{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f039bb78-5200-4bce-bdd3-f04f68fe344e",
   "metadata": {},
   "source": [
    "## Computational - 10 points\n",
    "\n",
    "- Add your answers in the same cell as the code or add another cell by copy pasting the existing cell\n",
    "- Outputs from the answer key have been left as they are for your reference. My personal suggestion would be to create a new cell with the same code copied and make sure that the output coming is the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "77f7a13b-b904-4087-9301-2153c549c4d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import the required libraries\n",
    "\n",
    "#TODO: import numpy below\n",
    "\n",
    "______________________________\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "17cddbaf-9083-491d-986b-a32e4b0fd298",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the breast cancer dataset from sklearn.datasets, read the documentation to see how to do the same\n",
    "data = _____________\n",
    "\n",
    "y = data.________  # Extracting the binary target variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1b79fd98-c435-4997-a0ba-13d2f84ac353",
   "metadata": {},
   "outputs": [],
   "source": [
    "#TODO: define the log likelihood function with the above given formula\n",
    "\n",
    "def log_likelihood(p, k):\n",
    "    return np._____(y * np.______(p) + (______) * np._____(______))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8648ef50-fb17-483a-b18e-6d8e7a8daef7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the log-likelihood function\n",
    "p_values = np.linspace(0.01, 0.99, 100)\n",
    "ll_values = [log_likelihood(p, y) for p in _________]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c90a7fcf-ad30-412f-a083-8308da5b150f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/Y9WqVRg5ciTatm0LQRDw/fffo7i4GHFxcbp23bt3x65du7BlyxYEBATA1dW1yb2y3t7eePHFF5GVlYWOHTti27Zt+OSTT/Diiy/q5gz6+/tj6NChWLx4MTw9PREWFobt27frzhK9mfaPrP/973944IEHIBaL0aNHD9jb29dp29jPEVkw881fJ2o87Vk0t/vRnl2zd+9eYfDgwYKzs7Pg6Ogo3H333cKWLVvqHG/v3r1Cv379BJlMJvj7+wszZswQ/ve//wkAdGebNUR7ZlV9P2FhYXox13cW3s1Onz4t+Pv7C3369NGdGXjixAlh9OjRQps2bQSpVCr4+/sLgwcPFlavXq3bz5Cz8IYPH17nOdR3FtapU6eEhx56SHB3dxfs7e2Fnj171nu23JUrV4SxY8cK3t7eglQqFTp16iQsWbJEd4agVk5OjjBq1CjBxcVFcHV1FUaNGiXs37+/WWfhCULjXufGnLlZ3+Pd/OPg4CB07NhReOWVV4Tc3Nw6+/zwww/CoEGDBDc3N0EmkwlhYWHCY489Jvz++++6Ng2dsQlAmDJlSp3tt56x1djnLAi1Z2f1799fcHZ2FoKCgoS5c+cKn376qUnOwtP+SCQSwdvbW4iJiRFmzZolZGZm1tnn1s/HX3/9JTz55JNCu3btBEdHR8Hd3V3o27evkJycrLff8ePHhQEDBghOTk4CAN1zaOj1buizuGvXLiE6OlqQyWRCQECAMGvWrDpnwObm5gqPPfaY4OXlJbi7uwtPP/207qzBm9/H1dXVwvPPPy/4+voKIpFI7zHre00b8zlq6HNw6+tFpiUShDucGkHUSsTHxyMzMxMZGRnmDoWIiCwch/CoVUpKSkLv3r0REhKCwsJCrF+/HqmpqVizZo25QyMiIivAAopaJbVajTlz5kAul0MkEiEyMhJffPEFnn76aXOHRkREVoBDeEREREQG4jIGRERERAZiAUVERERkIBZQRERERAbiJPIWoNFocO3aNbi6uhrlMhJERETU8gRBQGlpKQIDA++4qDILqBZw7dq1Ole0JyIiIuuQnZ2N4ODgBtuwgGoB2muVZWdn3/YK7I2hVCqRkpKC+Pj4Rl+JnJqO+TYt5tu0mG/TYr5Ny1j5VigUCAkJadQ1R1lAtQDtsJ2bm1uzCygnJye4ubnxA2gCzLdpMd+mxXybFvNtWsbOd2Om33ASOREREZGBWEARERERGYgFFBEREZGBOAfKjNRqNZRK5W3vVyqVkEgkqKqqglqtNmFkrRPzTUREjcUCygwEQYBcLkdxcfEd2/n7+yM7O5vrSZkA821agiDA1dUVvBwnEVkjFlBmoC2e2rRpAycnp9t+WWs0GpSVlcHFxeWOC3pR8zHfpiMIAsrKylBdXY28vLw7rrdCRGRpWECZmFqt1hVP3t7eDbbVaDSoqamBg4MDv9BNgPk2LZlMhqqqKigUCqjVaojFYnOHRETUaPyWMDHtnCcnJyczR0Jkfvb29gDQ4FxAIiJLxALKTDjHhoifAyKyXiygiIiIiAzEAoqs2q5duyASiXRnNCYnJ8PDw6PJx9u3bx/EYvFtjzdv3jz06tWrycdvjoEDB+KVV14xy2MTEZE+FlDUaImJiRg5cqTJHzc8PBwrVqyo977+/fsjNzcX7u7uLfLYTzzxBDIyMlrk2C2hpqYG77zzDnr27AknJyf4+PhgwIAB+OyzzzjPiIjIiHgWHlk1e3t7+Pv7t9jxHR0d4ejo2GLHN6aamhokJCTgxIkTePPNNzFgwAC4ubnhzz//xNKlS9G7d+8m954plUpeENUGqTUClGoNqlUaqDUC1BoBGuGff4F/5qmJAIjtRBDbiSDR/WsHe4kdxHacy0atDwsoMprdu3djxowZOHHiBLy8vDB+/Hi89dZbkEhq32alpaWYNGkSfvjhB7i5ueG1117Djz/+iF69et22h+lOdu3ahUGDBqGoqKjeobuCggI88MAD8Pf3x7fffguZTIYlS5Zg9erVyM3NRceOHfHf//4Xjz32WL3HT05OxiuvvFJn0dMvvvgC//3vf1FUVIQHHngAn3zyCVxdXQEA1dXVmDFjBr7++msoFApER0fj3XffxV133dXoXJWXl+PFF1/E999/D1dXV0yfPv2OuVixYgX27NmDw4cPo3fv3rrtbdu2xeOPP46amhoAtT16r7zyit5wYK9evTBy5EjMmzcPQO2X5kcffYRffvkFv//+O5KSkvDZZ5/hjTfewKRJk3T7HT16FFFRUbh48SLatm2LkpISzJgxAz/88AOqqqp0z71nz553jJ8aR6XWoLhSiaLyGhSW16CkUglFlQollUqUVCpRWqVEebUK5dVqlFarUF6tQmWNGpU1KhSVijH3+E5UqdRQqmsLJWOQ2Ikgk9QWU45SMRztxXCWSeAorf3X1UECNwdp7b+OUrg5SOHlLIWHkz28nO3h6WQPTycpJGIOipD1YAFlAQRBQKWy7qVDNBoNKmvUkNSoWmxdIkep2ChnQl29ehXDhg1DYmIiPv/8c/z111+YOHEiHBwcdF/KSUlJ+OOPP/DTTz/Bz88Pc+bMwdGjR1tsTlFOTg7i4+MRHR2NtWvXQiKRYPbs2fj+++/x0UcfoUOHDtizZw+efvpp+Pr64t57723UcS9evIgffvgBP//8M4qKijB69Gi8/fbbWLhwIQDgtddew6ZNm7Bu3TqEhYXhnXfeQUJCAi5cuAAvL69G5WrGjBnYuXMnNm/eDH9/f8yaNQtHjhxpMFfr16/H0KFD9YonLalUanAP0ty5c7F48WK8++67EIvFqKysxPr16/UKqA0bNiAmJgZt27aFIAgYPnw4vLy8sG3bNri7u+Pjjz/GkCFDkJGRAS8vL4MevzURBAFFFUrIS6pwvbQKeYoqXFdU40ZpNfLLtD81KCirhqJK1YxHEgFoeCjXTlTb0yQSiSACoCuxBEAjCFDVU3SpNAJUNWqU16hRdIfj3zYyEeDtbA8fFxl8XWXwdZHB390BAe4O8Hd3RIC7A4I8HOHhJOXZm2QRWEBZgEqlGpFzfjPLY6cvSICTffPfBqtWrUJISAg++OADiEQidO7cGdeuXcN//vMfzJkzB+Xl5Vi3bh02bNiAIUOGAAA+++wzBAYGNvux65ORkYG4uDg8/PDDeO+99yASiVBeXo7ly5djx44diImJAVDbO7Nv3z58/PHHjS6gNBoNkpOTdT1O48aNw/bt27Fw4UKUl5fjo48+QnJyMh544AEAwCeffILU1FSsWbMGM2bMuGOuKioqsGbNGnz++eeIi4sDAKxbt+6Oq3WfP38eAwcObGLG6ho7diyee+453e2nnnoKy5cvx5UrVxAWFgaNRoOvv/4as2bNAgDs3LkTp06dQl5eHmQyGQBg6dKl+OGHH7Bx40b861//Mlps1kap1iC3uArZRRXIKapATlElrhZXIre4CtdKKpFbUoUalcagY3o4SeHpZA93RyncHKVwd5TC3VECVwcpXGQSuMgkcJZJ4CITw9FeAqlIwNGDaRgy8D64OMpgL7GDvdgOUokdpOLa4Tg70Z2XlhAEARoBUGk0UKkF1KhqhwBrVBpUqdSoUqpRXq1GpbK2F6y8WoWyahUUf/eUlVapUFJZg6KK2l60oooaFFcqIQhAflkN8stq8Je89LaP7yKTINjTEcGeTgjxckSEjzPCvZ0R4eOMQA9HDieSydhkAVVdXY1+/frhxIkTOHbsmN5f7VlZWZgyZQp27NgBR0dHjB07FkuXLtUt6AcAp06dwtSpU3Hw4EF4eXnhhRdewH//+1/+1dOAs2fPIiYmRi9HAwYMQFlZGXJyclBUVASlUom+ffvq7nd3d0enTp10txctWoRFixbpbqenpyM0NNTgWCorK3HPPffgySefxHvvvad3vKqqKl1RolVTU1Nvr83thIeH64onAAgICEBeXh6A2t4ppVKJAQMG6O6XSqXo27cvzp49C6BxuaqpqdEVeQDg5eWll6v6CIJg1PdodHS03u3evXujc+fO+Oqrr/D6669j9+7dyMvLw+jRowEAR44cQVlZWZ0V9isrK3Hx4kWjxWWpalQaZBWW49KNclwpqEBmwT//5pZUNWq4zNvZHn5uDvBzk6GNqwN8XWXwcbGHj6sMPi61/9cWTYYOdymVStxIB9q3cWnWfDaRSASxCBDbiSGTAM6yJh9KR60RUFheg/yy2l63G6XVuF5aheslVcgtqYJcUYVrxVXIL6tGWbUKf8lL6y2y7MV2iPBxRns/F3Rs44oOfi7o6OeCcG9nDg+S0dlkAfXaa68hMDAQJ06c0NuuVqsxfPhw+Pr6Yt++fSgoKMD48eMhCALef/99AIBCoUBcXBwGDRqEQ4cOISMjA4mJiXB2dsarr77aIvE6SsVIX5BQZ7tGo0GpohSubq4tOoRnDPV9eQs3TUIVbpmQemsbAJg0aZLuyxhAk3unZDIZhg4diq1bt2LGjBm6nhuNpvYv/K1btyIoKKjOPo1165ePSCTSHbuh56nd1thcGapjx466Iq0hdnZ2dR6jvjP0nJ2d62x76qmnsGHDBrz++uvYsGEDEhIS4OPjA6A2vwEBAdi1a1ed/ZqztISlKa9W4XxeGc5fL8X5vDJczCvDpfxyZBVWNFgk2UvsdD0nwZ6OCPKo/Qlwd0CghyP83BxgL2mdX/JiO1HtsJ2rDF0Cbt+uSqlGTlHl3z15lcgqKMfl/NoiNaugAjVqDc5dL8W566XYilzdfjKJHTr5uyIywA1dAtzQLcgNXQPd4WCk33/UOtlcAfXLL78gJSUFmzZtwi+//KJ3X0pKCtLT05Gdna37cl62bBkSExOxcOFCuLm5Yf369aiqqkJycjJkMhm6deuGjIwMLF++HElJSS3SCyUSieodRtNoNFDZi+FkL7H4a7NFRkZi06ZNesXB/v374erqiqCgIHh4eEAqleLgwYMICQkBUFusnj9/HrGxsQBqe1mMMU/Gzs4OX3zxBcaOHYvBgwdj165dCAwMRGRkJGQyGbKysnSPeTNtEdQc7du3h729Pfbt24exY8cCqC1ODh8+rJu0fadceXp6QiqV4s8//9T1wBUVFSEjI6PeuLXGjh2LWbNm4dixY3V61FQqFaqrq+Hs7AxfX1/k5v7z5aJQKHD58uVGPb+xY8fijTfewJEjR7Bx40Z89NFHuvv69OkDuVwOiUSC8PDwRh3PkqnUGlzOL8dZeSn+ylXgL3kpzslLcbW48rb7ONmL0da3dkgp3NsZYd5OCPv7X18XGew4vNQsDlIx2rdxQfs2LnXuU2sEXCuuxIW8MpzPK8X562XI+LvQrahR42ROCU7mlOjai+1E6Ojnil4h7ugR7IGoME+093Xha0SNZlMF1PXr1zFx4kT88MMP9V5rLi0tDd26ddPr2UhISEB1dTWOHDmCQYMGIS0tDbGxsXo9EgkJCZg5cyYyMzMRERFR57jV1dWorq7W3VYoFABqvzhv/cteqVTWziHQaO74ha3tJdC2NzdBEFBSUoKjR4/qbffy8sKkSZOwYsUKTJ06FVOmTMG5c+cwd+5cTJs2DUBtb8YzzzyDGTNmwMPDA23atMG8efN0heGdnl9OTk6dxw0NDdXtp82n9rZIJNIronbs2AF/f3+8+uqrmDZtGlQqFe655x4oFAqkpaXp4tO69Xi39jDdHO/N2xwdHTFp0iTd8wwNDcWSJUtQUVGBZ599FhqN5o65cnJywnPPPYcZM2bA09MTfn5+eOONN3Q9R7fL1UsvvYStW7diyJAhWLBgAQYMGABXV1ccPnwYS5YswSeffIJevXph0KBBWLduHYYPHw5PT0/MmTMHYrG4zrHre4+GhYWhf//+mDBhAlQqFR566CFdm8GDByMmJgYjR47E4sWL0alTJ1y7dg2//PILHn744TpDgje/v5VKpVkvJlylVOMveSnSc0uRnqtAem4pzl0vu+28JB8Xe3Ro44L2vs5o5+uMtr61c3D8XGW3/SNLrVZBXfdcEZPR/i6y5fXA/F2l8Hf1xD3tPHXbNBoB2UWVSM9V4C95GdJzFThzTYEbZTU4m6vA2VwFvjqYDQBwc5Cgd6gHokI9EB3miR7B7pA1sVewNeTbkhgr34bsbzMFlCAISExMxKRJkxAdHY3MzMw6beRyOfz8/PS2eXp6wt7eHnK5XNfm1r+etfvI5fJ6C6jFixdj/vz5dbanpKTUKeQkEgn8/f1RVlamO638TkpLbz+h0pSUSiV27dqFqKgove1PPvkkVq1ahW+//RZz5szBp59+Ck9PTzz11FP497//rSso586di5KSEowYMQKurq546aWXcOXKFYhEIl2b+mg0GixbtgzLli3T2/7hhx/qemhKS0thZ2eHqqoqCIKgO97q1avx3HPPYfDgwdiyZQumT58ONzc3LF68GJmZmXB3d0fPnj0xbdo0vTzf7njV1dVQq9V68VZVVUGj0ei2zZw5E1VVVXjmmWdQVlaGXr16YePGjRCLxVAoFHB1db1jrt544w0UFRVh5MiRcHFxwZQpU1BYWIiampoGc/Xdd99h1apV+OijjzBjxgw4OjqiY8eOeP755xEaGgqFQoHJkycjIyMDDz30ENzc3DB79mxcvHgR1dXVeseurKys97EeeeQRzJgxA2PGjKnzR8KGDRvw1ltvYcKECcjPz0ebNm3Qv39/ODk53Tbuqqoq7NmzBypVc84uazy1BsitBLLKRLqf3ApAg7qFj72dgEAnINBZQKCTgAAnAQGOgLNUBaCitlEBUFQAFJkk+uZLTU01dwhm0wlAJ29gpBdQUgNc+fv1v1JW+39FlQq7M/KxOyMfACC1ExDhKqCju4AObgJCXACxgR1UrTnf5tDcfFdUVDS6rUho6oQLE5k3b169xcnNDh06hP379+Obb77Bnj17IBaLdb1FN08i/9e//oUrV67gt9/0z3izt7fH559/jjFjxiA+Ph4RERH4+OOPdfdfvXoVwcHBSEtLw913313n8evrgQoJCUF+fj7c3Nz02lZVVSE7Oxvh4eFwcHBo8HkJgoDS0lK4urra5AT28vJyhISEYMmSJZgwYYK5w7H5fFsaQRBQUFCAGzduIDQ09I6fh6a6UVqNY9nFOJ5dgmPZxTh9TYEqZd2eJW9ne0QGuKJroBsiA2rny4R4OtrMkI5SqURqairi4uK4KGo9lGoN/pKX4khWMY5eKcbBzCIUlOv/kevmIMGAdt64r6MP7m3vDT+3279nmW/TMla+FQoFfHx8UFJSUuf7+1YW3wM1depUjBkzpsE24eHheOutt/Dnn3/WmQwcHR2Np556CuvWrYO/vz8OHDigd7/27DBtL5O/v7+uN0pLe4bVrb1XWjKZrN5JyPWtvaNWqyESiWBnZ3fHeU03D0dZ+hyoxjh27Bj++usv9O3bFyUlJViwYAGA2h4NS3h+tpZvS3dzvpuyTlV9BEHAxRvlOJxZiEOZRTh8pRBXCur+RenqIEGP4Nq5Lz3//jfA3aFVFM7GyrWtkUqBPuEy9AmvPSlCEASczytD2sUC7L+Yjz8vFaKkUolfzlzHL2euAwAiA9wQF+mH+K5+iAxwq/f9w3ybVnPzbci+Fl9A+fj46M7yacjKlSvx1ltv6W5fu3YNCQkJ+Oabb9CvXz8AQExMDBYuXIjc3FwEBNSe6pGSkgKZTKYbloqJicGsWbNQU1OjW9ogJSUFgYGBNjEx1tyWLl2Kc+fOwd7eHlFRUdi7d2+jXl+i+mg0AjLySnHgUiEOXC7AwcuFyC/T7zUQiYBOfq7oHeqJ3qEe6BPqgbY+nCxMDROJaieZd/Rzxfj+4VBrBBzPLsbujBvYnXEDJ3OK/54vp8B7288jyMMRcZF+eKCbP+4K56KxrYHFF1CNdet6QS4utWdptGvXTncae3x8PCIjIzFu3DgsWbIEhYWFmD59OiZOnKjrqhs7dizmz5+PxMREzJo1C+fPn8eiRYswZ86cVvHXaUvq3bs3jhw5Yu4wyIoJgoArBRX442I+9l8oQNqlAhTeMswik9ihd6gH7gr3QnS4F3qHesDNgT0A1DxiOxGiwjwRFeaJpLiOKCirxq5zN/DbGTn2nL+Bq8WVSN6fieT9mfB3c8AD3fzgWYomL0tCls9mCqjGEIvF2Lp1KyZPnowBAwboLaSp5e7ujtTUVEyZMgXR0dHw9PREUlISkpKSzBg5UetVUqHEHxfzsSfjBvaez6+zjICjVIzocE/0i/DC3W290SPYo9Wup0Sm4+0iw6ioYIyKCkZljRr7LuTj19NypJyRQ66owmf7rwCQ4Nur+zCqTzAeiwpGiFfds8PJetlsARUeHl5v5R8aGoqff/65wX27d++OPXv2tFRoAPhXCRFQ/+dAoxFw+loJdv51A7sz8nA8uxg3r08pFYvQO9QTA9r5YEB7Fkxkfo72YsRF+iEu0g/Vqm7Yk5GPH4/lIOVMLnKKKvHe9vN4b/t53N3WC49FhWBYd3+jXEKLzIuvoIlpJ6hVVFTA0dHRzNEQmZd2KY9qNbDjVC52/JWHXeduIL+sWq9d+zYuuK+DL+7t6IN+EV788iGLJZPUFlMDO3hh85YciEN7Y/PxXPzx90T0Py8VYv5PZzAqKhhP3x2K9m1c73xQskj8LWRiYrEYHh4eujP7nJycbju3SqPRoKamBlVVVTwrzASYb9MRBAElpWW4ej0fB3OVeH/9DijV/3QzOduLcW8HXwzs5It7O/oiyIN/bJD1kYmBYT0DMCo6FFeLK7H5aA6+O5KDKwUVuvlSMW29MS4mDPGRfrxen5VhAWUG/v7+AP5ZHuF2BEFAZWUlHB0dOYHdBJjvlqdUa1ClVKOipvZn+6UyfH+2HAKACB9nDO7cBoM7t8Fd4V4cliObEuThiKmDO2DywPbYdyEfX/x5BdvPXkfapdqTIYI8HDHhngg8cVcInGX8arYGfJXMQCQSISAgAG3atGlw2XilUok9e/bgvvvu4zoiJsB8G58gCLicX47dGTew7/wNZP69JpNGAIqrNfB30GB6fEfc3z0Q7XzrXt+MyNbY2YlwX0df3NfRF1eLK/HVgSxsOJiFq8WVWPBzOt7bfh5P3x2K8f3D0ca1ZRaXJeNgAWVGYrG4wet/icViqFQqODg48AvdBJhv47l4oww/n8jFlpPXcCGvTLddYidC//Y+eKCbPwZ28MLBPdsx7N4I5ptapSAPR0xP6IQpg9pj09EcfLr3EjILKvDhzov4dO9lPNUvDJNi26JNAyuek/mwgCIio8gtqcRPx6/hx+PXkJ77z3Xv7MV2uK+jLx7o5o+hXfzg7lRbLPEiq0S1HO3FePruMDzZNxS/n72Oj3dfxNGsYqz94zLWH7jCQspCsYAioiZTVCnx62k5fjh2FWmXCqBdlUBiJ8I9HXzwYI9AxHf140KWRI0gthMhoas/4iP9sO9CPlb8fh5HrhTpCqnEAeGYPLA93B35ebIELKCIyCBqjYD9F/Ox8UgOfj0tR7Xqnwvz9g33wsO9AzGsWwA8ne3NGCWR9RKJRLi3gy/uae+jV0h9vPsSvj2UjX8P7oCn7w7jiRZmxgKKiBolq6AC3x7OxvdHc3CtpEq3vZ2vMx7tE4wRPQO50jKREd1cSO08l4fF2/7C+bwyLPg5HevSMvGf+zvjgW7+PGvYTFhAEdFt1ag0SEmX4+uD2dh3IV+33c1BghG9AvF4VAh6BLvzFzhRCxKJRBjc2Q/3dfDFd0dysCwlA1cKKjB5/VHc28EH80d0RVuexWpyLKCIqI4rBeXYcCALG4/koODvi/WKRMA97X0wOjoEcZF+cJDe/gxSIjI+idgOT/YNxYiegfh490Ws3nMJe8/n4/4VezEpti0mD2rPz6UJsYAiIgC1c5t2ncvDF39ewe6MG7oJ4W1cZXjirhCMjg7hEB2RBXCWSZAU3wmP9gnG3J/OYHfGDazccQGbj1/FwpHdcV9HX3OH2CqwgCJq5UoqlPj6UBa++PMKcooqddtjO/riqX6hGNy5DS8xQWSBwn2ckfzsXfjtjBzzt6Qju7ASz6w9iCf7hmL28C5w4YrmLYrZJWqlLuSVIXn/ZWw6chWVSjUAwN1RitHRwXiqXxjCfZzNHCER3YlIJML93QJwbwdfLPntHJL3Z+Krg1nYe/4G3nmsB/q38zF3iDaLBRRRKyIIAvZfLMAney9h17kbuu2d/V3x3IAIjOgVyDkURFbIWSbBvBFdkdDVHzM2nkBOUSXGfnIAif3D8foDnfm5bgEsoIhaAZVag22n5fi/PRdx+mrtKuEiETC0ix+eHRCOmLbePJOOyAbEtPPGr6/ch0XbzmLDgSwk78/EgcuF+HBsb56pZ2QsoIhsWJVSjW8OZeOTvZd085scpHYYHR2CCfdEIMybw3REtsZFJsGiR7ojoas/kr45jrO5Cjz0/j4sHtUDI3oGmjs8m8ECisgGlVYp8eWfWViz7xLyy2qXIfBytsf4mHCMiwmDF1cJJ7J5sR19se3le/HSV8dw4HJh7b+XCvDfByM5pGcELKCIbEhJhRJr/7iM5P2ZKKmsvVhvkIcjJsW2xWNRIXC05y9NotbEz80B65/vh/e2n8cHOy9g/YEsnMwpwSfPRMPfnRcnbg4WUEQ2oKRSibX7LmPtvssorVYBANr6OmPywPZ4uFcgpFyGgKjVkojt8Gp8J9wV7oWXvz6GU1dL8PCH+/DpM3ehe7C7ucOzWiygiKxYaZUSn/2RiU/3XoKiqrZw6uTnipeGdMD93fwhtuPEcCKqdV9HX/w45R5MWHcI5/PK8PjH+7F8dC8M6x5g7tCsEgsoIitUpVTj87RMrNp1EcUVtUN1Hf1c8PKQjnigmz/sWDgRUT1CvZ2waXJ//HvDMezOuIHJ64/i1biOmDq4Pc/ENRALKCIrolJrsPFIDlb8fh5yRRUAoJ2vM14Z2hHDuwewcCKiO3JzkGLN+Ggs3HYWn/2RiWWpGZArqvDmw934O8QALKCIrIAgCPjtzHW88+tfuJRfDqB2cvgrQzvg0T7BHKojIoNIxHaY+1BXtPV1wZwfT2P9gSyUV6uw5PGenDPZSCygiCzc8exiLNp6FgczCwHULkcwdVB7PHV3KGQSnlVHRE037u4wuDlI8Oq3J/DD8Wsor1Hj/Sd7c5mDRmABRWShcooq8M6v5/DTiWsAahfAnHhvW7wQ244XCSUio3m4VxBcZBK8uP4oUtOvY8K6Q/i/cdFw5u+ZBrGfjsjCVNaosTzlHAYv242fTlyDSASM6hOMndMH4tX4TiyeiMjohnTxQ/Kzd8HZXow/LhRg/NqDqKhRmTssi8YCishCCIKArSdzMWTZLqzccQE1Kg3ubuuFLVPvwbLRPRHg7mjuEInIhvVv54Mvn+8HNwcJDl8pwgtfHEG1Sm3usCwWCygiC5BxvRRPfvInpmw4imslVQjycMRHT/XBVxPvRrcgLnRHRKbRO9QTnz3bF45SMfaez8e0b45DrRHMHZZF4lgAkRlV1Kjw3vbzWLP3MlQaATKJHV4c2A4v3NeOl10hIrOICvPE/z0ThQnJh7HtlByuslN4e1R3rhN1CxZQRGbye/p1zP3pDK4WVwIA4iP9MOehSAR7Opk5MiJq7e7t4IuVT/bC5PVH8c3hbLg6SDB7eBcWUTdhAUVkYvKSKsz58TRS0q8DqF3Paf6Irhga6WfmyIiI/nF/twD8b1QPzNh4Ep/uuww/NwdMvK+tucOyGCygiExEEAR8fSgbi7aeRWm1ChI7EZ6/ty1eGtIeTvb8KBKR5Xk8OgQllUq8tfUsFv9yFh39XRHb0dfcYVkE/tYmMoErBeV4fdMppF0qAAD0DPHA/0Z1R2d/NzNHRkTUsAn3ROD89TJ8czgbUzccxY9TBqCtr4u5wzI7noVH1II0GgFr9l1Gwoo9SLtUAAepHd4Y3gXfv9ifxRMRWQWRSIQFI7siKswTpVUqPP/5YSiqlOYOy+xYQBG1kOzCCoz99E+8+XM6qpQaxLT1xm+v3Ifn723La9cRkVWRScRY/XQUAtwdcOlGOV7+6lirX96ABRSRkQmCgG8PZeOB9/biz0uFcJSK8dbIbtgwsR/CvJ3NHR4RUZP4usrwf+OiIZPYYee5G1jy2zlzh2RWLKCIjCi/rBoTPz+M1zadRFm1CtFhnvj1lXvx9N1hPP2XiKxe92B3vPNYDwDA6t0XsetcnpkjMh8WUERGsifjBu5fsRe/n82DvdgOrz/QGd+8EMNeJyKyKQ/3CsL4mDAAwIyNJ1FYXmPmiMyDBRRRM9WoNFi07SyeWXsQ+WXV6Ojngh+nDsCk2Hac60RENmnmsC5o38YFN0qr8fqmkxCE1jcfigUUUTNczi/HqI/24//2XAIAPH13KH6aeg+6BPAMOyKyXQ5SMd4b0wtSsQgp6dfx7eFsc4dkciygiJpo68lcPPT+Ppy6WgIPJyk+HheFt0Z2h4OU17AjItvXNdAd0+M7AQDmb0lHZn65mSMyLZsroLZu3Yp+/frB0dERPj4+ePTRR/Xuz8rKwkMPPQRnZ2f4+PjgpZdeQk2N/vjtqVOnEBsbC0dHRwQFBWHBggWtsnuS6lej0mDeT2cwZcNRlFWr0DfCC7+8fC8SuvqbOzQiIpN6/t62uLutFypq1Hjlm+NQqjXmDslkbGol8k2bNmHixIlYtGgRBg8eDEEQcOrUKd39arUaw4cPh6+vL/bt24eCggKMHz8egiDg/fffBwAoFArExcVh0KBBOHToEDIyMpCYmAhnZ2e8+uqr5npqZCGuFldiyvqjOJ5dDACYFNsO0+M7QiK2ub9FiIjuSGwnwvLRvZCwYg+OZxfj490XMXVwB3OHZRI2U0CpVCq8/PLLWLJkCSZMmKDb3qlTJ93/U1JSkJ6ejuzsbAQGBgIAli1bhsTERCxcuBBubm5Yv349qqqqkJycDJlMhm7duiEjIwPLly9HUlIST0Vvxfaev4F/f3UMxRVKuDlIsHx0L14AmIhavUAPRyx4uCumfXMCH+y8gJG9gxDs6WTusFqczRRQR48exdWrV2FnZ4fevXtDLpejV69eWLp0Kbp27QoASEtLQ7du3XTFEwAkJCSguroaR44cwaBBg5CWlobY2FjIZDK9NjNnzkRmZiYiIiLqPHZ1dTWqq6t1txUKBQBAqVRCqWz6cvfafZtzDGq82+VbEAR8tv8K/vdbBjQC0C3QDSvH9ECIpxNfm2bg+9u0mG/Tam35Ht61Db4K98TBzCLM/+kMVo3tZdLHN1a+DdnfZgqoS5dqz4KaN28eli9fjvDwcCxbtgyxsbHIyMiAl5cX5HI5/Pz0eww8PT1hb28PuVwOAJDL5QgPD9dro91HLpfXW0AtXrwY8+fPr7M9JSUFTk7Nr8JTU1ObfQxqvJvzXaMGvrlkh8P5tUN0fX01GB1SiFNpu3Dqdgcgg/D9bVrMt2m1pnwPcgcOQ4zUs3lYtuEXdPEw/dzh5ua7oqKi0W0tvoCaN29evcXJzQ4dOgSNpnbi2uzZszFq1CgAwGeffYbg4GB89913eOGFFwCg3iE4QRD0tt/aRjuB/HbDdzNnzkRSUpLutkKhQEhICOLj4+Hm1vTT2ZVKJVJTUxEXFwepVNrk41Dj3Jrv3JIqTN5wHKfzFRDbiTDrgU4Y1y+Ew7hGwve3aTHfptVa853nfA6f7b+CX/NcMXV0f8gkppkfaqx8a0eQGsPiC6ipU6dizJgxDbYJDw9HaWkpACAyMlK3XSaToW3btsjKygIA+Pv748CBA3r7FhUVQalU6nqZ/P39db1RWnl5tUvV39p7dfPj3DzkpyWVSo3ywTHWcahxpFIp0uXlmLDuMPLLquHpJMWHT/VB/3Y+5g7NJvH9bVrMt2m1tnwnxXfClpNyZBZUYN2f2ZgyqL1JH7+5+TZkX4s/dcjHxwedO3du8MfBwQFRUVGQyWQ4d+6fixsqlUpkZmYiLKx2yfmYmBicPn0aubm5ujYpKSmQyWSIiorStdmzZ4/e0gYpKSkIDAysM7RHtikl/Tqe+L805JdVo7O/K36aeg+LJyKiRnB1kGLWsM4AgA92XMDV4kozR9RyLL6Aaiw3NzdMmjQJc+fORUpKCs6dO4cXX3wRAPD4448DAOLj4xEZGYlx48bh2LFj2L59O6ZPn46JEyfqhtrGjh0LmUyGxMREnD59Gps3b8aiRYt4Bl4rIAgCdlwTYerXJ1Cl1GBQJ19sfLE/Qrxs/2wSIiJjeaR3EO4K90SlUo2FW9PNHU6LsZkCCgCWLFmCMWPGYNy4cbjrrrtw5coV7NixA56engAAsViMrVu3wsHBAQMGDMDo0aMxcuRILF26VHcMd3d3pKamIicnB9HR0Zg8eTKSkpL05jiR7VGpNZiz5Sx+vCKGIADj7g7DJ89Ew0Vm8aPcREQWRSQSYf6IbrATAdtOyXHkSpG5Q2oRNvXtIJVKsXTpUr2C6FahoaH4+eefGzxO9+7dsWfPHmOHRxaqskaNKRuOYsdfeRBBwMwHOmPife3Y40hE1ESRgW4Y1ScY3x3Jwfs7ziP52b7mDsnobKoHishQJRVKPL3mAHb8lQeZxA7PddLg2f5hLJ6IiJpp6uD2ENuJsOvcDZz4++oNtoQFFLVa8pIqPP7xfhy5UgQ3BwnWJUahhxeveUhEZAxh3s54uFftwtUrt583czTGxwKKWqWLN8ow6qP9yLheBj83Gb6b1B9RYZ7mDouIyKb8e3AH2ImA7X/l4fTVEnOHY1QsoKjVOXOtBI+vTsPV4kq09XHGphf7o5O/q7nDIiKyORE+zni4VxAA4D0b64ViAUWtysmcYoz95AAKy2vQI9gd302KaRUXvSQiMpcpg9pDJAJS06/jzDXb6YViAUWtxpErRXjqkwMoqVQiKswTXz7fD94udVeQJyIi42nfxgUP9aidC/X+9gtmjsZ4WEBRq/DnpQKMW3MApdUq9Ivwwrrn+sLNofVcXoGIyJz+Pbi2F+rXM3L8JW/89eYsGQsosnn7L+Qj8bODqKhR494OPkh+ti8XyCQiMqEOfq4Y1j0AAPDRrotmjsY4WECRTTt4uRDPrTukuzTLJ89Ew9FebO6wiIhanRdj2wEAfjklR1F5zR1aWz4WUGSzjmYV4dnPDqJKqcHATr5YPS4KDlIWT0RE5tAtyB3dgtxQo9Zg09Ecc4fTbCygyCadvlqC8WsPorxGjf7tvLH66SjIJCyeiIjM6cm+oQCArw9lQxCse+FiFlBkc87JS2snjFepcFe4Jz4dH82eJyIiCzCiZyAcpWJcyCvDYSu/yDALKLIpmfnleOrTAyiqUKJnsDvWJt4FJ3tOGCcisgSuDlI81LN2MvlXB7PMHE3zsIAim3GjtBrPrD2I/LJqdAlww7rn+sKVSxUQEVmUMX8P4209mYuSCqWZo2k6FlBkE8qqVXg2+SCyCisQ4uWIdc/dBQ8ne3OHRUREt+gd4oHO/q6oVmnww/Gr5g6nyVhAkdWrUWkw6YsjOH1VAW9ne3z+XD+0cXUwd1hERFQPkUiEMXeFAKgdxrPWyeQsoMiqaTQCZmw8gX0X8uFkL8Znz96FCB9nc4dFREQNeKR3MGQSO/wlL8Xx7GJzh9MkLKDIqr3961/48fg1SOxEWP10FHoEe5g7JCIiugN3J6luZfKvD2abOZqmYQFFVuvrg1n4vz2XAABLHu+B+zr6mjkiIiJqLO2aUFtOXkNplfVNJmcBRVYp7WIB3vjhNABg2tCOeKR3sJkjIiIiQ9wV7om2Ps6oqFFjx1955g7HYCygyOpk5pfjxfVHoNIIeKhnIF4a0t7cIRERkYFEIhHiu/oDALafZQFF1KJKKpWYsO4QiiuU6BnigSWP9YBIJDJ3WERE1ARDu7QBAOw8lwelWmPmaAzDAoqshkqtwdQNR3HxRjkC3B3wCS8OTERk1XqHesLL2R6lVSocyiw0dzgGYQFFVuOd385h7/l8OErF+HR8NNq4ca0nIiJrJrYTYWCn2hOArG0YjwUUWYVfTuXqzrhbPronuga6mzkiIiIyhrgufgCA7WevW9WimiygyOJdvFGGGRtPAgD+dV9bPPD32iFERGT97u3oC3uxHTILKnDxRrm5w2k0FlBk0cqrVZj0xRGUVavQL8ILryV0MndIRERkRC4yCfq19QJQ2wtlLVhAkcUSBAGvf38K5/PK0MZVhvfH9oZEzLcsEZGtGaobxrOeeVD8NiKLtW5/JracqL1My6qn+vACwURENmrI38sZHL5SiKLyGjNH0zgsoMginb5agoXbzgIAZg3rguhwLzNHRERELSXY0wmd/V2hEYBdGdbRC8UCiixORY0KL399DEq1gPhIPzw7INzcIRERUQvTDuP9ns4CiqhJ3vz5LC7eKIefmwz/G8WVxomIWgPtMN7ujBuoUVn+quQsoMii/Hpajq8OZkEkAt4d3QuezvbmDomIiEygZ7AHfFxkKKtW4eBly1+VnAUUWYzckkq8/n3tek8v3NcO/dv7mDkiIiIyFTs7EQZ3rl2V/HcrWM6ABRRZBLVGQNI3J1BcoUSPYHckxXU0d0hERGRigzvXzoPadyHfzJHcGQsosghr911G2qUCONmL8d6Y3rCX8K1JRNTaRIV5Aqi9AkVpldLM0TSM31JkdpdulGFpyjkAwJwHIxHh42zmiIiIyBx8XWUI8nCEIACnrpaYO5wGsYAis9JoBPxn00lUqzS4t4MPnrgrxNwhERGRGfUK8QAAnMhmAUV0W5+nZeJQZhGc7cVY/Gh3LllARNTK9Qh2BwCczCk2byB3wAKKzCa7sAL/+7V26O71YV0Q7Olk5oiIiMjceup6oIrNGsedsIAisxCE2qG7SqUad7f1wlN9Q80dEhERWYDuQe6wEwHXSqqQp6gydzi3xQKKzGLDwSzsv1gAR6kY/xvVA3Z2HLojIiLAWSZBhzauAIATOZY7D8qmCqiMjAw8/PDD8PHxgZubGwYMGICdO3fqtcnKysJDDz0EZ2dn+Pj44KWXXkJNjf6Vn0+dOoXY2Fg4OjoiKCgICxYsgCAIpnwqNi1PUYXF2/4CAMxI6IQwb551R0RE/9DOg7LkYTybKqCGDx8OlUqFHTt24MiRI+jVqxcefPBByOVyAIBarcbw4cNRXl6Offv24euvv8amTZvw6quv6o6hUCgQFxeHwMBAHDp0CO+//z6WLl2K5cuXm+tp2ZxF286irFqFniEeGN8/3NzhEBGRhdHNg7LgieQScwdgLPn5+bhw4QLWrl2LHj16AADefvttrFq1CmfOnIG/vz9SUlKQnp6O7OxsBAYGAgCWLVuGxMRELFy4EG5ubli/fj2qqqqQnJwMmUyGbt26ISMjA8uXL0dSUhLPEmumPy8V4Ifj1yASAW893A1iDt0REdEtet00kVwQBIv87rWZAsrb2xtdunTB559/jj59+kAmk+Hjjz+Gn58foqKiAABpaWno1q2brngCgISEBFRXV+PIkSMYNGgQ0tLSEBsbC5lMptdm5syZyMzMRERERJ3Hrq6uRnV1te62QqEAACiVSiiVTV9JVbtvc45hSZRqDeb8cBoAMCY6GJ39nCzqudlavi0d821azLdpMd/N09bbAfYSOyiqVLhwvQThd5jqYax8G7K/zRRQIpEIqampePjhh+Hq6go7Ozv4+fnh119/hYeHBwBALpfDz89Pbz9PT0/Y29vrhvnkcjnCw8P12mj3kcvl9RZQixcvxvz58+tsT0lJgZNT80/NT01NbfYxLMHOayJk5InhLBHQXcjEtm2Z5g6pXraSb2vBfJsW821azHfTBTqIkVkmwuc/70G0b+PmITc33xUVFY1ua/EF1Lx58+otTm526NAhREVFYfLkyWjTpg327t0LR0dHfPrpp3jwwQdx6NAhBAQEAEC93YC3dg/e2kY7gfx2XYgzZ85EUlKS7rZCoUBISAji4+Ph5ubWuCdaD6VSidTUVMTFxUEqlTb5OJbguqIKs1b+AUCN2Q92xeNRweYOqQ5byrc1YL5Ni/k2Lea7+Y4IfyHzzyyIfCIwbFjnBtsaK9/aEaTGsPgCaurUqRgzZkyDbcLDw7Fjxw78/PPPKCoq0hUtq1atQmpqKtatW4fXX38d/v7+OHDggN6+RUVFUCqVul4mf39/XW+UVl5eHgDU6b3SkslkekN+WlKp1CgfHGMdx5yWpJ5GebUavUI8MKZvuEUvW2AL+bYmzLdpMd+mxXw3XZ8wL3z+ZxZOX1M0OofNzbch+1p8AeXj4wMfH587ttN2u9nZ6Z9YaGdnB41GAwCIiYnBwoULkZubq+uRSklJgUwm082TiomJwaxZs1BTUwN7e3tdm8DAwDpDe9Q4aRcL8KN24vjIbhZdPBERkWXQnol3+poCSrUGUrFlLRxgWdE0Q0xMDDw9PTF+/HicOHECGRkZmDFjBi5fvozhw4cDAOLj4xEZGYlx48bh2LFj2L59O6ZPn46JEyfqeq3Gjh0LmUyGxMREnD59Gps3b8aiRYt4Bl4TaTQC3tqaDgB4ql8ougW5mzkiIiKyBuHeTnBzkKBGpcE5eam5w6nDZgooHx8f/PrrrygrK8PgwYMRHR2Nffv24ccff0TPnj0BAGKxGFu3boWDgwMGDBiA0aNHY+TIkVi6dKnuOO7u7khNTUVOTg6io6MxefJkJCUl6c1xosbbcvIazlxTwEUmwbShHc0dDhERWQmRSKTrhTpugQtqWvwQniGio6Px22+/NdgmNDQUP//8c4Ntunfvjj179hgztFapWqXGkt9qLxY8KbYtvF3qzhMjIiK6nZ7BHth7Ph8nsovx9N1h5g5Hj830QJHl+fLPLOQUVaKNqwzP3VN3+QciIqKGaHugTlrgNfFYQFGLKKlU4oMd5wEA0+I6wsnepjo7iYjIBHr+fU28jLxSlFWrzByNPhZQ1CJW776Iogol2rdxscg1n4iIyPK1cXNAgLsDBAE4ZWG9UI3uFjBkEjUvvNu65ZZUYu2+ywCA/9zfGRILO/WUiIisR2SAG3JLqnApvwwx7bzNHY5OowuoY8eO6d0+cuQI1Go1OnXqBADIyMiAWCzWradErde7qRmoVmlwV7gnhnZpY+5wiIjIigV5OgIArhZVmjkSfY0uoHbu3Kn7//Lly+Hq6op169bB09MTQO2K3s8++yzuvfde40dJVuPijTJsPJIDAHj9gS5cO4uIiJolyOPvAqrYsgqoJo2tLFu2DIsXL9YVT0DtRXnfeustLFu2zGjBkfX5cOcFaARgaJc2iArzvPMOREREDbDUHqgmFVAKhQLXr1+vsz0vLw+lpZa3WiiZRlZBBX48fg0A8NKQDmaOhoiIbIFN9UA98sgjePbZZ7Fx40bk5OQgJycHGzduxIQJE/Doo48aO0ayEqt2XYBaIyC2oy96BHuYOxwiIrIB2h6o64oqKNUaM0fzjyYtzrN69WpMnz4dTz/9NJRKZe2BJBJMmDABS5YsMWqAZB1yiip0c59eGtLezNEQEZGt8HGWwV5ihxqVBvKSKoR4OZk7JABNLKCcnJywatUqLFmyBBcvXoQgCGjfvj2cnZ2NHR9ZidW7L0KlEdC/nTeiwrzMHQ4REdkIOzsRgjwccTm/HDlFlRZTQDVrgR5nZ2d4eXnBx8eHxVMrJi+pwreHanuf/j2Yc5+IiMi4LHEeVJMKKI1GgwULFsDd3R1hYWEIDQ2Fh4cH3nzzTWg0ljM+Sabx8Z6LqFHXrvt0d1v2PhERkXHpCigLOhOvSUN4s2fPxpo1a/D2229jwIABEAQBf/zxB+bNm4eqqiosXLjQ2HGShbpRWo0NB7IA1PY+cd0nIiIyNt1SBsUVZo7kH00qoNatW4dPP/0UI0aM0G3r2bMngoKCMHnyZBZQrciafZdRrdKgZ4gH7u3gY+5wiIjIBtnMEF5hYSE6d+5cZ3vnzp1RWFjY7KDIOlTUqLDhwBUAwNRB7dn7RERELcISF9NsUgHVs2dPfPDBB3W2f/DBB+jZs2ezgyLrsOnoVSiqVAjzdsKQzrzmHRERtQxtD9S14ipoNIKZo6nVpCG8d955B8OHD8fvv/+OmJgYiEQi7N+/H9nZ2di2bZuxYyQLpNEISP7jMgBgfEw47OzY+0RERC3D390BdiKgRq1Bflk12rg5mDukpvVAxcbGIiMjA4888giKi4tRWFiIRx99FOfOnePFhFuJvRfycfFGOVxkEjweHWzucIiIyIZJxXbw/7toyrGQeVBN6oECgMDAQE4Wb8U++7v36bGoYLg6SM0cDRER2bogT0dcK6nC1aJK9Ak1/8Xqm1xAFRcXY82aNTh79ixEIhEiIyPx3HPPwd3d3ZjxkQW6dKMMu87dgEgEJPYPN3c4RETUCgR5OOIQiizmTLwmDeEdPnwY7dq1w7vvvovCwkLk5+dj+fLlaNeuHY4ePWrsGMnCrNufCQAY3KkNwn24Aj0REbU8SzsTr0k9UNOmTcOIESPwySefQCKpPYRKpcLzzz+PV155BXv27DFqkGQ5FFVK3UWDnx0QYeZoiIiotQjyqL0GnqX0QDWpgDp8+LBe8QQAEokEr732GqKjo40WHFmebw9lo7xGjY5+LhjQ3tvc4RARUSthaT1QTRrCc3NzQ1ZWVp3t2dnZcHV1bXZQZJnUGgHr0jIBAIn9I7hwJhERmczNq5ELgvnXgmpSAfXEE09gwoQJ+Oabb5CdnY2cnBx8/fXXeP755/Hkk08aO0ayEHvO30B2YSXcHaV4pHeQucMhIqJWRFtAlVWroKhUmTmaJg7hLV26FCKRCM888wxUqtonIZVK8eKLL+Ltt982aoBkOb47nA0AeLRPEBztxWaOhoiIWhNHezG8ne1RUF6DnOIKuDuZ96z/JhVQ9vb2eO+997B48WJcvHgRgiCgffv2cHJyMnZ8ZCEKy2uQmn4dAPB4VIiZoyEiotYoyNMRBeU1uFpUia6BVlhAaTk5OaF79+7GioUs2I/Hr0KpFtA10A2RgW7mDoeIiFqhIA9HnMwpsYgz8ZpUQJWXl+Ptt9/G9u3bkZeXB41Go3f/pUuXjBIcWY7vDtcuXTA6mr1PRERkHrqJ5BZwJl6TCqjnn38eu3fvxrhx4xAQEMCzsWzcmWslSM9VwF5sh4d7BZo7HCIiaqV0SxlYaw/UL7/8gq1bt2LAgAHGjocskLb3KS7SDx5O9maOhoiIWqublzIwtyYtY+Dp6QkvLy9jx0IWqFqlxg/HrwIAHosONnM0RETUmlnSYppNKqDefPNNzJkzBxUVFcaOhyzM9rN5KK5Qwt/NAfd18DV3OERE1IoF/305l4LyGlTWqM0aS6OH8Hr37q031+nChQvw8/NDeHg4pFKpXlteUNh23Lz2k9iOc92IiMh83BwlcJFJUFatwtXiSrRv42K2WBpdQI0cObIFwyBLJC+pwu6MGwCAx6I4fEdEROYlEokQ5OGIc9dLraeAmjt3bkvGQRbo+2M50AjAXeGeaOtrvjcpERGRVpDn3wWUmedBNWkOFLUOPxz7e/I4e5+IiMhC/HMmnnnnYTe6B8rLywsZGRnw8fGBp6dng2s/FRYWGiU4Mp8LeWXIuF4GqViE+7sFmDscIiIiAJZzJl6jC6h3330Xrq6uAIAVK1a0VDxkIX49nQsAGNDeB+6O0ju0JiIiMg1LWQuq0QXU+PHj6/0/2aZtp+QAgGHsfSIiIgtidT1QCoWi0Qd1c+PFZq3ZlYJypOcqILYTIS7Sz9zhEBER6YR4OqF7kDtCvZ0gCILZLifX6EnkHh4e8PT0bPBH26YlLFy4EP3794eTkxM8PDzqbZOVlYWHHnoIzs7O8PHxwUsvvYSamhq9NqdOnUJsbCwcHR0RFBSEBQsWQBAEvTa7d+9GVFQUHBwc0LZtW6xevbpFnpOl+uV0be9TTFtveDrz0i1ERGQ5fF1l2PLve/Dh2D5mvRZvo3ugdu7c2ZJx3FFNTQ0ef/xxxMTEYM2aNXXuV6vVGD58OHx9fbFv3z4UFBRg/PjxEAQB77//PoDaXrS4uDgMGjQIhw4dQkZGBhITE+Hs7IxXX30VAHD58mUMGzYMEydOxJdffok//vgDkydPhq+vL0aNGmXS52wuv5yqnf90fzd/M0dCRERkmRpdQMXGxrZkHHc0f/58AEBycnK996ekpCA9PR3Z2dkIDAwEACxbtgyJiYlYuHAh3NzcsH79elRVVSE5ORkymQzdunVDRkYGli9fjqSkJIhEIqxevRqhoaG6ifJdunTB4cOHsXTp0lZRQOUUVeBETglEIiChKwsoIiKi+jS6gLrV3r178fHHH+PSpUv47rvvEBQUhC+++AIRERG45557jBljo6SlpaFbt2664gkAEhISUF1djSNHjmDQoEFIS0tDbGwsZDKZXpuZM2ciMzMTERERSEtLQ3x8vN6xExISsGbNGiiVyjqXrQGA6upqVFdX625r54splUoolcomPyftvs05hqG2nbwGALgrzBMeDnYmfWxzM0e+WzPm27SYb9Nivk3LWPk2ZP8mFVCbNm3CuHHj8NRTT+Ho0aO64qG0tBSLFi3Ctm3bmnLYZpHL5fDz05/w7OnpCXt7e8jlcl2b8PBwvTbafeRyOSIiIuo9jp+fH1QqFfLz8xEQUPestMWLF+t6yG6WkpICJyen5jwtAEBqamqzj9FYX50WAxAhBPlmeR0tgSnzTcy3qTHfpsV8m1Zz811R0fjFOZtUQL311ltYvXo1nnnmGXz99de67f3798eCBQsafZx58+bVW3jc7NChQ4iOjm7U8eqbTHbrDP1b22gnkBva5mYzZ85EUlKS7rZCoUBISAji4+ObdUaiUqlEamoq4uLi6u35Mja5ogqX0/YAAF55fBD83Rxa/DEtianz3dox36bFfJsW821axsq3ISsONKmAOnfuHO677746293c3FBcXNzo40ydOhVjxoxpsM2tPUa34+/vjwMHDuhtKyoqglKp1PUo+fv763qjtPLy8gDgjm0kEgm8vb3rfWyZTKY3LKgllUqN8sEx1nHuZMe52ku3RIV5IsTbtcUfz1KZKt9Ui/k2LebbtJhv02puvg3Zt0kFVEBAAC5cuFCnuNm3bx/atm3b6OP4+PjAx8enKSHUERMTg4ULFyI3N1c3zJaSkgKZTIaoqChdm1mzZqGmpgb29va6NoGBgbrnEhMTgy1btugdOyUlBdHR0Tb/Idj299l3D/DsOyIiogY16WLCL7zwAl5++WUcOHAAIpEI165dw/r16zF9+nRMnjzZ2DECqF3j6fjx48jKyoJarcbx48dx/PhxlJWVAQDi4+MRGRmJcePG4dixY9i+fTumT5+OiRMn6obRxo4dC5lMhsTERJw+fRqbN2/GokWLdGfgAcCkSZNw5coVJCUl4ezZs1i7di3WrFmD6dOnt8jzshQ3SqtxMLP2GoZcvoCIiKhhTeqBeu2111BSUoJBgwahqqoK9913H2QyGaZPn46pU6caO0YAwJw5c7Bu3Trd7d69ewOoXZ9q4MCBEIvF2Lp1KyZPnowBAwbA0dERY8eOxdKlS3X7uLu7IzU1FVOmTEF0dDQ8PT2RlJSkN38pIiIC27Ztw7Rp0/Dhhx8iMDAQK1eutPklDHb+lQdBAHoEuyPYs/kT34mIiGxZkwqompoaLFy4ELNnz0Z6ejo0Gg0iIyPh4uKC/Px8ow3L3Sw5Ofm2a0BphYaG4ueff26wTffu3bFnz54G28TGxuLo0aOGhmjV9py/AQAY2KmNmSMhIiKyfE0awhs9ejQ0Gg2cnJwQHR2Nvn37wsXFBdevX8fAgQONHCK1NLVGwL4L+QCA+zoYv/glIiKyNU0qoHJzczFhwoQ62wYOHIjOnTsbJTAyndNXS1BcoYSrTIKeIR7mDoeIiMjiNamA2rZtGw4ePIhp06YBAK5evYqBAweie/fu+Pbbb40aILW8vX8P3/Vv7w2puElvCSIiolalSXOgvL298dtvv+ku2bJ161b06dMH69evh50dv4CtzZ7ztcN393bwNXMkRERE1qHJ18ILDg5Gamoq7rnnHsTFxeGLL7647UrdZLlKq5Q4eqUIAHAfCygiIqJGaXQB5enpWW+BVFFRgS1btuit0l1YWGic6KjF/XmpECqNgDBvJ4R6c/kCIiKixmh0AbVixYoWDIPMRTv/ib1PREREjdfoAmr8+PEtGQeZyV7d/CcuX0BERNRYjS6gFAqF7pIod7pasbYdWbbswgpczi+H2E6EmHb1XyiZiIiI6jJoDlRubi7atGkDDw+PeudDCYIAkUgEtVpt1CCpZWhXH+8T6gFXB9u+UDIREZExNbqA2rFjB7y8vADUXn+OrN/eDC5fQERE1BSNLqBiY2Pr/f/NioqKsGXLluZHRS1Opdbgj4t/X76lIwsoIiIiQxh11cusrCw8++yzxjwktZATOSUorVLB3VGK7kHu5g6HiIjIqnDZ8FZqT0bt/Kd72vtAbMcFUImIiAzBAqqV0q7/xOULiIiIDMcCqhWqUqpxMqcEANC/HQsoIiIiQxl0LbyVK1c2eP/Vq1ebFQyZxqmrJVBpBPi4yBDi5WjucIiIiKyOQQXUu+++e8c2oaGhTQ6GTEN78eA+ofWv50VEREQNM6iAunz5ckvFQSZ0NOvvAirM08yREBERWadmz4HKycmBRqMxRixkAoIg4GhWMQAgigUUERFRkzS7gIqMjERmZqYRQiFTyCmqxI3SakjsRFz/iYiIqImaXUAJgmCMOMhEtMN3XQPd4CAVmzkaIiIi68RlDFqZY38P3/UO5fAdERFRUzW7gJo1a5buIsNk+TiBnIiIqPkMOguvPjNnzjRGHGQCVUo10q8pANQuYUBERERN06QCKikpqd7tIpEIDg4OaN++PR5++GH2TFmYkzm1C2i2cZUhyIMLaBIRETVVkwqoY8eO4ejRo1Cr1ejUqRMEQcD58+chFovRuXNnrFq1Cq+++ir27duHyMhIY8dMTaQbvgv15AKaREREzdCkOVAPP/wwhg4dimvXruHIkSM4evQorl69iri4ODz55JO4evUq7rvvPkybNs3Y8VIzHNGuQB7mYd5AiIiIrFyTCqglS5bgzTffhJubm26bm5sb5s2bh3feeQdOTk6YM2cOjhw5YrRAqXkEQcCxm3qgiIiIqOmaVECVlJQgLy+vzvYbN25AoaidpOzh4YGamprmRUdGk11YifyyGkjFInTjAppERETN0uQhvOeeew6bN29GTk4Orl69is2bN2PChAkYOXIkAODgwYPo2LGjMWOlZtDOf4oMdOcCmkRERM3UpEnkH3/8MaZNm4YxY8ZApVLVHkgiwfjx4/Huu+8CADp37oxPP/3UeJFSs2gLqCgO3xERETVbkwooFxcXfPLJJ3j33Xdx6dIlCIKAdu3awcXFRdemV69exoqRjOCfBTQ9zBsIERGRDWjWQpouLi7w8vKCSCTSK57IslTUqHA2txQAJ5ATEREZQ5PmQGk0GixYsADu7u4ICwtDaGgoPDw88Oabb0Kj0Rg7RmqmkzklUGsE+Ls5IJALaBIRETVbk3qgZs+ejTVr1uDtt9/GgAEDIAgC/vjjD8ybNw9VVVVYuHChseOkZjiZUwwA6M3LtxARERlFkwqodevW4dNPP8WIESN023r27ImgoCBMnjyZBZSFOScvAwB0CXC7Q0siIiJqjCYN4RUWFqJz5851tnfu3BmFhYXNDoqMK+N67fynjn6uZo6EiIjINjSpgOrZsyc++OCDOts/+OAD9OjRo9lBkfGoNQLO59UWUJ38WUAREREZQ5OG8N555x0MHz4cv//+O2JiYiASibB//35kZ2dj27Ztxo6RmiG7sAJVSg1kEjuEejmZOxwiIiKb0KQeqNjYWGRkZOCRRx5BcXExCgsL8eijj+LMmTP47LPPjB0jNcO5v4fvOvi5QGwnMnM0REREtqHJ60AFBgbWmSx+4sQJrFu3DmvXrm12YGQcGXLOfyIiIjK2JvVAmcPChQvRv39/ODk5wcPDo879J06cwJNPPomQkBA4OjqiS5cueO+99+q0O3XqFGJjY+Ho6IigoCAsWLAAgiDotdm9ezeioqLg4OCAtm3bYvXq1S31tFqctgeqEwsoIiIio2nWSuSmVFNTg8cffxwxMTFYs2ZNnfuPHDkCX19ffPnllwgJCcH+/fvxr3/9C2KxGFOnTgUAKBQKxMXFYdCgQTh06BAyMjKQmJgIZ2dnvPrqqwCAy5cvY9iwYZg4cSK+/PJL/PHHH5g8eTJ8fX0xatQokz5nY9CdgccJ5EREREZjNQXU/PnzAQDJycn13v/cc8/p3W7bti3S0tLw/fff6wqo9evXo6qqCsnJyZDJZOjWrRsyMjKwfPlyJCUlQSQSYfXq1QgNDcWKFSsAAF26dMHhw4exdOlSqyugalQaXLpRDoA9UERERMZkUAH16KOPNnh/cXFxc2IxupKSEnh5eelup6WlITY2FjKZTLctISEBM2fORGZmJiIiIpCWlob4+Hi94yQkJGDNmjVQKpWQSqV1Hqe6uhrV1dW62wqFAgCgVCqhVCqbHL9236Ye4/z1Uqg0AlxkEvg4iZsVS2vQ3HyTYZhv02K+TYv5Ni1j5duQ/Q0qoNzd3e94/zPPPGPIIVtMWloavv32W2zdulW3TS6XIzw8XK+dn5+f7r6IiAjI5XLdtpvbqFQq5OfnIyAgoM5jLV68WNdDdrOUlBQ4OTV/6YDU1NQm7Xc0XwRADF97JX755Zdmx9FaNDXf1DTMt2kx36bFfJtWc/NdUVHR6LYGFVDGXqJg3rx59RYeNzt06BCio6MNOu6ZM2fw8MMPY86cOYiLi9O7TyTSP5VfO4H85u2NaXOzmTNnIikpSXdboVAgJCQE8fHxcHNr+uVTlEolUlNTERcXV2/P15389ft54Pxl9O0UgmHDIpscR2vR3HyTYZhv02K+TYv5Ni1j5Vs7gtQYZp0DNXXqVIwZM6bBNrf2GN1Jeno6Bg8ejIkTJ+KNN97Qu8/f3x9yuVxvW15eHoB/eqJu10YikcDb27vex5TJZHrDglpSqdQoH5ymHufCjdpKukuAGz/ABjDW60aNw3ybFvNtWsy3aTU334bsa9YCysfHBz4+PkY73pkzZzB48GCMHz++3gsax8TEYNasWaipqYG9vT2A2mG2wMBAXaEWExODLVu26O2XkpKC6Ohoq/sQ8Aw8IiKilmE160BlZWXh+PHjyMrKglqtxvHjx3H8+HGUlZUBqC2eBg0ahLi4OCQlJUEul0Mul+PGjRu6Y4wdOxYymQyJiYk4ffo0Nm/ejEWLFunOwAOASZMm4cqVK0hKSsLZs2exdu1arFmzBtOnTzfL826qihoVsgpre6B4Bh4REZFxWc0yBnPmzMG6det0t3v37g0A2LlzJwYOHIjvvvsON27cwPr167F+/Xpdu7CwMGRmZgKoneSempqKKVOmIDo6Gp6enkhKStKbvxQREYFt27Zh2rRp+PDDDxEYGIiVK1da3RIGF/LKIAiAj4s9vF3qDi8SERFR01lNAZWcnHzbNaCA2gnp8+bNu+Nxunfvjj179jTYJjY2FkePHjUwQstyjpdwISIiajFWM4RHhtHNf2IBRUREZHQsoGzUueu1c8M6cQI5ERGR0bGAslEZHMIjIiJqMSygbFBJhRJyRRUAoKOfi5mjISIisj0soGxQRl5t71OQhyNcHaxr7SoiIiJrwALKBmnPwOvA3iciIqIWwQLKBmnPwOMCmkRERC2DBZQN4hpQRERELYsFlA3S9UBxCQMiIqIWwQLKxiiqlCiqUAIAInyczRwNERGRbWIBZWOuFlUCADydpHCWWc2VeoiIiKwKCygboy2ggjwdzRwJERGR7WIBZWNyiioA1K4BRURERC2DBZSNuVr8dw+Uh5OZIyEiIrJdLKBsjK6A4hAeERFRi2EBZWN0c6A4hEdERNRiWEDZGG0PVDB7oIiIiFoMCygbUqVUI7+sBgB7oIiIiFoSCygbou19crYXw8NJauZoiIiIbBcLKBty8xpQIpHIzNEQERHZLhZQNuSfJQw4fEdERNSSWEDZEK5CTkREZBosoGwIF9EkIiIyDRZQNoQ9UERERKbBAsqGcA4UERGRabCAshEqtQZyRRUALqJJRETU0lhA2Qi5ogpqjQB7sR18XWTmDoeIiMimsYCyEdr5TwEeDrCz4xpQRERELYkFlI3g/CciIiLTYQFlI3KKWEARERGZCgsoG8ElDIiIiEyHBZSN4BAeERGR6bCAshG6Aoo9UERERC2OBZQN0GgEXQEV4snLuBAREbU0FlA2IL+8GjUqDexEgL+7g7nDISIisnksoGyAdgK5n5sDpGK+pERERC2N37Y2gBPIiYiITIsFlA3gEgZERESmxQLKBrAHioiIyLRYQNkA9kARERGZFgsoG8AeKCIiItNiAWUDtD1QweyBIiIiMgmrKaAWLlyI/v37w8nJCR4eHg22LSgoQHBwMEQiEYqLi/XuO3XqFGJjY+Ho6IigoCAsWLAAgiDotdm9ezeioqLg4OCAtm3bYvXq1UZ+NsZTUqlEabUKABDIHigiIiKTsJoCqqamBo8//jhefPHFO7adMGECevToUWe7QqFAXFwcAgMDcejQIbz//vtYunQpli9frmtz+fJlDBs2DPfeey+OHTuGWbNm4aWXXsKmTZuM+nyMRdv75OVsDyd7iZmjISIiah2s5ht3/vz5AIDk5OQG23300UcoLi7GnDlz8Msvv+jdt379elRVVSE5ORkymQzdunVDRkYGli9fjqSkJIhEIqxevRqhoaFYsWIFAKBLly44fPgwli5dilGjRrXEU2sWzn8iIiIyPaspoBojPT0dCxYswIEDB3Dp0qU696elpSE2NhYymUy3LSEhATNnzkRmZiYiIiKQlpaG+Ph4vf0SEhKwZs0aKJVKSKXSOsetrq5GdXW17rZCoQAAKJVKKJXKJj8f7b4NHSOroAwAEOAua9ZjUePyTcbDfJsW821azLdpGSvfhuxvMwVUdXU1nnzySSxZsgShoaH1FlByuRzh4eF62/z8/HT3RUREQC6X67bd3EalUiE/Px8BAQF1jrt48WJdD9nNUlJS4OTU/Iv7pqam3va+P67YAbBDdZEc27Zta/ZjUcP5JuNjvk2L+TYt5tu0mpvvioqKRrc1awE1b968eguPmx06dAjR0dF3PNbMmTPRpUsXPP300w22E4lEere1E8hv3t6YNrc+dlJSku62QqFASEgI4uPj4ebmdsfYb0epVCI1NRVxcXH19nwBwN7NZ4BrVxHVtSOGxbZt8mNR4/JNxsN8mxbzbVrMt2kZK9/aEaTGMGsBNXXqVIwZM6bBNrf2GN3Ojh07cOrUKWzcuBHAP0WPj48PZs+ejfnz58Pf3x9yuVxvv7y8PAD/9ETdro1EIoG3t3e9jy2TyfSGBbWkUqlRPjgNHUdRVXsGnrerAz+kRmKs140ah/k2LebbtJhv02puvg3Z16wFlI+PD3x8fIxyrE2bNqGyslJ3+9ChQ3juueewd+9etGvXDgAQExODWbNmoaamBvb29gBqh9kCAwN1hVpMTAy2bNmid+yUlBRER0db5IeguLJ2vNbD0d7MkRAREbUeVrOMQVZWFo4fP46srCyo1WocP34cx48fR1lZ7STqdu3aoVu3brqfiIgIALVn0bVp0wYAMHbsWMhkMiQmJuL06dPYvHkzFi1apDsDDwAmTZqEK1euICkpCWfPnsXatWuxZs0aTJ8+3TxP/A5KKv4uoJwsr7gjIiKyVVYziXzOnDlYt26d7nbv3r0BADt37sTAgQMbdQx3d3ekpqZiypQpiI6OhqenJ5KSkvTmL0VERGDbtm2YNm0aPvzwQwQGBmLlypUWuYQBABRV1AAA3B1ZQBEREZmK1RRQycnJd1wD6mYDBw6ss8I4AHTv3h179uxpcN/Y2FgcPXrU0BBNThCEf4bw2ANFRERkMlYzhEd1VSk1qFFpAAAeTpwDRUREZCosoKxYcWXt8J3ETgRne7GZoyEiImo9WEBZseKbJpDfbo0qIiIiMj4WUFZMW0BxAjkREZFpsYCyYiV/D+Fx/hMREZFpsYCyYtoeKE+egUdERGRSLKCsmHYJA3euQk5ERGRSLKCsWDFXISciIjILFlBWrPjvVcg9OImciIjIpFhAWTH2QBEREZkHCygrpl1I051n4REREZkUCygrpuuB4hAeERGRSbGAsmIlvJAwERGRWbCAsmL/9EBxCI+IiMiUWEBZqSqlGpVKNQDAnT1QREREJsUCykop/h6+E9uJ4OYgMXM0RERErQsLKCv1zyrkUohEIjNHQ0RE1LqwgLJSPAOPiIjIfFhAWamiCu0aUCygiIiITI0FlJUqYQ8UERGR2bCAslLaVcg9uAo5ERGRybGAslLaOVDu7IEiIiIyORZQVqqYq5ATERGZDQsoK8U5UERERObDAspKcQ4UERGR+bCAslK6OVAcwiMiIjI5FlBWSltAebIHioiIyORYQFmpkkrOgSIiIjIXFlBWqEalQVm1CgDPwiMiIjIHFlBWSNv7JBIBrg4soIiIiEyNBZQVKvn7DDw3BynEdiIzR0NERNT6sICyQtoJ5By+IyIiMg8WUFaomItoEhERmRULKCukvYyLO5cwICIiMgsWUFaouOLvVcjZA0VERGQWLKCsUAkvJExERGRWLKCs0D+TyDmER0REZA4soKxQMVchJyIiMisWUFZINweKQ3hERERmwQLKCnEdKCIiIvNiAWWFiv9eidzdkXOgiIiIzMFqCqiFCxeif//+cHJygoeHx23bJScno0ePHnBwcIC/vz+mTp2qd/+pU6cQGxsLR0dHBAUFYcGCBRAEQa/N7t27ERUVBQcHB7Rt2xarV69uiafUZOyBIiIiMi+JuQNorJqaGjz++OOIiYnBmjVr6m2zfPlyLFu2DEuWLEG/fv1QVVWFS5cu6e5XKBSIi4vDoEGDcOjQIWRkZCAxMRHOzs549dVXAQCXL1/GsGHDMHHiRHz55Zf4448/MHnyZPj6+mLUqFEmea4NUak1KK1SAeAkciIiInOxmgJq/vz5AGp7mOpTVFSEN954A1u2bMGQIUN027t27ar7//r161FVVYXk5GTIZDJ069YNGRkZWL58OZKSkiASibB69WqEhoZixYoVAIAuXbrg8OHDWLp0qUUUUIq/iycAcGcBRUREZBZWM4R3J6mpqdBoNLh69Sq6dOmC4OBgjB49GtnZ2bo2aWlpiI2NhUwm021LSEjAtWvXkJmZqWsTHx+vd+yEhAQcPnwYSqXSJM+lIdoz8FxlEkjENvPyERERWRWr6YG6k0uXLkGj0WDRokV477334O7ujjfeeANxcXE4efIk7O3tIZfLER4errefn58fAEAulyMiIgJyuVy37eY2KpUK+fn5CAgIqPPY1dXVqK6u1t1WKBQAAKVS2ayiS7vvzcfIL60EALg7SiyioLMl9eWbWg7zbVrMt2kx36ZlrHwbsr9ZC6h58+bphuZu59ChQ4iOjr7jsTQaDZRKJVauXKnrQfrqq6/g7++PnTt3IiEhAQAgEon09tNOIL95e2Pa3Gzx4sX1Po+UlBQ4OTndMfY7SU1N1f3/TJEIgBgiZSW2bdvW7GNTXTfnm1oe821azLdpMd+m1dx8V1RUNLqtWQuoqVOnYsyYMQ22ubXH6Ha0PUORkZG6bb6+vvDx8UFWVhYAwN/fH3K5XG+/vLw8AP/0RN2ujUQigbe3d72PPXPmTCQlJeluKxQKhISEID4+Hm5ubo2Kvz5KpRKpqamIi4uDVFo730l5/Brw12mE+vtg2LCoJh+b6qov39RymG/TYr5Ni/k2LWPlWzuC1BhmLaB8fHzg4+NjlGMNGDAAAHDu3DkEBwcDAAoLC5Gfn4+wsDAAQExMDGbNmoWamhrY29euoZSSkoLAwEBdoRYTE4MtW7boHTslJQXR0dG3fVFkMpnevCotqVRqlA/OzcdRVGsAAJ7O9vxQthBjvW7UOMy3aTHfpsV8m1Zz823IvlYzCzkrKwvHjx9HVlYW1Go1jh8/juPHj6OsrAwA0LFjRzz88MN4+eWXsX//fpw+fRrjx49H586dMWjQIADA2LFjIZPJkJiYiNOnT2Pz5s1YtGiR7gw8AJg0aRKuXLmCpKQknD17FmvXrsWaNWswffp0sz33m+mug8c1oIiIiMzGaiaRz5kzB+vWrdPd7t27NwBg586dGDhwIADg888/x7Rp0zB8+HDY2dkhNjYWv/76q66idHd3R2pqKqZMmYLo6Gh4enoiKSlJb/gtIiIC27Ztw7Rp0/Dhhx8iMDAQK1eutIglDACgRHsdPK5CTkREZDZWU0AlJyffdg0oLTc3N6xZs+a2C20CQPfu3bFnz54GjxMbG4ujR482JcwWxx4oIiIi87OaITyqpb2MCxfRJCIiMh8WUFbmnx4oDuERERGZCwsoK6ObA8UhPCIiIrNhAWVldD1QHMIjIiIyGxZQVkSjEVDCITwiIiKzYwFlRUqrVPj7qjKcRE5ERGRGVrOMAQGl1Uq4OUigEQB7CWtfIiIic2EBZUWCPZ1wcl4C1BrB3KEQERG1auzGsEJiO5G5QyAiImrVWEARERERGYgFFBEREZGBWEARERERGYgFFBEREZGBWEARERERGYgFFBEREZGBWEARERERGYgFFBEREZGBWEARERERGYgFFBEREZGBWEARERERGYgFFBEREZGBWEARERERGUhi7gBskSAIAACFQtGs4yiVSlRUVEChUEAqlRojNGoA821azLdpMd+mxXyblrHyrf3e1n6PN4QFVAsoLS0FAISEhJg5EiIiIjJUaWkp3N3dG2wjEhpTZpFBNBoNrl27BldXV4hEoiYfR6FQICQkBNnZ2XBzczNihFQf5tu0mG/TYr5Ni/k2LWPlWxAElJaWIjAwEHZ2Dc9yYg9UC7Czs0NwcLDRjufm5sYPoAkx36bFfJsW821azLdpGSPfd+p50uIkciIiIiIDsYAiIiIiMhALKAsmk8kwd+5cyGQyc4fSKjDfpsV8mxbzbVrMt2mZI9+cRE5ERERkIPZAERERERmIBRQRERGRgVhAERERERmIBRQRERGRgVhAmdmqVasQEREBBwcHREVFYe/evQ223717N6KiouDg4IC2bdti9erVJorUNhiS7++//x5xcXHw9fWFm5sbYmJi8Ntvv5kwWutn6Ptb648//oBEIkGvXr1aNkAbY2i+q6urMXv2bISFhUEmk6Fdu3ZYu3atiaK1fobme/369ejZsyecnJwQEBCAZ599FgUFBSaK1rrt2bMHDz30EAIDAyESifDDDz/ccZ8W/74UyGy+/vprQSqVCp988omQnp4uvPzyy4Kzs7Nw5cqVettfunRJcHJyEl5++WUhPT1d+OSTTwSpVCps3LjRxJFbJ0Pz/fLLLwv/+9//hIMHDwoZGRnCzJkzBalUKhw9etTEkVsnQ/OtVVxcLLRt21aIj48XevbsaZpgbUBT8j1ixAihX79+QmpqqnD58mXhwIEDwh9//GHCqK2Xofneu3evYGdnJ7z33nvCpUuXhL179wpdu3YVRo4caeLIrdO2bduE2bNnC5s2bRIACJs3b26wvSm+L1lAmVHfvn2FSZMm6W3r3Lmz8Prrr9fb/rXXXhM6d+6st+2FF14Q7r777haL0ZYYmu/6REZGCvPnzzd2aDapqfl+4oknhDfeeEOYO3cuCygDGJrvX375RXB3dxcKCgpMEZ7NMTTfS5YsEdq2bau3beXKlUJwcHCLxWirGlNAmeL7kkN4ZlJTU4MjR44gPj5eb3t8fDz2799f7z5paWl12ickJODw4cNQKpUtFqstaEq+b6XRaFBaWgovL6+WCNGmNDXfn332GS5evIi5c+e2dIg2pSn5/umnnxAdHY133nkHQUFB6NixI6ZPn47KykpThGzVmpLv/v37IycnB9u2bYMgCLh+/To2btyI4cOHmyLkVscU35e8mLCZ5OfnQ61Ww8/PT2+7n58f5HJ5vfvI5fJ626tUKuTn5yMgIKDF4rV2Tcn3rZYtW4by8nKMHj26JUK0KU3J9/nz5/H6669j7969kEj4q8kQTcn3pUuXsG/fPjg4OGDz5s3Iz8/H5MmTUVhYyHlQd9CUfPfv3x/r16/HE088gaqqKqhUKowYMQLvv/++KUJudUzxfckeKDMTiUR6twVBqLPtTu3r2071MzTfWl999RXmzZuHb775Bm3atGmp8GxOY/OtVqsxduxYzJ8/Hx07djRVeDbHkPe3RqOBSCTC+vXr0bdvXwwbNgzLly9HcnIye6EayZB8p6en46WXXsKcOXNw5MgR/Prrr7h8+TImTZpkilBbpZb+vuSfeWbi4+MDsVhc56+VvLy8OlWzlr+/f73tJRIJvL29WyxWW9CUfGt98803mDBhAr777jsMHTq0JcO0GYbmu7S0FIcPH8axY8cwdepUALVf8IIgQCKRICUlBYMHDzZJ7NaoKe/vgIAABAUFwd3dXbetS5cuEAQBOTk56NChQ4vGbM2aku/FixdjwIABmDFjBgCgR48ecHZ2xr333ou33nqLIwhGZorvS/ZAmYm9vT2ioqKQmpqqtz01NRX9+/evd5+YmJg67VNSUhAdHQ2pVNpisdqCpuQbqO15SkxMxIYNGzhXwQCG5tvNzQ2nTp3C8ePHdT+TJk1Cp06dcPz4cfTr189UoVulpry/BwwYgGvXrqGsrEy3LSMjA3Z2dggODm7ReK1dU/JdUVEBOzv9r1yxWAzgn54RMh6TfF8abTo6GUx7GuyaNWuE9PR04ZVXXhGcnZ2FzMxMQRAE4fXXXxfGjRuna689LXPatGlCenq6sGbNGi5jYABD871hwwZBIpEIH374oZCbm6v7KS4uNtdTsCqG5vtWPAvPMIbmu7S0VAgODhYee+wx4cyZM8Lu3buFDh06CM8//7y5noJVMTTfn332mSCRSIRVq1YJFy9eFPbt2ydER0cLffv2NddTsCqlpaXCsWPHhGPHjgkAhOXLlwvHjh3TLRthju9LFlBm9uGHHwphYWGCvb290KdPH2H37t26+8aPHy/Exsbqtd+1a5fQu3dvwd7eXggPDxc++ugjE0ds3QzJd2xsrACgzs/48eNNH7iVMvT9fTMWUIYzNN9nz54Vhg4dKjg6OgrBwcFCUlKSUFFRYeKorZeh+V65cqUQGRkpODo6CgEBAcJTTz0l5OTkmDhq67Rz584Gfx+b4/tSJAjsOyQiIiIyBOdAERERERmIBRQRERGRgVhAERERERmIBRQRERGRgVhAERERERmIBRQRERGRgVhAERERERmIBRQRERGRgVhAERERERmIBRQRERGRgSTmDoCIyBoMHDgQ3bp1AwB8+eWXEIvFePHFF/Hmm29CJBKZOToiMjX2QBERNdK6desgkUhw4MABrFy5Eu+++y4+/fRTc4dFRGbAiwkTETXCwIEDkZeXhzNnzuh6nF5//XX89NNPSE9PN3N0RGRq7IEiImqku+++W2+4LiYmBufPn4darTZjVERkDiygiIiIiAzEAoqIqJH+/PPPOrc7dOgAsVhspoiIyFxYQBERNVJ2djaSkpJw7tw5fPXVV3j//ffx8ssvmzssIjIDLmNARNRIzzzzDCorK9G3b1+IxWL8+9//xr/+9S9zh0VEZsACioiokaRSKVasWIGPPvrI3KEQkZlxCI+IiIjIQCygiIiIiAzEhTSJiIiIDMQeKCIiIiIDsYAiIiIiMhALKCIiIiIDsYAiIiIiMhALKCIiIiIDsYAiIiIiMhALKCIiIiIDsYAiIiIiMhALKCIiIiID/T/NQ8/2uEHZLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(p_values, ll_values, label='Log-Likelihood Curve')\n",
    "plt.xlabel('p')\n",
    "plt.ylabel('Log-Likelihood')\n",
    "plt.title('Log-Likelihood for Bernoulli Distribution')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7157b3ed-1d8e-4676-bdc0-619bc02dd692",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum log-likelihood is at p = 0.63\n"
     ]
    }
   ],
   "source": [
    "# Find its maximum using scipy\n",
    "result = minimize(lambda p: -log_likelihood(p, y), 0.5, bounds=[(0.01, 0.99)])\n",
    "print(f\"The maximum log-likelihood is at p = {result.x[0]:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f9ea698-6198-49f3-b6ad-7bf18c8e03e8",
   "metadata": {},
   "source": [
    "# Data Cleaning and likelihood estimation - 10 points\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3feb171f-6914-499b-be67-d9415f5145cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the titanic dataset\n",
    "titanic = sns.load_dataset(_______)\n",
    "\n",
    "# Drop rows where 'survived' is missing and 'age' is missing as we do not want information of people without an age\n",
    "titanic_cleaned = titanic._______(subset=[________])\n",
    "titanic_cleaned = titanic_cleaned._______(subset=[_____])\n",
    "num_survived = titanic_cleaned['survived'].______\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "890c153c-506b-4bd9-98fb-ec573895521e",
   "metadata": {},
   "outputs": [],
   "source": [
    "total_passengers = _____(titanic_cleaned)\n",
    "p_MLE = num_survived / total_passengers\n",
    "\n",
    "print(f\"The MLE for the probability of survival is: {p_MLE:.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1c7be693-5803-4188-904c-ae31968f5693",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Count of Titanic dataset before cleaning: 891\n",
      "Count of Titanic dataset after cleaning: 714\n",
      "The MLE for the probability of survival is: 0.41\n"
     ]
    }
   ],
   "source": [
    "# Load the titanic dataset\n",
    "titanic = sns.load_dataset('titanic')\n",
    "\n",
    "print(f\"Count of Titanic dataset before cleaning: {len(titanic)}\")\n",
    "\n",
    "# Drop rows where 'survived' and 'age' is missing below\n",
    "\n",
    "\n",
    "num_survived = titanic_cleaned['survived'].sum()\n",
    "\n",
    "print(f\"Count of Titanic dataset after cleaning: {len(titanic_cleaned)}\")\n",
    "\n",
    "total_passengers = _________ # Get the total passengers\n",
    "p_MLE = __________ # Get the p_MLE for the passengers\n",
    "\n",
    "print(f\"The MLE for the probability of survival is: {p_MLE:.2f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "466b3f36-708c-4992-bf1d-ee3ddde81548",
   "metadata": {},
   "source": [
    "**Code the likelihood function - 4 points**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56f598d6-0842-4ab5-8144-2f131eac7bcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a range of possible p values (from 0 to 1 in increments of 0.01)\n",
    "p_values = _____________________\n",
    "\n",
    "# Define the likelihood function\n",
    "def likelihood(p, n, k):\n",
    "    return ________________________"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "25edfa15-b657-4989-8aea-d3c0acb9d256",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute likelihood values for each p\n",
    "L_values = _____________________\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(p_values, L_values, label='Likelihood Function', color='blue')\n",
    "plt.axvline(x=p_MLE, color='red', linestyle='--', label=f'MLE at p = {p_MLE:.2f}')\n",
    "plt.xlabel('p (Probability of Survival)')\n",
    "plt.ylabel('Likelihood')\n",
    "plt.title('Likelihood Function of Survival Probability')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dfeb0849-2025-4c16-82e8-87173c4d2cae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a range of possible p values (from 0 to 1 in increments of 0.01)\n",
    "p_values = np.linspace(0, 1, 100)\n",
    "\n",
    "# Define the likelihood function\n",
    "def likelihood(p, n, k):\n",
    "    return __________________\n",
    "\n",
    "# Compute likelihood values for each p\n",
    "L_values = [likelihood(p, total_passengers, num_survived) for p in p_values]\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(p_values, L_values, label='Likelihood Function', color='blue')\n",
    "plt.axvline(x=p_MLE, color='red', linestyle='--', label=f'MLE at p = {p_MLE:.2f}')\n",
    "plt.xlabel('p (Probability of Survival)')\n",
    "plt.ylabel('Likelihood')\n",
    "plt.title('Likelihood Function of Survival Probability')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}