Programming Exercise 3 - Multi-class Classification and Neural Networks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Exercise 3: Multi-class Classification and Neural Networks\n",
    "\n",
    "> In this exercise, you will implement one-vs-all logistic regression and neural networks to recognize hand-written digits.\n",
    "\n",
    "## 1. Multi-class Classification\n",
    "\n",
    "> For this exercise, you will use logistic regression and neural networks to recognize handwritten digits (from 0 to 9). Automated handwritten digit recognition is widely used today - from recognizing zip codes (postal codes) on mail envelopes to recognizing amounts written on bank checks. This exercise will show you how the methods you’ve learned can be used for this classification task.\n",
    "In the first part of the exercise, you will extend your previous implementation of logistic regression and apply it to one-vs-all classification.\n",
    "\n",
    "### 1.1 Dataset\n",
    "\n",
    "> You are given a data set in ex3data1.mat that contains 5000 training examples of handwritten digits,  where each training example is a 20 pixel by 20 pixel grayscale image of the digit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'X': array([[ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "        ..., \n",
       "        [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ...,  0.,  0.,  0.]]),\n",
       " '__globals__': [],\n",
       " '__header__': b'MATLAB 5.0 MAT-file, Platform: GLNXA64, Created on: Sun Oct 16 13:09:09 2011',\n",
       " '__version__': '1.0',\n",
       " 'y': array([[10],\n",
       "        [10],\n",
       "        [10],\n",
       "        ..., \n",
       "        [ 9],\n",
       "        [ 9],\n",
       "        [ 9]], dtype=uint8)}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.io\n",
    "mat = scipy.io.loadmat('data/ex3data1.mat')\n",
    "mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Visualizing the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UKYuiUV8UOni///57c6mIf9+rVy/jNOcqn0ImeN++fS1zVVmrCxcutAzkhoAWpDbKokWLzKzWmH311Vc5y/HYEJSjoE341ltvGREgVdn07sXFxdZlUO4LHXKvvfaa5XyogFxBQUENV8gNN9yQ1ZInwQJ8Olg0Z2vWrMlpbpByR7RuTz/9dAYOHAhgpcX//e9/Z5T9ldhLumnTpnZ5yHUzYMAAwDtw1QhLrkTwDz8Fak877bSULrH8/HxjNikYfvbZZ9vBP3XqVMBrTgQ+UURyg+c6UzBeuQvTp0/P2jwmVh444ogjOOGEEwCv8yB4+U16fqYuKud6cnBwcHBIikZtUQihUMjMUmnHDdH+VBZFv379jML38MMPA5kxy9OBrK///ve/gBfEPeaYYwCfRnj55ZebJtcQJa3D4bDNo9rY7rvvvtaLOVUufNAqkFalpk2iVX/00Uc2f7VZLhqPqqqqrLrn9I4tWrQwTV7B/EgkkhOLT3tH1rDcgSNGjLB8nGuvvRao3igoEy65YO4PeDW2FFTX3v73v/8NeC4llfMOauj6DmXaP/DAA+Zyrc/4hUIh08zV0vfNN9+0dsJy3Yp22rx5c/t+uZamT5/O2WefXU3uSCSStf2l58rNdNVVV9meV+5Gfn5+xtewsygcHBwcHJIilMvAXatWrVJ+mKiwoi4uWrQo5SS3devWhQBatGhRL3nkx/7LX/7CvvvuC/h+yWD7w/qitLQ0JXlqgzSO/v37W70ZxXKuuOIKo2Ims8gkD0CHDh0yukCkwSmYPXjwYKMmJjaACWL58uUhgDZt2iSVR++v7womTWVSyyouLg4BtGzZsl7jE7SaFCPQOl6xYkXKmmhJSYm9XF33meZCweSioiKriqoYUjqacV33mVp5ao8HZUj2fFnR0Wi0RhvQ2s41reuioqIav9TngxRlBflVq6xly5aW8SxLZ8mSJaxcuRLwCTZ1HbO1a9fanDVv3rxOcyb5Bg0aBMCECRO44447AN+i+fzzz1O2ztevX1/rHziLwsHBwcEhKTYai0KaojSHdFgFqVoUQVkkTyYosZm0KIRoNGoySsOpa1wnmxaFIGZRKBSqk1x1tShyhVQtiiCCYwDpxd1SsSgE7alga9tM+NiT7bNgDafg84E/lCGx/lM8Hq+T5pzMoggisQdGsgZcwdpQ9UU6FsWxxx4LeE2bZN0oPvf888+nXCl2QxbFRhHMhobvKxxEsJFSY0Ww/3FjREPlnDQmNJYx0DrJ5XoJHrr1fX7igZ3pwG0mLu5sQWvm7bffBmDgwIFWaWD+/PlAdtIFGvdp5+Dg4ODQ4Mip68nBwcHBYeODsygcHBwcHJLCXRQODg4ODkmR02haOgyRTEIMkcYmT7NmzRqFPGVlZRYdbGxj1Lp160Yhz5o1axolCwvSYxdmEmI9NbY11BjnrK6sp2xjo2c91YbEAlnxeDyj9L5U5RGtLtiBryHlcqiO4LpJjNHl5eXlbI5qW7/1pTL/L0Aso9r6pyQmjoVCIbeHAojH4zXou7WNX7rreqO+KLR4tthiC8CrxaLMY2WW5qqsdjwet8xtlbi+8847jaqmpiKffPIJkHql1A0hWJIdPL616k8l8s7/ryKxdW7nzp1tjDRuK1asYP369dU+l601pLWx+eabA9XLjKvPeK4ptOLp62dhYWHWe4cn9nwOVmFWGXjVVisvL7c9roOvSZMm/+fWtrL5W7RoYeOg8WvdurWNh363ZMkSq6+VyoXhrmYHBwcHh6TY6CwKaYUVFRUcf/zxAFx33XWA1wDmuOOOA2Dy5MlA9ntVSBMtKCiwKpKDBw8GYM8997SGQtIMs2E2h0Ihk0OVOP/0pz9Zm89cNnoX4vG4aT3SGPPz820capMlm/IFs+mV1XrbbbdZnSNZoPfccw/33HMPkF03YSQSYf/99wf8jNpu3bpZJdnzzjsP8Jr55MoNVVVVRc+ePQG/cdHHH3/MwoULgey4w2KxmPXlUMXaPfbYA/DGaPvttwfgm2++ATxLS/1E1Cfiu+++MyskV5ZFsJlRba5mnTuZtgj1jCOOOAKAQw891GpMae522WWXGln/r7zyCn/7298Av3JvffabsygcHBwcHJJio7EopJ2q4uaZZ57JiBEjAN+P+c4771hnrmz7dnVjq7H6Oeecw+mnn15NngULFnDhhRcCmHafDbmCQVC1RTz55JNNY1V3wFz4u6XxNG/enPPPPx/wtdOpU6dahUtVCI1EIjVq/GRScw1qeX/9618Br4oueNU21a9CPTuGDh3KM888A/i9LLIxbpFIxKw/remysjKrTqrKv6eeeio///wzkHnrWGOjtbzXXnuZda7qvldeeaX1atAaC1ZrTUReXl69xisej5tGrFhNjx49AC8eocqs6lWx3XbbWb8IeRRuvfVWJk2aZM/PBdTDo127duy4447VZCwrK+Ppp58G4NNPPwUyZ51q3LWGd955Z5s/9Xi5++676dChAwAHH3ww4Fke6vuiPiT1WU+N+qLQQq6qqqJbt24A3HvvvYBX40QLUgHiUaNGWTOTbB6KFRUV1q5RC6J169Y2YS+88ALgbTKZ7dl0gQU32y677JK159QFmrNWrVpZi8i+ffsCcPjhh1uTlS+++ALw3AaqVaOFnBisTAWJZaMHDx5sh+DXX38NwJgxYxg6dGi1z/fs2ZNbbrkFgL///e+Ab6pn4hDSc9q2bWsHjN4zFovZGtpmm20Ar1y82nVmCpJBe0QX+XXXXWftSL/66ivAU3Akk9C5c2ebU5Ey9A5z586tl7zhcNjcfldeeSXg932vqqpizpw5gL+uN9tsM+uVffvttwOeu3DmzJkA1hc9G27DaDRK7969Ab9JUFFREatXrwawS61r167WhkCK4ptvvgmk3+BM76VxmTZtGt9++y3gN8D69NNPza0kt+Z5553HrrvuCniFBKF+Z5JzPTk4ODg4JEWjtCikwbRu3RqAI4880lwqffr0AbxWn0uWLAG8RkLgUVDlXshGAFfurx49enDppZcCflOTtWvXmoYji2Lp0qU5aW0JHk0OYNtttwW84GxiQCsXkNZdXFzMTTfdBPgNXXr37m0aq4JxQ4cONS1JGqW0tYKCgpRl17srwDdq1CizVB5//HHA06C1dmTSRyIRa4EprfCNN94APG0u3bHUuhw+fLi5TmSFvf7667ZejjzySACGDRvG66+/DvjWUToyBMt6n3TSSYDXThO88ZYLR1rnzJkzzfIZPnw44Fk5skIk0+zZswG46667rIppXaE1I+tbrtKgS/Xdd98FPPfOOeecU+3vV61alXMascgyCxYsMOtYltSDDz5o89elSxeADbrq6guN1SWXXAJ46zXYbEmfEannkEMOATyrWJaHo8c6ODg4OGQcjcqi0M2oQJF8xX369DH/n2iDb731lmmNDz74IAAHHXSQWSHyVWZCm5YlsfXWW9vzpBlLU3jiiSdMDr1Htqm5QjAjXUk333zzjSWO5dKi0LMqKyst5iCf+JQpU3jkkUcAv3H9nXfeaY3iFeBOh+Io7Vx+bLWq7dq1KzfeeCPgB00HDRpka2jWrFmAN25HH3004PvfExP10pFLwepjjjnG5uqVV14B4IILLjAN8LDDDgM8urPmNlFzTAXRaJQtt9wS8IPBCnzedtttPPTQQ9XkvfDCC7ngggsA7O+WLFnCP/7xj2qyK0GwpKSk3hqrrCy9n9ZDq1atbD8fddRRgKchy9f+5ZdfAp4nQTT0bO65vLw8o+mOGjUK8MZTSZKSS0FtyB5dV+dOsHGSiDV//etfbW7btWsHeNbquHHjgNTGyFkUDg4ODg5J0agsCmnu0qpEk/vXv/7Fk08+CfiJN+D7/3STfv311yklk2wIurVVIuSf//wn4Fk8paWlADz33HMAXHPNNfbMXFkSQigUqtG2sbKyMiOacDoyKTYhVFZWGutDsaTOnTubpjNx4kTAH79U5lDaqXzEogiPHTuWH374AcDonsuWLbOkLSXZ7bHHHsaESpYcWF/IclGsbf/99+c///kPAKNHjwagtLTUNHOt41gsllGtNBaLmcXev39/wGfu3XvvvXTu3BnA4kuDBg0yjVnr/4UXXjCWkRDsQFmf8QqFQhxwwAGAH0+SZr799ttbzE1rec2aNWbN6EyYP39+jbWWLUh7DybZ9erVC4Bzzz0X8BInFesROynTZ4LGuKqqyixg0dF33XVXY3+++OKLANxxxx02j6nI0qguCh0iCqTp4Pjiiy9ss+gl4/G4ZRrusMMOAJx99tm2wdKdmHg8bt+hza0aTtFolGeffRaAm2++GWjYYmWxWMzcKY2pmFwiRXWLLbaw7FvRi6dOnWruobKyMiB1anM0GjVXhYLlCmCPGzfO1osuk4suusgCkXJ7DR8+3DahNpsOhVQuDP2t5kcuy1AoZGtIbq+CggI7qJWLs3Tp0oy7DjdUoHK//fbj4osvBmC33XYDPKrlv/71L8CneJaXl2eMpBGPx62SwamnngpgSlgkEjHlUc/Lz883GmgwuJ+Yi5Pq5ZosRyT4vSKPDBw40C4IXXT333+/uaFVoypbpJZIJMKwYcMAn3xRUlJiNHS5WxcsWJDWmehcTw4ODg4OSdGoLAppA6LXSXPIz8+3W17a1TnnnMMpp5wC+Cbo5MmTM6bVV1VVWZ0ZBYYk35tvvmmBdiWLpZtIkwqCFWOVraoA6XfffWfaTENYGbFYjPLycsDTugBGjhxp7o4JEyYAXiBS2k+q7gNpeZFIhL322gvwXCbgW6WVlZWWtCVq45tvvmnz1r59e8DLSBbtWnOb6vgFSQYXXXQR4NXgAli9ejUffPBBNfmDVqm0v4qKioy6nvLz8+39Fbg++eSTAS8pUTWTPvvsMwBOP/10mx/9LpPacSwWM7ffjBkzgOp1lOT23XPPPQHP3XzXXXcBsHz5csCj5I4fPx6oPw01kXLcvn17s/42JC/AkCFDABgxYoSNy48//gh460pJhNmm7RYWFtpZpLWz00472TqTG/X2229PSxZnUTg4ODg4JEWjsigSNSfdkK1atbKSBooTjBw50pJw5OMuLS3NqPac6MuV9vHaa6+ZxqBSBqtWrTJKrv4u27TUYKMSWT/S9latWmXy5tKikDbYrFkz02YUx+nYsaMF/0UvXLZsWcYCkS1atDAapWITY8aMATwLQ5RZ+Y+bN29eg0DRt29fS5xU7CDYH6E+iMVilpC53XbbAb6lMHnyZCuTIU2vSZMmZnFJc506dWpGk0fD4bCNjYLTevctt9zS1pQIIrfccotZZaLCZjJwnJeXZ9RWBdWD76n1pLnr0aOHWY2KOY0ZM8aqAN92220AdaomG4vFLHB+4IEHAh6ZQXGiYGVofZf2kizQcDhsnwsSAWRBKgkvW/HLcDjM999/D8CJJ54IeJRm7S+9X8eOHe3MSkWWRnNRBDNGd9ppJwAL0gwYMMCClNp4zZs3t2xQFW/LdMBI8ujA1YYeOHCguVPEIJk/f74t0vfffx/IfoBb8nXt2tVqYanuzOLFi3OaP6HDTLztCy+80OrcaIHedNNNdjgpUJwJNogO1S5dulj+gdaGWES9evVi+vTpgJ9jU1FRYVnHKrK2atUqXn75ZSD9AzEajVrujS4KueN+/PFHcw3qOQcffLCteeUNvfXWW7b+MrW+tW4UsNacffXVV7z99tuA77o76qijLHtd+RaPPfaYretU15j+rqKiwg51HcJaS+C/sy70uXPn2txqnz344IPG+NHl/s477wDJ5zAWi9mebdOmDeAxuuRC0tyddtppgHeR6qwRU2/GjBmmvIph17VrVwtsy41e13Mg2DIgqOglY+Dpu7W2SkpKbI51wRYWFqblwnSuJwcHBweHpGg0FkU0GjU+sEx/BZWi0ahpG+Jvx2Ixq/mioPf48eMzFlTOz883s1EUSuVtHHnkkTU0hA4dOhhn+eqrrwY87n5iED6TCFKG1fxFGvT333+fdbpusGmLKMpyAw4YMMCCkxqPadOm2TxmklcerIaq+Vdpbq2hvffe26ifsnD69Oljssl1d8UVV/D7779nRMa8vDyzODfddFPAt34///zzauW9waMySrMVQePHH3/MeEA0sQ5Hjk1oAAAgAElEQVSW1sndd99t1pRKUR9++OFcf/31gN+Qa+LEiRbwr69sQUsCvFwOkUVUUytoDST2zC4oKDBNW1WAly9fbmXRlXeh/Jg/sgpFyVZgfPHixVYhVq5TzcmHH35o46L6W6FQyIgZskCaN2+ecrOnWCxm36N3WbhwobmXaqvfpvGQ6+vII480K01tF3777be0zkZnUTg4ODg4JEWDWxS6Iffcc0/zF0r70u8qKyvNJ6iszO7du/Pqq68CWN+D119/vYYGkirC4bAl/khLlna42Wabmc9UGkNlZaX5U0VXKy4uNtpeNmhywXeUVijf9sKFC7MWxA4m0sl/rbr3CvLdfPPNFrhOl/76R5BVs91229kzpLHuvPPOAPz+++82NupLcfzxx5sWpiTPJ598Mm0ygsanadOmVtMqMXO+Xbt2ZhHrZ7du3XjrrbcAf52XlZVl1DKMxWIW79O7K140c+ZMe3dVcH3ooYcslqFKCen4u4OWBHi9J2Th3XHHHYAflwiFQvYcyZWfn2/7XU159thjD7NeP/zwQ5OxLpCFoOz4fffd12JH+i7FtiZPnmxEgNqqByjTPhj0ru8aikajVg9MMkUiEYvLiEocrASredH5udtuu5kXRJZPuudPg18U2kA9evSwoJoGV0GlMWPG2KWgQnfLli3jpZdesr8Fr4Ca3AaZOJg12fPmzQP88uHDhg2z7mTi2sstBb4Zm+0SGsHNmhjsymYgW+60IUOGmJtQh5kCf//+979t/LJdXkHP+eqrr+xSUpllXfZFRUXG2pEJ/sUXX5jrSe6OqqqqjF2w4XDY2DiJ7J2HH37Ycl40Pp988gmXXXYZ4B/UmSZohMNhK+WgsRJTbMSIEXaw6DPt2rUzt5wu2nQuL60dFc7r3LmzBcnlulXZi6qqKttD6gK49957m5s1OO8KZmuvBplKG0JeXp6V2pArrWPHjvYdOn+C+zjZ2sjEusnPz7cLSlnVl1xyCYceeijg9xNX4Doej9ua0vn52WefcfbZZ1d7hyZNmrhgtoODg4ND9tDgFkUQ0hQUiLrmmmsAL8tYGkKw9LP4+dLulyxZkhUXj54p7XPy5MlWCEyF5hQAA7+N5JdffpnVHAZpdevWrWPu3LmAb3GlUu75j5AYBB05cqRpW6KXSjNv0qRJzui5es/58+fbHCnbWEHOZs2aGVXx448/BjyXoqiymuNMzFcwYCtXkoog6vubNm3K559/DviFJefMmWNkhGw2vNJ3yy0q6u6VV15pzYw0LkVFRUYIELV5yZIlKcsn62nq1KmApzWrRpFykkSMCGrAGtPvvvvOiAoitkycONFyMbT/66I9B2tEqbd1sFlSNnq41wWSSR6ML774wqpQnHHGGYBfij0cDlvAWtbDE088Yf+ui2VVFziLwsHBwcEhKULZaqxRG1q2bFnjYXp+UVGRBbHlL1Ty2Ia0F/k79bOuWk5JSUloQ/LUBRUVFaZdS4MJNqAPZtrWRauWPM2aNUtJnng8bgEw+cSnTZuWsjZRVlZmQmuM4vG40fDUhvH22283yunDDz8MVC83nUlojFq3br3Blwn6klV9VZpXfn6++d0VvC0tLU2ZArtmzZoQQJs2bTYoTzweNw1aVm9wPSgwKiuioKAgZXmKi4vti1u1alWnCRchQzGC448/3qruyt+9evVqHn30UcCrSADefqvLul63bl2Nfaa/C9ZkUnBdP2tbt/q7devWWdxJlaI39DeJ0BpKNme5RHDOmjdvvkGZqqqqzNui2lfBhEfFjrS+q6qqUt5/69evr3VinUXh4ODg4JAUDW5RCLFYzLSMDdXLzxTStSgyjVQtCmlZwcQ3IS8vL2W/5IYsCj2jT58+gMeWEWtEpROyVS2zLhaF5ITqjWUEjVcmrJ66WBRBeRKrmtbmC08HqVgUgsZoQ5VXNW71pXzWZlEkfmdwXdWFJRgKhWrMY5BGmwwbq0UBG15HQI1yKunEBjdkUTSaYHY4HG6wxj8bK4KbI3HsMq0AhEIhOygUOJ8+fbq5+3Ld1W9DSDzUGrqRk+TJdrnpdJAtd2Ey1LZ2U31+LpXdhkJDryN3Mjs4ODg4JEVOXU8ODg4ODhsfnEXh4ODg4JAU7qJwcHBwcEiKnEZGGhvL6I8YNBtCPB43DrqYGvn5+UmbiySDGDRFRUWNYnzWrl1rL9C2bdtGIdPq1atDAC1atGgU8pSWlqa1hjINrSGoP+spWxDrqbGt68Z2DkHjlCmIxkvFaITQpVBUVGRFupQkNHv2bCvdoYSgTDMU9PwgtTD4/6FhGCy1oT60x1Qv2FQRlCtXbWuTyRHsWdJY2FGSKTh3uZ6nxojEPRePx2vQUnOx92qjy2ZzLTeOVVkPBAdI2dDBwVImbDY2nJ7dpEkTuyiUU9CsWTMrM3zDDTcAXjXQdGv2aNJjsZhlZ+p99Y7t2rWzxanGOKWlpQ1y6AQ3krKjlXG/oc+rUqo2XzY2WiQSscxyNaLZZJNNrKZRtiv9JiIajdKiRQvAb65UWlpq1Y+DjXpyheDlrppCgwYNsoZCzz77rMn+f/GyqKqqsvWtCgj5+fm2H5UZXV5enrXLIrGNQufOne3/qaJFNuBiFA4ODg4OSbHRWBSJ9Zy22morq2mv1oHRaJR3330XwNqYZvJml2m3atUqq7KpWkLHHXccZ511FuDXPbrgggusUmkqLRHB719w0kknWQMZNXqR22v//fe371f11vvuuy/r2dJBSKsJtve84IILAKy5UVALDVpK6sHwzDPP2P+DzMyd5Nltt92sOumAAQMAr3nOfffdB/iNgrI9VpKnadOm3HTTTQCceuqpgNfSV02y1Kjmhx9+MMsjF9A62n333QFv7vRvzfGTTz6ZVTdUbTWe6vo32ZBHc9ajRw9rlqSaWE2aNLF1qj4Sd999t7mfM21Z6BxUbbfnn3/e2p4OHz4c8CrsZjrR1FkUDg4ODg5JsVFYFPF43HyCJ554IuB1V5NGrd8VFBRYi0C1BVQtokxrGvo+VW685557+O677wBP4wIvVqHuYfJf1lUOfU6ayeabb25tPdXtS/0VJk2aZBqV2kRuvfXWnHDCCYDXWB2yW85C/n+1uHz44YfZcsstAb9KaW0yhEIh6+Sl+NJjjz0GVA8U1hfSAnfddVcAHn/8cWtQL2tzyy23ZNiwYYBvUWQLGh9V/3ziiSes70JZWRngdUmUHIqdPP/882b1ZCtYKS01HA5bTER9TaLRqFkPqhr8008/8cknnwDpx1BisZjNVbCFLHjrQRVig+zCxCThYN2sRA0+nbGSXOqXcfPNN5uld++99wLe/h84cCDg772nn37a4pWZtij07oqNbrHFFjYHWlvffPNNxvd6o7wogiwQ8BaoNrRMrry8PB555BHAb+nYpUsXunbtCvj9rbWgV69enZUAk76zsLCQ999/H4CxY8cCXrMaucXU3rGuExh0zQCMGjXKDhEtCAWBdZmAP3ZnnHGGtU3U57JxUQTLxANceOGFAHTt2tUOGz03FouZ2yxIStBFf+yxxwLw8ssvA56LL1WXnVrTSp5bb73V2nyqJ/LBBx/MlVdeCWSPqZJ4+MnNtMcee9j46DPhcJi2bdsCfsD9sssu47333gO8AwAy5x7Tc/WscDjMyJEjAb9V6ejRoznyyCMB38V7wgknWNOlVF0++rvmzZtbCXYpQuozvtdee9ma/+yzzwDvAtVYBt1fxx9/POC77NQwKhNkgB133BHw2vuqZ7XWcdu2bRkxYgTgt2HN1lkD/jpVT+wffvjBXKpyUVZWVmbcNehcTw4ODg4OSdGoLAqZ52qacs455wBw+umn1+qyGDJkCOBriKtXr7Zg4Ntvvw34mly2uc3hcNhcLJMnTwY8DVmushkzZgD11+qDGoG0GDW80e8ikYhp5fvttx/gVXidPn26yZYtyDyXtilXT2VlpY29GvP861//slwTjdVOO+3EVVddBfjz3rlzZ8B366Uiz7bbbgv47Ts//PDDGpVujzrqKPt8tqi5shpEdFCL1vXr19uzJMO7775r73zggQcC3piIHHHeeecBvnWaKvVa2rx+Xn755QCsWLHCyCByn3777bfmUlUDo/79+xuld9GiRUD9NVft9QMPPNBaGm+//fZA9YZkcrvJa/Ddd98Z7VrzGA6HjeihgLI07uLi4pQtaWnlGou1a9faOmnZsiXgtUc+5JBDAD+YvGLFiqy1stU4q6nbl19+aRbPueeeC3jjIpd7eXk5kP66dhaFg4ODg0NSNBqLory8nJ122gnwA9HSCseMGUOPHj0AP2D07bff8sorrwC+j/68884zi+Knn34C/EBuLhOXgsHBbt26AZlJ6EqsSa/vHDx4sPmWFeg+77zzTBOU9pMNJMZS9LNZs2b89a9/BXzrbtWqVWb9SSs8+uijbW7S7W0RjUZN091zzz0B36IoKCgwLVaxm/79+xuFNxuIxWKWbCitU/MTi8VsXKQ1z50719byFVdcAXjavvaFtGZZp6lorbFYzP7uuuuuA+Dss88GPP++4muyAps0aWL+/o8++gjwrFZpz9qrsh7/CLJitIabN29ue0Ta78SJEwEvyC8LVeN22GGHmTUa3GcaN62ddPa71rAsPclVVFRkVq8IGNttt53tvZkzZwKpW3p1gSwDBfmnTZtmpBWtj0gkYpahiBJpPzcj3+Lg4ODg8D+LBrcopB3069fPGAXSMOSTLS8vZ++99wZ8Tev555+379DN/9tvv/HUU08BGEtK35kO1bKukIYjFkKnTp1MG8vEs/X922yzDeAzaA477DAbM8UA1q5da3L8/PPPgDfW0rQyPRa10RPlRxXrqkmTJuy1116AXyJiyJAhRouVRpZqsmQoFLIxGj9+PFA9niN2j3zyH3zwAV9++SWQWUZYkL4pq2r//fcHfO10wYIFXHvttYDPZiooKDDK9y677AJ4vvzEVpfpIBqNmnYuZqA04M8++8zKQAQtBFG7ZVHss88+tG/fHqjfHMXjcZsfxRfvvvtuG/sXX3wR8Gm4wTI0SnTbYYcdbEw1n8uXL+fOO+8EPGYS+KVs6ssQC1pcoqD269cPgL333tuSD8WunDRpkq1zjVl5eXnWOytqz3z++edG+5ZFEYvFMt71r8EvCgVBr7rqKnr16gX4JrFogTfffLNRJseNGwdgdY/ANzM/++wzJkyYAMBpp50G+BfKkiVL6jV5sVjMXBWJg56fn1+D0x6Px83FI1dBcXGxmfKZMEf1LAW15Zpr166dHYjKXXjooYfMzSPa3qRJkyzQLtM17SDX//97HTDKY+nYsaNd9AsXLgSgZ8+eRkft2bMn4AV1dQDdfvvtgO/2CM5xXWXRplVQOEjNVSBZh9y5555rSkY2MrKbNWtmlF/JsXz5csBTguQeVWZtNBq1w6ZDhw4md7J+yalAB5/cuZq7d999t9ZLSWM0ZcoUwAvISwkRiWLFihXV3rM2xONxo3CKctu+fXu71JWhr8tUhyHAa6+9BnjrViQX7bcrr7ySBx98EPDHMpULAjwixV133QV4bqXgOy5cuND2c7B//P333w/4LtbbbrutTuORDjRPK1eurEFuCf4+Y8/L6Lc5ODg4OPzPoUEsimAl1GuuuQaAQw89lFGjRgF+AFLa1ZgxY0wT+6OgmTJapS1J6wiWlE6GYAKZNAo9U1rE/PnzrcpnMPClpJ/BgwcDXpKcaHp1DfYlg7QEjcXVV18NeAErvacohrvvvrslb/Xu3Rvw3HAKDqrCbaYsC7mL7rjjDsBztcgUFlWvoKDAND1Za4WFheY2+Prrr4H6WxJBSKvSXOs5O+ywgwVtRcdctGhRNa01G1AtMMml8f70009rPDsajXLMMccAmHUdDof59NNPAV+jT0XmYGKcEtyk3b/55puAVyesNss3mByn56fiDovH47YPpKWHw2FzOcoa1HOCz5Zce++9tyV3ijL75Zdf2u9T1eCDyYd6N7mxZCl8/PHHZu0IeXl55o6SRXzDDTdw0UUXATVbA2Qa8XjcXE9KVNx2223NqzF16tSMPMdZFA4ODg4OSdHgMQppAh999JHVu5dWIJ/swoULk2owQcqdgoDS3ORfrW8Vyosvvth87NLgJM/s2bMt6UlUvqqqKs4//3wA0wA/+ugjs0qUmFRRUVEveWqDxkKxh6DcCmaPGzfOPieL4plnnrFELlltinfUNygJ3thKY1Y1XVH1otGoaVMav5UrVxotVv75CRMmWIXdbFCYZVHstddeFj+RZp4tGqPeW1RK8Nf0Bx98YP8dTJgEz4oVCSOYjKc1pthNOvGUJk2amFWp9Txt2rSk76L5Gzp0KOCVkJGVKOu2LusnFArZ2Mh6/O6773jppZeA2q3uxITOww8/3P6fKKpz585Ney41P9988w3HHXccQI0ulgUFBfa5YNKiqKgPPfQQ4CUK612UcJkthEIhW2eSbeXKlRnvTdFgrie5RWS2jR071g7TxAPjjxahDt99993XDkLV9ZEr6o++Q4tCRe2GDRtmGbGJB8uf//xnK1UdLDcsU14m8ZNPPmm1pm655RbAD9RlwhQNvlPioZOXl2dMKC38Dh06mGypyJGY0TtkyBBjXumC1qFSXl5eI+9j9uzZvPrqq4CfC/DLL79khYklGeWS22233exCUvAvW24nzcHhhx9uz5dioYKH4XDYPqe9cO2115rLSYdTWVmZBXszgYKCAiNBJMtG1/hVVlaaTGJJlZWVWU0lvUNdxjIcDpsCJ8ZXNBq1yzxRjng8bt97/fXXA55rVYFildGPxWIZIyOEQqEa9avk0mnSpIm5oYIXkz4ndtimm25qv1d+R7ZcT9Fo1OpuaZ8vW7aMBQsWZPS5zvXk4ODg4JAUDe560u0dbM5S14qUMp1V6fLkk09mzZo1gFfGGfw6UH8UTNZ3qepo27ZtmTt3LuAHhKQl/Prrr2ZSKq/jq6++4oUXXgB866S0tNQsG1k9qQaNg+WYEwO2sVjMnqnM5KOPPtpyFVTOevny5ZZXouBzfUx2aX5yXVx33XVWl0kWSm2uNck2cOBAC8Art6OwsDAr2lZiFdm+ffva/AT7HScik7K0bNnS1p0Co1pToVDIaLpqYHTiiSdaJq3m+qWXXrIgbyYoj7FYrEb9H2njFRUVtg+0tnr37m10Ua2jiRMnGs06VXdhMCic7L00DvpMXl6eue9Egc5WKW/lm4ic8uyzz9ZYH/F43MZK1PRff/01o56DZDIWFBRYKwNZX6FQyDUucnBwcHDILRrEogiHw+YnFn106NChprmrnWdtNdWD/kxpZErUGTx4MI8//jjg16Wvqx9az1LA85tvvrG4ggK10r47duxoQVz5nO+9917z/wf7CwRv+VQg7bdnz54ceuihgN+wSNVh+/bta/WL5Efu27evjZXoczfffLMFIVMJ/un7VK2yS5cu9aolE41GTdPJVhMeQXOg4HnPnj056KCDAD8+sn79+hprLBiETxX6rgULFpiFpZ4Foi1GIhHLLNZ4lpWVGfXzueeeAzyKdXA9pYvy8nIjMogmLNmUFQ5+f5EDDzzQYhraG2PGjDFtPtUgcl3eJRKJ2JypMkNZWZn1qFCsokmTJjVqjqWzrmQB69nydsyYMcO+P2gxKIaj5MpZs2bVoNFmE9mqthBEg1wUoVDIBlLBoQMPPNCyK2WKi00QPGC0aHv27GnZ1zLvTzvtNCuZEXxWXaDBFpPosssus4NZQWG5dd544w3LFNchHIlEMpIrkQi5Arbbbjvb0HonudW6du1q3HO53p5//nkrj6ycjyVLlmS9J3TQbagxVQDzrrvuMlmyXeJAB5FcbG+88QZ/+9vfAKqVpBZ5QfJMmDDBymmnWgZB7/3GG2+Y+09NeZQ/AP6hpjmOx+N2kYtIUVpampF1pTUTCoWsVIaUHeWXqCICVC81omC6WD2zZ8/OauE7IRKJWHFHZap//fXXNVxx+fn5lj/0ww8/VJM/E4enOtzdd9995krWmu7bt6+Nn/bjww8/bC6zXBQjzXS5jtrgXE8ODg4ODknRYBaFIBM7FouZKawWp3KtlJWVmSasonJr16612/3pp58GvAJZ6bp69Jw5c+ZYxmhi8DMvL88+J000W5qDvnfixIlmEquonTKYX331VRsruaVmzZpln8+UjPp7UT0XLFhgwWK5pYRwOGyF2VQfZ9y4cTVkyhYSyzFfccUV9uzDDjsM8KxTaaCybOfNm2eySSusL4L9zlXGXJm6slKbNm1ao07W448/bla1NOJMW6nhcNjWscqbizYs6wp87fjrr7+2ooVCtrVk7bfWrVtbhQXRTBcsWFDDvRSNRs0NJdnScf3oDFHdOFl8Rx11lLmjte6XLVvGM888A/jtV3/++eesW+5B6FnBnxkv+pnRb3NwcHBw+J9DKBf+LaFly5Y1Hqbnx2IxyyCWX1IB2pKSEtP8pLnOmjXLAtb1bfBeUlISAmjdunXuXj4J1qxZEwIoKiraoDzBMulK0JIGsWrVqhqJPcEAX32xdu1a+8O2bduaTIlB1Y4dOybVeKXVKekxEomkbEmsXr06BNCiRYuU5iwajVocR3GC/Px8C8qKXBGLxeqkMZeWltZpDUkbTXx2cBxECFi0aFG1WEJ9oDUE0KpVq3qNkSwt/YTq/v9Ug6Xr1q37w3WdTJ6ddtrJsra170866aRaGwQFmxhtSFat69rOodqQGEMqKiqyIL/mc/369RZ3S6xL9UfQOVQfmWqDYqfBMufac5K9vmdjIpxF4eDg4OCQFA2ecKebLhwOW/0X1StSrGJDf5dtimVjQvAd5Y8VwuFwVhhXG5JBmtbvv/+elHGRmBiY7bhEMuTl5ZnmrmS/eDxeo+FSpmXU9+nZiiEFERynhljL0oBzwWSqCzRmK1assERFlebZ0HrLxtpKtE5KS0st5hX0YtRG488l1O45KFOmz8YGvyiE4IA7JEdDHrhQs3f3xoLauvD9X3j2xgat74ULFxpxQ7kmv/zyS87XXdAd2BjnLxfj0fje2sHBwcGhUSGnwWwHBwcHh40PzqJwcHBwcEgKd1E4ODg4OCSFuygcHBwcHJIip/SB9u3bN4qAyIoVK0IAHTt2bBTyLF26tF6JQNlGphKBMonGmiTZrl27RiHPypUrbc5STUrMNOqalJgraM46deqUMXnKysqMLh7sqVMXLFq0yOasvkmJ2UIw2TaIjYvf2EAQPU6B/6qqqhq5AY4UUB2xWKzWBkEar1zRDIOZ/3UpH56NOjkO/zsIrieAM8880zKjb7/9diDz9PV4PF6nfKX/uTLjGxu0KJTUtuOOO/Ljjz8CflnvJk2aNNhlUVvXsmx1jvsjqNRC8+bNrZ+2ysFPnz6dG264AfC67UH2LgzNRbAv9QEHHAD4yVu9evWyJM9nn30W8AoeJuslnS6CZSESiw7m5+c3ePKWQ3KovMghhxwCeC0R1A9Hc5upi0J7qUmTJnb2JPatj0Qi9rlsljZ3MQoHBwcHh6T4n7MoNqTVp6OhSVNQIbD777/fNHhpyz///LOVQMiVZSG52rZty4ABAwC/vMdHH31k3dVy0TxFxcfUQ/vqq69m6NCh1T7Ts2dPs8CuuuqqrMpTW39vNaCZNWsW4PWvTuxUeM0111h5ac1nJrR7yaMGPJtvvrl1RhPmzZtnXeQ0npnKuq3vmsyWRZPojoxEIhss5x6s1qCfDZkZHYvF2HTTTQG4/vrrAXjhhResF3umLAmNxzbbbAN47q1OnToB/rjJsikuLrY9/+qrrwJeJ8KMl6fP6Lc5ODg4OPzPYaO1KOLxeI0ywLFYrEYxLP0u2GyovtDfya8+YMAA6zv82muvAV6/bhV8y7YGH2ygBF4rS9XEUdGy8ePHW0MnNRrKRo0oaTby+1977bUA9OnThzfffBOADz74APDayx5++OGA32zq+++/z6jWrDXRvXt3wOtlDtC7d29r1KM2o7///rs9e9SoUYCnKaqk/U8//QSkp9VrfAYNGgTAeeedB3iWhUqOS+ZFixbZM9XAaObMmRlZT/qO/Px8s270XsFWrIl7KhKJVCs5ng7i8TgtW7YE/HLrf/7znznyyCOBmlbMokWLbA2pKVBZWVmD1TqrrKw0WSXDfffdl9Ge5uCX51dM7fzzz2fu3LmAV9YcsIZOhYWF1mhJDbnuuOMOG7f6tmDYEDaKiyIej9vClTsFoF27dgBsueWWgLf4dthhBwBatWoFeB2xAD799FP7dyrPB3+zlZSUcPLJJwNYd6vnn3+egw8+GPC7g2XLTE5kYX366af89a9/BeBPf/oTAKeeeioDBw4E4PTTTwdg2rRpGb/EdLDIpdKnTx8APvvsM/7+978Dfq+H/fbbzxZ/+/btq71DJhCJRIyBosrDW221FeC5CCdPngz4bqDCwkJbTzLbhw0bxgknnABggfdUN1ssFuOcc84BsJ+bbbYZ4B18999/P4D1ODjnnHM45phjAN9l9swzzzB69OhqctQV8XjcDjQpEqeccop1Q9x6660Bv6f6+vXrzTWofgY//vgjn3zySbXPpXpQRyIRPvzwQ8BfL4sXL2bhwoXVvldybb311hx11FGA34Xv3HPPZdGiRUDuilJqvXTv3p1LLrkEwBTFX375JeNuHh38n3/+OeApMVKsND8qkti6dWv23ntvAP7yl78Anmu8pKQEgKlTp1b7zlThXE8ODg4ODknRqC2KYOCrZ8+eABx33HGAF1iWe2G77bYDoFOnTqYJCdJW4vF4rb0A6gNpdPn5+RZwOv/88wGYMmUKw4YNA3xtI1eBt/fff79GJ6sOHTpw/PHHA9C1a1fAC3Bn2qLQOyrwJu1qxYoVpv3IumvevHmtuRXpIsht32+//QDo27cvgPU4fvnll0224BhI01IPlA8//JAjjjgC8CmzokLXdez0jl26dDFrThq0rJTHH3/cxkedHK42LYYAACAASURBVPv27cuYMWMA2H333QGPhilXmXpa1Mey0bpQ3+sVK1aYG0y/23bbbe3zwf4w+szEiRMBOOusswDPNZKKKyMvL89yDdSR8bvvvjNXn54pt0r79u258847Adhrr70A2H777fn111+B7FsUWlcap2HDhpkF+sorrwDZcTPrO0Xdnj17do0ug1988YXJKPKFXE9jx461Hu3ff/894FmI6ZxHzqJwcHBwcEiKRmlRJGqdw4cP58orrwR8imppaakFaW+77TbAoxcuXry42ncpMFRZWZm2ny4IWRT/+c9/AJg0aRKXXnopAI8++mjGnlMX5Ofnm7agMgJt2rQx/6R885l8f/A0LcUa5DOVlldRUWGBXMWNdtxxR/NDK5YQjUYtwKl3UMCurlqr1knHjh25+OKLAU9TBd8qKCgoqPX7EuM9n3zyifl6ZYlJK6tr1rY00H79+hldWGv0H//4BwAtW7a095bFMnLkSIsDHH300YDXIzpVhEIhe6/XX38d8Hz9ss7btGkDYBTh5s2b27qWBTRixAizbvR3c+bMSUmbD4fDFtMLNr+SpRcMoANcfPHFtq7U6W7WrFk15ixbVF7JI8/F8OHDueeeewA/9pnpPRVEss6QwfHXOCh2s3LlSvOyBGNBzqJwcHBwcMgaGpVFkUj7VGr8aaedxhtvvAHAXXfdZZ9dsmQJ4FsgoVCohnaRjTaGoVDIaHI777wz4LGMgr2Ycw1pP/KJ77fffsbMKi4uBjLfEzkvL4+VK1cCmB9brJ7x48ebP1dW3Zo1a4xBImuwoKCgGpMN6m9J6DtPOeUUunXrBvhrR8lIf+RLlob28ccfm4ar75JlVFftUfKXlJTYvIgO2qxZM8CbL61bMdWGDBlifukhQ4YAnp9a45eK5pz4N8uXL68RxwsiUUvv2rWrJZWqbMX06dNTjg/II5Ds2eeeey4ARx55pI3RnnvuCcCtt95qMZvZs2cD3rrOhlWhZ4u9t3z5cosH6P2DlGIhHA7ntASLLDBZ6VtttZVZPJk6ixrVRaENKUrcyJEjAc8doMWhRV5ZWWkHX65ocsEMbQUd5Xq6+uqrjUaY656+VVVVRik888wzAS9Y+vbbbwPZzevQuyq499577wGeaa7NInfYpptuyn//+1/AbwifzuWdmA1+xBFHWGB0ypQp1b7/jzaufr9y5Upbh7vssgvgH5Aff/xxnQ4AKTpffPGFZVqfeOKJ1X73wgsvmOtHAe527dpZ0Fb5OePGjauWC5Qu8vLy6vQ9cv+VlJTYYaNgerYguZ577jnAG+/WrVsDcOihhwIwdOhQ9t9/fwCuuOIKwBurTGZu6321buV6e+yxx1i2bBngkzbatm1rSoAoqQsXLsy6W0yIRCLm/pViGI1GLedLilK64+JcTw4ODg4OSdGoLApBGp1q8vTo0cOCWfPmzQNg9OjRpr3m6vbWrVxSUmKuFlEL33nnHaPiyrzOtgtKFk7Lli2NRqhnjh8/vlpiWbZlUFKdNLttttmG1atXA34iUJs2bSxwK9nSmTO5rKRh7rDDDlZDSm7JP3p3jZfcO4ceeqhpkqJiq77PBx98UCfNTO9UXFzMzTffDPgZ2YMHDwY8q1mfk3Y6duxYyyRXhn0oFMppJrLcGHK77bzzzkYQ+eijj4DMuzAFja2oynPmzLExksXar18/s+bvvvtuwFtzcgll4izQ2lS1ASVEBt2SSsq89NJLrQ6T5uziiy+28yFb1YD1noWFheZ5Ee25pKTEEvQU4E7Xq+AsCgcHBweHpGg0FkWw3IDqusii6N27t/mhVSbjoYce4uqrrwaw6o25qJIKni/1uuuuA7AaLKNHj2bEiBFA9eB6NpCoNZ177rmmtYtG/MUXX5hmnC3Lpqqqii5dugBYDSeVDenYsaPFk0QvrKystBo0shoLCgpq9H+oqz9V76WEvvz8fLM4haB/P7HpTDQaNe1YMYRLLrnEPjdp0iTAp7bW188bDoetZIXkUpXfW2+9tUbPjMLCQosNZLO3QDJobHbaaSfAozSLsisrLduJpLXF+DSPH330kVGGRVUdPXq0yS3LIx2rR2vzz3/+M+C/76JFiyyepJI59957L9OmTQOw8ivDhw+3GFmm915iN70bbrjBEu2ESZMmZbyibYNfFMFGHOJpK4io7MMpU6aYm0Em5rhx48w01KDkCqFQyLJqFXh//fXXLetUXP7CwsKsHNJaLApiHX744XawaIFms5FSME9ArhLxtsWCKi4uNqaK5F26dKkVvZMJ36xZMzPtxc6qbwZysEx18HvBPzBWrVplG155A/369bNsY9XLadmypR2IyrAXQ0vfWR/I9aXvFFMnFAqZu07ve+KJJxoDSqyt77//PqeuJ425FLNmzZoZYUMXf7YvimTzXlhYaK4pZR+/9tprnHHGGYCfL5KOC0p/q7Ujt2Tv3r1NoVDG/+jRo83FuttuuwFehnTi32ZKadTek0I4fPhwW/Mir9xwww12XmZq7TjXk4ODg4NDUjS4RaHA0cknn8yFF14I+Ca/Knq2adPG8hUUsNl555154IEHci2uQS6BmTNnAl55bQUu77jjDsDTrrPhfgoGssDLXdC///a3vwFeBnC61T43BGkrf/vb38z6mzFjBuDXvmrVqhVPPPEE4Ff5jcViFmyWNt22bVury6R5v+mmmwCPoplMe5UmpQz0adOmmZappknSwF599VWrIbTPPvvYT32HrJ7KykpefPFFwLckNLbpaKeaA1lZhYWF5oZTcPbaa68194Ws0zPOOMMombmobSSXhuiokUiE8ePH278h9+6wRMiyU/2qp556ilNOOQXwtH7wXcKpuKD0fl9++SXg57Tss88+FtBXo6u8vDzzIIiaPmrUKKtlla05k1usSZMmJpNK5f/+++/2Dlr/ULPfd33KxzuLwsHBwcEhKRrcopCWcsQRR1iMQnQzaeh9+/a1hDJpPE8//XS1Wz3TCIVCJpuCW8HaK/q3buXp06dbUFUZksuWLcuKRqFnSyu/5JJLLHtUQbbp06czduxYIHk2bCrQO3344Yfm22/bti3g0wY333xzGw9ZjW3atLFgrsatqqrK4j0a57rGViSHkvjOP/988x0ruC7taeDAgRbTCdYU0u8l41NPPWXBa/mXM7G+ZI2I5j148GBLJlP/kssuu8zqPyn+NmLECAvaZhuxWMzas6rGUmVlpdW6yjWCGc+1WZaa//nz59saF5U5MVu6PpAVoqRHZaafffbZ9hyRONauXWu1zFQ14uWXX67RQC1bCIVCVhVb1nH//v0tmVN7a+3atWyxxRaAT33Wunv99df/MO7U4BeFzPrLL7/cAn5qNqMA6axZs3jqqacA38WhABtk56KIxWKWI9G/f3/A73j2n//8x7jlGvwLLrjAZEpsxJJpaPHpYH3llVfsIlXJ6pYtW2YtmK2N9Pjjj1tw9pprrgH8ACNg5aDVWe7bb7+1xkYyzX/66Sc76BMLOtY1aCp55s+fb9mpclWqpEiPHj2MGaZgdnl5ubGR5CabNWtWRjOhBX2XNvXYsWPtYJHr7aWXXrJDWa6F4447Lq0y4/VBPB63yz04psryzVVZiqBrVQd+bVnhusibNm1qv9fBmI6sWndao2o6dfHFF1s5fT1n5syZ1j9brspgkc5sQYU+u3btagF25ehEo1FTqHUZlJWV2ViqUKYC/3WBcz05ODg4OCRFg1sU0rT++9//cvbZZwO+e0mm+dKlS01DCLp8sqnhxONxC5opCCrqYuvWrY3vLhkLCwstjyJYiC4XBQLD4bDx3vW8NWvW5CRTXRRmBdGlCRcUFFipb7V0rKystGz6YIOc+uZPbAjBnAzJpf/Oz883V6WswLVr11qgWAH6/Pz8rNJRtabefvttDjroIMAnaFx11VU1XCZTpkzJOMUyGRKfH4vFLDAq10aQjpxJJOaVHHHEEey7776AT3SIxWJm8cnFe8EFF5g1qgB3JgLucm2pmsDpp59uz9ZaDbqhE5sLZQN6lrLS8/LyzJsQzN/SepYHprS01Cx35afJ3VqXfecsCgcHBweHpAjlsiR2+/bt6/SwxMZFmbYeVqxYEQLo2LHjBuUJhUIWA9BPBUM7duxoVo/quyxevNj8pNIs6jq2S5cuDQG0bNmyXpMRLGEtiqVKnd94440md33HrqSkxP6grjJJCwyWDJdGJn93OnMomVq3bp3Sgg2Wgw5qhalaM2vWrAkBtGvXrl7yaAwikYglGm6//faAR50VkUPW2MSJE+tUAXTlypU2uC1atEhpjCKRiGnwosRWVlYaDV0/Kyoq6jSXpaWl9ZqzYPIteAQJVYgVrTgSiVhAWQHb//73v0YnFlW6Nlqs5qxTp0657wNQCxYtWmSDWFRUVC+ZgrRrxXmD543+rRhFNBo1ayTZfly7dm2tE+ssCgcHBweHpGjwGEVtyDZjoC6Ix+NmGein4hLz58+vUSIgHA5Xa2aSC0hDWLFihVU6Dfrkc9k8Re+e614cdUWwCmsuS2IkIqgJyhr97LPPqv0MImj15AKKhwQtRMml9Z+tOQ42GQOP/q3KqJqzeDxuLWpFJZ47d679TbYq2zY26H2j0aixs2pDpipHN85d3UiRGFBvTGgMh6BD/ZCpIH6mkJeXZ/TcY489FvCCoGq+lGslIFjIMah8/fLLL0DDKUWNCbV19cwGGscKdXBwcHBotMhpMNvBwcHBYeODsygcHBwcHJLCXRQODg4ODkmR0+hUqhz4TEN86vrmLWQLyhFobPJA45Npk002aRTyrFq1KgTQqlWrRiHPunXr0s6jyDSUR9HY1lBjnLPGKFMQjvWUIhJruwdjPZmsHJn4nCAS6YSZemZdZcrV8xxyh8T1FovFaqyzbJfPSQeS6//SGg3OFdR+FqXLrHMXRQqoqKgwfrIqkbZp08YmSg2DIpFIyrkV+rwywPPy8mo0IxHnvbKyskb9nWzQZBNzRxwRInVEIhGrtRNUAjRvWl/hcDjr46zvr6qqsjWmKgRt27a17F6tt9LS0ho1jxoawXcAf0ybNWuWVsnxxo7y8nJrx6AS/5FIhGuvvRbwq8xWVlamV1E3TTkdHBwcHP7HsVFYFNFotIamUFBQYNp6tk1LaSvSovbcc0+r/a4GL3379rU6R+of8OCDD1rWZH01L2lvasBz6qmnWnMg1ZRasGAB4FXXVS+Pl156yf5fJhOkYrGY9Sq45JJLAK+yqbJ26/KsSCRiY5mrdprBFqeJFlF+fn7OksgSrYJevXpZwxs12wmHwzanam9ZUlKS1f4T4M9F9+7d2W+//QCsEnK/fv2s7tSiRYsAL4N89OjRQPZ7ZCRDcF+qKq962Kg21IIFC6zlbDaeHURDjEFBQYHt+eLiYsBr0qVKybIyJkyYYNV/U4GzKBwcHBwckqJRWhTS3FX9tG/fvtaOULXXn332WSZMmADUbBaeaUh7UPPy4cOHmwav2EBVVZXd2GpLunbtWrMu6gv5qhXv6Natm9Xf13uqm10oFDIZd9llF8DrGKjOZJmIV0SjUfbff38ALrzwQgCWLFlSa32iRGiM9t57bzp06ADAG2+8YbJnA7JA1drztNNOs2frd+PHj+fDDz8EasZfMg19/3XXXQd43cgUB5AlmpeXZ2tIYzxu3LiM1etJhPbZPvvsA8Add9xha0xdGu+//35KSkoAzKIcMmQIr776KoCV/MhW6ZjE2FssFrP1r3Hp378/V111FeC3KFU9qKuvvtreM5Py6Nn5+flmVek5uSx1kpeXZyVW1Gfi5ZdfttiEPBLvvvuunaepnJON6qLQQKuM8FlnnQXApZdeauWz9Zm77rrLGgnddNNNWZVH7Q/VSvPOO+/k+eefB/xL6uCDD+bee+8FoF27doBXk0YLq74bScXN5s6dC3ibWQtQfarVVrRr167Wb1w1esBv4Sg3VroLWJtP41LXDagFeuihhzJ06FDA77GtFreQmUNa86G+wA8++CAAnTt35rfffgP8A+8vf/mLmeh33HFHxmQQ4vG4jbmUh3PPPRfwXEtq9jRz5kzAO/BULluNqF544YWMySNo3rbcckvAf/eOHTtaW0+t7yBRQhfbDjvsYO4yuaUygUSSRCwWo3PnzoC/drt06WLu3uHDhwOw7bbbsnLlSsAvj67L95VXXknL5RKUp6qqykrCq696jx49rLe21tJvv/2W05prGhsVSfz1119tHOR62mKLLaxVcyoXhXM9OTg4ODgkRaOxKIItF6+++moAczddfvnlPPnkk4CvHR922GE899xzgK/VPPvssxbUygR08y5duhSAiy66yJ6nILW0rD333NPaoqrl4IIFC9J2h0mbKS0ttX/L5aafzZo1M5eBtMNDDjmEM888E4AXX3wR8MqRpyPPbrvtVu2/Y7FYnaibwZLIklNus+eeey7lBkuJiMfj9h1nnHEGAJttthkAI0eONDeZ5uyAAw5gyJAhgE8j/OqrrzLmOgiWqu/fvz/gB38vueQSfvjhB8C3HufNm2euxq+++grwtNhMa6eaM7niOnbsCHja+KOPPgr4WmqwgmvQtSJNP5PUU32/KOGXXHKJtdaVq6dr1652BsgSe/TRR5k9ezYAc+bMqfad6ZRpT8wpOeCAA7jxxhtNDvDm57LLLgN8qvzIkSNNxoagD4fDYT744APAdz2l/Z0Z+RYHBwcHh/9ZNBqLIhKJMGDAAMCjgoJP0Zs8ebJpFNK+/v3vf1v7z1tuuQXwtIl58+ZV+1w6kHa6evVqwLcs2rZty4EHHgj4Vsbuu+9uWphkWLhwYcY0imDd+cTvrKysNO1UvsnDDz/caKxqDv/WW2+lNS7SzoWioqIa/QKSWQWffPJJNZ8peGO5ePHiWt8rFSSOkTT6iooKayk6f/58ANasWcNJJ50EwPHHHw/At99+m7HAdrDJ/bvvvgv4lsXdd99tPm397oQTTjCr9J133gGy04hH76XGSUEiRL9+/QD48ssvAc8CkgV2yimnANC6dWuLGaY7Z6FQyDR2WVunn346AFdeeSVr1qwBvJaw+n/ytUv+ZcuW1Wi7G0SqCYuycHr06AHAPffcY94LrZe2bdvyyiuvAJiV1aRJE3uXhkAoFLI1rmZTnTp1snMgFTiLwsHBwcEhKRrcotBt37JlS0vikU99ypQpgHdDJ2p3eXl5xpi55pprAI8pkg0WhjQFWTwDBgywhB4xDaLRqGkgskCi0Whuuk8F/LDy9wcZN5nycT/wwAMAPPTQQ4AXB1C3MdElg13bpCnKd3vAAQeYTGJp9enTx6iY6SKond53330AFrMaPXq0ae6TJk0CPIqq6JSau2CcIxPyaH3ff//9AKYhn3HGGYwdOxaAt99+G/CSxf7xj38AfnJbYWFhxkt4JFrKU6dOBeDoo4/m5ZdfribvL7/8Ym12Bw0aBHjU3WnTpgHpM+lisZjN0ZFHHgn4DLHp06dz5513Ar5FAf4a03s0b948K2Vl9F1iD65fv95igFo3F1xwgcV4Hn/8cQCWL1+e0VhpfREKhYwCrvnp1KlTWt/ZaC6KgoICO5AVyJP51qJFCzsAg+0PxZGXedWrVy9zNaTrPojFYuYGUHBd1M6mTZtasEoTEo/H7UA+5JBD7HOiQ+pz2bg44vG4mdy6zIJZ0NpY6WyicDhsOQczZswAYK+99jI6pSjEOmh+++03W6Ryzw0fPryaYgAeCUAHZSZcPpqDZcuWAf7czZw50w4i1cbZZJNNzJ2o7N1YLJYVHrzmR8rNxx9/bLLJ/bV69WojQmRizjYEfbcopcoP6t69OzvvvDOA5SUEg9XKAXnppZcyGqSVq1mB4vfffx+Ayy67zFyqorgGL98gslkPS2dKt27d+Oc//wlgZ0O7du1sb8uFmg0kBtZro6YHSQdaw3Ibrl69Or39n/JfOjg4ODj8n0CDWxTSHquqqqzOjQJ+0vIikYi5L7bddlsA9t1332oaPniZwpnMsNV3FRUVmRwAn3/+Od988w3gB/2Ki4st2KdM1yOOOILp06cDvrsmG8HJ8vJyjjnmGHsmeJqH5BXlMh0XVF5entWSueuuuwBPc5ELTlaDamAtWrTItE65mYJzItkGDRpkLhhp0+nIqTmTRqVg8nPPPWeBftGGr732WnO7fPLJJ0D2a1Dp+3/99VfLnJebacmSJWZxiHI5YcKErKwZ8C0LPf+DDz5g1113Bfw9FQ6Hzb2oLOxg6fFUIc24e/fu9q7SkuXiXLx4sckhj0JBQUFWra0gtA7l/lq6dKl5EkRYOemkk6y+1HvvvQdkfo/H43FbxzoHlSxZUFBQw3NQVlZmluFWW21V7XepwlkUDg4ODg5J0WgsirKyMm699VYAC+jpVly1apUluCgA9/TTT/PII48AmDb91ltvpa1lSNMJhUJGv5NGobIGc+bMsQBssJyFaq48++yzgFfq4IADDgD84GomtQ1p5VtvvTWXXnop4JfGWLFiBXfffTfg14ApKCgweVPR2vU3qmw6f/5882UfdNBBgB/kUwkN8McoFouZ1Sh6bIcOHYx+KNpjJoLviVpWkF4siw/8RLtcVSDWc8455xyjCitW8e6775p1pbjBt99+a+OSqbWjNa4g7MUXXwx4ZWhEBlHweNttt2XgwIEARjYZOnSoxREzIZNom6rjdvLJJ9tPWZn/j73vDoyi6t5+ZjcJJCQkNOnlpSkIgkjvVZqKIFgAFQUEFFQsSBFUQBBFEbDr+4IgglQbCIh0UIqKgkgTgdCkJARCSNny/THfc2ayCUuSndks/u7zTzRZdu7ce+69pzznHMrcrl27xLK1O5nN1+J65ZVXZM8xDtmyZUvZA5Rtq2pzmanntNhZb42WhdPplMA5A9YpKSny959++gkAcPjw4YBib/l+URAOh0Pq2lAoePhUq1ZNLhEexsePH0etWrUAGDVfoqKiAr4oWAcoLS1NglTM9jQfuL5C6nK5pEYVXVUej8eWMsy+5aEHDRqEOnXqyDMB/dClG4PCXbhwYXk/MzMrt+DhcOrUKbzwwgsAjMuUpbNr166d5bA+fvy4BNfobtA0TXjzdG3QVWZlUNnr9Yq5TvfKzp075WC0+9DhPPNymDx5sigP5rpKvPDJ/Js5cybuvfdeAEZVgkBliW4cZj0zmP7OO+9gzpw5ACB1sQoWLChj5hrXqFEDu3fvDmgMnO8jR45IMJsXF/dMnTp1hHHFn8OHD5fL3S6X3NXGWrBgQXEBcb/FxsbKYWy1DPH86datm7iUyUaj3JrJFxzTpEmT5Jzs27cvAH1PBeJWVa4nBQUFBQW/CBmLwkx7own38ccfZ/mc+XanpkxtLTY2Nk8WhdvtlmqYpL/Nnz9ftDp+J10ibrdbxkFzr1GjRqL18LtSUlKknLaV2jHfl3Vc+vfvn6Wx09KlS8WyYYC5TZs28g40ZdnmMk+lh8PCRMulBsq1++6777J83uVySfCbaxcWFibVcBs3bgwAUsPL6sZLrP9EzWr27NlCaQy0wmhOng8YmvHvv/8udZW4ngUKFBBNnXIzePBgcc3R3WNVXkxcXBwAo+LA+++/LwF2ztHFixeFRss1S0lJCdhyp1XkcrlEZpjtTfzyyy+Sn0PySMuWLbFq1aqAnp1XeDwecYHTPbZ8+XJxQ1u1LpxbWkyPPfaYVKgl/ZzuLZfLJVRz0pdPnz4t4+O+DNT6UhaFgoKCgoJfhIxFAWRuUXktmBsF0e9N32tu4fV65VamdlutWjUJ4jHBjIG1qlWrSoMgBm2rVKki/n9Wlt20aZMkk1ntbweM6rqRkZFiUfDngw8+KP5J1tAHIMFSJikG6u82Z2JfC06nUzRmBvz79OmTqQmM1aAWXLFiRbRs2RKAEQtZt26d7X5uWhIM8rNe1tixY0We+N7p6emSdEoa+JkzZ6RJllX9Okh4YIyPst+kSRNJqqSlWKVKFUkaZQOj+Pj4gC0KrkurVq1E6yUt3vzdJLSwoqy5x0uwYhRERkaGWMS0LF5//XUkJCQAgGXZ2L4eDPPvzJWYAT0uwWA6YzsPP/ywWGlWzVFIXRS5hbl/NmA0PMotnE6nbNqxY8cC0ANCdBPcfffdAIyFCA8Pl2dxMRMSEiTYzSDlmjVr5EC2I1hqzlKnAPHnzTffLBcpWSJPPvmkmK6+ZRCCAYfDIXNIt2KrVq2kEB1dZVby47mhOnbsiCpVqgDQi7sBOjPMru5xBNeILkrO+6VLl0SGWO67dOnSwoBi7+qxY8eKa8iKi9ThcEgZEZaiZqn1Dz/8UNw6dEvVqVNHLhayEQ8dOhRwvomZ6EDSBQ81cv8jIiJkfVh25auvvgpqUyDAWMOYmBhpDMZg8o8//mh57g1lhJf14sWLpYwIlVAqHA8//LAoo7wwUlNTrR+Tpd+moKCgoPCvw3VrUZjzHKgx33nnndKcJjcZ2uZicgyknjt3Tkxh0vbYbMfj8UgOB7NWz58/L8FGlvjNjkZrBfhOLEIWHR0t42DeRmRkpBRVZDvV1atX257Nei1QGyQ9d+3atTh48CAAI8vdCm2IlgRdg3fffbe4cObOnWvZc64Fvi/pigwWv/POO/I7upvKlCkjY2J731mzZlkuQ7RMaD2wJWuHDh2ECss9tXv3bqGmc2+kp6cHPCaOYefOnWKB06VE68tMMGBex9mzZ+XfBkuW6c6tW7eutB8mWePgwYN59mRcC5SF+fPni1udc0L5HjNmjFhbvrR5K6EsCgUFBQUFv9CCqWHGxsZa9jC32y2+Xfro1qxZgxEjRgBAFp+9GUlJSRoAREdHy3h8g0RpaWkSQKOftFixYgD0m5tJYeYYBG/y3PqSk5OTs4wnJ+DzChUqJOPgnDgcDmnUQ1+nmdabk/HkZUw5Bec7IiJCNCEmM2W3ZhxT0aJFczQeaqdM7Bs7dqw0ciItNZBAX0JCggYAMTExORoP5YrEgqZNmwptmbL0ducxmgAAIABJREFU22+/SdyAAXdzVWJ/e/XSpUsyaYUKFcrRmGhFc95LlCgh1G7OX1JSklhBlOucWhOXL1++qlxzjT0ej8gnweeY5cBMdMnrmUUZyuma+T7npZdeQteuXQEYFW93796d55iJec38jcnr9WZphMS1czqdmSrrBgrzmMxQFoWCgoKCgl9ctzEKh8MhdL1p06YBMGIDQO5vV99yE5GRkaIFkmnAmAhg+J5pdeQH6LdMTU2V9z169Kj83ZfZlB+N3q8GzrdZU7JyfPyubdu2AdBLH7DPQX7MA+WFbJk9e/ZkSSg1N03i5x0Oh22+eLOsA7r1wNiR+TO0XO0oQ6NpWq5opcH0gHD/s+9Njx49JE5jdfKjP2iaZlscJMdjuF5dTwCyuCycTmeOAjnZuZ7yE3l1PdmFYLiecovcup54qPEyTU9PFxPdimBobl1PdiMvrie74c/1lB/IreuJ7h3mad10001CuLCC9p5T11MwoVxPCgoKCgp5QlAtCgUFBQWF6w/KolBQUFBQ8At1USgoKCgo+EVQWU+BBLUYsDYXBMtrBiKDWkWKFAkJv1tiYqIGWBPsNxcHJJskt2wVBvuB0AuMFixYMCTGk5qaGpKBWiD0AqNxcXEhMZ4LFy5Yts+sgHmfhdpZ5IuQpseSdeBwONCrVy8ARjXJFStWYPv27QByV67j3wpeoGzz2bx5cykzEkjPiUDAdSHNUNO0oBd0u97AOeN6Op3OkKI1BxNer1fOAP4EDDnOD1niOLKT6X/z+ROSF4VZKADghRdewKBBgwBAylQ3aNBAGtEwszU/BIcafFpaWpZ8hYIFCwZFeDwej1D42Cpx8+bNlpUSzw3MDWlIR2WtrOTkZGmCoy6MrDATS9isyJzbkB8HUXp6ulCMSSsuUKCArWPhJenxeKSKLasihIWFyXwEe148Ho9UOGYFhIyMDKkhxrPAzvH4PuNqVSDM/baBwJXE/5uqioKCgoJCjhGSFgU1ijvuuAOAXq/nf//7HwCjReTtt98ut3t+gKZnjRo1AOj9A2gJnTlzBoBenZN1bOxoykOkp6dL60NmkU+aNCmLJhgMcF7i4uKk7la/fv0AAPv375fGSfwZzLFlB1/NS9O0fHMhuFwuqSXENrxDhgyRfg12984wg7LcsGFDadLFlp/r1q0TubZyrig7pUuXBgC0bdtW2v2ycnNcXBwmTpwIAHjttdcA2D8vlI0CBQrIs1nr6dy5c1Jdl65eO6q38kysXbs2AKNKRHx8fBZrwev1yr7iT3P1hrxAWRQKCgoKCn4RUhYF/W916tQBAEyePBmA3lFr+vTpAIx6TmvXrpXbMtj+bq/XK4yikSNHAgDuueceufV523/88cfS+4CtCa0MTFLrK1asGDp06AAAmDNnjjzPqtaMOYGvL3Tw4MF44oknABhxk3LlykkXrp07dwLQ+zQEa/18A8WapkkchT/T0tLEEguWZWFuffnwww8DMNb28OHDQa1vxLkpV64cAL1iavv27QHoew7QWwPTcrXCIuQzWTeN/SmaNGkiNY44Hy6XS8bGz6emptpqmZpLebD7nrlDI/t57NmzB4AeH7TaquActWvXDoBxRj755JNZKstGRUVh/PjxAIz2tZMnTxYrMC9nUEhdFDQ9O3fuDAAoW7YsAKB///44fPgwAGNDmwuoBQvmDc22kNxEiYmJIhz8+dhjj2HXrl0AjAZHVl4UFJ5mzZpJeWg2VAmmmwLIXDYa0N93y5YtAIB3330XgL6pGjZsCMBoWxusQ9DMoKlcuTIA3bXJ1pZsk7plyxY89dRTAIBTp04BsJ8tRgWpU6dO0gKVrrnt27fni8uJB1LNmjWFgMAmUPXq1RM5CxRut1t6zb/xxhsAjP0PGI2euP/LlCmD3r17AzCKGY4aNUrGaMeFQdk+e/astKr99ddfAQBPPPEEXnrpJQDArbfeCgDYsGGDpReFx+OR/cI+53TFRUdHC2nFLEeUazY3S0lJCUghU64nBQUFBQW/CBmLwkw9o1lFbXzVqlVZmszkF1UQAG688UZpiUjNwePxSAMlaqw0U62GObgG6C1gSRs+efJkls8Fc66ofS9ZskRabdI0btSokcwhzXS73U7mXA42LqJGCgA//PADAIMk8eCDDwol0zyXdoAWIanNTz/9tGjEX331FQDdFRYsi8LtdktJ7fvvvx+ALmO0MmJjYwHoAeVALUGzDFMjZ64U86Pmz58vAXRWba1ZsyZGjRqVaYxXrlzB8OHDAWTOvQoU/C56Me644w7R6Cm/P/30k7h3mMM0b948aSVrlXxTLmhF0ZWdnJycZX87HA6xLv755x8A+tkVSKlyZVEoKCgoKPhFyFgUbrcbFSpUAGD44egHTUlJCahtZaCg5sd4xPTp0yXh5siRIwD0oDb9llOnTgUAVK9e3ZbxUNNhIlujRo2EKkh/ZWRkpIyb2lsw59Dr9Yp/uW7dugCA1q1bi6bMcdoVhOQ704Lp168fXnzxRQDAW2+9BUBfRz7/1VdfBQD8/PPPOHjwIAD7YxMc46OPPgoAaNOmDRYtWgTAaLgUzDW7cuWKBGbr168PQNdYqVFTq9+yZUvAVipls1atWuJPZ5xh3LhxADJ7Emi5x8fHS7yP69i7d2/88ccfAIAPP/wQgP9WyNcC14UaOC2eu+++Gy+88AIAIx6we/duaUbFMyE6OjpLA6hA4HK50KxZMwCQGBbnICIiQvZSdjDPQyBJeMqiUFBQUFDwi5CxKMxJIvTJ0ld5La3Abl88v5+MnZIlS8qz/vzzTwDAN998I75m3tS+pUisAr+XvvTIyEihm7Zt2xaArmXRT0otddeuXUFLcPN6veLTpkYWEREh9F274yZk0FEzfvbZZ/Hee+8BMFhYjRo1EoYT5+3hhx8WGqGd2rzH40H58uUBGBZFYmKiJG2RYh0Mi4Laffny5YX9ZaYIU/73798PAEhISMiztUXZ5R5/4IEHJDZJGvWGDRsAAIULF84iJ06nUyjyjDnNmjULQ4cOBQD8+OOPAIz4Zl7iO5wPxkofeOABAPo+WrJkiYyDP7lGvhq7VdA0TRhn3PNkgV24cCHLWpjPHe6DtLQ0YZfRUkpKSpLvvxZC6qIoVaoUAAjVs2LFitl+DtAX00xXJTgx5oUMFPzOMmXKANAXgsL05ZdfAtAFklmkjRo1kn9nZ7CW83XhwgXhlL/88ssAdDcBN+D7778PQM9kpevHbpdPZGSkZKyykOOLL74omzxYQWxSFqtUqSIXOTOdGzRoIO4CHtDLly8PymWalpYmQXUeApMmTcJPP/0EwJ7sXl/4HmydO3cWdykPm8jISOzYsQMAMrk3A70oihYtCgBo2rQpzp07BwDYunVrpvFkd4BpmiZzc+jQIQC6u2natGkAgIEDBwKAVAVIT0/P81hJEeYBe/z4cblAud/S0tLExcpxWeWyNLuMuYd47qxfvx6AnkPCvcSxlSxZUi4vBtjj4+Plv+kqY7WLnCgjyvWkoKCgoOAXIWNRaJomJj+DM6yg6fV6s9Qtqlq1qriCSEN1OBwScKMWFEhQiZYEM0H5PMCoxfP999/L+BmUo5Z67tw5qftkh6uF83Py5EncddddACDupueff16eSbN86NCh2LhxIwCj9LjV4+I6NW7cGD179gQASbyj2W5+rl0Jd9TqGBRevXq1aIFcx8KFC4u1xWB2SkqKrdo8Zaps2bK4/fbbARhuhCVLlkiQNBiUWI6ldevWAIBhw4bJu5PSfOLECbHASBdmcDuQZ3JPFS9eXGSScnKtd6fscKxLly7FvffeC0CvkAAYyXvHjh3Ls4ZPC5Qums2bN4v2zfcoX768eBpIggjENWcG90Z0dLTQ8RMSEgAY9NgaNWqIXNMa7N+/v1gZrNjQtm1boYLTBauC2QoKCgoKliFkLAqn04l9+/YBMJJZGIiMiIgQ/1q3bt0A6I15mBwUHx8PQPdZ9u3bF4B++wO6Zg3oWkFublBzcJ1+T/qSr1y5gvnz5wMwbvjy5ctL8Ja3+fLlyyW4Zoffm5ZUbGwsWrZsCQCS5ObxeOSZy5YtAwD06dNH5oy+cKtjBfy+/fv3Y968eQD0kgKAnhjIGIndpTs4DspSr1698OSTTwIw/LazZ8/GhAkTABhVd+2yJnzjAX369JGqrKRT79q1S7TDYIBjoSZatmxZ+R0TtV588UUJLlth5Zi1ZEC3Tjj3tEZzWqOMlkV6eroEr7m2tFioeecU5h4YpJ9zXNnRUHv16iUVXSnbFy5cCMjqIvh+V65cEfpvtWrVABixyIIFC8p4WXU3NTVVYhlcu4ULF2LdunUAIDGh3JxJIXVRMCjEIAs30Nq1a2XRKGh79uwRHrW57gwZLQxE8fBOTEzM1UVhbgbEPAAePhkZGVlcNl27dpVDmGwtsjjsAhe+T58+4iogv9rpdIqwEOfPn5cmK1a5nPg9NMXZYCYhIUEKAFIBGDdunJjnv//+OwD7guoMmtJV8Mgjj0hGL91NkydPDlopdt+y9I888oisz4oVKwDkX30usxuQe4Sth//++2+ZSyuUCn4/cyYuXrworkAeuAy25pTx5Xa7RVnkHDZo0ACAESDPKcxzQPAgrlu3rrgyWX2hc+fOwlCjUmJVMJvrkpaWhtdffx2A0cKAeRWpqalyiXBPVa9eXS5bBvnXrFkjSkheZF25nhQUFBQU/CJkLAoAWercsOFN27Zt5bakK2nr1q1ivlKTv++++8TNsXTpUgCGmZXbW95cnZbjoobzyy+/SP4EA7bPPfec3OIc6+nTp20JYvNdGLA/cOCAVJOklnrlyhVxlTGbdOXKlZJJbpXLyTc4ycDovHnzhJxAi++xxx5Djx49ABhzZBeoBT/77LMAgLFjx0qAc8qUKQD0uQpWiXOOh/WMKleuLC4Xc9nzYI6lSJEiAIw183g88je6TM+ePWvpHPG7aAGcPn1aqJ8M2FI2wsPD/c6J2WqkVcI53bRpU57HR2uHVG42UGvYsKG0DWCGdJkyZYTYQne31bkv5twRWum0cpxOp5xxtI7fe+89ccHTo1KgQAFVPVZBQUFBwT6ElEVB7YGaKJOgKleuLNoPG3JcunRJknZITzt37pwEJxcsWADA0DCs9K+mpaVJUJ3aeunSpaUCKf2CbrfblnpBfBdqEgsWLJAkP2aR1q1bV6hxzKilNmQl6MumpUB6bmpqqlh8Dz74IAA96Y3rYReoVdGyHDx4MAA9+MfmV1b63K8FxtSYtEXSQVhYmFi9XB+7a0v5ghm6DJCax3D06FEAegzBisCs7/eTtr5ixQqxBpgkxzjW9u3bszQnc7vdYoFx/w8fPhxdunQBYNBiWU05kDVm7TbK9O233y7f37FjRwB6gJsxAu4FO+JdvgnE3EderzdLbOvQoUNyhnIPBoqQuigIMk++/fZbALrAsIkRD6Q6deqIsJF/PWPGDGE5+LqNAgGFm5PfunVrtGnTBoBhZp4+fVouiOPHjwMIjG+eE3Ce5s+fL4JDHnlsbKwcjGRCXb582fLDkQchTVwWdAQgeSXMjv7qq6+kkYodh2JGRoZk848dOxYAhKM/c+bMoF4QBEkGjz/+OAA9ExnQ3YVUhIJRMiQ7+DKxnE6nuIQOHDgAwPpDj/uS6z9v3jxhKpGAwryNSZMmCWuHJIzy5csLu4cKSKdOnSQ3gDLvW6EhN+A7033Fi7xu3brSK5ulxceOHYuFCxfm+Vl5hb+ih8eOHZN3oLL47bffykWWl72nXE8KCgoKCn4RkhYFwZvvzJkzolGQnmYufMXPRUREWMaDdzqdYnLSpcRgW4ECBeQ5NHFHjBghNNBg0RzNlg5zFqiNORwO0XDs7C1OLfibb74BYLTwfPDBB/Hzzz8DgLSPXLRokWSEc/6szKfQNA3du3cHYLgBWLI6IyMjaAURzeD7MVufazZr1qxMQdv8BLXSqKgooZevWbMGQM5zGnILyuL58+elcgDduOwbPnPmTPz2228ADHfUjTfeKIUL6YIaM2aMBJT5LgEFbv//GrEV7iuvvAJAt3BImWcm/+effy7/Lj+aqWWHsLAwsah4PqWmpgZkxSuLQkFBQUHBL0LaoiAcDofchsHSCjVNk8Ao/epMWLnnnnvEL8kM582bN0twMNiahaZpotkH289NbZiBPwaRo6OjpUaOud6VHZaEOduXMSxqeqQDBzuZjaBG/s477wAwCAWnTp0KqLlOIODzWFWAc9W7d29JdgtWYD0sLEy8BWwsRavG4XDIfudPl8sl3gRmSp84cSJL7MMKUFYZ5+revbvEHdmiFQgdS4JW1JEjR4TevHbtWgCZ6f55gbIoFBQUFBT8QrO75o4Z0dHRwXuYHyQnJ2sAUKRIkRyNh3NEv595zqjBBOITTUxM1AAgNjY2JOYnKSlJVI9ChQrlakycI4/HY8ncEJcvX9YAoGDBglnGQ191mzZtMGDAAABGfS4yiqzWkFNTUzUg5zJtnhdAnxMrx0SZBoCYmJg8yzU1dyu05EuXLmkAEBcXl6PxcG44npwiLCwsR+O9cOFCQPvM7XZn6YETyDyZ91lOz6KcwOPxZGF95VTWeBb54rpwPeU3rKTa/tthZcOo3D7z0KFDUizN7p7cuUV+zMu1EGpyzcMs2PkkOUUorZ0/mF31ln2npd+moKCgoPCvQ1BdTwoKCgoK1x+URaGgoKCg4BfqolBQUFBQ8At1USgoKCgo+EVQ6Q5FixYNiYBIQkKCBuScRmg3SCOMjIwMifFcuXJFKHKhRmnOLV3XLpCuG2rjAdSaXQ2co1CbHwCIiooKiTGlpKQoeqwdMPPjfTnVTqczZLI27YZvnoCmafLu/F12tL3/K/OjoBAsuN1u2XNW5cWE1EWRkZEBwCjoxrIL+V00LTtwjCx//tRTT0mNepYnHjNmjKX9MAJFamqqjIOlPgJlvVEg2SubP1NTU6WoIvsGJCcnS9kIc4nr/OTNs0wLxxAeHm5peZHrAeZEN9+kt+zmwul02l5C/2pwu91Z+j7YXbaGc5KRkZGlD31YWJicT/md/8FxFi9eXPr3nDx5EoBe7l6V8FBQUFBQsA35blGYNcubb74ZANC8eXMARkOivXv3iiacnYYTbPeFy+WSrmCTJk0CoDfu+fDDDwEYjXqqVq2KX375BUD+WhTUdLp16ybFzFjiOhAtKCMjA//5z38A6GWzAUinvTNnzsgz+Ls///wTW7duBQApPrd06VLbymxcC263WxoJ0frZv39/vq2VWbaDKdO0DsqXLy8WIeU7KipKxsLxHTp0COvXr8/0O7tBC6dkyZLS4Iilx3/++Wdb5ovPZFOumjVrombNmpk+s3fvXulwx0Zq+dWAiuMdN26cNHViv+9NmzYF5JlRFoWCgoKCgl/ku0VBuN1u0TynTp0KwCjNPGrUqJDw8dM/GRkZKb1z2ZDmoYcekpaJ1atXB6D75O2so2P2l2b3HPpy2Wryk08+wfDhwwEYZcED0eLdbjcqVKgAQG8TCRilq0+dOoVLly4B0FugAkDFihWlNWPfvn0B6PELlnGnZWG3Ns24RLt27aSFJtvFPvfcc6Kh5XYcvsF7s8+fMFvQvj52c3yEY7QD/O727dsDgDQOKlmypJRF57jj4+PF+uvZsycAXZNnHI5xRbvWjPPBuXr88celwRFLtj/++OOyF6ywSvnupUqVAgBMmDABANCsWTOUKVMGgBE/PXLkiDRX+t///gfAaPoEBMcyNMcmAKBy5cqyLlZZfPl+UZhr8q9cuRKAUf+dh09MTIwcOuxudeedd4qg0OSz6zLhQrDfxMSJE1GjRg0ARg/vv/76S/7OHghWVwjlXFEIbrrpJnnOn3/+CSDzRuF/N2vWDIBeQ/+HH34AYE0huPDwcHkuu9j99ddfAIAdO3bImpnHw0PxmWeeAQA8++yzMl+8UOwiL3Ad2XD+4YcfRuXKlQEYl6rL5crz3HBdqCi0aNFC3G88yOjGKFGihHRMrFevHgB9Pdm7o3fv3gB0WbJarumi4Lu3bt0agN6lkEoa+75funRJlCG+w+XLl2W+7FbgOFaSRlq0aIGzZ88CAHbu3CmfsepA9ng8cgnwQmIf+oyMDCk2yY6Ot956K+68804Ahgxt3rxZeqUH04Vo7tnDC4IyGfB3W/ItCgoKCgr/WuS7RUFomiZUUrovqHFFRkZKt7QmTZoA0M1NWiDnz58HYJ92Q62mW7duAIAhQ4Zg0KBBAIA9e/YA0E1Rag92acTUDipVqgTACKQfPXpUtB9zPkP58uUBGBrRtm3bZK6ssHScTqes1cyZMzN9rzmHxEwv5BqVK1cOgN41kNbZ0qVLAdg3f9SIqfE3bdpU+iJv2LABgD5/ebUo+J7UwEeMGCE0RV+LIjk5Wdx/dFkmJCSgc+fOAAya8d9//52nsfgD55fdGWnBV6lSRSx2WooZGRminZII0aNHD6xbtw6AodXbtfco8yVLlgSgr92BAwcAAPPnzwdgLcXa6/XK/Nxwww3yO/78/vvvAQB9+vQBAIwePVr2HueuVKlSOHToEIDgEDQ4PlrrMTExEuinbAXqQVAWhYKCgoKCX4SMRQEYNyO1L9L2ypQpg8OHDwMwfH5xcXHo2rUrAINqaRc4HlIp161bh6+//hqAdZmP14JZ03niiScAAA0aNAAALF++XPyj/Izb7RaNiNrY+vXrM2VJWwG+N/26tGjS09PlGdSi+/bti169egEAbrvtNgDAypUr8emnnwIIHq2Q1M+yZctKUJbB7EB6a3P81LI7dOgg8RCC83/x4kVcvHgRgGFB9+nTR2SMiVJ2aKSU2V27dgGANHv65JNPMH36dAAQksKcOXNkzEOGDAGQOdBuJz3W4/EgLi4OAITuGRsbK94FcxUAK+HbFY7ztWnTJowePTrTZxcuXCgyfeONNwLQ46ecx7wSI3IDjrNfv34AdE8MOz1StgLtGa8sCgUFBQUFvwgZi8LhcMjtR/8eS2K0atVKaHvJyckAgLNnz6JTp04AgI8//hiAzsawUgOjdkzfI1lYb731Fv755x8AhtWTXa0nK7UIj8cj1FbGR/hz7ty5mcYB6H7K5557DoBhcS1fvtw2nymfS+ulRo0aEofo0qULAJ1dQw2b7KipU6eK7ztQrccfvF4vChUqBAB49NFHAeia8ebNmwEYVmMg8RGuN+UmPj4+Cz2WMK8D37tDhw44ffo0AMhPO33clBkys7p37y69xkeOHAkA6Nq1q8QE+PkZM2aI1WQn/dvtdouWzJjA/v37MW7cOAAQVp2VY3C5XMKwqlWrFgAIg2nlypU4evQoAMN6PHz4MFavXg1Aj5sCevzNX4KwlfB4PGKx33fffQB0ud6+fTsA62JHIXNRaJomm4JBPga3BwwYgGHDhgEwhCMqKkoOcF4oCxYssLQGDd05d999NwBjoxw8eFBcJzxgTp06JQJlzjQOVIgpaEWKFMHgwYMBGBnrDKxFRUXJ4cRDp0ePHpKV+eabb8q47DKB+XwzpTC7Wjw8ALmpfvzxx6C5nChfdD1duXJFXIhWzIvvoeB0Ov1uVF4iVIIqVKgg8s35DEYwlM+Ij4/H+PHjAQD79u0DADz//PNo1aoVAOCzzz4DACxZssRWVwr3VMWKFYV+zgv8iy++EJeZlaQHc74G6cLMo2BgeM2aNbKe5vcnIcL8XcHKWPd4PDJHJLnMmjXLctelcj0pKCgoKPhFyFgUgKF5rl27FgCkLlDDhg3FVUG6odPpFI2iYsWKAAwtzAp4PB6xIHhT8+fcuXNF66G7rHDhwlIvaPbs2QCAH374QZIBidxqYnynevXqyXuWLl0agEFvPH36tNSbYRZ2+fLlJTno22+/BRCcSq1mqp5vIFfTNBkT3XinTp3CsWPHbB0ToM8jrcCYmBgA+rwEk8Z4NVCOCxQogHPnzuXbOACj0m/jxo0B6KQRyjjlr0SJEhKIt2PeKPPt27eXZES6Uj744INstXqroGmauCj5bqQo//XXX1ksRPPngwmeP8WKFRN3IT0aixYtEhe9VR4WZVEoKCgoKPhFSFkU1BBIv2NCWbFixSSgxkDTq6++Ksl3dvgD3W63VEZlDSr63GfPni10SmrIzZo1k0SuJ598EoBekoF1YvKq/fDfnT59WpKcWHqBsZCYmBihVZprvFBTp7/ZTq2ZmtbkyZMB6FTC2rVrAzAsRafTiTZt2gAwKJkPPfSQxFC++OKLTJ+3EpqmCcWSMYGNGzcK1ZK/CyaoOZPGXKlSJSxevDhoz/elo8fGxkqMgnWdVq1ahe+++w6AHq8A9NpQvgmeVmj3ZiIGoJMfuOco++fPn7dlrTj+tLQ08WiQPMIAttki59yFh4dLiRzzd/lW3LUKvnTb++67T6pur1ixAoCeBGz1Hgqpi4LgocOsQo/HIwtE03z37t1yONoFLgrHwyDyzJkz5UDm3w4ePCifp5n8xhtvYNmyZQAMZklug9v8/r179wqroXDhwgCMS8Htdstmp+tp5MiRmDhxIgCDFBBoYJ0bmSauw+EQtwm/m+uzePFiqd1EuN1ucR0y0D5p0iSplTNv3jwA1l4UVDoaNmwo5et5cQZaejlQ8JAlO6xMmTIiO3bCt2AcySAvvPCC/O6hhx4CoLtPWcOMLLqqVavKfrTS3cvvogy3b99elB1eVnavl6Zp8r4EA8MejyeL68nj8chFzz24a9cumWOrWWHcg8wv6d27t/zu9ddfB6C7w62+KJTrSUFBQUHBL0LSoiCy0x6oIX711VdCC7MDTqdTNIndu3cDMNwTkZGRWUxuc4loBr0dDodoGYGa5g6HQ9wkDJCbzVs+m1TGjIwMqeFjlVuAlgzzEE6ePCmWEskG1GTM7865Kl++vAQnWeI6PDxc5teOekHUtm655RYpEU2a5759+7Joj8GEL1338OHD4uawy03odrvFRcrcBOYjbdu2TVwM2R+uAAAgAElEQVSHrB4LGFnatCRjYmJkrayqTmoG6ejR0dGyVqTE2lVTykyPZY05WgMMVpv3GeWqZs2a4iqj9bNz507bMrL5XHoXGjZsiBkzZgCANEmzw+pSFoWCgoKCgl+EtEWRHXjLHz58WIK51HhiYmIsa2CiaZpoUAxu8eZ+9dVX8cEHHwAwMsVr1aollT+p1b/33nsShLdCQ+R3+H6X1+sVKmrLli0BANOmTRMLxAoNwxxfYM+C5ORkeb9t27YBMKqwpqamyloxHlGrVi3JdqWPdceOHRKEs9Kfa26dCegaGNfz888/BxD8lpW+4Lo0bNgQAPDHH39Iwp3VFgU13IIFC+LFF18EoGdiA0YDoKeffjpLnbXatWuL75sJrs8//7xlca/sYK5Xxt4TdsOcVc/YKOWFMZz//ve/klxHK+Kpp56S84fJmydPnrTd8nnkkUcA6PuMcVBad1YmHRPX3UVBpKenS5Yve+jedNNNktUdaDkITdPkOxYsWADAKHHerl07KQRGN5DH45FSFGziYy6ZYSfjyOv1SmlrsrCsDopqmiYXM4PBN910k/DtyQyjW8rj8ciGp8vO6/UiPj4egDGn7777rritrNxc3FBkydWuXVvWhx3J8rNrotfrlYuXxR2nTp0q+QlWM3t4iAwYMEDKutN9QZJG3bp1hZXG9WzUqJEcnHRVbdiwwda5M7MfmUtFl7Mdh6AZTqcTP/74IwCjUCSbSL3//vt45ZVXABgtB7p27SpKCc+CjIwMy11O5q6MAISReejQITkH7VwT5XpSUFBQUPCL686ioGaemJgoxe4YIC1cuLClvGVqBXwm6YGVK1eWHAEWBzS7YagVhoeHB6UVotvtlgAcs8P/+ecfSzUMp9Mp1Fdmgnbr1k3asVKrotUVEREhBffopvj999+lrDeDkxkZGba4LygH1Nbj4uKk0U2wenP7g9frFdcXmxRxXHbCTGeli5Qac6tWrSS4Tyvi888/x7Rp0wAYdboiIiKCUjY7KipKMvhp9dgNh8MhNd7YjItupo4dO4o1RpcmAGkvzJ7ZKSkplgeUuW7MmWAhwBkzZohFbmeBRmVRKCgoKCj4xXVnURDmsuT0Y546dcoWPx21Jwb69u7dK7RQcwwiu2qpdsKcfEPt8KWXXgKgWxYchxVWlqZp8jxaA3v37s0UfwCMWkHmNqnUhpKTk7NUubVLC+K6cJ1+/vlnCTbSX5+fyXaaponlyXnl3NkB7ott27aJf5tBdAaMn3vuOdFOSY9NSEgQubezDDxg7DPWJqtUqZJQU81lu+20ZjRNExkl3XTo0KEA9MA1YwS03NeuXSuWB+fRDrlibIZ0YSYgnj17VmTdVivPtm9WUFBQUPhXQAtW3XQAKFq0qKUP481PjczpdOaIXZSQkKABQExMTPBe3g8uXbqkAUBkZGSex8M58C07khdcuXJFVJPo6Oirjim7uvvmcfhqOuYaOLlFcnKyBgCFChXK1RxxPG63O0uLy0Bw+fLlPI2H8Hq9Yo0xye69997DqFGjAOSe3cPxAP7XzOPxZEkWNa+hea0Afa6CvWbmfc21ssJTwDnyNz/XGk928GU25nS+OD8AEBUVlaMxmeUZyPmZl1OkpKRkO/jr1vUEGMKTnzTHUEF+lMnO7uDPz3Ld2SEY9OS8QNM0oTwyE/nEiRO2uy0dDkfIzYUvQm1fh9J48kueQ1tiFBQUFBTyHUF1PSkoKCgoXH9QFoWCgoKCgl+oi0JBQUFBwS+CGswuUqRISPi5EhMT88R+sAtkP4Ta/AB5Z/VYjUBZRlaD4ylRokRIjOfs2bM5Yj0FE5TrnDJ67AYZPaG4zwoXLhwSY7p48eK/j/WUn/ClFjIpCQhdpk1+wUzpyyuV8HqE1+vNRN2+XuFLD3U4HNf1+/xbYe6VwbUy05wDOY+um4uCL846LC6XSyaBGaPBzLT1XYhKlSrJ81kTJyUlJWi1nki15KY21/ShgBQsWDBoc+TxeGRMzDguVaqUlNFmFmtaWpqtGb+cf4/HI2Wjmb/gcDhs6bfO74yKipKy6izDfr0oD3yHtLQ03H777QD09roAMGfOHGlb+3/pwnC73ZnyF/jTN4fpWrBaBnxzK2JjY6UyMcd07tw5OTvzciZdH1KroKCgoJBvuC4sCo/HI4152GylSpUqckOybvz+/fuDouG43W65qR988EEAwMSJE6UZz/vvvw9Ab3DEyqlWahF8NquNxsXFSdMk9l+oXr26PJMVbhcuXIi///4bgH3WF11wxYoVQ/369QEYTVa6d++OPXv2AADWr18PAPjmm2+koixhpRVGLato0aK4//77AQBLly4FoGvL5hpCVoGW1BNPPIGaNWsCgLyj3f0UAoXvPDRp0gTjx48HAKlQvH79epEtO1p+mq1h3/3s9Xpl35vb7toBjoMyXbp0aWnexL4qf//9t1SS5Z7yJ0vmGl9WwOVyyRzxDHj00UelTwytjddff13Opby4fZVFoaCgoKDgFyFtUfA2LFCgAN5++20ARmep1atXiwZPTXHw4MFS2dQKjdns3wYMTbFSpUoYNGgQAOChhx4CoPsFqYHQp/vpp59KzwwrtB5qKvzJlpZDhgyRZ7PD3enTp0XzYiez3r17o3///gD0aqqAddVbWZG1YsWKAPQqtl26dAGgt60FgJdffhmFCxcGANx1110A9PIVr732GgB9vgBkqUUUCPhdJUqUwKRJkwAAt956KwBgypQpOH/+PAB7LL7OnTvjo48+AhCYL98cpAz0u671HK4j29e+/PLLqFy5MgDdQgb0mlQck5XzxvejFRYXFyd9KPjOsbGxeOaZZwBA4iT79u2zdE4oM7SgevbsCQCoX78+ypUrBwDSEvXQoUOoWrUqAPit1sx5Cg8Px/Dhw3M9Jl/SDH/eeOONEjvq2rUrAL0vD+uHsfNlVFRUQFZzSF8UPOg6deqUpcnK6tWrpclKjx49AABdunQRN8uZM2cABCbInFgGWzt06ABAP6B52Jw8eRKAfshRYFi+uVq1avjjjz/y/HxfcCOxTDQ3zJgxY7Bw4UIAhgClpqZK8Jam8eHDh8VV9tNPPwEI/KLgmOjyYi/x5s2bSy9sCvKRI0fk8OelMG3aNLnweKGsXr0agDVlrc29kHnRs6Xn559/LvJiRY0lfj/biDZu3BhDhgwBkPfDPS0tTZQeNqthy007muN06tQJADB9+nQAQPHixTF58mQAkN7ZmqbZclnxkho8eDAA/XBjS1/Kcu3atTFgwAAAwLFjxwDopeStah3rcrlQvHhxABDFgs24zMyhSpUqAQDq1KkjcpudgkOZoJwdP35cyC45hbm0Oi8qjmnixIkoVaoUAKOk/qeffipzSVf9F198Id+ngtkKCgoKCpYjJC0KavLUEu68805s2LABALBy5Ur5DKmWH3/8MQCgQoUKonlY6bagO+XNN98EAJQpUwZr1qwBALzxxhsA9GAlg0Vt27YFAHGzWAVqM2wq07dvXwDAgQMHpE0pPxMREYE2bdoAgGhgZ8+eFVeIFRq0x+MRrZbmdNOmTQEACxYskJLZHJtZA6alNX78eCxYsACA4XIgOcEuXK1cdKCgNcf2sMnJyeLayqk8mmmpANC+fXuxHBlIZXOqxYsXW+I65LNuu+02kecyZcoAABYtWoR33nknyxjNORWBwtcqpUU+b968LIHre++9VwgZy5YtA2BtQ6WwsDCZb5IxOIb169fj119/zfTMP//8Uxoc0Xowzwn/LT0PXq831+N1uVzizaCVU6FCBQDAmjVr8NVXXwEwWrJGRkZKW9ZFixYB0IPvgViByqJQUFBQUPCLkLQoqGGw6XzDhg0l4En85z//EQ2VN/jFixczUesCBbXA5ORkAEYA69dffxW/O7Wb6Oho0YhIf6M2afV4+I6MAURERKB169YADJ9kkyZNRENna8mOHTtKq0srtDCv1yvBfMY+OKYJEyZIUl121gt/t2PHDvFDk9JHkkJKSoplwVKzf5n+2/T0dEtpnbQGaEmuXr1aKMw5/ff8DloNDz30EObOnQtADyIDhlZJjTqvoByVLl1annnjjTcC0Ft8Anp7VLb95HsVKVIESUlJACD070DiJbTEKMO0kpYvXy5jZOJix44dJcDN/WgF5dicJElyjG/b3nPnzkmchp93u90yXn+ylJf9ZqYeMw5BcsyTTz4JQCel8LzhZ4YOHSqknlmzZgHQY2SByLqyKBQUFBQU/CIkLQrz7Q7orB1S9Ogv7d27t1ge/Hn06FGxPKhtBeKX47+lf5E0OZfLJZoUNePy5cuLBk82xsGDB20p4cH5iYmJAaD7+fv16wfA8FPOnj1b4ii0IpxOp2WWBKD7Qkmj5O9IYz569KjfOIjZOqL207JlSwDGnHKOAwGfk5KSIv5iMuJ+//13SzvKUQMlKy0pKSmLj90f0tPTZT4Z8+nUqRM2b94MwPBLW8Xw4ZrRJ9++fXtJiKRFc+LECYl1PfDAAwB0y2/Hjh0AIIwoJqDlNmZi9tnz3enz37dvn1gq3HsVKlTAs88+C8BemrAZjD20adNG6PmMC9iZQEnZDQsLkzjeZ599BsCwisuVK4dhw4YBMNIEatSogaFDh2b6XKByHpIXha/LZ//+/UKhPHDgAACd083AEjej0+mUQ9oKIfLNOqWJZy4AyIWoV6+eHNx09Rw/ftyyPAUzeCDR1TVgwADJ66CpWaBAAREOq2spcV7i4uLEJUCXEw+a3Ly3Hdm9hHnt6EKhAlK4cGFLyQ9UWAoVKgQg57Wk+JmiRYtKFnSvXr0A6DRmuszuueceAMDOnTsBZHZ75AY8+EiGoPswISEBzz//PABD2ZkzZ45cFHQJOhwOCazTRUVlJC/j8c0TIfe/UqVKaNGiBQA9yx0AfvvtN6F225WR7btm3G833HCDjINKWGpqalDqufnmrbBSxciRI2Xvf/nllwD085Ku8X379gHQ5SgQ96ByPSkoKCgo+EVIWhS8Pam11K1bF7t37wZgZPSeOXMmS6YyYATVArUoNE2T76XVQG2pdu3acqPffPPNAIBnn31WtFOaiVeuXPGbrZlXUKtgsHjr1q2Sfc1ktaSkJNtMc2pY/fr1EyuKFoWv1n41mOeDVEy6mqzMzOZcJSUliUVId8GFCxcsdR1wvJSDAgUK5Ogd+PknnnhCNHm6EB0OhyRyvvDCCwD0ADOQN5qv2+2WxD26c/j/L774Ig4dOgQA+O9//wtAdzN9+OGHAAxL+qmnnpKgKvdlXrVVTdNkf5G6PWLECAC6+5SVBigv33//vSSvBatyLdfQ5XKhRo0aAAzixXfffSfnAufATsuYa07rrnTp0kJD5/ylp6dj3bp1ACCJyps3b1YWhYKCgoKCfQhJi4K3JmuXpKenS1p9nTp1AOiahR19DMxBVmosHAetmaZNm4oWxpvd4/FIQI/Bb6fTaaklwe/iuKi9P/bYY5KktnjxYgB6faeEhAQA1tVzIjhHjRs3FiuAAeKcannUInv37i2a7YwZMwBAqJdWaIy0TsqVKyfBYGqkVoMaG4PzY8aMkb4AXAtamGaLlWjdurX4mRlHKFeunCR6kqDxzTffAMh7PIAB2WbNmgEwemUcPHhQSqtQcx4/fjy+//57AEZ5loSEBAl279+/P9O75wX8twzaM/ZYtGhRsUwZPK5SpYrsPSbcWq3BX03uvF6v/I0EgHr16kndNP68ePGipTFSs+VIC5nyNHDgwCykD5fLJRYf61XFxsYKVTsvsZ2Quig4MRQEHtBTp04VfjdLVq9bt86WICgXpWDBglJzhiwL4sCBA8IpZyDd4XDIOOwwiT0eT5b35KETHx8vjBGyUYYOHYpx48ZlGo/VG0rTNCEc5DQDmcLKWlkvvPACfvvtNwAGo4PfYcV4+e7Hjx+XmjwMwN9yyy2SIW5F3SS6sXjYDxs2TC5u8u8ZBDVvbl4KhQsXFoWIh3ivXr3koGa2LV1Audnw3Cvh4eHijiB7auPGjQB0VyLrVNF14fF4pE4QmYcff/yxjMlKWefFR1fc4cOHhWnF2kpRUVG44YYbABgKhdWFCfm9ZK9RqcnIyJB5rFevHgA9X4kuzT///BMAMG7cOLl888I28lUIo6Oj5Xu43ygzly9fzrJfNE3D1q1bAehKJKDX7GKhwLzMl3I9KSgoKCj4RUhZFNSU6tatCwCiXf35559Yvnw5AOCTTz4BoGtcbH5jhwuqX79+GD16NACDjkit8NixY5LPQQ1M0zQJcFerVg2ArhEFyl82U1EZ9KUWTI0jIiJC6Ilff/01AN319NZbbwEwtFerLZ2//vpLgnq0EOh2CQsLy2IRpKenSy2oV155BYCuhZMSeuTIEXkfq8AxpKWliWZI68FquaGmxvnu1q2b5EOwhhLpivHx8TIOWlklSpQQ+iWJHJ999plkIlPjDqj3cViYaOfUSlmRuUiRIqKxkqTRrFkz0bAp/++++66lVp8v+H5hYWHiXuK4kpOTJcBtJcxEBK4ZrXRWX65Tp47sM1qK1atXF3oxa1S9/fbbePTRRwHo7jzzO+UElFOeg6NGjZJ/zzwlWoHm7zW7qnzzdwJ1PyuLQkFBQUHBL0LKovClfvFmPXDggPj/GOhq3Lix+HutzDbmd/Xs2VOC04xRUFN87bXXRJNmgtmFCxdEW2a1WSuqlDIYe+uttwp10VeLM1fz5PjPnDkTUDN1f6AW895770lVSwb3qKWuXLlSnk/ffb9+/eRz9DOPGTNGgphWWhKE2d/LmlIdO3YEoGf58ndW0phpuf3zzz94+umnARjJkazFVaFCBbGguT6vv/66WK9MLHW73ZbOS1pamsw3NWAG3L1erzyLMafPPvtMrFTGksztN+1EWFiYVI1mv5VWrVqJrNtlzTA+Q6p5+/btAejxEc4B18fhcEi9twkTJgDQYzm1a9cGYFiQubEofGvdtWzZUiwrxk1IS7506ZKcEebzkxWsGSs5cuRIQFZFSF0UFFKaVeSUd+7cWVwazB2oW7euBJR5oVgR1OKkx8fHS9CTnHK6wkqWLCnjIWOnXr16csGRCWLFZuJh0rFjR1l0vq/5UGvXrh0ASBbtU089JSa61WUGOM8HDx6UBjfkvrPU+tGjR6UcOk33atWqSdMdZgDPnTvXlux1X4SHh0vJ5ZdffhmA7l5h/2wr2WmE0+mULG2WWuf8ZHfIeTwekRmr8oEIMw+f7CW6l8jmS0lJwZIlSwAAM2fOBKBfDjyArHB95Rbcj5ShTZs22dKV0AzOFfNXJk6cCEBnGpF9RXJNRkaGFOPjPEVERARUnJTKHnNpXn75Zcm+JgOOyuv27dvFHcazon379iI33GculysghUO5nhQUFBQU/CKkLAre5NQ6WeBv3LhxopHddtttAPQAMwNcVhRJ47PpOnn77bdFa6AZyWJlS5YsEaoi8wc2bNggGjRveCsol9RSSpUqJW4MUt+oeXTp0kWKArIU9ddffy1/t6sWjcPhkKZRNIUZxGvevLlYOcxbWLhwoWj1rBEUaPnj3ICuMKJz586iXTMnxS4tldp4MKwnf3A6nbIeY8aMAQChuiYnJ+O7774DYPD0w8PD83XMZooooNN26QK2qjiiL3zlkXTdBg0aCLXYbIH6ZuR//fXXklORF4uQ38dnvPvuu+KCo9uULWu7dOkia0VX+fbt2zF79mwARjA9UPelsigUFBQUFPxCs8M3ezUUKVIkRw/zrbE0bNgwPP744wCMBuITJkzIc7JUYmKiBgDR0dF+x8MqloyF0NJJSkoSSiNvao/HIz5Cc82XnMxvcnKyBmQ/P/zOBg0aCI20QYMGAAz/7ZYtWySjljWXAgk4cn4AoFChQjlaM1pi9MkXL15cND7O1ZkzZ0Tryu2aXb58WcvNeLID54s1k/r16yfURga1c6o9czwlSpQI3gbyg7Nnz8qaXUuuCXMDJ0CXV8azrLCsKNdRUVF5miNzcJ2xgSVLlgg1PbcWRUpKylX32dWeDxhB5dKlS0umM+OXDodDLFUGwbdt25YjSrp5nxUuXPiqY/J6vbJWtDY4ppiYGFk/7q2kpCTxROR2n128eDFb815ZFAoKCgoKfhGSFgVhbjfo67czt7bMLXJqUVAD9S0VYi7XYQX8WRSEuQeG77M9Ho+M0QpmSl4sCvNYfMdkLm2S13kL1KIwW3fmufRtY5nT/fBvsCjsRqAWBWDIcf/+/QHoyab01+dWW86tRUH4ngPXQk7PppxaFGb41n8yl/ax4ny6mkURUsFsX5g7POUHglXGOCfwNwehNE5ukGBSKHMC8ybPbi6DqTAp5Bw8EFkwMiwszJbS/f4QSvvLt55csMYWWrtZQUFBQSHkEFTXk4KCgoLC9QdlUSgoKCgo+IW6KBQUFBQU/CKoUeKcRvbtBiP7/yZ2iJUgOwQAYmJiQmJMly5d0gA1nquB4wGAYsWKhcSYzp8/H5JzZMU+o8s+NTVViBvMQcmpO9+8z0LtbPRFSLOeFBQUFEIJZGGxReugQYOkJApb1YYa488KXNcXhS8v3pwdTZib1NjRv5pZx/lB2yNcLleWPIpg1U9S+HfB3DMe0LO2+d+UrYiICDkM/6+RYTgXzNAeNWoU5s6dC8BoZvRvvCj+fW+koKCgoGAprhuLwjcjUdM0qfXCKq9RUVFSY5/aPRsdbd26NeCbntaK2+2Wmkb33HMPAL0HBSuoBkujYP2XSpUqSXVNVq7NyMjIF6uC6+NyubJktJqtrvwAx2HO+Pdt+uJwOGypumt+JqCvj2+fh/Dw8HzVRjVNExln75WmTZtKkyk2ztq+fbv0OrEy4ct3fa41/9lVcLVT5r1er3goxo4dCwA4ceKE1FkLdUvC1/rLzVyF9pspKCgoKOQ7QsqiMHfhAjLXWOFNzraEjz/+uGj1rPIaFhYm2iA74bFGe158qb5aYPPmzQEA3bp1Q7Vq1QBA6tMvXLgQTz75JABkaXFpNTg/7Po1duxY1KlTB4De2Q7QK8pa0Q/DH8waOS2Fm266CQDQtm1bNGnSBIDRS+DHH3/EtGnTABiVLoNlYXg8Hpm32NhYAECTJk2kHeitt94KQLdA33jjDQCZq6rmFb5WFdepf//+0taS/SAWL14s8mpFe9+cgu/ncrlk/d566y0Aui+e68eeHStXrpReMUePHgUQmDbNdaF1QvaQx+ORNTDXeKMFZrZmfCvh2qHdZ2RkSLXhRo0aAQC+/PJL6cQZynFBs/xz3nJquQEhdFFomiabii6lHj16ANBfiO0amzVrBkBvXLRjxw4AkLak8fHx0r82KSkJgHFoB2Ii33fffQCAyZMnA9B70p48eRKAEcy+7bbbUKZMGQB6f9pAn5kTXLx4EQBw8uRJ9OnTBwDw3HPPAdBLHZvdKVaCAla8eHG5PG+//Xb5HQDs3bsXe/fuBWC4VpKSkqTxCnuN//3337bOk7lv+QMPPABAL1sP6H2r2YuY8lKjRg1pRsW2pXm9cD0ej8zHY489BgBSLt/pdMozeXn07t0bI0eOBGA0dgrGRWouSc3nV65cGQDw6quvSmMclrfv1KkTpkyZAsBoVMWLP7eHpbn964svvggAeOSRRwDo7WO5t/n9RYoUQbly5QAYfcjDwsKkTfDw4cMB6C4h/i1Q8BJq2bIlXnrpJRk3oJf1Z0nxYKyVbxtk897Jbh/xTNU0TQorVqxYEQBEIbp8+fI1zwjlelJQUFBQ8IuQsSg8Ho9obk888QQAiHZz6dIlcTO98sorAIDZs2dLIyHepObyuoEGt9LT06UFKgNXvM1Hjhwp7UjpbnrggQfQvXt3AMDrr7+eaVxWg7c/teEtW7ZgwIABAAyTeMCAAfjvf/8LIHcmZk5A875nz54YNWoUAEhA79VXXwVguCTMcLlc+PrrrwEARYsWBaBr2ocPHwZg7Xz5mtlDhgyRRvPUTl999VVpb8vxVqlSRWQtLya6+fMej0esGDZLYqvRWbNmicuCZIxJkyaJlkfL68KFC7YHSTne2NhYlC9fHgCk1e9bb70lmvJHH30EAJg/f7407mE+AYPbebEoSAihW4cehZIlS4o8m114fAY/FxYWhurVqwMw3NB04QUCPjMmJgaAfi7R3ct1WrVqVVCqW3PP0UXKMR0+fFjOTcqw1+vN4mbt378/JkyYAAD49ttv5XM5hbIoFBQUFBT8ImQsCrfbLT5QahbUNCdOnCi35b59+wDosQEGvewCx1O1alUAwE8//QQA+OSTTyQ2QY303nvvFX8txzV37lwcP34cgD3WBTWJQ4cOiXZar149AECLFi3w2WefAci7/9gX1ECoRdarVw9ffvklAGDMmDEADGsnu2CspmlieSxatAiA3lLywIEDAKydI2qDDz/8sIyPskOLdc+ePfI5PvvEiRPynnmVL3MLzYEDBwKAtO195plnAOiyTU2UfvjatWvL33v16gUA+PDDD4NC/eS4aTUzcO10OuV9OKZWrVpJTID++dyOjd8ZHh6OO++8EwBQqlQpAIZmPHPmTGmBaia4kEhCGQIgzYxIUbeCyMExcnxdunSR2NqHH34IQLfquY6cO7fbbSnFOj09HaVLlwagW50AULNmTQDA+fPnxeKjfO/cuVN+xzOsRYsWOH36NABg+vTpAIy4XE6IE8qiUFBQUFDwi3y3KHhrFyhQQLQp0gYbN24MQE/w4a1tLlFBbZBarJUal9PpRHJyMgAIC4aaTLdu3bBgwQIAOi0W0K2O+++/H4ChcScnJ9uqBfK9T5w4gfPnz2f6m28pEytAjYl+0rJlywrLhGPJzl/LdSpZsiSGDh0KwNB+Dh48aKkPns+ir50ytWrVKjz99NMAdDYNoGudvuO1wt9M7bdmzZrCMFm6dCkAyDpFRkbKe9O/f/bsWdEEqcUuXrxYWEfB6GZGTZxxk9jYWLHASL3evn27xKZorfrGc64Fc6mQefPmAfAcom0AAB+SSURBVDDmgaUwVq1aleWdU1NTJR7Hv6WmpmLlypUADBkNhIHEeAAtKMZFjx49KrRg0u/NFlfdunUBAKVLlxYLh+PJCyjL0dHREq9t3bo1ACMG89FHH4m83XHHHQD084nxywoVKgDQz1eWGtm8eTMAI8aTE+T7RUE4HA4JcFKIbrvtNgBAmTJlZAObBZHFuGgOulwuyw5mh8MhZm/hwoUBGALzxhtvyIbi5M+bNw9du3YFAKGF/vPPPxIYtaMmDoWwRYsWEszjBWFnAJTvkpaWlmnD+IIbjoG3xx9/XC5/zu2RI0dsCWLzouD/z5o1Sy58u12WlMGkpCRRNui+5FycPHkyS20wcxCSfwsPDw9aPSWXyyXyQ5fF7Nmz0bJlSwDAF198AQB48803hR7OfZDXMTocDskjWb16dabvMrtE6Opt1aoVevfuDcC41JcsWYJ169ZlGk9e4XK5hHbLC7JSpUoA9AD/qlWrMo0xLS1N5uedd94BoFPESXJhocDcjMs3N2ncuHEYNGgQAEPBIjHju+++k73OC7ZQoUIi4yQgJCcny3/nJUdHuZ4UFBQUFPwi3y0Kal8ZGRlC26IWTlM3LCxMzNK4uDgAupbPW5oayVNPPeVXw83tuKjdkWZ66tQpAMCUKVMkIERto1SpUqLhMOnPbm2Q44uLi5PsWWqEiYmJoplYBb4fa/5cvnxZMpsZ1OaauN1uqbDJRJ/Y2FipRUUSQFJSUq5M4GuB686AKBOvoqOjs9QLs8vq4vfu2bNHLE4m3JE+bNbKuWalSpXKIrfBsCb4/KJFi4omSvqrpmmSAEf3DoBsLfy8wh+lnWNjxviIESNE46d757XXXhMXWKAWhaZpkmBL65eB+48++kieQ8uwXbt2kkRJq9HlckmwmfsipzDPJ6nVAwYMEFcTXak88yIjIzNZsIB+TlHOSPEfNmyYyJuyKBQUFBQULEe+WxRmUEunX4/lDwoUKCC3JRNebrjhBvTs2ROAkZzUtm1bzJ8/H4A1gT/e1NRSmCx1/PhxCeYxyORwOMTHSrqj3Yk4HNevv/4qVgy1mo0bNwp10aq6QdSUuRbvv/++vH+xYsUAGAFJj8cjFsXBgwcB6EG0jz/+GABsocSax0hL4t133wWgrxMtVcZH0tLSbLEqzDXLWNuKcstSK82aNRN/M0uxNG/eXGIay5cvBwAkJCRYOkdmS5naeps2bQAAo0ePliD29u3bAeiNeUhTt6tExdXiim63WyizLBnSrl07oXnS5x4fHy8EkrzCHBdhPTnOE33/27Ztk700YsQIAMDgwYMlRjpnzhwAekXpvCa5ut1uia8xJnrhwgUhgbC0Cy2/7Kyv5s2bC7GGY1+xYkVA51FIXRS+bgMefoAxIb///jsA3VXFWk9r1qwBoDNFyC4x1zixCjxUfvnlF2EOdO7cWcZOdgqDzMHgvQO6cHMTU7iTk5Mz1TmyEhS4rVu34oMPPgBgzAPdc9988w02btwIwGCN0X0AGDx9u+aIY1yxYgUAfe1ottOtMm7cOMuz1s1wOp1yqDG4+cknnwAAunfvLpc6D8OCBQvKvPzwww8AdEKAlcUdPR6PvPOQIUMAGIdeWlqaKAG8yPft2ydulvxoyEXmUYsWLQDoeQu8fOkKs9J1qWlaFsWK7lJN04Rwwzp0ZmIECSWJiYmiEOVFrvhvqEhMmzZN5Di7C4LnDZW1cePGifyzXtnFixcDkiPlelJQUFBQ8IuQsiiInJhITqdTKHP8Wb9+fdGsGXSyAr6a1KBBg4SeRq3G6XSKVk2a7LJly2ytKElTs3r16lK51je3xE44nU5xkVDjMYNaD+fArAXZnRPAZ3Eeli1bJgFBBme7du0qbihqW1ZbFpRl8to3bdokP0kfZuBzyZIlMi+sQGy1+9Llcgntc/To0QAMGZ4yZYrUpKLmGhYWFnRLgnu3UaNG6NevHwBDhj799FOpQ+VbzysQmEutk97OOlOs3VazZk1xpzKgnpGRIYQOWh5DhgwRUk1utfiwsDBxm7Iis6Zp2VoSgH42UUbobmrXrp3IOBu3BUoJVxaFgoKCgoJfhIxF4Xa7RUPw1WAcDkcWDdnsazVrYVZTQjk2wPDDjxs3TmIU1M5KlCghWjX9qmvXrpWAsp0avnku+JxgtWXMicZrx5rkFNTAChYsKAHabt26AdDrczG+lZaWlunzVoMyatZ+OS9sNVq2bFmxJBjgDtQi5fvQeunYsaNk0zMjety4cQB0Tb5IkSIAIPG2YIJrwP4c48aNE78/rZ7p06eLT94Osojb7Za+MwyQU17Gjh2bpTZYUlJSptpUALBu3bqA1s2XROMPGRkZ6NKlCwBjHb/99ls5i6yKb+XbRcFLgcymVq1aiXnEQBqF+9y5c1JS3LyR27VrB8AoLTxv3jwRNjsOSuYDxMfHi4nODZWYmCgltJlmX6pUKXkXuw9ufj/N9sTExJDs4csNxk0YLLdGRkaGlIbhxj9//ryMg+7LYML3EE9JSZEqACwXc/jw4YBcK77KVN++fSVgzcJ2ZNkMHDhQGhbxb8Eooc0xVqlSBYDB9mnVqpUQVtjU6NixY7a6cx0Oh1R8YLCfuTC33367lGAhIWLt2rVCoOEFZndnSQCZepuTjEDl4qWXXhJXp1VzFXoniYKCgoJCSCHfXU9mCifzImgV3HzzzQB0zY9ZhdSSw8PDpTgdA4Rz5syxVUNlnsTIkSOlHzTH5fF4xLogTc2cDWwnzK659957D4DOgw9WP+rcgJqtnTWwzN9LWSpbtqy4FGrUqAFAL19PDTEYBfd8wTVjkcJjx46Jdk9KqrlVaCAwF9Cjq4vZu9xniYmJ0uqTsm63ReFyuaRwIvt00yI/ffo0xo8fD8ConxaMXuK+802a99q1azPlyAD6/JgLlZp/2gFfOvddd90ltPM333wTgJ5CwP1lFZRFoaCgoKDgF/lmUfDWphb+xRdfSGCRmjB9yi1btpQgG+lp4eHhkplJH+KxY8ds8Q9S8yOVskOHDlLfhYlAp06dQtOmTQFA2qSePXvW1jgBv/vy5cv4888/ARjWVUZGRlB8pbkFtVkGKa0OdPsG9RkYffHFF3H33XcDgMSSKDeA/cmR2YF7gBbF2bNnpTaPVUlk5nLeADB+/PgsQWPWMlu2bJkEZu2WHfM69e3bF4BhSXB8H330kWjz+Wkd+7Y4yE9wHVndd/z48di/fz8AI65kZQIioSwKBQUFBQW/yLcr0lfzi4iIEDYG/0b2AVuQXu07qJnZpQX5+pJ79uwpzzRbDEzMMScC2amF0F+7ceNGtGrVCoCh9YSSNUGt9uLFi1LCgtVj7ZofMuiYtHTq1CmhD7K8woULF/JVS+S8kHG1aNEiSdqiVh0ofPfIyZMnMWzYsKuOxzfx0O4YW1hYmMRIyNR5++23AQAzZswIWhvY6w1cp4MHD2LChAkArKNUZwctmFmXhQsXDm6K51Vw8eJFDQCio6NDYjzJyckaAERFRYXEeFJSUmRXxsTEWDYmr9crRQMp6AUKFMjRYXTp0iUtN+Phd5Iu7PF45LChaR6IWzC348kJUlNThfZozozOzXgAoFixYiEhR+fPn8/RHLHmFUvl//bbbwB0N4uVrlvOUSjus5yejb7B7GLFikl9MMpOIJcqz0ZfKNeTgoKCgoJfBNWiUFBQUFC4/qAsCgUFBQUFv1AXhYKCgoKCX6iLQkFBQUHBL4LKDSxUqFBIBEQuX76sAUBsbGxIjCcpKUkDQo8VBgBFixYNiTElJCSE5BxZyXoKBGbWU6iNKdT2fVxcXEiM58KFCyG7z3yR/6mG1ylIAjBnFvtyvkOxequCwvUI7rf8LKkfSjC3ZPBteaxpmuVzoy6KXMBcDoFJLSzL7Ha7kZycDMDgM58/f1548FywfzvLjHkLTqczJIsShgpcLpeUpTZvdCbGMZnS4XAEVWZ8n5WRkSHKUHb9YijXzE2xMjHO7XZLCXbOR5EiRSTHhAUdU1JSZN7sTKDMyMiQvW1OFA5mMiCfz70VGxsrpek5ppSUFEkO5n4MDw8PaJz/965iBQUFBYVcISQtCmos/OlyueQmJcLDw4NepoKaVZEiRfD0008DgBQHTEtLw99//w0AUopk+fLlUniOne7s0D40TRNtz6zxZPcsX63QXLIhEM2V//a+++4DABw9ehS7du2S7/b9XCiUZDC/r3lcdozNd25vuukmKV3BQokOhwPHjh0DYJS2Tk5Otn2uKBMZGRkyTmqstWrVkoZC5cqVk79Re2WZ/W+//RaArsEG6u6gDJcrV05aCbCUdrt27aRf9dq1awHoJX42bNgAQC9NDljjcvHtP3/LLbdIiXo+Z+fOnbZ3RwSMpkj0YAwePBgAUL9+fSkkSavr2LFj0hGQ58/BgwcDauqmLAoFBQUFBb8IGYvC5XJlagYCQEqL33XXXdKvmrf2ggULsGzZsky/s1vzor+0fv36eOihhzL97a+//sL8+fMBQMqNjxw5UvypLBhoZeMVc8wkNjYWgN4TGdD7h8fHxwPIHPSjZsa6OmxQk5KSEtD8UQscM2YMAL1ez2OPPQYg+yKJvhai3fB6vaKVEQ6HQ9aHPu709HQZr5XyRE2djYF69OghbYCp6TmdThnPk08+CQD47LPPbGvWwzWgj3vgwIGinbL5VtGiRXH8+HEAkHLWR48eRdGiRQEYZfb5mS1btuRZm/e1unr37i1tPs3rxHE/+uij8rlp06YBgDSnCgRcf1ouL7/8MgCgbt268rszZ84AAAYNGoQffvgBgLGnwsLCLI0rud1umW/ur3vvvReA3p+b4ytVqhQAIC4uDnfddRcAoFmzZgCAESNGSAuCvKxPvl8UNO/KlSsnfYLbtm0LAKhXrx4A/WXpIuHnb7nlFgnY0Oy0uxIov79BgwaIi4sDYLiZPvroI8yaNQuAUd8/JiZGBMaOzW4+0IYPHw4AeOqpp2RcHC83GatzAnrvA0DvhAfoLg4rOqlt27YNgL4+dKnQJffoo4/KwcJ+xHZ3luPlEBYWJpdk/fr1AQBlypSRxvRlypQBAHz++eeYNGkSgMDdZF6vV9bg2WefBWC4Kjdu3Cjuy507dwIAGjVqhNdeew0AxOWyYMGCPD3bHyg3DECPHTsWADB06FDs2bMHAMR1sWTJErkgWOXW5XLJYWMOugOBrSfH1b17dwC6G5PKGd2YV65ckV4mpUuXBqDLN3uNcL5YhTcv7mkGgAcOHAgAuP/++wHo1aM5B+xEePfdd8u7UzE7ceKEpUwsl8slyie7gHI+hg8fjoMHDwIw3IUulwsPPvggAKPr3YABA2Rv5kURUq4nBQUFBQW/CJl+FMOGDZObm/1eeXt/+eWXop1SG7zhhhskuGY3fZBWDDvuderUSW7lHTt2ANAD19ReaBonJibKd9jhFuNz+vXrJz0GGFT89NNPxbVBF97x48fFzUEthEE5qzR7uiBatWol60itukWLFtKh0OyOsgO0JGhFDBw4ULQyrsXGjRtFc2YQPi4uzjJ58nq9IhONGjUCYGirzzzzjGjq1AT37dsn8/f777/Le1g5R+Zy67RuaLl/8cUXYtGw1HeBAgWy9F4x0565N/gzEDnnd/AcqFy5Mp577jkAwDfffANAn1MGlOlmqlOnjlgZvXv3zvQ3r9eb6zH5BvT5/6dOnRLrnH/r168fhg4dmumZL730EqKionL1TH/jCA8PlzXiHLGL5oEDB0TGuLfLly8vljL3wYYNG7JQe3MDZVEoKCgoKPhFvlgUXq9Xbss+ffoA0H1vDMhSS6d/bcWKFXJD/u9//wNgv2/bDGokzzzzDADgxhtvFN8p+2ifO3fO9gQz345o9OVOmTIF3333HQCDNnfmzBm/3cqs7gPM72ZA7/Dhw9KhkOOghWEnqDXRcmFf9UuXLmH06NEAgF9//RWA3vucmhrHuHPnzixJXnmFpmmi5THgScti6tSp0u2Pf+vTp4/sAd/+8YHCTDVngJPyw7jWr7/+KhorNeJg0Jj5zEqVKgEAatasCUCnv5IgwmRWp9Mpc8N/98knnwhtlE2QuHapqam5fgfO+ffffw8AuOeeewDocVTf5EOPxyNaO+MW0dHRllhYhNPplLkhzZ6eA7fbLWQExnYHDx4snR2XLFmS6Wdex6QsCgUFBQUFv8i3GAX9ZNToSpYsKbdlxYoVAeh0NECPDdAvGcxELWphpAo2aNAAgD52+pfpOw1GvRlfbfmVV14BoGsVpLnSVxsVFSXxB1oNdiaS0Vpg7+6VK1cKK43WX3x8vMSVfOvTWDkWwKBOUrO86667ZD747N27d4sPnJporVq1xLoIlPVkTmKcOXMmAIMlN2DAAMyePRuAQVGuUaOGWNFMZMtpq9jcgBooWUOkoC5cuFCsG8bXwsLCbN9zfD/KDi3md955R1rnmi0ryvOpU6cA6NYGv4NnSCDyRZmhRTFlyhQAOjXVN27hdDqFKUZvR3p6uqUMzIyMDHlGjx49AECs4woVKoglQSsiPT1d+sJPnz4dQOCsxny7KLiQDNr9888/ciAzcE1+sKZpEgS0qul8TsCDuVatWgCAEiVKAMgcELzjjjsA6PzxQ4cOAUAWl49V4Lt36NABgO4CA/QcCPLzucmSkpLw9ddfAzCEJS9m+LVAs5v5G8zivXTpEmJiYgBAOOBFixYVHjqVgN27d1vq/uJmYACfa3Ls2DF5DoP89957ryglpDb+8ssvtmSP84D59NNPAQCbNm0STjypjImJiThy5AgA62uD8V3Cw8Oxfv16AEYAn5Tl+++/X+iXM2bMAKAHTX2D2VYiIyNDSCJPPPEEAMgh9/3330vwmPB6vXKQ9+vXD4Ae9OYFvHnzZgDI9oLJKXyD2e+//z4AnUJNN505MEz6N39aNU9cM4/HI8oE14z7p1atWjJOurvmzJmDqVOnAgAuXrwIIPOFr1xPCgoKCgqWI18sCvONxgSZLVu2CMXTV8N0uVwSgGSiVtWqVW3P7qUm9ccffwDQE2kA3U3GOj00S0+fPi30OLqj3G63pW4DalLLly8HYGgL4eHhokFRM+7UqZPQH6ltvfvuu5YnJVKLYSCPQdDRo0dj3LhxACAuqOLFi8uc1qlTB4AeQLVqTOaaV3RL0FRv06aNWD9Mfrvzzjtx9OhRAJkT4ThGO1wutDaPHj0qSY90M50+fVosjueffx6ATpawkiShaZrsGyZg8WfJkiWlAgLdmmvXrsXbb78NIHMGuVVwuVzyfnPmzAGgZ6Pj/7V3LiFRvWEYf5yx0VJLXCQVuCuDZAgiUbMwdBNhriqCECGx2nchyE0SbVq6aNFlUZuyJCgiicqKykArE7EsiiCismzMyhic8b8YnndOo/+DzpzRhOe3UbrMfOe7nPf+fpjaGohGo7bXmOCSm5uL9vZ2APGgrRd7ime3qKgIQMz1zLljenlBQQFqa2sBxFPDDx06NMkSSoVAIGAFdq2trQBgRaHZ2dlmwXC/1tXVmXv67t27AGKu4Ldv3wJIbv1kUQghhHBlzmIUlH5MRXz9+rWldibi9EvSP7969WpLo3NeauKlH5WSl31djh8/DgAoKyuzcdMHXl5ebloY/fTOYFyy43KW23M8bE/AgDr/3snNmzctyFVTUwMg5h9PdTyJJI6JWktvb6/1lhkYGAAA1NfXW0yHGpmX2qlzDuhXpuXnbIXBFNSxsTHrwcVOpFlZWWkN+vOz9+/fb6nhjFXcvn3bAty0xvr7+22PeZ1+nfh5w8PD1oaGBXcnT560NaL1nEwRG0nsDL1hwwaLTXKNnHeaJDI+Pm5FlExACIVCZoXwXHphUdB6YOC4srLS1qKxsRFALJWXMcDy8nIAsfNPS9WLcUQiEWsxs2nTJgDxuXny5Al6enoAxOMWq1atsrFs3rwZQMz64vuVXoeZjG3Oez1xw/n9fus9MxVcNGYWBINB68XCSWxpabE2zV6anvysjo4OAPEsFee42tvbzTRnQ7f+/v6ks6I4L5wT58VIzjkDYsKE4+BYd+zYYbnXDx8+BBA7gF6/BPmyoVCgO+D79+8IhUIA4oc3GAyiqqoKQLzXlNcBUs4J98GePXsAACtXrkRlZSUA4MiRIwBilch8OfE50pXhQxcdhcOJEycsYMxagXA4bFlYFy9eBBDLlmIDOCYqpDrGRHeo03VBhYyu3oMHD5rw4JqdOXMm6YA/54G1CY2NjTh8+DCAuCt1KgHBs7VixQpzP/Ozrl+/boLeC8UjMZOPdSfhcNiUQSbhDAwMYO/evQCA0tJSAMCWLVtw6tQpz8YRiURMQGzfvh0A8PjxYwCxgP7w8DCAeNJIYWEhCgsLAcRdmBUVFaboco9xPaczZ3I9CSGEcGXOLYrpQqnH3OZ79+5ZehwDcLdu3TKTz0sS+1JNTExMqrwcHR21aklqGNu2bbNeQjMJakciEctxZ/vknz9/Wn8Xum0YXM/PzzeripW/TU1N5g5iACwajaatop0WDQOzPp/PNDLOW25urv09UwnTNR5aVtSaPn36ZJooK8bPnj1rWnq6q+rpQmQfoxcvXljVOPdSVlYW+vr6AMBSm/ft22cuFmqxqXZoZfo5P4dr4vf7bT9zPnp6eszqogvz/PnzSV3WE4lE7LtpRbx588asP36ms1M09xXrrY4ePWqp2Lxm4MCBA+au8sKTwKQHum2oqT9//hxPnz4FEE8siUajuHHjBoC4RbFmzZpJtTipkJWVherqavs+IO4q/fjx46SrYYeGhixBgWt8+vRpayHPd8tM+rzJohBCCOHKvLEoCKXfyMiIaRHsL7R27VpLj/OiaCrx4nhqKwUFBVaEx8KukpISS0mjRlJaWmr3VtCPOJ3xZGRk2GdQyyouLkZZWRmAuMbFGEBeXp4FaDk/HR0dVnSTSlrcdOFzOTU6rgE1nuLiYpvTdHePJZzHjRs3Woyira0NQKyv02xZEkyx5OUyzc3NVlzHOQuHw5b6yWLKL1++mOaXyl529npiajLHxMC/8/pc509qp+vWrUv6+4HYXPA8cAxLly61GAgtLMZHgsGgafVbt24FEJsX3qHCWNO3b988TyEG4rE14rzbgu+e7Oxsi7txb797984sIS/2dzgctsrs3bt3A4BZB8Fg0CwyZ1yTFxft2rULQCxtnfeeDA4OAphnwezp4qxSBGKVo9xsdLfU19fbZFy6dAkAks5njkajFnBj1gNfxj6fz0xPboRAIGC/84KgUCiUVCsBn89nLRQYjM3MzLQaBVYTM/sjMzPTaj2Yyx0KhUzIpPtCp/8jscaipKTkr0ytdJJ4Oc/OnTvtoLOdxmy0p+A46Brky2R0dNTWkxX/y5YtswwotrNobm42V1kq6+h88dMlySA5A6Pd3d32HRx3Tk6O3eZId2HiC3S6+Hw+U5joOqmqqjLXMSvEuW8XLVpkc8Q/6+3ttTYnfA6vLwXjPmGVN1/E69evt8p1Cs/a2lprX//y5UsAsTonLxQhZzNPvte4BnV1dQBiQWomuZBAIGCZZHz/PXr0yOqH6G6dydjkehJCCOHKvLEoCDWyDx8+WJtmXma0cOFCawbX1dUFIF6hO1PJPjExYf+XAXJaLp8/f7Z8ampgY2NjZh5SA3n27Jml/KWadx4Oh02To1bG/GkAk6ozfT7fnFkShGOnVp+fn5+2+58ToTXDvdHQ0GCaKK2u2WjkmFjdz+B6a2ur/RktruXLl5s229LSAgA4d+6cp+PMzMw0Tfz+/fsAYne7A0BnZ6ftV65TdXW1jYmJFckmRfj9fusS4Lz7mXVHTAFlEsSDBw/sDFJbv3z5sp3HdO8l7t9jx44BiKW9s/sCLYbx8XH7ncksr169SuoK1v8jEAiYBUPrjgF9Zxo8ef/+vSXRMAHm2rVrlrSQzNhkUQghhHBl3lkUxO/3m2+VldNFRUXWQpkdQqk9zlQD8vv9VqjGtER+5p8/f6ydMTX4SCRi2pizs6RXmoXTIuGzzOblTclATZhpe52dndZ7Jl2xAWf7ZyDebbO/v9+CprMVSAfiz8mKePqJKyoqrA8Vg4ttbW3W2ZXV7M6OuF6kWmZkZNi6sJqZlnBDQ4MlZFBrv3PnjhWNsmdXKnuaz0BruK+vzyxOni8+79evX82fzhhFJBLxVFt3g+Ogdj44OGjV6Wzn393djatXrwKIF7amw1LlMzPQz58XLlyYdCHY79+/zXJjrHPBggUpzZssCiGEEK5keH0pihs5OTmefdnExIRJbqaK1dTUmHRnPxP69Z0a7K9fvzIAYMmSJdMaj/PaQ37WVBpxsprEyMhIBgAsXrx49hbDhR8/ftjDFRQUpDwmZyuCxPYj02V4eHhac5QYF6Fv+8qVK2hqagIAuycjFThHeXl5M5of51WaiXvI2UNpph1sR0dH7R9Od0zOdSGJ1+Y6z9lM14xjcjv3zmuReb6cBa5TpesmC899fn5+Uns6Go26XnHKeZrueyAUCiV9zpxrl/gOd1qNM503nrNE5q3ryXl7GM3Yrq4uC3AlTlQqzHQDiL+ZqsYi3VBBYG+loaEhS7WcS/4lt+FcrMtUY3AmYPzL+Hy+f2aMs712/8ZTCyGE+GeZVdeTEEKI+YcsCiGEEK5IUAghhHBFgkIIIYQrEhRCCCFckaAQQgjhigSFEEIIVyQohBBCuCJBIYQQwhUJCiGEEK5IUAghhHBFgkIIIYQrEhRCCCFckaAQQgjhigSFEEIIVyQohBBCuCJBIYQQwhUJCiGEEK5IUAghhHBFgkIIIYQrEhRCCCFckaAQQgjhigSFEEIIVyQohBBCuPIfwTOxm8YKnBcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "rows = 10\n",
    "cols = 10\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "indexes = np.random.choice(5000, rows*cols)\n",
    "count = 0\n",
    "for i in range(0,rows):\n",
    "    for j in range(0,cols):\n",
    "        ax1 = fig.add_subplot(rows, cols, count+1)\n",
    "        ax1.imshow(mat['X'][indexes[count]].reshape(20,20).T, cmap='gray')\n",
    "        ax1.autoscale(False)\n",
    "        ax1.set_axis_off()\n",
    "        count+=1\n",
    "plt.subplots_adjust(wspace=.1, hspace=.1, left=0, right=1, bottom=0, top=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Vectorizing Logistic Regression\n",
    "\n",
    "#### 1.3.1 Vectorizing Regularized Logistic Regression\n",
    "\n",
    "$$J(\\theta) = -\\frac{1}{m}\\sum_{i=1}^m[y^i log(h_\\theta(x^i))+(1-y^i)log(1-h_\\theta(x^i))] + \\frac{\\lambda}{2m} \\sum_{j=1}^n\\theta_j^2$$\n",
    "\n",
    "Gradient:\n",
    "\n",
    "$$\\frac{\\partial J(\\theta)}{\\partial \\theta_0} = \\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)} - y^{(i)})\\cdot x_j^{(i)} \\ \\text{for j=0}$$\n",
    "\n",
    "$$\\frac{\\partial J(\\theta)}{\\partial \\theta_0} = (\\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)} - y^{(i)})\\cdot x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j \\ \\text{for j$\\ge$1}$$\n",
    "\n",
    "Recall that:\n",
    "\n",
    "$h_\\theta(x^{(i)}) = g(\\theta^Tx^{(i)})$\n",
    "\n",
    "$g(z) = \\frac{1}{1+e^{-z}}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def sigmoid(z):\n",
    "    z = np.array(z)\n",
    "    return 1 / (1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lr_cost_function(theta, X, y, lambda_reg):\n",
    "    m = y.shape[0]\n",
    "    theta = theta[:, np.newaxis] \n",
    "    h = sigmoid(X.dot(theta))\n",
    "    J = (1/m) * (-y.T.dot(np.log(h)) - (1-y).T.dot(np.log(1-h))) + (lambda_reg/(2*m)) * np.sum(theta[1:]**2)\n",
    "\n",
    "    diff_hy = h - y\n",
    "    grad = (1/m) * diff_hy.T.dot(X) + ((lambda_reg/m) * theta.T)\n",
    "    grad[0, 0] = (1/m) * diff_hy.T.dot(X[:, 0])\n",
    "\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing Cost Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_t = np.array([-2, -1, 1, 2])\n",
    "X_t = np.hstack((np.ones((5,1)), (np.arange(1,16).reshape(3,5)).T / 10))\n",
    "y_t = np.array([1, 0, 1, 0, 1]).reshape(5, -1)\n",
    "lambda_t = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost: [[ 2.5348194]]\n",
      "Expected cost: 2.534819\n",
      "Gradients:\n",
      "[[ 0.14656137]\n",
      " [-0.54855841]\n",
      " [ 0.72472227]\n",
      " [ 1.39800296]]\n",
      "Expected gradients:\n",
      " 0.146561\n",
      " -0.548558\n",
      " 0.724722\n",
      " 1.398003\n"
     ]
    }
   ],
   "source": [
    "J, grad = lr_cost_function(theta_t, X_t, y_t, lambda_t)\n",
    "print('Cost:', J)\n",
    "print('Expected cost: 2.534819')\n",
    "print('Gradients:')\n",
    "print(grad.T)\n",
    "print('Expected gradients:')\n",
    "print(' 0.146561\\n -0.548558\\n 0.724722\\n 1.398003')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 One-vs-all Classification\n",
    "\n",
    "> In this part of the exercise, you will implement one-vs-all classification by training multiple regularized logistic regression classifiers, one for each of the $K$ classes in our dataset. In the handwritten digits dataset, $K = 10$, but your code should work for any value of K."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt\n",
    "def one_vs_all(X, y, num_labels, lambda_reg):\n",
    "    m, n = X.shape\n",
    "    all_theta = np.zeros((num_labels, n+1))    \n",
    "    X = np.hstack((np.ones((m,1)), X))\n",
    "    \n",
    "    for i in range(num_labels):\n",
    "        initial_theta = np.zeros(shape=(n+1))\n",
    "        opt_results = opt.minimize(lr_cost_function, initial_theta, args=(X, y==i+1, lambda_reg), \n",
    "                                   method='TNC', jac=True, options={'maxiter':50})\n",
    "        all_theta[i, :] = opt_results['x']\n",
    "        \n",
    "    return all_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4.1 One-vs-all Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_one_vs_all(all_theta, X):\n",
    "    m, n = X.shape\n",
    "    X = np.hstack((np.ones((m,1)),X))\n",
    "    \n",
    "    pred = sigmoid(X.dot(all_theta.T))\n",
    "    y_pred = np.argmax(pred, axis=1)+1\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_r = 0.1\n",
    "num_labels = 10\n",
    "all_theta = one_vs_all(mat['X'], mat['y'], num_labels, lambda_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Train accuracy: 95.39999999999999'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = predict_one_vs_all(all_theta, mat['X'])\n",
    "accuracy = np.mean(y_pred == mat['y'].T)\n",
    "f'Train accuracy: {accuracy * 100}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4.2 Similar Code using Scikit-Learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=50, multi_class='ovr', n_jobs=None,\n",
       "          penalty='l2', random_state=None, solver='newton-cg', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver='newton-cg', max_iter=50, multi_class='ovr')\n",
    "log_reg.fit(mat['X'], mat['y'].T[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9446"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.score(mat['X'], mat['y'].T[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Neural Networks\n",
    "\n",
    "> In this part of the exercise, you will implement a neural network to rec- ognize handwritten digits using the same training set as before. The neural network will be able to represent complex models that form non-linear hypotheses. For this week, you will be using parameters from a neural network that we have already trained. Your goal is to implement the feedforward propagation algorithm to use our weights for prediction. In next week’s ex- ercise, you will write the backpropagation algorithm for learning the neural network parameters.\n",
    "\n",
    "### 2.1 Model Representation\n",
    "\n",
    "<img src=\"neural_network.png\">\n",
    "\n",
    "> You have been provided with a set of network parameters $(\\Theta^{(1)},\\Theta^{(2)})$ already trained by us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat_weights = scipy.io.loadmat('data/ex3weights.mat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 401), (10, 26))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat_weights['Theta1'].shape, mat_weights['Theta2'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Feedforward Propagation and Prediction\n",
    "\n",
    "The formulas to find $h_\\theta(x^{(i)})$ are in the neural network figure above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_nn(theta1, theta2, X):\n",
    "    m, n = X.shape\n",
    "    a1 = np.hstack((np.ones((m,1)),X)) #with a0\n",
    "    \n",
    "    z2 = a1.dot(theta1.T)\n",
    "    a2 = sigmoid(z2)\n",
    "    \n",
    "    z3 = np.hstack((np.ones((m,1)),a2)).dot(theta2.T) #with a0\n",
    "    a3 = sigmoid(z3)\n",
    "    h = np.argmax(a3, axis=1)+1 #get label with largest h(x)\n",
    "    \n",
    "    return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Train accuracy: 97.52'"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = predict_nn(mat_weights['Theta1'], mat_weights['Theta2'], mat['X'])\n",
    "accuracy = np.mean(y_pred == mat['y'].T)\n",
    "f'Train accuracy: {accuracy * 100}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.1 Similar Code using Scikit-Learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/sklearn/neural_network/multilayer_perceptron.py:562: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLPClassifier(activation='logistic', alpha=0.0001, batch_size='auto',\n",
       "       beta_1=0.9, beta_2=0.999, early_stopping=False, epsilon=1e-08,\n",
       "       hidden_layer_sizes=(25,), learning_rate='constant',\n",
       "       learning_rate_init=0.001, max_iter=200, momentum=0.9,\n",
       "       n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,\n",
       "       random_state=None, shuffle=True, solver='adam', tol=0.0001,\n",
       "       validation_fraction=0.1, verbose=False, warm_start=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neural_network import MLPClassifier\n",
    "nn = MLPClassifier(hidden_layer_sizes=(25,), activation='logistic')\n",
    "nn.fit(mat['X'], mat['y'].T[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98760000000000003"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn.score(mat['X'], mat['y'].T[0])"
   ]
  }
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