ETH.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": 11,
   "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",
    "from collections import defaultdict\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": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load data and chech size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 8)"
      ]
     },
     "execution_count": 13,
     "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": 14,
   "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": 15,
   "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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "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": 17,
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 8)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = np.cov(data.T)\n",
    "cov.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 19,
     "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": 20,
   "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 len(y)==1: # if y is a int\n",
    "        y = int(y[0]) # convert to 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",
    "        y = list(y)\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": 21,
   "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": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def remove_edges(nodes,cov):\n",
    "    \n",
    "    G = complete_graph(nodes)\n",
    "    S = defaultdict(set)\n",
    "    l = 0\n",
    "    loop_cond = True\n",
    "    nodes = G.nodes()\n",
    "\n",
    "    while loop_cond:\n",
    "        \n",
    "        loop_cond = False\n",
    "        \n",
    "        for i, j in permutations(nodes, 2):  # for each edge \n",
    "\n",
    "            neigh_i = set(complete_graph(nodes).neighbors(i))\n",
    "\n",
    "            if not (j in neigh_i and len(neigh_i - {j}) >= l):  # that are adjacent and |adj(G,i)\\{j}| >= l\n",
    "                continue\n",
    "\n",
    "            neigh_i_not_j = neigh_i - {j}\n",
    "\n",
    "            for k in combinations(neigh_i_not_j, l):  # choose k \\subset adj(G, i) - {j} with |k| = l\n",
    "\n",
    "                partial_corr = cond_part_corr_normal (cov, [i,j] , k)\n",
    "                t = threshold(alpha,n, [k])\n",
    "\n",
    "                if partial_corr<t: # i ind j | k\n",
    "                    S[(i, j)] = S[(i, j)] | set(k)\n",
    "                    S[(j, i)] = S[(j, i)] | set(k)\n",
    "                    if G.has_edge(i, j):\n",
    "                        print(f\"Remove {i,j} | {k}\")\n",
    "                        G.remove_edge(i, j)\n",
    "                    break\n",
    "\n",
    "            loop_cond = True  # There were some k s.t. |k| > l\n",
    "        l += 1\n",
    "    return G, S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.01791869975853449, 0.019606503322882374)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partial_corr = cond_part_corr_normal (cov, [3,6] , [0, 1, 4, 7])\n",
    "t = threshold(alpha,n, [0, 1, 4, 7])\n",
    "\n",
    "partial_corr,t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Remove (0, 1) | ()\n",
      "Remove (0, 1) | () : partial_corr:0.0002170749629688407 t:0.01960356094974014\n",
      "Remove (1, 0) | ()\n",
      "Remove (1, 2) | ()\n",
      "Remove (1, 2) | () : partial_corr:0.0014608955105152172 t:0.01960356094974014\n",
      "Remove (1, 3) | ()\n",
      "Remove (1, 3) | () : partial_corr:0.01312989871385623 t:0.01960356094974014\n",
      "Remove (1, 4) | ()\n",
      "Remove (1, 4) | () : partial_corr:0.0037363713516547093 t:0.01960356094974014\n",
      "Remove (1, 5) | ()\n",
      "Remove (1, 5) | () : partial_corr:0.002426094159300246 t:0.01960356094974014\n",
      "Remove (1, 7) | ()\n",
      "Remove (1, 7) | () : partial_corr:0.002906184797217224 t:0.01960356094974014\n",
      "Remove (2, 1) | ()\n",
      "Remove (3, 1) | ()\n",
      "Remove (4, 1) | ()\n",
      "Remove (5, 1) | ()\n",
      "Remove (7, 1) | ()\n",
      "Remove (0, 1) | (2,)\n",
      "Remove (0, 3) | (2,)\n",
      "Remove (0, 3) | (2,) : partial_corr:0.015139517669008866 t:0.01960356094974014\n",
      "Remove (0, 6) | (4,)\n",
      "Remove (0, 6) | (4,) : partial_corr:0.006629856543928722 t:0.01960356094974014\n",
      "Remove (1, 0) | (2,)\n",
      "Remove (1, 2) | (0,)\n",
      "Remove (1, 3) | (0,)\n",
      "Remove (1, 4) | (0,)\n",
      "Remove (1, 5) | (0,)\n",
      "Remove (1, 7) | (0,)\n",
      "Remove (2, 1) | (0,)\n",
      "Remove (2, 5) | (4,)\n",
      "Remove (2, 5) | (4,) : partial_corr:0.0169188111239302 t:0.01960356094974014\n",
      "Remove (2, 6) | (4,)\n",
      "Remove (2, 6) | (4,) : partial_corr:0.0032460708441151617 t:0.01960356094974014\n",
      "Remove (3, 0) | (2,)\n",
      "Remove (3, 1) | (0,)\n",
      "Remove (3, 5) | (4,)\n",
      "Remove (3, 5) | (4,) : partial_corr:0.005228258927283728 t:0.01960356094974014\n",
      "Remove (4, 1) | (0,)\n",
      "Remove (5, 1) | (0,)\n",
      "Remove (5, 2) | (4,)\n",
      "Remove (5, 3) | (4,)\n",
      "Remove (5, 6) | (4,)\n",
      "Remove (5, 6) | (4,) : partial_corr:0.00027927066914888835 t:0.01960356094974014\n",
      "Remove (5, 7) | (4,)\n",
      "Remove (5, 7) | (4,) : partial_corr:0.016671427721548067 t:0.01960356094974014\n",
      "Remove (6, 0) | (4,)\n",
      "Remove (6, 2) | (4,)\n",
      "Remove (6, 5) | (4,)\n",
      "Remove (6, 7) | (4,)\n",
      "Remove (6, 7) | (4,) : partial_corr:0.00723845302567809 t:0.01960356094974014\n",
      "Remove (7, 1) | (0,)\n",
      "Remove (7, 5) | (4,)\n",
      "Remove (7, 6) | (4,)\n",
      "Remove (0, 1) | (2, 3)\n",
      "Remove (0, 3) | (1, 2)\n",
      "Remove (0, 5) | (2, 4)\n",
      "Remove (0, 5) | (2, 4) : partial_corr:0.014318591127294118 t:0.01960356094974014\n",
      "Remove (0, 6) | (1, 4)\n",
      "Remove (1, 0) | (2, 3)\n",
      "Remove (1, 2) | (0, 3)\n",
      "Remove (1, 3) | (0, 2)\n",
      "Remove (1, 4) | (0, 2)\n",
      "Remove (1, 5) | (0, 2)\n",
      "Remove (1, 7) | (0, 2)\n",
      "Remove (2, 1) | (0, 3)\n",
      "Remove (2, 4) | (0, 3)\n",
      "Remove (2, 4) | (0, 3) : partial_corr:0.0011148698670067887 t:0.01960356094974014\n",
      "Remove (2, 5) | (0, 3)\n",
      "Remove (2, 6) | (0, 3)\n",
      "Remove (3, 0) | (1, 2)\n",
      "Remove (3, 1) | (0, 2)\n",
      "Remove (3, 5) | (0, 4)\n",
      "Remove (4, 1) | (0, 2)\n",
      "Remove (4, 2) | (0, 3)\n",
      "Remove (5, 0) | (2, 4)\n",
      "Remove (5, 1) | (0, 2)\n",
      "Remove (5, 2) | (0, 3)\n",
      "Remove (5, 3) | (0, 4)\n",
      "Remove (5, 6) | (0, 4)\n",
      "Remove (5, 7) | (0, 4)\n",
      "Remove (6, 0) | (1, 4)\n",
      "Remove (6, 2) | (0, 3)\n",
      "Remove (6, 5) | (0, 4)\n",
      "Remove (6, 7) | (0, 4)\n",
      "Remove (7, 1) | (0, 2)\n",
      "Remove (7, 5) | (0, 4)\n",
      "Remove (7, 6) | (0, 4)\n",
      "Remove (0, 1) | (2, 3, 4)\n",
      "Remove (0, 3) | (1, 5, 6)\n",
      "Remove (0, 5) | (1, 2, 4)\n",
      "Remove (0, 6) | (1, 2, 4)\n",
      "Remove (0, 7) | (1, 2, 6)\n",
      "Remove (0, 7) | (1, 2, 6) : partial_corr:0.015185161505030673 t:0.01960356094974014\n",
      "Remove (1, 0) | (2, 3, 4)\n",
      "Remove (1, 2) | (0, 3, 4)\n",
      "Remove (1, 3) | (0, 2, 4)\n",
      "Remove (1, 4) | (0, 2, 3)\n",
      "Remove (1, 5) | (0, 2, 3)\n",
      "Remove (1, 7) | (0, 2, 3)\n",
      "Remove (2, 1) | (0, 3, 4)\n",
      "Remove (2, 4) | (0, 1, 3)\n",
      "Remove (2, 5) | (0, 1, 3)\n",
      "Remove (2, 6) | (0, 1, 3)\n",
      "Remove (3, 0) | (1, 5, 6)\n",
      "Remove (3, 1) | (0, 2, 4)\n",
      "Remove (3, 5) | (0, 1, 4)\n",
      "Remove (4, 1) | (0, 2, 3)\n",
      "Remove (4, 2) | (0, 1, 3)\n",
      "Remove (5, 0) | (1, 2, 4)\n",
      "Remove (5, 1) | (0, 2, 3)\n",
      "Remove (5, 2) | (0, 1, 3)\n",
      "Remove (5, 3) | (0, 1, 4)\n",
      "Remove (5, 6) | (0, 1, 4)\n",
      "Remove (5, 7) | (0, 1, 4)\n",
      "Remove (6, 0) | (1, 2, 4)\n",
      "Remove (6, 2) | (0, 1, 3)\n",
      "Remove (6, 5) | (0, 1, 4)\n",
      "Remove (6, 7) | (0, 1, 4)\n",
      "Remove (7, 0) | (1, 2, 6)\n",
      "Remove (7, 1) | (0, 2, 3)\n",
      "Remove (7, 5) | (0, 1, 4)\n",
      "Remove (7, 6) | (0, 1, 4)\n",
      "Remove (0, 1) | (2, 3, 4, 5)\n",
      "Remove (0, 5) | (1, 2, 3, 4)\n",
      "Remove (0, 6) | (1, 2, 3, 4)\n",
      "Remove (0, 7) | (1, 2, 3, 4)\n",
      "Remove (1, 0) | (2, 3, 4, 5)\n",
      "Remove (1, 2) | (0, 3, 4, 5)\n",
      "Remove (1, 3) | (0, 2, 4, 5)\n",
      "Remove (1, 4) | (0, 2, 3, 5)\n",
      "Remove (1, 5) | (0, 2, 3, 4)\n",
      "Remove (1, 7) | (0, 2, 3, 4)\n",
      "Remove (2, 1) | (0, 3, 4, 5)\n",
      "Remove (2, 4) | (0, 1, 3, 5)\n",
      "Remove (2, 5) | (0, 1, 3, 4)\n",
      "Remove (2, 6) | (0, 1, 3, 4)\n",
      "Remove (3, 1) | (0, 2, 4, 5)\n",
      "Remove (3, 5) | (0, 1, 2, 4)\n",
      "Remove (3, 6) | (0, 1, 4, 7)\n",
      "Remove (3, 6) | (0, 1, 4, 7) : partial_corr:0.01791869975853449 t:0.01960356094974014\n",
      "Remove (4, 1) | (0, 2, 3, 5)\n",
      "Remove (4, 2) | (0, 1, 3, 5)\n",
      "Remove (5, 0) | (1, 2, 3, 4)\n",
      "Remove (5, 1) | (0, 2, 3, 4)\n",
      "Remove (5, 2) | (0, 1, 3, 4)\n",
      "Remove (5, 3) | (0, 1, 2, 4)\n",
      "Remove (5, 6) | (0, 1, 2, 4)\n",
      "Remove (5, 7) | (0, 1, 2, 4)\n",
      "Remove (6, 0) | (1, 2, 3, 4)\n",
      "Remove (6, 2) | (0, 1, 3, 4)\n",
      "Remove (6, 3) | (0, 1, 4, 7)\n",
      "Remove (6, 5) | (0, 1, 2, 4)\n",
      "Remove (6, 7) | (0, 1, 2, 4)\n",
      "Remove (7, 0) | (1, 2, 3, 4)\n",
      "Remove (7, 1) | (0, 2, 3, 4)\n",
      "Remove (7, 5) | (0, 1, 2, 4)\n",
      "Remove (7, 6) | (0, 1, 2, 4)\n",
      "Remove (0, 1) | (2, 3, 4, 5, 6)\n",
      "Remove (0, 5) | (1, 2, 3, 4, 6)\n",
      "Remove (0, 6) | (1, 2, 3, 4, 5)\n",
      "Remove (0, 7) | (1, 2, 3, 4, 5)\n",
      "Remove (1, 0) | (2, 3, 4, 5, 6)\n",
      "Remove (1, 2) | (0, 3, 4, 5, 6)\n",
      "Remove (1, 3) | (0, 2, 4, 5, 6)\n",
      "Remove (1, 4) | (0, 2, 3, 5, 7)\n",
      "Remove (1, 5) | (0, 2, 3, 4, 6)\n",
      "Remove (1, 7) | (0, 2, 3, 4, 5)\n",
      "Remove (2, 1) | (0, 3, 4, 5, 6)\n",
      "Remove (2, 4) | (0, 1, 3, 5, 6)\n",
      "Remove (2, 5) | (0, 1, 3, 4, 6)\n",
      "Remove (2, 6) | (0, 1, 3, 4, 5)\n",
      "Remove (3, 1) | (0, 2, 4, 5, 6)\n",
      "Remove (3, 5) | (0, 1, 2, 4, 6)\n",
      "Remove (3, 6) | (0, 1, 2, 4, 7)\n",
      "Remove (4, 1) | (0, 2, 3, 5, 7)\n",
      "Remove (4, 2) | (0, 1, 3, 5, 6)\n",
      "Remove (5, 0) | (1, 2, 3, 4, 6)\n",
      "Remove (5, 1) | (0, 2, 3, 4, 6)\n",
      "Remove (5, 2) | (0, 1, 3, 4, 6)\n",
      "Remove (5, 3) | (0, 1, 2, 4, 6)\n",
      "Remove (5, 6) | (0, 1, 2, 3, 4)\n",
      "Remove (5, 7) | (0, 1, 2, 3, 4)\n",
      "Remove (6, 0) | (1, 2, 3, 4, 5)\n",
      "Remove (6, 2) | (0, 1, 3, 4, 5)\n",
      "Remove (6, 3) | (0, 1, 2, 4, 7)\n",
      "Remove (6, 5) | (0, 1, 2, 3, 4)\n",
      "Remove (6, 7) | (0, 1, 2, 3, 4)\n",
      "Remove (7, 0) | (1, 2, 3, 4, 5)\n",
      "Remove (7, 1) | (0, 2, 3, 4, 5)\n",
      "Remove (7, 5) | (0, 1, 2, 3, 4)\n",
      "Remove (7, 6) | (0, 1, 2, 3, 4)\n",
      "Remove (0, 1) | (2, 3, 4, 5, 6, 7)\n",
      "Remove (0, 5) | (1, 2, 3, 4, 6, 7)\n",
      "Remove (0, 6) | (1, 2, 3, 4, 5, 7)\n",
      "Remove (0, 7) | (1, 2, 3, 4, 5, 6)\n",
      "Remove (1, 0) | (2, 3, 4, 5, 6, 7)\n",
      "Remove (1, 2) | (0, 3, 4, 5, 6, 7)\n",
      "Remove (1, 3) | (0, 2, 4, 5, 6, 7)\n",
      "Remove (1, 5) | (0, 2, 3, 4, 6, 7)\n",
      "Remove (1, 7) | (0, 2, 3, 4, 5, 6)\n",
      "Remove (2, 1) | (0, 3, 4, 5, 6, 7)\n",
      "Remove (2, 5) | (0, 1, 3, 4, 6, 7)\n",
      "Remove (2, 6) | (0, 1, 3, 4, 5, 7)\n",
      "Remove (3, 1) | (0, 2, 4, 5, 6, 7)\n",
      "Remove (3, 5) | (0, 1, 2, 4, 6, 7)\n",
      "Remove (3, 6) | (0, 1, 2, 4, 5, 7)\n",
      "Remove (5, 0) | (1, 2, 3, 4, 6, 7)\n",
      "Remove (5, 1) | (0, 2, 3, 4, 6, 7)\n",
      "Remove (5, 2) | (0, 1, 3, 4, 6, 7)\n",
      "Remove (5, 3) | (0, 1, 2, 4, 6, 7)\n",
      "Remove (5, 6) | (0, 1, 2, 3, 4, 7)\n",
      "Remove (5, 7) | (0, 1, 2, 3, 4, 6)\n",
      "Remove (6, 0) | (1, 2, 3, 4, 5, 7)\n",
      "Remove (6, 2) | (0, 1, 3, 4, 5, 7)\n",
      "Remove (6, 3) | (0, 1, 2, 4, 5, 7)\n",
      "Remove (6, 5) | (0, 1, 2, 3, 4, 7)\n",
      "Remove (6, 7) | (0, 1, 2, 3, 4, 5)\n",
      "Remove (7, 0) | (1, 2, 3, 4, 5, 6)\n",
      "Remove (7, 1) | (0, 2, 3, 4, 5, 6)\n",
      "Remove (7, 5) | (0, 1, 2, 3, 4, 6)\n",
      "Remove (7, 6) | (0, 1, 2, 3, 4, 5)\n"
     ]
    }
   ],
   "source": [
    "G,S = remove_edges(nodes,cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot skeleton:\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>"
   ]
  },
  {
   "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": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def statistical_orientation(G, S):\n",
    "\n",
    "    di_G = G.to_directed() # completely directed graph\n",
    "\n",
    "    for i, j in combinations(di_G.nodes() , 2):  # for all couples i,j\n",
    "\n",
    "        # a successor of n is a node m such that there exists a directed edge from n to m\n",
    "        adj_i = set(di_G.successors(i))\n",
    "        adj_j = set(di_G.successors(j))\n",
    "\n",
    "        if j in adj_i or i in adj_j:\n",
    "            continue  # that are nonadjacent (i.e no edge i-j)\n",
    "\n",
    "        for k in (adj_i & adj_j):  # with common neighbour k\n",
    "            if k not in S[(i, j)]:\n",
    "                print(f\"v-struct {i} -> {k} <- {j}\")\n",
    "                di_G.remove_edges_from([(k, i), (k, j)])  # replace i <-> k <-> j by i -> k <- j\n",
    "\n",
    "    return di_G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v-struct 0 -> 4 <- 3\n",
      "v-struct 1 -> 6 <- 4\n",
      "v-struct 2 -> 7 <- 4\n"
     ]
    }
   ],
   "source": [
    "di_G = statistical_orientation(G, S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3KiM3ZBfCzKRgCmFkx44do127djg6OvLzzz/j6qo/EnRycmL37t2UK1eOwGbuONgUeab27XQwupm7MSMLIfJBCqYQRpCVlcWPP/7ISy+9xCuvvMLp06eZPHkyycnJzJ8/Hzs7O1atWoWXlxcANV5yZmwHbxxtn+5X0FZRubQyjB4t6zFt2jQSExNN8XGEEDlQ1DxuN1K7dm113759ZowjRMFy8uRJ3n33XdauXYtOp+ONN97g+++/x83N7aHlbt26hZOT02PrP+lpJfcpgINtEcZ28ObtTnVITEzEzs4OAD8/P9atW0fx4sWN+dGEKLQURdmvqmrtR1+XI0whnlJWVhYhISFUqlQJb29vTpw4QUhICCkpKSxYsOCxYgnkWCxB/9SRP/zr07ZaOextdDjYPPwr6WCjw0ZRKfHPKf7wr0//+pUYN24cNjY23L17l6ysLIoVK4ajo6NJPqsQ4n/kKlkh8un06dO8++67rFy5EoAOHTqwYcMGqlSp8lzt+ro6E9G/NteT04k8cIHYv29zK+0eTg62eP+rBB2rlaZm1SEUe/d1wJlevXrx4YcfAvoLi1q2bEmRIs82HiqEyD8pmELkISsriylTpvDtt9/y119/4ebmxvfff09QUBA6nXFP0LxY3J6RTXIuvkOHDiU8PJwff/wRFxcX/Pz8UFWV7t278/7775OZmcm4ceOMmkcI8TApmELk4Ny5c7z33nssX76czMxM2rRpw8qVK/H29tYkz+jRo6lVqxbjx4+nWLFirFq1CkdHR+zs7ChRogQBAQGkp6fzxRdfaJJPiMJAxjCFMMjKymLmzJl4eXlRqVIldu7cyfjx40lJSWHFihWaFUsANzc3GjduzJw5cwAoWbLkg4t+/P39mT59OhMmTOD999/XLKMQ1k6OMEWhd+nSJT744AMWL17MvXv3aNGiBQsXLsTX11fraA8JDg7m3//+N/7+/iiP3PVg0KBB2NnZ0b9/f9LT0/n11181SimE9ZIjTFFo/f7771SrVg1XV1eio6MZO3YsqamprFmzxuKKJUDz5s1RVZVNmzbl+H6fPn1YsGABYWFh+Pv7mzecEIWAFExRqFy9epUhQ4ZQvHhxBgwYgIuLC3v27OHSpUuMHTsWGxvLPemiKApBQUGEhITkuky3bt34888/mTp1KoMHDzZfOCEKASmYolBYsmQJvr6+uLi4EBUVxTvvvENKSgrR0dHUrv3Y/GSLNWDAADZv3szZs2dzXaZjx46sXr2aOXPm0Lt3bzOmE8K6ScEUVispKYmAgACcnJzo3r07zs7ObN++nStXrjB+/PgHF80UJMWLF2fgwIFERETkuVzr1q3ZsGEDixYtomvXrmZKJ4R1k4IprE5UVBR+fn6ULl2ayMhIRo0axe3bt9myZQsNGjTQOt5zCwwMZOrUqaSmpua5XNOmTdm0aRMrVqygQ4cOZkonhPWSgimswq1btwgODsbZ2ZlOnTphb29PdHQ0iYmJfPvttxQtWlTriEbj7u5OnTp1mD9//hOXfe2119i5cyfr16+nZcuWZkgnhPWSgikKtA0bNlC3bl2cnZ2ZO3cuQ4cO5Z9//mHnzp00a9ZM63gmExwcTEhICHk9POG+2rVrs2/fPrZv307jxo3JysoyQ0IhrI8UTFHgpKSk8O6771KqVClat26NqqqsXr2apKQkfvrpp0Lx1I42bdqQnJzMjh078rW8r68vBw8eZN++fTRo0ECKphDPQAqmKDC2bNlCw4YNKVGiBFOnTqVPnz4kJSWxd+9e2rRpo3U8s9LpdAQGBuY5xeRRVatW5ciRIxw9epRatWpJ0RTiKUnBFBYtLS2Njz/+mDJlytCsWTNSU1NZunQpN2/eJCwsDGdnZ60jambw4MGsXbuWS5cu5XsdDw8PTpw4QXx8PL6+vmRkZJgwoRDWRQqmsEi7d++madOmFCtWjNDQULp27UpiYiIHDx6kU6dOWsezCCVLlqRPnz789ttvT7Wem5sbsbGxnDt3Dh8fH+7evWuihEJYFymYwmLcvXuXzz//HBcXFxo0aMCNGzdYsGABt2/fZtKkSZQqVUrriBYnKCiISZMmPXXRc3V1JS4ujitXrlC1alXS09NNlFAI6yEFU2juwIEDtGzZkqJFi/LDDz/Qrl07Ll++zJEjR+jWrZvW8Sxa1apVqV69OgsXLnzqdV1cXEhISODmzZt4enqSkpJigoRCWA8pmEITGRkZTJgwgfLly1O7dm0uXbrEzJkzSU5OZsaMGZQtW1briAXG/Skmz6J06dKcOnWK1NRUPDw8SE5ONnI6IayHFExhVseOHaNdu3Y4OjoyYcIEmjdvzvnz5zlx4gT9+vXTOl6B9Prrr3PlyhX27t37TOs7OzuTkJBAVlYW7u7u3Lp1y8gJhbAOUjCFyWVlZfHjjz/y0ksv8corr/DXX38xadIkkpOTmTt3LhUqVNA6YoFWpEgRRo8e/cxHmQBOTk6cOnUKGxsbqlSpQlJSkhETCmEdpGAKkzl58iSdOnXCwcGBsWPHUr9+fc6cOUNcXBxDhgxBp5MfP2MZNmwYy5cv5+rVq8/cRtGiRUlISKBYsWK4u7s/V1tCWCPZYwmjysrKIiQkhEqVKuHt7U1MTAwhISGkpKSwcOFC3NzctI5olUqVKkX37t2ZPHnyc7Xj4OBAXFwcpUqVwsPD46nmeAph7aRgCqM4ffo0b775Jo6Ojrz33nu8+uqrJCQkcOrUKUaOHClHk2YQHBzMxIkTuXfv3nO1Y2dnR2xsLOXLl8fLy4tz584ZKaEQBZvsxcQzy8rKYtKkSVSpUoXKlStz4MABvvvuO1JTU1myZAlVqlTROmKh4uvrS5UqVVi6dOlzt2VjY8PRo0d5+eWXqVatGqdPnzZCQiEKNimY4qmdO3eOnj17UqxYMYKCgh6cej1z5gxjxoyRo0kNBQUFPdfFP9nZ2Nhw6NAhvL298fHx4eTJk0ZpV4iCSvZsIl9UVWXmzJl4eXlRqVIlduzYwfjx40lJSWHlypVUrVpV64gC6NKlC3/99ReHDx82Sns6nY49e/ZQo0YNatSowbFjx4zSrhAFkRRMkadLly7Rv39/ihUrxvDhw6lUqRKHDh3iwoULvP/++9jY2GgdUWRja2vLqFGjjHaUCfqiuX37durXr0+tWrU4dOiQ0doWoiCRgilyNH/+fHx8fHB1dSU6Opr/+7//IzU1lTVr1uDr66t1PJGHESNGsGjRIqPOpdTpdGzatImmTZtSt27dZ75JghAFmRRM8cC1a9cYOnQoxYsXp3///pQrV449e/Zw6dIlxo0bJ0eTBUTZsmV54403mDp1qtHbXrt2LW3btqVhw4Zs27bN6O0LYcmkYAqWLFmCr68v5cqVY+XKlbzzzjukpKQQHR1N7dq1tY4nnkFwcDDh4eFkZmYave3ly5fTuXNnmjVrRnR0tNHbF8JSScEspJKSkggICMDJyYnu3bvj7OzM9u3buXLlCuPHj8fOzk7riOI51K5dGxcXF1asWGGS9iMjI+nVqxdt2rRh1apVJulDCEsjBbOQiYqKws/Pj9KlSxMZGcmoUaO4ffs2W7ZsoUGDBlrHE0ZkzCkmOZk7dy4DBw6kY8eOLFu2zGT9CGEppGAWArdu3SI4OBhnZ2c6deqEvb090dHRJCYm8u2331K0aFGtIwoT6NGjB8ePHycmJsZkfUybNg1/f3+6du1KZGSkyfoRwhLIVRwWIDE5ncj9F4i9fItbaRk4Odjg7eJEj1quvFjc/pnb3bBhAx9//DH79u3D2dmZoUOHMn78eIoXL27E9MJS2dnZ4e/vT1hYGGFhYSbrZ+LEiTg4ONCrVy9mzZolj2kzAlPtE8TzUVRVzfXN2rVrq/v27TNjnMLl8PmbhG1KYHPcNQDSM7IevOdgo0MFmnmVYXRTd2q85PzY+vcf9pu9AKakpPDJJ58wY8YMbty4Qa1atZgwYQJt2rQx7YcRFunSpUtUr16d06dPU7JkSZP29eGHH/L9998zZcoUhg4datK+rNXz7hOEcSiKsl9V1ceueJRTshqZs+sMvSfvYt2JK6RnZD30iwGQZnhtbcwVek/exZxdZx56/59//qFmzZoMHz4cgK1bt/Laa69RokQJpk6dSp8+fbhx4wZ79+6VYlmIlS9fnrZt2zJjxgyT9/Xtt98ybtw4hg8fzsSJE03en7V53n2CMD05JauBObvOMCHqBKn3sp64rKpC6r1MJkSdAKB//UrcvXuXdu3ace7cOc6cOUPp0qVJSkqiRo0aLF26lE6dOpn6I4gCJDg4mEGDBhEcHGzy+/yOHz8eR0dHAgMDSU9P56233jJpf9biefcJwjykYJrZ4fM3mRAV+9gvRuLyH0g7c5ise2kUKfYCTvW7UaJG2wfvp97LYkJULK9UKMlbA99k9+7d3D+d7unpyYoVKyhVqpRZP4soGBo0aECJEiVYs2YN7du3N3l/H3/8MXZ2drzzzjvcvXuXDz74wOR9FmQ57RNu7V/OnaMbuHvtDMWqNqV0x7cfW+/+PsHX1RlfVzk9aw5SMM0sbFMCaRmPTyZ3qt+DF9uPQbGx5d7181ye9zF25apg7+L+YJm0e5l0+b+JnNm0CZ1Oh4ODAxkZGfz9999SLEWuFEUhODiYkJAQsxRMgHfffRd7e3v+/e9/k5aWxqeffmqWfguinPYJNsVfpGTDXqSePoB6726u66ZlZBK+KYGI/nKDEXOQgmlGicnpbI67Rk7XWdmVccv2lYKCQsaNvx8qmCpQxNWXles3U7RIFteuXSMxMVFuMiCeqHfv3nz44YfEx8fj4eFhlj6DgoKws7MjICCA9PR0JkyYYJZ+C5Lc9glFvRoCkH45gcx7ibmur6qw8eQ1rieny9WzZiAF04wi91/I8/3ra8K5c3QDakY6duWq4Fjl8b8abW2KcN62AiObyMOZRf45OjoybNgwwsPD+fnnn83Wr7+/Pw4ODgwePJi0tDR+/PFHs/VdEDxpn5AfChB54ILsE8xACqYZxV6+9diVb9m92HY0pVqPJP1iLGnnjqIUsX1smbSMLGL/vm3KmMJKjRo1ildffZUvvvjCrHNxBw4ciL29PX379iUtLc2kc0ILmiftE/JD9gnmI9NKzOhWWsYTl1F0RXB4yYfM24ncPhiVSzv3jB1NFAIVK1akWbNmzJ492+x99+rVi8jISCIiIhgxYoTZ+7dU+dkn5K8d2SeYgxRMM3JyeIoD+qwsMm78nUs7jx95CpEfwcHBhIaGktcNS0yla9euLF++nGnTpjFw4ECz92+JnmqfkGc7sk8wBymYZuTt4oS9zeObPPPOTe7EbCbrbipqViapf+3nzonNOLjVeGxZBxsd3v8qYY64wgo1bdoUnU6n2WO5OnTowOrVq5k3bx49e/bUJIMlyW2foGZlombchaxMULNQM+6iZuX8qDbZJ5iPFEwz6l7LNec3FIXbB1dxIWww5//bmxsbp/FCyxEU9az/2KIq0N0vl3aEeAJFUUz+FJMnad26NdHR0SxZsoQuXbpolsMS5LZP+Gf7fM798Ca3dkVy5/hGzv3wJv9sn5/jsrJPMB+5l6yZ+c/ex7oTV3KcWvIkigJtq5WTOVfiudy5cwc3Nzf27dtHpUqVNMuxc+dOmjZtSosWLVi9erVmObQm+wTLI/eStRCBzdxxsCnyTOs62BRhdDP3Jy8oRB6KFSvGoEGDNL/fa4MGDdi5cycbN26kRYsWmoyrWgLZJxQcUjDNrMZLzozt4I2j7dNtevVeOvXtL+EjYxXCCAIDA5k2bRqpqama5qhVqxb79u1jx44dNGrUiKys55tiURA96z7B0VbH2A7ecls8M5KCqYH+9SsxtkNVHG2LgJr3DkJRwNG2CGUvbmPGuGEUL16c/v37ExUVRXp6upkSC2tTuXJl6tevz7x587SOwiuvvMLBgwc5cOAA9erVK5RF81n2CWM7VJUbr5uZjGFqKPpQAv2/nkNxj7roFIW0HJ5919yrDKObuVPWJg1XV1cyM/VXytnY2DBo0CCmTJmiUXpR0K1du5YPPviAgwcPoiiK1nE4deoUvr6+eHh4cODAAZM/WcUSzV+3kw9nbMChci0UyHOfIEeWppPbGKbc6UdDW570FnUAACAASURBVJbO4Y0XLjPho5ZEHrhA7N+3uZV2DycHW7z/VYLufg8/Xd3Pz4+9e/cC4OTkJPfmFM+lVatWpKamsm3bNho3bqx1HKpUqUJMTAzVq1enevXqHDlyBBubwrWLWjUngtG+1Rge2CJf+wRhXnKEqZG7d+/i5ubGunXrqF69er7WmTp1KgEBATg4OJCcnMxvv/2Gv7+/iZMKaxYSEsLWrVtZsGCB1lEeuHDhAj4+PpQrV45jx44VmocLXL16FS8vLxISEnjxxRe1jlOoyVWyFmbRokVUrVo138USoFu3brRo0YKYmBi++OILAgICNJ1PJwq+QYMGsX79ei5evKh1lAdcXV05efIk165dw8vLi7S0NK0jmcWUKVN48803pVhaMCmYGgkJCSE4OPip1nF2dmbNmjW89NJLjBs3jm+//ZYxY8bwww8/mCilsHZOTk7069ePiIgIraM8xMXFhfj4eG7duoWnpycpKSlaRzKpjIwMJk6cSFBQkNZRRB6kYGpg//79XLhwgU6dOj1XO++//z4///wzH3zwgYxnimcWFBTE5MmTLe6q69KlS3Pq1CnS09Nxd3cnOTlZ60gms3TpUtzc3Hj11Ve1jiLyIAVTAyEhIYwePdooFzSMGTOGiRMn8sknn8hT7cUz8fLyokaNGhY1jnmfs7Mzp06dAvQXBd28eVPjRKbxLGechPlJwTSza9eusXTpUoYPH260NkeOHMm0adP48ssv+fDDD43Wrig8tL6/bF6KFy9OQkICdnZ2uLu7c/36da0jGdWRI0dISEjgzTff1DqKeAIpmGY2efJk3nzzTUqXLm3UdgcPHsycOXP44YcfGDNmjFHbFtavQ4cOJCYmsnv3bq2j5Kho0aLEx8dTokQJ3N3duXr1qtaRjCYkJISAgABsbeURXZaucE1y0tj9gf1ly5aZpP2+fftib29Pz549SU9Pt7gLOYTlKlKkCIGBgYSGhlKvXj2t4+TIwcGBkydP4uPjg4eHBydOnKB8+fJax3ouSUlJREZGEhsbq3UUkQ9yhGlGf/75p8kH9rt168aSJUuYPHkyQ4YMMVk/wvoMHTqUlStXcuXKFa2j5MrOzo4TJ05QoUIFvLy8OHv2rNaRnsu0adPo2LEj5cqV0zqKyAcpmGYUEhJilsvG33jjDaKiopg9ezZ9+/Y1eX/COrzwwgv06NGDSZMmaR0lTzY2Nhw7dozKlStTrVq1BxcFFTSZmZmEhYXJxT4FiBRMMzly5Ajx8fF069bNLP21bduWdevWsWDBArP1KQq+oKAgIiIiuHfvntZR8qTT6Th48OCDm38UxFOaK1eupEyZMtStW1frKCKfpGCaSWhoKCNHjjTrwH7z5s3ZvHkzy5Yto2PHjmbrVxRcr7zyCp6enixevFjrKE+k0+nYs2cPfn5+1KxZk6NHj2od6anIVJKCRwqmGSQlJbFw4UJN7vv62muvsWPHDtauXUurVq3M3r8oeCx5ismjdDodW7dupWHDhtSuXZsDBw5oHSlfTpw4wdGjR+nZs6fWUcRTkIJpBtOmTeP111/HxcVFk/7r1KnDnj172LZtG02aNCmUzxsU+de5c2fOnTvHwYMHtY6SLzqdjujoaJo3b079+vUtdmpMdqGhoYwYMQJ7e3nySEEiBdPELGVgv2bNmuzfv5+9e/fSsGFDKZoiVzY2NowaNYrQ0FCtozyV1atX0759exo1asTWrVu1jpOrf/75h3nz5hEQEKB1FPGUpGCaWFRUFGXKlLGIuW0+Pj4cOXKEI0eOULt2bSmaIlcjRoxg8eLFBe6uOn/++SddunShefPmbNiwQes4OZo5cyZt2rShQoUKWkcRT0kKpomZaypJfnl4eHD8+HHi4uKoUaMGGRkZWkcSFqh06dJ06dKFKVOmaB3lqS1cuJDevXvTtm1boqKitI7zkKysLEJDQy1qnyDyTwqmCcXGxnL48GF69eqldZSHvPzyy8TGxnL27FmqV68uRVPkKDg4mPDw8AL58zFnzhwGDx5Mp06dWLJkidZxHli7di1FixalUaNGWkcRz0AKpglZ8sC+q6srcXFxXL58GW9vb+7evat1JGFh/Pz8qFChAsuXL9c6yjOZMmUKAQEBdO/e3WKexHJ/KomiKFpHEc9A7iVrIrdu3WLevHkcOXJE6yi5uv+QXm9vbzw9PYmNjcXBwUHrWMKCBAcHExISQteuXbWO8kzCwsKwt7enT58+pKenM2DAAM2yJCQksGfPHiIjIzXLIJ6PHGGayIwZM2jVqhWurq5aR8lTmTJliI+P586dO7i7u3Pnzh2tIwkL0q1bN2JjYzl27JjWUZ7ZTz/9xIcffsigQYM0HZMNCwtj6NChODo6apZBPB8pmCaQlZVlEVNJ8qtUqVKcOnWKzMxMqlSpwq1bt7SOJCyEnZ0dI0eOJCwsTOsoz+Wrr77is88+w9/fn/DwcLP3n5yczKxZsxg9erTZ+xbGIwXTBNatW4ejo2OBGth3cnIiPj4eGxsbqlSpQlJSktaRhIUYOXIkf/zxBzdv3tQ6ynP57LPP+OqrrwgKCuKnn34ya99z5syhSZMmuLm5mbVfYVxSME3g/lSSgjawf//J9sWKFcPDw4PExEStIwkL4OLiQvv27Zk+fbrWUZ7bRx99xI8//sh7773H119/bZY+VVWVqSRWQgqmkZ06dYrdu3cX2MdqOTg4EBcXh7OzM+7u7ly+fFnrSMICBAcHExYWZhU3u3j77bcJDQ1l7NixfP755ybvb+PGjaiqSosWLUzelzAtKZhGFhYWxpAhQyhatKjWUZ6ZnZ0dJ0+exMXFBU9PT86fP691JKGxevXq4ezszKpVq7SOYhSjR49m8uTJjB8/no8++sikfRXUM07icTKtxIiSk5OZOXMm+/fv1zrKc7v/kN5XX32VqlWrcvToUV5++WWtYwmNKIryYIrJ66+/rnUcoxg2bBj29vYMGjSI9PR0fv75Z6P3cfbsWbZs2cLs2bON3rYwPznCNKI5c+bQuHFjKlWqpHUUo7CxseHw4cN4eXnh4+NDfHy81pGEhnr16sXBgweJi4vTOorR9O/fn99//51ff/3VJFewTpw4kYEDB1K8eHGjty3MTwqmkdwf2C8oU0nyS6fTsXfvXnx9ffH19eX48eNaRxIacXBwYPjw4QV+ismjevbsyeLFi/ntt98YNmyY0dpNTU1l2rRpBAYGGq1NoS0pmEayadMmsrKyrHJgX6fTsWPHDurWrYufnx+HDh3SOpLQyKhRo5gzZw63b9/WOopRde7cmRUrVjBz5kz69+9vlDZ///136tSpg7u7u1HaE9qTgmkk1j6wr9Pp2Lx5M02aNKFu3brs3btX60hCA66urrRo0YJZs2ZpHcXo2rdvz5o1a5g/fz49evR4rrZUVbW4JxWJ5ycF0wjOnj3L5s2bGThwoNZRTG7dunW0adOGhg0bsn37dq3jCA0EBQURGhqKqqpaRzG6li1bsmnTJpYuXUqnTp2euZ3t27dz584d2rZta8R0QmtSMI1g4sSJDBgwoNAM7K9YsYI33niDpk2bsmnTJq3jCDNr0qQJtra2rF+/XusoJtGoUSO2bdvGmjVrnrnghYSEEBgYiE4nu1hrIt/N55SamsrUqVML3cD+okWL6NmzJ61atWLt2rVaxxFmlH2KibWqV68eu3btYtOmTTRr1uypbthw8eJF1q5dy+DBg00XUGhCCuZzuj+w7+HhoXUUs5s3bx4DBgygffv2BfaZieLZ9OvXjx07dnD69Gmto5iMn58f+/fvZ9euXTRq1CjfRfO3336jb9++lCxZ0sQJhblJwXwO9wf2rW0qydOYPn06/v7+dOnShUWLFmkdR5hJ0aJFGTJkiCZP/jCn6tWrc/jwYQ4dOkTdunWfWDTT09OZNGmSXOxjpaRgPocdO3aQnJxc6Af2J06cSFBQED179mTevHlaxxFmMnr0aKZPn05KSorWUUzKy8uLo0ePcuLECWrWrElGRkauyy5cuJDq1atTtWpVMyYU5iIF8znIwP7//PLLL7z33nv079/fKp5qIZ7s5Zdf5rXXXmPu3LlaRzG5KlWqcOLECU6fPs0rr7ySa9Es7GecrJ3s6Z/RpUuXWLNmDUOGDNE6isX49ttvGTduHMOGDeO3337TOo4wg6CgIEJCQqxyismjKlasyMmTJ7l06RLe3t7cvXv3off37NnD1atX6dixo0YJhalJwXxGERER9OnTRwb2HzF+/Hi++OILRo0axa+//qp1HGFirVq14t69e2zZskXrKGZRvnx54uPjSUpKwtPTk7S0tAfvhYSEMHr0aIoUKaJhQmFK8rSSZ3B/YD86OlrrKBZp7NixODg48NZbb5GWlsYHH3ygdSRhIoqiPLiRQdOmTbWOYxZly5YlISEBT09PPDw8OHnyJLdv32bFihX88ssvWscTJiRHmM8gMjKS6tWrU61aNa2jWKx3332XX3/9lY8++ogvv/xS6zjChAYOHEh0dHShem5qqVKlSEhI4O7du1SpUoWQkBC6d+9OqVKltI4mTEgK5jOQgf38CQoKIiIigk8//ZRPPvlE6zjCREqUKEH//v2JiIjQOopZOTs7c+rUKRRF4euvvy4Ut8Ys7KRgPqW9e/dy+fJlGdjPJ39/f6ZPn86ECRN4//33tY4jTCQwMJApU6Y8NKZXGBQvXpxvvvkGW1tbunTpQmJiotaRhAlJwXxKMrD/9AYNGsTvv//OTz/9JEfmVsrT05NXX32VP/74Q+soZjd58mSmTp2Ks7MzHh4eXL58WetIwkSkYD6Fq1evsnz5cqM+ZLaw6NWrF5GRkYSHh+Pv7691HGEC9+8vWximmNx36NAhTp8+Tc+ePTlx4gRlypTB09OTCxcuaB1NmIAUzKcwadIkunXrxosvvqh1lAKpa9euLF++nKlTp8qNqa1Q+/btuXnzJrt27dI6itmEhIQwatQobG1tsbOzIyYmhpdeeglvb2/Onj2rdTxhZFIw8+nevXtERETIKcXn1KFDB1avXs2cOXPo3bu31nGEEel0OgIDAwkNDdU6illcv36dxYsXM2LEiAev2djYcPToUTw8PKhWrRoJCQkaJhTGJgUzn5YuXUrlypWpUaOG1lEKvNatWxMdHc2iRYvo2rWr1nGEEQ0ZMoRVq1YVinG8qVOn8sYbb1C2bNmHXtfpdOzfvx8fHx9eeeUVYmJiNEoojE0KZj6FhITIEwiMqEmTJmzZsoUVK1bQoUMHreMII3F2dqZXr15Wf2vEzMxMwsPDcz3jpNPp2LVrF7Vq1cLPz48jR46YOaEwBSmY+XD48GH++usvORoysgYNGrBz507Wr19Py5YttY4jjCQoKIjffvvtsXutWpPly5fj4uJC7dq1c11Gp9Oxbds2XnvtNerUqcO+ffvMmFCYghTMfAgJCSEgIABbW1uto1id2rVrs2/fPrZv307jxo2f6sn2wjL5+Pjg7e1t1c9HfZqbl2zYsIEWLVo8+ANRFFxSMJ/g+vXrLFq0SKZCmJCvry8HDx5k3759NGjQQIqmFbg/xcQaHT9+nJiYGHr06JHvdVatWsXrr79OkyZN2Lx5swnTCVOSgvkEU6dOpVOnTo8N7Avjqlq1KkeOHOHo0aPUqlVLimYB16lTJy5evMj+/fu1jmJ0oaGh+Pv7Y2dn91TrLV26lG7dutGyZUvWrVtnonTClKRg5uFJA/vCuDw8PDhx4gTx8fH4+vrm+WR7YdlsbGwYPXq01U0xuXnzJvPnz2fkyJHPtP78+fPp168f7dq1Y8WKFUZOJ0xNCmYeVqxYgYuLC3Xq1NE6SqHh5uZGbGws586dw8fHx6ovHLF2w4cPZ+nSpVy7dk3rKEYzY8YM2rVrR/ny5Z+5jZkzZzJs2DA6d+7MkiVLjJhOmJoUzDzIVBJtuLq6EhcXx9WrV6latWqhu6G3tXjxxRd58803mTJlitZRjCIrK4uwsDCj7BMmTZrE6NGj6d69O/PnzzdCOmEOUjBzERMTw7Fjx55qYF8Yj4uLC/Hx8dy8eRMvLy9SUlK0jiSeQVBQEBMnTrSK0+urV6+mRIkSNGzY0CjthYSE8M4779C3b19mzpxplDaFaUnBzMX9gX17e3utoxRapUuX5tSpU6SmpuLh4UFycrLWkcRTevXVV6lYsSJ//vmn1lGe2/2pJIqiGK3N77//no8//pghQ4YwadIko7UrTMNG6wCW6J9//uH333/n+PHjWkcp9JydnUlISMDLywt3d3fi4uJwcnLSOpZ4CvenmHTr1k3rKM8sLi6O/fv3s3jxYqO3PWHCBBwcHAgICCA9PV0uMrRgcoSZgxkzZtC2bdvnGtgXxuPk5MSpU6ewsbGhcuXKJCUlaR1JPIU333yT+Ph4jh49qnWUZxYeHs6wYcNwdHQ0SfuffPIJ33zzDWPGjOGHH34wSR/i+ckR5iOysrIIDQ1lxowZWkcR2RQtWpSEhAS8vb1xd3cnNjZW5sYWELa2tgQEBBAaGlog7zGbnJzM7NmzOXjwoEn7+eCDD7C3t+ftt98mPT2dsWPHmrQ/8fTkCPMRa9asMerAvjAeBwcH4uLiePHFF/Hw8ODSpUtaRxL55O/vz8KFC7lx44bWUZ7arFmzaNasGRUrVjR5X2PGjCEsLIxPPvmETz/91OT9iacjBfMR96eSGHNgXxiPnZ0dJ06coHz58nh5eXHu3DmtI4l8KFeuHK+//jrTpk3TOspTUVWV0NBQs04vGzVqFFOnTuXLL7/kww8/NFu/4smkYGYTHx/P3r176dOnj9ZRRB5sbGw4fvw4L7/8MtWqVeP06dNaRxL5EBQURFhYGJmZmVpHybcNGzZQpEgRmjVrZtZ+hwwZwuzZs/nhhx8YM2aMWfsWuZOCmY2pB/aF8eh0Og4dOoS3tzc+Pj6cPHlS60jiCerVq0fp0qWJiorSOkq+aXnGqV+/fvzxxx+EhoYSEBBg9v7F46RgGiQnJzNr1ixGjRqldRSRTzqdjj179lCzZk1q1KjBsWPHtI4kniA4OLjA3F/29OnTbNu2jf79+2uWoXv37ixZsoTJkyczZMgQzXIIPSmYBrNnz6Zp06a4ublpHUU8hfsP6W3QoAG1atUy+ZWM4vn07NmTw4cPF4gzAhMnTmTw4MEUK1ZM0xxvvPEGUVFRzJ49m759+2qapbCTgsn/BvZlwnDBpNPp2LhxI82aNaNevXrs2bNH60giF/b29owYMcLijzJTUlKYPn06gYGBWkcBoG3btqxdu5YFCxYU6BtAFHRSMIHo6GgURTH7wL4wrjVr1tC2bVtee+01tm3bpnUckYuAgADmzp3LrVu3tI6Sq3nz5lG/fn0qV66sdZQHWrRowebNm1m2bBkdO3bUOk6hJAUTmUpiTZYvX07nzp1p1qwZ0dHRWscROahQoQKtW7e22BuOq6pqsU8qeu2119ixYwdr166lVatWWscpdAp9wTxz5gxbt27VdGBfGFdkZCS9e/emTZs2rFq1Sus4IgdBQUGEhoaSlZWldZTHbN26lbS0NFq3bq11lBzVqVOHPXv2sHXrVpo0aWKR29BaFfqCOXHiRAYNGkTx4sW1jiKMaM6cOQwcOJCOHTuybNkyreOIRzRq1AhHR0fWrVundZTH3D+61Oksd/dYs2ZNDhw4wN69e2nYsKEUTTOx3J8IM0hNTWXatGkWM7AvjGvatGmMHDmSrl27EhkZqXUckY2iKBY5xeTChQts2LCBQYMGaR3liXx8fDh8+DBHjhyhdu3aUjTNoFAXzHnz5lGvXj2qVKmidRRhIuHh4fz73/+mV69ezJ07V+s4Ipu+ffuya9cu/vrrL62jPBAREUG/fv0KzCPkPD09OX78OHFxcdSoUcMqHtRtyQptwbw/sC9TSazfzz//zAcffMCAAQOYOnWq1nGEgaOjI0OHDiUsLEzrKACkpaUxefLkAnfG6eWXXyYmJoazZ89SvXp1KZomVGgL5rZt20hJSbHYgX1hXF9//TWffvopI0aMIDw8XOs4wmDUqFHMnDmTO3fuaB2FBQsWUKNGDby9vbWO8tQqVqxIbGwsly9fxtvbm7t372odySoV2oJ5/wkEljywL4zr888/Z8KECQQFBfHf//5X6zgCqFSpEo0aNWLOnDma5rCGM07ly5cnLi6OpKQkPD09SUtL0zqS1SmU1eLixYusW7eOwYMHax1FmNnHH3/M999/zzvvvMN3332ndRyB/v6yISEhqKqqWYbdu3dz/fp1OnTooFkGYyhbtiwJCQncuXMHd3d3kpOTtY5kVQplwYyIiKBv374FZmBfGNe7777Lr7/+ykcffcR//vMfreMUei1atEBVVTZt2qRZhpCQEAIDAylSpIhmGYylVKlSnDp1ioyMDNzd3S36jkoFjY3WAcwtPT2dyZMna/rLKbQXFBSEg4MD/v7+pKen89VXX2kdqdBSFOXBjQyaN29u9v4vX75MVFSUxU1xeR5OTk4kJCTg7e1NlSpVOHnyJKVKldI6VoFX6I4wFyxYgK+vb4Ec2BfGNXz4cGbNmsW3337Lu+++q3WcQm3AgAFs2rSJc+fOmb3vSZMm0bNnT1544QWz921KxYsXJyEhgaJFi+Lh4UFiYqLWkQq8QlcwC/rAvjCu/v378/vvv/Pf//63wE0nsCbFixdn4MCBTJw40az93r17l4iICIu8b6wxODg4EB8fj7OzM+7u7ly+fFnrSAVaoSqYe/bs4dq1awV+YF8YV8+ePYmMjCQiIoIRI0ZoHafQCgwMZOrUqaSmppqtz8WLF+Pp6ckrr7xitj7Nzc7OjtjYWMqVK4enp6cmR/HWolAVTGsa2BfG1bVrV5YvX8706dMZOHCg1nEKJXd3d2rXrs38+fPN1mdhOeNka2vL8ePHqVixItWqVeP06dNaRyqQCk3BvHLlCitWrGDo0KFaRxEWqkOHDqxZs4Z58+bRs2dPreMUSuacYnLgwAHOnz9P586dTd6XJbCxseHIkSN4enri4+NDfHy81pEKnEJTMCdNmkSPHj3kSjGRp5YtW7Jx40aWLFlCly5dtI5T6LRt25bk5GR27Nhh8r5CQ0MZNWoUNjaFZ7KATqdj3759+Pr64uvry/Hjx7WOVKAUioJ57949IiIiCsWpF/H8GjduzNatW4mKiqJdu3ZaxylUdDodgYGBJp/ikZiYyJIlSwrlmLVOp2PHjh3UqVMHPz8/Dh06pHWkAqNQFMzFixfj4eFh1QP7wrjq16/Prl272LhxIy1atJBHJ5nR4MGDWbNmDZcuXTJZH1OmTKFLly6ULl3aZH1YMp1Ox5YtW2jcuDF169Zl7969WkcqEApFwQwNDZWjS/HU/Pz82L9/Pzt27KBx48ZSNM2kZMmS9OnTh99++80k7WdkZBAeHi77BGD9+vW0bt2ahg0bsn37dq3jWDyrL5iHDh3izJkzhWZgXxhX9erVOXjwIAcOHKBevXpSNM0kMDCQSZMmmeSpG8uWLcPV1RU/Pz+jt10QrVy5kk6dOtG0aVO5A9oTWH3BDAkJKXQD+8K4qlatyrFjx4iJicHPz0+KphlUq1YNHx8fFi5caPS2C8tUkqexePFievToQatWrVizZo3WcSyWVRfM69evs3jx4kI5sC+Mq0qVKsTExHDq1Cl5SK+Z3J9iYkxHjx7l5MmTdOvWzajtWoPff/+dAQMG0KFDB5YtW6Z1HItk1QVzypQpdO7cmTJlymgdRVgBNzc3Tp48ycWLF6lWrZo8pNfEOnbsyJUrV4x6QUpYWBgjR47Ezs7OaG1ak+nTpzNixAi6du3KokWLtI5jcay2YGZmZsrAvjC68uXLEx8fz7Vr1/Dy8pKH9JpQkSJFGD16tNGmmNy4cYM//viDkSNHGqU9a3X/3ro9e/Zk3rx5WsexKFY7sLd8+XIqVKhArVq1tI4irEzZsmWJj4/H29sbT09PYmNjKVq0qNaxrNKwYcOoUqUKV69epWzZss/V1vTp0+nQoQMuLi5GSme9fvnlF+zt7enfvz/p6ekMGTJE60gWwWqPMENCQqz2CQRCe6VLlyYhIYH09HR5sr0JlSpViu7duzN58uTnaiczM5OwsDDZJzyF7777jnHjxjFs2DCTTfEpaKyyYB4/fpyYmBi6d++udRRhxZydnTl16hSgvyjo5s2bGieyTkFBQUycOJF79+49cxurVq3ihRdeoH79+kZMZv3Gjx/PF198wahRo/jll1+0jqM5qyyYoaGhMrAvzOL+Q3rt7e1xd3eXh/SaQI0aNahcuTJLly595jbuTyVRFMWIyQqHsWPH8t133/H222/z3XffaR1HU1Y3hnnz5k3mz59PTEyM1lFEIVG0aFHi4uKoVq0aHh4enDx58rnH28TDgoODCQ0NpUePHk+97smTJzl06BB//vmnCZIVDu+99x729vaMGTOGu3fvMm7cOK0jacLqjjBnzJhB+/bt+de//qV1FFGIODg4EBsbS5kyZfDw8DDpfVALoy5duvDXX39x5MiRp143LCyM4cOH4+DgYIJkhUdwcDARERF8+umnfPLJJ1rH0YRVHWFmZWURFhbGrFmztI4iCiE7OztiYmLw9fXFy8uLY8eO4ebmpnUsq2Bra0tAQAAhISFPdQHQ7du3mTNnzjMVWvE4f39/7O3tGTJkCGlpaXz//fdaRzIrqzrCXL16NSVLlpSBfaEZGxsbjh07RuXKlalWrdqDi4LE8xsxYgSRkZEkJSXle52ZM2fSsmVLXF1dTZiscBk0aBDz5s3jp59+KnTz3At8wVRVlS+++IJdu3bx66+/EhQUJAP7QlM6nY6DBw9SrVo1qlevTmxsrNaRrELZsmXp1KkTU6dOzdfyWVlZhIaGylQSE+jduzcLFy4kPDwcf39/reOYTYEvmAD/+c9/aN68OevXrycjI4P09HStI4lCTqfTsXv3bvz8/KhZsybHjh3TOpJV0y6P4wAAIABJREFUCA4OJjw8nMzMzCcuu379euzs7GjSpIkZkhU+b775Jn/++SdTp05l0KBBWscxiwJfMBVFwdHRkbS0NDIzMxk5cmShHZAWlkWn07Ft2zYaNmxIrVq1OHDggNaRCrw6depQrlw5VqxY8cRlZSqJ6XXs2JFVq1Yxd+5cevfu/eD1GzduaJjKdAp8wQQe3JbM0dGR1q1b89lnn2mcSAg9RVGIjo6mefPm1K9fn927d2sdqcC7P8UkL3/99Rc7d+6kX79+ZkpVeLVp04YNGzawaNEiunbtyieffIKrqyspKSlaRzM6qyiYqqqiKAr+/v5ERUVRrFgxrSMJ8ZDVq1fToUMHGjVqxJYtW7SOU6D16NGDY8eOceLEiVyXCQ8PZ8iQIXKPXzNp2rQpmzdv5s8//+Srr74C9A+mtjYFalpJYnI6kfsvEHv5FrfSMnBysMHbxYmKHtUYOrQ+33zzjdYRhcjV0qVL6dmzJy1atGDNmjW0bNlS60gFkp2dHf7+/oSGhhIWFvbY+3fu3GHGjBlGfSyYeLJdu3ZhZ2dHeno6KSkpTJ48+bEbTeS2D+9Ry5UXi9trlDz/FFVVc32zdu3a6r59+8wYJ2eHz98kbFMCm+OuAZCe8b8n3jvY6FCBZl5lGN3UnRovOWuUUoj8GThwIPPmzWPZsmV06NBB6zgF0qVLl6hevTqnT5+mZMmSD703adIkVq5cKXf2MbOAgABmzJiBjY0Nd+7cQVEUrl+/zgsvvFDg9uGKouxXVbX2o69b/CnZObvO0HvyLtaduEJ6RtZDGxogzfDa2pgr9J68izm7zmgTVIh8mjVrFoMHD6ZTp04sWbJE6zgFUvny5WnTpg0zZsx46HVVVeVJRRqJiIggKSmJuXPn0rp1a1RVpWfPnszeaT37cIsumHN2nWFC1AlS72WSx4EwAKoKqfcymRB1wqI3uBAAU6ZMISAggO7du7NgwQKt4xRI9y/+ycr63w548+bNZGRk0KpVKw2TFV5Fixalc+fOrF27lqtXr3LRsTKf/3nEavbhFlswD5+/yYSoWFLvZeX4/r2ki5z9viuJy3946PXUe1lMiIrlyAV51JKwbGFhYbz11lv07t2b2bNnax2nwGnYsCElSpRg7dq1D167f3QpU0m0dynNlqwaXchUijz0embqba4u+pJzP3bjQvgQ7hzf9ND7lrwPt9iCGbYpgbSM3CcnJ62NwP5fHjm+l5aRSfimBFNFE8JofvzxRz766CMGDRrElClTtI5ToCiKQnBwMCEhIQCcO3eOjRs3MnDgQI2TCdDvw9MzHz/gSVo7EaWILa7Bcyjd6T2urw3n7rWzDy1jqftwiyyYicnpbI67lush/J2YzegciuHgViPH91UVNp68xvXkh+/4k5ycTF4XOQmhha+++orPPvsMf39/wsPDtY5ToPTu3Zu9e/eSkJBAREQEAwYMoESJElrHKvRy24dn3U0j5eQOnJv0R2fniMNLPhR1r8ed4xsfWi63fbjWLLJgRu6/kOt7Wekp3Nw6lxdaDMuzDQWIPKBv59y5cwwePBhnZ2eOHj1qzKhCGMVnn33GV199RVBQED/99JPWcQoMR0dHhg0bxi+//MKUKVMIDAzUOpIg9314RtJFFJ0O21IVHrxmW/Zl7j1yhAkP78MthUXOw4y9fOuxK6nuu7llNsVrtMHGqUyebaRlZLEr9jxr/vs+UVFRZGZmYm9vT1xcnExmFhape/fu3L59m/fee4+LFy8yatQorSMVCO3bt6d9+/bUrFkTnU5HQoLlncorbPbGX8pxH551LxXF/uH9r86+KFl3Ux9bNi0ji9i/b5ss47OwyIJ5Ky0jx9fvXvmLtLOH+deQX/LVzpade/kr22X7mZmZvPXWW/IgWWHRSpUqxU8//X97dx5XY9r/Afxzn85pk5QsRYppUZZQkaikwkiWqUxMoYyUhBlmhsHMwxhmMMNQSdkJIT22slQquxn7VlH2fRm0b+dcvz88/MYoneqcc5/q+3695vV6ntN9X9cndH+77vu+rmsJ1q5dCz09Pb7jKD3GGIqKinDlyhV8+umnfMchAMS9A4FWnT74XCDSACt5vziykkIIVDUqbCe3uEwu+WpKKQumtnrFsYrvXkb56ye4vyIAAMBKiwEmwaPnUyosokM+dUOfof/Ft99+i8ePH6OsrAw7d+6EnZ2dXPMTUltr1qxBYGAggoOD8csvv/AdR6mdOHECw4cPh46ODq5cuUJvyCqBr7adx64LDz/4XNi0NZhEjLK/H7y7LVv69BZEzSveaF1bXSTXnNWllM8wLfS1oSb8MJpW1wFoHbQarQLC0CogDI27DYSGiS1a+Pz0wbHqQgEsDLQxbNgwXL9+HZs2bYK1tTX09fUV8S0QUitffvklNm3ahEWLFmHq1Kl8x1Fq4eHhmDZtGgQCAVJTU6s+gchdZddwgao6NNvb49XRzZCUFqP4/jUUZp9Go459Pzj2zTVcuV7gUsqC6W1T8e7oApE6VLR03/3HidTBCVWhotnkg2NLSkuh/vACysrKwHEchg0bhhMnTsDYuOLfZAhRNr6+vti6dSuWLVuGkJAQvuMopUePHmH//v0YO3YsQkND300xIfyq7BoOAE37h4CVl+J+mC+e71kMvf4hUK1ghMkAeFtX3g4flHYt2fGbziAp40mVq0NUhANgqV2K/P1LcePGDXz55ZcIDAykYknqpN27d8PT0xNjxozB2rVr+Y6jVObMmYMnT54gMjISBQUFMDY2xtmzZ+lnXQnU6hrOAQM6tMRKvw+Wc1WIOreW7ERnU6gLVao+sALqIhX8Oqovjhw5gpSUFOTl5cHa2hru7u7YvXs3yssrfqmIEGU0dOhQ7Nu3Dxs3boSfnx/fcZRGaWkpoqKi3q0b26hRI4wZM4bmsiqJWl3DhSoIcTaVcaLaU9qC2aWNDma5W0BDVM2I5aUI6aUPK8M3K9536NABy5Ytw7179+Dj44Nff/0Vbdu2xZw5c3D/vnLN8SGkMgMHDsTBgwcRGxv7wZZJDVVcXBwsLS3RsWPHd5+FhIRg7dq1KCr6cJoCUayaXsM1RALMcrd4dw1XJkpbMAHAr2dbzHK3hIZIBVW9+MZxgIZIBX20X+CPiV64c+f9ibCampoYM2YMTp48icTERDx79gxWVlYYOnTou3mahCgzV1dXpKWlYdeuXRg8eDDfcXgXFhaGSZMmvfeZiYkJ7OzssGXLFp5SkX+qyTV8lrsl/Hq2VUi+6lLaZ5j/dOn+K6xIy0Zq1jNweDOh9S1VFQ4lJSXo16kVJru2h5WhDpYvX44lS5YgJSUFJiYmlbabn5+P2NhYREVF4dmzZwgMDMTYsWNhYGCggO+KkJo5ffo0HB0d4ezs/N7C4w3JmTNn4OXlhZycHAiF709DO3jwIKZPn47z58/TFBMl8bFr+Nv9MPu2b44QZ1OlGFlW9gyzThTMt17klyDu3H1kPspDbnEZtNVFsDBojCmD7dBSpxEyMzOhofFmAuzKlSsxf/58pKSkwNzcvMq2z549i6ioKOzYsQMuLi4IDg6Gq6srBAKlHoSTBurChQuws7ODvb09Dh8+3OD+nfr7+8PS0hLTp0//4GsSiQSWlpZYs2YNHBwceEhHKlPZNdzb2hB6Wmp8x3unsoIJxlil/9nY2LC6QEdHhwFgHTt2ZI8ePXr3+Zo1a1irVq3Y1atXpW7r9evXLDIyknXp0oV98skn7Ndff2VPnjyRR2xCauXy5ctMTU2N2dvbM7FYzHcchXn69CnT0dFhz58/r/SY5cuXs88//1yBqUh9AuAMq6Am1otfS9/eksnMzISVlRWuXr0KABg7diwWLlwINzc3XLp0Saq2tLW1ERwcjPPnz2PLli3IysqCubk5RowYgdTUVNrthCiNTp064eLFi7hw4QJ69Ojx3kbK9dmqVavg6en50WUDx4wZg6SkJDx48ECByUh9Vy8KZkFBAYA3a8W+evUKSUlJ777m5+eHpUuXon///jh37pzUbXIcBzs7O6xduxa3b99G7969MWnSJFhYWGDJkiV48eKFzL8PQqqrffv2uHz5MjIyMtC1a9d6P2WqvLwckZGR76aSVEZbWxu+vr5YuXKlgpKRBqGiYSerQ7dkJRIJEwgETEtLiwFgSUlJFR4XHx/PWrRowU6fPl2rvo4ePcr8/PxYkyZNmK+vLzty5AiTSCQ1bpMQWbhz5w7T0tJiFhYWrKysjO84crNjxw7Wu3dvqY7NyMhgLVu2ZMXFxXJOReob1NdbshzH4dSpU3j+/DksLCywYMGCCo/77LPPsGbNGnh4eOD48eM17svBwQGbNm1CTk4ObGxsMG7cOHTq1AnLly/Hy5cva/OtEFJjRkZGyMrKwsOHD2FhYYHS0lK+I8lFRVNJKmNhYQErKyts375dzqlIg1FRFWV1aIT5T3FxcUwgELC8vLxKjzlw4ABr3rw5S0tLk0mfEomEpaamshEjRrAmTZowf39/dvLkSRp1El48efKE6erqMmNjY1ZUVMR3HJm6ePEia9WqFSstLZX6nD179rAePXrIMRWpj1BfR5j/5OXlBW1tbcyaNavSYwYMGIDY2Fh4e3sjOTm51n1yHAdnZ2ds3boV169fh6WlJfz8/NC1a1dERkYiNze31n0QIq0WLVogOzsb+fn5MDMzQ2FhId+RZCY8PBzBwcEQiaTf8snd3R3Pnj3Dn3/+KcdkpKGoVwUTAAIDA7Fu3bqPHuPi4oL4+Hh88cUX2L9/v8z6btGiBb777jtcv34dv//+O1JSUmBsbIzAwECcPXtWZv0Q8jFNmzZFdnY2SktLYWJiUi9+afv777+xY8cOjB8/vlrnqaioYOLEibSLCZGJelcwf/rpJxQWFla5NJajoyN2796NMWPGYM+ePTLNIBAI4Obmhri4OFy7dg3t2rWDl5cXbG1tsWrVKuTn58u0P0L+TUdHBzk5ORAIBDA1NcWrV6/4jlQra9euhYeHB1q2bFntc8eOHYt9+/bhyZMnckhGGpJ6VzDV1dXh5uaG//znP1Uea29vj4SEBAQGBmLnzp1yyWNgYICZM2ciJycH8+bNQ0JCAoyMjBASEoKLFy/KpU9CAEBLSws3btyAhoYGTExM8Pz5c74j1YhYLEZERESVU0kqo6uri+HDhyM6OlrGyUhDU+8KJgAsW7YM2dnZyMrKqvLY7t274+DBgwgNDcXWrVvllklFRQUDBw7Erl27cOnSJbRs2RIeHh6wt7fH+vXr69WzJqI8NDU1kZWVBR0dHZiZmeHx48d8R6q2hIQENG/eHHZ2djVuY9KkSVi5ciXKyspkmIw0NPWyYLZv3x6mpqaYMmWKVMd37doVSUlJmDZtGjZs2CDndIChoSH+85//4NatW5g5cyZ27NiBNm3aYPLkye9WKSJEVtTV1ZGRkYHmzZvD3Ny8zm1rV52pJJXp3LkzzMzMEB8fL6NUpCGqlwUTeLMTe3JyMoqLi6U6vlOnTjh8+DBmzZqF1atXyzndG0KhEIMHD0ZCQgLOnTuHJk2aoF+/fnB0dERMTIzU2QmpiqqqKq5duwYjIyNYWFh8sP2dssrMzMTly5fx+eef17qtSZMmITw8XAapSENVbwumr68vNDU1pXqW+ZaFhQVSU1Px008/KXzXdmNjY8ybNw937tzB119/jU2bNqFNmzaYNm2aVLeWCamKUCjEpUuXYGZmBktLS2RnZ/MdqUrh4eEIDAyEmlrtd7IYOnQo7ty5gwsXLsggGWmI6m3BBN5sAVTdB/1mZmZIT0/H4sWL8ccff8gpWeVEIhE8PT1x8OBBnDp1CiKRCE5OTnBxccG2bdvq7QouRDEEAgHOnj2Lzp07o3PnzsjIyOA7UqVyc3OxZcsWBAcHy6Q9oVCICRMm0BQTUnMVrWbA6uhKP/+Wl5fHBAIB27lzZ7XPvXPnDjMxMWG//vqrHJJVT0lJCYuNjWV9+/ZlLVq0YNOnT2fZ2dl8xyJ1mFgsZg4ODkxNTY1dvHiR7zgVWrZsmcy36JJmazBC0BBW+vk3LS0tODk5Yfbs2dU+18jICOnp6Vi3bh3mzZsnh3TSU1VVhY+PDw4fPoyjR4+ivLwcPXv2RP/+/REfH09v/pFqEwgEOHr0KHr37o3u3btDmTaKB95sAh0eHl7jqSSVad68OYYOHaqw9xRIPVNRFWX1ZITJ2Jv1JzmOYzdv3qzR+Y8ePWIdOnRgs2bNUqr1YYuKilhMTAxzdHRkBgYGbNasWez27dt8xyJ10MCBA5lQKGQnTpzgO8o7+/fvZ126dJHLz9yZM2eYkZFRvd7VhdQOGuIIEwCsrKxgZGSEr776qkbn6+vrIy0tDXv37sX06dOVZgNpdXV1+Pr64siRI0hOTkZeXh6sra0xaNAg7Nmzp97vi0hkJzExER4eHnBycsKRI0f4jgPg/6eScBwn87ZtbGzQunVr7Nu3T+Ztk3quoirK6tEIkzHGVq1axYRCISspKalxG8+fP2fW1tZsypQpSjXS/KeCggK2bt061rNnT2ZoaMjmzJnD7t27x3csUkf4+PgwFRUVdujQIV5z3LhxgzVr1owVFhbKrY8tW7YwFxcXubVP6jY01BEm8GYtSVVVVcyfP7/Gbejp6SElJQWnTp1CSEgIJBKJDBPKhqamJvz9/XHy5Ens27cPT58+hZWVFYYOHYr9+/dDLBbzHZEosdjYWPj6+uLTTz/ldfS1YsUKjB07FhoaGnLrw8vLCxkZGbRQCKkWjn3kFqOtrS1TtpcBamr8+PGIj4+v9Xqaubm5cHd3R/v27REdHQ0VFRUZJZSP/Px8xMbGIioqCs+ePUNgYCDGjh0LAwMDvqMRJTV+/HisWbMGcXFx+OyzzxTad35+PoyNjXHu3DkYGxvLta+5c+fi8ePHiIyMlGs/pO7hOO4sY8z23583iBEmACxatAh///13rbfz0tbWxoEDB3Dz5k34+/sr/bNCLS0tjBs3Dn/99Rd27tyJO3fuoEOHDvD29kZSUpJSjpQJv6KjoxESEgJvb2+5rq9ckZiYGDg5Ocm9WAJAUFAQYmNj6/xOLkRxGkzB1NHRgb29PWbMmFHrtrS0tJCQkIAnT57Az8+vzkzrsLGxQXR0NO7cuQM3Nzd8++23MDc3x6JFi/D06VO+4xElEhYWhqlTp8LX11ch6ysDb96nkMdUksro6+tj4MCBVe6fS8hbDaZgAsAff/yBy5cv48GDB7VuS1NTE3v27EFeXh58fHzq1Ao82traCA4Oxvnz57F582ZkZmbC3NwcI0aMQFpamtK8CUz4tXjxYsycORMBAQEK2RorNTUVjDG4uLjIva+3Jk2ahIiICLrTQqTSoApm9+7d0apVqxpPMfk3dXV1xMfHQyKRwMvLq84tls5xHOzs7LB27Vrcvn0bvXv3RmhoKCwtLbFkyRK8ePGC74iEZz///DN++uknBAcHy31JubejS3lMJalMz549oaOjgwMHDiisT1KHVfTqLKtn00r+afny5UxVVZWVl5fLrM3S0lI2fPhw1r9/f7m+Cq8IEomEHT16lPn5+bEmTZowPz8/dvToUaWdSkMUY+HChYzjOLZo0SK5tH/79m3WtGlTlpeXJ5f2P2b9+vXs008/VXi/RHmhIU8r+aeJEydCIBBg0aJFMmtTJBJhy5YtaNasGTw8PFBQUCCzthWN4zg4ODhg06ZNyMnJQbdu3fDll1+ic+fOCAsLoxckGqjvvvsOS5cuxfTp02s1PasykZGRGD16NLS0tGTedlV8fHxw7tw5XL9+XeF9kzqmoirK6vEIkzHGRo0axVq2bCnzdsvLy5m/vz9zdHRkubm5Mm+fLxKJhKWmprIRI0awJk2aMH9/f3bq1CkadTZAkZGRjOM49sMPP8iszcLCQtasWTN248YNmbVZXTNnzmSTJ0/mrX+iXFDJCLNBFsxnz54xjuNYamqqzNsWi8Vs/PjxzN7enr169Urm7fPtyZMnbOHChczExIR16dKFrVixgr1+/ZrvWESB1q5dyziOY999951M2luzZg0bOHCgTNqqqbt37zJdXd169YsuqTkqmP9ia2vL5PX9SSQSFhoaymxtbdmLFy/k0gffxGIxS0pKYl5eXkxHR4cFBgayM2fO8B2LKEhMTAwTCAS1HpVJJBLWtWtXlpiYKKNkNefl5cXCw8P5jkGUABXMf0lPT2ccx7EnT57IpX2JRMKmTp3Kunbtyp49eyaXPpTFw4cP2fz585mxsTGzsbFhq1at4uXlDaJYcXFxTCAQsKCgoBq3cfToUWZmZsbEYrEMk9VMWloas7CwoEcNhF76+TcnJye0bNkSU6dOlUv7HMfht99+w8CBA9G3b188efJELv0oAwMDA8ycORM5OTmYN28e9u3bByMjI0ycOBGXLl3iOx6REy8vL/z3v//FqlWrEBAQUKM2wsPD372IxzcnJyeIRCKkpKTwHYUoKf7/lfLo66+/RlxcnNwmLXMch/nz58Pb2xvOzs54+PChXPpRFioqKhg4cCB27dqFS5cuoUWLFhg0aBDs7e2xfv16FBYW8h2RyNiQIUOQmJiITZs24YsvvqjWuQ8fPsShQ4fg7+8vn3DVxHEcJk2aJPf5pqQOq2jYyRrALVnG3jyHU1VVZUuXLpV7XwsWLGCmpqbs7t27cu9LmZSVlbHdu3czd3d3pqenxyZPnsyuXr3KdywiYykpKUxFRYV5enpKfc4PP/zAQkJC5Jiq+goKClizZs1qvOE8qR9At2Q/JBAIMHToUCxevFjufX3//fcIDg5Gnz59cPv2bbn3pyyEQiGGDBmChIQEnD17Ftra2nBzc4OTkxM2b95c51ZHIhVzcXFBeno69uzZg0GDBlV5fElJCaKjozFx4kQFpJPe2y3yVqxYwXcUoowqqqKsgYwwGWPswYMHjOM4dvLkSYX0t3z5cmZkZMSys7MV0p8yKi0tZTt37mT9+/dnzZo1Y9OmTWNZWVl8xyIy8OeffzKRSMRcXV0/etymTZuqPIYvOTk5TE9PjxUUFPAdhfAENMKsWKtWrWBlZSW3l3/+bdKkSZg1axacnZ2RlZWlkD6VjUgkgqenJw4ePIhTp05BKBTC0dERLi4u2L59e51ayJ68r3v37vjzzz9x9OhRODk5Vfp+QFhYGCZNmqTgdNL55JNP0KtXL2zevJnvKETZVFRFWQMaYTLG2IEDBxjHcezly5cK63Pt2rWsVatW7MqVKwrrU5mVlJSw2NhY1rdvX9ayZUs2ffp0lpOTw3csUkNXrlxh6urqzM7O7oMpI6dPn2Zt27aV6XrOsnbo0CFmZWVFU0waKNAIs3IDBgyAnp4evvnmG4X1GRAQgEWLFsHNzQ0XL15UWL/KSlVVFT4+Pjh8+DDS09NRVlYGOzs7DBgwAPHx8XVmz1HyRseOHXHp0iVcunQJtra27400w8PDERISAhUVFR4TfpybmxtKS0tx9OhRvqMQZVJRFWUNbITJGGNz5sxhGhoaCp9AvW3bNtaiRQtaJacCRUVFLCYmhjk6OjIDAwM2e/Zsdvv2bb5jkWq4efMma9SoEevUqRMrKytjT548YTo6OnViBazw8HDm7e3NdwzCA9AI8+NmzZqFsrIyrF69WqH9fv7554iKisLAgQNx+vRphfat7NTV1eHr64sjR44gKSkJubm5sLGxwaBBg7B3716Ul5fzHZFUoV27dsjIyMCdO3fQqVMnrFixAt7e3mjatCnf0ao0evRopKSk4N69e3xHIUqCe1NMK2Zra8vOnDmjwDj8GjZsGM6fP487d+4ovO+EhAQEBAQgPj4eDg4OCu+/rigsLMT27dsRFRWF+/fvY9y4cRg3bhxat27NdzTyEY8ePYKFhQUKCgpw8uRJdO/ene9IUpk8eTIaN24sly3NiPLiOO4sY8z235/TCPMfli1bhnv37uH8+fMK73vQoEGIiYmBp6cn0tLSFN5/XfF2ntzJkyexb98+PH36FJ07d8awYcOwf/9+iMViviOSChgYGOC3334Dx3EYPnx4nZl/GxoaitWrV9eZvES+qGD+g7GxMSwtLfH111/z0n///v2xbds2DB8+HElJSbxkqEu6dOmCiIgI3L17Fx4eHvjxxx9hamqKBQsW4PHjx3zHI/+yceNGREdHo6CgAKampsjPz+c7UpXMzc3RrVs3bNu2je8oRAlQwfyXBQsW4OjRo7z9MPft2xfx8fHw9fVFYmIiLxnqGi0tLYwbNw5//fUX4uLicPv2bVhaWsLb2xvJyclyWyuYSO/ChQu4desW/Pz8kJOTg/LycpiamiI3N5fvaFV6u77sxx5fkYaBCua/DB06FE2aNMGMGTN4y+Do6Ig9e/bA398fu3fv5i1HXWRjY4Po6GjcuXMHrq6u+Oabb2Bubo5Fixbh2bNnfMdrsMLDwzFhwgSIRCJoa2sjOzsbQqEQJiYm+Pvvv/mO91EDBw7Eq1ev6KU8QgWzIkFBQdiwYQOvGXr27In9+/cjKCgIO3bs4DVLXaStrY0JEybg/Pnz2Lx5MzIyMmBmZoaRI0ciLS2NRgsK9OLFC+zcuROBgYHvPtPS0kJ2djY0NTVhZmaG58+f85jw4wQCASZOnEi7mBAqmBX5z3/+g6KiImzatInXHDY2Njh48CAmT56MLVu28JqlruI4DnZ2dli3bh1u376NXr16ITQ0FJaWlli6dKnSj27qgzVr1mDw4MFo0aLFe5+rq6vjxo0b0NHRgampqVI/dw4ICEBiYqJSZyTyRwWzAurq6ujXrx/mzp3LdxR06dIFSUlJ+Oabb7B+/Xq+49RpOjo6mDRpEi5fvozVq1fj3LlzMDExwahRo3D8+HEadcqBWCzGihUrKl03VlVVFVlZWdDX14e5uTnu3r2r4ITS0dHRgY+PD6KioviOQnhEBbMSy5cvx82bN5GRkcF3FHTq1AmHDx/G7NmzER0dzXecOo9rca2lAAAgAElEQVTjODg4OGDTpk3Izs5Gt27dMHbsWHTu3BlhYWF49eoV3xHrjb1790JfX/+j8y6FQiGuXLkCIyMjdOjQAbdu3VJgQumFhoYiKiqKNgdowKhgVsLMzAympqaYMmUK31EAABYWFkhLS8P8+fMRHh7Od5x6Q09PD1OnTkVmZibCw8Nx4sQJtGvXDmPHjsXp06dp1FlL4eHhUu1KIhQKcenSJZibm6Njx464ceOGAtJVT6dOnWBhYYH4+Hi+oxCeUMH8iHnz5uHw4cNKM2nZ1NQUaWlp+P3337FkyRK+49QrHMfB2dkZW7duRVZWFiwsLODr6wtra2usXLkSeXl5fEesc65du4arV69i+PDhUh0vEAhw5swZWFlZwcrKClevXpVzwup7O8WENExUMD/Cx8cHjRo1wuzZs/mO8k67du2Qnp6OyMhI/PLLL3zHqZdatGiB7777DtevX8eiRYuQnJwMIyMjBAUF4dy5c3zHqzPCw8Mxfvx4qKqqSn2OQCDAiRMn0L17d1hbW+PChQtyTFh9gwcPxv379+nfQQNFBbMK/v7+Cl+QvSpGRkZIT0/Hhg0bMHfuXLptKCcCgQD9+vVDXFwcrl27BiMjI3h6eqJ79+5YvXo1CgoK+I6otF6/fo2tW7ciKCio2ucKBAIcOXIEjo6O6NGjB/766y85JKwZoVCIkJAQGmU2VBVtYcIa4PZelSkoKGACgYDt2LGD7ygfePz4MevYsSObOXMmbXSrIOXl5SwxMZENHTqU6erqspCQEHbx4kW+YymdpUuXMh8fn1q3M2jQICYUCtmxY8dkkEo2nj9/znR0dNjTp0/5jkLkBLS9V81oamrC2dkZP/zwA99RPtCyZUukpqYiISEB3377LY00FUBFRQUDBw7Erl27cOnSJbRo0QKDBg1Cr169sGHDBhQVFfEdkXcSiQQRERFSvexTlX379mHw4MHo06eP0mxKoKenh88++0zp7jwRBaioijIaYb7n8uXLjOM4lp2dzXeUCr148YLZ2NiwSZMm0UiTB2VlZWz37t3M3d2d6enpscmTJ7OrV6/yHYs3CQkJrFu3bjL9tzhy5EimoqLCDhw4ILM2a+PcuXOsTZs2rKysjO8oRA5AI8ya69SpE9q2bas0U0z+rWnTpkhOTsZff/2F4OBgWmxcwYRCIYYMGYKEhAScOXMGjRs3hpubG5ycnLBlyxaUlJTwHVGh3k4l4ThOZm1u2bIFo0aNgru7O/bs2SOzdmuqW7duMDIyUoosRIEqqqKMRpgfWLt2LRMKhaykpITvKJXKzc1lDg4OzN/fn5WXl/Mdp0ErLS1lO3fuZP369WPNmzdn06ZNY1lZWXzHkrvr16+z5s2bs8LCQrm0HxQUpDTvFMTGxjJnZ2e+YxA5AI0waycgIABqamr46aef+I5SqcaNG+PAgQO4c+cORo8ejfLycr4jNVgikQienp44dOgQTp48CaFQCEdHR7i6umL79u31drWYiIgIfPnll9DQ0JBL+ytXrkRoaCh8fHywefNmufQhLU9PT1y/fh2XL1/mNQdRoIqqKKMRZoWCgoJY06ZN+Y5RpYKCAta/f382fPhwVlpayncc8j8lJSUsNjaW9e3bl7Vs2ZJNnz6d5eTk8B1LZvLy8ljTpk3Z7du35d7Xt99+yziOY2vXrpV7Xx/z008/sfHjx/OagcgeaIRZe4sWLcKrV6+QkJDAd5SP0tTUxO7du1FYWIjPP/+8wT1DU1aqqqrw8fHB4cOHkZ6ejrKyMtjZ2WHAgAGIj49HWVkZ3xFrZePGjejTpw+MjY3l3teiRYswe/ZsfPnll7wuiB4YGIjt27fj5cuXvGUgClRRFWU0wqyUg4MD69y5M98xpFJSUsKGDRvG3N3dWVFREd9xSAWKiopYTEwMc3BwYK1atWKzZ89WyAhN1iQSCbO0tGSHDx9WaL8///wz4ziO/fHHHwrt9598fX3Zb7/9xlv/RPZAI0zZWLp0Ka5cuYL79+/zHaVKqqqq2L59O7S0tDBkyBAUFhbyHYn8i7q6Onx9fXH06FEcOnQIubm5sLa2hoeHB/bu3QuxWMx3RKmkpKRARUUFzs7OCu131qxZWLRoEb7++mssWrRIoX2/NWnSJERERNSZvytSc1Qwq8nW1haGhoZKO8Xk30QiETZv3oyWLVti0KBByM/P5zsSqUTHjh2xbNky3Lt3D97e3liwYAHatm2LuXPn4sGDB3zH+6jw8HCEhobKdCqJtL755hssW7YMM2bMwM8//6zw/u3s7NCsWTPs379f4X0TBato2MnoluxHRUREMJFIVKcmLZeXl7OAgADm4ODAXr9+zXccIqULFy6wCRMmMF1dXTZ06FCWmJiodFOGbt26xfT09Fh+fj6vOaKiohjHcWz27NkK73vjxo2sf//+Cu+XyAcquSVLBbMGxGIxU1dXZz///DPfUapFLBazoKAgZmdnx16+fMl3HFINeXl5bNWqVczGxoa1bduWzZ8/nz169IjvWIyxN2+sTp06le8YjDHG1q9fzziOY998841C+y0uLmYtW7ZkmZmZCu2XyEdlBZNuydaAQCCAj48Pli9fzneUahEIBIiMjESPHj3g5uaGv//+m+9IREpaWloYN24czpw5g7i4ONy+fRuWlpYYPnw4kpOTeVvdqbCwEGvXrkVISAgv/f/bmDFjsGXLFixZskQma9lKS01NDYGBgbS5e31XURVlNMKs0osXLxjHcSwlJYXvKNUmkUjYN998w7p06UI7LtRhr1+/ZitWrGBdunRhJiYmbOHChQr/+1y1ahUbNGiQQvuUxs6dO5lAIGCBgYEK6/PevXtMV1eXHnnUA6ARpmw1bdoU3bt3x7fffst3lGrjOA6LFi3CoEGD0LdvXzx+/JjvSKQGtLW1MWHCBJw/fx4xMTHIyMiAubk5Ro4cibS0NLnvXsMYQ1hYmEJHctLy9PTE7t27sWbNGvj7+yukT0NDQ7i5uWHDhg0K6Y/woKIqymiEKZVjx44xjuOU5llSdUkkEjZ37lzWvn17dv/+fb7jEBn4+++/2bJly1iHDh1Y+/bt2ZIlS9iLFy/k0teRI0eYubk5E4vFcmlfFg4dOsRUVFRksjenNOrCnwmpGmiEKXu9e/eGvr4+pk6dyneUGuE4Dj/++CP8/f3Rp08f3L17l+9IpJZ0dXUxefJkXLlyBatXr8a5c+fwySefYNSoUTh+/LhMR51hYWEIDQ2FQKC8l5F+/fohJSUFO3fuxGeffSb3/hwcHKChoYHk5GS590V4UFEVZTTClNrixYuZmppanf+NcsmSJaxt27bs5s2bfEchMvb8+XP2+++/M3Nzc9axY0e2fPnyWr8lXdee1x0/fpwJhUI2cOBAufe1evVq5uHhIfd+iPyAppXIh1gsZmpqauz333/nO0qthYeHMyMjI3bjxg2+oxA5kEgk7PDhw8zHx4fp6OiwgIAAdurUqRpt9Dxr1iw2ceJEOaSUn7/++ouJRCLm4uIi134KCwtZs2bN6tXC+g1NZQVTee+l1BECgQCfffYZfvvtN76j1NrEiRMxe/ZsODs7IzMzk+84RMY4jkPfvn0RGxuLrKwstG/fHl988QWsra2xcuVK5OXlSdVOcXExVq1ahdDQUDknli1bW1ucOXMGx48fh6Ojo9ym4mhoaCAgIAARERFyaZ/wqKIqymiEWS2PHj1iHMexY8eO8R1FJtatW8cMDAzY5cuX+Y5C5EwsFrNDhw4xLy8vpqOjw8aPH8/Onj370XM2bNjA+vXrp6CEsnft2jWmrq7OunfvLrdHKcqy+hGpGdAIU3709fXRtWtXTJs2je8oMuHv74/ffvsNbm5uuHDhAt9xiBwJBAL069cPcXFxuHbtGoyMjODp6Ynu3btj9erVKCgoeO94psRTSaRlaWmJS5cu4cqVK7CxsZHLSLNt27ZwcHBATEyMzNsmPKqoijIaYVZbcnIy4zhObq/w82HHjh2sRYsW7K+//uI7ClGg8vJylpCQwIYMGcJ0dXVZSEgIu3jxImOMsVOnTrF27dop3Xq2NXH79m3WqFEj1rFjR7msC52cnMw6depUo2fEhF+gEaZ8ubq6olmzZvVmlAkA3t7eiI6Ohru7O06ePMl3HKIgKioqcHd3x+7du3Hx4kU0b94c7u7u6NWrF77++muMHz8eKioqfMesNWNjY2RmZuLu3bvo2LEjSktLZdq+i4sLJBIJ0tPTZdou4Q8VTBmaNGkStm3bxtu6nvIwdOhQrF+/HkOGDMHRo0f5jkMUrE2bNpgzZw5u376NoKAg/PXXX1i8eDGmTJmCa9eu8R2v1gwNDXH9+nU8efIElpaWKC4ullnbHMchNDQUYWFhMmuT8IsKpgx9//33KC8vR1RUFN9RZMrd3R1btmyBp6cnDh8+zHccwgOhUIg7d+4gICAAZ8+eRePGjeHm5gYnJyds3rxZpoVG0fT19ZGdnY1Xr17B3Nxcphutjxo1CmlpabQoSD3BsY+s/GFra8vOnDmjwDh1n6enJ86cOVMvf0DS0tIwfPhwxMTEYMCAAXzHIQpUWlqKtm3b4uDBg+jcuTMAoKysDHv27EFUVBQuXLiA0aNHY/z48TA3N+c5bc28LZgikQhZWVnQ0tKSSbtfffUVNDQ08Msvv8ikPSJ/HMedZYzZ/vtzGmHK2B9//IH79+/j3LlzfEeROWdnZ+zatQujRo3Cvn37+I5DFCg+Ph7m5ubviiUAiEQieHl54dChQzhx4gRUVFTg6OgIV1dXbN++XebPBOVNR0cH2dnZkEgkMDU1RW5urkzanThxItasWYOioiKZtEf4QwVTxoyMjNCxY0d89dVXfEeRi969e2Pv3r0YO3Ys/vvf//IdhyhIeHj4R6eSmJqaYuHChbh79y7Gjx+PyMhIGBkZYcaMGbh586YCk9aOtrY2cnJyIBQK8cknn8hkz1gzMzPY2tpi27ZtMkhI+EQFUw5++eUXHD9+XGa/oSobOzs77N+/HxMmTMD27dv5jkPk7Pz587h79y6GDh1a5bFqamrw8fFBamoq0tPTUVZWBjs7OwwYMADx8fEoKytTQOLa0dTURHZ2NrS0tGBqaoqnT5/Wus1JkyYhLCxM7luuEfmigikHHh4e0NHRwYwZM/iOIjc2NjY4ePAgpkyZQpOz67mwsDBMmDABQqGwWue1b98ev//+O+7du4dRo0Zh6dKlMDY2xg8//IA7d+7IKa1sqKur4/r162jatCnMzMzw8OHDWrU3YMAA5OXl0fSsOo4KppwEBwdj48aNfMeQqy5duiA5ORnTp0/HunXr+I5D5OD58+eIj4/HuHHjatyGuro6/Pz8cPToUSQlJeH169ewtraGh4cH9u7dC7FYLMPEsqOqqorMzEy0atUK7du3r9WLfAKBABMnTqQpJnVdRasZMFrpp9ZKSkqYUChk69ev5zuK3GVmZjJDQ0O2cuVKvqMQGfvll1/YmDFjZN5uQUEBW7duHbOzs2OGhoZszpw5SruJeXl5OevcuTPT1NSs1fZ3r169Yrq6uuzBgwcyTEfkAbTSj2Kpqqqif//++Omnn/iOInft27dHamoqFixYQL9B1yPl5eVYsWKFXNaN1dTUhL+/P06dOoV9+/bhyZMn6Ny5M4YNG4b9+/cr1ahTRUUFFy5cgIWFBTp27IisrKwatdOkSROMGDGi3s3TblAqqqKMRpgykZ2dzTiOY1euXOE7ikLcunWLtWvXji1evJjvKEQGdu7cyezt7RXWX15eHouOjmY2Njasbdu2bP78+ezRo0cK678qYrGY2dvbMzU1tRrv5HP16lWmr6/PSkpKZJyOyBJohKl4JiYmMDc3x5QpU/iOohBt27ZFeno6oqOjMX/+fL7jkFqqaiqJrGlpaSEwMBBnzpzBjh07cOvWLVhaWsLb2xvJycm8LzkpEAhw7Ngx9OzZEzY2NjWaa92hQwd07NgRcXFxckhI5K6iKspohCkz27dvZwKBgBUUFPAdRWEePnzILCws2I8//kg7NdRRly9fZgYGBryPhF69esUiIiKYlZUVMzExYQsXLmRPnz7lNRNjjPXr14+JRCJ26tSpap+7a9cu1rNnTzmkIrICGmHyY/jw4dDS0sLs2bP5jqIwBgYGSEtLQ3x8PGbOnElzz+qg8PBwBAUFQVVVldccTZo0QUhICC5cuICYmBhkZGTAzMwMI0eORFpaGm//tg4dOoQBAwbAwcEBx44dq9a5Hh4eePz4MWjZ0bqHCqYCjBs3DmvWrOE7hkK1bNkSqampOHDgAKZNm0ZFsw55+fIltm3bhvHjx/Md5R2O49CzZ0+sW7cOt27dgr29PSZOnAhLS0ssXbpUJivyVNfevXsxdOhQODs7V2tTAhUVFYSEhNALcnVRRcNORrdkZaqgoIAJBAK2bds2vqMo3IsXL5itrS2bOHEiE4vFfMchUvj999/ZyJEj+Y5RJYlEwo4ePcp8fX1ZkyZNmJ+fHzt27JjCHwP4+voyFRUVlpiYKPU5z58/Zzo6OuzJkydyTEZqCnRLlj+amppwcXHBDz/8wHcUhWvatCmSk5Nx7tw5BAcH8/7iBvk4sViMiIgIhb7sU1Mcx8HBwQExMTHIyclBt27dMHbsWHTu3BlhYWF49eqVQnLExMRg9OjR8PDwwJ49e6Q6R09PD15eXli1apWc0xGZqqiKMhphytyVK1cYx3Hs+vXrfEfhRW5uLnNycmJjxoxh5eXlfMchldi7dy+zsbGpsy9rSSQSdvjwYebj48OaNGnCAgIC2KlTpxTy/QQHBzOBQMC2b98u1fEXLlxgrVu3ZqWlpXJORqoLNMLkV8eOHdGuXbt6u4tJVRo3bozExETcu3cPo0ePRnl5Od+RSAXeTiXhOI7vKDXCcRz69u2L2NhYXL9+He3bt8cXX3yBbt26YeXKlcjLy5Nb35GRkZg8eTJGjBiBzZs3V3l8ly5d8Mknn2D37t1yy0RkrKIqymiEKRfr169nKioqvL+qz6fCwkI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      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "nx.draw_networkx(di_G, pos = pos)\n",
    "plt.title(\"Directed graph after orienting v-structures\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Meek Rules <a name=\"meek\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def not_directed(edge,di_G): # check if a<->b return True\n",
    "    a = edge[0]\n",
    "    b = edge[1]\n",
    "    \n",
    "    if (a,b) in di_G.edges and (b,a) in di_G.edges:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_directed(edge,di_G): # check if a->b return True\n",
    "    a = edge[0]\n",
    "    b = edge[1]\n",
    "    \n",
    "    if (a,b) in di_G.edges and (b,a) not in di_G.edges:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def no_edge(a,b,di_G): # check if no edge a-b return True\n",
    "    if (a,b) not in di_G.edges and (b,a) not in di_G.edges:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check if the edge a-b is already directed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_1(edge, G, di_G):\n",
    "    \n",
    "    if not_directed(edge,di_G)==False: # already directed\n",
    "        return 0\n",
    "    \n",
    "    a = edge[0]\n",
    "    b = edge[1]\n",
    "\n",
    "    # list of possible c\n",
    "    neghs_a = set(G.neighbors(a)) - {b} # neigbours of a\n",
    "\n",
    "    # c if exists c->a\n",
    "    c_linked_a = [c for c in neghs_a if is_directed([c,a],di_G)]\n",
    "    # c cannot be linked to b in G\n",
    "    c = [c for c in c_linked_a if no_edge(c,b,di_G)]\n",
    "    \n",
    "    # if c is not empty\n",
    "    if len(c)>0:\n",
    "        di_G.remove_edge(b,a) # from a<->b to a->b\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": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_2(edge, G, di_G):\n",
    "    \n",
    "    if not_directed(edge,di_G)==False: # already directed\n",
    "        return 0\n",
    "    \n",
    "    a = edge[0]\n",
    "    b = edge[1]\n",
    "    \n",
    "    # list of possible c\n",
    "    neghs_a = set(G.neighbors(a)) - {b} # neigbours of a\n",
    "    \n",
    "    # c if exists a->c\n",
    "    c_linked_a = [c for c in neghs_a if is_directed([a,c],di_G)]\n",
    "    \n",
    "    # c if exist c->b\n",
    "    c = [c for c in c_linked_a if is_directed([c,b],di_G)]\n",
    "    \n",
    "    # if c is not empty\n",
    "    if len(c)>0:\n",
    "        di_G.remove_edge(b,a) # from a<->b to a->b\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": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_3(edge, G, di_G):\n",
    "    \n",
    "    if not_directed(edge,di_G)==False: # already directed\n",
    "        return 0\n",
    "    \n",
    "    a = edge[0]\n",
    "    b = edge[1]\n",
    "\n",
    "    # list of possible c or d\n",
    "    neghs_a = set(G.neighbors(a)) - {b} # neigbours of a\n",
    "    \n",
    "    # c(d) if exist c(b)->b\n",
    "    c_or_d = [c for c in neghs_a if is_directed([c,b],di_G)]\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 no_edge(c,d,di_G)]\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.remove_edge(b,a) # from a<->b to a->b\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": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def meek_rule_4(edge, G, di_G):\n",
    "    \n",
    "    if not_directed(edge,di_G)==False: # already directed\n",
    "        return 0\n",
    "    \n",
    "    a = edge[0]\n",
    "    b = edge[1]\n",
    "    \n",
    "    # list of possible c or d\n",
    "    neghs_a = set(G.neighbors(a)) - {b} # neigbours of a\n",
    "    \n",
    "    # c if exist c->b\n",
    "    c_list = [c for c in neghs_a if is_directed([c,b],di_G)]\n",
    "    \n",
    "    flag = 0\n",
    "    for c in c_list:\n",
    "        \n",
    "        # d if d-a and d->c\n",
    "        possible_d = [d for d in neghs_a-{c} if is_directed([d,c],di_G)]\n",
    "            \n",
    "        if possible_d is not None:\n",
    "\n",
    "            # d not linked to b\n",
    "            possible_d = [ d for d in possible_d if no_edge(d,b,di_G)]\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.remove_edge(b,a) # from a<->b to a->b\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": 36,
   "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",
    "        for edge in di_G.edges(): # for each edge\n",
    "\n",
    "            if not_directed(edge,di_G): # if not directed\n",
    "\n",
    "                # try to orient \n",
    "                a = edge[0]\n",
    "                b = edge[1]\n",
    "\n",
    "                meek1= meek_rule_1(edge, G, di_G)\n",
    "                meek2= meek_rule_2(edge, G, di_G)\n",
    "                meek3= meek_rule_3(edge, G, di_G)\n",
    "                meek4= meek_rule_4(edge, 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 di_G"
   ]
  },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Meek2 3->7: exist 4 such that 3->4 and 4->7 (avoid cycle)\n",
      "Meek1 4->5: exist 0 such that 0->4 and (0,5) not in G\n"
     ]
    }
   ],
   "source": [
    "di_G = meek_rules(G,di_G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</svg>\r\n"
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      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
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     },
     "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": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# check if we have a dag between the directed eges\n",
    "def is_dag(di_G):\n",
    "\n",
    "    directed = [edge for edge in di_G.edges() if not_directed(edge,di_G)==False]\n",
    "    di_G_un = nx.DiGraph()\n",
    "    di_G_un.add_edges_from(di_G_un)\n",
    "\n",
    "    try:\n",
    "        find_cycle(di_G_un)\n",
    "    except:\n",
    "        # print(\"No cycles (GOOD)\")\n",
    "        return True"
   ]
  },
  {
   "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": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def undirected_edges(G,di_G):\n",
    "    \n",
    "    undirected = []\n",
    "\n",
    "    for edge in G.edges():\n",
    "        if not_directed(edge,di_G): # not directed\n",
    "            undirected.append(edge)\n",
    "    \n",
    "    return undirected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 2), (2, 3)]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "undirected_edges(G,di_G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 42,
     "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": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equivalence_classes(equi_classes, G, di_G):\n",
    "    \n",
    "    undirected = undirected_edges(G,di_G)\n",
    "    directed = [edge for edge in di_G.edges() if not_directed(edge,di_G)==False]\n",
    "    \n",
    "    if len(undirected)==0: # all already directed\n",
    "        print(\"a\")\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.remove_edge(undirected[0][1],undirected[0][0])\n",
    "        G2.remove_edge(undirected[0][0],undirected[0][1])\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",
    "        # equivalent graph\n",
    "        equivalent_G = nx.DiGraph()\n",
    "        equivalent_G.add_edges_from(di_G.edges())\n",
    "        \n",
    "        #### we try to add one edge in one direction\n",
    "        added_edge = undirected[0]\n",
    "        print(f\"ADD EDGE: {added_edge}\")\n",
    "        \n",
    "        equivalent_G.remove_edge(added_edge[1], added_edge[0]) # add 0->1\n",
    "        \n",
    "        # now we check if other edges are still undirected or if we can direct some:    \n",
    "        \n",
    "        print(\"\\nMeek 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(f\"\\nAdding {added_edge}, all 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",
    "        equivalent_G1 = nx.DiGraph()\n",
    "        equivalent_G1.add_edges_from(di_G.edges())\n",
    "        \n",
    "        print(f\"\\n\\nADD EDGE: {added_edge[1],added_edge[0]}\")\n",
    "        \n",
    "        equivalent_G1.remove_edge(added_edge[0], added_edge[1]) # add 1->0\n",
    "        \n",
    "        # now we check if other edges are still undirected or if we can direct some:\n",
    "        \n",
    "        print(\"\\nMeek Rules:\")\n",
    "        meek_rules(G, equivalent_G)\n",
    "\n",
    "        if not undirected_edges(G,equivalent_G1) and is_dag(equivalent_G1) == True: # all directed and it is a DAG\n",
    "            print(f\"\\nAdding {added_edge[1],added_edge[1]}, all directed \\n\")\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",
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--------------------------\n",
      "Unidrected edge: [(0, 2), (2, 3)]\n",
      "\n",
      "ADD EDGE: (0, 2)\n",
      "\n",
      "Meek Rules:\n",
      "Meek1 2->3: exist 0 such that 0->2 and (0,3) not in G\n",
      "\n",
      "Adding (0, 2), all directed \n",
      "\n",
      "\n",
      "\n",
      "ADD EDGE: (2, 0)\n",
      "\n",
      "Meek Rules:\n",
      "\n",
      "--------------------------\n",
      "Unidrected edge: [(2, 3)]\n",
      "\n",
      "Only one undirected edge\n"
     ]
    }
   ],
   "source": [
    "equi_classes = []\n",
    "equi_classes = equivalence_classes(equi_classes, G, di_G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def num_equivalence_class(equi_classes):    \n",
    "    return len(equi_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have found the number of equivalent classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num = num_equivalence_class(equi_classes)\n",
    "num"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot equivalent classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "text/plain": [
       "<Figure size 432x1296 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if num>1:\n",
    "    fig, axes = plt.subplots(nrows=num, ncols=1, figsize = ( 6 , num*6))\n",
    "    ax = axes.flatten()\n",
    "    for i in range(num):\n",
    "        nx.draw_networkx(equi_classes[i], pos = pos, ax=ax[i])\n",
    "        ax[i].set_axis_off()\n",
    "\n",
    "    plt.show()\n",
    "else:\n",
    "    fig, axes = plt.subplots(figsize = ( 6 , num*6))\n",
    "    nx.draw_networkx(equi_classes[i], pos = pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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