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<h3>Course Project - Practical Machine Learning</h3>
<h1></h1>
<h3>Building a machine learning algorithm to predict activity quality from activity monitors.</h3>
<p>Human Activity Recognition - <b>HAR</b> - has emerged as a key research area in the last years and is gaining increasing attention by the pervasive computing research community, especially for the development of context-aware systems. Further details can be found <a href= http://groupware.les.inf.puc-rio.br/har>here</a>. <br>
The data <a href= http://groupware.les.inf.puc-rio.br/har>they</a> have provided was collected from accelerometers on the belt, forearm, arm, and dumbell of 6 participants. They were asked to perform barbell lifts correctly and incorrectly in 5 different ways. </p>
<pre><code class="r">library(caret)
</code></pre>
<pre><code>## Loading required package: lattice
## Loading required package: ggplot2
</code></pre>
<pre><code class="r">trainingData <- read.csv("~/Courses/Practical Machine Learning//pml-training.csv",
na.strings = c("NA", ""))
testingData <- read.csv("~/Courses/Practical Machine Learning//pml-testing.csv")
</code></pre>
<p>The goal of this project is to predict the manner in which they did the exercise. The manner has been divided into following classes:</p>
<pre><code class="r">levels(trainingData$classe)
</code></pre>
<pre><code>## [1] "A" "B" "C" "D" "E"
</code></pre>
<p><br></p>
<h3>Cleaning and setting the data:</h3>
<p>Removing columns with missing values:</p>
<pre><code class="r"># trainingData <- trainingData[,!sapply(data,function(x) any(is.na(x)))]
trainingData <- trainingData[, which(colSums(is.na(trainingData)) == 0)]
</code></pre>
<p>Also, we remove any variables(columns) that doesn't seem relative(non-sensor data) to the prediction model:</p>
<pre><code class="r">trainingData <- trainingData[, -grep("timestamp|X|user_name|new_window|num_window",
names(trainingData))]
</code></pre>
<p>After removing the columns with missing values, we get following number of variables:</p>
<pre><code class="r">names(trainingData)
</code></pre>
<pre><code>## [1] "roll_belt" "pitch_belt" "yaw_belt"
## [4] "total_accel_belt" "gyros_belt_x" "gyros_belt_y"
## [7] "gyros_belt_z" "accel_belt_x" "accel_belt_y"
## [10] "accel_belt_z" "magnet_belt_x" "magnet_belt_y"
## [13] "magnet_belt_z" "roll_arm" "pitch_arm"
## [16] "yaw_arm" "total_accel_arm" "gyros_arm_x"
## [19] "gyros_arm_y" "gyros_arm_z" "accel_arm_x"
## [22] "accel_arm_y" "accel_arm_z" "magnet_arm_x"
## [25] "magnet_arm_y" "magnet_arm_z" "roll_dumbbell"
## [28] "pitch_dumbbell" "yaw_dumbbell" "total_accel_dumbbell"
## [31] "gyros_dumbbell_x" "gyros_dumbbell_y" "gyros_dumbbell_z"
## [34] "accel_dumbbell_x" "accel_dumbbell_y" "accel_dumbbell_z"
## [37] "magnet_dumbbell_x" "magnet_dumbbell_y" "magnet_dumbbell_z"
## [40] "roll_forearm" "pitch_forearm" "yaw_forearm"
## [43] "total_accel_forearm" "gyros_forearm_x" "gyros_forearm_y"
## [46] "gyros_forearm_z" "accel_forearm_x" "accel_forearm_y"
## [49] "accel_forearm_z" "magnet_forearm_x" "magnet_forearm_y"
## [52] "magnet_forearm_z" "classe"
</code></pre>
<p>The variable we are predicting is “<b>classe</b>”.
Now, we partition the data into training set(70%) and cross-validation set(30%).</p>
<pre><code class="r">set.seed(1)
inTrain <- createDataPartition(y = trainingData$classe, p = 0.7, list = FALSE)
training <- trainingData[inTrain, ]
cv <- trainingData[-inTrain, ]
</code></pre>
<p>Feature density plot:</p>
<pre><code class="r">featurePlot(x = training[, -53], y = training$classe, plot = "density", auto.key = list(columns = 5))
</code></pre>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAALQCAIAAAA2NdDLAAAACXBIWXMAAAsSAAALEgHS3X78AAAgAElEQVR4nOzdeVwU9f8H8PfsLjcoIDcKeB+pkQeBAiqaGeB9VCZmaqVpN1pZpl8lb/3lnSmmaEp5kkZaiqao4BFqooSiIIdyCyLn7s7vj8V1heVadmbY5fV8+Kjdz85+Pu/3Z2Zn3zvMzjIsyxIAAAAAl0RCBwAAAAD6DwUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBYduY1m2c+fONjY2FRUVQscivKKiIuYpiUTi7u4eGxsrdFDCY1l269at7u7upqam7dq1W7ZsGX6ykYgsLS0Vm4qxsbGXl9fp06eFjqhJsLGxYZ53584doYMCPYGCQ7fFxcUVFhZaWlpGRUUJHUtTkZycnJ+fn5qaGhgYOGHCBLy5rl69esmSJd99911iYuKmTZs2bdq0ceNGoYNqEs6cOZOfn//ff/+99dZbgYGBV65cETqiJiEqKipfRdu2bYWOCPQEg92xTpszZw4RGRkZpaen//TTT0KHI7CioiILC4v8/HxLS0siysnJsbW1LSoqMjMzEzo0weTn57u5uZ09e7Znz56Klj179hw4cODAgQPCBiY4S0vL06dPu7u7K+7Omzfv9u3b+/btEzYqwdnY2Bw7dqxPnz5CBwJ6CEc4dJhcLg8PDw8KCnrjjTcOHTpUVlYmdERNCMuy+/fv9/Hxac7VBhFdvXrVxcVFWW0Q0cSJE1FtVIcjHABckwgdAGju3LlzNjY2ivcSZ2fn48ePjxgxop7PDbtGD4q4DO4pR3Oa/CIfAym5uroyDFNaWlpRUXH27NkGPDOM6AFnYalyJJrMy0BE9+7dc3JyakwPYRfCHhTwMS+OLR0ne/E1L9XY2dllZGQ04AlhYfSAl83F0ZEm8zotAwcOlEgq3xrMzMzS09Pr+8x7YVTCy5yYOFJbwTYV0BgKDh22d+/ehIQEBwcHInr06NEvv/xS/4Kjiw05WXAZ3FMtjPgYRdXZs2dbtGjBsmx8fPywYcMuXbrUuXPnej2zC1Gj3prrrQUvoxARkYuLS5X30SdPnmzdunXGjBnGxsb16aGLQxcnSz7mpYUxj/NSTVZWVsMqsy5dqHGVXH214Hta9uzZozwkxjBMA57ZoguZ8DInBkJuKqAxFBy6qqKiYt++fceOHVO8myYkJAQGBhYXF5uamtbn6R7OHMcnHBcXF8U5HG3btu3Tp8+pU6fqW3B4cBuYINzd3e/evRsXF/fSSy8pWo4dO7Zq1aqPP/64nj14tNXHeanm6NGjvXv3bsATPPR2WpycnNzc3DR5Ziu9nRPQChQcuurkyZMWFha+vr6KjyD29vY2NjaRkZHjxo0TOjSBFRQUEBHLsjdv3rxw4cL//vc/oSMSko2Nzfz580eOHLl+/fqXXnrp6tWrH3zwweeff96wT6566vHjx48ePSosLDxy5Mi6devOnDkjdERNgmJalHdNTU0NDQ0FjAf0BgoOXRUeHj569Gjl2wbDMKNGjQoPD0fBofxwZm9vv3DhQh8fH0HDEd6cOXNMTU2//PLL5ORkZ2fnzz///PPPPxc6qCbB19eXiIyMjNzd3Y8ePdqrVy+hI2oS/Pz8VO/u2rVr0qRJQgUD+gRfiwUAAADO4WuxAAAAwDkUHAAAAMA5FBwAAADAORQcAAAAwDkUHAAAAMA5FBwAAADAORQcAAAAwDkUHAAAAMA5FBwAAADAORQcAAAAwDkUHAAAAMA5FBwAAADAORQcAAAAwDkUHAILCQnZv38/EbEsO2vWLD8/v4CAgKysrNrv1tRbPRfjaHRQS4uTjPULALpLvHDhQqFjaKZkMtmgQYN27do1bty4bt26nTp16syZM0ePHi0rKzt69KhYLK7l7pAhQ9T2WaWTmhbjaHSoQuuTjPULALoLRzgEIxKJTp48OXfuXMXd6OhoLy8vIvL09Dx//nztd2vqs56LcTQ6VKH1Scb6BQDdhYJDMAzDSCQSkahyFeTk5Li6uhKRq6trTk5O7Xdr6rOei3E0OlSh9UnG+gUA3YWCg28//fTTuHHjQkJCqrRbWVmlpKQQUUpKirW1de13a+q8novV+UTNRgcF7lYx1i8A6C4UHHx755139u/f/80331Rp9/X1vXjxIhFdvnzZ29u79rs1dV7Pxep8omajgwJ3qxjrFwB0l0ToAKDSoEGDIiIiAgICJBJJaGiotbV1LXfr2QnPo0PtGj/JWL8AoLsYlmWFjgEAAAD0HP6kAgAAAJxDwQEAAACcQ8EBAAAAnNOBgiMvL68xTy8oKJDJZAIGUFJSUlxczNtwMpns0aNHjemhkQE0tIf8/PxGnkjUyICLiorKy8t5C6C8vLyoqIi34apjWTY/P1/AAACgeWrqBcfjx4+nT5/emB42bNgQHR3dmB7eeOONxjz90KFDv/76K2/DXbhwYd26dY3p4f33329MyZKenv7555/Xf/mQkJAbN25oPBw1esZ27Nhx7Ngx3gI4fvz4Tz/9xNtw1cXHxy9evLgxPcydO/f+/fuN6QEAmqGmXnDI5XK5XN6YHmQyWSOPcFRUVPAZQOOHa+SMNXLOGxqAXC7XrRXUyACawgbZ+C2kkSkAQDPU1AsOAAAA0AMoOAAAAIBzKDgAAACAcwJcafTu3bs/btlcz4XLy8tPRUW9OmyYxsP9c+WKg4Ojk7OTxj0cOXJk+PDhGj894VbC48eP+3r05We4BxkP0jPS+/Tpo3EPf/755wBfXyNjY82eXlRUlJWW3K5du3oun5KSYmtra2pqqtlwRHTz1q1uXbtq/PSHmZlGhoZWVlYa95CRdt/BubWIqVf5np+fX1ZW5uDgoPFwjcy3uKQkOytL8fOwmkm6e/eTz+b2HzBI4x4AoBkSoOAICwtLuho9Yqgvz+MK5fqt23sOHV82b7bQgfBnevDibavmCx0Ff75evmnWlPFO9rZCB8KTI3+dde3U4533m9EmDQCNJ8yPt7m2duzdU/OPaLqlvLzCsqVF88mXiCQSSbPKVywWde/coa2L5kfRdMu/CXeIEToIANA1OIcDAAAAOIeCoxnZfSBy0of1+kvH1fjE7n4TFLclLh5SaVO86MKjwseWXQZq9ly1U6HB/KhOFA/mLF5r1XVQVg4u9AkAugcFB4DO2Lbn8K2/99vZWAsdCABAg+lAwTH1s0UrN4cpbi9YteWj+SuJaOvPh9p6jjBp188zcMp/SSlE1Nd/cmTUOSJauTnM0NWztKyciPzGzwjb/3tNPVfv5EZC0sBx74WsDe05+I2EO8n9R04NXvS9TffB3qOmXbhyva//ZItOvp8sWK27KZeUlr0xc17LLgM8A6fcSEhSNJ6NjXtp6ESzDt7D3vow/WGW6vJD35wlk8nb9xv5pLikiaSwfvsvbfr4t+njvz38N0VLzD//egZOqXK7ztWndioaOj985j56WnDB4yKPgMnZufkHI6M6+4xp2WXA2HfnZufm0/Obbk0xN9kNHgCaAx0oOAKHeEeePKe4ffjY6XEBg1MzMmd/vWLn9wtTL0d27dh2zY8/E5Ff/z7RF68SUcw/N4yMDP/5N6FCKr14NX6wt/rvo6rthIiu3khMSk7bu2mJoqtePbokRh8qLSsfNTV4/4/L/wrfuHbbXsUuXudSJqKDkVF+/fvcOXd4gFevCTO+lMnkufkFo6cFL5ozI+1KZAe3NpNmP/c3hT/3bhSLRUnnI8xMTZpCCmdj4xas2vLzhpCYozt+P1HHT+TUvvqqT4UG88Nn7odCV7UwN7t5el/Rk5Kpny3a8N0X92KOtDA3+/CblYoFlJuu2pib8gYPAM2BMN9SaZBXfD0nf7yg4HFRbl5BZk5u/77uFVLp7XOHXJwdnhSX2FhbpmZkEpFf/77frdvOsuzlazffHh94/vI1QwOJi7ODs4Od2m5tW1lV74SISkrLflj+lZGhYcKdZEc7m4mjhxHREB+PRwWPXVs7Kv4VPC6ybaX5ZRuESpmIevXo8t6kMUQU8sUH2/Ycvn3vfmzcjYH9eg9/xZeIVn37SasX/BRvvU0zhQORUe8HjfH17EVEi+fO9J/0US0x1LL61E6FtuaHu9WnEHH89KhhA1/xfZmIVnzzkXOv1xQhKTfdnfuOVo+5KW/wANAc6EDBYWFu2r/vi3+dib2f/nDMa35isYhlxdv2HP7j1PmWFuZGhgYW5mZE5O3hfjX+vzvJqbatrIYO8Nzx6xFDA4MhPh41dSsRq+mEiNo42RsZGipum5uZKBd2sLNR3uYwWyLiLGUiUn5100AicWvj9DA7NzUj88+/Y9xerrzUmKGBQVauFs5J5CiFh1m5ykfbuThXX0D1ujK1r77qU6G2UYP54W71VU5Cdq5bm8o4bVtZGRoaKI5AKDddtTHbWls12Q0eAJoDHSg4iChwiM/vJ6KTUtIWfv4eEe07euL3k9F/hW+ytmyx+0Dk0RPRRGRmauL+QucNP/3q2atHvz493//iOwOJ5K0xr9XUp9pOiEgiaRK7Vy5SJqJ79zMUNyqk0pS0B22c7B3tbF7x9TywdQURyWTyuBsJDratMrO1UHNwkYKTvU1SSlplLqnpynbp0x8vTXtQ9zkWlU+vNhVpGZnamh+OVp+Cg22razdvK25n5+aXlZfbWFvm5D1SbrpqYw6P+LMpb/AAoPd04BwOIgoc4hNx/O/Euym+L/ciotz8AnMzUxNjo6ycvPXbfykpLVUs5te/b+jeCM9e3W2sLa1atjh++sIAr1419VlTJ00EFykT0dX4xG17DufkPfp62aa2Ls7tXJwDBnufjY2LjDqXk/foyyXrP1mwmmGqXtSpqLi4iaQwLnDIll0Hz8bGZWRmf7vyB0WoLS3Mr91MvBqfmJtfsHHHr/UMr/pUaDw//OSuNHyo78E/ok5GX8wvKAxe9P3oYYOqFA1qY27iGzwA6D3dKDjaujg5OdiMGDpAsWMNGudvZGjQuvdro6cFz/90emzcjV37I4nIr3+fJ8Ulnr17EJG3h3u3Tu1aWpjX1GdNnTQRXKRMRNMnjvr9ZHQ7rxEx//wbvnkJwzAOdq12r188N2Stq0fgleu3wtYuqvKUsf6DXfoGNPRbKhyl0K9Pz0VzZkyc9bWH/9sTRw9TnMrapYPbzMnjfEZPHzTu/dnvvF7P8KpPhWbzw1vuSu1dW29fveCDr5a5egQWFj3Z8N3cKguojbmJb/AAoPeE+S0VaU7S1DdGNOhZ/UZMXfj5e0MHeHIUFXcuXL6+ZuuefVuWNfSJuptyX//JlyLDSJdTaJCAyR9vCPmiyqXN9Tj3Hb8eIVObKe/ht1QAoAEEOIeDZdns3Py7Kel1L0pERMWlpf/eunP3frpbG8f6P0sp8W7KD7sOVGk0MTb67otZDe1KM+mZ2U+KixsUua6nLJPJbvyXpNMpNIhcJk/NeKis3XV99dUpOzffxsRG6CgAQMcIcIRj6dKlf//5u5GRYT2Xf5CZff1W4ovdOitPm9cthUVPCgoK2zg71v8pup7yk+InhY+LdTqFBikpLZFIDAwkleW7rq++OpWXl/sPH/nhp3OEDgQAdIkARzicnZ0nBE2dOnUq/0ML4sKFC0FBQRHHooQOhD9WVlb5+c3oUlGdOnUKDQ318fEROhCe7NixQ+gQAED36MZJowAAAKDTUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnGlVwhISE7N+/n4hYlp01a5afn19AQEBWVpaWYgMAAAA9oWHBIZPJBgwYsHDhQsXdU6dOZWdnR0VFjR07ds2aNVqLDgAAAPSCRLOniUSikydPfvvtt4q70dHRXl5eROTp6bljx44qC589e7asrEx5Nz4+vk2bNpqNCwCCKy4uTk5OPnHihLLF0NDQ19dXwJAAoOnTsOBgGEYikYhElQdIcnJyunfvTkSurq45OTmqS7IsGxsbK5PJlC3JycktW7bUNGAAEFhhYWFycvKVK1eULWKx2NvbW7lDAACoTsOCoworK6uUlBQiSklJsba2Vn2IYZjg4GDVlrCwMKlUqpVxAYB/Dg4O/v7+U6ZMEToQANAl2vlE4uvre/HiRSK6fPmyt7e3VvoEAAAAvaGdIxyDBg2KiIgICAiQSCShoaFa6RMAAAD0RqMKjpCQEMUNkUi0bt06bcQDAAAAeggneQEAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA57RTcJSVlVlaWrq7u7u7u69cuVIrfQIAAIDekGill7t3744cOXLnzp1a6Q0AAAD0jHaOcNy+fTshIWHUqFETJkxITU3VSp8AAACgN7RzhMPW1jY4OHj8+PHh4eGzZ8+OiIhQPsSy7KhRo4qLi5UtDx48GDVqlFbGBQD+3b1798CBAz///LOyxcTE5PDhwyIRzgkDgBppp+Dw8vJS3Bg5cuS8efNUH2IYRrX+IKKwsDCpVKqVcQGAf+3atZszZ86UKVOEDgQAdIl2PpEsX75806ZNRBQTE9O9e3et9AkAAAB6QztHON59991p06aFh4cbGxtv3rxZK30CAACA3tBOwWFtbX3o0CGtdAUAAAD6Byd5AQAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnJEIHoH1yOfVfdu+bhzNf8/iLGCKGiIhYogq6frNlxrAz/n7dBQ5R6357QpeyZF07MsSybGXGREQMVZwUSbZWiPWusPznxm/uV0aTwfOtLEXGvBu4/gdhYuLMzWtpnaLdRFYssSqtT1dz1MMZQz7bKERcAAANoJ03IpZlZ82a5efnFxAQkJWVpZU+NRP/gC3caXTBrV2A53GRSC5i5CKSi0guYuQiQ7m7e77/wx7/rXQSMELt+3QMPTanru3EJBORXMzIRcp/JDcaLBWHM0vDC4WOUptk20S9ro8UGTxdufRsLQd6bWH36FV5Vf69Ubf4NhIrWeVmrLJyFf+GOGzSs5QBQC9pZz916tSp7OzsqKiosWPHrlmzRit9aka0s5OlUXnty3R2fnAoeDs/8XDO+zz1OaRyTEO9L8steYmGD9u+nSM2ZWtZgCH27P+m8hYP1wzt6tieiYgh9p+/9GWTBgA9pZ0/qURHR3t5eRGRp6fnjh07qjyalpZWXv5sp5mdnW1hYaGVcavr0uZOfRbz7PAJkV68J/l9VZ+lGElt79C65a27a6hLHct4t99BpA9vwHK5vJ6fCdyz3uVtk5ZKpfn5+Xfv3lW2GBoatm7dmp/RAUBHaafgyMnJ6d69OxG5urrm5OSoPsSy7NKlS6VSqbIlMTHR19dXK+NWx9T1WV+hgClz5CgCnlnfr/Pwhp4xsKpH8aQvcyIrK6/vQUgeU05PTz99+vSdO8+Ke7FYvGHDBpEIf9kBgBppp+CwsrJKSUkhopSUFGtra9WHGIbZuPG5M9rCwsJU6w/tkrKMhKn7DWlr7MjV73MUAr+uBdIrG+peTH8OcFBuXF97r4u1L5NxtYvzW/yEwy0DE+N6Lpmd2tKe01BUuLq6vv3221OmTOFrQADQB9r5ROLr63vx4kUiunz5sre3t1b61MzlbX/VuUzREwr6NpyHYPjw3gKSGdS5VPk6MQ+x8MM+/Lc6lzF//18eImlSbD4V8mRtAIA6aafgGDRokK2tbUBAwIEDB4KDg7XSp2Y8Tw2O2H2iWF7j8eX8u6KDnRLc3fTl2K+XDZnepTtetSwi3Sk2jOXqkJIAWtuzfePZGv6EwBLz+52jLTvoT4Eln1BSU7IKLDHHK0LFhnr4FXcA0CcMy/J9tH3p0qUrV640MzPleVyhlJWV5eXlOzo6CB0Ifx48eOBoz9sBfuFlZmVbWrY0MjQUOhCeFD5+7Obq2rlzR6ED4YlUKi14VNDKppXQgfDHSCQvK9ejTyl1MTc1evykhGH05YNoPXzz7cKevfryPKgAn4ocHBzefXO4v19//ocWxI3/7v7y21+L5+jHOSP1MvOrZZuXfil0FPz5ZuXmWW+Pd7SzEToQnqzcvMvnZffxga8IHQhPLl2L//ngsWWfvyN0IPx584N5ezctEToK/sz8aun8T6Y72dsKHQhP9h09cS3ucrMoOMRicef2bgO8evM/tCAMDQxOX7jSfPIlIjNTk2aVbwtzs5df6tHWRb8uKFezXQci7W1btXN1FjoQnqQ9yDIzNWk++RKRRCJuVvmKRCIXZwcX5+ZyHNrGWpgrM+nVEaSr8Ynd/Sao3tBv9cx394HISR/Ob1CHRCRx8ZBKZVqJsz4j1n+VPSp8bNlloGbDqZ0KDeZHWxtY/Tucs3itVddBWTl5jR+UU7VsNny+KnkbSyfy1WwPUGe32iXsHqC0rKwxITWe3uwBaqdXBQeAvtq25/Ctv/fb2VjXvSgA6B392APoUsFxIyFp4Lj3QtaG9hz8BhEdjIzq7DOmZZcBY9+dm52b36Cutv58qK3nCJN2/TwDp/yXlFKl84Q7yf1HTg1e9L1N98Heo6ZduHK9r/9ki06+nyxYzUliNdBiviWlZW/MnNeyywDPwCk3EpIUjWdj414aOtGsg/ewtz5Mf/jclyqHvjlLJpO37zfySXFJE0lh/fZf2vTxb9PHf/vTr8XG/POvZ+CUKrfrXHdqp6Kh88Nz+qOnBRc8LvIImJydm1+9kyqjqA1b6xt8WXlF9UhUN5vqI9ZJ7VN+PfJXx/6jW73gN/PLpWXl5WpbNFhTDZqQ+MSk0rIync63oVt4cUlpU0uB0z2ATCbfe/h4k12DXOwB0jIy6pOjdulSwUFEV28kJiWn7d205N79jKmfLdrw3Rf3Yo60MDf78JuV9e8kNSNz9tcrdn6/MPVyZNeObdf8+HOVzoko5p8bvXp0SYw+VFpWPmpq8P4fl/8VvnHttr0NfZtsJK3kS0QHI6P8+ve5c+7wAK9eE2Z8KZPJc/MLRk8LXjRnRtqVyA5ubSbNfu4w4597N4rFoqTzEWamJk0hhbOxcQtWbfl5Q0jM0R2/n4iufeHa1131qVDbWPv88Jz+odBVLczNbp7eV/SkRG0nylHUhs3FBl/4+En1SJSbTd6jQrUj1kJtkIl373/w1bKwdf+7FLnr0rWbuw/8Ub1FgzXV0An5etkmqVSmu/lSw7fwB1m5TSoFrvcApWVl81dsbrJrkKM9AP907Lv7JaVlPyz/ysjQ8Pute0YNG/iK78tEtOKbj5x7vabYburDtpXV7XOHXJwdnhSX2FhbpmZkVuk84U6yo53NxNHDiGiIj8ejgseurR0V/woeF9m2suIou+q0ki8R9erR5b1JY4go5IsPtu05fPve/di4GwP79R7+ii8Rrfr2k1Yv+DWoQ55TOBAZ9X7QGF/PXkS0eO5M/0kf1bJwLeuO1E2F2kZtzY+21qBCxPHTajtRjrJz39HqYXOxwcfdSKgeiVhc+QGmphFrofYpvx75a+LoYV69exJR6Or5BYVF1VuOnjjb0DXV0Am55XAvNSNLd/Olhm/hMlnd52/xmQLXewAjQ8MzB7d69u7RZNeggnb3APzTsYKjjZO94moHD7Nz3dpUfinAtpWVoaFB/Y89SMTibXsO/3HqfEsLcyNDAwtzsyqdE5G5mYlyYYenX3eUiPm+nJRW8iUi5RcoDCQStzZOD7NzUzMy//w7xu3l4Yp2QwODrFxOTkfSSgoPs3KH+HgobrdzUXPyvOrlZGpfd9WnQm2jtuZHW2tQoaZOlKOoDdvW2krrG3zB46K+L75QJRIHu1bKJ6odsRZqn5KWkdmxnYtigRe7dSKiPYeOVWk5ExvX0DXV0D1AK8uWt++lVp95XcmXuNnC+UyB6z2ASCTaG3H8w/krm+warJwHre4B+KdjBYdEUrnRONi2unbztuJ2dm5+WXm5jbWlYtOp076jJ34/Gf1X+CZryxa7D0QefXqATtl506GVfIno3v3KP9dVSKUpaQ/aONk72tm84ut5YOsKIpLJ5HE3EhxsW2Vma7/m0EoKTvY2SSlpitv3UtOV7dKnn8PSHtT3HIvqU5GWkcnd/GhrDdbSSU7eI+UoasMOj/hT6xt8SwvzlLQHVSJRPlrTS6wWap9ib9tKuWYvXLl+515a9RYN1pQGewBjIyPdzZe42QPwmQLXe4CsnLyoc5f+PrC1ya5BBe3uAfinY+dwKA0f6nvwj6iT0RfzCwqDF30/etig+u89c/MLzM1MTYyNsnLy1m//paS0XqdHCasx+RLR1fjEbXsO5+Q9+nrZprYuzu1cnAMGe5+NjYuMOpeT9+jLJes/WbCaqfZLu0XFxU0khXGBQ7bsOng2Ni4jM/vblT8oQm1pYX7tZuLV+MTc/IKNO36tZ1fVp0JtY33mp0EauQbr2YnasLnY4N1f6FxTJEXFxRqMqPYpYwP8du3/PTbuxt2U9E++XZ2T/6h6iwZrSoPwnB1sdTdfavgWLpfXfZCfzxS43gOUV1SYmZg05TWo0HT2AJrR1YKjvWvr7asXfPDVMlePwMKiJxu+m1v/5waN8zcyNGjd+7XR04Lnfzo9Nu7Grv2R3IWqFY3Jl4imTxz1+8nodl4jYv75N3zzEoZhHOxa7V6/eG7IWlePwCvXb4WtXVTlKWP9B7v0DWjkt1S0lUK/Pj0XzZkxcdbXHv5vTxw9THEqa5cObjMnj8XclEYAACAASURBVPMZPX3QuPdnv/N6PbuqPhVqG+ucn4Zq5BqsZydqw+Zig2/ZwlxtJIrNZoz/oIaOqDbInl07rln42ZsfzHvp1YkvdG4/a8r46i0arCkNJsTYyEh386WGb+GPnxQ3qRS43gM42LYybNprUEFbe4ALV4T5eUsBfkslLCxMmpM09Y0RPI8rlAuXr6/ZumfflmVCB8Kfvv6TL0WGCR0FfwImf7wh5Ivmc6XR6cGLvT3cp0wYLnQgPDkTE7c5bP/eTd8JHQh/+o+cei5iu9BR8Oe1SR9tWT6v+VxpNHRvhKGlY9C0mTyPq2PncDTIjYSkZRt3VGk0NTH+ccXXQoTDOT3IVw9SaIzmkD6fOTaF+dSDfPUghcZo5ulrlwBHOLZt25Zw+e9hg/rxPK5Q4v9LOvjHqfmfTBc6EP58/r//W73gU6Gj4M+KTTsnjwtwaD4/3rYp7MUXOg0d4Cl0IDy5fjPxyInorz+aKnQg/Pniu3XLv67tq6d6ZtnGHVNfH6Hr1/Gsv2Onzr/wksc773/I87gCFBwrVqw4f+q4mZlg38zhWX5BYU5Obsf2bYUOhD9ZmZl2zern6TMzLS0tjYyMhA6EJ9du3HRxdrSy4u+CNMLKe1SQn5fXvh1ewnorKzOzpZWlkWFzeQkXlxS/6j9ixiy+a0qBzuGQSqdObS4fFy5cuBAUFHTnzh2hA+GPlZVVfj6vl2QVVqdOnUJDQ318fIQOhCfTp08nom3btgkdCE/OnDkzffr0xMREoQPhT3N7CXfo0GH37t2ens3loF1oaKihoWFQUBDP4+rqt1QAAABAh6DgAAAAAM6h4AAAAADOoeAAAAAAzqHgAAAAAM6h4AAAAADOoeAAAAAAzqHgAAAAAM6h4AAAAADOoeAAAAAAzqHgAAAAAM6h4AAAAADOoeAAAAAANUJCQvbv309ELMvOmjXLz88vICAgKytLs95QcAAAAMBzZDLZgAEDFi5cqLh76tSp7OzsqKiosWPHrlmzRrM+UXAAAADAc0Qi0cmTJ+fOnau4Gx0d7eXlRUSenp7nz5/XrE+J1qKrAcuyYWFhZWVlypaYmJhu3bpxPS4AAABUl5eXd+vWrZKSEmWLkZHR5MmTGYZRtjAMI5FIRKLKoxI5OTndu3cnIldX15ycHM3G5bzgYBjGwsLC1NRU2WJqaqqaFQAAAPCGYRgzMzMrKytli1gsrv192crKKiUlhYhSUlKsra01G5fzgoOIxowZo3q3pKREKpXyMC4AAABUYWVlZW9vP378+Po/xdfXd9u2bUR0+fJlb29vzcblo+AAAAAA3TVo0KCIiIiAgACJRBIaGqpZJyg4AAAAQI2QkBDFDZFItG7dukb2hm+pAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAAOdQcAAAAADnUHAAAAAA51BwAAAAwHPKysosLS3d3d3d3d1XrlyplT4lWukFAAAA9Mbdu3dHjhy5c+dOLfaJIxwAAADwnNu3byckJIwaNWrChAmpqala6ZPzIxwsyw4bNiw3N1fZkpeXFxQUxPW4AAAAUF1ycvLu3bvXrl2rbLG3tz969CjDMMoWW1vb4ODg8ePHh4eHz549OyIiovHjcl5wMAxz/Phx1ZawsDCpVMr1uAAAAFCdm5vbokWLav/k7+XlpbgxcuTIefPmaWVc/EkFAAAAnrN8+fJNmzYRUUxMTPfu3bXSJ04aBQAAgOe8++6706ZNCw8PNzY23rx5s1b6RMEBAAAAz7G2tj506JB2+8SfVAAAAIBzKDgAAACAcyg4AAAAgHMoOAAAAIBzKDgAAACAcyg4AAAAgHMoOAAAAIBzKDgAAACAcyg4AAAAgHMoOAAAAIBzKDgAAACAcyg4AAAAgHMoOAAAAIBzKDgAAACAcyg4AAAAgHMoOAAAAIBzKDgAAACAcxKhA9A+mYxe/+Lfla0mu7leq/5oZMo7AV+F8h8VPwpmmrXwKSEiOTEiYomIJUY0USZ0XFpWVlF2da2Zh6OcmKoPlZ9oZ7T9jhBBcajsMyPDPhXPNbGkzF0uZ8ST9G0VK139ssOLPe8qbqcWrHOZOVvYeLh29H+jAzpGEBFLJJooo+qbuN6R7xEzxBJRTmIr24XZQofDuXPzuvbr/l/lHf9yxlIP34Vrom9HOG5nUuFWy/29erZ1vcoQW/1fgOt2+c/6lrUC+7OopU+xIk0xyRU3RCSnPXq1z3pwP9ton/HLTjKGUbN+jYYksfq1ftk9IqM+5VUzVcldLJKze/QqZSXZHol7zyRlpi4tPyzaZCJ0UBx6st0ssOPhp69clvaIiC0WOiiO7WFET3dWtp1y5HvEQgfELdnP4v7dE569kCMNsvceFjoo9ViWnTVrlp+fX0BAQFZWllb61Lf9lP03H1q1KKh9GRHDfvpNND/x8OfMAYZha3x0j/4U0eYn7GtfgGHYlLn7+QmGB4oPf3UuU7bBiIdgeCamqkduzC1LBYmEH6bGJVVa2L3mgkTCj+rlhYjkgkTCj0fFJGaqJmjLjpbV/RIXwKlTp7Kzs6OiosaOHbtmzRqt9MnH+9DZs2fLysqUd+Pj49u0acPRWBYDN9ZnsWXObxClcRSDMM5MoHZERLJ8kdiqcptmWeZpFaI/L2Nz47pfnW3KphGN4yEYrlXkZhnUb0kDaym3oQgq7lwP9/7/Vh6pq5CTgb59UlJQFJdyEuX+LbEZUFGfWlOnKRO8dqZ9D997imoj+4nM1kw/j3PYrSgq71R5+9yfL/QfGq+4/cNlmtWX10iKi4tv37594sQJZYuRkZGPj4/qMtHR0V5eXkTk6em5Y8cOrYzLecHBsmxsbKxM9uyTSnJycsuWLTkarrZP+SokhvkcBSAYu8r/M1dYGvK0Ua/+llKpPjnJi/Tk2B0rK6t7IX3HEiMnUyKG9P0NWEHOijIN2rei//S+4FBgiSHGXFYkFpnLiejsffGYrkLHxA2WqTxexRJjaPbs2FVsypNZfc34jKSwsPDevXtXrlxRtojFYm9vb4Z5tn/Nycnp3r07Ebm6uubk5GhlXM4LDoZhgoODVVvCwsKkUq4+jcmKrMXmeXUudi1mfq9pHIUgEHkA0REiEg15tpNS2WHpT+khZ0lUVzY37y7tyUswXDO0q++xQLZUf1ZxFQyxvfvHPruvp4c36OmpwBJG2r3fLaFj4Q9D7Is+z07wtzQWMBZurRpKdI+IiCG2r8ombWPBa7VBRA4ODi4uLkFBQbUsY2VllZKSQkQpKSnW1tZaGVffXrrb4v6reyEi2++C615It8z4rbZHJ5bzFQfnzjr8WPsCLFHPEx/wEwwP2PoVi6J39GcVK8mr7aDUfDFJj8iqfQK8V/CyIJHw4/do/yotLDE+roLEwoePvdS8nMtlks+8BAmnDr6+vhcvXiSiy5cve3t7a6VPfSs43t9sszntSXqebU27aRkruu1d0sZOf06ifOZNmTLr526MTiXSn7+JDhj87inHbTWtX5ZlmLFyPUqXmIny2msOlpiC3v8wjL69lolINFEmU1mXMlYkmqg/ZyNVJ5lYIWUrd00sMY9zzdrNvCBsSJwK3HQ0O66lcvOWk6h0glx/D2AREclflyvLaJaovEJSPL6idQthg1Jv0KBBtra2AQEBBw4cqPJnCo0xLMv3nwlDQkIWL14skejRe0KtZDJ5eXm5iYn+Hiispqy0zMhID780UZOy8nIDiUQk0us9pYqy8nKGyNDIUOhAeNIcX8JlZUaGeAnrLZlMtmD+vK++WcDzuAJ80Hdxcdm89Mupb4zgf2hBXLh8fc3WPfu2LBM6EP709Z98KTJM6Cj4EzD54w0hX7R1cRI6EJ5MD17s7eE+ZcJwoQPhyZmYuM1h+/du+k7oQPjTf+TUcxHbhY6CP69N+mjL8nkuzg5CB8KT0L0RhpZ2dS+nbc2loAMAAAAB6XDBIXHxkErrvqLzo8LHll0GajbE7gORkz6cX59Gta7GJ3b3m0BEXPzdqvb05yxea9V1UFZO3V/Y0RXIV5VO53v52s0+r1WeHl9Tmgl3krv4juU3Lg5pN2UNdkG1jFtP3K21prCLlstrOzdI67nr9Ou3MXS44IBabNtz+Nbf++1stPNdpqYP+eqQti7Oi+bMEDoKXulBynqQgsa0nrtOv34bQ8iCY8evR9xeHu728vCd+466vTyciBLuJHuPmrbqh13OvV5r6zki6twlxZJnY+NeGjrRrIP3sLc+TH+YRURD35wlk8nb9xv5pLjqxYAV1m//pU0f/zZ9/LeHV35fNOaffz0Dp1S5nXAnuf/IqcGLvrfpPth71LQLV6739Z9s0cn3kwWrFUuWlJa9MXNeyy4DPAOn3EhIqqWxepBK9+5ntPUcYdKun2fglP+SUrhOf/S04ILHRR4Bk7Nz8w9GRnX2GdOyy4Cx787Nzs0nohsJSQPHvReyNrTn4DdqCnvrz4eqBKz6rDonLTs3v1nlm5qe6Tvm3eaTb/3tPhD57pyQyR9/a9llYP+RUxVj3buf/u3KH6qk+euRvzr2H93qBb+ZXy4tKy8nIpZlQ9aG2r841O3l4cq5Uou3dJpOyg3dBdW5w6wiKSWN6xSa1C5aiYfVp0OvX60TrOD4N+HOnMVrf92y7Pxv27ftefbrNVfjE6VS2e1zhyYMH/LN8s1ElJtfMHpa8KI5M9KuRHZwazNp9nwi+nPvRrFYlHQ+wsxUzY85nY2NW7Bqy88bQmKO7vj9RB0/mxLzz41ePbokRh8qLSsfNTV4/4/L/wrfuHbbXsXqPxgZ5de/z51zhwd49Zow40uZTK62UW2QKkkl7Px+YerlyK4d26758Weu0z8UuqqFudnN0/uKnpRM/WzRhu++uBdzpIW52YffrKwc5UZiUnLa3k1L1HaempE5++sVVQJWfVadk3Y//WGzyjc+8e6qbz9uPvk2yI5fj3j17nn73CFvD/fXZ3yl+udFZZrpD7M/+GpZ2Lr/XYrcdenazd0H/iCi2/dSxSJRcuyR6RNHLVi1pab+eU6nKaRMDd8F1b5FVZeVk89pCk1tF62K69WnW69f7RKs4AiP+POd10d4uL/gZG87Z+ZkZbtYLAqeEWRqYhw0NiDvUQERHT1xdmC/3sNf8bVq2WLVt59cvBqv2KRqcSAy6v2gMb6evZwd7BbPnVn7wo52NhNHD7O2bDHEx2P0sIGurR09e/Vwbe1Y8LiIiHr16PLepDG2raxCvvggMzv39r37ahtrD/LVgf18PXuZGBvZWFsWFBZxnb5SxPHTo4YNfMX3ZWvLFiu++ehgZJTiuSWlZT8s/+qFzu3Udm7byur2uUNVAlZ9Vp2T1qNLh2aV7wCvXh7u3ZtPvg3SrWO7mZPHKV4sqRkP7ySnVl/m1yN/TRw9zKt3z3auzqGr53ds24aILMxN58ycbGJsNOa1QfkFhTX1z3M6TSFlavguqKFMTYw4TaGp7aJV8bD6FHTi9atdgl3/Kv1BVl/3borbql9GcrBtpbhEh/JCHakZmX/+HaM4KE1EhgYGWbl5jnY2tXT+MCt3iI+H4nY7F+fqC6gWreZmlSW/RCx2eNqtRFw5uvK7jgYSiVsbp4fZuWob1QapHCI5NaOv/+SWFuZGhgYW5mZcp/9sHrJz3dpUhmrbysrQ0EBR4bZxsjcyNKypc1trq217Dv9x6rxqwKrPqnPSsvPym1W+aRmZI6d+btfKqpnk2yBVXizpD7PNq33ITsvI7NjORXH7xW6diCjhTrJyrmq/OoJELOYznfrgOuXqQ9S5C2oo5dRxlEJT20Wr4mH1VU6CLrx+tUuwgsPR3uZ++kPF7dSMh8p21R+PqVzSzuYVX88DW1cQkUwmj7uR4GDbqvbOnextklIqfwz2Xmq6sl369Dfk0h6o/wNedffuZyhuVEilKWkP2jjZp2VkVm9UG2RmduUG/SArJ+l8hLVli90HIo+eiOY6fSUH21bXbt5W3M7OzS8rL7extszJe6R8t1PbeXjEn7+fjP4rfJNqwKTyHlmngsKiG1G/Np98M3PyTu//8aXunZtJvg2ifLFIpbL76Q8d7WweFz2psoy9bSvlS/LClet37qX1de9Wfa7U2nf0BJ/p1AfXKZO6/VLtu6CGUpyUwF0KTW0XrbZD7lafgk68frVLsD+pjAsY/NMvRy5fu/kgK2f1lt21LBkw2PtsbFxk1LmcvEdfLln/yYLVyvVaVFysvvPAIVt2HTwbG5eRmf3tyh8Uy7e0ML92M/FqfGJufsHGHb/WM86r8Ynb9hzOyXv09bJNbV2cFcV49cZagiQiiVhsYmyUlZO3fvsvJaWlXKevNHyo78E/ok5GX8wvKAxe9P3oYYOqbJRqO8/NLzA3M60ScIOIRaJmla9ELDY2akb5Nsj1W7e37D6Yk/do/srNTva2ioPPqoqKi8cG+O3a/3ts3I27KemffLs6J/9R/fvnOZ364DplavguSDluPft/UlzKaQpNbRetiofVp6ATr1/tEqbguHD5eu+eXRfPnTliymcDx7735qhhykNA1TnYtdq9fvHckLWuHoFXrt8KW7tI0T7Wf7BL3wC1J13369Nz0ZwZE2d97eH/9sTRwxTnSXXp4DZz8jif0dMHjXt/9juv1zPU6RNH/X4yup3XiJh//g3fvESxjVZvrClIBZFI1Lr3a6OnBc//dHps3I1d+yM5TV+pvWvr7asXfPDVMlePwMKiJxu+m1ufzoPG+RsZGlQJuJ7TpcCImGaVr0gk6jdiSvPJt0H8/fqfOBPbzmvE6fNXwjcvqXK0WZFme9fWaxZ+9uYH8156deILndvPmjK+/v3znE59cJ0yNXwXRPXbopSsWrbgNIWmtotWxcPqU9CJ1692CfBbKmFhYdKcpH59emZm5w3w6kVEf/4ds3T9T6f213ZWtu5Se2nzhDvJepx+9Uub63e+1S9trt/51v/S5opDvuGbl/AQFXcadGlz/UjZtseQ7H9PCB0Ff5SXNteP1Ven0L0RhpaOQdPqOF1X6wQ7hyO/oPDND+Zd/WuPhbnZ+u2/+A/ur0EnNxKSlm3cUaXR1MT4xxVfayFELulr+oqQqp/+rd/5lpSWVWnX73xj/7nh7eEuyNBVGnXixa4xPUhZD1LQWHPOvSYCHOHYsGHDpb+P9e/74rHTF06du0xEPbp2mDD8FUMDffzJeKLb91JPnbv03qQxVdr1OP21oeEfT3ujSqMe5/vrkb/8+ve1sbZUbdTjfLeH/9a1Y1uv3j3qXDI27sb1W3fenTiKh6i4819SytnYuOn1y0I/Uv7iu/XLv/5Q6Cj488tvf77i62lt2UI/Vl+dzl265j1w8LuzPuV5XAF2glKplDEwvp2e175j5/YdOysaU7Lq/tayjsoqKDEwNLydXvV0aD1O38baslnlWy6VpWQ+yi957riOHucrZ0SFxaXVV3F11nZOA+2c6rNkU5ZdWCIxMKhnFvqRcs9unXQ9hQaRyuTJD/Nzn0j1Y/XViTEwJrGRAOMKcw6HVDp16lSexxXKhQsXgoKC7ty5I3Qg/LGyssrPF/iSdnzq1KlTaGioj4+P0IHwZPr06US0bds2oQPhyZkzZ6ZPn56YmCh0IPxpbi/hDh067N6929PTU+hAeBIaGmpoaBgUFMTzuPjxNgAAAOAcCg4AAADgHAoOAAAA4BwKDgAAAOAcCg4AAADgHAoOAAAA4BwKDgAAAOAcCg4AAADgHAoOAAAA4BwKDgAAAOAcCg4AAADgHAoOAAAA4FyjCo6QkJD9+/cTEcuys2bN8vPzCwgIyMrK0lJsAAAAoCc0LDhkMtmAAQMWLlyouHvq1Kns7OyoqKixY8euWbNGa9EBAACAXtCw4BCJRCdPnpw7d67ibnR0tJeXFxF5enqeP39ea9EBAACAXpBo9jSGYSQSiUhUWa/k5OR0796diFxdXXNyclSXZFl24cKFZWVlypYbN24oqhMAAADgWUZGxsWLF+Pj45UtRkZGCxcuZBiG03E1LDiqsLKySklJIaKUlBRra2vVhxiGGT16tEwmU7aYmppaWlpqZVwAAABoECsrKw8PD39/f2WLWCzmutogbRUcvr6+27ZtI6LLly97e3tXedTd3V31bnx8vFQq1cq4AAAA0CAmJiYtW7bs3bs3z+Nqp+AYNGhQREREQECARCIJDQ3VSp8AAACgNxpVcISEhChuiESidevWaSMeAAAA0EO48BcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHAOBQcAAABwDgUHAAAAcA4FBwAAAHBOOwVHWVmZpaWlu7u7u7v7ypUrtdInAAAA6A2JVnq5e/fuyJEjd+7cqZXeAAAAQM9o5wjH7du3ExISRo0aNWHChNTUVK30CQAAAHpDO0c4bG1tg4ODx48fHx4ePnv27IiICOVDLMsOGzYsNzdX2ZKXlxcUFKSVcQEAAKBBkpOTd+/evXbtWmWLvb390aNHGYbhdFztFBxeXl6KGyNHjpw3b57qQwzDHD9+XLUlLCxMKpVqZVwAAABoEDc3t0WLFvH/yV87f1JZvnz5pk2biCgmJqZ79+5a6RMAAAD0hnaOcLz77rvTpk0LDw83NjbevHmzVvoEAAAAvaGdgsPa2vrQoUNa6QoAAAD0Dy78BQAAAJxDwQEAAACcQ8EBAAAAnEPBAQAAAJxDwQEAAACcQ8EBAAAAnEPBAQAAAJxDwQEAAACcQ8EBAAAAnEPBAQAAAJxDwQEAAACcQ8EBAAAAnEPBAQAAAJxDwQEAAACcQ8EBAAAAnEPBAQAAAJxDwQEAAACck2ilF5ZlZ8+efevWLRMTk59++snOzk4r3WpgX8zZzE9Ov+W5wrLnEzJWtwRLxKjcrSAm/CT9MYin+KqIfp1SD5HYgF76P7L1JPP2lP4bJf1HC38kq4dsF2LdxIy5jMQadc4SsUSlRAYq65mpnAGpnE4+7nWsfHKS0ZAjM7ppLSNNFV4PM477xkCSRgyR/PlKmH0W9nON9HwLEcmJmKeNbLVHq2Dp0h0byh7u3PIfAyaj/EmxyPSJY3siMVE2MYVDyfg8uRUREVl2oWHXSGTQ6CyJiCg9gs69SayMnEZSSTYVlVFxNwq7WnE3UTK6iLoQVVD5H2RgTdSdZOXEWJHYQl2yGmAp5UHr1BNB7rGfWUxpRSFEZo3ukzP/fP3PSy/0UW3ZfM78vbWFEu3stJqi+FHO3SY8UN6NThrkM/+kgPFw6u7xbS6Z74slrGoju/Xlh2v2O73kLFRUnJoYQWPWHB/7/mvKlvI7ZkbfPhYwJJ5p57V76tSp7OzsqKio7du3r1mzZtmyZVrptqFGznyn1HTX8Q9lte2aqzxkQBTkRxYT6fHP3AZXXbghySuIiKQVdOl9IhERS1IJiStoRmWkDEk171/x1muqrp3IQETDWl4ZRlfSpc5Ba5bv+uwtzQdqHLmspHivVQtRGSnf0Kscd2NU/lulsQpRXQs834NHx2zquF3NQ05ETsef3X10i8INaXwxGZjU1WldTgygrDOVt1P3Vd4QXaC3yUAZsAkZvf70kcaO9zyG3JxS3SYvYScv+eSWiWO/BXPt5jIRjJqNRGg7/LZNmf5ulcYP+j9+skQk+0JuZCRIUNwq/MzwhQkVqi0+7aOkYQaSyRU1PUV33VwzsJvD39Xff5h3Yxzj2qT9sLT1li+EiItD7dfQ5v0/DJ09U7XRqEMR+7OIeUsuVFQ8084OLTo62svLi4g8PT3Pnz+vlT4bKuNRxtGKsN971Fpt1GThHtqr/ZBqU5pZWW08IydiSVKhhQ+yDeEsSV9r91FpIwqbRkqKfM1cVCbY8PT0YEmddjlpYSxltVEFvyudIfq/riWLey9c/2A9fcrr0PX09jtVqw0Fsw7sBi9hPs9wrUUfNYWFRCKlslz+g+HUvTxZN/u/a3qUMWZbZ62m27f5DIkHdx/TK7M/qN7OMOzNiFv8xyMI7RzhyMnJ6d69OxG5urrm5OSoPsSybFhYWFnZs3eUmJiYbt20fww/4UCCnJFLDDV6sgNRKNGbWg5JPekTSt5Dj2Ir74qMyciaSjKeW6bOPwdolSWTv37PmoHtLF58+Q0ysOB8vLJcOn+AkonSb6Tn/9f2xTNa2gy1QUYkUpn8TKJCoo5ERGT8iLZPIoYhIrKypsDvSGJe324VK11Z2hg5U2k6EUMMS0RUTqTcbouITPk4t4ohWtWt9EGrpXRkAP34IhHR60QtOR+3npia/4zYruBroi95jEVop4fTq8J8iuPIwe17P6+9eh+ZQ/Hx1LEjTwHxhVH5cFMhFRlIKg9suBwbQyN5rTny8vJu3bpVUlKibDEyMpo8eTLDcPvGo509vZWVVUpKChGlpKRYW1urPsQwjIWFhanps4O2pqamXGTVNbWr5k9miTy0F0qdDC2JffqWYmBKFc//Da+eH7i1h2UYC3GZyLgNcby1VWIYMrQiUyITa1mxDVt5gkbTIHq+1MslKlG5a2pbOUXGLRtcEhpaPrttYE5lVJk1S6R6coicv1pTwlCuTE5lhmTF04ha0V3fPvCrwRLz7M1J1HTqce1oU+cSDNELL/AQiYAY9tlO70l6u3p/dtHS6AxjZmZmZfXslS8Wi7muNkhbBYevr++2bduI6PLly97e3lUeHTNmjOrdkpISqVT7R/AdpzqKF4krMmUG9g1/8hWGPtJ6RDWQmJHLeLIbQLe3EhGV5T33KL/HNhSypXYTJ8wyNm7B03iG1tR/PBERjXchyrjk6nR7KU9D5YSTsgAAIABJREFUq8XUcJuIVI/EFbeg6f+n4RCKla5U9F/VEZXnyfK1Elii9Wn0+e8rqXVXGl/38jxjZQwjVl+Gzu/VO5znaHin+lGYBh0RLhBOjJ4xhg4EUc0nYbPpTozeHd6g5+tIicGzVVy2eA/PkVhZWdnb248fz/crXzuHbgcNGmRraxsQEHDgwIHg4GCt9NlgLhR2/Xi3WJEmn5YjQqmt9iOqjbEdmVQ/E5vhv9oolLf4KHs9f9VGNU59lzyQW9e9HEekT7/OUweGJj3UwnBeu2rqnmcn8om932Pyw8kUxffQ9ZF6KEFtu2wFhR2/yHMw/Hh0XM07cFmFGUmazB+6tMTA3PT2sRk1PcrKGeZTPVzFrc3p2ldq/jTGFjIuL+rbKq6Jdo5wiESidevWaaWrxph4cbDznuLVy5aM8F7VoX+J+p3481+5ZB8yopJbdLcTXzGqGJ1GmafoykdkYEl9NlBJOhX+R1IXijtDsVvY1ArpHVPm7VKxk0zzsrCCpKUklZCRATGiyhYSkZyh1Eei0KLZ8YYD441e+e9zgb8c6Tgp98LFHQaXV/WyuFXT59qq34Nln/5XSiRWWacskYhI9nRhUW0Hjf7d2qLQlOK7GhXfMXjt3xwHz3KLfiSTUmmEieEjS+NXWXItJFM5df2A+q7SSqbUdhI5+dNxDyrJIKuXqMN0YroURYQ/uJRqcfKi/ZsZ9BKRnMp2kewOGb9NjAsxxlo7pYMlSisWx2Wbn8pvPaxw1fVJr9J+AWqd+nA52Kkg/EkL+XNHmn9ZKhl/rdxQTy8eZLmz/MyIDj5v3FW2nH08x/f95QKGxJ2OezfLrn9UEdPdyPy513vZkenGP2/U2lfQm5LUz+ntjp6j5t8Z9cWzgzflf1kY/VQgYFQ8Y1iW7z+fh4SEhCxeLJZodnEJ3SOTySsqKoyN9fGbfDWoKK8wMNDDXUZNpDKpiBGJRHr6TlhNeUU5EWNo2FxWsUwmq6iQ4iWsx5rbS1gmky2Y/9VX3yzkeVwBTkdycXHZtPTLqW+M4H9oQVy4fH3N1j37tujnd/nU6us/+VJkmNBR8Cdg8scbQr5o66KN783qgunBi7093KdMGC50IDw5ExO3OWz/3k3fCR0If/qPnHouQt0lavTUa5M+2rJ8nouzg9CB8CR0b4ShpQZnOzZWcynoAAAAQEDNpeCQuHhIpTKho+BPc8uXml/KteS7+0DkpA/n16eTq/GJ3f0m1NlhE9HcUtaDfOs54qPCx5ZdBmo2hNqp0Gx+Gk+H8r2fmqZZAI3RXAoOAAAAEJAwBcfS9duDF31v032w96hpF65c7+s/2aKT7ycLVise3frzobaeI0za9fMMnPJfUoqiccevR9xeHu728vCd+466vTyciBLuJHuPmrbqh13OvV5r6zki6twlxZJnY+NeGjrRrIP3sLc+TH+YRURD35wlk8nb9xv5pLhEXThqRryRkDRw3Hsha0N7Dn4j4U5y/5FTawm4up37jvqMns6yrEwmn/LpwlPnLul3vlM/W7Ryc+VJGwtWbSkuKa29Bz1Iec+hY5ZdBir+ZWbnjntvbpPKt6S07I2Z81p2GeAZOOVGQlJN/SjV3qHq9tzr1bfupz98kJnT1FaxdlNW3aR/Cv8tv6BQv/NV3Z4Z5z4lpWU8pLB++y9t+vi36eO/Pfw3RUvMP/96Bk6pcrvOl6faqWjQ/CgjbCb5CkWYgiMpJb1Xjy6J0YdKy8pHTQ3e/+Pyv8I3rt22Nzs3PzUjc/bXK3Z+vzD1cmTXjm3X/PgzEf2bcGfO4rW/bll2/rft2/YcVvZzNT5RKpXdPndowvAh3yzfTES5+QWjpwUvmjMj7UpkB7c2k2bPJ6I/924Ui0VJ5yPMTNX8+JbaEYno6o3EpOS0vZuWEFHMPzdqClhtgpPHBRDRnkPHfti138nBNu9RgX7nGzjEO/LkOcXtw8dOM0xtPehHyhNHD3uUcPpRwundGxYzjOhqfGLTyZeIDkZG+fXvc+fc4QFevSbM+FImk6vtR6n2DlW353auzopz65rUKtZ6yqqb9NmLcSJGpN/5qm7PHdzaZGTmcJ3C2di4Bau2/LwhJObojt9PRKvNUan2l2f1qWjo/CSnZjSrfIUiTMFh2cJi4uhh1pYthvh4jB420LW1o2evHq6tHQseF9m2srp97pCvZy8TYyMba8uCwiIiCo/4853XR3i4v+Bkbztn5mRlP2KxKHhGkKmJcdDYgLxHBUR09MTZgf16D3/F16pli1XffnLxarxiZdRC7YhEVFJa9sPyr17o3I6IHO1sagpYbZ8Mw2xe+tVXSzes2BT2ybsTjY2M9DvfV3w9L127WfC46G5KemZOLkNMLT3oR8oKaQ+y3pvznbGRoV0rq6aTLxH16tHlvUljbFtZhXzxQWZ27u179zXrR0F1e167qPLKfk1qFWs9ZdVNOq+gkBE1rU1a6/kqKLbnvZu+k8lkXKdwIDLq/aAxvp69nB3sFs+dWfvCtb88q09FQ+dHceJF88lXKMJcpd/IqPIb3hKx2MHORnlb8d9tew7/cep8SwtzI0MDC3MzIkp/kNXXvfIq06rfXHKwbSWRiIlI8vSqHqkZmX/+HaM4FEZEhgYGWbl5jk+HUEvtiETUxsneyLDyN7XMzUxqCrgm3bu079jWxcba0s7aShmevuZrYW7av++Lf52JvZ/+cMxrfmdj42rpQT9SJiKpVDZx1tfBM4Mijv9tamLcdPIlIuV3dA0kErc2Tg+zc9X2U3snqpTbs7ODnaKlSa1iraesukn7vtyrQirV73xJZXvu82Jl2Jym8DArd4hP5U9YtXOpftllUr1GVO0vz+pTobaxzvlpbvnyr8n9LNC+oyd+Pxn9V/gma8sWuw9EHj0RTUSO9jb30ysvLJ2a8ewK09V/bMbRzuYVX88DW1cQkUwmj7uR4GDbSoMRSWXb0szfF/7JyXv0X1JKwOCqPy5T5+i6mG/gEJ/fT0QnpaQt/Py9s7FxDQ1AF1Ne9H9bzc1MPpn+ZsTxGn9ru6bROc2XiO7dr/z94QqpNCXtQRsne7X9ZGbXdwek3J6vxifWubB+pKzcpMf6D/rzTG0X29aPfJXb87PAuEzByd4mKaXyixL3UtOV7VJZ5bc80h7U95yD6lORlpGpwfw0t3z51+S+pZKbX2BuZmpibJSVk7d++y8lpaVENC5g8E+/HLl87eaDrJzVW3bX8vSAwd5nY+Mio87l5D36csn6TxasVm4rRcXF9R+xkcrKy2d8uWTDd3OXfDVr1ZbaLoGlH/kSUeAQn4jjfyfeTfF9uVftS+pHylHnLv30y287v/9fnVcn5D9fIroan7htz+GcvEdfL9vU1sW5nYtzLf0o1dSh6vY8a17dl7DTg5RJZZN+sVsdP32gB/lW2Z7lcjnXKYwLHLJl18GzsXEZmdnfrvxBsXxLC/NrNxOvxifm5hds3PFrLSPWPhUNnR9ZM8tXKE2u4Aga529kaNC692ujpwXP/3R6bNyNXfsje/fsunjuzBFTPhs49r03Rw1THm6qzsGu1e71i+eGrHX1CLxy/VbY2kWK9rH+g136Bqg9eVjtiI3MYsWmsN49u/q8/NKkMa/J5bX9Nph+5EtEbV2cnBxsRgwdUOdhA/1IOWzf7w+yctp6jjDv6FPTSelC5UtE0yeO+v1kdDuvETH//Bu+eQnDMDX1o1RLh89vz+zte6m1T44epEwqm7RI1OQ2aa3nq7o9m3f0efykmOsU+vXpuWjOjImzvvbwf3vi6GGKEy27dHCbOXmcz+jpg8a9P/ud12sars6paOj8FBQ+Phh5qvnkKxQBfkslLCxMmpPUoEubJ9xJzszOG+DVi4j+/Dtm6fqfTu3fwlmAWqbBpc11NN9+I6Yu/Py9oQM8Nbi0uY6mrKDBpc11Ol/NLm2uiykrNmljIyMNLm2ui/kqKS5trtMpNIji0ubFJaXNJN/QvRGGlo5B0+o4d1Xrmtw5HGrlFxS++cG8q3/tsTA3W7/9F//B/TXo5EZC0rKNO6o0mpoY/7jia40D46JP0sF8/2/hZ5eu3byf/nBQ/z6a9axzKevlKuYoWQXdSll1k75w+V8NetatfNV22DRT4E5zy5d/AhzhWL169cnIgz27dqx7URUxV/698m8CQ9TOtfVgn74GEt0olYgoNSPzn38TRr46oEHP0q18E+/e//PvmFcHenVs24aIIo7/3dB8SddSVnUxLr5ze9eWLczrXlSF7uYbcfzvdi7OPbp2aOgTdShl1U06Oe3B9Zu3Rwz1bWgnOpRvFUdPnA0c4kO6nEKDxMbd6NqhbQsLs2aS7/VbtwOHj/zgk7k8jytAwfHDDz8k/BvXuXMd52HpjdTUtJNRJ6e8/bbQgfAndPv2aVOnCh0Ff3bs3Pnq0KGOjo5CB8KT/Qcj7P6fvTsPi6ps/wB+n5lh2GUHN8A9NTJ3QRFFrVRMMdTSxMqtVOrtV7hkb2lKpZm+qaWZ4kKKuKW4VZrggru5FCqioIPIOmyyw8yc3x9jEwKynmWY+X4ur8szz5x5nvs+nDNzz9nG0dbHp941ZROlSEqKPnnq7SmBYgcinNDQzdOmGdMmvHXryBEjnF1E+AFVUcTHx3fr2eedqdMFHlekczhUqqlG84F0/vz5wMDAe/fuiR2IcOzs7HJyqr9Bp0Hq1KlTaGjowIEDxQ5EINOnTyeiTZs2iR2IQE6fPj19+vT4+NqvBzYYxrYJd+jQYfv27Z6enmIHIpDQ0FC5XB4YKHQNrXdXqQAAAIDhQcEBAAAAvEPBAQAAALxDwQEAAAC8Q8EBAAAAvEPBAQAAALxDwQEAAAC8Q8EBAAAAvEPBAQAAALxDwQEAAAC8Q8EBAAAAvEPBAQAAALxDwQEAAADVCAkJ2bt3LxGxLDtnzpwhQ4b4+fllZGQ0rDcUHAAAAPAUtVo9aNCgxYsXax9GR0dnZmZGRUUFBASsWrWqYX2i4AAAAICnSCSSEydOzJs3T/swJibGy8uLiDw9Pc+dO9ewPmWcRfcMLMu+9dZbJSUluhaFQvHKK6/wPS4AAABU9eDBg2PHjh06dEjXYmZmtm3bNoZhdC0Mw8hkMonkyV4JpVLp4eFBRO7u7kqlsmHj8l5wMAyzdu1ajUaja4mIiDAxMeF7XAAAAKjKzc3tnXfeef3113UtEomkYrVRlZ2dnUKhICKFQmFvb9+wcXkvOIjIxsam4kNLS0uVSiXAuAAAAFCJRCIxMzOzs7Or+0t8fHw2bdpERFeuXPH29m7YuEIUHAAAANB0+fr6RkZG+vn5yWSy0NDQhnWCggMAAACqERISop2QSCRr1qxpZG+4SgUAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAACeUlpaamtr27179+7du69YsYKTPmWc9AIAAAAGIzExccyYMdu2beOwTyEKjrS0tKKiIt3DzMxMW1tbAcYFAACASliWzcjISExM1LVYWFg0b9684jx3796Ni4vz9/eXy+UrV650dXVt/Li8Fxwsyy5YsKBiwZGUlDR8+HC+xwUAAICqkpKSfv/994sXL+pamjVrtnHjRoZhdC1OTk7BwcHjx4+PiIgICgqKjIxs/Li8FxwMw2zdurViS1hYmEql4ntcAAAAqMrd3T0oKCgwMLCGeby8vLQTY8aMWbhwISfj4qRRAAAAeMry5cvXrVtHRBcuXPDw8OCkT5w0CgAAAE+ZMWPGtGnTIiIizMzM1q9fz0mfKDgAAADgKfb29vv37+e2TxxSAQAAAN6h4AAAAADeoeAAAAAA3qHgAAAAAN6h4AAAAADeoeAAAAAA3qHgAAAAAN6h4AAAAADeoeAAAAAA3qHgAAAAAN6h4AAAAADeoeAAAAAA3qHgAAAAAN6h4AAAAADeoeAAAAAA3qHgAAAAAN6h4AAAAADeycQOoKEKC2lWa/LNJVNeumeJYUcqJLauvPTeeI9vqQ/2lEpKG/BStpzZu2HO5jlrPx9MXq04j4w7v32ryZrHMMQQyxIREcNFr6yG5tLFbyf35aIzoZX+z97UJadSI0ukyncwcTal8hxSlxFjQs2eI+/d1KyTKEEKZPlyWv0pfauu+kzpVVPTb0uEj6gWAQGU+gsFPXsGFUMtZpDPV2Tq8KRFU0Y5N4gtp78XU1EatZ9Cz31ETNP4lli+2d7ErPK6Wi1Wu2Wz2i2cZYg0LMMwLEPEEsMQ+++cKtKMPC919OQn5Aa6v/65NjZ3K8ZJRMRSSa7EbFwJuZhUfkE20arH5Z3sTGSaWjtniWG+vU5Xu3EXb12xLBsUFHT79m1zc/MtW7Y4Ozs3vs+mse5WplLRd1Y0nK9qg4gYYiVH3ai8gK8BGiPlMB1+vmHVBhExJuz4oO/773+u/ybq+iO3kXHnUC/KnithWO1mzHBUbRARI6FvJf0mbTjPUX/CYbfIq1YbRMQQmVhnUXEKqYqJVZOmhHJv0JEuVPxI+CAF8sILtGFBtdUGEZn2LNWMlwocUS3c3Sm9xmqDiGQsZf5Ev3Sig+1ptyXtMqNdFhQ1lI4NoNTjlPc3XZ1Lv/YSKODGYXeY1LHaICKGWIZYhmEZYrWbuYR5MlHpU5yRkfSYF6Ue5jTYRinbIW1rE1+52iAihszsNHRCTsp0XdvfGfR/4VTYqZi62tSl2iDtEgh+kdziOYy5jqKjozMzM6OiogICAlatWsVJn02z4Jj8JrUVYhzNOnshhqmvk2Ma38dnr8UPUNDtdNp4rfGdca0sl/Kv8jrCBtOXNVXeIvRaVgZjWl6P+VkNnR7LWzRii42lkJqel4yt07u5cJKSaHbd5mSzqSSN+ocTSYmIyvOJiIh5smMj9zqVKnmKkUMMo+KvczaKgzdAThSW5suZWtY0zW/ttBMPcum9wzT3L7Jc0LPeIy3r3IDwGikmJsbLy4uIPD09z507x0mfvB9SYVl28eLFpaX/fh2PjY319GzoPrFb+4p2LDEz+1uYQkniVH7vg1Y3bToO/8/vpo687U6pF1URETdvpl/e3zrY/e2Ff9CMHpz0x4WCBNqzkfIUxMHeu5pYywvUX7xBXXzo9Tp+DojtWGS9X5J9nYc49MClS3WarayM5HKeQ+EJQ8qzpC4h5p/v+ebNqfwxqUuJVVHBAzJ1FDnAGpQRLTpDL/A4AsNoKKGY2pvzOEbdJMXv6FLbPBJJ0b0PWhGRWkNbGCorI3ohpf5DsaThcv9ASkrKpUuXbt68qWsxNTVdvHgxw/y7K1mpVHp4eBCRu7u7UslNmct7wcEwzNixY9Xqf3d+WlhY2NnZNbC7lr2pxxzV5f/KKZOb+GrEEpPt/p5D645yG71555KacdXTLWsVEan06qugmQt1H095jyklgtdxWA3D9nqHOrbhdRQute5MD+v5Eoarw1B6Rl39kZTK9KfaUNXz676JDTl6k2QNkZpYIoYluQ2ZWNPje0RE9vrz/aA6JkRmbXgfxUUvvv65t+pPf9c+W7b7e0R0O5OcLKl1BmnKvpaYFvMeXI3s7Oz69u07cuRIXYtUKmWefsews7NTKBREpFAo7O252dkvxEmj3bt3r/jw5s2bqvpugTq27hbjZlJXL7ouxEk0muQWfed9JsBA9cBINBJTiaaBJ3BU9HE3fyJa8XLje+KOzIp69CIiNpyp5rAod6LvTxjy2Sv89c89b2/aWc+XOA/iJRLRdRPhBLpGkdXnbVZDxGoo4yRJzag8j7TnTOfF/TsDo2enp1TCEH3gSr/yOEKxxMncSi9OBrCwr8OeHJl5348/IyJZKn1ygnYGk+TlbjTLv55DMdye/mBubm5jY9OrV02nBPn4+GzatImIrly54u3tzcm4evFnq7euL9BfQrzpSOfp42l3klc4OJx26MqAYhNHFyuarpffl5iAVJaz80QrY1XMlWH87kHhHsNQyTf1mF9uR4OP8BaNqCwtyc+PPqppFvWvk4SKpm7Gj6epdZitlMh1HVm0pMRtxKrJzIVkFk/N4L2bn/g4ZUfsw8H8dW8+XsFf5/XEPGQG1DLLyFjt/z1b0P950sR99GrgmMQ7tR6Kedqh/AaF1yi+vr5OTk5+fn779u0LDg7mpM8me1nssht0/ypFzmGlCYVMtqWt5snHE0tsKTEMqcooJ42xVbNSBypVMTIrVmZBjIRYNTEskfTJKVlExGo/2Z7+dCv+y95imb6enGXXkyaW50Z/wyQst5bnM5J/c6mL/ALmZLO/L7/a9c+u1NOFtyAbydSFmaTJP7HO5MH/yc3KGQ2Vq4lIIpOxjIQlDbFlDKmIMWFZCRFDDEPEEqmJGCIpsUSMpLorW1j67uKPs1bNnNcUV/ypcyl3muaIE8NUvgAv2+prB9/XqCiJknaR1JzazyJbEc4yE87hw3TjBo0cSQvTye6p039ZYiRDHkknNRcttmrt3k1Xr5KfH01TUld1NfvuNMSYhdC4YJLLiWY9aSx6RHm3idGQxILkzci6E4dHVHnFzI+mG3fLbzxXw84dVs0wrIQtclBTW7a0sLyc1eS6ljRLlzR7aGVWImPZ8gJzNlNm5pDJ2qoZIjaL9mm8xgfHcHfJGgdcJ8YUZf2tiexvIS8ilYyRlpOEqJRKskk1aLV1n6CK0Q7vQMM7aCdv5d6OK/v9eScHtuZ3b7bQRjI8h8SonyUSyZo1a7jtk2FZoU/WDwkJWfb1V6amenOElWfl5ari4pJmzazEDkQ4hYXFlpbin9IlmLLSMqlUKpXp975u7hQUFEkkEguLpvHh13jl5arikpJm1sa0CRcVW1oY0SZcWlomk0mlUmPZhMtKyxYuCP7ksyUCjyvCFz03N7c1S+dOfWO08EOL4vyVv1ZtDN+zYZnYgQinz8gpl4+GiR2FcPym/Of7kPlt3VqKHYhApgcv9e7b/e0Jr4odiEBOX7i2PmzvznVfih2IcAaMmXo2crPYUQhnxOQPNixf6NZKz3aM8SZ0Z6TctoXw4zbNczgAAACgSTHGgmP7vqOT36/TtSfXb8Z7DJmgnZa59VWp6nY9np4xsHxzH+fbdh7csNdWuygasHwqLii+GVu+ZJQpz1262q6Lb4YyW7ARRWdsKRtbvtUyxoIDAECvbAo/cPvUXmdHvby1MT+MLWVjy7da+lJwbN19qE2/V9v0e3XbnsNt+r1KRFM/WrJi/ZPzABZ9u+GDz1bExiUMHjczZHVot6FvENEvR6OeG/iaTedBATPmZWblEJFKpZ614Gu7Lr6OHkOXfrephuGKS0rfmLXQpvMgz1Fvx8YlaBvPXLzW4+VJlh28h7/5/qO0jIrzvzxxjlqtad9/TGFRNTdsqRqqYecbvv83286Dtf+YVr0P/Hay6jycp7B28y7X3iNde4/cHHFQ23Lh6t+eo96uNB1378GAMVODl3zn6DHU23/a+T//6jNyinUnnw8XraxhUdR3+VT13cZwo8qXjO9PzN8WOnZacF5+QV+/KZlZOVU7qTRKtTFv3LG/redo83b9PUe9fSdBUelVtS6xqv78K86oUj51/k+jypeIzl+8/Kyn+KMXBcffcffmLl29e8Oycwc3bwo/oG0cNcz76Imz2ukDv50c5zeUiK7Hxic8SN657qv7SSlTP1ry/Zfz71841MzK8v3/riCi/b9FR5+7cu3YjuMR675cvTlBkfysEX85GjVkQO97Zw8M8uo54b0FarUmKydv7LTgJXPfS/7zaIc2rpODntoBe2znD1KpJOFcZLVnblcbqgHnO2ns8Ny4k7lxJ7d/v7RDG9chA/pUnYfbFM5cvLbo2w07vg+5cHjrkT9ial68F67G9nyhc3zM/pLSMv+pwXt/Wn484ofVm3Zqt+2qi6IBy6eqY6cvGFW+ZHx/Yv620P2h3zazsrx1ck9BYXHVTiqOUm3MD1PSgz79Ztt3ix9eOdqlY9tVP+2o9KpalxhSNsJ8vfpV877NN724HUFE5LF3Xh/dt/vzRDR31hTtHoKXfDyn/GdRXn5BVnZeujJrQJ/ut+/eLy4p/XH5J6Zy+Xcbw/2HD37Jpx8RffPfD1r1HKF9WylXqTKycvq82DX5z6PNrC2fNWLPFzrPnPwaEYXMn70p/MDd+0kXr8UO7t/r1Zd8iOjbzz90eH6ItsO6qBqqYeerlZyaMXPulwe3rqo6bmlpWUZWNocp7Dsa9W7gaz6ePYlo6bxZIyd/UENgLZwdJ40dTkTDBvbNzct3b91C+y8vv6DaRdH45VNUXKLMzjWefIkoU5nD7Vqq/ynzuoVqRf5+stpOdKNs23O4asxODnZ3z+53a9W8sKjY0d72YcqTnyfVvSru3oMalpiTwzN/aMLYUja2fIWnFwXHo9SMPt27aqd1FyZZW1kM6PPi8dMXkx6lvTZiiFQqISLXli6mcjkRpWVmtXF9chWik4OdXG6SmZXz2oghj/MLZ879Ml2ZNeftCR+/O5lMqh9RdwWjiUzWxrVlWmbWw5T0Y6cuaI9uEJHcxCQjq65n91QbqgHnS0QqlXrSnE+DZwX2frFr1WdzH+dzm0JaRtawgX210+3cWlWdoeLtZKz+uQWITCpt7uyom37Woqi2sV7LJz0z+5XBXsaTLxFdjY0zqj8x8byFPlkI1XVScZRqY3ayt9sUfuDX6HM21lamchNrqyefebpX1brEkLJx5is8vSg4Wrg4Jj1K004/TEnTtY8aNvDIHzEJiuTFH8/Utsj+ubdScyeHG7fuaqczs3JKy8oc7W0Tk5KHDOgzbeKYpEdp42fOt21mHfRO9eeZ30968nt95SqVIjnVtaVLC2fHl3w89238hojUas212LjmTg7pmXX9DK4aqmHnu+R/G60szT+cPrEkZq4YAAAgAElEQVTaZ3Pz8seNGsphCi1dHHX7Ku8//Pd+86p/fscrObX2cw6evLzKokhOSW/k8knPzBo5pL/x5EtEV/++s37ZAqNKmfjcQmvoRJmdqxul2pgjIo8dORFzPGKdvW2z7fuOHv7ngJSMizvRGVvKxpavwPTiHI5xfkO37Dp05cat1Azlyg3bde2jhg2M/P1UfKLCp1/PSi959WWfX36NOhFzKSfvcfCS78YO95XJpAePnZ44e2F6ZrZarSktKzc3e+YvCl6/Gb8p/IAyO/fTZevaurVq59bKb6j3mYvXjkadVWbnLvhq7YeLVjJVfmyzoKjoWR3WEKrh5Rt19vKWXQe3ffeFRFL9+lNSWsZtCuNGDdvw8y9nLl5LSc/8fMWP2lBtrK1u3Iq/fjM+Kyfvh611/Y2JqouiwctHp7CouG93D+PJl4jSMpVG9SfW4m8LraGTijNUG3NWTp6VpYW5mWmGMnvt5l3FJSV1XFB1YWwpG0++t+LuNL6T+tKLgqNXty5L580a/fZHgwNmTvQfrts11NatZcvmjqNfHlS1jmvv3nrzykWzP1nm3nfU44LC77+cR0TvTn6thYtj+/5jeo+Y7NXrhSnj/Z414vRJ/kdOxLTzGn3h6t8R679iGKa5s8P2tUvnhax27zvqz79uh62ufM/XgJFD3fr4VXvVRs2hGl6+YXuOpGYo23qOtuo40KrjwOU/bKs0g62NNbcp9O/dbcnc9ybN+bTvyLcmjR2uPZW1c4c2s6aMGzh2uu+4d4Peef1Zude6KBq2fCpydrSvelNkA86XiHp4dDaqP7EWf1toDZ1UVG3MgeNGmspNWvcaMXZa8Gf/N/3itdif9x6t47J6Ft1xYSNJWVrheJwx5EtEMecuNrKHBhDht1TCwsJUyoSKtzaPu/cgPTN7kFdPIjp26sLXa7dE792gfar/6KmLP5758iBPgYNsgGeFWvXW5oaRbw2eG/janTO/iB2FcPr5vRWx/mujurW5rY31t599KHYgAql4a3PD2EJrZdt5cG7cSe20MaTs8PyQa8fCtWfUGUO+2lubB06bVfusnNKLczhy8h5PnL3w+vFwayvLtZt3jRw6gIgKi4ov37iV9CjNd0DvhnUbG5ew7IetlRotzM1++uZTbjv83+KP6hVqU8+31g515zQJNqIodNFamDfwZ8yaaL4Xr8YuCHq7kZ1UpOcpZyhzbKwt9XALbbxnhWRrY016+abUeNWGZGfbjIwp34cp6dOnTxc+GBH2cHz99de/H9r7XPs2FRuvx96JvZPAMIxrS5f+vbvJZLIHSSkxl6979+2uO6dXb9Ucamq68uadhGE+/So2Nul8a3X6wlXt9Y1GIj4xqYWzQ4PLrCbn+KkL7q1bdGrvLnYgAklOTY9PSGrn1spgttBanbl4dWC/nob0plSz23fvu7Z0UWblGkm+dxIeBASMe//jTwQeV4Q9HM2bN39p+KjBgwdXbJwifBxCuXX7dtLa76fMCKrYaMD5EtEfMW9VytewvTtr9uS3pnbu3FnsQASiLFBZWVlMmVH7BVmG4e+bsT/9+NPnS78SOxDhnDC2Tfi996bOGNuxY0exAxHIyZOnbJxEKKpEKDikUmmL1u4DfHyFH1oUEhOzgpIy48mXiLJz840q37JydacuHgMGDhQ7EIFsCdtBRMbzJ1aTtKC41HjyJaIsI9uES8rUnZ/v5ulpyOdtVBR3N5FhRLhkRC+uUgEAAADDZvgFh6p+N+wGAAAA7hl+wfHtOTqTJHYQAAAAxs3wC44yNZWrxQ4CAADAuBl+wQEAAACiQ8EBAAAAvEPBAQAAALxDwQEAAAC8M/yCo7gsR6UpFzsKAAAAo2b4Bcel+B9uPjwrdhQAAABGzfALDlaj0RBu/gUAACAmvfh5el45JJOps9hBAAAAGLdG7eEICQnZu3cvEbEsO2fOnCFDhvj5+WVkZHAUGzeslSRXih0EAACAcWtgwaFWqwcNGrR48WLtw+jo6MzMzKioqICAgFWrVnEWHQAAABiEBhYcEonkxIkT8+bN0z6MiYnx8vIiIk9Pz3PnznEWHQAAABiEBp7DwTCMTCaTSJ7UK0ql0sPDg4jc3d2VyqcOYLAs6+/vX1RUpGtJTU319/dvaMAAAADQcImJiZGRkWFhYboWCwuLAwcOMAzD67jcnDRqZ2enUCiISKFQ2NvbV3yKYZjIyMiKLWFhYSqVipNxAQAAoF7atWs3f/78wMBAgcfl5rJYHx+fS5cuEdGVK1e8vb056RMAAAAMBjd7OHx9fSMjI/38/GQyWWhoKCd9AgAAgMFoVMEREhKinZBIJGvWrOEiHgAAADBAhn+nUQAAABAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOCd4RcclqXFEjV+nBYAAEBMhl9wDLl9qXlCrNhRAAAAGDXDLzgYYolYsaMAAAAwaoZfcAAAAIDoUHAAAAAA7wy/4GAkxnU8JU5J2/8SOwgAAICnycQOgHcdeyflWt8XOwrhpBfSvWyxgwAAAHia4e/hkEhZiUQtdhQAAABGjZuCo7S01NbWtnv37t27d1+xYgUnfQIAAIDB4OaQSmJi4pgxY7Zt28ZJbwAAAGBguCk47t69GxcX5+/vL5fLV65c6erqWvHZCxcuFBQU6B7evHmzTZs2nIwLAAAA9VJaWnr37t0//vhD12JlZeXp6cn3uNwUHE5OTsHBwePHj4+IiAgKCoqMjNQ9xbLsr7/+Wlpaqmu5deuWjY0NJ+NCVQ8yb11LOE+Dp4kdCAAA6KPs7OybN29WbLG0tOzXrx/DMLyOy03B4eXlpZ0YM2bMwoULKz7FMMwXX3xRsSUsLEylwo+b8CWvODOv8KHYUQAAgJ5q0aLFhAkTAgMDBR6Xm5NGly9fvm7dOiK6cOGCh4cHJ30CAACAweBmD8eMGTOmTZsWERFhZma2fv16TvqEhpHmsDaZYgcBAADwNG4KDnt7+/3793PSFTSSWQrZPRI7CAAAgKcZ/o2/AAAAQHQoOAwNa1w/HQMAAE0DCg5DY/44u0MGrlIBAAD9goLD0NimJXk8ShA7CgAAgKeg4AAAAADeGUfBgfMaAAAARGUcBQeAAXn/V7EjAACoPxQcAE3M3+liRwAAUH8oOACaGBwgBICmCAUHQNODs5IAoMlBwWFoTE3yHVrliR2FoH65+ovYIQhqeMxmsUMQVPSvmxUPb4kdBQA0ljEUHKxRfR+0MstwapMjdhSCWhu1VuwQBOVzbJ7YIQiKCQvLPfWH2FEAQGMZQ8FhXFjjO8Q/7aiR3eiMVWuMqYZmWGJZjdhRAEBjoeAwPEb0UaT1QnK+2CEIzpgKDlITod4AaPpQcECT1/aNArFDEJrGmMpKZ6s0s0dpYkchnHIN5ZSIHQQAD1BwGBzj+y4oNRE7AmExUrEjEJaFTbFMYkQ15bXfrp3+7zqxowAefbz1PbFDEAcKDkPDiB2ACIws5+cnFxrVERVjk3L3mCppu9hRAI+m/rRT7BDEIeOkF5Zlg4KCbt++bW5uvmXLFmdnZ066baST320c5Pxu5/4s0U9s+EZmkuF/92fDJZ5dWe3Eifivhy2eL3ZE/FKHy6SktmxHFM6UsGZmbxaLHRG/SnaYmTGlNl2JdsvUJJVOUokdEb/2fvFqQMcj7n1Zoh/Y8HW6TfjvDDqRSK425N+ZpIZVbrLhEn8nlvyJDZf8Er8wYHGI2BHxSxMulfyzV7aMlcvfLBU3Hr6V7jAzZUqfDyIKZ4xhE66Emz0c0dHRmZmZUVFRAQEBq1at4qTPxhvk/C7zz6FuhlhNuIHvidaESyvmO7TTJ+LGw5PYDFp8kr44RSU7zKWk1rWbMYZ/3NuM+fftWErq0h1mIgYjgICOR6puwluu06JocrKkW5k0ZieVG9D3iEqb8GudvhI3Hr6pwk0kFY4By5kyVlVIRDkltPkarb9CyY/FC44H5WoyfXoTLtlhNv0gDdlGAbvpVqaIoQmEm4IjJibGy8uLiDw9Pc+dO8dJn433ZNP9Z+ezxNDPbqiUIGOI5xXGJNFHv5OPO/V3fWrT1SrbYSpKVMIoD5dXapEzZSkGfYFOpXVYu4Zv/JN2j6c3X6DPfGiAGx2OFyk4HhjDJlyR7gsD+89hUc1um6Q8euVnMpORiyW9sZcuPRIvPq4xEZVPNzNlyia9QFFv0VdDadpByjPw/TscHVJRKpUeHh5E5O7urlQqKz7Fsuxbb71VUvLvt0+FQvHKK69wMm6t1CS9e8E91+6Vfp1/NPitl4hYYq7cec82+0g7r0cVv/0bjDUXaYs/JT+mledoGBERBVLxhvtWpa7N7GQ5UsYAU9bRfhrlsjYmDwo+cE0LlTkR0YE4mt1H7Mj4pCbp/Yst/9SMmuD1I0PsuN2UmEOT9pFMQlv9qZMDPTKUL8G5JWRLxBLz2+V32qt/7+CZavDfkbTuOPzR9uZLGhczM6aEIfbln6mlNR2Io/d6094JNPsI/fK62CFyhGFYIsott5E/KnivZVqY3ImIfrxCu27ShlHk35nOP6ThHYSI5MGDB8eOHTt06JCuxczMbNu2bQzD7xFKbgoOOzs7hUJBRAqFwt7evuJTDMOsXbtWo/l3y4mIiDAxEei6AimpXZ9P72Cx0RiqDSJiiO3x3MayfLlBVhtElF9GDubkYkkbXiX6hYhoG1k+NG/uJksVOzSB2DCPU6UuG2Uu2odqQ1+vpaRu0TY7wPnJJrxxNE3YQ58MpLa2JJPQvls031vsEDliYUJExBD7Up+w8jIT46g2WCLqmPVSRr6DS/MsbVM3F1rsSy2syEpOMoZyDe5IqY3J40eSFlvlTzbhDa8+OQ+pVEVyoQ77u7m5vfPOO6+//m8pJ5FI+K42iKtDKj4+PpcuXSKiK1eueHtXfgOwsbGxq8DS0lIiEe7qGMtmhTKZiirstTNU2gRlpLKwLhI7Fr6M6EBrLpJMQramT/KVkMa9eYr20yjsbqDYAfLol7v+RMQQ29ItTftpxBLzaiexw+KfpXOhjJ5swnZmtGEU/TeKxu8h3230cnt60UXs+Dgil/67CZvLDfz0539oN2G2eUeldhMuKLYc1o723CQ7MzKRUHgs9W4pdozcuZrYiYgYYlu7peg24X23qFRNv96jPxJpgJtAkUgkEktLy4qfyzY2NgKMy80eDl9f38jISD8/P5lMFhoaykmfjaciqazCF/20nOYtRIyGf5nFjs7m/553pCIpN39dfRLUl746Qy/9TCxLIzqqP7r/b03OEvPOoi1iBsez8Yv2suGSivvqbgxR97AVMSLeqUlacV9dckZzV6J2dnRkEhWWk4WM+P9KJqiscntHkyzdQzVJDftEd2aShsL//ROyxDSb9ng6S3OPk1coyaXk2ox+elXEADnW57+3Km3CJePVGRfo/aPkakN7JpCpYf+9uSo4JBLJmjVr6jizWq2+c+fOqVOnOBm6Jq1OZIX8p5vf3yzLpPQ8Qa0oXoBBq4iNjS0qKhIi3w57bhO1vDqUYdi/Dnk4fL6GxMiXiFQqFX/5DiQaqP0eUEanW51seWUoI2FLyDSr569i5VtYWHj9+vWKxw350ira4erLZqRiNUxK7xN059SpO7yPWVVKSgoRCbMJl+2Z2rbDA5aYlB4nqBUlivEnvnHjhkCbcJt9RNTy2lCG2Dt/tLWaG2qQm/BTWp1scXWohNhSMlX+swmPNqXR/5zKcFmQixCKioquXr1aWsr/SZutou2ujrSgErWGSet9gs6dGkA0wImIKO4KxfE+/BPx8fFdunQRarR/MazgtxD68ssvf1i72raZtcDjiqWwuDhDmd3WtZXYgQjn3oOkDm2E2jmoB+4nPWrh4mhmasjXyFSUnJpmKpc7OdjXPqtBKCwsyszOaWNMm/D9pOS2bq3FjkI495OSW7o4m5pWvhDMUOU+zg+a/d7Cz5cIPK4IO91dXV1D5s2a+sZo4YcWxfkrf63aGL5nwzKxAxFO+/5jbp3cLXYUwuk9InDPhuVt3QzoaHONpgcv9e7b/e0JBrSzu0anL1xbH7Z357ovxQ5EOD1fefPq7zvEjkI4vYZP3h/6rVur5mIHIpDQnZFyWxFOMcCtzQEAAIB3TaPguH4z3mPIhLrMmfs437bz4IaNsn3f0cnvf1aXxmrpgqx7tHVUa4dzl6626+KboczmcFARId9KDCxfAKikAR80RCRz66tSNaU7IDSNggNqtin8wO1Te50djeWYOvIFAGhyxCk4PvhsxawFX5eWlRHR7kPHOw4Y6/D8EF3LmYvXerw8ybKD9/A333+UllGXDtdu3uXae6Rr75GbIw5qWy5c/dtz1NuVpuPuPRgwZmrwku8cPYZ6+087/+dffUZOse7k8+Gildo5i0tK35i10KbzIM9Rb8fGJdTQWK8gCwqe3BijarKNT3/stOC8/IK+flMys3J+ORr13MDXbDoPCpgxLzMrh4hi4xIGj5sZsjq029A3ntX5xh3723qONm/X33PU23cSFJVeVetCq6qkpMyo8tXtezCSfBMeJFdt3Lr7UJt+r7bp9+q2PYfb9HuViKZ+tGTF+jDts4u+3fDBZysqRVs1HZVKPWvB13ZdfB09hi79blMNi4XzpLbtOTxw7HSWZdVqTc9X3jx0/HTNf5emnm/VaA073/D9v9l2Hqz9x7TqfeC3kzXnK3zK9f2geXniHLVa077/mMKiau7aUt/1WRjiFByffTj98o1b2/f9Gp+YNPuTZWFrvrh89GdtS1ZO3thpwUvmvpf859EObVwnB9W+l+nMxWuLvt2w4/uQC4e3HvkjpuaZL1yN7flC5/iY/SWlZf5Tg/f+tPx4xA+rN+3Urhy/HI0aMqD3vbMHBnn1nPDeArVaU21jfYOMT1QQUdVkOUl/f+i3zawsb53cU1BYPPWjJd9/Of/+hUPNrCzf/++Td5DrsfEJD5J3rvuq2s4fpqQHffrNtu8WP7xytEvHtqt+2lHpVbUutKoKCouMLN9io8q3fZvK1y/8HXdv7tLVuzcsO3dw86bwA9rGUcO8j544q50+8NvJcX5DK457Pymlajr7f4uOPnfl2rEdxyPWfbl6c4KimsqGp6SmjPMjovD9v/3489527q1efcmnhj+KAeRbbbQGnO+kscNz407mxp3c/v3SDm1chwyo5RcBBE6Z6v9Bc2znD1KpJOFcpKWFedXe6rU+C0acW0M5OdiFrvws73HB7kPHJ40d7tWrGxFpWw7/cWZw/17apfPt5x86PD9E+6lfg31Ho94NfM3HsycRLZ03a+TkD2qYuYWz46Sxw4lo2MC+uXn57q1baP/l5RcQUc8XOs+c/BoRhcyfvSn8wN37SdU2XrwWW68gy1UqIqqaLCfp60T+ftJ/+OCXfPoR0Tf//aBVzxHa1xaXlP64/BNTuXzbnsNVO3dysLt7dr9bq+aFRcWO9rYPU9K1veleFXfvQQ0LzcnBrmokGlZjVPlq72FrRPlWERF57J3XR/ft/jwRzZ01Rft1+SUfzyn/WZSXX5CVnZeuzBrQp/vtu/d14363MbzadMpVqoysnD4vdk3+82gza8tqh+MjKYZh1n/9ycjADxiGOXdws8HnWzVaw85XKzk1Y+bcLw9uXfWsocVKmbj4oKmoXuuzYES7F+WLXTsRUfj+3zq2c6vYcvritWOnLmj3XxGR3MQkI6uWc+XSMrKGDeyrnW7nVs218hXvNWJl+aQYlEmlzZ0dddPaCd2VjSYyWRvXlmmZWdU2PkxJr2+QRJSckl4pWU7S10nLzGrj+iRUJwc7udxEW+y7tnQxlcuJqNqwneztNoUf+DX6nI21lancxNrqyfage1WtCw35Gme+FT1KzejTvat2WndtobWVxYA+Lx4/fTHpUdprI4ZIpZKK41abzmsjhjzOL5w598t0Zdactyd8/O5kqu5nl2RSKR9JeXRu37Gtm6O9bavmzgafb7XRGnC+RKRSqSfN+TR4VmDvF7vWMJsoKRN3HzQ6dV+fBSNawXH+z7/u3U92cXJITs2o2NLC2fElH899G78hIrVacy02rrmTQ3pmTUu5pYujbj/V/Yf//pixSv3k9F3dELW6n5SinShXqRTJqa4tXZJT0qs2NiBIIqqaLCfp6zR3crhx6652OjMrp7SszNHeVpmdK5M92Qir7Twi8tiREzHHI9bZ2zbbvu/o4X+OSele1WDI17DzraiFi2PSozTt9MOUNF37qGEDj/wRk6BIXvzxzErjVptOYlLykAF9pk0ck/QobfzM+bbNrIPeqeb6nT2H/+AjqVPnryqzc+8kKK7fjO/+fE2/UmMY+VaN9lkMI98l/9toZWn+4fSJdZlZ4JSpuk+fxrxdUH3WZ8GIcw5HZlbOh5+vVObkBvgN+XnvkYvXYhMVj7QtfkO9z1y8djTqrDI7d8FXaz9ctLLWn7AbN2rYhp9/OXPxWkp65ucrftTOb2NtdeNW/PWb8Vk5eT9sretNqK7fjN8UfkCZnfvpsnVt3Vpp95dUbaxvkNr9YFWT5SR9nVdf9vnl16gTMZdy8h4HL/lu7HDfSttntZ1n5eRZWVqYm5lmKLPXbt5VXMLBjzNqNKxR5csaWb6p6cpKLeP8hm7ZdejKjVupGcqVG7br2kcNGxj5+6n4RIVPv551SefgsdMTZy9Mz8xWqzWlZeXmZtXfvJWPpErLyt5b8NX3X8776pM5cxYuq/lG9QaQb83RVmIA+Uadvbxl18Ft331Rx58OFThlaugHTUFR9T/VWa/1WTDiFBxfrPrp+efaz3l7fLcuHVct/mji7IU9XpmkbWnu7LB97dJ5Iavd+47686/bYatrv/dq/97dlsx9b9KcT/uOfGvS2OHaM2g6d2gza8q4gWOn+457N+id12vtRGv6JP8jJ2LaeY2+cPXviPVfaf+6VRvrG2R2bt7Pe49WTZaT9HXau7fevHLR7E+Wufcd9big8Psv51WaodrOA8eNNJWbtO41Yuy04M/+b/rFa7E/7z1a90GrVVpaZlT5FhYV7/812njy1Z7bVFGvbl2Wzps1+u2PBgfMnOg/XLe7u61by5bNHUe/PKjqd9Nq03l38mstXBzb9x/Te8Rkr14vTBnvV20AfCT1zbqwXt26DOzXY/JrIzQa9ud9NXVoAPnWHG0lBpBv2J4jqRnKtp6jrToOtOo4cPkP2/QqZWrQB03AyKFuffyqvUqlXuuzYET4LZWwsDCVMgG3Njdg7fuPSTgXKXYUwsGtzePuPUjPzB7k1ZOIjp268PXaLdF7N2if6j966uKPZ748yFOcWLlQ9dbmBpPvs6KtdGtzg8n3Ware2tywU9be2jxw2iyBx21KP2AeG5ew7IetlRotzM1++uZTMcKphS5aZXaOhXk1ly01uMOKxE3/WSHx2rke5stJ1d6E8q06Z07e44mzF14/Hm5tZbl2866RQwcQUWFR8eUbt5IepfkO6M1tAI1ZJpz0aQD5/m/xR3WP1gDyrW+fTSVlPXzfqIEIezi++OKL3eFhLV0cBR5XLDl5+Y9SMzw6txc7EOHExiUYVb5xCQ/cW7Wo4eisgblx666Tg12lTfjBw1Tt5YuO9rad2rtJJZKMrJy4ew+6dGjr5GArUqTcyMrJS81Qejz31Crd1POtOdrEpEeVrvhr6vnWLD4xya1Vc7Onfy3WgFNOSVfOmDb1w3lCFyUiHVJRqaZOnSrwuGI5f/58YGDgvXv3xA5EOHZ2djk51d9+xyB16tQpNDR04MCBYgcikOnTpxPRpk013TbRkJw+fXr69Onx8fFiByIcY9uEO3TosH37dk/PJnyUpF5CQ0PlcnlgYKDA4+K3VAAAAIB3KDgAAACAdyg4AAAAgHcoOAAAAIB3KDgAAACAdyg4AAAAgHcoOAAAAIB3KDgAAACAdyg4AAAAgHcoOAAAAIB3KDgAAACAdyg4AAAAgHcoOAAAAIB3KDgAAACgGiEhIXv37iUilmXnzJkzZMgQPz+/jIyMhvWGggMAAACeolarBw0atHjxYu3D6OjozMzMqKiogICAVatWNaxPFBwAAADwFIlEcuLEiXnz5mkfxsTEeHl5EZGnp+e5c+ca1qeMs+iegWVZf3//oqIiXUtqaqq/vz/f4wIAAEBViYmJkZGRYWFhuhYLC4sDBw4wDKNrYRhGJpNJJE/2SiiVSg8PDyJyd3dXKpUNG5f3goNhmMjIyIotYWFhKpWK73EBAACgqnbt2s2fPz8wMLDuL7Gzs1MoFESkUCjs7e0bNi4OqQAAAEBNfHx8Ll26RERXrlzx9vZuWCe87+EAAACAJs3X1zcyMtLPz08mk4WGhjasExQcAAAAUI2QkBDthEQiWbNmTSN7wyEVAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADhXEgWOwKRoOAAAAAQzicnxI6gDkpLS21tbbt37969e/cVK1Zw0qeMk14AAADAYCQmJo4ZM2bbtm0c9ilEwXHw4MHS0lLdw0uXLnXo0EGAcQEAAPRNWkYY0RQRA3j8+HFiYqKZmZmuxdTUdPTo0RXnuXv3blxcnL+/v1wuX7lypaura+PH5b3gYFk2KyurvLxc11JUVFTxIQAAgPFIS98ibsFRXl5eWFiYk5OjazExMWFZlmEYXYuTk1NwcPD48eMjIiKCgoIiIyMbPy7vBQfDMO+8807FFjMzM5VKxfe4AAAAUJWDg4Ovr29gYGAN83h5eWknxowZs3DhQk7GxUmjAAAAwnEqKhM7hNotX7583bp1RHThwgUPDw9O+sRJowAAAMtIzskAACAASURBVMLZdOS22CHUbsaMGdOmTYuIiDAzM1u/fj0nfaLgAAAAEI6EZcUOoXb29vb79+/ntk8cUgEAABCO3FivmkDBAQAAIBypWuwIRIKCAwAAQDhM7bMYJhQcAAAAwDsUHAAAAMA7FBwAAADAOxQcAAAAwjFvYaRnjaLgAAAAEE7rgGKxQxAHCg4AAADgHQoOAAAA4eCyWAAAAAC+oOAAAAAA3qHgAAC9llNC5RqxgxDQ1VT6/pLYQQjrWILYEYAgUHAAgF5bc5HOPRQ7CAHllVKWMV3EoGFpWYzYQYAgUHAAgF5jWWoKv+bNGaNKFowKCg4AAAABGetlKig4AAD0iMb49nC0eLBC7BAEZnx/YyIikokdAEdKMujvxX9cvzvM4o+ai8dr997uyW7RTrewopSPhYiOK0XlxMx3MO+d3bCXlxa0M/U9RB27chsVL/Lv0aUZVKig0sdUmkcSVeO7VBUzZeowi5mTG98V78qy6eybbOpxhup6C2TFpQ5uY+IZX4P66vR4m1Uzk8LFRJRC7DmGmWT4546y4ZJhxA4jonBS5jo6zs4UOyJ+acKlEtLs6EgUPk9FMtmkcrEj4pdqh4mMUVm1JwpnNCSRTNLfe5yzLBsUFHT79m1zc/MtW7Y4Ozs3vk9D2cNxedZ/znUeWlu1QUQ9Omz1ll7QTqcW0Ng9vIfGlXIN5bzZv8HVBhGZWiWy53tSWhSHUfGC1dApP2JMSWpBZTmcVBtEJDNnzc0D2aOntA83XaW+G2loGL2ynRR5nIzAkfQo+qUFpf5W92qDiNz73nsjtEtZbBl/cQmvmUmhbpohlg03lPerZ2DDJUyF776OtkoRgxFA+Q65hP4tImXEzZauz2TMvzlKSFO2w1TEYGoWHR2dmZkZFRUVEBCwatUqTvo0iA1YXUJFye8028LU7dvdSTcf3YyRt3iLimtn76tb+Z9vZCeMrJSiAjiJh0cF96jsMfn8QvnJxHD5pZaRUsmWBUT0ZyodvUtnp9GJKbR8GM0+wuEgjZNxii5OJ01D6oadI+M3btjIeUSiY4lhiSEixtB3RGsTZI3mCH/FT1+t8h1yUSIRRnl45exMGP3doxMTE+Pl5UVEnp6e586d46RP3g+psCzr7+9fVFSka0lNTfX39+dyDImMCu67yer6dVAqKx/ajjQsRd3nMgq+FSenc9RTHuX+TbYvcNQbDxR7qCybTr1K6kLO33vNXr4y82vNKWuJuYxG7iAiYohKVKTSkEwfyu+7G6g8v2EvZYg9k3NmDs3hNiLRaAqISE3SpMtOmfJBfV7cbfAFBxGxxFyKm9YsN7qT5wNpfXZxNV0FL2WXrWlxXOr/eqddEk6/YOgb7e6cr+I/f1f1jcPSAtop2ikNiYmJkZGRYWFhuhYLC4sDBw4wFb61K5VKDw8PInJ3d1cqudnZxnvCDMNERkZWbAkLC1OpON11xsjIxDpdZWIvrdPhBpZlvN3pi2guQxBAr14t6FFjO2FZhiETKterQwhVeHxK934k+55UkECFCo47/3PMTz9K9tyiR4/pQ08iIpWGhmzTj2qDiNTF1H4G3fq6AS9lienRvQfnEYmGkRGRlNTufTLakFFUG0TEENun82ZiqeKxBsNmedzBvItkAu0SOxDeadfgTzot1ZCE3Wki4o6sdu3azZ8/PzAwsIZ57OzsFAoFESkUCnt7e07G1ZN32Ubz+DyftanjvBfzhi6OfvK3d7bmLyaOOVsxxYq65vgsDDEktyfbFzkJiUevXKC0aFIVc7uKsixD6nVENPo5irxDay/R0bv0xl56qzuHgzSOWwCxDTwP47+xZsEfBXMbjpgYM+3/EtIYybEGbYIS0hj2F30dzT9HyqSk1v5p8/okihsSrxLs/6Z/82WJSKPHH8E+Pj6XLl0ioitXrnh7e3PSp/5mWz/t3vLwnPqg3K3WGVlifDKPaqcZorSPeA6MU+af5LL5jfiTsRIysSOv9WSi93WWeSsacYUC0mmSWsO8xEmXKo3k8bE/mZ+cichUSr9PJhdLis+izwfRNP3ZL9BmMll3Ittu9X2dukSy+INcqUTKR1BiUdNT6fxy9y2xIhFG6N1pFR+WsyZiRSIM6SR1xSJSQxL7jrW/hzddzw3vUrHCYImRTtLf82R9fX2dnJz8/Pz27dsXHMzNNxmGFfy2dj/++OOJEyf69OnDR+dqllIKNRa3NrXU5OcXdrTt2t/50dq8EutmppLsZv0Kn/PUkJSIHhRbuZkVShghclcoFDt37lywYAF3XbL5Sfftc+5bPrYsNbV77GRmnnvbISUljVqUO2SzJbIya/dsiVRiJrPSyBJNHQpsXAY3Y1m5TEbFKsacuzCeadGiRV988QWHHTLEStgSIomsSEN5GRJJlmmmPFdmK1OV5MpN81RFFkyhorCZZ9FfCU6tWz9KVTI55qyqtcY2rWWromauzVxsGDMrhrfvx8uWLXv99dfbtm3Lec8Stsz8cXH23TOty/56bNaszGSsmrnZUXUxvrBlzovvUnaWWeLvj+W9XHt3UsuFO96/a9cuInr99deFGe75jM9L8mQJHT8XZriq7t+/v3v37vnz5wszXNuHIeam5becudyC6ovzTbgGEkVCV4stsU4hwgxXrWXLlk2cONHd3V2Y4TzSP7uteVfdorUww1V1+fLlYcOGvfvuuwKPK0LBsWLFip83/9S6pYvA44olOyf37v2H/Xrq8UmaXDt1/s9BXr3EjkI45y7feKFLR2srC7EDEci12LhmVpbt27iKHYhAlNk5CYpH/Xp4iB2IcM5euj6gr/4caOTd2cs3unftZGkpxPcxffAwJf2tKVOCP/lM4HFFOEvWxcXlwxmTpr4xWvihRXH+yl+rNobv2bBM7ECE077/mKM/rxY7CuH0HhEYtvqLtm4txQ5EINODl3r37f72hFfFDkQgpy9cWx+2d+e6L8UORDg9X3nTqDbhXsMn/7x2iVur5mIHIpDQnZFyW0fhxzWUczgAAABAjxlgwXH9ZrzHkAliRyEcY8uXjC/lmvPdvu/o5PfrtGu0Yj8yt74qlf7e5sHYUjaAfOu+VeY+zrftPLhho1S7KBqwfBr/HmJs+XLCAAsOAAAA0Df6UnBs3LG/redo83b9PUe9fSfhyb2edh863nHAWIfnh8xa8HVpWVm1LWcuXuvx8iTLDt7D33z/UVpGw8aKjUsYPG5myOrQbkPfiLv3YMCYqcFLvnP0GOrtP+38n3/1GTnFupPPh4tWPqvDbXsODxw7nWVZtVrT85U3Dx0/bdj5Tv1oyYr1T25Rt+jbDR98VqdfemzSKYfv/82282DtP6ZV7wO/ndSrfItLSt+YtdCm8yDPUW/HxiVoG2vo5+WJc9RqTfv+YwqLiqv21oD1uamnrP+rNLf51ro+34q/z3kKazfvcu090rX3yM0RB7UtF67+7Tnq7UrTtW6e1S6K+i6fSm7eSXxx2BvGk69Y9KLgeJiSHvTpN9u+W/zwytEuHduu+mkHEcUnJs3+ZFnYmi8uH/358o1b2/f9WrUlKydv7LTgJXPfS/7zaIc2rpODat/LVO1YRHQ9Nj7hQfLOdV8R0YWrsT1f6Bwfs7+ktMx/avDen5Yfj/hh9aadmVk51fY5ZZwfEYXv/+3Hn/e2c2/16ks+hp3vqGHeR0+c1U4f+O3kOL+hDQujCaU8aezw3LiTuXEnt3+/tEMb1yEDarmoW8h8ieiXo1FDBvS+d/bAIK+eE95boFZrau7n2M4fpFJJwrlIS4tqTsuv7/psACnr+SrNeb61rs/urVtwm8KZi9cWfbthx/chFw5vPfJHTM0z17x5Vl0UDVg+lbRxbXFo23fGk69Y9OLn6Z0c7O6e3e/WqnlhUbGjve3DlHQi2n3o+KSxw716dSOi0JWf5T0uqNpy+I8zg/v30r4hfvv5hw7PD9H+Meo7FhEVl5T+uPwTU7k87t6DFs6Ok8YOJ6JhA/vm5uW7t26h/ZeXX+DkYFe1T4Zh1n/9ycjADxiGOXdws8Hn+5KP55T/LMrLL8jKzktXZg3oU/vlc009Za3k1IyZc788uHVVM2tL/cmXiHq+0Hnm5NeIKGT+7E3hB+7eT7p4LbYB/WjVd302gJT1fJXmPF+tGtZnSwuzdu6tOExh39GodwNf8/HsSURL580aOfmDGmauYfOsdlE0fvlYWpi7tWpuPPmKRS8KDplUuin8wK/R52ysrUzlJtZWlkSUnJLesd2Tu8692LUTEYXv/61Sy+mL146dutCm35PL8+QmJhlZtfycSrVjEZFrSxdT+ZOf8rP652psmVTa3NlRN11Dtx6d23ds6+Zob9uqubPB52ttZTGgz4vHT19MepT22oghUmnt+8maespEpFKpJ835NHhWYO8Xu+pVvkSkuyLXRCZr49oyLTPrYUp6A/rRqdf6rNWkU9bzVZrzfKlu6zOHKaRlZA0b2Fc73c6tVdUZKt4RqubNs+qiqLaxAcvH2PIVnl4UHHsO/3HkRMzxiHX2ts227zt6+I8YInJxckhOfXIU6vyff927n1y1pYWz40s+nvs2fkNEarXmWmxccyeH9MyalnK1YxGRTNaoe0KfOn9VmZ17J0Fx/WZ89+c7GXy+o4YNPPJHTIIiefHHM+syvwGkvOR/G60szT+cPrEuMwuZLxHdT0rRTpSrVIrkVNeWLg3rR6de67NhpKzPqzQf+dZlfeYwhZYujgmK5Ce5PPz3VyhV6ifX0eiGqFXVRZGcks7J8jG2fIWnF+dwZOXkWVlamJuZZiiz127eVVxSQkQBfkN+3nvk4rXYRMWjDz9fqczJrdriN9T7zMVrR6POKrNzF3y19sNFKyv+um7dx2qk0rKy9xZ89f2X8776ZM6chcs0mlp2ZDX1fIlo1LCBkb+fik9U+PTrWZf5m3rKUWcvb9l1cNt3X0gkddpkhMyXiK7fjN8UfkCZnfvpsnVt3Vq1c2tVl34Kioqq7a2+67MBpEz6vUpznm+t63NRcQm3KYwbNWzDz7+cuXgtJT3z8xU/aue3sba6cSv++s34rJy8H7burnUhPGtRNHj56BQWFSc9SjOefMWiFwVH4LiRpnKT1r1GjJ0W/Nn/Tb94LfbnvUe7dem4avFHE2cv7PHKpOefaz/n7fFVW5o7O2xfu3ReyGr3vqP+/Ot22OolDRurkfF/sy6sV7cuA/v1mPzaCI2G/XlfLR029XyJqK1by5bNHUe/PKiOuw2aesphe46kZijbeo626jjQquPA5T9s0598iWj6JP8jJ2LaeY2+cPXviPVfMQxTaz8BI4e69fGr9hKG+q7PBpAy6fcqzXm+ta7P9x+mcJtC/97dlsx9b9KcT/uOfGvS2OHaU1k7d2gza8q4gWOn+457N+iduv40T9VF0bDlU9GDhykjJn9gPPmKRYTfUgkLC1MpE3Br86au/+ipiz+e+fIgz6pPte8/JuFcpPAhiaX3iMA9G5bj1uZN3bNWaeO8tfnV33eIHYVweg2fvD/0WyO7tXmLwGmzBB5XL87h4ENsXMKyH7ZWarQwN/vpm0/1qk+uCJnv/xZ/dPnGraRHab4Deje488bDn5gaF5s+J6slWMqGukoL/yfW/5WqIl20uXn5jeyhIv3PN+FBskRuJnzBIcIejiVLlhw9sMd4flrzcUFhQWFxSxcRfimHJxlZOXH3HnTp0NbJwbbaGRIUj9q7V3NitqG6n5Ti2tKlkSelNiG37z5o3cLZkDbhmlfpvMeFRcXFLQxoE65Vbl6+rY212FEI58HD1NYtnI1nE84vKHrzzTff/3iBwOOKdEhFpZo6darA44rl/PnzgYGB9+7dEzsQ4djZ2eXkVH8HLYPUqVOn0NDQgQMHih2IQKZPn05EmzZtEjsQgZw+fXr69Onx8fFiByIcY9uEO3TosH37dk/Pag4QG6TQ0FC5XB4YGCjwuHpx0igAAAAYNhQcAAAAwDsUHAAAAMA7FBwAAADAOxQcAAAAwDsUHAAAAMA7FBwAAADAOxQcAAAAwDsUHAAAAMA7FBwAAADAOxQcAAAAwDsUHAAAAMA7FBwAAADAu0YVHCEhIXv37iUilmXnzJkzZMgQPz+/jIwMjmIDAAAAA9HAgkOtVg8aNGjx4sXah9HR0ZmZmVFRUQEBAatWreIsOgAAADAIsoa9TCKRnDhx4vPPP9c+jImJ8fLyIiJPT8+tW7dWmrmwsLCsrKziQ1NT04aNCwAAAI1UWFiYk5OjeyiXyy0tLfketIEFB8MwMplMInmyg0SpVHp4eBCRu7u7UqmsOKf2aEtRUZGuRaFQDB8+vKEBAwAAQMMpFIrff/89KipK12JhYbFlyxaGYXgdt4EFRyV2dnYKhYKIFAqFvb19xacYhqm0zyMsLEylUnEyLgAAANSLu7t7UFBQYGCgwONyc5WKj4/PpUuXiOjKlSve3t6c9AkAAAAGg5s9HL6+vpGRkX5+fjKZLDQ0lJM+AQAAwGA0quAICQnRTkgkkjVr1nARDwAAABgg3PgLAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHiHggMAAAB4h4IDAAAAeIeCAwAAAHjHTcFRWlpqa2vbvXv37t27r1ixgpM+AQAAwGDIOOklMTFxzJgx27Zt46Q3AAAAMDDc7OG4e/duXFycv7//hAkTHj58yEmfAAAAYDC42cPh5OQUHBw8fvz4iIiIoKCgyMhI3VMsy65evbq0tFTXcvXq1R49enAyLgAAANRLRkbG9evXU1JSdC2mpqb/+c9/GIbhdVxuCg4vLy/txJgxYxYuXFjxKYZhXnzxRbVarWvJzs42NzfnZFwAAACoF3Nz87Zt2/bq1UvXIpVK+a42iKuCY/ny5dbW1rNnz75w4YKHh0elZ319fSs+TElJUalUnIwLAAAA9WJtbe3g4DBs2DCBx+Wm4JgxY8a0adMiIiLMzMzWr1/PSZ8AAABgMLgpOOzt7ffv389JVwAAAGB4cOMvAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgHQoOAAAA4B0KDgAAAOAdCg4AAADgnYyTXliWDQoKun37trm5+ZYtW5ydnTnptu4e3zvV7NLgBr74KNHKNHJx4TIgAZTn0clXSXmWWE0dX3GjbfSLXoP5jIkjhRQ7LXZD2sDvBuRKn29IB5pCU8mMEq7DEpW6lN1lxlRt77yBes4UPhwhFNyng+2qaX+9mKRmgkfDj8h2VHi/phmuEQ3YT/7+QgXEi4IyCr1GWUU0qA29uSMjnGYPabevltfEe9PiM4JEJ4S08ObNKb3W2VJiB7ScG0N2AkQkDm72cERHR2dmZkZFRQUEBKxatYqTPuvh8e2GVxtENJLItzlnwQjmtz6UWY9qg4hevO9bUtYEPoaL3izafb/X2sAGVhtEJLEspe1mVKrkNC4xaXZZVlNtEFHcuwJHIhBNGR3sWO0z7C5LKnggbDT8SD9RS7VBRD2IJo4VJBq+lKrJL5ys5TSyI434WfOb85jaqw0i6hRD73zMf3RCKNrXoi7VBhG19Dh7eepcvuMRETcFR0xMjJeXFxF5enqeO3eOkz7rqiCR/d27sZ1M5yISIZVlU0EiUT2qDa3D3+/lIxxuHbhzYKG0jMwb14uklKKGUXk+NzGJ69FhCamf/TQrXCSCyblOz0iZIQ2dGCRwOLw4VbdK4n2ilBSeQ+HR8QQa2ZGm9iDP1tRRdqez6c26vnLIWsrmMzJhqEssStPqPnvXsauoHrM3MdwcUlEqlR4eHkTk7u6uVD71tZJlWX9//6KiIl1LamqqP4d7CO+HUVkeVf/tr84cicrLycSEm5AEUP64Ya8ruprEbSB8iHKOep2Tg3JlOZT2O7mO46IvUSl21vTs3RPUcZhQoQiFefqtiaWntvHyfCrNov9v7+5jojjzOID/hl0YXuVYdikoAoqlSlNPwvUOo0UWX1KzMUox7f3hG21SUiUVY0/9wx7aYppLGivpaU3FcqyckpxU8LD2qAs99WxreE2qibWybpaWZHmzyovgLnN/YAhlV5ydmWd2C9/PX8zuM7/nNzP77P52nhmWj1Y3J6U5+5/4VDvR+GxSClFfH82erUpOyusapLhwKvySbnTRnMCOQI3ok6ycixqJ1rBMTgV9LV41D9YI3n+R9Fp7e3tNTY3ZbB5/JDQ0tLq6muNkfpQ+hTIFR1RUlM1mIyKbzabT6SY+xXFcTU3NxEfMZrPT6VSkXyKi0RGnJiJw9J6sIPeIRtkfZAWFxJEmmJwD3q73R2E1i3SUlfww+X4bRck/kZyyg5xDCiTkc5xmymcfqZWHiqIW/2px0tugNpgE5d5DfEUTQq5Bz09NvHbFSvRagioJMZGZSPn/pnN/poggink/TeBEn5B7EEO5LDNTR0SKV807+vlE9rXl/Pnz9+7du3nzZuY9/ZoyUyqZmZnXr18nosbGxuXLZU9weCV+vTYyWWYM4VOOeF6RdFQSwFPy60RTfg65eeDkFv7lRUYZKejN9998PSmS5H2MCo4g6qyj2Gnx1X/+NtcU3w0WrFUxFbVwWuLneHxmlNNS+HMU/Fu7ytvdsn+KanaMKCKCcSoMJUfRzgxaW0ErzdTH6RsGjaJWEwKookTuvKo/4KMFjRcfLg8bmtjl4nPKFBxGo9FgMJhMpqqqqnfeeUeRmGJF/4n7/cGRkHmSAwj/4pyXfoOTZukltLySNHqRzXudAQPtLbSEaU7KiF4T/ddNDa9d+MPQkMTze8Iwx6WtpSV/o5A4ZXPzjWeyNdkXBY8Thy+WqZ6NWnLtgjB5kwXiAlIKKPOcTzJSWPwGmrXwKW2+JPpvmyrZMLQuha6+TpYt9Gg/re34sqJv01NW6E2gv1fS/15VJTvmuFcH+8W9Ud//zz+eq0hlnY8PcYKg9hVnZrPZYrEsW7ZMTGNBEKxW6/z5nu6OE6ezszMyMjI0NFRyhPb2djkJtLW1VVZWfvDBB+p0Nzg4+Msvv8TFSf+gtVqtSUlJkifznE7n7t27S0pKRLbv6OgwGAy8jDNMMvdYV1cXz/OzZs2SHGHfvn1vvPHGs896vqtikgcPHjx8+NBgMEjuTub2joyMOByO+Ph4yRE++eST0NDQrVu3imksCMLdu3fnzZP+lcDnQ7i5ubmqqurQoUPqdPdbHMIxMTFBQUHSuiMlhnBwcHCEjPNAe/fuzc/PF5nD/fv3R0ZG9HqxX/bcydze4eHhrq4uOUP4/Pnzubm5eXl5kiNIo8w1HF5ZtWpVSIjYM2WDg4P19fXp6emSu7NYLAsXLpwzx/PpWTFqa2uLiookr05EK1eujIoSe2+1zO46Oztv3LiRmiq9TP7ss8/y8/PDw8Olrd7d3f3888+L397z58+vWLEiNlb6ncky99g333yj1+sTExMlR9DpdOnp6RqNqBmuH3/80eFwpKR4N7M7kczttdlsTU1NL7zwguQIoaGhJpNJ5CEeGBior6+Xc+Lz0qVLqampPhzCHMepOYR//vnnmzdvyhnCpaWl27dvDwsLk7Z6V1eXV0O4uro6Ozv7Gan/ykgQBJl77Nq1azExMQkJ0q90iY6OXrJkicgh/MMPP/T29or8guGRzO21Wq3Nzc1yhnB/f//YfR5qE/zbvXv31q9fLyfCwYMHLRaLnAhZWVlyVjebzaWlpap19/XXXxcVFcmJ8Morr/T09Ehe3WazbdmyRXz7wsLClpYWyd0JsvfYkSNHPv/8c9USOHfu3EcffaRad+5aW1t37twpJ0JeXl57e7vIxr29vTk5OXK6KyoqamhokBNB5h4rKysrKytTrbv6+voDBw7IibBhw4a+vj7Jq1ut1m3btolv//bbb7e1tUnubnR01Gg0Sl5dEITDhw9XV1fLieDVIauqqiopKVGtO3fNzc27du2SE2Hr1q13796VE0Ea/GtzAAAAYA4FBwAAADCHggMAAACY88FFo17RarXBwbJ+qCkoKEjO5dNEJPnaq/EEVO4uUN6/TOV5XquV/sIIDAz0apO9be9O/h5TMwF/eEHKfIV4FUGr1cq5BYn8Y4+p3J3M7cUQZpqAP7wg1RzCCvLBbbEAAAAw02BKBQAAAJhDwQEAAADMoeAAAAAA5lBwAAAAAHN+V3AUFxefPXuWiARB2LFjR3Z2tslkcjgcUy96DCWmDaOu4UmU3ck4xH4IQ3h6wxAGyTQHDhzwdQ6PuVwuo9F46tSpjRs3pqamNjQ0XL58uba2dnh4uLa2VqPRTLG4apWHXyGfFMFjG0ZdgzsWOxmH2K9gCE9vGMIgkx+d4QgICLBYLHv27BlbvHr16tKlS4koIyPj2rVrUy96DCimDaOuwR2LnYxD7FcwhKc3DGGQyY8KDo7jtFptQMDjlLq7u8d+wDMxMbG7u3vqRY8BxbRh1DW4Y7GTcYj9Cobw9IYhDDL5vuAoKyvbuHFjcXHxpMejoqJsNhsR2Ww2nU439aLHyGLaiFlRQtcwjt3xdQ8iPiscYgVhCE9vGMKgFN8XHHl5eWfPnt2/f/+kxzMzM69fv05EjY2Ny5cvn3rRY2QxbcSsKKFrGMfu+LoHEZ8VDrGCMISnNwxhUIr//paK0WisqakxmUxarfbkyZM6nW6KRTER1OwankqRnYxD7M8whKc3DGHwFn5LBQAAAJjz/ZQKAAAATHsoOAAAAIA5FBwAAADAHAoOAAAAYA4FBwAAADCHggMAAACYQ8EBAAAAzKHgAAAAAOZQcAAAAABzKDgAAACAORQcAAAAwBwKDoAZSq/XcxOEh4d7tbpWUv0kMgAAAphJREFUq3U6nYxyA4Dpx39/LRYAWKuvr09LS/N1FgAwI+AMB8DMFRER8bsJiOjKlStpaWlhYWEvv/zyTz/9NNbsxIkT8+bNCwkJycjIuHXrFhGtWbPG5XIlJydbLJaMjIyxZt9+++3Y399//31WVlZxcfHixYufFBMAZhoUHADwWE9PT05OznvvvdfR0bFgwYJNmzYRkd1uLygoKC8vt9vtixYtOnz4MBHV1dVpNJo7d+6EhYV5DNXa2nrnzp0zZ854jAkAMxCmVABmrqysLK328ZvAsWPHHj16lJWVtW7dOiL68MMPo6OjXS6XwWC4fft2QkLCwMCAXq+32+1iIg8NDR0/fpzn+fLycveYGo2G3UYBgH9CwQEwc50+fXps1oOI9Hr9kSNH6urqkpKSxh4JCgpyOBwGg6G0tPTixYuRkZE8z0dERDwpmiAI43/PnTuX53kistvt7jHj4uLYbBAA+C8UHAAz1+zZs8dLASKKi4tbvXp1VVUVEblcrpaWltjY2MrKygsXLnz11Vc6na6ioqK2tnZSkPF7VTo6OsYfHD9x4jEmy20CAD+FazgA4DGTyXTlypUvvviiu7t73759hYWFHMf19PSEh4eHhIQ4HI6PP/54aGhovH1/f39kZGRbW1tra2tPT8/Ro0dFxlRxmwDAX6DgAIDHYmNjKyoq9uzZk5iY2NTUZDabiWjz5s08z8fHx+fk5Lz77rvffffdqVOniCg3NzchIWHu3LlvvfXWSy+9ZDQaCwoKRMYEgBmImzjtCgAAAMACznAAAAAAcyg4AAAAgDkUHAAAAMAcCg4AAABgDgUHAAAAMIeCAwAAAJhDwQEAAADMoeAAAAAA5lBwAAAAAHMoOAAAAIA5FBwAAADA3P8B6Fae2414C50AAAAASUVORK5CYII=" alt="plot of chunk densityPlot"/> </p>
<p><br></p>
<h3>Building the prediction model:</h3>
<p>Rather than using the default training method(bootstrapping), we are using <i>cross-validation</i> method with 5 folds to train the data as it seems to be more efficient and fast.</p>
<pre><code class="r">tctrl <- trainControl(method = "cv", number = 5)
modFit <- train(classe ~ ., data = training, method = "rf", trControl = tctrl)
</code></pre>
<pre><code>## Loading required package: randomForest
## randomForest 4.6-7
## Type rfNews() to see new features/changes/bug fixes.
</code></pre>
<p><br>
Summary of our fitted model:</p>
<pre><code class="r">modFit
</code></pre>
<pre><code>## Random Forest
##
## 3927 samples
## 52 predictors
## 5 classes: 'A', 'B', 'C', 'D', 'E'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
##
## Summary of sample sizes: 3142, 3142, 3142, 3142, 3140
##
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa Accuracy SD Kappa SD
## 2 1 1 0.008 0.01
## 30 1 1 0.008 0.01
## 50 1 1 0.01 0.02
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 27.
</code></pre>
<pre><code class="r">plot(modFit)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-7"/> </p>
<p>We can see from above that we have achieved accuracy of 100% using 5 fold Cross-Validated resampling with just 52 predictors.
<br></p>
<h3>Prediction and errors:</h3>
<p>As for the prediction statistics on cross-validation set:</p>
<pre><code class="r">prediction <- predict(modFit, newdata = cv)
</code></pre>
<pre><code>## Loading required package: randomForest
## randomForest 4.6-7
## Type rfNews() to see new features/changes/bug fixes.
</code></pre>
<pre><code class="r">confusionMatrix(prediction, cv$classe)
</code></pre>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1660 21 0 0 0
## B 10 1097 29 0 8
## C 1 20 991 19 7
## D 2 1 6 942 6
## E 1 0 0 3 1061
##
## Overall Statistics
##
## Accuracy : 0.977
## 95% CI : (0.973, 0.981)
## No Information Rate : 0.284
## P-Value [Acc > NIR] : < 2e-16
##
## Kappa : 0.971
## Mcnemar's Test P-Value : 0.000241
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.992 0.963 0.966 0.977 0.981
## Specificity 0.995 0.990 0.990 0.997 0.999
## Pos Pred Value 0.988 0.959 0.955 0.984 0.996
## Neg Pred Value 0.997 0.991 0.993 0.996 0.996
## Prevalence 0.284 0.194 0.174 0.164 0.184
## Detection Rate 0.282 0.186 0.168 0.160 0.180
## Detection Prevalence 0.286 0.194 0.176 0.163 0.181
## Balanced Accuracy 0.993 0.977 0.978 0.987 0.990
</code></pre>
<p>With an accuracy of 97.7%, our <i><b>out-of-sample error</b> is about <b>2.3 %</b></i>
<br>
<br></p>
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