problem1_Meek_Rules.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1: \n",
    "### Anita Mezzetti\n",
    "\n",
    "See PDF file for details\n",
    "\n",
    "index:\n",
    "1. [Complete undirected graph from nodes](#complete)\n",
    "2. [Conditional independence tests and delete edges](#direct)\n",
    "    - [Threshold](#threshold)\n",
    "    - [Partial correlation function (Gaussian)](#partial)\n",
    "    - [Partial correlation function (Pingouin) (not used)](#partialp)\n",
    "    - [Remove Edges](#delete)\n",
    "3. [Orient V-structures](#orient)\n",
    "    - [Find all undirected v structures](#findv)\n",
    "    - [Unshielded Colliders function](#unshielded)\n",
    "\n",
    "4. [Meek rules](#meek)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.io import loadmat\n",
    "import networkx as nx\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import det, inv\n",
    "import math\n",
    "import pingouin as pg\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "import numpy as N, networkx as nx\n",
    "import sys \n",
    "from networkx import DiGraph\n",
    "from itertools import combinations, permutations, chain\n",
    "from networkx.algorithms.cycles import find_cycle, simple_cycles\n",
    "import warnings\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)\n",
    "warnings.simplefilter(action='ignore', category=DeprecationWarning)\n",
    "import itertools "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define $\\alpha$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load data and chech size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 8)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = loadmat(\"Data.mat\")['D']\n",
    "n = data.shape[0] # sample size\n",
    "num_nodes = data.shape[1]\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes = np.array(range(num_nodes))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Complete undirected graph from nodes <a name=\"complete\"></a>\n",
    "\n",
    "I created a function. Then, I discovered that there was a function in Networkx which does the same (_nx.complete_graph(n)_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this function create a complete graph (with all possible edges)\n",
    "def complete_graph(nodes):\n",
    "    G = nx.Graph()\n",
    "\n",
    "    G.add_nodes_from(nodes)\n",
    "    for (i, j) in combinations(nodes, 2):\n",
    "        G.add_edge(i, j)\n",
    "\n",
    "    return G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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u9si7uAXf6MVgzdAvMNHVHl3afQVHR0ccOHBAjVfGURmc6FYh3FtKnl/JDz+AF4GDkX49BFkP/8GLwMHgh5f/Z+PmaWqWmzdvok+fPhgyZAj69u0rldgCRYkbnp6e8PPzQ8eOHbF27VoMHz4cVlZWJWUKCgpQu3btMvVmzpyJlStXgsRNeeHQCFx4oQrBMzbE140tcO7xm3LTxkw6fQeTTt9VWJ+bp6k5bt68iUWLFuHevXuYM2cOjhw5UqnQlsbf3x+Wlpbw8/MDn8/H5s2bcevWrTJlCgoKUKtWrTLHevToAX9/f4SFhaFXr15KuRYOxeB6ulWMKZ0dYKQnOVW0InSEAkz6YKoYh2q5desW+vXrh8GDB8PNzQ2xsbHw8fGRSXBDQkJw/Phx7Ny5E4wxbNq0Cb169UKDBg3KlCsoKICpadn1GRhjJb1dDu2AE90qhktdE8zsbg8mEJ91JgldCPD+763wG+OBzMxMFXnHIeL27dvo378/Bg4ciF69euHJkycyiy2AEpE+fPgwTE1NkZubi6CgIMyePbtcWVFG3ocMHToUT548we3bt+W+Hg7lwYluFaOwsBDHA/3QIO0ujPR1UFkCFgNQTV8XiwY0x2/TPREeHg4XFxc8f/5cHe5+cojEdsCAAejRowdiY2MxZcoUuRI/cnJy4O7ujoULF6JVq6LU7Z07d6Jly5Zo1qxZufICgQBmZmbljuvr6+OHH37gertaAie6VQgiwsSJE5GXl4e/fp+HQxPaoefnVjDU04HRB7MajPR0wISFcDDKwsEJbeHVtj68vb1x8uRJvH37Fl988QUuXbqkoSv5+Lhz5w4GDBiA/v37o3v37oiNjcXUqVMVyrKbPn06nJ2dMXnyZABFX7grVqwQ28sFAKFQKFZ0AWD8+PE4f/48nj59Krc/HEqCiCT+tGzZkji0hzlz5lDr1q0pIyOjzPF3Gbm06VIsOY9eRo4T1tAPB/6jTZdiKfTsP+To6EhCobBM+Xv37pGFhQUZGxvThg0b1HkJHx137tyhAQMGkK2tLa1bt45ycnKUYnfnzp3UuHFjSk9PLzm2f/9+6tixo9jyBQUFBIDevn0r0ebs2bNp6tSpSvGPo2IA3CIJusqJbhUhKCiIHB0dKTk5WWIZFxcXcnNzK3ktFAqpWbNmdO7cuXJl4+Pjyd7enszMzGjixImUl5enEr8/Vv777z8aMGAA2djY0Nq1ayk7O1tpth88eEA8Ho8iIyNLjgmFQnJxcaGTJ0+KrZOWlkYAKCsrS6LdxMREMjU1rfAzxKEcKhJdLrxQBdi3bx9WrVqFs2fPgsfjSSyXlZVVZsoQYwxTpkzB77//Xq7sZ599hoiICDRu3BihoaHo1q0bkpOTVeL/x8Tdu3cxaNAguLm5oUuXLoiLi8P06dNRrZr4XRpkJTMzE+7u7li5cmWZuO1ff/0FgUAANzc3ifUAVBjOsLGxweDBg7Fhwwal+MohJ5LUmLierlbw119/kZWVFT148KDSsra2tjRx4sQyxzIyMsjMzIyePXsmtk52djYNGjSIPvvsM/rss8/o3r17ynD7o+Pu3bs0aNAgsrGxoaCgIKX2bEUIhUL69ttvacyYMeXOubq60p49eyTWjYyMJMZYpW08evSILC0tVeI/x/8B19OtmkRERMDb2xtHjhxBkyZNKi2fk5NTbp6msbExRowYgU2bNomtU61aNRw+fBj9+vUDEaFz5844cuSIUvz/GLh37x6GDBmC3r17w9XVFXFxcfj++++V1rMtzZYtW3D//n389ttvZY5fu3YNL168wNChQyXWTUlJkWrXCmdnZ7Rt2xY7duxQ1F0OeZGkxsT1dDXK48ePydraWmIMTxzVq1enFStWlDseExNDPB6vwkEeoVBIy5YtI2tra7K2tqYFCxaQQCCQy/ePgXv37tHgwYPJ2tqaVq9eXWGsVBncvn2beDweRUdHlzvXv39/Wr9+fYX1jxw5QgYGBlK1deXKFbK3t6fCwkK5fOWoHHADaVWLhIQEqlevHu3YsUOmerq6urRt2zax53r16iWVvV27dhGPx6OmTZvS4MGDy82U+Ni5d+8eDRkyhKytrWnVqlUqF1siotTUVGrYsCEdPHiw3Ln79++TlZVVpeGA4OBgqlatmlTtCYVCateuHYWEhMjlL0flVCS6XHhBy0hJSUGvXr0wZcoUjBw5Uup6BQUFEAgE5cILIqZOnYrffvut0oVPvL29sXfvXiQlJSE1NRUdOnT4JBIp7t+/Dw8PD/Ts2RPt27dHXFwcZsyYgerVq6u0XSLC6NGj4ebmBk9Pz3LnV6xYIVU4Iy0tTer1kEWpwStWrOAWwtEAnOhqEdnZ2ejXrx969eqFmTNnylQ3PT0denp6MDY2Fnu+V69eSE1NRURERKW2evTogbCwMERHR6NRo0Zo167dR5tI8eDBA3h4eKB79+5o27YtYmNj1SK2ItasWYNXr14hMDCw3Ln4+HicOnWqJDmiIkTbJUlL//79kZqaiitXrsjkL4ficKKrJRQUFMDT0xP29vZYsWKFzPXT0tKgq6srUSx0dXXh4+MjdvqYOFq0aIErV64gMjISX3/9NTw8PCQOxlVFHjx4AE9PT3Tr1g1t2rRBXFwcfH19UaNGDbX5cO3aNQQEBODQoUNi12QIDAzEuHHjxK6n8CF8Pl+m7ZJ0dXXh5+fHpQZrAklxB+JiumpDKBTSyJEjyc3NjfLz8+Wycfv2bTIyMqI7d+5ILPP+/XsyMTGhpKQkqe0mJydTmzZtaODAgeTk5ESTJ0+W20dt4MGDB+Tp6UlWVla0cuVKyszM1IgfycnJVLduXQoNDRV7/s2bN2RqakqJiYlS2Rs7dizVr19fJh9ycnLIysqKHj58KFM9jsoBF9PVbmbNmoXo6GgcOnRI7n3K+Hw+GGMVPhabmZnB3d0df/zxh9R2eTweLly4AIFAABsbGzx79gzdu3evcokUDx8+xLBhw/DNN9+gVatWiIuLg5+fn1p7tiKEQiG8vLwwfPhw9O3bV2yZ3377DZ6enrCxsZHKZkZGhszrPBgZGWHatGliQxscKkSSGhPX01ULgYGB5OzsTO/evVPIzpEjR8jIyIgSEhIqLPfff/+RnZ0dFRQUyGS/oKCAxo8fT19++SVNmzaN6tevXyUSKR4+fEhDhw4lS0tLCggI0IrZGEuWLKFOnTpJfA/S09PJ3Nycnjx5IrVNNzc3+uKLL2T25f3792RqakovX76UuS6HZMD1dLWTXbt2Yd26dQgLC4O5ublCtvh8PoRCYaUDQF988QXq16+P48ePy2RfT08PmzdvxqBBgxAaGoqpU6eia9euWptI8ejRIwwfPhxdunTBl19+ibi4OPj7+0scaFQXFy5cwPr167F//37o6YnfuGXz5s3o1q0bHBwcpLabnZ0tV8KGmZkZvL29sW7dOpnrcsiJJDUmrqerUk6dOkVWVlb06NEjpdgLCgoiHR0dqVa5OnDgAHXu3Fnutv744w+ysrKi4OBgqlu3Li1cuFBrEikePXpEw4cPJ0tLS1q+fLlW9GxFJCYmko2NjdgFiETk5uaSra0t/ffffzLZbt26NXXr1k0uv549e0bm5ubE5/Plqs9RHnA9Xe3i33//xahRo3Ds2DE4Ozsrxeb79+9BRFLtTDBo0CBER0fjwYMHcrU1duxYbNu2Df7+/liyZAnCwsLg6emp0R0poqKi8N133+Hrr79G8+bNERsbi1mzZmm8ZyuisLAQw4YNw6RJk9CtWzeJ5Xbv3o3mzZvjiy++kMl+Tk6O3PHp+vXro0ePHtiyZYtc9TlkgxNdNfPo0SMMGjQIO3fuRNu2bZVmNyUlBQYGBmCVbSUBwMDAABMnTsT69evlbq9Pnz44deoUZs+ejW+//Ra1atXSSCKFSGxdXV3RtGlTxMXFYfbs2ahZU7u2mf/5559haGiIefPmSSwjEAgqXKS8InJychT6gpk5cyaCgoKQny/bNlAcssOJrhpJSEhAr169EBgYiN69eyvV9vv372WapzlhwgQcOHAAaWlpcrfZunVrXLlyBUFBQahTpw5Gjx6Ndu3a4fLly3LblJbo6Gh4eXnB1dUVTZo0QVxcHObMmaN1YgsAp06dwu7du7F3717o6kreVPTIkSMwNzeHq6urzG3k5eUpdO1ffvklnJ2dsX//frltcEiJpLgDcTFdpfLu3TtycnKiVatWqcR+z549ycLCQqY6w4YNo6CgIIXbTkpKolatWtGYMWPo1KlTZGlpSZs2bVLYrjiioqLIy8uLLCwsaOnSpVofh3z+/DlZWlrSlStXKiwnFAqpRYsWdPz4cbnasbS0pJkzZ8pVV0RYWBg1bdq03E4jHLIDLqarWbKystCnTx/0798fM2bMUEkbaWlpMqeuTp06FevXr4dQKFSobSsrK/zzzz9ITEzE+vXrcfbsWaxduxY+Pj4oKChQyLaImJgYeHt7o2PHjnByckJsbCzmzp1bZtF2bSM/Px+enp6YOXMmOnbsWGHZ8+fPIzc3V+K8XWnaql27tlx1RXTv3h26urr466+/FLLDUTGc6KqYgoICeHh4wNnZGcuXL1dZO3w+X+aBlPbt26N69eo4d+6cwu0bGxvjxIkTsLS0xPjx4xEaGooXL16gR48eePfundx2Y2JiMGLECHTo0AGOjo6Ii4vDvHnztFpsRcycORM2Njbw9fWttOyyZcswa9YsqdbEFUd+fr7C96T0QjgcqoMTXRUiFAoxZswY6OrqYuvWrVINcslLenq6zAMpjDFMnTpV6vUYKkNfXx/BwcHo2bMnevXqhdWrV6Nt27Zo3bo1IiMjZbL15MkTjBw5Eh06dEDjxo0RGxuL+fPnVwmxBYCQkBCEhoZi+/btlb7vN27cQFxcHIYPHy53e4WFhVKt0VAZnp6eePr0KW7evKmwLQ4JSIo7EBfTVQihUEgzZsygDh06qGVN1lq1alHXrl1lrpeVlUXm5uYUFxenVH82btxINjY2FBERQfv27SMej0dHjhyptN6TJ09o5MiRxOPxaPHixZSWlqZUv9SBaNH4mzdvSlV+0KBBtG7dOoXa1NHRoRMnTihkQ8SaNWvIw8NDKbY+VcAtYq5+AgICqGnTppSSkqLytoRCIenq6tKgQYPkqu/r60t+fn5K9oro2LFjxOPx6PTp03Tz5k2ys7OjRYsWiU2kEImtubk5LVq0iFJTU5XujzrIzs6m5s2bV7rTgwjRnmWKfDELhUICQFevXpXbRmkyMjJU8kX8KcGJrprZvn071a9fX2357NnZ2aSnp0cjRoyQq35sbCzxeDyV9MjDw8PJ0tKSgoODKTExkdq2bUtDhgwpWd0rNjaWRo0aRebm5rRw4cIqK7Yixo0bR8OGDZN6BsCoUaNo8eLFCrWZnZ1NjDG6e/euQnZKM3fuXJoyZYrS7H1qcKKrRk6cOEHW1tYUFRWltjZfv35NNWvWpEmTJslto0+fPhK3+lGUx48fU/369WnJkiWUk5NDo0aNImdnZ/Lw8PhoxJaIaOfOneTo6Ejp6elSlX/x4gWZmpoq/DSUnJxMOjo6FBMTo5Cd0rx+/ZpMTU0pOTlZaTY/JSoSXW4gTYlcvXoVY8eOxYkTJ+Do6Ki2dtPS0mBoaKjQbgfSbucjD05OTrh27Rr+/PNPjB07FkKhEPHx8Thz5gx27dqFBQsWKGUQSJM8ePAAvr6+CAkJkTpJYfXq1RgzZozELZakJSsrq9JlPWXF2toa7u7uCmUtckhAkhoT19OVicjISLK0tKSwsDC1t339+nWytbWl+fPny21DIBCQg4MDhYeHK9Gz/xMXF0deXl6kr69Pjo6O9PLlSwoLCyNLS0vavHmzStpUFxkZGeTk5CTTRqLJyclKW1Lx4cOHpKOjQ+/fv1fYVmmioqIUjjd/qoDr6aqW+Ph4uLm5ISgoCD169FB7+6KtWhRZkFtHRwdTpkxR2vQxEc+ePcO4cePQunVrNGzYEAkJCWjVqhU8PDzQsmVLXL16FWvWrMGUKVOUlkihTogIEydORPv27WXaSPT333/HkCFDUKdOHYV9yMrKAhEpfV83R0dHtGvXDjt27FCq3U8eSWpMXE9XKt6+fUuNGzemtWvXasyHg2YZUVUAACAASURBVAcPkr29vcI+pKamkomJidRbxFTE06dPady4cWRubk4//fRTmV6YQCAgf39/cnR0pGfPnlFaWhr16dOHOnfuXOViiBs3bqTmzZtXukV6aTIyMojH41F0dLRSfDh//jwBUEn6bnh4ODVs2JAKCwuVbvtjBlxPVzVkZmaiT58+cHd3x/Tp0zXmB5/Pr3BTSmkxMTHB0KFDsXXrVrltPH/+HOPHj0erVq1gbW2NmJgYLF68GGZmZiVldHR0EBAQAB8fH3To0AFPnz7F8ePH0aZNG7Ru3Rr3799X6DrUxe3bt/HTTz/h8OHDMi0gvnXrVnTu3BmNGzdWih+pqanQ1dVVSfJN+/btYW1trbWL1VdJJKkxcT3dCsnLy6Pu3bvTuHHjNL5AyMqVK8nR0ZH27dunsK3IyEiytbWVefPJZ8+e0fjx48nMzIzmzZsndXzx8OHDZGFhUbKw9969e8nCwoKOHj0qs+/qJDU1lRo2bEiHDh2SqV5eXh7Z2dnRrVu3lObL1q1bycDAQGn2PuTYsWP01VdfafxzXpUA19NVLkKhEKNGjUKNGjWwceNGlab3SkNaWprSRq+bNWuGRo0a4ejRo1KVj4+Px8SJE9GyZUtYWloiJiYGv/zyS5mebUW4u7sjJCQE3333Hfbu3Ytvv/0Wp0+fxrRp07BkyRKVzKZQFCLC6NGj0adPH3h4eMhUd+/evXB2dkbLli2V5k9qaqrErX+UQb9+/ZCeno5Lly6prI1PCU50ZYSI8OOPP+Lly5fYt2+fSj/s0iLt/mjSIs16DCKxbdGiBXg8XonYyrPXm6urKy5cuIA5c+ZgxYoVaNmyJSIiInD69Gl4enoiKytL3ktRCWvWrMGrV6+wcuVKmeoJhUIEBATItUh5RaSnp8u0lrKs6OjowNfXV+br5RAPJ7oysmzZMly8eBEnTpyQayNAVZCWlqZU0R0wYACePn2Ke/fulTv34sULTJo0CS1atIC5uTmio6OxdOlShTfWbNKkCa5du4bdu3fj+++/h6WlJf755x8YGxujQ4cOiI+PV8i+srh27RoCAgJw6NAhqbZGKs2xY8dQq1YtdOnSRak+qVp0AcDb2xt37tyRe4snjv/Dia4M/PHHH/jjjz/w119/adVkfj6fj8LCQoWmjJVGX18fkyZNKjMx/sWLF5g8eTK+/PJLmJmZITo6Gr/++it4PJ5S2gQAOzs7XLlyBZGRkRg2bBgAIDg4GCNHjkTbtm1x5coVpbUlD8nJyRg2bBi2bduG+vXry1SXiLB8+XLMnj1b6eGo9PR0mb8AZMXIyAjTpk1DYGCgStv5JJAU7CVuIK0MR48eJRsbG6WmWioLV1dXsrOzU9oUJKKi3SBMTEwoMjKSJk+eTGZmZjR79my1TOnKzc0lT09P6tSpU0mKrCiRYsuWLSpvXxwCgYB69OhBs2bNkqv+33//TY6OjirZNXnIkCHk4OCgdLsfkpKSQqamppSQkKDytqo64AbSFOPy5cuYMGECQkND0ahRI027U460tDTk5eUpdXJ8fn4+LCws0KZNG9SqVQtRUVFYtmyZUnu2kjA0NMT+/fvRsmVLdOzYEQkJCejRoweuXr2K1atXY+rUqWpPpFi6dClycnLwyy+/yFVf0UXKKyIzM1MtoS5TU1OMHDkSa9euVXlbHzWS1Ji4ni4REd27d6/MlCZtpF69elSrVi2lpIEmJCSQj48PmZmZkZeXF9WrV08lvTNpCQwMpLp161JkZCQREaWlpZGbmxt16dJFbYkU58+fJxsbG3r16pVc9UXLWubl5SnZsyI6duxIrVu3VontD3n+/DmZmZlVyXWO1Qm4nq58PHv2DG5ubvj999/RrVs3TbsjET6fj9zcXIViui9fvsTUqVPh4uICY2NjREVFYdeuXTA3N9fonlm+vr4ICAhA165dcfHiRdSuXRsnTpxA69at1ZJIkZiYCG9vb+zevRu2trZy2QgICICvr6/KBruys7OVngIsiXr16qF3797YsmWLWtr7KJGkxvSJ93TfvHlDjRo1ot9//13TrlSIQCAgxhjp6OjINXn95cuXNGXKFDI1NaWZM2fSmzdvypwPDg6m3r17K8tdufn777/JwsKCDhw4UHJsz549xOPxVJZIUVBQQK6urrRo0SK5bURHRxOPx6OMjAwlelYWZ2dncnNzU5n9D7l79y7Z2tqqrOf+MQBuPV3ZSE9Pp5YtW9JPP/2kaVcqhc/nU40aNcjY2Fimei9fvqSpU6eSqakp+fn5lRNbEdnZ2cTj8ejJkyfKcFch7t69S3Xq1KE1a9aUHIuIiCA7OztasmSJ0jOmZs+eTT169FAovDJ27FhasGCB8pwSQ/369cnT01OlbXxI9+7dafv27WptsyrBia4M5ObmUteuXWnChAlVIu3xxYsXZGNjQ5aWllKVf/XqFU2bNo1MTU3J19eXkpKSKq3j7+9PP/74o6KuKoXnz5+Tk5MT+fr6lohhYmIitWnThjw8PEp2pFCU0NBQsrOzo7dv38pt4+XLl2Rqakrv3r1Tik+SsLa2prFjx6q0jQ85d+4cff755xqN92szFYkuF9MthUAggLe3N2rXro0NGzZoPL1XGtLS0mBsbFxpPDcxMRHff/89mjZtCgMDAzx+/BiBgYGwsrKqtI3Jkydj165dWpEZVq9ePYSHh+P69evw8vJCXl4ebGxscPHiRVSvXh0dO3ZUOJEiPj4eY8eOxYEDB2BhYSG3nTVr1mDkyJEKJ45URn5+vtQLpyuLrl27wsDAAGfOnFFrux8DnOgWQ0SYPn06kpOTsXfvXujq6mraJang8/moUaOGxIGU169fl4itnp4eHj16JLXYiqhfvz46dOiAffv2KctthTAzM8O5c+eQm5sLNzc38Pl8GBkZYfv27RgxYoRCiRT5+fnw9PSEv78/OnToILePKSkpCA4OxowZM+S2IS35+fmoXbu2ytspDWMM/v7+XGqwHHCiW8ySJUtw7do1HD9+HEZGRpp2R2rS0tJQvXr1cqL7+vVr/PDDD2jSpAl0dXXx6NEjrFq1CtbW1nK1I1qPgbRkAZpq1arh8OHDcHJygqurKxITE8EYw48//ogdO3bA3d1driUqZ86cCRsbG4XFcv369RgwYADq1q2rkB1pyM/PR61atVTezod4eHjg+fPniIiIUHvbVRpJcQf6hGK6GzduJHt7e3r9+rWmXZGZPXv20DfffENff/01ERXFN3/44QcyNTWlH3/8UWnXJBAIyNHRkS5fvqwUe8pCKBTSr7/+SvXq1aNHjx6VHI+OjiZHR0eaOnWq1MtUHjp0iBo0aKDwRpGZmZlkYWFRxh9VoqOjQ8HBwWpp60OCgoLI3d1dI21rM+BiupL5888/sWTJEoSFhcndC9QkokdrPT09zJgxA02aNAEAPHz4EKtXr1baNalqOx9FYYxhzpw5WLRoETp37oyrV68CABo3bowbN27g6dOn6NmzJ96/f1+hnZiYGPj4+ODw4cMKbxQZHByMjh07wtnZWSE70lBYWAihUKj2mK6IsWPH4uLFi4iNjdVI+1USSWpMn0BP98KFC2RhYUF37tzRtCtyM3v2bLK3tyd9fX36/vvvlbLVjiT4fL7SNlNUBX/99RfxeDw6cuRIybHCwkLy9/enhg0b0v3798XWy87OpubNm9OGDRsU9iE/P58+++wzun79usK2pCEtLY10dXXp9OnTamlPHPPmzaPJkydrrH1tBNyUsfLcuXOHLCws6MKFC5p2RS6SkpJoxowZZGhoSA4ODmp7xPPx8aGff/5ZLW3Jw61bt8jGxobWr19f5vju3buJx+PRsWPHytUZO3YsDR8+XClTBHfu3EldunRR2I60vHr1ivT19enixYtqa/NDkpKSyNTUVKHpdR8bnOh+QGxsLNnY2FBISIimXZGZpKQk8vX1JTMzM5o+fTp5eXnRsGHDaNKkSWpp/+HDh2Rtba3V2UhxcXHUqFEjmjNnThkhFZdIsWPHDnJ0dKT09HSF2xUIBPT555/T2bNnFbYlLTExMWRoaEg3btxQW5vimDBhglZ/GaubikT3k4vpJiUloUePHliwYAGGDBmiaXek5u3bt/Dz84OzszPy8/MRGRmJtWvXoqCgADo6OkpbS7cyPv/8c3z++ef4888/1dKePDRs2BDh4eH4+++/MWrUqJIVyb766itERETg5MmTGDp0KCIiIuDn54eQkBClxERDQ0NhZGSk1nU6RHOn1bX2giR8fX2xceNGZGdna9SPqsAnJbp8Ph+9e/fGyJEjMXHiRE27IxVv377FzJkz4eTkhLy8PNy/fx/r1q1DnTp1ABRdk7L2R5MWabbz0TQWFha4cOECUlJS0LdvX2RkZABASSKFnp4eXF1dMWfOHDRt2lTh9ogIy5YtU8ki5RUhEl1N72LSuHFjdOzYEdu3b9eoH1WBT0Z0c3NzMXDgQHTo0AE//fSTpt2plLdv38Lf3x/Ozs7Izc1FZGQkfvvttxKxFcHn8wGot6fTr18/JCQk4M6dO2prUx5q1KiBo0ePol69eujcuTOSkpIAFK3XKxQK4eLigsDAwJIZD4pw+fJlpKSkYPDgwQrbkoXs7GwQkcZ7ukDRHOdVq1ahsLBQ065oNZ+E6AoEAnz33XewsLDA2rVrtTq9Nzk5GbNmzYKzszOys7Nx7949/Pbbb7CzsxNbPi0tTe3/dHp6epg8eXKZ7Xy0FT09PWzevBkDBgxA+/btERMTg02bNuHx48e4ePEitm/fjiFDhsiVSFGa5cuXw9/fX+2ZjFlZWRAKhRrv6QJAu3btUKdOHRw5ckTTrmg3koK99JEMpAmFQpo4cSJ17dqVcnNzNe2ORN6+fUv+/v5kZmZGPj4+9OLFC6nq2dra0tChQ+mPP/5QsYdlefv2LZmYmKh8MRdlsnXrVjI3N6fatWuX2XZJnkSK0ty5c4dsbW018vnas2cPMca0ZmDz+PHj1LJlyyqxWJQqwac8kLZw4ULcvHkTR48eVfnmffLw7t07zJ49G05OTsjIyMDdu3exfv16qdNH+Xw+BAKB2h8vLSws0L9/fwQHB6u1XUUYMmQI9PT0IBQKER0dXXJclEgRFxeHXr16VZpI8SEBAQH48ccfNfL5Sk9PB1C0mag20LdvX2RlZeHixYuadkVr+ahFd8OGDdi3bx/OnDmjsYwdSbx79w5z5syBo6Mj0tPT8d9//2HDhg0y5eoXFBQgNzdX6fujScvUqVOxYcMGCAQCtbctK0SE0aNHw9PTE+fOncP48ePLhBRq166N0NBQtGrVCq1bt5Z6q/HY2FicP39eYwOzaWlp0NPT05qQmY6ODvz8/LiFcCpCUheYqnh44eDBg1SnTh16+vSppl0pQ3JyMs2ePZvMzMxo0qRJFB8fL7etd+/ekZmZGXXt2lWtc0NL89VXX9GJEyc00rYsBAYGUuvWrUsew2NiYqhhw4a0YMGCco/Cu3fvJgsLC7GJFB8yYcIEmj9/vkp8loZZs2ZR9erVNda+OHJzc8nGxqZkX7tPEXxqyRHnz58nCwsLunv3rqZdKeHdu3c0Z84cMjMzo4kTJ9Lz588VthkbG0sNGjSgdu3aUXh4uBK8lJ2dO3dSjx49NNK2tFy9epUsLS3L3fOkpCRq2bIljR07lgoKCsqcu3HjBtnZ2dEvv/wiMT6ZmJhIJiYmGs3EmjRpEpmYmGisfUksW7aMRowYoWk3NEZFovvRhRdu376N4cOHIyQkBC4uLpp2B+/fv8e8efPQuHFjpKSk4M6dO9i0aRPq1aunsG0+n4/atWsjKytLY1OGPD098d9//5WJkWoTycnJGDZsGIKDg8vdcysrK1y8eBEvX77EwIEDyyzS3rp1a9y4cQMnTpzAsGHDxC7gHhQUBG9vb4UWOleU9PR0rRyrmDRpEkJDQ5GQkKBpV7SOj0p0nzx5gr59+2LLli1wdXXVqC8pKSmYP38+GjdujHfv3ilVbEXw+XyYmJiodTfYDzEyMsK4ceOwYcMGjbRfEQKBAF5eXvDy8kKfPn3EljE2NkZoaCh4PB6++eYbJCcnl5yztbXFpUuXYGRkhE6dOuHFixcl59LS0vDHH3/A19dX5ddREZmZmVopuiYmJhg1ahTWrl2raVe0D0ldYKpi4YVXr15RgwYNaOvWrRr14/379zRv3jwyMzOj8ePH07Nnz1TW1pEjR2jAgAFka2tLCQkJKmunMuLj48nMzEylO97Kw+LFi8nV1bVc6EAcQqGQ5s6dS40aNaK4uLhy51atWkU2NjZ05coVIiJaunQpeXt7q8RvWejSpQs5Ojpq2g2xiD4XqampmnZF7eBjj+mmpqZSs2bN6JdfftGYD+/fv6f58+eTmZkZjRs3TqViK2L79u00YsQIMjExUXjhbUUZNGgQbdy4UaM+lOb8+fNkY2NDr169kqnehg0byMbGhm7dulXu3JkzZ8jCwoLWr19PVlZW9ODBA2W5Kzdt2rQhFxcXTbshES8vL1q+fLmm3VA7H7XoZmdnU6dOnWjatGkamZCdkpJCP/30E5mbm9O4cePUOlsiKCiIpk+fTvr6+hpP/Pj777+pSZMmWjEp/tWrV2RtbU3nz5+Xq/7Ro0eJx+PRmTNnyp2LiooiKysratCggVyJFMqmWbNm1L59e027IZF79+5pLHFEk1QkulU6pltYWIjhw4fDzs4OQUFBap2rmJqaip9//hmNGjVCYmIiIiIisHXrVjRo0EBtPoh2AhYIBDAwMFBbu+Lo0qULhEIhLl26pFE/CgsLMWzYMPj4+KBr165y2Rg4cCCOHTuGkSNHYufOnWXO2dvbw8DAAFZWVnIlUiib7Oxsta0wJw/NmzdHs2bNsHfvXk27ojVUWdElIkyaNAk5OTnYsWMHdHTUcympqalYsGABGjVqhFevXiEiIgJ//PEHGjZsqJb2S8Pn80s2pdT05HjGmFasPjZ//nxUr14d8+bNU8hOhw4dcPHiRSxYsAC//vpr0WMhgIMHD6JBgwa4evUqWrZsidatW+Phw4fKcF0ucnJytFp0gaKFcAIDAyEUCjXtinYgqQtMWh5emDt3Ln311VdqG7xJTU2lBQsWkLm5OY0ZM6bcYIsmGDNmDK1atYqsrKw07QoREaWnp5OpqanU60Yom9DQUKpbt65S582+evWKXFxcyMfHhwoKCqhp06Zlwg6iRIrjx48rrU1ZMDMz04oBvYoQCoXUokULCg0N1bQragMfW3hh3bp1CAkJwalTp2BsbKzSttLS0rBo0SI4ODjgxYsXuHHjBrZt26aRnq043wwMDLRiWT8AqFmzJry8vLB582a1t/38+XOMHTsWBw4cUOq8WdG0sejoaHTq1AmMMfTs2bPkvJeXF06ePAkfHx8sXbq0pEesLvLy8rQuxf1DGGOYOXMmVqxYoWlXtIIqJ7r79+/HypUrcfbsWZVOSufz+SVi+/z5c1y/fh3BwcGwt7dXWZuywufzYWhoqDWiCwA+Pj7YunUr8vLy1NZmfn4+PD094e/vj/bt2yvdfu3atXH69GnExsYiLy8PKSkpZc63bt0aEREROHHiBIYPH67W3RPy8/NRq1YttbUnL+7u7khISMD169c17YrGqVKie/bsWfzwww84c+aMUpMMSsPn87F48WI4ODjg2bNnuH79OrZv3w4HBweVtKcIosVOtEl0nZyc4OLigsOHD6utTT8/P9SpUwczZsxQWRsRERGoWbMm+vXrh44dOyI+Pr7MeVGP2MDAAB07diyTSKEqiAgFBQVVQnT19PQwY8YMbiEcoOrEdG/cuEEWFhYlk9OVTVpaGi1evJh4PB6NHDmyzHqr2oqDgwPt3LmTOnfurGlXynD8+HFq06aNWto6dOgQNWzYUOUT8Pv06UObNm0ioqKpenXq1KH//vuvXDmhUEiBgYFkY2NDV69eValPWVlZpKOjQ+vWrVNpO8oiMzOTeDxelfjfUhRU9Xm6UVFRZG1trZLVrPh8Pi1ZsoR4PB6NGDGiSn0gLCwsaPfu3eTm5qZpV8pQWFhI9erVo4iICJW2Ex0dTTweT2wigzK5d+8eWVtbU05OTsmxgwcPkoWFhcS5wKJEClUuLv/27VsyMDDQeBamLPz0009q27lak1Rp0X358iXVq1ePgoODlWq3tNh6e3tTdHS0Uu2rGqFQSPr6+rRnzx5yd3fXtDvlCAgIoJEjR6rMfnZ2NjVv3lwtWXDffvut2KyqixcvkoWFBe3du1dsvaioKGrcuDFNmzZNqlRkWXn+/DlVr15dYvvayJs3b8jU1JTevHmjaVdUSkWiq9Ux3dTUVPTq1QuTJ0/G6NGjlWIzPT0dS5cuhb29PaKjoxEeHo5du3ahcePGSrGvLnJzc6Gjo4OCggKtiumKGDt2LI4fP15mARllMm3aNDRp0kTli4c/ffoUYWFhmDx5crlzX3/9NS5cuIDZs2cjMDCw3MwFR0dH3LhxA0+ePFFJIkVWVhZ0dHS08v2XhKWlJTw9PTU+n1uTaK3oZmdno1+/fujevTv8/f0Vtpeeno5ff/0VDg4OiIqKwtWrV7F79+4qJ7YiSq8wpo2T483NzTFo0CBs27ZN6bZ37tyJ8PBwbNmyReVJIatWrcKECRMkDlY1bdoU4eHh2LFjB3788cdyCQAmJiY4efIkvvzyS7Rp00apiRRZWVlgjGnFppSy4Ovri40bN4pdLvOTQFIXmDQYXigoKKC+ffuSl5cXCQQChWylp6fT0qVLycLCgr777jt6/PixkrzULI8fP6bGjRvTihUryNfXV9PuiOX27dv02WefKfXROjIykng8nloWm0lKSiITExNKSkqqtGxqaiq5urqSh4dHmdhvaXbt2kUWFhZKG5v4559/qFatWnT58mWl2FMngwcPrjIDgPKAqhReICJMmDABhYWFCA4Olju9NyMjA8uWLYO9vT0ePnyIy5cvY8+ePXByclKyx5pBtIC5JtfSrYwWLVrA1tYWJ0+eVIq9jIwMeHh4YNWqVWjSpIlSbFbE2rVrMXz4cFhZWVVa1sTEBGFhYQCAXr16IS0trVwZb29vnDx5EpMnTy6TWiwvop5iVevpAoC/vz9Wr16NwsJCTbuidrROdOfMmYNHjx4hJCRErh1OMzIysHz5ctjb2+PBgwe4dOkS9u7d+9GIrQhtWMBcGpS1HoPoy7hTp04YMWKEEjyrGD6fjy1btmDmzJlS1zEyMsKBAwfg4uKCjh074uXLl+XKiBIpjh07pnAiRVZWFohIq99/SbRp0wZ169ZFSEiIpl1RO1oluqtXr8bx48dx6tQpmeOUmZmZCAgIgIODAyIjI0vE1tnZWUXeapa0tLSSnq42xnRFuLu748GDB3j8+LFCdjZt2oTHjx9j3bp1SvKsYjZv3oyePXvKvGqcjo4OgoKCMGrUKLRv317srsKiRAp9fX106tRJ7i1tsrKyIBQKq2RPFyhaCGflypVqT53WNFojurt370ZQUBDCwsJgbm4udT2R2Nrb2+Pu3bv4559/sG/fvo9WbEWIerqa3B9NGgwNDTF+/HisX79ebhu3bt3CggULcPjwYbUITG5uLoKCgjBr1iy56jPG4Ofnh+XLl6Nr1664fPlyuTLVqlXDrl27MHz4cLRp0wbh4eEyt5OVlQWBQKDV739F9OnTBzk5Obhw4YKmXVEvkoK9pMaBtNOnT5OlpSU9fPhQ6joZGRkUEBBAlpaWNHToUJnqfgysXLmSfH19aejQobRv3z5Nu1MhCQkJZGpqSnw+X+a6KSkp1KBBAzp8+LAKPBPPpk2bqE+fPkqxJdqZ+tChQxLLnD59miwsLGjbtm0y2V6+fDnp6+tTenq6om5qjG3btlHPnj017YbSgTYPpF2/fh0jRozAsWPH8Pnnn1daPisrCytXroSDgwPu3LmDCxcu4MCBA1LV/ZgoHV7Q9p6OnZ0dunbtit27d8tUj4gwevRo9OvXD+7u7iryriyFhYVYsWIFZs+erRR7Xbt2xdmzZ/Hjjz9KDI307t0bV65cQUBAAL7//nupB5cyMzNRWFhYZcMLAPDdd9/h/v37iIyM1LQrakOjovv48WMMHDgQO3bsQLt27SosKxJbe3t73Lp1C+fPn8eBAwfUMoqtjWj7PN0PEQ2okQzxu1WrVuH169dqXSQlJCQENjY26Nixo9JsfvHFF7h69So2bNgAf39/sYt5ixIpoqOj0bt373IrmYkjMzMTOjo60NPTU5qv6sbQ0BDTp0//pBbC0ZjoJiQkoGfPnlixYoXE7bGBIrENDAyEvb09bt68ifPnz+PgwYNo2rSpGr3VPkQ9XW2P6YpwdXWFnp6e1PG78PBwrFy5EocOHVLbVkREhOXLlyutl1ua+vXrIzw8HOHh4RgxYgTy8/PLlTExMcGpU6fg4uIi1Y4UfD5frhk+2sbEiRNx+vRpuQcUqxoaEd3379+jZ8+emD59usTpP9nZ2Vi1ahXs7e0RERGBc+fO4dChQ5+82IqoCvN0SyPLdj7JyckYNmwYgoODVbaEpzjCwsIgEAgq7AQogrm5Oc6fP4+srCy4ubkhPT29XBldXV0EBgbi559/RpcuXRAaGirRXnp6OgwNDVXiqzoxMTHB6NGjERQUpGlX1IOkYC/JMZCWnJFLGy/G0vcH7tDoHRH0/YE7tPFiLL3L+P9OoJmZmdS2bVvy8/MTayMrK4tWrVpF1tbW5O7uTpGRkTL58Kng6upKFy9eJAcHhyqzWE9GRgaZmZnR8+fPJZYpLCykHj160OzZs9XoWRFff/017dmzR+XtFBYW0uTJk8nFxYUSExMllrt+/TrVqVOHfv31V7G7LPfo0YMsLS1V6araePHiBZmamqp8iU51AVUPpN1LSMOE3bfQIeAC1pyPwbG7ibgQ9RbH7iYi6HwM2gdcwMQ9t3D7+Tt4eHjA0dERAQEBZWxkZ2dj9erVsLe3x7VrxAUrPgAAIABJREFU1xAWFobDhw+jWbNmynDxo6OqzNMtjbGxMUaMGIFNmzZJLLN06VLk5eVhyZIlavQM+PfffxEfH4+hQ4eqvC1dXV2sX78enp6eaN++PaKiosSWa9OmDW7cuIGjR4/i22+/LZdIkZmZWaUH0UpTt25d9OvXr8LPxseCwqK75/pzDNt6Hecev0FeoRB5hWUHCXKLj5199AYeG8ORat4UW7duLUnvzc7Oxpo1a2Bvb4/w8HCEhYUhJCQEzZs3V9S1jxpReKGqxHRF+Pj4YNu2bcjNzS137vz589i0aRP279+v9sGh5cuXY+bMmWprlzGGuXPnYsGCBejcuTOuXbsmtlydOnVw6dIl6OnplUukyMrKgpGRkVr8VQd+fn5Yt26dWrd60gQKie6e68+x9PRj5BQIUNmgNBEg1NFDaoMuOHj7FXJychAUFAQHBwdcvXoVf/31F/78809ObKWkqqQBf0ijRo3QsmVLHDx4sMzxxMREeHt7Y8+ePbCxsVGrTw8fPsSNGzeUtnyoLIwaNQo7duzAgAEDcOzYMbFlRIkUw4YNQ5s2bUoEuqp94VZGs2bN4OLigj179mjaFZUi99f6vYQ0LD0dhZyCsj3bd6GByH1+D8KCXOjWMEWttkNQ0+X/u6fmFgix8Ph9zBo/HG0a2eD06dP44osv5L+CTxChUIj09HRUq1YNAoFAbaP7ymLq1KlYsGABRowYAcYYCgsLMWzYMEyZMgXffPON2v0JCAjA9OnTNfao3qtXL5w5cwb9+/dHUlISJk2aVK6MaEfdJk2aYODAgVi+fDlycnJgbW2tAY9Vh7+/P3x8fDB69Gi5F7vSduS+qvUXY5FbKCh3vFZbD9SZHIzPZhyGpftPSLu8G3lJsWXKFBLQaeIvOHLkCCe4cpCZmYnq1asjPz8fNWrUUPmassqmV69eSE1NRUREBABg/vz5qF69OubOnat2X+Lj43Hq1Cn4+Piove3StGrVClevXsXq1asxf/58ifOZ3dzccPnyZQQEBODdu3cfTUxXROfOnVGjRg2lrUynjcgluu8y83ApJllsSMHAoh6YnmjuIAMDQ2Hq67KFmA7+e5OP95kfd+xGVVSVdRckoaurCx8fH/z+++84efIk9u3bhz179mikZ7Nq1SqMGzcOJiYmam/7Qxo2bIjw8HCcO3cOY8aMQUFBQbky7zLzcPGNPrrO34Xa/WbhUe2vsPrM/Y/mf4kxBn9//486WUKu8ELI7fJL1pXmfdgGZN3/G1SYBwMre1Szb1WuDAMQcuclJrray+PCJ01VSgGWxOjRo9GgQQP89ddfOH78OHg8ntp9SE5Oxp49e5S6m4OiWFhY4MKFCxg6dCj69++Pw4cPw9jYGPcS0rD+YiwuxRRtf5RXKEQ1h9YAgHUXYrHxagK+cbaEz9cOcKmr+S8QRRg8eDBmz56Nf//9t9JM1aqIXKIblZRebpZCacx7+sCs+0TkvYpC7ov7YLrls2ZyC4XYfeIC4k5uhqGhIYyMjGBoaFjyI89rAwODKveoLQ9VdRCtNDVq1ICBgQG++uortG/fXiM+rFu3Dh4eHmofuKuMGjVq4NixY5g0aRI6d+6MMcu247crr5BbKGHAWs8ABULC2YdJuBzzDvPcnODVtr663VYaenp6mDFjBlauXIkjR45o2h2lI5fopudWviAH09GFUd0myHr4DzL+O41arfqXK6NfoxbMq5sjLy8PWVlZSElJQV5eHvLy8pCbm1vyt7SvCwoKYGBgoDQRV+S1oaEhdHV15bm9lVIV5+h+iJ+fH5o2bYr79++jsLBQ7VPEMjIysHHjRly/fl2t7UqLnp4etm7diuE/bcCKs7GAXuWDpQSGnAIBlp4uWru4Kgvv6NGjsXjxYsTExFTZfQwlIdcnvZaRDNWEwvIx3WJexz/FG7NktG/fHu3bt4etra087pRqSoj8/Hy5Rbv064yMDIXq5+bmQk9PTyWifuvWLfD5fJw7dw65ubm4dOlSpfX19PS05ing0KFDOH36NG7fvo2+ffvi+PHjGDJkiFp92LJlC7p16wYHBwe1tisLkS/5uKdjD+iVH7AGgIKUV0jcNhU1nDqA18+v5HhOgRC/nH6M5nYmaG5XNUMNNWrUwOTJk7Fq1Sps3rxZ0+4oFSZplBQAWrVqRbdu3Sp3fNOlOKw5H1MuxCDISkNu/D1Uc2gNpmeA3Od3kXz0V/D6zUT1xm3LlDXU08FAez2YvL6Fa9eu4dq1a6hZsybatWtXIsLNmzevsgt6EBEKCgoUEm1Jr+/fv4/379/D3Nwcz549w+eff15heVEigrp6+hWde/HiBbp06YKwsDC0aNECBw4cwObNm/HPP/+o7b3Jy8tDw4YNS3bp1VYm7L6Fc4/fSJwD/+bAT6DCPOjVtiwjugAAoRBfO5hg5/hOqndURSQnJ8PR0RGPHz+Wap86bYIxdpuIyg9mQc6erntLO6w5HyOuJWT8dwbvwzYAJIRebUuYdh1fTnBF+Lu7wty4O4AikXry5EmJAG/evBnx8fFo1apViQi3bdtWpl0lNAljDAYGBjAwMEDNmjWVavvXX39FRkYGvvzySxw+fBiHDx+utE5hYaFSRF8UBlKkPgC0b9++RIjfv3+Pev9j76zDotq+Pv6lBAkJhxZRGgVBRQQDMRAVExEVsRUMroHX7sYuVFTEvhZ2Xb22VxBERCyw26uISNfMWe8f/JgXpGaYM4H3fp6H59GZfdZeMGfW2XvtFaam0NDQkIjr59ixY7CxsYGNjQ0YhpHJeNDKIoQAIPvJDcirqEGprg24P8rZScrL4/qzb/jz2t/o0p69MpWSRFdXFwMGDMCmTZuwZMkSaavDGtUyuhx1ZbSz0i3zFFZQ1YTBoJAqr5cD0N5aF3XV/79CkpycHKysrGBlZYVhw4YBANLS0hATE4OoqCisW7cOsbGxMDY25hvhVq1awdraWia/NOIkPT0d2traQvl0FRUVoaioKFUf8MiRI5GXl4e9e/fy3UD5+fkICQnBly9fMHPmTKGNeEZGhtAPkU+fPkFFRQXa2trIz8+HkpKSVP3/Jf9f7NuuLEKIyc/Bj1sHoD9wKbIeXKpwXC2lWhixZDuWvH6GESNGsP55SoLg4GC4urpixowZUFdXl7Y6rFDt04vx7ha49fwbcgvL9zdVBq8wD1qfYgGUu/rmo62tjS5duqBLly5F1/F4ePToEaKionD9+nUsW7YMaWlpcHFx4RthZ2fnX+bDqYj09HQ0bNiwRsXp7t69G1FRUbh79y4UFBRQu3ZtfmB/cabV1q1boampKVY9IiMjsWbNGkRFRUFOTg5EVOoBIMouIC0tTWTXEVDUVVizy0TUsmpd7u/w4+Y+qDt0hmId3Up/10ICug4YiZCQ0UhMTMTq1atrXMFzCwsLuLu7IyIiAhMmTJC2OqxQ7U/AwUQLs7vZ/K/2QsXhYz9TW0keTirfsGrmb/iQGIV9+/YJfMCjoKAABwcHODg4YOzYsQCAf/75B9HR0YiKisLcuXORkJAAa2vrUqthU1NTmTlEYoPi6IUPHz7UCKP78OFDTJ06FdevXy/3gWhkZARPT0/s2bNHrF8sIsLy5csxb948/v0gJyfHX2XKAlwuF3l5eRh78AFuvfpR5v2CL6+Q9/YBDIdvEExgLVXExMRgwIAB6Nq1Kw4fPgwdHR2WtRYvU6dOha+vL8aNG1fjHhrlIdK+3N+lAWZ3s0VtJQVUbdMItZUUMLubLfbND8SZM2dw5MgRNGvWrEzJOmEwMDBAnz59sGrVKty+fRvfv3/H5s2bYWZmhuPHj8PV1RVGRkbo27cv1qxZg+joaP6KoqZSkwqYZ2Zmol+/fli7dm2lrZWCgoKwefPmclvZsMXly5eRl5eHHj16iG0OUVFUVIS6ujrq1in/c8179xDc9C/4sGU43m/yR0bsCeQkR+Hzronljq+jogRtbW2cO3cOTZo0QcuWLfH06VNx/gqs4+zsjAYNGgh0dlETEPmx4e/SAE3qaWHL9Re4lpwCORQlPhSjoigPHsOg4E0C/lg2Fk1Niw7CunXrhsePH8PZ2Rmmpqa4e/cuGjRoIKo6UFZWhqurK1xdXREcHAwiwtu3b/kHdAcOHEBycjIcHR35K2FXV9caVTikZHKELK9aiAgBAQFo27YtBg8eXOnY1q1bo3bt2rh8+TI6d+4sFn1CQkIwffr0GnEGYGNQB8qKn5HPLX2Spu7oCTVbN/7/M2KPg5v+BTqe48vIUFGUh41h0SGuoqIi1qxZgyZNmqBdu3aIiIhA9+7dxftLsMjUqVMxZ84cDBgwoMbvWlm5+5rU00KYvxOipnfAZA8r9HE0RkcbPfRxNMZkDyvcmdkJ9d9dxPOYK6Wus7S0xLt378DhcGBtbY3Lly+zoU4p5OTk0KBBA/j5+SE0NBTx8fH48uULFi9eDC0tLYSHh6NRo0YwNzeHv78/tmzZgoSEBIE7skqDmtIfbevWrUhKSqqwC25JhGnnUx1iY2Px4sULDBw4UCzy2SQlJQXP/tyLvLyyOzJ5JRUoqGvzf+SUVCCnWAsKqmV94QTAp1m9Uq8NHToUp0+fRmBgIEJCQoRqFCpNunbtioKCAly5cqXqwTJOteJ0q8OJEycQEhKCO3fulHlS8Xg89O3bF2fOnMGqVasQHBzMypyCwjAMkpOT+avhqKgofPz4Ec7OzqXC1WShKApQVNg6NjYWc+fORevWrTFy5Ehpq1SGuLg4dOvWDVFRUQInIOTk5KB+/fq4e/cuGjZsyKo+3t7ecHd3l+nDmE+fPmH16tXYvXs3fH19kdXUD7ffZlZZq7pciIGHrT52DHUu9+2PHz+id+/esLS0RHh4uEw/vIvZvXs3Dh48iIsXL0pblSqpLE5XYvusnj174tu3b4iOji7znoKCAk6ePIm5c+di6tSpGDRokFh9ez8jLy8PW1tbjBw5Ejt37sTTp0/x+vVrTJ48GTweDytWrICJiQns7OwwevRo7Nq1C8nJyVJbJci6TzctLQ39+vXD1q1bhcr4UlVVxbBhw7B161ZW9Xn69Clu376NUaNGsSqXLd68eYNx48bBzs4ORISHDx8iLCwMU7s1gYpi9VLJ5YnBrW1zkZiYWO77xsbGuHnzJuTk5ODm5oYPHyovYiUL+Pn54fHjx0hISJC2KiIhMaOroKCASZMmYe3atRWOWbBgASIjI3H06FE0b94cWVlZklKvDHXr1oWXlxeWLl2Ka9euIS0tDXv37oWDgwP++usveHp6QldXFz169MDy5ctx48YNkQ4EBaWwsBB5eXlQU1OTydoLRIRhw4ahV69e1UrtHTt2LHbt2sXq33LVqlUICgqSuQfUs2dF8bPNmzeHpqYmkpKSsG7dOhgbGwP4/wghRTnhFiC1leSxsLcDZo0ZhI4dO2LDhg3lLhBq166N/fv3w9fXFy1btix3QSRL1KpVCxMmTMDq1aulrYpISMy9ABQV327QoAFiY2NhZmZW4bjHjx+jVatWqFWrFu7cuQNzc9ks//jx40d+uFpUVBQePnyIRo0alUplNjExYdXxn5qaCisrK6SmpqJjx46YOXMmOnXqxJp8UVm9ejUiIyNx8+bNane06N69O7y9vVkJ6H///j0cHBzw4sULmTl0fPjwIZYtW4bLly8jKCgIv/32W4W63bt3D90nr0Adt2EoYKhSV4OcHKCiqFCqytjLly8xaNAgaGtrY/fu3RWm0547dw7Dhw/HihUrpNK2SFDS09NhZmaG+Ph4mJqaSludCpEJ9wJQ1A125MiRVR6sNG7cGK9evYKWlhYaN24ssz4cY2Nj+Pj4YO3atbhz5w6+ffuG9evXw8TEBIcPH0aLFi1gYmICX19frF+/HrGxsSgoKBBpzuJDNAAy5174+++/sXr1ahw5ckSkFkJBQUHYtGkTK+6btWvXYvjw4TJhcOPi4tCnTx94eHjA0dERL1++xPz58yvULT09Hb6+vtgQ5IOjY1rBs5E+lBXloaJY+muroigPZUV5eDbSx+EAl1LVxczNzXHr1i00b94cTZs2xfnz58udy8vLCzdu3MDy5csxefJkmT1I1tTUxIgRI7B+/Xppq1J9KurNTkRo3rw56/3g379/T9ra2vTjx48qx+bn55OnpycpKCjQihUrWNdF3DAMQy9evKC9e/fSmDFjqEmTJqSmpkZt27al6dOn08mTJ+nLly9Cybx37x45OjoSEVGTJk0oISFBHKoLzdevX6levXp07tw5kWXxeDyysLCg27dviyTn27dvpK2tTR8+fBBZJ1H4+++/qUuXLmRsbEwbNmyg7OzsKq9hGIZ8fHxo3LhxpV7/lplHYTdeUIsJoaTnM48mHbpPYTde0LfMvCpl3rhxg+rXr0+//fYb5ebmljvm+/fv1LlzZ/Lw8KDU1FTBfkEJU2xDvn//Lm1VKgRAHFVgVyVudImI/Pz8aPXq1QKNZRiGpk2bRgoKCjRgwAAqLCwUi06SIj09nS5dukQLFy4kT09P0tTUJAsLCxoyZAiFhYVRYmIicbncCq+/evUqubu7ExGRhYUFPXv2TFKqVwiXyyUPDw+aOXMmazLXrVtHAwcOFEnG/PnzaeTIkSxpJBwMw9Dly5fJ3d2dGjZsSNu2baO8vKoNYzGhoaHUtGnTCo2jj48PqaqqCq3X9+/fydfXl+zs7Ojhw4fljiksLKTg4GCysLCgJ0+eCD2HJBg6dCgtXbpU2mpUiMwZ3bt371L9+vWFMqAHDhwgJSUlcnBwoLS0NLHoJQ24XC49fPiQtm3bRkOHDiVLS0vS1NSkzp0704IFC+jSpUuUnp7OH3/8+HHq1asXEREZGhpKfRVHRLRgwQJq164dqw/EtLQ00tLSok+fPlXr+szMTOJwOJSUlMSaToLAMAydOXOGXFxcyNramvbs2UMFBQVCyYiLiyMOh0PPnz+vcEyXLl1IW1u72jpGREQQh8OhTZs2EcMw5Y7btWsX6erq0tmzZ6s1jzh5+PAhGRgYVPhQkjYyZ3SJiNzc3OjQoUNCXXP37l1SV1eXypdJknz9+pVOnTpFM2bMIDc3N1JTUyN7e3sKDAykUaNGUe/evYlhGNLU1JT6Fuuvv/4iQ0PDahvHyggMDKSFCxdW69p169aRj48PyxpVDI/Ho6NHj5KjoyM1adKEDh8+XOmOpSJ+/PhBZmZmdPjw4UrHubm5kaGhYXXVJSKiZ8+ekZOTE3l5eVXo5oqKiiIjIyMKCQmp0DhLi27dutH27dulrUa5yKTRPXnyJLVo0ULoD/LTp09kampKKioqMvkEFgf5+fkUGxtL69evJ0dHR1JTUyNdXV2Sk5OjpUuX0q1btygnJ0fien348IEMDAzo6tWrYpGfmJhIRkZGQq8U8/PzqV69enT37l2x6FWSwsJC2rdvH9na2lKLFi3o9OnT1TZOFflxy8PJyYkaNmxYrXlKkp+fTzNmzCAjIyP6888/yx3z/v17at68Ofn5+UnlPquIa9eukbW1NfF4PGmrUgaZNLpcLpcsLCzo77//Fvra7OxsateuHSkpKdGSJUtk7gksThYsWEBz586lly9fkpycHP3222/UokULUlVVpZYtW9KkSZPoyJEjYnc7FBYWUps2bWjJkiVincfNza3KVd/PREREUKdOncSkURH5+fm0Y8cOMjMzIzc3N7p06ZLI92FVftySNG7cmBo1aiTSfCW5evUqmZiY0KRJk8r1Pefk5JCfnx81b96c3r9/z9q8osAwDLVo0YJOnjwpbVXKIJNGl6joJvP29q7WtTwej8aPH09KSkrk4+ND+fn5LGsnm0yePJlWr15NP378IA0NDf7r2dnZdOPGDVq+fDn16NGD6tatS/Xr16cBAwbQxo0bKS4uTugVY2VMmzaNunTpIvZVxpEjR6ht27YCj+fxeGRtbU2XL18Wiz45OTm0adMmMjExoc6dO9ONGzdYkSuIH7ck5ubmxPb3MzU1lby9vcnBwYEeP35c5n2GYSgkJISMjIwoKiqK1bmry5EjR6hVq1bSVqMMMmt0s7KyqG7duvTixYtqywgLC6NatWqRvb09ff36lUXtZJMRI0ZQeHg4ffr0ifT19SscxzAMJScn065du2j06NFkZ2dH6urq5O7uTjNnzqQzZ87Qt2/fqqXDqVOnyMTEhFJSUqr7awhMQUEBGRkZ0YMHDwQaf/z48Wq5raoiIyODVq5cSQYGBtSzZ0+KiYlhTbagftySGBsbk5ubG2s6FMMwDO3YsYM4HA5t2bKl3L/jmTNnSFdXl3bt2sX6/MLC5XLJzMysWjtmcSKzRpeIaMaMGTRhwgSRZNy4cYPU1NSobt26lJiYyJJmsom3tzcdPXqUXrx4QWZmZkJdm5aWRn/++SfNmzePOnXqRBoaGmRtbU3Dhw+nHTt20OPHj6tcub5+/Zr09PQkutJZtGgRBQQEVDmueLt57Ngx1uZOS0ujRYsWka6uLvXv319g4y8owvhxS1K3bl3q0qULq7qUJCkpiZo1a0Y9e/Ys9+H65MkTsrCwoMmTJ0s9jHPz5s38iB5ZQaaN7ocPH0hbW1vkMLCXL1+SkZERqaiosPqlkzU6duxIf/31FyUmJpKdnZ1IsrhcLiUkJNCWLVvI39+fzMzMSEtLi7p27UqLFy+my5cvU0ZGBn98Xl4eOTk50dq1a0X9NYTi8+fPpKWlVWWkxpUrV1g7WPn69SvNmjWLdHR0aOjQofT06VORZZaHMH7ckmhoaIg9OiM/P5+mTp1KRkZGdOnSpTLvf//+nTw8PMjDw0OqUTTZ2dmkp6cnUxFNMm10iYj8/f1p5cqVIstJS0sjZ2dnUlZWpnnz5v2SB2zNmzen2NhYio6OJmdnZ9blf/78mY4fP05Tp06l1q1bk6qqKjk6OtK4cePIw8ODOnfuLJXTYj8/vyqNvYeHB0VERIg0z8ePHyk4OJi0tbUpMDCQXr16JZK8yrh37x7p6uoK7MctibKyMg0bNkwMWpXl8uXLZGxsTFOmTClzyFZYWEiTJ0+WeiLFggULaPTo0VKb/2dk3ujeu3eP6tWrx8pBT2FhIQ0ePJhUVFSoZ8+eMhXiwgYWFhaUnJxMV65c4WemiZO8vDyKjo6mwYMHk5qaGunr65OBgQF5e3vT6tWr6fbt2xIJUI+KiiJzc/MKDX5cXBzVq1ev2geqb968obFjx5K2tjZNnDhR7Cf0P378IHNzc6EjM4qRl5en3377jWWtKubbt2/Uu3dvatq0abmr/oiICKkmUqSkpJC2tjZ9/vxZKvP/jMwbXSIid3d3+uOPP1iRxTAMrV69mlRUVMjW1pY+fvzIilxZQFdXl758+UJnzpwhLy8vicyZnJxMHA6H7t27RwzD0OvXr+nAgQMUFBREzZo1I1VVVXJ1daUpU6bQsWPHxJIowTAMNWvWjM6fP1/u+z4+PtVyezx79oyGDx9OOjo6NH36dPrnn39EVbVKGIahfv36Ce3HLaawsJDk5ORYTbsWBIZhKCwsjDgcDm3btq3MTlLaiRTjxo2jWbNmSXze8qgRRvfUqVPk5OTE6od19uxZUlVVJR0dHYqNjWVNrrRgGIaUlJQoLy+PDh8+TP369RP7nNnZ2WRvb09hYWEVjsnMzKSrV6/SkiVLqFu3bqStrU0NGzakQYMG0ebNm+n+/fusHLZERERQt27dyrxe/FDIzMwUWNbDhw9p4MCBxOFwaMGCBRIt7rJ582ZydHSs9g4hIyODlJSUaPHixSxrJhhPnjwhR0dH6tOnT5kIGGkmUrx48ULo+0Bc1AijW1xZ6ubNm6zKTUxMJF1dXVJVVaX9+/ezKlvS5OTkkLKyMhEVGaChQ4eKfc7hw4fToEGDhHoY8ng8evLkCYWHh9OIESPI1taWNDQ0qEOHDjRnzhw6f/58tQ5ecnJyyo1lHTVqFM2fP18gGXFxcdSnTx/S19enkJCQUnUtJMG9e/eIw+GIVKjo69evpKKiQmvWrGFRM+HIy8uj4OBgqlevHl25cqXUezk5OTRw4EBycnKSeCJFv379aN26dRKdszxqhNElKloB9O7dm3W5//zzD9nb25OamhpNnTpVJtMGBeHz58/82NzQ0FAaO3asWOeLiIggW1tbVlYOqampdO7cOZo9eza1b9+e1NXVqVGjRjRq1CiKiIigpKQkgQz7tGnTKDg4mP//4uiXqmKGS5ZXXL9+vUDlFdmm2I8rbM2Rn3n79i2pqanRli1bWNKs+ly8eJGMjIxo2rRppfzpJRMpoqOjJaZPbGws1a9fn9VEoOpQY4xuVlaWUFk5wpCbm0t9+vQhDQ0N8vT0lIktiLA8ffqUrKysiIho5cqV9Pvvv4ttrsTEROJwOOVmJrFBYWEh3bt3jzZt2kQDBw6kBg0aUN26dal79+60dOlSunbtGmVlZZW57vXr11S3bl3+e1OmTKGJEyeWOwfDMPwDxwYNGlBYWJhQ5RXZpNiPy8aDMikpiTQ0NGj37t0saCY6X79+pe7du1Pz5s0pOTm51HvFiRSS1NXd3V3qu9oaY3SJiGbOnElBQUFikc0wDM2dO5fU1NTIysqKXr9+LZZ5xMWdO3eoRYsWRFQUIjNv3jyxzJORkUFWVla0b98+sciviI8fP1JkZCQFBweTi4sLqaqqUvPmzem3336jgwcP0tu3b4lhGOrZsydt376dUlNTSVtbm969e1dKDsMwdPbsWXJ1da12eUW2EdWPW5KEhATS1NSsduSDOGAYhjZv3kwcDofCw8NL7VoeP35MFhYWFBwcLJFEinPnzpGDg4NUQ0ZrlNH9+PGjQIHwovDHH3+QmpoaaWtrs+5DFicXL14kDw8PIiKaOnUqhYSEsD4HwzDUv39/mYh5zM3Npb///ptWrlxJvXv3Jj09PX76q6GhIY0ePZoGDx7MH8/j8SgyMpKaNm1K9vb21S6vyDZs+HFLEh0dTZqamnT370EzAAAgAElEQVTmzBlW5LHJo0ePyN7envr27VvqcDI1NZU6depEnTt3FnsiBcMwZGdnV25Ch6SoUUaXiGjw4MFiMSgliY6OJh0dHVJXV6cdO3aIdS62OHz4MD8Lafz48bRx40bW5wgNDWVtRcY2DMPQy5cvac+ePaSpqUny8vJUu3Ztat26NXl5eZGJiQk5OjrSqVOnZMZvz5YftyTXrl0jLS2tMgdYskJubi5NnDiRTExM6Nq1a/zXCwsLadKkSWRpaSn2RIrdu3eLvdJcZdQ4oxsfH0/GxsZirxz25s0bfqeG3377Teo55FWxfft2GjVqFBEVRRXs3LmTVfmxsbHVzpCSNH379iUjIyPatGkTGRkZkampKTVv3pzq1KlTqv3RgwcPpLbaZdOPW5Lz58+TpqamzFT6qogLFy6QoaEhzZw5s5R7pziRgo1+ehVRXFM5Pj5ebHNURmVGV6LdgAWladOmsLKywtGjR8U6j6mpKeLi4uDs7IwDBw6gc+fO+PHjh1jnFIX09HSxdQJOS0uDr68vwsLCYGFhwZpccZCRkYErV67g8+fPiIyMxMGDB/HmzRvExcUhLS0NJ0+eRJs2bXDnzh3069cPOjo66Ny5MxYsWIBLly4hPT1dInpu3boVz58/x9q1a1mVm5ubCyKSqU7Q5dGlSxfcv38fDx48QOvWrfHixQsAwPDhw3Hy5EmMGjUKK1euLFr9sUytWrUwceJErFq1inXZIlORNSYprnSJik49mzVrJhFnOJfLpQkTJvCD+n8+gZUVZs+eTYsWLSIiou7du9OpU6dYkcswDPXo0YMmTZrEijxxkZmZSatWrSJNTU3icDjUt29fgQ4Tv379SqdPny63/dGePXvo2bNnrN9nbPtxS3LgwAFSV1eX2fv0ZxiGoY0bNxKHw6Fdu3bx/9bv3r2j5s2b06BBg8SSSJGenk46Ojr05s0b1mVXBWqae4Go6FDEysqKtSLRgrB161bS0NAgbW1tunjxosTmFZSgoCC+H7dDhw70119/sSJ35cqV5OLiIrOF4NPS0mjx4sWkq6tLvr6+ZGZmRhcvXqRHjx6RgYGB0HqXbH/Uv39/MjExIQ6HQz179qSQkBC6efOmSEZAHH7ckoSHh1Pt2rVlpoODoCQmJlLjxo3J19eXX1UwOzubBgwYQE5OTmLpdjJt2rQKQwrFSY00ukRFRlDSdTIvXbpEmpqapKmpSevXr5epSmX+/v60Z88eIiJycXFhxad38+ZN0tfXp7dv34osi21SUlJo9uzZVLduXX55xVOnTpXaAbVv356Vmh3v3r2jw4cP08SJE/ntj5ydnfntjwQ1cOLy45Zk06ZNpKysXO0i9NIkJyeHgoKCyNTUlB85xDAMLV++XCyJFB8/fiRtbW2JpnkT1WCjm52dTbq6umLZolXGkydPyMTEhHR1dWnkyJEyswLs0aMHvx+Uvb09JSQkiCTvy5cvZGxsXGERGWnx6dMnmjJlSpnyigzDkIuLCx05coQ/9tixY2Jp1/Jz+yMOh0MmJibUv39/2rBhA929e7fc2N8tW7aIPfpj1apVpKCgUKMr6J09e5YMDAxozpw5/L+juBIphg8fLvZefj9TY40uUZEfc/z48RKfNyUlhVxdXcnQ0JBatWolE62A3Nzc6Pr160RU1CNLlIcRl8ulTp06yUxVJqKiaJJx48ZVWF7x+vXrZGFhUSoaobCwUCKn1AzD0LNnz2j37t0UEBBAdnZ2pKamRu3ateO3P7py5YpEFgkLFy4kADK1C6sOnz9/Jk9PT3JxcaGXL18SUVEihbm5OauJFI8fPyZ9fX2JhkHWaKP76dMnqWwPiIqKegwZMoT09fXJxMSE9VYtwtKkSRO6f/8+EREZGhqK5ANbsGABubu7y0SY3LNnz2jEiBFVllfs0qULbd++vczrS5cupZEjR4pbzTKUbH/k7u5OcnJyZGhoSMOGDaPt27fTo0ePxBIv/Pvvv5OioiLrcqUBj8ejdevWEYfDob179xLDMPxECk9PT9YSKby8vGjbtm2syBKEGm10iYiGDh1Ky5cvl8rcxf4mHR0d0tLSkmq7Z1NTU/5WW1NTs9otji5dukRGRkZiqXsrDI8ePSI/Pz+Byivev3+fjIyMyq2d8OXLF9LS0pLKg5mo6B7x9fWlwMBAevDgAW3dupUGDx5M5ubmpKWlRV26dKFFixaVaX9UXcaMGUOqqqosaC47JCQkUKNGjWjgwIH048cPKiwspIkTJ5KlpSUrrZJu3LhBVlZWEovZrvFGNyEhgYyMjKTqW42MjCRNTU3S0dGhpUuXSmVrVzI9WlFRsVp/jw8fPpCBgQFdvXqVbfUE5t69e+Tt7S1UecUBAwbQqlWrKnx/8ODBlb4vTrZs2UIODg7lbl//+ecfOnHiRLntj/bv308vX74U+l7y9/cnLS0tttSXGbKzs2ns2LHUoEEDfnffnTt3spJIwTAMOTs70/Hjx9lQtUpqvNElKmrIKOkCLD9z9+5dMjAwoHr16tHAgQMlepDB4/FIXl6euFwuFRQUkIKCgtBf1oKCAmrTpo3EDxWKuX37NnXt2lXo8orPnz+nunXrVrpKjImJoYYNG0o8+yw+Pl6oeNy8vDy6c+cOrV27lnx8fMjQ0JD09fWpT58+tGrVKoHaHxXXA/5VOXXqFOnr69P8+fOpsLCQbt++TUZGRrRixQqRFjuRkZHk4uIikQXTL2F0z507R02bNpX64cH79++pSZMmZGZmRk5OThJrBZSenk7q6upEVBQHqqGhIbSMqVOnUpcuXSRal6C4vGL79u2rXV4xMDCQ5syZU+W4Fi1aSLQITHp6Opmbm9PBgwerLYNhGHrz5g398ccfArc/6ty5M9WvX19U9WWajx8/UqdOnahVq1b0+vVrevfuHTVr1kykRAoul0sWFhZ069YtlrUtyy9hdHk8HtnY2JQqoCEtMjMzqWfPntSgQQMyMjKSSCugd+/eUb169Yio6HDRwMBAqOtPnTpF9evXr7LYN1swDEPnzp0Tubxi8UGqINEje/bsIU9Pz+qoKzTFftwxY8awLjsrK4uuXbtGS5cuJS8vL9LW1qYGDRqQn58fvyBRcV3lXxkej0erV68mXV1dOnDgAD+RokWLFtU+RN6yZQv17NmTZU3L8ksYXSKibdu2UY8ePaStBhEV3RDTpk0jAwMD0tbWZq2pZkUUZ/MQFW23zczMBL721atXpKenJ5ECKTwej44dO8ZaecVp06YJXF85NzeXdHV1JZIeW5kfl214PB49ffqUdu7cSSNHjiQVFRWSl5cXuf1RTSE+Pp6sra3J39+ffvz4QcuWLSNjY2O6c+eO0LJycnJIT0+PlcO5yvhljG5OTo7EvlSCEh4eTjo6OmRgYECzZs0S29b91q1b1Lp1ayIievDgAdnZ2Ql0XV5eHjk5OYm9b1RhYSHt37+fGjVqRC1atGClvGJaWhrp6OgIVWx+5syZYk/7FNaPyzaNGjUiJycnOnfuHM2ZM4c6dOhA6urqZGtrSyNHjqSdO3fS06dPpe6KY5OsrCwKCAggMzMzio6OptOnT5Ouri4/Q1MYFi5cKPYQw1/G6BIRzZkzR+y9wYTl2rVrxOFwyMLCgnr16sVKWNDPnDlzht8JNzo6mpydnQW6bvz48eTt7S22L2B+fj6Fh4eTubk5tW3bli5evMjaXMuWLStVpFwQ3r59Szo6OmJrx8SGH1dUzMzMqGPHjqVeKywspPj4eAoNDSU/Pz9q0KAB6ejokJeXV6Xtj2oax48fJz09PVq0aBElJiZWK5EiJSWFtLW1xRoy+UsZ3c+fP5OWlpbM5Z0/e/aMLCwsyM7Ojuzt7VlvBbR//34aOHAgERH/YKoqDh06RObm5vTjxw9WdSEq2nWEhoZS/fr1qXPnzqwXJsrJySF9fX16+PCh0Nf26dOHtm7dyqo+ROL14wqDsbGxQG628tofNWvWjIKCguiPP/6gN2/e1MjV8IcPH6hDhw7Upk0bSkhIoI4dO5Knp6dQcetBQUE0Y8YMsen4SxldIqJhw4bR0qVLpa1GGVJTU8nd3Z0aN25M+vr6rBqizZs381f4p0+fJi8vr0rHJyUlEYfDYT09NjMzk1avXk2GhobUs2dPiomJYVV+MZs3b662//7KlSvUuHFj1g2KJP24lcHhcPgPYGHIzc2l27dv06pVq/hhZ0ZGRuTj40Nr166lO3fuyEydkarg8Xi0YsUK/iHbhAkTyMrKipKSkgS6/tWrV1WGIYrCL2d0Hzx4QIaGhlLr7FoZ+fn5NGrUKGrYsCFxOBzWWgEtXbqU/2Q+dOgQ9evXr8Kx2dnZZGdnx2raY1paGi1ZsoRfXlHUYjuVUVhYSA0aNKj2wR/DMGRra8tqpIu0/bgl0dTUZKWHXXH7o3379tHYsWPJwcGBVFVVqU2bNjR16lQ6ceJEhSnZskJcXBxZWlrS0KFDKTQ0lHR1dQUu4NS/f39au3atWPT65YwuEVGnTp2q5USXBAzD0OrVq0lPT4/q169PEydOFLnGwbRp0/ip0BERETR06NAKxw4fPpz8/f1ZWemVLK84ZMgQsZ/6EhUV6XZzcxNJxubNm6lv376s6JOenk4WFhZS9eOWpHbt2hQcHCwW2RkZGXT58mVatGgRdenShTQ1Ncnc3JwGDx5MW7dulWr7o4rIzMykkSNHkrm5OW3fvp0MDQ1p5cqVVd7/cXFxZGJiIpZO0b+k0T1//rzU2yxXxalTp0hHR4eaNGlCHh4eIoX1BAYG8v2UoaGhNG7cuHLHRUREkK2trcgHST+XVyyuAiVuGIYhe3t7kctNZmRklNuevTr69O/fX+p+3JIoKirS/PnzJTIXj8ejR48e0fbt22nYsGFkZWVFderUIQ8PD5o/fz5dvHhRLGcG1SEyMpL09PRo2rRp1LRpU/L3968ykaJ9+/ZiyXStzOjKZI80QfD09ERBQQGuXbsmbVUqpGfPnrhy5Qq+f/+OrKwsuLi4IDk5uVqyfvz4we+Plp2dXW5/rMTEREybNg2RkZFQV1ev1jzv3r1DUFAQGjduDC6Xi8TERISFhcHMzKxa8oTl/PnzkJeXR5cuXUSSo6GhgUGDBmHbtm0iydm2bRuSkpKwbt06keSwBRGBy+WiTp06EplPXl4ejRs3xujRo7Fr1y4kJyfj5cuXmDBhAgoKCrBs2TIYGxvD3t4egYGB2LNnD54/f160opMwffv2RVxcHGJiYqCuro709HS0a9cOHz9+rPCaadOmia1PW4VUZI1Jxle6REXdcas6UJIFPn36RE5OTtSyZUvS09OrViugLl268It+zJ8/v0xvsPT0dLKysqr2U/v58+c0cuTIKssrips2bdqwto1/+vQp6enpVdv3Hx8fL5Ui+pWRl5dH8vLyFBYWJm1V+BQUFNDdu3dpw4YNYml/JCxcLpeWLVtGenp6NHDgwEoTKYp3Vn/++SerOuBXdC8QSS67hA2ys7PJx8eH7OzsSE9PT+hWQK6urnT79m0iKqqhEBISwn+vOJQpICBAaL1KllecP3++1MojEhUlgJiZmbFa47dTp07VehDJmh+3mLS0NFJSUqK9e/dKW5VKef/+PR05coQmTZpEzs7OpKqqSi1atKCJEyfS4cOHJdLfLSYmhszNzcnDw4M4HE6FZ0B79+4tE/csKr+s0SUimjdvnkz52yqDx+PRnDlzqF69emRpaSlUKyBbW1t69OgRERUlPGzatIn/XnE+vjChTCXLKy5fvlyg8orixsvLi/X42pMnT1LLli2FuqbYjxsYGMiqLmzw+fNnUlZWpsjISGmrIhQ5OTl08+ZNCgkJoZ49ewrc/khUMjIyaNiwYWRqakrGxsY0ZcqUMgeBBQUFVK9ePbp37x5r8/7SRveff/4hLS0tiRVyYYO9e/cSh8MhV1dXatu2rUDFXIyMjPhFPoYNG0Y7d+4kIqLY2FjS1dWlFy9eCDR3VFQUdevWTejyiuLmwYMHZGBgwHoMLJfLpfr169Pdu3cFvmbr1q3k4OAgkz3IXr16RSoqKiLXl5U2JdsfBQYGkr29PampqZGbmxvNmDGDTp8+zep3+tChQ8ThcMjc3LzcRIrVq1fTgAEDKCUzj7Zef0ETD8XT8N2xNPFQPG29/oK+ZQrnoqrM6MpRJQ5kJycniouLk5B3ufqMHDkSZmZmmD17trRVEZi///4bPj4+cHR0RHJyMk6dOoUmTZqUGvMtKx+R9z4g6Z8MHD5xBn17dIVdPR1cClsI317d4OnpiWbNmmHNmjXw9vaucC4iwvXr17FkyRK8evUKM2bMwLBhw6CsrCzuX1Ng/P39YW9vj+nTp7Mue8WKFUhKSsKuXbuqHHv//n107twZt2/fhpWVFeu6iMqTJ0/g5OSE8+fPw93dXdrqsEp6ejpiYmIQFRWFqKgoxMTEwMDAAK1ateL/2NraQl6+euf/b9++hb+/P968eQMlJSVcuHAB1tbWAICopI/wXRAOVYsWkJOTQz6X4V+noigPAuBurYtx7SzgYKJV5VxycnL3iMip3Pd+BaP76NEjdO7cGa9fv5YpQ1IVr169Qvfu3VGvXj3cv38f4eHh6NWrFx68/4HN11/gxrMUAChzA+QXFMCurjxy407C3rhOhSfrRIQLFy5gyZIlSE1NxaxZs+Dn5wclJSWJ/H6C8vr1azg5OeHVq1f8CA02+fbtGywtLfH8+XNwOJwKx2VkZKB58+ZYtGgRBg4cyLoebBAfH4+2bdvi6tWraNmypbTVESs8Hg+PHz9GVFQUoqOjERUVhW/fvqFly5Z8I9yyZUtoaGgIJXP58uVYuXIl5OTkcOjQIaRq22Lp+STkFnABObkKr5WTA1QUFTC7mw38XRpUOs8vb3SBohAyPz8/DB06VNqqCMWPHz/g6+uLzMxMvHv3Du1Hz0UcY4p8LoNKo1iIARguFvRsgmFtzEu9xTAMTp48iSVLloDL5WL27Nnw8fGBgoKCeH+ZajJ+/HjUqVMHy5cvF9scw4cPh42NTYUraSLCwIEDoaWlhbCwMLHpISq3b9+Gh4cHYmJiYG9vL211JM7Xr1/5BjgqKgrx8fGwtLQstRpu2LAh5CoxngBw584d9O3bF3n1WkC7wwhwIfh3o7aSPGZ3s63U8P4rjO7Fixcxbdo0JCQkVPkHlzW4XC4mTpyIP19kg9ekF6BYS+BrS94AXC4XR44cwdKlS6Gqqoq5c+eie/fu1d6OSYIvX77A1tYWT58+hb6+vtjmuXfvHry9vfHq1atyHz5hYWEICwtDdHQ0ateuLTY9ROXKlSvo3r07Hj58CAsLC2mrI3UKCgpw//59vhGOiooCj8dDq1at4OrqilatWqF58+ZQUVEpc21U0kf474oDI6/If424hUi9tAV5bxLA5GVBUcsQ2u2GoLZ5aftZW0kBhwNc0KRe+a6Gf4XRJSLY2dlh48aN6Nixo7TVEZoH73+g75Zb4P6Ur/LPgRnI/5QMOfkiQ6GgURfGAaUD/lWU5OFvkII96xbDwMAAc+fOhYeHR414+MyePRtpaWnYsmWL2OdydXXFjBkz0KtXr1Kvy7oftyRnz56Fj48PXr16BSMjI2mrI3MQEd69e1dqNfz06VM0adKk1GrY0NAQAfvi8NfTL6V2lExBHjJijkHdvhMUNHWR+zIO306vgtGIUChq/f+iQE4O8GykjzD/cu1qpUZXsbwXayJycnIIDg7G2rVra6TR3Xz9BXhy8kA5z0CdzmOg4eBZ4bW5+VwcTEzDzp074ebmJkYt2SUjIwPbtm1DbGysROYLCgpCaGhoKaObkZEBX19fbNy4UeYNLgDk5uaCx+OVm5H4H0V2wNTUFKamphgwYACAogzOu3fvIioqCrt27UJAQAA0dI0g13spSK70rke+lgq02g7i/1/VwhmKmvrI/+dFKaNLBFxLTkFqVj7qqgt3jiS7+85qMGjQINy7dw9Pnz6VtipC8S0rHzeepVTuw60EOXl5cHWt0LhZzTpYCQsLQ+fOnSWWYuzj44OHDx/y7w8iQkBAADp27CizB2c/k5eXBx6PJ9MuEFlDTU0N7u7umDVrFs6ePYuUlBSMWLwdCvJV7wR52Wko/P4RtXTrl3lPDkBk/Aeh9fllVroAoKKigrFjx2L9+vUi59xLksh7lX9wP67vwY/re6CkYwwtt8FQMW1SZkzxDRDoZl5WgAySl5eH9evX488//5TYnMrKyhg9ejS2bNmCTZs28esqREdHC3Q9EYFhGNZ+eDye0NfExcWBiHD16tVK9amObHHqLSvyi2UruY2CkmXryj9vHhffTq+Gun1HKNU1KfN+HpdB0udMoe/DX8roAsDYsWNhbW2NJUuWQFdXV9rqCETSPxmlwsJKot1+OJTqmkBOQQnZT2/i67HFMBy+EUrahqXG5XEZXL77FAZpj2T2Ri/5U1z4Z+nSpRL9ghYWFuLz5884ePAgvn//Di0tLZiYmAgkGygqAMPmj4KCglDj379/DwDYsGED67Kr+lFUVBSrfEnKnnLqOW69+lHhd5KIwbezawAFReh4jKlwXEZeoVDfdeAXNLp6enro27cvwsLCMHfuXGmrIxAZedwK31M2sub/W92+I7Kf3EDuyzgoOfUoMzbp1VtE3Lwk9hv95y+fsLKJCBcvXsTYsWPRqFEjiX9BR40ahfj4eGzevBl9+/YVWL4sHEzOmTMHa9eulegO4Vekbp2PAMo3ukSE1PMbwcv+Ab1+CyCnULGZrKMifMz7L2d0AWDy5Mno2LEjpk6dWm6oiKxRR0WIj0FODuWetgHo5NYa6/qPZ0cpMXL48GFYWVlh4cKFEp+b/lcakcfjYcyYMTJhSIUhKytL5pJbaiI2BnWgJP8JheVsML9f3IzC1PfQH7AE8koVH5KpKMrDxlDwxIxifqmDtGIaN24MR0dHHDx4UNqqCISNQR0oK5b9KJi8LOS+ugfiFoAYHrIeX0P++0eo3bBZmbHVvQEkDREhJCQEM2bMkMr827dvx/fv32FkZISrV69KRQdRyMrKqlFZl7JIQkICTq6dgYLCsq4BbvpXZCX8iYIvr/Bh02C8W+ODd2t8kPW4bN1uAuDTrJ7Q8/+SK10ACA4OxpQpUzBs2DCZX834NK+HdZeflXmdGB5+3NyPwu8fADl5KNWtB13vOVCqW/aDru4NIGkuXrwILpeLbt26SXzuhIQEzJkzB7dv38a1a9cQGhpa48ILs7OzUauW4Mkz//H/PHv2DPPnz8e1a9cwa9Ys1NM0wpXk0lFDipp6MJ1xtkpZcnJAe2tdocPFgF/Y6Hp4eICIcPnyZXh4eEhbnUrhqCujnZVumUBtBVVNGA4ToGMBMWhtplOtG0DShISEYPr06ZCXl+wm6+d4XCMjI8yaNQtv376FqampRHURhezs7BrhMpMl3r9/j0WLFuHEiRMIDg7Gjh07oK6ujgfvf+Dm8xQU8ISXqaKogHHu1csI/CXdC0DpZImawHh3C6goVq82ghzxcHPrnGq3ApIU0dHRePv2LT9oXVIUx+O2b9+eH4+rrq6OwYMHy3SdhfLIycn5z+gKSEpKCoKDg+Ho6AgOh4Nnz55h1qxZ/FZWqnkpyL61D7WEtIJFqfc2FaYAV8Uva3QBwM/PD/fv38fjx4+lrUqVOJhoYXY3G9RWEu4jqaUAFMYehmN9bbRt2xaXLl0Sk4aiExISgt9//x2KipLdYG3fvh1Pnz7F+vXrS70+btw47Ny5E3l5eRLVRxT+M7pVk56ejvnz58PGxgYFBQV49OgRli9fDh0dHf6Yr1+/omvXrpg/qAPm9WiM2koKlRUYA1DkUqitpFBlsZuq+KWNroqKCsaNG1fmyyar+Ls0wOxutkLdAPO6N8adfavw9u1bODg4YMiQIdiwYYNUGgNWxuPHjxETE4Phw4dLdN5iP+6RI0fKZHFZWVmhWbNmOHz4sER1EoXc3Nz/UoArIDc3F6tWrYKlpSXevHmDuLg4hIaGwtCwdEx7dnY2unfvjoEDByIgIAD+Lg1wOMAFno30oawoD5WfDrVVFOWhrCgPz0b6OBzgIpLBBX6hgjcVkZKSAisrKyQnJ0NPT0/a6ghE4ocf2HL9Ba4lp0AORYkPxSjKEXg8HjztjTHO3YK/xcnNzUVAQAASEhJQWFiINm3aYMuWLTJz6DJ06FBYW1tj1qxZEpszIyMDTk5OWLhwYYVpvmfPnsXChQtx9+5dieklCo0aNYKJiQkuXrwobVVkhsLCQuzcuROLFy+Gi4sLFi1ahMaNG5c7lsvlok+fPtDR0cHu3bvLHLKnZuUjMv4Dkj5nIiOvEHVUlGBjqAGfZvWEOjOprOBNjW/XIwijR4+mBQsWSFsNofmWmUdhN15Q6ynbqP38wzTp0H0aufog+Q0vvwElwzC0evVqMjAwoDZt2lCbNm3oy5cvEta6LG/evCEdHZ0yLVLECfO/PmdVNevkcrnUsGFDiomJkZBmotGwYUPq06ePtNWQCbhcLu3fv5/MzMzIw8ODYmNjKx3PMAwFBgaSh4eHwL0JqwsqadfzS7sXipk0aRK2bt1ao3x3AFBXXRmBbuZwyH2AvropWNffEY7K36BVu3yfqJycHKZMmYLdu3fj2bNnqFOnDlq2bInExEQJa16aNWvWYOTIkdDSqt7BQ3WoyI/7MwoKChg3bhxCQ0MlpJloFBQUQE1NTdpqSBUiwunTp+Ho6IjQ0FCEh4fj0qVLaNGiRaXXLV++HHfu3EFkZKRUd4D/CqPbqFEjNGvWDH/88Ye0VakWPB6PH2KVk5NTpU/P09MTf//9N16/fg1LS0t06NABJ0+elISqZUhJScG+ffswadIkic1ZmR+3PEaMGIEzZ87g69evEtBONPLz8/mn7/9Grl69CldXV8yZMwfLli1DVFQU2rdvX+V1e/fuxfbt23H+/HnUqVNHAppWzL/C6ALgh4+RjB0wCbAJCcwAACAASURBVALDMPxuB4IYXQCwtLTEnTt3oKysDFNTU4wbNw5Lly6V+O+/adMm+Pr6Sqzgdsl43OKmg1Who6ODvn37Ijw8XMzaiU5hYaFQPcF+FWJjY+Hh4YGAgABMmDABCQkJ6NGjh0CJT3/99RemTp2K8+fPy0Th93+N0e3YsSPk5eXx119/SVsVofl5pSvo9rJOnTo4deoUunTpAkVFRRw8eBB+fn7Izc0Vp7p8MjMzsWXLFkydOlUi8xERAgMDS8XjCsr48eOxdetWcLkVFx+SBf5tRvfx48fo06cPvL290a9fPzx9+hR+fn4CJ9c8ePAAgwYNwtGjR9GoUSMxaysY/xqjW9OSJUpScqWbnZ0tVMiQvLw8li5dilWrVuHr16/48OED3Nzc8PHjR3Gpy2f79u3o2LGjxHp57dixA0+ePKlWiGDTpk1hamqK06dPi0Ez9uByuVLfHkuC169fY8iQIejQoQPatGmD58+fIyAgQKhiP+/evYOXlxdCQ0NlqqPKv8boAsDAgQPx4MEDPHr0SNqqCIWwPt3y6N+/Py5duoT3799DQ0MDzs7OYm2Tk5+fj7Vr10qssM2DBw8we/Zsgf245VHczkeW+dWN7ufPnzF+/Hg4OTnBzMwMz58/x5QpU4T+TNPS0tC1a1cEBwfD19dXTNpWj3+V0VVWVsb48eNrTLJEMdXx6ZaHo6MjYmNjweVyYWxsjG7duontcHH//v2wt7dH06ZNxSK/JJmZmejXr59Qftzy8Pb2RlJSksxmMBYXU9fU1JS2Kqzz/ft3TJ8+HY0bN4aKigqSkpKwYMGCaj1g8vPz0adPH3h4eGDy5Mli0FY0/lVGFwDGjBmDY8eO4cuXL9JWRWCq69MtDz09PVy+fBnNmzeHlpYWpk+fjpkzZ/I7I7ABj8fDihUrJLLKFcWP+zO1atVCQEAANm/ezJJ27JKXlwd5eflfKiMtKysLS5YsgZWVFX78+IHExESsWbOm2l1fGIbB0KFDweFwsGbNGpmsMPivM7ocDgf9+/fH1q1bpa2KwIji0y2PWrVqYevWrfj999+Rl5eHs2fPok+fPsjMFL7fU3mcOHECOjo6aNeuHSvyKmPHjh14/Pgxa7uXgIAAHDx4EOnp6azIY5Pc3Nxfxujm5eVhw4YNsLCwwJMnTxAdHY1t27ahXj3RypNOnz4dHz58wL59+/jfGVnjX2d0gf9PlpDUKb6osOHTLY8xY8bg+PHjSE1NxZcvX+Dq6orXr1+LJJP+V6R85syZYl9lsOHH/RkjIyN4enpiz549rMhjk7y8PMjJydXoTsBcLhcRERGwtrbG5cuXcfHiRfzxxx+wtLQUWfbGjRtx9uxZnD59Wqb/Rv9Ko2tjY4MWLVrgwIED0lZFINjy6ZZH27ZtER0djfz8fKiqqsLV1RU3b96strzLly8jJycHPXqU7eHGJsV+3PXr14vkxy2PoKAgbN68mVWXCxsULxJq4kqXYRgcOXIEjRs3xt69e3Hw4EGcOXMGDg4OrMg/fvw4VqxYgQsXLpSqJiaL/CuNLlDUR62mJEuw6dMtD1NTU9y+fRtmZmbQ0tKCt7c3duzYUS1ZkihSXuzHdXd3x6BBg1iX37p1a9SuXRuXL19mXbYoFKex1ySjS0S4cOECnJycsHLlSmzatAnXrl1Dq1atWJvj9u3bCAwMxJkzZ9CgQQPW5IqNiooy0C9U8KY8GIahJk2a0IULF6StSpV0796dTp8+TUREBgYG9PHjR7HMwzAMLVu2jPT19cnExIQmTJhAhYWFAl8fExND9evXp4KCArHoV8y2bdvI3t6ecnJyxDbHjh07qEePHmKTXx1iY2NJUVGRPn/+LG1VBOLWrVvUpk0bsrGxocjISGIYhvU5kpKSSF9fX+a+x6ik4M2/1ugSEe3evZs8PDykrUaVdO3alc6ePUtERHXq1BF7ta4zZ84Qh8MhOzs78vDwoO/fvwt0nbe3N23YsEGsuiUkJBCHw6GkpCSxzpOdnU1169alV69eiXUeYbhx4wbJy8tTenq6tFWplPj4eOratSuZmprS7t27icvlimWez58/U8OGDWnnzp1ikS8KlRndf617AQAGDBiAR48e4eHDh9JWpVJ+9umKu8pU9+7dcfPmTeTn5yMlJQXOzs5VtgJKSkrCrVu3MHLkSLHpJU4/7s+oqqpi6NChMhXlkpubC4ZhZPaQKDk5Gf3790e3bt3QrVs3JCcnY+jQoWKJIsjKykL37t0xdOhQjBgxgnX54uRfbXSLkyXWrROg+aMUKfbpFv6vZbQwqZDVxdbWFjExMdDX14eSkhJat25daeHslStXIigoSGwPBBKzH7c8xo4di4iICOTk5EhkvqrIzMyEnJycRD5/YXj37h1GjRqFNm3awNHRES9evEBQUJDYWsUXFhbC19cXDg4OmDdvnljmECf/aqMLAIGBgThx4gT++ecfaatSIcUrXTZidIVBW1sb586dQ/fu3aGsrIxBgwZh/fr1ZQ4f379/j5MnTyIoKEhsuuzYsQOPHj3Chg0bxDbHz1hYWKBly5Y4dOiQxOasjIyMDJmKPf369SsmTZqEpk2bQl9fH8+ePcPMmTPFuhMjIowdOxZEhLCwMJlMfqiKf73R5XA4GDBgALZs2SJtVSqkeKXLdriYICgoKGDlypVYsWIFAGD9+vUYNWoU8vPz+WPWrVuH4cOHiy1Upzge9+jRoxLfWhfXY/j5QSMNMjIyJN7UszzS09Mxd+5c2NragmEYPH78GEuXLoW2trbY5168eDHu37+Po0ePytyKX2AqcvbSv+AgrZikpCTS1dUV62m4KLRt25Zu3LhBz58/J3Nzc6npcffuXTI2NiYbGxtq3bo1ffnyhb59+0ba2tr0/v17scyZkZFBlpaWtH//frHIrwoej0fm5uYUFRUllflLsmjRItLQ0JDa/NnZ2bRixQrS1dWlYcOG0evXryU6f0REBDVs2LBGRG/gv4O0yrG2tkbLli2xb98+aatSLtJc6ZbEyckJcXFx0NbWRmpqKpycnDBnzhx4e3uLnL5ZHiQFP+7PyMvLY/z48TJRfSwzM1Mqq7uCggJs2bIFlpaWiI2NxY0bN7Br1y6JxsRevHgRM2fOxIULF2BgYCCxecXBf0b3fwQHB2PdunUyl4UESM+nWx4GBgb84Hb6n1/N0dFRLHOFh4dL3I9bHsOGDcP58+el7vfPysqSaG8vHo+Hffv2wcbGBqdPn8apU6cQGRkJW1tbiekAAPHx8fD398exY8fEHrUiCf4zuv/D3d0dKioq+PPPP6WtShlkZaVbjLKyMsLDw+Hs7IxatWph4cKFWLJkCat+zwcPHmDWrFlS8eP+jLa2Nnx9faudpccWkjK6RISTJ0/CwcEBYWFh2LVrF/788084OZXfUVycvHnzBj169EBYWBhat24t8fnFwX9G93/IcmeJ4pWuJGJ0BaWwsBCxsbFYv3495OTksGPHDgwcOJCV8KrMzEz4+vpKJB5XUMaPH4+wsDB+2J40yMnJgYqKiljnuHLlClxcXDB//nysWLECf//9t0SqxZXH9+/f0bVrV0yfPh19+/aVig7i4D+jW4L+/fvj6dOnUm9Z/jOyttIFgD/++AM2NjYYO3YsYmJiUKdOHcTFxaFNmzYitQIq9uO6ublJzY9bHk2aNIGFhYXUuioDRWU9xRX7eufOHXTs2BFjxozB5MmTcf/+fXh5eUktJCsvLw+9evWCl5cXJkyYIBUdxMV/RrcEtWrVQlBQkMwlS8iST7dYn5JFyhs2bIjo6Gg4ODjg+/fvcHJyqnYroGI/7saNG9lUmRWk3c4nJyeHdVfLo0eP0Lt3b/Tr1w8DBgzAkydPMGDAALEWLKoKhmHg7+8PY2NjrFy5Ump6iIv/jO5PBAYG4uTJk/j8+bO0VeEjayvdU6dOQV1dHR06dOC/pq6ujqNHj2LEiBHgcrnw9PQUuhVQsR+Xzfq4bNK7d2+8ePFCajuhvLw81v4uL1++xODBg9GxY0e0a9cOz58/x+jRo2Ui9nXKlCn49u0b9uzZI1XjLy5+vd9IRHR0dODn5ydTyRKy5NOlSoqUy8vLY968edixYwfk5OQwadIkgVsBlfTj2tjYiEt9kVBSUsKYMWOk1s4nLy9P5Ifup0+fMHbsWLRs2RKWlpZ4/vw5Jk+eLHZfsaCsW7cOly5dwokTJ8TmSpE2/xndcpg4cSK2bdsmMzn3srTSvX79OtLT09G7d+8Kx/Tu3Rs3b96Eqqoq9u/fj969e1faCkhW/bjlMXr0aBw5cgRpaWkSnzsvL6/aD93U1FRMmzYNdnZ2UFdXR1JSEubNmydTnYWPHDmCNWvW4MKFCxLJbpMW/xndcrCysoKrq6vMJEvIkk93+fLlmDZtWpXbPjs7O9y7dw+Wlpa4f/8+WrZsWWErIFn24/6MgYEBunXrht27d0t87uLuHsKQmZmJxYsXw9raGhkZGXj48CFWrVoFDocjJi2rx82bNxEUFISzZ8+ifv360lZHrPxndCtAlpIlZGWle+/ePTx58gT+/v4Cja9bty4uXboEb29vpKamwtnZGTdu3Cg1Rtb9uOUhrXY+BQUF0NDQEGhsXl4e1q9fD0tLSyQnJ+POnTsICwuDsbGxmLUUnidPnqBfv344cOCA2BJtZIn/jG4FuLm5QU1NDRcuXJC2KjLj012xYgWmTJkiVIC+oqIiNmzYgJCQEBQWFqJXr17Yvn07gJrhxy0PFxcXaGpqVlrqUhwUFBRU+flzuVyEh4fDysoK165dw6VLl7B//35YWFhISEvh+PTpE7p164ZVq1bBw8ND2upIBOmXLJJRSiZLeHl5SVUXWVjpPn/+HNeuXUNERES1rh8+fDhsbGzQu3dvzJ49G4mJiUhNTa0RftyfkZOT44ePde3aVWLzFhYWVuiDZRgGR48exdy5c2FsbIzDhw/D1dVVYrpVh4yMDHh5eWH06NEYMmSItNWRHBVVwqF/UZWxisjPzydjY2O6f/++VPUwMjKiDx8+kJeXF79XmqQZNWoUzZs3T2Q5Hz58oGbNmlGdOnVITU1NbP3exE1OTg5xOBx6/vy5xOZUVVUt0w6JYRg6d+4cOTo6UosWLeivv/4SSy8ytikoKCAPDw8KCAioEfoKC/6rMlY9ZCVZQtor3Y8fP+LYsWP47bffRJZlbGyMsLAw5OfnQ1lZGa1bt0ZSUhILWkqW2rVrY/jw4RJt58PlcqGpqcn//61bt+Dm5oapU6di3rx5iImJQadOnWS+sDcRYfTo0VBWVsbmzZtlXl+2+c/oVkFAQABOnz6NT58+SU0Haft0169fjyFDhrBy4p2ZmYnBgwcjPDwcs2fPRlpaGlxcXGSy0FBVjB07Frt370Z2drZE5uPxeNDU1ER8fDy6du2KIUOGYPTo0UhMTESfPn1qjPGaP38+njx5gkOHDslEUXaJU9ESmP5zL/AZP348zZo1S2rz6+joUEpKCtnZ2dGDBw8kOvf3799JW1ub3r59K7IshmHIz8+PRo0axX/t4sWLpK2tTXXq1KG1a9fWuK1mjx49aPv27RKZCwC5ubmRoaEhhYaGUn5+vkTmZZPt27eTubk5ffnyRdqqiBX814JdNJ49e0YcDoeysv6vvTOPi7Le/vhnYABLQPbFAEF2EQkBQbSrmbdCM0HU3M3lKpJSLj9xKbzmNdTKFFMxXHC5FKZo5pIaKqZgIoKAhKCE4lUDNYd9YGbO7w8vXIkZGGaeWdDv+/Xq9Zrm+S4HcD5znvN8zznVGtnfxMSEHj9+TD179lRrDJGIaNWqVTR16lRO1kpISCBvb+9WHTqKiorIxcWFzM3NaerUqVRfX8/Jfurg5MmT1KdPH5V+WZSWltLUqVMJAM2dO1dj/w6V5ejRo2RtbU1FRUWaNkXlMNHlgJEjR9KWLVs0sreRkRE9efKEbGxs1PrgqaamhqysrKigoEDpta5du0YWFhb022+/Sb0uEAgoJCSEzM3NqV+/fp3GExKLxeTm5ka//PIL52s/ePCAoqKiyMzMjBYtWkQ8Ho+Tv4UmyMzMJAsLC8rIyNC0KWqhLdFlMV050WSyhKZiujt37kRwcLDSnQKazuN+9dVXMs/jGhsb4+jRo5g9ezZu3LiBV199FdeuXVNqX3WginY+T548wccff4xevXqBx+OhoKAAixcvBo/H03hGoiKUlJTg3Xffxfbt2xEUFKRpczSPLDUm5um2QCKRkJ+fn0aObHXp0oWqq6tJV1eXGhoa1LJnQ0MD9ejRgy5duqTUOk1x3BkzZsg9Jzk5mYyNjcnIyIhSUlKU2l8dPHnyhExMTJS+C6murqbY2FiysLCg6dOnU2lpafO127dvk46OTqe5A2iioqKCXF1d6euvv9a0KWoFLLzADf/+979p8ODBat9XX1+fKisric/nq23PPXv20Ouvv670OgkJCdS7d2+qqanp0Lzs7GyytbUlIyMjWrlypdY/YJszZw6tWLFCoblCoZC+/vprsrW1pTFjxkgNwRQWFhKPx6OqqiolLVUfNTU1FBQURNHR0Zo2Re0w0eWIhoYGsrOzo6ysLLXuq6urS+Xl5WRsbKyW/cRiMXl5edHJkyeVWqe9OG57lJeXU1BQEJmYmFB4eHiHhVud5Ofnk42NTYdOFIhEItq9ezc5OjrS22+/3ea/q+zsbAJAIpGIC3NVjkgkotDQUJo4cSKJxWJNm6N22hJdFtPtAHp6epg3b57akyUkEgmEQqHa4rlHjx6Fvr6+Urnw8sRx28PS0hLnz5/HmDFjcPr0afTr10+pVkCqxMvLC56enkhJSWl3LBHh0KFD6NOnD7755hvs3r0bJ06cQN++fWXOEQgE4PF40NXV5dJslUBE+PDDD1FZWYmdO3c+l4XIlUKWGhPzdKXSdG717t27atlPIpEQALpx4wY5OzurZb+goCBKTk5Wao2OxnHbY+vWrWRoaEjm5uZKx5lVxcGDB2nAgAEyr0skEjp16hT5+/uTj48PHTt2TO6wyQ8//EC6urpcmapS1q1bR97e3vTkyRNNm6IxwMIL3DJv3jxasmSJWvYSiUSko6NDOTk55O3trfL90tLSyMXFRanbWEXjuO1x/vx5MjMzo65du9LevXs5XZsLGhsbyc7Ojq5evdrqWnp6Og0ePJhcXV3pu+++6/At9549e8jAwIArU1VGUlIS2dvbU1lZmaZN0ShMdDnm5s2bakuWEAqFxOfzKT09nQIDA1W+X0hIiFIZVsrGcdvj9u3b5OnpSYaGhrRo0SKtixeuXr26hYefm5tLI0aMIHt7e9q+fTs1NjYqtO6mTZuoa9euXJmpEs6cOUOWlpaUm5uraVM0DhNdFRAWFkabN29W+T51dXVkYGBAP//8Mw0ZMkSle2VnZ1P37t0VzgirrKwkd3d3lXuhNTU1FBYWRkZGRjR06FCqrKxU6X4d4Y8//iATExPKzMykCRMmkLW1NX311VdUV1en1LqxsbHUrVs3jqzkntzcXLK0tKTU1FRNm6IVtCW6LMKtIOpKlmiqMKaOVj1r167F/PnzFWoISESIiIjAwIED5e4soSgvv/wyDh48iOjoaKSnp8PHxwclJSUq3VNeGhsbYWlpiUGDBsHDwwPFxcX46KOPlG78WFlZqRWdeqVx9+5dDB8+HBs2bGjRIZohHSa6CjJgwACYmpri6NGjKt3n2Ww0VYrurVu3cPr0acyaNUuh+Tt27EBubq7a+pzxeDwsX74cycnJqKiogK+vb6tWQOrk4cOHWLRoEby9vREYGAgLCwssW7ZM7vY67VFdXd2hjh3qQiAQYNiwYZg7dy4mTJigaXM6BUx0FeTZzhKqRF21dD///HNEREQo1B02Ly8PS5cuxffff6/2NNV33nkHmZmZMDY2RkhIiFrr2wJPj8atXLkS7u7uqK2tRX5+Pvbu3Qtra2tOWz3V1NRoneg2NDRg1KhRzTV9GfLBRFcJwsPDUVJSgqysLJXtoY66C/fv30dycjKioqI6PLe6uhpjxoxR6jyusnh4eCAvLw/+/v5YtGgRZs6cCZFIpNI96+rqsH79eri4uODmzZu4fPkytmzZgu7duwNAczsfrqipqVE6RMElRITp06fDyMgIGzdu7DS1fLUBJrpKoKenh6ioKJUmS6gjprtx40ZMmjQJVlZWHZpHRJgzZ45a4rjtYWJigrNnz2LGjBlISkrCwIED8fjxY873aWxsREJCAtzc3HD+/HmkpqZi7969cHZ2bjFu7NixuHr1KoqKijjZt6amRqFYu6pYvnw5bt26haSkpE6RsKFNvIBl27ll5syZ6NmzJ+7evQs7OzvO11d1TFcgECAhIUEhb33nzp3IycnBr7/+yrldiqCrq4u4uDj4+/sjIiICXl5eOHv2LCceuEQiQXJyMmJiYuDg4IADBw4gMDBQ5vguXbpgxowZ2LJlCzZs2KD0/nV1dVrTon7r1q04cOAA0tPTO2XVM03DPF0lMTExweTJkzm9lXwWVcd0t2zZgmHDhsHR0bFD8/Ly8rBkyRLs379f6z54U6ZMwfnz59HQ0AA/Pz8cO3ZM4bWICEePHoWvry82bNiA+Ph4pKamtim4TURERGDPnj2orq5WeP8m6urqtCK8cOTIEaxatQonTpzgpH3TC4mss2TEzunKza1bt8jc3FwlFaDKysrolVdeocjISM7L49XW1pK1tTXl5eV1aF5VVRW5u7vT7t27ObWHa+7fv0+9e/cmAwMDio2N7XClsnPnzlFwcDB5eXnR4cOHFap0FhoaSlu3bu3wvL/i6+tLw4cPV3odZcjIyCALCwu6fPmyRu3oDICd01UtPXv2xKBBg5CYmMj52qqM6SYmJqJfv37o3bu33HPov3HcAQMGYMqUKZzawzU2Nja4cuUKQkNDsXLlSowdOxZCobDdeVlZWXjrrbcwbdo0zJkzB9euXcPIkSMVelg0d+5cbN68+WkmkhIIhUKNhheKi4sRFhaGXbt2ISAgQGN2PBfIUmNinm6HuHDhAjk7O3Neeq+kpIQcHR1pzJgx9N1333G2bmNjIzk5OdHFixc7NG/79u3k5eWl1WUW/4pEIqEvvviCDAwMyMvLS2Yh8IKCAgoPD6fu3bvTli1bOGn8KJFIyMPDg86dO6fUOj179qT3339faXsU4Y8//iBnZ2fatm2bRvbvjIB5uqonODgY5ubm+PHHHzldV1Ux3f3798POzg7BwcFyz2mK42riPK4y8Hg8LFy4EMeOHUNpaSk8PDyQk5PTfL20tBTvv/8+/va3v6Ffv34oLi7GnDlzODkXy+PxODk+1tDQoJHfeU1NDd555x2MHz9e4cQZRkuY6HKEqpIlVHFOl4iwZs0aLF26VO45Tedxv/zyS6V7pmmKN954A3l5eTAyMkJQUBC2bduGqKgo+Pn5wcHBATdv3sTixYs5F7cpU6YgNTUVd+/eVXiNhoYGzrLb5EUkEmHcuHHw9PTEp59+qta9n2eY6HJIeHg4bt++jczMTM7WVEVM98SJE+DxeHj77bflGk+dKI7bHk5OTrhw4QJsbGwQERGB9PR0FBQU4NNPP0W3bt1UsqeRkREmTpyIbdu2KbxGY2OjQtmCikJEmDt3LoRCIRISEljyA4cw0eUQPp/PebKEKs7pxsbGYsmSJXJ/kHbu3Ins7Gxs2rSJk/01RU1NDWJjY9G3b1+88cYbmD17NvLy8jB58mTU1taqdO8PPvgACQkJcj3Ik4ZIJIKhoSHHVslmzZo1uHTpEg4cOKB16cedHlnBXmIP0hTiyZMnZGpqSnfu3OFkvWvXrlHv3r2pZ8+eVFxcrPR6v/zyC/Xs2VPuuq65ublkYWFBBQUFSu+tKerr6ykuLo5sbGxo7NixVFhY2HwtOTmZDAwMyNHRUeWFt4cOHUr79u1TaO5LL71EiYmJHFsknT179pCDg4PS3Y1fZMAepKmPbt26YerUqZx5hVzHdNeuXYv/+7//A5/ffjJiZ4/jisViJCYmwt3dHT/99BOOHz+O5ORkuLu7N48ZO3YsMjMzUVlZCQ8PD6Snp6vMHmUeqIlEIpWFP57l559/xqJFi3D8+PHmOhIMjpGlxsQ8XYUpKSkhMzMzToprX7lyhXx9fcnIyEjpnlO5ublkY2MjV0FtiURCkyZNounTpyu1pyaQSCR04MAB8vT0pNdee41++eWXduc8evSIfHx8SE9Pj+Lj41Vil0gkIgcHB8rMzOzwXF1dXTpz5owKrPofOTk5ZGlpqfTxNgbrHKERRo8eTRs3blR6ncuXL5O/vz/p6upSQ0ODUmtNnDiRYmNj5Rq7Y8eOTnke9+TJk+Tn50e+vr504sSJDmWRNTY20qRJk4jP59OMGTNU0u58zZo1Cp235fF4UnuvccXt27fplVdeUaohKeN/MNHVAOnp6eTk5KT0BzcjI4MCAgKIz+crtU6T9y2Pt9wZ47gXL16kQYMGkbu7O+3fv1+p3mlxcXGkp6dHAQEBJBAIOLSSqKKigkxMTKiiokLuOU0doX///XdObWni8ePH1KtXL/ryyy9Vsv6LSFuiy2K6KqJ///6wtrbGDz/8oNQ6Te2AlI3nfvnll5g1a1a7ccHq6mqMHTu208Rxr1271nx4f8qUKcjPz8eYMWOgo6P4P+158+YhNTUVBQUFcHV1xa1btziz18LCAqGhodixY4fccxoaGgBAJacXhEIhwsLC8Pe//x3z58/nfH2GFGSpMTFPV2n2799PAwcOVGqN8+fPU0BAANna2iq8xoMHD8jExITu37/f5rimOO60adMU3ktdFBUV0fjx48na2po2btyocDPNtigrK6MePXqQgYEBnThxgrN1r1y5Qg4ODnLfBf35558EgPNQj1gspnHjxlF4eLhKQikvMmCermYICwtDWVkZLl++rPAaTZ6uMmd04+LiMG7cONjY2LQ5bteuXcjOzlZZmUouuHv3R4TsOAAAEgFJREFULmbNmoX+/fvDy8sLN2/eRFRUlEoKfNvZ2aGwsBCvvfYaRowYgTVr1nCyrp+fH7p37y53f72mM8Rcl3ZcsmQJysrKsHfvXlaIXJ3IUmNini4nrF+/nsaNG6fw/NTUVPL39ydvb2+F5gsEAjI3N6dbt261Oa4pjnv9+nWF9lE15eXltGDBAjI1NaXo6Gh69OiR2vaWSCS0dOlS4vP5NGrUKLnPOLfFvn37aOjQoXKNvX79Oj39qHJHXFwcubu708OHDzldl/EUsAdpmkMgEJCZmRndvn1bofmnTp0if39/CgoKUmj+2rVrafz48W2OqaqqIg8PD62sjysQCCgmJobMzMwoMjKS7t27pzFbUlJSSF9fn9zd3ZUW/fr6erKyspLrYeWFCxdIR0dHqf2e5eDBg9S9e3cqKSnhbE1GS9oSXRZeUDHGxsZ4//33FU6WkEgkkEgkCoUX6uvrsWHDBkRHR8scQ/+tq9C/f3+tqqtQV1eHL774Ai4uLigtLUVmZiY2b94MW1tbjdkUFhaG3NxcVFRUwMnJCbm5uQqvZWBggH/84x/YsmVLu2MFAgFnt/8XL17E7NmzceTIETg5OXGyJqODyFJjYp4uZ5SWliqcLHHs2DHq27cvvfPOOx2eu23bNho2bFibY7TtPG5DQwPFx8fTK6+8QmFhYZSfn69pk1ohEAjo1VdfJT09PUpKSlJ4nTt37pCpqWm7x9KSkpKoS5cuCu/TRGFhIVlbW3P6UJAhHTBPV7P06NEDQ4cOxc6dOzs8V1FPVywWY926dViyZInMMXl5eYiOjtaKPmcSiQRJSUnw9PTEgQMHkJKSgpSUFHh5eWnULmkYGxsjKysLEyZMwOTJk7Fw4UKFOkPY29tjyJAh2Lt3b5vjKisr5UrbbosHDx4gJCQEn332mdzV5RgqQpYaE/N0OSUjI4McHR07fDTn8OHD5OPj0+FjXN999x0FBwfLzMjSljiuRCKhH374gby9vSkwMJBSU1M1ak9H2bx5M/H5fBo0aJBCx9bOnj1Lnp6ebWbOrVu3jkxMTBS2saqqivz8/Oif//ynwmswOgaYp6t5goKCYGtri8OHD3doniKeLtHTIuWyyjeSlsRxz549i+DgYCxfvhz/+te/kJGRgSFDhmjMHkWIjIxEWloaMjMz4ezsjPv373do/qBBg6Cjo4OzZ8/KHFNVVQU9PT2F7BOJRBg7dix8fHwQExOj0BoMbmGiq0YU6SwhFos7LLqnTp2CSCTC8OHDpV7X9HnczMxMvPnmm5g5cybmzp2LnJwcvPvuu522UHZwcDBKSkrA5/Ph7OyMCxcuyD1XnnY+1dXVColu05crESE+Pr7T/n6fN5joqpHQ0FDcu3cPly5dknuOIp5ubGwsoqOjpabCajKOW1BQgFGjRiE0NBSjRo1CYWEhJk6c+FwczLe2tkZxcTFee+01DB48uENfaJMmTUJaWhru3Lkj9Xp1dbVCyR+rVq3C1atX8f333yvsKTO4h4muGuHz+fjwww871FmiydOVt/ZCRkYGSktL8d5777W69mxdhV69esltg7L8/vvvmDp1KgYPHozg4GDcvHkTERERz50Q6Onp4eTJk4iOjsaHH36IKVOmyPWAzdDQEJMnT0Z8fLzU64qI7q5du7Br1y4cO3ZMrR0nGHIgK9hL7EGaSmhKlpC3YtS+ffvIxcWFvv76a7nGjxw5UupYiURCkydPVmtdhXv37tEHH3xAZmZmFBMTo3Q94M7EoUOHSE9Pj3x8fKi6urrd8Tdu3CBLS0uptY5HjhxJPj4+cu/9008/kZWVFf32228dspnBHWAP0rQHY2NjTJs2Te5kiY7EdAsKCpCRkYFp06a1upaYmIirV6+qJY77+PFjLF26FL1794a+vj4KCwuxcuVKtXQ+0BZCQ0ORn5+PsrIyODg4oLi4uM3xbm5u6Nu3L/bv39/qWm1trdx1F65evYpJkyYhJSUFHh4eCtnOUC1MdDXAvHnzsGvXLlRWVrY7ViKRQCwWyyW6a9euRVRUVKux+fn5WLx4scrjuNXV1Vi9ejXc3Nzw6NEj5OTkYP369bC0tFTZntqMm5sb7ty5A3t7e3h5eeHIkSNtjpf1QK2urk6uv1tpaSlGjBiB+Ph4DBgwQGG7GaqFia4G6NGjB9588025aqqKxWKIxeJ2Y7q3b9/Gjz/+iMjIyBbvN/U5++KLL1QWxxUKhYiLi4Orqyvy8/ORnp6Ob775Bvb29irZrzPRtWtXZGdnY8KECQgLC2vz2FZISAgePnzYqipdfX09XnrppTb3efz4MUJCQhAdHY3w8HBObGeoBia6GmLBggXYuHEjRCJRm+Pk9XTXr1+PmTNnwtTUtPk9IkJkZCSCgoIwdepUTux+FpFIhF27dsHNzQ2nTp3CiRMn8O2338LNzY3zvTozPB4PiYmJ2LRpE1avXo1hw4ZBLBa3Gqerq4vIyMhW3m59fX2bf//6+nqMHDkSw4cPR1RUFOf2M7hFudxChsL069cPdnZ2OHToEMaMGSNznFgshkgkavND9/DhQ+zduxf5+fkt3k9MTERWVpZS9XylIZFIcPDgQXzyySewtrZGUlISu52Vg8jISPj6+uKNN96Ai4sLsrKyYGZm1mLM9OnT4ezsjPLyclhZWQF4eich605HIpFg8uTJ6N69O9atW6fyn4GhPMzT1SDyJEvI4+nGxcVh9OjRLVpmN8Vxv//+e05atwNPPeeffvoJAQEBWLNmDTZu3Ihz584xwe0A/fv3R2lpKcRiMRwcHJCVldXiupmZGcLDw7F9+3Y8rBYiPu0WhH3HocDib/goORvxabfwqFrYPH7hwoUoLy/H7t27lWpRxFAfzNPVICNHjsSiRYuQkZGB/v37Sx3T5OnKEs6qqips3boVGRkZze+pIo578eJFLF26FBUVFVi1ahXCw8NZhpOCWFlZoaSkBCEhIQgMDMQ333yD6dOnN19/c/w/sGjnaexeewYAwHMKRDmAwzn30IX/AF/9XITB7pYwuXcZp06dwoULFzjvKsFQHeyrUYPo6urio48+atPblUgkaGxslOnpJiQkYMiQIXBxcQHAfRw3JycHw4cPx8SJEzF9+nTk5eVh9OjRTHCVhM/n4/Tp01i8eDFmzpyJiIgIAMC+S6VYkfYndOx9IBRJIBRJWsyr/+97p64/wHcVNpj9+b4WcXyG9sM8XQ0zbdo0rFy5Er///rvUotJtxXSFQiHWr1/f4igSV3HcoqIixMTEIC0tDcuWLUNKSopK+pC96Hz22WcICAjA2LFjceEPHkTe76K+UQLw2vaHCDzw+AbYeukBzMxKMSnIUT0GM5SGia6GMTIywowZM7Bp0yapHm9bortv3z54eXmhb9++AP4Xx01LS1M4jltWVoZPP/0Uhw4dwoIFC7B9+3aWRqpiwsLCcPDcFcw7dAu8xv95tne+HN1iHIkaYOQ7DGZvRjS/V9cowerjhehjZ4I+diZqs5mhOCy8oAXMmzcPu3fvhkAgaHWtsbERPB6vVZ2CpiLlS5cuBaB8HLe8vBzz58/Hq6++CktLSxQXF2PZsmVMcNXE0ZJG6Oi1vJNwWHig+T+7efvA4+vjZY+BrebWi8TYcu6mukxlKAkTXS3A3t4eb731ltRkifr6eqmFYQ4fPgxTU1MMGjRIqTiuQCBATEwMPD09IRKJcP36dXz22WcsTqhGHlYLkVZUgbZK49TeuAjdl7vBwL51Jw0i4OyNihanGhjaCxNdLUFWskR9fX2rVi1EhNjY2OYi5U1x3I7UVaitrcXnn38OV1dX3LlzB1lZWdi0aRNsbGw4+XkY8nMg6267Y6rzUtG19xCZDzB5AA5cbX8dhuZhoqsl+Pv7o0ePHkhJSWnxvlAohL6+fov3UlNTUVtbi3fffRfXr1/v0HnchoYGbN26Fa6urrh06RLOnTuHxMREODo6cvnjMDpA4YPKVqcUnkUkKIewLB9dvd+QOaZeJEHh/SpVmMfgGPYgTYtYsGABYmNjMWbMmGaPRlp4Yc2aNYiOjkZdXZ3ccVyxWIxvv/0WK1asgIuLCw4fPoyAgACV/SyMp0gkEvz5558oLy9HeXk5Kioqml83/X++2UDAzEXmGtX5Z2Bg1wt6Jm3fhVTWN3JtPkMFMNHVIkaMGIGFCxciIyMDwcHBAFp7upmZmSgqKsL48eMxa9YsBAYGthnHJSIcOXIEH3/8MYyMjLBjxw4MHjxY1T/KcwsRobKyspWAShPT8vJyPHr0CEZGRrCysoKVlRUsLS2bX/fq1QtWVlbgPzBGxv3WtRiaqMk/g25Bo2Veb8K4y/NVFP55hYmuFvFssoRbHz8cyLqLfCM/6A7xxEfJ2fCwMcbxzRuwcOFCJCUlITMzs83zuGfOnMGyZctQV1eH2NhYDB8+nCU1SKGmpkamgEoTUwMDg1YCamlpCScnJwQGBrZ438LCot0OGY/TbuFqRZHUEEP93d8grn4k9dTCs3Th68DD1kip3wNDPTDR1TL83wrH2ouPEbwmFTweD0LDnoDh0xRQfd37EPYYjS48Q6StXY4zB/ZLjeP++uuvWL58OUpLS7Fq1Sq89957L1RevlAoREVFhUzv86+vJRJJs0g+K6a2trbo06dPi/ctLS3bLbPYUUb72eGrn4ukXqvJT8XLbsHQMWi7yhwBGN3XjlO7GKqBia4Wse9SKVYfLwTf0Q8NYgL+coioQUzg8fVx+T/1MA6LQXZVVzx7gCg/Px+ffPIJMjMzERMTg2nTpj0XfchEIhEePXrU7q180+va2tpmgfyrkLq6urbyUrt27arROwALQwMMcrPE6d/+wF9bqpm/Pbfd+Twe8Lq7JcwNWcZgZ4CJrpbwVHB/Q12j5OmnqC10dNBIwOrjvwEAgq0kWLFiRXNTxKSkJM69MS559uGSPHFRgUAAU1NTqXHRvn37tvJSTUxMOl0Y5YPBLvil+CHqGmXHdmXRha+LyMGyH8QxtAsetdGt1N/fn65cuaJGc15MrpU9wbiES1I/cDUFaXhy8VuIKyug29UU5sM/Qhf73s3XdUmEykOrMHfCCMyfPx/GxsbqNB3A04dLVVVVct3KV1RU4OHDh80Pl6R5o399bWZm9ly0aW+PFl+8cvKSng6WD/NktRe0DB6Pl0VE/tKuMU9XC9h87ibqRa0Ft+73bPx5LhGWI6Oh390N4urHrcaIoYN3FsdhxYxgTm2qra2V61a+6bW+vr5UwXRyckK/fv1aXLOwsGh19piBZuFcfbwQ9SJxq1DDs/B4Tz3c5cM8mOB2MpjoapjmFFApHzDBhX+j24DxMHjlaVdXvpFF60E8HaSXCvCoWthmTK+hoUGuW/mm1yKRCNbW1q28T2tra3h7e7cQV1U8XHpRmRTkiD52Jthy7ibO3qgAD08TH5rowtcB4WkMN3KwCyty0wlhoqthZKWAkkQM4f2beMklEP+J/wdI3ICXXYNg8vr0VoVRJBIJPt55FJ74j0wxra2thYWFhVRv1MXFpVVc1NDQsNPFRZ8X+tiZIH6SPx5VC3Hg6l0U3q9CZX0jjLvowcPWCKP72rGHZp0YJroaRlYKqLjmCSARofbGRVhPWgueji4qDv4LgvRkmA6a0mJsowTILPoP+LxiWFpawtfXt5WwdsaHSy865oYGmP03Z02bweAYJroaprJeejdg3n+9WSO/EeAbPm1eaBQQKlV0AcAnoD82TWWdYBkMbefFOTGvpRh3kf69p9vFELrSYrgy1+n853EZjBcBJroaxsPGGAZ86X8GQ++hqMo6CnHNE4jrq1F15Qe87NK6SA1LAWUwOg9MdDXMaD/ZqZvdBoyDvq0r/vPNbNxLiIC+tTO6Bb/XahxLAWUwOg8spqth2koB5enyYf5WJMzfipQ5n6WAMhidC+bpagEfDHZBF75iGVcsBZTB6Fww0dUCfOxNsHyYB17S69if42kKqAc7IM9gdCJYeEFLYCmgDMaLARNdLYKlgDIYzz9MdLUMlgLKYDzfMNHVUlgKKIPxfMIepDEYDIYaYaLLYDAYaoSJLoPBYKgRJroMBoOhRtrskcbj8SoA3FafOQwGg/Fc0IOILKVdaFN0GQwGg8EtLLzAYDAYaoSJLoPBYKgRJroMBoOhRpjoMhgMhhphostgMBhq5P8Bg+F8XJzwR4MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = complete_graph(nodes) # or nx.complete_graph(nodes)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "nx.draw_networkx(G)\n",
    "plt.title(\"Complete undirected graph (1)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Perform conditional independence tests at a given significance level and delete edges based on the tests <a name=\"direct\"></a>\n",
    "\n",
    "See all the datails in the PDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Threshold\n",
    "This function finds the threshold:  <a name=\"threshold\"></a> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def threshold(alpha,n,s):\n",
    "    if isinstance(s,int):\n",
    "        #print(\"s is int\")\n",
    "        abs_s = 1\n",
    "    else: \n",
    "        abs_s = len(s)\n",
    "    num = norm.ppf(1-alpha/2)\n",
    "    den = math.sqrt(n-abs_s-3)\n",
    "    return num/den"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample partial correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Covariance matrix $\\Sigma$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 8)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = np.cov(data.T)\n",
    "cov.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#check if the covariance matrix is symmetric\n",
    "(cov.transpose() == cov).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- This function finds $\\Sigma_{X|Y}$ for a multivariate sample and calculate the partial correlation (see PDF): <a name=\"partial\"></a> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cond_part_corr_normal(cov,x,y):\n",
    "    \n",
    "    # for this algorithm x always has two nodes\n",
    "    \n",
    "    if len(x)!=2:\n",
    "        print(\"X should contain two nodes\")\n",
    "        return 0\n",
    "\n",
    "    if not y: # empty\n",
    "        return abs(cov[x[0], x[1]] / np.sqrt(cov[x[0], x[0]] * cov[x[1], x[1]]))\n",
    "        \n",
    "    #conditional cov\n",
    "    sigma_x = cov[x][:,x]\n",
    "\n",
    "    if isinstance(y,int): # if y is a int\n",
    "        sigma_y = cov[y][y]\n",
    "        sigma_xy = cov[x,y].reshape(2,1)\n",
    "        sigma_yx = cov[y,x]\n",
    "\n",
    "        cond_cov = sigma_x - sigma_xy * (np.reciprocal(sigma_y)) * sigma_yx\n",
    "\n",
    "    else: # if y is a list\n",
    "        sigma_y = cov[y][:,y]\n",
    "        inv_sigma_y = inv(sigma_y)\n",
    "        sigma_xy = cov[x][:,y]\n",
    "        sigma_yx = cov[y][:,x]\n",
    "\n",
    "        cond_cov = sigma_x - sigma_xy @ inv_sigma_y @ sigma_yx # formula in the pdf\n",
    "  \n",
    "    aij = cond_cov[0,1]\n",
    "    aii = cond_cov[0,0]\n",
    "    ajj = cond_cov[1,1]\n",
    "\n",
    "    partial_corr = aij / (math.sqrt(abs(aii*ajj)))\n",
    "\n",
    "    partial_corr = abs(partial_corr)\n",
    "    \n",
    "    partial_corr = 0.5* np.log((1+partial_corr)/(1-partial_corr))\n",
    "\n",
    "    return partial_corr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Partial correlation suing **pingouin**: <a name=\"partialp\"></a> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def part_corr_pingouin (data,a,z):\n",
    "    \n",
    "    values = [data[: , a[0]]] # shape 10000x1\n",
    "    values = np.concatenate((values, [data[: , a[1]]])) \n",
    "    values = np.concatenate((values, [data[: , z[0]]])) \n",
    "    \n",
    "    # we have to use these names to make it work\n",
    "    name = [\"x\",\"y\",str(z[0])]\n",
    "    \n",
    "    if len(z)>1:\n",
    "        for i in z[1:]:\n",
    "            values = np.concatenate((values, [data[: , i]])) \n",
    "            name =  np.concatenate((name, [str(i)] ))\n",
    "\n",
    "    df = pd.DataFrame(values.T, columns=name)\n",
    " \n",
    "    result = df.pcorr()\n",
    "\n",
    "    return abs(result.y.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remove edges \n",
    "In the nex cell we remove edges from the completed undirected graph: <a name=\"delete\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Remove edges:\n",
      "0 - 1 : 0 ⟂ 1 | []  (part_corr = 0.0002 threshold = 0.0196 )\n",
      "0 - 3 : 0 ⟂ 3 | [2]  (part_corr = 0.0151 threshold = 0.0196 )\n",
      "0 - 5 : 0 ⟂ 5 | [2 4]  (part_corr = 0.0143 threshold = 0.0196 )\n",
      "0 - 6 : 0 ⟂ 6 | [4]  (part_corr = 0.0066 threshold = 0.0196 )\n",
      "0 - 7 : 0 ⟂ 7 | [1 2 6]  (part_corr = 0.0152 threshold = 0.0196 )\n",
      "1 - 2 : 1 ⟂ 2 | []  (part_corr = 0.0015 threshold = 0.0196 )\n",
      "1 - 3 : 1 ⟂ 3 | []  (part_corr = 0.0131 threshold = 0.0196 )\n",
      "1 - 4 : 1 ⟂ 4 | []  (part_corr = 0.0037 threshold = 0.0196 )\n",
      "1 - 5 : 1 ⟂ 5 | []  (part_corr = 0.0024 threshold = 0.0196 )\n",
      "1 - 7 : 1 ⟂ 7 | []  (part_corr = 0.0029 threshold = 0.0196 )\n",
      "2 - 4 : 2 ⟂ 4 | [0 3]  (part_corr = 0.0011 threshold = 0.0196 )\n",
      "2 - 5 : 2 ⟂ 5 | [4]  (part_corr = 0.0169 threshold = 0.0196 )\n",
      "2 - 6 : 2 ⟂ 6 | [4]  (part_corr = 0.0032 threshold = 0.0196 )\n",
      "3 - 5 : 3 ⟂ 5 | [4]  (part_corr = 0.0052 threshold = 0.0196 )\n",
      "3 - 6 : 3 ⟂ 6 | [0 1 4 7]  (part_corr = 0.0179 threshold = 0.0196 )\n",
      "5 - 6 : 5 ⟂ 6 | [4]  (part_corr = 0.0003 threshold = 0.0196 )\n",
      "5 - 7 : 5 ⟂ 7 | [4]  (part_corr = 0.0167 threshold = 0.0196 )\n",
      "6 - 7 : 6 ⟂ 7 | [4]  (part_corr = 0.0072 threshold = 0.0196 )\n"
     ]
    }
   ],
   "source": [
    "#import time\n",
    "#start = time.time()\n",
    "\n",
    "print(\"Remove edges:\")\n",
    "\n",
    "nodes = set(G.nodes())\n",
    "\n",
    "for i in list(nodes):\n",
    "    for j in list(nodes):\n",
    "        if j>i: # no the node itself and no repeat\n",
    "\n",
    "            # all the nodes which are not i or j:\n",
    "            other_nodes = nodes - {i,j}\n",
    "\n",
    "            x = [i,j]\n",
    "    \n",
    "            # all the possible combinations of all other nodes:\n",
    "            combinationss = chain( *(combinations(other_nodes, l) for l in range(0, len(other_nodes) + 1)))\n",
    "            combinationss = (np.array(x) for x in combinationss)\n",
    "\n",
    "            for comb in combinationss:\n",
    "\n",
    "                # check if i is indipendent from j given s\n",
    "                partial_corr = cond_part_corr_normal (cov,x,list(comb))\n",
    "                t = threshold(alpha,n, list(comb))\n",
    "\n",
    "                if partial_corr<t: # Independence!\n",
    "                    print(\"%d - %d : %d ⟂ %d | %s  (part_corr = %.4f threshold = %.4f )\" %(i, j, i, j, str(comb), partial_corr, t))\n",
    "                    G.remove_edge(i,j)\n",
    "                    break # go to the next edge\n",
    "\n",
    "#print(time.time() - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot undirected graph:\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "if nx.check_planarity(G, counterexample=False)[0]==True: # if planar\n",
    "    pos = nx.circular_layout(G)\n",
    "    nx.draw(G, pos=pos, with_labels=True)\n",
    "else: # if not planar\n",
    "    pos = nx.draw_networkx(G)\n",
    "    \n",
    "plt.title(\"Undirected graph after the indipendence test (2)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Orient V-structures <a name=\"orient\"></a>\n",
    "\n",
    "Find unshielded colliders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "di_G = nx.DiGraph() # directed graph\n",
    "di_G.add_nodes_from(G.nodes()) # add all nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find all undirected v structures: <a name=\"findv\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_v_struct(nodes,G):\n",
    "\n",
    "    v_struct = set() # save all v structures\n",
    "    \n",
    "    for edge1 in G.edges():\n",
    "        for edge2 in G.edges():\n",
    "            if edge1 != edge2:\n",
    "                if edge1[0]==edge2[0] and not G.has_edge(edge1[1],edge2[1]):\n",
    "                    if (edge2[1], edge2[0], edge1[1]) not in v_struct:\n",
    "                        v_struct.add((edge1[1], edge2[0], edge2[1]))\n",
    "                        \n",
    "                elif edge1[0]==edge2[1] and not G.has_edge(edge1[1],edge2[0]):\n",
    "                    if (edge2[0], edge2[1], edge1[1]) not in v_struct:\n",
    "                        v_struct.add((edge1[1], edge2[1], edge2[0]))\n",
    "                    \n",
    "                elif edge1[1]==edge2[1] and not G.has_edge(edge1[0],edge2[0]):\n",
    "                    if (edge2[0], edge2[1], edge1[0]) not in v_struct:\n",
    "                        v_struct.add((edge1[0], edge2[1], edge2[0]))\n",
    "                    \n",
    "                elif edge1[1]==edge2[0] and not G.has_edge(edge1[0],edge2[1]):\n",
    "                    if (edge2[1], edge2[0], edge1[0]) not in v_struct:\n",
    "                        v_struct.add((edge1[0], edge2[0], edge2[1]))\n",
    "    \n",
    "    return v_struct"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function which say if in a v structure ( _i->j>-v_ ) j is a **collider**: <a name=\"unshielded\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_unshielded_collider(G, triple, alpha, n, cov):\n",
    "    \n",
    "    i = triple[0]\n",
    "    j = triple[1]\n",
    "    v = triple[2]\n",
    "    \n",
    "    # check that i and v are not linked (this should be true by constructions, but it is better to check)\n",
    "    if G.has_edge(i,v)==True: \n",
    "        return False # j cannot be a collider\n",
    "    \n",
    "    # check that i and v are linked to j (this should be true by constructions, but it is better to check)\n",
    "    if G.has_edge(i,j)==False or G.has_edge(v,j)adding==False:\n",
    "        return False # j cannot be a collider\n",
    "    \n",
    "    # other nodes apart i,j,v:\n",
    "    other_nodes = G.nodes - {i, j, v}\n",
    "    \n",
    "    # combination of all other nodes:    \n",
    "    combinationss = chain( *(combinations(other_nodes, l) for l in range(1, len(other_nodes) + 1)))\n",
    "    combinationss = (np.array(x) for x in combinationss)\n",
    "    \n",
    "    for comb in combinationss:\n",
    "        \n",
    "        # check if i is indipendent from j given s\n",
    "        partial_corr = cond_part_corr_normal (cov,[i,v],list(comb))\n",
    "        t = threshold(alpha,n, comb)\n",
    "        \n",
    "        # we want to find all subsets for which they are ind \n",
    "        if partial_corr < t: # zero corr: indipendent\n",
    "            \n",
    "            # we want to see if, adding j we have dependence. \n",
    "            # In this case j is a collider. Otherwise we continue to check with other combinations of subsets\n",
    "            if len(comb) < 1: # if comb is the empty set\n",
    "                comb_with_j = int(j)\n",
    "            else:\n",
    "                comb_with_j = list(np.concatenate((comb , [j])))\n",
    "                \n",
    "            partial_corr_with_j = cond_part_corr_normal (cov,[i,v],comb_with_j)\n",
    "            t_with_j = threshold(alpha, n, comb_with_j)\n",
    "            \n",
    "            #if they are dependent j is a collider\n",
    "            if partial_corr_with_j > t_with_j:\n",
    "                print(f\"For the v-struct {i}->{j}<-{v} : {i} ⟂ {v} given {comb} but {i} not ⟂ {v} given {comb_with_j} \")\n",
    "                # print(f\"part corr of {i},{v} given {comb} = {partial_corr}\")\n",
    "                #print(f\"Threshold of {comb} = {t}\")\n",
    "                #print(f\"part corr of {i},{v} given {comb_with_j} = {partial_corr_with_j}\")\n",
    "                #print(f\"Threshold of {comb_with_j} = {t_with_j} \\n\")\n",
    "                #if we arrive to this point at least once, j is a collider\n",
    "                return True\n",
    "            \n",
    "        #else: positive partial corr => they are dependend => not a collider\n",
    "        \n",
    "    return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Delete double headed edges:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "def double_headed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Statistical orientation**:  <a name=\"stat\"></a>\n",
    "Function to find unshielded colliders and create edges:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def statistical_orientation(nodes,G,di_G,alpha,n,cov):\n",
    "    \n",
    "    v_struct = find_v_struct(nodes,G)\n",
    "\n",
    "    for v in v_struct:\n",
    "\n",
    "        v_collider_bool = is_unshielded_collider(G, v, alpha, n, cov)\n",
    "\n",
    "        #if v[1] is an unshielded collider \n",
    "        if v_collider_bool==True :\n",
    "            di_G.add_edge(v[0],v[1])\n",
    "            di_G.add_edge(v[2],v[1])\n",
    "    \n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the v-struct 0->4<-7 : 0 ⟂ 7 given [1 2 6] but 0 not ⟂ 7 given [1, 2, 6, 4] \n",
      "For the v-struct 0->2<-3 : 0 ⟂ 3 given [1 5 6] but 0 not ⟂ 3 given [1, 5, 6, 2] \n",
      "For the v-struct 2->7<-4 : 2 ⟂ 4 given [0 3] but 2 not ⟂ 4 given [0, 3, 7] \n",
      "For the v-struct 0->4<-3 : 0 ⟂ 3 given [2] but 0 not ⟂ 3 given [2, 4] \n",
      "For the v-struct 1->6<-4 : 1 ⟂ 4 given [0] but 1 not ⟂ 4 given [0, 6] \n"
     ]
    }
   ],
   "source": [
    "statistical_orientation(nodes,G,di_G,alpha,n,cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "#nx.draw_planar(di_G, with_labels=True)\n",
    "nx.draw_networkx(di_G, pos = pos)\n",
    "plt.title(\"Directed graph after statistical orientation\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function find the colliders (attention: we mean colliders already created in the directed graph)  <a name=\"findcc\"></a>\n",
    "\n",
    "note: we do not save them directly before when we do the statistical orientation because this function can be useful is different situations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Meek Rules <a name=\"meek\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check if the edge a-b is already directed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def already_directed(a,b,di_G):\n",
    "    if (a,b) in di_G:\n",
    "        return True\n",
    "    if (b,a) in di_G:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_1(a,b, G,di_G):\n",
    "    \n",
    "    if already_directed(a,b,di_G)==True: # already directed\n",
    "        return 0\n",
    "    \n",
    "    # list of possible c\n",
    "    neghs_a = list(G.neighbors(a)) # neigbours\n",
    "\n",
    "    # c if exists c->a\n",
    "    c_linked_a = [c for c in neghs_a if (c,a) in di_G.edges]\n",
    "    \n",
    "    # c cannot be linked to b in G\n",
    "    c_linked_a = [c for c in c_linked_a if (c,b) not in G.edges]\n",
    "    c = [c for c in c_linked_a if (b,c) not in G.edges]\n",
    "    \n",
    "    # if c is not empty\n",
    "    if len(c)>0:\n",
    "        di_G.add_edge(a,b) # add edge\n",
    "        print(f\"Meek1 {a}->{b}: exist {c[0]} such that {c[0]}->{a} and ({c[0]},{b}) not in G\")\n",
    "        return 1\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_2(a,b, G,di_G):\n",
    "\n",
    "    if already_directed(a,b,di_G)==True: # already directed\n",
    "        return 0\n",
    "    \n",
    "    # list of possible c\n",
    "    neghs_a = list(G.neighbors(a)) # neigbours\n",
    "    \n",
    "    # c if exists a->c\n",
    "    c_linked_a = [c for c in neghs_a if (a,c) in di_G.edges]\n",
    "    \n",
    "    # c if exist c->b\n",
    "    c = [c for c in c_linked_a if (c,b) in di_G.edges]\n",
    "    \n",
    "    # if c is not empty\n",
    "    if len(c)>0:\n",
    "        di_G.add_edge(a,b) # add edge\n",
    "        print(f\"Meek2 {a}->{b}: exist {c[0]} such that {a}->{c[0]} and {c[0]}->{b} (avoid cycle)\")\n",
    "        return 1\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_3(a,b, G,di_G):\n",
    "\n",
    "    if already_directed(a,b,di_G)==True: # already directed\n",
    "        return 0\n",
    "    \n",
    "    # list of possible c or d\n",
    "    neghs_a = list(G.neighbors(a)) # neigbours\n",
    "    \n",
    "    # c(d) if exist c(b)->b\n",
    "    c_or_d = [c for c in neghs_a if (c,b) in di_G.edges]\n",
    "    \n",
    "    flag = 0\n",
    "    for c in c_or_d:\n",
    "        \n",
    "        possible_d = c_or_d.remove(c)\n",
    "        \n",
    "        if possible_d is not None:\n",
    "            # c not linked to d\n",
    "            d = [d for d in possible_d if (c,d) not in G.edges]\n",
    "\n",
    "            if len(d)>0: # we have found at least one d\n",
    "                flag=1\n",
    "                break\n",
    "\n",
    "    \n",
    "    if flag==1:\n",
    "        di_G.add_edge(a,b) # add edge\n",
    "        print(f\"Meek3 {a}->{b}: exist {c},{d[0]} such that {a}-{c}, {a}-{d[0]}, {c}->{b}, {d[0]}->{b} and ({c},{d[0]}) not in G\")\n",
    "        return 1\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_4(a,b, G,di_G):\n",
    "\n",
    "    if already_directed(a,b,di_G)==True: # already directed\n",
    "        return 0\n",
    "    \n",
    "    # list of possible c or d\n",
    "    neghs_a = list(G.neighbors(a)) # neigbours\n",
    "    \n",
    "    # c if exist c->b\n",
    "    c_list = [c for c in neghs_a if (c,b) in di_G.edges]\n",
    "    \n",
    "    flag = 0\n",
    "    for c in c_list:\n",
    "        \n",
    "        possible_d = c_list.remove(c)\n",
    "        \n",
    "        if possible_d is not None:\n",
    "            # d not linked to b\n",
    "            possible_d = [ d for d in possible_d if (d,b) in G.edges]\n",
    "\n",
    "            if possible_d is not None:\n",
    "                # d->c\n",
    "                d = [d for d in possible_d if (d,c) in di_G.edges]\n",
    "\n",
    "                if len(d)>0: # we have found at least one d\n",
    "                    flag=1\n",
    "                    break\n",
    "\n",
    "    \n",
    "    if flag==1:\n",
    "        di_G.add_edge(a,b) # add edge\n",
    "        print(f\"Meek4 {a}->{b}: exist {c},{d[0]} such that {a}-{c}, {a}-{d[0]}, {c}->{b}, {d[0]}->{c} and ({b},{d[0]}) not in G\")\n",
    "        return 1\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function which find all unidrected edges:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def only_undirected_edges(G,di_G):\n",
    "    \n",
    "    directed_edges = list(di_G.edges()) # directed\n",
    "    directed_edges2 = [(e[1],e[0]) for e in directed_edges] # directed other sense\n",
    "    \n",
    "    # total directed both direction\n",
    "    tot_directed = directed_edges + directed_edges2\n",
    "    \n",
    "    undirected_edges = [e for e in list(G.edges()) if e not in tot_directed] \n",
    "    \n",
    "    #undirected_edges = set(G.edges()) - set(directed_edges) - set(directed_edges2)\n",
    "    \n",
    "    return undirected_edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(3, 7), (4, 5)]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "only_undirected_edges(G,di_G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rules(G,di_G):\n",
    "    \n",
    "    flag = 0 \n",
    "\n",
    "    while flag == 0: # continue till you don't add any other edges\n",
    "        \n",
    "        flag = 1 # it will become 1 if we'll add other edges\n",
    "\n",
    "        # find all undirected nodes\n",
    "        still_undirected = only_undirected_edges(G,di_G)\n",
    "\n",
    "        # try to orient all undirect edges\n",
    "        for edge in still_undirected: \n",
    "            a = edge[0]\n",
    "            b = edge[1]\n",
    "\n",
    "            meek1 = meek_rule_1(a, b, G ,di_G)\n",
    "            meek2 = meek_rule_2(a, b, G, di_G)\n",
    "            meek3 = meek_rule_3(a, b, G, di_G)\n",
    "            meek4 = meek_rule_4(a, b, G, di_G)\n",
    "\n",
    "            # if we have added atr least one edge we have to re-check everything\n",
    "            if meek1==1 or meek2==1 or meek3==1 or meek4==1:\n",
    "                flag = 0\n",
    "            \n",
    "        return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Meek2 3->7: exist 2 such that 3->2 and 2->7 (avoid cycle)\n",
      "Meek1 4->5: exist 0 such that 0->4 and (0,5) not in G\n"
     ]
    }
   ],
   "source": [
    "meek_rules(G,di_G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "nx.draw_networkx(di_G, pos = pos)\n",
    "plt.title(\"Directed graph after Meek Rules\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equivalence classes <a name=\"equivalence\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, we find all the undirected edges. They are the edges which are in G and not in di_G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def undirected_edges(G,di_G):\n",
    "    edges_G = G.edges\n",
    "    edges_di_G = di_G.edges\n",
    "    \n",
    "    #print(edges_G)\n",
    "    #print(edges_di_G)\n",
    "    \n",
    "    undirected = [x for x in edges_G if x not in edges_di_G ] # remove edges directed in one directed\n",
    "    undirected = [x for x in undirected if reversed(x) not in edges_di_G ] # or in the other direction\n",
    "    \n",
    "    return undirected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "undirected_edges(G,di_G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(undirected_edges(G,di_G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point we can think that, for each undirected edge we have two opportunity (one direction and the other). So if we have $n$ undirected edges, one can think that $2^n$ is the answer.\n",
    "\n",
    "However, if we have more than one undirected edge, if we direct one, this can direct also the others. For example, if we have two undirected edges, it can happen that if we direct one, the other one has to be directed in order to avoid cycles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function return how many DAGs are in the corresponding equivalence class "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equivalence_classes(equi_classes, G, di_G):\n",
    "    \n",
    "    undirected = undirected_edges(G,di_G)\n",
    "    \n",
    "    if len(undirected)==0: # all already directed\n",
    "        print(\"All edges are already directed\")\n",
    "        print(di_G)\n",
    "        return [di_G]\n",
    "\n",
    "    \n",
    "    equi_classes = []\n",
    "    \n",
    "    print(f\"\\n--------------------------\\nUnidrected edge: {undirected}\\n\")\n",
    "    \n",
    "    if len(undirected)==1: # only one undirected edge\n",
    "        \n",
    "        print(\"only one undirected edge\")\n",
    "        \n",
    "        # we are sure not to create unshielded colliders or cycles, otherwise we would have detected it before\n",
    "        \n",
    "        #return 2\n",
    "        G1 = nx.DiGraph()\n",
    "        G2 = nx.DiGraph()\n",
    "        \n",
    "        G1.add_edges_from(di_G.edges)\n",
    "        G2.add_edges_from(di_G.edges)\n",
    "        \n",
    "        G1.add_edge(undirected[0][0],undirected[0][1])\n",
    "        G2.add_edge(undirected[0][1],undirected[0][0])\n",
    "        \n",
    "        equi_classes.append(G1)\n",
    "        equi_classes.append(G2)\n",
    "        \n",
    "        return equi_classes\n",
    "        \n",
    "    elif len(undirected)>1: # more than one\n",
    "        \n",
    "        # num_equi = 0 # number of equivalent classes\n",
    "        equi_classes = []\n",
    "        \n",
    "        # equivalent graph\n",
    "        equivalent_G = nx.DiGraph()\n",
    "        equivalent_G.add_edges_from(di_G.edges) # add all edges from gi_G\n",
    "        \n",
    "        #### we try to add one edge in one direction\n",
    "        \n",
    "        added_edge = undirected[0]\n",
    "        print(f\"ADD EDGE: {added_edge}\")\n",
    "        \n",
    "        equivalent_G.add_edge(added_edge[0], added_edge[1])\n",
    "        \n",
    "        # now we check if other edges are still undirected or if we can direct some:\n",
    "        \n",
    "        print(\"\\nAVOID UNSHIELDED COLLIDERS:\")\n",
    "        logical_orientation(G, equivalent_G)\n",
    "        \n",
    "        print(\"\\Meek Rules:\")\n",
    "        meek_rules(G, equivalent_G)\n",
    "\n",
    "        # at this point we can have all directed, or no new directed, or some of them directed\n",
    "        \n",
    "        if not undirected_edges(G,equivalent_G) and is_dag(equivalent_G) == True: # all directed and it is a DAG\n",
    "            print(\"\\nAll directed \\n\")\n",
    " \n",
    "            # we added one edge and this directed all the others. we add this final configuration\n",
    "            equi_classes.append(equivalent_G)\n",
    "            \n",
    "        elif is_dag(equivalent_G) == True: # some not directed but it is a DAG\n",
    "            # recall the function\n",
    "            new = equivalence_classes(equi_classes,G,equivalent_G)\n",
    "       \n",
    "            for graph in new:\n",
    "                equi_classes.append(graph)\n",
    "            \n",
    "            \n",
    "        #else: it is not a DAG and therefore this edge cannot be added\n",
    "\n",
    "        #### we try to add one edge in the other direction\n",
    "\n",
    "        equivalent_G1 = nx.DiGraph()\n",
    "        equivalent_G1.add_edges_from(di_G.edges) # add all edges from gi_G\n",
    "        added_edge = (undirected[0][1], undirected[0][0])\n",
    "        \n",
    "        print(f\"\\n\\nADD EDGE: {added_edge}\")\n",
    "        \n",
    "        equivalent_G1.add_edge(added_edge[0], added_edge[1])\n",
    "        \n",
    "        # now we check if other edges are still undirected or if we can direct some:\n",
    "        \n",
    "        print(\"\\nAVOID UNSHIELDED COLLIDERS:\")\n",
    "        logical_orientation(G,equivalent_G1)\n",
    "        \n",
    "        print(\"\\nAVOID CYCLES:\")\n",
    "        avoid_cycles(G, equivalent_G1)\n",
    "\n",
    "        if not undirected_edges(G,equivalent_G1) and is_dag(equivalent_G1) == True: # all directed and it is a DAG\n",
    "            print(\"\\nAll directed\")\n",
    "            # we added one edge and this directed all the others. we add this final configuration\n",
    "            equi_classes.append(equivalent_G1)\n",
    "            \n",
    "        elif is_dag(equivalent_G1) == True: # some not directed but it is a DAG\n",
    "            # recall the function\n",
    "            new = equivalence_classes(equi_classes,G,equivalent_G1)\n",
    "\n",
    "            for graph in new:\n",
    "                equi_classes.append(graph)\n",
    "            \n",
    "         #else: it is not a DAG and therefore this edge cannot be added\n",
    "        \n",
    "    # drop duplicates\n",
    "    if len(equi_classes)==1: # no duplicates\n",
    "        return equi_classes\n",
    "    \n",
    "    \n",
    "    equi_classes_unique = []\n",
    "    for G1 in equi_classes:\n",
    "        for G2 in equi_classes:\n",
    "\n",
    "            if nx.is_isomorphic(G1,G2): #equal\n",
    "                equi_classes_unique.append(G2)\n",
    "                equi_classes = [x if x is not G2 else nx.DiGraph() for x in equi_classes] # substitude all the other occurence in order not having more      \n",
    "                break\n",
    "\n",
    "    return equi_classes_unique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All edges are already directed\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equi_classes = []\n",
    "equi_classes = equivalence_classes(equi_classes, G, di_G)\n",
    "equi_classes\n",
    "len(equi_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def num_equivalence_class(G,di_G):\n",
    "    \n",
    "    equi_classes = []\n",
    "    equi_classes = equivalence_classes(equi_classes, G, di_G)\n",
    "    \n",
    "    if len(equi_classes)==1: # no duplicates\n",
    "        return 1\n",
    "    \n",
    "    return len(equi_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All edges are already directed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "num_equiv_class = num_equivalence_class(G,di_G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have found the number of equivalent classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_equiv_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
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   "source": []
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   "cell_type": "code",
   "execution_count": null,
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   "source": []
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   "cell_type": "code",
   "execution_count": null,
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   "source": []
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   "cell_type": "code",
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   "cell_type": "code",
   "execution_count": null,
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": []
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