Miniprojet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a82d14c7",
   "metadata": {},
   "source": [
    "# Mini projet"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c65ce831",
   "metadata": {},
   "source": [
    "## Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8e241931",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math \n",
    "import numpy as np \n",
    "from sklearn import linear_model \n",
    "from os import mkdir \n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cc74674",
   "metadata": {},
   "source": [
    "# Exercice 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd8475e5",
   "metadata": {},
   "source": [
    "## Question 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "002a4676",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Date', 'Location', 'Cost (millions 2013US$)', 'INES',\n",
      "       'Smyth Magnitude', 'Region', 'Description', 'Fatalities'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv('/Users/jeanlucas/Documents/Telecom/2A/MDI/MDI220/Miniprojet/NuclearPowerAccidents2016.csv')\n",
    "print(df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bdcba040",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     1986-04-26\n",
      "1     2011-03-11\n",
      "2     1995-12-08\n",
      "3     1979-03-28\n",
      "4     1957-09-11\n",
      "         ...    \n",
      "211   1997-11-03\n",
      "212   1996-05-15\n",
      "213   1978-03-11\n",
      "214   1990-09-25\n",
      "215   1992-08-02\n",
      "Name: Date, Length: 216, dtype: datetime64[ns]\n"
     ]
    }
   ],
   "source": [
    "df['Date']=pd.to_datetime(df['Date'])\n",
    "#df['Date'].rename(columns={'Cost (millions 2013US$)': 'Cost'})\n",
    "print(df['Date'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a4d22a69",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(175, 9)\n",
      "(175, 10)\n",
      "False    120\n",
      "True      55\n",
      "dtype: int64\n",
      "(175,)\n",
      "(55,)\n"
     ]
    }
   ],
   "source": [
    "date0=pd.to_datetime(pd.DataFrame(['03/28/1979'])[0])\n",
    "\n",
    "\n",
    "print(df.shape)\n",
    "df = df.dropna(subset=['Cost (millions 2013US$)']).reset_index()\n",
    "print(df.shape)\n",
    "\n",
    "n,m=df.shape\n",
    "date1= [date0 for k in range(n)]\n",
    "date1= pd.DataFrame(date1,index=[k for k in range(n)])\n",
    "\n",
    "\n",
    "s= df['Date']<date1[0]\n",
    "print(s.value_counts())\n",
    "\n",
    "costs = df['Cost (millions 2013US$)']\n",
    "print(costs.shape)\n",
    "costs_filtered= costs[s]\n",
    "print(costs_filtered.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4d11510b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4      8189.0\n",
      "5      4400.0\n",
      "6      3500.0\n",
      "7      2900.0\n",
      "8      2500.0\n",
      "10     1964.5\n",
      "11     1900.0\n",
      "12     1733.4\n",
      "13     1500.0\n",
      "14     1330.0\n",
      "15     1300.0\n",
      "17     1100.0\n",
      "18     1100.0\n",
      "21      990.0\n",
      "24      800.0\n",
      "25      793.9\n",
      "26      788.4\n",
      "29      541.4\n",
      "30      511.5\n",
      "33      425.2\n",
      "38      277.1\n",
      "41      180.0\n",
      "44      150.0\n",
      "52      100.0\n",
      "53      100.0\n",
      "54       99.5\n",
      "55       98.0\n",
      "56       89.9\n",
      "58       87.7\n",
      "60       84.5\n",
      "62       77.0\n",
      "70       60.1\n",
      "73       52.4\n",
      "86       38.0\n",
      "87       37.5\n",
      "95       25.7\n",
      "96       25.7\n",
      "101      17.1\n",
      "103      16.1\n",
      "106      15.0\n",
      "108      13.9\n",
      "115      11.8\n",
      "121      11.4\n",
      "130       6.1\n",
      "135       4.4\n",
      "157       1.2\n",
      "158       1.1\n",
      "161       0.0\n",
      "162       0.0\n",
      "163       0.0\n",
      "164       0.0\n",
      "165       0.0\n",
      "166       0.0\n",
      "167       0.0\n",
      "168       0.0\n",
      "Name: Cost (millions 2013US$), dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(costs_filtered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "54034ac6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    index  Cost (millions 2013US$)\n",
      "0       4                   8189.0\n",
      "1       5                   4400.0\n",
      "2       6                   3500.0\n",
      "3       7                   2900.0\n",
      "4       8                   2500.0\n",
      "5      10                   1964.5\n",
      "6      11                   1900.0\n",
      "7      12                   1733.4\n",
      "8      13                   1500.0\n",
      "9      14                   1330.0\n",
      "10     15                   1300.0\n",
      "11     17                   1100.0\n",
      "12     18                   1100.0\n",
      "13     21                    990.0\n",
      "14     24                    800.0\n",
      "15     25                    793.9\n",
      "16     26                    788.4\n",
      "17     29                    541.4\n",
      "18     30                    511.5\n",
      "19     33                    425.2\n",
      "20     38                    277.1\n",
      "21     41                    180.0\n",
      "22     44                    150.0\n",
      "23     52                    100.0\n",
      "24     53                    100.0\n",
      "25     54                     99.5\n",
      "26     55                     98.0\n",
      "27     56                     89.9\n",
      "28     58                     87.7\n",
      "29     60                     84.5\n",
      "30     62                     77.0\n",
      "31     70                     60.1\n",
      "32     73                     52.4\n",
      "33     86                     38.0\n",
      "34     87                     37.5\n",
      "35     95                     25.7\n",
      "36     96                     25.7\n",
      "37    101                     17.1\n",
      "38    103                     16.1\n",
      "39    106                     15.0\n",
      "40    108                     13.9\n",
      "41    115                     11.8\n",
      "42    121                     11.4\n",
      "43    130                      6.1\n",
      "44    135                      4.4\n",
      "45    157                      1.2\n",
      "46    158                      1.1\n",
      "47    161                      0.0\n",
      "48    162                      0.0\n",
      "49    163                      0.0\n",
      "50    164                      0.0\n",
      "51    165                      0.0\n",
      "52    166                      0.0\n",
      "53    167                      0.0\n",
      "54    168                      0.0\n"
     ]
    }
   ],
   "source": [
    "print(costs_filtered.reset_index())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c66faf7b",
   "metadata": {},
   "source": [
    "## Question 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b135e46",
   "metadata": {},
   "source": [
    "![](images/ex1-2a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "f1364c98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (18,12)\n",
    "\n",
    "x = plt.subplot(224)\n",
    "data = costs_filtered\n",
    "res = scipy.stats.probplot(data, plot=plt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d452613",
   "metadata": {},
   "source": [
    "## Question 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4683aa67",
   "metadata": {},
   "source": [
    "![](images/ex1-3a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "6d77c128",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = plt.subplot(224)\n",
    "data = costs_filtered\n",
    "res = scipy.stats.probplot(data, plot=plt,dist=scipy.stats.expon)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cce494f",
   "metadata": {},
   "source": [
    "C'est clairement la loi exponentielle qui se rapproche le plus de notre cas, on remarque cependant des écarts de plus en plus grand avec la théorie pour des valeurs théorique des quantiles assez grandes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "403a2177",
   "metadata": {},
   "source": [
    "# Exercice 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a7c0458",
   "metadata": {},
   "source": [
    "## Question 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "748ee49e",
   "metadata": {},
   "source": [
    "![](images/ex2-1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "f1ca4aeb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda is equal to 0.0013767725947156965\n"
     ]
    }
   ],
   "source": [
    "print(\"lambda is equal to\", 1/costs_filtered.values.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b0ab876",
   "metadata": {},
   "source": [
    "## Question 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "e0d2558a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambd = 1/np.mean(costs_filtered)\n",
    "x=np.arange(0,8000,8000/len(costs_filtered))\n",
    "L = [lambd * np.exp(-lambd*k) for k in x]\n",
    "plt.clf()\n",
    "plt.hist(costs_filtered, density=  True)\n",
    "plt.plot(x,L)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b6aa819",
   "metadata": {},
   "source": [
    "## Question 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cd603d1",
   "metadata": {},
   "source": [
    "![](images/ex2-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51219e59",
   "metadata": {},
   "source": [
    "## Question 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "39d1d0c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0013767725947156967"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#g1(lambda) vaut:\n",
    "1/np.mean(costs_filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75f07d16",
   "metadata": {},
   "source": [
    "## Question 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65e220ab",
   "metadata": {},
   "source": [
    "![](images/ex2-5-part1.png)\n",
    "![](images/ex2-5-part2.png)\n",
    "![](images/ex2-5-part3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd74803e",
   "metadata": {},
   "source": [
    "## Question 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "1f7c0ad4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "503.45800259270857\n",
      "89.9\n"
     ]
    }
   ],
   "source": [
    "#L'estimateur vaut:\n",
    "print(np.log(2)*np.mean(costs_filtered))\n",
    "\n",
    "#médiane empirique:\n",
    "\n",
    "costs_sorted = costs_filtered.tolist().sort()\n",
    "print(sorted(costs_filtered.tolist())[len(costs_filtered)//2])\n",
    "#print(costs_sorted[len(costs_sorted)//2])\n",
    "\n",
    "# --> on observe une différence conséquente liée aux limites du modèle employé"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e80fe8d",
   "metadata": {},
   "source": [
    "## Question 7"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d4e9f92",
   "metadata": {},
   "source": [
    "![](images/ex2-7.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d8ceef6",
   "metadata": {},
   "source": [
    "# Exercice 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379b657c",
   "metadata": {},
   "source": [
    "### Question 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7671eb13",
   "metadata": {},
   "source": [
    "![](images/ex3-1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44f20727",
   "metadata": {},
   "source": [
    "### Question 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70f25e61",
   "metadata": {},
   "source": [
    "![](images/ex3-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36755feb",
   "metadata": {},
   "source": [
    "### Question 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "851180a9",
   "metadata": {},
   "source": [
    "![](images/ex3-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22395d89",
   "metadata": {},
   "source": [
    "### Question 3: suite et code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "8e50d5ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha=0.05\n",
    "n=len(x)\n",
    "lambd = np.arange(0,1,1/1000)[1:]\n",
    "F=[]\n",
    "\n",
    "for l in lambd:\n",
    "    add = sum([-np.exp((alpha-1)/l)*(1-alpha)**k/(l**(k)*np.math.factorial(k)) for k in range(n)])+1\n",
    "    F.append(add)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "063435c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "plt.plot(F)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "4dca5014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Costs ( 39948.49999999999 ) are lower than the quantile of the experimental values ( 67383.01326778876 ) so H0 is accepted\n",
      "\n",
      " Finally, the p-value is:  0.9862825135767351\n"
     ]
    }
   ],
   "source": [
    "lam0 = 10**(-3)\n",
    "exp = np.random.gamma(n,1/lam0,5000)\n",
    "\n",
    "q = np.quantile(exp,0.95)\n",
    "if sum(costs_filtered)<=q:\n",
    "    print (\"Costs (\", sum(costs_filtered),\") are lower than the quantile of the experimental values (\",\n",
    "           q, \") so H0 is accepted\")\n",
    "else:\n",
    "    print (\"Costs (\", sum(costs_filtered),\") are higher than the quantile of the experimental values (\",\n",
    "           q, \") so H0 is rejected\")\n",
    "\n",
    "    \n",
    "print(\"\\n Finally, the p-value is: \", 1-scipy.stats.gamma.cdf(sum(costs_filtered),n,scale=1/lam0))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c446773",
   "metadata": {},
   "source": [
    "### Question 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9125dce2",
   "metadata": {},
   "source": [
    "![](images/ex3-4.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "35287642",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1225\n"
     ]
    },
    {
     "data": {
      "image/png": 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GZad5dNslaxfl+W4+r1yrl2fqW48fZoksAABwDIEEAAAxrLF7WA+/1q4PnFeu3IyURXnOFLdLn7x0rV47NqAnDrFEFgAAOINAAgCAGPZvTzYq1e3Shy9Y3OWs795WppV5GfrOH1glAQAAnEEgAQBAjOoeGtOvXmnVDWetUqE3bVGfO9Xj0m2XrNErR/r1fGPfoj43AABAJAgkAACIUT/feVQTAatbzq9Ykue/fscqLctM0U+fbV6S5wcAADgdAgkAAGJQIGh17wtHdP7afK0tzF6S10hPceuGs1br0f0dOtY/siSvAQAAcCoEEgAAxKCnDnXrWP+I3ndO+ZK+zvvPXS1Juuf5liV9HQAAgJMRSAAAEIPueaFFhd40vWVD8ZK+TtmyTF1eW6yfvXhEoxOBJX0tAACA6QgkAACIMT3DY/pTXbfes61MKe6l/1H9gfPKddw/occPdC75awEAAEwhkAAAIMY8uLtNgaDVu7etjMrrnb+2QCty03X/rtaovB4AAIBEIAEAQMz5r1fbVFuao+pib1Rez+0yeve2Mj11qFsdA6NReU0AAAACCQAAYkhTj0+vHu3Xu7auiOrrvmd7mYJW+vUrx6L6ugAAIHkRSAAAEEP+65VjMka65szobNeYUlmQpbMqlun+XUdlrY3qawMAgOREIAEAQAx5+LV2nVO5XCW56VF/7XduXamGbp/2tw9G/bUBAEDyIZAAACBGNHQP63DXsK7eWOrI61+1oURul9GDe9odeX0AAJBcCCQAAIgRj+zrkCS9ZUOxI6+fn52m89fm68E9bWzbAAAAS45AAgCAGPHI3g6duSpPpbkZjtXw9s2lOto3oj2tA47VAAAAkgOBBAAAMaCtf0S7Wwd01YYSR+u4ckOJPC6jB/e0OVoHAABIfAQSAADEgEfD2zWudGi7xpS8zFRdWFWg3+/rYNsGAABYUgQSAADEgD/WdWtNYZbWFGY7XYresr5ER/tGdLBjyOlSAABAAiOQAADAYf7xST3f2Ks31RQ5XYok6fL1RTJGemx/p9OlAACABEYgAQCAw55r6NX4ZFCXxkggUeRN19ZVeQQSAABgSRFIAADgsD/VdSkz1a2zKpc5XcoJV6wv0WvHBtTWP+J0KQAAIEERSAAA4CBrrf50sFsXnFGgNI/b6XJOeEu4uebjB1glAQAAlgaBBAAADqrvGtax/hFdFiPbNaasLcxWZUGW/niwy+lSAABAgiKQAADAQU8d7pEkXVxd4HAlb3RJdaGeb+zV6ETA6VIAAEACIpAAAMBBzzX0qCI/U2XLMp0u5Q0uqSnU6ERQLzb1OV0KAABIQAQSAAA4ZDIQ1AuNfTpvbeytjpCkcyvzlepx6clD3U6XAgAAEhCBBAAADnnt2ICGxiZ1/tp8p0uZUUaqW+dULieQAAAAS4JAAgAAhzzb0CtJOi9GAwkp1EeivmtYrcf9TpcCAAASDIEEAAAOea6hV+tKvCrITnO6lFO6tKZQkvTUoR6HKwEAAImGQAIAAAeMTgT0UnNfTK+OkELjP1fmZejJQ4z/BAAAi4tAAgAAB7xypF9jk0FdEKMNLacYY3RxdaGeqe/VRCDodDkAACCBEEgAAOCA5xp65DLS2WuWO13KrC6pLtTw2KRebjnudCkAACCBEEgAAOCAZxt6taksTznpKU6XMqvz1ubLZaRnwk04AQAAFgOBBAAAUeYfn9SrR/tjdtznyXIzUrRxZa6eJ5AAAACLiEACAIAoe/VIvyaDVudUxv52jSnnrcnXK0ePa2Q84HQpAAAgQRBIAAAQZS81H5cx0rbyZU6XErFz1+ZrImC1iz4SAABgkRBIAAAQZTtb+lRT7I2L/hFTzqpYLrfL6NmGHqdLAQAACYJAAgCAKAoErV450q/tcbQ6QpKy0zw6syxXzzXSRwIAACwOAgkAAKKormNIw2OT2lERX4GEFJq2sad1QMNjk06XAgAAEgCBBAAAUbSzpU+StKM8fhpaTjlvTYECQauXmvucLgUAACQAAgkAAKJoZ/NxFeekqWxZhtOlzNn28mVKdbv0HOM/AQDAIiCQAAAgina1HNeO8uUyxjhdypxlpLq1ZXUegQQAAFgUBBIAAERJ+8CIjvWPxF1Dy+nOW5OvvW0DGhiZcLoUAAAQ5wgkAACIkp3NxyUpLhtaTjmncrmslV4+ctzpUgAAQJwjkAAAIEp2NvcpM9Wt9aU5Tpcyb1tW58ntMtpJY0sAALBABBIAAETJriPHtWVVnjzu+P3xm5nq0cYVOXqpmRUSAABgYeL3NyIAAOLI6ERAB9uHtGVVntOlLNiOiuXafbRfY5MBp0sBAABxjEACAIAo2Nc2qMmg1ZkJEEicVbFMY5NB7T026HQpAAAgjhFIAAAQBbuP9ktSQqyQ2F6+XJLoIwEAABaEQAIAgCjY09qvkpx0FeekO13KghV601RZkEUfCQAAsCAEEgAARMHu1gFtLst1uoxFs6N8mXa19CkYtE6XAgAA4hSBBAAAS6zfP66mHl9C9I+YclbFch33T6ixZ9jpUgAAQJwikAAAYIntaR2QlBj9I6bsqFgmSWzbAAAA80YgAQDAEptqaLkpgbZsVBZkKT8rVS/R2BIAAMwTgQQAAEtsd2u/1hZmKSc9xelSFo0xRtvLl2lXCyskAADA/BBIAACwhKy1evXogM4sy3O6lEW3rXyZWnr96vONO10KAACIQwQSAAAsofaBUfUMjyVUQ8spW8Pv6dWjrJIAAABzRyABAMASmuofkYiBxKayXLldRq8c6Xe6FAAAEIcIJAAAWEKvtvYrxW1UW+p1upRFl5nq0boSL4EEAACYFwIJAACW0L5jg6op8SrN43a6lCWxdXWeXj3ar0DQOl0KAACIMwQSAAAsEWut9rUNaENp4oz7PNnWVcs0PDaphu5hp0sBAABxhkACAIAl0jYwquP+CW1cmeN0KUtm6+o8SdIrR2hsCQAA5oZAAgCAJbLv2IAkaf2KxF0hUVmQpdyMFPpIAACAOSOQAABgiextG5TLKCEbWk4xxmjr6jwCCQAAMGcEEgAALJH9bQNaW5itzFSP06Usqa2rlulQ15CGRiecLgUAAMQRAgkAAJbI3mOD2rAicftHTNm6Ok/WSntaB5wuBQAAxBECCQAAlkDP8Jg6Bke1cWXi9o+YcuaqPEnSyy00tgQAAJEjkAAAYAnsaxuUJG1I4IaWU3IzUrSmMEu7WSEBAADmgEACAIAlsK9tasJG4m/ZkKTNK3P12rF+p8sAAABxhEACAIAlsO/YoFYvz1RuRorTpUTF5rI8dQ6OqXNw1OlSAABAnCCQAABgCextG0iKhpZTNpeFtqa8xrYNAAAQIQIJAAAW2eDohFp6/UnR0HLK+hU5chlpT2u/06UAAIA4QSABAMAi2x9uaJks/SMkKTPVo6oir/YcY4UEAACIDIEEAACL7GB7eMJGafIEElJo28ZrrQOy1jpdCgAAiAMEEgAALLKDHUNanpWqQm+a06VE1eayXPX6xtU2QGNLAAAwOwIJAAAW2cGOIa0r8coY43QpUbWpLE+StOdov6N1AACA+EAgAQDAIgoGreo6hlRT4nW6lKirLfUqxW3oIwEAACJCIAEAwCI60ufXyERAtSXJ1T9CktI8btWUeBn9CQAAIkIgAQDAIjrYEWpoua40+VZISNKmlXna09pPY0sAADArAgkAABbRwY4huYxUVZScgcTmslwNjk6qpdfvdCkAACDGEUgAALCIDrYPqSI/SxmpbqdLccTmslxJoo8EAACYVUSBhDHmKmNMnTGm3hjzuRkeN8aY74Qf32OM2TbbtcaYbxhjDobP/7UxJi98vMIYM2KMeTX8decivE8AAKLiYMdg0m7XkKTqYq9SPS691trvdCkAACDGzRpIGGPckr4r6WpJ6yXdZIxZf9JpV0uqCn/dKun7EVz7mKSN1trNkg5J+vy052uw1m4Jf9023zcHAEA0+ccn1dLn17okbGg5JcXt0vrSHO2msSUAAJhFJCskzpZUb61ttNaOS7pP0rUnnXOtpLttyPOS8owxpae71lr7qLV2Mnz985LKFuH9AADgmEOdw7JWWpeEIz+n21yWq33HBhQI0tgSAACcWiSBxEpJR6fdbw0fi+ScSK6VpA9L+t20+5XGmFeMMU8aYy6aqShjzK3GmJ3GmJ3d3d0RvA0AAJbWwfbwhI0kXiEhSZvL8uQbD6ixe9jpUgAAQAyLJJAwMxw7+a88TnXOrNcaY74gaVLSPeFD7ZJWW2u3SvprSfcaY97wm5219i5r7Q5r7Y7CwsJZ3gIAAEvvYMeQslLdKluW4XQpjtq4MvRje1/boMOVAACAWBZJINEqadW0+2WS2iI857TXGmNukfR2Se+z4YHl1toxa21v+PYuSQ2SqiN5MwAAOOlA+6BqSrxyuWbK45PH2sJspXpc2tdGHwkAAHBqkQQSL0mqMsZUGmNSJd0o6YGTznlA0s3haRvnShqw1raf7lpjzFWSPivpGmvtiWHlxpjCcDNMGWPWKNQos3FB7xIAgCVmrVVd55Bqkny7hhRqbLmuxMsKCQAAcFqe2U6w1k4aY26X9Igkt6QfW2v3GWNuCz9+p6SHJb1VUr0kv6QPne7a8FP/q6Q0SY8ZYyTp+fBEjYslfdkYMykpIOk2a23fYr1hAACWQufgmPr9E6pN4pGf021YkaOHX+uQtVbhn/MAAACvM2sgIUnW2ocVCh2mH7tz2m0r6VORXhs+fsYpzv+lpF9GUhcAALHiQAcNLadbvyJXP3vxqI71j6hsWabT5QAAgBgUyZYNAAAwi4PtQ5KkmiQf+Tll44pQMLP3GNs2AADAzAgkAABYBHUdg1qRm67cjBSnS4kJ60py5DLSfhpbAgCAUyCQAABgERzsGNK6UrZrTMlIdWttYTaNLQEAwCkRSAAAsEATgaAauofZrnGSDStyCCQAAMApEUgAALBALb0+TQSsqouznS4lpmxYkauOwVH1Do85XQoAAIhBBBIAACzQoc5hSVJVESskptsQbmzJKgkAADATAgkAABbocOewjJHWFrJCYroNK3IlEUgAAICZEUgAALBAh7qGtGpZpjJS3U6XElNyM1NUtixD+5i0AQAAZkAgAQDAAtV3DtM/4hRobAkAAE6FQAIAgAWYCATV2DOsM+gfMaMNK3LV1OPT8Nik06UAAIAYQyABAMACtPT6mbBxGlONLQ+0s0oCAAC8HoEEAAALcLhzSBITNk7lRGPLY/SRAAAAr0cgAQDAAhzuCk3YOKOIFRIzKc5JU0F2Kn0kAADAGxBIAACwAIc6h1S2LIMJG6dgjNH6FbkEEgAA4A0IJAAAWID6rmFVs13jtNaX5qi+a1gTgaDTpQAAgBhCIAEAwDxNBoJq7PbpDBpanlZtqVfjgaAauoedLgUAAMQQAgkAAOappc+v8UCQFRKzqC0NTdo42D7kcCUAACCWEEgAADBPJyZssELitCoLspTqdjH6EwAAvA6BBAAA83S4M7QFgQkbp5fidqmqOFv7CSQAAMA0BBIAAMzToa5hlS3LUGaqx+lSYt66khwd7GDLBgAA+AsCCQAA5ulw55Cqi+kfEYnaUq+6h8bUMzzmdCkAACBGEEgAADAPUxM2qtiuEZH14caW9JEAAABTCCQAAJiHI+EJG/SPiMw6Jm0AAICTEEgAADAPh8INLdmyEZnlWakqzkljhQQAADiBQAIAgHmo7wr9TT8rJCK3riRHB2hsCQAAwggkAACYh/quYa3My1BWGhM2IlVbmqP6riGNTwadLgUAAMQAAgkAAOahoduntayOmJPaUq8mAlYN3cNOlwIAAGIAgQQAAHNkbeh/qtcUZDldSlypnWps2UEfCQAAQCABAMCcdQyOyj8eYIXEHK0pyFKq26UDTNoAAAAikAAAYM4aunySpLWFrJCYC4/bparibCZtAAAASQQSAADMWWNPqAfCGYWskJir2tIcVkgAAABJBBIAAMxZQ9ewstM8KvSmOV1K3FlX4lXP8Ji6h8acLgUAADiMQAIAgDlq6PZpbWGWjDFOlxJ31ocbW7JtAwAAEEgAADBHDd3DWst2jXlZx6QNAAAQRiABAMAc+MYm1T4wyoSNeVqelarinDT6SAAAAAIJAADmoqknNGFjTQETNuYr1NiSFRIAACQ7AgkAAOagoTs0YYMVEvO3riRHDd3DGp8MOl0KAABwEIEEAABz0NA1LJeRyvMznS4lbtWWejURsKrvGna6FAAA4CACCQAA5qCh26fVyzOV5nE7XUrcqmXSBgAAEIEEAABz0tA9rDVM2FiQNQVZSnW7dKiTxpYAACQzAgkAACIUCFo19fi0tpCGlgvhcbu0tihbBzsIJAAASGYEEgAARKitf0Rjk0GtZYXEgtUUZ6uOQAIAgKRGIAEAQITqmbCxaGpKctQxOKoB/4TTpQAAAIcQSAAAEKHGbp+kUA8ELExNSSjUqaOPBAAASYtAAgCACDV0DysvM0XLs1KdLiXu1ZSEJm0QSAAAkLwIJAAAiFBD17DWFmbLGON0KXFvRW66vGke1XUw+hMAgGRFIAEAQIQaupmwsViMMaou8epQx7DTpQAAAIcQSAAAEIGBkQn1DI9pDRM2Fk1NiVcHOwZlrXW6FAAA4AACCQAAItA4NWGDQGLR1BR7NTg6qY7BUadLAQAADiCQAAAgAg3hCRts2Vg8NSVeSVJdB40tAQBIRgQSAABEoKF7WCluo1XLM50uJWHUFBNIAACQzAgkAACIQEPXsMrzs5Ti5kfnYlmWlaoibxqjPwEASFL8VgUAQAQae3xaU8B2jcVWU+JlhQQAAEmKQAIAgFlMBIJq6fVpbRENLRdbTbFXh7uGFQgyaQMAgGRDIAEAwCyO9vk1EbCskFgCNSVejU8G1dzrc7oUAAAQZQQSAADMoqkn9D/Laxj5ueiYtAEAQPIikAAAYBYnAglWSCy6qiKvjCGQAAAgGRFIAAAwi6Yen/IyU7QsK9XpUhJORqpbFflZBBIAACQhAgkAAGbR1ONTRT6rI5ZKdXG2DjH6EwCApEMgAQDALJoY+bmkakpy1Nzr0+hEwOlSAABAFBFIAABwGiPjAbUPjKqSQGLJ1BR7FbTS4c5hp0sBAABRRCABAMBpTI2jrCwkkFgqJyZtsG0DAICkQiABAMBpTE3YYIXE0qnIz1Sqx6W6jkGnSwEAAFFEIAEAwGlMBRI0tVw6HrdLZxRmq44tGwAAJBUCCQAATqOx26finDRlpXmcLiWhrSvxskICAIAkQyABAMBpNPf62K4RBdUlXnUOjqnfP+50KQAAIEoIJAAAOI2mHp8qC7KdLiPhnWhs2UFjSwAAkgWBBAAAp9DvH1efb1yVBZlOl5Lw1jFpAwCApEMgAQDAKfxlwgYrJJZaSU66vOkeVkgAAJBECCQAADiF5l5GfkaLMSbc2JJAAgCAZEEgAQDAKTR1++Qy0urlbNmIhupir+o6h2StdboUAAAQBQQSAACcQmOPT2XLMpXq4cdlNNSUeDU0OqnOwTGnSwEAAFHAb1gAAJxCaMIG2zWipaqIxpYAACQTAgkAAGZgrVUzgURUVReHmoceJpAAACApEEgAADCD7qEx+cYDWlNIIBEt+dlpys9K1SECCQAAkgKBBAAAM2gMj/ysyCeQiKbqYq8OdQ47XQYAAIgCAgkAAGbQ1MPITydUF2frMJM2AABICgQSAADMoLnHp1SPSyvyMpwuJalUFXvlGw/oWP+I06UAAIAlRiABAMAMGnt8qsjPlNtlnC4lqVQXhyZtHGbbBgAACY9AAgCAGTT1+Ogf4YCpSRs0tgQAIPERSAAAcJJA0OpIr1+VTNiIurzMVBV501RHIAEAQMIjkAAA4CRt/SMaDwS1hoaWjqgu9rJlAwCAJEAgAQDASRpPTNjIdriS5FRVnK36rmEFg0zaAAAgkRFIAABwkqbu0N/OM/LTGTXFXo1MBNR6nEkbAAAkMgIJAABO0tTjU3aaRwXZqU6XkpSqwpM26CMBAEBiI5AAAOAkTb1+VRRkyhhGfjqhikkbAAAkBQIJAABO0tzjo3+Eg3LSU1Sam67DBBIAACQ0AgkAAKYZnwyq9bhfFfmZTpeS1KqLvTrEpA0AABIagQQAANMc6x9R0Erl+TS0dFJ1cbbqu4cVYNIGAAAJi0ACAIBpmntDIz9ZIeGsqmKvxieDagn/+wAAAIknokDCGHOVMabOGFNvjPncDI8bY8x3wo/vMcZsm+1aY8w3jDEHw+f/2hiTN+2xz4fPrzPGXLnA9wgAQMRaesKBBCM/HVUdnrTBtg0AABLXrIGEMcYt6buSrpa0XtJNxpj1J512taSq8Netkr4fwbWPSdpord0s6ZCkz4evWS/pRkkbJF0l6Xvh5wEAYMk19/qVneZRfhYjP51UVRRqKkpjSwAAElckKyTOllRvrW201o5Luk/StSedc62ku23I85LyjDGlp7vWWvuotXYyfP3zksqmPdd91toxa22TpPrw8wAAsOSae30qz2fkp9Oy0jwqW5ahOgIJAAASViSBxEpJR6fdbw0fi+ScSK6VpA9L+t0cXk/GmFuNMTuNMTu7u7sjeBsAAMyupdevChpaxoTqYq8Os2UDAICEFUkgMdNfEZ3c8vpU58x6rTHmC5ImJd0zh9eTtfYua+0Oa+2OwsLCGS4BAGBuJgNBHe3zq5yGljGhqjhbjT3DmggEnS4FAAAsgUgCiVZJq6bdL5PUFuE5p73WGHOLpLdLep+1dip0iOT1AABYdMf6RzQZtDS0jBE1xV5NBCyTNgAASFCRBBIvSaoyxlQaY1IVajj5wEnnPCDp5vC0jXMlDVhr2093rTHmKkmflXSNtdZ/0nPdaIxJM8ZUKtQo88UFvEcAACLS3Bv6ccSWjdgwNWmjroNtGwAAJCLPbCdYayeNMbdLekSSW9KPrbX7jDG3hR+/U9LDkt6qUANKv6QPne7a8FP/q6Q0SY+FG4c9b629LfzcP5e0X6GtHJ+y1gYW7R0DAHAKU38TX8GWjZiwtjBbxkiHOof0NpU6XQ4AAFhkswYSkmStfVih0GH6sTun3baSPhXpteHjZ5zm9b4q6auR1AYAwGJp7vErI8WtQm+a06VAUkaqW6uXZ+pwF5M2AABIRJFs2QAAICm0MPIz5lQXe3WISRsAACQkAgkAAMKaen2qpKFlTKkuzlZTj09jk+zeBAAg0RBIAAAgKRC04ZGfBBKxpLrYq0DQqqmHSRsAACQaAgkAACS19Y9oImBpaBljqopCkzbYtgEAQOIhkAAAQFJLeOQnKyRiy5rCLLldRoc7aWwJAECiIZAAAEBS89TIzwJWSMSS9BS3yvMzVddBIAEAQKIhkAAAQFJzj0/pKS4Ve9OdLgUnqS7y6nAXWzYAAEg0BBIAAEhq7vWrfHmWXC5Gfsaa6uJstfT6NDrBpA0AABIJgQQAAJJaen0qp6FlTKou8SpopYZuVkkAAJBICCQAAEkvGLRq6fOrooCGlrGounhq0gZ9JAAASCQEEgCApNcxOKrxySArJGJURX6WPC7D6E8AABIMgQQAIOk194QmbFQy8jMmpXpcWlOYxehPAAASDIEEACDpNff6JUnlbNmIWVXFXlZIAACQYAgkAABJr6XXp1SPS6U5jPyMVdVFXh3p88s/Pul0KQAAYJEQSAAAkl5zr0+rl2cy8jOGVRdnS5Lqu1glAQBAoiCQAAAkvZZevypoaBnTqkumJm0QSAAAkCgIJAAASS0YtGru9amChpYxrXx5plLdLhpbAgCQQAgkAABJrWtoTKMTQRpaxjiPOzRpo45AAgCAhEEgAQBIas29oZGfbNmIfdXFXh1mywYAAAmDQAIAkNRaTgQSrJCIdTUlXh3rH9HwGJM2AABIBAQSAICk1tzrV4rbqDSXkZ+xrqooNGmDPhIAACQGAgkAQFJr7vFp1fJMedz8SIx11cVTkzYIJAAASAT89gUASGrNvX62a8SJVcszleZxMfoTAIAEQSABAEha1lq19PpUTkPLuOB2GVUVZ7NCAgCABEEgAQBIWt3DY/KPB1ghEUeqi5i0AQBAoiCQAAAkrZZevySxQiKOVBV71TE4qgH/hNOlAACABSKQAAAkraae0MjPygJWSMSLmpLwpI0utm0AABDvCCQAAEmrpdcnj8toZV6G06UgQlVFoUkbdfSRAAAg7hFIAACSVnOvX2XLMhj5GUdW5mUoK9VNHwkAABIAv4EBAJJWaMIG2zXiictldEaxV3UdrJAAACDeEUgAAJKStVYtPX5V0NAy7tQUZ9NDAgCABEAgAQBISr2+cQ2NTaqChpZxp7rYq57hcfUOjzldCgAAWAACCQBAUmrpDU3YqGDLRtypLg41tjxEHwkAAOIagQQAICk19/glSeVs2Yg7fwkk2LYBAEA8I5AAACSlll6fXEYqW0YgEW+Kc9KUk+4hkAAAIM4RSAAAklJzr18rl2Uo1cOPwnhjjFF1sZdAAgCAOMdvYQCApNTc66N/RByrLvHqUOewrLVOlwIAAOaJQAIAkHSstWrqIZCIZ9VF2RoYmVDXEJM2AACIVwQSAICk0++f0NDoJA0t41h1CY0tAQCIdwQSAICk08zIz7g3NWmjroNAAgCAeEUgAQBIOi29oZGfFQUEEvGqIDtN+VmpOtw57HQpAABgnggkAABJp6nHJ2OkVcsznC4FC1Bd7FUdWzYAAIhbBBIAgKTT0uvTitwMpXncTpeCBaguztbhziEmbQAAEKcIJAAASae516+KAhpaxrvqEq984wEd6x9xuhQAADAPBBIAgKTT0utTOQ0t495UY0v6SAAAEJ8IJAAASWXAP6Hj/glVEkjEveqi8KQN+kgAABCXCCQAAEllauRneT5bNuJdbmaKinPSdIhAAgCAuEQgAQBIKlOBBCM/E0N1sZdAAgCAOEUgAQBIKi29fknS6uWskEgE1cVe1XcNKxBk0gYAAPGGQAIAkFSae30qzU1XegojPxNBTbFXoxNBHe3zO10KAACYIwIJAEBSaen1q4KGlgmjqjhbkti2AQBAHCKQAAAkleYenyoK2K6RKKrCoz8JJAAAiD8EEgCApDE4OqFe37jKWSGRMLLTPFqZl6FDncNOlwIAAOaIQAIAkDSOhBtaVjDyM6HUlDBpAwCAeEQgAQBIGlMjP1khkViqirPV2O3TRCDodCkAAGAOCCQAAEljauRnOSskEkpNsVfjgaBawoETAACIDwQSAICk0dTjU3FOmjJTPU6XgkVUfaKxJX0kAACIJwQSAICk0dLrU/lytmskmjOKsmWMVNdBHwkAAOIJgQQAIGk09/oZ+ZmA0lPcKl+eqcNdBBIAAMQTAgkAQFLwjU2qe2iMhpYJqrrYywoJAADiDIEEACApTDW0rCwgkEhE1cVeNff6NTYZcLoUAAAQIQIJAEBS+MvIT7ZsJKLqEq8CQavGbiZtAAAQLwgkAABJ4S+BBCskElHNiUkbbNsAACBeEEgAAJJCS49fBdlpyk5j5GciqizIksdlCCQAAIgjBBIAgKTQ3OtTJRM2Elaqx6XKgiwd6hx2uhQAABAhAgkAQFJo7vWxXSPBVRd7WSEBAEAcIZAAACQ8//ikOgfHVEFDy4RWXezVkT6/RsaZtAEAQDwgkAAAJLwjfaGRn6yQSGzVxdmyVqrvYtsGAADxgEACAJDwmntCgUQFgURCqy5h0gYAAPGEQAIAkPBapkZ+0tQyoZUvz1Sq20UgAQBAnCCQAAAkvOZen/KzUpWTnuJ0KVhCHrdLa4uyCSQAAIgTBBIAgITX3ONXOQ0tk0J1cTajPwEAiBMEEgCAhNfS66N/RJKoLvbqWP+IhkYnnC4FAADMgkACAJDQRicCahsYZcJGkqguDjW2PMykDQAAYh6BBAAgoU2N/KygoWVSqAkHEoc66CMBAECsI5AAACS05p7QhA22bCSHsmUZykhx00cCAIA4QCABAEhoLb3hFRIEEknB5TKqKmbSBgAA8YBAAgCQ0Jp7fcrLTFFuJiM/k0VVkZdAAgCAOEAgAQBIaM1M2Eg6NSXZ6hoaU79/3OlSAADAaRBIAAASWnOPXxX5NLRMJlOTNupobAkAQEwjkAAAJKyxyYDaBkYY+ZlkakrCgQTbNgAAiGkEEgCAhHW0b0TWMvIz2ZTkpCs3I0UHWSEBAEBMI5AAACSslt7QyE9WSCQXY4xqSrxs2QAAIMYRSAAAElZTTyiQqCSQSDrrSrw61DEka63TpQAAgFMgkAAAJKyWXr9y0j3KY+Rn0qkp8WpobFLH+kecLgUAAJwCgQQAIGE19/pUUZAlY4zTpSDK1pUwaQMAgFhHIAEASFgtvX76RySpqdGfNLYEACB2EUgAABLS+GRQrcf9qsxnwkYy8qanaGVeBoEEAAAxjEACAJCQWo/7FbRM2Ehm60q8qusYdLoMAABwCgQSAICE1NLrlyRVFLBCIlnVlHjV2O3T+GTQ6VIAAMAMIgokjDFXGWPqjDH1xpjPzfC4McZ8J/z4HmPMttmuNcZcb4zZZ4wJGmN2TDteYYwZMca8Gv66c6FvEgCQfJp7QyM/WSGRvGpKvJoMWjV0DztdCgAAmMGsgYQxxi3pu5KulrRe0k3GmPUnnXa1pKrw162Svh/BtXslvVvSUzO8bIO1dkv467Y5vysAQNJr6fUrO82j/KxUp0uBQ9aV5Ehi0gYAALEqkhUSZ0uqt9Y2WmvHJd0n6dqTzrlW0t025HlJecaY0tNda609YK2tW7R3AgDANE09PlUUZDLyM4mtKcxSitvQ2BIAgBgVSSCxUtLRafdbw8ciOSeSa2dSaYx5xRjzpDHmogjOBwDgdVp6fWzXSHIpbpfWFmbT2BIAgBgVSSAx018t2QjPieTak7VLWm2t3SrpryXda4zJeUNRxtxqjNlpjNnZ3d09y1MCAJLJRCCo1uMjqmDkZ9KrKfGyZQMAgBgVSSDRKmnVtPtlktoiPCeSa1/HWjtmre0N394lqUFS9Qzn3WWt3WGt3VFYWBjB2wAAJIu2/hFNBi0rJKB1JTlqGxjVwMiE06UAAICTRBJIvCSpyhhTaYxJlXSjpAdOOucBSTeHp22cK2nAWtse4bWvY4wpDDfDlDFmjUKNMhvn9K4AAEmtqSc0YaOygEAi2a0r8UqSDnWySgIAgFgzayBhrZ2UdLukRyQdkPRza+0+Y8xtxpipCRgPKxQa1Ev6gaRPnu5aSTLGvMsY0yrpPEkPGWMeCT/XxZL2GGN2S7pf0m3W2r5FebcAgKTQ0uuXJJWzZSPp1YQDCRpbAgAQezyRnGStfVih0GH6sTun3baSPhXpteHjv5b06xmO/1LSLyOpCwCAmTT3+pSZ6lZhdprTpcBhpbnp8qZ7dLCdxpYAAMSaSLZsAAAQV1p6/SrPz2LkJ2SM0ToaWwIAEJMIJAAACae518eEDZxQU+JVXeeQQgs6AQBArCCQAAAklMlAUEf7/KqgoSXCakpyNDQ6qbaBUadLAQAA0xBIAAASSvvAqCYClhUSOGFq0kZdB30kAACIJQQSAICE0twbGvlZns8KCYRUFzNpAwCAWEQgAQBIKM3hkZ8VBBIIy81I0YrcdBpbAgAQYwgkAAAJpbnHp/QUl4pzGPmJv6hh0gYAADGHQAIAkFBaen2qYOQnTlJTkqOG7mFNBIJOlwIAAMIIJAAACaW5169yGlriJOtKvJoIWDV2+5wuBQAAhBFIAAASRiBodaTXT/8IvMG60qnGlkzaAAAgVhBIAAASRvvAiMYDQSZs4A3WFGTL4zL0kQAAIIYQSAAAEkZzT2jCRmUBgQReL9Xj0trCbEZ/AgAQQwgkAAAJo6lnWBKBBGZWW+rVgXa2bAAAECsIJAAACaOpx6+MFDcjPzGj2tIctQ+Mqt8/7nQpAABABBIAgATS1DOsigJGfmJmtaU5kqT9rJIAACAmEEgAABJGc69fa9iugVOYCiQOtNNHAgCAWEAgAQBICBOBoI70+VVRkOl0KYhRhd40FWSn0UcCAIAYQSABAEgIR/v8CgStKguynS4FMay21Kv9bQQSAADEAgIJAEBCaO71SZIqWSGB01hfmqP6rmFNBIJOlwIAQNIjkAAAJITG7qlAghUSOLXa0hyNB4Jq6B52uhQAAJIegQQAICE09/qUm5GiZZkpTpeCGPaXxpZs2wAAwGkEEgCAhNDU42PkJ2a1pjBLqW4XkzYAAIgBBBIAgITQ3MPIT8wuxe1SVXE2KyQAAIgBBBIAgLg3OhHQsf4RVeQTSGB2taU5BBIAAMQAAgkAQNxr6fVLkioLCSQwu9rSHPUMj6traNTpUgAASGoEEgCAuNfUE5qYUMkKCUSgttQrSfSRAADAYQQSAIC419QTWiFRUZDpcCWIB+uZtAEAQEwgkAAAxL2mnmEVZKfJm87IT8wuLzNVpbnpBBIAADiMQAIAEPeYsIG5Wk9jSwAAHEcgAQCIe409PrZrYE5qS3PU0O3T6ETA6VIAAEhaBBIAgLg2NDqhnuExVRZkO10K4khtaY4CQav6rmGnSwEAIGkRSAAA4lpzuKFlJSskMAdTkzb2s20DAADHEEgAAOJa49TIT1ZIYA7K87OUkeLW/jYCCQAAnEIgAQCIa1MrJMrzWSGByLldRjUlXhpbAgDgIAIJAEBca+oZ1sq8DKWnuJ0uBXGmNjxpw1rrdCkAACQlAgkAQFxr6vWrkpGfmIf1pV4Njk6qbWDU6VIAAEhKBBIAgLhlrVVT9zAjPzEvtaU5kqQD9JEAAMARBBIAgLh13D+hwdFJGlpiXtZNBRL0kQAAwBEEEgCAuNV0YsIGKyQwd9lpHq1enqkDHQQSAAA4gUACABC3msITNlghgfmqLfXqQPuQ02UAAJCUCCQAAHGrqWdYbpdR2bIMp0tBnKotzVFzr0/+8UmnSwEAIOkQSAAA4lZTj0+rl2cqxc2PM8zP+tIcWStWSQAA4AB+gwMAxK2mHr8q8ukfgfnbsDJXkrS/bcDhSgAASD4EEgCAuGStVXOPj/4RWJAVuelalpmivcdobAkAQLQRSAAA4lLn4JhGJgJM2MCCGGO0YUWu9rWzQgIAgGgjkAAAxKXGEyM/WSGBhdmwMkd1HUManww6XQoAAEmFQAIAEJeawyM/K1ghgQXasCJXEwGrw100tgQAIJoIJAAAcampZ1ipHpdW5DLyEwuzcUWOJGkffSQAAIgqAgkAQFxq7PapMj9LLpdxuhTEuYr8LGWlurWPSRsAAEQVgQQAIC419vi0tijL6TKQAFwuo/UrcrS3jRUSAABEE4EEACDujE8GdaTPrzU0tMQi2bAiVwfaBxUIWqdLAQAgaRBIAADizpE+nwJBqzWFrJDA4tiwIkf+8YCaenxOlwIAQNIgkAAAxJ2G7tD/NK4tZIUEFseGFbmSRB8JAACiiEACABB3GrqHJYkVElg0VcXZSnW7tJ8+EgAARA2BBAAg7jR2+1TkTZM3PcXpUpAgUtwu1ZR4tZcVEgAARA2BBAAg7jR2D7M6Aotu48oc7WsblLU0tgQAIBoIJAAAccVaq4Zun9bQPwKLbP2KXPX7J3Ssf8TpUgAASAoEEgCAuNLnG9fAyAQNLbHoNq7IkSTto48EAABRQSABAIgrjeGxjGzZwGJbV5Ijl5H2HaOPBAAA0UAgAQCIKw1doQkbZ7BCAossI9WtM4qyWSEBAECUEEgAAOJKY49PqR6XVuRlOF0KEtCGFblM2gAAIEoIJAAAcaWxe1iV+Vlyu4zTpSABbViRo87BMfUMjzldCgAACY9AAgAQVxq6fVpbRP8ILI0NK3Il0dgSAIBoIJAAAMSN8cmgjvT5taaA/hFYGuvDkzb20tgSAIAlRyABAIgbR/p8CgQtEzawZHIzUrR6eab20UcCAIAlRyABAIgbDd2hkZ9rmbCBJbRpZa5eY4UEAABLjkACABA3GsOBBCsksJQ2l+XqaN+IjvvGnS4FAICERiABAIgbDd3DKvKmyZue4nQpSGCbykKNLVklAQDA0iKQAADEjcbuYVZHYMltXBkKJPa09jtbCAAACY5AAgAQF6y1auj2aQ39I7DEctJTtKYgS3taWSEBAMBSIpAAAMSFPt+4BkYmaGiJqNhURmNLAACWGoEEACAuNPbQ0BLRs7ksT+0Do+oaGnW6FAAAEhaBBAAgLjR2D0uS1hawQgJLb/NUY0u2bQAAsGQIJAAAcaGh26dUj0srl2U4XQqSwPrSHLmM6CMBAMASIpAAAMSFxu5hVeZnye0yTpeCJJCV5tEZRdn0kQAAYAkRSAAA4kJjt09ri+gfgejZtDJPe1oHZK11uhQAABISgQQAIOaNTwbV0ufXGvpHIIrOXJWrnuExtQ/Q2BIAgKVAIAEAiHlH+vwKBC0TNhBVm1aGGlvSRwIAgKVBIAEAiHn1XUOSpDOKWCGB6KktzZHHZfTasX6nSwEAICERSAAAYl59V3jkZyGBBKInPcWt6mIvKyQAAFgiBBIAgJh3uGtYK/MylJXmcboUJJkzV+XqtWM0tgQAYCkQSAAAYl591zDbNeCITSvz1O+f0NG+EadLAQAg4RBIAABiWjBo1dBNIAFnbC4LN7akjwQAAIuOQAIAENOO9Y9odCKoKgIJOKC62KtUt0uv0UcCAIBFRyABAIhph5mwAQelelyqLfVqd2u/06UAAJBwCCQAADFtasIGgQScsrksT3uPDSoYpLElAACLiUACABDTDncOqyA7TXmZqU6XgiS1qSxXw2OTaur1OV0KAAAJhUACABDT6ruH6R8BR001ttx9tN/ZQgAASDAEEgCAmGWtVX0nEzbgrKoir7JS3XqVQAIAgEVFIAEAiFldQ2MaGptUVTGBBJzjdhltKsslkAAAYJERSAAAYtbhznBDy0ICCThr6+pl2t82qNGJgNOlAACQMCIKJIwxVxlj6owx9caYz83wuDHGfCf8+B5jzLbZrjXGXG+M2WeMCRpjdpz0fJ8Pn19njLlyIW8QABC/6qdGfrJCAg7bsipPk0GrfW0DTpcCAEDCmDWQMMa4JX1X0tWS1ku6yRiz/qTTrpZUFf66VdL3I7h2r6R3S3rqpNdbL+lGSRskXSXpe+HnAQAkmcNdw8pJ96gwO83pUpDktq7KkyS9cqTf0ToAAEgkkayQOFtSvbW20Vo7Luk+SdeedM61ku62Ic9LyjPGlJ7uWmvtAWtt3Qyvd62k+6y1Y9baJkn14ecBACSZ+q5QQ0tjjNOlIMkV5aRrRW46fSQAAFhEkQQSKyUdnXa/NXwsknMiuXY+rydjzK3GmJ3GmJ3d3d2zPCUAIB7Vdw2rqsjrdBmAJGnL6jwCCQAAFlEkgcRMfy1lIzwnkmvn83qy1t5lrd1hrd1RWFg4y1MCAOJNn29cvb5xRn4iZmxZlafW4yPqGR5zuhQAABJCJIFEq6RV0+6XSWqL8JxIrp3P6wEAElx9V3jCBg0tESO2rFomSXqVPhIAACyKSAKJlyRVGWMqjTGpCjWcfOCkcx6QdHN42sa5kgaste0RXnuyByTdaIxJM8ZUKtQo88U5vCcAQAI4EUgw8hMxYtPKXLldhm0bAAAsEs9sJ1hrJ40xt0t6RJJb0o+ttfuMMbeFH79T0sOS3qpQA0q/pA+d7lpJMsa8S9L/k1Qo6SFjzKvW2ivDz/1zSfslTUr6lLWWod8AkGQOdw0pI8WtlXkZTpcCSJIyUt1aV+LVK0ePO10KAAAJYdZAQpKstQ8rFDpMP3bntNtW0qcivTZ8/NeSfn2Ka74q6auR1AYASEz1XcNaW5Qll4sJG4gdW1bl6YFX2xQMWv7bBABggSLZsgEAQNQxYQOxaMuqPA2NTaqhe9jpUgAAiHsEEgCAmDMwMqH2gVFVFxNIILZsXZ0nSXqFPhIAACwYgQQAIOYc7hySJNWU0NASsWVNQba86R4aWwIAsAgIJAAAMacuHEiwQgKxxuUy2rIqj9GfAAAsAgIJAEDMOdQxpKxUJmwgNm1dlaeDHYPyjU06XQoAAHGNQAIAEHPqOodUXeKVMUwxQOzZVr5MQSvtZtsGAAALQiABAIgp1lrVdQyphu0aiFFbVy+TJO1qOe5wJQAAxDcCCQBATOkZHtdx/4SqCCQQo3IzUlRdnK1dRwgkAABYCAIJAEBMOTFhg0ACMWx7+XK93HJcwaB1uhQAAOIWgQQAIKacmLDByE/EsO3lyzQ4Oqn67mGnSwEAIG4RSAAAYsqhziEty0xRYXaa06UAp7S9nD4SAAAsFIEEACCm1HUMqbqYCRuIbRX5mcrPStXOZgIJAADmi0ACABAzrLU61DmsmhL6RyC2GWO0rXyZXqaxJQAA80YgAQCIGW0Doxoem2TCBuLC9vJlaurxqXd4zOlSAACISwQSAICYcaiDCRuIH1N9JF4+0u9sIQAAxCkCCQBAzDgxYaOYCRuIfZtW5irFbbSzpc/pUgAAiEsEEgCAmHGoc0jFOWnKy0x1uhRgVukpbm1cmauXmbQBAMC8EEgAAGLGoc7QhA0gXmxfvUy7Wwc0Phl0uhQAAOIOgQQAICYEglaHO4fpH4G4sqNimcYng9rbNuB0KQAAxB0CCQBATDjS59fYZJAVEogr21aHG1uybQMAgDkjkAAAxIS68ISN6hICCcSPopx0rVqeoZeaaWwJAMBcEUgAAGLCofCEjaoiJmwgvpxdka+Xmo/LWut0KQAAxBUCCQBATDjQPqjy/ExlpXmcLgWYk3Mql6vPN66G7mGnSwEAIK4QSAAAYsKB9kHVluQ4XQYwZ2dVLpckvdDEtg0AAOaCQAIA4Djf2KRa+vyqLSWQQPypyM9UoTdNLxFIAAAwJwQSAADH1XUOyVqptpSGlog/xhidXblcLzT10UcCAIA5IJAAADjuQPugJLFCAnHrnMrlah8YVevxEadLAQAgbhBIAAAcd6B9UN40j8qWZThdCjAvZ1WE+ki8yLYNAAAiRiABAHDcgfYhrSv1yhjjdCnAvNQUe5WT7tFLzQQSAABEikACAOCoYNCqrmOI7RqIay5XqI8EKyQAAIgcgQQAwFGtx0c0PDZJIIG4d1bFcjX2+NQ1NOp0KQAAxAUCCQCAo/aHG1quK2HCBuLb2ZWhPhIvNR13uBIAAOIDgQQAwFEH2gdljFRDIIE4t3FlrjJS3PSRAAAgQgQSAABHHewYVGV+ljJTPU6XAixIitulbeV5eoE+EgAARIRAAgDgqAPtNLRE4ji7Il8HOwY14J9wuhQAAGIegQQAwDFDoxM60udXbSnbNZAYzq5cLmvFtg0AACJAIAEAcExdx5AkaV0JKySQGLauzlOqx6XnGnudLgUAgJhHIAEAcMyBcCBRu4JAAokhPcWtHeXL9GwDgQQAALMhkAAAOOZA+6By0j1akZvudCnAojl/bb4OtA+qzzfudCkAAMQ0AgkAgGMOtA+qtjRHxhinSwEWzXlrCyRJz7NtAwCA0yKQAAA4Ihi0qutgwgYSz+ayXGWmuvUc2zYAADgtAgkAgCNa+vzyjweYsIGEk+J26ezK5Xq2ocfpUgAAiGkEEgAAR+w9NiBJ2rAi1+FKgMV3/tp8NXT7ND4ZdLoUAABiFoEEAMARe9sGlOp2qbqYFRJIPOeH+0gMjk44XAkAALGLQAIA4Ii9xwZUU+JVqocfRUg8taU5ykn3aGBk0ulSAACIWfwWCACIOmut9h4b1MaVNLREYnK7jM5dk88KCQAAToNAAgAQda3HRzQwMkH/CCS089fma2wioNEJ+kgAADATAgkAQNRNNbTctJJAAonr/DPoIwEAwOkQSAAAom5v24DcLqOaEhpaInFVFWUrxe3S4AiBBAAAMyGQAABE3d5jg6oqylZ6itvpUoAlY4xRTkaKBkYmZK11uhwAAGIOgQQAIKpCDS0H2K6BpJCbkaKJQFCHu4adLgUAgJhDIAEAiKqOwVH1+sa1kUACSSA3I0WS9NShbocrAQAg9hBIAACiau+xQUli5CeSQprHpfQUt5463ON0KQAAxBwCCQBAVO09NiCXkWpLCSSQHPIyU/RCY69GJwJOlwIAQEwhkAAARNXeYwNaW5itzFSP06UAUZGbkaqxyaBeau5zuhQAAGIKgQQAIKr2tg3QPwJJJSfdo1S3S0+zbQMAgNchkAAARE3X0Kg6B8e0YQXbNZA83C6jHRXLaGwJAMBJCCQAAFGzL9zQkpGfSDYXVRXqYMeQugZHnS4FAICYQSABAIiavccGJEnrWSGBJHNRVYEksW0DAIBpCCQAAFGzt21AlQVZ8qanOF0KEFXrS3NUkJ2qpw+zbQMAgCkEEgCAqNnTSkNLJCeXy+jCMwr05/oeBYPW6XIAAIgJBBIAgKjoHBxV+8CoziwjkEByuqiqUD3D49rfPuh0KQAAxAQCCQBAVOw+2i9J2rIqz9E6AKdM9ZF4im0bAABIIpAAAETJntYBuV1GG1awQgLJqSgnXetLc/REHYEEAAASgQQAIEp2t/ZrXYlXGalup0sBHPOmdUXa1XJcA/4Jp0sBAMBxBBIAgCUXDFrtPtqvM9mugSR32boiBYJWT7JtAwAAAgkAwNJr7vVpcHRSW8rynC4FcNSWVXlanpWqPx3scroUAAAcRyABAFhyu1v7JYkVEkh6bpfRpdWFeqKuSwHGfwIAkhyBBABgye0+OqDMVLfOKMp2uhTAcW+qLdJx/4RePXrc6VIAAHAUgQQAYMm9erRfm1bmyu0yTpcCOO6iqkK5XUZ/OMC2DQBAciOQAAAsqfHJoPa3DWoL2zUASVJuRorOqlimP9JHAgCQ5AgkAABL6mDHoMYDQfpHANO8aV2RDnYM6Vj/iNOlAADgGAIJAMCS2n20XxINLYHp3rSuWJKYtgEASGoEEgCAJfXKkX4VZKdpRW6606UAMWNtYZZWL89k2wYAIKkRSAAAltSuI8e1vTxPxtDQEphijNGb1hXpmfoejYwHnC4HAABHEEgAAJZMz/CYWnr92l6+zOlSgJjz5toijU0G9Ux9j9OlAADgCAIJAMCSebnluCQRSAAzOKcyX950jx7Z1+F0KQAAOIJAAgCwZHYdOa4Ut9GGFblOlwLEnFSPS29eV6THD3RqMhB0uhwAAKKOQAIAsGRebjmujStzlZ7idroUICZduaFEx/0TerG5z+lSAACIOgIJAMCSGJ8Mak/rgLatZrsGcCqX1BQqzePSo/s6nS4FAICoI5AAACyJ/e2DGpsM0j8COI3MVI8uri7UI/s6ZK11uhwAAKKKQAIAsCR20dASiMiVG0rUPjCqPa0DTpcCAEBUEUgAAJbEy0eOa2Vehopz0p0uBYhpl9cWye0yTNsAACQdAgkAwJJ4ueW4trE6AphVXmaqzl2znEACAJB0CCQAAIuurX9E7QOj2r46z+lSgLhw5YYSNXT7VN815HQpAABEDYEEAGDR7TzRP2K5w5UA8eEt60skSY8wbQMAkEQIJAAAi+7Fpl5lp3lUW+p1uhQgLpTkpuvMVXn6/V62bQAAkgeBBABg0b3Y1Kft5cvkcfNjBojUWzeW6LVjA2rp9TldCgAAUcFvigCARXXcN65DncM6u5LtGsBcvG1zqSTpwT3tDlcCAEB0EEgAABbVS819kkQgAcxR2bJMbS9fpt/ubnO6FAAAoiKiQMIYc5Uxps4YU2+M+dwMjxtjzHfCj+8xxmyb7VpjzHJjzGPGmMPh78vCxyuMMSPGmFfDX3cuxhsFAETHi019SvW4tLks1+lSgLjzjs2lOtgxpEOdTNsAACS+WQMJY4xb0nclXS1pvaSbjDHrTzrtaklV4a9bJX0/gms/J+kP1toqSX8I35/SYK3dEv66bb5vDgAQfS8292nrqjyledxOlwLEnbduLpXLSA+ySgIAkAQiWSFxtqR6a22jtXZc0n2Srj3pnGsl3W1DnpeUZ4wpneXaayX9NHz7p5LeubC3AgBw2vDYpPYeG9A5bNcA5qXIm65z1+Trt3vaZa11uhwAAJZUJIHESklHp91vDR+L5JzTXVtsrW2XpPD3omnnVRpjXjHGPGmMuSiCGgEAMWBXy3EFrXR2Zb7TpQBx6x1nrlBTj0/72gadLgUAgCUVSSBhZjh2cmR/qnMiufZk7ZJWW2u3SvprSfcaY3LeUJQxtxpjdhpjdnZ3d8/ylACAaHixqVcel9G28jynSwHi1lUbSuRxGf12D9s2AACJLZJAolXSqmn3yySd/BPyVOec7trO8LYOhb93SZK1dsxa2xu+vUtSg6Tqk4uy1t5lrd1hrd1RWFgYwdsAACy1F5v6tHFlrjJTPU6XAsStZVmpuqiqQA/uZtsGACCxRRJIvCSpyhhTaYxJlXSjpAdOOucBSTeHp22cK2kgvA3jdNc+IOmW8O1bJP1GkowxheFmmDLGrFGoUWbjvN8hACAqRsYD2n10gHGfwCJ4x5krdKx/RC8f6Xe6FAAAlsysf4VlrZ00xtwu6RFJbkk/ttbuM8bcFn78TkkPS3qrpHpJfkkfOt214af+mqSfG2M+IumIpOvDxy+W9GVjzKSkgKTbrLV9i/JuAQBLZlfLcY0HgjpvLf0jgIW6Yn2x0jwu/ebVY9pevszpcgAAWBIRram11j6sUOgw/did025bSZ+K9Nrw8V5Jb57h+C8l/TKSugAAseOZhh55XEZnV7BCAlgob3qKrlhfrAd2t+kLb6tljC4AICFFsmUDAIBZPVvfo62r85SVRv8IYDFct71M/f4J/elgl9OlAACwJAgkAAALNjAyodeODej8tQVOlwIkjIuqClXkTdP9u445XQoAAEuCQAIAsGDPN/YqaKXz6R8BLBq3y+hd21bqibou9QyPOV0OAACLjkACALBgzzX0KiPFra2rab4HLKbrtpVpMmj1m1dPnrgOAED8I5AAACzYM/U9OqtyuVI9/FgBFlNVsVeby3J1/65Wp0sBAGDR8ZsjAGBBugZHdbhrWBewXQNYEtdtL9OB9kHtaxtwuhQAABYVgQQAYEGebeiVJF1wBg0tgaXwjs0rlOI2+iXNLQEACYZAAgCwIM/U9yg3I0XrS3OcLgVISMuyUnV5bbF+8+oxTQSCTpcDAMCiIZAAAMybtVZPH+7R+Wvz5XIZp8sBEtZ128vU6xvXHw50Ol0KAACLhkACADBvhzqH1TE4qktrCp0uBUhol1QXqjQ3Xfe8cMTpUgAAWDQEEgCAeXuirkuSdHE1gQSwlDxul248a7WePtyjll6f0+UAALAoCCQAAPP25KFurSvxqjQ3w+lSgIR3w1mr5HYZ3fsiqyQAAImBQAIAMC++sUm91NynS1gdAURFSW66Lq8t0i92tmpsMuB0OQAALBiBBABgXp5t6NVEwOoS+kcAUfO+c8rV5xvX7/d2OF0KAAALRiABAJiXJw91KSvVrR3ly50uBUgaF55RoPL8TJpbAgASAoEEAGDOrLV6oq5b559RoFQPP0qAaHG5jN579mq92NSnw51DTpcDAMCC8FskAGDOGnt8aj0+Qv8IwAHXbS9TqtvFKgkAQNwjkAAAzNkTdd2SRCABOCA/O01XbyrRL3e1anhs0ulyAACYNwIJAMCcPb6/U9XF2Vq1PNPpUoCk9KELKjU0Nqlf7DzqdCkAAMwbgQQAYE76/eN6sblPV6wvdroUIGltWZWnbavz9JNnmxUIWqfLAQBgXggkAABz8qe6LgWCVpfXEkgATvrIhWvU0uvXHw50Ol0KAADzQiABAJiTx/Z3qsibpjPL8pwuBUhqV24o1orcdP34mSanSwEAYF4IJAAAERubDOjJum69ubZYLpdxuhwgqXncLt1yfoWeb+zTvrYBp8sBAGDOCCQAABF7tqFXvvGA3kL/CCAm3Hj2amWmuvXDp1klAQCIPwQSAICIPba/U5mpbp23Nt/pUgBIys1I0Y1nrdYDu9vUetzvdDkAAMwJgQQAICLBoNXj+zt1SXWh0lPcTpcDIOxjF1fKZaQfPNXodCkAAMwJgQQAICK7W/vVNTTGuE8gxpTmZuidW1bqvpeOqmd4zOlyAACIGIEEACAiD7/WrhS30ZvXEUgAsebjl6zVeCConzzT7HQpAABEjEACADCrYNDqoT3turiqULmZKU6XA+AkZxRl68r1Jbr7uWYNjU44XQ4AABEhkAAAzOqVo/1qGxjV2zaXOl0KgFP45GVrNTg6qbufa3G6FAAAIkIgAQCY1YN72pTqcdE/Aohhm8vydFlNoX7wdCOrJAAAcYFAAgBwWsGg1cOvteuS6kJ509muAcSyz1xerX7/hH76bLPTpQAAMCsCCQDAae06clydg2N6O9s1gJh35qo8vXldkX7wdJMGWSUBAIhxBBIAgNN6cHeb0jwuvbmW7RpAPPj/rqjWwMgEEzcAADGPQAIAcEqBoNXDezv0pnVFyk7zOF0OgAhsXJmrK9YX64dPN2rAzyoJAEDsIpAAAJzS04e71T00pmvOXOF0KQDm4K+vqNbQ2KS+92S906UAAHBKBBIAgFP65cvHlJeZojfVFjldCoA5qC3N0bu2rtS/P9Ostv4Rp8sBAGBGBBIAgBkNjEzo0X0duubMFUrzuJ0uB8Ac/c1baiRJ33zskMOVAAAwMwIJAMCMHtrTrrHJoN6zrczpUgDMw8q8DH3w/Ar98uVWHewYdLocAADegEACADCjX77cqjOKsrW5LNfpUgDM0ycvXStvmkf/+PBBp0sBAOANCCQAAG/Q1OPTrpbjes+2MhljnC4HwDzlZabq02+u0pOHuvXHg51OlwMAwOsQSAAA3uBXL7fKZaR3bV3pdCkAFujm8yq0tjBL//vBAxqbDDhdDgAAJxBIAABeZzIQ1C92turCqkKV5KY7XQ6ABUr1uPTFd2xQU49P//5Ms9PlAABwAoEEAOB1Hj/QpY7BUb3/nNVOlwJgkVxSXajLa4v1//5wWF2Do06XAwCAJAIJAMBJ7nmhRaW56XrTuiKnSwGwiP7X22s1EbD6ykMHnC4FAABJBBIAgGmaenx6+nCP3nv2annc/IgAEkl5fpY+celaPbC7TU/UdTldDgAABBIAgL+45/kWeVxGN5y9yulSACyBT162VmsKs/Q//2uv/OOTTpcDAEhyBBIAAEnS6ERAv9jVqis3lKjISzNLIBGledz6P+/apNbjI/r244edLgcAkOQIJAAAkqTf7m7TwMiE3ncuzSyBRHbumnzdsGOVfvjnJu09NuB0OQCAJEYgAQCQtVY/+nOTaoq9Om9NvtPlAFhin3/rOi3PStXf/Hy3xiYDTpcDAEhSBBIAAD15qFsHO4b0sYvXyBjjdDkAllheZqq+/p7Nqusc0r88xtYNAIAzCCQAAPq3JxtVkpOua85c4XQpAKLksnVFuvGsVbrrqQbtaulzuhwAQBIikACAJPda64Cea+zVhy+sUKqHHwtAMvnC22pVmpuhv/75bg2PMXUDABBd/OYJAEnu355qkDfNo5vOppklkGy86Sn65l+dqaN9fn3xv/Y6XQ4AIMkQSABAEjvS69fDr7Xrveesljc9xelyADjgnDX5+vSbq/SrV47p/l2tTpcDAEgiBBIAkMS+88fDSnG79OELK50uBYCD/tubqnTumuX6X/+1V/Vdw06XAwBIEgQSAJCkGruH9auXW/X+c8tVnJPudDkAHOR2GX37xq3KSHXrU/e8LB/9JAAAUUAgAQBJ6tt/OKw0j1u3XbLW6VIAxIDinHR9+8YtOtw1pP/xyz2y1jpdEgAgwRFIAEASOtQ5pAd2t+nm88tV6E1zuhwAMeKiqkJ99qp1emhPu+58stHpcgAACY5AAgCS0LcfP6zMFLc+fjGrIwC83q0Xr9E7zlyhrz9yUH+q63K6HABAAiOQAIAk8/KR43rotXZ95MJKLc9KdbocADHGGKN/es8m1Zbk6PZ7Xtb+tkGnSwIAJCgCCQBIIsGg1T/8dr+KvGn6OL0jAJxCZqpHP/7gWcrJSNGHf/KS2gdGnC4JAJCACCQAIIn8+pVj2n20X//jqnXKSvM4XQ6AGFaSm64ff/AsDY9N6kP//pIGRyecLgkAkGAIJAAgSfjGJvVPvz+oM8ty9e6tK50uB0AcqC3N0fffv031XcP68L+/JP8440ABAIuHQAIAksT3nqhX19CYvviO9XK5jNPlAIgTF1UV6ts3btXLR47roz/dqdGJgNMlAQASBIEEACSBA+2D+rcnG/XurSu1vXy50+UAiDNv21yqf77+TD3X2KtP/McujU8GnS4JAJAACCQAIMFNBoL67C/3KDcjRf/z7eudLgdAnHr3tjJ99Z2b9Ke6bn36Z68QSgAAFoxAAgAS3L8/06w9rQO645oNjPkEsCDvPWe1vvSO9fr9vg599O6d9JQAACwIgQQAJLDmHp/+72N1ury2WG/fXOp0OQASwIcuqNTX37NZfz7crff/8AUN+Jm+AQCYHwIJAEhQ45NB/ff7XlGK26WvvHOjjKGRJYDF8VdnrdL33rdNe48N6oa7nlPX4KjTJQEA4hCBBAAkqG88clC7Wwf0jes2qyQ33elyACSYqzaW6scfPEtH+vy69rvPaO+xAadLAgDEGQIJAEhAfzzYqR883aQPnFuuqzayVQPA0riwqkC/uO08GUnX3fmsHtrT7nRJAIA4QiABAAnmWP+I/vYXe7SuxKsvvK3W6XIAJLgNK3L1m9sv1IYVufrUvS/rXx47pGDQOl0WACAOEEgAQAIZHpvUR37ykiYmg/rX925Teorb6ZIAJIFCb5ru/dg5un57mb79h8O65d9fVPfQmNNlAQBiHIEEACSIQNDqM/e9okOdQ/rX923TGUXZTpcEIImkedz6+nWb9X/etUkvNvXp6m8/pacOdTtdFgAghhFIAECC+MeHD+jxA12645oNuqS60OlyACQhY4zee85q/fa/XajlWam6+ccv6qsP7dfoRMDp0gAAMYhAAgASwP/7w2H98M9NuuW8ct18XoXT5QBIctXFXj1w+4V63zmr9YOnm3T1t5/W8429TpcFAIgxBBIAEOfueqpB//exQ3r31pX60js2OF0OAEiS0lPc+uq7Numej56jQNDqxrue19//+jUNjk44XRoAIEYQSABAHPvRn5v0fx4+qLdtLtXXr9ssl8s4XRIAvM4FZxTo95+5SB+9sFL3vXhEl33jCd3zQosCTOIAgKRHIAEAcchaq6/97qD+94P7ddWGEn3rhi3yuPkjHUBsykz16H++fb0euP1CrS3M1hd+vVdv+87T+vPhHqdLAwA4iN9eASDOTASC+ptf7NadTzbofees1nfft00phBEA4sDGlbn6z4+fq++9b5uGxyb1/h+9oPf+4Hm92NTndGkAAAd4nC4AABC5joFR3X7vy9rZclx/c0W1bn/TGTKGbRoA4ocxRm/dVKo3rSvSfzzfojufbNRf/dtzOn9tvv7bm6p07prl/LkGAEmCQAIA4sSz9T369H2vyD8e0Hdu2qprzlzhdEkAMG/pKW599KI1et855brnhVAwcdMPnteGFTn6yIWVevvmFUr1sPoLABKZsTb+Gwrt2LHD7ty50+kyAGBJjIwH9M3H6vSjPzdpTWG27nz/Np1R5HW6LACRePzS0PfLn3CyirgwOhHQr14+ph8/06T6rmEVetN0w45Vum57mSoKspwuDwCwAMaYXdbaHScfZ4UEAMSwFxp79dlf7lFzr1/vPWe1vvDWWmWl8Uc3gMSTnuLWe89ZrZvOXqWnD/fo359p0veeqNe//qleZ1cs13U7yvTWTaXK5s9AAEgY/IkOADHoSK9f//T7g3rotXatWp6hez96js4/o8DpsgBgyRljdHF1oS6uLlTHwKh+9Uqr7t/Zqv9x/x598Td7dUl1oa7cUKI3rytWbmaK0+UCABaAQAIAYkhb/4jueqpR975wRG6X0Wcur9KtF69RZip/XANIPiW56frkpWfoE5es1ctH+vWbV4/p0X2demRfpzwuo/PW5utN64p0UVWB1hZm0wwTAOIMv+ECQAzY3zaonzzbpF+/ckzWSu/etlJ/85YaFeekO10aADjOGKPt5cu0vXyZ7njHBu1u7dcj+zr1yL4O/cNv90uSSnLSdcEZBbqwKl87yperbFkGAQUAxDgCCQBwyHHfuH6/r0P3vXRUu4/2K83j0vvOKddHL6pU2bJMp8sDgJjkchltXb1MW1cv0+euXqejfX79ub5Hf67v0R8PduqXL7dKkgqyU7Vl1TJtXZ2nravztGllrrzpbPEAgFhCIAEAUdQxMKrHDnTq93vb9XxjnwJBq6qibH3x7ev17m0rlZeZ6nSJABBXVi3P1E1nr9ZNZ69WMGh1oGNQrxzpD30dPa7HD3SeOHdlXobWlXi1rtSrmpIc1RR7VZ6fqfQUt4PvAACSF4EEACyRYNDqSJ9fu1v79Xxjr55v7FNTj0+StKYgSx+/eI2u2liiTStzWVYMAIvA5TLasCJXG1bk6v3nlkuS+v3jeuVov/a3Depgx5DqOgb15KFuTQbtietKc9O1enmmyvMzVZ6fpfL8TK3Iy1BJTroKvWlKcbuceksAkNAiCiSMMVdJ+rYkt6QfWmu/dtLjJvz4WyX5JX3QWvvy6a41xiyX9J+SKiQ1S/ora+3x8GOfl/QRSQFJn7bWPrKgdwkAS2giEFR7/6iO9PnV0udTXceQ9rcN6kD7oHzjAUmSN92jcyqX633nrNZFVYWqLqb5GgBEQ15mqi6rKdJlNUUnjo1NBtTY7dOhziG19PrV3OvTkV6//niwWz3Dra+73hgpPytNJblpKvamqzg3XYXZaVqWmaJlWanKy0wN3c5MVV5mirLTPPz5DgARmjWQMMa4JX1X0hWSWiW9ZIx5wFq7f9ppV0uqCn+dI+n7ks6Z5drPSfqDtfZrxpjPhe9/1hizXtKNkjZIWiHpcWNMtbU2sDhvGQBObTIQlG8soOHxSfnGJjU0GvruG5tUr29cPcNj6hkeU+9w6HbH4Kja+kcVmPY3bdlpHtWWenXd9jKtX5GjDStyVVuaI7eLX1ABIBakedyqLc1RbWnOGx7zjU2qpdev9oERdQ6G/pzvGhwN/Xk/MKpXjvarzzd+yudOcRvlZqQqO82trDSPslI9ygrfzk7zKDPVc+KxzDSP0jyu8Jf7L7dTXEp1u5WWErqfGn481eOSx2Xkdhl5XIbgA0Dci2SFxNmS6q21jZJkjLlP0rWSpgcS10q621prJT1vjMkzxpQqtPrhVNdeK+nS8PU/lfSEpM+Gj99nrR2T1GSMqQ/X8Nz832bs+f4TDWrp9Z3ycWtP+VDocZ3+hNmvn+XxBb5+JC8yew2zvMdZr3f29SM5acH/HmP8v5NI/ikt9b+noJUmg0FNTFpNBIOaCIRvB4Kh++Hb44GgxieDGpsMzlpzXmaKCrLTVJCdqq2rlunaMzO1enmmVi3P1Or8TJXmpMtF+AAAcSkrzaP1K3K0fsUbw4opk4Gg+kcm1O8f13H/hI77xtXvn9Dx8P2BkXENjwXkH5vU8NikuofH1NLr13A44J5aPbdQLiN5XK4TAYXbbaYFFtOOTx1zG7lMKMgw4ev/cttIJnxMRi5X6LsJnxM6/pfbUviYUfg5//JcU99PNlN+MvN5bzw640/VGZ9vhmvNyedEWtvsz3WqY8BSKc5J12cur3a6jEUTSSCxUtLRafdbFVoFMds5K2e5ttha2y5J1tp2Y8zUOrqVkp6f4blexxhzq6RbJWn16tURvI3YsqvluF471n/ac2b+o3za47P84Tfbn40LTdUjuXz2Gp19j7O+hQW+/mLUsNT/DGez1PVHcs5C3qORlOJ2yeM2yk7xKNXtUorbpRSPSyluoxSXSykeoxS3S6luV+hvs9L+8rdXWWkeecPfl2elanlWKnuJASDJedyucDCdNq/rg0GrkYmAfOOTGpsIheGhUDww7Xbo/onbEwGNB4IKBKVAMKjJoFUgaP/yPWBnPh4MHw+EbgetlbVSMBzoT78f+i5ZG5QNhI8pdEzWhh7T9PNCt63sSfffaKa/QJj5vBmOzXDmjOdF8vdlUagDWEpnFGU7XcKiiiSQmOlX/ZM/eqc6J5Jr5/N6stbeJekuSdqxY0fc/VHww1t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      "text/plain": [
       "<Figure size 1296x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=np.linspace(0,2200,1000)\n",
    "n=55\n",
    "lam0=10**(-3)\n",
    "limit = math.floor(q/n)\n",
    "print(limit)\n",
    "f = scipy.stats.gamma.pdf(t,n,scale=1/(n*lam0))\n",
    "\n",
    "plt.clf()\n",
    "plt.plot(t,f, label='densité')\n",
    "plt.axvline(x=limit,color='orange', label='barriere de rejet')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "797aa283",
   "metadata": {},
   "source": [
    "### Question 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "57d5f36d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size=500\n",
    "lam = np.linspace(10**-5,10**-1.5,size)\n",
    "\n",
    "\n",
    "\n",
    "Ns = [10, 50, 100, 500, 100000]\n",
    "for n in Ns:\n",
    "    res = []\n",
    "    for l in lam:\n",
    "        exp = scipy.stats.gamma.rvs(n, scale = 1/l,  size = size)\n",
    "        lim = np.quantile(exp,0.95)\n",
    "        add = 1 - scipy.stats.gamma.cdf(costs_filtered.sum(), n, scale=1/l)\n",
    "        res.append(add)  \n",
    "    plt.plot(lam,res, label = n)\n",
    "    \n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0dfa130",
   "metadata": {},
   "source": [
    "Nous pouvons constater que lorsque n croit, la puissance reste plus longtemps égale (ou presque) à 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9a0cb7",
   "metadata": {},
   "source": [
    "### Question 6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b29581d2",
   "metadata": {},
   "source": [
    "![](images/ex3-6.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "db46d3f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y ( -0.0008654004036731705 ) is lower than the quantile of the experimental values ( 1.6681766191065321 ) so H0 is accepted\n"
     ]
    }
   ],
   "source": [
    "exp = scipy.stats.norm.rvs(size = 10000)\n",
    "qlim = np.quantile(exp,0.95)\n",
    "\n",
    "if (qlim > (costs_filtered.mean()-1/lam0) * (lam0) * np.sqrt(n) / n):\n",
    "    print (\"Y (\",(costs_filtered.mean()-1/lam0) * (lam0) * np.sqrt(n) / n ,\") is lower than the quantile of the experimental values (\",\n",
    "           qlim, \") so H0 is accepted\")\n",
    "else:\n",
    "    print (\"Y (\", (costs_filtered.mean()-1/lam0) * (lam0) * np.sqrt(n) / n,\") is higher than the quantile of the experimental values (\",\n",
    "           qlim, \") so H0 is rejected\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd5f0e94",
   "metadata": {},
   "source": [
    "H0 is also accepted in this test"
   ]
  }
 ],
 "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}