{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bec17a8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "34c4d638-d143-4c8e-a70a-bf2f757522fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 1.0 True\n",
      "3 0.926829268292683 False\n",
      "4 0.5 False\n",
      "5 -1.9487179487179487 False\n",
      "6 -17.789473684210527 False\n",
      "7 -135.02702702702703 False\n",
      "8 -1118.7777777777778 False\n",
      "9 -10366.742857142857 False\n",
      "10 -106728.11764705883 False\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import factorial\n",
    "factorial(5)\n",
    "\n",
    "for i in range(2,11):\n",
    "    x=(factorial(i)-44)/(i-44)\n",
    "    print(i,x,x.is_integer())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1817799e",
   "metadata": {},
   "source": [
    "SciPy is a scientific computation library that uses NumPy underneath.\n",
    "\n",
    "SciPy stands for Scientific Python.\n",
    "\n",
    "It provides more utility functions for optimization, stats and signal processing.\n",
    "\n",
    "One of its cooler features is an huge list of physical constants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "617a0e83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.141592653589793\n",
      "1.6605390666e-27\n",
      "0.017453292519943295\n",
      "31536000.0\n",
      "1e-15\n",
      "0.0037854117839999997\n",
      "1.602176634e-19\n",
      "1e-05\n"
     ]
    }
   ],
   "source": [
    "from scipy import constants\n",
    "\n",
    "print(constants.pi)\n",
    "# mass\n",
    "print(constants.atomic_mass) #1.66053904e-27\n",
    "# angle\n",
    "print(constants.degree)     #0.017453292519943295\n",
    "# time\n",
    "print(constants.year)        #31536000.0\n",
    "#length\n",
    "print(constants.fermi)             #1e-15\n",
    "# volume\n",
    "print(constants.gallon)           #0.0037854117839999997\n",
    "# energy\n",
    "print(constants.eV)            #1.6021766208e-19\n",
    "# force\n",
    "print(constants.dyne)            #1e-05"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "889ff483-57be-4253-9d11-a48c84c42cfb",
   "metadata": {},
   "source": [
    "Use a for loop to estimate $\\pi$ from the first 20 terms of the Madhava series:\n",
    "\n",
    "$$ \\pi = \\sqrt{12}(1 - {1 \\over {3\\cdot3}} + {1 \\over {5\\cdot3^2}} - {1 \\over {7\\cdot3^3}} +\\, ...) $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "64a8972c-baa3-4315-bf9a-ea52e7001f41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pi =  3.1415926535714034\n",
      "error =  1.8389734179891093e-11\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "pi = 0\n",
    "for k in range(20):\n",
    "    pi += pow(-3, -k) / (2*k+1)\n",
    "pi *= math.sqrt(12)\n",
    "\n",
    "print('pi = ', pi)\n",
    "print('error = ', abs(pi - math.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0a05f05-cfb2-4006-9b53-3387a0e80df8",
   "metadata": {},
   "source": [
    "#### Optimizing Functions:\n",
    "\n",
    "Essentially, all of the algorithms in Machine Learning are nothing more than a complex equation that needs to be minimized with the help of given data.\n",
    "\n",
    "Roots of an Equation:\n",
    "\n",
    "NumPy is capable of finding roots for polynomials and linear equations, but it can not find roots for non linear equations, like this one:\n",
    "\n",
    "x + cos(x)\n",
    "\n",
    "For that you can use SciPy's optimze.root function.\n",
    "\n",
    "This function takes two required arguments:\n",
    "\n",
    "- fun - a function representing an equation.\n",
    "- x0 - an initial guess for the root.\n",
    "\n",
    "The function returns an object with information regarding the solution. The actual solution is given under attribute x of the returned object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "465cfabc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.73908513] [0.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import root\n",
    "from math import cos\n",
    "\n",
    "def eqn(x):\n",
    "  return x + cos(x)\n",
    "\n",
    "myroot = root(eqn, 0)\n",
    "print(myroot.x,eqn(myroot.x))\n",
    "\n",
    "r=np.linspace(-10,10,100)\n",
    "s=r+np.cos(r)\n",
    "plt.plot(r,s)\n",
    "plt.plot([-10,10],[0,0],'k--');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0242660a",
   "metadata": {},
   "source": [
    "#### Finding Minima:\n",
    "\n",
    "We can use scipy.optimize.minimize() function to minimize the function. The minimize() function takes the following arguments:\n",
    "\n",
    "- fun - a function representing an equation.\n",
    "- x0 - an initial guess for the root.\n",
    "- method - name of the method to use. \n",
    "\n",
    "Legal values:\n",
    "\n",
    "    'CG'\n",
    "    'BFGS'\n",
    "    'Newton-CG'\n",
    "    'L-BFGS-B'\n",
    "    'TNC'\n",
    "    'COBYLA'\n",
    "    'SLSQP'\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5a0ec35f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: Optimization terminated successfully.\n",
      "  success: True\n",
      "   status: 0\n",
      "      fun: 1.75\n",
      "        x: [-5.000e-01]\n",
      "      nit: 2\n",
      "      jac: [ 0.000e+00]\n",
      " hess_inv: [[ 5.000e-01]]\n",
      "     nfev: 8\n",
      "     njev: 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "def eqn(x):\n",
    "  return x**2 + x + 2\n",
    "\n",
    "mymin = minimize(eqn, 0, method='BFGS')\n",
    "print(mymin)\n",
    "x=np.linspace(-2,2,50)\n",
    "plt.plot(x,eqn(x));"
   ]
  },
  {
   "attachments": {
    "J6zXU.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d93c22d8",
   "metadata": {},
   "source": [
    "![J6zXU.png](attachment:J6zXU.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "074a02b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, array([0, 0, 0, 1, 1, 1, 1], dtype=int32))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# some of the power of scipy, consider the above network and\n",
    "# its adjency matrix below\n",
    "\n",
    "import numpy as np\n",
    "from scipy.sparse.csgraph import connected_components\n",
    "from scipy.sparse import csr_matrix\n",
    "\n",
    "arr = np.array([\n",
    "    [0, 1, 1, 0, 0, 0, 0],\n",
    "    [1, 0, 1, 0, 0, 0, 0],\n",
    "    [1, 1, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 1, 0, 1],\n",
    "    [0, 0, 0, 1, 0, 1, 0],\n",
    "    [0, 0, 0, 0, 1, 0, 1],\n",
    "    [0, 0, 0, 1, 0, 1, 0]])\n",
    "\n",
    "newarr = csr_matrix(arr)\n",
    "\n",
    "connected_components(newarr)\n",
    "\n",
    "# answer = 2 networks, labeled by node"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50742689",
   "metadata": {},
   "source": [
    "#### Triangulation:\n",
    "\n",
    "A triangulation of a polygon is to divide the polygon into multiple triangles with which we can compute an area of the polygon. A triangulation with points means creating surface composed triangles in which all of the given points are on at least one vertex of any triangle in the surface. One method to generate these triangulations through points is the Delaunay() triangulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8307761c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.spatial import Delaunay\n",
    "\n",
    "points = np.array([\n",
    "  [2, 4],\n",
    "  [3, 4],\n",
    "  [3, 0],\n",
    "  [2, 2],\n",
    "  [4, 1]\n",
    "])\n",
    "\n",
    "simplices = Delaunay(points).simplices\n",
    "\n",
    "plt.triplot(points[:, 0], points[:, 1], simplices)\n",
    "plt.scatter(points[:, 0], points[:, 1], color='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17f826c2",
   "metadata": {},
   "source": [
    "#### Convex Hull:\n",
    "\n",
    "A convex hull is the smallest polygon that covers all of the given points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "79dd8094",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 9]\n",
      " [1 6]\n",
      " [1 0]\n",
      " [2 9]\n",
      " [2 6]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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jx+PTTz+Fr6+v6ByiGqGhoUhISMClS5dEpxA1mgad0KkuPKGTGkNaWhqmTp2KVatW1bw6JZEm8fDwgJ6eHr7++mvRKUQN0igndBJpquTkZEyZMgVfffUVhwVprKVLl2Lz5s345ZdfRKcQNQqOC9IZ27Ztg7u7OzZu3Ag3NzfROURPZGZmBg8PDwQHB4tOIWoUHBekEzZs2AAvLy9s374dkydPFp1D9EyBgYFISkpCTk6O6BQiteO4IK23du1azJ49G0lJSRg/frzoHKI66d69O7y9vREUFCQ6hUjtOC5Iq61cuRLz5s1DamoqRo8eLTqHqF4WL16M77//HllZWaJTiNSK44K01rJly+Dv74/vvvsOdnZ2onOI6q1Lly7w9fVFYGCg6BQiteK4IK0UHh6OyMhIHDx4EEOHDhWdQ9RgCxYswD//+U8cOXJEdAqR2nBckFZRqVQICAjAihUrcPjwYdja2opOInounTp1wrx58+Dv7w+Blx0iUiuOC9IaKpUKCxYsQEJCAjIyMtC/f3/RSURq8f777+PMmTPYv3+/6BQiteC4IK1QXV0NX19fbNu2DZmZmTA3NxedRKQ2hoaGNS+ux6MXpAs4LkjjVVVVwcfHB2lpacjMzETv3r1FJxGp3Zw5c5CXl4eUlBTRKUTPjeOCNNrDhw8xffp0ZGZmIiMjA6ampqKTiBpF27ZtsWTJEgQGBqK6ulp0DtFz4bggjaVUKuHu7o5Tp04hIyMDJiYmopOIGpWPjw9u376NHTt2iE4hei4cF6SRKisrMXXqVFy4cAGHDx9Gly5dRCcRNbpWrVohMDAQQUFBePjwoegcogbjuCCNc//+fUyaNAlXr17FwYMHYWxsLDqJqMm8/fbbUCqV2LRpk+gUogbjuCCNUlZWBmdnZ9y9exf79++HXC4XnUTUpPT19bF06VKEhITgwYMHonOIGoTjgjRGaWkpxo0bB5VKhfT0dHTo0EF0EpEQ06ZNg4GBAb7++mvRKUQNwnFBGqG4uBhjxoxB27ZtkZqainbt2olOIhJGT08PoaGhCAsLQ0VFhegconrjuCDhCgsL4ejoiM6dOyM5ORmtW7cWnUQk3BtvvAFjY2PExcWJTiGqN44LEurGjRtwcHCAmZkZduzYAQMDA9FJRBpBJpMhLCwMkZGRuHfvnugconrhuCBhrly5Ant7ewwYMACbN29Gy5YtRScRaRRnZ2f07NkTsbGxolOI6oXjgoTIz8+HnZ0dRowYgXXr1qFFixaik4g0jiRJCA8PxyeffII7d+6IziGqM44LanIXL16EnZ0dxo0bhy+//BJ6enqik4g0lqOjI6ysrBATEyM6hajOOC6oSZ07dw729vaYMmUKYmNjIZPxS5Doaf44ehETE4PCwkLROUR1wn/Zqcnk5ubC3t4e06dPx7JlyyBJkugkIq0wYsQIDB8+HJ9++qnoFKI64bigJpGdnQ0HBwf4+voiIiKCw4KonsLCwhAbG4tr166JTiF6Jo4LanQnTpyAo6MjFi5ciICAANE5RFpp4MCBGDt2LCIjI0WnED0TxwU1qiNHjmDs2LEIDQ3FggULROcQabXQ0FDEx8fj8uXLolOInorjghrNgQMHMH78eHz66afw9fUVnUOk9fr374/JkycjLCxMdArRU3FcUKNIS0vDxIkTsXLlSnh7e4vOIdIZwcHB2LBhAy5evCg6heiJOC5I7ZKTkzFlyhR89dVX8PDwEJ1DpFP69OkDd3d3hISEiE4heiKOC1Krbdu2wd3dHRs3boSbm5voHCKdFBQUhB07dkChUIhOIXqsOo+LW7duwdnZGe3bt8fAgQPx888/P/G+N2/exFtvvYW5c+fCy8sLxcXFaoklzbZhwwZ4eXlh+/btmDx5sugcIp1lamoKLy8vBAUFiU4heqw6j4uPPvoIc+fOxe7du1FeXo4333zzsferrq6Gs7MzZs6ciRUrVuD111/HP/7xD7UFk2Zau3YtZs+ejeTkZIwfP150DpHO8/f3x969e5GdnS06hagWSaVSqZ51p4qKChQWFsLExAQAsH37dsycOfOxL6Szc+dOzJ8/H5cuXQIAqFQqyOVy7N69G3Z2do/ct7S0FIaGhigpKUGHDh3U8OmQCCtXrsSSJUuwZ88ejBw5UnQOUbPxwQcf4JdffsGePXtEp1Az86zv33U6ctGqVauaYQEASqUSs2bNeux9d+/ejX79+tX8WZIkWFlZISUlpb7tpAWio6MREBCAffv2cVgQNbFFixYhIyMDx48fF51C9Ih6n9BZUFCAjRs3wt/f/7FvVygUMDY2fuQ2uVyO8+fPP/F9mpubw8TEBCYmJvjss8/qm0SChIeH46OPPsKBAwcwdOhQ0TlEzc4LL7wAPz8/XvmWNE6L+tz59OnTCAgIQFpaGhwcHHD06FEYGBg8cp+SkhIYGRk9cpuBgcFTT+o8e/Ysfy2iRVQqFQIDA/Hll1/i8OHD6N+/v+gkombrgw8+QM+ePXHw4EG89tpronOIANTzyIW1tTX27NmDb7/9FidPnsTOnTtr3cfIyAiVlZWP3Hb//n3I5fLnKyWNoFKpsGDBAiQkJCAjI4PDgkgwuVyO+fPnIzAwEHU4hY6oSTToOheTJ0+Gvb09rl69WuttZmZmKCwsfOS2W7duoW/fvg0rJI1RXV0NX19fbNu2DZmZmTA3NxedREQA/Pz8cP78eaSlpYlOIQLwHBfR6tixI6ysrGrdPmXKFGRlZdX8ubq6GufOncOECRMa+qFIA1RVVcHHxwdpaWnIzMxE7969RScR0X+0b98eixYtQkBAAI9ekEao07goLS3FunXrUFpaCgDIycnBgwcPMHbsWDx8+BAjR45ERkYGAMDZ2RmtWrWquchWSkoKRowYwRP+tNjDhw8xffp0ZGZmIiMjA6ampqKTiOhPZs2ahevXr2PXrl2iU4jqdkLnjRs3EBwcjAULFmDUqFEwMzPDli1bAPz+E21eXl7NCZv6+vpISUmBv78/unfvjtLSUmzevLnxPgNqVEqlEtOmTYNCoUBGRga6dOkiOomIHqNNmzbw9/dHUFAQJk6cCD09PdFJ1IzV6SJajYUX0dJslZWVcHNzQ35+Pr7//vtaTzEmIs1SWVmJvn37IiIiAtOmTROdQzpMLRfRoubn/v37mDRpEq5evYqDBw9yWBBpAQMDAwQFBSE4OBhKpVJ0DjVjHBdUS1lZGZydnXH37l3s37+fTyMm0iIeHh6QJAnr168XnULNGMcFPaK0tBTjxo2DSqVCeno6f11FpGVatGiBkJAQhIaG1rrmEFFT4bigGsXFxRgzZgzatm2L1NRUtGvXTnQSETWAm5sbOnTogPj4eNEp1ExxXBAAoLCwEI6OjujcuTOSk5PRunVr0UlE1EAymQyhoaGIiIhAeXm56BxqhjguCDdu3ICDgwPMzMywY8eOWq8XQ0TaZ9KkSejWrRtWrVolOoWaIY6LZu7KlSuwt7fHgAEDsHnzZrRs2VJ0EhGpgSRJCA8PR1RUFO7evSs6h5oZjotmLD8/H3Z2dhgxYgTWrVuHFi3q9SK5RKThnJyc8Morr2D58uWiU6iZ4bhopi5evAg7OzuMGzcOX375Ja/mR6SD/jh6ER0djdu3b4vOoWaE46IZOnfuHOzt7TFlyhTExsZCJuOXAZGuGjVqFAYOHIjo6GjRKdSM8LtKM5Obmwt7e3tMnz4dy5YtgyRJopOIqJGFh4fj888/x82bN0WnUDPBcdGMZGdnw8HBAb6+voiIiOCwIGomhg4dCgcHB0RFRYlOoWaC46KZOHHiBBwdHbFw4UIEBASIziGiJhYWFoa4uDhcuXJFdAo1AxwXzcCRI0cwduxYhIaGYsGCBaJziEgAa2trODs7IyIiQnQKNQMcFzruwIEDGD9+PJYtWwZfX1/ROUQkUEhICBISEnDp0iXRKaTjOC50WFpaGiZOnIiVK1di5syZonOISDBzc3O4uroiNDRUdArpOI4LHZWcnIwpU6bgq6++goeHh+gcItIQS5cuxebNm/HLL7+ITiEdxnGhg7Zt2wZ3d3ds2rQJbm5uonOISIOYmZnB09MTwcHBolNIh3Fc6JgNGzbAy8sL27dvx6RJk0TnEJEGCggIQFJSEnJyckSnkI7iuNAha9euxezZs5GcnIzx48eLziEiDdW9e3d4e3sjKChIdArpKI4LHbFy5Up88MEH2Lt3LxwdHUXnEJGGW7x4Mb7//ntkZWWJTiEdxHGhA6KjoxEQEIB9+/Zh5MiRonOISAt06dIFvr6+CAwMFJ1COojjQsuFh4fjo48+woEDBzB06FDROUSkRRYsWIB//vOfOHLkiOgU0jEcF1pKpVIhICAAK1aswOHDh2Frays6iYi0TKdOnTBv3jz4+/tDpVKJziEdwnGhhVQqFRYsWICEhARkZGSgf//+opOISEu9//77OHPmDPbv3y86hXQIx4WWqa6uhq+vL7Zv347MzEyYm5uLTiIiLWZoaIiFCxfy6AWpFceFFqmqqoKPjw/S0tKQmZmJ3r17i04iIh0wZ84c5OfnIyUlRXQK6QiOCy3x8OFDTJ8+HZmZmcjMzESPHj1EJxGRjmjbti2WLFmCwMBAVFdXi84hHcBxoQWUSiXc3d1x6tQpZGRkoFu3bqKTiEjH+Pj44Pbt29ixY4foFNIBHBcarrKyElOnTsWFCxdw+PBhdOnSRXQSEemgVq1aITAwEEFBQXj48KHoHNJyHBca7P79+5g0aRKuXr2KgwcPwtjYWHQSEemwt99+G0qlEps2bRKdQlquTuMiPz8fTk5OaN++PWxsbHDo0KGn3t/LywuSJEGSJOjr6+Pq1atqiW1OysrK4OzsjLt372L//v2Qy+Wik4hIx+nr62Pp0qUICQnBgwcPROeQFnvmuFCpVJg5cyZGjx6NVatWQaVSwdnZGf/+978fe/9r167hzp07iImJQUxMDDZu3IiuXbuqPVyXlZaWYty4cVCpVEhPT0eHDh1EJxFRMzFt2jQYGBjg66+/Fp1CWkxSPeOJzbm5ubh582bNi2HdvHkTvXr1QkREBPz8/Grdf/HixfDy8sLLL7/8zA9eWloKQ0NDlJSU8BvofxQXF2PcuHGQy+XYtWsXWrduLTqJiJqZ7du34/3338fFixfRqlUr0TmkgZ71/fuZRy769u37yKtsvvjii7CwsICBgUGt+969exerV6/GkCFD4OnpiWvXrj1nfvNSWFgIR0dHdO7cGcnJyRwWRCTEG2+8AWNjY8TFxYlOIS31zHHRsmXLWrcVFxfD2dm51u0VFRVYs2YNvL29sWfPHgwYMAC5ubnqKdVxN27cgIODA8zMzLBjx47HjjcioqYgk8kQFhaGyMhI3Lt3T3QOaaF6P1skMzMTr7/+OkxMTGq97YUXXoCbmxuioqLwyy+/4C9/+Qv+7//+75nv09zcHCYmJjAxMcFnn31W3yStd+XKFdjb22PAgAHYvHnzYwcdEVFTcnZ2Rs+ePREbGys6hbTQM8+5+F9KpRJz587F8uXL6/ST9enTp/Hqq6+itLQUbdu2rfV2nnPx+zNxXnvtNTg4OGDNmjXQ09MTnUREBADYv38/XF1d8euvv6Jjx46ic0iDPPc5F/8rOjoaS5YsqfMhe2tra8jlcj6l6QkuXrwIOzs7jBs3Dl9++SWHBRFpFEdHR1hZWSEmJkZ0CmmZOo+LtWvXYty4cejevTuA368cWVVV9dT/p7S0FP369eM1Gh7j3LlzsLe3x5QpUxAbGwuZjNczIyLNIkkSwsPDERMTg8LCQtE5pEXq9B1t1apV+PXXX3H9+nWkp6fj22+/xYwZM1BVVYWRI0ciIyMDAPDNN98gJiYGSqUS5eXleP/997Fy5cpG/QS0UW5uLuzt7fH2229j2bJlkCRJdBIR0WONGDECw4cPxyeffCI6hbSJ6hm++uorFYBa//n6+qoqKipUJiYmql27dqlUKpVq/fr1KiMjI1W3bt1UU6dOVV24cOGp77ukpEQFQFVSUvKsDJ1x8uRJVadOnVRhYWGiU4iI6iQrK0vVpk0b1dWrV0WnkIZ41vfvep3QqW7N7YTOEydOYNy4cfD398f8+fNF5xAR1dnkyZPRvXt3rFixQnQKaQC1ntBJDXfkyBGMHTsWYWFhHBZEpHVCQ0MRHx+Py5cvi04hLcBx0QQOHDiA8ePHY9myZZgzZ47oHCKieuvfvz8mT56MsLAw0SmkBTguGllaWhomTpyIlStXYubMmaJziIgaLDg4GBs2bMDFixdFp5CG47hoRMnJyZgyZQq++uoreHh4iM4hInouffr0gbu7O0JCQkSnkIbjuGgk27Ztg7u7OzZt2gQ3NzfROUREahEUFIQdO3ZAoVCITiENxnHRCDZs2AAvLy9s374dkyZNEp1DRKQ2pqam8PLyQlBQkOgU0mAcF2q2du1azJ49G8nJyRg/frzoHCIitfP398fevXuRnZ0tOoU0FMeFGq1cuRIffPAB9u7dC0dHR9E5RESNomvXrpg1axaPXtATcVyoSXR0NAICArBv3z6MHDlSdA4RUaNatGgRMjIycPz4cdEppIE4LtQgPDwcH330EQ4cOIChQ4eKziEianQvvPAC/Pz8EBAQIDqFNBDHxXNQqVQICAjAF198gcOHD8PW1lZ0EhFRk/nggw9w8uRJHDx4UHQKaRiOiwZSqVRYsGABEhISkJGRgf79+4tOIiJqUnK5HAsWLEBgYCAEvkwVaSCOiwaorq6Gr68vtm/fjszMTLzyyiuik4iIhJg7dy7Onz+PtLQ00SmkQTgu6qmqqgo+Pj5IS0tDZmYmevfuLTqJiEiY9u3bY9GiRQgICODRC6rBcVEPDx8+xPTp05GZmYnMzEz06NFDdBIRkXCzZ8/G9evXsWvXLtEppCE4LupIqVTC3d0dp06dQkZGBrp16yY6iYhII7Ru3RoBAQEICgpCVVWV6BzSABwXdVBZWYmpU6fiwoULOHz4MLp06SI6iYhIo7zzzju4d+8etmzZIjqFNADHxTPcv38fkyZNwtWrV3Hw4EEYGxuLTiIi0jgGBgYICgpCcHAwlEql6BwSjOPiKcrKyuDs7Iy7d+9i//79kMvlopOIiDSWh4cHJEnC+vXrRaeQYBwXT1BaWopx48ZBpVIhPT0dHTp0EJ1ERKTRWrRogZCQEISGhqKyslJ0DgnEcfEYxcXFGDNmDNq2bYvU1FS0a9dOdBIRkVZwc3NDhw4dEB8fLzqFBOK4+JPCwkI4OjqiS5cuSE5ORuvWrUUnERFpDZlMhtDQUERERKC8vFx0DgnCcfE/bty4AQcHB/Tu3Rs7duyAgYGB6CQiIq0zadIkdOvWDatWrRKdQoJwXPzHlStXYG9vD2tra3zzzTfQ19cXnUREpJUkSUJ4eDiioqJQWloqOocE4LgAkJ+fDzs7O4wYMQKJiYlo0aKF6CQiIq3m5OSEV155BZ9//rnoFBKg2Y+Lixcvws7ODuPGjcOXX34JPT090UlERFrvj6MX0dHRuH37tugcamLNelycO3cO9vb2mDJlCmJjYyGTNeuHg4hIrUaNGoVBgwYhOjpadAo1sWb73TQ3Nxf29vZ4++23sWzZMkiSJDqJiEjnhIWF4fPPP8fNmzdFp1ATapbjIjs7Gw4ODvD19UV4eDiHBRFRIxk6dCgcHBwQFRUlOoWaULMbFydOnICjoyMWLVqEgIAA0TlERDovLCwMcXFxuHLliugUaiLNalwcOXIEY8eORVhYGObPny86h4ioWbC2toazszMiIiJEp1ATaTbj4sCBAxg/fjyWLVuGOXPmiM4hImpWQkJCkJCQgEuXLolOoSZQp3GRn58PJycntG/fHjY2Njh06NAT73vz5k289dZbmDt3Lry8vFBcXKy22IZKS0vDxIkTsXLlSsycOVN0DhFRs2Nubg5XV1eEhoaKTqEmIKlUKtXT7qBSqeDk5IQxY8agS5cuiI6OxoULF5CTkwMzM7NH7ltdXY2hQ4di2bJlsLOzw549exAbG4v09PTHvu/S0lIYGhqipKREba86qlKp8FN+MfIKy2Bq3BZXTmdi2rRpSEhIgJubm1o+Bv2uuroaG09cxpkrJejXzRBvDnmJT+dtBH/+mh7YQ86TkEkr/fvf/4alpSV+/vln9O3bV3QOPYdnff9+5rjIzc3FzZs34ejoCOD3IxO9evVCREQE/Pz8Hrnvzp07MX/+/JrDXiqVCnK5HLt374adnV294+qroLgcHgk/4rfb5dDXk+F2bgZupS7HmoREzHiTw0Kdfsq7jX/E/wBl1X+/fPT1JGyeORQDTY0ElumWP39NK6uq0d2oDdZ7DYaJvI3oPKJ68/HxQWlpKTZv3iw6hZ7Ds75/P/PHzL59+9YMCwB48cUXYWFh8dgX9dq9ezf69etX82dJkmBlZYWUlJSG9teZSqWCR8KPyC8qh7JKhRs/puJm6nK8OHkxNt/ojGdsKKqH6urqWsMCAJRVKvwj/gdUV1cLKtMtf/6aLn9QBWWVCvlF5fBM+JFf06SVAgICkJSUhJycHNEp1IieOS5atmxZ67bi4mI4OzvXul2hUMDY2PiR2+RyOc6fP/8ciXXzU34xCm7fR1W1CmXnjuL2vli0sxmPlqa2uHy7HD/liz/3Q1dsPHG51rD4g7JKhY0nLjdxkW7636/p/1VVreLXNGmt7t27w9vbG0FBQaJTqBHV+xfkmZmZeP3112FiYlLrbSUlJTAyevSQuIGBAcrLy5/6Ps3NzWFiYgITExN89tln9U0CAOQVlqGF3u+/h277yggYjfNFueIwbm4Lgqr0JvIKyxr0fqm2M1dKnuvtVDf/+zX9Z/p6Mn5Nk9ZavHgxvv/+e2RlZYlOoUZSr3GhVCqxefPmJ57ta2RkhMrKykduu3//PuRy+VPf79mzZ1FQUICCggLMmzevPkk1TI3bQln138Px7Qc4oeuM1Whh2Bm/rpmFfyavR1VVVYPeNz2qXzfD53o71c2fv6b/l7KqGqbGbZu4iEg9unTpAl9fX17IUIfVa1xER0djyZIljz3fAgDMzMxQWFj4yG23bt1qkrOCB/aQo7tRG+jJ/vuTnsygLV4c7wvrGZHYsyURw4cPx5kzZxq9Rde9OeQl6D/xJ2oJbw55qYmLdNPjvqYBQE8m4SWjNhjY4+mjnUiTLViwAMePH0dmZqboFGoEdR4Xa9euxbhx49C9e3cAQGVlZa0jAVOmTHnkMFd1dTXOnTuHCRMmqCn3ySRJwnqvwejRqQ309SS0aakHfT0Jpp3aIOUjH+Tk5GDUqFEYPHgwli5dWusIC9WdTCbD5plDaw0MfT0JW7yH8emoavK0r+n17wzh01FJq3Xq1Anz5s1DQEAAT07WQc98KioArFq1CgUFBTVPJy0vL8euXbvw1VdfwdHREeHh4bC3t4dSqYS1tTW++eYbDBgwAMnJyYiPj8eePXse+36b4joXf74mQHZ2NmbMmIHKykqsXbsWw4YNU8vHbY54nYumwetckK4qKSlBr169sGXLFowZM0Z0DtXDc1/nIiEhAe+8806t2319ffHpp5+id+/e+OKLLzBp0iQAwK+//gp/f390794dpaWl+PTTT9G+ffsGxTUWpVKJzz77DKGhoZgxYwYiIiLQrl27Jvv4RET0u48//hg7d+7EiRMnOJq1yHOPi8Ykalz84fz585g5cyby8/OxZs0aODk5NXkDEVFzVlZWhl69eiE+Ph4uLi6ic6iOnvsiWrqsT58+OHToEBYvXgxXV1d4eHigqKhIdBYRUbPRtm1bLFmyBIGBgbwAnw5p1uMC+P3kRB8fHygUCpSUlMDc3Bxbt27lCUZERE3Ex8cHt2/fxo4dO0SnkJo0+3Hxh27duiEpKQmxsbGYO3cuJk6ciIKCAtFZREQ6r1WrVggMDERQUBAePnwoOofUgOPif0iSBFdXVygUCsjlclhaWiIuLo6H6oiIGtnbb78NpVKJTZs2iU4hNeC4eIxOnTph3bp12LZtG6KiouDg4NAkr49CRNRc6evrIzg4GCEhIXjw4IHoHHpOHBdP4eTkhDNnzsDGxgY2NjaIjIyEUqkUnUVEpJPc3d1hYGCAr7/+WnQKPSeOi2do164dli9fjv3792Pjxo0YPHgwsrOzRWcREekcPT09hIaGIiwsDBUVFaJz6DlwXNTRsGHDkJ2djYkTJ2LEiBFYuHAh7t+/LzqLiEinvPHGGzA2NkZcXJzoFHoOHBf1YGBggODgYGRlZSEjIwNWVlY4fPiw6CwiIp0hk8kQHh6OyMhI3Lt3T3QONRDHRQNYWlri2LFjePfdd+Hs7Axvb2/cuXNHdBYRkU6YMGECevbsiS+++EJ0CjUQx0UD6enp4b333kNubi7y8vJgYWGBpKQk0VlERFpPkiSEh4fjk08+4Q9uWorj4jn17NkT+/btQ2RkJLy8vODq6oobN26IziIi0mqOjo4YMGAAYmJiRKdQA3BcqIEkSfD09MTZs2chSRLMzc2RmJjIS4gTETXQH0cvYmJiUFhYKDqH6onjQo06d+6MrVu3IjExEf7+/nBycsKlS5dEZxERaaURI0Zg+PDh+OSTT0SnUD1xXDQCFxcXKBQK9OzZE/3790dMTAyqqqpEZxERaZ2wsDCsXLkS165dE51C9cBx0UgMDQ2xZs0apKamYtWqVRg+fDjOnDkjOouISKsMHDgQY8eORWRkpOgUqgeOi0Zmb2+PnJwcjBo1CoMHD8bSpUtRWVkpOouISGuEhoYiPj4ely9fFp1CdcRx0QRat26NqKgoHD16FCkpKbC1tcXx48dFZxERaYX+/ftj8uTJCAsLE51CdcRx0YRsbW1x4sQJeHh4YPTo0fDz8+MV6IiI6iA4OBgbNmzAxYsXRadQHXBcNDF9fX0sXLgQp06dwunTp9GvXz/s27dPdBYRkUbr06cPpk2bhpCQENEpVAccF4L06dMHhw4dwuLFi+Hq6goPDw8UFRWJziIi0liBgYHYsWMHFAqF6BR6Bo4LgWQyGXx8fKBQKFBSUgJzc3Ns3bqVF98iInoMU1NTeHl5ISgoSHQKPYOkEvidrLS0FIaGhigpKUGHDh1EZWgElUqF7du3w9fXF0OGDMGqVatgYmIiOouISKNcvXoVvXv3xtGjR2Frays6p9l61vdvHrnQEJIkwdXVFQqFAnK5HJaWloiLi0N1dbXoNCIijdG1a1fMnj2bRy80HI9caKh9+/bBx8cHPXr0QHx8PPr06SM6iYhII9y6dQu9evXCd999h2HDhonOaZZ45EJLOTk54cyZM7CxsYGNjQ0iIyOhVCpFZxERCffCCy/Az88PAQEBolPoCTguNFi7du2wfPly7N+/Hxs3bsTgwYNx8uRJ0VlERMJ98MEHOHnyJA4ePCg6hR6D40ILDBs2DNnZ2Zg4cSJGjhyJhQsX4v79+6KziIiEkcvlWLBgAQIDA/kMOw3EcaElDAwMEBwcjKysLGRkZMDKygqHDx8WnUVEJMzcuXNx/vx5pKWliU6hP+G40DKWlpY4duwY3n33XTg7O8Pb2xt37twRnUVE1OTat2+PRYsWISAggEcvNAzHhRbS09PDe++9h9zcXOTl5cHCwgJJSUmis4iImtzs2bNx/fp17Nq1S3QK/Q+OCy3Ws2dP7Nu3D5GRkfDy8sLUqVNx/fp10VlERE2mdevWCAgIQFBQEKqqqkTn0H/Ua1wUFhZiwYIFmD179jPv6+XlBUmSIEkS9PX1cfXq1QZH0pNJkgRPT0+cPXsWMpkMFhYWSExM5CFCImo23nnnHdy7dw9btmwRnUL/UedxoVQqcfToUSQnJ6O8vPyp97127Rru3LmDmJgYxMTEYOPGjejatetzx9KTde7cGVu3bkViYiL8/f3h5OSES5cuic4iImp0BgYGCAoKQnBwMK8HpCHqPC709fUxadIkDBo06Jn3XbFiBT7++GO89957eO+99+Dm5vZckVR3Li4uUCgU6NWrF/r374+YmBgeKiQinefh4QFJkrB+/XrRKYQGnHOhr6//1LffvXsXq1evxpAhQ+Dp6Ylr1641OI4axtDQEHFxcUhNTcWqVaswfPhwnDlzRnQWEVGjadGiBUJCQhAaGorKykrROc2e2k/orKiowJo1a+Dt7Y09e/ZgwIAByM3Nfer/Y25uDhMTE5iYmOCzzz5Td1KzZW9vj5ycHIwaNQqDBw/G0qVL+ZeOiHSWm5sbOnTogPj4eNEpzV69X7hs+vTpAIDExMRn3rewsBCOjo5o164djh07VuvtfOGyppOdnY0ZM2agoqICX331FV/sh4h00q5duzB79mz8+9//Rps2bUTn6CyhL1xmbGyMdevW4YcffkBZWVljfih6BltbW5w4cQKenp4YPXo0/Pz8cO/ePdFZRERqNWnSJHTr1g2rVq0SndKsNfp1LqytrSGXy/HgwYPG/lD0DPr6+li4cCFOnTqF06dPo1+/fti3b5/oLCIitZEkCeHh4YiKikJpaanonGar0cdFaWkp+vXrB7lc3tgfiuqoT58+OHToEBYvXgxXV1d4eHigqKhIdBYRkVo4OTnhlVdeweeffy46pdmq97ioqqpCdXV1zZ8fPnyIkSNHIiMjAwDwzTffICYmBkqlEuXl5Xj//fexcuVK9RWTWshkMvj4+EChUKCkpATm5ubYsmULL75FRFrvj6MX0dHRuH37tuicZqle42Lr1q3IzMzEkSNHsH37dgC/j428vDwUFxfX/Dk8PBw9e/bE9OnTsXjxYlhaWqq/nNSiW7duSEpKQmxsLPz8/ODi4oKCggLRWUREz2XUqFEYNGgQoqOjRac0S/V+tog68dkimqWoqAjz5s1DUlISPv74Y3h7e0Mm48vPEJF2+uGHHzB69Gj8+uuvePHFF0Xn6BShzxYh7dKpUyesW7cO27ZtQ1RUFBwcHHD+/HnRWUREDTJ06FA4ODggKipKdEqzw3FBtTg5OeHMmTOwsbGBjY0NIiMjeb1+ItJKYWFhiIuLw5UrV0SnNCscF/RY7dq1w/Lly7F//35s3LgRgwcPxsmTJ0VnERHVi7W1NZydnRERESE6pVnhuKCnGjZsGLKzszFx4kSMHDkSH3744TNfFZeISJOEhIQgISGBrxTdhDgu6JkMDAwQHByMrKwsZGZmYsCAATh8+LDoLCKiOjE3N4erqytCQ0NFpzQbHBdUZ5aWljh27BjmzJmD//f//h+8vb1x584d0VlERM+0dOlSbN68Gb/88ovolGaB44LqRU9PD35+fsjJyUFeXh4sLCyQlJQkOouI6KnMzMzg6emJpUuXik5pFjguqEF69uyJffv2ITIyEl5eXpg6dSquX78uOouI6IkCAgKQnJyMnJwc0Sk6j+OCGkySJHh6euLs2bOQyWSwsLBAYmIiLyFORBqpe/fu8Pb2RlBQkOgUnccrdJLa7N69G7NmzYKlpSXWrFmDnj17ik4iInrE9evXYWZmhsOHD2PQoEGic7QWr9BJTcbFxQUKhQK9evVC//79ERMTg6qqKtFZREQ1unTpAl9fXwQEBIhO0Wk8ckGNIiMjAzNmzECnTp2wdu1a9OvXT3QSERGA319HqVevXkhJSYGdnZ3oHK3EIxckhL29PXJycjBq1CgMHjwYS5cuRWVlpegsIiJ06tQJ8+bNQ0BAAM8RayQcF9RoWrdujaioKBw9ehQpKSmwsbHB8ePHRWcREeG9997Dv/71L+zfv190ik7iuKBGZ2trixMnTsDT0xOjR4/G3Llzce/ePdFZRNSMGRoa4sMPP4S/vz+PXjQCjgtqEvr6+li4cCFOnTqFn3/+Gf369cO+fftEZxFRMzZnzhxcvnwZKSkpolN0DscFNak+ffrg0KFDWLx4MVxdXeHh4YGioiLRWUTUDLVt2xZLlixBYGAgqqurRefoFI4LanIymQw+Pj5QKBQoKSmBubk5tmzZwkOTRNTkvL29cfv2bezYsUN0ik7huCBhunXrhqSkJMTGxsLPzw8uLi4oKCgQnUVEzUirVq0QGBiIoKAgPHz4UHSOzuC4IKEkSYKrqysUCgWMjIxgaWmJuLg4HqIkoibz9ttvQ6lUYtOmTaJTdAbHBWmETp06Yd26ddi2bRuioqLg4OCA8+fPi84iomZAX18fwcHBCAkJwYMHD0Tn6ASOC9IoTk5OOHPmDGxsbGBjY4PIyEgolUrRWUSk49zd3WFgYICEhATRKTqB44I0Trt27bB8+XLs378fGzduxODBg3Hy5EnRWUSkw/T09BAaGoqwsDDcv39fdI7W47ggjTVs2DBkZ2dj4sSJGDlyJD788EOUl5eLziIiHfXGG2/ghRdewJo1a0SnaD2OC9JoBgYGCA4ORlZWFjIzM2FlZYVDhw6JziIiHSSTyRAeHo7IyEheRfg5cVyQVrC0tMSxY8fg6+sLFxcXeHt7486dO6KziEjHTJgwAT179sQXX3whOkWrcVyQ1tDT04Ofnx9ycnKQl5cHCwsLJCUlic4iIh0iSRLCw8PxySef8AeY58BxQVqnZ8+e2LdvHyIjI+Hl5YWpU6fi+vXrorOISEc4OjrC2toaMTExolO0FscFaSVJkuDp6YmzZ89CJpPBwsICiYmJvIQ4ET03SZIQFhaGmJgYFBYWis7RShwXpNU6d+6MrVu3IjExEf7+/nBycsKlS5dEZxGRlhsxYgSGDx+OTz75RHSKVuK4IJ3g4uIChUKBXr16oX///oiJiUFVVZXoLCLSYmFhYVi5ciWuXbsmOkXrSKp6HEcuLCzExx9/jLKyMqxateqJ97t58yY++OADyOVy3Lt3D9HR0ZDL5bXuV1paCkNDQ5SUlKBDhw4N+wyI/iQjIwMzZsxAp06dsHbtWvTr1090EhFpqddffx0mJiZYsWKF6BSN8qzv33U+cqFUKnH06FEkJyc/9UJG1dXVcHZ2xsyZM7FixQq8/vrr+Mc//tGweqIGsLe3R05ODkaNGoXBgwdj6dKlqKysFJ1FGk6lUiEr7za2//QbsvJu8/ydRqJtj3NISAji4+Nx+fJl0SlapV5HLgBg2rRp0NfXR2Ji4mPfvnPnTsyfP7/m994qlQpyuRy7d++GnZ3dI/flkQtqbNnZ2ZgxYwYqKirw1VdfYdiwYaKTSAMVFJfDI+FH/Ha7HPp6MiirqtHdqA3Wew2GibyN6Dydoa2Ps7u7O9q2bYv4+HjRKRpDbUcu/qCvr//Ut+/evfuRw9CSJMHKygopKSn1/VBEz83W1hYnTpyAp6cnRo8ejblz5/LKe/QIlUoFj4QfkV9UDmWVCuUPqqCsUiG/qByeCT9q/E/W2kKbH+fg4GBs2LABFy9eFJ2iNdR+QqdCoYCxsfEjt8nlcr58Ngmjr6+PhQsX4tSpU/j5559haWmJ9PR00VmkIX7KL0bB7fuoqn70m1tVtQqXb5fjp/xiQWW6RZsf5z59+mDatGkICQkRnaI11D4uSkpKYGRk9MhtBgYGTz1Pw9zcHCYmJjAxMcFnn32m7iQiAL//A3Ho0CEsWbIEbm5u8PDwQFFRkegsEiyvsAwt9KTHvk1fT4a8wrImLtJN2v44BwYGYseOHfjXv/4lOkUrqH1cGBkZ1Tp57v79+499tsgfzp49i4KCAhQUFGDevHnqTiKqIZPJ4OPjA4VCgZKSEpibm2PLli0afUiWGpepcVsoq6of+zZlVTVMjds2cZFu0vbH2dTUFF5eXli6dKnoFK2g9nFhZmZW64pmt27dQt++fdX9oYgarFu3bkhKSkJsbCz8/Pzg4uKCgoIC0VkkwMAecnQ3agM92aM/VevJJLxk1AYDezz5ByOqO114nP39/bF3715kZ2eLTtF4ah8XU6ZMQVZWVs2fq6urce7cOUyYMEHdH4rouUiSBFdXVygUChgZGcHS0hKrV69GdfXjf7oi3SRJEtZ7DUaPTm2gryehTUs96OtJMO3UBuvfGQJJevyhfKofXXicu3btitmzZyMoKEh0isar91NR33rrrd+/SNavBwA8fPgQDg4OCA8Ph729PZRKJaytrfHNN99gwIABSE5ORnx8PPbs2VPrffGpqKRJ9u3bBx8fH7z00ktYu3Yt+vTpIzqJmpBKpcJP+cXIKyyDqXFbDOwh14pveNpG2x/nW7duoVevXvjuu++a9VPb1fpU1K1btyIzMxNHjhzB9u3bAQBVVVXIy8tDcfHvZ/rq6+sjJSUFUVFR+PDDD5GWlobNmzer4VMhalxOTk44c+YMbG1tYWNjg8jISCiVStFZ1EQkScIgUyNMHdgdg0yNtOobnjbR9sf5hRdegJ+fHwICAkSnaLR6H7lQJx65IE11/PhxzJgxAy1btsTatWvx6quvik4iIg1x584d9OzZEzt37sRrr70mOkcItV9Ei6g5GDZsGLKzszFx4kSMHDkSH3744VOfTk1EzUfHjh0xf/58BAYG8plmT8BxQfQEBgYGCA4ORlZWFjIzM2FlZYVDhw6JziIiDTB37lycP38eaWlpolM0EscF0TNYWlri2LFj8PX1hYuLC7y9vXHnzh3RWUQkUPv27bFo0SIEBATw6MVjcFwQ1YGenh78/PyQm5uL/Px8WFhYICkpSXQWEQk0e/ZsXL9+Hbt27RKdonE4LojqwdTUFOnp6YiMjISXlxemTp2K69evi84iIgFat26NgIAABAUFoaqqSnSORuG4IKonSZLg6emJs2fPQiaTwcLCAomJiTw0StQMvfPOO7h37x62bNkiOkWjcFwQNVDnzp2xdetWJCYmwt/fH05OTrh06ZLoLCJqQgYGBggKCkJwcDCvi/M/OC6InpOLiwsUCgV69eqF/v37IyYmhodIiZoRDw+PR65cTRwXRGphaGiIuLg4pKamYtWqVfjrX/+KM2fOiM4ioibQokULhISEIDQ0tNargjdXHBdEamRvb4+cnBw4ODhg8ODBWLp0Kf+xIWoG3Nzc0KFDB8THx4tO0QgcF0Rq1rp1a0RFReHo0aNISUmBjY0Njh8/LjqLiBqRTCZDWFgYIiIieDVfcFwQNRpbW1ucOHECnp6eGD16NObOnYt79+6JziKiRjJx4kR069YNq1atEp0iHMcFUSPS19fHwoULcfr0aeTk5MDS0hLp6emis4ioEUiShPDwcERFRaG0tFR0jlAcF0RN4OWXX8bBgwexZMkSuLm5wcPDA0VFRaKziEjNnJyc8Morr+Dzzz8XnSIUxwVRE5HJZPDx8YFCoUBJSQnMzc2xZcsWXnyLSIdIkoSIiAhER0fj9u3bonOE4bggamLdunVDUlISYmNj4efnBxcXFxQUFIjOIiI1sbe3x6BBgxAdHS06RRiOCyIBJEmCq6srFAoFjIyMYGlpidWrV6O6ulp0GhGpQVhYGD7//HPcvHlTdIoQHBdEAnXq1Anr1q3Dtm3b8PHHH2PUqFH45ZdfRGcR0XMaOnQoHBwcEBUVJTpFCI4LIg3g5OSEM2fOwNbWFra2toiMjOTrFBBpubCwMMTFxeHKlSuiU5ocxwWRhmjXrh2WL1+O/fv3Y+PGjRg8eDBOnjwpOouIGsja2hrOzs6IiIgQndLkOC6INMywYcOQnZ2NiRMnYuTIkfjwww95xT8iLRUSEoKvv/662b1iMscFkQYyMDBAcHAwsrKykJmZCSsrKxw6dEh0FhHVk7m5OVxdXREaGio6pUlxXBBpMEtLSxw7dgy+vr5wcXGBt7c37ty5IzqLiOohKCgImzdvblYna3NcEGk4PT09+Pn5ITc3F/n5+bCwsEBSUpLoLCKqIzMzM3h6emLp0qWiU5oMxwWRljA1NUV6ejoiIyPh5eWFqVOn4vr166KziKgOAgICkJycjJycHNEpTYLjgkiLSJIET09PnD17FjKZDBYWFkhMTOQlxIk0XPfu3eHj44OgoCDRKU1CUgn8V6m0tBSGhoYoKSlBhw4dRGUQaa3du3dj1qxZsLS0xJo1a9CzZ0/RSUT0BNevX4eZmRkOHz6MQYMGic55Ls/6/s0jF0RazMXFBQqFAr169UL//v0RExODqqoq0VlE9BhdunSBr68vAgICRKc0Oh65INIRGRkZmDFjBoyMjLB27Vr0799fdBIR/UlRURF69eqFlJQU2NnZic5pMB65IGom7O3tkZOTAwcHBwwZMgRLly5FZWWl6Cwi+h+dOnXCvHnzEBAQoNPnSnFcEOmQ1q1bIyoqCkePHkVKSgpsbGxw/Phx0VlE9D/ee+89/Otf/8L+/ftFpzQajgsiHWRra4sTJ07A09MTo0ePxty5c3Hv3j3RWUQEwNDQEB9++CH8/f119uhFvcZFZGQkZs6ciWnTpuHgwYNPve9rr70GSZIgSRKMjY1RUVHxXKFEVD/6+vpYuHAhTp8+jZycHFhaWiI9PV10FhEBmDNnDi5fvoyUlBTRKY2iRV3vGBsbiwsXLiAhIQEVFRWwtrZGamoqzMzMat335MmTMDExQUxMDACgb9++aNWqlfqqiajOXn75ZRw8eBDx8fFwc3ODi4sLYmJiYGxsLDqNqNlq27YtlixZgsDAQDg7O0Mm061fJNTp2SIPHjxA165dsXPnTtjb2wMA/Pz8cPfuXSQkJNS6/zvvvIPPPvsMhoaGT32/fLYIUdO6cuUKZs+ejePHj2PFihVwc3ODJEmis4iapYqKCrz88stYtmwZ3NzcROfUi1qeLXLs2DEUFRWhX79+NbcNGDAAe/bsqXXfS5cuYd26dXjllVfg6+uL0tLS58gnInXq1q0bkpKSEBsbCz8/P7i4uKCgoEB0FlGz1KpVKwQGBmLp0qV4+PCh6By1qtO4UCgUkMlkkMvlNbfJ5XLcunULxcXFj75DmQzr1q3DlClTkJCQAGtra1y7du2p79/c3BwmJiYwMTHBZ5991oBPg4jqSpIkuLq6QqFQwMjICJaWlli9ejWqq6tFpxE1O2+//TaUSiU2bdokOkWt6jQuSkpK0LFjx0d+J2RgYAAAKC8vf+S+PXr0wLRp0/DFF18gJycHSqUS8+fPf+r7P3v2LAoKClBQUIB58+bV93Mgogbo1KkT1q1bh23btuHjjz/GqFGjmtVLQhNpAn19fQQHByMkJAQPHjwQnaM2dRoXRkZGtS7Gc//+fQB45GjGn5mZmeGLL77Q6efyEmk7JycnnDlzBra2trCxscFHH30EpVIpOouo2XB3d4eBgcFjz2HUVnUaF2ZmZigrK3vk6aS3bt2CiYkJ2rRp89T/19HRkVcJJNJw7dq1w/Lly3HgwAFs2rQJgwYNwsmTJ0VnETULenp6CA0NRVhYWM0P7tquTuNi1KhRMDY2RlZWVs1tCoUCEyZMeOb/+9tvv8HZ2bnhhUTUZIYNG4bs7GxMmjQJI0eOxIcffljrV59EpH5vvPEGXnzxRaxZs0Z0ilrUaVzo6+vj/fffx7fffgsAKCsrw/fff49FixahqKgIAwcOrPld7YoVK5CYmAiVSoWioiKEhYUhOjq68T4DIlIrAwMDBAcHIysrC5mZmbCyssKhQ4dEZxHpNJlMhrCwMERGRurE1XTrfNWOhQsXokWLFvDz88O7776LtWvXwtTUFJWVlcjLy8Pdu3cB/H4uxty5c9G7d2/Mnz8fy5cvR+fOnRvtEyCixmFpaYljx47B19cXLi4u8Pb2xp07d0RnEemsCRMmoGfPnvjiiy9Epzw3vuQ6ET1TXl4efHx8kJubi1WrVmHSpEmik4h00v79+zF16lRcunQJHTt2FJ3zRHzJdSJ6bqampkhPT0dkZCS8vLwwdepUXL9+XXQWkc5xdHSEtbV1zctnaCuOCyKqE0mS4OnpibNnz0Imk8HCwqLm/CoiUg9JkhAWFoaYmBgUFhaKzmkwjgsiqpfOnTtj69atSExMhL+/P5ycnHDp0iXRWUQ6Y8SIERg+fDg++eQT0SkNxnFBRA3i4uIChUKBXr16oX///oiJiUFVVZXoLCKdEB4ejpUrVz7z5TM0FccFETWYoaEh4uLikJqailWrVuGvf/0rcnNzRWcRab1XX30VTk5OiIyMFJ3SIBwXRPTc7O3tkZOTAwcHBwwZMgRBQUG8Mi/RcwoJCUF8fDwuX74sOqXeOC6ISC1at26NqKgoHD16FHv27IGNjQ3++c9/is4i0lr9+/fH5MmTERYWJjql3jguiEitbG1tceLECXh6emLMmDGYO3euTlxxkEiE4OBgbNiwARcvXhSdUi8cF0Skdvr6+li4cCFOnz6NnJwcWFpaIj09XXQWkdbp06cPpk2bhpCQENEp9cJxQUSN5uWXX8bBgwfh7+8PNzc3vPXWW1r93H0iEQIDA7Fjxw7861//Ep1SZxwXRNSoZDIZvL29oVAoUFpaCgsLC2zevJkX3yKqI1NTU3h5eWHp0qWiU+qMry1CRE1GpVJh+/bt8PX1xeDBg7F69WqYmJiIziLSeFevXkXv3r1x9OhR2Nrais7ha4sQkeaQJAmurq5QKBQwMjKCpaUlVq9ejerqatFpRBqta9eumD17NoKCgkSn1AmPXBCRMPv27YOPjw9eeuklxMfHo2/fvqKTiDTWrVu30KtXL3z33XcYNmyY0BYeuSAijeXk5IQzZ87A1tYWtra2+Oijj6BUKkVnEWmkF154AX5+fggICBCd8kwcF0QkVLt27bB8+XIcOHAAmzZtwqBBg3Dy5EnRWUQaaf78+cjOzsbBgwdFpzwVxwURaYShQ4ciOzsbkyZNwsiRI/Hhhx+ivLxcdBaRRunYsSPmz5+PwMBAjX7GFccFEWkMAwMDBAcHIysrC5mZmbCyssKhQ4dEZxFplLlz5+L8+fNIS0sTnfJEHBdEpHEsLS1x7Ngx+Pr6wsXFBd7e3rhz547oLCKN0L59eyxevBgBAQEae/SC44KINJKenh78/PyQm5uL/Px8WFhYICkpSXQWkUaYNWsWrl+/jl27dolOeSyOCyLSaKampkhPT0dUVBS8vLwwdepUXL9+XXQWkVCtW7dGQEAAAgMDUVVVJTqnFo4LItJ4kiTBw8MDZ8+ehUwmg4WFBb7++muNPSRM1BRmzJiBsrIybNmyRXRKLRwXRKQ1OnfujK1btyIxMREBAQEYO3Ysfv31V9FZREK0bNkSS5cuRXBwsMZdH4bjgoi0jouLCxQKBczMzGBlZYWYmBiNPDRM1NjeeustSJKE9evXi055BMcFEWklQ0NDxMXFITU1FatXr8Zf//pX5Obmis4ialItWrRASEgIQkNDUVlZKTqnBscFEWk1e3t7/Pzzz3BwcMCQIUMQFBSkUf/IEjU2Nzc3dOjQAfHx8aJTanBcEJHWa926NaKionD06FHs2bMHNjY2+Oc//yk6i6hJyGQyhIWFISIiQmOuastxQUQ6w9bWFidOnICnpyfGjBmDuXPn4t69e6KziBrdxIkT0a1bN6xatUp0CgCOCyLSMfr6+li4cCFOnz6NnJwcWFpaIj09XXQWUaOSJAnh4eGIiopCaWmp6ByOCyLSTS+//DIOHjwIf39/uLm54a233kJhYaHoLKJG4+TkhFdeeQWff/656BSOCyLSXTKZDN7e3lAoFCgtLYWFhQU2b97Mi2+RTpIkCREREYiOjsbt27eFtnBcEJHO69atG5KSkhAbG4v33nsPLi4u+O2330RnEamdvb09Bg0ahOjoaKEd9RoXkZGRmDlzJqZNm4aDBw8+8X4XLlyAu7s75syZgzlz5vBpYUQknCRJcHV1hUKhgJGRESwtLbF69WpUV1cDAFQqFbLybmP7T78hK+82j26Q1goPD8fnn3+OfT/9IuzrWVLV8SPGxsYiOzsbCQkJqKiogLW1NVJTU2FmZvbI/crKymBtbY20tDT07t0bsbGxOHPmDOLi4mq9z9LSUhgaGqKkpAQdOnRQz2dERFQH+/btg4+PD1566SWELVuBkCN38NvtcujryaCsqkZ3ozZY7zUYJvI2olOJ6qWguBzWI8bgYbsX0dXJp1G+np/1/btORy4ePHiA4OBgeHp6AgBatWoFJycnRERE1LpvXFwcTExM0Lt3bwCAu7s74uPjkZeX9xyfBhGRejk5OeHMmTOwsbHBayOG4XTK13jwQInyB1VQVqmQX1QOz4QfeQSDtIpKpYJHwo9oNfTvKM1OQ2nRDSFfzy3qcqdjx46hqKgI/fr1q7ltwIABWLRoUa377t69G1ZWVjV/NjIyQrdu3ZCamop3331XDclEROrRrl07vPn+UnxbYoobe5bjriITRqP/Dwade6EaQN61chw+k49XexiJTiWqk5P5t5F/rQiyDl3QytQGd45sRKe/+aGqGrh8uxw/5RdjkGnjfz3XaVwoFArIZDLI5fKa2+RyOW7duoXi4uJHblcoFHjttdce+f/lcjnOnz//xPdvbm4OSZIAAPPmzcO8efPq9UkQETVUXmEZ2r9kDtn0z3Hn6De4ufnRH5peE3teHNFzk782E3qt2kJfT4a8wjLNGRclJSXo2LEjZLL//hbFwMAAAFBeXv7IuCgpKYGR0aPhBgYGT70k6dmzZ3nOBREJYWrcFsqqakgt9NHR3gOGw6bWvE1fT8Jaz4E8ckFa42T+bcxY9xOUVf/99YfUsjUAQFlVDVPjtk3SUadxYWRkVOsZH/fv3weAR4bF0+775/sREWmCgT3k6G7UBvlF5aiqBiSD309405NJMO3UBqP69ag5skqk6Ub1a48ef8n7z9fzfweGnkzCS0ZtMLBH03wvrtMJnWZmZigrK0NFRUXNbbdu3YKJiQnatGlT675/vgrerVu30LdvXzXkEhGplyRJWO81GD06tYG+noQ2LfWgr/f7sFj/zhAOC9IqmvL1XKcjF6NGjYKxsTGysrIwcuRIAL+fWzFhwoRa950yZQr27NlT8+eioiIUFRXByclJTclEROplIm+DA/Ps8VN+MfIKy2Bq3BYDe8g5LEgracLXc52vc/HRRx/h1q1biImJQVlZGQYOHIi0tDS0b98eTk5O2LRpE/r27Yvi4mJYW1vjxx9/ROfOnfH555/jwoULiI2NrfU+eZ0LIiIi7fOs7991OnIBAAsXLsSiRYvg5+eHkpISrF27Fqamprh69Sry8vJw9+5dAL+fg7Fz506899576Nq1KyRJQkxMjPo+IyIiItJodT5y0Rh45IKIiEj7qOUKnURERER1xXFBREREasVxQURERGrFcUFERERqxXFBREREasVxQURERGqls+Pis88+E53QbPCxbhp8nJsGH+emwce5aYh6nHX2OhcmJiYoKChQ6/ukx+Nj3TT4ODcNPs5Ng49z02isx5nXuSAiIqImVefLfzeGPw6alJaWNsr7boz3S7XxsW4afJybBh/npsHHuWk01uP8x/t80i8/hP5apKCgAN27dxf14YmIiOg5/PbbbzAxMal1u9BxUV1djatXr6J9+/Z8aWMiIiItoVKpcPfuXXTt2hUyWe0zLISOCyIiItI9PKGTiIiI1IrjgoiIiNRKJ8dFZGQkZs6ciWnTpuHgwYOic3RaYWEhFixYgNmzZ4tO0Un5+flwcnJC+/btYWNjg0OHDolO0lm3bt2Cs7Mz2rdvj4EDB+Lnn38WnaTT9u7di549e4rO0GmZmZmQJKnmv08//bTJPrbOnXMRGxuL7OxsJCQkoKKiAtbW1khNTYWZmZnoNJ2jVCqRmpqKDz/8EH/961+RmJgoOkmnqFQqODk5YcyYMejSpQuio6Nx4cIF5OTk8Ou5Ebz//vv429/+Bn19fbz77rvQ09NDbm6u6CydVFxcjEGDBuHhw4fIy8sTnaOzvLy8YGVlVfNnT09PyOXyJvnYOjUuHjx4gK5du2Lnzp2wt7cHAPj5+eHu3btISEgQXKe7pk2bBn19fY4LNcvNzcXNmzfh6OgIALh58yZ69eqFiIgI+Pn5Ca7TLRUVFSgsLKx5St327dsxc+ZM3LlzR2yYjnr33XfRuXNnJCQkcFw0krNnz2Lz5s0IDQ0V8vF16tcix44dQ1FREfr161dz24ABA7Bnzx6BVbpPX19fdIJO6tu3b82wAIAXX3wRFhYWMDAwEFilm1q1avXIc/WVSiVmzZolsEh3JSUlYdCgQXjppZdEp+i0ZcuW4aOPPoKdnR327t3b5B9fp8aFQqGATCZ75LCPXC7HrVu3UFxcLLCMqP5atmxZ67bi4mI4OzsLqGk+CgoKsHHjRvj7+4tO0TmFhYVITU3F9OnTRafovClTpmDZsmWorKzEhAkTEBkZ2aQfX6fGRUlJCTp27PjIBT3++CmvvLxcVBaRWmRmZuL1119/7NXwSD1Onz6N//u//0NaWhocHBxQWVkpOkmnBAYGIiwsTHRGs/C3v/0N7733Hn744Qf4+/sjKCgI586da7KPr1PjwsjIqNY/Bvfv3weAJjuJhagxKJVKob8/bS6sra2xZ88efPvttzh58iR27twpOklnbN26FaNGjUKXLl1EpzQrkiQhLCwM/fr1a9Jnm+nUuDAzM0NZWRkqKipqbrt16xZMTEzQpk0bgWVEzyc6OhpLlizh+RZNZPLkybC3t8fVq1dFp+iMuLg4/P3vf695WuTbb7+N/Px8SJKEw4cPi87TaZIk4bXXXmvSI3FCXxVV3UaNGgVjY2NkZWVh5MiRAH4/D2PChAmCy4gabu3atRg3blzNi/xVVlaiRYsW0NPTE1ym2zp27PjI0/jo+cTHx+PevXs1f969ezfi4uKwd+9e9O7dW2BZ83Dt2jXMnDmzyT6eTh250NfXx/vvv49vv/0WAFBWVobvv/8eixYtElym26qqqlBdXS06QyetWrUKv/76K65fv4709HR8++23mDFjBl/oT81KS0uxbt26mpeRzsnJwYMHDzB27FjBZbqjd+/esLa2rvnvpZdeQsuWLWFtbY127dqJztMply9fhq+vLy5fvgzg919JWVpa4pVXXmmyBp0aFwCwcOFCtGjRAn5+fnj33Xexdu1amJqais7SWVu3bkVmZiaOHDmC7du3i87RKQkJCXj33XcRGRmJv/3tb/jb3/6GN954A3K5/LGvQkgNd+PGDQQHB6N3795wdXXF5s2bsWXLFtFZRA3SokULZGRkwMLCAvb29nj48GGTP/tJpy6iRUREROLxxx8iIiJSK44LIiIiUiuOCyIiIlIrjgsiIiJSK44LIiIiUiuOCyIiIlIrjgsiIiJSK44LIiIiUiuOCyIiIlIrjgsiIiJSK44LIiIiUqv/D2Wk5lbLKp76AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.spatial import ConvexHull\n",
    "\n",
    "points = np.array([\n",
    "  [2, 4],\n",
    "  [3, 4],\n",
    "  [3, 0],\n",
    "  [2, 2],\n",
    "  [4, 1],\n",
    "  [1, 2],\n",
    "  [5, 0],\n",
    "  [3, 1],\n",
    "  [1, 2],\n",
    "  [0, 2]\n",
    "])\n",
    "\n",
    "hull = ConvexHull(points)\n",
    "hull_points = hull.simplices\n",
    "print(hull_points)\n",
    "\n",
    "plt.scatter(points[:,0], points[:,1])\n",
    "for simplex in hull_points:\n",
    "  plt.plot(points[simplex,0], points[simplex,1], 'k-');\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2bfa74bf-c5c5-419b-a118-62bab423708b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The shoelace algorithm\n",
    "\n",
    "def polygon_area(vertices):\n",
    "    \"\"\"\n",
    "    Return the area of the polygon enclosed by vertices using the shoelace\n",
    "    algorithm.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    a = np.vstack((vertices, vertices[0]))\n",
    "    S1 = sum(a[:-1,0] * a[1:,1])\n",
    "    S2 = sum(a[:-1,1] * a[1:,0])\n",
    "    return abs(S1-S2)/2\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "vertices = np.array([(3,4), (5,11), (12,8), (9,5), (5,6)])\n",
    "polygon = plt.Polygon(vertices, alpha=0.1, closed=True)\n",
    "ax.add_patch(polygon)\n",
    "simplices = Delaunay(vertices).simplices\n",
    "plt.triplot(vertices[:, 0], vertices[:, 1], simplices, color='g')\n",
    "plt.scatter(list(list(zip(*vertices))[0]),list(list(zip(*vertices))[1]),color='m')\n",
    "print(polygon_area(vertices))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9291bb5b-8223-4efc-83c3-580365e2a65d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://scipython.com/book2/chapter-4-the-core-python-language-ii/additional-problems/the-olympic-heptathlon/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a378f090",
   "metadata": {},
   "source": [
    "#### 1D Interpolation:\n",
    "\n",
    "The function interp1d() is used to interpolate a distribution with 1 variable. It takes x and y points and returns a callable function that can be called with new x and returns corresponding y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7172d6c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "\n",
    "xs = np.arange(10)\n",
    "ys = 2*xs + 1\n",
    "\n",
    "plt.scatter(xs,ys)\n",
    "\n",
    "interp_func = interp1d(xs, ys)\n",
    "\n",
    "newarr = interp_func(np.arange(2.1, 3, 0.1))\n",
    "plt.scatter(np.arange(2.1, 3, 0.1),newarr);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f867486e",
   "metadata": {},
   "source": [
    "#### Spline Interpolation:\n",
    "\n",
    "In 1D interpolation the points are fitted for a single curve whereas in Spline interpolation the points are fitted against a piecewise function defined with polynomials called splines. The UnivariateSpline() function takes xs and ys and produce a callable funciton that can be called with new xs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "885e666a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import UnivariateSpline\n",
    "\n",
    "xs = np.arange(10)\n",
    "ys = xs**2 + np.sin(xs) + 1\n",
    "\n",
    "interp_func = UnivariateSpline(xs, ys)\n",
    "\n",
    "newarr = interp_func(np.arange(2., 3., 0.1))\n",
    "\n",
    "plt.scatter(xs,ys)\n",
    "plt.scatter(np.arange(2., 3., 0.1),newarr);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "133e8e40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a closer look of that bad interpolation\n",
    "\n",
    "plt.xlim(1.9,3.1)\n",
    "plt.ylim(5,11)\n",
    "plt.scatter(xs,ys)\n",
    "plt.scatter(np.arange(2., 3., 0.1),newarr);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fc1e923",
   "metadata": {},
   "source": [
    "#### Interpolation with Radial Basis Function:\n",
    "\n",
    "Radial basis function is a function that is defined corresponding to a fixed reference point. The Rbf() function also takes xs and ys as arguments and produces a callable function that can be called with new xs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3dd716ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import Rbf\n",
    "\n",
    "xs = np.arange(10)\n",
    "ys = xs**2 + np.sin(xs) + 1\n",
    "\n",
    "interp_func = Rbf(xs, ys)\n",
    "\n",
    "newarr = interp_func(np.arange(2.1, 3, 0.1))\n",
    "plt.xlim(1.9,3.1)\n",
    "plt.ylim(5,11)\n",
    "plt.scatter(xs,ys)\n",
    "plt.scatter(np.arange(2.1, 3, 0.1),newarr);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "501f3c60-1ace-4187-8f19-6e6eae0bf96d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# numerical interpolation\n",
    "\n",
    "xs = np.linspace(-3, 3, 5)\n",
    "def fun(x):\n",
    "  \"\"\"A simple 4-th order polynomial.\"\"\"\n",
    "  return x**4\n",
    "ys = fun(xs)\n",
    "\n",
    "x=np.linspace(-3,3,100)\n",
    "plt.scatter(xs,ys, color='k',label='data')\n",
    "plt.plot(x,fun(x), color='k',label='actual')\n",
    "\n",
    "from scipy.interpolate import interp1d\n",
    "\n",
    "interp = interp1d(xs, ys)\n",
    "plt.plot(x,interp(x),color='r',label='linear')\n",
    "\n",
    "interp = interp1d(xs, ys, kind='nearest')\n",
    "plt.plot(x,interp(x),color='g',label='nearest')\n",
    "\n",
    "interp = interp1d(xs, ys, kind='cubic')\n",
    "plt.plot(x,interp(x),color='b',label='cubic')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c784dde7-b351-45e6-93a6-b8d10ab9b8e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "\n",
    "A, nu, k = 10, 4, 2\n",
    "\n",
    "def f(x, A, nu, k):\n",
    "    return A * np.exp(-k*x) * np.cos(2*np.pi * nu * x)\n",
    "\n",
    "xmax, nx = 0.5, 8\n",
    "x = np.linspace(0, xmax, nx)\n",
    "y = f(x, A, nu, k)\n",
    "\n",
    "f_nearest = interp1d(x, y, kind='nearest')\n",
    "f_linear  = interp1d(x, y)\n",
    "f_cubic   = interp1d(x, y, kind='cubic')\n",
    "\n",
    "x2 = np.linspace(0, xmax, 100)\n",
    "plt.plot(x, y, 'o', color='k', label='data')\n",
    "plt.plot(x2, f(x2, A, nu, k), color='k', label='exact')\n",
    "plt.plot(x2, f_nearest(x2), color='g', label='nearest')\n",
    "plt.plot(x2, f_linear(x2), color='r', label='linear')\n",
    "plt.plot(x2, f_cubic(x2), color='b', label='cubic')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e4d787cf-a664-47c6-bbab-c5e2d2267aa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import griddata\n",
    "\n",
    "x = np.linspace(-1,1,100)\n",
    "y =  np.linspace(-1,1,100)\n",
    "X, Y = np.meshgrid(x,y)\n",
    "\n",
    "def f(x, y):\n",
    "    s = np.hypot(x, y)\n",
    "    phi = np.arctan2(y, x)\n",
    "    tau = s + s*(1-s)/5 * np.sin(6*phi) \n",
    "    return 5*(1-tau) + tau\n",
    "\n",
    "T = f(X, Y)\n",
    "# Choose npts random point from the discrete domain of our model function\n",
    "npts = 400\n",
    "px, py = np.random.choice(x, npts), np.random.choice(y, npts)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=2, ncols=2)\n",
    "# Plot the model function and the randomly selected sample points\n",
    "ax[0,0].contourf(X, Y, T)\n",
    "ax[0,0].scatter(px, py, c='k', alpha=0.2, marker='.')\n",
    "ax[0,0].set_title('Sample points on f(X,Y)')\n",
    "\n",
    "# Interpolate using three different methods and plot\n",
    "for i, method in enumerate(('nearest', 'linear', 'cubic')):\n",
    "    Ti = griddata((px, py), f(px,py), (X, Y), method=method)\n",
    "    r, c = (i+1) // 2, (i+1) % 2\n",
    "    ax[r,c].contourf(X, Y, Ti)\n",
    "    ax[r,c].set_title(\"method = '{}'\".format(method))\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68e68ab-83d6-42ee-b718-9c82761d1bc0",
   "metadata": {},
   "source": [
    "A quick review of data distributions:\n",
    "\n",
    "https://makemeanalyst.com/normal-distribution-binomial-distribution-poisson-distribution/\n",
    "\n",
    "#### Bernoulli trial & Binomial Distribution\n",
    "\n",
    "Every random variable has a corresponding probability distribution. The probability distribution applies the theory of probability to describe the behavior of the random variable. A discrete random variable X has a finite number of possible integer values. The probability distribution of X lists the values and their probabilities in a table\n",
    "\n",
    "$x_1 \\rightarrow p_1$ ;\n",
    "$x_2 \\rightarrow p_2$ ;\n",
    "$x_3 \\rightarrow p_3$\n",
    "\n",
    "Every probability $p$ is a number between 0 and 1. The sum of the probabilities must be 1.\n",
    "\n",
    "#### Bernoulli trial or Binomial Trial\n",
    "\n",
    "Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, “success” and “failure”, in which the probability of success is the same every time the experiment is conducted.\n",
    "\n",
    "- The event (or trial) results in only one of two mutually exclusive outcomes – success/failure\n",
    "- Probability of success is known, P(success) = $p$\n",
    "\n",
    "examples:\n",
    "\n",
    "- A single coin toss (heads or tails), P(heads) = $p$ = 0.5\n",
    "- Survival of an individual after CABG surgery, P(survival) = $p$ = 0.98\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbd834b6",
   "metadata": {},
   "source": [
    "#### Binomial Distribution\n",
    "\n",
    "The binomial distribution is a discrete probability distribution that is used to model the number of successes in a fixed number of independent trials. It is characterized by two parameters – the probability of success in a single trial, and the number of trials. The binomial distribution is widely used in fields such as finance, biology, and quality control. A distribution is said to be binomial distribution if the following conditions are met.\n",
    "\n",
    "- Each trial has a binary outcome (One of the two outcomes is labeled a ‘success’)\n",
    "- The probability of success is known and constant over all trials\n",
    "- The number of trials is specified\n",
    "- The trials are independent. That is, the outcome from one trial doesn’t affect the outcome of successive trials\n",
    "\n",
    "If all the above conditions met then the binomial distribution describes the probability of X successes in n trials.\n",
    "\n",
    "A classic example of the binomial distribution is the number of heads (X) in n coin tosses.\n",
    "\n",
    "The Notation for a binomial distribution is\n",
    "\n",
    "X ~ B (n, $p$)\n",
    "\n",
    "which is read as ‘X is distributed binomial with n trials and probability of success in one trial equal to $p$ ’.\n",
    "\n",
    "Using this formula, the probability distribution of a binomial random variable X can be calculated if n and $p$ are known.\n",
    "\n",
    "$$ P(X) = {n! \\over X!(n-X)!}p^X(1-p)^{n-X} $$\n",
    "\n",
    "P(X) = # of Scenario * Single Scenario\n",
    "\n",
    "The first factorial terms gives the number of scenario and the second term describes the probability of success to power of number of successes and probability of failure to the power of number of failures.\n",
    "\n",
    "example:\n",
    "\n",
    "What is the probability of 2 heads in 6 coin tosses?\n",
    "\n",
    "- Success = ‘heads’\n",
    "- n = 6 trials\n",
    "- $p$ = 0.5\n",
    "- X = number of heads in 6 tosses which is 2 here.\n",
    "- X has a binomial distribution with n = 6 and $p$ = 0.5\n",
    "- X ~ B (6, 0.5)\n",
    "\n",
    "$$ P(X=2) = {6! \\over 2!(6-2)!} 0.5^2(1-0.5)^{6-2} = 0.234 $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "78f85ec0-2f38-4ad4-8de6-0c260d7eafc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "[[2 4 3 3]\n",
      " [3 1 2 3]\n",
      " [0 0 2 1]\n",
      " [1 2 2 1]]\n"
     ]
    }
   ],
   "source": [
    "# np.random.binomal provides a method to sample a binomical distribution given by n and p\n",
    "\n",
    "print(np.random.binomial(4,0.5))\n",
    "print(np.random.binomial(4,0.5,(4,4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de7c0ea7-8e83-4958-b382-1176363bcab6",
   "metadata": {},
   "source": [
    "There are two stable isotopes of carbon, $^{12}$C\n",
    " and $^{13}$C\n",
    " (the radioactive $^{14}$C\n",
    " nucleus is present in nature in only trace amounts of the order of parts per trillion). Taking the abundance of $^{13}$C\n",
    " to be $x=0.0107$\n",
    " (i.e. about 1\\%), we will calculate the relative amounts of buckminster fullerene, C$_{60}$\n",
    ", with exactly zero, one, two, three and four $^{13}$C\n",
    " atoms. (This is important in nuclear magnetic resonance studies of fullerenes, for example, because only the $^{13}$C\n",
    " nucleus is magnetic and so detectable by NMR).\n",
    "\n",
    "The number of $^{13}$C\n",
    " atoms in a population of carbon atoms sampled at random from a population with natural isotopic abundance follows a binomial distribution: the probability that, out of n\n",
    " atoms, m\n",
    " will be $^{13}$C\n",
    " (and therefore n−m\n",
    " will be $^{12}$C\n",
    ") is\n",
    "\n",
    "$$ P_m(n) = {\\binom nk}p^m(1-p)^{n-m} $$\n",
    "\n",
    "We can, of course, calculate $P_m(60)$\n",
    " exactly from this formula for $0<m<4$\n",
    ", but we can also simulate the sampling with the np.random.binomial method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "606d0716-3d3a-42e6-83f0-0bd04076f688",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Abundances of C60 as (13C)[m](12C)[60-m]\n",
      "m   \"Exact\"    Estimated\n",
      "------------------------\n",
      "0   0.5244      0.5284\n",
      "1   0.3403      0.3444\n",
      "2   0.1086      0.1099\n",
      "3   0.0227      0.0247\n",
      "4   0.0035      0.0035\n"
     ]
    }
   ],
   "source": [
    "n, x = 60, 0.0107\n",
    "mmax = 4\n",
    "m = np.arange(mmax+1)\n",
    "\n",
    "# Estimate the abundances by random sampling from the binomial distribution\n",
    "ntrials = 10000\n",
    "pbin = np.empty(mmax+1)\n",
    "for r in m:\n",
    "    pbin[r] = np.sum(np.random.binomial(n, x, ntrials)==r)/ntrials\n",
    "\n",
    "# Calculate and store the binomial coefficients nCm\n",
    "nCm = np.empty(mmax + 1)\n",
    "nCm[0] = 1\n",
    "for r in m[1:]:\n",
    "    nCm[r] = nCm[r-1] * (n - r + 1)/ r\n",
    "# The \"exact\" answer from binomial distribution\n",
    "p = nCm * x**m * (1-x)**(n-m)\n",
    "\n",
    "print('Abundances of C60 as (13C)[m](12C)[60-m]')\n",
    "print('m   \"Exact\"    Estimated')\n",
    "print('-'*24)\n",
    "for r in m:\n",
    "    print('{:1d}   {:6.4f}      {:6.4f}'.format(r, p[r], pbin[r]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09ea1ba0",
   "metadata": {},
   "source": [
    "#### Normal distribution\n",
    "\n",
    "The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is often used to describe natural phenomena such as heights and weights. It is characterized by its bell-shaped curve, which is symmetric and centered around the mean. The standard deviation determines the width of the curve and describes the variability of the data.\n",
    "\n",
    "$$ P(x) = { 1 \\over \\sigma\\sqrt{2\\pi} } e^{-(x-\\mu)^2/(x\\sigma^2)} $$\n",
    "\n",
    "$\\mu$ is the mean, $\\sigma$ is the standard deviation, $\\sigma^2$ is the variance.  scipy provides a function to make normal distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1e134066",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "mu = 1\n",
    "variance = 2\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)\n",
    "plt.plot(x, stats.norm.pdf(x, mu, sigma));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7f5cebe9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = stats.norm.cdf(x,mu,sigma)\n",
    "\n",
    "#plot normal CDF\n",
    "plt.plot(x, y)\n",
    "plt.plot([-4,4],[0.5,0.5],label='midpoint')\n",
    "plt.plot([mu,mu],[0,1.],label='$\\mu$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "14bed64c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 5\n",
    "variance = 5\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)\n",
    "plt.plot(x, stats.norm.pdf(x, mu, sigma))\n",
    "px=np.arange(7,12,.1)\n",
    "plt.fill_between(px,stats.norm.pdf(px, mu, sigma),color='r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0da4a2e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probablity of waiting longer than 7 hours 0.18554668476134872\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = stats.norm.cdf(x,mu,sigma)\n",
    "p=stats.norm(mu,sigma).cdf(7)\n",
    "plt.plot(x, y)\n",
    "plt.plot([7,7],[0,p])\n",
    "plt.plot([-2,7],[p,p]);\n",
    "print('probablity of waiting longer than 7 hours',1-p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "03d6d8cf-c09f-410e-8c3c-8147b9a3d57a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# two sigmas covers 95% of the area\n",
    "\n",
    "mu = 5\n",
    "variance = 5\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)\n",
    "plt.plot(x, stats.norm.pdf(x, mu, sigma))\n",
    "px=np.arange(mu-2.*sigma,mu+2.*sigma,.1)\n",
    "plt.fill_between(px,stats.norm.pdf(px, mu, sigma),color='r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "175ae0ed-d61e-4554-97d5-a5e96bc46b13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# np.random.normal can select random samples from a normal distribution\n",
    "\n",
    "plt.hist(np.random.normal(100.,5.,size=1000));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e59a3ab-39c0-4daf-ada8-6e3266017ddf",
   "metadata": {},
   "source": [
    "#### Poisson Distribution\n",
    "\n",
    "Another probability distribution for discrete variables is the Poisson distribution. The Poisson distribution is used to determine the probability of the number of events occurring over a specified time or space.\n",
    "\n",
    "Examples of events over space or time: \n",
    "\n",
    "- number of cells in a specified volume of fluid\n",
    "- number of calls/hour to a help line\n",
    "- number of emergency room beds filled/ 24 hours\n",
    "\n",
    "Like the binomial distribution and the normal distribution, there are many Poisson distributions. Each Poisson distribution is specified by the average rate at which the event occurs. The rate is notated with $\\lambda$ and there is only one parameter for the Poisson distribution.\n",
    "\n",
    "The probability that there are exactly X occurrences in the specified space or time is equal to\n",
    "\n",
    "$$ P(X) = { \\lambda^xe^{-\\lambda} \\over X! } $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "40213521-085f-4210-8194-6676ea24badf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "from scipy.special import factorial\n",
    "import matplotlib.pyplot as plt\n",
    "from math import *\n",
    "\n",
    "poisson_pmf = lambda y, μ: μ**y/factorial(y)*exp(-μ)\n",
    "\n",
    "y_values = range(0, 25)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "\n",
    "for μ in [1, 5, 10]:\n",
    "    distribution = []\n",
    "    for y_i in y_values:\n",
    "        distribution.append(poisson_pmf(y_i, μ))\n",
    "    ax.plot(y_values,\n",
    "            distribution,\n",
    "            label=f'$\\mu$={μ}',\n",
    "            alpha=0.5,\n",
    "            marker='o',\n",
    "            markersize=8)\n",
    "\n",
    "ax.grid()\n",
    "ax.set_xlabel('$y$', fontsize=14)\n",
    "ax.set_ylabel('$f(y \\mid \\mu)$', fontsize=14)\n",
    "ax.axis(xmin=0, ymin=0)\n",
    "ax.legend(fontsize=14);\n",
    "\n",
    "# Notice that the Poisson distribution begins to resemble a normal \n",
    "# distribution as the mean of y increases\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b21720d",
   "metadata": {},
   "source": [
    "The horizontal axis is the index X. The function is defined only at integer values of X. The connecting lines are only guides for the eye and do not indicate continuity. Notice that as λ increases the distribution begins to resemble a normal distribution.\n",
    "\n",
    "- If λ is 10 or greater, the normal distribution is a reasonable approximation to the Poisson distribution\n",
    "- The mean and variance for a Poisson distribution are the same and are both equal to λ\n",
    "- The standard deviation of the Poisson distribution is the square root of λ\n",
    "\n",
    "example:\n",
    "\n",
    "A large urban hospital has, on average, 80 emergency department admits every Monday. What is the probability that there will be more than 100?\n",
    "\n",
    "If we put λ =80 and  x= 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bd477523",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00393945815919926\n"
     ]
    }
   ],
   "source": [
    "print(poisson_pmf(100, 80))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c5065e5f-2c9d-4685-bf90-047563962634",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 5 3 3 3 2 2 3]\n"
     ]
    }
   ],
   "source": [
    "# again, np.random.poisson allows for sampling of an expected (average) number of events \n",
    "# within a certain interval\n",
    "\n",
    "# for example, let's say I get, on average, 2.5 emails per hour.  Over 8 hours I can \n",
    "# expect:\n",
    "\n",
    "print(np.random.poisson(2.5,8))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "225ddb2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=10000, minmax=(-3.7651910449819384, 3.523018761425625), mean=0.004007595664588842, variance=0.9907831493383192, skewness=-0.025325376472731767, kurtosis=0.024912723075367182)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy stats\n",
    "\n",
    "from scipy import stats\n",
    "a = np.random.normal(size=10000)\n",
    "s = stats.describe(a)\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6ff95c20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.004007595664588842"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9ab191f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(a, bins=20,histtype='step',color='red',density=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "080b2f63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.56356771, -0.08323872,  0.85385098, -0.3925777 , -1.17146125,\n",
       "        0.13586795,  0.65803925,  0.38149972, -0.77303176,  0.34450235])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "norm.rvs(size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1752e998",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.0, 2.0, array([6.81503002, 5.45397784, 1.63722614, 6.31747701, 7.84634104]))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gauss = norm(loc=5, scale=2)\n",
    "gauss.mean(), gauss.std(),gauss.rvs(size=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8c18aff3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 5.0\n",
      "median: 5.0\n",
      "standard deviation: 2.0\n",
      "variance: 4.0\n",
      "1st moment = mean: 5.0\n",
      "2 sigma bracket: (0.9999951122007928, 9.000004887799205)\n",
      "expectation value = mean: 5.0\n"
     ]
    }
   ],
   "source": [
    "print('mean:', gauss.mean())\n",
    "print('median:', gauss.median())\n",
    "print('standard deviation:', gauss.std())\n",
    "print('variance:', gauss.var())\n",
    "print('1st moment = mean:', gauss.moment(1))\n",
    "print('2 sigma bracket:', gauss.interval(0.9545))\n",
    "print('expectation value = mean:', gauss.expect(lambda x: x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cda50a59",
   "metadata": {},
   "source": [
    "#### Statistical Significance\n",
    "\n",
    "In statistics, statistical significance means that the result that was produced has a reason behind it, it was not produced randomly, or by chance.  SciPy provides us with a module called scipy.stats, which has functions for performing statistical significance tests.\n",
    "\n",
    "Hypothesis is an assumption about a parameter in population. \n",
    "\n",
    "- Null Hypothesis: It assumes that the observation is not statistically significant. \n",
    "- Alternate Hypothesis: It assumes that the observations are due to some reason. It's alternate to Null Hypothesis.\n",
    "\n",
    "Example:\n",
    "\n",
    "```\n",
    "For an assessment of a student we would take:\n",
    "\"student is worse than average\" - as a null hypothesis, and:\n",
    "\"student is better than average\" - as an alternate hypothesis.\n",
    "```\n",
    "\n",
    "One tailed test: When our hypothesis is testing for one side of the value only, it is called \"one tailed test\".\n",
    "\n",
    "Example:\n",
    "\n",
    "```\n",
    "For the null hypothesis:\n",
    "\"the mean is equal to k\", we can have alternate hypothesis:\n",
    "\"the mean is less than k\", or:\n",
    "\"the mean is greater than k\"\n",
    "```\n",
    "\n",
    "Two tailed test: When our hypothesis is testing for both side of the values.\n",
    "\n",
    "Example:\n",
    "\n",
    "```\n",
    "For the null hypothesis:\n",
    "\"the mean is equal to k\", we can have alternate hypothesis:\n",
    "\"the mean is not equal to k\"\n",
    "In this case the mean is less than, or greater than k, and both sides are to be checked.\n",
    "```\n",
    "\n",
    "Alpha value: Alpha value is the level of significance.\n",
    "\n",
    "Example:\n",
    "\n",
    "```\n",
    "How close to extremes the data must be for null hypothesis to be rejected.\n",
    "(It is usually taken as 0.01, 0.05, or 0.1.)\n",
    "```\n",
    "\n",
    "P value: P value tells how close to extreme the data actually is.\n",
    "\n",
    "P value and alpha values are compared to establish the statistical significance.\n",
    "\n",
    "If p value <= alpha we reject the null hypothesis and say that the data is statistically significant. otherwise we accept the null hypothesis.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a522c3ce",
   "metadata": {},
   "source": [
    "#### T-Test\n",
    "\n",
    "T-tests are used to determine if there is significant deference between means of two variables and lets us know if they belong to the same distribution.\n",
    "\n",
    "It is a two tailed test.\n",
    "\n",
    "The function ttest_ind() takes two samples of same size and produces a tuple of t-statistic and p-value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9475a176",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TtestResult(statistic=0.8897276517954502, pvalue=0.37469187426069217, df=198.0)\n",
      "0.37469187426069217\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import ttest_ind\n",
    "\n",
    "v1 = np.random.normal(size=100)\n",
    "v2 = np.random.normal(size=100)\n",
    "plt.hist(v1, density=True, alpha=0.5, bins=10, label='v1')\n",
    "plt.hist(v2, density=True, alpha=0.5, bins=10, label='v2');\n",
    "\n",
    "res = ttest_ind(v1, v2)\n",
    "print(res)\n",
    "print(ttest_ind(v1, v2).pvalue)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1c876e3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TtestResult(statistic=-6.651787980243725, pvalue=2.763232215620924e-10, df=198.0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = np.random.normal(size=100)\n",
    "v2 = np.random.normal(size=100)+1.\n",
    "plt.hist(v1, density=True, alpha=0.5, bins=10, label='v1')\n",
    "plt.hist(v2, density=True, alpha=0.5, bins=10, label='v2');\n",
    "\n",
    "res = ttest_ind(v1, v2)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4cbf5dd7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KstestResult(statistic=0.9472498680518208, pvalue=3.3372269494050743e-128, statistic_location=2, statistic_sign=-1)\n",
      "KstestResult(statistic=0.1420333364816072, pvalue=0.031874553306884934, statistic_location=-0.5302576183724408, statistic_sign=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# KS test\n",
    "\n",
    "# One Sample Kolmogorov-Smirnov Test\n",
    "\n",
    "from numpy.random import seed\n",
    "from numpy.random import poisson\n",
    "\n",
    "# set seed (e.g. make this example reproducible)\n",
    "seed(42)\n",
    "\n",
    "# generate dataset of 100 values that follow a Poisson distribution \n",
    "# with mean=5\n",
    "data1 = poisson(5, 100)\n",
    "data2 = np.random.normal(size=100)\n",
    "\n",
    "plt.hist(data1, density=True, alpha=0.5, bins=10, label='poisson')\n",
    "plt.hist(data2, density=True, alpha=0.5, bins=10, label='normal')\n",
    "plt.legend();\n",
    "\n",
    "from scipy.stats import kstest\n",
    "\n",
    "# perform Kolmogorov-Smirnov test for if it is a normal distribution\n",
    "print(kstest(data1, 'norm'))\n",
    "print(kstest(data2, 'norm'))\n",
    "\n",
    "# pvalue < 0.05, so reject null hypothesis\n",
    "\n",
    "# test for N=1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "30901f7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KstestResult(statistic=0.99, pvalue=4.417521386399011e-57, statistic_location=2.2697546239876076, statistic_sign=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Two Sample Kolmogorov-Smirnov Test\n",
    "\n",
    "from numpy.random import randn\n",
    "from numpy.random import lognormal\n",
    "\n",
    "# set seed (e.g. make this example reproducible)\n",
    "seed(0)\n",
    "\n",
    "# generate two datasets\n",
    "data1 = randn(100)\n",
    "data2 = lognormal(3, 1, 100)\n",
    "\n",
    "plt.hist(data1, density=True, alpha=0.5, bins=10, label='random')\n",
    "plt.hist(data2, density=True, alpha=0.5, bins=10, label='lognormal')\n",
    "plt.legend();\n",
    "\n",
    "from scipy.stats import ks_2samp\n",
    "\n",
    "# perform Kolmogorov-Smirnov test\n",
    "print(ks_2samp(data1, data2))\n",
    "\n",
    "# again, pvalue is < 0.05, so we reject the two samples\n",
    "# come from same distributions\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "4fe72bf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "linear PearsonRResult(statistic=0.9781263195065708, pvalue=1.2224930469035162e-68)\n",
      "sine PearsonRResult(statistic=0.6247081524680771, pvalue=3.759049769891642e-12)\n",
      "cloud PearsonRResult(statistic=0.030338350638072116, pvalue=0.7644531393689991)\n"
     ]
    },
    {
     "data": {
      "image/png": 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gC0T8WlpaAPh6sADAGWecgWuvvRY7duxAeXk5Bg8ejAEDBqC6uhoTJkzQ6tsiojSh5N240smU/gvx1WcW48n3vkZtizbbSI2UFJqI9J2hAID+DuC2Kl8CZsse3zKHY3zKgwnAl/NQXl6O0aNHw2634+6778bEiRMxevRotLe3Y926dTjrrLPwi1/8AjfddBMA4OGHH0ZtbS2+853vYMGCBQCAhx56CE6nEw8//DCef/55FBYWYsWKFWhvb8eUKVPw9NNPp/C7JCKzUvJuXK1kSq37ZuglKVQt6R1QAL7gofQ7KUvAlDJo0KCIkfFXX33V47HDhw/3eGzGjBk9HsvIyMDixYuxePHi5AdJRBSFkm3A1Uqm1LpVuR6SQtWUvkseRESkGiXvxuVUj0z1GOVQ6/vQC85QEBGR4pS+G1ejYVcqZgxS2XhMbZyhICIixalxNx6teqRexij3fZX8PvSCMxRERKQKI9yNG2GMRsGAgoiIVKO3WglSjDBGI2BAQUREppFsnwxKHAMKIiIyBaUqc1JimJRJRESGp2RlTkoMAwoiIjI8OVUvSV0MKIiIKKWU6Eiaij4ZSozbTJhDQUREKaNU3oPWVS+Zr9ETZyiIiCgllMx78Fe9tFpCZynUqHrJfA1pDCgM6J///CemTJmCWbNmafJ+R44cwcKFC1FQUKDJ+xFRelAy70HLqpfM15DGJQ+DaWlpwaFDh/D222/juuuu0+Q93377bbzyyiuSXU2JiBKldLdPrapeat2l1CgYUBhMXl4err32Wtx9992aved1112HrVu34j//+Y9m70lE5pds3kOkIlZqVL0Mfq9Ol0f2uNOp0BYDCoOy2bT90fXq1UvT9yMi80um26eWSZHh79Xt9kAQBFgFAR4x8rjTLXGTORQki1kjaiJKnUTzHrRMipR6L7fXly9hsSDiuNMxcTPtAwpRFLH54Gas2rUKmw9u1tUP+bXXXsMFF1yACRMm4PTTT8crr7wS9fWHDh3CD3/4Q1x88cUYMmQIrrjiCmzfvh0AsGHDBgwdOhSCIOCmm24CAGzbtg1lZWUhj/mtX78e5557LiZMmIALLrgAX331lRrfIhGpTO+1Evx5Dy/NGY+HK7+Nl+aMx/vzz0NR/94Rv0bLpMhI7+UVfZ/tzyedLjnudEzcTOslj8ZjjZi7bi72HdsHm8UGt9eNor5FWHrxUhT2LUzp2JYvX47FixfjX//6F/Ly8nDXXXfhBz/4AYYMGYKzzz67x+vb29txzjnnYOHChbjmmmtw/PhxTJ48GRMmTMCmTZtw1lln4auvvsLAgQMDXzNq1Cjs3LkTAwYMCDnWp59+issvvxzvvvsuJkyYgN27d+PMM89U/XsmImUZZco93rwHLZMio71Xhs2K3nYrpo8rSekY9SJtZyhEUcTcdXNR314Pl9eFTncnXF4X6tvrMW/dvJRG8R0dHZg/fz7uu+8+5OX5fuGmTp2K/v374+jRo5Jf8+tf/xqCIOCaa64B4Mt5+O1vf4sjR47g5z//OQAgIyMD/fr1C/m6jIyMwHv4zZs3D1OnTsWECRMAAMOGDUNlZaWi3yMRqcvMU+5aFrFK9L20LrSlB2kbUFQfqsa+Y/vgEUPDR4/oQcOxBlQfqk7RyIBPPvkEbW1tGDNmTOCx7373u2hpacHFF18s+TUrV67EqaeeGvLYyJEjMWrUKLzzzjuy33vLli3Ytm0bxo8fH/L40KFD5X8DRJRyZp5y17KIVaLvpeUY9SJtA4q69jrYLNIrPnaLHXXtdRqP6CR/vYfu7m7ZX1NbW4uOjp616ktLS9HS0oKuri5Zx/HnSuTn58t+byLSn1T0ttCKlkWsEn0vLceoF2mbQ+HIdsDtdUs+5/K64Mh2aDyik/xLEF9++WWP3IV9+/ahqKiox9cUFRVh9+7dPR7Pzs5GYWEhMjMzAcTerZGRkRF4HyIyLrNPuWtVxCqZ99JyjHqQtjMU5QXlKOpbBKtgDXncKlhR3LcY5QXlKRoZMH78eGRmZuLpp5+G13vyhNDY2Ih//etfkl9TWVmJffv24d///nfI43v27MG1114b+HtWVhaOHz/e4+v966lnnXUWLBYL3nrrLcn3CR4PEelXOky5+5M5p48rQUVZnqoX6kTfS8sxpprsgKK2thaXXnopsrOzUV5ejg8//DDk+UceeQSCIAT+VFVVKT5YJQmCgKUXL0VJdgnsFjuybFmwW+xwZDuw9OKlKf2h5+bmYsGCBdi8eTOuv/56bNiwAW+++Sbmz5+PK6+8EsePH0dzczMaGxsDX3Pfffdh0KBBuPvuu9He3g4A+OCDD9DY2Iif/vSngdeNGjUKGzduDCynvPLKK2htbUVzczMAoLi4GHPmzMFHH32EZ555BoBv6WXTpk0AfAGKy+XS5HMgosSl45Q7pZYgykj1FUURl156KS6++GIMGjQIixcvxjfffIOtW7di2LBhOH78OK699lqcf/75AIA+ffpgzpw5ksc6evQo+vXrh7a2NuTk5Ei+xuPxYOfOnfjWt74Fq9Uq+RqliKKI6kPVqGuvgyPbgfKCcl38QxNFEb/61a/w+9//Hp2dnbj88suxePFi2Gw2nHPOOdi1axcA4Oyzz8bnn38OANi1axfmz5+PrVu34tRTT8XgwYOxaNEiFBcXB467a9cuTJs2DR6PBxMmTMBPfvITTJ06FUVFRbj11lsxdepUuN1uPPDAA1i+fDlOPfVUVFRUoKOjAxs3bsS0adMwe/ZsFBbG3lar5c+RiKSlU+lnUles67esgGLbtm04dOgQJk6cCMBXQGno0KFYuHAhbr/9dvzxj3/E8OHDcdFFFyU9IIAXIrPgz5GIyDxiXb9lLXmMGDEiEEwAQEFBAU4//XRkZmbC6/ViyZIlmDJlCqZNm4avv/5audETERGRIcgKKPyZ/8FaW1sxadIkdHZ2YuHChViwYAGqqqpw5pln4oMPPoh5zJEjR6K4uBjFxcVYsmRJ/CMnIiIi3Uho2+j69esxderUwNr89OnTAQALFizA5MmTMXPmTOzZsyfqNPeOHTsiLnkQERGRscS9bdTlcuHll1/GI4880uO5rKwsvPDCCzh06BB27typyACJiIhI/+IOKBYvXowHHnggUCgp3KBBg3D66afLrsxIRERExhdXQLFs2TJcdtllKCnxdVbr6uqCxxPWC8PjQUZGBkaNGqXcKImIiEjXZOdQPPPMM2hoaEBxcTHWrl0Lp9OJN954AzfccAM+/fRTLFiwAJmZmXjggQfw6KOPcpsgERFRGpEVUCxfvhy33norAOCxxx4LPP7jH/8YFosFf/rTn/D0009j/PjxePDBB1FRUaHOaImIKGWUKpKlZbEtFvbSjqyAYubMmZg5c2bE54NLQBMRkfk0tDoxY/kG1Lc4Ybda4PJ4UZKXhRUzz0Jxbpbmx9Hbe1EaNwcjIiJ5RFHEjOUbUNvshMsjwtntgcsjorbZiRuXb4CMgsuKHkdv70U+DCiIiCiqjbWtaGjphMcbehH2eEXUtTixsbZV0+Po7b3IJ6HCVlphq2xj48+PyBxqmjpgswro9vR8zm61oKapAxVleZodRw4t34t8dBlQCIIAm80W6KhJxmWz2ZgARWRwZQP6wOWRvkFwebwoG9BH8eMkm0yp1JjVoNcu18nSZUBhsVgwbNgwrnGZgCAIsFi4skZkZONKc1GSl4XaZmfIEoLVIsCRl4VxpbmKHkeJZEqlxqy0xmONmLtuLvYd2webxQa3142ivkVYevFSFPYtTMmYlCKrfbmS5LQvJyIifZG6yDvysrBi1tko6t9bseOIooiJSz6WDATK8rPw/vzzZN/NKzVmpYiiiMpVlahvr4dHPLkWYxWscGQ7sHrKal3PVMS6futyhoKIiPSlODcLH8w/L+maDrGOIyeZUm7ug1JjVkr1oWrsO7YvJJgAAI/oQcOxBlQfqsbYgWNTMjYlMKAgIiJZBEFARVle4IIuiiKqalrivliHHyeY0smU0d5La3XtdbBZbHB5XT2es1vsqGuvY0BBRETGoUT1SLWKRuk5mTJZjmwH3F635HMurwuObIfGI1IWAwoiojSiRCAQXDTK4xXhOtEk0l80Kp48h3B6TaZUQnlBOYr6FknmUBT3LUZ5QXkKR5c8pt8TEaUJpapHqlk0ShAErJh5Fkrzs2C3CsjKsMJu9SVkrph1tq6TFmMRBAFLL16KkuwS2C12ZNmyYLfY4ch2YOnFSw39vQGcoSAiShtKJTyqXTRKb8mUSirsW4g1U9awDgURERmXUoGAFnkOekqmVJogCBg7cKyhEzClcMmDiChNKBUI+PMcrJbQu2oz5DlQ4hhQEBGlCaUCATPnOVDiWCmTiCiNKFk9Uontp2Qcsa7fDCiIiNIMAwFKBEtvExGlmFrdJRMNDMyc8Eipw4CCiEhFanWXVKtSpR9nMSheXPIgIlKJWt0llezIKUXtYIWMKdb1m7s8iIhUIqe7ZCLUrFSpVDVNSj8MKIiIVOLvLinF310yEf4CVZLHPVGgKlFqBitkbgwoiIhUolZ3STUrVaoZrJC5MaAgIlKJv7ukVbCGPJ5sd0k1K1WauX04qYsBBRGRStTqLqlmpUqW1aZEcZcHEZHK9FaHIhYlq2mSebBSJhGRziQaCKhZGyL82Gc6+mNT3RHWoaAAVsokItKRRGs8qFkbItqxWU2T5GIOBRGRRhKt8aBmbQjWnSClMKAgItJIojUe1KwNwboTpBQGFEREGkm0xoOatSFYd4KUwoCCiEgjidZ4ULM2BOtOkFIYUBARaSRajYeS3N4QRRErN9ajqqYlJHdBzdoQrDtBSuG2USIiDUntqBjcrxcAAfvbOiPu4FCzNgTrTpAcrENBRKQzwTUfSvOzcN9r21DbErsVuZZ1KFh3gsKxDgURmYZaFSe1JggCKsryUFGWh6qaFjS0Rt9l4a8FEfx1ao6JKBFxBRS1tbW4+eab8emnn2L48OFYsmQJLrjgAgCA0+nE7bffjt69e6OlpQULFy5EaWmpKoMmovTTeKwRc9fNxb5j+2Cz2OD2ulHUtwhLL16Kwr6FqR5eVNHu/v27LLo9Pb/Ov8uCF3kyAtlJmaIoYs6cObjooovwzDPPQBRFTJo0Cbt37wYAzJgxA+eeey5+97vf4d5778WVV14Jl8ul2sCJKH2Iooi56+aivr0eLq8Lne5OuLwu1LfXY966ebouvtTQ6sTEJR/jB89+jl+s+S9+8OznmLjkYzS0OgFE32XR5fZgb1NHjyRNIj2SHVD85z//wb333osFCxbghhtuwHvvvQdBEPDWW29h06ZNePvtt3HNNdcAAEaNGgVBEPDyyy+rNnAiSh/Vh6qx79g+eMTQ23iP6EHDsQZUH6pO0ciik1OFMtIuCwDweIHnPq3pEYQQ6ZHsgGLEiBGYOHFi4O8FBQU4/fTTkZmZiTVr1mD48OHIzMwMPD969Gi8+eabyo6WiNJSXXsdbBbpFVq7xY669jqNRySPnCqU4a3Ie9tDT8sshU1GITugyMjI6PFYa2srJk2ahO3bt2PAgAEhz+Xm5mLnzp0Rjzdy5EgUFxejuLgYS5YsiWPIRJRuHNkOuL1uyedcXhcc2Q6NRySP3CqUxblZ+GD+eXhpznj88LtDYJOcrWApbNK3hHd5rF+/HlOnTkVxcTHa2tqQlxeaNJSZmQmnM/L03I4dO7htlIhkKS8oR1HfItS314cse1gFK4r7FqO8oDyFo4ssniqU/l0WNU0dyLBZ4JbI0jRCkia3n6avhAIKl8uFl19+Gb/97W8BAHl5eTh27FjIazo7O5GbywprRJQ8QRCw9OKlgV0edosdLq8LxX2LsfTipbq9YPnzI2qbe9aYiFSF0silsNVssU76l1BAsXjxYjzwwAOBnIlhw4bhgw8+CHnN4cOHMWLEiORHSEQEoLBvIdZMWWOoOhT+/IhIVSilxp5IEKIHwQmoHq8Il8c3w+LP/Qgu0EXmFHelzGXLlmHcuHEYM2YMAKCrqwv/+c9/cO6556K1tTUQZJxxxhl44IEHcO2114Z8PStlElG6iXcZwIilsKtqWnDds1+gW2J2xW4V8NKc8bpeqqHYFK2U+cwzz6ChoQHFxcVYu3YtnE4n3njjDTz//POYMGEC1q5di8mTJ2PLli2wWCyYPn26Yt8IEZFStF7nj7cKpT9J00i5CCzQRbIDiuXLl+PWW28FADz22GOBx3/84x/DYrHgpZdewp133olPPvkETU1N+Mc//gGr1ar8iImIkqDkOr+agYnRSmEbOfeDlMHmYESUNkRRxMQlH0vmJ4Q34oqFCYihlPxsSZ9iXb9l16EgIjI6OYWm5JBTATPdhBfoysqwwm71BRORElDJXNht1ATM0oGRSG1KrfPLCUyMslThp8R5xIi5H6QcBhQGp3YHRgYrZCZKrfObLQFRyfOI0XI/SDkMKAwsuAOjR/TA5fV1d/V3YFw9ZXVSF38jt4smkqJUjQczJSCqfR6h9MEcCgNTswOjkdtFE0Wi1Dp/pA6hei8+JcWonVxJfzhDYWD+Doz+O4pg/g6MYweOTejYck4yiR6bKJWUWOdPpAKmXql5HqH0woDCwNTswMiTDJmZEuv8ZklANGonV9IfBhQGpmYHRp5kSI/01snSDAmIRu3kSvrDgMLA1OzAyJMM6Q0LSanDqJ1cSX9YKdME1NraGbzLI/wkM7jvYAVGTiQPqzCqj1vEKZZY128GFBQVTzKUKsHLG50uDx59awc7WRKlkKLdRin9CIKAsQPHMgGTNBW+vNHl8sAb4dbHiIWkiMyIAQUFcDaC9CC4T4bHK8LlkShHGUTLQlJ6Swql2Hhe0w4DCgLAqpikH5H6ZEhRs5BUePAwKKcXbvwLk0KNhOc1bTGHgiCKIipXVUru6HBkO1h6lzS1cmM9frHmv3BKNMoQAFgsAjJtoYWkivr3VnQM4Usu3W4PBEGA1wt4RCaFGgHPa8pjDgXFxKqYpCfR+mRYLcCDV56O3naraksOkZdcet57Gbm7qNnxvKY99vKgQFVMKf6qmERaidYnozS/D24YX4rp40pQUZanyh1mPEsuwMmkUNIXnte0x4CCWBWTdEWpBl6J8rcml8to3UXTBc9r2uOSB7EqJulOKvtkRFtyCWfE7qLpguc17XGGggKld0uyS2C32JFly4LdYocj28HSu5Qy/j4Zai5vSIm05GIRfEW0UjFrQvHjeU173OVBAdyvTeQj1TfEkZeF52eehf1tx1mHwkB4XlMOS28TESWARax64sU5vXHbKBFRAszQmlxJLBKVmHQKwhhQEFFEvEsnwPd7MHfd3ECCo8vrAgDUt9dj3rp5LBIVQboFYQwoiEiSVB4BS02nJxaJil86BmHc5UFEAHwnwKqaFqzcWI8Ne5sx48++apEujwhntwcuj4jaZiduXL4B0VKvgo9TVdMS9bVkDCwSFT85QZjZcIaCiHq2C3d7IFWKIVapac5qmBOLRMXPH4T5ZyaC+YMws83qcIaCKM0F967wz0ZEq+sUqdS01HEizWpwFkM9any2/iJRVsEa8jiLREWWjkEYZyiI0ly8vSsilZqOdJzwWQ3OYqhHrc/WXyTKn2Bot9jh8rpQ3LeYRaIiSMdKnZyhIEpz8fSuiFZqOtpx/LMa8cxiaM3osyZqf7aFfQuxZsoaLLtkGe4/+34su2QZVk9ZjcF9Byv0HZhLOlbq5AwFUZqL1bvCZhGQYTtZLTJSqelox/HPasidxdCaGWZNtPhsBUHA2IFjTbf2rxZ/EMY6FESUFvy9K2qbnSEXI6tFQGleb/xq2hmobXbGrEMR7Tj+WY2/b2qAzSqg29Pz6/2zGFoHFMF39h6vCJfHNzj/nf37888zxAXAP0OU6s82nQo5yZFOQRgDCqI0528XLtW7YsWss1HUvzfOGpKf9HEEQZA1ixGvZItvKX1nn6piYGp8tvFKt0JOUtI5oGJAQUSKtQuPdZxosxglub0hiiJWbqyX/f5KLFUoeWefyqUTOTNEakrHQk7h0j2gYnMwItKU1EV3cL9eAATsb+uUfSEWRRETl3wseQEty8+SvVRRVdOCHzz7OVyenqdCu1XAS3PGywoolBpPMiJ1SfXPNKlp88HNmP3e7Ih1F5ZdsszU0/6iKKJyVaXkrg5HtsMUARWbgxGRroTPYpTmZ+G+17ahtiW+HAalliqUurPXQ8KpUjNNiUimkJMZlglYnjyBbaNNTU1YsGABbrnllh7PPfLIIxAEIfCnqqpKkUESkbn4O3lOH1cCQRDQ0Br9QixFzjZVuWNZMfMslOZnwW4VkJVhhd3qm1WItKNFzfEkK/izrSjL0+zCnGghp8ZjjahcVYnZ783Goi8WYfZ7s1G5qhKNxxrVHK7iWJ48zhkKl8uFf//731i9ejXOOeeckOeOHz+OzZs34ze/+Q0AoE+fPqioqFBupERkSonmMCiZhKjEnb0ekiKVFO+sQSKFnMyUd5GOlTHDxRVQ2O12TJkyBStXruzx3HPPPYfbbrsNF110kWKDIyLzS/RCrHQSov/OPtFliVQnRSopkeTCRKppmmmZIB0rY4ZLqFKm3W4P+bvX68WSJUswZcoUTJs2DV9//bUigyMSRRGbD27Gql2rsPngZsNVL6TY/BdiqyX0ghPrQqzUUoVS9DaeRAXPGri8LnS6O+HyugKzBtH+DcZbTdNMywTpWBkznCJJmZ2dnVi4cCG2b9+OP//5zzjzzDOxevVqTJw4UYnDk85olUCV7luw0oWc+hWRpDIJ0QjjSUSyswbxFHIy2zJBulXGDJfQttGbbroJgG+ZI5zT6cTkyZOxc+dO7NmzB1ZraHc6/7aTwsLCwIc8f/58zJ8/P/7Rk+a0usinwxYsCqVUQahUFZYyi1W7VmHRF4vQ6e7s8VyWLQv3n30/pgyfosh78d+5sWi+bTQrKwsvvPAChgwZgp07d2LkyJGSr9uxYwfrUBiMlglUZlpbJXmSzWEAIheWev6HFThwtItBhgxazhqwi6m5qFKHYtCgQTj99NPR1dWlxuEpRbS8yCezpz1RZtgLH0mqvzctZg0i9eSoaerAhYs/BgDDNv7SktbJhcksE6T695pCqRJQeDweZGRkYNSoUWocnlJEy4u81murZs7XSPX3plU56kiFpbwi4D1RBdOojb+0lIpZg0QaaKX695p6SmiXh8fjgdd7cpvX+++/j4ceeggdHR1wu924//778eijj/bInyBj0/Ii779Lsgqhv0Nq3CUlk9Ue6Xh62Zmi9PeWyPv7Zg064M3Yi+7eX8CbsRe1zR24cfkGRd8/WmGpcLGKZqW7eHdraC3Vv9ckLe4ZildffRXr16+HxWLBypUrMX36dADAn/70Jzz99NMYP348HnzwQVMXtVJzmk3PU3haToVqeZek5FJOPHdNWvysU52LsrG2FQ1HG5FZtgwWewsgWgHBA68rD3X7ZilajjpaPQspqWqXbhR6brud6t9rkhZ3QHHNNdfgmmuuCXnsoosuQmOjscqkJkrNaTa9T+FpPRWq1RYspZZy4kla1epnnYpclGB7Dx9DRvEywN4MQfAC8F0ALBnNyCxejr2Hz1Xsgh6psFQkRqxeST6p/r0maWnVHCzZO0I1dzkYpQSt1vustbhLUmopp/pQNRoi3DXVt5+8a9LyZ53qff6ujD2AreVEMHGSIHgh2pp9z0OZMUjVs+h2eyAIArxewCMau3qlYYkiUPc50LIHyBsKOMZDBJI6h6T695qkpU1AocQdoZrTbEaawtPzVGgilFrKqTtaB7dbkMxM8ngE1B313TVp+bNOdTngPllHIMAK/8xEMAus6JN1RNH3kyosNSinF278S/xFs0gBR+qAF6YCR2oBqx3wuNCY68DcwQXY5zyY8Lk41b/XJC2hpEyjUSqBR80ysWYqQWs0SpXM7XD2hyhx4QQALzzocPYHoO3POtXlgB05Dtis0v++rDYRjhzl7yTDu22W5PmCjJfmjMfDld/GS3PG4/3556Gof2/F35uCiKIvmGjZC3i6ge4OiJ5uzM3sQH17Q1Ln4lT/XpO0tJihUOqOUM1pNk7hpZYSSzn27qGAOw9iIF/ARxQtgDvf9zy0/1mnshxweUE5irOl7yRLNLyTVKJoFsWp7nPfzIR48ne9OjMT++w2eMJ+9RKZnUv3Mtd6lBYzFErdEaq5lVHpY+tp66JR+JdypgyfgrEDx8Z9YhpySl90NcyCtzsfotcK0ZMB0WuFtzsfXQ0zMeSUvgC03RLrl+z3lsz78k4yTbXs8S1zBKmz22CLcC5KZHYuVb/XJC0tZiiUuiNUc5eDksfW+24RsxpXmouSnCLU1twFZNZAyGiC2D0A6CpDWX6fQAJgupUb5p1kmsobCnhCd2E4XG64I/zcXZ5uOA58Bdg/AxzjAf5+GE5CzcGSEau5iBqUbkCj5zoUbLaTWlJVIf0JgOFr9uE/6zGnjMGmuiPsN0H6JbFjI+KFXxSBpyp8ORQnlj1EAJVFg1Fvt4cse1hFwOF2Y/WhNggeF9C/FLjhdaA/l3r1JNb1Oy0CCiD0rj38jlAv1d+UsPngZsx+b3bE/dnLLllmmt0ZepVI3wqtylMTJUxix0bMC3/w11jsgNeFxrxSzB10CvY5D/rOxS4nil0uLD1wCINPlEaHYAPyhwK3btBmpiKeQCmNMaAIoucqlErRsvUwKUMURUxc8nGPgkxWi4Cy/Cz2m6DUk5htACDvwh+tDsXeD+FYvxjlzg70+GprBjBjDVD6HZW+qRMSCZTSlObty/XMbPUTpKRit0g6BGpqitTUKrjfhF52J2jRNZR0IjgQcDl77NjwvcYNtNb4Xhfpwi8IvueCnhcA37m4cQcgfbryzWi07FE3oAje2iq6fdtbAd/f/zpNuxkSk0irgCIdaF3whQmgyfM3teqWKGGhp34TXJZJI+F37a7jgBihT0oyF36JxM0Ar8v3vAoCN0F7P4SjsxHlojt0hkROoEQ9pMW20XSi5TY9dvxTRrSmVkr1mxBFEVU1LVi5sR5VNS0JdVD1dQ11wuUR4ez2wOURA23A+bM2EYmCVBA98KVUSgi/8IsiUPsZUP2i77/Rfjcc433LC0LYva1gA3LLfM8rrPFYIypXVWL2e7Ox6JsXMbsgD5VFg9FoC+uO7Q+USDbOUJiQVtv0jFQuXM8iNbVSqt+EEjMLRlqWoSRJFKSKKPzCH28+giD4ngtL3ERuGXD967GXG+JMpuzRR+fEGOrtNswbWIDV+/afnKlQcYbErBhQmJQW+SLs+KcMqaZW8fSbCM9rONPRP7D9tDQ/C/e9tg21Lb5gxXUii94/syA34dMoyzKkAH9BKn8+QQgBsFgAa6+eF/4I+Qhiy15Uv3wV6i76ORw5Ejc3/R3AbVXx77JIIJky4k2QIKDBbkN1ZibGdnWpOkNiZgwoKGEsF56c8EDg/Tu/F3cdivDZB393TcB3oe9yeyC1mhLvzIIWyzKkE9HyGiw24LLHAHtWzwu/xMxGo82KuQNPwT57F2yfPwo3vNI5VhKJm1ElmEwZ9SZIFFHXqw/GukX5MyQUggEFJYwd/xIXbRlC7p1+cF5D8OyDf6375N+lhc8sRNuto/SyDHcGaSjeGgv+vAapLaJ5Q4CK2dJfHzazIQKYO7AA9XYbPIIAl7cLAAI5VkkV2Yu0LBMjmTLqTZA1A46KG4CS81iHIkEMKChh6VZCOpJ4t1JGCgTiXYaIlNcgV/DMQqzdOskuywTjziANxbMsEBx4XPgz4J+PxpfXEDazcbIRWOjrFcmxirYsE2XXSdSboOwSlH/3XgYSSWBAQUlJ9z4NiSQ8KpXgGC2vIZbgmYUeiWonpoPD7ySLc31twJOpQyH3vUgB8SwLSAUe/RzA1Gd9uzwSmNnwNwJzSXxN0jlWCW435U2QuhhQUNLSoWCYlERnGpRKcIyW1yDFZhGQYes5s7D54GbZu3Wk2oDHM0PDnUEakrssECnwaK0BPlwov7hT2I4Nh2iL3Ags2RyraMsyMZIp0/0mSE0MKNIE16yVl+hMg1IJjpHyGsJZLQJK83rjV9POQG2zs8dFP5ndOvHO0HBnkIbkLgskmI8gKWjHRnnzbhTteh71xw8rn2OV5HbTdL0JUltaBxRyLrJmuBBzzVodic40KJXgKJXXEL7LI7zb6VlD8nscJ9HdOonM0HBnkIbkLgskmI8Q0YkdG0Lpd7D0Wxeqt7yQ6HZTUk3aBhRyLrJmuBBzzVo9ic40JJPgKLW8EJ7XEFyHQk6eQ6K7dRKZoYnnvcwQzKeU3GUBFctfK768ILVjJZ7tpqSqtOo26ieKIipXVUqe1BzZDqyeshoAYr7GCCc3tjNXz8kuoR1AZg2EjCaI3QOArjKU5feJuVsj3t0havbSCA6ew+8kB/cdLPk1KzfW4xdr/gunxBRNVoYVD1d+G9PHlST0XmYI5nVBon04csuA614Dju7zXZhzhwBv/iSxTqJaYlfQlGO3UQlyEsMAmCJ5jGvW6hEEAU9cW4JZa2+G29IMwArAA5s3H09c/mzMgFMqwTESpbaaRpLInWSiMzSR3gvwBcC1R2vxzJfP4LDzMGfVkiW1LJBTCPw17MKcXQj0LwaONsZf/loL7ApqCGkZUMi5yAIwxYU4XdeslZouj3YcURTx0IY7AHszBNED4ETwaW3GQ1/coeiFT4teGvEmqiWTCxL+XsEzEoIgoFtiPd9owbxuBFehFEXgqYqeF+a2Bl/Rqhmrfc/pLR9BycTRRMVbICwNpWVAIfcia4YLcTpWs1RqujzWcbTcAqnHXhpKFbsKz/OJxkjBvBqSDpSjXZiP1AIQgPLr4hlQYhfZeL9O6cRROYLHmNHnZKEvLrdElJYBhdyLrBkuxOlWyEWpJFQ5x9FyOUmvvTSUKHYVKTCTYqRgXmmKBMpKXpgTzWlI5OtUTByNNEbxhatQ3bkfdfYMOI47Ud7V5etEyuWWiCypHkAq+C+yJdklsFvsyLJlwW6xw5HtCFxk5bzGKPxr1ssuWYb7z74fyy5ZhtVTVkdMtjMyufkxShxHy+Uk//KC1RL6e6dUi/Nk+HNBpo8rQUVZXtz/NvyBWSzJBPOiKGLzwc1YtWsVNh/cDI1z0ZMWHOC6vC50ujvh8roCAa7s70epC3NwToOn21dN09N98iIbaTyJfp1/x4oQ9nsipyuoKAK1nwHVL/r+G+uzEkU0/vUqVPbqwOyCPCzq3wezBxegsmgwGm3WoNcFLbcQgDSdoQDkJaGZqaJauhRyUWrWQM5xJg+brNksVjzLC0bbbhktMAOATGsmvKI34Vk1NXeMaPVZRw1w2+tR/cnjGCunqVUSFSZDJJrTkOjXJVrIKoHZELH2M8zt5US97URTsxPHrrfbMG9gAVbv24/Au6m13GJQaRtQAPIusulyITYLpWYN5BxHi+WkeFucG3G7ZaQlSAssGJg1ELeMuQWOnMQu1mrWYdHys44a4Hq6UbdxKcZ+uDj20kGSFSYDEl06SWbJJd5CVgnuDKluWI99NmvPpmaCgAa7DdWZmRjb5eucqspyi4GldUCR7ox2JyuHUkmo5QXlGJhViIb2ekAIyl0QLRiUVRg4jpqzWPG2ODdqEbNYgVkyS3NqJc5q/VlHDXAFAY7OsKWDaOv6SlSYTHTpJNkll+AdK7EkOBtSZ7NHbmomiqiz23wBRbyzOmmAAUWa0vpOVqvgRclZA2fdTHj7PAXB3gKIVkDwQHTlwVk3s8d7Kj2LlUjdCSM33lIrMFMrcVbrzzpioCyKKHa5Ue6/Y5a7jTKeC7OURJdO4vm6ZHeQbHkRECKkCUaZDXGUnQ/3V89JfplLEOAQbYA1Q191OnSCAUUa0vruSm7wolTQocTFaWNtK/Y39Ub3wfmw9q4NVMH0dJai22pRpO5DrPePt+6E0YuYqRGYqZU4q/Vn3SNQBuDydKPY5cbSA4cQ8putxbp+oksncr9OiR0kggVwH5d+XZTZkPKBY1GUXYz69gZ4gr4NqwgU9y5A+cT7gPxhrEMhgQFFGtLy7kpu8KL0jEmyF6eTdR8EeDrLgM6ywHNq1X0IDqh27+sFmxVx1Z1I1yJm0ahVhyUVn3VIoLz3QzjWL0a5swM9LmlaresnunQS6+sSrYoZ/nWRxJhFEQQBSy/9s+981N4AuyDAJYoozinxzXKacHecUhhQKMBouQha3l3JCV7KC8p1t/avdd2H8IDK5XFDKO4PoW4mRHfoltBI7x9v461kakcYhVqJs6kqGBcIlAvKgaqXgc4kd2skP6DElk6ifZ3SO0j8bL0A0Xuyl0mUQMhMO/y0xIAiSUbMqtfy7kpumXO9rf0r1WJcjkizOJaMZmQ5lqNjz3zgxH1otPeXe/FUs8mYHqlxcUh5wTildmvokRo7SKy9gFHTgTHXSfcykVhO4Q6/+MUdUDQ1NeHxxx9HR0cHnnnmmcDjTqcTt99+O3r37o2WlhYsXLgQpaWlig5Wb4yaVa/l3ZWc4EWPa/9KlZWWI2KlSMELS0YLMvrUwuYaJuv9Y1081W4ypldqXBxSfhcbaekA8BVwMmrPCTV2kMDrCyYc46V7mSRa9ZL9PULEFVC4XC78+9//xurVq3HOOeeEPDdjxgxUVlZixowZ2LZtG6688kps2rQJdrtd0QHriVGz6qPdXd0y8nH8fVODYtPgcoMXPa79K1FW2i/asli0gCrLnomZF/dHse3bst8/2sVTiyZj6STld7HhSwdmaPGt5g4SJZuMmeGzVlhcAYXdbseUKVOwcuXKkMc3bdqEt99+Gy+++CIAYNSoURAEAS+//DJmzJih3Gh1Ro931nKF3131QgEeX92FH2/cq+g0uJypYT03MIunxXgksZbFYs3inDdkJMYOLEn4/YPpsckYKcQsLb7V3EGiVC8Ts3zWCksohyJ81mHNmjUYPnw4MjMzA4+NHj0ab775pqkDCqNn1fvvrsoLyjFxyceoa+5UZRo81tRwytejVSRnWUzLgEqvTca0ZrREaln00OJbKWrtIImwLCICqLYDdV0H4Di4Ofbvg5k+awUpkpS5fft2DBgwIOSx3NxcfPnll0ocXrf0fGcdDy2mwWNNDad8PVolcpfFtAqotEw21SsjJlLLkooW32pSYweJxLJIo82KuQMLsM9uh233q3B/82Ls3wezfdYKUaTbaFtbG/LyQi84mZmZcDqdEb9m5MiRKC4uRnFxMZYsWaLEMDRnlo6k/mlwKf5pcC34g44pw6dg7MCxhvn8oonWSTN4l0syHWHj6aTpTzYtzc+C3SogK8MKu1VAWb7yyaZ6pFjXTj3SusW3EfmXRfKGANYMiPY+mDtoIOrtdrgEyP99iPZZe7oBl1N+d1Mo1w031V11FZmhyMvLw7Fjx0Ie6+zsRG5u5LudHTt2ICcnR4m3Tykz3FlzGlw98SyLJZLgl8jddnFuFt6/83t4edt6bD+0B6cXDMX/jfoeLJbE7i+MtHxg1ERqWZTqJGp2Qcsi1fUfY9+eV+EJW7qI+fsQ6bOG1bfD+90HZCdqKjVjpoeZN0VmKIYNG4ampqaQxw4fPowRI0YocXjdM/qdtX8a3GoJHbfa0+Cpjqa14F8WswrWkMeVWBZL9G678VgjJq+ejMVb52PdoT9i8db5mLx6MhqPNcY9hsZjjahcVYnZ783Goi8WYfZ7s1G5qjKhY2lB7oyRLoii7w5X7p1u2N037H18/80favzaFEo7sSxSN+g02KzSOxGj/j5IfdYWO2C1AF6vb5aiO6xhm8TPT6kZM73MvCkSUFx99dXYunUruvwNauDLq7jiiiuUODypLBXT4Ea7ECVKzWUxOXfb4ZQ88ejlJBYPwyRSH6nz1UtYUQm8s8D336cqfI9H47/7nrEG+P4Tvv/eugHor8wuIbNJ6vch/LO+7DEAAhBeTyY4UTNMIv+GpSh1nGQltOTh8XhCToTl5eWYMGEC1q5di8mTJ2PLli2wWCyYPn26YgMldSlZcyEWoxYES5SeOmkqOeVvxOUDQyRSJ7slMdlOomkk6d+H4M+6+sW4EzVj/hve+yHGNu7w5WyUnA3UfyG5e0UvJQziDiheffVVrF+/HhaLBStXrgwEDS+99BLuvPNOfPLJJ2hqasI//vEPWK3WGEczLyOtK/spUXNBDiNeiJKll06aSp549HISi4chtihH25LYsheoWgbYs1iZUQGK/j4kkBQb9d+wywnH+sWAG4A7KEixZZzMzbj+NeBoIxwHvoJbKpCBtjNvcQcU11xzDa655poejw8YMAAvvPCCIoMyOj0kx+iZES9EepTI3ZWSU/6GWT4Io/tE6mhbEr1uYO29vkZXrMyoCMV+HxJIio34b1gEil0ulDsldth1nzhvNu8BnjoTgIByqx1FBf1Qb7OFtlzXeOZNkRwKOkmLdWWjJzMa9UKkN4nkZyiZJKpmwqnadJ1IHbUnhQh4PbIS/kg+RX4f4kmKPZFwK2x5CUtPnxv6b1iwweF2Y+mBQz1b04fw+H5PPN0Qujuw9MBBlLhcsItIWQkDQdT4anT06FH069cPbW1tptg2Gm7zwc2Y/d7siHffyy5ZltTdtxlmP0RRROWqSsk7a0e2w3Q5FGqLd3kt+HcofIpXTt0LtY6V9vyNppp3Ax8/Bhw9ELkVdzBrhi8xkDkT+hCrYZhEDxCxvwPV338UdWIXHAe+Qvn630Hojr/+jwigOqsP6r53FxxDLlB85i3W9ZsBhcJW7VqFRV8sQqe7s8dzWbYs3H/2/ZgyfEpCxzbThTjRC5Eoiqoljqp5bL1RMsfHiPlCuhN+kQleM7dmAO7jgOiF75IRxt7Ht8ug/DrJQ/PnoyOiGNrt1E+w+WYybt3gC0ZWVEoveckR4/chGbGu34oUtqKT1JzON1MyYyLrlg2tzh7txJVoYKb2sfVIySTRlHfcNLpIuzpgBfoVAuffB7g6fcWSJPMqIlfBNMOMpqnI6QESsWiWTCmsisocCoUpva4cnC/xr4Z/GacojwzxrFuKoogZyzegttkJl0eEs9sDl0cMNDBLZKJNFEVU1bTgb1V1+N+lnyl6bCLZIl1k4AGOHQTyhgEVs30XGSHs33+UhD8j1gkxPX/CrRT/1tKIRbPsvv8G/z3sOpPqqqicoVCYktuQwu8uuj3dPWYn/MyezBhvA7NYyxfBMxIWQUCXu2fpcSWboxGFCF5nb94lr35BnC29zTSjaRpyt5ZKdU0Nr0ORU+hLyI2nxbvKGFCoQIltSJGKP0kxQlZ9ovyBwcqN9bBE+Pj8Dcz8F/1YyxfBsx2+ACXynVr4sYmS1iNfosu3HVRKrItMlDoU3J6tvrjzU+LZWipVoCz874m0eFcRAwqVJLuuHOnuws8m2JBhzdBfUR4FyZlFAEIbmIUHCy6P7/PzL1+8f6IaqNRsR6xjEyUs0g6OaIl3ci8yEXB7troSyk/xL2fEMdMUVfjvg7//S4oCDAYUOhXt7qK3tTeuO/06lOaUmjZrW+4sQngDMzlLI/527d3SsVrEY/vHpeVOEGbom0DwjIRg8e3YiMRiA6yZikxfG6LMuEEl1T4g2nLG3vWJBwIS21G1LnzGgEKnot1duEU3zi0611DTlfFeiGPNImTaLPCKIhx5oQ3MogUL/uWLaO3aox1b650gzNA3gfAdHNHYsoDx84D84YrcXRqizHic9BJgx5WfEqkuhX9m4Ugd8PRZyQUCyfZ/UQgDCp0y091FIhfiaIFBps2CyWMKMX1cSY/AJFqw4F++8LdrPzn74WMRgEH9euHOi77VI+iRs5Si5Ikt3RqoGUXcF7SIOzikDu4GTr1E0QJVui8zHgc9Bdiy81NizRooFQjI2Y6qQeEzbhvVKTXbXmspnu2e/m2cKzfWo9PliRgYeEUR08eVoKIsr8fn4A8WrGEZnFYLMKhgP/a51qP6UDWe/2FFj3btQwb0wcp550geW85SipL00o6YTmo81ojKVZWY/d5sLPpiEWa/NxuVqyrReKwx8hdF2yYYTMXtfrouMy6T3rbAyspPCQ4WPN3S5dLlBAJyyNmOqgHOUOiYGe4u5G73DJ/F6HZ7IAgCrIIAT9DJQiqvIZggCFgx86zQGRGhGX0cy3EsoxWLNpy8s3nh5j+isbm3rGUYOUspSu4EYYa+fFpMgyc8YxS1Lwd8Tb5Eb8q3++md3rbAyppBlhMsRGsEF6HluaQEOp2qgQGFzhm9CqGcC/G40lzJ5QSLIMJqEWCBEFgqCc9rkFKcm4UPTuzm2Hv4GJ7d+yMcPt4Mt9cDd9CF4Efv/wirp6yWFQjIWUpREjP05dFqGjyeC1pIgNO3BOX9HRBaasIuLEFVMPOGpXy7n97pLcCWlZ8iJ1hQKhBIoNOpGhhQkKrkXIgjzWJ4RcAiinjwym+jt90a164KQRBQUZYHa+8aNH+1P+k7m0h5F7FmTBJlphwatSidZxJtpkPuBU0ywCkciKUCUNha13ObYP8SRT4Ls9NjgB1zBllOsBBHIBB1Jk7p7agJYkBBqpJzIf77poaIsxgZNit6262YPi7yiTfaDhKl7mwkl1JkzpgkwowZ+kpTcho81kyHnAtaxACnYz/mFTmwetLvIbTuVb0+gF52QihJrwF21BlkOcGCzEBA1kxcnIXP1MCAglQl50KczHJCQ6sTNyz/Avuc22Hv1QLX8TwUZZ2OF2aejeLcLEXvbIKXUrSoQ2GGHBo1KRUsypnpkHNB8wU4DRECnHpU9+6FsWXKd4AMpqedEEoyZIAtd9YgRiAQ10xcHIXP1MCAglQX60Kc6HKCKIq47rm1aMp+Chl5LYBoRYbgwSFXHq5/7jZ8eMdVit/Z+JdS4k3ATLQgltFzaNSkVLAod6YjcEFrb4BdEOASRRRnl2Dp6TdD2PIS6rr2w+ZxwyXxY7V73Kg7qu46v9m3GhsywJY7axAlENBbQmo0pggozDjFZzbRLsRxLScEFYnZ0ZWPpj5PQchohiB4AZz4B5fRjMN4ClU15+GsIfkpv7NJt9boWlEqWJQ701HodmNNQyOqOw+iLiMTjq7jKK+ph7DtU8CWAYdVhHtgPoCev1MuiHA4jyb8vcphpAtPogwZYCc5a6C3hNRoDB9QmHWKL93IWk4IKxLjtIjIGJgPd1hQIAheIKMF/6qrwllDLkvpnY3WBbHSiVLT4PHUFBBaajBWdGOssyP0hd0ulAMocvVDvd0GT9B7W0URxW4Pyj3qlv0x0oWH5NNjQmokhg4ozD7Fl26iLidIVJRr6NsHdohwS9wRwmuFJbM55NipuLOJt+06xUeJYDGpmgJBBABLDx7C3IEF2Ge3wS6KcAkCil1uLD3cCiF/WDLfakxGuvCQfHpNSJVi6EqZpqwm6O8WV/2i778aV4DTLYkTusPl7jE74SdYPPhe2WlajS4ifx0OKf46HJScZCtByqpKK7PiZaHbgzX79mPZ/kO4v7kVy/YfwurGwxic41C9FoD/wmMVrCGP6/HCQ7GJoojNBzdj9e7V+HH5jw1RNdnQMxSmm+JTsltceEMafze7aIlBkZrY6IFEkZjyri4Uudw9ppghWlCSXaKLn73WBbEoMUnVFAgjABjr8mCs1+YrppI/VJNaAIbcCUGSpJbyC/sU4lfn/gpOt1O3uYKGDihMNcWnZLe48MDEHVSpzZYhHahECmaufw042hh/kKF0cCJxQg9MMQ8aiIaMTAiCHaLoQUmOfk6gWhfEosQlVFOgx0FsQN4QoPJ3vtdqHJjLXQJiIrt+RVrKbzjWgKeqn9L1Ur4gatxV5ejRo+jXrx/a2tqQk5OT1LFEUUTlqkrJtSVHtkPXH3wPtZ8BKyqly7RaM4AZa+RlCYsi8FRFfCe+5j3Ax48BRw/0LA9stQAQ4psxUXKmJdb3Jdgg5g9B9dVLUXesXpcnR6ldHv4dLEX9e6d6eCRX8O+15cRsmQBAhO/fqEEqYDKRXd82H9yM2e/NjjjzvuySZSmbfY11/TZ0QAGE/uMIn+Ib3HewAiPWSPWLwDsLfB3pwtn7AN9/AiiXURQnWmAixWLz/XEfl/d6weabwo00YxLlwh/16+QIP6HHcQJPtA6EUlL9/qSQRJYSdcRUN2EmtWrXKiz6YhE63Z09nsuyZeH+s+/HlOFTtB8YYl+/Db3kARi02IkUpZrERGtII3lst++PXMGd8qRmTOR02Eu0iluCpWX1UAci0YJYpDNSNQVSWJkwXulQq8LojLyUb+hdHn7JZnnrgn+NVgiL8eLtFhdH8ljC/J3ypETLho/2dXL5T+jl1/n+G+NnHVwHwuUR4ez2wOURA3UgNJ6gMzx/5vmqXauw+eBmfn4K0uKz9SeyS/EnslNqGXm3juFnKIwiZhJUMt3igqdhc4fISx5LRrQZE6VmWhTCOhDK4dq7erT6bI1895sujLxbhwGFBmSfLBKZ0pdKgMwuBPoX+3ZnSCWPebogeiXLQUEEINh6AV6P72u8XiB4elSw+QIWiL68j/AxxtGOVwv+OhBSnUz9dSAYUMTGInLq0fKzNVKRpHRm1KV8BhQqi/tkEU/d90hbTdsafDs4Zqw+uXUtKHlMzC1D/fNzMNi7H3bhZI0ElyigWRiAgd9/yFfVL6fQt2U1eMYkp8iXc7FisvQOjhMzLeILUyG21sAj2GEVXRDyhkDQYC9+ONaBUAbX3tWj5Wdr5LvfdGPEviUMKFSm6skiWgLkkVoAQujOkBOBysaaFizovg/LrIvgwGG4YIUdHtSJBZjpvh+L876PilLfXbt46wZ8VbUO7Y07kT34VJxW9TMIYQGM2LIXx/8yBW9NWIWyU/piUM4A3Nj1BAq6qzHUcgh7vAU4dLwcK8R8FCf2nSaMdSCUYboiclJSVNhN68/WqHe/pH8MKFSm6ski2o4OfwKkxExHTVMHDlkLcFH3kxgnfI0yy0HUeAdiozgCWRm2wDLAyd0RHtitp+KMTduxwrYXGQgNYATRDduRGrS8+XP83XMGNuM0eL0C9ogj8DlGAACsLZ0paYYVVydTisj0a+9SS4f9HMDEn/u2cqsYYKTis1Xq7pcFsigYAwqVqXKy8N9JNe8C3F3Sr4mSAHlyGUDARvE0bPSc7HnhXwaQ6pJZbD0Al2hFhtDz+7HBg5uEt/BD21uoE0/BjZ77sA+nBJ5PZRKkrE6mFJWp194jVqndBay8Ecjoo0xxtgiM+tmqnUjKYMV4TLFtVM8U3wJ0pM5XOGpFJfDFH6VrSMRIgPQvA1gtof84g5cBpHZH1HgHwg6J7Eb4btwyBTcyBDdKhYN4PuNx+FI8T0plMyx/HYjp40pQUZbHE1OcZDXQMqpYnUS7O3xBhr8MvsLbOY342Qbnhrm8LnS6O+HyugK5YclueW081ojKVZWY/d5sLPpiEWa/NxuVqyrReKxRoe+A1MAZCpUlmwQVUmExPwvj3praI4chwN5H1lZTOcsAUrsjNoojUCeegjIchE2QTnQEALvghQOHME74GhvFnrMfZBzhd4mrJ6/GlsNbzHXXKLcYnBLF2fyHkrj7NlJeg5q5YdxRZFwMKNQSlOBVmDcUayavRnX4iRjwlcqOkAQWXuHxDK90DgMAX/nss+cCp14ia6031jKA9O4IATd234cVmb/CEEsTAAGCp1vyrVywosxyMLCcYrUA38+pwbjWFkAYZrxupyek0zRstCltwydgBotQO0UEUJ2ZiTq7DQ6XG+VdXRCi5CbJFetzNcJnq2ZuGHcUGZeiAcX69etx3nnnBf7+61//GgsWLFDyLYxBIsFL6F+KsTe8fvIfQowGWvHmMMCaCeQPj+tEF60cdKTdEQcsBbg5+w94f3om8M178Pz7d7BJLIPY4UGDMAhZGVac4jmIFzIeR0nXYQjvRGgWpkZDMYWlU2En098lxigG12izYu7AAuyz22ATRbgFAUUuN5YebkVhEsXZzPK5qplImhY7ikxK0YDiueeew29+85vA32+88UYlD28MctqQAzFfE28Og9JVKGMui/TvDTi+A/G/b8LdujckqHDDCiGvDHdV3oiapg5M+tf96NV+EILXDXTH+Xm8MDWxVtAKz3aY5UIgl6nvEmMUgxMFG+YO7Id6uw0eQYDrxM+13m7DvEEDsbrkbMmicHKY5XNVM5HU9DuKFKS3GVPFAoodO3aguLgYd9xxh1KHNCY5zbGAmK+paSo+kcMgBm3tLJDOYZBRhTKRbpcxd0cIAuw3vgHxhanwBhWxsp4oYlXRPx8Vlp1AR0Pin0fzN8DzVwK2zJS2TzfLhUAu094lyigGV12/Hvv2vNLzZy0IaLBbUX14S8Lfu1k+VzULZOl114veLt56nDFVLKB48skn8fzzz+Ojjz7Cfffdh+9///tKHdpYoiZ4WYAtLwJ9ToHXYoNF4jVeix2Wlj0oGzACp3gO4s8Zj8EhnCw+1SjmYh8GoMTSCos1Q1YSZjLdNmN2yezvgHBbFYS6z2GRmg2QUysDiJ4U53UD3SeCjeCZjUjt02PNECVwEjDLhUCuZO4S9XbiDSGjGFzdoNNgq82AS6J9tN2SkdTP2kx332oVyNJjNU+9Xbz1OmOqWEBx9dVXY9SoUXj55ZdxxRVXYNGiRbj//vsjvn7kyJGBb3j+/PmYP3++UkNJrWjNsTzHgW0rfX00IpxU3K4u2POGYFxJf7yQ8TgGew/CLngDiZhFaEajMBjCjNW+O/wY0/lSuRgAAt02FSk0Fa1ceNTPoxtwOX09RyLV0wiXovbpZroQyJHoXaLeTrw9yAhwHYUjVftZ6/XuO1FqlYfWUzVPPV689Tpjqlgdissvvxx33HEHPv/8c/z0pz/Fgw8+iK+++iri63fs2IGGhgY0NDSYJ5gAIrch93Mf9wUTYs/t7C7RgjqxABu9IyDUf4ESy+GQXhvAiS2ZlsMQBIusFt5yum2qKuLnYfU1H3v3gcj1NCJJQft0I7cUTkQitRHUrk2gCBndcNX8WRux5kSq+IOVKcOnYOzAsSn7bORcvLWm1zb0ihe2EgQBv/zlL/E///M/+PDDD5U+vGyiKGLzwc1YtWsVNh/crN3JzN+GPG+Ir7OntVfElwGAS7SiQ8xEt2hDrTgIc8WfoqbZCbTsgRDhwihY5V8Y/fUkpGhSaCr887D38V3YrRZfJ1P/LEXIwPr4tsFGkoL26el4IfDfJS67ZBnuP/t+LLtkGVZPWY3BfQdLvl6PJ94eIgW4QXlIav+s4/1cKbX0ePHW64ypKnUoBEHAhRdeiK4umdPYCkv5tGtwG/ItLwLbVgLu4z1e5kQG/uK5DDXi4EAvDbvV4iv+JChzYdRFt83wtuwup29mQpTYseKvpzH8YuDNn8TfBj1S+3RYgb4DgZbdJ18X54VBT9OwWolnStsQeSb+ANeftOvvohuWh6T2z9qInSTTlR4v3npdOlOtsNX+/fsxZ84ctQ4fkW7Wu/x5BQCw9VXJl9jhxUeeMYFqkqEdMCNcGGXs6AimRrfNRHaMhORZVL8YeR3bX0+j7BxZJ37J9wn/Ok+3b3ml/QDwzj1J7fpI9YVAzwmPejzxSgoPcCPkIaX6Z036oMeLtx4TVwGFAoq6ujo88cQTWLBgARwOB1599VV8+9vfxmmnnRb7ixWmu2SVCHfMomDFfmEQvrSchiyrVboDZiIX1DBKd9tMZsdIQN5QiO5uyb38oscFwT/7IvPE30Pw1zXvBj5+DDh6wPf5d5+4e05y10cqpHzmLQY9nngjipZITBRErxdvPc6YCqICyQWNjY247LLLsGfPHpx55pm4+eabcd1110m+9ujRo+jXrx/a2tqQk5OT7Fv3sGrXKiz6YhE6JbZ8ZdmycP/Z92PK8CmKv29UwXURggID8frXsPFI35A7fQChd/+O/hDqv0i6QFNCswoSx5i45GPJ2Y6y/CzZO0ZErxf1v/wfDPbuD0k6dYkWNFoK4fj5NggWhdJ7aj/zNVKTnA3JAGasMcRFRRRFVK6qlLxYO7IduimsFRz0hJ94mSNARqbn2UGtxLp+KzJDUVhYiK1btypxqKTpcto1wp22IAio6I9AjYeod/9JXvRi1pOQQc6OETnH31h3BAu678My6yI4cLLGRp1YgJnd92Jx3RHlWpzLqYNhgIBCdzNvEejxrolICVwCi810zcF0O+0aY4pV6XoRSsxIhJPqQOrn3zEiJxCoaerAIWsBLup+MqgKqC8pNSvDJvs4sqi060Nrhkh4PIEnXqL0ZLqAQq/rXbEodfcPKJTnIEGpHSMnjyNgo3haoCNpvMcJiNa3I9KujziTW1NNlzNvRERBTBdQAMacdlXq7l/NyphK7RhRdOdJrL4dMrcJAtB1+3TdzrwREZ1gyoACMN60q1J3/0rOdIRTaseIYjtP5PbtkLNbROft040680ZE6cO0AYXRKHXXrtRMRyQxO5BqeZx4+nZEy2FRqaGY0ow486YbOp59IjILBhQ6odRduxaVMZXYMaLIcZTawaFSQzE1GG3mTRd0PvtEZBYMKHREibt2NSpj6pZSOzhMsrWUJBhk9onIDBRvDmZ4ougrhlT9ou+/GndI9N+1Tx9XgoqyvIhdHatqWrByYz2qalpCGp/5ZzpK87NgtwrIyrDCbvUVnkqkMqauyWj0JItJtpaSBDmzT0SkCM5QBFNwalSNOhCAvC2hSuU56F48OzgkBCrfdR+EI78E5YdrIRh4aylJ4OwTkWYUKb0dD7VLb0cT9SIvisBTFdL1CvKHxjU1qlYdCKVKX5tOAgl3PftiuFDkcmPpgUMoFK2hgUn/Em2+D1KeSUqvE+mBJqW3jSDmRV6hxLx46kDEWxtezS2hhhZno6eIHWltVsw79QysHnYjhPxh3AlgVMEBZu4QUxQ2IzKCtAgoZF3kk5kaDTqBfdU9AA0tnpgX/UQ6R6q9JTRdRO2LcbwZ1UWncxeFUUktW2YXAv2LgaONCXftJaLY0iKgkHVnn2hiXtgJ7Fuubqy1nYIbPPdiH04JealFELByYz1EUcQvt0jcIbfXY966eRE7R2qxJTQdGKkvBsUh0o6OtgYgbwgwY7XvOdahIFJFWuzy8N/ZS/Hf2cMxHq4cB9ywhjzvhgXurFOAlt09d30En8A83UB3B6yiCyU4gOczHgcQGsB0ub1Ys6UR1//1FdS0NUTtHCnFvyXUagn9Xky5JVRF7IthUtGWLY/UAhCA8ut8M40MJogUlxYBhZw7exHAjO57USsWoFu0oUPMRLdohVe0QGw/CPGde3zJXU9V+GYlgIgnMLvghUM4hHHC1z3e77jbC6+tCaJX+qP33yFLibQltDSvN+66ZAT+vqmhxzZS6snfF8MqhAaP7IuhITW2Z/uXLaX4ly2JSDXmXfIIymsYlzcEJbm9URu27GERgFOyM1HT1IEd+49i05FsTPT4W2ofwJ3W11AgtMIOL9B9ImgILogTJe/CLdgwzHoI23A6utyhwYzYPQAQJBIhEPsOOXxLaJ9MG55892vc/kq1ojtKzEzxvhgs6xwftSpXsp4IUUqZc9uoxAnLlePAjO57sfFIX9itFnS7PYELh91qQZfLA694cpFinPAVXsxYhExBYmrcYgcue8yX5PXp7wCJ6XPRmoGvLvkr/lI/CGu2NOJ4SFAhImvoElgymiEIJx+3ClY4sh0Rcyh6vAe3kSYl3l02kljWOT4Kbs/W9NhEFPP6bb4lD4m8Bni6YT9Sg5d6P4GXZp+Nh648HQU5veAVAZdHhLPbA48YmvFQZjnYI58iwOsG1t4LfPFHyWACgg1CbhlGnnUJpo8rgadHzCags24mxO582AQ7smxZsFvscGQ74rpDlpNsSpEJAMYe78KU9g6MPd6FuC81EX7XArNY8cbqKa7Sqgk1K1f6C53lDfHVmLD38f03fyh3dBBpwHxLHlFOWEJrDSosO4FTRqCpvbvHhThYjXcg7JBelgBEwOsBvM7Qh+19emxJi9Rbw+LNw8D2n+OJyhzUH6tP6A6Z20iToMTMgpJNxdJlpkPtypVyWtUTkSrMN0MhIzEr2q4PAb4lg+3201GPUyLPUvQ4tg04e66v8t6tGwLVFaP11nhh1nicOehMTBk+BWMHjo17up3bSBOk1MyCUkmASs906JkWeQ7+Qmfc0UGkKfPNUMg4YZWJkS/EVgvw4JWno7fdimO9/gbrhzNP9olwH4coeiGg5wnea82EJX+45N2VWr010qqzqJKUmllQ6uJooPbpSfM3dEu0ciUTYIl0y3wBhYwT1jgg4oW4ND8LN4wvPXGxLwG+fXL6VHR1wPWP+5GBnnkTblcX7HlDIq7D+7uIKrkE4Z/9CC8p7sgzYWdRJSk17Z7sxVHp8RhBMg3d0mVZiMigzBdQyDhhCYD8C3FQn4iNe5uRJ/4GDhyAPWh3hku0oA4FaPWOQIXG327adBZVklIzC0l2O1V8PEaRSJ5DpCqYwdu4+TtPlFLm3DYKyJoajbfF+MqN9Vi65iP8EQvhEA7DBSvs8KBOLMBc/BTzKs/D9HHsTKl7Sm8vlDMNH+013O4YG7uGEqVc+nYbldGBMt5liLIBfVDrycdFgeJXB1HjHYiN4gjYrRYmQRqFUjMLwceL9rsWa6pe6fGYUTotCxEZlHkDigRFK3YUnAS50XsaNnpOA8AkSEOSO+2ebBKg3Kn6SOMBfHfn6Z6EmG7LQkQGlF4BRfjFoeRsoP6LwN8b8xyY+/68iC3FmQRpMsnOLMgRzw6O8PGkexJi8L/X3CHKJMASkWrMm0MRLvzk7A6aOrVlQPS4UFk0CPU2a0gXUKly2PHmXpABKZXXUP0i8M4CX22JcPY+wPef8NVLUOv9jUoqmMou9BWKOdrYc1moP3OXiNSWvjkUwSJNO/t1u1CdmYl9FjFqS/GxA8cCUGcLKOlMqmtVpFNtinCR/r22NfjKas9Y7XuOy0JEupIeAUWkk3PwS+w22EQRLokTkb+luD+goDSQ6loV6ZyEGC2YOlILQDg5q5Puy0JEOmK+0ttSopVIPsHhcsMd4a4mVktxURRRVdOClRvrUVXTAo1XkUgNSteqiLdhVTomIfqbo215ERAinJqCS5qnU8lyIgNIjxmKaCfnE8q7ulDkcqPeboMn6CRvFawo7luM8oJyya9raHX2SNIsycvCiplnoTg3S9FvgzSkVBVMILFCTkq+vxEEzzQIFsB9XPp1wcFUOi8LEelQesxQ+E/OQuT4SQCw9GALSrwW2C3yWoqLoogZyzegttkZaIPu8oiobXbixuUbOFNhZEq3wo63YZVeW3FLtVhPtu16+ExDpGAiPJhSqjkbESkiPWYopAoHebp9UYQI34na60Jh/1Ksueo1VHc3SdahCLexthUNLZ092qB7vCLqWpzYWNvKxE0jS3Ur7FS/f7hYOy+U3lrrZ+sFiN6ehb7ScVmISMfSI6AApE/OYXUo4BgPQRAwFg5ZCZj+Nujdnp7P2a0W1DR1MKAwOhkVV039/n6Rdl4cqTn5mkT7a0RLQLX2AkZNB8Zc1zOYSrdlISKdS5+AApA+OSdxsi4bELkNusvjZSluMg8ZO6UClNxaC68vmJA6DkuWE+mKogHFY489hj179sDpdGLWrFm48MILlTy87gSX4g5vg85S3GQq0WYRpGjVBl5vy0JEaUyxgOKpp57CN998g+XLl+P48eMYM2YM3n77bQwbNkypt9AdluKmpCTbJ0QL/jE27wLcXfK/Tss28HpZFkqBaL2HiLSmSOnt7u5uFBYW4rXXXsN5550HALj99tvR3t6O5cuXh7xWq9LbWpbHZiluipsRCjIFj9FiA1xOeV+nZht4Cmg81oi56+ZG7D1EpLRY129FAooPP/wQF154IZqampCfnw8AWL58Oe677z4cOnQorgEpgbUhSNeM0Kcj0hj97H18swg5Rb6/H93H/hoaEkURlasqUd9eH7P3EJFSNOnlsX37dlgsFuTmnswZyM3NxeHDh9Ha2hryuN/IkSMDv/Dz58/H/PnzlRhKSG0Ij1eEy+P7x+avDfH+/PP4D41SywgFmaIlYVpswNlzgVMvOZnfwJkFTVUfqsa+Y/tk9R4i0ooiAUVbWxv69+8Pi+VknazMzEwAgNPplAwoduzYocoMBWtD6ENar+3GmrpPpk+HVssCUbdyZgL5wyPvlvIXumKAoZq69jrYLDa4vD13x7D3EKWKIgFFXl4eurpCE7Y6OzsBQDKYUBNrQ6ReWq/tysmNSLQgk5Z5F0YYYxpzZDvg9kpv4Y3Ve4hILYqU3h42bBg6Ojpw/PjJkrmHDx9GcXExsrK0zVlgbYjUEkURc9fNRX17PVxeFzrdnXB5Xahvr8e8dfOMX448Wplpuc2qIpWCj7ZNUulGWLFKaIti6sdIEZUXlKOobxGsgjXk8Vi9h4jUpMgMxfnnn48BAwagqqoK5557LgBfXsUVV1yhxOFjCt5lUZqfhZLcLNS2sDZEKph6bTfW3bfc3IhEtkkmm3cRvFSS0Qf456OxS2hnFwL9i32PJTvGlr1A1TLAnsVlEAUIgoClFy8NzATaLXa4vC4U9y2O2HuISG2KBBR2ux133nknXn/9dZx77rno6OjAunXr8M477yhx+KikdnQM6tcLRf17Y39bJ2tDaMy0a7uRSk8Hl5mOJzci3oJM0Y4t2IBv3ot8nGjbP6OV0G5r8DUnm7Ha930mM0avG1h7r68vB5dBFFHYtxBrpqxJ31wl0h3FClvde++9uO+++3D77bejra0Ny5YtQ1lZmVKHlxRpR0fjkeMozeuNF2efjdpmJ2tDaMi0a7tyZgjizTuIpyBTtGO7ncCnvwNsmT0v1pECITlEt+97huDrkprMGCECXo9vGQSIv99HHNIpIVgQBIwdONaYQTqZjmIBhdVqxRNPPKHU4WSJtqOjvrUTgiBg+jjuhdeSf21Xan+8odd25cw+jPmBes2qIpWn9vO6ge4TjwdfrOPpwSFFiRLaUlTaIpvWCcFEKaZIUmaq+Hd0SPHv6CBt+dd2S7JLYLfYkWXLgt1ihyPbYey1XTmzD/7ciLwhgDXDV/zJmuErVpVssyqpY1ts8CU+hAm+WPsDoUQlUkI7eIyCVXqMwMlgRSGmTwgm0jlDdxs9uaNDxDjha5RZDqLGOxAbxRHc0ZFCplzbldvASs1mVeHHbt4FbFh6chkhmP9iHXUZIoZEZlbCx+hyAu8+ECGvIo5gRQZTJwQTGYChA4pxpbkY1/8YHj32IEpwGC5YYYcH9TgFP+v7CHd0pJDp1nbj2ZmhZrOq4GPXfgZ89pT06/wX61jLEHJKaMcbDAWPURSBL5aqswwUxmwJwemUC0LmYOiAQgCwIuNxCMIh2OBBBnwnrFIc8j2O6akdIJmL3lplRwwWrEDfgUDLbt9fr3/Nl1MRHAj1LwUu/DnQfezk9wEo/70l20k0DmZKCGYuCBmRIs3B4qFoc7Daz4AVlRHKA2cAM9akvicCkZpCtoSeSBoVAIgAbBknd31c/5qvnkSqAiENSoabpWGWWb4PMp9Y129DJ2VGTThTKOFLFEVU1bRg5cZ6VNW0MLGL9MU/azJjDXD5r4HsgYBX9M0CBFeqfPFq30W8/LqTxbW05F8GUfH9zZIQLCcXhEiPDL3kkXC/AZnYBp0MwX+xBoBjh/TdxVRlZkgINlsuCKUPY89QJNITQabgolkujwhntwcujxhog86ZCtIdDWbsjMCfEDxl+BSMHTjWUMEEYK5cEEovxg4oVNz3L6cNOpGuqDxjR9pg4y8yKmMveQCqZd6zDToZjtxaGaRrbPxFRmX8gAJQZd8/26CT4Wi4RZPUZYZcEEo/5ggoVDCuNBcleVmBxmN+bINOuqa3WhmUMNMVhyPTM3YOhYoEQcCKmWehND8LdquArAwr7FYBZflsg046p8EWTSKicJyhiKI4NwsfzD8PG2tbUdPUwTboREREETCgiEEQBFSU5TEBk4iIKAoueRAREVHSGFAQERFR0hhQEBERUdIYUBAREVHSGFAQERFR0rjLg4iITEMURVYYTREGFEREZAqNxxoDPVBsFhvcXjeK+hZh6cVLUdi3MNXDMz0ueRARkeGJooi56+aivr0eLq8Lne5OuLwu1LfXY966eRBFMfZBKCkMKIiIyPCqD1Vj37F98IihLaI9ogcNxxpQfag6RSNLHwwoyFBEUcTmg5uxatcqbD64mXcdRAQAqGuvg80ivYpvt9hR116n8YjSD3MoyDC4PkpEkTiyHXB73ZLPubwuOLIdGo8o/XCGggyB66NEFE15QTmK+hbBKlhDHrcKVhT3LUZ5QXmKRpY+GFCQIXB9lIiiEQQBSy9eipLsEtgtdmTZsmC32OHIdmDpxUu5dVQDXPIgQ/Cvj7q8rh7P+ddHxw4cm4KREZFeFPYtxJopa1iHIkUYUJAhcH2UiOQQBAFjB47lDUYKcMmDDIHro0RE+saAggyB66NERPrGJQ8yDK6PEhHpFwMKMhSujxIR6ROXPIiIiChpDCiIiIgoaYoFFI888ggEQQj8qaqqUurQREREpHOK5FAcP34cmzdvxm9+8xsAQJ8+fVBRUaHEoYmIiMgAFAkonnvuOdx222246KKLlDgcERERGUzSSx5erxdLlizBlClTMG3aNHz99ddKjIuIiIgMJOmAorOzEwsXLsSCBQtQVVWFM888Ex988IESYyMiIiKDEMQYfZ/vuusufPnllxGfv+OOOzBp0iQAgNPpxOTJk7Fz507s2bMHVqu1x+uPHj2Kfv36obCwMFCQaP78+Zg/f34y3wcRERGpyH/9bmtrQ05OTs8XiArbv3+/2KtXL3H79u2Sz7e1tYkAxLa2NqXfWly8eLHixyRp/Ky1wc9ZG/yctcHPWRtqfc6xrt8xZygSceaZZ+LPf/4zxowZE3+Ek4Ti4mI0NDQoekySxs9aG/yctcHPWRv8nLWh1ucc6/qteGErj8eDjIwMjBo1SulDExERkU4lvW30/fffx7///W8sWLAAmZmZeOCBB/Doo49K5k8AgH9C5OjRo8m+teSx1Tgu9cTPWhv8nLXBz1kb/Jy1odbn7D9mxIWNZNdU1q1bJw4ePFgcMGCAOGnSJHHDhg1RX19fXy8C4B/+4R/+4R/+4R8D/qmvr9cuhyIar9eLxsZGZGdns+00ERGRQYiiiPb2dhQWFsJi6ZkxoXlAQURERObDbqNERESUNAYURERElDRFmoPpwWOPPYY9e/bA6XRi1qxZuPDCC1M9JNOpra3FzTffjE8//RTDhw/HkiVLcMEFF6R6WKb2j3/8A7feeiv27t2b6qGYWltbG55//nnk5eWhqKiIv9cKOnbsGO69917k5OTA7Xajq6sLTzzxBDIzM1M9NNNoamrC448/jo6ODjzzzDOBx51OJ26//Xb07t0bLS0tWLhwIUpLS9UbSLK7PPTg97//vfjDH/5QFEVR7OzsFEeMGCHu2rUrxaMyF6/XK1588cXir3/9a3HFihXi6NGjxaysLH7OKmppaRGHDRsmlpaWpnooprZr1y7x2muvFZuamlI9FFO65ZZbQio33nrrreLPfvazFI7IXLq7u8U33nhDPPXUU8Ubb7wx5Llp06aJzz//vCiKorh161Zx1KhRYnd3t2pjMfySR3d3Nx566CHceOONAIBevXrh0ksvxcKFC1M8MnP5z3/+g3vvvRcLFizADTfcgPfeew+CIOCtt95K9dBM62c/+xlmzJiR6mGYWmtrK2bMmIHf/va3yM/PT/VwTOmjjz4KuSseNWoUtm7dmsIRmYvdbseUKVNQUVER8vimTZvw9ttv45prrgHg+9wFQcDLL7+s2lgMH1B88sknaG5uxv/8z/8EHhs9ejQvdAobMWIEJk6cGPh7QUEBTj/9dE5bqmTVqlWoqKiAw+FI9VBM7Re/+AWGDh2Kxx57DOPHj8c999wDt9ud6mGZyhlnnIFnnnkGXq8XALBx40bMmzcvxaMyH7vdHvL3NWvWYPjw4SHn6NGjR+PNN99UbQyGDyi2b98Oi8WC3NzcwGO5ubk4fPgwWltbUzgyc8nIyOjxWGtra6DTLCmnqakJb7/9Nm666aZUD8XUnE4nli1bhrFjx+I3v/kNnnvuOfzhD3/Avffem+qhmcqSJUuwZ88ezJgxA59++immTJmCyy+/PNXDMr3t27djwIABIY/l5uZi586dqr2n4QOKtrY29O/fP6TIhj8iczqdqRqW6a1fvx5Tp05FcXFxqodiOj//+c/xy1/+MtXDML0vvvgCnZ2duO666yAIAk477TRcc801+MMf/hC4m6bkDR48GK+++ir69euH73//+/xsNdLW1oa8vLyQxzIzM1W9Lho+oMjLy0NXV1fIY52dnQAQMmtBynG5XHj55ZfxyCOPpHoopvPqq6/i/PPPx6BBg1I9FNM7cOAAAKBPnz6Bx84//3x0dnZi3759qRqW6ezYsQOfffYZnn76aTz55JOYOnUq3n333VQPy/QiXRvVvC4aPqAYNmwYOjo6cPz48cBjhw8fRnFxMbKyslI4MvNavHgxHnjgAeZPqOCPf/wjrr32WgiCAEEQ8MMf/hC1tbUQBAEfffRRqodnKtnZ2QAQsjRaUFAAgDcjSpo9ezbOPffcwP/fdtttuPvuu1M8KvMbNmwYmpqaQh47fPgwRowYodp7Gj6gOP/88zFgwABUVVUFHtu+fTuuuOKKFI7KvJYtW4bLLrsMJSUlAICuri54PJ4Uj8o8nn32WVRXVwf+PPzwwxg8eDCqq6sxbty4VA/PVL7zne/Abrdjw4YNgcdaWlpQXl6Ovn37pnBk5vLll1+G5GDNmjUL9fX1KRxRerj66quxdevWkFkKta+Nhg8o7HY77rzzTrz++usAgI6ODqxbtw733XdfikdmPs888wz27NmDAwcOYO3atXj99dcxe/ZsNnlT0PDhwzFmzJjAH4fDgYyMDIwZM4YXOYXl5+fj9ttvxx/+8IfAY2+88QZ++tOfpnBU5nP55ZfjnXfeCfz966+/ZjK3CjweT0h+Snl5OSZMmIC1a9cCALZs2QKLxYLp06erNgZTNAfzeDy477770N3djba2NsyZMwff/e53Uz0sU1m+fDlmzZrV4/Ef//jH+N3vfpeCEaWH5557Dg899BBqampSPRRTcrvduOeee+B0OpGTk4PS0lLceuutqR6WqbS1teHuu+9GYWEh+vbtiwMHDuDBBx9Ev379Uj0003j11Vdxzz33wGKx4Ne//nUgaGhqasKdd96JwYMHo6mpCY8++igKCwtVG4cpAgoiIiJKLcMveRAREVHqMaAgIiKipDGgICIioqQxoCAiIqKkMaAgIiKipDGgICIioqQxoCAiIqKkMaAgIiKipDGgICIioqQxoCAiIqKkMaAgIiKipP1/UrKJ5IScxyEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# correlation tests\n",
    "\n",
    "# https://www.scribbr.com/statistics/correlation-coefficient/\n",
    "\n",
    "# https://online.stat.psu.edu/stat501/lesson/1/1.9\n",
    "\n",
    "n = 100\n",
    "x = np.linspace(0, 10, n)\n",
    "linear = 3 * x + np.random.normal(loc=0, scale=2, size=n)\n",
    "sine = x + 5*np.sin(x) + np.random.normal(loc=0, scale=1, size=n)\n",
    "cloud = np.random.normal(loc=10, scale=5, size=n)\n",
    "plt.scatter(x,linear,label='linear')\n",
    "plt.scatter(x,sine,label='sine')\n",
    "plt.scatter(x,cloud,label='cloud')\n",
    "plt.legend();\n",
    "print('linear', stats.pearsonr(x, linear))\n",
    "print('sine', stats.pearsonr(x, sine))\n",
    "print('cloud', stats.pearsonr(x, cloud))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "4ea5da39",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['HAge', 'HHght', 'WAge', 'WHght', 'HAgeMar']\n",
      "PearsonRResult(statistic=0.9382381733457485, pvalue=6.932617920993003e-79)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from astropy.io import ascii\n",
    "data=ascii.read('data/husbandwife.csv',format='csv')\n",
    "print(data.colnames)\n",
    "plt.scatter(data['HAge'],data['WAge'])\n",
    "plt.plot([10,70],[10,70],color='r') # line of unity\n",
    "plt.xlabel('Husband Age')\n",
    "plt.ylabel('Wife Age');\n",
    "print(stats.pearsonr(data['HAge'],data['WAge']))"
   ]
  }
 ],
 "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": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
