{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b246b6ac",
   "metadata": {},
   "source": [
    "## A.I. Assignment 4\n",
    "\n",
    "## Learning Goals\n",
    "\n",
    "By the end of this lab, you should be able to:\n",
    "* Get familiar with tensors in pytorch\n",
    "* Get familiar with the activation functions for ANN \n",
    "* Create a simple perceptron model with pytorch\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8247d8bb",
   "metadata": {},
   "source": [
    "## Common activation functions for ANN:\n",
    "\n",
    "##### Sigmoid:\n",
    "\n",
    "The sigmoid function is a popular choice for activation functions in neural networks. It has an $S-shaped$ curve:\n",
    "$$f(x) = \\frac{1}{1+e^{-x}}.$$\n",
    "\n",
    "It has a number of appealing qualities:\n",
    "\n",
    "1. *Nonlinearity*: Because the sigmoid function is nonlinear, it enables the neural network to simulate nonlinear interactions between inputs and outputs. A neural network would simply be a linear model without a nonlinear activation function like sigmoid, which would significantly restrict its capacity to describe complex relationships.\n",
    "\n",
    "1. *Smoothness*: As the sigmoid function is differentiable and smooth, its derivative exist at every point. This is significant because it makes it possible for neural network training techniques based on gradients (such as backpropagation) to perform well.\n",
    "\n",
    "1. *Boundedness*: The sigmoid function is bounded between 0 and 1, it means  its outputs can be interpreted as probabilities.  It is most useful in applications like binary classification, where the goal is to predict whether an input belongs to one of two classes.\n",
    "\n",
    "1. *Monotonicity*: The sigmoid function is monotonic, which means that its outputs are always increasing or always decreasing with respect to its inputs. This makes it easy to interpret the effect of changes in input variables on the output of the network.\n",
    "\n",
    "##### ReLU (Rectified Linear Unit):\n",
    "\n",
    "The ReLU function is defined as $$f(x) = max(0, x).$$\n",
    "\n",
    "It is a widely used activation function in deep learning due to its simplicity and effectiveness.\n",
    "\n",
    "##### Tanh (Hyperbolic Tangent):\n",
    "\n",
    "The $\\tanh$ function is similar to the sigmoid function but produces outputs in the interval $[-1, 1]$:  \n",
    "$$f(x) = \\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}.$$\n",
    "\n",
    "##### Softmax:\n",
    "\n",
    "The softmax function is commonly used in the output layer of a neural network for multi-class classification problems. It normalizes the output into a probability distribution over the classes.\n",
    "\n",
    "Given a vector $\\vec{z}$ of $n$ real numbers, the softmax function calculates a vector $\\vec{s}$ of $n$ real numbers with the components:\n",
    "$$s_j = \\frac{e^{z_j}}{\\sum_{k=1}^{n} {e^{z_k}}}.$$\n",
    "\n",
    "\n",
    "##### Leaky ReLU:\n",
    "\n",
    "The Leaky ReLU is a variation of the ReLU function that introduces a small non-zero gradient for negative inputs. It is defined as \n",
    "$$f(x) = max(0.01 \\cdot x, x).$$\n",
    "\n",
    "##### ELU (Exponential Linear Unit):\n",
    "\n",
    "The ELU function is another variation of the ReLU function that introduces a small negative saturation value for negative inputs. It is defined as \n",
    "\n",
    "$$ f(x) = \\biggl\\{ \\begin{matrix} x, & for & x > 0 \\\\\n",
    "                      \\alpha \\cdot (e^{x} - 1), & for & x \\leq 0 \\end{matrix}$$\n",
    "where $\\alpha$ is a hyperparameter.\n",
    "\n",
    "##### Swish:\n",
    "\n",
    "The Swish function is a recent activation function that is a smooth approximation of the ReLU function. It is defined as f(x) = x * sigmoid(x)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "68931328",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "torch.cuda.is_available()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93017ce5",
   "metadata": {},
   "source": [
    "create a tensor with requires_grad=True to tell PyTorch to track gradients for this tensor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a14b6a39",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([2.], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([2.0], requires_grad=True)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56340210",
   "metadata": {},
   "source": [
    "You can perform any operations on this tensor as usual:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "99cb5a71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([9.], grad_fn=<AddBackward0>)\n"
     ]
    }
   ],
   "source": [
    "y = x ** 2 + 2 * x + 1\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af8a18dc",
   "metadata": {},
   "source": [
    "To compute the gradients of y with respect to x, you need to call backward() on y:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8c244acf",
   "metadata": {},
   "outputs": [],
   "source": [
    "y.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0e9b7e33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([6.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "87ce525b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([1., 1., 1.])\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "# Create a tensor with requires_grad=True\n",
    "x = torch.tensor([1., 2., 3.], requires_grad=True)\n",
    "\n",
    "# Compute a function of x\n",
    "y = x.sum()\n",
    "\n",
    "# Compute gradients of y with respect to x\n",
    "y.backward()\n",
    "\n",
    "# Print gradients of x\n",
    "print(x.grad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30804b8c",
   "metadata": {},
   "source": [
    "Exercise 1.\n",
    "\n",
    "Compute the gradient for the sigmoid activation function in 2 points using pytorch and check it with the known explicit formula "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2dc94902",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0.1966, 0.1050])\n",
      "tensor([0.1966, 0.1050])\n",
      "tensor([0.1966, 0.1050], grad_fn=<DivBackward0>)\n"
     ]
    }
   ],
   "source": [
    "# your code here\n",
    "import torch\n",
    "\n",
    "x = torch.tensor([1.0, 2.0], requires_grad=True)\n",
    "y = 1 / (1 + torch.exp(-x))\n",
    "y.backward(torch.ones_like(x))\n",
    "print(x.grad)\n",
    "\n",
    "x_2 = torch.tensor([1.0, 2.0], requires_grad=True)\n",
    "y_2 = torch.sigmoid(x_2)\n",
    "y_2.backward(torch.ones_like(x_2))\n",
    "print(x_2.grad)\n",
    "\n",
    "x_3 = torch.tensor([1.0, 2.0], requires_grad=True)\n",
    "y_3 = torch.exp(-x_3) / ((torch.exp(-x_3) + 1 ) ** 2)\n",
    "print(y_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e77a45c",
   "metadata": {},
   "source": [
    "Exercise 2.\n",
    "\n",
    "Compute the gradient for the linear activation function in 2 points using pytorch and check it with the known explicit formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7054039e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([1., 1.])\n",
      "tensor([1., 1.])\n"
     ]
    }
   ],
   "source": [
    "# your code here\n",
    "import torch\n",
    "\n",
    "x = torch.tensor([1.0, 2.0], requires_grad=True)\n",
    "y = x\n",
    "y.backward(torch.ones_like(x))\n",
    "print(x.grad)\n",
    "\n",
    "\n",
    "x_3 = torch.tensor([1.0, 2.0], requires_grad=True)\n",
    "y_3 = torch.tensor([1.0, 1.0])\n",
    "print(y_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dab117e3",
   "metadata": {},
   "source": [
    "Execise 3.\n",
    "\n",
    "Compute the gradient for the relu activation function in 2 points using pytorch and check it with the known explicit formula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1f69f4c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0., 1.])\n",
      "tensor([-1.,  2.])\n",
      "tensor([0., 1.])\n"
     ]
    }
   ],
   "source": [
    "# your code here\n",
    "\n",
    "x = torch.tensor([-1.0, 2.0], requires_grad=True)\n",
    "y = torch.max(torch.tensor(0),x)\n",
    "y.backward(torch.ones_like(x))\n",
    "print(x.grad)\n",
    "\n",
    "\n",
    "x_2 = torch.tensor([-1.0, 2.0], requires_grad=True)\n",
    "y_2 = torch.relu(x_2)\n",
    "y_2.backward(torch.ones_like(x_2))\n",
    "print(x_2.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef985f68",
   "metadata": {},
   "source": [
    "Exercise 4. \n",
    "\n",
    "Write in python a function to plot the sigmoid activation function and its gradient using matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6c645aaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code here\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def plot_sigmoid_and_gradient():\n",
    "    x = np.linspace(-10, 10, 100)\n",
    "    x_tensor = torch.tensor(x, requires_grad=True)\n",
    "    sig = torch.sigmoid(x_tensor)\n",
    "    sig.backward(torch.ones_like(x_tensor))\n",
    "    sig_grad = x_tensor.grad\n",
    "\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    \n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(x, sig.detach().numpy(), label='Sigmoid', color='blue')\n",
    "    plt.title('Sigmoid Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('Sigmoid(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(x, sig_grad, label='Sigmoid Derivative', color='red')\n",
    "    plt.title('Gradient of Sigmoid Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('Sigmoid\\'(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "plot_sigmoid_and_gradient()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51202a51",
   "metadata": {},
   "source": [
    "Exercise 5. \n",
    "\n",
    "Write in python a function to plot the ReLU activation function and its gradient using matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "99e49c47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code here\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def plot_relu_and_gradient():\n",
    "    x = np.linspace(-10, 10, 100)\n",
    "    x_tensor = torch.tensor(x, requires_grad=True)\n",
    "    sig = torch.relu(x_tensor)\n",
    "    sig.backward(torch.ones_like(x_tensor))\n",
    "    sig_grad = x_tensor.grad\n",
    "\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    \n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(x, sig.detach().numpy(), label='ReLU', color='blue')\n",
    "    plt.title('ReLU Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('ReLU(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(x, sig_grad, label='ReLU Derivative', color='red')\n",
    "    plt.title('Gradient of ReLU Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('ReLU\\'(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "plot_relu_and_gradient()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c81684ff",
   "metadata": {},
   "source": [
    "Exercise 6. \n",
    "\n",
    "Write in python a function to plot the tanh activation function and its gradient using matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "559d421d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code here\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def plot_tanh_and_gradient():\n",
    "    x = np.linspace(-10, 10, 100)\n",
    "    x_tensor = torch.tensor(x, requires_grad=True)\n",
    "    sig = torch.tanh(x_tensor)\n",
    "    sig.backward(torch.ones_like(x_tensor))\n",
    "    sig_grad = x_tensor.grad\n",
    "\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    \n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(x, sig.detach().numpy(), label='Tanh', color='blue')\n",
    "    plt.title('Tanh Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('tanh(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(x, sig_grad, label='Tanh Derivative', color='red')\n",
    "    plt.title('Gradient of Tanh Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('tanh\\'(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "plot_tanh_and_gradient()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8740a0a8",
   "metadata": {},
   "source": [
    "Exercise 7. \n",
    "\n",
    "Write in python a function to plot the leaky ReLU activation function and its gradient using matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7b455646",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jR8Le3t7gGk0IIXr27Ck8PDyEWq02+RppvddVqlQxuMbRMVWX16tXTxQpUsTg+jIxMVFUrVpVlChRQr9f3XsxatQog30uWrRIABCRkZGpHQ4hxJv/j5Q/xYsXTzU2HQBi1qxZRvt6W91+7NgxAUD4+fmlGZslHi9LxRZvyhZxcXH45Zdf0KVLFzg5ORl8O9euXTvExcXht99+02+/fft2NGzYEPny5YOdnR2USiXWr1+PK1euGO375s2bqF+/PqKjo/Hbb7+hRo0aBo+PHz8eFy5cwIkTJwBou9p9/fXXGDhwIPLly/fW2GNiYqBUKqFUKlGoUCF8/PHH6NWrFwICAvTbHDhwAImJiRgwYIBB2RwcHNC0aVMpM0i/fPkS3333HRo0aKCf6Ktp06YoW7YsNm7cCI1GA0A7lu769euZ/vbdlGrVqqF27doGrTBXrlzB6dOnMWTIEINtM/Jep8fVq1dx79499O/fHzY2bz7S8uXLh27duuG3334zGnrQqVMng7+rV6+OuLg4PHjw4K2v5+joiDNnzhj8rF+/PlOxKxQKdOzY0SiW27dv6//+6aef4ODgYHQcMyunjxdRbla7dm19faFUKrF06VKjbbp162a07sGDBxg5ciRKliyp/xwsXbo0AOg/C2NiYnDmzBl07drV4LNa1zr0Nj/88AOqVq2KmjVrGtRTrVu3NtlFvHnz5nBxcdH/7eHhgSJFihh8HmVEZj5rzOWHH35A8+bN4enpaVD2tm3bAtC2uukcOnQI77//Ptzc3GBrawulUomZM2fi8ePHRp9xjx8/RosWLXD69Gl9d9nkxo8fjwcPHmD79u0AtN10g4OD0b59+3TPxF20aFEolUoUKFAAPXv2RO3atbFp0yb94ydPnsSTJ08wcOBAg7JpNBq0adMGZ86cMRpKkN2EEPru5a1atQKgHY7QrFkzg95wsbGxOHr0KHr27InChQub5bULFiyIjh07YtOmTfrrnKdPn2LPnj0YMGAA7OzeTGeVkfc6PWJiYvD777+je/fuBteXtra26N+/P+7cuYOrV68aPMdUfQog3efZwYMHDa4/9u/fn+G404oled3+008/AUCme4umJON4WRom3pQtHj9+jMTERCxfvtzgokSpVKJdu3YAoB/LtmvXLvTs2RPFixfHN998g1OnTuHMmTMYMmSIyfFQp0+fxj///INevXqhRIkSRo937twZXl5e+q5rGzduRExMTLo/OJInVvv27UOzZs2wZcsWLFiwQL+Nrkt23bp1jcq3bdu2VG8dZoquUkitu1BiYqJBxZGabdu24eXLl+jZsyeePXuGZ8+e4fnz5+jZsyf+++8/hIWFAdDOHgvA5LHLiiFDhuDUqVP4+++/AQAhISFQqVTo3bu3fpuMvtfp8fjxYwAw2QXU09MTGo0GT58+NVhfsGBBg79VKhUA4NWrV299PRsbG9SpU8fgp0KFCpmK3cnJyejLD5VKZXAsHj58CE9PT4ML16zI6eNFZO0KFSoER0dHkxd6mzdvxpkzZ/TjHVNycnIymmlco9HAx8cHu3btwqeffopffvkFp0+f1n8ZrTuvnj59Co1Gg6JFixrt19S6lO7fv4+LFy8a1VEuLi4QQhjVUynPc0B7rmf2PM/MZ4253L9/H/v27TMqu26eF13ZT58+DR8fHwDAunXrcOLECZw5cwZ+fn4AjD/j/vnnH/z+++9o27YtqlatavS6uvHGuuuPH374Abdu3crQrT11idWBAwfQrVs3HDt2TN/FX1c2AOjevbtR+RYuXAghBJ48eZKu10rP9QeAt86mrhvS1qNHD0RHR+uvQXr27InY2Fhs2bIFgPZ/OikpKVuuP+7evau/ztmyZQvi4+MN5jzI6HudHk+fPoUQItX/ceDNeaCT1fq0Ro0aBtcfukQ0M94Wy8OHD2Fra5uuz5v0kHG8LA1nNadsUaBAAf03WKklvLrZwb/55ht4e3tj27ZtBvclTTnBlE6vXr1QtGhR+Pn5QaPRYPr06QaP29jYYPTo0Zg2bRqWLl2KVatWoWXLlulOjnSJlU6rVq1Qu3ZtzJkzB3379kXJkiX1M0ru2LFD30qRWR4eHgCAu3fvmnz87t27+m3Somt1nTBhgn6StJSPt27dWv8t8507dzIZsWm9e/fGpEmTsHHjRgQEBODrr7/GBx98gAIFCui3yeh7nR66D+XIyEijx+7duwcbGxuDGLKTLolOWZ6MfBGTUuHChXH8+HFoNBqzJN+WdLyIrIGtrS1atGiB0NBQREZGGlw06u7wkNp9jlPeaxsALl26hD///BMbN27EwIED9ev//fdfg+0KFCgAhUJh8h7O6bmvs+4Lg9Qm2MzumZFlftYUKlQI1atXN+iplpzuIn/r1q1QKpX44YcfDL4E/f77700+r379+ujRoweGDh0KAAgODjb6XB43bhx69OiBP/74AytWrED58uX1rcDpUaNGDf1706pVK7Ru3Rpr167F0KFDUbduXf1jy5cvT3XG6PRcMwDa42Rra5vm9Yetra3JL2WS011/LFu2DMuWLTP5+IgRI+Du7g5bW1uzX3+0bt0anp6eCAkJQevWrRESEoL33nvP4A4sGX2v06NAgQKwsbFJ9X8cyP7zTCe164+UiWxGFC5cGElJSYiKisrw/BamWNLxkoUt3pQtnJyc0Lx5c5w/fx7Vq1c3aiGsU6eO/oNcoVDA3t7e4AIlKioqzVnNp0+fjqCgIMycORO+vr5Gjw8bNgz29vbo27cvrl69mqFvm1NSqVRYuXIl4uLiMG/ePADaD3k7Oztcv37dZNmSJ+5vU65cOZQuXRrbt283muzm4cOHOHz4MN5///0093HlyhWcOnUK3bp1w+HDh41+dJN3PX78GOXLl0fZsmWxYcOGNBPejH6rWKBAAXzwwQf46quv8MMPPyAqKsqoe3RG3uv0trRUqFABxYsXx+bNmw2OX0xMDHbu3KmfTTcn6LoSXrx40WB9aq1h6dG2bVvExcWZnKk0OWs8XkTWwtfXF0lJSRg5cqTB5GeZofv8033G6qSclMvZ2Rnvvvsudu3aZdAL5sWLF9i3b99bX6dDhw64fv06ChYsaLKOSm/X5+QyUi/I/Kzp0KEDLl26hLJly5osuy7xVigUsLOzg62trf65r169wtdff53qvgcOHIitW7ciJCQEAwYMMGot7tKlC0qVKoXJkyfj4MGDGDVqlMkvYNJDoVBg5cqVsLW11TcyNGzYEPnz50d4eHiq1x+pzbyfkoODAxo2bIi9e/ca9TqLi4vD3r170ahRozSHpT19+hS7d+9Gw4YNTV5/9O3bF2fOnMGlS5fg6OiIpk2bYvv27Wl+IZ3R6w9dQ8/333+PX3/9FWfPnjV5/ZHe9zq99amzszPee+897Nq1y2B7jUaDb775BiVKlMix+9F7eHjAwcHB6PojPXcISo1uaEZwcHCa21nj8ZKFLd6UJYcOHTL5TX+7du3wxRdfoFGjRmjcuDE+/vhjeHl54cWLF/j333+xb98+HDp0CIC2gty1axdGjRqF7t2747///sPcuXNRrFgxo1kqkxs/fjzy5cuHjz76CC9fvsT//d//6Su3/PnzY8CAAQgODkbp0qXTNR4uLU2bNkW7du0QEhKCqVOnwtvbG/7+/vDz88ONGzfQpk0bFChQAPfv38fp06fh7OxsMHM7AOzbt89g/JxO9+7dsWTJEvTs2RMtW7bE8OHDUbRoUVy7dg0LFiyAvb09ZsyYkWZ8um+bP/30U7z77rtGj7948QK//PILvvnmG4wfPx4rV65Ex44dUa9ePUycOBGlSpVCREQEDhw4gG+//RaAdtw2AHzxxRcYOHAglEolKlSoYLIMOkOGDMG2bdswZswYlChRwugLg4y819WqVcORI0ewb98+FCtWDC4uLiZ7LdjY2GDRokXo27cvOnTogBEjRiA+Ph6LFy/Gs2fPDIYIZLeiRYvi/fffR2BgIAoUKIDSpUvjl19+wa5duzK9z969eyMkJAQjR47E1atX0bx5c2g0Gvz++++oVKkSPvzwQwDWebyIrEXDhg2xcuVKjB07Fv/73//w0UcfoUqVKvrWm507dwKAUbdyUypWrIiyZcti6tSpEELA3d0d+/bt03eTTW7u3Llo06YNWrVqhcmTJyMpKQkLFy6Es7PzW7sTT5gwATt37kSTJk0wceJEVK9eHRqNBhEREQgNDcXkyZPx3nvvZeg4ZKReyO7PmuTzxCTXtGlT+Pv7IywsDA0aNMC4ceNQoUIFxMXF4datW9i/fz9Wr16NEiVKoH379li2bBn69OmDjz76CI8fP8aSJUuMvhRJqXv37nByckL37t3x6tUrbNmyRZ/s2traYvTo0fjss8/g7OxsdIu3jCpXrhw++ugjrFq1CsePH0ejRo2wfPlyDBw4EE+ePEH37t1RpEgRPHz4EH/++ScePnxolCilda22YMECNG/eHPXr18eECRP01wNBQUG4f/8+tm7dmmZ83377LeLi4jBu3DiTt4ErWLAgvv32W6xfvx6ff/45li1bhkaNGuG9997D1KlT8c477+D+/fvYu3cv1qxZAxcXF303/rVr18LFxQUODg7w9vZOs+V9yJAhWLhwIfr06QNHR0f06tXL4PGMvNfVqlXD1q1bsW3bNpQpUwYODg76//2UAgMD0apVKzRv3hxTpkyBvb09Vq1ahUuXLmHLli2Z/tIloxQKBfr164cNGzagbNmyqFGjBk6fPm10l5+MaNy4Mfr374958+bh/v376NChA1QqFc6fPw8nJyf9EAhrPF7SyJrVjaybbrbB1H50M2DevHlTDBkyRBQvXlwolUpRuHBh0aBBAzFv3jyD/S1YsEB4eXkJlUolKlWqJNatW6efdTE5vJ7VPLktW7YIOzs7MXjwYIOZU48cOSIAiAULFqS7XLpZzU3566+/hI2NjRg8eLB+3ffffy+aN28uXF1dhUqlEqVLlxbdu3c3mOk0tZkodT86Bw8eFD4+PiJ//vzCzs5OFCtWTPTr109cu3YtzZgTEhJEkSJFjGZyTy4xMVGUKFFCVKtWTb/u1KlTom3btsLNzU2oVCpRtmxZMXHiRIPn+fr6Ck9PT2FjY2Mww2jKWc11kpKSRMmSJdOcBTO97/WFCxdEw4YNhZOTkwCgf73UZg7//vvvxXvvvSccHByEs7OzaNmypThx4oTBNqnNMK/7f37bzK1p/X/oREZGiu7duwt3d3fh5uYm+vXrJ86ePWtyVnNT+zJ1LF69eiVmzpwpypUrJ+zt7UXBggVFixYtxMmTJ/XbWOLxIsptLly4IAYPHiy8vb2FSqUSDg4O4p133hEDBgwQv/zyi8G2aX1ehIeHi1atWgkXFxdRoEAB0aNHDxEREWE0+7AQQuzdu1dUr15d2Nvbi1KlSokFCxaY/JxIOau5EEK8fPlSTJ8+XVSoUEHY29sLNzc3Ua1aNTFx4kQRFRWl385U3ZraPlOrF1KTns+azMxqntqPLp6HDx+KcePGCW9vb6FUKoW7u7uoXbu28PPzEy9fvtTvb8OGDaJChQpCpVKJMmXKiMDAQLF+/XqjzzjdrOYpY8mXL59o06aNiI2N1a+/deuWACBGjhz51vLopHUHlPv374t8+fKJ5s2b69cdPXpUtG/fXri7uwulUimKFy8u2rdvb3AM03utdvbsWdGlSxdRqFAhYWtrKwoVKiS6dOkizp0799a4a9asaTSTe0r16tUThQoV0m8THh4uevToIQoWLKj/vx40aJCIi4vTPycoKEh4e3sLW1tbg/oz5azmyTVo0EAAEH379jX5eHrf61u3bgkfHx/h4uIiAOhfL7WZw3/99VfRokUL4ezsLBwdHUW9evXEvn37DLZJbYb51OrolN52hxwhhHj+/LkYNmyY8PDwEM7OzqJjx476/0VTs5qnp25PSkoSn3/+uahatar+M6R+/foG5bPE42WpFEKYuLM9US4wefJkBAcH47///nvr+CQiIiIic1i+fDnGjRuHS5cu6Sd0IyJiV3PKdX777Tf8888/WLVqFUaMGMGkm4iIiLLd+fPncfPmTfj7+6Nz585MuonIAFu8KddRKBRwcnLSj8lOz727iYiIiLLCy8sLUVFRaNy4Mb7++muz3YaJiHIHJt5ERERERERE2Yi3EyMiIiIiIiLKRky8iYiIiIiIiLIRE28iIiIiIiKibJTrZzXXaDS4d+8eXFxccv9N2YmIyGoJIfDixQt4enrCxiZvfy/OupuIiKxBRuruXJ9437t3DyVLlpQdBhERUbr8999/KFGihOwwpGLdTURE1iQ9dXeuT7xdXFwAaA+Gq6trlvalVqsRGhoKHx8fKJVKc4SX41gGy2DtZbD2+AGWwRJYe/yAecsQHR2NkiVL6uutvIx1tyGWQT5rjx9gGSyBtccPsAwpZaTuzvWJt66Lmqurq1kqbycnJ7i6ulr1PxrLIJ+1l8Ha4wdYBktg7fED2VMGdq1m3Z0SyyCftccPsAyWwNrjB1iG1KSn7s7bg8iIiIiIiIiIshkTbyIiIiIiIqJsxMSbiIiIiIiIKBvl+jHe6ZWUlAS1Wp3mNmq1GnZ2doiLi0NSUlIORWZeLIMhpVIJW1tbM0VGREQ5RaPRICEh4a3bsd6zDNZeBmuOn9c6RJYhzyfeQghERUXh2bNn6dq2aNGi+O+//6x28huWwVj+/PlRtGhRqz0eRER5TUJCAm7evAmNRvPWbVnvWQZrL4O1x58/f34ULFhQdhhEeVqeT7x1SXeRIkXg5OSU5oepRqPBy5cvkS9fvrfeIN1SsQxvCCEQGxuLBw8eAACKFStmrhCJiCibCCEQGRkJW1tblCxZ8q31AOs9y2DtZbDW+JNf61hbSz1RbpOnE++kpCR90p2ebwF13docHBys6kM3OZbBkKOjIwDgwYMHKFKkCLtiERFZuMTERMTGxsLT0xNOTk5v3Z71nmWw9jJYc/y6a5379+9bZWs9UW5hXZ8cZqYb052eiptyL937/7Yx/kREJJ+u1c7e3l5yJETWQ3etwwYGInnydOKtw2//8ja+/0RE1oef3UTpx/OFSD4m3kRERERERETZiIk3Gbl16xYUCgUuXLggOxQiIiJKB9bd5jdo0CB88MEH2f46GzduRP78+bP9dYhILqmJ97Fjx9CxY0d4enpCoVDg+++/N3hcCIHZs2fD09MTjo6OaNasGS5fviwnWAuSUxWBOTVr1gwKhQIKhQL29vYoW7YsfH19ER8fn+59pHVRceTIESgUCpO3hatZsyZmz56d+eCJiPKot9XTphw9ehS1a9eGg4MDypQpg9WrV2d/oFaAdfcFo8eyUnfPnj1bH5udnR0KFSqEJk2aICgoKEPxpeWLL77Axo0bzbIvHS8vLwQFBRms69WrF/755x+zvg4RWR6piXdMTAxq1KiBFStWmHx80aJFWLZsGVasWIEzZ86gaNGiaNWqFV68eJHDkZI5DB8+HJGRkfj333+xaNEirFy5kgkxEZEFe1s9ndLNmzfRrl07NG7cGOfPn8e0adMwbtw47Ny5M5sjpexiyXV3lSpVEBkZiYiICBw+fBg9evRAYGAgGjRokKVrxaSkJGg0Gri5ueVIS7SjoyOKFCmS7a9DRHJJTbzbtm2LefPmoWvXrkaPCSEQFBQEPz8/dO3aFVWrVsWmTZsQGxuLzZs3S4jWeoSHh6Ndu3bIly8fPDw80L9/fzx69Ej/+MGDB9GkSRPkz58fBQsWRIcOHXD9+vVU96fRaDB8+HCUL18eR48ehY2NDc6ePWuwzfLly1G6dGkIIVLdj5OTE4oWLYpSpUqhW7duaNWqFUJDQ/WPCyGwaNEilClTBo6OjqhRowZ27NiRhSNBRERZkVY9bcrq1atRqlQpBAUFoVKlShg2bBiGDBmCJUuWZHOk1o91d8bZ2dmhaNGi8PT0RLVq1TB27FgcPXoUly5dwsKFC/XbJSQk4NNPP0Xx4sXh7OyM9957D0eOHNE/ruvq/cMPP6By5cpQqVS4ffu2QS+FNWvWoHLlytBoNAYxdOrUCQMHDgQAXL9+HZ07d4aHhwfy5cuHunXr4uDBg/ptmzVrhtu3b2PixIn61vrkrw8AV69ehUKhwN9//23wOsuWLYOXl5f+vXrb/wsRWR6LvY/3zZs3ERUVBR8fH/06lUqFpk2b4uTJkxgxYkS2vK4QQGys6cc0GiAmBrC1Bcx9C0cnJ8AcE05GRkaiadOmGD58OJYtW4ZXr17hs88+Q8+ePXHo0CEAQGxsLCZMmIAaNWogJiYGM2fORJcuXXDhwgWje1MmJCSgT58+uH79Oo4fP44iRYrg/fffR0hICOrUqaPfLiQkBIMGDUr3rJl//vknTpw4AS8vL/266dOnY9euXQgODka5cuVw7Ngx9OvXD4ULF0bTpk2zfnCIiMzs228VsLHhba10Tp06ZVBvA0Dr1q2xfv16qNVqKJVK879oWhU3YBWVN+tu86lYsSLatm2LXbt2Yd68eQCAwYMH49atW9i6dSs8PT2xe/dutGnTBn/99RfKlSsHQHt8AwMD8eWXX6JgwYJGLdA9evTAhAkTcPjwYbRq1QoA8PTpUxw4cAD79u0DALx8+RLt2rXDvHnz4ODggE2bNqFjx464evUqSpUqhV27dqFGjRr46KOPMHz4cJPxV6hQAbVr18a3336LuXPn6tdv3rwZffr0gUKhSNf/S5ru3AHu3s3wsbUEisREuIeHQ+HmBthZbBqTKmuPH8g9ZXCKjMzx17XYoxUVFQUA8PDwMFjv4eGB27dvp/q8+Ph4g7E90dHRALT3aE55n2a1Wg0hBDQajf4bzJgYwNU1tYrZBkD+jBUknaKjNXB2Tt+2Qgh93CmtWrUKtWrV0lc2APDll1+idOnS+Pvvv1GuXDl06tQJLi4u+op23bp1KFq0KC5duoSqVavq9xsdHY127dohLi4Ohw4dgpubGzQaDYYMGYJRo0ZhyZIlUKlU+PPPP3HhwgXs2LHDZEzJY/vyyy+hVquRkJAAGxsbLF++HBqNBjExMVi2bBkOHjyI+vXrA9COg/r111+xevVqNG7cWL9v3be9yY9B8t+mYkjteOmeI4SAWq3Osftb6v4XrfXe4dYeP8AyWAJrj//PP4EhQ+zg6Pg+mjVTo1ixrO3PWo9DclFRUSbr7cTERDx69AjFUjlIWaq7Y2Jg4+qaakzZV3MDmuhopLfyZt1t3rpbtz9Tj1eoUAGhoaHQaDS4fv06tmzZgoiICHh6egIAJk2ahJ9//hkbNmxAQEAANBoN1Go1VqxYgRo1aph8zwoUKICWLVtiy5YtaNmyJQBg27ZtcHd3R/PmzaHRaFCtWjVUq1ZN/3x/f3/s3r0be/bswejRo5E/f37Y2toiX758+sQ+edl1v/v06YOVK1dizpw5AIB//vkH586dw8aNG6HRaN76/1K+fHmjY6K71lE9ewa78uWBxESTx9XS2QFoLDuILLD2+IHcU4ay7dpBPWBAlveVkbrbYhNvnZTfwgoh0vxmNjAwUP9BlVxoaCicnJwM1um6KL18+RIJCQkAtIl39lXRqYuOjkZSUvq2VavVSExM1F+YJPf777/jyJEjcDVxEfLXX3+haNGiuHnzJgICAnD27Fk8efJE/0H/999/o1SpUnj58iUAoHfv3ihevDi+//57KBQK/eu1aNECtra22Lx5M7p164Y1a9agcePGcHd3NxkTACQmJqJHjx6YPHkyXrx4gS+++AIuLi5o1aoVoqOj8ccffyAuLg6tW7c2eF5CQgKqV6+O6OhofVyxr1s2ko/fSr4u5Tf/SUlJiI+PTzW2hIQEvHr1CseOHUNiDldEYWFhOfp65mbt8QMsgyWw1vjnzn0PQhRF7dr3cf78OZw/n7X9xabVamtFTNXbptYnl6W6OyZGQq2tFR0djfRW3qy7zVt3x8fHIykpyeTjcXFx+rKfOHECQghUrFjR6Pmurq6Ijo5GXFwc7O3t4eXlZbC/lO+ZrtU7MDAQKpUKX3/9Nbp06YIY7cUjYmJisHDhQoSGhiIyMhJJSUl49eoVrl27pt+HRqNBXFycwevExcVBCKFf165dO3z66af45ZdfULduXYSEhKBatWooUaIEoqOj0/X/klJCQgLi4uLg8PgxFImJ0NjaIjbFl2REeUm8m5tZrj8yUndbbOKt+9CIiooy+Ib8wYMHRt+mJ+fr64tJkybp/46OjkbJkiXh4+Nj9AEVFxeH//77D/ny5YODgwMAwMVF2/psihACL168MPjG2VycnFzT3VtNqVTCzs7O5AeujY0NOnTogAULFhg9VqxYMTg5OaF3794oVaoU1q1bB09PT2g0GlSvXl2/z3z58gEA2rdvj2+//Rbh4eFo0aKFwb769++Pbdu2oW/fvti5cyeWLVtmMh4d3YyjNWvWBADUq1cP1apVw/bt2zF06FA4OjoCAPbt24fixYsbPFelUhnEpbsIS/4+6P5fNBqNURwvXrxAkSJFUo0vLi4Ojo6OaNKkif7/ILup1WqEhYWhVatW2dP1MptZe/wAy2AJrDn+X39V4Nw5O9jZCfTp87dZypBagmFNihYtqu+xpvPgwQPY2dmhYMGCqT4vS3W3i4u25TkV2Vl3u2agqznrbvPW3SqVCra2tiYfv3HjBry9veHq6qrf7syZM0a92vLlywdXV1c4ODjA0dERbm5uBo8nf8+EEGjTpg2EEPj1119Rt25dnDp1CkFBQfoYfH19ERoaikWLFuGdd96Bo6MjevbsCYVCod/GxsYGDg4OBnE7ODgYbOPq6opmzZph7969aNmyJXbv3o2PPvrIYB9p/b84m+iFERcXBwcHB8TpvggrUwYqK7xTkDXXG4D1xw/knjL8Y6YyZKTuttjE29vbG0WLFkVYWBhq1aoFQPtt3dGjRw0mzEhJpVJBpVIZrVcqlUYHNikpCQqFAjY2NgbftLq4mN63tjsQkC+fwuib2Zykm5DDVAy1a9fGzp07UaZMGdiZGHfx8OFDXL16FWvWrNGPvTp+/DgA6I+Dbr+jRo1CtWrV8MEHH+DHH380GKs1fPhwVK1aFatXr4ZarUb37t3fekySx6xSqTBt2jT4+vqib9++qFq1KlQqFe7cuYPmzZubfL7uuboKO/n+KlSoABsbG5w7dw7e3t7650RGRuLu3buoWLFiqvHZ2NhAoVCY/B/JbjJe05ysPX6AZbAE1ha/EMCMGdrlIUM0KFYsxixlsKZjkJr69evrx7vqhIaGok6dOmmWL8t1d2oVN15339VooMiXj3V3Lqq7dftL+fjff/+NAwcOwNfXFzY2NqhduzaSkpLw6NEjNG5suoOsbh8p95X8PdNoNHB0dESXLl2wZcsW3LhxA+XLl0fdunX12x8/fhyDBg1Ct27dAGjHfN+6dQvNmjXT79ve3h4ajcbgtUy9fr9+/fDZZ5/px+r37t1b//jb/l9SK6NCodDOeQBAYWdn1Z851lZvpGTt8QMsQ/J9pJfUxPvly5f4999/9X/fvHkTFy5cgLu7O0qVKoUJEyZg/vz5KFeuHMqVK4f58+fDyckJffr0kRi1ZXj+/LnRPTHd3d0xevRorFu3Dr1798Ynn3yCQoUK4d9//8XWrVuxbt06FChQAO7u7li3bh2KFy+OiIgITJ06NdXXGTt2LJKSktChQwf89NNPaNSoEQCgUqVKqFevHj777DMMGTJE/613RvTp0wfTpk3DqlWrMGXKFEyZMgUTJ06ERqNBo0aNEB0djZMnTyJfvnz6GUMB7YyfMTExcHZ21ldClStXxogRIzB58mTY2dmhRo0auHfvHvz8/FCpUiWjyX6IiDJr3z7g5EnA0RGYNk0DE7cnzjXeVk/7+vri7t27+OqrrwAAI0eOxIoVKzBp0iQMHz4cp06dwvr167FlyxZZRbAorLvNW3cnJiYiKioKGo0Gjx8/xpEjRzBv3jzUrFkTn3zyCQCgfPny6Nu3LwYMGIClS5eiVq1aePToEQ4dOoRq1aqhXbt2GS5/586dcfnyZfTr18/gsXfeeQe7du1Cx44doVAoMGPGDKMx6F5eXjh27Bg+/PBDqFQqFCpUyOTrdO3aFR9//DE+/vhjNG/e3KBHwdv+X9Kar0ahi0fil1BEeZaQ6PDhwwKA0c/AgQOFEEJoNBoxa9YsUbRoUaFSqUSTJk3EX3/9laHXeP78uQAgnj9/bvTYq1evRHh4uHj16lW69pWUlCSePn0qkpKSMhSDuQ0cODDN4/bPP/+ILl26iPz58wtHR0dRsWJFMWHCBKHRaERSUpLYvXu3qFSpklCpVKJ69eriyJEjAoDYvXu3EEKImzdvCgDi/Pnz+tdcunSpcHFxESdOnNCvW79+vQAgTp8+/daYmzZtKsaPH2+0PiAgQBQuXFi8ePFCaDQa8cUXX4gKFSoIpVIpChcuLFq3bi2OHj1qEJepn5s3b4q4uDjh7+8vKlWqJBwdHUXp0qXFoEGDRGRkZJqxZfT/wBwSEhLE999/LxISEnLsNc3J2uMXgmWwBNYYf2KiEFWqCAEI4etr3jKkVV/J8rZ6euDAgaJp06YGzzly5IioVauWsLe3F15eXiI4ODjDr8u6m3X32+ruWbNm6fdja2sr3N3dRaNGjcTnn38u4uLiDLZNSEgQM2fOFF5eXkKpVIqiRYuKLl26iIsXLwohhAgJCRFubm5GrzFw4EDRuXNnIcSb/6OEhARRrFgxAUBcv37dYPubN2+K5s2bC0dHR1GyZEmxYsUKo2N46tQpUb16daFSqYTuMjy11+/Ro4cAIDZs2GD0WFr/L6a8evVKXL58WZxcvFj7AVa9emqH1qJZY72RnLXHLwTLkFJG6m6FEGncvDEXiI6OhpubG54/f25ynNjNmzfh7e2drrG9Go0G0dHRcHV1ldpdLSvMWYaAgABs3boVf/31l5miSx9zvw8Z/T8wB7Vajf3796Ndu3ZW2U3H2uMHWAZLYI3xf/UVMHAgUKAAcOMG4OxsvjKkVV/lNay7DbHuls/a44+Li8ONGzfw/McfUf/TT4FatYA//pAdVoZZY72RnLXHD7AMKWWk7ra+Tw6S7uXLlzhz5gyWL1+OcePGyQ6HiChHxMcDM2dql6dOBfLnlxoOUYaw7iYgWVfzHLp9KhG9wcSbMmzMmDFo1KgRmjZtiiFDhsgOh4goR6xeDdy+DXh6AmPGyI6GKGNYdxPAMd5EMlnsrOZkuTZu3IiNGzfKDoOIKMe8eAHMm6ddnj0bSHFraSKLx7qbAEChG2HKFm+iHMevu4iIiN5i2TLg0SOgfHlg8GDZ0RARZRK7mhNJw8SbiIgoDQ8fAkuWaJfnzQPSedtcIiKLw67mRPLwrAOM7rFIeQvffyJKS0AA8PIlULs20K2b7GhIJ5fflIXIrHTXOoqkJO0KtngT5bg8/b29vb09bGxscO/ePRQuXBj29vZQKBSpbq/RaJCQkIC4uDirvJUEwDIkJ4RAQkICHj58CBsbG9jb25sxSiLKDW7fBoKDtcsLFrCRyBIolUooFAo8fPgQhQsXTrPeBljvWQprL4O1xp/yWkcRE6N9gIk3UY7L04m3jY0NvL29ERkZiXv37r11eyEEXr16BUdHx7dW9JaKZTDm5OSEUqVKWVVFSkQ5Y9YsICEBaNkSeP992dEQANja2qJEiRK4c+cObt269dbtWe9ZBmsvg7XH7+TkBE9PT/ydmKhdwcSbKMfl6cQb0LZ6lypVComJiUjSdb9JhVqtxrFjx9CkSROrvmE8y/CGra0t7OzsrLISJaLsdekS8NVX2uXAQLmxkKF8+fKhXLlyUKvVb92W9Z5lsPYyWHP8umudxMREjvEmkijPJ94AoFAooFQq3/pBamtri8TERDg4OFjdh64Oy0BElD7TpwNCaMd1160rOxpKydbWFrbpaLXLDXUGyyCftcevx1nNiaTh111EREQpnDwJ7NmjvTYNCJAdDRGReSiYeBNJw8SbiIgoGSGAqVO1y4MHAxUqyI2HiMhcmHgTycPEm4iIKJmffwZ+/RVQqbSTqxER5RYc400kD886IiKi1zQawNdXuzx2LFCihNx4iIjMiS3eRPIw8SYiInpt61bgzz8BN7c3CTgRUa4hhPY3E2+iHMfEm4iICNr7dc+YoV3+9FPA3V1uPERE5sau5kTy8KwjIiIC8OWXwI0bgIcHMH687GiIiMyPXc2J5GHiTUREeV5MDODvr12eORNwdpYbDxFRdmDiTSQPE28iIsrzgoKA+/eBsmWB4cNlR0NElD2YeBPJw8SbiIjytMePgUWLtMtz5wJKpdx4iIiyC8d4E8nDs46IiPK0BQuA6GigRg2gVy/Z0RARZR+2eBPJw8SbiIjyrDt3gOXLtcuBgWwEIqJcjrcTI5KGlxhERJRnzZ4NxMcDTZsCbdrIjoaIKHuxqzmRPDzriIgoT/r7byAkRLscGAgoFHLjISLKboqkJO0CW7yJchwTbyIiypOmTwc0GqBTJ6B+fdnREBFlP47xJpKHiTcREeU5Z84AO3dqW7nnz5cdDRFRzlBwjDeRNEy8iYgoTxECmDpVuzxgAFClitx4iIhyCsd4E8nDs46IiPKUgweBQ4cAe3tgzhzZ0RAR5Rx2NSeSh4k3ERHlGRoN4OurXR41CihdWm48REQ5il3NiaRh4k1ERHnGzp3AuXNAvnzAtGmyoyEiylmc1ZxIHibeRESUJ6jVgJ+fdnnKFKBwYbnxEBHlNI7xJpKHZx0REeUJISHAtWvahHvSJNnREBHlPI7xJpKHiTcREeV6sbFvJlKbPh1wcZEbDxGRDLydGJE8TLyJiCjXW74cuHdPO5naiBGyoyEikoRdzYmk4VlHRES52tOnwIIF2mV/f0ClkhsPEZEs7GpOJA8TbyIiytUWLQKePQOqVgX69pUdDRGRPEy8ieRh4k1ERLnWvXvAF19ol+fP57UmEeVtTLyJ5GHiTUREuZa/P/DqFdCgAdChg+xoiIjk4u3EiOThWUdERLnStWvAl19qlwMDAYVCbjxERLKxxZtIHibeRESUK82YASQlAe3bA02ayI6GiMgC8HZiRNIw8SYiolzn3Dlg2zZtK/f8+bKjISKyDGzxJpKHiTcREeU606Zpf/fpA1SvLjcWIiJLwTHeRPLwrCMiolzl0CEgNBRQKrWTqxERkRZbvInkYeJNRES5hhCAr692ecQIoEwZufEQEVkSJt5E8jDxJiKiXGP3buD0acDZGZg+XXY0RESWhV3NieThWUdERLlCYiLg56ddnjgR8PCQGw8RkaVhizeRPEy8iYgoV/jqK+Dvv4GCBYEpU2RHQ0RkgXg7MSJpmHgTEZHVi4sDZs3SLk+bBri5yY2HiMgSscWbSB4m3kREZPVWrgTu3AFKlABGjZIdDRGRZeIYbyJ5eNYREZFVe/4cmD9fuzxnDuDgIDceIiJLxRZvInmYeBMRkVVbsgR48gSoVAkYMEB2NERElouJN5E8TLyJiMhq3b8PLFumXQ4IAOzs5MZDRGTJmHgTycPEm4iIrNbcuUBsLPDee8AHH8iOhojIsnGMN5E8POuIiMgq3bgBrFmjXQ4MBBQKufEQEVk8tngTScPEm4iIrNLMmUBiItC6NdC8uexoiIgsn4L38SaShok3ERFZnT//BDZv1i7rZjQnIqK0sas5kTw864iIyOr4+QFCAL16Af/7n+xoiIisAydXI5KHiTcREVmVX38FfvxRO4P53LmyoyEish5MvInkYeJNRERWQwjA11e7PGwYUK6c3HiIiKwKE28iaZh4ExGR1fjhB+DECcDREZgxQ3Y0RETWhWO8ieThWUdERFYhKQmYNk27PH484OkpNx4iImvDruZE8jDxJiIiq7B5M3DpEpA/P/Dpp7KjISKyPrydGJE8Fp14JyYmYvr06fD29oajoyPKlCkDf39/aHTf1hERUZ4QH6+9bzcATJ0KFCggNx4iImvEFm8ieexkB5CWhQsXYvXq1di0aROqVKmCs2fPYvDgwXBzc8P48eNlh0dERDlkzRrg1i1t9/KxY2VHQ0RknTjGm0geiz7rTp06hc6dO6N9+/bw8vJC9+7d4ePjg7Nnz8oOjYiIcsiLF8C8edrlWbMAJye58eRFq1atgre3NxwcHFC7dm38+uuvaW7/7bffokaNGnByckKxYsUwePBgPH78OIeiJaLUsMWbSB6LTrwbNWqEX375Bf/88w8A4M8//8Tx48fRrl07yZEREVFO+fxz4OFD7a3DBg+WHU3es23bNkyYMAF+fn44f/48GjdujLZt2yIiIsLk9sePH8eAAQMwdOhQXL58Gdu3b8eZM2cwbNiwHI6ciIww8SaSxqK7mn/22Wd4/vw5KlasCFtbWyQlJSEgIAC9e/dO9Tnx8fGIj4/X/x0dHQ0AUKvVUKvVWYpH9/ys7kcmlsEyWHsZrD1+gGWwBOmJ/+FDYMkSOwAKzJ6dCEDAkoprzvfAUt/HZcuWYejQofrEOSgoCAcOHEBwcDACAwONtv/tt9/g5eWFcePGAQC8vb0xYsQILFq0KEfjJiJjNuxqTiSNRSfe27ZtwzfffIPNmzejSpUquHDhAiZMmABPT08MHDjQ5HMCAwMxZ84co/WhoaFwMlP/xLCwMLPsRyaWwTJYexmsPX6AZbAEacW/fn1VvHhRFmXLPoOj41Hs35+DgWWAOd6D2NhYM0RiXgkJCTh37hymTp1qsN7HxwcnT540+ZwGDRrAz88P+/fvR9u2bfHgwQPs2LED7du3T/V1+KV52lgG+aw9fgBQx8dDqVvWaGBR32Kmk7W/D9YeP8AypLav9FAIobuvgOUpWbIkpk6ditGjR+vXzZs3D9988w3+/vtvk88xVXmXLFkSjx49gqura5biUavVCAsLQ6tWraBUKt/+BAvEMlgGay+DtccPsAyW4G3x374NVKlih4QEBX78MRGtWlledWXO9yA6OhqFChXC8+fPs1xfmcu9e/dQvHhxnDhxAg0aNNCvnz9/PjZt2oSrV6+afN6OHTswePBgxMXFITExEZ06dcKOHTtSPUazZ882+aX55s2bzfalOVFep0hKQqdu3QAA+7/+GmoXF8kREVm/2NhY9OnTJ111t0W3eMfGxsImRVcYW1vbNG8nplKpoFKpjNYrlUqzXZiac1+ysAyWwdrLYO3xAyyDJUgt/oAAICEBaNECaNvWDgqFhODSyRzvgSW/h4oUB18IYbROJzw8HOPGjcPMmTPRunVrREZG4pNPPsHIkSOxfv16k8/x9fXFpEmT9H/rvjT38fHhl+ZgGSyBtccPAOqXL/XLrdq0AdzcJEaTOdb+Plh7/ADLkJKuh1Z6WHTi3bFjRwQEBKBUqVKoUqUKzp8/j2XLlmHIkCGyQyMiomx0+TLw1Vfa5cBAWHTSnZsVKlQItra2iIqKMlj/4MEDeHh4mHxOYGAgGjZsiE8++QQAUL16dTg7O6Nx48aYN28eihUrZvQcfmmePiyDfFYdf7LGLKVKBVhrOWDl7wOsP36AZUi+j/Sy6JkVli9fju7du2PUqFGoVKkSpkyZghEjRmDu3LmyQyMiomzk56edfLdbN+Ddd2VHk3fZ29ujdu3aRmPYw8LCDLqeJ5dabzVA21JORJIkJb1Z5qzmRDnOolu8XVxcEBQUhKCgINmhEBFRDjl1CtizR9s4o7t/N8kzadIk9O/fH3Xq1EH9+vWxdu1aREREYOTIkQC03cTv3r2Lr153UejYsSOGDx+O4OBgfVfzCRMm4N1334Wnp6fMohDlbcmHajLxJspxFp14ExFR3iIEoJtAe/BgoGJFufEQ0KtXLzx+/Bj+/v6IjIxE1apVsX//fpQuXRoAEBkZaXBP70GDBuHFixdYsWIFJk+ejPz586NFixZYuHChrCIQEWDY4s3biRHlOCbeRERkMX7+GTh2DFCpgNmzZUdDOqNGjcKoUaNMPrZx40ajdWPHjsXYsWOzOSoiyhB2NSeSil93ERGRRdBoAF9f7fLYsUCJEnLjISLKVdjiTSQVzzoiIrII27YBf/4JuLq+6W5ORERm8nqMt2BrN5EUTLyJiEi6hARg+nTt8qefAgULyo2HiCjX0bV4s7WbSAqeeUREJN2XXwI3bgAeHsCECbKjISLKhXSJN1u8iaRg4k1ERFLFxAD+/trlmTMBZ2e58RAR5Uq624kx8SaSgok3ERFJtXy5De7fB8qUAYYNkx0NEVEuxRZvIqmYeBMRkTTR0UosWaKtiubOBeztJQdERJRbcYw3kVQ884iISJpdu8ohOlqBGjWADz+UHQ0RUS7GFm8iqZh4ExGRFHfuAD/+WAYAEBjIRhgiomzFMd5EUvEyh4iIpJg3zxZqtS0aN9agTRvZ0RAR5XLsak4kFc88IiLKcX//DWzcqAAABARooFBIDoiIKLdjizeRVEy8iYgox02fDmg0Crz7biTq1ROywyEiyvUUHONNJBUTbyIiylFnzgA7dwIKhUC/fldkh0NElDewxZtIKibeRESUo3x9tb/79RMoVeqF3GCIiPIKjvEmkopnHhER5ZiwMOCXX7T36545M0l2OEREeQcTbyKpeOYREVGO0GjetHZ//DFQurTceIiI8hR2NSeSiok3ERHliJ07gXPngHz5AD8/2dEQEeUxnFyNSCom3kRElO3U6jfJ9pQpQOHCcuMhIspz2NWcSCqeeURElO02bgSuXdMm3JMmyY6GiCgPYos3kVRMvImIKFvFxgKzZ2uXp08HXFykhkNElDe9HuMtmHgTScHEm4iIstWKFcC9e9rJ1EaMkB0NEVEexa7mRFLxzCMiomzz7BmwYIF22d8fUKmkhkNElHexqzmRVEy8iYgo2yxaBDx9ClSpAvTtKzsaIqI8jLcTI5KKiTcREWWLyEggKEi7HBjIaz0iIqnY4k0kFRNvIiLKFv7+wKtXQIMGQIcOsqMhIsrjOMabSCqeeUREZHbXrgHr1mmXFywAFAq58RAR5Xls8SaSiok3ERGZ3cyZ2mu8du2Axo1lR0NERBzjTSQXE28iIjKr8+eBrVu1rdzz58uOhoiIADDxJpKMiTcREZmVr6/2d58+QI0acmMhIqLXdF3NOfaHSAom3kREZDaHDwMHDgB2dtrJ1YiIyDIoOMabSCom3kREZBZCvGntHjECKFNGbjxERJQMu5oTScXEm4iIzGLPHuD33wEnJ2D6dNnREBGRAd5OjEgqnnlERJRlSUnAtGna5UmTgKJF5cZDREQpsKs5kVRMvImIKMu+/hq4cgVwdwemTJEdDRERGWFXcyKpmHgTEVGWxMVp79sNaFu93dzkxkNERCawxZtIKibeRESUJcHBwH//ASVKAKNGyY6GiIhM4hhvIql45hERUaZFRwMBAdrl2bMBR0ep4RARUWrY4k0kFRNvIiLKtCVLgMePgYoVgYEDZUdDRESp4hhvIqmYeBMRUabcvw8sW6ZdnjcPsLOTGw8REaXhdYu3YFdzIil45hERUaYEBAAxMUDdukDXrrKjISKiNLGrOZFUTLyJiCjDbtwAVq/WLi9YACgUcuMhIqK3YOJNJBUTbyIiyrBZswC1GvDxAVq0kB0NERG9Fcd4E0nFxJuIiDLk4kXg22+1y/Pny42FiIjSibcTI5KKZx4REWWInx8gBNCzJ1C7tuxoiIgoXXQt3ky8iaTgmUdEROl2/Djwww/anopz58qOhoiI0o1dzYmkYuJNRETpIgQwdap2edgwoHx5ufEQEVEGcHI1IqmYeBMRUbr8+CNw4gTg4ADMnCk7GiIiyhCO8SaSimceERG9VVIS4OurXR4/HvD0lBsPERFlEFu8iaRi4k1ERG+1eTNw6RKQPz/w2WeyoyEiooxScIw3kVRMvImIKE3x8W+6lk+dChQoIDceIiLKBHY1J5KKZx4REaVpzRrg1i2gWDFg7FjZ0RARUaawqzmRVEy8iYgoVS9eAPPmaZdnzQKcnOTGQ0REmcTEm0gqJt5ERJSqzz8HHj4E3nkHGDJEdjRERJRpHONNJBUTbyIiMunhQ2DJEu1yQACgVMqNh4iIsoBjvImk4plHREQmBQZqu5r/739A9+6yoyEioixhV3MiqZh4ExGRkYgIYOVK7XJgIBtIiIisHruaE0nFSykiIjIyezaQkAA0bw60aiU7GiIiyrLXLd6CiTeRFEy8iYjIQHg4sGmTdnnBAkChkBsPERGZAcd4E0llJzsAIiKyLH5+2h6JXbsC774rOxrKCrVajaioKMTGxqJw4cJwd3eXHRIRycKu5kRS8SsvIiLS++034PvvtQ0iuvt3k3V5+fIl1qxZg2bNmsHNzQ1eXl6oXLkyChcujNKlS2P48OE4c+aM7DCJKKfpEm+2eBNJkekW7//++w+3bt3Sf4tepUoVqFQqc8ZGREQ5SAhg6lTt8qBBQKVKUsOhTPj8888REBAALy8vdOrUCVOnTkXx4sXh6OiIJ0+e4NKlS/j111/RqlUr1KtXD8uXL0e5cuVkh01EOYFdzYmkylDiffv2baxevRpbtmzBf//9ByGE/jF7e3s0btwYH330Ebp16wYbM53Ud+/exWeffYaffvoJr169Qvny5bF+/XrUrl3bLPsnIiKtAweAo0cBlUo7uRpZn5MnT+Lw4cOoVq2aycffffddDBkyBMHBwdiwYQOOHj3KxJsor+DtxIikSnd2PH78eFSrVg3Xrl2Dv78/Ll++jOfPnyMhIQFRUVHYv38/GjVqhBkzZqB69epm6cb29OlTNGzYEEqlEj/99BPCw8OxdOlS5M+fP8v7JiKiNzQawNdXuzx6NFCypNx4KHO2b9+eatKdnIODA0aNGoVhw4blQFREZBE4xptIqnS3eNvb2+P69esoXLiw0WNFihRBixYt0KJFC8yaNQv79+/H7du3Ubdu3SwFt3DhQpQsWRIhISH6dV5eXlnaJxERGfvuO+DCBcDVFZg2TXY0ZA7379+Hh4eHyccuXryI6tWr53BERCQVW7yJpEp34r148eJ077Rdu3aZCialvXv3onXr1ujRoweOHj2K4sWLY9SoURg+fHiqz4mPj0d8fLz+7+joaADamV3VanWW4tE9P6v7kYllsAzWXgZrjx9gGQz3A0yfbgdAgUmTkuDqqkFOHBa+B6b3ZS7VqlXDl19+iU6dOhmsX7JkCWbMmIFXr16le1+rVq3C4sWLERkZiSpVqiAoKAiNGzdOdfv4+Hj4+/vjm2++QVRUFEqUKAE/Pz8MGTIk0+UhoiziGG8iqTI1udrly5dRpUoVk4/9/PPPaNOmTZaC0rlx4waCg4MxadIkTJs2DadPn8a4ceOgUqkwYMAAk88JDAzEnDlzjNaHhobCycnJLHGFhYWZZT8ysQyWwdrLYO3xAywDAPz0kxeuX6+B/PnjUKHCQezfn2SmyNKH74FWbGysGSJ547PPPkOvXr0wcOBAfP7553jy5An69++Py5cvY9u2benez7Zt2zBhwgSsWrUKDRs2xJo1a9C2bVuEh4ejVKlSJp/Ts2dP3L9/H+vXr8c777yDBw8eIDEx0VxFI6LMYIs3kVSZSrzr1KmDRYsWYezYsfp18fHxmDx5MtavX5+hb9HTotFoUKdOHcyfPx8AUKtWLVy+fBnBwcGpJt6+vr6YNGmS/u/o6GiULFkSPj4+cHV1zVI8arUaYWFhaNWqFZRKZZb2JQvLYBmsvQzWHj/AMujExAAjR2qrgjlzlOjWrbU5Q0wT3wNDuh5a5jJ58mS8//776NevH6pXr44nT56gXr16uHjxYqpd0E1ZtmwZhg4dqh8PHhQUhAMHDiA4OBiBgYFG2//88884evQobty4ob9vOIeJEVkAjvEmkipTife3336Ljz76CPv370dISAiioqLQp08fAMCJEyfMFlyxYsVQuXJlg3WVKlXCzp07U32OSqUyeVszpVJptgs7c+5LFpbBMlh7Gaw9foBlCA4GoqIAb29g5EhbKJU5f0GW19+D5PswtzJlyqBKlSr6erNnz54ZSroTEhJw7tw5TNXdZ+41Hx8fnDx50uRz9u7dq/+C/uuvv4azszM6deqEuXPnwtHR0eRzOEwsbSyDfNYePwDYvu51kigEhJWWw9rfB2uPH2AZUttXemQq8e7atSvq1auHgQMHomrVqoiJicHgwYOxdOnSVCvVzGjYsCGuXr1qsO6ff/5B6dKlzfYaRER51ZMnwMKF2uW5cwF7e7nxkHmdOHEC/fr1Q8GCBXHx4kWcOHECY8eOxY8//og1a9agQIECb93Ho0ePkJSUZJSse3h4ICoqyuRzbty4gePHj8PBwQG7d+/Go0ePMGrUKDx58gQbNmww+RwOE0sflkE+a46/2fPncAPwx4ULeKhQyA4nS6z5fQCsP36AZdDJyDCxTCXeAJCUlISEhAQkJSUhKSkJRYsWNdnSnBUTJ05EgwYNMH/+fPTs2ROnT5/G2rVrsXbtWrO+DhFRXrRwIfD8OVC9OtC7t+xoyNxatGiBiRMnYu7cuVAqlahUqRKaN2+O/v37o1q1arhz506696VIcZEuhDBap6PRaKBQKPDtt9/Czc0NgLa7evfu3bFy5UqTX9BzmFjaWAb5rD1+ALB9fc/I/9WtC1sfH8nRZI61vw/WHj/AMqSUkWFimUq8t27dio8//hiNGzfGP//8gwsXLmDw4ME4cOAAvv76a5QpUyYzuzVSt25d7N69G76+vvD394e3tzeCgoLQt29fs+yfiCivunsX+L//0y4HBnKS29woNDQUTZs2NVhXtmxZHD9+HAEBAenaR6FChWBra2vUuv3gwYNUu6wXK1YMxYsX1yfdgHaYmBACd+7cQbly5Yyew2Fi6cMyyGfN8QshAAB2KhXsrLQMOtb8PgDWHz/AMiTfR3pl6lJr6NChmD9/Pvbu3YvChQujVatW+Ouvv1C8eHHUrFkzM7tMVYcOHfDXX38hLi4OV65cSfNWYkRElD5z5gBxcUDjxkDbtrKjoeyQMunWsbGxwYwZM9K1D3t7e9SuXduoO15YWBgaNGhg8jkNGzbEvXv38PLlS/26f/75BzY2NihRokQ6oycis+PtxIikytSZ98cff+Djjz82WFegQAF89913WLlypVkCIyKi7HH1KqAbartgAWDlQ/0oma1bt6Z72//++y9dE6JOmjQJX375JTZs2IArV65g4sSJiIiIwMiRIwFou4knv9NInz59ULBgQQwePBjh4eE4duwYPvnkEwwZMsSs88AQUQZxVnMiqTKVeFeoUCHVx/r375/pYIiIKPtNn65t+OjUCUil0ZKsVHBwMCpWrIiFCxfiypUrRo8/f/4c+/fvR58+fVC7dm08efLkrfvs1asXgoKC4O/vj5o1a+LYsWPYv3+/fqLTyMhIRERE6LfPly8fwsLC8OzZM9SpUwd9+/ZFx44d8X+6sQ1EJAcTbyKp0j3Ge8GCBRg3bly6Zhf9/fff8ejRI7Rv3z5LwRERkXmdOQPs2KFt5U7nMF+yIkePHsUPP/yA5cuXY9q0aXB2doaHhwccHBzw9OlTREVFoXDhwhg8eDAuXbqEIkWKpGu/o0aNwqhRo0w+tnHjRqN1FStWzBUz3hLlKrqu5ky8iaRId+IdHh6OUqVKoUePHujUqRPq1KmDwoULAwASExMRHh6O48eP45tvvkFkZCS++uqrbAuaiIgyZ9o07e/+/YGqVeXGQtmjQ4cO6NChAx4/fozjx4/j1q1bePXqFQoVKoRatWqhVq1asOEYT6K853XiLXj+E0mR7sT7q6++wsWLF7Fy5Ur07dsXz58/h62tLVQqlf7+ZbVq1cJHH32EgQMHmv3WYkRElDUHD2p/7O21k6tR7lawYEF07txZdhhEZCk4uRqRVBm6nVj16tWxZs0arF69GhcvXjT4Fr1mzZooVKhQdsVJRERZIAQwdap2eeRIwMtLajhERJTTOMabSKpM3cdboVCgRo0aqFGjhrnjISKibLBzJ3DuHJAvH+DnJzsayk7e3t5QJJuq/saNGxKjISKLwRZvIqkylHgnn7U0OTc3N7i5uZklICIiMq/ExDfJ9uTJQDrn0yIrZWqyMyIiTq5GJFeGEm8vLy+Db9GTK1y4MD799FNMmjTJLIEREZF5hIQA//wDFCoE8CM692vatKnsEIjIEjHxJpIqQ4n3+fPnTa5/9uwZTp8+jYCAADg5OWHkyJFmCY6IiLLm1Stg9mztsp8f4OoqNRzKAeydRkQmcYw3kVQZSrzTGtPdtGlTFCtWDEuWLGHiTURkIZYvB+7dA0qVAj7+WHY0lBPYO42ITOIYbyKpMjW5WmoaNGjASVyIiCzE06dAYKB2ec4cgHd5zBvYO42ITGJXcyKpzJp4P336FPnz5zfnLomIKJMWLwaePQMqVwb695cdDeUU9k4jIpPY1ZxIKrP1NUlISMCiRYtQr149c+2SiIgyKTISCArSLs+fz+sseoO904jyJgVbvImkylCLd9euXU2uf/78OS5dugQ7Ozv8+uuvZgmMiIgyb+5c7cRq9esDnTrJjoYsCXunEeVButZugGO8iSTJUOKd2myoJUuWRPfu3dG3b1+4cspcIiKp/v0XWLdOu7xgAZDKPFuUB7F3GlEepWvtBtjiTSRJhhLvkJCQNB+/fv06PvjgAxw6dChLQRERUebNmAEkJgJt2wJNmsiOhnIae6cRkZHkLd5MvImkMOvkai9fvsTRo0fNuUsiIsqA8+eBrVu1y/Pny42F5GDvNCIykrzFm13NiaQwa+JNRERyTZum/d2nD1CzptRQSBL2TiMiI+xqTiQdv/IiIsoljhwBfv4ZsLMD/P1lR0OWir3TiPIgJt5E0jHxJiLKBYQAfH21yx99BJQtKzceIiKyIBzjTSRdhrqa16pVC4o0pseNjY3NckBERJRxe/cCv/0GODlpJ1cjIiLS4xhvIukylHh/8MEH2RQGERFlVlLSm7HdEycCRYvKjYeIiCwME28i6TKUeM+aNSu74iAiokz69lsFwsMBd3fgk09kR0OysXcaERl53dVcw6SbSJpMz2qemJiII0eO4Pr16+jTpw9cXFxw7949uLq6Il++fOaMkYiIUpGQYAN/f+14PV9fIJU7SVEewt5pRGTkdYu3YOJNJE2mEu/bt2+jTZs2iIiIQHx8PFq1agUXFxcsWrQIcXFxWL16tbnjJCIiE37+2QsREQqUKAGMHi07GrIE7J1GREZ0Xc2ZeBNJk6mzb/z48ahTpw6ePn0KR0dH/fouXbrgl19+MVtwRESUuuhoYMeO8gCA2bOBZB/HRAC0vdMOHjyINWvW4MWLFwCAe/fu4eXLl5IjI6IcxRZvIuky1eJ9/PhxnDhxAvb29gbrS5cujbt375olMCIiStvnn9sgOlqJ8uUFBg5MfUwv5U3snUZEeq/HeDPxJpInU2efRqNBUvLZEV+7c+cOXFxcshwUERGl7cEDIChI+xHu758Eu0zP2EG5FXunEZGersU7jYkXiSh7ZSrxbtWqFYKCgvR/KxQKvHz5ErNmzUK7du3MFRsREaUiIACIiVHgnXeeoksXITscskDHjx/H9OnT2TuNiNjVnMgCZKqN5PPPP0fz5s1RuXJlxMXFoU+fPrh27RoKFSqELVu2mDtGIiJK5uZNIDhYu9y/fzgUinflBkQWib3TiEiPXc2JpMtU4u3p6YkLFy5gy5Yt+OOPP6DRaDB06FD07dvXoDsbERGZ36xZgFoNvP++BjVqPJIdDlkoXe+0tWvXAmDvNKI8jbOaE0mX6VGBjo6OGDJkCIYMGaJfFxkZiU8++QQrVqwwS3BERGTor7+Ab77RLs+dq8H9+3LjIcvF3mlEpMeu5kTSZTjxDg8Px+HDh6FUKtGzZ0/kz58fjx49QkBAAFavXg1vb+/siJOIiAD4+QFCAD16ALVrC+zfLzsislTsnUZEeky8iaTLUOL9ww8/oFu3blCr1QCARYsWYd26dejZsyeqVq2K7du3o0OHDtkSKBFRXnf8OLBvH2BrC8ydKzsasgbsnUZEADjGm8gCZOjsCwgIwMiRIxEdHY0lS5bgxo0bGDlyJHbu3InDhw8z6SYiyiZCAFOnapeHDAEqVJAbD1m28PBwrFy5EmvXrsWzZ88AAI8ePcLEiRNRpkwZHDp0SG6ARJSz2OJNJF2Gzr4rV65g9OjRyJcvH8aNGwcbGxsEBQWhSZMm2RUfEREB2L8fOHECcHDQTq5GlJoffvgBtWrVwtixYzFy5EjUqVMHhw8fRqVKlXDhwgVs374d4eHhssMkopykm1yN9/EmkiZDiXd0dDTy588PALCzs4OjoyPKly+fHXEREdFrSUmAr692edw4oHhxufGQZWPvNCIywhZvIukyNblaVFQUAEAIgatXryImJsZgm+rVq5snOiIiwpYt2tnM3dyAzz6THQ1ZuitXrmDTpk363mmffvope6cR5XUc400kXYYT75YtW0IIof9b9825QqGAEAIKhQJJuu4sRESUJQkJwIwZ2uXPPgPc3eXGQ5aPvdOIyAhbvImky1DiffPmzeyKg4iITFizBrh1CyhWDBg/XnY0ZC3YO42IDDDxJpIuQ4l36dKlsysOIiJK4cWLN7cNmzkTcHKSGw9ZD/ZOIyID7GpOJF2Gu5oDgJeXF4YMGYJBgwahVKlS5o6JiIgABAUBDx8C77wDDB0qOxqyFuydRkRG2OJNJF2mEu/Jkydj48aN8Pf3R/PmzTF06FB06dIFKpXK3PEREeVJjx4Bixdrl+fNA5RKufGQ9WDvNCIywtuJEUmXqa+9xo4di3PnzuHcuXOoXLkyxo0bh2LFimHMmDH4448/zB0jEVGeM3++tqt5rVpAjx6yoyFr5OXlBX9/f0RERMgOhYhkY4s3kXRZOvtq1KiBL774Anfv3sWsWbPw5Zdfom7duqhRowY2bNhgML6MiIjSJyICWLlSuxwYCPA6iTJj8uTJ2LNnD8qUKYNWrVph69atiI+Plx0WEcnAMd5E0mXp7FOr1fjuu+/QqVMnTJ48GXXq1MGXX36Jnj17ws/PD3379jVXnEREecbs2drbiDVrBvj4yI6GrBV7pxGRHlu8iaTL1Nn3xx9/YOzYsShWrBjGjh2LKlWq4NKlSzh+/DgGDx4MPz8/7N27F7t37zZ3vEREuVp4OLBpk3Z5wQIOx6OsY+80ImLiTSRfpiZXq1u3Llq1aoXg4GB88MEHUJqY9ady5cr48MMPsxwgEVFe4uen7RHYpQvw3nuyo6HcQK1WY/fu3QgJCUFYWBjq1auHoUOH4t69e/Dz88PBgwexefNm2WESUXZi4k0kXaYS78OHD6NJkyYmH/vtt99Qr149ODs7IyQkJEvBERHlJb/9Bnz/vXZMd0CA7GjI2v3xxx8ICQnBli1bYGtri/79++Pzzz9HxYoV9dv4+PikWp8TUS7CMd5E0mXq7Pvoo4/w+PFjo/UnTpxAmzZtshwUEVFeIwQwdap2edAgoFIlqeFQLlC3bl1cu3YNwcHBuHPnDpYsWWKQdAPsnUaUZ/B2YkTSZSrxbty4MXx8fPDixQv9umPHjqFdu3aYNWuW2YIjIsorQkOBo0cBlQrgxyiZw+HDh/Hzzz+jR48eRkPCfvvtNwBg7zSivIJdzYmky9TZt3btWnh7e6N9+/aIi4vD4cOH0b59e/j7+2PixInmjpGIKFfTaN60do8eDZQqJTceyh3YO42I9NjVnEi6TJ19CoUCW7ZsgYODA1q2bIlOnTohMDAQ48ePN3d8RES53nffARcuAK6ugK+v7Ggot2DvNCLSY4s3kXTpnlzt4sWLRutmzZqF3r17o1+/fmjSpIl+m+rVq5svQiKiXEytBqZP1y5PmQIUKiQ3Hso91q5dix49eqB9+/YIDQ3FqVOn0KlTJ8ybN49flBPlNUy8iaRLd+Jds2ZNKBQKg/t96v5es2YN1q5dCyEEFAoFknQTOBARUZrWrweuXweKFAE4UofMSdc7rX379mjZsiUuXryIwMBAjBkzRnZoRJTTmHgTSZfuxPvmzZvZGQcRUZ4TGwvMmaNdnjEDyJdPbjxk/dg7jYhMej3GG0y8iaRJd+JdunTp7IyDiCjP+b//A6KiAG9v4KOPZEdDuQF7pxGRSboWb95OjEiadCfepoSHhyMiIgIJCQkG6zt16pSloIiIcrunT4GFC7XLc+cC9vZy46Hcgb3TiMgkdjUnki5TifeNGzfQpUsX/PXXXwbfrCtef4vGb9GJiNK2cCHw7BlQvTrQu7fsaCi3YO80IjKJiTeRdJlKvMePHw9vb28cPHgQZcqUwenTp/H48WNMnjwZS5YsMXeMRES5yt27wBdfaJfnz+eQO8pe7J1GRPr7eNvaSg6EKO/KVOJ96tQpHDp0CIULF4aNjQ1sbGzQqFEjBAYGYty4cTh//ry54yQiyjX8/YG4OKBRI6BdO9nRUG7F3mlEpKc73znGm0iaTLWzJCUlId/r6XcLFSqEe/fuAdB2cbt69ar5okshMDAQCoUCEyZMyLbXICLKTv/8o72FGAAsWMBrIMo+ut5p9+/fh5OTEy5fvoxjx46hTp06OHLkiOzwiCgnsas5kXSZavGuWrUqLl68iDJlyuC9997DokWLYG9vj7Vr16JMmTLmjhEAcObMGaxdu5a3PyEiqzZ9uvb6p2NHoGFD2dFQbsbeaUSkp+tqzsSbSJpMnX3Tp0+H5vUJPG/ePNy+fRuNGzfG/v378X//939mDRAAXr58ib59+2LdunUoUKCA2fdPRJQTzp4Ftm/XtnIHBMiOhnI7Wb3TiMgCscWbSLpMtXi3bt1av1ymTBmEh4fjyZMnKFCggH7smDmNHj0a7du3x/vvv4958+aluW18fDzi4+P1f0dHRwMA1Go11Gp1luLQPT+r+5GJZbAM1l4Ga48fkFMGX19bADbo00eDihWTkNWXtvb3wdrjB8xbBnMfBxm904jIQvE+3kTSZek+3v/++y+uX7+OJk2awN3dXT9xizlt3boVf/zxB86cOZOu7QMDAzFnzhyj9aGhoXBycjJLTGFhYWbZj0wsg2Ww9jJYe/xAzpXhzz8L4eDBhrCz06BJk1+wf3+s2fZt7e+DtccPmKcMsbHm+58AtL3TYmJiAGh7p3Xo0AGNGzdGwYIFsW3btgzta9WqVVi8eDEiIyNRpUoVBAUFoXHjxm993okTJ9C0aVNUrVoVFy5cyEwxiMgcdIk3ZzUnkiZTiffjx4/Rs2dPHD58GAqFAteuXUOZMmUwbNgw5M+fH0uXLjVLcP/99x/Gjx+P0NBQODg4pOs5vr6+mDRpkv7v6OholCxZEj4+PnB1dc1SPGq1GmFhYWjVqhWUSmWW9iULy2AZrL0M1h4/kLNlEAKYO1d7sTNihMDgwc3Msl9rfx+sPX7AvGXQ9dAyF3P1Ttu2bRsmTJiAVatWoWHDhlizZg3atm2L8PBwlCpVKtXnPX/+HAMGDEDLli1x//79LJWFiLKIY7yJpMtU4j1x4kQolUpERESgUqVK+vW9evXCxIkTzZZ4nzt3Dg8ePEDt2rX165KSknDs2DGsWLEC8fHxsE3xzZ1KpYJKpTLal1KpNNuFnTn3JQvLYBmsvQzWHj+QM2XYuRM4dw5wdgZmzrSFUmneFgdrfx+sPX7APGXIrmOQ1d5py5Ytw9ChQzFs2DAAQFBQEA4cOIDg4GAEBgam+rwRI0agT58+sLW1xffff5+VIhBRVvF2YkTSZeprr9DQUCxcuBAlSpQwWF+uXDncvn3bLIEBQMuWLfHXX3/hwoUL+p86deqgb9++uHDhglHSTURkaRITAT8/7fLkyUCRInLjobzj8ePHaNmyJcqXL4927dohMjISADBs2DBMnjw5XftISEjAuXPn4OPjY7Dex8cHJ0+eTPV5ISEhuH79OmbNmpX5AhCR+XByNSLpMtXiHRMTY3K89KNHj0y2NmeWi4sLqlatarDO2dkZBQsWNFpPRGSJNm4Erl4FChbUJt5EOcUcvdMePXqEpKQkeHh4GKz38PBAVFSUyedcu3YNU6dOxa+//go7u/RdZnBi1LSxDPJZe/y2ajVsoE28rbUMgPW/D9YeP8AypLav9MhU4t2kSRN89dVXmDt3LgBAoVBAo9Fg8eLFaNasWWZ2SUSU67x6BcyerV328wOyOM0EUYaEhobiwIEDZumdlnJMuBDC5DjxpKQk9OnTB3PmzEH58uXTvX9OjJo+LIN81hp/zdu3URraxNtay5CctZfB2uMHWAadjEyMmqnEW5dgnz17FgkJCfj0009x+fJlPHnyBCdOnMjMLtPtyJEj2bp/IiJzWbkSuHsXKFkS+Phj2dFQXmOO3mmFChWCra2tUev2gwcPjFrBAeDFixc4e/Yszp8/jzFjxgAANBoNhBCws7NDaGgoWrRoYfQ8ToyaNpZBPmuP33bnTgDaxNtaywBY//tg7fEDLENKGZkYNVOJd+XKlXHx4kUEBwfD1tYWMTEx6Nq1K0aMGIFZs2Zhw4YNmdktEVGu8ewZMH++dtnfH0jnjRmIzMYcvdPs7e1Ru3ZthIWFoUuXLvr1YWFh6Ny5s9H2rq6u+OuvvwzWrVq1CocOHcKOHTvg7e1t8nU4MWr6sAzyWW38rydVFDY21luGZKy9DNYeP8AyJN9HemX6Pt5FixY16hb2559/YtOmTUy8iSjPW7wYePoUqFwZ6N9fdjSUF5mrd9qkSZPQv39/1KlTB/Xr18fatWsRERGBkSNHAtC2Vt+9exdfffUVbGxsjOZgKVKkCBwcHDg3C5FMvJ0YkXQ8+4iIzCwyEggK0i4HBAC8AQPJoOud9u6776JVq1b63mlnzpxBQEBAuvfTq1cvBAUFwd/fHzVr1sSxY8ewf/9+lC5dGgAQGRmJiIiI7CoGEZmD7nZiTLyJpMl0izcREZk2bx4QGwu89x5gojcuUY4xV++0UaNGYdSoUSYf27hxY5rPnT17NmbrZhkkIjl0txPjfbyJpOHXXkREZvTvv8DatdrlhQsBXuMQEZF0vI83kXQZavHu2rVrmo8/e/YsK7EQEVm9mTOBxESgTRugaVPZ0RAREYFjvIksQIYSbzc3t7c+PmDAgCwFRERkrS5cALZs0S7rZjQnIiKSji3eRNJlKPEOCQnJrjiIiKzetGna3717A7VqyY2F8i72TiMiI5xcjUg6Tq5GRGQGR48CP/0E2Nlp79tNJAt7pxGREXY1J5KOiTcRURYJAUydql0ePhx45x258VDext5pRGSEXc2JpOPZR0SURXv3Ar/9Bjg6AjNmyI6GiIgoBd5OjEg6Jt5ERFmQlPRmbPfEiUCxYnLjISIiMsIWbyLpePYREWXB118D4eFAgQLAJ5/IjoaIiMgEjvEmko5nHxFRJsXFAbNmaZd9fYH8+aWGQ0REZBpbvImk49lHRJRJq1cDERFA8eLAmDGyoyEiIkoFbydGJB3PPiKiTIiOBgICtMuzZ2snViMiIrJIbPEmko5nHxFRJixdCjx6BJQvDwwaJDsaIiKiNHCMN5F0PPuIiDLowQNg2TLtckAAYGcnNx4iIqI08XZiRNIx8SYiyqCAAODlS6BOHaBbN9nREBERvQW7mhNJx7OPiCgDbt0CgoO1ywsWAGw8ICIii8eu5kTS8ewjIsqAWbMAtRp4/32gZUvZ0RAREaUDW7yJpOPZR0SUTn/9BXz9tXY5MFBuLEREROnG24kRScezj4gonfz8ACGAHj2047uJiIisAlu8iaTj2UdElA4nTgD79gG2tsDcubKjISIiygCO8SaSjmcfEdFbCAH4+mqXhwwBKlSQGw8REVGG8HZiRNIx8SYieouffgJ+/RVwcNBOrkZERGRV2NWcSDqefUREadBo3rR2jxsHFC8uNx4iIqIMY+JNJB3PPiKiNGzZAly8CLi5AZ99JjsaIiKiTHg9xhu2tnLjIMrDmHgTEaUiIQGYMUO7/NlngLu73HiIiIgyhWO8iaRj4k1ElIp164CbN4GiRbXdzImIiKwSu5oTScezj4jIhJcvAX9/7fLMmYCzs9x4iIiIMo23EyOSjmcfEZEJQUHAgwdA2bLAsGGyoyEiIsoCtngTScezj4gohUePgMWLtctz5wJKpdx4iIiIsoRjvImkY+JNRJTCggVAdDRQsybQq5fsaIiIiLLodeLNWc2J5GHiTUSUTEQEsGKFdjkwEGCvPCIisnoc400kHc8+IqJk5swB4uOBpk2B1q1lR0NERJRFunt4g13NiWRi4k1E9NqVK8DGjdrlBQsAXp8QEZHV03UzB1u8iWTi2UdE9Nr06dqGgQ8+AOrVkx0NERGRGTDxJrIIPPuIiAD8/juwa5d2THdAgOxoiIiIzCR5V3Mm3kTS8OwjojxPCMDXV7s8cCBQubLceIiIiMwmWYs3ZwwlkodnHxHleWFhwOHDgL09MHu27GiIiIjMiF3NiSwCzz4iytM0GmDqVO3y6NFAqVJy4yEiIjIrdjUnsgg8+4goT9uxQ4Hz5wEXF2DaNNnREBERmRlbvIksAs8+IsqzEhMVmD3bFgDwySdAoUKSAyIiIjK35GO8eZ9MImmYeBNRnnXwYGn8+68ChQsDEyfKjoaIiCgbvE68ha2t5ECI8jYm3kSUJ8XGAtu2VQAAzJgB5MsnOSAiIqLsoBvjzcSbSCo72QEQEcmwYoUNnj5VwstL4KOP2PWOiIhyKV1Xc47vJpKKZyAR5TlPnwJLlmg//mbOTIJKJTkgIiKi7KJLvNniTSQVE28iynMWLACePVOgdOnn6N1byA6HiIgo+7CrOZFFYOJNRHnK3bvA//2fdrlfvyu8DiEiotyNLd5EFoGJNxHlKf7+QFwc0KCBBnXq3JcdDhERUfbiGG8ii8AzkIjyjH/+Adav1y4HBGh4O1MiIsr92OJNZBGYeBNRnjF9uvb6o0MHoGFDju0mIqI8gGO8iSwCE28iyhPOngW2bwcUCiAgQHY0REREOYQt3kQWgYk3EeUJ06Zpf/ftC1SvLjcWIiKiHMMx3kQWgWcgEeV6v/wChIUBSqV2cjUiIqI8gy3eRBaBiTcR5WpCAL6+2uWRIwFvb7nxEBER5SiO8SayCEy8iShX270bOHMGcHYG/PxkR0NERJTDdC3evJUHkVRMvIko10pMfDO2e9IkwMNDbjxEREQ5jl3NiSwCE28iyrU2bQKuXgUKFgSmTJEdDRERkQTsak5kEZh4E1Gu9OoVMHu2dtnPD3B1lRoOERGRHGzxJrIITLyJKFdatQq4cwcoWRL4+GPZ0RAREUnC24kRWQSLPgMDAwNRt25duLi4oEiRIvjggw9w9epV2WERkYV7/hyYP1+7PGcO4OAgNx4iIiJpXifegi3eRFJZdOJ99OhRjB49Gr/99hvCwsKQmJgIHx8fxMTEyA6NiCzY4sXAkydA5crAgAGyoyEiIpKIY7yJLIKd7ADS8vPPPxv8HRISgiJFiuDcuXNo0qSJpKiIyJJFRQGff65dDgjgdQYREeVx7GpOZBEsOvFO6fnz5wAAd3f3VLeJj49HfHy8/u/o6GgAgFqthlqtztLr656f1f3IxDJYBmsvgyXH7+9vg9hYW7z7rgbt2iUhtRAtuQzpZe1lsPb4AfOWwZqPAxFZME6uRmQRrCbxFkJg0qRJaNSoEapWrZrqdoGBgZgzZ47R+tDQUDg5OZkllrCwMLPsRyaWwTJYexksLf6oKCesXdsSANCx40n89NPjtz7H0sqQGdZeBmuPHzBPGWJjY80QCRFRCky8iSyC1STeY8aMwcWLF3H8+PE0t/P19cWkSZP0f0dHR6NkyZLw8fGBaxbvJ6RWqxEWFoZWrVpBqVRmaV+ysAyWwdrLYKnxDxhgi6QkG/j4aPDZZ++lua2lliEjrL0M1h4/YN4y6HpoERGZFcd4E1kEq0i8x44di7179+LYsWMoUaJEmtuqVCqoVCqj9Uql0mwXdubclywsg2Ww9jJYUvx//gls3apdXrDABkpl+sayWVIZMsvay2Dt8QPmKYMlH4NVq1Zh8eLFiIyMRJUqVRAUFITGjRub3HbXrl0IDg7GhQsXEB8fjypVqmD27Nlo3bp1DkdNRAA4xpvIQlj0GSiEwJgxY7Br1y4cOnQI3t7eskMiIgs1bZr2d69eQK1acmMhyk22bduGCRMmwM/PD+fPn0fjxo3Rtm1bREREmNz+2LFjaNWqFfbv349z586hefPm6NixI86fP5/DkRMRAHY1J7IQFt3iPXr0aGzevBl79uyBi4sLoqKiAABubm5wdHSUHB0RWYpjx4D9+wE7O2DePNnREOUuy5Ytw9ChQzFs2DAAQFBQEA4cOIDg4GAEBgYabR8UFGTw9/z587Fnzx7s27cPtfitGFHOY1dzIotg0Yl3cHAwAKBZs2YG60NCQjBo0KCcD4iILI4QwNSp2uVhw4B33pEbD1FukpCQgHPnzmGq7iR7zcfHBydPnkzXPjQaDV68eME7kmQByyCfNcevSEiAHQCNQgHAOsugY83vA2D98QMsQ2r7Sg+LTryFELJDICILt28fcOoU4OgIzJwpOxqi3OXRo0dISkqCh4eHwXoPDw99L7S3Wbp0KWJiYtCzZ89Ut+EdSdKHZZDPGuMv/eefqAng4aNHAKyzDClZexmsPX6AZdDJyB1JLDrxJiJKS1LSm7HdEyYAxYpJDYco11K8binTEUIYrTNly5YtmD17Nvbs2YMiRYqkuh3vSJI2lkE+a47f5vV8DIVfV5LWWAYda34fAOuPH2AZUsrIHUmYeBOR1frmG+DyZaBAAeDTT2VHQ5T7FCpUCLa2tkat2w8ePDBqBU9p27ZtGDp0KLZv3473338/zW15R5L0YRnks8r4X39JZmOnvey3yjKkYO1lsPb4AZYh+T7Sy6JnNSciSk18/Juu5VOnAvnzSw2HKFeyt7dH7dq1jbrjhYWFoUGDBqk+b8uWLRg0aBA2b96M9u3bZ3eYRJQW3k6MyCKwxZuIrNLq1UBEBODpCYwdKzsaotxr0qRJ6N+/P+rUqYP69etj7dq1iIiIwMiRIwFou4nfvXsXX331FQBt0j1gwAB88cUXqFevnr613NHREW5ubtLKQZRn8XZiRBaBiTcRWZ3o6De3DZs1SzuxGhFlj169euHx48fw9/dHZGQkqlativ3796N06dIAgMjISIN7eq9ZswaJiYkYPXo0Ro8erV8/cOBAbNy4MafDJyIm3kQWgYk3EVmdZcuAR4+A8uWBIUNkR0OU+40aNQqjRo0y+VjKZPrIkSPZHxARpR/v401kETjYg4isyoMHwNKl2uV58wA7fn1IRESUOo7xJrIIPAOJyKrMnw+8fAnUrg107y47GiIiIgvHruZEFoGJNxFZjVu3gOBg7fKCBfo7pBAREVFqXnc1F0y8iaRi4k1EVmPWLCAhAWjZEnjLbYGJiIgIYIs3kYVg4k1EVuHSJeDrr7XLgYFyYyEiIrIaHONNZBF4BhKRVfDzA4QAunUD6taVHQ0REZGVYIs3kUVg4k1EFu/ECWDvXu01Q0CA7GiIiIisCG8nRmQRmHgTkUUTApg6Vbs8eDBQoYLceIiIiKyKrsWbM5ISScXEm4gs2k8/AcePAw4O2snViIiIKAPY1ZzIIjDxJiKLpdEAvr7a5bFjgRIl5MZDRERkdZh4E1kEJt5EZLG2bAEuXgTc3N50NyciIqIM4BhvIovAxJuILFJCAjBjhnb5008Bd3e58RAREVkl3k6MyCLwDCQii7RuHXDzJlC0KDB+vOxoiIiIrBS7mhNZBCbeRGRxXr4E5s7VLs+YATg7y42HiIjIarGrOZFFYOJNRBbniy+A+/eBsmWB4cNlR0NERGTF2OJNZBGYeBORRXn8GFi0SLs8dy6gVMqNh4iIyKpxjDeRReAZSEQWJTAQiI4GatYEevWSHQ0REZGVY4s3kUVg4k1EFuO//4AVK7TLgYH8cp6IiCjLOMabyCLwspaILMacOUB8PNC0KdC6texoiIiIcgF2NSeyCDwDicgi/P03EBKiXV6wAFAo5MZDRESUK7CrOZFFYOJNRBZh+nRtb7jOnYF69WRHQ0RElEu87moumHgTScXEm4ikO30a2LlT2wsuIEB2NERERLkIW7yJLAITbyKSSghg6lTt8oABQJUqcuMhIiLKVTjGm8gi8AwkIqkOHgQOHwbs7YHZs2VHQ0RElMsw8SayCDwDiUgajeZNa/eoUUDp0nLjISIiynV4OzEii8DEm4ik2bED+OMPwMUFmDZNdjRERES5EMd4E1kEJt5EJIVarZ3JHACmTAEKF5YbDxERUa7EruZEFoFnIBFJsWEDcO2aNuGeOFF2NERERLkUW7yJLAITbyLKcbGxwJw52uXp07VdzYmIiCgbcIw3kUVg4k1EOW75ciAyUjuZ2ogRsqMhIiLKxdjVnMgi8Awkohz19CmwYIF22d8fUKnkxkNERJSrsas5kUVg4k1EOWrhQuDZM6BqVaBvX9nREBER5XLsak5kEZh4E1GOuXsX+OIL7fL8+bwGICIiynZs8SayCEy8iSjHzJ0LxMUBDRoAHTrIjoaIiCgP4BhvIovAM5CIcsS1a8CXX2qXFywAFAq58RAREeUJbPEmsghMvIkoR0yfrq3727UDGjeWHQ0REVEewTHeRBaBiTcRZbtz54DvvtO2cgcGyo6GiIgoD2FXcyKLwDOQiLLdtGna3336ANWry42FiIgoT2FXcyKLwMSbiLLVoUNAaCigVGrv201EREQ5iIk3kUVg4k1E2UYIwNdXuzxiBFCmjNx4iIiI8pzXY7wFE28iqZh4E1G22b0bOH0acHbWTq5GREREOUzX4s3biRBJxcSbiLJFYiLg56ddnjgR8PCQGw8REVGexK7mRBaBiTcRZYuvvgL+/htwdwemTJEdDRERUR7F24kRWQQm3kRkdq9eAbNmaZf9/AA3N7nxEBER5Vls8SayCEy8icjsVq0C7twBSpQARo2SHQ0REVEexvt4E1kEnoFEZFbPnwPz52uX58wBHBzkxkNERJSnscWbyCIw8SYis1qyBHjyBKhUCRgwQHY0REREeRzHeBNZBCbeRGQ2UVHAsmXa5YAAwM5ObjxERER5HruaE1kEnoFEZDbz5gGxscB77wEffCA7GiIiImJXcyLLwMSbiMzixg1g7VrtcmAgoFDIjYeIiCjPE4JdzYksBBNvIjKLmTMBtRpo3Rpo3lx2NERERAQh3iwz8SaSiok3EWXZn38CmzdrlwMD5cZCREREr+m6mQMc400kGc9AIsqyadO0X6p/+CFQq5bsaIiIiAiAYeLNFm8iqZh4E1GWHDsG7N+vncF87lzZ0RAREZGebnw3wMSbSDIm3kSUaUIAvr7a5WHDgHfekRsPERERJcMWbyKLwcSbiDLtxx8VOHkScHQEZsyQHQ0REREZ4BhvIothFWfgqlWr4O3tDQcHB9SuXRu//vqr7JCI8ryHDx0xebL22/MJEwBPT7nxEBERUQps8SayGBafeG/btg0TJkyAn58fzp8/j8aNG6Nt27aIiIiQHRpRnvXvv8C0aY1w86YCpUsDn34qOyIiIiIywjHeRBbD4hPvZcuWYejQoRg2bBgqVaqEoKAglCxZEsHBwbJDI8qTLl0CWrSww8OHTihXTuDXX4H8+WVHRUREREaSt3grFPLiICLYyQ4gLQkJCTh37hymTp1qsN7HxwcnT56UFBWRddBoALXa8CcxMX3rUlsfGwvMng08eaJA6dLPceiQE0qUUMouKhEREZmiS7zZ2k0knUUn3o8ePUJSUhI8PDwM1nt4eCAqKsrkc+Lj4xEfH6//Ozo6GgCgVquhVquzFI/u+Vndj0wsg2lJSelNUhXpSlQTE7XbmtpPQoL25/r1qvj5ZyApKQlqtcJoPymfp/377dvp1mk02ffNdp06SRg//gTc3ZvBWv+VeC7IZ+3xA+YtgzUfByKyULqu5ky8iaSz6MRbR5Gia4wQwmidTmBgIObMmWO0PjQ0FE5OTmaJJywszCz7kSmzZRBCm9AlJiqQlGSj/52UZPi3udZr/36znJio+/0/LF36JNnfb35r40vfet1+hcjp7le2AMrm8GsCNjYa2NkJ2Nq++W1ra+pvATs7jYm/BYoWjcGHH16Fo2Ninj4XLIm1l8Ha4wfMU4bY2FgzREJElAxbvIkshkUn3oUKFYKtra1R6/aDBw+MWsF1fH19MWnSJP3f0dHRKFmyJHx8fODq6pqleNRqNcLCwtCqVSsolW/vXitEaq2Wxj9JSQqT61O2omqXTbe6altZk68zbh1NSBC4f/8RXF0LvU5ATW+beqtu3hkfZGcnoFQCSiVgZwf9csq/k2+n+7G1hdG65NsqFBrcvXsL5cp5QaWyMdq/UilS3Y9xLKnHmXKd4fdVCmi/AMioQlCrPTN0LliijJ7Plsjay2Dt8QPmLYOuhxYRkdnoEm/eSoxIOotOvO3t7VG7dm2EhYWhS5cu+vVhYWHo3LmzyeeoVCqoVCqj9UqlMssXRf/3fzYIDm4KZ2fHVLsRp0xeLZPpLy2y4m3JYWrrMrrezg6wsUnCv/9eQbVqleDgYJvmPjIai+4xOzvjnhapy/iXEWq1Bvv3h6NdOy8oldb7LbQ5zivZWAb5rD1+wDxlsORjsGrVKixevBiRkZGoUqUKgoKC0Lhx41S3P3r0KCZNmoTLly/D09MTn376KUaOHJmDEb9h2707moSHw3buXKudXMpWCDR5/pxlkMhq44+L0/5mizeRdBadeAPApEmT0L9/f9SpUwf169fH2rVrERERIaUCv3sXuH49f5b2oVBkLAHMynpTf9vYJCI8/CL+97/qcHS0y1IsunW2tjlbB2mT1uto166CVSetRETWQHdbz1WrVqFhw4ZYs2YN2rZti/DwcJQqVcpo+5s3b6Jdu3YYPnw4vvnmG5w4cQKjRo1C4cKF0a1btxyPX3H5Mgpcv57jr2tONgAKyA4ii6y9DNYeP0qXlh0BUZ5n8Yl3r1698PjxY/j7+yMyMhJVq1bF/v37UVrCB8jAgRo4O59B/fp14Ohol6mWVNlfOKrVAvv3/4d27arBghtXiIjIQiS/rScABAUF4cCBAwgODkZgYKDR9qtXr0apUqUQFBQEAKhUqRLOnj2LJUuWSEm8k4KDcfbYMdSpUwd2dhZ/2WNSYmIizp49yzJIZO3x4733ZEdAlOdZxSfHqFGjMGrUKNlhoHJloE6d+2jVSjBpJSKiXC8zt/U8deoUfHx8DNa1bt0a69evh1qtzvEu9aJZM9yPjYVo1w7WWnkLtRr3AZZBImuPHwCs9jYkRLmEVSTeRERElPMyc1vPqKgok9snJibi0aNHKFasmNFzeCvQtLEM8ll7/ADLYAmsPX6AZUhtX+nBxJuIiIjSlJHbeqa2van1OrwVaPqwDPJZe/wAy2AJrD1+gGXQycitQJl4ExERkUmZua1n0aJFTW5vZ2eHggULmnyOJd0K1BKxDPJZe/wAy2AJrD1+gGVIKSO3AmXiTURERCZl5rae9evXx759+wzWhYaGok6dOqle4GTnrUCzY1+ysAzyWXv8AMtgCaw9foBlSL6P9LLJ0isRERFRrjZp0iR8+eWX2LBhA65cuYKJEyca3NbT19cXAwYM0G8/cuRI3L59G5MmTcKVK1ewYcMGrF+/HlOmTJFVBCIiIunY4k1ERESpetttPSMjIxEREaHf3tvbG/v378fEiROxcuVKeHp64v/+7/+k3EqMiIjIUjDxJiIiojSldVvPjRs3Gq1r2rQp/vjjj2yOioiIyHqwqzkRERERERFRNmLiTURERERERJSNmHgTERERERERZSMm3kRERERERETZiIk3ERERERERUTZi4k1ERERERESUjZh4ExEREREREWUjJt5ERERERERE2chOdgDZTQgBAIiOjs7yvtRqNWJjYxEdHQ2lUpnl/cnAMlgGay+DtccPsAyWwNrjB8xbBl09pau38jLW3YZYBvmsPX6AZbAE1h4/wDKklJG6O9cn3i9evAAAlCxZUnIkREREb/fixQu4ubnJDkMq1t1ERGRN0lN3K0Qu/2pdo9Hg3r17cHFxgUKhyNK+oqOjUbJkSfz3339wdXU1U4Q5i2WwDNZeBmuPH2AZLIG1xw+YtwxCCLx48QKenp6wscnbI8FYdxtiGeSz9vgBlsESWHv8AMuQUkbq7lzf4m1jY4MSJUqYdZ+urq5W+4+mwzJYBmsvg7XHD7AMlsDa4wfMV4a83tKtw7rbNJZBPmuPH2AZLIG1xw+wDMmlt+7O21+pExEREREREWUzJt5ERERERERE2YiJdwaoVCrMmjULKpVKdiiZxjJYBmsvg7XHD7AMlsDa4wdyRxlyu9zwHrEM8ll7/ADLYAmsPX6AZciKXD+5GhEREREREZFMbPEmIiIiIiIiykZMvImIiIiIiIiyERNvIiIiIiIiomzExDuFgIAANGjQAE5OTsifP7/JbSIiItCxY0c4OzujUKFCGDduHBISEtLcb3x8PMaOHYtChQrB2dkZnTp1wp07d7KhBIaOHDkChUJh8ufMmTOpPm/QoEFG29erVy/b4zXFy8vLKJapU6em+RwhBGbPng1PT084OjqiWbNmuHz5cg5FbOjWrVsYOnQovL294ejoiLJly2LWrFlv/Z+R/R6sWrUK3t7ecHBwQO3atfHrr7+muf3Ro0dRu3ZtODg4oEyZMli9enUORWosMDAQdevWhYuLC4oUKYIPPvgAV69eTfM5qZ0rf//9dw5FbWj27NlGsRQtWjTN51jSe2DqvFUoFBg9erTJ7S3h+B87dgwdO3aEp6cnFAoFvv/+e4PHM/u5snPnTlSuXBkqlQqVK1fG7t27s6kEeRPrbS3ZdUZKrLtZd2cE62359TbAuju5bKm7BRmYOXOmWLZsmZg0aZJwc3MzejwxMVFUrVpVNG/eXPzxxx8iLCxMeHp6ijFjxqS535EjR4rixYuLsLAw8ccff4jmzZuLGjVqiMTExGwqiVZ8fLyIjIw0+Bk2bJjw8vISGo0m1ecNHDhQtGnTxuB5jx8/ztZYU1O6dGnh7+9vEMuLFy/SfM6CBQuEi4uL2Llzp/jrr79Er169RLFixUR0dHQORf3GTz/9JAYNGiQOHDggrl+/Lvbs2SOKFCkiJk+enObzZL4HW7duFUqlUqxbt06Eh4eL8ePHC2dnZ3H79m2T29+4cUM4OTmJ8ePHi/DwcLFu3TqhVCrFjh07ciTelFq3bi1CQkLEpUuXxIULF0T79u1FqVKlxMuXL1N9zuHDhwUAcfXqVYNjnt3naGpmzZolqlSpYhDLgwcPUt3e0t6DBw8eGMQeFhYmAIjDhw+b3N4Sjv/+/fuFn5+f2LlzpwAgdu/ebfB4Zj5XTp48KWxtbcX8+fPFlStXxPz584WdnZ347bffsrk0eQfrbS1LqreFYN3NujtjWG/Lr7eFYN2tk111NxPvVISEhJiswPfv3y9sbGzE3bt39eu2bNkiVCqVeP78ucl9PXv2TCiVSrF161b9urt37wobGxvx888/mz32tCQkJIgiRYoIf3//NLcbOHCg6Ny5c84E9RalS5cWn3/+ebq312g0omjRomLBggX6dXFxccLNzU2sXr06GyLMuEWLFglvb+80t5H5Hrz77rti5MiRBusqVqwopk6danL7Tz/9VFSsWNFg3YgRI0S9evWyLcaMePDggQAgjh49muo2usrj6dOnORdYGmbNmiVq1KiR7u0t/T0YP368KFu2bKqJg6Ud/5SVd2Y/V3r27CnatGljsK5169biww8/NHvMeR3rbcupt4Vg3S1Dbqq7WW9bBtbdb5ij7mZX8ww6deoUqlatCk9PT/261q1bIz4+HufOnTP5nHPnzkGtVsPHx0e/ztPTE1WrVsXJkyezPebk9u7di0ePHmHQoEFv3fbIkSMoUqQIypcvj+HDh+PBgwfZH2AqFi5ciIIFC6JmzZoICAhIs6vXzZs3ERUVZXC8VSoVmjZtmuPHOzXPnz+Hu7v7W7eT8R4kJCTg3LlzBscPAHx8fFI9fqdOnTLavnXr1jh79izUanW2xZpez58/B4B0HfNatWqhWLFiaNmyJQ4fPpzdoaXp2rVr8PT0hLe3Nz788EPcuHEj1W0t+T1ISEjAN998gyFDhkChUKS5rSUd/+Qy+7mS2vtiKZ9FeQHrbXlYd7PuzizW2/KvnVh3m7/uZuKdQVFRUfDw8DBYV6BAAdjb2yMqKirV59jb26NAgQIG6z08PFJ9TnZZv349WrdujZIlS6a5Xdu2bfHtt9/i0KFDWLp0Kc6cOYMWLVogPj4+hyJ9Y/z48di6dSsOHz6MMWPGICgoCKNGjUp1e90xTfk+yTjeply/fh3Lly/HyJEj09xO1nvw6NEjJCUl/X979xbS9P/Hcfz9q+aBNKmspkkaBvPCItOySQdMiELpV9HxorzposigjMi76qKoiOomhEJGh5tOFpWBbtCKkqTDMMugwjLNpJKC6Hx4/y/8bf9cm7np132r5wOE+h62z/fzWZ+X7+/aPiH1X6B/F6NGjZKvX7/Kq1evDGtrT6iqlJaWyrRp0yQzMzPocUlJSXLw4EE5ffq0VFZWis1mk4KCArly5Uo/tvb/cnNz5ciRI1JdXS2HDh2S9vZ2ycvLk46OjoDHm3kMzp49K2/evOm2cDBb//sLd14JNi5mmIv+FuR2/+e2CNlNdoeP3I58bouQ3UbMRYN6dfZvYuvWrbJt27Zuj7lx44bk5OT06PEC3fVR1V/eDeqLc7zCuabW1laprq6WEydO/PLxly5d6vtzZmam5OTkSGpqqlRVVcnChQvDavOPQmn/hg0bfNsmTJggQ4cOlUWLFvnupAfj37e96e9AwhmDtrY2mTNnjixevFhWrVrV7blGj8GvhNp/gY4PtL2/lZSUyJ07d+Tq1avdHmez2cRms/n+brfbpaWlRfbs2SMzZswwupk/mTt3ru/P48ePF7vdLunp6XL48GEpLS0NeI5Zx6CiokLmzp3b5R1Hf2br/2DCmVeMnov+ROR2JzPltgjZTXb3D3I78rktQnYbMRf9FYV3SUmJLFu2rNtj0tLSevRYVqtV6urqumx7/fq1fPny5ac7Iz+e8/nzZ3n9+nWXu+cvXryQvLy8Hj2vv3CuyeFwyPDhw2XevHkhP19SUpKkpqbKw4cPQz43kN6MiffbQR89ehQwvL3fINne3i5JSUm+7S9evAg6RuEI9Rra2tokPz9f7Ha7HDx4MOTn6+sxCCYxMVEGDhz401297vrParUGPH7QoEHd/oJltHXr1sm5c+fkypUrkpKSEvL5U6dOlWPHjhnQstANHjxYxo8fH3T8zToGzc3N4nK5pLKyMuRzzdT/4c4rwcalL+eiPxG53clMuS1CdpPdxiO3I5/bImS3Udn9VxTeiYmJkpiY2CePZbfbZfv27fL8+XPfANbU1Eh0dLRkZ2cHPCc7O1ssFos4nU5ZsmSJiIg8f/5c7t69K7t37w6rHaFek6qKw+GQlStXisViCfn5Ojo6pKWlpcuLtjd6MyYej0dEJGhbxo4dK1arVZxOp2RlZYlI5+dULl++LLt27QqvwQGEcg3Pnj2T/Px8yc7OFofDIQMGhP4pj74eg2CioqIkOztbnE6nLFiwwLfd6XTKv//+G/Acu90u58+f77KtpqZGcnJywnq99Zaqyrp16+TMmTPidrtl7NixYT2Ox+MxvL976tOnT3L//n2ZPn16wP1mGwMvh8MhI0eOlMLCwpDPNVP/hzuv2O12cTqdXd79q6mpCbt4+1uQ2+bLbRGym+w2DrndyQy5LUJ2G5bdvfpqtj9Qc3Ozejwe3bZtm8bFxanH41GPx+NbAsO7LElBQYHevn1bXS6XpqSkdFmWpLW1VW02m9bV1fm2rV69WlNSUtTlcunt27d11qxZ/bIsiZfL5VIR0cbGxoD7bTabVlZWqqrq27dvdePGjVpbW6uPHz/WS5cuqd1u19GjR/f7kh61tbW6d+9e9Xg82tTUpMePH9fk5GSdN29e0Pardi4dkJCQoJWVldrQ0KDLly+P2JIkz54903HjxumsWbO0tbW1y3ILPzLTGHiXJKmoqNDGxkZdv369Dh48WJ88eaKqqmVlZbpixQrf8d4lMTZs2KCNjY1aUVER0SUx1qxZowkJCep2u7v09/v3733H+F/Dvn379MyZM/rgwQO9e/eulpWVqYjo6dOnI3EJunHjRnW73drU1KTXr1/XoqIijY+P/23GQFX127dvOmbMGN28efNP+8zY/2/fvvXN+SLim3u8S/H0ZF5ZsWJFl28Qvnbtmg4cOFB37typ9+/f1507d7KcWB8jtyOfGf7IbrI7VOS2OXJblexWNS67Kbz9FBcXq4j89PPj+nXNzc1aWFiosbGxOmzYMC0pKdGPHz/69j9+/Pincz58+KAlJSU6bNgwjY2N1aKiIn369Gm/Xdfy5cs1Ly8v6H4RUYfDoaqq79+/19mzZ+uIESPUYrHomDFjtLi4uF/b63Xr1i3Nzc3VhIQEjYmJUZvNplu2bNF3794Fbb9q5/IBW7ZsUavVqtHR0TpjxgxtaGjo59Z3cjgcAV9T/ve9zDYGBw4c0NTUVI2KitJJkyZ1WdKjuLhYZ86c2eV4t9utWVlZGhUVpWlpaVpeXt5vbfUXrL9/fI34X8OuXbs0PT1dY2JidOjQoTpt2jStqqrq/8b/x7vOpMVi0eTkZF24cKHeu3fPt9/sY6CqWl1d7Vvf058Z+9+7LIr/T3Fxsar2bF6ZOXOm73ivkydPqs1mU4vFohkZGRH7pfBPRW6bIzN+RHaT3aEit82R26pkt5cR2f2P6n+f4gcAAAAAAH2O5cQAAAAAADAQhTcAAAAAAAai8AYAAAAAwEAU3gAAAAAAGIjCGwAAAAAAA1F4AwAAAABgIApvAAAAAAAMROENAAAAAICBKLwBAAAAADAQhTcAAAAAAAai8AYAAAAAwEAU3gB65OXLl2K1WmXHjh2+bXV1dRIVFSU1NTURbBkAAAiE7AbM4x9V1Ug3AsDv4eLFizJ//nypra2VjIwMycrKksLCQtm/f3+kmwYAAAIguwFzoPAGEJK1a9eKy+WSyZMnS319vdy4cUNiYmIi3SwAABAE2Q1EHoU3gJB8+PBBMjMzpaWlRW7evCkTJkyIdJMAAEA3yG4g8viMN4CQNDU1SVtbm3z//l2am5sj3RwAAPALZDcQebzjDaDHPn/+LFOmTJGJEydKRkaG7N27VxoaGmTUqFGRbhoAAAiA7AbMgcIbQI9t2rRJTp06JfX19RIXFyf5+fkSHx8vFy5ciHTTAABAAGQ3YA78V3MAPeJ2u2X//v1y9OhRGTJkiAwYMECOHj0qV69elfLy8kg3DwAA+CG7AfPgHW8AAAAAAAzEO94AAAAAABiIwhsAAAAAAANReAMAAAAAYCAKbwAAAAAADEThDQAAAACAgSi8AQAAAAAwEIU3AAAAAAAGovAGAAAAAMBAFN4AAAAAABiIwhsAAAAAAANReAMAAAAAYCAKbwAAAAAADPQ/g1dK+bLEliwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code here\n",
    "# your code here\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def plot_relu_and_gradient():\n",
    "    x = np.linspace(-10, 10, 100)\n",
    "    x_tensor = torch.tensor(x, requires_grad=True)\n",
    "    sig = torch.nn.LeakyReLU()(x_tensor)\n",
    "    sig.backward(torch.ones_like(x_tensor))\n",
    "    sig_grad = x_tensor.grad\n",
    "\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    \n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(x, sig.detach().numpy(), label='Leaky ReLU', color='blue')\n",
    "    plt.title('Leaky ReLU Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('LeakyReLU(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(x, sig_grad, label='Leaky ReLU Derivative', color='red')\n",
    "    plt.title('Gradient of Leaky ReLU Activation Function')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('LeakyReLU\\'(x)')\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "plot_relu_and_gradient()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e33119c",
   "metadata": {},
   "source": [
    "## Perceptron\n",
    "\n",
    "We define a class called *Perceptron* that inherits from *torch.nn.Module*. \n",
    "\n",
    "In the constructor, we define a single fully-connected linear layer with $input_dim$ inputs and $output_dim$ outputs, and a $sigmoid$ activation function. In the forward method, we apply the linear transformation to the input $x$, and then apply the sigmoid activation function to the output.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "aa86d7c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "input_size = 2\n",
    "output_size = 1\n",
    "\n",
    "class Perceptron(torch.nn.Module):\n",
    "    def __init__(self, input_dim, output_dim):\n",
    "        super(Perceptron, self).__init__()\n",
    "        self.linear = torch.nn.Linear(input_dim, output_dim)\n",
    "        self.activation = torch.nn.Sigmoid()\n",
    "        \n",
    "    def forward(self, x):\n",
    "        x = self.linear(x)\n",
    "        x = self.activation(x)\n",
    "        return x\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a178820e",
   "metadata": {},
   "source": [
    " We create an instance of this model and use it to make predictions like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "78513e21",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0.2733], grad_fn=<SigmoidBackward0>)\n"
     ]
    }
   ],
   "source": [
    "perceptron = Perceptron(input_size, output_size)\n",
    "x = torch.tensor([0.5, 0.2])\n",
    "y = perceptron(x)\n",
    "print(y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "54070b51",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [100/1000], Loss: 0.5374\n",
      "Epoch [200/1000], Loss: 0.5336\n",
      "Epoch [300/1000], Loss: 0.5328\n",
      "Epoch [400/1000], Loss: 0.5326\n",
      "Epoch [500/1000], Loss: 0.5326\n",
      "Epoch [600/1000], Loss: 0.5326\n",
      "Epoch [700/1000], Loss: 0.5325\n",
      "Epoch [800/1000], Loss: 0.5325\n",
      "Epoch [900/1000], Loss: 0.5325\n",
      "Epoch [1000/1000], Loss: 0.5325\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Define the loss function and optimizer\n",
    "criterion = nn.BCELoss()  # Binary cross-entropy loss\n",
    "optimizer = torch.optim.SGD(perceptron.parameters(), lr=0.1)  # Stochastic gradient descent optimizer\n",
    "\n",
    "# Generate some random input data and labels\n",
    "input_data = torch.randn((10, input_size))\n",
    "labels = torch.randint(0, 2, (10, output_size)).float()\n",
    "\n",
    "# Train the model\n",
    "num_epochs = 1000\n",
    "for epoch in range(num_epochs):\n",
    "    # Forward pass\n",
    "    outputs = perceptron(input_data)\n",
    "    loss = criterion(outputs, labels)\n",
    "\n",
    "    # Backward pass and optimization\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    # Print the loss every 100 epochs\n",
    "    if (epoch + 1) % 100 == 0:\n",
    "        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75b840f4",
   "metadata": {},
   "source": [
    "Exercise 8: \n",
    "\n",
    "Implement a binary classification model using the Perceptron class in PyTorch for the logic OR. \n",
    "\n",
    "Your task is to create a Perceptron instance and train it using a proper  dataset and the binary cross-entropy loss with stochastic gradient descent optimizer. \n",
    "\n",
    "Here are the steps you can follow:\n",
    "\n",
    "Define a Perceptron class that inherits from torch.nn.Module and implements a binary classification model.\n",
    "\n",
    "Define a binary cross-entropy loss function using the torch.nn.BCEWithLogitsLoss module.\n",
    "\n",
    "Define a stochastic gradient descent optimizer using the torch.optim.SGD module.\n",
    "\n",
    "Train the Perceptron model on the training set using the binary cross-entropy loss and stochastic gradient descent optimizer.\n",
    "\n",
    "Evaluate the trained model compute the accuracy.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "dc3c5d3e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [100/1000], Loss: 0.3704\n",
      "Epoch [200/1000], Loss: 0.2844\n",
      "Epoch [300/1000], Loss: 0.2289\n",
      "Epoch [400/1000], Loss: 0.1907\n",
      "Epoch [500/1000], Loss: 0.1628\n",
      "Epoch [600/1000], Loss: 0.1417\n",
      "Epoch [700/1000], Loss: 0.1252\n",
      "Epoch [800/1000], Loss: 0.1119\n",
      "Epoch [900/1000], Loss: 0.1011\n",
      "Epoch [1000/1000], Loss: 0.0921\n",
      "tensor([[0.1913],\n",
      "        [0.9240],\n",
      "        [0.9277],\n",
      "        [0.9985]], grad_fn=<SigmoidBackward0>)\n",
      "Accuracy: 1.00\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "\n",
    "input_size = 2\n",
    "output_size = 1\n",
    "\n",
    "class Perceptron(torch.nn.Module):\n",
    "    def __init__(self, input_dim, output_dim):\n",
    "        super(Perceptron, self).__init__()\n",
    "        self.linear = torch.nn.Linear(input_dim, output_dim)\n",
    "        self.activation = torch.nn.Sigmoid()\n",
    "        \n",
    "    def forward(self, x):\n",
    "        x = self.linear(x)\n",
    "        x = self.activation(x)\n",
    "        return x\n",
    "\n",
    "perceptron = Perceptron(input_size, output_size)\n",
    "\n",
    "\n",
    "criterion = nn.BCELoss()  # Binary cross-entropy loss\n",
    "optimizer = torch.optim.SGD(perceptron.parameters(), lr=0.1)  # Stochastic gradient descent optimizer\n",
    "\n",
    "# Generate some random input data and labels\n",
    "input_data = torch.tensor([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=torch.float32)\n",
    "labels = torch.tensor([[0], [1], [1], [1]], dtype=torch.float32)\n",
    "\n",
    "# Train the model\n",
    "num_epochs = 1000\n",
    "for epoch in range(num_epochs):\n",
    "    # Forward pass\n",
    "    outputs = perceptron(input_data)\n",
    "    loss = criterion(outputs, labels)\n",
    "\n",
    "    # Backward pass and optimization\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    # Print the loss every 100 epochs\n",
    "    if (epoch + 1) % 100 == 0:\n",
    "        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')\n",
    "\n",
    "test_data = torch.tensor([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=torch.float32)\n",
    "test_labels = torch.tensor([[0], [1], [1], [1]], dtype=torch.float32)\n",
    "\n",
    "outputs = perceptron(test_data)\n",
    "print(outputs)\n",
    "accuracy = ((outputs > 0.5) == test_labels).sum().item() / test_labels.size(0)\n",
    "print(f'Accuracy: {accuracy:.2f}')\n"
   ]
  }
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