diff --git "a/src/theory/ActivationFunctions.ipynb" "b/src/theory/ActivationFunctions.ipynb" new file mode 100644--- /dev/null +++ "b/src/theory/ActivationFunctions.ipynb" @@ -0,0 +1,960 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Define the range for the input data\n", + "x = np.linspace(-10, 10, 100)\n", + "import numpy as np\n", + "\n", + "def identity(x):\n", + " \"\"\"\n", + " Compute the Identity activation function.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : the input itself, unmodified.\n", + " \"\"\"\n", + " return x\n", + "\n", + "def sigmoid(x):\n", + " \"\"\"\n", + " Compute the sigmoid of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : Sigmoid function output.\n", + " \"\"\"\n", + " return 1 / (1 + np.exp(-x))\n", + "\n", + "def tanh(x):\n", + " \"\"\"\n", + " Compute the hyperbolic tangent of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : Hyperbolic tangent function output.\n", + " \"\"\"\n", + " return np.tanh(x)\n", + "\n", + "def relu(x):\n", + " \"\"\"\n", + " Compute the Rectified Linear Unit activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : ReLU function output where negative values are zero.\n", + " \"\"\"\n", + " return np.maximum(0, x)\n", + "\n", + "def leaky_relu(x, alpha=0.01):\n", + " \"\"\"\n", + " Compute the Leaky Rectified Linear Unit activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + " alpha : Slope of the negative part of the function.\n", + "\n", + " Returns:\n", + " numpy array : Leaky ReLU function output.\n", + " \"\"\"\n", + " return np.where(x > 0, x, x * alpha)\n", + "\n", + "def arctan(x):\n", + " \"\"\"\n", + " Compute the arctangent of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : ArcTan function output.\n", + " \"\"\"\n", + " return np.arctan(x)\n", + "\n", + "def softplus(x):\n", + " \"\"\"\n", + " Compute the Softplus activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : Softplus function output.\n", + " \"\"\"\n", + " return np.log1p(np.exp(x))\n", + "\n", + "def mish(x):\n", + " \"\"\"\n", + " Compute the Mish activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : Mish function output, derived as x * tanh(softplus(x)).\n", + " \"\"\"\n", + " return x * np.tanh(softplus(x))\n", + "\n", + "def selu(x, alpha=1.6732632423543772848170429916717, scale=1.0507009873554804934193349852946):\n", + " \"\"\"\n", + " Compute the Scaled Exponential Linear Unit activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + " alpha : Scale for the negative factor.\n", + " scale : Scale for the positive factor.\n", + "\n", + " Returns:\n", + " numpy array : SELU function output.\n", + " \"\"\"\n", + " return scale * np.where(x > 0, x, alpha * (np.exp(x) - 1))\n", + "\n", + "def silu(x):\n", + " \"\"\"\n", + " Compute the Sigmoid Linear Unit (SiLU) activation of x, also known as Swish.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : SiLU function output, derived as x / (1 + exp(-x)).\n", + " \"\"\"\n", + " return x / (1 + np.exp(-x))\n", + "\n", + "def softmax(x):\n", + " \"\"\"\n", + " Compute the SoftMax activation of x, typically used for multi-class classification.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : SoftMax function output.\n", + " \"\"\"\n", + " e_x = np.exp(x - np.max(x))\n", + " return e_x / e_x.sum()\n", + "\n", + "def softsign(x):\n", + " \"\"\"\n", + " Compute the SoftSign activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : SoftSign function output, derived as x / (1 + |x|).\n", + " \"\"\"\n", + " return x / (1 + np.abs(x))\n", + "\n", + "def elu(x, alpha=1.0):\n", + " \"\"\"\n", + " Compute the Exponential Linear Unit activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + " alpha : The scaling factor for negative inputs.\n", + "\n", + " Returns:\n", + " numpy array : ELU function output.\n", + " \"\"\"\n", + " return np.where(x >= 0, x, alpha * (np.exp(x) - 1))\n", + "\n", + "def prelu(x, alpha=0.01):\n", + " \"\"\"\n", + " Compute the Parametric Rectified Linear Unit activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + " alpha : The learned parameter that scales the output when x is negative.\n", + "\n", + " Returns:\n", + " numpy array : PReLU function output.\n", + " \"\"\"\n", + " return np.where(x >= 0, x, alpha * x)\n", + "\n", + "def gelu(x):\n", + " \"\"\"\n", + " Compute the Gaussian Error Linear Unit activation of x.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : GELU function output, derived using the Gaussian distribution function for smoothing.\n", + " \"\"\"\n", + " return 0.5 * x * (1 + np.tanh(np.sqrt(2 / np.pi) * (x + 0.044715 * np.power(x, 3))))\n", + "\n", + "def sqnl(x):\n", + " \"\"\"\n", + " Compute the Square Nonlinearity (SQNL) activation function.\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : SQNL function output, which is bounded between -1 and 1.\n", + " \"\"\"\n", + " return np.where(x > 2, 1, np.where(x >= 0, x - (x**2) / 4, np.where(x >= -2, x + (x**2) / 4, -1)))\n", + "\n", + "\n", + "def swish(x):\n", + " \"\"\"\n", + " Compute the Swish activation function, also known as the Sigmoid Linear Unit (SiLU).\n", + "\n", + " Parameters:\n", + " x : A scalar or numpy array.\n", + "\n", + " Returns:\n", + " numpy array : Swish function output. The function is unbounded above and bounded below by zero.\n", + " \"\"\"\n", + " return x * sigmoid(x)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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IiODWW281OzwR8XIVPfd6/PHHadGiBa+++irjx48His6/+vXrxz//+c9Sj1lQUMCYMWPKPFfTpk255557uOWWW4iIiODFF1/kxRdf5Pjx4zRs2JD777+fMWPGVNlUMlL9LIZmORQpZdWqVcTHx/PBBx9wyy23mB2OiJho1KhRvPnmm2RnZ590smARERERETl7moNK5G/efvttatWqxdVXX212KCJSjf6+GsyhQ4f48MMPOf/889WcEhERERE5x3SJn8gJX3/9NevXr+ett95i5MiRJ11JS0S8U/fu3enduzetW7cmPT2dd999l6ysrHKHmIuIiIiISNXSJX4iJ8TFxZGenk7//v358MMPCQ4ONjskEalGTzzxBJ999hl79uzBYrHQqVMnxo0bR2JiotmhiYiIiIh4PTWoRERERERERETEVJqDSkRERERERERETKUGlYiIiIiIiIiImMrrJkl3uVzs27eP4OBgLBaL2eGISAUZhsGxY8eoX78+Vqv39s5Vo0Q8k2qUiLgz1SgRcWcVrVFe16Dat28fMTExZochImdo9+7dNGzY0OwwzhnVKBHPpholIu5MNUpE3NnpapTXNaiKV17bvXs3ISEhp9zX4XAwb948+vXrh6+vb3WEVy28NS/w3tyUF2RlZRETE+P1qyeqRnlvXuC9uSkv1ajy6OfC83hrbspLNao8+rnwPN6am/KqeI3yugZV8VDPkJCQChWtwMBAQkJCvO4HxRvzAu/NTXn9yduHa6tGeW9e4L25Ka8/qUb9ST8Xnsdbc1Nef1KN+pN+LjyPt+amvP50uhrlvRcoi4iIiIiIiIiIR1CDSkRERERERERETFXtDapffvmFK664gvr162OxWPjyyy9L3W8YBmPHjqVevXoEBASQmJjIli1bqjtMEakBTlePyrNgwQI6deqE3W6nWbNmTJs27ZzHKSI1k2qUiIiI1CTV3qDKycmhY8eOTJkypdz7X3zxRf79738zdepUFi9eTFBQEP379ycvL6+aIxURb3e6evR3O3bsYMCAAfTp04eVK1cyatQobr/9dr7//vtzHKmI1ESqUSIiIlKTVPsk6ZdeeimXXnppufcZhsGkSZN48sknufLKKwH44IMPiIqK4ssvv+SGG26ozlBFpAoYhtkRnNyp6lF5pk6dSuPGjXnllVcAaN26Nb/++iuvvvoq/fv3P1dhikgNpRolIiIiNYlbreK3Y8cO0tLSSExMLNkWGhpKQkICixYtKrdBlZ+fT35+fsntrKwsoGhGeYfDccrnK77/dPt5Gm/NC7w3N2/N6z+Ld/HFFiuJBQWn3dcTcl+0aFGp+gTQv39/Ro0addJjVKPK8ta8wHtzO11eLpdBrsNJboGT4wVOjjuK/hUUushzOHE4DQoKXTicLhwug0KnQaHLRaHLwOUySv7vNIoey2UYuAxO/N/AMMCg6IOsUl9Dye2/dsOLvyreZFC6U1683eVysWePlc6ZOUSFBVXoe+DOVKOqhrfmBebm5nIZHMkt4HCOgyPHC8jOd5KTX0iew0mew0WB04WjsKhGOP/yr7gGFNeFv/6+F9cAl8vF7t1WFv13LVZr+ReIuPMHZidTXKMSjuVSNzjwlPt648+riLi3Z+ds5OAeC/2cLqpqcUK3alClpaUBEBUVVWp7VFRUyX1/l5yczPjx48tsnzdvHoGBpy7kxVJSUioZqWfw1rzAe3PzlrxcBny1y8pP+62AlZc+mU+n8FOfGebm5lZPcGchLS2t3PqUlZXF8ePHCQgIKHOMatTJeWte4B25GQYcc8ChfDiSbyGzwMIXb8/nmAOyHZBTaCG3EI4XQp4TDDx1aXMr3//4M+H+p95LNerkvOHnvTzemhec+9yOOWDLUQu7cyzsz4WDxy0cKQCncS7rhBXS953DxzeLlXnzFxDqd+q9PKFGiYj3WLDpANMXpQI2huw5yj+aRVbJ47pVg+pMjB49mqSkpJLbWVlZxMTE0K9fP0JCQk55rMPhICUlhb59++JbVS0/N+CteYH35uZNeWXnF5I0azU/7c8A4NKGTh694WL8/E59ZlX8qb23UY0qy1vzAs/NLd/hZN3+Y6zdl8W6fVlsPZDNtowccvKdlXociwUCfW0E+Nnw97Xh72PFz8eK3ceKj82Kn82Kj82Cr9WCj82KzWrBx2rBarVgs1iwWcFqsRT9s1qwAFZL0TaLBSyWom0WC1g4sQ3gL7dLYvlLTEW3//bG2AIup5Nt27ZxWWJvwkNO3YxRjSrLU3/eT8db84Jzm9uR3AL+u2o/X6zYx/r9x066X1iAL2GBvgT7+xDkd6Je+Niw+1jx9SmqC75/qQsWC9isFixYsFoo8/tuAZwuFzu2b6dJkyb42GyVD95N++vFNerSxD6E1SrbYP4rb61RIuJ+juQU8OhnqwG4MNpF59jaVfbYbtWgio6OBiA9PZ169eqVbE9PTyc+Pr7cY+x2O3a7vcx2X1/fCv/hrcy+nsRb8wLvzc3T89pzJJfbpy9lY9ox7D5WXri6HZbdy/Hz8zttXp6Qd3R0NOnp6aW2paenExISUu7IBFCNOhVvzQvcPzeXy2DtvqMs2HSQ/205yKrdRylwusrsZ7FAvRB/6of548o+zHmtGhMVGkDdIDt1gvwICfAlNMCXEH8favn7EOBrw2Jx03d65XA4HMwp2Ep4SKBq1N+oRnlvXlC1uR3Lc/D6T1t5/7edFBT+WUdaRQfTJa42raJDaBZZi4a1A4gK8cfXVvVrNDkcDubM2cplfVt41WtWXKPCagV4RY0SEc9nGAZPfrmWA8fyaRIexBWNjlbp47tVg6px48ZER0czf/78koZUVlYWixcv5u677zY3OBE5peWpR7jjg6VkZBcQXsvOO0O70DY6iDm7zY6s6nTv3p05c+aU2paSkkL37t1NikikcjanH+Pz5Xv4ZtV+9mYeL3VfeC0/4mPCaFM/lNbRwTSLrEWjuoHYfWwn3vzN4bJLWupNkBtTjZLqlrI+ndGz15CRXTSPWZt6IdzQLYbL2tcjvFbZxqd4t19++YWXXnqJZcuWsX//fr744gsGDhxYcr9hGIwbN463336bzMxMevbsyRtvvEHz5s3NC1pEKuXLlXv5ds1+fKwWXrm2Pamrfq3Sx6/2BlV2djZbt24tub1jxw5WrlxJnTp1aNSoEaNGjeLZZ5+lefPmNG7cmDFjxlC/fv1SxU1E3Mt/V+7lkc9WU1DoonW9EN4d2oX6YQFuP2Hn6erR6NGj2bt3Lx988AEAd911F6+//jqPPvoot956Kz/++COffvop3377rVkpiJyWy2WQsiGd93/bwe/bD5dsD/KzcX7zcHq1iKR707rE1Q30qNFPNYFqlLgrwzB465ftPD93I4YBjcODeHJAay5qFak6UoPl5OTQsWNHbr31Vq6++uoy97/44ov8+9//Zvr06SXv8/r378/69evx9z/NRIAiYrq9mccZ+991ANx/cXPaNQghdVXVPke1N6iWLl1Knz59Sm4Xz3swdOhQpk2bxqOPPkpOTg533HEHmZmZnH/++cydO1dFS8QNuVwGk+Zv4d/ztwCQ2DqK126IJ8juVoMzT+p09Wj//v2kpqaW3N+4cWO+/fZbHnzwQV577TUaNmzIO++8o+XbxS0ZhsH8DQeYmLKZ9fuL5iaxWS1c3CqSq85rQJ9Wkfj7nsFcLVJtVKPEHRmGwfiv1zNt4U4ABv+jEWMvb4ufT9Vfuiee5dJLL+XSSy8t9z7DMJg0aRJPPvkkV155JQAffPABUVFRfPnll+Wu1i4i7sPlMnj401UcyyvkvEZh3NO7KYarcnOVVkS1v4vs3bs3xinWebVYLDz99NM8/fTT1RiViFRWnsPJQ7NW8e3q/QDceWETHr2kFTar53xyerp6NG3atHKPWbFixTmMSuTspR7KZcx/1/Lz5oMA1LL7MKR7LIP/EUv9sFNPtCvuQzVK3NFHi1OZtnAnFguMvbwNw3rEadSUnNaOHTtIS0sjMTGxZFtoaCgJCQksWrRIDSoRN/febztYtP0QAb42Xr0+Hh+bFYc3NKhExPMdyMpjxIfLWLU7E1+bhQlXtef6LjFmhyVS4xmGwYe/72LCtxvIL3ThZ7My/Pw47rqwKbWDTrNGuYjIaSzefojxXxVd3vFI/5YM79nY5IjEU6SlpQEQFRVVantUVFTJfeXJz88nPz+/5HbxaoUOh+O0U0kU3+/uU05UlrfmBd6bm6fntSU9mxe/3wTA6Etb0CDUr9TvYEXyqmjualCJSKWs23eU26cvZf/RPMICfZk6uDP/aFLX7LBEaryjxx089tlq5q4rOtHv0bQuzwxsR9OIWiZHJiLeICvPwb0zVlDoMri8Qz3u7tXU7JCkBkhOTmb8+PFlts+bN4/AwMAKPUZKSkpVh+UWvDUv8N7cPDGvQhdMXGOjoNBCmzAXIQfWMGfOmlL7VCSv3NzcCj2fGlQiUmHz1qUxauZKcgucNI0I4t2hXYkLDzI7LJEab8+RXIa9v4StB7LxtVkYfWlrhvfUZTciUnX+76dtZGQXLSv+0rUdVV+kUqKjowFIT0+nXr16JdvT09NLVm8vz+jRo0vm34OiEVQxMTH069ePkJCQUz6nw+EgJSWFvn37etUKtN6aF3hvbp6c1yspW9ibu4Pagb68c0cPIoL/XKG1MnkVj348HTWoROS0/r5azwXNw3n9pk6EBnhWgRXxRuv3ZTHs/T84cCyfeqH+vHlLZzo0DDM7LBHxIrsP5/LerzsAeOKy1gT4aYEFqZzGjRsTHR3N/PnzSxpSWVlZLF68mLvvvvukx9ntdux2e5ntvr6+FX6jX5l9PYm35gXem5un5bV052He+l9R7U++uj3165Q/Kr8ieVU0bzWoROSUCgpd/OuLNcxatgeAW/4Ry7gr2uBj02o9ImbblHaMG9/+naPHHbSMCmbarV2pF6pJ0EWkar34/SYKnC56NK3Lxa0jzQ5H3FR2djZbt24tub1jxw5WrlxJnTp1aNSoEaNGjeLZZ5+lefPmNG7cmDFjxlC/fn0GDhxoXtAiUq6c/EKSPl2Fy4BrOjXkknb1Tn9QFVCDSkRO6nBOAXd9tIw/dhzGaoFxV7RlaI84s8MSEWBnRg6D313M0eMO4mPCmH5rN41qFJEqt2F/Fl+v2ofFAv8a0FqX9slJLV26lD59+pTcLr40b+jQoUybNo1HH32UnJwc7rjjDjIzMzn//POZO3cu/v7+ZoUsIifx7LfrST2cS4OwAMb9s021Pa8aVCJSrq0HjnHrtKWkHs4l2O7D5JvOo3dLfWoq4g4O5xQw+N3FHDyWT6voYKYPV3NKRM6N//yRCsCl7aJpWz/U5GjEnfXu3RvDME56v8Vi4emnn+bpp5+uxqhEpLJ+WJ/Of/7YjcUCr1zfkRD/6jvHVINKRMr4ZfNB7p2xnGN5hcTUCeC9oV1pHhVsdlgiAhQ6Xdz3n+XsOXKc2LqBfHhbAqGBak6JSNU7XuDkixV7AbipW6zJ0YiIyLmWkZ3P47NXA3D7+Y2rfbV2NahEpJQPF+3kqa/X43QZdI2rzdTBnalbq+zklCJijpe+38RvWw8R6GfjrVu6lFpNRUSkKn27Zn/Jh1U9mlbvmxQREalehmEwevYaMrILaBkVzEP9WlZ7DGpQiQhQNCrjmW/WM33RLgCu7tSA5KvbY/fRSj0i7uKnjQd485ftALx0bUdaRmtko4icO8WX993QtRFWq+aeEhHxZrOW7iFlfTq+NguvDorH37f63weqQSUiZOU5GDljBb9sPojFAo/0b8ndvZpqIlQRN3I011Ey5Hp4zzgGdKie1VREpGbanH6MZbuOYLNauK5zQ7PDERGRc2j34VzGf70OgKS+LWlTP8SUONSgEqnhUg/lcuv0JWw9kE2Ar41XB8VzSbtos8MSkb8Z//U60rPyaRIexGOXtDI7HBHxct+s3g9An5aRRIZolTUREW/ldBkkfbqSnAIn3eLqcMeFTUyLRQ0qkRrsjx2HufPDpRzJdRAd4s87Q7vQroFW6BFxNz9uTGf2ir1YLfDy9R1NGXItIjXLz5sOANCvbZTJkYiIyLn01i/bWbLzCLXsPrxyfUdsJl7SrQaVSA01a+lunvhiDQ6nQYeGobw9pAtR+oRUxO0UFLp45psNANx2fmM6NaptckQi4u0ysvNZtecoAL1bRJgcjYiInCvr9h1lYsomAMZe0YaYOoGmxqMGlUgN43IZvPj9Jqb+vA2Ay9pH88p18QT4aUSGiDuavnAnOzJyCK9l54HEFmaHIyI1wC+bDwLQpl6ILu8TEfFSeQ4nSTNX4XAa9G8b5RbzDapBJVKD5OQX8uDMlcxbnw7AyD7NSOrbQivziLipjOx8/j1/CwCP9m9JLbv+bIvIubdgU1GDqk8rjZ4SEfFWr8zbxKb0Y4TXsvPcVe3dYoEsnemK1BD7Mo9z+/SlrN+fhZ/NygvXtueq88zvkovIyb32wxaO5RfSrkEI17rBp1oi4v2cLoNfthQ1qHq3jDQ5GhERORcWbsvgnV93APDCNe2pW8tuckRF1KASqQFW7c7k9g+WcvBYPnWD/HhrSGc6x9YxOywROYX9R48zc8luAJ64rLVGOopItVi5O5PMXAch/j6cFxNmdjgiIlLFsvIcPDJrNYYBN3aL4eLW7rMYhhpUIl7u29X7Sfp0JfmFLlpGBfPO0C6mT34nIqc3dcE2CpwuujWuQ4+m4WaHIyI1xM8n5p+6oEUEPjarydGIiEhVe+qrdezNPE6jOoE8OaCN2eGUogaViJcyDIPJP25lYspmAC5qFclrN8QT7O9rcmQicjrpWXn858ToqQcubm5yNCJSkyzdeRiAHk3rmhyJiIhUtTlr9jN7+V6sFnh1UEeC3Gx+U/eKRkSqRJ7DyWOfr+a/K/cBcGvPxvxrQGtsukRIxCNM/XkbBYUuusTW1ptEEak2TpfB6j1HATgvprbJ0YiISFU6kJXHE1+sAeCuXk3dcsoXNahEvMzBY/nc+eFSlqdmYrNaeObKdtyU0MjssESkgrLyHCVzT913cXO3WFFFRGqGbQezyc4vJMDXRouoWmaHIyIiVcQwDB79fDWZuQ7a1g9hVGILs0MqlxpUIl5kY1oWt01byt7M44T4+zB1cGd6NNPcNSKeZNbSPeQWOGkeWYsLm+v3V0Sqz8rUTADaNwzV/FMiIl7k48WpLNh0ED8fK5MGxePn4541Xg0qES/x48Z07puxgpwCJ43Dg3h3aBeaROjTTxFP4nQZTF+4E4BhPeM0ekpEqtWK3ZkAWr1PRMSLbD+YzYRvNwDwaP+WNI8KNjmik1ODSsTDGYbBu7/u4Lk5G3AZ0L1JXd4Y3ImwQD+zQxORSvpp4wFSD+cSGuDLVec1MDscEalhVp5oUMWrQSUi4hUKnS6SPl3FcYeTHk3rcmvPxmaHdEruOa5LRCqkoNDFE1+s4dlvi5pTN3aL4YPbuqk5VQlTpkwhLi4Of39/EhIS+OOPP065/6RJk2jZsiUBAQHExMTw4IMPkpeXV03RirebdmL01A1dYwj002dIIlJ9cgsK2ZSWBUB8ozBzgxERkSrxfwu2sXJ3JsH+Prx8XUesbr5olhpUIh4qM7eAoe/9wX/+2I3FAk8OaM1zV7XHV3NGVNjMmTNJSkpi3LhxLF++nI4dO9K/f38OHDhQ7v4zZszg8ccfZ9y4cWzYsIF3332XmTNn8sQTT1Rz5OKNUg/l8uvWDCwWGPyPWLPDEZEaZs2eo7gMiAqxUy80wOxwxEs5nU7GjBlD48aNCQgIoGnTpjzzzDMYhmF2aCJeZ/WeTF6bvwWAZwe2o36Y+9d2fTwr4oG2H8zmtulL2ZGRQ5CfjX/feB4Xt44yOyyPM3HiREaMGMHw4cMBmDp1Kt9++y3vvfcejz/+eJn9Fy5cSM+ePbnpppsAiIuL48Ybb2Tx4sXVGrd4p8+WFa3cd36zcGLqBJocjYjUNLq8T6rDCy+8wBtvvMH06dNp27YtS5cuZfjw4YSGhnL//febHZ6I1zhe4GTUzJU4XQYDOtTjnx3rmx1ShWiohYiHWbg1g4FTfmNHRg4NwgL47O4eak6dgYKCApYtW0ZiYmLJNqvVSmJiIosWLSr3mB49erBs2bKSywC3b9/OnDlzuOyyy6olZvFeLpfB58v3AnBdlxiToxGRmujPBlVtcwMRr7Zw4UKuvPJKBgwYQFxcHNdeey39+vU77RQLIlI5z3+3ge0Hc4gMtjNhYDuPWXhHI6hEPMiMxamM/e9aCl0GnRqF8eYtXYgItpsdlkfKyMjA6XQSFVW6uRcVFcXGjRvLPeamm24iIyOD888/H8MwKCws5K677jrlJX75+fnk5+eX3M7KKprfw+Fw4HA4Thlj8f2n28/TeGtecOa5/bbtEHszjxPs70Of5nXc7nvjra9ZZfLyttxF/m79/qK/Tx0ahpociXizHj168NZbb7F582ZatGjBqlWr+PXXX5k4caLZoYl4jV82H2T6ol0AvHRdR4+an1gNKhEP4HQZTPh2A+/9tgOAgfH1ef6aDvj72kyOrGZZsGABzz33HP/3f/9HQkICW7du5YEHHuCZZ55hzJgx5R6TnJzM+PHjy2yfN28egYEVu4wrJSXlrOJ2V96aF1Q+tw+2WAErHUIL+DHl+3MTVBXw1tesInnl5uZWQyQi5jhe4CT1cNHPeAs3Xn5cPN/jjz9OVlYWrVq1wmaz4XQ6mTBhAjfffHO5++uDvrK8NS/w3tyqM6/MXAcPz1oFwOCEGHo0Djtnz3suPuhTg0rEzR3Lc/DAJyv5cWPRxN0P9W3ByIuaecwwTXcVHh6OzWYjPT291Pb09HSio6PLPWbMmDHccsst3H777QC0b9+enJwc7rjjDv71r39htZa9anr06NEkJSWV3M7KyiImJoZ+/foREhJyyhgdDgcpKSn07dsXX1/fyqbotrw1Lziz3I7lOXh0yc+AiwcHdqejG45e8NbXrDJ5Fb8pEvFG2w5mYxhQO9CX8Fqe80m7eJ5PP/2Ujz/+mBkzZtC2bVtWrlzJqFGjqF+/PkOHDi2zvz7oOzlvzQu8N7dznZdhwPQtVg4csxLpb9DR2MGcOTvO6XNC1X7QpwaViBvbfTiX26cvZVP6Mew+ViZeH8+ADvXMDssr+Pn50blzZ+bPn8/AgQMBcLlczJ8/n5EjR5Z7TG5ubpkmlM1WNIrtZKvP2O127Payl2H6+vpW+I1+Zfb1JN6aF1Qut59Wp5Nf6KJpRBCd4+q6dfPZW1+ziuTljXmLFNucfgyA5lHBbl2DxPM98sgjPP7449xwww1A0Yd9u3btIjk5udwGlT7oK8tb8wLvza268vpq1X5W/L4Gm9XCG0MTzvkl2+figz41qETc1LJdh7nzw2VkZBcQGWznnaFd6NAwzOywvEpSUhJDhw6lS5cudOvWjUmTJpGTk1Oyqt+QIUNo0KABycnJAFxxxRVMnDiR8847r+QSvzFjxnDFFVeUNKpEKuvbNfsBuKJjfb0xFBFTbE7PBqClLu+Tc+xkH/a5XK5y99cHfSfnrXmB9+Z2LvPaf/Q447/ZAMD9FzWnc+Pwc/I85anKD/rUoBJxQ1+u2Mujn62mwOmiTb0Q3h3WhXqhAWaH5XUGDRrEwYMHGTt2LGlpacTHxzN37tySidNTU1NLnUQ9+eSTWCwWnnzySfbu3UtERARXXHEFEyZMMCsF8XBHcx38b8tBAAa01+hIETHHlhMjqFpE1TI5EvF2xedNjRo1om3btqxYsYKJEydy6623mh2aiMdyuQwenrWKrLxCOsaEcW+fpmaHdMbKTphisqeeegqLxVLqX6tWrcwOS6RauFwGr8zbxKiZKylwuujXJorP7u6u5tQ5NHLkSHbt2kV+fj6LFy8mISGh5L4FCxYwbdq0kts+Pj6MGzeOrVu3cvz4cVJTU5kyZQphYWHVH7h4hXnr03A4DVpGBdNcIxfkJKZMmUJcXBz+/v4kJCSccjn2adOmlTmP8vf3r8ZoxRNtPvDnJX4i59LkyZO59tprueeee2jdujUPP/wwd955J88884zZoYl4rGkLd/Lb1kP4+1p59fqO+Njcrs1TYW45gqpt27b88MMPJbd9fNwyTJEqVeCEBz5dzdx1RZN23927KY/0a4nVqkt+RLxV8eV9mltOTmbmzJkkJSUxdepUEhISmDRpEv3792fTpk1ERkaWe0xISAibNm0qua1LR+VUcvIL2X34OKAV/OTcCw4OZtKkSUyaNMnsUES8wpb0Yzw/dyMA/xrQhiYRnj0S1i07Pz4+PiddRUvEG6Vn5fHvdTZ256Tja7Pw3FXtua5LjNlhicg5lJlbwK9bMgC4TJf3yUlMnDiRESNGlMyNN3XqVL799lvee+89Hn/88XKPsVgsOo+SCtt6oGj+qfBaftQJ0gp+IiKeoqDQVXTlTaGLXi0iGJzQyOyQzppbNqi2bNlC/fr18ff3p3v37iQnJ9OoUfnf7Pz8fPLz80tuF88O73A4cDgcp3ye4vtPt5+n8da8wDtzW7cvizs/WkF6joWwAF/+76Z4usbV9oocK/N6eUO+IpWRsj6dQpdBq+hgmkV69qddcm4UFBSwbNkyRo8eXbLNarWSmJjIokWLTnpcdnY2sbGxuFwuOnXqxHPPPUfbtm3L3VfnUWV5a15Qfm4b9mUC0CwiyGNz9tbXTOdRInIq/56/hXX7sggL9OWlazt4xYhpt2tQJSQkMG3aNFq2bMn+/fsZP348F1xwAWvXriU4uOyw4+TkZMaPH19m+7x58wgMDKzQc6akpJx13O7IW/MC78lt1SELH221UuCyEBVgcEer4xxcv4g5682OrGpV5PXKzc2thkhE3McPG4ou572knUa6SPkyMjJwOp0lCzcUi4qKYuPGjeUe07JlS9577z06dOjA0aNHefnll+nRowfr1q2jYcOGZfbXedTJeWteUDq3eTutgBXf44eYM2eOeUFVAW99zXQeJSJ/t2zXYf5vwVYAnruqPZEh3jHfpNs1qC699NKSrzt06EBCQgKxsbF8+umn3HbbbWX2Hz16NElJSSW3s7KyiImJoV+/foSEhJzyuRwOBykpKfTt29erlrH01rzAe3IzDIO3/reT9xZtAeD8pnUYUOcAV17q2Xn9XWVer+JP7UVqgjyHk182F13el9g66jR7i1Rc9+7d6d69e8ntHj160Lp1a958881yJyHWeVRZ3poXlJ/b7A+WAxn07daWy7p65vQC3vqa6TxKRMqTk19I0qercBlw9XkNvGqqCLdrUP1dWFgYLVq0YOvWreXeb7fbsdvtZbb7+vpW+A9UZfb1JN6aF3h2bvmFTkZ/sYbZy/cCMKxHHI/1a8a87+d6dF6nUpG8vDFvkZNZtO0Qxx1OokP8aVv/1E0AqbnCw8Ox2Wykp6eX2p6enl7hOaZ8fX0577zzdB51Brw1Lyid29aDOQC0rh/m8fl662um8ygR+atnv93ArkO51A/156kry7+E31O5/fqD2dnZbNu2jXr1vKcrKDXXoex8Br+zmNnL92KzWnjmyrY89c+2Hr0UqIhUXsqJy/sS20R6xXwBcm74+fnRuXNn5s+fX7LN5XIxf/78UqOkTsXpdLJmzRqdR0m5jhc42ZtZtIJfMw9f+UlEpCaYvyGd//yRisUCr1wfT4i/dzWn3W4E1cMPP8wVV1xBbGws+/btY9y4cdhsNm688UazQxM5K5vTj3Hb9CXsPnycYH8f/u/mTlzQPMLssESkmhmGwfziBpUu75PTSEpKYujQoXTp0oVu3boxadIkcnJySlb1GzJkCA0aNCA5ORmAp59+mn/84x80a9aMzMxMXnrpJXbt2sXtt99uZhriplIPF81bFOLvQ22t4Cci4tYOZefz2OdrALj9/MZ0b1rX5Iiqnts1qPbs2cONN97IoUOHiIiI4Pzzz+f3338nIkJv5MVzLdh0gPtmrOBYfiGxdQN5d2gXmkWWnfRfRLzf2r1ZpGflE+Rn88oTC6lagwYN4uDBg4wdO5a0tDTi4+OZO3duycTpqampWK1/jsI9cuQII0aMIC0tjdq1a9O5c2cWLlxImzZtzEpB3NjOQ0WX98WFB5kciYiInIphGIyevYaM7HxaRgXzUL+WZod0Trhdg+qTTz4xOwSRKmMYBtMX7uTpb9bjMqBb4zq8ObizPqUUqcGKL++7sEUEdh+bydGIJxg5ciQjR44s974FCxaUuv3qq6/y6quvVkNU4g12nWhQxdZVg0pExJ19tmwP89an42uz8OqgePx9vfMc0u0aVCLewuF0Mf7rdXz0eyoA13dpyLMD2+Pno/mmRGqynzcfBKBPy0iTIxGRmm7XoaJL/OLqBpociYiInMzuw7mM/3o9AEl9W9LGixfYUYNK5Bw4etzByBnL+d+WDCwWePySVtxxYRNNhixSwx3OKWD1nkygaASViIiZihtUjeqoQSUi4o6cLoOHPl1Fdn4hXeNqc8eFTcwO6ZxSg0qkiu3MyOG26UvYdjCHQD8bkwbF069txZYDFxHv9uvWDAwDWkUHEx3qb3Y4IlLDaQ4qERH39vb/tvPHzsME+dl45bp4bFbvHvCgBpVIFVq8/RB3fbSMI7kO6oX6887QLrStH2p2WCLiJn45cXmfRk+JiNkKCl3syzwOQKwu8RMRcTsb9mcxcd5mAMZd0ZZGNaBWq0ElUkU+Xbqbf32xBofToGPDUN4e0oXIEI2QEJEihmGUNKh6qUElIibbcyQXlwGBfjYiatnNDkdERP4iz+HkwZkrKXC6SGwdxXVdGpodUrVQg0rkLDldBi/O3cibv2wHYECHerxyXUevXVlBRM7MxrRjHDiWT4CvjS5xtc0OR0RquL/OP6U5MkVE3MvElM1sTDtG3SA/nr+mfY2p02pQiZyFnPxCHvhkJT+cWDb+/oubM+ri5li9/NpgEam84tX7ujeti91HDWwRMVfJ/FN1Nf+UiIg7+X37Id7+X9Hgh+ev6UB4DRrlqgaVyBnam3mc26cvZcP+LPx8rLx0bQeujG9gdlgi4qb+t+XE/FPNw02ORETkzxFUseHeP6eJiIinyMpz8NCnqzAMGNQlhr5toswOqVqpQSVyBlakHmHEB8vIyM4nvJadt4Z0plMjXbIjIuXLczhZsvMIAOc31/xTImI+jaASEXE/479az97M48TUCWDMFW3MDqfaqUElUknfrN7HQ5+uIr/QRavoYN4Z2oWGtfXpo4ic3LJdRygodBEVYqdphN4Mioj5UotHUNWAVaFERDzBd2v28/nyPVgtMPH6eGrZa167xmp2ACKewjAMJv2wmZEzVpBf6OLiVpF8dncPNadE5LQWbssAoEfT8BozyaWIuK9Cp4vdR4obVGqaS/Xau3cvgwcPpm7dugQEBNC+fXuWLl1qdlgipjqQlccTX6wB4K5eTekaV8fkiMxR81pyImcgz+Hkkc9W8/WqfQCMuKAxj1/aGpsmQxeRCvht6yEAejSta3IkIiKwPysPh9PAz2YlOsTf7HCkBjly5Ag9e/akT58+fPfdd0RERLBlyxZq19ZUGVJzGYbBY5+v5kiugzb1QhiV2MLskEyjBpXIaRw4lscdHyxj5e5MfKwWnhnYjhu7NTI7LBHxEFl5DlbvyQSgRzNNkC4i5tt7JA+AhnUC9GGbVKsXXniBmJgY3n///ZJtjRs3NjEiEfPN+COVnzYdxM/HyquD4vHzqbkXuqlBJXIKG/Zncdu0Jew7mkdogC9vDO5Ej6Z6gykiFffH9sO4DIirG0iDsACzwxERYU/mcQDVJKl2X331Ff379+e6667j559/pkGDBtxzzz2MGDGi3P3z8/PJz88vuZ2VlQWAw+HA4XCc8rmK7z/dfp7GW/MC783tVHntPJTDs9+sB+Dhvs1pUtffY/KvzOtV0ZzUoBI5ifkb0rn/PyvIKXDSJDyId4d1pXG45mkQkcr5rXj+KY2eEhE3sfdIUYNK82hKddu+fTtvvPEGSUlJPPHEEyxZsoT7778fPz8/hg4dWmb/5ORkxo8fX2b7vHnzCAys2M9vSkrKWcftjrw1L/De3P6el9OA19baOO6w0DzERcSRdcyZs86k6M5cRV6v3NzcCj2WGlQif2MYBu/8bwfPfbcBw4Cezeryfzd1JjTQ1+zQRMQDLTwx/1RPjb4UETexN7O4QaURVFK9XC4XXbp04bnnngPgvPPOY+3atUydOrXcBtXo0aNJSkoquZ2VlUVMTAz9+vUjJCTklM/lcDhISUmhb9+++Pp6z3m8t+YF3pvbyfJ6/adt7MreRi27D++M6E59DxvVWpnXq3j04+moQSXyFwWFLsZ8uZaZS3cDcFNCI8b/sy2+tpp7HbC3mzJlCi+99BJpaWl07NiRyZMn061bt5Pun5mZyb/+9S9mz57N4cOHiY2NZdKkSVx22WXVGLV4ikPZ+WxKPwbAP5rUzNVYRMT97Mk8MQeVGlRSzerVq0ebNm1KbWvdujWff/55ufvb7XbsdnuZ7b6+vhVuYFRmX0/irXmB9+b217xW78lkyoLtADwzsC2xEaduuLqzirxeFX091aASOeFITgF3fbSMxTsOY7XAkwPaMLxnnJaE92IzZ84kKSmJqVOnkpCQwKRJk+jfvz+bNm0iMjKyzP4FBQX07duXyMhIPvvsMxo0aMCuXbsICwur/uDFI/yx4zAALaOCqVur7Am2iIgZ9mkElZikZ8+ebNq0qdS2zZs3Exsba1JEItXveIGTB2eupNBlcFn7aAbGNzA7JLehBpUIsO1gNrdNW8LOQ7nUsvsw+cbz6NOqbINCvMvEiRMZMWIEw4cPB2Dq1Kl8++23vPfeezz++ONl9n/vvfc4fPgwCxcuLPkUIC4urjpDFg+z+ESDKkGjp0TETTgNSMsqmnRac1BJdXvwwQfp0aMHzz33HNdffz1//PEHb731Fm+99ZbZoYlUmxfmbmTbwRwig+1MGNheAyL+Qg0qqfF+3ZLB3R8v41heIQ1rB/Du0K60jA42Oyw5xwoKCli2bBmjR48u2Wa1WklMTGTRokXlHvPVV1/RvXt37r33Xv773/8SERHBTTfdxGOPPYbNZiv3GK0+U5a35gVlc/v9xATpXRqFenS+3vqanYvVZ0TcXWY+OF0GfjYrERrZKdWsa9eufPHFF4wePZqnn36axo0bM2nSJG6++WazQxOpFv/bcpBpC3cC8OK1Hagd5GduQG5GDSqp0T76fRfjvlqH02XQObY2b97SmXCdrNUIGRkZOJ1OoqKiSm2Piopi48aN5R6zfft2fvzxR26++WbmzJnD1q1bueeee3A4HIwbN67cY7T6zMl5a15QlFuOAzamF/2Zzdq2nDmpJgdVBbz1NavK1WdE3N3h/KJP6hvUDsBq1af2Uv0uv/xyLr/8crPDEKl2mbkOHp61CoDB/2hE75a6Yufv1KCSGqnQ6eLZbzeUdK+vOq8ByVe3x9+3/FEwIlC08kxkZCRvvfUWNpuNzp07s3fvXl566aWTNqi0+kxZ3poXlM5twZYjsHQlTSOCGHRlT7NDOyve+pqdi9VnRNzd4RODejX/lIhI9Xrqmw2kZ+XTODyIJy5rbXY4bkkNKqlxsvIc3P+fFSzYdBCAR/q35J7eTXXtbw0THh6OzWYjPT291Pb09HSio6PLPaZevXr4+vqWupyvdevWpKWlUVBQgJ9f2SG6Wn3m5Lw1LyjKbUlqJgDdm9b1mjy99TWrytVnRNxdcYOqgYctZy4i4smWZ1j4dksaNquFidd3JNBPrZjyWM0OQKQ67T6cyzX/t5AFmw7i72vljZs7cW+fZmpO1UB+fn507tyZ+fPnl2xzuVzMnz+f7t27l3tMz5492bp1Ky6Xq2Tb5s2bqVevXrnNKanZFm8/MUF647omRyIi8qfiS/w0gkpEpHrsP5rHp9uLWi8j+zTjvEa1TY7IfalBJTXGkp2HuXLKb2w5kE1UiJ1Zd/bg0vb1zA5LTJSUlMTbb7/N9OnT2bBhA3fffTc5OTklq/oNGTKk1CTqd999N4cPH+aBBx5g8+bNfPvttzz33HPce++9ZqUgburocQcb0oouCdMKfiLiTv68xE8r+ImInGsul8HjX6zluNNC+wYhjLyomdkhuTWNK5Ma4fNlexg9ew0FThftGoTwzpCuRIf6mx2WmGzQoEEcPHiQsWPHkpaWRnx8PHPnzi2ZOD01NRWr9c8+fkxMDN9//z0PPvggHTp0oEGDBjzwwAM89thjZqUgbmpZaiaGAU3Cg4gMVq0REfehEVQiItXng0U7WbjtML5Wg5evaY+vTWOETkUNKvFqLpfBy/M28X8LtgFwSdtoJg7SNb/yp5EjRzJy5Mhy71uwYEGZbd27d+f3338/x1GJp1uy8wgA3Rpr9JSIuI9Cp4vM4jmo1KASETmnth44RvJ3RauDXxnroklEkMkRuT+9SxevlVtQyEOfruK7tWkA3NunKQ/1bakllUXknFu6Sw0qEXE/B47l48KCr82i0Z0iIueQw+niwZmryC90cX6zupwfnn76g0RzUIl3Sjuax/VvLuK7tWn42axMvL4jj/RvpeaUiJxz+U5Yu7do/qmucWpQiYj72JN5HIB6of7YdE4kInLOTJ6/hTV7jxIa4MvzV7VFa3JVjEZQiddZs+cot3+whPSsfOoE+fHWLZ3pojeJIlJNdmVbKHQZ1A/11xwvIuJW9h7JA6BBmGqTiMi5sjz1CK//tBWACVe1IypEI1YrSg0q8SrfrdnPg5+uJM/honlkLd4b1pWYOlqlRkSqz7asoo/Iujaug0Ufl4mIG9l3tKhBVT9Mb5ZERM6FnPxCkmauxGXAlfH1ubxDfRwOh9lheQw1qMQrGIbBlJ+28vK8zQD0ahHB5JvOI8Tf1+TIRKSm2VZ0dZ/mnxIRt7PvxCV+DUI1gkpE5FyYMGcDOw/lUi/Un6evbGd2OB5HDSrxePmFTkZ/vobZK/YCMLxnHP+6rDU+WsJTRKpZQaGLndlFo6YS1KASETezN7NoBFU9jaASEalyP208wIzFqQC8cl1HQgM0WKKy1KASj5aRnc+dHy5j2a4j2KwWxv+zLYP/EWt2WCJSQ63bl4XDZaF2oC9NI2qZHY6ISCn7j54YQaUGlYhIlTqcU8Ajn60G4LbzG9OjWbjJEXkmtx1iMmXKFOLi4vD39ychIYE//vjD7JDEzWxKO8bAKb+xbNcRgv19mD68m5pTImKqJbuOANAltrbmn5IqU9lzolmzZtGqVSv8/f1p3749c+bMqaZIxZ0ZhvHnHFS6xE9EpMoYhsHo2avJyM6neWQtHunf0uyQPJZbNqhmzpxJUlIS48aNY/ny5XTs2JH+/ftz4MABs0MTN7Fg80GueWMhe44cJ65uIF/e25Pzm6tLLSLmWlrSoAozNxDxGpU9J1q4cCE33ngjt912GytWrGDgwIEMHDiQtWvXVnPk4m4O5xSQ53ABEB2qEVQiIlXl8+V7+X5dOr42C68Oisff12Z2SB7LLRtUEydOZMSIEQwfPpw2bdowdepUAgMDee+998wOTUxmGAYL9lu486MVZOcX8o8mdfjinp66lEZETOdyGSxPzQSKRlCJVIXKnhO99tprXHLJJTzyyCO0bt2aZ555hk6dOvH6669Xc+TibvaemCA9xNfA7uOWbwFERDzO7sO5PPXVOgBGJbagXYNQkyPybG7316mgoIBly5aRmJhYss1qtZKYmMiiRYtMjEzM5nC6GPv1Br7YacNlwKAuMXxwawK1g/zMDk1EhM0HjnH0eCF+VoM29YLNDke8wJmcEy1atKjU/gD9+/fXOZSUrOBX225yICIiXsLpMnho1iqy8wvpHFubOy9sYnZIHs/tJknPyMjA6XQSFRVVantUVBQbN24ss39+fj75+fklt7Oyitb3djgcOByOUz5X8f2n28/TeGNeR487uP+TVSzcfhgLBg8lNuOOC5tgMZw4HE6zwztr3viaQeXy8rbcpeZZsuMwAHHBhlYRlSpR2XMigLS0tHL3T0tLK3d/nUeV5a15pR7KAaCO3fC63Lz1NdN5lIh7e/fX7fyx4zCBfjYmXt9R539VwO0aVJWVnJzM+PHjy2yfN28egYGBFXqMlJSUqg7LLXhLXgeOw9sbbRzIs+BnNRjS3EVMzia++26T2aFVOW95zf6uInnl5uZWQyQi584fO4vmn2oabJgciUjF6Tzq5Lwtr992WgErtf28L7diNTkvnUeJVK8N+7N4+fvNAIy5vA2xdYNMjsg7uF2DKjw8HJvNRnp6eqnt6enpREdHl9l/9OjRJCUlldzOysoiJiaGfv36ERIScsrncjgcpKSk0LdvX3x9fasmATfgTXn9vv0wYz9ZydG8QuqF+jNlUHt2r1nkFbn9lTe9Zn9VmbyKP7UX8USGYZSMoGp66j89IhVW2XMigOjo6Ertr/Oosrw1r29mrIT9B6htN7wuN299zbz9POr5559n9OjRPPDAA0yaNMnscEQqLL/QyYMzV1LgdHFxq0hu6Bpjdkhew+0aVH5+fnTu3Jn58+czcOBAAFwuF/Pnz2fkyJFl9rfb7djtZS+m9/X1rfAfqMrs60k8Pa///JHKmC/XUugyiI8J460hnantb2P3Gs/P7WRqcl7emLfUHHuOHCctKw9fm4XYWhpBJVWjsudEAN27d2f+/PmMGjWqZFtKSgrdu3cvd3+dR52ct+W1PysPKJqDyttyK1aT8/K0vJcsWcKbb75Jhw4dzA5FpNImpmxmY9ox6gT58fw1HbBYLGaH5DXc8iLJpKQk3n77baZPn86GDRu4++67ycnJYfjw4WaHJtXA6TJ49pv1jJ69hkKXwRUd6/PJHf8gMlhLIouIe1qys2j0VNv6IfhpZWGpQqc7JxoyZAijR48u2f+BBx5g7ty5vPLKK2zcuJGnnnqKpUuXnrShJTXHvsyiBlUdu5roYq7s7Gxuvvlm3n77bWrX1qq34lkWbz/EW79sByD56vZEBGvliarkdiOoAAYNGsTBgwcZO3YsaWlpxMfHM3fu3DKTfor3yc4v5IH/rGD+xgMAjEpszgMXN1dXWkTcWnGDqktsbXAeMjka8SanOydKTU3Fav3z88YePXowY8YMnnzySZ544gmaN2/Ol19+Sbt27cxKQdxAbkEhh3MKAK3iJ+a79957GTBgAImJiTz77LOn3FcLOZTlrXmB++d2LK+Qhz5diWHANZ3qc1GLupVaxMBd8zpT52IhB7dsUAGMHDlSn/bVMHuO5HL79KVsTDuG3cfKS9d15J8d65sdlojIaS0+Mf9U17ja5G0zORjxOqc6J1qwYEGZbddddx3XXXfdOY5KPEnx6Kkgu40AW6HJ0UhN9sknn7B8+XKWLFlSof21kMPJeWte4L65zdhqZU+mlTp2g262VObMSa3U8e6a19mqyoUc3LZBJTXL8tQj3PHBUjKyCwivZeftIZ05r5GG/IqI+zt4LJ/tB3OwWKBzozB+U4NKRNzM3szjADQIDcBiyT/N3iLnxu7du3nggQdISUnB379iU3doIYeyvDUvcO/c5q1PZ/GiVVgs8PrgbnSNq/h7VXfO62yci4Uc1KAS0/135V4e+Ww1BYUuWtcL4Z2hXWgQFmB2WCIiFbL0xOV9LaOCCQ3wnpMOEfEe+040qOqFaT5PMc+yZcs4cOAAnTp1KtnmdDr55ZdfeP3118nPz8dmKz2RoxZyODlvzQvcL7cDx/IY89UGAO68sCk9mkee0eO4W15VpSoXclCDSkxjGAav/rCFf8/fAkBi6yheuyGeILt+LEXEcxRf3tetcR2TIxERKd/eI0UNqvqhalCJeS6++GLWrFlTatvw4cNp1aoVjz32WJnmlIg7MAyD0Z+v4XBOAa2ig3mwb3OzQ/Jq6gSIKfIcTh6atYpvV+8H4M4Lm/DoJa2wWTUZuoh4lj/UoBIRN1dyiV9YAGSbHIzUWMHBwWUWbAgKCqJu3bpayEHc1idLdjN/4wH8bFYm3RCP3UeN1HNJDSqpdgey8hjx4TJW7c7E12ZhwsD2XN81xuywREQqLSvPwYa0omvqu8WpQSUi7mnPkaLJaRvWVoNKRKSidmbk8Mw36wF4uH8LWkWfet4zOXtqUEm1WrfvKLdPX8r+o3mEBfoydXBn/tGkrtlhiYickWU7j2AYEFc3kMgQf69bPlhEvMOeI8UjqPzZt9vkYET+oryVSEXcQaHTRdKnK8ktcPKPJnW4/fwmZodUI6hBJdVm3ro0Rs0s+iVvGhHEu0O7EhceZHZYIiJn7I+durxPRNxbQaGLtKw8oGgE1T6T4xER8QRTf97G8tRMgu0+vHxdR6yaiqZaWM0OQLyfYRhM/Xkbd360jNwCJxc0D2f2PT3VnBK3MWXKFOLi4vD39ychIYE//vijQsd98sknWCwWBg4ceG4DFLe1ePshALrq8j4RcVNpR/MwDLD7WKkb5Gd2OCIibm/t3qNM+qFoIa9x/2xLw9qBJkdUc6hBJedUQaGLRz9bzfPfbcQwYPA/GvHesK5ail3cxsyZM0lKSmLcuHEsX76cjh070r9/fw4cOHDK43bu3MnDDz/MBRdcUE2RirvJLShk9Z6jALpUWUTcVvH8Uw1qB2CxaASAiMip5DmcjJq5kkKXwaXtormmUwOzQ6pR1KCSc+ZwTgGD313MrGV7sFpg/D/b8uzA9vja9GMn7mPixImMGDGC4cOH06ZNG6ZOnUpgYCDvvffeSY9xOp3cfPPNjB8/niZNdD16TbVs1xEKXQYNwgKKJh4WEXFDxfNPaQSAiMjpvTB3I1sPZBMRbGfCVe3V2K9m6hTIObH1wDGu+r/f+GPHYYLtPrw3rCtDe8SZHZZIKQUFBSxbtozExMSSbVarlcTERBYtWnTS455++mkiIyO57bbbqiNMcVOLtxfNP5XQuI5OXkTEbZVawU9ERE7qt60ZvP/bTgBevKYDdXRZdLXTJOlS5X7ZfJB7ZyznWF4hMXUCeG9oV5pHBZsdlkgZGRkZOJ1OoqKiSm2Piopi48aN5R7z66+/8u6777Jy5coKPUd+fj75+fklt7OysgBwOBynXfGt+H5vWxnOW/JatC0DgC6xYWVy8vTc/k55eV/uUnPsySweQaUGlYjIyRzNdfDwrFUA3JzQiD6tIk2OqGZSg0qq1IeLdvLU1+txugy6xtVm6uDO1K1lNzsskSpx7NgxbrnlFt5++23Cw8MrdExycjLjx48vs33evHkEBlbscouUlJRKxekpPDmvAies3G0DLBzftYo56atK3e/JuZ1KTc4rNze3GiIRqXq6xE9E5PTGfrWW/UfziKsbyL8GtDY7nBpLDSqpEoVOF898s57pi3YBcE2nhjx3dTvsPjaTIxM5ufDwcGw2G+np6aW2p6enEx0dXWb/bdu2sXPnTq644oqSbS6XCwAfHx82bdpE06ZNSx0zevRokpKSSm5nZWURExNDv379CAkJOWV8DoeDlJQU+vbti6+v9yws4A15Ldp+COcfy4gKsXPLVX1LLvHzhtzKo7z+HP0o4mn2HtEIKhGRU/l61T7+u3IfNquFiYPiCfRTm8Qs+s7LWcvKczByxgp+2XwQiwUe7d+Ku3o10Zws4vb8/Pzo3Lkz8+fPZ+DAgUBRw2n+/PmMHDmyzP6tWrVizZo1pbY9+eSTHDt2jNdee42YmJgyx9jtduz2sqMIfX19K/xGvzL7ehJPzmvprqLV+7o3qYufX9n5CTw5t1OpyXl5Y97i/RxOF/uPnmhQhalBJSLyd2lH83jyy7UA3Nu7KZ0a1TY5oppNDSo5K6mHcrl1+hK2HsgmwNfGq4PiuaRd2ZEnIu4qKSmJoUOH0qVLF7p168akSZPIyclh+PDhAAwZMoQGDRqQnJyMv78/7dq1K3V8WFgYQJnt4t1+33FigvQmdU2ORETk5NKO5uEywM/HSngtO05nodkhiYi4DZfL4JHPVnH0uIP2DUK57+LmZodU46lBJWfsjx2HufPDpRzJdRAd4s87Q7vQrkGo2WGJVMqgQYM4ePAgY8eOJS0tjfj4eObOnVsycXpqaipWqxY8lT8dL3CyMjUTKFrBT0TEXZXMPxUWgNVqwek0OSARETfy4e+7+N+WDOw+Vl4dFI+vTef8ZlODSs7IZ8v2MHr2ahxOg/YNQnlnaBeiQvzNDkvkjIwcObLcS/oAFixYcMpjp02bVvUBiVtbuuswBU4X9UL9aRweZHY4IiIntedI0eT+DTT/lIhIKVsPZPPcnA0APHFZa5pF1jI5IgE1qKSSXC6DF7/fxNSftwEwoH09Xr6uIwF+mgxdRGqG37YeAqBH03DNtScibk0r+ImIlOVwukj6dCX5hS4uaB7OLf+INTskOUENKqmw3IJCHpy5ku/XFa14dt9FzXgwsQVWq96giUjNsXBbBgA9m2n+KRFxb3u0gp+ISBmTf9zK6j1HCfH34aVrO+r9rBtRg0oqZP/R49w2bSnr92fhZ7Py4rUdGHheA7PDEhGpVkdzHazdW7SCX4+m4SZHIyJyasWX+KlBJSJSZHnqEab8tBWACVe1JzpU09S4EzWo5LRW7c5kxAdLOXAsn7pBfrw1pDOdYzUxsIjUPL/vOITLgCYRQTqhERG3t+tQUYMqtq7myxMRyS0o5KFPV+F0GVwZX58rOtY3OyT5GzWo5JS+Wb2Phz5dRX6hi5ZRwbw7rIvmMRCRGmvh1hOX92n0lIi4uTyHk7SsPADi6urcTUTkuTkb2JGRQ3SIP0//s53Z4Ug51KCSchmGweQftzIxZTMAF7WK5N83nkctu35kRKTm+m1b0QTpmn9KRNxd6uGi0VMh/j6EBfqZHI2IiLl+2nSAj35PBeDl6zoSGuhrckRSHqvZAYj7yXM4GTVzZUlz6rbzG/P2kC5qTolIjZaelcfWA9lYLPCPJmpQiYh725mRA0BcuC7vE/eRnJxM165dCQ4OJjIykoEDB7Jp0yazwxIvdzingEc/Ww3A8J5xnN9cI+HdlRpUUsrBY/nc+Pbv/HflPnysFpKvbs+Yy9tg08oGIlLD/bz5IAAdGoRqNIKIuD3NPyXu6Oeff+bee+/l999/JyUlBYfDQb9+/cjJyTE7NPFShmHwry/WcPBYPs0ia/HYJa3MDklOQUNipMTGtCxum7aUvZnHCfH3YergzvRopu6yiAjALycaVL1aRJgciYjI6e08VPSGP7aO5p8S9zF37txSt6dNm0ZkZCTLli3jwgsvNCkq8WZfrNjLd2vT8LFaePX6ePx9bWaHJKegBpUAMH9DOvf/ZwU5BU4ahwfx7tAuNImoZXZYIiJuweky+PXEBOkXqkElIh7gzxFUalCJ+zp69CgAdepohXCpenuO5DLuv+sAGJXYnPYNQ02OSE5HDaoazjAM3v11BxPmbMAwoHuTurwxuJMuXxER+YvVezLJzHUQ7O9DfEyY2eGIiJxW8QgqzUEl7srlcjFq1Ch69uxJu3blr6iWn59Pfn5+ye2srCwAHA4HDofjlI9ffP/p9vM03poXVG1uLpfBQ5+u5Fh+IefFhHJbj0amfc+89TWrTF4VzV0NqhqsoNDF2P+u5ZMluwG4sVsMT1/ZDl+bpiYTEfmrXzYXjZ46v1k4PqqRIuLmCgpd7Ms8DmgElbive++9l7Vr1/Lrr7+edJ/k5GTGjx9fZvu8efMIDKzYz3ZKSsoZx+jOvDUvqJrcftpnYfEuG35WgwF1DzHv+7mnP+gc89bXrCJ55ebmVuix1KCqoTJzC7j7o+Us2n4IiwX+dVlrbju/MRaLJkMXEfm7nzcfADT/lIh4hj1HcnEZEOhnI6KW3exwRMoYOXIk33zzDb/88gsNGzY86X6jR48mKSmp5HZWVhYxMTH069ePkJCQUz6Hw+EgJSWFvn374uvrW2Wxm81b84Kqy21LejaPLPkdcDHm8rbc0PXkP2PVwVtfs8rkVTz68XTUoKqBth/M5rbpS9mRkUOQn43JN53HRa2izA5LRMQtHc11sHJ3JqD5p0TEMxTPP9WoTqA+fBS3YhgG9913H1988QULFiygcePGp9zfbrdjt5dtsvr6+lb4jX5l9vUk3poXnF1u+YVOHvp8LQWFLi5qFcng7nFuUwe99TWrSF4VzVsNqhrmt60Z3P3RMrLyCmkQFsC7w7rQKvrUnz6IiNRkv2w5iMuAZpG1qB8WYHY4IiKnVTL/VF3NPyXu5d5772XGjBn897//JTg4mLS0NABCQ0MJCNDfWDl7k37Ywob9WdQO9OX5a9q7TXNKKkYNqhpkxuJUxvx3LU6XQadGYbw1pAvhGvYtInJKP2xIB+Di1pEmRyIiUjFawU/c1RtvvAFA7969S21///33GTZsWPUHJF5lyc7DvPnzNgCSr25PZLC/yRFJZalBVQM4XQbPzdnAu7/uAODK+Pq8cE0H/H1tJkcmIuLeHE4XP20smn+qb2tdCi0inqF4BFWsRlCJmzEMw+wQxEtl5xeS9OlKXAZc27khl7SrZ3ZIcgbcbimiuLiia0T/+u/55583OyyPdSzPwYgPlpY0px7q24JJg+LVnBIRqYClO4+QlVdInSA/zmtU2+xwpIY5fPgwN998MyEhIYSFhXHbbbeRnZ19ymN69+5d5jzqrrvuqqaIxV2knhhBFacRVCJSQzzz9Xp2Hz5Og7AAxl3Rxuxw5Ay55Qiqp59+mhEjRpTcDg4ONjEaz7XnyHHu+nglm9KPYfexMvH6eAZ0UCdZRKSiii/vu6hVJDar5jCQ6nXzzTezf/9+UlJScDgcDB8+nDvuuIMZM2ac8rgRI0bw9NNPl9yu6FLs4h0KCl2kHj7RoArXCCoR8X7z1qUxc+luLBaYeH1Hgv29byLymsItG1TBwcFER0ebHYZH23EMxr/5O4dzHEQE23lnSBc6xoSZHZaIiMcwDKOkQZWo+aekmm3YsIG5c+eyZMkSunTpAsDkyZO57LLLePnll6lfv/5Jjw0MDNR5VA22IyOHQpdBsN2HeqGaf0VEvFtGdj6jZ68B4I4LmpDQpK7JEcnZcMsG1fPPP88zzzxDo0aNuOmmm3jwwQfx8Sk/1Pz8fPLz80tuZ2VlAeBwOHA4HKd8nuL7T7efp5m9fDeT19lwGg7a1Atm6s3nUS/U3yvy9NbXTHl5X+7i+bYeyGbXoVz8bFYuaB5hdjhSwyxatIiwsLCS5hRAYmIiVquVxYsXc9VVV5302I8//piPPvqI6OhorrjiCsaMGXPSUVQ6jyrL0/PasC8TgKaRQRQWFpa6z9NzOxnl5X25i1SEYRg8/vkaDuUU0Co6mKR+LcwOSc6S2zWo7r//fjp16kSdOnVYuHAho0ePZv/+/UycOLHc/ZOTkxk/fnyZ7fPmzavwkPaUlJSzitlduAz4breVeXutgIX2tV3cEnOEFb/9yAqzg6ti3vKa/V1Nzis3N7caIhGpuHnri0ZPdW9alyC72/25FC+XlpZGZGTpkXs+Pj7UqVOnZFn28tx0003ExsZSv359Vq9ezWOPPcamTZuYPXt2ufvrPOrkPDWvOalWwIp//hHmzJlT7j6emtvp1OS8dB4lNdGnS3fzw4Z0/GxWXh0Uj91H8yx7umo543788cd54YUXTrnPhg0baNWqFUlJSSXbOnTogJ+fH3feeSfJycnY7fYyx40ePbrUMVlZWcTExNCvXz9CQkJO+ZwOh4OUlBT69u2Lr69nX6d6vMDJo7PXMm/vieXQ67t47baLsPv5mRxZ1fKm1+yvlNefn9qLuItvV+8H4NJ2ulRKqk5Fz4nO1B133FHydfv27alXrx4XX3wx27Zto2nTpmX213lUWZ6e1zczVsLeA1zUuTWX9YgtdZ+n53YyykvnUVLzpB7K5emv1wPwUL8WtK536r9Z4hmqpUH10EMPMWzYsFPu06RJk3K3JyQkUFhYyM6dO2nZsmWZ++12e7mNK19f3wr/garMvu4oPSuPER8sZfWeo/jaLDzzzzYEpK3C7ufn0Xmdiqe/ZidTk/PyxrzFc20/mM36/Vn4WC30b6sGlVSdip4TRUdHc+DAgVLbCwsLOXz4cKXml0pISABg69at5TaodB51cp6a17aDOQC0qhd60vg9NbfTqcl5eWPeIifjdBkkfbqSnAIn3RrX4fYLyu8liOeplgZVREQEERFnNn/HypUrsVqtZYa5S5G1e49y+/SlpGXlUTvQlzdv6cJ5DYOZM2eV2aGJiHisOWuKRk/1bBZO7SDvGokq5qroOVH37t3JzMxk2bJldO7cGYAff/wRl8tV0nSqiJUrVwJQr55W8a0J8hxOdh4qalC1jNYq2CLind78ZRtLdx2hlt2HV67rqJWWvYhbTaqxaNEiFi9eTJ8+fQgODmbRokU8+OCDDB48mNq1a5sdntuZuzaNB2eu5LjDSbPIWrw7tAuxdYM0SaKIyFn65sTlfQM66E29mKN169ZccskljBgxgqlTp+JwOBg5ciQ33HBDyQp+e/fu5eKLL+aDDz6gW7dubNu2jRkzZnDZZZdRt25dVq9ezYMPPsiFF15Ihw4dTM5IqsP2gzm4DAjx9yEyuOzIOBERT7d271FeTdkMwFP/bEtMnYrNlyiewWp2AH9lt9v55JNP6NWrF23btmXChAk8+OCDvPXWW2aH5lYMw+CNBdu466NlHHc4uaB5OLPv6UFs3SCzQxPxSFOmTCEuLg5/f38SEhL4448/Trrv22+/zQUXXEDt2rWpXbs2iYmJp9xfPM/WA9lsTDuGr81C/za6vE/M8/HHH9OqVSsuvvhiLrvsMs4///xS50QOh4NNmzaVTI7s5+fHDz/8QL9+/WjVqhUPPfQQ11xzDV9//bVZKUg123LgGAAtooKxWDSiQES8S57DyYMzV+JwGvRvG8U1nRqYHZJUMbcaQdWpUyd+//13s8Nwa/mFTkbPXsPs5XsBGNo9ljGXt8HH5la9RhGPMXPmTJKSkpg6dSoJCQlMmjSJ/v37s2nTpnIvLV6wYAE33ngjPXr0wN/fnxdeeIF+/fqxbt06GjTQH0lvUDw5+vnNwgkN1JweYp46deowY8aMk94fFxeHYRglt2NiYvj555+rIzRxU5vTixpUzaN0eZ+IeJ+Xv9/ElgPZhNey89xV7dWI90LqaniQQ9n5DH5nMbOX78VmtfD0lW0Zf2U7NadEzsLEiRMZMWIEw4cPp02bNkydOpXAwEDee++9cvf/+OOPueeee4iPj6dVq1a88847uFwu5s+fX82Ry7lgGAZfrNgDwOUd6pscjYhI5WxOzwagRVQtkyMREalaC7dm8M6vOwB48dr21K2ly5i9kVuNoJKT25x+jNumL2H34eME+/sw5aZOXNjizCaeF5EiBQUFLFu2jNGjR5dss1qtJCYmsmjRogo9Rm5uLg6Hgzp16pR7f35+Pvn5+SW3i5eBdjgcp50vrvh+b5tXzp3zWrrrCDsP5RLkZyOxVd1Kx+jOuZ0N5eV9uYt32pL+5yV+IiLe4uhxBw/PKloE7KaERlzUKsrkiORcUYPKAyzYdID7ZqzgWH4hjeoE8t6wLjSL1ImHyNnKyMjA6XQSFVX6j1xUVBQbN26s0GM89thj1K9fn8TExHLvT05OZvz48WW2z5s3j8DAik3qmJKSUqH9PI075jVjqxWw0i7UwYIf5p3x47hjblWhJudVPM+TiLvKczhJPVz0c9pcI6hExIs89dU69h3NI7ZuIP+6rLXZ4cg5pAaVGzMMg+kLd/L0N+txGdCtcR2mDu5MHS15LuIWnn/+eT755BMWLFiAv79/ufuMHj2apKSkkttZWVnExMTQr18/QkJCTvn4DoeDlJQU+vbti6+v98yF5K555RYU8sSynwEnD/wzga5xlV891l1zO1vK68/RjyLuav3+LFwG1A3yI0KXvoiIl/h29X6+WLEXqwUmXh9PkF0tDG+mV9dNOZwuxn+9jo9+TwXgus4NmXBVe/x8NN+USFUJDw/HZrORnp5eant6ejrR0adeve3ll1/m+eef54cffjjl8u12ux27vewbBV9f3wq/0a/Mvp7E3fL6YXU6OQVOYusG0r1ZxFlNvOluuVWVmpyXN+Yt3mVlaiYAHWPCNHGwiHiF9Kw8/vXlGgDu7dOMzrGV//BQPIu6HW7o6HEHt05bwke/p2KxwOOXtuLFazuoOSVSxfz8/OjcuXOpCc6LJzzv3r37SY978cUXeeaZZ5g7dy5dunSpjlClGny6dDcA13ZqqDd3IuJxVu7OBCA+JszUOEREqoJhGDzy2Woycx20axDCfRc1NzskqQYaQeVmdmbkcOv0JWw/mEOgn41Jg+Lp1/bUIzlE5MwlJSUxdOhQunTpQrdu3Zg0aRI5OTkMHz4cgCFDhtCgQQOSk5MBeOGFFxg7diwzZswgLi6OtLQ0AGrVqkWtWprzw1NtTMti8Y7D2KwWrunc0OxwREQqTQ0qEfEmH/2+i182H8TuY2XSoHgN1qgh1KByI79vP8RdHy0jM9dBvVB/3hnahbb1Q80OS8SrDRo0iIMHDzJ27FjS0tKIj49n7ty5JROnp6amYrX++QfxjTfeoKCggGuvvbbU44wbN46nnnqqOkOXKjR94U4A+reNon5YgLnBiIhU0qHs/JIJ0juqQSUiHm5HRg4T5mwAiq4m0gJhNYcaVG7i0yW7+deXa3A4DTrGhPH2LZ2JDCl/0mURqVojR45k5MiR5d63YMGCUrd37tx57gOSanUkp4AvVuwFYFiPxiZHIyJSeav2ZALQJCKI0ADNlybub8qUKbz00kukpaXRsWNHJk+eTLdu3cwOS9yA0wUPf7aGPIeLns3qMrR7nNkhSTXSODmTOV0GyXM28Ojnq3E4DQZ0qMfMO/6h5pSISDWZuXQ3eQ4XbeqFnNHKfSIiZiueIF2X94knmDlzJklJSYwbN47ly5fTsWNH+vfvz4EDB8wOTdzAvL0WVu/NIsTfh5ev64jVqnlBaxI1qEyUk1/InR8u481ftgPwwMXNef3G8/D3tZkcmYhIzeBwuvhw0S4AhvWM0+ToIuKRVpyYf+o8NajEA0ycOJERI0YwfPhw2rRpw9SpUwkMDOS9994zOzQx2bp9WczbU9SieGZgO+qFatqFmkYNKpPszTzOtVMX8cOGdPx8rLx2QzwP9m2hN0ciItXoixV72Zt5nLpBfvyzY32zwxERqTSXy2BVyQTpGgUq7q2goIBly5aRmJhYss1qtZKYmMiiRYtMjEzMZhgGL3y/GRcWLmkbxZXxDcwOSUygOahMsHJ3JrdPX0pGdj7htfx4a0gXOjXSCYWISHUqdLqY8tNWAO64sIlGr4qIR9pxKIesvELsPlZa1dNEwuLeMjIycDqdJYvRFIuKimLjxo1l9s/Pzyc/P7/kdlZWFgAOhwOHw3HK5yq+/3T7eRpvzet/WzNYtP0wNovBQxc39qr8vPU1q0xeFc1dDapq9tWqfTwyaxX5hS5aRQfzztAuNKwdaHZYIiI1zn9X7mPXoVzqBPlxS/dYs8MRETkjf+w4DED7BqH42nRxhHiX5ORkxo8fX2b7vHnzCAys2HuolJSUqg7LLXhTXi4DXlljAyycH22wfsmvrDc7qHPAm16zv6pIXrm5uRV6LDWoqolhGLw2fwuTftgCwMWtInntxvOoZddLICJS3QqdLl4/MXpqxAVNCPRTLRYRz7RgU9HE0he2iDA5EpHTCw8Px2azkZ6eXmp7eno60dHRZfYfPXo0SUlJJbezsrKIiYmhX79+hISEnPK5HA4HKSkp9O3bF19f71nd0hvz+mb1fvb8voYgPxv9GhR6VW7gna8ZVC6v4tGPp6Mz8mqQ53Dy6Ger+WrVPgBGXNCYxy9tjU0rEoiImGLWsj3syMghLNBXo6dExGMVFLr4beshAHq3VINK3J+fnx+dO3dm/vz5DBw4EACXy8X8+fMZOXJkmf3tdjt2u73Mdl9f3wq/0a/Mvp7EW/IqdLqY/FPRomG3nx9HreObvCa3v6vJeVU0bzWozrEDx/K444NlrNydiY/VwoSr2jGoayOzwxIRqbGy8hy8/P0mAO67qLlGsoqIx1q66zDZ+YWE1/KjXf1Qs8MRqZCkpCSGDh1Kly5d6NatG5MmTSInJ4fhw4ebHZqY4KtV+9h+4kPDYT1i+WX+JrNDEhPprPwcWr8vi9unL2Hf0TxCA3x5Y3AnejQNNzssEZEabfL8LRzKKaBpRBBDNHpKRDzYz5sOAkWX91k1Ml88xKBBgzh48CBjx44lLS2N+Ph45s6dW2bidPF+hU4Xr80vmgLnjgub6ENDUYPqXElZn84Dn6wgt8BJk/Ag3h3WlcbhQWaHJSJSo20/mM20hTsBePLyNppQWEQ82oITDareLSNNjkSkckaOHFnuJX1Ss8xesbdkwZqh3eMAw+yQxGRqUFUxwzB465ftPD93I4YBPZrW5Y2bOxMa6H3XmoqIeBKny+Cxz1fjcBr0bhlBH72hExEPti/zOJvSj2G1wIXNNUJfRDxLdn4hE+dtBuDOC5sQZPfB4XCYHJWYTQ2qKlRQ6OLJL9fw6dI9ANyU0Ijx/2yrT+hFRNzA+7/tYMnOIwT52XjmynZmhyMiclZ+3Fi0et95jWoTFuhncjQiIpXzyrxNpGXl0ahOIEN7xJkdjrgJNaiqyJGcAu76aBmLdxzGaoEnB7RheM84LBbNByAiYrZtB7N56cTE6P8a0IaYOoEmRyQicnY+X170gWi/Npq3R0Q8y9q9R5l+YsqFZwa2w9/XZm5A4jbUoKoCWw9kc9v0Jew6lEstuw+TbzpPl46IiLiJ3IJC7v14OfmFLi5oHs6N3WLMDklE5KxsTMtiRWrRCtFXd2podjgiIhVWUOhi9Ow1uAy4vEM9erWIMDskcSNqUJ2lX7dkcPfHyziWV0iDsADeG9aVltHBZoclIiIUzQv42Odr2Jh2jPBafrx0bUeNbBURj/fJH7sB6Nc2iohgu8nRiIhU3HNzNrBm71FCA3wZe3kbs8MRN6MG1Vn46PddjPtqHU6XQZfY2ky9pTPhtXSSICLiLt76ZTtfr9qHj9XC/93cmehQf7NDEhE5K3kOJ7NPXN53Q9dGJkcjIlJxc9bsL1lNeeL1HYkM0XmZlKYG1RkodLp49tsNJb9cV5/XgORr2mP30bWzIiLu4tOlu0n+biMAYy5vQ7fGdUyOSETk7M1Zs5+svEIa1g7g/GZavU9EPMO6fUd59LPVANzVqykXt9b8eVKWGlSVdCzPwX3/WcGCTQcBeKR/S+7p3VSXjIiIuJE5a/bz+OdFJ0G3n9+YId1jTY5IROTsOV0Gb/68HYAbusZgter8U0Tc346MHIa+9wfZ+YX8o0kdHu7XwuyQxE2pQVUJuw/nctv0JWxOz8bf18qr18dzaft6ZoclIiJ/MXNJKk98sRaXUfQG7l8DWutDBBHxCp8u3c2m9GOEBvgy+B9qvIuI+9t9OJfB7ywmI7uAtvVDeGtIF3xsVrPDEjelBlUFLd15mDs+XMbhnAKiQuy8M6Qr7RuGmh2WiIic4HIZvDZ/C6/N3wLAtZ0bMuGq9mpOiYhXyM4v5JV5mwF44OLmhAX6mRyRiMiprd6Tya3TlpCRXUCT8CCm39qNEH9fs8MSN6YGVQXMXr6Hxz9fQ4HTRfsGobw9pIsm2hURcSOHsvN5aNaqksuv77uoGUl9W6g5JSJe440FW8nIzieubqBGT4mI2/tm9T4embWa4w4nbeqF8P7wrlpQTE5LDapTcLkMXknZxJSftgFwabtoJl4fT4CfJkMXEXEX89alMea/a0nPysfuY+WZK9txfdcYs8MSEakyv23NYOqJuacev7Q1fj66PEZE3FNOfiFPfbWOWcuKVhu9oHk4bwzuTC27Wg9yevopOYncgkKSZq5i7ro0AO7t05SH+rbUZJQiIm5iR0YOE75dzw8bDgDQLLIWr990Hq2iQ0yOTESk6qQeyuXeGctxugyu7tSA/m218pWIuB/DMPhq1T6S52wkLSsPqwXu7dOM+y9ujq/mnJIKUoOqHGlH87j9gyWs3ZuFn83K89e05+pODc0OS0REKGpM/d9PW5m9Yi9Ol4GvzcKIC5pw30XNNcJVRLxK8TlpZq6Djg1DeU7z6omImzEMgx83HmDyj1tZuTsTgJg6Abx8bUcSmtQ1NzjxOGpQ/c2aPUe5/YMlpGflUyfIj7du6UyXuDpmhyUiUqPlFzpZsOkgMxan8vPmgyXb+7SM4InLWtM8KtjE6EREqt7avUe5bXrROWlEsJ2pt3TG31dNeBFxD5m5BXy5Yi//+aNodVEAf18r9/ZuxogLm6heyRmp1rF2EyZMoEePHgQGBhIWFlbuPqmpqQwYMIDAwEAiIyN55JFHKCwsrJb4vluzn+veXEh6Vj4tomrx33t7qjklUgNMmTKFuLg4/P39SUhI4I8//jjl/rNmzaJVq1b4+/vTvn175syZU02R1ixHjzv4dvV+Hvp0FV2e/YE7P1zGz5sPYrHARa0imX1PD94f3k3NKfFKFTln+jvDMBg7diz16tUjICCAxMREtmzZcm4DlSqX53Dy7/lbuHZq0Tlp88hazL67B/VCA8wOTURquH2Zx/nkj1SGv/8H3SbM56mv17Mp/RhBfjbuvLAJvzzSh/subq7mlJyxah1BVVBQwHXXXUf37t159913y9zvdDoZMGAA0dHRLFy4kP379zNkyBB8fX157rnnzllchmEw5aetvPT9JgB6t4xg8o3nEawlMEW83syZM0lKSmLq1KkkJCQwadIk+vfvz6ZNm4iMjCyz/8KFC7nxxhtJTk7m8ssvZ8aMGQwcOJDly5fTrl07EzLwDvmFTrYdyGHdvqOs2XuUpTuPsDEtC5fx5z7RIf78M74+Nyc0IrZukHnBilSD050zlefFF1/k3//+N9OnT6dx48aMGTOG/v37s379evz9tfqwuzt4LJ/Zy/fwwaJd7M08DkCvFhFMvuk8LcsuItUut6CQzenZrNt3lJWpmSzbdYTtGTml9mkVHcyN3RoxML4BoYGqU3L2qrVBNX78eACmTZtW7v3z5s1j/fr1/PDDD0RFRREfH88zzzzDY489xlNPPYWfn1+Vx+RwwSOfr+W/q/YDMKxHHE8OaI2PJnITqREmTpzIiBEjGD58OABTp07l22+/5b333uPxxx8vs/9rr73GJZdcwiOPPALAM888Q0pKCq+//jpTp06t1tg9hctlkJXnICO7gIzsfPYdyeHnfRaWfrOBPZl57DyUS+rhXJx/7Uad0CyyFr1bRJDYJopucXW0UIXUGKc7Z/o7wzCYNGkSTz75JFdeeSUAH3zwAVFRUXz55ZfccMMN5ypUOQOGYXDwWD4b046xIjWT37ZlsHzXEQpP1MH6of48fllrruhQT3NOiUiVc7oMMnMLOJxTwMFj+aQfy2NfZh77jx5n16Fcdh7KYc+R4xh/OzWzWqB9wzASW0VySbtojWKXKudWc1AtWrSI9u3bExX15+ok/fv35+6772bdunWcd955Vfp8h7LzmbLexo5j+7FZLYz/Z1sG/yO2Sp9DRNxXQUEBy5YtY/To0SXbrFYriYmJLFq0qNxjFi1aRFJSUqlt/fv358svv6zy+Nbty2LnMVixOxMfn6Jy/eeJgvG328VbirYZhoFR/DUGJ/4ruW0Y4DL+/L+r+P8uA6dh4HQZuAyDQmfR1w6XgdPpwuE0cLhcFBS6cDhd5Dtc5BU6yXO4OO5wkptfSE6Bk5z8Qo7lFXIsz8HR4w7K9p5ssGt3qS3Bdh/a1A+hbf1QOsfWpktcbaJCNOpDpCJ27NhBWloaiYmJJdtCQ0NJSEhg0aJF56RBtXZvUY1a+Zca5Y7Ktr7L2ecvtbWw0Mn2LFi26wg+Pj5/1s6/1VXDKHqT5zxROwtdRTXT4SyqkXmFTo4X18P8QjJzHRzKKSD9aB77Mo9zLL/sFBbnNQpjUJcYroxvoEUfRM7Smr1Hy9SoitSDv/t7k4ZyHql4H+Pvt098YZTap/R5maukthgl9cXpKj5PK/q6uM44XQb5jkJWpVs4sjgVF1YKXUXnZ/mFRbUnv9BJfqGLPEdRDcotcJJbUHRelp1fSNZxB8fyC0+SV2nhtey0rhdMx4ZhxMeE0bVxHUIDNFJKzh23OptIS0sr1ZwCSm6npaWVe0x+fj75+fklt7OysgBwOBw4HI6TPtfhnAKueXMxe49ZCPH34d83dKRn07qnPMZTFOfgDbn8nbfmprzMyT0jIwOn01lu3dm4cWO5x5ysTlV1jQK4e8YK9h/14dW1p54Ty1OE+PtQJ8iPiFp+uHIOc16LOGLDa9GoTgBNI4KIDLaXGSngab8T+l32LO5eoyqjuAZVpj7B2dWo2z9cxqEc76lRpfnw2rol5/QZrBaIrRNIm3ohJDSpTY8mdYmtG3jiXhcOh6vKn1O/y57Fm2oUwM6dO3nmmWf48ccfSUtLo379+gwePJh//etf5+RKmSHvLyM731trlA22l3+uWhmhAb5EBNuJqGWnXpg/9UMDaFQnkLjwIJpEBBFey14FsYpU3Fk3qB5//HFeeOGFU+6zYcMGWrVqdbZPVa7k5OSSYfB/NW/ePAIDA8s5oohhQCM/K/n+Fu5olcfRTYuZs+mchGialJQUs0M4Z7w1t5qcV25ubjVEUv3OtEYB+Lts1C3nvMDyty8s5d0H/LXXY/nLNsuJ28X3W098bT1xX9H/DWyWou22E/fZ/vLPx1r0f19r0dd+VgM/a9FtfxvYbRDgY+BvgyAfCPQBH2shkPdnUMZ2OAiZB2GZ6q9HqMl5VUWNMvucqTxnU6MCsYEXvXcpcyHd32roX+tm8W3rX+qkhRM10mrgY6GkJtpP1MRavgaBPhDmB7XtBrX9wM+WBWTBwT2sOwjrzn2aQM3+XfZE3nIetXHjRlwuF2+++SbNmjVj7dq1jBgxgpycHF5++eUqf76GYf4czDxGQGAgFb1S1lK2EhRtP8Xxf55jWUrdLvc8zWIpqSUWLH+ei1ksJ87FLFhP7GArvm0t2mazWrCe2J5x8AAN6kXj5+uDr9WCn48VH5sFu48NPx8r/j427L5WAv1sBPjaCLL7EGT3oZbdh9AAX0IDfKkd6KtpbcTtnHWD6qGHHmLYsGGn3KdJkyYVeqzo6Ogyq2elp6eX3Fee0aNHl7rcJisri5iYGPr160dISMgpn693Xj5zvp/PwMv64uvrPUMVHQ4HKSkp9O3rXXmB9+amvP781L46hYeHY7PZSupMsfT09JPWnOjo6ErtfzY1qm9f/Vx4Gm/NTXlVTY2qynOmvyuuQenp6dSrV69ke3p6OvHx8Sc9TjWqLG/9eQfvzU15mXMeVVmXXHIJl1xyScntJk2asGnTJt54441z0qD6emQP5syZw2WXXeB1PxdFecV7VV4iUAUNqoiICCIiIqoiFrp3786ECRM4cOBAyepZKSkphISE0KZNm3KPsdvt2O1lP77z9fU97S9sEBDkW7F9PZG35gXem1tNzsuMvP38/OjcuTPz589n4MCBALhcLubPn8/IkSPLPaZ79+7Mnz+fUaNGlWxLSUmhe/fu5e5/NjXqTPb1JN6aF3hvbjU5r6rIuyrPmf6ucePGREdHM3/+/JKGVFZWFosXL+buu+8+6XGqUSfnrXmB9+ZWk/Py1LyPHj1KnTp1Tnr/2VyGrEs/PY+35qa8Kp57tc5BlZqayuHDh0lNTcXpdLJy5UoAmjVrRq1atejXrx9t2rThlltu4cUXXyQtLY0nn3ySe++9t9yTJxGRs5WUlMTQoUPp0qUL3bp1Y9KkSeTk5JSs6jdkyBAaNGhAcnIyAA888AC9evXilVdeYcCAAXzyyScsXbqUt956y8w0RMTLnO6cCaBVq1YkJydz1VVXYbFYGDVqFM8++yzNmzencePGjBkzhvr165c04EVE3MnWrVuZPHnyKUdPnc1lyMVq8qWfnspbc6vJeVX0MuRqbVCNHTuW6dOnl9wuXpXvp59+onfv3thsNr755hvuvvtuunfvTlBQEEOHDuXpp5+uzjBFpAYZNGgQBw8eZOzYsaSlpREfH8/cuXNLJhpOTU3Fav3z+vwePXowY8YMnnzySZ544gmaN2/Ol19+Sbt27cxKQUS80OnOmQA2bdrE0aNHS/Z59NFHycnJ4Y477iAzM5Pzzz+fuXPn4u+v1TBF5Nw5k/n19u7dyyWXXMJ1113HiBEjTnrc2VyGrEs/PY+35qa8Kn4ZcrU2qKZNm8a0adNOuU9sbCxz5sypnoBERICRI0ee9JK+BQsWlNl23XXXcd11153jqESkJqvIOZPxtzXCLRYLTz/9tD7YE5FqVdn59fbt20efPn3o0aPHaUeg6zLkk/PWvMB7c6vJeVU072ptUImIiIiIiIj3qMz8env37qVPnz507tyZ999/v9QodRERNahERERERETknNq7dy+9e/cmNjaWl19+mYMHD5bcd7LVkEWkZvG6BlXxcPeKXOPocDjIzc0lKyvLq4baeWte4L25Ka8/f2f/fsmKt1GN8t68wHtzU16qUeXRz4Xn8dbclJdn1KiUlBS2bt3K1q1badiwYan7Khq3apT35gXem5vyqniNshjuXMXOwJ49e4iJiTE7DBE5Q7t37y5z0uJNVKNEPJtqlIi4M9UoEXFnp6tRXtegcrlc7Nu3j+DgYCwWyyn3LV4FYvfu3addBcKTeGte4L25Ka+ibvqxY8eoX7++V89HoBrlvXmB9+amvFSjyqOfC8/jrbkpL9Wo8ujnwvN4a27Kq+I1yusu8bNarZX+1CAkJMSrflCKeWte4L251fS8QkNDqyEac6lG/clb8wLvza2m56UaVb6a/nPhibw1t5qel2pU+Wr6z4Un8tbcanpeFalR3tteFxERERERERERj6AGlYiIiIiIiIiImKpGN6jsdjvjxo3DbrebHUqV8ta8wHtzU15SHm/9/nlrXuC9uSkvKY+3fv+8NS/w3tyUl5THW79/3poXeG9uyqvivG6SdBERERERERER8Sw1egSViIiIiIiIiIiYTw0qERERERERERExlRpUIiIiIiIiIiJiKjWoRERERERERETEVDW2QTVhwgR69OhBYGAgYWFh5e6TmprKgAEDCAwMJDIykkceeYTCwsLqDbQKxMXFYbFYSv17/vnnzQ6r0qZMmUJcXBz+/v4kJCTwxx9/mB3SWXvqqafKvDatWrUyO6xK++WXX7jiiiuoX78+FouFL7/8stT9hmEwduxY6tWrR0BAAImJiWzZssWcYD2EapRqlDtQjZKTUY1SjXIHqlFyMqpRqlFm85b6BNVbo2psg6qgoIDrrruOu+++u9z7nU4nAwYMoKCggIULFzJ9+nSmTZvG2LFjqznSqvH000+zf//+kn/33Xef2SFVysyZM0lKSmLcuHEsX76cjh070r9/fw4cOGB2aGetbdu2pV6bX3/91eyQKi0nJ4eOHTsyZcqUcu9/8cUX+fe//83UqVNZvHgxQUFB9O/fn7y8vGqO1HOoRqlGuQvVKCmPapRqlLtQjZLyqEapRrkDb6hPUM01yqjh3n//fSM0NLTM9jlz5hhWq9VIS0sr2fbGG28YISEhRn5+fjVGePZiY2ONV1991ewwzkq3bt2Me++9t+S20+k06tevbyQnJ5sY1dkbN26c0bFjR7PDqFKA8cUXX5TcdrlcRnR0tPHSSy+VbMvMzDTsdrvxn//8x4QIPYtqlGdQjfIcqlFVSzXKM6hGeQ7VqKqlGuUZvLFGeWN9MoxzX6Nq7Aiq01m0aBHt27cnKiqqZFv//v3Jyspi3bp1JkZ2Zp5//nnq1q3Leeedx0svveRRw1cLCgpYtmwZiYmJJdusViuJiYksWrTIxMiqxpYtW6hfvz5NmjTh5ptvJjU11eyQqtSOHTtIS0sr9fqFhoaSkJDgFa+fWVSj3IdqlGdTjTo3VKPch2qUZ1ONOjdUo9yHN9cob69PUPU1yqcqg/MmaWlppQoWUHI7LS3NjJDO2P3330+nTp2oU6cOCxcuZPTo0ezfv5+JEyeaHVqFZGRk4HQ6y309Nm7caFJUVSMhIYFp06bRsmVL9u/fz/jx47ngggtYu3YtwcHBZodXJYp/X8p7/Tztd8mdqEa5D9Uoz6YadW6oRrkP1SjPphp1bqhGuQ9vrVE1oT5B1dcorxpB9fjjj5eZiOzv/zz5h/yvKpNrUlISvXv3pkOHDtx111288sorTJ48mfz8fJOzkEsvvZTrrruODh060L9/f+bMmUNmZiaffvqp2aHJOaAapRrlaVSjahbVKNUoT6MaVbOoRqlGeRLVpzPjVSOoHnroIYYNG3bKfZo0aVKhx4qOji6zckB6enrJfWY7m1wTEhIoLCxk586dtGzZ8hxEV7XCw8Ox2Wwl3/9i6enpbvFaVKWwsDBatGjB1q1bzQ6lyhS/Runp6dSrV69ke3p6OvHx8SZFZQ7VqNJUozyPapR3U40qTTXK86hGeTfVqNJUozyLN9YnqPoa5VUNqoiICCIiIqrksbp3786ECRM4cOAAkZGRAKSkpBASEkKbNm2q5DnOxtnkunLlSqxWa0le7s7Pz4/OnTszf/58Bg4cCIDL5WL+/PmMHDnS3OCqWHZ2Ntu2beOWW24xO5Qq07hxY6Kjo5k/f35JkcrKymLx4sUnXVnFW6lGVYxqlPtSjfJuqlEVoxrlvlSjvJtqVMWoRrknb6xPUPU1yqsaVJWRmprK4cOHSU1Nxel0snLlSgCaNWtGrVq16NevH23atOGWW27hxRdfJC0tjSeffJJ7770Xu91ubvCVsGjRIhYvXkyfPn0IDg5m0aJFPPjggwwePJjatWubHV6FJSUlMXToULp06UK3bt2YNGkSOTk5DB8+3OzQzsrDDz/MFVdcQWxsLPv27WPcuHHYbDZuvPFGs0OrlOzs7FKfBuzYsYOVK1dSp04dGjVqxKhRo3j22Wdp3rw5jRs3ZsyYMdSvX7/kj5CUpRqlGuUOVKMGmhe0m1ONUo1yB6pRA80L2s2pRqlGmc1b6hNUc42qiqUGPdHQoUMNoMy/n376qWSfnTt3GpdeeqkREBBghIeHGw899JDhcDjMC/oMLFu2zEhISDBCQ0MNf39/o3Xr1sZzzz1n5OXlmR1apU2ePNlo1KiR4efnZ3Tr1s34/fffzQ7prA0aNMioV6+e4efnZzRo0MAYNGiQsXXrVrPDqrSffvqp3N+noUOHGoZRtPzomDFjjKioKMNutxsXX3yxsWnTJnODdnOqUapR7kA1Sk5GNUo1yh2oRsnJqEapRpnNW+qTYVRvjbIYhmFUvq0lIiIiIiIiIiJSNbxqFT8REREREREREfE8alCJiIiIiIiIiIip1KASERERERERERFTqUElIiIiIiIiIiKmUoNKRERERERERERMpQaViIiIiIiIiIiYSg0qERERERERERExlRpUIiIiIiIiIiJiKjWoRERERERERETEVGpQiYiIiIiIiIiIqdSgEhERERERERERU6lBJSIiIiIiIiIiplKDSkRERERERERETKUGlYiIiIiIiIiImEoNKhERERERERERMZUaVCIiIiIiIiIiYio1qERERERERERExFRqUInpXnrpJZo0aYLNZiM+Pt7scERESpyL+rRz504sFgvTpk2rkscTETkVi8XCU089ValjevfuTbt27c5NQCIip7BgwQIsFgsLFiyo1HEWi4WRI0eem6Ck2qhBJZW2Zs0arr32WmJjY/H396dBgwb07duXyZMnV/qx5s2bx6OPPkrPnj15//33ee6559i3bx9PPfUUK1euLLP/sGHDsFgshISEcPz48TL3b9myBYvFgsVi4eWXXz6T9ETEg5lZnwC+/vprevXqRWRkJIGBgTRp0oTrr7+euXPnnmVmIlLTTZs2reQc59dffy1zv2EYxMTEYLFYuPzyy02IUERqkqo85xIp5mN2AOJZFi5cSJ8+fWjUqBEjRowgOjqa3bt38/vvv/Paa69x3333VerxfvzxR6xWK++++y5+fn4ALF26lPHjxxMXF1fuiAUfHx9yc3P5+uuvuf7660vd9/HHH+Pv709eXt4Z5yginsns+vTyyy/zyCOP0KtXL0aPHk1gYCBbt27lhx9+4JNPPuGSSy4BIDY2luPHj+Pr61sleYtIzeLv78+MGTM4//zzS23/+eef2bNnD3a7vdT248eP4+OjU34RqTpVfc71VxdeeCHHjx8vOfeSmkV/raRSJkyYQGhoKEuWLCEsLKzUfQcOHKj04x04cICAgIBKFSC73U7Pnj35z3/+U6ZBNWPGDAYMGMDnn39e6VhExLOZWZ8KCwt55pln6Nu3L/PmzSv3sYpZLBb8/f0rHY+ICMBll13GrFmz+Pe//12q8TRjxgw6d+5MRkZGqf1Vb0SkqlX1OddfWa1W1a0aTJf4SaVs27aNtm3blilEAJGRkSVfF79Za9q0KXa7nbi4OJ544gny8/NL9rFYLLz//vvk5OSUDFmfNm0aXbt2BWD48OGltv/VTTfdxHfffUdmZmbJtiVLlrBlyxZuuummMrEdPnyYhx9+mPbt21OrVi1CQkK49NJLWbVqVan9hg4dir+/Pxs2bCi1vX///tSuXZt9+/ZV9FslItXMzPqUkZFBVlYWPXv2LDe2vz7/yeagmjVrFm3atMHf35927drxxRdfMGzYMOLi4soc+/LLL/PWW2+V5NC1a1eWLFlyBt81EfE0N954I4cOHSIlJaVkW0FBAZ999lm550B/n4Pq2LFjjBo1iri4OOx2O5GRkfTt25fly5eXOXb9+vX06dOHwMBAGjRowIsvvnhOchIRz1KRc66rr76aTp06lbrviiuuwGKx8NVXX5VsW7x4MRaLhe+++w4ofw6qLVu2cM011xAdHY2/vz8NGzbkhhtu4OjRo2We/8svv6Rdu3bY7Xbatm2raRY8jBpUUimxsbEsW7aMtWvXnnK/22+/nbFjx9KpUydeffVVevXqRXJyMjfccEPJPh9++CEXXHABdrudDz/8kA8//JDWrVvz9NNPA3DHHXeUbL/wwgtLPf7VV1+NxWJh9uzZJdtmzJhBq1atyhRCgO3bt/Pll19y+eWXM3HiRB555BHWrFlDr169SjWdXnvtNSIiIhg6dChOpxOAN998k3nz5jF58mTq169f+W+aiFQLM+tTZGQkAQEBfP311xw+fLjSsX/77bcMGjQIX19fkpOTufrqq7nttttYtmxZufvPmDGDl156iTvvvJNnn32WnTt3cvXVV+NwOCr93CLiWeLi4ujevTv/+c9/SrZ99913HD16tFQdO5m77rqLN954g2uuueb/2bvz8KjKs4/j38lk3wkJCYFA2HfZQXClAhERwapVq4JotVVxeVM3lEVARVGUqlSqraItqLVV3BBJUQRlFURklSXsSSCE7MlkMnPeP0IGYgIkZDkzk9/nuqLMmWdm7jsJN2fueZ7n8Ne//pWHH36YoKCgSh/OnThxgiuvvJKePXsye/ZsOnfuzGOPPeZ6EykijVd1zrkuueQSfvrpJ3Jzc4GyffK+//57fHx8WLlypWvcypUr8fHxOeOHfCUlJSQlJbFmzRruv/9+5s6dy913383evXsrTFYA+O6777j33nu56aabmDVrFsXFxVx33XUcP3689klLwzBEamDp0qWG1Wo1rFarMWjQIOPRRx81vvrqK6OkpMQ1ZtOmTQZg/OEPf6jw2IcfftgAjK+//tp1bNy4cUZISEiFcevXrzcA4+233670+qePv/76640rrrjCMAzDcDgcRlxcnDFt2jQjNTXVAIwXXnjB9bji4mLD4XBUeK7U1FQjICDAmD59eoXjX331lQEYTz/9tLF3714jNDTUGDNmTA2+SyJiBrPr05QpUwzACAkJMUaMGGE888wzxoYNGyqNK69Rpz9Hjx49jJYtWxp5eXmuY8uXLzcAo3Xr1pUe27RpUyMrK8t1/JNPPjEA47PPPjvn90lEPNPbb79tAMb69euN1157zQgLCzMKCwsNwzCMG264wRgyZIhhGIbRunVrY+TIka7HAcbUqVNdtyMiIoz77rvvrK912WWXGYDx7rvvuo7ZbDYjLi7OuO666+owKxHxRNU55yo/Z1q8eLFhGIaxefNmAzBuuOEGY+DAga5x11xzjdG7d2/X7W+++cYAjG+++cYwDMP48ccfDcD48MMPzxoTYPj7+xu7d+92Hfvpp58MwHj11VfrIm1pAJpBJTUybNgwVq9ezTXXXMNPP/3ErFmzSEpKokWLFq6pmosXLwYgOTm5wmP//Oc/A2UzBerC73//e5YvX056ejpff/016enpVU5th7J9q3x8yn7dHQ4Hx48fJzQ0lE6dOlWa0j58+HD++Mc/Mn36dH77298SGBjI3/72tzqJWUTqj9n1adq0aSxcuJDevXvz1Vdf8eSTT9K3b1/69OlTaWbC6Y4cOcLPP//M2LFjCQ0NdR2/7LLL6NGjR5WPufHGG2nSpInr9iWXXAKUzRYVEe/3u9/9jqKiIj7//HPy8vL4/PPPz3gO9GuRkZGsXbv2nNsWhIaGcuutt7pu+/v7M2DAANUZEanWOVfv3r0JDQ1lxYoVQNlMqZYtWzJ27Fg2btxIYWEhhmHw3Xffuc5jqhIREQHAV199RWFh4VnjGjp0KO3atXPdvuCCCwgPD1fd8iBqUEmN9e/fn48++ogTJ06wbt06Jk6cSF5eHtdffz3btm1j//79+Pj40L59+wqPi4uLIzIykv3799dJHFdddRVhYWF88MEHLFiwgP79+1d6zXJOp5OXX36ZDh06EBAQQHR0NDExMWzevLnKtcsvvvgiUVFRbNq0iVdeeaXC/jEi4r7Mrk8333wzK1eu5MSJEyxdupTf//73/Pjjj4waNeqMVxctf82q6teZalqrVq0q3C5vVp04caI24YuIh4iJiWHo0KEsXLiQjz76CIfDwfXXX1+tx86aNYstW7aQkJDAgAEDeOqpp6p889ayZUssFkuFY02aNFGdERHg3OdcVquVQYMGuZbzrVy5kksuuYSLL74Yh8PBmjVr2LZtG1lZWWdtULVp04bk5GT+/ve/Ex0dTVJSEnPnzq3yPdyvz49AdcvTqEEl583f35/+/fvz7LPP8vrrr2O32/nwww9d9//6pKauBQQE8Nvf/pZ33nmHjz/++KyfHD777LMkJydz6aWX8q9//YuvvvqKlJQUunXrhtPprDT+xx9/dF2B4ueff663HESkfphdn8LDwxk2bBgLFixg3Lhx7Nmzh7Vr19bZ81ut1iqPG4ZRZ68hIu6t/IIx8+bNY8SIEVVuVlyV3/3ud+zdu9e1t+YLL7xAt27dKu0tpTojItVxtnOuiy++mPXr11NcXOxqUEVGRtK9e3dWrlzpal6drUEFMHv2bDZv3swTTzxBUVERDzzwAN26dePQoUMVxqlueT41qKRO9OvXD4C0tDRat26N0+lk165dFcZkZGSQnZ1N69atz/pcNXnjWD47IS8v76wbg/7nP/9hyJAh/OMf/+Cmm25i+PDhDB06tNLGegAFBQWMHz+erl27cvfddzNr1ixdHUvEg5lVn6p6/aqUv+bu3bsr3VfVMRERgGuvvRYfHx/WrFlT7eV95Zo3b869997LokWLSE1NpWnTpjzzzDP1FKmINBa/Pue55JJLKCkp4b333uPw4cOuRtSll17qalB17NiR2NjYcz53jx49mDRpEitWrGDlypUcPnyYefPm1V8yYgo1qKRGvvnmmyo70OX7unTq1ImrrroKgDlz5lQY89JLLwEwcuTIs75GSEgIQJXNo18bMmQIM2bM4LXXXiMuLu6M46xWa6W4P/zwQw4fPlxp7GOPPcaBAwd45513eOmll0hMTGTcuHEVLkEvIu7HzPpUWFjI6tWrq3xM+ayETp06VXl/fHw83bt359133yU/P991/Ntvv9UMThE5o9DQUF5//XWeeuopRo0aVa3HOByOSstimjVrRnx8vM5zRKTaqnPOBTBw4ED8/Px4/vnniYqKolu3bkBZ42rNmjV8++2355w9lZubS2lpaYVjPXr0wMfHR3XLC/maHYB4lvvvv5/CwkKuvfZaOnfuTElJCatWreKDDz4gMTGR8ePHExkZybhx43jjjTfIzs7msssuY926dbzzzjuMGTOGIUOGnPU12rVrR2RkJPPmzSMsLIyQkBAGDhxImzZtKo318fFh0qRJ54z76quvZvr06YwfP57Bgwfz888/s2DBAtq2bVth3Ndff81f//pXpk6dSp8+fQB4++23ufzyy5k8eTKzZs2qwXdLRBqSmfUpLCyMwYMHc+GFF3LllVeSkJBAdnY2ixYtYuXKlYwZM4bevXuf8XmfffZZRo8ezUUXXcT48eM5ceIEr732Gt27d6/QtBIROd24ceNqND4vL4+WLVty/fXX07NnT0JDQ/nf//7H+vXrmT17dj1FKSLepjrnXADBwcH07duXNWvWMGrUKNdM9EsvvZSCggIKCgrO2aD6+uuvmTBhAjfccAMdO3aktLSUf/7zn1itVq677rp6z1UalhpUUiMvvvgiH374IYsXL+aNN96gpKSEVq1ace+99zJp0iTX/gd///vfadu2LfPnz+fjjz8mLi6OiRMnMnXq1HO+hp+fH++88w4TJ07kT3/6E6Wlpbz99ttVNqiq64knnqCgoICFCxfywQcf0KdPH7744gsef/xx15i8vDzuuOMOevfuzZNPPuk6fskll/Dggw8ye/Zsfvvb33LhhReedxwiUn/MrE+33norb775Jl988QVvv/026enpWK1WOnXqxAsvvMADDzxw1ucdNWoU7733Hk899RSPP/44HTp0YP78+bzzzjts3bq1Lr49IiIEBwdz7733snTpUj766COcTift27fnr3/9K/fcc4/Z4YmIh6juORecmi118cUXu47FxcXRvn17du/efc4GVc+ePUlKSuKzzz7j8OHDBAcH07NnT7788ku9L/NCFkM7homIiLilXr16ERMTQ0pKitmhiIiIiIjUK+1BJSIiYjK73V5pf4Xly5fz008/cfnll5sTlIiIiIhIA9IMKhEREZPt27ePoUOHcuuttxIfH8+OHTuYN28eERERbNmyhaZNm5odooiIiIhIvdIeVCIiIiZr0qQJffv25e9//zvHjh0jJCSEkSNH8txzz6k5JSIiIiKNgpb4iUijtWLFCkaNGkV8fDwWi4VFixad8zHLly+nT58+BAQE0L59e+bPn1/vcYr3i4iI4IMPPuDQoUPYbDaysrL48MMPadeundmhiYiIiIg0CDWoRKTRKigooGfPnsydO7da41NTUxk5ciRDhgxh06ZNPPTQQ/zhD3/gq6++qudIRUREREREvJv2oBIRASwWCx9//DFjxow545jHHnuML774gi1btriO3XTTTWRnZ7NkyZIGiFJERERERMQ7ed0eVE6nkyNHjhAWFobFYjE7HBGpJsMwyMvLIz4+Hh8f95zcuXr1aoYOHVrhWFJSEg899NAZH2Oz2bDZbK7bTqeTrKwsmjZtqhol4kE8oUbVBZ1HiXgm1SgRcWfVrVFe16A6cuQICQkJZochIufp4MGDtGzZ0uwwqpSenk5sbGyFY7GxseTm5lJUVERQUFClx8ycOZNp06Y1VIgiUs/cuUbVBZ1HiXg21SgRcWfnqlFe16AKCwsDyhIPDw8/61i73c7SpUsZPnw4fn5+DRFeg/DWvMB7c1NekJubS0JCguvvsLeYOHEiycnJrts5OTm0atWK1NTUc+Zqt9v55ptvGDJkiNf9XnhjXuC9uSkvyMvLo02bNl5Xo35N51Hemxd4b27Ky3vPo35NNcp78wLvzU15Vb9GeV2DqnyqZ3h4eLWKVnBwMOHh4V73i+KNeYH35qa8TnHn6dpxcXFkZGRUOJaRkUF4eHiVs6cAAgICCAgIqHQ8Kiqq2jWqadOmXvl74W15gffmprxw3e/ONaou6DzKe/MC781NeZ2iGnWKfi88j7fmprxOOVeN8t4FyiIidWzQoEEsW7aswrGUlBQGDRpkUkQiIiIiIiLeQQ0qEWm08vPz2bRpE5s2bQIgNTWVTZs2ceDAAaBsed7YsWNd4//0pz+xd+9eHn30UXbs2MFf//pX/v3vf/N///d/ZoQvIiIiIiLiNdSgEpFG64cffqB379707t0bgOTkZHr37s2UKVMASEtLczWrANq0acMXX3xBSkoKPXv2ZPbs2fz9738nKSnJlPhFpPFZsWIFo0aNIj4+HovFwqJFiyrcbxgGU6ZMoXnz5gQFBTF06FB27dplTrAi0qioPolIbalBJSKN1uWXX45hGJW+5s+fD8D8+fNZvnx5pcf8+OOP2Gw29uzZw+23397gcYtI41VQUEDPnj2ZO3dulffPmjWLV155hXnz5rF27VpCQkJISkqiuLi4gSMVkcZG9UlEasvrNkkXERER8VYjRoxgxIgRVd5nGAZz5sxh0qRJjB49GoB3332X2NhYFi1axE033dSQoYpILR3Ns+Fwmh1F9ak+iTQuGbnFOI26fU41qESk3gyf8x3Hc62065NH94Qos8MRkUaisKSUzLwSjuXbOJ5v43hBiev/Wb/6ysyzMvBSG3FNPP+qOqmpqaSnpzN06FDXsYiICAYOHMjq1aurfANos9mw2Wyu27m5uUDZlXnsdvtZX6/8/nON8zTemhd4b27emJfTaXDPgh/JPGGlXe8TdG3R5Kzj3T3386lPoBpVFW/NC7w3N2/Mq9Th5K5/biQvz0qHPtl0ah551vHVzV0NKhGpN0fzbBTYLQT6Wc0ORUS8QLHdQUZuMWk5xaTnFJORW0x6bjFH82wcy7VxLN/G0dxiCkocNXhWC1mFduLO/t7PI6SnpwMQGxtb4XhsbKzrvl+bOXMm06ZNq3R86dKlBAcHV+t1U1JSahipZ/DWvMB7c/OmvFZlWNh82EqAFX5av5p9P519fGFhYcMEdp7Opz6BatTZeGte4L25eVNeK9IsbE+3EmSFTetWseccn/NVt0apQSUi9cLucLreJIYHqdSIyLnlFNk5mFXIoRNFHDpRyOHsIg6fKOJIThFHsovJKiip9nMF+vkQHRpAdGgATUP8aRrqT1RIANGh/jQJ9icq1J9wfx82rfuexKbVe5PjjSZOnEhycrLrdm5uLgkJCQwfPpzw8PCzPtZut5OSksKwYcPw8/P8GWjlvDUv8N7cvC2v4/k2przyPVDKVQlOrh957rzKZxZ5G9Woyrw1L/De3Lwtr6N5Np78S1mNurqVk99eVXc1Su8aRaRe5BadmsYZFqBSIyJlcorspGYWsPdYPvsyC0g9Xsj+4wUcyCoku/Dc078D/XxoHhFEbHgAceGBxIYH0iw8kGZhAWVf4YFEh/oTGuCLxWI563PZ7XYObQY/q3dcMyYuLg6AjIwMmjdv7jqekZFBr169qnxMQEAAAQEBlY77+flV+yS6JmM9ibfmBd6bm7fk9ULKNnKKSukSF8YlcSeqlZe7530+9QlUo87GW/MC783NW/J6/qst5NtKuaBlOINjs+q0Ruldo4jUi9ziUgACrAa+XvLmT0SqL6fIzs70PHam57LraD67MvLZfSyfY3m2sz6uaYg/LaOCadkkiJZNgmgRWfbVPCKI+MhAIoL8ztl4aqzatGlDXFwcy5Ytc73hy83NZe3atdxzzz3mBici1bJ273H+u/EQFgtMu6YLaT+vMjukOqH6JOIdvt+dyac/HcHHAtOu7sqBn76r0+dXg0pE6kXOyRlUwdp+SsTrZeQWs/lQDlsO57D1SC7b03I5nF10xvHNwgJoGxNCm+gQEpuG0LppCInRwSQ0CSZEMy7PKj8/n927d7tup6amsmnTJqKiomjVqhUPPfQQTz/9NB06dKBNmzZMnjyZ+Ph4xowZY17QIlItJaVOJi3aAsBN/VvROyGStJ9NDqoGVJ9EvJut1MHkkzXqtgtb071FOAfOsT9eTeksUETqhatBpSoj4lWK7Q42H8ph44ETbNx/gp8OZZORW/WsqBaRQXSMDaVjXBgdm4XRvlkobWNCCAv0/OntZvnhhx8YMmSI63b53izjxo1j/vz5PProoxQUFHD33XeTnZ3NxRdfzJIlSwgMDDQrZBGppn98l8quo/k0DfHnsSs7mR1Ojak+iXi3N1fsZW9mAdGhAfw5qX5qlN46iki9KG9QBfkaJkciIrVRbHewZs9xPj/gwztvrmPL4VxKHM4KY3ws0KFZGN1bRNAtPpxu8eF0bh5ORJAaUXXt8ssvxzDOXFctFgvTp09n+vTpDRiViNTWoROFvLJsFwATr+pCZLC/x12SXvVJxHsdzCrk1a/LZkhOvroL4YF+9VKj1KASkXqhGVQinskwDHYfzeebnUf59pdjrN93gpJSJ+ADZAMQExZAv9ZN6N0qkl4JTejeIpxgf/1lFxE5X099uo0iu4MBbaK4rk8Ls8MREXExDIMpn2zBVupkcLumXNMzvt5eS2eTIlIvyq/iF6Q9qETcnsNpsH5fFku3ZrB0WzqHTlTcPyo2PIBW/kX89pIeDG4fQ6uoYG1ULiJSR1K2ZfC/7Rn4+lh4ekx31VcRcStLt2Xwzc5j+FktTB9dvzVKDSoRqReuBpWqjIhbMgyDjQey+XTTYRZvSa9wdT1/Xx8GtW3KZR1juLRjDK0i/fnyyy+5qk8Lr7g8soiIuygsKeWpT7cC8IdL2tIxNszkiERETimwlTLtZI3646XtaN8stF5fT28dRaRenFripz2oRNxJRm4xH/5wkP9sOMS+44Wu4xFBfgztEsvwbrFc0iG6wpI9T9sHRUTEU7yybDeHs4toERnEA1e0NzscEZEKXvl6F0dyimnZJIj7htR/jVKDSkTqhfagEnEfhmGwNjWL+d/vI2V7Bg5nWeM4yM/Kld3juKZXPBe1i8bf18fkSEVEGo9fMvL4+8q9ADx1TTft5ScibmVneh7/WJkKwLRruhHkX/97t6gKiki9yNEeVCKmK3U4WbwlnXnL97AtLdd1vF/rJtw0oBUjuscREqBTARGRhmYYBpMWbaHUaTC0SyzDusaaHZKIiIthGEw+WaOGd43lii4NU6N0Vioi9UIzqETM43AafLLpMH9Ztov9J5fxBflZ+W2fFowbnKg9TkRETPbfjYdZl5pFkJ+Vp67panY4IiIV/HfjYdbtK6tRU6/p1mCvq7eOIlIvXDOotAeVSIMxDINl24/y3JId7D6aD0CTYD/GX9SGsYNaExnsb3KEIiKSXVjCs4u3A/DAFR1o2STY5IhERE7JLixh5ska9eDQDrSIDGqw11aDSkTqhWZQiTSsXRl5TPtsG9/tzgQgMtiPP13WjrGDWmtfExERN/L8kp1kFZTQoVkod17cxuxwREQqeOGrnRw/WaPuuKhha5TOWEWkzjmdBvm2UkB7UInUt2K7g7nf7Gbet3uwOwz8rT7ceUkb7rm8HeGBfmaHJyIip9l44ATvrTsAwNNjuuviFCLiVjYdzGahiTVKDSoRqXN5xaUYJ1f2aQaVSP3ZcjiHhz7Y5FrON7RLM6aO6kZClJaLiIi4m1KHk0kfbwHguj4tGdi2qckRiYic4nAaTFr0M4YBv+3TwpQapbeOIlLnXPtP+fmgDwZF6p5hGLy5ci8vfLUTu8MgJiyA6dd048rucVgsFrPDExGRKryzej/b0nIJD/Rl4lWdzQ5HRKSCf63Zz5bDJ2vUiC6mxKAGlYjUufIGVXiQH1BibjAiXibfVsrD//6JJVvTARjeNZbnrruAqBBtgC4i4q7Sc4p5aelOAB4b0Zno0ACTIxIROeVoXjEvflVWox65sjMxYebUKDWoRKTOuRpUgSoxInXpYFYh4+evZ/fRfPysFqaO6sYtA1tp1pSIiJub8cU2Ckoc9EqI5Ob+rcwOR0Skgme+2E6erZSeLSP4/QDzapTePYpInStvUEUEaYNmkbqy5XAOt7+9nsx8G3Hhgfz11j70adXE7LBEROQcVvxyjC82p+FjKdt02MdHHyqIiPtYtTuTTzYdOVmjemA1sUapQSUidS63uHwGlRpUInVhzd7j3Dl/PQUlDro0D2f++P7EhgeaHZaIiJxDsd3BlE/KNkYfNziR7i0iTI5IROSUklInk07WqFsvbE2PlubWKDWoRKTOnZpBpRIjUlvrUrO4Y/56CkscDG7XlL/d1pcwNX9FRDzC68v3sO94IbHhASQP62h2OCIiFby5ci97jxUQHRrAn4d3MjscNahEpO5V3CRdRM7XxgMnGP/2OgpLHFzSIZo3x/Yj0M9qdlgiIlINqZkFvL58DwCTr+6qDxdExK0czCrk1a93ATBpZBe32J5FF4AXkTrnmkGlEzGR87b/eAF/eOcHCkocXNS+qZpTIiIexDAMpnyyhRKHk0s6RDOyR3OzQxIRqWDaZ1sptjsZ1LYpo3vFmx0OoAaViNSD8gZVmJb4iZyXnEI74+evJ6ughB4tItScEhHxMJ9vTmPlrkz8fX2YMbq7rrYqIm4lZVsG/9t+FD+rhRljurlNjVKDSkTqXK5mUImcN6fTYMJ7G9l7rID4iED+Ma4fwf5q9oqIeIq8YjszPt8GwL2XtyMxOsTkiERETiksKeWpT7cCcNclbWnfLMzkiE6pdYNq7ty5JCYmEhgYyMCBA1m3bt0Zx27dupXrrruOxMRELBYLc+bMqTTmqaeewmKxVPjq3LlzbcMUkQaU69qDSm+qRWrq9W/3sHJXJkF+Vv5xe3+a6Wp9IiIeZfbSXziaZyOxaTB/uqyd2eGIiFTw6te7OZxdRIvIIO7/TQezw6mgVg2qDz74gOTkZKZOncrGjRvp2bMnSUlJHD16tMrxhYWFtG3blueee464uLgzPm+3bt1IS0tzfX333Xe1CVNEGtipq/hpBpVITazfl8XspTsBmD66G12ah5sckYiI1MSWwzm8u3ofADPGdNfybBFxK7sy8nhzxV4AnrqmG0H+7lWjatWgeumll7jrrrsYP348Xbt2Zd68eQQHB/PWW29VOb5///688MIL3HTTTQQEBJzxeX19fYmLi3N9RUdH1yZMEWlg2iRdpObybaU8+N6POA24tncLru/b0uyQRESkBhxOgycXbcFpwNUXNOeSDjFmhyQi4mIYBpM/2UKp02Bol1iGdY01O6RKzrtBVVJSwoYNGxg6dOipJ/PxYejQoaxevbpWQe3atYv4+Hjatm3LLbfcwoEDB2r1fCLScAzDILe4FNASP5GamL10J0dyikmICmLGGG2oK+fH4XAwefJk2rRpQ1BQEO3atWPGjBkYhmF2aCJe7711B/jpYDahAb5Mvrqr2eG4JdUoEfMs2nSYNXuzCPTzYeoo96xR5/3uMTMzE4fDQWxsxa5bbGwsO3bsOO+ABg4cyPz58+nUqRNpaWlMmzaNSy65hC1bthAWVnnzLpvNhs1mc93Ozc0FwG63Y7fbz/pa5fefa5yn8da8wHtz86a88opLcTjLTjLK+1PVycsbchc5X5sPZfPOqn0APDOmB6EBau7K+Xn++ed5/fXXeeedd+jWrRs//PAD48ePJyIiggceeMDs8ES81rE8G7OWlL0H+vPwjsRq/8AqqUaJmCOnyM4zX2wH4P7fdCAhKtjkiKrmdmfAI0aMcP35ggsuYODAgbRu3Zp///vf3HnnnZXGz5w5k2nTplU6vnTpUoKDq/dNT0lJOf+A3Zi35gXem5s35JVlA/DFajFY+c3XWCzVy6uwsLDeYxNxR6UOJxM/+hmnAaN7xXNpRy0JkfO3atUqRo8ezciRIwFITEzkvffeO+tFbESk9mYu3k5ucSnd4sO57cLWZofjtlSjRMwxe+lOMvNLaBcTwl2XtDU7nDM67wZVdHQ0VquVjIyMCsczMjLOugF6TUVGRtKxY0d2795d5f0TJ04kOTnZdTs3N5eEhASGDx9OePjZN5e12+2kpKQwbNgw/Py8Z68cb80LvDc3b8pry+Fc2LiG6LBAhg8fXO28ymc/ijQ2H208zNYjuUQE+WlJiNTa4MGDeeONN/jll1/o2LEjP/30E9999x0vvfSS2aGJeK3Ve47z0Y+HsVjgmWt74Gut9YXSvZZqlEjD+/lQDv9csx+AGaO74+/rvjXqvBtU/v7+9O3bl2XLljFmzBgAnE4ny5YtY8KECXUVH/n5+ezZs4fbbrutyvsDAgKq3HDdz8+v2m/0azLWk3hrXuC9uXlDXjk2BwBRIQGuXKqTl6fnLXI+iu0O5vzvFwAmDGlPdOiZLyAiUh2PP/44ubm5dO7cGavVisPh4JlnnuGWW26pcry2SqjMW/MC783NzLxKSp1MWvQzADf1a0m3uJA6i6MmeXnKz1Q1qva8NS/w3tzMzMvhNHjy480YBoy6II7+rSPcukbVaolfcnIy48aNo1+/fgwYMIA5c+ZQUFDA+PHjARg7diwtWrRg5syZQNnG6tu2bXP9+fDhw2zatInQ0FDat28PwMMPP8yoUaNo3bo1R44cYerUqVitVm6++ebahCoiDeREYQkATUP8TY5ExP0tWHuAIznFNI8I5LZBWhIitffvf/+bBQsWsHDhQrp168amTZt46KGHiI+PZ9y4cZXGa6uEM/PWvMB7czMjr5TDFvYcsxLqa3AB+1i8eF/dv4YXbZWgGlV3vDUv8N7czMjru3QLmw9bCbQa9Pc7xOLFh+r8NeqyRtWqQXXjjTdy7NgxpkyZQnp6Or169WLJkiWujdMPHDiAj8+p6WNHjhyhd+/ertsvvvgiL774IpdddhnLly8H4NChQ9x8880cP36cmJgYLr74YtasWUNMjPbkEPEEx/PLGlRNPKhBNXfuXF544QXS09Pp2bMnr776KgMGDKhy7Pz5811N+HIBAQEUFxc3RKjiRfJtpcz9pmz5+oNXdCDQz2pyROINHnnkER5//HFuuukmAHr06MH+/fuZOXNmlW/+tFVCZd6aF3hvbmbldehEEY+9+j3gZOroHozpFV+nz1+TvDxlqwTVqNrz1rzAe3MzK6/j+TYm/+V7oJRHruzCzRe2qtPnr48aVetN0idMmHDGJX3lTadyiYmJ57yE6Pvvv1/bkETERFkFnjWD6oMPPiA5OZl58+YxcOBA5syZQ1JSEjt37qRZs2ZVPiY8PJydO3e6blssloYKV7zIwrX7ySoooW10CNf3bWl2OOIlCgsLK3w4CGC1WnE6nVWO11YJZ+ateYH35tbQeT3z5SaK7U4ubBvF9f1a1dv5gDdtlaAaVXe8NS/w3twaOq8XUra5Lt4wbnCbetsfry5rlNtdxU9EPFv5Er8oD2lQvfTSS9x1112uWVHz5s3jiy++4K233uLxxx+v8jEWi6VOLwYhjU+pw8k7q8o2q/zTZe20oa7UmVGjRvHMM8/QqlUrunXrxo8//shLL73EHXfcYXZoIl5l6dZ0/rf9KL4+Fp4e010fVlWTapRIw1i79zj/3XgIiwWeHtPdY8411aASkTrlSUv8SkpK2LBhAxMnTnQd8/HxYejQoaxevfqMj8vPz6d169Y4nU769OnDs88+S7du3aocq809K/PWvKD6uX25JZ3D2UU0Cfbjqm4xbv+98NafmTduQPzqq68yefJk7r33Xo4ePUp8fDx//OMfmTJlitmhiXiNwpJSpn1Wtq/u3Ze2pX2zMJMj8hyqUSL1z+5wMvmTLQDc1L8VvVs1MTmi6lODSkTqlCdtkp6ZmYnD4XDtm1cuNjaWHTt2VPmYTp068dZbb3HBBReQk5PDiy++yODBg9m6dSstW1ZepqXNPc/MW/OCc+f2ly1WwEL/JjaWpXzVMEHVAW/9mXnTBsRhYWHMmTOHOXPmmB2KiNf6y7JdHM4uokVkEPf/poPZ4XgU1SiR+vfWd6n8kpFPVIg/j13ZyexwakQNKhGpU8dP7kHVJNj9G1TnY9CgQQwaNMh1e/DgwXTp0oW//e1vzJgxo9J4be5ZmbfmBdXL7efDOexdvRY/q4Upv7+c2PDABo6y5rz1Z+aNGxCLSP36JSOPf6xMBWDaNd0I8tcFLkTEfRzJLmLO/3YB8PiIzkR62HsyNahEpE6dKN8kPdT9i2F0dDRWq5WMjIwKxzMyMqq9x5Sfnx+9e/dm9+7dVd6vzT3PzFvzgrPn9u8NRwAY2aM5LZt61rIQb/2ZedMGxCJSfwzDYNKiLZQ6DYZ1jWVo19hzP0hEpAFN/2wbRXYH/Vo34fo+nncRHs/YKUtEPILDaZBdVLZPiyfMoPL396dv374sW7bMdczpdLJs2bIKs6TOxuFw8PPPP9O8efP6ClO8iK3UweKf0wC4sX/dXupXRETq1383HmZdahZBflaeuqbqvSdFRMzyzc6jLNmajtXHwowx3fHx8byLN2gGlYjUmezCEgyj7M9Ngv0wnA5zA6qG5ORkxo0bR79+/RgwYABz5syhoKDAdVW/sWPH0qJFC2bOnAnA9OnTufDCC2nfvj3Z2dm88MIL7N+/nz/84Q9mpiEeYvnOY+QWlxIXHsiANlFmhyMiItWUXVjCs4u3A/Dg0A60iAwyOSIRkVOK7Q6mfrIVgPGDE+nS/OxbibgrNahEpM5knVzeFxHkh6/VB7sHNKhuvPFGjh07xpQpU0hPT6dXr14sWbLEtXH6gQMH8PE5Ndn0xIkT3HXXXaSnp9OkSRP69u3LqlWr6Nq1q1kpiAf5dFPZ8r5RPZtj9cBPtUREGqvnl+wkq6CEjrGh3HlxG7PDERGp4PXleziQVUhseAAPDetodjjnTQ0qEakz5Ruke8IV/E43YcIEJkyYUOV9y5cvr3D75Zdf5uWXX26AqMTb5BXb+d/2sv3ORvdqYXI0IiJSXRsPnOC9dQcAeHpMD/ys2iVFRNxHamYBr3+7B4DJV3clNMBz2zyqriJSZ8o3SI/ysAaVSENYujUDW6mTdjEhdIv3zGnXIiKNTanDyZMfbwHg+r4ttTxbRNyKYRhM/XQrJaVOLukQzcgenr0vrhpUIlJnymdQNVGDSqSSzzaXLe8b3asFFouW94mIeIJ3Vu9ne1ouEUF+TBzR2exwREQq+HJLOit+OYa/1Yfpo7t7/DmmGlQiUmdOeOgSP5H6Vmx3sHrPcQCSusWZHI2IiFRHek4xLy3dCcDjIzrTNDTA5IhERE7Jt5Uy/bNtAPzxsra0iQ4xOaLaU4NKROqMZlCJVG1daha2Uidx4YF0jA01OxwREamGGZ9vo6DEQZ9WkdzYL8HscEREKnhl2S7Sc4tJiAriviHtzQ6nTqhBJSJ15kShZlCJVGXFL8cAuLRjtMdPvRYRaQy+/eUYX/ychtXHwtNjeuCjK6+KiBvZmZ7HP75LBWD6Nd0J9LOaHFHdUINKROpMVvkMqmA1qEROt2JXeYMqxuRIRETkXIrtDqZ8UrYx+u2DE+mqC1uIiBsxDIPJi7bgcBokdYtlSOdmZodUZ9SgEpE6U96gigpVg0qkXFpOEb9k5ONjgYvbR5sdjoiInMNfl+9h//FC4sID+b9hHc0OR0Skgo82HmbdviyC/KxMGdXN7HDqlBpUIlJnsrRJukglK3/JBOCClpFEanahiIhb23ssn3nL9wAwZVRXQgN8TY5IROSUnEI7zy7eDsADV3SgRWSQyRHVLTWoRKROGIZxapN0vQkXcflWy/tERDyCYRhM/XQrJQ4nl3aMYUR3XXVVRNzLi0t3cryghPbNQrnz4jZmh1Pn1KASkTpRWOKgpNQJQFMt8RMByt7srNpdNoPqso5a3ici4s4+25zGyl2Z+Pv6MP2abrqohYi4lc2HsvnX2v0ATB/dDX9f72vneF9GImKK8uV9Ab4+BHnJVSREamvf8UJOFNrx9/WhR4tIs8MREZEzyC22M+PzbQDcd3l7EqNDTI5IROQUh7NsY3TDgNG94hnczjs/+FSDSkTqxOn7T+kTR5EyPx3MBqB7fLhXfsolIuItXlr6C8fybLSJDuFPl7c1OxwRkQreX3+Anw7lEBbgy5NXdTE7nHqjs2URqRPlDaom2iBdxGXTyQZVz4RIU+MQEZEz23I4h3dX7wNgxujuBPhqJriIuI/j+TZmLdkJQPLwjjQLDzQ5ovqjBpWI1IljeTYAYsICTI5ExH2UN6h6qUElIuKWHE6DJz/+GacBo3rGc3EH71w2IyKe67kvd5BTZKdr83Buu7C12eHUKzWoRKROZOQWA9BMDSoRAEpKnWw7kgtAz5aR5gYjIiJVWrju1LKZySO9d9mMiHimH/Zl8eGGQwDMGNMdX6t3t3C8OzsRaTBHT86gahbmvVNORWpiR3ouJQ4nkcF+tG4abHY4IiLyK8fybMxasgOAP3v5shkR8TylDieTFm0B4MZ+CfRt3cTkiOqfGlQiUieO5p2cQRWuGVQicNr+Uy0jdeEAERE39Ozi7eQVl9ItPpzbBiWaHY6ISAXvrN7PjvQ8IoP9eGxEZ7PDaRBqUIlIndAMKpGKtEG6iIj7WrUnk49/PIzFAs9c2wOrjz5IEBH3kZFbzMspvwDwaFJnohrJhajUoBKROnE092SDSjOoRIBTDarealBJAzt8+DC33norTZs2JSgoiB49evDDDz+YHZaI2ygpdTL55LKZ3w9opQtZiIjbeXbxdvJtpfRMiOSm/glmh9Ng1KASkVozDMN1FT9tki4CecV29h4rAOCClhEmRyONyYkTJ7jooovw8/Pjyy+/ZNu2bcyePZsmTbx/3wqR6npz5V72HCsgOtSfR5Max7IZd6ImusjZrdqTySebjmCxwNOju+PTiGZ4+podgIh4vuxCOyUOJwAxalCJsOtoWXOqeUQgTUP1d0IazvPPP09CQgJvv/2261ibNm1MjEjEvRzMKuTVr3cB8MRVXYgI9jM5osalvIk+ZMgQvvzyS2JiYti1a5ea6CInlZQ6mfLJVgBuGdiKHo3sg041qESk1sr3n4oM9iPA12pyNCLm23Ny9lS7mFCTI5HG5tNPPyUpKYkbbriBb7/9lhYtWnDvvfdy1113mR2aiOkMw+CpT7dSbHdyYdsoru3dwuyQGh010UXO7q3vU9l9NJ+mIf48MrzxzfBUg0pEas11BT/NnhIBIDWzvEEVYnIk0tjs3buX119/neTkZJ544gnWr1/PAw88gL+/P+PGjas03mazYbPZXLdzc3MBsNvt2O32s75W+f3nGudpvDUv8N7cqptXyrajLNtxFD+rhakjO1NaWtoQ4Z23mvy8POVnWtMmumpUZd6aF3hvbtXNKy2nmFeWlc3wfGR4B4L93Pt7UR81Sg0qEam1jJMbpMeG6wp+IgB7yxtUzTSDShqW0+mkX79+PPvsswD07t2bLVu2MG/evCobVDNnzmTatGmVji9dupTg4OBqvWZKSkrtgnZT3poXeG9uZ8vL5oBnN1kBC5fFOfjlhxX80nCh1Up1fl6FhYUNEEnt1bSJrhp1Zt6aF3hvbufK6+2dPhSW+NAmzCAg7ScWL/6pgSKrnbqsUWpQiUitlc+g0v5TImXKZ1C1jVaDShpW8+bN6dq1a4VjXbp04b///W+V4ydOnEhycrLrdm5uLgkJCQwfPpzw8PCzvpbdbiclJYVhw4bh5+c9+/h4a17gvblVJ6/nv/qF7JJ9tIwM5KU7LiLI3/23JKjJz6t8ZpG7q2kTXTWqMm/NC7w3t+rktXJ3JptWb8THAn+5bTBdmoc1cJQ1Vx81Sg0qEam1o7nlV/DTDCoRhxMOZBUB0K6ZlvhJw7rooovYuXNnhWO//PILrVu3rnJ8QEAAAQGVP1zw8/Or9puDmoz1JN6aF3hvbmfKa2d6HvNX7Qdg2ujuhId41vlKdX5envLzrGkTXTXqzLw1L/De3M6Ul63UwYwvyv7tHjc4kQtaRTV0aLVSlzXKpy4CEpHG7VheeYNKM6hEMm1Q6jQI9rcSp2Wv0sD+7//+jzVr1vDss8+ye/duFi5cyBtvvMF9991ndmgipnA6DSYt+plSp8HwrrFc0SXW7JAatZo20UUag7+vTCU1s4CYsAD+b1hHs8MxlRpUIlJrrk3Sw9WgEjlaZAGgbUwIFovF5Giksenfvz8ff/wx7733Ht27d2fGjBnMmTOHW265xezQREzx342HWL/vBEF+VqZe083scBo9NdFFKjp0opBXvy7bGP3Jq7oQHuh9M8dqQkv8RKTWMrTET8Qlo2x1H+1itP+UmOPqq6/m6quvNjsMEdOdKChh5pc7AHhoaAdaRAaZHJGUN9EnTpzI9OnTadOmjZro0qjN+HwbxXYnA9pEMbpXvNnhmE4NKhGpFcMwXDOoYjWDSoSMkzOo1KASETHXrK92kFVQQqfYMO64uI3Z4chJaqKLlPlm51G+2pqB1cfCjNHdNfOeOljiN3fuXBITEwkMDGTgwIGsW7fujGO3bt3KddddR2JiIhaLhTlz5tT6OUXEXHm2UortTkAzqETg1BI/NahERMyzYf8J3lt3EICnr+2On1U7m4iI+yi2O5j26VYAxg9OpFOc+1+1ryHUqlJ/8MEHJCcnM3XqVDZu3EjPnj1JSkri6NGjVY4vLCykbdu2PPfcc8TFxdXJc4qIucqv4BcW4OsRl2wWqU+GYXD05BK/tjG6gp+IiBlKHU4mLdoCwPV9W9I/0bOuiCUi3u/NFXvZd7yQZmEBPDi0g9nhuI1aNaheeukl7rrrLsaPH0/Xrl2ZN28ewcHBvPXWW1WO79+/Py+88AI33XRTlZcLPZ/nFBFzHc0tW94Xo+V9ImQVlFDosGCxQJtoNahERMwwf9U+tqflEhHkx8QRnc0OR0SkgoNZhcxdvhuAJ0d2IayRb4x+uvNuUJWUlLBhwwaGDh166sl8fBg6dCirV692m+cUkfp1NK98g3Q1qET2ZhYC0CIyiEA/zSgUEWlo6TnFvJzyCwCPj+hM01Cdn4iIeynfGH1gmyiu6amN0U933pukZ2Zm4nA4iI2NrXA8NjaWHTt2NNhz2mw2bDab63Zubi4Adrsdu91+1tcrv/9c4zyNt+YF3pubJ+eVll32hjw6xL9S/DXJyxNzF/m1A1llfx9aRwWbHImISOM0/fOtFJQ46NMqkhv7JZgdjohIBct3HmXptpMbo4/Rxui/5vFX8Zs5cybTpk2rdHzp0qUEB1fvDUJKSkpdh+UWvDUv8N7cPDGv1ak+gA+Fx4+wePGhKsdUJ6/CwsI6jkyk4R3JLlvy2iJSFwwQEWloK3ZlsvjndKw+Fp4e0wMfH73xExH3YSt18tRpG6N3jNXG6L923g2q6OhorFYrGRkZFY5nZGSccQP0+njOiRMnkpyc7Lqdm5tLQkICw4cPJzw8/KyvZ7fbSUlJYdiwYfj5ec+6T2/NC7w3N0/O6/OFmyD9KJf06cpVA1tVuK8meZXPfhTxZEdyyhpU8ZFBJkciItK4lDjgqc+2A3D74ES6xp/9fYCISEN76/t97DteSIw2Rj+j825Q+fv707dvX5YtW8aYMWMAcDqdLFu2jAkTJjTYcwYEBFS54bqfn1+13+jXZKwn8da8wHtz88S8yt+QJ0SFnjH26uTlaXmLVOVIdtkl/OIjNINKRKQh/e+IDwdPFBEXHsj/DetodjgiIhVk2eCvP+wF4MmrtDH6mdRqiV9ycjLjxo2jX79+DBgwgDlz5lBQUMD48eMBGDt2LC1atGDmzJlA2Sbo27Ztc/358OHDbNq0idDQUNq3b1+t5xQR93L45BvyFk00Y0Tk1AwqNahERBpKamYB/ztctpxvyqiuhAZ4/C4mIuJlFu3zodjuZECbKEb30sboZ3LeV/EDuPHGG3nxxReZMmUKvXr1YtOmTSxZssS1yfmBAwdIS0tzjT9y5Ai9e/emd+/epKWl8eKLL9K7d2/+8Ic/VPs5RcR9FNhKyS4s29zckxtUc+fOJTExkcDAQAYOHMi6devOOv7DDz+kc+fOBAYG0qNHDxYvXtxAkYo7czoNNahERBqYYRg89fl2HIaFSzs0ZUT389tqRESkvny3+zg/Zflg9bEwfXQ3bYx+FrX+eGHChAlnXH63fPnyCrcTExMxDKNWzyki7qN89lRYoC/hHjpN9YMPPiA5OZl58+YxcOBA5syZQ1JSEjt37qRZs2aVxq9atYqbb76ZmTNncvXVV7Nw4ULGjBnDxo0b6d69uwkZiLs4XlBCSakTCwZx4WpQiYg0hM82p7FqTxa+FoMpV3fRGz8RcSslpU5mfFG2P96tAxPoHKf98c6mVjOoRKRxcy3v8+ANoV966SXuuusuxo8fT9euXZk3bx7BwcG89dZbVY7/y1/+wpVXXskjjzxCly5dmDFjBn369OG1115r4MjF3ZT/fQj3Bz+r/nkVEalvucV2Znxetn3IsBZOWkdV7wreIiIN5R/fpbI3s5BQP4MHf9PO7HDcnhZoi8h5O3yi7A15Sw9d3ldSUsKGDRuYOHGi65iPjw9Dhw5l9erVVT5m9erVFa4cCpCUlMSiRYuqHG+z2bDZbK7b5VcrtNvt2O32s8ZXfv+5xnkab83rQGYeAFEB3pebt/7MapKXt+Uu4g1eWvoLx/JsJDYN5ooWuhqwiLiXtJwiXv16FwCjWzm1MXo1qEElIuetfMZIvIfOoMrMzMThcFTa4y42NpYdO3ZU+Zj09PQqx6enp1c5fubMmUybNq3S8aVLlxIcXL1PelNSUqo1ztN4W17fHLEAVpr4G16XW7nGnFdhYWEDRCIi1bXlcA7vrt4HwFOjupCzc625AYmI/Mqzi3dQWOKgT6tI+sVkmh2OR1CDSkTOW/kMKk9e4lffJk6cWGHGVW5uLgkJCQwfPpzw8LOvQbfb7aSkpDBs2DD8/LznExdvzWvDFztg/wGaBOB1uXnrz6wmeZXPfhQR8zmcBk8u2oLTgFE947moXVMW7zQ7KhGRU1bvOc5nPx3BYoEpIzuzf9N3ZofkEdSgEpHz5tqDykOX+EVHR2O1WsnIyKhwPCMjg7i4qq8CFBcXV6PxAQEBBAQEVDru5+dX7Tf6NRnrSbwtr/TcsqWcTQIMr8utXGPOyxvzFvFU7607wE8HswkN8GXyyC5mhyMiUkGpw8lTn24F4JaBregWH87+TebG5Cm0i6uInDdPn0Hl7+9P3759WbZsmeuY0+lk2bJlDBo0qMrHDBo0qMJ4KFsedKbx0niUN2yjKvcjRUSkjmTm25i1pGwZ/p+Hd6SZrpoqIm7mn2v2szMjjybBfjw8vJPZ4XgUzaASkfNidzjJyCsGPHcGFUBycjLjxo2jX79+DBgwgDlz5lBQUMD48eMBGDt2LC1atGDmzJkAPPjgg1x22WXMnj2bkSNH8v777/PDDz/wxhtvmJmGuIEjJxtUTfwNkyMREfFezy7eTm5xKd3iw7ntwtZmhyMiUkFmvo2XUn4B4OGkTkQG++tCKzWgBpWInJf0nGIMA/x9fYgO8dwpIzfeeCPHjh1jypQppKen06tXL5YsWeLaCP3AgQP4+JyabDp48GAWLlzIpEmTeOKJJ+jQoQOLFi2ie/fuZqUgbqCwpJQThWUnH5pBJSJSP9bsPc5HGw9jscAz1/bA16rFICLiXmYt2UFecSndW4RzU/9WZofjcdSgEpHzcui05X0+PhaTo6mdCRMmMGHChCrvW758eaVjN9xwAzfccEM9RyWepHz2VFigL4G+pSZHIyLifUpKnUxetAWAmwe0oldCpLkBiYj8yqaD2fz7h0MATLumO1YPf49kBn3sICLnpXy/nfhI7f0g4mrYRujvg4hIffjHd6nsOppP0xB/HkvqbHY4IiIVOJ0GU09ujP7bPi3o27qJyRF5JjWoROS8ePoG6SJ16Uh22X5szdWwFRGpc4dOFPLKsl0APHFVFyKCdVVNEXEv/914yHV10cevVBP9fKlBJSLnpXxJU4vIYJMjETHfwROFgBq2IiL1Ydpn2yiyOxjQJorf9mlhdjgiIhXkFtt5/uTVRR+4or2uLloLalCJyHk5kFX2hrylB1/BT6Su7D2WD0BiUzVsRUTq0v+2ZZCyLQNfHwtPj+mOxaI9XUTEvbzyv11k5pfQNiaE2we3MTscj6YGlYicl9TMAgDaxISYHImI+fYeK/v70FZ/H8TNPPfcc1gsFh566CGzQxGpsaISB099Vranyx8uaUvH2DCTI5K6pPok3mD30Tzmr9oHwJSru+LvqxZLbei7JyI1VlhSSnpu2Z47baP1hlwat1KHk33HyxpU7fT3QdzI+vXr+dvf/sYFF1xgdigi5+W1b3Zx6EQR8RGBPHBFe7PDkTqk+iTewDAMpn22jVKnwdAusVzeqZnZIXk8NahEpMb2ZZYt74sM9iMy2N/kaETMdfBEEXaHQaCfD3Hac0DcRH5+PrfccgtvvvkmTZroSkLieXYfzeONFXsBmHpNN4L9fU2OSOqK6pN4i5RtGazclYm/1YfJV3cxOxyvoEovIjXmWt6n2SIirv2n2kaH4uOjvVHEPdx3332MHDmSoUOH8vTTT59xnM1mw2azuW7n5uYCYLfbsdvtZ32N8vvPNc7TeGte4Dm5GYbBpI9/xu4wGNIpmiEdos4as6fkVVM1ycuTcq9ufRJxZ8V2B09/sR2AOy9pQ+umel9UF9SgEpEaS80se0OuBpUI7DnZoGrXLNTkSETKvP/++2zcuJH169efc+zMmTOZNm1apeNLly4lOLh6m/6npKTUOEZP4K15gfvn9sMxC2tSrfhZDC4JTufLL7+s1uPcPa/zVZ28CgsLGyCS2qtJfQI10avirXmBZ+X25rd7OZBVSGxYAH+8uLWa6NUcey5qUIlIjaWeXOKn/adEYM/Rk/tPaYN0cQMHDx7kwQcfJCUlhcDAcy85nThxIsnJya7bubm5JCQkMHz4cMLDw8/6WLvdTkpKCsOGDcPPz6/WsbsLb80LPCO3vGI7M/7yPVDCfb/pwG2Xtz3nYzwhr/NRk7zKGzfurKb1CdREPxtvzQvcP7ecEnj1RytgYVhsId8uW1qtx7l7XuerLpvoalCJSI2Vz6BKVINKxDWDqm2MZlCJ+TZs2MDRo0fp06eP65jD4WDFihW89tpr2Gw2rFar676AgAACAgIqPY+fn1+13+jXZKwn8da8wL1ze+XLX8ou1x4dwj1D2uPnaz33g05y57xqozp5eULeNa1PoCZ6Vbw1L/Cc3B75z8+UONPolRDB5NsGnHOLB0/Jq6bqo4muBpWI1Jj2oBI5ZW+mZlCJ+7jiiiv4+eefKxwbP348nTt35rHHHqv05k/EnWw5nMO7q/cBMH10dwJq0JwS93c+9UlN9DPz1rzAvXPbeOAEi35KA2DaNd0JCKj+BaPcOa/aqMsmuhpUIlIj2YUlnCgsW0OcqM0ApZHLKighq6AEKNskHZzmBiSNXlhYGN27d69wLCQkhKZNm1Y6LuJOnE6DJxdtwWnAqJ7xXNwh2uyQpI6pPomnczoNpn22DYDr+7akZ0KkuQF5IR+zAxARz1I+eyo2PICQAPW4pXErv4Jfi8gggvz1Sb+IyPl6f/1BfjqYTWiAL5NG6nLtIuJ+Fm06zE8Hswnxt/JoUiezw/FKencpIjWi5X0ip+w9Vvb3oa2W94kbW758udkhiJzV8Xwbzy/ZAUDysI7EhldvA23xfKpP4ikKbKU892VZnZrwmw40U52qF5pBJSI1cqpBpQ2hRco3SG+nDdJFRM7b80t2kFNkp0vzcMYOam12OCIilby+fA9H82y0igrmjosTzQ7Ha6lBJSI1Ur4hdFvNoBJh19HyBpX+PoiInI8N+7P49w+HAHh6TDd8rXp7IiLu5WBWIW+s3AvAE1d10QUc6pH+BRCRGtl3skGVqAaVNHKGYbD5UDYA3VpEmBuMiIgHKnU4efLjLQD8rl9L+raOMjkiEZHKnluyg5JSJ4PaNiWpW6zZ4Xg1NahEpNocToPdmjEiAsDh7CIy80vws1ro2jzc7HBERDzOO6v3syM9j8hgPx4foY3RRcT9rEvN4ovNafhYYMqorlgsFrND8mpqUIlIte07XoCt1EmQn5XWTdWgksZt08FsALo0DyfQT1O9RURq4mhuMS+n/ALAo0mdiQrxNzkiEZGKnE6D6Z9vBeDG/q3oog8k650aVCJSbTvS8gDoGBeG1UefHkjj9tPJBlXPlpGmxiEi4omeWbydfFspPRMiual/gtnhiIhU8t+Nh9hyOJewAF/+PLyj2eE0CmpQiUi17UjPBaBLXJjJkYiY76eDOQD0TIg0NxAREQ+zak8mn2w6gsUCT4/ujo8+9BIRN1NgK2XWVzsBuP+K9kSHBpgcUeOgBpWIVNv2tLIGVWc1qKSRK3U4+flwWYOqlxpUIiLVZnc4mfJJ2ZKZWwe2pkdLXWRCRNzPvG/3cCzPRuumwYwbnGh2OI2GGlQiUm3bTy7x66z119LI/ZKRT5HdQViAL211RUsRkWp7+/tUdh/Np2mIPw8P72R2OCIilRzOLuKNFXsBmDiiCwG+2mu0oahBJSLVklts53B2EQBd4tSgksbtp0PZAFyQEKGlKSIi1ZSWU8Sc/+0C4LERnYkI9jM5IhGRymYt2YGt1MnANlEkdYs1O5xGRQ0qEamWnells6fiIwJ1QimNnjZIFxGpuWe+2E5hiYO+rZtwfZ+WZocjIlLJjwdOuPbIm3x1VywWfRDZkNSgEpFq2VG+/5SW94mw6WSDSvtPiYhUz/e7M/l8cxo+Fpg+uptmn4qI2zEMgxmfbwPguj4t6d5Ce+Q1NDWoRKRatp+cQaUN0qWxO5ZnY8fJvw99WjcxORoREfdXUupkyidbALjtwtZ0i9ebPhFxP1/8nMbGA9kE+Vl5JEl75JlBDSoRqRbNoBIps3LXMQC6twjXJYdFRKrh7e9T2XOsgKYh/iRrY3QRcUPFdgfPL9kBwJ8ua0dseKDJETVOalCJyDk5nYZrxkgXzaCSRm7FL2UNqks7xJgciYiI+0vPKeYvy07bGD1I+1iKiPt5Z9U+DmYVERceyF2XtjE7nEar1g2quXPnkpiYSGBgIAMHDmTdunVnHf/hhx/SuXNnAgMD6dGjB4sXL65w/+23347FYqnwdeWVV9Y2TBGphb2ZBRSWOAjw9aFNdIjZ4YiYxuk0WLkrE4BLO6pBJSJyLs8uLtsYvXerSG2MLiJu6Xi+jde+3g3Aw0mdCPb3NTmixqtWDaoPPviA5ORkpk6dysaNG+nZsydJSUkcPXq0yvGrVq3i5ptv5s477+THH39kzJgxjBkzhi1btlQYd+WVV5KWlub6eu+992oTpojU0o8HTgBlVyzztWripTRe29JyOV5QQoi/lT6ttP+UiMjZrNl7nE9/Krsa1ozR3bUxuoi4pTn/20WerZTuLcL5be8WZofTqNXqneZLL73EXXfdxfjx4+natSvz5s0jODiYt956q8rxf/nLX7jyyit55JFH6NKlCzNmzKBPnz689tprFcYFBAQQFxfn+mrSRG8CRMy08UA2AL1bRZoah4jZvj25vG9Qu2j8fdWsFRE5k1KHk6c+3QrA7we00tWwRMQt7T6ax8J1BwB48qquaqSb7LzPrktKStiwYQNDhw499WQ+PgwdOpTVq1dX+ZjVq1dXGA+QlJRUafzy5ctp1qwZnTp14p577uH48ePnG6aI1IHyGVS9NWNEGrny/acu6xhtciQiIu7tX2v2syM9j8hgPx7Wxugi4qZmLt6Bw2kwtEssg9o1NTucRu+8F1dmZmbicDiIjY2tcDw2NpYdO3ZU+Zj09PQqx6enp7tuX3nllfz2t7+lTZs27NmzhyeeeIIRI0awevVqrFZrpee02WzYbDbX7dzcsiuN2e127Hb7WXMov/9c4zyNt+YF3pubO+eVbyvll4yyDdJ7xIfWKMaa5OWOuYucLrfYzob9Zc1a7T8lInJmx/NtvJTyCwAPD+9EkxB/kyMSEals1e5Mlu04iq+PhYlXdTY7HKEWDar6ctNNN7n+3KNHDy644ALatWvH8uXLueKKKyqNnzlzJtOmTat0fOnSpQQHB1frNVNSUs4/YDfmrXmB9+bmjnn9kmPBaViJCjD4YeWy83qO6uRVWFh4Xs8t0lC+2pJOqdOgfbNQWjfVxQJERM7kxaU7yS0upVt8ODcPaGV2OCIilTidBk9/sR2AWwa2ol1MqMkRCdSiQRUdHY3VaiUjI6PC8YyMDOLi4qp8TFxcXI3GA7Rt25bo6Gh2795dZYNq4sSJJCcnu27n5uaSkJDA8OHDCQ8PP2sOdrudlJQUhg0bhp+f91zy1lvzAu/NzZ3z2rd8L2zbzaAOzbnqqgtq9Nia5FU++1HEXX2y6QgAY3rFmxyJiIj7+vlQDu+vPwjAtGu6YdV+LiLihj768TDb0nIJC/TlwaEdzQ5HTjrvBpW/vz99+/Zl2bJljBkzBgCn08myZcuYMGFClY8ZNGgQy5Yt46GHHnIdS0lJYdCgQWd8nUOHDnH8+HGaN29e5f0BAQEEBARUOu7n51ftN/o1GetJvDUv8N7c3DGvzYfLGkd9E6POO7bq5OVueYuc7mhuMav2ZAJwTU9d3UVEpCpOp8HUT7dgGGXN/H6JUWaHJCJSSVGJgxe/2gnAhCHtidIyZLdRq0sQJScn8+abb/LOO++wfft27rnnHgoKChg/fjwAY8eOZeLEia7xDz74IEuWLGH27Nns2LGDp556ih9++MHV0MrPz+eRRx5hzZo17Nu3j2XLljF69Gjat29PUlJSbUIVkfNgGAY/HswGdAU/adw+35yG04A+rSJp1bR6y8dFRBqbT346zMYD2QT7W3l8RBezwxERqdLfV+4lPbeYFpFBjBucaHY4cppaNahuvPFGXnzxRaZMmUKvXr3YtGkTS5YscW2EfuDAAdLS0lzjBw8ezMKFC3njjTfo2bMn//nPf1i0aBHdu3cHwGq1snnzZq655ho6duzInXfeSd++fVm5cmWVs6REpH7tP15IVkEJ/r4+dIv3vstDZ2VlccsttxAeHk5kZCR33nkn+fn5Z33M5ZdfjsViqfD1pz/9qYEiFrN88lPZ8r7RvTR7StzbzJkz6d+/P2FhYTRr1owxY8awc+dOs8OSRqDAVspzX5ZdKOm+Ie2Jiwg0OSIRkcqO5hXz+rd7AHhsRGcC/SpfiE3MU+tN0idMmHDGJX3Lly+vdOyGG27ghhtuqHJ8UFAQX331VW1DEpE6smbvcQAuaBGBv2+t+tlu6ZZbbiEtLY2UlBTsdjvjx4/n7rvvZuHChWd93F133cX06dNdt6t7QQbxTKmZBfx0MBurj4WRF1S93FzEXXz77bfcd9999O/fn9LSUp544gmGDx/Otm3bCAnR5v5Sf+Z+s5uMXButooK58+I2ZocjbmrmzJl89NFH7Nixg6CgIAYPHszzzz9Pp06dzA5NGok5/9tFYYmDngmRjNJ5ndtxu6v4iYj7WLmrbM+di9pHmxxJ3du+fTtLlixh/fr19OvXD4BXX32Vq666ihdffJH4+DNvhB0cHHzWizuId/nn6v0AXNohmuhQzeYV97ZkyZIKt+fPn0+zZs3YsGEDl156qUlRibc7cLyQv69MBWDSyC6akSBnpCa6mOmXjDzeX3cAgCev6oLFoos4uBs1qESkSg6nwfcnN4W+tKP3NahWr15NZGSkqzkFMHToUHx8fFi7di3XXnvtGR+7YMEC/vWvfxEXF8eoUaOYPHnyGWdR2Ww2bDab63b51Qrtdjt2u/2sMZbff65xnsaT8sorLuWDH8pOZG4bmKCfWSPOy1Nzz8nJASAqSptVS/15ZvE2ShxOLukQzbCusWaHI25MTXQx08zF23EakNQtlgFt9O+iO1KDSkSqtPVIDtmFdsICfOnZMtLscOpceno6zZo1q3DM19eXqKgo0tPTz/i43//+97Ru3Zr4+Hg2b97MY489xs6dO/noo4+qHD9z5kymTZtW6fjSpUurvTQwJSWlWuM8jSfk9W2ahQKbldggg9xf1rF4V/Ue5wm5nY/GnFdhYWEDRFK3nE4nDz30EBdddJFrv89fUxO9Mm/NC+ontzV7s/hqawZWHwsTkzpSWlpaZ89dXd76M1MTXTWqKt6aF9Rvbt/vOc43O4/h62Ph4WHtG/T7560/s/qoUWpQiUiVypf3XdiuKb5Wz9l/6vHHH+f5558/65jt27ef9/Pffffdrj/36NGD5s2bc8UVV7Bnzx7atWtXafzEiRNJTk523c7NzSUhIYHhw4cTHh5+1tey2+2kpKQwbNgw/Pz8zjtmd+MpeTmcBrP/8h1QxL1DuzJyQMI5H+MpudWU8jr1psiT3HfffWzZsoXvvvvujGPURD8zb80L6i43pwEvbLYCFgbHONi1YQXV7OPXC2/9mTXmJrpq1Jl5a15Q97k5DXixvFY1c7Bt7bdsq9NXqB5v/ZnVZY1Sg0pEqvTdyQbVJR08a3nfn//8Z26//fazjmnbti1xcXEcPXq0wvHS0lKysrJqtL/UwIEDAdi9e3eVDaqAgIAqr0Lq5+dX7Tf6NRnrSdw9r2+2pnMgq4jwQF9u6N8KP7/q/5Pp7rmdr8acl6flPWHCBD7//HNWrFhBy5YtzzhOTfTKvDUvqPvc3l9/iCOF24gI8mX2HRfTJNi/DqKsOW/9mamJrhpVFW/NC+ovt/9uPMzhNVsJC/TlhdsvJiqkYWuVt/7M6qNGqUElIpUUlpTyw/4sAC72sA3SY2JiiImJOee4QYMGkZ2dzYYNG+jbty8AX3/9NU6n09V0qo5NmzYB0Ly5rgLiTZxOg5f/VzYP4PcDWxPsr38uxTMYhsH999/Pxx9/zPLly2nT5uxXU1MT/cy8NS+om9xyi+3MWbYbgAev6EizCPM3uPbWn1ljbqKrRp2Zt+YFdZtbYUkpL5+sVff/pj2xkebVKm/9mdVljfKcdTsi0mDWpmZhdxi0iAyiTbT5J5z1oUuXLlx55ZXcddddrFu3ju+//54JEyZw0003ua7gd/jwYTp37sy6desA2LNnDzNmzGDDhg3s27ePTz/9lLFjx3LppZdywQUXmJmO1LHPNh9he1ouYQG+/PHStmaHI1Jt9913H//6179YuHAhYWFhpKenk56eTlFRkdmhiZeZ+81ujheU0DYmhNsGtTY7HPEQhmEwYcIEPv74Y77++utzNtFFauuNFXvJyLWREBXEuMGJZocj56CPhEWkkmXbM4Cyq/d58+VXFyxYwIQJE7jiiivw8fHhuuuu45VXXnHdb7fb2blzp2vNtL+/P//73/+YM2cOBQUFJCQkcN111zFp0iSzUpB6YHc4eSnlFwDuvrQtTRp4GrhIbbz++usAXH755RWOv/322+dc/ixSXfuPF/D2d/sAmDSyC34etFelmOu+++5j4cKFfPLJJ64mOkBERARBQUEmRyfeJiO3mL99uxeAx6/sQoCv1eSI5FzUoBKRChxOgyVbyhpUV3b37mVrUVFRLFy48Iz3JyYmYhiG63ZCQgLffvttQ4QmJvpg/UH2Hy8kOtSfOy7WJ7viWU6vWSL1ZebiHZQ4nFzSIZohnZqd+wEiJ6mJLg3pha92UmR30Ld1E67qUf09ZsU8alCJSAXrUrPIzLcREeTH4HZNzQ5HpEEdz7fx4tKdAEwY0p6QAP0zKSJyurV7j7Nkazo+FnhyZBevnmktdU9NdGkoWw7n8N+NhwDVKk+i+bgiUsGXW9IAGN41VlP2pdF5+ovtZBfa6do8nFsv1J4qIiKnczoNnv5iOwA3DWhF57izX0VNRMQMhmEw/fNtGAaM7hVPn1ZNzA5JqknvPkXExeE0+HJL2V4AV/Xw7uV9Ir+2ctcxPv7xMD4WmPnbHviqQSsiUsHHPx7m58M5hAb4kjyso9nhiIhU6aut6axLzSLA14dHr+xsdjhSAzr7FhGXH/ZlcSzPRnigLxe1jzY7HJEGk1Nk5/H//gzA2EGJ9EyINDcgERE3U1hSygtflS2Bvm9Ie6JDA0yOSESkMlupg2cX7wDKLnbTIlKb73sSNahExOWLn8uW9w3rGoe/r8qDNA6GYfD4fzdzOLuIVlHBPJzUyeyQRETczhsr9pKeW0zLJkGMvyjR7HBERKr01nf7OJBVSLOwAP50WTuzw5Ea0jtQEQGgqMTBxz8eBuCaXvEmRyPScP619gBfbknHz2rhtd/3JlQbo4uIVJCec9ql2kd0JtBPl2oXEfdzNLeY177eBZTVKl3sxvOoQSUiAHy2+Qh5xaUkRAVxiZb3SSOxfl8WMz7bBsBjV3bmgpaR5gYkIuKGXlx66lLtI7VHpYi4qVlf7aSgxEGvhEjG9GphdjhyHtSgEhEAFq49AMDvB7TGx0eXYRXvty+zgLvf/YESh5Mru8Vx58VtzA5JRMTtnH6p9km6VLuIuKkfD5zgPxvKatXUUV31fsZDqUElImw9ksOmg9n4WS3c0K+l2eGI1LvMfBt3zF/PiUI7PVtG8PKNvfSmS0TkV06/VPs1PePprUu1i4gbcjgNpnyyFYDr+rRUrfJgalCJiGv2VFK3OF2VR7xeVkEJt7y5lr2ZBbSIDOLNcf0I8td+KiIiv7ZkS9ml2gP9fHh8hC7VLiLu6YP1B/n5cA5hgb6qVR5ODSqRRu5oXrFrOuwtA1ubHI1I/coqKOGWv69lZ0YezcIC+NcfBtIsLNDssERE3E6x3cGzX24H4O5L2xGvS7WLiBs6UVDCrK92AJA8rCMxYfqw3ZNpW3uRRu7NFXuxlTrp3SqSC9tGmR2OSL05cLyQcW+vIzWzgOjQAN67+0LaRIeYHZaIiFt66/tUDmYVERsewJ8ua2t2OCIiVZr55XayC+10jgvjtgv1YbunU4NKpBHLzLfxzzX7AXjgig7ag0e81k8Hs7nznR/IzLfRIjKId+4YQLuYULPDEhFxS+k5xbz29W6g7Aqnwf56yyAi7mddahb//qFsJcgz13bH16oFYp5O/9qINGJvrthLsd1Jz5YRXN4xxuxwROrFv9cfZNInWygpddKleTjzx/cnNlzL+kREzuT5JTsoLHHQp5Uu1S4i7qmk1MkTH/8MwM0DWtG3tVaCeAM1qEQaqSPZRby7umz21INDNXtKvE+BrZTpn23jgx8OAjC0Sywv39iTsEA/kyMTEXFfG/Zn8fGPh7FY4KlruulS7SLiluZ9u4fdR/OJDvXn8Su1Mbq3UINKpJGa8fk2iuwO+rVuwpBOzcwOR6RO/XjgBP/3wSb2HS/EYoHkoR25b0h7vdESETmLUoeTyYvKLtV+Q9+WXNAy0tyARESqsDM9j1e/3gXA5Ku7EhGsDx+9hRpUIo3Qt78c48st6Vh9LMwY012zp8RrFNhKmb30F+avSsVpQPOIQGb/rieD20WbHZqIiNt7d/V+tqXlEhHkx2OakSAibqjU4eSR//yE3WEwtEss1/SMNzskqUNqUIk0MsV2B1M/2QLAuEGJdGkebnJEIrVnGAafbU7jucXbOZJTDMCYXvFMu6a7PlUTEamGjNxiXkr5BSjbGL1pqC7VLiLu542Ve9l8KIfwQF+euVYftHsbNahEGpkZn29j3/FCmoUF8H/DOpgdjkitrd17nOeX7GDjgWwAWjYJ4plre3CZNv4XEam26Z9vI99WSq+ESG7qn2B2OCIilWw5nMPLJxvpk6/uqoveeCE1qEQakS82p7Fg7QEAXrxBm0WLZ1u/L4tXlu1i5a5MAIL9rdx7eTv+cElbAv2sJkcnIuI5lmxJ54vNaVh9LDw9prv26xMRt1NU4uCB93/E7jC4slsc1/dtaXZIUg/UoBJpJFIzC3j8v5sBuPfydlyq2SXigRxOg2XbM3hjxV5+2H8CAF8fCzcNSOD+33TQJ2kiIjWUXVjCpEVlS///eGlbureIMDkiEZHKZnyxjb3HCogND2Dmb3toaZ+XUoNKpBE4mlfMuLfWkWcrpV/rJiQP62h2SCI1cjzfxn83HuKfa/ZzMKsIAH+rD9f1bcG9l7cnISrY5AhFRDzT9M+2kZlvo32zUB64Qkv/RcT9fLTxEAtPWwXSJMTf5IikvqhBJeLl8ort3P7Weg5kFdIqKpi/3toHX6uP2WGJnJPd4eTbncf46MdDpGzLwO4wAIgI8uPmAa0Yf1GiZkyJiNTCJ5sO89GPh7FYYNb1F2h5tIi4nW1Hcnni458BeOCKDlzSQatAvJkaVCJeLDPfxh3z17MtLZfo0AD+eecAmoXpDb24r1KHk3WpWXz+cxpLtqSTVVDiuu+ClhHcPKAVY3q1IMhfb6JERGpj//ECnvy4bGnf/UPa06dVE5MjEhGp6Hi+jT/9awPFdieXdYzhQc3y9HpqUIl4qf3HCxj71jr2Hy8kKsSfd+7oT+umIWaHJVJJbrGd73dl8r/tR1m2I4PsQrvrvuhQf67p2YLr+ragW7z2RRERqQu2UicPvPcj+bZS+ic20dI+EXE7RSUO7nznBw5kFZIQFcScG3th1QUcvJ4aVCJe6Muf03j0v5vJKy4lISqId+8YSJtoNafEPZQ6nOzLg7nL97JqbxYb95+g1Gm47o8M9uPKbnGMvKA5g9o21ZJUkfMwd+5cXnjhBdLT0+nZsyevvvoqAwYMMDsscQOGAU8u2spPh3KICPJjzk29VWelwalGydmUOpw8+O+f2HQwm8hgP+aPH6B9pxoJNahEvEh2YQnPfbmD99cfBKB3q0j+dmtfmmmfHjFRsd3Bz4dzWJeaxfp9WaxPzaKgxBe27HaNaRsTwpBOzRjWNZZ+rZvozZJILXzwwQckJyczb948Bg4cyJw5c0hKSmLnzp00a9bM7PDEZCmHLXxxMA2rj4XXft+bFpFBZockjYxqlJyNwwnJH/7M0m0Z+Pv68ObYfrSLCTU7LGkgalCJeIFSh5P/bDjErK92uvbsuefydiQP64if3uhLA3I4DfYey2fzoRw2H8pm08FstqXlujY4LxdsNbioYyyXdWrGJR2itfxUpA699NJL3HXXXYwfPx6AefPm8cUXX/DWW2/x+OOPmxydmOnfPxzii4Nle/hNu6abNhsWU6hGyZmUlDqZv8uHzVkZ+FktzP19H/onRpkdljQgNahEPFix3cGiHw/z1+V7OJBVCECHZqHMGNOdC9s2NTk68Xa5xXZ+Sc9jR3oe29NyT37lUWR3VBobHRpA/8Qm9E+Mok9COKk/fsfVI3vh5+dnQuQi3qukpIQNGzYwceJE1zEfHx+GDh3K6tWrK4232WzYbDbX7dzcXADsdjt2u73S+NMNen45x/Ot/N+apRWOWywV9wixVLiPKsdaTt5nqXTMgsUCPhawUP5nCz4n/8/J/1st4ONjwWqx4ONjwdfHgo/Fgq+17M9WHwt+Vh/8rBZ8fcr+7+/rg7+vDwG+PgT4Wgn09SHQz4q/FVIzLBRvPEhEUAAhAb6EBfoSGuhLeKAvYQG+HjnLc8G6gzz12XYAxl2YwI1948/5M/YU5Xl4Sz7lapKXp+Re0xpVG3//bh9bDlnYt3wvVqtPpdpUlfIhlpOV61RdOnXc9eeTtchy2p85rT75WMqOl9Wl8mMn65PPqdrk6+ODr9VyWn3ywd+3rGYF+FrLapSfD4G+Vny8eA+mY3k2/vTPH9icVVaj/3ZbX37TOdbssKSBqUEl4mEMw+CnQzks+vEwH208RG5xKQBNQ/y55/J2jBucqFlTUmcMw+Bono29xwrYm5nP7qOnvtJyiqt8TLC/la7Nw+mZEMkFLSPo06oJLZsEuU4M7XY7+zc1YBIijUhmZiYOh4PY2Ion9bGxsezYsaPS+JkzZzJt2rRKx5cuXUpwcPBZX6vYZsXAgmH86o5KB86mJmMbkpV/791+xnuDrAbBvhDmB6F+BmF+EO4PEf4Gkf4Q6W8QFQBBbnCm7TTgq0MWlhwqmzl1WXMnvUll8eJUkyOreykpKWaHUC+qk1dhYWEDRFJ7Na1RtWmiz12+h3yblS8O7j7rOE/iZ7UQ5GfF4rQy55fvCA30JcTfSmiAL6EBvoQH+RER5EtEkB+Rwf5EhfjRNMSf6NAAooL93La5/uOBbB7892bScooJshq8elNPLmkX5TGN13NRE736udf6n82abnD34YcfMnnyZPbt20eHDh14/vnnueqqq1z3G4bB1KlTefPNN8nOzuaiiy7i9ddfp0MHXV1EGq/swhLW7M3i+92ZfL3jKIezi1z3tYgMYvxFifx+YCuC/d3gTFg8jq3UwZHsYg5mFXLwRCEHsgo5cLyQfccL2X+8gMKSyjOiyjWPCKRjbBhdmofTpXkY3eLDaRMdqqusiHiIiRMnkpyc7Lqdm5tLQkICw4cPJzw8/KyP7TO4gOXLv+XSyy7F17fibEijiiaV4bqv4rjTj5ffchplD3AaxsnjJ8eeHONwlv3f6SwbU/ZVtszY4TRwGIbrz6UOg1KnE/vJ/5c6DEocZbdtdgclDifFdie2UidFdgeFtlIOHE4jJLIpRXYn+bZS8m2l5BWXuuphkcNCkQOO26DiHLGKwgN9SYgKolWTYBKjg2kbHVL2FRNCaED9/5t9vKCER/7zMysPHQfgzsGt6OHcy/Dhw7xqBqvdbiclJYVhwxpvXuWNG29TmyZ6nyY+2J1V31dVParqftefy+vQ6ceN057n5H/KX6782i/Ok2OcRvmfLa4/O0+OdzhP/d9hlH2VOqHUKPtyGqdqjN1hYHeUAhZyjtesKWmhrJkecbKJ3iQAmgQYNA2ApoEG0YEQaK3RU9aazQGLD/rwbZoFAwvNAg3+0NlBwd4NLN7bsLE0BDXRz61W/zLWdIO7VatWcfPNNzNz5kyuvvpqFi5cyJgxY9i4cSPdu3cHYNasWbzyyiu88847tGnThsmTJ5OUlMS2bdsIDNRGz+LdHE6DtOOF7MnM55eTy6Y2H8phb2ZBhXHB/laGdG7G9X1bcmmHGDUD5IxKHU6O5dtIzykmI7eYI9nFpOUUcSSnmCPZRRw+UcTRPNtZn8PqYyGhSRBtokNoFxNKu2ahdIwNpX1MGBHB3vNGQMQbREdHY7VaycjIqHA8IyODuLi4SuMDAgIICAiodNzPz++cb4jjIkMI94f4JqFe1xRYvPgwV13Vv1JedoeT3CI7JwrtnCgsIaughMx8G8fybBzNs3E0t5i0k/X1RKGd3OJSth7JY+uRvEqv0yIyiE5xYXSKC6NzXFmjv210SJ3McCgpdfLu6n28smwXucWlBPr58PSYHoy+IJbFi/dW6+friRpzXp6Sd01rVG2a6MO8pHFZ6ihroNtKnRTbHeQV2Vi+chUX9OmPzQn5xaXknWyi5xWXkl1kJ6fQTnaRnayCEo4XlNUqp2Eh1w65djhYUPV7h+hQfxKbBrsa6e1OfrWICKrT5YVFJQ7eW3+QN7/bR2Z+2f651/ZqzmPD27F25XKP/5n9mpro1W+i16pBVdMN7v7yl79w5ZVX8sgjjwAwY8YMUlJSeO2115g3bx6GYTBnzhwmTZrE6NGjAXj33XeJjY1l0aJF3HTTTbUJV6RBGUbZJ7SFNgf5tlIKSkrJLSolp6jspPbEyZPao3k20nOK2H3EysPr/ldpM+ly7WJCuLh9NJd0iOHiDtEE+jXwRxziNgzDIKfITmZ+CcfzbWTml3Asr/jk/20cy7eRkVvM0Twbmfm2aq22CfTzIaFJMAlRwbQ6+ZUYHUxi0xBaNgnG39c9p4SLSEX+/v707duXZcuWMWbMGACcTifLli1jwoQJ5gbnBfysPjQNDaBpaOWm3q8V2Eo5dKKI/ccLOJBVyN7MAvYey2f30QIy820czi7icHYRX+846nqMv68PHWND6RRbNiu1fbNQOsSG0Tw88JxvDp1Og50ZeXz60xE+2niIjNyyDx86x4Xx8o296NI83OuWl4jnqWmNqk0T/XzGuiM/Pzj9Wpt2u509oTCofUy183I4DY4X2DiaW/ahZVpOEYezizl0opCDJ4o4mFV4suFe9vXD/uwKjw/086FdTCjtm4XSPiaUtjGhtI0JoVVUMCHVnA2aU2hnw4EsFv+czldb0smzlW1T0rJJEDPGdGdIp2auGuXpP7Mzacx5VTfv825Qnc8Gd6tXr67QAQdISkpi0aJFAKSmppKens7QoUNd90dERDBw4EBWr15dZYOqNuuS//rNbn7c58PGL7Zj9fGeN18Op5P9+z0rr7O9fz59mYDT6WT/AR82fL4Ny2m5lQ8xfnWgqmUDp5YKlI1wGmV/dp5cZmA4jZPTbsuWDDicpy0bOG3JgN1xarmAvbSsGVVS/ulGqQOb3UmpsxqdARcLYODv60PrqCA6NAulU2wYXePD6NkygibB/qeNdWI/05xlN+KNm3s2pHnf7mXdXh+WfrCZE6d9CnaioKRGv1u+PhaahQUQGxFIfEQQcRGBNI8IpGWTIJpHBNGySRBRIf7V2jxURNxfcnIy48aNo1+/fgwYMIA5c+ZQUFDg+kBRGkZIgK9rhtSvZReW8EtGPjsz8tiRlsuO9LL/F5Q42HI4ly2HK37SHODrQ8smQcRHBtE0xJ+IID+sPj44DYMThSWk5xSz7Uiu6w0fQExYAH8e1pEb+iVoprW4FdWohmf1sdAsLJBmYYF0bxFR5ZjcYjv7MwvZm5nPnqP57MksYM/RfPYeK6DY7mTrkVy2Hqk8CyYqxJ/mEYHEhAUQFexPkL8Vf18f7A4nRSVOMnLLGmH7frUksVVUMPcNacdv+7TU/rnict4NqppucAeQnp5e5fj09HTX/eXHzjTm12qzLnnBj1aOFvtA2sGzjvNM3poXlOV2yOwgasTPYhBgLdssNdgXgn0NQn0hxK9sQ9Vwv7I14FEBZevCfSwlQA4UQuFuWO3hezt60+aeDWnBuoOk5/pARtX1LyzAl+iwAJqG+BMTFkB0aADNwgKICQugWXgAzcICiQ0PpGmIv1df9UVEKrrxxhs5duwYU6ZMIT09nV69erFkyZJK51dinshgfwa0iWJAm1OXT3c6DQ6eKGT7yYbVzvQ8dh3NZ19mAbZSJ3uOFbDnWMFZnhWC/KwMbteU6/u25IousZr9Km5JNco9hQf60aNlBD1aVmxglTqcHDxRxK6MPHYfK7tQzr7MAvZmFpBdWPYBalZBSbVeo010CBe1b8roXi3o26qJzk+lEo/fUbk265IPhOxh07ZdJCYm4uMhM42qw+l0sm/fPlPyqosJGJazbDbqdDpI3bePNomJWK3WiiOruCzsaYdPXib21EELZZd7Lb9kNYCPT9kYq8+p47++dLXfaZeGLb9kddn/yy5V7e/rQ5CflQA/H4L9rAT5W8/5qYDWJXvv5p61cXP/BLbt+IX+PbsQHVY2yykqxJ+mof40CfbXMk8ROaMJEyZoSZ+H8fGx0LppCK2bhnBl9+au43aHk7TsYg5kFZKeW0xWgY2cIrtrE+aoYH+iw/zpGBtGp9gwt71Kl8jpVKM8h6/VhzbRIbSJDmH4r+7LLbZzKKuIjNxijuXZOFFYQmFJ2cUnyt8bxYYHEh8RSOfm4USF+Ff5GiLlzrtBVdMN7gDi4uLOOr78/xkZGTRv3rzCmF69elX5nLVZl/yny9qxuGAnV43o7HVNgcWL93pdXnBabld6X26gdclS0b2Xt2Vx4Q6uGtRa3x8RkUbKz+pDq6bBtGp69pUBIiINLTzQj67xfnSNP/vEEJHqOu+PWE7f4K5c+QZ3gwYNqvIxgwYNqjAeypb+lI9v06YNcXFxFcbk5uaydu3aMz6niIiIiIiIiIh4tlot8TvXBndjx46lRYsWzJw5E4AHH3yQyy67jNmzZzNy5Ejef/99fvjhB9544w0ALBYLDz30EE8//TQdOnSgTZs2TJ48mfj4eNdVHkRERERERERExLvUapH6jTfeyIsvvsiUKVPo1asXmzZtqrDB3YEDB0hLS3ONHzx4MAsXLuSNN96gZ8+e/Oc//2HRokV0797dNebRRx/l/vvv5+6776Z///7k5+ezZMkSAgMDaxOqiEgFzzzzDIMHDyY4OJjIyMhqPcYwDKZMmULz5s0JCgpi6NCh7Nq1q34DFRERERERaQRqvUn62Ta4W758eaVjN9xwAzfccMMZn89isTB9+nSmT59e29BERM6opKSEG264gUGDBvGPf/yjWo+ZNWsWr7zyCu+8845rhmdSUhLbtm1TE11ERERERKQWPP4qfiIi52PatGkAzJ8/v1rjDcNgzpw5TJo0idGjRwPw7rvvEhsby6JFi7jpppvqK1QRERERERGvp+vQiohUQ2pqKunp6QwdOtR1LCIigoEDB7J69WoTIxMREREREfF8XjeDyjAMoOzqf+dit9spLCwkNzfXqy7h7q15gffmprxO/Z0t/zvsbtLT0wFce+yVi42Ndd1XFZvNhs1mc93OyckBICsrC7vdftbXLP/+HT9+3Ct/L7wtL/De3JQX5OXlAe5bo+qKzqO8Ny/w3tyUl/ufR9UV1SjvzQu8NzflVf0a5XUNqvITyISEBJMjEZHzkZeXR0RExHk99vHHH+f5558/65jt27fTuXPn83r+8zFz5kzXcsLTtWnTpsFiEJG6U5sa5Ql0HiXi2VSjRMSdnatGeV2DKj4+noMHDxIWFobFYjnr2NzcXBISEjh48CDh4eENFGH989a8wHtzU15l3fS8vDzi4+PP+/X+/Oc/c/vtt591TNu2bc/ruePi4gDIyMigefPmruMZGRn06tXrjI+bOHEiycnJrttOp5OsrCyaNm2qGuVleYH35qa86qZGeQKdR3lvXuC9uSkv1aiq6PfC83hrbsqr+jXK6xpUPj4+tGzZskaPCQ8P96pflHLemhd4b26NPa/afuIXExNDTExMrZ7jTNq0aUNcXBzLli1zNaRyc3NZu3Yt99xzzxkfFxAQQEBAQIVjkZGRNXrtxv574Ym8NbfGnpc3z0oop/OoU7w1L/De3Bp7XqpRVWvsvxeeyFtza+x5VadGaZN0EWmUDhw4wKZNmzhw4AAOh4NNmzaxadMm8vPzXWM6d+7Mxx9/DIDFYuGhhx7i6aef5tNPP+Xnn39m7NixxMfHM2bMGJOyEBERERER8Q5eN4NKRKQ6pkyZwjvvvOO63bt3bwC++eYbLr/8cgB27tzp2tQc4NFHH6WgoIC7776b7OxsLr74YpYsWUJgYGCDxi4iIiIiIuJtGnWDKiAggKlTp1ZafuPpvDUv8N7clFfDmz9/PvPnzz/rmF9fZcJisTB9+nSmT59ej5Gd4s7fv9rw1rzAe3NTXlIVb/3+eWte4L25KS+pird+/7w1L/De3JRX9VkMb78WqYiIiIiIiIiIuDXtQSUiIiIiIiIiIqZSg0pEREREREREREylBpWIiIiIiIiIiJiq0TaonnnmGQYPHkxwcDCRkZFVjjlw4AAjR44kODiYZs2a8cgjj1BaWtqwgdaBxMRELBZLha/nnnvO7LBqbO7cuSQmJhIYGMjAgQNZt26d2SHV2lNPPVXpZ9O5c2ezw6qxFStWMGrUKOLj47FYLCxatKjC/YZhMGXKFJo3b05QUBBDhw5l165d5gTrIVSjVKPcgWqUnIlqlGqUO1CNkjNRjVKNMpu31Cdo2BrVaBtUJSUl3HDDDdxzzz1V3u9wOBg5ciQlJSWsWrWKd955h/nz5zNlypQGjrRuTJ8+nbS0NNfX/fffb3ZINfLBBx+QnJzM1KlT2bhxIz179iQpKYmjR4+aHVqtdevWrcLP5rvvvjM7pBorKCigZ8+ezJ07t8r7Z82axSuvvMK8efNYu3YtISEhJCUlUVxc3MCReg7VKNUod6EaJVVRjVKNcheqUVIV1SjVKHfgDfUJGrhGGY3c22+/bURERFQ6vnjxYsPHx8dIT093HXv99deN8PBww2azNWCEtde6dWvj5ZdfNjuMWhkwYIBx3333uW47HA4jPj7emDlzpolR1d7UqVONnj17mh1GnQKMjz/+2HXb6XQacXFxxgsvvOA6lp2dbQQEBBjvvfeeCRF6FtUoz6Aa5TlUo+qWapRnUI3yHKpRdUs1yjN4Y43yxvpkGPVfoxrtDKpzWb16NT169CA2NtZ1LCkpidzcXLZu3WpiZOfnueeeo2nTpvTu3ZsXXnjBo6avlpSUsGHDBoYOHeo65uPjw9ChQ1m9erWJkdWNXbt2ER8fT9u2bbnllls4cOCA2SHVqdTUVNLT0yv8/CIiIhg4cKBX/PzMohrlPlSjPJtqVP1QjXIfqlGeTTWqfqhGuQ9vrlHeXp+g7muUb10G503S09MrFCzAdTs9Pd2MkM7bAw88QJ8+fYiKimLVqlVMnDiRtLQ0XnrpJbNDq5bMzEwcDkeVP48dO3aYFFXdGDhwIPPnz6dTp06kpaUxbdo0LrnkErZs2UJYWJjZ4dWJ8r8vVf38PO3vkjtRjXIfqlGeTTWqfqhGuQ/VKM+mGlU/VKPch7fWqMZQn6Dua5RXzaB6/PHHK21E9usvT/4lP11Nck1OTubyyy/nggsu4E9/+hOzZ8/m1VdfxWazmZyFjBgxghtuuIELLriApKQkFi9eTHZ2Nv/+97/NDk3qgWqUapSnUY1qXFSjVKM8jWpU46IapRrlSVSfzo9XzaD685//zO23337WMW3btq3Wc8XFxVW6ckBGRobrPrPVJteBAwdSWlrKvn376NSpUz1EV7eio6OxWq2u73+5jIwMt/hZ1KXIyEg6duzI7t27zQ6lzpT/jDIyMmjevLnreEZGBr169TIpKnOoRlWkGuV5VKO8m2pURapRnkc1yrupRlWkGuVZvLE+Qd3XKK9qUMXExBATE1MnzzVo0CCeeeYZjh49SrNmzQBISUkhPDycrl271slr1EZtct20aRM+Pj6uvNydv78/ffv2ZdmyZYwZMwYAp9PJsmXLmDBhgrnB1bH8/Hz27NnDbbfdZnYodaZNmzbExcWxbNkyV5HKzc1l7dq1Z7yyirdSjaoe1Sj3pRrl3VSjqkc1yn2pRnk31ajqUY1yT95Yn6Dua5RXNahq4sCBA2RlZXHgwAEcDgebNm0CoH379oSGhjJ8+HC6du3KbbfdxqxZs0hPT2fSpEncd999BAQEmBt8DaxevZq1a9cyZMgQwsLCWL16Nf/3f//HrbfeSpMmTcwOr9qSk5MZN24c/fr1Y8CAAcyZM4eCggLGjx9vdmi18vDDDzNq1Chat27NkSNHmDp1KlarlZtvvtns0GokPz+/wqcBqampbNq0iaioKFq1asVDDz3E008/TYcOHWjTpg2TJ08mPj7e9Y+QVKYapRrlDlSjxpgXtJtTjVKNcgeqUWPMC9rNqUapRpnNW+oTNHCNqotLDXqicePGGUClr2+++cY1Zt++fcaIESOMoKAgIzo62vjzn/9s2O1284I+Dxs2bDAGDhxoREREGIGBgUaXLl2MZ5991iguLjY7tBp79dVXjVatWhn+/v7GgAEDjDVr1pgdUq3deOONRvPmzQ1/f3+jRYsWxo033mjs3r3b7LBq7Jtvvqny79O4ceMMwyi7/OjkyZON2NhYIyAgwLjiiiuMnTt3mhu0m1ONUo1yB6pRciaqUapR7kA1Ss5ENUo1ymzeUp8Mo2FrlMUwDKPmbS0REREREREREZG64VVX8RMREREREREREc+jBpWIiIiIiIiIiJhKDSoRERERERERETGVGlQiIiIiIiIiImIqNahERERERERERMRUalCJiIiIiIiIiIip1KASERERERERERFTqUElIiIiIiIiIiKmUoNKRERERERERERMpQaViIiIiIiIiIiYSg0qERERERERERExlRpUIiIiIiIiIiJiKjWoRERERERERETEVGpQiYiIiIiIiIiIqdSgEhERERERERERU6lBJSIiIiIiIiIiplKDSkRERERERERETKUGlYiISA0lJiZy++23mx2GiIiIiIjXUINK6txf//pXLBYLAwcOrNPntVgs1fpavnx5nb6uiDQuP//8M9dffz2tW7cmMDCQFi1aMGzYMF599dUzPmb58uVYLBb+85//nHGMxWJhwoQJVd73n//8R/VLRM4qNTWVCRMm0LFjR4KDgwkODqZr167cd999bN68ucbPp7olIrVV3XMmu93OK6+8Qv/+/QkLCyM0NJT+/fvz6quvUlpaWul5ExMTsVgs3H///ZXuq6p2zZ8/H4vFwg8//FD3SUqD8jU7APE+CxYsIDExkXXr1rF7927at29fJ8/7z3/+s8Ltd999l5SUlErHu3TpUievJyKNz6pVqxgyZAitWrXirrvuIi4ujoMHD7JmzRr+8pe/uE6Udu7ciY+PPuMRkYbx+eefc+ONN+Lr68stt9xCz5498fHxYceOHXz00Ue8/vrrpKam0rp1a7NDFZFGorrnTAUFBYwcOZJvv/2Wq6++mttvvx0fHx+WLFnCAw88wKJFi/jss88IDg6u9BpvvvkmEydOJD4+vqHTE5OoQSV1KjU1lVWrVvHRRx/xxz/+kQULFjB16tSzPqa0tBSn04m/v/9Zx916660Vbq9Zs4aUlJRKx0VEztczzzxDREQE69evJzIyssJ9R48edf05ICCggSMTkcZqz5493HTTTbRu3Zply5bRvHnzCvc///zz/PWvf1XTXEQaVHXPmZKTk/n222959dVXK8zIvOeee5g7dy4TJkzgkUceYe7cuRWeo1u3buzcuZPnnnuOV155pV5zEfehf8mkTi1YsIAmTZowcuRIrr/+ehYsWFDh/n379mGxWHjxxReZM2cO7dq1IyAggG3btgGwY8cOfve73xETE0NQUBCdOnXiySefrPbrv/322/zmN7+hWbNmBAQE0LVrV15//fVK4xITE7n66qv57rvvGDBgAIGBvoTrIgAAdBBJREFUgbRt25Z33323dt8AEfFoe/bsoVu3bpVOtACaNWvm+rP2oBKRhjJr1iwKCgp4++23KzWnAHx9fXnggQdISEhwHduxYwfXX389UVFRBAYG0q9fPz799NOGDFtEvFx1zpkOHTrEP/7xD37zm99UuVz4vvvuY8iQIbzxxhscPny4wn2JiYmMHTuWN998kyNHjtRLDuJ+1KCSOrVgwQJ++9vf4u/vz80338yuXbtYv359pXFvv/02r776KnfffTezZ88mKiqKzZs3M3DgQL7++mvuuusu/vKXvzBmzBg+++yzar/+66+/TuvWrXniiSeYPXs2CQkJ3HvvvZU68gC7d+/m+uuvZ9iwYcyePZsmTZpw++23s3Xr1lp9D0TEc7Vu3ZoNGzawZcsWs0MREQHKlve1b9++2nt7bt26lQsvvJDt27fz+OOPM3v2bEJCQhgzZgwff/xxPUcrIo1Fdc6ZvvzySxwOB2PHjj3jmLFjx1JaWsqSJUsq3ffkk09SWlrKc889Vycxi/vTEj+pMxs2bGDHjh2uTfEuvvhiWrZsyYIFC+jfv3+FsYcOHWL37t3ExMS4jt12220YhsHGjRtp1aqV63hNCtK3335LUFCQ6/aECRO48soreemll7jvvvsqjN25cycrVqzgkksuAeB3v/sdCQkJvP3227z44ovVT1xEvMbDDz/MiBEj6NWrFwMGDOCSSy7hiiuuYMiQIfj5+Zkdnog0Mrm5uRw5coQxY8ZUui87O7vC5sIhISEEBQXx4IMP0qpVK9avX+9ajnzvvfdy8cUX89hjj3Httdc2VPgi4sWqc85UvkqmZ8+eZ3ye8vvKx56ubdu23Hbbba69qKqaRSreRTOopM4sWLCA2NhYhgwZApRd+eXGG2/k/fffx+FwVBh73XXXVWhOHTt2jBUrVnDHHXdUaE6VP091nd6cysnJITMzk8suu4y9e/eSk5NTYWzXrl1dzSmAmJgYOnXqxN69e6v9eiLiXYYNG8bq1au55ppr+Omnn5g1axZJSUm0aNFCy2NEpMHl5uYCEBoaWum+yy+/nJiYGNfX3LlzycrK4uuvv+Z3v/sdeXl5ZGZmkpmZyfHjx0lKSmLXrl2VltGIiJyP6pwz5eXlARAWFnbG5ym/r3zsr02aNEmzqBoRNaikTjgcDt5//32GDBlCamoqu3fvZvfu3QwcOJCMjAyWLVtWYXybNm0q3C5vCnXv3r1WcXz//fcMHTqUkJAQIiMjiYmJ4YknngCo1KD6dSMMoEmTJpw4caJWMYiIZ+vfvz8fffQRJ06cYN26dUycOJG8vDyuv/76Kj/dq0s1aciLiPcrf+OWn59f6b6//e1vpKSk8K9//ct1bPfu3RiGweTJkys0r2JiYlwXrTl98+K6oLol0nid65zpXM2n0+87fa/P05XPonrjjTdIS0ur+yTErWiJn9SJr7/+mrS0NN5//33ef//9SvcvWLCA4cOHu26fPtOpruzZs4crrriCzp0789JLL5GQkIC/vz+LFy/m5Zdfxul0VhhvtVqrfB7DMOo8NhHxPP7+/vTv35/+/fvTsWNHxo8fz4cffnjOK5OeSUBAAEVFRVXeV1hYCEBgYOB5xysi3iciIoLmzZtXucdL+Z5U+/btcx0rP9d5+OGHSUpKqvI527dvX+3XV90Skeo40zlT165dAdi8eTO9evWq8rGbN28GyhpRZ/Lkk0/yz3/+k+eff77KJc/iPdSgkjqxYMECmjVrVuVm5B999BEff/wx8+bNO+PjywtSbTYm/uyzz7DZbHz66acVZkd988035/2cIiIA/fr1A6jVJ3etW7dm586dVd5Xfrx169bn/fwi4p1GjhzJ3//+d9atW8eAAQPOOrb8fMrPz4+hQ4fW+rVVt0Skpk4/Z7rzzjuxWq3885//PONG6e+++y7+/v6MHj36jM/Zrl07br31Vv72t79V+4IR4pm0xE9qraioiI8++oirr76a66+/vtLXhAkTyMvLO+v+LTExMVx66aW89dZbHDhwoMJ91Z3RVD4j6vTxOTk5vP322+eRlYg0Rt98802VNWfx4sUAdOrU6byf+6qrrmLNmjVs2LChwvHs7GwWLFhAr169iIuLO+/nFxHv9OijjxIcHMwdd9xBRkZGpftPr1nNmjXj8ssv529/+1uVDfVjx47V6LVVt0TkTKpzztSyZUvuvPNO/ve///H6669XGjtv3jy+/vpr/vjHP9K0adOzvt6kSZOw2+3MmjWrbhIQt6QZVFJrn376KXl5eVxzzTVV3n/hhRcSExPDggULztrxfuWVV7j44ovp06cPd999N23atGHfvn188cUXbNq06ZxxDB8+HH9/f0aNGsUf//hH8vPzefPNN2nWrJnWK4tItdx///0UFhZy7bXX0rlzZ0pKSli1ahUffPABiYmJjB8//qyP/+9//8uOHTsqHR83bhyPP/44H374IZdeeil//OMf6dy5M0eOHGH+/PmkpaWpmS4iVerQoQMLFy7k5ptvplOnTtxyyy307NkTwzBITU1l4cKF+Pj40LJlSwDmzp3LxRdfTI8ePbjrrrto27YtGRkZrF69mkOHDvHTTz9VeH7VLRE5H9U9Z3rppZfYsWMH9957L0uWLOHKK68E4KuvvuKTTz7hN7/5DS+88MI5X698FtU777xzxjFvvfUWS5YsqXT8wQcfPOtG7eJGDJFaGjVqlBEYGGgUFBScccztt99u+Pn5GT/88IMBGC+88EKV47Zs2WJce+21RmRkpBEYGGh06tTJmDx5cpVj77vvPuPXv8KffvqpccEFFxiBgYFGYmKi8fzzzxtvvfWWARipqamuca1btzZGjhxZ6Tkvu+wy47LLLjt30iLilb788kvjjjvuMDp37myEhoYa/v7+Rvv27Y3777/fyMjIcI1r3bq1MW7cONftb775xgDO+LVy5UrDMAzj0KFDxh/+8AejRYsWhq+vrxEVFWVcffXVxpo1axo6VRHxMLt37zbuueceo3379kZgYKARFBRkdO7c2fjTn/5kbNq0qcLYPXv2GGPHjjXi4uIMPz8/o0WLFsbVV19t/Oc//3GNUd0Skdqo7jmTYRhGSUmJMWfOHKNv375GcHCwq86MGzfOcDgclZ77TO/Vdu3aZVitVgMwPvzwQ9fxt99++6z17ODBg3X/DZB6YTEM7QgtIiIiIiIiIvUvNzeXyy67jD179rBixYozbqAujY8aVCIiIiIiIiLSYNLT0xk8eDDFxcWsXr1aF1wQQA0qERERERERERExma7iJyIiIiIiIiIiplKDSkRERERERERETKUGlYiIiIiIiIiImEoNKhERERERERERMZUaVCIiIiIiIiIiYipfswOoa06nkyNHjhAWFobFYjE7HBGpJsMwyMvLIz4+Hh8f7+2dq0aJeCbVKBFxZ6pRIuLOqlujvK5BdeTIERISEswOQ0TO08GDB2nZsqXZYdQb1SgRz6YaJSLuTDVKRNzZuWqU1zWowsLCgLLEw8PDzzrWbrezdOlShg8fjp+fX0OE1yC8NS/w3tyUF+Tm5pKQkOD6O+ytVKO8Ny/w3tyUl2pUVfR74Xm8NTflpRpVFf1eeB5vzU15Vb9G1WuDasWKFbzwwgts2LCBtLQ0Pv74Y8aMGXPG8cuXL2fIkCGVjqelpREXF1et1yyf6hkeHl6tohUcHEx4eLjX/aJ4Y17gvbkpr1O8fbq2apT35gXem5vyOkU16hT9Xngeb81NeZ2iGnWKfi88j7fmprxOOVeNqtcFygUFBfTs2ZO5c+fW6HE7d+4kLS3N9dWsWbN6ilBERERERERERMxWrw2qESNG8PTTT3PttdfW6HHNmjUjLi7O9eXNG/2JiHtZsWIFo0aNIj4+HovFwqJFiyrcbxgGU6ZMoXnz5gQFBTF06FB27dplTrAi0uioRomIuzhXParK8uXL6dOnDwEBAbRv35758+fXe5wi4jncsvPTq1cvmjdvzrBhw/j+++/NDkdEGpFzzfycNWsWr7zyCvPmzWPt2rWEhISQlJREcXFxA0cqIo2RapSIuIuarpZJTU1l5MiRDBkyhE2bNvHQQw/xhz/8ga+++qqeIxURT+FWm6Q3b96cefPm0a9fP2w2G3//+9+5/PLLWbt2LX369KnyMTabDZvN5rqdm5sLlK2HtNvtZ3298vvPNc7TeGte4L25KS/3yX3EiBGMGDGiyvsMw2DOnDlMmjSJ0aNHA/Duu+8SGxvLokWLuOmmmxoyVBFphFSjRMRdnK0eVWXevHm0adOG2bNnA9ClSxe+++47Xn75ZZKSkuorTBHxIG7VoOrUqROdOnVy3R48eDB79uzh5Zdf5p///GeVj5k5cybTpk2rdHzp0qUEBwdX63VTUlLOL2A35615gffm5ul5GQbYnFBcCkUOKHZAUamFkiUp+FvP/tjCwsKGCbIWUlNTSU9PZ+jQoa5jERERDBw4kNWrV+vNn4iHWbkrk4P5ZkdRd1SjRLzL8l+OcbjA7CjqzurVqyvUJ4CkpCQeeughcwKSRiE9p5jMfBt5xaUYhmFKDKWOUn7JsdBk73F8rW7VgqmV8ryGOZzU1d7vbv/dGTBgAN99990Z7584cSLJycmu2+WXLxw+fHi1ruyQkpLCsGHDvG43fW/MC7w3N3fLy+k0yCm2c6LAzonCEk4U2jlRaCe7qIScwlKyi+zkFtnJKbaTW1RKTpGdvOJS8mylOJyVC//i+wbSIS7irK9ZPvvRnaWnpwMQGxtb4XhsbKzrvl/TLM/KvDUv8N7cvDGvvGI7j360heP5Vjr0SOc3Xc5+tWBPyF01qm54a17gvbl5Y17ZhXYe/e8WcgqtdOl5lIs7nv2iUZ6Qe3p6epX1KTc3l6KiIoKCgio9RjWqMm/NC+o2t+xCO499tIWvdx6r9XPVjf9v787jo6rv/Y+/ZpLJZN8gZIFAwhp2EARBq1iW4E5rvdrSitTi1Uq9iq1KfwoCKi5VUevV2tai91arva0riEQUV3aN7HvYAkmAkD2ZTGbO748sGAkhgUzOzMn7+Xikdc6ck3w+TPgy5zPf7+cbxPNbN5gdhA8EMbW8CkdQ892jWvqa+n2BKjs7m+Tk5NM+73Q6cTqdpxx3OBwtvtFvzbmBxKp5gXVz82VehmFQVOGmoNRFfkkVBaUujtZ/lbk4XubieFk1x8tdnKhwN1loaqkgu43o0GAinMEYrgrsQcFnzMuKrydolmdzrJoXWDc3K+X1rxw7x8rsJIRC2Z6vWZrT/PmBMMvzbGiMOj2r5gXWzc1Keb2x186JCjtJYXBi53qW7m7+fI1Rp2el34vvsmpecO65HSyDl3cGUeiyYcMgygGhQWC3tVGA0shnK1cSdobKUkvHKJ8WqMrKyti9++RompOTQ3Z2NvHx8XTv3p3Zs2eTm5vLq6++CsCiRYtIT09n4MCBVFVV8Ze//IWPP/6Y5cuX+zJMEUuocns4dKKSQycqyC2q5HBRJYeLqjhcVEleSRV5xVW4aryt+p5RocHEhYcQFxFCfLiD2PAQYsMdxIQ5iA1zEFP33/VfUaEOokMdhDrs2Gw23G43S5cupVdChI+ybl9JSbUzLPLz8xsVzvPz8xk2bFiT12iW56msmhdYNzer5bXlcAlfrF4NwHXpXi7LPHNegTDLU2NU27BqXmDd3KyW18ZDxaxavQaA63p6mGyhMSo/P7/Rsfz8fKKjo5ucPQUao5pi1bygbXIrrnST+cyXFLqq6R4fxrPXD2VgSvO/K75m1desNXm1dIzyaYFq/fr1XHrppQ2P6weXadOmsXjxYo4cOcKBAwcanq+urubuu+8mNzeX8PBwhgwZwkcffdToe4h0ZFVuD/uOl5NztJy9x8rZd6yc/ccr2F9YTn6J68zfAIgLd9AlKpQu0U4Souq+Ip10rvuKjwihU2QIceEhhAT75UafpklPTycpKYkVK1Y03OyVlJSwZs0abrvttiav0SzP07NqXmDd3KyQl9drMPf97XgNuGJwEv0iD7Uor0DIW2NU27JqXmDd3KyQl8drMG/JdgwDrhmaTO/wg5YZo8aMGcPSpUsbHcvKymLMmDGnvUZj1OlZNS84t9yeen87x8ur6ZUQwVu3X0h0qP/8GVn1NWvLMcqnBapx48Y124hs8eLFjR7fc8893HPPPb4MSSQgeLwG+46Xs/VwCTvyStmRX8qu/FIOFFbQ3Mq7SGcw3eLC6BobRte4MJJjwkiJDSU5Joyk6NqiVKjjDN3KO7gzzfy88847eeihh+jTpw/p6ek88MADpKSkMGXKFPOCFpEWe33dAb49WESkM5jZk/uy4YtDZofUKhqjRKzt9bUH2HiomChnMPdm9mXd5wfNDum0Wrta5tZbb+WPf/wj99xzD7/85S/5+OOPefPNN1myZIlZKYjFbNh/gtfW1E6AefhHg/2qOCUt4/c9qESszjAM9hdWsP6ojQ1LtrP1SClbDpdQ6fY0eX5UaDC9EiLp2TmC9M4RdO8UTlqnCLrHhxMb7sBm0+Lqc3GmmZ/33HMP5eXl3HLLLRQVFXHRRRexbNkyQkNDzQpZRFroWJmLx5ftAODuSX1JjA68v7cao0Ss63iZiyc+rB2jZk3qS0LUqTOH/ElrV8ukp6ezZMkS7rrrLp555hm6devGX/7yFzIzM9s9drEer9fg/rc3A/CTEd24oGcnkyOSs6EClUg783oNtueVsnrvcdbmFLJ+fyHHyqqBINh98h/xUIedjKRo+idH0S8xir6JUfROjCQh0qkilA+daeanzWZj/vz5zJ8/vx2jEpG2sHDpdoor3QxIjuYXF/TA8Db9QYA/0xglYl2PfhBYY1RrV8vUX/PNN9/4MCrpqL7YfYxtR0qIcgbz+8v7mx2OnCUVqETawbEyFyt3HOXTnUf5cvcxCsurGz3vCLKREublkkE9GNY9jsFdY+iZEEmQtpoQEWkTa3MK+dfXh7DZ4OEfDSI4yI7bz2/+RKTj2LC/kH9uqF1yvGCKxiiR1vr7mv0AXDuiG/ERISZHI2dLBSoRHzlYWMGyzXl8sPkI3xws4rsfMIWHBHF+WjwX9OzE+WlxZHQJZ0XWh1x+eYYlG+eJiJjJ7fFy/9ubALjh/O4M7x5nckQiIifVeLz8v7dqlyb9x8hujOihMUqkNfJLqvhoWwEAPxvd3eRo5FyoQCXShoor3Ly78TBvfX2Irw8UNXpuYEo0l/brwsV9ExjePRZH0Mkd8txudztHKiLScbz8RQ4788uIjwjh3sn9zA5HRKSRV1ftZ3teKTFhDu6dnGF2OCIB5411B/F4DUalxdM3McrscOQcqEAl0gY27D/B31fvZ8mmI7hqvADYbTA6vROXD05i4oAkkmLUoFZEpL0dLqpk0Ue7AJh9WQax4Zr2LyL+o6CkiqeydgJwz+R+dIr078boIv6mxuPl9bW1fXynXqDZU4FOBSqRs+T1GizbksefP9/LN9+ZLZWRFMVPRnTj6qEpdAnAHaJERKxk/ntbqXR7OD8tjmvP62Z2OCIijTy8dBtlrhqGdovhhvN1cy3SWqv2HudIcRVx4Q4mD0oyOxw5RypQibSS12uwdPMRnvloF7sKygAICbJz9bAUpo7uzrDUWO2yJyLiBz7ZXsCyLXkE2W0smDIIuzaeEBE/smrPcd7JPozNVtsYXZvjiLTeR1vzAZg8KAlncJDJ0ci5UoFKpBXW7D3OQ0u2sSm3GIDo0GBuGpvGL8akkRClKdkiIv6iyu1hzru1TYdvviidjKRokyMSETnJ7fEy553aMWrq6O4M6RZrbkAiAcgwjIbm6OMzEk2ORtqCClQiLXCszMWC97fyTvZhACKdwfzqB+lMvzCdmDDtuici4m+e/2Q3BwsrSY4J5b/G9zE7HBGRRl7+IoddBbWbN/x2kjZvEDkb2/NKyS2qxBls58Lenc0OR9qAClQiZ/D2N7k8+N4Wiirc2G3w01HduWtiXzqriaWIiF/ac7SMP326F4A5Vw4gwqm3OyLiP44UV/LMitrNG+7T5g0iZ23FttrlfRf17kxYiJb3WYHesYmcRmmVmznvbOGtb3IBGJAczaPXDtYUbBERP2YYBnPf2UK1x8u4fglqmCoifmfB+1upqPYwokccP9HmDSJnrX5534QBWt5nFSpQiTRhd0EZM15dT86xcoLsNu74YR9+fWkvHEF2s0MTEZFmvL/xCF/sPoYz2M78qwdp0woR8Suf7TzK0k152G2w4Bpt3iBytgpKq8g+WATA+Iwu5gYjbUYFKpHv+WznUW5/7WtKq2roGhvGMzcMY2RavNlhiYjIGZRWuVnw/lYAbr+0N907hZsckYjISa4aD3Pf3QLAtLFpDEjR5g0iZ2vljqMADOkWQ5foUJOjkbaiApXId7yTncusN7/F4zU4Py2OF38+gk7qNSUiEhCeytpJQamL9M4R/OclPc0OR0SkkT9/tpecY+UkRDm5a2Jfs8MRCWir9x4H4Ad91BzdSlSgEqnz5rqD3PvvjRgG/Gh4Vx69djDOYDXbExEJBJtzi3nlq30AzL9moMZvEfErBwsr+OMnuwG4/4r+RIdqF2iRc7FuXyEAo9I7mRyJtCUVqESAf204xD3/2gjAzy/ozvyr1RNARCRQeL0G97+9Ga8BVw5J5gd9EswOSUSkkXnvbaXK7eWCnvFcPTTF7HBEAtqR4koOFlZit8GIHnFmhyNtSAUq6fA+23mUe+uKUzeNTWPuVQPUVFdEJIC8sf4g2QeLiHQG88CVA8wOR0SkkRXb8vloWz7BdhsLrtHmDSLnam1O7eypgSkxRDpV0rASbUkmHdrWwyXc9r8bqPEaXD00hTlXqjglIhJIjpe5ePSD7QDMmtiXRDVKFRE/UuX28OB7tY3Rb74onT6JUSZHJBL46gtUo9K1kZXVqEAlHVZJlZtb/3cD5dUexvbqxBPXDdGyPhGRAPPoB9sprnTTPzmaG8f0MDscEZFG/nvlHg4WVpIcE8od4/uYHY6IJdT3nzpfO61bjk8LVJ999hlXXXUVKSkp2Gw23n777TNes3LlSs477zycTie9e/dm8eLFvgxROijDMLj3/zZyoLCCbnFhvDB1hBrqiogEmHX7CvnnhkMAPDRlEMFB+txNRPzHvmPlvPjpHgAeuHIAEVqKJHLOTpRXszO/DIDz09R/ymp8+k6uvLycoUOH8vzzz7fo/JycHK644gouvfRSsrOzufPOO/nVr37Fhx9+6MswpQP6n9X7+WBzHo4gG8//7DxiwrWTiohIIHF7vNz/1mYAbjg/VU1SRcSvGIbBg+9tobrGyw/6dOayQUlmhyRiCfWzp3p3iaRTpNPkaKSt+bSMf9lll3HZZZe1+PwXX3yR9PR0nnzySQD69+/PF198wdNPP01mZqavwpQO5mBhBQuX1vYrmX1Zf4amxpobkIiItNriL/exI7+UuHAH907OMDscEZFGPtySz8odRwkJsjPv6oHqcSrSRuoLVOo/ZU1+NRd+1apVTJgwodGxzMxMVq1aZVJEYjWGUbsVeaXbw+j0eKZfmGZ2SCIi0kpHiit5+qOdQO0HDXERISZHJCJyUkV1DfPrGqPfcnFPeiZEmhyRiHV8e7AYgPO6a+a0FfnVQui8vDwSExMbHUtMTKSkpITKykrCwsJOucblcuFyuRoel5SUAOB2u3G73c3+vPrnz3ReoLFqXnDuub2/8Qif7jyKI8jG/Kv6U1NT05bhnTWrvmatyctquYuI7yx4fysV1R5G9IjjJyO6mR2OiEgjz328m8PFVXSNDeP2S3ubHY6IZXi9BlsO1xaoBneNMTka8QW/KlCdjYULFzJv3rxTji9fvpzw8PAWfY+srKy2DssvWDUvOLvcXB546JsgwMaE5Bq2r/uU7W0f2jmx6mvWkrwqKiraIRIRCXQrdxSwdFMeQXYbD00ZpN1XRcSv7C4o4y+f7wXgwasHEhaiTXhE2sreY+WUV3sIcwTRKyHC7HDEB/yqQJWUlER+fn6jY/n5+URHRzc5ewpg9uzZzJo1q+FxSUkJqampTJo0iejo6GZ/ntvtJisri4kTJ+JwWKdJtlXzgnPL7cVP91Li3k23uDCeuPlCnMH+s8LVqq9Za/Kqn/0oInI6VW4Pc9+tXTYzfWwa/ZOb/3deRKQ9GYbBnHc24/YYjM/owsQBiWe+SERabHNu7eypASnR2rnXovyqQDVmzBiWLl3a6FhWVhZjxow57TVOpxOn89Tu/Q6Ho8U3+q05N5BYNS9ofW7FFW7+/MU+AO6e1JfIMP/c8cGqr1lL8gqUvD0eDw8++CD/+7//S15eHikpKdx0003cf//9aoAq4mMvrNzD/uMVJEY7uXNiX7PD8Usao0TM8/7GI3y15zjOYDsPXj3Q7HBELGdTrpb3WZ1PC1RlZWXs3r274XFOTg7Z2dnEx8fTvXt3Zs+eTW5uLq+++ioAt956K3/84x+55557+OUvf8nHH3/Mm2++yZIlS3wZpnQAL32+h5KqGvomRnL10K5mhyMB7LHHHuOFF17glVdeYeDAgaxfv57p06cTExPDHXfcYXZ4IpaVc6ycFz7dA8CcKwcS6fSrz9j8hsYoEXOUuWp4aMlWAH49rjep8S1rNSIiLVdfoBqkApVl+fTd3fr167n00ksbHtcvxZs2bRqLFy/myJEjHDhwoOH59PR0lixZwl133cUzzzxDt27d+Mtf/kJmZqYvwxSLKyyv5uW62VO/ndSPIPUrkXPw1Vdfcc0113DFFVcAkJaWxuuvv87atWtNjkzEugzDYO67W6iu8fKDPp25fHCS2SH5LY1RIuZYlLWT/BIXPTqF85+X9DQ7HBHL8XoNtmgGleX5tEA1btw4DMM47fOLFy9u8ppvvvnGh1FJR/P62gNUuj0M6hqtXgByzsaOHctLL73Ezp076du3L99++y1ffPEFTz31VJPna6fRU1k1L7Bubmbn9cHmPD6r24F1zhX92mwHVivuNNraMUpEzt32vBL+9tU+AOZdPZBQhxqji7S1+gbpoQ67GqRbmObHi6W5PV7+Z9V+AH55Ybr6b8g5u++++ygpKSEjI4OgoCA8Hg8PP/wwU6dObfJ87TR6elbNC6ybmxl5VXngkezaHVh/mOxh65pP2drGP8NKO422doxSEf1UVs0LrJubmXkZhsH9b23C4zWYNKALF/aMa7M4rFhEFzlbDQ3Sk9Ug3cpUoBJL+3BLHnklVXSOdHLFkGSzwxELePPNN/n73//Oa6+9xsCBA8nOzubOO+8kJSWFadOmnXK+dho9lVXzAuvmZmZejy7bQXH1flLjwvjDL8e26cwEK+402toxSkX007NqXmDd3MzIa+1RG+v3BxFiNxgTepilSw+3+c+wUhFd5GypQXrHoAKVWNriL/cBMHV0d5zBmm4t5+53v/sd9913HzfccAMAgwcPZv/+/SxcuLDJmz/tNHp6Vs0LrJtbe+e1Pa+Exatqe1XOnzKIqPBQn/wcK+002toxSkX0U1k1L7BubmblVVLpZv4zXwLV3DG+Lz+/OL1Nv78Vi+giZ2uzGqR3CCpQiWVtzi1m/f4TOIJsTB3d3exwxCIqKiqw2xtPKw4KCsLr9ZoUkYg1eb0GD7y9GY/XYPLAJC7t18XskAJCa8coFdFPz6p5gXVza++8nl26g+Pl1fRKiOCWS3rjCPbNsiMrFdFFzoZhGOzILwVgQErzH55IYFOBSizrX18fAiBzYBJdon3zqbt0PFdddRUPP/ww3bt3Z+DAgXzzzTc89dRT/PKXvzQ7NBFL+dfXh1i37wRhjiDmXDXA7HAChsYokfaxObeY/1ld2+d0wTWDCPFRcUpE4Gipi6IKN3Yb9EqINDsc8SEVqMSSPF6D9749AsCPz+tqcjRiJc899xwPPPAAv/71rykoKCAlJYX//M//ZM6cOWaHJmIZRRXVLPxgOwB3TuhDSmyYyREFDo1RIr7n9Rrc//ZmvAZcNTSFsb07mx2SiKXVz55K6xyhXTItTqV+saSv9hzjWJmLuHAHP+iTYHY4YiFRUVEsWrSI/fv3U1lZyZ49e3jooYcICQkxOzQRy3j8wx0UllfTp0skv7yobXu6WJ3GKBHfe3P9QbIPFhHpDOb+K/qbHY7pnn/+edLS0ggNDWX06NGsXbv2tOcuXrwYm83W6Cs0VCsdpHk78moLVP0So0yORHxNBSqxpHeya3dQuXxwMg5tQyoiEjC+OXCC19fWNkZ/aMogjeEi4ldOlFfz2LKTMzwTO3gbiTfeeINZs2Yxd+5cvv76a4YOHUpmZiYFBQWnvSY6OpojR440fO3fv78dI5ZAtLNuBlUfFagsT+/6xHKq3B6Wbc4DYMpwLe8TEQkUnrplM4YBPx7eldE9O5kdkohII49/uIMTFW76JUZx09g0s8Mx3VNPPcWMGTOYPn06AwYM4MUXXyQ8PJyXX375tNfYbDaSkpIavhITE9sxYglEO/PLAM2g6gjUg0os55PtBZS5augaG8aI7nFmhyMiIi30v6v3s+VwCdGhwcy+XMtmRMS/ZB8s4h/ramd4LpgyiOAOPsOzurqaDRs2MHv27IZjdrudCRMmsGrVqtNeV1ZWRo8ePfB6vZx33nk88sgjDBw4sMlzXS4XLper4XFJSQkAbrcbt9vdbHz1z5/pvEBj1byg6dy8XoNddTOoenYKDci8rfqatSavluauApVYzodbamdPXTkkGbvdZnI0IiLSEgWlVfzhwx0A/G5yBglRTpMjEhE5qXaG56baGZ7ndWVUerzZIZnu2LFjeDyeU2ZAJSYmsn379iav6devHy+//DJDhgyhuLiYP/zhD4wdO5YtW7bQrVu3U85fuHAh8+bNO+X48uXLCQ8Pb1GcWVlZLTov0Fg1L2ic2/EqKK8OJshmsG3tZ+wM4LqwVV+zluRVUVHRou+lApVYisdr8OnOowCM76/pwiIigeKRJdsoddUwpFsMPxvV3exwREQaeW3NfjbnlhAVGszsyzTD82yNGTOGMWPGNDweO3Ys/fv3509/+hMLFiw45fzZs2cza9ashsclJSWkpqYyadIkoqOjm/1ZbrebrKwsJk6ciMPhaLskTGbVvKDp3D7ecRS++YbeXaK46sqxJkd4dqz6mrUmr/rZj2eiApVYyreHijhR4SYqNJjzuseaHY6IiLTAV3uO8Xb2YWy22sboQZr9KiJ+5FiZiyfqZ3hm9tMMzzqdO3cmKCiI/Pz8Rsfz8/NJSkpq0fdwOBwMHz6c3bt3N/m80+nE6Tz1z9vhcLT4Rr815wYSq+YFjXPbe6wSgH5J0QGfr1Vfs5bk1dK8A3iCnMipVm6v3THk4r4JHb4vgIhIIKiu8fLA25sB+PnoHgzpFmtuQCIi37Nw6XZKqmoY1DWaqaN7mB2O3wgJCWHEiBGsWLGi4ZjX62XFihWNZkk1x+PxsGnTJpKTk30VpgS4+h38+iWpQXpHoBlUYimf7Khd3ndpvy4mRyIiIi3xly/2sudoOZ0jQ/jtpH5mhyMi0si6fYX86+tD2Gyw4BrN8Py+WbNmMW3aNEaOHMmoUaNYtGgR5eXlTJ8+HYAbb7yRrl27snDhQgDmz5/PBRdcQO/evSkqKuKJJ55g//79/OpXvzIzDfFjO/JqC1R9ukSaHIm0BxWoxDIKSqvYlFsMwCV9E0yORkREzuTQiQqeW1G7rGP2Zf2JCbfetHcRCVw1npMzPG84P5Xh2h36FNdffz1Hjx5lzpw55OXlMWzYMJYtW9bQOP3AgQPY7SdXNZw4cYIZM2aQl5dHXFwcI0aM4KuvvmLAgAFmpSB+zOM12H20DIC+iZpB1RGoQCWW8Wnd7Kkh3WLUG0BEJADMf28rlW4Po9Lj+fF5Xc0OR0SkkcVf7WN7Ximx4Q7uycwwOxy/NXPmTGbOnNnkcytXrmz0+Omnn+bpp59uh6jECg4XVVJd4yUk2E5qfMt2bZTApiY9Yhkr63bvG6flfSIifm/FtnyWb80n2G5jwTWDsNm0bEZE/Ed+SRWLPtoFwL2TM4iLCDE5IpGOZ++xcgDSOoVreW0HoQKVWIJhGKzZexyAi3p3NjkaERFpTpXbw4PvbQHg5ovS1fhURPzOw0u2UeaqYVhqLNePTDU7HJEOKadueV965wiTI5H2ogKVWELOsXKOlVUTEmxnSLcYs8MREZFm/PcnuzlYWElyTCh3jO9jdjgiIo18tfsY7357GJsNHpoyCLtmboiYIqduBlV6ZzVI7yjapUD1/PPPk5aWRmhoKKNHj2bt2rWnPXfx4sXYbLZGX6Ghoe0RpgSwdfsKARjWLZZQR5DJ0YiIyOnkHCvnxU/3AjDnygFEONUOU0T8R3WNlwfeqW2M/vPRPRjUVR98ipilfolfT82g6jB8XqB64403mDVrFnPnzuXrr79m6NChZGZmUlBQcNproqOjOXLkSMPX/v37fR2mBLi1OScAOD9du6uIiPgrwzCY885mqj1eLu6bwORBSWaHJCLSyF+/yGHP0XI6RYTw20n9zA5HpEPbe7RuBlWCClQdhc8LVE899RQzZsxg+vTpDBgwgBdffJHw8HBefvnl015js9lISkpq+KrfplTkdNbuq+0/NSq9k8mRiIjI6XywOY/Pdx0jJMjOvKsHqjG6iPiV3KJKnl1R2xh99uX9iQl3mByRSMdV5fZwuLgSUA+qjsSnBarq6mo2bNjAhAkTTv5Au50JEyawatWq015XVlZGjx49SE1N5ZprrmHLli2+DFMCXF5xFQcLK7Hb4LzusWaHIyIiTShz1TD/va0A3Dqul95siojfeej9rVS6PZyfFse153U1OxyRDm3/8QoMA6JCg+mkXTQ7DJ82fjh27Bgej+eUGVCJiYls3769yWv69evHyy+/zJAhQyguLuYPf/gDY8eOZcuWLXTr1u2U810uFy6Xq+FxSUkJAG63G7fb3Wx89c+f6bxAY9W8oOncVu2uXS7aPzmK0KDAzNuqr1lr8rJa7iLS2LMrdpFXUkVqfBi/HtfL7HBERBr5dOdRPticR5DdxvxrBmmGp4jJco7V7uDXMyFSfx87EL/rTDpmzBjGjBnT8Hjs2LH079+fP/3pTyxYsOCU8xcuXMi8efNOOb58+XLCw8Nb9DOzsrLOPmA/ZtW8oHFu/7fXDtjp7C1m6dKl5gXVBqz6mrUkr4qKinaIRETMsCOvlL9+kQPA/KsHaTMLEfErVW4Pc+sao08bk0b/5GiTIxIRNUjvmHxaoOrcuTNBQUHk5+c3Op6fn09SUssaozocDoYPH87u3bubfH727NnMmjWr4XFJSQmpqalMmjSJ6Ojm/3Fxu91kZWUxceJEHA7rrDG3al7QdG7PP/cVUMZ144aTOTAw+5VZ9TVrTV71sx9FxFoMw+CBdzbj8RpMGpDIpRldzA5JRKSRlz7by77jFSREOblrYh+zwxERIKe+QboKVB2KTwtUISEhjBgxghUrVjBlyhQAvF4vK1asYObMmS36Hh6Ph02bNnH55Zc3+bzT6cTpdJ5y3OFwtPhGvzXnBhKr5gUncyt31bDraO30z1G9Ogd8vlZ9zVqSlxXzFhF465tc1uYUEuYIYs5VA8wOR0SkkYOFFTz/Se0H4fdf0Z+oUL0fEfEHOcdUoOqIfL7Eb9asWUybNo2RI0cyatQoFi1aRHl5OdOnTwfgxhtvpGvXrixcuBCA+fPnc8EFF9C7d2+Kiop44okn2L9/P7/61a98HaoEoC2HSzAMSI4JpUtUqNnhiIjIdxRXunlk6TYAfjO+N93iWrb0XkSkvTz47hZcNV7G9OzE1UNTzA5HROqoQNUx+bxAdf3113P06FHmzJlDXl4ew4YNY9myZQ2N0w8cOIDdfnIzwRMnTjBjxgzy8vKIi4tjxIgRfPXVVwwYoE9d5VQbDxUBMLhrjLmBiIjIKZ5avoNjZdX0SojgVxf1NDscEZFGsrbms2J7AY4gGwumDFQjZhE/UVzp5nh5NaACVUfTLk3SZ86cedolfStXrmz0+Omnn+bpp59uh6jECjYeKgZgSDcVqERE/Mnm3GL+Z/V+AOZfM4iQYPsZrhARaT+V1R4efHcLADdf1JPeXaJMjkhE6u07Xrt5UpcoJxFOv9vXTXxI7xYloG3KrS1QDe4Wa24g0qHk5uby85//nE6dOhEWFsbgwYNZv3692WGJ+A2v1+D+tzfjNeCqoSlc2Luz2SGJiDTy3yt3k1tUSUpMKHeM7212OCLyHQcLawtUaZ00e6qjUYFKAlZxpbthbbKW+El7OXHiBBdeeCEOh4MPPviArVu38uSTTxIXF2d2aCJ+4831B8k+WERESBD/7/L+ZofT4aiILtK8nGPl/OnTvQDMuWoA4SGaoSHiTw6eqAQgNV69KzsajcYSsLbUzZ7qFhdGfESIydFIR/HYY4+RmprK3/72t4Zj6enpJkYk4l9OlFfz2LLtANw1sS9JMdrAoj3VF9EvvfRSPvjgAxISEti1a5eK6CJ1DMNgzjubqfZ4uaRvApkDk8wOSUS+51Bdgaq7ClQdjgpUErA21hWohmp5n7Sjd999l8zMTK677jo+/fRTunbtyq9//WtmzJhhdmgifuHxD3dwosJNv8Qopo1NMzucDkdFdJHmfbA5j893HSMkyM68q9UYXcQfnZxBFWZyJNLeVKCSgLXpUH3/KS3vk/azd+9eXnjhBWbNmsXvf/971q1bxx133EFISAjTpk075XyXy4XL5Wp4XFJSAoDb7cbtdjf7s+qfP9N5gcaqeYF1c2tpXt8eKuYf6w4AMOfKfuD14PZ6fB7f2WrN6xUor6mK6CKnV+6qYf57WwG49ZKepGl3MBG/VN+DSjOoOh4VqCRgfXuoCIAh6j8l7cjr9TJy5EgeeeQRAIYPH87mzZt58cUXmyxQLVy4kHnz5p1yfPny5YSHt+wf3aysrHML2k9ZNS+wbm7N5eU14KlNQRiGjfM7ezm2dTVLt7ZjcOegJa9XRUVFO0Ry7lREP3dWzQusm1tL81qUtZO8kiq6xYUx46Iefv/nYMUiusiZeLxwuLgKUIGqI1KBSgLSiYrqhrXJA1WgknaUnJzMgAEDGh3r378///rXv5o8f/bs2cyaNavhcUlJCampqUyaNIno6Ohmf5bb7SYrK4uJEyficDjOPXg/YdW8wLq5tSSv19Ye5GD5NiKdwTx784V0jnS2c5St15rXq75w4+9URG87Vs0LrJtbc3nlVcBfNwYBNi7rUsbHWR+2X2DnyEpFdJEzOVFd+6GXM9hOQpT/v5eQtqUClQSk7XmlQG1VPSbMOjeB4v8uvPBCduzY0ejYzp076dGjR5PnO51OnM5T/3F1OBwtLmC05txAYtW8wLq5nS6v42UunvpoNwC/ndSX5LjI9g7tnLTk9QqU11NF9HNn1bzAurmdKS/DMPjF39bjNU7ww34J3PPz4SZE2XpWLKKLnMmxqtq+cN3jw9UjrgNSgUoC0va8MgAykqJMjkQ6mrvuuouxY8fyyCOP8B//8R+sXbuWl156iZdeesns0ERM89iy7RRXuhmQHM3PL2i6WCvtQ0X0tmPVvMC6uZ0ur3eyc1mTcwJnsJ151wwKuNytVEQXOZPjdavOtbyvY7KbHYDI2dhWN4Oqf3Lzn+6KtLXzzz+ft956i9dff51BgwaxYMECFi1axNSpU80OTcQUG/af4M31hwBYMGUgwUF6a2Gmu+66i9WrV/PII4+we/duXnvtNV566SVuv/12s0MTMUVJlZuHlmwDYOalvUnVTa+IXzteN4NKf1c7Js2gkoC0QwUqMdGVV17JlVdeaXYYIqbzeA0eeHszAP8xshsjesSbHJHUF9Fnz57N/PnzSU9PVxFdOrSns3ZytNRFWqdwbrmkp9nhiMgZHK/tj64ZVB2UClQScDxe2FVQu8RvgApUIiKm+fua/Ww9UkJ0aDD3Ts4wOxypoyK6SK2th0t45at9AMy7ZhDO4CBzAxKRMzrmOtmDSjoezcOXgJNfBW6PQaQzmG5xYWaHIyLSIR0rc/HEh7W9jn43OYNOAbBrn4h0HF6vwZx3NuM14LJBSVzSN8HskESkBRpmUHVSgaojUoFKAs7h8tqqekZSFHa7dnYQETHDox9sp7SqhoEp0fxsVHezwxERaeRfXx9i/f4ThIcE8cCVA858gYiYrrjSTaWn9v5OExE6JhWoJODkVtQVqJK1g5+IiBk27C/k/zbUN0YfRJA+LBARP1Jc4ebRD7YDcMf4PqTE6kZXJBAcOlEJQOfIEMJD1I2oI1KBSgLO4fLa/1eDdBGR9lfbGH0LANePTOW87nEmRyQi0tgTy7dzvLya3l0i+eWF6WaHIyItdKCwAoBUzZ7qsFSgkoBzuG4GlQpUIiLtr74xekyYg3sm9zM7HBGRRjYdKubvaw4AsOCaQYQE63ZHJFAcKqqdQaXlfR2XRmwJKMfLXJS4bdhstT2oRESk/Rz/TmP032b2U2N0EfErXq/B/e9sxjDg6qEpjOnVyeyQRKQVDhfVdkjvqmW5HZYKVBJQtueXAdA9LlzrkkVE2tkTWbsoraphUFc1RhcR//Pmhly+PVhEpDOY+6/ob3Y4ItJKuXUzqFJiQ02ORMyiO3wJKDvySgHolxRpciQiIh1LTin8a/NhAOZdrcboIuJfytzwZNYuAO6a2Jcu0brBFQk0mkEl7TKD6vnnnyctLY3Q0FBGjx7N2rVrmz3/n//8JxkZGYSGhjJ48GCWLl3aHmFKANhRN4OqX6IKVCIi7cXjNfi/nCAAfjKiGyN6qDG6iPiX9w7YKap0k5EUxbQxPcwOp0PRvZ60BcMwGnpQqUDVcfm8QPXGG28wa9Ys5s6dy9dff83QoUPJzMykoKCgyfO/+uorfvrTn3LzzTfzzTffMGXKFKZMmcLmzZt9HaoEgJ11Baq+ieo/JSLSXt5Yf4hD5TaiQoO577IMs8MREWnkmwNFrC6ova15aMoggoPUxaS96F5P2kpJZQ3lLg8AKTGaAdlR+Xz0fuqpp5gxYwbTp09nwIABvPjii4SHh/Pyyy83ef4zzzzD5MmT+d3vfkf//v1ZsGAB5513Hn/84x99Har4OY/XYFeBZlCJiLSnwvJqnvqodtnMneN701mN0UXEj9R4vMx9bxsAPx6ewsi0eJMj6lh0rydt5VBRBQCRwQZhIUEmRyNm8WmBqrq6mg0bNjBhwoSTP9BuZ8KECaxatarJa1atWtXofIDMzMzTni8dx/7j5bhqvDjsBt3jw80OR0SkQ3jiwx0UV9aQEm7ws/O7mR2OiEgj/7t6P9vySgkLMrhnUh+zw+lQdK8nbSn3RO3yvjh9Dtah+bRJ+rFjx/B4PCQmJjY6npiYyPbt25u8Ji8vr8nz8/Lymjzf5XLhcrkaHpeUlADgdrtxu93Nxlf//JnOCzRWzWtLbhEASWHg9dTgdlunQa9VX7PW5GW13EWsYOOhIv6x7gAAP0n3aNmMiPiVo6Uunly+E4Aru3vppBme7Ur3euawal77j9eulIl3GpbLzaqvmS/u9QJ+F7+FCxcyb968U44vX76c8PCWzbLJyspq67D8gtXy+uCgHbCTHG5YLrd6HTmvioqKdohERFrK6zWY884WDAOuHpJMr4iDZockItLIwqXbKHXVMLhrNGMTC80OR3xA93qnZ7W8vtxXe68X57RebvU6cl4tvdfzaYGqc+fOBAUFkZ+f3+h4fn4+SUlJTV6TlJTUqvNnz57NrFmzGh6XlJSQmprKpEmTiI6ObjY+t9tNVlYWEydOxOFwtCSlgGDVvJa+ng0UkBJuWC43q75mrcmr/hMxEfEP//f1IbIPFhEREsS9k/uy/nMVqETEf6zZe5x/f5OLzQYPXtmfQxu/NDukDkf3euawal5LXs+GIwV0cupeL1D44l7PpwWqkJAQRowYwYoVK5gyZQoAXq+XFStWMHPmzCavGTNmDCtWrODOO+9sOJaVlcWYMWOaPN/pdOJ0njqd1+FwtPjFb825gcRqee0qKAcgOdx6udXryHlZMW+RQFVc6eaxD2qXZ9w5oS9dorRsRkT8h9vjZc47WwC44fzuDOkWw6GNJgfVAelez1xWy+tIce1Szjin9XKr15HzamnePl/iN2vWLKZNm8bIkSMZNWoUixYtory8nOnTpwNw44030rVrVxYuXAjAf/3Xf3HJJZfw5JNPcsUVV/CPf/yD9evX89JLL/k6VPFjVW4P+47XFqhSwg2ToxERsbans3ZyvLyaXgkRTBubBobH7JBERBq88tU+duSXEhfu4J7MfmaH06HpXk/ayqETtUvA4p261+vIfF6guv766zl69Chz5swhLy+PYcOGsWzZsobmeAcOHMBuP9l0dezYsbz22mvcf//9/P73v6dPnz68/fbbDBo0yNehih/blV+G14C4cAdRjhqzwxERsawdeaX8z+r9ADx49UBCgu243SpQiYh/yCuu4ums2sbo912WQVxEiOUaDwcS3etJW6ioruFERe3fY+3i17G1S5P0mTNnnnaa58qVK085dt1113Hdddf5OCoJJNvzates9kuMxGarNDkaERFrMgyDue9uxuM1mDwwiR/0STA7JBGRRh5aspXyag/ndY/luhGpZocj6F5Pzl3uidr7u0hnMOHBmozQkWm/aAkI2/NKAeibGGVyJCIi1rVk0xFW7y3EGWzn/13R3+xwREQa+XL3Md7feAS7DRZMGYTdbjM7JBFpA4eKagtU3WJDTY5EzKYClQSEbUdqZ1BlJKlAJSLiCxXVNTyyZBsAt43rRWp8y7bvFhFpD9U1Xh54ZzMAv7igBwNTYkyOSETayqG6GVQpsWEmRyJmU4FK/J5hGN8pUEWaHI2IiDW9sHIPh4ur6Bobxq2X9DI7HBGRRv7yxV72Hi2nc6STWZPUGF3ESuqX+HXVDKoOTwUq8XsFpS5OVLix26BPFxWoRETa2oHjFfzps70APHBlf0IdQSZHJCJyUm5RJc+t2A3A7y/PICbMetu0i3RkB+t28OsapxlUHZ0KVOL3ttbNnuqZEKmbJhERH3hoyVaqa7xc2LsTmQOTzA5HRKSR+e9todLtYVR6PD8a3tXscESkjR0qrC1QdY9Te4GOTgUq8Xv1y/v6J0ebHInIqR599FFsNht33nmn2aGInJXPdh5l+dZ8guw2HrxqIDabmg6LiP/4ZEcBH26pHaMWXDNIY5SIBR2oK1B10wyqDk8FKvF724/U7uCnBunib9atW8ef/vQnhgwZYnYoImfF7fEy770tANw4pgd9tFOq5aiILoGsyu3hwXdrx6hfXphGP70XFLGckio3JyrcgApUogKVBID6GVQDNINK/EhZWRlTp07lz3/+M3FxcWaHI3JWXvlqH3uOlhMfEcKdE/qaHY60MRXRJdC9+Oke9h+vIDHayX9pjBKxpIN1s6fiI0KICg02ORoxm34DxK9VuT3sPVYOaImf+Jfbb7+dK664ggkTJvDQQw+d9jyXy4XL5Wp4XFJSW3B1u9243e5mf0b982c6L9BYNS8IrNyOl7lY9NEuAGZN6E148OnjDqS8WqM1eQVa7t8tojc3Ron4qwPHK/jvlXsAuP+KAUQ6ddsiYkX1BarUePWfEhWoxM/tLijD4zWIDXeQGO2kpqbG7JBE+Mc//sHXX3/NunXrznjuwoULmTdv3inHly9fTnh4y/4hzsrKanWMgcCqeUFg5PaPPXbKXHa6RRhE5G9k6dKNZ7wmEPI6Gy3Jq6Kioh0iaTsqop89q+YFgZObYRjMeWcT1TVexvaKJ7N/52ZjDpS8WsvKRXSRevX9p7qrQCWoQCV+rn4Hv/5J0WqKKX7h4MGD/Nd//RdZWVmEhoae8fzZs2cza9ashsclJSWkpqYyadIkoqObnxXodrvJyspi4sSJOBzW2VLbqnlB4OS25XAJq1evBuCJn45iZI/ml6kGSl6t1Zq86gs3gUBF9LZh1bzA/3PbVGhj5c4ggmwG46IK+OCDD1p0nb/ndbasWEQXqXewsBKA7vHqPyUqUImf0w5+4m82bNhAQUEB5513XsMxj8fDZ599xh//+EdcLhdBQUENzzmdTpxO5ynfx+FwtPhGvzXnBhKr5gX+nZthGDz8wQ4MA64emsKY3l1afK0/53UuWpJXoOStIvq5s2peEBi5VVZ7ePy5L4EqZvygJ9Mn9jnjNYGQ19mwahFd5Ls0g0q+SwUq8WtbDtcXqLRri/iH8ePHs2nTpkbHpk+fTkZGBvfee2+j4pSIP3p/4xHW7TtBqMPOfZdlmB2OtDEV0duOVfMC/87tmY/3kltURdfYMO6Y0BeHo+W3K/6c17mwUhFd5PvUg0q+SwUq8Vser8GW3GIAhqbGmhuMSJ2oqCgGDRrU6FhERASdOnU65biIv6ms9rBw6TYAfj2uNymxmk5vNSqiSyDbe7SMlz7bC8ADVw4gPES3KiJW5vEaHDpRv8RPBSpRgUr8WM6xMsqrPYQ5guiVEGl2OCIiAe9Pn+3hcHHtzIRbLu5pdjjiAyqiS6AyDIO5726h2uNlXL8EMgcmmh2SiPhYfkkV1R4vwXYbyTFheD3aEKujU4FK/NbGQ7WzpwZ1jSbIrgbp4r9WrlxpdggiZ3S4qJIXP63dsn325RmEOjSTRkT8xweb8/h81zFCgu08eNVAbY4j0gHU95/qFhdGkN2G12NyQGI6FajEb9UXqAZ3jTU3EBERC3hs2Xaq3F5GpcVzxeBks8ORdqQiuvi7clcN89/bCsBtl/QirXOEyRGJSHs4oP5T8j12swMQOZ2Nh4oAGNItxtxAREQC3Ib9J3gn+zA2G8y5aoBmJoiIX3l2xS7ySqpIjQ/jtnG9zA5HRNrJIRWo5HtUoBK/VOPxNuzgpwKViMjZ83oN5r9fOzPhuhHdGNRVY6qI+I9d+aX89YscAOZdPVDLj0U6kPoZVGqQLvVUoBK/tKugDFeNlyhnMGmdNM1bRORsvZ2dy7cHi4gICeK3mf3MDkdEpIFhGMx5Zws1XoMJ/RP5YYYao4t0JPtVoJLv8WmBqrCwkKlTpxIdHU1sbCw333wzZWVlzV4zbtw4bDZbo69bb73Vl2GKH9rU0CA9BrsapIuInJWK6hoeW7YdgNt/2JsuUaEmRyQictJ7G4+wau9xnMF25l41wOxwRKSd5RwrByBdfeekjk+bpE+dOpUjR46QlZWF2+1m+vTp3HLLLbz22mvNXjdjxgzmz5/f8Dg8XBXVjmZjbhGg5X0iIufixU/3kl/ioltcGL+8MN3scEREGpRWuXmobvnxzEt7qweNSAdzoryaogo3gFbMSAOfFai2bdvGsmXLWLduHSNHjgTgueee4/LLL+cPf/gDKSkpp702PDycpKQkX4UmAaBhBz8VqEREzsrhokpe+mwPAL+/vL/6uoiIX3nmo10UlLpI6xTOjIt7mh2OiLSzvXWzp1JiQgkL0XsUqeWzJX6rVq0iNja2oTgFMGHCBOx2O2vWrGn22r///e907tyZQYMGMXv2bCoqKnwVpvihiuoattY1SB+WGmtuMCIiAerxZdupcnsZlRbPZYP0oY+I+I8deaX87at9ADyoxugiHVLD8r4EzZ6Sk3w2gyovL48uXbo0/mHBwcTHx5OXl3fa6372s5/Ro0cPUlJS2LhxI/feey87duzg3//+d5Pnu1wuXC5Xw+OSktrChtvtxu12Nxtj/fNnOi/QBHpe6/Yep8ZrkBwTSmKko1EegZ7b6Sgv6+UuYqbsg0W8nX0Ymw0euHIANpt6+YmIfzAMgwfe2YzHa5A5MJFx/bqc+SIRsZycY7W9qdV/Sr6r1QWq++67j8cee6zZc7Zt23bWAd1yyy0N/z148GCSk5MZP348e/bsoVevXqecv3DhQubNm3fK8eXLl7e4d1VWVtZZx+vPAjWvDw7aATspjgqWLl3a5DmBmtuZdOS8NFNSpG0YhsGCur4uPx7eTUulRcSvvJN9mLU5hYQ67DxwpRqji3RUe4/WzqDq2TnS5EjEn7S6QHX33Xdz0003NXtOz549SUpKoqCgoNHxmpoaCgsLW9VfavTo0QDs3r27yQLV7NmzmTVrVsPjkpISUlNTmTRpEtHR0c1+b7fbTVZWFhMnTsThcLQ4Jn8X6Hm9/vI64ATXjB3I5eenNnou0HM7HeV1cvajiJybJZuOsGH/CcIcQdwzuZ/Z4YiINCitcvPw0toPsmde2ptucWqMLtJRaYmfNKXVBaqEhAQSEhLOeN6YMWMoKipiw4YNjBgxAoCPP/4Yr9fbUHRqiezsbACSk5ObfN7pdOJ0Ok857nA4Wnyj35pzA0kg5lVd4yW7rkH6mF4Jp40/EHNriY6clxXzFmlvVW4Pj36wHYBbL+lFYnSoyRGJiJy06KNdHC11kd45Qo3RRTowr9doKFD11BI/+Q6fNUnv378/kydPZsaMGaxdu5Yvv/ySmTNncsMNNzTs4Jebm0tGRgZr164FYM+ePSxYsIANGzawb98+3n33XW688UYuvvhihgwZ4qtQxY9sPlxMldtLXLiD3l003VNEpDUWf7WPQycqSYoO5Rbd/ImIH9mRV8riusboc68agDNYjdFFOqojJVW4arw4gmx0jQ0zOxzxIz4rUEHtbnwZGRmMHz+eyy+/nIsuuoiXXnqp4Xm3282OHTsaes+EhITw0UcfMWnSJDIyMrj77ru59tpree+993wZpviRdTmFAIxMi1dTXxGRVjhW5uL5j3cD8LvMftqyWUT8hmEYzH1XjdFFpFZOXf+p7vHhBAf5tCQhAcZnu/gBxMfH89prr532+bS0NAzDaHicmprKp59+6suQxM+trStQjU6PNzkSEZHAsuijnZS6ahjUNZofDe9qdjgiIg3e33iE1XsLcQarMbqIfHcHP62YkcZUrhS/4fUarN9/AoDz01SgEhFpqd0Fpby+9iAA918xALtdM1BFxD+Uu2p4eEltY/Tb1RhdRIC9df2neqlBunyPClTiNzblFlNc6SbSGcyAlOZ3YBQRkZMeWbodj9dg4oBELujZyexwREQa/PGT3eSVVNE9Ply98UQEgL11S/zS1SBdvkcFKvEbn+woAOAHfTrj0FpkEZEW+WLXMT7eXkCw3cbsyzLMDkdEpEHOsXL+8vleAB64cgChDvXGExEadvBTgUq+T1UA8Ruf7DgKwKVqnCki0iIer8FDS7YC8PMLetAzQb0cRMR/LHh/K26Pwbh+CUzor/d3IgJVbg+HTtRukqb3LfJ9KlCJXzhW5mLjoSIALumXYG4wIiIB4l9fH2J7XinRocH81/g+ZocjItLg4+35fLy9AEeQjQeuHKDdmS2msLCQqVOnEh0dTWxsLDfffDNlZWXNXjNu3DhsNlujr1tvvbWdIhZ/sbugDK8BceEOOkeGmB2O+Bmf7uIn0lKf7TyKYcDAlGgSo0PNDkdExO9VVNfwhw93APCbH/YhLkJv8kTEP7hqPMx/r3Z25y8vTKeXZklYztSpUzly5AhZWVm43W6mT5/OLbfc0uwO7gAzZsxg/vz5DY/Dw9U0v6PZmV8KQN/EKBWu5RQqUIlf0PI+EZHW+fNnORSUukiND+PGsT3MDkdEpMHfvtzHvuMVJEQ5+Y1md1rOtm3bWLZsGevWrWPkyJEAPPfcc1x++eX84Q9/ICUl5bTXhoeHk5SU1F6hih/aUVeg6pcUZXIk4o+0xE9MV+Px8tnOugJVhpb3iYicSUFJFX/6bA8A907OwBmsxsMi4h8KSqt4bsUuoHZ8inTq83CrWbVqFbGxsQ3FKYAJEyZgt9tZs2ZNs9f+/e9/p3PnzgwaNIjZs2dTUVHh63DFz+zKr10K2jdRBSo5lf7FENNt2H+C4ko3seEOhqXGmR2OiIjfeyprJxXVHoZ3j+WKwclmhyMi0uCJZTsor/YwNDWWHw/vanY44gN5eXl06dJ41UNwcDDx8fHk5eWd9rqf/exn9OjRg5SUFDZu3Mi9997Ljh07+Pe//33aa1wuFy6Xq+FxSUkJAG63G7fb3Wyc9c+f6bxAE+h57cirfQ17dgo7JYdAz+10lFfLc1eBSkz37reHAZjQP5Egu9Yhi39buHAh//73v9m+fTthYWGMHTuWxx57jH79+pkdmnQQ2/NKeHP9QQDuv6K/+jeIiN/YeKiIf244BMDcqwZg1/u6gHLffffx2GOPNXvOtm3bzvr733LLLQ3/PXjwYJKTkxk/fjx79uyhV69eTV6zcOFC5s2bd8rx5cuXt7h/VVZW1tkF7OcCMa8qD+QW1ZYg9n27iqNbmz4vEHNriY6cV0tnS6pAJaaqrvGyZNMRAKYM06ds4v8+/fRTbr/9ds4//3xqamr4/e9/z6RJk9i6dSsRERFmhycdwCNLt+M14PLBSYzoEW92OCIiABiG0dAY/UfDu3Jed82KDzR33303N910U7Pn9OzZk6SkJAoKChodr6mpobCwsFX9pUaPHg3A7t27T1ugmj17NrNmzWp4XFJSQmpqKpMmTSI6OrrZ7+92u8nKymLixIk4HI4Wx+XvAjmv7INFsHYtiVFOrrtm0inPB3JuzVFeJ2c/nokKVGKqz3cdpajCTedIJ2N6dTI7HJEzWrZsWaPHixcvpkuXLmzYsIGLL77YpKiko/hs51E+23kUR5CNeydnmB2O+CHN8hSzLNl0hPX7TxDmCOKeyfp9C0QJCQkkJJy5H+yYMWMoKipiw4YNjBgxAoCPP/4Yr9fbUHRqiezsbACSk0+/VN3pdOJ0Ok857nA4Wnyj35pzA0kg5rX3eCUAfZOimo09EHNriY6cV0vzVpN0MdU72bXL+64amqzlfRKQiouLAYiP10wW8S2P1+CRpbVLK35xQRo9OmnGnpyqfpbn6tWrG7Z/nzRpEuXl5WaHJhZW5fawcOl2AP7zkp4kx4SZHJH4Uv/+/Zk8eTIzZsxg7dq1fPnll8ycOZMbbrihYQe/3NxcMjIyWLt2LQB79uxhwYIFbNiwgX379vHuu+9y4403cvHFFzNkyBAz05F2tCNPDdKleZpBJaYpd9WQtTUfgGu0vE8CkNfr5c477+TCCy9k0KBBTZ6j5p6nsmpe4Nvc/rnhENvzSokJC+a2i9Pa9c/Pqq+ZL5p7mk2zPMUMf/0ih9yiSpJjQvnPi5teqiXW8ve//52ZM2cyfvx47HY71157Lc8++2zD8263mx07djT0nQkJCeGjjz5i0aJFlJeXk5qayrXXXsv9999vVgpigp35pQD0U4FKTkMFKjHNh1vyqHR7SOsUztBuMWaHI9Jqt99+O5s3b+aLL7447Tlq7nl6Vs0L2j43lwce/SYIsHFpFxdfrTTnz86qr1lbNvf0N2ea5aki+qmsmhf4JrfjZS7+e+VuAGZN6E2wzYvb7W2z798SVn3N/LmIHh8fz2uvvXba59PS0jAMo+Fxamoqn376aXuEJn6svkDVJzHS5EjEX6lAJaZ5ddV+AK49r5t2oZKAM3PmTN5//30+++wzunXrdtrz1NzzVFbNC3yX27Mf76bEvZfUuDAeuulCnMHtu0Lfqq+ZL5p7+pOWzPJUEf30rJoXtG1ub+61U+6ykxphEJybzdLD2W32vVvLqq+ZlYvo0nEUVVRTUFr7gUgfzaCS01CBSkzxzYETZB8sIiTIzk9Hdzc7HJEWMwyD3/zmN7z11lusXLmS9PT0Zs9Xc8/Ts2pe0La55RVX8Zcvagv6sy/vT2TYqb9P7cWqr1lbNvf0Jy2Z5aki+qmsmhe0fW67CspYvWYVYLDw+vMZnW5OP0arvmZWL6JLx7LlcO3vaGp8GJFOlSGkafrNEFP87ct9AFw1NIXOkebdbIm01u23385rr73GO++8Q1RUFHl5eQDExMQQFqamsNL2/rB8B5VuDyN7xHHZoJZv3y0dW0tneaqIfnpWzQvaLrcns3bj8RpMHJDIRX0T2yCyc2PV18yqRXTpWDbl1i45H9xVrV3k9LSLn7S7/JIqlm46AsD0C9PMDUaklV544QWKi4sZN24cycnJDV9vvPGG2aGJBW3OLeZfXx8C4P9d0V/LoeWMDMNg5syZvPXWW3z88cdnnOUpcrZW7TnOiu0FBNlt3HdZhtnhiIifqy9QDVKBSpqhGVTS7l5dtY8ar8H5aXEaoCTgfLfhp4gvGYbBQ0u2Yhi1s02Hd48zOyQJAJrlKe3B6zVY+ME2AH42qju9EtTwWESat1kzqKQFfDaD6uGHH2bs2LGEh4cTGxvbomsMw2DOnDkkJycTFhbGhAkT2LVrl69CFBMcL3OxuG55380X6VNdEZHTWb41n9V7CwkJtnPv5H5mhyMBQrM8pT0s2XSEjYeKiQgJ4o7xfcwOR0T8XHGlm/3Haxv5D0pRgUpOz2cFqurqaq677jpuu+22Fl/z+OOP8+yzz/Liiy+yZs0aIiIiyMzMpKqqyldhSjt7YeUeyqs9DO4aQ+ZA9VIREWlKdY2XhUtrZyfM+EE63eJatpuaiGEYTX7ddNNNZocmFlFd4+WJD3cA8J+X9CIhSr1ERaR5W+pmT3WLCyMuIsTkaMSf+WyJX/2WxYsXL27R+YZhsGjRIu6//36uueYaAF599VUSExN5++23ueGGG3wVqrSTw0WVvLq6dieq32b2Uy8VEZHTeHXVPvYdryAhyslt43qbHY6ISIPX1x7gQGHt+PSrH2g2vIicmRqkS0v5TZP0nJwc8vLymDBhQsOxmJgYRo8ezapVq0yMTNrKMx/torrGy6j0eC7u09nscERE/NLxMhfPrKhd3v7bSX21FbOI+I0yVw3P1o1Pd07oQ3iIxicROTM1SJeW8pt/VeqbeCYmNt6iNjExseG5prhcLlwuV8PjkpISANxuN263u9mfWf/8mc4LNP6Y1zcHinhzw0EAZo3vRU1NzVl9H3/MrS0oL+vlLnK2nszaSWlVDQNTovnJiFSzwxERafDnz/ZyvLyanp0j+I+RGp9EpGXqG6QP6aYClTSvVQWq++67j8cee6zZc7Zt20ZGRvttNbtw4cKG5YTftXz5csLDW9azIysrq63D8gv+kleNF/6wMQjDsDEqwUv+llUs3XJu39NfcmtrHTmvioqKdohExL9tOVzM62sPADD3qoEE2bUUWkT8w9FSF3/+fC8Av8vshyPIbxZiiIgfK6lys08N0qWFWlWguvvuu8/YZLNnz55nFUhSUm3D7Pz8fJKTkxuO5+fnM2zYsNNeN3v2bGbNmtXwuKSkhNTUVCZNmkR0dHSzP9PtdpOVlcXEiRNxOBxnFbc/8re8Xvh0L0cqdxMX7uCPv7qQuPCzb4znb7m1FeV1cvajSEdlGAbz39uKYcCVQ5IZlR5vdkgiIg2e+3gXFdUehqbGMnmQNroRkZbZrAbp0gqtKlAlJCSQkJDgk0DS09NJSkpixYoVDQWpkpIS1qxZ0+xOgE6nE6fz1N1DHA5Hi2/0W3NuIPGHvDbnFvPHlbWfts25agBdYiLa5Pv6Q26+0JHzsmLeIq3x3sYjrMkpxBlsZ/bl/c0OR0Skwf7j5by2pnZ2532TM7TRjYi02IZ9JwAY2i3W3EAkIPhsbu6BAwfIzs7mwIEDeDwesrOzyc7OpqysrOGcjIwM3nrrLQBsNht33nknDz30EO+++y6bNm3ixhtvJCUlhSlTpvgqTPGhkio3t7/2NdU1Xib0T2TKsK5mhyQi4pfKXDU8vGQrALdf2puusWEmRyQictKTy3dS4zW4pG8CY3p1MjscEQkga/cVAmhmuLSIz5qkz5kzh1deeaXh8fDhwwH45JNPGDduHAA7duyguLi44Zx77rmH8vJybrnlFoqKirjoootYtmwZoaGhvgpTfMQwDGb/axP7j1fQNTaMP1w3RJ+2iYicxnMf7yK/xEWPTuHccvHZLZUXEfGFzbnFvPvtYQDumdzP5GhEJJDUeLx8vb92BpUKVNISPitQLV68mMWLFzd7jmEYjR7bbDbmz5/P/PnzfRWWtJNFH+1iyaYjOIJs/PFnw4k9h75TIiJWtruglJe/yAFg7lUDCHUEmRyRiMhJjy3bDsA1w1IYqAbHItIKW4+UUF7tITo0mH6JUWaHIwFA229Im/vH2gM8s2IXAPOuHsTw7nEmRyQi4p8Mw+D3b23G7TGY0L8LP8xINDskEZEGn+86yue7jhESZOe3kzR7SkRaZ21O7fK+89PisWtnYmkBFaikTS3ddIT/9/ZmAGZe2pufje5uckQiIv7rnxsOsTankDBHEA9ePdDscEREGni9Bo9+UDt76ucX9CA1PtzkiEQk0DQUqLS8T1rIZ0v8pON5+5tcZr2ZjdeAn4zoxt2T+podkoiI3yosr2bh0m0A3DWxD93idPMnIv7j3W8Ps+VwCVHOYGb+sLfZ4YhIgPF6DdapQbq0kmZQSZt4ddU+7qorTl03ohuPXaum6CIizZn33hZOVLjJSIpi+oXpZocjItKgyu3h8breU7eO60V8hHqJikjr7DlaxokKN6EOO4PUv05aSDOo5Jy4PV7mvbeF/119AICfX9Cd+VcP0hpjEZFmZG3N553sw9ht8Ni1Q3AE6fMiEfEff/0ih8PFVaTEhHLzRSqgi0jrralb3nde9zhCgvU+R1pGBSo5a7lFldz1j2zW7ivEZoN7J2fwnxf31MwpEZFmFFe4+X9vbQJgxsU9GZoaa25AIiLfcazMxQsr9wDwu8n9tLOoiJyVz3YeBWB0eieTI5FAogKVnJWlm44w+9+bKK50ExESxKIbhjNxgHafEhE5kwff20JBqYuenSO4a4J69YmIf3ly+U7KXDUM7hrDNUO7mh2OiASgKreHz3cdA2B8/y4mRyOBRAUqaZW84irmvLOZ5VvzARjaLYZnfzqcHp0iTI5MRMT/vfvtYd76Jhe7DZ64bohmJoiIX9l0qJh/rKtt23D/Ff3VskFEzsqqPcepdHtIjgllYEq02eFIAFGBSlqkyu3hr1/k8N+f7Ka82kOw3catl/TijvF9tKZYRKQFcosqG5b2zfxhH0b00I42IuI/vF6Due9uxjDgmmEpjO6pZTkicnY+2lY7meGHGV3U/kVaRQUqaVZ1jZd/fX2IP368m9yiSgCGd49l4Y8Hk5GkariISEu4PV7u/Mc3lFbVMCw1lju0ZbuI+Jl/f5PL1weKiAgJ4veX9zc7HBEJUIZhsGJbAQAT1AJGWkkFKmlSuauGf64/yJ8/z2koTCXHhHLv5AyuHpqiKd8iIq2wcOl21u07QZQzmEXXDyNYu/aJiB85XubikaXbAPjN+D4kRoeaHJGIBKoth0vIK6kiPCSIMZqJKa2kApU0svdoGa+vPcAb6w5SUlUDQOdIJ7eN68XU0d3VL0VEpJXe+/YwL3+ZA8CT/zGUtM7q2Sci/mXee1spLK8mIymKX16YbnY4IhLA6pf3XdS7s+4dpdVUoBJKqtws3XiEf3+Ty9qcwobjaZ3C+eVF6Vw3IpWwEA0uIiKtlX2wiN/937cA3DauF5MGJpkckYhIYx9tzefdbw9jt8HjPxmi3qIictYMw+Ddbw8DWt4nZ0cFqg7qeJmLj7cXsGxzHp/vOka1xwuA3QaX9uvCz0Z359J+XbSUT0TkLO0/Xs7Ni9dR5fZySd8E7p7Y1+yQREQaOVbm4vd1mzfMuLgnQ7rFmhuQiAS01XsL2Xu0nIiQIC4fnGx2OBKAVKDqIDxeg025xXy+8ygrdx7l6wMnMIyTz/dNjORHw7sxZXgKyTFh5gUqEiCef/55nnjiCfLy8hg6dCjPPfcco0aNMjss8RMFpS5u+tt6jpdXMzAlmuennqe+UyLiV7xeg7veyKag1EXvLpHcNUFFdBE5N39fsx+AKcO7EulUqUFaT781FlXjrV1akn2olDU5x1mTU0hpXU+pegOSo5k0MJErBifTJzHKpEhFAs8bb7zBrFmzePHFFxk9ejSLFi0iMzOTHTt20KVLF7PDE5MVuWDqX9ex73gFXWPD+NtN5+tNmoj4nf9euZvPdx0j1GHnv6eep14xInJOjpW5+HBLHgBTR/cwORoJVHrHbAEer0HOsXI25xazKbeYbw6cYNPBINxr1jY6L8oZzNjenfhBnwQuzehC11jNlBI5G0899RQzZsxg+vTpALz44ossWbKEl19+mfvuu8/k6MRM+49X8NyWII65aotT/7jlArpoNywxgWZ5SnOWb83nqaydACy4ZhB99UGliJyjf64/hNtjMLx7LANSos0ORwKUClQBxDAM8ktc7C4oY2d+KTvzS9meV8r2vBKq3N7vnW0jNszByLR4zk+LY0yvTgxMiSFIPaVEzkl1dTUbNmxg9uzZDcfsdjsTJkxg1apVp5zvcrlwuVwNj0tKSgBwu9243e5mf9b0xevJORLEf+/9Cpvt5N/d7/8t/s5TDf9tqzvr5OPa/7Fhw2arfWyz2er+vy4Pmw27rfb/bXX/bbPVnhdksxFkrz0WZK/97yCbjaAgG8F2O8F2G8FBNoLtNkKC7DiC7IQEn/xyBtsJDbYT5ggi2G6QUwqbD50gOtxJpDOYSGdwwDfm/XLPce74x7eUuGx0iw3lf28eSVKU44yvcyCoz8EKuXxXa/IKpNw1y1Oas6vYxkv/3ITXgJ+N7s51I1PNDklEAlxltYf/WbUP0OwpOTcqUPkZwzA4WubiYGEFBworyDlWwf7j5ew9Wk7OsXLKXDVNXhfqsDMgOZrBXWMYlBJF0Z5spv14IiEhIe2cgYi1HTt2DI/HQ2Ji451JEhMT2b59+ynnL1y4kHnz5p1yfPny5YSHhzf7s7YcDOJEtQ0qys4taL8UzKLN6xofsRmEB0NYMIQHQ0SwQUQwRDkgKsQg2gHRDoNYJ8SEgMNP6lk1Xliea2f5IRsGNnpEGtzcq4xvv/qEb80Oro1lZWWZHYJPtCSvioqKdoikbWiWp5zOmpxC/rzDTrXHS+bAROZfPdDskETEAp5ZsYvDxVV0jQ3jyiFqji5nTwWqdlbmqiGvuIr8kiqOFFdxpKiSw8VV5BZVknuigkMnKnHVfH821ElBdhs9OoXTOyGSjKQo+iRGMSAlmrROEQ2zo9xuN0sPZzeacSEi5pg9ezazZs1qeFxSUkJqaiqTJk0iOrr56c9xfY+yau16Rpx3Hvbg7/UGMU49v/6QUbcDggEYxveO1z3wGmBg1P5//fkGeA0Dg9rmuQa1jz3e2nM8hoHXa1Djrb2uxuvF6wW3x0uN16DGY1Dj9eL2GFR7vLg9XlxuL9UeL64aLy63h0q3l8rqGo4Xl0Gwk4rqGirrZoDWGDZK3FDSMFGl+TGsU0QIKbGhdIsNIzU+jB7x4fToFE5ap3C6RDnbZQxck1PIvPe3saugHIApQ5O4KPQQl2dOxOFw+Pzntxe3201WVhYTJ3bcvOpnP/q79pzlmfnMF+QXBTE3+xOs9JbDMMDtPre8bHUzVk/OSqVupqmdkCA7ToedUEcQ4SFBRDqDiQ1zEBvuoEuUk6SYUFLrxrW27Av12tqDLFiynRqvjdFpsTx57SAMrwe319NmP8MsmuXZ/rk//PDDLFmyhOzsbEJCQigqKjrjNYZhMHfuXP785z9TVFTEhRdeyAsvvECfPn18H7D4zI68Uv7y+V4A5l09UP3s5Jz4rEB1NoPWTTfdxCuvvNLoWGZmJsuWLfNRlOfOMAzKqz0UllVzvNzF8br/P1ZWzdFSF8fKXBSUujha6qKgpIry6jO/CbDbIDmm9o1JeucIusdHkN45gl4JEXTvFI7z+zeqItJuOnfuTFBQEPn5+Y2O5+fnk5SUdMr5TqcTp9N5ynGHw3HGG+IxvRM4sdPgkoxEyxUFli5dyuWXj8PhcODxGpS5aiitclNSWUNxpZuiimoKK6rrxtZqjpa5OFrioqC0irySKqrcXo6X1z63KffUwkGkM5j0zhH07hJJ7y6R9Kn7/+7x4ee8m57b4+WLXcf402d7WL23EKgtls2/ZhATMzrxwQeHWvT6BqKOnFeg5N2eszwLioMor7FBjbWKArX8I694p0FyuEHXcOgWYdA90iA2hFYVzgoq4d39djadqB37RnT28pMux1iR9aGPojaPZnm2n+rqaq677jrGjBnDX//61xZd8/jjj/Pss8/yyiuvkJ6ezgMPPEBmZiZbt24lNFT9GgNRuauG2f/eSI3XIHNgIhMGJJ75IpFm+KxAdTaDFsDkyZP529/+1vC4qRs7X6iu8dbeHFU1vkkqqXLX3Sy5Ka6s5kS5m6LKaooq3JyoqH1c7Tn9jKemRDmDSYwJJbnuKykmjG6xYXSNCyM1LpykmNCA78UiYlUhISGMGDGCFStWMGXKFAC8Xi8rVqxg5syZ5gYXoILsNmLCHMSEOSDuzOcbhkFRhbt25mlRZcOS6P3HK9h3vJxDJyopc9WwqW7jiO8KCbKT1jmcnp0j6ZkQQY9O4aTGhZMcG0ZClJOIkKBTZl6VVtX+rI0Hi1m/v5CPthVQWF4NgCPIxn+MTOXuSf2Ijwix3Kf3Yn3nMsuzz3nFfP7Fl4wdO5bgYOtMyq+pqeGrr746q7y+O2O1dlZq7UxUr2E0zDR1180qrXJ7KK/2UFpVQ1GFm8KK2g83jxRXcfBEJaVVNRS6bBS6bGw5cfJndIlyMqRrNANTohmQEk3PzuF0jQ3DUVd8NwyDwgo36/ad4MMt+Xy4NR+3xyDIbuM349JJq9jJpEkddzZkIPHnWZ71he3Fixe36HzDMFi0aBH3338/11xzDQCvvvoqiYmJvP3229xwww2+ClV8ZFd+Kbf9/Wt2F5QRERLE3Ku0ZFjOnc/eTbR20KrndDqbnIXgC1P/uo5tuUHcs+6jZpfVtUSYI4j4iBA6RYbQKSKETpFOOkc66RwZQpfoULpEOWu/okO13bhIgJs1axbTpk1j5MiRjBo1ikWLFlFeXt7Q70V8y2azERcRQlxECIO6xpzyfHWNlwOF5ewuKGfP0TJ25Zey+2gZuwvKqHJ72Zlfxs78pvt6hQTbCQ8Jwhlsp8ZjNNxAfl/nyBCuHtqVX/0gnRTtiCp+pD1nefZJimFXOGSkxFquKLDX5LwMw6CwvJpdBWXsyCtly+FiNh4qZldBGQWlLj7afpSPth9tON9ugwhnMKGOIEqr3KdsnnNpvwR+f3l/0uJDWbp0Z4eeDRmIrDDLMycnh7y8PCZMmNBwLCYmhtGjR7Nq1arTFqjOZRny5Ge/4HhxEAu3fGqp1ieGYVBVZV5eXq9BqauGirr3R4lRTp65fggJEcHn/EGdlusGFl8sQ/a7SsnKlSvp0qULcXFx/PCHP+Shhx6iU6dOPvlZheXVlLptwMl/xCNCgogOcxAVGtzwiX50mIO48BBiwhzEhTuICQ8hLrz2WFxE7X+Hh/jdH6WI+Mj111/P0aNHmTNnDnl5eQwbNoxly5adsqRGzBESbKd3lyh6d2m8bbrXa5BbVMnuo2Xk1G08caCwgoMnKsgvrl2CXV3jpbqJDyyiQ4PJSIrmvB5xjO3VibG9Op3zUkERX9AsT2uw2Wx0inTSKdLJBT1Pvg+uqK5hy+ESvj1YxNbDJWw9UsK+4+VUub2UVtVQWnVyM520TuFMGpjE5YOTGZYaC1jv5kgCR15eHkCTy4/rn2vKuSxDzi0Mospjg2pXs+cFJv/IKyPGy8/7lJO/ZRVLt7Td9+3Iy3UDUVsuQ/arqsrkyZP58Y9/THp6Onv27OH3v/89l112GatWrSIoqOm+S+dSVX/sR/1Zs3o1Ey65iLjIMCKdQWd5w2H41T/4Vq3QgnVzU16Bl/vMmTN1sxdg7HYbqfHhpMaHc2m/U58vd9VwoqKaymoPrhovjiA7IcF2ukQ5idDMVwkgmuVpXeEhwZyfFs/5afENx+p3gC6rqqHK7SU8JIjk2FD1LJVWu++++3jssceaPWfbtm1kZGS0U0Tntgy566BCVq9ezejRF1huGfKaNeblZbPV9vqMqdvcoS1puW5g8cUy5Fb9Rvt60Pru1M7BgwczZMgQevXqxcqVKxk/fnyT15xLVR2gawRsW//FWcXr76xaoQXr5taR8wqkLdzFmiKcwSpEiSVolmfHYrPZ6BIVyvcmjYq02t13381NN93U7Dk9e/Y8q+9dv8Q4Pz+f5OTkhuP5+fkMGzbstNedyzLkod3jyd0Mw3rEW64ocHiL9fL6ro68XDcQteUy5Fa9E/floHW679W5c2d279592gLVuVTVVckMPFbNTXkFzhbuIiKBQLM8RaS1EhISSEhI8Mn3Tk9PJykpiRUrVjQUpEpKSlizZg233XabT36miASeVhWofDloNeXQoUMcP368UZX9+86lqn425wYSq+YF1s2tI+dlxbxFRERErOjAgQMUFhZy4MABPB4P2dnZAPTu3ZvIyEgAMjIyWLhwIT/60Y+w2WzceeedPPTQQ/Tp04f09HQeeOABUlJSGvrliYj4bC1DawetsrIy5s2bx7XXXktSUhJ79uzhnnvuoXfv3mRmZvoqTBEREREREWmFOXPm8MorrzQ8Hj58OACffPIJ48aNA2DHjh0UFxc3nHPPPfdQXl7OLbfcQlFRERdddBHLli0jNDS0XWMXEf/lswJVawetoKAgNm7cyCuvvEJRUREpKSlMmjSJBQsWNDlDSkRERERERNrf4sWLWbx4cbPnGIbR6LHNZmP+/PnMnz/fh5GJSCDzWYGqtYNWWFgYH374oa/CERERERERERERP2W57Yrqi14tabjsdrupqKigpKTEUv1vrJoXWDc35XXy7+z3P22zGo1R1s0LrJub8tIY1RT9XgQeq+amvDRGNUW/F4HHqrkpr5aPUZYrUJWWlgKQmppqciQicjZKS0uJiYkxOwyf0RglEtg0RomIP9MYJSL+7ExjlM2wWJnd6/Vy+PBhoqKisNlszZ5bUlJCamoqBw8eJDo6up0i9D2r5gXWzU151VbTS0tLSUlJwW63t1OE7U9jlHXzAuvmprw0RjVFvxeBx6q5KS+NUU3R70XgsWpuyqvlY5TlZlDZ7Xa6devWqmuio6Mt9YtSz6p5gXVz6+h5WfkTv3oao06yal5g3dw6el4ao5rW0X8vApFVc+voeWmMalpH/70IRFbNraPn1ZIxyrrldRERERERERERCQgqUImIiIiIiIiIiKk6dIHK6XQyd+5cnE6n2aG0KavmBdbNTXlJU6z652fVvMC6uSkvaYpV//ysmhdYNzflJU2x6p+fVfMC6+amvFrOck3SRUREREREREQksHToGVQiIiIiIiIiImI+FahERERERERERMRUKlCJiIiIiIiIiIipVKASERERERERERFTddgC1cMPP8zYsWMJDw8nNja2yXMOHDjAFVdcQXh4OF26dOF3v/sdNTU17RtoG0hLS8NmszX6evTRR80Oq9Wef/550tLSCA0NZfTo0axdu9bskM7Zgw8+eMprk5GRYXZYrfbZZ59x1VVXkZKSgs1m4+233270vGEYzJkzh+TkZMLCwpgwYQK7du0yJ9gAoTFKY5Q/0Bglp6MxSmOUP9AYJaejMUpjlNmsMj5B+45RHbZAVV1dzXXXXcdtt93W5PMej4crrriC6upqvvrqK1555RUWL17MnDlz2jnStjF//nyOHDnS8PWb3/zG7JBa5Y033mDWrFnMnTuXr7/+mqFDh5KZmUlBQYHZoZ2zgQMHNnptvvjiC7NDarXy8nKGDh3K888/3+Tzjz/+OM8++ywvvvgia9asISIigszMTKqqqto50sChMUpjlL/QGCVN0RilMcpfaIySpmiM0hjlD6wwPkE7j1FGB/e3v/3NiImJOeX40qVLDbvdbuTl5TUce+GFF4zo6GjD5XK1Y4TnrkePHsbTTz9tdhjnZNSoUcbtt9/e8Njj8RgpKSnGwoULTYzq3M2dO9cYOnSo2WG0KcB46623Gh57vV4jKSnJeOKJJxqOFRUVGU6n03j99ddNiDCwaIwKDBqjAofGqLalMSowaIwKHBqj2pbGqMBgxTHKiuOTYfh+jOqwM6jOZNWqVQwePJjExMSGY5mZmZSUlLBlyxYTIzs7jz76KJ06dWL48OE88cQTATV9tbq6mg0bNjBhwoSGY3a7nQkTJrBq1SoTI2sbu3btIiUlhZ49ezJ16lQOHDhgdkhtKicnh7y8vEavX0xMDKNHj7bE62cWjVH+Q2NUYNMY5Rsao/yHxqjApjHKNzRG+Q8rj1FWH5+g7ceo4LYMzkry8vIaDVhAw+O8vDwzQjprd9xxB+eddx7x8fF89dVXzJ49myNHjvDUU0+ZHVqLHDt2DI/H0+TrsX37dpOiahujR49m8eLF9OvXjyNHjjBv3jx+8IMfsHnzZqKioswOr03U/31p6vULtL9L/kRjlP/QGBXYNEb5hsYo/6ExKrBpjPINjVH+w6pjVEcYn6DtxyhLzaC67777TmlE9v2vQP4l/67W5Dpr1izGjRvHkCFDuPXWW3nyySd57rnncLlcJmchl112Gddddx1DhgwhMzOTpUuXUlRUxJtvvml2aOIDGqM0RgUajVEdi8YojVGBRmNUx6IxSmNUINH4dHYsNYPq7rvv5qabbmr2nJ49e7boeyUlJZ2yc0B+fn7Dc2Y7l1xHjx5NTU0N+/bto1+/fj6Irm117tyZoKCghj//evn5+X7xWrSl2NhY+vbty+7du80Opc3Uv0b5+fkkJyc3HM/Pz2fYsGEmRWUOjVGNaYwKPBqjrE1jVGMaowKPxihr0xjVmMaowGLF8QnafoyyVIEqISGBhISENvleY8aM4eGHH6agoIAuXboAkJWVRXR0NAMGDGiTn3EuziXX7Oxs7HZ7Q17+LiQkhBEjRrBixQqmTJkCgNfrZcWKFcycOdPc4NpYWVkZe/bs4Re/+IXZobSZ9PR0kpKSWLFiRcMgVVJSwpo1a067s4pVaYxqGY1R/ktjlLVpjGoZjVH+S2OUtWmMahmNUf7JiuMTtP0YZakCVWscOHCAwsJCDhw4gMfjITs7G4DevXsTGRnJpEmTGDBgAL/4xS94/PHHycvL4/777+f222/H6XSaG3wrrFq1ijVr1nDppZcSFRXFqlWruOuuu/j5z39OXFyc2eG12KxZs5g2bRojR45k1KhRLFq0iPLycqZPn252aOfkt7/9LVdddRU9evTg8OHDzJ07l6CgIH7605+aHVqrlJWVNfo0ICcnh+zsbOLj4+nevTt33nknDz30EH369CE9PZ0HHniAlJSUhn+E5FQaozRG+QONUVPMC9rPaYzSGOUPNEZNMS9oP6cxSmOU2awyPkE7j1FtsdVgIJo2bZoBnPL1ySefNJyzb98+47LLLjPCwsKMzp07G3fffbfhdrvNC/osbNiwwRg9erQRExNjhIaGGv379zceeeQRo6qqyuzQWu25554zunfvboSEhBijRo0yVq9ebXZI5+z66683kpOTjZCQEKNr167G9ddfb+zevdvssFrtk08+afLv07Rp0wzDqN1+9IEHHjASExMNp9NpjB8/3tixY4e5Qfs5jVEao/yBxig5HY1RGqP8gcYoOR2NURqjzGaV8ckw2neMshmGYbS+rCUiIiIiIiIiItI2LLWLn4iIiIiIiIiIBB4VqERERERERERExFQqUImIiIiIiIiIiKlUoBIREREREREREVOpQCUiIiIiIiIiIqZSgUpEREREREREREylApWIiIiIiIiIiJhKBSoRERERERERETGVClQiIiIiIiIiImIqFahERERERERERMRUKlCJiIiIiIiIiIipVKASERERERERERFT/X8iCxysuISGwQAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-overview\n", + "#| fig-cap: \"Overview\"\n", + "\n", + "plt.figure(figsize=(12, 8))\n", + "\n", + "rows = 3\n", + "columns = 4\n", + "\n", + "\n", + "plt.subplot(rows, columns, 1)\n", + "plt.plot(x, identity(x), label=\"Identity\")\n", + "plt.title(\"Identity\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 2)\n", + "plt.plot(x, sigmoid(x), label=\"Sigmoid\")\n", + "plt.title(\"Sigmoid\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 3)\n", + "plt.plot(x, tanh(x), label=\"Tanh\")\n", + "plt.title(\"Tanh\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 4)\n", + "plt.plot(x, selu(x), label=\"SeLU\")\n", + "plt.title(\"SeLU\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 5)\n", + "plt.plot(x, softmax(x), label=\"SoftMax\")\n", + "plt.title(\"SoftMax\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 6)\n", + "plt.plot(x, softsign(x), label=\"SoftSign\")\n", + "plt.title(\"SoftSign\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 7)\n", + "plt.plot(x, mish(x), label=\"Mish\")\n", + "plt.title(\"Mish\")\n", + "plt.grid(True)\n", + "\n", + "\n", + "plt.subplot(rows, columns, 8)\n", + "plt.plot(x, swish(x), label=\"Swish\")\n", + "plt.title(\"Swish\")\n", + "plt.grid(True)\n", + "\n", + "\n", + "plt.subplot(rows, columns, 9)\n", + "plt.plot(x, arctan(x), label=\"arctan\")\n", + "plt.title(\"ArcTan\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 10)\n", + "plt.plot(x, silu(x), label=\"silu\")\n", + "plt.title(\"SiLU\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 11)\n", + "plt.plot(x, gelu(x), label=\"gelu\")\n", + "plt.title(\"GeLU\")\n", + "plt.grid(True)\n", + "\n", + "plt.subplot(rows, columns, 12)\n", + "plt.plot(x, sqnl(x), label=\"SQNL\")\n", + "plt.title(\"SQNL\")\n", + "plt.grid(True)\n", + "\n", + "# Add a legend\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Define the activation functions as described previously\n", + "# Define x as input values\n", + "x = np.linspace(-10, 10, 200)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-identity\n", + "#| fig-cap: \"Identity\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "\n", + "plt.plot(x, identity(x), label=\"Identity\")\n", + "plt.title(\"Identity Function\")\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"f(x)\")\n", + "plt.grid(True)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-sigmoid\n", + "#| fig-cap: \"Sigmoid Functions\"\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, sigmoid(x), label=\"Sigmoid\")\n", + "plt.title(\"Sigmoid\")\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"f(x)\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-tanh\n", + "#| fig-cap: \"Hyperbolic Tangent\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, tanh(x), label=\"Tanh\")\n", + "plt.title(\"Tanh\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-arctan\n", + "#| fig-cap: \"Arc Tangent\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, arctan(x), label=\"Arctan\")\n", + "plt.title(\"Arctan\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-softsign\n", + "#| fig-cap: \"SoftSign\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "# 3. Hyperbolic Tangent Functions\n", + "plt.plot(x, softsign(x), label=\"SoftSign\")\n", + "plt.title(\"SoftSign\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-softmax\n", + "#| fig-cap: \"SoftMax\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "# 3. Hyperbolic Tangent Functions\n", + "plt.plot(x, softmax(x), label=\"SoftMax\")\n", + "plt.title(\"SoftMax\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-softplus\n", + "#| fig-cap: \"SoftPlus\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "# 3. Hyperbolic Tangent Functions\n", + "plt.plot(x, softplus(x), label=\"SoftPlus\")\n", + "plt.title(\"SoftPlus\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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TFBt+PsyKL/Zgs9ip3qACA19uTXCN69+PuyTdcKJOS0ujefPmfPLJJ3mOf/fdd/noo4/47LPP2Lx5Mz4+PvTq1YvMzMwbDra8GD58ODqdDp1Oh8lkolatWvz73/8u9LI5duwYFSpUYOfOnbnGrVmzBp1Ol+clazVr1mTmzJk3F7wQQpRDmalWfpu1kx0rTwDQskcN7n62OV6+Hi6O7CZ2fffp04c+ffrkOU4pxcyZM/nPf/7DvffeC8A333xD5cqVWbJkCYMHD77R2ZYbvXv3JjIyEqvVyrZt2xg2bBg6nY533nnH1aEJIcQt5VxcCss+iyblQiZGDz13PdqQeq0r56pnzUhxQXQldIw6NjaW+Ph4unfv7igLCAigbdu2bNy4Md9EbbFYsFgsjuHk5GQg+4zea+88ZrVaUUqhaRqaphUqLqWU429hpykJSik8PDwICQkBoFq1anTr1o2oqCimT5+Opmm8++67fPHFF8THx1O/fn1eeeUVHnzwwev2I2c4v+Xi6r5frTjWh6ZpKKVcetZ3zmezMHfHc2fSD/ci/Sgdh7cm8Ne8Q9itGn5BnvQa1YiKVX2c4j1/JpYNYx/ClGElvU8/vL19b3q+RVkeJZKo4+PjAahc2fkXSeXKlR3j8jJ9+nSmTp2aq3zlypW5LsMyGo2EhoaSmppKVlYWkP2Fn2m9/hd+xoXE69YpCk+TvkhnH1utVmw2m+OHyL59+9iwYQNhYWEkJyczY8YMFixYwIwZM6hTpw4bNmzg0UcfxcfHh44dO5KWlgZAenq6o40c6enpAKSkpOS6NlnTNDIzM3NN42opKTf+KzUrK4uMjAzWrl2LzWYrxqiKLioqyqXzLy7SD/ci/SgZSoOkGDOpx7J3bZuDbPg1P8emnX/Bziv1Lh5aT83F/6PRBdB0sPCjfxPUrP9Nzz/nu7ow3Oqs70mTJjFu3DjHcM6DtXv27JnredSZmZnExcXh6+uLp6cnAOlZNlq+U/ofhj2v9cDbo/CL0mQysWLFCqpXr47NZsNisaDX65k1axZms5kPPviAlStX0r59ewCaNWvGtm3b+O677+jTpw8+PtnX8eU8G/VqOT9o/Pz8co3T6/V4enoWy7O9i4NSipSUFPz8/G74MqvMzEy8vLzo1KmT43NQ2qxWK1FRUfTo0aPMP29X+uE+pB8lJyMli1WRB0g9lgRAi55htO4Xjl7v/D20eOojtPhlN55WSPKBPf1uZ+j4D4ulH0XZYCqRRB0aGgrA2bNnnW7tePbsWVq0aJHvdGazGbPZnKvcZDLlWjB2ux2dToder3dsObrqLl1Xx1AYOp2Orl27Mnv2bNLS0vjggw8wGo0MHDiQvXv3kp6eTq9evZymycrKomXLluj1V7bec/p/bSwFxZTXNK6Ss7v7ZmLKWR55fUZKmzvEUBykH+5F+lG8Eo4ns2xONKkXLZjMBroNb0idliFOdRIvnCHq6X403Z0BQGyYnppvfUTw6dRi60dR2iiRRF2rVi1CQ0NZtWqVIzEnJyezefNmnn766ZKYJQBeJgP7pvXKd7ymaaQkp+Dn71esycrLVPRjoz4+PtStWxeAr7/+mubNm/PVV1/RpEkTAH7//XeqVavmNE1eP2KulbO1nJSURGBgoNO4xMREAgICihyrEEKUBwc2nmHN9zHYbRoBIV70faoZFas632lsy8ofSHp9Gk3OgQZEt6/IfZ9GoTeaOHTaNRdS33CiTk1N5fDhw47h2NhYdu7cScWKFalRowZjx47ljTfeoF69etSqVYtXX32VqlWrMmDAgOKIO086na7AXdCapmHzMODtYXSbrUrI3ip8+eWXGTduHAcPHsRsNnPixAk6d+5c5Lbq1auHXq9n27ZthIeHO8qPHj1KUlIS9evXL87QhRDC7dntGusXHCZ6zUkAajatRPfHGmP2cs4Xi14fRs0F/1AtC1K8IP7RHgx+4SPAtSfD3XCi3rp1K127dnUM5xxbHjZsGHPnzuXf//43aWlpPPHEEyQmJnLHHXewfPlylx1HdHcDBw7kpZdeYs6cObz44ou88MILaJrGHXfcQVJSEuvXr8ff359hw4Y5pomJicn1g6Nx48aMHDmS8ePHYzQaadq0KXFxcUyYMIF27drRoUOH0u6aEEK4THpyFss/j+bM4ezj0bf3q8nt/Wqhu+p4dGrSRZY+3Yum21MBOF5VR/W3/ss97fK+BLm03XCi7tKli+PymrzodDqmTZvGtGnTbnQWtxSj0ciYMWN49913iY2NJTg4mOnTp3P06FECAwNp1aoVL7/8stM0Q4cOzdVOXFwcH374IW+//TYTJkzg+PHjhIaG0qNHD9588025N7YQ4pYRH5vE8jl7SEu04OFpoPuIRtRqHuxUZ+e6X0h4dRJN47Pz2e7b/en/6Up8/NznMKFbnfV9q5g7d26e5RMnTmTixIkAPP/88zz//PN51qtZsyaXLl3C398/3134r732Gq+99lpxhCuEEGXOvvWn+euHGDSbokKoN32eakqFUOfj0YvffYqweX8RlglpZogbcieDJn7uoojzJ4laCCFEuWG3aqz76SB7150GoHaLYLoNa4jHVcejM9KS+fXpnjT7J3t3eFxlHcHT3uS+zve5JObrkUQthBCiXEhLtLD882jijyaDDtreU5vbeoU7HY/eu3klJ14eS7NT2bu6o1v60PvTpfhXCMmvWZeTRC2EEKLMO3M4keWf7yE9OQuzt5EejzUmvEklpzr/+3AsIf+3gprpkOEBRx+8nYcmf+OiiAtPErUQQogySynF3nWnWffjQTS7omJVn+znR4dcue20JSOdxaN70HTDRfTA6WDwe/UVHuz5iOsCLwJJ1EIIIcokm9XO2h8Osn/DGQDqtArhrkcb4OF5JbXF7FzL4X8/TfMT2XdC3NPUi+6f/o8KwdXybNMdSaIWQghR5qRczGT5nGgSjqeg00G7++rQskcNp0tQf589iUpfLqF2GlhMcPCepjz05k8ujPrGSKIWQghRppw+dInln+8hI8WK2cdIr8ebENaoomO8NcvComd70XTtWfQK4iuBecI4HrpnlAujvnGSqIUQQpQJSil2rz7JhoWH0TRFpeq+9H2qKf5BXo46x/ZvJfqFYTQ/lr2re19DDzp/uoSgKrVcFfZNk0QthBDC7dmy7Kz5PoaYzfEA1Lu9Ml3/1QCTx5WHIq2c+zo+n8yjbgpkGeFAn/o8OH0RBmPZTnVlO3qRy7Fjx6hVqxY7duwo8JGiQghRViRfyGD5nD2cO5GCTq+jw/11aN4tzHE82m6zsWBsHxr/eRKjBgkVQI17hkEDn3Vx5MXDfR4hdYsYPnx4iT5BrCR06dIFnU6HTqfD09OT+vXrM3369ALv9X6tNWvWoNPpSExMzDVu7ty5uR7JmUOn07FkyZIbC1wIUeadPHCRBW9t5dyJFDx9TdzzfAtadL9y0ljckT38b0BLmv+RnaQP1DNRf/5iupSTJA2yRS0KadSoUUybNg2LxcKff/7JE088QWBgYIk+X1wIcetSSrFrVRwbFh1GKQiu4Uefp5riV/HKExj/nDcD04dfEZEENj3s7VmTgTP+V+Z3dV9LtqjdzJ49e+jTpw++vr5UrlyZf/3rX5w/f94xfvny5XTq1Inw8HCCg4Pp378/R44cybc9u93OY489RoMGDVi7di16vZ6tW7c61Zk5cybh4eFompZvO97e3oSGhhIeHs6IESNo1qwZUVFRjvEWi4UXX3yRatWq4ePjQ9u2bVmzZs2NLwghxC3LarET9dVe1i/MTtIN2oVy/4utHEnabrMxf1w/gt78iqAkuOAPZycNY/DMZeUuSUN5S9RKQVZawS9r+vXrFPVVhF3ABUlMTOSuu+6iZcuWbN26leXLl3P27FkeeughR520tDTGjh3L6tWriYqKQq/Xc9999+WZZC0WCwMHDmTnzp2sW7eOTp060b17dyIjI53qRUZGMnz48HyfxHU1pRTr1q3jwIEDeHh4OMrHjBnDxo0bmT9/Prt372bgwIH07t2bQ4cO3cQSEULcapLOZbDo3W0c2pqAXq+j0+D63DWsIcbLJ43FnzjErw+0ovnSo5jscLC2gRrfz6f7vya6OPKSU75+eljT4a2q+Y7WA4ElMd+XT4OHz/XrXcfHH39My5YteeuttxxlX3/9NWFhYRw8eJD69evzwAMPoGkaycnJ+Pv78/XXXxMcHMy+ffto0qSJY7rU1FT69euHxWJh9erVBARkP1t15MiRPPXUU7z//vuYzWa2b99OdHQ0v/zyS4Gxffrpp3z55ZdkZWVhtVrx9PTkueeeA+DEiRNERkZy4sQJqlbNXv4vvvgiy5cvJzIy0qk/QgiRnxP7LrDyy71Y0m14+Zno/URTqtYLdIxf9/MnaO99TINLYNfBnruqMvDDFeVyK/pq5WuLuozbtWsXq1evxtfX1/Fq0KABgGP39qFDhxg6dCgtWrQgMDCQmjVrAtnJ8mpDhgwhLS2NlStXOpI0wIABAzAYDCxevBjIPpGra9eujnby8/DDD7Nz507Wr19Pnz59eOWVV+jQoQMA0dHR2O126tev7xT7X3/9VeBueSGEgOw9ddtXHOe3WbuwpNuoXMufh15u45Skf5x4H/6TPybkElzyg5PjH2LwJ6vKfZKG8rZFbfLO3rrNh6ZpJKek4O/nV6jdvEWabzFITU3l7rvv5p133sk1rkqVKgDcfffd1KhRgw8//JC6desC0KRJE7Kyspzq9+3bl++++46NGzdy1113Oco9PDx49NFHiYyM5P7772fevHl8+OGH140tICDAMb+ffvqJunXr0q5dO7p3705qaioGg4Ft27ZhMBicpvP19b1u2/7+/qSlpaFpmtN6yTlD/OofGkKI8iUr08af3+znyPZzADTqWIVOgyMwmLK/Cy7En2DNM/fQbJ8FgCPhehr+90s6NGnvsphLW/lK1DpdwbugNQ1M9uw6xZmoi0mrVq1YtGgRNWvWxJjHr8QLFy4QExPDnDlzaN68Of7+/mzYsCHPtp5++mmaNGnCPffcw++//07nzp0d40aOHEmTJk349NNPsdls3H///UWK09fXl+eff54XX3yRHTt20LJlS+x2OwkJCdx5551F6zQQERGBzWZj586dtGrVylG+fft2AOrXr1/kNoUQ7i/xbDrL5kRz8XQaekP28ejGd155WMaG3yOxvPUujS6ApoPddwbz4MdRmDzMLoy69JVYtrLb7bz66qvUqlULLy8v6tSpw+uvv16ka2/Lq6SkJHbu3On0iouLY/To0Vy8eJEhQ4awZcsWjhw5wooVKxgxYgR2u50KFSpQqVIlvvjiC44ePcqff/7JuHHj8p3Ps88+yxtvvEH//v35+++/HeUNGzakXbt2TJgwgSFDhuDl5ZVvG/l58sknOXjwIIsWLaJ+/fo8/PDDPProo/z888/Exsbyzz//MH36dH7//Xen6aKjo536HR0dTePGjenZsyePPfYYq1atIjY2luXLl/PMM88waNAgqlUrO0+5EUIUzrHo8yx4eysXT6fhHeDBfeNbOSXpn14djNfEdwm9AEneEDumP0M+X3vLJWkowS3qd955h9mzZ/N///d/NG7cmK1btzJixAgCAgIcJyHdqtasWUPLli2dyh5//HG+/PJL1q9fz4QJE+jZsycWi4Xw8HB69+6NXq9Hp9Mxf/58nnvuOTp06EBERAQfffQRXbp0yXdeY8eORdM0+vbty/Llyx3HlR9//HE2bNjAY489dkN9qFixIo8++iivvfYa999/P5GRkbzxxhuMHz+eU6dOERQURLt27ejfv7/TdJ06dXIaNhgMZGVl8eOPPzJlyhSefPJJTp8+TfXq1bnvvvt49dVXbyg+IYR7Uppi67Jj/PNbLCgIrR1A7yeb4BOQnYATL5wh6pl+NN2VAUBsdT113vuEdi27uC5oF9OpEtrE7d+/P5UrV+arr75ylD3wwAN4eXnx3XffFaqN5ORkAgICSEpKwt/f32lcZmYmsbGx1KpVC09Pz3xacHb12dLFeoy6lBVHP15//XUWLFjA7t27izm6wiuOftzI56C4Wa1Wli5dSt++fTGZTC6JoThIP9xLeeyHsun4Y+4+Yndl3xuiSadq3PFQPQzG7P//ravmkzh1KtUSQAOi21fkvk+jMHsVz3lAN6O410dB+e1aJZatOnTowKpVqzh48CCQfUbz33//TZ8+fUpqlqIQUlNT2bNnDx9//DHPPlt+brEnhHBvifHpLHxnK7G7zqM36uj6rwZ0HhrhSNKL3hyO7oXsJJ3iBUee7MHgyPVukaRdrcR2fU+cOJHk5GQaNGiAwWDAbrfz5ptv8vDDD+c7jcViwWKxOIaTk5OB7F8yVqvVqa7VakUphaZpBd5R62o5Ow9ypiurbqYfo0ePZv78+dx7770MHz7cpcuhONaHpmkopbBarbnOOC8tOZ/Naz+jZY30w72Up35knDWyeMZOrBY7PoEe9Hi8ESE1/bBaraQmXyTq2f403Z4KwPGqOkJff5c+bXq5Vd+Le30UpZ0S2/U9f/58XnrpJd577z0aN27Mzp07GTt2LO+//z7Dhg3Lc5rXXnuNqVOn5iqfN28e3t7Ov6qMRiOhoaGEhYU53SFL3FqysrKIi4sjPj4em83m6nCEEFdRCpIPeZByJPv4s0cFG5VaZmIwZ6edxLhdVFk4n7D47OHtrXwwDxiPyVz+t6LT09MZOnRooXZ9l1iiDgsLY+LEiYwePdpR9sYbb/Ddd99x4MCBPKfJa4s6LCyM8+fP53mMOi4ujpo1axb62KRSipSUFPz8/BxPXimLpB9XZGZmcuzYMcLCwlx6jDoqKooePXqU+WOJ0g/3Udb7YUm3sfqbGE7svQhAoztD6fBAHfSG7F3d//vvaGrMX4dPJqSZ4cSgjtz90mxXhlyg4l4fycnJBAUFFSpRl9iu7/T09FwnCBkMhgJ3cZrNZszm3Kfem0ymXAvGbrej0+nQ6/WFPhEpZ94505VV0o8rcs6Gz+szUtrcIYbiIP1wL2WxHxdOp7JsdjRJ5zIwmPT4N0zjjofqYTKZyEhL5tene9LsnyQA4kJ1BE99k/s73+fiqAunuNZHUdoosUR999138+abb1KjRg0aN27Mjh07eP/992/4ciAhhBDu7/C2BFZ9sx+bxY5vRTM9Rzbin+i1AOz/J4pjk56n2ansHbnRLX3o/elS/CuEuDJkt1diiXrWrFm8+uqrPPPMMyQkJFC1alWefPJJJk+eXFKzFEII4SKaptj8y1G2rzgOQPUGFeg5sjFGsw6iYenHLxL67UpqpkOGBxx98HYemvyNi6MuG0osUfv5+TFz5kxmzpxZUrMQQgjhBjLTrER9tZcT+7KPR7foUYP2A2qjN+hJTU4iedFbtPonGT1wOhj8Xn2FB3s+4tqgy5Dyda9vIYQQper8yRSWfRZN8vlMjCY9dz3akHq3VwYgZudaDr/0NK3jss9H2dvUk26f/kaFYLktcFFIohZCCHFDDm05y5/f7Mdm1fAP8qTPU00Jqu4HwNLPXqbCF4upnQYWE8Tc3ZhBby10ccRlU9k9ZbgMGz58ODqdDp1Oh4eHB3Xr1mXatGnYbDbWrFnjGKfT6QgODqZv375ER0cXaR5dunRh7NixeY6rWbNmnockXnvtNVq0aFH0DgkhbimaXWP9wkOs/GovNqtGWKOKDJx0O0HV/bBmWfjhqS6Ef7iYwDSIrwg7hvXn/qk/uDrsMku2qF2kd+/eREZGYrFYWLp0KaNHj8ZkMtG+ffYzVmNiYvD39+f06dO89NJL9OvXj8OHD8vNXYQQLpWRmsWKL/ZyKuYSAK16h9P2ntro9TqO7d9K9LjhtIi1A7CvoQcdPlxA8o79rgy5zJMtahcxm82EhoYSHh7O008/Tffu3fn1118d40NCQggNDaVVq1aMHTuWuLg4pxvFbNy4kc6dO+Pl5UVYWBjPPfccaWlpruiKEOIWce5ECgve2sqpmEsYzQZ6jWpC+wF10Ot1rJz7Oqce/Rd1Y+1kGWH33fUZsGAbQVVquTrsMq9cbVErpciwZeQ7XtM0MmwZGK3GYr1RiJfR66bvEObl5cWFCxdylSclJTF//nwAx9b0kSNHGDhwIK+//jpff/01586dY8yYMYwZM4bIyMibikMIIfISs+kMq7+PwW7VCAjxos9TTalU1Re7zcaCsX1o/OdJjBokVAA17hkGDcx+6I/mRvfrLqvKVaLOsGXQdl7bUp/v5qGb8Tbd2L1plVKsWrWKFStWOD3Nqnr16gCOreR77rmHBg0aAPD222/z4IMP8vzzz6PX66lXrx4fffQRnTt3Zvbs2S67laYQovyx2zU2LDzM7tUnAQhvWokeIxph9jYRd2QP254fQvPD2ffZP1DPRLuPf6JKeANXhlzulKtEXZb89ttv+Pr6YrVa0TSNoUOH8tprr7FlyxYA1q1bh7e3N5s2beKtt97is88+c0y7e/dudu/ezcKFV86gzHkCVWxsLA0bNiz1/gghyp/05CxWfLGH04cSAWjdryZt+tVCp9fx5w//xTTzSyKSwKaHvT3DGTjjNwxGSSvFrVwtUS+jF5uHbs53vKZpjodAFPeu76Lq2rUrs2fPxsPDg6pVq2K85sNdq1YtAgMDiYiIICEhgUGDBrF2bfZt+FJTUxk+fDjjx4/P1Y8aNWpcd97+/v4kJSXlKk9MTCQgIKDIfRFClD9njyWzfE40qZcsmDwNdB/eiNotgrN3db94L41WHMVkhwv+kPnsMAb/a6KrQy63ylWi1ul0Be6C1jQNm9GGt8nb5Q+z8PHxoW7duoWqO3r0aKZPn87ixYu57777aNmyJTExMdStW/eG+hEREcG2bdtylW/fvp2IiIgityeEKF/2rT/N2h8OYrdpBFb2pu/TTakQ6kP8iUNsePYBmsdkH3c+VNtAiw+/p0a95i6OuHwrV4m6vPL29mbUqFFMmTKFAQMG8O9//5sOHTrw7LPPMmrUKHx8fNi3bx9RUVF8/PHHjunOnTvHzp07ndqqUqUKL7zwAnfeeSdvvvkm999/P3a7nR9++IGNGzfy6aeflnLvhBDuwm7T+PunQ+xZewqAWs2D6D68ER5eRtb9/Anaex/T8BLYdbDnrqoM/HCF7OouBXJ5VhkxZswY9u/fz4IFC2jWrBm//fYbBw8e5M4776Rly5ZMnjyZqlWrOk0zb948WrZs6fT64osv6NChA8uWLWPZsmV07NiRLl26sGHDBlatWkWTJk1c1EMhhCulJVlY8v6O7CStg7b31KLPk03x8DLy48T78Jv8MSGX4JIvnBr/EIM/WSVJupTIUnaBuXPn5juuS5cuKKVylYeFhWG9fJmDpmm0atWKFStW5Lvre82aNQXG0LNnT3r27FnomIUQ5Vf80SSWzYkmPSkLDy8jPR5rRM2mQVw8G8fqZ+6m2V4LAEfC9TSc8QUdmnZwccS3FknUQghxC9uz9hTrfjyIZldUqOJD36eaEljZmw2/R5I5/V0anQdNB7vvDObBj6MweZhdHfItRxK1EELcguxWjbXzY9i3/gwAdVoFc9ejDfHwNPLTq4Opt2QXFayQ5A3nH+/PkNHvuTjiW5ckaiGEuMWkXrKw/PNozsYmo9NBuwF1aNmzBkkX4/llWD+a7sq+w2NsdT113vuEdi27uDTeW50kaiGEuIWcPpTI8i/2kJGchdnbSM+RjanRqBJbV80ncepUmiSABkS3r8i9nyzHy9vP1SHf8iRRCyHELUApRfSaU6xfcAhNU1Sq5kufp5oSEOzFojeHU/PHzVTLghQvOPNIdwaPn+XqkMVlkqiFEKKcs2XZ+WteDAc2xQNQ7/bKdH2kAZbMJH56uBNNt6UCcLyqjqpvvMe9Hfq5MlxxjRK9jvrUqVM88sgjVKpUCS8vL5o2bcrWrVtLcpZCCCGuknIxk59nbOfApnh0Ouj4YF16PNaI/VuXsv7eOxxJendrf+78ZSPNJEm7nRLbor506RIdO3aka9euLFu2jODgYA4dOkSFChVKapZCCCGucjLmEiu+2ENmqhVPHxO9RjWmeoOKLHnvKap9/xc1MiHNDCcGd2TQpC9dHa7IR4kl6nfeeYewsDCn5yPXqiUPEBdCiJKmlGLXqjg2/HwEpSmCwrKPR5s8rcwf1p7mmxMBOFlZR9Brr3N/1wdcG7AoUInt+v71119p3bo1AwcOJCQkxHH7SiGEECXHmmUn6ut9rF94GKUpItqF8sBLt3Hq6HrW3NPOkaSjW/rQdskaWkqSdnsltkV99OhRZs+ezbhx43j55ZfZsmULzz33HB4eHgwbNizPaSwWCxaLxTGcnJwMgNVqddw+M4fVanU8g1nTtELFlHNrzpzpXGXEiBF88803ucp79uzJsmXLqF27Ns8//zzPP/98rjoGg4FFixZx1113OfVjxIgRJCYmsnjx4hKPv7gUx/rQNA2lFFarFYPBUJzhFVrOZ/Paz2hZI/1wLzfSj+TzmUR9uY8Lp9LQ6aH9/bVp3Kkqv38yjtBvV1IzHTI84Mj9rbnvla+L3P6NuJXXR2HaK4wSS9SaptG6dWveeustAFq2bMmePXv47LPP8k3U06dPZ+rUqbnKV65cibe38+MrjUYjoaGhpKamkpWVVaTYUlJSilS/uFmtVrp168Ynn3ziVG42m0lOTkbTNDIzMx0/VK6VkZF9M4Kr+2G1WrHZbPlO485uZn1kZWWRkZHB2rVrsdlsxRhV0UVFRbl0/sVF+uFeCtuPzPMGLu70QrPq0HtoVGqRydHELewZOYNW/ySjB04HQ9z991OhdhuWLl1asoFf41ZbH9eTnp5e6LollqirVKlCo0aNnMoaNmzIokWL8p1m0qRJjBs3zjGcnJxMWFgYPXv2xN/f36luZmYmcXFx+Pr64unpWaiYlFKkpKTg5+eHTqcrQm+Kl8lkwsfHh3r16uU5Xq/X4+npmavPOby8vACc+mEymTAajflO446KY31kZmbi5eVFp06dCv05KG5Wq5WoqCh69OiByWRySQzFQfrhXgrbj+zj0SfZsvUYSkFwDV96jGzE2VPbODJhAo1OZO+t2tPUky4fLaFTUNV82yoJt9r6KKyibFSVWKLu2LEjMTExTmUHDx4kPDw832nMZjNmc+4bvptMplwLxm63o9Pp0Ov1jidIKaVQl7c286I0DS0jA2U0osvnqVM3QuflVaREo9PpHLEXVKeg8dfWKUyb7iZnd/fNxK3X69HpdHl+RkqbO8RQHKQf7qWgfmRl2lj9bQyHtyUA0LBDFToNqc/Kr16lwheLqZ0GFhPE3N2YQW8tLM2wc7kV1kdR2ymsEkvUL7zwAh06dOCtt97ioYce4p9//uHzzz/n888/L6lZojIyiGl123XrnS3m+UZs34buml3z1/Pbb7/h6+vrVPbyyy/z8ssvF2doQohyKjEhnWWfRXPxdBp6g447B9WnfttKLHi2O03/isegIL4imCa8wKB7n3B1uOImlFiivv3221m8eDGTJk1i2rRp1KpVi5kzZ/Lwww+X1CzLlK5duzJ79mynsooVK7ooGiFEWXJ8zwWivt6LJd2Gt78HvZ9siiXrECsG9KJFrB2A/Q09uOPjnwmpVsfF0YqbVaK3EO3fvz/9+/cvyVk40Xl5EbF9W77jNU0jOSUFfz+/Yt1FrLt8zLgofHx8qFu3bpGn8/PzIykpKVd5YmIiAQEBRW5PCFF2KE2xbflxNv/vKCgIre1P7yeasn7Ju/h8Mo+6KZBlgAN96/Pg9EUYjHKX6PKgXK1FnU5X8C5oTUNvs6H39i5Tx3KvFhERwfbt27nvvvscZXa7nV27djFy5EgXRiaEKElZmTZWzd3P0Z3nAGjcqRod7q/Fzy/1p/GqOIwanAsE7YUnGTRorEtjFcWrXCXqssRisRAfH+9UZjQaCQoKArLvk75z506n8eHh4YwbN47HH3+c8PBw7r77bjIyMpg1axaXLl2SRC1EOXUpPo1ln0VzKT4dvVFH58ER+FW5yNIHb6P54ezLEg/UM9Hu45+oEt7AxdGK4iaJ2kWWL19OlSpVnMoiIiI4cOAAADNmzGDGjBlO47/99lseeeQR7HY7//3vf5k2bRre3t7cdtttrF27lsqVK5da/EKI0nEs+gJrvokhK9OOT6CZ3k82Yd+mL7kw/ksiksCmh709wxk44zfZ1V1OyVp1gblz5zJ37tx8xx87dqzA6YcOHUr//v3x9/cvs7vwhRAFU5oi6ZAHK5ftA6BK3QB6PNaQ398YSKMVRzHZ4YI/ZD47jMH/mujiaEVJkkQthBBuxpJhY+VX+0g5nH1fiaZdq1O3DUSNaEfzmOxbTx6qbaDFh99To15zV4YqSoEkaiGEcCMXT6ex9LPdJCVkgF7RZWgEFxN+4eDDH9PwIth1EH1XVR76cIXs6r5FyFoWQgg3cWRHAqvm7sdqseNbwYx3w4vs+d9zRPy+H7MNLvlCylMPMWRk7mciiPJLErUQQriYpin++fUo25YfB6BaRCCt+vqxeeIzNNuf/dChw+F6Gs34gg5NO7gyVOECkqiFEMKFMtOsRH29lxN7LwLQvHsYBq8NHH78bZqcB00H0XcE88AnUZg8cj8LQZR/kqiFEMJFzp9MZdlnu0k+n4nRpKfrvxqw67cXqLNkJ4FZkOQN54b3ZfBz/3V1qMKFJFELIYQLHNp6lj+/2Y8tS8Ovkid3DqnC1tf70mRX9hMAY6vruThwOIMeG+vaQIXLyUW4QghRijS7xoZFh1n55V5sWRphDStQr2McR565kqR3ta/IHQvX4hda38XRCncgW9RCCFFKMlOtrPhyDycPXAKgVa8anNr7Jh4TNxGYBSlecOaR7gwePwur1eriaIW7kEQthBCl4NyJFJbNiSblQiZGs4GOD1Rn35zBNN2WCsDxqjqqvvEe93bo5+JIhbuRXd8ucO7cOZ5++mlq1KiB2WwmNDSUXr16sX79egBq1qyZ/SSwa15vv/02kH2L0QoVKuR6aAfAmjVr0Ol0JCYm5hpXs2ZNZs6cWYI9E0LkJWZzPIve20bKhUz8g71o1iOF05PvdiTp3a39ufOXjTSTJC3yIFvULvDAAw+QlZXF//3f/1G7dm3Onj3LqlWruHDhgqPOtGnTGDVqlNN0fn5+pR2qEOIm2O0aGxcdYdefcQDUaFwJa/rXGP+zkrBMSDPDicEdGTTpSxdHKtyZJOpSlpiYyLp161izZg2dO3cGsh9f2aZNG6d6fn5+hIaGuiJEIUQxSE/OYsUXezh9KBGA5t2rEPe/x2mxOfv49MnKOoJee537uz7gwihFWVCuErVSCluWlu94TdOwZdmxWuzo9arY5mv00KPT6QpV19fXF19fX5YsWUK7du0wm+UGBkKUNwnHk1n2WTSplyyYzAYa3GElZfYDtDiV/b0T3cKH3rOX4l8hxMWRirKgXCVqW5bG58//VerzfeLDzpjMhkLVNRqNzJ07l1GjRvHZZ5/RqlUrOnfuzODBg2nWrJmj3oQJE/jPf/7jNO2yZcu48847izV2IUTx2r/hDH/Ni8Fu0wis7I2X71LM0xcQnA4ZHnD0/tt46LXvXB2mKEPKVaIuKx544AH69evHunXr2LRpE8uWLePdd9/lyy+/ZPjw4QC89NJLjvc5qlWrVvrBCiEKxW7TWL/gENF/nQKgRpMKpOx4iYj1p9ADp4PB95VJPNj7UdcGKsqcUkvUb7/9NpMmTeL5558vsTOPjR56nviwc77jNU0jJSUZPz9/9PriO+Hd6FH0tjw9PenRowc9evTg1VdfZeTIkUyZMsWRnIOCgqhbt26R2/X39wcgKSmJwMBAp3GJiYkEBAQUuU0hRMHSkiys+GIPZw4nAVDndgO2H/9FyxN2APY28aTb7N+oECw/tkXRlUqi3rJlC3PmzHHatVsSdDpdgbugNU2H0WLAZDYUa6IuDo0aNWLJkiU33U69evXQ6/Vs27aN8PBwR/nRo0dJSkqifn2505EQxSn+aBLL50STlpSFh6eBClW2EfDpFwSmgcUEB+9uzENvLXR1mKIMK/FEnZqaysMPP8wXX3zBG2+8UdKzc3sXLlxg4MCBPPbYYzRr1gw/Pz+2bt3Ku+++y7333uuol5KSQnx8vNO03t7eji1mgJiYmFw/OBo3bszIkSMZP348RqORpk2bEhcXx4QJE2jXrh0dOsgj8oQoLnvXnWLt/INodkWFUC+0+Bk0mLsPg4L4imCa8AIP3fuEq8MUZVyJJ+rRo0fTr18/unfvft1EbbFYsFgsjuHk5GQArFZrrtvpWa1WlFJomoam5X+m99WUUo6/hZ2muHl7e9OmTRs++OADjhw5gtVqJSwsjJEjRzJp0iRHXJMnT2by5MlO0z7xxBPMnj3b0Y+hQ4fmav/48eN88MEHvPPOO0yYMIHjx48TGhrqWP5KKcf0rlYc60PTNJRSWK1WDIbCndBX3HI+m2X9lo/Sj8KzWzXWLzrCgfXZP6ZDahswrRlDxNF0APY39KDtBwsIqVbrhuOQ9eFeirsfRWlHp0rwW3v+/Pm8+eabbNmyBU9PT7p06UKLFi3yPUb92muvMXXq1Fzl8+bNw9vb26nMaDQSGhpKWFgYHh4eJRG+KAOysrKIi4sjPj4em83m6nDELcCeqePCDi+yEg2AwuAfTZPVc6iUAlkG2Na5GhW6PYPe6JofjqJsSE9PZ+jQoSQlJTntKc1LiSXquLg4WrduTVRUlOPY9PUSdV5b1GFhYZw/fz5XRzIzM4mLi6NmzZp4enoWKialFCkpKfj5+RX6umd3JP24IjMzk2PHjhEWFlboz0Fxs1qtREVF0aNHD0wmk0tiKA7Sj+uLP5JE1Ff7yUix4uFlwCNrHq1Wr8WowblAsI4dRacHni2Wecn6cC/F3Y/k5GSCgoIKlahLbNf3tm3bSEhIoFWrVo4yu93O2rVr+fjjj7FYLLl2VZrN5jxvAGIymXItGLvdjk6nQ6/XF/rEsJzdqznTlVXSjyv0+uybzeT1GSlt7hBDcZB+5KaUYs9fp/j7p0NomsI/2IjX7sk0jjkLwIH6Rtp89CPVajYqlvldTdaHeymufhSljRJL1N26dSM6OtqpbMSIETRo0IAJEya47HiiEEIUhc1q568fDnJgwxkA/IMvUeOPaYRcysKmhz09wnnov79hMMptKUTJKLFPlp+fH02aNHEq8/HxoVKlSrnKhRDCHaVczGT5nGgSjqeg04GX8S+a/vwTZjtc8IfMMf9iyKMvuzpMUc6V+Z+A7nIGs3ANWf+ipJyKucSKL/dcPh6tx/fkx7SI3gvAodoGWnzwDTUiWl2nFSFuXqkm6jVr1hRbWzn799PT0/Hy8iq2dkXZkp6efTlMeTj2JdyDUordf55k/aLDKE3h6ZdJ2D9vEnb2InYd7OlalYEfrZBd3aLUlNlPmsFgIDAwkISEBCD7+uTrnTmsaRpZWVlkZmaW+ZOwbvV+KKVIT08nISGBwMBAOedBFAtrlp013x/g4Obsk8TMpgO0WPEZ3llWLvlCylMPMXhk7ktIhShJZTZRA47nNeck6+tRSpGRkYGXl1eZv6xJ+pEtMDBQntstikXy+QyWzYnmfFwqOj34Ji+m9dY/0AFHwvU0nPEFHZrKnf1E6SvTiVqn01GlShVCQkIKdZcXq9XK2rVr6dSpU5neVSr9yGYymWRLWhSLuP0XWfnlXjLTrBg97FSNmUXd44fQdLD7jmAe+CQKk4c8O164RplO1DkMBkOhvrANBgM2mw1PT88yneCkH0IUD6UUO6Pi2Lj4MEqB0XiOZhtmEpiaSJI3nH+sH4PHzHB1mOIWVy4StRBCFJXVYufPb/dzeGv2oTNPyz+0Xfs9Bs1GbHUdtd/5hHa3dXVxlEJIohZC3IKSzqWz7LNoLpxKQ6dTBJ/+kcYx69ABu9pX4N6Pl+PlU/BtHYUoLZKohRC3lON7LxD11V4s6Tb0+gwa7J5N6PkjpHjB6UfuYvD4T1wdohBOJFELIW4JSim2LT/O5l+PggKj/ThtN8zBnJXEiSo6qrz5HgM69HN1mELkIolaCFHuZWXaWPV/+zm64xwA/ol/02rXAvTKxu7WfvSfHYWPX4CLoxQib5KohRDlWuLZdJZ+Fs2lM2mAnZpH51P7xAbSzHBicEcGTfrS1SEKUSBJ1EKIcuvY7vNEfb2XrEw7epVMyx1zCEg+xsnKOoJee537uz7g6hCFuC5J1EKIckcp2LbsONuWngDAM+Mwt+34CnNWMtEtfOg9eyn+FUJcHKUQhSOJWghRrmRl2Liw3ZNTCdlJOvjsXzQ+sAiLyc7ewbfx0GvfuThCIYpGErUQoty4eCaNpbN3k5lgAmUlImY+1eI3cToYfF+ZxIO9H3V1iEIUmSRqIUS5cHTHOf6Yuw+rxY7BdpGWu77AP+UEe5t40m32b1QIrubqEIW4IZKohRBlmqYptvwWy9alxwDwTTlIi91foUgl+v7GPPTWQtcGKMRNkkQthCizMtOsRH29jxN7LwBQ7eSf1DuymIQKGsYXn+Oh+592cYRC3DxJ1EKIMunCqVSWfhZN8rkMdFoWDQ/MIzRhC/sbeGB94Dnuv1uOR4vyQe/qAIQQoqgOb0tg4bvbSD6Xgclygdbb/0vFC1vY3b8efX/YhKd/kKtDFKLYlGiinj59Orfffjt+fn6EhIQwYMAAYmJiSnKWQohyTNMUG34+zIov9mCz2Am8tJ+2W98h03iSS5OfZNCMXzEYZUehKF9KNFH/9ddfjB49mk2bNhEVFYXVaqVnz56kpaWV5GyFEOVQZqqV32btZMfK7Ouja5yIosXuT4mtaaHOD4voMmisawMUooSU6E/P5cuXOw3PnTuXkJAQtm3bRqdOnUpy1kKIcuRcXArLPosm5UImOruFRge+o9KF7ezuGc5D//1NtqJFuVaqn+6kpCQAKlasWJqzFUKUYQf/iWf1twewWTU8M87RbM/nWAynOTvxXwx59GVXhydEiSu1RK1pGmPHjqVjx440adIkzzoWiwWLxeIYTk5OBsBqtWK1Wm86hpw2iqMtV5J+uBfpR8nQ7IrNv8QSvfoUABUv7KXx/rnE1rDQ5L1vqFG/RZ6xuls/bpT0w70Udz+K0o5OKaWKZa7X8fTTT7Ns2TL+/vtvqlevnmed1157jalTp+YqnzdvHt7e3iUdohDCTdgtOi7u9MRyMXtbIvz4csKP/ca2DhXx6zsWo9Hk4giFuDnp6ekMHTqUpKQk/P39C6xbKol6zJgx/PLLL6xdu5ZatWrlWy+vLeqwsDDOnz9/3Y4UhtVqJSoqih49emAyld1/dOmHe5F+FK9zJ1JY+eV+0i5Z0NsyaXTgG0yZu7j0xAP0HDHlutO7Sz9ulvTDvRR3P5KTkwkKCipUoi7RXd9KKZ599lkWL17MmjVrCkzSAGazGbPZnKvcZDIV6wou7vZcRfrhXqQfN+/AxjOs/v4Amk3hlX6WZns+Jz44gYazv6JD0w5FakvWh3uRfuRup7BKNFGPHj2aefPm8csvv+Dn50d8fDwAAQEBeHl5leSshRBliN2usX7BYaLXnASg0vloGh6Yy/52vtw3awtmLzn0JW5dJZqoZ8+eDUCXLl2cyiMjIxk+fHhJzloIUUakJ2ex/PNozhzOviqk5rHfqZiwjLin+jJ4zAwXRyeE65X4rm8hhMhPfGwSy2bvIj3ZhsGWQaP9/0eq1x4qfPEx7W+7y9XhCeEW5C4BQgiX2Lf+NGu+34/SdHinxdN0zxwOt7By78eb8PK5+ZNHhSgvJFELIUqV3aqx7qeD7F13GtARfG4nYce/5dQjHRg8/hNXhyeE25FELYQoNWmJFn6fvZNzx9NAadSO/Q2dNQqfj97l3g79XB2eEG5JErUQolScOZzI/z7ZijVDj9GaTuP9kZyqHUf/2Rvw8QtwdXhCuC1J1EKIEqWUYu+60/w1bz+gxyf1FHUPfUHCgHoMmrTI1eEJ4fYkUQshSozNaufPb/dy6J/zgJ6QhO34X/wOr+n/4f67HnR1eEKUCZKohRAlIuViJovfX0/KeR0ojTpHfyGp0gbaL16Jf4UQV4cnRJkhiVoIUexOH7rELzM3odnNGK2p1DsYycVu3gx6bZurQxOizJFELYQoNkoptq88yqafj4LOjG/qSSqf+hyfV57grt6Pujo8IcokSdRCiGJhy7Lz68frOHNQA52Byme3oAyLaPvTYioEV3N1eEKUWZKohRA3LflCBj++sYKsDH90yk74scWktkpg0PR/XB2aEGWeJGohxE05tucsSz/egsIfU1YKVeO+ImBMf/rd+4SrQxOiXJBELYS4IUop1vywkX1/pYPOG7+U43hlzKXN3K8JqVbH1eEJUW5IohZCFJnVYmfetIWkXggGnZ6Qs5uw1f6H+99ZhcEoXytCFCf5jxJCFMml+BR+nPo7dhWCTrNT5fRCAh5pwF2Dl7g6NCHKJUnUQohC2/HnDjbOP4nSh2DKSsY/KZI2s6ZTrVYjV4cmRLkliVoIcV1KKRa++z0JR0NB74NfciyGoGUM/HyR7OoWooTJf5gQokCZaRa+/XckWfb6oIOK59dTqb+RnsMXujo0IW4JkqiFEPk6svsAf3y4DZupPjrNRuClhXR88ylqRLRydWhC3DL0JT2DTz75hJo1a+Lp6Unbtm355x+5AYIQZcHSz79l5azD2ExV8LAk4mf4loHfz5IkLUQpK9FE/eOPPzJu3DimTJnC9u3bad68Ob169SIhIaEkZyuEuAlKU0SOnU7stipoBm98Uo9Q5fa9/Gv2t5g8zK4OT4hbTokm6vfff59Ro0YxYsQIGjVqxGeffYa3tzdff/11Sc5WCHGD0hMT+eap2aRntgWdHt/kdXR8sRH9n3nV1aEJccsqsWPUWVlZbNu2jUmTJjnK9Ho93bt3Z+PGjSU12wJtO36Jw8nwz7GLGA1l9/C8zW6TfriR4uqH0jQUGkrZQWkoZUNpGig7GjbQ7CilgbKhKbujnqbscHlYaXYUl8ehstvMGYf98vDlMi63rexomp2jm1dR8eAALJ5N0WlWvNXvDP7qbcxe3sW3sIQQRVZi347nz5/HbrdTuXJlp/LKlStz4MCBPKexWCxYLBbHcHJyMgBWqxWr1XrTMT32zXbSs4zM2rv1ptsqPhp6NPTY0es0dFe916PBVe/1KHQ6Ozo0dCgWxPyEXn+5Dgo92uXxKrudy+3p0NDpFLrL9XCUc3nc5dfl6XQ6DRzvs//mHs5+D+rKX0fb2cNO76+qnz3uyjS7fv3UMUwedXJeSqcuL7Mr4xRc9V6BjivvwTFNzjjFlemUYzi73pXW1eVxV97j6MXV45zrLv0LNKe6OMZpOWWOYd01w6B0upv6JN0wpeizzZNGl8aQ5lsNU1YiFSL2MGDcfwGK5X+vNOXEW9bivpb0w70Udz+K0o5bbcZMnz6dqVOn5ipfuXIl3t43/6u+Zeg0rHo7cOWrPOfL2vHFq7vqfZ7DV31Bc+WLtihfzFwerxXyi1m7/BLu4Np15qLkCuiUQkf28SsdoL/8O0WPchp21FE41dcp8EtXDFluICvgSZICamCwp+Df+hIe1ZqzdOlSF/WseERFRbk6hGIh/XAvxdWP9PT0QtctsUQdFBSEwWDg7NmzTuVnz54lNDQ0z2kmTZrEuHHjHMPJycmEhYXRs2dP/P39bzqmt757hXR9Ub9Y86vvmi9ovVJ5fDFf9WWN8xf31eXZX9q6a+rrsv/qdNnt6a4qQ+c8HuBymV6X05ZzHUdZzntdzngdel3Ouyt109PS8fP1Ra8zXDONHp3uyjR6nf7yeP3lMtDp9JfLr9RxKtPpL8eS/V7nKDdcmY/OcFW5PjsOvXNd/eVynU6PXp/zPqcNA5pS7N8XQ5MmTTGaTJf7YkCnNzjqXj2dXn/VX/SX52dArzc6yvU6Y/b0ej06nfGaMmP2Utbf+CkmStNIWbKE819/SHTle0gKqIPJYKdCRx39HhiCyWS64bZdzWq1EhUVRY8ePaQfbkD6kbecPcaFUWKJ2sPDg9tuu41Vq1YxYMAAADRNY9WqVYwZMybPacxmM2Zz7rNKTSZTsSyYybUe4GjsEWrVrI3RYLzyBXz5S9T5i1l/+Yv26i95Q+76l7+Mr/5idnwRO770DY7pdZe/cK/+sr7y3ni5Th5fzLorX8xWq5WlS5fSt2/fMv/BLy/9OBO3lGaNy0Y/MnbtIv6NN8mMjuZYjZ6crdwGnQ56Pt2CXUc2FNv/m6tJP9yL9CN3O4VVoru+x40bx7Bhw2jdujVt2rRh5syZpKWlMWLEiJKcbb56dvwPS5OW0uuOsvGFKkRxssTGcuGzz0j65VcA4sM7cbTWvQB0GlyfahGB7DriygiFEHkp0UQ9aNAgzp07x+TJk4mPj6dFixYsX7481wlmQoiSkxkTw4U5c0hethxU9ilz6f1GsT+jBWjQvFsYTTpXL/Mn+whRXpX4yWRjxozJd1e3EKJkKJuN1LXrSPzxR1L/+stR7tu1K5n9HmfL8hSUphHRNpSOD9R1YaRCiOtxq7O+hRA3J+vkSRIXLSJp0c/Ycu4AqNPh17sXQU8+Sbw1iD/mRKPZFLWaB9H10QboinyCpRCiNEmiFqKMsxw9SsrKlaSsjCJz3z5HuaFCBQIGDCDwoYGYa9UiZnM8f/5fNJqmqN0ymJ6PN8ZgKPHb/QshbpIkaiHKGHtSEmn//EP6xk2kbdhA1rFjV0bq9fi0a0vgwIH4duuG3sMDpRTbVxxn4+LsM8XqtQ6h24hGkqSFKCMkUQvhxpRSZB07Rubu3WTs2kXGrt1k7t8P2lW3wDGZ8GnfDr8ePfDr1g1jxYqOUbYsO6u/P8DBzdn3M2jePYyO99eV3d1ClCGSqIVwA0opbAnnsBw+RNbhw1gOH8ZyKPuvlpqaq75H7dr4tGuHT4f2eLdti8HPL1edxLPprPhyD+fjUtHpddwxsC7NuoaVRneEEMVIErUQpUBlZWG7eBHbufNY489gPXUK66nTl/9mv/JKyAA6Dw88GzfGq1kzvFo0x6tlS0z53N0PspN+zKZ41s4/iNVix9PHRK8nmlA9okJJdU8IUYIkUQtRSMpmQ8vIQEvPQGWkY09NQ0tOIuviJQI2/8Ol+HhIS8eenISWnIzt4iVs589hP3cee1LS9Weg1+NRowbmenXxqFsXc926mOvWw1yrJjoPj0LFmHQunb9+OEjcvosAVK0XSI/HGuFbwfNmui6EcKFbKlHbzp/HkJyM7dw5yPU4QnXNYAHDBY3LY7RT29eZtqBhdfm9zWbDdO4cWbGxaMar77B2MzFfOx7yLShiH5zavuqtzWbDfPIkmdHR2PT67Ec6ahrKrmU/5tFuB01lP95R00Cp3GXXTqNpYNdQmh1sdpTVmvtls6GsWXmOw2pFy7SgZWSg0tPRMjOzk3NGBhRwQ5DKwIV8x15mNGKsWBFjaCimalXxqFYN09Wv6tXR53EL3cKw2zV2Rp1gy+/HsFs1DEY9t/evScue4ejleLQQZdotlaiP9+tPnfR0jr35lqtDuWm1gBMz/uvqMG5aOHBy1seuDqNo9Hr0np7o/fww+Puj8/PjfEYGVerVxRgYiMHPH0OAP4YKFTEGVcIYFIQhKAhDQMBNPUgjL0pTHN15js2/HuVSfPbTeKpFVKDL0AgCK8tzpIUoD26pRK3T69F0OnQ5j5e89jGT1xnWFTCuSMMFtVvIaa1Wa/b9yksr5lxxXDMqV0Eh+q8UGZmZePn4ZCcwQ/bDT9Dr0Rn0oNODwZC9vgwG0OvQ6Q3Z4/XX1rs8bU49nR6dyZT98sj+i9F4pcxkQmfyQJerzIjO0xO9lxd6Ly90l/9ePazz8LjyGSJ7XexeupQWpfhwEaUUx6MvsPl/Rzkfl31s29PXxB0P1qV+21Cn+IQQZdstlahrb9xQbp7WJP24NdmtGoe3nWX36pMkHE8BwORpoPldYbToHobZW5ajEOXNLZWohSirki9ksHfdafavP01GSvaxcqOHnmZdq9OyRzievpKghSivJFEL4abSkiwc2X6Ow1vPcubIlbPGfSuYadypGo06VsXbv3Bngwshyi5J1EK4CaUUF0+ncXzvBU7sucDpQ4lXTqDXQbX6FWjWpTo1m1VCL7f/FOKWIYlaCBdRmuJSfDrxR5M4cziRuP0XSUvKcqoTUtOfeq1DqHtbiFwLLcQtShK1EKXAbtdIjE/nwqlULpxK5fzJVM7GJmNJtznVM5r0VIuoQI3GFQlvEkRAsJeLIhZCuAtJ1EIUE6UpUi5mknw+4/Irk6RzGVw8k8alM2lo9lx3kcFo0hNS058qdQKoWj+QqvUCMZoMLoheCOGuJFELUQClKSwZNizpVizpNjJTraSnZJGelEVakoX0pCxSEzM5f8aHr6LWo9lyJ+McJk8DQdV8qVTNl0rVfQmu4UdQmK88blIIUSBJ1KJMUkqhaQrNprDbNOw2Dc2e/d5RZr/83q5ht2rYsjSsFju2LDtWix3r5b+2y+9tFg2rxZadkNNtWNKsWDJsedxONS96QKHX6/Cr5Il/sBf+lTzxD/IisLI3QdV98avkKTciEUIU2S2VqP/+6TAXY838demg860c87kXda5Bp2oFTJPfF/vV9+3ONS6/6XMHpCmNC2c8WXl6H/qcfjhNn39mKUxsueZahNiufqs0hVIKpXH5r8p+jPLlJKs0RVKSNz/t2ApKl3d9dU07mspOyHatkAm0eBg99Hj6mDB7G/Hy88AnwIx3QPZfs4+B3fu3071vZwKDfOSMbCFEsSqRRH3s2DFef/11/vzzT+Lj46latSqPPPIIr7zyCh6FfApQSTj0TwJWiwcxJ8+6LIbiY+LY2es+BqIMMJCYmlE8LRn16I06DEY9BoMOvVGf/d6oQ2/QY/TQYzIbMHkYMJoNzu89DJjMeoxmA2bv7ITs6W3C7JP912DKP/larVZiztrxq+gpSVoIUexKJFEfOHAATdOYM2cOdevWZc+ePYwaNYq0tDRmzJhRErMslFZ9arB/3wEiIiJyHRfMd5ek0+2tC7jXdX6TF6bd3Df7LrBdu93O3r17adKkMQaDId+ZF7SXVVfAfbvznl6X/7h8mtLps++rrtPr0Om58l6XPU7T7Pzzzz+0a98Wk8nkKM+u5/xef/V7Q3YC1ht0jkScU1cIIcqbEknUvXv3pnfv3o7h2rVrExMTw+zZs12aqJt3q84py25a9gwr0/eWtlqtHE/dSaM7q5b5fuw+aqdqvcAy3Q8hhChJpXaMOikpiYoVKxZYx2KxYLFYHMPJyclA9he6tYBnARdWThvF0ZYrST/ci/TDvUg/3Iv0o+D2CkOnCjrzqJgcPnyY2267jRkzZjBq1Kh867322mtMnTo1V/m8efPw9pZn6wohhCgf0tPTGTp0KElJSfj7+xdYt0iJeuLEibzzzjsF1tm/fz8NGjRwDJ86dYrOnTvTpUsXvvzyywKnzWuLOiwsjPPnz1+3I4VhtVqJioqiR48eZXpXq/TDvUg/3Iv0w71IP/KWnJxMUFBQoRJ1kXZ9jx8/nuHDhxdYp3bt2o73p0+fpmvXrnTo0IHPP//8uu2bzWbMZnOucpPJVKwruLjbcxXph3uRfrgX6Yd7kX7kbqewipSog4ODCQ4OLlTdU6dO0bVrV2677TYiIyOvXO8rhBBCiEIrkZPJTp06RZcuXQgPD2fGjBmcO3fOMS40NLQkZimEEEKUSyWSqKOiojh8+DCHDx+mevXqTuOKcu5aTt2cs79vltVqJT09neTk5DK9C0b64V6kH+5F+uFepB95y8lrhcmJpXLW9406efIkYWFhrg5DCCGEKBFxcXG5Nmiv5daJWtM0Tp8+jZ+fX7HcdSrnLPK4uLhiOYvcVaQf7kX64V6kH+5F+pE3pRQpKSlUrVr1uudwufVDOfR6/XV/adwIf3//Mv2BySH9cC/SD/ci/XAv0o/cAgICClVPTsUWQggh3JgkaiGEEMKN3VKJ2mw2M2XKlDxvqlKWSD/ci/TDvUg/3Iv04+a59clkQgghxK3ultqiFkIIIcoaSdRCCCGEG5NELYQQQrixcpWo33zzTTp06IC3tzeBgYF51jlx4gT9+vXD29ubkJAQXnrpJWw2W4HtXrx4kYcffhh/f38CAwN5/PHHSU1NLYEe5G3NmjXodLo8X1u2bMl3ui5duuSq/9RTT5Va3HmpWbNmrpjefvvtAqfJzMxk9OjRVKpUCV9fXx544AHOnj1bShHnduzYMR5//HFq1aqFl5cXderUYcqUKWRlZRU4nTusj08++YSaNWvi6elJ27Zt+eeffwqsv2DBAho0aICnpydNmzZl6dKlpRRp3qZPn87tt9+On58fISEhDBgwgJiYmAKnmTt3bq7l7unpWUoR5+21117LFdPVjwfOi7utC8j7/1mn0zF69Og867vLuli7di133303VatWRafTsWTJEqfxSikmT55MlSpV8PLyonv37hw6dOi67Rb1/6vQVDkyefJk9f7776tx48apgICAXONtNptq0qSJ6t69u9qxY4daunSpCgoKUpMmTSqw3d69e6vmzZurTZs2qXXr1qm6deuqIUOGlFAvcrNYLOrMmTNOr5EjR6patWopTdPyna5z585q1KhRTtMlJSWVWtx5CQ8PV9OmTXOKKTU1tcBpnnrqKRUWFqZWrVqltm7dqtq1a6c6dOhQShHntmzZMjV8+HC1YsUKdeTIEfXLL7+okJAQNX78+AKnc/X6mD9/vvLw8FBff/212rt3rxo1apQKDAxUZ8+ezbP++vXrlcFgUO+++67at2+f+s9//qNMJpOKjo4utZiv1atXLxUZGan27Nmjdu7cqfr27atq1KhR4GcoMjJS+fv7Oy33+Pj4Uow6tylTpqjGjRs7xXTu3Ll867vjulBKqYSEBKc+REVFKUCtXr06z/rusi6WLl2qXnnlFfXzzz8rQC1evNhp/Ntvv60CAgLUkiVL1K5du9Q999yjatWqpTIyMvJts6j/X0VRrhJ1jsjIyDwT9dKlS5Ver3f6YMyePVv5+/sri8WSZ1v79u1TgNqyZYujbNmyZUqn06lTp04Ve+yFkZWVpYKDg9W0adMKrNe5c2f1/PPPl05QhRQeHq4++OCDQtdPTExUJpNJLViwwFG2f/9+BaiNGzeWQIQ35t1331W1atUqsI6r10ebNm3U6NGjHcN2u11VrVpVTZ8+Pc/6Dz30kOrXr59TWdu2bdWTTz5ZonEWRUJCggLUX3/9lW+d/L4PXGnKlCmqefPmha5fFtaFUko9//zzqk6dOvluQLjjurg2UWuapkJDQ9V7773nKEtMTFRms1n98MMP+bZT1P+voihXu76vZ+PGjTRt2pTKlSs7ynr16kVycjJ79+7Nd5rAwEBat27tKOvevTt6vZ7NmzeXeMx5+fXXX7lw4QIjRoy4bt3vv/+eoKAgmjRpwqRJk0hPTy+FCAv29ttvU6lSJVq2bMl7771X4KGHbdu2YbVa6d69u6OsQYMG1KhRg40bN5ZGuIWSlJRExYoVr1vPVesjKyuLbdu2OS1HvV5P9+7d812OGzdudKoP2f8v7rbcgesu+9TUVMLDwwkLC+Pee+/N9/+9NB06dIiqVatSu3ZtHn74YU6cOJFv3bKwLrKysvjuu+947LHHCnw2gzuui6vFxsYSHx/vtLwDAgJo27Ztvsv7Rv6/isKt7/Vd3OLj452SNOAYjo+Pz3eakJAQpzKj0UjFihXznaakffXVV/Tq1eu690EfOnQo4eHhVK1ald27dzNhwgRiYmL4+eefSynS3J577jlatWpFxYoV2bBhA5MmTeLMmTO8//77edaPj4/Hw8Mj1zkHlStXdtnyv9bhw4eZNWsWM2bMKLCeK9fH+fPnsdvteX7+Dxw4kOc0+f2/uMty1zSNsWPH0rFjR5o0aZJvvYiICL7++muaNWtGUlISM2bMoEOHDuzdu7dEniVQGG3btmXu3LlERERw5swZpk6dyp133smePXvw8/PLVd/d1wXAkiVLSExMZPjw4fnWccd1ca2cZVqU5X0j/19F4faJeuLEibzzzjsF1tm/f/91T8RwRzfSt5MnT7JixQp++umn67b/xBNPON43bdqUKlWq0K1bN44cOUKdOnVuPPBrFKUf48aNc5Q1a9YMDw8PnnzySaZPn+7yOxfdyPo4deoUvXv3ZuDAgYwaNarAaUtrfdwqRo8ezZ49e/j7778LrNe+fXvat2/vGO7QoQMNGzZkzpw5vP766yUdZp769OnjeN+sWTPatm1LeHg4P/30E48//rhLYrpZX331FX369KFq1ar51nHHdVEWuH2iHj9+fIG/0ABq165dqLZCQ0NznYWXc/ZwaGhovtMkJCQ4ldlsNi5evJjvNIV1I32LjIykUqVK3HPPPUWeX9u2bYHsLcDiTAw3s47atm2LzWbj2LFjRERE5BofGhpKVlYWiYmJTlvVZ8+evenlf62i9uP06dN07dqVDh068Pnnnxd5fiW1PvISFBSEwWDIdbZ8QcsxNDS0SPVL05gxY/jtt99Yu3ZtkbfETCYTLVu25PDhwyUUXdEFBgZSv379fGNy53UBcPz4cf74448i7x1yx3WRs0zPnj1LlSpVHOVnz56lRYsWeU5zI/9fRXLTR7nd0PVOJrv6LLw5c+Yof39/lZmZmWdbOSeTbd261VG2YsUKl5xMpmmaqlWr1nXPLs7P33//rQC1a9euYo7sxn333XdKr9erixcv5jk+52SyhQsXOsoOHDjg8pPJTp48qerVq6cGDx6sbDbbDbVR2uujTZs2asyYMY5hu92uqlWrVuDJZP3793cqa9++vUtPYNI0TY0ePVpVrVpVHTx48IbasNlsKiIiQr3wwgvFHN2NS0lJURUqVFAffvhhnuPdcV1cbcqUKSo0NFRZrdYiTecO64J8TiabMWOGoywpKalQJ5MV5f+rSDHedAtu5Pjx42rHjh1q6tSpytfXV+3YsUPt2LFDpaSkKKWuXJ7Vs2dPtXPnTrV8+XIVHBzsdHnW5s2bVUREhDp58qSjrHfv3qply5Zq8+bN6u+//1b16tUr1cuzcvzxxx8KUPv378817uTJkyoiIkJt3rxZKaXU4cOH1bRp09TWrVtVbGys+uWXX1Tt2rVVp06dSjtshw0bNqgPPvhA7dy5Ux05ckR99913Kjg4WD366KOOOtf2Q6nsy7Nq1Kih/vzzT7V161bVvn171b59e1d0wRFj3bp1Vbdu3dTJkyedLjW5uo67rY/58+crs9ms5s6dq/bt26eeeOIJFRgY6LgK4l//+peaOHGio/769euV0WhUM2bMUPv371dTpkxx+SVBTz/9tAoICFBr1qxxWu7p6emOOtf2Y+rUqY5L6bZt26YGDx6sPD091d69e13RBaWUUuPHj1dr1qxRsbGxav369ap79+4qKChIJSQkKKXKxrrIYbfbVY0aNdSECRNyjXPXdZGSkuLID4B6//331Y4dO9Tx48eVUtmXZwUGBqpffvlF7d69W9177725Ls+666671KxZsxzD1/v/uhnlKlEPGzZMAbleV1/Td+zYMdWnTx/l5eWlgoKC1Pjx451+Ba5evVoBKjY21lF24cIFNWTIEOXr66v8/f3ViBEjHMm/NA0ZMiTf64djY2Od+nrixAnVqVMnVbFiRWU2m1XdunXVSy+95NLrqLdt26batm2rAgIClKenp2rYsKF66623nPZmXNsPpZTKyMhQzzzzjKpQoYLy9vZW9913n1NSLG2RkZF5fs6u3kHlrutj1qxZqkaNGsrDw0O1adNGbdq0yTGuc+fOatiwYU71f/rpJ1W/fn3l4eGhGjdurH7//fdSjfda+S33yMhIR51r+zF27FhHnytXrqz69u2rtm/fXvrBX2XQoEGqSpUqysPDQ1WrVk0NGjRIHT582DG+LKyLHCtWrFCAiomJyTXOXddFzvf8ta+cWDVNU6+++qqqXLmyMpvNqlu3brn6Fx4erqZMmeJUVtD/182Qp2cJIYQQbuyWuo5aCCGEKGskUQshhBBuTBK1EEII4cYkUQshhBBuTBK1EEII4cYkUQshhBBuTBK1EEII4cYkUQshhBBuTBK1EEII4cYkUQshhBBuTBK1EEII4cYkUQtxCzt37hyhoaG89dZbjrINGzbg4eHBqlWrXBiZECKHPJRDiFvc0qVLGTBgABs2bCAiIoIWLVpw77338v7777s6NCEEkqiFEMDo0aP5448/aN26NdHR0WzZsgWz2ezqsIQQSKIWQgAZGRk0adKEuLg4tm3bRtOmTV0dkhDiMjlGLYTgyJEjnD59Gk3TOHbsmKvDEUJcRbaohbjFZWVl0aZNG1q0aEFERAQzZ84kOjqakJAQV4cmhEAStRC3vJdeeomFCxeya9cufH196dy5MwEBAfz222+uDk0Igez6FuKWtmbNGmbOnMm3336Lv78/er2eb7/9lnXr1jF79mxXhyeEQLaohRBCCLcmW9RCCCGEG5NELYQQQrgxSdRCCCGEG5NELYQQQrgxSdRCCCGEG5NELYQQQrgxSdRCCCGEG5NELYQQQrgxSdRCCCGEG5NELYQQQrgxSdRCCCGEG5NELYQQQrix/wdpAb71tH9FlAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-relu-variants\n", + "#| fig-cap: \"ReLU and Variants\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, relu(x), label=\"ReLU\")\n", + "plt.plot(x, leaky_relu(x), label=\"Leaky ReLU\")\n", + "plt.plot(x, prelu(x, 0.01), label=\"PReLU\")\n", + "plt.plot(x, elu(x), label=\"ELU\")\n", + "plt.plot(x, selu(x), label=\"SELU\")\n", + "plt.title(\"ReLU and Variants\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-relu\n", + "#| fig-cap: \"ReLU and Variants\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, relu(x), label=\"ReLU\")\n", + "plt.title(\"ReLU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-leaky_relu\n", + "#| fig-cap: \"Leaky Relu\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, leaky_relu(x), label=\"Leaky ReLU\")\n", + "plt.title(\"Leaky-ReLU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-prelu\n", + "#| fig-cap: \"PReLU\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, prelu(x, 0.01), label=\"PReLU\")\n", + "plt.title(\"PReLU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-elu\n", + "#| fig-cap: \"ELU\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, elu(x), label=\"ELU\")\n", + "plt.title(\"ELU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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geEQA3n6yEzRO/DZkqTGoiYgaOCEEVuw4gdV7zgEAJj4SgtcGt4OSs43JAoOaiKgBM5otmPPNH/j29ysAgLkDwzC1ZyvONiYjDGoiogZKZzDhb5//jt0nr0OlVODNJzriyYdaSF0W3YVBTUTUAN0qNGDCuiSkXsqBs1qJ/xvdBY+F+UpdFlWgTs4SuHLlCsaMGQMvLy+4uLigQ4cOSE5OrotNERFRDV3JKcKTH8Uj9VIOPF3V+HzywwxpGbP5EfWtW7fwyCOP4NFHH8WOHTvQrFkznD59Gk2aNLH1poiIqIZOZuRj7NoEZObpEeDhjPWTuqONj5vUZVEVbB7Ub775JgIDAxEbG2tdFhISYuvNEBFRDSWdv4lJ65KQV2xCW5/GWD+pO/w9XKQui+7B5i99f//99+jatSueeuop+Pj4oHPnzvjkk09svRkiIqqBuGOZGPNpAvKKTega3ARbXujBkLYTNj+iPnfuHFatWoVZs2bhn//8J5KSkjBjxgxoNBqMGzeu3Hi9Xg+9Xm+9npeXBwAwGo0wGo21rqd0HbZYl9QcpRf2IT+O0gv7qNhXyZcx//tjsAjgsdBmiBnZES5qRb08TtwnVa+vOhRCCGGTrd6m0WjQtWtXxMfHW5fNmDEDSUlJOHDgQLnxixYtwuLFi8st37RpE1xdOQE8EdH9EgL4+YoC2y+pAACRzSx4urUFKn5EWnI6nQ6jRo1Cbm4u3N2r/kYymx9R+/v748EHHyyzrF27dvjmm28qHD9v3jzMmjXLej0vLw+BgYHo16/fPYuvDqPRiLi4OPTt2xdqtbrW65OSo/TCPuTHUXphH3+yWASWbj+B7ZcuAQBe7BmCl6Pb1PtEJtwnFSt99bg6bB7UjzzyCE6ePFlm2alTpxAcHFzheK1WC622/LeyqNVqm+5UW69PSo7SC/uQH0fppaH3YTBZMPubVPzwxzUoFMDCIQ9i/CPSntTb0PdJReupLpsH9csvv4yoqCi88cYbGDlyJBITE/Hxxx/j448/tvWmiIjoLoV6E17YmIK9p7OhVinw75ERGNYpQOqyqBZsftZ3t27d8N133+GLL75AeHg4Xn/9dcTExGD06NG23hQREd3hVqEBoz9NwN7T2XDVqLBmXDeGtAOokylEhwwZgiFDhtTFqomIqAJXc4owdm0izmQVwNNVjdjx3dA5iBNNOQLO9U1EZOfOZBVg7JoEXM0thr+HMzZwtjGHwqAmIrJjqZdyMCE2Ebd0RrRq1ggbJkWiuScnMnEkDGoiIju19/R1TN2QAp3BjE4tPBA7oTuaNtJIXRbZGIOaiMgO/fDHVbz8ZSqMZoG/tvXGR2MeQiMt/0t3RNyrRER2ZsPBC1iw7QiEAAZ39MfKkZ2gdVJJXRbVEQY1EZGdEELgvV2nEfPLaQDAmIeDsHhYOFRKzgnqyBjURER2wGIRWPzfo/jswAUAwEt92mJmdNt6nxKU6h+DmohI5gwmC2ZvScN/065CoQAWDW2PcVEtpS6L6gmDmohIxnQGE17Y+Dv2nLrOKUEbKAY1EZFM3dIZ8PzGVKReyoGLWoXVzz2Eng80k7osqmcMaiIiGbqlB579NAlnrxdyStAGjkFNRCQzZ68XIuaICjmGQvh7OGP9xO5o68spQRsqBjURkYykXcrB+NhE5BgUaOXtig2TH+aUoA0cg5qISCb2nc7G8xuSoTOYEdRI4IvJ3eHLkG7wGNRERDKw4/A1zNh8CEazQFTrphjulcV5uwkAoJS6ACKihu6rpEuYtul3GM0Cgzv44+MxXeDMGUHpNh5RExFJ6JM957Bs+3EAwLPdA7F0RAdYzCaJqyI5YVATEUlACIF//3wK//n1DABgaq9WmDsgDAqFAhazxMWRrDCoiYjqmcUisOi/R7H+9rzdrw4Ixd96t5G4KpIrBjURUT0ymi14ZUsatqaWzNv9+vBwjHk4WOqySMYY1ERE9aTYaMb0Tb/jl+NZcFIq8O+RnTA8ornUZZHMMaiJiOpBfrERkz9LRkL6TWidlFg1pgseC/OVuiyyAwxqIqI6drPQgPGxifjjci7ctE74dFxXRLbykrosshMMaiKiOnQttwjPrUnEmawCNG2kwfqJ3RHe3EPqssiOMKiJiOrI+exCjP40AVdyiuDv4YwNkyLRxqex1GWRnWFQExHVgePX8vDcmkRkF+gR4t0IGyZ1R4smrlKXRXaozqcQXbFiBRQKBWbOnFnXmyIikoWUCzfx9OoDyC7Q40F/d2x5oQdDmu5bnR5RJyUlYfXq1ejYsWNdboaISDb2nLqOqRtSUGQ0o2twE6wZ3w0eLmqpyyI7VmdH1AUFBRg9ejQ++eQTNGnSpK42Q0QkG9sPX8Okz5JQZDSj1wPNsGFSJEOaaq3OjqinTZuGwYMHIzo6GkuXLq10nF6vh16vt17Py8sDABiNRhiNxlrXUboOW6xLao7SC/uQH0fpRco+vvn9Cv659SgsAhgU7ou3n+gAJ4UFRqOlxutylP0BOE4vtu6jJutRCCGETbZ6h82bN2PZsmVISkqCs7MzevfujYiICMTExJQbu2jRIixevLjc8k2bNsHVle/pEJH87c1Q4Ov0ku+l7OFjwchWFigVEhdFsqbT6TBq1Cjk5ubC3d29yrE2P6K+dOkSXnrpJcTFxcHZ2fme4+fNm4dZs2ZZr+fl5SEwMBD9+vW7Z/HVYTQaERcXh759+0Kttu+XoBylF/YhP47SixR9rN6Tjq/TTwMAJkQFY96AB6BQ1C6lHWV/AI7Ti637KH31uDpsHtQpKSnIyspCly5drMvMZjP27NmD//znP9Dr9VCp/vxGdK1WC61WW249arXapjvV1uuTkqP0wj7kx1F6qY8+hBBYGXcKH/yv5GsqZzzWBi/3rX1I38lR9gfgOL3Yqo+arMPmQd2nTx8cPny4zLIJEyYgLCwMc+bMKRPSRET2SAiBpT8ex5p96QCAOQPC8GLv1hJXRY7K5kHt5uaG8PDwMssaNWoELy+vcsuJiOyNxSLwr61H8EXiRQDA4mHtMS6qpbRFkUPjzGRERNVkMlvwytd/4LtDV6BUACue6IiRXQOlLoscXL0E9e7du+tjM0REdUZvMuOlL1Kx82gGnJQKvPt0BIZ2CpC6LGoAeERNRHQPxUYzpm5IwW+nrkOjUuL/RndB9IP8LmmqHwxqIqIqFOhNmPxZEg6euwkXtQqfjO2Kv7T1lrosakAY1ERElcjVGTF+XSIOXcxBY60TYid0Q7eWTaUuixoYBjURUQVuFOjx3JpEHLuWB09XNdZP7I6OLTylLosaIAY1EdFdMnKLMWZNAs5kFcC7sQYbJ0cizK/2MyUS3Q8GNRHRHS7d1GH0pwm4eFMHfw9nfD45Eq2aNZa6LGrAGNRERLdduFGIUZ8k4EpOEYKauuLzyZEIbMovByJpMaiJiACkZxfi2Y8PIiOvGK2aNcKmyQ/Dz+PeXyxEVNcY1ETU4J3JKsCoTw4iK1+Ptj6N8fmUSPi4MaRJHhjURNSgncrMx6hPEpBdoEeYnxs2To6Ed+Py3+hHJBUGNRE1WMev5WHMpwm4UWhAO393fD45Ek0baaQui6gMBjURNUhHr+ZizKcJuKUzIry5OzZOioSnK0Oa5IdBTUQNzuHLuRizJgG5RUZ0auGB9RMj4eGqlrosogoxqImoQTl08RbGrk1EfrEJXYI8sW5id7g7M6RJvhjURNRgpFy4iXFrk1CgN6FbyyaIndAdjbX8b5Dkjb+hRNQgJKbfxITYRBQazHi4VVOsGdcNjRjSZAf4W0pEDu/A2RuYuC4JRUYzHmnjhU/HdoOLRiV1WUTVwqAmIoe273Q2Jq9PQrHRgp4PNMPHzz0EZzVDmuyHUuoCiIjqym+nrmPSZyUh/WgoQ5rsE4+oicgh/e9EJl7Y8DsMZgui2/niw9GdoXViSJP9YVATkcP55XgWZnyZBqNZYEB7P7z/bGdonPgCItknBjUROZTUGwpsSEiDySIwuIM/Yp6JgFrFkCb7xaAmIofx4+EMfHZKCQsEhkcE4N9PdYITQ5rsHIOaiBzC1kNXMGvLH7BAgccj/PHOyAiolAqpyyKqNf6pSUR27+uUy3j5q1RYBBDZzILlj4czpMlh2Dyoly9fjm7dusHNzQ0+Pj4YMWIETp48aevNEBEBAL5MuohXvk6DEMAz3VrgmdYWhjQ5FJsH9W+//YZp06bh4MGDiIuLg9FoRL9+/VBYWGjrTRFRA7fx4AXM+eYwhADG9gjGkqHtwIwmR2Pz96h37txZ5vq6devg4+ODlJQU9OzZ09abI6IG6rP481j4/VEAwIRHWmLBkAdhMpkkrorI9ur8ZLLc3FwAQNOmTSu8Xa/XQ6/XW6/n5eUBAIxGI4xGY623X7oOW6xLao7SC/uQH3vrJTb+At7YUfKW2qRHgjGnf1uYTCa766MyjtIH4Di92LqPmqxHIYQQNtlqBSwWC4YNG4acnBzs27evwjGLFi3C4sWLyy3ftGkTXF1d66o0IrJTu64o8P3FkhnGoptbMCTQAgVf7iY7o9PpMGrUKOTm5sLd3b3KsXUa1C+++CJ27NiBffv2oUWLFhWOqeiIOjAwENnZ2fcsvjqMRiPi4uLQt29fqNX2/eXwjtIL+5Afe+nlw93nELPrDABgeu9WmPFYayjuSGl76eNeHKUPwHF6sXUfeXl58Pb2rlZQ19lL39OnT8cPP/yAPXv2VBrSAKDVaqHVasstV6vVNt2ptl6flBylF/YhP3LtRQiBd+NO4f3/lYT07L4P4O992lY6Xq591JSj9AE4Ti+26qMm67B5UAsh8Pe//x3fffcddu/ejZCQEFtvgogaECEEVuw8gdW/nQMAzBsYhqm9WktcFVH9sXlQT5s2DZs2bcK2bdvg5uaGjIwMAICHhwdcXFxsvTkicmBCCCz54Rhi958HACwY8iAm/oV//FPDYvPPUa9atQq5ubno3bs3/P39rT9ffvmlrTdFRA7MYhGYv+2INaSXjghnSFODVCcvfRMR1YbZIvDPbw/jy+RLUCiAN/9fR4zsFih1WUSS4JdyEJGsmC0Cr2xJw7eHrkCpAP49shMe71z5CalEjo5BTUSyYTRbMOurNPw37SpUSgVino7A0E4BUpdFJCkGNRHJgsFkwYwvDmHn0QyoVQp88GwXDAj3k7osIskxqIlIcsVGM6Z9/jt2nciCRqXEqjFd0Kedr9RlEckCg5qIJFWgN2HKZ8k4cO4GtE5KfDy2K3o90Ezqsohkg0FNRJK5VWjA+NhEpF3ORWOtEz4d1xUPt/KSuiwiWWFQE5EkMvOKMebTBJzOKkATVzXWT4xEhxYeUpdFJDsMaiKqdxdv6DB6zUFculkEP3dnbJjUHW193aQui0iWGNREVK9OZuTjuTUJyMrXI9jLFRsnRSKwKb/SlqgyDGoiqjdJ529i8mfJyC0yIszPDesndoePu7PUZRHJGoOaiOrF9sPXMPPLVBhMFnQO8kTs+G7wdNVIXRaR7DGoiajOrdmXjqU/HoMQQN8HffH+M53holFJXRaRXWBQE1GdsVgElm0/jjX70gEAzz0cjEXD2kOlVEhcGZH9YFATUZ0oNpox+6s0/Hj4GgBg7sAwTO3ZCgoFQ5qoJhjURGRzNwr0eGFjCpLO34JapcA7T3XC8IjmUpdFZJcY1ERkU8ev5WHK+mRcvlUEN60TVo99CFGtvaUui8huMaiJyGZ2HsnArK9SoTOYEezlik/HduVEJkS1xKAmolqzWAT+8+sZrIw7BQB4pI0XPhzVhR+/IrIBBjUR1cqtQgNmfZWKX09eBwCMj2qJ1wa3g5NKKXFlRI6BQU1E9+33i7cw/fPfcTW3GFonJV4fHo6R3QKlLovIoTCoiajGLBaBtfvTsWLHCZgsAiHejfDhqC54MMBd6tKIHA6Dmohq5GpOEV79+g/sO5MNABjc0R8r/l8HuDmrJa6MyDExqImoWoQQ+O7QFSz8/ijyi01wVivxr0HtMObhYE5iQlSHGNREdE8ZucVY+P0R/HQ0EwAQEeiJlSM7oVWzxhJXRuT4GNREVCmj2YJ1+88j5pdTKDSYoVYpMDP6AUzt2YpndRPVkzp7pn344Ydo2bIlnJ2dERkZicTExLraFBHVgYPnbmDw+3uxbPtxFBrM6BzkiW3T/oJpj7ZhSBPVozo5ov7yyy8xa9YsfPTRR4iMjERMTAz69++PkydPwsfHpy42SUQ2cvRqLlb+fAq7TmQBAJq4qjF3YBieeigQSn7rFVG9q5M/i1euXIkpU6ZgwoQJePDBB/HRRx/B1dUVa9eurYvNEZENZOiAGZvTMPj9fdh1IgtKBTAqMgj/m90bT3cLYkgTScTmR9QGgwEpKSmYN2+edZlSqUR0dDQOHDhQbrxer4der7dez8vLAwAYjUYYjcZa1/N18iV8c1qJX75Kg0pZ8neJ9QTV2xfuugoFFHdcLntb6ZLKbldUcnvl2yq9rqhgW3/eBgDCYsH5C0oc3nECSpWyim2Vr0UBQKlUQKlQQKUoWadKqYBSUXZ56eWSH0ClVJSMVaBkmVIBleLO+8G6zEmlgFqlhEalhJOy5PKfyxRwUimhVikAixlCwCb7V0ql9dtzH0II7Dt7A+vjL+C30yoIZEKhAAaH+2HGY60R4t0IgP306Aj7BHCcPgDH6cXWfdRkPQohhLDJVm+7evUqmjdvjvj4ePTo0cO6/NVXX8Vvv/2GhISEMuMXLVqExYsXl1vPpk2b4OrqWut6vk5XYm8G30+TI5VCQKVAyY8ScLp9Wa0s+dEoAY1K/HlZCahVt/9Vitv/Aprby7QqwEUl4KwCnFWAi1PJcn5yqLwCI/B7tgL7MpXILPrzAerQxIJBgRYENJKwOKIGQKfTYdSoUcjNzYW7e9UTBUl+1ve8efMwa9Ys6/W8vDwEBgaiX79+9yy+OtxOZcFrTwraPvAAVCoVSv8sESi5YL1+x58rpX+7CJS9TVRyOypbZ7n7i7vG/3l75ff9szCz2YLzFy4gODgYytuvDtyr1tIFFgFYhLj9A5gtAkIImC2AWZReFmXHWUoum4WApcxtd9z/9jizRcBkscBoFjCaS/69+/rdzEIB62JzuZtvq13KqpQKNNaq0FjrBDetExo7O8HN2QluWjU8XJzQxFWDJo3U8HRRo0kjDZq4qkuWuarhrFZVuW6j0Yi4uDj07dsXarX8J/vI0RkRdzwL249k4MC5mzBbSh78RloVRnTyQ7DhAsYMs49eKmNv+6QyjtIH4Di92LqP0lePq8PmQe3t7Q2VSoXMzMwyyzMzM+Hn51duvFarhVarLbdcrVbb5MH46wM+yD8jMKhna7v+JQFKflG2b0/HoEHt7K4XIQRMlpLQLio2YMfPcejZ+zEolCoYzBYYzRaYzAJ6kwV6kxnFRjOKDBYUGc0oMppRbDBbLxcZzNCbSv4tWWZBkcGEAr0Z+cVG5BebUKA3wWwp+eMjt8iE3CJTjWt2UatKgruRBk0badDEteRfr0YaNG2sgYdWhbN5QGiOAb4eTvBwUcvqfVydwYTk87dw8NwNHDh3A39czrWGMwC0D3DHUw+1wBMPtYCzCti+/YLNnndSYx/y4yi92KqPmqzD5kGt0Wjw0EMPYdeuXRgxYgQAwGKxYNeuXZg+fbqtN0d2QqFQQH37/Wq1QsBNDfh7ONfZE1cIgSKjGfnFJmt4//lTcj23yIibOgNuFRpwS2fArcI/r5ssJfcvyjXjam5xFVtywvtH9wMoOXpv4qqGVyMtmt4Oc69Gd4T77eVet5d7umqgqmWwCyGQozPiWm4xruQU4VRmPk5k5ONkRh7OXS+EyVL2lYwwPzcM7RSAQR38re8/A/b//iGRI6uTl75nzZqFcePGoWvXrujevTtiYmJQWFiICRMm1MXmiMpRKBRw1TjBVeMEX3fnGt1XCIECvenP4NYZcLOg5N8bhSWXbxQacKOgGJeu50APNfKLS47gswsMyC4wVLNGoImrBp6uarioVXBWq27/q4SzWgWNU+nbG7j9NgOg05e8WlCgL/mjIzOvGHqTpdJtBHg44+HWXujRygs9WnuhRZPan/dBRPWrToL66aefxvXr17FgwQJkZGQgIiICO3fuhK+vb11sjsimFAoF3JzVcHNWI8ir8mAreStiOwYN6g+hUOGWzoDsAj1uFhpws9CAGwW3/y004Gah/o7LBuTojBAC1rG15dVIAz8PZ7TxaYwwP3eE+bkh1M8N/h7OnIebyM7V2clk06dP50vd1GBonJTwdXeu9tG7yWzBLZ3xdmgbSt6HN1pK3ps3lrxHrzdZoEDJkXfpR+YaaVVopHVCI03JSXE+bs7wcdfe88Q3IrJfkp/1TdQQOamUaOamRTO38idSEhHdiR8wJiIikjEGNRERkYwxqImIiGSMQU1ERCRjDGoiIiIZY1ATERHJmOw+nlX6JRM1mbC8KkajETqdDnl5eXY/z6yj9MI+5MdRemEf8uMovdi6j9KMq84XWMouqPPz8wEAgYGBEldCRERUt/Lz8+Hh4VHlGJt/H3VtWSwWXL16FW5ubjaZ+rD0azMvXbpkk6/NlJKj9MI+5MdRemEf8uMovdi6DyEE8vPzERAQYP3a4srI7ohaqVSiRYsWNl+vu7u7Xf+S3MlRemEf8uMovbAP+XGUXmzZx72OpEvxZDIiIiIZY1ATERHJmMMHtVarxcKFC6HV2v+XHzhKL+xDfhylF/YhP47Si5R9yO5kMiIiIvqTwx9RExER2TMGNRERkYwxqImIiGTMIYJ62bJliIqKgqurKzw9PSscc/HiRQwePBiurq7w8fHBK6+8ApPJVOV6b968idGjR8Pd3R2enp6YNGkSCgoK6qCD8nbv3g2FQlHhT1JSUqX36927d7nxL7zwQr3UXJWWLVuWq2vFihVV3qe4uBjTpk2Dl5cXGjdujCeeeAKZmZn1VHF558+fx6RJkxASEgIXFxe0bt0aCxcuhMFgqPJ+ctknH374IVq2bAlnZ2dERkYiMTGxyvFbtmxBWFgYnJ2d0aFDB2zfvr2eKq3Y8uXL0a1bN7i5ucHHxwcjRozAyZMnq7zPunXryj32zs7O9VRxxRYtWlSuprCwsCrvI7d9Uaqi57VCocC0adMqHC+X/bFnzx4MHToUAQEBUCgU2Lp1a5nbhRBYsGAB/P394eLigujoaJw+ffqe663pc6zahANYsGCBWLlypZg1a5bw8PAod7vJZBLh4eEiOjpaHDp0SGzfvl14e3uLefPmVbneAQMGiE6dOomDBw+KvXv3ijZt2ohnn322jrooS6/Xi2vXrpX5mTx5sggJCREWi6XS+/Xq1UtMmTKlzP1yc3PrpeaqBAcHiyVLlpSpq6CgoMr7vPDCCyIwMFDs2rVLJCcni4cfflhERUXVU8Xl7dixQ4wfP1789NNP4uzZs2Lbtm3Cx8dHzJ49u8r7yWGfbN68WWg0GrF27Vpx9OhRMWXKFOHp6SkyMzMrHL9//36hUqnEW2+9JY4dOyZee+01oVarxeHDh+u17jv1799fxMbGiiNHjojU1FQxaNAgERQUVOXvUWxsrHB3dy/z2GdkZNRj1eUtXLhQtG/fvkxN169fr3S8HPdFqaysrDJ9xMXFCQDi119/rXC8XPbH9u3bxb/+9S/x7bffCgDiu+++K3P7ihUrhIeHh9i6datIS0sTw4YNEyEhIaKoqKjSddb0OVYTDhHUpWJjYysM6u3btwulUlnmF2LVqlXC3d1d6PX6Ctd17NgxAUAkJSVZl+3YsUMoFApx5coVm9d+LwaDQTRr1kwsWbKkynG9evUSL730Uv0UVQPBwcHi3Xffrfb4nJwcoVarxZYtW6zLjh8/LgCIAwcO1EGF9+ett94SISEhVY6Rwz7p3r27mDZtmvW62WwWAQEBYvny5RWOHzlypBg8eHCZZZGRkWLq1Kl1WmdNZGVlCQDit99+q3RMZf8nSGnhwoWiU6dO1R5vD/ui1EsvvSRat25d6cGEHPfH3UFtsViEn5+fePvtt63LcnJyhFarFV988UWl66npc6wmHOKl73s5cOAAOnToAF9fX+uy/v37Iy8vD0ePHq30Pp6enujatat1WXR0NJRKJRISEuq85rt9//33uHHjBiZMmHDPsZ9//jm8vb0RHh6OefPmQafT1UOF97ZixQp4eXmhc+fOePvtt6t86yElJQVGoxHR0dHWZWFhYQgKCsKBAwfqo9xqyc3NRdOmTe85Tsp9YjAYkJKSUuaxVCqViI6OrvSxPHDgQJnxQMlzRm6PPYB7Pv4FBQUIDg5GYGAghg8fXulzvj6dPn0aAQEBaNWqFUaPHo2LFy9WOtYe9gVQ8nu2ceNGTJw4scrvaZDj/rhTeno6MjIyyjzmHh4eiIyMrPQxv5/nWE3Ibq7vupCRkVEmpAFYr2dkZFR6Hx8fnzLLnJyc0LRp00rvU5fWrFmD/v3733Me9FGjRiE4OBgBAQH4448/MGfOHJw8eRLffvttPVVasRkzZqBLly5o2rQp4uPjMW/ePFy7dg0rV66scHxGRgY0Gk25cw58fX0lefwrcubMGXzwwQd45513qhwn9T7Jzs6G2Wyu8Dlw4sSJCu9T2XNGLo+9xWLBzJkz8cgjjyA8PLzScaGhoVi7di06duyI3NxcvPPOO4iKisLRo0fr5DsFqiMyMhLr1q1DaGgorl27hsWLF+Ovf/0rjhw5Ajc3t3Lj5b4vSm3duhU5OTkYP358pWPkuD/uVvq41uQxv5/nWE3INqjnzp2LN998s8oxx48fv+dJGHJzP31dvnwZP/30E7766qt7rv/555+3Xu7QoQP8/f3Rp08fnD17Fq1bt77/witQk15mzZplXdaxY0doNBpMnToVy5cvl3zGovvZJ1euXMGAAQPw1FNPYcqUKVXetz73SUMxbdo0HDlyBPv27atyXI8ePdCjRw/r9aioKLRr1w6rV6/G66+/XtdlVmjgwIHWyx07dkRkZCSCg4Px1VdfYdKkSZLUZAtr1qzBwIEDERAQUOkYOe4PeyDboJ49e3aVf5kBQKtWraq1Lj8/v3Jn35WePezn51fpfbKyssosM5lMuHnzZqX3qY776Ss2NhZeXl4YNmxYjbcXGRkJoOToz9ahUJt9FBkZCZPJhPPnzyM0NLTc7X5+fjAYDMjJySlzVJ2ZmVmrx78iNe3j6tWrePTRRxEVFYWPP/64xtury31SEW9vb6hUqnJnzFf1WPr5+dVofH2aPn06fvjhB+zZs6fGR2FqtRqdO3fGmTNn6qi6mvP09MQDDzxQaU1y3helLly4gF9++aXGrxLJcX+UPq6ZmZnw9/e3Ls/MzERERESF97mf51iN1Ppdbhm518lkd559t3r1auHu7i6Ki4srXFfpyWTJycnWZT/99FO9n0xmsVhESEjIPc8srsy+ffsEAJGWlmbjympn48aNQqlUips3b1Z4e+nJZF9//bV12YkTJyQ/mezy5cuibdu24plnnhEmk+m+1iHFPunevbuYPn269brZbBbNmzev8mSyIUOGlFnWo0cPSU9gslgsYtq0aSIgIECcOnXqvtZhMplEaGioePnll21c3f3Lz88XTZo0Ee+9916Ft8txX9xt4cKFws/PTxiNxhrdTw77A5WcTPbOO+9Yl+Xm5lbrZLKaPMdqVGOt1yADFy5cEIcOHRKLFy8WjRs3FocOHRKHDh0S+fn5Qog/P57Vr18/kZqaKnbu3CmaNWtW5uNZCQkJIjQ0VFy+fNm6bMCAAaJz584iISFB7Nu3T7Rt27bePp5V6pdffhEAxPHjx8vddvnyZREaGioSEhKEEEKcOXNGLFmyRCQnJ4v09HSxbds20apVK9GzZ896rflu8fHx4t133xWpqani7NmzYuPGjaJZs2Zi7Nix1jF39yJEycezgoKCxP/+9z+RnJwsevToIXr06CFFC9Ya27RpI/r06SMuX75c5iMmd46R4z7ZvHmz0Gq1Yt26deLYsWPi+eefF56entZPQjz33HNi7ty51vH79+8XTk5O4p133hHHjx8XCxculPwjQS+++KLw8PAQu3fvLvPY63Q665i7+1i8eLH143QpKSnimWeeEc7OzuLo0aNStCCEEGL27Nli9+7dIj09Xezfv19ER0cLb29vkZWVJYSwj31xJ7PZLIKCgsScOXPK3SbX/ZGfn2/NCQBi5cqV4tChQ+LChQtCiJKPZ3l6eopt27aJP/74QwwfPrzcx7Mee+wx8cEHH1iv3+s5VhsOEdTjxo0TAMr93PlZvvPnz4uBAwcKFxcX4e3tLWbPnl3mr79ff/1VABDp6enWZTdu3BDPPvusaNy4sXB3dxcTJkywhn99efbZZyv97HB6enqZPi9evCh69uwpmjZtKrRarWjTpo145ZVXJP8cdUpKioiMjBQeHh7C2dlZtGvXTrzxxhtlXs24uxchhCgqKhJ/+9vfRJMmTYSrq6t4/PHHy4RifYuNja3w9+zOF6bkvE8++OADERQUJDQajejevbs4ePCg9bZevXqJcePGlRn/1VdfiQceeEBoNBrRvn178eOPP9ZzxWVV9tjHxsZax9zdx8yZM609+/r6ikGDBonff/+9/ou/w9NPPy38/f2FRqMRzZs3F08//bQ4c+aM9XZ72Bd3+umnnwQAcfLkyXK3yXV/lP5/f/dPaa0Wi0XMnz9f+Pr6Cq1WK/r06VOuv+DgYLFw4cIyy6p6jtUGvz2LiIhIxhrE56iJiIjsFYOaiIhIxhjUREREMsagJiIikjEGNRERkYwxqImIiGSMQU1ERCRjDGoiIiIZY1ATERHJGIOaiIhIxhjUREREMsagJmqgrl+/Dj8/P7zxxhvWZfHx8dBoNNi1a5eElRHRnfilHEQN2Pbt2zFixAjEx8cjNDQUERERGD58OFauXCl1aUR0G4OaqIGbNm0afvnlF3Tt2hWHDx9GUlIStFqt1GUR0W0MaqIGrqioCOHh4bh06RJSUlLQoUMHqUsiojvwPWqiBu7s2bO4evUqLBYLzp8/L3U5RHQXHlETNWAGgwHdu3dHREQEQkNDERMTg8OHD8PHx0fq0ojoNgY1UQP2yiuv4Ouvv0ZaWhoaN26MXr16wcPDAz/88IPUpRHRbXzpm6iB2r17N2JiYrBhwwa4u7tDqVRiw4YN2Lt3L1atWiV1eUR0G4+oiYiIZIxH1ERERDLGoCYiIpIxBjUREZGMMaiJiIhkjEFNREQkYwxqIiIiGWNQExERyRiDmoiISMYY1ERERDLGoCYiIpIxBjUREZGMMaiJiIhk7P8DzxiCtvad68wAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-silu\n", + "#| fig-cap: \"SILU\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, silu(x), label=\"SILU\")\n", + "plt.title(\"SILU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-selu\n", + "#| fig-cap: \"SELU\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, selu(x), label=\"SELU\")\n", + "plt.title(\"SELU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-gelu\n", + "#| fig-cap: \"GeLU\"\n", + "\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, gelu(x), label=\"GeLU\")\n", + "plt.title(\"GeLU\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "\n", + "# Adjust layout and show the plot\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-mish\n", + "#| fig-cap: \"Mish\"\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, mish(x), label=\"Mish\")\n", + "plt.title(\"Mish\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "# Adjust layout and show the plot\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-swish\n", + "#| fig-cap: \"Swish\"\n", + "plt.figure(figsize=(5, 3))\n", + "plt.plot(x, swish(x), label=\"Swish\")\n", + "plt.title(\"Swish\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "# Adjust layout and show the plot\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-sqnl\n", + "#| fig-cap: \"SQNL\"\n", + "plt.plot(x, sqnl(x), label=\"SQNL\")\n", + "plt.title(\"SQNL\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.legend()\n", + "# Adjust layout and show the plot\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-nonlinear\n", + "#| fig-cap: \"Advanced Non-linear Functions\"\n", + "# 5. Advanced Non-linear Functions\n", + "plt.plot(x, mish(x), label=\"Mish\")\n", + "plt.plot(x, sqnl(x), label=\"SQNL\")\n", + "plt.plot(x, gelu(x), label=\"GeLU\")\n", + "plt.title(\"Advanced Non-linear Functions\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.legend()\n", + "# Adjust layout and show the plot\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| label: fig-maxout\n", + "#| fig-cap: \"Maxout plot\"\n", + "\n", + "\n", + "# Corrected Maxout function\n", + "def maxout_demo(x):\n", + " weights = np.array([[1, -0.5], [0.5, 1]]) # Two sets of weights for two neurons\n", + " biases = np.array([0.5, -0.5]) # Biases for each set\n", + " x_reshaped = np.tile(x, (2, 1)).T # Duplicate x to match weight shape\n", + " neuron_outputs = np.dot(x_reshaped, weights.T) + biases\n", + " return np.max(neuron_outputs, axis=1)\n", + "\n", + "# Plotting the activation functions\n", + "plt.figure(figsize=(5,3))\n", + "plt.plot(x, maxout_demo(x), label=\"Maxout\")\n", + "plt.title(\"Maxout\")\n", + "plt.xlabel(\"x\")\n", + "plt.grid(True)\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "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": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}