{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# renvoie le quotient et le reste de la division euclidienne de a par b\n",
    "def diveucl(a,b):\n",
    "    r=a\n",
    "    q=0\n",
    "    while r>b-1:\n",
    "        q=q+1\n",
    "        r=r-b\n",
    "    return [q,r] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#détermine le plus petit diviseur premier de n\n",
    "def mindiv(n): \n",
    "    r=2\n",
    "    while r <= math.sqrt(n): \n",
    "        if n%r!=0: # si r ne divise par n on augmente r de 1\n",
    "            r=r+1\n",
    "        else: # sinon cela signifie que r est le premier recherché\n",
    "            return r\n",
    "    return n    \n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "29\n"
     ]
    }
   ],
   "source": [
    "print(mindiv(27))\n",
    "print(mindiv(29))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fournit la liste des diviseurs premiers de n, avec multiplicité et par ordre croissant\n",
    "def decompo(n): \n",
    "    d=[] # liste des diviseurs premiers\n",
    "    a=n\n",
    "    while a>1:\n",
    "        d=d+[mindiv(a)] # on ajoute le plus petit diviseur premier de a à la liste d\n",
    "        a= a//d[-1]  # on divise a par p (élément d'indice \"-1\" de la liste d) et on recommence jusqu'à atteindre a=1\n",
    "    return d   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 3, 3]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decompo(27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def produitliste(c):\n",
    "    p=1\n",
    "    for i in range(len(c)): # i va de 0 à la (longueur de c) -1\n",
    "        p=p*c[i]\n",
    "    return p    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 11, 647]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "14234"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(decompo(14234))\n",
    "produitliste(decompo(14234))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fournit une liste de n premiers nombres (question e))\n",
    "def premiereuclide(n): \n",
    "    d=[2]\n",
    "    while len(d)<n:\n",
    "        N=produitliste(d)+1 #N contient un facteur premier qui n'est pas dans la liste d\n",
    "        d=d+[mindiv(N)] #on ajoute à la liste le plus petit facteur premier de N\n",
    "    return d  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 7, 43, 13, 53, 5, 6221671]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "premiereuclide(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def crible(n):\n",
    "    L=list(range(n+1))\n",
    "    L[1]=0\n",
    "    \n",
    "    for p in range(2,n+1):\n",
    "        for i in range(2*p,n+1,p):\n",
    "            L[i]=0  \n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crible(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42.075817584991455\n"
     ]
    }
   ],
   "source": [
    "# Mesurons le temps que prend l'algorithme\n",
    "start=time.time()\n",
    "\n",
    "crible(20000000)\n",
    "\n",
    "end=time.time()\n",
    "duree=end-start\n",
    "print(duree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# On optimise un peu l'algo précédent à deux endroits\n",
    "# renvoie une liste c de longueur n+1 telle que c[k] = k si k est premier et 0 sinon\n",
    "def crible2(n):\n",
    "    d=list(range(n+1)) # d est la liste des entiers entre 0 et n\n",
    "    if n > 0: # 1 n'est pas premier\n",
    "        d[1]=0\n",
    "    r=2 #on initialise à p=2\n",
    "    while r<math.sqrt(n)+1: # on peut arrêter le crible dès qu'on est plus grand que racine de n (1ère optimisation)\n",
    "        if d[r]!=0: # on vérifie que le d[r] n'a pas déjà été supprimé (2ème optimisation)\n",
    "            for i in range(r*r,n+1,r): #on \"supprime\" les multiples de r (en commençant à r^2) en mettant leur valeur à 0\n",
    "                d[i]=0\n",
    "        r=r+1   \n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crible2(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.719168186187744\n"
     ]
    }
   ],
   "source": [
    "# Mesurons le temps pris par le 2ème algo\n",
    "start=time.time()\n",
    "\n",
    "crible2(20000000)\n",
    "\n",
    "end=time.time()\n",
    "duree=end-start\n",
    "print(duree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# L = liste d'entiers. On supprime de L tous les multiples de p\n",
    "def supprMult(p,L):\n",
    "    for i in L:\n",
    "        if i%p == 0:\n",
    "            L.remove(i)\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# renvoie la liste des premiers <= n en utilisant le crible d'Eratosthène récursif (sur une liste)\n",
    "def cribleRecListe(L):\n",
    "    if len(L) == 1 or L[0] > L[-1]^2:\n",
    "        return L\n",
    "    else:\n",
    "        return [L[0]]+cribleRecListe(supprMult(L[0],L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# crible récursif à partir d'un entier n (et en utilisant l'algo précédent)\n",
    "def cribleRec(n):\n",
    "    if n > 1:\n",
    "        return cribleRecListe(list(range(2,n+1)))\n",
    "    else:\n",
    "        return []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cribleRec(40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# renvoie pi(n)\n",
    "def PiIteratif(n):\n",
    "    c=crible2(n)\n",
    "    return len(c) - c.count(0)  # on compte tous les nombres premiers (c'est-à-dire le nombres de valeurs non nulles dans le tableau renvoyé par crible1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# codage en récursif (fonction intermédiaire qui travaille sur les listes)\n",
    "def PiRecListe(L):\n",
    "    # si L[0]² est plus grand que le dernier élément de L il ne reste que des nombres premiers\n",
    "    if len(L) == 1 or L[0]**2 > L[-1]: # on initialise (L[-1] = dernier élément de L)\n",
    "        return len(L)\n",
    "    else:\n",
    "        return 1+PiRecListe(supprMult(L[0],L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pi(n) en récursif en utilisant l'algo précédent\n",
    "def PiRecursif(n):\n",
    "    if n > 1:\n",
    "        return PiRecListe(list(range(2,n+1)))\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0\n",
      "0 0\n",
      "1 1\n",
      "2 2\n",
      "2 2\n",
      "3 3\n",
      "3 3\n",
      "4 4\n",
      "4 4\n",
      "4 4\n",
      "4 4\n",
      "5 5\n"
     ]
    }
   ],
   "source": [
    "for n in range(12):\n",
    "    print(PiIteratif(n),PiRecursif(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VEhyi6d2mq2q5qrZjwQtQ4AAAAICrkJ2XrRfWvKDP9nymvvX6anzH8QrwDbAdC16CAgcAAAAU0qnMU4pZEaONqRsV3iJcYbeFyRhjOxa8CAUOAAAAKIS9aXsVGR+po+eOamLniQqtF2o7ErwQBQ4AAAC4grUpazVy5Uj5+fhpXp95CgkOsR0JXooplAAAAMBlfLTrIw1bPkzVA6trSb8llDdYxQ4cAAAAcAl5+Xl6fcPrWrBtgTrW6qjJnScryD/Idix4uSvuwBlj6hhjVhhjthljkowx0QXrzxtjDhljNhf86HvRa8YaY3YbY3YaY3qX5G8AAAAAKG4ZORmKWRmjBdsW6M83/1lvdH+D8gaXUJgduFxJoxzH2WiMuU7SBmPM8oLnXnccZ/LFFxtjmkp6SFIzSTdIijPGNHYcJ684gwMAAAAl4ci5I4pKiNKuU7s0tu1Y/e8t/2s7EvCrKxY4x3FSJKUUPD5rjNkuqdZlXnKfpL87jpMlaZ8xZrektpLWFENeAAAAoMQkHU9SVEKUMnIzNKvHLHWq1cl2JOA3rmqIiTGmrqSWkr4vWIo0xvxojJlnjKlcsFZL0sGLXpasyxc+AAAAwLrlvyzXgGUD5O/rr9jQWMobXFKhC5wxJkjSx5JiHMc5I+ktSQ0ktdCFHbopV/MLG2OGGGPWG2PWHzt27GpeCgAAABQbx3H07k/vauTKkWpSpYkW912sRpUb2Y4FXFKhCpwxxk8Xyttix3H+KUmO4xx1HCfPcZx8SXN04TZJSTokqc5FL69dsPYbjuO84zhOa8dxWgcHB1/L7wEAAAAokpy8HI37bpymb5yu0Hqhmtt7rqqWq2o7FvC7CjOF0kiaK2m74zhTL1qvedFlD0jaWvD4M0kPGWMCjDH1JDWS9EPxRQYAAACu3enM0/rr8r/q0z2fKjwkXK/d+ZoCfANsxwIuqzBTKDtKelTST8aYzQVrT0v6szGmhSRH0n5JQyXJcZwkY8yHkrbpwgTLCCZQAgAAwJXsT9uviPgIHTl3RK/d+Zr61u975RcBLqAwUyi/lWQu8dSXl3nNBEkTriEXAAAAUCLWHVmnmBUxKuNTRnN7z1WL61vYjgQU2lVNoQQAAADc2ae7P9WQ5UNUrVw1Leq7iPIGt1OYWygBAAAAt5bv5OuNTW9ozk9z1K5mO03tOlUV/CvYjgVcNQocAAAAPFpmbqbGfTdOy/Yv0x8a/UHPtH9Gfj5+tmMBRUKBAwAAgMc6cf6Ehq8Yrp+O/aSRt4/UgGYDdGHIOuCeKHAAAADwSHtO71FEfIROnD+hqV2n6q6b7rIdCbhmFDgAAAB4nNWHV2vUylEqW6as3uvznppXa247ElAsmEIJAAAAj/LRro8UHheumkE1taTvEsobPAo7cAAAAPAI+U6+Xt/wuuYnzVenWp00qfMkBfkH2Y4FFCsKHAAAANxeRk6Gxn4zVgkHE/RQk4f0ZNsnVcaHb3XhefhTDQAAALeWmpGqqIQo7Ti5Q0+1fUoP3/Kw7UhAiaHAAQAAwG3tPLlTEfEROpN9RjO6zVCXOl1sRwJKFENMAAAA4JYSkxP12NLH5MjRwtCFlDd4BQocAAAA3M7i7YsVlRClmyrcpPf7va+bq9xsOxJQKriFEgAAAG4jNz9XE9dN1Ps73lfXOl312p2vKdAv0HYsoNRQ4AAAAOAWzuWc0+hVo/XNoW/0WNPHNPL2kfL18bUdCyhVFDgAAAC4vCPnjigiPkJ7Tu/RuPbj1L9Jf9uRACsocAAAAHBpSceTFJkQqczcTL3Z4011qNXBdiTAGoaYAAAAwGXFH4jXgGUD5O/jr4WhCylv8HrswAEAAMDlOI6jBUkLNHXDVN1a7VZN7z5d1cpVsx0LsI4CBwAAAJeSk5+jl79/WR/t+ki9buqlCZ0mqGyZsrZjAS6BAgcAAACXcSb7jEatHKW1KWs1+NbBimoZJR/Du36Af6PAAQAAwCUkn01WZHykfjnzi8Z3GK8HGj1gOxLgcihwAAAAsG5z6mZFr4hWTn6OZvecrbY129qOBLgk9qMBAABg1bJ9yzToq0Eq71dei/suprwBl8EOHAAAAKxwHEdzfpqjmZtmquX1LTW923RVLlvZdizApVHgAAAAUOpy8nL0/Jrn9dmez9Svfj+N7zBe/r7+tmMBLo8CBwAAgFKVlpWmmBUxWn90vcJDwhUWEiZjjO1YgFugwAEAAKDU/HLmF0XER+hw+mG9cucrurv+3bYjAW6FAgcAAIBSseHoBkWviJaR0bu93lWr6q1sRwLcDlMoAQAAUOI+3/O5Bn89WJUDKmtJ3yWUN6CI2IEDAABAiXEcR7M2z9LsH2erbY22mtp1qioGVLQdC3BbFDgAAACUiKy8LI37bpyW7luq+xver+faPyc/Xz/bsQC3RoEDAABAsTuZeVLRCdHafGyzoltFa1DzQUyaBIoBBQ4AAADFam/aXkXERejY+WOa3GWyetftbTsS4DEocAAAACg2646sU/SKaPn5+Gle73m6Lfg225EAj8IUSgAAABSLT3d/qiHLhyi4XLAW911MeQNKADtwAAAAuCaO4+jNLW/q7S1vq12Ndprabaoq+FewHQvwSBQ4AAAAFFl2XrbGfTdOX+77kkmTQCmgwAEAAKBITmeeVvSKaG1M3ajhLYdr8K2DmTQJlDAKHAAAAK7agTMHFB4frpT0FE3sPFGh9UJtRwK8AgUOAAAAV2Xj0Y2KXhEtSXq397tqeX1Ly4kA78EUSgAAABTal3u/1OCvB6tSQCUt7ruY8gaUMnbgAAAAcEWO42jOT3M0c9NM3V79dk3rOk2VylayHQvwOhQ4AAAAXFZOXo5eWPOCPt3zqe6uf7de6PCC/H39bccCvBIFDgAAAL8rLStNI1eO1A9HftCwkGEaFjKMSZOARRQ4AAAAXFLy2WSFx4fr4NmDernTy7qnwT22IwFejwIHAACA/7Ll2BYNTxiu3PxcvdPzHbWp0cZ2JABiCiUAAAD+w9f7v9agrwYpsEygFvVdRHkDXAg7cAAAAJB0YdLk/KT5mrphqkKCQzSj+wxVKVvFdiwAF6HAAQAAQDn5OXr5+5f10a6P1Ltub03oNEEBvgG2YwH4DxQ4AAAAL3c2+6yeWPWEVh9ercG3DlZUyyj5GN5pA7giChwAAIAXS0lPUXh8uPan7df4DuP1QKMHbEcCcBkUOAAAAC+VdCJJkfGRyszN1Jt3vak7brjDdiQAV8DeOAAAgBdKOJCggcsGyt/HX7GhsZQ3wE1Q4AAAALyI4zhatG2RYlbEqEHFBlrcb7EaVm5oOxaAQuIWSgAAAC+Rm5+riesm6v0d76vHjT30yp2vqFyZcrZjAbgKFDgAAAAvkJGTodGJo5WYnKgBzQZoxO0jmDQJuCEKHAAAgIc7eu6oIhMi9fOpnzWu/Tj1b9LfdiQARUSBAwAA8GA7T+5UeHy40rPT9UaPN9SpVifbkQBcA/bNAQAAPFRicqIeW/qYjIwWhi6kvAEegAIHAADggT7Y8YGiEqJ0U4WbtKTfEjWp0sR2JADFgFsoAQAAPEhefp6mbpiqhdsWqkvtLprYeaIC/QJtxwJQTChwAAAAHiIjJ0NjvxmrhIMJeviWhzW69Wj5+vjajgWgGFHgAAAAPMDx88cVGR+p7Se366m2T+nhWx62HQlACaDAAQAAuLmfT/2siPgInc46rendpqtrna62IwEoIRQ4AAAAN7b68GqNWjlK5cqU0/w+89W0alPbkQCUIKZQAgAAuKmPd32siLgI1QyqqSX9llDeAC/ADhwAAICbyXfyNXPTTL3707vqWKujJneerCD/INuxAJQCChwAAIAbycrL0rhvx2np/qX6Y+M/6ul2T6uMD9/SAd6C/7cDAAC4idOZpxW9IlobUzdqxO0jNLDZQBljbMcCUIoocAAAAG7g4JmDGhY/TCnpKZrUZZL61O1jOxIACyhwAAAALm5z6mYNTxguR47e7f2uWl7f0nYkAJYwhRIAAMCFLf9luQZ/PVjX+V+nRX0XUd4AL8cOHAAAgAtyHEcLty3UlPVTFBIcohndZ6hy2cq2YwGwjAIHAADgYnLzc/XqD6/qg50fqNdNvfTynS8rwDfAdiwALoACBwAA4EIycjI0OnG0EpMTNbD5QMW0ipGP4V0vAC6gwAEAALiI1IxURcZHauepnRrXfpz6N+lvOxIAF0OBAwAAcAE/n/pZ4fHhSstK08zuM9W5dmfbkQC4IAocAACAZWsOr9HIlSMVWCZQC/os0C1Vb7EdCYCL4oZqAAAAiz75+ROFx4WrZlBNLe63mPIG4LLYgQMAALDAcRzN2jxLs3+crTtq3qGpXacqyD/IdiwALo4CBwAAUMqy87L1t9V/0xd7v9D/NPofPdv+Wfn5+NmOBcANUOAAAABKUVpWmkasHKF1R9YpqmWU/nrrX2WMsR0LgJugwAEAAJSS5LPJCo8PV/LZZL1y5yu6u/7dtiMBcDMUOAAAgFKw9fhWRcRHKDc/V7N7zlabGm1sRwLghphCCQAAUMISDiRo4LKBKlemnGL7xlLeABQZBQ4AAKAELd6+WDErYtSociMt7rtY9SvWtx0JgBvjFkoAAIASkJefp8nrJ2vR9kXqcWMPvXLnKypXppztWADcHAUOAACgmJ3PPa+nEp9SwsEEPdr0UY26fZR8fXxtxwLgAShwAAAAxej4+eOKio/StpPb9FTbp/TwLQ/bjgTAg1DgAAAAisne03sVHh+uk5knNa3rNHW7sZvtSAA8DAUOAACgGKw7sk7RK6Ll7+Ov93q/p2bVmtmOBMADMYUSAADgGn2+53MNWT5EweWCtbjfYsobgBLDDhwAAEAROY6j2T/O1qzNs9S2Rlu93u11VfCvYDsWAA9GgQMAACiCnPwcjV8zXv/a/S/d2+BePX/H8/Lz9bMdC4CHo8ABAABcpbPZZzVy5UitTVmr8JBwhYWEyRhjOxYAL0CBAwAAuAop6SkKjw/X/rT9eqnjS7qv4X22IwHwIhQ4AACAQtp2Ypsi4iOUlZult3u+rXY129mOBMDLMIUSAACgEFYdXKUBywbIz8dPC0MXUt4AWEGBAwAAuIK/7/i7hq8YrnoV62lJvyVqWLmh7UgAvBS3UAIAAPyOfCdfr294XfOT5qtr7a56rfNrCvQLtB0LgBejwAEAAFxCVl6Wnvn2GX21/ys91OQhPdX2Kfn6+NqOBcDLUeAAAAD+w+nM04peEa2NqRv1ROsn9FjTxzgmAIBLoMABAABc5ODZgwqPC9fh9MOa1GWS+tTtYzsSAPyKAgcAAFBg6/GtioiPUJ6Tpzm95qhV9Va2IwHAbzCFEgAAQNLKgyv1l6/+onJlyik2NJbyBsAlUeAAAIDX+/uOvyt6RbQaVGygRX0XqV7FerYjAcAlcQslAADwWvlOvqZtnKb3tr7HMQEA3AIFDgAAeKWsvCw9++2zWrZ/mf7U5E8a23YsxwQAcHkUOAAA4HXSstI0PGG4NqZu1MjbR2pAswEcEwDALVDgAACAV0k+m6xhccN0KP2QJnWepD71OCYAgPugwAEAAK+RdDxJEfERysnP0Zxec3R79dttRwKAq8IUSgAA4BVWHVylgV8NVNkyZRUbGkt5A+CWKHAAAMDjfbjzQw1fMVz1KtbTor6LVL9SfduRAKBIuIUSAAB4rHwnX9M3Tte8rfPUpXYXTew8kWMCALg1ChwAAPBI2XnZevbbZ7V0/1L1b9xfY9uNVRkfvvUB4N74KgYAADxOWlaaoldEa8PRDYppFaO/NP8LxwQA8AgUOAAA4FEOpR9SeFy4Dp49qNfufE196/e1HQkAig0FDgAAeIykE0mKiItQdn62ZvecrTY12tiOBADF6opTKI0xdYwxK4wx24wxScaY6IL1KsaY5caYnwt+rlywbowxM4wxu40xPxpjWpX0bwIAACAxOVEDlw1UgG+AFoUuorwB8EiFOUYgV9Iox3GaSmovKcIY01TSU5LiHcdpJCm+4GNJCpXUqODHEElvFXtqAACAi/xj1z8UlRCluhXqanG/xRwTAMBjXbHAOY6T4jjOxoLHZyVtl1RL0n2SFhRctkDS/QWP75O00LlgraRKxpiaxZ4cAAB4vX8fEzCNqX3mAAAgAElEQVR+zXh1vKGj5veZr2rlqtmOBQAl5qreA2eMqSuppaTvJVV3HCel4KkjkqoXPK4l6eBFL0suWEsRAABAMcnOy9a478bpy31f6sHGD+qZds9wTAAAj1for3LGmCBJH0uKcRznzMWjeB3HcYwxztX8wsaYIbpwi6VuvPHGq3kpAADwcmlZaYpZEaP1R9crulW0BjUfxDEBALxCYd4DJ2OMny6Ut8WO4/yzYPnov2+NLPg5tWD9kKQ6F728dsHabziO847jOK0dx2kdHBxc1PwAAMDLHE4/rMeXPq7Nxzbr1Ttf1eBbB1PeAHiNwkyhNJLmStruOM7Ui576TNLjBY8fl/TpReuPFUyjbC8p7aJbLQEAAIps24ltevjLh5Wakap3er6jfvX72Y4EAKWqMLdQdpT0qKSfjDGbC9aelvSqpA+NMYMk/SKpf8FzX0rqK2m3pAxJA4s1MQAA8ErfJH+jUatGqVJAJc0JnaOGlRvajgQApe6KBc5xnG8l/d59CT0ucb0jKeIacwEAAPzqo10f6aW1L6lx5caa1WOWggN5+wUA78SoJgAA4LIcx9HMTTM156c56lSrk6Z0maJAv0DbsQDAGgocAABwSTl5ORq3epz+b+//6Q+N/qBn2z/LMQEAvB5fBQEAgMs5k31GI1aM0A9HftDwlsOZNAkABShwAADApaSkpyg8Plz7z+zXy51e1j0N7rEdCQBcBgUOAAC4jB0ndyg8LlyZuZmafddsta3Z1nYkAHAphTrIGwAAoKStPrRajy99XL4+vloQuoDyBgCXQIEDAADWfbr7U0XER6j2dbW1KHSRGlVuZDsSALgkbqEEAADWOI6jOT/N0cxNM9WuZjtN6zpNQf5BtmMBgMuiwAEAACty83M14fsJ+mjXR7q7/t0a32G8/Hz9bMcCAJdGgQMAAKUuIydDYxLHaFXyKg2+dbCGtxzOMQEAUAgUOAAAUKpOnD+hyPhIbTu5Tc+2e1Z/uvlPtiMBgNugwAEAgFLzy5lfFLY8TMfPH9e0rtPU7cZutiMBgFuhwAEAgFKx5dgWRcVHSZLe7f2uQoJDLCcCAPfDMQIAAKDErTiwQoO/Gqwg/yDF9o2lvAFAEVHgAABAifpgxweKWRmjhpUaKjY0VjdVuMl2JABwW9xCCQAASoTjOJq+cbrmbp2rLrW7aGLniQr0C7QdCwDcGgUOAAAUu5y8HD23+jl9sfcL/bHxH/V0u6dVxodvOwDgWvGVFAAAFKuz2Wc1YuUIfZ/yvYa3HK7Btw7mjDcAKCYUOAAAUGyOnjuq8Phw7T29VxM6TdC9De61HQkAPAoFDgAAFIufT/2sYXHDlJ6Trll3zVKHGzrYjgQAHocCBwAArtm6I+sUnRCtsmXKan6f+bq5ys22IwGAR+IYAQAAcE2W7luqocuHKjgwWIv7Lqa8AUAJYgcOAAAUieM4WpC0QFM2TNHt1W/X9G7TVTGgou1YAODRKHAAAOCq5eXnadL6SVq8fbF61+2tCZ0mKMA3wHYsAPB4FDgAAHBVMnMzNfabsYo7EKfHmj6mUa1HycfwrgwAKA0UOAAAUGinM08rKiFKW45t0Zg2Y/Ro00dtRwIAr0KBAwAAhZJ8NlnD4obpcPphTeoySb3r9rYdCQC8DgUOAABcUdKJJEXERSgnP0fv9HpHt1e/3XYkAPBK3LAOAAAu65vkbzRw2UAF+AYoNjSW8gYAFlHgAADA7/rk508UlRCluhXqalHfRapfqb7tSADg1biFEgAA/BfHcfT2lrf15pY31eGGDpradarK+5W3HQsAvB4FDgAA/EZOfo5eXPOiPtn9ie5rcJ/+1uFv8vPxsx0LACAKHAAAuEhGToZGrhqp7w59p7CQMIWHhMsYYzsWAKAABQ4AAEiSjp8/rvC4cO06tUt/u+NverDxg7YjAQD+AwUOAABoX9o+DYsbppOZJzWj+wx1rt3ZdiQAwCVQ4AAA8HKbUzcrMiFSvsZX83rPU/NqzW1HAgD8Do4RAADAiyUcSNDgrweron9FLQpdRHkDABdHgQMAwEt9uPNDjVg5Qo0rN1Zs31jVqVDHdiQAwBVwCyUAAF7GcRzN2jxLs3+crc61O2tS50kK9Au0HQsAUAgUOAAAvMjFZ7w90PABPXfHcyrjw7cDAOAu+IoNAICXyMjJ0BOrntA3h77hjDcAcFMUOAAAvMDJzJOKiIvQtpPb9Nwdz+mPjf9oOxIAoAgocAAAeLiDZw4qLC5MqRmpmtZ1mrrd2M12JABAEVHgAADwYEnHkxQeH648J09zes1Ri+tb2I4EALgGHCMAAICH+u7Qdxr41UCV9S2r2NBYyhsAeAAKHAAAHuizPZ8pMj5SN1W4SYv6LlK9ivVsRwIAFANuoQQAwIM4jqO5W+dq+sbpal+zvV7v+rqC/INsxwIAFBMKHAAAHiIvP0+v/PCKPtj5gfrW66uXOr4kP18/27EAAMWIAgcAgAfIzM3U2G/GKu5AnAY2G6iY22PkY3inBAB4GgocAABuLi0rTcMThmtT6iY92eZJPdL0EduRAAAlhAIHAIAbS0lPUVhcmA6ePaiJXSaqT90+tiMBAEoQBQ4AADe169QuDVs+TOdzz2t2z9lqU6ON7UgAgBLGzfEAALihdUfW6fGlj0tGmh86n/IGAF6CAgcAgJtZtm+Zhi4fquqB1bW472I1rtzYdiQAQCmhwAEA4EZit8VqdOJo3VrtVi0IXaAa5WvYjgQAKEW8Bw4AADeQ7+Rr6vqpWrBtge668S692vlVBfgG2I4FAChlFDgAAFxcTl6Onv3uWX2570s91OQhPdX2Kfn6+NqOBQCwgAIHAIALS89OV8zKGH2f8r2iW0VrUPNBMsbYjgUAsIQCBwCAizqWcUzD4oZpz+k9mtBpgu5tcK/tSAAAyyhwAAC4oL1pezVs+TCdyjqlN3q8oY61OtqOBABwARQ4AABczObUzYpMiJSv8dV7fd5Ts6rNbEcCALgIjhEAAMCFJBxI0OCvB6uif0Ut6ruI8gYA+A0KHAAALuLDnR9qxMoRaly5sWL7xqrOdXVsRwIAuBhuoQQAwDLHcTRr8yzN/nG2OtfurEmdJynQL9B2LACAC6LAAQBgUU5+jl5c86I+2f2JHmj4gJ674zmV8eGvZwDApfE3BAAAlmTkZGh04mglJicqLCRM4SHhnPEGALgsChwAABacyjylyPhIbT2xVePaj1P/Jv1tRwIAuAEKHAAApexw+mENXT5Uh9MPa2rXqepxYw/bkQAAboICBwBAKdp5cqeGxQ1TZl6m5vSao1bVW9mOBABwIxwjAABAKVl3ZJ0GLhsoY4wW9FlAeQMAXDUKHAAApSDulziFLQ9TcGCwFoUuUqPKjWxHAgC4IQocAAAl7IMdH2jkypG6peotWtBngWoG1bQdCQDgpngPHAAAJeTiA7q71O6iSV0mqVyZcrZjAQDcGAUOAIASkJufq5fWvqSPf/6YA7oBAMWGv0kAAChmmbmZGp04WisPrtSQ24YoskUkB3QDAIoFBQ4AgGKUlpWmqIQobU7drKfbPa0/3/xn25EAAJJOpGcpPStXPsaoTpVA23GKjAIHAEAxOXLuiMKWh+nA2QOa1GWSetftbTsSAEDSodPn1XXSCuXkOaoWFKD1z95lO1KRUeAAACgGe07v0dDlQ3Uu55zevuttta3Z1nYkAECB+O1HlZPn6IV7m6laUIDtONeEAgcAwDXalLpJkfGR8vf11/w+89WkShPbkQDAq323+7i+Sjry68ff7j6u+tXK6/EOde2FKiYUOAAArsGKAys0OnG0apavqbd7vq1aQbVsRwIAr/fC50nafzxD5QN8f12L6NbQYqLiQ4EDAKCIPt71scavHa9mVZvpjR5vqErZKrYjAYBXcRxHufnOb9YOnTqvXUfT9Wy/WzT4zvqWkpUcChwAAFfJcRy98+M7emPzG+pYq6OmdpmqQD/3nWgGAO5qaOwGfb3t6CWf63FL9VJOUzoocAAAXIW8/Dy98sMr+mDnB7q3wb16vsPz8vPxsx0LALzOqXPZitt+VF2bBKv1TZV/89wNlcqpXrXylpKVLAocAACFlJWXpbHfjNXyX5ZrYPOBGtFqBAd0A0ApOZOZo4/WJysnL1+StOdYuvIdKeauxmpRp5LldKWHAgcAQCGcyT6j6IRorT+6XmPajNGjTR+1HQkAvMritQf02rIdv1mrX628bqtV0VIiOyhwAABcQWpGqsLiwrQvbZ9eu/M19a3f13YkAPA68duPqmnNCvpo2B2/rgWU8ZWPj3fdCUGBAwDgMval7VPY8jCdzjqtWT1mqcMNHWxHAgCP5ziOBry3TttTzvy6lno2S8N7NFKgv3dXGO/+3QMAcBk/HvtREfER8jE+mtdnnppVbWY7EgB4hV1H07Vq1zHd2aiaalcuJ0ny8/XRw+1utJzMPgocAACXkJicqCdWPaFq5app9l2zVadCHduRAMDjbTpwSodOn9eqncckSZMeDFGNimUtp3ItFDgAAP7Dv3b/S8+vfl6NKzfWm3e9qWrlqtmOBAAe73RGtvrPXqOcvAsHc7e6sRLl7RIocAAAFHAcR/O2ztO0jdPUvmZ7Tes2TeX9PPMcIQBwNat2HVNOnqO3Hm6lhtcHqWalcrYjuSQKHAAAkvKdfE1aN0mLti9SaL1QTeg4QX6+HNANANfqw3UH9f66A1e87tCp86pa3l+9m9XwusmSV4MCBwDwetl52Xrm22e0bP8yPXLLIxrdZrR8jI/tWADg9hzH0Rsrdis7N1+Nqgdd9tomNa5TaPOalLcroMABALxaena6YlbG6PuU7zXy9pEa0GyAjOGbBwAoqp1HziojO1fShdH/B05m6KX7m+uR9jdZTuYZKHAAAK91/PxxhceF6+dTP+vlTi/rngb32I4EAG5t7d4Teuidtb9Z8zFS95uvt5TI81DgAABe6eDZgxq6fKiOnz+uGd1n6M7ad9qOBABu76ukIwoo46O3Hmn1690MwUEBuoGBJMWGAgcA8Do7T+5UWFyYcvJzNKfXHIUEh9iOBABu6f0fDui73cd//fi73cfVsWE1db+5usVUno0CBwDwKuuOrNPwhOEq71dec/vMVf1K9W1HAgC3lJWbp5e+2KYAP19VCrwwtbdqUIAeaX+j5WSejQIHAPAa8QfiNWbVGNW+rrZm95ytGuVr2I4EAG4nKzdPaRk5Wv/LKZ3LztOMP7dUj1vYcSstFDgAgFf4eNfHGr92vJpXa65Z3WepUtlKtiMBgNtxHEf3z1qt7SlnJEll/XzUoUE1y6m8CwUOAODRHMfRuz+9qxmbZqhTrU6a0mWKAv0CbccCALe09/g5bU85o/6tayukTiU1DA5SOX9f27G8CgUOAOCx8p18TVw3UYu3L9bd9e/W+I7j5efjZzsWALiFf6w/qN3H0n+ztuvIWUlS9F2NVYvJklZQ4AAAHiknL0fPfPeMlu5bqkebPqonWj8hH+NjOxYAuIXUs5ka/dGPKuNj5OtjfvNcl8bBlDeLKHAAAI+TkZOhEStHaPXh1YppFaO/NP/Lr+cRAQCubMWOVEnSZ5Gd1PSGCpbT4GIUOACARzmVeUoR8RFKOpGk8R3G64FGD9iOBAAu6Z3EPZr81S45cv7rudx8RzUrltUtNa+zkAyXQ4EDAHiMlPQUDVk+RCnnUjSt6zR1u7Gb7UgA4LI+WHdQN1UNVM+mlz4CoGPDaty94IIocAAAj7D71G4NjRuq8znnNbvnbN1e/XbbkQDAJexOTdeaPcd/s3YuO097jp3T8/c01YCO9SwlQ1FQ4AAAbm9z6mZFxEcowDdA7/V5T02qNLEdCQBcxpiPtmjjgdP/te5fxkd3/c7uG1wXBQ4A4NYSkxM1auUoVS9fXW/f9bZqX1fbdiQAcBkn0rO06eBpDevaQIM6/XanrZyfr8oHUAfcDf/FAABu67M9n+m5755TkypN9GaPN1W1XFXbkQDAJUyL26V/bTqkzJx8OY7U79aaqhYUYDsWigEFDgDglhYkLdDk9ZPVrmY7Te82XeX9ytuOBAAuIScvX3O/3aeaFcsqpE4l3VCpnJpxFIDHoMABANyK4zh6fcPrei/pPfWu21svd3pZ/r7+tmMBQLHbceSMDp8+f9Wv23vsnM5m5mryH5uod7MaJZAMNlHgAABuIzc/V8+vfl6f7vlUf2ryJ41tO1a+Pr62YwFAsTuTmaN73/hO2bn5RXp9eX9fdWpYrZhTwRVQ4AAAbuF87nmNXjVaq5JXKTwkXGEhYZxPBMBjfbPruLJz8zXljyFqeH3QVb8++LoABpR4KP6rAgBcXlpWmqISorQ5dbPGtR+n/k36244EAMUuL9/R2H/+qEOnz2v/8QxVCvTT/S1rydeHf6zC/0eBAwC4tKPnjiosLky/nPlFk7tMVq+6vWxHAoASsSX5tD5cn6wm1a9TzYpl1ffWmpQ3/BcKHADAZe1L26ew5WFKy07TW3e9pXY129mOBAAlIicvX/O+3SdfH6MPhrZXpUCGM+HSKHAAAJe09fhWhceFyxijeb3nqWnVprYjAUCJmbhsh774MUXt61ehvOGyfGwHAADgP60+vFp/+eovCvQL1MLQhZQ3AB7NcRwt3XpENSuW1et/amE7DlzcFQucMWaeMSbVGLP1orXnjTGHjDGbC370vei5scaY3caYncaY3iUVHADgmZbuW6qI+AjVua6OYkNjdVOFm2xHAoAS8cO+kxrz0RbFfLBZyafOa3iPRqpZsZztWHBxhbmFcr6kNyQt/I/11x3HmXzxgjGmqaSHJDWTdIOkOGNMY8dx8oohKwDAwy3ZvkSv/vCqWlVvpRndZ6iCfwXbkQCgxEz+aqe2JJ9WlfL+alL9OvVsWt12JLiBKxY4x3ESjTF1C/n57pP0d8dxsiTtM8bsltRW0poiJwQAeDzHcTRr8yzN/nG2utfprtc6v6ayZcrajgUARZKZk6ecvMsfwH02M1frfzmpiG4NNapXk1JKBk9wLUNMIo0xj0laL2mU4zinJNWStPaia5IL1gAAuKS8/Dy9/P3L+nDXh/qfRv+jce3HqYwPM7YAuKeNB07pwbdWK98p3PXdb76+ZAPB4xT1b8i3JL0oySn4eYqkv1zNJzDGDJE0RJJuvPHGIsYAALiz7Lxsjf1mrL7+5WsNaj5I0a2iZQxnHgFwX59vOawyvj4a3auJrvTlrEp5f7WoU6l0gsFjFKnAOY5z9N+PjTFzJH1R8OEhSXUuurR2wdqlPsc7kt6RpNatWxfy3ygAAJ4iIydDMStitCZljZ5o/YQeb/a47UgAUCRnM3O0aO0BZefm68ufUtSxQVX9tXN927HgoYpU4IwxNR3HSSn48AFJ/55Q+ZmkJcaYqbowxKSRpB+uOSUAwKOczjytiPgIJZ1I0osdX9T9De+3HQkAiuyDdQf12rIdkiQfI93fl3cQoeRcscAZY96X1FVSNWNMsqS/SepqjGmhC7dQ7pc0VJIcx0kyxnwoaZukXEkRTKAEAFzsyLkjGrp8qJLPJmtq16nqfmN325EA4JrEb09V4+pBWhbdWZLk48Ot4Cg5hZlC+edLLM+9zPUTJE24llAAAM+0P22/hiwfojPZZ/R2z7fVpkYb25EA4JoMjV2vNXtPaFjXBhQ3lArGfAEASsW2E9s0LG6YJGle73lqWrWp5UQAcG2OpGXqq6SjuqlqoB6/o67tOPASFDgAQIlbd2SdohKiVNG/omb3nK26FevajgQARbb54GntTk3X5oOnJElzHmutGhU5uxKlgwIHAChR8QfiNWbVGNW5ro5m95yt6uWr244EAEWWmZOnh+es1bnsC2MeGgSXV6PrgyyngjehwAEASswnP3+i59c8r+ZVm2tWj1mqVJbzjgC4t7V7T+hcdp6m9g9Rm7pVVDXIn/MrUaoocACAEjF/63xN2TBFHW7ooNe7vq5Av0DbkQDgd3225bDeXrlHVzqc+ER6lsr5+arvrTVV1s+3VLIBF6PAAQCKleM4mrZxmuZtnafedXvrlU6vyM/Xz3YsALisud/s1bH0LLWoc/k7BWpXLqeODapS3mANBQ4AUGxy83P14toX9c+f/6n+jfvr6XZPy9eHb3IAuIYfk08rPSv3v9bPZ+dpS3KanujVWJHdG1lIBhQeBQ4AUCyy8rL0VOJTijsQp6G3DVVEiwjeFwLAZazff1IPvr3mstf0bFqjlNLAivOnpM1LpBO7pbtft52myChwAIBrdi7nnKITovX9ke/1ZJsn9UjTR2xHAoDf+HrbUfn5Gr03oK3K+P73Py5VLOenJjWus5AMJS5li/TDHOmnj6Tc89KNd0i5WVKZANvJioQCBwC4JiczTyo8Llw7Tu7Qy51e1j0N7rEdCQB+4+MNyXonca/ubFRNnRpVsx0HpSE3S0r6l7RujpS8TvILlG7rL7UZLNW8zXa6a0KBAwAUWUp6ioYsH6KUcyma3m26utTpYjsSAPyG4zh6bdkOSdL/Y+++w6us7/+PP8/J3iEkJGyI7Cl7IwIBRK3WWb+2dUCYouIu1lqrtmLFBbJCcP9aZ9UqKhABZQfCJuyZEJKQkL1Ozrl/fxykoiAryX3G63Fdvey5z+G6XtWa5JX7c7/fd/dvYW4YqX0FR2DDQkh7B8ryoH4rGPUCdL0DgjxjlY0KnIiIXJIDBQcYt2QcZbYy5iXMo0dsD7MjiYicVmGzk1NUyf7cEnKKK5lxa1eGtY81O5bUBocDDnwHqcmw5xvntbajnXfbWl4FVqu5+WqYCpyIiFy07Se2M3HpRHwsPrw56k3aRrU1O5KIyBnuWriedQfzAfCxWhjSNsbkRFLjfhxKkroA8g9ASAwMfAh63A2RTc1OV2tU4ERE5KKsObaGB5Y9QFRgFEkJSTQN99xvkiLinnKLK1l3MJ8br2zEoNYxNKkXRP1Q9xxYIWfx86EkTfvCkGnQ4TduO5jkYqjAiYjIBVtyeAmPf/84LSJaMG/4PGKC9RttEXEthWU27nlrPQDjBl9Bh0bhJieSGuHBQ0kulgqciIhckI/3fMyza5+lS3QXZg2bRURAhNmRRER+4eO0DLZnFtG1aSTtG2otgNvzgqEkF0sFTkREfpVhGCRvT+a1tNcY2HggM66aQbBfsNmxRMSLGYaBwzj7eynp2bSJDeXzyQPqNpTUHC8bSnKxVOBEROScDMNgxoYZvL3zbUa3HM1zA5/Dz+pndiwR8WKGYXDNaz+w63jxOT8z/qr4OkwkNcZLh5JcLBU4ERE5q2pHNX9d/Vc+3/85d7S7gyd6P4HV4t2/9RQR8+04VsSu48XccGUjrogJ/cX7PlYLt/XUD/tuxcuHklwsFTgREfmFiuoKHv3+UZYfXc6krpOY0HUCFovF7Fgi4uVOlFTyyEdbsFjgqes6EK3Jku6rugp2fg7r50PGeq8eSnKxVOBEROQMJVUlTPluChuzNzKtzzTuaHeH2ZFERACYu3w/u44XM7hNjMqbuyrMhI1vwsa3oDQXoq6Akf+AK//Pa4eSXCwVOBEROS2/Ip8JSyaw9+ReXhj0AqPjR5sdSUTktJRdOfRpGcVbd/cyO4pcDMOAQz84j0nu+goMB7QZBb3HQvxQrx9KcrFU4EREBIDjpcdJXJxIVmkWrw19jcFNBpsdSUS8yLtrD/PGd/vO+b6BQXZRJfcMaIHVqiPdbqGyGLb82zmUJHcXBEVB//ug571Qr4XZ6dyWCpyIiHCo8BDjloyjuKqYeQnz6BHbw+xIIuJl3ll9CH9fK/3i65/zM4F+Vm7o2rgOU8klyd3tvNu25d9QVQyNusGNc6Djb8EvyOx0bk8FTkTEy+3K38X4JeMBSB6ZTIf6HUxOJCKeyDAMlu/JpazS/ov3Sipt7M0p4anrOjBmYEsT0slls1fDnq+dQ0kOfg8+/tDxJug9Dprol4I1SQVORMSLpWWnMTllMqH+ocxPmE/LCP3gJCK1Y8WeXO55M/Wc7/tYLYzoEFuHiaRGlORC2tuw4U0oyoCIpjDsL9D9LgiJNjudR1KBExHxUiszVzJ12VTiQuKYnzCfhqENzY4kIh5syc5sgv19+GRif3zO8gxbWKAvDSN0vM4tGAZkbHDebdv5GdirIH4IXDPdOZzERxWjNunvroiIF/rm4Df8aeWfaB3ZmjnD51A/6NzPnIiI/Jq//XcnWzIKzvu5XVlFDGodTfuG4XWQSmqFrRy2f+IsbllbwD8Metzj3N0W08bsdF5DBU5ExMt8vOdj/rbmb3Rr0I1Zw2YR5h9mdiQRcVPZRRUsXHWQNrGhNAgL/NXPdm9ejzED4+somdSok4cgNRk2vQvlJyGmPVw7A7rcDgH6HlLXVOBERLzIwu0LeWXjKwxsPJCXh7xMkK+OK4nIxcsqLCe7qJLlu3MAmHlHd9rG6Qd5j+JwwP4U5zTJvYvBYoX210GvRGgxECxa5WAWFTgRES9gGAavpb1G8vZkrmlxDc8PfB4/Hz+zY4mIG6qw2Rn16g8UltsAaBYVTJvYUJNTSY0pPwmb3ocNyZB/AEIawOBHocfdEKEVDq5ABU5ExMPZHXaeX/c8H+35iNva3Ma0PtPwsfqYHUtE3NS6g/kUltt4bFRb2seF06pBKBbdjXF/WVshNQm2fgTV5dC0L1z9JLT/Dfj6m51OfkIFTkTEg9nsNqatnMY3h75hbOex3N/tfv2gJSIXxOEwmP7NLrIKK864vie7mEA/K/cOaEmgn34Z5NaqqyD9C+cxyaNrwTcIutzqPCbZsIvZ6eQcVOBERDxUeXU5Dy1/yLkuoMdU7u10r9mRRMSNbMssZN73B2gYEfiLonZ3f5U3t1Z0zLm3beNbUJoD9VrCiOeh250QVM/sdHIeKnAiIh6ouKqY+1LuY1POJp7u9zS3tLnF7Egi4iZKK6spq7KzaFsWVgssun8Q9UJ0hM7tGQYcXuVcAQOf1EsAACAASURBVJD+JRgOaD0Ceo+DK4aC1Wp2QrlAKnAiIh4mrzyPCUsnsK9gHy9e9SKjWowyO5KIuImc4gquenE55TY7AL1a1FN5c3eVJbD137B+AeSmQ2Ak9JsEPcdAVEuz08klUIETEfEgWSVZjFsyjuOlx5k5dCYDGw80O5KIuJHv0nMot9l5ZEQbIoL9GXBFfbMjyaXK3QOpC2DLv6CyCBp2hd/Mgk43g3+w2enkMqjAiYh4iIOFBxm3ZBylVaXMS5hH99juZkcSEReXduQkS3Zmn369bFcOjSODmHx1Kw08ckf2atjzjXOa5IHlYPWDjr91HpNs0lO72zyECpyIiAfYmbeTCUsmYLFYWDhqIe2i2pkdSUTcwNOf72D7sUL8fvL8k8qbGyo9AWlvOweTFB6F8MYw9M/Q/S4IbWB2OqlhKnAiIm5uw/ENTPluCmH+YcxPmE+LiBZmRxIRN5BdVMG2zEIeG9WWSUNamR1HLkXGRudQkh2fgr0KWg6GUf+ANteAj37M91T6Jysi4sa+z/ieh5Y/RKPQRsxPmE9cSJzZkUTEBT304Wa+3Jp1xjXDMAAY2k53aNyKrRy2f+o8JnlsE/iHOu+09RoLDXT6whuowImIuKlFBxbx5MonaV2vNXMT5hIVGGV2JBFxQcUVNv675Rjdm9WjW7Mzd3w1jAikbWyYScnkopw8DBuSIe1dKM+H6LYw+iXo+jsI0D9Db6ICJyLihj7c/SHPrX2O7rHdmTV0FqH+oWZHEhEXs+VoAVszC9mfU4LNbvBQQhv6xGuqpFtxOODAMlif5BxOYrFCu9HOoSQtBmkoiZdSgRMRcSOGYZC8PZnX0l5jcJPBzLhqBoG+gWbHEhEX43AYjH1nA7nFlYDzTluP5vXO86fEZVQUOcf/r58PefsgJAYGPQw974GIJmanE5OpwImIuAnDMHhl4yu8ueNNRrcczXMDn8PP6md2LBFxQdsyC8ktruS5GzsxsmMcYYG++PpYz/8HxVy5u51327b8C6pKoHFPuCkJOtwAvgFmpxMXoQInIuIG7A47z659lk/2fsLtbW9nWp9pWC36YUxEnDYezudPn26j2u4cTFJUUY3VAtd2bki9EH+T08mvctidxyPXz3fubvPxdy7b7p0IjXuYnU5ckAqciIiLs9lt/Gnln/j20Lckdk5kSrcp2tEkImf4IPUomSfLGdo+9vS1zo3DVd5cWVk+pL0DqclQeOTU7ranoMfdEBJtdjpxYSpwIiIurKK6gqnLp7IycyUP93iYuzvdbXYkEXEBu48Xc6yg/PTr73blMrR9LDPv6GZiKrkgWVth/TzY9jFUVziHkYx8Dtpeq91tckH0/xIRERdVUlXClO+msDF7I3/p9xdubXOr2ZFExAWUVFZzwxsrqbA5zrg+smPsOf6EmM5ug/QvYN18OLoW/IKh6x3OY5KxHc1OJ25GBU5ExAUVVBQwcelE0vPTeWHQC4yOH212JBFxET/syaXC5uDFm7vQJs65/8vfx0r7htoF5nKKs2HjW7BhIZQch3otYeTf4cr/gyBNBZVLowInIuJicstyGbdkHEeKjvDq1a8ypOkQsyOJiAlsdgdPfLKNnOKKM64fyislPNCX33ZvjJ8mS7oew4CMVOdQkh2fgcMGrYZD75nOv1r1z0wujwqciIgLySzJJHFxIifKTzB7+Gz6NOxjdiQRMUnqoXw+ScugXVwYwf4+p6/HhAbwx74tVN5cja0Ctn/iLG5ZmyEgHHqNdR6TrH+F2enEg6jAiYi4iIOFB0lcnEhZdRlJI5LoGtPV7EgiUssqbHaO5Jed9b0vNh/D39fKJxP7ExKgH9lcVsFR2JAMG9+G8nyIaQfXvgxdboeAULPTiQfSVwMRERewK38X45eMB+DNkW/SNqqtyYlEpC5M+dcmluzMPuf7Q9rGqLy5IsOAQz/Aunmwe5HzWtvR0Ge8c6qkVr1ILdJXBBERk23O2cykpZMI9gsmaUQSLSNamh1JROpAaWU1K3bnck2nOK7r0uisn+nZQoMuXEplCWz9ANYnQW46BEXBgAeg5xiIbGp2OvESKnAiIiZam7WW+7+7n5igGJJGJNEo9Ow/xImIe/tiyzFW7ztxxrUTJVVU2R38oW9z+rfS4maXlrffWdo2vw+VRdCwK9wwGzrdDH6BZqcTL6MCJyJikmVHlvHwiodpEdGC+QnziQ7SD3Ainqja7uCpz7ZTbXcQGnjmj17dm0XSs0WUScnkVzkcsG+pc+n2vqVg9YOON0LvcdCkl45JimlU4ERETPDVga94cuWTdKjfgTnD5xAREGF2JBG5TBU2O3aH8YvraUdOUlhuY86d3bmmc0MTkslFKS9w3mlbnwQnD0JoHAyZBj3ugrA4s9OJqMCJiNS1D3d/yHNrn6NnXE9mDp1JiF+I2ZFE5DJ9vjmTB/69+Zzv+/lYGNhad9ldWvZO5wqArR+ArQya9oVhT0G768HX3+x0IqepwImI1KE3t7/JyxtfZnCTwcy4agaBvnp2QsQTfLH5GLHhAYwZePYhRK0bhBEW6FfHqeS87NWw+yvn3bZDP4BvIHS+xXlMsqFWuYhrUoETEakDhmEwa/Ms5m+dz8gWI/nHwH/g56Mf5kTczdH8Mj7fnMnPT0qu2n+C3/VqxrjBWtjsFkpPwMa3YMNCKMqEiGYw/Bno/kcI1jOJ4tpU4EREapnDcPBi6ou8n/4+N7e+maf6PoWP1cfsWCJyCV5ZuodP0zJ/cd3fx8r1XfV8m8vLTHMek9z+CdirIH4IjP4ntBkF+rosbkIFTkSkFtkddv665q98tu8z/tDhDzza81Esmlwm4pbsDoPlu3O54cpGvHzblWe8ZwGsVv277ZKqK2Hn586l25kbwD8Uut8FvRMhpq3Z6UQumgqciEgtsdltPPHDEyw+vJhJXScxoesElTcRN1JcYeO3s1dzoqQSAIfDoKiimuHtY/FRWXN9Rcdgw5vOo5KlOVC/FVzzInS9AwLDzU4ncslU4EREakF5dTkPLX+IlZkreaTnI9zV8S6zI4nIRVqxJ5d9OSX8tltjwk/tbwsJ8CWhQ6zJyeScDAOOrHEek0z/Lzjs0GakcyhJ/NVgtZqdUOSyqcCJiNSwkqoSJqdMZlPOJp7u9zS3tLnF7EgichFS0rMpKLPx6aYM6gX78dKtXXXHzdVVlcH2j2HdfMjeBoER0GcC9BoLUWefDCrirlTgRERqUEFFAROWTmB3/m6mD57ONS2vMTuSiFyEzUcLGPP2htOv7+jdVOXNlRUcgdQFkPYOlJ+EBh3h+teg823gH2x2OpFaoQInIlJDcstyGbdkHEeKjvDq1a9yVdOrzI4kIhdp6c5sfKwWvrp/IMF+vjSK1K5Gl2MYcGglrJ8Hu74CLND+Oug9Hpr3Bz1rLB5OBU5EpAZklmSSuDiRvPI85gyfQ++Gvc2OJCI/czivlKkfbKay2nHOzxzJK6NH83q0i9OQC5dTVQbbPnJOk8zZAUFRMOAB6DkGIpuanU6kzqjAiYhcpgOFB0hcnEhFdQVJI5LoEtPF7EgichafpmWy6WgBQ9s2OOdNmoYRQfyxX/O6DSa/7sdjkhvfhooCiO0Mv5kFnW8BvyCz04nUORU4EZHLkJ6XzoSlE7BgYeHIhbSN0k4hEVeUXVTB22sO0b1ZPZLv7mV2HDmfH49JrpsLuxdx+phknwnQrJ+OSYpXU4ETEblEm3M2M2npJEL8Q0hKSKJFRAuzI4nIWRiGwR1Jaykos2kFgKurKoNtHzqnSZ4+Jvkg9BoDEU3MTifiElTgREQuQerxVCanTCYmKIakEUk0Cm1kdiQROYf9uaUcyC3l5u5NuHeARsq7pJOH/zdNsqIA4jrDDW9Ap5t1TFLkZ1TgREQu0srMlTy47EGahDYhaUQSMcExZkcSkZ/Yn1vCy4v3YLM7h5VkFVYA8NCINvj7apGzyzAMOPSDcyjJ6WOS10Of8TomKfIrVOBERC5CyuEUHvn+EVpHtmZuwlyiAqPMjiQiP/Pe2sN8u+M4rRqEnr52e8+mNI7UnRyXcPqY5DzI2aljkiIXSQVOROQCfXngS/688s90iu7E7OGzCffXmHERV1BcYaOgzHb6dUp6DoNaR/PmPVrn4VJ0TFKkRqjAiYhcgI/3fMzf1vyNXnG9mDl0JsF+wWZHEhGgqtrBkH8uJ6+06ozr4wbHm5RIznDOY5IToFlfHZMUuQQqcCIi5/HezveYnjqdgY0H8sqQVwj0DTQ7koicsv5gPnmlVUwccgXx0SEA+PtaGdUpzuRkXq6qDLZ+AOvn/++Y5MCpzqXbEY3NTifi1lTgRER+RdLWJF7f9DrDmw1n+uDp+Pv4mx1JxOsZhsHCVYc4ml/GlowCAnyt3D+0NUH+PmZHk5OHITUJ0t49dUyyC9ww+9QxSf3yS6QmqMCJiJyFYRi8vul1FmxbwHXx1/HsgGfxtepLpogrOHCilGe/3Emwvw++Vgu39myi8mYmw4CD3zvvtv14TLLDb6D3eB2TFKkF+mlERORnDMNgeup03k9/n1va3MJTfZ/CatHocRFXkZKeDcDiqYNpUk/Po5qmqhS2npommZsOwfV1TFKkDqjAiYj8hN1h59m1z/LJ3k/4ffvf81ivx7Dot8ciLmPhyoP8fdEu2sWFqbyZ5fQxyXegolDHJEXqmAqciMgp1Y5qnlz5JIsOLiKxcyJTuk1ReRNxMZ+kZWCxwD9u6mx2FO/y4zHJdfNgz9ecPibZZwI07aNjkiJ1SAVORASoslfx2PePkXIkhQe6P8DYzmPNjiTilRwOg483ZlBUYfvFe1V2BzuOFfHENe3o1qyeCem8UFWpc5rkuvk/OSb5EPS8V8ckRUyiAiciXq+8upypy6eyKnMVT/R+gjvb32l2JBGvteZAHo99svWc7/v7WhnZUSsCat3JQz9Zuq1jkiKuRAVORLxaqa2UKd9NYcPxDTzT/xluan2T2ZFEvNrS9GwCfK2semIoAb6/HB7k52Ml0E8TJ2uFYcDBFc67bbsXgcUKHW6APuN1TFLEhajAiYjXKqwsZFLKJHac2ME/Bv2Da+OvNTuSiEdLzypi4nsbqap2nPMzJ0qrGHBFfaJDA+owmZf7xTHJaBj0sI5JirgoFTgR8Ur5FfmMXzKe/QX7mTFkBsOaDTM7kojH+8+mTDILyrnxynOXAosF7ujdrA5TebGTh2B9Emx613lMsmFXuHEOdLxJxyRFXJgKnIh4nZyyHMYtHkdGSQYzh85kQOMBZkcS8Xj7ckpY8MMBBrSK5p+3djU7jvcyDDj0A6yd+7NjkhOgaW8dkxRxAypwIuJVjpUcY+ziseSV5zFn+Bx6xfUyO5KIx3M4DO5csBaHAaM6aQCJKWzlsO0j5xqA7O3OaZKDHoZeYyC8kdnpROQiqMCJiNc4XHSYsYvHUmorZf6I+XSN0V0Akbqw41gR2UWV3Hd1K+7opeORdaow0zlNcuNbUJ4PsZ3hhjeg0y06JiniplTgRMQr7Du5j8QlidgddhaOXEi7qHZmRxLxeH9flM6mIyfJLa7EYoF7B7bEatURvVpnGJCRCmvnwM7PAQPajoa+E6H5AB2TFHFzKnAi4vF25u1k/JLx+Fn9eGvUW8RHxpsdScTj5RZXMv/7A1wRE0KjyCCu69KIqBB/s2N5tuoq2PmZs7gdS4OACGdp6z0O6jU3O52I1BAVOBHxaJtzNjNx6UTC/cNZMGIBTcObmh1JxCNV2x3sOl6MwzAA+H5PLgCv39GNjo0izIzm+UpyYMObsCEZSrKhfmsY/RJ0vQMCQs1OJyI1TAVORDxW6vFUJqdMpkFwA5ISkmgY2tDsSCIea/4PB3jxm91nXGscGUSHhuEmJfICWVuc0yS3fwz2KmiVAH0nQPxQsP5yCbqIeAYVOBHxSKsyV/HAsgdoEtqEpBFJxATHmB1JxKN9u/047eLCeHRk29PXWjUIxaLnrWqWvRp2fQnr5sKRNeAXAt3vgj7jIbq12elEpA6owImIx1lxdAVTl08lPiKe+SPmExUYZXYkEY9iGAYvfrubYwXlp17DloxCHhnRhmHtY01O56HK8iHtHedEycKjENkcRv4drrwTgiLNTicidUgFTkQ8ypLDS3hsxWO0jWrLvIR5RATo2RuRmrbjWBFzlu8nNjyAID8fANrFhfGbro1NTuaBctKdd9u2fADV5dBiEFwzHdqMAquP2elExAQqcCLiMb468BVPrnySztGdmT18NmH+YWZHEvE4hmHwSVoGFgt8df8gokMDzI7keRwO2LsY1s2BA8vBNxA63wp9JkBcJ7PTiYjJVOBExCP8Z+9/eHr10/SM68msobMI9gs2O5KIR3plyR7eXHWIbs0iVd5qWkURbP5/sH4e5B+AsEYw9CnocQ+E1Dc7nYi4CBU4EXF7H+7+kGfXPku/hv14behrBPkGmR1JxGP9d2sWYQG+/POWrmZH8Rx5+2F9Emx6D6qKoUlvGPpnaP8b8PEzO52IuBgVOBFxa+/tfI/pqdMZ3GQwLw95mQAf3REQqSl2h0HyygMUlNkAqLA5OHiilGdv6EirBtovdlkMw3k8ct1c2PMtWH2h42+dawAa9zA7nYi4MBU4EXFbyduSeTXtVYY1G8Y/B/8TP/2mWqRGrT2Qx98X7cLXauHHbQD1Q/xJ6BBnbjB3VlUGWz+AdfMgNx1CYuCqx6DnvRCmv68icn4qcCLidgzDYO6WuczeMptrWlzD84Oex8+q8iZS01LSc/D3tbL5LwkE++tHhstScBRSk2Dj21BRAHFd4MY50PEm8As0O52IuBF9NRYRt2IYBq9vep0F2xZwwxU38Ez/Z/DRKG2RGvHXL3bw79Qjp19XVju4qk2MytulMgw4stY5TTL9S8CAdtdB34nQrB9oybmIXAJ9RRYRt2EYBv/c8E/e3fkut7S5haf6PoXVYjU7lohHqKp28PHGDNrFhdOnZZTzogVu0G63i1ddCds/cT7flrUFAiOg32TonQiRzcxOJyJuTgVORNyCw3Dw93V/54PdH3Bn+zt5vNfjWPTba5GLUmGz88WWY9jsjl+8l3mynJLKau67uhXDO8SakM4DFGfDhmTYsBBKcyGmHVz3CnS5HfxDzE4nIh5CBU5EXJ7dYeeZNc/wn33/4Z5O9zC1+1SVN5FL8EHqUZ7+Ysc5348M9qN/K+0bu2iZac67bds/BYcNWo90TpOMv1rHJEWkxqnAiYhLq3ZU8+dVf+arA18xoesEJnWdpPImcolSduUQHx3Cv8f1Pev7oYG+et7tQtltkP4FrJ0LGevBPxR6jYHe46D+FWanExEPpq/SIuKybHYbj//wOEsOL+H+bveT2CXR7EgibmXqB5vZmlFw+vWhvDLuHdCCBuGaenjJyvIh7W3n4u2iTKjXEka9AFfeCYHhZqcTES+gAiciLqnKXsXDyx9mecZyHun5CHd1vMvsSCJu5UheGf/ZlEm3ZpE0igwCoHPjCH7ft7nJydxU7m7nMcnN/4Lqcmh5FVw7A1qPAE3CFZE6pAInIi6norqCB5c9yKpjq5jWZxp3tLvD7EgibqXCZufFb3cB8MptV9IiWgM0LolhwP4UWDsH9i0FnwDocptzDUBsR7PTiYiXUoETEZdSZitjyndTSD2eyjP9n+Gm1jeZHUnE7SSvPMiXW7NoGxum8nYpqspg6wfO4nZiN4TGwtVPQs97ISTa7HQi4uVU4ETEZZRUlTApZRJbcrfw/MDnuf6K682OJOKWFu/MJiYsgP+X2MfsKO6l6Jjz2baNb0L5SYjrAr+dBx1/C74BZqcTEQFU4ETERRRWFjJx6UTS89J5cfCLjGwx0uxIIm7BMAz+/Nl2juSXnb625WgBDye0oX6oSscFydgIa2fDzs/AcEC7a6HvJGjWT2sARMTlqMCJiOlOVpxk/JLx7C3Yy4whMxjabKjZkUTcxo5jRby/7gitGoQSFuj8tt43PoobuzU2OZmLs1efWgMwx7kGICAc+kyA3olQr4XZ6UREzkkFTkRMlVeex9jFYzlSdITXr36dQU0GmR1JxKXZ7A4O55UBBgCfbcrEYoF/JfYlJkx33M6r/CSkvQPr5kNRxqk1ANOh250QEGZ2OhGR81KBExHTnCg/wZhvx3Cs5Bizhs2iX6N+ZkcScXnPf5XOW6sPnXGtW7NIlbfzObH31BqA/we2MmgxCEb/E9qM1BoAEXErKnAiYoqcshzGfDuG7LJsZg+fTa+4XmZHEnF5hmHw9fYs+rSMOmOf25VNI01M5cIMAw4scx6T3LsYfPyh823QdwLEdTY7nYjIJTlvgbNYLAuB64AcwzA6nboWBXwAtAAOAbcZhnHSYrFYgNeA0UAZcLdhGGm1E11E3NXx0uOM+XYMJ8pPMHf4XLrHdjc7kojLKK+yM2Pxbkqrqn/xXlmVneyiSh4d2Y7ruzYyIZ2bsJWfWgMwF3LTIaQBDJkGPe+B0AZmpxMRuSwXcgfuLWAW8M5Prj0BpBiG8YLFYnni1OvHgWuA1qf+0weYc+qvIiIAHCs5xphvx3Cy8iTzEuZxZYMrzY4k4lK+3XGcBSsPEh3qj/UsExDbxoYxvL1KyFkVZUHqAtiwEMrznXfZbpwLnW7SGgAR8RjnLXCGYXxvsVha/OzyDcCQU//9bWA5zgJ3A/COYRgGsNZisURaLJaGhmFk1VRgEXFfGcUZjPl2DMVVxSQlJNE5RkeYRAzDoMLmOP16yc5sokP9WT9tOFarRthfkMw05zHJHZ+Cw35qDcBEaD5AawBExONc6jNwsT8pZceB2FP/vTFw9Cefyzh1TQVOxMsdLTrKvYvvpcxWRtLIJDrW72h2JBGXMPbtDaTsyjnj2q09mqi8nY+9GnZ96SxuR9eCfxj0Huf8T1RLs9OJiNSayx5iYhiGYbFYjIv9cxaLZRwwDqBZs2aXG0NEXNihwkOMWTyGKnsVySOTaRfVzuxIIi7hZGkVy3bnMKxdA3q1jALAaoHruuj5tnMqL4BN7zrXABQegcjmMOoFuPJOCAw3O52ISK271AKX/ePRSIvF0hD48VeHmUDTn3yuyalrv2AYxnxgPkDPnj0vugCKiHs4UHiAsd+OpdpRzYIRC2gb1dbsSCK1IrOgnM82ZeJ8iuDCHMgtxWHA/cNa01WTJH9d3n7nGoBN74OtFJoPhFH/gLbXaA2AiHiVSy1wXwB3AS+c+uvnP7l+n8Vi+TfO4SWFev5NxHvtO7mPsYvHYmCwcORCWtVrZXYkkVrz6pI9fLQx46L/XKsGoXRuHFELiTyAYcDBFc5jknu+BR8/6HSLcw1Aw65mpxMRMcWFrBH4F86BJdEWiyUDeBpncfvQYrGMAQ4Dt536+CKcKwT24VwjcE8tZBYRN7Dn5B4SFyditVhZOGIh8ZHxZkcSqTUOh8Gy3Tlc16Uhr9x+cZNVfSwWPe/2c7Zy2PaRs7jl7ITgaLjqceh5L4TFnv/Pi4h4sAuZQnnHOd4adpbPGsDkyw0lIu5tV/4uEhcn4u/jT/KIZFpEtDA7kkitqay2M2zGCk6UVJHQIRY/H6vZkdxX8XFITYYNyVCWB7Gd4IbZ0Olm8As0O52IiEu47CEmIiI/tSNvB+MWjyPYL5iFIxbSNLzp+f+QiBtbdyCfjJPl9L+iPiM7xpkdxz0d2+y827b9E3BUO59r6zsJWgzUGgARkZ9RgRORGrMtdxvjl4wnzD+M5JHJNAlrYnYkkctiGAYp6TkUV9rO+Zmvth4n0M/Kwrt7EeinYRoXzGGH3YtgzWw4shr8Q6HXGOcagPpXmJ1ORMRlqcCJSI3YnLOZiUsnEhkQSfLIZBqFagy6uL+1B/IZ+86G837umk5xKm8XqrLYOUly3Rw4eQgim8HIv0O330OghrmIiJyPCpyIXLa07DQmLp1IdFA0ySOTiQvRMTLxDCnp2fj7WPny/oH4/8qzbY0ig+owlZsqOArr58HGd6CyEJr2hYS/QdtrwUc/joiIXCh9xRSRy5J6PJXJKZOJDY5lwYgFxIZoQpy4r9nL97Fo2/+23xzMLaXfFfVpExtmYio3l7EB1syCnV84X3e8EfpOhiY9zM0lIuKmVOBE5JKty1rHfSn30Si0EQtGLCAmOMbsSCKXrKrawZxl+4kOCyA+OgSAuPBAxgzUCoyLZq+GXV/CmjcgYz0EREC/yc7n2yI12EhE5HKowInIJVmduZr7l91P07CmJI1IIjoo2uxIIpckp7iCQyfK2J1dTHFlNTNu68oITZO8NBVFsOldWDsXCo9AvRZwzYtw5f9BgO5iiojUBBU4EbloP2T8wIPLHqRFRAuSRiQRFRhldiSRS/b7BevYk10CQJCfDwNa6ZcRF+3kIVg3D9LehapiaNYfRv3DuQ7AquEuIiI1SQVORC7KiqMrmLp8Kq0iWzE/YT6RgZFmRxK5ZAdPlLInu4TEQS0Z0rYBDSMCCQnQt8YLYhhwdL3z+bZdX4LFCh1/69zf1ri72elERDyWvkuJyAVbdmQZD614iLb12jIvYR4RARr5Le7jjWX72JpRcMa144UVAPyxXwuaRgWbEcv92Ksh/XPn822ZG52j/wc8AL0SIaKx2elERDyeCpyIXJDvjnzHwysepn1Ue+YmzCXcP9zsSCIX7ERJJS8t3k1sWCCRwX5nvHdLjyYqbxeivADS3nEelSzKgKh4GP0SdL0DAkLNTici4jVU4ETkvFKOpPDI8kfoUL8DcxPmEuavYQTiHkorqykot7F4x3EMAxbc1ZNOjXXn+KLkH3CWtk3vQVUJtBgE174ErUeC9dy78UREpHaowInIr1J5E3dlszsY8tJycosrAedKgI6NdOf4ghgGHFnjPCa56yuw+kKnm6HfJGjY1ex0IiJeTQVORM4p5XAKj6x4hA7RHZg7XOVN3EvqwXxyiysZNzieVjGhdGwcjsViMTuWa7PbYMdnsPYNOLYJOn+SbgAAIABJREFUgurBoIecz7eFNzQ7nYiIoAInIuew9PBSHl3xKB2iOzBv+DxC/fWMi7gmwzBY8MNBsk4NJPnRlowC/H2sPDCstSZLnk/5Sdj4FqybD8XHoH5ruPZl5/Nt/no+UETEleg7moj8wpLDS3hsxWN0jO7I3OFzVd7Epe3MKuL5RekE+fngaz3zDtvNPRqrvP2avP2wdg5sfh9sZdDyKrj+VWiVoOfbRERclL6ricgZlhxewqMrHqVTdCeVN3EL36XnYLHA949dTUxYgNlxXJ9hwKGVsHY27P4afPyg863QdyLEdTY7nYiInIcKnIic9mN56xzdmTnD56i8iekOnSjlupkrKams/tXPdW0aqfJ2PtVVsONT52CS41shKAoGPwq9xkJYrNnpRETkAqnAiQgAiw8t5rHvH6NzdGfmJswlxC/E7EgiLNqeRUllNZOGXIGvz7mP9CW0VwE5p7J82LAQ1idByXGIbgvXvwZdbge/ILPTiYjIRVKBExG+PfQtj3//OF1iujBn+ByVNzGVze7gow0ZlNvs/Cctk06Nw3lsVDuzY7mfE3udxyQ3/wuqyyH+arjhDbhiqJ5vExFxYypwIl7um0Pf8MT3T6i8ictYtC2Laf/Zdvr1tNEqbxfMMODg985jknu/BZ8A6HIr9J0EsR3NTiciIjVABU7Ei/1Y3rrGdGX28Nkqb+ISUtJzqB/iT8rDV+FjtRAW6Gd2JNd3+vm2WXB8GwRHw5A/Qc8xEBpjdjoREalBKnAiXuqbg9/wxA8qb+Janv1yJ19sOcYtPZoQGexvdhzXd3p/2zwozoKYdvCbmdD5NvALNDudiIjUAhU4ES/00/I2Z/gcgv20qFfMV1ZVzbtrDxMW6Mu4wfFmx3Ft+Qed+9s2vQe2Uuf+tt/MhCuG6fk2EREPpwIn4mW+Pvg1T/zwBFfGXKnyJi7hQG4Je7JL2H28mKpqB2/e3Ys2sWFmx3JNR9fD6pmw60uwWKHTLdBvMjTsYnYyERGpIypwIl5k0YFF/Gnln+jWoBuzh81WeRPTGYbBH5LXk1lQDkC9YD96tYgyOZWLcdidhW31LMhYD4ER0P9+6DMewhuZnU5EROqYCpyIl1B5E1e0M6uIzIJyHh3ZlqvbNiAmLAB/Xx0BBKCyBDa/71wFcPIQRDaHUdOh2+8hINTsdCIiYhIVOBEv8NWBr5i2cprKm5jqr1/sYOexojOu5ZZUYrHAbT2bEhMWYFIyF1OUBevnOZdvVxRCk96Q8Ddodx1YfcxOJyIiJlOBE/FwXx74kidXPkn3Bt15Y9gbKm9iioyTZby1+hCtG4QSHfq/ohYXHsioTnEqb+Ac/7/mDdj2MRh2Z2HrPwWa9jY7mYiIuBAVOBEP9mN56xHbg1lDZ6m8SZ2x2R3syS7GMJyvF+84DsC8P/QgPkbH/04zDNi31DmY5OAK8AuBnvdC34kQ1dLsdCIi4oJU4EQ81FcHvlJ5E9PM/G4fr6fsPeNafEyIytuPbBWw7UPnHbfcXRDWEIY9DT3vgaB6ZqcTEREXpgIn4oG+OfgN01ZOo3uD7ipvYopvtmfRpUkEU4a2Pn2tXZxWA1CaBxuSYf18KM2F2M7w23nQ8Sbw1eJyERE5PxU4EQ+z+NDi03ve9Myb1KW0Iyd5b81hqh0Ge7JL+PO17UnoEGt2LNdwYh+sfQM2/wuqy6FVAvS/z7mA22IxO52IiLgRFTgRD5JyOIXHv3+cztGdmT1c0yalbs1M2cvq/XnEhgfSLi6Ma7s0NDuSuQwDDq9yHpPc/TX4+EGX26HffdCgndnpRETETanAiXiI7458xyMrHqFDdAfmDJ9DiF+I2ZHEw5VX2amw2QGorHawen8ed/Zpzl+u72ByMpPZbbDzc1gzC45tgqAoGPwo9E6E0AZmpxMRETenAifiAVYcXcHDKx6mff32zB0+l1B/DYqQ2pVVWM7VLy2nwuY44/qw9l5cUCoKIe0dWDsXijKgfiu47hXo8jvw191wERGpGSpwIm7u+4zvmbp8Km3rtWVuwlzC/DUoQmrf0p3ZVNgcPDKiDaEBzm8l4UF+9L+ivsnJTFBwFNbNhY1vQ1UxNB8I174ErUeC1Wp2OhER8TAqcCJubFXmKqYum0qryFbMS5hHuH+42ZHEC2zNKODZL9NpUT+YyVe3wuKtQzgy05zHJHd85nzd8bfQbzI07m5uLhER8WgqcCJuas2xNdz/3f3ER8aTNCKJiIAIsyOJl/jrFzuosju4tWdT7ytvDgfs+cZZ3A6vgoBw59LtPhMgsqnZ6URExAuowIm4oXVZ65jy3RSaRzRnfsJ8lTepM3kllWw6WsCDw1sz+epWZsepO7Zy2PIv50TJvH0Q0RRGPA/d/wiBuvMtIiJ1RwVOxM2kHk/lvpT7aBrWlAUjFlAvsJ7ZkcTDpGcV8X9Ja38xoATAbhgYBgxr5yX73UrzIHWBc/F22Qlo1A1uToYON4KPvoWKiEjd03cfETey4fgGJqdMpnFoYxaMWEBUYJTZkcQDfbHlGMUV1dwzoMVZj0g2CAugU2MPv+uUtx/WzoZN7zsXb7cZBf2nQPMBWrwtIiKmUoETcRObcjYxKWUScSFxLBi5gPpBXjjtT2rdjmOFzFm+n37x9XnyWi/c53Y0FVa/BulfavG2iIi4JBU4ETewOWczE5ZMIDY4luQRyUQHRZsdSTyQYRgkvr0BgNFdGpqcpg45HLDna1j1OhxdC4ERMOgh6D0OwuLMTiciInIGFTgRF7c1dysTlk4gOiiaBSMWEBMcY3Yk8VDpWcUcK6zg0ZFt+X2fZmbHqX0/H0wS2QxGTYduv4eAULPTiYiInJUKnIgL235iO+OXjCcqMIrkkcnEhnjJ4AipNesP5vOXz7dT7TB+8V5xhQ2AW3s28ez1AD8fTNLwSrhlIbS/QYNJRETE5ek7lYiL2pG3g3FLxhEREMHCkQuJC9FRLrl8/2/dYTJOlnNVm7Pfye3QKJwGYYF1nKqO/HwwSeuRzsEkLQZqMImIiLgNFTgRF5Sel864xeMI8wtTeZNLUlpZTdqRkxg/udFmAMv35DKiYywv33aladnq3NFUWP06pP/31GCS204NJmlvdjIREZGLpgIn4mJ25+8mcUkiIX4hJI9MplFoI7MjiRt6afFu3lx16KzvjezoBb8Q+HEwyeqZcGSNczDJwKnQZ7wGk4iIiFtTgRNxIftO7iNxcSKBPoEkj0ymSVgTsyOJGzIMgyU7s+kXX59HRrY5470AXx86NvLgHW62ilODSWY5B5NENINRL0C3P2gwiYiIeAQVOBEXcbDwIGMXj8XX6svCkQtpGtbU7EjiZlbsyeXNVQex2R1knCxn0pBW9GjuJcvey/L/N5ikNFeDSURExGPpu5qICzhadJSx347FwGDByAU0C/eCEe5S495Yto/0rCLiY0IZ0Ko+ozp5wVHB/AOwZjZseu/UYJIR0P9+DSYRERGPpQInYrJjJccYs3gMVY4qFo5cSHxEvNmRxMVVVtvJOFl+xrXyKjsbD59k0pAreHhEW5OS1aGMDf8bTGL11WASERHxGipwIiY6Xnqce7+9lxJbCckjkmldr7XZkcQNPPzhFr7cmnXW94a19+BdgQ4H7Pnm1GCS1RAQAQMegD4TNJhERES8hgqciElyy3IZu3gsBZUFJCUk0b6+7hzI+VXY7KSk5zC8fQOu73rmhNLIYH+ubBppUrJaZKuArf+G1bMgby9ENIWR/4Duf4CAMLPTiYiI1CkVOBET5Ffkk7g4kZyyHOYlzKNzTGezI4mLKqms5pUleyi32QE4WVpFuc3OnX2bc3XbBianq2Vl+ZCaDOvnnRpM0hVuToYON2owiYiIeC19BxSpYwUVBSQuTiSzJJPZw2fTrUE3syOJC/vvlmMkrzxIdKg/4BzK0blxBP3i65sbrDblH4S1pwaT2MqgVQIMuB9aDNJgEhER8XoqcCJ1qKiqiHFLxnGo8BAzh82kV1wvsyOJi6qqduAwDJbuzKZxZBArH78ai6eXl2ObYNVrsPNzsPhAl9uh32SI7WB2MhEREZehAidSR0ptpUxcMpG9BXt57erX6N+ov9mRxEVtOJTP7fPXYncYAPyhb3PPLW+GAftTnMXt4PcQEO5cA9BnAoQ3NDudiIiIy1GBE6kDZbYyJi2dxI68Hcy4agaDmww2O5K4sC+3ZuHnY+HhEW3wtVq48crGZkeqeXYb7PjMWdyyt0FYQ0h4FnrcDYHhZqcTERFxWSpwIrWsorqC+7+7n825m5k+eDrDmg8zO5K4mBV7ctmeWXj69dfbsxjYKppJQ1qZmKqWVJVC2ruw5g0oPALRbeGG2dD5VvD1NzudiIiIy1OBE6lFVfYqHlz2IOuPr+f5gc8zqsUosyOJi6mw2Zn43kbKquynr1ks8BtPu+tWkgvr50NqEpSfhGb9YPSL0HokWK1mpxMREXEbKnAitcRmt/Hw8odZdWwVz/R/huuvuN7sSOKC1h3Mp6zKTtIfezK4TTQAFiz4+3pIqck/4Nzftvl9qK6Edtc6n3Fr1sfsZCIiIm5JBU6kFlQ7qnn8h8dZnrGcJ/s8yU2tbzI7kriIlPRsnvh0G45TA0rKbXaC/HwY1DqaAF8fk9PVoMw05/Nt6V+A1Re6/g76TYGYNmYnExERcWsqcCI1zO6wM23lNJYcXsKjPR/ld+1+Z3YkcSEfpB7F7jAY3Tnu9LXuzeoR6OcB5c0wYF8KrHoVDv0AAREw4AHnRMmwuPP/eRERETkvFTiRGuQwHDy9+mm+Pvg1D3R/gD92/KPZkcQk+aVV/LA394xrhgEr953g5u5NePbGTiYlqwV2G2z/FFa/DtnbIawRjHgOut+liZIiIiI1TAVOpIYYhsGza5/l8/2fM6nrJMZ2Hmt2JDHRC1+n8+GGjLO+d00nD7kbVVkCae84J0oWZUBMO7hxDnS6RRMlRUREaokKnEgNMAyD6anT+XjPx4zpNIYJXSeYHUlM5HAYpKTnkNAhlj9d0+6M9wL9fGgUGWRSshpSkgvr5kLqAqgogGb94doZ0HqEJkqKiIjUMhU4kRowc9NM3k9/n9+3/z0PdH8Ai8VidiSpQ2VV1Ux8L42TZVUAVFU7yCut4rouDYmPCTU5XQ3K2w9rZsGm98Fe5ZwoOeABaNrb7GQiIiJeQwVO5DIlbU0iaVsSN7e+mcd6Paby5oVW7M5lxZ5c+rSMItjfOYykTWwYw9rHmpyshmRudE6U3PkF+PhB1zug/xSIbm12MhEREa+jAidyGd7b+R6vb3qda+Ov5am+T6m8eZndx4sprrDxn02ZRAT58f7YPvj6eMgRQsOAfUudxe3HiZIDp0Kf8ZooKSIiYiIVOJFL9MmeT5ieOp1hzYbx3IDn8LF6wBh4uWDbMwu5bubK069v6tbYM8qb3QbbP4FVr0POjlMTJZ+HHndBQJjZ6URERLyeCpzIJVh0YBHPrHmGAY0H8OLgF/G16l8lb7N4ZzZWC8z/Q08C/Kx0bRppdqTLU1l8aqLk7FMTJdtroqSIiIgL0k+dIhfpuyPfMW3lNHrE9uCVIa/g76Mfbr3NV1uzeD1lLz2b12N4Bzd/zq0kB9bNg9QkqCiE5gPgupehVYImSoqIiLggFTiRi7AqcxWPrHiEjvU7MmvYLIJ83XwcvFw0wzB44Zt0AO4Z0NLkNJch/yCsngmb3nNOlGx/HfR/AJr2MjuZiIiI/AoVOJELtOH4Bh5c9iDxEfHMHj6bEL8QsyNJLTpRUklVteMX14/ml3E0v5znbuzEtV0ampDsMh3fBitfhR2fgtUXuv7OWdyiW5mdTERERC6ACpzIBdiWu437vruPhqENmZcwj4iACLMjSS1atjuHe95M/dXPDG3XoI7S1ADDgMOrYOUrzsmS/qHQ7z7oOwnC3bCEioiIeDEVOJHz2J2/mwlLJxAZEElSQhL1g+qbHUlq2aKtWYQF+vLna9uf9f2GEUE0inSD47MOB+z52lncMlIhOBqGPgW9xkBQPbPTiYiIyCVQgRP5FQcKDzBuyTiCfINYMGIBsSFuPrBCzuqzTZlszyw8/XpJejZD2jbg9l7NTEx1GaqrYNtHzh1uJ3ZDZHO4dgZceSf4uUHxFBERkXNSgRM5h4ziDBIXJwKQNCKJJmFNTE4ktaG4wsajH2/BggU/H+cidh+rhZu7NzY52SWoLDm1CmAWFGVCbCe4ORk63Ag++nIvIiLiCfQdXeQsskuzGbt4LBXVFSwcuZCWEW48bVB+1cq9J7DZDT4Y14c+8W56PLY0D9bPh/XzoPwkNB8I178GrYaDxWJ2OhEREalBKnAiP5NXnkfikkQKKgtYMGIBbaPamh1JLsH87/fzwte7MM7zOcOA8EBfejR3w2fCCo4677alvQO2Mmh7LQx8EJr2NjuZiIiI1BIVOJGfKKwsZNyScWSVZDE3YS6dojuZHUku0UcbMoiPCWV0p7jzfrZb83r4+rjR0uqcdOfzbds+cr7ufBsMeAAatDM3l4iIiNQ6FTiRU0ptpUxcOpGDhQeZNXQWPWJ7mB1JLtKhE6Us251Duc3O3pwSnrquA2MGetDx16PrnRMldy8Cv2DoPc65CiCyqdnJREREpI6owIkA5dXlTE6ZzM68nbw85GX6N+5vdiS5BH/97w6W784FwN/XyogOHjA11DBg7xJY9apzl1tQPRjyJ2d5C44yO52IiIjUMRU48Xo2u42Hlj9EWnYaLwx6gaHNhpodSS5BaWU1q/fl8cd+zXkooQ0Bvj4E+fuYHevS2athx3+cxS17O4Q3gVEvQPc/gn+I2elERETEJCpw4tXsDjvTVk5jZeZKnu73NKPjR5sdSS5BQVkVQ15aTpXdwaiOcUQG+5sd6dLZymHTe7D6dSg4AjHt4MY50OkW8HXj/10iIiJSI1TgxGsZhsGza5/lm0Pf8FCPh7ilzS1mR5JLtDQ9h4IyG9d0iqN3Szc9Vlh+ElIXwNq5UHYCmvSCUdOhzSiwutGAFREREalVKnDilQzD4OWNL/PJ3k9I7JzIPZ3uMTuSXCTDMFhzII+Simo+TcsgNjyA2Xd2x+Jue8+KsmDtG7DhTagqgVYJMHAqNO+vHW4iIiLyCypw4pUWbFvAWzve4va2tzOl2xSz48glWH8wn/9LWnf69R/7NXev8pa33/l825Z/g6MaOt3sXAUQ19nsZCIiIuLCVODE6/x71795fdPrXBd/HdP6THOvH/rltKXp2fj7WPlgfF/8fa20ahBqdqQLk7UVVr4MOz8HH3/nUJJ+90GUB607EBERkVqjAide5b/7/8vz655nSJMh/G3A37Ba9GyRq3np292kHso/7+fSs4roe0V9ujWrVwepasDhNc7itncx+Ic577b1nQShDcxOJiIiIm5EBU68xrIjy3hq1VP0juvNS0News/qZ3Yk+ZmTpVXMXr6P5vVDaBAW8Kuf7dAonMRBLn7XyjBgXwr8MAOOrIbg+jD0Keg1FoIizU4nIiIibkgFTrzCuqx1PLLiEdpHtef1oa8T4PPr5UBqT7XdwZ7sEhyG8Yv3Vu07gcOAV2+/kq5N3bjgOOyQ/gX88DIc33pqh9v0Uzvcgs1OJyIiIm5MBU483rbcbUz5bgrNwpsxZ/gcQvy0BNlMbyzbzytL95zz/QZhAXRuHFGHiWpQdRVs+xBWvgJ5+6B+K7jhDeh8m3a4iYiISI1QgROPtvfkXiamTCQqMIp5CfOIDHTjuzoe4psdx+nUOJz7h7Y+6/tXNAjFanWzwTJVZZD2DqyeCUUZENcFbn0L2v8GrD5mpxMREREPogInHuv/t3ffYVaUBxvG79mFpfcuXaSKIF2kC4JYY1diEjWJDXtBsfcSC4piQwQ15YsxMQkxYqGINKWISheR3payS122zffHWQmIKLDn7Nmze/+uy4udObMzz16ZDPswM++7atsqrvzoSlKSUhjZfyQ1yzpYRDyFYcgDYxewcN02hg5sQf9ja8c7Uv7tToOZI2HGS7BrMzTsBmc8B8f0dQ43SZIUExY4FUkbdm7g9x/9nszcTMYMGEP9CvXjHanYW7JhB2OmLSc5KeD0tkfFO07+7NgIM16Ez1+DzO3QtD90vxkado13MkmSVMRZ4FTkpGWkceVHV7I1YyujBozimCrHxDtSsZaRlUNGVg7vz1sHwNTbT6J2pdJxTnWE0lbC1OHwxVuQvQeOPRu63wR12sQ7mSRJKiYscCpSdmTu4KqPr2LV9lW81O8lWldvHe9IxVrarkx6/GEi2zOyAWhdt2JilrfUxTDl2cgAJQTQ9iLodiNU9x8HJElSwbLAqcjIyM7gugnXsWjLIp7t8yyd63SOd6Ri75MlqWzPyGZwnyZUL1+Krk2qxTvS4VkzJzL59sL/QMky0PkK6HotVKob72SSJKmYssCpSMjOzea2ybcxe8NsHu3xKL3r9453pGJp3pp0Ppy/fu/ypCWpVC+fwi0nN0+ckSXDEJZPiUy+vWwilK4EPW+DLldBuQQroJIkqcixwCnhhWHI/dPuZ9KqSQztPJTTjz493pGKrQfGzmfm8q37DcB4Rc+jE6O8hSEsGRcpbqtnQrma0O8B6Hg5lK4Y73SSJEmABU5FwDOzn+Ff3/6Lq9tezaCWg+Idp9jaujOT2Su2cv1Jx3Bz/+bxjnPocrJh/ruRybc3zofKDeC0p+H4X0Yem5QkSSpELHBKaK/Pe50x88dwUfOLuLrt1fGOU2xt2JZBl0fHA3BSy1pxTnOIsvfAl3+JDE6y9Tuo0QLOfhVanwPJJeOdTpIk6UdZ4JSw3v3mXYbNHsYpjU5haJehBE6cHDffv/d26YmNaFuvUpzT/IzMXTDnTZg2HLatgaPaQf8/QfNTISkp3ukkSZJ+kgVOCWn8yvHcP/1+TjzqRB7t/ihJgb94F6SlG7cze8XWvcvvzF5N4+rluP/MY+OY6mfs2Q4zX4PpI2BnKjTsBme9AEf3Acu/JElKEBY4JZyZ62cy5JMhHFvtWIb1HkZJH3crcNf++QsWrd++37rBfZrEKc3P2L0VPnsFZrwEGWnQ5CTocSs06hbvZJIkSYfNAqeEsnDzQq6bcB11K9RlRN8RlC1ZNt6Rip1VW3axaP12buzXlAs61gciN7BqVyxkE3TvSIUZI+Dz1yBzOzQ/DXreAnU7xDuZJEnSEbPAKWGs3LaSqz6+igopFXj15FepUrpKvCMVC0s3bufGv84lMzsXgJ17cgA4s+1RHFW5EI7SmL4Gpj0Ps8dAdkZkUJIet0CtQvx4pyRJ0iGywCkhpO5K5YqPriA3zOWVk1+hdrna8Y5UbLwzew2L1m3n5Fb/G13yrOOP4uga5eOY6kds+Q6mPgtz/wxhLrS5ELrfBNWbxjuZJElS1FjgVOil70nnyo+vZEvGFkb1H8XRlY6Od6QibeXmXazYsnPv8ofz19OpUVVeuqSQPnqYuhg+fQa+/hskJUO7X0G3G6BKw3gnkyRJijoLnAq13dm7uW7CdXyX/h0v9n2R42ocF+9IRVpObsg5L01l047M/db/umshLEPrvoJPn4YF/4pMuH3C1dD1WqhYJ97JJEmSYsYCp0IrKzeLWz+5lbkb5/JkryfpelTXeEcq8uas3MqmHZncMbAFHRtG3jFMTgo4rm4hmttt1Uz49ClYMg5KVYQeN8MJ10C56vFOJkmSFHMWOBVKuWEu9029j8mrJ3PPCfcwoNGAeEcqMmYu38LLk74lNwwP+Gz11t2USAoY1KUBFUsXoukZwhBWTIXJT8KySVCmCvS5Gzr/HspUjnc6SZKkAmOBU6EThiFPzXqKscvGMvj4wVzQ/IJ4RypSXvlkGdOXbeaYmgcOQlImJZnf9zy68JS3MISl4yPFbdUMKFcTTn4IOl4OpQrZICqSJEkFwAKnQmfUvFG8teAtBrUYxJVtrox3nCJlXfpuPl64gV93bciDZ7WOd5yDy82Fxe/B5Kdg3VyoWA9OfQraXRJ5302SJKmYssCpUHn3m3d5bs5znNr4VG7vfDtBEMQ7UpGRviuLro9NAKBvy1o/s3Wc5GTD/Hcjg5OkLoSqR8OZL0SmBCiREu90kiRJcWeBU6ExefVkHpj+AF3rdOXhbg+TFCTFO1KRMmnJRgCuP+kYejYtZAN+5GTBV3+NFLcty6BGSzjnNTj2bEj2MiVJkvS9fP1mFATBcmA7kANkh2HYMQiCqsBfgUbAcuCCMAy35i+mirqvUr/ilkm30KxKM4b1GUbJ5ELyDlYCm71iK+9+sXrv8qzlW6lWLoUb+zUrPHc2szPhyz9HilvaSqjTFi78IzQ/DZIs8JIkST8UjX/a7hOG4aZ9lu8Axodh+HgQBHfkLd8eheOoiPou/TsGjx9M9TLVebHfi5QrWS7ekYqEJ8YtYu7KNCqU/t//zS85oSFJSYWgvGXvgS/egk+HwbbVULdD5B23pv2hsJRLSZKkQigWzyadBfTO+/oNYBIWOB1E6q5UrvroKpKCJF45+RWqlylkj/YlmDAMyczJZdvubGav2Mo1vZtwS//m8Y71P1m7YfYbMPU52L4W6neBM5+DJn0tbpIkSYcgvwUuBD4MgiAEXgnD8FWgVhiG6/I+Xw8U0tESFG/bM7dz9cdXs3XPVkYPGE2Dig3iHSnhPTB2AWOmLd+7fFKLmvELs6/MnTBrdKS47dwIDbvB2S9D454WN0mSpMOQ3wLXPQzDNUEQ1AQ+CoJg0b4fhmEY5pW7AwRBcAVwBUCDBv7iXtxk5mRy08Sb+DbtW17o+wLHVj823pESXnZOLv+cu4YODatwUouaVCuXwvH14zzJ9Z4dMPM1mPY87NoEjXtBr9HQqHt8c0mSJCWofBW4MAzX5P25MQiCd4HOwIYgCOqEYbguCII6wMaDfO+rwKsAHTt2/NGSp6IpN8zlril38dn6z3i0+6N0q9st3pESXk5uyF3vziNtVxaXd2vMaW2Kyb44AAAgAElEQVTqxDdQxjb4/FWYPgJ2b4k8ItlrCDQ4Ib65JEmSEtwRF7ggCMoBSWEYbs/7uj/wIPBv4DfA43l//isaQVU0hGHIkzOfZNzycdzc4WbOaHJGvCMVCZ8s2chfZ60iOSmgR7M4vke4Ow0+ewVmjICMdGg6IFLc6nWMXyZJkqQiJD934GoB7+YNR14C+HMYhuOCIJgJvB0EwW+BFcAF+Y+pomLM/DH8ceEfuaTlJVx67KXxjlNkjF+4kVIlkph7b3/KpCQXfIBdW2DGi5HytmdbZBqAXrfBUe0KPoskSVIRdsQFLgzDZUDbH1m/Geibn1AqmsZ+O5ZnZj/DKY1O4bZOtxWeucgS1IrNO/nVqM/ZlZlD2q5M+rWsVfDlbecmmP4CfD4SMndAq7Og521Q+7iCzSFJklRMxGIaAekAU9dM5d6p99Kldhce6f4ISYGTNOfXf75ax8otu7i4c32SgoBBXQpwMKAdG2HacJg5KjI1QOtzoMetUKtVwWWQJEkqhixwirn5m+Zz06SbaFK5Cc/2eZaU5JR4Ryr0MrJymLBoI1k5uQfdZuyXa2lTrxKPndOm4IJtWxcpbrNeh5xMOO78SHGr0azgMkiSJBVjFjjF1MptK7lm/DVUKVWFl/q9RPmU8vGOlBDemr6CR/678Ge3G3JKAU3Snb4apjwLc96E3GxoexH0uAWqNSmY40uSJAmwwCmGNu/ezFUfX0VumMvLJ79MjbI14h0pYXy0cAMtaldgxC/bH3SbpCCgYdWysQ2SthI+fQa++CMQwvGDoPvNULVxbI8rSZKkH2WBU0zszt7NdROuI3VXKq8NeI3GlfyF/3vjF27g+QlL+anJD79encbgPsfQpEac7limrYRPn44UtyAJ2v8aut8IlQvwPTtJkiQdwAKnqMvJzeH2ybczb9M8hvUZRtsaBwxWWqyNmvIdKzbvpE29ygfdpm/LWpzfoX4Bpsqzt7j9CYIAOlwG3W+CSnULPoskSZIOYIFTVIVhyBMzn2DiqokM7TyUvg2cUWJfX61OY9q3m7mqVxPuGNgi3nH+Z99HJYMAOlxqcZMkSSqELHCKqjfmv8FfFv2F37T6DYNaDop3nEJl47YMznxhKgAnt6oV5zR50lbt86hkAB1+k1fc6sU7mSRJkn6EBU5RM275OJ6e/TT9G/bn5o43xztOoTN+0UYAHj/nODo0rBLfMGmrYMozMOetyHL7X0OPmy1ukiRJhZwFTlExe8Ns7vz0TtrXbM+jPR51ou48WTm5PDh2AVt2ZvL1mnTqVi7DhZ3i8G7b936suHW/CSrHMZMkSZIOmQVO+bYsfRnXT7ieuuXrMvyk4ZRKLhXvSIXGtG8389aMFTSoWpaUEklc0qUBQRAUfJD01ZF33Oa8GVlu/6vIdAAWN0mSpIRigVO+bNq9iWs+voYSSSV4qd9LVCpVKd6RCo3c3JC3Z62idMkkPrypJ6VLJhd8CIubJElSkWKB0xHblbWLweMHsyVjC6MHjKZeBd+f2tfd/5rHe1+to1/LmgVf3tLX5D0q+SaEIbS7JPKOm/O4SZIkJTQLnI5Idm42t02+jUVbFjG8z3COrX5svCMVKjm5Ie9/vY6jKpXmgbNaF9yB09fAlGEw5w2LmyRJUhFkgdNhC8OQxz57jMmrJ3PPCffQq36veEeKi12Z2bz8yTIysnIO+CxtVyZbd2Xx0KDW1K1cJvZh9ituuXnF7RaLmyRJUhFjgdNhGzVvFG8veZvLW1/OBc0viHecuBn75VqGj/+G0iWTCDhwYJIGVcvSs1mN2IbYtjZS3GaP+V9x634zVGkY2+NKkiQpLixwOizvLXuP5+Y8x8DGA7mh/Q3xjhNXHy/cSN3KZZhye5+CH1ly27rIO27fF7fjfxm542ZxkyRJKtIscDpks9bP4p6p99CxVkce7vZwsZ7r7do/z+GjBRu45IQCnhZgR2rkjtusUZCbDW0vhp63QpVGBZdBkiRJcWOB0yFZsW0FN066kbrl6/Jsn2dJSU6Jd6S4Sd+Vxfvz1lO/ahmu7n1MwRx01xaY+hx8/ipkZ0Cbi6DXEKjauGCOL0mSpELBAqeflZaRxjUfX0MSSbzY98ViN9fbzj3Z/HPuGrKycwH4ZuMOcnJDnr2wXewHKNmdBtNHwIyXIHMHHHce9LodqjeN7XElSZJUKFng9JMyczK5YeINrNu5jlEDRlG/YvGbAPpPn63g0f8u2m9dvSplOL5+5dgddM92mPEyTH8eMtKh1VnQeyjUbBm7Y0qSJKnQs8DpoMIw5L5p9zFn4xye6PEE7Wq2i3ekuBi/cCMtalfgL78/Ye+6cqVKkJwUg3ffMnfC5yMjj0vu3gLNT40Utzpton8sSZIkJRwLnA7q5a9e5j/L/sPg4wdz6tGnxjtOgQjDkKv+OJuF67bvXbdq6y4G9z6GKuVi+N5f1m6Y9XpkgJKdqXBMP+hzJ9TtELtjSpIkKeFY4PSj3lv2Hi/OfZEzm5zJlW2ujHecAvNt6g4+mL+Bzo2r7n2/7YSjq3JxlxhNiJ29B+a8CZ8+DdvXQeNe0OcuaNAlNseTJElSQrPA6QBzNszhnqn30KFWB+7rel/Bz3EWB/PXprM2LYOJizcC8OyFx3NULAcoycmCuX+CyU9B+ipo0BXOGQmNe8TumJIkSUp4FjjtZ+W2ldww8QaOKn8Uz/YuHtMFpO/O4uwR08jMiYwy2aZepdiVt5xs+Ppt+OQJ2Loc6naEM4fD0X2gGBRlSZIk5Y8FTnul70ln8PjBhISM6DuCyqVjOMpiITJ5SSqZObkMu7AtTWtWoH6VstE/SG4OzH8XJj0Gm5dCnbYw6G1o2t/iJkmSpENmgRMAWTlZ3DTpJlbvWM1r/V+jYcWG8Y4UMxMXb2Tk5GWEYWR55ZZdVC2Xwplt60Z/ZMncXFg0FiY+BqkLoeaxcOEfocXpFjdJkiQdNgucCMOQB6Y/wMz1M3m0+6N0qFW0Rz585ZNvWbhuO81rVQCgbuUynHpc7eiWtzCEbz6CCQ/C+q+hejM4bzS0+gUkJUXvOJIkSSpWLHDita9f41/f/our2l7FGU3OiHecqFu9dRfbdmcDkJGdw8zlW7my59EMOaVFbA64fAqMfxBWfQZVGsHZr8Bx50NScmyOJ0mSpGLDAlfMfbziY4Z/MZyBjQdyTdtr4h0n6r7btJO+T08iN9x//cmtakX/YGtmw4SH4dsJUKEOnD4M2v0KkktG/1iSJEkqlixwxdjCzQu5c8qdtKnehoe6PVQkpwv4aMF6ckN45oK2lE2JnO4Vy5SgXYMq0TvIxoWR4rboP1CmKvR/GDr9DkrGcBoCSZIkFUsWuGJq0+5NXDfhOiqmVOS5k56jVHKpeEeKuslLUnn0v4toWaci57SvF/0DbFkGkx6Hr96GlPLQ+0444WooXTH6x5IkSZKwwBVLe3L2cMOEG9iWuY03TnmD6mWqxztSTDz+/iIAftM1yiNqblsLk5+EOW9CUgk48TrofhOUrRrd40iSJEk/YIErZsIw5L5p9/HVpq8Y1nsYLau1jHekfNmVmU1WTnjA+tTte1iwbhtDB7bgos4NonOwnZthyjMw8zXIzYYOl0KPW6FinejsX5IkSfoZFrhiZtS8Uby37D2uPf5a+jXsF+84+TJ7xRbOf3n6AQOU7Ktvy5r5P1DGNpg+IvJf1k5ocyH0uh2qNs7/viVJkqTDYIErRsavHM9zc55jYOOBXNHminjHybexX66jZHIStw1o/qMDsNSqWIpjalY48gNk7oKZI2HKMNi9FVqeCX3ugpoxmn5AkiRJ+hkWuGJi8ZbFDP10KK2rtebBEx9M+BEnP/0mlTHTlnNSi5r8rsfR0d15diZ88SZ88iTsWA9N+sJJd0Pd9tE9jiRJknSYLHDFwKbdm7h2wrVUSKnA8JOGU7pE6XhHypec3JAb/m8uAGe3qxu9HefmwNd/g4mPQtoKqH8CnPc6NOoWvWNIkiRJ+WCBK+IyczK5aeJNpGWk8cbAN6hRtka8I+Xb3FVpbNmZyfCL23FG26Pyv8MwhMXvw/gHIXUh1G4Dv3wHjukHCX6nUpIkSUWLBa4IC8OQB6Y/wNzUuTzd62laVWsV70hHZNrSTQz+8xyy80abzMzJJTkpoFfTKJTRFdPh4/th1Qyo2gTOGw2tfgFJSfnftyRJkhRlFrgibMz8Mfz7239zzfHX0L9R/3jHOWLvzFlNdm7I+R3r713Xsk4FKpUteeQ73TA/csdtyTgoXxtOHwbtfgXJ+dinJEmSFGMWuCJqypopDJs9jAGNBnBVm6viHeewbc/I4sP5G8jJDZm4aCN9W9Tk3jOicAdx64rIO25f/RVKVYS+90KXqyGlbP73LUmSJMWYBa4IWrFtBUMmD6FZlWYJO+LkyMnLGD5h6d7lU4/L52TZOzfB5Kdg1igggBOvhe43Q9mq+duvJEmSVIAscEXMzqyd3DDhBpKDZJ476TnKlkzMO0sfL9xIh4ZVGH5xO0omB9SscIQjZ+7ZEZmAe9rzkUm4jx8EvYdCpXrRDSxJkiQVAAtcEZIb5nLnp3eyfNtyXjn5FeqWj+IQ+1GwKzOb3785i807Mn9yuzCExRu2M3RgC+pWLnNkB8vOhNljYPIfYGcqtDg98rhkjeZHtj9JkiSpELDAFSGvfPkKE1ZN4PZOt9OlTpd4xznA5CWbmLp0M92PqU65Usk/uW3z2hU4u/0RFNDcXJj3d5j4MGxdDg27w0V/gfqdjiy0JEmSVIhY4IqICSsn8OKXL3JmkzP5ZctfxjvOfr5enc62jCz+Pmc1FUuXYPRlnSiZHOVh+sMQln4MHz8AG76GWsc5l5skSZKKHAtcEfBt2rcM/XQorau15t6u9xaqQUvmr03njBem7F0+u13d6Je3VTMjc7mtmAKVG8I5r0Hrc53LTZIkSUWOBS7Bbcvcxg0Tb6BMiTIM6zOMUsml4h1pPx/O30AQwJjLOlOmZDKtjqoYvZ1v/jZS3Bb+G8rVgIFPQodLoURK9I4hSZIkFSIWuASWk5vD7ZNvZ82ONbw+4HVql6sd70j7GfvlWp4b/w0dGlahV7Ma0dvxjlT45AmYPRqSS0VGlew6GEpViN4xJEmSpELIApfAnv/ieaasmcI9J9xDu5rt4h1nP2EY8tSHiwH4XffG0dlp5i6YMQKmPAdZuyJ323rfAeVrRmf/kiRJUiFngUtQ45aPY9S8UZzf7HwuaH5BvOPslZGVw/r0DNam72bF5l089IvWDMzvJNy5OTD3zzDxEdi+Lm9KgPugRrPohJYkSZIShAUuAX2z9RvunXov7Wq2Y2jnofGOs5+r/jibSYtTgcjgjye1yMfdse9HlvzoXti4AOp1gvNGQ8OuUUorSZIkJRYLXILZnrmdmyfdTLmS5Xi619OUTC4Z70h7pe/OYso3mzj1uNqc3KoWtSqWPvKJuNfOhY/uge8mQ5XGcP4b0OospwSQJElSsWaBSyBhGHL3lLtZtX0VowaMokbZKA4Mkk879mRz6ejPyc4NubxbYzo2qnpkO9q6AiY8DF+/DWWqwsA/QIfLHFlSkiRJwgKXUF6f9zoTVk1gSKchdKjVId5x9jP2y7V8sTKNpjXL065BlcPfwe6t8OnT8NkrECRB95uh+41QulL0w0qSJEkJygKXID5b9xnDvxjOKY1O4ZKWl8Q7zl45uSG5Ycj4hRuoW7kMH97U8/AmEs/eA5+/CpOfgox0OH4Q9LkLKtWNXWhJkiQpQVngEsD6nesZMnkIjSo24oETHzi8ghRDs5Zv4eKRM8jKCQH4ddeGh54tDGH+PyITcaethGP6Qb8HoHbr2AWWJEmSEpwFrpDLzMnklkm3kJGdwbBThlG2ZNl4R9pr7JdrSU4KuKFvU5KSAs5tX+/QvnHVTPhgKKyeCbWOg1/9E5r0iW1YSZIkqQiwwBVyf5j5B77a9BXP9H6GoysdHZcMW3dm8vc5q8nODfdbP27+erofU51rT2p6aDtKWxm54zbv71C+Fpw1AtpeDEnJ0Q8tSZIkFUEWuEJs7Ldj+eviv3LZsZdxcsOT45Zj9NTvGD5h6Y9+dvdph/CuWsY2mDIMpo+IDFDS63Y48XooVT7KSSVJkqSizQJXSC3espgHpz9Ip9qduL799XHNMn7RRjo2rMJbv+2y3/oggNIlf+LuWU42fPEWTHwEdqZCm4ug7z1Q6RAftZQkSZK0HwtcIbQjcwe3fHILFVIq8Ieef6BEUsH9z5SbGzLotRksS925d93G7Xu4Y2ALyqQcxqOOS8fDh3fDxgXQ4EQY9DbUbR+DxJIkSVLxYYErZMIw5IHpD0Qm6+4/iuplqhfo8b9ak86MZVvo07wGtSuVBiAlOYnzOhziXbONiyLFbelHUKURXPAmtDwzcrtOkiRJUr5Y4AqZvy35G+OWj+OG9jfQsXbHAjvurOVbWJeewccLN5AUwLALj6dy2ZRD38HOTTDpMZg1GlLKQ/+HofMVUKJU7EJLkiRJxYwFrhBZuHkhT3z+BN2O6sblrS8vsONu2JbBBa9M5/tBJrsfU/3Qy1v2Hvjs5chE3Jk7odNvodcdUK5a7AJLkiRJxZQFrpDYkbmDWz+5lcqlK/Noj0dJCpIK7NgTFm0kN4TRl3WifpUy1K18CHPNhSEs/i98cBds/Q6aDoD+D0GN5rEPLEmSJBVTFrhCIAxD7p9+P2t2rOH1Aa9TtXTVmB5v7JdreX3qd3uXV23ZTd3KZejdrAbBobyrtnERjLsDlk2E6s3hkn/AMX1jmFiSJEkSWOAKhbcXv80Hyz/ghvY30L5W7EdqfGXyt6xP30PLOhUAaFmnAme3q/vz5W33Vpj0OHw+MjKH2ylPRB6ZTC4Z88ySJEmSLHBxt2DzAp6Y+QTd6hbMe2/Tvt3EvDXbuP2UFlzdu8mhfVNuDsweAxMehow06HAp9LkLyhXsCJmSJElScWeBi6Ptmdu59ZNbqVK6Co91fyzm770tS93BoJGfAdCvZc1D+6blU+D9O2DD19CwG5zyONRpE8OUkiRJkg7GAhcnYRjy0IyHWLtjLa8PeJ0qpavE/JgfLdgAwMuXdKBprQo/vXHaSvjwHljwT6hUH84fA61+4XxukiRJUhxZ4OJk7LKxvP/d+ww+fnBM33vbnZnDg/+Zz7aMbOas2EqrOhU5pXXtg39D5i6Y+hxMfRYIoPedcOJ1kHIII1NKkiRJiikLXBys3LaSR2Y8QodaHfj9cb+P6bE+XriBv3y+iobVylI2JZnLuzf+8Q3DEOb/Az68F7athmPPgZMfhMr1Y5pPkiRJ0qGzwBWwrJwshkweQomkEjze43GSk5Kjuv/snFy27Mzcuzxu/nqqlkthwi29SU46yOOPGxfCf2+D5Z9C7ePgnFehUbeo5pIkSZKUfxa4AvbC3BeYv3k+z/R+htrlfuJRxiP0+zdnMXFx6n7rzmlf98fL257t8MkTMOMlSCkPpz0NHS6DKJdKSZIkSdFhgStAM9bNYPS80Zzb9FxObnhy1PefviuLyd9sYsCxtejZrAYAAcGBI06GIcz7O3x4N2xfB+1/DX3vh3LVop5JkiRJUvRY4ArI1oyt3PnpnTSq1IghnYZEff8792Tz+7dmkZMbckXPJnRoeJBRLTcugv/eGnlcsk5buOAtqN8p6nkkSZIkRZ8FrgCEYci9U+8lbU8aL/Z7kbIloz+i47tfrOHz77ZwdPVyHF+/8oEbHPC45DORCbl9XFKSJElKGBa4AvD24reZtHoSQzoNoUXVFjE5xoRFG2lQtSzjb+lFsO9cbT98XLLdr6Df/VCuekxySJIkSYodC1yMrdi2gqdnP82JR53IJS0vidp+f/P650z7dtPe5ayckEtPbLR/edv3ccnabXxcUpIkSUpwFrgYys7N5q4pd1EiqQQPnvjg/uUqH9am7eaTJan0aV6DlnUqApCcFDCoS4PIBpm7Io9LTn8BUso5uqQkSZJURFjgYmjM/DF8mfolT/R4glrlah3xftJ3ZfGfr9eSkxsC8NXqdADuOq0lx9SssP/G33wE790MaSvh+F9GJuP2cUlJkiSpSLDAxcjiLYsZMXcEAxoNYGDjgfna18hPl/HCxKX7rWtRuwJNapT/34rt62HcHTD/XajeDC59Dxp1z9dxJUmSJBUuFrgYyMzJZOiUoVQuVZm7u9yd70cnP164gU6NqvDyJR32rqtQumRkv7k5MOt1GP8gZO+BPndDt+uhRKn8/hiSJEmSChkLXAyMmDuCb7Z+w4i+I6hc+keG9D8EExdt5KH/LCAnDFmxeRd3ntqCauV/UMrWfw1jb4Q1s6BxLzh9GFRrEoWfQJIkSVJhZIGLsjkb5jB63mjObXouPev1POL9/HHGCrbuyqRnsxp0aVyVc9rX+9+HmTth0mMw/UUoUwXOGQnHnQ9RGiRFkiRJUuFkgYui3dm7uXvq3RxV/ihu63TbEe9n9oqtjF+0kUtPbMT9Zx67/4dLPoD3boX0ldD+19DvAShbNZ/JJUmSJCUCC1wUjfhiBKu2r2JU/1GUK1nuiPaRtiuTc1+aBkD/Y/cZuXLnJnh/SGRS7hot4LJx0LBrNGJLkiRJShAWuCj5OvVr3lr4Fuc1O4/OdTof8X4mLU4F4Mnz2nBik+oQhvD1O5Hytmc79LkLut0IJVKiFV2SJElSgrDARUFWThb3TruX6mWqc3OHmw/7+7Nzchny969Yn57B8k07qV4+hXPb14P0NZE53ZaMg7od4awXoGbLGPwEkiRJkhKBBS4KRn49kqVpSxnRdwQVUir8/Df8wJyVafxjzhpa1K5A3SplOKNNbZLmjIGP7oWcLBjwKHS5CpKSox9ekiRJUsKwwOXTkq1LGPnVSE47+rRDHnVyT3YO323auXf53S/WUCIp4G9XdaXCzpUw9npY/ik07glnDIeqjWMVX5IkSVICscDlQ3ZuNvdOvZeKpSpye6fbD/n77np3Hu/MXr3fup7HVKHCnJdhwiOQXDJS3Nr/2qkBJEmSJO1lgcuHPy/8M/M3z+fJnk9SpXSVQ/qe7JxcPlqwgV7NanBRp/oAlN2xgq5f3w0fzoRmA+H0Z6DiUbGMLkmSJCkBWeCO0IadGxgxdwQ96vZgQKMBh/Q9mdm5XPHWLNJ3Z3FRp/oMbF0bZr4GE+6N3HU7+1Voc4F33SRJkiT9KAvcEXpq1lPkhDkM7TKU4BAL1+QlqUxanErNCqXoWTsT3joblk2EJn3hzOehUt0Yp5YkSZKUyCxwR2Da2mmMWz6OwccPpn6F+gfdLgxDduzJ3rv84YL1lEtJYtrAjZR47XLIzYbTnoGOl3vXTZIkSdLPssAdpsycTB797FEaVmzIZa0v+8ltr/+/uYz9cu3e5Wqk88dqf6LEv6dAg67wixeh6tGxjixJkiSpiLDAHabR80azYtsKXun3CqWSSx10u12Z2Xwwfz09mlanV7Ma1Ns0hV4L7qP07h1w8kPQdbDzukmSJEk6LBa4w7Bq+ypGfj2SAY0GcGLdE390m+nfbuaz7zazNm03mdm5XN29Hicuex6+fAlqHgvnvga1WhVwckmSJElFgQXuEIVhyGOfPUZykMxtHW876DY3vz2XdekZAPSovJkTJlwAG+ZBl6ug3wNQsnRBxpYkSZJUhFjgDtGEVRP4dM2n3NrxVmqVq/Wj2yxYt4116Rn84ZzjOD/4GD64k2B7ORj0NjQ7tKkGJEmSJOlgLHCHYFfWLh7//HGaVmnKoJaDfnSb+WvTOW34FCqyg7OW3E6w9L/Q5CT4xUtQoXYBJ5YkSZJUFFngDsHLX77M+p3reaLHE5RMKvmj2/zzizW0Dpbxl8ovUWrZBuj/MJwwGJKSCjitJEmSpKLKAvcTcnJzWLR1EW8seINzm55L+1rt9/s8IyuHD+avJzMrh5S5b/BuqVGULFkTBr0P9TvHKbUkSZKkosoCdxD/Wvov3l7yNhnZGVQrXY2bO958wDZ/nbmKx/89m0dKvs5tyVNYV70bdS57C8pVi0NiSZIkSUWdBe4gKpWqxIJNCwgJef6k56mYUvGAbeZ9NZv3y95Hw9zVbO86hNon3+HcbpIkSZJixgJ3EL3r92Zk/5GEhHSq3emAz8e8MZJ71t1LiZIpBL98lwpN+sQhpSRJkqTixAL3EzrW7njgyjBkx6Rn+dWyB1gaNKDsoL9R9ujmBR9OkiRJUrFjgTsMKzdsofQHN1Nz2bv8N7czjX/3FvUbOkWAJEmSpIJhgTtEmVvXkvbSmbThG57JOo93K1zM5AY/PqG3JEmSJMWCBe5QrPoc/vxLmoTpfNTmaU5sdzYXVytLEATxTiZJkiSpGLHAHczGRbB2DmTuJHfcUNbnVOGanIf42xmXUSbFkSYlSZIkFTwL3MF88RZMfwGAJeU7c+Gm3/Hrk463vEmSJEmKGwvcwZz8EDTqwc6MTM56O5kBbY/ilv6ONilJkiQpfpLiHaDQSkoi4+iT6fBOSfbkQL9WDlgiSZIkKb4scD/hs++2kJGVy6AuDTi1tdMFSJIkSYqvmBW4IAhOCYJgcRAES4MguCNWx4mlCQs3UKZkMvee3ooSyXZdSZIkSfEVk1YSBEEyMAIYCLQCLg6CoFUsjhUrYRjy8cKNdDumOqVLOnCJJEmSpPiL1W2lzsDSMAyXhWGYCfwfcFaMjhUTSzbsYE3abvq2rBnvKJIkSZIExK7A1QVW7bO8Om9dwhi/aAMAJ7WwwEmSJEkqHOL2YlcQBFcEQTArCIJZqamp8YpxUJ0bVeWWk5tRq2LpeEeRJEmSJCB288CtAervs1wvb91eYRi+CrwK0LFjxzBGOY5Yx0ZV6dioarxjSJIkSdJesboDNxNoGgRB4yAIUoCLgH/H6FiSJEmSVCzE5A5cGIbZQRBcC3wAJAOvh2E4PxbHkiRJkqTiIlaPUBKG4X+B/8Zq/5IkSZJU3Dg7tSRJkiQlCFE0WE8AAAY6SURBVAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCUIC5wkSZIkJQgLnCRJkiQlCAucJEmSJCWIIAzDeGcgCIJUYEW8c/xAdWBTvEOoyPL8Uqx5jimWPL8Ua55jiqXCen41DMOwxs9tVCgKXGEUBMGsMAw7xjuHiibPL8Wa55hiyfNLseY5plhK9PPLRyglSZIkKUFY4CRJkiQpQVjgDu7VeAdQkeb5pVjzHFMseX4p1jzHFEsJfX75DpwkSZIkJQjvwEmSJElSgrDA/UAQBKcEQbA4CIKlQRDcEe88SkxBENQPgmBiEAQLgiCYHwTBDXnrqwZB8FEQBN/k/Vklb30QBMHwvPPuqyAI2sf3J1AiCIIgOQiCL4Ig+E/ecuMgCD7LO4/+GgRBSt76UnnLS/M+bxTP3Cr8giCoHATBO0EQLAqCYGEQBF29fimagiC4Ke/vx3lBEPwlCILSXsOUH0EQvB4EwcYgCObts+6wr1tBEPwmb/tvgiD4TTx+lp9jgdtHEATJwAhgINAKuDgIglbxTaUElQ3cEoZhK+AEYHDeuXQHMD4Mw6bA+LxliJxzTfP+uwJ4qeAjKwHdACzcZ/kJYFgYhscAW4Hf5q3/LbA1b/2wvO2kn/IcMC4MwxZAWyLnmdcvRUUQBHWB64GOYRi2BpKBi/AapvwZA5zyg3WHdd0KgqAqcB/QBegM3Pd96StMLHD76wwsDcNwWRiGmcD/AWfFOZMSUBiG68IwnJP39XYiv/zUJXI+vZG32RvAL/K+Pgt4M4yYAVQOgqBOAcdWAgmCoB5wGvBa3nIAnAS8k7fJD8+v78+7d4C+edtLBwiCoBLQExgFEIZhZhiGaXj9UnSVAMoEQVACKAusw2uY8iEMw8nAlh+sPtzr1gDgozAMt4RhuBX4iANLYdxZ4PZXF1i1z/LqvHXSEct71KMd8BlQKwzDdXkfrQdq5X3tuafD9SwwBMjNW64GpIVhmJ23vO85tPf8yvs8PW976cc0BlKB0XmP6L4WBEE5vH4pSsIwXAM8BawkUtzSgdl4DVP0He51KyGuZxY4KYaCICgP/B24MQzDbft+FkaGgHUYWB22IAhOBzaGYTg73llUJJUA2gMvhWHYDtjJ/x47Arx+KX/yHkk7i8g/FhwFlKMQ3uVQ0VKUrlsWuP2tAervs1wvb5102IIgKEmkvP0pDMN/5K3e8P2jRXl/bsxb77mnw9ENODMIguVEHvU+icg7S5XzHkeC/c+hvedX3ueVgM0FGVgJZTWwOgzDz/KW3yFS6Lx+KVr6Ad+FYZgahmEW8A8i1zWvYYq2w71uJcT1zAK3v5lA07xRkFKIvFD77zhnUgLKezZ/FLAwDMNn9vno38D3Ixr9BvjXPut/nTcq0glA+j63/KX9hGE4NAzDemEYNiJynZoQhuEvgYnAeXmb/fD8+v68Oy9v+yLxr5CKvjAM1wOrgiBonreqL7AAr1+KnpXACUEQlM37+/L7c8xrmKLtcK9bHwD9gyCoknenuH/eukLFibx/IAiCU4m8W5IMvB6G4SNxjqQEFARBd+BT4Gv+947SnUTeg3sbaACsAC4Iw3BL3l9gLxB5hGQXcFkYhrMKPLgSThAEvYFbwzA8PQiCo4nckasKfAFcEobhniAISgNvEXkXcwtwURiGy+KVWYVfEATHExkgJwVYBlxG5B99vX4pKoIgeAC4kMiozV8AvyPyrpHXMB2RIAj+AvQGqgMbiIwm+U8O87oVBMHlRH5nA3gkDMPRBflzHAoLnCRJkiQlCB+hlCRJkqQEYYGTJEmSpARhgZMkSZKkBGGBkyRJkqQEYYGTJEmSpARhgZMkSZKkBGGBkyRJkqQEYYGTJEmSpATx/7w6MEK9UttjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On trace sur le même graphique Pi(x) et x/log(x) pour x entre 2 et N\n",
    "\n",
    "fig=plt.figure()\n",
    "\n",
    "fig.set_figheight(15)\n",
    "fig.set_figwidth(15)\n",
    "\n",
    "N=1000\n",
    "\n",
    "c=crible2(N)\n",
    "x=list(range(2,N+1))\n",
    "y=[len(c[0:i])-c[0:i].count(0) for i in range(2,N+1)]  #permet de tracer pi(x). On n'utilise pas PiRecursif pour gagner du temps de calcul\n",
    "z=[i/math.log(i) for i in range(2,N+1)] # on trace x/log(x)\n",
    "t=[2*i/math.log(i) for i in range(2,N+1)] # on trace 2x/log(x)\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.plot(x,z)\n",
    "plt.plot(x,t)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}