From_Math_To_Models_Linear_Family_and_Grdient_Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Python 2&3 compartibility\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# imports\n",
    "import numpy as np\n",
    "import os\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "\n",
    "# stable output across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# pretty figures\n",
    "%matplotlib inline\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Ignore useless warnings\n",
    "import warnings\n",
    "warnings.filterwarnings(action=\"ignore\", module=\"scipy\", message=\"^internal gelsd\")\n",
    "pd.options.mode.chained_assignment = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x (150,) float64\n",
      "y (150,) float64\n"
     ]
    }
   ],
   "source": [
    "#to replicate class output I will keep random state 1 \n",
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(150)\n",
    "print('x', x.shape, x.dtype)\n",
    "y = 2 * x - 5 + rng.randn(150) # generate noise from a standard normal distribution\n",
    "print('y', y.shape, y.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x, y) \n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.154927422232134 [2.0501849]\n",
      "-5.154927422232134 [2.0501849]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#using sckit learn linear regression to fit the data (closed form solution)\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lr = LinearRegression(fit_intercept=True)\n",
    "lr.fit(x.reshape(-1,1),y) # or create a new axis np.newaxis\n",
    "\n",
    "print(lr.intercept_, lr.coef_)\n",
    "\n",
    "lr.fit(x[:,np.newaxis],y)\n",
    "\n",
    "print(lr.intercept_, lr.coef_)\n",
    "\n",
    "xfit = np.linspace(0,10,1000)\n",
    "yfit = lr.predict(xfit[:,np.newaxis])\n",
    "\n",
    "sns.scatterplot(x,y)\n",
    "plt.plot(xfit,yfit)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2)\n",
      "[-5.15492742  2.0501849 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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f4H2CEShoiZaLaIJbKbUQyNBa31Dz++eAQq31PbWesxZ4Rmv9YmPvJQluIVpH7WonpRRGBQaDwVv15K8aqrDM5nOj3IMXD+O7/BJWrN9Lhc3BLaf14/ZzBhAfY2x2VVWoEu0dUVvdlFcOJNd7LBkoi8BYhOjwfF2EF2WPYPm6Pfx28mDvxdjXfgV/S0MPf5RHXkEZJ/ey8OepJzH4xON/5VMTY70Bo6jCHnTACNUmO+FftC1DbQNGen6jlEoE+tc8LoQIM1+J47vf2EJ2Vs86CWSHw8WBEit7iyo4UGLF4XD5XBoCOHjM/V4FpVW4wJvH8LVslVdQFnRFkydo9UhJIL1T++vNFGmRKp2NUUrFA0bAqJSKV0rFAG8Bw5VS2TU/vx/YorXeHolxCtGeBJNsrs/f7MBiNnkTyJ49ErXLVrcXlGGJj2HZjCxSEkze154/rCt9UhMB2F9SVSfgSEVTdIvUzOI+wArcA0yv+ff7tNaFQDbwR6AYGA9cHaExCtFuNPeu3V/i2HOGQ2yMkcPltjp7JPKLrdz68ka+2nOU+9/eRnFlNcO6J/PMzCwKSm1s2X/M+161K5akoim6RSRnobWej7ss1tfP/g+QUlkhQqi5h/2kJsay4qZx7C2qJCHWSKXdSUqiicWf7/JWK+0rriS/2MronhZuPbM/cUYDL2/Yyw0vfEOyOYZF2SeRPTqDw+U2Csttdd6/dsVSpA9REo2LtgS3EKIZAvVnasldu83h8p4xnZFiZumMLP6SPQKL2f0ZJqOBczO7MHNCH27/9yaOVlQDcP6wbvxx6nBSk9zBqFtyfKP9m6S/U3STYCFEGxdM2Whz79p9zUhmv7SRt+ZM8pbNxhgU10/oy03Lv8HmcHlfu/XAMWqvcgWqWJKKpugWbdVQQogmCiYx3NyjTxubkbhcms35JZzz1y+Y+cLXdQJF7efVFqhiSSqaopfMLIRo44JZYmruXXtjM5K3Nu3nrje24HRpTunXmb1FlRw8VtXgecFoDyfOtXcysxCijfKUwjq15oUbxjK6p8X7M18XaoNBkZoYS2yM0bvpLVA1lK8ZyYJLh3PPG1u487XNOGteb6t28egVI+s8b8VN49DogKW6Ld1fIcJDzrMQog3ylad45PIRPPxhHoXlNp+tLjyvefyTPLKzepKaGEuXTnF0P8Hc6LkPnrv+8qpqXs3J5/m1ezAaFLec1o83Nu5jf4l7NjG6p4XbzxlI/y5JJMUZKSi1BdV+w19bkECVWiI02mq7DyFEEHzlKea+voWVs07xu4xTVGHn8U/yuH5iX+5+Y0ud6qah3ZL9LvsYDIrth0p54O1t/HikggtP6sa8KZl07RTPBcO7ecdRWG6j2wnxZFjMTSrVlf0VbYMECyHaIH8XWMDv3bjd4SQ7q6c3UHhe46lu8vW6Q8eqWPBeLu9tOUif1ASW3zSOMwale3/uLw/SlAAg+yvaBgkWQrRBzbnAei7mwVzEq50uXlz7E3/7vx04XJrfTR7ErNP7EW9qmAfxFWSaMj7ZX9E2SLAQog1qzgU2NTEWq90R8CL+9Z6jzFu1lbyCMs4e0oX5Fw+jV2pCg/drrIKpKeOT/RVtgyS4hWijmlNu6nC4yDtcxuyXNjZIPBdV2PnzBz/w5rf76WEx88DFmUzO7IpSDd8zmI2AUg7bNgSb4JZgIUQH4nJpfiqqqNPrKSPFzLrdRTz6cR5V1U5mnd6P284aiDnW/5KWVDC1H1INJYRooKjCzsznv65zkTcZFdVOzaQBqTx4yXAGdEkK+D4ul4t5UzKxmE2UWKtZsmY3m/aVSAVTOybBQog2qLlLPL6qlKqdmgcvzmTmxD4+l5x8ffaRCjsL3s1tcHpeSyqYZNkqukmwEKKNacl50zFGAykJJoorq72PdbfEc+GI7kEFCnDPTjw5Dzh+et4rt4xvdgWTnKEd/aTdhxBtTHNPlMs9UMqcl7+luLKaWKP7r35Gipnnrh/bpIu8vz0URoNq9oVdTsmLfjKzEKKNaeqO57Kqah7/ZCfL1//ECWYTD2eP4IzB6TicrmYt97TGJjrZxR39JFgI0cYEe7HWWrN68wH++N4PFJbbuHZcL+aeNxhLQss2uzW2h6K5eQfZxR39pHRWiDYmmPX9XYfLuP/tbazbXcRJPU5g4WXDGVmrK20oxlA/KADNzjtIziJyZJ+FEO2Yvzv4SruDpz7bxbP//RGzycjc84dw7bheGMNwwW3p3guphooM2WchRDtWvyeT1pqPth3ioXdy2V9i5fKsDO65YAhpSeHbINfSvIO/PlMiOkiwECLKBbrj/rmokvnvbOOz7YcZ3LUTr906gbF9Ood9nJJ3aN8kWAgRxRpby7c7XSz94kcWr9lFjEFx30VDuX5iH0zGyFTES/fY9k1yFkJEWGMzh8NlVUxbvK7B3frc8wbz+Cc7+KmokiknncivzuyPJcEU8bV+yTu0PZKzEKINCFQFVFXtOw/wm39/R7+0RFbcNI6MFDN7iyoptzmotDvpnZpAn9TEiFykJe/QfskObiEiyN/O5UOlVbhcGqNSZKSY67xGAbec1pf3bj+V4T2SKSitYt7bW7lq2VfMe3srBaVVlFhl57MILQkWQkSQvwqiAyVW8grKiI81MOfM/sTUzBLiTQYev2oUPxdVUG5zYrU7mft63WNS576+Batddj6L0JJlKCEiyF8FUVGFnV//axOje1l4//tDpCbGcvOpfenfJcnbDvyBi504tfYZbJztIxUpoojMLISIIE8FkWepKSPFzJ+mnsSCd3I5eKyKT3ILuGFiH568elSdQOEpSY03GRssU2WkmIk3yV9tEVpSDSVEhLlcmkOlVRwosfLNT0d58tNdWKudpCbG8udpJ/GQj3Mjfjt5MIO7dgKa32JDCJB2H0K0KUXlNu59aysfbjsEQOfEWN761QSue+7rBktUr86eQJekOIqt1dgdTsyxRhwuTbWjeV1kRccmpbNCtAEul+bVnH0s+nA7pVYHV43N4OZJfUnrFIfV7jv5rbVmZ2G5zCZEWMnCphARsu3AMbKXrOOeN7+nh8VMWqdYVn6Tz03LcygotWGKMfjMRyil5KAgEXYSLIQIMZdLU1hmY39xJYVlNlyuuku9pVXVzF+9jYuf+pJ9RyuZf3EmxZV2CkptwPGLf4xBNUh+PzNzDEaFHBQkwk6WoYQIocZ2ZCsFb393gIXv/UBRhY0Zp/TmznMHU15Vzfx3cuu8T36xFavdyeCunXhrzqQ67TOKKuzSsE+EXVTOLJRSa5RSVUqp8ppfeZEekxDB8Lcj+5ufjnLNM19xx8rv6Jocx7Mzx/DrswfSKS7Gu9eiNs/F39M+o0dKAumd4jAYlM9yW2nYJ1pbVFZDKaXWAC9rrZ8N9jVSDSWaorUa3u0vrmTSos8bPG40KJLiYpg5oTdvfpvP/pIq70V+YHpSkxPW0rBPhIpUQwnhR2se4elrRzbARSedyG1nDeCm5d+wv6QKOD7reGvOJJ/LTeA+fc5XQJCGfSLconIZqsaflVJHlFJrlVJn+nqCUmqWUipHKZVTWFgY5uGJtsrfUlEoqolSE2N58JJhxMW4/2qZjIrHrhjJ364aRWKc0W9iuv5yE7g3201dvJZJiz5n6uK15BWUNUiWCxEu0Ros7gb6AT2AZcA7Sqn+9Z+ktV6mtR6jtR6Tnp4e7jGKNqqlx3/6U1Xt5IlPd/Krf35LjEHxm3MG8J+7zmLq6B4YDKrR3ER9rRnQhGiOqFyG0lpvqPXb5Uqpa4ALgaciNCTRjrTG8Z+fbz/MA6u38fPRSi4Z2Z17LxpK1+T4Os8JdJJc7TyEvwaBUh4rIiUqg4UPGncbfyFaLJTHf+4vsfLQO9v4aFsB/dMTeeWW8UwckObzuQaD8pmbMBhUgzzKCzeMlfJYEVWCDhZKqVXAs8D7WmtXaw1IKWUBxgNfAA7gKuB04I7W+kzRsTR20Q6W3eHi2S9/5KlPdwFw1/mDueXUfsTGNL6y6y8xXX/Z6clPd/LI5SO8Z1VIeayItKbMLCqAlcAxpdSLwAta652tMCYTsBAYAjiB7cBlWmvZayFCon7ZaYrZ1KQy1HW7jzBv1VZ2F1ZwbmZX7r84k4yUhBaNo/6y06Z9JTz8YR4rZ50CIOWxIuKCDhZa6+uUUsnAdcCNwD1KqS9xzzZe01pbG32D4D+nEBgbivcSwldgqL2n4dzMLtx+ziBufXljwDLaw6VVLHzvB1ZvPkCvzgm8cMNYzhrSpdnjCrTsVFhuIzbGKCWyIio0qRpKa12qtX5aaz0OOAnYCCwFDimlliqlhrbGIIVoDs8FuXb56YFj1jrLPdlZPb2BAnxXHTmcLp7/cg9nP/YFH247xG/OGcjHvz292YEC/C87ya5sEa2aleBWSnUHLgWm4M4rvA70BLYopf6gtX40dEMUonl8lZ8eLrPVuXu3mE1+q45cLs1neYf5ywfb2XW4nDMGpfPgJcPok5bY4rHVL9+VZScR7ZqS4DbhDhA3AZOBTcDDwL+01uU1z7kS974ICRYi4nztp6jfhK/EWu2z6qjc5uDWlzfycW4B4K6guvv8wfTq3PTchC++yndl2UlEs6YsQx3EveS0G8jSWo/TWj/jCRQ1PgGKQzlAIZrL1ya4NzbuY+mMLO/jb2zcx5Lpx3/fwxLP1NE9uGLJem+gAHeQmfXSxpBtipNmgKKtCbqRoFJqBu5EdlXrDql5pJGgqM9fD6iB6UneI0k9Se9iazVb8kv46yc72HaglNE9LWzaV9LgPdfefRY9mlH55G980gxQRFrIGwlqrV9q2ZCECK/G9lOkd4rzXqx3FZbx3Jc/8fq3+aQmxvG3q0YxsX8q055eR3pSHLee2R+L2USl3X3edSjHJ0tOoq1oKzu4hWgWfxdkl0uz50g5//p6H69tzKe0qprLRvXggSmZWBJjcbk0K24aR0FpVYONcRazzABExxOtjQSFaFU5e4/yP69s4tkv93DMWk16UhxXjsnAhXtZ1mBQJMXHeAMFSDM/0bFJsBBRL9CZ1k1RbnOw8N1crlm2gfxiKzNO6c2ojBM4XGZj7utbsNqPN+qrdrikmZ8QNWQZSkS1UB1UpLXm/e8PseDdXA6VVpEYa6Tc5uDzvMMsyh7Box/lsWlfCc5acag1utMK0VbJzEJEtZae6+ByaXJ+OsqVS9fzP698iyXBRHqnOCpqZhD5xVbufmMLt57Zn4wUM/Gm438lpLxViONkZiGiWksOKqqocrDw/Vz+9fU+wL1b++HsETywehuFZbY67+cJDGmJx5PhoehOK0R7ITMLEdWacrpcbZ/+UMDkx7/wBgpw79ae88q33H7OwAbv191i9rm0Vf+4UwkUoqOSYCGiWlOXgvYdreSW5TncvDzH59kS+cVW+qYlNni/bsnxEgiEaIQsQ4moFuxSkM3h5Nn/7uGpz3aiUNxzwRAuGdmdK5eub5CgTogzytKSEE0kwUJEvUA7nb/ceYT7397Kj0cquGB4N+69cChxJiN2h5NXbhnPwvdy+Tj3sHcWkZYoy0lCNJUECxH1/PVQOnSsioXv5fLuloP0Tk3gxRvHcvrAdPIKyrj6ma+8pbZLZ2Sx4NLhGAwGmUUI0UwSLERU87XP4unrTmb9j0U88X87qXZpfvuLQcw+ox/xJiOFZbYGpbazX9rIW3MmSR8mIVpAgoWIar72WUx7eh3VTs1Zg9OZf8kweqceP4wo2FJb6fgqRNNIsBBRzdfFv9qp+fPU4Vw9rhdK1b3AN7brunaAcLp0g1xGU3eFC9GRSOmsCEoo+zM1hdFgwJJgqvNYd0s8v8js1iBQgP9S2xSzqc553Nc+u4HrJ/ZldE+LNAgUIggysxB1+FqeAYLuzxTK5Z3N+0q4b9VWSiqriYsxYHO4ODezC/ddlInd4aSwzNbg/f2V2vpazrr7jS3Mm5LJ7Jc2SoNAIQKQYCG8/DXt65oc57M/U/2kcVOb/vkLLMcqq3n4o+288vXPpCUdP4xIa82RCjvXPruh0ff3VWrrL5dhMbtnLdIgUIjGSbAQXv6a9q2cdUpQSeOiCjuPf5LHvCmZWMwmSqzVPP5JHn+cOqLBxdtXYFk6I4tt+0tZ9OF2iivt3DCxD7+dPIgQ7SpBAAAW3UlEQVTkePcFvbDM5p0F1B5fMJVO/nIZJdZqaRAoRBAkWAgvf3ffTk1QrbpdLhfXT+zL3W8cP1luUfYIXC5Xg8/yFZim/mMddqeLrN4pvHTpeDK7Jwc1vmCWjzy5jPrBKS0xlrfmTJJqKCECkGAhvPzdfcebDA0utL7uxJ0ab6CA43mBV2dPaPBZvi78sTEG7pg8kOyTM0hPajhTaMn5EtJBVoiWkWoo4eWvkigtMc57oV1791m8NWdSnTyBp1Kq2un7ZDmtG1ZOmYwGOicer3I6e0gXkuNjePjDPLKfXkdeQVmDiquWni8hHWSFaD6ZWQivQHffvvICtXMP86ZkBnXnv7uwnHmrtnK0ohqTUXHnuYN5+au9HDhWBfjPRcjsQIjIkWAh6gjUtK++2rmHJWt2syh7RJ2cRe07f6vdyVOf7eSZ//5IvMnIg5cM47xh3bA5nPzlg+113tdfLqKp4xNChIYEC9EitXMPm/aV8OhH7mqood06ER9rxGiAfcUVrN9dxBOf7uLgsSqmndyDP1ww1HvRLyyzyVnXQkQ5yVmIFql/kt2mfSUseDeX+FgjReV2LnriS8545AvueXMrRoPi8atG8ujlI+vMDuSsayGin8wsRIv4Kkl9ZuYYXC7NVUvXU1rl8D5Xa43F7N5NLbkIIdoWCRYdUDAtOYJt2+HrQp974BizVuTUCRQA+0uqSIg1Si5CiDZIgkUHE0xLjqa27fBc6A8es/LA6q28//0henVOIC0pliPlx5vzZaSYqbQ7m5SLkFbiQkQHyVl0MP5aetTuuBrMc2qrdrpY9p/dnPPYF3z6w2HunDyIj+44jZduHl8nD/HI5SPo2dmMy+UKqnOtJ2h5OsVOXbzW5/4LIUTri8qZhVKqM/AccC5wBPiD1vqVyI4q+gVzFx5My4ymtNX4ancR/7vqe34srOC0gWksvHQ4vdPchxEN7tqJN+dMpKrahVGBQcEDq7fxce5hb/dYo0H5Hau/oCWn3gkRflEZLIB/AHagKzAKeE8ptVlrvS2yw4pewS4dBdMyI5jnFJbZ+NP7P/DWpv0Ya95/z5EKKquduFwag0FhMCi6dIr3Pn/q4rXkF1sZ3dPC9RP7Buwe25JeUEKI0Iq6ZSilVCKQDczTWpdrrb8EVgMzIjuy6BbM0pHLpdFoXr55PC/cMJbRPS0+y1QbK2V1ujTL1/3E2Y+t4Z3NB+gUH4OzZlmoseWq2hf+W8/s36CHlK/X1S/L9YxF9l8IEX7ROLMYBDi11jtqPbYZOKP+E5VSs4BZAL169QrP6KJUoLtwny3Bp2dxoiUeizm4A4Q255cw7+2tbN1fyqkD0phzZn+ufXaD38+srfZsxWI2BTVj8FeWK/svhAi/aAwWScCxeo8dAzrVf6LWehmwDGDMmDEdOusZaOnI18xj9ssbeWvOpEYrnACKK+zcu+p7/v3NPrp0iuOpa0YzZcSJHCm3B73zuvaF33OGRKDXyf4LIaJH1C1DAeVAcr3HkoGyCIylzQi0C9rXzCM9KQ67w+n3XG2XS7Pym585+7E1vJqTz82T+vLpnWdy8cjuKKWatPO69oV/VMYJLJ2RFfTrpFOsEJGnfLWPjqSanEUxMExrvbPmsRXAAa31Pf5eN2bMGJ2TkxOmUbaeluwraOy1tRPMAKN7Wrjr/MHMfX2LzyTztgPHmLdqK9/+XMLYPiksuGw4Q7rVj+HNH6/snxAiOiilNmqtxwR8XrQFCwCl1L8BDdyCuxrqfWBiY9VQ7SFYNHUzXEve+4UbxjLv7a0NloJeumk8y9f/xIr1P5GSEMsfLhxK9sk9UEou5EK0R209WHQGngcmA0XAPYH2WbSHYFH/7h/cF/Bg9xUEuluv/XOn1pz+8JoG75GaGMvRSjvXje/F3HOHcEKCqcFzhBDtR7DBIhoT3GitjwKXRXoc4daSfQXBzEpqJ619tQUH6Joczws3jmVEhiVE30oI0R5EY4K7w2rJvoKmtuhITYzlqWtG0ynOfb+gFNx21gDe/p9JEiiEEA1IsIgiLTnXoSmzEq01H+ceYs4/v6XM5uCik7rx0W9O53eTB2GKkT8SQoiGonIZqqNqyb4Cf/ssTDEGCsts3vcrr6rmwXdzWZNXyJBunXjymtGM7dO5Nb+WEKIdkGARZZp7roO/3c7lVQ5mPv81+cVWOsXHUFXtJNZo4L6LhnLDxD7EGGUmIYQITIJFO+FrVmI0wCV/P15dVVblwGwy8tqtE8ns3nDPhBBC+CPBoh2pPyv5du/RBnkMa7WTE8zyv10I0TRy1WgDHA4Xh8ttVDtdmIwGEmINVNgaO7PCxXNf7uGJT3egcO9u9JCurUKI5pBgEeUcDhfbC8q49eWN3lzE09OziI9R7Cgop3dqAn1SE70BY/3uIua9vZVdh8uZPLQr153Si/tWbZWurUKIFpFgEeUOl9u8gQLc5bC/enmjt13HI5ePwJJgwuHU/PH9H3j7uwP07Gzm+RvGcPaQrrhcWrq2CiFaTIJFlKt2unzun4gxKPKLrfz+tc1ckdWT577cg83h4vazBzDnrAHEm9xLTc2trgJp9ieEOE6CRZSLMSif+yeMNSWv+0uq+NunOzltYBoPXTqcvjXnX7dUazY1FEK0PVJkH+XiYgwsvu7kOru6/zLtJP70fi4ARgWLsofz2BUjiTUqn+dSNEdT24cIIdo3mVlEOY3ivc37eeGGsSgF724+yM3Lc6h2ukiKi+Hfs8ZjNBiY9vS6kM4AWtLUUAjR/kiwiJBg8wEpZhPXndKHr34s4ukvfmTPkQqGd0/m3guHMKBrMhrNtMXrGswAgm1r7k+gY1qFEB2LBIsICDYf4HJpNuWXcMMLX1Nhc2JQcOfkQdx6ej9MNQns/cWVrTID8Nc+RMpuheiYJFhEgL98gGc24HJpjpTbeHfLARa+9wOeFIRLw8qcfVw9rhfpNcGitWYALWlqKIRofyRYhEH9JafG8gEul7t9+O3//g67w9XgverPGlpzBtCSslshRPsiwaKV+VpyeuWW8T5nAw6X5v7V23j5q70ATD+lF59vP8z+kqo6z6s9a5AZgBAiHKR0tpX5WnJa+F4uS2dkecthe1jiufnUvlyxZL03UABs21/Kw5ePDHgYkmcG0CMlgfROcRIohBAhJzOLVuZryamwzE5aYiwrZ53CT0WVPPXZTh58JxeTUXHXeYN55eufyS+2smlfCY9+lMeCS4fTv0sSZpPMGoQQkSHBopXVT0CP7mnhrvMHM+3pdd7lpYRYIyeYTRyzVvNJbgGLskdw9xtbyC+2Ulhuo9sJ8WRYzBIkhBARo7Ru+W7faDBmzBidk5MT6WE0UD9n8cINY/n9a5vr7IR+ZkYWv3xpo/f3o3tauPXM/gzt1glzbIx32Un6NAkhQk0ptVFrPSbQ82Rm0cpqJ6B/Lqrg8f/b0aBlhgvqzD427Sthwbu5vDp7AnaHkyMVtjrHo0qfJiFEuEmCOwwcLs2rOfu47rkN5OwtJtkcw8iME1g6I4uVs06hc0JsnYR3RoqZJdOzmL96K5MWfc60xesoKK0iPcldxip9moQQ4SYziwDq75FIMZsotlYHvRy0dtcR5r29lR8LKzh/WDfuvWgo1U4XBaVVzH19i3emsOKmcbw5ZyLVDhdKKeav3srHuYcBd3CY+/oW5k3JZHbNcpX0aRJChJMEi0bUzzecm9mF288ZVOfUOn/LQQWlVSx87wfe2XyA3qkJvHDjWM4a3AWAw2VVzHx+S51y2pnPf81bcybRIyWB/cWV3kDhkV9sxWI2eX8vfZqEEOEkwaIR9fdIZGf1bHBq3S9X5PDq7Al0S47HYFA4nC6Wr9/L45/swO50cccvBnLrGf29hxEBVDtcdaqjbj2zPxazybuD218Lj0q70/vv0qdJCBFOEizqqb3s5NS6zgXbYjb5bNNxoMRKcaWdcquDB97ZxvZDZZwxKJ2HLh1G79SGhxF5gkF6Uhy/P2+wt0zWEwQGpif5bOHRNTmOtXefJdVQQoiw69DBwlc+YmdheZ0y19p3+CXWap93/D8VVXD/29uotDs58YR4lkw/mfOGdUMp3xdzTz+nQ8eqvIECjs9U3pwzkdSkWF755XiMSmGONWIx1wSH0ByEJ4QQTdJhg4W/nk21l50++P4gi687mTn//Jb8YitvbNzHkulZ3qWoHpZ4Jmd25e43vsfp0lw2qju/mzyYXqkJjX62p5w2Mc7oc6ZSaXMy/bkNdWYVFrMsOQkhIqfDBgtfPZsOl9nIL7Z6d1knxcXw1Gc7mTclk9TEWLp0iuPE5HhenT2B/+wo5OkvdvPC2p8A6JocxwUnnYgxyGJkg0FhNsX4nKnsOVIR8sOMhBCiJTpssPDVs6mq2sm5mV24fmJfqqpdzH3dPaPwVCZlpJhZfuM4nl+7h1c2/IxnlamHJZ6HLx/J8nV7OLnXCL+f6WvZq35uYun0LO5btbXO66RMVggRaR02WPiqOIqLMXLPBUOZ+fzXPHbFSJ9LRNlL1lFqrWbmhN5cNbYnlXYnRRV2lq/bw28nD/ZboeTvdLyB6Ul12osbDVBYbqvzWimTFUJEWofdwe1JMtfeNZ3eKY5j1mryi63eZHZ9PVMSeOfXp/LgpcMZ0i2Z3qmJDO+ezB+njmi0/Ya/0/GKrdV12otbzA3HJWWyQohI67AzC1+HBmk0e464g8SSNbuZf/Ew7lj5HeU2BwYFt589kNvOGkBMjMH7HsHmERo7HS/QuKRMVggRaVEVLJRSa4BTAEfNQ/u11oNb6/PqX+xdLk3v1AQezj6J2/61iV/9cyMOp+biESfy63MGMiA9qdGLdv2cRO2LfFPOypbjTIUQ0SaqgkWN27TWz0bigw0GhculeeLTXRytqGZglyT+cOEQzhzUJeCdvb+chGdpqjXPyhZCiNYWjcEiIqx2J//4fBdL/7ObeJORuecO5uKRJ2KODe4/kb+chKfkVZaXhBBtWTQGiz8rpf4C5AH3aq3XtPYHfpJbwPzV29hfYmXq6B5ckZXBXW9s4ZGP84I+OyKYnIQsLwkh2qpoq4a6G+gH9ACWAe8opfr7e7JSapZSKkcplVNYWNjkD3M4XdyyPIdfrsghIdbIv24Zz9zzBhMbY2DelExG97TUOTvC5dIUltnYX1xJYZkNl+v4KYOenERtUvIqhGgvwhYslFJrlFLaz68vAbTWG7TWZVprm9Z6ObAWuNDfe2qtl2mtx2itx6Snpzd5TDFGAxkpZv73wiG8++tTsSTGcuXS9Vy+ZD0L3s3l9+cN9gYMu8NJXkEZUxevZdKiz5m6eC15BWXegOGrFFdyEkKI9iKqz+BWSn0AfKC1fjLQc1t6BndhmY2pi9c2qFaaNyXTe8TplUvXN/h57TYcjVVDCSFENGpzZ3ArpSzAeOAL3KWzVwGnA3eE4/P95Rw8MwajQnISQogOK5pyFiZgIVAIHAF+DVymtc4Lx4f7yzl0t5hrktsGyUkIITqsqAkWWutCrfVYrXUnrbVFa32K1vqTcH2+v5yD5wQ8yUkIITqyqM5ZNEVzcxa18wzmWCMOl6ba4UIphVGBwWDw5h4kJyGEaG/aXM4iEnztul5x0zhsDpffndiSkxBCdERRswwVCb52Xe8tqvS5E/tQaVWdfRVCCNGRdOhg4asCKiHW91GnB0qsdfZVCCFER9Khg4WvCqhKu9Nn1ZNnFlJUYQ/nEIUQIip06GDhq8Kpd2pCg8cWZY9gyZrdfo83bawNiBBCtAcdOsHtrxMswKuzJ3CgxEpRhZ1HP8pj074Sn/sqArUmF0KI9qBDzyzg+K5rz7GmBoPCYFB0S44nMS6GBe/megOFr30V/lqTy3KVEKI96dAzi8YEe/5EsMelCiFEWybBohHB7KtoynGpQgjRVnX4ZaiWkjYgQoiOQGYWLSTHpQohOgIJFiEgbUCEEO2dLEMJIYQISIKFEEKIgCRYCCGECEiChRBCiIAkWAghhAio3ZyUp5QqBPY28+VpuM/97kjkO3cMHe07d7TvCy3/zr211umBntRugkVLKKVygjlWsD2R79wxdLTv3NG+L4TvO8sylBBCiIAkWAghhAhIgoXbskgPIALkO3cMHe07d7TvC2H6zpKzEEIIEZDMLIQQQgQkwUIIIURAHTpYKKU6K6XeUkpVKKX2KqWujfSYWpNSKk4p9VzNdy1TSm1SSl0Q6XGFg1JqoFKqSin1cqTHEi5KqauVUj/U/PnerZQ6LdJjai1KqT5KqfeVUsVKqUNKqb8rpdpVV22l1G1KqRyllE0p9WK9n52jlNqulKpUSn2ulOod6s/v0MEC+AdgB7oC1wFPK6WGRXZIrSoG2AecAZwAzANeVUr1ieCYwuUfwDeRHkS4KKUmA4uAG4FOwOnAjxEdVOtaDBwGTgRG4f4zPieiIwq9A8BC4PnaDyql0oA3cf997gzkACtD/eEdNlgopRKBbGCe1rpca/0lsBqYEdmRtR6tdYXWer7W+iettUtr/S6wB8iK9Nhak1LqaqAE+DTSYwmjB4GHtNZf1fy/3q+13h/pQbWivsCrWusqrfUh4EOgXd34aa3f1FqvAorq/WgasE1r/ZrWugqYD4xUSg0J5ed32GABDAKcWusdtR7bTDv7A9YYpVRX3P8dtkV6LK1FKZUMPATcGemxhItSygiMAdKVUruUUvk1yzLmSI+tFT0BXK2USlBK9QAuwB0wOoJhuK9dgPumENhNiK9lHTlYJAHH6j12DPeUvd1TSpmAfwLLtdbbIz2eVrQAeE5rvS/SAwmjroAJuBw4DfeyzGjgvkgOqpV9gfviWArk416KWRXREYVPWK5lHTlYlAPJ9R5LBsoiMJawUkoZgJdw52tui/BwWo1SahTwC+DxSI8lzKw1/3xKa31Qa30E+CtwYQTH1Gpq/jx/hHvdPhF3Y70U3DmbjiAs17KOHCx2ADFKqYG1HhtJO16SAVBKKeA53Hef2Vrr6ggPqTWdCfQBflZKHQJ+D2Qrpb6N5KBam9a6GPfddUfZcdsZ6An8XWtt01oXAS/QToOjD9twX7sAbz62PyG+lnXYYFGzrvcm8JBSKlEpNQm4FPcdd3v2NDAUuFhrbQ305DZuGe6/NKNqfi0B3gPOi+SgwuQF4NdKqS5KqRTgDuDdCI+pVdTMnPYAv1JKxSilLMD11FrHbw9qvls8YASMSqn4mvLgt4DhSqnsmp/fD2wJ9fJyhw0WNeYAZtwld/8CfqW1brczi5ra69m4L5yHlFLlNb+ui/DQWoXWulJrfcjzC/d0vUprXRjpsYXBAtylwjuAH4BNwB8jOqLWNQ04HygEdgEO4LcRHVHo3Yd7ifEeYHrNv99X8+c5G/f/32JgPHB1qD9cekMJIYQIqKPPLIQQQgRBgoUQQoiAJFgIIYQISIKFEEKIgCRYCCGECEiChRBCiIAkWAghhAhIgoUQQoiAJFgIIYQISIKFECGmlEpXSh1USt1f67ERNce6Xh7JsQnRXNLuQ4hWoJQ6D3gH9/Ge3+E+X+FrrfWNER2YEM0kwUKIVqKU+htwCe6DeU4DRmmtyyM7KiGaR4KFEK1EKRWHu032QGCi1npDhIckRLNJzkKI1tMH96E8GugX2aEI0TIysxCiFdSccb4e2AlsAOYDI7TWP0dyXEI0lwQLIVqBUuovwLXACOAY8AHug7bO0lq7Ijk2IZpDlqGECDGl1BnAncBMrXWJdt+R3YD7ONu7Izk2IZpLZhZCCCECkpmFEEKIgCRYCCGECEiChRBCiIAkWAghhAhIgoUQQoiAJFgIIYQISIKFEEKIgCRYCCGECEiChRBCiID+H2szCfe6P5oLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_b = np.c_[np.ones((x.shape[0],1)), x[:,np.newaxis]] #initialize x with bias 1\n",
    "print(x_b.shape)\n",
    "x_b[:10]\n",
    "\n",
    "#lets use the closed form equation to solve the regression first this is also usin sklearn LinearReg class\n",
    "weights_best = np.linalg.inv(x_b.T.dot(x_b)).dot(x_b.T).dot(y)\n",
    "print(weights_best) #looks pretty good. exactly same as our scikit learn linear closed form model\n",
    "\n",
    "#lets prdict and plot \n",
    "yfit = xfit.dot(weights_best[1]) + weights_best[0]\n",
    "\n",
    "sns.scatterplot(x,y)\n",
    "plt.plot(xfit,yfit)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y'); #looks good "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-5.15492742  2.0501849 ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-5.15492742,  2.0501849 ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#we can also use scipy.linalg.lstsq() to predict the model parameters\n",
    "weights_best, _, _, _ = np.linalg.lstsq(x_b, y, rcond=1e-6)\n",
    "print(weights_best)\n",
    "\n",
    "np.linalg.pinv(x_b).dot(y) #same solution another way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.97130082] [2.01716603]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#using sckit learn gradient descent class\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "lr_gd = SGDRegressor(penalty=None, max_iter=1000, tol=1e-3)\n",
    "lr_gd.fit(x[:, np.newaxis],y)\n",
    "\n",
    "print(lr_gd.intercept_, lr_gd.coef_)\n",
    "\n",
    "yfit = lr_gd.predict(xfit[:,np.newaxis])\n",
    "\n",
    "sns.scatterplot(x,y)\n",
    "plt.plot(xfit,yfit)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.05003441] -5.153916861526987\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#using model taught in class gradient descent approach\n",
    "\n",
    "class MyLRModel():\n",
    "    def __init__(self, niter=1000, alpha=0.03):\n",
    "        self.niter = niter\n",
    "        self.alpha = alpha\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        N, m = X.shape #N=rows, m= features, I prefer to name them in opposite order this is giving me a headache #Damnit\n",
    "        self.w = np.random.rand(m) #initialize the weights (m defines how many attribute so that many features)\n",
    "        self.b = 0  #initialize bias\n",
    "        for i in range(self.niter): # we chose 50 iterations so loop will run 50 times\n",
    "            y_ = np.dot(X, self.w) + self.b #predict y \n",
    "            z = np.average(y_ - y)\n",
    "            loss = 0.5 * np.average((y_ - y) * (y_ - y))\n",
    "            db = z #change bias \n",
    "            dw = np.dot((y_ - y).T, X) / N #compute gradient\n",
    "            self.w = self.w - self.alpha * dw\n",
    "            self.b = self.b - self.alpha * db\n",
    "            #print(loss)\n",
    "        self.coef_ = self.w\n",
    "        self.intercept_ = self.b\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return np.dot(X, self.w) + self.b\n",
    "    \n",
    "lr_my_model1 = MyLRModel()\n",
    "lr_my_model1.fit(x[:,np.newaxis],y)\n",
    "print(lr_my_model1.coef_, lr_my_model1.intercept_)\n",
    "\n",
    "yfit = lr_my_model1.predict(xfit[:, np.newaxis])\n",
    "\n",
    "sns.scatterplot(x,y)\n",
    "plt.plot(xfit,yfit)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y'); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#so lets fix this implementation and fix my headache \n",
    "#from now on m = no. of examples and n = no. of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope [1.84814464] intercept [-5.18501519]\n"
     ]
    }
   ],
   "source": [
    "#Now let's do gradient descent implementation using a different approch \n",
    "#Batch gradient descent algorithm \n",
    "#try differnt learning rates see how the algorithm diverges or converges\n",
    "eta = 0.03 #consider it as alpha - learning rate but remember I call it eta cause alpha is usded as regularization hyperparameter in many cases\n",
    "n_epochs = 1000\n",
    "m = x_b.shape[0]\n",
    "weights = np.random.randn(x_b.shape[1],1) #initialize weights\n",
    "\n",
    "for i in range(n_epochs):\n",
    "    gradients = 2/m * x_b.T.dot(x_b.dot(weights) - y.reshape(-1,1))\n",
    "    weights = weights - eta * gradients\n",
    "    \n",
    "print('slope', weights[1], 'intercept', weights[0]) #we arrived at the same answer with lot lesser codes\n",
    "# what I exactly did is instead of computing bias and weights separately I added a bias term to data then initilized a weight for the bias term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights_path = []\n",
    "def plot_gradient_descent(weights, eta, weights_path=None):\n",
    "    m = len(x_b)\n",
    "    plt.plot(x,y, 'b.')\n",
    "    n_iter = 1000\n",
    "    for i in range(n_iter):\n",
    "        if i < 10: \n",
    "            y_pred = xfit_b.dot(weights)\n",
    "            style = 'b-' if i >0 else 'r--'\n",
    "            plt.plot(xfit,y_pred,style)\n",
    "        gradients = 2/m * x_b.T.dot(x_b.dot(weights)-y)\n",
    "        weights = weights - eta*gradients\n",
    "        if weights_path is not None:\n",
    "            weights_path.append(weights)\n",
    "    plt.xlabel('x', fontsize=18)\n",
    "    plt.ylabel('y', fontsize=18)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights_path_bgd = []\n",
    "x_new = np.linspace(0,10,2)\n",
    "x_new_b = np.c_[np.ones((x_new.shape[0],1)), x_new[:,np.newaxis]]\n",
    "\n",
    "def plot_gradient_descent(weights, eta, weights_path=None):\n",
    "    m = len(x_b)\n",
    "    plt.plot(x, y, \"b.\")\n",
    "    n_iterations = 300\n",
    "    for iteration in range(n_iterations):\n",
    "        if iteration <10 or iteration>295:\n",
    "            y_predict = x_new_b.dot(weights)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(x_new, y_predict, style)\n",
    "        gradients = 2/m * x_b.T.dot(x_b.dot(weights) - y.reshape(-1,1))\n",
    "        weights = weights - eta * gradients\n",
    "        if weights_path is not None:\n",
    "            weights_path.append(weights)\n",
    "    plt.xlabel(\"x\", fontsize=18)\n",
    "    plt.ylabel('y', fontsize=18)\n",
    "    plt.title('eta = {}'.format(eta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mGE2zZmFxBfD557GdBpONCyzHqQKMGQM77mh5xADjx8M776R2TFWY/YF8Vf0l4thsYgungcDxIrKHiGwPXAZ8kIQxOk7KCBwCDz0UZs2yqNWECbD33qkemeM4VYnsbOjd235WhOLs18FSAOvUsY2gSLZuhZtuqvg944WnCDpOJadDB3jvPXter56ZWwR5xfHiP/+BYcNsEVUDdqfrYel+kawFdohx7S/A78BiIB/4Hrg51oeKSDegG0Djxo3jNVbHSSq//WZRqv/+13rOvPaaCyvHccpPWdP7SiLaTTB4/9dfw9FHh23X09LCPa7ANokimw2nAo9gOU4lJSfHolaBuDr9dFi/Pv7i6rbb4NJLYdIkWLAgvp9dSdkARLdfrg+sj3HtK0AdIAuoC4yhmAiWqvZX1Raq2mKXXXaJ43AdJ/EEtVaHHWZRqwED4IMPXFw5jlMxypLeVxZatoR77w2LpZdeghYtwuIKTFx16GB1omlpULt24vtclYYLLMephEyebKHvdevs9ciR5hQYT7ZutQmoTx8TbV99BfvsE997VFJ+ATJEZL+IY82BaIOL4PgQVf1TVXMwg4tjRGTnJIzTcZLCb7/ZTvPNN8MJJ1it1TXX1IhotuM4CaKk9L7yEqQann66zVNgzYS32y78+XfdZTbtvXolzymwJDxF0HEqGZddBm++ac+33976OMTbyGLZMtsBWrwY9t3XxFXDhvG9R2VFVTeKyBjgERH5B+Yi2BFoFePyr4AuIjIF2ATcCCxR1VXJGq/jJIpQCF55Be6+2xYpAwa4iYXjOOUnO7toGl9x6X0V+exTT4XNm8PHHnrImg8Xd9/ysHYtnH8+DB4c34bpLrAcp5KQnw+77QarCpbuJ51U8ZB6SUybBm3bwpYt0L49jBtni6saxo3AIGAFsBq4QVXniMiJwAeqGkjaO4AXgLlALeAH4NwUjNdx4sr8+SampkzxWivHcSpOSbVW0dbosQRRaXz4YWFxddVVJq5ifX55yM21zwo2tNu3h+++q9hnxcJTBB2nEvDll5CZGRZXQ4YkRlz17Wt2y1u22AT1/vs1UlxRkPLXSVXrqmpjVX2z4PjUCHGFqq5W1ctUdVdVbaCqJ6jql6kbueNsG0Gt1aGHWqH4a695rZXjOBWnrLVWgRB74AH7Gbj8leQ0+L//WXPggMxMOO64bXMmVIX777f0wkBcgTUxjicewXKcFHPddeGeDbVrw8qVsEMsP7ttQBW6doXhw22CGj3aCkIdx6k5zJ9vtVWffmqLiddeAze8dBxnWwhqrYIIVnG1VsUJseKiX8OHQ5cu9rxhQ7j1Vth1V+jeveLOhIMGwQ032PsD0tNtTH//e/l+79JwgeU4KWTPPWHJEnt+zDEwY0b877Fpk01A331nk9SXX1pjPsdxagahELz6qhWBp6WZsHITC8dx4kFZa61iCbFYoqtlS+jY0coXAE480cwrwCJXsa4vjY8/hs6dw8ZhYHNhKAT77w+PPgqdOlXwH6AYPEXQcVLADz/Yrkkgrl58MTHi6tdfLfXnu++geXNYtMjFlePUJObPh9NOs8abrVrZ3POPf7i4chwnPpS1rioQYj17hiNPsZwGDzwwLK7S0+GJJ8KfEX19VlbJ6YI//mjGFW3bhsVVMPftvTcMHQrffmtibcuWbfpnKIJHsBwnydx+Ozz7rD3PzDSRtXMCTL/Hj4fzzoO8PAuzDxniiyrHqSmEQtCvH9x5p+3U9u/vwspxnPhS3mbC0aYUkdGv44+Hs86Cv/4q/J7IKFXk9VlZxacLrlhhoiqWacWuu8KDD5rJz7hxcPjhVus1YIBF9uOFR7AcJ0moWp+pQFwdcohNDIkQVw89BOecY2H0vn1tl8YXVo5TM1iwwKJWN94Yjlpde63PAY7jxJfyNhOOZWjRsiVcfLEJtb/+suhUZmbx/bOCxsOzZlnUKfLemzebK2qjRkXFVYMG8Pjjltmz++5WlnHRRTYvvv22OQrGE49gOU4S+PVXC3vn59vrxx6zCSLe5OebecUHH1ij4o8/tl0hx3GqPx61chwnmZTV4AKKj3aNGWP1UWB14suXW2/OktIOs7PNsELVXqenW5lF3brhYwHbbQe33WbZQ9OmmZPyrFlWe/Xmm3DhhYlxU3aB5TgJ5sEHwzaj6ekwbx40aRL/+/z5pzUPnj/fzDNmzrS+Wo7jVH8WLLD0lk8+sejVwIHuEOg4TmIpTzPhWNGuUaPCWT1HHWXrluBzS/usYMMaYOtWePfdwtdkZppjYBDtatfOPr9ZMxg2DC65BDISqIJcYDlOglC1qNUvv9jrZs1g7tzE7CZ/843tymzcaA2KJ02yycVxnOqNajhqBfbc0wEdx9kWytMQuKzNfqOjXSNGwOzZdu6668zptKy0aVM4UhX5XASuvNI2t+fOhXPPhenToWlTi3pdcUVihVVAymuwRKS2iAwUkYUisl5EZonImRHnTxWRn0Rkk4h8KiIJ2Pt3nPgyf75NIIG4uvNOSxNMxKJnyBA4+mgTV7fdZpOiiyvHqf4EtVY33GDNN3/4Abp1c3HlOE7FKa4h8LYSRLseeshKGAJxNXx4+cTVgAFw8smWEh3N+eebc+AVV9ijXTtYvNg2nn7+2eqskiGuoHJEsDKARcBJwO9Ae+BtETkU2ACMAf4BjAd6AiOA41IzVMcpnd694b777HlamlmAHnpo/O+jCjffDC+/bKmH//mPFYo6jlO9iY5avfqqCyvHceJDcb2p4sE++1jJxNattj764Qc46CA7V1rUbOFC20hatqzouaCeavNmM/f59FPYYw946SVLna5dOz7jLw8pF1iquhHoEXHoPRGZDxwFZAFzVHUkgIj0AFaJyIGq+lOyx+o4JaEKhx1mEwbYH/fChYnZLcnJsUlo+nSoXx8+/9xcCR3Hqd4sXGgLhsmTLXo1YEBiajodx6mZlMe4ojx89JE5/AHssAOsXBkWPiXZva9fb+e++ir259aqZQYW995r5RGNGsHzz9umU5068Rl7RUh5imA0ItII2B+YAxwMzA7OFYixeQXHY723m4jMFJGZK1euTMZwHQewRU/t2mFxdc01FpZOhLj64w9bUE2fDgccAL//7uLKcao7QdTqkEPMLevVV23B4uLKcZx4Eqsh8Lby0ENhcXXwwdb0NzKqFCtqtnUrdOpkm8ixxFVGhtVXHXWU1XB9+y088wz89hvcckvZxdXChdZPa8mSbf0to8YX34/bNkQkE3gDGKqqP4lIPSBaKa0Fdoj1flXtD/QHaNGihca6xnHizTPPwB132HMR+OwzOOGExNzrk0+gfXuLYJ13HowcaWF2x3GqLwsXmt36xx/bTu6AAVaw7TiOkwjKalxRFs44Az780J43bw6vvFL0msioWWam1WfVrl3Ucr1ZM+ja1azcZ8+GsWPN2v3xx61kom7dso9r9mx46il46y1bu7VqZZbt8aLSLM1EJA0YDuQCNxcc3gDUj7q0PrA+iUNznJiEQnDkkWFxlZVlRhOJEldPP20pQbm5Vuc1erSLK8epzkRGraZPt4XJpEkurhzHqTzEah4MNn81bhwWVxkZluUTyzgjiJq1b2+RqxEjCourPfaA116zhsDffmu1VT/8AL16manY3XeXTVypWn3WGWfA4YebtXv37vYZ8RRXUEkiWCIiwECgEdBeVbcWnJoDdI24ri7QrOC446SMBQssPS8311537mz9HBKBqplXvP227fCMH2/OOI7jVF8io1annGJ9rVxYOY5TmSiuduqvv2D33S3bRsScTvv1K944Y+JEW0dt2lT48xs2hPvvtwjX449bC4r69aFHDxNGO+5YtnHm51u068knLd2wUSN47DG4/nrYaac4/WNEUVn2v18BDgI6qOrmiONjgUNEpLOI1AEeBL5zgwsnlbzwgjnhBOJqzJjEiasNGyxf+e23YZddzPbdxZXjVF9UoX9/cx4NolYff+ziynGcykes2qnPP7eMnpwc2H57q7e6/HITYOnphY0zfvjB1jZnnllYXG2/PTz8sNWZzpxpdVYTJpjYWrDAarrKIq62bDFhd+CBcMEFJvz69bPPuPfexIkrqAQRrIK+VtcBOcAyCfvMXqeqb4hIZ6Av8DowA3AjaiclhEJmERoUW9arZ3+kWVmJud///mc7PGvXWp+rqVNTYzXqOE5y+P13i1pNmuRRK8dxKj/RjoOLF4fLJPbdF+bNs+dBCmBgw96sGey3n/UHjSQzE/71L7joInjxRTjmGDOruOsuK8fYeeeyjeuvv2xz6vnnYcUKW0ONGmWmGenpcfrlSyHlAktVFwLFdu9Q1Y+BA5M3IscpyoIF1qthyxZ7fcoptqucqL4zo0dbWmBenrnjvPKK97hxnOqKqhlX3H67beS8/LL93XuNpeM4yaa0flSRtGwJzz1na5YVK6w2CqBjR3jnnaLXHnGEpRR+8UXhcyI253XtanPhcceZ2Lr1VhNXu+5atrEvWmTj6d/fMoDOPNPef9JJyV9D+fTtOKXQt6+lBAbiqn9/24lJ1B/rPfdYN/JQyCaaV191ceU41ZXffzf74m7dbJf1hx+sXsHFVc1ARG4uaC+TIyJDos6dKiI/icgmEfm0IOPHcRJGUFP1wAOxzShiXd+9u6XyffutHXv88aLiShXatoXttisqri69FP77X7vmxBPh9dfNEfC338zcqyzias4cuPJKi5o9/7xFqmbPtrTCNm1Ss4byKdxxiiE/32w7//lPe12njjnNXHttYu6Xl2cT2hNPWP7x9OnWT8uJPyLSUETGishGEVkoIpeWcO2RIvKZiGwQkeUi8q9kjtWpnqiaK9Yhh9iC4+WX3SGwhrIE6AUMijwoIjsDY4AHgIbATGBE0kfn1Chi1VSVxMSJsDnCOeHaa83RL5IHHrC0vI8/Lny8Qweb83bayRySBw2yKNa8eRaF2n33ku+taqUTHTrYPDpyJNx0k71/+HA47LCy/taJIeUpgo5TGZk3z4rMg4njiCPgyy8T0zgYrKP5UUdZeLtJEyvqLGuusVMhXsJaQjQCDgfeF5HZqlrIobRgkTMRuBUYBdQC9kryWJ1qxu+/20Lko4/g5JOt1mqffVI9KicVqOoYABFpQeG55TxgjqqOLDjfA1glIge60ZeTKKJrqtq0KT5l8NtvrRlxQGYmXHVV+PXQoVZTmpdX9D5dupiwOvtsE3NXXw3//rfZupdGKATjxtlm9PTptlZ65BG48cbE1cRXBBdYjhNF377hqBXAo4/Cffcl7n7Tp1tN1+bNlir0/vvJK8KsiRS0e+gMHKKqG4BpIjIOuAK4J+ry24APVfWNgtc5wP+SNlinWhFda/XSS2YT7OmATgwOBmYHL1R1o4jMKzheRGCJSDegG0DjsqxSHScG0WYUENuGvV8/m7vAXAC7d7fNopYtLap05pnWFzQaEZvvRoww4dW1qzkDlmWDKSfH0gefegp+/tne89JLlhq4/fZx+geIIy6wHKeAvDybUD7/3F5nZppjYPPmibtnv35Wb6Fquze9eiXuXs7/sz+Qr6q/RBybDZwU49rjgO9F5Avgb5iT6U2q+nv0hb7AcUoiMmrVpo2lw3jUyimBesDKqGNrgR1iXayq/YH+AC1atNBY1zhOLKIjVMEDrIFwkDKYk2P9p0TCzYPbtrU5DaxmqlEjM7uIZP/9bX0zaZK1nMnLM5fABx6Av/2t9PGtXWtrpeeeg6VLLaPorbesb1aisoriQSUemuMkj19/NSEV9GH429+sQDJRuyKqFjofNMgmiJEjrSjTSQr1sIVKJMUtXPYCjgTaAt8DTwL/AY6PvtAXOE4sVC0F8LbbPGrllIsNQP2oY/WB9SkYi1NN6d/f6pZCIWsDE0SoAoKUwZwcuyYQU2CRp5497dhll8GqVYU/e4897Jo//rB7bNxo7sgPPQQHHFD62JYsMVH16quwfr2JuWHDLKJWFYy/XGA5NZ7olMBbbjEXmkSxZQscfzx88w00aAAzZtgOj5M0yrNw2QyMVdWvAETkYawOYkdVjRZpjlOIRYssavXhh7ZQGTjQXK4cpwzMAboGLwpSm5sVHHecbSY729z6ghqpnJywqUVkRGvyZBNKn3wSfm/79iaUjjxutodDAAAgAElEQVQSZs0q/Lk77WQRq7VrrZnv2rXW5Pehh+Dgg0sf108/WRrg8OEWObvwQrNaP+KIOPzSScQFllNjyc21nZBp0+x1Wlq4wWeimD/fGuetWmWuN9OnQ926ibufE5NfgAwR2U9V5xYca07shct3QGQ0KnheBfbPnFShatHp226zxUvfvm697sRGRDKwtVg6kC4idYA8YCzwlIh0Bt4HHgS+c4MLp6yU1s9qyhQTMAFpaWYS0aYNbN1qZRJTpkDDhkXdBCdOtPPRnHqqNRp+9FFr9nvuuZZWWBZHv+xsM654912zc+/WzepVq2oqtU/3To3k559t0gjE1W67mZNfIsXVxIkWFl+1yvo+fPedi6tUoKobMfvjR0SkrogcD3QEhse4fDBwrogcLiKZmGXyNFVdk7wRO1WJRYtsd/cf/7Ad1++/t/QYF1dOMdyPRcrvAS4veH6/qq7EzHgeBf4CjgUuTtUgnapFWfpZtWljaYFpaSaWXnrJolG5ubZJlJtrkasDD7T0wDp1wu8NhYp+Xnq6OSA//LCJrK+/hjFjShZXoRCMH2/9r1q1MoOMBx+EhQvDPUirKj7lOzWOF16wCSNwuLnoIsv1bdgwcfd89FFz1cnLgz594I03qkYOcTXmRmA7YAVWU3WDqs4RkRNFZENwkap+AtyH7SCvwIwuiu2Z5dRcglqrQw6Bzz6zxcEnn3hKoFMyqtpDVSXq0aPg3MeqeqCqbqeqbVR1QWpH61QVytLPqmVLq3E67TSbr7p1K3pNkBa4//6x7davv976ddatG+4dOmOG2agfeWTx48vNhSFDrB3OOefYxtQLL5gZ0MMPmzNhVcdTBJ0aQ06OFUlOnWqvReDNN63oMlGEQnDeeRbyrl3bikFbt07c/Zyyoap/AkVsRVR1KmaCEXnsFeCVJA3NqYL88YfVWk2cCCedZOmBLqwcx0kGsVIBY/WzivW+7t3tmqlTTex06WIbRVu3hq9LT4dffin83nbtwnbty5bZ2urhh2OnIkayfr0Za/TpA4sXW3TrjTesRitWymFVxgWWUyP48Uc49ljYUBCbaNDAUvT23jtx91y7Flq0MIfC3Xe30PkeeyTufo7jJBdVGDwYbr3VdndffNGaXXo6oOM4ySBIBYzuUxXdz6q4GqzoKNeddxadvyLrtDp2NMflgQNtw/ikk6ynVWkbx8uWWYTq5ZdtbRQ0WG/Xrvpm87jAcqo9zz9vuzQBp50GEyYkdrfku+8sB3n9evs5ebJNfo7jVA8io1atW1vUqlmzVI/KcZyaRCyRFIipyH5WsYiOch10kNVZRQqqyGuPP96c/d59N/z85JNLHt/cufD00zB0qN2nc2dzBDz66Ir9vlUJF1hOtWXzZjj99HBKIJjYuuWWxN73zTctzJ6fD//6l+U4O45TPVC12oFbb7U0mhdecBMLx3FSQ1lSAYsjMsqVlmaOf9Hsv78df/ttu+7YY2HAANuoFineqfDLL+HJJ83kolYtuPJKuOOOsjUWri64wHKqJd9/b3/sgZHF9tubJfqhhyb2vt27m4hLT7fdncsvT+z9HMdJHn/8YYXgH3zgUSvHcVJLIG6eew5Wr46dCliaVXvLltZCYvbsoudOOAGWLjXr9D33tEjUbbeFU/qi0xM//tjS/5580u7ZoAHcd5/1GW3UKK6/epXABZZT7Xj6acsjDjjiCLNj3377xN1z61azeJ82DerVg88/L1vfB8dxKj8etXIcpzJRXO1Vea555hmLKhXHtGmw33723qVLzfK9VavwZ0SmJ27ZYul/y5bBXnvBs89aq4oddoj7r15l8K8Hp9qwaZPtuESKq/vus14MiRRXS5dCkyY2Gf3tb2Y36uLKcaoHixfD2WfD1Vdbcfd339mOrIsrx3FSRVls2KdMMffk/Hz7GVwzbpzNX5HiqnZts1xv2tRe77svjB4NXbva+0Ohovc59tjwPKhqzYGHDoV582wzqiaLK3CB5VQTvv0Wdt3VIkcQ7kD+6KOJdaj57DObiJYutV4OP/9sYXHHcao2gUPgwQfDp59a6u+nn3pKoOM4qSeovUpPL772Kisr3BA4FLK69B12MCdA1fB1HTtapOrVV00kjRhh5hTnnWeZOdH3WbHCmgFfcIFF9Js2haeeMsfkLl3c0CvAUwSdKo2q5fvec0/42L77WoFlVlZi7/3887ZLowo9e1rHc8dxqj6LF1ut1YQJcOKJVmtVk4qzHcep3JTFhn31aoswBSKrZ8/C5zMy4IADzBVwv/2sH9VFF5mYinWf/faD11+3+TAnBzp1soyh0npf1VQqhcASkZuBK4FDgf+o6pUFx5sC84GNEZc/oapR/5s4NZENG6yHQnZ2+NjVV8NrryU2fUfVzCvefNMiZe++C2eembj7lZfSilrj9R7HqW6oWopL0Hzz+efh5ps9HdBxnMpHaTbsrVqFxVU0tWubSNq82epLL7vMBFestUDt2maCcf/9dk2XLpZeeMABcf6FUkAoZAZoI0da6nc8G8RXCoEFLAF6AacD28U430BV85I7JKcy8/XXNgEEjYPT0+Gtt+D88xN7302b4LjjzKUwK8siZfH8g9xWiitqLUlAlaVY1nGqO4sXw3XXwfvve9TKcZyqzemnWyPg4thtNzOt6NIl3BM0ci2QmQmPPw7vvWfugPXrW7Tqlltgjz2S8zskilDIyklGjbI6s8WLbe3TqlU1FFiqOgZARFoAe6V4OE4lRhV694Z//zt8bNddTeg0aZLYe8+da0Wdf/0FRx5pf6B16iT2nuUluvB12DB7DBpkx2IJqJIaFTpOdUfV/kb+9S/7//+559zEwnGcqsmNN8IrrxR/vn59K6u46qqitVKBKUYoZOuB7t1h993t+m7dYMcdEzr0hJKfb0ZkgahautQic2ecYTb0HTrYv008qRQCqwwsFBEFJgF3quqqWBeJSDegG0Djxo2TODwnGaxbZ7sy06eHj519tv2xJLqo8p13rKAzLw+uucbSEBNpnlFRIpsOpqXZOEOhcEHrli22mIwUUNvSqNBxqjJLltjC4f33zYF08GCPWjmOU/V47jm4/fbCKYE77WQbwgEnnACTJsXeGN60yRxSg/eLwL33mplF7dqJHXuiyMuDqVMt/W/MGFi+3H739u0t2+nssxPrdFjZBdYq4GjgWyALeAl4A0slLIKq9gf6A7Ro0UJjXeNUTWbMMDebTZvstQi89JI1yEs0DzwAvXqZYHn1VUsjSjZlrZEKClKHDTNxlZ9f+HzgjNalS+HUwZIaFTpOdSOIWnXvbju2HrVyHKcqEXx3Z2ZaO5qtW8Pn9t7bhMOPP4aPZWRYJCpaXK1ebWupPn1gzRo7lp4OffuabXtZx1FZ1g55eTaeUaNMVK1cac6IZ51lm+Tt21uv0mRQqQWWqm4AZha8XF5ghrFUROqr6roUDs1JEoFD30MPhY/Vr2+h3kMPTey9QyH7o5w40f5AP/3UUgSTTXlrpFq2tAkm0oY10kkomIDAa6+cmkd01GrQIHPHchzHqQpkZ0Pr1vZdHknDhjaXzZgRPtaokaU/RwugBQtMVA0YYBvXBx5oWULBOiEy8lXSOCrDGmLrVlufjRoFY8fCqlXW+/Tss01UnXkm1K2b/HFVaoEVg2DJWAmTs5x4s2aNuQR+9VX4WMuWVriZ6B2I1auhRQubhPbe20w1dtklsfeMJtgZ+v33stdIBe/Jygq7BKWlwW23wYsv2msRO++1V05NQhWGD7fFRk6OLS5uucWjVo7jVB3+/NPWRZHiKiMDDj8cZs60tUpAhw7WVDiS2bMtkjVihM19l11m5hVr1xYWS2UpFUjlGiI3Fz75xNL/3nnH/l3q1QuLqjPOMJGVSiqFwBKRDGws6UC6iNQB8oCjgDXAXGAn4AVgiqquTdVYneTwxRfQtm04JRAsF7hHj8TXPn39NZx0EmzcaBPOxIk2gSWTyJ2hjIxwX4qSJr7o3aTotL9mzcxyOihefe45r71yagZLllhq73vvwfHHW5qsR60cx6kqbN1qIioy7S8gL8+a/GZl2Xc+mBlY0B9U1cTPE0/Ahx+aEOne3R57RdjKRffVKi39L9n127m55mg4cqS1x/nrL0uFPOccq6k6/XTLNqosVAqBBdwPRCSBcTnwMPAz8BiwK7AOM7m4JOmjc5KGqtU8Pfpo+FidOiZyTjop8fcfNAiuvdbC5HffbTalqSByZwhsTADLllntCBSd8KJ3k1avtiLVgNWr7VwoZDv4q1eX3qjQcaoyqtYY85ZbwlGrf/6zcCNNx3Gcyky05boING0K8+dblOaWW+CFF2xDWsS+01u3tu/7sWMtYvXVV5Yu+NhjVlu1005F7xPZV6ss6X9laXa8reTk2O8+apSJqrVrrUykY0eLVLVtW/ncnAMqhcBS1R5Aj2JO/yd5I3FSyerVFvr+5pvwsQMPhM8+S0563g03mIlFerrtkCS6p1ZJRO8MHXGELQxzc+384MGWc1weN8CsrHB+dShkr0trVOg4VRWPWjmOU5UJ1iSRHHQQ/PQTrFhh5hZnnGHf9aGQfe8vWWKi69VX4emnYd48m/f69TNzq7KKkbKm/yViDbFli0XaRo2yFMd166BBA+jUyUTVaadVDWfDSiGwHOe//7VCxM2bw8euu87cbRK925yba41Fv/zS+jxMn27CLpVE7wxNmVLYJSjWhFfabtLq1WGzi7S0cCqB41QnIqNWW7bAs8/ac49aOY5TFXj2WbjjjsJGVfvsAwsX2uPOO+38u+9apAqs+e/s2SasXnjBBNjRR1taYKdO5Z//kp3+t3mzZSqNHAnjx8OGDRZlO/98e5x6auLb8cQbF1hOSgmFrGlwZCpeRga89RZ07pz4+y9aZGYWK1bYztCXXybPwrM0IneGvv/eRFGQMhhrwitLvnTt2l5zBSAiDYGBQDusHcS9qvpmCdfXAr4D6qmqN0OvpCxdahsz48dDq1YWtdp//1SPynEcp3TGj4fzzitsYLHHHta/aelSi97su6+ZV9x9t81vYHPdcceZCNuwwTar77rLyioqWrOejPS/TZvggw9MVL33ntW9Z2XBxRfb73ryyWZDX1VxgeWkjJUrLbd41qzwsT33tMZw++yT+PtPmmSOM7m5cOGFJuoqY/Pg7GwrRlW1XagOHWzyjCxCzcoK9/QJelh061b4c5IxYVYhXgJygUbA4cD7IjJbVecUc/2dwAqgkshvJxKPWjmOU1WZMweOOaawqVfDhpYat2oV3HijpcVdeKGtV3r3Dl93yCG2MTxjBlxyiUW3DjssPuNKRPrfxo3WImPUKPu5aRPsvLO5GV5wgYnCqiyqInGB5aSEyZNNKESmBHbqZCInGbm1Tz4Zdth5+mnrgJ4otrURX5ALHQrZgvGYY8LiKihCFbHolqpdd9NN1icsVlFqDRdWiEhdoDNwSEGvvWkiMg64ArgnxvX7YMY7twGvJXOsTuksXWpF2+PGedTKcZyqw+rVljmzcmX4WN269p2+bh0cdZQZVXXsaPVYOTlFP+O33yzq1aQJnHtu/MRVPNmwwSJUI0daxGrzZth1V+ja1dL/WrdOvlNzMqiGv5JTmcnPN2Hz9NPhYyJWa3XDDYm/v6rtkowebUJuwgQ45ZTE3S8ejfiKy4WOLEJNS7N/xyBnOxTyvlYlsD+Qr6q/RBybDRTnU/kicB+wuZjzAIhIN6AbQOPGjeMwTKckVOGNNyxStXkzPPOM9bjyqJXjOJWZnBxo3hx+/jl8rFatsMNv+/Zm8jBzpkWlJk8u2vg3I8Na1xx9tAms3FzLXElVs99o1q0Li6qJEy2zYLfd4OqrTVSdeGL1n6u9xaKTNJYtgyOPLCyudtrJUgSTIa7Wr4e//93EVaNG1jciXuIqO9vC9tnZhY/HcuIpLy1bWs+qU0+1n8HkGQiv9HQTi3fcYZNuWpq9rsk1VqVQD4jupbcW2CH6QhE5F8hQ1bGlfaiq9lfVFqraYpdkd6WuYSxdahHvK64wQ5pvv7Vm2tX9C9txnKqLqq056tQJi6u0NHvk5cHll9vx446z1/n5tnl09dXWGDiSPn2spc2sWSbK8vPtZ0XWGPFi7Vpr5t6xo0WoLrvM0hevvdbcoP/4w0RgmzY1Y672CJaTFD780MLXkSmBxx9vEaT69RN//x9/NGGybp39nDIlfo40JUWpYkWfypsyGNRg5eZafVqQ+herpqpTJ6+xKgMbgOj/6+oD6yMPFKQSPgm0T9K4nFJQhTfftJYFmzfbZk337jXjy9pxnKrLtdfCgAHh1yL2CIVMWD34YLiNRCBAAlOrn36yn7vsYpGsUMjqsI86Knb7lWSyZo25GY4aZf2qcnOtefENN1ikqmVLE5A1ERdYTkLJy7PIyvPPFz7+4IPQo0dyTCXefhsuvdQmqxtvtHTEeFJSv4hoEQSxxVhJoqu4KFhwfWQzYa+xKhO/ABkisp+qzi041hyINrjYD2gKTBX7H7UWsKOILAOOU9UFyRmuAxYBv+46q7Vq2dJqrQ44INWjchzHKZ4nngjXewcE4umii2wtdNBB4XNLllhz4EiLdrA5r0MHi1qFQoXXAsluv/Lnn2FRNWmStZBp3BhuvtlE1bHH1lxRFYkLLCdhLF5sTfB++CF8bPvtzTkmWelrd95pu9xpaTBkiBVVxpvS+kVEip7evWOLpZJEV1ZW4c/Pytr2uq6ajKpuFJExwCMi8g/MRbAj0Crq0h+AvSNetwL6AkcCK3GSgketHMepaowZY65/QRQKLIU/L8+yeR56yBwAA/73P5vbhg83wRJp+pCZaTWmEHutkYz2K6tXwzvvWE3V5Mn2ezRpYnWv559v5luV0YU5lbjAchLC++/bH92WLeFjBx9sf5iNGiX+/nl50K4dfPqpufJMnQpHHJG4+wXCrUuXksVOLDFWXIQqUkQ995xNcNHX5+RYJLBHDxdZ5eRGYBBmvb4auEFV54jIicAHqlpPVfOAZcEbRORPIKSqy2J+ohN3li0zh8B33/WoleM4lZ9vvrHyh8i1TxCxOussePhhM7gI+OILczV+913YbjsztXjzTVvDpKXZZlKQapedHXutkaj2KytXWjRt1Cj45BP7HfbZx+pdL7jAUhRdVBWPCywnrmzdCrfeWjQN7/rr4cUXk2PFuWKFmWksXmxN+WbONDONRBBdf9WlS+nviTVBlia6Vq8unApYq5ZN4KGQheinTvVIVnlQ1T+BTjGOT6WYXleqOgXwJsNJQBX+8x+LWm3cCE89ZfOKR60cx6mMLFliEalIt78gde+MM0xYHXWUHQ+FbBP6ySdh2jTrefXQQ1aDdfnlds2OO9paJqgVL2mtEc/SgBUrLPo2apStQ/LzoVkzywa64ALbqHZRVTY8S9KJG7//bjszkeIqM9NCyq+8khxxlZ1tYevFi83qdO7cxIkrKJ9LYDBBvvYaDB0aPh7UafXsGRZJkQ6B0WH/wFUwmORUU+8e5DjxYtkysx2+7DLrZ/Xtt1bH6eLKcZzKxqZNFtXZc8+wuAq+m9u2henTza78qKNsjTBkiBlVnXMOLFoEL7xga6ecnLC4at7czCO+/jrsThy91hg2LLZzcUVYtgxefhlOPhl2390MKhYtstqxWbNsHdW7t21cu7gqOx7BcuLC2LEW2o5shLf33pai16xZcsbwyivWYFfVdoN69Kj4Z5XV6a+0+qtISjPDiLxPLIfASGbNCjsHgS0+3ZbdqcqoWqPxm2/2qJXjOJWbUMgam8+YUfTcKadYxOr44+31unW2sdqnj23+Nm9uPfwuuMA2oU891VLwAK680lKhoyNWzz0XXmtkZMCgQbaWqGgd9pIlFqkaOdIyYFSt5cW//23jOuQQF1PbigssZ5vIzbUF0WuvFT5+3nnw+uuWU5xoVK1PxJAhNlmNGQNnn13xzytPc+DShFAkpYmxaFFXXNg/OxsGDix87NZbPT3QqbosW2a7pu+8Yz1gBg+2L3vHcZzKxkUXmTtxNK1bwyOPwEkFLeuXLbMI1csvW4+ok0+27+527Syy9eSTJpxWrbLrBwyAa66x57HKBIK1xu+/25or1mZtSfzxh/UBHTUKPv/c1k4HH2xOhhdcYM+d+OECy6kw8+dbbvEvv4SPpaVZrdWNNyZnDJs32y7RrFmWx/zll9seMSsp0hSLsuY/lyTGyiPqpkyxAtgAEWjQoPT7O05lIzpq9eST3jDYcSIRkSnAcUAw6y9WVbd6SQH33w+PPlr0eMuWluJ/yin2fTx3rjkCDh1q3+mdO1vfqqOPtuuzs02Ebd1qr0Vg9mxLHQyItSEbrDWys8OfXVrmzKJFJqhGjTJDDbD7PPywmWdEWsQ78cUFllMhRo60fOHc3PCxrCxrNHfkkckZw/z50KKF9WQ47DDbEYpHxKw8aX/loby9rooTWG3aWKQu+LdPpDWr4ySK5cstajV2rPVNGTLEo1aOUww3q+qA0i9zEsHQoXDVVUV7Ux1zjEWs2rUzkfTll7ZJNGaMfS9fdRXcfjv87W+F3zdwYFhcgfW2OvTQomuE4jZkS8ucWbDAIlUjR4ZTGJs3h169TFS5E2tycIHllIstWyw6NXhw4eMnnmgNQJMVSZkwATp1skmqSxdbnMUrX7g8aX9Qtnqt0iJU5RF1LVva/YYNs9elWcM7TmXCo1aO41QFpkwx8RQphsCc9Hr2NCOt7GwTUt9/bxbtDRrAffeZA2qsljSPP144xX+77SwTqLg1QknlCZHn5s+3KNXIkfDVV3bsyCPhscdMVO233zb9UzgVwAWWU2Z+/dUmgnnzCh9/8EEzlUhW5+6ePe2eItC3rxlbxJuypv2VNbWvtAhVeUVdPG1ZHSdZLF9uGzRjxljUavBgT1FxnDLQW0QeB34G/l3QMsJJEHPnmjjZsKHw8UMOsfVHx46Wpt+jh71WtfXILbdYlGiHHWJ/bocO5igIVo/Vtm34+75375LXCLE2cufNM0E1apQ5DoJl9TzxhKUlJstgzImNCyynTLz5prnbRO7k1K1rzfFOPTU5YwiFbGJ77z2oUwc+/jjs0pMqpkwx58RQKGyVHkv4lCVC5aLJqa6owogRFrXasMEWALfdlpzWDY5Txbkb+BHIBS4GxovI4apaaKtTRLoB3QAaN26c9EFWB/7800TU0qWFjx9wgAmn884zW/YXXoBnnzWziQAR2G234sXVvvtalAnMTbB798LnS1ojRG7kZmTYWmzGDGthAZaq+NRTFqlq2rTiv78TXypFHywRuVlEZopIjogMiTp3qoj8JCKbRORTEWmSomHWSDZvhiuusJ40keLq4IPN3CJZ4mrNGuuJ8957sMcelmOcSHGVnV22HhNZWWG79FDIXsci6F116qn204WUU1NYvty++C+5xHZUZ82ygm8XV45TOqo6Q1XXq2qOqg4FPgfax7iuv6q2UNUWu+yyS/IHWoXZssWEVVZWYXG1777W8HzOHHMI7NEDGjc2cdS0qYmaOnUsvbl27dgbp+vWwfbbm7gSsTVFtLiC2P0wA95+28aYn28buf36WWrhM8/YWmjGDOsV6OKqclFZvuKWAL2A04H/tykQkZ2BMcA/gPFAT2AE5qjjJJiffoIzz7Q/4Ei6dbPUvMzM5Izj22+txmvDBpvAJk1K7OKsPI5+q1eHu7Wnpdnr4j6ze3f7zKlTraDVRZZTnVG1hcFNN3nUynHiiALeoSgOhEJw+umWDRPJnntardQll8DChZb6N2iQiZtOnWyD6LiCVejxxxef2v/VV5YKrWpCbNky2HHH4scTmcXy448WJXvvPdukCsjMtHm1U6dt/e2dRFOurzoR+QUYCAxV1WXxGoSqjin4/BbAXhGnzgPmqOrIgvM9gFUicqCq/hSv+ztFGToU/vGPwnbgmZkwfLj1gEgWw4dbODwUssXZM88k/p6x6qWC49GTaJs2tnNVmjlFea3fawqJmlOc1LJihTkEjhlj6SuDB8Pf/57qUTlOxUnFXCUiDYBjgf9iNu0XAa2BGDEQpzx061a0f2dWlkWlrrjCbNMvu8xqnDIyzEzqjjuKOvAVl9rft68ZXYBFvRYsKNmIS9UiZUFN1Y8/hs9lZlpkKxQqW422Uzko717iVqA30FNEJgADgAmqGor7yIyDgdnBC1XdKCLzCo4XEVieg7ztbNxoje5GjCh8vHFjixztv3/yxvLPf9oklZ5uYfqLL47/PYLC0awsiz61aVM0FzoryyJaOTk2lr59bXKGsptTJMr6vRqQ7DnFSSCRUav1620X+PbbPWrlVAtSMVdlYtk9BwL52Lqnk6r+nMB7Vmt69zaXv0jq17e+VV27wn//a2Zekyfb8TvvtAjWHnuU/R6XXGJOqWBZQBMmxL5O1dwHA1H1008mwlq3NkOM9983URU87r23Yr+zkxrK9bWnqgeLyHHANcCFQAdgWUHd1KDooss4UA9YGXVsLRCzjFBV+wP9AVq0aKGxrnGKZ84cOOssC4lH0qkTvP66mVokg61bTYB88YUVjH7xheVHx5sgFTAwqUhLs2jU5MlWJzV6tDnxrF4dviYUMhe0WbPC9uiBqAoiXbFEVnldAmsKKZhTnASxYoX9bYwebQ01hwzxqJVTfUjFXKWqK4Gj4/25NZERIywilZ8fPrb99hax6toVxo+3tL9Zs2D33a19xHXXmcgqjkhnP7Dnr74aNr945BHrcRWJqpU9BJbqc+fa2qNNGxNy555r9VrDhlnkKi/PN2WrLKpaoQewPXAVMA0IYbsrnwCXArUr+Jm9gCERr58HXo665nugc2mfddRRR6lTNkIh1f79VdPTVe3P3x5paaovvmjnk8Xixaq77Wb3339/1XXrKv5ZX3yh+thj9jMWjz1W9HdOT1e9/nrVWrVURexnv36qmZmFrxNR3W47++wvvrDn6enhY9UZYKZWcN4o6ZGIOSVVj5o2/4wYobCbrrAAACAASURBVLrzzvb38vjjqlu3pnpETnUlUfNPeR6Vfa6qafNPSUydqlq7thb6/s7MVO3TR3X1atW+fVX32ceOH3ig6sCBqlu2FP95wbqiX7/w936tWkXXEpMnh98TCqnOnKl6992qzZrp/681TjtN9dVXVZcvL/z5kZ97/fXVf01RlSjP/FPhxA1V3QQMBgaLyP7AQ8AlwEnAiyIyDOijqr+X8DGlMQfoGrwQkbpAs4LjThxYv96a5I0eXfh4VhZMnGg9FZLFf/9rBac5OWaHOmpUxZsHl8Wook0bS/kLhWxKTEuza5cts/eB/fzgg3C/raAmTbVwfZbXV207SZpTnDiyYoX9XYwa5VErp+bgc1Xl59dfbU5asyZ8LC3Napm6dDHTigMOgFWr7Pu6Tx9Lyyupn2fkukIknNUSGRUDuOce63P11Vfh9L/58229ceqpdr5TJ9h556L3iKzXBivP8PVE1WSbbNpFJF1EzgWexYovFfgUmA78E/ifiHQsw+dkiEgdIB1IF5E6IpIBjAUOEZHOBecfBL5TN7iIC7Nn22IoWlydcAL8/HNyxVWfPjYh5eZajvTo0eUTV9G26sUZVUQT3CMz0+qqJk+2XhaRjB9vrn+ffQbXX29phOnp4bB9UF8VecypGPGaU5zE8/bb1q5h3Dj72/viCxdXTs3B56rKyapVsPfesN9+YXElYqLm++9tA/WAA+Chh0y4TJtmc1fHjiWLKyi8rgiF7Ds/mowMK7PYYw8z+Hn2WTjwQBg40NwAP/zQDMRiiSvw9US1oqyhrsgHVnD5FLAMC48vAx4HmkVc8zfgG+DnMnxeD2xyinz0KDh3GlbYuRmYAjQtyxg9RF48oZDqSy9ZCmBkSBtU//1v1fz85I7l4ovt3rVqqX70Ufk/I1aKXlnS9iJTBNPT7bWqhf5Fwv8maWnhc8H9olMPS0tHrE6QgBSdeM8pqX5U5/ln+XLV88+3v40WLVR/+CHVI3JqEomYf8rzqApzVXWef4pjyxbV5s21yJrmxhtVP/9c9dJL7Xs+M1P1yitV58wp/z2i1xXHHx++z847q+64oz3PyLB1g4hqnTrlXxfUpPVEVaM88095J5arsSZ3+QWPD4HOQEYx118J5JXnHvF61MQJpiysWaN6zjlFJ6G6dVU//DC5Y9mwQfXgg+3+u+yiunBhxT6nOKFU2iRVkjALBFZamr3u16/4z6ppk2E8FzhVaU4pz6O6zj9vvx2utXrsMa+1cpJPqgRWVZqrquv8E4v8fNXTT9cia5oLL1QdNy58rl491dtvV120aNvu98UXqr16qe61V+H71aql2qGD6rBhqg88EHtN4lR9yjP/lLcGa0DEbs1rqrqglOt/BIaX8x5Ogpg508LgS5YUPn7wwVZntPfeyRvLzz+bY8+aNZYnPXWqpd6Vl+xsc+wJQvWRIfXS3P1iOfv17m0pAFpQk3XaaeYkGDQJjq7nKk9TYicmPqdUAVautFqrkSMtdXjIEJs3HKcG4XNVJULVXP6ie1mdcoq5Bb7yCpxzDjRqBI89Zn35GjSo+P3y8+Hzz61lTL9+dn+wNMBbbrH6rcBxMDvbGqsHaYSe5lczKa/A6gyMU9X8Uq8EVPVL4Mtyj8qJK6rw/PPWqDeYFAKuvdYMHGrVSt54xoyxZsV5eXb//v0r9jmR4iYjwz4rsE4PzrdpY7bvmZmxzSeimwRG96vq0aPkJsHeQHibScmcIiINsaah7YBVwL2q+maM6+7EjHaaFFz3sqo+ta33r0qMHGn26+vW2ULlzju9r5VTI/H1TyXh0Ufh/vsLH2veHC691NYT11xjNVj9+tmaoE6dit0nP99qr0eNsnXLsoj20mlpVtM1bZpZqm/cGO6PCeH67ooadTlVn/L2wRqbqIE4ieGvv2w354MPCh+vVQsGD7YJKZncd59FidLSYMAAmwgrSmluO8OGFXYDHDasdPFTXL+q4poEewPhbSOFc8pLQC7QCDgceF9EZqtqtEOpAF2A7zAH049EZJGqvpXU0aaAlSvh5pvNzKJFC5svEtGPznGqAr7+ST3Dh8OVV1pkKKBxYzj/fOvVeffdlhHzxBPm0hfLhKI08vLM0TgQVStWwHbbwWGHhQVWVhYsXWpz4nXX2bGPPrKf3brZ+iEvzza08/J847Wm4vuQ1ZgZMywlcPnywscbNzbBlUzHr/x862g+aZI195syxSbCbaG84iZy96k8lNQkuDo1EF6+3NIpqjsF7R46A4eo6gZgmoiMA64A7om8VlWfjHj5s4i8CxwPVGuBNWqURa3WrLHd4rvu8qiV4zipYfJkOOssa+ESsNNOdmzsWHPqO/NME1itW5c/arR1K7z8MrzxhjX+XbPG1ilnnw0XXACffmrnwdYtXxbEJaMdmEePNoHlG68OUPFGw5X9UZOKPKPJz1d98snCTnjB45xztq15b0VYuVK1cWO7f+PGqqtWxe+zSzKY+OKLwg2Ca9Uq3YiipjUNXrNG9Y47VLOy7N8qN7f091AJGn1uywM4AtgcdewOYHwp7xNgFnB9Mee7ATOBmY0bNy7LP3+lY8UKKw4H1aOOUv3++1SPyHEKU9Xnn2Q8qsv65/vvVevX10JrmDp1VNu1M6e+9HTVyy9XnT27/J+dm6s6caLqNdeE3f8iTSk2brTrWrUKn7vxxsKfcdddhcfWr1/4XE0zv6oplGf+8T3Jasbq1XDJJRYpiiQtDZ55Bv71r+TmBH/1le3ebNpkTYTff79iYfviiK6hij53zTXhgtT8/JJD9dnZVnOVk2MpCGWtqcrOrloRLFWYMMF+16+/Dht6HHus1dlkZaV6hAmnHrA26thaYIdS3tcD6x04ONZJVe0P9Ado0aKFxrqmMjN6tBWCe9TKcZxU8scfZh6xdGn4WHq69aP89lure7rpJrj1VmjSpOyfm5sLH39sEfp33rESih12gGbN4LvvCqce1q4Nu+5qqdJg0a1LLw1/32dlwYsv2npKBO64o3ANVklrE6dm4F+f1Yhp0+C888ITQkBWljXLTfYf+4ABlp8cCsG//w29esX388sibLp0gaFDSw/VB4YZgbhKSytbaL8quQguXw4PPmguSOvX27FddzVzkLvvti+aGsIGoH7UsfrA+uLeICI3Y7VYJ6pqTnHXVUVWrbLFyttvw1FHwSefeK2V4zjJZ+1acxf+6afwMRHYay9YtAgWL4aePW0jqKwbgTk5tuE8ciS8+67do359K5+44AJo2xZmzSr8PX7wwVZ3tXWrCbs5c6w5ceT3fVqabdoGG5Tb4lDoVE9cYFUDQiEzjoh21QE4/njLUd5ll+SOqVs3s0/NyLCd8U6d4vv5ZRU2Za2RCgwzAnF12mkW4SlNLFV2F8FQyARV7972JQH236RtW4tSbGsdXBXlFyBDRPZT1bkFx5oD0QYXAIjI1VhtVmtV/SNJY0wKkVGrXr0sapWZmepROdWZnBxrrbFwoT0WLAj/HDu2RkTQnShycqBdO3Psi2THHU0QZWZaDdSVV5rwKY0tW8x0YuRIGDfOMjMaNLB1yAUX2Pd7ZFuYyHVCnTomvsCE2IoV4Wsjv+8DYSXidVZObFxgVXFWrDDL86DXUyT33mu7PfFMySuNnBw44QTrudWggRlt7L9//O9THmFTllB9LHt2MGFSkjCrrMWsv/1mUcN334XNm+1Y48bwz3/aoyI9x6oLqrpRRMYAj4jIPzAXwY5Aq+hrReQy4DHgZFX9LbkjTRyrVplD4IgRHrVy4sumTbHFU/AzMu0LbJG6116W6rV+vQusmkR+vpU0jBxZ+HjwndqsmWVXnHde6enKmzfDhx/aZ40fb/8v7bSTOQyef75tyJbUjqZlS0udv+8+e33IIWbDHkn09/1zz1lZRlUpD3CSiwusKsyUKTZxrF5d+Hjdupbu0759csezcKFFRFautMlpxgxz4kkE8RY20ZEuiG+ELBls3Wo9QJ591gQWmJA691zrX3TggakbWyXkRmAQsAJYDdygqnNE5ETgA1WtV3BdLyAL+ErCxYuvq+r1yR5wvBgzxqJWf/3lUSun/KxbV7KAik5Rz8y0JvZNm8IZZ9jPJk3CP/fc0///q2moWv3U888XPi5i59q0sXnplFNKrhnftMkckUeNgvfegw0bTKBfdJFFqk4+uez/b7VrF65dD0oLoqlM3/dO5ccFVhUkP98iUw8/XPTc3/9uRhJNmyZ3TB99ZJ3Mc3NtR+qNNxJrppGIiS4y0tW7d3wjZInk++8tWvnRRyaywKKGd91lKRXJjGBWFVT1T6BI4qqqTsVMMILX+yRzXIlk1SqLXr71Fhx5pBV7H3poqkflVCZUTXgXJ54WLrTzkdSpY0KpSRM4/PCiAmr33X0OcsI8+aRFpWJx8cXWyPyII4p//8aNFmkaOdLWOps2wc47mwHFBRfASSeVT7CHQpbdsXixvX711XBvq0gia77vvbfsn+/UXFxgVTGWLrXdmalTi567+mp46aWKdy2vKI8/bhOOCPTpA927J+5e/ftb3UjnzlbnlShhU1lT/wK2bDFXyJdfhiVL7FjduvYl06uXpdw4TkBk1KpnT1vgeNSg5qFqEaaSBNT6KKuXunXDYqlVq8LiqWlTM8pJpjOtUzUZNgyuuqqwUx/YPHTddXDbbbBPMdtZGzaYmBo50sTV5s32/13XrpbF07p1xRxPV6+2CGpOjv0/fOON1lA4mqpkZuVUHlxgVSEmTTJxFb2DmJlphhJduyZ3PKomdMaOtVS0jz6yiS5eRLsE9u8fu2t6ImzSK2sqwLRpZmYybZpF10Rs1/iBBywV0Bc6TiTRUatJk2IvIJzqQShkDdWLE08LF4ZrMgMaNDCx1KyZpWRFC6iGDX1ecSpOZHZLJHXrmrX5TTfFNuFav95qqUaNsjTALVtgt91sI/n88+HEE7ctMjp1qkW7/q+9Mw9vqsz++PdNureUStkELaCiKCIIuBRkLA4yijo6ouOCgtugoI6474qI4K7jLooMuDEzoigjuKH4QygqirsiKpujLAIF2pIuyfn9cXK9N2mSbmm2fj/Pc582997cvNlO3vOec75HRBelvV6NXj3zTF0HKtHFrEhiQgcrCaitBW69VetogtlzT13ZiXWqz44dwMCB2vW8c2fg0081FSRaOGXT3W7gkUdCd03v00cdoJoadTSjafjinfpnsWOHRh1mzLDr7QoKgLPP1s8Fi8JJKF55BbjoIkatUonaWo1Yh3Og1q2rO5Ft316dpd69tS43OIWvbduYPw3SCvjkE3XYd+wI3L/bbioidf756mQ52b7ddqreeEN//7t00VYip56qEdRopJs60xT32UedtptvDu9AhctoSbYemCS20MFKcH7+WQ3LsmV1jx1/PPDcc7H/gfzqKzV0O3eqDPyiRdFvSLpokd2TyufTVa7TTgs8p18/TTuwJhTV1Xo7FQydiK7a3XprYDPgQYOASZPqL/4lrZctWzRq9eKLWsvAqFXyUF2t/X7CRZ/Wr9dJoJPOndVZGjBA1dacDlRREZCXV+dhCGkxfvhBf6eCxU7at1cBptNPD1zoKStTKfWXXlIVwOpqTXEfN04jVcXF+tsXLU46SdV1Af2+zJmjjlKkkoBQGS3Tpum8xOfTDB6mDZJg6GAlMPPnq2BE8AqQywXcdRdw5ZWxn2TPng2cdZb+yF96KfDQQy3zOCUlulJl5Wv7fBotszBGozjBr02ys2mTpgDOnm3XQnTqpCt4111Xd8WPECfOqNWkSfqZYdQqcdi1y+4BFSoK9csvuphiYYzWiHTvrotZwdGnoqLY19wSEopff9XP6OrVgfs7dNAShj//2Z6vbNumTs5//qMLQDU1+lm+5BJ1qg47rH6nqrHRIxGgZ0/gxx/19r336hwKaFhJgDOjpbRUx1pbq7erqpg2SOpCBysBqanRXgz33lv3WGGhTqKGDIn9uK68Uleg3G7g2WfV0Wopios1LdBaIUpL027rFunp9irTjBn2ytPo0S03ppYiXDPg4cM1LXTAgPiOjyQ+jFolBuXl4aNPa9YAGzcGnu922xLmw4bVdaD22CNy7x5C4s327Vp7/cUXgfsLCzXD5phj9PaWLcDcuRqpeucddU66dwcuu0yzdA45JPKCsdOhAiKLTgQ7Xzt36kLlrl36GIsXqzPoxHKgSkvr73+5aFFgJNnlSjwhLBJ/6GAlGGvX6grO8uV1jxUXqxpY586xHVNtrRqz//s/TTdZsiQ2k7c+fYALLrBvP/WU/jVGc6YBNXQPPZSczf5Wr1b1xddeswvPu3WzmwFzYkUawty5GrXaupVRq5amrCyyAl9wT8KMDFvC/IQTAp2nbt20viTa6dWExAKPR52n998P3J+frw3MjzlGRXaeekqdqoUL1SnZay9VDDz1VF08bEgWTrCK35gx4UUngs995BGdR1hiFq+8onMZl6vufKGhaoElJZoW6KwRT6a5B4kNNO0JxKuvqnBBsEwuoL0hpkyJ/Y/xhg1qBH/5RVWmPvkkejVfkUL8wYbuwQcDc6QPPjg5ZVNra1Wp6IEHApsBn3yyrprtu298x0eShy1bgL//HXjhBa1HfOstRq2ag4i+puGiT2vX6mq9k+xs22E69NC6CnydOkW3foSQeFNdrc7Ra68F7s/O1syWIUPUiRk2zI707LOP9mU85RT97W5saUOwih8QvmbKWb+9a5eKaQAaDZ49Gzj66PDzhoaqBSaqyjBJLJLCwTLGLAJwOAB/xiv+JyL7xW9E0aW6Wh2oUPVMOTk6gTrxxNiP64MP1Bh5PLr6+uqr0av5qm+lKNjQbdkSaNCSTTb1iy807dPZDHi//VTJaPRoNuIkjePVV7VlwZYt2nD8+usZtaoPEU3RCxd9WrNGm5Y6adNGHaXu3TUNKjiFr317is2Q1oHXq5kjs2YF7k9P18XfnBztw/nXv6pzs+++Gk0/5RSgb9/mfU+CVfxGj9YtlINTWFi319bw4SqgMXVq5HlDY/pfJorKMElcksLB8nOJiDwd70FEm59+0l5Sn31W99j++6tk6d57x35cjz6qaWoiKvF8002hz2uqTGkoB8naX1IS2tAFG7REbgQM6OrZffcBjz8e2Ax41ChtBty1a3zHR5KP4KjVm2/q5IWoLfnll/A1UGvX6sq2k3bt1FHabz+dhAU7UAUFdKBI60ZE5wKPPhq43+XSNMDyco1OiQC9egE33qgRrgMPjN53J1zEKNScIzhN96ij1E4CgfMKt1sFZ0pLA6/HyBSJFsnkYKUcL70EnHNO3VVTQFdnnnhCw+6xRETzm599VlemXn0VOPbY0Oc2p7t5sANVWFj3WsGGLtiZS1RDuGSJ/sg4mwEffLD22TjpJE7YSNNwRq0mTtSIaGuKWtXUaNuKcNGn9ettVS+Ljh3VWerbV7MAgmug2rSJ+dMgJCkQ0QjU3XfXPdapk0aD58/X/mq33KJOVe/eLTeehkSM3ntPW5tYpKfrYqbzGgsXahRuxgytD5s5M3DuwsgUiRbJ5GBNNcbcCWAlgBtFZFHwCcaYsQDGAkBRUVFsR9cIPB4t8nz88brH0tN1v5U3HEt27QIOP1zT2QoLVWije/fw5zcnTS/YQQp1reuvD1+4ahnERDGEoZoB77abOsq33qr/E9IUtm7VqNXzz6d21KqqSleUQ9U+rVkD/O9/gak/xmhz8+7d1W6dfnpdCfOcnLg8FUKSFhFdDJwyJbBlgJOOHVXh95RTNNMmEXjhBc0OsTj7bO2lFTxHKC7W+UVtbfKUGJDkJFkcrGsBfAOgGsDpAOYZY/qJyI/Ok0RkGoBpADBw4MAwpiG+rFqlKYFffln32B57aOHowQfHflw//qgyqdu2Af37A0uXqvhCJBqTrxyKhqT8WVGrdesSr+ZKRFfwJk4MbAZ8xBGq5jZ0aHzHR5KfVIpaVVZGVuD79dfA891utYnduul3KTj6tOee9dsoQkjDEFEbc/vtoR2rXr20Ncspp2hKbSIxa5Zm3jjJzdX9s2bpQmdTa60IaSpJ4WCJyIeOmzONMWcAGAHg4TgNqUm8+KJGpjyeuseOPVZXqOMR6Zg3T52+mhrg3HOBZ55p2P2imaYX6lrOqJXbbSsoxtsgbtqkKYD/+pet+Ni5MzB2rIpWcNWcNJetW7U/zHPPabTqjTc0epXI7NgRPvq0di2weXPg+enpGmXq1k3tX7ACX9eulDAnpKUR0SyLyZPrOlbp6Spxfvnl2qQ3EbnoIuDJJ/V/Y3SRMy0NmD7dFpR65pnARdlELjEgqUOy/nwJgKSpZKms1BSf6dPrHjMGuOMOnZjHQ8731ls12uJyAY89piH1SIQTtfjyy+Ybq+BO6RMn2nKrAPC3v+mELB4G0efTFIQ77wxsBvynP6kyUTyijiQ1ee01jVr99pt+P2+4If490UQ0uh1Jga+sLPA+WVm2s9S/f2D0qXt3XZSgeiYh8aG2Fhg/3u4v6SQrS1ujXHhh7MfVGAYO1OwRQMsuTjnFznixnC5AHa3grJdEKjEgqUnCO1jGmAIAhwF4HyrTfhqAPwCYEM9xNZRvv9Xo0LffBu43RhWq5syJTyqZzwccfzywYIEKabz7rtYxRCJUb6oJE2wnyOXSlJ3m9qSyHsd5XUuaNdYGMVQz4O7d1WG+5JLkTdciiUdw1GrBgthFrUQ0Mhsu+rRmjaqFOcnLs52lQYPqKvB17EhBF0ISkU2bgE6d6q5TZ2So8u348Yndv62mRoU2tm3T2y+9pPMswM5+mTHDVg1NT2caIIk9Ce9gAUgHMBlALwBeAN8BOElEVsZ1VA1g5kwNXwdLAwPalHLOnPhIdW/bps2DV6/WGodPPwU6dKj/fsFCFHPm6F8rwuTzhZZcb6xTZD2O5VwNG6bRrFg5V6GaAWdl6erY1KnaNJGQaDJvnqaYtlTUyufTGqdwztO6dfYCgkVBgTpLe++tCx7O6FO3bipxTgeKkOQjWG3TBS+uaj8Tt+/3HDL2vAxwnQhs2KBpLW3bqjEoKND/DzpIV0+8XjUsLbTKGCpbprRU5x0PPKAPnZYGfP890KNH4H2Li1VR0OrZVd/ibFPbzRASiYR3sERkM4BD4j2OxlBRoal2zz6rt4MnIRMmqPRpPKIfn36qDTMrKrQ/xFtvNTxNJ7gwdORIYPHiupGmUJLrjTFawY8TK+fqyy81WuVsBtyrl0rVnn12Yq/okeRk2zaNWj37rM5b5s9vWrppba2q7EWSMK+uDrxP+/bqLB14oEazg0Uk2rZt9tMjhCQg+fnWf4Iz9v0UTwx4Cvm7NgJljiKs9etDF2a9+KJKdi5erOk3OTmBDth99+kP9ldfaWF5sINWXKz/WxOHrKw6k6RQqsGAzl0s57BNGxX/CTePCi45mDo1tAPVnHYzhEQi4R2sZOPLL9XxWLXK3iei9iM7W6Nap5wSn7H9858qsuHzac3XnXc27v6hCkP79NHbhYVq7IIl1z0eXUVqjMGKZQGqxwPcc49GrKxmwHl56lDdcYfWiZDUwxjTDsB0AMMB/AbgehF5IcR5BsCdAC7w75oO4FqRcALGDWfePK1x2LxZ+8jceGP4qFV1tc53wtVA/fyzft+c7L67OkqHHKI2J9iBys1t7jMghLQ0DbVVjSEvD3juOYOhQ4EuXQYAGFD3pEMOUW+mvFwLLLdv17+WhGBRkUoOlpUFHreM2MqV6mxZq5UWy5YBhx2mztf558OXlo5dmQVwtStAdqe2wL/+hUWL9sKgqvfwJ9987PS0xc6pBXhsZQlqa61GWwa3XrET6bsEcOdFXP2sz4FqTrsZQiJBBytKiKiIxcUX1w2/A8C++6rkcrzkTS++WKP9bjfwn/803ckLLgwtLlancs4cdSytY263GiwRzYVubP1USxeghmoG3L+/pmedcAJTn1oBj0LbPnQC0A/A68aYz0Xk66DzxgI4CUBfqLjO2wB+AvBEcx581SptfJubq71bXnlFo9oZGTpX6NpVF3i3blWRnGDlUZdL03qzsnQRoLBQFS09Hr3dubPOdzZv1oWD5cvVCSsoAG67DTjgAJ143H23Hj///LqLJYWFwIoV+nijR+vfWbM0c6hzZ420WYsqVt2DddyJ89yyMuCzz9RWWI9n1UZYYykp0XEGL644r29d87HHdB6Xk6Or29dcEzgWa+yhbElwWpDztvVcly3TtM0zz9Qm4ePHa9rwCSfo402frpOy6mq18dbjO8f7zTf6vpx/vqaBBjNtml6nSxdVU1ywQB+3vFxX6Q87TK/92Wdak7djR+DzuvZavUZtrdqwO++s+7otWmS/9h066Odi5Eh7PKFeL+e+gw/Wca1YoZ/Zgw/WbIht2zRV9LLL9P0Mfr7WPus927kT+PBD4OSTgbvussfmXKDj5LYODbVVjcLZMyosLpeGu+yQl81eewE33RT+viNHqhHzeGwnrKzM7kY8YADWjrsT/36qDG0qy7CbZzuG71GG3XJyUFICbHF/gfG+x5ArlfjDvPewGHq/LOyCyc7BaWvuAtreoT/WbdvCk12A7WiLNS+U4rCSbGD2bGDZMni/bItxngJslQLs8BRg4sS/aFbMvlsAY1ByRD4yMtIo2U6ij4ik5DZgwACJFTt2iJx+ugggYoxu6lroduaZIuXlMRtOAFVVIocfruNo21bkm2/Cn7t0qciUKfq3oVxzTeBzffJJ3X/RRfbr4HbrdePNjh0iV14pUlhoj7ddO5EJE0S2bYv36JIHAMslAb7jTd0A5EInLPs69j0L4M4Q5y4FMNZx+3wAy+p7jPrszz33WJ9Bn3+TEJsvwsbjTT9e3+vL4/F5b0Sys+v//Ul2+9OYrTG2qjH2J1GYMkXnB6HmCUuXitx+u8huBd7fPzO3n/ejTJ1cq5+RJUtE7r1X5Kab5JdTLpHn3WfJq/izZGf59PhVV+mkx2FUdyBPXC79nG0++ozfMHDo8QAAIABJREFU99fm5Mn2tnvI9n5/sAfwwAMi48eLXH+9yF136eRm3jz7+Pr1Ihs2iOzaFauXiyQAjbE/jGA1kxUrNBpkiSGI6IKKMRrFeeghFbqIR0Tk559VzGLTJq0lWr48fFpQU/KQS0uBe+8N3Ddnjq6Kjh6t6ZDxXhUSCd0MeMgQlafnalWrZF8AXhH53rHvcwBHhji3t/+Y87zeIc6DMWYsNOKFoqKiiAN47bXf7+XYK86rRbw/IakIU7Tq0GBb1Rj7kyiEa/hbWqo28t57gdpaF1wu4MsvDQ44YC/HvQepfCmAf04Fbn5FVdDcliT7Pfdo/r/Xi48W7sQjk8uw4oOK38W43trzfJz5j8OBsjK4y8qQX1amdRwWy5drA8KyMjv/uk8fLVgFgFNP1VAzoPLJBQUa1v73v3XfNddoGoGzBm2//XSiBag6h1W/lpvLtJlUpKGeWLJtLb2C4/OJPPqoSFqaiMsVsEgixoh06SLy0UctOoSILFwokpmp4zn1VB1vJCKtJDlxRrmmTKkbrbMiWMHnxpqNG0UuuECkTRt7bLvvLnLbbSKVlbEfTyqBJF9BBjAEwIagfX8DsCjEuV4AvRy3e8Lfhy/SY9RnfyZNCvzexHo79NC6dsvlsr/Pwd/r9HTdgq9jrQY/+aRIRkbjxpCerrYmM9O2PcHXtWzH0qW2PavvmsFjycysa4OWLtXru932+K3bGRmhn2tDtrQ0vXa48Trto4jebup7mJkpMmpU3f1ud+Drlp1d9/10jmfp0rqvV1Pez7S00GMJd/6oUTo263MY/J6HI9ntT2O2xtgq55YsESyRuvOEpUsDv385OfUHiYK/z6E+Qw05JyQ+n8jOnRqx+ukne/9//yvy2GM6+GuuERk7VmTyZPv4UUeJdOokkpVlP5kTT7SPd+wY+EVp107k0kvt42eeKXLuuSKXXy4ycaLIgw+KfPCBPaYVK0RWr9b0m9raBj4Z0lwaY38YwWoCZWXa3XzOHDta5eToo7UpbWFhfMZ3333A1Vfr//fcA1x1Vf33CbeS5CRUH6ysLFuG/qqrAmsMYt3IT0TrZqdO1ToAQBWGjjlG6xL69o3dWEhCUw4guKggH8DOBpybD6Dcb2ibzM03A7vtBjzzjNqPr76yVf7S0lQafZ99NNpqqXx27qxKg7/+qrU4lZVaQ5iZqX321q7VBdOsLP3cV1Tolpam51ZV6fVycoAvvsDv7RUsnLedzy4tTWuBcnNtKffcXO1DAwA9e2qUfPx4rfGpqNDHT0vTrUsXjaRXVGj9UFNqsJyyyw2pwbJqf4DQNViRBHuiVYNljTdSDZZ1uzk1WF27hq/Bcj7PSDVYixbVfb2cryFrsOJGY2xVUhI8T7jppkBdjJtuUptW3zXqE8ZqsniWMaoKkpcXuP+44yLfz5I+BPQLsX17oGF97DH90FviIGVltoSsiBa3b9umx3f63+4JE4DBg9WgB8vN5udrf49rr9VrnX22HTmztqOO0vvt2qU/Ok51x3h3s09BTDPnCQnLwIEDZfny5VG/7scfa2R47Vp7n9PBmjhRDUI8JL1FgNNOUxGLjAz9QTzqqIbfv75eEFOn6sTQ69VJ3+2326qB8fxhXL1apdTnzQtsBnzZZdoMOI3LCFHFGPOJiAyM9ziaijEmF8A2AL1FZJV/3ywAv4jIdUHnLgUwQ0Se8t8+D1qTFbEtd1Psz6pVms66YIF+p6qq1HEYOlQn3iNG1O330hxqavR3e+dOnbQ352+wCEc4cnJ0HtCmTfP+5uU1vL0ESS2S3f40hsbYKictNf9paY45BnjzTft2RgZw3nmNF8lKOWpr1di6XOoQVVcDr78eqN5YVgYMH64/FL/8og6gdXz7dl1Be/hhnRR99ZWufjjJzgaeekrVT779FrjiikAHrKBAV2V69lT1pZUrA49nZ7eKNMfG2B9OPRuICPCPf2hkKJRP2lbVRTF8eOzHBujq8CGH6PeiY0dNH95zz+hdv7RUm5FakxoryhXrKJWF16sLQA88oA4WoKtcp56qjuDee8d+TCQ5EJEKY8zLACYZYy6AKnOdCGBQiNNnAbjCGDMfgAC4EsDDLTGunj11UeCyy3SB8r331NlasEB/SwFN4R8xQh2uP/xBo1dNJT1dow/t2jV/7Jaz5nS8GuqcrV0beDtUY/ZQ5OY231Fr04bOGklcGmmrEorGNO/1+XRRdP16vX3FFWoDZ8zQOf/Mma28P1VaWqChzsgA/vKX8Od36WJLwAL6ApeX26vNRUW6Ih3soPXqpcd37dLo2o8/6vFt29TI9+mjP1QffKAyuE7S04F33tEfprff1hB1sIP2t79pKHv9ep24OY+3aZNyzUbpYDWArVuBc87Rz2OolMABAzRdMF51pd9+q4Zn+3bg8MOB999vfLQ3ksiF81hamn5H4rWi9MUX2gz47bftNIL999cI1llnpdz3k7Qc4wE8A2ATgC0AxonI18aYIQAWiIiVD/IkgL0AfOm//bR/X4uSk6MLkMcdpws6339vO1vWwkJOjn4vjz1Wt+7dW3pU4Ymms1Zd3fRo2tq1gbeDmyuHIzc3epE12iASZULaqvgOKTINFc0qLdWo/V136e+5McBHHwEDB+pCaW0t+1NFBUtu3yI/3xbrCEX//vpGWIhomoLloB1+uP4YBTto3brp8dpaddJ+/dU+VlmpinCdOwMvv6zpjk6MUaerWzf1rGfOrOugXXedRsq++Uav7Tzetm34rtNxgg5WPZSWAn/9qyryWTgjWBdfDNx/f/zSV196SZuqe73AuHE6+WoKkZrtOY8BtiM5dWpscuerqtQAP/GEfqcAndCMHq3NgK1aEEIaiohshfa3Ct6/GECe47YAuMa/xQVjNHK13376m1RRYUe35s/XhR9AFxosZ2vIkOZFt+JJRobalWjUsFZVNT0NcvXqwGhccL/UcOTlRS+yRmeNhLNViUxDmveWlgJHHml/rzIztTawTRu93ZC6cBIjjAlUWOzYUfM5w2H9EDmpqbFTBU45BTjwwLoOWvv2etzl0on26tX28e3bdXUdAJ58UiW6nbhc+hgulzZ7fOutQAesUydtdApoIWhZWaDztttuUf/RpIMVBp9PJUKvvz7wR05Eb2dmaoH6GWfEb4xnnw0895yOZ8YMjbIBjQvNW0QyZsHHCgt1daqqSl8n6/WIdgh/8WKtZ1uyxG4GPGCA1rkdd1yrSPclpA65ubr4ePzxao9WrrSdrUce0QWf3NzA6Ja1sNjayMzUzfrdbg6WsxbJMQt3bPPmwHNCNaMPRV5e0xy04H25uXTWSOxoiHN0++2Bixa33GI7V0AzRClIYuKMLnXtqls4xozRzYlV/A9oDunJJwc6aJWVtpHLy1OHcONGTf8oK9OUD8vBmjwZ+O9/A69/0UXA44837zkGQQcrBJs3a3TkjTd0Eh+strX33sDcucABB8R2XJbjNGSIrmR/8onuT0/X1W3rnMb2swJsY2apRoU6Zhk6a3XKel2svhLRCOHv2KGLDzNnamQMUIduzBj9boRqKE9Ia8UYTZvv1Qu4/HJNs3dGt6x+WwccYAtlHHEEBaOaQrScNZGGOWvh/m7eHHi7Ic6aJYQWjTRItuwh9VGfczRypNooi+xsFfMJdR06VgRAYKFst26RVw2vvFI3J87Us4ce0uiJFTnbvt2uP4sidLCCWLxYUwI3bdLbwT8kp56qkrrOlZZYYDlOHk9dkY3aWtu5sdTHfD79G+z01BfdspoDBxeVBhu6jIzACFZzQ/ivv64O1Kef6vNzu7VWcvJkdSgJIfWTl6cS4iecoN+j776zna2HHtIWDnl5gdGtJOlJmjIYo4I8WVkqmd4cLGetqeqPGzcGRtasNPD6xt+mTXTSIOmspS6hnCMRbTnwww96+6KL1P5Yc4epUxmtIi2E09D06BFdSd4w0MHy4/PZMuRutx2dEdH3xe3W1JtLL43PD8KiRYHOVVGR/jjW1gY6N4WFgZElZx2DM7rldteVP21I3jQQuDrVnBqsTZuAG29U9UWrzUOXLmp0r7kmeWtICEkEjNG6rP3314yK8nLg3XdtKfhXX9Xzeve2o1uDBzO6lUw4nbWOHZt3LauOvalpkL/+Gni7Ic6ayxUYWZs/P75iLaTlKC/XMpjKSv3cvvuuPW9pauYNIYkMHSyoo3LWWaowadXWWRijP1xz5gCD4iiMum2bPa60NGD2bP3fGY0qLbWbH1u1YlaanXWu5UB5vVon6IxUNaaotKmhexGtG7vzzsBmwCNGqIN70EGNvyYhpH7y8oA//1k3EVUftZytf/xDa07z8oBhw2wp+D32iPeoSayw6tizs6PjrO3a1fioWm5udJ4LSSxWrND6aRFdOP3558BU24Yu7hKSTLR6B+vdd1Wo4rff7H1OB6ukBHjxxeb/4DSH885TEQu3GzjzTFULdKbuAfYKUFVVoBBHKLEKKxImEmjMWrKo1GoG/NprdlPSHj20bmTcODYDJiSWGKN1WQccAFx1lU5wFy60peDnztXz+vSxUwkHD044FVySoBijNeU5OVR5be1MmwZceKH+37Wr9tMMFlyhYiBJRVrttNbrBSZN0i09va6QBaDpa7fdFr8mlB6PTmo+/VQVJD/+OHwDXafwhMulq9AjR6poxaxZdiqgJWQxY0bd9EIgukWltbUqG//gg3Yz4OxsrXGbOhXYa6/oPA4hpHm0aQOcdJJuIsDXX9vO1v33A3ffreccfbTtcEUSgSKEkDFjbOGsdu2AUaO05UrwAi4VA0kqYiRYMSFFGDhwoCxfvjzs8ZdfVgfE5dLVNitf3OXSicTzz6sUeLxYs0ab7W3Zomlzy5YFtiEIJjiH+cEHgb//XSNagO5zht2bIuXeUL78Erj2Wk25tGRYDzhARVtGjWJRc7JjjPlERAbGexyJTH32J5nYsSMwumX1BDzoINvZGjSI0S0SG2h/6icR7E+fPsBXX4U+FjwfISRZaIz9abURLCtiZcQLn88A0Jh1366/Yc7b+eixX4bq52/cqInhOTn233btWtRLWLBA6yRqa7WXm1PONJxjFE5K3aKmJtCgBUeqmutwVVVpXdWTT9rNgPPzdQVrypTmq2URQuJDfj7wl7/oJqKTJsvZuu8+XZHOzw+MbnXpEu9RE0LigcejaaE7dujtfv2Azz4LPKe6WiNbdLBIKpMUDpYxph2A6QCGA/gNwPUi8kJzrmnVXPkcAbw/4h1cuP4JfL/qRaz9Fch6dB6yXnoWWfDYm7sWmTt/Q2Ym4LpkvKpKOJ2vTp2AefP0go8/rrMRp4PWsaPdQO3jj1Vax3H/O57uiJum5vmfN/D+++r8WCIWkZR2wkmpA1rjtG6dfS0nzVHwCdUMeOBAuxkwISR1MEZXpvv0UaXPHTs0Um1Jwc+Zo+f17WsrExYXs8aSkNbAypWareLzaUR79WptDxHsYDWHlsy+ISSaJMvP3qMAqgF0AtAPwOvGmM9F5OumXnDlSv0rsAusFmIYFmIYcIK150r/5sALIEf/TXc/jCzXfcjeUY0sU40sU4WslTXIPNQvnfvjEGT91gNZ3grd4EFWW4PMr/zHn/8cWau/RRY8yIAHj2McVqAH3G51Vh6Si9Fr13cwww1+6OBCRqUbt+46CNfhLhWzuPY6YP9tQG4uft6agx9+zUHnoQeg13UnobgY+PTOt/D2OwYbduTgndJcvDctF3Ont8NJ5xc2SZ7dYscOdaBmzQpsBnzOOdrLKtY9wggh8SE/Hzj5ZN1END3YUia85x6Nardtq9GtESM0Ir/77vEeNSEk2jz/vKoxA5qx8ssvurBSUGArG1tkZmpdeGOhnDtJJhLewTLG5AIYCeBAESkH8IEx5jUAZwO4runXbf7Yarxu1HizsbMm+/daLlMNmM+s6x+omxsQl1oXqQB891spiheEvK5VD3YpHtV/yv2bA58POGLxFKQvrkEGqn/fat9yI+tRNWpZ33VAZm05slCJztiC7vDgV9/ueOKJIXjqKeAaczfauCqRke7FRK/AB4MVcgiM+TPemO9D1r2TkZXr1q1NOj7Y1BMPfzUUX65uo82AXT4ceeA23HHROgw+zKtRuNrOAHazrSkLrghpFRijdVkHHaSKodu3a3TLcrheeknP69fPloE//HBGtwhJdi6+WAWtAHV4li61j5WU6IJydbV+188913auGttYmHLuJJlIeJELY8zBAJaKSLZj31UAjhSRE4LOHQtgLAAUFRUNWLt2bdjrPvMMcP75LTPmhhC8opO8+GDggwsCF3wwbgN3RgbSXF64KrYjDV64jQ/pxgu3y4f0wnyk75aPDHiQvmE9MtJ8yEwXZGYIsjJ9yOq+OzI7t0MOKpG1eR3y8gyy8lzIa+tGTts05Ba1R9tOOcjN8aJtG0Fe2zRkZKjhdrv1rzG2X+f07xqyr6nHonGtZIFF5vWTCEXmiYQI8MUXtrO1dKlOkgoKgOHD1dk65higc+d4j5QkOrQ/9RNL+3PooVrtAKiw1j/+Ufec4LS+pkaiGMEi8SbVRC7yAGwP2rcdQJ1ENBGZBmAaoAYm0kULC6M1vKaRGs4VAL9r5YVmT8ILYBcAuAG001PEv/kAbPRvyALQs+7lvrf+yQHQK8Ljxkk7P0YEO12RHLJoOX55ecCGDU0fMyHhMEbrsvr2VTXRsjLg7bdtsYx//1vP69/fFso47DBGtwhJVGpqNN3XKhO4/XZd5AxV5x1MUyNRlHMnyUQy/HyVA8gP2pcPYGdzLnrkkSrQANjOTvDfxh5z/v/117pi26ePFn0Gn//EE9p01xjgiCNUNXD//YFvv9X+W7W1djM+n08nGpMmAb16hX7slSu1/uHAA4F99w0/rpUrdWwHHFD3vI0btanyp5/a8uodOugK85FH2lE3r1fH5Pwrov9bm3VMRK9VWxv41+vV/6urVYijqgqoqRZUVQtqa12o8XhRXV6F2hpBTY2gtgbw1gpq07PhRRq8nhp4d1X5H8fAJ4BXDHzpmRC44av1QmpqITDwwUCgnoQYNwADO3KbmOGjYAc8Fg65JYhCSEtTUACceqpuPh/w+ee2szV1KnDHHdr7zxndYsNaQhKDNWuAnj31N9zt1nnDmDGhI0uhok7NaSwczV6dhLQkyeBgfQ8gzRjTU0RW+ff1BdBkgQtAf+CPOKLZYwtJaSlwww2hjU1NDTB0qKrutWmjecvr12tD4eJiVd4bPFhXaNatA556KtBhOfHE6I7V6wUeeUTD+s5mwCNH6kSne/foPl5kDGyHx43f1URCku7fwuFGnSjX73VhAHbsBDZsgK+8EtVllfBsr4KnzIOqQUNVL/LDz+FZ9hk8O2tQWe5FRbmgosKg8rRzUVGTgcp3S1H5yXeorHZjV3UadtWkYZc3DZ5j/oKqKgPPV6vg2ViGamSiChmoQiZqkIGaDl1RXQ3UlHtQ4zWoRToEruDBNxL5/WnZ4SlxOGUNcyKTLVWRpAYuF3DwwbrdcAOwbVtgdOtf/9LzBgywlQkPPTR+DeAJac3MnastGwDNerjqKuDdd+tGpAB7HhN87PrrGYkiqU/CO1giUmGMeRnAJGPMBVAVwRMBDIrvyMITLvz966+aArNhg0aPHnlEHaZgR8zaSkuBmTObtspTH6GaAffurYbvzDNTdLLtfFL5+UB+PlzQZMWs4HP36wuM7hv+WlcVA4jwq1DWAdiWBlRUAJU79G9NDTC8qx6f/65K+FdUoLbcA8/OGlSl58FzwyR4PIBn8r3wfPQFPLsEnkofPB6gqsMe8Nx2l3189S+/NxCoQiY8nbrDc+JpevzVt+DZ7oEHWdiFbHhcOdiV1wGejt30+ObtqKpNg8eXjhrJAABkpvuAZjt7hDSP3XYD/vpX3Xw+lXi2ZOCnTAEmT9ZWhMOHq7P1pz9p9wtCSMty7bXA3Xfr//vsA/zvf3ZqoJXOm5GhJRhW1Cr4mDWPYSSKpDoJ72D5GQ/gGQCbAGwBMK45Eu0tTajw9//9n04Iqqp09eell7RBZ6Q85GjnG1dVaVRq2rTAZsDnnKMpOWwGHEUKCnQLx4gRukG/hHn+7XdmXBX5+idfoHr5lZV+J65StW8P9R+fvU11cp3H99kHuPRSPX76hRo6raiAVFSiuqIGVa/MB7B/k54uIS2By6WLUv37a+r01q2B0a3Zs3XdZMAAW5nwkEMY3SIk2pSUaF9OADjvPP05uflmW/X4b38Dior0POcic/AxOlWktZAUDpaIbAVwUrzH0VCCHaOPPgIuv1yPTZmiUSKgriNWWFhXtjQaqzyLF+vkZMkSXRE2RichEyf+PscnyUZ9Dtzpp0e+/+zZv/9rAGT6N0ISmXbtgNNO083nA1assJUJJ0/WOtXCQo1qHXus/uXCESFNx+sF9tjDFkCaPl0drNLSwPmL1VuztFTTAp1RK2ffTUJaC0nhYCUjxcXa4+Wss4AXXlAjM2+eRrGc51iOWGEhMGFC9ORHrWbAM2fqqi8AtG9vNwPOy4t0b0JSE2NMOwDTAQwH8BuA60XkhTDnXg1gDIBu/nMfE5F7YjVWEhmXSyNXAwboSvqWLcBbb6mz9cYbanetxSRLmXDgQEa3CGkoGzdq5Km6Wr9vn32mwl1A3fnLokVaemDNY9xujVzRuSKtFTpYLURlpcoMf/WVBhqOOw54/HHglVcCDY4VoZo6NToN9F57DbjtNl3ZFVEjV1KikTMaOULwKIBqAJ2g9ZyvG2M+D5NybACMBvAFgL0BvGWMWS8is0OcS+JMYSFwxhm6+XzAJ5/YqYSTJqldbN8+MLrVvn28R01IYrJwITBsmP6fl6fOVk6Q7pQ1p7DqrYyxlYQBdc6sqBYFLUhrgw5WC/D99+pclZWprPqqVcDzz9vHn35aa7KchqY5sqUbN6r61n/+A+z0i9d37QqMGwdcfbVej5DWjjEmF8BIAAeKSDmAD4wxrwE4G8B1weeLyN2OmyuNMa8CGAyADlaC43Jp5OqQQ4BbbgF++y0wuvX88zoZPPTQwOiWixovhOD22/V7A6gg13ffhRe+ctZbuVy6qGuMPY9hc2DSWqGDFWXmztXeLrW1Gh53u9U4OamtBWbNarqgRWkp8N57gMejYhnffqv709OB44/XaNiBB0b7mRGS9OwLwCsi3zv2fQ7gyPruaIwxAIYAeDLCOWMBjAWAoqKi5o2URJX27VUd9cwzdXV9+XI7unXbbZpO3aFDYHQr3s3oCYkHI0bo9wLQuYzVBDwc1uJwVZU6WJdfrlk71iLxxIl6zOdrXnYOIckGHawocvPNWmjtcmn/qgsu0ChSOILD5g0RtJgzx5Yvtth7b+CKK4ALL2R9ASERyAOwPWjfdgBtGnDfiVAN+xnhThCRaQCmAcDAgQNj0BqaNAWXSyNXhx6q9aibN9vRrQULgOees8+x+m7178/oFkltfD6gRw8VqACABx8ELrus/vsVF+u5l1yiUayHH9bFYkAjV5Zz5XJFv90MIYkMfzKigM8HHHOMOlc5OcCyZepcAVpvFZyil5mpTTX/+Ed1yv74R3W2wuH1qgHr0QM45ZRA5+rqq4EffgDGj6dzRVo3xphFxhgJs30AoBxAftDd8gHsrOe6l0BrsY4TkaqWGT2JFx06AKNGqWO1caPab0t+euJETTPcfXdgzBgV37REgwhJFbZtA3Jzbedq2jR1rkpLNSMm0vwEUIEZq/bKilJZqYOWczVsGNMDSeuCEaxmsnWrrm6uXQt06qSOVW2tfby4WFd05swB+vWzQ+fhmhE7+eILbey3cKHdDHivvbR9kderjprVUZ2Q1o6IlEQ67q/BSjPG9BSRVf7dfQGE7alnjDkPWp/1BxH5OVpjJYmJ2631s4cdps7V5s3Am2+qFPx//6up3S6XHrf6bh18MKNbJHkpLQUGD1ZRLIvLLtPbEyZoBMrtBh55BBg7NvQ1nGmCxmh6bZ8+gXXlEyfSuSKtC/4sNINnngE6d1bn6tBDVdTizjvtiFRpqaYI/v3v6iQ9/LCdDmgZJLc7MGxeVaWGqEsXoG9fLcjOydH0v82bgR9/1GZ/kydzNYiQxiAiFQBeBjDJGJNrjBkM4EQAz4Y63xgzCsAUAEeLyE+xGylJFDp0sFttbNqkNv3GG3XB6+abVRijSxdtf/Gvf2kkgJBk4YEHgEGD1JnKyrL3V1frorCV3ldTA1x8cfhIlpUm6Hbr+RMm6P6FC1Uwg3MV0hphBKuJ3HCDhs4BbajXv7/KAlsRqVmztAeVx2OvDDkjVcGiFrW1wJAhasC8Xlvh6rbbNP3QSTSaDxPSShkP4BkAmwBsATDOkmg3xgwBsEBErC5xkwEUAvjY2BJaz4nIRbEdMkkE3G7tbXj44Sr7vnGjRrcWLND2GDNnaiSruNhWJuzXj9EtkpgcdZSKZQH6Ga2utv/PyABGjtTjVkmC1xtZoCI4TXDWLJVppzQ7aa3QwWoCF10EPOnQErMcKCsc7nYDn36qqz/WMadsqUXv3qrQc/zxgc2Azz1Xi69zc2PydAhpNYjIVgAnhTm2GCqEYd3uEatxkeSjUyetsR09WhfIPvrIFsq46SbdOnfWBbJjjwWOPhrYbbd4j5oQrSW0nCsLn0/nKXvtpbXdY8dqxszd/mYVIpGVNZ2tZtLSNMPH66U0O2m90MFqBNXVwBFHAB9/rI33amr0hzUjQ/PwAWDDBv2BXb7cLu5MSwPOO89uMMxmwIQQkjqkpWmq1aBBmhK1YYMd3Zo7F/jnP9XOW9GtESM0BTxcbyFCWpLVq+3/XS77cyiiTtWECVpDVVCgx625zJYt4a/pzMpZt06VlCPVmBOS6tDBaiDr1mm+/ebNGnn68EMVoVi0SFd1Jkyo28nc5dL79O+vUuqXXqo9qyor9Zp77KHqf1ddpT2sCCGEJD+dO6vq4Jgxugj34Yd2dOvGG3XbfXeNbo0YodE8KwGsAAASbUlEQVSttm3jPWrSWigpAbKz7Ywbr9c+JqLZN1b5QmamLVQRSmI9VLuZ0lJNmY10P0JSHTpYDeDttzWNr7oaOOMM4Pnn1ZGyjMnUqbYiIKAGy+1WB+uTTzR1xMngwZpi2Lt37J8LIYSQ2JGWpjZ/8GAVJ9qwQcWLFiwAXn4ZmDFDfy8GDbKVCQ86iNEt0nIER5ucJQ+AnVUTXCseHIUqLVVRL8uRslIB67sfIa0BOlhBOFdjAE3le/NN/bF74AFbHcdJSUndVaCiIjVczn2AXue44+hcEUJIa6RzZ1UdPOccjW4tW6bO1vz5wPXX69aliy2UMWwYo1sk+jijTc88Y4tcWJLsllMUSVQrUrsZinGR1g4dLAfO1Rhj1GhYIhWXXx7auQLUiJxzjjbnA/R+q1draN26DWhEKzOT4XJCCCEa3TriCN3uuAP49VeNbs2fD7z0EjB9uh0BsxyuPn0Y3WotGGMWATgcgNVd838isl80H6O4WB2jWbP0tlUr3hCcwhZMBSQkkFbtYAVHqyZOtPs+BPPgg8B++9VttPfZZ8B11wHvvBO4Py0NeOghFbIAVARjyxaGywkhhIRm991VRfbcc1VEadkydbYWLNDfmeuuA7p2DYxu5efHe9SkhblERJ5uyQdoaLQpVL0VUwEJCU2rdbCc0Sq3WyNVNTXhz/f5tNFenz4qWjFlikasNmzQ423b6g/fN98Eni+iKzuNWRUihBDSuklP196IQ4Zone///mfXbv3738DTT9sRMEuZsHdvRrdIyxCp3opzG0Lq0mpbIAbnDgc7V8YA11wT2CSytlZFLnJy7EaThx0G3H8/cO21wGWXqTKPJXLh8wXmJhNCCCFNoWtX4PzzNXXwt9/0N+XKK7WH4rXX6uJfUZFmWcydC+zcGe8Rkygx1RjzmzFmiTGmJNxJxpixxpjlxpjlmzdvbvSDlJaqI19aGvp4qHorQkh4Wm0Ey5k7LFI3LdDl0h4Q990HXHGFXYu1di3QoYOmcNxyi0q1O1d1HnxQUwGd0u3MTSaEEBIt0tOBI4/U7c47gZ9/tqNbs2drD6L0dI1uWcqEBxzA6FYSci2AbwBUAzgdwDxjTD8R+TH4RBGZBmAaAAwcOFAa8yDholNOWG9FSONIaAerJQs8rdzhhQttp8h+XHWw/vlPYNUqda5cLqBnT+Coo4Czz7aNT/CqzpYtqgIF6Ioic5MJIYS0JHvsAVxwgW7V1cDSpbYy4dVX61ZUZNdu/fGPQF5evEfduvHPb44Mc3iJiBwhIh869s00xpwBYASAh6M1jtLSwPpzZ3SK9VaENJ2EdrD8tFiB5157AaeeWte5SkvTlMHvv7ebAQ8erE0hp01Tx8ta4Ym0qsPcZEIIIbHE+h0qKQHuugtYv95WJnz+ee15lJ4O/OEPtsO1//6MbsUaESlpyt0ARO2dsiJXlnPlcunnp7CQ9VaENJdWW4O1dCnQvbsWDvfrB3TsqPtF9Ifmz39WwYr16zUitWRJ6Pxja1Xn9ttDh9UJIYSQeLHnnsDf/ga88oouJr77rqavb9gAXHWVCmP06AGMGwe89hpQXh7vERMAMMYUGGP+ZIzJMsakGWNGAfgDgDej9RhWBo7lXA0bpvOYLVtYb0VIc0mGCNZUY8ydAFYCuFFEFoU70RgzFsBYACgqKop40fffBzweFaP47DN7f1qa/gC5XFooXFbGSBUhhJDkJyMDGDpUt7vvBtats6Nbzz4LPPGEnmNFt0aM0PYkjG7FhXQAkwH0AuAF8B2Ak0RkZbQeIHheM3GiPZdhvRUhzSPRHawGF3gCjSvytEQt0tP1f0vEwucDnnsOmDmzbnic+ceEEEJSBUt1cOxYTRP74AOt3VqwQBUKr7xSMz0sZ2voUCA3N96jbh2IyGYAh7TkY4Sb13C+Q0jziVuKoDFmkTFGwmwfAICIfCgiO0WkSkRmAlgCLfBsNldfrb1EbrklcHXOkmUPlw54/fU0NoQQQlKLzEytu7n3XuDrr4E1a4DHHwcOOgiYNQs44QSgXTtg+HDggQeAlSvthUmSvFjzGiBQpp3zHUKaR9wiWPEu8MzIUIGL0lL9Yamq0nTBRx5R9T9nBIvhcUIIIa2Jbt2Aiy7SraoKWLzYjm5dcYVuPXrYMvBDh2qPSJIclJbaESqgfpl2QkjjSNgUQWNMAYDDALwPlWk/DVrgOSFaj2EZmAcfBFas0H19+jA8TgghhFhkZqoAwrBh2htyzRrb2ZoxA3j0UT2npMRWJuzZk7VbiUpw36sxY+pm7XDeQ0jzSFgHCy1c4Ok0MG63/hDU1mrkyilJSgghhBCb7t1VdXDcOBWLsqJb8+erQuGECcDee9vOVkkJo1uJRHD/TkAdraoqLZMoLIzr8AhJCRJWpl1ENovIISLSRkQKRORwEXk7Wtd3GpiaGvv/qipV0rHykAkhhBASmqws4OijgfvvB777DvjpJ41o9eoFTJ8OHHecTtiPPRZ46CFg1ap4j5hY6oFut/4dPVozeVwunQdNmMA5ECHNJWEdrJbGaWDS0/V/l0tVBN95R6NbTgNTWhpYAEoIST6MMe2MMa8YYyqMMWuNMWc24D4ZxpjvjDE/x2KMhCQzPXoA48cD//0vsHUr8OabwIUXquN12WXAvvtq+uDf/64S8bt2xXvErY9Q/Tu3bFHREp8vdO8rzoEIaRyJnCLYogTXWQEauXrnnUADU1xcN1+ZBaCEJC2PQts+dALQD8DrxpjPReTrCPe5GsAmAHkxGB8hKUNWlqoODh+uEZIff7Rrt55+Gnj4YT1n6FCNcI0apUqFpOUJLoOI1OuTcyBCGk+rjWABgTKkxcXqYGVm2mFzy8AE5yuzqzkhyYcxJhfASAA3i0i5iHwA4DUAZ0e4Tw8AZwGYGptREpK67L03cMklwOuva8TkjTe0B9cPP2hEa+fOeI+w9RIqqmXBORAhjafVRrBCEU49MNLKDiEkadgXgFdEvnfs+xzAkRHu8zCAGwDUm8hkjBkLYCwAFBUVNWOYhKQ+2dnAn/6k2z/+ocqE3brFe1Stm3DiXpwDEdJ46GAFEcrAULadkJQgD8D2oH3bAbQJdbIx5i8A0kTkFWNMSX0XF5FpAKYBwMCBA9mClZBG0L17vEdAwsE5ECGNhw5WA6FsOyGJjTFmEcJHo5YAuBRAftD+fAB1EpP86YR3AxgRxSESQkhSwjkQIY2DDhYhJCUQkZJIx/1OU5oxpqeIWGLRfQGEErjoCaA7gMVGu6VmAGhrjNkA4HARWROlYRNCCCEkxaCDRQhpFYhIhTHmZQCTjDEXQFUETwQwKMTpXwHY03F7EIBHAPQHsLmlx0oIIYSQ5KVVqwgSQlod4wFkQ2XXXwQwzpJoN8YMMcaUA4CI1IrIBmsDsBWAz3/bG6/BE0IIISTxYQSLENJqEJGtAE4Kc2wxwvS6EpFFAPZouZERQgghJFVgBIsQQgghhBBCogQdLEIIIYQQQgiJEkYkNdu1GGM2A1hbz2ntAfwWg+G0JHwOiUFreg7dRKRDSw8mmWmg/QFa1+cmkUn255Ds4wdof6IG7U/SweeQGDTkOTTY/qSsg9UQjDHLRWRgvMfRHPgcEgM+B9IUUuE153OIP8k+fiA1nkOykQqvOZ9DYsDnUBemCBJCCCGEEEJIlKCDRQghhBBCCCFRorU7WNPiPYAowOeQGPA5kKaQCq85n0P8SfbxA6nxHJKNVHjN+RwSAz6HIFp1DRYhhBBCCCGERJPWHsEihBBCCCGEkKhBB4sQQgghhBBCogQdLEIIIYQQQgiJEinvYBlj2hljXjHGVBhj1hpjzgxznjHG3GWM2eLf7jbGmFiPN8S4Mo0x0/1j32mMWWGMOTbMuecYY7zGmHLHVhLjIYfEGLPIGONxjGtlmPMS9X0oD9q8xpiHw5ybEO+DMeYSY8xyY0yVMeafQcf+aIz5zhhTaYx5zxjTLcJ1uvvPqfTfZ1iLDz5FoP2h/YkGyWh//GOhDYojtD+0P9GA9qdp9iflHSwAjwKoBtAJwCgAjxtjeoc4byyAkwD0BXAQgOMBXBirQUYgDcB6AEcCaAvgZgD/NsZ0D3N+qYjkObZFMRllw7jEMa79wpyTkO+D8zWFfpZ2AfhPhLskwvvwC4DJAJ5x7jTGtAfwMvSz1A7AcgD/inCdFwGsAFAI4EYALxljGtTJnND+xGSUDYP2J/bQBsUX2p/EgfYn9sTV/qS0g2WMyQUwEsDNIlIuIh8AeA3A2SFOHwPgPhH5WUT+B+A+AOfEbLBhEJEKEZkoImtExCci/wWwGsCAeI+thUjI9yGIUwBsArA43gOJhIi8LCJzAWwJOnQygK9F5D8i4gEwEUBfY0yv4GsYY/YF0B/ArSKyS0TmAPgS+r0iEaD9SUoS8n0IIinsD0AbFE9of5KShHwfgqD9aaD9SWkHC8C+ALwi8r1j3+cAQq3g9PYfq++8uGKM6QR9Xl+HOeVgY8xvxpjvjTE3G2PSYji8+pjqH9uSCCHjZHgfxgCYJZF7HCTy+xDwGotIBYAfEf578ZOI7HTsS8T3JBGh/Umszz3tT+JAG9Ty0P4k1uee9idxiIn9SXUHKw/A9qB92wG0acC52wHkJUL+q4UxJh3A8wBmish3IU75PwAHAugI9a7PAHB17EYYkWsB7AWgK7SZ2zxjzN4hzkvo98EYUwRNV5gZ4bREfh+A5n0vIp1LAqH9SZzPPe1PYkEb1PLQ/iTO5572J7GIif1JdQerHEB+0L58ADsbcG4+gPJ6vPSYYYxxAXgWmk99SahzROQnEVntD6V/CWASNJwbd0TkQxHZKSJVIjITwBIAI0KcmtDvA4DRAD4QkdXhTkjk98FPc74Xkc4lgdD+JMjnnvYnMd4HB7RBLQ/tT4J87ml/EuN9cBAT+5PqDtb3ANKMMT0d+/oidHj5a/+x+s6LOf7Vi+nQ4sKRIlLTwLsKgIRY+QhBuLEl7PvgZzQir96EItHeh4DX2J+rvzfCfy/2MsY4V2sS7T1JVGh/Eutz74T2J77QBrU8tD+J97m3oP2JL7GxPyKS0huA2VAFkFwAg6Ghvd4hzrsIwLfQEG4X/4t3UbzH7x/bEwCWAcir57xjAXTy/98LwFfQwrx4j78AwJ8AZEFVgUYBqACwX5K9D4P8426TDO+D/7XOAjAVuvpnvf4d/N+Dkf59dwFYFuE6ywDc6z/3LwDKAHSI9/uRDBvtD+1PFJ9HUtkf/+PTBsX3M0P7E//x0/60UvsT9zctBi9wOwBz/R+MdQDO9O8fAg29WucZAHcD2Orf7gZgEmD83aArAB5oqNLaRgEo8v9f5D/3XgAb/c/1J2hoNj0BnkMHAB9DQ6pl/g/r0cn0PvjH9iSAZ0PsT8j3AaqMI0HbRP+xYQC+g8qtLgLQ3XG/JwA84bjd3X/OLgArAQyL93uRLBvtD+1PFJ9HUtkf/1hog+L7maH9if9zoP1ppfbH+O9MCCGEEEIIIaSZpHoNFiGEEEIIIYTEDDpYhBBCCCGEEBIl6GARQgghhBBCSJSgg0UIIYQQQgghUYIOFiGEEEIIIYRECTpYhBBCCCGEEBIl6GARQgghhBBCSJSgg0UIIYQQQgghUYIOFiGEEEIIIYRECTpYhBBCCCGEEBIl6GCRmGOMSTPGLDHGlBtjegUdG2uMEWPMpHiNjxCSutD+EELiBe1P68GISLzHQFohxphuAD4DsBbA4SLiMcb0BvAxgE8AlIiIN55jJISkJrQ/hJB4QfvTOmAEi8QFEVkL4HwAfQHca4zJBjAbgAfAKBoXQkhLQftDCIkXtD+tA0awSFwxxjwGYByApQAGARgpIi/Hd1SEkNYA7Q8hJF7Q/qQ2dLBIXDHGZAH4CsDeAJ4SkbFxHhIhpJVA+0MIiRe0P6kNUwRJvDkIQJH//wONMWnxHAwhpFVB+0MIiRe0PykMHSwSN4wx+dC8498A3AigGMBtcR0UIaRVQPtDCIkXtD+pD71lEk+eBNANwNEi8q4xph+A64wx74jIe3EeGyEktaH9IYTEC9qfFIc1WCQuGGPOB/A0gCkicqN/XwFUujQdwEEisiWOQySEpCi0P4SQeEH70zqgg0Vijr+53idQY3KkiNQ6jhUD+D8AC0Tkz3EaIiEkRaH9IYTEC9qf1gMdLEIIIYQQQgiJEhS5IIQQQgghhJAoQQeLEEIIIYQQQqIEHSxCCCGEEEIIiRJ0sAghhBBCCCEkStDBIoQQQgghhJAoQQeLEEIIIYQQQqIEHSxCCCGEEEIIiRJ0sAghhBBCCCEkStDBIoQQQgghhJAo8f9pBDgJpWNp5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "weights = np.random.randn(2,1)\n",
    "\n",
    "plt.figure(figsize=(12,4))\n",
    "plt.subplot(131)\n",
    "plot_gradient_descent(weights,0.03)\n",
    "plt.subplot(132)\n",
    "plot_gradient_descent(weights,0.05)\n",
    "plt.subplot(133)\n",
    "plot_gradient_descent(weights,0.01, weights_path=weights_path_bgd) #with a higher learning rate algorithm is converging much faster in much fewer iterations\n",
    "# 0.03 took 1000 iterations 0.01 converged within 300 \n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x219ff1ab518>]"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Stochastic Gradient Descent #Simulated Annealing \n",
    "weights_path_sgd = []\n",
    "m = x_b.shape[0]\n",
    "np.random.seed(42)\n",
    "\n",
    "n_epochs = 11\n",
    "t0, t1 = 5, 100 #learning shcedule hyperparameters\n",
    "\n",
    "def annealing(t):\n",
    "    return t0/(t+t1)\n",
    "\n",
    "eta=0.01\n",
    "weights = np.random.randn(2,1) \n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch ==0 and i<10:\n",
    "            y_predict = x_new_b.dot(weights)\n",
    "            style = \"b-\" if i > 0 else \"r--\"         # not shown\n",
    "            plt.plot(x_new, y_predict, style)\n",
    "        rand_instance = np.random.randint(m) #choose a random training instance\n",
    "        xi = x_b[rand_instance:rand_instance+1]\n",
    "        yi = y[rand_instance:rand_instance+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(weights)-yi)\n",
    "        eta = annealing(eta*m+1)\n",
    "        weights = weights - eta*gradients\n",
    "        weights_path_sgd.append(weights)\n",
    "        \n",
    "\n",
    "plt.plot(x,y,'b.')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Add Ridge Lasso - Models with Contours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}