbol(${(n=e.description)!=null?n:t})`:e};/** +* @vue/reactivity v3.4.27 +* (c) 2018-present Yuxi (Evan) You and Vue contributors +* @license MIT +**/let we;class ji{constructor(t=!1){this.detached=t,this._active=!0,this.effects=[],this.cleanups=[],this.parent=we,!t&&we&&(this.index=(we.scopes||(we.scopes=[])).push(this)-1)}get active(){return this._active}run(t){if(this._active){const n=we;try{return we=this,t()}finally{we=n}}}on(){we=this}off(){we=this.parent}stop(t){if(this._active){let n,r;for(n=0,r=this.effects.length;n=4))break}this._dirtyLevel===1&&(this._dirtyLevel=0),et()}return this._dirtyLevel>=4}set dirty(t){this._dirtyLevel=t?4:0}run(){if(this._dirtyLevel=0,!this.active)return this.fn();let t=Xe,n=ct;try{return Xe=!0,ct=this,this._runnings++,Qr(this),this.fn()}finally{Zr(this),this._runnings--,ct=n,Xe=t}}stop(){this.active&&(Qr(this),Zr(this),this.onStop&&this.onStop(),this.active=!1)}}function Ui(e){return e.value}function Qr(e){e._trackId++,e._depsLength=0}function Zr(e){if(e.deps.length>e._depsLength){for(let t=e._depsLength;t{const n=new Map;return n.cleanup=e,n.computed=t,n},mn=new WeakMap,at=Symbol(""),ur=Symbol("");function ve(e,t,n){if(Xe&&ct){let r=mn.get(e);r||mn.set(e,r=new Map);let s=r.get(n);s||r.set(n,s=io(()=>r.delete(n))),so(ct,s)}}function Ve(e,t,n,r,s,o){const i=mn.get(e);if(!i)return;let l=[];if(t==="clear")l=[...i.values()];else if(n==="length"&&k(e)){const c=Number(r);i.forEach((a,f)=>{(f==="length"||!ft(f)&&f>=c)&&l.push(a)})}else switch(n!==void 0&&l.push(i.get(n)),t){case"add":k(e)?xr(n)&&l.push(i.get("length")):(l.push(i.get(at)),yt(e)&&l.push(i.get(ur)));break;case"delete":k(e)||(l.push(i.get(at)),yt(e)&&l.push(i.get(ur)));break;case"set":yt(e)&&l.push(i.get(at));break}Rr();for(const c of l)c&&oo(c,4);Or()}function Bi(e,t){const n=mn.get(e);return n&&n.get(t)}const ki=wr("__proto__,__v_isRef,__isVue"),lo=new Set(Object.getOwnPropertyNames(Symbol).filter(e=>e!=="arguments"&&e!=="caller").map(e=>Symbol[e]).filter(ft)),es=Ki();function Ki(){const e={};return["includes","indexOf","lastIndexOf"].forEach(t=>{e[t]=function(...n){const r=J(this);for(let o=0,i=this.length;o{e[t]=function(...n){Ze(),Rr();const r=J(this)[t].apply(this,n);return Or(),et(),r}}),e}function Wi(e){ft(e)||(e=String(e));const t=J(this);return ve(t,"has",e),t.hasOwnProperty(e)}class co{constructor(t=!1,n=!1){this._isReadonly=t,this._isShallow=n}get(t,n,r){const s=this._isReadonly,o=this._isShallow;if(n==="__v_isReactive")return!s;if(n==="__v_isReadonly")return s;if(n==="__v_isShallow")return o;if(n==="__v_raw")return r===(s?o?sl:ho:o?fo:uo).get(t)||Object.getPrototypeOf(t)===Object.getPrototypeOf(r)?t:void 0;const i=k(t);if(!s){if(i&&Y(es,n))return Reflect.get(es,n,r);if(n==="hasOwnProperty")return Wi}const l=Reflect.get(t,n,r);return(ft(n)?lo.has(n):ki(n))||(s||ve(t,"get",n),o)?l:de(l)?i&&xr(n)?l:l.value:Z(l)?s?On(l):Rn(l):l}}class ao extends co{constructor(t=!1){super(!1,t)}set(t,n,r,s){let o=t[n];if(!this._isShallow){const c=$t(o);if(!yn(r)&&!$t(r)&&(o=J(o),r=J(r)),!k(t)&&de(o)&&!de(r))return c?!1:(o.value=r,!0)}const i=k(t)&&xr(n)?Number(n)e,An=e=>Reflect.getPrototypeOf(e);function Yt(e,t,n=!1,r=!1){e=e.__v_raw;const s=J(e),o=J(t);n||(Je(t,o)&&ve(s,"get",t),ve(s,"get",o));const{has:i}=An(s),l=r?Lr:n?Pr:Ht;if(i.call(s,t))return l(e.get(t));if(i.call(s,o))return l(e.get(o));e!==s&&e.get(t)}function Jt(e,t=!1){const n=this.__v_raw,r=J(n),s=J(e);return t||(Je(e,s)&&ve(r,"has",e),ve(r,"has",s)),e===s?n.has(e):n.has(e)||n.has(s)}function Qt(e,t=!1){return e=e.__v_raw,!t&&ve(J(e),"iterate",at),Reflect.get(e,"size",e)}function ts(e){e=J(e);const t=J(this);return An(t).has.call(t,e)||(t.add(e),Ve(t,"add",e,e)),this}function ns(e,t){t=J(t);const n=J(this),{has:r,get:s}=An(n);let o=r.call(n,e);o||(e=J(e),o=r.call(n,e));const i=s.call(n,e);return n.set(e,t),o?Je(t,i)&&Ve(n,"set",e,t):Ve(n,"add",e,t),this}function rs(e){const t=J(this),{has:n,get:r}=An(t);let s=n.call(t,e);s||(e=J(e),s=n.call(t,e)),r&&r.call(t,e);const o=t.delete(e);return s&&Ve(t,"delete",e,void 0),o}function ss(){const e=J(this),t=e.size!==0,n=e.clear();return t&&Ve(e,"clear",void 0,void 0),n}function Zt(e,t){return function(r,s){const o=this,i=o.__v_raw,l=J(i),c=t?Lr:e?Pr:Ht;return!e&&ve(l,"iterate",at),i.forEach((a,f)=>r.call(s,c(a),c(f),o))}}function en(e,t,n){return function(...r){const s=this.__v_raw,o=J(s),i=yt(o),l=e==="entries"||e===Symbol.iterator&&i,c=e==="keys"&&i,a=s[e](...r),f=n?Lr:t?Pr:Ht;return!t&&ve(o,"iterate",c?ur:at),{next(){const{value:h,done:m}=a.next();return m?{value:h,done:m}:{value:l?[f(h[0]),f(h[1])]:f(h),done:m}},[Symbol.iterator](){return this}}}}function Ue(e){return function(...t){return e==="delete"?!1:e==="clear"?void 0:this}}function Yi(){const e={get(o){return Yt(this,o)},get size(){return Qt(this)},has:Jt,add:ts,set:ns,delete:rs,clear:ss,forEach:Zt(!1,!1)},t={get(o){return Yt(this,o,!1,!0)},get size(){return Qt(this)},has:Jt,add:ts,set:ns,delete:rs,clear:ss,forEach:Zt(!1,!0)},n={get(o){return Yt(this,o,!0)},get size(){return Qt(this,!0)},has(o){return Jt.call(this,o,!0)},add:Ue("add"),set:Ue("set"),delete:Ue("delete"),clear:Ue("clear"),forEach:Zt(!0,!1)},r={get(o){return Yt(this,o,!0,!0)},get size(){return Qt(this,!0)},has(o){return Jt.call(this,o,!0)},add:Ue("add"),set:Ue("set"),delete:Ue("delete"),clear:Ue("clear"),forEach:Zt(!0,!0)};return["keys","values","entries",Symbol.iterator].forEach(o=>{e[o]=en(o,!1,!1),n[o]=en(o,!0,!1),t[o]=en(o,!1,!0),r[o]=en(o,!0,!0)}),[e,n,t,r]}const[Ji,Qi,Zi,el]=Yi();function Ir(e,t){const n=t?e?el:Zi:e?Qi:Ji;return(r,s,o)=>s==="__v_isReactive"?!e:s==="__v_isReadonly"?e:s==="__v_raw"?r:Reflect.get(Y(n,s)&&s in r?n:r,s,o)}const tl={get:Ir(!1,!1)},nl={get:Ir(!1,!0)},rl={get:Ir(!0,!1)};const uo=new WeakMap,fo=new WeakMap,ho=new WeakMap,sl=new WeakMap;function ol(e){switch(e){case"Object":case"Array":return 1;case"Map":case"Set":case"WeakMap":case"WeakSet":return 2;default:return 0}}function il(e){return e.__v_skip||!Object.isExtensible(e)?0:ol(Ri(e))}function Rn(e){return $t(e)?e:Mr(e,!1,Gi,tl,uo)}function ll(e){return Mr(e,!1,Xi,nl,fo)}function On(e){return Mr(e,!0,zi,rl,ho)}function Mr(e,t,n,r,s){if(!Z(e)||e.__v_raw&&!(t&&e.__v_isReactive))return e;const o=s.get(e);if(o)return o;const i=il(e);if(i===0)return e;const l=new Proxy(e,i===2?r:n);return s.set(e,l),l}function Rt(e){return $t(e)?Rt(e.__v_raw):!!(e&&e.__v_isReactive)}function $t(e){return!!(e&&e.__v_isReadonly)}function yn(e){return!!(e&&e.__v_isShallow)}function po(e){return e?!!e.__v_raw:!1}function J(e){const t=e&&e.__v_raw;return t?J(t):e}function dn(e){return Object.isExtensible(e)&&Js(e,"__v_skip",!0),e}const Ht=e=>Z(e)?Rn(e):e,Pr=e=>Z(e)?On(e):e;class go{constructor(t,n,r,s){this.getter=t,this._setter=n,this.dep=void 0,this.__v_isRef=!0,this.__v_isReadonly=!1,this.effect=new Ar(()=>t(this._value),()=>Ot(this,this.effect._dirtyLevel===2?2:3)),this.effect.computed=this,this.effect.active=this._cacheable=!s,this.__v_isReadonly=r}get value(){const t=J(this);return(!t._cacheable||t.effect.dirty)&&Je(t._value,t._value=t.effect.run())&&Ot(t,4),Nr(t),t.effect._dirtyLevel>=2&&Ot(t,2),t._value}set value(t){this._setter(t)}get _dirty(){return this.effect.dirty}set _dirty(t){this.effect.dirty=t}}function cl(e,t,n=!1){let r,s;const o=K(e);return o?(r=e,s=xe):(r=e.get,s=e.set),new go(r,s,o||!s,n)}function Nr(e){var t;Xe&&ct&&(e=J(e),so(ct,(t=e.dep)!=null?t:e.dep=io(()=>e.dep=void 0,e instanceof go?e:void 0)))}function Ot(e,t=4,n){e=J(e);const r=e.dep;r&&oo(r,t)}function de(e){return!!(e&&e.__v_isRef===!0)}function re(e){return mo(e,!1)}function Fr(e){return mo(e,!0)}function mo(e,t){return de(e)?e:new al(e,t)}class al{constructor(t,n){this.__v_isShallow=n,this.dep=void 0,this.__v_isRef=!0,this._rawValue=n?t:J(t),this._value=n?t:Ht(t)}get value(){return Nr(this),this._value}set value(t){const n=this.__v_isShallow||yn(t)||$t(t);t=n?t:J(t),Je(t,this._rawValue)&&(this._rawValue=t,this._value=n?t:Ht(t),Ot(this,4))}}function yo(e){return de(e)?e.value:e}const ul={get:(e,t,n)=>yo(Reflect.get(e,t,n)),set:(e,t,n,r)=>{const s=e[t];return de(s)&&!de(n)?(s.value=n,!0):Reflect.set(e,t,n,r)}};function _o(e){return Rt(e)?e:new Proxy(e,ul)}class fl{constructor(t){this.dep=void 0,this.__v_isRef=!0;const{get:n,set:r}=t(()=>Nr(this),()=>Ot(this));this._get=n,this._set=r}get value(){return this._get()}set value(t){this._set(t)}}function dl(e){return new fl(e)}class hl{constructor(t,n,r){this._object=t,this._key=n,this._defaultValue=r,this.__v_isRef=!0}get value(){const t=this._object[this._key];return t===void 0?this._defaultValue:t}set value(t){this._object[this._key]=t}get dep(){return Bi(J(this._object),this._key)}}class pl{constructor(t){this._getter=t,this.__v_isRef=!0,this.__v_isReadonly=!0}get value(){return this._getter()}}function gl(e,t,n){return de(e)?e:K(e)?new pl(e):Z(e)&&arguments.length>1?ml(e,t,n):re(e)}function ml(e,t,n){const r=e[t];return de(r)?r:new hl(e,t,n)}/** +* @vue/runtime-core v3.4.27 +* (c) 2018-present Yuxi (Evan) You and Vue contributors +* @license MIT +**/function Ye(e,t,n,r){try{return r?e(...r):e()}catch(s){Kt(s,t,n)}}function Se(e,t,n,r){if(K(e)){const s=Ye(e,t,n,r);return s&&zs(s)&&s.catch(o=>{Kt(o,t,n)}),s}if(k(e)){const s=[];for(let o=0;o>>1,s=pe[r],o=Vt(s);oPe&&pe.splice(t,1)}function bl(e){k(e)?vt.push(...e):(!We||!We.includes(e,e.allowRecurse?ot+1:ot))&&vt.push(e),bo()}function os(e,t,n=jt?Pe+1:0){for(;nVt(n)-Vt(r));if(vt.length=0,We){We.push(...t);return}for(We=t,ot=0;ote.id==null?1/0:e.id,wl=(e,t)=>{const n=Vt(e)-Vt(t);if(n===0){if(e.pre&&!t.pre)return-1;if(t.pre&&!e.pre)return 1}return n};function wo(e){fr=!1,jt=!0,pe.sort(wl);try{for(Pe=0;Pese(v)?v.trim():v)),h&&(s=n.map(lr))}let l,c=r[l=un(t)]||r[l=un($e(t))];!c&&o&&(c=r[l=un(dt(t))]),c&&Se(c,e,6,s);const a=r[l+"Once"];if(a){if(!e.emitted)e.emitted={};else if(e.emitted[l])return;e.emitted[l]=!0,Se(a,e,6,s)}}function Eo(e,t,n=!1){const r=t.emitsCache,s=r.get(e);if(s!==void 0)return s;const o=e.emits;let i={},l=!1;if(!K(e)){const c=a=>{const f=Eo(a,t,!0);f&&(l=!0,ie(i,f))};!n&&t.mixins.length&&t.mixins.forEach(c),e.extends&&c(e.extends),e.mixins&&e.mixins.forEach(c)}return!o&&!l?(Z(e)&&r.set(e,null),null):(k(o)?o.forEach(c=>i[c]=null):ie(i,o),Z(e)&&r.set(e,i),i)}function Mn(e,t){return!e||!kt(t)?!1:(t=t.slice(2).replace(/Once$/,""),Y(e,t[0].toLowerCase()+t.slice(1))||Y(e,dt(t))||Y(e,t))}let ce=null,Pn=null;function vn(e){const t=ce;return ce=e,Pn=e&&e.type.__scopeId||null,t}function eu(e){Pn=e}function tu(){Pn=null}function Cl(e,t=ce,n){if(!t||e._n)return e;const r=(...s)=>{r._d&&vs(-1);const o=vn(t);let i;try{i=e(...s)}finally{vn(o),r._d&&vs(1)}return i};return r._n=!0,r._c=!0,r._d=!0,r}function kn(e){const{type:t,vnode:n,proxy:r,withProxy:s,propsOptions:[o],slots:i,attrs:l,emit:c,render:a,renderCache:f,props:h,data:m,setupState:v,ctx:C,inheritAttrs:I}=e,$=vn(e);let q,D;try{if(n.shapeFlag&4){const y=s||r,M=y;q=Ae(a.call(M,y,f,h,v,m,C)),D=l}else{const y=t;q=Ae(y.length>1?y(h,{attrs:l,slots:i,emit:c}):y(h,null)),D=t.props?l:xl(l)}}catch(y){Nt.length=0,Kt(y,e,1),q=oe(_e)}let p=q;if(D&&I!==!1){const y=Object.keys(D),{shapeFlag:M}=p;y.length&&M&7&&(o&&y.some(Er)&&(D=Sl(D,o)),p=Qe(p,D,!1,!0))}return n.dirs&&(p=Qe(p,null,!1,!0),p.dirs=p.dirs?p.dirs.concat(n.dirs):n.dirs),n.transition&&(p.transition=n.transition),q=p,vn($),q}const xl=e=>{let t;for(const n in e)(n==="class"||n==="style"||kt(n))&&((t||(t={}))[n]=e[n]);return t},Sl=(e,t)=>{const n={};for(const r in e)(!Er(r)||!(r.slice(9)in t))&&(n[r]=e[r]);return n};function Tl(e,t,n){const{props:r,children:s,component:o}=e,{props:i,children:l,patchFlag:c}=t,a=o.emitsOptions;if(t.dirs||t.transition)return!0;if(n&&c>=0){if(c&1024)return!0;if(c&16)return r?is(r,i,a):!!i;if(c&8){const f=t.dynamicProps;for(let h=0;he.__isSuspense;function To(e,t){t&&t.pendingBranch?k(e)?t.effects.push(...e):t.effects.push(e):bl(e)}const Ol=Symbol.for("v-scx"),Ll=()=>wt(Ol);function Hr(e,t){return Nn(e,null,t)}function su(e,t){return Nn(e,null,{flush:"post"})}const tn={};function Ne(e,t,n){return Nn(e,t,n)}function Nn(e,t,{immediate:n,deep:r,flush:s,once:o,onTrack:i,onTrigger:l}=ee){if(t&&o){const O=t;t=(...N)=>{O(...N),M()}}const c=ue,a=O=>r===!0?O:lt(O,r===!1?1:void 0);let f,h=!1,m=!1;if(de(e)?(f=()=>e.value,h=yn(e)):Rt(e)?(f=()=>a(e),h=!0):k(e)?(m=!0,h=e.some(O=>Rt(O)||yn(O)),f=()=>e.map(O=>{if(de(O))return O.value;if(Rt(O))return a(O);if(K(O))return Ye(O,c,2)})):K(e)?t?f=()=>Ye(e,c,2):f=()=>(v&&v(),Se(e,c,3,[C])):f=xe,t&&r){const O=f;f=()=>lt(O())}let v,C=O=>{v=p.onStop=()=>{Ye(O,c,4),v=p.onStop=void 0}},I;if(Gt)if(C=xe,t?n&&Se(t,c,3,[f(),m?[]:void 0,C]):f(),s==="sync"){const O=Ll();I=O.__watcherHandles||(O.__watcherHandles=[])}else return xe;let $=m?new Array(e.length).fill(tn):tn;const q=()=>{if(!(!p.active||!p.dirty))if(t){const O=p.run();(r||h||(m?O.some((N,T)=>Je(N,$[T])):Je(O,$)))&&(v&&v(),Se(t,c,3,[O,$===tn?void 0:m&&$[0]===tn?[]:$,C]),$=O)}else p.run()};q.allowRecurse=!!t;let D;s==="sync"?D=q:s==="post"?D=()=>me(q,c&&c.suspense):(q.pre=!0,c&&(q.id=c.uid),D=()=>In(q));const p=new Ar(f,xe,D),y=to(),M=()=>{p.stop(),y&&Cr(y.effects,p)};return t?n?q():$=p.run():s==="post"?me(p.run.bind(p),c&&c.suspense):p.run(),I&&I.push(M),M}function Il(e,t,n){const r=this.proxy,s=se(e)?e.includes(".")?Ao(r,e):()=>r[e]:e.bind(r,r);let o;K(t)?o=t:(o=t.handler,n=t);const i=qt(this),l=Nn(s,o.bind(r),n);return i(),l}function Ao(e,t){const n=t.split(".");return()=>{let r=e;for(let s=0;s{lt(r,t,n)});else if(Ys(e))for(const r in e)lt(e[r],t,n);return e}function ou(e,t){if(ce===null)return e;const n=jn(ce)||ce.proxy,r=e.dirs||(e.dirs=[]);for(let s=0;s{e.isMounted=!0}),Mo(()=>{e.isUnmounting=!0}),e}const Ee=[Function,Array],Ro={mode:String,appear:Boolean,persisted:Boolean,onBeforeEnter:Ee,onEnter:Ee,onAfterEnter:Ee,onEnterCancelled:Ee,onBeforeLeave:Ee,onLeave:Ee,onAfterLeave:Ee,onLeaveCancelled:Ee,onBeforeAppear:Ee,onAppear:Ee,onAfterAppear:Ee,onAppearCancelled:Ee},Pl={name:"BaseTransition",props:Ro,setup(e,{slots:t}){const n=Hn(),r=Ml();return()=>{const s=t.default&&Lo(t.default(),!0);if(!s||!s.length)return;let o=s[0];if(s.length>1){for(const m of s)if(m.type!==_e){o=m;break}}const i=J(e),{mode:l}=i;if(r.isLeaving)return Kn(o);const c=cs(o);if(!c)return Kn(o);const a=dr(c,i,r,n);hr(c,a);const f=n.subTree,h=f&&cs(f);if(h&&h.type!==_e&&!it(c,h)){const m=dr(h,i,r,n);if(hr(h,m),l==="out-in"&&c.type!==_e)return r.isLeaving=!0,m.afterLeave=()=>{r.isLeaving=!1,n.update.active!==!1&&(n.effect.dirty=!0,n.update())},Kn(o);l==="in-out"&&c.type!==_e&&(m.delayLeave=(v,C,I)=>{const $=Oo(r,h);$[String(h.key)]=h,v[qe]=()=>{C(),v[qe]=void 0,delete a.delayedLeave},a.delayedLeave=I})}return o}}},Nl=Pl;function Oo(e,t){const{leavingVNodes:n}=e;let r=n.get(t.type);return r||(r=Object.create(null),n.set(t.type,r)),r}function dr(e,t,n,r){const{appear:s,mode:o,persisted:i=!1,onBeforeEnter:l,onEnter:c,onAfterEnter:a,onEnterCancelled:f,onBeforeLeave:h,onLeave:m,onAfterLeave:v,onLeaveCancelled:C,onBeforeAppear:I,onAppear:$,onAfterAppear:q,onAppearCancelled:D}=t,p=String(e.key),y=Oo(n,e),M=(T,F)=>{T&&Se(T,r,9,F)},O=(T,F)=>{const w=F[1];M(T,F),k(T)?T.every(j=>j.length<=1)&&w():T.length<=1&&w()},N={mode:o,persisted:i,beforeEnter(T){let F=l;if(!n.isMounted)if(s)F=I||l;else return;T[qe]&&T[qe](!0);const w=y[p];w&&it(e,w)&&w.el[qe]&&w.el[qe](),M(F,[T])},enter(T){let F=c,w=a,j=f;if(!n.isMounted)if(s)F=$||c,w=q||a,j=D||f;else return;let A=!1;const G=T[nn]=le=>{A||(A=!0,le?M(j,[T]):M(w,[T]),N.delayedLeave&&N.delayedLeave(),T[nn]=void 0)};F?O(F,[T,G]):G()},leave(T,F){const w=String(e.key);if(T[nn]&&T[nn](!0),n.isUnmounting)return F();M(h,[T]);let j=!1;const A=T[qe]=G=>{j||(j=!0,F(),G?M(C,[T]):M(v,[T]),T[qe]=void 0,y[w]===e&&delete y[w])};y[w]=e,m?O(m,[T,A]):A()},clone(T){return dr(T,t,n,r)}};return N}function Kn(e){if(Wt(e))return e=Qe(e),e.children=null,e}function cs(e){if(!Wt(e))return e;const{shapeFlag:t,children:n}=e;if(n){if(t&16)return n[0];if(t&32&&K(n.default))return n.default()}}function hr(e,t){e.shapeFlag&6&&e.component?hr(e.component.subTree,t):e.shapeFlag&128?(e.ssContent.transition=t.clone(e.ssContent),e.ssFallback.transition=t.clone(e.ssFallback)):e.transition=t}function Lo(e,t=!1,n){let r=[],s=0;for(let o=0;o1)for(let o=0;o!!e.type.__asyncLoader;/*! #__NO_SIDE_EFFECTS__ */function iu(e){K(e)&&(e={loader:e});const{loader:t,loadingComponent:n,errorComponent:r,delay:s=200,timeout:o,suspensible:i=!0,onError:l}=e;let c=null,a,f=0;const h=()=>(f++,c=null,m()),m=()=>{let v;return c||(v=c=t().catch(C=>{if(C=C instanceof Error?C:new Error(String(C)),l)return new Promise((I,$)=>{l(C,()=>I(h()),()=>$(C),f+1)});throw C}).then(C=>v!==c&&c?c:(C&&(C.__esModule||C[Symbol.toStringTag]==="Module")&&(C=C.default),a=C,C)))};return jr({name:"AsyncComponentWrapper",__asyncLoader:m,get __asyncResolved(){return a},setup(){const v=ue;if(a)return()=>Wn(a,v);const C=D=>{c=null,Kt(D,v,13,!r)};if(i&&v.suspense||Gt)return m().then(D=>()=>Wn(D,v)).catch(D=>(C(D),()=>r?oe(r,{error:D}):null));const I=re(!1),$=re(),q=re(!!s);return s&&setTimeout(()=>{q.value=!1},s),o!=null&&setTimeout(()=>{if(!I.value&&!$.value){const D=new Error(`Async component timed out after ${o}ms.`);C(D),$.value=D}},o),m().then(()=>{I.value=!0,v.parent&&Wt(v.parent.vnode)&&(v.parent.effect.dirty=!0,In(v.parent.update))}).catch(D=>{C(D),$.value=D}),()=>{if(I.value&&a)return Wn(a,v);if($.value&&r)return oe(r,{error:$.value});if(n&&!q.value)return oe(n)}}})}function Wn(e,t){const{ref:n,props:r,children:s,ce:o}=t.vnode,i=oe(e,r,s);return i.ref=n,i.ce=o,delete t.vnode.ce,i}const Wt=e=>e.type.__isKeepAlive;function Fl(e,t){Io(e,"a",t)}function $l(e,t){Io(e,"da",t)}function Io(e,t,n=ue){const r=e.__wdc||(e.__wdc=()=>{let s=n;for(;s;){if(s.isDeactivated)return;s=s.parent}return e()});if(Fn(t,r,n),n){let s=n.parent;for(;s&&s.parent;)Wt(s.parent.vnode)&&Hl(r,t,n,s),s=s.parent}}function Hl(e,t,n,r){const s=Fn(t,e,r,!0);$n(()=>{Cr(r[t],s)},n)}function Fn(e,t,n=ue,r=!1){if(n){const s=n[e]||(n[e]=[]),o=t.__weh||(t.__weh=(...i)=>{if(n.isUnmounted)return;Ze();const l=qt(n),c=Se(t,n,e,i);return l(),et(),c});return r?s.unshift(o):s.push(o),o}}const De=e=>(t,n=ue)=>(!Gt||e==="sp")&&Fn(e,(...r)=>t(...r),n),jl=De("bm"),xt=De("m"),Vl=De("bu"),Dl=De("u"),Mo=De("bum"),$n=De("um"),Ul=De("sp"),Bl=De("rtg"),kl=De("rtc");function Kl(e,t=ue){Fn("ec",e,t)}function lu(e,t,n,r){let s;const o=n;if(k(e)||se(e)){s=new Array(e.length);for(let i=0,l=e.length;it(i,l,void 0,o));else{const i=Object.keys(e);s=new Array(i.length);for(let l=0,c=i.length;lEn(t)?!(t.type===_e||t.type===ye&&!Po(t.children)):!0)?e:null}function au(e,t){const n={};for(const r in e)n[/[A-Z]/.test(r)?`on:${r}`:un(r)]=e[r];return n}const pr=e=>e?ei(e)?jn(e)||e.proxy:pr(e.parent):null,Lt=ie(Object.create(null),{$:e=>e,$el:e=>e.vnode.el,$data:e=>e.data,$props:e=>e.props,$attrs:e=>e.attrs,$slots:e=>e.slots,$refs:e=>e.refs,$parent:e=>pr(e.parent),$root:e=>pr(e.root),$emit:e=>e.emit,$options:e=>Vr(e),$forceUpdate:e=>e.f||(e.f=()=>{e.effect.dirty=!0,In(e.update)}),$nextTick:e=>e.n||(e.n=Ln.bind(e.proxy)),$watch:e=>Il.bind(e)}),qn=(e,t)=>e!==ee&&!e.__isScriptSetup&&Y(e,t),Wl={get({_:e},t){if(t==="__v_skip")return!0;const{ctx:n,setupState:r,data:s,props:o,accessCache:i,type:l,appContext:c}=e;let a;if(t[0]!=="$"){const v=i[t];if(v!==void 0)switch(v){case 1:return r[t];case 2:return s[t];case 4:return n[t];case 3:return o[t]}else{if(qn(r,t))return i[t]=1,r[t];if(s!==ee&&Y(s,t))return i[t]=2,s[t];if((a=e.propsOptions[0])&&Y(a,t))return i[t]=3,o[t];if(n!==ee&&Y(n,t))return i[t]=4,n[t];gr&&(i[t]=0)}}const f=Lt[t];let h,m;if(f)return t==="$attrs"&&ve(e.attrs,"get",""),f(e);if((h=l.__cssModules)&&(h=h[t]))return h;if(n!==ee&&Y(n,t))return i[t]=4,n[t];if(m=c.config.globalProperties,Y(m,t))return m[t]},set({_:e},t,n){const{data:r,setupState:s,ctx:o}=e;return qn(s,t)?(s[t]=n,!0):r!==ee&&Y(r,t)?(r[t]=n,!0):Y(e.props,t)||t[0]==="$"&&t.slice(1)in e?!1:(o[t]=n,!0)},has({_:{data:e,setupState:t,accessCache:n,ctx:r,appContext:s,propsOptions:o}},i){let l;return!!n[i]||e!==ee&&Y(e,i)||qn(t,i)||(l=o[0])&&Y(l,i)||Y(r,i)||Y(Lt,i)||Y(s.config.globalProperties,i)},defineProperty(e,t,n){return n.get!=null?e._.accessCache[t]=0:Y(n,"value")&&this.set(e,t,n.value,null),Reflect.defineProperty(e,t,n)}};function uu(){return ql().slots}function ql(){const e=Hn();return e.setupContext||(e.setupContext=ni(e))}function as(e){return k(e)?e.reduce((t,n)=>(t[n]=null,t),{}):e}let gr=!0;function Gl(e){const t=Vr(e),n=e.proxy,r=e.ctx;gr=!1,t.beforeCreate&&us(t.beforeCreate,e,"bc");const{data:s,computed:o,methods:i,watch:l,provide:c,inject:a,created:f,beforeMount:h,mounted:m,beforeUpdate:v,updated:C,activated:I,deactivated:$,beforeDestroy:q,beforeUnmount:D,destroyed:p,unmounted:y,render:M,renderTracked:O,renderTriggered:N,errorCaptured:T,serverPrefetch:F,expose:w,inheritAttrs:j,components:A,directives:G,filters:le}=t;if(a&&zl(a,r,null),i)for(const X in i){const V=i[X];K(V)&&(r[X]=V.bind(n))}if(s){const X=s.call(n,n);Z(X)&&(e.data=Rn(X))}if(gr=!0,o)for(const X in o){const V=o[X],He=K(V)?V.bind(n,n):K(V.get)?V.get.bind(n,n):xe,zt=!K(V)&&K(V.set)?V.set.bind(n):xe,tt=ne({get:He,set:zt});Object.defineProperty(r,X,{enumerable:!0,configurable:!0,get:()=>tt.value,set:Le=>tt.value=Le})}if(l)for(const X in l)No(l[X],r,n,X);if(c){const X=K(c)?c.call(n):c;Reflect.ownKeys(X).forEach(V=>{ec(V,X[V])})}f&&us(f,e,"c");function U(X,V){k(V)?V.forEach(He=>X(He.bind(n))):V&&X(V.bind(n))}if(U(jl,h),U(xt,m),U(Vl,v),U(Dl,C),U(Fl,I),U($l,$),U(Kl,T),U(kl,O),U(Bl,N),U(Mo,D),U($n,y),U(Ul,F),k(w))if(w.length){const X=e.exposed||(e.exposed={});w.forEach(V=>{Object.defineProperty(X,V,{get:()=>n[V],set:He=>n[V]=He})})}else e.exposed||(e.exposed={});M&&e.render===xe&&(e.render=M),j!=null&&(e.inheritAttrs=j),A&&(e.components=A),G&&(e.directives=G)}function zl(e,t,n=xe){k(e)&&(e=mr(e));for(const r in e){const s=e[r];let o;Z(s)?"default"in s?o=wt(s.from||r,s.default,!0):o=wt(s.from||r):o=wt(s),de(o)?Object.defineProperty(t,r,{enumerable:!0,configurable:!0,get:()=>o.value,set:i=>o.value=i}):t[r]=o}}function us(e,t,n){Se(k(e)?e.map(r=>r.bind(t.proxy)):e.bind(t.proxy),t,n)}function No(e,t,n,r){const s=r.includes(".")?Ao(n,r):()=>n[r];if(se(e)){const o=t[e];K(o)&&Ne(s,o)}else if(K(e))Ne(s,e.bind(n));else if(Z(e))if(k(e))e.forEach(o=>No(o,t,n,r));else{const o=K(e.handler)?e.handler.bind(n):t[e.handler];K(o)&&Ne(s,o,e)}}function Vr(e){const t=e.type,{mixins:n,extends:r}=t,{mixins:s,optionsCache:o,config:{optionMergeStrategies:i}}=e.appContext,l=o.get(t);let c;return l?c=l:!s.length&&!n&&!r?c=t:(c={},s.length&&s.forEach(a=>bn(c,a,i,!0)),bn(c,t,i)),Z(t)&&o.set(t,c),c}function bn(e,t,n,r=!1){const{mixins:s,extends:o}=t;o&&bn(e,o,n,!0),s&&s.forEach(i=>bn(e,i,n,!0));for(const i in t)if(!(r&&i==="expose")){const l=Xl[i]||n&&n[i];e[i]=l?l(e[i],t[i]):t[i]}return e}const Xl={data:fs,props:ds,emits:ds,methods:At,computed:At,beforeCreate:ge,created:ge,beforeMount:ge,mounted:ge,beforeUpdate:ge,updated:ge,beforeDestroy:ge,beforeUnmount:ge,destroyed:ge,unmounted:ge,activated:ge,deactivated:ge,errorCaptured:ge,serverPrefetch:ge,components:At,directives:At,watch:Jl,provide:fs,inject:Yl};function fs(e,t){return t?e?function(){return ie(K(e)?e.call(this,this):e,K(t)?t.call(this,this):t)}:t:e}function Yl(e,t){return At(mr(e),mr(t))}function mr(e){if(k(e)){const t={};for(let n=0;n1)return n&&K(t)?t.call(r&&r.proxy):t}}const $o={},Ho=()=>Object.create($o),jo=e=>Object.getPrototypeOf(e)===$o;function tc(e,t,n,r=!1){const s={},o=Ho();e.propsDefaults=Object.create(null),Vo(e,t,s,o);for(const i in e.propsOptions[0])i in s||(s[i]=void 0);n?e.props=r?s:ll(s):e.type.props?e.props=s:e.props=o,e.attrs=o}function nc(e,t,n,r){const{props:s,attrs:o,vnode:{patchFlag:i}}=e,l=J(s),[c]=e.propsOptions;let a=!1;if((r||i>0)&&!(i&16)){if(i&8){const f=e.vnode.dynamicProps;for(let h=0;h{c=!0;const[m,v]=Do(h,t,!0);ie(i,m),v&&l.push(...v)};!n&&t.mixins.length&&t.mixins.forEach(f),e.extends&&f(e.extends),e.mixins&&e.mixins.forEach(f)}if(!o&&!c)return Z(e)&&r.set(e,mt),mt;if(k(o))for(let f=0;f-1,v[1]=I<0||C-1||Y(v,"default"))&&l.push(h)}}}const a=[i,l];return Z(e)&&r.set(e,a),a}function hs(e){return e[0]!=="$"&&!_t(e)}function ps(e){return e===null?"null":typeof e=="function"?e.name||"":typeof e=="object"&&e.constructor&&e.constructor.name||""}function gs(e,t){return ps(e)===ps(t)}function ms(e,t){return k(t)?t.findIndex(n=>gs(n,e)):K(t)&&gs(t,e)?0:-1}const Uo=e=>e[0]==="_"||e==="$stable",Dr=e=>k(e)?e.map(Ae):[Ae(e)],rc=(e,t,n)=>{if(t._n)return t;const r=Cl((...s)=>Dr(t(...s)),n);return r._c=!1,r},Bo=(e,t,n)=>{const r=e._ctx;for(const s in e){if(Uo(s))continue;const o=e[s];if(K(o))t[s]=rc(s,o,r);else if(o!=null){const i=Dr(o);t[s]=()=>i}}},ko=(e,t)=>{const n=Dr(t);e.slots.default=()=>n},sc=(e,t)=>{const n=e.slots=Ho();if(e.vnode.shapeFlag&32){const r=t._;r?(ie(n,t),Js(n,"_",r,!0)):Bo(t,n)}else t&&ko(e,t)},oc=(e,t,n)=>{const{vnode:r,slots:s}=e;let o=!0,i=ee;if(r.shapeFlag&32){const l=t._;l?n&&l===1?o=!1:(ie(s,t),!n&&l===1&&delete s._):(o=!t.$stable,Bo(t,s)),i=t}else t&&(ko(e,t),i={default:1});if(o)for(const l in s)!Uo(l)&&i[l]==null&&delete s[l]};function wn(e,t,n,r,s=!1){if(k(e)){e.forEach((m,v)=>wn(m,t&&(k(t)?t[v]:t),n,r,s));return}if(bt(r)&&!s)return;const o=r.shapeFlag&4?jn(r.component)||r.component.proxy:r.el,i=s?null:o,{i:l,r:c}=e,a=t&&t.r,f=l.refs===ee?l.refs={}:l.refs,h=l.setupState;if(a!=null&&a!==c&&(se(a)?(f[a]=null,Y(h,a)&&(h[a]=null)):de(a)&&(a.value=null)),K(c))Ye(c,l,12,[i,f]);else{const m=se(c),v=de(c);if(m||v){const C=()=>{if(e.f){const I=m?Y(h,c)?h[c]:f[c]:c.value;s?k(I)&&Cr(I,o):k(I)?I.includes(o)||I.push(o):m?(f[c]=[o],Y(h,c)&&(h[c]=f[c])):(c.value=[o],e.k&&(f[e.k]=c.value))}else m?(f[c]=i,Y(h,c)&&(h[c]=i)):v&&(c.value=i,e.k&&(f[e.k]=i))};i?(C.id=-1,me(C,n)):C()}}}let Be=!1;const ic=e=>e.namespaceURI.includes("svg")&&e.tagName!=="foreignObject",lc=e=>e.namespaceURI.includes("MathML"),rn=e=>{if(ic(e))return"svg";if(lc(e))return"mathml"},sn=e=>e.nodeType===8;function cc(e){const{mt:t,p:n,o:{patchProp:r,createText:s,nextSibling:o,parentNode:i,remove:l,insert:c,createComment:a}}=e,f=(p,y)=>{if(!y.hasChildNodes()){n(null,p,y),_n(),y._vnode=p;return}Be=!1,h(y.firstChild,p,null,null,null),_n(),y._vnode=p,Be&&console.error("Hydration completed but contains mismatches.")},h=(p,y,M,O,N,T=!1)=>{T=T||!!y.dynamicChildren;const F=sn(p)&&p.data==="[",w=()=>I(p,y,M,O,N,F),{type:j,ref:A,shapeFlag:G,patchFlag:le}=y;let fe=p.nodeType;y.el=p,le===-2&&(T=!1,y.dynamicChildren=null);let U=null;switch(j){case Et:fe!==3?y.children===""?(c(y.el=s(""),i(p),p),U=p):U=w():(p.data!==y.children&&(Be=!0,p.data=y.children),U=o(p));break;case _e:D(p)?(U=o(p),q(y.el=p.content.firstChild,p,M)):fe!==8||F?U=w():U=o(p);break;case Pt:if(F&&(p=o(p),fe=p.nodeType),fe===1||fe===3){U=p;const X=!y.children.length;for(let V=0;V{T=T||!!y.dynamicChildren;const{type:F,props:w,patchFlag:j,shapeFlag:A,dirs:G,transition:le}=y,fe=F==="input"||F==="option";if(fe||j!==-1){G&&Me(y,null,M,"created");let U=!1;if(D(p)){U=Wo(O,le)&&M&&M.vnode.props&&M.vnode.props.appear;const V=p.content.firstChild;U&&le.beforeEnter(V),q(V,p,M),y.el=p=V}if(A&16&&!(w&&(w.innerHTML||w.textContent))){let V=v(p.firstChild,y,p,M,O,N,T);for(;V;){Be=!0;const He=V;V=V.nextSibling,l(He)}}else A&8&&p.textContent!==y.children&&(Be=!0,p.textContent=y.children);if(w)if(fe||!T||j&48)for(const V in w)(fe&&(V.endsWith("value")||V==="indeterminate")||kt(V)&&!_t(V)||V[0]===".")&&r(p,V,null,w[V],void 0,void 0,M);else w.onClick&&r(p,"onClick",null,w.onClick,void 0,void 0,M);let X;(X=w&&w.onVnodeBeforeMount)&&Ce(X,M,y),G&&Me(y,null,M,"beforeMount"),((X=w&&w.onVnodeMounted)||G||U)&&To(()=>{X&&Ce(X,M,y),U&&le.enter(p),G&&Me(y,null,M,"mounted")},O)}return p.nextSibling},v=(p,y,M,O,N,T,F)=>{F=F||!!y.dynamicChildren;const w=y.children,j=w.length;for(let A=0;A{const{slotScopeIds:F}=y;F&&(N=N?N.concat(F):F);const w=i(p),j=v(o(p),y,w,M,O,N,T);return j&&sn(j)&&j.data==="]"?o(y.anchor=j):(Be=!0,c(y.anchor=a("]"),w,j),j)},I=(p,y,M,O,N,T)=>{if(Be=!0,y.el=null,T){const j=$(p);for(;;){const A=o(p);if(A&&A!==j)l(A);else break}}const F=o(p),w=i(p);return l(p),n(null,y,w,F,M,O,rn(w),N),F},$=(p,y="[",M="]")=>{let O=0;for(;p;)if(p=o(p),p&&sn(p)&&(p.data===y&&O++,p.data===M)){if(O===0)return o(p);O--}return p},q=(p,y,M)=>{const O=y.parentNode;O&&O.replaceChild(p,y);let N=M;for(;N;)N.vnode.el===y&&(N.vnode.el=N.subTree.el=p),N=N.parent},D=p=>p.nodeType===1&&p.tagName.toLowerCase()==="template";return[f,h]}const me=To;function ac(e){return Ko(e)}function uc(e){return Ko(e,cc)}function Ko(e,t){const n=Qs();n.__VUE__=!0;const{insert:r,remove:s,patchProp:o,createElement:i,createText:l,createComment:c,setText:a,setElementText:f,parentNode:h,nextSibling:m,setScopeId:v=xe,insertStaticContent:C}=e,I=(u,d,g,_=null,b=null,S=null,L=void 0,x=null,R=!!d.dynamicChildren)=>{if(u===d)return;u&&!it(u,d)&&(_=Xt(u),Le(u,b,S,!0),u=null),d.patchFlag===-2&&(R=!1,d.dynamicChildren=null);const{type:E,ref:P,shapeFlag:B}=d;switch(E){case Et:$(u,d,g,_);break;case _e:q(u,d,g,_);break;case Pt:u==null&&D(d,g,_,L);break;case ye:A(u,d,g,_,b,S,L,x,R);break;default:B&1?M(u,d,g,_,b,S,L,x,R):B&6?G(u,d,g,_,b,S,L,x,R):(B&64||B&128)&&E.process(u,d,g,_,b,S,L,x,R,ht)}P!=null&&b&&wn(P,u&&u.ref,S,d||u,!d)},$=(u,d,g,_)=>{if(u==null)r(d.el=l(d.children),g,_);else{const b=d.el=u.el;d.children!==u.children&&a(b,d.children)}},q=(u,d,g,_)=>{u==null?r(d.el=c(d.children||""),g,_):d.el=u.el},D=(u,d,g,_)=>{[u.el,u.anchor]=C(u.children,d,g,_,u.el,u.anchor)},p=({el:u,anchor:d},g,_)=>{let b;for(;u&&u!==d;)b=m(u),r(u,g,_),u=b;r(d,g,_)},y=({el:u,anchor:d})=>{let g;for(;u&&u!==d;)g=m(u),s(u),u=g;s(d)},M=(u,d,g,_,b,S,L,x,R)=>{d.type==="svg"?L="svg":d.type==="math"&&(L="mathml"),u==null?O(d,g,_,b,S,L,x,R):F(u,d,b,S,L,x,R)},O=(u,d,g,_,b,S,L,x)=>{let R,E;const{props:P,shapeFlag:B,transition:H,dirs:W}=u;if(R=u.el=i(u.type,S,P&&P.is,P),B&8?f(R,u.children):B&16&&T(u.children,R,null,_,b,Gn(u,S),L,x),W&&Me(u,null,_,"created"),N(R,u,u.scopeId,L,_),P){for(const Q in P)Q!=="value"&&!_t(Q)&&o(R,Q,null,P[Q],S,u.children,_,b,je);"value"in P&&o(R,"value",null,P.value,S),(E=P.onVnodeBeforeMount)&&Ce(E,_,u)}W&&Me(u,null,_,"beforeMount");const z=Wo(b,H);z&&H.beforeEnter(R),r(R,d,g),((E=P&&P.onVnodeMounted)||z||W)&&me(()=>{E&&Ce(E,_,u),z&&H.enter(R),W&&Me(u,null,_,"mounted")},b)},N=(u,d,g,_,b)=>{if(g&&v(u,g),_)for(let S=0;S<_.length;S++)v(u,_[S]);if(b){let S=b.subTree;if(d===S){const L=b.vnode;N(u,L,L.scopeId,L.slotScopeIds,b.parent)}}},T=(u,d,g,_,b,S,L,x,R=0)=>{for(let E=R;E{const x=d.el=u.el;let{patchFlag:R,dynamicChildren:E,dirs:P}=d;R|=u.patchFlag&16;const B=u.props||ee,H=d.props||ee;let W;if(g&&nt(g,!1),(W=H.onVnodeBeforeUpdate)&&Ce(W,g,d,u),P&&Me(d,u,g,"beforeUpdate"),g&&nt(g,!0),E?w(u.dynamicChildren,E,x,g,_,Gn(d,b),S):L||V(u,d,x,null,g,_,Gn(d,b),S,!1),R>0){if(R&16)j(x,d,B,H,g,_,b);else if(R&2&&B.class!==H.class&&o(x,"class",null,H.class,b),R&4&&o(x,"style",B.style,H.style,b),R&8){const z=d.dynamicProps;for(let Q=0;Q{W&&Ce(W,g,d,u),P&&Me(d,u,g,"updated")},_)},w=(u,d,g,_,b,S,L)=>{for(let x=0;x{if(g!==_){if(g!==ee)for(const x in g)!_t(x)&&!(x in _)&&o(u,x,g[x],null,L,d.children,b,S,je);for(const x in _){if(_t(x))continue;const R=_[x],E=g[x];R!==E&&x!=="value"&&o(u,x,E,R,L,d.children,b,S,je)}"value"in _&&o(u,"value",g.value,_.value,L)}},A=(u,d,g,_,b,S,L,x,R)=>{const E=d.el=u?u.el:l(""),P=d.anchor=u?u.anchor:l("");let{patchFlag:B,dynamicChildren:H,slotScopeIds:W}=d;W&&(x=x?x.concat(W):W),u==null?(r(E,g,_),r(P,g,_),T(d.children||[],g,P,b,S,L,x,R)):B>0&&B&64&&H&&u.dynamicChildren?(w(u.dynamicChildren,H,g,b,S,L,x),(d.key!=null||b&&d===b.subTree)&&Ur(u,d,!0)):V(u,d,g,P,b,S,L,x,R)},G=(u,d,g,_,b,S,L,x,R)=>{d.slotScopeIds=x,u==null?d.shapeFlag&512?b.ctx.activate(d,g,_,L,R):le(d,g,_,b,S,L,R):fe(u,d,R)},le=(u,d,g,_,b,S,L)=>{const x=u.component=wc(u,_,b);if(Wt(u)&&(x.ctx.renderer=ht),Ec(x),x.asyncDep){if(b&&b.registerDep(x,U),!u.el){const R=x.subTree=oe(_e);q(null,R,d,g)}}else U(x,u,d,g,b,S,L)},fe=(u,d,g)=>{const _=d.component=u.component;if(Tl(u,d,g))if(_.asyncDep&&!_.asyncResolved){X(_,d,g);return}else _.next=d,vl(_.update),_.effect.dirty=!0,_.update();else d.el=u.el,_.vnode=d},U=(u,d,g,_,b,S,L)=>{const x=()=>{if(u.isMounted){let{next:P,bu:B,u:H,parent:W,vnode:z}=u;{const pt=qo(u);if(pt){P&&(P.el=z.el,X(u,P,L)),pt.asyncDep.then(()=>{u.isUnmounted||x()});return}}let Q=P,te;nt(u,!1),P?(P.el=z.el,X(u,P,L)):P=z,B&&fn(B),(te=P.props&&P.props.onVnodeBeforeUpdate)&&Ce(te,W,P,z),nt(u,!0);const ae=kn(u),Te=u.subTree;u.subTree=ae,I(Te,ae,h(Te.el),Xt(Te),u,b,S),P.el=ae.el,Q===null&&Al(u,ae.el),H&&me(H,b),(te=P.props&&P.props.onVnodeUpdated)&&me(()=>Ce(te,W,P,z),b)}else{let P;const{el:B,props:H}=d,{bm:W,m:z,parent:Q}=u,te=bt(d);if(nt(u,!1),W&&fn(W),!te&&(P=H&&H.onVnodeBeforeMount)&&Ce(P,Q,d),nt(u,!0),B&&Un){const ae=()=>{u.subTree=kn(u),Un(B,u.subTree,u,b,null)};te?d.type.__asyncLoader().then(()=>!u.isUnmounted&&ae()):ae()}else{const ae=u.subTree=kn(u);I(null,ae,g,_,u,b,S),d.el=ae.el}if(z&&me(z,b),!te&&(P=H&&H.onVnodeMounted)){const ae=d;me(()=>Ce(P,Q,ae),b)}(d.shapeFlag&256||Q&&bt(Q.vnode)&&Q.vnode.shapeFlag&256)&&u.a&&me(u.a,b),u.isMounted=!0,d=g=_=null}},R=u.effect=new Ar(x,xe,()=>In(E),u.scope),E=u.update=()=>{R.dirty&&R.run()};E.id=u.uid,nt(u,!0),E()},X=(u,d,g)=>{d.component=u;const _=u.vnode.props;u.vnode=d,u.next=null,nc(u,d.props,_,g),oc(u,d.children,g),Ze(),os(u),et()},V=(u,d,g,_,b,S,L,x,R=!1)=>{const E=u&&u.children,P=u?u.shapeFlag:0,B=d.children,{patchFlag:H,shapeFlag:W}=d;if(H>0){if(H&128){zt(E,B,g,_,b,S,L,x,R);return}else if(H&256){He(E,B,g,_,b,S,L,x,R);return}}W&8?(P&16&&je(E,b,S),B!==E&&f(g,B)):P&16?W&16?zt(E,B,g,_,b,S,L,x,R):je(E,b,S,!0):(P&8&&f(g,""),W&16&&T(B,g,_,b,S,L,x,R))},He=(u,d,g,_,b,S,L,x,R)=>{u=u||mt,d=d||mt;const E=u.length,P=d.length,B=Math.min(E,P);let H;for(H=0;HP?je(u,b,S,!0,!1,B):T(d,g,_,b,S,L,x,R,B)},zt=(u,d,g,_,b,S,L,x,R)=>{let E=0;const P=d.length;let B=u.length-1,H=P-1;for(;E<=B&&E<=H;){const W=u[E],z=d[E]=R?Ge(d[E]):Ae(d[E]);if(it(W,z))I(W,z,g,null,b,S,L,x,R);else break;E++}for(;E<=B&&E<=H;){const W=u[B],z=d[H]=R?Ge(d[H]):Ae(d[H]);if(it(W,z))I(W,z,g,null,b,S,L,x,R);else break;B--,H--}if(E>B){if(E<=H){const W=H+1,z=WH)for(;E<=B;)Le(u[E],b,S,!0),E++;else{const W=E,z=E,Q=new Map;for(E=z;E<=H;E++){const be=d[E]=R?Ge(d[E]):Ae(d[E]);be.key!=null&&Q.set(be.key,E)}let te,ae=0;const Te=H-z+1;let pt=!1,zr=0;const St=new Array(Te);for(E=0;E=Te){Le(be,b,S,!0);continue}let Ie;if(be.key!=null)Ie=Q.get(be.key);else for(te=z;te<=H;te++)if(St[te-z]===0&&it(be,d[te])){Ie=te;break}Ie===void 0?Le(be,b,S,!0):(St[Ie-z]=E+1,Ie>=zr?zr=Ie:pt=!0,I(be,d[Ie],g,null,b,S,L,x,R),ae++)}const Xr=pt?fc(St):mt;for(te=Xr.length-1,E=Te-1;E>=0;E--){const be=z+E,Ie=d[be],Yr=be+1{const{el:S,type:L,transition:x,children:R,shapeFlag:E}=u;if(E&6){tt(u.component.subTree,d,g,_);return}if(E&128){u.suspense.move(d,g,_);return}if(E&64){L.move(u,d,g,ht);return}if(L===ye){r(S,d,g);for(let B=0;Bx.enter(S),b);else{const{leave:B,delayLeave:H,afterLeave:W}=x,z=()=>r(S,d,g),Q=()=>{B(S,()=>{z(),W&&W()})};H?H(S,z,Q):Q()}else r(S,d,g)},Le=(u,d,g,_=!1,b=!1)=>{const{type:S,props:L,ref:x,children:R,dynamicChildren:E,shapeFlag:P,patchFlag:B,dirs:H}=u;if(x!=null&&wn(x,null,g,u,!0),P&256){d.ctx.deactivate(u);return}const W=P&1&&H,z=!bt(u);let Q;if(z&&(Q=L&&L.onVnodeBeforeUnmount)&&Ce(Q,d,u),P&6)Si(u.component,g,_);else{if(P&128){u.suspense.unmount(g,_);return}W&&Me(u,null,d,"beforeUnmount"),P&64?u.type.remove(u,d,g,b,ht,_):E&&(S!==ye||B>0&&B&64)?je(E,d,g,!1,!0):(S===ye&&B&384||!b&&P&16)&&je(R,d,g),_&&qr(u)}(z&&(Q=L&&L.onVnodeUnmounted)||W)&&me(()=>{Q&&Ce(Q,d,u),W&&Me(u,null,d,"unmounted")},g)},qr=u=>{const{type:d,el:g,anchor:_,transition:b}=u;if(d===ye){xi(g,_);return}if(d===Pt){y(u);return}const S=()=>{s(g),b&&!b.persisted&&b.afterLeave&&b.afterLeave()};if(u.shapeFlag&1&&b&&!b.persisted){const{leave:L,delayLeave:x}=b,R=()=>L(g,S);x?x(u.el,S,R):R()}else S()},xi=(u,d)=>{let g;for(;u!==d;)g=m(u),s(u),u=g;s(d)},Si=(u,d,g)=>{const{bum:_,scope:b,update:S,subTree:L,um:x}=u;_&&fn(_),b.stop(),S&&(S.active=!1,Le(L,u,d,g)),x&&me(x,d),me(()=>{u.isUnmounted=!0},d),d&&d.pendingBranch&&!d.isUnmounted&&u.asyncDep&&!u.asyncResolved&&u.suspenseId===d.pendingId&&(d.deps--,d.deps===0&&d.resolve())},je=(u,d,g,_=!1,b=!1,S=0)=>{for(let L=S;Lu.shapeFlag&6?Xt(u.component.subTree):u.shapeFlag&128?u.suspense.next():m(u.anchor||u.el);let Vn=!1;const Gr=(u,d,g)=>{u==null?d._vnode&&Le(d._vnode,null,null,!0):I(d._vnode||null,u,d,null,null,null,g),Vn||(Vn=!0,os(),_n(),Vn=!1),d._vnode=u},ht={p:I,um:Le,m:tt,r:qr,mt:le,mc:T,pc:V,pbc:w,n:Xt,o:e};let Dn,Un;return t&&([Dn,Un]=t(ht)),{render:Gr,hydrate:Dn,createApp:Zl(Gr,Dn)}}function Gn({type:e,props:t},n){return n==="svg"&&e==="foreignObject"||n==="mathml"&&e==="annotation-xml"&&t&&t.encoding&&t.encoding.includes("html")?void 0:n}function nt({effect:e,update:t},n){e.allowRecurse=t.allowRecurse=n}function Wo(e,t){return(!e||e&&!e.pendingBranch)&&t&&!t.persisted}function Ur(e,t,n=!1){const r=e.children,s=t.children;if(k(r)&&k(s))for(let o=0;o>1,e[n[l]]0&&(t[r]=n[o-1]),n[o]=r)}}for(o=n.length,i=n[o-1];o-- >0;)n[o]=i,i=t[i];return n}function qo(e){const t=e.subTree.component;if(t)return t.asyncDep&&!t.asyncResolved?t:qo(t)}const dc=e=>e.__isTeleport,Mt=e=>e&&(e.disabled||e.disabled===""),ys=e=>typeof SVGElement<"u"&&e instanceof SVGElement,_s=e=>typeof MathMLElement=="function"&&e instanceof MathMLElement,_r=(e,t)=>{const n=e&&e.to;return se(n)?t?t(n):null:n},hc={name:"Teleport",__isTeleport:!0,process(e,t,n,r,s,o,i,l,c,a){const{mc:f,pc:h,pbc:m,o:{insert:v,querySelector:C,createText:I,createComment:$}}=a,q=Mt(t.props);let{shapeFlag:D,children:p,dynamicChildren:y}=t;if(e==null){const M=t.el=I(""),O=t.anchor=I("");v(M,n,r),v(O,n,r);const N=t.target=_r(t.props,C),T=t.targetAnchor=I("");N&&(v(T,N),i==="svg"||ys(N)?i="svg":(i==="mathml"||_s(N))&&(i="mathml"));const F=(w,j)=>{D&16&&f(p,w,j,s,o,i,l,c)};q?F(n,O):N&&F(N,T)}else{t.el=e.el;const M=t.anchor=e.anchor,O=t.target=e.target,N=t.targetAnchor=e.targetAnchor,T=Mt(e.props),F=T?n:O,w=T?M:N;if(i==="svg"||ys(O)?i="svg":(i==="mathml"||_s(O))&&(i="mathml"),y?(m(e.dynamicChildren,y,F,s,o,i,l),Ur(e,t,!0)):c||h(e,t,F,w,s,o,i,l,!1),q)T?t.props&&e.props&&t.props.to!==e.props.to&&(t.props.to=e.props.to):on(t,n,M,a,1);else if((t.props&&t.props.to)!==(e.props&&e.props.to)){const j=t.target=_r(t.props,C);j&&on(t,j,null,a,0)}else T&&on(t,O,N,a,1)}Go(t)},remove(e,t,n,r,{um:s,o:{remove:o}},i){const{shapeFlag:l,children:c,anchor:a,targetAnchor:f,target:h,props:m}=e;if(h&&o(f),i&&o(a),l&16){const v=i||!Mt(m);for(let C=0;C0?Re||mt:null,gc(),Dt>0&&Re&&Re.push(e),e}function du(e,t,n,r,s,o){return Xo(Qo(e,t,n,r,s,o,!0))}function Yo(e,t,n,r,s){return Xo(oe(e,t,n,r,s,!0))}function En(e){return e?e.__v_isVNode===!0:!1}function it(e,t){return e.type===t.type&&e.key===t.key}const Jo=({key:e})=>e??null,hn=({ref:e,ref_key:t,ref_for:n})=>(typeof e=="number"&&(e=""+e),e!=null?se(e)||de(e)||K(e)?{i:ce,r:e,k:t,f:!!n}:e:null);function Qo(e,t=null,n=null,r=0,s=null,o=e===ye?0:1,i=!1,l=!1){const c={__v_isVNode:!0,__v_skip:!0,type:e,props:t,key:t&&Jo(t),ref:t&&hn(t),scopeId:Pn,slotScopeIds:null,children:n,component:null,suspense:null,ssContent:null,ssFallback:null,dirs:null,transition:null,el:null,anchor:null,target:null,targetAnchor:null,staticCount:0,shapeFlag:o,patchFlag:r,dynamicProps:s,dynamicChildren:null,appContext:null,ctx:ce};return l?(Br(c,n),o&128&&e.normalize(c)):n&&(c.shapeFlag|=se(n)?8:16),Dt>0&&!i&&Re&&(c.patchFlag>0||o&6)&&c.patchFlag!==32&&Re.push(c),c}const oe=mc;function mc(e,t=null,n=null,r=0,s=null,o=!1){if((!e||e===xo)&&(e=_e),En(e)){const l=Qe(e,t,!0);return n&&Br(l,n),Dt>0&&!o&&Re&&(l.shapeFlag&6?Re[Re.indexOf(e)]=l:Re.push(l)),l.patchFlag|=-2,l}if(Tc(e)&&(e=e.__vccOpts),t){t=yc(t);let{class:l,style:c}=t;l&&!se(l)&&(t.class=Tr(l)),Z(c)&&(po(c)&&!k(c)&&(c=ie({},c)),t.style=Sr(c))}const i=se(e)?1:Rl(e)?128:dc(e)?64:Z(e)?4:K(e)?2:0;return Qo(e,t,n,r,s,i,o,!0)}function yc(e){return e?po(e)||jo(e)?ie({},e):e:null}function Qe(e,t,n=!1,r=!1){const{props:s,ref:o,patchFlag:i,children:l,transition:c}=e,a=t?_c(s||{},t):s,f={__v_isVNode:!0,__v_skip:!0,type:e.type,props:a,key:a&&Jo(a),ref:t&&t.ref?n&&o?k(o)?o.concat(hn(t)):[o,hn(t)]:hn(t):o,scopeId:e.scopeId,slotScopeIds:e.slotScopeIds,children:l,target:e.target,targetAnchor:e.targetAnchor,staticCount:e.staticCount,shapeFlag:e.shapeFlag,patchFlag:t&&e.type!==ye?i===-1?16:i|16:i,dynamicProps:e.dynamicProps,dynamicChildren:e.dynamicChildren,appContext:e.appContext,dirs:e.dirs,transition:c,component:e.component,suspense:e.suspense,ssContent:e.ssContent&&Qe(e.ssContent),ssFallback:e.ssFallback&&Qe(e.ssFallback),el:e.el,anchor:e.anchor,ctx:e.ctx,ce:e.ce};return c&&r&&(f.transition=c.clone(f)),f}function Zo(e=" ",t=0){return oe(Et,null,e,t)}function hu(e,t){const n=oe(Pt,null,e);return n.staticCount=t,n}function pu(e="",t=!1){return t?(zo(),Yo(_e,null,e)):oe(_e,null,e)}function Ae(e){return e==null||typeof e=="boolean"?oe(_e):k(e)?oe(ye,null,e.slice()):typeof e=="object"?Ge(e):oe(Et,null,String(e))}function Ge(e){return e.el===null&&e.patchFlag!==-1||e.memo?e:Qe(e)}function Br(e,t){let n=0;const{shapeFlag:r}=e;if(t==null)t=null;else if(k(t))n=16;else if(typeof t=="object")if(r&65){const s=t.default;s&&(s._c&&(s._d=!1),Br(e,s()),s._c&&(s._d=!0));return}else{n=32;const s=t._;!s&&!jo(t)?t._ctx=ce:s===3&&ce&&(ce.slots._===1?t._=1:(t._=2,e.patchFlag|=1024))}else K(t)?(t={default:t,_ctx:ce},n=32):(t=String(t),r&64?(n=16,t=[Zo(t)]):n=8);e.children=t,e.shapeFlag|=n}function _c(...e){const t={};for(let n=0;nue||ce;let Cn,vr;{const e=Qs(),t=(n,r)=>{let s;return(s=e[n])||(s=e[n]=[]),s.push(r),o=>{s.length>1?s.forEach(i=>i(o)):s[0](o)}};Cn=t("__VUE_INSTANCE_SETTERS__",n=>ue=n),vr=t("__VUE_SSR_SETTERS__",n=>Gt=n)}const qt=e=>{const t=ue;return Cn(e),e.scope.on(),()=>{e.scope.off(),Cn(t)}},bs=()=>{ue&&ue.scope.off(),Cn(null)};function ei(e){return e.vnode.shapeFlag&4}let Gt=!1;function Ec(e,t=!1){t&&vr(t);const{props:n,children:r}=e.vnode,s=ei(e);tc(e,n,s,t),sc(e,r);const o=s?Cc(e,t):void 0;return t&&vr(!1),o}function Cc(e,t){const n=e.type;e.accessCache=Object.create(null),e.proxy=new Proxy(e.ctx,Wl);const{setup:r}=n;if(r){const s=e.setupContext=r.length>1?ni(e):null,o=qt(e);Ze();const i=Ye(r,e,0,[e.props,s]);if(et(),o(),zs(i)){if(i.then(bs,bs),t)return i.then(l=>{ws(e,l,t)}).catch(l=>{Kt(l,e,0)});e.asyncDep=i}else ws(e,i,t)}else ti(e,t)}function ws(e,t,n){K(t)?e.type.__ssrInlineRender?e.ssrRender=t:e.render=t:Z(t)&&(e.setupState=_o(t)),ti(e,n)}let Es;function ti(e,t,n){const r=e.type;if(!e.render){if(!t&&Es&&!r.render){const s=r.template||Vr(e).template;if(s){const{isCustomElement:o,compilerOptions:i}=e.appContext.config,{delimiters:l,compilerOptions:c}=r,a=ie(ie({isCustomElement:o,delimiters:l},i),c);r.render=Es(s,a)}}e.render=r.render||xe}{const s=qt(e);Ze();try{Gl(e)}finally{et(),s()}}}const xc={get(e,t){return ve(e,"get",""),e[t]}};function ni(e){const t=n=>{e.exposed=n||{}};return{attrs:new Proxy(e.attrs,xc),slots:e.slots,emit:e.emit,expose:t}}function jn(e){if(e.exposed)return e.exposeProxy||(e.exposeProxy=new Proxy(_o(dn(e.exposed)),{get(t,n){if(n in t)return t[n];if(n in Lt)return Lt[n](e)},has(t,n){return n in t||n in Lt}}))}function Sc(e,t=!0){return K(e)?e.displayName||e.name:e.name||t&&e.__name}function Tc(e){return K(e)&&"__vccOpts"in e}const ne=(e,t)=>cl(e,t,Gt);function br(e,t,n){const r=arguments.length;return r===2?Z(t)&&!k(t)?En(t)?oe(e,null,[t]):oe(e,t):oe(e,null,t):(r>3?n=Array.prototype.slice.call(arguments,2):r===3&&En(n)&&(n=[n]),oe(e,t,n))}const Ac="3.4.27";/** +* @vue/runtime-dom v3.4.27 +* (c) 2018-present Yuxi (Evan) You and Vue contributors +* @license MIT +**/const Rc="http://www.w3.org/2000/svg",Oc="http://www.w3.org/1998/Math/MathML",ze=typeof document<"u"?document:null,Cs=ze&&ze.createElement("template"),Lc={insert:(e,t,n)=>{t.insertBefore(e,n||null)},remove:e=>{const t=e.parentNode;t&&t.removeChild(e)},createElement:(e,t,n,r)=>{const s=t==="svg"?ze.createElementNS(Rc,e):t==="mathml"?ze.createElementNS(Oc,e):ze.createElement(e,n?{is:n}:void 0);return e==="select"&&r&&r.multiple!=null&&s.setAttribute("multiple",r.multiple),s},createText:e=>ze.createTextNode(e),createComment:e=>ze.createComment(e),setText:(e,t)=>{e.nodeValue=t},setElementText:(e,t)=>{e.textContent=t},parentNode:e=>e.parentNode,nextSibling:e=>e.nextSibling,querySelector:e=>ze.querySelector(e),setScopeId(e,t){e.setAttribute(t,"")},insertStaticContent(e,t,n,r,s,o){const i=n?n.previousSibling:t.lastChild;if(s&&(s===o||s.nextSibling))for(;t.insertBefore(s.cloneNode(!0),n),!(s===o||!(s=s.nextSibling)););else{Cs.innerHTML=r==="svg"?`${e}`:r==="mathml"?`${e}`:e;const l=Cs.content;if(r==="svg"||r==="mathml"){const c=l.firstChild;for(;c.firstChild;)l.appendChild(c.firstChild);l.removeChild(c)}t.insertBefore(l,n)}return[i?i.nextSibling:t.firstChild,n?n.previousSibling:t.lastChild]}},ke="transition",Tt="animation",Ut=Symbol("_vtc"),ri=(e,{slots:t})=>br(Nl,Ic(e),t);ri.displayName="Transition";const si={name:String,type:String,css:{type:Boolean,default:!0},duration:[String,Number,Object],enterFromClass:String,enterActiveClass:String,enterToClass:String,appearFromClass:String,appearActiveClass:String,appearToClass:String,leaveFromClass:String,leaveActiveClass:String,leaveToClass:String};ri.props=ie({},Ro,si);const rt=(e,t=[])=>{k(e)?e.forEach(n=>n(...t)):e&&e(...t)},xs=e=>e?k(e)?e.some(t=>t.length>1):e.length>1:!1;function Ic(e){const t={};for(const A in e)A in si||(t[A]=e[A]);if(e.css===!1)return t;const{name:n="v",type:r,duration:s,enterFromClass:o=`${n}-enter-from`,enterActiveClass:i=`${n}-enter-active`,enterToClass:l=`${n}-enter-to`,appearFromClass:c=o,appearActiveClass:a=i,appearToClass:f=l,leaveFromClass:h=`${n}-leave-from`,leaveActiveClass:m=`${n}-leave-active`,leaveToClass:v=`${n}-leave-to`}=e,C=Mc(s),I=C&&C[0],$=C&&C[1],{onBeforeEnter:q,onEnter:D,onEnterCancelled:p,onLeave:y,onLeaveCancelled:M,onBeforeAppear:O=q,onAppear:N=D,onAppearCancelled:T=p}=t,F=(A,G,le)=>{st(A,G?f:l),st(A,G?a:i),le&&le()},w=(A,G)=>{A._isLeaving=!1,st(A,h),st(A,v),st(A,m),G&&G()},j=A=>(G,le)=>{const fe=A?N:D,U=()=>F(G,A,le);rt(fe,[G,U]),Ss(()=>{st(G,A?c:o),Ke(G,A?f:l),xs(fe)||Ts(G,r,I,U)})};return ie(t,{onBeforeEnter(A){rt(q,[A]),Ke(A,o),Ke(A,i)},onBeforeAppear(A){rt(O,[A]),Ke(A,c),Ke(A,a)},onEnter:j(!1),onAppear:j(!0),onLeave(A,G){A._isLeaving=!0;const le=()=>w(A,G);Ke(A,h),Ke(A,m),Fc(),Ss(()=>{A._isLeaving&&(st(A,h),Ke(A,v),xs(y)||Ts(A,r,$,le))}),rt(y,[A,le])},onEnterCancelled(A){F(A,!1),rt(p,[A])},onAppearCancelled(A){F(A,!0),rt(T,[A])},onLeaveCancelled(A){w(A),rt(M,[A])}})}function Mc(e){if(e==null)return null;if(Z(e))return[zn(e.enter),zn(e.leave)];{const t=zn(e);return[t,t]}}function zn(e){return Ii(e)}function Ke(e,t){t.split(/\s+/).forEach(n=>n&&e.classList.add(n)),(e[Ut]||(e[Ut]=new Set)).add(t)}function st(e,t){t.split(/\s+/).forEach(r=>r&&e.classList.remove(r));const n=e[Ut];n&&(n.delete(t),n.size||(e[Ut]=void 0))}function Ss(e){requestAnimationFrame(()=>{requestAnimationFrame(e)})}let Pc=0;function Ts(e,t,n,r){const s=e._endId=++Pc,o=()=>{s===e._endId&&r()};if(n)return setTimeout(o,n);const{type:i,timeout:l,propCount:c}=Nc(e,t);if(!i)return r();const a=i+"end";let f=0;const h=()=>{e.removeEventListener(a,m),o()},m=v=>{v.target===e&&++f>=c&&h()};setTimeout(()=>{f(n[C]||"").split(", "),s=r(`${ke}Delay`),o=r(`${ke}Duration`),i=As(s,o),l=r(`${Tt}Delay`),c=r(`${Tt}Duration`),a=As(l,c);let f=null,h=0,m=0;t===ke?i>0&&(f=ke,h=i,m=o.length):t===Tt?a>0&&(f=Tt,h=a,m=c.length):(h=Math.max(i,a),f=h>0?i>a?ke:Tt:null,m=f?f===ke?o.length:c.length:0);const v=f===ke&&/\b(transform|all)(,|$)/.test(r(`${ke}Property`).toString());return{type:f,timeout:h,propCount:m,hasTransform:v}}function As(e,t){for(;e.lengthRs(n)+Rs(e[r])))}function Rs(e){return e==="auto"?0:Number(e.slice(0,-1).replace(",","."))*1e3}function Fc(){return document.body.offsetHeight}function $c(e,t,n){const r=e[Ut];r&&(t=(t?[t,...r]:[...r]).join(" ")),t==null?e.removeAttribute("class"):n?e.setAttribute("class",t):e.className=t}const Os=Symbol("_vod"),Hc=Symbol("_vsh"),jc=Symbol(""),Vc=/(^|;)\s*display\s*:/;function Dc(e,t,n){const r=e.style,s=se(n);let o=!1;if(n&&!s){if(t)if(se(t))for(const i of t.split(";")){const l=i.slice(0,i.indexOf(":")).trim();n[l]==null&&pn(r,l,"")}else for(const i in t)n[i]==null&&pn(r,i,"");for(const i in n)i==="display"&&(o=!0),pn(r,i,n[i])}else if(s){if(t!==n){const i=r[jc];i&&(n+=";"+i),r.cssText=n,o=Vc.test(n)}}else t&&e.removeAttribute("style");Os in e&&(e[Os]=o?r.display:"",e[Hc]&&(r.display="none"))}const Ls=/\s*!important$/;function pn(e,t,n){if(k(n))n.forEach(r=>pn(e,t,r));else if(n==null&&(n=""),t.startsWith("--"))e.setProperty(t,n);else{const r=Uc(e,t);Ls.test(n)?e.setProperty(dt(r),n.replace(Ls,""),"important"):e[r]=n}}const Is=["Webkit","Moz","ms"],Xn={};function Uc(e,t){const n=Xn[t];if(n)return n;let r=$e(t);if(r!=="filter"&&r in e)return Xn[t]=r;r=Tn(r);for(let s=0;sYn||(Gc.then(()=>Yn=0),Yn=Date.now());function Xc(e,t){const n=r=>{if(!r._vts)r._vts=Date.now();else if(r._vts<=n.attached)return;Se(Yc(r,n.value),t,5,[r])};return n.value=e,n.attached=zc(),n}function Yc(e,t){if(k(t)){const n=e.stopImmediatePropagation;return e.stopImmediatePropagation=()=>{n.call(e),e._stopped=!0},t.map(r=>s=>!s._stopped&&r&&r(s))}else return t}const Fs=e=>e.charCodeAt(0)===111&&e.charCodeAt(1)===110&&e.charCodeAt(2)>96&&e.charCodeAt(2)<123,Jc=(e,t,n,r,s,o,i,l,c)=>{const a=s==="svg";t==="class"?$c(e,r,a):t==="style"?Dc(e,n,r):kt(t)?Er(t)||Wc(e,t,n,r,i):(t[0]==="."?(t=t.slice(1),!0):t[0]==="^"?(t=t.slice(1),!1):Qc(e,t,r,a))?kc(e,t,r,o,i,l,c):(t==="true-value"?e._trueValue=r:t==="false-value"&&(e._falseValue=r),Bc(e,t,r,a))};function Qc(e,t,n,r){if(r)return!!(t==="innerHTML"||t==="textContent"||t in e&&Fs(t)&&K(n));if(t==="spellcheck"||t==="draggable"||t==="translate"||t==="form"||t==="list"&&e.tagName==="INPUT"||t==="type"&&e.tagName==="TEXTAREA")return!1;if(t==="width"||t==="height"){const s=e.tagName;if(s==="IMG"||s==="VIDEO"||s==="CANVAS"||s==="SOURCE")return!1}return Fs(t)&&se(n)?!1:t in e}const $s=e=>{const t=e.props["onUpdate:modelValue"]||!1;return k(t)?n=>fn(t,n):t};function Zc(e){e.target.composing=!0}function Hs(e){const t=e.target;t.composing&&(t.composing=!1,t.dispatchEvent(new Event("input")))}const Jn=Symbol("_assign"),gu={created(e,{modifiers:{lazy:t,trim:n,number:r}},s){e[Jn]=$s(s);const o=r||s.props&&s.props.type==="number";gt(e,t?"change":"input",i=>{if(i.target.composing)return;let l=e.value;n&&(l=l.trim()),o&&(l=lr(l)),e[Jn](l)}),n&>(e,"change",()=>{e.value=e.value.trim()}),t||(gt(e,"compositionstart",Zc),gt(e,"compositionend",Hs),gt(e,"change",Hs))},mounted(e,{value:t}){e.value=t??""},beforeUpdate(e,{value:t,modifiers:{lazy:n,trim:r,number:s}},o){if(e[Jn]=$s(o),e.composing)return;const i=(s||e.type==="number")&&!/^0\d/.test(e.value)?lr(e.value):e.value,l=t??"";i!==l&&(document.activeElement===e&&e.type!=="range"&&(n||r&&e.value.trim()===l)||(e.value=l))}},ea=["ctrl","shift","alt","meta"],ta={stop:e=>e.stopPropagation(),prevent:e=>e.preventDefault(),self:e=>e.target!==e.currentTarget,ctrl:e=>!e.ctrlKey,shift:e=>!e.shiftKey,alt:e=>!e.altKey,meta:e=>!e.metaKey,left:e=>"button"in e&&e.button!==0,middle:e=>"button"in e&&e.button!==1,right:e=>"button"in e&&e.button!==2,exact:(e,t)=>ea.some(n=>e[`${n}Key`]&&!t.includes(n))},mu=(e,t)=>{const n=e._withMods||(e._withMods={}),r=t.join(".");return n[r]||(n[r]=(s,...o)=>{for(let i=0;i{const n=e._withKeys||(e._withKeys={}),r=t.join(".");return n[r]||(n[r]=s=>{if(!("key"in s))return;const o=dt(s.key);if(t.some(i=>i===o||na[i]===o))return e(s)})},oi=ie({patchProp:Jc},Lc);let Ft,js=!1;function ra(){return Ft||(Ft=ac(oi))}function sa(){return Ft=js?Ft:uc(oi),js=!0,Ft}const _u=(...e)=>{const t=ra().createApp(...e),{mount:n}=t;return t.mount=r=>{const s=li(r);if(!s)return;const o=t._component;!K(o)&&!o.render&&!o.template&&(o.template=s.innerHTML),s.innerHTML="";const i=n(s,!1,ii(s));return s instanceof Element&&(s.removeAttribute("v-cloak"),s.setAttribute("data-v-app","")),i},t},vu=(...e)=>{const t=sa().createApp(...e),{mount:n}=t;return t.mount=r=>{const s=li(r);if(s)return n(s,!0,ii(s))},t};function ii(e){if(e instanceof SVGElement)return"svg";if(typeof MathMLElement=="function"&&e instanceof MathMLElement)return"mathml"}function li(e){return se(e)?document.querySelector(e):e}const bu=(e,t)=>{const n=e.__vccOpts||e;for(const[r,s]of t)n[r]=s;return n},wu="/BioMarkovChains.jl/dev/logo.png",oa="modulepreload",ia=function(e){return"/BioMarkovChains.jl/dev/"+e},Vs={},Eu=function(t,n,r){let s=Promise.resolve();if(n&&n.length>0){document.getElementsByTagName("link");const o=document.querySelector("meta[property=csp-nonce]"),i=(o==null?void 0:o.nonce)||(o==null?void 0:o.getAttribute("nonce"));s=Promise.all(n.map(l=>{if(l=ia(l),l in Vs)return;Vs[l]=!0;const c=l.endsWith(".css"),a=c?'[rel="stylesheet"]':"";if(document.querySelector(`link[href="${l}"]${a}`))return;const f=document.createElement("link");if(f.rel=c?"stylesheet":oa,c||(f.as="script",f.crossOrigin=""),f.href=l,i&&f.setAttribute("nonce",i),document.head.appendChild(f),c)return new Promise((h,m)=>{f.addEventListener("load",h),f.addEventListener("error",()=>m(new Error(`Unable to preload CSS for ${l}`)))})}))}return s.then(()=>t()).catch(o=>{const i=new Event("vite:preloadError",{cancelable:!0});if(i.payload=o,window.dispatchEvent(i),!i.defaultPrevented)throw o})},la=window.__VP_SITE_DATA__;function kr(e){return to()?(Di(e),!0):!1}function Fe(e){return typeof e=="function"?e():yo(e)}const ci=typeof window<"u"&&typeof document<"u";typeof WorkerGlobalScope<"u"&&globalThis instanceof WorkerGlobalScope;const ca=Object.prototype.toString,aa=e=>ca.call(e)==="[object Object]",Bt=()=>{},Ds=ua();function ua(){var e,t;return ci&&((e=window==null?void 0:window.navigator)==null?void 0:e.userAgent)&&(/iP(?:ad|hone|od)/.test(window.navigator.userAgent)||((t=window==null?void 0:window.navigator)==null?void 0:t.maxTouchPoints)>2&&/iPad|Macintosh/.test(window==null?void 0:window.navigator.userAgent))}function fa(e,t){function n(...r){return new Promise((s,o)=>{Promise.resolve(e(()=>t.apply(this,r),{fn:t,thisArg:this,args:r})).then(s).catch(o)})}return n}const ai=e=>e();function da(e,t={}){let n,r,s=Bt;const o=l=>{clearTimeout(l),s(),s=Bt};return l=>{const c=Fe(e),a=Fe(t.maxWait);return n&&o(n),c<=0||a!==void 0&&a<=0?(r&&(o(r),r=null),Promise.resolve(l())):new Promise((f,h)=>{s=t.rejectOnCancel?h:f,a&&!r&&(r=setTimeout(()=>{n&&o(n),r=null,f(l())},a)),n=setTimeout(()=>{r&&o(r),r=null,f(l())},c)})}}function ha(e=ai){const t=re(!0);function n(){t.value=!1}function r(){t.value=!0}const s=(...o)=>{t.value&&e(...o)};return{isActive:On(t),pause:n,resume:r,eventFilter:s}}function pa(e){return Hn()}function ui(...e){if(e.length!==1)return gl(...e);const t=e[0];return typeof t=="function"?On(dl(()=>({get:t,set:Bt}))):re(t)}function fi(e,t,n={}){const{eventFilter:r=ai,...s}=n;return Ne(e,fa(r,t),s)}function ga(e,t,n={}){const{eventFilter:r,...s}=n,{eventFilter:o,pause:i,resume:l,isActive:c}=ha(r);return{stop:fi(e,t,{...s,eventFilter:o}),pause:i,resume:l,isActive:c}}function Kr(e,t=!0,n){pa()?xt(e,n):t?e():Ln(e)}function Cu(e,t,n={}){const{debounce:r=0,maxWait:s=void 0,...o}=n;return fi(e,t,{...o,eventFilter:da(r,{maxWait:s})})}function xu(e,t,n){let r;de(n)?r={evaluating:n}:r={};const{lazy:s=!1,evaluating:o=void 0,shallow:i=!0,onError:l=Bt}=r,c=re(!s),a=i?Fr(t):re(t);let f=0;return Hr(async h=>{if(!c.value)return;f++;const m=f;let v=!1;o&&Promise.resolve().then(()=>{o.value=!0});try{const C=await e(I=>{h(()=>{o&&(o.value=!1),v||I()})});m===f&&(a.value=C)}catch(C){l(C)}finally{o&&m===f&&(o.value=!1),v=!0}}),s?ne(()=>(c.value=!0,a.value)):a}function di(e){var t;const n=Fe(e);return(t=n==null?void 0:n.$el)!=null?t:n}const Oe=ci?window:void 0;function Ct(...e){let t,n,r,s;if(typeof e[0]=="string"||Array.isArray(e[0])?([n,r,s]=e,t=Oe):[t,n,r,s]=e,!t)return Bt;Array.isArray(n)||(n=[n]),Array.isArray(r)||(r=[r]);const o=[],i=()=>{o.forEach(f=>f()),o.length=0},l=(f,h,m,v)=>(f.addEventListener(h,m,v),()=>f.removeEventListener(h,m,v)),c=Ne(()=>[di(t),Fe(s)],([f,h])=>{if(i(),!f)return;const m=aa(h)?{...h}:h;o.push(...n.flatMap(v=>r.map(C=>l(f,v,C,m))))},{immediate:!0,flush:"post"}),a=()=>{c(),i()};return kr(a),a}function ma(e){return typeof e=="function"?e:typeof e=="string"?t=>t.key===e:Array.isArray(e)?t=>e.includes(t.key):()=>!0}function Su(...e){let t,n,r={};e.length===3?(t=e[0],n=e[1],r=e[2]):e.length===2?typeof e[1]=="object"?(t=!0,n=e[0],r=e[1]):(t=e[0],n=e[1]):(t=!0,n=e[0]);const{target:s=Oe,eventName:o="keydown",passive:i=!1,dedupe:l=!1}=r,c=ma(t);return Ct(s,o,f=>{f.repeat&&Fe(l)||c(f)&&n(f)},i)}function ya(){const e=re(!1),t=Hn();return t&&xt(()=>{e.value=!0},t),e}function _a(e){const t=ya();return ne(()=>(t.value,!!e()))}function hi(e,t={}){const{window:n=Oe}=t,r=_a(()=>n&&"matchMedia"in n&&typeof n.matchMedia=="function");let s;const o=re(!1),i=a=>{o.value=a.matches},l=()=>{s&&("removeEventListener"in s?s.removeEventListener("change",i):s.removeListener(i))},c=Hr(()=>{r.value&&(l(),s=n.matchMedia(Fe(e)),"addEventListener"in s?s.addEventListener("change",i):s.addListener(i),o.value=s.matches)});return kr(()=>{c(),l(),s=void 0}),o}const ln=typeof globalThis<"u"?globalThis:typeof window<"u"?window:typeof global<"u"?global:typeof self<"u"?self:{},cn="__vueuse_ssr_handlers__",va=ba();function ba(){return cn in ln||(ln[cn]=ln[cn]||{}),ln[cn]}function pi(e,t){return va[e]||t}function wa(e){return e==null?"any":e instanceof Set?"set":e instanceof Map?"map":e instanceof Date?"date":typeof e=="boolean"?"boolean":typeof e=="string"?"string":typeof e=="object"?"object":Number.isNaN(e)?"any":"number"}const Ea={boolean:{read:e=>e==="true",write:e=>String(e)},object:{read:e=>JSON.parse(e),write:e=>JSON.stringify(e)},number:{read:e=>Number.parseFloat(e),write:e=>String(e)},any:{read:e=>e,write:e=>String(e)},string:{read:e=>e,write:e=>String(e)},map:{read:e=>new Map(JSON.parse(e)),write:e=>JSON.stringify(Array.from(e.entries()))},set:{read:e=>new Set(JSON.parse(e)),write:e=>JSON.stringify(Array.from(e))},date:{read:e=>new Date(e),write:e=>e.toISOString()}},Us="vueuse-storage";function Wr(e,t,n,r={}){var s;const{flush:o="pre",deep:i=!0,listenToStorageChanges:l=!0,writeDefaults:c=!0,mergeDefaults:a=!1,shallow:f,window:h=Oe,eventFilter:m,onError:v=w=>{console.error(w)},initOnMounted:C}=r,I=(f?Fr:re)(typeof t=="function"?t():t);if(!n)try{n=pi("getDefaultStorage",()=>{var w;return(w=Oe)==null?void 0:w.localStorage})()}catch(w){v(w)}if(!n)return I;const $=Fe(t),q=wa($),D=(s=r.serializer)!=null?s:Ea[q],{pause:p,resume:y}=ga(I,()=>O(I.value),{flush:o,deep:i,eventFilter:m});h&&l&&Kr(()=>{Ct(h,"storage",T),Ct(h,Us,F),C&&T()}),C||T();function M(w,j){h&&h.dispatchEvent(new CustomEvent(Us,{detail:{key:e,oldValue:w,newValue:j,storageArea:n}}))}function O(w){try{const j=n.getItem(e);if(w==null)M(j,null),n.removeItem(e);else{const A=D.write(w);j!==A&&(n.setItem(e,A),M(j,A))}}catch(j){v(j)}}function N(w){const j=w?w.newValue:n.getItem(e);if(j==null)return c&&$!=null&&n.setItem(e,D.write($)),$;if(!w&&a){const A=D.read(j);return typeof a=="function"?a(A,$):q==="object"&&!Array.isArray(A)?{...$,...A}:A}else return typeof j!="string"?j:D.read(j)}function T(w){if(!(w&&w.storageArea!==n)){if(w&&w.key==null){I.value=$;return}if(!(w&&w.key!==e)){p();try{(w==null?void 0:w.newValue)!==D.write(I.value)&&(I.value=N(w))}catch(j){v(j)}finally{w?Ln(y):y()}}}}function F(w){T(w.detail)}return I}function gi(e){return hi("(prefers-color-scheme: dark)",e)}function Ca(e={}){const{selector:t="html",attribute:n="class",initialValue:r="auto",window:s=Oe,storage:o,storageKey:i="vueuse-color-scheme",listenToStorageChanges:l=!0,storageRef:c,emitAuto:a,disableTransition:f=!0}=e,h={auto:"",light:"light",dark:"dark",...e.modes||{}},m=gi({window:s}),v=ne(()=>m.value?"dark":"light"),C=c||(i==null?ui(r):Wr(i,r,o,{window:s,listenToStorageChanges:l})),I=ne(()=>C.value==="auto"?v.value:C.value),$=pi("updateHTMLAttrs",(y,M,O)=>{const N=typeof y=="string"?s==null?void 0:s.document.querySelector(y):di(y);if(!N)return;let T;if(f&&(T=s.document.createElement("style"),T.appendChild(document.createTextNode("*,*::before,*::after{-webkit-transition:none!important;-moz-transition:none!important;-o-transition:none!important;-ms-transition:none!important;transition:none!important}")),s.document.head.appendChild(T)),M==="class"){const F=O.split(/\s/g);Object.values(h).flatMap(w=>(w||"").split(/\s/g)).filter(Boolean).forEach(w=>{F.includes(w)?N.classList.add(w):N.classList.remove(w)})}else N.setAttribute(M,O);f&&(s.getComputedStyle(T).opacity,document.head.removeChild(T))});function q(y){var M;$(t,n,(M=h[y])!=null?M:y)}function D(y){e.onChanged?e.onChanged(y,q):q(y)}Ne(I,D,{flush:"post",immediate:!0}),Kr(()=>D(I.value));const p=ne({get(){return a?C.value:I.value},set(y){C.value=y}});try{return Object.assign(p,{store:C,system:v,state:I})}catch{return p}}function xa(e={}){const{valueDark:t="dark",valueLight:n="",window:r=Oe}=e,s=Ca({...e,onChanged:(l,c)=>{var a;e.onChanged?(a=e.onChanged)==null||a.call(e,l==="dark",c,l):c(l)},modes:{dark:t,light:n}}),o=ne(()=>s.system?s.system.value:gi({window:r}).value?"dark":"light");return ne({get(){return s.value==="dark"},set(l){const c=l?"dark":"light";o.value===c?s.value="auto":s.value=c}})}function Qn(e){return typeof Window<"u"&&e instanceof Window?e.document.documentElement:typeof Document<"u"&&e instanceof Document?e.documentElement:e}function Tu(e,t,n={}){const{window:r=Oe}=n;return Wr(e,t,r==null?void 0:r.localStorage,n)}function mi(e){const t=window.getComputedStyle(e);if(t.overflowX==="scroll"||t.overflowY==="scroll"||t.overflowX==="auto"&&e.clientWidth1?!0:(t.preventDefault&&t.preventDefault(),!1)}const Zn=new WeakMap;function Au(e,t=!1){const n=re(t);let r=null,s="";Ne(ui(e),l=>{const c=Qn(Fe(l));if(c){const a=c;if(Zn.get(a)||Zn.set(a,a.style.overflow),a.style.overflow!=="hidden"&&(s=a.style.overflow),a.style.overflow==="hidden")return n.value=!0;if(n.value)return a.style.overflow="hidden"}},{immediate:!0});const o=()=>{const l=Qn(Fe(e));!l||n.value||(Ds&&(r=Ct(l,"touchmove",c=>{Sa(c)},{passive:!1})),l.style.overflow="hidden",n.value=!0)},i=()=>{const l=Qn(Fe(e));!l||!n.value||(Ds&&(r==null||r()),l.style.overflow=s,Zn.delete(l),n.value=!1)};return kr(i),ne({get(){return n.value},set(l){l?o():i()}})}function Ru(e,t,n={}){const{window:r=Oe}=n;return Wr(e,t,r==null?void 0:r.sessionStorage,n)}function Ou(e={}){const{window:t=Oe,behavior:n="auto"}=e;if(!t)return{x:re(0),y:re(0)};const r=re(t.scrollX),s=re(t.scrollY),o=ne({get(){return r.value},set(l){scrollTo({left:l,behavior:n})}}),i=ne({get(){return s.value},set(l){scrollTo({top:l,behavior:n})}});return Ct(t,"scroll",()=>{r.value=t.scrollX,s.value=t.scrollY},{capture:!1,passive:!0}),{x:o,y:i}}function Lu(e={}){const{window:t=Oe,initialWidth:n=Number.POSITIVE_INFINITY,initialHeight:r=Number.POSITIVE_INFINITY,listenOrientation:s=!0,includeScrollbar:o=!0}=e,i=re(n),l=re(r),c=()=>{t&&(o?(i.value=t.innerWidth,l.value=t.innerHeight):(i.value=t.document.documentElement.clientWidth,l.value=t.document.documentElement.clientHeight))};if(c(),Kr(c),Ct("resize",c,{passive:!0}),s){const a=hi("(orientation: portrait)");Ne(a,()=>c())}return{width:i,height:l}}var er={BASE_URL:"/BioMarkovChains.jl/dev/",MODE:"production",DEV:!1,PROD:!0,SSR:!1},tr={};const yi=/^(?:[a-z]+:|\/\/)/i,Ta="vitepress-theme-appearance",Aa=/#.*$/,Ra=/[?#].*$/,Oa=/(?:(^|\/)index)?\.(?:md|html)$/,he=typeof document<"u",_i={relativePath:"404.md",filePath:"",title:"404",description:"Not Found",headers:[],frontmatter:{sidebar:!1,layout:"page"},lastUpdated:0,isNotFound:!0};function La(e,t,n=!1){if(t===void 0)return!1;if(e=Bs(`/${e}`),n)return new RegExp(t).test(e);if(Bs(t)!==e)return!1;const r=t.match(Aa);return r?(he?location.hash:"")===r[0]:!0}function Bs(e){return decodeURI(e).replace(Ra,"").replace(Oa,"$1")}function Ia(e){return yi.test(e)}function Ma(e,t){return Object.keys((e==null?void 0:e.locales)||{}).find(n=>n!=="root"&&!Ia(n)&&La(t,`/${n}/`,!0))||"root"}function Pa(e,t){var r,s,o,i,l,c,a;const n=Ma(e,t);return Object.assign({},e,{localeIndex:n,lang:((r=e.locales[n])==null?void 0:r.lang)??e.lang,dir:((s=e.locales[n])==null?void 0:s.dir)??e.dir,title:((o=e.locales[n])==null?void 0:o.title)??e.title,titleTemplate:((i=e.locales[n])==null?void 0:i.titleTemplate)??e.titleTemplate,description:((l=e.locales[n])==null?void 0:l.description)??e.description,head:bi(e.head,((c=e.locales[n])==null?void 0:c.head)??[]),themeConfig:{...e.themeConfig,...(a=e.locales[n])==null?void 0:a.themeConfig}})}function vi(e,t){const n=t.title||e.title,r=t.titleTemplate??e.titleTemplate;if(typeof r=="string"&&r.includes(":title"))return r.replace(/:title/g,n);const s=Na(e.title,r);return n===s.slice(3)?n:`${n}${s}`}function Na(e,t){return t===!1?"":t===!0||t===void 0?` | ${e}`:e===t?"":` | ${t}`}function Fa(e,t){const[n,r]=t;if(n!=="meta")return!1;const s=Object.entries(r)[0];return s==null?!1:e.some(([o,i])=>o===n&&i[s[0]]===s[1])}function bi(e,t){return[...e.filter(n=>!Fa(t,n)),...t]}const $a=/[\u0000-\u001F"#$&*+,:;<=>?[\]^`{|}\u007F]/g,Ha=/^[a-z]:/i;function ks(e){const t=Ha.exec(e),n=t?t[0]:"";return n+e.slice(n.length).replace($a,"_").replace(/(^|\/)_+(?=[^/]*$)/,"$1")}const nr=new Set;function ja(e){if(nr.size===0){const n=typeof process=="object"&&(tr==null?void 0:tr.VITE_EXTRA_EXTENSIONS)||(er==null?void 0:er.VITE_EXTRA_EXTENSIONS)||"";("3g2,3gp,aac,ai,apng,au,avif,bin,bmp,cer,class,conf,crl,css,csv,dll,doc,eps,epub,exe,gif,gz,ics,ief,jar,jpe,jpeg,jpg,js,json,jsonld,m4a,man,mid,midi,mjs,mov,mp2,mp3,mp4,mpe,mpeg,mpg,mpp,oga,ogg,ogv,ogx,opus,otf,p10,p7c,p7m,p7s,pdf,png,ps,qt,roff,rtf,rtx,ser,svg,t,tif,tiff,tr,ts,tsv,ttf,txt,vtt,wav,weba,webm,webp,woff,woff2,xhtml,xml,yaml,yml,zip"+(n&&typeof n=="string"?","+n:"")).split(",").forEach(r=>nr.add(r))}const t=e.split(".").pop();return t==null||!nr.has(t.toLowerCase())}function Iu(e){return e.replace(/[|\\{}()[\]^$+*?.]/g,"\\$&").replace(/-/g,"\\x2d")}const Va=Symbol(),ut=Fr(la);function Mu(e){const t=ne(()=>Pa(ut.value,e.data.relativePath)),n=t.value.appearance,r=n==="force-dark"?re(!0):n?xa({storageKey:Ta,initialValue:()=>typeof n=="string"?n:"auto",...typeof n=="object"?n:{}}):re(!1),s=re(he?location.hash:"");return he&&window.addEventListener("hashchange",()=>{s.value=location.hash}),Ne(()=>e.data,()=>{s.value=he?location.hash:""}),{site:t,theme:ne(()=>t.value.themeConfig),page:ne(()=>e.data),frontmatter:ne(()=>e.data.frontmatter),params:ne(()=>e.data.params),lang:ne(()=>t.value.lang),dir:ne(()=>e.data.frontmatter.dir||t.value.dir),localeIndex:ne(()=>t.value.localeIndex||"root"),title:ne(()=>vi(t.value,e.data)),description:ne(()=>e.data.description||t.value.description),isDark:r,hash:ne(()=>s.value)}}function Da(){const e=wt(Va);if(!e)throw new Error("vitepress data not properly injected in app");return e}function Ua(e,t){return`${e}${t}`.replace(/\/+/g,"/")}function Ks(e){return yi.test(e)||!e.startsWith("/")?e:Ua(ut.value.base,e)}function Ba(e){let t=e.replace(/\.html$/,"");if(t=decodeURIComponent(t),t=t.replace(/\/$/,"/index"),he){const n="/BioMarkovChains.jl/dev/";t=ks(t.slice(n.length).replace(/\//g,"_")||"index")+".md";let r=__VP_HASH_MAP__[t.toLowerCase()];if(r||(t=t.endsWith("_index.md")?t.slice(0,-9)+".md":t.slice(0,-3)+"_index.md",r=__VP_HASH_MAP__[t.toLowerCase()]),!r)return null;t=`${n}assets/${t}.${r}.js`}else t=`./${ks(t.slice(1).replace(/\//g,"_"))}.md.js`;return t}let gn=[];function Pu(e){gn.push(e),$n(()=>{gn=gn.filter(t=>t!==e)})}function ka(){let e=ut.value.scrollOffset,t=0,n=24;if(typeof e=="object"&&"padding"in e&&(n=e.padding,e=e.selector),typeof e=="number")t=e;else if(typeof e=="string")t=Ws(e,n);else if(Array.isArray(e))for(const r of e){const s=Ws(r,n);if(s){t=s;break}}return t}function Ws(e,t){const n=document.querySelector(e);if(!n)return 0;const r=n.getBoundingClientRect().bottom;return r<0?0:r+t}const Ka=Symbol(),wi="http://a.com",Wa=()=>({path:"/",component:null,data:_i});function Nu(e,t){const n=Rn(Wa()),r={route:n,go:s};async function s(l=he?location.href:"/"){var c,a;l=rr(l),await((c=r.onBeforeRouteChange)==null?void 0:c.call(r,l))!==!1&&(he&&l!==rr(location.href)&&(history.replaceState({scrollPosition:window.scrollY},""),history.pushState({},"",l)),await i(l),await((a=r.onAfterRouteChanged)==null?void 0:a.call(r,l)))}let o=null;async function i(l,c=0,a=!1){var m;if(await((m=r.onBeforePageLoad)==null?void 0:m.call(r,l))===!1)return;const f=new URL(l,wi),h=o=f.pathname;try{let v=await e(h);if(!v)throw new Error(`Page not found: ${h}`);if(o===h){o=null;const{default:C,__pageData:I}=v;if(!C)throw new Error(`Invalid route component: ${C}`);n.path=he?h:Ks(h),n.component=dn(C),n.data=dn(I),he&&Ln(()=>{let $=ut.value.base+I.relativePath.replace(/(?:(^|\/)index)?\.md$/,"$1");if(!ut.value.cleanUrls&&!$.endsWith("/")&&($+=".html"),$!==f.pathname&&(f.pathname=$,l=$+f.search+f.hash,history.replaceState({},"",l)),f.hash&&!c){let q=null;try{q=document.getElementById(decodeURIComponent(f.hash).slice(1))}catch(D){console.warn(D)}if(q){qs(q,f.hash);return}}window.scrollTo(0,c)})}}catch(v){if(!/fetch|Page not found/.test(v.message)&&!/^\/404(\.html|\/)?$/.test(l)&&console.error(v),!a)try{const C=await fetch(ut.value.base+"hashmap.json");window.__VP_HASH_MAP__=await C.json(),await i(l,c,!0);return}catch{}if(o===h){o=null,n.path=he?h:Ks(h),n.component=t?dn(t):null;const C=he?h.replace(/(^|\/)$/,"$1index").replace(/(\.html)?$/,".md").replace(/^\//,""):"404.md";n.data={..._i,relativePath:C}}}}return he&&(history.state===null&&history.replaceState({},""),window.addEventListener("click",l=>{if(l.target.closest("button"))return;const a=l.target.closest("a");if(a&&!a.closest(".vp-raw")&&(a instanceof SVGElement||!a.download)){const{target:f}=a,{href:h,origin:m,pathname:v,hash:C,search:I}=new URL(a.href instanceof SVGAnimatedString?a.href.animVal:a.href,a.baseURI),$=new URL(location.href);!l.ctrlKey&&!l.shiftKey&&!l.altKey&&!l.metaKey&&!f&&m===$.origin&&ja(v)&&(l.preventDefault(),v===$.pathname&&I===$.search?(C!==$.hash&&(history.pushState({},"",h),window.dispatchEvent(new HashChangeEvent("hashchange",{oldURL:$.href,newURL:h}))),C?qs(a,C,a.classList.contains("header-anchor")):window.scrollTo(0,0)):s(h))}},{capture:!0}),window.addEventListener("popstate",async l=>{var c;l.state!==null&&(await i(rr(location.href),l.state&&l.state.scrollPosition||0),(c=r.onAfterRouteChanged)==null||c.call(r,location.href))}),window.addEventListener("hashchange",l=>{l.preventDefault()})),r}function qa(){const e=wt(Ka);if(!e)throw new Error("useRouter() is called without provider.");return e}function Ei(){return qa().route}function qs(e,t,n=!1){let r=null;try{r=e.classList.contains("header-anchor")?e:document.getElementById(decodeURIComponent(t).slice(1))}catch(s){console.warn(s)}if(r){let s=function(){!n||Math.abs(i-window.scrollY)>window.innerHeight?window.scrollTo(0,i):window.scrollTo({left:0,top:i,behavior:"smooth"})};const o=parseInt(window.getComputedStyle(r).paddingTop,10),i=window.scrollY+r.getBoundingClientRect().top-ka()+o;requestAnimationFrame(s)}}function rr(e){const t=new URL(e,wi);return t.pathname=t.pathname.replace(/(^|\/)index(\.html)?$/,"$1"),ut.value.cleanUrls?t.pathname=t.pathname.replace(/\.html$/,""):!t.pathname.endsWith("/")&&!t.pathname.endsWith(".html")&&(t.pathname+=".html"),t.pathname+t.search+t.hash}const sr=()=>gn.forEach(e=>e()),Fu=jr({name:"VitePressContent",props:{as:{type:[Object,String],default:"div"}},setup(e){const t=Ei(),{site:n}=Da();return()=>br(e.as,n.value.contentProps??{style:{position:"relative"}},[t.component?br(t.component,{onVnodeMounted:sr,onVnodeUpdated:sr,onVnodeUnmounted:sr}):"404 Page Not Found"])}}),$u=jr({setup(e,{slots:t}){const n=re(!1);return xt(()=>{n.value=!0}),()=>n.value&&t.default?t.default():null}});function Hu(){he&&window.addEventListener("click",e=>{var n;const t=e.target;if(t.matches(".vp-code-group input")){const r=(n=t.parentElement)==null?void 0:n.parentElement;if(!r)return;const s=Array.from(r.querySelectorAll("input")).indexOf(t);if(s<0)return;const o=r.querySelector(".blocks");if(!o)return;const i=Array.from(o.children).find(a=>a.classList.contains("active"));if(!i)return;const l=o.children[s];if(!l||i===l)return;i.classList.remove("active"),l.classList.add("active");const c=r==null?void 0:r.querySelector(`label[for="${t.id}"]`);c==null||c.scrollIntoView({block:"nearest"})}})}function ju(){if(he){const e=new WeakMap;window.addEventListener("click",t=>{var r;const n=t.target;if(n.matches('div[class*="language-"] > button.copy')){const s=n.parentElement,o=(r=n.nextElementSibling)==null?void 0:r.nextElementSibling;if(!s||!o)return;const i=/language-(shellscript|shell|bash|sh|zsh)/.test(s.className),l=[".vp-copy-ignore",".diff.remove"],c=o.cloneNode(!0);c.querySelectorAll(l.join(",")).forEach(f=>f.remove());let a=c.textContent||"";i&&(a=a.replace(/^ *(\$|>) /gm,"").trim()),Ga(a).then(()=>{n.classList.add("copied"),clearTimeout(e.get(n));const f=setTimeout(()=>{n.classList.remove("copied"),n.blur(),e.delete(n)},2e3);e.set(n,f)})}})}}async function Ga(e){try{return navigator.clipboard.writeText(e)}catch{const t=document.createElement("textarea"),n=document.activeElement;t.value=e,t.setAttribute("readonly",""),t.style.contain="strict",t.style.position="absolute",t.style.left="-9999px",t.style.fontSize="12pt";const r=document.getSelection(),s=r?r.rangeCount>0&&r.getRangeAt(0):null;document.body.appendChild(t),t.select(),t.selectionStart=0,t.selectionEnd=e.length,document.execCommand("copy"),document.body.removeChild(t),s&&(r.removeAllRanges(),r.addRange(s)),n&&n.focus()}}function Vu(e,t){let n=!0,r=[];const s=o=>{if(n){n=!1,o.forEach(l=>{const c=or(l);for(const a of document.head.children)if(a.isEqualNode(c)){r.push(a);return}});return}const i=o.map(or);r.forEach((l,c)=>{const a=i.findIndex(f=>f==null?void 0:f.isEqualNode(l??null));a!==-1?delete i[a]:(l==null||l.remove(),delete r[c])}),i.forEach(l=>l&&document.head.appendChild(l)),r=[...r,...i].filter(Boolean)};Hr(()=>{const o=e.data,i=t.value,l=o&&o.description,c=o&&o.frontmatter.head||[],a=vi(i,o);a!==document.title&&(document.title=a);const f=l||i.description;let h=document.querySelector("meta[name=description]");h?h.getAttribute("content")!==f&&h.setAttribute("content",f):or(["meta",{name:"description",content:f}]),s(bi(i.head,Xa(c)))})}function or([e,t,n]){const r=document.createElement(e);for(const s in t)r.setAttribute(s,t[s]);return n&&(r.innerHTML=n),e==="script"&&!t.async&&(r.async=!1),r}function za(e){return e[0]==="meta"&&e[1]&&e[1].name==="description"}function Xa(e){return e.filter(t=>!za(t))}const ir=new Set,Ci=()=>document.createElement("link"),Ya=e=>{const t=Ci();t.rel="prefetch",t.href=e,document.head.appendChild(t)},Ja=e=>{const t=new XMLHttpRequest;t.open("GET",e,t.withCredentials=!0),t.send()};let an;const Qa=he&&(an=Ci())&&an.relList&&an.relList.supports&&an.relList.supports("prefetch")?Ya:Ja;function Du(){if(!he||!window.IntersectionObserver)return;let e;if((e=navigator.connection)&&(e.saveData||/2g/.test(e.effectiveType)))return;const t=window.requestIdleCallback||setTimeout;let n=null;const r=()=>{n&&n.disconnect(),n=new IntersectionObserver(o=>{o.forEach(i=>{if(i.isIntersecting){const l=i.target;n.unobserve(l);const{pathname:c}=l;if(!ir.has(c)){ir.add(c);const a=Ba(c);a&&Qa(a)}}})}),t(()=>{document.querySelectorAll("#app a").forEach(o=>{const{hostname:i,pathname:l}=new URL(o.href instanceof SVGAnimatedString?o.href.animVal:o.href,o.baseURI),c=l.match(/\.\w+$/);c&&c[0]!==".html"||o.target!=="_blank"&&i===location.hostname&&(l!==location.pathname?n.observe(o):ir.add(l))})})};xt(r);const s=Ei();Ne(()=>s.path,r),$n(()=>{n&&n.disconnect()})}export{yu as $,su as A,Dl as B,ka as C,nu as D,lu as E,ye as F,Fr as G,Pu as H,oe as I,ru as J,yi as K,Ei as L,_c as M,wt as N,Lu as O,Sr as P,Su as Q,Ln as R,Ou as S,ri as T,he as U,On as V,iu as W,Eu as X,Au as Y,ec as Z,bu as _,Zo as a,au as a0,mu as a1,uu as a2,Rn as a3,gl as a4,br as a5,hu as a6,wu as a7,Vu as a8,Ka as a9,Iu as aA,Mu as aa,Va as ab,Fu as ac,$u as ad,ut as ae,vu as af,Nu as ag,Ba as ah,Du as ai,ju as aj,Hu as ak,di as al,kr as am,xu as an,Ru as ao,Tu as ap,Cu as aq,qa as ar,Ct as as,Mo as at,ou as au,gu as av,de as aw,fu as ax,dn as ay,_u as az,Yo as b,du as c,jr as d,pu as e,ja as f,Ks as g,ne as h,Ia as i,Qo as j,yo as k,tu as l,La as m,Tr as n,zo as o,eu as p,hi as q,cu as r,re as s,Za as t,Da as u,Ne as v,Cl as w,Hr as x,xt as y,$n as z}; diff --git a/dev/assets/chunks/framework.D1rHXXmm.js b/dev/assets/chunks/framework.D1rHXXmm.js deleted file mode 100644 index 419cc6e..0000000 --- a/dev/assets/chunks/framework.D1rHXXmm.js +++ /dev/null @@ -1,17 +0,0 @@ -/** -* @vue/shared v3.4.21 -* (c) 2018-present Yuxi (Evan) You and Vue contributors -* @license MIT -**/function Sr(e,t){const n=new Set(e.split(","));return t?r=>n.has(r.toLowerCase()):r=>n.has(r)}const ee={},_t=[],xe=()=>{},Si=()=>!1,Wt=e=>e.charCodeAt(0)===111&&e.charCodeAt(1)===110&&(e.charCodeAt(2)>122||e.charCodeAt(2)<97),Tr=e=>e.startsWith("onUpdate:"),ce=Object.assign,Ar=(e,t)=>{const n=e.indexOf(t);n>-1&&e.splice(n,1)},Ti=Object.prototype.hasOwnProperty,Y=(e,t)=>Ti.call(e,t),U=Array.isArray,vt=e=>An(e)==="[object Map]",Qs=e=>An(e)==="[object Set]",q=e=>typeof e=="function",se=e=>typeof e=="string",At=e=>typeof e=="symbol",Z=e=>e!==null&&typeof e=="object",Zs=e=>(Z(e)||q(e))&&q(e.then)&&q(e.catch),eo=Object.prototype.toString,An=e=>eo.call(e),Ai=e=>An(e).slice(8,-1),to=e=>An(e)==="[object Object]",Rr=e=>se(e)&&e!=="NaN"&&e[0]!=="-"&&""+parseInt(e,10)===e,bt=Sr(",key,ref,ref_for,ref_key,onVnodeBeforeMount,onVnodeMounted,onVnodeBeforeUpdate,onVnodeUpdated,onVnodeBeforeUnmount,onVnodeUnmounted"),Rn=e=>{const t=Object.create(null);return n=>t[n]||(t[n]=e(n))},Ri=/-(\w)/g,$e=Rn(e=>e.replace(Ri,(t,n)=>n?n.toUpperCase():"")),Li=/\B([A-Z])/g,ft=Rn(e=>e.replace(Li,"-$1").toLowerCase()),Ln=Rn(e=>e.charAt(0).toUpperCase()+e.slice(1)),hn=Rn(e=>e?`on${Ln(e)}`:""),Ze=(e,t)=>!Object.is(e,t),pn=(e,t)=>{for(let n=0;n{Object.defineProperty(e,t,{configurable:!0,enumerable:!1,value:n})},ur=e=>{const t=parseFloat(e);return isNaN(t)?e:t},Oi=e=>{const t=se(e)?Number(e):NaN;return isNaN(t)?e:t};let ns;const no=()=>ns||(ns=typeof globalThis<"u"?globalThis:typeof self<"u"?self:typeof window<"u"?window:typeof global<"u"?global:{});function Lr(e){if(U(e)){const t={};for(let n=0;n{if(n){const r=n.split(Mi);r.length>1&&(t[r[0].trim()]=r[1].trim())}}),t}function Or(e){let t="";if(se(e))t=e;else if(U(e))for(let n=0;nse(e)?e:e==null?"":U(e)||Z(e)&&(e.toString===eo||!q(e.toString))?JSON.stringify(e,so,2):String(e),so=(e,t)=>t&&t.__v_isRef?so(e,t.value):vt(t)?{[`Map(${t.size})`]:[...t.entries()].reduce((n,[r,s],o)=>(n[qn(r,o)+" =>"]=s,n),{})}:Qs(t)?{[`Set(${t.size})`]:[...t.values()].map(n=>qn(n))}:At(t)?qn(t):Z(t)&&!U(t)&&!to(t)?String(t):t,qn=(e,t="")=>{var n;return At(e)?`Symbol(${(n=e.description)!=null?n:t})`:e};/** -* @vue/reactivity v3.4.21 -* (c) 2018-present Yuxi (Evan) You and Vue contributors -* @license MIT -**/let be;class Hi{constructor(t=!1){this.detached=t,this._active=!0,this.effects=[],this.cleanups=[],this.parent=be,!t&&be&&(this.index=(be.scopes||(be.scopes=[])).push(this)-1)}get active(){return this._active}run(t){if(this._active){const n=be;try{return be=this,t()}finally{be=n}}}on(){be=this}off(){be=this.parent}stop(t){if(this._active){let n,r;for(n=0,r=this.effects.length;n=4))break}this._dirtyLevel===1&&(this._dirtyLevel=0),ht()}return this._dirtyLevel>=4}set dirty(t){this._dirtyLevel=t?4:0}run(){if(this._dirtyLevel=0,!this.active)return this.fn();let t=Ye,n=ct;try{return Ye=!0,ct=this,this._runnings++,rs(this),this.fn()}finally{ss(this),this._runnings--,ct=n,Ye=t}}stop(){var t;this.active&&(rs(this),ss(this),(t=this.onStop)==null||t.call(this),this.active=!1)}}function Di(e){return e.value}function rs(e){e._trackId++,e._depsLength=0}function ss(e){if(e.deps.length>e._depsLength){for(let t=e._depsLength;t{const n=new Map;return n.cleanup=e,n.computed=t,n},vn=new WeakMap,at=Symbol(""),hr=Symbol("");function _e(e,t,n){if(Ye&&ct){let r=vn.get(e);r||vn.set(e,r=new Map);let s=r.get(n);s||r.set(n,s=uo(()=>r.delete(n))),co(ct,s)}}function Ve(e,t,n,r,s,o){const i=vn.get(e);if(!i)return;let l=[];if(t==="clear")l=[...i.values()];else if(n==="length"&&U(e)){const c=Number(r);i.forEach((a,f)=>{(f==="length"||!At(f)&&f>=c)&&l.push(a)})}else switch(n!==void 0&&l.push(i.get(n)),t){case"add":U(e)?Rr(n)&&l.push(i.get("length")):(l.push(i.get(at)),vt(e)&&l.push(i.get(hr)));break;case"delete":U(e)||(l.push(i.get(at)),vt(e)&&l.push(i.get(hr)));break;case"set":vt(e)&&l.push(i.get(at));break}Mr();for(const c of l)c&&ao(c,4);Pr()}function Bi(e,t){var n;return(n=vn.get(e))==null?void 0:n.get(t)}const Ui=Sr("__proto__,__v_isRef,__isVue"),fo=new Set(Object.getOwnPropertyNames(Symbol).filter(e=>e!=="arguments"&&e!=="caller").map(e=>Symbol[e]).filter(At)),os=ki();function ki(){const e={};return["includes","indexOf","lastIndexOf"].forEach(t=>{e[t]=function(...n){const r=J(this);for(let o=0,i=this.length;o{e[t]=function(...n){dt(),Mr();const r=J(this)[t].apply(this,n);return Pr(),ht(),r}}),e}function Ki(e){const t=J(this);return _e(t,"has",e),t.hasOwnProperty(e)}class ho{constructor(t=!1,n=!1){this._isReadonly=t,this._isShallow=n}get(t,n,r){const s=this._isReadonly,o=this._isShallow;if(n==="__v_isReactive")return!s;if(n==="__v_isReadonly")return s;if(n==="__v_isShallow")return o;if(n==="__v_raw")return r===(s?o?rl:yo:o?mo:go).get(t)||Object.getPrototypeOf(t)===Object.getPrototypeOf(r)?t:void 0;const i=U(t);if(!s){if(i&&Y(os,n))return Reflect.get(os,n,r);if(n==="hasOwnProperty")return Ki}const l=Reflect.get(t,n,r);return(At(n)?fo.has(n):Ui(n))||(s||_e(t,"get",n),o)?l:de(l)?i&&Rr(n)?l:l.value:Z(l)?s?Mn(l):In(l):l}}class po extends ho{constructor(t=!1){super(!1,t)}set(t,n,r,s){let o=t[n];if(!this._isShallow){const c=St(o);if(!bn(r)&&!St(r)&&(o=J(o),r=J(r)),!U(t)&&de(o)&&!de(r))return c?!1:(o.value=r,!0)}const i=U(t)&&Rr(n)?Number(n)e,On=e=>Reflect.getPrototypeOf(e);function Qt(e,t,n=!1,r=!1){e=e.__v_raw;const s=J(e),o=J(t);n||(Ze(t,o)&&_e(s,"get",t),_e(s,"get",o));const{has:i}=On(s),l=r?Nr:n?Hr:Dt;if(i.call(s,t))return l(e.get(t));if(i.call(s,o))return l(e.get(o));e!==s&&e.get(t)}function Zt(e,t=!1){const n=this.__v_raw,r=J(n),s=J(e);return t||(Ze(e,s)&&_e(r,"has",e),_e(r,"has",s)),e===s?n.has(e):n.has(e)||n.has(s)}function en(e,t=!1){return e=e.__v_raw,!t&&_e(J(e),"iterate",at),Reflect.get(e,"size",e)}function is(e){e=J(e);const t=J(this);return On(t).has.call(t,e)||(t.add(e),Ve(t,"add",e,e)),this}function ls(e,t){t=J(t);const n=J(this),{has:r,get:s}=On(n);let o=r.call(n,e);o||(e=J(e),o=r.call(n,e));const i=s.call(n,e);return n.set(e,t),o?Ze(t,i)&&Ve(n,"set",e,t):Ve(n,"add",e,t),this}function cs(e){const t=J(this),{has:n,get:r}=On(t);let s=n.call(t,e);s||(e=J(e),s=n.call(t,e)),r&&r.call(t,e);const o=t.delete(e);return s&&Ve(t,"delete",e,void 0),o}function as(){const e=J(this),t=e.size!==0,n=e.clear();return t&&Ve(e,"clear",void 0,void 0),n}function tn(e,t){return function(r,s){const o=this,i=o.__v_raw,l=J(i),c=t?Nr:e?Hr:Dt;return!e&&_e(l,"iterate",at),i.forEach((a,f)=>r.call(s,c(a),c(f),o))}}function nn(e,t,n){return function(...r){const s=this.__v_raw,o=J(s),i=vt(o),l=e==="entries"||e===Symbol.iterator&&i,c=e==="keys"&&i,a=s[e](...r),f=n?Nr:t?Hr:Dt;return!t&&_e(o,"iterate",c?hr:at),{next(){const{value:h,done:p}=a.next();return p?{value:h,done:p}:{value:l?[f(h[0]),f(h[1])]:f(h),done:p}},[Symbol.iterator](){return this}}}}function Ue(e){return function(...t){return e==="delete"?!1:e==="clear"?void 0:this}}function Xi(){const e={get(o){return Qt(this,o)},get size(){return en(this)},has:Zt,add:is,set:ls,delete:cs,clear:as,forEach:tn(!1,!1)},t={get(o){return Qt(this,o,!1,!0)},get size(){return en(this)},has:Zt,add:is,set:ls,delete:cs,clear:as,forEach:tn(!1,!0)},n={get(o){return Qt(this,o,!0)},get size(){return en(this,!0)},has(o){return Zt.call(this,o,!0)},add:Ue("add"),set:Ue("set"),delete:Ue("delete"),clear:Ue("clear"),forEach:tn(!0,!1)},r={get(o){return Qt(this,o,!0,!0)},get size(){return en(this,!0)},has(o){return Zt.call(this,o,!0)},add:Ue("add"),set:Ue("set"),delete:Ue("delete"),clear:Ue("clear"),forEach:tn(!0,!0)};return["keys","values","entries",Symbol.iterator].forEach(o=>{e[o]=nn(o,!1,!1),n[o]=nn(o,!0,!1),t[o]=nn(o,!1,!0),r[o]=nn(o,!0,!0)}),[e,n,t,r]}const[Yi,Ji,Qi,Zi]=Xi();function Fr(e,t){const n=t?e?Zi:Qi:e?Ji:Yi;return(r,s,o)=>s==="__v_isReactive"?!e:s==="__v_isReadonly"?e:s==="__v_raw"?r:Reflect.get(Y(n,s)&&s in r?n:r,s,o)}const el={get:Fr(!1,!1)},tl={get:Fr(!1,!0)},nl={get:Fr(!0,!1)},go=new WeakMap,mo=new WeakMap,yo=new WeakMap,rl=new WeakMap;function sl(e){switch(e){case"Object":case"Array":return 1;case"Map":case"Set":case"WeakMap":case"WeakSet":return 2;default:return 0}}function ol(e){return e.__v_skip||!Object.isExtensible(e)?0:sl(Ai(e))}function In(e){return St(e)?e:$r(e,!1,qi,el,go)}function il(e){return $r(e,!1,zi,tl,mo)}function Mn(e){return $r(e,!0,Gi,nl,yo)}function $r(e,t,n,r,s){if(!Z(e)||e.__v_raw&&!(t&&e.__v_isReactive))return e;const o=s.get(e);if(o)return o;const i=ol(e);if(i===0)return e;const l=new Proxy(e,i===2?r:n);return s.set(e,l),l}function wt(e){return St(e)?wt(e.__v_raw):!!(e&&e.__v_isReactive)}function St(e){return!!(e&&e.__v_isReadonly)}function bn(e){return!!(e&&e.__v_isShallow)}function _o(e){return wt(e)||St(e)}function J(e){const t=e&&e.__v_raw;return t?J(t):e}function Mt(e){return Object.isExtensible(e)&&_n(e,"__v_skip",!0),e}const Dt=e=>Z(e)?In(e):e,Hr=e=>Z(e)?Mn(e):e;class vo{constructor(t,n,r,s){this.getter=t,this._setter=n,this.dep=void 0,this.__v_isRef=!0,this.__v_isReadonly=!1,this.effect=new Ir(()=>t(this._value),()=>Pt(this,this.effect._dirtyLevel===2?2:3)),this.effect.computed=this,this.effect.active=this._cacheable=!s,this.__v_isReadonly=r}get value(){const t=J(this);return(!t._cacheable||t.effect.dirty)&&Ze(t._value,t._value=t.effect.run())&&Pt(t,4),jr(t),t.effect._dirtyLevel>=2&&Pt(t,2),t._value}set value(t){this._setter(t)}get _dirty(){return this.effect.dirty}set _dirty(t){this.effect.dirty=t}}function ll(e,t,n=!1){let r,s;const o=q(e);return o?(r=e,s=xe):(r=e.get,s=e.set),new vo(r,s,o||!s,n)}function jr(e){var t;Ye&&ct&&(e=J(e),co(ct,(t=e.dep)!=null?t:e.dep=uo(()=>e.dep=void 0,e instanceof vo?e:void 0)))}function Pt(e,t=4,n){e=J(e);const r=e.dep;r&&ao(r,t)}function de(e){return!!(e&&e.__v_isRef===!0)}function re(e){return bo(e,!1)}function Vr(e){return bo(e,!0)}function bo(e,t){return de(e)?e:new cl(e,t)}class cl{constructor(t,n){this.__v_isShallow=n,this.dep=void 0,this.__v_isRef=!0,this._rawValue=n?t:J(t),this._value=n?t:Dt(t)}get value(){return jr(this),this._value}set value(t){const n=this.__v_isShallow||bn(t)||St(t);t=n?t:J(t),Ze(t,this._rawValue)&&(this._rawValue=t,this._value=n?t:Dt(t),Pt(this,4))}}function wo(e){return de(e)?e.value:e}const al={get:(e,t,n)=>wo(Reflect.get(e,t,n)),set:(e,t,n,r)=>{const s=e[t];return de(s)&&!de(n)?(s.value=n,!0):Reflect.set(e,t,n,r)}};function Eo(e){return wt(e)?e:new Proxy(e,al)}class ul{constructor(t){this.dep=void 0,this.__v_isRef=!0;const{get:n,set:r}=t(()=>jr(this),()=>Pt(this));this._get=n,this._set=r}get value(){return this._get()}set value(t){this._set(t)}}function fl(e){return new ul(e)}class dl{constructor(t,n,r){this._object=t,this._key=n,this._defaultValue=r,this.__v_isRef=!0}get value(){const t=this._object[this._key];return t===void 0?this._defaultValue:t}set value(t){this._object[this._key]=t}get dep(){return Bi(J(this._object),this._key)}}class hl{constructor(t){this._getter=t,this.__v_isRef=!0,this.__v_isReadonly=!0}get value(){return this._getter()}}function pl(e,t,n){return de(e)?e:q(e)?new hl(e):Z(e)&&arguments.length>1?gl(e,t,n):re(e)}function gl(e,t,n){const r=e[t];return de(r)?r:new dl(e,t,n)}/** -* @vue/runtime-core v3.4.21 -* (c) 2018-present Yuxi (Evan) You and Vue contributors -* @license MIT -**/function Je(e,t,n,r){try{return r?e(...r):e()}catch(s){qt(s,t,n)}}function Se(e,t,n,r){if(q(e)){const o=Je(e,t,n,r);return o&&Zs(o)&&o.catch(i=>{qt(i,t,n)}),o}const s=[];for(let o=0;o>>1,s=he[r],o=Ut(s);oPe&&he.splice(t,1)}function vl(e){U(e)?Et.push(...e):(!qe||!qe.includes(e,e.allowRecurse?ot+1:ot))&&Et.push(e),xo()}function us(e,t,n=Bt?Pe+1:0){for(;nUt(n)-Ut(r));if(Et.length=0,qe){qe.push(...t);return}for(qe=t,ot=0;ote.id==null?1/0:e.id,bl=(e,t)=>{const n=Ut(e)-Ut(t);if(n===0){if(e.pre&&!t.pre)return-1;if(t.pre&&!e.pre)return 1}return n};function So(e){pr=!1,Bt=!0,he.sort(bl);try{for(Pe=0;Pese(y)?y.trim():y)),h&&(s=n.map(ur))}let l,c=r[l=hn(t)]||r[l=hn($e(t))];!c&&o&&(c=r[l=hn(ft(t))]),c&&Se(c,e,6,s);const a=r[l+"Once"];if(a){if(!e.emitted)e.emitted={};else if(e.emitted[l])return;e.emitted[l]=!0,Se(a,e,6,s)}}function To(e,t,n=!1){const r=t.emitsCache,s=r.get(e);if(s!==void 0)return s;const o=e.emits;let i={},l=!1;if(!q(e)){const c=a=>{const f=To(a,t,!0);f&&(l=!0,ce(i,f))};!n&&t.mixins.length&&t.mixins.forEach(c),e.extends&&c(e.extends),e.mixins&&e.mixins.forEach(c)}return!o&&!l?(Z(e)&&r.set(e,null),null):(U(o)?o.forEach(c=>i[c]=null):ce(i,o),Z(e)&&r.set(e,i),i)}function Fn(e,t){return!e||!Wt(t)?!1:(t=t.slice(2).replace(/Once$/,""),Y(e,t[0].toLowerCase()+t.slice(1))||Y(e,ft(t))||Y(e,t))}let le=null,$n=null;function En(e){const t=le;return le=e,$n=e&&e.type.__scopeId||null,t}function Qa(e){$n=e}function Za(){$n=null}function El(e,t=le,n){if(!t||e._n)return e;const r=(...s)=>{r._d&&xs(-1);const o=En(t);let i;try{i=e(...s)}finally{En(o),r._d&&xs(1)}return i};return r._n=!0,r._c=!0,r._d=!0,r}function Gn(e){const{type:t,vnode:n,proxy:r,withProxy:s,props:o,propsOptions:[i],slots:l,attrs:c,emit:a,render:f,renderCache:h,data:p,setupState:y,ctx:v,inheritAttrs:I}=e;let N,K;const k=En(e);try{if(n.shapeFlag&4){const _=s||r,M=_;N=Re(f.call(M,_,h,o,y,p,v)),K=c}else{const _=t;N=Re(_.length>1?_(o,{attrs:c,slots:l,emit:a}):_(o,null)),K=t.props?c:Cl(c)}}catch(_){jt.length=0,qt(_,e,1),N=oe(we)}let g=N;if(K&&I!==!1){const _=Object.keys(K),{shapeFlag:M}=g;_.length&&M&7&&(i&&_.some(Tr)&&(K=xl(K,i)),g=et(g,K))}return n.dirs&&(g=et(g),g.dirs=g.dirs?g.dirs.concat(n.dirs):n.dirs),n.transition&&(g.transition=n.transition),N=g,En(k),N}const Cl=e=>{let t;for(const n in e)(n==="class"||n==="style"||Wt(n))&&((t||(t={}))[n]=e[n]);return t},xl=(e,t)=>{const n={};for(const r in e)(!Tr(r)||!(r.slice(9)in t))&&(n[r]=e[r]);return n};function Sl(e,t,n){const{props:r,children:s,component:o}=e,{props:i,children:l,patchFlag:c}=t,a=o.emitsOptions;if(t.dirs||t.transition)return!0;if(n&&c>=0){if(c&1024)return!0;if(c&16)return r?fs(r,i,a):!!i;if(c&8){const f=t.dynamicProps;for(let h=0;he.__isSuspense;function Lo(e,t){t&&t.pendingBranch?U(e)?t.effects.push(...e):t.effects.push(e):vl(e)}const Rl=Symbol.for("v-scx"),Ll=()=>xt(Rl);function Ur(e,t){return Hn(e,null,t)}function nu(e,t){return Hn(e,null,{flush:"post"})}const rn={};function Ne(e,t,n){return Hn(e,t,n)}function Hn(e,t,{immediate:n,deep:r,flush:s,once:o,onTrack:i,onTrigger:l}=ee){if(t&&o){const L=t;t=(...F)=>{L(...F),M()}}const c=ue,a=L=>r===!0?L:lt(L,r===!1?1:void 0);let f,h=!1,p=!1;if(de(e)?(f=()=>e.value,h=bn(e)):wt(e)?(f=()=>a(e),h=!0):U(e)?(p=!0,h=e.some(L=>wt(L)||bn(L)),f=()=>e.map(L=>{if(de(L))return L.value;if(wt(L))return a(L);if(q(L))return Je(L,c,2)})):q(e)?t?f=()=>Je(e,c,2):f=()=>(y&&y(),Se(e,c,3,[v])):f=xe,t&&r){const L=f;f=()=>lt(L())}let y,v=L=>{y=g.onStop=()=>{Je(L,c,4),y=g.onStop=void 0}},I;if(Xt)if(v=xe,t?n&&Se(t,c,3,[f(),p?[]:void 0,v]):f(),s==="sync"){const L=Ll();I=L.__watcherHandles||(L.__watcherHandles=[])}else return xe;let N=p?new Array(e.length).fill(rn):rn;const K=()=>{if(!(!g.active||!g.dirty))if(t){const L=g.run();(r||h||(p?L.some((F,T)=>Ze(F,N[T])):Ze(L,N)))&&(y&&y(),Se(t,c,3,[L,N===rn?void 0:p&&N[0]===rn?[]:N,v]),N=L)}else g.run()};K.allowRecurse=!!t;let k;s==="sync"?k=K:s==="post"?k=()=>me(K,c&&c.suspense):(K.pre=!0,c&&(K.id=c.uid),k=()=>Nn(K));const g=new Ir(f,xe,k),_=oo(),M=()=>{g.stop(),_&&Ar(_.effects,g)};return t?n?K():N=g.run():s==="post"?me(g.run.bind(g),c&&c.suspense):g.run(),I&&I.push(M),M}function Ol(e,t,n){const r=this.proxy,s=se(e)?e.includes(".")?Oo(r,e):()=>r[e]:e.bind(r,r);let o;q(t)?o=t:(o=t.handler,n=t);const i=zt(this),l=Hn(s,o.bind(r),n);return i(),l}function Oo(e,t){const n=t.split(".");return()=>{let r=e;for(let s=0;s0){if(n>=t)return e;n++}if(r=r||new Set,r.has(e))return e;if(r.add(e),de(e))lt(e.value,t,n,r);else if(U(e))for(let s=0;s{lt(s,t,n,r)});else if(to(e))for(const s in e)lt(e[s],t,n,r);return e}function ru(e,t){if(le===null)return e;const n=Un(le)||le.proxy,r=e.dirs||(e.dirs=[]);for(let s=0;s{e.isMounted=!0}),Fo(()=>{e.isUnmounting=!0}),e}const Ee=[Function,Array],Io={mode:String,appear:Boolean,persisted:Boolean,onBeforeEnter:Ee,onEnter:Ee,onAfterEnter:Ee,onEnterCancelled:Ee,onBeforeLeave:Ee,onLeave:Ee,onAfterLeave:Ee,onLeaveCancelled:Ee,onBeforeAppear:Ee,onAppear:Ee,onAfterAppear:Ee,onAppearCancelled:Ee},Ml={name:"BaseTransition",props:Io,setup(e,{slots:t}){const n=Bn(),r=Il();return()=>{const s=t.default&&Po(t.default(),!0);if(!s||!s.length)return;let o=s[0];if(s.length>1){for(const p of s)if(p.type!==we){o=p;break}}const i=J(e),{mode:l}=i;if(r.isLeaving)return zn(o);const c=hs(o);if(!c)return zn(o);const a=gr(c,i,r,n);mr(c,a);const f=n.subTree,h=f&&hs(f);if(h&&h.type!==we&&!it(c,h)){const p=gr(h,i,r,n);if(mr(h,p),l==="out-in")return r.isLeaving=!0,p.afterLeave=()=>{r.isLeaving=!1,n.update.active!==!1&&(n.effect.dirty=!0,n.update())},zn(o);l==="in-out"&&c.type!==we&&(p.delayLeave=(y,v,I)=>{const N=Mo(r,h);N[String(h.key)]=h,y[Ge]=()=>{v(),y[Ge]=void 0,delete a.delayedLeave},a.delayedLeave=I})}return o}}},Pl=Ml;function Mo(e,t){const{leavingVNodes:n}=e;let r=n.get(t.type);return r||(r=Object.create(null),n.set(t.type,r)),r}function gr(e,t,n,r){const{appear:s,mode:o,persisted:i=!1,onBeforeEnter:l,onEnter:c,onAfterEnter:a,onEnterCancelled:f,onBeforeLeave:h,onLeave:p,onAfterLeave:y,onLeaveCancelled:v,onBeforeAppear:I,onAppear:N,onAfterAppear:K,onAppearCancelled:k}=t,g=String(e.key),_=Mo(n,e),M=(T,$)=>{T&&Se(T,r,9,$)},L=(T,$)=>{const E=$[1];M(T,$),U(T)?T.every(j=>j.length<=1)&&E():T.length<=1&&E()},F={mode:o,persisted:i,beforeEnter(T){let $=l;if(!n.isMounted)if(s)$=I||l;else return;T[Ge]&&T[Ge](!0);const E=_[g];E&&it(e,E)&&E.el[Ge]&&E.el[Ge](),M($,[T])},enter(T){let $=c,E=a,j=f;if(!n.isMounted)if(s)$=N||c,E=K||a,j=k||f;else return;let A=!1;const G=T[sn]=ie=>{A||(A=!0,ie?M(j,[T]):M(E,[T]),F.delayedLeave&&F.delayedLeave(),T[sn]=void 0)};$?L($,[T,G]):G()},leave(T,$){const E=String(e.key);if(T[sn]&&T[sn](!0),n.isUnmounting)return $();M(h,[T]);let j=!1;const A=T[Ge]=G=>{j||(j=!0,$(),G?M(v,[T]):M(y,[T]),T[Ge]=void 0,_[E]===e&&delete _[E])};_[E]=e,p?L(p,[T,A]):A()},clone(T){return gr(T,t,n,r)}};return F}function zn(e){if(Gt(e))return e=et(e),e.children=null,e}function hs(e){return Gt(e)?e.children?e.children[0]:void 0:e}function mr(e,t){e.shapeFlag&6&&e.component?mr(e.component.subTree,t):e.shapeFlag&128?(e.ssContent.transition=t.clone(e.ssContent),e.ssFallback.transition=t.clone(e.ssFallback)):e.transition=t}function Po(e,t=!1,n){let r=[],s=0;for(let o=0;o1)for(let o=0;o!!e.type.__asyncLoader;/*! #__NO_SIDE_EFFECTS__ */function su(e){q(e)&&(e={loader:e});const{loader:t,loadingComponent:n,errorComponent:r,delay:s=200,timeout:o,suspensible:i=!0,onError:l}=e;let c=null,a,f=0;const h=()=>(f++,c=null,p()),p=()=>{let y;return c||(y=c=t().catch(v=>{if(v=v instanceof Error?v:new Error(String(v)),l)return new Promise((I,N)=>{l(v,()=>I(h()),()=>N(v),f+1)});throw v}).then(v=>y!==c&&c?c:(v&&(v.__esModule||v[Symbol.toStringTag]==="Module")&&(v=v.default),a=v,v)))};return kr({name:"AsyncComponentWrapper",__asyncLoader:p,get __asyncResolved(){return a},setup(){const y=ue;if(a)return()=>Xn(a,y);const v=k=>{c=null,qt(k,y,13,!r)};if(i&&y.suspense||Xt)return p().then(k=>()=>Xn(k,y)).catch(k=>(v(k),()=>r?oe(r,{error:k}):null));const I=re(!1),N=re(),K=re(!!s);return s&&setTimeout(()=>{K.value=!1},s),o!=null&&setTimeout(()=>{if(!I.value&&!N.value){const k=new Error(`Async component timed out after ${o}ms.`);v(k),N.value=k}},o),p().then(()=>{I.value=!0,y.parent&&Gt(y.parent.vnode)&&(y.parent.effect.dirty=!0,Nn(y.parent.update))}).catch(k=>{v(k),N.value=k}),()=>{if(I.value&&a)return Xn(a,y);if(N.value&&r)return oe(r,{error:N.value});if(n&&!K.value)return oe(n)}}})}function Xn(e,t){const{ref:n,props:r,children:s,ce:o}=t.vnode,i=oe(e,r,s);return i.ref=n,i.ce=o,delete t.vnode.ce,i}const Gt=e=>e.type.__isKeepAlive;function Nl(e,t){No(e,"a",t)}function Fl(e,t){No(e,"da",t)}function No(e,t,n=ue){const r=e.__wdc||(e.__wdc=()=>{let s=n;for(;s;){if(s.isDeactivated)return;s=s.parent}return e()});if(jn(t,r,n),n){let s=n.parent;for(;s&&s.parent;)Gt(s.parent.vnode)&&$l(r,t,n,s),s=s.parent}}function $l(e,t,n,r){const s=jn(t,e,r,!0);Vn(()=>{Ar(r[t],s)},n)}function jn(e,t,n=ue,r=!1){if(n){const s=n[e]||(n[e]=[]),o=t.__weh||(t.__weh=(...i)=>{if(n.isUnmounted)return;dt();const l=zt(n),c=Se(t,n,e,i);return l(),ht(),c});return r?s.unshift(o):s.push(o),o}}const Be=e=>(t,n=ue)=>(!Xt||e==="sp")&&jn(e,(...r)=>t(...r),n),Hl=Be("bm"),Rt=Be("m"),jl=Be("bu"),Vl=Be("u"),Fo=Be("bum"),Vn=Be("um"),Dl=Be("sp"),Bl=Be("rtg"),Ul=Be("rtc");function kl(e,t=ue){jn("ec",e,t)}function ou(e,t,n,r){let s;const o=n&&n[r];if(U(e)||se(e)){s=new Array(e.length);for(let i=0,l=e.length;it(i,l,void 0,o&&o[l]));else{const i=Object.keys(e);s=new Array(i.length);for(let l=0,c=i.length;lSn(t)?!(t.type===we||t.type===ye&&!$o(t.children)):!0)?e:null}function lu(e,t){const n={};for(const r in e)n[t&&/[A-Z]/.test(r)?`on:${r}`:hn(r)]=e[r];return n}const yr=e=>e?ei(e)?Un(e)||e.proxy:yr(e.parent):null,Nt=ce(Object.create(null),{$:e=>e,$el:e=>e.vnode.el,$data:e=>e.data,$props:e=>e.props,$attrs:e=>e.attrs,$slots:e=>e.slots,$refs:e=>e.refs,$parent:e=>yr(e.parent),$root:e=>yr(e.root),$emit:e=>e.emit,$options:e=>Kr(e),$forceUpdate:e=>e.f||(e.f=()=>{e.effect.dirty=!0,Nn(e.update)}),$nextTick:e=>e.n||(e.n=Pn.bind(e.proxy)),$watch:e=>Ol.bind(e)}),Yn=(e,t)=>e!==ee&&!e.__isScriptSetup&&Y(e,t),Kl={get({_:e},t){const{ctx:n,setupState:r,data:s,props:o,accessCache:i,type:l,appContext:c}=e;let a;if(t[0]!=="$"){const y=i[t];if(y!==void 0)switch(y){case 1:return r[t];case 2:return s[t];case 4:return n[t];case 3:return o[t]}else{if(Yn(r,t))return i[t]=1,r[t];if(s!==ee&&Y(s,t))return i[t]=2,s[t];if((a=e.propsOptions[0])&&Y(a,t))return i[t]=3,o[t];if(n!==ee&&Y(n,t))return i[t]=4,n[t];_r&&(i[t]=0)}}const f=Nt[t];let h,p;if(f)return t==="$attrs"&&_e(e,"get",t),f(e);if((h=l.__cssModules)&&(h=h[t]))return h;if(n!==ee&&Y(n,t))return i[t]=4,n[t];if(p=c.config.globalProperties,Y(p,t))return p[t]},set({_:e},t,n){const{data:r,setupState:s,ctx:o}=e;return Yn(s,t)?(s[t]=n,!0):r!==ee&&Y(r,t)?(r[t]=n,!0):Y(e.props,t)||t[0]==="$"&&t.slice(1)in e?!1:(o[t]=n,!0)},has({_:{data:e,setupState:t,accessCache:n,ctx:r,appContext:s,propsOptions:o}},i){let l;return!!n[i]||e!==ee&&Y(e,i)||Yn(t,i)||(l=o[0])&&Y(l,i)||Y(r,i)||Y(Nt,i)||Y(s.config.globalProperties,i)},defineProperty(e,t,n){return n.get!=null?e._.accessCache[t]=0:Y(n,"value")&&this.set(e,t,n.value,null),Reflect.defineProperty(e,t,n)}};function cu(){return Wl().slots}function Wl(){const e=Bn();return e.setupContext||(e.setupContext=ni(e))}function ps(e){return U(e)?e.reduce((t,n)=>(t[n]=null,t),{}):e}let _r=!0;function ql(e){const t=Kr(e),n=e.proxy,r=e.ctx;_r=!1,t.beforeCreate&&gs(t.beforeCreate,e,"bc");const{data:s,computed:o,methods:i,watch:l,provide:c,inject:a,created:f,beforeMount:h,mounted:p,beforeUpdate:y,updated:v,activated:I,deactivated:N,beforeDestroy:K,beforeUnmount:k,destroyed:g,unmounted:_,render:M,renderTracked:L,renderTriggered:F,errorCaptured:T,serverPrefetch:$,expose:E,inheritAttrs:j,components:A,directives:G,filters:ie}=t;if(a&&Gl(a,r,null),i)for(const X in i){const V=i[X];q(V)&&(r[X]=V.bind(n))}if(s){const X=s.call(n,n);Z(X)&&(e.data=In(X))}if(_r=!0,o)for(const X in o){const V=o[X],He=q(V)?V.bind(n,n):q(V.get)?V.get.bind(n,n):xe,Yt=!q(V)&&q(V.set)?V.set.bind(n):xe,tt=ne({get:He,set:Yt});Object.defineProperty(r,X,{enumerable:!0,configurable:!0,get:()=>tt.value,set:Oe=>tt.value=Oe})}if(l)for(const X in l)Ho(l[X],r,n,X);if(c){const X=q(c)?c.call(n):c;Reflect.ownKeys(X).forEach(V=>{Zl(V,X[V])})}f&&gs(f,e,"c");function D(X,V){U(V)?V.forEach(He=>X(He.bind(n))):V&&X(V.bind(n))}if(D(Hl,h),D(Rt,p),D(jl,y),D(Vl,v),D(Nl,I),D(Fl,N),D(kl,T),D(Ul,L),D(Bl,F),D(Fo,k),D(Vn,_),D(Dl,$),U(E))if(E.length){const X=e.exposed||(e.exposed={});E.forEach(V=>{Object.defineProperty(X,V,{get:()=>n[V],set:He=>n[V]=He})})}else e.exposed||(e.exposed={});M&&e.render===xe&&(e.render=M),j!=null&&(e.inheritAttrs=j),A&&(e.components=A),G&&(e.directives=G)}function Gl(e,t,n=xe){U(e)&&(e=vr(e));for(const r in e){const s=e[r];let o;Z(s)?"default"in s?o=xt(s.from||r,s.default,!0):o=xt(s.from||r):o=xt(s),de(o)?Object.defineProperty(t,r,{enumerable:!0,configurable:!0,get:()=>o.value,set:i=>o.value=i}):t[r]=o}}function gs(e,t,n){Se(U(e)?e.map(r=>r.bind(t.proxy)):e.bind(t.proxy),t,n)}function Ho(e,t,n,r){const s=r.includes(".")?Oo(n,r):()=>n[r];if(se(e)){const o=t[e];q(o)&&Ne(s,o)}else if(q(e))Ne(s,e.bind(n));else if(Z(e))if(U(e))e.forEach(o=>Ho(o,t,n,r));else{const o=q(e.handler)?e.handler.bind(n):t[e.handler];q(o)&&Ne(s,o,e)}}function Kr(e){const t=e.type,{mixins:n,extends:r}=t,{mixins:s,optionsCache:o,config:{optionMergeStrategies:i}}=e.appContext,l=o.get(t);let c;return l?c=l:!s.length&&!n&&!r?c=t:(c={},s.length&&s.forEach(a=>Cn(c,a,i,!0)),Cn(c,t,i)),Z(t)&&o.set(t,c),c}function Cn(e,t,n,r=!1){const{mixins:s,extends:o}=t;o&&Cn(e,o,n,!0),s&&s.forEach(i=>Cn(e,i,n,!0));for(const i in t)if(!(r&&i==="expose")){const l=zl[i]||n&&n[i];e[i]=l?l(e[i],t[i]):t[i]}return e}const zl={data:ms,props:ys,emits:ys,methods:It,computed:It,beforeCreate:pe,created:pe,beforeMount:pe,mounted:pe,beforeUpdate:pe,updated:pe,beforeDestroy:pe,beforeUnmount:pe,destroyed:pe,unmounted:pe,activated:pe,deactivated:pe,errorCaptured:pe,serverPrefetch:pe,components:It,directives:It,watch:Yl,provide:ms,inject:Xl};function ms(e,t){return t?e?function(){return ce(q(e)?e.call(this,this):e,q(t)?t.call(this,this):t)}:t:e}function Xl(e,t){return It(vr(e),vr(t))}function vr(e){if(U(e)){const t={};for(let n=0;n1)return n&&q(t)?t.call(r&&r.proxy):t}}function ec(e,t,n,r=!1){const s={},o={};_n(o,Dn,1),e.propsDefaults=Object.create(null),Vo(e,t,s,o);for(const i in e.propsOptions[0])i in s||(s[i]=void 0);n?e.props=r?s:il(s):e.type.props?e.props=s:e.props=o,e.attrs=o}function tc(e,t,n,r){const{props:s,attrs:o,vnode:{patchFlag:i}}=e,l=J(s),[c]=e.propsOptions;let a=!1;if((r||i>0)&&!(i&16)){if(i&8){const f=e.vnode.dynamicProps;for(let h=0;h{c=!0;const[p,y]=Do(h,t,!0);ce(i,p),y&&l.push(...y)};!n&&t.mixins.length&&t.mixins.forEach(f),e.extends&&f(e.extends),e.mixins&&e.mixins.forEach(f)}if(!o&&!c)return Z(e)&&r.set(e,_t),_t;if(U(o))for(let f=0;f-1,y[1]=I<0||v-1||Y(y,"default"))&&l.push(h)}}}const a=[i,l];return Z(e)&&r.set(e,a),a}function _s(e){return e[0]!=="$"&&!bt(e)}function vs(e){return e===null?"null":typeof e=="function"?e.name||"":typeof e=="object"&&e.constructor&&e.constructor.name||""}function bs(e,t){return vs(e)===vs(t)}function ws(e,t){return U(t)?t.findIndex(n=>bs(n,e)):q(t)&&bs(t,e)?0:-1}const Bo=e=>e[0]==="_"||e==="$stable",Wr=e=>U(e)?e.map(Re):[Re(e)],nc=(e,t,n)=>{if(t._n)return t;const r=El((...s)=>Wr(t(...s)),n);return r._c=!1,r},Uo=(e,t,n)=>{const r=e._ctx;for(const s in e){if(Bo(s))continue;const o=e[s];if(q(o))t[s]=nc(s,o,r);else if(o!=null){const i=Wr(o);t[s]=()=>i}}},ko=(e,t)=>{const n=Wr(t);e.slots.default=()=>n},rc=(e,t)=>{if(e.vnode.shapeFlag&32){const n=t._;n?(e.slots=J(t),_n(t,"_",n)):Uo(t,e.slots={})}else e.slots={},t&&ko(e,t);_n(e.slots,Dn,1)},sc=(e,t,n)=>{const{vnode:r,slots:s}=e;let o=!0,i=ee;if(r.shapeFlag&32){const l=t._;l?n&&l===1?o=!1:(ce(s,t),!n&&l===1&&delete s._):(o=!t.$stable,Uo(t,s)),i=t}else t&&(ko(e,t),i={default:1});if(o)for(const l in s)!Bo(l)&&i[l]==null&&delete s[l]};function xn(e,t,n,r,s=!1){if(U(e)){e.forEach((p,y)=>xn(p,t&&(U(t)?t[y]:t),n,r,s));return}if(Ct(r)&&!s)return;const o=r.shapeFlag&4?Un(r.component)||r.component.proxy:r.el,i=s?null:o,{i:l,r:c}=e,a=t&&t.r,f=l.refs===ee?l.refs={}:l.refs,h=l.setupState;if(a!=null&&a!==c&&(se(a)?(f[a]=null,Y(h,a)&&(h[a]=null)):de(a)&&(a.value=null)),q(c))Je(c,l,12,[i,f]);else{const p=se(c),y=de(c);if(p||y){const v=()=>{if(e.f){const I=p?Y(h,c)?h[c]:f[c]:c.value;s?U(I)&&Ar(I,o):U(I)?I.includes(o)||I.push(o):p?(f[c]=[o],Y(h,c)&&(h[c]=f[c])):(c.value=[o],e.k&&(f[e.k]=c.value))}else p?(f[c]=i,Y(h,c)&&(h[c]=i)):y&&(c.value=i,e.k&&(f[e.k]=i))};i?(v.id=-1,me(v,n)):v()}}}let ke=!1;const oc=e=>e.namespaceURI.includes("svg")&&e.tagName!=="foreignObject",ic=e=>e.namespaceURI.includes("MathML"),on=e=>{if(oc(e))return"svg";if(ic(e))return"mathml"},ln=e=>e.nodeType===8;function lc(e){const{mt:t,p:n,o:{patchProp:r,createText:s,nextSibling:o,parentNode:i,remove:l,insert:c,createComment:a}}=e,f=(g,_)=>{if(!_.hasChildNodes()){n(null,g,_),wn(),_._vnode=g;return}ke=!1,h(_.firstChild,g,null,null,null),wn(),_._vnode=g,ke&&console.error("Hydration completed but contains mismatches.")},h=(g,_,M,L,F,T=!1)=>{const $=ln(g)&&g.data==="[",E=()=>I(g,_,M,L,F,$),{type:j,ref:A,shapeFlag:G,patchFlag:ie}=_;let fe=g.nodeType;_.el=g,ie===-2&&(T=!1,_.dynamicChildren=null);let D=null;switch(j){case Tt:fe!==3?_.children===""?(c(_.el=s(""),i(g),g),D=g):D=E():(g.data!==_.children&&(ke=!0,g.data=_.children),D=o(g));break;case we:k(g)?(D=o(g),K(_.el=g.content.firstChild,g,M)):fe!==8||$?D=E():D=o(g);break;case Ht:if($&&(g=o(g),fe=g.nodeType),fe===1||fe===3){D=g;const X=!_.children.length;for(let V=0;V<_.staticCount;V++)X&&(_.children+=D.nodeType===1?D.outerHTML:D.data),V===_.staticCount-1&&(_.anchor=D),D=o(D);return $?o(D):D}else E();break;case ye:$?D=v(g,_,M,L,F,T):D=E();break;default:if(G&1)(fe!==1||_.type.toLowerCase()!==g.tagName.toLowerCase())&&!k(g)?D=E():D=p(g,_,M,L,F,T);else if(G&6){_.slotScopeIds=F;const X=i(g);if($?D=N(g):ln(g)&&g.data==="teleport start"?D=N(g,g.data,"teleport end"):D=o(g),t(_,X,null,M,L,on(X),T),Ct(_)){let V;$?(V=oe(ye),V.anchor=D?D.previousSibling:X.lastChild):V=g.nodeType===3?Zo(""):oe("div"),V.el=g,_.component.subTree=V}}else G&64?fe!==8?D=E():D=_.type.hydrate(g,_,M,L,F,T,e,y):G&128&&(D=_.type.hydrate(g,_,M,L,on(i(g)),F,T,e,h))}return A!=null&&xn(A,null,L,_),D},p=(g,_,M,L,F,T)=>{T=T||!!_.dynamicChildren;const{type:$,props:E,patchFlag:j,shapeFlag:A,dirs:G,transition:ie}=_,fe=$==="input"||$==="option";if(fe||j!==-1){G&&Me(_,null,M,"created");let D=!1;if(k(g)){D=Wo(L,ie)&&M&&M.vnode.props&&M.vnode.props.appear;const V=g.content.firstChild;D&&ie.beforeEnter(V),K(V,g,M),_.el=g=V}if(A&16&&!(E&&(E.innerHTML||E.textContent))){let V=y(g.firstChild,_,g,M,L,F,T);for(;V;){ke=!0;const He=V;V=V.nextSibling,l(He)}}else A&8&&g.textContent!==_.children&&(ke=!0,g.textContent=_.children);if(E)if(fe||!T||j&48)for(const V in E)(fe&&(V.endsWith("value")||V==="indeterminate")||Wt(V)&&!bt(V)||V[0]===".")&&r(g,V,null,E[V],void 0,void 0,M);else E.onClick&&r(g,"onClick",null,E.onClick,void 0,void 0,M);let X;(X=E&&E.onVnodeBeforeMount)&&Ce(X,M,_),G&&Me(_,null,M,"beforeMount"),((X=E&&E.onVnodeMounted)||G||D)&&Lo(()=>{X&&Ce(X,M,_),D&&ie.enter(g),G&&Me(_,null,M,"mounted")},L)}return g.nextSibling},y=(g,_,M,L,F,T,$)=>{$=$||!!_.dynamicChildren;const E=_.children,j=E.length;for(let A=0;A{const{slotScopeIds:$}=_;$&&(F=F?F.concat($):$);const E=i(g),j=y(o(g),_,E,M,L,F,T);return j&&ln(j)&&j.data==="]"?o(_.anchor=j):(ke=!0,c(_.anchor=a("]"),E,j),j)},I=(g,_,M,L,F,T)=>{if(ke=!0,_.el=null,T){const j=N(g);for(;;){const A=o(g);if(A&&A!==j)l(A);else break}}const $=o(g),E=i(g);return l(g),n(null,_,E,$,M,L,on(E),F),$},N=(g,_="[",M="]")=>{let L=0;for(;g;)if(g=o(g),g&&ln(g)&&(g.data===_&&L++,g.data===M)){if(L===0)return o(g);L--}return g},K=(g,_,M)=>{const L=_.parentNode;L&&L.replaceChild(g,_);let F=M;for(;F;)F.vnode.el===_&&(F.vnode.el=F.subTree.el=g),F=F.parent},k=g=>g.nodeType===1&&g.tagName.toLowerCase()==="template";return[f,h]}const me=Lo;function cc(e){return Ko(e)}function ac(e){return Ko(e,lc)}function Ko(e,t){const n=no();n.__VUE__=!0;const{insert:r,remove:s,patchProp:o,createElement:i,createText:l,createComment:c,setText:a,setElementText:f,parentNode:h,nextSibling:p,setScopeId:y=xe,insertStaticContent:v}=e,I=(u,d,m,b=null,w=null,S=null,O=void 0,x=null,R=!!d.dynamicChildren)=>{if(u===d)return;u&&!it(u,d)&&(b=Jt(u),Oe(u,w,S,!0),u=null),d.patchFlag===-2&&(R=!1,d.dynamicChildren=null);const{type:C,ref:P,shapeFlag:B}=d;switch(C){case Tt:N(u,d,m,b);break;case we:K(u,d,m,b);break;case Ht:u==null&&k(d,m,b,O);break;case ye:A(u,d,m,b,w,S,O,x,R);break;default:B&1?M(u,d,m,b,w,S,O,x,R):B&6?G(u,d,m,b,w,S,O,x,R):(B&64||B&128)&&C.process(u,d,m,b,w,S,O,x,R,pt)}P!=null&&w&&xn(P,u&&u.ref,S,d||u,!d)},N=(u,d,m,b)=>{if(u==null)r(d.el=l(d.children),m,b);else{const w=d.el=u.el;d.children!==u.children&&a(w,d.children)}},K=(u,d,m,b)=>{u==null?r(d.el=c(d.children||""),m,b):d.el=u.el},k=(u,d,m,b)=>{[u.el,u.anchor]=v(u.children,d,m,b,u.el,u.anchor)},g=({el:u,anchor:d},m,b)=>{let w;for(;u&&u!==d;)w=p(u),r(u,m,b),u=w;r(d,m,b)},_=({el:u,anchor:d})=>{let m;for(;u&&u!==d;)m=p(u),s(u),u=m;s(d)},M=(u,d,m,b,w,S,O,x,R)=>{d.type==="svg"?O="svg":d.type==="math"&&(O="mathml"),u==null?L(d,m,b,w,S,O,x,R):$(u,d,w,S,O,x,R)},L=(u,d,m,b,w,S,O,x)=>{let R,C;const{props:P,shapeFlag:B,transition:H,dirs:W}=u;if(R=u.el=i(u.type,S,P&&P.is,P),B&8?f(R,u.children):B&16&&T(u.children,R,null,b,w,Jn(u,S),O,x),W&&Me(u,null,b,"created"),F(R,u,u.scopeId,O,b),P){for(const Q in P)Q!=="value"&&!bt(Q)&&o(R,Q,null,P[Q],S,u.children,b,w,je);"value"in P&&o(R,"value",null,P.value,S),(C=P.onVnodeBeforeMount)&&Ce(C,b,u)}W&&Me(u,null,b,"beforeMount");const z=Wo(w,H);z&&H.beforeEnter(R),r(R,d,m),((C=P&&P.onVnodeMounted)||z||W)&&me(()=>{C&&Ce(C,b,u),z&&H.enter(R),W&&Me(u,null,b,"mounted")},w)},F=(u,d,m,b,w)=>{if(m&&y(u,m),b)for(let S=0;S{for(let C=R;C{const x=d.el=u.el;let{patchFlag:R,dynamicChildren:C,dirs:P}=d;R|=u.patchFlag&16;const B=u.props||ee,H=d.props||ee;let W;if(m&&nt(m,!1),(W=H.onVnodeBeforeUpdate)&&Ce(W,m,d,u),P&&Me(d,u,m,"beforeUpdate"),m&&nt(m,!0),C?E(u.dynamicChildren,C,x,m,b,Jn(d,w),S):O||V(u,d,x,null,m,b,Jn(d,w),S,!1),R>0){if(R&16)j(x,d,B,H,m,b,w);else if(R&2&&B.class!==H.class&&o(x,"class",null,H.class,w),R&4&&o(x,"style",B.style,H.style,w),R&8){const z=d.dynamicProps;for(let Q=0;Q{W&&Ce(W,m,d,u),P&&Me(d,u,m,"updated")},b)},E=(u,d,m,b,w,S,O)=>{for(let x=0;x{if(m!==b){if(m!==ee)for(const x in m)!bt(x)&&!(x in b)&&o(u,x,m[x],null,O,d.children,w,S,je);for(const x in b){if(bt(x))continue;const R=b[x],C=m[x];R!==C&&x!=="value"&&o(u,x,C,R,O,d.children,w,S,je)}"value"in b&&o(u,"value",m.value,b.value,O)}},A=(u,d,m,b,w,S,O,x,R)=>{const C=d.el=u?u.el:l(""),P=d.anchor=u?u.anchor:l("");let{patchFlag:B,dynamicChildren:H,slotScopeIds:W}=d;W&&(x=x?x.concat(W):W),u==null?(r(C,m,b),r(P,m,b),T(d.children||[],m,P,w,S,O,x,R)):B>0&&B&64&&H&&u.dynamicChildren?(E(u.dynamicChildren,H,m,w,S,O,x),(d.key!=null||w&&d===w.subTree)&&qr(u,d,!0)):V(u,d,m,P,w,S,O,x,R)},G=(u,d,m,b,w,S,O,x,R)=>{d.slotScopeIds=x,u==null?d.shapeFlag&512?w.ctx.activate(d,m,b,O,R):ie(d,m,b,w,S,O,R):fe(u,d,R)},ie=(u,d,m,b,w,S,O)=>{const x=u.component=bc(u,b,w);if(Gt(u)&&(x.ctx.renderer=pt),wc(x),x.asyncDep){if(w&&w.registerDep(x,D),!u.el){const R=x.subTree=oe(we);K(null,R,d,m)}}else D(x,u,d,m,w,S,O)},fe=(u,d,m)=>{const b=d.component=u.component;if(Sl(u,d,m))if(b.asyncDep&&!b.asyncResolved){X(b,d,m);return}else b.next=d,_l(b.update),b.effect.dirty=!0,b.update();else d.el=u.el,b.vnode=d},D=(u,d,m,b,w,S,O)=>{const x=()=>{if(u.isMounted){let{next:P,bu:B,u:H,parent:W,vnode:z}=u;{const gt=qo(u);if(gt){P&&(P.el=z.el,X(u,P,O)),gt.asyncDep.then(()=>{u.isUnmounted||x()});return}}let Q=P,te;nt(u,!1),P?(P.el=z.el,X(u,P,O)):P=z,B&&pn(B),(te=P.props&&P.props.onVnodeBeforeUpdate)&&Ce(te,W,P,z),nt(u,!0);const ae=Gn(u),Ae=u.subTree;u.subTree=ae,I(Ae,ae,h(Ae.el),Jt(Ae),u,w,S),P.el=ae.el,Q===null&&Tl(u,ae.el),H&&me(H,w),(te=P.props&&P.props.onVnodeUpdated)&&me(()=>Ce(te,W,P,z),w)}else{let P;const{el:B,props:H}=d,{bm:W,m:z,parent:Q}=u,te=Ct(d);if(nt(u,!1),W&&pn(W),!te&&(P=H&&H.onVnodeBeforeMount)&&Ce(P,Q,d),nt(u,!0),B&&Wn){const ae=()=>{u.subTree=Gn(u),Wn(B,u.subTree,u,w,null)};te?d.type.__asyncLoader().then(()=>!u.isUnmounted&&ae()):ae()}else{const ae=u.subTree=Gn(u);I(null,ae,m,b,u,w,S),d.el=ae.el}if(z&&me(z,w),!te&&(P=H&&H.onVnodeMounted)){const ae=d;me(()=>Ce(P,Q,ae),w)}(d.shapeFlag&256||Q&&Ct(Q.vnode)&&Q.vnode.shapeFlag&256)&&u.a&&me(u.a,w),u.isMounted=!0,d=m=b=null}},R=u.effect=new Ir(x,xe,()=>Nn(C),u.scope),C=u.update=()=>{R.dirty&&R.run()};C.id=u.uid,nt(u,!0),C()},X=(u,d,m)=>{d.component=u;const b=u.vnode.props;u.vnode=d,u.next=null,tc(u,d.props,b,m),sc(u,d.children,m),dt(),us(u),ht()},V=(u,d,m,b,w,S,O,x,R=!1)=>{const C=u&&u.children,P=u?u.shapeFlag:0,B=d.children,{patchFlag:H,shapeFlag:W}=d;if(H>0){if(H&128){Yt(C,B,m,b,w,S,O,x,R);return}else if(H&256){He(C,B,m,b,w,S,O,x,R);return}}W&8?(P&16&&je(C,w,S),B!==C&&f(m,B)):P&16?W&16?Yt(C,B,m,b,w,S,O,x,R):je(C,w,S,!0):(P&8&&f(m,""),W&16&&T(B,m,b,w,S,O,x,R))},He=(u,d,m,b,w,S,O,x,R)=>{u=u||_t,d=d||_t;const C=u.length,P=d.length,B=Math.min(C,P);let H;for(H=0;HP?je(u,w,S,!0,!1,B):T(d,m,b,w,S,O,x,R,B)},Yt=(u,d,m,b,w,S,O,x,R)=>{let C=0;const P=d.length;let B=u.length-1,H=P-1;for(;C<=B&&C<=H;){const W=u[C],z=d[C]=R?ze(d[C]):Re(d[C]);if(it(W,z))I(W,z,m,null,w,S,O,x,R);else break;C++}for(;C<=B&&C<=H;){const W=u[B],z=d[H]=R?ze(d[H]):Re(d[H]);if(it(W,z))I(W,z,m,null,w,S,O,x,R);else break;B--,H--}if(C>B){if(C<=H){const W=H+1,z=WH)for(;C<=B;)Oe(u[C],w,S,!0),C++;else{const W=C,z=C,Q=new Map;for(C=z;C<=H;C++){const ve=d[C]=R?ze(d[C]):Re(d[C]);ve.key!=null&&Q.set(ve.key,C)}let te,ae=0;const Ae=H-z+1;let gt=!1,Zr=0;const Lt=new Array(Ae);for(C=0;C=Ae){Oe(ve,w,S,!0);continue}let Ie;if(ve.key!=null)Ie=Q.get(ve.key);else for(te=z;te<=H;te++)if(Lt[te-z]===0&&it(ve,d[te])){Ie=te;break}Ie===void 0?Oe(ve,w,S,!0):(Lt[Ie-z]=C+1,Ie>=Zr?Zr=Ie:gt=!0,I(ve,d[Ie],m,null,w,S,O,x,R),ae++)}const es=gt?uc(Lt):_t;for(te=es.length-1,C=Ae-1;C>=0;C--){const ve=z+C,Ie=d[ve],ts=ve+1{const{el:S,type:O,transition:x,children:R,shapeFlag:C}=u;if(C&6){tt(u.component.subTree,d,m,b);return}if(C&128){u.suspense.move(d,m,b);return}if(C&64){O.move(u,d,m,pt);return}if(O===ye){r(S,d,m);for(let B=0;Bx.enter(S),w);else{const{leave:B,delayLeave:H,afterLeave:W}=x,z=()=>r(S,d,m),Q=()=>{B(S,()=>{z(),W&&W()})};H?H(S,z,Q):Q()}else r(S,d,m)},Oe=(u,d,m,b=!1,w=!1)=>{const{type:S,props:O,ref:x,children:R,dynamicChildren:C,shapeFlag:P,patchFlag:B,dirs:H}=u;if(x!=null&&xn(x,null,m,u,!0),P&256){d.ctx.deactivate(u);return}const W=P&1&&H,z=!Ct(u);let Q;if(z&&(Q=O&&O.onVnodeBeforeUnmount)&&Ce(Q,d,u),P&6)xi(u.component,m,b);else{if(P&128){u.suspense.unmount(m,b);return}W&&Me(u,null,d,"beforeUnmount"),P&64?u.type.remove(u,d,m,w,pt,b):C&&(S!==ye||B>0&&B&64)?je(C,d,m,!1,!0):(S===ye&&B&384||!w&&P&16)&&je(R,d,m),b&&Jr(u)}(z&&(Q=O&&O.onVnodeUnmounted)||W)&&me(()=>{Q&&Ce(Q,d,u),W&&Me(u,null,d,"unmounted")},m)},Jr=u=>{const{type:d,el:m,anchor:b,transition:w}=u;if(d===ye){Ci(m,b);return}if(d===Ht){_(u);return}const S=()=>{s(m),w&&!w.persisted&&w.afterLeave&&w.afterLeave()};if(u.shapeFlag&1&&w&&!w.persisted){const{leave:O,delayLeave:x}=w,R=()=>O(m,S);x?x(u.el,S,R):R()}else S()},Ci=(u,d)=>{let m;for(;u!==d;)m=p(u),s(u),u=m;s(d)},xi=(u,d,m)=>{const{bum:b,scope:w,update:S,subTree:O,um:x}=u;b&&pn(b),w.stop(),S&&(S.active=!1,Oe(O,u,d,m)),x&&me(x,d),me(()=>{u.isUnmounted=!0},d),d&&d.pendingBranch&&!d.isUnmounted&&u.asyncDep&&!u.asyncResolved&&u.suspenseId===d.pendingId&&(d.deps--,d.deps===0&&d.resolve())},je=(u,d,m,b=!1,w=!1,S=0)=>{for(let O=S;Ou.shapeFlag&6?Jt(u.component.subTree):u.shapeFlag&128?u.suspense.next():p(u.anchor||u.el);let kn=!1;const Qr=(u,d,m)=>{u==null?d._vnode&&Oe(d._vnode,null,null,!0):I(d._vnode||null,u,d,null,null,null,m),kn||(kn=!0,us(),wn(),kn=!1),d._vnode=u},pt={p:I,um:Oe,m:tt,r:Jr,mt:ie,mc:T,pc:V,pbc:E,n:Jt,o:e};let Kn,Wn;return t&&([Kn,Wn]=t(pt)),{render:Qr,hydrate:Kn,createApp:Ql(Qr,Kn)}}function Jn({type:e,props:t},n){return n==="svg"&&e==="foreignObject"||n==="mathml"&&e==="annotation-xml"&&t&&t.encoding&&t.encoding.includes("html")?void 0:n}function nt({effect:e,update:t},n){e.allowRecurse=t.allowRecurse=n}function Wo(e,t){return(!e||e&&!e.pendingBranch)&&t&&!t.persisted}function qr(e,t,n=!1){const r=e.children,s=t.children;if(U(r)&&U(s))for(let o=0;o>1,e[n[l]]0&&(t[r]=n[o-1]),n[o]=r)}}for(o=n.length,i=n[o-1];o-- >0;)n[o]=i,i=t[i];return n}function qo(e){const t=e.subTree.component;if(t)return t.asyncDep&&!t.asyncResolved?t:qo(t)}const fc=e=>e.__isTeleport,$t=e=>e&&(e.disabled||e.disabled===""),Es=e=>typeof SVGElement<"u"&&e instanceof SVGElement,Cs=e=>typeof MathMLElement=="function"&&e instanceof MathMLElement,wr=(e,t)=>{const n=e&&e.to;return se(n)?t?t(n):null:n},dc={name:"Teleport",__isTeleport:!0,process(e,t,n,r,s,o,i,l,c,a){const{mc:f,pc:h,pbc:p,o:{insert:y,querySelector:v,createText:I,createComment:N}}=a,K=$t(t.props);let{shapeFlag:k,children:g,dynamicChildren:_}=t;if(e==null){const M=t.el=I(""),L=t.anchor=I("");y(M,n,r),y(L,n,r);const F=t.target=wr(t.props,v),T=t.targetAnchor=I("");F&&(y(T,F),i==="svg"||Es(F)?i="svg":(i==="mathml"||Cs(F))&&(i="mathml"));const $=(E,j)=>{k&16&&f(g,E,j,s,o,i,l,c)};K?$(n,L):F&&$(F,T)}else{t.el=e.el;const M=t.anchor=e.anchor,L=t.target=e.target,F=t.targetAnchor=e.targetAnchor,T=$t(e.props),$=T?n:L,E=T?M:F;if(i==="svg"||Es(L)?i="svg":(i==="mathml"||Cs(L))&&(i="mathml"),_?(p(e.dynamicChildren,_,$,s,o,i,l),qr(e,t,!0)):c||h(e,t,$,E,s,o,i,l,!1),K)T?t.props&&e.props&&t.props.to!==e.props.to&&(t.props.to=e.props.to):cn(t,n,M,a,1);else if((t.props&&t.props.to)!==(e.props&&e.props.to)){const j=t.target=wr(t.props,v);j&&cn(t,j,null,a,0)}else T&&cn(t,L,F,a,1)}Go(t)},remove(e,t,n,r,{um:s,o:{remove:o}},i){const{shapeFlag:l,children:c,anchor:a,targetAnchor:f,target:h,props:p}=e;if(h&&o(f),i&&o(a),l&16){const y=i||!$t(p);for(let v=0;v0?Le||_t:null,pc(),kt>0&&Le&&Le.push(e),e}function uu(e,t,n,r,s,o){return Xo(Qo(e,t,n,r,s,o,!0))}function Yo(e,t,n,r,s){return Xo(oe(e,t,n,r,s,!0))}function Sn(e){return e?e.__v_isVNode===!0:!1}function it(e,t){return e.type===t.type&&e.key===t.key}const Dn="__vInternal",Jo=({key:e})=>e??null,gn=({ref:e,ref_key:t,ref_for:n})=>(typeof e=="number"&&(e=""+e),e!=null?se(e)||de(e)||q(e)?{i:le,r:e,k:t,f:!!n}:e:null);function Qo(e,t=null,n=null,r=0,s=null,o=e===ye?0:1,i=!1,l=!1){const c={__v_isVNode:!0,__v_skip:!0,type:e,props:t,key:t&&Jo(t),ref:t&&gn(t),scopeId:$n,slotScopeIds:null,children:n,component:null,suspense:null,ssContent:null,ssFallback:null,dirs:null,transition:null,el:null,anchor:null,target:null,targetAnchor:null,staticCount:0,shapeFlag:o,patchFlag:r,dynamicProps:s,dynamicChildren:null,appContext:null,ctx:le};return l?(Gr(c,n),o&128&&e.normalize(c)):n&&(c.shapeFlag|=se(n)?8:16),kt>0&&!i&&Le&&(c.patchFlag>0||o&6)&&c.patchFlag!==32&&Le.push(c),c}const oe=gc;function gc(e,t=null,n=null,r=0,s=null,o=!1){if((!e||e===Ao)&&(e=we),Sn(e)){const l=et(e,t,!0);return n&&Gr(l,n),kt>0&&!o&&Le&&(l.shapeFlag&6?Le[Le.indexOf(e)]=l:Le.push(l)),l.patchFlag|=-2,l}if(Sc(e)&&(e=e.__vccOpts),t){t=mc(t);let{class:l,style:c}=t;l&&!se(l)&&(t.class=Or(l)),Z(c)&&(_o(c)&&!U(c)&&(c=ce({},c)),t.style=Lr(c))}const i=se(e)?1:Al(e)?128:fc(e)?64:Z(e)?4:q(e)?2:0;return Qo(e,t,n,r,s,i,o,!0)}function mc(e){return e?_o(e)||Dn in e?ce({},e):e:null}function et(e,t,n=!1){const{props:r,ref:s,patchFlag:o,children:i}=e,l=t?yc(r||{},t):r;return{__v_isVNode:!0,__v_skip:!0,type:e.type,props:l,key:l&&Jo(l),ref:t&&t.ref?n&&s?U(s)?s.concat(gn(t)):[s,gn(t)]:gn(t):s,scopeId:e.scopeId,slotScopeIds:e.slotScopeIds,children:i,target:e.target,targetAnchor:e.targetAnchor,staticCount:e.staticCount,shapeFlag:e.shapeFlag,patchFlag:t&&e.type!==ye?o===-1?16:o|16:o,dynamicProps:e.dynamicProps,dynamicChildren:e.dynamicChildren,appContext:e.appContext,dirs:e.dirs,transition:e.transition,component:e.component,suspense:e.suspense,ssContent:e.ssContent&&et(e.ssContent),ssFallback:e.ssFallback&&et(e.ssFallback),el:e.el,anchor:e.anchor,ctx:e.ctx,ce:e.ce}}function Zo(e=" ",t=0){return oe(Tt,null,e,t)}function fu(e,t){const n=oe(Ht,null,e);return n.staticCount=t,n}function du(e="",t=!1){return t?(zo(),Yo(we,null,e)):oe(we,null,e)}function Re(e){return e==null||typeof e=="boolean"?oe(we):U(e)?oe(ye,null,e.slice()):typeof e=="object"?ze(e):oe(Tt,null,String(e))}function ze(e){return e.el===null&&e.patchFlag!==-1||e.memo?e:et(e)}function Gr(e,t){let n=0;const{shapeFlag:r}=e;if(t==null)t=null;else if(U(t))n=16;else if(typeof t=="object")if(r&65){const s=t.default;s&&(s._c&&(s._d=!1),Gr(e,s()),s._c&&(s._d=!0));return}else{n=32;const s=t._;!s&&!(Dn in t)?t._ctx=le:s===3&&le&&(le.slots._===1?t._=1:(t._=2,e.patchFlag|=1024))}else q(t)?(t={default:t,_ctx:le},n=32):(t=String(t),r&64?(n=16,t=[Zo(t)]):n=8);e.children=t,e.shapeFlag|=n}function yc(...e){const t={};for(let n=0;nue||le;let Tn,Er;{const e=no(),t=(n,r)=>{let s;return(s=e[n])||(s=e[n]=[]),s.push(r),o=>{s.length>1?s.forEach(i=>i(o)):s[0](o)}};Tn=t("__VUE_INSTANCE_SETTERS__",n=>ue=n),Er=t("__VUE_SSR_SETTERS__",n=>Xt=n)}const zt=e=>{const t=ue;return Tn(e),e.scope.on(),()=>{e.scope.off(),Tn(t)}},Ss=()=>{ue&&ue.scope.off(),Tn(null)};function ei(e){return e.vnode.shapeFlag&4}let Xt=!1;function wc(e,t=!1){t&&Er(t);const{props:n,children:r}=e.vnode,s=ei(e);ec(e,n,s,t),rc(e,r);const o=s?Ec(e,t):void 0;return t&&Er(!1),o}function Ec(e,t){const n=e.type;e.accessCache=Object.create(null),e.proxy=Mt(new Proxy(e.ctx,Kl));const{setup:r}=n;if(r){const s=e.setupContext=r.length>1?ni(e):null,o=zt(e);dt();const i=Je(r,e,0,[e.props,s]);if(ht(),o(),Zs(i)){if(i.then(Ss,Ss),t)return i.then(l=>{Ts(e,l,t)}).catch(l=>{qt(l,e,0)});e.asyncDep=i}else Ts(e,i,t)}else ti(e,t)}function Ts(e,t,n){q(t)?e.type.__ssrInlineRender?e.ssrRender=t:e.render=t:Z(t)&&(e.setupState=Eo(t)),ti(e,n)}let As;function ti(e,t,n){const r=e.type;if(!e.render){if(!t&&As&&!r.render){const s=r.template||Kr(e).template;if(s){const{isCustomElement:o,compilerOptions:i}=e.appContext.config,{delimiters:l,compilerOptions:c}=r,a=ce(ce({isCustomElement:o,delimiters:l},i),c);r.render=As(s,a)}}e.render=r.render||xe}{const s=zt(e);dt();try{ql(e)}finally{ht(),s()}}}function Cc(e){return e.attrsProxy||(e.attrsProxy=new Proxy(e.attrs,{get(t,n){return _e(e,"get","$attrs"),t[n]}}))}function ni(e){const t=n=>{e.exposed=n||{}};return{get attrs(){return Cc(e)},slots:e.slots,emit:e.emit,expose:t}}function Un(e){if(e.exposed)return e.exposeProxy||(e.exposeProxy=new Proxy(Eo(Mt(e.exposed)),{get(t,n){if(n in t)return t[n];if(n in Nt)return Nt[n](e)},has(t,n){return n in t||n in Nt}}))}function xc(e,t=!0){return q(e)?e.displayName||e.name:e.name||t&&e.__name}function Sc(e){return q(e)&&"__vccOpts"in e}const ne=(e,t)=>ll(e,t,Xt);function Cr(e,t,n){const r=arguments.length;return r===2?Z(t)&&!U(t)?Sn(t)?oe(e,null,[t]):oe(e,t):oe(e,null,t):(r>3?n=Array.prototype.slice.call(arguments,2):r===3&&Sn(n)&&(n=[n]),oe(e,t,n))}const Tc="3.4.21";/** -* @vue/runtime-dom v3.4.21 -* (c) 2018-present Yuxi (Evan) You and Vue contributors -* @license MIT -**/const Ac="http://www.w3.org/2000/svg",Rc="http://www.w3.org/1998/Math/MathML",Xe=typeof document<"u"?document:null,Rs=Xe&&Xe.createElement("template"),Lc={insert:(e,t,n)=>{t.insertBefore(e,n||null)},remove:e=>{const t=e.parentNode;t&&t.removeChild(e)},createElement:(e,t,n,r)=>{const s=t==="svg"?Xe.createElementNS(Ac,e):t==="mathml"?Xe.createElementNS(Rc,e):Xe.createElement(e,n?{is:n}:void 0);return e==="select"&&r&&r.multiple!=null&&s.setAttribute("multiple",r.multiple),s},createText:e=>Xe.createTextNode(e),createComment:e=>Xe.createComment(e),setText:(e,t)=>{e.nodeValue=t},setElementText:(e,t)=>{e.textContent=t},parentNode:e=>e.parentNode,nextSibling:e=>e.nextSibling,querySelector:e=>Xe.querySelector(e),setScopeId(e,t){e.setAttribute(t,"")},insertStaticContent(e,t,n,r,s,o){const i=n?n.previousSibling:t.lastChild;if(s&&(s===o||s.nextSibling))for(;t.insertBefore(s.cloneNode(!0),n),!(s===o||!(s=s.nextSibling)););else{Rs.innerHTML=r==="svg"?`${e}`:r==="mathml"?`${e}`:e;const l=Rs.content;if(r==="svg"||r==="mathml"){const c=l.firstChild;for(;c.firstChild;)l.appendChild(c.firstChild);l.removeChild(c)}t.insertBefore(l,n)}return[i?i.nextSibling:t.firstChild,n?n.previousSibling:t.lastChild]}},Ke="transition",Ot="animation",Kt=Symbol("_vtc"),ri=(e,{slots:t})=>Cr(Pl,Oc(e),t);ri.displayName="Transition";const si={name:String,type:String,css:{type:Boolean,default:!0},duration:[String,Number,Object],enterFromClass:String,enterActiveClass:String,enterToClass:String,appearFromClass:String,appearActiveClass:String,appearToClass:String,leaveFromClass:String,leaveActiveClass:String,leaveToClass:String};ri.props=ce({},Io,si);const rt=(e,t=[])=>{U(e)?e.forEach(n=>n(...t)):e&&e(...t)},Ls=e=>e?U(e)?e.some(t=>t.length>1):e.length>1:!1;function Oc(e){const t={};for(const A in e)A in si||(t[A]=e[A]);if(e.css===!1)return t;const{name:n="v",type:r,duration:s,enterFromClass:o=`${n}-enter-from`,enterActiveClass:i=`${n}-enter-active`,enterToClass:l=`${n}-enter-to`,appearFromClass:c=o,appearActiveClass:a=i,appearToClass:f=l,leaveFromClass:h=`${n}-leave-from`,leaveActiveClass:p=`${n}-leave-active`,leaveToClass:y=`${n}-leave-to`}=e,v=Ic(s),I=v&&v[0],N=v&&v[1],{onBeforeEnter:K,onEnter:k,onEnterCancelled:g,onLeave:_,onLeaveCancelled:M,onBeforeAppear:L=K,onAppear:F=k,onAppearCancelled:T=g}=t,$=(A,G,ie)=>{st(A,G?f:l),st(A,G?a:i),ie&&ie()},E=(A,G)=>{A._isLeaving=!1,st(A,h),st(A,y),st(A,p),G&&G()},j=A=>(G,ie)=>{const fe=A?F:k,D=()=>$(G,A,ie);rt(fe,[G,D]),Os(()=>{st(G,A?c:o),We(G,A?f:l),Ls(fe)||Is(G,r,I,D)})};return ce(t,{onBeforeEnter(A){rt(K,[A]),We(A,o),We(A,i)},onBeforeAppear(A){rt(L,[A]),We(A,c),We(A,a)},onEnter:j(!1),onAppear:j(!0),onLeave(A,G){A._isLeaving=!0;const ie=()=>E(A,G);We(A,h),Nc(),We(A,p),Os(()=>{A._isLeaving&&(st(A,h),We(A,y),Ls(_)||Is(A,r,N,ie))}),rt(_,[A,ie])},onEnterCancelled(A){$(A,!1),rt(g,[A])},onAppearCancelled(A){$(A,!0),rt(T,[A])},onLeaveCancelled(A){E(A),rt(M,[A])}})}function Ic(e){if(e==null)return null;if(Z(e))return[Qn(e.enter),Qn(e.leave)];{const t=Qn(e);return[t,t]}}function Qn(e){return Oi(e)}function We(e,t){t.split(/\s+/).forEach(n=>n&&e.classList.add(n)),(e[Kt]||(e[Kt]=new Set)).add(t)}function st(e,t){t.split(/\s+/).forEach(r=>r&&e.classList.remove(r));const n=e[Kt];n&&(n.delete(t),n.size||(e[Kt]=void 0))}function Os(e){requestAnimationFrame(()=>{requestAnimationFrame(e)})}let Mc=0;function Is(e,t,n,r){const s=e._endId=++Mc,o=()=>{s===e._endId&&r()};if(n)return setTimeout(o,n);const{type:i,timeout:l,propCount:c}=Pc(e,t);if(!i)return r();const a=i+"end";let f=0;const h=()=>{e.removeEventListener(a,p),o()},p=y=>{y.target===e&&++f>=c&&h()};setTimeout(()=>{f(n[v]||"").split(", "),s=r(`${Ke}Delay`),o=r(`${Ke}Duration`),i=Ms(s,o),l=r(`${Ot}Delay`),c=r(`${Ot}Duration`),a=Ms(l,c);let f=null,h=0,p=0;t===Ke?i>0&&(f=Ke,h=i,p=o.length):t===Ot?a>0&&(f=Ot,h=a,p=c.length):(h=Math.max(i,a),f=h>0?i>a?Ke:Ot:null,p=f?f===Ke?o.length:c.length:0);const y=f===Ke&&/\b(transform|all)(,|$)/.test(r(`${Ke}Property`).toString());return{type:f,timeout:h,propCount:p,hasTransform:y}}function Ms(e,t){for(;e.lengthPs(n)+Ps(e[r])))}function Ps(e){return e==="auto"?0:Number(e.slice(0,-1).replace(",","."))*1e3}function Nc(){return document.body.offsetHeight}function Fc(e,t,n){const r=e[Kt];r&&(t=(t?[t,...r]:[...r]).join(" ")),t==null?e.removeAttribute("class"):n?e.setAttribute("class",t):e.className=t}const Ns=Symbol("_vod"),$c=Symbol("_vsh"),Hc=Symbol(""),jc=/(^|;)\s*display\s*:/;function Vc(e,t,n){const r=e.style,s=se(n);let o=!1;if(n&&!s){if(t)if(se(t))for(const i of t.split(";")){const l=i.slice(0,i.indexOf(":")).trim();n[l]==null&&mn(r,l,"")}else for(const i in t)n[i]==null&&mn(r,i,"");for(const i in n)i==="display"&&(o=!0),mn(r,i,n[i])}else if(s){if(t!==n){const i=r[Hc];i&&(n+=";"+i),r.cssText=n,o=jc.test(n)}}else t&&e.removeAttribute("style");Ns in e&&(e[Ns]=o?r.display:"",e[$c]&&(r.display="none"))}const Fs=/\s*!important$/;function mn(e,t,n){if(U(n))n.forEach(r=>mn(e,t,r));else if(n==null&&(n=""),t.startsWith("--"))e.setProperty(t,n);else{const r=Dc(e,t);Fs.test(n)?e.setProperty(ft(r),n.replace(Fs,""),"important"):e[r]=n}}const $s=["Webkit","Moz","ms"],Zn={};function Dc(e,t){const n=Zn[t];if(n)return n;let r=$e(t);if(r!=="filter"&&r in e)return Zn[t]=r;r=Ln(r);for(let s=0;s<$s.length;s++){const o=$s[s]+r;if(o in e)return Zn[t]=o}return t}const Hs="http://www.w3.org/1999/xlink";function Bc(e,t,n,r,s){if(r&&t.startsWith("xlink:"))n==null?e.removeAttributeNS(Hs,t.slice(6,t.length)):e.setAttributeNS(Hs,t,n);else{const o=$i(t);n==null||o&&!ro(n)?e.removeAttribute(t):e.setAttribute(t,o?"":n)}}function Uc(e,t,n,r,s,o,i){if(t==="innerHTML"||t==="textContent"){r&&i(r,s,o),e[t]=n??"";return}const l=e.tagName;if(t==="value"&&l!=="PROGRESS"&&!l.includes("-")){const a=l==="OPTION"?e.getAttribute("value")||"":e.value,f=n??"";(a!==f||!("_value"in e))&&(e.value=f),n==null&&e.removeAttribute(t),e._value=n;return}let c=!1;if(n===""||n==null){const a=typeof e[t];a==="boolean"?n=ro(n):n==null&&a==="string"?(n="",c=!0):a==="number"&&(n=0,c=!0)}try{e[t]=n}catch{}c&&e.removeAttribute(t)}function mt(e,t,n,r){e.addEventListener(t,n,r)}function kc(e,t,n,r){e.removeEventListener(t,n,r)}const js=Symbol("_vei");function Kc(e,t,n,r,s=null){const o=e[js]||(e[js]={}),i=o[t];if(r&&i)i.value=r;else{const[l,c]=Wc(t);if(r){const a=o[t]=zc(r,s);mt(e,l,a,c)}else i&&(kc(e,l,i,c),o[t]=void 0)}}const Vs=/(?:Once|Passive|Capture)$/;function Wc(e){let t;if(Vs.test(e)){t={};let r;for(;r=e.match(Vs);)e=e.slice(0,e.length-r[0].length),t[r[0].toLowerCase()]=!0}return[e[2]===":"?e.slice(3):ft(e.slice(2)),t]}let er=0;const qc=Promise.resolve(),Gc=()=>er||(qc.then(()=>er=0),er=Date.now());function zc(e,t){const n=r=>{if(!r._vts)r._vts=Date.now();else if(r._vts<=n.attached)return;Se(Xc(r,n.value),t,5,[r])};return n.value=e,n.attached=Gc(),n}function Xc(e,t){if(U(t)){const n=e.stopImmediatePropagation;return e.stopImmediatePropagation=()=>{n.call(e),e._stopped=!0},t.map(r=>s=>!s._stopped&&r&&r(s))}else return t}const Ds=e=>e.charCodeAt(0)===111&&e.charCodeAt(1)===110&&e.charCodeAt(2)>96&&e.charCodeAt(2)<123,Yc=(e,t,n,r,s,o,i,l,c)=>{const a=s==="svg";t==="class"?Fc(e,r,a):t==="style"?Vc(e,n,r):Wt(t)?Tr(t)||Kc(e,t,n,r,i):(t[0]==="."?(t=t.slice(1),!0):t[0]==="^"?(t=t.slice(1),!1):Jc(e,t,r,a))?Uc(e,t,r,o,i,l,c):(t==="true-value"?e._trueValue=r:t==="false-value"&&(e._falseValue=r),Bc(e,t,r,a))};function Jc(e,t,n,r){if(r)return!!(t==="innerHTML"||t==="textContent"||t in e&&Ds(t)&&q(n));if(t==="spellcheck"||t==="draggable"||t==="translate"||t==="form"||t==="list"&&e.tagName==="INPUT"||t==="type"&&e.tagName==="TEXTAREA")return!1;if(t==="width"||t==="height"){const s=e.tagName;if(s==="IMG"||s==="VIDEO"||s==="CANVAS"||s==="SOURCE")return!1}return Ds(t)&&se(n)?!1:t in e}const Bs=e=>{const t=e.props["onUpdate:modelValue"]||!1;return U(t)?n=>pn(t,n):t};function Qc(e){e.target.composing=!0}function Us(e){const t=e.target;t.composing&&(t.composing=!1,t.dispatchEvent(new Event("input")))}const tr=Symbol("_assign"),hu={created(e,{modifiers:{lazy:t,trim:n,number:r}},s){e[tr]=Bs(s);const o=r||s.props&&s.props.type==="number";mt(e,t?"change":"input",i=>{if(i.target.composing)return;let l=e.value;n&&(l=l.trim()),o&&(l=ur(l)),e[tr](l)}),n&&mt(e,"change",()=>{e.value=e.value.trim()}),t||(mt(e,"compositionstart",Qc),mt(e,"compositionend",Us),mt(e,"change",Us))},mounted(e,{value:t}){e.value=t??""},beforeUpdate(e,{value:t,modifiers:{lazy:n,trim:r,number:s}},o){if(e[tr]=Bs(o),e.composing)return;const i=s||e.type==="number"?ur(e.value):e.value,l=t??"";i!==l&&(document.activeElement===e&&e.type!=="range"&&(n||r&&e.value.trim()===l)||(e.value=l))}},Zc=["ctrl","shift","alt","meta"],ea={stop:e=>e.stopPropagation(),prevent:e=>e.preventDefault(),self:e=>e.target!==e.currentTarget,ctrl:e=>!e.ctrlKey,shift:e=>!e.shiftKey,alt:e=>!e.altKey,meta:e=>!e.metaKey,left:e=>"button"in e&&e.button!==0,middle:e=>"button"in e&&e.button!==1,right:e=>"button"in e&&e.button!==2,exact:(e,t)=>Zc.some(n=>e[`${n}Key`]&&!t.includes(n))},pu=(e,t)=>{const n=e._withMods||(e._withMods={}),r=t.join(".");return n[r]||(n[r]=(s,...o)=>{for(let i=0;i{const n=e._withKeys||(e._withKeys={}),r=t.join(".");return n[r]||(n[r]=s=>{if(!("key"in s))return;const o=ft(s.key);if(t.some(i=>i===o||ta[i]===o))return e(s)})},oi=ce({patchProp:Yc},Lc);let Vt,ks=!1;function na(){return Vt||(Vt=cc(oi))}function ra(){return Vt=ks?Vt:ac(oi),ks=!0,Vt}const mu=(...e)=>{const t=na().createApp(...e),{mount:n}=t;return t.mount=r=>{const s=li(r);if(!s)return;const o=t._component;!q(o)&&!o.render&&!o.template&&(o.template=s.innerHTML),s.innerHTML="";const i=n(s,!1,ii(s));return s instanceof Element&&(s.removeAttribute("v-cloak"),s.setAttribute("data-v-app","")),i},t},yu=(...e)=>{const t=ra().createApp(...e),{mount:n}=t;return t.mount=r=>{const s=li(r);if(s)return n(s,!0,ii(s))},t};function ii(e){if(e instanceof SVGElement)return"svg";if(typeof MathMLElement=="function"&&e instanceof MathMLElement)return"mathml"}function li(e){return se(e)?document.querySelector(e):e}const _u=(e,t)=>{const n=e.__vccOpts||e;for(const[r,s]of t)n[r]=s;return n},vu="/BioMarkovChains.jl/dev/logo.png",sa="modulepreload",oa=function(e){return"/BioMarkovChains.jl/dev/"+e},Ks={},bu=function(t,n,r){let s=Promise.resolve();if(n&&n.length>0){const o=document.getElementsByTagName("link"),i=document.querySelector("meta[property=csp-nonce]"),l=(i==null?void 0:i.nonce)||(i==null?void 0:i.getAttribute("nonce"));s=Promise.all(n.map(c=>{if(c=oa(c),c in Ks)return;Ks[c]=!0;const a=c.endsWith(".css"),f=a?'[rel="stylesheet"]':"";if(!!r)for(let y=o.length-1;y>=0;y--){const v=o[y];if(v.href===c&&(!a||v.rel==="stylesheet"))return}else if(document.querySelector(`link[href="${c}"]${f}`))return;const p=document.createElement("link");if(p.rel=a?"stylesheet":sa,a||(p.as="script",p.crossOrigin=""),p.href=c,l&&p.setAttribute("nonce",l),document.head.appendChild(p),a)return new Promise((y,v)=>{p.addEventListener("load",y),p.addEventListener("error",()=>v(new Error(`Unable to preload CSS for ${c}`)))})}))}return s.then(()=>t()).catch(o=>{const i=new Event("vite:preloadError",{cancelable:!0});if(i.payload=o,window.dispatchEvent(i),!i.defaultPrevented)throw o})},ia=window.__VP_SITE_DATA__;function zr(e){return oo()?(Vi(e),!0):!1}function Fe(e){return typeof e=="function"?e():wo(e)}const ci=typeof window<"u"&&typeof document<"u";typeof WorkerGlobalScope<"u"&&globalThis instanceof WorkerGlobalScope;const la=Object.prototype.toString,ca=e=>la.call(e)==="[object Object]",Qe=()=>{},xr=aa();function aa(){var e,t;return ci&&((e=window==null?void 0:window.navigator)==null?void 0:e.userAgent)&&(/iP(ad|hone|od)/.test(window.navigator.userAgent)||((t=window==null?void 0:window.navigator)==null?void 0:t.maxTouchPoints)>2&&/iPad|Macintosh/.test(window==null?void 0:window.navigator.userAgent))}function ua(e,t){function n(...r){return new Promise((s,o)=>{Promise.resolve(e(()=>t.apply(this,r),{fn:t,thisArg:this,args:r})).then(s).catch(o)})}return n}const ai=e=>e();function fa(e,t={}){let n,r,s=Qe;const o=l=>{clearTimeout(l),s(),s=Qe};return l=>{const c=Fe(e),a=Fe(t.maxWait);return n&&o(n),c<=0||a!==void 0&&a<=0?(r&&(o(r),r=null),Promise.resolve(l())):new Promise((f,h)=>{s=t.rejectOnCancel?h:f,a&&!r&&(r=setTimeout(()=>{n&&o(n),r=null,f(l())},a)),n=setTimeout(()=>{r&&o(r),r=null,f(l())},c)})}}function da(e=ai){const t=re(!0);function n(){t.value=!1}function r(){t.value=!0}const s=(...o)=>{t.value&&e(...o)};return{isActive:Mn(t),pause:n,resume:r,eventFilter:s}}function ha(e){return e||Bn()}function ui(...e){if(e.length!==1)return pl(...e);const t=e[0];return typeof t=="function"?Mn(fl(()=>({get:t,set:Qe}))):re(t)}function fi(e,t,n={}){const{eventFilter:r=ai,...s}=n;return Ne(e,ua(r,t),s)}function pa(e,t,n={}){const{eventFilter:r,...s}=n,{eventFilter:o,pause:i,resume:l,isActive:c}=da(r);return{stop:fi(e,t,{...s,eventFilter:o}),pause:i,resume:l,isActive:c}}function Xr(e,t=!0,n){ha()?Rt(e,n):t?e():Pn(e)}function wu(e,t,n={}){const{debounce:r=0,maxWait:s=void 0,...o}=n;return fi(e,t,{...o,eventFilter:fa(r,{maxWait:s})})}function Eu(e,t,n){let r;de(n)?r={evaluating:n}:r=n||{};const{lazy:s=!1,evaluating:o=void 0,shallow:i=!0,onError:l=Qe}=r,c=re(!s),a=i?Vr(t):re(t);let f=0;return Ur(async h=>{if(!c.value)return;f++;const p=f;let y=!1;o&&Promise.resolve().then(()=>{o.value=!0});try{const v=await e(I=>{h(()=>{o&&(o.value=!1),y||I()})});p===f&&(a.value=v)}catch(v){l(v)}finally{o&&p===f&&(o.value=!1),y=!0}}),s?ne(()=>(c.value=!0,a.value)):a}function yt(e){var t;const n=Fe(e);return(t=n==null?void 0:n.$el)!=null?t:n}const Te=ci?window:void 0;function De(...e){let t,n,r,s;if(typeof e[0]=="string"||Array.isArray(e[0])?([n,r,s]=e,t=Te):[t,n,r,s]=e,!t)return Qe;Array.isArray(n)||(n=[n]),Array.isArray(r)||(r=[r]);const o=[],i=()=>{o.forEach(f=>f()),o.length=0},l=(f,h,p,y)=>(f.addEventListener(h,p,y),()=>f.removeEventListener(h,p,y)),c=Ne(()=>[yt(t),Fe(s)],([f,h])=>{if(i(),!f)return;const p=ca(h)?{...h}:h;o.push(...n.flatMap(y=>r.map(v=>l(f,y,v,p))))},{immediate:!0,flush:"post"}),a=()=>{c(),i()};return zr(a),a}let Ws=!1;function Cu(e,t,n={}){const{window:r=Te,ignore:s=[],capture:o=!0,detectIframe:i=!1}=n;if(!r)return Qe;xr&&!Ws&&(Ws=!0,Array.from(r.document.body.children).forEach(p=>p.addEventListener("click",Qe)),r.document.documentElement.addEventListener("click",Qe));let l=!0;const c=p=>s.some(y=>{if(typeof y=="string")return Array.from(r.document.querySelectorAll(y)).some(v=>v===p.target||p.composedPath().includes(v));{const v=yt(y);return v&&(p.target===v||p.composedPath().includes(v))}}),f=[De(r,"click",p=>{const y=yt(e);if(!(!y||y===p.target||p.composedPath().includes(y))){if(p.detail===0&&(l=!c(p)),!l){l=!0;return}t(p)}},{passive:!0,capture:o}),De(r,"pointerdown",p=>{const y=yt(e);l=!c(p)&&!!(y&&!p.composedPath().includes(y))},{passive:!0}),i&&De(r,"blur",p=>{setTimeout(()=>{var y;const v=yt(e);((y=r.document.activeElement)==null?void 0:y.tagName)==="IFRAME"&&!(v!=null&&v.contains(r.document.activeElement))&&t(p)},0)})].filter(Boolean);return()=>f.forEach(p=>p())}function ga(e){return typeof e=="function"?e:typeof e=="string"?t=>t.key===e:Array.isArray(e)?t=>e.includes(t.key):()=>!0}function xu(...e){let t,n,r={};e.length===3?(t=e[0],n=e[1],r=e[2]):e.length===2?typeof e[1]=="object"?(t=!0,n=e[0],r=e[1]):(t=e[0],n=e[1]):(t=!0,n=e[0]);const{target:s=Te,eventName:o="keydown",passive:i=!1,dedupe:l=!1}=r,c=ga(t);return De(s,o,f=>{f.repeat&&Fe(l)||c(f)&&n(f)},i)}function ma(){const e=re(!1),t=Bn();return t&&Rt(()=>{e.value=!0},t),e}function ya(e){const t=ma();return ne(()=>(t.value,!!e()))}function di(e,t={}){const{window:n=Te}=t,r=ya(()=>n&&"matchMedia"in n&&typeof n.matchMedia=="function");let s;const o=re(!1),i=a=>{o.value=a.matches},l=()=>{s&&("removeEventListener"in s?s.removeEventListener("change",i):s.removeListener(i))},c=Ur(()=>{r.value&&(l(),s=n.matchMedia(Fe(e)),"addEventListener"in s?s.addEventListener("change",i):s.addListener(i),o.value=s.matches)});return zr(()=>{c(),l(),s=void 0}),o}const an=typeof globalThis<"u"?globalThis:typeof window<"u"?window:typeof global<"u"?global:typeof self<"u"?self:{},un="__vueuse_ssr_handlers__",_a=va();function va(){return un in an||(an[un]=an[un]||{}),an[un]}function hi(e,t){return _a[e]||t}function ba(e){return e==null?"any":e instanceof Set?"set":e instanceof Map?"map":e instanceof Date?"date":typeof e=="boolean"?"boolean":typeof e=="string"?"string":typeof e=="object"?"object":Number.isNaN(e)?"any":"number"}const wa={boolean:{read:e=>e==="true",write:e=>String(e)},object:{read:e=>JSON.parse(e),write:e=>JSON.stringify(e)},number:{read:e=>Number.parseFloat(e),write:e=>String(e)},any:{read:e=>e,write:e=>String(e)},string:{read:e=>e,write:e=>String(e)},map:{read:e=>new Map(JSON.parse(e)),write:e=>JSON.stringify(Array.from(e.entries()))},set:{read:e=>new Set(JSON.parse(e)),write:e=>JSON.stringify(Array.from(e))},date:{read:e=>new Date(e),write:e=>e.toISOString()}},qs="vueuse-storage";function Yr(e,t,n,r={}){var s;const{flush:o="pre",deep:i=!0,listenToStorageChanges:l=!0,writeDefaults:c=!0,mergeDefaults:a=!1,shallow:f,window:h=Te,eventFilter:p,onError:y=E=>{console.error(E)},initOnMounted:v}=r,I=(f?Vr:re)(typeof t=="function"?t():t);if(!n)try{n=hi("getDefaultStorage",()=>{var E;return(E=Te)==null?void 0:E.localStorage})()}catch(E){y(E)}if(!n)return I;const N=Fe(t),K=ba(N),k=(s=r.serializer)!=null?s:wa[K],{pause:g,resume:_}=pa(I,()=>L(I.value),{flush:o,deep:i,eventFilter:p});h&&l&&Xr(()=>{De(h,"storage",T),De(h,qs,$),v&&T()}),v||T();function M(E,j){h&&h.dispatchEvent(new CustomEvent(qs,{detail:{key:e,oldValue:E,newValue:j,storageArea:n}}))}function L(E){try{const j=n.getItem(e);if(E==null)M(j,null),n.removeItem(e);else{const A=k.write(E);j!==A&&(n.setItem(e,A),M(j,A))}}catch(j){y(j)}}function F(E){const j=E?E.newValue:n.getItem(e);if(j==null)return c&&N!=null&&n.setItem(e,k.write(N)),N;if(!E&&a){const A=k.read(j);return typeof a=="function"?a(A,N):K==="object"&&!Array.isArray(A)?{...N,...A}:A}else return typeof j!="string"?j:k.read(j)}function T(E){if(!(E&&E.storageArea!==n)){if(E&&E.key==null){I.value=N;return}if(!(E&&E.key!==e)){g();try{(E==null?void 0:E.newValue)!==k.write(I.value)&&(I.value=F(E))}catch(j){y(j)}finally{E?Pn(_):_()}}}}function $(E){T(E.detail)}return I}function pi(e){return di("(prefers-color-scheme: dark)",e)}function Ea(e={}){const{selector:t="html",attribute:n="class",initialValue:r="auto",window:s=Te,storage:o,storageKey:i="vueuse-color-scheme",listenToStorageChanges:l=!0,storageRef:c,emitAuto:a,disableTransition:f=!0}=e,h={auto:"",light:"light",dark:"dark",...e.modes||{}},p=pi({window:s}),y=ne(()=>p.value?"dark":"light"),v=c||(i==null?ui(r):Yr(i,r,o,{window:s,listenToStorageChanges:l})),I=ne(()=>v.value==="auto"?y.value:v.value),N=hi("updateHTMLAttrs",(_,M,L)=>{const F=typeof _=="string"?s==null?void 0:s.document.querySelector(_):yt(_);if(!F)return;let T;if(f&&(T=s.document.createElement("style"),T.appendChild(document.createTextNode("*,*::before,*::after{-webkit-transition:none!important;-moz-transition:none!important;-o-transition:none!important;-ms-transition:none!important;transition:none!important}")),s.document.head.appendChild(T)),M==="class"){const $=L.split(/\s/g);Object.values(h).flatMap(E=>(E||"").split(/\s/g)).filter(Boolean).forEach(E=>{$.includes(E)?F.classList.add(E):F.classList.remove(E)})}else F.setAttribute(M,L);f&&(s.getComputedStyle(T).opacity,document.head.removeChild(T))});function K(_){var M;N(t,n,(M=h[_])!=null?M:_)}function k(_){e.onChanged?e.onChanged(_,K):K(_)}Ne(I,k,{flush:"post",immediate:!0}),Xr(()=>k(I.value));const g=ne({get(){return a?v.value:I.value},set(_){v.value=_}});try{return Object.assign(g,{store:v,system:y,state:I})}catch{return g}}function Ca(e={}){const{valueDark:t="dark",valueLight:n="",window:r=Te}=e,s=Ea({...e,onChanged:(l,c)=>{var a;e.onChanged?(a=e.onChanged)==null||a.call(e,l==="dark",c,l):c(l)},modes:{dark:t,light:n}}),o=ne(()=>s.system?s.system.value:pi({window:r}).value?"dark":"light");return ne({get(){return s.value==="dark"},set(l){const c=l?"dark":"light";o.value===c?s.value="auto":s.value=c}})}function nr(e){return typeof Window<"u"&&e instanceof Window?e.document.documentElement:typeof Document<"u"&&e instanceof Document?e.documentElement:e}function Su(e,t,n={}){const{window:r=Te}=n;return Yr(e,t,r==null?void 0:r.localStorage,n)}function gi(e){const t=window.getComputedStyle(e);if(t.overflowX==="scroll"||t.overflowY==="scroll"||t.overflowX==="auto"&&e.clientWidth1?!0:(t.preventDefault&&t.preventDefault(),!1)}const fn=new WeakMap;function Tu(e,t=!1){const n=re(t);let r=null;Ne(ui(e),i=>{const l=nr(Fe(i));if(l){const c=l;fn.get(c)||fn.set(c,c.style.overflow),n.value&&(c.style.overflow="hidden")}},{immediate:!0});const s=()=>{const i=nr(Fe(e));!i||n.value||(xr&&(r=De(i,"touchmove",l=>{xa(l)},{passive:!1})),i.style.overflow="hidden",n.value=!0)},o=()=>{var i;const l=nr(Fe(e));!l||!n.value||(xr&&(r==null||r()),l.style.overflow=(i=fn.get(l))!=null?i:"",fn.delete(l),n.value=!1)};return zr(o),ne({get(){return n.value},set(i){i?s():o()}})}function Au(e,t,n={}){const{window:r=Te}=n;return Yr(e,t,r==null?void 0:r.sessionStorage,n)}function Ru(e={}){const{window:t=Te,behavior:n="auto"}=e;if(!t)return{x:re(0),y:re(0)};const r=re(t.scrollX),s=re(t.scrollY),o=ne({get(){return r.value},set(l){scrollTo({left:l,behavior:n})}}),i=ne({get(){return s.value},set(l){scrollTo({top:l,behavior:n})}});return De(t,"scroll",()=>{r.value=t.scrollX,s.value=t.scrollY},{capture:!1,passive:!0}),{x:o,y:i}}function Lu(e={}){const{window:t=Te,initialWidth:n=Number.POSITIVE_INFINITY,initialHeight:r=Number.POSITIVE_INFINITY,listenOrientation:s=!0,includeScrollbar:o=!0}=e,i=re(n),l=re(r),c=()=>{t&&(o?(i.value=t.innerWidth,l.value=t.innerHeight):(i.value=t.document.documentElement.clientWidth,l.value=t.document.documentElement.clientHeight))};if(c(),Xr(c),De("resize",c,{passive:!0}),s){const a=di("(orientation: portrait)");Ne(a,()=>c())}return{width:i,height:l}}var rr={BASE_URL:"/BioMarkovChains.jl/dev/",MODE:"production",DEV:!1,PROD:!0,SSR:!1},sr={};const mi=/^(?:[a-z]+:|\/\/)/i,Sa="vitepress-theme-appearance",Ta=/#.*$/,Aa=/[?#].*$/,Ra=/(?:(^|\/)index)?\.(?:md|html)$/,ge=typeof document<"u",yi={relativePath:"",filePath:"",title:"404",description:"Not Found",headers:[],frontmatter:{sidebar:!1,layout:"page"},lastUpdated:0,isNotFound:!0};function La(e,t,n=!1){if(t===void 0)return!1;if(e=Gs(`/${e}`),n)return new RegExp(t).test(e);if(Gs(t)!==e)return!1;const r=t.match(Ta);return r?(ge?location.hash:"")===r[0]:!0}function Gs(e){return decodeURI(e).replace(Aa,"").replace(Ra,"$1")}function Oa(e){return mi.test(e)}function Ia(e,t){var r,s,o,i,l,c,a;const n=Object.keys(e.locales).find(f=>f!=="root"&&!Oa(f)&&La(t,`/${f}/`,!0))||"root";return Object.assign({},e,{localeIndex:n,lang:((r=e.locales[n])==null?void 0:r.lang)??e.lang,dir:((s=e.locales[n])==null?void 0:s.dir)??e.dir,title:((o=e.locales[n])==null?void 0:o.title)??e.title,titleTemplate:((i=e.locales[n])==null?void 0:i.titleTemplate)??e.titleTemplate,description:((l=e.locales[n])==null?void 0:l.description)??e.description,head:vi(e.head,((c=e.locales[n])==null?void 0:c.head)??[]),themeConfig:{...e.themeConfig,...(a=e.locales[n])==null?void 0:a.themeConfig}})}function _i(e,t){const n=t.title||e.title,r=t.titleTemplate??e.titleTemplate;if(typeof r=="string"&&r.includes(":title"))return r.replace(/:title/g,n);const s=Ma(e.title,r);return n===s.slice(3)?n:`${n}${s}`}function Ma(e,t){return t===!1?"":t===!0||t===void 0?` | ${e}`:e===t?"":` | ${t}`}function Pa(e,t){const[n,r]=t;if(n!=="meta")return!1;const s=Object.entries(r)[0];return s==null?!1:e.some(([o,i])=>o===n&&i[s[0]]===s[1])}function vi(e,t){return[...e.filter(n=>!Pa(t,n)),...t]}const Na=/[\u0000-\u001F"#$&*+,:;<=>?[\]^`{|}\u007F]/g,Fa=/^[a-z]:/i;function zs(e){const t=Fa.exec(e),n=t?t[0]:"";return n+e.slice(n.length).replace(Na,"_").replace(/(^|\/)_+(?=[^/]*$)/,"$1")}const or=new Set;function $a(e){if(or.size===0){const n=typeof process=="object"&&(sr==null?void 0:sr.VITE_EXTRA_EXTENSIONS)||(rr==null?void 0:rr.VITE_EXTRA_EXTENSIONS)||"";("3g2,3gp,aac,ai,apng,au,avif,bin,bmp,cer,class,conf,crl,css,csv,dll,doc,eps,epub,exe,gif,gz,ics,ief,jar,jpe,jpeg,jpg,js,json,jsonld,m4a,man,mid,midi,mjs,mov,mp2,mp3,mp4,mpe,mpeg,mpg,mpp,oga,ogg,ogv,ogx,opus,otf,p10,p7c,p7m,p7s,pdf,png,ps,qt,roff,rtf,rtx,ser,svg,t,tif,tiff,tr,ts,tsv,ttf,txt,vtt,wav,weba,webm,webp,woff,woff2,xhtml,xml,yaml,yml,zip"+(n&&typeof n=="string"?","+n:"")).split(",").forEach(r=>or.add(r))}const t=e.split(".").pop();return t==null||!or.has(t.toLowerCase())}function Ou(e){return e.replace(/[|\\{}()[\]^$+*?.]/g,"\\$&").replace(/-/g,"\\x2d")}const Ha=Symbol(),ut=Vr(ia);function Iu(e){const t=ne(()=>Ia(ut.value,e.data.relativePath)),n=t.value.appearance,r=n==="force-dark"?re(!0):n?Ca({storageKey:Sa,initialValue:()=>typeof n=="string"?n:"auto",...typeof n=="object"?n:{}}):re(!1),s=re(ge?location.hash:"");return ge&&window.addEventListener("hashchange",()=>{s.value=location.hash}),Ne(()=>e.data,()=>{s.value=ge?location.hash:""}),{site:t,theme:ne(()=>t.value.themeConfig),page:ne(()=>e.data),frontmatter:ne(()=>e.data.frontmatter),params:ne(()=>e.data.params),lang:ne(()=>t.value.lang),dir:ne(()=>e.data.frontmatter.dir||t.value.dir),localeIndex:ne(()=>t.value.localeIndex||"root"),title:ne(()=>_i(t.value,e.data)),description:ne(()=>e.data.description||t.value.description),isDark:r,hash:ne(()=>s.value)}}function ja(){const e=xt(Ha);if(!e)throw new Error("vitepress data not properly injected in app");return e}function Va(e,t){return`${e}${t}`.replace(/\/+/g,"/")}function Xs(e){return mi.test(e)||!e.startsWith("/")?e:Va(ut.value.base,e)}function Da(e){let t=e.replace(/\.html$/,"");if(t=decodeURIComponent(t),t=t.replace(/\/$/,"/index"),ge){const n="/BioMarkovChains.jl/dev/";t=zs(t.slice(n.length).replace(/\//g,"_")||"index")+".md";let r=__VP_HASH_MAP__[t.toLowerCase()];if(r||(t=t.endsWith("_index.md")?t.slice(0,-9)+".md":t.slice(0,-3)+"_index.md",r=__VP_HASH_MAP__[t.toLowerCase()]),!r)return null;t=`${n}assets/${t}.${r}.js`}else t=`./${zs(t.slice(1).replace(/\//g,"_"))}.md.js`;return t}let yn=[];function Mu(e){yn.push(e),Vn(()=>{yn=yn.filter(t=>t!==e)})}function Ba(){let e=ut.value.scrollOffset,t=0,n=24;if(typeof e=="object"&&"padding"in e&&(n=e.padding,e=e.selector),typeof e=="number")t=e;else if(typeof e=="string")t=Ys(e,n);else if(Array.isArray(e))for(const r of e){const s=Ys(r,n);if(s){t=s;break}}return t}function Ys(e,t){const n=document.querySelector(e);if(!n)return 0;const r=n.getBoundingClientRect().bottom;return r<0?0:r+t}const Ua=Symbol(),bi="http://a.com",ka=()=>({path:"/",component:null,data:yi});function Pu(e,t){const n=In(ka()),r={route:n,go:s};async function s(l=ge?location.href:"/"){var c,a;l=ir(l),await((c=r.onBeforeRouteChange)==null?void 0:c.call(r,l))!==!1&&(ge&&l!==ir(location.href)&&(history.replaceState({scrollPosition:window.scrollY},document.title),history.pushState(null,"",l)),await i(l),await((a=r.onAfterRouteChanged)==null?void 0:a.call(r,l)))}let o=null;async function i(l,c=0,a=!1){var p;if(await((p=r.onBeforePageLoad)==null?void 0:p.call(r,l))===!1)return;const f=new URL(l,bi),h=o=f.pathname;try{let y=await e(h);if(!y)throw new Error(`Page not found: ${h}`);if(o===h){o=null;const{default:v,__pageData:I}=y;if(!v)throw new Error(`Invalid route component: ${v}`);n.path=ge?h:Xs(h),n.component=Mt(v),n.data=Mt(I),ge&&Pn(()=>{let N=ut.value.base+I.relativePath.replace(/(?:(^|\/)index)?\.md$/,"$1");if(!ut.value.cleanUrls&&!N.endsWith("/")&&(N+=".html"),N!==f.pathname&&(f.pathname=N,l=N+f.search+f.hash,history.replaceState(null,"",l)),f.hash&&!c){let K=null;try{K=document.getElementById(decodeURIComponent(f.hash).slice(1))}catch(k){console.warn(k)}if(K){Js(K,f.hash);return}}window.scrollTo(0,c)})}}catch(y){if(!/fetch|Page not found/.test(y.message)&&!/^\/404(\.html|\/)?$/.test(l)&&console.error(y),!a)try{const v=await fetch(ut.value.base+"hashmap.json");window.__VP_HASH_MAP__=await v.json(),await i(l,c,!0);return}catch{}o===h&&(o=null,n.path=ge?h:Xs(h),n.component=t?Mt(t):null,n.data=yi)}}return ge&&(window.addEventListener("click",l=>{if(l.target.closest("button"))return;const a=l.target.closest("a");if(a&&!a.closest(".vp-raw")&&(a instanceof SVGElement||!a.download)){const{target:f}=a,{href:h,origin:p,pathname:y,hash:v,search:I}=new URL(a.href instanceof SVGAnimatedString?a.href.animVal:a.href,a.baseURI),N=new URL(location.href);!l.ctrlKey&&!l.shiftKey&&!l.altKey&&!l.metaKey&&!f&&p===N.origin&&$a(y)&&(l.preventDefault(),y===N.pathname&&I===N.search?(v!==N.hash&&(history.pushState(null,"",h),window.dispatchEvent(new HashChangeEvent("hashchange",{oldURL:N.href,newURL:h}))),v?Js(a,v,a.classList.contains("header-anchor")):window.scrollTo(0,0)):s(h))}},{capture:!0}),window.addEventListener("popstate",async l=>{var c;await i(ir(location.href),l.state&&l.state.scrollPosition||0),(c=r.onAfterRouteChanged)==null||c.call(r,location.href)}),window.addEventListener("hashchange",l=>{l.preventDefault()})),r}function Ka(){const e=xt(Ua);if(!e)throw new Error("useRouter() is called without provider.");return e}function wi(){return Ka().route}function Js(e,t,n=!1){let r=null;try{r=e.classList.contains("header-anchor")?e:document.getElementById(decodeURIComponent(t).slice(1))}catch(s){console.warn(s)}if(r){let s=function(){!n||Math.abs(i-window.scrollY)>window.innerHeight?window.scrollTo(0,i):window.scrollTo({left:0,top:i,behavior:"smooth"})};const o=parseInt(window.getComputedStyle(r).paddingTop,10),i=window.scrollY+r.getBoundingClientRect().top-Ba()+o;requestAnimationFrame(s)}}function ir(e){const t=new URL(e,bi);return t.pathname=t.pathname.replace(/(^|\/)index(\.html)?$/,"$1"),ut.value.cleanUrls?t.pathname=t.pathname.replace(/\.html$/,""):!t.pathname.endsWith("/")&&!t.pathname.endsWith(".html")&&(t.pathname+=".html"),t.pathname+t.search+t.hash}const lr=()=>yn.forEach(e=>e()),Nu=kr({name:"VitePressContent",props:{as:{type:[Object,String],default:"div"}},setup(e){const t=wi(),{site:n}=ja();return()=>Cr(e.as,n.value.contentProps??{style:{position:"relative"}},[t.component?Cr(t.component,{onVnodeMounted:lr,onVnodeUpdated:lr,onVnodeUnmounted:lr}):"404 Page Not Found"])}}),Fu=kr({setup(e,{slots:t}){const n=re(!1);return Rt(()=>{n.value=!0}),()=>n.value&&t.default?t.default():null}});function $u(){ge&&window.addEventListener("click",e=>{var n;const t=e.target;if(t.matches(".vp-code-group input")){const r=(n=t.parentElement)==null?void 0:n.parentElement;if(!r)return;const s=Array.from(r.querySelectorAll("input")).indexOf(t);if(s<0)return;const o=r.querySelector(".blocks");if(!o)return;const i=Array.from(o.children).find(a=>a.classList.contains("active"));if(!i)return;const l=o.children[s];if(!l||i===l)return;i.classList.remove("active"),l.classList.add("active");const c=r==null?void 0:r.querySelector(`label[for="${t.id}"]`);c==null||c.scrollIntoView({block:"nearest"})}})}function Hu(){if(ge){const e=new WeakMap;window.addEventListener("click",t=>{var r;const n=t.target;if(n.matches('div[class*="language-"] > button.copy')){const s=n.parentElement,o=(r=n.nextElementSibling)==null?void 0:r.nextElementSibling;if(!s||!o)return;const i=/language-(shellscript|shell|bash|sh|zsh)/.test(s.className),l=[".vp-copy-ignore",".diff.remove"],c=o.cloneNode(!0);c.querySelectorAll(l.join(",")).forEach(f=>f.remove());let a=c.textContent||"";i&&(a=a.replace(/^ *(\$|>) /gm,"").trim()),Wa(a).then(()=>{n.classList.add("copied"),clearTimeout(e.get(n));const f=setTimeout(()=>{n.classList.remove("copied"),n.blur(),e.delete(n)},2e3);e.set(n,f)})}})}}async function Wa(e){try{return navigator.clipboard.writeText(e)}catch{const t=document.createElement("textarea"),n=document.activeElement;t.value=e,t.setAttribute("readonly",""),t.style.contain="strict",t.style.position="absolute",t.style.left="-9999px",t.style.fontSize="12pt";const r=document.getSelection(),s=r?r.rangeCount>0&&r.getRangeAt(0):null;document.body.appendChild(t),t.select(),t.selectionStart=0,t.selectionEnd=e.length,document.execCommand("copy"),document.body.removeChild(t),s&&(r.removeAllRanges(),r.addRange(s)),n&&n.focus()}}function ju(e,t){let n=!0,r=[];const s=o=>{if(n){n=!1,o.forEach(l=>{const c=cr(l);for(const a of document.head.children)if(a.isEqualNode(c)){r.push(a);return}});return}const i=o.map(cr);r.forEach((l,c)=>{const a=i.findIndex(f=>f==null?void 0:f.isEqualNode(l??null));a!==-1?delete i[a]:(l==null||l.remove(),delete r[c])}),i.forEach(l=>l&&document.head.appendChild(l)),r=[...r,...i].filter(Boolean)};Ur(()=>{const o=e.data,i=t.value,l=o&&o.description,c=o&&o.frontmatter.head||[],a=_i(i,o);a!==document.title&&(document.title=a);const f=l||i.description;let h=document.querySelector("meta[name=description]");h?h.getAttribute("content")!==f&&h.setAttribute("content",f):cr(["meta",{name:"description",content:f}]),s(vi(i.head,Ga(c)))})}function cr([e,t,n]){const r=document.createElement(e);for(const s in t)r.setAttribute(s,t[s]);return n&&(r.innerHTML=n),e==="script"&&!t.async&&(r.async=!1),r}function qa(e){return e[0]==="meta"&&e[1]&&e[1].name==="description"}function Ga(e){return e.filter(t=>!qa(t))}const ar=new Set,Ei=()=>document.createElement("link"),za=e=>{const t=Ei();t.rel="prefetch",t.href=e,document.head.appendChild(t)},Xa=e=>{const t=new XMLHttpRequest;t.open("GET",e,t.withCredentials=!0),t.send()};let dn;const Ya=ge&&(dn=Ei())&&dn.relList&&dn.relList.supports&&dn.relList.supports("prefetch")?za:Xa;function Vu(){if(!ge||!window.IntersectionObserver)return;let e;if((e=navigator.connection)&&(e.saveData||/2g/.test(e.effectiveType)))return;const t=window.requestIdleCallback||setTimeout;let n=null;const r=()=>{n&&n.disconnect(),n=new IntersectionObserver(o=>{o.forEach(i=>{if(i.isIntersecting){const l=i.target;n.unobserve(l);const{pathname:c}=l;if(!ar.has(c)){ar.add(c);const a=Da(c);a&&Ya(a)}}})}),t(()=>{document.querySelectorAll("#app a").forEach(o=>{const{hostname:i,pathname:l}=new URL(o.href instanceof SVGAnimatedString?o.href.animVal:o.href,o.baseURI),c=l.match(/\.\w+$/);c&&c[0]!==".html"||o.target!=="_blank"&&i===location.hostname&&(l!==location.pathname?n.observe(o):ar.add(l))})})};Rt(r);const s=wi();Ne(()=>s.path,r),Vn(()=>{n&&n.disconnect()})}export{Zl as $,nu as A,Vl as B,Ba as C,eu as D,ou as E,ye as F,Vr as G,Mu as H,oe as I,tu as J,mi as K,wi as L,yc as M,xt as N,Lu as O,Lr as P,Cu as Q,xu as R,Pn as S,ri as T,Ru as U,ge as V,Mn as W,su as X,bu as Y,Tu as Z,_u as _,Zo as a,gu as a0,lu as a1,pu as a2,cu as a3,In as a4,pl as a5,Cr as a6,fu as a7,vu as a8,ju as a9,mu as aA,Ou as aB,Ua as aa,Iu as ab,Ha as ac,Nu as ad,Fu as ae,ut as af,yu as ag,Pu as ah,Da as ai,Vu as aj,Hu as ak,$u as al,yt as am,zr as an,Eu as ao,Au as ap,Su as aq,wu as ar,Ka as as,De as at,Fo as au,ru as av,hu as aw,de as ax,au as ay,Mt as az,Yo as b,uu as c,kr as d,du as e,$a as f,Xs as g,ne as h,Oa as i,re as j,Rt as k,Qo as l,wo as m,Or as n,zo as o,Qa as p,Za as q,iu as r,La as s,Ja as t,ja as u,di as v,El as w,Ne as x,Ur as y,Vn as z}; diff --git a/dev/assets/chunks/theme.BWgOxzZE.js b/dev/assets/chunks/theme.BWgOxzZE.js deleted file mode 100644 index f03a3bc..0000000 --- a/dev/assets/chunks/theme.BWgOxzZE.js +++ /dev/null @@ -1,7 +0,0 @@ -function __vite__mapDeps(indexes) { - if (!__vite__mapDeps.viteFileDeps) { - __vite__mapDeps.viteFileDeps = ["assets/chunks/VPLocalSearchBox.CaalGK9M.js","assets/chunks/framework.D1rHXXmm.js"] - } - return indexes.map((i) => __vite__mapDeps.viteFileDeps[i]) -} -import{d as _,o as a,c as u,r as c,n as N,a as F,t as w,b as P,w as p,T as pe,e as f,_ as g,u as We,i as Je,f as Ye,g as he,h as y,j as I,k as G,l as v,m as i,p as B,q as H,s as K,v as le,x as z,y as ee,z as fe,A as Le,B as Xe,C as Qe,D as R,F as M,E,G as Te,H as te,I as b,J as W,K as we,L as se,M as Q,N as J,O as Ze,P as Ie,Q as xe,R as ce,S as Ne,U as Me,V as oe,W as et,X as tt,Y as st,Z as Ae,$ as _e,a0 as ot,a1 as nt,a2 as at,a3 as Ce,a4 as rt,a5 as it,a6 as lt}from"./framework.D1rHXXmm.js";const ct=_({__name:"VPBadge",props:{text:{},type:{default:"tip"}},setup(s){return(t,e)=>(a(),u("span",{class:N(["VPBadge",t.type])},[c(t.$slots,"default",{},()=>[F(w(t.text),1)])],2))}}),ut={key:0,class:"VPBackdrop"},dt=_({__name:"VPBackdrop",props:{show:{type:Boolean}},setup(s){return(t,e)=>(a(),P(pe,{name:"fade"},{default:p(()=>[t.show?(a(),u("div",ut)):f("",!0)]),_:1}))}}),vt=g(dt,[["__scopeId","data-v-b06cdb19"]]),L=We;function pt(s,t){let e,o=!1;return()=>{e&&clearTimeout(e),o?e=setTimeout(s,t):(s(),(o=!0)&&setTimeout(()=>o=!1,t))}}function ue(s){return/^\//.test(s)?s:`/${s}`}function me(s){const{pathname:t,search:e,hash:o,protocol:n}=new URL(s,"http://a.com");if(Je(s)||s.startsWith("#")||!n.startsWith("http")||!Ye(t))return s;const{site:r}=L(),l=t.endsWith("/")||t.endsWith(".html")?s:s.replace(/(?:(^\.+)\/)?.*$/,`$1${t.replace(/(\.md)?$/,r.value.cleanUrls?"":".html")}${e}${o}`);return he(l)}function X({removeCurrent:s=!0,correspondingLink:t=!1}={}){const{site:e,localeIndex:o,page:n,theme:r,hash:l}=L(),d=y(()=>{var m,k;return{label:(m=e.value.locales[o.value])==null?void 0:m.label,link:((k=e.value.locales[o.value])==null?void 0:k.link)||(o.value==="root"?"/":`/${o.value}/`)}});return{localeLinks:y(()=>Object.entries(e.value.locales).flatMap(([m,k])=>s&&d.value.label===k.label?[]:{text:k.label,link:ht(k.link||(m==="root"?"/":`/${m}/`),r.value.i18nRouting!==!1&&t,n.value.relativePath.slice(d.value.link.length-1),!e.value.cleanUrls)+l.value})),currentLang:d}}function ht(s,t,e,o){return t?s.replace(/\/$/,"")+ue(e.replace(/(^|\/)index\.md$/,"$1").replace(/\.md$/,o?".html":"")):s}const ft=s=>(B("data-v-792811ca"),s=s(),H(),s),_t={class:"NotFound"},mt={class:"code"},bt={class:"title"},kt=ft(()=>v("div",{class:"divider"},null,-1)),$t={class:"quote"},gt={class:"action"},yt=["href","aria-label"],Pt=_({__name:"NotFound",setup(s){const{site:t,theme:e}=L(),{localeLinks:o}=X({removeCurrent:!1}),n=I("/");return G(()=>{var l;const r=window.location.pathname.replace(t.value.base,"").replace(/(^.*?\/).*$/,"/$1");o.value.length&&(n.value=((l=o.value.find(({link:d})=>d.startsWith(r)))==null?void 0:l.link)||o.value[0].link)}),(r,l)=>{var d,h,m,k,$;return a(),u("div",_t,[v("p",mt,w(((d=i(e).notFound)==null?void 0:d.code)??"404"),1),v("h1",bt,w(((h=i(e).notFound)==null?void 0:h.title)??"PAGE NOT FOUND"),1),kt,v("blockquote",$t,w(((m=i(e).notFound)==null?void 0:m.quote)??"But if you don't change your direction, and if you keep looking, you may end up where you are heading."),1),v("div",gt,[v("a",{class:"link",href:i(he)(n.value),"aria-label":((k=i(e).notFound)==null?void 0:k.linkLabel)??"go to home"},w((($=i(e).notFound)==null?void 0:$.linkText)??"Take me home"),9,yt)])])}}}),St=g(Pt,[["__scopeId","data-v-792811ca"]]);function Be(s,t){if(Array.isArray(s))return Z(s);if(s==null)return[];t=ue(t);const e=Object.keys(s).sort((n,r)=>r.split("/").length-n.split("/").length).find(n=>t.startsWith(ue(n))),o=e?s[e]:[];return Array.isArray(o)?Z(o):Z(o.items,o.base)}function Vt(s){const t=[];let e=0;for(const o in s){const n=s[o];if(n.items){e=t.push(n);continue}t[e]||t.push({items:[]}),t[e].items.push(n)}return t}function Lt(s){const t=[];function e(o){for(const n of o)n.text&&n.link&&t.push({text:n.text,link:n.link,docFooterText:n.docFooterText}),n.items&&e(n.items)}return e(s),t}function de(s,t){return Array.isArray(t)?t.some(e=>de(s,e)):K(s,t.link)?!0:t.items?de(s,t.items):!1}function Z(s,t){return[...s].map(e=>{const o={...e},n=o.base||t;return n&&o.link&&(o.link=n+o.link),o.items&&(o.items=Z(o.items,n)),o})}function O(){const{frontmatter:s,page:t,theme:e}=L(),o=le("(min-width: 960px)"),n=I(!1),r=y(()=>{const C=e.value.sidebar,T=t.value.relativePath;return C?Be(C,T):[]}),l=I(r.value);z(r,(C,T)=>{JSON.stringify(C)!==JSON.stringify(T)&&(l.value=r.value)});const d=y(()=>s.value.sidebar!==!1&&l.value.length>0&&s.value.layout!=="home"),h=y(()=>m?s.value.aside==null?e.value.aside==="left":s.value.aside==="left":!1),m=y(()=>s.value.layout==="home"?!1:s.value.aside!=null?!!s.value.aside:e.value.aside!==!1),k=y(()=>d.value&&o.value),$=y(()=>d.value?Vt(l.value):[]);function V(){n.value=!0}function S(){n.value=!1}function A(){n.value?S():V()}return{isOpen:n,sidebar:l,sidebarGroups:$,hasSidebar:d,hasAside:m,leftAside:h,isSidebarEnabled:k,open:V,close:S,toggle:A}}function Tt(s,t){let e;ee(()=>{e=s.value?document.activeElement:void 0}),G(()=>{window.addEventListener("keyup",o)}),fe(()=>{window.removeEventListener("keyup",o)});function o(n){n.key==="Escape"&&s.value&&(t(),e==null||e.focus())}}function wt(s){const{page:t,hash:e}=L(),o=I(!1),n=y(()=>s.value.collapsed!=null),r=y(()=>!!s.value.link),l=I(!1),d=()=>{l.value=K(t.value.relativePath,s.value.link)};z([t,s,e],d),G(d);const h=y(()=>l.value?!0:s.value.items?de(t.value.relativePath,s.value.items):!1),m=y(()=>!!(s.value.items&&s.value.items.length));ee(()=>{o.value=!!(n.value&&s.value.collapsed)}),Le(()=>{(l.value||h.value)&&(o.value=!1)});function k(){n.value&&(o.value=!o.value)}return{collapsed:o,collapsible:n,isLink:r,isActiveLink:l,hasActiveLink:h,hasChildren:m,toggle:k}}function It(){const{hasSidebar:s}=O(),t=le("(min-width: 960px)"),e=le("(min-width: 1280px)");return{isAsideEnabled:y(()=>!e.value&&!t.value?!1:s.value?e.value:t.value)}}const ve=[];function He(s){return typeof s.outline=="object"&&!Array.isArray(s.outline)&&s.outline.label||s.outlineTitle||"On this page"}function be(s){const t=[...document.querySelectorAll(".VPDoc :where(h1,h2,h3,h4,h5,h6)")].filter(e=>e.id&&e.hasChildNodes()).map(e=>{const o=Number(e.tagName[1]);return{element:e,title:Nt(e),link:"#"+e.id,level:o}});return Mt(t,s)}function Nt(s){let t="";for(const e of s.childNodes)if(e.nodeType===1){if(e.classList.contains("VPBadge")||e.classList.contains("header-anchor")||e.classList.contains("ignore-header"))continue;t+=e.textContent}else e.nodeType===3&&(t+=e.textContent);return t.trim()}function Mt(s,t){if(t===!1)return[];const e=(typeof t=="object"&&!Array.isArray(t)?t.level:t)||2,[o,n]=typeof e=="number"?[e,e]:e==="deep"?[2,6]:e;s=s.filter(l=>l.level>=o&&l.level<=n),ve.length=0;for(const{element:l,link:d}of s)ve.push({element:l,link:d});const r=[];e:for(let l=0;l=0;h--){const m=s[h];if(m.level{requestAnimationFrame(r),window.addEventListener("scroll",o)}),Xe(()=>{l(location.hash)}),fe(()=>{window.removeEventListener("scroll",o)});function r(){if(!e.value)return;const d=window.scrollY,h=window.innerHeight,m=document.body.offsetHeight,k=Math.abs(d+h-m)<1,$=ve.map(({element:S,link:A})=>({link:A,top:Ct(S)})).filter(({top:S})=>!Number.isNaN(S)).sort((S,A)=>S.top-A.top);if(!$.length){l(null);return}if(d<1){l(null);return}if(k){l($[$.length-1].link);return}let V=null;for(const{link:S,top:A}of $){if(A>d+Qe()+4)break;V=S}l(V)}function l(d){n&&n.classList.remove("active"),d==null?n=null:n=s.value.querySelector(`a[href="${decodeURIComponent(d)}"]`);const h=n;h?(h.classList.add("active"),t.value.style.top=h.offsetTop+39+"px",t.value.style.opacity="1"):(t.value.style.top="33px",t.value.style.opacity="0")}}function Ct(s){let t=0;for(;s!==document.body;){if(s===null)return NaN;t+=s.offsetTop,s=s.offsetParent}return t}const Bt=["href","title"],Ht=_({__name:"VPDocOutlineItem",props:{headers:{},root:{type:Boolean}},setup(s){function t({target:e}){const o=e.href.split("#")[1],n=document.getElementById(decodeURIComponent(o));n==null||n.focus({preventScroll:!0})}return(e,o)=>{const n=R("VPDocOutlineItem",!0);return a(),u("ul",{class:N(["VPDocOutlineItem",e.root?"root":"nested"])},[(a(!0),u(M,null,E(e.headers,({children:r,link:l,title:d})=>(a(),u("li",null,[v("a",{class:"outline-link",href:l,onClick:t,title:d},w(d),9,Bt),r!=null&&r.length?(a(),P(n,{key:0,headers:r},null,8,["headers"])):f("",!0)]))),256))],2)}}}),Ee=g(Ht,[["__scopeId","data-v-3f927ebe"]]),Et=s=>(B("data-v-c14bfc45"),s=s(),H(),s),Dt={class:"content"},Ft={class:"outline-title",role:"heading","aria-level":"2"},Ot={"aria-labelledby":"doc-outline-aria-label"},Ut=Et(()=>v("span",{class:"visually-hidden",id:"doc-outline-aria-label"}," Table of Contents for current page ",-1)),jt=_({__name:"VPDocAsideOutline",setup(s){const{frontmatter:t,theme:e}=L(),o=Te([]);te(()=>{o.value=be(t.value.outline??e.value.outline)});const n=I(),r=I();return At(n,r),(l,d)=>(a(),u("div",{class:N(["VPDocAsideOutline",{"has-outline":o.value.length>0}]),ref_key:"container",ref:n,role:"navigation"},[v("div",Dt,[v("div",{class:"outline-marker",ref_key:"marker",ref:r},null,512),v("div",Ft,w(i(He)(i(e))),1),v("nav",Ot,[Ut,b(Ee,{headers:o.value,root:!0},null,8,["headers"])])])],2))}}),Gt=g(jt,[["__scopeId","data-v-c14bfc45"]]),zt={class:"VPDocAsideCarbonAds"},Kt=_({__name:"VPDocAsideCarbonAds",props:{carbonAds:{}},setup(s){const t=()=>null;return(e,o)=>(a(),u("div",zt,[b(i(t),{"carbon-ads":e.carbonAds},null,8,["carbon-ads"])]))}}),Rt=s=>(B("data-v-6d7b3c46"),s=s(),H(),s),qt={class:"VPDocAside"},Wt=Rt(()=>v("div",{class:"spacer"},null,-1)),Jt=_({__name:"VPDocAside",setup(s){const{theme:t}=L();return(e,o)=>(a(),u("div",qt,[c(e.$slots,"aside-top",{},void 0,!0),c(e.$slots,"aside-outline-before",{},void 0,!0),b(Gt),c(e.$slots,"aside-outline-after",{},void 0,!0),Wt,c(e.$slots,"aside-ads-before",{},void 0,!0),i(t).carbonAds?(a(),P(Kt,{key:0,"carbon-ads":i(t).carbonAds},null,8,["carbon-ads"])):f("",!0),c(e.$slots,"aside-ads-after",{},void 0,!0),c(e.$slots,"aside-bottom",{},void 0,!0)]))}}),Yt=g(Jt,[["__scopeId","data-v-6d7b3c46"]]);function Xt(){const{theme:s,page:t}=L();return y(()=>{const{text:e="Edit this page",pattern:o=""}=s.value.editLink||{};let n;return typeof o=="function"?n=o(t.value):n=o.replace(/:path/g,t.value.filePath),{url:n,text:e}})}function Qt(){const{page:s,theme:t,frontmatter:e}=L();return y(()=>{var m,k,$,V,S,A,C,T;const o=Be(t.value.sidebar,s.value.relativePath),n=Lt(o),r=Zt(n,U=>U.link.replace(/[?#].*$/,"")),l=r.findIndex(U=>K(s.value.relativePath,U.link)),d=((m=t.value.docFooter)==null?void 0:m.prev)===!1&&!e.value.prev||e.value.prev===!1,h=((k=t.value.docFooter)==null?void 0:k.next)===!1&&!e.value.next||e.value.next===!1;return{prev:d?void 0:{text:(typeof e.value.prev=="string"?e.value.prev:typeof e.value.prev=="object"?e.value.prev.text:void 0)??(($=r[l-1])==null?void 0:$.docFooterText)??((V=r[l-1])==null?void 0:V.text),link:(typeof e.value.prev=="object"?e.value.prev.link:void 0)??((S=r[l-1])==null?void 0:S.link)},next:h?void 0:{text:(typeof e.value.next=="string"?e.value.next:typeof e.value.next=="object"?e.value.next.text:void 0)??((A=r[l+1])==null?void 0:A.docFooterText)??((C=r[l+1])==null?void 0:C.text),link:(typeof e.value.next=="object"?e.value.next.link:void 0)??((T=r[l+1])==null?void 0:T.link)}}})}function Zt(s,t){const e=new Set;return s.filter(o=>{const n=t(o);return e.has(n)?!1:e.add(n)})}const D=_({__name:"VPLink",props:{tag:{},href:{},noIcon:{type:Boolean},target:{},rel:{}},setup(s){const t=s,e=y(()=>t.tag??(t.href?"a":"span")),o=y(()=>t.href&&we.test(t.href));return(n,r)=>(a(),P(W(e.value),{class:N(["VPLink",{link:n.href,"vp-external-link-icon":o.value,"no-icon":n.noIcon}]),href:n.href?i(me)(n.href):void 0,target:n.target??(o.value?"_blank":void 0),rel:n.rel??(o.value?"noreferrer":void 0)},{default:p(()=>[c(n.$slots,"default")]),_:3},8,["class","href","target","rel"]))}}),xt={class:"VPLastUpdated"},es=["datetime"],ts=_({__name:"VPDocFooterLastUpdated",setup(s){const{theme:t,page:e,frontmatter:o,lang:n}=L(),r=y(()=>new Date(o.value.lastUpdated??e.value.lastUpdated)),l=y(()=>r.value.toISOString()),d=I("");return G(()=>{ee(()=>{var h,m,k;d.value=new Intl.DateTimeFormat((m=(h=t.value.lastUpdated)==null?void 0:h.formatOptions)!=null&&m.forceLocale?n.value:void 0,((k=t.value.lastUpdated)==null?void 0:k.formatOptions)??{dateStyle:"short",timeStyle:"short"}).format(r.value)})}),(h,m)=>{var k;return a(),u("p",xt,[F(w(((k=i(t).lastUpdated)==null?void 0:k.text)||i(t).lastUpdatedText||"Last updated")+": ",1),v("time",{datetime:l.value},w(d.value),9,es)])}}}),ss=g(ts,[["__scopeId","data-v-9da12f1d"]]),os=s=>(B("data-v-87be45d1"),s=s(),H(),s),ns={key:0,class:"VPDocFooter"},as={key:0,class:"edit-info"},rs={key:0,class:"edit-link"},is=os(()=>v("span",{class:"vpi-square-pen edit-link-icon"},null,-1)),ls={key:1,class:"last-updated"},cs={key:1,class:"prev-next"},us={class:"pager"},ds=["innerHTML"],vs=["innerHTML"],ps={class:"pager"},hs=["innerHTML"],fs=["innerHTML"],_s=_({__name:"VPDocFooter",setup(s){const{theme:t,page:e,frontmatter:o}=L(),n=Xt(),r=Qt(),l=y(()=>t.value.editLink&&o.value.editLink!==!1),d=y(()=>e.value.lastUpdated&&o.value.lastUpdated!==!1),h=y(()=>l.value||d.value||r.value.prev||r.value.next);return(m,k)=>{var $,V,S,A;return h.value?(a(),u("footer",ns,[c(m.$slots,"doc-footer-before",{},void 0,!0),l.value||d.value?(a(),u("div",as,[l.value?(a(),u("div",rs,[b(D,{class:"edit-link-button",href:i(n).url,"no-icon":!0},{default:p(()=>[is,F(" "+w(i(n).text),1)]),_:1},8,["href"])])):f("",!0),d.value?(a(),u("div",ls,[b(ss)])):f("",!0)])):f("",!0),($=i(r).prev)!=null&&$.link||(V=i(r).next)!=null&&V.link?(a(),u("nav",cs,[v("div",us,[(S=i(r).prev)!=null&&S.link?(a(),P(D,{key:0,class:"pager-link prev",href:i(r).prev.link},{default:p(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(t).docFooter)==null?void 0:C.prev)||"Previous page"},null,8,ds),v("span",{class:"title",innerHTML:i(r).prev.text},null,8,vs)]}),_:1},8,["href"])):f("",!0)]),v("div",ps,[(A=i(r).next)!=null&&A.link?(a(),P(D,{key:0,class:"pager-link next",href:i(r).next.link},{default:p(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(t).docFooter)==null?void 0:C.next)||"Next page"},null,8,hs),v("span",{class:"title",innerHTML:i(r).next.text},null,8,fs)]}),_:1},8,["href"])):f("",!0)])])):f("",!0)])):f("",!0)}}}),ms=g(_s,[["__scopeId","data-v-87be45d1"]]),bs=s=>(B("data-v-83890dd9"),s=s(),H(),s),ks={class:"container"},$s=bs(()=>v("div",{class:"aside-curtain"},null,-1)),gs={class:"aside-container"},ys={class:"aside-content"},Ps={class:"content"},Ss={class:"content-container"},Vs={class:"main"},Ls=_({__name:"VPDoc",setup(s){const{theme:t}=L(),e=se(),{hasSidebar:o,hasAside:n,leftAside:r}=O(),l=y(()=>e.path.replace(/[./]+/g,"_").replace(/_html$/,""));return(d,h)=>{const m=R("Content");return a(),u("div",{class:N(["VPDoc",{"has-sidebar":i(o),"has-aside":i(n)}])},[c(d.$slots,"doc-top",{},void 0,!0),v("div",ks,[i(n)?(a(),u("div",{key:0,class:N(["aside",{"left-aside":i(r)}])},[$s,v("div",gs,[v("div",ys,[b(Yt,null,{"aside-top":p(()=>[c(d.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":p(()=>[c(d.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":p(()=>[c(d.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":p(()=>[c(d.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":p(()=>[c(d.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":p(()=>[c(d.$slots,"aside-ads-after",{},void 0,!0)]),_:3})])])],2)):f("",!0),v("div",Ps,[v("div",Ss,[c(d.$slots,"doc-before",{},void 0,!0),v("main",Vs,[b(m,{class:N(["vp-doc",[l.value,i(t).externalLinkIcon&&"external-link-icon-enabled"]])},null,8,["class"])]),b(ms,null,{"doc-footer-before":p(()=>[c(d.$slots,"doc-footer-before",{},void 0,!0)]),_:3}),c(d.$slots,"doc-after",{},void 0,!0)])])]),c(d.$slots,"doc-bottom",{},void 0,!0)],2)}}}),Ts=g(Ls,[["__scopeId","data-v-83890dd9"]]),ws=_({__name:"VPButton",props:{tag:{},size:{default:"medium"},theme:{default:"brand"},text:{},href:{},target:{},rel:{}},setup(s){const t=s,e=y(()=>t.href&&we.test(t.href)),o=y(()=>t.tag||t.href?"a":"button");return(n,r)=>(a(),P(W(o.value),{class:N(["VPButton",[n.size,n.theme]]),href:n.href?i(me)(n.href):void 0,target:t.target??(e.value?"_blank":void 0),rel:t.rel??(e.value?"noreferrer":void 0)},{default:p(()=>[F(w(n.text),1)]),_:1},8,["class","href","target","rel"]))}}),Is=g(ws,[["__scopeId","data-v-14206e74"]]),Ns=["src","alt"],Ms=_({inheritAttrs:!1,__name:"VPImage",props:{image:{},alt:{}},setup(s){return(t,e)=>{const o=R("VPImage",!0);return t.image?(a(),u(M,{key:0},[typeof t.image=="string"||"src"in t.image?(a(),u("img",Q({key:0,class:"VPImage"},typeof t.image=="string"?t.$attrs:{...t.image,...t.$attrs},{src:i(he)(typeof t.image=="string"?t.image:t.image.src),alt:t.alt??(typeof t.image=="string"?"":t.image.alt||"")}),null,16,Ns)):(a(),u(M,{key:1},[b(o,Q({class:"dark",image:t.image.dark,alt:t.image.alt},t.$attrs),null,16,["image","alt"]),b(o,Q({class:"light",image:t.image.light,alt:t.image.alt},t.$attrs),null,16,["image","alt"])],64))],64)):f("",!0)}}}),x=g(Ms,[["__scopeId","data-v-35a7d0b8"]]),As=s=>(B("data-v-955009fc"),s=s(),H(),s),Cs={class:"container"},Bs={class:"main"},Hs={key:0,class:"name"},Es=["innerHTML"],Ds=["innerHTML"],Fs=["innerHTML"],Os={key:0,class:"actions"},Us={key:0,class:"image"},js={class:"image-container"},Gs=As(()=>v("div",{class:"image-bg"},null,-1)),zs=_({__name:"VPHero",props:{name:{},text:{},tagline:{},image:{},actions:{}},setup(s){const t=J("hero-image-slot-exists");return(e,o)=>(a(),u("div",{class:N(["VPHero",{"has-image":e.image||i(t)}])},[v("div",Cs,[v("div",Bs,[c(e.$slots,"home-hero-info-before",{},void 0,!0),c(e.$slots,"home-hero-info",{},()=>[e.name?(a(),u("h1",Hs,[v("span",{innerHTML:e.name,class:"clip"},null,8,Es)])):f("",!0),e.text?(a(),u("p",{key:1,innerHTML:e.text,class:"text"},null,8,Ds)):f("",!0),e.tagline?(a(),u("p",{key:2,innerHTML:e.tagline,class:"tagline"},null,8,Fs)):f("",!0)],!0),c(e.$slots,"home-hero-info-after",{},void 0,!0),e.actions?(a(),u("div",Os,[(a(!0),u(M,null,E(e.actions,n=>(a(),u("div",{key:n.link,class:"action"},[b(Is,{tag:"a",size:"medium",theme:n.theme,text:n.text,href:n.link,target:n.target,rel:n.rel},null,8,["theme","text","href","target","rel"])]))),128))])):f("",!0),c(e.$slots,"home-hero-actions-after",{},void 0,!0)]),e.image||i(t)?(a(),u("div",Us,[v("div",js,[Gs,c(e.$slots,"home-hero-image",{},()=>[e.image?(a(),P(x,{key:0,class:"image-src",image:e.image},null,8,["image"])):f("",!0)],!0)])])):f("",!0)])],2))}}),Ks=g(zs,[["__scopeId","data-v-955009fc"]]),Rs=_({__name:"VPHomeHero",setup(s){const{frontmatter:t}=L();return(e,o)=>i(t).hero?(a(),P(Ks,{key:0,class:"VPHomeHero",name:i(t).hero.name,text:i(t).hero.text,tagline:i(t).hero.tagline,image:i(t).hero.image,actions:i(t).hero.actions},{"home-hero-info-before":p(()=>[c(e.$slots,"home-hero-info-before")]),"home-hero-info":p(()=>[c(e.$slots,"home-hero-info")]),"home-hero-info-after":p(()=>[c(e.$slots,"home-hero-info-after")]),"home-hero-actions-after":p(()=>[c(e.$slots,"home-hero-actions-after")]),"home-hero-image":p(()=>[c(e.$slots,"home-hero-image")]),_:3},8,["name","text","tagline","image","actions"])):f("",!0)}}),qs=s=>(B("data-v-f5e9645b"),s=s(),H(),s),Ws={class:"box"},Js={key:0,class:"icon"},Ys=["innerHTML"],Xs=["innerHTML"],Qs=["innerHTML"],Zs={key:4,class:"link-text"},xs={class:"link-text-value"},eo=qs(()=>v("span",{class:"vpi-arrow-right link-text-icon"},null,-1)),to=_({__name:"VPFeature",props:{icon:{},title:{},details:{},link:{},linkText:{},rel:{},target:{}},setup(s){return(t,e)=>(a(),P(D,{class:"VPFeature",href:t.link,rel:t.rel,target:t.target,"no-icon":!0,tag:t.link?"a":"div"},{default:p(()=>[v("article",Ws,[typeof t.icon=="object"&&t.icon.wrap?(a(),u("div",Js,[b(x,{image:t.icon,alt:t.icon.alt,height:t.icon.height||48,width:t.icon.width||48},null,8,["image","alt","height","width"])])):typeof t.icon=="object"?(a(),P(x,{key:1,image:t.icon,alt:t.icon.alt,height:t.icon.height||48,width:t.icon.width||48},null,8,["image","alt","height","width"])):t.icon?(a(),u("div",{key:2,class:"icon",innerHTML:t.icon},null,8,Ys)):f("",!0),v("h2",{class:"title",innerHTML:t.title},null,8,Xs),t.details?(a(),u("p",{key:3,class:"details",innerHTML:t.details},null,8,Qs)):f("",!0),t.linkText?(a(),u("div",Zs,[v("p",xs,[F(w(t.linkText)+" ",1),eo])])):f("",!0)])]),_:1},8,["href","rel","target","tag"]))}}),so=g(to,[["__scopeId","data-v-f5e9645b"]]),oo={key:0,class:"VPFeatures"},no={class:"container"},ao={class:"items"},ro=_({__name:"VPFeatures",props:{features:{}},setup(s){const t=s,e=y(()=>{const o=t.features.length;if(o){if(o===2)return"grid-2";if(o===3)return"grid-3";if(o%3===0)return"grid-6";if(o>3)return"grid-4"}else return});return(o,n)=>o.features?(a(),u("div",oo,[v("div",no,[v("div",ao,[(a(!0),u(M,null,E(o.features,r=>(a(),u("div",{key:r.title,class:N(["item",[e.value]])},[b(so,{icon:r.icon,title:r.title,details:r.details,link:r.link,"link-text":r.linkText,rel:r.rel,target:r.target},null,8,["icon","title","details","link","link-text","rel","target"])],2))),128))])])])):f("",!0)}}),io=g(ro,[["__scopeId","data-v-d0a190d7"]]),lo=_({__name:"VPHomeFeatures",setup(s){const{frontmatter:t}=L();return(e,o)=>i(t).features?(a(),P(io,{key:0,class:"VPHomeFeatures",features:i(t).features},null,8,["features"])):f("",!0)}}),co=_({__name:"VPHomeContent",setup(s){const{width:t}=Ze({includeScrollbar:!1});return(e,o)=>(a(),u("div",{class:"vp-doc container",style:Ie(i(t)?{"--vp-offset":`calc(50% - ${i(t)/2}px)`}:{})},[c(e.$slots,"default",{},void 0,!0)],4))}}),uo=g(co,[["__scopeId","data-v-c43247eb"]]),vo={class:"VPHome"},po=_({__name:"VPHome",setup(s){const{frontmatter:t}=L();return(e,o)=>{const n=R("Content");return a(),u("div",vo,[c(e.$slots,"home-hero-before",{},void 0,!0),b(Rs,null,{"home-hero-info-before":p(()=>[c(e.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":p(()=>[c(e.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":p(()=>[c(e.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":p(()=>[c(e.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":p(()=>[c(e.$slots,"home-hero-image",{},void 0,!0)]),_:3}),c(e.$slots,"home-hero-after",{},void 0,!0),c(e.$slots,"home-features-before",{},void 0,!0),b(lo),c(e.$slots,"home-features-after",{},void 0,!0),i(t).markdownStyles!==!1?(a(),P(uo,{key:0},{default:p(()=>[b(n)]),_:1})):(a(),P(n,{key:1}))])}}}),ho=g(po,[["__scopeId","data-v-cbb6ec48"]]),fo={},_o={class:"VPPage"};function mo(s,t){const e=R("Content");return a(),u("div",_o,[c(s.$slots,"page-top"),b(e),c(s.$slots,"page-bottom")])}const bo=g(fo,[["render",mo]]),ko=_({__name:"VPContent",setup(s){const{page:t,frontmatter:e}=L(),{hasSidebar:o}=O();return(n,r)=>(a(),u("div",{class:N(["VPContent",{"has-sidebar":i(o),"is-home":i(e).layout==="home"}]),id:"VPContent"},[i(t).isNotFound?c(n.$slots,"not-found",{key:0},()=>[b(St)],!0):i(e).layout==="page"?(a(),P(bo,{key:1},{"page-top":p(()=>[c(n.$slots,"page-top",{},void 0,!0)]),"page-bottom":p(()=>[c(n.$slots,"page-bottom",{},void 0,!0)]),_:3})):i(e).layout==="home"?(a(),P(ho,{key:2},{"home-hero-before":p(()=>[c(n.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":p(()=>[c(n.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":p(()=>[c(n.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":p(()=>[c(n.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":p(()=>[c(n.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":p(()=>[c(n.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":p(()=>[c(n.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":p(()=>[c(n.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":p(()=>[c(n.$slots,"home-features-after",{},void 0,!0)]),_:3})):i(e).layout&&i(e).layout!=="doc"?(a(),P(W(i(e).layout),{key:3})):(a(),P(Ts,{key:4},{"doc-top":p(()=>[c(n.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":p(()=>[c(n.$slots,"doc-bottom",{},void 0,!0)]),"doc-footer-before":p(()=>[c(n.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":p(()=>[c(n.$slots,"doc-before",{},void 0,!0)]),"doc-after":p(()=>[c(n.$slots,"doc-after",{},void 0,!0)]),"aside-top":p(()=>[c(n.$slots,"aside-top",{},void 0,!0)]),"aside-outline-before":p(()=>[c(n.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":p(()=>[c(n.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":p(()=>[c(n.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":p(()=>[c(n.$slots,"aside-ads-after",{},void 0,!0)]),"aside-bottom":p(()=>[c(n.$slots,"aside-bottom",{},void 0,!0)]),_:3}))],2))}}),$o=g(ko,[["__scopeId","data-v-91765379"]]),go={class:"container"},yo=["innerHTML"],Po=["innerHTML"],So=_({__name:"VPFooter",setup(s){const{theme:t,frontmatter:e}=L(),{hasSidebar:o}=O();return(n,r)=>i(t).footer&&i(e).footer!==!1?(a(),u("footer",{key:0,class:N(["VPFooter",{"has-sidebar":i(o)}])},[v("div",go,[i(t).footer.message?(a(),u("p",{key:0,class:"message",innerHTML:i(t).footer.message},null,8,yo)):f("",!0),i(t).footer.copyright?(a(),u("p",{key:1,class:"copyright",innerHTML:i(t).footer.copyright},null,8,Po)):f("",!0)])],2)):f("",!0)}}),Vo=g(So,[["__scopeId","data-v-c970a860"]]);function Lo(){const{theme:s,frontmatter:t}=L(),e=Te([]),o=y(()=>e.value.length>0);return te(()=>{e.value=be(t.value.outline??s.value.outline)}),{headers:e,hasLocalNav:o}}const To=s=>(B("data-v-47ad05d4"),s=s(),H(),s),wo={class:"menu-text"},Io=To(()=>v("span",{class:"vpi-chevron-right icon"},null,-1)),No={class:"header"},Mo={class:"outline"},Ao=_({__name:"VPLocalNavOutlineDropdown",props:{headers:{},navHeight:{}},setup(s){const t=s,{theme:e}=L(),o=I(!1),n=I(0),r=I(),l=I();xe(r,()=>{o.value=!1}),ce("Escape",()=>{o.value=!1}),te(()=>{o.value=!1});function d(){o.value=!o.value,n.value=window.innerHeight+Math.min(window.scrollY-t.navHeight,0)}function h(k){k.target.classList.contains("outline-link")&&(l.value&&(l.value.style.transition="none"),Ne(()=>{o.value=!1}))}function m(){o.value=!1,window.scrollTo({top:0,left:0,behavior:"smooth"})}return(k,$)=>(a(),u("div",{class:"VPLocalNavOutlineDropdown",style:Ie({"--vp-vh":n.value+"px"}),ref_key:"main",ref:r},[k.headers.length>0?(a(),u("button",{key:0,onClick:d,class:N({open:o.value})},[v("span",wo,w(i(He)(i(e))),1),Io],2)):(a(),u("button",{key:1,onClick:m},w(i(e).returnToTopLabel||"Return to top"),1)),b(pe,{name:"flyout"},{default:p(()=>[o.value?(a(),u("div",{key:0,ref_key:"items",ref:l,class:"items",onClick:h},[v("div",No,[v("a",{class:"top-link",href:"#",onClick:m},w(i(e).returnToTopLabel||"Return to top"),1)]),v("div",Mo,[b(Ee,{headers:k.headers},null,8,["headers"])])],512)):f("",!0)]),_:1})],4))}}),Co=g(Ao,[["__scopeId","data-v-47ad05d4"]]),Bo=s=>(B("data-v-070ab83d"),s=s(),H(),s),Ho={class:"container"},Eo=["aria-expanded"],Do=Bo(()=>v("span",{class:"vpi-align-left menu-icon"},null,-1)),Fo={class:"menu-text"},Oo=_({__name:"VPLocalNav",props:{open:{type:Boolean}},emits:["open-menu"],setup(s){const{theme:t,frontmatter:e}=L(),{hasSidebar:o}=O(),{headers:n}=Lo(),{y:r}=Me(),l=I(0);G(()=>{l.value=parseInt(getComputedStyle(document.documentElement).getPropertyValue("--vp-nav-height"))}),te(()=>{n.value=be(e.value.outline??t.value.outline)});const d=y(()=>n.value.length===0),h=y(()=>d.value&&!o.value),m=y(()=>({VPLocalNav:!0,"has-sidebar":o.value,empty:d.value,fixed:h.value}));return(k,$)=>i(e).layout!=="home"&&(!h.value||i(r)>=l.value)?(a(),u("div",{key:0,class:N(m.value)},[v("div",Ho,[i(o)?(a(),u("button",{key:0,class:"menu","aria-expanded":k.open,"aria-controls":"VPSidebarNav",onClick:$[0]||($[0]=V=>k.$emit("open-menu"))},[Do,v("span",Fo,w(i(t).sidebarMenuLabel||"Menu"),1)],8,Eo)):f("",!0),b(Co,{headers:i(n),navHeight:l.value},null,8,["headers","navHeight"])])],2)):f("",!0)}}),Uo=g(Oo,[["__scopeId","data-v-070ab83d"]]);function jo(){const s=I(!1);function t(){s.value=!0,window.addEventListener("resize",n)}function e(){s.value=!1,window.removeEventListener("resize",n)}function o(){s.value?e():t()}function n(){window.outerWidth>=768&&e()}const r=se();return z(()=>r.path,e),{isScreenOpen:s,openScreen:t,closeScreen:e,toggleScreen:o}}const Go={},zo={class:"VPSwitch",type:"button",role:"switch"},Ko={class:"check"},Ro={key:0,class:"icon"};function qo(s,t){return a(),u("button",zo,[v("span",Ko,[s.$slots.default?(a(),u("span",Ro,[c(s.$slots,"default",{},void 0,!0)])):f("",!0)])])}const Wo=g(Go,[["render",qo],["__scopeId","data-v-4a1c76db"]]),De=s=>(B("data-v-b79b56d4"),s=s(),H(),s),Jo=De(()=>v("span",{class:"vpi-sun sun"},null,-1)),Yo=De(()=>v("span",{class:"vpi-moon moon"},null,-1)),Xo=_({__name:"VPSwitchAppearance",setup(s){const{isDark:t,theme:e}=L(),o=J("toggle-appearance",()=>{t.value=!t.value}),n=y(()=>t.value?e.value.lightModeSwitchTitle||"Switch to light theme":e.value.darkModeSwitchTitle||"Switch to dark theme");return(r,l)=>(a(),P(Wo,{title:n.value,class:"VPSwitchAppearance","aria-checked":i(t),onClick:i(o)},{default:p(()=>[Jo,Yo]),_:1},8,["title","aria-checked","onClick"]))}}),ke=g(Xo,[["__scopeId","data-v-b79b56d4"]]),Qo={key:0,class:"VPNavBarAppearance"},Zo=_({__name:"VPNavBarAppearance",setup(s){const{site:t}=L();return(e,o)=>i(t).appearance&&i(t).appearance!=="force-dark"?(a(),u("div",Qo,[b(ke)])):f("",!0)}}),xo=g(Zo,[["__scopeId","data-v-ead91a81"]]),$e=I();let Fe=!1,ie=0;function en(s){const t=I(!1);if(oe){!Fe&&tn(),ie++;const e=z($e,o=>{var n,r,l;o===s.el.value||(n=s.el.value)!=null&&n.contains(o)?(t.value=!0,(r=s.onFocus)==null||r.call(s)):(t.value=!1,(l=s.onBlur)==null||l.call(s))});fe(()=>{e(),ie--,ie||sn()})}return et(t)}function tn(){document.addEventListener("focusin",Oe),Fe=!0,$e.value=document.activeElement}function sn(){document.removeEventListener("focusin",Oe)}function Oe(){$e.value=document.activeElement}const on={class:"VPMenuLink"},nn=_({__name:"VPMenuLink",props:{item:{}},setup(s){const{page:t}=L();return(e,o)=>(a(),u("div",on,[b(D,{class:N({active:i(K)(i(t).relativePath,e.item.activeMatch||e.item.link,!!e.item.activeMatch)}),href:e.item.link,target:e.item.target,rel:e.item.rel},{default:p(()=>[F(w(e.item.text),1)]),_:1},8,["class","href","target","rel"])]))}}),ne=g(nn,[["__scopeId","data-v-8b74d055"]]),an={class:"VPMenuGroup"},rn={key:0,class:"title"},ln=_({__name:"VPMenuGroup",props:{text:{},items:{}},setup(s){return(t,e)=>(a(),u("div",an,[t.text?(a(),u("p",rn,w(t.text),1)):f("",!0),(a(!0),u(M,null,E(t.items,o=>(a(),u(M,null,["link"in o?(a(),P(ne,{key:0,item:o},null,8,["item"])):f("",!0)],64))),256))]))}}),cn=g(ln,[["__scopeId","data-v-48c802d0"]]),un={class:"VPMenu"},dn={key:0,class:"items"},vn=_({__name:"VPMenu",props:{items:{}},setup(s){return(t,e)=>(a(),u("div",un,[t.items?(a(),u("div",dn,[(a(!0),u(M,null,E(t.items,o=>(a(),u(M,{key:o.text},["link"in o?(a(),P(ne,{key:0,item:o},null,8,["item"])):(a(),P(cn,{key:1,text:o.text,items:o.items},null,8,["text","items"]))],64))),128))])):f("",!0),c(t.$slots,"default",{},void 0,!0)]))}}),pn=g(vn,[["__scopeId","data-v-97491713"]]),hn=s=>(B("data-v-e5380155"),s=s(),H(),s),fn=["aria-expanded","aria-label"],_n={key:0,class:"text"},mn=["innerHTML"],bn=hn(()=>v("span",{class:"vpi-chevron-down text-icon"},null,-1)),kn={key:1,class:"vpi-more-horizontal icon"},$n={class:"menu"},gn=_({__name:"VPFlyout",props:{icon:{},button:{},label:{},items:{}},setup(s){const t=I(!1),e=I();en({el:e,onBlur:o});function o(){t.value=!1}return(n,r)=>(a(),u("div",{class:"VPFlyout",ref_key:"el",ref:e,onMouseenter:r[1]||(r[1]=l=>t.value=!0),onMouseleave:r[2]||(r[2]=l=>t.value=!1)},[v("button",{type:"button",class:"button","aria-haspopup":"true","aria-expanded":t.value,"aria-label":n.label,onClick:r[0]||(r[0]=l=>t.value=!t.value)},[n.button||n.icon?(a(),u("span",_n,[n.icon?(a(),u("span",{key:0,class:N([n.icon,"option-icon"])},null,2)):f("",!0),n.button?(a(),u("span",{key:1,innerHTML:n.button},null,8,mn)):f("",!0),bn])):(a(),u("span",kn))],8,fn),v("div",$n,[b(pn,{items:n.items},{default:p(()=>[c(n.$slots,"default",{},void 0,!0)]),_:3},8,["items"])])],544))}}),ge=g(gn,[["__scopeId","data-v-e5380155"]]),yn=["href","aria-label","innerHTML"],Pn=_({__name:"VPSocialLink",props:{icon:{},link:{},ariaLabel:{}},setup(s){const t=s,e=y(()=>typeof t.icon=="object"?t.icon.svg:``);return(o,n)=>(a(),u("a",{class:"VPSocialLink no-icon",href:o.link,"aria-label":o.ariaLabel??(typeof o.icon=="string"?o.icon:""),target:"_blank",rel:"noopener",innerHTML:e.value},null,8,yn))}}),Sn=g(Pn,[["__scopeId","data-v-717b8b75"]]),Vn={class:"VPSocialLinks"},Ln=_({__name:"VPSocialLinks",props:{links:{}},setup(s){return(t,e)=>(a(),u("div",Vn,[(a(!0),u(M,null,E(t.links,({link:o,icon:n,ariaLabel:r})=>(a(),P(Sn,{key:o,icon:n,link:o,ariaLabel:r},null,8,["icon","link","ariaLabel"]))),128))]))}}),ye=g(Ln,[["__scopeId","data-v-ee7a9424"]]),Tn={key:0,class:"group translations"},wn={class:"trans-title"},In={key:1,class:"group"},Nn={class:"item appearance"},Mn={class:"label"},An={class:"appearance-action"},Cn={key:2,class:"group"},Bn={class:"item social-links"},Hn=_({__name:"VPNavBarExtra",setup(s){const{site:t,theme:e}=L(),{localeLinks:o,currentLang:n}=X({correspondingLink:!0}),r=y(()=>o.value.length&&n.value.label||t.value.appearance||e.value.socialLinks);return(l,d)=>r.value?(a(),P(ge,{key:0,class:"VPNavBarExtra",label:"extra navigation"},{default:p(()=>[i(o).length&&i(n).label?(a(),u("div",Tn,[v("p",wn,w(i(n).label),1),(a(!0),u(M,null,E(i(o),h=>(a(),P(ne,{key:h.link,item:h},null,8,["item"]))),128))])):f("",!0),i(t).appearance&&i(t).appearance!=="force-dark"?(a(),u("div",In,[v("div",Nn,[v("p",Mn,w(i(e).darkModeSwitchLabel||"Appearance"),1),v("div",An,[b(ke)])])])):f("",!0),i(e).socialLinks?(a(),u("div",Cn,[v("div",Bn,[b(ye,{class:"social-links-list",links:i(e).socialLinks},null,8,["links"])])])):f("",!0)]),_:1})):f("",!0)}}),En=g(Hn,[["__scopeId","data-v-9b536d0b"]]),Dn=s=>(B("data-v-5dea55bf"),s=s(),H(),s),Fn=["aria-expanded"],On=Dn(()=>v("span",{class:"container"},[v("span",{class:"top"}),v("span",{class:"middle"}),v("span",{class:"bottom"})],-1)),Un=[On],jn=_({__name:"VPNavBarHamburger",props:{active:{type:Boolean}},emits:["click"],setup(s){return(t,e)=>(a(),u("button",{type:"button",class:N(["VPNavBarHamburger",{active:t.active}]),"aria-label":"mobile navigation","aria-expanded":t.active,"aria-controls":"VPNavScreen",onClick:e[0]||(e[0]=o=>t.$emit("click"))},Un,10,Fn))}}),Gn=g(jn,[["__scopeId","data-v-5dea55bf"]]),zn=["innerHTML"],Kn=_({__name:"VPNavBarMenuLink",props:{item:{}},setup(s){const{page:t}=L();return(e,o)=>(a(),P(D,{class:N({VPNavBarMenuLink:!0,active:i(K)(i(t).relativePath,e.item.activeMatch||e.item.link,!!e.item.activeMatch)}),href:e.item.link,noIcon:e.item.noIcon,target:e.item.target,rel:e.item.rel,tabindex:"0"},{default:p(()=>[v("span",{innerHTML:e.item.text},null,8,zn)]),_:1},8,["class","href","noIcon","target","rel"]))}}),Rn=g(Kn,[["__scopeId","data-v-ed5ac1f6"]]),qn=_({__name:"VPNavBarMenuGroup",props:{item:{}},setup(s){const t=s,{page:e}=L(),o=r=>"link"in r?K(e.value.relativePath,r.link,!!t.item.activeMatch):r.items.some(o),n=y(()=>o(t.item));return(r,l)=>(a(),P(ge,{class:N({VPNavBarMenuGroup:!0,active:i(K)(i(e).relativePath,r.item.activeMatch,!!r.item.activeMatch)||n.value}),button:r.item.text,items:r.item.items},null,8,["class","button","items"]))}}),Wn=s=>(B("data-v-492ea56d"),s=s(),H(),s),Jn={key:0,"aria-labelledby":"main-nav-aria-label",class:"VPNavBarMenu"},Yn=Wn(()=>v("span",{id:"main-nav-aria-label",class:"visually-hidden"},"Main Navigation",-1)),Xn=_({__name:"VPNavBarMenu",setup(s){const{theme:t}=L();return(e,o)=>i(t).nav?(a(),u("nav",Jn,[Yn,(a(!0),u(M,null,E(i(t).nav,n=>(a(),u(M,{key:n.text},["link"in n?(a(),P(Rn,{key:0,item:n},null,8,["item"])):(a(),P(qn,{key:1,item:n},null,8,["item"]))],64))),128))])):f("",!0)}}),Qn=g(Xn,[["__scopeId","data-v-492ea56d"]]);function Zn(s){const{localeIndex:t,theme:e}=L();function o(n){var A,C,T;const r=n.split("."),l=(A=e.value.search)==null?void 0:A.options,d=l&&typeof l=="object",h=d&&((T=(C=l.locales)==null?void 0:C[t.value])==null?void 0:T.translations)||null,m=d&&l.translations||null;let k=h,$=m,V=s;const S=r.pop();for(const U of r){let j=null;const q=V==null?void 0:V[U];q&&(j=V=q);const ae=$==null?void 0:$[U];ae&&(j=$=ae);const re=k==null?void 0:k[U];re&&(j=k=re),q||(V=j),ae||($=j),re||(k=j)}return(k==null?void 0:k[S])??($==null?void 0:$[S])??(V==null?void 0:V[S])??""}return o}const xn=["aria-label"],ea={class:"DocSearch-Button-Container"},ta=v("span",{class:"vp-icon DocSearch-Search-Icon"},null,-1),sa={class:"DocSearch-Button-Placeholder"},oa=v("span",{class:"DocSearch-Button-Keys"},[v("kbd",{class:"DocSearch-Button-Key"}),v("kbd",{class:"DocSearch-Button-Key"},"K")],-1),Pe=_({__name:"VPNavBarSearchButton",setup(s){const e=Zn({button:{buttonText:"Search",buttonAriaLabel:"Search"}});return(o,n)=>(a(),u("button",{type:"button",class:"DocSearch DocSearch-Button","aria-label":i(e)("button.buttonAriaLabel")},[v("span",ea,[ta,v("span",sa,w(i(e)("button.buttonText")),1)]),oa],8,xn))}}),na={class:"VPNavBarSearch"},aa={id:"local-search"},ra={key:1,id:"docsearch"},ia=_({__name:"VPNavBarSearch",setup(s){const t=tt(()=>st(()=>import("./VPLocalSearchBox.CaalGK9M.js"),__vite__mapDeps([0,1]))),e=()=>null,{theme:o}=L(),n=I(!1),r=I(!1);G(()=>{});function l(){n.value||(n.value=!0,setTimeout(d,16))}function d(){const $=new Event("keydown");$.key="k",$.metaKey=!0,window.dispatchEvent($),setTimeout(()=>{document.querySelector(".DocSearch-Modal")||d()},16)}function h($){const V=$.target,S=V.tagName;return V.isContentEditable||S==="INPUT"||S==="SELECT"||S==="TEXTAREA"}const m=I(!1);ce("k",$=>{($.ctrlKey||$.metaKey)&&($.preventDefault(),m.value=!0)}),ce("/",$=>{h($)||($.preventDefault(),m.value=!0)});const k="local";return($,V)=>{var S;return a(),u("div",na,[i(k)==="local"?(a(),u(M,{key:0},[m.value?(a(),P(i(t),{key:0,onClose:V[0]||(V[0]=A=>m.value=!1)})):f("",!0),v("div",aa,[b(Pe,{onClick:V[1]||(V[1]=A=>m.value=!0)})])],64)):i(k)==="algolia"?(a(),u(M,{key:1},[n.value?(a(),P(i(e),{key:0,algolia:((S=i(o).search)==null?void 0:S.options)??i(o).algolia,onVnodeBeforeMount:V[2]||(V[2]=A=>r.value=!0)},null,8,["algolia"])):f("",!0),r.value?f("",!0):(a(),u("div",ra,[b(Pe,{onClick:l})]))],64)):f("",!0)])}}}),la=_({__name:"VPNavBarSocialLinks",setup(s){const{theme:t}=L();return(e,o)=>i(t).socialLinks?(a(),P(ye,{key:0,class:"VPNavBarSocialLinks",links:i(t).socialLinks},null,8,["links"])):f("",!0)}}),ca=g(la,[["__scopeId","data-v-164c457f"]]),ua=["href","rel","target"],da={key:1},va={key:2},pa=_({__name:"VPNavBarTitle",setup(s){const{site:t,theme:e}=L(),{hasSidebar:o}=O(),{currentLang:n}=X(),r=y(()=>{var h;return typeof e.value.logoLink=="string"?e.value.logoLink:(h=e.value.logoLink)==null?void 0:h.link}),l=y(()=>{var h;return typeof e.value.logoLink=="string"||(h=e.value.logoLink)==null?void 0:h.rel}),d=y(()=>{var h;return typeof e.value.logoLink=="string"||(h=e.value.logoLink)==null?void 0:h.target});return(h,m)=>(a(),u("div",{class:N(["VPNavBarTitle",{"has-sidebar":i(o)}])},[v("a",{class:"title",href:r.value??i(me)(i(n).link),rel:l.value,target:d.value},[c(h.$slots,"nav-bar-title-before",{},void 0,!0),i(e).logo?(a(),P(x,{key:0,class:"logo",image:i(e).logo},null,8,["image"])):f("",!0),i(e).siteTitle?(a(),u("span",da,w(i(e).siteTitle),1)):i(e).siteTitle===void 0?(a(),u("span",va,w(i(t).title),1)):f("",!0),c(h.$slots,"nav-bar-title-after",{},void 0,!0)],8,ua)],2))}}),ha=g(pa,[["__scopeId","data-v-28a961f9"]]),fa={class:"items"},_a={class:"title"},ma=_({__name:"VPNavBarTranslations",setup(s){const{theme:t}=L(),{localeLinks:e,currentLang:o}=X({correspondingLink:!0});return(n,r)=>i(e).length&&i(o).label?(a(),P(ge,{key:0,class:"VPNavBarTranslations",icon:"vpi-languages",label:i(t).langMenuLabel||"Change language"},{default:p(()=>[v("div",fa,[v("p",_a,w(i(o).label),1),(a(!0),u(M,null,E(i(e),l=>(a(),P(ne,{key:l.link,item:l},null,8,["item"]))),128))])]),_:1},8,["label"])):f("",!0)}}),ba=g(ma,[["__scopeId","data-v-c80d9ad0"]]),ka=s=>(B("data-v-40788ea0"),s=s(),H(),s),$a={class:"wrapper"},ga={class:"container"},ya={class:"title"},Pa={class:"content"},Sa={class:"content-body"},Va=ka(()=>v("div",{class:"divider"},[v("div",{class:"divider-line"})],-1)),La=_({__name:"VPNavBar",props:{isScreenOpen:{type:Boolean}},emits:["toggle-screen"],setup(s){const{y:t}=Me(),{hasSidebar:e}=O(),{frontmatter:o}=L(),n=I({});return Le(()=>{n.value={"has-sidebar":e.value,home:o.value.layout==="home",top:t.value===0}}),(r,l)=>(a(),u("div",{class:N(["VPNavBar",n.value])},[v("div",$a,[v("div",ga,[v("div",ya,[b(ha,null,{"nav-bar-title-before":p(()=>[c(r.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":p(()=>[c(r.$slots,"nav-bar-title-after",{},void 0,!0)]),_:3})]),v("div",Pa,[v("div",Sa,[c(r.$slots,"nav-bar-content-before",{},void 0,!0),b(ia,{class:"search"}),b(Qn,{class:"menu"}),b(ba,{class:"translations"}),b(xo,{class:"appearance"}),b(ca,{class:"social-links"}),b(En,{class:"extra"}),c(r.$slots,"nav-bar-content-after",{},void 0,!0),b(Gn,{class:"hamburger",active:r.isScreenOpen,onClick:l[0]||(l[0]=d=>r.$emit("toggle-screen"))},null,8,["active"])])])])]),Va],2))}}),Ta=g(La,[["__scopeId","data-v-40788ea0"]]),wa={key:0,class:"VPNavScreenAppearance"},Ia={class:"text"},Na=_({__name:"VPNavScreenAppearance",setup(s){const{site:t,theme:e}=L();return(o,n)=>i(t).appearance&&i(t).appearance!=="force-dark"?(a(),u("div",wa,[v("p",Ia,w(i(e).darkModeSwitchLabel||"Appearance"),1),b(ke)])):f("",!0)}}),Ma=g(Na,[["__scopeId","data-v-2b89f08b"]]),Aa=_({__name:"VPNavScreenMenuLink",props:{item:{}},setup(s){const t=J("close-screen");return(e,o)=>(a(),P(D,{class:"VPNavScreenMenuLink",href:e.item.link,target:e.item.target,rel:e.item.rel,onClick:i(t),innerHTML:e.item.text},null,8,["href","target","rel","onClick","innerHTML"]))}}),Ca=g(Aa,[["__scopeId","data-v-27d04aeb"]]),Ba=_({__name:"VPNavScreenMenuGroupLink",props:{item:{}},setup(s){const t=J("close-screen");return(e,o)=>(a(),P(D,{class:"VPNavScreenMenuGroupLink",href:e.item.link,target:e.item.target,rel:e.item.rel,onClick:i(t)},{default:p(()=>[F(w(e.item.text),1)]),_:1},8,["href","target","rel","onClick"]))}}),Ue=g(Ba,[["__scopeId","data-v-7179dbb7"]]),Ha={class:"VPNavScreenMenuGroupSection"},Ea={key:0,class:"title"},Da=_({__name:"VPNavScreenMenuGroupSection",props:{text:{},items:{}},setup(s){return(t,e)=>(a(),u("div",Ha,[t.text?(a(),u("p",Ea,w(t.text),1)):f("",!0),(a(!0),u(M,null,E(t.items,o=>(a(),P(Ue,{key:o.text,item:o},null,8,["item"]))),128))]))}}),Fa=g(Da,[["__scopeId","data-v-4b8941ac"]]),Oa=s=>(B("data-v-c9df2649"),s=s(),H(),s),Ua=["aria-controls","aria-expanded"],ja=["innerHTML"],Ga=Oa(()=>v("span",{class:"vpi-plus button-icon"},null,-1)),za=["id"],Ka={key:1,class:"group"},Ra=_({__name:"VPNavScreenMenuGroup",props:{text:{},items:{}},setup(s){const t=s,e=I(!1),o=y(()=>`NavScreenGroup-${t.text.replace(" ","-").toLowerCase()}`);function n(){e.value=!e.value}return(r,l)=>(a(),u("div",{class:N(["VPNavScreenMenuGroup",{open:e.value}])},[v("button",{class:"button","aria-controls":o.value,"aria-expanded":e.value,onClick:n},[v("span",{class:"button-text",innerHTML:r.text},null,8,ja),Ga],8,Ua),v("div",{id:o.value,class:"items"},[(a(!0),u(M,null,E(r.items,d=>(a(),u(M,{key:d.text},["link"in d?(a(),u("div",{key:d.text,class:"item"},[b(Ue,{item:d},null,8,["item"])])):(a(),u("div",Ka,[b(Fa,{text:d.text,items:d.items},null,8,["text","items"])]))],64))),128))],8,za)],2))}}),qa=g(Ra,[["__scopeId","data-v-c9df2649"]]),Wa={key:0,class:"VPNavScreenMenu"},Ja=_({__name:"VPNavScreenMenu",setup(s){const{theme:t}=L();return(e,o)=>i(t).nav?(a(),u("nav",Wa,[(a(!0),u(M,null,E(i(t).nav,n=>(a(),u(M,{key:n.text},["link"in n?(a(),P(Ca,{key:0,item:n},null,8,["item"])):(a(),P(qa,{key:1,text:n.text||"",items:n.items},null,8,["text","items"]))],64))),128))])):f("",!0)}}),Ya=_({__name:"VPNavScreenSocialLinks",setup(s){const{theme:t}=L();return(e,o)=>i(t).socialLinks?(a(),P(ye,{key:0,class:"VPNavScreenSocialLinks",links:i(t).socialLinks},null,8,["links"])):f("",!0)}}),je=s=>(B("data-v-362991c2"),s=s(),H(),s),Xa=je(()=>v("span",{class:"vpi-languages icon lang"},null,-1)),Qa=je(()=>v("span",{class:"vpi-chevron-down icon chevron"},null,-1)),Za={class:"list"},xa=_({__name:"VPNavScreenTranslations",setup(s){const{localeLinks:t,currentLang:e}=X({correspondingLink:!0}),o=I(!1);function n(){o.value=!o.value}return(r,l)=>i(t).length&&i(e).label?(a(),u("div",{key:0,class:N(["VPNavScreenTranslations",{open:o.value}])},[v("button",{class:"title",onClick:n},[Xa,F(" "+w(i(e).label)+" ",1),Qa]),v("ul",Za,[(a(!0),u(M,null,E(i(t),d=>(a(),u("li",{key:d.link,class:"item"},[b(D,{class:"link",href:d.link},{default:p(()=>[F(w(d.text),1)]),_:2},1032,["href"])]))),128))])],2)):f("",!0)}}),er=g(xa,[["__scopeId","data-v-362991c2"]]),tr={class:"container"},sr=_({__name:"VPNavScreen",props:{open:{type:Boolean}},setup(s){const t=I(null),e=Ae(oe?document.body:null);return(o,n)=>(a(),P(pe,{name:"fade",onEnter:n[0]||(n[0]=r=>e.value=!0),onAfterLeave:n[1]||(n[1]=r=>e.value=!1)},{default:p(()=>[o.open?(a(),u("div",{key:0,class:"VPNavScreen",ref_key:"screen",ref:t,id:"VPNavScreen"},[v("div",tr,[c(o.$slots,"nav-screen-content-before",{},void 0,!0),b(Ja,{class:"menu"}),b(er,{class:"translations"}),b(Ma,{class:"appearance"}),b(Ya,{class:"social-links"}),c(o.$slots,"nav-screen-content-after",{},void 0,!0)])],512)):f("",!0)]),_:3}))}}),or=g(sr,[["__scopeId","data-v-382f42e9"]]),nr={key:0,class:"VPNav"},ar=_({__name:"VPNav",setup(s){const{isScreenOpen:t,closeScreen:e,toggleScreen:o}=jo(),{frontmatter:n}=L(),r=y(()=>n.value.navbar!==!1);return _e("close-screen",e),ee(()=>{oe&&document.documentElement.classList.toggle("hide-nav",!r.value)}),(l,d)=>r.value?(a(),u("header",nr,[b(Ta,{"is-screen-open":i(t),onToggleScreen:i(o)},{"nav-bar-title-before":p(()=>[c(l.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":p(()=>[c(l.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":p(()=>[c(l.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":p(()=>[c(l.$slots,"nav-bar-content-after",{},void 0,!0)]),_:3},8,["is-screen-open","onToggleScreen"]),b(or,{open:i(t)},{"nav-screen-content-before":p(()=>[c(l.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":p(()=>[c(l.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3},8,["open"])])):f("",!0)}}),rr=g(ar,[["__scopeId","data-v-f1e365da"]]),Ge=s=>(B("data-v-2ea20db7"),s=s(),H(),s),ir=["role","tabindex"],lr=Ge(()=>v("div",{class:"indicator"},null,-1)),cr=Ge(()=>v("span",{class:"vpi-chevron-right caret-icon"},null,-1)),ur=[cr],dr={key:1,class:"items"},vr=_({__name:"VPSidebarItem",props:{item:{},depth:{}},setup(s){const t=s,{collapsed:e,collapsible:o,isLink:n,isActiveLink:r,hasActiveLink:l,hasChildren:d,toggle:h}=wt(y(()=>t.item)),m=y(()=>d.value?"section":"div"),k=y(()=>n.value?"a":"div"),$=y(()=>d.value?t.depth+2===7?"p":`h${t.depth+2}`:"p"),V=y(()=>n.value?void 0:"button"),S=y(()=>[[`level-${t.depth}`],{collapsible:o.value},{collapsed:e.value},{"is-link":n.value},{"is-active":r.value},{"has-active":l.value}]);function A(T){"key"in T&&T.key!=="Enter"||!t.item.link&&h()}function C(){t.item.link&&h()}return(T,U)=>{const j=R("VPSidebarItem",!0);return a(),P(W(m.value),{class:N(["VPSidebarItem",S.value])},{default:p(()=>[T.item.text?(a(),u("div",Q({key:0,class:"item",role:V.value},nt(T.item.items?{click:A,keydown:A}:{},!0),{tabindex:T.item.items&&0}),[lr,T.item.link?(a(),P(D,{key:0,tag:k.value,class:"link",href:T.item.link,rel:T.item.rel,target:T.item.target},{default:p(()=>[(a(),P(W($.value),{class:"text",innerHTML:T.item.text},null,8,["innerHTML"]))]),_:1},8,["tag","href","rel","target"])):(a(),P(W($.value),{key:1,class:"text",innerHTML:T.item.text},null,8,["innerHTML"])),T.item.collapsed!=null&&T.item.items&&T.item.items.length?(a(),u("div",{key:2,class:"caret",role:"button","aria-label":"toggle section",onClick:C,onKeydown:ot(C,["enter"]),tabindex:"0"},ur,32)):f("",!0)],16,ir)):f("",!0),T.item.items&&T.item.items.length?(a(),u("div",dr,[T.depth<5?(a(!0),u(M,{key:0},E(T.item.items,q=>(a(),P(j,{key:q.text,item:q,depth:T.depth+1},null,8,["item","depth"]))),128)):f("",!0)])):f("",!0)]),_:1},8,["class"])}}}),pr=g(vr,[["__scopeId","data-v-2ea20db7"]]),ze=s=>(B("data-v-ec846e01"),s=s(),H(),s),hr=ze(()=>v("div",{class:"curtain"},null,-1)),fr={class:"nav",id:"VPSidebarNav","aria-labelledby":"sidebar-aria-label",tabindex:"-1"},_r=ze(()=>v("span",{class:"visually-hidden",id:"sidebar-aria-label"}," Sidebar Navigation ",-1)),mr=_({__name:"VPSidebar",props:{open:{type:Boolean}},setup(s){const{sidebarGroups:t,hasSidebar:e}=O(),o=s,n=I(null),r=Ae(oe?document.body:null);return z([o,n],()=>{var l;o.open?(r.value=!0,(l=n.value)==null||l.focus()):r.value=!1},{immediate:!0,flush:"post"}),(l,d)=>i(e)?(a(),u("aside",{key:0,class:N(["VPSidebar",{open:l.open}]),ref_key:"navEl",ref:n,onClick:d[0]||(d[0]=at(()=>{},["stop"]))},[hr,v("nav",fr,[_r,c(l.$slots,"sidebar-nav-before",{},void 0,!0),(a(!0),u(M,null,E(i(t),h=>(a(),u("div",{key:h.text,class:"group"},[b(pr,{item:h,depth:0},null,8,["item"])]))),128)),c(l.$slots,"sidebar-nav-after",{},void 0,!0)])],2)):f("",!0)}}),br=g(mr,[["__scopeId","data-v-ec846e01"]]),kr=_({__name:"VPSkipLink",setup(s){const t=se(),e=I();z(()=>t.path,()=>e.value.focus());function o({target:n}){const r=document.getElementById(decodeURIComponent(n.hash).slice(1));if(r){const l=()=>{r.removeAttribute("tabindex"),r.removeEventListener("blur",l)};r.setAttribute("tabindex","-1"),r.addEventListener("blur",l),r.focus(),window.scrollTo(0,0)}}return(n,r)=>(a(),u(M,null,[v("span",{ref_key:"backToTop",ref:e,tabindex:"-1"},null,512),v("a",{href:"#VPContent",class:"VPSkipLink visually-hidden",onClick:o}," Skip to content ")],64))}}),$r=g(kr,[["__scopeId","data-v-c3508ec8"]]),gr=_({__name:"Layout",setup(s){const{isOpen:t,open:e,close:o}=O(),n=se();z(()=>n.path,o),Tt(t,o);const{frontmatter:r}=L(),l=Ce(),d=y(()=>!!l["home-hero-image"]);return _e("hero-image-slot-exists",d),(h,m)=>{const k=R("Content");return i(r).layout!==!1?(a(),u("div",{key:0,class:N(["Layout",i(r).pageClass])},[c(h.$slots,"layout-top",{},void 0,!0),b($r),b(vt,{class:"backdrop",show:i(t),onClick:i(o)},null,8,["show","onClick"]),b(rr,null,{"nav-bar-title-before":p(()=>[c(h.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":p(()=>[c(h.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":p(()=>[c(h.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":p(()=>[c(h.$slots,"nav-bar-content-after",{},void 0,!0)]),"nav-screen-content-before":p(()=>[c(h.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":p(()=>[c(h.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3}),b(Uo,{open:i(t),onOpenMenu:i(e)},null,8,["open","onOpenMenu"]),b(br,{open:i(t)},{"sidebar-nav-before":p(()=>[c(h.$slots,"sidebar-nav-before",{},void 0,!0)]),"sidebar-nav-after":p(()=>[c(h.$slots,"sidebar-nav-after",{},void 0,!0)]),_:3},8,["open"]),b($o,null,{"page-top":p(()=>[c(h.$slots,"page-top",{},void 0,!0)]),"page-bottom":p(()=>[c(h.$slots,"page-bottom",{},void 0,!0)]),"not-found":p(()=>[c(h.$slots,"not-found",{},void 0,!0)]),"home-hero-before":p(()=>[c(h.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":p(()=>[c(h.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":p(()=>[c(h.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":p(()=>[c(h.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":p(()=>[c(h.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":p(()=>[c(h.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":p(()=>[c(h.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":p(()=>[c(h.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":p(()=>[c(h.$slots,"home-features-after",{},void 0,!0)]),"doc-footer-before":p(()=>[c(h.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":p(()=>[c(h.$slots,"doc-before",{},void 0,!0)]),"doc-after":p(()=>[c(h.$slots,"doc-after",{},void 0,!0)]),"doc-top":p(()=>[c(h.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":p(()=>[c(h.$slots,"doc-bottom",{},void 0,!0)]),"aside-top":p(()=>[c(h.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":p(()=>[c(h.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":p(()=>[c(h.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":p(()=>[c(h.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":p(()=>[c(h.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":p(()=>[c(h.$slots,"aside-ads-after",{},void 0,!0)]),_:3}),b(Vo),c(h.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),P(k,{key:1}))}}}),yr=g(gr,[["__scopeId","data-v-a9a9e638"]]),Se={Layout:yr,enhanceApp:({app:s})=>{s.component("Badge",ct)}},Pr=s=>{if(typeof document>"u")return{stabilizeScrollPosition:n=>async(...r)=>n(...r)};const t=document.documentElement;return{stabilizeScrollPosition:o=>async(...n)=>{const r=o(...n),l=s.value;if(!l)return r;const d=l.offsetTop-t.scrollTop;return await Ne(),t.scrollTop=l.offsetTop-d,r}}},Ke="vitepress:tabSharedState",Y=typeof localStorage<"u"?localStorage:null,Re="vitepress:tabsSharedState",Sr=()=>{const s=Y==null?void 0:Y.getItem(Re);if(s)try{return JSON.parse(s)}catch{}return{}},Vr=s=>{Y&&Y.setItem(Re,JSON.stringify(s))},Lr=s=>{const t=rt({});z(()=>t.content,(e,o)=>{e&&o&&Vr(e)},{deep:!0}),s.provide(Ke,t)},Tr=(s,t)=>{const e=J(Ke);if(!e)throw new Error("[vitepress-plugin-tabs] TabsSharedState should be injected");G(()=>{e.content||(e.content=Sr())});const o=I(),n=y({get(){var h;const l=t.value,d=s.value;if(l){const m=(h=e.content)==null?void 0:h[l];if(m&&d.includes(m))return m}else{const m=o.value;if(m)return m}return d[0]},set(l){const d=t.value;d?e.content&&(e.content[d]=l):o.value=l}});return{selected:n,select:l=>{n.value=l}}};let Ve=0;const wr=()=>(Ve++,""+Ve);function Ir(){const s=Ce();return y(()=>{var o;const e=(o=s.default)==null?void 0:o.call(s);return e?e.filter(n=>typeof n.type=="object"&&"__name"in n.type&&n.type.__name==="PluginTabsTab"&&n.props).map(n=>{var r;return(r=n.props)==null?void 0:r.label}):[]})}const qe="vitepress:tabSingleState",Nr=s=>{_e(qe,s)},Mr=()=>{const s=J(qe);if(!s)throw new Error("[vitepress-plugin-tabs] TabsSingleState should be injected");return s},Ar={class:"plugin-tabs"},Cr=["id","aria-selected","aria-controls","tabindex","onClick"],Br=_({__name:"PluginTabs",props:{sharedStateKey:{}},setup(s){const t=s,e=Ir(),{selected:o,select:n}=Tr(e,it(t,"sharedStateKey")),r=I(),{stabilizeScrollPosition:l}=Pr(r),d=l(n),h=I([]),m=$=>{var A;const V=e.value.indexOf(o.value);let S;$.key==="ArrowLeft"?S=V>=1?V-1:e.value.length-1:$.key==="ArrowRight"&&(S=V(a(),u("div",Ar,[v("div",{ref_key:"tablist",ref:r,class:"plugin-tabs--tab-list",role:"tablist",onKeydown:m},[(a(!0),u(M,null,E(i(e),S=>(a(),u("button",{id:`tab-${S}-${i(k)}`,ref_for:!0,ref_key:"buttonRefs",ref:h,key:S,role:"tab",class:"plugin-tabs--tab","aria-selected":S===i(o),"aria-controls":`panel-${S}-${i(k)}`,tabindex:S===i(o)?0:-1,onClick:()=>i(d)(S)},w(S),9,Cr))),128))],544),c($.$slots,"default")]))}}),Hr=["id","aria-labelledby"],Er=_({__name:"PluginTabsTab",props:{label:{}},setup(s){const{uid:t,selected:e}=Mr();return(o,n)=>i(e)===o.label?(a(),u("div",{key:0,id:`panel-${o.label}-${i(t)}`,class:"plugin-tabs--content",role:"tabpanel",tabindex:"0","aria-labelledby":`tab-${o.label}-${i(t)}`},[c(o.$slots,"default",{},void 0,!0)],8,Hr)):f("",!0)}}),Dr=g(Er,[["__scopeId","data-v-9b0d03d2"]]),Fr=s=>{Lr(s),s.component("PluginTabs",Br),s.component("PluginTabsTab",Dr)},Ur={extends:Se,Layout(){return lt(Se.Layout,null,{})},enhanceApp({app:s,router:t,siteData:e}){Fr(s)}};export{Ur as R,Zn as c,L as u}; diff --git a/dev/assets/chunks/theme.CNBIs78H.js b/dev/assets/chunks/theme.CNBIs78H.js new file mode 100644 index 0000000..977a7c5 --- /dev/null +++ b/dev/assets/chunks/theme.CNBIs78H.js @@ -0,0 +1,2 @@ +const __vite__fileDeps=["assets/chunks/VPLocalSearchBox.DqWxI-Ji.js","assets/chunks/framework.Cvv1S4VC.js"],__vite__mapDeps=i=>i.map(i=>__vite__fileDeps[i]); +import{d as _,o as a,c as u,r as c,n as N,a as F,t as w,b as y,w as p,e as f,T as pe,_ as $,u as Je,i as Ye,f as Xe,g as he,h as g,j as v,k as i,p as B,l as H,m as z,q as le,s as I,v as O,x as ee,y as K,z as fe,A as Le,B as Qe,C as Ze,D as R,F as M,E,G as Te,H as te,I as k,J as W,K as we,L as se,M as Q,N as J,O as xe,P as Ie,Q as ce,R as Ne,S as Me,U as oe,V as et,W as tt,X as st,Y as Ae,Z as _e,$ as ot,a0 as nt,a1 as at,a2 as Ce,a3 as rt,a4 as it,a5 as lt}from"./framework.Cvv1S4VC.js";const ct=_({__name:"VPBadge",props:{text:{},type:{default:"tip"}},setup(s){return(e,t)=>(a(),u("span",{class:N(["VPBadge",e.type])},[c(e.$slots,"default",{},()=>[F(w(e.text),1)])],2))}}),ut={key:0,class:"VPBackdrop"},dt=_({__name:"VPBackdrop",props:{show:{type:Boolean}},setup(s){return(e,t)=>(a(),y(pe,{name:"fade"},{default:p(()=>[e.show?(a(),u("div",ut)):f("",!0)]),_:1}))}}),vt=$(dt,[["__scopeId","data-v-b06cdb19"]]),L=Je;function pt(s,e){let t,o=!1;return()=>{t&&clearTimeout(t),o?t=setTimeout(s,e):(s(),(o=!0)&&setTimeout(()=>o=!1,e))}}function ue(s){return/^\//.test(s)?s:`/${s}`}function me(s){const{pathname:e,search:t,hash:o,protocol:n}=new URL(s,"http://a.com");if(Ye(s)||s.startsWith("#")||!n.startsWith("http")||!Xe(e))return s;const{site:r}=L(),l=e.endsWith("/")||e.endsWith(".html")?s:s.replace(/(?:(^\.+)\/)?.*$/,`$1${e.replace(/(\.md)?$/,r.value.cleanUrls?"":".html")}${t}${o}`);return he(l)}function X({correspondingLink:s=!1}={}){const{site:e,localeIndex:t,page:o,theme:n,hash:r}=L(),l=g(()=>{var d,m;return{label:(d=e.value.locales[t.value])==null?void 0:d.label,link:((m=e.value.locales[t.value])==null?void 0:m.link)||(t.value==="root"?"/":`/${t.value}/`)}});return{localeLinks:g(()=>Object.entries(e.value.locales).flatMap(([d,m])=>l.value.label===m.label?[]:{text:m.label,link:ht(m.link||(d==="root"?"/":`/${d}/`),n.value.i18nRouting!==!1&&s,o.value.relativePath.slice(l.value.link.length-1),!e.value.cleanUrls)+r.value})),currentLang:l}}function ht(s,e,t,o){return e?s.replace(/\/$/,"")+ue(t.replace(/(^|\/)index\.md$/,"$1").replace(/\.md$/,o?".html":"")):s}const ft=s=>(B("data-v-951cab6c"),s=s(),H(),s),_t={class:"NotFound"},mt={class:"code"},bt={class:"title"},kt=ft(()=>v("div",{class:"divider"},null,-1)),$t={class:"quote"},gt={class:"action"},yt=["href","aria-label"],Pt=_({__name:"NotFound",setup(s){const{theme:e}=L(),{currentLang:t}=X();return(o,n)=>{var r,l,h,d,m;return a(),u("div",_t,[v("p",mt,w(((r=i(e).notFound)==null?void 0:r.code)??"404"),1),v("h1",bt,w(((l=i(e).notFound)==null?void 0:l.title)??"PAGE NOT FOUND"),1),kt,v("blockquote",$t,w(((h=i(e).notFound)==null?void 0:h.quote)??"But if you don't change your direction, and if you keep looking, you may end up where you are heading."),1),v("div",gt,[v("a",{class:"link",href:i(he)(i(t).link),"aria-label":((d=i(e).notFound)==null?void 0:d.linkLabel)??"go to home"},w(((m=i(e).notFound)==null?void 0:m.linkText)??"Take me home"),9,yt)])])}}}),St=$(Pt,[["__scopeId","data-v-951cab6c"]]);function Be(s,e){if(Array.isArray(s))return Z(s);if(s==null)return[];e=ue(e);const t=Object.keys(s).sort((n,r)=>r.split("/").length-n.split("/").length).find(n=>e.startsWith(ue(n))),o=t?s[t]:[];return Array.isArray(o)?Z(o):Z(o.items,o.base)}function Vt(s){const e=[];let t=0;for(const o in s){const n=s[o];if(n.items){t=e.push(n);continue}e[t]||e.push({items:[]}),e[t].items.push(n)}return e}function Lt(s){const e=[];function t(o){for(const n of o)n.text&&n.link&&e.push({text:n.text,link:n.link,docFooterText:n.docFooterText}),n.items&&t(n.items)}return t(s),e}function de(s,e){return Array.isArray(e)?e.some(t=>de(s,t)):z(s,e.link)?!0:e.items?de(s,e.items):!1}function Z(s,e){return[...s].map(t=>{const o={...t},n=o.base||e;return n&&o.link&&(o.link=n+o.link),o.items&&(o.items=Z(o.items,n)),o})}function U(){const{frontmatter:s,page:e,theme:t}=L(),o=le("(min-width: 960px)"),n=I(!1),r=g(()=>{const C=t.value.sidebar,T=e.value.relativePath;return C?Be(C,T):[]}),l=I(r.value);O(r,(C,T)=>{JSON.stringify(C)!==JSON.stringify(T)&&(l.value=r.value)});const h=g(()=>s.value.sidebar!==!1&&l.value.length>0&&s.value.layout!=="home"),d=g(()=>m?s.value.aside==null?t.value.aside==="left":s.value.aside==="left":!1),m=g(()=>s.value.layout==="home"?!1:s.value.aside!=null?!!s.value.aside:t.value.aside!==!1),V=g(()=>h.value&&o.value),b=g(()=>h.value?Vt(l.value):[]);function P(){n.value=!0}function S(){n.value=!1}function A(){n.value?S():P()}return{isOpen:n,sidebar:l,sidebarGroups:b,hasSidebar:h,hasAside:m,leftAside:d,isSidebarEnabled:V,open:P,close:S,toggle:A}}function Tt(s,e){let t;ee(()=>{t=s.value?document.activeElement:void 0}),K(()=>{window.addEventListener("keyup",o)}),fe(()=>{window.removeEventListener("keyup",o)});function o(n){n.key==="Escape"&&s.value&&(e(),t==null||t.focus())}}function wt(s){const{page:e,hash:t}=L(),o=I(!1),n=g(()=>s.value.collapsed!=null),r=g(()=>!!s.value.link),l=I(!1),h=()=>{l.value=z(e.value.relativePath,s.value.link)};O([e,s,t],h),K(h);const d=g(()=>l.value?!0:s.value.items?de(e.value.relativePath,s.value.items):!1),m=g(()=>!!(s.value.items&&s.value.items.length));ee(()=>{o.value=!!(n.value&&s.value.collapsed)}),Le(()=>{(l.value||d.value)&&(o.value=!1)});function V(){n.value&&(o.value=!o.value)}return{collapsed:o,collapsible:n,isLink:r,isActiveLink:l,hasActiveLink:d,hasChildren:m,toggle:V}}function It(){const{hasSidebar:s}=U(),e=le("(min-width: 960px)"),t=le("(min-width: 1280px)");return{isAsideEnabled:g(()=>!t.value&&!e.value?!1:s.value?t.value:e.value)}}const ve=[];function He(s){return typeof s.outline=="object"&&!Array.isArray(s.outline)&&s.outline.label||s.outlineTitle||"On this page"}function be(s){const e=[...document.querySelectorAll(".VPDoc :where(h1,h2,h3,h4,h5,h6)")].filter(t=>t.id&&t.hasChildNodes()).map(t=>{const o=Number(t.tagName[1]);return{element:t,title:Nt(t),link:"#"+t.id,level:o}});return Mt(e,s)}function Nt(s){let e="";for(const t of s.childNodes)if(t.nodeType===1){if(t.classList.contains("VPBadge")||t.classList.contains("header-anchor")||t.classList.contains("ignore-header"))continue;e+=t.textContent}else t.nodeType===3&&(e+=t.textContent);return e.trim()}function Mt(s,e){if(e===!1)return[];const t=(typeof e=="object"&&!Array.isArray(e)?e.level:e)||2,[o,n]=typeof t=="number"?[t,t]:t==="deep"?[2,6]:t;s=s.filter(l=>l.level>=o&&l.level<=n),ve.length=0;for(const{element:l,link:h}of s)ve.push({element:l,link:h});const r=[];e:for(let l=0;l=0;d--){const m=s[d];if(m.level{requestAnimationFrame(r),window.addEventListener("scroll",o)}),Qe(()=>{l(location.hash)}),fe(()=>{window.removeEventListener("scroll",o)});function r(){if(!t.value)return;const h=window.scrollY,d=window.innerHeight,m=document.body.offsetHeight,V=Math.abs(h+d-m)<1,b=ve.map(({element:S,link:A})=>({link:A,top:Ct(S)})).filter(({top:S})=>!Number.isNaN(S)).sort((S,A)=>S.top-A.top);if(!b.length){l(null);return}if(h<1){l(null);return}if(V){l(b[b.length-1].link);return}let P=null;for(const{link:S,top:A}of b){if(A>h+Ze()+4)break;P=S}l(P)}function l(h){n&&n.classList.remove("active"),h==null?n=null:n=s.value.querySelector(`a[href="${decodeURIComponent(h)}"]`);const d=n;d?(d.classList.add("active"),e.value.style.top=d.offsetTop+39+"px",e.value.style.opacity="1"):(e.value.style.top="33px",e.value.style.opacity="0")}}function Ct(s){let e=0;for(;s!==document.body;){if(s===null)return NaN;e+=s.offsetTop,s=s.offsetParent}return e}const Bt=["href","title"],Ht=_({__name:"VPDocOutlineItem",props:{headers:{},root:{type:Boolean}},setup(s){function e({target:t}){const o=t.href.split("#")[1],n=document.getElementById(decodeURIComponent(o));n==null||n.focus({preventScroll:!0})}return(t,o)=>{const n=R("VPDocOutlineItem",!0);return a(),u("ul",{class:N(["VPDocOutlineItem",t.root?"root":"nested"])},[(a(!0),u(M,null,E(t.headers,({children:r,link:l,title:h})=>(a(),u("li",null,[v("a",{class:"outline-link",href:l,onClick:e,title:h},w(h),9,Bt),r!=null&&r.length?(a(),y(n,{key:0,headers:r},null,8,["headers"])):f("",!0)]))),256))],2)}}}),Ee=$(Ht,[["__scopeId","data-v-3f927ebe"]]),Et={class:"content"},Dt={"aria-level":"2",class:"outline-title",id:"doc-outline-aria-label",role:"heading"},Ft=_({__name:"VPDocAsideOutline",setup(s){const{frontmatter:e,theme:t}=L(),o=Te([]);te(()=>{o.value=be(e.value.outline??t.value.outline)});const n=I(),r=I();return At(n,r),(l,h)=>(a(),u("nav",{"aria-labelledby":"doc-outline-aria-label",class:N(["VPDocAsideOutline",{"has-outline":o.value.length>0}]),ref_key:"container",ref:n},[v("div",Et,[v("div",{class:"outline-marker",ref_key:"marker",ref:r},null,512),v("div",Dt,w(i(He)(i(t))),1),k(Ee,{headers:o.value,root:!0},null,8,["headers"])])],2))}}),Ot=$(Ft,[["__scopeId","data-v-b38bf2ff"]]),Ut={class:"VPDocAsideCarbonAds"},jt=_({__name:"VPDocAsideCarbonAds",props:{carbonAds:{}},setup(s){const e=()=>null;return(t,o)=>(a(),u("div",Ut,[k(i(e),{"carbon-ads":t.carbonAds},null,8,["carbon-ads"])]))}}),Gt=s=>(B("data-v-6d7b3c46"),s=s(),H(),s),zt={class:"VPDocAside"},Kt=Gt(()=>v("div",{class:"spacer"},null,-1)),Rt=_({__name:"VPDocAside",setup(s){const{theme:e}=L();return(t,o)=>(a(),u("div",zt,[c(t.$slots,"aside-top",{},void 0,!0),c(t.$slots,"aside-outline-before",{},void 0,!0),k(Ot),c(t.$slots,"aside-outline-after",{},void 0,!0),Kt,c(t.$slots,"aside-ads-before",{},void 0,!0),i(e).carbonAds?(a(),y(jt,{key:0,"carbon-ads":i(e).carbonAds},null,8,["carbon-ads"])):f("",!0),c(t.$slots,"aside-ads-after",{},void 0,!0),c(t.$slots,"aside-bottom",{},void 0,!0)]))}}),qt=$(Rt,[["__scopeId","data-v-6d7b3c46"]]);function Wt(){const{theme:s,page:e}=L();return g(()=>{const{text:t="Edit this page",pattern:o=""}=s.value.editLink||{};let n;return typeof o=="function"?n=o(e.value):n=o.replace(/:path/g,e.value.filePath),{url:n,text:t}})}function Jt(){const{page:s,theme:e,frontmatter:t}=L();return g(()=>{var m,V,b,P,S,A,C,T;const o=Be(e.value.sidebar,s.value.relativePath),n=Lt(o),r=Yt(n,j=>j.link.replace(/[?#].*$/,"")),l=r.findIndex(j=>z(s.value.relativePath,j.link)),h=((m=e.value.docFooter)==null?void 0:m.prev)===!1&&!t.value.prev||t.value.prev===!1,d=((V=e.value.docFooter)==null?void 0:V.next)===!1&&!t.value.next||t.value.next===!1;return{prev:h?void 0:{text:(typeof t.value.prev=="string"?t.value.prev:typeof t.value.prev=="object"?t.value.prev.text:void 0)??((b=r[l-1])==null?void 0:b.docFooterText)??((P=r[l-1])==null?void 0:P.text),link:(typeof t.value.prev=="object"?t.value.prev.link:void 0)??((S=r[l-1])==null?void 0:S.link)},next:d?void 0:{text:(typeof t.value.next=="string"?t.value.next:typeof t.value.next=="object"?t.value.next.text:void 0)??((A=r[l+1])==null?void 0:A.docFooterText)??((C=r[l+1])==null?void 0:C.text),link:(typeof t.value.next=="object"?t.value.next.link:void 0)??((T=r[l+1])==null?void 0:T.link)}}})}function Yt(s,e){const t=new Set;return s.filter(o=>{const n=e(o);return t.has(n)?!1:t.add(n)})}const D=_({__name:"VPLink",props:{tag:{},href:{},noIcon:{type:Boolean},target:{},rel:{}},setup(s){const e=s,t=g(()=>e.tag??(e.href?"a":"span")),o=g(()=>e.href&&we.test(e.href)||e.target==="_blank");return(n,r)=>(a(),y(W(t.value),{class:N(["VPLink",{link:n.href,"vp-external-link-icon":o.value,"no-icon":n.noIcon}]),href:n.href?i(me)(n.href):void 0,target:n.target??(o.value?"_blank":void 0),rel:n.rel??(o.value?"noreferrer":void 0)},{default:p(()=>[c(n.$slots,"default")]),_:3},8,["class","href","target","rel"]))}}),Xt={class:"VPLastUpdated"},Qt=["datetime"],Zt=_({__name:"VPDocFooterLastUpdated",setup(s){const{theme:e,page:t,frontmatter:o,lang:n}=L(),r=g(()=>new Date(o.value.lastUpdated??t.value.lastUpdated)),l=g(()=>r.value.toISOString()),h=I("");return K(()=>{ee(()=>{var d,m,V;h.value=new Intl.DateTimeFormat((m=(d=e.value.lastUpdated)==null?void 0:d.formatOptions)!=null&&m.forceLocale?n.value:void 0,((V=e.value.lastUpdated)==null?void 0:V.formatOptions)??{dateStyle:"short",timeStyle:"short"}).format(r.value)})}),(d,m)=>{var V;return a(),u("p",Xt,[F(w(((V=i(e).lastUpdated)==null?void 0:V.text)||i(e).lastUpdatedText||"Last updated")+": ",1),v("time",{datetime:l.value},w(h.value),9,Qt)])}}}),xt=$(Zt,[["__scopeId","data-v-9da12f1d"]]),De=s=>(B("data-v-b88cabfa"),s=s(),H(),s),es={key:0,class:"VPDocFooter"},ts={key:0,class:"edit-info"},ss={key:0,class:"edit-link"},os=De(()=>v("span",{class:"vpi-square-pen edit-link-icon"},null,-1)),ns={key:1,class:"last-updated"},as={key:1,class:"prev-next","aria-labelledby":"doc-footer-aria-label"},rs=De(()=>v("span",{class:"visually-hidden",id:"doc-footer-aria-label"},"Pager",-1)),is={class:"pager"},ls=["innerHTML"],cs=["innerHTML"],us={class:"pager"},ds=["innerHTML"],vs=["innerHTML"],ps=_({__name:"VPDocFooter",setup(s){const{theme:e,page:t,frontmatter:o}=L(),n=Wt(),r=Jt(),l=g(()=>e.value.editLink&&o.value.editLink!==!1),h=g(()=>t.value.lastUpdated&&o.value.lastUpdated!==!1),d=g(()=>l.value||h.value||r.value.prev||r.value.next);return(m,V)=>{var b,P,S,A;return d.value?(a(),u("footer",es,[c(m.$slots,"doc-footer-before",{},void 0,!0),l.value||h.value?(a(),u("div",ts,[l.value?(a(),u("div",ss,[k(D,{class:"edit-link-button",href:i(n).url,"no-icon":!0},{default:p(()=>[os,F(" "+w(i(n).text),1)]),_:1},8,["href"])])):f("",!0),h.value?(a(),u("div",ns,[k(xt)])):f("",!0)])):f("",!0),(b=i(r).prev)!=null&&b.link||(P=i(r).next)!=null&&P.link?(a(),u("nav",as,[rs,v("div",is,[(S=i(r).prev)!=null&&S.link?(a(),y(D,{key:0,class:"pager-link prev",href:i(r).prev.link},{default:p(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(e).docFooter)==null?void 0:C.prev)||"Previous page"},null,8,ls),v("span",{class:"title",innerHTML:i(r).prev.text},null,8,cs)]}),_:1},8,["href"])):f("",!0)]),v("div",us,[(A=i(r).next)!=null&&A.link?(a(),y(D,{key:0,class:"pager-link next",href:i(r).next.link},{default:p(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(e).docFooter)==null?void 0:C.next)||"Next page"},null,8,ds),v("span",{class:"title",innerHTML:i(r).next.text},null,8,vs)]}),_:1},8,["href"])):f("",!0)])])):f("",!0)])):f("",!0)}}}),hs=$(ps,[["__scopeId","data-v-b88cabfa"]]),fs=s=>(B("data-v-83890dd9"),s=s(),H(),s),_s={class:"container"},ms=fs(()=>v("div",{class:"aside-curtain"},null,-1)),bs={class:"aside-container"},ks={class:"aside-content"},$s={class:"content"},gs={class:"content-container"},ys={class:"main"},Ps=_({__name:"VPDoc",setup(s){const{theme:e}=L(),t=se(),{hasSidebar:o,hasAside:n,leftAside:r}=U(),l=g(()=>t.path.replace(/[./]+/g,"_").replace(/_html$/,""));return(h,d)=>{const m=R("Content");return a(),u("div",{class:N(["VPDoc",{"has-sidebar":i(o),"has-aside":i(n)}])},[c(h.$slots,"doc-top",{},void 0,!0),v("div",_s,[i(n)?(a(),u("div",{key:0,class:N(["aside",{"left-aside":i(r)}])},[ms,v("div",bs,[v("div",ks,[k(qt,null,{"aside-top":p(()=>[c(h.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":p(()=>[c(h.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":p(()=>[c(h.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":p(()=>[c(h.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":p(()=>[c(h.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":p(()=>[c(h.$slots,"aside-ads-after",{},void 0,!0)]),_:3})])])],2)):f("",!0),v("div",$s,[v("div",gs,[c(h.$slots,"doc-before",{},void 0,!0),v("main",ys,[k(m,{class:N(["vp-doc",[l.value,i(e).externalLinkIcon&&"external-link-icon-enabled"]])},null,8,["class"])]),k(hs,null,{"doc-footer-before":p(()=>[c(h.$slots,"doc-footer-before",{},void 0,!0)]),_:3}),c(h.$slots,"doc-after",{},void 0,!0)])])]),c(h.$slots,"doc-bottom",{},void 0,!0)],2)}}}),Ss=$(Ps,[["__scopeId","data-v-83890dd9"]]),Vs=_({__name:"VPButton",props:{tag:{},size:{default:"medium"},theme:{default:"brand"},text:{},href:{},target:{},rel:{}},setup(s){const e=s,t=g(()=>e.href&&we.test(e.href)),o=g(()=>e.tag||e.href?"a":"button");return(n,r)=>(a(),y(W(o.value),{class:N(["VPButton",[n.size,n.theme]]),href:n.href?i(me)(n.href):void 0,target:e.target??(t.value?"_blank":void 0),rel:e.rel??(t.value?"noreferrer":void 0)},{default:p(()=>[F(w(n.text),1)]),_:1},8,["class","href","target","rel"]))}}),Ls=$(Vs,[["__scopeId","data-v-14206e74"]]),Ts=["src","alt"],ws=_({inheritAttrs:!1,__name:"VPImage",props:{image:{},alt:{}},setup(s){return(e,t)=>{const o=R("VPImage",!0);return e.image?(a(),u(M,{key:0},[typeof e.image=="string"||"src"in e.image?(a(),u("img",Q({key:0,class:"VPImage"},typeof e.image=="string"?e.$attrs:{...e.image,...e.$attrs},{src:i(he)(typeof e.image=="string"?e.image:e.image.src),alt:e.alt??(typeof e.image=="string"?"":e.image.alt||"")}),null,16,Ts)):(a(),u(M,{key:1},[k(o,Q({class:"dark",image:e.image.dark,alt:e.image.alt},e.$attrs),null,16,["image","alt"]),k(o,Q({class:"light",image:e.image.light,alt:e.image.alt},e.$attrs),null,16,["image","alt"])],64))],64)):f("",!0)}}}),x=$(ws,[["__scopeId","data-v-35a7d0b8"]]),Is=s=>(B("data-v-955009fc"),s=s(),H(),s),Ns={class:"container"},Ms={class:"main"},As={key:0,class:"name"},Cs=["innerHTML"],Bs=["innerHTML"],Hs=["innerHTML"],Es={key:0,class:"actions"},Ds={key:0,class:"image"},Fs={class:"image-container"},Os=Is(()=>v("div",{class:"image-bg"},null,-1)),Us=_({__name:"VPHero",props:{name:{},text:{},tagline:{},image:{},actions:{}},setup(s){const e=J("hero-image-slot-exists");return(t,o)=>(a(),u("div",{class:N(["VPHero",{"has-image":t.image||i(e)}])},[v("div",Ns,[v("div",Ms,[c(t.$slots,"home-hero-info-before",{},void 0,!0),c(t.$slots,"home-hero-info",{},()=>[t.name?(a(),u("h1",As,[v("span",{innerHTML:t.name,class:"clip"},null,8,Cs)])):f("",!0),t.text?(a(),u("p",{key:1,innerHTML:t.text,class:"text"},null,8,Bs)):f("",!0),t.tagline?(a(),u("p",{key:2,innerHTML:t.tagline,class:"tagline"},null,8,Hs)):f("",!0)],!0),c(t.$slots,"home-hero-info-after",{},void 0,!0),t.actions?(a(),u("div",Es,[(a(!0),u(M,null,E(t.actions,n=>(a(),u("div",{key:n.link,class:"action"},[k(Ls,{tag:"a",size:"medium",theme:n.theme,text:n.text,href:n.link,target:n.target,rel:n.rel},null,8,["theme","text","href","target","rel"])]))),128))])):f("",!0),c(t.$slots,"home-hero-actions-after",{},void 0,!0)]),t.image||i(e)?(a(),u("div",Ds,[v("div",Fs,[Os,c(t.$slots,"home-hero-image",{},()=>[t.image?(a(),y(x,{key:0,class:"image-src",image:t.image},null,8,["image"])):f("",!0)],!0)])])):f("",!0)])],2))}}),js=$(Us,[["__scopeId","data-v-955009fc"]]),Gs=_({__name:"VPHomeHero",setup(s){const{frontmatter:e}=L();return(t,o)=>i(e).hero?(a(),y(js,{key:0,class:"VPHomeHero",name:i(e).hero.name,text:i(e).hero.text,tagline:i(e).hero.tagline,image:i(e).hero.image,actions:i(e).hero.actions},{"home-hero-info-before":p(()=>[c(t.$slots,"home-hero-info-before")]),"home-hero-info":p(()=>[c(t.$slots,"home-hero-info")]),"home-hero-info-after":p(()=>[c(t.$slots,"home-hero-info-after")]),"home-hero-actions-after":p(()=>[c(t.$slots,"home-hero-actions-after")]),"home-hero-image":p(()=>[c(t.$slots,"home-hero-image")]),_:3},8,["name","text","tagline","image","actions"])):f("",!0)}}),zs=s=>(B("data-v-f5e9645b"),s=s(),H(),s),Ks={class:"box"},Rs={key:0,class:"icon"},qs=["innerHTML"],Ws=["innerHTML"],Js=["innerHTML"],Ys={key:4,class:"link-text"},Xs={class:"link-text-value"},Qs=zs(()=>v("span",{class:"vpi-arrow-right link-text-icon"},null,-1)),Zs=_({__name:"VPFeature",props:{icon:{},title:{},details:{},link:{},linkText:{},rel:{},target:{}},setup(s){return(e,t)=>(a(),y(D,{class:"VPFeature",href:e.link,rel:e.rel,target:e.target,"no-icon":!0,tag:e.link?"a":"div"},{default:p(()=>[v("article",Ks,[typeof e.icon=="object"&&e.icon.wrap?(a(),u("div",Rs,[k(x,{image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])])):typeof e.icon=="object"?(a(),y(x,{key:1,image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])):e.icon?(a(),u("div",{key:2,class:"icon",innerHTML:e.icon},null,8,qs)):f("",!0),v("h2",{class:"title",innerHTML:e.title},null,8,Ws),e.details?(a(),u("p",{key:3,class:"details",innerHTML:e.details},null,8,Js)):f("",!0),e.linkText?(a(),u("div",Ys,[v("p",Xs,[F(w(e.linkText)+" ",1),Qs])])):f("",!0)])]),_:1},8,["href","rel","target","tag"]))}}),xs=$(Zs,[["__scopeId","data-v-f5e9645b"]]),eo={key:0,class:"VPFeatures"},to={class:"container"},so={class:"items"},oo=_({__name:"VPFeatures",props:{features:{}},setup(s){const e=s,t=g(()=>{const o=e.features.length;if(o){if(o===2)return"grid-2";if(o===3)return"grid-3";if(o%3===0)return"grid-6";if(o>3)return"grid-4"}else return});return(o,n)=>o.features?(a(),u("div",eo,[v("div",to,[v("div",so,[(a(!0),u(M,null,E(o.features,r=>(a(),u("div",{key:r.title,class:N(["item",[t.value]])},[k(xs,{icon:r.icon,title:r.title,details:r.details,link:r.link,"link-text":r.linkText,rel:r.rel,target:r.target},null,8,["icon","title","details","link","link-text","rel","target"])],2))),128))])])])):f("",!0)}}),no=$(oo,[["__scopeId","data-v-d0a190d7"]]),ao=_({__name:"VPHomeFeatures",setup(s){const{frontmatter:e}=L();return(t,o)=>i(e).features?(a(),y(no,{key:0,class:"VPHomeFeatures",features:i(e).features},null,8,["features"])):f("",!0)}}),ro=_({__name:"VPHomeContent",setup(s){const{width:e}=xe({initialWidth:0,includeScrollbar:!1});return(t,o)=>(a(),u("div",{class:"vp-doc container",style:Ie(i(e)?{"--vp-offset":`calc(50% - ${i(e)/2}px)`}:{})},[c(t.$slots,"default",{},void 0,!0)],4))}}),io=$(ro,[["__scopeId","data-v-7a48a447"]]),lo={class:"VPHome"},co=_({__name:"VPHome",setup(s){const{frontmatter:e}=L();return(t,o)=>{const n=R("Content");return a(),u("div",lo,[c(t.$slots,"home-hero-before",{},void 0,!0),k(Gs,null,{"home-hero-info-before":p(()=>[c(t.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":p(()=>[c(t.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":p(()=>[c(t.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":p(()=>[c(t.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":p(()=>[c(t.$slots,"home-hero-image",{},void 0,!0)]),_:3}),c(t.$slots,"home-hero-after",{},void 0,!0),c(t.$slots,"home-features-before",{},void 0,!0),k(ao),c(t.$slots,"home-features-after",{},void 0,!0),i(e).markdownStyles!==!1?(a(),y(io,{key:0},{default:p(()=>[k(n)]),_:1})):(a(),y(n,{key:1}))])}}}),uo=$(co,[["__scopeId","data-v-cbb6ec48"]]),vo={},po={class:"VPPage"};function ho(s,e){const t=R("Content");return a(),u("div",po,[c(s.$slots,"page-top"),k(t),c(s.$slots,"page-bottom")])}const fo=$(vo,[["render",ho]]),_o=_({__name:"VPContent",setup(s){const{page:e,frontmatter:t}=L(),{hasSidebar:o}=U();return(n,r)=>(a(),u("div",{class:N(["VPContent",{"has-sidebar":i(o),"is-home":i(t).layout==="home"}]),id:"VPContent"},[i(e).isNotFound?c(n.$slots,"not-found",{key:0},()=>[k(St)],!0):i(t).layout==="page"?(a(),y(fo,{key:1},{"page-top":p(()=>[c(n.$slots,"page-top",{},void 0,!0)]),"page-bottom":p(()=>[c(n.$slots,"page-bottom",{},void 0,!0)]),_:3})):i(t).layout==="home"?(a(),y(uo,{key:2},{"home-hero-before":p(()=>[c(n.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":p(()=>[c(n.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":p(()=>[c(n.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":p(()=>[c(n.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":p(()=>[c(n.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":p(()=>[c(n.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":p(()=>[c(n.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":p(()=>[c(n.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":p(()=>[c(n.$slots,"home-features-after",{},void 0,!0)]),_:3})):i(t).layout&&i(t).layout!=="doc"?(a(),y(W(i(t).layout),{key:3})):(a(),y(Ss,{key:4},{"doc-top":p(()=>[c(n.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":p(()=>[c(n.$slots,"doc-bottom",{},void 0,!0)]),"doc-footer-before":p(()=>[c(n.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":p(()=>[c(n.$slots,"doc-before",{},void 0,!0)]),"doc-after":p(()=>[c(n.$slots,"doc-after",{},void 0,!0)]),"aside-top":p(()=>[c(n.$slots,"aside-top",{},void 0,!0)]),"aside-outline-before":p(()=>[c(n.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":p(()=>[c(n.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":p(()=>[c(n.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":p(()=>[c(n.$slots,"aside-ads-after",{},void 0,!0)]),"aside-bottom":p(()=>[c(n.$slots,"aside-bottom",{},void 0,!0)]),_:3}))],2))}}),mo=$(_o,[["__scopeId","data-v-91765379"]]),bo={class:"container"},ko=["innerHTML"],$o=["innerHTML"],go=_({__name:"VPFooter",setup(s){const{theme:e,frontmatter:t}=L(),{hasSidebar:o}=U();return(n,r)=>i(e).footer&&i(t).footer!==!1?(a(),u("footer",{key:0,class:N(["VPFooter",{"has-sidebar":i(o)}])},[v("div",bo,[i(e).footer.message?(a(),u("p",{key:0,class:"message",innerHTML:i(e).footer.message},null,8,ko)):f("",!0),i(e).footer.copyright?(a(),u("p",{key:1,class:"copyright",innerHTML:i(e).footer.copyright},null,8,$o)):f("",!0)])],2)):f("",!0)}}),yo=$(go,[["__scopeId","data-v-c970a860"]]);function Po(){const{theme:s,frontmatter:e}=L(),t=Te([]),o=g(()=>t.value.length>0);return te(()=>{t.value=be(e.value.outline??s.value.outline)}),{headers:t,hasLocalNav:o}}const So=s=>(B("data-v-bc9dc845"),s=s(),H(),s),Vo={class:"menu-text"},Lo=So(()=>v("span",{class:"vpi-chevron-right icon"},null,-1)),To={class:"header"},wo={class:"outline"},Io=_({__name:"VPLocalNavOutlineDropdown",props:{headers:{},navHeight:{}},setup(s){const e=s,{theme:t}=L(),o=I(!1),n=I(0),r=I(),l=I();function h(b){var P;(P=r.value)!=null&&P.contains(b.target)||(o.value=!1)}O(o,b=>{if(b){document.addEventListener("click",h);return}document.removeEventListener("click",h)}),ce("Escape",()=>{o.value=!1}),te(()=>{o.value=!1});function d(){o.value=!o.value,n.value=window.innerHeight+Math.min(window.scrollY-e.navHeight,0)}function m(b){b.target.classList.contains("outline-link")&&(l.value&&(l.value.style.transition="none"),Ne(()=>{o.value=!1}))}function V(){o.value=!1,window.scrollTo({top:0,left:0,behavior:"smooth"})}return(b,P)=>(a(),u("div",{class:"VPLocalNavOutlineDropdown",style:Ie({"--vp-vh":n.value+"px"}),ref_key:"main",ref:r},[b.headers.length>0?(a(),u("button",{key:0,onClick:d,class:N({open:o.value})},[v("span",Vo,w(i(He)(i(t))),1),Lo],2)):(a(),u("button",{key:1,onClick:V},w(i(t).returnToTopLabel||"Return to top"),1)),k(pe,{name:"flyout"},{default:p(()=>[o.value?(a(),u("div",{key:0,ref_key:"items",ref:l,class:"items",onClick:m},[v("div",To,[v("a",{class:"top-link",href:"#",onClick:V},w(i(t).returnToTopLabel||"Return to top"),1)]),v("div",wo,[k(Ee,{headers:b.headers},null,8,["headers"])])],512)):f("",!0)]),_:1})],4))}}),No=$(Io,[["__scopeId","data-v-bc9dc845"]]),Mo=s=>(B("data-v-070ab83d"),s=s(),H(),s),Ao={class:"container"},Co=["aria-expanded"],Bo=Mo(()=>v("span",{class:"vpi-align-left menu-icon"},null,-1)),Ho={class:"menu-text"},Eo=_({__name:"VPLocalNav",props:{open:{type:Boolean}},emits:["open-menu"],setup(s){const{theme:e,frontmatter:t}=L(),{hasSidebar:o}=U(),{headers:n}=Po(),{y:r}=Me(),l=I(0);K(()=>{l.value=parseInt(getComputedStyle(document.documentElement).getPropertyValue("--vp-nav-height"))}),te(()=>{n.value=be(t.value.outline??e.value.outline)});const h=g(()=>n.value.length===0),d=g(()=>h.value&&!o.value),m=g(()=>({VPLocalNav:!0,"has-sidebar":o.value,empty:h.value,fixed:d.value}));return(V,b)=>i(t).layout!=="home"&&(!d.value||i(r)>=l.value)?(a(),u("div",{key:0,class:N(m.value)},[v("div",Ao,[i(o)?(a(),u("button",{key:0,class:"menu","aria-expanded":V.open,"aria-controls":"VPSidebarNav",onClick:b[0]||(b[0]=P=>V.$emit("open-menu"))},[Bo,v("span",Ho,w(i(e).sidebarMenuLabel||"Menu"),1)],8,Co)):f("",!0),k(No,{headers:i(n),navHeight:l.value},null,8,["headers","navHeight"])])],2)):f("",!0)}}),Do=$(Eo,[["__scopeId","data-v-070ab83d"]]);function Fo(){const s=I(!1);function e(){s.value=!0,window.addEventListener("resize",n)}function t(){s.value=!1,window.removeEventListener("resize",n)}function o(){s.value?t():e()}function n(){window.outerWidth>=768&&t()}const r=se();return O(()=>r.path,t),{isScreenOpen:s,openScreen:e,closeScreen:t,toggleScreen:o}}const Oo={},Uo={class:"VPSwitch",type:"button",role:"switch"},jo={class:"check"},Go={key:0,class:"icon"};function zo(s,e){return a(),u("button",Uo,[v("span",jo,[s.$slots.default?(a(),u("span",Go,[c(s.$slots,"default",{},void 0,!0)])):f("",!0)])])}const Ko=$(Oo,[["render",zo],["__scopeId","data-v-4a1c76db"]]),Fe=s=>(B("data-v-b79b56d4"),s=s(),H(),s),Ro=Fe(()=>v("span",{class:"vpi-sun sun"},null,-1)),qo=Fe(()=>v("span",{class:"vpi-moon moon"},null,-1)),Wo=_({__name:"VPSwitchAppearance",setup(s){const{isDark:e,theme:t}=L(),o=J("toggle-appearance",()=>{e.value=!e.value}),n=g(()=>e.value?t.value.lightModeSwitchTitle||"Switch to light theme":t.value.darkModeSwitchTitle||"Switch to dark theme");return(r,l)=>(a(),y(Ko,{title:n.value,class:"VPSwitchAppearance","aria-checked":i(e),onClick:i(o)},{default:p(()=>[Ro,qo]),_:1},8,["title","aria-checked","onClick"]))}}),ke=$(Wo,[["__scopeId","data-v-b79b56d4"]]),Jo={key:0,class:"VPNavBarAppearance"},Yo=_({__name:"VPNavBarAppearance",setup(s){const{site:e}=L();return(t,o)=>i(e).appearance&&i(e).appearance!=="force-dark"?(a(),u("div",Jo,[k(ke)])):f("",!0)}}),Xo=$(Yo,[["__scopeId","data-v-ead91a81"]]),$e=I();let Oe=!1,ie=0;function Qo(s){const e=I(!1);if(oe){!Oe&&Zo(),ie++;const t=O($e,o=>{var n,r,l;o===s.el.value||(n=s.el.value)!=null&&n.contains(o)?(e.value=!0,(r=s.onFocus)==null||r.call(s)):(e.value=!1,(l=s.onBlur)==null||l.call(s))});fe(()=>{t(),ie--,ie||xo()})}return et(e)}function Zo(){document.addEventListener("focusin",Ue),Oe=!0,$e.value=document.activeElement}function xo(){document.removeEventListener("focusin",Ue)}function Ue(){$e.value=document.activeElement}const en={class:"VPMenuLink"},tn=_({__name:"VPMenuLink",props:{item:{}},setup(s){const{page:e}=L();return(t,o)=>(a(),u("div",en,[k(D,{class:N({active:i(z)(i(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel},{default:p(()=>[F(w(t.item.text),1)]),_:1},8,["class","href","target","rel"])]))}}),ne=$(tn,[["__scopeId","data-v-8b74d055"]]),sn={class:"VPMenuGroup"},on={key:0,class:"title"},nn=_({__name:"VPMenuGroup",props:{text:{},items:{}},setup(s){return(e,t)=>(a(),u("div",sn,[e.text?(a(),u("p",on,w(e.text),1)):f("",!0),(a(!0),u(M,null,E(e.items,o=>(a(),u(M,null,["link"in o?(a(),y(ne,{key:0,item:o},null,8,["item"])):f("",!0)],64))),256))]))}}),an=$(nn,[["__scopeId","data-v-48c802d0"]]),rn={class:"VPMenu"},ln={key:0,class:"items"},cn=_({__name:"VPMenu",props:{items:{}},setup(s){return(e,t)=>(a(),u("div",rn,[e.items?(a(),u("div",ln,[(a(!0),u(M,null,E(e.items,o=>(a(),u(M,{key:o.text},["link"in o?(a(),y(ne,{key:0,item:o},null,8,["item"])):(a(),y(an,{key:1,text:o.text,items:o.items},null,8,["text","items"]))],64))),128))])):f("",!0),c(e.$slots,"default",{},void 0,!0)]))}}),un=$(cn,[["__scopeId","data-v-97491713"]]),dn=s=>(B("data-v-e5380155"),s=s(),H(),s),vn=["aria-expanded","aria-label"],pn={key:0,class:"text"},hn=["innerHTML"],fn=dn(()=>v("span",{class:"vpi-chevron-down text-icon"},null,-1)),_n={key:1,class:"vpi-more-horizontal icon"},mn={class:"menu"},bn=_({__name:"VPFlyout",props:{icon:{},button:{},label:{},items:{}},setup(s){const e=I(!1),t=I();Qo({el:t,onBlur:o});function o(){e.value=!1}return(n,r)=>(a(),u("div",{class:"VPFlyout",ref_key:"el",ref:t,onMouseenter:r[1]||(r[1]=l=>e.value=!0),onMouseleave:r[2]||(r[2]=l=>e.value=!1)},[v("button",{type:"button",class:"button","aria-haspopup":"true","aria-expanded":e.value,"aria-label":n.label,onClick:r[0]||(r[0]=l=>e.value=!e.value)},[n.button||n.icon?(a(),u("span",pn,[n.icon?(a(),u("span",{key:0,class:N([n.icon,"option-icon"])},null,2)):f("",!0),n.button?(a(),u("span",{key:1,innerHTML:n.button},null,8,hn)):f("",!0),fn])):(a(),u("span",_n))],8,vn),v("div",mn,[k(un,{items:n.items},{default:p(()=>[c(n.$slots,"default",{},void 0,!0)]),_:3},8,["items"])])],544))}}),ge=$(bn,[["__scopeId","data-v-e5380155"]]),kn=["href","aria-label","innerHTML"],$n=_({__name:"VPSocialLink",props:{icon:{},link:{},ariaLabel:{}},setup(s){const e=s,t=g(()=>typeof e.icon=="object"?e.icon.svg:``);return(o,n)=>(a(),u("a",{class:"VPSocialLink no-icon",href:o.link,"aria-label":o.ariaLabel??(typeof o.icon=="string"?o.icon:""),target:"_blank",rel:"noopener",innerHTML:t.value},null,8,kn))}}),gn=$($n,[["__scopeId","data-v-717b8b75"]]),yn={class:"VPSocialLinks"},Pn=_({__name:"VPSocialLinks",props:{links:{}},setup(s){return(e,t)=>(a(),u("div",yn,[(a(!0),u(M,null,E(e.links,({link:o,icon:n,ariaLabel:r})=>(a(),y(gn,{key:o,icon:n,link:o,ariaLabel:r},null,8,["icon","link","ariaLabel"]))),128))]))}}),ye=$(Pn,[["__scopeId","data-v-ee7a9424"]]),Sn={key:0,class:"group translations"},Vn={class:"trans-title"},Ln={key:1,class:"group"},Tn={class:"item appearance"},wn={class:"label"},In={class:"appearance-action"},Nn={key:2,class:"group"},Mn={class:"item social-links"},An=_({__name:"VPNavBarExtra",setup(s){const{site:e,theme:t}=L(),{localeLinks:o,currentLang:n}=X({correspondingLink:!0}),r=g(()=>o.value.length&&n.value.label||e.value.appearance||t.value.socialLinks);return(l,h)=>r.value?(a(),y(ge,{key:0,class:"VPNavBarExtra",label:"extra navigation"},{default:p(()=>[i(o).length&&i(n).label?(a(),u("div",Sn,[v("p",Vn,w(i(n).label),1),(a(!0),u(M,null,E(i(o),d=>(a(),y(ne,{key:d.link,item:d},null,8,["item"]))),128))])):f("",!0),i(e).appearance&&i(e).appearance!=="force-dark"?(a(),u("div",Ln,[v("div",Tn,[v("p",wn,w(i(t).darkModeSwitchLabel||"Appearance"),1),v("div",In,[k(ke)])])])):f("",!0),i(t).socialLinks?(a(),u("div",Nn,[v("div",Mn,[k(ye,{class:"social-links-list",links:i(t).socialLinks},null,8,["links"])])])):f("",!0)]),_:1})):f("",!0)}}),Cn=$(An,[["__scopeId","data-v-9b536d0b"]]),Bn=s=>(B("data-v-5dea55bf"),s=s(),H(),s),Hn=["aria-expanded"],En=Bn(()=>v("span",{class:"container"},[v("span",{class:"top"}),v("span",{class:"middle"}),v("span",{class:"bottom"})],-1)),Dn=[En],Fn=_({__name:"VPNavBarHamburger",props:{active:{type:Boolean}},emits:["click"],setup(s){return(e,t)=>(a(),u("button",{type:"button",class:N(["VPNavBarHamburger",{active:e.active}]),"aria-label":"mobile navigation","aria-expanded":e.active,"aria-controls":"VPNavScreen",onClick:t[0]||(t[0]=o=>e.$emit("click"))},Dn,10,Hn))}}),On=$(Fn,[["__scopeId","data-v-5dea55bf"]]),Un=["innerHTML"],jn=_({__name:"VPNavBarMenuLink",props:{item:{}},setup(s){const{page:e}=L();return(t,o)=>(a(),y(D,{class:N({VPNavBarMenuLink:!0,active:i(z)(i(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,noIcon:t.item.noIcon,target:t.item.target,rel:t.item.rel,tabindex:"0"},{default:p(()=>[v("span",{innerHTML:t.item.text},null,8,Un)]),_:1},8,["class","href","noIcon","target","rel"]))}}),Gn=$(jn,[["__scopeId","data-v-ed5ac1f6"]]),zn=_({__name:"VPNavBarMenuGroup",props:{item:{}},setup(s){const e=s,{page:t}=L(),o=r=>"link"in r?z(t.value.relativePath,r.link,!!e.item.activeMatch):r.items.some(o),n=g(()=>o(e.item));return(r,l)=>(a(),y(ge,{class:N({VPNavBarMenuGroup:!0,active:i(z)(i(t).relativePath,r.item.activeMatch,!!r.item.activeMatch)||n.value}),button:r.item.text,items:r.item.items},null,8,["class","button","items"]))}}),Kn=s=>(B("data-v-492ea56d"),s=s(),H(),s),Rn={key:0,"aria-labelledby":"main-nav-aria-label",class:"VPNavBarMenu"},qn=Kn(()=>v("span",{id:"main-nav-aria-label",class:"visually-hidden"},"Main Navigation",-1)),Wn=_({__name:"VPNavBarMenu",setup(s){const{theme:e}=L();return(t,o)=>i(e).nav?(a(),u("nav",Rn,[qn,(a(!0),u(M,null,E(i(e).nav,n=>(a(),u(M,{key:n.text},["link"in n?(a(),y(Gn,{key:0,item:n},null,8,["item"])):(a(),y(zn,{key:1,item:n},null,8,["item"]))],64))),128))])):f("",!0)}}),Jn=$(Wn,[["__scopeId","data-v-492ea56d"]]);function Yn(s){const{localeIndex:e,theme:t}=L();function o(n){var A,C,T;const r=n.split("."),l=(A=t.value.search)==null?void 0:A.options,h=l&&typeof l=="object",d=h&&((T=(C=l.locales)==null?void 0:C[e.value])==null?void 0:T.translations)||null,m=h&&l.translations||null;let V=d,b=m,P=s;const S=r.pop();for(const j of r){let G=null;const q=P==null?void 0:P[j];q&&(G=P=q);const ae=b==null?void 0:b[j];ae&&(G=b=ae);const re=V==null?void 0:V[j];re&&(G=V=re),q||(P=G),ae||(b=G),re||(V=G)}return(V==null?void 0:V[S])??(b==null?void 0:b[S])??(P==null?void 0:P[S])??""}return o}const Xn=["aria-label"],Qn={class:"DocSearch-Button-Container"},Zn=v("span",{class:"vp-icon DocSearch-Search-Icon"},null,-1),xn={class:"DocSearch-Button-Placeholder"},ea=v("span",{class:"DocSearch-Button-Keys"},[v("kbd",{class:"DocSearch-Button-Key"}),v("kbd",{class:"DocSearch-Button-Key"},"K")],-1),Pe=_({__name:"VPNavBarSearchButton",setup(s){const t=Yn({button:{buttonText:"Search",buttonAriaLabel:"Search"}});return(o,n)=>(a(),u("button",{type:"button",class:"DocSearch DocSearch-Button","aria-label":i(t)("button.buttonAriaLabel")},[v("span",Qn,[Zn,v("span",xn,w(i(t)("button.buttonText")),1)]),ea],8,Xn))}}),ta={class:"VPNavBarSearch"},sa={id:"local-search"},oa={key:1,id:"docsearch"},na=_({__name:"VPNavBarSearch",setup(s){const e=tt(()=>st(()=>import("./VPLocalSearchBox.DqWxI-Ji.js"),__vite__mapDeps([0,1]))),t=()=>null,{theme:o}=L(),n=I(!1),r=I(!1);K(()=>{});function l(){n.value||(n.value=!0,setTimeout(h,16))}function h(){const b=new Event("keydown");b.key="k",b.metaKey=!0,window.dispatchEvent(b),setTimeout(()=>{document.querySelector(".DocSearch-Modal")||h()},16)}function d(b){const P=b.target,S=P.tagName;return P.isContentEditable||S==="INPUT"||S==="SELECT"||S==="TEXTAREA"}const m=I(!1);ce("k",b=>{(b.ctrlKey||b.metaKey)&&(b.preventDefault(),m.value=!0)}),ce("/",b=>{d(b)||(b.preventDefault(),m.value=!0)});const V="local";return(b,P)=>{var S;return a(),u("div",ta,[i(V)==="local"?(a(),u(M,{key:0},[m.value?(a(),y(i(e),{key:0,onClose:P[0]||(P[0]=A=>m.value=!1)})):f("",!0),v("div",sa,[k(Pe,{onClick:P[1]||(P[1]=A=>m.value=!0)})])],64)):i(V)==="algolia"?(a(),u(M,{key:1},[n.value?(a(),y(i(t),{key:0,algolia:((S=i(o).search)==null?void 0:S.options)??i(o).algolia,onVnodeBeforeMount:P[2]||(P[2]=A=>r.value=!0)},null,8,["algolia"])):f("",!0),r.value?f("",!0):(a(),u("div",oa,[k(Pe,{onClick:l})]))],64)):f("",!0)])}}}),aa=_({__name:"VPNavBarSocialLinks",setup(s){const{theme:e}=L();return(t,o)=>i(e).socialLinks?(a(),y(ye,{key:0,class:"VPNavBarSocialLinks",links:i(e).socialLinks},null,8,["links"])):f("",!0)}}),ra=$(aa,[["__scopeId","data-v-164c457f"]]),ia=["href","rel","target"],la={key:1},ca={key:2},ua=_({__name:"VPNavBarTitle",setup(s){const{site:e,theme:t}=L(),{hasSidebar:o}=U(),{currentLang:n}=X(),r=g(()=>{var d;return typeof t.value.logoLink=="string"?t.value.logoLink:(d=t.value.logoLink)==null?void 0:d.link}),l=g(()=>{var d;return typeof t.value.logoLink=="string"||(d=t.value.logoLink)==null?void 0:d.rel}),h=g(()=>{var d;return typeof t.value.logoLink=="string"||(d=t.value.logoLink)==null?void 0:d.target});return(d,m)=>(a(),u("div",{class:N(["VPNavBarTitle",{"has-sidebar":i(o)}])},[v("a",{class:"title",href:r.value??i(me)(i(n).link),rel:l.value,target:h.value},[c(d.$slots,"nav-bar-title-before",{},void 0,!0),i(t).logo?(a(),y(x,{key:0,class:"logo",image:i(t).logo},null,8,["image"])):f("",!0),i(t).siteTitle?(a(),u("span",la,w(i(t).siteTitle),1)):i(t).siteTitle===void 0?(a(),u("span",ca,w(i(e).title),1)):f("",!0),c(d.$slots,"nav-bar-title-after",{},void 0,!0)],8,ia)],2))}}),da=$(ua,[["__scopeId","data-v-28a961f9"]]),va={class:"items"},pa={class:"title"},ha=_({__name:"VPNavBarTranslations",setup(s){const{theme:e}=L(),{localeLinks:t,currentLang:o}=X({correspondingLink:!0});return(n,r)=>i(t).length&&i(o).label?(a(),y(ge,{key:0,class:"VPNavBarTranslations",icon:"vpi-languages",label:i(e).langMenuLabel||"Change language"},{default:p(()=>[v("div",va,[v("p",pa,w(i(o).label),1),(a(!0),u(M,null,E(i(t),l=>(a(),y(ne,{key:l.link,item:l},null,8,["item"]))),128))])]),_:1},8,["label"])):f("",!0)}}),fa=$(ha,[["__scopeId","data-v-c80d9ad0"]]),_a=s=>(B("data-v-40788ea0"),s=s(),H(),s),ma={class:"wrapper"},ba={class:"container"},ka={class:"title"},$a={class:"content"},ga={class:"content-body"},ya=_a(()=>v("div",{class:"divider"},[v("div",{class:"divider-line"})],-1)),Pa=_({__name:"VPNavBar",props:{isScreenOpen:{type:Boolean}},emits:["toggle-screen"],setup(s){const{y:e}=Me(),{hasSidebar:t}=U(),{frontmatter:o}=L(),n=I({});return Le(()=>{n.value={"has-sidebar":t.value,home:o.value.layout==="home",top:e.value===0}}),(r,l)=>(a(),u("div",{class:N(["VPNavBar",n.value])},[v("div",ma,[v("div",ba,[v("div",ka,[k(da,null,{"nav-bar-title-before":p(()=>[c(r.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":p(()=>[c(r.$slots,"nav-bar-title-after",{},void 0,!0)]),_:3})]),v("div",$a,[v("div",ga,[c(r.$slots,"nav-bar-content-before",{},void 0,!0),k(na,{class:"search"}),k(Jn,{class:"menu"}),k(fa,{class:"translations"}),k(Xo,{class:"appearance"}),k(ra,{class:"social-links"}),k(Cn,{class:"extra"}),c(r.$slots,"nav-bar-content-after",{},void 0,!0),k(On,{class:"hamburger",active:r.isScreenOpen,onClick:l[0]||(l[0]=h=>r.$emit("toggle-screen"))},null,8,["active"])])])])]),ya],2))}}),Sa=$(Pa,[["__scopeId","data-v-40788ea0"]]),Va={key:0,class:"VPNavScreenAppearance"},La={class:"text"},Ta=_({__name:"VPNavScreenAppearance",setup(s){const{site:e,theme:t}=L();return(o,n)=>i(e).appearance&&i(e).appearance!=="force-dark"?(a(),u("div",Va,[v("p",La,w(i(t).darkModeSwitchLabel||"Appearance"),1),k(ke)])):f("",!0)}}),wa=$(Ta,[["__scopeId","data-v-2b89f08b"]]),Ia=_({__name:"VPNavScreenMenuLink",props:{item:{}},setup(s){const e=J("close-screen");return(t,o)=>(a(),y(D,{class:"VPNavScreenMenuLink",href:t.item.link,target:t.item.target,rel:t.item.rel,onClick:i(e),innerHTML:t.item.text},null,8,["href","target","rel","onClick","innerHTML"]))}}),Na=$(Ia,[["__scopeId","data-v-27d04aeb"]]),Ma=_({__name:"VPNavScreenMenuGroupLink",props:{item:{}},setup(s){const e=J("close-screen");return(t,o)=>(a(),y(D,{class:"VPNavScreenMenuGroupLink",href:t.item.link,target:t.item.target,rel:t.item.rel,onClick:i(e)},{default:p(()=>[F(w(t.item.text),1)]),_:1},8,["href","target","rel","onClick"]))}}),je=$(Ma,[["__scopeId","data-v-7179dbb7"]]),Aa={class:"VPNavScreenMenuGroupSection"},Ca={key:0,class:"title"},Ba=_({__name:"VPNavScreenMenuGroupSection",props:{text:{},items:{}},setup(s){return(e,t)=>(a(),u("div",Aa,[e.text?(a(),u("p",Ca,w(e.text),1)):f("",!0),(a(!0),u(M,null,E(e.items,o=>(a(),y(je,{key:o.text,item:o},null,8,["item"]))),128))]))}}),Ha=$(Ba,[["__scopeId","data-v-4b8941ac"]]),Ea=s=>(B("data-v-c9df2649"),s=s(),H(),s),Da=["aria-controls","aria-expanded"],Fa=["innerHTML"],Oa=Ea(()=>v("span",{class:"vpi-plus button-icon"},null,-1)),Ua=["id"],ja={key:1,class:"group"},Ga=_({__name:"VPNavScreenMenuGroup",props:{text:{},items:{}},setup(s){const e=s,t=I(!1),o=g(()=>`NavScreenGroup-${e.text.replace(" ","-").toLowerCase()}`);function n(){t.value=!t.value}return(r,l)=>(a(),u("div",{class:N(["VPNavScreenMenuGroup",{open:t.value}])},[v("button",{class:"button","aria-controls":o.value,"aria-expanded":t.value,onClick:n},[v("span",{class:"button-text",innerHTML:r.text},null,8,Fa),Oa],8,Da),v("div",{id:o.value,class:"items"},[(a(!0),u(M,null,E(r.items,h=>(a(),u(M,{key:h.text},["link"in h?(a(),u("div",{key:h.text,class:"item"},[k(je,{item:h},null,8,["item"])])):(a(),u("div",ja,[k(Ha,{text:h.text,items:h.items},null,8,["text","items"])]))],64))),128))],8,Ua)],2))}}),za=$(Ga,[["__scopeId","data-v-c9df2649"]]),Ka={key:0,class:"VPNavScreenMenu"},Ra=_({__name:"VPNavScreenMenu",setup(s){const{theme:e}=L();return(t,o)=>i(e).nav?(a(),u("nav",Ka,[(a(!0),u(M,null,E(i(e).nav,n=>(a(),u(M,{key:n.text},["link"in n?(a(),y(Na,{key:0,item:n},null,8,["item"])):(a(),y(za,{key:1,text:n.text||"",items:n.items},null,8,["text","items"]))],64))),128))])):f("",!0)}}),qa=_({__name:"VPNavScreenSocialLinks",setup(s){const{theme:e}=L();return(t,o)=>i(e).socialLinks?(a(),y(ye,{key:0,class:"VPNavScreenSocialLinks",links:i(e).socialLinks},null,8,["links"])):f("",!0)}}),Ge=s=>(B("data-v-362991c2"),s=s(),H(),s),Wa=Ge(()=>v("span",{class:"vpi-languages icon lang"},null,-1)),Ja=Ge(()=>v("span",{class:"vpi-chevron-down icon chevron"},null,-1)),Ya={class:"list"},Xa=_({__name:"VPNavScreenTranslations",setup(s){const{localeLinks:e,currentLang:t}=X({correspondingLink:!0}),o=I(!1);function n(){o.value=!o.value}return(r,l)=>i(e).length&&i(t).label?(a(),u("div",{key:0,class:N(["VPNavScreenTranslations",{open:o.value}])},[v("button",{class:"title",onClick:n},[Wa,F(" "+w(i(t).label)+" ",1),Ja]),v("ul",Ya,[(a(!0),u(M,null,E(i(e),h=>(a(),u("li",{key:h.link,class:"item"},[k(D,{class:"link",href:h.link},{default:p(()=>[F(w(h.text),1)]),_:2},1032,["href"])]))),128))])],2)):f("",!0)}}),Qa=$(Xa,[["__scopeId","data-v-362991c2"]]),Za={class:"container"},xa=_({__name:"VPNavScreen",props:{open:{type:Boolean}},setup(s){const e=I(null),t=Ae(oe?document.body:null);return(o,n)=>(a(),y(pe,{name:"fade",onEnter:n[0]||(n[0]=r=>t.value=!0),onAfterLeave:n[1]||(n[1]=r=>t.value=!1)},{default:p(()=>[o.open?(a(),u("div",{key:0,class:"VPNavScreen",ref_key:"screen",ref:e,id:"VPNavScreen"},[v("div",Za,[c(o.$slots,"nav-screen-content-before",{},void 0,!0),k(Ra,{class:"menu"}),k(Qa,{class:"translations"}),k(wa,{class:"appearance"}),k(qa,{class:"social-links"}),c(o.$slots,"nav-screen-content-after",{},void 0,!0)])],512)):f("",!0)]),_:3}))}}),er=$(xa,[["__scopeId","data-v-382f42e9"]]),tr={key:0,class:"VPNav"},sr=_({__name:"VPNav",setup(s){const{isScreenOpen:e,closeScreen:t,toggleScreen:o}=Fo(),{frontmatter:n}=L(),r=g(()=>n.value.navbar!==!1);return _e("close-screen",t),ee(()=>{oe&&document.documentElement.classList.toggle("hide-nav",!r.value)}),(l,h)=>r.value?(a(),u("header",tr,[k(Sa,{"is-screen-open":i(e),onToggleScreen:i(o)},{"nav-bar-title-before":p(()=>[c(l.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":p(()=>[c(l.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":p(()=>[c(l.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":p(()=>[c(l.$slots,"nav-bar-content-after",{},void 0,!0)]),_:3},8,["is-screen-open","onToggleScreen"]),k(er,{open:i(e)},{"nav-screen-content-before":p(()=>[c(l.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":p(()=>[c(l.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3},8,["open"])])):f("",!0)}}),or=$(sr,[["__scopeId","data-v-f1e365da"]]),ze=s=>(B("data-v-2ea20db7"),s=s(),H(),s),nr=["role","tabindex"],ar=ze(()=>v("div",{class:"indicator"},null,-1)),rr=ze(()=>v("span",{class:"vpi-chevron-right caret-icon"},null,-1)),ir=[rr],lr={key:1,class:"items"},cr=_({__name:"VPSidebarItem",props:{item:{},depth:{}},setup(s){const e=s,{collapsed:t,collapsible:o,isLink:n,isActiveLink:r,hasActiveLink:l,hasChildren:h,toggle:d}=wt(g(()=>e.item)),m=g(()=>h.value?"section":"div"),V=g(()=>n.value?"a":"div"),b=g(()=>h.value?e.depth+2===7?"p":`h${e.depth+2}`:"p"),P=g(()=>n.value?void 0:"button"),S=g(()=>[[`level-${e.depth}`],{collapsible:o.value},{collapsed:t.value},{"is-link":n.value},{"is-active":r.value},{"has-active":l.value}]);function A(T){"key"in T&&T.key!=="Enter"||!e.item.link&&d()}function C(){e.item.link&&d()}return(T,j)=>{const G=R("VPSidebarItem",!0);return a(),y(W(m.value),{class:N(["VPSidebarItem",S.value])},{default:p(()=>[T.item.text?(a(),u("div",Q({key:0,class:"item",role:P.value},nt(T.item.items?{click:A,keydown:A}:{},!0),{tabindex:T.item.items&&0}),[ar,T.item.link?(a(),y(D,{key:0,tag:V.value,class:"link",href:T.item.link,rel:T.item.rel,target:T.item.target},{default:p(()=>[(a(),y(W(b.value),{class:"text",innerHTML:T.item.text},null,8,["innerHTML"]))]),_:1},8,["tag","href","rel","target"])):(a(),y(W(b.value),{key:1,class:"text",innerHTML:T.item.text},null,8,["innerHTML"])),T.item.collapsed!=null&&T.item.items&&T.item.items.length?(a(),u("div",{key:2,class:"caret",role:"button","aria-label":"toggle section",onClick:C,onKeydown:ot(C,["enter"]),tabindex:"0"},ir,32)):f("",!0)],16,nr)):f("",!0),T.item.items&&T.item.items.length?(a(),u("div",lr,[T.depth<5?(a(!0),u(M,{key:0},E(T.item.items,q=>(a(),y(G,{key:q.text,item:q,depth:T.depth+1},null,8,["item","depth"]))),128)):f("",!0)])):f("",!0)]),_:1},8,["class"])}}}),ur=$(cr,[["__scopeId","data-v-2ea20db7"]]),Ke=s=>(B("data-v-ec846e01"),s=s(),H(),s),dr=Ke(()=>v("div",{class:"curtain"},null,-1)),vr={class:"nav",id:"VPSidebarNav","aria-labelledby":"sidebar-aria-label",tabindex:"-1"},pr=Ke(()=>v("span",{class:"visually-hidden",id:"sidebar-aria-label"}," Sidebar Navigation ",-1)),hr=_({__name:"VPSidebar",props:{open:{type:Boolean}},setup(s){const{sidebarGroups:e,hasSidebar:t}=U(),o=s,n=I(null),r=Ae(oe?document.body:null);return O([o,n],()=>{var l;o.open?(r.value=!0,(l=n.value)==null||l.focus()):r.value=!1},{immediate:!0,flush:"post"}),(l,h)=>i(t)?(a(),u("aside",{key:0,class:N(["VPSidebar",{open:l.open}]),ref_key:"navEl",ref:n,onClick:h[0]||(h[0]=at(()=>{},["stop"]))},[dr,v("nav",vr,[pr,c(l.$slots,"sidebar-nav-before",{},void 0,!0),(a(!0),u(M,null,E(i(e),d=>(a(),u("div",{key:d.text,class:"group"},[k(ur,{item:d,depth:0},null,8,["item"])]))),128)),c(l.$slots,"sidebar-nav-after",{},void 0,!0)])],2)):f("",!0)}}),fr=$(hr,[["__scopeId","data-v-ec846e01"]]),_r=_({__name:"VPSkipLink",setup(s){const e=se(),t=I();O(()=>e.path,()=>t.value.focus());function o({target:n}){const r=document.getElementById(decodeURIComponent(n.hash).slice(1));if(r){const l=()=>{r.removeAttribute("tabindex"),r.removeEventListener("blur",l)};r.setAttribute("tabindex","-1"),r.addEventListener("blur",l),r.focus(),window.scrollTo(0,0)}}return(n,r)=>(a(),u(M,null,[v("span",{ref_key:"backToTop",ref:t,tabindex:"-1"},null,512),v("a",{href:"#VPContent",class:"VPSkipLink visually-hidden",onClick:o}," Skip to content ")],64))}}),mr=$(_r,[["__scopeId","data-v-c3508ec8"]]),br=_({__name:"Layout",setup(s){const{isOpen:e,open:t,close:o}=U(),n=se();O(()=>n.path,o),Tt(e,o);const{frontmatter:r}=L(),l=Ce(),h=g(()=>!!l["home-hero-image"]);return _e("hero-image-slot-exists",h),(d,m)=>{const V=R("Content");return i(r).layout!==!1?(a(),u("div",{key:0,class:N(["Layout",i(r).pageClass])},[c(d.$slots,"layout-top",{},void 0,!0),k(mr),k(vt,{class:"backdrop",show:i(e),onClick:i(o)},null,8,["show","onClick"]),k(or,null,{"nav-bar-title-before":p(()=>[c(d.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":p(()=>[c(d.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":p(()=>[c(d.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":p(()=>[c(d.$slots,"nav-bar-content-after",{},void 0,!0)]),"nav-screen-content-before":p(()=>[c(d.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":p(()=>[c(d.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3}),k(Do,{open:i(e),onOpenMenu:i(t)},null,8,["open","onOpenMenu"]),k(fr,{open:i(e)},{"sidebar-nav-before":p(()=>[c(d.$slots,"sidebar-nav-before",{},void 0,!0)]),"sidebar-nav-after":p(()=>[c(d.$slots,"sidebar-nav-after",{},void 0,!0)]),_:3},8,["open"]),k(mo,null,{"page-top":p(()=>[c(d.$slots,"page-top",{},void 0,!0)]),"page-bottom":p(()=>[c(d.$slots,"page-bottom",{},void 0,!0)]),"not-found":p(()=>[c(d.$slots,"not-found",{},void 0,!0)]),"home-hero-before":p(()=>[c(d.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":p(()=>[c(d.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":p(()=>[c(d.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":p(()=>[c(d.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":p(()=>[c(d.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":p(()=>[c(d.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":p(()=>[c(d.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":p(()=>[c(d.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":p(()=>[c(d.$slots,"home-features-after",{},void 0,!0)]),"doc-footer-before":p(()=>[c(d.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":p(()=>[c(d.$slots,"doc-before",{},void 0,!0)]),"doc-after":p(()=>[c(d.$slots,"doc-after",{},void 0,!0)]),"doc-top":p(()=>[c(d.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":p(()=>[c(d.$slots,"doc-bottom",{},void 0,!0)]),"aside-top":p(()=>[c(d.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":p(()=>[c(d.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":p(()=>[c(d.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":p(()=>[c(d.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":p(()=>[c(d.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":p(()=>[c(d.$slots,"aside-ads-after",{},void 0,!0)]),_:3}),k(yo),c(d.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),y(V,{key:1}))}}}),kr=$(br,[["__scopeId","data-v-a9a9e638"]]),Se={Layout:kr,enhanceApp:({app:s})=>{s.component("Badge",ct)}},$r=s=>{if(typeof document>"u")return{stabilizeScrollPosition:n=>async(...r)=>n(...r)};const e=document.documentElement;return{stabilizeScrollPosition:o=>async(...n)=>{const r=o(...n),l=s.value;if(!l)return r;const h=l.offsetTop-e.scrollTop;return await Ne(),e.scrollTop=l.offsetTop-h,r}}},Re="vitepress:tabSharedState",Y=typeof localStorage<"u"?localStorage:null,qe="vitepress:tabsSharedState",gr=()=>{const s=Y==null?void 0:Y.getItem(qe);if(s)try{return JSON.parse(s)}catch{}return{}},yr=s=>{Y&&Y.setItem(qe,JSON.stringify(s))},Pr=s=>{const e=rt({});O(()=>e.content,(t,o)=>{t&&o&&yr(t)},{deep:!0}),s.provide(Re,e)},Sr=(s,e)=>{const t=J(Re);if(!t)throw new Error("[vitepress-plugin-tabs] TabsSharedState should be injected");K(()=>{t.content||(t.content=gr())});const o=I(),n=g({get(){var d;const l=e.value,h=s.value;if(l){const m=(d=t.content)==null?void 0:d[l];if(m&&h.includes(m))return m}else{const m=o.value;if(m)return m}return h[0]},set(l){const h=e.value;h?t.content&&(t.content[h]=l):o.value=l}});return{selected:n,select:l=>{n.value=l}}};let Ve=0;const Vr=()=>(Ve++,""+Ve);function Lr(){const s=Ce();return g(()=>{var o;const t=(o=s.default)==null?void 0:o.call(s);return t?t.filter(n=>typeof n.type=="object"&&"__name"in n.type&&n.type.__name==="PluginTabsTab"&&n.props).map(n=>{var r;return(r=n.props)==null?void 0:r.label}):[]})}const We="vitepress:tabSingleState",Tr=s=>{_e(We,s)},wr=()=>{const s=J(We);if(!s)throw new Error("[vitepress-plugin-tabs] TabsSingleState should be injected");return s},Ir={class:"plugin-tabs"},Nr=["id","aria-selected","aria-controls","tabindex","onClick"],Mr=_({__name:"PluginTabs",props:{sharedStateKey:{}},setup(s){const e=s,t=Lr(),{selected:o,select:n}=Sr(t,it(e,"sharedStateKey")),r=I(),{stabilizeScrollPosition:l}=$r(r),h=l(n),d=I([]),m=b=>{var A;const P=t.value.indexOf(o.value);let S;b.key==="ArrowLeft"?S=P>=1?P-1:t.value.length-1:b.key==="ArrowRight"&&(S=P(a(),u("div",Ir,[v("div",{ref_key:"tablist",ref:r,class:"plugin-tabs--tab-list",role:"tablist",onKeydown:m},[(a(!0),u(M,null,E(i(t),S=>(a(),u("button",{id:`tab-${S}-${i(V)}`,ref_for:!0,ref_key:"buttonRefs",ref:d,key:S,role:"tab",class:"plugin-tabs--tab","aria-selected":S===i(o),"aria-controls":`panel-${S}-${i(V)}`,tabindex:S===i(o)?0:-1,onClick:()=>i(h)(S)},w(S),9,Nr))),128))],544),c(b.$slots,"default")]))}}),Ar=["id","aria-labelledby"],Cr=_({__name:"PluginTabsTab",props:{label:{}},setup(s){const{uid:e,selected:t}=wr();return(o,n)=>i(t)===o.label?(a(),u("div",{key:0,id:`panel-${o.label}-${i(e)}`,class:"plugin-tabs--content",role:"tabpanel",tabindex:"0","aria-labelledby":`tab-${o.label}-${i(e)}`},[c(o.$slots,"default",{},void 0,!0)],8,Ar)):f("",!0)}}),Br=$(Cr,[["__scopeId","data-v-9b0d03d2"]]),Hr=s=>{Pr(s),s.component("PluginTabs",Mr),s.component("PluginTabsTab",Br)},Dr={extends:Se,Layout(){return lt(Se.Layout,null,{})},enhanceApp({app:s,router:e,siteData:t}){Hr(s)}};export{Dr as R,Yn as c,L as u}; diff --git a/dev/assets/getstarted.md.BxUYlh-U.js b/dev/assets/getstarted.md.EJuNxDSJ.js similarity index 88% rename from dev/assets/getstarted.md.BxUYlh-U.js rename to dev/assets/getstarted.md.EJuNxDSJ.js index 8474fee..9db306b 100644 --- a/dev/assets/getstarted.md.BxUYlh-U.js +++ b/dev/assets/getstarted.md.EJuNxDSJ.js @@ -1,8 +1,8 @@ -import{_ as i,c as s,l as a,a as t,a7 as n,o as e}from"./chunks/framework.D1rHXXmm.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),o={name:"getstarted.md"},l=n(`

Get started ​

Installation ​

You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:

julia
]add BioMarkovChains

If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.

Create a BioMarkovChain of DNA ​

julia
using BioSequences, BioMarkovChains
+import{_ as i,c as s,j as a,a as t,a6 as n,o as e}from"./chunks/framework.Cvv1S4VC.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),o={name:"getstarted.md"},l=n(`
Get started ​
Installation ​
You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:
julia
]add BioMarkovChains
If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.
Create a BioMarkovChain of DNA ​
julia
using BioSequences, BioMarkovChains
 
 sequence = dna"CCTCCCGGACCCTGGGCTCGGGAC"
 
-BioMarkovChain(sequence)
BioMarkovChain of DNAAlphabet{4}() and order 1:
+BioMarkovChain(sequence)
BioMarkovChain of DNAAlphabet{4}() and order 1:
   - Transition Probability Matrix --> Matrix{Float64}(4 × 4):
    0.0     1.0     0.0     0.0
    0.0     0.5     0.2     0.3
@@ -12,7 +12,7 @@ import{_ as i,c as s,l as a,a as t,a7 as n,o as e}from"./chunks/framework.D1rHXX
    0.087
    0.4348
    0.3478
-   0.1304
Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.
`,9),r=a("em",null,"n-step transition probability matrix",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 1044.2","aria-hidden":"true"},T=n('𝓂',1),h=[T],Q=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])]),a("mo",null,"="),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",{stretchy:"false"},"("),a("mi",null,"n"),a("mo",{stretchy:"false"},")"),a("mo",{stretchy:"false"},")")])],-1),c={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g=a("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[a("g",{"data-mml-node":"math"},[a("g",{"data-mml-node":"mi"},[a("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),u=[g],x=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"n")])],-1),_={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"1.744ex",role:"img",focusable:"false",viewBox:"0 -721 1216 771","aria-hidden":"true"},w=n('',1),v=[w],b=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")])])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.985ex",height:"1.957ex",role:"img",focusable:"false",viewBox:"0 -661 2645.6 865","aria-hidden":"true"},C=n('',1),M=[C],L=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null," ")]),a("mo",{stretchy:"false"},"→"),a("mi",null,"j")])],-1),H=a("em",null,"n",-1),A=n(`
julia
BioMarkovChain(sequence, 2)
BioMarkovChain of DNAAlphabet{4}() and order 2:
+   0.1304
Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.
`,9),r=a("em",null,"n-step transition probability matrix",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 1044.2","aria-hidden":"true"},T=n('𝓂',1),h=[T],Q=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])]),a("mo",null,"="),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",{stretchy:"false"},"("),a("mi",null,"n"),a("mo",{stretchy:"false"},")"),a("mo",{stretchy:"false"},")")])],-1),c={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g=a("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[a("g",{"data-mml-node":"math"},[a("g",{"data-mml-node":"mi"},[a("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),u=[g],x=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"n")])],-1),_={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"1.744ex",role:"img",focusable:"false",viewBox:"0 -721 1216 771","aria-hidden":"true"},w=n('',1),b=[w],v=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")])])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.985ex",height:"1.957ex",role:"img",focusable:"false",viewBox:"0 -661 2645.6 865","aria-hidden":"true"},C=n('',1),M=[C],L=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null," ")]),a("mo",{stretchy:"false"},"→"),a("mi",null,"j")])],-1),H=a("em",null,"n",-1),A=n(`
julia
BioMarkovChain(sequence, 2)
BioMarkovChain of DNAAlphabet{4}() and order 2:
   - Transition Probability Matrix --> Matrix{Float64}(4 × 4):
    0.0     0.5     0.2     0.3
    0.05    0.475   0.325   0.15
@@ -22,4 +22,4 @@ import{_ as i,c as s,l as a,a as t,a7 as n,o as e}from"./chunks/framework.D1rHXX
    0.087
    0.4348
    0.3478
-   0.1304
`,2);function D(j,E,B,S,P,V){return e(),s("div",null,[l,a("p",null,[t("A very nice nice property of the transition probability matrix is that the "),r,t(),a("mjx-container",p,[(e(),s("svg",d,h)),Q]),t(", that is the "),a("mjx-container",c,[(e(),s("svg",m,u)),x]),t("th power of "),a("mjx-container",_,[(e(),s("svg",k,v)),b]),t(" represents "),a("mjx-container",f,[(e(),s("svg",y,M)),L]),t(" transitions in "),H,t(" steps. We can also have higher order transition models as:")]),A])}const I=i(o,[["render",D]]);export{G as __pageData,I as default};
+   0.1304
`,2);function D(j,E,B,S,P,V){return e(),s("div",null,[l,a("p",null,[t("A very nice nice property of the transition probability matrix is that the "),r,t(),a("mjx-container",p,[(e(),s("svg",d,h)),Q]),t(", that is the "),a("mjx-container",c,[(e(),s("svg",m,u)),x]),t("th power of "),a("mjx-container",_,[(e(),s("svg",k,b)),v]),t(" represents "),a("mjx-container",f,[(e(),s("svg",y,M)),L]),t(" transitions in "),H,t(" steps. We can also have higher order transition models as:")]),A])}const I=i(o,[["render",D]]);export{G as __pageData,I as default}; diff --git a/dev/assets/getstarted.md.BxUYlh-U.lean.js b/dev/assets/getstarted.md.EJuNxDSJ.lean.js similarity index 95% rename from dev/assets/getstarted.md.BxUYlh-U.lean.js rename to dev/assets/getstarted.md.EJuNxDSJ.lean.js index 82d5d8c..46a71f4 100644 --- a/dev/assets/getstarted.md.BxUYlh-U.lean.js +++ b/dev/assets/getstarted.md.EJuNxDSJ.lean.js @@ -1 +1 @@ -import{_ as i,c as s,l as a,a as t,a7 as n,o as e}from"./chunks/framework.D1rHXXmm.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),o={name:"getstarted.md"},l=n("",9),r=a("em",null,"n-step transition probability matrix",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 1044.2","aria-hidden":"true"},T=n("",1),h=[T],Q=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])]),a("mo",null,"="),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",{stretchy:"false"},"("),a("mi",null,"n"),a("mo",{stretchy:"false"},")"),a("mo",{stretchy:"false"},")")])],-1),c={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g=a("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[a("g",{"data-mml-node":"math"},[a("g",{"data-mml-node":"mi"},[a("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),u=[g],x=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"n")])],-1),_={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"1.744ex",role:"img",focusable:"false",viewBox:"0 -721 1216 771","aria-hidden":"true"},w=n("",1),v=[w],b=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")])])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.985ex",height:"1.957ex",role:"img",focusable:"false",viewBox:"0 -661 2645.6 865","aria-hidden":"true"},C=n("",1),M=[C],L=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null," ")]),a("mo",{stretchy:"false"},"→"),a("mi",null,"j")])],-1),H=a("em",null,"n",-1),A=n("",2);function D(j,E,B,S,P,V){return e(),s("div",null,[l,a("p",null,[t("A very nice nice property of the transition probability matrix is that the "),r,t(),a("mjx-container",p,[(e(),s("svg",d,h)),Q]),t(", that is the "),a("mjx-container",c,[(e(),s("svg",m,u)),x]),t("th power of "),a("mjx-container",_,[(e(),s("svg",k,v)),b]),t(" represents "),a("mjx-container",f,[(e(),s("svg",y,M)),L]),t(" transitions in "),H,t(" steps. We can also have higher order transition models as:")]),A])}const I=i(o,[["render",D]]);export{G as __pageData,I as default}; +import{_ as i,c as s,j as a,a as t,a6 as n,o as e}from"./chunks/framework.Cvv1S4VC.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),o={name:"getstarted.md"},l=n("",9),r=a("em",null,"n-step transition probability matrix",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 1044.2","aria-hidden":"true"},T=n("",1),h=[T],Q=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"n")])]),a("mo",null,"="),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"m")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"i"),a("mi",null,"j")])]),a("mo",{stretchy:"false"},"("),a("mi",null,"n"),a("mo",{stretchy:"false"},")"),a("mo",{stretchy:"false"},")")])],-1),c={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g=a("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[a("g",{"data-mml-node":"math"},[a("g",{"data-mml-node":"mi"},[a("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),u=[g],x=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"n")])],-1),_={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"1.744ex",role:"img",focusable:"false",viewBox:"0 -721 1216 771","aria-hidden":"true"},w=n("",1),b=[w],v=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"script"},"M")])])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.985ex",height:"1.957ex",role:"img",focusable:"false",viewBox:"0 -661 2645.6 865","aria-hidden":"true"},C=n("",1),M=[C],L=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"i"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",null," ")]),a("mo",{stretchy:"false"},"→"),a("mi",null,"j")])],-1),H=a("em",null,"n",-1),A=n("",2);function D(j,E,B,S,P,V){return e(),s("div",null,[l,a("p",null,[t("A very nice nice property of the transition probability matrix is that the "),r,t(),a("mjx-container",p,[(e(),s("svg",d,h)),Q]),t(", that is the "),a("mjx-container",c,[(e(),s("svg",m,u)),x]),t("th power of "),a("mjx-container",_,[(e(),s("svg",k,b)),v]),t(" represents "),a("mjx-container",f,[(e(),s("svg",y,M)),L]),t(" transitions in "),H,t(" steps. We can also have higher order transition models as:")]),A])}const I=i(o,[["render",D]]);export{G as __pageData,I as default}; diff --git a/dev/assets/home.md.nGdy1Xvl.js b/dev/assets/home.md.DYCAAGxb.js similarity index 85% rename from dev/assets/home.md.nGdy1Xvl.js rename to dev/assets/home.md.DYCAAGxb.js index eae020a..feb9f98 100644 --- a/dev/assets/home.md.nGdy1Xvl.js +++ b/dev/assets/home.md.DYCAAGxb.js @@ -1 +1 @@ -import{_ as t,c as a,o,l as e,a8 as s,a as r}from"./chunks/framework.D1rHXXmm.js";const O=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"home.md","filePath":"home.md","lastUpdated":null}'),n={name:"home.md"},i=e("p",{align:"center"},[e("img",{src:s,height:"150"}),e("br"),e("i",null,"Representing biological sequences as Markov chains")],-1),c=e("hr",null,null,-1),l=e("h2",{id:"Overview",tabindex:"-1"},[r("Overview "),e("a",{class:"header-anchor",href:"#Overview","aria-label":'Permalink to "Overview {#Overview}"'},"​")],-1),d=e("blockquote",null,[e("p",null,"This package aim to represent BioSequences types as Markov chains to perform different operations and predictions")],-1),h=[i,c,l,d];function _(p,m,u,v,f,g){return o(),a("div",null,h)}const b=t(n,[["render",_]]);export{O as __pageData,b as default}; +import{_ as t,c as a,o,j as e,a7 as s,a as r}from"./chunks/framework.Cvv1S4VC.js";const O=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"home.md","filePath":"home.md","lastUpdated":null}'),n={name:"home.md"},i=e("p",{align:"center"},[e("img",{src:s,height:"150"}),e("br"),e("i",null,"Representing biological sequences as Markov chains")],-1),c=e("hr",null,null,-1),l=e("h2",{id:"Overview",tabindex:"-1"},[r("Overview "),e("a",{class:"header-anchor",href:"#Overview","aria-label":'Permalink to "Overview {#Overview}"'},"​")],-1),d=e("blockquote",null,[e("p",null,"This package aim to represent BioSequences types as Markov chains to perform different operations and predictions")],-1),h=[i,c,l,d];function _(p,m,u,v,f,g){return o(),a("div",null,h)}const b=t(n,[["render",_]]);export{O as __pageData,b as default}; diff --git a/dev/assets/home.md.nGdy1Xvl.lean.js b/dev/assets/home.md.DYCAAGxb.lean.js similarity index 85% rename from dev/assets/home.md.nGdy1Xvl.lean.js rename to dev/assets/home.md.DYCAAGxb.lean.js index eae020a..feb9f98 100644 --- a/dev/assets/home.md.nGdy1Xvl.lean.js +++ b/dev/assets/home.md.DYCAAGxb.lean.js @@ -1 +1 @@ -import{_ as t,c as a,o,l as e,a8 as s,a as r}from"./chunks/framework.D1rHXXmm.js";const O=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"home.md","filePath":"home.md","lastUpdated":null}'),n={name:"home.md"},i=e("p",{align:"center"},[e("img",{src:s,height:"150"}),e("br"),e("i",null,"Representing biological sequences as Markov chains")],-1),c=e("hr",null,null,-1),l=e("h2",{id:"Overview",tabindex:"-1"},[r("Overview "),e("a",{class:"header-anchor",href:"#Overview","aria-label":'Permalink to "Overview {#Overview}"'},"​")],-1),d=e("blockquote",null,[e("p",null,"This package aim to represent BioSequences types as Markov chains to perform different operations and predictions")],-1),h=[i,c,l,d];function _(p,m,u,v,f,g){return o(),a("div",null,h)}const b=t(n,[["render",_]]);export{O as __pageData,b as default}; +import{_ as t,c as a,o,j as e,a7 as s,a as r}from"./chunks/framework.Cvv1S4VC.js";const O=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"home.md","filePath":"home.md","lastUpdated":null}'),n={name:"home.md"},i=e("p",{align:"center"},[e("img",{src:s,height:"150"}),e("br"),e("i",null,"Representing biological sequences as Markov chains")],-1),c=e("hr",null,null,-1),l=e("h2",{id:"Overview",tabindex:"-1"},[r("Overview "),e("a",{class:"header-anchor",href:"#Overview","aria-label":'Permalink to "Overview {#Overview}"'},"​")],-1),d=e("blockquote",null,[e("p",null,"This package aim to represent BioSequences types as Markov chains to perform different operations and predictions")],-1),h=[i,c,l,d];function _(p,m,u,v,f,g){return o(),a("div",null,h)}const b=t(n,[["render",_]]);export{O as __pageData,b as default}; diff --git a/dev/assets/index.md.Ba-cgBKx.js b/dev/assets/index.md.Ba-cgBKx.js new file mode 100644 index 0000000..b491f4d --- /dev/null +++ b/dev/assets/index.md.Ba-cgBKx.js @@ -0,0 +1 @@ +import{_ as t,c as e,o as a,a6 as i}from"./chunks/framework.Cvv1S4VC.js";const _=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"BioMarkovChains.jl","text":"Representing biological sequences as Markov chains","tagline":null,"image":{"src":"/logo.png","alt":"BioMarkovChains"},"actions":[{"theme":"brand","text":"Get Started","link":"/getstarted.md"},{"theme":"alt","text":"View on Github","link":"https://github.com/camilogarciabotero/BioMarkovChains.jl"}]}},"headers":[],"relativePath":"index.md","filePath":"index.md","lastUpdated":null}'),s={name:"index.md"},o=i('

<div class="vp-doc" style="width:90%; margin:auto">

Install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the add BioMarkovChains command.

julia
(@v1.10) pkg> add BioMarkovChains

For more information, see the Getting Started section.

</div>

',5),n=[o];function d(l,r,h,p,c,k){return a(),e("div",null,n)}const m=t(s,[["render",d]]);export{_ as __pageData,m as default}; diff --git a/dev/assets/index.md.mmk1IapY.lean.js b/dev/assets/index.md.Ba-cgBKx.lean.js similarity index 60% rename from dev/assets/index.md.mmk1IapY.lean.js rename to dev/assets/index.md.Ba-cgBKx.lean.js index aab1a46..733f74f 100644 --- a/dev/assets/index.md.mmk1IapY.lean.js +++ b/dev/assets/index.md.Ba-cgBKx.lean.js @@ -1 +1 @@ -import{_ as t,c as e,o as a,a7 as i}from"./chunks/framework.D1rHXXmm.js";const m=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"BioMarkovChains.jl","text":"Representing biological sequences as Markov chains","tagline":null,"image":{"src":"/logo.png","alt":"BioMarkovChains"},"actions":[{"theme":"brand","text":"Get Started","link":"/getstarted.md"},{"theme":"alt","text":"View on Github","link":"https://github.com/camilogarciabotero/BioMarkovChains.jl"}]}},"headers":[],"relativePath":"index.md","filePath":"index.md","lastUpdated":null}'),s={name:"index.md"},o=i("",7),n=[o];function l(d,p,r,h,c,k){return a(),e("div",null,n)}const _=t(s,[["render",l]]);export{m as __pageData,_ as default}; +import{_ as t,c as e,o as a,a6 as i}from"./chunks/framework.Cvv1S4VC.js";const _=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"BioMarkovChains.jl","text":"Representing biological sequences as Markov chains","tagline":null,"image":{"src":"/logo.png","alt":"BioMarkovChains"},"actions":[{"theme":"brand","text":"Get Started","link":"/getstarted.md"},{"theme":"alt","text":"View on Github","link":"https://github.com/camilogarciabotero/BioMarkovChains.jl"}]}},"headers":[],"relativePath":"index.md","filePath":"index.md","lastUpdated":null}'),s={name:"index.md"},o=i("",5),n=[o];function d(l,r,h,p,c,k){return a(),e("div",null,n)}const m=t(s,[["render",d]]);export{_ as __pageData,m as default}; diff --git a/dev/assets/index.md.mmk1IapY.js b/dev/assets/index.md.mmk1IapY.js deleted file mode 100644 index 54f4d2d..0000000 --- a/dev/assets/index.md.mmk1IapY.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as t,c as e,o as a,a7 as i}from"./chunks/framework.D1rHXXmm.js";const m=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"BioMarkovChains.jl","text":"Representing biological sequences as Markov chains","tagline":null,"image":{"src":"/logo.png","alt":"BioMarkovChains"},"actions":[{"theme":"brand","text":"Get Started","link":"/getstarted.md"},{"theme":"alt","text":"View on Github","link":"https://github.com/camilogarciabotero/BioMarkovChains.jl"}]}},"headers":[],"relativePath":"index.md","filePath":"index.md","lastUpdated":null}'),s={name:"index.md"},o=i('

<p style="margin-bottom:2cm"></p>

<div class="vp-doc" style="width:80%; margin:auto">

<h2> Get Started </h2>

Install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the add BioMarkovChains command.

julia
(@v1.10) pkg> add BioMarkovChains

For more information, see the Getting Started section.

</div>

',7),n=[o];function l(d,p,r,h,c,k){return a(),e("div",null,n)}const _=t(s,[["render",l]]);export{m as __pageData,_ as default}; diff --git a/dev/assets/style.BSicJgYg.css b/dev/assets/style.BSicJgYg.css new file mode 100644 index 0000000..47e281a --- /dev/null +++ b/dev/assets/style.BSicJgYg.css @@ -0,0 +1 @@ +@import"https://fonts.googleapis.com/css?family=Space+Mono:regular,italic,700,700italic";@import"https://fonts.googleapis.com/css?family=Space+Grotesk:regular,italic,700,700italic";@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-cyrillic-ext.BBPuwvHQ.woff2) format("woff2");unicode-range:U+0460-052F,U+1C80-1C88,U+20B4,U+2DE0-2DFF,U+A640-A69F,U+FE2E-FE2F}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-cyrillic.C5lxZ8CY.woff2) format("woff2");unicode-range:U+0301,U+0400-045F,U+0490-0491,U+04B0-04B1,U+2116}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-greek-ext.CqjqNYQ-.woff2) format("woff2");unicode-range:U+1F00-1FFF}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-greek.BBVDIX6e.woff2) format("woff2");unicode-range:U+0370-0377,U+037A-037F,U+0384-038A,U+038C,U+038E-03A1,U+03A3-03FF}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-vietnamese.BjW4sHH5.woff2) format("woff2");unicode-range:U+0102-0103,U+0110-0111,U+0128-0129,U+0168-0169,U+01A0-01A1,U+01AF-01B0,U+0300-0301,U+0303-0304,U+0308-0309,U+0323,U+0329,U+1EA0-1EF9,U+20AB}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-latin-ext.4ZJIpNVo.woff2) format("woff2");unicode-range:U+0100-02AF,U+0304,U+0308,U+0329,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-latin.Di8DUHzh.woff2) format("woff2");unicode-range:U+0000-00FF,U+0131,U+0152-0153,U+02BB-02BC,U+02C6,U+02DA,U+02DC,U+0304,U+0308,U+0329,U+2000-206F,U+2074,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-cyrillic-ext.r48I6akx.woff2) format("woff2");unicode-range:U+0460-052F,U+1C80-1C88,U+20B4,U+2DE0-2DFF,U+A640-A69F,U+FE2E-FE2F}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-cyrillic.By2_1cv3.woff2) format("woff2");unicode-range:U+0301,U+0400-045F,U+0490-0491,U+04B0-04B1,U+2116}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-greek-ext.1u6EdAuj.woff2) format("woff2");unicode-range:U+1F00-1FFF}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-greek.DJ8dCoTZ.woff2) format("woff2");unicode-range:U+0370-0377,U+037A-037F,U+0384-038A,U+038C,U+038E-03A1,U+03A3-03FF}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-vietnamese.BSbpV94h.woff2) format("woff2");unicode-range:U+0102-0103,U+0110-0111,U+0128-0129,U+0168-0169,U+01A0-01A1,U+01AF-01B0,U+0300-0301,U+0303-0304,U+0308-0309,U+0323,U+0329,U+1EA0-1EF9,U+20AB}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-latin-ext.CN1xVJS-.woff2) format("woff2");unicode-range:U+0100-02AF,U+0304,U+0308,U+0329,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-latin.C2AdPX0b.woff2) format("woff2");unicode-range:U+0000-00FF,U+0131,U+0152-0153,U+02BB-02BC,U+02C6,U+02DA,U+02DC,U+0304,U+0308,U+0329,U+2000-206F,U+2074,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}@font-face{font-family:Punctuation SC;font-weight:400;src:local("PingFang SC Regular"),local("Noto Sans CJK SC"),local("Microsoft YaHei");unicode-range:U+201C,U+201D,U+2018,U+2019,U+2E3A,U+2014,U+2013,U+2026,U+00B7,U+007E,U+002F}@font-face{font-family:Punctuation SC;font-weight:500;src:local("PingFang SC Medium"),local("Noto Sans CJK SC"),local("Microsoft YaHei");unicode-range:U+201C,U+201D,U+2018,U+2019,U+2E3A,U+2014,U+2013,U+2026,U+00B7,U+007E,U+002F}@font-face{font-family:Punctuation SC;font-weight:600;src:local("PingFang SC Semibold"),local("Noto Sans CJK SC Bold"),local("Microsoft YaHei Bold");unicode-range:U+201C,U+201D,U+2018,U+2019,U+2E3A,U+2014,U+2013,U+2026,U+00B7,U+007E,U+002F}@font-face{font-family:Punctuation SC;font-weight:700;src:local("PingFang SC Semibold"),local("Noto Sans CJK SC Bold"),local("Microsoft YaHei Bold");unicode-range:U+201C,U+201D,U+2018,U+2019,U+2E3A,U+2014,U+2013,U+2026,U+00B7,U+007E,U+002F}:root{--vp-c-white: #ffffff;--vp-c-black: #000000;--vp-c-neutral: var(--vp-c-black);--vp-c-neutral-inverse: var(--vp-c-white)}.dark{--vp-c-neutral: var(--vp-c-white);--vp-c-neutral-inverse: var(--vp-c-black)}:root{--vp-c-gray-1: #dddde3;--vp-c-gray-2: #e4e4e9;--vp-c-gray-3: #ebebef;--vp-c-gray-soft: rgba(142, 150, 170, .14);--vp-c-indigo-1: #3451b2;--vp-c-indigo-2: #3a5ccc;--vp-c-indigo-3: #5672cd;--vp-c-indigo-soft: rgba(100, 108, 255, .14);--vp-c-purple-1: #6f42c1;--vp-c-purple-2: #7e4cc9;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .14);--vp-c-green-1: #18794e;--vp-c-green-2: #299764;--vp-c-green-3: #30a46c;--vp-c-green-soft: rgba(16, 185, 129, .14);--vp-c-yellow-1: #915930;--vp-c-yellow-2: #946300;--vp-c-yellow-3: #9f6a00;--vp-c-yellow-soft: rgba(234, 179, 8, .14);--vp-c-red-1: #b8272c;--vp-c-red-2: #d5393e;--vp-c-red-3: #e0575b;--vp-c-red-soft: rgba(244, 63, 94, .14);--vp-c-sponsor: #db2777}.dark{--vp-c-gray-1: #515c67;--vp-c-gray-2: #414853;--vp-c-gray-3: #32363f;--vp-c-gray-soft: rgba(101, 117, 133, .16);--vp-c-indigo-1: #a8b1ff;--vp-c-indigo-2: #5c73e7;--vp-c-indigo-3: #3e63dd;--vp-c-indigo-soft: rgba(100, 108, 255, .16);--vp-c-purple-1: #c8abfa;--vp-c-purple-2: #a879e6;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .16);--vp-c-green-1: #3dd68c;--vp-c-green-2: #30a46c;--vp-c-green-3: #298459;--vp-c-green-soft: rgba(16, 185, 129, .16);--vp-c-yellow-1: #f9b44e;--vp-c-yellow-2: #da8b17;--vp-c-yellow-3: #a46a0a;--vp-c-yellow-soft: rgba(234, 179, 8, .16);--vp-c-red-1: #f66f81;--vp-c-red-2: #f14158;--vp-c-red-3: #b62a3c;--vp-c-red-soft: rgba(244, 63, 94, .16)}:root{--vp-c-bg: #ffffff;--vp-c-bg-alt: #f6f6f7;--vp-c-bg-elv: #ffffff;--vp-c-bg-soft: #f6f6f7}.dark{--vp-c-bg: #1b1b1f;--vp-c-bg-alt: #161618;--vp-c-bg-elv: #202127;--vp-c-bg-soft: #202127}:root{--vp-c-border: #c2c2c4;--vp-c-divider: #e2e2e3;--vp-c-gutter: #e2e2e3}.dark{--vp-c-border: #3c3f44;--vp-c-divider: #2e2e32;--vp-c-gutter: #000000}:root{--vp-c-text-1: rgba(60, 60, 67);--vp-c-text-2: rgba(60, 60, 67, .78);--vp-c-text-3: rgba(60, 60, 67, .56)}.dark{--vp-c-text-1: rgba(255, 255, 245, .86);--vp-c-text-2: rgba(235, 235, 245, .6);--vp-c-text-3: rgba(235, 235, 245, .38)}:root{--vp-c-default-1: var(--vp-c-gray-1);--vp-c-default-2: var(--vp-c-gray-2);--vp-c-default-3: var(--vp-c-gray-3);--vp-c-default-soft: var(--vp-c-gray-soft);--vp-c-brand-1: var(--vp-c-indigo-1);--vp-c-brand-2: var(--vp-c-indigo-2);--vp-c-brand-3: var(--vp-c-indigo-3);--vp-c-brand-soft: var(--vp-c-indigo-soft);--vp-c-brand: var(--vp-c-brand-1);--vp-c-tip-1: var(--vp-c-brand-1);--vp-c-tip-2: var(--vp-c-brand-2);--vp-c-tip-3: var(--vp-c-brand-3);--vp-c-tip-soft: var(--vp-c-brand-soft);--vp-c-note-1: var(--vp-c-brand-1);--vp-c-note-2: var(--vp-c-brand-2);--vp-c-note-3: var(--vp-c-brand-3);--vp-c-note-soft: var(--vp-c-brand-soft);--vp-c-success-1: var(--vp-c-green-1);--vp-c-success-2: var(--vp-c-green-2);--vp-c-success-3: var(--vp-c-green-3);--vp-c-success-soft: var(--vp-c-green-soft);--vp-c-important-1: var(--vp-c-purple-1);--vp-c-important-2: var(--vp-c-purple-2);--vp-c-important-3: var(--vp-c-purple-3);--vp-c-important-soft: var(--vp-c-purple-soft);--vp-c-warning-1: var(--vp-c-yellow-1);--vp-c-warning-2: var(--vp-c-yellow-2);--vp-c-warning-3: var(--vp-c-yellow-3);--vp-c-warning-soft: var(--vp-c-yellow-soft);--vp-c-danger-1: var(--vp-c-red-1);--vp-c-danger-2: var(--vp-c-red-2);--vp-c-danger-3: var(--vp-c-red-3);--vp-c-danger-soft: var(--vp-c-red-soft);--vp-c-caution-1: var(--vp-c-red-1);--vp-c-caution-2: var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, "Menlo", "Monaco", "Consolas", "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root:where(:lang(zh)){--vp-font-family-base: "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: var(--vp-c-text-1);--vp-custom-block-warning-bg: var(--vp-c-warning-soft);--vp-custom-block-warning-code-bg: var(--vp-c-warning-soft);--vp-custom-block-danger-border: transparent;--vp-custom-block-danger-text: var(--vp-c-text-1);--vp-custom-block-danger-bg: var(--vp-c-danger-soft);--vp-custom-block-danger-code-bg: var(--vp-c-danger-soft);--vp-custom-block-caution-border: transparent;--vp-custom-block-caution-text: var(--vp-c-text-1);--vp-custom-block-caution-bg: var(--vp-c-caution-soft);--vp-custom-block-caution-code-bg: var(--vp-c-caution-soft);--vp-custom-block-details-border: var(--vp-custom-block-info-border);--vp-custom-block-details-text: var(--vp-custom-block-info-text);--vp-custom-block-details-bg: var(--vp-custom-block-info-bg);--vp-custom-block-details-code-bg: var(--vp-custom-block-info-code-bg)}:root{--vp-input-border-color: var(--vp-c-border);--vp-input-bg-color: var(--vp-c-bg-alt);--vp-input-switch-bg-color: var(--vp-c-default-soft)}:root{--vp-nav-height: 64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: var(--vp-c-bg);--vp-local-search-result-bg: var(--vp-c-bg);--vp-local-search-result-border: var(--vp-c-divider);--vp-local-search-result-selected-bg: var(--vp-c-bg);--vp-local-search-result-selected-border: var(--vp-c-brand-1);--vp-local-search-highlight-bg: var(--vp-c-brand-1);--vp-local-search-highlight-text: var(--vp-c-neutral-inverse)}@media (prefers-reduced-motion: reduce){*,:before,:after{animation-delay:-1ms!important;animation-duration:1ms!important;animation-iteration-count:1!important;background-attachment:initial!important;scroll-behavior:auto!important;transition-duration:0s!important;transition-delay:0s!important}}*,:before,:after{box-sizing:border-box}html{line-height:1.4;font-size:16px;-webkit-text-size-adjust:100%}html.dark{color-scheme:dark}body{margin:0;width:100%;min-width:320px;min-height:100vh;line-height:24px;font-family:var(--vp-font-family-base);font-size:16px;font-weight:400;color:var(--vp-c-text-1);background-color:var(--vp-c-bg);font-synthesis:style;text-rendering:optimizeLegibility;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}main{display:block}h1,h2,h3,h4,h5,h6{margin:0;line-height:24px;font-size:16px;font-weight:400}p{margin:0}strong,b{font-weight:600}a,area,button,[role=button],input,label,select,summary,textarea{touch-action:manipulation}a{color:inherit;text-decoration:inherit}ol,ul{list-style:none;margin:0;padding:0}blockquote{margin:0}pre,code,kbd,samp{font-family:var(--vp-font-family-mono)}img,svg,video,canvas,audio,iframe,embed,object{display:block}figure{margin:0}img,video{max-width:100%;height:auto}button,input,optgroup,select,textarea{border:0;padding:0;line-height:inherit;color:inherit}button{padding:0;font-family:inherit;background-color:transparent;background-image:none}button:enabled,[role=button]:enabled{cursor:pointer}button:focus,button:focus-visible{outline:1px dotted;outline:4px auto -webkit-focus-ring-color}button:focus:not(:focus-visible){outline:none!important}input:focus,textarea:focus,select:focus{outline:none}table{border-collapse:collapse}input{background-color:transparent}input:-ms-input-placeholder,textarea:-ms-input-placeholder{color:var(--vp-c-text-3)}input::-ms-input-placeholder,textarea::-ms-input-placeholder{color:var(--vp-c-text-3)}input::placeholder,textarea::placeholder{color:var(--vp-c-text-3)}input::-webkit-outer-spin-button,input::-webkit-inner-spin-button{-webkit-appearance:none;margin:0}input[type=number]{-moz-appearance:textfield}textarea{resize:vertical}select{-webkit-appearance:none}fieldset{margin:0;padding:0}h1,h2,h3,h4,h5,h6,li,p{overflow-wrap:break-word}vite-error-overlay{z-index:9999}mjx-container{overflow-x:auto}mjx-container>svg{display:inline-block;margin:auto}[class^=vpi-],[class*=" vpi-"],.vp-icon{width:1em;height:1em}[class^=vpi-].bg,[class*=" vpi-"].bg,.vp-icon.bg{background-size:100% 100%;background-color:transparent}[class^=vpi-]:not(.bg),[class*=" vpi-"]:not(.bg),.vp-icon:not(.bg){-webkit-mask:var(--icon) no-repeat;mask:var(--icon) no-repeat;-webkit-mask-size:100% 100%;mask-size:100% 100%;background-color:currentColor;color:inherit}.vpi-align-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M21 6H3M15 12H3M17 18H3'/%3E%3C/svg%3E")}.vpi-arrow-right,.vpi-arrow-down,.vpi-arrow-left,.vpi-arrow-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5l7 7-7 7'/%3E%3C/svg%3E")}.vpi-chevron-right,.vpi-chevron-down,.vpi-chevron-left,.vpi-chevron-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 18 6-6-6-6'/%3E%3C/svg%3E")}.vpi-chevron-down,.vpi-arrow-down{transform:rotate(90deg)}.vpi-chevron-left,.vpi-arrow-left{transform:rotate(180deg)}.vpi-chevron-up,.vpi-arrow-up{transform:rotate(-90deg)}.vpi-square-pen{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3H5a2 2 0 0 0-2 2v14a2 2 0 0 0 2 2h14a2 2 0 0 0 2-2v-7'/%3E%3Cpath d='M18.375 2.625a2.121 2.121 0 1 1 3 3L12 15l-4 1 1-4Z'/%3E%3C/svg%3E")}.vpi-plus{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5v14'/%3E%3C/svg%3E")}.vpi-sun{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='4'/%3E%3Cpath d='M12 2v2M12 20v2M4.93 4.93l1.41 1.41M17.66 17.66l1.41 1.41M2 12h2M20 12h2M6.34 17.66l-1.41 1.41M19.07 4.93l-1.41 1.41'/%3E%3C/svg%3E")}.vpi-moon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3a6 6 0 0 0 9 9 9 9 0 1 1-9-9Z'/%3E%3C/svg%3E")}.vpi-more-horizontal{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='1'/%3E%3Ccircle cx='19' cy='12' r='1'/%3E%3Ccircle cx='5' cy='12' r='1'/%3E%3C/svg%3E")}.vpi-languages{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6'/%3E%3C/svg%3E")}.vpi-heart{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M19 14c1.49-1.46 3-3.21 3-5.5A5.5 5.5 0 0 0 16.5 3c-1.76 0-3 .5-4.5 2-1.5-1.5-2.74-2-4.5-2A5.5 5.5 0 0 0 2 8.5c0 2.3 1.5 4.05 3 5.5l7 7Z'/%3E%3C/svg%3E")}.vpi-search{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='11' cy='11' r='8'/%3E%3Cpath d='m21 21-4.3-4.3'/%3E%3C/svg%3E")}.vpi-layout-list{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='7' height='7' x='3' y='3' rx='1'/%3E%3Crect width='7' height='7' x='3' y='14' rx='1'/%3E%3Cpath d='M14 4h7M14 9h7M14 15h7M14 20h7'/%3E%3C/svg%3E")}.vpi-delete{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M20 5H9l-7 7 7 7h11a2 2 0 0 0 2-2V7a2 2 0 0 0-2-2ZM18 9l-6 6M12 9l6 6'/%3E%3C/svg%3E")}.vpi-corner-down-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 10-5 5 5 5'/%3E%3Cpath d='M20 4v7a4 4 0 0 1-4 4H4'/%3E%3C/svg%3E")}:root{--vp-icon-copy: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3C/svg%3E");--vp-icon-copied: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3Cpath d='m9 14 2 2 4-4'/%3E%3C/svg%3E")}.vpi-social-discord{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.317 4.37a19.791 19.791 0 0 0-4.885-1.515.074.074 0 0 0-.079.037c-.21.375-.444.864-.608 1.25a18.27 18.27 0 0 0-5.487 0 12.64 12.64 0 0 0-.617-1.25.077.077 0 0 0-.079-.037A19.736 19.736 0 0 0 3.677 4.37a.07.07 0 0 0-.032.027C.533 9.046-.32 13.58.099 18.057a.082.082 0 0 0 .031.057 19.9 19.9 0 0 0 5.993 3.03.078.078 0 0 0 .084-.028c.462-.63.874-1.295 1.226-1.994a.076.076 0 0 0-.041-.106 13.107 13.107 0 0 1-1.872-.892.077.077 0 0 1-.008-.128 10.2 10.2 0 0 0 .372-.292.074.074 0 0 1 .077-.01c3.928 1.793 8.18 1.793 12.062 0a.074.074 0 0 1 .078.01c.12.098.246.198.373.292a.077.077 0 0 1-.006.127 12.299 12.299 0 0 1-1.873.892.077.077 0 0 0-.041.107c.36.698.772 1.362 1.225 1.993a.076.076 0 0 0 .084.028 19.839 19.839 0 0 0 6.002-3.03.077.077 0 0 0 .032-.054c.5-5.177-.838-9.674-3.549-13.66a.061.061 0 0 0-.031-.03zM8.02 15.33c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.956-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.956 2.418-2.157 2.418zm7.975 0c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.955-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.946 2.418-2.157 2.418Z'/%3E%3C/svg%3E")}.vpi-social-facebook{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M9.101 23.691v-7.98H6.627v-3.667h2.474v-1.58c0-4.085 1.848-5.978 5.858-5.978.401 0 .955.042 1.468.103a8.68 8.68 0 0 1 1.141.195v3.325a8.623 8.623 0 0 0-.653-.036 26.805 26.805 0 0 0-.733-.009c-.707 0-1.259.096-1.675.309a1.686 1.686 0 0 0-.679.622c-.258.42-.374.995-.374 1.752v1.297h3.919l-.386 2.103-.287 1.564h-3.246v8.245C19.396 23.238 24 18.179 24 12.044c0-6.627-5.373-12-12-12s-12 5.373-12 12c0 5.628 3.874 10.35 9.101 11.647Z'/%3E%3C/svg%3E")}.vpi-social-github{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12'/%3E%3C/svg%3E")}.vpi-social-instagram{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M7.03.084c-1.277.06-2.149.264-2.91.563a5.874 5.874 0 0 0-2.124 1.388 5.878 5.878 0 0 0-1.38 2.127C.321 4.926.12 5.8.064 7.076.008 8.354-.005 8.764.001 12.023c.007 3.259.021 3.667.083 4.947.061 1.277.264 2.149.563 2.911.308.789.72 1.457 1.388 2.123a5.872 5.872 0 0 0 2.129 1.38c.763.295 1.636.496 2.913.552 1.278.056 1.689.069 4.947.063 3.257-.007 3.668-.021 4.947-.082 1.28-.06 2.147-.265 2.91-.563a5.881 5.881 0 0 0 2.123-1.388 5.881 5.881 0 0 0 1.38-2.129c.295-.763.496-1.636.551-2.912.056-1.28.07-1.69.063-4.948-.006-3.258-.02-3.667-.081-4.947-.06-1.28-.264-2.148-.564-2.911a5.892 5.892 0 0 0-1.387-2.123 5.857 5.857 0 0 0-2.128-1.38C19.074.322 18.202.12 16.924.066 15.647.009 15.236-.006 11.977 0 8.718.008 8.31.021 7.03.084m.14 21.693c-1.17-.05-1.805-.245-2.228-.408a3.736 3.736 0 0 1-1.382-.895 3.695 3.695 0 0 1-.9-1.378c-.165-.423-.363-1.058-.417-2.228-.06-1.264-.072-1.644-.08-4.848-.006-3.204.006-3.583.061-4.848.05-1.169.246-1.805.408-2.228.216-.561.477-.96.895-1.382a3.705 3.705 0 0 1 1.379-.9c.423-.165 1.057-.361 2.227-.417 1.265-.06 1.644-.072 4.848-.08 3.203-.006 3.583.006 4.85.062 1.168.05 1.804.244 2.227.408.56.216.96.475 1.382.895.421.42.681.817.9 1.378.165.422.362 1.056.417 2.227.06 1.265.074 1.645.08 4.848.005 3.203-.006 3.583-.061 4.848-.051 1.17-.245 1.805-.408 2.23-.216.56-.477.96-.896 1.38a3.705 3.705 0 0 1-1.378.9c-.422.165-1.058.362-2.226.418-1.266.06-1.645.072-4.85.079-3.204.007-3.582-.006-4.848-.06m9.783-16.192a1.44 1.44 0 1 0 1.437-1.442 1.44 1.44 0 0 0-1.437 1.442M5.839 12.012a6.161 6.161 0 1 0 12.323-.024 6.162 6.162 0 0 0-12.323.024M8 12.008A4 4 0 1 1 12.008 16 4 4 0 0 1 8 12.008'/%3E%3C/svg%3E")}.vpi-social-linkedin{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.447 20.452h-3.554v-5.569c0-1.328-.027-3.037-1.852-3.037-1.853 0-2.136 1.445-2.136 2.939v5.667H9.351V9h3.414v1.561h.046c.477-.9 1.637-1.85 3.37-1.85 3.601 0 4.267 2.37 4.267 5.455v6.286zM5.337 7.433a2.062 2.062 0 0 1-2.063-2.065 2.064 2.064 0 1 1 2.063 2.065zm1.782 13.019H3.555V9h3.564v11.452zM22.225 0H1.771C.792 0 0 .774 0 1.729v20.542C0 23.227.792 24 1.771 24h20.451C23.2 24 24 23.227 24 22.271V1.729C24 .774 23.2 0 22.222 0h.003z'/%3E%3C/svg%3E")}.vpi-social-mastodon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.268 5.313c-.35-2.578-2.617-4.61-5.304-5.004C17.51.242 15.792 0 11.813 0h-.03c-3.98 0-4.835.242-5.288.309C3.882.692 1.496 2.518.917 5.127.64 6.412.61 7.837.661 9.143c.074 1.874.088 3.745.26 5.611.118 1.24.325 2.47.62 3.68.55 2.237 2.777 4.098 4.96 4.857 2.336.792 4.849.923 7.256.38.265-.061.527-.132.786-.213.585-.184 1.27-.39 1.774-.753a.057.057 0 0 0 .023-.043v-1.809a.052.052 0 0 0-.02-.041.053.053 0 0 0-.046-.01 20.282 20.282 0 0 1-4.709.545c-2.73 0-3.463-1.284-3.674-1.818a5.593 5.593 0 0 1-.319-1.433.053.053 0 0 1 .066-.054c1.517.363 3.072.546 4.632.546.376 0 .75 0 1.125-.01 1.57-.044 3.224-.124 4.768-.422.038-.008.077-.015.11-.024 2.435-.464 4.753-1.92 4.989-5.604.008-.145.03-1.52.03-1.67.002-.512.167-3.63-.024-5.545zm-3.748 9.195h-2.561V8.29c0-1.309-.55-1.976-1.67-1.976-1.23 0-1.846.79-1.846 2.35v3.403h-2.546V8.663c0-1.56-.617-2.35-1.848-2.35-1.112 0-1.668.668-1.67 1.977v6.218H4.822V8.102c0-1.31.337-2.35 1.011-3.12.696-.77 1.608-1.164 2.74-1.164 1.311 0 2.302.5 2.962 1.498l.638 1.06.638-1.06c.66-.999 1.65-1.498 2.96-1.498 1.13 0 2.043.395 2.74 1.164.675.77 1.012 1.81 1.012 3.12z'/%3E%3C/svg%3E")}.vpi-social-npm{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M1.763 0C.786 0 0 .786 0 1.763v20.474C0 23.214.786 24 1.763 24h20.474c.977 0 1.763-.786 1.763-1.763V1.763C24 .786 23.214 0 22.237 0zM5.13 5.323l13.837.019-.009 13.836h-3.464l.01-10.382h-3.456L12.04 19.17H5.113z'/%3E%3C/svg%3E")}.vpi-social-slack{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M5.042 15.165a2.528 2.528 0 0 1-2.52 2.523A2.528 2.528 0 0 1 0 15.165a2.527 2.527 0 0 1 2.522-2.52h2.52v2.52zm1.271 0a2.527 2.527 0 0 1 2.521-2.52 2.527 2.527 0 0 1 2.521 2.52v6.313A2.528 2.528 0 0 1 8.834 24a2.528 2.528 0 0 1-2.521-2.522v-6.313zM8.834 5.042a2.528 2.528 0 0 1-2.521-2.52A2.528 2.528 0 0 1 8.834 0a2.528 2.528 0 0 1 2.521 2.522v2.52H8.834zm0 1.271a2.528 2.528 0 0 1 2.521 2.521 2.528 2.528 0 0 1-2.521 2.521H2.522A2.528 2.528 0 0 1 0 8.834a2.528 2.528 0 0 1 2.522-2.521h6.312zm10.122 2.521a2.528 2.528 0 0 1 2.522-2.521A2.528 2.528 0 0 1 24 8.834a2.528 2.528 0 0 1-2.522 2.521h-2.522V8.834zm-1.268 0a2.528 2.528 0 0 1-2.523 2.521 2.527 2.527 0 0 1-2.52-2.521V2.522A2.527 2.527 0 0 1 15.165 0a2.528 2.528 0 0 1 2.523 2.522v6.312zm-2.523 10.122a2.528 2.528 0 0 1 2.523 2.522A2.528 2.528 0 0 1 15.165 24a2.527 2.527 0 0 1-2.52-2.522v-2.522h2.52zm0-1.268a2.527 2.527 0 0 1-2.52-2.523 2.526 2.526 0 0 1 2.52-2.52h6.313A2.527 2.527 0 0 1 24 15.165a2.528 2.528 0 0 1-2.522 2.523h-6.313z'/%3E%3C/svg%3E")}.vpi-social-twitter,.vpi-social-x{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M18.901 1.153h3.68l-8.04 9.19L24 22.846h-7.406l-5.8-7.584-6.638 7.584H.474l8.6-9.83L0 1.154h7.594l5.243 6.932ZM17.61 20.644h2.039L6.486 3.24H4.298Z'/%3E%3C/svg%3E")}.vpi-social-youtube{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.498 6.186a3.016 3.016 0 0 0-2.122-2.136C19.505 3.545 12 3.545 12 3.545s-7.505 0-9.377.505A3.017 3.017 0 0 0 .502 6.186C0 8.07 0 12 0 12s0 3.93.502 5.814a3.016 3.016 0 0 0 2.122 2.136c1.871.505 9.376.505 9.376.505s7.505 0 9.377-.505a3.015 3.015 0 0 0 2.122-2.136C24 15.93 24 12 24 12s0-3.93-.502-5.814zM9.545 15.568V8.432L15.818 12l-6.273 3.568z'/%3E%3C/svg%3E")}.visually-hidden{position:absolute;width:1px;height:1px;white-space:nowrap;clip:rect(0 0 0 0);clip-path:inset(50%);overflow:hidden}.custom-block{border:1px solid transparent;border-radius:8px;padding:16px 16px 8px;line-height:24px;font-size:var(--vp-custom-block-font-size);color:var(--vp-c-text-2)}.custom-block.info{border-color:var(--vp-custom-block-info-border);color:var(--vp-custom-block-info-text);background-color:var(--vp-custom-block-info-bg)}.custom-block.info a,.custom-block.info code{color:var(--vp-c-brand-1)}.custom-block.info a:hover,.custom-block.info a:hover>code{color:var(--vp-c-brand-2)}.custom-block.info code{background-color:var(--vp-custom-block-info-code-bg)}.custom-block.note{border-color:var(--vp-custom-block-note-border);color:var(--vp-custom-block-note-text);background-color:var(--vp-custom-block-note-bg)}.custom-block.note a,.custom-block.note code{color:var(--vp-c-brand-1)}.custom-block.note a:hover,.custom-block.note a:hover>code{color:var(--vp-c-brand-2)}.custom-block.note code{background-color:var(--vp-custom-block-note-code-bg)}.custom-block.tip{border-color:var(--vp-custom-block-tip-border);color:var(--vp-custom-block-tip-text);background-color:var(--vp-custom-block-tip-bg)}.custom-block.tip a,.custom-block.tip code{color:var(--vp-c-tip-1)}.custom-block.tip a:hover,.custom-block.tip a:hover>code{color:var(--vp-c-tip-2)}.custom-block.tip code{background-color:var(--vp-custom-block-tip-code-bg)}.custom-block.important{border-color:var(--vp-custom-block-important-border);color:var(--vp-custom-block-important-text);background-color:var(--vp-custom-block-important-bg)}.custom-block.important a,.custom-block.important code{color:var(--vp-c-important-1)}.custom-block.important a:hover,.custom-block.important a:hover>code{color:var(--vp-c-important-2)}.custom-block.important code{background-color:var(--vp-custom-block-important-code-bg)}.custom-block.warning{border-color:var(--vp-custom-block-warning-border);color:var(--vp-custom-block-warning-text);background-color:var(--vp-custom-block-warning-bg)}.custom-block.warning a,.custom-block.warning code{color:var(--vp-c-warning-1)}.custom-block.warning a:hover,.custom-block.warning a:hover>code{color:var(--vp-c-warning-2)}.custom-block.warning code{background-color:var(--vp-custom-block-warning-code-bg)}.custom-block.danger{border-color:var(--vp-custom-block-danger-border);color:var(--vp-custom-block-danger-text);background-color:var(--vp-custom-block-danger-bg)}.custom-block.danger a,.custom-block.danger code{color:var(--vp-c-danger-1)}.custom-block.danger a:hover,.custom-block.danger a:hover>code{color:var(--vp-c-danger-2)}.custom-block.danger code{background-color:var(--vp-custom-block-danger-code-bg)}.custom-block.caution{border-color:var(--vp-custom-block-caution-border);color:var(--vp-custom-block-caution-text);background-color:var(--vp-custom-block-caution-bg)}.custom-block.caution a,.custom-block.caution code{color:var(--vp-c-caution-1)}.custom-block.caution a:hover,.custom-block.caution a:hover>code{color:var(--vp-c-caution-2)}.custom-block.caution code{background-color:var(--vp-custom-block-caution-code-bg)}.custom-block.details{border-color:var(--vp-custom-block-details-border);color:var(--vp-custom-block-details-text);background-color:var(--vp-custom-block-details-bg)}.custom-block.details a{color:var(--vp-c-brand-1)}.custom-block.details a:hover,.custom-block.details a:hover>code{color:var(--vp-c-brand-2)}.custom-block.details code{background-color:var(--vp-custom-block-details-code-bg)}.custom-block-title{font-weight:600}.custom-block p+p{margin:8px 0}.custom-block.details summary{margin:0 0 8px;font-weight:700;cursor:pointer;-webkit-user-select:none;user-select:none}.custom-block.details summary+p{margin:8px 0}.custom-block a{color:inherit;font-weight:600;text-decoration:underline;text-underline-offset:2px;transition:opacity .25s}.custom-block a:hover{opacity:.75}.custom-block code{font-size:var(--vp-custom-block-code-font-size)}.custom-block.custom-block th,.custom-block.custom-block blockquote>p{font-size:var(--vp-custom-block-font-size);color:inherit}.dark .vp-code span{color:var(--shiki-dark, inherit)}html:not(.dark) .vp-code span{color:var(--shiki-light, inherit)}.vp-code-group{margin-top:16px}.vp-code-group .tabs{position:relative;display:flex;margin-right:-24px;margin-left:-24px;padding:0 12px;background-color:var(--vp-code-tab-bg);overflow-x:auto;overflow-y:hidden;box-shadow:inset 0 -1px var(--vp-code-tab-divider)}@media (min-width: 640px){.vp-code-group .tabs{margin-right:0;margin-left:0;border-radius:8px 8px 0 0}}.vp-code-group .tabs input{position:fixed;opacity:0;pointer-events:none}.vp-code-group .tabs label{position:relative;display:inline-block;border-bottom:1px solid transparent;padding:0 12px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-code-tab-text-color);white-space:nowrap;cursor:pointer;transition:color .25s}.vp-code-group .tabs label:after{position:absolute;right:8px;bottom:-1px;left:8px;z-index:1;height:2px;border-radius:2px;content:"";background-color:transparent;transition:background-color .25s}.vp-code-group label:hover{color:var(--vp-code-tab-hover-text-color)}.vp-code-group input:checked+label{color:var(--vp-code-tab-active-text-color)}.vp-code-group input:checked+label:after{background-color:var(--vp-code-tab-active-bar-color)}.vp-code-group div[class*=language-],.vp-block{display:none;margin-top:0!important;border-top-left-radius:0!important;border-top-right-radius:0!important}.vp-code-group div[class*=language-].active,.vp-block.active{display:block}.vp-block{padding:20px 24px}.vp-doc h1,.vp-doc h2,.vp-doc h3,.vp-doc h4,.vp-doc h5,.vp-doc h6{position:relative;font-weight:600;outline:none}.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:28px}.vp-doc h2{margin:48px 0 16px;border-top:1px solid var(--vp-c-divider);padding-top:24px;letter-spacing:-.02em;line-height:32px;font-size:24px}.vp-doc h3{margin:32px 0 0;letter-spacing:-.01em;line-height:28px;font-size:20px}.vp-doc .header-anchor{position:absolute;top:0;left:0;margin-left:-.87em;font-weight:500;-webkit-user-select:none;user-select:none;opacity:0;text-decoration:none;transition:color .25s,opacity .25s}.vp-doc .header-anchor:before{content:var(--vp-header-anchor-symbol)}.vp-doc h1:hover .header-anchor,.vp-doc h1 .header-anchor:focus,.vp-doc h2:hover .header-anchor,.vp-doc h2 .header-anchor:focus,.vp-doc h3:hover .header-anchor,.vp-doc h3 .header-anchor:focus,.vp-doc h4:hover .header-anchor,.vp-doc h4 .header-anchor:focus,.vp-doc h5:hover .header-anchor,.vp-doc h5 .header-anchor:focus,.vp-doc h6:hover .header-anchor,.vp-doc h6 .header-anchor:focus{opacity:1}@media (min-width: 768px){.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:32px}}.vp-doc h2 .header-anchor{top:24px}.vp-doc p,.vp-doc summary{margin:16px 0}.vp-doc p{line-height:28px}.vp-doc blockquote{margin:16px 0;border-left:2px solid var(--vp-c-divider);padding-left:16px;transition:border-color .5s}.vp-doc blockquote>p{margin:0;font-size:16px;color:var(--vp-c-text-2);transition:color .5s}.vp-doc a{font-weight:500;color:var(--vp-c-brand-1);text-decoration:underline;text-underline-offset:2px;transition:color .25s,opacity .25s}.vp-doc a:hover{color:var(--vp-c-brand-2)}.vp-doc strong{font-weight:600}.vp-doc ul,.vp-doc ol{padding-left:1.25rem;margin:16px 0}.vp-doc ul{list-style:disc}.vp-doc ol{list-style:decimal}.vp-doc li+li{margin-top:8px}.vp-doc li>ol,.vp-doc li>ul{margin:8px 0 0}.vp-doc table{display:block;border-collapse:collapse;margin:20px 0;overflow-x:auto}.vp-doc tr{background-color:var(--vp-c-bg);border-top:1px solid var(--vp-c-divider);transition:background-color .5s}.vp-doc tr:nth-child(2n){background-color:var(--vp-c-bg-soft)}.vp-doc th,.vp-doc td{border:1px solid var(--vp-c-divider);padding:8px 16px}.vp-doc th{text-align:left;font-size:14px;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-doc td{font-size:14px}.vp-doc hr{margin:16px 0;border:none;border-top:1px solid var(--vp-c-divider)}.vp-doc .custom-block{margin:16px 0}.vp-doc .custom-block p{margin:8px 0;line-height:24px}.vp-doc .custom-block p:first-child{margin:0}.vp-doc .custom-block div[class*=language-]{margin:8px 0;border-radius:8px}.vp-doc .custom-block div[class*=language-] code{font-weight:400;background-color:transparent}.vp-doc .custom-block .vp-code-group .tabs{margin:0;border-radius:8px 8px 0 0}.vp-doc :not(pre,h1,h2,h3,h4,h5,h6)>code{font-size:var(--vp-code-font-size);color:var(--vp-code-color)}.vp-doc :not(pre)>code{border-radius:4px;padding:3px 6px;background-color:var(--vp-code-bg);transition:color .25s,background-color .5s}.vp-doc a>code{color:var(--vp-code-link-color)}.vp-doc a:hover>code{color:var(--vp-code-link-hover-color)}.vp-doc h1>code,.vp-doc h2>code,.vp-doc h3>code{font-size:.9em}.vp-doc div[class*=language-],.vp-block{position:relative;margin:16px -24px;background-color:var(--vp-code-block-bg);overflow-x:auto;transition:background-color .5s}@media (min-width: 640px){.vp-doc div[class*=language-],.vp-block{border-radius:8px;margin:16px 0}}@media (max-width: 639px){.vp-doc li div[class*=language-]{border-radius:8px 0 0 8px}}.vp-doc div[class*=language-]+div[class*=language-],.vp-doc div[class$=-api]+div[class*=language-],.vp-doc div[class*=language-]+div[class$=-api]>div[class*=language-]{margin-top:-8px}.vp-doc [class*=language-] pre,.vp-doc [class*=language-] code{direction:ltr;text-align:left;white-space:pre;word-spacing:normal;word-break:normal;word-wrap:normal;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-hyphens:none;-moz-hyphens:none;-ms-hyphens:none;hyphens:none}.vp-doc [class*=language-] pre{position:relative;z-index:1;margin:0;padding:20px 0;background:transparent;overflow-x:auto}.vp-doc [class*=language-] code{display:block;padding:0 24px;width:fit-content;min-width:100%;line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-block-color);transition:color .5s}.vp-doc [class*=language-] code .highlighted{background-color:var(--vp-code-line-highlight-color);transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .highlighted.error{background-color:var(--vp-code-line-error-color)}.vp-doc [class*=language-] code .highlighted.warning{background-color:var(--vp-code-line-warning-color)}.vp-doc [class*=language-] code .diff{transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .diff:before{position:absolute;left:10px}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){filter:blur(.095rem);opacity:.4;transition:filter .35s,opacity .35s}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){opacity:.7;transition:filter .35s,opacity .35s}.vp-doc [class*=language-]:hover .has-focused-lines .line:not(.has-focus){filter:blur(0);opacity:1}.vp-doc [class*=language-] code .diff.remove{background-color:var(--vp-code-line-diff-remove-color);opacity:.7}.vp-doc [class*=language-] code .diff.remove:before{content:"-";color:var(--vp-code-line-diff-remove-symbol-color)}.vp-doc [class*=language-] code .diff.add{background-color:var(--vp-code-line-diff-add-color)}.vp-doc [class*=language-] code .diff.add:before{content:"+";color:var(--vp-code-line-diff-add-symbol-color)}.vp-doc div[class*=language-].line-numbers-mode{padding-left:32px}.vp-doc .line-numbers-wrapper{position:absolute;top:0;bottom:0;left:0;z-index:3;border-right:1px solid var(--vp-code-block-divider-color);padding-top:20px;width:32px;text-align:center;font-family:var(--vp-font-family-mono);line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-line-number-color);transition:border-color .5s,color .5s}.vp-doc [class*=language-]>button.copy{direction:ltr;position:absolute;top:12px;right:12px;z-index:3;border:1px solid var(--vp-code-copy-code-border-color);border-radius:4px;width:40px;height:40px;background-color:var(--vp-code-copy-code-bg);opacity:0;cursor:pointer;background-image:var(--vp-icon-copy);background-position:50%;background-size:20px;background-repeat:no-repeat;transition:border-color .25s,background-color .25s,opacity .25s}.vp-doc [class*=language-]:hover>button.copy,.vp-doc [class*=language-]>button.copy:focus{opacity:1}.vp-doc [class*=language-]>button.copy:hover,.vp-doc [class*=language-]>button.copy.copied{border-color:var(--vp-code-copy-code-hover-border-color);background-color:var(--vp-code-copy-code-hover-bg)}.vp-doc [class*=language-]>button.copy.copied,.vp-doc [class*=language-]>button.copy:hover.copied{border-radius:0 4px 4px 0;background-color:var(--vp-code-copy-code-hover-bg);background-image:var(--vp-icon-copied)}.vp-doc [class*=language-]>button.copy.copied:before,.vp-doc [class*=language-]>button.copy:hover.copied:before{position:relative;top:-1px;transform:translate(calc(-100% - 1px));display:flex;justify-content:center;align-items:center;border:1px solid var(--vp-code-copy-code-hover-border-color);border-right:0;border-radius:4px 0 0 4px;padding:0 10px;width:fit-content;height:40px;text-align:center;font-size:12px;font-weight:500;color:var(--vp-code-copy-code-active-text);background-color:var(--vp-code-copy-code-hover-bg);white-space:nowrap;content:var(--vp-code-copy-copied-text-content)}.vp-doc [class*=language-]>span.lang{position:absolute;top:2px;right:8px;z-index:2;font-size:12px;font-weight:500;color:var(--vp-code-lang-color);transition:color .4s,opacity .4s}.vp-doc [class*=language-]:hover>button.copy+span.lang,.vp-doc [class*=language-]>button.copy:focus+span.lang{opacity:0}.vp-doc .VPTeamMembers{margin-top:24px}.vp-doc .VPTeamMembers.small.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}.vp-doc .VPTeamMembers.small.count-2 .container,.vp-doc .VPTeamMembers.small.count-3 .container{max-width:100%!important}.vp-doc .VPTeamMembers.medium.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}:is(.vp-external-link-icon,.vp-doc a[href*="://"],.vp-doc a[target=_blank]):not(.no-icon):after{display:inline-block;margin-top:-1px;margin-left:4px;width:11px;height:11px;background:currentColor;color:var(--vp-c-text-3);flex-shrink:0;--icon: url("data:image/svg+xml, %3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24' %3E%3Cpath d='M0 0h24v24H0V0z' fill='none' /%3E%3Cpath d='M9 5v2h6.59L4 18.59 5.41 20 17 8.41V15h2V5H9z' /%3E%3C/svg%3E");-webkit-mask-image:var(--icon);mask-image:var(--icon)}.vp-external-link-icon:after{content:""}.external-link-icon-enabled :is(.vp-doc a[href*="://"],.vp-doc a[target=_blank]):after{content:"";color:currentColor}.vp-sponsor{border-radius:16px;overflow:hidden}.vp-sponsor.aside{border-radius:12px}.vp-sponsor-section+.vp-sponsor-section{margin-top:4px}.vp-sponsor-tier{margin:0 0 4px!important;text-align:center;letter-spacing:1px!important;line-height:24px;width:100%;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-sponsor.normal .vp-sponsor-tier{padding:13px 0 11px;font-size:14px}.vp-sponsor.aside .vp-sponsor-tier{padding:9px 0 7px;font-size:12px}.vp-sponsor-grid+.vp-sponsor-tier{margin-top:4px}.vp-sponsor-grid{display:flex;flex-wrap:wrap;gap:4px}.vp-sponsor-grid.xmini .vp-sponsor-grid-link{height:64px}.vp-sponsor-grid.xmini .vp-sponsor-grid-image{max-width:64px;max-height:22px}.vp-sponsor-grid.mini .vp-sponsor-grid-link{height:72px}.vp-sponsor-grid.mini .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.small .vp-sponsor-grid-link{height:96px}.vp-sponsor-grid.small .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.medium .vp-sponsor-grid-link{height:112px}.vp-sponsor-grid.medium .vp-sponsor-grid-image{max-width:120px;max-height:36px}.vp-sponsor-grid.big .vp-sponsor-grid-link{height:184px}.vp-sponsor-grid.big .vp-sponsor-grid-image{max-width:192px;max-height:56px}.vp-sponsor-grid[data-vp-grid="2"] .vp-sponsor-grid-item{width:calc((100% - 4px)/2)}.vp-sponsor-grid[data-vp-grid="3"] .vp-sponsor-grid-item{width:calc((100% - 4px * 2) / 3)}.vp-sponsor-grid[data-vp-grid="4"] .vp-sponsor-grid-item{width:calc((100% - 12px)/4)}.vp-sponsor-grid[data-vp-grid="5"] .vp-sponsor-grid-item{width:calc((100% - 16px)/5)}.vp-sponsor-grid[data-vp-grid="6"] .vp-sponsor-grid-item{width:calc((100% - 4px * 5) / 6)}.vp-sponsor-grid-item{flex-shrink:0;width:100%;background-color:var(--vp-c-bg-soft);transition:background-color .25s}.vp-sponsor-grid-item:hover{background-color:var(--vp-c-default-soft)}.vp-sponsor-grid-item:hover .vp-sponsor-grid-image{filter:grayscale(0) invert(0)}.vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.dark .vp-sponsor-grid-item:hover{background-color:var(--vp-c-white)}.dark .vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.vp-sponsor-grid-link{display:flex}.vp-sponsor-grid-box{display:flex;justify-content:center;align-items:center;width:100%}.vp-sponsor-grid-image{max-width:100%;filter:grayscale(1);transition:filter .25s}.dark .vp-sponsor-grid-image{filter:grayscale(1) invert(1)}.VPBadge{display:inline-block;margin-left:2px;border:1px solid transparent;border-radius:12px;padding:0 10px;line-height:22px;font-size:12px;font-weight:500;transform:translateY(-2px)}.VPBadge.small{padding:0 6px;line-height:18px;font-size:10px;transform:translateY(-8px)}.VPDocFooter .VPBadge{display:none}.vp-doc h1>.VPBadge{margin-top:4px;vertical-align:top}.vp-doc h2>.VPBadge{margin-top:3px;padding:0 8px;vertical-align:top}.vp-doc h3>.VPBadge{vertical-align:middle}.vp-doc h4>.VPBadge,.vp-doc h5>.VPBadge,.vp-doc h6>.VPBadge{vertical-align:middle;line-height:18px}.VPBadge.info{border-color:var(--vp-badge-info-border);color:var(--vp-badge-info-text);background-color:var(--vp-badge-info-bg)}.VPBadge.tip{border-color:var(--vp-badge-tip-border);color:var(--vp-badge-tip-text);background-color:var(--vp-badge-tip-bg)}.VPBadge.warning{border-color:var(--vp-badge-warning-border);color:var(--vp-badge-warning-text);background-color:var(--vp-badge-warning-bg)}.VPBadge.danger{border-color:var(--vp-badge-danger-border);color:var(--vp-badge-danger-text);background-color:var(--vp-badge-danger-bg)}.VPBackdrop[data-v-b06cdb19]{position:fixed;top:0;right:0;bottom:0;left:0;z-index:var(--vp-z-index-backdrop);background:var(--vp-backdrop-bg-color);transition:opacity .5s}.VPBackdrop.fade-enter-from[data-v-b06cdb19],.VPBackdrop.fade-leave-to[data-v-b06cdb19]{opacity:0}.VPBackdrop.fade-leave-active[data-v-b06cdb19]{transition-duration:.25s}@media (min-width: 1280px){.VPBackdrop[data-v-b06cdb19]{display:none}}.NotFound[data-v-951cab6c]{padding:64px 24px 96px;text-align:center}@media (min-width: 768px){.NotFound[data-v-951cab6c]{padding:96px 32px 168px}}.code[data-v-951cab6c]{line-height:64px;font-size:64px;font-weight:600}.title[data-v-951cab6c]{padding-top:12px;letter-spacing:2px;line-height:20px;font-size:20px;font-weight:700}.divider[data-v-951cab6c]{margin:24px auto 18px;width:64px;height:1px;background-color:var(--vp-c-divider)}.quote[data-v-951cab6c]{margin:0 auto;max-width:256px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.action[data-v-951cab6c]{padding-top:20px}.link[data-v-951cab6c]{display:inline-block;border:1px solid var(--vp-c-brand-1);border-radius:16px;padding:3px 16px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:border-color .25s,color .25s}.link[data-v-951cab6c]:hover{border-color:var(--vp-c-brand-2);color:var(--vp-c-brand-2)}.root[data-v-3f927ebe]{position:relative;z-index:1}.nested[data-v-3f927ebe]{padding-right:16px;padding-left:16px}.outline-link[data-v-3f927ebe]{display:block;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-2);white-space:nowrap;overflow:hidden;text-overflow:ellipsis;transition:color .5s}.outline-link[data-v-3f927ebe]:hover,.outline-link.active[data-v-3f927ebe]{color:var(--vp-c-text-1);transition:color .25s}.outline-link.nested[data-v-3f927ebe]{padding-left:13px}.VPDocAsideOutline[data-v-b38bf2ff]{display:none}.VPDocAsideOutline.has-outline[data-v-b38bf2ff]{display:block}.content[data-v-b38bf2ff]{position:relative;border-left:1px solid var(--vp-c-divider);padding-left:16px;font-size:13px;font-weight:500}.outline-marker[data-v-b38bf2ff]{position:absolute;top:32px;left:-1px;z-index:0;opacity:0;width:2px;border-radius:2px;height:18px;background-color:var(--vp-c-brand-1);transition:top .25s cubic-bezier(0,1,.5,1),background-color .5s,opacity .25s}.outline-title[data-v-b38bf2ff]{line-height:32px;font-size:14px;font-weight:600}.VPDocAside[data-v-6d7b3c46]{display:flex;flex-direction:column;flex-grow:1}.spacer[data-v-6d7b3c46]{flex-grow:1}.VPDocAside[data-v-6d7b3c46] .spacer+.VPDocAsideSponsors,.VPDocAside[data-v-6d7b3c46] .spacer+.VPDocAsideCarbonAds{margin-top:24px}.VPDocAside[data-v-6d7b3c46] .VPDocAsideSponsors+.VPDocAsideCarbonAds{margin-top:16px}.VPLastUpdated[data-v-9da12f1d]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 640px){.VPLastUpdated[data-v-9da12f1d]{line-height:32px;font-size:14px;font-weight:500}}.VPDocFooter[data-v-b88cabfa]{margin-top:64px}.edit-info[data-v-b88cabfa]{padding-bottom:18px}@media (min-width: 640px){.edit-info[data-v-b88cabfa]{display:flex;justify-content:space-between;align-items:center;padding-bottom:14px}}.edit-link-button[data-v-b88cabfa]{display:flex;align-items:center;border:0;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.edit-link-button[data-v-b88cabfa]:hover{color:var(--vp-c-brand-2)}.edit-link-icon[data-v-b88cabfa]{margin-right:8px}.prev-next[data-v-b88cabfa]{border-top:1px solid var(--vp-c-divider);padding-top:24px;display:grid;grid-row-gap:8px}@media (min-width: 640px){.prev-next[data-v-b88cabfa]{grid-template-columns:repeat(2,1fr);grid-column-gap:16px}}.pager-link[data-v-b88cabfa]{display:block;border:1px solid var(--vp-c-divider);border-radius:8px;padding:11px 16px 13px;width:100%;height:100%;transition:border-color .25s}.pager-link[data-v-b88cabfa]:hover{border-color:var(--vp-c-brand-1)}.pager-link.next[data-v-b88cabfa]{margin-left:auto;text-align:right}.desc[data-v-b88cabfa]{display:block;line-height:20px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.title[data-v-b88cabfa]{display:block;line-height:20px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.VPDoc[data-v-83890dd9]{padding:32px 24px 96px;width:100%}@media (min-width: 768px){.VPDoc[data-v-83890dd9]{padding:48px 32px 128px}}@media (min-width: 960px){.VPDoc[data-v-83890dd9]{padding:48px 32px 0}.VPDoc:not(.has-sidebar) .container[data-v-83890dd9]{display:flex;justify-content:center;max-width:992px}.VPDoc:not(.has-sidebar) .content[data-v-83890dd9]{max-width:752px}}@media (min-width: 1280px){.VPDoc .container[data-v-83890dd9]{display:flex;justify-content:center}.VPDoc .aside[data-v-83890dd9]{display:block}}@media (min-width: 1440px){.VPDoc:not(.has-sidebar) .content[data-v-83890dd9]{max-width:784px}.VPDoc:not(.has-sidebar) .container[data-v-83890dd9]{max-width:1104px}}.container[data-v-83890dd9]{margin:0 auto;width:100%}.aside[data-v-83890dd9]{position:relative;display:none;order:2;flex-grow:1;padding-left:32px;width:100%;max-width:256px}.left-aside[data-v-83890dd9]{order:1;padding-left:unset;padding-right:32px}.aside-container[data-v-83890dd9]{position:fixed;top:0;padding-top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + var(--vp-doc-top-height, 0px) + 48px);width:224px;height:100vh;overflow-x:hidden;overflow-y:auto;scrollbar-width:none}.aside-container[data-v-83890dd9]::-webkit-scrollbar{display:none}.aside-curtain[data-v-83890dd9]{position:fixed;bottom:0;z-index:10;width:224px;height:32px;background:linear-gradient(transparent,var(--vp-c-bg) 70%)}.aside-content[data-v-83890dd9]{display:flex;flex-direction:column;min-height:calc(100vh - (var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px));padding-bottom:32px}.content[data-v-83890dd9]{position:relative;margin:0 auto;width:100%}@media (min-width: 960px){.content[data-v-83890dd9]{padding:0 32px 128px}}@media (min-width: 1280px){.content[data-v-83890dd9]{order:1;margin:0;min-width:640px}}.content-container[data-v-83890dd9]{margin:0 auto}.VPDoc.has-aside .content-container[data-v-83890dd9]{max-width:688px}.VPButton[data-v-14206e74]{display:inline-block;border:1px solid transparent;text-align:center;font-weight:600;white-space:nowrap;transition:color .25s,border-color .25s,background-color .25s}.VPButton[data-v-14206e74]:active{transition:color .1s,border-color .1s,background-color .1s}.VPButton.medium[data-v-14206e74]{border-radius:20px;padding:0 20px;line-height:38px;font-size:14px}.VPButton.big[data-v-14206e74]{border-radius:24px;padding:0 24px;line-height:46px;font-size:16px}.VPButton.brand[data-v-14206e74]{border-color:var(--vp-button-brand-border);color:var(--vp-button-brand-text);background-color:var(--vp-button-brand-bg)}.VPButton.brand[data-v-14206e74]:hover{border-color:var(--vp-button-brand-hover-border);color:var(--vp-button-brand-hover-text);background-color:var(--vp-button-brand-hover-bg)}.VPButton.brand[data-v-14206e74]:active{border-color:var(--vp-button-brand-active-border);color:var(--vp-button-brand-active-text);background-color:var(--vp-button-brand-active-bg)}.VPButton.alt[data-v-14206e74]{border-color:var(--vp-button-alt-border);color:var(--vp-button-alt-text);background-color:var(--vp-button-alt-bg)}.VPButton.alt[data-v-14206e74]:hover{border-color:var(--vp-button-alt-hover-border);color:var(--vp-button-alt-hover-text);background-color:var(--vp-button-alt-hover-bg)}.VPButton.alt[data-v-14206e74]:active{border-color:var(--vp-button-alt-active-border);color:var(--vp-button-alt-active-text);background-color:var(--vp-button-alt-active-bg)}.VPButton.sponsor[data-v-14206e74]{border-color:var(--vp-button-sponsor-border);color:var(--vp-button-sponsor-text);background-color:var(--vp-button-sponsor-bg)}.VPButton.sponsor[data-v-14206e74]:hover{border-color:var(--vp-button-sponsor-hover-border);color:var(--vp-button-sponsor-hover-text);background-color:var(--vp-button-sponsor-hover-bg)}.VPButton.sponsor[data-v-14206e74]:active{border-color:var(--vp-button-sponsor-active-border);color:var(--vp-button-sponsor-active-text);background-color:var(--vp-button-sponsor-active-bg)}html:not(.dark) .VPImage.dark[data-v-35a7d0b8]{display:none}.dark .VPImage.light[data-v-35a7d0b8]{display:none}.VPHero[data-v-955009fc]{margin-top:calc((var(--vp-nav-height) + var(--vp-layout-top-height, 0px)) * -1);padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px) 24px 48px}@media (min-width: 640px){.VPHero[data-v-955009fc]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 48px 64px}}@media (min-width: 960px){.VPHero[data-v-955009fc]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 64px 64px}}.container[data-v-955009fc]{display:flex;flex-direction:column;margin:0 auto;max-width:1152px}@media (min-width: 960px){.container[data-v-955009fc]{flex-direction:row}}.main[data-v-955009fc]{position:relative;z-index:10;order:2;flex-grow:1;flex-shrink:0}.VPHero.has-image .container[data-v-955009fc]{text-align:center}@media (min-width: 960px){.VPHero.has-image .container[data-v-955009fc]{text-align:left}}@media (min-width: 960px){.main[data-v-955009fc]{order:1;width:calc((100% / 3) * 2)}.VPHero.has-image .main[data-v-955009fc]{max-width:592px}}.name[data-v-955009fc],.text[data-v-955009fc]{max-width:392px;letter-spacing:-.4px;line-height:40px;font-size:32px;font-weight:700;white-space:pre-wrap}.VPHero.has-image .name[data-v-955009fc],.VPHero.has-image .text[data-v-955009fc]{margin:0 auto}.name[data-v-955009fc]{color:var(--vp-home-hero-name-color)}.clip[data-v-955009fc]{background:var(--vp-home-hero-name-background);-webkit-background-clip:text;background-clip:text;-webkit-text-fill-color:var(--vp-home-hero-name-color)}@media (min-width: 640px){.name[data-v-955009fc],.text[data-v-955009fc]{max-width:576px;line-height:56px;font-size:48px}}@media (min-width: 960px){.name[data-v-955009fc],.text[data-v-955009fc]{line-height:64px;font-size:56px}.VPHero.has-image .name[data-v-955009fc],.VPHero.has-image .text[data-v-955009fc]{margin:0}}.tagline[data-v-955009fc]{padding-top:8px;max-width:392px;line-height:28px;font-size:18px;font-weight:500;white-space:pre-wrap;color:var(--vp-c-text-2)}.VPHero.has-image .tagline[data-v-955009fc]{margin:0 auto}@media (min-width: 640px){.tagline[data-v-955009fc]{padding-top:12px;max-width:576px;line-height:32px;font-size:20px}}@media (min-width: 960px){.tagline[data-v-955009fc]{line-height:36px;font-size:24px}.VPHero.has-image .tagline[data-v-955009fc]{margin:0}}.actions[data-v-955009fc]{display:flex;flex-wrap:wrap;margin:-6px;padding-top:24px}.VPHero.has-image .actions[data-v-955009fc]{justify-content:center}@media (min-width: 640px){.actions[data-v-955009fc]{padding-top:32px}}@media (min-width: 960px){.VPHero.has-image .actions[data-v-955009fc]{justify-content:flex-start}}.action[data-v-955009fc]{flex-shrink:0;padding:6px}.image[data-v-955009fc]{order:1;margin:-76px -24px -48px}@media (min-width: 640px){.image[data-v-955009fc]{margin:-108px -24px -48px}}@media (min-width: 960px){.image[data-v-955009fc]{flex-grow:1;order:2;margin:0;min-height:100%}}.image-container[data-v-955009fc]{position:relative;margin:0 auto;width:320px;height:320px}@media (min-width: 640px){.image-container[data-v-955009fc]{width:392px;height:392px}}@media (min-width: 960px){.image-container[data-v-955009fc]{display:flex;justify-content:center;align-items:center;width:100%;height:100%;transform:translate(-32px,-32px)}}.image-bg[data-v-955009fc]{position:absolute;top:50%;left:50%;border-radius:50%;width:192px;height:192px;background-image:var(--vp-home-hero-image-background-image);filter:var(--vp-home-hero-image-filter);transform:translate(-50%,-50%)}@media (min-width: 640px){.image-bg[data-v-955009fc]{width:256px;height:256px}}@media (min-width: 960px){.image-bg[data-v-955009fc]{width:320px;height:320px}}[data-v-955009fc] .image-src{position:absolute;top:50%;left:50%;max-width:192px;max-height:192px;transform:translate(-50%,-50%)}@media (min-width: 640px){[data-v-955009fc] .image-src{max-width:256px;max-height:256px}}@media (min-width: 960px){[data-v-955009fc] .image-src{max-width:320px;max-height:320px}}.VPFeature[data-v-f5e9645b]{display:block;border:1px solid var(--vp-c-bg-soft);border-radius:12px;height:100%;background-color:var(--vp-c-bg-soft);transition:border-color .25s,background-color .25s}.VPFeature.link[data-v-f5e9645b]:hover{border-color:var(--vp-c-brand-1)}.box[data-v-f5e9645b]{display:flex;flex-direction:column;padding:24px;height:100%}.box[data-v-f5e9645b]>.VPImage{margin-bottom:20px}.icon[data-v-f5e9645b]{display:flex;justify-content:center;align-items:center;margin-bottom:20px;border-radius:6px;background-color:var(--vp-c-default-soft);width:48px;height:48px;font-size:24px;transition:background-color .25s}.title[data-v-f5e9645b]{line-height:24px;font-size:16px;font-weight:600}.details[data-v-f5e9645b]{flex-grow:1;padding-top:8px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.link-text[data-v-f5e9645b]{padding-top:8px}.link-text-value[data-v-f5e9645b]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.link-text-icon[data-v-f5e9645b]{margin-left:6px}.VPFeatures[data-v-d0a190d7]{position:relative;padding:0 24px}@media (min-width: 640px){.VPFeatures[data-v-d0a190d7]{padding:0 48px}}@media (min-width: 960px){.VPFeatures[data-v-d0a190d7]{padding:0 64px}}.container[data-v-d0a190d7]{margin:0 auto;max-width:1152px}.items[data-v-d0a190d7]{display:flex;flex-wrap:wrap;margin:-8px}.item[data-v-d0a190d7]{padding:8px;width:100%}@media (min-width: 640px){.item.grid-2[data-v-d0a190d7],.item.grid-4[data-v-d0a190d7],.item.grid-6[data-v-d0a190d7]{width:50%}}@media (min-width: 768px){.item.grid-2[data-v-d0a190d7],.item.grid-4[data-v-d0a190d7]{width:50%}.item.grid-3[data-v-d0a190d7],.item.grid-6[data-v-d0a190d7]{width:calc(100% / 3)}}@media (min-width: 960px){.item.grid-4[data-v-d0a190d7]{width:25%}}.container[data-v-7a48a447]{margin:auto;width:100%;max-width:1280px;padding:0 24px}@media (min-width: 640px){.container[data-v-7a48a447]{padding:0 48px}}@media (min-width: 960px){.container[data-v-7a48a447]{width:100%;padding:0 64px}}.vp-doc[data-v-7a48a447] .VPHomeSponsors,.vp-doc[data-v-7a48a447] .VPTeamPage{margin-left:var(--vp-offset, calc(50% - 50vw) );margin-right:var(--vp-offset, calc(50% - 50vw) )}.vp-doc[data-v-7a48a447] .VPHomeSponsors h2{border-top:none;letter-spacing:normal}.vp-doc[data-v-7a48a447] .VPHomeSponsors a,.vp-doc[data-v-7a48a447] .VPTeamPage a{text-decoration:none}.VPHome[data-v-cbb6ec48]{margin-bottom:96px}@media (min-width: 768px){.VPHome[data-v-cbb6ec48]{margin-bottom:128px}}.VPContent[data-v-91765379]{flex-grow:1;flex-shrink:0;margin:var(--vp-layout-top-height, 0px) auto 0;width:100%}.VPContent.is-home[data-v-91765379]{width:100%;max-width:100%}.VPContent.has-sidebar[data-v-91765379]{margin:0}@media (min-width: 960px){.VPContent[data-v-91765379]{padding-top:var(--vp-nav-height)}.VPContent.has-sidebar[data-v-91765379]{margin:var(--vp-layout-top-height, 0px) 0 0;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPContent.has-sidebar[data-v-91765379]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.VPFooter[data-v-c970a860]{position:relative;z-index:var(--vp-z-index-footer);border-top:1px solid var(--vp-c-gutter);padding:32px 24px;background-color:var(--vp-c-bg)}.VPFooter.has-sidebar[data-v-c970a860]{display:none}.VPFooter[data-v-c970a860] a{text-decoration-line:underline;text-underline-offset:2px;transition:color .25s}.VPFooter[data-v-c970a860] a:hover{color:var(--vp-c-text-1)}@media (min-width: 768px){.VPFooter[data-v-c970a860]{padding:32px}}.container[data-v-c970a860]{margin:0 auto;max-width:var(--vp-layout-max-width);text-align:center}.message[data-v-c970a860],.copyright[data-v-c970a860]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.VPLocalNavOutlineDropdown[data-v-bc9dc845]{padding:12px 20px 11px}@media (min-width: 960px){.VPLocalNavOutlineDropdown[data-v-bc9dc845]{padding:12px 36px 11px}}.VPLocalNavOutlineDropdown button[data-v-bc9dc845]{display:block;font-size:12px;font-weight:500;line-height:24px;color:var(--vp-c-text-2);transition:color .5s;position:relative}.VPLocalNavOutlineDropdown button[data-v-bc9dc845]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPLocalNavOutlineDropdown button.open[data-v-bc9dc845]{color:var(--vp-c-text-1)}.icon[data-v-bc9dc845]{display:inline-block;vertical-align:middle;margin-left:2px;font-size:14px;transform:rotate(0);transition:transform .25s}@media (min-width: 960px){.VPLocalNavOutlineDropdown button[data-v-bc9dc845]{font-size:14px}.icon[data-v-bc9dc845]{font-size:16px}}.open>.icon[data-v-bc9dc845]{transform:rotate(90deg)}.items[data-v-bc9dc845]{position:absolute;top:40px;right:16px;left:16px;display:grid;gap:1px;border:1px solid var(--vp-c-border);border-radius:8px;background-color:var(--vp-c-gutter);max-height:calc(var(--vp-vh, 100vh) - 86px);overflow:hidden auto;box-shadow:var(--vp-shadow-3)}@media (min-width: 960px){.items[data-v-bc9dc845]{right:auto;left:calc(var(--vp-sidebar-width) + 32px);width:320px}}.header[data-v-bc9dc845]{background-color:var(--vp-c-bg-soft)}.top-link[data-v-bc9dc845]{display:block;padding:0 16px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.outline[data-v-bc9dc845]{padding:8px 0;background-color:var(--vp-c-bg-soft)}.flyout-enter-active[data-v-bc9dc845]{transition:all .2s ease-out}.flyout-leave-active[data-v-bc9dc845]{transition:all .15s ease-in}.flyout-enter-from[data-v-bc9dc845],.flyout-leave-to[data-v-bc9dc845]{opacity:0;transform:translateY(-16px)}.VPLocalNav[data-v-070ab83d]{position:sticky;top:0;left:0;z-index:var(--vp-z-index-local-nav);border-bottom:1px solid var(--vp-c-gutter);padding-top:var(--vp-layout-top-height, 0px);width:100%;background-color:var(--vp-local-nav-bg-color)}.VPLocalNav.fixed[data-v-070ab83d]{position:fixed}@media (min-width: 960px){.VPLocalNav[data-v-070ab83d]{top:var(--vp-nav-height)}.VPLocalNav.has-sidebar[data-v-070ab83d]{padding-left:var(--vp-sidebar-width)}.VPLocalNav.empty[data-v-070ab83d]{display:none}}@media (min-width: 1280px){.VPLocalNav[data-v-070ab83d]{display:none}}@media (min-width: 1440px){.VPLocalNav.has-sidebar[data-v-070ab83d]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.container[data-v-070ab83d]{display:flex;justify-content:space-between;align-items:center}.menu[data-v-070ab83d]{display:flex;align-items:center;padding:12px 24px 11px;line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.menu[data-v-070ab83d]:hover{color:var(--vp-c-text-1);transition:color .25s}@media (min-width: 768px){.menu[data-v-070ab83d]{padding:0 32px}}@media (min-width: 960px){.menu[data-v-070ab83d]{display:none}}.menu-icon[data-v-070ab83d]{margin-right:8px;font-size:14px}.VPOutlineDropdown[data-v-070ab83d]{padding:12px 24px 11px}@media (min-width: 768px){.VPOutlineDropdown[data-v-070ab83d]{padding:12px 32px 11px}}.VPSwitch[data-v-4a1c76db]{position:relative;border-radius:11px;display:block;width:40px;height:22px;flex-shrink:0;border:1px solid var(--vp-input-border-color);background-color:var(--vp-input-switch-bg-color);transition:border-color .25s!important}.VPSwitch[data-v-4a1c76db]:hover{border-color:var(--vp-c-brand-1)}.check[data-v-4a1c76db]{position:absolute;top:1px;left:1px;width:18px;height:18px;border-radius:50%;background-color:var(--vp-c-neutral-inverse);box-shadow:var(--vp-shadow-1);transition:transform .25s!important}.icon[data-v-4a1c76db]{position:relative;display:block;width:18px;height:18px;border-radius:50%;overflow:hidden}.icon[data-v-4a1c76db] [class^=vpi-]{position:absolute;top:3px;left:3px;width:12px;height:12px;color:var(--vp-c-text-2)}.dark .icon[data-v-4a1c76db] [class^=vpi-]{color:var(--vp-c-text-1);transition:opacity .25s!important}.sun[data-v-b79b56d4]{opacity:1}.moon[data-v-b79b56d4],.dark .sun[data-v-b79b56d4]{opacity:0}.dark .moon[data-v-b79b56d4]{opacity:1}.dark .VPSwitchAppearance[data-v-b79b56d4] .check{transform:translate(18px)}.VPNavBarAppearance[data-v-ead91a81]{display:none}@media (min-width: 1280px){.VPNavBarAppearance[data-v-ead91a81]{display:flex;align-items:center}}.VPMenuGroup+.VPMenuLink[data-v-8b74d055]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.link[data-v-8b74d055]{display:block;border-radius:6px;padding:0 12px;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);white-space:nowrap;transition:background-color .25s,color .25s}.link[data-v-8b74d055]:hover{color:var(--vp-c-brand-1);background-color:var(--vp-c-default-soft)}.link.active[data-v-8b74d055]{color:var(--vp-c-brand-1)}.VPMenuGroup[data-v-48c802d0]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.VPMenuGroup[data-v-48c802d0]:first-child{margin-top:0;border-top:0;padding-top:0}.VPMenuGroup+.VPMenuGroup[data-v-48c802d0]{margin-top:12px;border-top:1px solid var(--vp-c-divider)}.title[data-v-48c802d0]{padding:0 12px;line-height:32px;font-size:14px;font-weight:600;color:var(--vp-c-text-2);white-space:nowrap;transition:color .25s}.VPMenu[data-v-97491713]{border-radius:12px;padding:12px;min-width:128px;border:1px solid var(--vp-c-divider);background-color:var(--vp-c-bg-elv);box-shadow:var(--vp-shadow-3);transition:background-color .5s;max-height:calc(100vh - var(--vp-nav-height));overflow-y:auto}.VPMenu[data-v-97491713] .group{margin:0 -12px;padding:0 12px 12px}.VPMenu[data-v-97491713] .group+.group{border-top:1px solid var(--vp-c-divider);padding:11px 12px 12px}.VPMenu[data-v-97491713] .group:last-child{padding-bottom:0}.VPMenu[data-v-97491713] .group+.item{border-top:1px solid var(--vp-c-divider);padding:11px 16px 0}.VPMenu[data-v-97491713] .item{padding:0 16px;white-space:nowrap}.VPMenu[data-v-97491713] .label{flex-grow:1;line-height:28px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.VPMenu[data-v-97491713] .action{padding-left:24px}.VPFlyout[data-v-e5380155]{position:relative}.VPFlyout[data-v-e5380155]:hover{color:var(--vp-c-brand-1);transition:color .25s}.VPFlyout:hover .text[data-v-e5380155]{color:var(--vp-c-text-2)}.VPFlyout:hover .icon[data-v-e5380155]{fill:var(--vp-c-text-2)}.VPFlyout.active .text[data-v-e5380155]{color:var(--vp-c-brand-1)}.VPFlyout.active:hover .text[data-v-e5380155]{color:var(--vp-c-brand-2)}.VPFlyout:hover .menu[data-v-e5380155],.button[aria-expanded=true]+.menu[data-v-e5380155]{opacity:1;visibility:visible;transform:translateY(0)}.button[aria-expanded=false]+.menu[data-v-e5380155]{opacity:0;visibility:hidden;transform:translateY(0)}.button[data-v-e5380155]{display:flex;align-items:center;padding:0 12px;height:var(--vp-nav-height);color:var(--vp-c-text-1);transition:color .5s}.text[data-v-e5380155]{display:flex;align-items:center;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.option-icon[data-v-e5380155]{margin-right:0;font-size:16px}.text-icon[data-v-e5380155]{margin-left:4px;font-size:14px}.icon[data-v-e5380155]{font-size:20px;transition:fill .25s}.menu[data-v-e5380155]{position:absolute;top:calc(var(--vp-nav-height) / 2 + 20px);right:0;opacity:0;visibility:hidden;transition:opacity .25s,visibility .25s,transform .25s}.VPSocialLink[data-v-717b8b75]{display:flex;justify-content:center;align-items:center;width:36px;height:36px;color:var(--vp-c-text-2);transition:color .5s}.VPSocialLink[data-v-717b8b75]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPSocialLink[data-v-717b8b75]>svg,.VPSocialLink[data-v-717b8b75]>[class^=vpi-social-]{width:20px;height:20px;fill:currentColor}.VPSocialLinks[data-v-ee7a9424]{display:flex;justify-content:center}.VPNavBarExtra[data-v-9b536d0b]{display:none;margin-right:-12px}@media (min-width: 768px){.VPNavBarExtra[data-v-9b536d0b]{display:block}}@media (min-width: 1280px){.VPNavBarExtra[data-v-9b536d0b]{display:none}}.trans-title[data-v-9b536d0b]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.item.appearance[data-v-9b536d0b],.item.social-links[data-v-9b536d0b]{display:flex;align-items:center;padding:0 12px}.item.appearance[data-v-9b536d0b]{min-width:176px}.appearance-action[data-v-9b536d0b]{margin-right:-2px}.social-links-list[data-v-9b536d0b]{margin:-4px -8px}.VPNavBarHamburger[data-v-5dea55bf]{display:flex;justify-content:center;align-items:center;width:48px;height:var(--vp-nav-height)}@media (min-width: 768px){.VPNavBarHamburger[data-v-5dea55bf]{display:none}}.container[data-v-5dea55bf]{position:relative;width:16px;height:14px;overflow:hidden}.VPNavBarHamburger:hover .top[data-v-5dea55bf]{top:0;left:0;transform:translate(4px)}.VPNavBarHamburger:hover .middle[data-v-5dea55bf]{top:6px;left:0;transform:translate(0)}.VPNavBarHamburger:hover .bottom[data-v-5dea55bf]{top:12px;left:0;transform:translate(8px)}.VPNavBarHamburger.active .top[data-v-5dea55bf]{top:6px;transform:translate(0) rotate(225deg)}.VPNavBarHamburger.active .middle[data-v-5dea55bf]{top:6px;transform:translate(16px)}.VPNavBarHamburger.active .bottom[data-v-5dea55bf]{top:6px;transform:translate(0) rotate(135deg)}.VPNavBarHamburger.active:hover .top[data-v-5dea55bf],.VPNavBarHamburger.active:hover .middle[data-v-5dea55bf],.VPNavBarHamburger.active:hover .bottom[data-v-5dea55bf]{background-color:var(--vp-c-text-2);transition:top .25s,background-color .25s,transform .25s}.top[data-v-5dea55bf],.middle[data-v-5dea55bf],.bottom[data-v-5dea55bf]{position:absolute;width:16px;height:2px;background-color:var(--vp-c-text-1);transition:top .25s,background-color .5s,transform .25s}.top[data-v-5dea55bf]{top:0;left:0;transform:translate(0)}.middle[data-v-5dea55bf]{top:6px;left:0;transform:translate(8px)}.bottom[data-v-5dea55bf]{top:12px;left:0;transform:translate(4px)}.VPNavBarMenuLink[data-v-ed5ac1f6]{display:flex;align-items:center;padding:0 12px;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.VPNavBarMenuLink.active[data-v-ed5ac1f6],.VPNavBarMenuLink[data-v-ed5ac1f6]:hover{color:var(--vp-c-brand-1)}.VPNavBarMenu[data-v-492ea56d]{display:none}@media (min-width: 768px){.VPNavBarMenu[data-v-492ea56d]{display:flex}}/*! @docsearch/css 3.6.0 | MIT License | © Algolia, Inc. and contributors | https://docsearch.algolia.com */:root{--docsearch-primary-color:#5468ff;--docsearch-text-color:#1c1e21;--docsearch-spacing:12px;--docsearch-icon-stroke-width:1.4;--docsearch-highlight-color:var(--docsearch-primary-color);--docsearch-muted-color:#969faf;--docsearch-container-background:rgba(101,108,133,.8);--docsearch-logo-color:#5468ff;--docsearch-modal-width:560px;--docsearch-modal-height:600px;--docsearch-modal-background:#f5f6f7;--docsearch-modal-shadow:inset 1px 1px 0 0 hsla(0,0%,100%,.5),0 3px 8px 0 #555a64;--docsearch-searchbox-height:56px;--docsearch-searchbox-background:#ebedf0;--docsearch-searchbox-focus-background:#fff;--docsearch-searchbox-shadow:inset 0 0 0 2px var(--docsearch-primary-color);--docsearch-hit-height:56px;--docsearch-hit-color:#444950;--docsearch-hit-active-color:#fff;--docsearch-hit-background:#fff;--docsearch-hit-shadow:0 1px 3px 0 #d4d9e1;--docsearch-key-gradient:linear-gradient(-225deg,#d5dbe4,#f8f8f8);--docsearch-key-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 2px 1px rgba(30,35,90,.4);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 1px 0 rgba(30,35,90,.4);--docsearch-footer-height:44px;--docsearch-footer-background:#fff;--docsearch-footer-shadow:0 -1px 0 0 #e0e3e8,0 -3px 6px 0 rgba(69,98,155,.12)}html[data-theme=dark]{--docsearch-text-color:#f5f6f7;--docsearch-container-background:rgba(9,10,17,.8);--docsearch-modal-background:#15172a;--docsearch-modal-shadow:inset 1px 1px 0 0 #2c2e40,0 3px 8px 0 #000309;--docsearch-searchbox-background:#090a11;--docsearch-searchbox-focus-background:#000;--docsearch-hit-color:#bec3c9;--docsearch-hit-shadow:none;--docsearch-hit-background:#090a11;--docsearch-key-gradient:linear-gradient(-26.5deg,#565872,#31355b);--docsearch-key-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 2px 2px 0 rgba(3,4,9,.3);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 1px 1px 0 rgba(3,4,9,.30196078431372547);--docsearch-footer-background:#1e2136;--docsearch-footer-shadow:inset 0 1px 0 0 rgba(73,76,106,.5),0 -4px 8px 0 rgba(0,0,0,.2);--docsearch-logo-color:#fff;--docsearch-muted-color:#7f8497}.DocSearch-Button{align-items:center;background:var(--docsearch-searchbox-background);border:0;border-radius:40px;color:var(--docsearch-muted-color);cursor:pointer;display:flex;font-weight:500;height:36px;justify-content:space-between;margin:0 0 0 16px;padding:0 8px;-webkit-user-select:none;user-select:none}.DocSearch-Button:active,.DocSearch-Button:focus,.DocSearch-Button:hover{background:var(--docsearch-searchbox-focus-background);box-shadow:var(--docsearch-searchbox-shadow);color:var(--docsearch-text-color);outline:none}.DocSearch-Button-Container{align-items:center;display:flex}.DocSearch-Search-Icon{stroke-width:1.6}.DocSearch-Button .DocSearch-Search-Icon{color:var(--docsearch-text-color)}.DocSearch-Button-Placeholder{font-size:1rem;padding:0 12px 0 6px}.DocSearch-Button-Keys{display:flex;min-width:calc(40px + .8em)}.DocSearch-Button-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:3px;box-shadow:var(--docsearch-key-shadow);color:var(--docsearch-muted-color);display:flex;height:18px;justify-content:center;margin-right:.4em;position:relative;padding:0 0 2px;border:0;top:-1px;width:20px}.DocSearch-Button-Key--pressed{transform:translate3d(0,1px,0);box-shadow:var(--docsearch-key-pressed-shadow)}@media (max-width:768px){.DocSearch-Button-Keys,.DocSearch-Button-Placeholder{display:none}}.DocSearch--active{overflow:hidden!important}.DocSearch-Container,.DocSearch-Container *{box-sizing:border-box}.DocSearch-Container{background-color:var(--docsearch-container-background);height:100vh;left:0;position:fixed;top:0;width:100vw;z-index:200}.DocSearch-Container a{text-decoration:none}.DocSearch-Link{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;font:inherit;margin:0;padding:0}.DocSearch-Modal{background:var(--docsearch-modal-background);border-radius:6px;box-shadow:var(--docsearch-modal-shadow);flex-direction:column;margin:60px auto auto;max-width:var(--docsearch-modal-width);position:relative}.DocSearch-SearchBar{display:flex;padding:var(--docsearch-spacing) var(--docsearch-spacing) 0}.DocSearch-Form{align-items:center;background:var(--docsearch-searchbox-focus-background);border-radius:4px;box-shadow:var(--docsearch-searchbox-shadow);display:flex;height:var(--docsearch-searchbox-height);margin:0;padding:0 var(--docsearch-spacing);position:relative;width:100%}.DocSearch-Input{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:transparent;border:0;color:var(--docsearch-text-color);flex:1;font:inherit;font-size:1.2em;height:100%;outline:none;padding:0 0 0 8px;width:80%}.DocSearch-Input::placeholder{color:var(--docsearch-muted-color);opacity:1}.DocSearch-Input::-webkit-search-cancel-button,.DocSearch-Input::-webkit-search-decoration,.DocSearch-Input::-webkit-search-results-button,.DocSearch-Input::-webkit-search-results-decoration{display:none}.DocSearch-LoadingIndicator,.DocSearch-MagnifierLabel,.DocSearch-Reset{margin:0;padding:0}.DocSearch-MagnifierLabel,.DocSearch-Reset{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}.DocSearch-Container--Stalled .DocSearch-MagnifierLabel,.DocSearch-LoadingIndicator{display:none}.DocSearch-Container--Stalled .DocSearch-LoadingIndicator{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Reset{animation:none;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;right:0;stroke-width:var(--docsearch-icon-stroke-width)}}.DocSearch-Reset{animation:fade-in .1s ease-in forwards;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;padding:2px;right:0;stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Reset[hidden]{display:none}.DocSearch-Reset:hover{color:var(--docsearch-highlight-color)}.DocSearch-LoadingIndicator svg,.DocSearch-MagnifierLabel svg{height:24px;width:24px}.DocSearch-Cancel{display:none}.DocSearch-Dropdown{max-height:calc(var(--docsearch-modal-height) - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height));min-height:var(--docsearch-spacing);overflow-y:auto;overflow-y:overlay;padding:0 var(--docsearch-spacing);scrollbar-color:var(--docsearch-muted-color) var(--docsearch-modal-background);scrollbar-width:thin}.DocSearch-Dropdown::-webkit-scrollbar{width:12px}.DocSearch-Dropdown::-webkit-scrollbar-track{background:transparent}.DocSearch-Dropdown::-webkit-scrollbar-thumb{background-color:var(--docsearch-muted-color);border:3px solid var(--docsearch-modal-background);border-radius:20px}.DocSearch-Dropdown ul{list-style:none;margin:0;padding:0}.DocSearch-Label{font-size:.75em;line-height:1.6em}.DocSearch-Help,.DocSearch-Label{color:var(--docsearch-muted-color)}.DocSearch-Help{font-size:.9em;margin:0;-webkit-user-select:none;user-select:none}.DocSearch-Title{font-size:1.2em}.DocSearch-Logo a{display:flex}.DocSearch-Logo svg{color:var(--docsearch-logo-color);margin-left:8px}.DocSearch-Hits:last-of-type{margin-bottom:24px}.DocSearch-Hits mark{background:none;color:var(--docsearch-highlight-color)}.DocSearch-HitsFooter{color:var(--docsearch-muted-color);display:flex;font-size:.85em;justify-content:center;margin-bottom:var(--docsearch-spacing);padding:var(--docsearch-spacing)}.DocSearch-HitsFooter a{border-bottom:1px solid;color:inherit}.DocSearch-Hit{border-radius:4px;display:flex;padding-bottom:4px;position:relative}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--deleting{transition:none}}.DocSearch-Hit--deleting{opacity:0;transition:all .25s linear}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--favoriting{transition:none}}.DocSearch-Hit--favoriting{transform:scale(0);transform-origin:top center;transition:all .25s linear;transition-delay:.25s}.DocSearch-Hit a{background:var(--docsearch-hit-background);border-radius:4px;box-shadow:var(--docsearch-hit-shadow);display:block;padding-left:var(--docsearch-spacing);width:100%}.DocSearch-Hit-source{background:var(--docsearch-modal-background);color:var(--docsearch-highlight-color);font-size:.85em;font-weight:600;line-height:32px;margin:0 -4px;padding:8px 4px 0;position:sticky;top:0;z-index:10}.DocSearch-Hit-Tree{color:var(--docsearch-muted-color);height:var(--docsearch-hit-height);opacity:.5;stroke-width:var(--docsearch-icon-stroke-width);width:24px}.DocSearch-Hit[aria-selected=true] a{background-color:var(--docsearch-highlight-color)}.DocSearch-Hit[aria-selected=true] mark{text-decoration:underline}.DocSearch-Hit-Container{align-items:center;color:var(--docsearch-hit-color);display:flex;flex-direction:row;height:var(--docsearch-hit-height);padding:0 var(--docsearch-spacing) 0 0}.DocSearch-Hit-icon{height:20px;width:20px}.DocSearch-Hit-action,.DocSearch-Hit-icon{color:var(--docsearch-muted-color);stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Hit-action{align-items:center;display:flex;height:22px;width:22px}.DocSearch-Hit-action svg{display:block;height:18px;width:18px}.DocSearch-Hit-action+.DocSearch-Hit-action{margin-left:6px}.DocSearch-Hit-action-button{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:inherit;cursor:pointer;padding:2px}svg.DocSearch-Hit-Select-Icon{display:none}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Select-Icon{display:block}.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:background-color .1s ease-in}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{transition:none}}.DocSearch-Hit-action-button:focus path,.DocSearch-Hit-action-button:hover path{fill:#fff}.DocSearch-Hit-content-wrapper{display:flex;flex:1 1 auto;flex-direction:column;font-weight:500;justify-content:center;line-height:1.2em;margin:0 8px;overflow-x:hidden;position:relative;text-overflow:ellipsis;white-space:nowrap;width:80%}.DocSearch-Hit-title{font-size:.9em}.DocSearch-Hit-path{color:var(--docsearch-muted-color);font-size:.75em}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-action,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-icon,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-path,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-text,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-title,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Tree,.DocSearch-Hit[aria-selected=true] mark{color:var(--docsearch-hit-active-color)!important}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:none}}.DocSearch-ErrorScreen,.DocSearch-NoResults,.DocSearch-StartScreen{font-size:.9em;margin:0 auto;padding:36px 0;text-align:center;width:80%}.DocSearch-Screen-Icon{color:var(--docsearch-muted-color);padding-bottom:12px}.DocSearch-NoResults-Prefill-List{display:inline-block;padding-bottom:24px;text-align:left}.DocSearch-NoResults-Prefill-List ul{display:inline-block;padding:8px 0 0}.DocSearch-NoResults-Prefill-List li{list-style-position:inside;list-style-type:"» "}.DocSearch-Prefill{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:1em;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;font-size:1em;font-weight:700;padding:0}.DocSearch-Prefill:focus,.DocSearch-Prefill:hover{outline:none;text-decoration:underline}.DocSearch-Footer{align-items:center;background:var(--docsearch-footer-background);border-radius:0 0 8px 8px;box-shadow:var(--docsearch-footer-shadow);display:flex;flex-direction:row-reverse;flex-shrink:0;height:var(--docsearch-footer-height);justify-content:space-between;padding:0 var(--docsearch-spacing);position:relative;-webkit-user-select:none;user-select:none;width:100%;z-index:300}.DocSearch-Commands{color:var(--docsearch-muted-color);display:flex;list-style:none;margin:0;padding:0}.DocSearch-Commands li{align-items:center;display:flex}.DocSearch-Commands li:not(:last-of-type){margin-right:.8em}.DocSearch-Commands-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:2px;box-shadow:var(--docsearch-key-shadow);display:flex;height:18px;justify-content:center;margin-right:.4em;padding:0 0 1px;color:var(--docsearch-muted-color);border:0;width:20px}.DocSearch-VisuallyHiddenForAccessibility{clip:rect(0 0 0 0);clip-path:inset(50%);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}@media (max-width:768px){:root{--docsearch-spacing:10px;--docsearch-footer-height:40px}.DocSearch-Dropdown{height:100%}.DocSearch-Container{height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);position:absolute}.DocSearch-Footer{border-radius:0;bottom:0;position:absolute}.DocSearch-Hit-content-wrapper{display:flex;position:relative;width:80%}.DocSearch-Modal{border-radius:0;box-shadow:none;height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);margin:0;max-width:100%;width:100%}.DocSearch-Dropdown{max-height:calc(var(--docsearch-vh, 1vh)*100 - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height))}.DocSearch-Cancel{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;flex:none;font:inherit;font-size:1em;font-weight:500;margin-left:var(--docsearch-spacing);outline:none;overflow:hidden;padding:0;-webkit-user-select:none;user-select:none;white-space:nowrap}.DocSearch-Commands,.DocSearch-Hit-Tree{display:none}}@keyframes fade-in{0%{opacity:0}to{opacity:1}}[class*=DocSearch]{--docsearch-primary-color: var(--vp-c-brand-1);--docsearch-highlight-color: var(--docsearch-primary-color);--docsearch-text-color: var(--vp-c-text-1);--docsearch-muted-color: var(--vp-c-text-2);--docsearch-searchbox-shadow: none;--docsearch-searchbox-background: transparent;--docsearch-searchbox-focus-background: transparent;--docsearch-key-gradient: transparent;--docsearch-key-shadow: none;--docsearch-modal-background: var(--vp-c-bg-soft);--docsearch-footer-background: var(--vp-c-bg)}.dark [class*=DocSearch]{--docsearch-modal-shadow: none;--docsearch-footer-shadow: none;--docsearch-logo-color: var(--vp-c-text-2);--docsearch-hit-background: var(--vp-c-default-soft);--docsearch-hit-color: var(--vp-c-text-2);--docsearch-hit-shadow: none}.DocSearch-Button{display:flex;justify-content:center;align-items:center;margin:0;padding:0;width:48px;height:55px;background:transparent;transition:border-color .25s}.DocSearch-Button:hover{background:transparent}.DocSearch-Button:focus{outline:1px dotted;outline:5px auto -webkit-focus-ring-color}.DocSearch-Button-Key--pressed{transform:none;box-shadow:none}.DocSearch-Button:focus:not(:focus-visible){outline:none!important}@media (min-width: 768px){.DocSearch-Button{justify-content:flex-start;border:1px solid transparent;border-radius:8px;padding:0 10px 0 12px;width:100%;height:40px;background-color:var(--vp-c-bg-alt)}.DocSearch-Button:hover{border-color:var(--vp-c-brand-1);background:var(--vp-c-bg-alt)}}.DocSearch-Button .DocSearch-Button-Container{display:flex;align-items:center}.DocSearch-Button .DocSearch-Search-Icon{position:relative;width:16px;height:16px;color:var(--vp-c-text-1);fill:currentColor;transition:color .5s}.DocSearch-Button:hover .DocSearch-Search-Icon{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Search-Icon{top:1px;margin-right:8px;width:14px;height:14px;color:var(--vp-c-text-2)}}.DocSearch-Button .DocSearch-Button-Placeholder{display:none;margin-top:2px;padding:0 16px 0 0;font-size:13px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.DocSearch-Button:hover .DocSearch-Button-Placeholder{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Placeholder{display:inline-block}}.DocSearch-Button .DocSearch-Button-Keys{direction:ltr;display:none;min-width:auto}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Keys{display:flex;align-items:center}}.DocSearch-Button .DocSearch-Button-Key{display:block;margin:2px 0 0;border:1px solid var(--vp-c-divider);border-right:none;border-radius:4px 0 0 4px;padding-left:6px;min-width:0;width:auto;height:22px;line-height:22px;font-family:var(--vp-font-family-base);font-size:12px;font-weight:500;transition:color .5s,border-color .5s}.DocSearch-Button .DocSearch-Button-Key+.DocSearch-Button-Key{border-right:1px solid var(--vp-c-divider);border-left:none;border-radius:0 4px 4px 0;padding-left:2px;padding-right:6px}.DocSearch-Button .DocSearch-Button-Key:first-child{font-size:0!important}.DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"Ctrl";font-size:12px;letter-spacing:normal;color:var(--docsearch-muted-color)}.mac .DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"⌘"}.DocSearch-Button .DocSearch-Button-Key:first-child>*{display:none}.DocSearch-Search-Icon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' stroke-width='1.6' viewBox='0 0 20 20'%3E%3Cpath fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' d='m14.386 14.386 4.088 4.088-4.088-4.088A7.533 7.533 0 1 1 3.733 3.733a7.533 7.533 0 0 1 10.653 10.653z'/%3E%3C/svg%3E")}.VPNavBarSearch{display:flex;align-items:center}@media (min-width: 768px){.VPNavBarSearch{flex-grow:1;padding-left:24px}}@media (min-width: 960px){.VPNavBarSearch{padding-left:32px}}.dark .DocSearch-Footer{border-top:1px solid var(--vp-c-divider)}.DocSearch-Form{border:1px solid var(--vp-c-brand-1);background-color:var(--vp-c-white)}.dark .DocSearch-Form{background-color:var(--vp-c-default-soft)}.DocSearch-Screen-Icon>svg{margin:auto}.VPNavBarSocialLinks[data-v-164c457f]{display:none}@media (min-width: 1280px){.VPNavBarSocialLinks[data-v-164c457f]{display:flex;align-items:center}}.title[data-v-28a961f9]{display:flex;align-items:center;border-bottom:1px solid transparent;width:100%;height:var(--vp-nav-height);font-size:16px;font-weight:600;color:var(--vp-c-text-1);transition:opacity .25s}@media (min-width: 960px){.title[data-v-28a961f9]{flex-shrink:0}.VPNavBarTitle.has-sidebar .title[data-v-28a961f9]{border-bottom-color:var(--vp-c-divider)}}[data-v-28a961f9] .logo{margin-right:8px;height:var(--vp-nav-logo-height)}.VPNavBarTranslations[data-v-c80d9ad0]{display:none}@media (min-width: 1280px){.VPNavBarTranslations[data-v-c80d9ad0]{display:flex;align-items:center}}.title[data-v-c80d9ad0]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.VPNavBar[data-v-40788ea0]{position:relative;height:var(--vp-nav-height);pointer-events:none;white-space:nowrap;transition:background-color .5s}.VPNavBar[data-v-40788ea0]:not(.home){background-color:var(--vp-nav-bg-color)}@media (min-width: 960px){.VPNavBar[data-v-40788ea0]:not(.home){background-color:transparent}.VPNavBar[data-v-40788ea0]:not(.has-sidebar):not(.home.top){background-color:var(--vp-nav-bg-color)}}.wrapper[data-v-40788ea0]{padding:0 8px 0 24px}@media (min-width: 768px){.wrapper[data-v-40788ea0]{padding:0 32px}}@media (min-width: 960px){.VPNavBar.has-sidebar .wrapper[data-v-40788ea0]{padding:0}}.container[data-v-40788ea0]{display:flex;justify-content:space-between;margin:0 auto;max-width:calc(var(--vp-layout-max-width) - 64px);height:var(--vp-nav-height);pointer-events:none}.container>.title[data-v-40788ea0],.container>.content[data-v-40788ea0]{pointer-events:none}.container[data-v-40788ea0] *{pointer-events:auto}@media (min-width: 960px){.VPNavBar.has-sidebar .container[data-v-40788ea0]{max-width:100%}}.title[data-v-40788ea0]{flex-shrink:0;height:calc(var(--vp-nav-height) - 1px);transition:background-color .5s}@media (min-width: 960px){.VPNavBar.has-sidebar .title[data-v-40788ea0]{position:absolute;top:0;left:0;z-index:2;padding:0 32px;width:var(--vp-sidebar-width);height:var(--vp-nav-height);background-color:transparent}}@media (min-width: 1440px){.VPNavBar.has-sidebar .title[data-v-40788ea0]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}.content[data-v-40788ea0]{flex-grow:1}@media (min-width: 960px){.VPNavBar.has-sidebar .content[data-v-40788ea0]{position:relative;z-index:1;padding-right:32px;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .content[data-v-40788ea0]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2 + 32px);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.content-body[data-v-40788ea0]{display:flex;justify-content:flex-end;align-items:center;height:var(--vp-nav-height);transition:background-color .5s}@media (min-width: 960px){.VPNavBar:not(.home.top) .content-body[data-v-40788ea0]{position:relative;background-color:var(--vp-nav-bg-color)}.VPNavBar:not(.has-sidebar):not(.home.top) .content-body[data-v-40788ea0]{background-color:transparent}}@media (max-width: 767px){.content-body[data-v-40788ea0]{column-gap:.5rem}}.menu+.translations[data-v-40788ea0]:before,.menu+.appearance[data-v-40788ea0]:before,.menu+.social-links[data-v-40788ea0]:before,.translations+.appearance[data-v-40788ea0]:before,.appearance+.social-links[data-v-40788ea0]:before{margin-right:8px;margin-left:8px;width:1px;height:24px;background-color:var(--vp-c-divider);content:""}.menu+.appearance[data-v-40788ea0]:before,.translations+.appearance[data-v-40788ea0]:before{margin-right:16px}.appearance+.social-links[data-v-40788ea0]:before{margin-left:16px}.social-links[data-v-40788ea0]{margin-right:-8px}.divider[data-v-40788ea0]{width:100%;height:1px}@media (min-width: 960px){.VPNavBar.has-sidebar .divider[data-v-40788ea0]{padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .divider[data-v-40788ea0]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.divider-line[data-v-40788ea0]{width:100%;height:1px;transition:background-color .5s}.VPNavBar:not(.home) .divider-line[data-v-40788ea0]{background-color:var(--vp-c-gutter)}@media (min-width: 960px){.VPNavBar:not(.home.top) .divider-line[data-v-40788ea0]{background-color:var(--vp-c-gutter)}.VPNavBar:not(.has-sidebar):not(.home.top) .divider[data-v-40788ea0]{background-color:var(--vp-c-gutter)}}.VPNavScreenAppearance[data-v-2b89f08b]{display:flex;justify-content:space-between;align-items:center;border-radius:8px;padding:12px 14px 12px 16px;background-color:var(--vp-c-bg-soft)}.text[data-v-2b89f08b]{line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.VPNavScreenMenuLink[data-v-27d04aeb]{display:block;border-bottom:1px solid var(--vp-c-divider);padding:12px 0 11px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:border-color .25s,color .25s}.VPNavScreenMenuLink[data-v-27d04aeb]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupLink[data-v-7179dbb7]{display:block;margin-left:12px;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-1);transition:color .25s}.VPNavScreenMenuGroupLink[data-v-7179dbb7]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupSection[data-v-4b8941ac]{display:block}.title[data-v-4b8941ac]{line-height:32px;font-size:13px;font-weight:700;color:var(--vp-c-text-2);transition:color .25s}.VPNavScreenMenuGroup[data-v-c9df2649]{border-bottom:1px solid var(--vp-c-divider);height:48px;overflow:hidden;transition:border-color .5s}.VPNavScreenMenuGroup .items[data-v-c9df2649]{visibility:hidden}.VPNavScreenMenuGroup.open .items[data-v-c9df2649]{visibility:visible}.VPNavScreenMenuGroup.open[data-v-c9df2649]{padding-bottom:10px;height:auto}.VPNavScreenMenuGroup.open .button[data-v-c9df2649]{padding-bottom:6px;color:var(--vp-c-brand-1)}.VPNavScreenMenuGroup.open .button-icon[data-v-c9df2649]{transform:rotate(45deg)}.button[data-v-c9df2649]{display:flex;justify-content:space-between;align-items:center;padding:12px 4px 11px 0;width:100%;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.button[data-v-c9df2649]:hover{color:var(--vp-c-brand-1)}.button-icon[data-v-c9df2649]{transition:transform .25s}.group[data-v-c9df2649]:first-child{padding-top:0}.group+.group[data-v-c9df2649],.group+.item[data-v-c9df2649]{padding-top:4px}.VPNavScreenTranslations[data-v-362991c2]{height:24px;overflow:hidden}.VPNavScreenTranslations.open[data-v-362991c2]{height:auto}.title[data-v-362991c2]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-text-1)}.icon[data-v-362991c2]{font-size:16px}.icon.lang[data-v-362991c2]{margin-right:8px}.icon.chevron[data-v-362991c2]{margin-left:4px}.list[data-v-362991c2]{padding:4px 0 0 24px}.link[data-v-362991c2]{line-height:32px;font-size:13px;color:var(--vp-c-text-1)}.VPNavScreen[data-v-382f42e9]{position:fixed;top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 1px);right:0;bottom:0;left:0;padding:0 32px;width:100%;background-color:var(--vp-nav-screen-bg-color);overflow-y:auto;transition:background-color .5s;pointer-events:auto}.VPNavScreen.fade-enter-active[data-v-382f42e9],.VPNavScreen.fade-leave-active[data-v-382f42e9]{transition:opacity .25s}.VPNavScreen.fade-enter-active .container[data-v-382f42e9],.VPNavScreen.fade-leave-active .container[data-v-382f42e9]{transition:transform .25s ease}.VPNavScreen.fade-enter-from[data-v-382f42e9],.VPNavScreen.fade-leave-to[data-v-382f42e9]{opacity:0}.VPNavScreen.fade-enter-from .container[data-v-382f42e9],.VPNavScreen.fade-leave-to .container[data-v-382f42e9]{transform:translateY(-8px)}@media (min-width: 768px){.VPNavScreen[data-v-382f42e9]{display:none}}.container[data-v-382f42e9]{margin:0 auto;padding:24px 0 96px;max-width:288px}.menu+.translations[data-v-382f42e9],.menu+.appearance[data-v-382f42e9],.translations+.appearance[data-v-382f42e9]{margin-top:24px}.menu+.social-links[data-v-382f42e9]{margin-top:16px}.appearance+.social-links[data-v-382f42e9]{margin-top:16px}.VPNav[data-v-f1e365da]{position:relative;top:var(--vp-layout-top-height, 0px);left:0;z-index:var(--vp-z-index-nav);width:100%;pointer-events:none;transition:background-color .5s}@media (min-width: 960px){.VPNav[data-v-f1e365da]{position:fixed}}.VPSidebarItem.level-0[data-v-2ea20db7]{padding-bottom:24px}.VPSidebarItem.collapsed.level-0[data-v-2ea20db7]{padding-bottom:10px}.item[data-v-2ea20db7]{position:relative;display:flex;width:100%}.VPSidebarItem.collapsible>.item[data-v-2ea20db7]{cursor:pointer}.indicator[data-v-2ea20db7]{position:absolute;top:6px;bottom:6px;left:-17px;width:2px;border-radius:2px;transition:background-color .25s}.VPSidebarItem.level-2.is-active>.item>.indicator[data-v-2ea20db7],.VPSidebarItem.level-3.is-active>.item>.indicator[data-v-2ea20db7],.VPSidebarItem.level-4.is-active>.item>.indicator[data-v-2ea20db7],.VPSidebarItem.level-5.is-active>.item>.indicator[data-v-2ea20db7]{background-color:var(--vp-c-brand-1)}.link[data-v-2ea20db7]{display:flex;align-items:center;flex-grow:1}.text[data-v-2ea20db7]{flex-grow:1;padding:4px 0;line-height:24px;font-size:14px;transition:color .25s}.VPSidebarItem.level-0 .text[data-v-2ea20db7]{font-weight:700;color:var(--vp-c-text-1)}.VPSidebarItem.level-1 .text[data-v-2ea20db7],.VPSidebarItem.level-2 .text[data-v-2ea20db7],.VPSidebarItem.level-3 .text[data-v-2ea20db7],.VPSidebarItem.level-4 .text[data-v-2ea20db7],.VPSidebarItem.level-5 .text[data-v-2ea20db7]{font-weight:500;color:var(--vp-c-text-2)}.VPSidebarItem.level-0.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-1.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-2.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-3.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-4.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-5.is-link>.item>.link:hover .text[data-v-2ea20db7]{color:var(--vp-c-brand-1)}.VPSidebarItem.level-0.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-1.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-2.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-3.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-4.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-5.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-0.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-1.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-2.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-3.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-4.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-5.has-active>.item>.link>.text[data-v-2ea20db7]{color:var(--vp-c-text-1)}.VPSidebarItem.level-0.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-1.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-2.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-3.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-4.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-5.is-active>.item .link>.text[data-v-2ea20db7]{color:var(--vp-c-brand-1)}.caret[data-v-2ea20db7]{display:flex;justify-content:center;align-items:center;margin-right:-7px;width:32px;height:32px;color:var(--vp-c-text-3);cursor:pointer;transition:color .25s;flex-shrink:0}.item:hover .caret[data-v-2ea20db7]{color:var(--vp-c-text-2)}.item:hover .caret[data-v-2ea20db7]:hover{color:var(--vp-c-text-1)}.caret-icon[data-v-2ea20db7]{font-size:18px;transform:rotate(90deg);transition:transform .25s}.VPSidebarItem.collapsed .caret-icon[data-v-2ea20db7]{transform:rotate(0)}.VPSidebarItem.level-1 .items[data-v-2ea20db7],.VPSidebarItem.level-2 .items[data-v-2ea20db7],.VPSidebarItem.level-3 .items[data-v-2ea20db7],.VPSidebarItem.level-4 .items[data-v-2ea20db7],.VPSidebarItem.level-5 .items[data-v-2ea20db7]{border-left:1px solid var(--vp-c-divider);padding-left:16px}.VPSidebarItem.collapsed .items[data-v-2ea20db7]{display:none}.VPSidebar[data-v-ec846e01]{position:fixed;top:var(--vp-layout-top-height, 0px);bottom:0;left:0;z-index:var(--vp-z-index-sidebar);padding:32px 32px 96px;width:calc(100vw - 64px);max-width:320px;background-color:var(--vp-sidebar-bg-color);opacity:0;box-shadow:var(--vp-c-shadow-3);overflow-x:hidden;overflow-y:auto;transform:translate(-100%);transition:opacity .5s,transform .25s ease;overscroll-behavior:contain}.VPSidebar.open[data-v-ec846e01]{opacity:1;visibility:visible;transform:translate(0);transition:opacity .25s,transform .5s cubic-bezier(.19,1,.22,1)}.dark .VPSidebar[data-v-ec846e01]{box-shadow:var(--vp-shadow-1)}@media (min-width: 960px){.VPSidebar[data-v-ec846e01]{padding-top:var(--vp-nav-height);width:var(--vp-sidebar-width);max-width:100%;background-color:var(--vp-sidebar-bg-color);opacity:1;visibility:visible;box-shadow:none;transform:translate(0)}}@media (min-width: 1440px){.VPSidebar[data-v-ec846e01]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}@media (min-width: 960px){.curtain[data-v-ec846e01]{position:sticky;top:-64px;left:0;z-index:1;margin-top:calc(var(--vp-nav-height) * -1);margin-right:-32px;margin-left:-32px;height:var(--vp-nav-height);background-color:var(--vp-sidebar-bg-color)}}.nav[data-v-ec846e01]{outline:0}.group+.group[data-v-ec846e01]{border-top:1px solid var(--vp-c-divider);padding-top:10px}@media (min-width: 960px){.group[data-v-ec846e01]{padding-top:10px;width:calc(var(--vp-sidebar-width) - 64px)}}.VPSkipLink[data-v-c3508ec8]{top:8px;left:8px;padding:8px 16px;z-index:999;border-radius:8px;font-size:12px;font-weight:700;text-decoration:none;color:var(--vp-c-brand-1);box-shadow:var(--vp-shadow-3);background-color:var(--vp-c-bg)}.VPSkipLink[data-v-c3508ec8]:focus{height:auto;width:auto;clip:auto;clip-path:none}@media (min-width: 1280px){.VPSkipLink[data-v-c3508ec8]{top:14px;left:16px}}.Layout[data-v-a9a9e638]{display:flex;flex-direction:column;min-height:100vh}.VPHomeSponsors[data-v-db81191c]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPHomeSponsors[data-v-db81191c]{margin:96px 0}@media (min-width: 768px){.VPHomeSponsors[data-v-db81191c]{margin:128px 0}}.VPHomeSponsors[data-v-db81191c]{padding:0 24px}@media (min-width: 768px){.VPHomeSponsors[data-v-db81191c]{padding:0 48px}}@media (min-width: 960px){.VPHomeSponsors[data-v-db81191c]{padding:0 64px}}.container[data-v-db81191c]{margin:0 auto;max-width:1152px}.love[data-v-db81191c]{margin:0 auto;width:fit-content;font-size:28px;color:var(--vp-c-text-3)}.icon[data-v-db81191c]{display:inline-block}.message[data-v-db81191c]{margin:0 auto;padding-top:10px;max-width:320px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.sponsors[data-v-db81191c]{padding-top:32px}.action[data-v-db81191c]{padding-top:40px;text-align:center}.VPTeamPage[data-v-c2f8e101]{margin:96px 0}@media (min-width: 768px){.VPTeamPage[data-v-c2f8e101]{margin:128px 0}}.VPHome .VPTeamPageTitle[data-v-c2f8e101-s]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPTeamPageSection+.VPTeamPageSection[data-v-c2f8e101-s],.VPTeamMembers+.VPTeamPageSection[data-v-c2f8e101-s]{margin-top:64px}.VPTeamMembers+.VPTeamMembers[data-v-c2f8e101-s]{margin-top:24px}@media (min-width: 768px){.VPTeamPageTitle+.VPTeamPageSection[data-v-c2f8e101-s]{margin-top:16px}.VPTeamPageSection+.VPTeamPageSection[data-v-c2f8e101-s],.VPTeamMembers+.VPTeamPageSection[data-v-c2f8e101-s]{margin-top:96px}}.VPTeamMembers[data-v-c2f8e101-s]{padding:0 24px}@media (min-width: 768px){.VPTeamMembers[data-v-c2f8e101-s]{padding:0 48px}}@media (min-width: 960px){.VPTeamMembers[data-v-c2f8e101-s]{padding:0 64px}}.VPTeamPageTitle[data-v-e277e15c]{padding:48px 32px;text-align:center}@media (min-width: 768px){.VPTeamPageTitle[data-v-e277e15c]{padding:64px 48px 48px}}@media (min-width: 960px){.VPTeamPageTitle[data-v-e277e15c]{padding:80px 64px 48px}}.title[data-v-e277e15c]{letter-spacing:0;line-height:44px;font-size:36px;font-weight:500}@media (min-width: 768px){.title[data-v-e277e15c]{letter-spacing:-.5px;line-height:56px;font-size:48px}}.lead[data-v-e277e15c]{margin:0 auto;max-width:512px;padding-top:12px;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 768px){.lead[data-v-e277e15c]{max-width:592px;letter-spacing:.15px;line-height:28px;font-size:20px}}.VPTeamPageSection[data-v-d43bc49d]{padding:0 32px}@media (min-width: 768px){.VPTeamPageSection[data-v-d43bc49d]{padding:0 48px}}@media (min-width: 960px){.VPTeamPageSection[data-v-d43bc49d]{padding:0 64px}}.title[data-v-d43bc49d]{position:relative;margin:0 auto;max-width:1152px;text-align:center;color:var(--vp-c-text-2)}.title-line[data-v-d43bc49d]{position:absolute;top:16px;left:0;width:100%;height:1px;background-color:var(--vp-c-divider)}.title-text[data-v-d43bc49d]{position:relative;display:inline-block;padding:0 24px;letter-spacing:0;line-height:32px;font-size:20px;font-weight:500;background-color:var(--vp-c-bg)}.lead[data-v-d43bc49d]{margin:0 auto;max-width:480px;padding-top:12px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.members[data-v-d43bc49d]{padding-top:40px}.VPTeamMembersItem[data-v-f9987cb6]{display:flex;flex-direction:column;gap:2px;border-radius:12px;width:100%;height:100%;overflow:hidden}.VPTeamMembersItem.small .profile[data-v-f9987cb6]{padding:32px}.VPTeamMembersItem.small .data[data-v-f9987cb6]{padding-top:20px}.VPTeamMembersItem.small .avatar[data-v-f9987cb6]{width:64px;height:64px}.VPTeamMembersItem.small .name[data-v-f9987cb6]{line-height:24px;font-size:16px}.VPTeamMembersItem.small .affiliation[data-v-f9987cb6]{padding-top:4px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .desc[data-v-f9987cb6]{padding-top:12px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .links[data-v-f9987cb6]{margin:0 -16px -20px;padding:10px 0 0}.VPTeamMembersItem.medium .profile[data-v-f9987cb6]{padding:48px 32px}.VPTeamMembersItem.medium .data[data-v-f9987cb6]{padding-top:24px;text-align:center}.VPTeamMembersItem.medium .avatar[data-v-f9987cb6]{width:96px;height:96px}.VPTeamMembersItem.medium .name[data-v-f9987cb6]{letter-spacing:.15px;line-height:28px;font-size:20px}.VPTeamMembersItem.medium .affiliation[data-v-f9987cb6]{padding-top:4px;font-size:16px}.VPTeamMembersItem.medium .desc[data-v-f9987cb6]{padding-top:16px;max-width:288px;font-size:16px}.VPTeamMembersItem.medium .links[data-v-f9987cb6]{margin:0 -16px -12px;padding:16px 12px 0}.profile[data-v-f9987cb6]{flex-grow:1;background-color:var(--vp-c-bg-soft)}.data[data-v-f9987cb6]{text-align:center}.avatar[data-v-f9987cb6]{position:relative;flex-shrink:0;margin:0 auto;border-radius:50%;box-shadow:var(--vp-shadow-3)}.avatar-img[data-v-f9987cb6]{position:absolute;top:0;right:0;bottom:0;left:0;border-radius:50%;object-fit:cover}.name[data-v-f9987cb6]{margin:0;font-weight:600}.affiliation[data-v-f9987cb6]{margin:0;font-weight:500;color:var(--vp-c-text-2)}.org.link[data-v-f9987cb6]{color:var(--vp-c-text-2);transition:color .25s}.org.link[data-v-f9987cb6]:hover{color:var(--vp-c-brand-1)}.desc[data-v-f9987cb6]{margin:0 auto}.desc[data-v-f9987cb6] a{font-weight:500;color:var(--vp-c-brand-1);text-decoration-style:dotted;transition:color .25s}.links[data-v-f9987cb6]{display:flex;justify-content:center;height:56px}.sp-link[data-v-f9987cb6]{display:flex;justify-content:center;align-items:center;text-align:center;padding:16px;font-size:14px;font-weight:500;color:var(--vp-c-sponsor);background-color:var(--vp-c-bg-soft);transition:color .25s,background-color .25s}.sp .sp-link.link[data-v-f9987cb6]:hover,.sp .sp-link.link[data-v-f9987cb6]:focus{outline:none;color:var(--vp-c-white);background-color:var(--vp-c-sponsor)}.sp-icon[data-v-f9987cb6]{margin-right:8px;font-size:16px}.VPTeamMembers.small .container[data-v-fba19bad]{grid-template-columns:repeat(auto-fit,minmax(224px,1fr))}.VPTeamMembers.small.count-1 .container[data-v-fba19bad]{max-width:276px}.VPTeamMembers.small.count-2 .container[data-v-fba19bad]{max-width:576px}.VPTeamMembers.small.count-3 .container[data-v-fba19bad]{max-width:876px}.VPTeamMembers.medium .container[data-v-fba19bad]{grid-template-columns:repeat(auto-fit,minmax(256px,1fr))}@media (min-width: 375px){.VPTeamMembers.medium .container[data-v-fba19bad]{grid-template-columns:repeat(auto-fit,minmax(288px,1fr))}}.VPTeamMembers.medium.count-1 .container[data-v-fba19bad]{max-width:368px}.VPTeamMembers.medium.count-2 .container[data-v-fba19bad]{max-width:760px}.container[data-v-fba19bad]{display:grid;gap:24px;margin:0 auto;max-width:1152px}:root{--vp-plugin-tabs-tab-text-color: var(--vp-c-text-2);--vp-plugin-tabs-tab-active-text-color: var(--vp-c-text-1);--vp-plugin-tabs-tab-hover-text-color: var(--vp-c-text-1);--vp-plugin-tabs-tab-bg: var(--vp-c-bg-soft);--vp-plugin-tabs-tab-divider: var(--vp-c-divider);--vp-plugin-tabs-tab-active-bar-color: var(--vp-c-brand-1)}.plugin-tabs{margin:16px 0;background-color:var(--vp-plugin-tabs-tab-bg);border-radius:8px}.plugin-tabs--tab-list{position:relative;padding:0 12px;overflow-x:auto;overflow-y:hidden}.plugin-tabs--tab-list:after{content:"";position:absolute;bottom:0;left:0;right:0;height:2px;background-color:var(--vp-plugin-tabs-tab-divider)}.plugin-tabs--tab{position:relative;padding:0 12px;line-height:48px;border-bottom:2px solid transparent;color:var(--vp-plugin-tabs-tab-text-color);font-size:14px;font-weight:500;white-space:nowrap;transition:color .25s}.plugin-tabs--tab[aria-selected=true]{color:var(--vp-plugin-tabs-tab-active-text-color)}.plugin-tabs--tab:hover{color:var(--vp-plugin-tabs-tab-hover-text-color)}.plugin-tabs--tab:after{content:"";position:absolute;bottom:-2px;left:8px;right:8px;height:2px;background-color:transparent;transition:background-color .25s;z-index:1}.plugin-tabs--tab[aria-selected=true]:after{background-color:var(--vp-plugin-tabs-tab-active-bar-color)}.plugin-tabs--content[data-v-9b0d03d2]{padding:16px}.plugin-tabs--content[data-v-9b0d03d2]>:first-child:first-child{margin-top:0}.plugin-tabs--content[data-v-9b0d03d2]>:last-child:last-child{margin-bottom:0}.plugin-tabs--content[data-v-9b0d03d2]>div[class*=language-]{border-radius:8px;margin:16px 0}:root:not(.dark) .plugin-tabs--content[data-v-9b0d03d2] div[class*=language-]{background-color:var(--vp-c-bg)}.VPHero .clip{white-space:pre;max-width:500px}:root{--vp-font-family-base: "Barlow", "Inter var experimental", "Inter var", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", sans-serif;--vp-font-family-mono: "Fira Code", Menlo, Monaco, Consolas, "Courier New", monospace}:root{--julia-blue: #5fd7ff ;--julia-purple: #5fd7ff;--julia-red: #CB3C33;--julia-green: #0087d7;--vp-c-brand: #0087d7;--vp-c-brand-light: #0087d7;--vp-c-brand-lighter: #5fd7ff ;--vp-c-brand-lightest: #5fd7ff ;--vp-c-brand-dark: #5fd7ff;--vp-c-brand-darker: #5fd7ff ;--vp-c-brand-dimm: #212425}:root{--vp-button-brand-border: var(--vp-c-brand-light);--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand);--vp-button-brand-hover-border: var(--vp-c-brand-light);--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-light);--vp-button-brand-active-border: var(--vp-c-brand-light);--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-button-brand-bg)}:root{--vp-home-hero-name-color: transparent;--vp-home-hero-name-background: -webkit-linear-gradient( 120deg, #ff875f 30%, #ff875f 30% );--vp-home-hero-image-background-image: linear-gradient( -45deg, #0094ea11 15%, #0094ea11 15%, #0094ea11 );--vp-home-hero-image-filter: blur(10px)}@media (min-width: 640px){:root{--vp-home-hero-image-filter: blur(60px)}}@media (min-width: 960px){:root{--vp-home-hero-image-filter: blur(72px)}}:root.dark{--vp-custom-block-tip-border: var(--vp-c-brand);--vp-custom-block-tip-text: var(--vp-c-brand-lightest);--vp-custom-block-tip-bg: var(--vp-c-brand-dimm);--vp-c-black: hsl(220 20% 9%);--vp-c-black-pure: hsl(220, 24%, 4%);--vp-c-black-soft: hsl(220 16% 13%);--vp-c-black-mute: hsl(220 14% 17%);--vp-c-gray: hsl(220 8% 56%);--vp-c-gray-dark-1: hsl(220 10% 39%);--vp-c-gray-dark-2: hsl(220 12% 28%);--vp-c-gray-dark-3: hsl(220 12% 23%);--vp-c-gray-dark-4: hsl(220 14% 17%);--vp-c-gray-dark-5: hsl(220 16% 13%);--vp-c-bg: hsl(240, 2%, 11%);--vp-custom-block-info-bg: hsl(220 14% 17%);--vp-c-gutter: hsl(220 20% 9%);--vp-c-bg-alt: hsl(220 20% 9%);--vp-c-bg-soft: hsl(220 14% 17%);--vp-c-bg-mute: hsl(220 12% 23%)}.DocSearch{--docsearch-primary-color: var(--vp-c-brand) !important}mjx-container>svg{display:block;margin:auto}mjx-container{padding:.5rem 0}mjx-container{display:inline-block;margin:auto 2px -2px}mjx-container>svg{margin:auto;display:inline-block}:root{--vp-c-brand-1: #ff875f;--vp-c-brand-2: #ff875f;--vp-c-brand-3: #ff875f;--vp-c-sponsor: #ca2971;--vitest-c-sponsor-hover: #c13071}.dark{--vp-c-brand-1: #0087d7;--vp-c-brand-2: #0087d7;--vp-c-brand-3: #0087d7;--vp-c-sponsor: #ee4e95;--vitest-c-sponsor-hover: #e51370}.VPLocalSearchBox[data-v-f4c4f812]{position:fixed;z-index:100;top:0;right:0;bottom:0;left:0;display:flex}.backdrop[data-v-f4c4f812]{position:absolute;top:0;right:0;bottom:0;left:0;background:var(--vp-backdrop-bg-color);transition:opacity .5s}.shell[data-v-f4c4f812]{position:relative;padding:12px;margin:64px auto;display:flex;flex-direction:column;gap:16px;background:var(--vp-local-search-bg);width:min(100vw - 60px,900px);height:min-content;max-height:min(100vh - 128px,900px);border-radius:6px}@media (max-width: 767px){.shell[data-v-f4c4f812]{margin:0;width:100vw;height:100vh;max-height:none;border-radius:0}}.search-bar[data-v-f4c4f812]{border:1px solid var(--vp-c-divider);border-radius:4px;display:flex;align-items:center;padding:0 12px;cursor:text}@media (max-width: 767px){.search-bar[data-v-f4c4f812]{padding:0 8px}}.search-bar[data-v-f4c4f812]:focus-within{border-color:var(--vp-c-brand-1)}.local-search-icon[data-v-f4c4f812]{display:block;font-size:18px}.navigate-icon[data-v-f4c4f812]{display:block;font-size:14px}.search-icon[data-v-f4c4f812]{margin:8px}@media (max-width: 767px){.search-icon[data-v-f4c4f812]{display:none}}.search-input[data-v-f4c4f812]{padding:6px 12px;font-size:inherit;width:100%}@media (max-width: 767px){.search-input[data-v-f4c4f812]{padding:6px 4px}}.search-actions[data-v-f4c4f812]{display:flex;gap:4px}@media (any-pointer: coarse){.search-actions[data-v-f4c4f812]{gap:8px}}@media (min-width: 769px){.search-actions.before[data-v-f4c4f812]{display:none}}.search-actions button[data-v-f4c4f812]{padding:8px}.search-actions button[data-v-f4c4f812]:not([disabled]):hover,.toggle-layout-button.detailed-list[data-v-f4c4f812]{color:var(--vp-c-brand-1)}.search-actions button.clear-button[data-v-f4c4f812]:disabled{opacity:.37}.search-keyboard-shortcuts[data-v-f4c4f812]{font-size:.8rem;opacity:75%;display:flex;flex-wrap:wrap;gap:16px;line-height:14px}.search-keyboard-shortcuts span[data-v-f4c4f812]{display:flex;align-items:center;gap:4px}@media (max-width: 767px){.search-keyboard-shortcuts[data-v-f4c4f812]{display:none}}.search-keyboard-shortcuts kbd[data-v-f4c4f812]{background:#8080801a;border-radius:4px;padding:3px 6px;min-width:24px;display:inline-block;text-align:center;vertical-align:middle;border:1px solid rgba(128,128,128,.15);box-shadow:0 2px 2px #0000001a}.results[data-v-f4c4f812]{display:flex;flex-direction:column;gap:6px;overflow-x:hidden;overflow-y:auto;overscroll-behavior:contain}.result[data-v-f4c4f812]{display:flex;align-items:center;gap:8px;border-radius:4px;transition:none;line-height:1rem;border:solid 2px var(--vp-local-search-result-border);outline:none}.result>div[data-v-f4c4f812]{margin:12px;width:100%;overflow:hidden}@media (max-width: 767px){.result>div[data-v-f4c4f812]{margin:8px}}.titles[data-v-f4c4f812]{display:flex;flex-wrap:wrap;gap:4px;position:relative;z-index:1001;padding:2px 0}.title[data-v-f4c4f812]{display:flex;align-items:center;gap:4px}.title.main[data-v-f4c4f812]{font-weight:500}.title-icon[data-v-f4c4f812]{opacity:.5;font-weight:500;color:var(--vp-c-brand-1)}.title svg[data-v-f4c4f812]{opacity:.5}.result.selected[data-v-f4c4f812]{--vp-local-search-result-bg: var(--vp-local-search-result-selected-bg);border-color:var(--vp-local-search-result-selected-border)}.excerpt-wrapper[data-v-f4c4f812]{position:relative}.excerpt[data-v-f4c4f812]{opacity:75%;pointer-events:none;max-height:140px;overflow:hidden;position:relative;opacity:.5;margin-top:4px}.result.selected .excerpt[data-v-f4c4f812]{opacity:1}.excerpt[data-v-f4c4f812] *{font-size:.8rem!important;line-height:130%!important}.titles[data-v-f4c4f812] mark,.excerpt[data-v-f4c4f812] mark{background-color:var(--vp-local-search-highlight-bg);color:var(--vp-local-search-highlight-text);border-radius:2px;padding:0 2px}.excerpt[data-v-f4c4f812] .vp-code-group .tabs{display:none}.excerpt[data-v-f4c4f812] .vp-code-group div[class*=language-]{border-radius:8px!important}.excerpt-gradient-bottom[data-v-f4c4f812]{position:absolute;bottom:-1px;left:0;width:100%;height:8px;background:linear-gradient(transparent,var(--vp-local-search-result-bg));z-index:1000}.excerpt-gradient-top[data-v-f4c4f812]{position:absolute;top:-1px;left:0;width:100%;height:8px;background:linear-gradient(var(--vp-local-search-result-bg),transparent);z-index:1000}.result.selected .titles[data-v-f4c4f812],.result.selected .title-icon[data-v-f4c4f812]{color:var(--vp-c-brand-1)!important}.no-results[data-v-f4c4f812]{font-size:.9rem;text-align:center;padding:12px}svg[data-v-f4c4f812]{flex:none} diff --git a/dev/assets/style.COODeMdn.css b/dev/assets/style.COODeMdn.css deleted file mode 100644 index a2698dd..0000000 --- a/dev/assets/style.COODeMdn.css +++ /dev/null @@ -1 +0,0 @@ -@import"https://fonts.googleapis.com/css?family=Space+Mono:regular,italic,700,700italic";@import"https://fonts.googleapis.com/css?family=Space+Grotesk:regular,italic,700,700italic";@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-cyrillic-ext.BBPuwvHQ.woff2) format("woff2");unicode-range:U+0460-052F,U+1C80-1C88,U+20B4,U+2DE0-2DFF,U+A640-A69F,U+FE2E-FE2F}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-cyrillic.C5lxZ8CY.woff2) format("woff2");unicode-range:U+0301,U+0400-045F,U+0490-0491,U+04B0-04B1,U+2116}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-greek-ext.CqjqNYQ-.woff2) format("woff2");unicode-range:U+1F00-1FFF}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-greek.BBVDIX6e.woff2) format("woff2");unicode-range:U+0370-0377,U+037A-037F,U+0384-038A,U+038C,U+038E-03A1,U+03A3-03FF}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-vietnamese.BjW4sHH5.woff2) format("woff2");unicode-range:U+0102-0103,U+0110-0111,U+0128-0129,U+0168-0169,U+01A0-01A1,U+01AF-01B0,U+0300-0301,U+0303-0304,U+0308-0309,U+0323,U+0329,U+1EA0-1EF9,U+20AB}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-latin-ext.4ZJIpNVo.woff2) format("woff2");unicode-range:U+0100-02AF,U+0304,U+0308,U+0329,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:Inter;font-style:normal;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-roman-latin.Di8DUHzh.woff2) format("woff2");unicode-range:U+0000-00FF,U+0131,U+0152-0153,U+02BB-02BC,U+02C6,U+02DA,U+02DC,U+0304,U+0308,U+0329,U+2000-206F,U+2074,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-cyrillic-ext.r48I6akx.woff2) format("woff2");unicode-range:U+0460-052F,U+1C80-1C88,U+20B4,U+2DE0-2DFF,U+A640-A69F,U+FE2E-FE2F}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-cyrillic.By2_1cv3.woff2) format("woff2");unicode-range:U+0301,U+0400-045F,U+0490-0491,U+04B0-04B1,U+2116}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-greek-ext.1u6EdAuj.woff2) format("woff2");unicode-range:U+1F00-1FFF}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-greek.DJ8dCoTZ.woff2) format("woff2");unicode-range:U+0370-0377,U+037A-037F,U+0384-038A,U+038C,U+038E-03A1,U+03A3-03FF}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-vietnamese.BSbpV94h.woff2) format("woff2");unicode-range:U+0102-0103,U+0110-0111,U+0128-0129,U+0168-0169,U+01A0-01A1,U+01AF-01B0,U+0300-0301,U+0303-0304,U+0308-0309,U+0323,U+0329,U+1EA0-1EF9,U+20AB}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-latin-ext.CN1xVJS-.woff2) format("woff2");unicode-range:U+0100-02AF,U+0304,U+0308,U+0329,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:Inter;font-style:italic;font-weight:100 900;font-display:swap;src:url(/BioMarkovChains.jl/dev/assets/inter-italic-latin.C2AdPX0b.woff2) format("woff2");unicode-range:U+0000-00FF,U+0131,U+0152-0153,U+02BB-02BC,U+02C6,U+02DA,U+02DC,U+0304,U+0308,U+0329,U+2000-206F,U+2074,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}@font-face{font-family:Chinese Quotes;src:local("PingFang SC Regular"),local("PingFang SC"),local("SimHei"),local("Source Han Sans SC");unicode-range:U+2018,U+2019,U+201C,U+201D}:root{--vp-c-white: #ffffff;--vp-c-black: #000000;--vp-c-neutral: var(--vp-c-black);--vp-c-neutral-inverse: var(--vp-c-white)}.dark{--vp-c-neutral: var(--vp-c-white);--vp-c-neutral-inverse: var(--vp-c-black)}:root{--vp-c-gray-1: #dddde3;--vp-c-gray-2: #e4e4e9;--vp-c-gray-3: #ebebef;--vp-c-gray-soft: rgba(142, 150, 170, .14);--vp-c-indigo-1: #3451b2;--vp-c-indigo-2: #3a5ccc;--vp-c-indigo-3: #5672cd;--vp-c-indigo-soft: rgba(100, 108, 255, .14);--vp-c-purple-1: #6f42c1;--vp-c-purple-2: #7e4cc9;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .14);--vp-c-green-1: #18794e;--vp-c-green-2: #299764;--vp-c-green-3: #30a46c;--vp-c-green-soft: rgba(16, 185, 129, .14);--vp-c-yellow-1: #915930;--vp-c-yellow-2: #946300;--vp-c-yellow-3: #9f6a00;--vp-c-yellow-soft: rgba(234, 179, 8, .14);--vp-c-red-1: #b8272c;--vp-c-red-2: #d5393e;--vp-c-red-3: #e0575b;--vp-c-red-soft: rgba(244, 63, 94, .14);--vp-c-sponsor: #db2777}.dark{--vp-c-gray-1: #515c67;--vp-c-gray-2: #414853;--vp-c-gray-3: #32363f;--vp-c-gray-soft: rgba(101, 117, 133, .16);--vp-c-indigo-1: #a8b1ff;--vp-c-indigo-2: #5c73e7;--vp-c-indigo-3: #3e63dd;--vp-c-indigo-soft: rgba(100, 108, 255, .16);--vp-c-purple-1: #c8abfa;--vp-c-purple-2: #a879e6;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .16);--vp-c-green-1: #3dd68c;--vp-c-green-2: #30a46c;--vp-c-green-3: #298459;--vp-c-green-soft: rgba(16, 185, 129, .16);--vp-c-yellow-1: #f9b44e;--vp-c-yellow-2: #da8b17;--vp-c-yellow-3: #a46a0a;--vp-c-yellow-soft: rgba(234, 179, 8, .16);--vp-c-red-1: #f66f81;--vp-c-red-2: #f14158;--vp-c-red-3: #b62a3c;--vp-c-red-soft: rgba(244, 63, 94, .16)}:root{--vp-c-bg: #ffffff;--vp-c-bg-alt: #f6f6f7;--vp-c-bg-elv: #ffffff;--vp-c-bg-soft: #f6f6f7}.dark{--vp-c-bg: #1b1b1f;--vp-c-bg-alt: #161618;--vp-c-bg-elv: #202127;--vp-c-bg-soft: #202127}:root{--vp-c-border: #c2c2c4;--vp-c-divider: #e2e2e3;--vp-c-gutter: #e2e2e3}.dark{--vp-c-border: #3c3f44;--vp-c-divider: #2e2e32;--vp-c-gutter: #000000}:root{--vp-c-text-1: rgba(60, 60, 67);--vp-c-text-2: rgba(60, 60, 67, .78);--vp-c-text-3: rgba(60, 60, 67, .56)}.dark{--vp-c-text-1: rgba(255, 255, 245, .86);--vp-c-text-2: rgba(235, 235, 245, .6);--vp-c-text-3: rgba(235, 235, 245, .38)}:root{--vp-c-default-1: var(--vp-c-gray-1);--vp-c-default-2: var(--vp-c-gray-2);--vp-c-default-3: var(--vp-c-gray-3);--vp-c-default-soft: var(--vp-c-gray-soft);--vp-c-brand-1: var(--vp-c-indigo-1);--vp-c-brand-2: var(--vp-c-indigo-2);--vp-c-brand-3: var(--vp-c-indigo-3);--vp-c-brand-soft: var(--vp-c-indigo-soft);--vp-c-brand: var(--vp-c-brand-1);--vp-c-tip-1: var(--vp-c-brand-1);--vp-c-tip-2: var(--vp-c-brand-2);--vp-c-tip-3: var(--vp-c-brand-3);--vp-c-tip-soft: var(--vp-c-brand-soft);--vp-c-note-1: var(--vp-c-brand-1);--vp-c-note-2: var(--vp-c-brand-2);--vp-c-note-3: var(--vp-c-brand-3);--vp-c-note-soft: var(--vp-c-brand-soft);--vp-c-success-1: var(--vp-c-green-1);--vp-c-success-2: var(--vp-c-green-2);--vp-c-success-3: var(--vp-c-green-3);--vp-c-success-soft: var(--vp-c-green-soft);--vp-c-important-1: var(--vp-c-purple-1);--vp-c-important-2: var(--vp-c-purple-2);--vp-c-important-3: var(--vp-c-purple-3);--vp-c-important-soft: var(--vp-c-purple-soft);--vp-c-warning-1: var(--vp-c-yellow-1);--vp-c-warning-2: var(--vp-c-yellow-2);--vp-c-warning-3: var(--vp-c-yellow-3);--vp-c-warning-soft: var(--vp-c-yellow-soft);--vp-c-danger-1: var(--vp-c-red-1);--vp-c-danger-2: var(--vp-c-red-2);--vp-c-danger-3: var(--vp-c-red-3);--vp-c-danger-soft: var(--vp-c-red-soft);--vp-c-caution-1: var(--vp-c-red-1);--vp-c-caution-2: var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Chinese Quotes", Inter, ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji", "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: var(--vp-c-text-1);--vp-custom-block-warning-bg: var(--vp-c-warning-soft);--vp-custom-block-warning-code-bg: var(--vp-c-warning-soft);--vp-custom-block-danger-border: transparent;--vp-custom-block-danger-text: var(--vp-c-text-1);--vp-custom-block-danger-bg: var(--vp-c-danger-soft);--vp-custom-block-danger-code-bg: var(--vp-c-danger-soft);--vp-custom-block-caution-border: transparent;--vp-custom-block-caution-text: var(--vp-c-text-1);--vp-custom-block-caution-bg: var(--vp-c-caution-soft);--vp-custom-block-caution-code-bg: var(--vp-c-caution-soft);--vp-custom-block-details-border: var(--vp-custom-block-info-border);--vp-custom-block-details-text: var(--vp-custom-block-info-text);--vp-custom-block-details-bg: var(--vp-custom-block-info-bg);--vp-custom-block-details-code-bg: var(--vp-custom-block-info-code-bg)}:root{--vp-input-border-color: var(--vp-c-border);--vp-input-bg-color: var(--vp-c-bg-alt);--vp-input-switch-bg-color: var(--vp-c-default-soft)}:root{--vp-nav-height: 64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: var(--vp-c-bg);--vp-local-search-result-bg: var(--vp-c-bg);--vp-local-search-result-border: var(--vp-c-divider);--vp-local-search-result-selected-bg: var(--vp-c-bg);--vp-local-search-result-selected-border: var(--vp-c-brand-1);--vp-local-search-highlight-bg: var(--vp-c-brand-1);--vp-local-search-highlight-text: var(--vp-c-neutral-inverse)}@media (prefers-reduced-motion: reduce){*,:before,:after{animation-delay:-1ms!important;animation-duration:1ms!important;animation-iteration-count:1!important;background-attachment:initial!important;scroll-behavior:auto!important;transition-duration:0s!important;transition-delay:0s!important}}*,:before,:after{box-sizing:border-box}html{line-height:1.4;font-size:16px;-webkit-text-size-adjust:100%}html.dark{color-scheme:dark}body{margin:0;width:100%;min-width:320px;min-height:100vh;line-height:24px;font-family:var(--vp-font-family-base);font-size:16px;font-weight:400;color:var(--vp-c-text-1);background-color:var(--vp-c-bg);font-synthesis:style;text-rendering:optimizeLegibility;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}main{display:block}h1,h2,h3,h4,h5,h6{margin:0;line-height:24px;font-size:16px;font-weight:400}p{margin:0}strong,b{font-weight:600}a,area,button,[role=button],input,label,select,summary,textarea{touch-action:manipulation}a{color:inherit;text-decoration:inherit}ol,ul{list-style:none;margin:0;padding:0}blockquote{margin:0}pre,code,kbd,samp{font-family:var(--vp-font-family-mono)}img,svg,video,canvas,audio,iframe,embed,object{display:block}figure{margin:0}img,video{max-width:100%;height:auto}button,input,optgroup,select,textarea{border:0;padding:0;line-height:inherit;color:inherit}button{padding:0;font-family:inherit;background-color:transparent;background-image:none}button:enabled,[role=button]:enabled{cursor:pointer}button:focus,button:focus-visible{outline:1px dotted;outline:4px auto -webkit-focus-ring-color}button:focus:not(:focus-visible){outline:none!important}input:focus,textarea:focus,select:focus{outline:none}table{border-collapse:collapse}input{background-color:transparent}input:-ms-input-placeholder,textarea:-ms-input-placeholder{color:var(--vp-c-text-3)}input::-ms-input-placeholder,textarea::-ms-input-placeholder{color:var(--vp-c-text-3)}input::placeholder,textarea::placeholder{color:var(--vp-c-text-3)}input::-webkit-outer-spin-button,input::-webkit-inner-spin-button{-webkit-appearance:none;margin:0}input[type=number]{-moz-appearance:textfield}textarea{resize:vertical}select{-webkit-appearance:none}fieldset{margin:0;padding:0}h1,h2,h3,h4,h5,h6,li,p{overflow-wrap:break-word}vite-error-overlay{z-index:9999}mjx-container>svg{display:inline-block;margin:auto}[class^=vpi-],[class*=" vpi-"],.vp-icon{width:1em;height:1em}[class^=vpi-].bg,[class*=" vpi-"].bg,.vp-icon.bg{background-size:100% 100%;background-color:transparent}[class^=vpi-]:not(.bg),[class*=" vpi-"]:not(.bg),.vp-icon:not(.bg){-webkit-mask:var(--icon) no-repeat;mask:var(--icon) no-repeat;-webkit-mask-size:100% 100%;mask-size:100% 100%;background-color:currentColor;color:inherit}.vpi-align-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M21 6H3M15 12H3M17 18H3'/%3E%3C/svg%3E")}.vpi-arrow-right,.vpi-arrow-down,.vpi-arrow-left,.vpi-arrow-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5l7 7-7 7'/%3E%3C/svg%3E")}.vpi-chevron-right,.vpi-chevron-down,.vpi-chevron-left,.vpi-chevron-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 18 6-6-6-6'/%3E%3C/svg%3E")}.vpi-chevron-down,.vpi-arrow-down{transform:rotate(90deg)}.vpi-chevron-left,.vpi-arrow-left{transform:rotate(180deg)}.vpi-chevron-up,.vpi-arrow-up{transform:rotate(-90deg)}.vpi-square-pen{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3H5a2 2 0 0 0-2 2v14a2 2 0 0 0 2 2h14a2 2 0 0 0 2-2v-7'/%3E%3Cpath d='M18.375 2.625a2.121 2.121 0 1 1 3 3L12 15l-4 1 1-4Z'/%3E%3C/svg%3E")}.vpi-plus{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5v14'/%3E%3C/svg%3E")}.vpi-sun{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='4'/%3E%3Cpath d='M12 2v2M12 20v2M4.93 4.93l1.41 1.41M17.66 17.66l1.41 1.41M2 12h2M20 12h2M6.34 17.66l-1.41 1.41M19.07 4.93l-1.41 1.41'/%3E%3C/svg%3E")}.vpi-moon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3a6 6 0 0 0 9 9 9 9 0 1 1-9-9Z'/%3E%3C/svg%3E")}.vpi-more-horizontal{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='1'/%3E%3Ccircle cx='19' cy='12' r='1'/%3E%3Ccircle cx='5' cy='12' r='1'/%3E%3C/svg%3E")}.vpi-languages{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6'/%3E%3C/svg%3E")}.vpi-heart{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M19 14c1.49-1.46 3-3.21 3-5.5A5.5 5.5 0 0 0 16.5 3c-1.76 0-3 .5-4.5 2-1.5-1.5-2.74-2-4.5-2A5.5 5.5 0 0 0 2 8.5c0 2.3 1.5 4.05 3 5.5l7 7Z'/%3E%3C/svg%3E")}.vpi-search{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='11' cy='11' r='8'/%3E%3Cpath d='m21 21-4.3-4.3'/%3E%3C/svg%3E")}.vpi-layout-list{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='7' height='7' x='3' y='3' rx='1'/%3E%3Crect width='7' height='7' x='3' y='14' rx='1'/%3E%3Cpath d='M14 4h7M14 9h7M14 15h7M14 20h7'/%3E%3C/svg%3E")}.vpi-delete{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M20 5H9l-7 7 7 7h11a2 2 0 0 0 2-2V7a2 2 0 0 0-2-2ZM18 9l-6 6M12 9l6 6'/%3E%3C/svg%3E")}.vpi-corner-down-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 10-5 5 5 5'/%3E%3Cpath d='M20 4v7a4 4 0 0 1-4 4H4'/%3E%3C/svg%3E")}:root{--vp-icon-copy: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3C/svg%3E");--vp-icon-copied: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3Cpath d='m9 14 2 2 4-4'/%3E%3C/svg%3E")}.vpi-social-discord{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.317 4.37a19.791 19.791 0 0 0-4.885-1.515.074.074 0 0 0-.079.037c-.21.375-.444.864-.608 1.25a18.27 18.27 0 0 0-5.487 0 12.64 12.64 0 0 0-.617-1.25.077.077 0 0 0-.079-.037A19.736 19.736 0 0 0 3.677 4.37a.07.07 0 0 0-.032.027C.533 9.046-.32 13.58.099 18.057a.082.082 0 0 0 .031.057 19.9 19.9 0 0 0 5.993 3.03.078.078 0 0 0 .084-.028c.462-.63.874-1.295 1.226-1.994a.076.076 0 0 0-.041-.106 13.107 13.107 0 0 1-1.872-.892.077.077 0 0 1-.008-.128 10.2 10.2 0 0 0 .372-.292.074.074 0 0 1 .077-.01c3.928 1.793 8.18 1.793 12.062 0a.074.074 0 0 1 .078.01c.12.098.246.198.373.292a.077.077 0 0 1-.006.127 12.299 12.299 0 0 1-1.873.892.077.077 0 0 0-.041.107c.36.698.772 1.362 1.225 1.993a.076.076 0 0 0 .084.028 19.839 19.839 0 0 0 6.002-3.03.077.077 0 0 0 .032-.054c.5-5.177-.838-9.674-3.549-13.66a.061.061 0 0 0-.031-.03zM8.02 15.33c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.956-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.956 2.418-2.157 2.418zm7.975 0c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.955-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.946 2.418-2.157 2.418Z'/%3E%3C/svg%3E")}.vpi-social-facebook{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M9.101 23.691v-7.98H6.627v-3.667h2.474v-1.58c0-4.085 1.848-5.978 5.858-5.978.401 0 .955.042 1.468.103a8.68 8.68 0 0 1 1.141.195v3.325a8.623 8.623 0 0 0-.653-.036 26.805 26.805 0 0 0-.733-.009c-.707 0-1.259.096-1.675.309a1.686 1.686 0 0 0-.679.622c-.258.42-.374.995-.374 1.752v1.297h3.919l-.386 2.103-.287 1.564h-3.246v8.245C19.396 23.238 24 18.179 24 12.044c0-6.627-5.373-12-12-12s-12 5.373-12 12c0 5.628 3.874 10.35 9.101 11.647Z'/%3E%3C/svg%3E")}.vpi-social-github{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12'/%3E%3C/svg%3E")}.vpi-social-instagram{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M7.03.084c-1.277.06-2.149.264-2.91.563a5.874 5.874 0 0 0-2.124 1.388 5.878 5.878 0 0 0-1.38 2.127C.321 4.926.12 5.8.064 7.076.008 8.354-.005 8.764.001 12.023c.007 3.259.021 3.667.083 4.947.061 1.277.264 2.149.563 2.911.308.789.72 1.457 1.388 2.123a5.872 5.872 0 0 0 2.129 1.38c.763.295 1.636.496 2.913.552 1.278.056 1.689.069 4.947.063 3.257-.007 3.668-.021 4.947-.082 1.28-.06 2.147-.265 2.91-.563a5.881 5.881 0 0 0 2.123-1.388 5.881 5.881 0 0 0 1.38-2.129c.295-.763.496-1.636.551-2.912.056-1.28.07-1.69.063-4.948-.006-3.258-.02-3.667-.081-4.947-.06-1.28-.264-2.148-.564-2.911a5.892 5.892 0 0 0-1.387-2.123 5.857 5.857 0 0 0-2.128-1.38C19.074.322 18.202.12 16.924.066 15.647.009 15.236-.006 11.977 0 8.718.008 8.31.021 7.03.084m.14 21.693c-1.17-.05-1.805-.245-2.228-.408a3.736 3.736 0 0 1-1.382-.895 3.695 3.695 0 0 1-.9-1.378c-.165-.423-.363-1.058-.417-2.228-.06-1.264-.072-1.644-.08-4.848-.006-3.204.006-3.583.061-4.848.05-1.169.246-1.805.408-2.228.216-.561.477-.96.895-1.382a3.705 3.705 0 0 1 1.379-.9c.423-.165 1.057-.361 2.227-.417 1.265-.06 1.644-.072 4.848-.08 3.203-.006 3.583.006 4.85.062 1.168.05 1.804.244 2.227.408.56.216.96.475 1.382.895.421.42.681.817.9 1.378.165.422.362 1.056.417 2.227.06 1.265.074 1.645.08 4.848.005 3.203-.006 3.583-.061 4.848-.051 1.17-.245 1.805-.408 2.23-.216.56-.477.96-.896 1.38a3.705 3.705 0 0 1-1.378.9c-.422.165-1.058.362-2.226.418-1.266.06-1.645.072-4.85.079-3.204.007-3.582-.006-4.848-.06m9.783-16.192a1.44 1.44 0 1 0 1.437-1.442 1.44 1.44 0 0 0-1.437 1.442M5.839 12.012a6.161 6.161 0 1 0 12.323-.024 6.162 6.162 0 0 0-12.323.024M8 12.008A4 4 0 1 1 12.008 16 4 4 0 0 1 8 12.008'/%3E%3C/svg%3E")}.vpi-social-linkedin{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.447 20.452h-3.554v-5.569c0-1.328-.027-3.037-1.852-3.037-1.853 0-2.136 1.445-2.136 2.939v5.667H9.351V9h3.414v1.561h.046c.477-.9 1.637-1.85 3.37-1.85 3.601 0 4.267 2.37 4.267 5.455v6.286zM5.337 7.433a2.062 2.062 0 0 1-2.063-2.065 2.064 2.064 0 1 1 2.063 2.065zm1.782 13.019H3.555V9h3.564v11.452zM22.225 0H1.771C.792 0 0 .774 0 1.729v20.542C0 23.227.792 24 1.771 24h20.451C23.2 24 24 23.227 24 22.271V1.729C24 .774 23.2 0 22.222 0h.003z'/%3E%3C/svg%3E")}.vpi-social-mastodon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.268 5.313c-.35-2.578-2.617-4.61-5.304-5.004C17.51.242 15.792 0 11.813 0h-.03c-3.98 0-4.835.242-5.288.309C3.882.692 1.496 2.518.917 5.127.64 6.412.61 7.837.661 9.143c.074 1.874.088 3.745.26 5.611.118 1.24.325 2.47.62 3.68.55 2.237 2.777 4.098 4.96 4.857 2.336.792 4.849.923 7.256.38.265-.061.527-.132.786-.213.585-.184 1.27-.39 1.774-.753a.057.057 0 0 0 .023-.043v-1.809a.052.052 0 0 0-.02-.041.053.053 0 0 0-.046-.01 20.282 20.282 0 0 1-4.709.545c-2.73 0-3.463-1.284-3.674-1.818a5.593 5.593 0 0 1-.319-1.433.053.053 0 0 1 .066-.054c1.517.363 3.072.546 4.632.546.376 0 .75 0 1.125-.01 1.57-.044 3.224-.124 4.768-.422.038-.008.077-.015.11-.024 2.435-.464 4.753-1.92 4.989-5.604.008-.145.03-1.52.03-1.67.002-.512.167-3.63-.024-5.545zm-3.748 9.195h-2.561V8.29c0-1.309-.55-1.976-1.67-1.976-1.23 0-1.846.79-1.846 2.35v3.403h-2.546V8.663c0-1.56-.617-2.35-1.848-2.35-1.112 0-1.668.668-1.67 1.977v6.218H4.822V8.102c0-1.31.337-2.35 1.011-3.12.696-.77 1.608-1.164 2.74-1.164 1.311 0 2.302.5 2.962 1.498l.638 1.06.638-1.06c.66-.999 1.65-1.498 2.96-1.498 1.13 0 2.043.395 2.74 1.164.675.77 1.012 1.81 1.012 3.12z'/%3E%3C/svg%3E")}.vpi-social-npm{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M1.763 0C.786 0 0 .786 0 1.763v20.474C0 23.214.786 24 1.763 24h20.474c.977 0 1.763-.786 1.763-1.763V1.763C24 .786 23.214 0 22.237 0zM5.13 5.323l13.837.019-.009 13.836h-3.464l.01-10.382h-3.456L12.04 19.17H5.113z'/%3E%3C/svg%3E")}.vpi-social-slack{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M5.042 15.165a2.528 2.528 0 0 1-2.52 2.523A2.528 2.528 0 0 1 0 15.165a2.527 2.527 0 0 1 2.522-2.52h2.52v2.52zm1.271 0a2.527 2.527 0 0 1 2.521-2.52 2.527 2.527 0 0 1 2.521 2.52v6.313A2.528 2.528 0 0 1 8.834 24a2.528 2.528 0 0 1-2.521-2.522v-6.313zM8.834 5.042a2.528 2.528 0 0 1-2.521-2.52A2.528 2.528 0 0 1 8.834 0a2.528 2.528 0 0 1 2.521 2.522v2.52H8.834zm0 1.271a2.528 2.528 0 0 1 2.521 2.521 2.528 2.528 0 0 1-2.521 2.521H2.522A2.528 2.528 0 0 1 0 8.834a2.528 2.528 0 0 1 2.522-2.521h6.312zm10.122 2.521a2.528 2.528 0 0 1 2.522-2.521A2.528 2.528 0 0 1 24 8.834a2.528 2.528 0 0 1-2.522 2.521h-2.522V8.834zm-1.268 0a2.528 2.528 0 0 1-2.523 2.521 2.527 2.527 0 0 1-2.52-2.521V2.522A2.527 2.527 0 0 1 15.165 0a2.528 2.528 0 0 1 2.523 2.522v6.312zm-2.523 10.122a2.528 2.528 0 0 1 2.523 2.522A2.528 2.528 0 0 1 15.165 24a2.527 2.527 0 0 1-2.52-2.522v-2.522h2.52zm0-1.268a2.527 2.527 0 0 1-2.52-2.523 2.526 2.526 0 0 1 2.52-2.52h6.313A2.527 2.527 0 0 1 24 15.165a2.528 2.528 0 0 1-2.522 2.523h-6.313z'/%3E%3C/svg%3E")}.vpi-social-twitter,.vpi-social-x{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M18.901 1.153h3.68l-8.04 9.19L24 22.846h-7.406l-5.8-7.584-6.638 7.584H.474l8.6-9.83L0 1.154h7.594l5.243 6.932ZM17.61 20.644h2.039L6.486 3.24H4.298Z'/%3E%3C/svg%3E")}.vpi-social-youtube{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.498 6.186a3.016 3.016 0 0 0-2.122-2.136C19.505 3.545 12 3.545 12 3.545s-7.505 0-9.377.505A3.017 3.017 0 0 0 .502 6.186C0 8.07 0 12 0 12s0 3.93.502 5.814a3.016 3.016 0 0 0 2.122 2.136c1.871.505 9.376.505 9.376.505s7.505 0 9.377-.505a3.015 3.015 0 0 0 2.122-2.136C24 15.93 24 12 24 12s0-3.93-.502-5.814zM9.545 15.568V8.432L15.818 12l-6.273 3.568z'/%3E%3C/svg%3E")}.visually-hidden{position:absolute;width:1px;height:1px;white-space:nowrap;clip:rect(0 0 0 0);clip-path:inset(50%);overflow:hidden}.custom-block{border:1px solid transparent;border-radius:8px;padding:16px 16px 8px;line-height:24px;font-size:var(--vp-custom-block-font-size);color:var(--vp-c-text-2)}.custom-block.info{border-color:var(--vp-custom-block-info-border);color:var(--vp-custom-block-info-text);background-color:var(--vp-custom-block-info-bg)}.custom-block.info a,.custom-block.info code{color:var(--vp-c-brand-1)}.custom-block.info a:hover,.custom-block.info a:hover>code{color:var(--vp-c-brand-2)}.custom-block.info code{background-color:var(--vp-custom-block-info-code-bg)}.custom-block.note{border-color:var(--vp-custom-block-note-border);color:var(--vp-custom-block-note-text);background-color:var(--vp-custom-block-note-bg)}.custom-block.note a,.custom-block.note code{color:var(--vp-c-brand-1)}.custom-block.note a:hover,.custom-block.note a:hover>code{color:var(--vp-c-brand-2)}.custom-block.note code{background-color:var(--vp-custom-block-note-code-bg)}.custom-block.tip{border-color:var(--vp-custom-block-tip-border);color:var(--vp-custom-block-tip-text);background-color:var(--vp-custom-block-tip-bg)}.custom-block.tip a,.custom-block.tip code{color:var(--vp-c-tip-1)}.custom-block.tip a:hover,.custom-block.tip a:hover>code{color:var(--vp-c-tip-2)}.custom-block.tip code{background-color:var(--vp-custom-block-tip-code-bg)}.custom-block.important{border-color:var(--vp-custom-block-important-border);color:var(--vp-custom-block-important-text);background-color:var(--vp-custom-block-important-bg)}.custom-block.important a,.custom-block.important code{color:var(--vp-c-important-1)}.custom-block.important a:hover,.custom-block.important a:hover>code{color:var(--vp-c-important-2)}.custom-block.important code{background-color:var(--vp-custom-block-important-code-bg)}.custom-block.warning{border-color:var(--vp-custom-block-warning-border);color:var(--vp-custom-block-warning-text);background-color:var(--vp-custom-block-warning-bg)}.custom-block.warning a,.custom-block.warning code{color:var(--vp-c-warning-1)}.custom-block.warning a:hover,.custom-block.warning a:hover>code{color:var(--vp-c-warning-2)}.custom-block.warning code{background-color:var(--vp-custom-block-warning-code-bg)}.custom-block.danger{border-color:var(--vp-custom-block-danger-border);color:var(--vp-custom-block-danger-text);background-color:var(--vp-custom-block-danger-bg)}.custom-block.danger a,.custom-block.danger code{color:var(--vp-c-danger-1)}.custom-block.danger a:hover,.custom-block.danger a:hover>code{color:var(--vp-c-danger-2)}.custom-block.danger code{background-color:var(--vp-custom-block-danger-code-bg)}.custom-block.caution{border-color:var(--vp-custom-block-caution-border);color:var(--vp-custom-block-caution-text);background-color:var(--vp-custom-block-caution-bg)}.custom-block.caution a,.custom-block.caution code{color:var(--vp-c-caution-1)}.custom-block.caution a:hover,.custom-block.caution a:hover>code{color:var(--vp-c-caution-2)}.custom-block.caution code{background-color:var(--vp-custom-block-caution-code-bg)}.custom-block.details{border-color:var(--vp-custom-block-details-border);color:var(--vp-custom-block-details-text);background-color:var(--vp-custom-block-details-bg)}.custom-block.details a{color:var(--vp-c-brand-1)}.custom-block.details a:hover,.custom-block.details a:hover>code{color:var(--vp-c-brand-2)}.custom-block.details code{background-color:var(--vp-custom-block-details-code-bg)}.custom-block-title{font-weight:600}.custom-block p+p{margin:8px 0}.custom-block.details summary{margin:0 0 8px;font-weight:700;cursor:pointer;-webkit-user-select:none;user-select:none}.custom-block.details summary+p{margin:8px 0}.custom-block a{color:inherit;font-weight:600;text-decoration:underline;text-underline-offset:2px;transition:opacity .25s}.custom-block a:hover{opacity:.75}.custom-block code{font-size:var(--vp-custom-block-code-font-size)}.custom-block.custom-block th,.custom-block.custom-block blockquote>p{font-size:var(--vp-custom-block-font-size);color:inherit}.dark .vp-code span{color:var(--shiki-dark, inherit)}html:not(.dark) .vp-code span{color:var(--shiki-light, inherit)}.vp-code-group{margin-top:16px}.vp-code-group .tabs{position:relative;display:flex;margin-right:-24px;margin-left:-24px;padding:0 12px;background-color:var(--vp-code-tab-bg);overflow-x:auto;overflow-y:hidden;box-shadow:inset 0 -1px var(--vp-code-tab-divider)}@media (min-width: 640px){.vp-code-group .tabs{margin-right:0;margin-left:0;border-radius:8px 8px 0 0}}.vp-code-group .tabs input{position:fixed;opacity:0;pointer-events:none}.vp-code-group .tabs label{position:relative;display:inline-block;border-bottom:1px solid transparent;padding:0 12px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-code-tab-text-color);white-space:nowrap;cursor:pointer;transition:color .25s}.vp-code-group .tabs label:after{position:absolute;right:8px;bottom:-1px;left:8px;z-index:1;height:2px;border-radius:2px;content:"";background-color:transparent;transition:background-color .25s}.vp-code-group label:hover{color:var(--vp-code-tab-hover-text-color)}.vp-code-group input:checked+label{color:var(--vp-code-tab-active-text-color)}.vp-code-group input:checked+label:after{background-color:var(--vp-code-tab-active-bar-color)}.vp-code-group div[class*=language-],.vp-block{display:none;margin-top:0!important;border-top-left-radius:0!important;border-top-right-radius:0!important}.vp-code-group div[class*=language-].active,.vp-block.active{display:block}.vp-block{padding:20px 24px}.vp-doc h1,.vp-doc h2,.vp-doc h3,.vp-doc h4,.vp-doc h5,.vp-doc h6{position:relative;font-weight:600;outline:none}.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:28px}.vp-doc h2{margin:48px 0 16px;border-top:1px solid var(--vp-c-divider);padding-top:24px;letter-spacing:-.02em;line-height:32px;font-size:24px}.vp-doc h3{margin:32px 0 0;letter-spacing:-.01em;line-height:28px;font-size:20px}.vp-doc .header-anchor{position:absolute;top:0;left:0;margin-left:-.87em;font-weight:500;-webkit-user-select:none;user-select:none;opacity:0;text-decoration:none;transition:color .25s,opacity .25s}.vp-doc .header-anchor:before{content:var(--vp-header-anchor-symbol)}.vp-doc h1:hover .header-anchor,.vp-doc h1 .header-anchor:focus,.vp-doc h2:hover .header-anchor,.vp-doc h2 .header-anchor:focus,.vp-doc h3:hover .header-anchor,.vp-doc h3 .header-anchor:focus,.vp-doc h4:hover .header-anchor,.vp-doc h4 .header-anchor:focus,.vp-doc h5:hover .header-anchor,.vp-doc h5 .header-anchor:focus,.vp-doc h6:hover .header-anchor,.vp-doc h6 .header-anchor:focus{opacity:1}@media (min-width: 768px){.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:32px}}.vp-doc h2 .header-anchor{top:24px}.vp-doc p,.vp-doc summary{margin:16px 0}.vp-doc p{line-height:28px}.vp-doc blockquote{margin:16px 0;border-left:2px solid var(--vp-c-divider);padding-left:16px;transition:border-color .5s}.vp-doc blockquote>p{margin:0;font-size:16px;color:var(--vp-c-text-2);transition:color .5s}.vp-doc a{font-weight:500;color:var(--vp-c-brand-1);text-decoration:underline;text-underline-offset:2px;transition:color .25s,opacity .25s}.vp-doc a:hover{color:var(--vp-c-brand-2)}.vp-doc strong{font-weight:600}.vp-doc ul,.vp-doc ol{padding-left:1.25rem;margin:16px 0}.vp-doc ul{list-style:disc}.vp-doc ol{list-style:decimal}.vp-doc li+li{margin-top:8px}.vp-doc li>ol,.vp-doc li>ul{margin:8px 0 0}.vp-doc table{display:block;border-collapse:collapse;margin:20px 0;overflow-x:auto}.vp-doc tr{background-color:var(--vp-c-bg);border-top:1px solid var(--vp-c-divider);transition:background-color .5s}.vp-doc tr:nth-child(2n){background-color:var(--vp-c-bg-soft)}.vp-doc th,.vp-doc td{border:1px solid var(--vp-c-divider);padding:8px 16px}.vp-doc th{text-align:left;font-size:14px;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-doc td{font-size:14px}.vp-doc hr{margin:16px 0;border:none;border-top:1px solid var(--vp-c-divider)}.vp-doc .custom-block{margin:16px 0}.vp-doc .custom-block p{margin:8px 0;line-height:24px}.vp-doc .custom-block p:first-child{margin:0}.vp-doc .custom-block div[class*=language-]{margin:8px 0;border-radius:8px}.vp-doc .custom-block div[class*=language-] code{font-weight:400;background-color:transparent}.vp-doc .custom-block .vp-code-group .tabs{margin:0;border-radius:8px 8px 0 0}.vp-doc :not(pre,h1,h2,h3,h4,h5,h6)>code{font-size:var(--vp-code-font-size);color:var(--vp-code-color)}.vp-doc :not(pre)>code{border-radius:4px;padding:3px 6px;background-color:var(--vp-code-bg);transition:color .25s,background-color .5s}.vp-doc a>code{color:var(--vp-code-link-color)}.vp-doc a:hover>code{color:var(--vp-code-link-hover-color)}.vp-doc h1>code,.vp-doc h2>code,.vp-doc h3>code{font-size:.9em}.vp-doc div[class*=language-],.vp-block{position:relative;margin:16px -24px;background-color:var(--vp-code-block-bg);overflow-x:auto;transition:background-color .5s}@media (min-width: 640px){.vp-doc div[class*=language-],.vp-block{border-radius:8px;margin:16px 0}}@media (max-width: 639px){.vp-doc li div[class*=language-]{border-radius:8px 0 0 8px}}.vp-doc div[class*=language-]+div[class*=language-],.vp-doc div[class$=-api]+div[class*=language-],.vp-doc div[class*=language-]+div[class$=-api]>div[class*=language-]{margin-top:-8px}.vp-doc [class*=language-] pre,.vp-doc [class*=language-] code{direction:ltr;text-align:left;white-space:pre;word-spacing:normal;word-break:normal;word-wrap:normal;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-hyphens:none;-moz-hyphens:none;-ms-hyphens:none;hyphens:none}.vp-doc [class*=language-] pre{position:relative;z-index:1;margin:0;padding:20px 0;background:transparent;overflow-x:auto}.vp-doc [class*=language-] code{display:block;padding:0 24px;width:fit-content;min-width:100%;line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-block-color);transition:color .5s}.vp-doc [class*=language-] code .highlighted{background-color:var(--vp-code-line-highlight-color);transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .highlighted.error{background-color:var(--vp-code-line-error-color)}.vp-doc [class*=language-] code .highlighted.warning{background-color:var(--vp-code-line-warning-color)}.vp-doc [class*=language-] code .diff{transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .diff:before{position:absolute;left:10px}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){filter:blur(.095rem);opacity:.4;transition:filter .35s,opacity .35s}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){opacity:.7;transition:filter .35s,opacity .35s}.vp-doc [class*=language-]:hover .has-focused-lines .line:not(.has-focus){filter:blur(0);opacity:1}.vp-doc [class*=language-] code .diff.remove{background-color:var(--vp-code-line-diff-remove-color);opacity:.7}.vp-doc [class*=language-] code .diff.remove:before{content:"-";color:var(--vp-code-line-diff-remove-symbol-color)}.vp-doc [class*=language-] code .diff.add{background-color:var(--vp-code-line-diff-add-color)}.vp-doc [class*=language-] code .diff.add:before{content:"+";color:var(--vp-code-line-diff-add-symbol-color)}.vp-doc div[class*=language-].line-numbers-mode{padding-left:32px}.vp-doc .line-numbers-wrapper{position:absolute;top:0;bottom:0;left:0;z-index:3;border-right:1px solid var(--vp-code-block-divider-color);padding-top:20px;width:32px;text-align:center;font-family:var(--vp-font-family-mono);line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-line-number-color);transition:border-color .5s,color .5s}.vp-doc [class*=language-]>button.copy{direction:ltr;position:absolute;top:12px;right:12px;z-index:3;border:1px solid var(--vp-code-copy-code-border-color);border-radius:4px;width:40px;height:40px;background-color:var(--vp-code-copy-code-bg);opacity:0;cursor:pointer;background-image:var(--vp-icon-copy);background-position:50%;background-size:20px;background-repeat:no-repeat;transition:border-color .25s,background-color .25s,opacity .25s}.vp-doc [class*=language-]:hover>button.copy,.vp-doc [class*=language-]>button.copy:focus{opacity:1}.vp-doc [class*=language-]>button.copy:hover,.vp-doc [class*=language-]>button.copy.copied{border-color:var(--vp-code-copy-code-hover-border-color);background-color:var(--vp-code-copy-code-hover-bg)}.vp-doc [class*=language-]>button.copy.copied,.vp-doc [class*=language-]>button.copy:hover.copied{border-radius:0 4px 4px 0;background-color:var(--vp-code-copy-code-hover-bg);background-image:var(--vp-icon-copied)}.vp-doc [class*=language-]>button.copy.copied:before,.vp-doc [class*=language-]>button.copy:hover.copied:before{position:relative;top:-1px;transform:translate(calc(-100% - 1px));display:flex;justify-content:center;align-items:center;border:1px solid var(--vp-code-copy-code-hover-border-color);border-right:0;border-radius:4px 0 0 4px;padding:0 10px;width:fit-content;height:40px;text-align:center;font-size:12px;font-weight:500;color:var(--vp-code-copy-code-active-text);background-color:var(--vp-code-copy-code-hover-bg);white-space:nowrap;content:var(--vp-code-copy-copied-text-content)}.vp-doc [class*=language-]>span.lang{position:absolute;top:2px;right:8px;z-index:2;font-size:12px;font-weight:500;color:var(--vp-code-lang-color);transition:color .4s,opacity .4s}.vp-doc [class*=language-]:hover>button.copy+span.lang,.vp-doc [class*=language-]>button.copy:focus+span.lang{opacity:0}.vp-doc .VPTeamMembers{margin-top:24px}.vp-doc .VPTeamMembers.small.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}.vp-doc .VPTeamMembers.small.count-2 .container,.vp-doc .VPTeamMembers.small.count-3 .container{max-width:100%!important}.vp-doc .VPTeamMembers.medium.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}:is(.vp-external-link-icon,.vp-doc a[href*="://"],.vp-doc a[target=_blank]):not(.no-icon):after{display:inline-block;margin-top:-1px;margin-left:4px;width:11px;height:11px;background:currentColor;color:var(--vp-c-text-3);flex-shrink:0;--icon: url("data:image/svg+xml, %3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24' %3E%3Cpath d='M0 0h24v24H0V0z' fill='none' /%3E%3Cpath d='M9 5v2h6.59L4 18.59 5.41 20 17 8.41V15h2V5H9z' /%3E%3C/svg%3E");-webkit-mask-image:var(--icon);mask-image:var(--icon)}.vp-external-link-icon:after{content:""}.external-link-icon-enabled :is(.vp-doc a[href*="://"],.vp-doc a[target=_blank]):after{content:"";color:currentColor}.vp-sponsor{border-radius:16px;overflow:hidden}.vp-sponsor.aside{border-radius:12px}.vp-sponsor-section+.vp-sponsor-section{margin-top:4px}.vp-sponsor-tier{margin:0 0 4px!important;text-align:center;letter-spacing:1px!important;line-height:24px;width:100%;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-sponsor.normal .vp-sponsor-tier{padding:13px 0 11px;font-size:14px}.vp-sponsor.aside .vp-sponsor-tier{padding:9px 0 7px;font-size:12px}.vp-sponsor-grid+.vp-sponsor-tier{margin-top:4px}.vp-sponsor-grid{display:flex;flex-wrap:wrap;gap:4px}.vp-sponsor-grid.xmini .vp-sponsor-grid-link{height:64px}.vp-sponsor-grid.xmini .vp-sponsor-grid-image{max-width:64px;max-height:22px}.vp-sponsor-grid.mini .vp-sponsor-grid-link{height:72px}.vp-sponsor-grid.mini .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.small .vp-sponsor-grid-link{height:96px}.vp-sponsor-grid.small .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.medium .vp-sponsor-grid-link{height:112px}.vp-sponsor-grid.medium .vp-sponsor-grid-image{max-width:120px;max-height:36px}.vp-sponsor-grid.big .vp-sponsor-grid-link{height:184px}.vp-sponsor-grid.big .vp-sponsor-grid-image{max-width:192px;max-height:56px}.vp-sponsor-grid[data-vp-grid="2"] .vp-sponsor-grid-item{width:calc((100% - 4px)/2)}.vp-sponsor-grid[data-vp-grid="3"] .vp-sponsor-grid-item{width:calc((100% - 4px * 2) / 3)}.vp-sponsor-grid[data-vp-grid="4"] .vp-sponsor-grid-item{width:calc((100% - 12px)/4)}.vp-sponsor-grid[data-vp-grid="5"] .vp-sponsor-grid-item{width:calc((100% - 16px)/5)}.vp-sponsor-grid[data-vp-grid="6"] .vp-sponsor-grid-item{width:calc((100% - 4px * 5) / 6)}.vp-sponsor-grid-item{flex-shrink:0;width:100%;background-color:var(--vp-c-bg-soft);transition:background-color .25s}.vp-sponsor-grid-item:hover{background-color:var(--vp-c-default-soft)}.vp-sponsor-grid-item:hover .vp-sponsor-grid-image{filter:grayscale(0) invert(0)}.vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.dark .vp-sponsor-grid-item:hover{background-color:var(--vp-c-white)}.dark .vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.vp-sponsor-grid-link{display:flex}.vp-sponsor-grid-box{display:flex;justify-content:center;align-items:center;width:100%}.vp-sponsor-grid-image{max-width:100%;filter:grayscale(1);transition:filter .25s}.dark .vp-sponsor-grid-image{filter:grayscale(1) invert(1)}.VPBadge{display:inline-block;margin-left:2px;border:1px solid transparent;border-radius:12px;padding:0 10px;line-height:22px;font-size:12px;font-weight:500;transform:translateY(-2px)}.VPBadge.small{padding:0 6px;line-height:18px;font-size:10px;transform:translateY(-8px)}.VPDocFooter .VPBadge{display:none}.vp-doc h1>.VPBadge{margin-top:4px;vertical-align:top}.vp-doc h2>.VPBadge{margin-top:3px;padding:0 8px;vertical-align:top}.vp-doc h3>.VPBadge{vertical-align:middle}.vp-doc h4>.VPBadge,.vp-doc h5>.VPBadge,.vp-doc h6>.VPBadge{vertical-align:middle;line-height:18px}.VPBadge.info{border-color:var(--vp-badge-info-border);color:var(--vp-badge-info-text);background-color:var(--vp-badge-info-bg)}.VPBadge.tip{border-color:var(--vp-badge-tip-border);color:var(--vp-badge-tip-text);background-color:var(--vp-badge-tip-bg)}.VPBadge.warning{border-color:var(--vp-badge-warning-border);color:var(--vp-badge-warning-text);background-color:var(--vp-badge-warning-bg)}.VPBadge.danger{border-color:var(--vp-badge-danger-border);color:var(--vp-badge-danger-text);background-color:var(--vp-badge-danger-bg)}.VPBackdrop[data-v-b06cdb19]{position:fixed;top:0;right:0;bottom:0;left:0;z-index:var(--vp-z-index-backdrop);background:var(--vp-backdrop-bg-color);transition:opacity .5s}.VPBackdrop.fade-enter-from[data-v-b06cdb19],.VPBackdrop.fade-leave-to[data-v-b06cdb19]{opacity:0}.VPBackdrop.fade-leave-active[data-v-b06cdb19]{transition-duration:.25s}@media (min-width: 1280px){.VPBackdrop[data-v-b06cdb19]{display:none}}.NotFound[data-v-792811ca]{padding:64px 24px 96px;text-align:center}@media (min-width: 768px){.NotFound[data-v-792811ca]{padding:96px 32px 168px}}.code[data-v-792811ca]{line-height:64px;font-size:64px;font-weight:600}.title[data-v-792811ca]{padding-top:12px;letter-spacing:2px;line-height:20px;font-size:20px;font-weight:700}.divider[data-v-792811ca]{margin:24px auto 18px;width:64px;height:1px;background-color:var(--vp-c-divider)}.quote[data-v-792811ca]{margin:0 auto;max-width:256px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.action[data-v-792811ca]{padding-top:20px}.link[data-v-792811ca]{display:inline-block;border:1px solid var(--vp-c-brand-1);border-radius:16px;padding:3px 16px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:border-color .25s,color .25s}.link[data-v-792811ca]:hover{border-color:var(--vp-c-brand-2);color:var(--vp-c-brand-2)}.root[data-v-3f927ebe]{position:relative;z-index:1}.nested[data-v-3f927ebe]{padding-right:16px;padding-left:16px}.outline-link[data-v-3f927ebe]{display:block;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-2);white-space:nowrap;overflow:hidden;text-overflow:ellipsis;transition:color .5s}.outline-link[data-v-3f927ebe]:hover,.outline-link.active[data-v-3f927ebe]{color:var(--vp-c-text-1);transition:color .25s}.outline-link.nested[data-v-3f927ebe]{padding-left:13px}.VPDocAsideOutline[data-v-c14bfc45]{display:none}.VPDocAsideOutline.has-outline[data-v-c14bfc45]{display:block}.content[data-v-c14bfc45]{position:relative;border-left:1px solid var(--vp-c-divider);padding-left:16px;font-size:13px;font-weight:500}.outline-marker[data-v-c14bfc45]{position:absolute;top:32px;left:-1px;z-index:0;opacity:0;width:2px;border-radius:2px;height:18px;background-color:var(--vp-c-brand-1);transition:top .25s cubic-bezier(0,1,.5,1),background-color .5s,opacity .25s}.outline-title[data-v-c14bfc45]{line-height:32px;font-size:14px;font-weight:600}.VPDocAside[data-v-6d7b3c46]{display:flex;flex-direction:column;flex-grow:1}.spacer[data-v-6d7b3c46]{flex-grow:1}.VPDocAside[data-v-6d7b3c46] .spacer+.VPDocAsideSponsors,.VPDocAside[data-v-6d7b3c46] .spacer+.VPDocAsideCarbonAds{margin-top:24px}.VPDocAside[data-v-6d7b3c46] .VPDocAsideSponsors+.VPDocAsideCarbonAds{margin-top:16px}.VPLastUpdated[data-v-9da12f1d]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 640px){.VPLastUpdated[data-v-9da12f1d]{line-height:32px;font-size:14px;font-weight:500}}.VPDocFooter[data-v-87be45d1]{margin-top:64px}.edit-info[data-v-87be45d1]{padding-bottom:18px}@media (min-width: 640px){.edit-info[data-v-87be45d1]{display:flex;justify-content:space-between;align-items:center;padding-bottom:14px}}.edit-link-button[data-v-87be45d1]{display:flex;align-items:center;border:0;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.edit-link-button[data-v-87be45d1]:hover{color:var(--vp-c-brand-2)}.edit-link-icon[data-v-87be45d1]{margin-right:8px}.prev-next[data-v-87be45d1]{border-top:1px solid var(--vp-c-divider);padding-top:24px;display:grid;grid-row-gap:8px}@media (min-width: 640px){.prev-next[data-v-87be45d1]{grid-template-columns:repeat(2,1fr);grid-column-gap:16px}}.pager-link[data-v-87be45d1]{display:block;border:1px solid var(--vp-c-divider);border-radius:8px;padding:11px 16px 13px;width:100%;height:100%;transition:border-color .25s}.pager-link[data-v-87be45d1]:hover{border-color:var(--vp-c-brand-1)}.pager-link.next[data-v-87be45d1]{margin-left:auto;text-align:right}.desc[data-v-87be45d1]{display:block;line-height:20px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.title[data-v-87be45d1]{display:block;line-height:20px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.VPDoc[data-v-83890dd9]{padding:32px 24px 96px;width:100%}@media (min-width: 768px){.VPDoc[data-v-83890dd9]{padding:48px 32px 128px}}@media (min-width: 960px){.VPDoc[data-v-83890dd9]{padding:48px 32px 0}.VPDoc:not(.has-sidebar) .container[data-v-83890dd9]{display:flex;justify-content:center;max-width:992px}.VPDoc:not(.has-sidebar) .content[data-v-83890dd9]{max-width:752px}}@media (min-width: 1280px){.VPDoc .container[data-v-83890dd9]{display:flex;justify-content:center}.VPDoc .aside[data-v-83890dd9]{display:block}}@media (min-width: 1440px){.VPDoc:not(.has-sidebar) .content[data-v-83890dd9]{max-width:784px}.VPDoc:not(.has-sidebar) .container[data-v-83890dd9]{max-width:1104px}}.container[data-v-83890dd9]{margin:0 auto;width:100%}.aside[data-v-83890dd9]{position:relative;display:none;order:2;flex-grow:1;padding-left:32px;width:100%;max-width:256px}.left-aside[data-v-83890dd9]{order:1;padding-left:unset;padding-right:32px}.aside-container[data-v-83890dd9]{position:fixed;top:0;padding-top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + var(--vp-doc-top-height, 0px) + 48px);width:224px;height:100vh;overflow-x:hidden;overflow-y:auto;scrollbar-width:none}.aside-container[data-v-83890dd9]::-webkit-scrollbar{display:none}.aside-curtain[data-v-83890dd9]{position:fixed;bottom:0;z-index:10;width:224px;height:32px;background:linear-gradient(transparent,var(--vp-c-bg) 70%)}.aside-content[data-v-83890dd9]{display:flex;flex-direction:column;min-height:calc(100vh - (var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px));padding-bottom:32px}.content[data-v-83890dd9]{position:relative;margin:0 auto;width:100%}@media (min-width: 960px){.content[data-v-83890dd9]{padding:0 32px 128px}}@media (min-width: 1280px){.content[data-v-83890dd9]{order:1;margin:0;min-width:640px}}.content-container[data-v-83890dd9]{margin:0 auto}.VPDoc.has-aside .content-container[data-v-83890dd9]{max-width:688px}.VPButton[data-v-14206e74]{display:inline-block;border:1px solid transparent;text-align:center;font-weight:600;white-space:nowrap;transition:color .25s,border-color .25s,background-color .25s}.VPButton[data-v-14206e74]:active{transition:color .1s,border-color .1s,background-color .1s}.VPButton.medium[data-v-14206e74]{border-radius:20px;padding:0 20px;line-height:38px;font-size:14px}.VPButton.big[data-v-14206e74]{border-radius:24px;padding:0 24px;line-height:46px;font-size:16px}.VPButton.brand[data-v-14206e74]{border-color:var(--vp-button-brand-border);color:var(--vp-button-brand-text);background-color:var(--vp-button-brand-bg)}.VPButton.brand[data-v-14206e74]:hover{border-color:var(--vp-button-brand-hover-border);color:var(--vp-button-brand-hover-text);background-color:var(--vp-button-brand-hover-bg)}.VPButton.brand[data-v-14206e74]:active{border-color:var(--vp-button-brand-active-border);color:var(--vp-button-brand-active-text);background-color:var(--vp-button-brand-active-bg)}.VPButton.alt[data-v-14206e74]{border-color:var(--vp-button-alt-border);color:var(--vp-button-alt-text);background-color:var(--vp-button-alt-bg)}.VPButton.alt[data-v-14206e74]:hover{border-color:var(--vp-button-alt-hover-border);color:var(--vp-button-alt-hover-text);background-color:var(--vp-button-alt-hover-bg)}.VPButton.alt[data-v-14206e74]:active{border-color:var(--vp-button-alt-active-border);color:var(--vp-button-alt-active-text);background-color:var(--vp-button-alt-active-bg)}.VPButton.sponsor[data-v-14206e74]{border-color:var(--vp-button-sponsor-border);color:var(--vp-button-sponsor-text);background-color:var(--vp-button-sponsor-bg)}.VPButton.sponsor[data-v-14206e74]:hover{border-color:var(--vp-button-sponsor-hover-border);color:var(--vp-button-sponsor-hover-text);background-color:var(--vp-button-sponsor-hover-bg)}.VPButton.sponsor[data-v-14206e74]:active{border-color:var(--vp-button-sponsor-active-border);color:var(--vp-button-sponsor-active-text);background-color:var(--vp-button-sponsor-active-bg)}html:not(.dark) .VPImage.dark[data-v-35a7d0b8]{display:none}.dark .VPImage.light[data-v-35a7d0b8]{display:none}.VPHero[data-v-955009fc]{margin-top:calc((var(--vp-nav-height) + var(--vp-layout-top-height, 0px)) * -1);padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px) 24px 48px}@media (min-width: 640px){.VPHero[data-v-955009fc]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 48px 64px}}@media (min-width: 960px){.VPHero[data-v-955009fc]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 64px 64px}}.container[data-v-955009fc]{display:flex;flex-direction:column;margin:0 auto;max-width:1152px}@media (min-width: 960px){.container[data-v-955009fc]{flex-direction:row}}.main[data-v-955009fc]{position:relative;z-index:10;order:2;flex-grow:1;flex-shrink:0}.VPHero.has-image .container[data-v-955009fc]{text-align:center}@media (min-width: 960px){.VPHero.has-image .container[data-v-955009fc]{text-align:left}}@media (min-width: 960px){.main[data-v-955009fc]{order:1;width:calc((100% / 3) * 2)}.VPHero.has-image .main[data-v-955009fc]{max-width:592px}}.name[data-v-955009fc],.text[data-v-955009fc]{max-width:392px;letter-spacing:-.4px;line-height:40px;font-size:32px;font-weight:700;white-space:pre-wrap}.VPHero.has-image .name[data-v-955009fc],.VPHero.has-image .text[data-v-955009fc]{margin:0 auto}.name[data-v-955009fc]{color:var(--vp-home-hero-name-color)}.clip[data-v-955009fc]{background:var(--vp-home-hero-name-background);-webkit-background-clip:text;background-clip:text;-webkit-text-fill-color:var(--vp-home-hero-name-color)}@media (min-width: 640px){.name[data-v-955009fc],.text[data-v-955009fc]{max-width:576px;line-height:56px;font-size:48px}}@media (min-width: 960px){.name[data-v-955009fc],.text[data-v-955009fc]{line-height:64px;font-size:56px}.VPHero.has-image .name[data-v-955009fc],.VPHero.has-image .text[data-v-955009fc]{margin:0}}.tagline[data-v-955009fc]{padding-top:8px;max-width:392px;line-height:28px;font-size:18px;font-weight:500;white-space:pre-wrap;color:var(--vp-c-text-2)}.VPHero.has-image .tagline[data-v-955009fc]{margin:0 auto}@media (min-width: 640px){.tagline[data-v-955009fc]{padding-top:12px;max-width:576px;line-height:32px;font-size:20px}}@media (min-width: 960px){.tagline[data-v-955009fc]{line-height:36px;font-size:24px}.VPHero.has-image .tagline[data-v-955009fc]{margin:0}}.actions[data-v-955009fc]{display:flex;flex-wrap:wrap;margin:-6px;padding-top:24px}.VPHero.has-image .actions[data-v-955009fc]{justify-content:center}@media (min-width: 640px){.actions[data-v-955009fc]{padding-top:32px}}@media (min-width: 960px){.VPHero.has-image .actions[data-v-955009fc]{justify-content:flex-start}}.action[data-v-955009fc]{flex-shrink:0;padding:6px}.image[data-v-955009fc]{order:1;margin:-76px -24px -48px}@media (min-width: 640px){.image[data-v-955009fc]{margin:-108px -24px -48px}}@media (min-width: 960px){.image[data-v-955009fc]{flex-grow:1;order:2;margin:0;min-height:100%}}.image-container[data-v-955009fc]{position:relative;margin:0 auto;width:320px;height:320px}@media (min-width: 640px){.image-container[data-v-955009fc]{width:392px;height:392px}}@media (min-width: 960px){.image-container[data-v-955009fc]{display:flex;justify-content:center;align-items:center;width:100%;height:100%;transform:translate(-32px,-32px)}}.image-bg[data-v-955009fc]{position:absolute;top:50%;left:50%;border-radius:50%;width:192px;height:192px;background-image:var(--vp-home-hero-image-background-image);filter:var(--vp-home-hero-image-filter);transform:translate(-50%,-50%)}@media (min-width: 640px){.image-bg[data-v-955009fc]{width:256px;height:256px}}@media (min-width: 960px){.image-bg[data-v-955009fc]{width:320px;height:320px}}[data-v-955009fc] .image-src{position:absolute;top:50%;left:50%;max-width:192px;max-height:192px;transform:translate(-50%,-50%)}@media (min-width: 640px){[data-v-955009fc] .image-src{max-width:256px;max-height:256px}}@media (min-width: 960px){[data-v-955009fc] .image-src{max-width:320px;max-height:320px}}.VPFeature[data-v-f5e9645b]{display:block;border:1px solid var(--vp-c-bg-soft);border-radius:12px;height:100%;background-color:var(--vp-c-bg-soft);transition:border-color .25s,background-color .25s}.VPFeature.link[data-v-f5e9645b]:hover{border-color:var(--vp-c-brand-1)}.box[data-v-f5e9645b]{display:flex;flex-direction:column;padding:24px;height:100%}.box[data-v-f5e9645b]>.VPImage{margin-bottom:20px}.icon[data-v-f5e9645b]{display:flex;justify-content:center;align-items:center;margin-bottom:20px;border-radius:6px;background-color:var(--vp-c-default-soft);width:48px;height:48px;font-size:24px;transition:background-color .25s}.title[data-v-f5e9645b]{line-height:24px;font-size:16px;font-weight:600}.details[data-v-f5e9645b]{flex-grow:1;padding-top:8px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.link-text[data-v-f5e9645b]{padding-top:8px}.link-text-value[data-v-f5e9645b]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.link-text-icon[data-v-f5e9645b]{margin-left:6px}.VPFeatures[data-v-d0a190d7]{position:relative;padding:0 24px}@media (min-width: 640px){.VPFeatures[data-v-d0a190d7]{padding:0 48px}}@media (min-width: 960px){.VPFeatures[data-v-d0a190d7]{padding:0 64px}}.container[data-v-d0a190d7]{margin:0 auto;max-width:1152px}.items[data-v-d0a190d7]{display:flex;flex-wrap:wrap;margin:-8px}.item[data-v-d0a190d7]{padding:8px;width:100%}@media (min-width: 640px){.item.grid-2[data-v-d0a190d7],.item.grid-4[data-v-d0a190d7],.item.grid-6[data-v-d0a190d7]{width:50%}}@media (min-width: 768px){.item.grid-2[data-v-d0a190d7],.item.grid-4[data-v-d0a190d7]{width:50%}.item.grid-3[data-v-d0a190d7],.item.grid-6[data-v-d0a190d7]{width:calc(100% / 3)}}@media (min-width: 960px){.item.grid-4[data-v-d0a190d7]{width:25%}}.container[data-v-c43247eb]{margin:auto;width:100%;max-width:1280px;padding:0 24px}@media (min-width: 640px){.container[data-v-c43247eb]{padding:0 48px}}@media (min-width: 960px){.container[data-v-c43247eb]{width:100%;padding:0 64px}}.vp-doc[data-v-c43247eb] .VPHomeSponsors,.vp-doc[data-v-c43247eb] .VPTeamPage{margin-left:var(--vp-offset, calc(50% - 50vw) );margin-right:var(--vp-offset, calc(50% - 50vw) )}.vp-doc[data-v-c43247eb] .VPHomeSponsors h2{border-top:none;letter-spacing:normal}.vp-doc[data-v-c43247eb] .VPHomeSponsors a,.vp-doc[data-v-c43247eb] .VPTeamPage a{text-decoration:none}.VPHome[data-v-cbb6ec48]{margin-bottom:96px}@media (min-width: 768px){.VPHome[data-v-cbb6ec48]{margin-bottom:128px}}.VPContent[data-v-91765379]{flex-grow:1;flex-shrink:0;margin:var(--vp-layout-top-height, 0px) auto 0;width:100%}.VPContent.is-home[data-v-91765379]{width:100%;max-width:100%}.VPContent.has-sidebar[data-v-91765379]{margin:0}@media (min-width: 960px){.VPContent[data-v-91765379]{padding-top:var(--vp-nav-height)}.VPContent.has-sidebar[data-v-91765379]{margin:var(--vp-layout-top-height, 0px) 0 0;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPContent.has-sidebar[data-v-91765379]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.VPFooter[data-v-c970a860]{position:relative;z-index:var(--vp-z-index-footer);border-top:1px solid var(--vp-c-gutter);padding:32px 24px;background-color:var(--vp-c-bg)}.VPFooter.has-sidebar[data-v-c970a860]{display:none}.VPFooter[data-v-c970a860] a{text-decoration-line:underline;text-underline-offset:2px;transition:color .25s}.VPFooter[data-v-c970a860] a:hover{color:var(--vp-c-text-1)}@media (min-width: 768px){.VPFooter[data-v-c970a860]{padding:32px}}.container[data-v-c970a860]{margin:0 auto;max-width:var(--vp-layout-max-width);text-align:center}.message[data-v-c970a860],.copyright[data-v-c970a860]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.VPLocalNavOutlineDropdown[data-v-47ad05d4]{padding:12px 20px 11px}@media (min-width: 960px){.VPLocalNavOutlineDropdown[data-v-47ad05d4]{padding:12px 36px 11px}}.VPLocalNavOutlineDropdown button[data-v-47ad05d4]{display:block;font-size:12px;font-weight:500;line-height:24px;color:var(--vp-c-text-2);transition:color .5s;position:relative}.VPLocalNavOutlineDropdown button[data-v-47ad05d4]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPLocalNavOutlineDropdown button.open[data-v-47ad05d4]{color:var(--vp-c-text-1)}.icon[data-v-47ad05d4]{display:inline-block;vertical-align:middle;margin-left:2px;font-size:14px;transform:rotate(0);transition:transform .25s}@media (min-width: 960px){.VPLocalNavOutlineDropdown button[data-v-47ad05d4]{font-size:14px}.icon[data-v-47ad05d4]{font-size:16px}}.open>.icon[data-v-47ad05d4]{transform:rotate(90deg)}.items[data-v-47ad05d4]{position:absolute;top:40px;right:16px;left:16px;display:grid;gap:1px;border:1px solid var(--vp-c-border);border-radius:8px;background-color:var(--vp-c-gutter);max-height:calc(var(--vp-vh, 100vh) - 86px);overflow:hidden auto;box-shadow:var(--vp-shadow-3)}@media (min-width: 960px){.items[data-v-47ad05d4]{right:auto;left:calc(var(--vp-sidebar-width) + 32px);width:320px}}.header[data-v-47ad05d4]{background-color:var(--vp-c-bg-soft)}.top-link[data-v-47ad05d4]{display:block;padding:0 16px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.outline[data-v-47ad05d4]{padding:8px 0;background-color:var(--vp-c-bg-soft)}.flyout-enter-active[data-v-47ad05d4]{transition:all .2s ease-out}.flyout-leave-active[data-v-47ad05d4]{transition:all .15s ease-in}.flyout-enter-from[data-v-47ad05d4],.flyout-leave-to[data-v-47ad05d4]{opacity:0;transform:translateY(-16px)}.VPLocalNav[data-v-070ab83d]{position:sticky;top:0;left:0;z-index:var(--vp-z-index-local-nav);border-bottom:1px solid var(--vp-c-gutter);padding-top:var(--vp-layout-top-height, 0px);width:100%;background-color:var(--vp-local-nav-bg-color)}.VPLocalNav.fixed[data-v-070ab83d]{position:fixed}@media (min-width: 960px){.VPLocalNav[data-v-070ab83d]{top:var(--vp-nav-height)}.VPLocalNav.has-sidebar[data-v-070ab83d]{padding-left:var(--vp-sidebar-width)}.VPLocalNav.empty[data-v-070ab83d]{display:none}}@media (min-width: 1280px){.VPLocalNav[data-v-070ab83d]{display:none}}@media (min-width: 1440px){.VPLocalNav.has-sidebar[data-v-070ab83d]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.container[data-v-070ab83d]{display:flex;justify-content:space-between;align-items:center}.menu[data-v-070ab83d]{display:flex;align-items:center;padding:12px 24px 11px;line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.menu[data-v-070ab83d]:hover{color:var(--vp-c-text-1);transition:color .25s}@media (min-width: 768px){.menu[data-v-070ab83d]{padding:0 32px}}@media (min-width: 960px){.menu[data-v-070ab83d]{display:none}}.menu-icon[data-v-070ab83d]{margin-right:8px;font-size:14px}.VPOutlineDropdown[data-v-070ab83d]{padding:12px 24px 11px}@media (min-width: 768px){.VPOutlineDropdown[data-v-070ab83d]{padding:12px 32px 11px}}.VPSwitch[data-v-4a1c76db]{position:relative;border-radius:11px;display:block;width:40px;height:22px;flex-shrink:0;border:1px solid var(--vp-input-border-color);background-color:var(--vp-input-switch-bg-color);transition:border-color .25s!important}.VPSwitch[data-v-4a1c76db]:hover{border-color:var(--vp-c-brand-1)}.check[data-v-4a1c76db]{position:absolute;top:1px;left:1px;width:18px;height:18px;border-radius:50%;background-color:var(--vp-c-neutral-inverse);box-shadow:var(--vp-shadow-1);transition:transform .25s!important}.icon[data-v-4a1c76db]{position:relative;display:block;width:18px;height:18px;border-radius:50%;overflow:hidden}.icon[data-v-4a1c76db] [class^=vpi-]{position:absolute;top:3px;left:3px;width:12px;height:12px;color:var(--vp-c-text-2)}.dark .icon[data-v-4a1c76db] [class^=vpi-]{color:var(--vp-c-text-1);transition:opacity .25s!important}.sun[data-v-b79b56d4]{opacity:1}.moon[data-v-b79b56d4],.dark .sun[data-v-b79b56d4]{opacity:0}.dark .moon[data-v-b79b56d4]{opacity:1}.dark .VPSwitchAppearance[data-v-b79b56d4] .check{transform:translate(18px)}.VPNavBarAppearance[data-v-ead91a81]{display:none}@media (min-width: 1280px){.VPNavBarAppearance[data-v-ead91a81]{display:flex;align-items:center}}.VPMenuGroup+.VPMenuLink[data-v-8b74d055]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.link[data-v-8b74d055]{display:block;border-radius:6px;padding:0 12px;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);white-space:nowrap;transition:background-color .25s,color .25s}.link[data-v-8b74d055]:hover{color:var(--vp-c-brand-1);background-color:var(--vp-c-default-soft)}.link.active[data-v-8b74d055]{color:var(--vp-c-brand-1)}.VPMenuGroup[data-v-48c802d0]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.VPMenuGroup[data-v-48c802d0]:first-child{margin-top:0;border-top:0;padding-top:0}.VPMenuGroup+.VPMenuGroup[data-v-48c802d0]{margin-top:12px;border-top:1px solid var(--vp-c-divider)}.title[data-v-48c802d0]{padding:0 12px;line-height:32px;font-size:14px;font-weight:600;color:var(--vp-c-text-2);white-space:nowrap;transition:color .25s}.VPMenu[data-v-97491713]{border-radius:12px;padding:12px;min-width:128px;border:1px solid var(--vp-c-divider);background-color:var(--vp-c-bg-elv);box-shadow:var(--vp-shadow-3);transition:background-color .5s;max-height:calc(100vh - var(--vp-nav-height));overflow-y:auto}.VPMenu[data-v-97491713] .group{margin:0 -12px;padding:0 12px 12px}.VPMenu[data-v-97491713] .group+.group{border-top:1px solid var(--vp-c-divider);padding:11px 12px 12px}.VPMenu[data-v-97491713] .group:last-child{padding-bottom:0}.VPMenu[data-v-97491713] .group+.item{border-top:1px solid var(--vp-c-divider);padding:11px 16px 0}.VPMenu[data-v-97491713] .item{padding:0 16px;white-space:nowrap}.VPMenu[data-v-97491713] .label{flex-grow:1;line-height:28px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.VPMenu[data-v-97491713] .action{padding-left:24px}.VPFlyout[data-v-e5380155]{position:relative}.VPFlyout[data-v-e5380155]:hover{color:var(--vp-c-brand-1);transition:color .25s}.VPFlyout:hover .text[data-v-e5380155]{color:var(--vp-c-text-2)}.VPFlyout:hover .icon[data-v-e5380155]{fill:var(--vp-c-text-2)}.VPFlyout.active .text[data-v-e5380155]{color:var(--vp-c-brand-1)}.VPFlyout.active:hover .text[data-v-e5380155]{color:var(--vp-c-brand-2)}.VPFlyout:hover .menu[data-v-e5380155],.button[aria-expanded=true]+.menu[data-v-e5380155]{opacity:1;visibility:visible;transform:translateY(0)}.button[aria-expanded=false]+.menu[data-v-e5380155]{opacity:0;visibility:hidden;transform:translateY(0)}.button[data-v-e5380155]{display:flex;align-items:center;padding:0 12px;height:var(--vp-nav-height);color:var(--vp-c-text-1);transition:color .5s}.text[data-v-e5380155]{display:flex;align-items:center;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.option-icon[data-v-e5380155]{margin-right:0;font-size:16px}.text-icon[data-v-e5380155]{margin-left:4px;font-size:14px}.icon[data-v-e5380155]{font-size:20px;transition:fill .25s}.menu[data-v-e5380155]{position:absolute;top:calc(var(--vp-nav-height) / 2 + 20px);right:0;opacity:0;visibility:hidden;transition:opacity .25s,visibility .25s,transform .25s}.VPSocialLink[data-v-717b8b75]{display:flex;justify-content:center;align-items:center;width:36px;height:36px;color:var(--vp-c-text-2);transition:color .5s}.VPSocialLink[data-v-717b8b75]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPSocialLink[data-v-717b8b75]>svg,.VPSocialLink[data-v-717b8b75]>[class^=vpi-social-]{width:20px;height:20px;fill:currentColor}.VPSocialLinks[data-v-ee7a9424]{display:flex;justify-content:center}.VPNavBarExtra[data-v-9b536d0b]{display:none;margin-right:-12px}@media (min-width: 768px){.VPNavBarExtra[data-v-9b536d0b]{display:block}}@media (min-width: 1280px){.VPNavBarExtra[data-v-9b536d0b]{display:none}}.trans-title[data-v-9b536d0b]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.item.appearance[data-v-9b536d0b],.item.social-links[data-v-9b536d0b]{display:flex;align-items:center;padding:0 12px}.item.appearance[data-v-9b536d0b]{min-width:176px}.appearance-action[data-v-9b536d0b]{margin-right:-2px}.social-links-list[data-v-9b536d0b]{margin:-4px -8px}.VPNavBarHamburger[data-v-5dea55bf]{display:flex;justify-content:center;align-items:center;width:48px;height:var(--vp-nav-height)}@media (min-width: 768px){.VPNavBarHamburger[data-v-5dea55bf]{display:none}}.container[data-v-5dea55bf]{position:relative;width:16px;height:14px;overflow:hidden}.VPNavBarHamburger:hover .top[data-v-5dea55bf]{top:0;left:0;transform:translate(4px)}.VPNavBarHamburger:hover .middle[data-v-5dea55bf]{top:6px;left:0;transform:translate(0)}.VPNavBarHamburger:hover .bottom[data-v-5dea55bf]{top:12px;left:0;transform:translate(8px)}.VPNavBarHamburger.active .top[data-v-5dea55bf]{top:6px;transform:translate(0) rotate(225deg)}.VPNavBarHamburger.active .middle[data-v-5dea55bf]{top:6px;transform:translate(16px)}.VPNavBarHamburger.active .bottom[data-v-5dea55bf]{top:6px;transform:translate(0) rotate(135deg)}.VPNavBarHamburger.active:hover .top[data-v-5dea55bf],.VPNavBarHamburger.active:hover .middle[data-v-5dea55bf],.VPNavBarHamburger.active:hover .bottom[data-v-5dea55bf]{background-color:var(--vp-c-text-2);transition:top .25s,background-color .25s,transform .25s}.top[data-v-5dea55bf],.middle[data-v-5dea55bf],.bottom[data-v-5dea55bf]{position:absolute;width:16px;height:2px;background-color:var(--vp-c-text-1);transition:top .25s,background-color .5s,transform .25s}.top[data-v-5dea55bf]{top:0;left:0;transform:translate(0)}.middle[data-v-5dea55bf]{top:6px;left:0;transform:translate(8px)}.bottom[data-v-5dea55bf]{top:12px;left:0;transform:translate(4px)}.VPNavBarMenuLink[data-v-ed5ac1f6]{display:flex;align-items:center;padding:0 12px;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.VPNavBarMenuLink.active[data-v-ed5ac1f6],.VPNavBarMenuLink[data-v-ed5ac1f6]:hover{color:var(--vp-c-brand-1)}.VPNavBarMenu[data-v-492ea56d]{display:none}@media (min-width: 768px){.VPNavBarMenu[data-v-492ea56d]{display:flex}}/*! @docsearch/css 3.6.0 | MIT License | © Algolia, Inc. and contributors | https://docsearch.algolia.com */:root{--docsearch-primary-color:#5468ff;--docsearch-text-color:#1c1e21;--docsearch-spacing:12px;--docsearch-icon-stroke-width:1.4;--docsearch-highlight-color:var(--docsearch-primary-color);--docsearch-muted-color:#969faf;--docsearch-container-background:rgba(101,108,133,.8);--docsearch-logo-color:#5468ff;--docsearch-modal-width:560px;--docsearch-modal-height:600px;--docsearch-modal-background:#f5f6f7;--docsearch-modal-shadow:inset 1px 1px 0 0 hsla(0,0%,100%,.5),0 3px 8px 0 #555a64;--docsearch-searchbox-height:56px;--docsearch-searchbox-background:#ebedf0;--docsearch-searchbox-focus-background:#fff;--docsearch-searchbox-shadow:inset 0 0 0 2px var(--docsearch-primary-color);--docsearch-hit-height:56px;--docsearch-hit-color:#444950;--docsearch-hit-active-color:#fff;--docsearch-hit-background:#fff;--docsearch-hit-shadow:0 1px 3px 0 #d4d9e1;--docsearch-key-gradient:linear-gradient(-225deg,#d5dbe4,#f8f8f8);--docsearch-key-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 2px 1px rgba(30,35,90,.4);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 1px 0 rgba(30,35,90,.4);--docsearch-footer-height:44px;--docsearch-footer-background:#fff;--docsearch-footer-shadow:0 -1px 0 0 #e0e3e8,0 -3px 6px 0 rgba(69,98,155,.12)}html[data-theme=dark]{--docsearch-text-color:#f5f6f7;--docsearch-container-background:rgba(9,10,17,.8);--docsearch-modal-background:#15172a;--docsearch-modal-shadow:inset 1px 1px 0 0 #2c2e40,0 3px 8px 0 #000309;--docsearch-searchbox-background:#090a11;--docsearch-searchbox-focus-background:#000;--docsearch-hit-color:#bec3c9;--docsearch-hit-shadow:none;--docsearch-hit-background:#090a11;--docsearch-key-gradient:linear-gradient(-26.5deg,#565872,#31355b);--docsearch-key-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 2px 2px 0 rgba(3,4,9,.3);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 1px 1px 0 rgba(3,4,9,.30196078431372547);--docsearch-footer-background:#1e2136;--docsearch-footer-shadow:inset 0 1px 0 0 rgba(73,76,106,.5),0 -4px 8px 0 rgba(0,0,0,.2);--docsearch-logo-color:#fff;--docsearch-muted-color:#7f8497}.DocSearch-Button{align-items:center;background:var(--docsearch-searchbox-background);border:0;border-radius:40px;color:var(--docsearch-muted-color);cursor:pointer;display:flex;font-weight:500;height:36px;justify-content:space-between;margin:0 0 0 16px;padding:0 8px;-webkit-user-select:none;user-select:none}.DocSearch-Button:active,.DocSearch-Button:focus,.DocSearch-Button:hover{background:var(--docsearch-searchbox-focus-background);box-shadow:var(--docsearch-searchbox-shadow);color:var(--docsearch-text-color);outline:none}.DocSearch-Button-Container{align-items:center;display:flex}.DocSearch-Search-Icon{stroke-width:1.6}.DocSearch-Button .DocSearch-Search-Icon{color:var(--docsearch-text-color)}.DocSearch-Button-Placeholder{font-size:1rem;padding:0 12px 0 6px}.DocSearch-Button-Keys{display:flex;min-width:calc(40px + .8em)}.DocSearch-Button-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:3px;box-shadow:var(--docsearch-key-shadow);color:var(--docsearch-muted-color);display:flex;height:18px;justify-content:center;margin-right:.4em;position:relative;padding:0 0 2px;border:0;top:-1px;width:20px}.DocSearch-Button-Key--pressed{transform:translate3d(0,1px,0);box-shadow:var(--docsearch-key-pressed-shadow)}@media (max-width:768px){.DocSearch-Button-Keys,.DocSearch-Button-Placeholder{display:none}}.DocSearch--active{overflow:hidden!important}.DocSearch-Container,.DocSearch-Container *{box-sizing:border-box}.DocSearch-Container{background-color:var(--docsearch-container-background);height:100vh;left:0;position:fixed;top:0;width:100vw;z-index:200}.DocSearch-Container a{text-decoration:none}.DocSearch-Link{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;font:inherit;margin:0;padding:0}.DocSearch-Modal{background:var(--docsearch-modal-background);border-radius:6px;box-shadow:var(--docsearch-modal-shadow);flex-direction:column;margin:60px auto auto;max-width:var(--docsearch-modal-width);position:relative}.DocSearch-SearchBar{display:flex;padding:var(--docsearch-spacing) var(--docsearch-spacing) 0}.DocSearch-Form{align-items:center;background:var(--docsearch-searchbox-focus-background);border-radius:4px;box-shadow:var(--docsearch-searchbox-shadow);display:flex;height:var(--docsearch-searchbox-height);margin:0;padding:0 var(--docsearch-spacing);position:relative;width:100%}.DocSearch-Input{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:transparent;border:0;color:var(--docsearch-text-color);flex:1;font:inherit;font-size:1.2em;height:100%;outline:none;padding:0 0 0 8px;width:80%}.DocSearch-Input::placeholder{color:var(--docsearch-muted-color);opacity:1}.DocSearch-Input::-webkit-search-cancel-button,.DocSearch-Input::-webkit-search-decoration,.DocSearch-Input::-webkit-search-results-button,.DocSearch-Input::-webkit-search-results-decoration{display:none}.DocSearch-LoadingIndicator,.DocSearch-MagnifierLabel,.DocSearch-Reset{margin:0;padding:0}.DocSearch-MagnifierLabel,.DocSearch-Reset{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}.DocSearch-Container--Stalled .DocSearch-MagnifierLabel,.DocSearch-LoadingIndicator{display:none}.DocSearch-Container--Stalled .DocSearch-LoadingIndicator{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Reset{animation:none;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;right:0;stroke-width:var(--docsearch-icon-stroke-width)}}.DocSearch-Reset{animation:fade-in .1s ease-in forwards;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;padding:2px;right:0;stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Reset[hidden]{display:none}.DocSearch-Reset:hover{color:var(--docsearch-highlight-color)}.DocSearch-LoadingIndicator svg,.DocSearch-MagnifierLabel svg{height:24px;width:24px}.DocSearch-Cancel{display:none}.DocSearch-Dropdown{max-height:calc(var(--docsearch-modal-height) - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height));min-height:var(--docsearch-spacing);overflow-y:auto;overflow-y:overlay;padding:0 var(--docsearch-spacing);scrollbar-color:var(--docsearch-muted-color) var(--docsearch-modal-background);scrollbar-width:thin}.DocSearch-Dropdown::-webkit-scrollbar{width:12px}.DocSearch-Dropdown::-webkit-scrollbar-track{background:transparent}.DocSearch-Dropdown::-webkit-scrollbar-thumb{background-color:var(--docsearch-muted-color);border:3px solid var(--docsearch-modal-background);border-radius:20px}.DocSearch-Dropdown ul{list-style:none;margin:0;padding:0}.DocSearch-Label{font-size:.75em;line-height:1.6em}.DocSearch-Help,.DocSearch-Label{color:var(--docsearch-muted-color)}.DocSearch-Help{font-size:.9em;margin:0;-webkit-user-select:none;user-select:none}.DocSearch-Title{font-size:1.2em}.DocSearch-Logo a{display:flex}.DocSearch-Logo svg{color:var(--docsearch-logo-color);margin-left:8px}.DocSearch-Hits:last-of-type{margin-bottom:24px}.DocSearch-Hits mark{background:none;color:var(--docsearch-highlight-color)}.DocSearch-HitsFooter{color:var(--docsearch-muted-color);display:flex;font-size:.85em;justify-content:center;margin-bottom:var(--docsearch-spacing);padding:var(--docsearch-spacing)}.DocSearch-HitsFooter a{border-bottom:1px solid;color:inherit}.DocSearch-Hit{border-radius:4px;display:flex;padding-bottom:4px;position:relative}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--deleting{transition:none}}.DocSearch-Hit--deleting{opacity:0;transition:all .25s linear}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--favoriting{transition:none}}.DocSearch-Hit--favoriting{transform:scale(0);transform-origin:top center;transition:all .25s linear;transition-delay:.25s}.DocSearch-Hit a{background:var(--docsearch-hit-background);border-radius:4px;box-shadow:var(--docsearch-hit-shadow);display:block;padding-left:var(--docsearch-spacing);width:100%}.DocSearch-Hit-source{background:var(--docsearch-modal-background);color:var(--docsearch-highlight-color);font-size:.85em;font-weight:600;line-height:32px;margin:0 -4px;padding:8px 4px 0;position:sticky;top:0;z-index:10}.DocSearch-Hit-Tree{color:var(--docsearch-muted-color);height:var(--docsearch-hit-height);opacity:.5;stroke-width:var(--docsearch-icon-stroke-width);width:24px}.DocSearch-Hit[aria-selected=true] a{background-color:var(--docsearch-highlight-color)}.DocSearch-Hit[aria-selected=true] mark{text-decoration:underline}.DocSearch-Hit-Container{align-items:center;color:var(--docsearch-hit-color);display:flex;flex-direction:row;height:var(--docsearch-hit-height);padding:0 var(--docsearch-spacing) 0 0}.DocSearch-Hit-icon{height:20px;width:20px}.DocSearch-Hit-action,.DocSearch-Hit-icon{color:var(--docsearch-muted-color);stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Hit-action{align-items:center;display:flex;height:22px;width:22px}.DocSearch-Hit-action svg{display:block;height:18px;width:18px}.DocSearch-Hit-action+.DocSearch-Hit-action{margin-left:6px}.DocSearch-Hit-action-button{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:inherit;cursor:pointer;padding:2px}svg.DocSearch-Hit-Select-Icon{display:none}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Select-Icon{display:block}.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:background-color .1s ease-in}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{transition:none}}.DocSearch-Hit-action-button:focus path,.DocSearch-Hit-action-button:hover path{fill:#fff}.DocSearch-Hit-content-wrapper{display:flex;flex:1 1 auto;flex-direction:column;font-weight:500;justify-content:center;line-height:1.2em;margin:0 8px;overflow-x:hidden;position:relative;text-overflow:ellipsis;white-space:nowrap;width:80%}.DocSearch-Hit-title{font-size:.9em}.DocSearch-Hit-path{color:var(--docsearch-muted-color);font-size:.75em}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-action,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-icon,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-path,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-text,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-title,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Tree,.DocSearch-Hit[aria-selected=true] mark{color:var(--docsearch-hit-active-color)!important}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:none}}.DocSearch-ErrorScreen,.DocSearch-NoResults,.DocSearch-StartScreen{font-size:.9em;margin:0 auto;padding:36px 0;text-align:center;width:80%}.DocSearch-Screen-Icon{color:var(--docsearch-muted-color);padding-bottom:12px}.DocSearch-NoResults-Prefill-List{display:inline-block;padding-bottom:24px;text-align:left}.DocSearch-NoResults-Prefill-List ul{display:inline-block;padding:8px 0 0}.DocSearch-NoResults-Prefill-List li{list-style-position:inside;list-style-type:"» "}.DocSearch-Prefill{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:1em;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;font-size:1em;font-weight:700;padding:0}.DocSearch-Prefill:focus,.DocSearch-Prefill:hover{outline:none;text-decoration:underline}.DocSearch-Footer{align-items:center;background:var(--docsearch-footer-background);border-radius:0 0 8px 8px;box-shadow:var(--docsearch-footer-shadow);display:flex;flex-direction:row-reverse;flex-shrink:0;height:var(--docsearch-footer-height);justify-content:space-between;padding:0 var(--docsearch-spacing);position:relative;-webkit-user-select:none;user-select:none;width:100%;z-index:300}.DocSearch-Commands{color:var(--docsearch-muted-color);display:flex;list-style:none;margin:0;padding:0}.DocSearch-Commands li{align-items:center;display:flex}.DocSearch-Commands li:not(:last-of-type){margin-right:.8em}.DocSearch-Commands-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:2px;box-shadow:var(--docsearch-key-shadow);display:flex;height:18px;justify-content:center;margin-right:.4em;padding:0 0 1px;color:var(--docsearch-muted-color);border:0;width:20px}.DocSearch-VisuallyHiddenForAccessibility{clip:rect(0 0 0 0);clip-path:inset(50%);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}@media (max-width:768px){:root{--docsearch-spacing:10px;--docsearch-footer-height:40px}.DocSearch-Dropdown{height:100%}.DocSearch-Container{height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);position:absolute}.DocSearch-Footer{border-radius:0;bottom:0;position:absolute}.DocSearch-Hit-content-wrapper{display:flex;position:relative;width:80%}.DocSearch-Modal{border-radius:0;box-shadow:none;height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);margin:0;max-width:100%;width:100%}.DocSearch-Dropdown{max-height:calc(var(--docsearch-vh, 1vh)*100 - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height))}.DocSearch-Cancel{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;flex:none;font:inherit;font-size:1em;font-weight:500;margin-left:var(--docsearch-spacing);outline:none;overflow:hidden;padding:0;-webkit-user-select:none;user-select:none;white-space:nowrap}.DocSearch-Commands,.DocSearch-Hit-Tree{display:none}}@keyframes fade-in{0%{opacity:0}to{opacity:1}}[class*=DocSearch]{--docsearch-primary-color: var(--vp-c-brand-1);--docsearch-highlight-color: var(--docsearch-primary-color);--docsearch-text-color: var(--vp-c-text-1);--docsearch-muted-color: var(--vp-c-text-2);--docsearch-searchbox-shadow: none;--docsearch-searchbox-background: transparent;--docsearch-searchbox-focus-background: transparent;--docsearch-key-gradient: transparent;--docsearch-key-shadow: none;--docsearch-modal-background: var(--vp-c-bg-soft);--docsearch-footer-background: var(--vp-c-bg)}.dark [class*=DocSearch]{--docsearch-modal-shadow: none;--docsearch-footer-shadow: none;--docsearch-logo-color: var(--vp-c-text-2);--docsearch-hit-background: var(--vp-c-default-soft);--docsearch-hit-color: var(--vp-c-text-2);--docsearch-hit-shadow: none}.DocSearch-Button{display:flex;justify-content:center;align-items:center;margin:0;padding:0;width:48px;height:55px;background:transparent;transition:border-color .25s}.DocSearch-Button:hover{background:transparent}.DocSearch-Button:focus{outline:1px dotted;outline:5px auto -webkit-focus-ring-color}.DocSearch-Button:focus:not(:focus-visible){outline:none!important}@media (min-width: 768px){.DocSearch-Button{justify-content:flex-start;border:1px solid transparent;border-radius:8px;padding:0 10px 0 12px;width:100%;height:40px;background-color:var(--vp-c-bg-alt)}.DocSearch-Button:hover{border-color:var(--vp-c-brand-1);background:var(--vp-c-bg-alt)}}.DocSearch-Button .DocSearch-Button-Container{display:flex;align-items:center}.DocSearch-Button .DocSearch-Search-Icon{position:relative;width:16px;height:16px;color:var(--vp-c-text-1);fill:currentColor;transition:color .5s}.DocSearch-Button:hover .DocSearch-Search-Icon{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Search-Icon{top:1px;margin-right:8px;width:14px;height:14px;color:var(--vp-c-text-2)}}.DocSearch-Button .DocSearch-Button-Placeholder{display:none;margin-top:2px;padding:0 16px 0 0;font-size:13px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.DocSearch-Button:hover .DocSearch-Button-Placeholder{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Placeholder{display:inline-block}}.DocSearch-Button .DocSearch-Button-Keys{direction:ltr;display:none;min-width:auto}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Keys{display:flex;align-items:center}}.DocSearch-Button .DocSearch-Button-Key{display:block;margin:2px 0 0;border:1px solid var(--vp-c-divider);border-right:none;border-radius:4px 0 0 4px;padding-left:6px;min-width:0;width:auto;height:22px;line-height:22px;font-family:var(--vp-font-family-base);font-size:12px;font-weight:500;transition:color .5s,border-color .5s}.DocSearch-Button .DocSearch-Button-Key+.DocSearch-Button-Key{border-right:1px solid var(--vp-c-divider);border-left:none;border-radius:0 4px 4px 0;padding-left:2px;padding-right:6px}.DocSearch-Button .DocSearch-Button-Key:first-child{font-size:0!important}.DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"Ctrl";font-size:12px;letter-spacing:normal;color:var(--docsearch-muted-color)}.mac .DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"⌘"}.DocSearch-Button .DocSearch-Button-Key:first-child>*{display:none}.DocSearch-Search-Icon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' stroke-width='1.6' viewBox='0 0 20 20'%3E%3Cpath fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' d='m14.386 14.386 4.088 4.088-4.088-4.088A7.533 7.533 0 1 1 3.733 3.733a7.533 7.533 0 0 1 10.653 10.653z'/%3E%3C/svg%3E")}.VPNavBarSearch{display:flex;align-items:center}@media (min-width: 768px){.VPNavBarSearch{flex-grow:1;padding-left:24px}}@media (min-width: 960px){.VPNavBarSearch{padding-left:32px}}.dark .DocSearch-Footer{border-top:1px solid var(--vp-c-divider)}.DocSearch-Form{border:1px solid var(--vp-c-brand-1);background-color:var(--vp-c-white)}.dark .DocSearch-Form{background-color:var(--vp-c-default-soft)}.DocSearch-Screen-Icon>svg{margin:auto}.VPNavBarSocialLinks[data-v-164c457f]{display:none}@media (min-width: 1280px){.VPNavBarSocialLinks[data-v-164c457f]{display:flex;align-items:center}}.title[data-v-28a961f9]{display:flex;align-items:center;border-bottom:1px solid transparent;width:100%;height:var(--vp-nav-height);font-size:16px;font-weight:600;color:var(--vp-c-text-1);transition:opacity .25s}@media (min-width: 960px){.title[data-v-28a961f9]{flex-shrink:0}.VPNavBarTitle.has-sidebar .title[data-v-28a961f9]{border-bottom-color:var(--vp-c-divider)}}[data-v-28a961f9] .logo{margin-right:8px;height:var(--vp-nav-logo-height)}.VPNavBarTranslations[data-v-c80d9ad0]{display:none}@media (min-width: 1280px){.VPNavBarTranslations[data-v-c80d9ad0]{display:flex;align-items:center}}.title[data-v-c80d9ad0]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.VPNavBar[data-v-40788ea0]{position:relative;height:var(--vp-nav-height);pointer-events:none;white-space:nowrap;transition:background-color .5s}.VPNavBar[data-v-40788ea0]:not(.home){background-color:var(--vp-nav-bg-color)}@media (min-width: 960px){.VPNavBar[data-v-40788ea0]:not(.home){background-color:transparent}.VPNavBar[data-v-40788ea0]:not(.has-sidebar):not(.home.top){background-color:var(--vp-nav-bg-color)}}.wrapper[data-v-40788ea0]{padding:0 8px 0 24px}@media (min-width: 768px){.wrapper[data-v-40788ea0]{padding:0 32px}}@media (min-width: 960px){.VPNavBar.has-sidebar .wrapper[data-v-40788ea0]{padding:0}}.container[data-v-40788ea0]{display:flex;justify-content:space-between;margin:0 auto;max-width:calc(var(--vp-layout-max-width) - 64px);height:var(--vp-nav-height);pointer-events:none}.container>.title[data-v-40788ea0],.container>.content[data-v-40788ea0]{pointer-events:none}.container[data-v-40788ea0] *{pointer-events:auto}@media (min-width: 960px){.VPNavBar.has-sidebar .container[data-v-40788ea0]{max-width:100%}}.title[data-v-40788ea0]{flex-shrink:0;height:calc(var(--vp-nav-height) - 1px);transition:background-color .5s}@media (min-width: 960px){.VPNavBar.has-sidebar .title[data-v-40788ea0]{position:absolute;top:0;left:0;z-index:2;padding:0 32px;width:var(--vp-sidebar-width);height:var(--vp-nav-height);background-color:transparent}}@media (min-width: 1440px){.VPNavBar.has-sidebar .title[data-v-40788ea0]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}.content[data-v-40788ea0]{flex-grow:1}@media (min-width: 960px){.VPNavBar.has-sidebar .content[data-v-40788ea0]{position:relative;z-index:1;padding-right:32px;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .content[data-v-40788ea0]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2 + 32px);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.content-body[data-v-40788ea0]{display:flex;justify-content:flex-end;align-items:center;height:var(--vp-nav-height);transition:background-color .5s}@media (min-width: 960px){.VPNavBar:not(.home.top) .content-body[data-v-40788ea0]{position:relative;background-color:var(--vp-nav-bg-color)}.VPNavBar:not(.has-sidebar):not(.home.top) .content-body[data-v-40788ea0]{background-color:transparent}}@media (max-width: 767px){.content-body[data-v-40788ea0]{column-gap:.5rem}}.menu+.translations[data-v-40788ea0]:before,.menu+.appearance[data-v-40788ea0]:before,.menu+.social-links[data-v-40788ea0]:before,.translations+.appearance[data-v-40788ea0]:before,.appearance+.social-links[data-v-40788ea0]:before{margin-right:8px;margin-left:8px;width:1px;height:24px;background-color:var(--vp-c-divider);content:""}.menu+.appearance[data-v-40788ea0]:before,.translations+.appearance[data-v-40788ea0]:before{margin-right:16px}.appearance+.social-links[data-v-40788ea0]:before{margin-left:16px}.social-links[data-v-40788ea0]{margin-right:-8px}.divider[data-v-40788ea0]{width:100%;height:1px}@media (min-width: 960px){.VPNavBar.has-sidebar .divider[data-v-40788ea0]{padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .divider[data-v-40788ea0]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.divider-line[data-v-40788ea0]{width:100%;height:1px;transition:background-color .5s}.VPNavBar:not(.home) .divider-line[data-v-40788ea0]{background-color:var(--vp-c-gutter)}@media (min-width: 960px){.VPNavBar:not(.home.top) .divider-line[data-v-40788ea0]{background-color:var(--vp-c-gutter)}.VPNavBar:not(.has-sidebar):not(.home.top) .divider[data-v-40788ea0]{background-color:var(--vp-c-gutter)}}.VPNavScreenAppearance[data-v-2b89f08b]{display:flex;justify-content:space-between;align-items:center;border-radius:8px;padding:12px 14px 12px 16px;background-color:var(--vp-c-bg-soft)}.text[data-v-2b89f08b]{line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.VPNavScreenMenuLink[data-v-27d04aeb]{display:block;border-bottom:1px solid var(--vp-c-divider);padding:12px 0 11px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:border-color .25s,color .25s}.VPNavScreenMenuLink[data-v-27d04aeb]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupLink[data-v-7179dbb7]{display:block;margin-left:12px;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-1);transition:color .25s}.VPNavScreenMenuGroupLink[data-v-7179dbb7]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupSection[data-v-4b8941ac]{display:block}.title[data-v-4b8941ac]{line-height:32px;font-size:13px;font-weight:700;color:var(--vp-c-text-2);transition:color .25s}.VPNavScreenMenuGroup[data-v-c9df2649]{border-bottom:1px solid var(--vp-c-divider);height:48px;overflow:hidden;transition:border-color .5s}.VPNavScreenMenuGroup .items[data-v-c9df2649]{visibility:hidden}.VPNavScreenMenuGroup.open .items[data-v-c9df2649]{visibility:visible}.VPNavScreenMenuGroup.open[data-v-c9df2649]{padding-bottom:10px;height:auto}.VPNavScreenMenuGroup.open .button[data-v-c9df2649]{padding-bottom:6px;color:var(--vp-c-brand-1)}.VPNavScreenMenuGroup.open .button-icon[data-v-c9df2649]{transform:rotate(45deg)}.button[data-v-c9df2649]{display:flex;justify-content:space-between;align-items:center;padding:12px 4px 11px 0;width:100%;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.button[data-v-c9df2649]:hover{color:var(--vp-c-brand-1)}.button-icon[data-v-c9df2649]{transition:transform .25s}.group[data-v-c9df2649]:first-child{padding-top:0}.group+.group[data-v-c9df2649],.group+.item[data-v-c9df2649]{padding-top:4px}.VPNavScreenTranslations[data-v-362991c2]{height:24px;overflow:hidden}.VPNavScreenTranslations.open[data-v-362991c2]{height:auto}.title[data-v-362991c2]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-text-1)}.icon[data-v-362991c2]{font-size:16px}.icon.lang[data-v-362991c2]{margin-right:8px}.icon.chevron[data-v-362991c2]{margin-left:4px}.list[data-v-362991c2]{padding:4px 0 0 24px}.link[data-v-362991c2]{line-height:32px;font-size:13px;color:var(--vp-c-text-1)}.VPNavScreen[data-v-382f42e9]{position:fixed;top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 1px);right:0;bottom:0;left:0;padding:0 32px;width:100%;background-color:var(--vp-nav-screen-bg-color);overflow-y:auto;transition:background-color .5s;pointer-events:auto}.VPNavScreen.fade-enter-active[data-v-382f42e9],.VPNavScreen.fade-leave-active[data-v-382f42e9]{transition:opacity .25s}.VPNavScreen.fade-enter-active .container[data-v-382f42e9],.VPNavScreen.fade-leave-active .container[data-v-382f42e9]{transition:transform .25s ease}.VPNavScreen.fade-enter-from[data-v-382f42e9],.VPNavScreen.fade-leave-to[data-v-382f42e9]{opacity:0}.VPNavScreen.fade-enter-from .container[data-v-382f42e9],.VPNavScreen.fade-leave-to .container[data-v-382f42e9]{transform:translateY(-8px)}@media (min-width: 768px){.VPNavScreen[data-v-382f42e9]{display:none}}.container[data-v-382f42e9]{margin:0 auto;padding:24px 0 96px;max-width:288px}.menu+.translations[data-v-382f42e9],.menu+.appearance[data-v-382f42e9],.translations+.appearance[data-v-382f42e9]{margin-top:24px}.menu+.social-links[data-v-382f42e9]{margin-top:16px}.appearance+.social-links[data-v-382f42e9]{margin-top:16px}.VPNav[data-v-f1e365da]{position:relative;top:var(--vp-layout-top-height, 0px);left:0;z-index:var(--vp-z-index-nav);width:100%;pointer-events:none;transition:background-color .5s}@media (min-width: 960px){.VPNav[data-v-f1e365da]{position:fixed}}.VPSidebarItem.level-0[data-v-2ea20db7]{padding-bottom:24px}.VPSidebarItem.collapsed.level-0[data-v-2ea20db7]{padding-bottom:10px}.item[data-v-2ea20db7]{position:relative;display:flex;width:100%}.VPSidebarItem.collapsible>.item[data-v-2ea20db7]{cursor:pointer}.indicator[data-v-2ea20db7]{position:absolute;top:6px;bottom:6px;left:-17px;width:2px;border-radius:2px;transition:background-color .25s}.VPSidebarItem.level-2.is-active>.item>.indicator[data-v-2ea20db7],.VPSidebarItem.level-3.is-active>.item>.indicator[data-v-2ea20db7],.VPSidebarItem.level-4.is-active>.item>.indicator[data-v-2ea20db7],.VPSidebarItem.level-5.is-active>.item>.indicator[data-v-2ea20db7]{background-color:var(--vp-c-brand-1)}.link[data-v-2ea20db7]{display:flex;align-items:center;flex-grow:1}.text[data-v-2ea20db7]{flex-grow:1;padding:4px 0;line-height:24px;font-size:14px;transition:color .25s}.VPSidebarItem.level-0 .text[data-v-2ea20db7]{font-weight:700;color:var(--vp-c-text-1)}.VPSidebarItem.level-1 .text[data-v-2ea20db7],.VPSidebarItem.level-2 .text[data-v-2ea20db7],.VPSidebarItem.level-3 .text[data-v-2ea20db7],.VPSidebarItem.level-4 .text[data-v-2ea20db7],.VPSidebarItem.level-5 .text[data-v-2ea20db7]{font-weight:500;color:var(--vp-c-text-2)}.VPSidebarItem.level-0.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-1.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-2.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-3.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-4.is-link>.item>.link:hover .text[data-v-2ea20db7],.VPSidebarItem.level-5.is-link>.item>.link:hover .text[data-v-2ea20db7]{color:var(--vp-c-brand-1)}.VPSidebarItem.level-0.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-1.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-2.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-3.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-4.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-5.has-active>.item>.text[data-v-2ea20db7],.VPSidebarItem.level-0.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-1.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-2.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-3.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-4.has-active>.item>.link>.text[data-v-2ea20db7],.VPSidebarItem.level-5.has-active>.item>.link>.text[data-v-2ea20db7]{color:var(--vp-c-text-1)}.VPSidebarItem.level-0.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-1.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-2.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-3.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-4.is-active>.item .link>.text[data-v-2ea20db7],.VPSidebarItem.level-5.is-active>.item .link>.text[data-v-2ea20db7]{color:var(--vp-c-brand-1)}.caret[data-v-2ea20db7]{display:flex;justify-content:center;align-items:center;margin-right:-7px;width:32px;height:32px;color:var(--vp-c-text-3);cursor:pointer;transition:color .25s;flex-shrink:0}.item:hover .caret[data-v-2ea20db7]{color:var(--vp-c-text-2)}.item:hover .caret[data-v-2ea20db7]:hover{color:var(--vp-c-text-1)}.caret-icon[data-v-2ea20db7]{font-size:18px;transform:rotate(90deg);transition:transform .25s}.VPSidebarItem.collapsed .caret-icon[data-v-2ea20db7]{transform:rotate(0)}.VPSidebarItem.level-1 .items[data-v-2ea20db7],.VPSidebarItem.level-2 .items[data-v-2ea20db7],.VPSidebarItem.level-3 .items[data-v-2ea20db7],.VPSidebarItem.level-4 .items[data-v-2ea20db7],.VPSidebarItem.level-5 .items[data-v-2ea20db7]{border-left:1px solid var(--vp-c-divider);padding-left:16px}.VPSidebarItem.collapsed .items[data-v-2ea20db7]{display:none}.VPSidebar[data-v-ec846e01]{position:fixed;top:var(--vp-layout-top-height, 0px);bottom:0;left:0;z-index:var(--vp-z-index-sidebar);padding:32px 32px 96px;width:calc(100vw - 64px);max-width:320px;background-color:var(--vp-sidebar-bg-color);opacity:0;box-shadow:var(--vp-c-shadow-3);overflow-x:hidden;overflow-y:auto;transform:translate(-100%);transition:opacity .5s,transform .25s ease;overscroll-behavior:contain}.VPSidebar.open[data-v-ec846e01]{opacity:1;visibility:visible;transform:translate(0);transition:opacity .25s,transform .5s cubic-bezier(.19,1,.22,1)}.dark .VPSidebar[data-v-ec846e01]{box-shadow:var(--vp-shadow-1)}@media (min-width: 960px){.VPSidebar[data-v-ec846e01]{padding-top:var(--vp-nav-height);width:var(--vp-sidebar-width);max-width:100%;background-color:var(--vp-sidebar-bg-color);opacity:1;visibility:visible;box-shadow:none;transform:translate(0)}}@media (min-width: 1440px){.VPSidebar[data-v-ec846e01]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}@media (min-width: 960px){.curtain[data-v-ec846e01]{position:sticky;top:-64px;left:0;z-index:1;margin-top:calc(var(--vp-nav-height) * -1);margin-right:-32px;margin-left:-32px;height:var(--vp-nav-height);background-color:var(--vp-sidebar-bg-color)}}.nav[data-v-ec846e01]{outline:0}.group+.group[data-v-ec846e01]{border-top:1px solid var(--vp-c-divider);padding-top:10px}@media (min-width: 960px){.group[data-v-ec846e01]{padding-top:10px;width:calc(var(--vp-sidebar-width) - 64px)}}.VPSkipLink[data-v-c3508ec8]{top:8px;left:8px;padding:8px 16px;z-index:999;border-radius:8px;font-size:12px;font-weight:700;text-decoration:none;color:var(--vp-c-brand-1);box-shadow:var(--vp-shadow-3);background-color:var(--vp-c-bg)}.VPSkipLink[data-v-c3508ec8]:focus{height:auto;width:auto;clip:auto;clip-path:none}@media (min-width: 1280px){.VPSkipLink[data-v-c3508ec8]{top:14px;left:16px}}.Layout[data-v-a9a9e638]{display:flex;flex-direction:column;min-height:100vh}.VPHomeSponsors[data-v-db81191c]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPHomeSponsors[data-v-db81191c]{margin:96px 0}@media (min-width: 768px){.VPHomeSponsors[data-v-db81191c]{margin:128px 0}}.VPHomeSponsors[data-v-db81191c]{padding:0 24px}@media (min-width: 768px){.VPHomeSponsors[data-v-db81191c]{padding:0 48px}}@media (min-width: 960px){.VPHomeSponsors[data-v-db81191c]{padding:0 64px}}.container[data-v-db81191c]{margin:0 auto;max-width:1152px}.love[data-v-db81191c]{margin:0 auto;width:fit-content;font-size:28px;color:var(--vp-c-text-3)}.icon[data-v-db81191c]{display:inline-block}.message[data-v-db81191c]{margin:0 auto;padding-top:10px;max-width:320px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.sponsors[data-v-db81191c]{padding-top:32px}.action[data-v-db81191c]{padding-top:40px;text-align:center}.VPTeamPage[data-v-c2f8e101]{margin:96px 0}@media (min-width: 768px){.VPTeamPage[data-v-c2f8e101]{margin:128px 0}}.VPHome .VPTeamPageTitle[data-v-c2f8e101-s]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPTeamPageSection+.VPTeamPageSection[data-v-c2f8e101-s],.VPTeamMembers+.VPTeamPageSection[data-v-c2f8e101-s]{margin-top:64px}.VPTeamMembers+.VPTeamMembers[data-v-c2f8e101-s]{margin-top:24px}@media (min-width: 768px){.VPTeamPageTitle+.VPTeamPageSection[data-v-c2f8e101-s]{margin-top:16px}.VPTeamPageSection+.VPTeamPageSection[data-v-c2f8e101-s],.VPTeamMembers+.VPTeamPageSection[data-v-c2f8e101-s]{margin-top:96px}}.VPTeamMembers[data-v-c2f8e101-s]{padding:0 24px}@media (min-width: 768px){.VPTeamMembers[data-v-c2f8e101-s]{padding:0 48px}}@media (min-width: 960px){.VPTeamMembers[data-v-c2f8e101-s]{padding:0 64px}}.VPTeamPageTitle[data-v-e277e15c]{padding:48px 32px;text-align:center}@media (min-width: 768px){.VPTeamPageTitle[data-v-e277e15c]{padding:64px 48px 48px}}@media (min-width: 960px){.VPTeamPageTitle[data-v-e277e15c]{padding:80px 64px 48px}}.title[data-v-e277e15c]{letter-spacing:0;line-height:44px;font-size:36px;font-weight:500}@media (min-width: 768px){.title[data-v-e277e15c]{letter-spacing:-.5px;line-height:56px;font-size:48px}}.lead[data-v-e277e15c]{margin:0 auto;max-width:512px;padding-top:12px;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 768px){.lead[data-v-e277e15c]{max-width:592px;letter-spacing:.15px;line-height:28px;font-size:20px}}.VPTeamPageSection[data-v-d43bc49d]{padding:0 32px}@media (min-width: 768px){.VPTeamPageSection[data-v-d43bc49d]{padding:0 48px}}@media (min-width: 960px){.VPTeamPageSection[data-v-d43bc49d]{padding:0 64px}}.title[data-v-d43bc49d]{position:relative;margin:0 auto;max-width:1152px;text-align:center;color:var(--vp-c-text-2)}.title-line[data-v-d43bc49d]{position:absolute;top:16px;left:0;width:100%;height:1px;background-color:var(--vp-c-divider)}.title-text[data-v-d43bc49d]{position:relative;display:inline-block;padding:0 24px;letter-spacing:0;line-height:32px;font-size:20px;font-weight:500;background-color:var(--vp-c-bg)}.lead[data-v-d43bc49d]{margin:0 auto;max-width:480px;padding-top:12px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.members[data-v-d43bc49d]{padding-top:40px}.VPTeamMembersItem[data-v-f9987cb6]{display:flex;flex-direction:column;gap:2px;border-radius:12px;width:100%;height:100%;overflow:hidden}.VPTeamMembersItem.small .profile[data-v-f9987cb6]{padding:32px}.VPTeamMembersItem.small .data[data-v-f9987cb6]{padding-top:20px}.VPTeamMembersItem.small .avatar[data-v-f9987cb6]{width:64px;height:64px}.VPTeamMembersItem.small .name[data-v-f9987cb6]{line-height:24px;font-size:16px}.VPTeamMembersItem.small .affiliation[data-v-f9987cb6]{padding-top:4px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .desc[data-v-f9987cb6]{padding-top:12px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .links[data-v-f9987cb6]{margin:0 -16px -20px;padding:10px 0 0}.VPTeamMembersItem.medium .profile[data-v-f9987cb6]{padding:48px 32px}.VPTeamMembersItem.medium .data[data-v-f9987cb6]{padding-top:24px;text-align:center}.VPTeamMembersItem.medium .avatar[data-v-f9987cb6]{width:96px;height:96px}.VPTeamMembersItem.medium .name[data-v-f9987cb6]{letter-spacing:.15px;line-height:28px;font-size:20px}.VPTeamMembersItem.medium .affiliation[data-v-f9987cb6]{padding-top:4px;font-size:16px}.VPTeamMembersItem.medium .desc[data-v-f9987cb6]{padding-top:16px;max-width:288px;font-size:16px}.VPTeamMembersItem.medium .links[data-v-f9987cb6]{margin:0 -16px -12px;padding:16px 12px 0}.profile[data-v-f9987cb6]{flex-grow:1;background-color:var(--vp-c-bg-soft)}.data[data-v-f9987cb6]{text-align:center}.avatar[data-v-f9987cb6]{position:relative;flex-shrink:0;margin:0 auto;border-radius:50%;box-shadow:var(--vp-shadow-3)}.avatar-img[data-v-f9987cb6]{position:absolute;top:0;right:0;bottom:0;left:0;border-radius:50%;object-fit:cover}.name[data-v-f9987cb6]{margin:0;font-weight:600}.affiliation[data-v-f9987cb6]{margin:0;font-weight:500;color:var(--vp-c-text-2)}.org.link[data-v-f9987cb6]{color:var(--vp-c-text-2);transition:color .25s}.org.link[data-v-f9987cb6]:hover{color:var(--vp-c-brand-1)}.desc[data-v-f9987cb6]{margin:0 auto}.desc[data-v-f9987cb6] a{font-weight:500;color:var(--vp-c-brand-1);text-decoration-style:dotted;transition:color .25s}.links[data-v-f9987cb6]{display:flex;justify-content:center;height:56px}.sp-link[data-v-f9987cb6]{display:flex;justify-content:center;align-items:center;text-align:center;padding:16px;font-size:14px;font-weight:500;color:var(--vp-c-sponsor);background-color:var(--vp-c-bg-soft);transition:color .25s,background-color .25s}.sp .sp-link.link[data-v-f9987cb6]:hover,.sp .sp-link.link[data-v-f9987cb6]:focus{outline:none;color:var(--vp-c-white);background-color:var(--vp-c-sponsor)}.sp-icon[data-v-f9987cb6]{margin-right:8px;font-size:16px}.VPTeamMembers.small .container[data-v-fba19bad]{grid-template-columns:repeat(auto-fit,minmax(224px,1fr))}.VPTeamMembers.small.count-1 .container[data-v-fba19bad]{max-width:276px}.VPTeamMembers.small.count-2 .container[data-v-fba19bad]{max-width:576px}.VPTeamMembers.small.count-3 .container[data-v-fba19bad]{max-width:876px}.VPTeamMembers.medium .container[data-v-fba19bad]{grid-template-columns:repeat(auto-fit,minmax(256px,1fr))}@media (min-width: 375px){.VPTeamMembers.medium .container[data-v-fba19bad]{grid-template-columns:repeat(auto-fit,minmax(288px,1fr))}}.VPTeamMembers.medium.count-1 .container[data-v-fba19bad]{max-width:368px}.VPTeamMembers.medium.count-2 .container[data-v-fba19bad]{max-width:760px}.container[data-v-fba19bad]{display:grid;gap:24px;margin:0 auto;max-width:1152px}:root{--vp-plugin-tabs-tab-text-color: var(--vp-c-text-2);--vp-plugin-tabs-tab-active-text-color: var(--vp-c-text-1);--vp-plugin-tabs-tab-hover-text-color: var(--vp-c-text-1);--vp-plugin-tabs-tab-bg: var(--vp-c-bg-soft);--vp-plugin-tabs-tab-divider: var(--vp-c-divider);--vp-plugin-tabs-tab-active-bar-color: var(--vp-c-brand-1)}.plugin-tabs{margin:16px 0;background-color:var(--vp-plugin-tabs-tab-bg);border-radius:8px}.plugin-tabs--tab-list{position:relative;padding:0 12px;overflow-x:auto;overflow-y:hidden}.plugin-tabs--tab-list:after{content:"";position:absolute;bottom:0;left:0;right:0;height:2px;background-color:var(--vp-plugin-tabs-tab-divider)}.plugin-tabs--tab{position:relative;padding:0 12px;line-height:48px;border-bottom:2px solid transparent;color:var(--vp-plugin-tabs-tab-text-color);font-size:14px;font-weight:500;white-space:nowrap;transition:color .25s}.plugin-tabs--tab[aria-selected=true]{color:var(--vp-plugin-tabs-tab-active-text-color)}.plugin-tabs--tab:hover{color:var(--vp-plugin-tabs-tab-hover-text-color)}.plugin-tabs--tab:after{content:"";position:absolute;bottom:-2px;left:8px;right:8px;height:2px;background-color:transparent;transition:background-color .25s;z-index:1}.plugin-tabs--tab[aria-selected=true]:after{background-color:var(--vp-plugin-tabs-tab-active-bar-color)}.plugin-tabs--content[data-v-9b0d03d2]{padding:16px}.plugin-tabs--content[data-v-9b0d03d2]>:first-child:first-child{margin-top:0}.plugin-tabs--content[data-v-9b0d03d2]>:last-child:last-child{margin-bottom:0}.plugin-tabs--content[data-v-9b0d03d2]>div[class*=language-]{border-radius:8px;margin:16px 0}:root:not(.dark) .plugin-tabs--content[data-v-9b0d03d2] div[class*=language-]{background-color:var(--vp-c-bg)}.VPHero .clip{white-space:pre;max-width:500px}:root{--vp-font-family-base: "Barlow", "Inter var experimental", "Inter var", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", sans-serif;--vp-font-family-mono: "Fira Code", Menlo, Monaco, Consolas, "Courier New", monospace}:root{--julia-blue: #5fd7ff ;--julia-purple: #5fd7ff;--julia-red: #CB3C33;--julia-green: #0087d7;--vp-c-brand: #0087d7;--vp-c-brand-light: #0087d7;--vp-c-brand-lighter: #5fd7ff ;--vp-c-brand-lightest: #5fd7ff ;--vp-c-brand-dark: #5fd7ff;--vp-c-brand-darker: #5fd7ff ;--vp-c-brand-dimm: #212425}:root{--vp-button-brand-border: var(--vp-c-brand-light);--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand);--vp-button-brand-hover-border: var(--vp-c-brand-light);--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-light);--vp-button-brand-active-border: var(--vp-c-brand-light);--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-button-brand-bg)}:root{--vp-home-hero-name-color: transparent;--vp-home-hero-name-background: -webkit-linear-gradient( 120deg, #ff875f 30%, #ff875f 30% );--vp-home-hero-image-background-image: linear-gradient( -45deg, #0094ea11 15%, #0094ea11 15%, #0094ea11 );--vp-home-hero-image-filter: blur(10px)}@media (min-width: 640px){:root{--vp-home-hero-image-filter: blur(60px)}}@media (min-width: 960px){:root{--vp-home-hero-image-filter: blur(72px)}}:root.dark{--vp-custom-block-tip-border: var(--vp-c-brand);--vp-custom-block-tip-text: var(--vp-c-brand-lightest);--vp-custom-block-tip-bg: var(--vp-c-brand-dimm);--vp-c-black: hsl(220 20% 9%);--vp-c-black-pure: hsl(220, 24%, 4%);--vp-c-black-soft: hsl(220 16% 13%);--vp-c-black-mute: hsl(220 14% 17%);--vp-c-gray: hsl(220 8% 56%);--vp-c-gray-dark-1: hsl(220 10% 39%);--vp-c-gray-dark-2: hsl(220 12% 28%);--vp-c-gray-dark-3: hsl(220 12% 23%);--vp-c-gray-dark-4: hsl(220 14% 17%);--vp-c-gray-dark-5: hsl(220 16% 13%);--vp-c-bg: hsl(240, 2%, 11%);--vp-custom-block-info-bg: hsl(220 14% 17%);--vp-c-gutter: hsl(220 20% 9%);--vp-c-bg-alt: hsl(220 20% 9%);--vp-c-bg-soft: hsl(220 14% 17%);--vp-c-bg-mute: hsl(220 12% 23%)}.DocSearch{--docsearch-primary-color: var(--vp-c-brand) !important}mjx-container>svg{display:block;margin:auto}mjx-container{padding:.5rem 0}mjx-container{display:inline-block;margin:auto 2px -2px}mjx-container>svg{margin:auto;display:inline-block}:root{--vp-c-brand-1: #ff875f;--vp-c-brand-2: #ff875f;--vp-c-brand-3: #ff875f;--vp-c-sponsor: #ca2971;--vitest-c-sponsor-hover: #c13071}.dark{--vp-c-brand-1: #0087d7;--vp-c-brand-2: #0087d7;--vp-c-brand-3: #0087d7;--vp-c-sponsor: #ee4e95;--vitest-c-sponsor-hover: #e51370}.VPLocalSearchBox[data-v-f5c68218]{position:fixed;z-index:100;top:0;right:0;bottom:0;left:0;display:flex}.backdrop[data-v-f5c68218]{position:absolute;top:0;right:0;bottom:0;left:0;background:var(--vp-backdrop-bg-color);transition:opacity .5s}.shell[data-v-f5c68218]{position:relative;padding:12px;margin:64px auto;display:flex;flex-direction:column;gap:16px;background:var(--vp-local-search-bg);width:min(100vw - 60px,900px);height:min-content;max-height:min(100vh - 128px,900px);border-radius:6px}@media (max-width: 767px){.shell[data-v-f5c68218]{margin:0;width:100vw;height:100vh;max-height:none;border-radius:0}}.search-bar[data-v-f5c68218]{border:1px solid var(--vp-c-divider);border-radius:4px;display:flex;align-items:center;padding:0 12px;cursor:text}@media (max-width: 767px){.search-bar[data-v-f5c68218]{padding:0 8px}}.search-bar[data-v-f5c68218]:focus-within{border-color:var(--vp-c-brand-1)}.local-search-icon[data-v-f5c68218]{display:block;font-size:18px}.navigate-icon[data-v-f5c68218]{display:block;font-size:14px}.search-icon[data-v-f5c68218]{margin:8px}@media (max-width: 767px){.search-icon[data-v-f5c68218]{display:none}}.search-input[data-v-f5c68218]{padding:6px 12px;font-size:inherit;width:100%}@media (max-width: 767px){.search-input[data-v-f5c68218]{padding:6px 4px}}.search-actions[data-v-f5c68218]{display:flex;gap:4px}@media (any-pointer: coarse){.search-actions[data-v-f5c68218]{gap:8px}}@media (min-width: 769px){.search-actions.before[data-v-f5c68218]{display:none}}.search-actions button[data-v-f5c68218]{padding:8px}.search-actions button[data-v-f5c68218]:not([disabled]):hover,.toggle-layout-button.detailed-list[data-v-f5c68218]{color:var(--vp-c-brand-1)}.search-actions button.clear-button[data-v-f5c68218]:disabled{opacity:.37}.search-keyboard-shortcuts[data-v-f5c68218]{font-size:.8rem;opacity:75%;display:flex;flex-wrap:wrap;gap:16px;line-height:14px}.search-keyboard-shortcuts span[data-v-f5c68218]{display:flex;align-items:center;gap:4px}@media (max-width: 767px){.search-keyboard-shortcuts[data-v-f5c68218]{display:none}}.search-keyboard-shortcuts kbd[data-v-f5c68218]{background:#8080801a;border-radius:4px;padding:3px 6px;min-width:24px;display:inline-block;text-align:center;vertical-align:middle;border:1px solid rgba(128,128,128,.15);box-shadow:0 2px 2px #0000001a}.results[data-v-f5c68218]{display:flex;flex-direction:column;gap:6px;overflow-x:hidden;overflow-y:auto;overscroll-behavior:contain}.result[data-v-f5c68218]{display:flex;align-items:center;gap:8px;border-radius:4px;transition:none;line-height:1rem;border:solid 2px var(--vp-local-search-result-border);outline:none}.result>div[data-v-f5c68218]{margin:12px;width:100%;overflow:hidden}@media (max-width: 767px){.result>div[data-v-f5c68218]{margin:8px}}.titles[data-v-f5c68218]{display:flex;flex-wrap:wrap;gap:4px;position:relative;z-index:1001;padding:2px 0}.title[data-v-f5c68218]{display:flex;align-items:center;gap:4px}.title.main[data-v-f5c68218]{font-weight:500}.title-icon[data-v-f5c68218]{opacity:.5;font-weight:500;color:var(--vp-c-brand-1)}.title svg[data-v-f5c68218]{opacity:.5}.result.selected[data-v-f5c68218]{--vp-local-search-result-bg: var(--vp-local-search-result-selected-bg);border-color:var(--vp-local-search-result-selected-border)}.excerpt-wrapper[data-v-f5c68218]{position:relative}.excerpt[data-v-f5c68218]{opacity:75%;pointer-events:none;max-height:140px;overflow:hidden;position:relative;opacity:.5;margin-top:4px}.result.selected .excerpt[data-v-f5c68218]{opacity:1}.excerpt[data-v-f5c68218] *{font-size:.8rem!important;line-height:130%!important}.titles[data-v-f5c68218] mark,.excerpt[data-v-f5c68218] mark{background-color:var(--vp-local-search-highlight-bg);color:var(--vp-local-search-highlight-text);border-radius:2px;padding:0 2px}.excerpt[data-v-f5c68218] .vp-code-group .tabs{display:none}.excerpt[data-v-f5c68218] .vp-code-group div[class*=language-]{border-radius:8px!important}.excerpt-gradient-bottom[data-v-f5c68218]{position:absolute;bottom:-1px;left:0;width:100%;height:8px;background:linear-gradient(transparent,var(--vp-local-search-result-bg));z-index:1000}.excerpt-gradient-top[data-v-f5c68218]{position:absolute;top:-1px;left:0;width:100%;height:8px;background:linear-gradient(var(--vp-local-search-result-bg),transparent);z-index:1000}.result.selected .titles[data-v-f5c68218],.result.selected .title-icon[data-v-f5c68218]{color:var(--vp-c-brand-1)!important}.no-results[data-v-f5c68218]{font-size:.9rem;text-align:center;padding:12px}svg[data-v-f5c68218]{flex:none} diff --git a/dev/biomarkovchains.html b/dev/biomarkovchains.html index 8ce5e22..217001d 100644 --- a/dev/biomarkovchains.html +++ b/dev/biomarkovchains.html @@ -5,20 +5,20 @@ Towards Markov Chains | BioMarkovChains.jl - - + + - + - - - + + + -
BioMarkovChains.jl

Appearance

Towards Markov Chains ​

DNA as a Markov chain ​

Several packages (e.g. MarkovChainsHammer.jl, DiscreteMarkovChains.jl, etc.) in the Julia ecosystem have been implemented to work with Markov chains with a state space of integers, those could be efficient in many ways, but they are clumsy to work with a specialized biological types as in the BioJulia ecosystem. Therefore, in the GeneFinder package we dedicated some implementations to work with BioSequence types so that we can expand the functionality in an efficient way (see complete API).

One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet A = {A, C, G, T} is draw as a four-vertex graph, where each letter of A is a state (vertex) and the edges of the graph represent transitions from one nucleotide to another in a sequence (e.g. A → T represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet A.

More formally a Markov chain is a random process where each state is a random variable Xt where t∈T is a discrete time in a finite sequence T and the probability to jump from one state into another is only dependent of the current state. Therefore a definition of this Markov property is given by:

P(Xt=j|Xt−1=i)

where i, j ∈ A . This property led us to generalize a way to calculate the probability of a sequence T from a process (X1...XT) where each random variable is a nucleotide from A so that:

P(X1=i1,...,XT=iT)=P(X1=i1)∏t=2TP(Xt=it|Xt−1=it−1)

Note that previous equations has two terms, a initial probability P(X1=i1) and the the product of all transitions beginning at t=2. So, to calculate the initial probability distribution of each of the nucleotides of a string T with the alphabet 𝒜 we can first calculate the transition probability matrix M^ out of the frequency count of the transitions. In an alphabet 𝒜 we got 42 transitions of one order, that is the AA, AC, AG, ... which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a 4x4 matrix representing all the transitions. For instance in a DNA sequence T of 24 nucleotides:

CCTCCCGGACCCTGGGCTCGGGAC

We can calculate each frequency nucleotide to any other nucleotide m^ij=cijci where cij is the actual count of the dinucleotide, and therefore ci is the counts of the nucleotide i to any other nucleotide and build the transition probability matrix:

[ACGTA0.001.000.000.00C0.000.560.220.30G0.250.120.620.00T0.000.670.330.00]

It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions cij over the total sum of the dinucleotide counts ck:

π^i=ci∑kck

That way for the previous example example we can can calculate the initial probabilities π^ = (0.08,0.43,0.34,0.13). Both set of probabilities composed a transition model that can be used to predict the probability of any DNA sequence using equation (2).

References ​

Axelson-Fisk, Marina. 2015. Comparative Gene Finding. Vol. 20. Computational Biology. London: Springer London. http://link.springer.com/10.1007/978-1-4471-6693-1.

- +
BioMarkovChains.jl

Appearance

Towards Markov Chains ​

DNA as a Markov chain ​

Several packages (e.g. MarkovChainsHammer.jl, DiscreteMarkovChains.jl, etc.) in the Julia ecosystem have been implemented to work with Markov chains with a state space of integers, those could be efficient in many ways, but they are clumsy to work with a specialized biological types as in the BioJulia ecosystem. Therefore, in the GeneFinder package we dedicated some implementations to work with BioSequence types so that we can expand the functionality in an efficient way (see complete API).

One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet A = {A, C, G, T} is draw as a four-vertex graph, where each letter of A is a state (vertex) and the edges of the graph represent transitions from one nucleotide to another in a sequence (e.g. A → T represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet A.

More formally a Markov chain is a random process where each state is a random variable Xt where t∈T is a discrete time in a finite sequence T and the probability to jump from one state into another is only dependent of the current state. Therefore a definition of this Markov property is given by:

P(Xt=j|Xt−1=i)

where i, j ∈ A . This property led us to generalize a way to calculate the probability of a sequence T from a process (X1...XT) where each random variable is a nucleotide from A so that:

P(X1=i1,...,XT=iT)=P(X1=i1)∏t=2TP(Xt=it|Xt−1=it−1)

Note that previous equations has two terms, a initial probability P(X1=i1) and the the product of all transitions beginning at t=2. So, to calculate the initial probability distribution of each of the nucleotides of a string T with the alphabet 𝒜 we can first calculate the transition probability matrix M^ out of the frequency count of the transitions. In an alphabet 𝒜 we got 42 transitions of one order, that is the AA, AC, AG, ... which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a 4x4 matrix representing all the transitions. For instance in a DNA sequence T of 24 nucleotides:

CCTCCCGGACCCTGGGCTCGGGAC

We can calculate each frequency nucleotide to any other nucleotide m^ij=cijci where cij is the actual count of the dinucleotide, and therefore ci is the counts of the nucleotide i to any other nucleotide and build the transition probability matrix:

[ACGTA0.001.000.000.00C0.000.560.220.30G0.250.120.620.00T0.000.670.330.00]

It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions cij over the total sum of the dinucleotide counts ck:

π^i=ci∑kck

That way for the previous example example we can can calculate the initial probabilities π^ = (0.08,0.43,0.34,0.13). Both set of probabilities composed a transition model that can be used to predict the probability of any DNA sequence using equation (2).

References ​

Axelson-Fisk, Marina. 2015. Comparative Gene Finding. Vol. 20. Computational Biology. London: Springer London. http://link.springer.com/10.1007/978-1-4471-6693-1.

+ \ No newline at end of file diff --git a/dev/getstarted.html b/dev/getstarted.html index d7d02e5..3f35946 100644 --- a/dev/getstarted.html +++ b/dev/getstarted.html @@ -5,23 +5,23 @@ Get started | BioMarkovChains.jl - - + + - + - - - + + + -
BioMarkovChains.jl

Appearance

Get started ​

Installation ​

You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:

julia
]add BioMarkovChains

If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.

Create a BioMarkovChain of DNA ​

julia
using BioSequences, BioMarkovChains
+    
BioMarkovChains.jl
Appearance
Get started ​
Installation ​
You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:
julia
]add BioMarkovChains
If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.
Create a BioMarkovChain of DNA ​
julia
using BioSequences, BioMarkovChains
 
 sequence = dna"CCTCCCGGACCCTGGGCTCGGGAC"
 
-BioMarkovChain(sequence)
BioMarkovChain of DNAAlphabet{4}() and order 1:
+BioMarkovChain(sequence)
BioMarkovChain of DNAAlphabet{4}() and order 1:
   - Transition Probability Matrix --> Matrix{Float64}(4 × 4):
    0.0     1.0     0.0     0.0
    0.0     0.5     0.2     0.3
@@ -31,7 +31,7 @@
    0.087
    0.4348
    0.3478
-   0.1304
Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.
A very nice nice property of the transition probability matrix is that the n-step transition probability matrix Mn=(mij(n)), that is the nth power of M represents i →j transitions in n steps. We can also have higher order transition models as:
julia
BioMarkovChain(sequence, 2)
BioMarkovChain of DNAAlphabet{4}() and order 2:
+   0.1304
Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.
A very nice nice property of the transition probability matrix is that the n-step transition probability matrix Mn=(mij(n)), that is the nth power of M represents i →j transitions in n steps. We can also have higher order transition models as:
julia
BioMarkovChain(sequence, 2)
BioMarkovChain of DNAAlphabet{4}() and order 2:
   - Transition Probability Matrix --> Matrix{Float64}(4 × 4):
    0.0     0.5     0.2     0.3
    0.05    0.475   0.325   0.15
@@ -41,8 +41,8 @@
    0.087
    0.4348
    0.3478
-   0.1304

-    
+   0.1304
+ \ No newline at end of file diff --git a/dev/hashmap.json b/dev/hashmap.json index 117f06e..d2853f6 100644 --- a/dev/hashmap.json +++ b/dev/hashmap.json @@ -1 +1 @@ -{"home.md":"nGdy1Xvl","index.md":"mmk1IapY","article01.md":"BL6r3tif","getstarted.md":"BxUYlh-U","biomarkovchains.md":"DhkAaXJV","api.md":"CM80ZGQK"} +{"index.md":"Ba-cgBKx","getstarted.md":"EJuNxDSJ","home.md":"DYCAAGxb","article01.md":"BrGXw77Y","api.md":"BiqC9tVJ","biomarkovchains.md":"0rg0z1ev"} diff --git a/dev/home.html b/dev/home.html index aa407ee..a30e90c 100644 --- a/dev/home.html +++ b/dev/home.html @@ -5,20 +5,20 @@ BioMarkovChains.jl - - + + - + - - - + + + -
BioMarkovChains.jl

Appearance


Representing biological sequences as Markov chains

Overview ​

This package aim to represent BioSequences types as Markov chains to perform different operations and predictions

- +
BioMarkovChains.jl

Appearance


Representing biological sequences as Markov chains

Overview ​

This package aim to represent BioSequences types as Markov chains to perform different operations and predictions

+ \ No newline at end of file diff --git a/dev/index.html b/dev/index.html index c8bc34b..5988282 100644 --- a/dev/index.html +++ b/dev/index.html @@ -5,20 +5,20 @@ BioMarkovChains.jl - - + + - + - - - + + + -
BioMarkovChains.jl

Appearance

BioMarkovChains.jl

Representing biological sequences as Markov chains

Get Started
View on Github
BioMarkovChains

<p style="margin-bottom:2cm"></p>

<div class="vp-doc" style="width:80%; margin:auto">

<h2> Get Started </h2>

Install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the add BioMarkovChains command.

julia
(@v1.10) pkg> add BioMarkovChains

For more information, see the Getting Started section.

</div>

- +
BioMarkovChains.jl

Appearance

BioMarkovChains.jl

Representing biological sequences as Markov chains

Get Started
View on Github
BioMarkovChains

<div class="vp-doc" style="width:90%; margin:auto">

Install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the add BioMarkovChains command.

julia
(@v1.10) pkg> add BioMarkovChains

For more information, see the Getting Started section.

</div>

+ \ No newline at end of file