{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bd6616b0",
   "metadata": {},
   "source": [
    "# INF 5060/9060 \n",
    "<div class=\"container\">\n",
    "      <div class=\"text\">\n",
    "        <h1> Quantitative Performance Analysis </h1>\n",
    "      </div>\n",
    "      <div class=\"image\">\n",
    "        <img src=\"https://upload.wikimedia.org/wikipedia/en/thumb/3/31/University_of_Oslo_seal.svg/1200px-University_of_Oslo_seal.svg.png\" width=100>\n",
    "      </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a6495a1",
   "metadata": {},
   "source": [
    "# Requirements/Dependencies\n",
    "Intall these libraries if you haven't already installed them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "32f28ac3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# ! pip install numpy\n",
    "# ! pip install scipy\n",
    "# ! pip install matplotlib\n",
    "# ! pip install seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d92ec897",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import binom, beta, uniform\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "plt.rcParams.update({'font.size': 18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "58ef02bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "## A simple probability class\n",
    "\n",
    "\n",
    "\n",
    "class Probability:\n",
    "    def __init__(self, n_outcomes=2):\n",
    "        self.P = np.ones(n_outcomes) / n_outcomes\n",
    "        self.n_outcomes = n_outcomes\n",
    "            \n",
    "    def get_prob(self, x):\n",
    "        return self.P[x]\n",
    "\n",
    "    def get_sample_space(self):\n",
    "        return range(self.n_outcomes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0dd92878",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample: 28 , probability: 0.01\n",
      "sample: 87 , probability: 0.01\n",
      "sample: 72 , probability: 0.01\n",
      "sample: 32 , probability: 0.01\n",
      "sample: 96 , probability: 0.01\n",
      "sample: 86 , probability: 0.01\n",
      "sample: 62 , probability: 0.01\n",
      "sample: 56 , probability: 0.01\n",
      "sample: 41 , probability: 0.01\n",
      "sample: 98 , probability: 0.01\n"
     ]
    }
   ],
   "source": [
    "P = Probability(n_outcomes = 100)\n",
    "for r in range(10):\n",
    "    r = np.random.randint(100)\n",
    "    print('sample:', r, ', probability:', P.get_prob(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aaf6b532",
   "metadata": {},
   "source": [
    "### Binomial\n",
    "\n",
    "Binom takes n and p as shape parameters, where p is the probability of a single success and n is the number of occurances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "04ad0480",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 2\n",
    "p = 0.5\n",
    "binom_dist = binom(n, p)\n",
    "x = np.arange(n+1)\n",
    "\n",
    "plt.bar(x, binom_dist.pmf(x), color='b', width=0.1)\n",
    "plt.ylabel('Probability')\n",
    "plt.xlabel('x')\n",
    "plt.xticks(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5acf8ea6",
   "metadata": {},
   "source": [
    "## Histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "4010f868",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdf of x is 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "r = norm.rvs(size=10000, loc=100, scale = 20)\n",
    "\n",
    "ax.hist(r, bins='auto', histtype='bar', alpha=0.5)\n",
    "ax.set_title(\"Normally\")\n",
    "\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "sns.set(style=\"whitegrid\")\n",
    "np.random.seed(10)\n",
    "\n",
    "fig, axs=plt.subplots(1, 3, figsize=(15, 6))\n",
    "\n",
    "axs[0].hist(np.random.exponential(scale = 10, size = 10000), color = \"r\")\n",
    "axs[0].set_title(\"Exponentially\")\n",
    "\n",
    "axs[1].hist(np.random.randn(10000), color = \"m\") \n",
    "axs[1].set_title(\"Normally\")\n",
    "\n",
    "axs[2].hist(np.random.poisson(lam = 5, size = 10000), color = \"k\")\n",
    "axs[2].set_title(\"Poisson\")\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29604997",
   "metadata": {},
   "source": [
    "## uniform and normal distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "fe7eee05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm, uniform\n",
    "\n",
    "\n",
    "x = uniform.rvs(0.01,0.99,size=10000)\n",
    "\n",
    "# Probability Density Function\n",
    "\n",
    "plt.plot(x, uniform.pdf(x),\n",
    "       'b-', lw=5, alpha=0.6, label='uniform pdf')\n",
    "\n",
    "plt.ylabel('f(x)')\n",
    "plt.xlabel('x')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Cumulative Distribution Function\n",
    "\n",
    "plt.plot(x, uniform.cdf(x),\n",
    "       'b-', lw=5, alpha=0.6, label='uniform cdf')\n",
    "\n",
    "plt.ylabel('F(x)')\n",
    "plt.xlabel('x')\n",
    "plt.show()\n",
    "\n",
    "#linspace returns evenly spaced numbers over a specified interval\n",
    "x = np.linspace(norm.ppf(0.01), norm.ppf(0.99), 100) \n",
    "#print(x)\n",
    "\n",
    "# Probability Density Function\n",
    "\n",
    "\n",
    "plt.plot(x, norm.pdf(x),\n",
    "       'b-', lw=5, alpha=0.6, label='norm pdf')\n",
    "\n",
    "plt.ylabel('f(x)')\n",
    "plt.xlabel('x')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Cumulative Distribution Function\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x, norm.cdf(x),'b-', lw=5, alpha=0.6, label='norm cdf')\n",
    "plt.ylabel('F(x)')\n",
    "plt.xlabel('x')\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "07cc7d27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'x')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "498bcef1",
   "metadata": {},
   "source": [
    "## Indices of Central Tendency\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f923eb86",
   "metadata": {},
   "source": [
    "### mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "17d74b5c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean:  99.99818016614081\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# mean\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#The location (loc) keyword specifies the mean. The scale (scale) keyword specifies the standard deviation.\n",
    "r = norm.rvs(size=1000000, loc=100, scale = 10)\n",
    "\n",
    "ax.hist(r, bins='auto', histtype='bar', alpha=0.3)\n",
    "r_mean = np.mean(r)\n",
    "print('mean: ', r_mean)\n",
    "plt.vlines(r_mean, 0, 11000,  color= 'r', ls='--')\n",
    "\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "9cff829f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# skewed normal distribution\n",
    "\n",
    "from scipy.stats import skewnorm\n",
    "\n",
    "#rvs(a, loc=0, scale=1, size=1, random_state=None)\n",
    "#skewnorm takes a real number 'a' as a skewness parameter When a = 0 the distribution is identical to a normal distribution\n",
    "\n",
    "r_sk = skewnorm.rvs(10, size=1000000, loc=130, scale = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "784feb4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Value of Sample')"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k4iiBEjmDUC1tICIikUWTyEVERESCpARKREREJEgawhMJA1tCQn2HICIiYaQESiTErNHRXPX7V+o7DBERCSMN4YmIiIgESQmUiIiISJA0hCcSYl6nkx1PzAagy2PTsEZF1XNEIiISakqgRELNNDn638/9j0VEJPJoCE9EREQkSLoCJVID1e2NB9ofT0TkfKUESqQGTt0bD9D+eCIi5zElUCJB0N54IiICmgMlIiIiEjRdgRIJA4uWLhARiWj1fgXq0KFDZGZmkp6eTo8ePbjnnnvYtWuX/3hubi4ZGRl0796dfv36kZOTE3C+z+dj/vz59OnTh27dujFy5Ej27NkTUCcUbYjUlDU6mqvXrOTqNSuxRkfXdzgiIhIG9Z5AjRkzhr1797JkyRJef/11oqOjGT58OGVlZZSUlDBixAjatm3LunXrGDduHNnZ2axbt85//sKFC1m1ahWzZs1i9erVGIbB6NGjcblcACFpQ0RERORk9ZpAlZSUcOGFFzJz5kwuv/xy2rdvz/3338+BAwf48ssvWbNmDQ6HgxkzZtC+fXuGDBnC8OHDWbJkCQAul4tly5Yxbtw4+vbtS2pqKllZWRQVFbFx40aAkLQhIiIicrJ6TaCaN2/OvHnz6NixIwAHDx4kJyeHlJQUOnTowNatW0lLS8Nm+36qVnp6Ort37+bQoUPk5eVx4sQJ0tPT/ccTEhLo0qULW7ZsAQhJGyLB8Llc7HhiNjuemI1PVzFFRCJSg5lE/uijj/qvFi1atIjY2FgKCwvp1KlTQL1WrVoBsH//fgoLCwFo3bp1lToFBQUAIWlDJBimz0fJtn/7H4uISORpMAnUXXfdxdChQ3nttdcYO3YsK1eupLy8HIfDEVAv6ru7m5xOJ2VlZQDV1jly5AhASNqoDdM0KS0tPXvFRq6y/yr/BXC53DidTv96SabXgjfW5i879XljrWO1GLhc0VV+zt7ycv/j0tJSrHVIoqrrXwkt9XH4qY/DT30cGqZpYhhGjeo2mASqQ4cOAMycOZNPPvmEFStWEB0dXWUit9PpBCA2Npbo7+5wcrlc/seVdWJiYgBC0kZtuN1ucnNza31+Y5Ofnw+AxWLBtMawb18Jbo8XgJhoBw5rEvsLinC5PFWeN9Y6dpuVGGsZBwrK8X2XJJmmie+79xfAF198gXFKcl6X/pXwUR+Hn/o4/NTHdXfqBZXTqdcE6tChQ2zatIkf//jHWK1WoOIXcPv27SkuLiYlJYXi4uKAcyqfJycn4/F4/GUXX3xxQJ3U1FSAkLRRG3a73Z8URrKysjLy8/Np27atP+E8fNxNuS/Wf6XGYbOQkNCEC1pb8frMKs8bax271UKrVgmc/MdKTJQVm9fFZ98979y5c52WMqiufyW01Mfhpz4OP/VxaJy8jNLZ1GsCVVxczOTJk0lMTOTqq68GKq7c7Nixg/79+9OyZUtWrVqF1+v1J1ibNm2iXbt2JCYmEh8fT1xcHJs3b/YnP0ePHmXHjh1kZGQAkJaWVuc2asMwDGJjY2t9fmMTExPjf72lrlKioqK+TzRsFqxWq7/s1OeNuY7bCyXHnPh8pn9vvISTfu6xsbEhWQvq5P6V8FAfh5/6OPzUx3VT0+E7qOe78FJTU+nduzePP/44W7duZefOnTz88MMcPXqU4cOHM2TIEI4fP860adPYtWsX69evZ/ny5dx7771AxWW2jIwM5syZw/vvv09eXh4TJ04kJSWFAQMGAISkDZEzqdwfr3KTYRERiXy1ugK1YcMGmjdvTt++fcnNzeWhhx6ioKCAm266iRkzZtR4/NAwDJ5//nnmzp3LhAkTOHbsGL169eLVV1/lggsuAGDp0qXMnj2bwYMHk5SUxJQpUxg8eLC/jfHjx+PxeJg+fTrl5eWkpaWRk5PjjyExMbHObYiIiIicLOgE6pVXXuHZZ59l/Pjx9O3bl8cff5wjR45w++2388Ybb9CiRQseeuihGrcXHx/PjBkzmDFjRrXHu3btyurVq097vtVqJTMzk8zMzNPWCUUbIjVljY7mmjfXnb2iiIg0WkEP4a1Zs4ZRo0YxZswY9u/fzyeffML999/P1KlTmTx5Mu+++2444hQRERFpMIJOoL755huuvfZaAD766CMMw6B///4AXHrppRw6dCi0EYqIiIg0MEEP4bVo0YKDBw8C8OGHH3LppZeSkpICVKx507Jly9BGKNLI+FwudmbNB6DTxPFYNJdORCTiBJ1A9e/fn7lz57Jp0yY+/vhjJk6cCFTMjXrxxRe59dZbQx6kSGNyotTJoX9sAuDg8JHENY0nNtpez1GJiEgoBZ1ATZ06Fa/Xy5YtW/j5z3/OyJEjAVi1ahV9+/ZlwoQJoY5RpNEwgDKn2//8m+ITXBwVrQRKRCTCBJ1AORwOnnjiiSrlb731ln+PORGpoLWhREQiU61XIv/oo4/4xz/+QXFxMZMmTSI3N5fLLruMNm3ahDI+aQSCWblVREQkEgSdQJWVlTF27Fj+8Y9/EBcXx4kTJxg1ahSvvfYaO3bsYMWKFXTs2DEcsUoD5YhuwuHjbkpdpRiAy+2r75BERETCKuhlDObNm8fnn3/Ob3/7W/75z39imhVDFM8++yzJyclkZ2eHPEhp2Fwek71Fx9hTcIxvDpzA5fbWd0giIiJhFXQC9cc//pFJkyaRnp4eMHSTlJTEmDFj2LZtW0gDlMbB6/VpPzgRETlvBD2Ed/To0dPOc2ratCmlpaV1DkqkMTMcUUQ9kYXXZ4Jda0CJiESioK9AdezYkbfffrvaYx988IHmP8l5zzAMDEcUhiMKi8XA6/Vx8HCp/6u03H32RkREpEEL+grUmDFjeOCBBzh8+DDXXXcdhmGwZcsW1q9fz6pVq5g7d2444hRplAzDoMzppeRYKT6ficVicFFynNaFEhFp5IJOoG644Qaee+455s6dy0cffQTA008/TWJiIjNmzOCmm24KeZAijYnP7ca15neYmNhu+xUQhc9nVgzpiYhIRKjVOlCDBg1i0KBBfP311xw+fJiEhAQuvfRSLJagRwRFIo/Pi+/f/6x4fOsv6jcWEREJi1plPG+99RbTpk3j0ksvpWfPnhw+fJghQ4awcePGUMcnIiIi0uAEnUCtX7+eKVOmUFZW5i9LTEzkwgsv5MEHH1QSJSIiIhEv6ARq2bJljBo1innz5vnL2rVrxwsvvMCIESNYuHBhSAMUERERaWiCTqD27t1L7969qz3Wu3dvdu/eXeegRERERBqyoBOoVq1a8dlnn1V7bMeOHTRv3rzOQYmIiIg0ZEHfhfezn/2MRYsW0aRJE2644QZatGjBt99+y3vvvceCBQsYNmxYOOIUERERaTCCTqDuvfdevvrqK2bOnMmsWbP85aZpctNNNzFu3LiQBijS2BiOKKKmP6OtXEREIljQCZTNZmPevHmMGTOGrVu3cuTIEeLj47niiitITU0NR4wijYphGBhx8Rg+M2DDbRERiRy1WkgTKvbE0753IrVTWu4O2BMvNtqu7V1ERBqRoBMon8/H66+/zocffkhZWRk+ny/guGEYLF++PGQBijQ2Prcb94ZVmCbYbrkNiAo4blCRQO0tOq798UREGqmgE6g5c+awbNkyLrzwQlJSUqoMUZim9vuS85zPi/efH1c8HnTr6atpfzwRkUYr6ATqzTffZMSIETz88MPhiEdERESkwQt6HagTJ07Qr1+/MIQiIiIi0jgEnUBdccUV/Pvf/w5HLCIiIiKNQtBDeKNGjSIzMxOPx0O3bt2IiYmpUictLS0kwYmIiIg0REEnUCNGjADgxRdfBAiYRG6aFeve5Obmhig8ERERkYYn6ATqd7/7XTjiEBEREWk0gk6grrzyynDEIRIxDLsDx5SZ+EwTbFrbSUQkEtVqJfJvv/2WnJwc/vGPf3DgwAGWLl3Ke++9R2pqKjfccEOoYxRpVAyLBUuLREyfiWEJ+j4NERFpBIL+dN+7dy8//elPWbNmDcnJyRw6dAiv18vu3bsZP348f/nLX4Jq7/Dhwzz22GNce+219OzZk1/84hds3brVf3zq1Kl07tw54Ovaa6/1H/f5fMyfP58+ffrQrVs3Ro4cyZ49ewK+R25uLhkZGXTv3p1+/fqRk5MTcLwmbYiIiIhUCjqBeuaZZ0hMTOT9999nwYIF/pXH586dS//+/Vm8eHFQ7U2aNIlPP/2UefPm8frrr3PZZZdx991389VXXwHwxRdfcN999/G3v/3N/7Vhwwb/+QsXLmTVqlXMmjWL1atXYxgGo0ePxuVyAVBSUsKIESNo27Yt69atY9y4cWRnZ7Nu3boatyESDNPjwf2H9Xj/uB7T46nvcEREJAyCTqA2bdrE/fffT0JCQpVtXIYOHcqXX35Z47b27NnD3//+d37zm9/Qq1cvLr30UqZNm0ZycjLvvPMOXq+XXbt2cfnll5OUlOT/atGiBQAul4tly5Yxbtw4+vbtS2pqKllZWRQVFbFx40YA1qxZg8PhYMaMGbRv354hQ4YwfPhwlixZUuM2RIJhej14P34P31/fB5+3vsMREZEwqNUEDavVWm25y+WqklSdSfPmzXn55Zf5wQ9+4C8zDAPTNDly5Aj5+fk4nU7at29f7fl5eXmcOHGC9PR0f1lCQgJdunRhy5YtAGzdupW0tDRstu+ne6Wnp7N7924OHTpUozZEREREThb0JPJevXrx8ssv88Mf/pCoqIpd5g3DwOfz8dprr9GzZ88at5WQkEDfvn0Dyv74xz/yv//9j969e7Nz504Mw2D58uV8/PHHWCwW+vbty4QJE4iPj6ewsBCA1q1bB7TRqlUrCgoKACgsLKRTp05VjgPs37+/Rm3UhmmalJaW1vr8xqK8vBwAp9uF12diei14Y204nU7/RrmnlkVqHavFwOWOxuv6ftjO5XTi9Xqr1DFN/GV2qwWn083+4iMBfRsTZcXncQJQVlYWlp+ffN+36uPwUR+Hn/o4NCrXs6yJoBOoyZMn84tf/IIf/ehHXHXVVRiGQU5ODl999RV79uxh5cqVQQdcadu2bfz617/m+uuvp3///syfPx+LxUKbNm1YvHgxe/bs4ZlnnmHnzp0sX77c/0ZxOBwB7URFRXHkSMUvo/Ly8mqPQ8UvsJq0URtut/u8WFDUYrGANYaDxQdwe7zERDtwWJPYX1CE67tE4tSySK1jt1mJtZXjc34/d66gsJCoGGuVOqYJ+/Yd8vdZlM3Dnv0HcX/Xts1m5ZLWCRjeivdnfn5+mH+Soj4OP/Vx+KmP6+7UfOB0gk6gOnXqxLp163jhhRfYvHkzVquVf/zjH6SlpfHMM8/QuXPnoIMFeO+993jooYfo1q0b8+bNA2DcuHEMHz6chIQE//dOSkpi6NChbN++nejoaKBi6LDyMVQkRpVbzERHR1eZDO50VvxVHxsbW6M2asNut9OhQ4dan99YlJeXk/9NMS1bJWGz2nHYLCQkNOGC1lb/lZpTyyK1jtVikJzcFG+5k8p7OFunpJCQ0LRKHdOEMm90QNut3N+3bbUYpKQ0JdpWcYdr27Zt6/R+lNMrKysjPz9ffRxG6uPwUx+Hxq5du2pcN+gEasOGDaSnpzN37txgTz2tFStWMHv2bAYMGMCcOXP82Z9hGP7kqVLlcFxhYaF/2K24uJiLL77YX6e4uJjU1FQAUlJSKC4uDmij8nlycjKe7+6SOlMbtWEYBrGxsbU+v7GJsjuw2R3YbRasVitRUVH+ZODUskitY7UYOOx2vCdNHHdERVVbx4Qztm21GDgcdqIdFQtxxsTEnFfvp/qgPg4/9XH4qY/rJph53EFPIn/qqaf473//G+xpp7Vy5UpmzpzJr371K55//vmAS2eTJ0/m7rvvDqi/fft2ADp06EBqaipxcXFs3rzZf/zo0aPs2LGDXr16ARUbG2/btg2v9/tfaps2baJdu3YkJibWqA0RERGRkwV9BSoxMZGjR4+G5Jvv3r2bJ598kgEDBnDvvfdy6NAh/7Ho6GhuvvlmxowZw6JFixg4cCC7d+/miSee4Oabb/bfmZeRkcGcOXNo0aIFbdq04bnnniMlJYUBAwYAMGTIEJYuXcq0adMYNWoUn332GcuXL+fxxx8HKsY6z9aGSDAMuwPHxOn4fNrKRUQkUgWdQN1xxx088cQTbN68mY4dO9KyZcsqdX72s5/VqK0//elPuN1uNm7cWGXNpcGDB/P000+TnZ3N4sWLWbx4MfHx8QwaNIgJEyb4640fPx6Px8P06dMpLy8nLS2NnJwc/5WsxMREli5dyuzZsxk8eDBJSUlMmTKFwYMH17gNkWAYFguW5Au0lYuISAQLOoF6+umnAXjzzTerPW4YRo0TqPvuu4/77rvvjHVuvPFGbrzxxtMet1qtZGZmkpmZedo6Xbt2ZfXq1XVqQ0RERKRS0AnU+++/H444RCKG6fHg3vgOpgm2G34MRNV3SCIiEmJBJ1Bt2rQJRxwiEcP0evC+/4eKJ/1/VL/BiIhIWASdQC1YsOCsdR544IFaBSMiIiLSGIQ0gYqLi6NVq1ZKoERCyKKJ6CIiDU7QCVReXl6VstLSUrZt28aMGTN49NFHQxKYyPnMMMDr9XH4uBfTGsPh426wuImN1rIIIiINQUj+tI2NjaVPnz6MHTuWZ599NhRNipzXDMOgzOllb9Exvtpbwt6iY5SWu+s7LBER+U5IxwZat27NV199FcomRc5rXq8Pt8eL1+ur71BEROQkQQ/hVcc0TQoKCliyZInu0hMREZGIF3QClZqaetrN9kzT1BCenPcMuwPH2Cl4TbSVi4hIhAo6gRo7dmy1CVRcXBz9+vWjbdu2oYhLpNEyLBYsF7XVVi4iIhEs6ARq3LhxALjdbuz2ir+uS0tLcblcNGvWLKTBiYiIiDREQf957Ha7mT59OnfccYe/7JNPPqF3797Mnj0br9cb0gBFGhvT48Hz0Ua8H2/E9HjqOxwREQmDoBOo7Oxs/vCHPwRsGHzZZZfx8MMP88Ybb7BkyZJQxifS6JheD54/voHv/20AX2j+oLAYBl6vj4OHSwO+tLSBiEj9CHoI79133+Xhhx9m6NCh/rKmTZty5513YrFY+O1vf8t9990X0iBFzneGAWVOLyXHSvH5TAAsFoOLkuO0uKaISD0IOoEqKSnhwgsvrPZYu3btKCoqqnNQIlI9n8/E+10CJSIi9SfoIbz27dvzpz/9qdpjGzdu5JJLLqlzUCIiIiINWdBXoEaOHMnkyZM5fPgwN9xwA4mJiXz77be89957/PnPf+app54KR5wiIiIiDUbQCdTAgQM5duwYCxYs4M9//rO/vHnz5jz66KMBk8tFREREIlGttnL5+c9/ztChQ9m9ezeHDx8mISGBSy+9FIsWDRQREZHzQK0ynrfeeovp06dz6aWX0rNnTw4fPsyQIUPYuHFjqOMTaXQMuwP76AlYRz2orVxERCJU0AnU+vXrmTJlCmVlZf6yxMRELrzwQh588EElUXLeMywWrO07Ybm0k7ZyERGJUEF/ui9btoxRo0Yxb948f1m7du144YUXGDFiBAsXLgxpgCIiIiINTdAJ1N69e+ndu3e1x3r37s3u3bvrHJRIY2Z6PHg2fYR300eY2tpIRCQiBZ1AtWrVis8++6zaYzt27KB58+Z1DkqkMTO9Hjxvrsb39hrwhm8vPMOgyvYu2tpFROTcCPouvJ/97GcsWrSIJk2acMMNN9CiRQv/OlALFixg2LBh4YhTRE5hGEbA9i7a2kVE5NwJOoG69957+eqrr5g5cyazZs3yl5umyU033cS4ceNCGqCInJm2dxEROfeCTqBsNhvz5s1jzJgxbNu2jcOHDxMfH88VV1xBampqOGIUERERaVBqtZAmQMeOHbFYLBw7dozmzZtrDzwRERE5b9QqgXrnnXd45plnOHjwoL+sZcuWTJ48WVu5iIiISMQLOoH64IMPyMzMJD09nUmTJtGyZUuKi4t56623mDp1Ks2aNaNfv35hCFUaKsMw6jsEERGRcyroBGrRokXcdNNNZGVlBZQPGTKEiRMn8tJLLymBimCl5e6AW+XdbjdWmwO03JGfYbNjHz4Gnw+w1nqUXEREGrCg14HauXMngwcPrvbY4MGDycvLq3NQ0nCVlrvZW3ScPQXH2FNwjH3Fx/H66juqhsWwWrGmXo4l9QcYVmt9hyMiImEQ9J/HzZs35/Dhw9UeKykpweFw1DUmaeBOvm3e9PpQjiAiIueboK9AXX311bzwwgvs378/oHzfvn28+OKLXHPNNUG1d/jwYR577DGuvfZaevbsyS9+8Qu2bt3qP56bm0tGRgbdu3enX79+5OTkBJzv8/mYP38+ffr0oVu3bowcOZI9e/YE1AlFGyI1ZXo8eLZuwrdt0zndyqW6lcm1OrmISHgEnUBNmjQJp9PJTTfdxLBhw5g8eTLDhg3jxz/+MWVlZUyePDno9j799FPmzZvH66+/zmWXXcbdd9/NV199RUlJCSNGjKBt27asW7eOcePGkZ2dzbp16/znL1y4kFWrVjFr1ixWr16NYRiMHj0al8sFEJI2RIJhej14Xv893nUrwrqVy6kqVyY/eYh1b9FxJVAiImEQ9BBeUlISb7zxBsuWLWPLli3897//pWnTptx5552MGDGCli1b1ritPXv28Pe//53XXnuNnj17AjBt2jQ+/vhj3nnnHaKjo3E4HMyYMQObzUb79u3Zs2cPS5YsYciQIbhcLpYtW0ZmZiZ9+/YFICsriz59+rBx40YGDhzImjVr6tyGSGOilclFRMKvVrcIJSYmkpmZWedv3rx5c15++WV+8IMf+MsMw8A0TY4cOcJ///tf0tLSsNm+DzM9PZ2XXnqJQ4cOsW/fPk6cOEF6err/eEJCAl26dGHLli0MHDiQrVu31rkNERERkZPV6z3WCQkJ/qs+lf74xz/yv//9j969e5OVlUWnTp0Cjrdq1QqA/fv3U1hYCEDr1q2r1CkoKACgsLCwzm3UhmmalJaW1vr8hsrlcuN0Or+fRI4Xh9XA5Xbj9ZmYXgveWFtgnVPKIrWO1WLgckfjdX0/bOdyOvF6vVXqmCY1atvlrhh+c3rcAe3UNEarxcDlio7I92KolJWVBfwroac+Dj/1cWiYplnjtQ0b1CI127Zt49e//jXXX389/fv356mnnqpyV19UVBRQ8cun8o1SXZ0jR44AUF5eXuc2asPtdpObm1vr8xsii8WCaY1h374S3J6KydEx0Q7iL0zi4MEDuFweYqIdOKxJ7C8owvVdInFqWaTWsdusxNrK8Tm/nztXUFhIVIy1Sh3ThH37DuH2eM/Y9sGDBwA4dOAg8VFG0DHabVaiLaUUecvw+bTexJnk5+fXdwgRT30cfurjuqvpagINJoF67733eOihh+jWrRvz5s0DIDo6uspEbqfTCUBsbCzR0dEAuFwu/+PKOjExMSFrozbsdjsdOnSo9fkN1eHjbsp9sQFXoABatkzCarXhsFlISGjCBa2t/jqnlkVqHavFIDm5Kd5yJ5X3cLZOSSEhoWmVOqYJZd7os7bdsqWP/fsLSExqGdBOTWO0WgxSUprSLM4etvdEY1dWVkZ+fj5t27at0/95OT31cfipj0Nj165dNa5bowTqzTff5Nprr6V58+a1DupMVqxYwezZsxkwYABz5szxZ38pKSkUFxcH1K18npycjMfj8ZddfPHFAXVSU1ND1kZtGIZBbGxsrc9vqEpdpURFRZ00jOQGPDjsdmx2B3abBavVGlDn1LJIrWO1GDjsdry+75cucERFVVvHhBq17bBXJD5RNnutYrRaDBwOe0S+F0MtJiZG/RRm6uPwUx/XTTBbk9VoGYMZM2awe/duAK6//vqQrja+cuVKZs6cya9+9Suef/75gEtnaWlpbNu2De9Ja+ls2rSJdu3akZiYSGpqKnFxcWzevNl//OjRo+zYsYNevXqFrA2RYBg2O/ZfjsL6i7u1lYuISISq0ae7w+HgzTffxOPxsG/fPj755BOOHTt22vppaWk1+ua7d+/mySefZMCAAdx7770cOnTIfyw6OpohQ4awdOlSpk2bxqhRo/jss89Yvnw5jz/+uD+ujIwM5syZQ4sWLWjTpg3PPfccKSkpDBgwACAkbYgEw7BasXbtCT4Twxr0UmsiItII1CiBuv3221m6dClr1qzBMAx/8nGqytnrNZ08/ac//Qm3283GjRvZuHFjwLHBgwfz9NNPs3TpUmbPns3gwYNJSkpiypQpAXvxjR8/Ho/Hw/Tp0ykvLyctLY2cnBz/lazExMQ6tyEiIiJysholUA899BC33HILJSUlDBs2jMceeywkE6Tvu+8+7rvvvjPW6dq1K6tXrz7tcavVSmZm5hnXpQpFGyI1ZXq9eD/7Nz7TxOzao77DERGRMKjxBI2OHTsC8MADD3D99deTnJwctqBEGjPT48a9cmnFk8uer9dYTt4fr1JstJ3YaN2VJyJSF0HPcH3ggQdwuVysWrWKzZs3c/ToUZo3b06vXr0YPHiwf40lEal/lfvjlRwrxeczsVgMLkqOUwIlIlJHQSdQR48eZdiwYeTl5XHBBReQlJTE7t27eeedd3j11VdZuXIl8fHx4YhVRGpJ++OJiIRW0LcIzZ07l8LCQlasWMEHH3zA6tWr+eCDD1ixYgWHDh0iOzs7HHGKiIiINBhBJ1Dvv/8+EyZMqLJGUq9evRg/fjx//vOfQxaciIiISEMUdAJ14sQJLrroomqPXXTRRRw+fLiuMYmIiIg0aEEnUJdeeikffvhhtcfef/99LrnkkjoHJSIiItKQBT2J/O6772bSpEm4XC4GDRpEy5YtOXjwIG+//TZr165lxowZYQhTpPEwrDZst92JaZraykVEJEIF/en+k5/8hPz8fBYvXszatWuBihXIHQ4HY8eOZejQoSEPUqQxMWw2bL2uxqutXEREIlat/jy+//77ycjI4JNPPuHIkSM0bdqUbt260bRp01DHJyIiItLg1Hp8ISEhgWuvvTaUsYhEBNPrxZu3HZ8PzP+7rL7DCVDdyuSg1clFRIKlCRoiIWZ63Lh/u6jiyazn6zWWU526Mjmg1clFRGpBCZTIeUgrk4uI1I1muIqIiIgEKegEavHixXz55ZfhiEVERESkUQg6gVq6dCkFBQXhiEVERESkUQg6gWrbtq2uQImIiMh5LehJ5P369SMrK4sPP/yQjh07kpiYGHDcMAzGjh0bsgBFREREGpqgE6gFCxYAsHXrVrZu3VrluBIoOd8ZVhu2W4ZWLBOgrVxERCJS0J/ueXl54YhDJGIYNhu2q/tqKxcRkQhWpz+Pjx07RnFxMRdddBFWqxWr1RqquETkHKludXKtTC4icma1SqA2b97MnDlz+O9//4thGKxdu5YlS5aQkpLCI488EuoYRRoV0+fD+9VOfKaJ2aFTfYdzVqeuTq6VyUVEzi7o8YVNmzZx9913Ex0dzUMPPYRpVqxm3KVLF373u9/xyiuvhDxIkcbEdLtwL3ke79Js8LjrO5waq1yd3KcVykVEziroBOr555/n+uuv5/e//z133XWXP4G65557GDVqFGvXrg15kCIiIiINSdAJVG5uLkOGDAEqLv2f7JprrmHfvn2hiUxERESkgQo6gYqPj+fAgQPVHisoKCA+Pr7OQYmIiIg0ZEEnUNdffz1ZWVls377dX2YYBoWFhSxevJh+/fqFMj4RERGRBifou/AmT57Mp59+yh133EHLli0BmDRpEoWFhbRu3ZpJkyaFPEgRERGRhiToBKpp06asXbuWDRs28M9//pPDhw8THx/PnXfeya233kpMTEw44hQRERFpMGq1DpTD4eCOO+7gjjvuCHU8Io2eYbVh+/FgfKYJFi0uKyISiWqVQH311VcsWrSITZs2ceTIERITE0lPT2fMmDG0bds2xCGKNC6GzYat74CKrVxs2spFRCQSBZ1Abdq0idGjR9O8eXP69etHYmIiBw4c4KOPPuK9997j1VdfJTU1NRyxisg5UN3WLqDtXUREThZ0ApWVlUVaWhovvfQSDofDX37ixAlGjRrFk08+ye9+97uQBinSmJg+H769+fhMMC++pL7DCdqpW7sA2t5FROQUQY8v5OXlMXz48IDkCaBJkybcc889fPrpp7UOZuHChdx5550BZVOnTqVz584BX9dee63/uM/nY/78+fTp04du3boxcuRI9uzZE9BGbm4uGRkZdO/enX79+pGTkxNwvCZtiNSU6XbhevFZvAufbVRbuZyqcmsXbe8iIlJV0AlU69at2b9/f7XHTpw44V/aIFi//e1vmT9/fpXyL774gvvuu4+//e1v/q8NGzb4jy9cuJBVq1Yxa9YsVq9ejWEYjB49GpfLBUBJSQkjRoygbdu2rFu3jnHjxpGdnc26detq3IaIiIjIyYJOoDIzM3n++ef54x//iNfr9Zdv3ryZefPm8dBDDwXVXlFREaNGjSI7O5t27doFHPN6vezatYvLL7+cpKQk/1eLFi0AcLlcLFu2jHHjxtG3b19SU1PJysqiqKiIjRs3ArBmzRocDgczZsygffv2DBkyhOHDh7NkyZIatyEiIiJyshrNgUpNTQ3Y9840TSZNmoTVaqVZs2YcO3YMl8uF1Wpl9uzZ/PjHP65xAJ9//jlNmzblrbfe4sUXXwzYSy8/Px+n00n79u2rPTcvL48TJ06Qnp7uL0tISKBLly5s2bKFgQMHsnXrVtLS0rDZvn+p6enpvPTSSxw6dIh9+/adtQ0RERGRk9UogRo7dmyVjYNDpX///vTv37/aYzt37sQwDJYvX87HH3+MxWKhb9++TJgwgfj4eAoLC4GKYcWTtWrVioKCAgAKCwvp1KlTleMA+/fvr1EbtWGaJqWlpWev2Mi4XG6cTife7+bEmHhxWA1cbjden4npteCNtQXWOaUsUutYLQYudzRel+f7/nI68Xq9VeqYJjVq2+WumEPl9LgD2jnXr9VqMXC5oiPyPV1WVhbwr4Se+jj81MehYZpmjfOdGiVQ48aNq1NAtfXll19isVho06YNixcvZs+ePTzzzDPs3LmT5cuX+98op05oj4qK4siRIwCUl5dXexwqfoHVpI3acLvd5Obm1vr8hshisWBaY9i3rwS3p2L4NibaQfyFSRw8eACXy0NMtAOHNYn9BUW4vkskTi2L1Dp2m5VYWzk+5/dz5woKC4mKsVapY5qwb98h3B7vGds+eLBi4+5DBw4SH2XU22u126xEW0op8pbh8/lC/t5qCPLz8+s7hIinPg4/9XHdnZoPnE6tFtJ0uVx8/fXXHDt2rNrjaWlptWm2inHjxjF8+HASEhIA6NSpE0lJSQwdOpTt27cTHR3tj6fyMVQkRpVbykRHR1eZDO50OgGIjY2tURu1Ybfb6dChQ63Pb6gOH3dT7osNuAIF0LJlElarDYfNQkJCEy5obfXXObUsUutYLQbJyU3xljupvIezdUoKCQlNq9QxTSjzRp+17ZYtfezfX0BiUsuAds71a7VaDFJSmtIsLvKWMSgrKyM/P5+2bdtqK6owUR+Hn/o4NHbt2lXjurVaSHPy5MmUlJQAFZe7oGLtmMpLX6G68mIYhj95qlQ5HFe5eTFAcXExF198sb9OcXGxfzHPlJQUiouLA9qofJ6cnIzH4zlrG7WNPTY2ttbnN1SlrlKioqJOGv5xAx4cdjs2uwO7zYLVag2oc2pZpNaxWgwcdjs+w8B6/U8wTXDExFZbx4Qate2wVyQsUTZ7vb5Wm9XAarVSetLfIpG2sGZMTExE/p9tSNTH4ac+rptgpisFnUA9+eSTNG/enBkzZtCsWbNgTw/K5MmTOXz4cMC6Tdu3bwegQ4cOXHTRRcTFxbF582Z/8nP06FF27NhBRkYGUHE1bNWqVXi9XqzWin3JNm3aRLt27UhMTCQ+Pv6sbYgEw7DZsA+4OaK2cjl1cU0trCki57ugE6j//e9/ZGVlnXbidyjdfPPNjBkzhkWLFjFw4EB2797NE088wc033+y/My8jI4M5c+bQokUL2rRpw3PPPUdKSgoDBgwAYMiQISxdupRp06YxatQoPvvsM5YvX87jjz8OVIx1nq0NEalQubimiMj5LugEqnPnzv7hu3C77rrryM7OZvHixSxevJj4+HgGDRrEhAkT/HXGjx+Px+Nh+vTplJeXk5aWRk5Ojn8SWGJiIkuXLmX27NkMHjyYpKQkpkyZwuDBg2vchkgwTJ8PX9F+TJ+J2fqC+g5HRETCIOgE6te//jUPPfQQFouFrl27VjtZ7YILavdL4+mnn65SduONN3LjjTee9hyr1UpmZiaZmZmnrdO1a1dWr15dpzZEasp0u3BlzQLAPut5QBM6RUQiTa3vwvv1r3992uORdvu+iIiIyMmCTqBmzJiB1Wpl4sSJJCUlhSMmERERkQYt6ATq66+/Jjs7m+uuuy4c8YiIiIg0eEHfY33JJZdoqXgRERE5rwWdQD344INkZWXx97//nRMnToQjJhEREZEGLeghvLlz53Lw4EFGjRpV7XHDMNixY0edAxORhsswwOv1cfBw4ObCkbY6uYjI6QSdQA0cODAccYhEDMNqw3rtDRXbHFms9R1OWJy6Mjmg1clF5LwSdAL1wAMPhCMOkYhh2GzYf3JrRG3lcjpamVxEzldBJ1D79+8/a53aLqQpIiIi0hgEnUD179//rLsVayFNOZ+ZPh++bw9hmiZmYmJ9hyMiImEQdAL15JNPVkmgSktL2bZtG//85z958sknQxacSGNkul24nn0U0FYuIiKRKugE6tZbb622/Fe/+hXPPPMMb7/9Nv369atrXCIiIiINVkhnuPbr14+//OUvoWxS6llpuZuDh0s5eLiUQ4dLcbl99R2SiIhIvavVZsKn88knn2CzhbRJqWel5W72Fh3H5zOx2Sw0beKo75BERETqXdDZztSpU6uU+Xw+CgoK2Lp1K7fddltIApOGo/JWdYtuVxcREQFqkUBt3ry5SplhGMTFxTF69Gjuu+++kAQmIo1LdauTa2VyEYlUQSdQH3zwQTjiEJFG7tTVybUyuYhEMk1YEgk1ixVr+rWYJmCJ7JXIq6PVyUXkfFCjBKq6eU+nYxiG1oKS85rFbsf+s5+fF1u5iIicr2qUQFU37+lUJSUllJWVKYESERGRiFejBOpM857cbjeLFi3i5ZdfpmXLlsyYMSNUsYk0SqZpYh4/hukzMZsm1Hc4IiISBnWaA5Wbm8sjjzzCzp07GThwII8++ihNmzYNVWwijZLpcuKc9TBQuZVLdL3GIyIioVerBMrj8fDiiy+yZMkSmjVrxoIFC7j++utDHZuINGLVLWsAWtpARCJD0AnUjh07mDp1Kl988QU//elPmT59OgkJGqYQkUCnLmsAaGkDEYkYNU6gPB4PCxYsYOnSpbRo0YJFixZx3XXXhTM2EYkAWtZARCJRjRKozz//nEceeYRdu3bxs5/9jGnTphEXFxfu2EREREQapBolUHfccQc+n4/4+Hj27dvH/ffff9q6hmGwfPnykAUoIiIi0tDUKIHq2bOn/7FpnvlS/NmOi4iIiDR2NUqgfv/734c7DpHIYbFi6ZmOiXlebuUiInI+0F54IiFmsdtx3DFMW7mIiEQwfbqLiIiIBElXoERCzDRNTJezYisXq1YhP1l1i2tqYU0RaYyUQImEmOly4nxsIqCtXE516uKaWlhTRBqrBjWEt3DhQu68886AstzcXDIyMujevTv9+vUjJycn4LjP52P+/Pn06dOHbt26MXLkSPbs2RPyNkQkdCoX1/RpgU0RaaQaTAL129/+lvnz5weUlZSUMGLECNq2bcu6desYN24c2dnZrFu3zl9n4cKFrFq1ilmzZrF69WoMw2D06NG4XK6QtSEiIiJysnpPoIqKihg1ahTZ2dm0a9cu4NiaNWtwOBzMmDGD9u3bM2TIEIYPH86SJUsAcLlcLFu2jHHjxtG3b19SU1PJysqiqKiIjRs3hqwNERERkZPVewL1+eef07RpU9566y26desWcGzr1q2kpaVhs30/VSs9PZ3du3dz6NAh8vLyOHHiBOnp6f7jCQkJdOnShS1btoSsDREREZGT1fsk8v79+9O/f/9qjxUWFtKpU6eAslatWgGwf/9+CgsLAWjdunWVOgUFBSFrozZM06S0tPTsFRs4l8uN0+nE6zMxvRa8sTb/cwATLw6rgcvtPn2dU8oitY7VYuByR+N1eb7vP6cTr9dbpY5pUqO2XW43AE6PO6Cd+n6tIe0zV3S9/l8pKysL+FdCT30cfurj0DBNE8MwalS33hOoMykvL8fhcASURUVFARW/fCrfKNXVOXLkSMjaqA23201ubm6tz28ILBYLpjWGfftKcHu8xEQ7cFiT2F9QhOu7JCEm2kH8hUkcPHgAl8tz2jonl0VqHbvNSqytHJ/z+7lzBYWFRMVYq9QxTdi379AZ+9VhrehXgEMHDhIfZTSY1xqqOlEOO01jTIqKnJimz99vDpuBq/zEOd0aKj8//5x9r/OV+jj81Md1d2o+cDoNOoGKjo6uMpHb6XQCEBsbS3R0xe3hLpfL/7iyTkxMTMjaqA273U6HDh1qfX5Dcfi4m3JfLF6ficNmISGhCRe0tgZcgQJo2TIJq9VWbZ1TyyK1jtVikJzcFK/LzZ4u3TCB1q0vICGhaZU6pgll3uiztt2ypY/9+wtITGoZ0E59v9ZQ1omObcJxlxWvryKBslotpLSMp1ncuVnaoKysjPz8fNq2bVun//Nyeurj8FMfh8auXbtqXLdBJ1ApKSkUFxcHlFU+T05OxuPx+MsuvvjigDqpqakha6M2DMMgNja21uc3FKWuUqKiovD6TOw2C1ar1f8cwPS6AQ8Oux2b3VFtnVPLIrWO1WLgsNsx7Xaih91b7Xn+OlCjth32iiQiymZvUK811HVsNjuGpaKO1WLgcNjP+f+fmJiYiPg/25Cpj8NPfVw3NR2+gwYwifxM0tLS2LZtG16v11+2adMm2rVrR2JiIqmpqcTFxbF582b/8aNHj7Jjxw569eoVsjZERERETtagE6ghQ4Zw/Phxpk2bxq5du1i/fj3Lly/n3nvvBSrGKTMyMpgzZw7vv/8+eXl5TJw4kZSUFAYMGBCyNkRERERO1qCH8BITE1m6dCmzZ89m8ODBJCUlMWXKFAYPHuyvM378eDweD9OnT6e8vJy0tDRycnL8k8BC0YZIMHzOcsofuR8A26zngah6jUdEREKvQSVQTz/9dJWyrl27snr16tOeY7VayczMJDMz87R1QtGGiIiISKUGPYQnIiIi0hApgRIREREJUoMawhMRMQzwen0cPPz96uSx0XZio8/NulAiIjWhBEpEGhTDMChzeik5VorPZ2KxGFyUHKcESkQaFCVQItIg+XymfwFOEZGGRgmUSKgZFiydL8P87rGIiEQeJVAiIWZxOHCMGIvXZ2LYlECJiEQifbqLiIiIBElXoESkQavurjzQnXkiUr+UQImEmM9ZTvmjEwCw/eZZtJVL3Zx6Vx6gO/NEpN4pgRIJB7erviOIOLorT0QaEs2BEhEREQmSEigRERGRIGkIT0QaHW33IiL1TQmUiDQ62u5FROqbEigRabQ0sVxE6osSKJFQMywY7Tp+99io31hERCQslECJhJjF4SDq3onaykVEJILp011EREQkSEqgRERERIKkITyREPM5yymfOQVMsP16FtrKJfy0X56InGtKoETC4cTx+o7gvKL98kTkXFMCJX6l5W5Ky93+5wbgcvvqLyCRIGlZAxE5V5RAiV9puZu9Rcf9f8HbbBaaNnHUc1QiIiINjxIoCXDyX/AW/SUvIiJSLd2FJyIiIhIkJVAiIiIiQdIQnkioGRaMCy8GE23lUo+qW9pAyxqISKgogRIJMYvDQdQDj2grl3p26tIGWtZAREJJCZSIRDQtbSAi4aA/j0VERESCpCtQIiHmczopf3o6ALaHfoO2chERiTxKoERCzoTD337/WBqE0+2XZzV8GJrsLyJBahRDePv27aNz585VvtauXQtAbm4uGRkZdO/enX79+pGTkxNwvs/nY/78+fTp04du3boxcuRI9uzZE1DnbG2ISONWOal8b9Fx9hQcY0/BMfYWHafM6VUCJSJBaxRXoL744guioqJ47733Aj7o4uPjKSkpYcSIEdxwww08/vjjfPLJJzz++OM0a9aMIUOGALBw4UJWrVrFU089RXJyMs899xyjR4/mnXfeweFw1KgNEYkMmlQuIqHQKBKonTt30q5dO1q1alXl2PLly3E4HMyYMQObzUb79u3Zs2cPS5YsYciQIbhcLpYtW0ZmZiZ9+/YFICsriz59+rBx40YGDhzImjVrztiGiEQ2i6VRXIwXkQakUXxqfPHFF3To0KHaY1u3biUtLQ2b7ftcMD09nd27d3Po0CHy8vI4ceIE6enp/uMJCQl06dKFLVu21KgNEYlMhgGmCT5LDIePuzl4uJTScnd9hyUijUCjuQKVlJTEL3/5S/Lz87nkkku4//776dOnD4WFhXTq1CmgfuWVqv3791NYWAhA69atq9QpKCgAOGsbiYmJQcdsmialpaVnr9iAuFxunE6nf3jD9Frwxtr8Zac+BzDx4rAauNzu09epSTsRUMdqMXC5o/G6PN/3qdOJ1+utUsc0qVHbLnfFL3Onxx3QTn2/1oipY7NwoszCnsIjHC63EBsdzUXJ8eDTYpuhVFZWFvCvhJ76ODRM06zxnMgGn0C5XC7y8/OJiYlhypQpxMbG8tZbbzF69GheeeUVysvLcTgcAedERVXcNu50Ov1vpurqHDlyBOCsbdSG2+0mNze3VufWB4vFgmmNYd++EtweLwAx0Q4c1iT2FxThcnmqPK+sE39hEgcPHjhjnZq009jr2G1WYm3l+Jwu3M0TMU2Tw4VFRMVYq9QxTdi37xBuj/eMbR88eACAQwcOEh9lNJjXGml1PB4vBfsLsdus2M3mFHnL8Pl8IfifJSfLz8+v7xAinvq47k7NB06nwSdQDoeDLVu2YLPZ/C/qBz/4AV999RU5OTlER0fjcrkCzqlMemJjY4mOjgYqErHKx5V1YmJiAM7aRm3Y7fbTDjs2VIePuyn3xfr/OnfYLCQkNOGC1la8PrPKc6i4AgXQsmUSVqut2jo1aScS6lgtBsnJTTFNKJ8wHa/P5IIz1CnzRp+17ZYtfezfX0BiUksSEpo2mNcaSXWaNIkGimiV3IrY6GhSUprSLE5XoEKprKyM/Px82rZt6//cldBSH4fGrl27aly3wSdQUH0S06lTJ/72t7+RkpJCcXFxwLHK58nJyXg8Hn/ZxRdfHFAnNTUV4Kxt1IZhGLVOvupLqauUqKgo/y8Xu82C1Wr1l536HMD0ugEPDrsdm91RbZ2atBMJdawWA4fdjgmnPa8mdU5u22Gv+EUeZbM3qNcaaXUAohxRREdHYbVaKQ38e0qbEIdITExMo/tcbGzUx3UTzJImDX4SeV5eHj169GDr1q0B5f/973/p0KEDaWlpbNu2Da/X6z+2adMm2rVrR2JiIqmpqcTFxbF582b/8aNHj7Jjxw569eoFcNY2ROT8cLq1ojSxXERO1eATqE6dOtGxY0cef/xxtm7dyldffcVTTz3FJ598wn333ceQIUM4fvw406ZNY9euXaxfv57ly5dz7733AhVDgBkZGcyZM4f333+fvLw8Jk6cSEpKCgMGDAA4axsiwfA5nTjnzcT9/EzMU4aGpXGoXCvK6zPxac0oEalGgx/Cs1gsLF68mDlz5jBhwgSOHj1Kly5deOWVV+jcuTMAS5cuZfbs2QwePJikpCSmTJnC4MGD/W2MHz8ej8fD9OnTKS8vJy0tjZycHP+cqsTExLO2IVJzJmZxgf+xiIhEngafQAG0aNGCJ5988rTHu3btyurVq0973Gq1kpmZSWZmZq3bEBEREanU4IfwRERERBqaRnEFSkSkvhgGeL0+Dh7+fmFc3ZUnIkqgRETOoPLOvJJjpfh8JhaLwUXJcUqgRM5zSqBERGqg8s48ERFQAiUSBgY0a/H9Y4ko1Q3pgYb1RM43SqBEQswSFUX0I7Pw+kwMm+7TiDSnDukBGtYTOQ8pgRIRqQUN6Ymc3/TnsYiIiEiQdAVKJMR8LhfOBU+DCbb7JwNR9R2ShJmWOhA5/yiBEgk104f5zf++e6whnvOBljoQOf8ogRIRCRHNixI5f2gOlIiIiEiQdAXqPFZa7qa03A1UrFbkcvvqNyCRCKG1okQinxKo81hpuZu9Rcfx+UxsNgtNmzjqOySRiKC1okQinxKo81zlnA2L5m2IhNzJc6J0p55IZFECJRIOTeJAOamcRHfqiUQWJVAiIWaJiib60We1lYtUS3fqiUQGJVAiIvVAE81FGjclUCIi9UATzUUaNyVQIiHmc7lwvpQFgG3UA2grFzkTTTQXaZyUQImEmunD3P3ld48110VqThPNRRoPJVAiIg2MJpqLNHxKoEREGihNNBdpuJRAiYg0UJpoLtJwKYESEWngNNFcpOFRAiUi0oicelXKajVonRjr3xi8kpIqkfBSAiUSDnZtzCzh5d/H0qJhPpH6oARKJMQsUdFEz3xeW7nIOaVhPpFzSwmUiEiE0XpSIuGnBEpEJEJVXpU63XIIVqsFr9fnf66rVCI1pwTqPFFa7g6YZGoALrfv9CdIrflcLlyvvIgJ2Ibdi7ZykfpW3XIINpuFpk0clBxz6iqVSC0ogTpPlJa72Vt0vMqHp4SB6cP3xef+xyINxcnzpCzf/atVz0VqRwnUeaS6D08RETj9quca5hOpnhKo7/h8PhYsWMDatWs5evQoV1xxBb/5zW+45JJL6js0EZGwq8kwX13WnDIMI2yxi9QH3WP9nYULF7Jq1SpmzZrF6tWrMQyD0aNH43K56js0EZFzpvJKtddn+hOpyjLThDKnl71Fx9lTcIw9Bcf4pvg4x044OXi41P91aoIFEBUTx+Hj7jPWEWlMdAUKcLlcLFu2jMzMTPr27QtAVlYWffr0YePGjQwcOLCeIxQRaTgCpgNYzr4yutvtxoudvUXHsNnsWj1dIoISKCAvL48TJ06Qnp7uL0tISKBLly5s2bKlUSZQJ991pzvuRCTczrQyuunzYKVijpVhqb5OdUnVqfOvqitT0iX1xTBN87yfTfznP/+ZcePG8emnnxIdHe0vf/DBBykvL+ell14Kqr1///vfmKaJ3V5//6l9PhOPzwSzYnKoxTC++4vxux+3YWA9uezU5zWtU1ENn1mRqNW6nUiog4HNaoBp4j50sKJK80SsFkvVOoDHe/a2PT4fXo8Xm816SjuNoD8aSR2LAW63B4vFgmGx1Hs8EVmHID4nzFM+t757XtmG5ZQ6Vks1c6uMiv+H3z+tqBPw666aOkYjnqZlmiYejwebzab5ZnXgdrsxDIOePXueta6uQAFlZWUAOByBt/VHRUVx5MiRoNurfPPW55vYajWwWgPLqvthn1pW2zpnOyeU36uh1wGwJiefvU6Nfj4WcNjOUif4GFUnkN1mPWudhhZzY6xztnNq+72qV93n76llkZNoGIZR5XeYBK8ika7Z+0IJFPivOrlcroArUE6nk5iYmKDb69GjR8hiExERkYZHd+EBrVu3BqC4uDigvLi4mJSUlPoISURERBowJVBAamoqcXFxbN682V929OhRduzYQa9eveoxMhEREWmINIRHxdynjIwM5syZQ4sWLWjTpg3PPfccKSkpDBgwoL7DExERkQZGCdR3xo8fj8fjYfr06ZSXl5OWlkZOTo4m5YmIiEgVWsZAREREJEiaAyUiIiISJCVQIiIiIkFSAiUiIiISJCVQIiIiIkFSAiUiIiISJCVQIiIiIkFSAiUiIiISJCVQckYLFy7kzjvvDCh79913GTRoEF27duWGG27g5Zdf5uTlxHw+H/Pnz6dPnz5069aNkSNHsmfPnnMdeqNRXR+fbPr06fTv3z+gTH0cnOr6eOrUqXTu3Dng69prr/UfVx8Hp7o+Li4uZtKkSfTq1YurrrqKyZMn8+233/qPq4+Dc2of33nnnVXew5VfGzZsANTHYWWKnMYrr7xidu7c2czIyPCX/eUvfzG7dOlirlixwvzf//5n/ulPfzK7d+9uvvLKK/46L7zwgnn11Vebf/nLX8zc3Fxz5MiR5oABA0yn01kPr6Jhq66PT7Zx40azU6dO5nXXXRdQrj6uudP18eDBg8158+aZxcXF/q9Dhw75j6uPa666PnY6nebAgQPN2267zfzss8/M//znP+ZNN91kjho1yl9HfVxz1fVxSUlJwPu3uLjYvOeee8ybbrrJPHbsmGma6uNwUgIlVRQWFpp333232b17d/Omm24K+A+7du1aMysrK6D+/fffb44ePdo0zYoPzR49epgrV670Hz9y5IjZtWtX85133jkn8TcGZ+rjSkVFRWZ6erqZkZERkECpj2vmTH3s8XjMyy+/3Ny4cWO156qPa+ZMfbxu3Tqze/fu5oEDB/xlH3/8sXn99debx44dUx/XUE0+Kyq9/fbbZpcuXcy8vDzTNPU+DjcN4UkVn3/+OU2bNuWtt96iW7duAcduu+02JkyYAIDX6+Xjjz/mX//6F9dccw0AeXl5nDhxgvT0dP85CQkJdOnShS1btpyz19DQnamPAUzT5JFHHuGWW27hyiuvDDimPq6ZM/Vxfn4+TqeT9u3bV3uu+rhmztTHf/3rX0lPT6dly5b+sj59+vDee+8RFxenPq6hs31WVCotLeXZZ5/lrrvuonPnzoDex+GmzYSliv79+1eZc3Oq/fv3c8MNN+D1eunduze/+MUvACgsLASgdevWAfVbtWpFQUFBeAJuhM7Wx7/97W85cOAAixcv5qWXXgo4pj6umTP18c6dOzEMg+XLl/Pxxx9jsVjo27cvEyZMID4+Xn1cQ2fq4/z8fHr16sWLL77Ihg0b8Hg89O7dm8zMTBISEtTHNVSTz2OAVatWceLECcaMGeMvUx+Hl65ASa0kJCTw+uuvk52dzRdffMGUKVMAKCsrA8DhcATUj4qKwul0nvM4G6O8vDwWLFjAc889V6UfQX0cCl9++SUWi4U2bdqwePFiHn74YT766CPuv/9+fD6f+jgEjh8/zoYNG/jiiy+YO3cuTzzxBNu2beP+++/HNE31cQh5vV5+//vf88tf/pL4+Hh/ufo4vHQFSmolLi6OLl260KVLF3w+HxMnTiQzM5Po6GgAXC6X/zGA0+kkJiamvsJtNJxOJw899BBjxowhNTW12jrq47obN24cw4cPJyEhAYBOnTqRlJTE0KFD2b59u/o4BOx2O7GxscydOxe73Q5A06ZNuf3229XHIfavf/2L/fv3c8cddwSUq4/DS1egJChbt25l+/btAWUdO3YEKm5ZrrxUXFxcHFCnuLiYlJSUcxNkI/bpp5/y5ZdfsmDBAnr06EGPHj146aWX2L9/Pz169OCtt95SH4eAYRj+5KlSp06dgIphD/Vx3aWkpNCuXTt/8gTff1Z888036uMQeu+99+jatSsXXXRRQLn6OLyUQElQli1bxlNPPRVQ9umnn2Kz2Wjbti2pqanExcWxefNm//GjR4+yY8cOevXqda7DbXS6du3Kn//8Z9588002bNjAhg0b+PnPf06rVq3YsGED/fv3Vx+HwOTJk7n77rsDyir/MOjQoYP6OAR69epFXl4e5eXl/rKdO3cCcMkll6iPQ2jbtm0BE8UrqY/DS0N4EpSRI0cybNgw5s+fzy233MLnn3/Oc889x7Bhw2jevDkAGRkZzJkzhxYtWtCmTRuee+45UlJSGDBgQD1H3/BFR0dzySWXBJQ1bdoUm80WUK4+rpubb76ZMWPGsGjRIgYOHMju3bt54oknuPnmm/135qmP6+bnP/85r776KpMnT+bBBx/k2LFjzJgxg6uuuorLLrsMUB+HgtfrZdeuXVX+IICKuU/q4/BRAiVB6dWrFy+99BLPP/88OTk5tGjRgpEjRzJ69Gh/nfHjx+PxeJg+fTrl5eWkpaWRk5NT7YRoqR31cd1cd911ZGdns3jxYhYvXkx8fDyDBg3yL9EB6uO6atGiBa+++ipPPfUUd9xxBw6HgxtuuIGpU6f666iP6+7w4cO43W6aNWtW7XH1cfgYpnnSHhwiIiIiclaaAyUiIiISJCVQIiIiIkFSAiUiIiISJCVQIiIiIkFSAiUiIiISJCVQIiIiIkFSAiUiIiISJCVQIlJnI0aM4Morr8Tlcp22zi233MLtt99eo/buvPNO7rzzzlCFFxJz5szhqquuonv37mzYsOG09davX8/Pf/5zevbsSbdu3Rg4cCBZWVkcP3783AVbA4888gj9+/ev7zBEGi0lUCJSZ7fddhtHjhzh448/rvZ4Xl4eeXl53Hbbbec4stDYuXMnS5Ys4Uc/+hFLly7l2muvrbbeggULeOyxx+jVqxdZWVksWrSIW265hddee4277roLt9t9jiMXkXDRVi4iUmcDBgygadOmvPXWW9xwww1Vjm/YsIHY2FgGDhxYD9HV3eHDhwEYOHDgaTdhdblcLFmyhJEjRzJp0iR/+Q9/+EMuvfRSxo4dy3vvvcePf/zjcxGyiISZrkCJSJ05HA4GDRrEhx9+yLFjxwKOeb1e3nnnHW666Sbi4uL49ttvefzxx7nuuuv4wQ9+wJVXXsnYsWP55ptvTtt+586deeGFFwLKXnjhBTp37hxQtnXrVjIyMujWrRtXXnklDz/8MN9+++1Z4//DH/7ArbfeSo8ePbjmmmt47LHHOHLkiP/7VA4n3nXXXacd9jp+/Djl5eVUtztW3759mThxIhdddJG/7JtvvmHKlCn07t2byy67jKuvvpopU6ZQUlLir9O/f38WLFjAU089xVVXXUWPHj2YPHkyJ06c4OWXX+baa6/liiuuYNy4cVXOy8rK4qmnnuLKK6/kyiuvJDMzM6BOddauXcvAgQP5wQ9+QL9+/XjhhRfweDxn7T+R85GuQIlISNx2222sWLGC//f//l/AXKe//e1vHDhwgNtuuw3TNLn33ns5cuQIkydPJikpidzcXLKzs3nsscdYtmxZrb//li1bGDFiBOnp6Tz//PMcOXKE7Oxshg0bxuuvv050dHS15y1cuJDs7Gx++ctfMnHiRPbu3Ut2djaffPIJa9as4fbbb6dFixY88cQTPPbYY/To0aPadlq0aEG3bt3IycmhuLiYAQMG0LNnT1q0aIHdbue+++7z1y0rK2PYsGE0b96c3/zmN8THx7Nt2zZefPFFoqKimDlzpr/uK6+8wg9/+EOysrLYvn078+bN4/PPPyc5OZmZM2eye/dunn32WVq2bMlvfvMb/3krV67kkksu4cknn+Tbb79l7ty5fP3116xduxaLperfzi+99BJZWVlkZGQwdepUcnNzeeGFFygoKODJJ5+s7Y9FJGIpgRKRkPi///s/unTpwttvvx2QQL3xxhu0b9+eK664gqKiImJiYnj44Yf9Q2FXXXUV33zzDatWrarT9587dy7t2rXjpZdewmq1Avgnca9bt45f/epXVc45cuQIixYt4vbbbw9IPjp16sSvfvUr1q9fzy9/+Us6dOgAQIcOHejSpctpY5g/fz6ZmZls2LCBDRs2YBgGHTt25IYbbmD48OE0bdoUgPz8fFJSUnj66ae5+OKLAUhPT2f79u3861//CmizSZMmZGVlYbPZ+OEPf8gbb7xBcXExa9euJT4+nr59+/LPf/6Tf//73wHnGYbBK6+8Qnx8PFCR4I0dO5aPP/6Yfv36BdQ9duwYixYtYujQoUyfPh2A3r1706xZM6ZPn86IESPo2LHjWX8GIucTDeGJSMjcdtttbNmyhcLCQqDiF/MHH3zgnzyenJzM7373O3r16sX+/fvZtGkTK1as4N///nedJliXlZXx6aef0rdvX0zTxOPx4PF4uOiii2jfvj1///vfqz3vk08+weVyMWjQoIDyXr160aZNGzZv3hxUHCkpKfz+97/n3Xff5eGHH6Zv377s27ePhQsX8pOf/IT8/HygItlcuXIlF154IXv37uWvf/0ry5Yt4+uvv67SD127dsVm+/5v3aSkJC699FJ/YgTQrFmzKkOn1113XUCd/v37Y7fb2bp1a5W4//Of/1BWVkb//v39fefxePzDlafrP5Hzma5AiUjIDBo0iGeeeYZ33nmHUaNG8Yc//AGfz8ctt9zir/PWW28xb948CgoKaNasGampqacdXqupo0eP4vP5WLJkCUuWLKlyPCoqqtrzKuc5tWzZssqxli1bVklKaqpDhw506NCBkSNH4na7Wb9+PU888QTz5s1j/vz5QMXQ3EsvvURJSQktW7bksssuIyYmpsr3jIuLq9J+TEzMWWNo1apVwHOLxUKzZs04evRolbqVk+TvueeeatsqLi4+6/cTOd8ogRKRkElISGDAgAG8/fbbjBo1ig0bNtC/f38SExOBikneDz/8MBkZGdx9992kpKQA8Oyzz7Jt27Yztu31egOel5aW+h83adIEwzAYPnx4tXf6nS7hqBxSO3jwIO3btw84duDAgYBJ32ezfPlyFi1axIcffhjw/ex2O0OHDuWjjz5i165dALz99ts8/fTTTJ48mdtuu40WLVoA8OCDD7J9+/Yaf88zqUyKKnm9XkpKSvzf62QJCQlAxVpXbdu2rXK8ugRT5HynITwRCanbbruNvLw8/vWvf/Gf//wnYO2n//znP/h8PsaPH+9PnrxeL//4xz8A8Pl81bYZFxfnHxasdPKcn7i4OLp06cLXX3/N5Zdf7v/q2LEjCxYsOO1QXLdu3XA4HLz99tsB5Vu3bmX//v307Nmzxq+7Q4cOlJSU8Pvf/77KMa/Xy969e+nUqRMA27ZtIz4+nnvuucef0Jw4cYJt27adtg+C9de//jVgYdP3338fj8fD1VdfXaVut27dsNvtFBUVBfSf3W5n7ty5Z7xDUuR8pStQIhJS6enpXHjhhTz66KOkpKTQu3dv/7GuXbsC8MQTTzBkyBCOHj3KihUryMvLAyquKlU3ZNWvXz/effddunbtSrt27XjjjTfYs2dPQJ1JkyZxzz33MHnyZH7605/i9XpZtmwZn376KWPGjKk21mbNmnHPPfewYMEC7HY7119/Pd988w3Z2dl06NCBW2+9tcav+5prruHmm29m3rx5fPHFF9x44420aNGCwsJCVq1aRWFhIc8//7y/H1577TWefvpprrvuOoqLi8nJyeHgwYP+q2J1VVhYyJgxYxg2bBgFBQXMmzeP3r17c9VVV1Wp27x5c0aNGkV2djbHjx/nqquuoqioiOzsbAzDIDU1NSQxiUQSJVAiElKGYXDrrbcyf/58xo4dG3DL/FVXXcVjjz3GK6+8wv/7f/+Pli1bctVVV7FgwQLGjh3Ltm3b6Nu3b5U2p06disfj4bnnnsNms/GTn/yEyZMn++8Yg4q7xnJycliwYAHjx4/Hbrdz2WWX8corr9C9e/fTxjtu3DhatmzJihUrWLt2Lc2aNeOmm25iwoQJNZprdLLnnnuOq666ijfffJPp06dTWlpKixYtuOaaa3jqqaf8Q4KDBw/mm2++Yd26daxcuZLk5GT69u3LL3/5Sx599FF27drlv/OvtgYOHEhCQgITJkwgNjaWwYMHM3HixNPWnzBhAklJSaxcuZKlS5fStGlTrr76aiZNmhQwGV1EKhhmdau+iYhIo9W/f3+uvPJKnn766foORSRiaQ6UiIiISJCUQImIiIgESUN4IiIiIkHSFSgRERGRICmBEhEREQmSEigRERGRICmBEhEREQmSEigRERGRICmBEhEREQmSEigRERGRICmBEhEREQmSEigRERGRIP1/ZcFTb3tqsUIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "heights,bins = np.histogram(r_sk,bins=100)\n",
    "plt.bar(bins[:-1],heights,width=(max(bins) - min(bins))/len(bins), alpha=0.3)\n",
    "\n",
    "r_sk_mean = np.mean(r_sk)\n",
    "plt.vlines(r_sk_mean, 0, heights.max(), color= 'r', ls='--')\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83bd3870",
   "metadata": {},
   "source": [
    "### median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "5ad1a37b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# median\n",
    "\n",
    "plt.bar(bins[:-1],heights,width=(max(bins) - min(bins))/len(bins), alpha=0.3)\n",
    "\n",
    "r_sk_median = np.median(r_sk)\n",
    "plt.vlines(r_sk_mean, 0, heights.max(),  color= 'r', ls='--')\n",
    "plt.vlines(r_sk_median, 0, heights.max(),  color= 'k', ls='-')\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40fe2f64",
   "metadata": {},
   "source": [
    "### mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "13cc8500",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mode is 132.319\n"
     ]
    }
   ],
   "source": [
    "mode_index = heights.argmax()\n",
    "r_sk_mode = bins[mode_index]\n",
    "print('mode is %.3f' % r_sk_mode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "a6d83594",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(bins[:-1], heights, width=(max(bins) - min(bins))/len(bins), alpha=0.3)\n",
    "\n",
    "\n",
    "plt.vlines(r_sk_mean, 0, heights.max(),  color= 'r', ls='--')\n",
    "plt.vlines(r_sk_median, 0, heights.max(),  color= 'k', ls='-')\n",
    "plt.vlines(r_sk_mode, 0, heights.max(),  color= 'b', ls='-.')\n",
    "\n",
    "plt.text(140, heights.max() - 1500, 'mean', color='r', rotation = 10)\n",
    "plt.text(135, heights.max() + 700, 'median', color='k', rotation = 10)\n",
    "plt.text(127, heights.max() + 1000, 'mode', color='b', rotation = 10)\n",
    "\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.ylim(0, heights.max() + 6000)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "4596a4f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_hist = plt.hist(r, bins='auto', histtype='bar', alpha=0.3)\n",
    "\n",
    "r_max_height = 11000\n",
    "\n",
    "r_median = np.median(r)\n",
    "\n",
    "# mode\n",
    "r_heights = r_hist[0]\n",
    "r_bins = r_hist[1]\n",
    "r_mode = r_bins[r_heights.argmax()]\n",
    "\n",
    "plt.vlines(r_mean, 0, r_max_height,  color= 'r', ls='--')\n",
    "plt.vlines(r_median, 0, r_max_height,  color= 'k', ls='-')\n",
    "plt.vlines(r_mode, 0, r_max_height,  color= 'b', ls='-.')\n",
    "\n",
    "plt.text(r_mean - 8, r_max_height + 2500, 'mean', color='r')\n",
    "plt.text(r_mean - 8, r_max_height + 1250, 'median', color='k')\n",
    "plt.text(r_mean - 8, r_max_height+ 100, 'mode', color='b')\n",
    "\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.ylim(0, r_max_height + 3500)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "2af49589",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_lsk = skewnorm.rvs(-100, size=1000000, loc=130, scale = 10)\n",
    "\n",
    "\n",
    "lsk_heights, lsk_bins = np.histogram(r_lsk,bins=100)\n",
    "plt.bar(lsk_bins[:-1],lsk_heights, width=(max(lsk_bins) - min(lsk_bins))/len(lsk_bins), alpha=0.3)\n",
    "\n",
    "r_lsk_mean = np.mean(r_lsk)\n",
    "r_lsk_median = np.median(r_lsk)\n",
    "\n",
    "r_lsk_mode = lsk_bins[lsk_heights.argmax()]\n",
    "\n",
    "plt.vlines(r_lsk_mean, 0, lsk_heights.max(),  color= 'r', ls='--')\n",
    "plt.vlines(r_lsk_median, 0, lsk_heights.max(),  color= 'k', ls='-')\n",
    "plt.vlines(r_lsk_mode, 0, lsk_heights.max(),  color= 'b', ls='-.')\n",
    "\n",
    "plt.text(112, lsk_heights.max() - 2000, 'mean', color='r', rotation = 10)\n",
    "plt.text(115, lsk_heights.max() + 1500, 'median', color='k', rotation = 10)\n",
    "plt.text(123, lsk_heights.max() + 1000, 'mode', color='b', rotation = 10)\n",
    "\n",
    "\n",
    "\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.ylim(0, heights.max() + 7500)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "402dbdad",
   "metadata": {},
   "outputs": [],
   "source": [
    "r2 = norm.rvs(size=1000000, loc=190, scale = 10)\n",
    "bimodal_r = np.append(r, r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "e1db028f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rb_hist = plt.hist(bimodal_r, bins='auto', histtype='bar', alpha=0.3)\n",
    "\n",
    "rb_mean = np.mean(bimodal_r)\n",
    "rb_median = np.median(bimodal_r)\n",
    "\n",
    "# mode\n",
    "rb_heights = rb_hist[0]\n",
    "rb_bins = rb_hist[1]\n",
    "rb_mode = rb_bins[rb_heights.argmax()]\n",
    "rb_mode2 = rb_bins[np.argsort(rb_heights)[-2]]\n",
    "\n",
    "\n",
    "\n",
    "rb_max_height = rb_heights.max()\n",
    "\n",
    "plt.vlines(rb_mean, 0, 1000,  color= 'r', ls='--')\n",
    "plt.vlines(rb_median, 0, 1000,  color= 'k', ls='-')\n",
    "plt.vlines(rb_mode, 0, rb_max_height,  color= 'b', ls='-.')\n",
    "plt.vlines(rb_mode2, 0, rb_max_height,  color= 'b', ls='-.')\n",
    "\n",
    "plt.text(rb_mean - 15, 20000, 'mean', color='r')\n",
    "plt.text(rb_mean - 15, 15000, 'median', color='k')\n",
    "plt.text(rb_mean - 15, rb_max_height+ 100, 'modes', color='b')\n",
    "\n",
    "\n",
    "plt.ylabel('Number of occurences')\n",
    "plt.xlabel('Value of Sample')\n",
    "plt.ylim(0, rb_max_height + 3500)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95b520a4",
   "metadata": {},
   "source": [
    "### geometric mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "c3c6189f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13072506625797775"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import gmean\n",
    "\n",
    "gmean([1.18, 1.13, 1.11, 1.08, 1.1, 1.28, 1.05]) - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d93515ae",
   "metadata": {},
   "source": [
    "## Indices of Dispersion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "f8003ce7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[33.4514179  43.2740947  49.97405024 56.71080888 66.42708213]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate some example data\n",
    "np.random.seed(42)\n",
    "\n",
    "\n",
    "data = np.random.normal(loc=50, scale=10, size=10000)\n",
    "#data = skewnorm.rvs(100, size=10000, loc=50, scale = 10)\n",
    "\n",
    "# Define percentiles\n",
    "percentiles = [5, 25, 50, 75, 95]\n",
    "\n",
    "# Calculate percentiles\n",
    "percentile_values = np.percentile(data, percentiles)\n",
    "print(percentile_values)\n",
    "\n",
    "# Create a histogram\n",
    "plt.hist(data, bins=100, density=True, alpha=0.7, color='blue', label='Data')\n",
    "\n",
    "# Plot vertical lines at the percentiles\n",
    "for percentile in percentile_values:\n",
    "    plt.axvline(x=percentile, color='red', linestyle='--')\n",
    "\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Percentiles Illustration')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e9c580f",
   "metadata": {},
   "source": [
    "### range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "cb103e6e",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range: 99.25\n"
     ]
    }
   ],
   "source": [
    "range = np.max(r) - np.min(r)\n",
    "print('range: %.2f' % range)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c57a6dbd",
   "metadata": {},
   "source": [
    "### variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "9a88cac9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.94666782686112"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97a26d07",
   "metadata": {},
   "source": [
    "### standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "724f9715",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.99733303570813"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9f8eac6",
   "metadata": {},
   "source": [
    "### Coefficient of Variation (C.O.V. )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "65037e4d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Variation: 0.10\n"
     ]
    }
   ],
   "source": [
    "cv = np.std(r) / np.mean(r)\n",
    "print('Coefficient of Variation: %.2f' % cv)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4f831ea",
   "metadata": {},
   "source": [
    "### Mean Absolute Deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "fd4cc26f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mad(x):\n",
    "    return np.mean(np.absolute(x - np.mean(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "8301b763",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Deviation: 7.96\n"
     ]
    }
   ],
   "source": [
    "print('Mean Absolute Deviation: %.2f' % mad(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efea5c66",
   "metadata": {},
   "source": [
    "### percentiles\n",
    "\n",
    "<img src='https://online-learning-college.com/wp-content/uploads/2022/04/Interquartile-range-scaled.jpg'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "941e8cd4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10- and 90-percentile: 87.19, 112.78\n",
      "(Semi-)interquartile range (SIQR): 6.73\n",
      "\n",
      "median: The 50-percentile: 99.99, or .5-quantile: 99.99\n"
     ]
    }
   ],
   "source": [
    "r_p10 = np.percentile(r, 10)\n",
    "r_p90 = np.percentile(r, 90)\n",
    "\n",
    "print('10- and 90-percentile: %.2f, %.2f' % (r_p10, r_p90))\n",
    "\n",
    "r_Q1 = np.percentile(r, 25)\n",
    "r_Q2 = np.percentile(r, 50)\n",
    "r_Q3 = np.percentile(r, 75)\n",
    "\n",
    "print('(Semi-)interquartile range (SIQR): %.2f' % ((r_Q3 - r_Q1) / 2))\n",
    "\n",
    "r_q50 = np.quantile(r, 0.5)\n",
    "\n",
    "print()\n",
    "print('median: The 50-percentile: %.2f, or .5-quantile: %.2f' % (r_Q2, r_q50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "71d38988",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "a0beccd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'x')"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cumulative Distribution Function\n",
    "\n",
    "sns.ecdfplot(r, lw=5, alpha=0.6)\n",
    "\n",
    "\n",
    "plt.hlines(0.5, 80, r_median,  color= 'k', ls='-')\n",
    "plt.vlines(r_median, 0, 0.5,  color= 'k', ls='-')\n",
    "\n",
    "plt.hlines(0.25, 80, r_Q1,  color= 'k', ls='-')\n",
    "plt.vlines(r_Q1, 0, 0.25,  color= 'k', ls='-')\n",
    "\n",
    "plt.hlines(0.75, 80, r_Q3,  color= 'k', ls='-')\n",
    "plt.vlines(r_Q3, 0, 0.75,  color= 'k', ls='-')\n",
    "\n",
    "plt.ylabel('F(x)')\n",
    "plt.xlabel('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5b9674",
   "metadata": {},
   "source": [
    "### PDF and CDF of Normal Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "a023c355",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The location (loc) keyword specifies the mean. The scale (scale) keyword specifies the standard deviation.\n",
    "\n",
    "ax = plt.figure(figsize=(7, 5))\n",
    "\n",
    "x = np.linspace(norm.ppf(0.00001),\n",
    "                norm.ppf(0.99999), 1000)\n",
    "\n",
    "plt.plot(x, norm.pdf(x, loc=1, scale = 0.44), label = '$\\mu=0, \\sigma^{2}=0.2$')\n",
    "plt.plot(x, norm.pdf(x, loc=0, scale = 1), label = '$\\mu= 0, \\sigma^{2}=1.0$')\n",
    "plt.plot(x, norm.pdf(x, loc=0, scale = 2.24), label = '$\\mu=0, \\sigma^{2}=5.0$')\n",
    "plt.plot(x, norm.pdf(x, loc=-2, scale = 0.7), label = '$\\mu=-2, \\sigma^{2}=0.5$')\n",
    "plt.xlim(-5, 5)\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$\\phi_{\\mu,\\sigma^{2}}(x)$')\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "89d8b46c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The location (loc) keyword specifies the mean. The scale (scale) keyword specifies the standard deviation.\n",
    "\n",
    "ax = plt.figure(figsize=(7, 5))\n",
    "\n",
    "x = np.linspace(norm.ppf(0.00001),\n",
    "                norm.ppf(0.99999), 1000)\n",
    "\n",
    "plt.plot(x, norm.cdf(x, loc=0, scale = 0.44), label = '$\\mu=0, \\sigma^{2}=0.2$')\n",
    "plt.plot(x, norm.cdf(x, loc=0, scale = 1), label = '$\\mu= 0, \\sigma^{2}=1.0$')\n",
    "plt.plot(x, norm.cdf(x, loc=0, scale = 2.24), label = '$\\mu=0, \\sigma^{2}=5.0$')\n",
    "plt.plot(x, norm.cdf(x, loc=-2, scale = 0.7), label = '$\\mu=-2, \\sigma^{2}=0.5$')\n",
    "plt.xlim(-5, 5)\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$\\phi_{\\mu,\\sigma^{2}}(x)$')\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f8863ad",
   "metadata": {},
   "source": [
    "# Comparing Systems\n",
    "\n",
    "### Confidence Interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "f0a33098",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "def mean_confidence_interval(data, confidence=0.95):\n",
    "    return stats.t.interval(0.95, len(data)-1, loc=np.mean(data), scale=stats.sem(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "9fdb5177",
   "metadata": {},
   "outputs": [],
   "source": [
    "r3 = norm.rvs(size=1000, loc=0, scale = 1)\n",
    "\n",
    "r_ci = mean_confidence_interval(r3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ffd694a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x110a5cdd0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 5))\n",
    "plt.hist(r3, bins='auto', histtype='step', alpha=0.8)\n",
    "\n",
    "# plt.vlines(r_ci[0], 0, r_max_height)\n",
    "# plt.vlines(r_ci[1], 0, r_max_height)\n",
    "plt.fill_betweenx(np.arange(0,120), x1=r_ci[0], x2=r_ci[1], color='b', label='Confidence Interval')\n",
    "plt.legend(loc='upper right', fontsize=14)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b0a8629f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
