chapter_4_exercises.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4 exercises"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
      "0                5.1               3.5                1.4               0.2   \n",
      "1                4.9               3.0                1.4               0.2   \n",
      "2                4.7               3.2                1.3               0.2   \n",
      "3                4.6               3.1                1.5               0.2   \n",
      "4                5.0               3.6                1.4               0.2   \n",
      "\n",
      "   target  \n",
      "0       0  \n",
      "1       0  \n",
      "2       0  \n",
      "3       0  \n",
      "4       0  \n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Load the Iris dataset\n",
    "iris = load_iris()\n",
    "\n",
    "# Convert to a DataFrame for easier handling\n",
    "iris_df = pd.DataFrame(data=iris.data, columns=iris.feature_names)\n",
    "iris_df['target'] = iris.target\n",
    "\n",
    "# Display the first few rows of the dataset\n",
    "print(iris_df.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data\n",
    "#y = (iris.target == 0).astype(np.float32)  # Binary classification: class 0 vs. others\n",
    "y = iris.target  # Multi-class classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Split the dataset into training and testing sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "# Standardize the features\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## full Numpy implementation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: Loss = 1.098612288668107, Accuracy = 80.00%\n",
      "Iteration 100: Loss = 0.6506742980421142, Accuracy = 86.67%\n",
      "Iteration 200: Loss = 0.5302555472930268, Accuracy = 90.00%\n",
      "Iteration 300: Loss = 0.4724024346027137, Accuracy = 90.00%\n",
      "Iteration 400: Loss = 0.4363672529615082, Accuracy = 90.00%\n",
      "Iteration 500: Loss = 0.4107698557498471, Accuracy = 90.00%\n",
      "Iteration 600: Loss = 0.3910721536497021, Accuracy = 93.33%\n",
      "Iteration 700: Loss = 0.37506773688897777, Accuracy = 93.33%\n",
      "Iteration 800: Loss = 0.36154785648979737, Accuracy = 93.33%\n",
      "Iteration 900: Loss = 0.3497953555890682, Accuracy = 93.33%\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Initialize the weights\n",
    "def initialize_weights(n_features, n_classes):\n",
    "    weights = np.zeros((n_features, n_classes))\n",
    "    bias = np.zeros(n_classes)\n",
    "    return weights, bias\n",
    "\n",
    "# Compute the softmax function\n",
    "def softmax(z):\n",
    "    exp_z = np.exp(z - np.max(z, axis=1, keepdims=True))\n",
    "    return exp_z / np.sum(exp_z, axis=1, keepdims=True)\n",
    "\n",
    "# Compute the model predictions\n",
    "def predict(X, weights, bias):\n",
    "    linear_output = np.dot(X, weights) + bias\n",
    "    return softmax(linear_output)\n",
    "\n",
    "# Train the model using gradient descent\n",
    "def train(X, y, X_test, y_test, learning_rate, num_iterations):\n",
    "    n_samples, n_features = X.shape\n",
    "    n_classes = len(np.unique(y))\n",
    "    weights, bias = initialize_weights(n_features, n_classes)\n",
    "    losses = []\n",
    "    accuracies = []\n",
    "    \n",
    "    # One-hot encode the labels\n",
    "    y_one_hot = np.eye(n_classes)[y]\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        predictions = predict(X, weights, bias)\n",
    "        \n",
    "        # Compute gradients\n",
    "        dw = (1 / n_samples) * np.dot(X.T, (predictions - y_one_hot))\n",
    "        db = (1 / n_samples) * np.sum(predictions - y_one_hot, axis=0)\n",
    "        \n",
    "        # Update weights and bias\n",
    "        weights -= learning_rate * dw\n",
    "        bias -= learning_rate * db\n",
    "        \n",
    "        # Compute loss\n",
    "        loss = -np.mean(np.sum(y_one_hot * np.log(predictions + 1e-15), axis=1))\n",
    "        losses.append(loss)\n",
    "        \n",
    "        # Compute accuracy on the test set\n",
    "        test_predictions = predict(X_test, weights, bias)\n",
    "        test_predictions = np.argmax(test_predictions, axis=1)\n",
    "        accuracy = np.mean(test_predictions == y_test)\n",
    "        accuracies.append(accuracy)\n",
    "        \n",
    "        if i % 100 == 0:\n",
    "            print(f\"Iteration {i}: Loss = {loss}, Accuracy = {accuracy * 100:.2f}%\")\n",
    "    \n",
    "    return weights, bias, losses, accuracies\n",
    "\n",
    "# Train the model\n",
    "learning_rate = 0.01\n",
    "num_iterations = 1000\n",
    "weights, bias, losses, accuracies = train(X_train, y_train, X_test, y_test, learning_rate, num_iterations)\n",
    "\n",
    "# Plot the loss function\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(losses)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss Function During Training')\n",
    "\n",
    "# Plot the accuracy on the test set\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(accuracies)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy on Test Set During Training')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pytorch implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: Loss = 0.6162369251251221, Accuracy = 83.33%\n",
      "Iteration 100: Loss = 0.4973093271255493, Accuracy = 90.00%\n",
      "Iteration 200: Loss = 0.44637373089790344, Accuracy = 90.00%\n",
      "Iteration 300: Loss = 0.41590896248817444, Accuracy = 93.33%\n",
      "Iteration 400: Loss = 0.3943862020969391, Accuracy = 93.33%\n",
      "Iteration 500: Loss = 0.3776877820491791, Accuracy = 93.33%\n",
      "Iteration 600: Loss = 0.36394789814949036, Accuracy = 96.67%\n",
      "Iteration 700: Loss = 0.35218557715415955, Accuracy = 96.67%\n",
      "Iteration 800: Loss = 0.3418320417404175, Accuracy = 96.67%\n",
      "Iteration 900: Loss = 0.3325329124927521, Accuracy = 96.67%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert to PyTorch tensors\n",
    "X_train = torch.tensor(X_train, dtype=torch.float32)\n",
    "X_test = torch.tensor(X_test, dtype=torch.float32)\n",
    "y_train = torch.tensor(y_train, dtype=torch.long)\n",
    "y_test = torch.tensor(y_test, dtype=torch.long)\n",
    "\n",
    "# Define the model\n",
    "class SoftmaxRegression(nn.Module):\n",
    "    def __init__(self, n_features, n_classes):\n",
    "        super(SoftmaxRegression, self).__init__()\n",
    "        self.linear = nn.Linear(n_features, n_classes)\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.linear(x)\n",
    "\n",
    "# Train the model\n",
    "def train(model, criterion, optimizer, X_train, y_train, X_test, y_test, num_iterations):\n",
    "    losses = []\n",
    "    accuracies = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        # Forward pass\n",
    "        outputs = model(X_train)\n",
    "        loss = criterion(outputs, y_train)\n",
    "        \n",
    "        # Backward pass and optimization\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        # Record the loss\n",
    "        losses.append(loss.item())\n",
    "        \n",
    "        # Compute accuracy on the test set\n",
    "        with torch.no_grad():\n",
    "            test_outputs = model(X_test)\n",
    "            _, predicted = torch.max(test_outputs, 1)\n",
    "            accuracy = (predicted == y_test).float().mean().item()\n",
    "            accuracies.append(accuracy)\n",
    "        \n",
    "        if i % 100 == 0:\n",
    "            print(f\"Iteration {i}: Loss = {loss.item()}, Accuracy = {accuracy * 100:.2f}%\")\n",
    "    \n",
    "    return losses, accuracies\n",
    "\n",
    "# Define model, criterion, and optimizer\n",
    "n_features = X_train.shape[1]\n",
    "n_classes = len(torch.unique(y_train))\n",
    "model = SoftmaxRegression(n_features, n_classes)\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = optim.SGD(model.parameters(), lr=0.01)\n",
    "\n",
    "# Train the model\n",
    "num_iterations = 1000\n",
    "losses, accuracies = train(model, criterion, optimizer, X_train, y_train, X_test, y_test, num_iterations)\n",
    "\n",
    "# Plot the loss function\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(losses)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss Function During Training')\n",
    "\n",
    "# Plot the accuracy on the test set\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(accuracies)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy on Test Set During Training')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## jax implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax.numpy as jnp\n",
    "from jax import grad, jit\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: Loss = 1.0891655683517456, Accuracy = 80.00%\n",
      "Iteration 100: Loss = 0.6487720012664795, Accuracy = 86.67%\n",
      "Iteration 200: Loss = 0.5294882655143738, Accuracy = 90.00%\n",
      "Iteration 300: Loss = 0.4719635248184204, Accuracy = 90.00%\n",
      "Iteration 400: Loss = 0.43607038259506226, Accuracy = 90.00%\n",
      "Iteration 500: Loss = 0.41054868698120117, Accuracy = 90.00%\n",
      "Iteration 600: Loss = 0.3908964693546295, Accuracy = 93.33%\n",
      "Iteration 700: Loss = 0.3749217987060547, Accuracy = 93.33%\n",
      "Iteration 800: Loss = 0.3614225685596466, Accuracy = 93.33%\n",
      "Iteration 900: Loss = 0.34968510270118713, Accuracy = 93.33%\n"
     ]
    },
    {
     "data": {
      "image/png": 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nnnnGatyCBQvMkq7q9S/p/oviGDRo0BWPP3funDk3N9fcsGFD8xNPPGHZfy3PZ2Zz8efnojh79uxpdeynn35qlmRes2aN2Ww2m48dO2Z2dXU19+/f32pc0c95Sb9bwLYxfQ8oo1OnTmndunXq16+fqlevbtnv6OiogQMH6vDhw5ZS1LZt2+r777/X2LFj9euvv+rMmTNW56pZs6YaNGigV199VdOnT9fGjRuveg7+zz//rN9//92yLVmypMz3duedd1p93bJlS509e1ZpaWmSpO+//16S9Pjjj5f5Ghe6mtfycjFKuuYVVsxm8zUdLxV+elRaJpNJffr0sdrXsmVLq/tYvny5PD09i1X/3H///dcW6EVKijstLU3Dhw9XcHCwnJyc5OzsrJCQEEnSzp07r3jOgIAAtW3b1mrfxfd3OVf6WVy+fLkk6b777rMaV96vDQBcr2bPni13d3cNGDBAklS9enXde++9Wrlypfbs2WMZ9/3336tLly5q2rTpJc/1/fffq1GjRurWrVu5xljW96fTp09r+fLluu+++y7b9/DWW29VRESE1TSyd999VyaTSY8++uhlY1u6dKmaNWtW7L1u8ODBMpvNxSq4e/XqZVWNVR7PL//73/9kMpn04IMP6ty5c5YtICBAERERlqmSN9xwg2rUqKFnnnlG7777rnbs2FHma17o+eefV2JiouLi4vTYY4+pevXqevfdd9W6dWtLq4qzZ8/ql19+0d133y0PDw+rOHv27KmzZ8+WyzTGS7nW57uuXbuqRo0apR5/pefUSz2/9OvXT05O5TeZqaR/O+fOndNLL72kZs2aycXFRU5OTnJxcdGePXtK9WwnXfn57GqPlf5+bdauXaucnJxir027du1KnHIJ20dSCiij48ePy2w2lziHPigoSNLf8+zffPNNPfPMM/rqq6/UpUsX1axZU3379rU87JlMJv3yyy/q3r27pk6dqlatWsnPz08jR460lFNfSUREhNq0aWPZrnalkwtdXHZdNO2uKJl29OhROTo6KiAgoMzXuNDVvJaljbGsit4Qi65bFlezAp2Hh4fc3Nys9rm6ulqaVkqF9+7v71/s2JL2lZWHh0ex8vyCggJFR0dr8eLFevrpp/XLL79o/fr1lofG0rzWJZXwu7q6lvrv6Up/zxkZGXJyclLNmjWtxpXnawMA16u9e/dqxYoV6tWrl8xms06cOKETJ06oX79+kqyn4hw9evSKU6hKM+ZqXcv70/Hjx5Wfn1+qmEaOHKlffvlFu3btUl5enj744AP169fvis86GRkZhj+/pKamymw2y9/fX87Ozlbb2rVrLX22vL29tXz5ct1444169tln1bx5cwUFBWn8+PHKy8sr8/WlwvfdIUOG6N1339WWLVu0fPlyubi46L///a+kwtfh3Llzeuutt4rF2LNnT0kqsR9YeUlMTKy0ZzupdM8vUvHnFScnp0tOfyyLkuIePXq0nn/+efXt21fffvut1q1bp99//92ycmJpXMvPcVlfm0vtg+2jpxRQRjVq1JCDg4OSk5OLfa+okWHRiijVqlXTxIkTNXHiRKWmplqqpvr06WNp/BkSEmJpNLp79259+umnmjBhgnJzc/Xuu++WOc6ihMfFjbMvfki6Gn5+fsrPz1dKSspVv0mX5Gpey4pW1Kj9wiaKbm5uxV4/qfDhqaS4SruqSWnVqlVL69evL7b/Un2qyqKkmLdt26bNmzdrzpw5Vn1F9u7dW27XvVa1atXSuXPndOzYMavEVHm+NgBwvYqLi5PZbNbnn3+uzz//vNj3586dq8mTJ8vR0VF+fn6WZtiXUpoxl3ouuVRC4lren2rWrClHR8crxiRJDzzwgJ555hm98847ateunVJSUkpVEV6rVi3Dn198fX1lMpm0cuXKEvt3XrivRYsWWrhwocxms7Zs2aI5c+Zo0qRJcnd319ixY8stpltuuUXR0dH66quvlJaWpho1algq4C/1uoaFhZXb9S+0fv16paSkaOjQoZZ9l3u2K0lFPNtJhQnFOnXqWPafO3fump7RL1ZS3B9//LEGDRqkl156yWp/enq6fHx8yu3aZXXha3OxlJQUqqWuQ1RKAWVUrVo1RUZGavHixVafChQUFOjjjz9W3bp1S2zE5+/vr8GDB+v+++/Xrl27SlzdplGjRnruuefUokUL/fHHH9cUp7+/v9zc3LRlyxar/V9//XWZz9mjRw9J0syZMy87rrQVMWV9Lcvb5s2b9dJLLyk0NNSqZDg0NLTY67d79+5iUworSufOnZWdnW2ZNllk4cKFFXrdogeZix9w33vvvQq97tXo3LmzJFmtlihV/GsDALYuPz9fc+fOVYMGDbRs2bJi25gxY5ScnGx57+nRo4eWLVt22fe+Hj16aPfu3ZdddKToF8qL31eLPhQqjdK+P7m7u6tz58767LPPrliF4+bmpkcffVRz587V9OnTdeONN6pDhw5XjOW2227Tjh07ij2vzZs3TyaTSV26dCnNLV2T3r17y2w2Kykpyapqvmhr0aJFsWNMJpMiIiL0+uuvy8fHxyr+q6loTk1NLbHlRH5+vvbs2SMPDw/5+PjIw8NDXbp00caNG9WyZcsS4yxKRpRX9bskHTt2TMOHD5ezs7OeeOIJy/7Q0FClpaVZJT5yc3P1448/XvM1S+OWW26RVPz55fPPP7dauKgimEymYv92vvvuOyUlJVXodUsrMjJSrq6uxV6btWvXXnObDlRNVEoBV7B06VKrZe6L9OzZU1OmTNHtt9+uLl266Mknn5SLi4tiY2O1bds2LViwwPLQFBkZqd69e6tly5aqUaOGdu7cqY8++kjt27eXh4eHtmzZon//+9+699571bBhQ7m4uGjp0qXasmXLNX9qVdRjIC4uTg0aNFBERITWr1+vTz75pMzn7NSpkwYOHKjJkycrNTVVvXv3lqurqzZu3CgPDw/95z//kfT3p3GLFi1S/fr15ebmVuKDkaRSv5blJSEhQd7e3srLy9ORI0f0yy+/6KOPPlLt2rX17bffysXFxTJ24MCBevDBBzVixAjdc889OnjwoKZOnXrZ/hTl6aGHHtLrr7+uBx98UJMnT9YNN9yg77//3vLgdPFyy+WlSZMmatCggcaOHSuz2ayaNWvq22+/VXx8fIVcryzuuOMOdejQQWPGjFFWVpZat26tNWvWaN68eZIq7rUBAFv3/fff68iRI3rllVdKXGI9PDxcb7/9tmbPnq3evXtr0qRJ+v7773XLLbfo2WefVYsWLXTixAn98MMPGj16tJo0aaJRo0Zp0aJFuuuuuzR27Fi1bdtWZ86c0fLly9W7d2916dJFAQEB6tatm6ZMmaIaNWooJCREv/zyixYvXlzq2K/m/aloRb7IyEiNHTtWN9xwg1JTU/XNN9/ovffek6enp2XsiBEjNHXqVCUkJGjWrFmliuWJJ57QvHnz1KtXL02aNEkhISH67rvvFBsbq3/961+V8qFahw4d9Oijj2rIkCHasGGDbrnlFlWrVk3JyclatWqVWrRooX/961/63//+p9jYWPXt21f169eX2WzW4sWLdeLECd1+++2W87Vo0UK//vqrvv32WwUGBsrT0/OSK7J99NFHeu+99/TAAw/o5ptvlre3tw4fPqxZs2Zp+/bteuGFFyzPVG+88YY6duyoTp066V//+pdCQ0OVnZ2tvXv36ttvv7UkMxs0aCB3d3fNnz9fTZs2VfXq1RUUFHTF6Xd79uzR2rVrVVBQoIyMDK1bt06zZ89WVlaW5s2bp+bNm1vG9u/fXy+88IIGDBigp556SmfPntWbb76p/Pz8a/3rKJXmzZvr/vvv17Rp0+To6KiuXbtq+/btmjZtmry9vSv0+aV3796aM2eOmjRpopYtWyohIUGvvvpquU+9LauaNWtq9OjRlv9H3H333Tp8+LAmTpyowMBAnu2uQySlgCt45plnSty/f/9+de7cWUuXLtX48eM1ePBgFRQUKCIiQt9884169+5tGdu1a1d98803ev3113X69GnVqVNHgwYN0rhx4yQVNoNu0KCBYmNjdejQIZlMJtWvX1/Tpk2zJHiuxbRp0yRJU6dO1cmTJ9W1a1f973//u6by1zlz5qhVq1aaPXu25syZI3d3dzVr1kzPPvusZczEiROVnJysRx55RNnZ2QoJCSkxwSep1K9leSlqGu7q6qqaNWuqRYsWeuWVVzRkyBCrB1SpsKT/yJEjevfdd/Xhhx8qPDxcM2fO1MSJE8s9rpJUq1ZNS5cu1ahRo/T000/LZDIpOjpasbGx6tmzZ4WVWjs7O+vbb7/Vf//7Xz322GNycnJSt27d9PPPP6tevXoVcs2r5eDgoG+//VZjxozRyy+/rNzcXHXo0EEff/yx2rVrVyXK0AGgKpo9e7ZcXFw0ZMiQEr/v6+uru+++W59//rllitH69es1fvx4vfzyy8rIyJCfn586duxomT7t6empVatWacKECXr//fc1ceJE1ahRQzfffLNVw/CPPvpI//nPf/TMM88oPz9fffr00YIFC9SmTZtSxX41709FH8aNHz9eMTExys7OVkBAgLp27Wr1AZQk1alTRx07dtSWLVv0wAMPlCoWPz8/rV69WjExMYqJiVFWVpbq16+vqVOnavTo0aU6R3l477331K5dO7333nuKjY1VQUGBgoKC1KFDB0sT9oYNG8rHx0dTp07VkSNH5OLiosaNGxebBvnGG2/o8ccf14ABA3T69Gl17tzZ0iz9Yr169VJKSoqWLFmimTNn6vjx4/L09FTLli310Ucf6cEHH7SMbdasmf744w+9+OKLeu6555SWliYfHx81bNjQ0ldKKuwjFhcXp4kTJyo6Olp5eXkaP368JkyYcNnXoOgZ1MnJSd7e3mrUqJEefvhhPfroo5Ym+EXCwsL09ddf69lnn1W/fv0UGBio0aNH6+jRo5X2fPfhhx8qMDBQs2fP1uuvv64bb7xRn376qe64444KfX5544035OzsrClTpujkyZNq1aqVFi9erOeee67Crnm1/u///k/VqlWzPHs3adJEM2fO1Lhx43i2uw6ZzOWx1BQAoNK99NJLeu6555SYmFhlPt2qKj755BP985//1G+//aaoqCijwwEA2IC0tDSFhIToP//5j6ZOnWp0OLBDq1evVocOHTR//vxSJ0btxf79+9WkSRONHz/e6kNw2D6SUgBgA95++21JhVMW8vLytHTpUr355pvq37+/ZaqavVqwYIGSkpLUokULOTg4aO3atXr11Vd10003WZZcBgDgUg4fPqx9+/bp1Vdf1dKlS7V7926r5tNARYiPj9eaNWvUunVrubu7a/PmzXr55Zfl7e2tLVu2FFud2Z5s3rxZCxYsUFRUlLy8vLRr1y5NnTpVWVlZ2rZtG6vwXWeYvgcANsDDw0Ovv/66Dhw4oJycHNWrV0/PPPNMlSq1Noqnp6cWLlyoyZMn69SpUwoMDNTgwYM1efJko0MDANiAWbNmadKkSQoNDdX8+fNJSKFSeHl56aefftKMGTOUnZ0tX19f9ejRQ1OmTLHrhJRU2Lpiw4YNmj17tk6cOCFvb2/deuut+r//+z8SUtchKqUAAAAAAABQ6WhdDwAAUMXExsYqLCxMbm5uat26tVauXHnZ8e+8846aNm0qd3d3NW7cuNi03ltvvVUmk6nY1qtXL8uYCRMmFPt+QEBAhdwfAACAxPQ9AACAKmXRokUaNWqUYmNj1aFDB7333nvq0aOHduzYUeLKlzNnzlRMTIw++OAD3XzzzVq/fr0eeeQR1ahRQ3369JEkLV68WLm5uZZjMjIyFBERoXvvvdfqXM2bN9fPP/9s+drR0bGC7hIAAIDpewAAAFVKZGSkWrVqpZkzZ1r2NW3aVH379tWUKVOKjY+KilKHDh306quvWvaNGjVKGzZs0KpVq0q8xowZM/TCCy8oOTlZ1apVk1RYKfXVV19p06ZN5XtDAAAAl2B3lVIFBQU6cuSIPD09ZTKZjA4HAAAYyGw2Kzs7W0FBQXJwML6rQW5urhISEjR27Fir/dHR0Vq9enWJx+Tk5BRriuvu7q7169crLy9Pzs7OxY6ZPXu2BgwYYElIFdmzZ4+CgoLk6uqqyMhIvfTSS6pfv/4l483JyVFOTo7l64KCAh07dky1atXiOQsAADtW2mcsu0tKHTlyRMHBwUaHAQAAqpBDhw6pbt26Roeh9PR05efnF1tdyN/fXykpKSUe0717d82aNUt9+/ZVq1atlJCQoLi4OOXl5Sk9PV2BgYFW49evX69t27Zp9uzZVvsjIyM1b948NWrUSKmpqZo8ebKioqK0fft21apVq8RrT5kyRRMnTryGOwYAANezKz1j2V1SytPTU1LhC+Pl5WVwNAAAwEhZWVkKDg62PB9UFRdXGZnN5ktWHj3//PNKSUlRu3btZDab5e/vr8GDB2vq1Kkl9oSaPXu2wsPD1bZtW6v9PXr0sPx3ixYt1L59ezVo0EBz587V6NGjS7x2TEyM1fcyMzNVr149nrMAALBzpX3GsrukVNEDnZeXFw9LAABAUvEkkFF8fX3l6OhYrCoqLS2tWPVUEXd3d8XFxem9995TamqqAgMD9f7778vT01O+vr5WY0+fPq2FCxdq0qRJV4ylWrVqatGihfbs2XPJMa6urnJ1dS22n+csAAAgXfkZy/jmCQAAAJAkubi4qHXr1oqPj7faHx8fr6ioqMse6+zsrLp168rR0VELFy5U7969i/Vw+PTTT5WTk6MHH3zwirHk5ORo586dxab/AQAAlBe7q5QCAACoykaPHq2BAweqTZs2at++vd5//30lJiZq+PDhkgqnzCUlJWnevHmSpN27d2v9+vWKjIzU8ePHNX36dG3btk1z584tdu7Zs2erb9++JfaIevLJJ9WnTx/Vq1dPaWlpmjx5srKysvTQQw9V7A0DAAC7RVIKAACgCunfv78yMjI0adIkJScnKzw8XEuWLFFISIgkKTk5WYmJiZbx+fn5mjZtmnbt2iVnZ2d16dJFq1evVmhoqNV5d+/erVWrVumnn34q8bqHDx/W/fffr/T0dPn5+aldu3Zau3at5boAAADlzWQ2m81GB1GZsrKy5O3trczMTHodAABg53guKF+8ngAAQCr9MwE9pQAAAAAAAFDpSEoBAAAAAACg0hmalFqxYoX69OmjoKAgmUwmffXVV5cdn5ycrAceeECNGzeWg4ODRo0aVSlxAgAAAAAAoHwZmpQ6deqUIiIi9Pbbb5dqfE5Ojvz8/DRu3DhFRERUcHQAAAAAAACoKIauvtejRw/16NGj1ONDQ0P1xhtvSJLi4uIqKiwAAAAAAABUMEOTUpUhJydHOTk5lq+zsrIMjAYAAAAAAACSHTQ6nzJliry9vS1bcHCw0SEBAAAAAADYves+KRUTE6PMzEzLdujQIaNDAgAAAAAAsHvX/fQ9V1dXubq6Gh0GAAAAAAAALnDdV0oBAAAAAACg6jG0UurkyZPau3ev5ev9+/dr06ZNqlmzpurVq6eYmBglJSVp3rx5ljGbNm2yHHv06FFt2rRJLi4uatasWWWHX8zZvHztTs3WybPnFHWDr9HhAAAAAAAAG7MnNVsnzuRVyrUCvNwUXNOjUq5VEkOTUhs2bFCXLl0sX48ePVqS9NBDD2nOnDlKTk5WYmKi1TE33XST5b8TEhL0ySefKCQkRAcOHKiUmC/nYMZp3fn2b/J2d9bm8dFGhwMAAAAAAGxI/I5UPTJvQ6Vdb3jnBhrbo0mlXe9ihialbr31VpnN5kt+f86cOcX2XW680QK83SRJmWfydDYvX27OjgZHBAAAAAAAbMXBjFOSpOquTqrtWfH9sWtWc67wa1zOdd/ovDJ5uTnJ3dlRZ/LylZJ5VqG+1YwOCQAAAAAA2IiiOpzoZv6a3v9GQ2OpDDQ6L0cmk8lSLZWcedbgaAAAAAAAgC0pOJ+VMplMBkdSOUhKlbMAr8KkVGoWSSkAAAAAAFB6BecrpRzsIydFUqq8USkFAAAAAADKwqyiSimDA6kkJKXKmT+VUgAAAAAAoAzMlkop+8hKkZQqZ4HnK6VSqJQCAAAAAABXoaCASilcg6JKqWQqpQAAAAAAwFU4XyhFo3OUTVGlVCqVUgAAAAAA4CoUrb5Ho3OUSVGj86Mnc3Quv8DgaAAAAAAAgK0oWn3PJPvISpGUKme+1V3l6GBSfoFZ6SdzjQ4HAAAAAADYCiqlcC0cHUyq7ekqSUqhrxQAAAAAACglS6UUPaVQVkXNzlmBDwAAAAAAlJZZrL6HaxRgSUqdMTgSAAAAAABgK4oqpRzsJCtFUqoCFDU7T8nKMTgSAAAAAABgK4pW37OPlBRJqQpRlJRKpacUAAAAAAAoraJKKTvpdE5SqgIEnk9KJTN9DwAAAAAAlJKlUso+clIkpSpCUaPzVKbvAQAAAACAUrKsvmcnE/hISlWAgAtW3zOfz3ICAAAAAABcjtnS6NzYOCoLSakKUNRT6kxevrLOnDM4GgAAAAAAYAuKpu+x+h7KzM3ZUT4ezpKkFJqdAwAAAACAq2AnOSmSUhWlaAofzc4BAAAAAEBp/N3o3D6yUiSlKkiQj7skKTmTSikAAAAAAHBllqSUwXFUFpJSFSTIp7BS6sgJKqUAAAAAAMCV/d3o3D7SUiSlKkhRpVQSSSkAAAAAAFAKBay+h/JQ53xSikopAAAAAABQGmZLTymDA6kkJKUqSJAlKUVPKQAAAAAAcGVF0/dodI5r8nej8zMqKKq/AwAAAAAAuIQCKqVQHvw9XeVgkvLyzUo/mWN0OAAAAAAAoIoroNE5yoOTo4MCvApX4KPZOQAAAAAAuBKzCrNSNDrHNaOvFAAAAAAAKC1LTynZR1aKpFQFCmIFPgAAAAAAUEqsvodyU5SUYvoeAAC4GrGxsQoLC5Obm5tat26tlStXXnb8O++8o6ZNm8rd3V2NGzfWvHnzrL4/Z84cmUymYtvZs9bV3Fd7XQAAUL7oKYVyU8ensKcUlVIAAKC0Fi1apFGjRmncuHHauHGjOnXqpB49eigxMbHE8TNnzlRMTIwmTJig7du3a+LEiXr88cf17bffWo3z8vJScnKy1ebm5lbm6wIAgPLH6nsoN5bpe5kkpQAAQOlMnz5dQ4cO1bBhw9S0aVPNmDFDwcHBmjlzZonjP/roIz322GPq37+/6tevrwEDBmjo0KF65ZVXrMaZTCYFBARYbddyXQAAUP7OF0pRKYVrV6cGjc4BAEDp5ebmKiEhQdHR0Vb7o6OjtXr16hKPycnJsap4kiR3d3etX79eeXl5ln0nT55USEiI6tatq969e2vjxo3XdF0AAFD+6CmFclNUKXXsVK7O5OYbHA0AAKjq0tPTlZ+fL39/f6v9/v7+SklJKfGY7t27a9asWUpISJDZbNaGDRsUFxenvLw8paenS5KaNGmiOXPm6JtvvtGCBQvk5uamDh06aM+ePWW+rlSYEMvKyrLaAABA2RUUFP5pspOsFEmpCuTl5ixPVydJTOEDAACld/GDqNlsvuTD6fPPP68ePXqoXbt2cnZ21l133aXBgwdLkhwdHSVJ7dq104MPPqiIiAh16tRJn376qRo1aqS33nqrzNeVpClTpsjb29uyBQcHX+2tAgCAC5jPT+BzsI+cFEmpimZZge84SSkAAHB5vr6+cnR0LFadlJaWVqyKqYi7u7vi4uJ0+vRpHThwQImJiQoNDZWnp6d8fX1LPMbBwUE333yzpVKqLNeVpJiYGGVmZlq2Q4cOXc3tAgCAixStvmeSfWSlDE1KrVixQn369FFQUJBMJpO++uqrKx6zfPlytW7dWm5ubqpfv77efffdig/0GgSxAh8AACglFxcXtW7dWvHx8Vb74+PjFRUVddljnZ2dVbduXTk6OmrhwoXq3bu3HBxKftQzm83atGmTAgMDr+m6rq6u8vLystoAAEDZFfWUspdKKScjL37q1ClFRERoyJAhuueee644fv/+/erZs6ceeeQRffzxx/rtt980YsQI+fn5lep4I1hW4CMpBQAASmH06NEaOHCg2rRpo/bt2+v9999XYmKihg8fLqmwOikpKUnz5s2TJO3evVvr169XZGSkjh8/runTp2vbtm2aO3eu5ZwTJ05Uu3bt1LBhQ2VlZenNN9/Upk2b9M4775T6ugAAoOKdz0nZzep7hialevTooR49epR6/Lvvvqt69eppxowZkqSmTZtqw4YNeu2116p8UuowSSkAAFAK/fv3V0ZGhiZNmqTk5GSFh4dryZIlCgkJkSQlJycrMTHRMj4/P1/Tpk3Trl275OzsrC5dumj16tUKDQ21jDlx4oQeffRRpaSkyNvbWzfddJNWrFihtm3blvq6AACg4hWYLfP37IKhSamrtWbNmmJLFXfv3l2zZ89WXl6enJ2dDYrs0urWOJ+UoqcUAAAopREjRmjEiBElfm/OnDlWXzdt2lQbN2687Plef/11vf7669d0XQAAUPHOp6SolKqKUlJSSlyq+Ny5c0pPT7f0RbhQTk6OcnJyLF9X9lLFdWt4SJIOHztdqdcFAAAAAAC2pcC+CqVsb/W9kpYqLml/EaOXKg6uWVgplZx1VrnnCir12gAAAAAAwHZYGp3bXLambGzqNgMCAkpcqtjJyUm1atUq8Rijlyr2q+4qN2cHmc00OwcAAAAAAJdmb43ObSop1b59+2JLFf/0009q06bNJftJGb1UsclkskzhO3ScKXwAAAAAAKBklkbndsLQpNTJkye1adMmbdq0SZK0f/9+bdq0ybKiTExMjAYNGmQZP3z4cB08eFCjR4/Wzp07FRcXp9mzZ+vJJ580IvxSCz7f7PzQMSqlAAAAAABAyYqSUvZSKWVoo/MNGzaoS5culq9Hjx4tSXrooYc0Z86cYkseh4WFacmSJXriiSf0zjvvKCgoSG+++abuueeeSo/9agTXpFIKAAAAAABcXlGhlJ3kpIxNSt16662WJl4luXjJY0nq3Lmz/vjjjwqMqvwFF03fYwU+AAAAAABwCfSUQrkrWoHv0HGm7wEAAAAAgJKZVTR9z+BAKglJqUpQ1Oj8MJVSAAAAAADgEgosk8nsIytFUqoSFPWUyjiVq1M55wyOBgAAAAAAVEV/Nzo3OJBKQlKqEni7O8vLrbB912Gm8AEAAAAAgBLQUwoVwrICH1P4AAAAAABACYoWg7OTnBRJqcpiWYHvOEkpAAAAAABQXAGVUqgIlhX4jjF9DwAAAAAAFFe0+p6d9DknKVVZLNP3qJQCAAAAAAAlKCgo/JNKKZQry/Q9ekoBAAAAAIASsPoeKkRRpdTh42csjcsAAAAAAAAuZrKT+XskpSpJ3RruMpmkkznndPx0ntHhAAAAAACAKoZKKVQIN2dHBXq5SZIOZJwyOBoAAAAAAFDVFE2sMtFTCuUtpFY1SdKBdJJSAAAAAADAWlGllJ3kpEhKVaZQ38K+UgcyaHYOAAAAAACsFVVKsfoeyl3o+Uqpg0zfAwAAAAAAFylaFs1OclIkpSqTZfoelVIAAAAAAOAiNDpHhbFM36OnFAAAAAAAuMjfPaXsIytFUqoShdQsrJTKPJOnE6dzDY4GAAAAAABUJZbV94wNo9KQlKpE7i6OCvByk8QUPgAAAAAAYI1G56hQIbUKp/DR7BwAAAAAAFzo755SJKVQAYpW4NtPXykAAAAAAHABy/Q9+8hJkZSqbCG+RZVSTN8DAAAAAAB/+7vRucGBVBInowOwN2HnK6UOMH0PAAAAACzMZrPW7jumtOyzRocCGOZMXr4kyWQnrc5JSlWykPNJKSqlAAAAAOBva/7K0AOz1hkdBlAluDiRlEIFKGp0fuxUrjLP5Mnb3dngiAAAAADAeClZhRVS3u7OCq/jZXA0gHEa+XuqgV91o8OoFCSlKlk1Vyf5ebrqaHaODmacUsu6PkaHBAAAAACGKzjf4PnGYB/NfbitscEAqBQ0OjdAGCvwAQAAAIAVs501eAZAUsoQYb4kpQAAAADgQudzUnIgKwXYDZJSBmhQuzAp9ddRklIAAAAAIEkFRZVSBscBoPKQlDJAUcOyv9JOGhwJAAAAAFQN5wulZKJSCrAbJKUMUP98Umpf+kkVFHXzAwAAAAA7VlQp5UBOCrAbJKUMEFzDXc6OJp3NK1Dy+WVPAQAAAMCeFfWUolAKsB8kpQzg5Oig0PMr8DGFDwAAAAD+Xn2PRueA/SApZZD6fkXNzklKAQAAAEABq+8BdoeklEEszc5JSgEAAACApVKK5fcA+0FSyiBFSal9R08ZHAkAAAAAGI9KKcD+kJQySIPaVEoBAAAAQBFW3wPsD0kpgxT1lErNylH22TyDowEAAACAqoGcFGA/SEoZxMvNWX6erpKYwgcAAKzFxsYqLCxMbm5uat26tVauXHnZ8e+8846aNm0qd3d3NW7cWPPmzbP6/gcffKBOnTqpRo0aqlGjhrp166b169dbjZkwYYJMJpPVFhAQUO73BgCXUsDqe4DdMTwpVd4PXbakwflqqX3pTOEDAACFFi1apFGjRmncuHHauHGjOnXqpB49eigxMbHE8TNnzlRMTIwmTJig7du3a+LEiXr88cf17bffWsb8+uuvuv/++7Vs2TKtWbNG9erVU3R0tJKSkqzO1bx5cyUnJ1u2rVu3Vui9AsCFinpKUSoF2A9Dk1IV8dBlSywr8KVRKQUAAApNnz5dQ4cO1bBhw9S0aVPNmDFDwcHBmjlzZonjP/roIz322GPq37+/6tevrwEDBmjo0KF65ZVXLGPmz5+vESNG6MYbb1STJk30wQcfqKCgQL/88ovVuZycnBQQEGDZ/Pz8KvReAeBCZhqdA3bH0KRURTx02ZL655NSe9OolAIAAFJubq4SEhIUHR1ttT86OlqrV68u8ZicnBy5ublZ7XN3d9f69euVl1dy38rTp08rLy9PNWvWtNq/Z88eBQUFKSwsTAMGDNC+ffsuG29OTo6ysrKsNgAoKxqdA/bHsKRUZT10VeWHpYbnV+Dbk5ZtcCQAAKAqSE9PV35+vvz9/a32+/v7KyUlpcRjunfvrlmzZikhIUFms1kbNmxQXFyc8vLylJ6eXuIxY8eOVZ06ddStWzfLvsjISM2bN08//vijPvjgA6WkpCgqKkoZGRmXjHfKlCny9va2bMHBwWW4awCwZmL+HmA3DEtKVdZDV1V+WGrk7ylJOpBxWjnn8g2OBgAAVBWmi6aumM3mYvuKPP/88+rRo4fatWsnZ2dn3XXXXRo8eLAkydHRsdj4qVOnasGCBVq8eLHVh309evTQPffcoxYtWqhbt2767rvvJElz5869ZJwxMTHKzMy0bIcOHbraWwUAi4LzTaUcDO98DKCyGP7PvSIfuqSq/bDk7+UqLzcn5ReYWYEPAADI19dXjo6OxT6gS0tLK/ZBXhF3d3fFxcXp9OnTOnDggBITExUaGipPT0/5+vpajX3ttdf00ksv6aefflLLli0vG0u1atXUokUL7dmz55JjXF1d5eXlZbUBQFkVNTq/1O+DAK4/hiWlKvqhq0hVflgymUyWaqndqUzhAwDA3rm4uKh169aKj4+32h8fH6+oqKjLHuvs7Ky6devK0dFRCxcuVO/eveVwQbnBq6++qhdffFE//PCD2rRpc8VYcnJytHPnTgUGBpbtZgDgKplVmJUiJQXYD8OSUhX50GVLGgWQlAIAAH8bPXq0Zs2apbi4OO3cuVNPPPGEEhMTNXz4cEmFVeCDBg2yjN+9e7c+/vhj7dmzR+vXr9eAAQO0bds2vfTSS5YxU6dO1XPPPae4uDiFhoYqJSVFKSkpOnny78VWnnzySS1fvlz79+/XunXr1K9fP2VlZemhhx6qvJsHYNcKWH0PsDtORl589OjRGjhwoNq0aaP27dvr/fffL/bQlZSUpHnz5kkqfOhav369IiMjdfz4cU2fPl3btm27bK+Dqq7R+Wbnu1NZgQ8AAEj9+/dXRkaGJk2apOTkZIWHh2vJkiUKCQmRJCUnJysxMdEyPj8/X9OmTdOuXbvk7OysLl26aPXq1QoNDbWMiY2NVW5urvr162d1rfHjx2vChAmSpMOHD+v+++9Xenq6/Pz81K5dO61du9ZyXQCoaGZW3wPsjqFJqYp46LI1VEoBAICLjRgxQiNGjCjxe3PmzLH6umnTptq4ceNlz3fgwIErXnPhwoWlDQ8AKoSZnlKA3TE0KSWV/0OXrSnqKZV47LTO5ObL3aXkhu0AAAAAcD0rOJ+VIicF2A/bbMR0HfGt7qpa1VxkNkt705jCBwAAAMA+nS+UkolW54DdIClVBTT0L+wrtYspfAAAAADsVAE9pQC7Q1KqCmh8fgrfHpJSAAAAAOxUUU8pB7JSgN0gKVUFNDyflKJSCgAAAIC9Klp9j5QUYD9ISlUBjQOKKqXoKQUAAADAPhWw+h5gd0hKVQGNahcmpZJOnFHW2TyDowEAAACAykdPKcD+kJSqArw9nBXo7SZJ2pXCFD4AAAAA9sdsqZQyNg4AlYekVBXRLNBLkrTjSJbBkQAAAABA5TNbKqXISgH2gqRUFdH0fFJqZzJJKQAAAAD2x9JTytgwAFQiklJVRLOg85VSJKUAAAAA2CGzzq++R6UUYDdISlURRZVSu1KydS6/wOBoAAAAAKByFVVKMX0PsB8kpaqIkJoe8nBxVM65Au1PP2V0OAAAAABQqWh0DtgfklJVhIODyVItxRQ+AAAAAPbm70bnBgcCoNKQlKpCmgZ6SiIpBQAAAMD+FJjpKQXYG5JSVUizQG9J0o4jJKUAAAAA2Bem7wH2h6RUFVJUKbUzOdvgSAAAAACgctHoHLA/JKWqkCYBXnIwSeknc5SWfdbocAAAAACg0tBTCrA/JKWqEHcXR4X6VpPEFD4AAAAA9uV8oZRMIisF2AuSUlVMs/Mr8G0nKQUAAADAjvzd6NzgQABUGpJSVUzLuoXNzrclZRocCQAAAABUngJLo3OyUoC9IClVxbSo4yNJ2nKYpBQAAAAA+0FPKcD+kJSqYsLrFE7fSzpxRhkncwyOBgAAAAAqh5nV9wC7Q1KqivF0c1Z9v8Jm51uZwgcAAADATphFTynA3pCUqoJa1insK7WVKXwAAAAA7ERBQeGf9JQC7AdJqSqoRV0fSdIWKqUAAAAA2IkCekoBdoekVBVUtAIflVIAAAAA7MX5llIyiawUYC9ISlVBzQK95GCSUrLOKi37rNHhAAAAAECFY/U9wP6QlKqCqrk66Yba1SVJ25jCBwAAAMAOFLD6HmB3SEpVUS3q+EiStjCFDwAAAIAdKKqUYvYeYD9ISlVRRX2lSEoBAAAAsAdUSgH2h6RUFVWUlNp06MTfnxgAAAAAwHXq70bnAOwFSakqqlmQl1wcHXTsVK4Sj502OhwAAAAAqFCWRuf8lgrYDf65V1GuTo4Kr+MlSfoj8bjB0QAAAABAxSqwrL5HrRRgL0hKVWE31ashSfrj4AljAwEAAACACkbXEsD+kJSqwlqdT0ptPESlFAAAAIDrG5VSgP0hKVWF3VTPR5K0Mzlbp3PPGRsMAAAAAFQgVt8D7A9JqSosyMddAV5uyi8wa+vhTKPDAQAAAICKcz4pRU4KsB8kpaq4omqpPxJPGBoHAAAAAFSkv6fvGRwIgEpjeFIqNjZWYWFhcnNzU+vWrbVy5crLjp8/f74iIiLk4eGhwMBADRkyRBkZGZUUbeUr6ivFCnwAAAAArmcFlk7nZKUAe2FoUmrRokUaNWqUxo0bp40bN6pTp07q0aOHEhMTSxy/atUqDRo0SEOHDtX27dv12Wef6ffff9ewYcMqOfLKU1QptTHxhMwsRwEAAADgOlX02w6VUoD9MDQpNX36dA0dOlTDhg1T06ZNNWPGDAUHB2vmzJkljl+7dq1CQ0M1cuRIhYWFqWPHjnrssce0YcOGSo688oTX8Zazo0npJ3N06NgZo8MBAAAAgApBo3PA/hiWlMrNzVVCQoKio6Ot9kdHR2v16tUlHhMVFaXDhw9ryZIlMpvNSk1N1eeff65evXpd8jo5OTnKysqy2myJm7OjWtTxliStP3DM4GgAAAAAoIKcnxlCTgqwH4YlpdLT05Wfny9/f3+r/f7+/kpJSSnxmKioKM2fP1/9+/eXi4uLAgIC5OPjo7feeuuS15kyZYq8vb0tW3BwcLneR2VoG1ZLkrR+//XbOwsAAACAfaNSCrA/hjc6N130Pxyz2VxsX5EdO3Zo5MiReuGFF5SQkKAffvhB+/fv1/Dhwy95/piYGGVmZlq2Q4cOlWv8lSEyrKYkaf1+KqUAALAHV7sQzDvvvKOmTZvK3d1djRs31rx584qN+eKLL9SsWTO5urqqWbNm+vLLL6/5ugBQngqolALsjmFJKV9fXzk6OharikpLSytWPVVkypQp6tChg5566im1bNlS3bt3V2xsrOLi4pScnFziMa6urvLy8rLabE3r0BoymaQDGaeVmnXW6HAAAEAFutqFYGbOnKmYmBhNmDBB27dv18SJE/X444/r22+/tYxZs2aN+vfvr4EDB2rz5s0aOHCg7rvvPq1bt67M1wWA8la0rtOlihQAXH8MS0q5uLiodevWio+Pt9ofHx+vqKioEo85ffq0HBysQ3Z0dJSk63plOi83ZzULLEymUS0FAMD17WoXgvnoo4/02GOPqX///qpfv74GDBigoUOH6pVXXrGMmTFjhm6//XbFxMSoSZMmiomJ0W233aYZM2aU+boAUN6KKqVYfQ+wH05GXnz06NEaOHCg2rRpo/bt2+v9999XYmKiZTpeTEyMkpKSLCXoffr00SOPPKKZM2eqe/fuSk5O1qhRo9S2bVsFBQUZeSsVrm1YTW0/kqX1+4+pT8T1fa8AANirooVgxo4da7X/cgvB5OTkyM3NzWqfu7u71q9fr7y8PDk7O2vNmjV64oknrMZ0797dkpQqy3VRtW05fEJr/qIfKWxL+slcSfSUAuyJoUmp/v37KyMjQ5MmTVJycrLCw8O1ZMkShYSESJKSk5OtSsYHDx6s7Oxsvf322xozZox8fHzUtWtXq08Cr1eRYTX14W8HqJQCAOA6VpaFYLp3765Zs2apb9++atWqlRISEhQXF6e8vDylp6crMDBQKSkplz1nWa4rFSbEcnJyLF/b2irH17OH5/xu+QUfsDVuzo5GhwCgkhialJKkESNGaMSIESV+b86cOcX2/ec//9F//vOfCo6q6rk5tLDZ+a7UbB0/lasa1VwMjggAAFSUq1kI5vnnn1dKSoratWsns9ksf39/DR48WFOnTrW0OSjtOa/mulJhv8+JEyeW6p5QuY6fzpMk9WoRyC/4sCl1a7jrxmAfo8MAUEkMT0qhdGpVd9UNtatrb9pJ/X7gmKKbBxgdEgAAKGdlWQjG3d1dcXFxeu+995SamqrAwEC9//778vT0lK+vryQpICDgsucsy3WlwlYLo0ePtnydlZWl4ODg0t8wKkxRb57xdzZTbU+3K4wGAMAYhjU6x9VrG1ZYLfX7AabwAQBwPSrLQjBFnJ2dVbduXTk6OmrhwoXq3bu3ZYGY9u3bFzvnTz/9ZDlnWa97PaxyfL2yrGImevMAAKouKqVsSGRYTX2yLpG+UgAAXMeudiGY3bt3a/369YqMjNTx48c1ffp0bdu2TXPnzrWc87///a9uueUWvfLKK7rrrrv09ddf6+eff9aqVatKfV3YjgtXpWYVMwBAVUZSyoYUVUptTcpU5pk8ebs7GxwRAAAob1e7EEx+fr6mTZumXbt2ydnZWV26dNHq1asVGhpqGRMVFaWFCxfqueee0/PPP68GDRpo0aJFioyMLPV1YTsK/s5JsYoZAKBKM5kv/CjFDmRlZcnb21uZmZk2WWLe9bVftS/9lN4b2Frd6SsFAMA1sfXngqqG17NqOJdfoBvGfS9J2vTC7fLxYIEcAEDlKu0zAT2lbEzHhoUNS3/bm25wJAAAAKiKLqyUutzqiQAAGI2klI3pcENhUmoVSSkAAKqM0NBQTZo0yWpaHWCUAnpKAQBsBEkpG9Oufi05mKR9R0/pyIkzRocDAAAkjRkzRl9//bXq16+v22+/XQsXLlROTo7RYQFUSgEAqjSSUjbG291ZEcE+kqiWAgCgqvjPf/6jhIQEJSQkqFmzZho5cqQCAwP173//W3/88YfR4cHOUCkFALAVJKVsUMeiKXx7SEoBAFCVRERE6I033lBSUpLGjx+vWbNm6eabb1ZERITi4uJkZ+vLwCBWPaVEVgoAUHWRlLJBRX2lftubroICHm4BAKgq8vLy9Omnn+rOO+/UmDFj1KZNG82aNUv33Xefxo0bp3/+859Ghwg7cGHyk9l7AICqzMnoAHD1WtWrIXdnR2WcytWu1Gw1DWTJZQAAjPTHH3/oww8/1IIFC+To6KiBAwfq9ddfV5MmTSxjoqOjdcsttxgYJezFhZ9ZOpCVAgBUYVRK2SAXJwdF1q8piSl8AABUBTfffLP27NmjmTNn6vDhw3rttdesElKS1KxZMw0YMMCgCGFXLpy+R04KAFCFUSllozre4Ktfdx3Vyr3peuSW+kaHAwCAXdu3b59CQkIuO6ZatWr68MMPKyki2DPrRudkpQAAVReVUjbqlkZ+kqS1+zJ0OvecwdEAAGDf0tLStG7dumL7161bpw0bNhgQEewZq+8BAGwFSSkb1bB2ddXxcVfuuQKt3pthdDgAANi1xx9/XIcOHSq2PykpSY8//rgBEcGeXbgMjolKKQBAFUZSykaZTCZ1bVJbkrR0V5rB0QAAYN927NihVq1aFdt/0003aceOHQZEBHtWVClFPgoAUNWRlLJhRUmpZX+mWS39CwAAKperq6tSU1OL7U9OTpaTEy08UbmKHgvpJwUAqOpIStmw9g1qyc3ZQcmZZ/VnSrbR4QAAYLduv/12xcTEKDMz07LvxIkTevbZZ3X77bcbGBnsUVFSipQUAKCqIyllw9ycHRXVwFeStPRPpvABAGCUadOm6dChQwoJCVGXLl3UpUsXhYWFKSUlRdOmTTM6PNiZoul7VEoBAKo6klI2rssFU/gAAIAx6tSpoy1btmjq1Klq1qyZWrdurTfeeENbt25VcHCw0eHBzliaOpCTAgBUcTQ5sHFdm9TW85L+SDyu46dyVaOai9EhAQBgl6pVq6ZHH33U6DAAFRQUVUoZHAgAAFdAUsrG1fFxV2N/T+1KzdaKPUd11411jA4JAAC7tWPHDiUmJio3N9dq/5133mlQRLBHNDoHANgKklLXgS5NamtXarZ+3plGUgoAAAPs27dPd999t7Zu3SqTyWRZFdd0PimQn59vZHiwM+bzE/hISQEAqroy9ZQ6dOiQDh8+bPl6/fr1GjVqlN5///1yCwylF93cX1JhX6mcczz0AgBQ2f773/8qLCxMqamp8vDw0Pbt27VixQq1adNGv/76q9Hhwc4UUCkFALARZUpKPfDAA1q2bJkkKSUlRbfffrvWr1+vZ599VpMmTSrXAHFlN9b1kb+Xq07mnNPqvRlGhwMAgN1Zs2aNJk2aJD8/Pzk4OMjBwUEdO3bUlClTNHLkSKPDg50psFTqGRwIAABXUKak1LZt29S2bVtJ0qeffqrw8HCtXr1an3zyiebMmVOe8aEUHBxM6t48QJL0w7YUg6MBAMD+5Ofnq3r16pIkX19fHTlyRJIUEhKiXbt2GRka7FBRTykTWSkAQBVXpqRUXl6eXF1dJUk///yzpXlnkyZNlJycXH7RodTuOJ+U+mlHis7lFxgcDQAA9iU8PFxbtmyRJEVGRmrq1Kn67bffNGnSJNWvX9/g6GBvinqasfoeAKCqK1NSqnnz5nr33Xe1cuVKxcfH64477pAkHTlyRLVq1SrXAFE6bcNqqoaHs46fztP6A8eMDgcAALvy3HPPqaCg8EOhyZMn6+DBg+rUqZOWLFmiN9980+DoYG8KqJQCANiIMq2+98orr+juu+/Wq6++qoceekgRERGSpG+++cYyrQ+Vy8nRQbc389enGw7rx20pimrga3RIAADYje7du1v+u379+tqxY4eOHTumGjVqkBhApStafY9KKQBAVVemSqlbb71V6enpSk9PV1xcnGX/o48+qnfffbfcgsPVuSO8cArfj9tTVVD0ERkAAKhQ586dk5OTk7Zt22a1v2bNmiSkYIjzRXv8/AEAqrwyJaXOnDmjnJwc1ahRQ5J08OBBzZgxQ7t27VLt2rXLNUCUXlQDX1V3dVJK1lltPnzC6HAAALALTk5OCgkJUX5+vtGhAJL+rpQiJQUAqOrKlJS66667NG/ePEnSiRMnFBkZqWnTpqlv376aOXNmuQaI0nNzdlSXJoVJwf9toeE8AACV5bnnnlNMTIyOHaOvI4xXtPqeA5VSAIAqrkxJqT/++EOdOnWSJH3++efy9/fXwYMHNW/ePJp5GqxPy0BJ0v+2HFE+U/gAAKgUb775plauXKmgoCA1btxYrVq1stqAylTA6nsAABtRpkbnp0+flqenpyTpp59+0j/+8Q85ODioXbt2OnjwYLkGiKvTubGfvNyclJqVo/X7j6l9A1ZDBACgovXt29foEAALM6vvAQBsRJmSUjfccIO++uor3X333frxxx/1xBNPSJLS0tLk5eVVrgHi6rg6OapHeKAWbTikbzYnkZQCAKASjB8/3ugQAIuiSilyUgCAqq5M0/deeOEFPfnkkwoNDVXbtm3Vvn17SYVVUzfddFO5Boird9eNQZKkJVtTlHuuwOBoAAAAUJkK6CkFALARZaqU6tevnzp27Kjk5GRFRERY9t922226++67yy04lE1k/Vqq7emqtOwcrdh9VN2a+RsdEgAA1zUHB4fLTpViZT5ULiqlAAC2oUyVUpIUEBCgm266SUeOHFFSUpIkqW3btmrSpMlVnSc2NlZhYWFyc3NT69attXLlykuOHTx4sEwmU7GtefPmZb2N65Kjg0m9WxZWS32z+YjB0QAAcP378ssvtXjxYsu2aNEijR07VoGBgXr//feNDg92hkopAICtKFNSqqCgQJMmTZK3t7dCQkJUr149+fj46MUXX1RBQemniy1atEijRo3SuHHjtHHjRnXq1Ek9evRQYmJiiePfeOMNJScnW7ZDhw6pZs2auvfee8tyG9e1O89P4YvfkarTuecMjgYAgOvbXXfdZbX169dP//d//6epU6fqm2++MTo82JmC81kpUlIAgKquTEmpcePG6e2339bLL7+sjRs36o8//tBLL72kt956S88//3ypzzN9+nQNHTpUw4YNU9OmTTVjxgwFBwdr5syZJY739vZWQECAZduwYYOOHz+uIUOGlOU2rmsRdb0VUstDZ/Ly9cO2FKPDAQDALkVGRurnn382OgzYmfOFUkzfAwBUeWVKSs2dO1ezZs3Sv/71L7Vs2VIREREaMWKEPvjgA82ZM6dU58jNzVVCQoKio6Ot9kdHR2v16tWlOsfs2bPVrVs3hYSEXO0tXPdMJpPuaVVXkvTZhsMGRwMAgP05c+aM3nrrLdWtW9foUGBnilbfY/oeAKCqK1Oj82PHjpXYO6pJkyY6duxYqc6Rnp6u/Px8+ftbN+H29/dXSsqVK3uSk5P1/fff65NPPrnsuJycHOXk5Fi+zsrKKlV814N7WtfV6z/v1pp9GUrMOK16tTyMDgkAgOtSjRo1rBqdm81mZWdny8PDQx9//LGBkcEunS+VIicFAKjqypSUioiI0Ntvv60333zTav/bb7+tli1bXtW5Ll6pxmw2X3b1miJz5syRj4+P+vbte9lxU6ZM0cSJE68qputFHR93dbzBVyv3pOvzPw5r9O2NjA4JAIDr0uuvv271/OLg4CA/Pz9FRkaqRo0aBkYGe0SjcwCArShTUmrq1Knq1auXfv75Z7Vv314mk0mrV6/WoUOHtGTJklKdw9fXV46OjsWqotLS0opVT13MbDYrLi5OAwcOlIuLy2XHxsTEaPTo0Zavs7KyFBwcXKoYrwf3tgnWyj3p+iLhsEbd1lAODjycAABQ3gYPHmx0CIBF0fS90nzQCwCAkcrUU6pz587avXu37r77bp04cULHjh3TP/7xD23fvl0ffvhhqc7h4uKi1q1bKz4+3mp/fHy8oqKiLnvs8uXLtXfvXg0dOvSK13F1dZWXl5fVZk+im/nLy81JSSfOaPVfGUaHAwDAdenDDz/UZ599Vmz/Z599prlz5xoQEeyZpdG5oVEAAHBlZUpKSVJQUJD+7//+T1988YUWL16syZMn6/jx41f14DV69GjNmjVLcXFx2rlzp5544gklJiZq+PDhkgqrnAYNGlTsuNmzZysyMlLh4eFlDd9uuDk76q4b60iSPks4ZHA0AABcn15++WX5+voW21+7dm299NJLBkQEe2ZpdF7mJ30AACpHmabvlZf+/fsrIyNDkyZNUnJyssLDw7VkyRLLanrJyclKTEy0OiYzM1NffPGF3njjDSNCtkn3tQnWR2sP6vttKZp4Olc+Hpef8ggAAK7OwYMHFRYWVmx/SEhIsWcZoKKZWX0PAGAjDE1KSdKIESM0YsSIEr83Z86cYvu8vb11+vTpCo7q+hJex0vNAr20IzlLnycc1rBO9Y0OCQCA60rt2rW1ZcsWhYaGWu3fvHmzatWqZUxQsFvmotX3jA0DAIAroqjXDphMJj3YrrD6bP66RBUULckCAADKxYABAzRy5EgtW7ZM+fn5ys/P19KlS/Xf//5XAwYMMDo82JmiRz0anQMAqrqrSkr94x//uOz2xBNPVFScuEZ33RgkT1cn7U8/pd/+Sjc6HAAAriuTJ09WZGSkbrvtNrm7u8vd3V3R0dHq2rVrmXpKxcbGKiwsTG5ubmrdurVWrlx52fHz589XRESEPDw8FBgYqCFDhigj4+8FTm699VaZTKZiW69evSxjJkyYUOz7AQEBVx07jGe2rL5ncCAAAFzBVU3f8/b2vuL3S2pMDuNVc3XSP1rV0dw1B/XRmoPq1NDP6JAAALhuuLi4aNGiRZo8ebI2bdokd3d3tWjRwtIn82osWrRIo0aNUmxsrDp06KD33ntPPXr00I4dO1SvXr1i41etWqVBgwbp9ddfV58+fZSUlKThw4dr2LBh+vLLLyVJixcvVm5uruWYjIwMRURE6N5777U6V/PmzfXzzz9bvnZ0dLzq+GG8okopekoBAKq6q0pKffjhhxUVByrBg+1CNHfNQf28M1XJmWcU6O1udEgAAFxXGjZsqIYNG17TOaZPn66hQ4dq2LBhkqQZM2boxx9/1MyZMzVlypRi49euXavQ0FCNHDlSkhQWFqbHHntMU6dOtYypWbOm1TELFy6Uh4dHsaSUk5MT1VHXgb8bnRscCAAAV0BPKTvS0N9TkWE1VWCWFqxjJSAAAMpLv3799PLLLxfb/+qrrxZL/FxObm6uEhISFB0dbbU/Ojpaq1evLvGYqKgoHT58WEuWLJHZbFZqaqo+//xzq6l5F5s9e7YGDBigatWqWe3fs2ePgoKCFBYWpgEDBmjfvn2XjTcnJ0dZWVlWG4xX1D3URKtzAEAVR1LKzgxsXziN4JP1h5RzLt/gaAAAuD4sX768xCTQHXfcoRUrVpT6POnp6crPz5e/v7/Vfn9/f6WkpJR4TFRUlObPn6/+/fvLxcVFAQEB8vHx0VtvvVXi+PXr12vbtm2WSqwikZGRmjdvnn788Ud98MEHSklJUVRUlFVvqotNmTJF3t7eli04OLjU94qKU0BPKQCAjSApZWe6Nw9QgJeb0k/m6JtNR4wOBwCA68LJkyfl4uJSbL+zs3OZqocuXjXNbDZfciW1HTt2aOTIkXrhhReUkJCgH374Qfv379fw4cNLHD979myFh4erbdu2Vvt79Oihe+65Ry1atFC3bt303XffSZLmzp17yThjYmKUmZlp2Q4dOnQ1t4kKQk8pAICtICllZ5wdHfRQVKgkafaq/ZaeAwAAoOzCw8O1aNGiYvsXLlyoZs2alfo8vr6+cnR0LFYVlZaWVqx6qsiUKVPUoUMHPfXUU2rZsqW6d++u2NhYxcXFKTk52Wrs6dOntXDhwmJVUiWpVq2aWrRooT179lxyjKurq7y8vKw2GI/V9wAAtuKqGp3j+vBA23p6a+ke/ZmSrd/2ZqhjQ1+jQwIAwKY9//zzuueee/TXX3+pa9eukqRffvlFn3zyiT7//PNSn8fFxUWtW7dWfHy87r77bsv++Ph43XXXXSUec/r0aTk5WT/SFa2ad/GHT59++qlycnL04IMPXjGWnJwc7dy5U506dSp1/KgazFRKAQBsBJVSdsjbw1n3tSns+fDByss3MAUAAFd255136quvvtLevXs1YsQIjRkzRklJSVq6dKlCQ0Ov6lyjR4/WrFmzFBcXp507d+qJJ55QYmKiZTpeTEyMBg0aZBnfp08fLV68WDNnztS+ffv022+/aeTIkWrbtq2CgoKszj179mz17dtXtWrVKnbdJ598UsuXL9f+/fu1bt069evXT1lZWXrooYeu/gWBoegpBQCwFVRK2amHO4Rp7poDWr77qHanZquRv6fRIQEAYNN69eplaXZ+4sQJzZ8/X6NGjdLmzZuVn1/6xUX69++vjIwMTZo0ScnJyQoPD9eSJUsUElK4WElycrISE/9eRXfw4MHKzs7W22+/rTFjxsjHx0ddu3bVK6+8YnXe3bt3a9WqVfrpp59KvO7hw4d1//33Kz09XX5+fmrXrp3Wrl1ruS5sR1Gl1KX6kAEAUFWYzHbWVCgrK0ve3t7KzMy0+74Hwz9K0A/bU3Rfm7qa2i/C6HAAAKh05f1csHTpUsXFxWnx4sUKCQnRPffco3vuuUc33XRTOURb9fGcVTV8tuGQnvp8i25t7Kc5Q9pe+QAAAMpZaZ8JmL5nxx65pb4k6cuNSTpy4ozB0QAAYJsOHz6syZMnq379+rr//vtVo0YN5eXl6YsvvtDkyZPtJiGFqqPoE2fqpAAAVR1JKTvWOqSG2tevpbx8s95fQW8pAACuVs+ePdWsWTPt2LFDb731lo4cOaK33nrL6LBg54omQtDoHABQ1ZGUsnP/6XqDJGnB+kSlZZ81OBoAAGzLTz/9pGHDhmnixInq1auXZdU7wEgF9JQCANgIklJ2rn2DWmpVz0c55wo0e+V+o8MBAMCmrFy5UtnZ2WrTpo0iIyP19ttv6+jRo0aHBTv3d6NzY+MAAOBKSErZOZPJpP90bShJ+mjtQR0/lWtwRAAA2I727dvrgw8+UHJysh577DEtXLhQderUUUFBgeLj45WdnW10iLBDBZbpewYHAgDAFZCUgm5t7KfmQV46nZuvD3+jWgoAgKvl4eGhhx9+WKtWrdLWrVs1ZswYvfzyy6pdu7buvPNOo8ODnaGnFADAVpCUwvlqqcLeUh+uPqDM03kGRwQAgO1q3Lixpk6dqsOHD2vBggVGhwM7ZFl9j5wUAKCKIykFSVJ0swA1CfBU9tlzenfFX0aHAwCAzXN0dFTfvn31zTffGB0K7EzB+U7nNDoHAFR1JKUgSXJwMGlMdGNJ0oe/7VdaFivxAQAA2CLL6nvGhgEAwBWRlIJFt6a11aqej87mFejtZXuNDgcAAABlUDR9j55SAICqzsnoAFB1mEwmPdW9ie7/YK0WrE/UI53qK7imh9FhAQAAlMqWwyf05cYkmc1XHns9234kUxKr7wEAqj6SUrDSvkEtdWroq5V70vV6/G5N73+j0SEBAACUysRvdyjh4HGjw6gyPN2cjQ4BAIDLIimFYp7q3lgr96Try01JerRzfTUJ8DI6JAAAgCs6lXNOknRnRJDq2Xm1t6uTg+67OdjoMAAAuCySUiimZV0f9QgP0PfbUjT5fzv10dC2rN4CAACqvKJpe/e1CVbHhr7GBgMAAK6IRuco0dgeTeTi6KBVe9O19M80o8MBAAAoNT5LAwDANpCUQolCalXTkI6hkqT/+26ncs8VGBsQAADAFZjPrztHTgoAANtAUgqX9O8uN8i3uov2pZ/SR2sPGh0OAADAZdn7qnsAANgaklK4JE83Z42JbixJeuPn3Tp2KtfgiAAAAC7NkpOiVAoAAJtAUgqXdV+bYDUJ8FTW2XOa9tMuo8MBAAC4JLO5aPoeWSkAAGwBSSlclqODSRPubC5J+mR9ojYdOmFsQAAAAFdAo3MAAGwDSSlcUbv6tfSPVnVkNkvjvtyqc/k0PQcAAFVP0fQ9clIAANgGklIolWd7NpW3u7O2H8nSvDU0PQcAAFUQjc4BALApJKVQKr7VXTW2RxNJ0rSfdikl86zBEQEAAFizVEoxfw8AAJtAUgql1r9NsFrV89Gp3HxN/Ha70eEAAABYsTQ6JycFAIBNICmFUnNwMGly3xZydDDp+20p+n5rstEhAQAAFENOCgAA20BSClelWZCXRtzaQJL0/NfbdOxUrsERAQAAFPp7+p6hYQAAgFIyPCkVGxursLAwubm5qXXr1lq5cuVlx+fk5GjcuHEKCQmRq6urGjRooLi4uEqKFpL07643qJF/daWfzNWEb5jGBwAAqgazpdE5WSkAAGyBoUmpRYsWadSoURo3bpw2btyoTp06qUePHkpMTLzkMffdd59++eUXzZ49W7t27dKCBQvUpEmTSowark6Oeu3eCDk6mPTN5iP6cXuK0SEBAADIzPJ7AADYFEOTUtOnT9fQoUM1bNgwNW3aVDNmzFBwcLBmzpxZ4vgffvhBy5cv15IlS9StWzeFhoaqbdu2ioqKquTI0bKujx67pb4kadyXTOMDAADGK6qUYvoeAAC2wbCkVG5urhISEhQdHW21Pzo6WqtXry7xmG+++UZt2rTR1KlTVadOHTVq1EhPPvmkzpw5Uxkh4yL/7dZQDWtXV/rJHD3zxRbLijcAAABGsCSljA0DAACUkmFJqfT0dOXn58vf399qv7+/v1JSSp4Otm/fPq1atUrbtm3Tl19+qRkzZujzzz/X448/fsnr5OTkKCsry2pD+XB1ctSMATfKxdFB8TtS9cn6S0+7BAAAqCwmSqUAALAJhjc6v/ihwWw2X/JBoqCgQCaTSfPnz1fbtm3Vs2dPTZ8+XXPmzLlktdSUKVPk7e1t2YKDg8v9HuxZ8yBvPX1HY0nSi//bob1p2QZHBAAA7B0pKQAAbINhSSlfX185OjoWq4pKS0srVj1VJDAwUHXq1JG3t7dlX9OmTWU2m3X48OESj4mJiVFmZqZlO3ToUPndBCRJD3cIU6eGvjqbV6CRCzYp51y+0SEBAAA7RCsBAABsi2FJKRcXF7Vu3Vrx8fFW++Pj4y/ZuLxDhw46cuSITp48adm3e/duOTg4qG7duiUe4+rqKi8vL6sN5cvBwaRp90aoZjUX7UjO0qs/7DI6JAAAYIeKUlLM3gMAwDYYOn1v9OjRmjVrluLi4rRz50498cQTSkxM1PDhwyUVVjkNGjTIMv6BBx5QrVq1NGTIEO3YsUMrVqzQU089pYcfflju7u5G3QYk1fZy0yv3tJQkzVq1X/E7Ug2OCAAA2Ju/G52TlQIAwBYYmpTq37+/ZsyYoUmTJunGG2/UihUrtGTJEoWEhEiSkpOTlZj4d/Ps6tWrKz4+XidOnFCbNm30z3/+U3369NGbb75p1C3gArc389fDHcIkSaM/3aSDGacMjggAANgjKqUAALANJrOdTb7PysqSt7e3MjMzmcpXAfLyCzTg/bVKOHhcTQO99OWIKLk5OxodFgAAJeK5oHwZ/XpGvvSzUrNy9L//dFR4He8rHwAAACpEaZ8JDF99D9cXZ0cHvfNAK9Wq5qKdyVl6/qttRocEAADshGX6HpVSAADYBJJSKHcB3m566/6b5GCSPks4rAXrE698EAAAwDWyq/J/AACuAySlUCGibvDVmOjGkqQXvt6m9fuPGRwRAAC43tHoHAAA20JSChXmX50bqGeLAOXlmzX84wQdOnba6JAAAIAdYPoeAAC2gaQUKoyDg0nT7r1R4XW8dOxUrobN3aCTOeeMDgsAAFy3CkulSEoBAGAbSEqhQrm7OOqDQW1U29NVu1KzNWrhRuUX0PEBAACUP6bvAQBgW0hKocIFervr/UFt5OrkoJ93pun/vtsps5nEFAAAKF88XQAAYFtISqFS3Bjso1fvjZAkxf22Xx+s3GdwRAAAVF2xsbEKCwuTm5ubWrdurZUrV152/Pz58xURESEPDw8FBgZqyJAhysjIsHx/zpw5MplMxbazZ89e03WrmqIPvZi+BwCAbSAphUpzZ0SQnu3ZRJL00pI/9dXGJIMjAgCg6lm0aJFGjRqlcePGaePGjerUqZN69OihxMTEEsevWrVKgwYN0tChQ7V9+3Z99tln+v333zVs2DCrcV5eXkpOTrba3NzcynzdqqioUoqcFAAAtoGkFCrVI53qa2jHMEnSU59v1qo96QZHBABA1TJ9+nQNHTpUw4YNU9OmTTVjxgwFBwdr5syZJY5fu3atQkNDNXLkSIWFhaljx4567LHHtGHDBqtxJpNJAQEBVtu1XLcqo1IKAADbQFIKlcpkMmlcz6bqExGkvHyzHvtog7YlZRodFgAAVUJubq4SEhIUHR1ttT86OlqrV68u8ZioqCgdPnxYS5YskdlsVmpqqj7//HP16tXLatzJkycVEhKiunXrqnfv3tq4ceM1XVeScnJylJWVZbUZ6e+WlWSlAACwBSSlUOkcHEx67d6Wal+/lk7l5mtQ3HrtSc02OiwAAAyXnp6u/Px8+fv7W+339/dXSkpKicdERUVp/vz56t+/v1xcXBQQECAfHx+99dZbljFNmjTRnDlz9M0332jBggVyc3NThw4dtGfPnjJfV5KmTJkib29vyxYcHFzWWy8X9JQCAMC2kJSCIVydHPXeoNZqUcdbx07l6oFZ67Q//ZTRYQEAUCWYLsqqmM3mYvuK7NixQyNHjtQLL7yghIQE/fDDD9q/f7+GDx9uGdOuXTs9+OCDioiIUKdOnfTpp5+qUaNGVomrq72uJMXExCgzM9OyHTp06GpvtVyx+h4AALaFpBQM4+XmrHkPt1WTAE8dzc7RPz9Yq0PHThsdFgAAhvH19ZWjo2Ox6qS0tLRiVUxFpkyZog4dOuipp55Sy5Yt1b17d8XGxiouLk7JycklHuPg4KCbb77ZUilVlutKkqurq7y8vKw2Q53PSlEoBQCAbSApBUPVqOaij4dFqoFfNR3JPKsHZq1VcuYZo8MCAMAQLi4uat26teLj4632x8fHKyoqqsRjTp8+LQcH60c6R0dHSX9PZ7uY2WzWpk2bFBgYWObrVmWXq+4CAABVB0kpGM63uqs+eaSdQmp56NCxM3rgg3U6coLEFADAPo0ePVqzZs1SXFycdu7cqSeeeEKJiYmW6XgxMTEaNGiQZXyfPn20ePFizZw5U/v27dNvv/2mkSNHqm3btgoKCpIkTZw4UT/++KP27dunTZs2aejQodq0aZPVFL8rXdcWFKXgSEkBAGAbnIwOAJAkfy83ffJIO/V/b432p5/Sfe+t0YJH2im4pofRoQEAUKn69++vjIwMTZo0ScnJyQoPD9eSJUsUEhIiSUpOTlZiYqJl/ODBg5Wdna23335bY8aMkY+Pj7p27apXXnnFMubEiRN69NFHlZKSIm9vb910001asWKF2rZtW+rr2gIanQMAYFtM5kvVdV+nsrKy5O3trczMTOP7HqCYpBNn9M8P1upAxmkFertp/rBI1ferbnRYAIDrFM8F5cvo17PZCz/odG6+lj91q0JqVav06wMAgEKlfSZg+h6qlDo+7vr0sfa6oXZ1JWee1X3vrdXu1GyjwwIAADbAbGl0TqkUAAC2gKQUqpzaXm5a+Gg7NQnwVPrJHPV/b402HTphdFgAAMBGMH0PAADbQFIKVZJvdVctfLSdIup66/jpPN3//lot25VmdFgAAKAKM8uuulIAAGDzSEqhyvLxcNH8R9qpU0NfncnL17C5G/R5wmGjwwIAAFWUZfoelVIAANgEklKo0qq7Omn2Qzfr7pvqKL/ArCc/26x3lu2VnfXnBwAApVD0dGAiKwUAgE0gKYUqz8XJQdPujdBjnetLkl79cZde+Hq7zuUXGBwZAACoUvjMCgAAm0JSCjbBwcGkmB5N9XzvZpKkj9Ye1JA5vyvzTJ7BkQEAgKqGOikAAGwDSSnYlKEdw/Tug63k7uyolXvSdXfsbzqQfsrosAAAQBVQ1Oic2XsAANgGklKwOXeEB+qz4e0V6O2mfUdP6a53ftPqv9KNDgsAABjM0uicWikAAGwCSSnYpPA63vr68Q6KCPZR5pk8DZq9Xh+tOUADdAAA7Njfjc4NDQMAAJQSSSnYrNpeblr0aDv1iQjSuQKznv96u0Z/ullncvONDg0AABiAD6cAALAtJKVg09ycHfXmgBv1bM8mcnQw6cuNSbo79jftp88UAAB2x1IpZWgUAACgtEhKweaZTCY9eksDzR8WKd/qrvozJVt3vrVKP21PMTo0AABgBLJSAADYBJJSuG60q19L343sqDYhNZSdc06PfpSgKUt2KvdcgdGhAQCASkCjcwAAbAtJKVxX/L3ctODRdnq4Q5gk6b0V+9Tv3dU6wHQ+AADsBo3OAQCwDSSlcN1xdnTQC32a6d0HW8vb3VlbDmeq15srtfiPw0aHBgAAKsiFTc7JSQEAYBtISuG6dUd4gL7/bydFhtXUqdx8jf50s0Yt3Kjss3lGhwYAAMoZC+8BAGB7SErhuhbk465PHmmnMbc3kqODSV9tOqIeb6zU6r/SjQ4NAABUEBPz9wAAsAkkpXDdc3Qw6T+3NdSnj7VX3RruOnz8jB74YJ0mfLNdp3PPGR0eAAAoBxcWSpGSAgDANpCUgt1oHVJDP4y6Rf+MrCdJmrP6gHq8sVLr9x8zODIAAHCtrHpKkZUCAMAmkJSCXanu6qT/u7uFPhraVkHebjqYcVr931+jF/+3Q2dy840ODwAAlJF1pRRZKQAAbIHhSanY2FiFhYXJzc1NrVu31sqVKy859tdff5XJZCq2/fnnn5UYMa4HnRr66YcnbtF9berKbJZmr9qv7jNWaMXuo0aHBgAAyoBG5wAA2B5Dk1KLFi3SqFGjNG7cOG3cuFGdOnVSjx49lJiYeNnjdu3apeTkZMvWsGHDSooY1xMvN2dN7RehDwffrEBvNyUeO61Bcev134UbdTQ7x+jwAABAWVEoBQCATTA0KTV9+nQNHTpUw4YNU9OmTTVjxgwFBwdr5syZlz2udu3aCggIsGyOjo6VFDGuR12a1Fb86M4a0iFUDibp601HdNu0X7VgfaIKCvjYFQAAW2AWPaUAALA1hiWlcnNzlZCQoOjoaKv90dHRWr169WWPvemmmxQYGKjbbrtNy5Ytu+zYnJwcZWVlWW3Axaq7Oml8n+b66vEOah7kpayz5xSzeKv6v79GO47wMwMAQFV34fQ9clIAANgGw5JS6enpys/Pl7+/v9V+f39/paSklHhMYGCg3n//fX3xxRdavHixGjdurNtuu00rVqy45HWmTJkib29vyxYcHFyu94HrS8u6Pvr68Q56rldTebg46vcDx9X7rZV67qutOn4q1+jwAABAKZgolQIAwCY4GR3AxQ8NZrP5kg8SjRs3VuPGjS1ft2/fXocOHdJrr72mW265pcRjYmJiNHr0aMvXWVlZJKZwWU6ODhrWqb56tAjUS0t26rstyfp4baK+3ZysJ6Mb6f629eTkaPgaAQAA4AJUSgEAYHsM+83a19dXjo6Oxaqi0tLSilVPXU67du20Z8+eS37f1dVVXl5eVhtQGnV83PXOA6204JF2ahLgqcwzeXr+6+3q/dYqrfkrw+jwAADABS7sKQUAAGyDYUkpFxcXtW7dWvHx8Vb74+PjFRUVVerzbNy4UYGBgeUdHmDRvkEt/e8/HfXiXc3l4+GsP1Oydf8Ha/XIvA3am5ZtdHgAAOAizN4DAMA2GDp9b/To0Ro4cKDatGmj9u3b6/3331diYqKGDx8uqXDqXVJSkubNmydJmjFjhkJDQ9W8eXPl5ubq448/1hdffKEvvvjCyNuAHXBydNDA9qHq3TJI0+N365P1iYrfkapfdqaq/83BGtWtkfy93IwOEwAAu2U9fY+sFAAAtsDQpFT//v2VkZGhSZMmKTk5WeHh4VqyZIlCQkIkScnJyUpMTLSMz83N1ZNPPqmkpCS5u7urefPm+u6779SzZ0+jbgF2pkY1F73YN1wPRYVq6g9/6qcdqVqw/pC+3JikYR3r67HO9eXp5mx0mAAA2J0LJ+9RKQUAgG0wmc1mu5qAn5WVJW9vb2VmZtJfCtdsw4FjmvL9n0o4eFySVLOai/7d5QY9EFlPbs6OBkcHALgSngvKl5GvZ/bZPLWY8JMk6c8X7+B9GAAAA5X2mYAlxIBr0Ca0pj4f3l7vDWyt+n7VdOxUrib9b4c6v7pM89YcUM65fKNDBADALtjVp6wAAFwnSEoB18hkMql78wD9NOoWTflHCwV5uyk1K0cvfL1dt776qz5ee1C55wqMDhMAALvB9D0AAGwDSSmgnDg5Ouj+tvW07Klb9WLfcAV4uSk586ye+2qburz2qz5Zl0hyCgCACkKjcwAAbA9JKaCcuTo5amC7EP361K2aeGdz+Xu5KunEGT375VZ1ee1Xzfltv87kMq0PAIBydWFSipwUAAA2gaQUUEHcnB31UFSolj/VReP7NJOfZ2FyasK3O9ThlaV665c9yjydZ3SYAABcF8wXZKXISQEAYBtISgEVzM3ZUUM6hGnl0130Yt9wBdd017FTuZoWv1tRL/+il5bsVGrWWaPDBADApllN36NUCgAAm0BSCqgkbs6F0/qWjblVbwy4UU0CPHUqN1/vr9inTq8s09gvtmh3arbRYQIAAAAAUCmcjA4AsDdOjg6668Y6ujMiSMt2pSl22V/acPC4Fv5+SAt/P6RODX31cMcwdW7oJwcHPukFAKA0LiiUYvoeAAA2gqQUYBCTyaSuTfzVtYm/fj9wTLNX7tdPO1K0ck+6Vu5JV32/ahrSIUz3tKojDxf+qQIAcDnmC+bvMXsPAADbwG+6QBVwc2hN3RxaU4eOndac1Qe06PdD2nf0lJ7/apte/eFP3R9ZTw9Ghii4pofRoQIAUCVZVUqRlQIAwCbQUwqoQoJreuj53s20Jqarxvdppno1PZR19pzeW75Pt7y6TA/P+V1L/0xVfoH5yicDAMCOmHlrBADA5lApBVRBnm7OGtIhTIPah2rpn2mas3q/ftuboaV/pmnpn2mq4+OuByLr6b42wfLzdDU6XAAAAAAArhqVUkAV5uhg0u3N/DV/WDv9MqazhnUMk7e7s5JOnNGrP+5S1Mu/6PFP/tCavzKsemkAAGxbbGyswsLC5ObmptatW2vlypWXHT9//nxFRETIw8NDgYGBGjJkiDIyMizf/+CDD9SpUyfVqFFDNWrUULdu3bR+/Xqrc0yYMEEmk8lqCwgIqJD7qwjm8xP4mLkHAIDtICkF2IgGftX1XO9mWvfsbZp2b4RuquejvHyzvtuSrPs/WKuu05brnWV7lZJ51uhQAQDXYNGiRRo1apTGjRunjRs3qlOnTurRo4cSExNLHL9q1SoNGjRIQ4cO1fbt2/XZZ5/p999/17Bhwyxjfv31V91///1atmyZ1qxZo3r16ik6OlpJSUlW52revLmSk5Mt29atWyv0XsvV+c9myEkBAGA7TGY7K6/IysqSt7e3MjMz5eXlZXQ4wDXZfiRT89cl6uuNSTqVmy9JcjBJnRr66b42werWrLZcnRwNjhIAqq6q+FwQGRmpVq1aaebMmZZ9TZs2Vd++fTVlypRi41977TXNnDlTf/31l2XfW2+9palTp+rQoUMlXiM/P181atTQ22+/rUGDBkkqrJT66quvtGnTpjLHbuTrmZp1VpEv/SJHB5P+eqlnpV4bAABYK+0zAZVSgA1rHuStl+5uofXjuunVfi3VNqymCszS8t1H9fgnfyjypV804Zvt2paUaXSoAIBSyM3NVUJCgqKjo632R0dHa/Xq1SUeExUVpcOHD2vJkiUym81KTU3V559/rl69el3yOqdPn1ZeXp5q1qxptX/Pnj0KCgpSWFiYBgwYoH379l37TVUSM5VSAADYHBqdA9eBaq5OurdNsO5tE6wD6af0ecJhfZ5wWClZZzVn9QHNWX1ATQI81femOrozIkhBPu5GhwwAKEF6erry8/Pl7+9vtd/f318pKSklHhMVFaX58+erf//+Onv2rM6dO6c777xTb7311iWvM3bsWNWpU0fdunWz7IuMjNS8efPUqFEjpaamavLkyYqKitL27dtVq1atEs+Tk5OjnJwcy9dZWVlXc7vlqqinFAAAsB1USgHXmVDfanqye2P9Nrar5j7cVr1bBsrF0UF/pmTr5e//VIdXlqr/e2u0YH2iTpzONTpcAEAJTBd16zabzcX2FdmxY4dGjhypF154QQkJCfrhhx+0f/9+DR8+vMTxU6dO1YIFC7R48WK5ublZ9vfo0UP33HOPWrRooW7duum7776TJM2dO/eScU6ZMkXe3t6WLTg4+GpvtdzR6BwAANtBpRRwnXJ0MKlzIz91buSnE6dztWRrir7elKR1+49Zthe+3qZbG9dW3xvr6LamteXmTP8pADCSr6+vHB0di1VFpaWlFaueKjJlyhR16NBBTz31lCSpZcuWqlatmjp16qTJkycrMDDQMva1117TSy+9pJ9//lktW7a8bCzVqlVTixYttGfPnkuOiYmJ0ejRoy1fZ2VlGZaY+nv6HlkpAABsBUkpwA74eLjogch6eiCyno6cOKNvNh/RVxuT9GdKtuJ3pCp+R6qquzopupm/erYIVKdGvjRIBwADuLi4qHXr1oqPj9fdd99t2R8fH6+77rqrxGNOnz4tJyfrRzpHx8L/h1+4ns2rr76qyZMn68cff1SbNm2uGEtOTo527typTp06XXKMq6urXF1dr3iuymC5U3JSAADYDJJSgJ0J8nHX8M4NNLxzA+1KydbXm5L09aYjSjpxRos3JmnxxiRVd3VSt6a11aNFoDo38qOCCgAq0ejRozVw4EC1adNG7du31/vvv6/ExETLdLyYmBglJSVp3rx5kqQ+ffrokUce0cyZM9W9e3clJydr1KhRatu2rYKCgiQVTtl7/vnn9cknnyg0NNRSiVW9enVVr15dkvTkk0+qT58+qlevntLS0jR58mRlZWXpoYceMuBVuHpFCThyUgAA2A6SUoAdaxzgqafvaKInoxsrIfG4vtuSrO+3JSs1K0dfbTqirzYdUTUXR3Vt6q9eLQLUuVFtubuQoAKAitS/f39lZGRo0qRJSk5OVnh4uJYsWaKQkBBJUnJyshITEy3jBw8erOzsbL399tsaM2aMfHx81LVrV73yyiuWMbGxscrNzVW/fv2srjV+/HhNmDBBknT48GHdf//9Sk9Pl5+fn9q1a6e1a9darlvVWabvkZUCAMBmmMwX1nXbgaysLHl7eyszM1NeXl5GhwNUOQUFZm08dFxLtqbo+63JOpJ51vI9d2dHdW1SW93DA3RrYz95uTkbGCkAXDueC8qXka/noWOn1WnqMrk5O+jPF3tU6rUBAIC10j4TUCkFwIqDg0mtQ2qqdUhNjevZVJsPn9CSrclasjVFSSfO6Lutyfpua7KcHU1qV7+WujX1V7dm/qrj42506AAA0OgcAAAbQlIKwCU5OJh0U70auqleDT3bs6m2JmXqu63Jit+Rqn1HT2nlnnSt3JOu8d9sV7NAL3Vr5q/oZv5qHuR1yaXLAQCoCEzfAwDA9pCUAlAqJpNJLev6qGVdH8X0aKq/jp7ULzsLV+5LOHhcO5KztCM5S2/+skeB3m6WCqrIsJo0SgcAVDizaHQOAICtISkFoEwa+FVXA7/qevSWBso4maOlf6bp552pWrE7XcmZZ/XR2oP6aO1BuTk7qH39Wrq1cW3d2thPIbWqGR06AOA69HelFGkpAABsBUkpANesVnVX3dsmWPe2CdbZvHyt/itd8TtStezPo0rJOqtlu45q2a6jkqQw32rq3MhPtzb2U7v6taiiAgAAAAA7RVIKQLlyc3ZU1yb+6trEX2azWX+mZGv57qP6dVeaNhw4rv3pp7Q//ZTmrD4gVycHtW9QS7c28tMtjfwU5luNT7gBAGVStJw07yIAANgOklIAKozJZFLTQC81DfTS8M4NlH02T7/tzdDy3Wn6dddRJWee1a+7jurX81VUdXzc1eGGWupwg6+iGvjKz9PV4DsAANgKs2X+nrFxAACA0iMpBaDSeLo5647wAN0RHiCz2azdqSf1667CBFXCweNKOnFGn244rE83HJYkNQnwVIcbfNXxBl+1Daupaq78LwsAUDIqpQAAsD38hgfAECaTSY0DPNU4wFOPdW6g07nn9PuB41q9N12r9qZr+5Es/ZmSrT9TsjV71X45OZjUql4NRd1QSx1v8FVEsI+cHR2Mvg0AQBVBo3MAAGwPSSkAVYKHi5M6N/JT50Z+kqSMkzlasy9Dv+1N18o96Tp8/IzWHzim9QeOacbPe+Th4qjWITUUGVZTkfVrqWVdb7k60TQdAOxXYVaKnBQAALaDpBSAKqlWdVf1bhmk3i2DJEmJGae1am+6fvsrXav3puv46Tyt3FOYsJIkVycHtapXQ+3q11Jk/Zq6MdiHlf0AAAAAoAojKQXAJtSr5aEHatXTA5H1VFBg1u60bK3bd0zr9mdo3b5jyjiVqzX7MrRmX4YkycXJQTcG+6jd+UqqVvVqyN2FJBUAXK/ocw4AgO0hKQXA5jg4mNQkwEtNArz0UFSozGaz/jp6Umv3HdO6/ce0bl+G0rJztH7/Ma3ff0xaulfOjiY1D/JWm5Aaah1SQ61Da6i2p5vRtwIAKCeWRufM3wMAwGaQlAJg80wmk26o7akbanvqwXYhMpvNOpBxWuv2ZWjtvgyt239MyZlntenQCW06dEKzVu2XJAXXdFebkJqFSaqQGmrk7ylHB36ZAQBbRKUUAAC2h6QUgOuOyWRSmG81hflW04C29WQ2m3X4+BklHDyuDQePacOB49qVmq1Dx87o0LEkfbkxSZLk6eqkm0JqqHW9GmoTWkMRwT6q7sr/JgHAFphpdA4AgM0x/Let2NhYvfrqq0pOTlbz5s01Y8YMderU6YrH/fbbb+rcubPCw8O1adOmig8UgM0ymUwKrumh4Joe6ntTHUlS9tk8bUw8oQ0Hj+uPg8e1MfG4snPOacXuo1qx+6gkycEkNfL31E31fHRjsI8ign3UsDbVVAAAAABQHgxNSi1atEijRo1SbGysOnTooPfee089evTQjh07VK9evUsel5mZqUGDBum2225TampqJUYM4Hrh6easWxr56ZZGfpKkc/kF+jMlW38kHteGA8eVcPC4kk6c0Z8p2fozJVsL1h+SJHm4OKpFHW/dWM9HN9b10Y31fBTg5UYPEwAwWNH0PSbwAQBgO0xm899v4ZUtMjJSrVq10syZMy37mjZtqr59+2rKlCmXPG7AgAFq2LChHB0d9dVXX11VpVRWVpa8vb2VmZkpLy+vawkfwHUuJfOsNh06rk2HMrXp0HFtPZypU7n5xcbV9nS1VFLdFOyjFnW95enmbEDEAK4WzwXly8jXc8eRLPV8c6X8PF31+7hulXptAABgrbTPBIZVSuXm5iohIUFjx4612h8dHa3Vq1df8rgPP/xQf/31lz7++GNNnjz5itfJyclRTk6O5eusrKyyBw3ArgR4u+kO70DdER4oScovMGtv2kltPnRCG883Td+dmq207Bz9tCNVP+0orNw0maQb/KqrRR1vNa/jrRZ1vNUsyIv+VABQgSw9pQyOAwAAlJ5hvyGlp6crPz9f/v7+Vvv9/f2VkpJS4jF79uzR2LFjtXLlSjk5lS70KVOmaOLEidccLwA4OpjUOMBTjQM8dd/NwZKk07nntC0pS5vPJ6k2HTqhpBNntCftpPakndTi803UTSYpzLeaWpxPUjUP8lbzOl7yoqIKAMqFZfU9slIAANgMwz+2v7gPi9lsLrE3S35+vh544AFNnDhRjRo1KvX5Y2JiNHr0aMvXWVlZCg4OLnvAAHABDxcntQ2rqbZhNS370rLPauvhTG1NytS2pCxtS8pUStZZ7Tt6SvuOntLXm45Yxob5VlPzIC+rZJW3B4kqACgrE7VSAADYDMOSUr6+vnJ0dCxWFZWWllasekqSsrOztWHDBm3cuFH//ve/JUkFBQUym81ycnLSTz/9pK5duxY7ztXVVa6urhVzEwBQgtqebrqtqZtua/r3/8uOZudo25FMbTucWfhnUpaSTpzR/vRT2p9+Sv/bkmwZW6+mh5oHealpYNHmqTo+7jRTBwAAAHBdMSwp5eLiotatWys+Pl533323ZX98fLzuuuuuYuO9vLy0detWq32xsbFaunSpPv/8c4WFhVV4zABQVn6erurSuLa6NK5t2ZdxMkfbj2Sdr6gqTFYdOnZGicdOK/HYaX2/7e+kvZebkyVJ1ez8nw39q8vN2dGI2wGAKofpewAA2B5Dp++NHj1aAwcOVJs2bdS+fXu9//77SkxM1PDhwyUVTr1LSkrSvHnz5ODgoPDwcKvja9euLTc3t2L7AcAW1Kruqlsa+emWRn6WfSdO52pbUpZ2JhduO5KztDftpLLOntO6/ce0bv8xy1hHB5Pq+1YrTFQF/V1VVdvTzYjbAQBD0egcAADbY2hSqn///srIyNCkSZOUnJys8PBwLVmyRCEhIZKk5ORkJSYmGhkiAFQqHw8XdWzoq44NfS37cs7la2/aSe1MzrYkq3YmZ+n46TxLQ/VvNv/dp8q3uouaBnqpkb+nGvt7qlGApxrWrq5qrP4H4Dr2d6UUaSkAAGyFyWwuegu3D1lZWfL29lZmZqa8vLyMDgcAysRsNis1K8dSTbXjfKJqf/opXer/6nVruFuSVI39PdXI31P1/aoxBRB2jeeC8mXk67n50And9c5vquPjrt/GFu8zCgAAKk9pnwn42BwAbJDJZFKAt5sCvN3UpcnffarO5OZrV2q2/kzO0u7Uk9qdmq1dqdk6mp2jw8fP6PDxM/rlzzTLeAeTFOpbzZKkahxQ+GdoLQ85OToYcWsAUCZ29SkrAADXCZJSAHAdcXdx1I3BProx2Mdq/7FTudqdmq0955NUu1NOaldqtjLP5Gnf0VPad/SUVWN1F0cH1ferpkb+nrqhdnXLFlLLQ65OVFYBqHqKiv+ZvQcAgO0gKQUAdqBmNRe1q19L7erXsuwzm81Ky84prKZKyT5fVXVSe1KzdTo3X3+mZOvPlGyr8zg6mFSvpoca+FW3SlY18KsmTzfnyr4tALAoqpQiKQUAgO0gKQUAdspkMsnfy03+Xm7q1PDvFQALCsxKOnFGu1OztTv1pPamndTeoyf1V9pJncw5p/3pp7Q//ZR+3plqdT5/L9fCJJVfUaKq8E8/T1caDwOocJZG56y/BwCAzSApBQCw4uBgUnBNDwXX9NBtTf0t+4sqq/amnbRsfx0t/DMtO0epWYXbb3szrM7n6eZkSVaF+VVTfd9qCvMtnApIk3UA5YfpewAA2BqSUgCAUrmwsqrDDb5W38s88//t3Xl0VOX9x/HPZJvsk4SQDUIC2h6WSBFQSlCxFgVBFHtOjR5kqa09saIgdWvValUMUGtRW3A5Vi3SQlvQWn/WY1BMi6QGWRSNFmVLCAkhJExCVpJ5fn8ErowJyDIzNwPv1zk5JPc+c5fvJPHrJ8+995AVUG07PKvqy+qDKqttUkNLuzaVHdCmsgNf256U4YrSgN4x6p/81ceA5Fj1SYxSaAj/Zwng5PGbAwCA4EEoBQA4ba6ocA3vl6jh/RK9lrcc6tDO/Y3aVt2oL6sPauf+Rm2vadT2fQfV0NKuigPNqjjQrP98UeP1uojQEPXrFX04pDoqtOodo96xXA4IoCvD4/cAAAg6hFIAAL+JDA/VwLR4DUyL91pujFFtY5t21HSGVDtqGrVj3+F/9zeqrd1jXSL4dbHOMCukyk6OUXavaGX1ila/pBglx0YQWAFnqa9udM7vAAAAggWhFAAg4BwOh3rFOtUr1qmR2Ule6zo8RpXuZuuG6tuPhFU1jdpd16SDre3aUuHWlgp3l+3GRISqX68YZSVFKys5WllJMco6HFqlu7gkEDiTfXWjcwAAECwIpQAAPUpoiEN9E6PVNzHa66mAktTa3qHy2iavoGrX/iaV1TZpj7tZjW0d+qyyXp9V1nfZbnioQ5mJ0YdDqhj1S4pWdnLnDKvMpCg5w7jpOhDMDKkUAABBh1AKABA0nGGhOjclTuemxHVZ1xlYNaustjOo6vxo1K7aJpXXNulQh+m8n1VNo6R9Xq89ctP1fklfhVaZSVHKTOx8CmFidDiXBAFBgp9UAACCB6EUAOCM0BlYxerclNgu645cEmiFVbWN2lXTpF21TSrb36jGtg7rpuvF2/d3eX2sM0x9E6PUNzHaK6w68nmMk/+cAnbjPucAAAQfumgAwBnv6EsCx5zrvc4Yo5qDbdYMq537O4Oqstomldc1a19Dqw62tuvzqgZ9XtXQ7faTYiKUmRilvknRhwOrr4KrjIRILg0EAsC6eo9ZjQAABA1CKQDAWc3hcKh3nFO945wakZXUZX3LoQ7trusMqHYfDqrKa5tUXtek8tpmuZsPqbaxTbWNbfpod9ebrzscUmpcpBVUdQZXUcpMilafhCiluSIVHhoSiFMFzmjm8FwpIikAAIIHoRQAAMcRGX7s+1hJUn3Loc6Qqra5M7z6WnDVcsijqvoWVdW3aP3Oui6vD3FIqfGR6pMQpT6JUcpIiLI+75vQ+TWXBwInwJopZe9hAACAE0eXCwDAaYiPDNeQDJeGZLi6rDtyaWD54bBq91Fh1e66ZlUeaFFbh0eV7hZVulv04a6uoZUkJUSHdwZVh0OqvolRXiFWr5gILlkCDnMwVwoAgKBBKAUAgJ8cfWng8H6JXdZ7PEY1B1u1+0CzKuqatefwzdYr6pqtG683tLTrQNMhHWg6pE/31He7n8jwkK9mWB010+pIiMUlgjgbHLnROfksAADBg1AKAACbhIQ4lBIfqZT4yG5DK6nz8sBjBVYVdc2qbmhVyyGPtu9r1PZ9jd1uw+GQesc6lZ4QpQxXpNJckcpwdYZVGQmRSndFKSXOqTCCKwQxw+P3AAAIOoRSAAD0YPGR4YpPD9eg9Phu17e2d6jK3aKKuuauM64OfHWJYHVDq6obWvVReff7CXFIKXGRSk+IVLqrM6iy/j28LCUuUqEhTENBz2REKgUAQLAhlAIAIIg5w0KV1StGWb1iul3v8Rjtb2xTpbu5895VB5qte1hVupu150CL9ta3qN1jrBuybzrGvkJDHEqNcyrNFXnUrKujZl8lRCk51klw5QOLFy/Wb37zG1VWVmrIkCFatGiRLr744mOOX7ZsmRYuXKgvvvhCLpdLEyZM0OOPP65evXpZY1auXKkHHnhA27Zt0znnnKN58+bp2muvPa399iTGutE5338AAAQLQikAAM5gISFf3ddqaN/uxxy5t9Ued4uqDgdVVoh1OMja29CqDo/RHneL9rhbpLID3W4rLMSh1PhIpcZ3hlep8Z2zrFLjI5UWH2ktiwwP9d9JB7kVK1Zozpw5Wrx4scaMGaNnn31WV155pUpLS9WvX78u49euXavp06frd7/7nSZPnqyKigrl5+frJz/5iV599VVJUnFxsfLy8vTII4/o2muv1auvvqrrrrtOa9eu1ahRo05pvz2NdU8pW48CAACcDIcxZ9cV+PX19XK5XHK73YqP7/5SCAAA4K3DY7SvoVV73M2qcrdoz+EZV1XuFu1xd14mWN3QIs8JdhUJ0eFKi/9aaOWKtJaluSKVGB3u91kvPbEvGDVqlIYPH64lS5ZYywYNGqQpU6aooKCgy/jHH39cS5Ys0bZt26xlTz/9tBYuXKjy8s7rNfPy8lRfX69//etf1pgJEyYoMTFRf/nLX05pv92xs55FW/dpxh9LNCQjXv93e3DM7gIA4Ex1oj0BM6UAAMA3Cg1xdIZGrshjjmk/fO+qSnfnJYFVR/49/PmRf1vbPdYTBT+vajjm9iLCQjpnXMVHquAHQ3VuSqw/Tq1HaWtr04YNG3Tvvfd6Lb/iiiu0bt26bl+Tm5ur++67T2+++aauvPJKVVdX6+9//7smTZpkjSkuLtYdd9zh9brx48dr0aJFp7xfSWptbVVra6v1dX1990+I9IVfrPr4mE+glKSGlna/7RsAAPgHoRQAAPCJsNAQZSREKSMh6phjjDFyNx+yAqrO8KpVVfXeQdb+xja1tXtUXtus8tpmhYeeHRdl1dTUqKOjQ6mpqV7LU1NTVVVV1e1rcnNztWzZMuXl5amlpUXt7e26+uqr9fTTT1tjqqqqjrvNU9mvJBUUFOjXv/71SZ3jqdq2r1Ef73Z/47jjff8BAICehVAKAAAEjMPhUEJ0hBKiIzQw7dhTuVvbO1Rd32rNtDreDK0z0dcvWzTGHPNSxtLSUt1+++361a9+pfHjx6uyslJ33XWX8vPz9cILL5zUNk9mv5L0i1/8QnPnzrW+rq+vV2Zm5vFP7hTdM2Gg3M1txx0T4nDoguwkv+wfAAD4HqEUAADocZxhocpMilZmUrTdhxJQycnJCg0N7TI7qbq6ussspiMKCgo0ZswY3XXXXZKkoUOHKiYmRhdffLEeffRRpaenKy0t7bjbPJX9SpLT6ZTT6Tzp8zwVI7ISA7IfAAAQOCF2HwAAAAA6RUREaMSIESosLPRaXlhYqNzc3G5f09TUpJAQ75YuNLTz6YZHnmczevToLtt8++23rW2eyn4BAABOFzOlAAAAepC5c+dq2rRpGjlypEaPHq3nnntOZWVlys/Pl9R5yVxFRYX+9Kc/SZImT56sm2++WUuWLLEu35szZ44uvPBCZWRkSJJmz56tSy65RAsWLNA111yjf/zjH1q9erXWrl17wvsFAADwNUIpAACAHiQvL0/79+/Xww8/rMrKSuXk5OjNN99UVlaWJKmyslJlZWXW+JkzZ6qhoUG///3v9fOf/1wJCQm67LLLtGDBAmtMbm6uli9frvvvv18PPPCAzjnnHK1YsUKjRo064f0CAAD4msMcmdd9lqivr5fL5ZLb7VZ8/LFvsAoAAM589AW+RT0BAIB04j0B95QCAAAAAABAwBFKAQAAAAAAIOAIpQAAAAAAABBwhFIAAAAAAAAIOEIpAAAAAAAABByhFAAAAAAAAAKOUAoAAAAAAAABRygFAAAAAACAgCOUAgAAAAAAQMARSgEAAAAAACDgCKUAAAAAAAAQcGF2H0CgGWMkSfX19TYfCQAAsNuRfuBIf4DTQ58FAACkE++xzrpQqqGhQZKUmZlp85EAAICeoqGhQS6Xy+7DCHr0WQAA4Gjf1GM5zFn2p0GPx6M9e/YoLi5ODofD59uvr69XZmamysvLFR8f7/Pto3vU3R7U3R7U3R7U3T7+rL0xRg0NDcrIyFBICHc1OF3+7LP4GbQHdbcPtbcHdbcHdbdHT+ixzrqZUiEhIerbt6/f9xMfH88Pkw2ouz2ouz2ouz2ou338VXtmSPlOIPosfgbtQd3tQ+3tQd3tQd3tYWePxZ8EAQAAAAAAEHCEUgAAAAAAAAg4QikfczqdevDBB+V0Ou0+lLMKdbcHdbcHdbcHdbcPtYfE94FdqLt9qL09qLs9qLs9ekLdz7obnQMAAAAAAMB+zJQCAAAAAABAwBFKAQAAAAAAIOAIpQAAAAAAABBwhFI+tHjxYvXv31+RkZEaMWKE/vOf/9h9SEGtoKBAF1xwgeLi4pSSkqIpU6bof//7n9cYY4weeughZWRkKCoqSpdeeqk+/fRTrzGtra267bbblJycrJiYGF199dXavXt3IE8lqBUUFMjhcGjOnDnWMuruHxUVFbrxxhvVq1cvRUdHa9iwYdqwYYO1nrr7Xnt7u+6//371799fUVFRGjBggB5++GF5PB5rDHU/ff/+9781efJkZWRkyOFw6LXXXvNa76sa19XVadq0aXK5XHK5XJo2bZoOHDjg57NDoNBn+Q49Vs9AjxU49Fj2oM8KjKDvswx8Yvny5SY8PNw8//zzprS01MyePdvExMSYXbt22X1oQWv8+PHmxRdfNJ988onZvHmzmTRpkunXr585ePCgNWb+/PkmLi7OrFy50mzZssXk5eWZ9PR0U19fb43Jz883ffr0MYWFhWbjxo3me9/7nvnOd75j2tvb7TitoFJSUmKys7PN0KFDzezZs63l1N33amtrTVZWlpk5c6b54IMPzI4dO8zq1avNl19+aY2h7r736KOPml69epk33njD7Nixw/ztb38zsbGxZtGiRdYY6n763nzzTXPfffeZlStXGknm1Vdf9VrvqxpPmDDB5OTkmHXr1pl169aZnJwcc9VVVwXqNOFH9Fm+RY9lP3qswKHHsg99VmAEe59FKOUjF154ocnPz/daNnDgQHPvvffadERnnurqaiPJFBUVGWOM8Xg8Ji0tzcyfP98a09LSYlwul3nmmWeMMcYcOHDAhIeHm+XLl1tjKioqTEhIiHnrrbcCewJBpqGhwXzrW98yhYWFZuzYsVbDRN3945577jEXXXTRMddTd/+YNGmSuemmm7yW/eAHPzA33nijMYa6+8PXmyVf1bi0tNRIMv/973+tMcXFxUaS+fzzz/18VvA3+iz/oscKLHqswKLHsg99VuAFY5/F5Xs+0NbWpg0bNuiKK67wWn7FFVdo3bp1Nh3VmcftdkuSkpKSJEk7duxQVVWVV92dTqfGjh1r1X3Dhg06dOiQ15iMjAzl5OTw3nyDW2+9VZMmTdK4ceO8llN3/3j99dc1cuRI/fCHP1RKSorOP/98Pf/889Z66u4fF110kd555x1t3bpVkvTRRx9p7dq1mjhxoiTqHgi+qnFxcbFcLpdGjRpljfnud78rl8vF+xDk6LP8jx4rsOixAoseyz70WfYLhj4r7LReDUlSTU2NOjo6lJqa6rU8NTVVVVVVNh3VmcU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      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert to JAX arrays\n",
    "X_train = jnp.array(X_train)\n",
    "X_test = jnp.array(X_test)\n",
    "y_train = jnp.array(y_train)\n",
    "y_test = jnp.array(y_test)\n",
    "\n",
    "# Initialize the weights\n",
    "def initialize_weights(n_features, n_classes):\n",
    "    weights = jnp.zeros((n_features, n_classes))\n",
    "    bias = jnp.zeros(n_classes)\n",
    "    return weights, bias\n",
    "\n",
    "# Compute the softmax function\n",
    "def softmax(z):\n",
    "    exp_z = jnp.exp(z - jnp.max(z, axis=1, keepdims=True))\n",
    "    return exp_z / jnp.sum(exp_z, axis=1, keepdims=True)\n",
    "\n",
    "# Compute the model predictions\n",
    "def predict(X, weights, bias):\n",
    "    linear_output = jnp.dot(X, weights) + bias\n",
    "    return softmax(linear_output)\n",
    "\n",
    "def cross_entropy_loss(weights, bias, X, y, n_classes):\n",
    "    predictions = predict(X, weights, bias)\n",
    "    y_one_hot = jnp.eye(n_classes)[y]\n",
    "    return -jnp.mean(jnp.sum(y_one_hot * jnp.log(predictions + 1e-15), axis=1))\n",
    "\n",
    "def accuracy(weights, bias, X, y):\n",
    "    predictions = predict(X, weights, bias)\n",
    "    predicted_classes = jnp.argmax(predictions, axis=1)\n",
    "    return jnp.mean(predicted_classes == y)\n",
    "\n",
    "def update(weights, bias, X, y, learning_rate, n_classes):\n",
    "    loss_grad_weights = grad(cross_entropy_loss, argnums=0)(weights, bias, X, y, n_classes)\n",
    "    loss_grad_bias = grad(cross_entropy_loss, argnums=1)(weights, bias, X, y, n_classes)\n",
    "    weights -= learning_rate * loss_grad_weights\n",
    "    bias -= learning_rate * loss_grad_bias\n",
    "    return weights, bias\n",
    "\n",
    "update = jit(update, static_argnums=(5,))\n",
    "\n",
    "def train(X_train, y_train, X_test, y_test, learning_rate, num_iterations, n_classes):\n",
    "    n_features = X_train.shape[1]\n",
    "    weights, bias = initialize_weights(n_features, n_classes)\n",
    "    losses = []\n",
    "    accuracies = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        weights, bias = update(weights, bias, X_train, y_train, learning_rate, n_classes)\n",
    "        \n",
    "        # Compute loss\n",
    "        loss = cross_entropy_loss(weights, bias, X_train, y_train, n_classes)\n",
    "        losses.append(loss)\n",
    "        \n",
    "        # Compute accuracy on the test set\n",
    "        acc = accuracy(weights, bias, X_test, y_test)\n",
    "        accuracies.append(acc)\n",
    "        \n",
    "        if i % 100 == 0:\n",
    "            print(f\"Iteration {i}: Loss = {loss}, Accuracy = {acc * 100:.2f}%\")\n",
    "    \n",
    "    return weights, bias, losses, accuracies\n",
    "\n",
    "# Define model parameters\n",
    "learning_rate = 0.01\n",
    "num_iterations = 1000\n",
    "n_classes = len(jnp.unique(y_train))\n",
    "\n",
    "# Train the model\n",
    "weights, bias, losses, accuracies = train(X_train, y_train, X_test, y_test, learning_rate, num_iterations, n_classes)\n",
    "\n",
    "# Plot the loss function\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(losses)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss Function During Training')\n",
    "\n",
    "# Plot the accuracy on the test set\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(accuracies)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.title('Accuracy on Test Set During Training')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "scardapane_alice",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}