Gaussian Naive Bayes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples=20, centers=[(0,0), (5,5), (-5, 5)], random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x20a063adcc8>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fO4XJyJEjtWDBAm3dulXjxo3TSy+9FNCxr3O5XPL5fDpz5sx5P5f9+/fL5/N1eOXFxYqZrRzHjx/Xs88+q/nz52vBggX68MMPtWTJEknS3Llz250pKyvrzIgBicZMiE6cKwgE5wkCxbmCQHCeIFCcKwhEOM+T+Ph4ud3ugNc7LrlcPUoPBv0+LZcOUHNzc9BzHXnkkUd04403atKkSVq8eLFycnJkmqZ27dqlJ598Uvv27ZPf75ff71dzc7Pi4+OVkpKi559/Xunp6frss8/08MMPy+l0yuv1qrm5WeXl5Vq/fr2mTp2qSy+9VOXl5Tp06JDuuOMOlZaWdnisvc9rxIgRSkpK0i9+8Qv94he/kMPh0AcffKBRo0YpNzdX0ldlydy5c7V69Wp5PJ4Lfs6nT5/WF1980eb1rKysDmdippgwDEOjR4/WsmXLJElXXHGFjh49qj/96U8dFhPn+8StUFZWFnWZEJ04VxAIzhMEinMFgeA8QaA4VxCIcJ8n9fX1io+PD3i9cdNdMg6+H9QNMI2kNBk33RXU+1xIdna2duzYocLCQj3yyCP67LPPlJKSohEjRuiJJ55QfHy8HA6HHA7Hufd9/vnntXTpUk2aNElDhgzR8uXLdfvtt8vlcik+Pl7Jyck6fvy45s6dq+rqavXt21e33nqrFi1apNra2g6PuVyuNvn69eunl19+WcuWLdP3vvc92e12XXnllfre976n+Ph4eTwe/fCHP9Q999yj8ePHB/Q5JyYmasCAAUF9nWKmmLjkkkva3E9i6NCh524AAgAAAACAJJkp6fJnDpd9386AZ/yZw8P2qNCvu/TSS7Vy5UqtXLmy3eNPP/10q48nTpyod999t9VrJ0+ePPfvffv21QsvvNDur3W+Yx25+uqrtW3btjavm6ap+fPna8KECZo1a1ZQv2awYuYeE1dffbU+/vjjVq99/PHHQTcxAAAAAICuzzPvfvkzcwJa68/MkWfefRFOFFvee+89vfbaa+fuUzFu3Dh99NFHEXmvmLliYv78+ZoyZYpWrVqlm2++WQcPHtQf//hH/epXv7I6GgAAAAAg2rh7qGlJodxrHpXjSHG72zqMpDT5M4d/VUq4e1gQMnqNGTNGtbW1nfJeMVNMXHnllXrxxRf18MMPa+XKlbr88st133336e6777Y6GgAAAAAgGrl7yPPzX8tWUynX5hfkOHnsq0eCOp3y9x8s7/Q5Edm+geDETDEhSVOnTtXUqVOtjgEAAAAAiCFmSrpa7lhodQx0IGbuMQEAAAAAALoeigkAAAAAAGAZigkAAAAAAGAZigkAAAAAAGAZigkAAAAAAGCZmHoqBwAAALoGW02lXJvWyVFR/q9H9/XL+OrRfSnpVscDAHQiigkAAAB0Hk+T3GseleNIsex11a0OOUoPyrl/l/yZw+WZd7/k7mFRSABAZ2IrBwAAADqHp0k9Hr9Hrn3vtCklzrLXVcu1b6d6PH6P5Gnq5IAAACtwxQQAAAA6xdkrJQLhOFIs95pH5fn5ryOcCkB3YHiq5D22QUbjCZmmTzabU/Zeg+TKuE12d5ql2X784x+rpqZGr7zyiqU5rEQxAQAAgIiz1VQGXEqc5ThSLFttlcxka79pABC7TH+zPMUrZNSXymz515VapiSj/pD8le/Jnpgtd+5i2RzxEcnwxRdfqLCwUNu2bVNFRYVSU1OVm5uruXPnasqUKRF5z1jDVg4AAABEnGvTug63b3TEXlct16b1EUoEoKsz/c1q3r9U/srdrUqJVmtaquWv2q3m/Utl+pvDnqG8vFwTJ07UW2+9pWXLlmnXrl3auHGjpkyZooKCgrC/X6yimAAAAEDEOSrKQ5s7eSzMSQB0F57iFTJOlwS01jhdIk/xirBnWLRokUzT1Pbt23XTTTcpKytL2dnZmjt3rnbu3NnuTFFRka6//noNGjRIGRkZuvnmm1VaWtpqza5du3Tttdeqf//+GjhwoCZPnqzi4uILHutITU2NCgoKNHToUF1yySUaM2aM3nrrrfB8EQLAVg4AAABEns/XuXMAujXDUyWjvvTCC78+U18iw1Mtuzs1LBlqa2tVVFSkBx54QL169WpzPCkpqd25xsZG5efna8SIEWpqatKqVas0a9Ysvf/++4qLi5PP59Ps2bM1Z84crV27Vl6vVwcOHJDD4TjvsY6cPHlS1113nUaNGqX169crPT1d7777rnr37h2Wr0MgKCYAAAAQec4Q/9oZ6hyAbs17bEOH2zc6YrbUyHt8g9zZPwtLhqNHj8o0TQ0dOjSouRkzZrT6+A9/+IMGDBigffv2acyYMTpz5ozq6+s1bdo0DR48WJLOvUdtbW2HxzqycOFC5ebm6sUXX5TNZpMkDRkyRJI0ZcoUNTY2yjAMzZw5U0uWLAnqcwkUf9IDAAAg4vz9BslRejD4uf6DI5AGQFdnNJ4Iba4htG1n7TFNM6S5Y8eO6ZFHHtHevXtVXV0twzBkGIY+/fRTSVJycrJmz56tW265RRMnTtSECRM0c+ZMXX755ec91p5PPvlE//jHP7R9+/ZzpcTXvfrqq0pMTJTf79e0adN0/fXX61vf+lZIn9f5cI8JAAAARJx3+u0ykoK7PNpISpN3+pwIJQLQlZlmaNvAQp1rT2Zmpmw2mw4fPhzU3KxZs1RVVaUnnnhCRUVF2rFjh5xOp1paWs6teeqpp1RUVKSxY8fq9ddfV15ent58880LHvumgwcPyul0atSoUe0eT0xMlCS1tLS0ev9wo5gAAABAxJkp6fJnDg9qxp85nEeFAgiJzRba5oBQ59qTnJysyZMna+3atWpoaGhzvK6urs1rNTU1Ki0tVUFBgSZNmqTs7GydOXNGvnbutzNy5EgtWLBAW7du1bhx4/TSSy8FdOzrXC6XfD6fzpw50+HnMXnyZGVlZWnSpEkRuVpCopgAAABAJ/HMu1/+zJyA1vozc+SZd1+EEwHoquwJA0Ob6zUorDlWrVol0zR1zTXXaOPGjSorK9Phw4f17LPPaty4cW3WJyUlKTU1VevWrdPRo0e1c+dOFRQUyPm1++0cP35cDz30kN5//32dOHFCO3bs0EcffaTs7OzzHmtPXl6ekpKSVFBQoH/+8586fPiw1q1bpw8//PDcmjfffFPFxcX68MMPL/h0j1BxjwkAAAB0DncPNS0plHvNo3IcKZa9ru2N6YykNPkzh39VSrh7WBASQFfgGjxb/qr3g7oBpi0uVa6M2WHNkZGRobfffluFhYVatmyZPvvsM6WkpGjEiBH67W9/22a93W7Xc889p6VLl2rMmDEaMmSIli9frttvv/3cmp49e+rjjz/WnXfeqerqavXt21ff//73tWDBAtXW1nZ4rD0pKSl6+eWXtWzZMl133XWy2+268sorNXXq1FbrEhMTNWHCBL355pvKyQmsYA6Gra6uLrQ7ciBoZWVlysrKsjoGYgDnCgLBeYJAca4gEJ19nthqKuXa/IIcJ4999UhQp1P+/oPlnT6H7RtRjj9TEIhwnyf19fXq06dPUDPNBx+Wv2p3wOsd6WMVP/LBYKN1WXV1dfL7/UpNTVVzc7NuvfVWzZ8/X9OmTTvvXCi/V1wxAQAAgE5npqSr5Y6FVscA0IW5cxeref9SGadLLrjWnjhM7pzFnZAqdtTV1emOO+6Q1+uVaZqaOXPmBUuJUFFMIKoZnip5j22Q0XhCpumTzeaUvdcguTJuk93NT1MAAAAAtM/miFf86MfkKV4ho75EZktN2zVxqbL3yZY7Z7FsjngLUkavs9tQOgPFBKKS6W/+vz9ASlvtCzMlGfWH5K98T/bEbLlz+QMEAAAAQPtsjnjFj3zwqx94Hn9JRkP5N37gOVt2d3CPMkb4UUwg6pj+5gtecmW2VMtftVvN+5cqfvRjlBMAAAAAOmR3p8md/TOrY6ADFBOIOp7iFQHtA5Mk43SJPMUruEkNAAAAug1bTaVcm9bJUVH+r5vH9sv46uaxKelWxwOCRjGBqGJ4qmTUlwY3U18iw1PNJVgAAADo2jxNHT5u11F6UM79u/7vcbv387hdxBS71QGAr/Me2xDUs4YlyWypkff4hgglAgAAAKKAp0k9Hr9Hrn3vtCklzrLXVcu1b6d6PH6P5Gnq5IBA6CgmEFWMxhOhzTWUhzkJAAAAED3OXikRCMeRYrnXPBrhRJ3PNE2rI+ACQv09ophAVDFNX6fOAQAAANHOVlMZcClxluNIsWy1VRFK1Pni4+P15ZdfWh0D52Gapurq6pSQkBD0LPeYQFSx2ZwKpWOz2TiVAQAA0DW5Nq3rcPtGR+x11XJtWq+WOxZGKFXncrvd8vl8qq+vtzoKzqN3795yOoP/3ozv5hBV7AkDZdQfCn6u16AIpAEAAACs56gIbduy4+SxMCexVig/iUdsYCsHoopr8GzZ4oJ7uoYtLlWujNkRSgQAAABYzBfituVQ54BORjGBqGJ3p8memB3cTJ9sHhUKAACAriuES+Mvag7oZBQTiDru3MWyJw4LaK09cZjcOYsjnAgAAACwjr9faNuW/f0HhzkJEBlUaGjD8FTJe2yDjMYTMk2fbDan7L0GyZVxm+zutIi/v80Rr/jRj8lTvEJGfYnMlpq2a+JSZe+TLXfOYtkc8RHPBAAAAFjFO/12OffvDuoGmEZSmrzT50QwFRA+FBM4x/Q3/18ZUCqz5V9/6JmSjPpD8le+J3titty5kS8DbI54xY988KuS5PhLMhrKv1GSzGb7BgAAALoFMyVd/szhsu/bGfCMP3O4zOTI/1ARCAeKCUj6qpRo3r9UxumSjte0VMtftVvN+5cqfvRjnXKlgt2dJnf2zyL+PgAAAEA088y7X/bH75HjSPEF1/ozc+SZd18npALCg3tMQJK+ulLiPKXE1xmnS+QpXhHhRAAAAADOcfdQ05JCea8aLyOp/SuHjaQ0ea8ar6YlhZK7RycHBELHFROQ4amSUV8a3Ex9iQxPNdspAAAAgM7i7iHPz38tW02lXJtfkOPksa8eCep0yt9/sLzT57B9AzGJYgLyHtvQ6p4SgTBbauQ9voFtFgAAAEAnM1PS1XLHQqtjAGHDVg7IaDwR2lxDeZiTAAAAAAC6G4oJyDR9nToHAAAAAMBZFBOQzRbajp5Q5wAAAAAAOIvvLCF7wkAZ9YeCn+s1KAJpAJxPRUWFVq5cqdLSUp0+fVqJiYkaNmyYFi1apH79+lkdDwAAAAgaxQTkGjxb/qr3g7oBpi0uVa6M2RFMBeDrGhsblZ+frz179ujUqVOtju3evVt///vflZeXpzVr1ighIcGilAAAAEDw2MoB2d1psidmBzfTJ5tHhQKdpLGxUTNmzNDmzZvblBJnnTp1Slu2bNHMmTPV2NjYyQkBAACA0MVMMfGb3/xGSUlJrf4ZOnSo1bG6DHfuYtkThwW01p44TO6cxRFOBOCs/Px87d27N6C1e/bsUX5+foQTAQAAAOETU1s5srKytGXLlnMfOxwOC9N0LTZHvOJHPyZP8QoZ9SUyW2rarolLlb1Pttw5i2VzxFuQEuh+KioqtGfPnqBm9uzZo88++0yXXXZZhFIBAAAA4RNTxYTT6dQll1xidYwuy+aIV/zIB2V4quQ9/pKMhnKZpk82m1P2XoPkypjN9g2gk61cubLD7RsdOXXqlFauXKnVq1dHKBUAAAAQPjFVTBw/flzDhw+Xy+VSXl6eHnzwQWVkZFgdq8uxu9Pkzv6Z1TEASCotLQ1prqSkJMxJAAAAgMiw1dXVmVaHCMQbb7yhhoYGZWVlqaqqSitXrlRZWZnee+89paSktDtTVlbWySkBILzuuusuHToU/ON8R4wYoeeffz4CiQAAAIDgZWVldXgsZq6YuO6661p9nJeXp1GjRmnDhg366U9/2u7M+T5xK5SVlUVdJkQnzhWclZiYGPIc5xDO4s8UBILzBIHiXEEgOE8QjJh5Ksc39erVS8OGDdPRo0etjgIAEZOdHdyjfM8aNiywp+wAAAAAVouZKya+qbm5WWVlZRo/frzVUQAgYu699169/vrrQd0A87LLLtO9994bwVQAAODrbDWVcm1aJ0dFueTzSU6n/P0y5J0+R2ZKutXxgKgXM8XEAw88oGnTpunyyy8/d8Qw6C4AACAASURBVI+JL7/8UrfddpvV0QAgYvr166e8vLxWj0q+kLy8PB4VCgBAZ/A0yb3mUTmOFMteV93qkKP0oJz7d8mfOVyeefdL7h4Whex+KIpiT8wUExUVFbr77rtVXV2ttLQ05eXl6Y033tDAgQOtjgYAEbVmzRrNmDFDe/fuveDab3/723rmmWc6IRUAAN2cp0k9Hr9HjiPFHS6x11XLvm+n7I/fo6YlhZQTkUZRFLNipph47rnnrI4AAJZISEjQ3/72N+Xn52vPnj3tbuu47LLLlJeXp2eeeUYJCQkWpAQAoHs5+w1wIBxHiuVe86g8P/91hFN1YxRFMS1migkA6M4SEhK0fv16VVRUaNWqVSopKdHp06eVmJio4cOHa9GiRWHbvnHDDTdo69atYfm1AADoimw1lQGXEmc5jhTLVlslMzktQqm6N4qi2EYxAQAxpF+/flq9erWk8D6Ga/fu3fL5fJowYcK5195++225XC6NHTs2LO8BAEBX4dq0rs1WgQux11XLtWm9Wu5YGKFU3RdFUeyL2ceFAgAubOPGjerbt69OnDhx7rUlS5Zo1KhR+uKLL869NmDAAP3pT3/SokWL1NDQoEWLFunZZ5/VgAEDrIgNAEBUc1SUhzZ38liYk0C6uKII0YFiAucYnip5Sn6npn2L9OXeBWrat0ie0idleKqsjgYgRDNmzFBOTo5WrVolSXryySf117/+VX/961/Vt2/fc+sGDBigdevWqXfv3jpw4IB69+6tdevWUUwAANAen69z53BeFEWxj60ckOlvlqd4hYz6Upkt/2oaTUlG/SH5K9+TPTFb7tzFsjnirQsKIGg2m00PPvigbr31Vg0ePFiFhYXatGmTMjMzW607efKkHnjgASUnJ+uKK65QfX297rrrLi1fvlz9+/e3KD0AAFHKGeK3UaHO4fwoimIeV0x0c6a/Wc37l8pfubtVKdFqTUu1/FW71bx/qUx/cycnBHCxvvvd7+rKK6/U8uXL9fzzz+vKK69ss+b48eO68847tXr1avXq1UurV6/WnXfeqfLy0H4CAQBAV+bvNyi0uf6Dw5wEkiiKugCKiW7OU7xCxumSgNYap0vkKV4R4UQAwu3tt9/WoUOHZJqm0tPT213z7//+75o4cWKr1yZOnMiNLwEAaId3+u0yklKDmjGS0uSdPidCibo3iqLYRzHRjRmeKhn1pcHN1JfI8AR3YxkA1vnwww81Z84cPf7447rhhhv08MMPX3CGR4UCAHB+Zkq6/JnDg5rxZw7nCRARQlEU+ygmujHvsQ0dbt/oiNlSI+/xDRFKBCCcTpw4oVtvvVU/+clPNGfOHP3yl7/U9u3b9c4771gdDQCAmOeZd7/8mTkBrfVn5sgz774IJ+q+KIpiH8VEN2Y0nrjwovbmGthzDkS72tpa/cd//IemTp2qJUuWSJJycnI0c+bMgK6aAAAAF+DuoaYlhfJeNb7Dn9YbSWnyXjVeTUsKJXePTg7YvVAUxTbu9tGNmWZod6ENdQ5A50lOTtYHH3zQ5vXnn3/egjQAAHRR7h7y/PzXstVUyrX5ha8eP+nzSU6n/P0Hyzt9Dj+V7yz/VxS51zwqx5Fi2evaXhluJKXJnzn8q1KCoiiqUEx0YzabU2aIcwAAAAC+Yqakq+WOhVbHAEVRzOI7zG7MnjBQRv2h4Od6hXbXWwAAAACINIqi2MM9Jrox1+DZssUFd/daW1yqXBmzI5QIAAAAANDdUEx0Y3Z3muyJ2cHN9MmW3R1cmQEAAAAAQEcoJro5d+5i2ROHBbTWnjhM7pzFEU4EAAAAAOhOKCa6OZsjXvGjH5MjfaxscSntr4lLlSN9rOJHPyabI76TEwIAAAAAujJufomvyomRD8rwVMl7/CUZDeUyTZ9sNqfsvQbJlTGb7RsAAAAAgIigmMA5dnea3Nk/szoGAAAAAKAbYSsHAAAAAACwDMUEAAAAAACwDMUEAAAAAACwDMUEAAAAAACwDMUEAAAAAACwDMUEAAAAAACwDMUEAAAAAACwDMUEAAAAAACwDMUEAAAAAACwjNPqAAAAAACA6GarqZRr0zo5Ksoln09yOuXvlyHv9DkyU9KtjocYRzEBAAAAAGifp0nuNY/KcaRY9rrqVoccpQfl3L9L/szh8sy7X3L3sCgkYh1bOQAAAAAAbXma1OPxe+Ta906bUuIse121XPt2qsfj90iepk4OiK6CYgIAAAAA0MbZKyUC4ThSLPeaRyOcCF0VxQQAAAAAoBVbTWXApcRZjiPFstVWRSgRujKKCQAAAABAK65N6zrcvtERe121XJvWRygRujJufgkAAAAAUSJann7hqCgPbe7ksTAnQXdAMQEAAAAAVou2p1/4fJ07h26NrRwAAAAAYKVofPqFM8SfYYc6h26NYgIAAAAALBSNT7/w9xsU2lz/wWFOgu6AYgIAAAAALBKtT7/wTr9dRlJqUDNGUpq80+dEKBG6MooJAAAAALBItD79wkxJlz9zeFAz/szhMpPTIpQIXRnFBAAAAABYJJqffuGZd7/8mTkBrfVn5sgz774IJ0JXRTEBAAAAAFaJ5qdfuHuoaUmhvFeN73Bbh5GUJu9V49W0pLBznhaCLolbpgIAAACAVaL96RfuHvL8/Ney1VTKtfmFr67U8Pkkp1P+/oPlnT6H7Ru4aBQTAAAAAGARf79BcpQeDH6uk59+Yaakq+WOhZ36nug+2MoBAAAAABbh6RcAxQQAAAAAWIanXwAxXEwUFhYqKSlJ9957r9VRAAAAACBkPP0C3V1MFhN79uzRn//8Z+Xm5lodBQAAAAAuDk+/QDcXcze/rK+v149+9CM9+eSTWrFihdVxAAAAAODi8fQLdGMxV0wsWLBAM2bM0MSJEykmAAAAAHQpPP0C3VFMFRN//vOfdfToUa1Zsyag9WVlZRFOFLxozIToxLmCQHCeIFCcKwgE5wkCxbmCQHCe4OuysrI6PBYzxURZWZkefvhhvf7664qLiwto5nyfuBXKysqiLhOiE+cKAsF5gkBxriAQnCcIFOcKAsF5gmDETDHxwQcfqLq6WmPGjDn3mt/v1+7du/Xcc8+poqJCbrfbwoQAAAAAACBYMVNM3HDDDRo9enSr137yk58oMzNTBQUFAV9FAQAAAAAAokfMFBNJSUlKSkpq9VrPnj2VnJysnJzAnvkLAAAAAACii93qAAAAAAAAoPuKmSsm2rN161arIwAAAAAAgIvAFRMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyFBMAAAAAAMAyTqsDAAAAAACA87PVVMq1aZ0cFeWSzyc5nfL3y5B3+hyZKelWx7soFBMAAAAAAEQrT5Pcax6V40ix7HXVrQ45Sg/KuX+X/JnD5Zl3v+TuYVHIi8NWDgAAAAAAopGnST0ev0eufe+0KSXOstdVy7Vvp3o8fo/kaerkgOFBMQEAAAAAQBQ6e6VEIBxHiuVe82iEE0UGxQQAAAAAAFHGVlMZcClxluNIsWy1VRFKFDkUEwAAAAAARBnXpnUdbt/oiL2uWq5N6yOUKHIoJgAAAAAAiDKOivLQ5k4eC3OSyKOYAAAAAAAg2vh8nTtnIYoJAAAAAACijdPZuXMWopgAAAAAACDK+PsNCm2u/+AwJ4k8igkAAAAAAKKMd/rtMpJSg5oxktLknT4nQokih2ICAAAAAIAoY6aky585PKgZf+ZwmclpEUoUORQTAAAAAABEIc+8++XPzAlorT8zR55590U4UWRQTAAAAAAAEI3cPdS0pFDeq8Z3uK3DSEqT96rxalpSKLl7dHLA8Ii923UCAAAAANBduHvI8/Nfy1ZTKdfmF+Q4eeyrR4I6nfL3Hyzv9DkxuX3j6ygmAAAAAACIcmZKulruWGh1jIhgKwcAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALAMxQQAAAAAALCM0+oA3Z3hqZL32AYZjSdkmj7ZbE7Zew2SK+M22d1pVscDAAAAACCiKCYsYvqb5SleIaO+VGZL9b9el2TUH5K/8j3ZE7Plzl0smyPeuqAAAAAAAEQQWzksYPqb1bx/qfyVu1uVEq3WtFTLX7VbzfuXyvQ3d3JCAAAAAAA6B8WEBTzFK2ScLglorXG6RJ7iFRFOBAAAAACANSgmOpnhqZJRXxrcTH2JDE/7V1YAAAAAABDLYqaYWLt2rcaOHasBAwZowIABuu6667Rt2zarYwXNe2xDh9s3OmK21Mh7fEOEEgEAAAAAYJ2YKSb69eun//f//p/efvttbd++XRMmTNAPfvADHTp0yOpoQTEaT4Q211Ae5iQAAAAAAFgvZp7KccMNN7T6+Fe/+pWeffZZ7dmzRyNGjLAoVfBM09epcwAAAAAARLOYKSa+zu/3a+PGjWpsbNR3vvMdq+MExWZzygxxDgAAAACArsZWV1cXyvfJlvjoo480ZcoUNTc3KyEhQWvXrtXUqVM7XF9WVtaJ6QLTp+ZlJTTuCnquIWGcTqf8ZwQSAQAAAAAQWVlZWR0ei6lioqWlRZ9++qnq6+u1adMm/fnPf9aWLVuUk5NjdbSAlJWVKXNgspr3/CKoG2Da4lIV/+3fye5OjWA6RJOysrLz/ocLSJwnCBznCgLBeYJAca4gEJwnCEbM3PxSkuLi4jRkyBCNHj1ay5Yt08iRI/XUU09ZHSsodnea7InZwc30yaaUAAAAAAB0STFVTHyTYRhqaWmxOkbQ3LmLZU8cFtBae+IwuXMWRzgRAAAAAADWiJk7Kj700EOaMmWK+vfvr4aGBr366qvauXOn/vKXv1gdLWg2R7ziRz8mT/EKGfUlMltq2q6JS5W9T7bcOYtlc8RbkBIAAAAAgMiLmWLi888/19y5c/XFF18oMTFRubm5evXVVzV58mSro4XE5ohX/MgHZXiq5D3+koyGcpmmTzabU/Zeg+TKmM32DQAAAABAlxczxcTTTz9tdYSIsLvT5M7+mdUxAAAAAACwRMj3mGhubtZHH32kxsbGNsdeffXViwoFAAAAAAC6h5CKiT179ig3N1c33nijsrKy9Nvf/rbV8YULF4YlHAAAAAAA6NpCKibuv/9+LV++XEePHtX//M//aPPmzfrJT34iwzAkSaZphjUkAAAAAADomkIqJkpKSnTbbbdJkoYOHaqtW7fq888/1+233x6Tj+8EAAAAAADWCKmYSExMVEVFxbmPe/TooZdeeklOp1O33HLLuSsnAAAAAAAAziekYmLSpEl68cUXW73mcrn03HPPadCgQWpqagpLOAAAAAAA0LWF9LjQ1atXy+fztXndbrfr97//vZYsWXLRwQAAAAAAQNcX0BUT8+bNa1VExMXFqWfPnh2uHzBgwMUnAwAAAAAAXV5AxcTmzZs1c+ZM1dXVdbjmwIEDYQsFAAAAAAC6h4CLibKyMk2ZMkXHjx9vdeyjjz7Sf/3Xf+maa66JRD4AAAAAANCFBVRMXHXVVXrjjTfkdDp17bXX6oMPPlBpaanuuusuTZgwQTt27NDChQsjnRUAAAAAAHQxAd/8cuDAgdq2bZtuvfVW3XjjjfL7/erVq5fuvfde5efnKykpKZI5AQAAAABAFxRwMXH06FEVFhZq7969MgxDhmFo6dKlys/Pj2Q+AAAAAADQhQW0lWPu3Ln6zne+o40bNyo/P1/FxcW6++67dd9992n58uWRzggAAAAAALqogK6Y2LJli+bNm6cFCxYoPT1dkrRy5UoNHjxYv/rVr3Ts2DE9/fTTiouLi2hYAAAAAADQtQRUTOzfv1+XXHJJm9fnz5+vwYMH60c/+pFuvPFGbdu2LewBAQAAAABA1xXQVo72Somzrr/+em3ZskWffPJJ2EIBAAAAAIDuIaBi4kJGjRqloqKicPxSAAAAAACgGwlLMSFJ/fr1C9cvBQAAAAAAuomwFRMAAAAAAADBopgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWoZgAAAAAAACWcVodAAAAIJIqGv1aeeC0Sut8ajFMxdltGpbk1KIrEtUvwWF1PAAAuj2KCQAA0CU1eg3lv1OrPZUtOvWl0erY7s9b9PdPmpWXFqc1E5KV4OIiUgAArML/hQEAQJfT6DU0Y1uVNpc3tyklzjr1paEtJ5o1c1uVGr3trwEAAJFHMQEAALqc/HdqtbfSG9DaPZVe5b9TG+FEAACgIxQTAACgS6lo9GtPZUtQM3sqW/TZl/4IJQIAAOdDMQEAALqUlQdOd7h9oyOnvjS08n9PRygRAAA4H4oJAADQpZTW+UKaKwlxDgAAXByKCQAA0KW0GGanzgEAgItDMQEAALqUOLutU+cAAMDFoZgAAABdSnaSM6S5YSHOAQCAi0MxAQAAupR7r0jUpT2D+yvOZT3tundUYoQSAQCA86GYAAAAXUq/BIfy0uKCmslLj9NlPR0RSgQAAM6HYgIAAHQ5ayYkKy/dFdDab6e79Mz45AgnAgAAHaGYAAAAXU6Cy66/TU3TjYPiO9zWcVlPu24cFK+NU9OU4OKvRAAAWIW7PAEAgC4pwWXX+u+mqqLRr1UHTqukzqcWw1Sc3abhyU4tuiKR7RsAAEQBigkAANCl9UtwaPVYtmoAABCtYua6xdWrV+uaa67RgAEDlJmZqf/8z/9UcXGx1bEAAAAAAMBFiJliYufOnfrhD3+obdu2adOmTXI6nZo5c6Zqa2utjgYAAAAAAEIUM1s5XnvttVYfr1mzRgMHDtR7772n66+/3qJUAAAAAADgYsTMFRPf1NDQIMMwlJSUZHUUAAAAAAAQopgtJpYuXaqRI0fqO9/5jtVRAAAAAABAiGx1dXWm1SGCdd999+m1117Tf//3fysjI6PDdWVlZZ0XCgAAAAAAtCsrK6vDYzFXTPzyl7/Ua6+9ps2bN2vo0KFWxwlKWVnZeX8zgLM4VxAIzhMEinMFgeA8QaA4VxAIzhMEI2ZufilJS5Ys0WuvvaYtW7bEXCkBAAAAAADaipliYtGiRXrllVf0wgsvKCkpSZ9//rkkKSEhQb169bI4HQAAAAAACEXM3PzyT3/6k86cOaMZM2YoOzv73D9PPvmk1dEAAAAAAECIYuaKibq6OqsjAAAAAACAMIuZKyYAAAAAAEDXQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAsQzEBAAAAAAAs47Q6AAAAsE5Fo18rD5xWaZ1PLYapOLtNw5KcWnRFovolOKyOBwAAugGKCQAAuqFGr6H8d2q1p7JFp740Wh3b/XmL/v5Js/LS4rRmQrISXFxgCQAAIoe/aQAA0M00eg3N2FalzeXNbUqJs059aWjLiWbN3FalRm/7awAAAMKBYgIAgG4m/51a7a30BrR2T6VX+e/URjgRAADozigmAADoRioa/dpT2RLUzJ7KFn32pT9CiQAAQHdHMQEAQDey8sDpDrdvdOTUl4ZW/u/pCCUCAADdHcUEAADdSGmdL6S5khDnAAAALoRiAgCAbqTFMDt1DgAA4EIoJgAA6Ebi7LZOnQMAALgQigkAALqR7CRnSHPDQpwDAAC4EIoJAAC6kXuvSNSlPYP73/9lPe26d1RihBIBAIDujmICAIBupF+CQ3lpcUHN5KXH6bKejgglAgAA3R3FBAAA3cyaCcnKS3cFtPbb6S49Mz45wokAAEB3RjEBAEA3k+Cy629T03TjoPgOt3Vc1tOuGwfFa+PUNCW4+OsCAACIHO5kBQBAN5Tgsmv9d1NV0ejXqgOnVVLnU4thKs5u0/BkpxZdkcj2DQAA0CkoJgAA6Mb6JTi0eixbNQAAgHW4NhMAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFiGYgIAAAAAAFgmpoqJXbt2adasWRo+fLiSkpL04osvWh0JAAAAAABchJgqJhobG5WTk6PHHntMPXr0sDoOAAAAAAC4SE6rAwRjypQpmjJliiRp/vz5FqcBAAAAAAAXK6aumAAAAAAAAF2Lra6uzrQ6RCj69++vFStW6Ac/+EGHa8rKyjoxEQAAAAAAaE9WVlaHx2JqK0ewzveJW6GsrCzqMiE6ca4gEJwnCBTnCgLBeYJAca4gEJwnCAZbOQAAAAAAgGUoJgAAAAAAgGViaitHQ0ODjh49KkkyDEOffvqpDh48qOTkZA0YMMDidAAAAAAAIFgxdcXE/v37NWHCBE2YMEFNTU36zW9+owkTJujRRx+1OhoAAAAAAAhBTF0xMX78eNXV1VkdAwAAAAAAhElMXTEBAAAAAAC6FooJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGYoJAAAAAABgGafVAQAAQPAqGv1aeeC0Sut8ajFMxdltGpbk1KIrEtUvwWF1PAAAgIBRTAAAEEMavYby36nVnsoWnfrSaHVs9+ct+vsnzcpLi9OaCclKcP3/9u4/Nqvy/hv4py2tpFXSrnRQRDBzqOgUFMTpI5BhAjOKMBZ0zv0IAxVRE4MSwemzyNx0FFy26ALK2MzGEo1jOpzKtgQnjkyrEXRZIDCnMqFYoBVow7eld58/vpHIg2Ah3Fznvn29/qLnXBd5N7mS+/R9zrluD0YWOwUVAMVAMQEABaKtMxeTVu2I15o7DzumqT0Xz763Lyav2hFPT+irnChSCioAiolPKgAoEDPXtByxlPi4xubOmLmmJc+JSOGjgmrlu/sOKSU+8vGCqq3zk8cAQFYoJgCgAGxt64rG5o6jmtPY3BHb2rvylIhUFFQAFBvFBAAUgIb1uw97d/xwmtpz0bBud54SkYKCCoBipJgAgAKwsXX/Mc3bcIzzyCYFFQDFSDEBAAWgI9d9QueRTQoqAIqRYgIACkBFackJnUc2KagAKEaKCQAoAGdVH9s3fJ99jPPIJgUVAMVIMQEABWDOsD7Rv/LoPrbrK0tjzvA+eUpECgoqAIqRYgIACsCAqrIY2bfiqOaMrKuI+sqyPCUiBQUVAMVIMQEABWLJmJoYWVfeo7EX1ZXH4tE1eU7EiaagAqAYKSYAoEBUlZfGMxP6xsTBvQ9717y+sjQmDu4dT0/oG1XlPuaLkYIKgGLjhUMAKCBV5aXxm3G1sbWtKxau3x0bWvdHR647KkpLYmhNr7hzWB93x4vcRwXVzDUt0djcEU3tuUPG1FeWxsi6ilg8ukZBBUDmKSYAoAANqCqLhy51J/yzSkEFQDFRTAAAmbe1rSsa1u+OjR/7A/zs6v/9A3xA1Wf3D3AFFQDFQDEBAGRWW2fusK8srN3eEc9t2Rcj+1bEkjFeWQCAQuUTHADIpLbOXExatSNWvrvvE/dRiIhoas/Fs+/ti8mrdkRb5yePAQCyTTEBAGTSzDUt8VpzZ4/GNjZ3xsw1LXlOBADkg2ICAMicrW1d0djccVRzGps7Ylt7V54SAQD5opgAADKnYf3uw76+cThN7bloWLc7T4kAgHxRTAAAmbOxdf8xzdtwjPMAgHQUEwBA5nTkuk/oPAAgHcUEAJA5FaUlJ3QeAJCOYgIAyJyzqnsd07yzj3EeAJBOwRUTS5cujfPPPz/69esXY8eOjbVr16aOBAAcZ3OG9Yn+lUd3mVJfWRpzhvfJUyIAIF8KqphYsWJFzJ07N+6444546aWXYtSoUTF16tTYsmVL6mgAwHE0oKosRvatOKo5I+sqor6yLE+JAIB8Kahi4pFHHolvfvOb8d3vfjfOOuusaGhoiH79+sWyZctSRwMAjrMlY2piZF15j8ZeVFcei0fX5DkRAJAPBVNMdHR0xLp162LcuHEHHR83bly88soriVIBAPlSVV4az0zoGxMH9z7sax31laUxcXDveHpC36gqL5jLGgDgYwpmh6idO3dGV1dX1NXVHXS8rq4uPvjgg0+cs2nTphMR7ahkMRPZZK3QE9YJPVXIa+X/nhbxwedLYtmWXvF2e2l05iLKSyO+UJmL6aftj7qT9sbWd3aljlkUCnmdcGJZK/SEdcLHDRky5LDnCqaY+EhJycFfA9bd3X3IsY8c6RdPYdOmTZnLRDZZK/SEdUJPFcNaGRIR/+dLqVMUt2JYJ5wY1go9YZ1wNAqmmKitrY2ysrJDno7YsWPHIU9RAABsbeuKhvW7Y2Pr/ujIdUdFaUmcXd0r7hzWJwZU2SQTALKiYIqJioqKGD58eKxevTomT5584Pjq1avj6quvTpgMAMiSts5czFzTEo3NHdHUnjvo3NrtHfHcln0xsm9FLBlTY18KAMiAgikmIiJuueWWuOmmm2LEiBFx8cUXx7Jly6KpqSmmTZuWOhoAkAFtnbmYtGpHmSQ3qwAADupJREFUvNbcedgxTe25ePa9fTF51Q6bZgJABhRUMTFlypTYtWtXNDQ0xPbt22Po0KHx5JNPxqBBg1JHAwAyYOaaliOWEh/X2NwZM9e0xG/G1eY5FQBwJAVVTEREzJgxI2bMmJE6BgCQMVvbuqKxueOo5jQ2d8S29q6or7TnBACk4tlFAKAoNKzffcieEp+mqT0XDet25ykRANATigkAoChsbN1/TPM2HOM8AOD4UEwAAEWhI9d9QucBAMeHYgIAKAoVpSUndB4AcHwoJgCAonBW9bHt6X32Mc4DAI4PxQQAUBTmDOsT/SuP7tKmvrI05gzvk6dEAEBPKCYAgKIwoKosRvatOKo5I+sqfFUoACSmmAAAisaSMTUxsq68R2MvqiuPxaNr8pwIAPg0igkAoGhUlZfGMxP6xsTBvQ/7Wkd9ZWlMHNw7np7QN6rKXQoBQGp2ewIAikpVeWn8ZlxtbG3rioXrd8eG1v3RkeuOitKSGFrTK+4c1sfrGwCQIYoJAKAoDagqi4cu9aoGAGSd5xcBAACAZBQTAAAAQDKKCQAAACAZxQQAAACQjGICAAAASEYxAQAAACSjmAAAAACSUUwAAAAAySgmAAAAgGQUEwAAAEAyigkAAAAgGcUEAAAAkIxiAgAAAEhGMQEAAAAko5gAAAAAklFMAAAAAMkoJgAAAIBkFBMAAABAMooJAAAAIBnFBAAAAJCMYgIAAABIRjEBAAAAJKOYAAAAAJJRTAAAAADJKCYAAACAZBQTAAAAQDKKCQAAACAZxQQAAACQjGICAAAASEYxAQAAACSjmAAAAACS6ZU6AAAAx9/Wtq5oWL87Nrbuj45cd1SUlsTZ1b3izmF9YkBVWep4AHCAYgIAoIi0deZi5pqWaGzuiKb23EHn1m7viOe27IuRfStiyZiaqCr38CwA6fk0AgAoEm2duZi0akesfHffIaXER5rac/Hse/ti8qod0db5yWMA4ERSTAAAFImZa1ritebOHo1tbO6MmWta8pwIAD5dwRQTv/71r+Oqq66KQYMGRXV1dbz77rupIwEAZMbWtq5obO44qjmNzR2xrb0rT4kAoGcKpphob2+PcePGxdy5c1NHAQDInIb1uw/7+sbhNLXnomHd7jwlAoCeKZjNL2fNmhUREW+88UbiJAAA2bOxdf8xzdtwjPMA4HgpmCcmAAA4vI5c9wmdBwDHS8E8MXEsNm3alDrCIbKYiWyyVugJ64SeslaKX9f/nBQRZccwb9+B9WGd0FPWCj1hnfBxQ4YMOey5pMXE/fffHwsXLjzimJUrV8bo0aOP6f8/0i+ewqZNmzKXiWyyVugJ64SeslY+G4Y3t8Qbu9uPet4F9afEkCGDrBN6zFqhJ6wTjkbSYuLmm2+Oa6655ohjBg4ceILSAAAUrjnD+sTzW/Yd1QaY9ZWlMWd4nzymAoBPl7SYqK2tjdra2pQRAACKwoCqshjZtyKefW9fj+eMrKuI+sqjf/0DAI6ngtn8cvv27fHmm2/G5s2bIyJi48aN8eabb0ZLS0viZAAA2bBkTE2MrCvv0diL6spj8eiaPCcCgE9XMMXEsmXLYsyYMXHDDTdERMQ111wTY8aMieeeey5xMgCAbKgqL41nJvSNiYN7R//KT77Mq68sjYmDe8fTE/pGVXnBXAoCUMQK5ls55s2bF/PmzUsdAwAg06rKS+M342pja1tXLFy/Oza07o+OXHdUlJbE0JpeceewPl7fACBTCqaYAACg5wZUlcVDl3pVA4Ds8/weAAAAkIxiAgAAAEhGMQEAAAAko5gAAAAAklFMAAAAAMkoJgAAAIBkFBMAAABAMooJAAAAIBnFBAAAAJCMYgIAAABIRjEBAAAAJFPS2tranToEAAAA8NnkiQkAAAAgGcUEAAAAkIxiAgAAAEhGMQEAAAAko5gAAAAAklFMJPL666/H5MmT49RTT42BAwfG+PHjY+fOnaljkVHd3d3x9a9/Paqrq+OZZ55JHYcMaWlpiTlz5sRFF10U/fv3j3PPPTdmz54du3btSh2NDFi6dGmcf/750a9fvxg7dmysXbs2dSQy5qGHHoqvfOUrcdppp8UZZ5wR1157bfzrX/9KHYuMW7RoUVRXV8ecOXNSRyGDmpqaYubMmXHGGWdEv3794uKLL46XX345dSwyTjGRwGuvvRZf+9rX4rLLLou//OUv8eKLL8att94avXr1Sh2NjHr44YejrKwsdQwyaNu2bbFt27a47777Yu3atbFkyZJYu3ZtTJ8+PXU0EluxYkXMnTs37rjjjnjppZdi1KhRMXXq1NiyZUvqaGTIyy+/HNOnT49Vq1bFH//4x+jVq1dMnjw5WlpaUkcjoxobG+Pxxx+Pc889N3UUMqi1tTUmTJgQ3d3d8eSTT8Yrr7wSCxYsiLq6utTRyLiS1tbW7tQhPmvGjx8fo0ePjnvvvTd1FArAG2+8Ed/61rfixRdfjCFDhsTjjz8ekyZNSh2LDPvzn/8c1157bbz77rvRp0+f1HFI5PLLL49zzz03fv7znx84duGFF8akSZPiBz/4QcJkZNnevXtj0KBBsXz58rjiiitSxyFjPvzwwxg7dmz87Gc/iwULFsQ555wTDQ0NqWORIfPnz4+///3vsWrVqtRRKDCemDjBmpub49VXX41+/frFV7/61RgyZEhcccUV8be//S11NDJoz549MX369PjpT3+qaabH9uzZEyeddFJUVlamjkIiHR0dsW7duhg3btxBx8eNGxevvPJKolQUgr1790Yul4vq6urUUcig22+/PSZNmhRjx45NHYWM+tOf/hQjRoyIadOmxRe/+MW47LLL4tFHH43ubvfCOTLFxAn2zjvvRETEAw88ENdff3089dRTcckll8SUKVPirbfeShuOzJk9e3ZcfvnlMX78+NRRKBCtra3xox/9KL7zne94PewzbOfOndHV1XVIoVlXVxcffPBBolQUgrlz58Z5550Xo0aNSh2FjHn88cfj7bffju9///upo5Bh77zzTvzyl7+M008/PX7/+9/HzJkz47777ovHHnssdTQyzlXrcXL//ffHwoULjzhm5cqVUVFRERER06ZNi29/+9sRETFs2LB4+eWX41e/+lU89NBDec9KWj1dK++//37885//jNWrV5+gZGRJT9fJ6NGjD/zc1tYW1113XdTX18f8+fPzHZECUFJSctDP3d3dhxyDj9x9993xj3/8I1544QX7GnGQTZs2xfz58+P5558/cC0LnySXy8UFF1xw4JXBYcOGxdtvvx1Lly6NG2+8MXE6skwxcZzcfPPNcc011xxxzMCBAw/cqTrrrLMOOnfmmWfGf//737zlIzt6ulZ+97vfxYYNG+LUU0896Ny0adNi1KhR8cILL+QzJon1dJ18ZO/evTF16tSIiHjiiSeid+/eec1HttXW1kZZWdkhT0fs2LHDa2F8onnz5sWKFSti5cqVcfrpp6eOQ8a8+uqrsXPnzrjkkksOHOvq6oq1a9fGsmXLYuvWrXHSSSclTEhW9OvXz985HBPFxHFSW1sbtbW1nzpu8ODBUV9fH5s2bTro+L///e8455xz8hWPDOnpWrn33nvjtttuO+jYpZdeGj/84Q/jyiuvzFc8MqKn6yTif/eUmDp1anR3d8dTTz0VJ598cp7TkXUVFRUxfPjwWL16dUyePPnA8dWrV8fVV1+dMBlZdNddd8WKFSvi2WefjTPPPDN1HDLoyiuvjAsuuOCgY7fcckucccYZMXv2bE9RcMCXv/zl2Lx580HHNm/eHKeddlqiRBQKxcQJVlJSErfddls8+OCD8aUvfSnOP//8+MMf/hCNjY2xYMGC1PHIkAEDBsSAAQMOOT5w4EB3szhgz549MWXKlNizZ08sX7482tvbo729PSIiampqXCx+ht1yyy1x0003xYgRI+Liiy+OZcuWRVNTU0ybNi11NDLkzjvvjCeeeCJ++9vfRnV1dWzfvj0iIqqqqpScHFBdXX3IhqiVlZVRU1PjxhoHmTVrVowfPz4WLlwYU6ZMiTfffDMeffRR30bIp1JMJDBr1qzo7OyMe+65J3bt2hVnn312PPXUU3HeeeeljgYUmHXr1kVjY2NERIwYMeKgc///HhR8tkyZMiV27doVDQ0NsX379hg6dGg8+eSTMWjQoNTRyJClS5dGRBzyNdR33XVXzJs3L0UkoIBdeOGFsXz58pg/f340NDTEwIED4+67744ZM2akjkbGlbS2tvruFgAAACAJXxcKAAAAJKOYAAAAAJJRTAAAAADJKCYAAACAZBQTAAAAQDKKCQAAACAZxQQAAACQjGICAAAASEYxAQAAACSjmAAAkmpqaor6+vqYMWPGQcdff/31qK+vjxtvvDFRMgDgRFBMAABJ9e/fP6ZNmxYrVqyIzZs3R0TEe++9F9ddd10MHz48Hn744cQJAYB8UkwAAMndfvvt0bt371i0aFHs3r07vvGNb8Qpp5wSy5cvj4qKitTxAIA86pU6AADA5z//+fje974Xixcvjv/85z/R1NQUf/3rX+Nzn/tc6mgAQJ55YgIAyIRbb701crlcvP7667F8+fL4whe+cND5Rx99NEaPHh21tbXxwAMPJEoJABxvigkAIBMWLVoUuVwuurq6orq6+pDz9fX1cffdd8dVV12VIB0AkC+KCQAguV/84hfx2GOPxY9//OM45ZRT4sEHHzxkzMSJE+OKK66IPn36JEgIAOSLPSYAgKSef/75uOeee2L27Nkxa9as+PDDD2PBggXx1ltvxXnnnZc6HgCQZ56YAACSWbduXcyYMSOuvvrquPfeeyMi4uabb46TTz7ZPhIA8BmhmAAAknj//ffjuuuui6FDh8bixYujpKQkIiKqq6vjhhtuiOeeey7WrVuXOCUAkG8lra2t3alDAAD01G233RYDBgyIefPmpY4CABwHnpgAAArC/v37Y9++fdHV1RVdXV0H/g0AFDZPTAAABeGBBx6In/zkJwcde+SRR+L6669PlAgAOB4UEwAAAEAyXuUAAAAAklFMAAAAAMkoJgAAAIBkFBMAAABAMooJAAAAIBnFBAAAAJCMYgIAAABIRjEBAAAAJPP/ALpOESqQzjZ2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 8))\n",
    "for i in range(3):\n",
    "    plt.scatter(X[np.where(y==i), 0], X[np.where(y==i), 1], s=200, label=f'Class $c_{i+1}$')\n",
    "plt.scatter([-2], [5], c='k', s=200)\n",
    "plt.annotate('$x*$', (-1.9, 4.7))\n",
    "plt.xlabel('$x_1$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.base import BaseEstimator, ClassifierMixin\n",
    "from sklearn.utils.validation import check_X_y, check_array, check_is_fitted\n",
    "\n",
    "class GaussianNaiveBayesClassifier(BaseEstimator, ClassifierMixin):\n",
    "    def fit(self, X, y):\n",
    "        X, y = check_X_y(X, y)\n",
    "        self.priors_ = np.bincount(y) / len(y)\n",
    "        self.n_classes_ = np.max(y) + 1\n",
    "        \n",
    "        self.means_ = np.array([X[np.where(y==i)].mean(axis=0) for i in range(self.n_classes_)])\n",
    "        self.stds_ = np.array([X[np.where(y==i)].std(axis=0) for i in range(self.n_classes_)])\n",
    "        \n",
    "        \n",
    "        return self\n",
    "    \n",
    "    def predict_proba(self, X):\n",
    "        check_is_fitted(self)\n",
    "        X = check_array(X)\n",
    "        \n",
    "        res = []\n",
    "        for i in range(len(X)):\n",
    "            probas = []\n",
    "            for j in range(self.n_classes_):\n",
    "                probas.append((1/np.sqrt(2*np.pi*self.stds_[j]**2)*np.exp(-0.5*((X[i]-self.means_[j])/self.stds_[j])**2)).prod()*self.priors_[j])\n",
    "            probas = np.array(probas)\n",
    "            res.append(probas / probas.sum())\n",
    "            \n",
    "        \n",
    "        return np.array(res)\n",
    "    \n",
    "    def predict(self, X):\n",
    "        check_is_fitted(self)\n",
    "        X = check_array(X)\n",
    "        \n",
    "        res = self.predict_proba(X)\n",
    "        \n",
    "        return res.argmax(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8.06313823e-07, 1.36201957e-04, 9.99862992e-01],\n",
       "       [1.00000000e+00, 4.23258691e-14, 1.92051255e-11],\n",
       "       [4.30879705e-01, 5.69120295e-01, 9.66618838e-27]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_gauss = GaussianNaiveBayesClassifier()\n",
    "my_gauss.fit(X, y)\n",
    "my_gauss.predict_proba([[-2, 5], [0,0], [6, -0.3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 1], dtype=int64)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_gauss.predict([[-2, 5], [0,0], [6, -0.3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8.06313823e-07, 1.36201957e-04, 9.99862992e-01],\n",
       "       [1.00000000e+00, 4.23258691e-14, 1.92051255e-11],\n",
       "       [4.30879705e-01, 5.69120295e-01, 9.66618838e-27]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "gnb = GaussianNB(var_smoothing=0)\n",
    "gnb.fit(X, y)\n",
    "gnb.predict_proba([[-2, 5], [0,0], [6, -0.3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 1])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gnb.predict([[-2, 5], [0,0], [6, -0.3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mlxtend.plotting import plot_decision_regions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Decision Regions')"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 8))\n",
    "plot_decision_regions(X, y, clf=gnb, legend=0, colors='#1f77b4,#ff7f0e,#ffec6e')\n",
    "for i in range(3):\n",
    "    plt.scatter(X[np.where(y==i), 0], X[np.where(y==i), 1], s=200)\n",
    "plt.scatter([-2, 0, 6], [5, 0, -0.3], c='k', s=200)\n",
    "plt.xlabel('$x_1$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.title('Decision Regions')"
   ]
  },
  {
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}