01_intro_AI_on_Supercomputer/01_linear_regression_sgd.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Artificial intelligence in a nutshell\n",
    "\n",
    "In this notebook, we will talk about \n",
    "* What is AI training? \n",
    "* How does large language model work? \n",
    "* A simple AI model: linear regression\n",
    "\n",
    "**How to run this notebook on Polaris**\n",
    "* Go to https://jupyter.alcf.anl.gov, and click \"Login Polaris\"\n",
    "* After login, select ```ALCFAITP``` project and ```ALCFAITP``` queue during the lecture (use ```debug``` queue outside of the lecture)\n",
    "* Load the notebook and select \"datascience/conda-2023-01-10\" python kernel\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/jupyter1.png\" width=\"600\" />\n",
    "  <img src=\"figures/jupyter2.png\" width=\"600\" /> \n",
    "</p>\n",
    "\n",
    "**How to run this notebook on Google Colab**\n",
    "\n",
    "* Go to https://colab.research.google.com/, sign in or sign up\n",
    "* \"File\"-> \"open notebook\"\n",
    "* choose ```01_intro_AI_on_Supercomputer/01_linear_regression_sgd.ipynb``` from the list\n",
    "![Google Colab](figures/colab.png)\n",
    "\n",
    "## What is AI training?\n",
    "**Two ways of learning English** \n",
    "* through learning rules;\n",
    "* through hearing a lot of speakings\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/data_driven.png\" width=\"1000\" /> \n",
    "</p>\n",
    "\n",
    "I learned English in my middle school, and memorized a lot of grammar rules in my mind. Every time when I speak, I try to follow the grammar rules as much as I can. But I always break the rules. \n",
    "\n",
    "However, my daugher learned English differently. She learns speaking by hearing a lot of speaking from TV, teachers, classmates, and her older brother. The fact is that, she seldomly breaks grammar rules. This way of learning by observing patterns is very powerful! This is the essence of AI or data driven science. \n",
    "\n",
    "## How does large language model work? \n",
    "\n",
    "Large Language Models, like GPT, function by pre-training on extensive datasets to learn language patterns, utilizing transformer architecture for contextual understanding, and can be fine-tuned for specific tasks, enabling them to generate coherent and contextually relevant text based on provided inputs.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/llm2.png\" width=\"600\" />\n",
    "  <img src=\"figures/chatgpt_response.png\" width=\"160\" /> \n",
    "</p>\n",
    "\n",
    "**More complicated example**\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/chatgpt_poem.png\" width=\"400\" /> \n",
    "  <img src=\"figures/martin.png\" width=\"450\" /> \n",
    "</p>\n",
    "\n",
    "You can do this on https://chat.openai.com\n",
    "\n",
    "## Simplest AI model example: linear regression\n",
    "This example is adopted from Bethany Lusch, ALCF. \n",
    "\n",
    "Linear regression is the simplest example ``learning\" from existing data for future prediction. \n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/excel_linear_regression.jpg\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "We're going to review the math involved in this process to help understand how training an AI works.\n",
    "\n",
    "First we will load some tools that others wrote and we can use to help us work.\n",
    "* [Pandas](https://pandas.pydata.org/docs/): a toolkit for working with row vs. column data, like excel sheets, and CSV (Comma Seperated Values) files.\n",
    "* [Numpy](https://numpy.org/doc/): a toolkit for managing arrays, vectors, matrices, etc, doing math with them, slicing them up, and many other handy things.\n",
    "* [Matplotlib](https://matplotlib.org/stable/index.html): a toolkit for plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython.display as ipydis\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset\n",
    "We used a realestate dataset from Kaggle to produce this reduced dataset. This dataset contains the _sale price_ and _above ground square feet_ of many houses. We can use this data for our linear regression.\n",
    "\n",
    "We use Pandas to read the data file which is stored as Comma Separated Values (CSV). and print the column labels. CSV files are similar to excel sheets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Unnamed: 0', 'SalePrice', 'GrLivArea'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "! [ -e ./slimmed_realestate_data.csv ] || wget https://raw.githubusercontent.com/argonne-lcf/ai-science-training-series/main/01_intro_AI_on_Supercomputer/slimmed_realestate_data.csv\n",
    "data = pd.read_csv('slimmed_realestate_data.csv')\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now pandas provides some helpful tools for us to inspect our data. It provides a `plot()` function that, behind the scenes, is calling into the _Matplotlib_ library and calling the function [matplotlib.pyplot.plot()](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html). In this case, we simply tell it the names of the columns we want as our _x_ and _y_ values and the `style` (`'.'` tells `matplotlib` to use a small dot to represent each data point)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='GrLivArea'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(x='GrLivArea', y='SalePrice',style='.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theory of linear regression\n",
    "\n",
    "The goal of learning regression is to find a line that is closest to all the points. \n",
    "\n",
    "The slope and intercept of such a line $y = m x + b$ can be found as: \n",
    "\n",
    "$$m = { n (\\Sigma xy) - (\\Sigma x) (\\Sigma y) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "$$b = { (\\Sigma y) (\\Sigma x^2) - (\\Sigma x) (\\Sigma xy) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "Details derivation of this can be found [here](https://en.wikipedia.org/wiki/Simple_linear_regression). \n",
    "\n",
    "We'll break this calculation into a few steps to help make it easier.\n",
    "\n",
    "First lets define $x$ and $y$. $x$ will be our _above ground square footage_ and $y$ will be _sale price_. In our equations we have a few different values we need, such as $n$ which is just the number of points we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we need our $x$ and $y$ by selecting only the column we care about for each one. Note about data formats: `data` is a Pandas [DataFrame](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html#pandas.DataFrame) object which has rows and columns; `data['GrLivArea']` is a Pandas [Series](https://pandas.pydata.org/docs/reference/api/pandas.Series.html) object which only has rows; then we also convert from _Pandas_ data formats (in this case a _Series_) to _Numpy_ data formats using the `to_numpy()` function which is part of the Pandas _Series_ object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data['GrLivArea'].to_numpy()\n",
    "y = data['SalePrice'].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will calculate $\\Sigma xy$, $\\Sigma x$, $\\Sigma y$, and $\\Sigma x^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_xy = np.sum(x*y)\n",
    "sum_x = np.sum(x)\n",
    "sum_y = np.sum(y)\n",
    "sum_x2 = np.sum(x*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominator in the equation for $m$ and $b$ are the same so we can calculate that once:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "denominator = n * sum_x2 - sum_x * sum_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our fit values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 87.688145 * x + 34754.077892\n"
     ]
    }
   ],
   "source": [
    "m = (n * sum_xy - sum_x * sum_y) / denominator\n",
    "b = (sum_y * sum_x2 - sum_x * sum_xy) / denominator\n",
    "print('y = %f * x + %f' % (m,b))\n",
    "\n",
    "# saving these for later comparison\n",
    "m_calc = m\n",
    "b_calc = b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the fit results with our data to see how we did. \n",
    "\n",
    "First we define a plotting function because we're going to do this often and we want to reuse our code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x,y,m,b,plt = plt):\n",
    "   # plot our data points with 'bo' = blue circles\n",
    "   plt.plot(x,y,'bo')\n",
    "   # create the line based on our linear fit\n",
    "   # first we need to make x points\n",
    "   # the 'arange' function generates points between two limits (min,max)\n",
    "   linear_x = np.arange(x.min(),x.max())\n",
    "   # now we use our fit parameters to calculate the y points based on our x points\n",
    "   linear_y = linear_x * m + b\n",
    "   # plot the linear points using 'r-' = red line\n",
    "   plt.plot(linear_x,linear_y,'r-',label='fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now can use this function to plot our results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training through Stochastic Gradient Descent (SGD)\n",
    "\n",
    "SGD is a common method in AI for training deep neural networks on large datasets. It is an iterative method for optimizing a loss function that we get to define. We will use this simple linear regression to demonstrate how it works.\n",
    "\n",
    "#### The model\n",
    "\n",
    "In AI, neural networks are often referred to as a _model_ because, once fully trained, they should model (AKA predict) the behavior of our system. In our example, the system is how house prices vary based on house size. We know our system is roughly driven by a linear function:\n",
    "\n",
    "$$ \\hat{y_i}(x_i) = m * x_i + b $$\n",
    "\n",
    "We just need to figure out $m$ and $b$. Let's create a function that calculates our model given $x$, $m$, and $b$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x,m,b):\n",
    "   return m * x + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "#### The Loss Function\n",
    "\n",
    "A _loss function_, or _objective function_, is something we define and is based on what we want to achieve. In the method of SGD, it is our goal to minimize (or make close to zero) the values calculated from the _loss function_. In our example, we ideally want the prediction of our _model_ to be equal to the actual data, though we will settle for \"as close as possible\".\n",
    "\n",
    "So we will select our _loss function_ to be the [Mean Squared Error](https://en.wikipedia.org/wiki/Mean_squared_error) function:\n",
    "\n",
    "$$ L(y_i,\\hat{y_i}) = (y_i - \\hat{y_i}(x_i))^2 $$\n",
    "\n",
    "where $y_i$ is our $i^{th}$ entry in the `data['SalePrice']` vector and $\\hat{y_i}$ is the prediction based on evaluting $m * x_i + b$.\n",
    "\n",
    "This function looks like the figure below when we plot it with $x=y_i - \\hat{y_i}(x_i)$ and we we want to be down near $y_i - \\hat{y_i}(x_i) = 0$ which indicates that our $y_i$ is as close as possible to $\\hat{y_i}$.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/loss_func.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Here we crate a function that calculates this for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(x,y,m,b):\n",
    "   y_predicted = model(x,m,b)\n",
    "   return np.power( y - y_predicted, 2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Minimizing the Loss Function\n",
    "\n",
    "We want to use the loss function in order to guide how to update $m$ and $b$ to better model our system. In calculus we learn to minimize a function with respect to a variable you calculate the _partial derivative_ with respect to the variable you want to vary.\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = 0 $$\n",
    "\n",
    "The location of the solution to this is the minimum as shown in the figure above. We can write down the partial derivative of the loss function as:\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = -2 x_i (y_i - \\hat{y_i}(x_i)) $$\n",
    "$$ { \\partial L \\over \\partial b } = -2 (y_i - \\hat{y_i}(x_i)) $$\n",
    "\n",
    "We can use this to calculate an adjustment to $m$ and $b$ that will reduce the loss function, effectively improving our fitting parameters. This is done using this equation:\n",
    "\n",
    "$$ m' = m - \\eta { \\partial L \\over \\partial m }$$\n",
    "$$ b' = b - \\eta { \\partial L \\over \\partial b }$$\n",
    "\n",
    "Here our original $m$ and $b$ are adjusted by the partial derivative multiplied by some small factor, $\\eta$, called the _learning rate_. This learning rate is very important in our process and must be tuned for every problem.\n",
    "\n",
    "In our example, the selection of the learning rate essentially defines how close we can get to the minimum, AKA the best fit solution. This figure shows what happens when we pick a large learning rate. We first select a starting point in our loss function (typically randomly), then every update from $m$/$b$ to $m'$/$b'$ results in a shift to somewhere else on our loss function (following the red arrows). In this example, our learning rate ($\\eta$) has been selected too large such that we bounce back and forth around the minimum, never reaching it.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/parabola_largeLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "If we select a smaller learning we can see better behavior in the next figure.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/parabola_smallLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Though, keep in mind, too small a learning rate results is so little progress toward the minimum that you may never reach it!\n",
    "\n",
    "A pit fall of SGD that one must be aware of is when your loss function is complex, with many minima. The next figure shows such a case, in which we select a small learning rate and our starting point happens to be near a local minimum that is not the lowest minimum. As shown, we do reach a minimum, but it isn't the lowest minimum in our loss function. It could be that we randomly select a starting point near the minimum we care about, but we should build methods that are more robust against randomly getting the right answer.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_smallLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Then, if we increase our learning rate too much, we bounce around again.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_largeLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "What we want to do in this situation is start with a large learning rate and slowly reduce its size as we progress. That is shown in this next figure.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_variableLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "As you can see, this process is not perfect and could still land in a local minimum, but it is important to be aware of these behaviors as you utilize SGD in machine learning.\n",
    "\n",
    "So let's continue, we'll build functions we can use to update our fit parameters, $m$ and $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def updated_m(x,y,m,b,learning_rate):\n",
    "   dL_dm = - 2 * x * (y - model(x,m,b))\n",
    "   dL_dm = np.mean(dL_dm)\n",
    "   return m - learning_rate * dL_dm\n",
    "\n",
    "def updated_b(x,y,m,b,learning_rate):\n",
    "   dL_db = - 2 * (y - model(x,m,b))\n",
    "   dL_db = np.mean(dL_db)\n",
    "   return b - learning_rate * dL_db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Putting it together\n",
    "\n",
    "We can now randomly select our initial slope and intercept:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.00 * x + 1000.00\n"
     ]
    }
   ],
   "source": [
    "m = 5.\n",
    "b = 1000.\n",
    "print('y_i = %.2f * x + %.2f' % (m,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our Loss function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first 10 loss values:  [3.03421561e+10 3.55511025e+10 1.24579082e+10 1.91656336e+10\n",
      " 1.60604929e+10 2.04432804e+10 1.72410030e+10 1.76517796e+10\n",
      " 1.52769600e+10 2.18152900e+10]\n"
     ]
    }
   ],
   "source": [
    "l = loss(x,y,m,b)\n",
    "print('first 10 loss values: ',l[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.47 * x + 1000.00     previously calculated: y_i = 87.69 * x + 34754.08\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rate = 1e-9\n",
    "m = updated_m(x,y,m,b,learning_rate)\n",
    "b = updated_b(x,y,m,b,learning_rate)\n",
    "print('y_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f' % (m,b,m_calc,b_calc))\n",
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[029]  dy_i = 88.89 * x + 32912.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478200827.641291\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set our initial slope and intercept\n",
    "m = 5.\n",
    "b = 1000.\n",
    "# batch_size = 60\n",
    "# set a learning rate for each parameter\n",
    "learning_rate_m = 1e-7\n",
    "learning_rate_b = 1e-1\n",
    "# use these to plot our progress over time\n",
    "loss_history = []\n",
    "# convert panda data to numpy arrays, one for the \"Ground Living Area\" and one for \"Sale Price\"\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "# we run our loop N times\n",
    "loop_N = 30\n",
    "for i in range(loop_N):\n",
    "   # update our slope and intercept based on the current values\n",
    "   m = updated_m(data_x,data_y,m,b,learning_rate_m)\n",
    "   b = updated_b(data_x,data_y,m,b,learning_rate_b)\n",
    "\n",
    "   # calculate the loss value\n",
    "   loss_value = np.mean(loss(data_x,data_y,m,b))\n",
    "\n",
    "   # keep a history of our loss values\n",
    "   loss_history.append(loss_value)\n",
    "\n",
    "   # print our progress\n",
    "   print('[%03d]  dy_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f    loss: %f' % (i,m,b,m_calc,b_calc,loss_value))\n",
    "   \n",
    "   # close/delete previous plots\n",
    "   plt.close('all')\n",
    "   \n",
    "   # create a 1 by 2 plot grid\n",
    "   fig,ax = plt.subplots(1,2,figsize=(18,6),dpi=80)\n",
    "   # lot our usual output\n",
    "   plot_data(data_x,data_y,m,b,ax[0])\n",
    "\n",
    "   # here we also plot the calculated linear fit for comparison\n",
    "   line_x = np.arange(data_x.min(),data_x.max())\n",
    "   line_y = line_x * m_calc + b_calc\n",
    "   ax[0].plot(line_x,line_y,'b-',label='calculated')\n",
    "   # add a legend to the plot and x/y labels\n",
    "   ax[0].legend()\n",
    "   ax[0].set_xlabel('square footage')\n",
    "   ax[0].set_ylabel('sale price')\n",
    "\n",
    "   # plot the loss \n",
    "   loss_x = np.arange(0,len(loss_history))\n",
    "   loss_y = np.asarray(loss_history)\n",
    "   ax[1].plot(loss_x,loss_y, 'o-')\n",
    "   ax[1].set_yscale('log')\n",
    "   ax[1].set_xlabel('loop step')\n",
    "   ax[1].set_ylabel('loss')\n",
    "   plt.show()\n",
    "   # gives us time to see the plot\n",
    "   # time.sleep(2.5)\n",
    "   # clears the plot when the next plot is ready to show.\n",
    "   ipydis.clear_output(wait=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework\n",
    "## Mini Batch Training\n",
    "In AI, datasets are often very large and cannot be processed all at once as is done in the loop above. The data is instead randomly sampled in smaller _batches_ where each _batch_ contains `batch_size` inputs. How can you change the loop above to sample the dataset in smaller batches? Hint: Our `data` variable is a Pandas `DataFrame` object, search for \"how to sample a DataFrame\".\n",
    "\n",
    "Instead of using the entire dataset like \n",
    "```python\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "```\n",
    "Use \n",
    "```python\n",
    "data_batch = data.sample(batch_size)\n",
    "data_x = data_batch['GrLivArea'].to_numpy()\n",
    "data_y = data_batch['SalePrice'].to_numpy()\n",
    "```\n",
    "\n",
    "You also have to adjust the loop_N accordingly to make sure that it loop over the entire datasets the same number of times.\n",
    "```python\n",
    "loop_N = 30*len(data)//batch_size\n",
    "```\n",
    "\n",
    "Please plot your learning curve for different batch size, such as 32, 64, 128, 256, 512. \n",
    "\n",
    "## Learning rate issue (Bonus)\n",
    "As described above, if the learning rate is too large, it will affect the convergence. Do your training with (batch_size = 64, learning_rate_m = 1e-7, learning_rate_b = 1e-1). Then linearly increase the batch size and learning rate until you see the training does not converge. \n",
    "```\n",
    "(64, 1e-7, 1e-1)*1\n",
    "(64, 1e-7, 1e-1)*2\n",
    "(64, 1e-7, 1e-1)*4\n",
    "(64, 1e-7, 1e-1)*8\n",
    "...\n",
    "```\n",
    "\n",
    "**How to submit your homework**\n",
    "* Fork the github repo to your personal github \n",
    "* Make change to the 01_linear_regression_sgd.ipynb, and then push to your personal github\n",
    "* Provide the link of 01_linear_regression_sgd in the personal github. \n",
    "\n",
    "Follow the below instruction on how to do this: \n",
    "https://github.com/argonne-lcf/ai-science-training-series/blob/main/00_introToAlcf/03_githubHomework.md"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Submission"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Mini Batch Training\n",
    "\n",
    "The task here is to \"train\" our model using batches of data. We break the dataset into chunks of size `batch_size`. We train the model on a subset of the data, and run this \"inner loop\" enough times to see all of the data. In the \"outer loop\" of training, we compute the loss and log the results.\n",
    "\n",
    "The idea behind the \"inner loop\" of training with a subset of the data is the ability to distribute the work over multiple compute resources. Each compute resource would run the \"inner loop\", then communicate its parameters as part of the \"outer loop\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== BATCH_SIZE = 64 ===== \n",
      "[000]  dy_i = 89.16 * x + 32502.29     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478408177.654546\n",
      "[001]  dy_i = 88.67 * x + 33247.55     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478062102.037441\n",
      "[002]  dy_i = 88.35 * x + 33746.16     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477907194.733171\n",
      "[003]  dy_i = 88.13 * x + 34079.74     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477837856.785210\n",
      "[004]  dy_i = 87.98 * x + 34302.92     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477806820.475785\n",
      "[005]  dy_i = 87.89 * x + 34452.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477792928.335463\n",
      "[006]  dy_i = 87.82 * x + 34552.14     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477786710.084443\n",
      "[007]  dy_i = 87.78 * x + 34618.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477783926.737540\n",
      "[008]  dy_i = 87.75 * x + 34663.69     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782680.885618\n",
      "[009]  dy_i = 87.73 * x + 34693.60     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782123.230728\n",
      "[010]  dy_i = 87.71 * x + 34713.62     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781873.619221\n",
      "[011]  dy_i = 87.71 * x + 34727.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781761.890792\n",
      "[012]  dy_i = 87.70 * x + 34735.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781711.880110\n",
      "[013]  dy_i = 87.70 * x + 34741.96     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781689.494864\n",
      "[014]  dy_i = 87.69 * x + 34745.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781679.475020\n",
      "[015]  dy_i = 87.69 * x + 34748.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781674.990045\n",
      "[016]  dy_i = 87.69 * x + 34750.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.982528\n",
      "[017]  dy_i = 87.69 * x + 34751.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.083945\n",
      "[018]  dy_i = 87.69 * x + 34752.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.681731\n",
      "[019]  dy_i = 87.69 * x + 34752.99     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.501696\n",
      "[020]  dy_i = 87.69 * x + 34753.35     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.421111\n",
      "[021]  dy_i = 87.69 * x + 34753.59     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.385040\n",
      "[022]  dy_i = 87.69 * x + 34753.75     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.368895\n",
      "[023]  dy_i = 87.69 * x + 34753.86     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.361668\n",
      "[024]  dy_i = 87.69 * x + 34753.93     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.358433\n",
      "[025]  dy_i = 87.69 * x + 34753.98     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356985\n",
      "[026]  dy_i = 87.69 * x + 34754.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356337\n",
      "[027]  dy_i = 87.69 * x + 34754.03     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356047\n",
      "[028]  dy_i = 87.69 * x + 34754.05     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355917\n",
      "[029]  dy_i = 87.69 * x + 34754.06     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355859\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== BATCH_SIZE = 256 ===== \n",
      "[000]  dy_i = 89.16 * x + 32502.29     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478408177.654546\n",
      "[001]  dy_i = 88.67 * x + 33247.55     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478062102.037441\n",
      "[002]  dy_i = 88.35 * x + 33746.16     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477907194.733171\n",
      "[003]  dy_i = 88.13 * x + 34079.74     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477837856.785210\n",
      "[004]  dy_i = 87.98 * x + 34302.92     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477806820.475785\n",
      "[005]  dy_i = 87.89 * x + 34452.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477792928.335463\n",
      "[006]  dy_i = 87.82 * x + 34552.14     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477786710.084443\n",
      "[007]  dy_i = 87.78 * x + 34618.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477783926.737540\n",
      "[008]  dy_i = 87.75 * x + 34663.69     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782680.885618\n",
      "[009]  dy_i = 87.73 * x + 34693.60     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782123.230728\n",
      "[010]  dy_i = 87.71 * x + 34713.62     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781873.619221\n",
      "[011]  dy_i = 87.71 * x + 34727.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781761.890792\n",
      "[012]  dy_i = 87.70 * x + 34735.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781711.880110\n",
      "[013]  dy_i = 87.70 * x + 34741.96     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781689.494864\n",
      "[014]  dy_i = 87.69 * x + 34745.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781679.475020\n",
      "[015]  dy_i = 87.69 * x + 34748.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781674.990045\n",
      "[016]  dy_i = 87.69 * x + 34750.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.982528\n",
      "[017]  dy_i = 87.69 * x + 34751.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.083945\n",
      "[018]  dy_i = 87.69 * x + 34752.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.681731\n",
      "[019]  dy_i = 87.69 * x + 34752.99     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.501696\n",
      "[020]  dy_i = 87.69 * x + 34753.35     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.421111\n",
      "[021]  dy_i = 87.69 * x + 34753.59     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.385040\n",
      "[022]  dy_i = 87.69 * x + 34753.75     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.368895\n",
      "[023]  dy_i = 87.69 * x + 34753.86     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.361668\n",
      "[024]  dy_i = 87.69 * x + 34753.93     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.358433\n",
      "[025]  dy_i = 87.69 * x + 34753.98     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356985\n",
      "[026]  dy_i = 87.69 * x + 34754.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356337\n",
      "[027]  dy_i = 87.69 * x + 34754.03     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356047\n",
      "[028]  dy_i = 87.69 * x + 34754.05     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355917\n",
      "[029]  dy_i = 87.69 * x + 34754.06     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355859\n"
     ]
    },
    {
     "data": {
      "image/png": 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uW9wvu+yyIu9dX331VZnWW/z9HXC+x6ekpFRop9zS3uNdrcGxjpI+ZzRr1oxjx44VGRrtkJWVxbFjx2jevDkAI0eO5PTp0yxbtgzTNPnggw8YN24cAIcPH+bMmTOMHDmyyOeH9evXFxl70Lx58woFVQ6eflYp/tkjPT2d2267jYiICEJDQwkLC+PMmTOlfn4srDJeh1dffZXo6Gh+85vf0KJFC373u9+VGPAMHz7c2Q5XWoD6008/cerUKS5cuMCGDRt45ZVXeOeddwCrFe25556jS5cuNGrUiLCwMGbMmFHqY/fk59bdz70r1113HfPmzWP//v2kpKQQFRXF9ddff8lg8sLeeust3nvvPZYuXeoMpBMTE8nNzSU8PNz5c+D4XL5v3z63a66oqVOn8s4777By5UrnuAuAkJAQ+vTpQ1BQEPXq1eOuu+7it7/9rTNgDw0NBWDSpEl07NiRoKAgHnzwQcLDw1m8eLFX1yxlo8BKRDw2Z84c54dRsD40tW/fnu3bt3PmzBnnXyRM0wSs3v3iNmzYwAMPPMDf//53Dh06xOnTp3nuueect3ElPDycyy+/nH/9619kZGTQq1cvhg0b5gysrr322hJv62oNFTV27FiWLl3KoUOHuPnmmy853qZNG9LT04t8GE9OTgYgIiLC+YaamprqPF74vwFatmzJ7bffXuQD+5kzZ5wf/iuTN54jERGpOZo2bUrdunWd72UOycnJziqIyMhI3n33XdLS0li5ciXLli1zVg/Hxsby8ccfc+jQIRYsWMDbb79d5ophgAYNGnD27Nkilx04cKBM54iKimLPnj0uj3nyfljae3x5DBs2DMMw+Oijjy45Nnv2bGw2G0OHDgWsavfbb7+d9957j6+//prDhw87dzAOCwujbt26/O9//yvy+eHs2bNFZjeV533f1W08/axS/Lb33nsv+fn5bNy4kTNnznDy5ElCQ0Pdfn4srjJehyZNmvCPf/yD3bt3s2nTJlJTU5k8ebLL63711VfOwd2eBqg2m40ePXrQv39//vvf/wLwySef8Nprr/Hvf/+bY8eOcerUKSZMmFDkc7Crx+/u57YyREZG8tRTT3H69OlL/nfuMHfuXKZOncpXX31VJLxu2bIlQUFBHD16tMjPwvnz513urg2wZs2aS3YCLf7lbqaqaZr84Q9/YM6cOaxZs8ajENpmszmf544dOzrncIl/028pIlKqo0ePMmPGDB5++GH+/Oc/O1vgTp8+TWhoKA0bNuTEiRM88sgjRW7n2DmvcIvg6dOnCQgIoFmzZgQGBvLTTz/x1ltvlbqGoUOH8uKLL3L11VcTEBBA//792bVrF8uWLXN+iHOlZcuWJCcnk5eXV56H7lKjRo1YtWoVS5YsKfKXPYdf/epX2O12nnjiCc6fP8+hQ4f44x//yA033EDLli1p3bo1gwcP5tFHH+XkyZOcPHmSJ554osg57r//fhYsWMD8+fPJzs4mLy+PpKQkr/zVxxvPkYiIVE95eXlcuHChyBfA73//e55++mn27t1LdnY2//jHP0hKSuKOO+4ArAqrjIwMTNMkNDQUu92O3W4nOzubmTNnOnfYbdiwIQEBAS7fP0vTo0cPvvnmG37++WdycnJ47bXXyty+89BDD/HSSy/x9ddfk5eXxy+//MKqVasAq9LJZrO5HW1Q2nt8eTiGlf/xj3/kww8/5JdffuGXX35h9uzZTJ48mb/85S9FQphx48bx+eef8/LLLzNq1CgaNGgAWO2DEydO5NFHH2XXrl2Ypsn58+dZvXp1hcMOV58VyvtZ5fTp04SEhNCoUSPOnj3L448/XiTkqqrX4ZNPPiE5OZn8/HwaNGhAnTp1yvVz6c7mzZtZs2YN8fHxgPXY7XY7zZs3xzAMvvnmG2fVj0PLli0veb0eeugh3n//fRYuXEh2djYXLlwoMky/rD744APmzp3rrOw6evQo06ZNo1mzZi535FyxYgX33nsvn376KVdccUWRY/369aNr167cd999zvOdPHmShQsXlripUv/+/S/ZCbT4V0nBY25uLnfeeScrV65kzZo1RdotHdasWcOuXbvIy8sjOzubOXPm8PHHHzsDtDp16nDvvffyxhtvkJycTG5uLtOnT+fAgQNlbkEW71JgJSIuOXYnCQ0N5YorruDLL79k9uzZvPjii87rfPDBB8yfP58GDRrQu3fvS/4PPiYmhgcffJCrr76asLAwXnzxRYYOHcrEiRMZNGgQDRs25IknnmDMmDGlrmfo0KGcPn3aGU7VqVOHfv36kZ+fT0JCQom3Gz9+PGD9dTgsLKzSdsDr0aMHsbGxLo+FhoaybNkytmzZQnh4uLMF4l//+pfzOrNnzyYoKIioqCi6d+/O6NGji5yjZ8+eLFu2jHfffZfWrVs7d4MpvjNQZfDWcyQiItXPiy++SL169Yp8ff3117z66qsMHTqUq6++mubNm7Nw4UKWLVtGmzZtAGsnwKuuuoqQkBDi4uLo06ePc4v4BQsW0KVLF+rXr8/AgQMZO3asR+/9xd1xxx3cdtttJCQk0KZNG06dOkXfvn3LdI7x48fzwgsv8PDDD9OoUSM6dOjAokWLAKt66fnnn2fcuHGEhYVx//33X3J7T97jy+OZZ57h7bff5p///CetWrWiVatWvPXWW7zzzjs8+eSTRa7bvXt3unTpwtKlS53tgA6vvvoqv/3tb51tgVFRUbzwwgvk5ORUaH2uPiuU97PKG2+8wZYtW2jUqBGdO3emdevWRdq5qup12LJlC9dccw0NGjSgffv2hIWF8eqrr3p8+5I4djcMCQnhlltuYcyYMUydOhWwqvQHDx5MbGwsTZs25e23375k58tHHnmE3bt3O1sGwfocPGfOHF588UWaNWtGeHg4M2bMKPcaGzduzDvvvEPXrl2pX78+3bp149SpUyxfvpx69epdcv0PP/yQs2fPcsMNNxSpglqzZg0BAQEsW7aM4OBgevXqRYMGDYiLi+M///mPVyqY1q1bx8cff0xycjIdOnQosh6H3bt38+tf/5rQ0FBatmzJ66+/zocffsiNN97ovM7LL7/M8OHD6dOnD02bNuWjjz7iq6++chmAie8Yprs+HBERERERERERkSqmCisREREREREREfErCqxERERERERERMSvKLASERERERERERG/osBKRERERERERET8igIrERERERERERHxK3ZfL8Df1alTh2bNmvl6GSIiIuJFR48eJSsry9fLkEL0GUxERKRmK+3zlwKrUjRr1oyMjAxfL0NERES8KDw83NdLkGL0GUxERKRmK+3zl1oCRURERERERETEryiwEhERERERERERv6LASkRERERERERE/IpmWFVQfn4+pmn6ehm1imEYzi8RERERERERqXkUWJVTdnY26enp5OTk+HoptZJhGISFhdG8eXNsNhUKioiIiIiIiNQkCqzKKT09nQYNGtCkSRNV+vhATk4Ohw8fJi0tjbZt2/p6OSIiIiIiIiJSiRRYlUN+fj45OTk0adIEu11PoS8EBATQunVrEhMTyc/PV5WViIiIiIiISA2i3/LLwTGzSpVVvuV4/jVDTERERERERKRmUWAlIiIiIiIiIiJ+RYFVDfLZZ5/RqVMn4uPjCQgI4JdffgHgtdde49ChQz5enYiIiIiIiIiIZxRY1SBvv/02Tz/9NJs3byYvL48GDRoACqxEREREREREpHrRxPDKcOONkJzsvfO3bw+ff+72KpMmTWLNmjX8/PPPvPnmm2zYsIGTJ0/yxhtvcODAAUaPHk29evWYNWsW8fHx3luriIhIJTNNWLcOkpIgOhr69gWNkZTyME2TH9JOknrsLFFN69MjspFmkoqIiPgpBVY1xBtvvMHWrVt5+OGHufnmm50fvp5++mk++OAD5s6dq6BKRESqnbQ0GDYMUlIgKAiys6FtW1iyBCIjfb06qU4yTp7j7g++Z9+JcwQG2MjJy6dN42D+/furCG8U7OvliYiISDEKrCpDKdVPIiIiUnamaYVVycmQm2uFVWB9f911sHOnKq3EM6ZpcvcH35N2/Bx5+SY5eXkApB0/x5gPvmf55IGqtBIREfEzmmElIiIifmndOkhNtcKqwnJzYe9e67iIJ35IO0nGifPk5ZtFLs/LN0k/cY4f0k76aGUiIiJSEgVWtUBoaCinT5/29TJERETKJCkJAgNdHwsKso6LeCL12FnsAa4rqAIDbKQeO1vFKxIREZHSKLCqBSZNmsS9995LfHw8mzdv9vVyREREPBIdXdAGWFx2tnVcxBNRTeuTk5fv8lhOXj5RTetX8YpERESkNJphVYOsXLnS+d+mWVDyPm7cOMaNG+eDFYmIiJRf377WgHXHDCsHux3atbOOi3iiR2Qj2jQOds6wcgiwGUQ0DqZHZCMfrk5ERERcUYWViIiI+CXDsHYDbN/eagEMCbH+jY62LteMbPGUYRj8+/dXEdkk2PlzExhgENUkmH/f00sD10VERPyQKqxERETEb0VGwq5d1oD1pCQrrOrbV2GVlF14o2BWTB7IyBkb+CntJB/f25sekY0UVomIiPgpBVYiIiLi1wwD+vWzvkQqwjAMGgcHYRgGPaMa+3o5IiIi4oZaAkVERESk1jCMorM+RURExD8psBIRERGRWsNALYAiIiLVgQIrEREREalVVF8lIiLi/xRY1WKGYXDq1Kly337s2LG89tprpV5v0aJFfPvtt+W6j//9738MGjSoXLcVERER/5GTk8OoUaMYNGgQr7zyis/WYbUE+uzuRURExEMKrMTrKhJYiYiISM3w6aefkpCQwMqVK/nxxx85evSoT9ahTQFFRESqBwVWNciGDRvo168fcXFxdOvWjc8++4w//elP9OzZk/j4eAYMGMDu3btd3nbXrl0MGzaMbt260a1bN95++20ABg0axKJFi5zXGzFiBLNmzbrk9itWrKBPnz5cccUVdOnShffffx+AL7/8ks8//5xXXnmF+Ph43nvvPQA+/PBDevXqRffu3RkwYABbtmwBrL++3n///XTo0IGrrrqKb775phKfIREREfGVlJQUYmNjAejUqRMbN270yTocM6w0eF1ERMS/2X29gJrgxhshOdl752/fHj7/3P11Tpw4wc0338yCBQvo378/+fn5nDp1ioSEBF599VUAPvnkEx566CEWL15c5La5ubncdNNN/PWvf+W3v/0tAMeOHSvTGrt3787atWsJCAjgxIkTXHHFFQwbNozrr7+eG2+8kfj4eB5++GEA1q1bx5w5c1i9ejV16tRhzZo13H777ezYsYN33nmH3bt3s2PHDgCGDRtWpnWIiIjIpbKysnjkkUdYsmQJdevWJS4ujtmzZ5f7fJMmTeLzzz8nLS2NTZs2ER8f7zyWmJjImDFjOHbsGA0bNmTWrFl06dKFjh07smrVKq655hrWrFlDTExMJTyycrhYYWWaqrYSERHxZwqsaogNGzbQsWNH+vfvD4DNZqNx48Z8/PHHvPnmm/zyyy/k5+dz4sSJS267e/duLly44AyrAJo2bVqm+z9+/Dj33HMPe/bswW63c/z4cbZv3054ePgl1/3ss8/YsmULvXr1cl524sQJzp8/z4oVK7j77rsJCgoC4Pe//72zWktERETK57HHHsMwDPbs2YNhGBw6dOiS62RnZ7N//37atm3rvCwrK4uDBw8SFRVV5LojRozg0UcfpV+/fpecZ8KECYwfP56xY8eyYMECxo4dy8aNG7nxxhtZunQp1157Lc2aNaN58+aV/jg94cioVF8lIiLi3xRYVYLSqp98JT09nQceeICNGzfSvn17tm7dyoABA8p0DrvdTl5envP7CxcuuLzexIkTuf7661m4cCGGYdC9e/cSr2uaJmPGjOH5558v9f4N/elTRESkQs6ePcv7779PRkaG8321ZcuWl1xv586d3HrrrSxatIjY2FjOnTvHzTffzODBg5kyZUqR65b0eeLIkSP88MMPLF26FIBbb72VBx54gKSkJKKjo5k+fbrzc0CfPn1cnmP+/PnMnz+f8+fPV+Rhl8jxHFgtgfqcISIi4q80w6qGSEhIIDExkTVr1gCQn59PSkoKgYGBtGrVCtM0eeutt1zetmPHjgQHBzNnzhznZY6WwOjoaL777jvAmj2xdu1al+c4efIkkZGRGIbB6tWrnTOpAEJDQzl9+rTz+xtvvJHZs2eTnp7uXOsPP/wAwJAhQ5g9ezY5OTlkZ2czc+bM8j4lIiIiAiQnJ9O4cWOef/55evToQf/+/VmxYsUl14uPj+fDDz/kpptuYtWqVQwfPpz+/ftfEla5s2/fPlq1aoXdbv1N1DAMIiIiSE9PJz09nUGDBjF48GBGjBhBcHCwy3OMHDmSefPmUa9evfI94FKowkpERKR6UGBVQzRq1Ij//Oc/PPbYY3Tr1o3u3btz5swZbrvtNrp06ULPnj2JiIhweVu73c5nn33GzJkziY2NJS4ujoULFwLw6KOP8s033xAbG8vjjz9epI2vsBdffJHHHnuM+Ph4PvjggyLXu+uuu5g3bx5XXHEF7733Hv379+fll1/mlltuIS4uji5duvDJJ58AcO+999KhQwc6d+5Mv379iszEEBERkbLLzc0lLS2Nzp0788MPP/DGG28wevRoDh8+fMl1ExISmD59OoMGDaJz585MnTq10tYRERHBypUr+frrr7nxxhsr7bxlZRSaYSUiIiL+yzC1RYpb4eHhZGRkFLksLy+PPXv2EBMTQ0BAgI9WJnodRESksrh6v68pjh07RosWLcjOzna+X/bs2ZMXXniBIUOGXHLdYcOGMXToUObOncsHH3zAoEGDSjx3VFQUixYtcv6B6ciRI0RHR3PixAnsdjumadKqVSvWrl1LdHR0mdbtrdfk4U82sWjzAfY8O5wgu/52KyIi4iulvdfrXVpERESkBmvatCmDBw9myZIlgNXin5KSQqdOnYpc7/DhwwwePJj777+fF154gS+++IJx48Y5b+eJ5s2b0717d+cOhAsXLiQ8PLzMYVVVMNUUKCIi4tcUWImIiIjUcG+//TavvPIKsbGx3HzzzcyYMYPWrVsXuc6FCxd46qmnuOeeewDo1KkTixcv5ty5c5ecb8KECc6/ig4bNqxIIDVjxgxmzJhBTEwML774ot/NoywYuu7jhYiIiIhb2iVQREREpIZr164d33zzjdvrREZGEhkZWeSy6Ohol9VRM2bMKPE8HTt2ZMOGDeVbaBXQvoAiIiLVgyqsyqHodsjiK47n3/F6iIiIiJRKQ9dFRESqBa8GVsePHyc+Pt75FRMTg91u58SJExw5coTrrruODh060LVrV1avXu28XVUfKyubzUZgYCDHjx8nNzeXvLw8fVXx14ULF9i/fz9169bFZlPuKiIiIp4xLiZWmmElIiLi37zaEtikSRM2b97s/P7VV19l1apVNG7cmN///vf07t2bxYsXs3HjRm655RZSUlIIDAzkscceq9Jj5REREUF6ejonTpyopGdLysIwDMLCwmjevLmvlyIiIiLViKEKKxERkWqhSmdYvf/++7zwwgsAzJs3j6SkJMDaWvmyyy5j1apVDBkypMqPlUdQUBDR0dHk5+erNbCKGYbh/BIREREpC8enB316ExER8W9VFlitX7+ekydP8utf/5rjx4+Tk5NDy5YtncejoqJIT0+v8mMVpXY0ERERkeqjoMJKkZWIiIg/q7K05f333+fuu+/GbvfvjQmnTZtGeHi48yszM9PXSxIRERGRSlIww0pERET8WZUEVpmZmcybN4/f//73gDXbym63c+jQIed1UlNTiYiIqPJjxU2ePJmMjAznV0hISKU+FyIiIiLiO5ooICIiUj1USWA1d+5c4uLiuPzyy52XjRw5krfffhuAjRs3sn//fgYOHOiTYyIiIiJSu6gjUERExL9VSX/e+++/z7333lvkspdeeom77rqLDh06EBQUxOzZs5079lX1MRERERGpHQxNXRcREakWDFMTJ90KDw8nIyPD18sQERERL9L7vf/x1mvy+KfbmPN9Opufvpaw4KBKP7+IiIh4prT3em1xJyIiIiK1RsEugb5dh4iIiLinwEpEREREag11BIqIiFQPCqxEREREpNYoqLBSZCUiIuLPFFiJiIiISK1hXKyxUlwlIiLi3xRYiYiIiEitoRlWIiIi1YMCKxERERGpNQpmWCmxEhER8WcKrERERESk1jAcJVYiIiLi1xRYiYiIiEjtowIrERERv6bASkRERERqHeVVIiIi/k2BlYiIiIjUGhq6LiIiUj0osBIRERGRWsO4OHZdQ9dFRET8mwIrEREREak1VGElIiJSPSiwEhEREZFaw7FHoPIqERER/6bASkRERERqjYIKK0VWIiIi/kyBlYiIiIjUGsbFxEp5lYiIiH9TYCUiIiIitYZR+lVERETEDyiwEhEREZHaQ0PXRUREqgUFViIiIiIiIiIi4lcUWImIiIhIrWFcLLEytU+giIiIX1NgJSIiIiK1hqGWQBERkWpBgZWIiIiI1BqOoevKq0RERPybAisRERERqTUKKqwUWYmIiPgzBVYiIiIiUmsUzLASERERf6bASkRERERqDc2wEhERqR4UWImIiIhIrWE4/0uJlYiIiD+z+3oBIiIiIiIO8+fPZ/78+Zw/f947d3CxxEoVViIiIv5NFVYiIiIi4jdGjhzJvHnzqFevnlfOr10CRUREqgcFViIiIiJSaxhG6dcRERER31NgJSIiIiK1jloCRURE/JsCKxERERGpNYyLTYGmmgJFRET8mgIrEREREak1HC2BqrASERHxbwqsRERERKTWcA5dV2AlIiLi1xRYiYiIiEit4aywUkugiIiIX1NgJSIiIiK1hnExsVKFlYiIiH9TYCUiIiIiIiIiIn5FgZWIiIiI1Boaui4iIlI9KLASERERkVrDuDh2XTOsRERE/JsCKxERERGpNRwVViIiIuLfvB5YZWVl8cADD9ChQwdiY2O58847AUhMTCQhIYGYmBh69uzJjh07nLep6mMiIiIiUruoJVBERMS/eT2weuyxxzAMgz179rBt2zZeffVVACZMmMD48ePZs2cPU6ZMYezYsc7bVPUxEREREakdHAVWyqtERET8m2Ga3vv70tmzZ2nVqhUZGRmEhoY6Lz9y5AjR0dGcOHECu92OaZq0atWKtWvXEhoaWqXHoqOj3T6G8PBwMjIyvPUUiYiIiB/Q+73/8dZr8s7qZJ7/8mf+c38CV0Q0qvTzi4iIiGdKe6+3e/POk5OTady4Mc8//zzLly+nXr16/OUvfyEsLIxWrVpht1t3bxgGERERpKen07Bhwyo9VlpgJSIiIiI1R8HQdREREfFnXm0JzM3NJS0tjc6dO/PDDz/wxhtvMHr0aHJzc715txUybdo0wsPDnV+ZmZm+XpKIiIiIVBLH0HXNsBIREfFvXg2sIiIisNls3HHHHQBcccUVtG3blrS0NA4ePOgMrkzTJD09nYiICNq0aVOlx4qbPHkyGRkZzq+QkBBvPkUiIiIi4hNKrERERPyZVwOrpk2bMnjwYJYsWQJASkoKKSkp9O3bl+7duzN79mwAFi5cSHh4ONHR0TRv3rxKj4mIiIhI7WFcLLFShZWIiIh/8+rQdYC9e/dyzz33cOzYMWw2G08//TS33noru3fvZuzYsRw/fpzQ0FBmzpxJbGwsQJUfc0dDWEVERGo+vd/7H2+9Jh+sTeH//reT+RP70DOqcaWfX0RERDxT2nu91wOr6k4fYEVERGo+vd/7H2+9JjPXpfDX/+5k3oQ+XNVWgZWIiIivlPZe79WWQBERERERf2L4egEiIiLiEQVWIiIiIlLrqMlARETEvymwEhEREZFawzl03cfrEBEREfcUWImIiIhIrXExr9IugSIiIn5OgZWIiIiI1BqOGVamaqxERET8mgIrEREREak9nCVWvl2GiIiIuKfASkRERERqjYIKKxEREfFnCqxEREREpNbQDCsREZHqQYGViIiIiNQaBo5dApVYiYiI+DMFViIiIiJSa6jCSkREpHpQYCUiIiIitYZR+lVERETEDyiwEhEREZFaRwVWIiIi/k2BlYiIiIjUGgUtgYqsRERE/JkCKxERERGpNQqGrouIiIg/U2AlIiIiIrWHY4iVEisRERG/psBKRERERGqNgrxKiZWIiIg/U2AlIiIiIrWGcXGIlUZYiYiI+DcFViIiIiJSazgrrBRYiYiI+DUFViIiIiJSazh3CfTtMkRERKQUCqxEREREpNZwBlYqsRIREfFrCqxEREREpNYwnE2BIiIi4s8UWImIiIhIraP6KhEREf+mwEpEREREao2ClkDfrkNERETcU2AlIiIiIrWQEisRERF/psBKRERERGoN42KJlSqsRERE/JsCKxERERHxupycHEaNGsWgQYN45ZVXfLYOx8h15VUiIiL+TYGViIiIiHjdp59+SkJCAitXruTHH3/k6NGjPlmHZliJiIhUDwqsRERERMTrUlJSiI2NBaBTp05s3LjRJ+swLtZYmaqxEhER8WsKrERERERqiZkzZ2IYBosWLarQeSZNmkRUVBSGYbB58+YixxITE0lISCAmJoaePXuyY8cOADp27MiqVaswTZM1a9Zw+vTpCq2hvFRhJSIiUj0osBIRERGpBVJTU3n33Xfp3bu3y+PZ2dmkpKQUuSwrK4vU1NRLrjtixAjWrl1LZGTkJccmTJjA+PHj2bNnD1OmTGHs2LEA3HjjjRw9epRrr72WZs2a0bx5c5frmD9/PqNGjeL8+fNle4Ae0gwrERGR6kGBlYiIiEgNl5+fz7hx43jzzTepU6eOy+vs3LmTIUOGsG3bNgDOnTvHDTfcwNy5cy+57oABAwgPD7/k8iNHjvDDDz9w5513AnDrrbeyb98+kpKSCAgIYPr06SxbtozAwED69Onjch0jR45k3rx51KtXr7wP1y1HhZWIiIj4NwVWIiIiIjXctGnT6Nu3L1deeWWJ14mPj+fDDz/kpptuYtWqVQwfPpz+/fszZcoUj+9n3759tGrVCrvdDoBhGERERJCenk56ejqDBg1i8ODBjBgxguDg4Ao/roow1RMoIiLi1+y+XoCIiIiIeM/27dtZuHAhq1evLvW6CQkJTJ8+nUGDBjFx4kSmTp1aaeuIiIhg5cqVlXa+8lOJlYiISHWgCisRERGRGmzNmjWkpqbSoUMHoqKi+Pbbbxk/fjzTp0+/5LrHjh3jiSee4LHHHmPJkiVlDpjatGnDwYMHyc3NBawqpvT0dCIiIirjoVQKDV0XERGpHhRYiYiIiNRg9913HwcPHiQ1NZXU1FR69+7NO++8w3333VfkeocPH2bw4MHcf//9vPDCC3zxxReMGzeOJUuWeHxfzZs3p3v37syePRuAhQsXEh4eTnR0dKU+poooGLquxEpERMSfKbASERERES5cuMBTTz3FPffcA0CnTp1YvHgx586du+S6EyZMIDw8nIyMDIYNG1YkkJoxYwYzZswgJiaGF198kZkzZ1bZY/CEcbHEShVWIiIi/k0zrERERERqkZLa/CIjI4mMjCxyWXR0tMvqqBkzZpR4/o4dO7Jhw4YKrdGbnBVWCqxERET8miqsRERERKTWcM6w8u0yREREpBReD6yioqLo2LEj8fHxxMfHM3fuXAASExNJSEggJiaGnj17smPHDudtqvqYiIiIiNQOBUPXFVmJiIj4syqpsJo7dy6bN29m8+bNjB49GrBmH4wfP549e/YwZcoUxo4d67x+VR8TERERkdrBuNgUqLhKRETEvxmml/+8FBUVxaJFi4iPj3deduTIEaKjozlx4gR2ux3TNGnVqhVr164lNDS0So+VtmuNY6CoiIiI1Fx6v/c/3npNvtl9hN/N3MjLI7oxqkebSj+/iIiIeKa09/oqqbC6++67iY2N5Z577uHo0aPs27ePVq1aYbdbM98NwyAiIoL09PQqP1bctGnTCA8Pd35lZmZWxVMkIiIiIlVJJVYiIiJ+zeuB1erVq9m6dSs//fQTTZs2ZcyYMd6+ywqZPHkyGRkZzq+QkBBfL0lEREREKolzl0AlViIiIn7N7u07iIiIACAwMJCHH36YmJgY2rRpw8GDB8nNzXW26KWnpxMREUFoaGiVHhMRERGR2sO4OHVdM9dFRET8m1crrM6ePcupU6ec38+ZM4crrriC5s2b0717d2bPng3AwoULCQ8PJzo6usqPiYiIiEjtUVBhJSIiIv7Mq0PX9+7dy6233kpeXh6madKuXTtef/11oqKi2L17N2PHjuX48eOEhoYyc+ZMYmNjAar8mDsawioiIlLz6f3e/3jrNVmTeJS73v+e52+J5fZeqrYXERHxldLe672+S2B1pw+wIiIiNZ/e7/2Pt16TtYnHuPP973julq7c0Suy0s8vIiIinvGLXQJFRERERPzBxRFWmmElIiLi5xRYiYiIiEitoRlWIiIi1YPXdwkUERGpLUwT1q2DpCSIjoa+fQuqOUTETzgTK0VWIiIi/kyBlYiISCVIS4NhwyAlBYKCIDsb2raFJUsgUmNyRPyGgVJkERGR6kAtgSIiIhVkmlZYlZxsBVWZmda/yclw3XUq5BDxR/qfpYiIiH9TYCUiIlJB69ZBairk5ha9PDcX9u61jouIf9DQdRERkepBgZWIiEgFJSVBYKDrY0FB1nER8Q8FI6yUWImIiPgzBVYiIiIVFB1ttQC6kp1tHRcR/2BcLLFSXCUiIuLfFFiJiIhUUN++1oB1e7GtTOx2aNfOOi4i/kEtgSIiItWDAisREZEKMgxrN8D27a0WwJAQ69/oaOtyQ5uSifgNZ0ugT1chIiIipbGXfhUREREpTWQk7NplDVhPSrLCqr59FVaJ+JuCCitFViIiIv5MgZWIiEglMQzo18/6EhF/pRRZRESkOlBLoIiIiIjUGpphJSIiUj0osBIRERGRWkP1VSIiItWDAisRERERqXVMjV0XERHxawqsRERERKTWMC72BKolUERExL8psBIRERGRWsPREqi8SkRExL95HFgdPHiQlStXApCbm0t2dra31iQiIiIi4hUaui4iIlI9eBRYLViwgN69ezN27FgAduzYwc033+zFZYmIiIiIVD7jYo2VZliJiIj4N48CqxdeeIGffvqJRo0aARAXF0daWppXFyYiIiIiUtlUYSUiIlI9eBRYBQQE0KRJkyKXBQUFeWVBIiIiIiIiIiJSu3kUWDVo0IDDhw87d1VZsWIFjRs39urCREREREQqW0GFlUqsRERE/Jndkyu99NJLDB8+nL1799KvXz9SUlL44osvvL02EREREZFK5ZxhpbxKRETEr3kUWPXo0YNvvvmG9evXY5omCQkJhIWFeXlpIiIiIiKVy1FhJSIiIv7No5bAjRs3YrPZGD58ONdffz02m40ffvjB22sTEREREfEKFViJiIj4N48CqwkTJhAcHOz8Pjg4mIkTJ3ptUSIiIiIi3qBdAkVERKoHjwKr/Px8AgICnN/b7XZyc3O9tigREREREW9wzrBSjZWIiIhf8yiwCgoKIjEx0fn9nj17CAwM9NqiRERERES8QRVWIiIi1YNHQ9efeeYZ+vXrx/DhwwFYsmQJM2fO9OrCREREREQqm2PmuvIqERER/+ZRYPWrX/2KNWvWsHz5cgCmTp1K+/btvbowEREREZHK5twlUCVWIiIifs2jwAogJiaGmJgYb65FRERERMTLHDOsRERExJ+5Dax++9vfMmfOHK644goM55+jCvz0009eW5iIiIiISGXTDCsREZHqwW1g9ac//QmA1157rSrWIiIiIiLiVQUzrJRYiYiI+DO3gdWVV15JXl4e7733Hh9++GFVrUlERERExCtcdQ2IiIiI/7GVdoWAgAD27NlTFWsRERERKeLormPMuGM1gxv/xP4fDvp6OVKDqCVQRETEv5UaWAFcffXVjB8/nvXr17N161bnl4iIiEhlO5F8kvfGrGFokx9p1TmMiR8PYN3Jzvz4n3RfL82nZsyYwenTpwH4wx/+QI8ePVi9erWPV1X9FLQEioiIiD/zaJfAuXPnArBs2TLnZYZhsHfvXu+sSkTED5gmrFsHSUkQHQ19+xbaDl1EKtWptNMs+ts25n1eh2VH48mlP4Fkc32LHxn9m1xueCKW0PBevl6mT/3zn/9kwoQJrFu3ju3bt/Pcc8/xpz/9ie+//97XS6tWNHRdRESkevAosEpJSfH2OkRE/EpaGgwbBikpEBQE2dnQti0sWQKRkb5enUjNcCbjDJ8/t425nway5Eg8OfTDTg7XNtvM6JuyuOmpWMIia3dIVZjdbn1s+/rrr7n77rsZNmwYjz/+uI9XVf0YF2usNHRdRETEv3nUEgjw7bff8uyzz/Lcc8/x3XfflfmOZs6ciWEYLFq0CIAjR45w3XXX0aFDB7p27VqkpL2qj4mIFGaaVliVnGwFVZmZ1r/JyXDddfqrvEhFZB7K5JNJ67nlsm9p3iaIu97uy1dHunN1k628N2YNh5My+fJIT8a824+wyIa+Xq5fsdlszJ07l7lz5zJkyBAAsrOzfbyq6sdQT6CIiEi14FFg9eqrrzJ69GiOHz/OsWPHGD16NNOmTfP4TlJTU3n33Xfp3bu387LHHnuM3r17k5iYyMyZM7n99tvJycnxyTERkcLWrYPUVMjNLXp5bi7s3WsdFxHPnTt2jgWPbGBk+Aaat7Lx2zcT+PxgT/o22snbt6/m4M5TLDnWg3tm9adx+0a+Xq7feuutt5gzZw733nsvkZGR7Nmzh2uuucbXy6q2lFeJiIj4N49aAt955x1++uknmjRpAsDUqVPp3bs3kydPLvW2+fn5jBs3jjfffJNHHnnEefm8efNISkoCoGfPnlx22WWsWrWKIUOGVPkxEZHCkpIgMBCysi49FhRkHe/Xr+rXJVKdXDh1ga9e2My8T/L5b3o3ztIHg3z6N9zK6OtO85snOtGyW3dfL7Na6d27t7NS3TRNWrVqxRtvvOHbRVVDBTOsFFmJiIj4M48qrEJDQ51hFUDjxo0JDQ316A6mTZtG3759ufLKK52XHT9+nJycHFq2bOm8LCoqivT09Co/5mq94eHhzq/MzEyPHqfUfKYJa9fCrFnWv/qcW3NFR1stgK5kZ1vHReRSWWey+O/U77mr3VqaN8rmNy/35pP0BOIa7OX136wi48cjrDoVz/2fDKRlt+a+Xm61c88993Dq1Cmys7OJj4+nRYsW/L//9/98vaxqx7iYWOl9XERExL95VGF1zTXXMHbsWO655x4AZs2axZAhQ9i6dSsA3bp1c3m77du3s3Dhwmo1L2ry5MlFKsfCw8N9uBrxFxrAXbv07Wu9vsnJRdsC7XZo1846LiKW7MxsVkzbwtx/Z7EoOZbTXAXAVfW3M3rwMUY+EUObXq4/J0jZ/Pjjj4SFhfH5559zxRVXsGbNGvr168f999/v66VVKxphJSIiUj14FFjNnz8fgFWrVhW5fO7cuRiGwd69e13ebs2aNaSmptKhQwcADh06xPjx4/nrX/+K3W7n0KFDzqqn1NRUIiIiaNKkSZUeEylN4QHcubkFlTeOAdw7dxYa4Co1gmFYYWTxkLJdO+tyvd5S2+VeyOWb17Ywd+Y5Pk3sykmzJwBXBu9k1MBNjHoimqh+XX28yprH0cK2Zs0afv3rXxMaGkpAQICPV1X96P/DRUREqgePWgJTUlJK/CoprAK47777OHjwIKmpqaSmptK7d2/eeecd7rvvPkaOHMnbb78NwMaNG9m/fz8DBw4EqPJjIu5oAHftFBkJu3bBihXw5pvWvzt3gnJuqa3ysvP4+u+bmNh5Na2CTzH08St5f09/Iuoc4blrV5K4PI0fznbm0S8HEdVP1cne0LJlS+677z7mz5/PkCFDyMnJIS8vz9fL8lhOTg6jRo1i0KBBvPLKK75ejloCRURE/JxHFVbe8NJLL3HXXXfRoUMHgoKCmD17NoGBgT45JuKOBnDXXoZhvbZ6faW2ys/NZ+30bcx95xQLd3bicP4VAHSpk8ikvtsZ9acIOg7vCHT07UJriY8++ojZs2czZswYwsLCSE1N9WgDHH/x6aefkpCQwMMPP8xtt93G0aNHadasWZWvw7jYFGiqKVBERMSvVWlgtXLlSud/t2jRgqVLl7q8XlUfE3FHA7hFai7TtKokk5Ks/y337at2ofzcfL59fwdzp59g/raOHMyPA6Bj0F4m9N7JqMnhdLmpA9DBtwuthZo2bcr48ePZvHkz69evJz4+nrFjx/p6WR5LSUmhZ0+rfbRTp05s3LiR66+/vsrXUbBLYJXftYiIiJSBRy2BIrWZYwC3vVi8qwHcItVbWhp06gSDB8ODD1r/dupkXV7bmPkm372/nUd6rCSq7kH6TozljS0DCbZl8UTCSrbM38Ou823566pBdLlJKb2vrF+/nvbt2/OHP/yBP/zhD0RHR7NhwwaPbjt06FC6detGfHw8/fv3Z9OmTRVay6RJk4iKisIwDDZv3lzkWGJiIgkJCcTExNCzZ0927NgBQMeOHVm1ahWmabJmzRpOnz5doTWUVy3PpEVERKqNMgVWWa56okRqOMcA7vbtrRbAkBDr3+hoDeAWqa4Kb6aQnQ2Zmda/js0UakPlhZlv8uPsXUzptZJ2dTLoPa4r034cRICRz5ReK/lx9i4SsyJ4bt0guo2IwbDp/+x8bfLkySxYsIBNmzaxadMmFixYwB//+EePbjtv3jy2bt3K5s2bmTx5ssvKrOzsbFJSUopclpWVRWpq6iXXHTFiBGvXriXSxVa5EyZMYPz48ezZs4cpU6Y47+vGG2/k6NGjXHvttTRr1ozmzZu7XOv8+fMZNWoU58+f9+ixlZmzwqoW/A9dRESkGvMosNq6dStdu3alffv2gLWt8qOPPurVhYn4Ew3gFqlZautmCma+yZZ5u3kiYSUd6qTT465OvPz9IPJMG49cuZLvPtjB3qxwXvx2EN3v6KSQys+cP3+evoXKehMSErhw4YJHtw0LC3P+9+nTpzFc/LVl586dDBkyhG3btgFw7tw5brjhBubOnXvJdQcMGEB4+KXD9Y8cOcIPP/zAnXfeCcCtt97Kvn37SEpKIiAggOnTp7Ns2TICAwPp06ePy7WOHDmSefPmUa9ePY8eW1kVzLASERERf+ZRYDVp0iTefvtt52DM7t2788UXX3h1YSL+xjGAe+xY619VVolUX47NFFxxbKZQk+z4LImnB6ykU70U4kd35IUNgzifH8RD8atYP2MbqRda8eoPg7jqd10UUvmxkJAQli9f7vx+xYoV1K9f3+Pb33333bRp04apU6fy4YcfXnI8Pj6eDz/8kJtuuolVq1YxfPhw+vfvz5QpUzy+j3379tGqVSvsF/voDcMgIiKC9PR00tPTGTRoEIMHD2bEiBEEBwd7fN7KpBlWIiIi1YNHQ9czMzPpV2ibLMMwCAoK8tqiREREvKk2bKbw85d7mfdqOnPXh7MzKxqIpoXtCH+IXcXo8WH0nRiLzd7K18uUMnj99de59dZbCQgIACA/P59PP/3U49v/+9//BuBf//oXU6ZM4csvv7zkOgkJCUyfPp1BgwYxceJEpk6dWjmLByIiIopswOMrjkhWuwSKiIj4N48CK7vdTk5OjrN8fN++fc4PSyIiItWNYzOF5OSibYHVfTOFpBVpzH0xhXlrW7H1QkegHU2NY0zsvJpR9zRgwAPdCAga6OtlSjn16NGDpKQkdu/eDVhDzANLKhV0Y8yYMUycOJHjx4/TpEmTIseOHTvGE088wWOPPcbcuXNZuXIlgwYN8vjcbdq04eDBg+Tm5mK32zFNk/T0dCL8qIfe8XlWFVYiIiL+zaOWwAceeICbb76Zo0eP8tRTT9G/f3/NsBIRkWqrJm2mkLJ6Hy8NX8mVwbvoMCSSp5YPIiOrGeM6rmbZSz9x8FwY03cM4OrJVxAQpD82VUdnzpxxfp0/f56IiAgiIiI4f/48Z86cKfX2p06d4sCBA87vFy1aRJMmTWjcuHGR6x0+fJjBgwdz//3388ILL/DFF18wbtw4lixZ4vFamzdvTvfu3Zk9ezYACxcuJDw8nGg/KlusRv/zFhERqdU8qrC68847adeuHZ999hnZ2dnMnj27SIugiIhIdePYTGHdOmtmVXS0VVlVHcKq9A37mf98InO/acbGs12ANjTkNGOj1zB6TD0GT44jMHiAr5cplSQsLAzDMIrsauf43jAM8vLy3N7+9OnTjBw5kvPnz2Oz2WjWrBn/+9//Lhm8fuHCBZ566ilGjhwJQKdOnVi8eLFzCHthEyZM4IsvvuDQoUMMGzaMBg0akHRx+NuMGTMYO3Yszz//PKGhocycObOiT4FXqMBKRETEvxmm9vR1Kzw8nIyMDF8vQ0REarn9PxxkwfN7mLusMRsyYwFowBluaruV0XcGce2f4qgTWsfHq6y+9H7vf7z1mpw6l038/y3jt1dF8MJvYiv9/CIiIuKZ0t7r3VZY3XLLLS63PXYoy6BPERERV0yzelY5VYVDW4+w4G+7mLc0jLVnYjFpRX0yuS1iPaNvD+C6KXHUDVPFs0hZGIXGrouIiIj/chtY3XzzzVW0DBERqY3S0mDYMEhJsWZIZWdbw9CXLLFa9mqjo7uOsfBvO5n3VQNWnepGPgOpxzlGhH/HqFFw/eNxBDdN8PUyRaqvi3mVegxERET8m9vAasyYMVW1DhERqWVM0wqrHDv1ZWdblycnw3XXwc6dtafS6njiCf7z7A7m/S+Yr0/EkccA6nCBm1ptZPTIfH71eDdCWvbx9TJFagRDgZWIiEi14NHQdYB58+axefNmLly44Lxs2rRpXlmUiIjUfOvWQWqqFVYVlpsLe/dax2vy/h6n0k6z6G/bmPtZHZYfiyeX/gSRxfUtfmT0b3K54YlYQsN7+3qZIjVOQUOgEisRERF/5lFgNWnSJFJSUvjxxx/57W9/y/z587n22mu9vTYREanBkpIgMBCysi49FhRkHa9pgdWZjDN8/tw25n4ayJIj8eTQDzs5DG22mVE3ZXHTU7GERfby9TJFajTHfFZVWImIiPg3jwKrb775hi1btnDFFVfw97//nT//+c9qFxSRCtGgbYmOLmgDLC472zpeE2QeyuS/z21l3kIbXx2MJ4u+BJDL4CabGfXr89wytSuN2/f09TJFag2NXBcREakePAqs6tati81mwzAMcnJyaNmyJQcOHPD22kSkhtKgbQErpGzbtmCGlYPdDu3aWcerq3PHzvHF81uYOw++2B/PBRKwkcegRlsYfX0mtzzZmWadevh6mSK1kmZYiYiIVA8eBVYNGjTg3Llz9OvXjzvvvJOWLVsSHBzs7bWJSA2kQdueqQ0VaIZhhZTFw8t27azLq9vjPX/iPItf2sLcOfn8d18c5+iDQT79G25l9HWnufWpzrTo2t3XyxSp9Qyq2f+5iIiI1FIeBVZz5szBbrfzyiuvMG3aNE6ePMmCBQu8vTYRqYFq+6BtT9SmCrTISNi1q/qGc1lnsljy0mbmfZzLZ6ndyMQakt63wVZGXXuSEU925LLu8b5dpIi4pKHrIiIi/s2jwKpFixbO/37ggQfYt28fbdq08dqiRKTmqo2DtsuiNlagGYb1mleX1z07M5vlf9/CvA+zWJQcy2msIem96m9n9JBjjHg8hja9uvl4lSJSEkNDrERERKoFjwKr6667jk8++QS73U5cXBwAd999N//3f//n1cWJSM1TWwZtl5cq0PxTzrkcvnl9K3NnnuM/SV05aVpD0q8M3snoQZsY+Xg0Uf26+niVIlIWyqtERET8m82TKx0+fJiwsDC+/PJLbrrpJvbs2cN//vMfb69NRGogx6Bte7G4vCYM2q4Mjgo0VxwVaFI18rLz+Prvm5jQaTWtQs4w7Ikr+SCxP5F1D/P80JUkrUjjh7Od+fMXg4jqF+7r5YqIhwqGriuyEhER8WceVVjl5OQAsHr1aq677jqCgoKwF/9tU0RqBG8P+65pg7YrmyrQfCsvO4+107cx773TLNjRmSPmFQB0rZPIQ323MepPEXQcfjlwuW8XKiLl5hi6rrhKRETEv3mUOnXt2pXhw4eza9cuXn75Zc6dO+ftdYmID1TVsO/qPmjbmxwVaI4ZVg6qQPOe/Nx8Nry7nblvn2TB9o4czI8HoGPQXib23sGoyeF0uakD0MGn6xSRylFQYeXbdYiIiIh7HgVWs2bNYvHixcTFxREcHMz+/ft54YUXvL02EalCVT3su7oN2q4qqkCrGma+yfczdzD3/x1j/pYYMvKsIenRgak82Wclox6+jNjfdMCwtfPxSkWksmnmuoiISPXgUWBVt25dbr75Zuf3rVu3pnXr1t5ak4j4gIZ9+w9VoHmHmW/y4+xdzHvrCPN+iiYtzxqSHmXfx5ReKxn9UEviR3fEsEX5dqEi4lXGxf8z1QwrERER/6ZBVCICFAz7zsq69Jhj2LcCq6pTWgWat2eN1RRmvsmW+XuY9/pB5m1sS3JuZ6AzbQL288iVKxn9YHN63NUJw9bG10sVkSqiCisREZHqQYGViAAa9l2dVNWsseps+38SmTttP/O+i2RPTkegI5fZDvJQ/CpG39eYXr/vgs2uSmGR2shQYiUiIlItKLASEUDDvquLqp41Vp38/OVe5r6SzrwN4ezMsoakt7Ad4YHYVYwaH0bfibHY7K18vUwREREREfGAAisRATTsu7rQrLGiEpelMu/lVOauvYxtF2KAdjQzjjKx82pG3xtK//tjCQga6Otliogfcc6wUomViIiIX1NgJSJOvhj2rVlMZaNZY5Cyeh/zXkhm7qoWbDrfCYiisXGCcR1XM/r3IQya1A173QG+XqaI+DnNXBcREfFvCqxEpIjShn1XJs1i8kzhUO/cudo5ayx9w37mP5/I3G+asfFsF6ANYcYpftdhDaPursfgyXEEBiukEhHPGIYCKxEREX+nwEpEfEKzmDxTPNRzVFYFBEBeXsH1auKssf0/HGT+c3uYt7wxGzJjgdY04Ax3tVvLqDuCGPpoPEEh/X29TBGphgzUEigiIuLvFFiJiMcqs32vJsxi8nY7Y0mhXkBAwVdNmzV2aOsRFvxtF3OXhrH2TBzQivpk8tvIdYy+3c6wR+OoG+bnPxgi4vcMw1CFlYiIiJ9TYCUiHqns9r3qPoupKtoZSwr18vLAZoPXXoPg4Oo/++vIjqN8+twu5n7VgFWn4jAZSD3OMTJ8A6Nvg+sfj6de4xpUOiYiPmdVWImIiIg/U2AlIqXyRvtedHT1ncVUVe2M7kK9OnWssGrs2Irfjy8cTzzBp3/bzrwv6vP1iXjyGUAdLnBzq+8ZPTKfXz8ZR/3mfXy9TBGpoTTDSkRExP8psBKRUnmjfa9vX6siyRH6OFSHWUxV1c5YnUM9V06mnGLR37Yx7791WX4snlwGEEQWv275A6NuyeXGp7rR4LLevl6miNQChmqsRERE/J4CKxEplTfa9wzDap8r3lZXHWYxVVU7Y3UO9RxOp5/m8+e3Mfc/QSw9Ek8O/bGTw9Bmmxl9cxY3PhlLWGQvXy9TRGobVViJiIj4PQVWIlIqb1X6REbCrl3eHVzuDVVZ+fTss/Dgg3DsmNUGmJPj/6HeLwd+4X8vbGPuggAWH4oji34EkMvgJpsZfcN5bn6qK43b9/T1MkVERERExI/ZvH0HQ4cOpVu3bsTHx9O/f382bdoEQGJiIgkJCcTExNCzZ0927NjhvE1VHxMR9xyVPvZiEXdlVPoYhlWNNHas9a+/hjCFefP5cEhLg06d4I47IDPTel4aNICPPrJmZEVEVPw+KtPZI2eZ98f1jAjfQPPWdm5/K4H/HupBv0Y7mXHHag79fJolx3rw+5n9ady+ka+XKyK1nBoCRURE/J/XA6t58+axdetWNm/ezOTJkxl7cULwhAkTGD9+PHv27GHKlCnOy31xTETcc7TvtW9vtbyFhFj/Rkf7d6WPt3j7+Sg81D072wqscnKsKqupUyvnMVSG8yfO8+mj3zI6Yj3NW8Do1xL4dH8vejXczT9Hr+LAthMsP9Gd8bMH0LRjE18vV0TEyRq6rshKRETEnxlmFb5bz5o1i9dee42lS5cSHR3NiRMnsNvtmKZJq1atWLt2LaGhoVV6LLqU3p3w8HAyMjKq6BkS8W+m6f32vaq4j8rirbWuXQtDhpQ8I2vFisqZkVUeWWeyWPLSZuZ+lMvnad3IpAEAfRtsZfTQk9z6REcu697SN4urRNXp51Aqh97v/Y83X5NOUxfTq11jZv3uKq+cX0REREpX2nt9lcywuvvuu/nmm28A+PLLL9m3bx+tWrXCfrGfxjAMIiIiSE9Pp2HDhlV6rHhgNW3aNKZNm+b8PjMz07tPjkg14mjf81ZYkpZ26RD2tm2tqqXISO/cZ0V46/moqqHunsrOzGbZq1uY92EWi/bGcgZrSHqv+tsZPeQYIx6PoU2vblW3IC+rbj+HIlJ2hoaui4iI+L0qCaz+/e9/A/Cvf/2LKVOm8Le//a0q7rZcJk+ezOTJk53fh4eH+3A1IhVXXSpFCrfB5eYWDDVPTobrrrPmNpW07uryGD1VlUPdS5JzLoev/7GFef86z3+SunLStIak9wjeyahBmxj5eDRR/bp6fyFVrCI/hyJSfWiGlYiIiP+r0l0Cx4wZw8SJEwkPD+fgwYPk5uY6W/TS09OJiIggNDS0So+J1GTVqVJk3TpITbVCgsJyc2HvXuu4q6qi6vQYPeUY6u4ITRwqa6h7SQFf7oVcVr25lbkfZPLp7i4cN3sAEF/vZ/7cfwujprSl/TWdgc4VW4AfK+/PoYhUH6Zpkm/CodPn2Zh6gh6RjTCURIuIiPgdrw5dP3XqFAcOHHB+v2jRIpo0aULz5s3p3r07s2fPBmDhwoWEh4cTHR1d5cdEaipXg7uzswsqRfytFcLRBueKow2uuOr2GD3lzaHujt0HBw+GBx+EIVfnMazFZsZ1XE3r4JMMebQ77/48gFZBJ/jb4JXsXpzCpnOX8/iSQbS/ppomgGVQnp9DEak+Mk6eY/C0VZzPySPpSCa3v/stg6etIuPkOV8vTURERIrx6tD1tLQ0Ro4cyfnz57HZbDRr1oxXX32V+Ph4du/ezdixYzl+/DihoaHMnDmT2NhYgCo/5o6GsEp15c+Du11Zu9YKUVy1wpW03ur2GMuqslsdTdMKq5IT8+mUv51GnGQ3HTmMNST98qBkRvfZx6jJ4XS+sXYG+uX5OZSaQe/3/qeyXxPTNBk8bRVpx8+Rl1/w8TfAZhDVJJjlkweq0kpERKQKlfZeX6W7BFZH+gAr1dWsWVYFjat9A0JC4M03YezYql5VyZxhios2uOho17ODqttj9CUz32T24zt4/5Vj7DFjOMhlAESSShSpHA64jHe+7kD/AbX7l7Xy/BxKzaD3e/9T2a/JxtQT3PHud2Tn5V9yLDDA4ON7e9MzqnGl3Z+IiIi4V9p7vVdbAkXEd/xhcHdZlKcNrro9xqpm5pv88O+d/LnnSqKC9nP3y11ZZQ7CTi4DWUkMP5NGJKsYREa9GJL3KonxZjumiPhW6rGz2ANc/484MMBG6rGzVbwiERERcadKh66LSNXx9uDuymaasG8fTJkC589DvXrQoYP7Nrjq9hirgplvsmX+Hua+dpB5P7Rlb641JD0iIIMJl69kfWJztuV1Yh9FN51QwFcgMhJ27apZO0+KCEQ1rU+Oi+oqgJy8fKKa1q/iFYmIiIg7CqxEaihHpUjxHfTatfNtpYiruUzp6SXv9GcYJc9y8tfHWNXMfJPt/0lk3msHmPtdJIk5HYGOtLYd5OErVjFqYmN6/b4LRkA4nTqBXQFfqQzDmlWleVUiNUePyEa0aRzscoZVRONgekQ28uHqREREpDjNsCqFZlpIdVfZg7srIi3NdTCVk2OFVq5mBn35JQwaBAcOWLu35eUVhFmRFzet86fHWJV2/S+ZeX/fx9z1bdiV3R6AlrbDjOjyM6MnNiJhfFdsdqvz2/EcffutNdvr0KFLA76ICHf3JlKz6f3e/3jjNck4eY67P/ievUfPYjMKwqp/39OL1mH1KvW+RERExD0NXa8gfYAVqRwlDbMOCLBCKFfsF2tAC1/fcZsOHWrnAOzEZanMfSmVeesuY9uFGACaGUe5tdMuRt8bSv/7YwkICihym+JBYVYWtGwJkyZB7961J+ATcUfv9/7HW6+JaZp0/9syQuvaeXVUPD0iG2l3QBERER8o7b1eLYEiUiXWrYPU1EvDp5LCKrj0uoVvk5wMa9dC//6VtkS/tXdlOvNe3Mu81S3YdL4TEEVj4wT3Xr6aUb8LYdCkbtjrDnB5W9O0wipHUOgYUn/wILz/PjzyiMIqEaldDMOgXmAAjerX0a6AIiIifkyBlYhUiaQkq6UvK6tyzpeTA6NGWS1ujtZAd/ytbbC09aSty2D+C0nM/aY5P5zrDEQQZpzidx3WMHpMPa75YxyBwa5DqsJKCgpzc2HvXuu45jSJSG1jGAZqMhAREfFvCqxEpEpERxdU97hSvDXQZoN815s5OR09CtddV3prYEmzswrPwapKJa3nw5cPsm7mHuYub8y3mbFAOA04w13t1jL6rjpc+6c4gkLKVlLmLigMCrKOK7ASkdrGZoN85VUiIiJ+TYGViFSJvn2tUKb4DCu73QqNAgKsAMdutwKcJk3g+HH3LYN5eaVXCZXUEpec7FnYVdmKr6dh9mGu4GdO7w7jqpvigFaE8Au3R65j1O12hj0aR92w8idK7oLC7GzruIhIbWMzjCI7BYqIiIj/UWAl4iX+1oLma4ZhVTQVryxy7FCXnw8DB1q7AQYFwalT1l/ATdN9pZW7KiHThOnTLw3JwHctcevWwZm9R+mTu4szhLKVbqyhBcGcpQ/rGX2bwfh/xlOvcd9KuT93QWG7dtZxEZHaJsAwyFdLoIiIiF9TYCXiBf7Wglacr8K0yEjYtevS+wZrB8EDB6xQxRGsBARYwUpeXsmVViVVCTleg6Skkm+bk2PNwKqKwOrY7uP857kd/PvTEA7nxHGQAdTlPFfxPQb5bCGObSEJjB8G9SpxBnBpQWFtDlFFpPYyDOu9UERERPyXAiuRSlaZLWjeCJZ8HaYZhhUQFQ6J1q4teQfBgAB4/XV49llrZlXh8KmkKqHCr4G7lkLThDff9N5OeSdTTvGf/9vGvP/WY/nxePIYQBBZ9OAHAshlK934jt7O6weVo0XPk5+RkoJChVUiUlvZVGElIiLi9xRYiVSyytqVzRvBkr/Nc3IobTB4/fpWJZSnVUIlvQauHDxYuW2Bp9NP89mz25j3WRBLj8STQ38Cyea65j8x6qZsbnwylt7DelVKi15ZfkZcBYUiIrWVzTDIKW1nDxEREfEpBVYilawydmXzVrBUWWFaZfNkMHhZqoTcvQbF1alT8Z3yfjnwC/99bitzP7Wz+FA82fQjgFyGNNnMqBvOc8vTsTRqe5Xz+pXRouev4aOISHVgsxmYbipwRURExPcUWIlUssrYlc1dsJSYaA0Sv+++sgcSlRGmlYWnLY2eDgb3tErI3WtQXHl3yjt75CxfvLCFufNsfHkgjgv0xUYeVzfawuhfZ3LLk11o2rGHy9sWDt8SE+H8eahXD9LToU0bz15Xfw0fRUSqA5uBWgJFRET8nAIrkUpWGbuyuQuW8vLgoYfgjTfK3h7oLsjJyipfcFOSsrarVeZg8JJeg+LK2oZ3/sR5vnxhM/PmmvxvXxznSMAgnwENtzJ6+Bl+82QnWnTt7tG5DMMKp8aNK1/bZ1WHjyIiNYlmWImIiPg/BVYilawywpfSKoRyc8vX+uUIclztnGcYEB7u2XlKU552NU9a/jyt2HL1GmRlFewKVadO0dcErMHvrs574dQFlry8hXkf5/J5Wjcy6QNA3wZbGT30JCOeupxW8fFV8hwVVhmVfCIitZXNAI2wEhER8W8KrES8oKK7snlSIVSe1i/DgMWLISbm0sAqLw+GD6+c2Ufu2tWSkqxwqH//sp2zrEPoXb0GCQmwfn3R1yQ9HTp1Knre6Mhsnrh+C0v+m8Vne2M5Qy8AeodsY9Tg44x8siPhPbuV78m5qKItfZVRyVcab+xSKSLiDwxVWImIiPg9BVYihVTmL+gV2ZWtcIWQq2ooh/K0fmVkgM126eV5eZU3+8hdu1puLowaZe36VzhochdIRUSUrxrJ1WvgCHKSkqzX+957rfOYuTnEZG+hHufZnhjLna/3BKBH8E5GX72JkY9HE9k3tkLPS+Gfrz17KtbSV9ltlMV5Y5dKERF/EWBTYCUiIuLvFFiJXORvv6A7KoSmT7dmVrmqtHLV+lVa6FYVs49Ka2k8etR6rt991wqL2re3Zjnt3es6kHrnnYoPGDdNWLgQHnwQjh2z2gJzzufSJX8rvclkJ134CWtIekd+5gpjMw/9oy03P9QZ6Fzu58Kh8M9XQID1GEsKIj1t6atoJV9JtAOhiNR01tB1X69CRERE3FFgJYL//oJuGNZugG+84VnrV2mhm2nCuXNw4YLr+6us2UfuZmWBddnu3TB4sBUcZWVBTs6l13MEUl99VbGQzfG87N4NBnl0YxuhuWfYSSc2YQ1J78AeYtlGKpHs5nL217+cUw3L+QQU4/j5clct51DWlr6KVPKVRDsQikhNZxgGpiqsRERE/JqLxiCR6s80rTlJs2ZZ/5b2mdSTX9B9xdH61b69Fc6EhFj/RkcXbf0qHLplZ0NmpvWvI3RLTbVmNT38sOvQpDJnHznW3KyZ++vl5FjrdBVWOQQFWf+6293w3LmSX2vThGHX5lN3z1YGsIpmHGML8axhAA05w0BW0o4kEolhFYNIo63z/iprcLnj58tdWFXS6+oLjio8VxwBoYhIdWYzIE8lViIiIn5NFVZS45Snta8q2uQqwpPWL3ehW3IyDBwIBw5cetwwrMdeWbOPCq953jyrispdIFWa7GxrGPynn15aZRYQYK33j390Mfeqjcl3H+zg/ZePczoxht1YQ9KjSGEgK9nPZSTRgb20v+Q+KzO8A+s1czU3zMFms1oVr7/ePwabawdCEanprBlWvl6FiIiIuKPASmqU8rb2eeMX9MreYa201i93oRvA/v2uK3xsNvjHP6zWw8oOSvr1s4Kf3bvLd3tHcNSv36UDxrOyrPXm5Vlf1utnEpi4iwmXH2FXTjTpeV0BaEM6A1nJQVqxhxhSL1ZRFRYYaLUnVubgcofoaPehXZ061s6N/tJmVxU7EIqI+JJNuwSKiIj4PQVWUqOUd/ZOZf+CXpkD3F0FX3DpZdHRJYdV7sKSevUgOLjs4YwngZxhwLPPwsiRnp/Xboe6dS8NjopXmZ07B5MnQ16eSQy7acUh9tKW7fmd2X6hM21sGfypx0rihzXndy91Yl9uhMv7Cwiw1u8YAF9Zg8sL69sXLrsM0tNdH8/N9a+qJW/vQCgi4mvWDCtfr0JERETcUWAlNUp5W/sq8xf0yhzg7ir4Cg+3jmVkFA3D3nvP8zUWVp4KsuLrysqCli1h0iTo3bto4JOZCfXrw9mzpZ+3ZUt46inYtAm6d4eJE4u20jmqzPommLwxKZG+OQfYSyR7uJw9XE5LDjKAlWTWacoD/68Lv/t9OKYJf1twaRjpEB0NS5dCRAT071+258FThgGrVllVVMXDw4AAaz6Zv1UteWsHQhERf6AZViIiIv5PgZXUKBVp7ausX9A9qfLq27fk+3FULiUmwjPPWHOnClrerHMUfkxgnWfwYMjPL9taAwLKXkFWUiC3bx88+qgVGBauJiutHa4ww7CqpoKC4MMPrd0RC1el7fpfMnNf3ce8DW3YlR0DxNCcwwxgFSdpxDa6cohWBJnQIabgnK7aCZs2hTffhN/8pmpCmKgo2LMHBgywXtOgIOv5a9/ef6uWvLEDoYiIPwhQS6CIiIjfU2AlNUpFW/sq4xf00qq8vv0Wxo1z3S4IBcFKQACcP+/ZfTrmOJVVs2ZlD0tKCuTACrMK70y4c2fJr0lhAQFWJdWRI0XDueRkuKtfCtfGpDFvXWu2Z3UA2tPMOMrEzqtJPhrKyuOxrM4f6DyXq9faX6qFoqKs6jRfr0NEpLZTS6CIiIj/U2AlNYo/zN4prcrrjTfg4MFL2wWHDSv475KCncoUGGjt4hfherRTiUob7g6Xzgwr/JrY7db8KcOw5mfl5lqtgIcOFYRu4aTTnr0cym3JmozLWZPRlsbGCe69fDWjfx/CwAe7Ya87wGXLZEmvtb9UC/nLOkREajObgSqsRERE/JwCK6lxvF1NU9qwcXdVXo5gxlW7YHKydZ6qCKvsdqsVrTyhibtArrDCM8OKvybt21vXcQw5T0yE5+/P4DKSOEpzdtGZDCJoyCn6G2u47pZ6/PnDOAKDBxS5D3+pnBIRkepFuwSKiIj4PwVWUiN5q4rFk93/3FV5jRsHf/mLZ4FPZStc0VSRirO+fQvmMblTfGaYc2B6ofldTXIO8v0ru/locVOSsruSRDihnKYva8miDpuJ47vA/jz/RwgMLvlxqWJJRETKwmaDfBNM08TQXzlERET8kgIrEQ+VZfe/kip/1q0rOawqT2VVYKD7gebNm1uD0K+6qmCtFa1CMgx47jkYNYoS53+UNMw9LQ1GDTxMcPrPnDAbsZVuQCtC+IUE1pGDnS3EsQ4rffJ09piIiEhZ2C6+CZqmqnJFRET8lQIrEQ95svtf4SofV5U/ngwg91RgIAwdCl9/7Xo4e7168OKL8LvfFVzWv3/F7tMhMxPq17f+daX4MPdD244y4+GdfPZNQzab3TBpQTBn6c168rGxhTjWU5BKGUZB26K/7qAnIiLVlyOwyjdNbOhNRkRExB/ZfL0AkerCMWzcFce8ptI42gXbty/5XJ5whDlTppS8O2BeHnToUP77cMfdHCvHMPfg88d5587VXBP2E627NeYvXw9kl9mRq/ie3qzHBL4lge/pTRb1ipwjIABee82qWivrUHgREZHS2C5mVPkaYyUiIuK3VGEl4qHSdv8rPK/JHUe74JNPwrRp7nfbK0njxrB4sRXmlDTgvbRWutKGx7tTUqVYE9tJetfbzrO31GPF8XjyGEAQWfTgBwLIZSvd+I7epZ6/bl0IDlZllYiIeEfhCisRERHxT6qwEvGQI6SxF4t5PQ2H1q6FWbOsfwGuvx7y88u3luPHrXla6ekFFVtBQRASYv0bHe2+lS4tDTp1gsGD4cEHrX87dbIuL40j6Bo3Dlq1gjDbafrb1tKDjZzJr88XZ/rzzfFuXNf8J166cS0NAi/wPb3YQF/O0sCjx1eWAFBERKSsbDYFViIiIv5OFVYiHnK3+19p4ZCrnQW/+qr8a8nLKzrs3dWA9+LrcQRNiYnWToUHDpQ+PL6kx3Ik+Rdiza20yrNzmHjW0I8AcrnStpk7bj3PXS/F0qjtVcyaBVlfA24GwxenQesiIuJtagkUERHxfwqsRMqgpN3/Sgp43O0sOGhQybvseaL4sPfiA94Lr2HhQquS6vhxKxByNaS9pOHxDpmHz3Jf/BbCTtlIJZ7V9MVGHnFspj5n2UEXfrL14Mw2eDDKuo27NkqwZlUFBFhrrFPHswBQ/FtFWk1r47pExDfUEigiIuL/vNoSeOHCBW6++WZiYmKIi4vj2muvJeniZOojR45w3XXX0aFDB7p27crq1audt6vqYyLFFW/hK/x51rH739ix1r/uful1t7PggQNgq+D/AgMD4csvXa8TrIqoyy+HkSPh0CHIyXEdVjkEBFgVWA7njp1jwZ82cFPzDTRvafDVqQS+5yo6sYv+rKYRJ9jElaxlACdpUiT0gpLbKB1atYKff7Z2OnzzTVixQoPWq7OKtJrWxnWJiO8YjsBKJVYiIiJ+y+sVVuPHj2f48OEYhsFbb73FuHHjWLlyJY899hi9e/dm8eLFbNy4kVtuuYWUlBQCAwOr/JhIYSW18C1ZYlVYlYVjZ0FXg9UDA+HChYqt9exZePXVguqkwussXN3lqfPn4dmpFzA2bmHpl7l8nhbHWfoA0I0tNOQUP3M5m7mixHM4QjRHJcvixVar4e7dl1730CFrltfOna6ruqT6cFdNWFqraW1cl4j4VsDFPxgprxIREfFfXg2s6taty/XXX+/8vnfv3rz66qsAzJs3z1lt1bNnTy677DJWrVrFkCFDqvyYiENpv9zu2AHr13veVuSuJS4vD5o1gyNH3K/JMNy3DubkWF9gVUcNGGCFbevXW9VdeXnuzw9gJ5t4NhNENtv3x/K76b0AiDW20YQT/GzGsJW40k+E6xDtb3+DO+4oWKeDoyJr7Vrrcapdq/pyV03ortW0tq5LRHxLLYEiIiL+r0pnWL3++uvcdNNNHD9+nJycHFq2bOk8FhUVRXp6epUfK27atGlMmzbN+X1mZmalPX7xf+5+uU1OtsKXQ4c8r7xytMQ5AjAHx2DxL7+EDh1KDpUCA622uYMHrdubphXk2GzWDoPFP2fn51s7B0ZFwaRJJVd3AQSQQxxbqMd5thPLD1wFQCd20t3YxA1/jOaJf8aWeHt3Codoycnw0EPWc1Y8sHI8F6NGwYkTFa9o8we1dVaSu2rCoCDruC+CIX9dl4j4lgIrERER/1dlgdXzzz9PUlISK1as4Ly7ITo+NnnyZCZPnuz8Pjw83Ierkarm7pfb3FzYt88KJDxtKyptZ8GICKsqKibm0pAsIMC63jvvWG11pgnh4RAcbN3mzTehpDx1/37rePHHYSOXOLZSn0x20JWf6AFAR3YRz2aSaccuOrM3qDP1d7sPvOz2gjUHB1uPKy/v0hAtNxeOHSu5SuzcOes+8vKqf7tWSe2kixdDRkbNDrHcVRNmZ1vHfcFf1yUivuX4/+D8fN+uQ0REREpWJYHVq6++yqeffsry5csJDg4mODgYu93OoUOHnFVPqampRERE0KRJkyo9JlKYu19uXQUunrQVlbazYNu2VgA1cKA1iD0w0Apv2rSxzn/ttZdWHnXoAH//e8mPIz/fqgRr2RIO7c+jc/42QjnDTjqxie4AdGAP3dhKKpHsphO76eS8fVaWFbK4ayc0DCtUa9XKqqA6caLkEK1OHQgJgaNHi57TZrOe1+L3Ux3btUpqJ01Kgo4di+6EWJ0ryEpSWjVh375al0htl5OTwx133MGRI0f41a9+xZ///GefrUUVViIiIv7Pq7sEgtViN2fOHJYtW0ZYWJjz8pEjR/L2228DsHHjRvbv38/AgQN9ckzEobRd7VwJCrJa+2bOhP/3/6x/y7qzYFSU1Yr4zTfWOZYvt9aQlmYFHJmZ1r+OGVV9+ljrLHmXwXzi2EJC7ioa5R9jC/GsYQANOcMgVtKOZBKJYRWDSKOtyzOUNvsqJ8e6zqFD8P77MHy4+0qWqVMvXa9hWCGOK452reqipHZSR+VYTk7B6+ioIKtJvyc5qgnbt7deu5AQ69/oaOtyX1WU+eu6RGqjTz/9lISEBFauXMmPP/7I0aNHfbaWAJsCKxEREX/n1QqrjIwMHnnkEdq1a8fVV18NQJ06dfjuu+946aWXuOuuu+jQoQNBQUHMnj3buWNfVR8TcXDVwpeV5Xr2kkNmJrz0khU+OGZMOao3ylJF4wi1+vWzAi9X4YdjRlW7dvDxx3D77db3FpMubKcJJ9hDDBuz49h4EDoEpjC600ra9W9Nmj2aN95sX+YWiMBA6zG56uZ1VEOB+0qW1193HdCUtFNidWvXctdOWlx1rCDzRGnVhFqXSO2WkpJCz549AejUqRMbN24ssjlPVXL87195lYiIiP/yamAVHh6OWcIngRYtWrB06VK/OCb+r7yDrPPz4e234aefoHt3mDjRup27cxX/5XbPHnjtNddhTeH7KbzWnBzrtoXnMJXlMZQWfmRkwLhx8K9ZJo/esIvgs0dIIpodxALQhjSuq7uS52e2In5UDOn72jJsmHXesoZV9etbA9yPHLFCMlfPQ1CQFVSVNK/r2WetXQJdVR+B1VpYuKKrOrZruWsndaWmDvwuHLz6E39dl0hVuHDhArfddhs7d+6kXr16NG/enOnTpxNdgb8KTJo0ic8//5y0tDQ2bdpEfHy881hiYiJjxozh2LFjNGzYkFmzZtGlSxc6duzIqlWruOaaa1izZg0xMTGV8OjKRy2BIiIi/q9KdwmU2qcydkwraZB1adVL69bB1VcXVEe9/z48/LA11+nwYffnKvzL7YIF7sOqkuTlFVTRtGlT8BgcQVTTptbMp1tvvfQ5ad/eXaWOSXT+blr8fIi7r2nHPjoDnWlNBlcbKzlqa05O+07MWBZJRETBbKWkpNLb/FzJyQHHH8A//ND1dRzVUCVVsvzrXyUHcMHBEBpadJdAR3VaWYM+XyppVlJJqlsFmYhUb+PHj2f48OEYhsFbb73FuHHjWLlyZZHrZGdns3//ftq2LWgVz8rK4uDBg0RFRRW57ogRI3j00Ufp5yIFnjBhAuPHj2fs2LEsWLCAsWPHsnHjRm688UaWLl3KtddeS7NmzWjevLnLtc6fP5/58+d7dZOeix2B5OUrsBIREfFXhllSCZQAVpVYRkaGr5dRLZU3aCosP9+6TUZG0cogu936Zb+kXeTy86FuXfetfMXPtWMHrF9fNBgB6NQJdu/2bL3F1a1rzaR66SXXQYZhWDsEFn5O0tJg6FCrsquASTSJtOYAqUSRRhQALTlIDLs5RlN+NrrQvIXBvHlF52StXQuDB5et+qfw+lq0gHnzrOejc2fXLX/uXovS1hAUZM3sMoxLQ6nK+BmqSq7WC1ZQWLyCrLTnTESqVm16v//hhx8YMWIEqampRS7fvHkzt956K4sWLSI2NpZz585x8803M3jwYKZMmeLyXFFRUSxatMhZYXXkyBGio6M5ceIEdrsd0zRp1aoVa9eudVZ0mabJmDFjePvttwkODi5xnd58TaYt3c0bXyexfPJAopuHeOU+RERExL3S3utVYSVeUdKOaY5h0578op6aCr16Wa1oxeXmWudauxb697/0vv/0J8/CqsLnatvWGiBeOBh59lkrfCivCxdg3z6r0spV1Y1pFm0dBOt5c8yEakcSbchgH21IIoYkYmjOYQawihM0YjtdOUSriyezduHbutX6NjnZCkUSE62Wu/IwTThzBoYMsZ6P99+He+65tOWvtOHVpe3U5gjYCv+hvjJ+hqqaqwqz8HBrvWV9zkREvOX111/npptuuuTy+Ph4PvzwQ2666SZmzpzJ008/zZAhQ0oMq1zZt28frVq1wn5x9xLDMIiIiCA9PZ2goCDuvvtubDYbDz/8sNuwytuMi/8HrL/bioiI+C8FVuIVJe2Y5umw6dRUq/LIXeiUkwOjRsG33xatTho2zAppyiI3t6CKq3Aw8uCDngdfJfm//3Pfile4ddA0ITcphb55aeynNUl0YC/RNOEo/VnNaULZRixHcL3DZV4ePPCA9d/BwdbjatmyfNVVDufOWf8mJ1tzs3buvLQSrbTgxdUw+9KCm4r+DPmKq1lJGvgtIv7i+eefJykpiRUrVrg8npCQwPTp0xk0aBATJ05k6tSplXbfERERl7Qh+krBDCsfL0RERERKpMBKvMLd0PDShk2bJgwY4FlQdOgQXHONdT4oqMgp62Bxxw5/heXmWhVLFf3jqydzoyKNNP59Twqr97QimY4k05bGHKc/q/mFELbSjTUMKNP9OoKmAwcqJxxxBEXr15dveHVZd2qryM+Qv9HAbxHxB6+++iqffvopy5cvL7G66dixYzzxxBM89thjzJ07l5UrVzJo0CCP76NNmzYcPHiQ3NxcZ0tgeno6ERERlfQoKodmWImIiPg/BVbiFe52TCtt2PTChVYbnaf27rUGo7dq5boipyKK715XmVqTQXuSOEpzdmV1JnFPJA05RT/WcI5gtpQjpHIlN9dqvbPbK/7c2O2lh43uAqmyBDcV+RnydD3evr2IiL+YNm0ac+bMYfny5YSFhbm8zuHDhxk6dCiTJk3innvu4e677+aGG27gn//8J8OGDfPofpo3b0737t2ZPXs2Y8eOZeHChYSHh1doR0JvsNm0S6CIiIi/09D1UtSmIayVyTStYeVlHdBtmnDZZVblVFmEhsKIETBnTvl29CtJYKAVWJW1YqskLTlADHs4TlN20BWAUE4TyzYuUIctxJFLUOXcWSEhIfD00/DWW1bFleNxwaUDwW0294939WorcCoe5KSnV+6A9PL+DDlUdGB7dRv4LiIVU5Pf7zMyMmjTpg3t2rWjQYMGANSpU4fvvvuuyPXS0tL4/vvvGTlypPOypKQktm3bxi233FLkuhMmTOCLL77g0KFDNGnShAYNGpB0sdx59+7djB07luPHjxMaGsrMmTOJjY0t87q9+ZpMX5nMS4t/5r8P9CM2vKFX7kNERETcK+29XoFVKWryB9jKVrwaxd2w6ZI6AxYsgEKfk8uk8K5slSUoCJo0gYMHy3+O5hzicnZzkkZsoxsAIfxCN7aSg50txJFN3UpasWtBQbBihRUslfYatWhRcoWbYcDcuTB16qVBTk6OFVqVJ1wqiavQqLSfIah42FXR24tI9aP3e//jzddkxqpkXvjqZz77Q1/i2oR55T5ERETEPe0SKFWipGqUxYutYeaetFSZpjXkvLwqO6xynPOXX0qvOiquKUfpxE7O0JCtdOMILQnmLL1ZTz42thDHevpW/oJL0KZNwXNf2kDwxES4/35rh8Pi6tSBSZPg2LGiO/clJblunazogPSyzr1yqOjA9uo68F1ERDzjGLqep7/bioiI+C0FVlJhplkw7LxwiJGcDMOHW9Uonvxyv24dHD/u3bWWR2amZ9drxHG6sIOzhLCFONYwkLqc5yq+w8BkC3F8S4J3F1sOxUMs03QdVoF1uSOsKszdnK+KDkgvz8Dyig5sr+imAZp7JSLi3xz/v6xGAxEREf+lwEoqrLKqUZKSrDDAk90B/UVDThLLds5Rjy3Es5YBBJFFD34ggDy2Est39Kn0+7XZrC9Ph6jv21e2qiDDKHl3RJvNs3M4uBuQ7q1wp6ID28t7e829EhGpHgKcQ9d9vBAREREpkQIrKbPiIUNiomfVKIVv1769dTwpCc6dg/37rVDF1Tn8jWNIehZ12Ew8a+lPINlcwU8Ekc02YvmeXhW6D3eBkeP4ZZdZM6M84Xgdis+wchUQJSdDvXrW6+KKu9bL4rsq2u3WzKm+LrofvRnu9O1rncvVDKqS1lPR27urNLzuOs29EhHxJ46WwHwlViIiIn5LgZWUiauQoWXLkoMmRzVK4dvZ7SWHIf4qhDPEso1c7GwhnnX0w04OcWymLhfYRiybAq5y2xpXmsBAa0ZUaYPPHde9/Xb4+989q0jLyrJ2CuzUqfSAKDq69HO6CqYiI63LU1MvHZBePKjxdrhjGNb9ljSwvbRzl+f2mnslIlJ9XCywUoWViIiIH1NgJR7Lz4cBA6wh6vn5BSHDgQMFLWqFB5PbbNC4sXXZ0KHWL+2Fwwl/V4+zxLOFfGxsJp4N9MVGHnFspj5n2U5XfqSn8/qBNnjmGfh//8+a85SX575KyiEgwAqJ3nnHGlIP1u3+8Y+Sg8CcHCs0qVPHs8CqVSt48slLXwNXAVHfvtbOiIcOlfC81IOGDeHEiUuDnDZtPGvxq4pwp7wD28t7+4rOzRIRkapjOCqsNMNKRETEbymwEo+kpUH//q6rfnJzrV/Ui/8in58Pp0/D1VeXbYc9X6rLOeLYggFsIY4NJGCQTxxbaMAv7KQTm7jS5W1tNiuwyciw2vWOHPH8ft97D8aNK6jmuXDB/Xyq1q2tgfZ//3vp5zYMuOEG6z48CYgMA958E0aOdH2+vDyYN8+6nqsgx5MB6VUV7pRnYHt5b1/RuVkiIlJ1CmZYKbASERHxVwqspFSO9q39+0u+Tm6u68qT8+e9t67KEsQF4tlCALlsJc45JL0bW2jIKXbRic1cUep5srKsVsd27coWVuXlWaGeaVr/XVoFWlAQrF4NERFWS19Skvtd+gIDITS0bAHRrbdCTIxVgeVqJlW/fgVhTnmUJdypLrvuVXRuloiIVB21BIqIiPi/Mu73JbWRo33LXZWUaVafKiqAQLLowfcksJY6ZPM9vdhAX9qSwgBW0YKDbCWONQzkGM09Pu+DD7qfPVWS3Fz3oZNhWK2DbdrARx/BN99Yr8vixVaIYy8heg4IsMKS4cPLVv1jGLB0qXV5UJA1/yooyPr+2WfhX/+CtWut1900rf+eNavgstI4wp3i6y4e7qSlWXO3Bg+2ntvBg63v09JKv4+q5ph71b79pc+ZJ3OzRESk6qglUERExP+pwkpK9e231WfulDsB5BDHFupxnm104weuAqAzO2jKUZKIZjuxFboPb4V2hmENYg8OhjvuKDo0ffFiqw1xwwarRfD4cauaKi+v6GwpV9U/Nps1ND8h4dL7LD7DKSTEmoN1++0F9x8ebl03I6NsO/15MtS8Ou66V9G5WSIiUjW0S6CIiIj/M0xTf1pyJzw8nIyMDF8vw2dM0/olvDxVQ/7ARi5xbKE+Z9lBV07SGICO7KIlh0mmHRlE+HiVnnM12D483Ap9bLaS2+dMExYutKqUjh61zmGa1jFHVZO7kMk0rcqm4oGXK3a7dd+eBEru2v3WroUhQ0puY1yxQkPMRaTy1Pb3e3/kzdfkP5sy+OPcLbx7dw+u7dzCK/chIiIi7pX2Xq8KK3EbGqxbB4cP+3Z9ZWWQRze2Esov7KSzc0h6B/bQja2kEMVuOrGbTj5eadkVr+DKz4f0dIiKgjVrrMCp+JDwtLSCSiZH5ZWDaVq7DJZWtVTSrn6ulGWnP3dDzbXrnoiIeItNLYEiIiJ+T4FVLVc4zCje0tWmDcyYUV1mU+UTyzbCOMXPdGLLxSHp7UimK9tJpw2JxJBIjI/X6R0ZGdbruGtX0cCppLa64koKmRxh5qxZVgWXpyojUKouu+5Vl6HwIiJSwDHDSo0GIiIi/kuBVS2Tnw9vvw0//QRXXAGvv26FVcVnBA0YAAcPWtU3/iufruygMSfYTQzbiAMgihQ6s5IMWpNMNHtpX2n3eNllUK+eVdWUm+vZgPGqYJqwe7fV9jdiRMHlZamMKh4yFQ4zAwLKtuNjZQRK5d11ryoDJHeBr7sZXiIi4luOXQLzqsUf5URERGonBVa1yLp1cPXVpYdQublWIOOfTDqxk2YcJYkOziHpbUhjICs5SCv2EEMqbb1y74cPwz/+AQcOWHO9PvrIK3dTbpMmwa23FgQ07trqiiscMhWvzCqL0gIlT3kymL24qgyQquNQeBERsaglUERExP8psKol8vM9C6v8k0lHfr44JL09u+jCLqA1GQxkJYdpzs90Yh/eL2nJy7NCIcPwzzDi2LGibX3u2uoKKx4ylVaZFRRkPRctWkCdOrB/v2eBUlmVZde9qg6QSnqOyjLDS0REfEOBlYiIiP9TYFVLvP12dQurTKJJpDUHSC00JL0lBxnASo7RlJ10YT/hvlmd6T/tgIXVqVO0ra+ktjqwwpv69V2HTO4qswzDOledOlZA1ratVWmWmemdFjx3g9kLq+oASUPhRUSqL0dLoD++l4uIiIhFgVUt8eOPvl6BZ9qRRBsySCeCJGJIIobmHGYAqzhBI7bTlUO08vUyyywgAIKD4ZdfvHs/xWdHldRW17YtPPectZ72F0d8ff11QeDkrjLLEdY5ZlolJ8PUqb5vgavqAKm6DIUXEZFLqcJKRETE/ymwqiUaNvT1CkoWxV4iSWc/rUmiA3uJpilH6c8qTtOQbcRyhIG+Xma5GIYVorRrB88+C7fd5n4mlGGU/6+9AQHQsiUkJlrfOyqd3LXVlTTzafHikiuzivOXFrjo6JJndXkjQCrvUHgREfE9x863efkKrERERPyVAqtaomtXX6+gqAjSaEvKxSHpHUmlHY05Tn9W8wsN2Eosa6ppSFWYYVhD2u+7z/q+fXtrNz9X2rSBv/wFLlyAs2fhjTesnRoDAkqfQxUQYH0dPGjN2Co+bNxVW527mU/Dh1uh1XXXFYRZ589bs9BcBWr+0AIXXkJ3aECAdwKk8gyFFxER/+CosFKBlYiIiP9SYFWDmGbJw6ljYqxf3PPyfLe+1uyjPckcoQU/04l0IgnjJP1YwzmC2UI31jAAux3MPKAGfIisU8dqBXS8DkuWwDXXWBVJhbVvb7XkRUQUXPanPxW8nrt3w+uvF7ThFRYUBCEhcOaMFTw5ZpWVNmy8tJlPGRlFK7POnYM//tF1eObrFjjTtB5rvovtyQMCrPDNGwFSWYbCi4iI/1BLoIiIiP9TYFVDlNTa5aiw6dsXmjWDQ4eqdl0tOUAMey4OSe/KftoQymn6spYL1GELcaylf5HblNaCVhGVFdoZHg5rzcsrGuRERlrBxtq18NVX1mXDh1uVSYXPWTgAGTPG+n7aNNf3kZ9vzaIq67BxT2c+Ob5M06r68scWOEf4VtJru2+f9dx7g6dD4UVExH8UBFY+XoiIiIiUSIFVDeCutatwhc3998PTT3t/Pc05xOXs5iSN2EY3DnEZIfxCAuvIwc5m4llH1f92b7e7rsApi4AAq+UuNtaqOHrggZKvaxiuZ0oZBvTvb30VV9aZUnY7NG1q7dDnahdId616ZR0a7s8tcNqxT0REysKxS2CeKqxERET8lgKras40Yfp018Oxi1fYlDTjpzI05Sid2Mlpwi4OSW9JMGfpw3rysLGFONbj2ynUlVG5ZbdD3bowdqz1/bRpl7b3Fb5uSTOlXCnrTClHWPTss3D77a7P6a5VrzxDw/21BU479omISFnYbI4ZVgqsRERE/JUCq2rMUY3jbie3wtUlHTpYVSiuKnHKozHH6MxOMmnAVrqxhoHU5TxX8R0GsJk4NpBQOXfmJ7Ky4NVX4dNPrfDp669h6FArtAoIsF6HZs2sAOfIEatFzVszpRxhEZRvt7ryVkz5YwucduwTEZGycLYEqidQRETEbymwqqaKV+OUpHB1Sd++1k50JVUEeaIhJ4ll+8Uh6XGsZQBBZNGDHwggjy104zv6lP8OqoGcnKLh088/Fw2RTBOuvfbSeUolzZRyzKyaNatgm+3iXM2UKqy8rXr+WjFVVv7crigiIv7H0RKovEpERMR/KbCqptats34xdxdWBQRAkyZWIFKRivdQThPLNrKow2biWUt/AsmmOz8RSDbbiOV7epX/Dqqh4uFT4RBp1izP5ykVnlkVEOB6F0Aova2tIsGTP1ZMlUdNCd9ERMT7DO0SKCIi4vcUWFVTiYmlt/bl5cHp0zBkiNUu9eyz1m5pngjhDN3YRg52tlwckm4nhzg2U5cLbCOWjVxV8QdSjZU0zNvTeUqeVsl52tZWU4Kn0hTfRbFwKFVbngMREamYggorBVYiIiL+SoFVNXX+vPuqKcOwjp87Z32fnAwPPlhyyxlAMJnEsfXikPR41tMXG3nEsZn6nGM7XfiRnpX7QDzUoAG8/z488og1y8kfPl+WVPXk6TylkmZWOdSrZ4WOamsrUNIuiu6G2YuIiBQXYHNUWPl4ISIiIlIiN/FF5Zg0aRJRUVEYhsHmzZudlycmJpKQkEBMTAw9e/Zkx44dPjtWHdWr5z7AKB7o5ObCsWOXhiN1OUcvNtCbDZjY2EACG7mKTuyiP6tpxAk2cSVr6c8pGlf+A/HQ++/DyJEwZ44V/Piau6onxzyl9u2tUCUkxPo3Orpo8JSUZLUOulKvnrXz34oV1pysiAjvPZbqonBFWnY2ZGZa/zrmiflDiCkiItWD4yPUln2n2Jh6QrsFioiI+CGvB1YjRoxg7dq1RBYrf5gwYQLjx49nz549TJkyhbFjx/rsWHXUoUPZg5s6dawd7IK4wFV8Sx/WE0A+39GH7+hFBxLpzyqacIzNXMEaBnCcZt55AGU0dSrk58M995Q9mHBXVVYWAQElh0/FOeYprVgBb77pOnhy1zqYlwdjx1qtbaqsspS2i+K6dT5ZloiIVDMZJ89x30c/AbB812Fuf/dbBk9bRcbJcz5emYiIiBRmmFX0J6WoqCgWLVpEfHw8R44cITo6mhMnTmC32zFNk1atWrF27VpCQ0Or9Fi0u0nWQHh4OBkZGVXxFJWJaUKnTlaVTuHd6Gw2K9gpLpAsrrRtoVXTbJYf6cYvhALQlW005gS7ieEwrapo9WVnt8Ntt8HcuaXP7irMMODOO+HDDyu+hl/9CkaMqLxh3o7X0FXrYHS0FXAprCowa5bV1pqZeemxkBArGKzmObSI+JC/vt/XZt54TUzTZPC0VaQdO0teoU/AATaDqCbBLJ880DmQXURERLyrtPd6nzRX7du3j1atWmG/WCJkGAYRERGkp6fTsGHDKj1WWmDlrxxtZ8Xn+bRrZ/2bng7kZhPHFuqSxTZi+Tb/KjgCPevvYEjcUQ416MC/l8cWCbzKymazqraOHaPU8wQElH6dkuTmwiefuB9O7kpgINx7L3z//aXhnt1uVTzt2+dZCHb99ZUbiLh7DTWz6lKeDrMXEREpyQ9pJ8k4cb5IWAWQl2+SfuIcP6SdpGeU70YgiIiISAGvtwRWN9OmTSM8PNz5lemqnMNHTBPWrrUqTdautcKWwm1ny5fD/3szl9s7/kg/1hDCWX6kJ+voR7hxgGcGrWTvqn18n9mF59cNYsBtralXr3xrMQzrPnNy4LvvrNDKndLa8oKCrEDIndLCqoCAot875kz162cFQNHRl86Uevllz1oGg4Jg4sTSr1dWnrQOisUxzL54K6ynuyiKiIikHjuLPcD1X4QCA2ykHjtbxSsSERGRkvikwqpNmzYcPHiQ3NxcZ4teeno6ERERhIaGVumx4iZPnszkyZOd34eHh1flU+OSacLChVY71PHj1iyqwruj9bkqj8OLt/LXCb+wObszx7kSgBh2M6LDFoZPjOKWP3bCMDoVOa+7ipXStGkDN9xghT2RkTBvHlxzTcmhkmGUXl11/fXw1Vdln1Flt1trsNtLrlRyBEPr1lmVVo62vn/9y6rCysoq+fxBQfD66/Dvf1deO2BhhmGFav36Vd45ayJVpImISEVFNa1PTp6L2QlATl4+UU3rV/GKREREpCQ+qbBq3rw53bt3Z/bs2QAsXLiQ8PBwoqOjq/yYv0tNtcKWkSPh0CGrosnaHS2feolbGBezitb1jjPiuStYkT2AME4xkJVEsZe99o6sDRjELX+McvnLvKNipXhlkie/+B84UHRntn79rF3xile/BASUHlY5KmSCgylTxVedOgWVUl9/XXqlkiMYKjzM3F1oZ7NZQ94jI+Ghh6zAcPBga+5UWprn65TKo4o0ERGpiB6RjWjTOJiAYh92AmwGEY2D6RHZyEcrExERkeK8PnR9woQJfPHFFxw6dIgmTZrQoEEDkpKS2L17N2PHjuX48eOEhoYyc+ZMYmNjAar8mDu+HMKamgoxMYXnK+XTlR0Xh6R35DAtAWhvSyE8P419hLOXoiFcUJD1S33fvpdWF6WlQUICHDxYvvUFBsJrr1lBU3Q0hIdbIVbh6pfGjeH0aTh/3vU5AgKsHQ+XLLHmbg0e7FnVV2Ag/OlPVlVWRSqeSht8np9v7UCnoegiIjWbhq77H2+9Jhknz3Hne9+RevwcdpuBYUBE42D+fU8vWoeVc1aCiIiIlFlp7/VVtktgdeWrD7CmaVWT7Ntn0pkdNOUYSXTgAK0BaEMa7UjhIK04GBLDL5muk5PgYPjrX+G994oGSa1bQ0ZG2XbcK84wrMCpbt2CFsXFi63zOoKx/HwYOLDkc7z1Ftx/v3WuksIjVyIirECvMgKjtDTXbWbPPgt33OG6XdARBKqNT0SkZlBg5X+8+Zpk5+YR89Ri4tuE8eSvOtEjspF2BxQREalifrlLoLhn5pt8/MzPtN93GJP27KQrAK3JYCArOUwLfuZy9hEJQEAJ1UsA587BtGlw5IjVlueoXkpJqYR1mlaw5JhLn5QEw4dblUeOIGfNGvfn6NatIHQqPKOo+I5+hRkGTJpUEHIVrxwr6+fN8sy3Cgr6/+3dfXDU1b3H8c8mGxIhYOW5EkjAICXmYUt4EkQIDxGVodbrhd5RwZYRlUHH0WvRKVWHWqGj1gqtt1Z7oWA71wqY29EZvYIVKtIiFYqIqETARAjyECgB8rCb7/1ju0tCNiGbbHZ/2X2/ZhiSPb/d3/n+lsOefHPO9+c/loQVAACdTxd3spKTXOrbPZW7AgIA4FAkrBzC6k271n6mV35xWH/8YLBKvcMlDdc3dUjX6l0dU2/t0VX6Sk2LwF8sQdPWLX/h8vmkvXv9BeJvucX/WGmpf5XX2bNNj+/a1d8+YcL5xwLJo//6L3/dqFArrdxuacyY0CujAoXoMzPD63uowuct1beqrfW3AwCAzinVnaRqb+gC7AAAIPZiUnQd5338v/v06LXvavgl++WZPUxLt07S2fpUzcvepIKkXTqs/tqsSf9aZRU6MxWLTZ0tJcnuvfd8n7Kzm9/e5/WGTvq4XNI994Qu4u52+x8fN86frCot9SeP/IXo/d83LAbfHoGi9KH6MGSIvx0AAHROaSnJqqm7yC2MAQBAzJCwipG1D27VVWn7lHtTtn7yl0mqrOuuBbmbtGn5P1R2ro9e/GyiqofmKzn54m9R797+O9pFS3Jyy+c7dsy/vU5qe9InsD3wiiv8q6fS08/fEfCtt6T33/fXsLowGeb1+oukB87fHhfrA6UuAADovNJYYQUAgKORsIoRn9d0pPYyzf/WZm18eocOVffUrz6aqGvvLVByl+RgsiQ7++KJkQce8BdRjxS3W+rWrfm27GypT5/mn5+a6q/vJLUv6RPYHrhxo7Rihf/vPXv8Bdf37fPXlwolUF8qElrqAwAA6LxYYQUAgLNRwypGbl46SjcvlVK6XtvsMYFkyYMPSs8+2/xrpaf7VxsNHuy/Q199G35ZmJQkZWRImzadv8tferq0eHHTu+e99Za0bZv07/8e+rXq6hpv9WuuqHlrViiFqi0lRbe+VHN9AAAAnVcXd5KqSVgBAOBYJKxiwEz624cprUreuFxSXt75O+KFar/kEn/CafNmf12nTz8Nrz9ut/Tcc/66US6XlJV1Pjnzb/8WOtE0cKB05ZX+mlEN7+bX3Fa/SCd9AlsNS0sbbwukvhQAAGiNtJRknTpXF+tuAACAZpCwirK23Nlu6FB/IqYuxJzK7fa3S/7nv/iiNGVK6GNDCWzxCySrLtRcosnlkv7v/5rGEliBFan6TmahE2aBrYYdfX4AABCf0lJYYQUAgJORsIois/N3tvN6z29pC9zZbs+e0ImW8eP9iZhQq4muuKLxaqLSUn8NqVAJq0ANqaqqyCR4Qm31GzfOXxD9nXfC2/oXysWSe+3ZaggAABJbqjtZ1XUUXQcAwKlIWEXRli0Xv7NdqC1z4awmaqm2kySVlPiPj1SCp+EKrIMHpZyc8FaPNae1yT3qSwEAgLZIS0lStdcnM5OL33YBAOA4JKyiKHBnu5qapm2BO9s1l3hp7Wqii9V2uuaa80meSGrr6rHmtDW5BwAA0BppKckyk+p8pi5uElYAADhNUqw7kEjae2e7QKLpjjvOJ55CHfPWW/6tgoEtgF26+F+7I2s7tSbBFI5Aci+UQHIPAACgrdLcyZKkai91rAAAcCJWWEVRtO5sF4vaTu1ZPRZKe5N7AAAALUlN8f/etrrOpx5pzfyWDAAAxAwrrKIomqufXC5/kio7258s2rLFv22vo0Q6wRRI7rkvSKlGOrkHAAASU1qKf4VVDYXXAQBwJFZYRVm0Vj9d7A57kRbp1WPhFJoHAAAIh5npRJV/Wfj2gyeUcdklFF4HAMBhXGYdue6m88vIyFB5eXmsuxEWM2n48NDJo+zs8Augt1aoJFkgwTRoUNte0yy6WxsBAImpM37ex7uOek/KK89qzn9v08FjZ+QzyZ3k0qBeXbX6B6OVcVnXiJ8PAACEdrHPelZYxaFY3WGvI1aPBQrNc0dAAADQXmbmT1YdPyvfv35l6603HTx+VnP/e5s2PDCRlVYAADgENaziUCzvsNeaOxkCAADEwvaDlSo/cU6++sYbDHz1pi9PnNX2g5Ux6hkAALgQCas4xB32AAAAmjpw7IzcyaF/m5aSnKQDx85EuUcAAKA5JKziEHfYAwAAaCqrdzfV+ULfFbDW61NW725R7hEAAGgONaziUCzvsEeRdAAA4FQjMy/TwJ5ddeDYGV2wK1Deeumx//1Il12SIpfLpTM1PnXtkhT8ultqsnp266ITZ2qbtMXLcU7sU6Id58Q+xctxTuxToh3nxD7Fy3Edda7Ks3VKSU7SpGF9dNvYTCUlRXfNE3cJvIjOfNegaCePQt0lcPBgf5IsM7PjzgsAQHt15s/7eNVR70nZiTOa/Mwm1fmYAgMA0FruJJf+Z/5YjczqGbHXvNhnPVsC41g0C6Cb+ZNVpaX+RFVVlf/v0lJp+nR/OwAAQKxV/LNGYl4CAEBYvPWm/3jxr6qvD721viOQsEJEbNkiHTggeb2NH/d6pS++8LcDAADE2oFjZ5SURL0CAADCVeczvfy3L6N2PhJWiIh9+6SUlNBtXbr42wEAAGItq3c3eZspvA4AAFq2+6tTUTsXCStERHa2fwtgKLW1/nYAAIBYG5l5mfpdmhbrbgAA0CnlDrg0auciYYWIGD/eX2DdfcF9J91u/90Jx4+PTb8AAAAacrlcemX+WLmZBQMAEJaUZJduGzMoaufjoxoR4XL57wZ4xRX+LYDp6f6/s7P9j3dkwXcAAIBwDOzZTX/+zyL17ZEa664AANAp+O8SeLWSkqKXRnJf/BCgdTIzpU8+8RdY37fPn6waP55kFQAAcJ6BPbvqb49M0QcHTuidT45o91endKbGp65dkuRyuZp83S01WT27ddGJM7Vxe5wT+5RoxzmxT/FynBP7lGjHObFP8XJcR52r8mydUpKTNGlYH902NjOqySqJhBUizOWSrrnG/wcAAMDJXC6XRg/updGDe8W6KwAA4AJsCQQAAAA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\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== BATCH_SIZE = 1024 ===== \n",
      "[000]  dy_i = 89.16 * x + 32502.29     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478408177.654546\n",
      "[001]  dy_i = 88.67 * x + 33247.55     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478062102.037441\n",
      "[002]  dy_i = 88.35 * x + 33746.16     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477907194.733171\n",
      "[003]  dy_i = 88.13 * x + 34079.74     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477837856.785210\n",
      "[004]  dy_i = 87.98 * x + 34302.92     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477806820.475785\n",
      "[005]  dy_i = 87.89 * x + 34452.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477792928.335463\n",
      "[006]  dy_i = 87.82 * x + 34552.14     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477786710.084443\n",
      "[007]  dy_i = 87.78 * x + 34618.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477783926.737540\n",
      "[008]  dy_i = 87.75 * x + 34663.69     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782680.885618\n",
      "[009]  dy_i = 87.73 * x + 34693.60     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782123.230728\n",
      "[010]  dy_i = 87.71 * x + 34713.62     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781873.619221\n",
      "[011]  dy_i = 87.71 * x + 34727.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781761.890792\n",
      "[012]  dy_i = 87.70 * x + 34735.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781711.880110\n",
      "[013]  dy_i = 87.70 * x + 34741.96     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781689.494864\n",
      "[014]  dy_i = 87.69 * x + 34745.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781679.475020\n",
      "[015]  dy_i = 87.69 * x + 34748.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781674.990045\n",
      "[016]  dy_i = 87.69 * x + 34750.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.982528\n",
      "[017]  dy_i = 87.69 * x + 34751.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.083945\n",
      "[018]  dy_i = 87.69 * x + 34752.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.681731\n",
      "[019]  dy_i = 87.69 * x + 34752.99     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.501696\n",
      "[020]  dy_i = 87.69 * x + 34753.35     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.421111\n",
      "[021]  dy_i = 87.69 * x + 34753.59     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.385040\n",
      "[022]  dy_i = 87.69 * x + 34753.75     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.368895\n",
      "[023]  dy_i = 87.69 * x + 34753.86     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.361668\n",
      "[024]  dy_i = 87.69 * x + 34753.93     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.358433\n",
      "[025]  dy_i = 87.69 * x + 34753.98     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356985\n",
      "[026]  dy_i = 87.69 * x + 34754.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356337\n",
      "[027]  dy_i = 87.69 * x + 34754.03     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356047\n",
      "[028]  dy_i = 87.69 * x + 34754.05     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355917\n",
      "[029]  dy_i = 87.69 * x + 34754.06     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355859\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== BATCH_SIZE = 4096 ===== \n",
      "[000]  dy_i = 89.16 * x + 32502.29     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478408177.654546\n",
      "[001]  dy_i = 88.67 * x + 33247.55     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478062102.037441\n",
      "[002]  dy_i = 88.35 * x + 33746.16     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477907194.733171\n",
      "[003]  dy_i = 88.13 * x + 34079.74     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477837856.785210\n",
      "[004]  dy_i = 87.98 * x + 34302.92     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477806820.475785\n",
      "[005]  dy_i = 87.89 * x + 34452.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477792928.335463\n",
      "[006]  dy_i = 87.82 * x + 34552.14     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477786710.084443\n",
      "[007]  dy_i = 87.78 * x + 34618.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477783926.737540\n",
      "[008]  dy_i = 87.75 * x + 34663.69     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782680.885618\n",
      "[009]  dy_i = 87.73 * x + 34693.60     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782123.230728\n",
      "[010]  dy_i = 87.71 * x + 34713.62     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781873.619221\n",
      "[011]  dy_i = 87.71 * x + 34727.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781761.890792\n",
      "[012]  dy_i = 87.70 * x + 34735.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781711.880110\n",
      "[013]  dy_i = 87.70 * x + 34741.96     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781689.494864\n",
      "[014]  dy_i = 87.69 * x + 34745.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781679.475020\n",
      "[015]  dy_i = 87.69 * x + 34748.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781674.990045\n",
      "[016]  dy_i = 87.69 * x + 34750.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.982528\n",
      "[017]  dy_i = 87.69 * x + 34751.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.083945\n",
      "[018]  dy_i = 87.69 * x + 34752.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.681731\n",
      "[019]  dy_i = 87.69 * x + 34752.99     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.501696\n",
      "[020]  dy_i = 87.69 * x + 34753.35     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.421111\n",
      "[021]  dy_i = 87.69 * x + 34753.59     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.385040\n",
      "[022]  dy_i = 87.69 * x + 34753.75     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.368895\n",
      "[023]  dy_i = 87.69 * x + 34753.86     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.361668\n",
      "[024]  dy_i = 87.69 * x + 34753.93     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.358433\n",
      "[025]  dy_i = 87.69 * x + 34753.98     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356985\n",
      "[026]  dy_i = 87.69 * x + 34754.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356337\n",
      "[027]  dy_i = 87.69 * x + 34754.03     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356047\n",
      "[028]  dy_i = 87.69 * x + 34754.05     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355917\n",
      "[029]  dy_i = 87.69 * x + 34754.06     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355859\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set a learning rate for each parameter\n",
    "learning_rate_m = 1e-7\n",
    "learning_rate_b = 1e-1\n",
    "\n",
    "# for plotting entire data set\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "\n",
    "# iterate over batch sizes\n",
    "batch_sizes = [64, 256, 1024, 4096]\n",
    "for batch_size in batch_sizes:\n",
    "    print(' ===== BATCH_SIZE = %d ===== ' % (batch_size))\n",
    "    \n",
    "    # reset our initial slope and intercept\n",
    "    m = 5.\n",
    "    b = 1000.\n",
    "    \n",
    "    # use these to plot our progress over time\n",
    "    loss_history = []\n",
    "    data_batch = data\n",
    "\n",
    "    # begin training loop\n",
    "    N_inner = 20\n",
    "    N_outer = 30\n",
    "    for i in range(N_outer):\n",
    "        for j in range(N_inner):\n",
    "            # create subset of data using batch_size\n",
    "            r = batch_size / len(data['GrLivArea'])\n",
    "            data_batch.sample(frac=r, replace=True)\n",
    "            data_x_batch = data_batch['GrLivArea'].to_numpy()\n",
    "            data_y_batch = data_batch['SalePrice'].to_numpy()\n",
    "\n",
    "            # update our slope and intercept based on the current values\n",
    "            m = updated_m(data_x_batch,data_y_batch,m,b,learning_rate_m)\n",
    "            b = updated_b(data_x_batch,data_y_batch,m,b,learning_rate_b)\n",
    "\n",
    "            # calculate the loss value\n",
    "            loss_value = np.mean(loss(data_x_batch,data_y_batch,m,b))\n",
    "\n",
    "            # keep a history of our loss values\n",
    "            loss_history.append(loss_value)\n",
    "\n",
    "        # print our progress\n",
    "        print('[%03d]  dy_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f    loss: %f' % (i,m,b,m_calc,b_calc,loss_value))\n",
    "\n",
    "        # close/delete previous plots\n",
    "        plt.close('all')\n",
    "\n",
    "        # create a 1 by 2 plot grid\n",
    "        fig,ax = plt.subplots(1,2,figsize=(18,6),dpi=80)\n",
    "\n",
    "        # plot our usual output\n",
    "        plot_data(data_x,data_y,m,b,ax[0])\n",
    "\n",
    "        # here we also plot the calculated linear fit for comparison\n",
    "        line_x = np.arange(data_x.min(),data_x.max())\n",
    "        line_y = line_x * m_calc + b_calc\n",
    "        ax[0].plot(line_x,line_y,'b-',label='calculated')\n",
    "\n",
    "        # add a legend to the plot and x/y labels\n",
    "        ax[0].legend()\n",
    "        ax[0].set_xlabel('square footage')\n",
    "        ax[0].set_ylabel('sale price')\n",
    "\n",
    "        # plot the loss \n",
    "        loss_x = np.arange(0,len(loss_history))\n",
    "        loss_y = np.asarray(loss_history)\n",
    "        ax[1].plot(loss_x,loss_y, 'o-')\n",
    "        ax[1].set_yscale('log')\n",
    "        ax[1].set_xlabel('loop step')\n",
    "        ax[1].set_ylabel('loss')\n",
    "        ax[0].set_title('Data with Model Fit')\n",
    "        ax[1].set_title('Loss Function Over Iterations - Batch Size = %d' % (batch_size))\n",
    "\n",
    "    # show final results for batch size\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Learning Rate Issue\n",
    "\n",
    "The learning rate affects how large of a step to take when minimizing the loss function. When the step is too large, it can lead the minimization of the loss function to diverge. This is clearly shown in the example below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== RATE_MULTIPLIER = 1 ===== \n",
      "    batch_size = 64\n",
      "    learning_rate_m = 1.000000e-07\n",
      "    learning_rate_b = 1.000000e-01\n",
      "[000]  dy_i = 89.16 * x + 32502.29     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478408177.654546\n",
      "[001]  dy_i = 88.67 * x + 33247.55     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478062102.037441\n",
      "[002]  dy_i = 88.35 * x + 33746.16     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477907194.733171\n",
      "[003]  dy_i = 88.13 * x + 34079.74     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477837856.785210\n",
      "[004]  dy_i = 87.98 * x + 34302.92     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477806820.475785\n",
      "[005]  dy_i = 87.89 * x + 34452.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477792928.335463\n",
      "[006]  dy_i = 87.82 * x + 34552.14     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477786710.084443\n",
      "[007]  dy_i = 87.78 * x + 34618.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477783926.737540\n",
      "[008]  dy_i = 87.75 * x + 34663.69     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782680.885618\n",
      "[009]  dy_i = 87.73 * x + 34693.60     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477782123.230728\n",
      "[010]  dy_i = 87.71 * x + 34713.62     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781873.619221\n",
      "[011]  dy_i = 87.71 * x + 34727.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781761.890792\n",
      "[012]  dy_i = 87.70 * x + 34735.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781711.880110\n",
      "[013]  dy_i = 87.70 * x + 34741.96     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781689.494864\n",
      "[014]  dy_i = 87.69 * x + 34745.97     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781679.475020\n",
      "[015]  dy_i = 87.69 * x + 34748.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781674.990045\n",
      "[016]  dy_i = 87.69 * x + 34750.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.982528\n",
      "[017]  dy_i = 87.69 * x + 34751.65     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781672.083945\n",
      "[018]  dy_i = 87.69 * x + 34752.45     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.681731\n",
      "[019]  dy_i = 87.69 * x + 34752.99     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.501696\n",
      "[020]  dy_i = 87.69 * x + 34753.35     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.421111\n",
      "[021]  dy_i = 87.69 * x + 34753.59     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.385040\n",
      "[022]  dy_i = 87.69 * x + 34753.75     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.368895\n",
      "[023]  dy_i = 87.69 * x + 34753.86     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.361668\n",
      "[024]  dy_i = 87.69 * x + 34753.93     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.358433\n",
      "[025]  dy_i = 87.69 * x + 34753.98     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356985\n",
      "[026]  dy_i = 87.69 * x + 34754.01     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356337\n",
      "[027]  dy_i = 87.69 * x + 34754.03     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.356047\n",
      "[028]  dy_i = 87.69 * x + 34754.05     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355917\n",
      "[029]  dy_i = 87.69 * x + 34754.06     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355859\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== RATE_MULTIPLIER = 4 ===== \n",
      "    batch_size = 256\n",
      "    learning_rate_m = 4.000000e-07\n",
      "    learning_rate_b = 4.000000e-01\n",
      "[000]  dy_i = 91.17 * x + 29623.20     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1481169186.241553\n",
      "[001]  dy_i = 87.83 * x + 34544.82     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477787306.162822\n",
      "[002]  dy_i = 87.69 * x + 34745.54     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781680.728774\n",
      "[003]  dy_i = 87.69 * x + 34753.73     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.371403\n",
      "[004]  dy_i = 87.69 * x + 34754.06     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355838\n",
      "[005]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[006]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[007]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[008]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[009]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[010]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[011]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[012]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[013]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[014]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[015]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[016]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[017]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[018]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[019]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[020]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[021]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[022]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[023]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[024]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[025]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[026]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[027]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[028]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n",
      "[029]  dy_i = 87.69 * x + 34754.08     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1477781671.355812\n"
     ]
    },
    {
     "data": {
      "image/png": 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3T2amyspKLV68mGQVAAAAgKjFDCsAAAAAAAC4CpuuAwAAAAAAwFVIWAEAAAAAAMBVSFgBAAAAAADAVUhYAQAAAAAAwFVIWAEAAAAAAMBVSFgBAAAAAADAVUhYAQAAAAAAwFX+H094CADAO8zXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== RATE_MULTIPLIER = 8 ===== \n",
      "    batch_size = 512\n",
      "    learning_rate_m = 8.000000e-07\n",
      "    learning_rate_b = 8.000000e-01\n",
      "[000]  dy_i = 38338.27 * x + -55737106.53     previously calculated: y_i = 87.69 * x + 34754.08    loss: 405535151198538.000000\n",
      "[001]  dy_i = -2521935.41 * x + 4903228074.61     previously calculated: y_i = 87.69 * x + 34754.08    loss: 3575637398865951232.000000\n",
      "[002]  dy_i = -94266384.57 * x + 35563978232.91     previously calculated: y_i = 87.69 * x + 34754.08    loss: 11880835629321025486848.000000\n",
      "[003]  dy_i = 27869339663.14 * x + -41906894279189.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 220447724556251026421710848.000000\n",
      "[004]  dy_i = -1567286923758.16 * x + 3200246737503650.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1661831346947539312042525589504.000000\n",
      "[005]  dy_i = -91142769922369.67 * x + 66947089125077312.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 6049025119001616871232623924477952.000000\n",
      "[006]  dy_i = 20025253905661292.00 * x + -30986749902067556352.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 117937133644162725733434019044439097344.000000\n",
      "[007]  dy_i = -940201015086697728.00 * x + 2043393352974910619648.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 760648241733560466331461644693381176098816.000000\n",
      "[008]  dy_i = -80944286035061473280.00 * x + 76339749743775128223744.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 3215401717317366946117980377684252134341607424.000000\n",
      "[009]  dy_i = 14196076193224213921792.00 * x + -22577233757621897480110080.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 62058505057461031850852907183399517488033491320832.000000\n",
      "[010]  dy_i = -536771171677477844025344.00 * x + 1269885281923303703436066816.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 343464514860262637587210485179038780321971971360292864.000000\n",
      "[011]  dy_i = -68164903486048577605599232.00 * x + 73818201999313994026902880256.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1767093164685295563404741297398343181754964174308863115264.000000\n",
      "[012]  dy_i = 9929144570805902675493781504.00 * x + -16222878780761505109722164887552.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 32109299372765195172814563062742835366770379923809571606364160.000000\n",
      "[013]  dy_i = -283678203762636521211399503872.00 * x + 761823317781572119730800516136960.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 153446362730708570654589041463116640075498982570655414784582746112.000000\n",
      "[014]  dy_i = -55302008432217208035524026040320.00 * x + 65562471997910025530298623884001280.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 991321782837592248701195852131741462512228825276644309601946232160256.000000\n",
      "[015]  dy_i = 6849557884809190850739624055144448.00 * x + -11500691677558056318294253518712733696.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 16333652520799577100747443171575216376360300263569564292362289452471549952.000000\n",
      "[016]  dy_i = -129925698049896636349167652705402880.00 * x + 434959119765010364305107448509834985472.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 68154488915942188368404732174108919062886951498210640206472503654712615108608.000000\n",
      "[017]  dy_i = -43615537225046102126442708924421373952.00 * x + 55213927120285737867546832874514241552384.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 560879076442138087261396772459393599484987693291959795790097094392706968003280896.000000\n",
      "[018]  dy_i = 4656907384885128735156433919237186125824.00 * x + -8044022636172591106263129428354979892035584.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 8168448252890910466844707041748845775065966375698038622902893528419305944136888090624.000000\n",
      "[019]  dy_i = -40538481642404541457608210241939786694656.00 * x + 229894163745727598602363477739667955373834240.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 30317168725707375124650704491096743707117660359275883766026678511047598211462447692251136.000000\n",
      "[020]  dy_i = -33625716416742828525293527215609744365453312.00 * x + 44796329646133241080173890203411001207754326016.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 317049143130609892600453731605552044844546471082962740486740162790810002638501143523933290496.000000\n",
      "[021]  dy_i = 3116582759732424460249388838409268396432556032.00 * x + -5549195529978277229160959655823140360286663344128.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 4016081813468669269807461613603439361493789561107194401694495597625937090095757153471707320680448.000000\n",
      "[022]  dy_i = 8113987252866436609830775034538827501134675968.00 * x + 105313853594573770262067672099721867887578936508416.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 13645866309260481000945639136664356621879651567478749016055926061490442369147386605930524865527283712.000000\n",
      "[023]  dy_i = -25432657749748468047493748082504493937758287429632.00 * x + 35330802246813072870943055224451966772937564687958016.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 177885804589550485886885651859874404052285169674748594022656485712525293276925584610886782592543558205440.000000\n",
      "[024]  dy_i = 2049181540869688829114940391503777609742046900256768.00 * x + -3772867402334140581652458863277058816831391552096960512.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1941331959830004305527141393522029407497673213320144779338485947050723648395814375109471311206865451217846272.000000\n",
      "[025]  dy_i = 31736657559115888514868175386970581385536344363630592.00 * x + 32882751184184319111020019699115930232875256017877729280.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 6293282362300809415689901293912012736353208233303467363396886260365104214089280963946368576569996579904176521216.000000\n",
      "[026]  dy_i = -18916372847006862527095305113196622920457406791209189376.00 * x + 27239095228702494806773953368416573135809317126414708768768.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 98649062118777299569368925121470580169035054277590742671066567060185070615324793702235900507735673400921352417837056.000000\n",
      "[027]  dy_i = 1319970732663344386169607023308236014878572875641872449536.00 * x + -2524990310470748181196959484980606068610511168761872703815680.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 922790601733711016473255673602517605729728676312282484629523144073385895602297517227555769310164594680607247801501351936.000000\n",
      "[028]  dy_i = 40573629888904088071377980452704181452865576493911591878656.00 * x + -6543925691806839249090022349997145945615838849904433357127680.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 3010744623316848325148751094894072567804551064725437200230960680731036663087315401413722190680945359587759572352212603502592.000000\n",
      "[029]  dy_i = -13857894018617258297159790536522151109062405785004346949238784.00 * x + 20602527170731223899191065021685526274909516505391245749053816832.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 53937036214509765166088815654727953122926504554151613832162850308063946064753321567844329915327121890656803652472077443351445504.000000\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ===== RATE_MULTIPLIER = 12 ===== \n",
      "    batch_size = 768\n",
      "    learning_rate_m = 1.200000e-06\n",
      "    learning_rate_b = 1.200000e+00\n",
      "[000]  dy_i = 401351745654499.50 * x + -1010340053827229056.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 242490473523083146802602326519447552.000000\n",
      "[001]  dy_i = 687032543478023404975554560.00 * x + -1729496641849925720606215503872.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 710557104575729805101438570821020623798817899299814470844416.000000\n",
      "[002]  dy_i = 1176059951034469996463147640005838503936.00 * x + -2960546418414845721595758607110284096045056.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 2082108175895269857805745849078573651447108715046073675024807488165485530417865949184.000000\n",
      "[003]  dy_i = 2013175389662509006938591701029201565208210271371264.00 * x + -5067853202775683625479104232680048769801203568389128192.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 6101092267198431095499165161840685628819031231744599626357191762828882381752473509666087956337801367662886912.000000\n",
      "[004]  dy_i = 3446146725749704470216688799343199365624602601166668858231095296.00 * x + -8675133727048667310741014609468209351854355300403560161053570498560.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 17877710334076733303455400296797102900620817149759404947523277478961774409331972377201937857683035154033937712624744726563707552792576.000000\n",
      "[005]  dy_i = 5899102143001201748449241104909031806132049202406767838893070155492767039488.00 * x + -14850064153586390805767219203420243579271811075583024187829461492031288237883392.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 52386115926733255646200326020485378412992495841052440919599522136431422989043792294580717407785933737110154200659865328135751749032151168909751872792914034688.000000\n",
      "[006]  dy_i = 10098062811295652518707551552173340447570235659259824061336302341172365698692023798726656.00 * x + -25420288874400467174536798954166217004180071680143924632115331580590312692536138030670413824.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 153504284978720794211054077140537388614945279813464975143779994899076528812431368480503894289152587448061529424547815413379335913143207819334596894493182563350393538353928599452516352.000000\n",
      "[007]  dy_i = 17285829278588189880202182498452089986722135019088572508597371715996723478877631919957966985657057280.00 * x + -43514363289933006980858338697041735912097778379053437923719445309983378437022385148837600536804328472576.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 449805546564746638513966199675298028266321877102353165797805623050760833001694934996116378277477345182996408020194157398898080067888217821984369539654785880985129092099858064862587977026158591229491993903104.000000\n",
      "[008]  dy_i = 29589823259393879459744113912058580056132952450671843289652678486307990522563714193697015167223543041090446688256.00 * x + -74487737802032564274050954940033943006770596771596209857170005243825499021059791738328218526249027513740844261703680.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1318041576158326657199835496120524206694749454220094868950746876800992773050126247658637258130337724341075934047223281032816817796447997660343740410514605308570299438141693489656126009303028997430696901182804367141879117566357536768.000000\n",
      "[009]  dy_i = 50651757946418759954304055408302410267891552876205320076410779273812287189166600473636946818805718242315462532294653750804480.00 * x + -127507854036507880223552416621752062012274509376792785951912922050333011319526548222311172665265375383691061532544407702039691264.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 3862188027136443844380238977028801746366087872399034592379634364689426840940897201202521397400466798038482142476522825607220198597418284903018621412359113412017502625114473209380602293954837046680850101901871707050624194317660875847822498078920023572742144.000000\n",
      "[010]  dy_i = 86705505489901735572725359186466140531034782176851344982208337880742886551147419445718416014834963340808587300136807093293195690103537664.00 * x + -218267507119161846249017462463496103772019658845267055334927481468857989553639931405827167593788014613432062646462789427205194470360602378240.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 11317166792593104012288087299115911902299345627854106028435467995932823427759936005926243360749131456299704513876755673179933899275969420907807446818734106601939232425459870733192568359141633844016068099895154864728764821951272693857572546686109089211691681457878237804269915865088.000000\n",
      "[011]  dy_i = 148422186851086578302016399017508029651730587000177515947385648397028128857788254340476265155242137012345303072278021336869464015240555777708863258624.00 * x + -373629569911614440043829652303473193522554474951620984641872751256150615502037589800809304754809743550656161598001645734212312664175291399789541163270144.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: 33162099647005966042310238991585401595733192757287118349842262907813619580408381468929976941066052414832185716042139406375423626304824525145877312657534927383077542714663713680178792962423965465271290729422493766127680743569841079010086189617724012700408550368649042733989048529690687334629375736463491072.000000\n",
      "[012]  dy_i = 254068590283744394860156825361347350441709208862635778242971696760854069824548249941410045537148126065141265595840598150992711670568520998858507490590631265304576.00 * x + -639577816024280303830895238761433177884124071597669627081678483779977829351998232080158173989036729325563757737810520772004697338090727964653364808100320274475384832.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[013]  dy_i = 434913741255772472464518227628714513659306629075467665093841411784862670265154146293944544453140038678519080379700478808652864053078426744610219163765457060259143963262320640.00 * x + -1094827111374392354268787286021529616367974138541313826081528542063459353330650539881915210532791692220830375147853366805989829758602252706181143860592729362952897042882586738688.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[014]  dy_i = 744483850293536912001116733126021114032194153054384422685159838957891965739714349264030185544463281857767512329816268965903034596654304076534740424276712418299377978341771230595547922432.00 * x + -1874121293404730535891284111101815469081727727266031050211568995280151817448693644399678344644363148432842693995698408056233575822655618753343311400073303147497843506834959279336616531853312.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[015]  dy_i = 1274404900952375516486738828270366266583487451155970670851313486354592954025102552854688233810023563778105252319664549682335315538026588757984996789266562153324797030334042151062977263872545988280320.00 * x + -3208114400805999859029204592428599946682661332703641015417789205857649507424450839596347595966725583704821804558764312347319466472563276680985217538952621396622042715327725282278351210867528224074629120.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[016]  dy_i = 2181521937555892825255644870613285025344211403555473069438607383594256823092824428770409821435466675355553324022865327204678503676122267018738144222235094032384510001791366524753078975643470647747443953292541952.00 * x + -5491639225741491490571539418579757555856029311734278003428626695802484426211064376875213926966023758128733988394284584078512988170243341064389524911398113051025289622289298649927257179246669350305888878897236279296.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[017]  dy_i = 3734321768914374215113418848776395382423127116426589039466415055039103791298562186284968584711720196974512029769452990043779778923422380777185990775790887198934640228237547834561406663660994090021394690345558175779662069760.00 * x + -9400569187347496579089702448701706950386888354605230600004233741932809208020030886330239042442182586843268263130243401493448311636046379116915991806881505070633420083539067361551342911165241616161806992837333053494375242268672.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/tmp/pbs.1247291.polaris-pbs-01.hsn.cm.polaris.alcf.anl.gov/ipykernel_16567/3061333823.py:3: RuntimeWarning: overflow encountered in power\n",
      "  return np.power( y - y_predicted, 2 )\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[018]  dy_i = 6392399193295087354261699353726818628602098299876406138012824628597597386679435018738136496337791577881969207922657457153014321441279045436132929236456960819379591209918532533754531788358167832697862415457375891223520897523291315503104.00 * x + -16091862085892113193782975897795298913313597514842264256037643012600616404963433013823695490069957805984505053787011801050954509106570345045323587451592888309209484284909165575866331142754933615879779999084607837742908652724494699138646016.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[019]  dy_i = 10942487009714502144835929531662142383820761700953034726982396289747939988162574180000694514091849734123722229598179409318701933724288559567652367365318945001286580378196016652845905592010873225713416669166166229829622533280057700716743193587089408.00 * x + -27545994314886536427761347771962668401246642515022759086266658175113305580573374921969256876697955925458584082175013475731803671926167151641654089361316345286404452372718391491963142915024212318421772760498820795990429877471552166903950297922451537920.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[020]  dy_i = 18731311724612315459457160147869709246980017190917654552974524977321118111167230833377256676076021022398861833099032002910882636092469369858585195948604667570580204304315448473169644051776730839329961670568769019241489662907137135177939921038773158071895064576.00 * x + -47153138570643870905635866039237999048566028233057487476922195188087926969994446470979875353741512685009846248082997464184642595136761457178053039715879097524762991560210022227154030737983401461961241769076552989753414088801174134430134376087233764030033988419584.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[021]  dy_i = 32064195151715582772969951819426803912374685797847556569249556834719051398025190585091858997406746726193899102581715301003443941004109489280200194091523006308591630397138660512709196201098601063217202457057246656330477052987967819753667711716654186142111128342660571463680.00 * x + -80716580844596700806608359555673206340942010871649330662426082030142038926120199524886347402548850711607059644711400421276561967871742208392661425347578910709565444899428009015837023671668188611454137607987887875091806336919071355386293568240087259316250143079872359559069696.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[022]  dy_i = 54887379263268320108739164613449940254315707435355961535156880003527484001030337731807620381641409765805967186466184909285548691273355063753289187739675441135764829185428947992046200965848274732607374295771199265611620722469545013045595786049557217517442649432467895492237991218249728.00 * x + -138170366188486597423789298451336225686035941793612032295455969998363264100235165184547399742875673634019793474343593654327935278567828835478328998672906365853158469193663349396941947463958129063221223886870957089018874713319253310964415127604296184306185605072793725999247012305502732288.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[023]  dy_i = 93956027529625199466069863696159427899727313499395012228231948329152925665952407384841493327518955455412974922743919038278013948432864907402272989525853831656664670348089264924376691395679474569965096282931507980754328415478424332235709959890662970369347563555011507201689581861255597732357210112.00 * x + -236519558842766572295104397126932714966412835294786748486127293311523815304370055781961888437831218283018774592951801422226961235889859051256558212396756842855777651066018822636180108892823421859967902928448114055898508874953705722478718252411656742538033129010367976181744389986182847380848589668352.00     previously calculated: y_i = 87.69 * x + 34754.08    loss: inf\n",
      "[024]  dy_i = nan * x + nan     previously calculated: y_i = 87.69 * x + 34754.08    loss: nan\n",
      "[025]  dy_i = nan * x + nan     previously calculated: y_i = 87.69 * x + 34754.08    loss: nan\n",
      "[026]  dy_i = nan * x + nan     previously calculated: y_i = 87.69 * x + 34754.08    loss: nan\n",
      "[027]  dy_i = nan * x + nan     previously calculated: y_i = 87.69 * x + 34754.08    loss: nan\n",
      "[028]  dy_i = nan * x + nan     previously calculated: y_i = 87.69 * x + 34754.08    loss: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/tmp/pbs.1247291.polaris-pbs-01.hsn.cm.polaris.alcf.anl.gov/ipykernel_16567/4129302290.py:2: RuntimeWarning: invalid value encountered in add\n",
      "  return m * x + b\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[029]  dy_i = nan * x + nan     previously calculated: y_i = 87.69 * x + 34754.08    loss: nan\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set a learning rate for each parameter\n",
    "learning_rate_m = 1e-7\n",
    "learning_rate_b = 1e-1\n",
    "\n",
    "# for plotting entire data set\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "\n",
    "# iterate over batch sizes\n",
    "initial_rates = np.array([64, 1e-7, 1e-1])\n",
    "rate_multipliers = [1, 4, 8, 12]\n",
    "for rate_multiplier in rate_multipliers:\n",
    "    rates = initial_rates * rate_multiplier\n",
    "    batch_size = rates[0]\n",
    "    learning_rate_m = rates[1]\n",
    "    learning_rate_b = rates[2]\n",
    "    print(' ===== RATE_MULTIPLIER = %d ===== ' % (rate_multiplier))\n",
    "    print('    batch_size = %d' % batch_size)\n",
    "    print('    learning_rate_m = %e' % learning_rate_m)\n",
    "    print('    learning_rate_b = %e' % learning_rate_b)\n",
    "    \n",
    "    # reset our initial slope and intercept\n",
    "    m = 5.\n",
    "    b = 1000.\n",
    "    \n",
    "    # use these to plot our progress over time\n",
    "    loss_history = []\n",
    "    data_batch = data\n",
    "\n",
    "    # begin training loop\n",
    "    N_inner = 20\n",
    "    N_outer = 30\n",
    "    for i in range(N_outer):\n",
    "        for j in range(N_inner):\n",
    "            # create subset of data using batch_size\n",
    "            r = batch_size / len(data['GrLivArea'])\n",
    "            data_batch.sample(frac=r, replace=True)\n",
    "            data_x_batch = data_batch['GrLivArea'].to_numpy()\n",
    "            data_y_batch = data_batch['SalePrice'].to_numpy()\n",
    "\n",
    "            # update our slope and intercept based on the current values\n",
    "            m = updated_m(data_x_batch,data_y_batch,m,b,learning_rate_m)\n",
    "            b = updated_b(data_x_batch,data_y_batch,m,b,learning_rate_b)\n",
    "\n",
    "            # calculate the loss value\n",
    "            loss_value = np.mean(loss(data_x_batch,data_y_batch,m,b))\n",
    "\n",
    "            # keep a history of our loss values\n",
    "            loss_history.append(loss_value)\n",
    "\n",
    "        # print our progress\n",
    "        print('[%03d]  dy_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f    loss: %f' % (i,m,b,m_calc,b_calc,loss_value))\n",
    "\n",
    "        # close/delete previous plots\n",
    "        plt.close('all')\n",
    "\n",
    "        # create a 1 by 2 plot grid\n",
    "        fig,ax = plt.subplots(1,2,figsize=(18,6),dpi=80)\n",
    "\n",
    "        # plot our usual output\n",
    "        plot_data(data_x,data_y,m,b,ax[0])\n",
    "\n",
    "        # here we also plot the calculated linear fit for comparison\n",
    "        line_x = np.arange(data_x.min(),data_x.max())\n",
    "        line_y = line_x * m_calc + b_calc\n",
    "        ax[0].plot(line_x,line_y,'b-',label='calculated')\n",
    "\n",
    "        # add a legend to the plot and x/y labels\n",
    "        ax[0].legend()\n",
    "        ax[0].set_xlabel('square footage')\n",
    "        ax[0].set_ylabel('sale price')\n",
    "\n",
    "        # plot the loss \n",
    "        loss_x = np.arange(0,len(loss_history))\n",
    "        loss_y = np.asarray(loss_history)\n",
    "        ax[1].plot(loss_x,loss_y, 'o-')\n",
    "        ax[1].set_yscale('log')\n",
    "        ax[1].set_xlabel('loop step')\n",
    "        ax[1].set_ylabel('loss')\n",
    "        ax[0].set_title('Data with Model Fit')\n",
    "        ax[1].set_title('Loss Function Over Iterations - Rate Multiplier = %d' % (rate_multiplier))\n",
    "\n",
    "    # show final results for batch size\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "datascience/conda-2023-01-10",
   "language": "python",
   "name": "conda-2023-01-10"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  },
  "vscode": {
   "interpreter": {
    "hash": "ca11ad6395cdedf9566fae895615e536994dcaaccdd1d5f900a22af192bb117e"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}