C2W2_11DIJKSTRA'S_SHORTEST-PATH_ALGORITHM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Introduction\n",
    "The algorithm, given a directed graph and a starting vertex, it will find the shortest paths between the starting vertex and all vertices it can reach. The algorithm only works when the paths have non negative edges connecting the vertices.\n",
    "\n",
    "Thus, given a graph G = (V, E), a starting vertex s $\\in$ V and non negative edges of length $l_e$ where e $\\in$ E, the output of the algorithm is dist(s, v) for every vertex v $\\in$ V\n",
    "\n",
    "The dist(s, v) denotes the shortest distance from s to v and dist(s, v) = $\\infty$ if there is no path from s to a vertex v.\n",
    "***\n",
    "We have seen how BFS can be used to find the shortest path to any vertex from a vertex. This is a special case of graph where each edge has unit length. Djikstra's algorithm is more generic in a way where each edge can have a weight of non positive value.\n",
    "\n",
    "But can we reduce this graph to a graph where edges are of unit length? That is, if an edge between two vertices have a weight 5, we can replace this edge (with the two vertices) with 5 vertices connected one after other with each edge length of 1 as seen in the following graph\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "DG = nx.DiGraph()\n",
    "edges = [(1, 2, 5), (3, 4, 1), (4, 5, 2), (5, 6, 4), (6, 7, 1)]\n",
    "DG.add_weighted_edges_from(edges)\n",
    "pos = nx.spring_layout(DG,k=0.55,iterations=20)\n",
    "   # k controls the distance between the nodes and varies between 0 and 1\n",
    "    # iterations is the number of times simulated annealing is run\n",
    "    # default k =0.1 and iterations=50\n",
    "weights =nx.get_edge_attributes(DG, 'weight')\n",
    "nx.draw_networkx_edge_labels(DG, pos=pos,  edge_labels = weights)\n",
    "nx.draw(DG, pos=pos, with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x151da86050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = nx.spring_layout(DG)    # spring_layout randomness causes pos to be random\n",
    "nx.draw_networkx_edge_labels(DG, pos=pos,  edge_labels = weights)\n",
    "nx.draw(DG, pos=pos, with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XQa/mNaqcSSlnUsqZlAo6k3jhTim/wMvKlfkHBA0N/Qfce/3clStrfiGYMeVMSjmTUs6kVMCZxHmPu5zjx/M/Oz18OD8ZfsYMuOoqWLt2/P0/VowVZ1LKmZRyJqUCzSR2uCVpAorz4aQkCTDckhSO4ZakYAy3JAVjuCUpGMMtScEYbkkKxnBLUjCGW5KCMdySFIzhlqRgDLckBWO4JSkYwy1JwRhuSQrGcEtSMIZbkoIx3JIUjOGWpGAMtyQFY7glKRjDLUnBGG5JCsZwS1IwhluSgvl/Yepy/7wiDHQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x151e810e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "g1 = nx.DiGraph()\n",
    "g1.add_node(1, pos = (0, 5))\n",
    "g1.add_node(2, pos = (20, 5))\n",
    "g1.add_edge(1, 2, weight = 5)\n",
    "pos = nx.get_node_attributes(g1, 'pos')\n",
    "weights =nx.get_edge_attributes(g1, 'weight')\n",
    "nx.draw_networkx_edge_labels(g1, pos, edge_labels = weights)\n",
    "nx.draw(g1, pos, with_labels = True)\n",
    "\n",
    "g2 = nx.DiGraph()\n",
    "g2.add_node(1, pos = (0, 0))\n",
    "g2.add_node(2, pos = (5, 0))\n",
    "g2.add_node(3, pos = (10, 0))\n",
    "g2.add_node(4, pos = (15, 0))\n",
    "g2.add_node(5, pos = (20, 0))\n",
    "g2.add_edge(1, 2, weight = 1)\n",
    "g2.add_edge(2, 3, weight = 1)\n",
    "g2.add_edge(3, 4, weight = 1)\n",
    "g2.add_edge(4, 5, weight = 1)\n",
    "pos = nx.get_node_attributes(g2, 'pos')\n",
    "weights =nx.get_edge_attributes(g2, 'weight')\n",
    "nx.draw_networkx_edge_labels(g2, pos, edge_labels = weights)\n",
    "nx.draw(g2, pos, with_labels = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea sounds right and also works well for small graphs with small length edges. But imagine graphs with vertices of length order or magnitude larger than the number of vertices in a graph (e.g. two vertices connected by edge of length 100 gets transformed to a graoh with 100 vertices each of unit length).\n",
    "\n",
    "Though BFS runs in linear time of the input graph size, the transformed graph is way larger that the original graph and hence the time complexity is no longer linear with respect to the original input graph and thus this appoach, though clever doesn't practically scale to all graphs.\n",
    "***\n",
    "# Dijkstra's Shortest-Path Algorithm\n",
    "Let us now look at an implementation of Djikstra's algorithm. Though the implementation here can use heap, we will not use it and stick to the approach the Pseudo code gives in thic chapter. This implementation will use Heap in future notebook and we will be able to appreciate the how the choice of right datastructure is crucial even for the same algorithm\n",
    "\n",
    "## Dijkstra's Algorithm Naive implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex 1\n",
      "Vertex 1 is at distance 0\n",
      "Vertex 2 is at distance 1\n",
      "Vertex 3 is at distance 3\n",
      "Vertex 4 is at distance 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f696d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def djikstra_naive(DG, source):\n",
    "    #Naive implementation which does the following\n",
    "    #\n",
    "    # 1. For vertices in X, find all edges originating from them to all vertices not in X\n",
    "    # 2. Keep track of minimum value of len(w) + lwv\n",
    "    # 3. Return w, v and lwv\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                dji_greedy = A[edge[0]] + DG.edges[edge[0], edge[1]]['weight'] #djikstra's greedy criterion\n",
    "                if edge[1] not in A:\n",
    "                    A[edge[1]] = dji_greedy\n",
    "                elif dji_greedy < A[edge[1]]:\n",
    "                    A[edge[1]] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    w_overall = edge[1]  \n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "    print(\"Printing minimum distances from starting vertex {}\".format(source))\n",
    "    for node in A:\n",
    "        print(\"Vertex {} is at distance {}\".format(node, A[node]))\n",
    "        \n",
    "        \n",
    "\n",
    "DG = nx.DiGraph()\n",
    "DG.add_node(1, pos = (0, 5))\n",
    "DG.add_node(2, pos = (7, 10))\n",
    "DG.add_node(3, pos = (7, 0))\n",
    "DG.add_node(4, pos = (14, 5))\n",
    "DG.add_edge(1, 2, weight = 1)\n",
    "DG.add_edge(2, 3, weight = 2)\n",
    "DG.add_edge(3, 4, weight = 3)\n",
    "DG.add_edge(1, 3, weight = 4)\n",
    "DG.add_edge(2, 4, weight = 6)\n",
    "pos = nx.get_node_attributes(DG, 'pos')\n",
    "weights =nx.get_edge_attributes(DG, 'weight')\n",
    "nx.draw_networkx_edge_labels(DG, pos, edge_labels = weights)\n",
    "nx.draw(DG, pos, with_labels = True)\n",
    "\n",
    "djikstra_naive(DG, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex 1\n",
      "Vertex 1 is at distance 0\n",
      "Vertex 2 is at distance 1\n",
      "Vertex 3 is at distance 3\n",
      "Vertex 4 is at distance 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x151e6cead0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def djikstra_naive_nx(DG, source):\n",
    "    #Naive implementation which does the following\n",
    "    #\n",
    "    # 1. For vertices in X, find all edges originating from them to all vertices not in X\n",
    "    # 2. Keep track of minimum value of len(w) + lwv\n",
    "    # 3. Return w, v and lwv\n",
    "    X = [source]\n",
    "    A = [source]\n",
    "    all_nodes = list(DG.nodes)\n",
    "    for node in all_nodes:\n",
    "        DG.nodes[node]['shortest_dist'] = float('inf')\n",
    "    DG.nodes[source]['shortest_dist'] = 0\n",
    "    #print( DG.nodes.data() )\n",
    "    #print( DG.edges.data() )\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                #print(\"edge0: {}  edge1: {}\".format(edge[0], edge[1]))\n",
    "                dji_greedy = DG.nodes[edge[0]]['shortest_dist'] + DG.edges[edge[0], edge[1]]['weight'] #djikstra's greedy criterion\n",
    "                if edge[1] not in A:\n",
    "                    DG.nodes[edge[1]]['shortest_dist'] = dji_greedy\n",
    "                    A.append(edge[1])\n",
    "                elif dji_greedy < DG.nodes[edge[1]]['shortest_dist']:\n",
    "                    DG.nodes[edge[1]]['shortest_dist'] = dji_greedy\n",
    "                    A.append(edge[1])\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    w_overall = edge[1]  \n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "    print(\"Printing minimum distances from starting vertex {}\".format(source))\n",
    "    for node in all_nodes:\n",
    "        print(\"Vertex {} is at distance {}\".format(node, DG.nodes[node]['shortest_dist']))\n",
    "\n",
    "\n",
    "        \n",
    "        \n",
    "\n",
    "DG = nx.DiGraph()\n",
    "DG.add_node(1, pos = (0, 5))\n",
    "DG.add_node(2, pos = (7, 10))\n",
    "DG.add_node(3, pos = (7, 0))\n",
    "DG.add_node(4, pos = (14, 5))\n",
    "DG.add_edge(1, 2, weight = 1)\n",
    "DG.add_edge(2, 3, weight = 2)\n",
    "DG.add_edge(3, 4, weight = 3)\n",
    "DG.add_edge(1, 3, weight = 4)\n",
    "DG.add_edge(2, 4, weight = 6)\n",
    "pos = nx.get_node_attributes(DG, 'pos')\n",
    "weights =nx.get_edge_attributes(DG, 'weight')\n",
    "nx.draw_networkx_edge_labels(DG, pos, edge_labels = weights)\n",
    "nx.draw(DG, pos, with_labels = True)\n",
    "\n",
    "djikstra_naive_nx(DG, 1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex s\n",
      "Vertex s is at distance 0\n",
      "Vertex t is at distance 6\n",
      "Vertex w is at distance 3\n",
      "Vertex v is at distance 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f78a210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('v', pos = (5, 0))\n",
    "g.add_node('w', pos = (5, 5))\n",
    "g.add_node('t', pos = (10, 5))\n",
    "g.add_edge('s', 'v', weight = 1)\n",
    "g.add_edge('v', 't', weight = 6)\n",
    "g.add_edge('s', 'w', weight = 4)\n",
    "g.add_edge('v', 'w', weight = 2)\n",
    "g.add_edge('w', 't', weight = 3)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "djikstra_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Problem 9.2\n",
    "\n",
    "Consider a directed graph G with a source vertex ss, a destination t, and nonnegative edge lengths. Under what conditions is the shortest s-t path guaranteed to be unique?\n",
    "\n",
    "a. When all edge lengths are distinct powers of 2.\n",
    "Since the vertices are powers of two and unique, no two edges can add up to the length of any other edge. Thus the shortest path is unique and not other path is guaranteed to have that length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex s\n",
      "Vertex y is at distance 14\n",
      "Vertex s is at distance 0\n",
      "Vertex t is at distance 15\n",
      "Vertex w is at distance 12\n",
      "Vertex v is at distance 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f78ad90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('v', pos = (5, 0))\n",
    "g.add_node('w', pos = (10, 0))\n",
    "g.add_node('y', pos = (15, 0))\n",
    "g.add_node('t', pos = (20, 5))\n",
    "g.add_edge('s', 't', weight = 16)\n",
    "g.add_edge('s', 'v', weight = 8)\n",
    "g.add_edge('v', 'w', weight = 4)\n",
    "g.add_edge('w', 'y', weight = 2)\n",
    "g.add_edge('y', 't', weight = 1)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "djikstra_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Problem 9.3\n",
    "Consider a directed graph $G = (V,E)$ and a source vertex s with the following properties: edges that leave the source vertex s have arbitrary (possibly negative) lengths; all other edge lengths are nonnegative; and there are no edges from any other vertex to the source s. Does Dijkstra's shortest-path algorithm correctly compute shortest-path distances (from s) in this graph?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex s\n",
      "Vertex a is at distance -100\n",
      "Vertex c is at distance 8\n",
      "Vertex b is at distance 5\n",
      "Vertex e is at distance 1\n",
      "Vertex d is at distance -8\n",
      "Vertex g is at distance 4\n",
      "Vertex f is at distance -99\n",
      "Vertex i is at distance 26\n",
      "Vertex h is at distance 24\n",
      "Vertex s is at distance 0\n",
      "Vertex t is at distance -97\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f339250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('a', pos = (5, 10))\n",
    "g.add_node('b', pos = (10, 10))\n",
    "g.add_node('c', pos = (15, 10))\n",
    "g.add_node('d', pos = (5, 5))\n",
    "g.add_node('e', pos = (10, 5))\n",
    "g.add_node('f', pos = (15, 5))\n",
    "g.add_node('g', pos = (5, 0))\n",
    "g.add_node('h', pos = (10, 0))\n",
    "g.add_node('i', pos = (15, 0))\n",
    "g.add_node('t', pos = (20, 5))\n",
    "g.add_edge('s', 'a', weight = -100)\n",
    "g.add_edge('a', 'b', weight = 500)\n",
    "g.add_edge('b', 'c', weight = 3)\n",
    "g.add_edge('c', 't', weight = 4)\n",
    "g.add_edge('s', 'd', weight = -8)\n",
    "g.add_edge('d', 'e', weight = 9)\n",
    "g.add_edge('e', 'f', weight = 10)\n",
    "g.add_edge('f', 't', weight = 2)\n",
    "g.add_edge('s', 'g', weight = 4)\n",
    "g.add_edge('g', 'h', weight = 20)\n",
    "g.add_edge('h', 'i', weight = 2)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "g.add_edge('a', 'f', weight = 1)\n",
    "g.add_edge('b', 'f', weight = 1)\n",
    "g.add_edge('g', 'b', weight = 1)  # Changing\n",
    "g.add_edge('h', 'f', weight = 1)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "djikstra_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex s\n",
      "Vertex a is at distance -100\n",
      "Vertex c is at distance 403\n",
      "Vertex b is at distance 400\n",
      "Vertex e is at distance 1\n",
      "Vertex d is at distance -8\n",
      "Vertex g is at distance 4\n",
      "Vertex f is at distance -99\n",
      "Vertex i is at distance 26\n",
      "Vertex h is at distance 24\n",
      "Vertex s is at distance 0\n",
      "Vertex t is at distance -97\n"
     ]
    },
    {
     "data": {
      "image/png": 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DlLJNVScWi9GtWzf06tULP/30E+s4gsb30FVYeno6HB0dMW/ePEE3cwBo3rw5Ll++jH79+qFdu3ZYtWoVJBJJqda5Z88efPfdd0pr5gBgYGCA/fv3Y8qUKXj06JHStqvKvvnmG+zbtw+bNm3C6dOnWccRNL6HrsJcXFzw6tUrBAcHq/UdgoorMjISkyZNQlJSEnx9fWFhYVHsdRARWrZsidWrV6N79+4KSFmwTZs2wdvbG1euXIFecW/WLVD//PMPRowYgWvXrsHExIR1HEHie+gqas+ePTh58iT8/f01qpkDQIMGDXD27FlMmjQJ3bp1wy+//IL09PRirSMsLAwfP35E165dFZSyYN9//z2aN2+O6dOn83Oxs9jZ2WHWrFkYOnSoSk7eJgS8oauge/fuYdasWQgKCkLlypVZx2FCJBJh0qRJ+O+//xAWFgZra2uEhIQU+fXymIirNEQiEbZs2YJr167B19eXSQZV5ObmBkNDQ7i6urKOIkwsT7HhcktISKAmTZqQv78/6ygqQyqVUkBAANWoUYPmzJlT6CXlKSkpVLVqVXr27JmSEubv/v37ZGBgQDdu3GAdRWXEx8eTqakp7d27l3UUweF76CqEsibd6tSpE8aOHcs6jsoQiUQYPnw4wsPDERsbCwsLC5w9ezbf5Q8ePAgbGxvUqVNHiSnz1qRJE2zcuBGOjo54//496zgqQV9fH0FBQXBxcUFERATrOMLC+jcK98nLly+pdevWlJqayjqKSvvzzz/JxMSEJk6cSO/fv8/1fPfu3VVu72/mzJnUr18/yszMZB1FZfj4+JC5uTklJiayjiIYfA9dhVSpUgUnT56Erq4u6ygqrU+fPggPD4eOjg6aN2+Ow4cP5zwXFRWFW7duKWQirtLw9PREXFwcVq5cyTqKypgwYQLatGmDKVOm8APHcsJPW+TU2vnz5zFx4kRYW1tj/fr12LhxIz58+IB169axjpbLixcv0Lp1a+zZs4fZ2TeqJiUlBe3bt8eUKVMwbdo01nHUHm/ojBGRxp2WKG8pKSlYsmQJtm3bBqlUijNnzqBFixasY+Xp9OnTGDNmDEJDQ/kNlbM8fvwYHTp0wJ9//ok2bdqwjqPW+JALIzExMQDAm7kc6OnpYeXKlfj555+RkpKChQsXIjo6mnWsPPXo0QPTpk3DsGHD+A2Vs5iZmWHLli1wdHREXFwc6zhqjTd0BmbOnIkBAwZg4cKFSr/Zg5BdvHgRy5cvR4cOHWBtbY3Nmzer5IRQCxcuROXKlfHjjz+yjqIyBg4ciGHDhmHUqFHIzMxkHUd9sTwiq4l27dpFPXv2pJiYGPLx8aHevXvTkSNHiIj4GRClEBcXR5UrV8456+Xu3bvUrl07srW1pQcPHjBOl9u7d++oXr16FBwczDqKyhCLxdS5c2dasmQJ6yhqi++hK9nr16/Rr18/1KxZE6NHj8a4ceOwZMkSpKWlMbuqUQh2796NPn36oEqVKgAAc3NzXLx4EUOGDEGHDh2wcuXKfCf7EovFOHfuXKknAyuOqlWrYv/+/YiKisrzW0RmZiaePXumtDyqQEdHB3v37sWdO3f4XnpJsf6NInTBwcHk4eFB//77LxERHThwgBo2bPjFMhMnTqSFCxeyiCcIUqmULC0t6ezZs3k+HxkZSd27d6dWrVpRZGRkrucfPHhAXbt2JT09PaXvMed3w5JTp06Rubk5ubq6KjWPKkhLS8vzcf4NtnB8l1CB1qxZg/nz50NLSwtubm7YsGED+vfvDysrKyxZsgQAIJFI4OTkhHfv3uHDhw9sA6upmzdvIjExEXZ2dnk+b2pqitOnT2P69Om4detWrj1iIyMjHDt2DObm5qhRowYAKG3sXVtbO8/HbW1tsWTJEvj6+uLVq1dKyaIqypYtm+fjEokEMTExmD17Nm7cuKHkVOpBOLe/UTESiQTh4eEIDg6GpaUlWrZsiZMnT8Lb2xvLli1Djx49MHDgQLRo0QJ6enrIyMjIGS7giqcoE3GJRCKMHz8eUqk013IVK1bE5cuXIZVK0bFjRwBQ2vBXfmc5SaVSBAQEwNXVFbVq1coztya5desWfH19QUQ4ePAgUlJSsGXLFtaxVA5v6HKUnp6es3eho6MDbW1t7Ny5E56enujWrRtSUlJw7NgxfPvtt/j555/h4uKCwYMH49ChQ7CysoJEIoG2tjY/lbEYUlNTsW/fPoSFhRVp+fya4vHjx9GuXTsAsvHr/PaclcXb2xsJCQk5Z8Jo6nsiPDwcBw8exIcPH2BhYYGGDRsiOjoas2fPBsCv4/ia5v7Kl7NVq1Zh9OjRuHbtWs5jzs7OeP36NW7evAltbW20atUKRkZGuHnzJiZMmAB3d3ekp6fDyckJXl5e0NHR4W/OYjpw4ABat25d4om4pFIpUlJScP78eQwZMgQA++YZFhYGf39/LF++HIDsFwzrTCxkZGTA09MTR44cwerVqzFq1CgEBASgQ4cOMDc3B8D+/0rV8IYuBwcOHIC3tzfKli2L8+fP51wcUb9+fZibm2PHjh3IzMyEiYkJMjIyEBoaCkA24f+CBQswZcoUlvHVWmlvAq2lpYXXr18jKSkp53J8FkMbRITjx48DkB176du3L2xsbEBEzL8tsFKmTBmsXr0atWvXRrt27eDq6gqJRIL58+ezjqayeEOXg/bt2+PChQsYP348nj9/nnPfRBMTE/Tq1QvJyck5XxHj4+NhaGjIMq5gPHnyBLdv38aAAQNK9PqIiAhMnToVbm5usLGxYbq3l5SUhPXr18PY2Bg3b97EsmXLAECjJ63KzMyEgYEBDh48CHt7e/j7+0NHRyfnOS433tDloHr16jAyMoKdnR3MzMwQFhaG69evAwBatWoFDw8PPH/+HD169EBMTAymT5/OOLEw+Pv7w8nJKd+zIgpjbGyMxo0b4/Xr19i1axe8vLyQlJSU87wym2nFihVx/Phx/Pjjj4iOjsaRI0dARBp9IFRbWxtSqRTPnj3Dmzdv4Orqim7duuU8x+XGJ+eSAyLK+fBFRUVh06ZNqF69+he32UpLS0NycjKqVavGMKlwZGZmol69ejh27BgsLS1Lvb64uDhER0fDysoqp1mkpKTg9OnT6N+/v1L33l+8eIH79+/D3t6ejxEDSE5Oxu+//46ffvqJdRSVxxt6KX1+OllGRgbKlCmDc+fO4fTp03j37h3CwsJw5swZVKpUiXFSYTlx4gR+/vnnnOMRipCRkYG2bduiRo0a8Pb2Rt26dRW2rYLwMzk+ya4Fr0neNPf7nJxkN/PffvsNbm5uAIBmzZph165dCAkJwa+//sqbuQKU9mBoUZQpUwbXrl1D586dYW1tjQ0bNih9sq+0tDT4+fkpdZuqTCQSIT09HRs2bODj6Hnge+ilRETYsGEDzp8/j5UrV8LU1BS//fYboqOj4ePjwzqeIMXFxcHMzAxPnz5V2sVYERERmDBhAkQiEXx9fdG4cWOlbDcjIwNNmjTBihUr4OjoqJRtqjoiQvfu3WFra4tff/2VdRzVotyZBoTp6/taSiQSRkk0w9q1a8nJyUnp283MzCQvLy+qVq0aLVu2jDIyMpSy3evXr5OBgQFFREQoZXvqICYmhoyNjen48eOso6gUvocuR5p+ebYyEBGsrKywbt06Zrdxe/r0KaZMmYK3b9/C19cXLVu2VPg2t2zZgvXr1yMkJATly5dX+PbUwb///gtHR0eEhIQwO76hanj3kSPezBXvxo0bSEpKQpcuXZhlqFevHk6cOIFZs2ahV69eWLhwIdLS0hS6zUmTJsHa2hpTp07V6HPTP2dra4t58+bB0dER6enprOOoBN6BOLXi6+uL8ePHM//lKRKJMGbMGNy+fRsPHz5EixYtcPHiRYVub/Pmzbh16xa8vb0Vth11M3fuXNSuXRs//PAD6yiqge2Ij/qTSCT5zmnNyVdycjLp6+tTdHQ06yi5BAUFkZGREU2fPp0SEhIUtp0HDx6QoaEhhYaGKmwb6ubDhw9kZmZGu3fvZh2FOb6HXgpEhFmzZin1Tjea7MCBA2jbti1MTExYR8llyJAhCA8PR0pKCiwsLHDy5EmFbKdRo0b4448/4ODggHfv3ilkG+qmcuXKCAoKwqxZs3D37l3WcZjiDb0U1q5di5CQEOZf/zWFr68vJkyYwDpGvqpWrQo/Pz9s2bIFU6ZMwZgxYxAfHy/37QwePBhDhgyBs7OzSt4EmwUrKyt4enpiyJAhSExMZB2HGd6JSij7DvP79+9HmTJlWMcRvMjISNy9exf9+vVjHaVQPXv2RHh4OKpUqYLmzZsjKChI7ttYvnw5EhMTcybx4oCxY8fC1tYWEydO1NwDx6zHfNTR69evydjYmI4dO8Y6isZYtGgRzZ49m3WMYrt48SI1adKEBg8eTK9evZLrul++fElGRkZ06tQpua5XnaWmplLLli1p3bp1rKMwwRt6MYnFYuratSv99NNPrKNoDIlEQsbGxnT79m3WUUokNTWVFi1aRIaGhuTn50dSqVRu6/7777+pZs2aKnmgmJXIyEiqXr06Xbp0iXUUpeMNvZgWLFhA9vb2/GpQJfrrr7+odevWrGOUWlhYGLVq1Yp69OhBUVFRcluvh4cHtWvXjtLT0+W2TnV39OhRql27Nr1584Z1FKXiY+jFcPToUezatQt79uzh8zErkTIm4lKGFi1aICQkBN27d4eNjQ3Wr18vlwmm3NzcYGho+MV0zZqub9++cHZ2xsiRIzVqEi9+6X8RPXnyBO3bt8ehQ4fQvn171nE0xtu3b9GwYUM8e/YMlStXZh1Hbh4+fIiJEydCIpHA19cXTZs2LdX63r9/DxsbGyxbtgzDhg2TU0r1JpFI0LNnT3Ts2BG//fYb6zhKwffQiyAtLQ2Ojo5YuHAhb+ZKtnv3bvTr109QzRyQnU/+zz//YNSoUbC1tcX//vc/iMXiEq9PX18fQUFBcHFxQUREhByTqi8dHR0EBATA398ff/31F+s4SsH30Itg8uTJ+PjxI/bu3csn1VciIoKlpSW8vLxgZ2fHOo7CREdHY8qUKXj16hX8/PxgbW1d4nVt3boVv//+O0JCQlChQgU5plRfFy9exJAhQxASEoJ69eqxjqNYTEfw1YC/vz81adJEoZdzc3m7du0amZqaUmZmJusoCieVSmnnzp1UvXp1mj9/PqWkpJR4PWPHjqWRI0fK9Wwadbd69WqysbGhtLQ01lEUig+5FODWrVtwdXVFUFAQKlasyDqOxlGVibiUQSQSYdSoUbhz5w6ioqJgZWWFCxculGg9GzduRHh4ODZv3qyApOppzpw5qFu3LmbPns06imKx/o2iqviEP2xlT8T1/Plz1lGYOHjwIBkbG9O0adPo48ePxX79o0ePyNDQkEJCQhSQTj19/PiRGjZsSDt37mQdRWGEv+tTAkSEsWPHomfPnhg5ciTrOBopODgY7dq1Q+3atVlHYWLgwIEIDw9Heno6LCwscPz48WK93szMDN7e3hg6dCifxCtLpUqVEBwcjDlz5iA8PJx1HMVg/RtFFXl6elKbNm0EP96myrp06UJBQUGsY6iEM2fOUP369WnUqFH09u3bYr123rx59O2332rEcYii2r59OzVq1KhE33xUHd9D/8qFCxewatUqBAYGomzZsqzjaKTHjx/j3r17ajERlzJ0794dd+7cgYGBASwsLBAYGFjkyac8PDyQnJwMd3d3BadUH6NHj4adnR0mTJgguEm8+GmLn3n9+jWsra3h6+uLb7/9lnUcjbVo0SKkpqZizZo1rKOonKtXr2LChAlo2LAhNm3ahFq1ahX6mpiYGNjY2MDf3x89e/ZUQkrVl5aWho4dO8LZ2VlYB0rZfkFQHWKxmLp06UKLFy9mHUWjZU/EdefOHdZRVFZaWhotXryYDA0NaevWrUU6PfHcuXNUo0YNevbsmRISqocnT55Q9erV6eLFi6yjyA1v6Fnmz59PPXv25JNuMXbs2DFq06YN6xhq4datW2RjY0PdunWjyMjIQpdfsWIFtW3blk/i9Zk///xTUJN48TF0AIcPH8aePXuwe/duPukWY0KZiEsZLC0tceXKFfTu3Rtt2rTB2rVrC5yIytXVFTVr1sTcuXNrhq02AAAgAElEQVSVmFK19enTB2PGjMGIESOEMYkX698orD1+/JgMDQ3pypUrrKNovNjYWKpcuTJ9+PCBdRS18+jRI+rSpQu1bduWwsPD813u/fv31KBBAwoICKDk5GRat26dxt/kXCKRUPfu3WnhwoUkkUjojz/+KPbZRKpCoxt6SkoKWVlZ0fr161lH4YhozZo15OzszDqG2srMzKQ//viDDAwMaOnSpfkOrYSFhZG+vj4ZGxuTlpYW3bx5U8lJVc+bN2/IyMiImjZtSiKRiLZv3846Uolo9JCLi4sLmjZtChcXF9ZRNB4RqfxNoFWdlpYWpkyZgrCwMISEhMDGxgahoaG5lnv06BGSk5Px8uVL6Orq4ubNmwzSqpaoqCikpKTg/v37ICJcuXKFdaQS0diG7ufnhytXrsDHx4fPoKgCQkNDkZaWhs6dO7OOovZq166No0ePYsGCBejXrx9cXV2RkpICADh06BAmTpyYs2xKSgouXbrEKqrKmDNnTk6NANkMjepImOehx8YC27YBt28DHz8ClSsDlpbAuHGAoSH+++8/9OjRAxcuXCj1jQXURiE1YS0gIABly5bF4MGDlbdRFa+JPLx9+xazZs1CaGgo3N3dMW7cOOjr62PKlClYtWoVkpKSUL16dbx+/Vr2Ag2oSV4yMjKwY8cOLF68GLGxsSAiiMXiTxPDqUtdmA74yNu1a0SDBhHp6sp+gE8/5coR6epSep8+NNDYmAICAlinVY4i1IQGDZItx4hUKqWUlBTlXZ6uBjWRt8OHD1OZMmVIJBKRnp4eeXh4UHJyMi1cuJDq1aunkTXJi1gsJh8fHzIwMJBNDaBmdRFOQ9+0iUhPj0gk+rLoX/1kApSmoyNbXuiKWBMSiWTL8ZoItibbt2+nMmXKEAACQGXLlqVXr17JntTQmhRKDesijIaeXfiCiv71j4r8ByhMEWoyBqBFvCYa8T5ZsmQJ1apVi8qUKUM6OjoEgNq3b59vTSIAagFQBYDWCbQmBVLT94r6N/Rr14pf+M//A0JDFR7xw4cP1LdvX7K0tCRzc3Py8/NT7AaLWJNcDV2JNVE6FX2fjBs3jgwNDalZs2Y5j717947s7e3JzMyM7O3tKT4+Xm7bk0qlFB8fTyEhIRSxa1e+NRkP0GwV+OxER0eTnZ0dNWnShMzNzWnt2rUK32ZB75W6AJ1WgbrkR/0b+qBBhX8lyu9HJCIaPFjhEf/3v/+Rm5sbEckuntHX11fs5ddFrEmeDV1JNVE6FX2fnD9/nm7cuPFFQ3d1dSUPDw8iIvLw8Mh578hdATXpDpCPCnx2Xr16RTdu3CAiooSEBGrYsCHdvXtXsRstoC6FNnTGnx/1buhv3uQ+UJH1sxygWpB9ZWwE0Jn8/gN0dYliYxUac9myZfT999+TVCqlJ0+eUIMGDUp9ADA1NZWOHDmS+yq/AmpyE6CWWTUZCtCwvBq6EmoilUoVcr9LqVRKR44coaSkpC+fKKAmLwEaDJABQPWQx/CCEmoSFRX1RUNv1KhRzvj2q1evqFGjRqVa/9mzZ3PPVVJATboCpAVQWYDKA/SA4Wfna/3796dTp06Vej2hoaH08OHD3E8UUJdRAIkA0s2qywoVqks29W7oK1bkWfwIgGpnfVgJoCiAHudX/HLliFauVGjMhIQEsrOzo5o1a1L58uXpzz//LPU6L126RCKRiIyMjGjbtm2fGns+NUkHqA5AawDKAGg/QDr5NXQF1eT333+nc+fO5fxd3hOhJSQkEACqVKkSeXh4fGrs+dQkE6BWAP2aVZ9IgOoDdELJ75OvG3rlypW/eL5KlSqlWr+BgQGVLVuWZs6c+amx51OT7J8uKGQPXUmfnc9FRUWRiYmJXG5M0alTJ9LS0iIHB4cvG3shdSl0D51BXT6nw/ScydK6fRtIS8v1sDaAdAD3ABgCqFfQOlJTEbF/P86UK1eqKNOmTcv3ZsYnT55EixYt8PfffyMyMhI9evSAra0tKlWqlLNMeno6fHx8iry9J0+eQFdXFzExMZg8eTJmzpyJBQsW4Mfw8DxrchWAGMBsACIADgDynW1cDjVxcHBAzZo1c/6+Y8cO/PTTT6hfvz7GjBmDefPmQVtbG5mZmQVOiJaUlIRt27YVaZtpaWnQ1tZGQkICFi9ejF9//RWjRo2CT2pqnjUJBfAWwOKsv5sCmARgL4BeXy8sh5rI84rkx48f48SJE0VaNiUlBenp6di0aRM2b94MOzs7nDAwgFYeNSkWOX12sg0ePDjf+d2TkpIwZMgQrF279ovPTXR0NI4cOVLsbb18+RJSqRQHDhzAoUOHYGFhgaNHj8I4n55SLKmpwJ07pVtHCal3Q//4Mc+HzQCsBbAEwF3IPpxrAOR3KwBxbCwiIiJKFYWIvvj7xo0bcxq0vr4+li5dCpFIBDMzM9SvXx8RERFo06ZNzvJSqbRYGWJiYnJmh8vMzERycjLu3buXb01eATCGrJlnq1vA+ktbk6dPn+Y0dCJCVFQUtm/fjubNm2Pq1Km4desWfHx8oKurK9ueWIxvvvkm13rKlSuHBw8e5KpvXjIyMnKWk0gkyMzMlN070sAgz+WfQVaXKp89lgnANp/1y+N9UhQ1atRATEwMjIyMEBMTg+rVq+daJjExschZst8nEokE2traePjwIaQ6OnK5TFyeNUlNTc17G2IxhgwZAicnp1wXniUnJ5do+9nbkkql0NLSwrNnzxAfHw/jfD4/xfb+vXzWU1xMvhfIi5NTwV99APoI0PCs8a98l1PwhFBTp06lX375hYiIXr9+TbVq1Sr1bG6XLl0iHR0d0tPTo7lz535aXz41+QcgI4Cknz3WIb8hFwXUJPvsCiLZgeFJkyZRu3btKCoqijIyMsjHx6fUB4oTEhJIJBKRrq4ujRgx4tMc4fnU5DJAZoV9fVbC++TrIZd58+Z9cVDU1dW1VOuvVq0alSlThuzs7Cg0+wyMQj47RRpyUcJnRyqVkrOzM82aNUuu6+3YsSPp6OiQubk5/fXXX5+O6RRSl3pFGXJRQl3yo94NvYAx9LMApUE2NjoOsjM6WI13vXz5knr06EHNmzenZs2a0c6dO0u9zvj4eFq+fHnuXwwFjKGbALQWIDFAwVD+GPrn0tPTadOmTWRpaUmVKlWidevWlXqdmZmZtHz58tw3e8inJhLIxtCXA5SS9fc7AF1TYk2GDx9ONWvWJB0dHTI2NqatW7dSXFwcdevWjczMzKhbt2707t27Um1j8+bNnxp5NjUZQ//3338JAFlYWJCVlRVZWVnRsWPHSr3e4OBgOnbsWO6D84XUpS1A3ipQl/yod0PP54j0LYBaQ3Y2hz5AffDpAGmuH4ZHpBWigKP0ofh0scjQrB8WZ7l8rkuXLuTk5KTYjRRylstwgGoAVCXrA5vnHpgGvU+K3NCFVhOiQutyKGvHqDJAnipYF/Vu6EQqe34xU2pSk7CwMOratatCTmHMRU1qolS8JnlT47qo/2yLoaGAnR3w2dSXRaanB5w/D9jYyD0WU2pUk+TkZJQvX17xG1KjmigNr0ne1Lgu6j8feuvWwKpVskIWh56e7HVCfEOqUU2U0swBtaqJ0vCa5E2d68Lsu4G8FXFmNKlIRMkAPZgzh3VixVPD2eIUjtckh1QqpcDAQFrdsCGvyWeuXr1KNjY2lLZ2rdrVRTgNnUg2Kc7gwbKDEuXKfVn07LmLBw+mi2vXUq1atSgmJoZ1YsUrYk2UMaFQbGwsbdu2Te5XiBabCtWEhczMTDp06BA1btyYRCKR7MpUDa8JkexUYFtbW9LW1iaRSCQ7jVbN6qL+Y+h5eftWdneRO3dkJ/jr6wMWFsDYsTl3F1m8eDEuXLiAM2fOQEdHva+vKpIi1ETRFixYALFYjFWrVille4VSgZoom0QigaWlJZ49e5Zzy7WhQ4di3759sgU0sCYAMGjQIJw4cQJpWVeJNmjQAI8fP/60gLrUhfVvFFYkEgn16NGD5s+fzzqKRhCLxWRkZKT4mfK4Qi1ZsiTnZhe6urrk5eXFOhJzAQEBVK5cOQJkNwAZPXo060glov4HRUtIW1sbe/bswZ49e0o0FwRXPCdOnEDdunVhbm7OOorGGz9+PPT09FC+fHlkZmbC2tqadSTm+vfvj9q1a0NfXx/a2tro2LEj60glorENHQAMDAwQGBiIiRMnIjIyknUcQfPz88P48eNZx9B4GRkZcHR0xI8//oiIiAiMHTsWLVq0YB2LKSLCtGnT0KZNGzx9+hRTp05Fr165pmdTC8IcQy8mLy8v+Pn54fLlyygnp5njuE/evHmDxo0bIzo6+ouZ8jjlmzlzJp49e4ZDhw5BJBIV/gIN4OPjg3Xr1iEkJER5p9EqCG/okP2GHjlyJMqXL4+tW7eyjiM4q1evxp07d4o8DS6nGHv37sWiRYtw48YNVKlSpfAXaICbN2+iV69euHjxIho3bsw6Tqlp9JBLNpFIBB8fH1y6dAn+/v6s4wgKEcHX1xcTJkxgHUWj3b9/HzNmzEBQUBBv5lnev38PBwcHbNq0SRDNHFD3+dDlqEKFCggODkaXLl3QsmVLjR9XlJeQkBBIJBJ06tSJdRSNlX1ziOXLl6Nly5as46gEqVSK0aNHo3///nB0dGQdR274HvpnzM3NsX79ejg4OODDhw+s4wiCr68vxo8fz8drGSEiTJ48Ge3atePfkj6zYsUKvHv3DitXrmQdRa74GHoeZsyYgefPn+PgwYO8EZVCUlISTExMcO/ePRgZGbGOo5Gy75x15coVfsA/y7lz5zBy5EiEhoaidu3arOPIFd9Dz8Pq1avx+vVreHp6so6i1oKCgtCpUyfezBkJCQnBr7/+iqCgIN7Ms7x8+RJOTk7YuXOn4Jo5wBt6nsqUKYPAwECsWbMG58+fZx1HbfGDoezExcVh6NCh2LJlC8zMzFjHUQlisRjDhg3DtGnTYG9vzzqOQvAhlwKcOnUK48aNw/Xr1/leZjE9fPgQnTt3xvPnz/O8+TOnOJmZmejTpw8sLS0FN0ZcGnPnzkVERASOHj0KLS1h7ssK818lJz179sTkyZMxfPhwSCQS1nHUip+fH5ydnXkzZ8Dd3R2pqalYtmwZ6ygqIygoCAcOHMDOnTsF28wBvodeKKlUiu+++47v7RSDRCJBnTp1cPbsWTRt2pR1HI1y4sQJTJgwgX+r/MzDhw/RsWNHHD9+HDZCvSlHFuH+qpITLS0t7Nq1C/v27cOhQ4dYx1ELx48fR7169XgzV7Lo6GiMHTsWAQEBvJlnSU5OxpAhQ+Du7i74Zg7wPfQiu3btGvr27YvLly/zg0yFGDRoEPr06YOJEyeyjqIx0tPT0blzZzg4OMDV1ZV1HJVARBgzZgwAYPv27RpxCjJv6MXAz+ktXPZEXM+fP0fFihVZx9EYLi4uePnyJQ4cOKARjasovL29sWHDBoSEhECvuPcHVVO8oRcDEWHUqFEoW7Ys/Pz8WMdRSatWrcLdu3f5nDhKtGfPHixevBjXr1/n87RkuX79Onr37o1Lly6hUaNGrOMoDR9DLwaRSIQtW7YgJCQEvr6+rOOoHD4Rl/Ldu3cPs2bNQnBwMG/mWeLj4+Ho6IjNmzdrVDMH+ORcxVa+fHkEBwfD1tYWrVq14pMdfebKlSuQSqVqe7cXdZOYmIghQ4Zg5cqVsLKyYh1HJUilUjg7O2PQoEFwcHBgHUfp+B56CTRp0gQbN26Eg4MD3r9/zzqOysi+KxEfw1U8IsKkSZPQsWNHjBs3jnUcleHh4YGPHz9ixYoVrKMwwcfQS2HWrFmIiorCoUOHBH2xQlHwibiUi99lK7ezZ8/C2dkZoaGhMDY2Zh2HCc3uQqXk6emJuLg4fsERgP3798PW1pY3cyW4evUqfvvtNwQHB/NmnuXly5cYNWoUdu3apbHNHOANvVSyJ/Fat24dzp07xzoOU/xgqHK8ffsWQ4cOxdatW2Fqaso6jkoQi8UYOnQoZsyYgW7durGOwxQfcpGD06dPY8yYMbh+/Tpq1arFOo7SPXjwAF26dOETcSlYZmYmevfujVatWmH58uWs46iMOXPm4PHjxzh8+LDGD31q9r9eTnr06IFp06Zh2LBhEIvFrOMonZ+fH0aPHs2buYItXboUYrEY7u7urKOojP379+Pw4cPYsWOHxjdzgO+hy41UKkW/fv3QtGlTrFq1inUcpRGLxahTpw7OnTuHJk2asI4jWMePH8ekSZNw/fp11KxZk3UclRAREQFbW1ucOHEC1tbWrOOoBP4rTU60tLSwc+dOBAcH48CBA6zjKM3x48dhamrKm7kCPXv2LGfSLd7MZZKTk+Hg4IBly5bxZv4ZvocuZ9evX8d3332HGzduwMTEhHUchRs4cCD69evHD4gqiEQiQfv27TF8+HDMnTuXdRyVQERwdnaGjo4O/P39+XUPn+F76HJmY2MDd3d3aGtrs46icK9fv8b58+cxdOhQ1lEESyqVwt7eHj/88APrKCpDIpGgQYMG2LRpE2/mX+F76ApARMjIyEDZsmVzPSeVSgVz8MbT0xMRERF8XhsFE9J7Rl54TfLGK6IAIpEoz2YOyPYuYmJiMHv2bNy4cUPJyeQneyKu8ePHs44iCKmpqQBkpyZ+TVMbF69J8fGqKNGtW7cwb948LFu2DEFBQfD29mYdqcQuX74MAOjQoQPjJOpv6dKl6NixI2JjY6GtrQ2pVMo6EnO8JiXDZ1tUgvDwcBw8eBAfPnyAhYUFGjZsiOjoaMyePRuAbG9X3cYC+URc8hEQEIC///4bTZo0wdy5cwV/E+Oi4DUpOT6GrmAZGRmYNGkS7t27h9DQUKSmpmL27NkwNTXF/PnzWccrkcTERNSpUwf379/np9GVUkZGBh4/fgwTExP07NkTs2fPxrBhw5CZmakRB9bzwmtScryhK0FcXBwmTZqEmJgY2NjYIDU1Va0PJPr5+eHw4cM4fPgw6yiCcuDAAbi7u+PcuXOoXLmyWn5zkzdek+Lh32MULDMzEwYGBjh48CDs7e3h7+8PHR2dnOfUEZ+ISzEGDx4MGxubnJs8Z2RkqO17RF54TYqH76ErgVQqxfPnz+Hu7g5jY2M0bdoUw4YNYx2rRCIiItC1a1dER0fzuVsUICEhAb1790bjxo2Rnp4Od3d31K9fn3UspnhNio4fFFUCLS0tGBgYoG7duvjpp59YxykVPhGXYqWnp+PNmzdITk7GH3/8wRsXeE2Kg++hM1DQhUeqTCwWw8TEBP/88w+fu0VOvj7QN3/+fJQvXx6LFy9mmIqtry8a4jUpOt7QGSAiPHr0CLdv31arG9kePnwYnp6euHjxIusogvD06VOEhITAwcEhp6lr+pkcSUlJWL9+PVxdXXO+BWp6TYqDHxRlQCQSQSwWY9q0aXj48CHrOEWWfe45V3ppaWlwcHBAXFzcF81KkxsXEWHy5MmIjIz8YkhPk2tSXHwPnaEtW7bAy8sLV69eRfny5VnHKVBMTAzMzc3x/PlzVKhQgXUctTd16lS8e/cOgYGB/DS8LBs3boSPjw+uXLnC75VaQryhM0REGDt2LIgI27dvV+kP9sqVK/Hw4UNs3bqVdRS1t3PnTri7uyM0NBSVKlViHUclhISEoF+/frh8+TLMzMxYx1FbfMiFIZFIhM2bN+O///7Dli1bWMfJF5+IS37u3LmDH374AUFBQbyZZ4mLi8PQoUOxZcsW3sxLiZ+2yJienh6CgoLQqVMnWFtbw8bGhnWkXC5dugQtLS20b9+edRS1lpCQAAcHB6xZswYWFhas46iEzMxMjBo1CsOGDcPAgQNZx1F7fA9dBTRq1Ah//PEHHB0dER8fzzpOLnwirtIjIowfPx5du3aFs7Mz6zgqw93dHampqVi2bBnrKILAx9BVyNy5cxEREYGjR4+qzOxyiYmJMDExwYMHD1CjRg3WcdTW77//jt27d+PixYvQ1dVlHUclnDx5EuPHj8f169dhZGTEOo4gqEbX4AAAy5cvR0JCgkrtrQQGBsLOzo4381K4dOkSli9fjqCgIN7Ms0RHR2PMmDEICAjgzVyOeENXId988w327duHTZs24cyZM6zjAOATcZXWmzdvMGzYMPj5+aFevXqs46iE9PR0ODo6Yu7cuejcuTPrOILCh1xU0Llz5zBy5EiEhoaidu3azHLcv38f3bp1w/Pnz3NmiOSKTiKRoGfPnujYsSN+++031nFUhouLC16+fIkDBw7w4zJyxvfQVVDXrl0xc+ZMDB06FBkZGcxy+Pn5YcyYMbyZl9DixYuhra2NJUuWsI6iMvbs2YMTJ07A39+fN3MF4HvoKkoqlWLAgAFo0KAB1q5dq/TtZ0/Edf78eTRu3Fjp21d3R48exfTp03Hjxg0YGhqyjqMS7t27hy5duuDMmTOwsrJiHUeQ+B66itLS0sKOHTtw5MgRBAYGKn37x44dQ8OGDXkzL4EnT55g4sSJ2LdvH2/mWRITEzFkyBCsXLmSN3MF4nvoKu7mzZvo1asX/v33X6VOWdu/f38MGjQI48aNU9o2hSAtLQ0dO3bE6NGjMWvWLNZxVAIRYcSIEahQoQKfOkLBeENXAz4+Pli3bh1CQkKUMokXn4ir5CZPnoyPHz9i7969fIw4i5eXF/z8/HD58mU+6ZaC8YauBrKvMhSLxdi5c6fCG8Xy5csRGRkJHx8fhW5HaLZv3w4PDw+EhoaiYsWKrOOohKtXr2LAgAG4cuUKTE1NWccRPN7Q1URKSgrat2+PqVOn4vvvv1fYdogIjRs3xvbt2/ncLcVw+/ZtdO/eHf/88w+aNWvGOo5KePv2LaytrbFx40b069ePdRyNwM9HUxN6enoIDg5Ghw4dYGNjg9atWytkOxcvXoSOjg7atWunkPUL0cePHzFkyBCsXbuWN/MsmZmZcHJygpOTE2/mSsTPclEjZmZm8Pb2hqOjI969e6eQbfCJuIqHiDBu3Dj06NEDTk5OrOOojKVLl0IikfALqpSMD7moIVdXV4SHh+PYsWNyncQrISEBderU4RNxFcOqVasQGBiIf//9V+1u+q0ox48fx6RJk3Djxg3+PlIyvoeuhjw8PJCcnAx3d3e5rjcwMBBdu3blH8IiunDhAlatWoX9+/fzZp7l2bNnGDt2LAICAvj7iAHe0NWQjo4O9u3bB29vb5w6dUpu6+UTcRXd69evMWLECGzbtg1169ZlHUclpKenw8HBAW5ubrC1tWUdRyPxIRc19s8//2D48OEIDQ2FiYlJqdZ179492NvbIzo6ms/dUgiJRAJ7e3t06dIFv/76K+s4KmPatGl48+YNgoKC+DEYRvgeuhqzs7PDnDlz4OjoWOpJvPhEXEX3008/oWzZsli8eDHrKCpj9+7dOHPmDPz8/HgzZ4jvoas5IsLAgQNRt25drF+/vlivzczMRFpaGsqUKYPatWvj33//RaNGjRSUVBiOHDkCFxcX3Lx5EwYGBqzjqIS7d+/Czs4Of//9N79XKmN8D13NiUQibN++HceOHcPevXuL9dqjR4+iSpUqaN++PapXr87vuF6IyMhITJw4EYGBgbyZZ8medGv16tW8masAvocuEGFhYejZsycuXLiAqKgo3L9/H3Pnzi3wNWfPnsXAgQORlJQEXV1dVKxYEX///TeaN2+upNTqIzU1FR06dMD48eMxY8YM1nFUAhFh2LBh0NfXh7e3N+s4HPiVooLRsmVLLFu2DLa2tkhMTETFihULbehGRkbI/n1ORDA2Ni71wVWhmjFjBpo0aQIXFxfWUVTG+vXrERkZiUuXLrGOwmXhDV0g4uPj4e/vj48fP0IikSAhIQHv3r1DtWrV8n2NkZERUlNToaOjgw4dOuDPP/+Enp6eElOrB39/f1y6dAmhoaH8gF+Wy5cvY9myZbh69Sq/8bUK4WPoAnHv3j2EhYXlnKWira2NsLCwAl9TpUoVEBG6dOmCkydP8maeh//++w9ubm4IDg7mUwlniY2Nzbnxdf369VnH4T7Dx9AF5MOHD1i7di08PT2RkpKC6dOnY8OGDbInY2OBbduA27eBjx+BypUBS0ucrl0b3YYNg7a2NtPsTORTE4wbBxga4sOHD7CxscFvv/2GESNGsE6rHIXUJDMzE7169ULbtm3xv//9j3Va7iu8oQtQUlIS5syZgxo1asB9wADAwwM4flz2ZFrapwXLlQOIgN69gQULAAXN4KhyQkMLrQn17g3Xd++QbmkJLy8vNjmVqQg1Qe/e2FylCoKePcOpU6c0cydAxfGGLmSbNwPz5gGpqbIPZH5EItmHdtUqQIFzrauEItZEKhIhXSTCN+vWQUfoB0KLUZM0AJLly1HJzU15+bgi016yZMkS1iE4Bcj+kKakFG15sRg4dw6oWlW4e+p51KQegOYAvr6XjgjAN0TQOn9e42qSrVnWT72sv4sAfAOg7OXLwq6JOiNOeK5dI9LTI5LtbxXvR0+PKDRU7pGio6PJzs6OmjRpQubm5rR27VoiInr37h3Z29uTmZkZ2dvbU3x8vNy3TUT51qQuQKcZ1eRz+dVHoVTwfcKVDm/oQjRoEJFIVLIPqkhENHiw3CO9evWKbty4QURECQkJ1LBhQ7p79y65urqSh4cHERF5eHiQm5ub3LdNRPnWpEgNXUE1+Vx+9VEoFXyfcKXDG7rQvHlDpKub54fwBkAtAKoAkANAQwFalNeHVVeXKDZWoTH79+9Pp06dokaNGtGrV6+ISNbUGjVqVOJ1ZmZmkqenJ0VFRX35RAE1qQuQJ0AWAFXKqkkqo5p8Lrs+8rBlyxa6efPmlw8WUJMi/7JTck24wvHz0IVm27Y8H84AMAjAWADxAEYAOJjfOkSifNcjD0+fPkVYWBjatm2LN2/ewMjICIDsQqfY2NgSrzc5ORlubm5o2rQpnJ2d8fTpU9kThfxbAgGcABAF4DaAPJdWcE0+93l95GHBggVo134Tk1sAAARoSURBVK4d7O3tP12bII9/ixJrwhUNv1JUaG7f/vKUsyxXAUgAzITs4NZgAG3yW0dqKq75+mLX8+climBkZITZs2ejXLlyuZ5LSkrKuaFypUqVCl2XRCLB0aNHce7cuUKXzcjIgEgkQlpaGnbv3o2AgAC0a9cOF+vVy7Mm2WYCqJX1534A/stroVLW5GvLli3L80Klgupz/PhxHM8+rbAYkpOTkZGRgbNnz6J169YwMTHBo7ZtoVNATYokNRW4c6d06+Dkijd0ofn4Mc+HXwEwhqyZZyto1hYDHZ0Sz75YrVq1PO91KhaLMWTIEDg5OWHw4MEAgBo1aiAmJgZGRkaIiYlB9erVv3iNSCSCgYFBkbKkpaXlXJqvo6MDLS0t2XTAb98W+Lqan/1ZD7Ja5aU0NflaXudw51Wfz1WtWrVE28/+v9DW1oaWlhZMTU2hlZhY/NB5ef9ePuvh5IP1mA8nZ05OeY53/gNQLYCknz3WMb8xdIDI2VmusaRSKTk7O9OsWbO+eHzevHlfHBR1dXUt8TYSEhIIAFWsWJHc3d0pMTFR9kQ+NclrnPgXgJyUVJPP5VcfeTAwMKAyZcrQ9OnTKSYmRvZgATUp1gFjBdaEKz4+hi40lpZAHpMltQegDWADZEMvhwFcy28d5coBcp7b+tKlS9i5cyf+/vtvtGjRAi1atMBff/2FH3/8EadPn0bDhg1x+vRp/PjjjyXeRoUKFXDw4EG8evUKixYt+jSkkU9NikUBNflcfvWRhz179uDZs2fYsGEDatbM+j6iBjXhio9fKSo0sbFA3bp5jhlfBzARwGMAvQFkAmgJ4OevF9TVBaKjAUNDBYdVkgJqUg/AVgD2WX9fAll9dn29oAbVJFs9fFmbXIRWEwHge+hCU726bG6WPKZ5tYHsgF8SgP0AXgKo/fVCIhHw3XfC+pAWUJOn+LJhLUEezVzDapLtKQpo5kKsiQDwhi5ECxbIvg5/5TyA15ANuWyH7BS9b79eqFw52euFJp+aFAmvSW5CrYma4w1diFq3lk209dX85g8AWAGoDGA1gCAARp8voKcne52NjbKSKk8+NSkUr0luQq6JmuNj6ELGZ1vMjdckN14TweANXeiuX5fNc/3XX7IPZGrqp+ey57n+7jvZ12dN2ePiNcmN10QQeEPXFG/fyi7TvnNHdjGIvr7slLOxYzX3wBavSW68JmqNN3SO4ziB4AdFOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TCN7QOY7jBII3dI7jOIHgDZ3jOE4geEPnOI4TiP8DzLzUHEcKtocAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f339210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('a', pos = (5, 10))\n",
    "g.add_node('b', pos = (10, 10))\n",
    "g.add_node('c', pos = (15, 10))\n",
    "g.add_node('d', pos = (5, 5))\n",
    "g.add_node('e', pos = (10, 5))\n",
    "g.add_node('f', pos = (15, 5))\n",
    "g.add_node('g', pos = (5, 0))\n",
    "g.add_node('h', pos = (10, 0))\n",
    "g.add_node('i', pos = (15, 0))\n",
    "g.add_node('t', pos = (20, 5))\n",
    "g.add_edge('s', 'a', weight = -100)\n",
    "g.add_edge('a', 'b', weight = 500)\n",
    "g.add_edge('b', 'c', weight = 3)\n",
    "g.add_edge('c', 't', weight = 4)\n",
    "g.add_edge('s', 'd', weight = -8)\n",
    "g.add_edge('d', 'e', weight = 9)\n",
    "g.add_edge('e', 'f', weight = 10)\n",
    "g.add_edge('f', 't', weight = 2)\n",
    "g.add_edge('s', 'g', weight = 4)\n",
    "g.add_edge('g', 'h', weight = 20)\n",
    "g.add_edge('h', 'i', weight = 2)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "g.add_edge('a', 'f', weight = 1)\n",
    "g.add_edge('b', 'f', weight = 1)\n",
    "g.add_edge('b', 'g', weight = 1)  # Changing\n",
    "g.add_edge('h', 'f', weight = 1)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "djikstra_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Problem 9.8\n",
    "\n",
    "Consider a directed graph G and a source vertex ss. Suppose G contains a negative cycle (a directed cycle in which the sum of the edge lengths is negative) and also a path from s to this cycle. Suppose you run Dijkstra's algorithm on G (with source s). Which of the following statements are true?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex a\n",
      "Vertex a is at distance 0\n",
      "Vertex c is at distance -3\n",
      "Vertex b is at distance 1\n",
      "Vertex e is at distance 0\n",
      "Vertex d is at distance -6\n",
      "Vertex g is at distance -1\n",
      "Vertex f is at distance -1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f516210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('a', pos = (0, 5))\n",
    "g.add_node('b', pos = (10, 5))\n",
    "g.add_edge('a', 'b', weight = 1)\n",
    "\n",
    "g.add_node('c', pos = (15, 7))\n",
    "g.add_edge('b', 'c', weight = -8)\n",
    "\n",
    "g.add_node('d', pos = (15, 12))\n",
    "g.add_edge('c', 'd', weight = -3)\n",
    "\n",
    "g.add_node('e', pos = (7, 12))\n",
    "g.add_edge('d', 'e', weight = 6)\n",
    "\n",
    "g.add_node('f', pos = (5, 10))\n",
    "g.add_edge('e', 'f', weight = -1)\n",
    "g.add_edge('f', 'c', weight = 2)\n",
    "\n",
    "g.add_node('g', pos = (7, 7))\n",
    "g.add_edge('f', 'g', weight = 1)\n",
    "g.add_edge('g', 'c', weight = -2)\n",
    "g.add_edge('a', 'g', weight = -1)\n",
    "\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "djikstra_naive(g, 'a')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we see in the above graph, we have two directed cycles g -> c -> d -> e -> f -> g and c -> d -> e -> f -> c. Both have non negative sum of lengths. Still, the shortest distance using Djikstra algorithm for c will be calculated as -3 where the true shortest distance is -7. All vertices that gets pulled into frontier after c will be incorrect. For the above graph, except g and b, the distances will be incorrect. Following code snippet demonstrates the incorrect path lengths\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Problems\n",
    "\n",
    "**Problem 1: ** <br>\n",
    "In lecture we define the length of a path to be the sum of the lengths of its edges. Define the bottleneck of a path to be the maximum length of one of its edges. A mininum-bottleneck path between two vertices s and t is a path with bottleneck no larger than that of any other s-t path. Show how to modify Dijkstra's algorithm to compute a minimum-bottleneck path between two given vertices. The running time should be $O(m \\log n)$, as in lecture.\n",
    "\n",
    "\n",
    "    The running time should be O(m logn), as in lecture.\n",
    "    First we have implemented it using a loop over nodes and edges to get an  O(m n) implementation.\n",
    "    Later, we will use heap datastructure to get O(m logn) running time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex 1\n",
      "Vertex 1 has a minimum-bottleneck of 0 having path ['1']\n",
      "Vertex 2 has a minimum-bottleneck of 1 having path ['1', '2']\n",
      "Vertex 3 has a minimum-bottleneck of 2 having path ['1', '2', '3']\n",
      "Vertex 4 has a minimum-bottleneck of 3 having path ['1', '2', '3', '4']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def minimum_bottleneck_path_naive(DG, source):\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    B = {}\n",
    "    B[source] = str(source)\n",
    "    bottleneck = {}\n",
    "    bottleneck[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    v_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                dji_greedy = DG.edges[edge[0], edge[1]]['weight'] #bottleneck criterion\n",
    "                if edge[1] not in A:\n",
    "                    A[edge[1]] = dji_greedy\n",
    "                    bottleneck[edge[1]] = dji_greedy\n",
    "                    #print(\"from bottleneck[{}] = {} ,to bottleneck[{}] = {}\".format(edge[0] , bottleneck[edge[0]], edge[1] , bottleneck[edge[1]]))\n",
    "                elif dji_greedy < A[edge[1]]:\n",
    "                    A[edge[1]] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    if dji_greedy > bottleneck[edge[0]]:\n",
    "                        bottleneck[edge[1]] = dji_greedy\n",
    "                        #print(\"from bottleneck[{}] = {} ,to bottleneck[{}] = {}\".format(edge[0] , bottleneck[edge[0]], edge[1] , bottleneck[edge[1]]))\n",
    "                    else:\n",
    "                        bottleneck[edge[1]] = bottleneck[edge[0]]\n",
    "                    w_overall = edge[1] \n",
    "                    v_overall = edge[0] \n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "        B[w_overall] = B[v_overall] +','+ str(w_overall)\n",
    "        \n",
    "    print(\"Printing minimum-bottleneck path from starting vertex {}\".format(source))\n",
    "    for node in A:\n",
    "        print(\"Vertex {} has a minimum-bottleneck of {} having path {}\".format(node, bottleneck[node], B[node].split(',')))\n",
    "        \n",
    "        \n",
    "\n",
    "DG = nx.DiGraph()\n",
    "DG.add_node(1, pos = (0, 5))\n",
    "DG.add_node(2, pos = (7, 10))\n",
    "DG.add_node(3, pos = (7, 0))\n",
    "DG.add_node(4, pos = (14, 5))\n",
    "DG.add_edge(1, 2, weight = 1)\n",
    "DG.add_edge(2, 3, weight = 2)\n",
    "DG.add_edge(3, 4, weight = 3)\n",
    "DG.add_edge(1, 3, weight = 4)\n",
    "DG.add_edge(2, 4, weight = 6)\n",
    "pos = nx.get_node_attributes(DG, 'pos')\n",
    "weights =nx.get_edge_attributes(DG, 'weight')\n",
    "nx.draw_networkx_edge_labels(DG, pos, edge_labels = weights)\n",
    "nx.draw(DG, pos, with_labels = True)\n",
    "\n",
    "minimum_bottleneck_path_naive(DG, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex s\n",
      "Vertex s has a minimum-bottleneck of 0 having path ['s']\n",
      "Vertex v has a minimum-bottleneck of 1 having path ['s', 'v']\n",
      "Vertex w has a minimum-bottleneck of 2 having path ['s', 'v', 'w']\n",
      "Vertex t has a minimum-bottleneck of 3 having path ['s', 'v', 'w', 't']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('v', pos = (5, 0))\n",
    "g.add_node('w', pos = (5, 5))\n",
    "g.add_node('t', pos = (10, 5))\n",
    "g.add_edge('s', 'v', weight = 1)\n",
    "g.add_edge('v', 't', weight = 6)\n",
    "g.add_edge('s', 'w', weight = 4)\n",
    "g.add_edge('v', 'w', weight = 2)\n",
    "g.add_edge('w', 't', weight = 3)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "minimum_bottleneck_path_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex v\n",
      "Vertex v has a minimum-bottleneck of 0 having path ['v']\n",
      "Vertex t has a minimum-bottleneck of 3 having path ['v', 'w', 't']\n",
      "Vertex w has a minimum-bottleneck of 2 having path ['v', 'w']\n"
     ]
    }
   ],
   "source": [
    "start_vert = 'v'\n",
    "minimum_bottleneck_path_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex s\n",
      "Vertex s has a minimum-bottleneck of 0 having path ['s']\n",
      "Vertex a has a minimum-bottleneck of 5 having path ['s', 'a']\n",
      "Vertex d has a minimum-bottleneck of 8 having path ['s', 'd']\n",
      "Vertex g has a minimum-bottleneck of 4 having path ['s', 'g']\n",
      "Vertex h has a minimum-bottleneck of 20 having path ['s', 'g', 'h']\n",
      "Vertex b has a minimum-bottleneck of 5 having path ['s', 'a', 'b']\n",
      "Vertex f has a minimum-bottleneck of 5 having path ['s', 'a', 'f']\n",
      "Vertex t has a minimum-bottleneck of 5 having path ['s', 'a', 'f', 't']\n",
      "Vertex c has a minimum-bottleneck of 5 having path ['s', 'a', 'b', 'c']\n",
      "Vertex e has a minimum-bottleneck of 9 having path ['s', 'd', 'e']\n",
      "Vertex i has a minimum-bottleneck of 20 having path ['s', 'g', 'h', 'i']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('a', pos = (5, 10))\n",
    "g.add_node('b', pos = (10, 10))\n",
    "g.add_node('c', pos = (15, 10))\n",
    "g.add_node('d', pos = (5, 5))\n",
    "g.add_node('e', pos = (10, 5))\n",
    "g.add_node('f', pos = (15, 5))\n",
    "g.add_node('g', pos = (5, 0))\n",
    "g.add_node('h', pos = (10, 0))\n",
    "g.add_node('i', pos = (15, 0))\n",
    "g.add_node('t', pos = (20, 5))\n",
    "g.add_edge('s', 'a', weight = 5)\n",
    "g.add_edge('a', 'b', weight = 5)\n",
    "g.add_edge('b', 'c', weight = 3)\n",
    "g.add_edge('c', 't', weight = 4)\n",
    "g.add_edge('s', 'd', weight = 8)\n",
    "g.add_edge('d', 'e', weight = 9)\n",
    "g.add_edge('e', 'f', weight = 10)\n",
    "g.add_edge('f', 't', weight = 2)\n",
    "g.add_edge('s', 'g', weight = 4)\n",
    "g.add_edge('g', 'h', weight = 20)\n",
    "g.add_edge('h', 'i', weight = 2)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "g.add_edge('a', 'f', weight = 1)\n",
    "g.add_edge('b', 'f', weight = 1)\n",
    "g.add_edge('b', 'g', weight = 1)\n",
    "g.add_edge('h', 'f', weight = 1)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "minimum_bottleneck_path_naive(g, start_vert)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problem 2: ** <br>\n",
    "We can do better. Suppose now that the graph is undirected. Give a linear-time ($O(m)$) algorithm to compute a minimum-bottleneck path between two given vertices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex v\n",
      "Vertex s has a minimum-bottleneck of 1 having path ['v', 's']\n",
      "Vertex t has a minimum-bottleneck of 3 having path ['v', 'w', 't']\n",
      "Vertex w has a minimum-bottleneck of 2 having path ['v', 'w']\n",
      "Vertex v has a minimum-bottleneck of 0 having path ['v']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180dc850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def undirected_minimum_bottleneck_path_naive(DG, source):\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    B = {}\n",
    "    B[source] = str(source)\n",
    "    bottleneck = {}\n",
    "    bottleneck[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    v_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                edge_tail = edge[0]\n",
    "                edge_head = edge[1]\n",
    "            elif (edge[1] in X) and (edge[0] not in X):\n",
    "                edge_tail = edge[1]\n",
    "                edge_head = edge[0]\n",
    "            if ((edge[0] in X) and (edge[1] not in X))  or ((edge[1] in X) and (edge[0] not in X)):\n",
    "                dji_greedy = DG.edges[edge_tail, edge_head]['weight'] #bottleneck criterion\n",
    "                if edge_head not in A:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                    bottleneck[edge_head] = dji_greedy\n",
    "                elif dji_greedy < A[edge_head]:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    if dji_greedy > bottleneck[edge_tail]:\n",
    "                        bottleneck[edge_head] = dji_greedy\n",
    "                    else:\n",
    "                        bottleneck[edge_head] = bottleneck[edge_tail]\n",
    "                    w_overall = edge_head \n",
    "                    v_overall = edge_tail\n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "        B[w_overall] = B[v_overall] +','+ str(w_overall)\n",
    "        \n",
    "    print(\"Printing minimum-bottleneck path from starting vertex {}\".format(source))\n",
    "    for node in A:\n",
    "        print(\"Vertex {} has a minimum-bottleneck of {} having path {}\".format(node, bottleneck[node], B[node].split(',')))\n",
    "        \n",
    "        \n",
    "\n",
    "UDG = nx.Graph()\n",
    "UDG.add_node('s', pos = (0, 5))\n",
    "UDG.add_node('v', pos = (5, 0))\n",
    "UDG.add_node('w', pos = (5, 5))\n",
    "UDG.add_node('t', pos = (10, 5))\n",
    "UDG.add_edge('s', 'v', weight = 1)\n",
    "UDG.add_edge('v', 't', weight = 6)\n",
    "UDG.add_edge('s', 'w', weight = 4)\n",
    "UDG.add_edge('v', 'w', weight = 2)\n",
    "UDG.add_edge('w', 't', weight = 3)\n",
    "pos = nx.get_node_attributes(UDG, 'pos')\n",
    "weights =nx.get_edge_attributes(UDG, 'weight')\n",
    "nx.draw_networkx_edge_labels(UDG, pos, edge_labels = weights)\n",
    "nx.draw(UDG, pos, with_labels = True)\n",
    "\n",
    "undirected_minimum_bottleneck_path_naive(UDG, 'v')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex s\n",
      "Vertex a has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'f', 'a']\n",
      "Vertex c has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'c']\n",
      "Vertex b has a minimum-bottleneck of 4 having path ['s', 'g', 'b']\n",
      "Vertex e has a minimum-bottleneck of 9 having path ['s', 'd', 'e']\n",
      "Vertex d has a minimum-bottleneck of 8 having path ['s', 'd']\n",
      "Vertex g has a minimum-bottleneck of 4 having path ['s', 'g']\n",
      "Vertex f has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'f']\n",
      "Vertex i has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'f', 't', 'i']\n",
      "Vertex h has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'f', 'h']\n",
      "Vertex s has a minimum-bottleneck of 0 having path ['s']\n",
      "Vertex t has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'f', 't']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x151f6600d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "UDg = g.to_undirected()\n",
    "pos = nx.get_node_attributes(UDg, 'pos')\n",
    "weights =nx.get_edge_attributes(UDg, 'weight')\n",
    "nx.draw_networkx_edge_labels(UDg, pos, edge_labels = weights)\n",
    "nx.draw(UDg, pos, with_labels = True)\n",
    "\n",
    "undirected_minimum_bottleneck_path_naive(UDg, 's')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from source vertex v to destination vertex t\n",
      "Route v -> t has a minimum-bottleneck of 3 having path ['v', 'w', 't']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def undirected_minimum_bottleneck_route_naive(DG, source, destination):\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    B = {}\n",
    "    B[source] = str(source)\n",
    "    bottleneck = {}\n",
    "    bottleneck[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    v_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                edge_tail = edge[0]\n",
    "                edge_head = edge[1]\n",
    "            elif (edge[1] in X) and (edge[0] not in X):\n",
    "                edge_tail = edge[1]\n",
    "                edge_head = edge[0]\n",
    "            if ((edge[0] in X) and (edge[1] not in X))  or ((edge[1] in X) and (edge[0] not in X)):\n",
    "                dji_greedy = DG.edges[edge_tail, edge_head]['weight'] #bottleneck criterion\n",
    "                if edge_head not in A:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                    bottleneck[edge_head] = dji_greedy\n",
    "                elif dji_greedy < A[edge_head]:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    if dji_greedy > bottleneck[edge_tail]:\n",
    "                        bottleneck[edge_head] = dji_greedy\n",
    "                    else:\n",
    "                        bottleneck[edge_head] = bottleneck[edge_tail]\n",
    "                    w_overall = edge_head \n",
    "                    v_overall = edge_tail\n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "        B[w_overall] = B[v_overall] +','+ str(w_overall)\n",
    "        if w_overall == destination:\n",
    "            break\n",
    "        \n",
    "    print(\"Printing minimum-bottleneck path from source vertex {} to destination vertex {}\".format(source, destination))\n",
    "    for node in A:\n",
    "        if node == destination:\n",
    "            print(\"Route {} -> {} has a minimum-bottleneck of {} having path {}\".format(source, destination, bottleneck[node], B[node].split(',')))\n",
    "        \n",
    "        \n",
    "\n",
    "UDG = nx.Graph()\n",
    "UDG.add_node('s', pos = (0, 5))\n",
    "UDG.add_node('v', pos = (5, 0))\n",
    "UDG.add_node('w', pos = (5, 5))\n",
    "UDG.add_node('t', pos = (10, 5))\n",
    "UDG.add_edge('s', 'v', weight = 1)\n",
    "UDG.add_edge('v', 't', weight = 6)\n",
    "UDG.add_edge('s', 'w', weight = 4)\n",
    "UDG.add_edge('v', 'w', weight = 2)\n",
    "UDG.add_edge('w', 't', weight = 3)\n",
    "pos = nx.get_node_attributes(UDG, 'pos')\n",
    "weights =nx.get_edge_attributes(UDG, 'weight')\n",
    "nx.draw_networkx_edge_labels(UDG, pos, edge_labels = weights)\n",
    "nx.draw(UDG, pos, with_labels = True)\n",
    "\n",
    "undirected_minimum_bottleneck_route_naive(UDG, 'v', 't')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from source vertex s to destination vertex a\n",
      "Route s -> a has a minimum-bottleneck of 4 having path ['s', 'g', 'b', 'f', 'a']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "UDg = g.to_undirected()\n",
    "pos = nx.get_node_attributes(UDg, 'pos')\n",
    "weights =nx.get_edge_attributes(UDg, 'weight')\n",
    "nx.draw_networkx_edge_labels(UDg, pos, edge_labels = weights)\n",
    "nx.draw(UDg, pos, with_labels = True)\n",
    "\n",
    "undirected_minimum_bottleneck_route_naive(UDg, 's', 'a')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problem 3: ** <br>\n",
    "What if the graph is directed? Can you compute a minimum-bottleneck path between two given vertices faster than $O(m \\log n)$ ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum-bottleneck path from starting vertex s\n",
      "Route s -> a has a minimum-bottleneck of 5 having path ['s', 'a']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1514955090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def minimum_bottleneck_route_naive(DG, source, destination):\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    B = {}\n",
    "    B[source] = str(source)\n",
    "    bottleneck = {}\n",
    "    bottleneck[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    v_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                dji_greedy = DG.edges[edge[0], edge[1]]['weight'] #bottleneck criterion\n",
    "                if edge[1] not in A:\n",
    "                    A[edge[1]] = dji_greedy\n",
    "                    bottleneck[edge[1]] = dji_greedy\n",
    "                    #print(\"from bottleneck[{}] = {} ,to bottleneck[{}] = {}\".format(edge[0] , bottleneck[edge[0]], edge[1] , bottleneck[edge[1]]))\n",
    "                elif dji_greedy < A[edge[1]]:\n",
    "                    A[edge[1]] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    if dji_greedy > bottleneck[edge[0]]:\n",
    "                        bottleneck[edge[1]] = dji_greedy\n",
    "                        #print(\"from bottleneck[{}] = {} ,to bottleneck[{}] = {}\".format(edge[0] , bottleneck[edge[0]], edge[1] , bottleneck[edge[1]]))\n",
    "                    else:\n",
    "                        bottleneck[edge[1]] = bottleneck[edge[0]]\n",
    "                    w_overall = edge[1] \n",
    "                    v_overall = edge[0] \n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "        B[w_overall] = B[v_overall] +','+ str(w_overall)\n",
    "        if w_overall == destination:\n",
    "            break\n",
    "        \n",
    "    print(\"Printing minimum-bottleneck path from starting vertex {}\".format(source))\n",
    "    for node in A:\n",
    "        if node == destination:\n",
    "            print(\"Route {} -> {} has a minimum-bottleneck of {} having path {}\".format(source, destination, bottleneck[node], B[node].split(',')))        \n",
    "        \n",
    "\n",
    "DG = nx.DiGraph()\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('a', pos = (5, 10))\n",
    "g.add_node('b', pos = (10, 10))\n",
    "g.add_node('c', pos = (15, 10))\n",
    "g.add_node('d', pos = (5, 5))\n",
    "g.add_node('e', pos = (10, 5))\n",
    "g.add_node('f', pos = (15, 5))\n",
    "g.add_node('g', pos = (5, 0))\n",
    "g.add_node('h', pos = (10, 0))\n",
    "g.add_node('i', pos = (15, 0))\n",
    "g.add_node('t', pos = (20, 5))\n",
    "g.add_edge('s', 'a', weight = 5)\n",
    "g.add_edge('a', 'b', weight = 5)\n",
    "g.add_edge('b', 'c', weight = 3)\n",
    "g.add_edge('c', 't', weight = 4)\n",
    "g.add_edge('s', 'd', weight = 8)\n",
    "g.add_edge('d', 'e', weight = 9)\n",
    "g.add_edge('e', 'f', weight = 10)\n",
    "g.add_edge('f', 't', weight = 2)\n",
    "g.add_edge('s', 'g', weight = 4)\n",
    "g.add_edge('g', 'h', weight = 20)\n",
    "g.add_edge('h', 'i', weight = 2)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "g.add_edge('a', 'f', weight = 1)\n",
    "g.add_edge('b', 'f', weight = 1)\n",
    "g.add_edge('b', 'g', weight = 1)\n",
    "g.add_edge('h', 'f', weight = 1)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "dest_vert = 'a'\n",
    "minimum_bottleneck_route_naive(g, start_vert, dest_vert)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Challenging problem\n",
    "\n",
    "In this programming problem you'll code up Dijkstra's shortest-path algorithm.\n",
    "\n",
    "Download the following text file: dijkstraData.txt\n",
    "\n",
    "The file contains an adjacency list representation of an undirected weighted graph with 200 vertices labeled 1 to 200. Each row consists of the node tuples that are adjacent to that particular vertex along with the length of that edge. For example, the 6th row has 6 as the first entry indicating that this row corresponds to the vertex labeled 6. The next entry of this row \"141,8200\" indicates that there is an edge between vertex 6 and vertex 141 that has length 8200. The rest of the pairs of this row indicate the other vertices adjacent to vertex 6 and the lengths of the corresponding edges.\n",
    "\n",
    "Your task is to run Dijkstra's shortest-path algorithm on this graph, using 1 (the first vertex) as the source vertex, and to compute the shortest-path distances between 1 and every other vertex of the graph. If there is no path between a vertex vv and vertex 1, we'll define the shortest-path distance between 1 and vv to be 1000000.\n",
    "\n",
    "You should report the shortest-path distances to the following ten vertices, in order: 7,37,59,82,99,115,133,165,188,197. You should encode the distances as a comma-separated string of integers. So if you find that all ten of these vertices except 115 are at distance 1000 away from vertex 1 and 115 is 2000 distance away, then your answer should be 1000,1000,1000,1000,1000,2000,1000,1000,1000,1000. Remember the order of reporting DOES MATTER, and the string should be in the same order in which the above ten vertices are given.\n",
    "\n",
    "IMPLEMENTATION NOTES: This graph is small enough that the straightforward $O(mn)$ time implementation of Dijkstra's algorithm should work fine. OPTIONAL: For those of you seeking an additional challenge, try implementing the heap-based version. Note this requires a heap that supports deletions, and you'll probably need to maintain some kind of mapping between vertices and their positions in the heap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex s\n",
      "Vertex a is at distance 5\n",
      "Vertex e is at distance 16\n",
      "Vertex t is at distance 8\n",
      "Vertex i is at distance 9\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "def undirected_djikstra_naive(DG, source, destination):\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                edge_tail = edge[0]\n",
    "                edge_head = edge[1]\n",
    "            elif (edge[1] in X) and (edge[0] not in X):\n",
    "                edge_tail = edge[1]\n",
    "                edge_head = edge[0]\n",
    "            if ((edge_tail in X) and (edge_head not in X)) :\n",
    "                dji_greedy = A[edge_tail] + DG.edges[edge_tail, edge_head]['weight'] #djikstra's greedy criterion\n",
    "                if edge_head not in A:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                elif dji_greedy < A[edge_head]:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    w_overall = edge_head  \n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "    print(\"Printing minimum distances from starting vertex {}\".format(source))\n",
    "    for node in A:\n",
    "        if node in destination:\n",
    "            print(\"Vertex {} is at distance {}\".format(node, A[node]))\n",
    "        \n",
    "        \n",
    "\n",
    "\n",
    "pos = nx.get_node_attributes(UDg, 'pos')\n",
    "weights =nx.get_edge_attributes(UDg, 'weight')\n",
    "nx.draw_networkx_edge_labels(UDg, pos, edge_labels = weights)\n",
    "nx.draw(UDg, pos, with_labels = True)\n",
    "\n",
    "\n",
    "dest_verts = ['e', 'i', 't', 'a']\n",
    "undirected_djikstra_naive(UDg, 's', dest_verts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import urllib3\n",
    "\n",
    "def testcase():\n",
    "    challenge_graph = nx.Graph()\n",
    "    http = urllib3.PoolManager()\n",
    "    r1 = http.request('GET', \"https://d3c33hcgiwev3.cloudfront.net/_dcf1d02570e57d23ab526b1e33ba6f12_dijkstraData.txt?Expires=1562630400&Signature=ZOvhWVbzgyiVE3G--kHjTZFT88KvlX2Tg~FJ6XpH7EISRUhkXTLk2cBMie1fREsIUI3zJdd3gWkLasBOiU-bZO4Ud91saYKaj-wfcSsh05uGTglYjtKYNHVPDfG2MkKUiTgzRjdhokyrC-gPJQhHeiyGaeAlLKnz81x5rT7zv0M_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A\")\n",
    "    IntegerMatrixStringJoin = r1.data.decode('utf8').split('\\r\\n')\n",
    "    IntegerMatrixStringJoin.remove('')\n",
    "    edges = []\n",
    "    for i in IntegerMatrixStringJoin:\n",
    "        node_edges = i.split('\\t')\n",
    "        sourceint = int(node_edges[0])\n",
    "        dest_list = node_edges[1:-1]\n",
    "        challenge_graph = nx.Graph()\n",
    "        for edstr in dest_list:\n",
    "            edlist = edstr.split(',')\n",
    "            destint = int(edlist[0])\n",
    "            edgeweight = int(edlist[1])\n",
    "            edges.append((sourceint, destint, edgeweight))\n",
    "    challenge_graph.add_weighted_edges_from(edges)\n",
    "    nx.draw(challenge_graph, with_labels = True)\n",
    "    return challenge_graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/aishwaya/anaconda2/lib/python2.7/site-packages/urllib3/connectionpool.py:858: InsecureRequestWarning: Unverified HTTPS request is being made. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#ssl-warnings\n",
      "  InsecureRequestWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex 1\n",
      "Vertex 7 is at distance 2599\n",
      "Vertex 37 is at distance 2610\n",
      "Vertex 59 is at distance 2947\n",
      "Vertex 82 is at distance 2052\n",
      "Vertex 99 is at distance 2367\n",
      "Vertex 115 is at distance 2399\n",
      "Vertex 133 is at distance 2029\n",
      "Vertex 165 is at distance 2442\n",
      "Vertex 188 is at distance 2505\n",
      "Vertex 197 is at distance 3068\n"
     ]
    },
    {
     "data": {
      "image/png": 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Lo1gspkQiYZ06dejr60tPT0+q1WrK5XIGBQUxJiaG5cqV4+7du19Ym/R6PY8ePcopU6awfv36tLe3Z3R0NAcPHsxt27YJpsnnRK/Xc8uWLaxZsybd3d05efLkJ8489Xo9v//+e6rVavbv35+//vor1Wo1pVIpJ06cyLy8PPr4+NDGxoaHDh3isWPH6OrqygULFpAkBwwYwMTERHbr1o2tW7dm3bp1OWbMmFK3Ozk5mStXrmRubi4BmMT9559/Znh4eKmsLHq9nmPGjKGHhwcPHTpU6rYICLwrCOL8hjNlyhR26tTJ9P769et0cHCgubk5ra2tWblyZYrFYpqbm7NVq1Z0c3Nj1apV6e7uTnt7e9rb27Nt27ZUqVTs3bs38/LyXngb7969y61btzI9PZ1RUVG0t7dn/fr1OXXqVB47dkwwgT8FvV7Pn376iZUqVaK/vz+//fbbpz7gXL58mY0bN2ZwcDB37NjBMWPG0MrKiiqVinv27OGZM2dMoVI5OTk8ffo0PTw8OHPmTJLkkiVL6OXlxSVLltDDw4PffffdMzuBPcgHH3zAjIwMMjubH1ta8mB4OJmcTH2rVhwrl3Pn6tWlvubChQupVCq5ZcuWUp8rIPAuIIjzG86BAwcYEBBQYltGRgblcjktLCzo4uLCoKAgikQiWlpaslevXlSpVGzXrh2VSiWdnJyo0WhYo0YNpqam0t3d/aXHlubk5HDRokVs164dXVxc6O3tzS5dunDZsmWl8iZ/19Fqtfz+++8ZFhbG8PBwLlmyhFqt9onn6PV6zp8/nyqVioMHD+bZs2cZHx9PGxsb1qxZk7m5udy5c6cpVOru3bs8f/48fXx8OGXKFJLkoUOHqFAo+Msvv9DV1ZWZmZn09vbmxo0bn6sfMzp14uHAQFIqZeEDIYH3zM15VywmGzc2JN4pBZs2baJSqeTixYufq10CAm8zgji/4eh0Ojo5OfHSpUumbVqtlqGhobSysqKdnR3r1atHlUplSkxyP/510KBBlMlkDAoKopeXFxUKBT/77DMGBASwUaNGPH/+/Etvv16v56FDh/jll18yKSmJtra2rFy5MocPH86dO3e+kPXwt427d+9y1qxZ9Pf3Z+XKlbl27dpnsi6cP3+e9erVY1hYGPfs2cNffvmFcrmc1tbWHDdunMnMLZFIWL9+fep0Ol6+fJkBAQH84osvSJK5ubn08/Pj3Llz2axZM/bp04effPIJU1JSnq8z06fznoUFdU9JnqMXiQzx/KWMaT5w4ADd3NxM/RMQ+F9BEOe3gPr163PJkiUltv3+++90cnKinZ0dFQoFhw4dSjs7O4pEItrY2HDixIlUq9X89NNP6ePjw5iYGMrlcmo0GrZr147p6elUKBScPHnyU2drL5KCggJu2LCB/fv3Z2hoKJ2cnNi0aVN+8803/8m7/G0gPz+fkyZNopubG2vVqsWtW7c+k+Do9XrOmjWLCoWCw4cPZ35+PtPT02ljY2PK7EWyRKgUaQhRKlu2LEeMGEHS8KCXnJzMHj16cMGCBSxTpgz/+usvyuXy53tQe44Md88j0OfOnWPZsmXZq1evV/pdFRB4nQji/BYwfvx4du/e/aHtrVq1MuVGtre357Rp02hra0uRSERbW1vOnj2bXl5e/Pjjj5mYmMjIyEiqVCpGRETQx8eHixYtYtWqVVm+fHnu27fvNfTMkMRi3rx5bNmyJZVKJQMCAtizZ0/+9NNP/Pfff19Lm140ubm5HDVqFFUqFZs0aVIq57wzZ86wZs2ajIyM5IEDB3j27FlGR0fT0dGRNWrU4LVr10iyRKgUafCuL1euHAcNGmR6ABg+fDirVKnC48ePU6lU8s8//2SdOnVMs+pSUSw3/GKAQQCtAfoA/BXgYYBRAB2NrxrGbSaBLqWDYm5uLhMSEtikSRMWFBSUvr0CAm8Zgji/BWRlZTE0NPSh7RcvXqSTkxNtbW3p5OREf39/jh8/nk5OThSJRHRwcOAPP/zA0NBQ9ujRg3379qWHhwcrVKjAkJAQyuVyfvzxx5wxYwZVKhX79+//WvNt63Q67t27l59//jmrVatGW1tbJiQkcPTo0dyzZ89bl0EqOzub6enplMlkbNOmDQ8fPvzM5+p0Ok6fPp0KhYKjR49mUVERV6xYQUdHR9ra2nL06NHU6XTU6XSsUqWKKVSKNGR+q1ixInv37m0S5p9++omurq68ePGiKTXnypUrGRwc/Hze9Y0bkyIRNwD0ALgToA7gBeMrF+BpgHpj6tlJAEPvi7NIZMiIV0ru3LnDFi1aMDY21vRQIiDwriKI81tAUVER7ezsHvmDNHbsWIaEhFCtVtPPz4/t2rVjz549qVarKZFI6OjoyHXr1rFq1apMTU3lnDlzKJfLmZKSQrVazejoaJYvX547duwwzcTXrl37Gnr5MP/++y/XrFnDXr16MSgoiAqFgu+99x7nzJnDixcvvu7mPZZz586xV69edHJyYrdu3Xjq1KlSnX/ixAkmJCSwYsWKPHz4MAsLC5mWlkYHBwcqFApu27aNpGF87odK/fXXXyTJ27dvMy4ujl26dDEJ87Fjx6hUKrljxw5OmDCBsbGxzMvLo6enJ3/55ZfSdzA725BqFmAlgLOeYsouAjgVoFXx7VKpISNeKdHpdBwwYAADAwNLPa4CAm8Tgji/JdSqVeuRXtZ37tyhv78/g4KCKJfL6erqyjlz5rB27drUaDS0sLCgTCbj1q1b2bhxY9aoUYPbtm2jh4cHW7VqRRcXF9auXZsymYxff/01f/75Z/r4+DAlJaWEE9qbwJkzZzhz5kw2b96cTk5ODAkJYd++fbl+/fo3wtR59OhRdujQgTKZjAMGDCj1+Gm1Wn711VeUy+UcP348tVot//nnH5YpU4YKhYLx8fHMzs4mSVOolLOzsylrWGFhIRMTE/n++++brAz//vsvy5Yty+nTp5u8tE+ePMmPP/6Yqampz9fRsWNJqZRagOYAPwfoC9AVYHeABcVE2AGgBKAI4GfFxdnKypCq9jmZPHkyXVxcuGfPnue+hoDAm4wgzm8Jo0aNMuUtfpB169bRw8OD9vb2lMlklMlk3LNnj2lGbW1tTZlMxl27drFz586MjIzkoUOHWLVqVdasWZMJCQksX748Q0JCmJyczNOnT5scxjIyMt5Ic7JWq+WuXbv46aefMjY2lra2tqxZsybHjx/PgwcPlnS0ys42CEqrVmRysuHfsWOfa+b2KPbv38/U1FSTw9b169dLfY1//vmHlStXZlxcnKmYxdy5c+ng4EB7e3sOHz7c5Az1YKgUafAAr1evHlNTU03H6fV6pqSksH379rxz5w7Dw8M5a9YsHjt2jHK5/PmzcLVqRQK8CBDGteVLAK8CrAxw8CPKnE4DuObBWXWbNs93fyPLli2jQqEwmfMFBN4lBHF+S/jtt98YHR392P3169dnzZo16e3tzfDwcIaGhvLo0aPUaDSUy+V0cnKiQqHg3r17OWzYMPr6+vLIkSPs3r07AwIC2KtXLzo7OzM1NZXOzs5cvXo1Dx48yEqVKrFy5cpvfLammzdvcsWKFezatSu9vb2p0Wg4vF49nouOpt7S0mSGLTFzk0qfK/72Ptu3b2e9evWo0Wg4fvz450rwUlRUxLFjx1Iul3Py5MnU6XTMy8tjq1atqFQqqVAoStRGvh8q1aBBA9MDSFFREZs0acJGjRqVqO09btw4RkdHs7CwkOnp6WzQoAF1Oh2TkpI4bty45+ozSRbWrEkCvGEU57nFxvVHgBGPMG3rAMoAZhffnpz83G24z++//061Ws3Zs2f/52sJCLxJCOL8lnDnzh3a2Njw1q1bj9x//PhxyuVyBgYG0s3NjeXLl2daWhr/+OMPymQy2tnZ0cXFhWq1mocOHWJGRgY1Gg337t3LmTNnUqlUcvTo0XR1dWWbNm3o6enJzp0789atW8zIyKBCoeDgwYPfCPPxs5A9YsQzxd+ylPG3er2e69evZ3x8PL29vfn1118/d8Wuv/76i+XLl2f16tV58uRJkob6yD4+PnR1dWWVKlVKrK3fD5UqbkHRarV87733WLt2bd65c8e0fdOmTXR2dubZs2f522+/0dnZmdnZ2Vy+fDnLlClTQsSfxL1797hjxw5++OGHjIiIoLW1NecXGz83gPOeQZyLAEoB7n2BM+f7HDlyhN7e3hwxYoQQCy3wziCI81tEfHz8E014gwcPZlJSEmUyGZ2cnOju7s4ff/yRP/zwAzUaDaVSKf39/ens7MwjR47wxx9/NGWK2rFjB11cXJiens6aNWuycuXKbNasGf38/Lhr1y5eunSJzZs3p6+v73NnknplvIT4W51Ox+XLlzM6OpplypThggULnjuByr179/jZZ59RoVBwxowZ1Ov11Ov1/Oqrr+jo6EgnJycOHjy4xPXff//9EqFS99vUvn17Vq9evcRD05kzZ6hWq/nLL78wLy+P3t7eXLVqFfPz8+nh4cHNmzc/tm2XL1/m/Pnz2bRpU7q5uZmKqygUCtasWZP9+/fn95GRpnXloQCjjTPiGwCrAPwY4AajEGsB3gLYE6AGYKHxPP1/XHN+VLsjIyPZqVOn/8nENgLvHoI4v0UMHTqU6enpj91/+/Zturm5MTU1leHh4YyOjqZCoeCpU6c4evRoBgcH09zcnJGRkXR1deWxY8e4ZcsWKpVKLlmyhBcuXGCFChXYtGlTfvLJJ3R2duaQIUOoUqk4fPhwFhUVcc2aNfT09GTr1q2fWL7wtWGMv40HaAnQxvgKKCbEkwF6AbQzrpf+dn92Z2HBWw94L9+7d4/z589ncHAwo6OjuWLFiv+0Br9v3z5GREQwKSmJZ8+eJUleu3aNycnJdHNzo1wu57p160zHFw+V+vnnn03b9Xo9u3XrxtjY2BLhbwUFBYyKijKZrTt27MiOHTuSJIcMGcL33nvPdOzdu3e5a9cuDhs2jDExMbSzs6NEIqFEIqGPjw9bt27NlStX8tKlS/zmm29Yvnx5uru7c9yAASwyNzek5wTYzej4pTaKcCHApQADjWOvAFgH4IFin4HW3PyFrfnfJy8vj7Vr12bdunXfmRh5gf9dBHF+i9i0aRNjY2OfeMzixYsZGhpKLy8vBgUFsVGjRqxQoQLv3LnD999/n7GxsZRIJIyPj6e7uztPnjzJ/fv308XFhVOmTGFhYSHbt2/P0NBQLl68mK6uruzRowdr1KjBihUr8vjx47x9+zb79etHlUrF2bNnv1mmRGP8bTzAmY+YIe+CIVnGHhhicKcbxUNrXBddKZGwYsWKHDx4MPv3708vLy8mJCRww4YN/6mfd+/e5dChQ6lUKjlnzhzTtbZt20ZXV1d6e3uzYsWKJco13p/1Fg+VIg3C3LdvX5YvX77EModer2e7du2YmppKvV7PVatW0cfHh3l5eTx69CgdHR2ZkZHBNm3a0MfHhxKJhObm5pRKpYyMjOSgQYP4xx9/8N69e9Tr9dy9ezc/+OADOjo6smHDhly7di3PnTvH5s2bc42FBbWlsUwUX38WibhVLn/usXwS9+7dY/v27RkVFcUrV668lHsICLwKBHF+i7h9+zZtbGyeWkYwPj6evXr1okajoUwmY0JCAvv378+7d+8yPj6e9erVo1gsZr169ejl5cUzZ87w1KlT9Pf355AhQ6jT6Th58mSq1Wr+8MMPrFWrFqtUqcIRI0ZQoVBw5syZ1Ov13Lt3L6OjoxkfH89//vnnFY7EYygWf/s4cf4eYPli72/D4NR06b651dKS/dq2NWVds7OzY+PGjZmRkWFaFy4tWVlZDAkJYf369U1ryFqtliNGjKBcLqdSqWS/fv1KrAOf27OHQ6VS/iCV8k6tWiU8zIcMGcLw8PCHvMKnT5/OkJAQ3r59m2fOnKFcLmfXrl2ZkJBAMzMzkxjLZDImJSVx6tSpPHr0aImHjps3b3L69OksV64cvby8OHLkSF68eJFarZbTpk2jXC5nREQE462tmf+c4qy3tmYdpZL79+9/rvF8Gnq9nsOGDaOPjw+PHj36Uu4hIPCyEcT5LSMmJuaJa4akoViAUqlky5YtGR8fz4iICLq6unLt2rW8du0a/f39mZKSQrFYzNTUVPr4+PCse4HcAAAgAElEQVT8+fPMyclhdHQ0O3bsyKKiIm7evJlqtZpffvklR44cSbVazYyMDEZERLBBgwbMzs6mVqvlpEmTKJfLOWzYsBJOSa8cY/ztfXFWAJTDEN6zxSgMtwBGGmfQWqOJO8I4iyYMMboLwsJMwnHlyhUuWLCAbdq0MSV6SUtL48qVKx/rnHefwsJCfvTRR1SpVPzuu+9MInjhwgXGx8fTz8+PMpmsZPx6VhavVa3KQuChCk+0smKRmRk32Nnxxvr1plP0ej1/+OEH2tvbMzU1lf7+/hSJRDQ3N6eZmRmVSiUdHBy4aNGiR8Ze6/V67tq1ix06dKCjoyObNm3K9evXm8z3+/fvZ8WKFRkZGUl/f3+qVCr6+vpyuLOzYe24NOJsXNsfOXKkydz+spg1axbVajV37NjxUu8jIPAyEMT5LWPgwIEcPnz4U4/r3r07O3ToQI1GwwoVKrBDhw5Uq9W8cOECjx49SpVKxebNm1MsFvP9999nQEAAL126xLy8PNasWZMNGjRgQUEBT58+zYiICLZt25YbNmygm5sb+/fvzwEDBlCj0XDNmjUkDVmxGjZsyMDAQG7duvVlD8OjMcbf3jdf5wG8A0Oojy3AE0YRHgXQDIbkGHKAWQ8KyGO8iPV6Pffv388vvviCiYmJtLW1ZVxcHD/77DNmZWWVKMqwfft2BgYGsmnTpiXMq2vWrKFKpWJwcDCjoqJKZrmaPp1Fz2Au1otE1FpaMrNhQyYlJZkKnlhbW9PCwoIeHh5UqVRcs2YNL1++TA8Pj0d+Jrm5uZwyZQpDQ0Pp6+vLMWPGlGjr7du3OWDAACqVSnbp0oUymYwqlYoxMTEsU6YMs7OzuaJWLd42mqqfaMoGWCAWUzd1KklDalNHR8fnigkvDevWraNCoeCKFSte6n0EBF40gji/Zaxdu5bVq1d/6nHXr1+nSqXiuHHj6OvrS5VKxa5du7Jq1aosKirili1bqFKpmJycTDMzM3bu3JnBwcHMzs7m3bt32bJlS1apUoU3btxgfn4+U1NTGR0dzX379jEpKYmxsbFcunQpPTw82LVrV5NT0ooVK+jm5sYOHTq89B/e++j1el66dInZFSo8VhySjLPkb2DIZnXUKBiZAFUwJNQobfxtfn4+MzMz2adPH5YpU4YymYxNmzZlzZo1qVQq+cMPP5iOvXPnDvv06UO1Wk2NRsOePXuWtDJMn867RierZ33dBtjLwoKOjo6sWbMmd+3axSNHjlChUJji0tPT09mqVasSY/X777+zbdu2dHBwYGpqKn/55ZeHnNzWrVtHLy8vpqamsn379nRxcaFcLme9evVMwnz58mWKxWImyeXMiYtjAUDdA/Hk+TA4iP1sY8OO4eGcNGmS6R5t2rR5vqIbpWT37t3UaDScanwweO285KQ4Au8Ggji/Zdy8eZO2trbPVKxgxowZrFKlChs1asTGjRszODiY8fHx/OSTT0iSs2fPpo+PD6tWrUoLCwumpaUxNDSUV69epU6nY58+fVi2bFmeP3+eer2eY8aMoUaj4bZt2/j5559TrVZz6dKlbN26NQMCAphlTOZx69YtU1KTBQsWvFCHsXv37vHgwYNcsGAB+/fvz8TERCqVSsrlcm5Qqx8rZLVhKL7QHeCHD+wLB/jDM8ycn8bSpUupVCrp4eFBmUzG4OBgfvjhh5w1axYjIiIYFhZGmUzGpUuXljwxK4t3JJLnWr+9Y2bGPnFx1Ol01Gq1jI2N5YQJE0gaso7J5XJeunSJ165d48SJExkcHMzAwECOHz/+kd72ly5dYkpKCn18fDh37lxGRUWxfPnylMvlbNOmDYODg02z6woVKlAikTAzM5N9+/ZlWZWK53r14ndmZjwdGkq2acMpHh5UiUSMiooyLX/c91LPysqil5fXKykDefLkSQYEBPCjjz56fRnvsrIMDotS6UtJiiPwbiGI81tIuXLluH379qcep9VqGRkZyalTp1KpVDIpKYkffPABNRqNqeDBoEGDGBsby9DQUNra2rJ79+6MiIjg9evXqdfrOXbsWHp4ePDvv/8mSWZmZlKpVPLrr7/mb7/9Rnd3dw4YMIALFy6kUqnkZ599ZoozzcrKYnh4OBMTE3n8+PFS9/P69evcvHkzJ06cyHbt2rFcuXK0srJiYGAgU1JSOGrUKK5Zs4Zbt27l4MGDOdrRkYUiEXMB/mycsRUBXAiDh/Y/RhO3P8CTRhP3BhgKMhwp/iNZytncv//+y+7du9PFxcW0fqzVarl79242b96cZmZmFIvFtLW15YABA7hv3z6T012ZMmVoDrBtsR/q0zA4qdkUe31abP/7MOS0Nu2XSKjVak3VvHQ6HfV6PRMTE5mWlsaWLVvSwcGBrVq14rZt2x75sFS8CtbgwYO5ePFiKpVK1qlThx4eHuzZsyeDgoJ4+fJlkuTKlSspEokYHR1NvV5PHx8fxsbG8qeffqKlpSUXLVpEkhw9ejTNzMzYrVs3RkdH89NPP2XdunVNbahQocIjc8a/DK5evcpKlSqxZcuWr9434n7s/VPM/6VNiiPw7iKI81tI7969+fnnnz/Tsdu3b6erqyunTJnCcuXK0dXVlWPHjqWLiwuzs7Op0+nYtGlTtmjRgh4eHlQoFExLS2N0dDRv3rxJ0pDjWa1Wc+fOnSQNVY6Cg4PZuXNnXrx4kXXr1mWlSpW4a9cu1qhRg5UqVeKJEydIGlJLjhs3jnK5nKNGjXrkjF+n0/HYsWNcunQphwwZwuTkZLq7u9POzo6xsbFMS0vjjBkzuGvXLpP5PDs7m5MnT2b58uXp7OzMvn378uCmTdRLpcyBITGGLQzxtxWNIkyjIA8F6G7cHwSUyHhV2mpJGzdupJeXF9u1a8cbN26Ytt++fZvt27enp6cnPTw82K5dO86ZM4f169enTCajhYUFxWIxHQB2Mgrug+Jc9Jgf8PcBDnmgzQd/+YUKhYJnz55lTk4O27RpQwsLCwYHB/Orr7564hLDgQMHGBMTw8qVK3Pfvn3s3bs3PT09WadOHZYvX57p6ekMDAw0OZPduXOHDg4OtLS05J9//skDBw7Qy8uLHTp04IwZM0qUrzx9+jQBMDY2lkFBQczMzGRISAgXL15MklywYAETExOfebz/KwUFBWzUqBGrVavG3NzcV3PTl5AUR+DdRxDnt5Dly5ezTp06z3x8mzZtOHDgQFarVo2dOnWih4cH+/Tpw6SkJOp0Oubn57N8+fIcNGgQ5XI5vby82LVrV8bExJjyRa9Zs4YKhcJUTvLWrVts0KABY2NjefHiRY4dO5YqlYqrVq3ihAkTqFAo+O2335pmSKdPn2adOnUYHBzMGTNmcPr06ezSpQtjYmJoa2tLT09PNmzYkJ988gmXLVvGEydOPGR+LCgo4Pfff8969eqZZoI///xzyYxQjRtT/7TZyWNeWoC/q9XPlMDi5s2b7NSpE93d3UskDSEN3s1BQUEMDw+njY0N4+LiGBQURGtrawYFBTE0NJROTk4EwAEAB/5HcdZbWfELlYqDBg1iSkoKHRwcaG1tzWnTpj1xSSE/P58fffQRlUolv/nmG548eZIVKlRg7dq1GRMTw6ZNm/LTTz81OQveJy0tjRKJhM2aNSNJjhgxgh9++CE//vhjDh8+nCKRiH/88YfpeEtLS1pZWXHixIlMTEzkzp076ezszGvXrvHOnTtUq9Umy8yrQKvVsnv37gwJCeH58+df7s2MSXGe5/tIa2ty9+6X2z6BNxZBnN9CcnJy6ODg8MxrdZcuXaJcLufGjRspl8v53nvvsW3btqxcuTLHjh1rOsbDw4NTp06ljY0NIyIi+MEHHzAuLs40W925cyfVajXnzp1L0jDjHTZsGN3d3ZmVlcXff/+d7u7u7N+/P/fs2cOgoCDGxMRw0KBBbNq0Kf38/GhhYUFzc3MGBQVx7Nix3LZt2xNnMDqdjlu2bGGHDh3o5OTExMREzps375FFJrRaLTeMGsWC5xTnfJGINRwcaGFhYRqXR7Fu3Tq6u7uzc+fOJutCTk4OV69ezaSkJJqbm1MsFtPc3JwhISGMiIigk5OTqUzngAEDaG5uzrCwMGrfe49DHiPOLjCUYWwHQ8Wn4uLsZHxFwpDP+jszM4aGhnLq1Kns3bs3W7du/cTvxLp16+jt7c2WLVvyypUrXLVqFVVGgff19eVHH33EMWPGMCAgoER+72PHjlEikdDKysrkaR4REcFt27Zx2rRp7Ny5MwGYKmuRZHh4OENUKm5LTuYyKyvmxsUxKyCA30dFkTk5HDp0KNPS0p7Y3hfN/SUbd3d3Hjx48IVff8qUKYyKiqKFWFzisyXATTBkT7MCmADwTLF9FwA2MH62rgAzIiJeeNsE3g4EcX5LKVOmTKlq2X7xxResW7cuv/jiCyYkJNDHx4fffPMNVSqVKQ70wIEDVCgUXLhwIS0sLFijRg22a9eO1apVMyU++fvvv+nh4cGxY8eaZmVLliyho6MjO3bsyM6dO1Mmk1EikVChUNDLy4u2trYcOHAgDx8+zKKiIubm5rJr1650cXHhkiVLHjm7O3z4MAcNGkR3d3eGhYVx3Lhxjy1xePfuXc6aNYv+/v6MiYnhKDc33i6lMN8G2NPcnHZ2dnz//fdpZmZGNze3EjPA69evs23btvTy8mJGRganTp3K1q1b09fXl/b29qYZq7m5OSUSCcuWLcu0tDQuWrTIlPlr8eLFFIvF/19VKjn5IXH+F+Bu48z5CsCmAGsV2/8nwGvG/WthMM//VKYM9Xq9yVv7/trwg1y6dMkU2/7zzz/z3r177NevHz08PDht2jSq1WrOnDmT48aNo7+/f4kx1+v1DA0NpY2NDXv16kWSPHXqFJVKJbVaLVesWMG6desSwP8LelYWD/r5PTJuuwCg1sKCBbVrs5qtrelB51Xy3XffUalUPjV3QGlZtmwZV8yZw64SSYnP9ipAexjSmxYC7A/Dssv9/QkAe8OQFnW/UaQ3L1/+Qtsm8HYgiPNbSteuXU1euc/C3bt3GRgYyJUrVzIqKorp6el0dnbmvHnz6OnpaVovXbNmDTUaDRcvXkwzMzO2aNGCrVu3Zq1atVhYWMgrV65w4cKFVKvVDAoKYtmyZSmVSunn50dbW1tWqVKFa9eu5bBhw6hSqbh69Wpu3ryZHh4e7N69e4nsZtu3b2fZsmVZt25dnj59mleuXOHEiRMZGRlJFxcX9u/fnwcOHHhsn/Lz8zlp0iS6u7uzVq1a3Lp1KwcMGEC1Ws35lSuT1tZPjb/VArxrZsYeZmYEQDc3N5qbm3PkyJGsWrUqRSIRq1Wrxj59+tDW1pYajYbW1tYMDAxkjRo1mJiYSG9vb4pEIjo6OlIqlfLDDz8ssf58n88++4wikYj9+vX7/42tWj0kzg++Lhtn0rces78LwBRjzeeQkBD27dv3IaHT6XSm6mLp6enMz8/nuXPnWKlSJdatW5fTpk2jUqnkpk2b+OWXX9LPz+8hk+/s2bMpkUjo4ODAa3//TY4dy7+jorjP3Z1s1YpnundntZAQikQiQ/+Na61PW2bQi0S8I5Hwl+bNn/n7/CLZvHkzlUqlyYnthTF2LIc8IM4zAFZ64KFQCoND4r/Gzzmn2P4PJBK2jox8se0SeCsQxPlV8YJjGxcvXsxGjRqV6pzMzEz6+vryjz/+oFKpZI8ePdiwYUP26tWLjRo1Ms1gJ02axDJlynD06NEUi8WMioqis7MzLS0t6ejoyISEBHbp0oV+fn6sXbu2KVPWjRs3WKtWLVavXp3Xrl3j9u3b6eHhwb59+zI7O5stW7ZkUFBQiRl/bm4uU1JSTDmeW7duzY0bNz7RZJ+bm8tRo0ZRpVKxSZMm3G1cl5s3bx5VKhX9/PwMpvjdu7nZyYlac3MWisUlBcHKioUAs9zd+XHt2kxJSaGtrS0BsGzZshSLxXRzc6NCoSCMP5qenp6sVasWfXx86OjoyDp16rBWrVp0dHRk9erVGRAQ8NiHibZt21IsFjMjI6PE9ltDhnCQSPREcb5ivP/Nx+zvBLCKVMqAgABaW1szJCSENjY2VKlUplA6Dw8PBgYGctmyZSwoKODatWupVqs5ZswYDhkyhN7e3vz77785ceJE+vr6lsjxTRrW2G1sbJgkl/NIcPAjw4F0UikLAS4DWNS3b6nXWvNFIuqKVd16lRw8eJDu7u784osvXlzo3yMevHoB7PpAv8vCsDSRZ/yci9e87gQwwsnpxbRH4K1CEOeXzUuKbbxw4QLlcnmpYzYbNGjA0aNHMz09nY0bN2ZYWBgnTZrEgIAANmvWjB06dGBkZCTNzMxobW3NsLAwikQivv/++0xKSmLDhg1NOaALCgrYoEED1qpVy7QGrNVqOXDgQHp7e/PAgQOmiksVK1bkmTNnuGjRIgbL5VwSHc3fvb2ZaWbGTRoNt9arx0axsYyIiDDFSz9IdnY2Bw8ebIq5PXz4sGnfjh07TKUy//zzT9MYOTk58e6FC/xSo+FPTk5cb2nJw1FR5BdfcOqwYaxbty4VCgUbNWpkEmcAdHV1Nf0tlUppa2tLkUhEBwcHLliwgBcvXmSNGjUYHR3NoKAgtmjR4rHr4LGxsTQzM+N6Y8rNW7duce7cuaxevTo9ra3ZH2Br/H/o1y4Ywr50MJivU4zmzvvfmx+MsywdwPUwmLXHpqfTzs6O5cqVo42NDcPDw9m2bVvGxsbS2tralPUtKCjIVHkqIiKCvr6+9PT05Pz58zl48GB6e3ub4pCL07JlS6aJxcw3znSfZo3QA2wF0BmG6l/++P9c5wtRMkzMyjjOewAWWVq+Nieo8+fPMyQkhD169Hgmf46CggJevHiRhw4d4rZt27hixQp+++23HDduHAcPHswDHh4PiXMHgB89MF6VAc4x/h0LsIfxu/AnDGbtABubV9B7gTcNQZxfJi85ttHX19eUCepZ0Ol03Lx5M+3s7NijRw/a2NjQycmJIpGIZcqUoVQqZXp6Onfs2MHc3FzWrl2b3bp146BBgyiRSDhnzhwmJyezefPmJg/poqIiduzYkdHR0SWSWixatIgKhYJLly6lXq/n+PHjWcPenjs1GhYCpnrAxR9U9FIpz0ZFMUkuZ8+ePU0z8nPnzrFXr150cnJit27dSqa8NO53dnZmcHBwiYxT06ZNMzlGaTQaxsfHU6FQsFKlSmzatCldXFwoEokYGhpKOzs7NmvWjJaWliZRtrCwMHkar1q1iteuXWPVqlUJgJaWlmzQoAHlcjkzMjIeOdsqXlVq//79XL16NVNSUmhvb8/KlSvT3t7edK/7r2EAF8FQ0tLaKG5tYDBt3x+rKjCsW9oBDAM4JzSUAwcOZNu2bUkaljAmTJhAJycnuri40NHRkX5+fkxJSWFAQACrVKnCDRs2MDg4mJGRkUxLS2OZMmVoZmZGCwsL+vr6snbt2uzZsyenTJnCSZMmMU0kYn4pHe3+giF9KmEw26qNAvzgcXMA+hgFXQeQTZo883f6v6LX63nz5k2eOnWKe/bs4fLly1m2bFlGRERw+PDh7NevH9u3b89GjRqxatWqDAkJoYuLC6VSKS0sLKjRaFi2bFnGxsayWrVqjI+PZ4UKFejl5cVFEskjZ87dHuh/CAwzZ8LgHFYPhrzwFYxCXd3Z+ZWNh8Cbg4gkIfDiycgA+vcHCgqe/Rxra2D8eKBbt2c6vEOHDoiOjkZaWtpD+woKCnDo0CEcOHDA9Dp48CAcHR0hlUphYWGBlJQUTJ8+HV26dMFvv/2GTp06YdiwYdi7dy/s7OyQl5eH2NhYdOrUCXv37sWiRYuwYsUKTJs2DTKZDPPnz4dEIgFJDB06FEuXLsX69evh7e0NANi3bx8aNGiAwMBAJPzzD/pevAhLAJIndUokAqVSLIiIwMBTpxASEoK9e/eiY8eO6Nu3LzQaTYnD8/PzERcXB4VCAb1ejw0bNkAsFoMk4uLiUL58eWi1WkydOhUSiQRisRhKpRIpKSnIy8tDZmYmrl69CgcHB/j6+iIoKAgLFiyAtbU18vPz8dFHH2H16tU4c+YM0tLSIBKJMHfuXOTl5eHevXtIS0vD1KlTIRKJSrTr7NmziIiIgEQiQf369bFmzRoEBQUhNDQUmZmZOHfuHIKDg+F66RLW5uXBTKd7ps/8QQoBVAVw0MICJ0+ehJmZGfr06YM//vgD06dPR+3ataHX6zFz5kwMHDgQnp6euHLlCm7cuIGAgAB06dIFV65cwffff4+tW7dCo9Hg9OnTOH78OI4fP45//vkHh+fOxfp792BjvOdxAKEAmgFYaNw2BcAEANcBBAD4CkCVYu08CiABwCQAKQ/0oZpx3zDje72lJcTnzwNK5TOPQ1FREW7evIkbN2489MrNzX3s9ps3b8La2hpOTk6QyWSQyWRwdHTEgQMHUFhYiE6dOsHd3d20TyqV4saNG7h48SJOnjyJv//+GwcOHMCFCxdgaWmJoqIiFBUVAQD6AxADyAYw19jObwDMA7Dd+D4fgBLAXgBBj+hXS4kEnlWr4vPNm595LATeDQRxfhns3g0kJJROmO9jbQ1s2wZERz/10Hnz5iEzMxNffvkl9u/fX0KIz507h6CgIISHhyMiIgLh4eEICwuDTCZDfn4+goODsXDhQixatAharRZHjhxB8+bNcfjwYRQUFGDhwoUQiUQ4e/YsKlWqhBkzZmDatGnYsmULNm/ejGHDhsHNzQ2zZ8+GWCwGAEydOhVjxozBjz/+iBMnTmDBggXYtWsXupAYkZ8PK73+mYfhjkSCdHNzLLCxQcWKFTFjxgy4ubmVOEav1yMlJQUFBQXYs2cPpk+fjhMnTmDXrl3YuXMnrl69ivr168Pb2xtff/01PD09cfLkSej1eiQlJaFKlSoICQlBu3btsHTpUiQnJ8PT0xO9e/fGp59+ColEguzsbAwaNAj79u3D+vXrYWdnB1dXVwQGBsLHxweTJk2CSqXC0qVLERsbCwBYtGgR2rZtC7FYDF9fX7Ru3Ro2NjYYP348rly5ggoVKmDo0KFo164dFhYUoPrt2zgPIA3ATgCWMAjfVwDMin/eANoBmAmgEwxT7eM2NgjTalFUVASJRAJLS0v06NEDQ4cOhbW1NXQ6HYYPH47Zs2fju+++g06nQ8uWLTFgwACoVCrMmDEDWVlZsLKyQpUqVRAXF2d6qLG0tMS4cePg/9FHqE+aHqpqwfBQ4AmDOP8BoDqAXwFEAvgawCcArgDoCYMwFQIoZzzGtlifzgLwAXACgLdx212JBNd79cLxhg2fWWwLCgpKCGzxv4u/Htzu6OgIc3Pzh75/169fR+/evbFp0yYkJyfj4sWLOHLkCLKzs6FUKiESifDvv//i1q1b0Ov1kEgMo6PT6SCRSGBmZga7u3fRzjgOM42fZS4APwCzAdSD4YFkG4BdxvseAeBm/A4sBfAhgCN//w1lcPBDbRR4x3md0/Z3lsaNSZGIfwOsZjRB+gJcXsyU9dhYR5HosWa9u3fvcv/+/Zw3bx779OnDSpUqUSQSUalUsmbNmuzfvz8XLFjAQ4cOlagN/CiWLFnCsLAwXrt2jW5ubly4cCHlcjn37NnDsmXL8ttvvzUdu3PnTioUCu7Zs4eRkZG0srLiwYMHGR8fz06dOpnyOq9fv55xcXFUAZzs7s7TVapQW6kS9RLJY8diJ8BE49qaAmAzFKutbGXFu9u3c/jw4VQoFJw0aRK1Wi31ej2PHTvGRo0aUalUmszPMTEx7NWrF8eMGcPGjRtTo9FQo9FQqVTS1taWiYmJtLe3p4WFBQsLC0kazJrVqlWjh1TK2UFBXCuTUVevHo9VrMjPZTKGqNWmik9RUVEEQFtbW1P42dWrVxkfH08A9Pf3p4eHBwGYHO+mTp1KhUJBiUTChIQErl+/nj169KBEImF5T09qjcUu6hjNn4VGE3YIDLnA739fbhi/L2VRsk71HZGILubmVKlUFIlEFIlEDAgI4N9//81Lly4xISGBNWrU4JUrVzhr1iyqVCpThaqMjAx6eHjw1KlTzM7O5rJly/jhhx8yKiqKNjY2rFChAjUSCQuL3W8xwOZG83sr47an1cjWAvwN4GcwhAgVN+l+CkN5zwdN3YcsLblepWKWWs0dPj78qWpVThw8mBkZGVyyZAk3btzIP//8k6dOneLNmzefK1+2Xq/nlStXuHnzZk6bNo3du3dn9erV6ezsTFtbW0ZGRjIoKIjm5uZ0c3OjtbU1xWIxxWIx7e3tTX4IYrGYGo2Gbm5upprZVlZWj1yyIMCNxs9Sauz76WL9nmj8f2ANw/rz7mrVSt0vgXcDQZxfNNnZpFTKIhicYL40/jj9YvwPdxRPj3WkVMprR46YwlratGnDsLAwWllZsUyZMnzvvfc4ZswYrlu3ji4uLjy5c2epPcH1ej0TEhI4bdo0rlq1in5+fpw8eTKjoqK4f/9+KhSKEg5XS5Ysobu7O0+cOEEfHx86ODjwxIkTDA8PZ3h4OJ2dndkmKIjHQ0OpNTcvsab8pLFYZxyHWzBUMGoPQwWp4g8qt27d4rfffksvLy86ODjQ0dGRCoXC5JkcGxvLYcOGMSkpifb29gwODqanpyc/+OADnjp1ilu3bmWVKlU4duxY2tra0t/fn4cPH+bZs2fZo2JFbrSzYyFA/QMOe3eNwrQchnSgdnZ2/PLLL+ng4EBbW1uOGzeOs2fPNpWPNDOGY1WsWJGjR4+mvb09zczMWLNmTX711VesUaMG5XI55XI5P/zwwxL1p4NgiFm+f+/+ADsXe98F4DTjj3lxcc4H+JFYTCcnJ86fP5/+/v50cHCgSCSiVCrlkCFDeO/ePX700Uf08/Pj0aNHSRqKonh4ePDkyZOP/H7k5eUxOjqaA4z3oPEz8gd47gFxflqN7OJ9mPTANj+Asx8hzg+FwP0H50m9Xs+zZ8/y559/5oQJE9ipU6f/Y43GfOMAACAASURBVO+646Oq0vZz506fSZlMeiWNEAgtCRBqEnovIqIUO0VA1AVUQEFFBRHEip8FEUGsiPiBoq6wuoguVkAUwZXVxRVWUaQFSHm+P869d+7cKUkQcddv3t/v/JKZe+fce245z3nb87Jz5870eDyMi4tjly5deMUVV3D69Om86qqrWFlZyaSkJC1wzmaz0WQyMSkpSSPRcTgc7Nq1K3v37k2v10tJkpiRkcGcnBzm5eVx+fLlYoEcYQiLyBlKxKx9tmXhQmDuXHx28iTKABwFoHojewPoACADwtS3Vfn+OIB4AJ9A+J2qANxps+GdDh3QunVrrbVo0QIOh8N3rA8+wAfnnYe2338vzJ96v6XZDMgy0L8/MHMm0K5dwKnu3LkTPXr0wOeff47JkycjKysLO3fuRIcOHZCZmYl77rkH29avh/P554EdO7Dnww/x1Q8/oOWoUej6xBP47vRpJCYmAgDuyMjAJTt3QqpS9CydfAaEvBbzDOf0MYByZV8AOCVJKHA4kFFcjLKyMvz8889YvXo1qqurkZSUhH/9618oLS1Ft27d0LVrV3Tq1AlOpxMpKSn4xz/+gbi4OKxZswarV69Gv379MGnSJPTs2RNZWVlwrVyJ+adPw1xTAynMa1AL4CSAGZKEmiuvRJs2bXD99dfjxIkTSE1Nxfz587Fx40Y888wzyM7Oxtdffw0AKC4uRnFxMdatW4eioiKMGjUKDzzwAAYPHox58+YBY8YATz8NQJiCtyp/fwbQR7k2wwBsgzB5b4MwH4+BMGur8remTfHt7bdj0qRJWLp0Ke6//35s2bIFNpsNkiShWbNmcLvdePTRRzWf+bJlyzBjxgzIsoyffvoJhw4d0v4eOnQI3333HX788UesVI4HANcASAVwA4BbIEzRqyDUwvkQJloCiAXwGgDjE3clABeE3xkQftfeEGbfqJBX3yCSBDgcQWMzamtr8fXXX+OLL77A559/rv3dvXs3oqKiUFhYiObNm6NZs2aIi4vDkSNHsG3bNmzZsgVff/01zGYzqqurkZGRgezsbJhMJuzatQs//fQTamtrQRLdu3dHjx498Oyzz2LHjh2IiYlBaWkp/vWvf8FisWDWrFkYPny4ZuYGADz8MKqvuQYWxRfdIGlk/ElE/oDyOy8O/ngyejQJcAdEmohee+gJcCjC5zqqn+vqoV/k0qWkzRagnQRtNlvISPCrr76aEyZM4IEDB5iYmMiNGzcyMTGRny1fzm3p6TwtywEpYMcBnjKZ+LLJxOGZmfx5/vywlJnhroVx3yXwtyKclGX+bcQIjh8/ns2bN2dUVBRtNhvT0tIoSRLvvvvugDGtWbPGr5iCyuO9du1aAoJoZGZsbEDt4fraMUX7S0pK4uLFi1leXs6kpCTa7XZKkkSLxUKr1cqSkhJGRUURADMzM7lt2zYePnyY7dq147Rp03yR3QMHan1/rmifssA3XqJcrxqAJQC3KvsZNWcC3CDLbNeuHSsqKjQTfJs2bWi1Wv3MqjExMZr2V1FRwYsvvpjXXXcd582bx6VLl/LZZ5/lm2++ya1btzIhIYHJycncqJjdPwHYHOAp5Zh6zTlYjex4CE3/qDKGjRDWkpd15z0OIhL9TLTKWrudH155JW+99VaOHDmSrVq1ot1u1wp2TJs2jY8//ji3bt3Kr776iq+++ipvuukmduzYkS6Xi3a7nTabjVFRUezSpQsnTZrEiRMnCspNq5Vut5t2u509evTgE088wffff599+/bVXAddunThDTfcwKZNm7Jjx45cv359yPzov/3tb7zaYuFx5fqEHVukKlVEFImA89kWZcI9DTAb4F3K/69DlPnrjfpzHQnwHy1b8uWXX9YmlyNHjvhe/qVLSWXSbHCzWIK+8D/99BOTkpL48ccf88knn2SbNm34/qWX8oQkNYjZqUo3YYdq4a6Ffr/tEL7ndwzfP2ez8eabb+bWrVvZvn17zpkzhx07duS4ceOYm5vLESNG+BVmGDNmDB/SkVnccsstvOmmm7Q0KFmSOEY3tl0KAMYqrYfynXEcpwA2BWgFOGrUKH7wwQe0WCwa+KWlpdHj8bBXr1584YUX+NprrzExMVGjAh0xYgSffPJJXn/99RwwYADXKObOWogqWbdDpB79CMGvPAPCRHyZ7hyCgfPTSklKk8mk+UVVELHb7TSbzVoOt9ls5i233ML169fzgw8+4LfffhtQPvH666+ny+Xi8OHD+U5WlrZockKkQyVBLLbsANsieI3sFgALIaqCRUH40B/Vbb8HYiFiQSA7WjjuabUdglgA5CQmcuXKlfzwww957Ngxnjhxgu+++y6XLFnCoUOHaosR1cWQk5PDyy67jA899BAXLVrE888/n9HR0YyOjqbD4WBGRgavueYa/uUvf+Hx48d55513anEEmZmZvP7665mWlkaXy8Xu3btz06ZNYUlLfvrpJ6amptLlcrEyKopvx8cLl4/D4f8uKaQ4P1VWRkzZESEZAeezL4rmrIJNN4BxChCNhgDm+nIdCfCQ08lNaWm8PyODJZmZ2mp/YFJSvWAYFqCDvPiPPvooO3fuzNraWt7brBlPmc319vWAAmjWBk6u6rWIVSZ3m9JGQfgs90IUengqyLE2Wiy0WCxMSkpiixYtOGzYMJaWlvKbb77h0aNHOWvWLMbHx/Phhx9mVVUVPR6PHyf0qFGjmJOTw6ysLJpMJo5JSPCrn/wzRFCOqqneB7BlkPO4HWBXgF74B/qowJdhs/Gxpk35WZs2/CQjg68nJvJOj4cJun2dTifdbjdNJpPmz/0BgQxgayEAbojumiUpYBYNAYgEeNps5lynky6XizExMdy6dSvXrFmjFRfZsmUL77vvPsbExFCWZa1UZUFBgVZC1GKxMCYmhk2bNmVxcbFmBQCEhnxKOc/vdW0aBOf3v9GAGtlB2hpljBMNz0+98RhKu1K5F2UxMXziiSc4btw4FhQU0GKx0OPx0O120+VysaKigrfffjs3btzItWvX8tprr2VeXh6dTifj4+Nps9lYWVnJhx56iPv27SNJvv322+zatatW4GPEiBH89NNPuXDhQiYnJ7Nfv34sKytj3759w1Ywq6ur48CBA5mYmMjWrVvz7rvvps1mY7/SUlEzfOxYsZgfO5ZcuJAP3XILR44cedanpIj8d0oEnM+26IJ8jK0jwP+B4NftpPv+WLjJTAmEeaBVK7YtKKDVQPV4Spkks5QJfrPh933hz8ZkAZiamsqXXnqJW7Zs4Z49e3jo0CG2bNmSN/bo0eCKTmc6uV4FsBdEdO8SCC31CuX8Hw5xrJ8GDeLgwYNpNpuZkZFBq9XK4uJiJicn02q1Micnh+3bt2diYiLj4+OZnp7OzZs3c+/evVywYAGtVisvvfRSbt++nWkWC2cGqRSktmqADyr3Q//91xBBW69CLCKaKWN7CuDbAL+BsAoYyVVOQERUf922LUfm5BCABnyJEEFnhLAszFeO/zOEyX+U8r8eFDtCBNYd1vXfrbCQHo+HjzzyCKOjoxkfH8+//OUvvOqqq1hUVMTFixczNTWVl112GZOSkjh48GDKsqxVE9u9ezevvPJKxsXFaYuIUuUen0RgYBfhb9aut0Z2mGYk6QjHPa1+txVgGUQgWUeAzbxejTzl8ssv55NPPskvvviCH330ERcsWMDy8nI6HA6mpKQwNjaWycnJnDhxIjds2CC43g8e5LG5c/l+fj5fM5u5EuCSlBS+/NhjPHTokJYtMHLkSI2e9fTp07ziiitYXFwcssjIokWLmJ6ezpKSEmZkZPDTTz8lAC1a3ihHjhyh1+sNGaQXkf9fEgHnsy1KtDYhtMUqCK3jbgjWp5MQ2kY0hKZcBVHPN5h2oG9XAMyVJJog/Hvq909CaK8OgBKENgr4MzF9BKFlqODcJDWVQ4YM0QBNkiQCoBnw0yjrM/duggBVi/I33OT6sjLWXgCH6a7F7cq5Lwwx7hOSxGXNmjElJYUfffQRo6KitPKXJFlVVcU9e/bwjTfe0CKQZVlmYmIiLRYLJUnSzMpFRUWcAeFSCAbOMRCmVgki7Ue/bQBE1PZmiFJ+p+GLYm5Iq1GuxbU2m8ZCNnToUO4pKmINhE+3XLnOXoiUsoNB+imHz6xdA/Ct2FiOGzdOK2qRlJTEjIwMHjhwgHV1dRw9ejRNJhOfffZZkuSWLVuYl5fH0tJSulwu6i0AAChJEm9PT28QTefZaI3hnlbH3Bbi+V6uPGs7L76Yhw8f5v79+7l8+XJedNFF9Hq9TEpKYlZWFh0OBzt37syFCxdy165dmhm69v33+Y/iYp6UpIB7WWu387Qs838tFt46cKAW5a6Xuro63nLLLczOzubu3bv9tunpZNu2bcsVK1awf//+lGU57PQxa9asc14+MyL/mRIB599ClDzn6cpk64LQYPfqXv5wuY7BmqqpFsMfnPUtTQEelQqREJpsAgSf8W4FeJZVVHDkyJGMjo7mkCFDOH36dC6/916OM0yU9Zl7/wbhG+0IHziHmlwHK9fCBuEr/BAid7eJAgouQ1N/e1qWmWI2Mysri2VlZezRowenTJnC6OhotmnThqNGjWL//v1ZVlbGvLw8P6AxmUzMy8uj3W5n+/btWVZWxqeCAIK+HYMIZFqv++4l+NK7VHA+Y0ByOrmiY0e2aNGCkiSxVDnmmfR1QpK495lnmJCQwIqKCiYkJPDyyy/n3LlzWVJSwscff5wpKSl86KGH6PF4NPpSIxirJS7tdjtviInhCUORkF/TNErOEK2x3NP36J6v5RC5wCuVvGOHw8H8/HwmJyfT6/Xykksu4fPPPx9QL3zXrl18qGVLHlOe67Dn34AArWXLljExMZFbtmwhKXLfMzIyWFBQwHHjxom63TU1tNvtLCkpCTt1HDhwgB6PhwcPHvz181BE/qslAs6/hfya3MZ6mgkCYFUQM0Hw76rg3AbgLUoDwAshiioQ4K0QC4FddjvHjRvHG264gRdccAFbtGjBmbLM6xEatEKZe2dDaMMqONc3uX4HoYFLSuuJ0AFlNRAaEwAt8jgtLY1t2rRhmzZtGBcXR4fDwZYtW7Jdu3bMysqiJEl0uVxMTU1ldHS0ZhWQZZkmk4mvBAEEY6uFiBM4CAGceQD3wLf4sCC4r/0xiIWTCwLMv9NtWwJhuo6C4MvOUHJnAREB3liAPiFJfH3YMHq9Xk1jPnjwILOzs/nCCy+wS5culGWZ2dnZWv61CsbR0dGcMGECH3nkEebm5nLUqFFs3ry5tlAIR55zHMI14VW2d63nHO+x2fhtu3ZBtdPqIPciXDzGdxCLuUPwB+e3XC7abDa6XC46nU6OGDGCW7Zs8QvUqqqq4pw5c5iamsoJyrk16t2rB6Bfe+01xsfH88UXX2S/fv1YXl7O8vJyNm3alK+++ip37dpFAFy3bl2908eECRN48803n5WpKCL/vRIB599K1KIX9bz0Ro1RD7b7EKhVZsCnOR9Tvntb+Zyk/H6zMqGlQID1VAjt1gSwNcBtJhMHDx7MmTNnctWqVfzkk09YPXJkSNAKZ+41gnN9wW6dlO3HINJsJkAwTgW7NscgzOoqsFiUwLDk5GT27duXo0ePZq9evehwOFhQUECr1cpOnTrxs88+49/+9jfecsstbNGiBQHQ4XBw6tSp9WrOKmjYAX4MYW42K9c2Hr5UJ0BYKKqV39ypbHNAuChGQgTAqX1+BWGJIIRbo7USUW2321laWqoBdH2aXA0EsFxjs/GVV15hUlKS5meePn0627dvT6P1wGq1skmTJrzuuuvYrFkzXnrppTx16hRra2u5YcMGNmnShAD4ssnEkwhNGEMIP/NIZQw1CF7IQtWW387JYWlpKXNycphus3EawBUA1yl/PwxyL8LFY6yFsLyowXHREAulGIA5OTm8/vrruWnTJs6bN48FBQXawqN169Y0mUx0u92c068faw2R0o0C6DCR1B9++CGjoqKYnp5Or9fL22+/nZWVlayrq+OwYcNoMpkaVI5y7969jI+PDxtsFpE/vkTA+beUhlal0k1EerBVwblat09n+MD5SQhtTDVhR0GAb18ItqksCG06BiKNxQlhEiwBtFQbdRKvT6MMZu4NBs71Bbu5AH6q2/4J/M3YajuunKtqrgTAZs2a0eVyMS4uTgvQ6d69u5Y+pKYKqWOLjY1lYWEhrVYr27dvT0mSeC0QUKLxDQggroGIHL8aYmGjbleDsbpDRJ8nQ+ToxkKY+vcoIDFM2f9O+AL0vgoyth8hNFOXycQOHTpQjfjuGRvLFyGCvE4bIuaPQ5j4N7pcHJqeruVU9+jRg0lJSX6ArGrILVu2ZGpqKqdOnao9kt999x1LSkro9Xrpdru1yPEE5bg7EZiT3gvgTRBukSjlGtX3LNcpbRV8iwT9uQHgdJOJ0wz3Ilw8xkn4B8fdCxG4NsnwLKtR8bIsa89Efn4+77vvPlb160dKEk9CWHkyIYLY2kAE++nfO/2i+DYgLLUuSb7zzjv0er202WwsLy9namqqVmtctfA0VM4//3wuWbLkzOeeiPzXSwScf2v54APxQtvtAbmNxmYE2/rAuRI+vl5CaG6DlUYFIHIAXgqRejJWAQbjJC7LMldJUqPMvdXK5HkjhJk6swGTKyHAbYoCBCcgtGg9mNdAEI9MMpmYn5+vUSdef/31tFqtTEpK4pgxY+h0Omk2mxkdHc3rrruOPXv2pGr+njRpEvfu3csdO3Zw6dKldLvdjI+PZ0FBQQCIzYWILC9QJuF4CJ7r7UHG3wwiojoNYlHSAoJi8wHlvqkWg1r4AvP0pBtPQ4AblONcDLCgoIA2m41JSUmcPHmySO0pKtIiwd/1erkC4AxJ4vWXXcaJEycGjCE6OprZ2dna58GDB7Nz584cNWoU77rrLkZHR7OgoICxsbE0mUyUZZlxcXGMjY3l0KFDGR8fz8fy83kc4QljVkBYQa6FMGsb0/9CgfQqQNNc+/fvrxG0BLsXRMPjMZYD7CxJrDt4kJ9++imHDRtGu90etO+oqCgWJSZqPOHHlOPtU+7X/0KA9D4Ef++0ZrcHpcU9ePAg09LSOH78eJaVlTE9PZ2ZmZk8efKkZtJeuXJlg6eNbdu2MSMjo16O/Ij8cSUCzudK/v1vX25jWlrQycYItuokkaq0MRApSDkQZkYJIsXnJIT5UYLQ6r5QJsUsCOAcC6E9vwUfOE+ePNk/UOauuzhblhts7p17hpPr1wAHQoC8B8I3uwdCMzyhTPYlEJqPGtWsRl0XFxdrNZDVICYAtNvtLCoq0jisMzMz2atXL65evZqZmZmMj4/nnDlz6PV6aTabuVaS6jUfB2sPK9fyOIT5PhbCH3u/cl+8EKB+FL7YgNVB+tkDoYk+7nTSYrEwISGBWVlZGmPVNddcw7S0tKAgE6x5PB7Gx8f7WUP01gM1KjsuLo6dOnXikCFDOGTIEDZr1kzrQ019CkcYc4eyb57yPHkgTP47lN+OgyBpkeBPqFMH8DJZ1oLPCgsLtYj6NajflB+ySRJ/qqxk3759NUvCgAED+OGHH/JdpWBKaWmpZtqfjvAR9i2V5y8sODsc4j3WSU1NDXv16sWJEyfS6/Xy/fffp9frZa9evVhRUcEhQ4ZQkiTW1NQ0asqorKzkU089dTZmn4j8F0oEnH8P0dE2qu0bZUL/WvfdUYAfKJPEdUEm5Qz4NGTjtn3K9wshzNnJEIFX1ygTqrqfCmwX9ejBGWi4uZcQGkcVhDkwU/m/MQQpNZLE961WvpWWxrcHDmSuArwAGB8fT5PJxPbt2zM1NZUZGRmUJIler1fbx2azsWvXrhqIFxYWsl+/fuzcubOmnanb9O1MI6SNFJu5CvB8oVzjqfAFhAFCezaynantGYhcXfWcrFYrXS4XPR5P0BQnvQ9Zb8JV6TotFgv79+/Pjh07Mi8vTwNrWZY5cuRIjh8/nk6nk7169WLnzp2ZnZ2tLW5Ut4Z6bnrynGbKXxPEAkSCWKCo1bOilH0AYRH5M8Tiqh/AdGV7JoQFJSsriwUFBYyJidHM3B3N5jOOVj+u3MuCggI++uijAZWpampq+Nxzz7Fly5bMycnhphCLYgI8oNyvL+C/KE6DsDz9oN9/7Fi/49x2223s2rUru3XrxkWLFnHq1KmcMmUKa2pqOGXKFEqSxJycnEZPExs3bmRRUVGD/NQR+eNJBJx/D9GxiKltHvwDiIxtbpCJWjVfV0EJioHQ3tSAGROEdjNUmWhiIbRzYz/OIN/NRf3m3s1BflfewIn1GITvdwbAVZLEVyC0t+nKscJpii6Xi02aNNHIPBISEjTAioqKYmJiombKVn9jNpsZExNDQERuT5blRoGCkWLzT8rnGcr2FyDM3HEQIJ0HEdH9U4j+VkKAWmk9Yw3WzGazZr5VQc7r9TI5OVmLzLbZbH5R2vW1UKQha5RnoBuE9mwE8gyImIIUCIsJIVwvd8K3ANoPwcvds7CQ559/vsaopt7LiWj8YukYwEfatuWXX37Jr7/+mp988gk3b97Ml19+mcuWLdNynVNSUtirVy8OGTKEf/V4gvZ1GsLCpFYB0y+KD0CQ/PhRzQ4cqL3KmzZtYkpKCu+44w6WlZVxz5499Hq9WirU9u3bCQhe8x07djRqmqirq2Pr1q25YcOGszr9ROS/QyLg/HtIEBaxfIDLDJNGOcRqXg1KyVEmtNsggDcaAoSvBHgEwmStD5hJhwDYo0p/dcokpNcg10CYkxtCqLFHOZ/Ruu/+DfAiiMVBLASrVbg+aiAWEz+kpwc9rmreXgOhqek1RFWjVmsjb926lUOGDKHJZNKKFIQDIL3GKSt+7YZESBM+is0f4fO1l0PwR6v+953KNd6h3B99ycfH4CMV2QUBVtfCV0yjsQB9ttsNulSnYOQ5N0BozAkQQYe/QERPQzn/LPiD83Ld2PdD+KevlGW6XC6OHj1aS41TFxkPtWzJKpMpsFRkkOfnuO6aud1uZmZmsmXLliwuLmaTJk1otVoZFRXFrKwsZmRkaNSlqxU2Nn2rhYg+74fAWtNq+145lhYIp2jO33//PVNTU/nUU0/R6/Xyiy++4IUXXsjbbrtNe9UvvPBCSpLEFStWMCEhgW+99VbwOeHgwaBlX198+GF269btXMxKEfkPkwg4/x6iYxEjwHchtNcjhkmhLYRGXauAwgUQAVXdlXYcQjPrq0xWxklFP2HWQTCFqZNxQ1N39K0XwC7wB+cuECb3w8rk9nGI36qg+5HytyEpQ8cgIrZtNltANG44M6/e72o2m9mzZ09OmjQpYF8A7CDLfFmWQy4UTsPne8yG/+JGb2XYDOGzdEL42gsNY7wUgq7TqdyX6YBfcJIeoFXAMisFLWJiYvwKbARbdLhcLs3ErWrTFotFC5yrD5zVaG0q52Ykz1GDBdfBZ7YHhKVGjW8wgvN83b7ZALcAftq9eu42m42ZmZnsIMvcmprKKgTSoB4HWG028xWLhQsvuICtWrViYmIibTYbExMTtdrLXq+XFRUV7Nu3L1u2bEmPx6MdS1+bWn0nLoV4p4zH07cDyu8PQ6n5vXAha2pqWFlZyZtvvpk9evTgggUL+OGHHzIlJYXHjh0jKTRfp9PJ7OxskuTmzZuZkJDAp59+2jcXbNsmSIvs9kDaX4eDdXY7X3M6uWPZst9jporI7ygRcP69RGERI4SGNSbIpFCoTH6qz3gsxCreuN8aCM0kHNidhC9n+ExIL56ByEeeCx84v65MyqGAtlaSuBHgC04np0EUSzgT8+XVFgszMzNZVlamlUXU+56NWnGwz8a2aNEiLl68mC6Xiw6Hg9eMGsUZksRVJhM3mExcZTJxttXK0cXFomwmwlNsdoaI9vUo9/NMxtleAVW9L9jhcDAtLY2yLGvBcDabTStioe7Xq1cvlpSUMD4+nm3btvUze6elpQVEMUuSxMzMTK0QBpTnKNS9nA0RXa6a9n+Eb7EyA6E15zqIBdscgAeVHOARI0bQbDbT5XIxKiqKzzzzDPv06cPWrVuLAD6IBcKLTic3yDJXShKnAcyNjmaTJk2Ym5vLGTNmMCYmhvn5+ZQkienp6czKytICBa1Wq+beUMfcxOnkSZ1mPgEik+CoYazvQ6SNGRfFhFhQDe3cmZWVlSwtLeWDDz7Idu3a8fTp0+zRowcffvhh7RX/6KOPKEkS77jjDu27nTt3MiMjgwsWLGBdA1MtayWJVbIcKSP5/0wi4Px7SQNYxMoh/K9eiHSjzSH2uwbCNBeqnxPKRHSmdJG/QJjdv4U/ON8KX7WtOAgz+V90vzsOAciqCV1/3GAm8qchgoecENWYDun66eZ0Mjk5mUuXLuWIESMaBMBOpzPkNv1vMzMzWVFRwdzcXL766qts27Yt27Zty9jYWALgBpstrKbf2Apd6rZpEL5pt7LPFAj/uXpeOTk5LCws1ILanE4nnU4nJUnixIkTOXv2bHbq1Enb32KxMBHgbKuVr3q93GixcJVCI5tkMvlp3/oFgNrCPRuzlWdM1SD/pNx/tXpWKHBW23yIvOKLL75YiwtQx6UHUNXyMX78eD7++ONcsGAB4+Pj6Xa72aFDB65fv542m43Jycl+5y7LMtu3b8/Kykp6vV7t/sbExPCSSy7h3LlzmZKSwnfi41mj3AfA323kgkj7Wg1hyg9YFEsSTw8axFtvvZUul4s5OTmUJImVlZWcNGkSmzRpwlOnTmmv+OjRowmAv/zyi9+rv3//ft6WmsqTDaj+5gfSdnsEoP8fSQScf09ZulS8cCFexvchTN0nIXKg3QgktXgDQpP7MsjvVdOw3mRqLG6hgl8oSsZNEBGrNmUC1oPzOKXPxyHMv89A+J71ka0rACYmJvJVu90P4Iwm8s+U8b0NoclcBN+CowZCq9ODkDqxqyCTAPBWt5tr3e6A4LK0tDSaTKaQ2nZmZmbQ/FhZSf+ptkgVXwAAIABJREFUb0FzphW65kBEB9cq9zpWuX76c7DZbIyOjqbL5dJymRMgAPgZWdbGei8EQUx9fvxQAWgWi4UmkylkcJZq1larZ7WCWJDZIMz4avDhPIiF5KPKmFVe7duUsZtMJi2YTw/OWVlZXLx4MS0WC+12O0+fPs3t27fzkUce0Uz2qiVANf2rtKNFRUV+VoS4uDhOnDiRe/bs4b333suUlBQOGjSIkydPZrnT2aiCJX7N6eTBDRuYnJzMt956i3369OENN9zAlStXasQ4qampHDt2LJ988knN6hEg27axym4PSYKib7coY3pTdw6Res//PyQCzr+z1C1dyuMNzLvtA5FTq35+DwJ8/mzYrxr+OcPqpBUNETx2iWH/cJSMKyEivR9CIDhPhdAw9H0VwZ94Yx38/ZlEcBP5TAhAVvf5CiK/VvXDnwDYVOc/VCfpcEFtwUBJ1R4lSdKoPVVTqL7l5ORoedEAGhRRfCblD/WtP4S1JJS2H26sKiNXuPMLtlgzMsVZrVa/eAQ92cwYiEVEN4hnyQORs74TIviweZBz3gRRICUZwueu9wGrQDxx4kQuWrSI7du310zSamqZzWbzWzh16dKFs2bNot1u1xYUABgbG8uSkhIWFhZy//79GigPHTqUL774IktKStikSROmpqby7zNmNJ773ulkzYMPsmvXrpw3bx6XLVvGtm3b8vTp03zqqadYVlbG2tpa7t27lw8//DArKyu1hcLkyZO5du1aH6/AsGFhSVD074BKw6vFjtTDUhaRP45EwPk/QC7Kz+emuDiynmpAfSHoIgnhx0uAf1qL2j6AfzpSTk4Os7KyOAMIKG5RHyXjEgjzXiyEduSCAJi2EBpztmF/IzivAPzIH0KZyAcDXGDoywXfQkFvIldbY/iog0VFq6CkTv4tWrRgnz59aLfbg2rS9R2vseUP9e0EBIBNB5ienu53fo0Za0Oa/loYq1SprQRiITA7yLa5QfrMgg9AaiEWkh7lHuZDRHuri6oxY8Zw4cKFtFqt2uJHT+9pNps5ceJE3n333Rw0aJAfoOsXWNHR0ZwyZQpvv/12durUiUePHmVlZaWW871t2zYuWLCAcXFxLCwsZGVlpa/a09KlPCnL9V7PWoDHJYlV99zDG2+8kb179+a3337L+Ph4fvrpp6yqqmJWVhbfeecdv3d67NixBMDXX3+dd911F3v16kW3280+bdtqMQzGppKg6N93lYb3Tf2+IVjKIvLHkgg4/85ycOdOzrJY+Fp8PJmfr72APwPcCB8hyCoIkNwNoakkAnw2yAseDMTU9owsBwBIfZSMxyH8bc9BaEfTIPI+/w3hE46FMLnXQOT6euAza59U9tfn0E6FD4T14NwdgoFLP5ZU+PvZVyAQKM8UlM60lSjXJ5j22tjyh/p2MQSgvRzkmGcy1oZci5Igx1Kbw+GgLMtsmZzMOQ4Ht6B+zTxUq4Pw26q857IsayQxqluivLycDodDW5BER0fTYrEwOjo6INr8ggsu4MyZM9muXTvu3r2b27dvZ3p6Ot1uN3v37s0hQ4awRYsWbNOmDYuLi5mamso//elPPHHihEZUsmfPHraTJL4IsNZmC6TWdThYY7HwzzExvHXQIPbp04fp6ek8ePAgBwwYwLlz55IkFy9ezEGDBvm907W1tXQ6nUxMTPT7vqqqinvHjw/gTSf8SVAI4QrR0/DqwVmNGI/IH1vMiMjvIx98AMyfD88rr2AuAOuPPwI//qhtrgZwE4DdAGQAzQC8DKAAwGUAfgBwhdIAIAvALgASgI2ShOkkWgGIBXAYwA4AntragNPYD+AzAMMB/AvAewAGAGgOoBCAU2lxynm4AdgBJCi/fwXAJACTlXNcByBe2WYF4FLOAQA+BfBnAJ8EuRxuAEcM3x0BEKX7/K7yVwJwTOlblRMApgN4HuLatQbwjrLtbgArAHwDwAsgDcB3Qc6hPjGZTPiorg7nQ4zxEkC7xmVnOCYAmAFxDzZDXD+TyYS6ujrIsoySujosJjEBwFsAjkNcfyeA7wFcBGBpkLH3AHALgDcB9FSO8zyAeyHuQzsAMwGcrzsPj8eDn3/+GZIkobS0FPHx8Xj99ddxV10d7rLZ8OekJHT+9ltIDb5iAk1XA1glSWBNDQDA6/UiJycHn332Gdq0aYN33xV3tq6uDiTFdToirlx1dTUAwGKxoLq6WtyDjz7Crl278OWXX6Jjx444cuQIzGYzTp8+jU8++QQnTpzA8ePHIUkSSMJqteLBBx/Efffdh1rDOzBCkpBlNmNMbS1aWCxwVVfjpN2OLy0WvOT14rODBxH7/vv44YcfkJiYiNLSUvz44484cOAANmzYgO3bt6NVq1bo3r07zGYzZFnG4cOHceLECcTFxaFHjx6ora1FbW0t6urqcNOXXyJPuQ6qVAMYDfE8NYN4tmcBeCPENZVOngR27mzEXYjIf6X83quD/5eipFDUNbambD2tBoLwIZT/NVj93HsgfLt6HuGBEAFG+t+/CV/lKWOkdR1Eek0GhIl8JHxm8jqA/1L+V03kKoOZ3kQ+E/4EJn+Hv8+ZEPShgIgQNwa1hfOb3wWRX10NQQCiN/mbgqQvNaTJssz8/HyaTCZOgKAtbUz5Q/W7ORCm7h+VezQd/uZsNb3pMwhLBCFcGzEQFoxLgoz9ZQT6KtV7+Bx8db1PKNciJSWFK1as8LsWHo+HrVq10riwN23aRIfDwdVomH/bWJWqefPm3LJlC4uKimi32/nll1+yV69enDp1atCoe6vVyqlTp3Lv3r185513OGrUKE2Dzs3N5YgRI+h0OtmkSRN+/PHHJMmrr76aHo+HXbp04fDhwxkVFcVWrVpx8+bN3LhxI59//nkuW7aM48aN044zdOhQjh07lueddx67dOlCh8PBDh06sE2bNiwsLNTY59TKaGqZT7UgiyRJfiZ5Y1O3m81mWq1Wrje4roKRoKiR8Oo+Rs2ZAGv69/+dJ7GI/NYSAedzLQ2s83wmrQ71+yRnGQDkz2g8OBsjrZ+ESAX6FiLSejD8wVOdqFUTudr0JvLPIID9HQgQUwFHv7iYBuFnb6zf3NiuggDJxoCx2owm1lKI1CJ90FRDyh8SguIyD77FiwqWat/pVqtGVKJvuyH808MgqFmNYw/pq1TaYxDgfBzgXCXXWI2Ibtq0qQY+ANi/f39u376dHo+HFouFcXFxHAOxCAwG0up3+5VroY7FYrHw7rvv5uLFiwNSp/TX02QysaCggLIss02bNmzVqhWbNWvGzMzMANBr7H2z2WxaKpp6rIyMDObk5LBZs2Zs1qwZ7XY7y8vL2adPHw4dOlQ7l6FDh9Lj8dDr9fK+++7jokWL6Ha7+fTTT/O9997j559/zu+++45Hjx6l0+lkbGwsSfLkyZPctm0b77//fg4YMIAv6LIzQpGgtEZwGl59TMaesrLfeSKLyG8tEXA+l9KA3OZfA8zhthujblUAOQ1RrOE25fMWiKhRVbszFrdYAQGoc+ED5+EQBTbUY70LoVnXl7Ki74MQec4ZENr1YPjynFXgSjKZOB2B4NyYUoZ1yuTXEwir8YTSgoygYIZIKzLuG69cx0wI37m+Qtc9EJMuICZeJ3xWBH0f1+soNQn/RUVbCPKPLoaxZ0AsGIj6wVm9dqpWCIhgNDXlrD5msQKIgMSvIBZbXymfCxpxTfXHUX3MCQkJTEpKYvPmzTls2DCOHDmSZWVlmr9almXOnj2by5YtY2FhId1uN10ulxZgZrPZ+N5777Guro7V1dUcPnw4Bw0axFOnTnH+/PlalPcLL7zg93p+8cUXbNq0qfZ53bp1zMzM5P33388WLVqwefPmbNmyJZctW8bLL7+cN954ox/tZk3//tzTvj1nACzNymJubi7NZrNWW9pisfgFR4YiQamPhrfGauWC+PiAQh8R+WNJBJzPpQwb5kd44FIm5ym6FzNcznGwVgMBOOH63QVh4jROiq2V7Z9BaHCAqDpk14HA/wSbTJXJfSBEIQ2zcr4vKf1tUfbLhgCoQogUsEplTLm6fVcZzls9rt4sXQMBtoAILjOaj9VShnMhzMt/Ufr6PMj1mgMBpu8gdKRyQ5rJZAqamrYfwhLxqnJf1itjUpnENkIE830GQb1aDhE0FixAK1gxihqAf4XIJ74RAqTVsR+CyEl3KGNvCDivCzE+WZaDLl7UxcmQIUP8tFAj2N50000B/ek/JyQkcMCAAczLy9OisVNSUrh27Vp6vV6uW7eOnTp14pIlS7SUqN69e3PAgAGUZZmzZs3ifffdx5iYGHq9Xt5+++1MTEzk3LlzWVhYSJfLxaysLE6YMIHPP/88+/bty4EDB9LhcDApKYlerzeg2tOXX37J/Px8kuS+ffuYkJDArVu38p///CdNJhOXLVvGnTt3MjY2lj1jYvjvLl1YbTbzlCH6Wk3he9XhYB8dIQoAJkkSqxCeBMV4v4z3sc5uZ682bfjSSy/9HrNYRM6RRMD5XImBT5vKhOyCIN5QvwvnO9W3E5LEUyYT9yPQlG3s92cIja0OIqL6CggCiUtC9E2IiOJ4iBKJVghAzYPQsP+qm2StygQTpYDChxBaKRQAiYcAZwmCUKEGoq60E8GJU5ZDFPjQWwL0wPUKztxv/gBEXvY/lX3DRSs3pAXT4t+HML3rjxsPcKvy/0UQ/nV1258htOhgUeTB0uTUNgHC995ON3bVV6mOvSHgvCLIcQGRXmYsFJKWlsa0tDRKksTLL7+cXq+XsbGxtNvtfkCucprriUFUzViSJCYmJtLj8dBmszE3N5fvvPOO9rsDBw6wuLiY48ePpyRJ7N27t+ZTXrhwIUeMGKFpyZ07d+ZHH33E2NhY5ufn89tvvyVJ/vLLL0xLS+MTTzzBxYsXa2lMVqtV8wEvXrw44BXds2cPc3NzeerUKbZr107b57zzzmOHDh3YsmVLjh8/nlOUMpeN5YcvLS3lY489xs0ez6+qYc3zzuOLL77IDh06RMpJ/oElAs7nSoJUonoSQrtUgag+32k1hMa1AsL/OigvLyhhv7FfYx8PQmi74cC5AmKRoDJfWZQ+T8FX7xbKMWohNFK7cv7XKNsuhND8Ve3uXV3/vQDeFOK4t+g+18E/NcyoOT8AkUcLiHQdPTiPhK++cgsIP+3fle218GnjZ9qCafE1ECQd65T/10Jos2oqVCv4p8D9oOvP4/Hw6quv9us/1P25AgKYe8MHzqqvUl0sBfNV6sE5VNpdsOC4cePGcfTo0RrAmkwmDhkyhO3atQt5fdR+bDabFtBVVFREm83GhIQEFiUmcjrAfV268H8BPi1JvNluZ4bdzuzsbA4dOpSLFi3SXqE333xTY0kDwA0bNrBp06asrKxkz549/V63devWMS8vjydOnCBJbtmyxS+vOjExkWPHjuXTTz/Nfys5w1999RWzs7N50UUXsXXr1hw/frxG0ZmdnU2LxcJZcXGNTms7Kcv8x403csmSJXS5XCyT5V/FUsYPPmBNTQ3z8/P59ttvn7s5LCLnVCLgfK4kSA3nSvgTOjTEd7oCgg1JlmXeYDIFBWdjv2qLAShDaLHlCA3O/1Am9q+Vz7OVzxJ82rI6QTaD0EBjIQA/AcIUbgbYFMKc7Vb2jdedV0+IYKZwxyXEYkAPINcqn1W/+fMQ1oBoCApE1W/ugACmzyAWKw74fLFqMwZghWtqhSg98ATT4glBzuJSrrUDwrStbssB+Jru82mlv9atW/O6667z479W/ZMHIVjVjkIA/gal3+EQEe7ZynU9ALEocEKY7QN8lco1exhi0fSTMn5Vm1XzkNXjp6enCxNuz54aKOtdARkZGSwoKAh5zZo0aUKTycSKigouWLCAzZs3Z1xcHAckJvJ/LRatLKX+2lUpZt+XTSa+vWgR27VrR1KYmbt06UKTycTy8nJNE37iiSdYVVXFxMRE7t692++VGzFiBGfOnMm6ujqWlJTQ6XTSarUyLS2NF154Ie+//35WVFTQ4XAwISGBiYmJ2r3u3bs3+/fvT6vVypiYGGZlZXF006ZnnG9+wmRij5gYWq1WdujQgZNlmSfqIR0KCsw6bu1HHnmE/SNR239YiYDzuZKBA/1etG8QCEQN8Z2uA9ihQwcOHjw4qGal9vsFEJS79xhEKk46fOX8Nhv6uA0+s6cKzokQJu6LILRbdQJ2Q2ip90EAcjYEeMfBP8ApEcK3mgNhfrXAUMA+yHH1C5JQAKCC/XiIhYETwow+GOAkZVsT5dwAX/DVBARqjjk5OSGDxIKlzATTnN9Uxv4BhHa+DUJj/0TZ3goinUnd/8cwY1NpT/8NoY3HQGjECUH2TdONXfXnZ8HfrL08zLEKCws5c+ZM2u12yrLMjh07EhC+9csvv5y5ubkhf6teHz3jmloGEgA//fRTer1efvzxx5xiNrPKZGqQSfi4JPE6h4O33XYb4+PjeffddzM3N5elpaUaxefJkydJkrNmzeKUKVP8Xrnvv/+eCQkJvPPOO+nxeFhSUkJZljl27Fi6XC6azWYWFhZy5MiRHDZsmN8Yo6KimJCQwIqKCt50003MycmhBf5ZCO9BLDI9EIuc8+GLvCeEO+li5X4lQFhyJk6cSLvdzlatWvH0/ffzOHz84yGbJAUAMylITZKTk7ljx45zNo1F5NxJBJzPlRg053nKhKv/riG+05fcblosFg4ePDggZ1Lfbzju3ioIsOquAIcRnPMAPqH7PBvCRD0KAthiIMDeAbBMOWeT0qzKXxsEQKn0jar/2gGhZY+GWDyEO67a9EFLE5TrYzTZG0HyTxCBdern/crvXzb8zgj8qv+0rKyMRUVFAQFPCRAa7UoIrXym4bh3I9AiMET5nhCLm1m6bRsgQFUtsqFPMwLCl3H8NU3vxzebzczOzqYsy+zSpQuXL1+uga1+QWJcnKg+XCNQjxo1imPHjtXM2qdPn+a0adP4VKdOrLZaG32e19hs/PTTT3ngwAEmJCQwLy+PWVlZlGWZSxXA+uc//0mPx8NffvmF1dXV3L59O5ctW8auXbv6LSCaNGnC+fPnc968eUxKSmJaWhqdTieLi4vp9XrpdDq5c+dOXnHFFbTZbJolI8FqDQj+exXCMvELxELvMgiWN3X7pRCAfRzivcsBGGexMD8/n0ePHuX8+fPZQZZZPXgwa63WQCuYwyFcYeedF7LYxZ133smxY8eey5ksIudIIuB8ruSuu/yiOvMBLjO8jPXlHB8HeJMSqNO3b1/u69o1YDIL1q/aVO7eagiT6yAIjUsPzlsUsNCTf+iBrzeEyd0EX9GL7xGoSZkgNGEXhLaYCwHQKnjnQZi/wx3XCKDhaCyN4Pxn5Ty3Q2if4yHM8qsNvwsVrQyIFKPi4mK2aNGCA5OS/IpOhEpN+4tyXFVT/hhCk35d+fwaRADYLviitd26SkvGcziTEp8NAbwJgEaOoQ/+cjgctFgsNJvNjImJYXl5ecA5xcTEEACLior80rDUlpSUxBYtWmh9SpLEC7p39zNhPwZfPEAfgN/ptvWFfwSzBWC02cykpCT26NGDU6ZMYXx8PJs3b860tDR+8sknfOKJJ5ibm8usrCw6nU42a9aMo0ePZvfu3Wk2m5mZmUmTycSioiK6XC5269aN06ZNY3Z2NmfMmMGrrrqK5eXljIqKYmlpKSVJYkZGBqOjoynLclBeemP7CGIBrH72QlhO1M+3AMySZf744488deoU7XY7p0+fTpJ8fP58zouJ4bcVFcLKNnasoOish0P7559/ZlxcHL/55ptzMYtF5BxKBJzPkfz9vfc0Qol3ERyI6ss5roPQgNspk+CNhsCSUP2+AWHetEKY4q5SJr2LIHJw9VWtxsE/sEoFvmEQJtjzIMDWDmHeroIwzasT82UQWrmkTE4W+HzVcyEAXdWyN9dzXHVBMg31g1Qw3++DEIuABAjCj2gIX6x+n+cgNOGngIBSk3pt3RidOxeBYD5X2faAch/dEGb+RYZjLoYw80dBxAfExsZqGnmw8zhb3NrGAiB6rddsNrNPnz50uVx+Y1Jzix977DGed955ftumTp3K2bNn+5m0JUnizTffrHFnA6DX62V3XeW1vyj35DMI981EBFqR9K0bwAsliVFRURw+fDjz8vKYl5fHuLg4AmBqaipHjRrFyZMnMzMzkzt37uTKlSt54YUX+mn7GRkZ/Otf/6qZwmtqarh+/Xq63W6tpKiaJ20ymbRo8tjYWK6SpKDPmL4tgT/JjBeiIpf6+XaAsRYLSfKyyy5jVFSUlqt86aWXnrGJevr06bz22mvP3mQVkf8IiYDzOZIxY8bwi8JCUpI4HkLbCvaCfwZhKjb6D4NNsMZSjKH6Xa30Z0ZwZix1wqmCMFmrYK3XDrtCmMDNCqgMgCgRGA2hhat1iI9AmK1nQvg8VU3ZrPy1KOfQHT7QMh5X39SgLdW8+zmC50vPhijPGEob+1K5Bj/pvlNJWMKVmrwTZ19zVdsxiAVJQ0peLkDDqlIFY+1S+zGWEHU4HH7auh6s9eb1Fi1a8K233tI0ZhV4HQ6HFvSlT5u64IILmJqaqn0XYzb7PZfT4IsHoHKfgMBa5YQwB6sxFBk65rJu3bqxuLiYLpeLOTk5nDZtGrt3705Zlul0OtmuXTumpaXR5XKxa9eulCSJaWlpnDZtGocMGaKxgbnd7gDTvCRJtFqtlGWZ0dHRtFqtIYP/1LYdwvesX/yNhljUHgG4F8KsbTWZePDgQZpMJj7++OPa/KBGsR89erTRc8v+/fvp8Xh46NChszllReR3lgg4n03RsQVx4EDx9667uOfddxkfH8+jmzadNYYwFaDr80kG4+7VN6NZW9/mIhDIuyotBgJwkyEAZpuyPVX5OwgiTWg5wM66PmdC+OGS4R+1HKyp5CPqIqQawmy/GP750jsg/OE2CNPicQhNvAQCqL6BMB/PNPQfilXtAeW3VsNkXF8AEJXjd4VYICQiMNdaf/9WoXElL+9E6IpYKgC/AqHBrYAw2atpd8aodD3JiNGXbLPZtKjiYMA1Z84c5ufnB3yv/70KogA40OvlWB2PfEPjAQgfD/hxgDMkidHR0UH93DExMWzWrBmbNm3K5ORkVlZWailbbrdbi+42m81s0qQJW7duzYSEBO3ck5KSNB95eno6u3btyqysLO1YKxEanPdCPPfGAM1DynOZBLGQnQ0wx+1mZWUlMzIytGnj2LFjtNvtjI+PP+Op57LLLuNtt912NmaxiPyHSAScz4Zs20YOGyaCNwy5zHQ4eMpk4hfNm4v9ziK3tqp5hdLsQnH3NhSc9c3oY71BOfYbEH7Vw0o/kyFAaSiEf/orCHN4DUQAjRcikroP6qccVYOW1JSinRCgp/9dDgIXEHMhNGxAmN+TlPNuaGDVGvjyu/WTcX0BQD9ALCRWQRSpOIJAljIVaFVgbuz9nggBtNMArouNDQvADWlWq5WJiYkBhCHhmp57O1TTA+hQSTqjeABCWEKWK/8/o9BuulwutmvXjrIsMyUlhZWVlezduzdJ8vjx4/R6vczMzKTb7dbyoktKStivXz+N/lOWZVqtVr+gL3WRoicrcbvd9Hq9vNXtDupz/geEhchY7jRYm2k2c0jTppQkyS8/ecuWLSwsLGT79u3PeAr6/PPPmZiYqOV1R+S/XyLg/GtFBdt6KkzV6dMhli7lAxZLUO3sFET+apYysRmBcy6ExqoGy9gBLi4uDjrRh+LuJQR4VEGA8+vK/+HAcm6QCbg1BFgVKOcSD6Ghb4cvSGw5BHWoQ9l/OETUdn1FKvSme5UlbQcCwVnNl26MNtbQVp+P0RgANBOh3RV603K4BVV9rb46zI1tTqeTM2fOZFJSElVQjY6OZlZWlmauVoG2X79+zMrK0og8YmNjOWHChKB9PvLII1p/o2T5jOIB/qrcb/X53ZaUxHvvvZcul4sdO3bkmDFj2KlTJ8qyzLi4OD711FO89tprNVN9VFQUbTZbgKZts9k0s73X62VcXJzfOO12O0tKSpiSkqKN5/xu3Xi9yeQX/LcfYnG4EMHvVbCFaauMDJaWlvpNIUuWLGGPHj04cuTIXzUVDR48mA899NCv6iMi/zkSAedfI2eiBSsAveauu/hQaionIBCclygTU7A0p7nwLxZxUpKYarFwogIAKnD9Q52IEJy7NyvIRL2vEeOoD7gOKH0e1n2nL48Y6nd6E67qi1Wj109DBFjdpfz/Onz50uG0sVBman27RTlffV6wOsZDEAuPzobfGAOAKgFOhfB9JwDsr/S3AsLHruZaV8Cnxe+Cj8QlFmAP5Tu1z2CRy5lB7l04zTVYs9lsmg8ZgEZAEhUVxfj4eI4cOZKjR49mq1at6HK5NK0yJSWF8fHxHDhwYMBx9MxiTqdT+39wPc9KsHgAQvCW64MEX3Q6efLkSd5zzz10uVyMi4tjQkKCn1k+mEYvyzLz8vKYnJzsV5FKTflKTk6m2Wz2I1RRA8QmTZrEuXPnBvQ5V/fMGHnt1fN9Dv4L01UFBZQkifv27fObRkaPHs2hQ4eKQhq/Qt59911mZ2ezurr6V/UTkf8MiYBzI+WBBx5gSUkJrRYLL9GlRtXnj6yDSMWIU9r4wYN5s80WkCerb8FMzkZw1hNplMBXyq+hIKtvtQ34bagUovch6EdrIcD3AggQUn9nLI8YLmjpDoT2xW6HiN6NgwBlfb50KG1MNVMbF0Jq+wrB6x+r4HwlhB9ZD87BAoDyIXzx25TrcjV8BUU0kzD8tWs973kNBJlLyzDXvxyC9rSxJuxgKU+qlqj+X1BQwPz8fM6ZM4eSJLGoqIgXXngh4+Li+OWXXzI1NVUDO1XTNuZlG1tsbCw7m828SPesVEG4KMLFA5xQruVbuudjOsQiQmUpU0HZ4/GEpRGNj4+ny+Xi8OHD+frrrzM1NZV2u50ul4vJycnaoiIjI4M2m4379+/nM888Q5NwbXWgAAAgAElEQVTJxOXLl3PRokV0uVzsbLXyxBnWYK9zOtkjJobDhg0LmFMKCgo4ZMgQPvroo796furcuTOfffbZX91PRH5/iYBzI2XNmjVcu3YtJ2ZnN8of+T8QdJb/hKh7nA4B1uE00FDgHA0BDM0BLoU/kcavyYutVs49GLMYEbq61VwIDbUJhAakBol9r+sbEJqrXsMYicCgpcamDXWEf7602ozaWB0Ca1mrLVT949kQZvoyCHIUFZxDBQC1gvDxq5+DsX+VwX9xZbz+D0JoWsG274OIXN4FcKZCpxkKkKKiohgdHR3wfbBcaiPZiCzLdDgcjImJ4RVXXMEbb7yRtbW19Hg8AalWoZrH4wl6fnMhFiQtlfsTKh5gNcQzqC7iTgBMU/zinTp1YnR0NHv37h2UBxzw5WLn5ubypZde4smTJ/nGG28wNjbWb9zZ2dmMiYnh/v37efjwYUZHR7Ouro4VFRW8/PLLtWvRqlUrFhQU8E9OZ+PfL6eTrw4eTIvFEhCN/csvv2h512+++eavnp9eeeUVtm3bNlIQ4w8gEXA+Ezl4kLOD+NH0zeiP7AjwEd3nhwG2R+PBeRdE6kkNRF5zMgKLF5xJXuwxCFNxOGaxxmp5oZq+BKS+qQuLfRCgGKtM3pPhM20/B7FgsCvXJxU+/3k4baw6xLV+HsLsSgSC80wIDf1D+KLO/4HQAUBjIBZl6udDQcYYysSr5z2fF+K6qZHLhG9BFgqgrVYrJ06cqGm44fYFwIqKCubl5QXdlp+f72PKgtBgV0kSN1osXAlfPrbVatVyj43t1zCd1Sr3tolhYaDyfaempvpFn7vdbg2cb7jhBg4ePNjP3N2hQwc+9NBD9Hq9TE1N5WuvvUZSAKXb7eZzzz3H2NhYut1uOhwOOhwOxsXFaSlkMz0enpTl+sejxJmcvv9+P8IRvWzatImdOnViVlYWv/rqq189NdXW1rJ58+Z84403fnVfEfl9JQLOZyJ33VUvOBv9kdEQpl/1898gQG8CBMAa83b3wWcGVTXN24IcZz4EqOm1Hj1ANzRN50UEpueoTWUW039Xn5YXroUKalIn8H4QAFYFoX0XQSwETsFXmtIFkQeeonwfThurgYikNoLzUQizs8pvngUBzqrptTuEqboKophFO4QPAHoLYkHxCcRCZzLEAkI/xgsQejF2DOBD8C+UoW/6yOV18EUVqxzWasS1GoWsfx7UbWq+b0O0X+PCaQ1EjEOo+sVr4P8sBlt4NfZZUVuV0tbAR8Lj8Xh46aWXMikpyS94LS4ujiaTyY8YpaioiDExMdy5c6f2Gvfs2ZNxcXE8ffo0SfLIkSNafrPb7Wbv3r357LPP+vnP3W43Fy9ezJ/ffDNkWpuRdlMlHKmpqQmYShYuXMgpU6bQarVq5/FrZfny5QFVuiLy3ycRcD4TGT260YQEKpGC+nmP8rLHKhOXsc6xCs7BiDn07Tb4SiYaWwnqz4tViSlClSc8ABFUpj/3hmh5oVq1ckyjz1RPqNIMwsys/mY6RIDX6xCast5fnYH686WPQYD8bAhwTYYA+Vj4tGZCBJSlQARdGa/lEOVYQOgAIEK4GVKVvvtBPAcN0ZzVVguhrR80fG+MXA5WDMRisWim7GDUmnl5eX4BUQ0F5sYs9E6YTJyo/M54jKlW65mXStRdnypZ5j1KnrVqknc4HLRarX5VvWJjY+lyudirVy9arVbeeuut2iu8efNmpqWlaRWz9u7dq1GVyrLM1atX89FHH9Xyj9U+77nnHpLklClTaDKZmCzLvD8jg6vNZr4dExNAuxmMcEQvF1xwAe+++25mZWWdtenp1KlTTE9P54cffnjW+ozIuZcIOJ+JDBzYaEKCaPhT+b0PAcQW+AdW9YLQ+nYrk8Gr8E9zehnCj1qn9JcCoYGrhROCTa7xEAAXjpjilSBjOQ0RPTw+yLb6tLxwLZimpeYyE8JkPFb5vB8iwvsliMIgfQ19DUAgPabxPKcrY5kNAbIn4VsEqDSjKohGQwSk9VG2JSktWrlXSWiYeTaU6T6cz5nKM2CHyB3Xf6+PXA5VhzlcM5lMQf3NDQXmxt7fCYZ+cnNzaTKZGgz09bWTZjMnBRmTCs5ZWVksLy9ncnIy8/Ly2K1bNyYkJHDevHk8fPgwc3Jy+Morr/CLL76gw+Gg2+3W/NHr16/n5MmTabFYNHax2NhYrlq1igkJCdy6datm4s7NzWW3bt1488030+l0Bmi/FRUVfoQjRsnJyeGyZctYUVFxVqeoxYsX84ILLjirfUbk3EoEnM9EQmjO/0Bof2RHgI/qPg8OMhHOhYj4DkaxORzCNHshhGblgsgvvkKSmJuby+LiYo0T2Pjb/Px8tm3bNqy2ZFxM1Mcspu5j1PKqQ+wbCsDUfGb98T+HyIWWlXO7BGIxcptyTvo+RiF47Wp9StbHEIsBY4T5exAa+yMQ5B4u+Oofq3zh70Fo3fdCxAh8H+RYwVoo070D8ItcVklcaiCCCa+GWHBV6foyRi4b61A3RgtuTNObop+BWMw4IawPqlXoOER+uRdiAdO1nvED/hYddZzl8E/7a6p8XwfBSZ0BYe0YCV+O/DGAPXTpYNHR0RqDmNvt5uHDh9mvXz8C4Lx587hv3z727NmTycnJHDRoEDdt2sT8/HzGxsbSarXy4osvpiRJWu70n/70J63W9fHjx0mSr732mmadMJlMbN68OX/Zu5c7xo7l8zYbv2ndWmMG3PHWW5Qkie+8807QaeTHH39kVFQUH374YV5++eVndYo6cuQIvV7vWfFjR+T3kQg4N1Kqq6tZdfvtvFGWG0VI8LAyue2HCOhqDuGzDZW3exSi5GI1hGl5OALrH1cDLFPyU9U6vEOGDAk6Ie7evZtPPvkkAeF/TE9P9wuS0WuuDWEWU4+v1/JOQJj0Q4F5OCDbDh/gZ0BEflsVMJAhNNt7IBYL/4YAOJVCtK3hnIwpWXOCXA8157itcq3/pEz+akCYkcRkOQLznMONx6g5Bmtz4SNxsSnjlCGeo7W6/lZDWGMGQFhJohvQd32tXbt27NGjR1hgV2MA3oCInH5PuT/7lUYIK8BI5Z7UwEcYE8xyoD9WTEwME5T7XgsBzo8FuZZPKtfnW+U+DYavpnINwHVmM4uKimg2m7XAsLy8PHq9XkZHR9PlcrFNmzbMz89nly5duHr1ao3K0+120+PxcOLEiVq1KhXklyxZogGz3le8d+9ejYSlTJZZ1a8fabezxlgK0+FglSRxU2ysYAYMIq+//jrLy8t54403ct68eWd9rpo1axavuuqqs95vRM6NRMC5kXKmhAR1AGdAgIxH+b8O4fN29U1l3NIza73XgEnYWO1oJcA5djvXL1+uTUDqfioQh2IWq0/Lq4MAx30IHm39A8BOylhjIEy8W+Cvcf+gnHdn3WS9FsK0/TpEgFVngNdBEJxkQpCMqOf4ARqWklUD4cedB7GYaAilZH054MaqT6HaIPhbXfZDLMpeVY6xHkLDVi0SpyAAe7FyT15rwH033v+nTSa/alcJynabzaZpl8bfqfe1I0RAnHG8uyEWNKHY3owafrBjqM9cKHAeDv8F77sQCxl1IVkFsH12Nu12u5brvGTJEm7cuJGyLLN9+/aMiopicnIyZ82aRUmSaLPZmJWVRZvNxuLiYn777bfs3r27dl7z5s2jyWRiXFwcT506pb37X331FdPS0ihJkvZ81TWGGdAgd9xxB6dNm8aRI0dy1apVZ32uOnDgAGNjY3nw4MGz3ndEfnuJgPOZyrBh9VJ2hmq1CG3+DZW3a2TcOonwfkc1ujZUMFgVwPU2m1907RqAf1cnbQQyi4Wi6vSbjBA62roKPqKSOgjQ9SjXQk+Akq20/4GIwh4KYb4+BcHb7VHG8AAEOJ/SHXsO6jfH7oNvIWWG0NBvQ8MoJevgb3JWr2ewqk+hAMnI0fy+8r2+z3iAW5X/HwHYRbetPtBryP1Xff6dLBZGRUXRbrf75SbPgHjGaiAWDvMhosXTIBZbJyBiF4oAXguxsCmCf1R/fb5xvbWmXBmTF2IBt1n5/jwIy5La5xblt5/qrsX/5OayU6dOWulHj8fD8vJyJiUl8dlnn+WePXs0rVhNucrIyOCOHTs4b948zYKkppKpPuiffvpJe93//ve/MzMzk127dj2zEp5BAHrYsGF89tln2b59e7777ru/yTQ1YcIE3nTTTb9J3xH5bSUCzmcq27adcQGLKpNJA5TtymR/HODdEObck6ifcSvUBK1f1dcXdFMLf5D/tekuagsVbW089ivKcVUNUQXnTyA0awm+gC01xWwihLammoCbQ9QHVn+/GyLPuRahzbFGcLYo/5sATlH6+hICtLPhX4KyRrln9VV9CgdIRnCugbCerFP+XwsBguq9uAzCV95XuRZdIUy7oY7R2DS6YJr+e8o+ajnHEgh2N9X6MQvCbaBajk4p98EF/2Ifz/8fe+8dH2WZtY9fz7TMTNpMeoGQBAIBElro0pYmArqIIipdFFEBWYq6oIDAorKv6y6uBVnXAurqawNUVrFjW5BdsIIgqICKgkgJISHJ9fvj3PfMM5NnJgnFfX9fc38+9yeZp91PPdc55z7nOm53wJ2tea6zs7OZmZnJlabtPoAUCjkBcWXHQZjbVkCyEXZDFNPz1Zjvmfb9YdAgDho0KBCZ3alTJzocDk6ZMoXFxcWcPXt2YOzU1FT6fD4WFRUxISGBjRs3JiB0o3ou2el0hlBs7tq1i02aNOH06dPZCafxjXi95KZNgeM2atSIO3fuZEpKCr/77ruzIqZ27NghFfFOoRRlQ/vvtgZwPp12CtzaxwA+0bs3t7duzUolrH1KqA2CRHsT0Rm3KgE+q9xzGpD1PNipaPXVEHd1xyj7R+OnDg8KagbraGu9fTGC6UpXRjinSML6KrXf3yDu6CcgQP6jxTHC3bH71fafqGO8qO7v8xAFyAMBmK8hXMhetW05RCnoheiKkVUPj6B/FNZkKH9T74BdnYc5Cn4ARIl4SZ3LUgTd0pGAub7vpBmgDQQjw39Syx5Wvxeo300hMQBOdV8vUc/fCXlPtKv7Va9XSjIaBue6XIHplUfVvY10TucCXAZRquZBAi2z1ZiAzEHrbdcaRuA+FxQU0DAMjho1KhAclpubGwDdPXv28NixY7zuuusC16utbV3oIjExkUeOHCFJ7t69m02aNGH//v1pt9vpQHDOmwhV9Kz4CFqFrbMbBocOHcrvvvuOPp+PR44cocfjOauMXhdffHEgBayh/f+nNYDz6bY6VqWqBFjpdnPTxIm02WxcNmYMK8PLS9ZDmHZ1OGrUze1qt1sK5t6wjoQNB+jjSkhbWV6RyigSNYOC/hfW0dbmfcogCsjDqNs1a2E9DaK0mNcVoWb1KSt37BWQ+ep4dV4OiGI0HgJ4TggwpkMis81VrrQFuROnlsqk+xrUBOf1kHn4TRAw2ghRyP6j1l+AUK9JNURxsHJln061K11+cyBCAagRxEOgOcj96p6+qu7Z1RAF4rB6Ts0hMQH62iK516NF9g+CTIWEL9dxB1WmZY9AXNGGYQRYw7Syau4Oh4Px8fFMTU0N0HKaCUZ0j4uLY8uWLfnRRx8xNzeXc+fOpc/nY9eWLXll2LPbrfapS5ZCNcA8w+Ajd9/NF154gf379+dHH33Eli1bnlURtWnTJjZu3PiMkZw0tF+m2dDQTq9dcw3w1lvAhRfipMOBCocjZDXdblQ5nXg1NhbXtGyJkhUr8OCDD2L6Y49hWePGKDOMeg1XCuBGux2fejzo3bs3Tp48CUMdY3ZVFdwR9vsrgGOqb7dYbwDwALhT/e4NYB1E8gDAcADDACSH7bcdwBoADwBIVceZobYvBXAAwCEAN4bt5wZwGYDbAWyNfsmB8yOANur/2tp+ACcBPA1gA4AtALap6/oWwCYAZWrZUQC3AZgD4DiA7wH0CDuevg+fAPCq8ziV9rPFsi0AegHoCMAGoBOALgBeVeutrpmo2bYAuDZs2VMAWgKIB9AKwPNhx7gZQDaALMgz8QNoFzbeBAB3A5gE4BbIPeqizjkHwGsAzgfwMYB3AVwC4FN1/H6Q98YDuW/mpr+UnwG8DOAEgEoAjwF4G8C5AH4C8KU61meQd2se5D5BncvHAMrKyuD3+9G0aVO4XC7k5uYiOTkZU6dOBQDk5eVh7NixKC0txZEjR+B0OlFdXY3jx4/DZgsVgxUVFfj888/Rpk0bVFdXY9myZRg0aBD6bN+OpBp3ve7tbQA/kLjo8GF8+OGH6NSpE3bt2oX8/PzTOGrtrWPHjigoKMATTzxxVsdpaGe4/be1g/+X2vCePfnJ+PE8MGQI/+lyca3fz13XXsuKffvYuHFjNmvWjE8//TRJctiwYQTAv7RsyVLUkX3JMHitoiIEZA5v8uTJzMrKCol8DbdqXZCUpwIEI2Kj1Y3WOarmgB3dw62+8KCgQoQGrhHBaGur6zJTlup+COA/EUxTWwWxFLdB+Kp9EItbW+l+1HRrh7tjCQlWamdxDpvUtubgttqit1fj1Czn6RCr25yG96YaS1vK/4ZY0i+r39sgFv16dc23Q1z55uMmADWsutqiwHVJwy/VcWdBLPbwOfEKiDXtgHgV4hGMKfgEEiRog1jMj0JKZ94V4Xlb9R8gVn+cuq4ukHgBQub+m6vzzoFErJv3rYAEKmpX+QKvl63T0gI5vkVFRYGykHa7nW63my1btmRRURGTk5M5Y8YM2mw2zpkzh1988QWBIOWpdpVrOlSrKQltOWdBLPrxsJ5iISR2YBxAjhnDoUOH8plnnuFdd93FKVOmnHXZ9M9//pOtW7dmVVXVWR+roZ2Z1gDOZ6idOHGCsbGx/PHHH9m+fXs+9NBDHDduHFesWEGS/POf/8xevXoxLy+PS5cuZX5+Pq+66ioC4AC/nz/26sUy1ATYk04nywyDzxoGRzZtysTERPp8Pno8nkCgjc1mswRSLTx7QuZIfUpY34/odaN1jqoVpWe4cLIKCjIgbs2TCI22fl+NV66u83YlkPch6PaLJKyvQ3DOexBEIYiFzOm1gHU95EZq3DwIoPghc7XhLsgbUVOhIKJHb1vRZ55Kn6+OdzdEUYlT5xvOevaMWh+vnqdP7a9TpT4EapQfrS0K/HaAI0zrNqn7W1cOcr1+n7rvOoCvP4IR9GezV8O69OhJp5Or7Xb+edQoDh06lJMmTaJhGPT7/XQ4HLTb7Rw7diwLCwvpcDg4YcKEwHfsdDqZnZ3N9PT0ADVoXl4enU4n10a4N7XxEejziod8Z9VDhzI9PZ1ff/01p02bxjvvvPOsy6fq6mq2a9eOL7zwwlkfq6GdmdYAzmeobdiwgR06dODtt9/OAQMGsLq6mrfddhtnzpxJkjx69ChTUlJYWFhIv9/Pzz77jElJSfT7/QSkxN/KP/2JJ2+7jR+2asWXY2K4xufj9iuvZMW+fRw1ahRdLhf79u0bSAdxKAISAHwqJiaiENPBVR9BwC4GMn+o11tVvzqO0IjYSOCsg4LMgNcTAiQ+iEV4McRaexNSVjEOApS9AL5l2q8SkT0Ikea8rSplZUGA3K7O4QuIJd0GAj4xEKDtB8mbjYMAfHjNbZ2LToSWoKwtja22fjoVmrTiZJUqFf5saosC/wpCwrIdYoHOhgBL+HFmQCpi6aBAQOaY9foOapkLYkFD3Xfzef9OrYe6/2YWvfkQq9wcOPXlKd4f87UfA3hrZib79+/PhIQENmrUKBAkplnBBgwYEPiG9+zZQ8MwuGjRIvbq1Ytt2rQJlJUEIgfzmbsVHwEh/AJNIO/TseHDmZqayurqap5//vl89tlnfxEZ9fjjj7Nnz56/yFgN7fRbAzifobZo0SJOmDCBycnJ3LVrF0ny+eef5+DBgwPbDBkyhF6vl4mJiczNzWVqair/8pe/0Ov10mazceXKlYFt169fz9jYWPbp04cVFRU8efIkc3NzmZGRQcMwmJKSElJxyIobW/drEKQEbQ8BpWWm9VbgXA5rAAkXTjooyAzOQyF0l/UVpq8hNKDJKkJc82OXQMDSpnpjgK9DrF0HxBvgUNvEQ9yxYyHBZDogzEAwJesN0zKv6n5IIYuvIYQpBWpZNgTMTxWcTzdwawmsU6XqGwVeDgmwg1qfC8kjDj9OW4iSlYigO90FsbyJ4Lv1FEQBuFjde73/w+q+3gdRJMZDKkuZwTka3/jp9OM2G2d4vezUqRPtdjvff/99duvWjQCYmZkZcPPu2LGDjRo1os1mY1ZWFmNjY0OUX8A6DS68h/MR6N4f4C0A6fHw47Fjed5555EkW7duzS1btvwiMkrLkPfee+8XGa+hnV5rAOcz1Pr27cuioiLeddddgWXbtm1jfn4+SfLhhx9mZmYm4+LimJycTJvNxiuuuILNmzfnF198wcmTJ9Nut/Opp54K7L9s2TJmZmayQ4cOvOqqq5iQkMD09HSOHDmS2tp2Op1s2rQpHw8r42cFfpoRayBCI2GtwDm86zKK4fzUFRAreaH6/Q7EEv28luNZgU4JZH5ZW6tW1vJcCHXno5A5yHcg7nkbgpWydArUTZD5ykIEATkeYu1PgrjL7ep6dqv196pxDqn7YoMAew4EyCogc8JxOD139qmmPK2Ksl99o8DnQNLN9qhn9zfIHPS0sGd8AGIR6h4PyQDQDHJd1DUdgVjyHRDqTi9Uz1b/Nke+RwPnUQhWEDPHSxAyX16onkNLhNKdWt23S/LzOWHCBF5zzTUBwE1OTmZBQUGghKbOfLDZbCwqKmLbtm1DKnvpAjLme1MbHwHV/bXr63W7+Yfp0zlv3jxWV1czNjaWhw8f/sXk1N13381hw4b9YuM1tFNvDeB8BtqJEyfocrnYsWPHEB7eiooKxsTE8KGHHmJmZibfeust+v1+ulwuOhwOdu7cOYSFaNSoUXQ4HFy9ejVJcsuWLczMzGRiYiJjYmK4aNEixsfHs7i4mOeddx5Hjx5Nj8dDu93OlW3aWM45hwdX9YVYuttM29QFnK9F5PnSTyCWpVcJyvAAr7qAztWIbFGaQUf/r3OYzXWlj0G8AoNN244wAcEXAG9Wwt5Qy3XJSw3O75jG3aSE/1G17gfTugkQ9+yZAOjaXNx/gXg87KgJYisgypELQbeyvldXQwDFjaDbOE3dAyJY0etqtdwd5RmbewJC3dpvI+h1MNQ9Gxy2fQkkTiAD4IVqe53+Nl9t44fEENwLUdA+gSheJZB31g2ZW9+r7oWudW4+b83t/ToEJBMg7uQXYmICniYAdLvdgfQrwzDYvn17tm3bNgDSOqZDTx9FiheIxkeg+xIIw1u1YZDDh3PgwIFcs2YN9+/fz6SkpF9UVpWWljI1NZWff/75LzpuQ6t/awDnM9CeeeYZOhyOkELuumVnZzM5OZkvvvgi8/Ly2Lx5cwJgjx492L179xDygerqal544YV0OBy877772KNHDxqGwddee4333HMP7XY7mzdvzqysLD7//POMiYnhc889x6KiIrbLyrKM1g4PrkqFBGiZt6kNnE9CLJc7UbPudDRQqSsX9TlK2IUTPBBiISWrdS0hLtOxSljr4hWAgJILwUCpkQgF51kQS8sNAedhEIvvBQgxSR6CAOOBBJJ9gOD8IRBafWs8IhOB1KfXpeb2LAgAh+cfv6nOYQtkTjNPnfto9czuU7+9EIv4XxCFoljtvwACXK0g7F8r1H0sQXSFobagqELIvL9eb1fHXQ15H3PVtevI908RZF97FwJyep32nlyqnt2TsA50i0Nore9/Qbwry9U1moljDMNgfn4+4+Pj6ff7A7nOOsDS5XKxqKiII0eODCwzDIPJycmsePddljud9VI+dS+z2Vi2YQOTkpK4b98+vv/+++zYseMvKapIkgsWLDjjVbAa2plvDeB8mq26upotWrRg165da6x77rnnGBMTw2nTpjEzM5PDhg2j3W5ncXEx77zzTrZv355PPPFEyD4HDx5kTk4OAfB3v/sdO3TowPHjxzM7O5vr1q3jlVdeydjYWPbu3Zsej4dvvvkmX3nlFWZlZXGt0xkiVDUj1lEl+P6JICMWIYFNZRBwvhbijgxnAFuF4JxirOn/LhALLFoQ1Uk1RiTQMXNRR0sFGgkBpRcggFyEILglQ7iXW0J4mH+PINC7TOdrh6QUPYpg+phHnfO/IZZzLMQVPBwChl2V0CdEgZii7tdmiJWXgdMHZ7PLdCYi04JacXLPVM9tvsXx5qtt+qpnbkDA+xYEPQllkBS3WIjC0l49Uy+iu9xrC4q6HkGlhurZDkYw8v06tT6ct1z329QzIELjJZIQfJfDA91cEDd9+LHWq+etiWO09WwGXXPWg8Ph4PXXX8/k5GQmJibSbrfTbrezVatWzMjI4DPPPEPeey/LHY56AXO508m5ycm8qGdPLoyPJ0eN4p727flWTg55xx3kDz/8UiKLBw4coN/v5759+36xMRta/VsDOJ9m+8c//sHY2Fj5aE3thRdeYGpqKs877zx6vV5OnDiRhmHwT3/6Ezdu3MicnBy+/vrrzMnJYWlpKauqqvjggw8yPT2dkyZNYteuXel0OpmcnMzmzZvz+++/Dxz7j3/8IwGwa9euvPjii1ldXc1WrVqxT2wsT5pK172DYACPAZk3fQBiqZQgGFlr7qMsBO9HSoBXQ0on5kPcx8MgaVnNIfNqeyEgeR+CruraQEd3q2AbbSHNhbgLy5SgLlb76BSqD9X5tVTLDAQViQz116euuxWEG9oGsSLNJS+7QQLlxkBATVu2hEQ2D1Hn3RkC1G0s7l9tPbxKmK4SVRsdqNX9mYFQFjNd5vI3YducDwEo8zZaQduk7sc+CICNgChp0ebEawPn6WoMHRTVAxLtrdc/o9b/FGH/2yGub/27EqKctUewHKk50C1GPc9dFsfS4EwE09+s3NRpaWkBt3ZKSgpTU4hjxDUAACAASURBVFPZtWtXDho0iE6nk3FxcXzxxReZnZ3N119/nTNjY+vMT1AKcP8VV3Ct08kThlHTw+XxkG63FNOJUF7yTLdp06Zx9uzZv8hYDe3UWgM4n0Y7cOAAMzIy6Ha7eejQocDyl19+mampqbzjjjsYHx/PnJwcejweTp48ObBNnz59uGrVKo4YMYKTJk1i586d2aVLF3744YckyVdeeSVARXjBBReEjLtw4cJA5LbD4eDmzZt5++230263c+MVV5A2W1RXtFX6kXZ1WgneCgTrTveGgJeuO90N4jrU2/4NAl51qWds7lZpKtpCGgFrIExHMBBMKyA2dX6jIQFhjRF0eydCIr2zIKBsR7Dk5QYE5y49kHlPQILHrITuZWqcul5fXatEdYywv9X9sSJKAYIc4HqbBHWdVmQqhyEuY+1daAfwHvU7fE58h3rmWqm5Wt27DyCKz02QuWsD4rn4DuI9uV/d852QWIdUhJLSPA8B6mqIOzoLNWld50KUwL+gZqDb1ZD38T+o+ZzM4BxOHNOvX7+Q3xq0nU4nFy1axMTERObl5TE3N5cDBw4kSU6YMIEJCQkcPHgwL8jK4pvJySy322s80xN2O6tjYrirfXveFRPDUoRSjlr2KOUlz3TbvXs3k5KS+PPPP5/1sRraqbUGcD6NNmbMGI4YMYIdOnQILHvttdeYkpLCm266ienp6ezYsSNdLhfbt28fwm370ksvsVWrVrzssstoGAbvvPNOVlVVsaqqin/4wx+YkZHBtWvXMj8/n4ZhBNItvv/+eyYlJXHjxo1MTk5mUVER4+LiuHjxYjqdTs4eN450OPgxgtau/vgHIBgMpLs5oCoSOFMBQGclxHogWHc6QQlnvZ0OoqqLRWiz2QKW5B6LsfW8qRPBueDVEPaoq5SQPxfiDneocdNUDx/rfIQGcDkggL0Rwajbz5Wgj1HrG5vu32eQaORyyPxusjrnuighZ6JKlBUnN1GTKEWTtJi3maKux4pM5XKIB+QgZApiIUSp0+OWQKztajVO+HkNggB9OGOZ7pdBpkAM07KWCGXRuhQCtrEQz4cVp/ZcdV7TINXbzHETzSBKxR8t9rOynG02W0iKlNfrpcPhoMvlIoAA94DP56PT6WSnTp143333kSQvvfRSut1uxsXFMSkpiZmZmXx51SrenpzMlTYbX7TZuKNbNz7brRvbZGby06lTWV3f6nW/EECPGjWKt99++1kfp6GdWmsA51Ns69atY25uLm+++WbOmDGDJPn2228zJSWFkyZNYuPGjdmqVSsOHjyYALht27bAvpWVlYEAr2HDhnHmzJkcNWoUf/zxRw4aNIjnnHMO9+zZQ1LA2DAMejwefvLJJ7zmmms4ffp0kuTixYs5aNAgJiUlMTU1lTExMZzndvOE3R7iitYfff8woZaIYPqRjlqO5rJcCLGciWDdaRtC06a+UAKvGtEtwrqQaFhZpnGQIhXNTQLfpUDgYi1s1XX5IcD+gBL+SxEs7mDu8xEadauDyvS857cQS09PA3SEKCFEMAWsNmCuj3C2Aui6EGBsh4DwZWHLzQBlJlOhui5z0ZBDYeOaaWEjlQL9CfKu7YQogFp5I8DHAK5Tz/gnCJhfXYd7EB4vcal6ps8jlO70HYgV70eQ7tTq2o8bRg3iGDNAu91uNmvWjE6nk+np6SHbOZ1OvvLKK1y1ahVbtGjBTp060e12c+zYsSwuLuZzzz3HoUOH0u/3c9y4cWzVqhWHDx/O9UuWsNQwIlZ0262Ob1nRKqy85NloOhukrKzsrI7T0E6tNYDzKbQjR46wSZMmfPnll9mvXz+uWbOG7733HlNSUjhixAjm5+czMzOTixcvZrt27ejz+QL1Yd999122a9eOvXr14uLFi9m3b18ePXqUqampTEtL4+zZs2tUjykoKGBmZia9Xi/9fj8PHDhAUtIisrOzWVJSwgsvvJCGYQQoN82u6AoluLQrOhwI7lECU89DN7UQcluVAATEas2FWFoJELKQ9kro65Qc877hFmEkSzIcfMItJELc0n+MsL0GczON5VBIVaehEAvrC7X8HHXuVsDQEaFpS9+re/SeOv7usGt7GtbAfLpkI2bQt+LkLgP4MUQR+hLCzNbNtE05BGzvhXgBtkNc3r83jTMeooT8DHlPFiA0h9tMC3sfrEuBvgVR9C6DeB2S1LVbXdczkIC+2q7/B3WuCep8UiAWuL52TXeqPSbhdKdVatuXILEWPwHMtJhr1sFgqQBvNAyuBLje7a7h+fF6vXQ6nZw5cyYzMzPpdDrZvn17Llq0iHfccQdnzJjB1NRUTp8+nWVlZbzxxhv5YkwMqwwjIrudBmfLilYq7epst0GDBgUohhva/63WAM6n0KZOncrx48cH+LS1K3vAgAEsKChgUlISn332Wf7+97/n0KFD2b9/fz722GMcO3Yss7Oz+fjjj7O6upoVFRVs3Lgxf/e73zE+Pp4FBQWWxPSXXnop7777brrdbrrdbu7cuZOkgPPo0aPpcrnodDrpcDhCmMK2KgGXBAFl7YoOFwRVSsA9BAkGsgLnoQgFHV13up3a9yUlZP4CYZSKBDhWJBqRCE7MFhJRsyDESAjpAyHWexOIcnGD6TiDIW5dHwRw09UxdE5uOiSX9msIyC1TArkQNXOKT6ImOBOR6ztHo+l8Qo3hhVjz4ZHL0UBfW/uHILECXojVFb7NOItljcPO6QDEtZ0KAdhuCHVRm/nVP4N1KdDH1O8EiPIzGQLSr6DmdV+vnltdlZT5Ea6d6vkmQubVw/d7I8q9Mxe26OZw8JW4OEte+0ieH5fLxRYtWtAwDN5///0cN24c77//fmZmZgbjSvbvZ5UpOJOIXDQjYrlJt/usR3G/8cYbbN68eQg/Q0P7v9EawLme7d1332VmZiYPHjzIDRs2sLCwkKmpqezcuTMLCgqYlZXFzZs38+2332ZGRgb37t3LHj16MDY2ljfccEOgiDtJHjp0iMXFxfT7/dy5cyc7d+7MRx99tMaYd9xxBy+++GJmZ2czJSWFPp+PU6ZMYUpKCtu2bUun0xkQHCujCDrtig5fflIJ0/chkbv5CAKk3qYRJIK5CUKLHnSEAOheSMRvK4TyJod3q9znaALYqiCEBvPOECvdq9b1iCCMnRC6yFwIiDWGWFMaZC6HpJN5IZZYOwRzq3Mh7nB9n6zA2aq+c6QqYYSAVo6631Xq3u212C4c9E+Hk7su3Uoh0MpelbpviyEekwMQj8RsiPUMSAER/TybQ6z98Ov2IZgfb6WgRKuWdqo93Auh55brEwtQrp5XeIS9trw13WdmZibHjBnDF3v3ZkVYulV9K1pVezzk0qVnVZ5VV1ezU6dONbJNGtp/vzWAcz3aiRMn2LJlywDF5nXXXUePx8PCwkLm5uayQ4cO3LdvH3/++Wfm5ubyD3/4A1u1asXCwkJecsklIcf68MMPmZ+fz0mTJgXK27333nvMzs7m0aNHQ7Z9+eWXGR8fz8WLF/Oiiy6idseZg1h0vuYrAwawUmnsWyEgVgpxBWtX9CsQK7QSEq07FdZ0lBogV0GA6lXUBOdUhDI0NVGC20yvmI4gi5VZOBHRaRhPKAGfqYT6NRDXazQwN7OVNYIARrg7sRziAtYkJueq5dMgaTx3QOZSdT51GgRINDiPQJCvW5cwDK9SFalKGBFkN6sNVMJB/3Tc5KcCYmbL+Uf126oU6Bq1TntT5qMmOL8PATNt5UZSUKJVSzvVazLP3+t55lOJBQh/Nmar2mazMQ3gTXY7/9ft5j7DqLHPqVS02tWjB0+ePHlW5drTTz/Nzp07hxAiNbT/fmsA53q0W265hcOGDWN1dTU//fTTQB5yRkYGL774YpaWlpIkL7roIubn57NJkyZ89tln+eqrrwaqwVRXV/O+++5jSkoKn3zySZLknDlzeO2115IkL7/8ct58882BMauqqjht2jQCQVpBs/AcNWoUv/rqK7Zp04YA+PDSpaxWFapmQUAtFhKIo4XnU5Co2FglMM9DsJZxfcoFvqLOIQPiVt6ujjUMoXWE5yAIzOZj11ZveAHEGj4ImYPsAnDeKQhSq0AqPQ8YCwHn/0Csfl3qcCrEZZoJmeeegiA4d4TMYX4GAeh1qJmmY1VukxCFyAkh2mgKsZiuQ2QrOxz0TxdU6gpiVkpGnjrv8FKgmtvcA1FkNGlIM7XfvyFKnHnKpS4KSjYkiDESv7buC9R4ZqWxKuyaHA4Hk5KSGB8ff0aVnEr17P4N6zS52t5Dc7eqaPVOUhJzc3N5991389ixY2dFrlVWVrKgoIBvvvnmWTl+Qzu11gDOdWxbt25lSkoK9+3bx+3btzMtLY0AmJiYyJtvvplVVVU8ceIEL7vsMtpsNt50000BsN63bx9TU1N55MgRXnbZZWzTpg23b98eOPZ3331Hv9/PH374gd988w2TkpL42muvccyYMYyNjQ0ISpfLRZfLxeHDh/Pvf/874+LimJ2dze+//54rV64kAF500UXckJp6yu7PSOUC9e8mJiHYTQniBab1HypBalVHeBysSUbCt9OlKksgioRe9xjEGjYL4NooQmsTivEQcL4LYm2nq26HgKgTAqL3IQjOj5j2vxkyhxoOopGqhOmiDyWQKPAfIVMJVuxWRE3Qr4871qresRW4RAJm7Z4vU9u6UZO45goIIP1Lbasj6JtBFKqPIYD9j7Ax66KgZAP8O8SDQogCmI4gfzYhEeJFECUqHJzXwzqdz4maNLGvQhRWD4ST+yvTuicRfNd7R7nXp/MeEhEqWo0Zw/fff5/DVZnJefPm8YezMA+9fPnyQKWshvZ/ozWAs2779wuN3qhR5NCh8lfR6lVWVrJTp05csWIFd+7cybS0tAAx/qpVq0hKalVeXh5dLleN+qzV1dWMi4tjs2bNOHHiRB4/frzG8OPGjeOIESM4duxYut1uApLeYRgG7XY7vV4vJ0yYwIMHDwb22bhxI71eL3Nycrho0aKAy66r3c7jNtsZAWddLlCDlg0Stb1ECblcBMsoXgdJbfHBuo7wbFiTjESqN9xBCUa9/SolvL5FkP7zD6jdCqoLOJciWHXpAQhoXAQJcspTAnOPGv8dBAHrfyGu3fA550iW809q/cOmZU9D5rmttg8Hfd3rwsn9KoR8Jto2ZgrVSD18OqIc4k3QQPwGQt3RcRCLt1zdPyA0XUjnUdemoIRzvm+DWNHmd2IQJL2rCULBOfw6n1HP1Iom9ke1/Cn1XGdB3osYBAtrZEKU1Lywa3Gr+/Cjxdi6Rwp4rK2iVZlhcNe11wbczdu3b+ekSZPo9/t57bXXBgJDz0QrKytjRkYGt27desaO2dBOrzWA88aNQpvndks3f1iKVu+LoiJOLinhrl27mJ6ezpiYGLrdbl566aXctWsXf/vb37JZs2Zs164db7311hpDPPzww3Q4HJw7d25g2fHjx7l+/XreeOONLCkpCYC9w+EIWMtOp5MxMTF89NFHecstt3DOnDkkBezfe+89XnfddWzcuDHNc2kAmJGRwZleb71cd5EESHi5wEZKiOl85iaQQKFNELdzodrfqo6wFUhGqzc8VwntH9TYmgRF04LW1ZKsCzjr39qNPw3BlKrHYQ1ahLj2m8CajjSSi7MRQq3vSOBsFWgW3utCj1pXClWr7lbbmatdlUPSpnQEvAeh8QLZENIXXSXLUP9rnvK6KiganMPrketSlU9BgtKIyOCsu/YQPI2aNKjLIZax/n1MnffCsGOsgLwb5pzl+QilSyVqutnnW9xXQ11LLiJXtCoD2DotjU2bNuWCBQv45ZdfkhRP25w5c5icnMxLLrmEm85QPvRtt93G0aNHn5FjNbTTb79ucL73Xkn2twjeCP+wK2NiODs+ng6Hg7m5uezatSsvvfRSJicnc8mSJfyf//kfdu3aNSR4o7S0lFdccQULCwt5/vnnc+7cuVyyZAn79u3L2NhYdu/enZdffjmLiooC5escDgfz8/M5btw4pqWlceTIkXzzzTd5xRVXMC0tjdnZ2bTb7TQMg2lpaezTpw/79OkTAs4arOvq/owkQKZArAdzSpEWgmYBOw8iwHXZv2dRs45wPMQCNwt5TcN4DySAKEYJPU10cRziatTCzGlxjrp3RNCSvDNMgGpwXoVQq0cL/K5qvKXqHF2m68k2CVl9zebqVE9DFBIrd3CkeeRb1PnuV8fsgZrMbfr66wKgZ7NfAPEgNEcooGl+8mRIeUZzvEA2RKEphMQTZKt9J5j2r4uCYraczfXIKxA9FiJaP4mayto0SNCgeTuvxbIVkLgEc85yPkKVjEhudnOvhljgj0RYT0h5ySMDBjArK4sLFy4MZGf06NGDDzzwAA8dOsQjR47wrrvuYuPGjdm3b1/+85//PK2grkOHDjEpKYlfffXVmZCuDe00268XnDUw1+GDNn/YX3g8/LJ7d3HRDh7Mb775hp988glTUlJC3Eyff/45mzdvzo4dO/L888+nx+NhcnIyr7/+ej799NOBj0pbzE6nkx06dGBCQgInTZrELl26EJBAloSEhADlYIcOHdilSxfm5eUF3N86ncPcW7duTcMwuOLqq7k2JiYQtR0uJKJdbzjbU3iPJGCtyEM6QXJyzUL+j5A8ZLNLsRkkilfvN04JU0LSwGorNpECAZRpkOC0UajpDSBkHnOJ2scOmRftpsaPRZCn24AoHLer/TIRmr97CyTy2+pcIqU+VUCswUTIVMFUBN3kuteW52ylDJxKQY3aumYmKzY9t6/VfUlGKIDqeIFsiMLzrFqXCbGa30TwnYumoJirpb2s/tf7XQ3JpY8WC1FbDwfnKxBMA9Ndk58kQxSRNyDg3Nt0jEGQd+Woab/a3OxU9yEW0adjjgGc1r07b7nlFqalpfGpp55ieXk5V69ezYsuuogJCQm85JJL+MILL7C0tJQrV65kcXEx27Rpw5UrV9YgMqprmzVrFq+//vozJWUb2mm0Xyc4b9xYb2AO78cNg3S7WXnBBby8oIB/+9vf+N1333HVqlXs3bs3bTYb/X4/x48fz1WrVvHBBx9kv379OGnSJMbExATAVrvIfT4fW7duTa/Xy6SkpIB1DEiUdmpqKjUQJyQkMCUlhS6XiwUFBWzUqBG7detGp9MZKHHn8XiYmZnJDz/8kEOGDGG6zcaZAJ+Ji+OmzEx+5vEEIpOt+hOQlKH5iAzOkQTsmwglD9kIAbiREKtC1xvWQqqN2k6TjDghwT971TnMgaTcNIIAT10BJ9ti2Xw1Vo7FugIIYDeCALbOg45BkLzlRsg8+U/qHDMgDFuRrPkzxRAWzWNwOgU1auua09sMzosgCokmuHkVofECSRBljBBQ80MsxZNqX+3VaIGggjJOjacVo/DzmGR6LjooLQY1YyFuh3X09kyI4qUBt4dp3TSEVvciZH56JURReFjt9weEgnMzhIJ8Xd3sExA9MOy4zcbr7HY6HI6Q+JbBgwdz3bp1PH78OA8ePMj77ruPgzt25ILYWG4qLOShnj259ze/4f1Nm7JddjbvuuuuGmmZtbW9e/cGWQijxOE0tLPfflXgfPfdd7OkpIQum63Gx7FCfZA6tWZf2PrNSiDFQqysP6vlVQBLDYO3ZmbS5/MxPz+fycnJvPfee7l27VouXbqUF1xwQUjUNQDGx8ezcePGTE5ODgR82e12JiQk0OVy0eFwMCsri4Zh0Ov1MiEhgXa7nR06dOBNN93Ehx56iOvXr+cll1zCli1b8pZbbgkBdA3k4eXxnE4ns7Ky+Hx8fEThcBgCVN8gOjhHswDN5CE+1BS2GiR7I2ilaJKR1hCr8S0Ema9skPm5x9S+dbESL4giBK9HzXPqBgEBQiy1dhCgMQvZE0q4xqv34I+Q4KdI4Haq3Nqz6nCNZ6KgxqlYzgUAH4TEC2gPg44XOAYBUE2G8wYEROdDlLWmEMWvLlSWZn7tTyG82i5I4KEPYtGGx0JshbVbeR5EmaqCkH24AL6r1i1XxzLffw9COePPhfB791a/b4Dkyb+uftfVzV4KeXfeiPCcTjgc3DFzJl988UU2adKEAwcO5JQpU9ikSRMCYFxcHGNiYnhFcTG/KCpilcvFKpU6GfguHQ5WOp38IDub/RMTOWfOnJCSs7W1W4cO5WeFhVHjcH7J8pa/1varAudnnnmGzz30ECfb7SGC4U2IW/ATSLDLZISW3ftRrV8FEc5HIDmu5pf2hN3O6TExjI2NDdR/1e5os7Br164dR44cyQEDBrBx48aMi4tjy5YtWVBQwPj4+JDt4+PjmZGRQZvNxoyMDLpcLhqGwcTERKanp9Pv9wcsaU1JGBMTEwLQOTk5TElJocPhoNPpZI8ePThlyhS+7fNFFOaajIOIDs6n0uviUuwOoRIlRCk6ABHaLyLoHq2LlXgJIoOzrr5kxRWthXkbBNN4IvXwfNpoAF0XEI2WM2u+xiU4MwU1auuzIFzcGpzfhczHroYoLqmQiPCNEC/Co2o/P0Rh01SgyRALVB9zDmoHZ82vnQgBtCJIJP1eNW6JadsmEDCM5lY2Bz1mI5iz/QNEQXxarb8BEtxofi4DIF6cnmobHfCmvQCtEOpmT4coDOGpWSsRjGWIh3hwFhkGy+12PmsYwm+vlOoWLVqwefPm9Pl8vPPOO/nss88yISGBf2nZsk61pKsAVjidXHnOOfT7/Zw0aVJICqdlu/deVrndtcep/ILlLX+t7VcFziTJO+7g3DBwngnwWtNvnYu6U/3+PcQVWxfhN6xRI+bk5ATAEpASdJmZmTWCtszdZrMFytBpS7pZs2bMzs4OuLX0tna7PfDb4XDQ5/MxISGBgORC5+XlBfKwAZl/1hSffr+faWlpEWk+w8k45uPMgXOkYJxwl2KREpRWx7gaMt8YaQyzlRjNcm4GoaK04oq+G2Kl76nHtdUGfHVJfdqs/kYSjJGqG9VGeXkIktebCrG8M6OcZ3hPgYCVno64Uv29DQJQ5nlhj8X+F6jz/Q6icGlwvgnW4ByJyvIzhFYUi4VUITNf5wgE3dlNUBOc51uc33y1bj3Eze6GFEV5GMEYhUkW+8WpMXRwmB/BlMNU0zkuUterwb4/RNZoxWovJNJ9QKtWXLduHZ977rlABobdbmf37t05aNAgulwu2u12/t7nq7dSVgpwRUkJx44dy9TUVA4fPpwffPBBTdl4CnE4DQB99tqvD5xHjbIk2jADxF71cWnKyQwIiHRTH54uDhFOOVmfIB63282MjAy2aNGCbdu2ZevWrZmTkxOYizYMg/n5+Rw4cCDHjx9Pn8/H0aNHMy0tjYsXL6bP52Pv3r05aNAgFhcX11nYJiQksKSkJGKqTzgZh87lbG+x7QkIMNTVrfoBaoJzXVyK5j4Z4O/qIDROQqLNw8kmCMlT9kJAIJwrepBa/mV9BJTp3GubJ46U1jQTtVvCkaob1UZ5OR4CZKUQhTO9lnOM1ueqe2t1jFgEi5J8DKGi1PPDlQimhVmVv4xGZXkS4uW4U/1/P8SdPtS0/1bIt5qKyOCs+1iImzpSQOQPEO9LHMRq74JgEOBJdQ8NSK53GUR5H4mgi32pOpen1HUdg3xDb0AUwZ2msbTH5jyvNxAY2qlTJ86fP5+dO3cO3Fuv10u7YYQoyu9DwN4Pea8uhuSNm7/lPIiFngmwIDGRWVlZHDBgALOzs9mrVy+uXbtWiu2cThzOL1De8tfYfn3gPHRoDcHwKkTr3QqxXCapj28GRBAmqI90o/qwbBBQtqKcrG/6iwbi8ALwp9r18XSPtF2kVB8zGcd3EIF6kRJY4dseB9gPtVuET0MUGquyh5FcitpKdEAoIqsggj8OQpd5jXpmCRBXox5zEAR4vZDAMgPiCTC7S6+CuLyBUDam6Wq8GlMWEPd7jhq/HSRFKPx+1DfCWvf6Bo5Fy9sOJ+6guk8bTb8XIMgrfip9PgRUbAhGYqerY+rvYBsEtGLUPtUIpsXpILNI10CEUll+jJq1yTUg6d+5EA9PE0QH51mQd/Ew6sbqFd7nW9yPnqjpDYoLG7815D3WgWi3IRhPkQfwL4bB4uJiDhs2jJ07dw4QEOXl5TE7O5s2m40DEapsvgRRAA5DvrUJCM3Z3wnxmhDynRVB5qyLioqYlJTEvLw8NmrUiC1atOBXHTqw2jDYG0HylVhIdkX4PRivznuHXvYLlbf8tbVfHzhbWM4E+FeIqzMVMp+XAKmSM1cJgvFquw8gws4s2M2Uk6UAb7TZAlVqtNs5JSUlsMztdteYi3Y4HDQMg36/P0Bo4nQ6ee6553LChAm8/vrrmZ2dTZfLxczMTM6YMYNTpkzhwIEDGR8fH3BrJyYmMikpieeccw6zs7OjCtk1DketVu98WLu1w4HoVIgu5qtjmV2KvSEuTm0lZkBANh4yB/yEOp+RSuBUIpTOMZIA1WOZywyGc0V7IWBuzoXW88Xz1XlVAVwLEb67Le7LqeQmO1DTwi9FZAVkgBpfW0TTEVQ+IoHzv8LuTwzqfn563tn8zdRGvar7DnWMkwhazu+jflSWH6EmOPsQrBv+lLpHOo/ej9Dobb3PPAhIHsCpAXOkXt84Ct2rIfEF8wA+raxms5IdGxtLv98v2RrqmNHu2WYEiV7C+wEIWUqy18u4uDgC4jb3+XzMcjgCgZy9Yc1frvsGBFMHd5jX/QLlLX9t7dcHzhZzzuF9O0RQ/6Q+vHwECRQqIe5tqBc+nHKSCFIumitHeTyeQApVQkJCoMfHx9Pj8QQirTVom61fl8vFmJiYwDy2zWaj2+0OqUgVyYqOJHC9Xu8vkuoT3utb9jBc8G2DgNLhOuy7GyKkd0VY/x8ljHwQwX4xQglGovViWM+L14XVy9yt6CSJ6ArItRCGLkKKgvwGwepYVuA8CuCFkEDGHZD3uT6Ws5UbujbqVd01OOt5fANiQZpzzx+HWLpeiEfqUYRSWZ5Q1m/uQgAAIABJREFUzydXHWup6d79CJli2oxg1PaTCEZv6xzkJRDlW7t9l+HU5u/r8o7WN47iNojHJ9r3Ogs1mc3C+10IDWQjJLshHkEF+vGBA3n99dezW7dugfrwNxhGwOvVG5HB+STEa7QVFuD8C5S3/LU1B35FrbKyEpWXXoqqOXNQBeAEAAeASgA7AbQGsAfAJADXA/Cr/ZoBeA7ANLVNLAAbgHQALgD/q5bp5gNgGAZIoqqqCpWVlSHnUVpaCrvdHugulwsnTpxASkoK3G43nE4nnE4nAGDnzp1o1aoVqqqqsG3bNng8HgBA//798dlnn+HYsWP46aefkJSUhG+//Rb9+/dH165d4XK58PHHH2PLli3YsWNHYGy73Y6qqiocP34cB3JzsdzpxOQdO+Ctx30sBbAAwG/UffIB+BnARwAeBnDAtG0qgHEA2qjt7ACq1N9TaYsBnIQ8GyeAAnUuFwE4DmAWgKfUNj4APQHkQaTJTQD+po4zEcAdAN48hXPYD+ALyLsQ3ryQa61rmwR5l/ablm0HsAbAXgAJalmJab0f8gwAuS4b5P2N1JYBmAq5V8kALgPwIIDv63iOPotldgBjAVwO+Y6svgNzy1LjPgXgcdPyVer8ZwF4EsAuddyLATyhtnECSAKg3+Ib1N8jkPerD4AOpvNKUn/9AOLU8jnqHAvU7yrIO9MJQFnYufYAMB3AiAjXYm60WNYawCOm36UAvoT1+wI1/i6bDYkJCSgvL0dFRQWqqqoAiBwBgDYktkc5j48ALASwOmz55arvAPAogMNvvIGnP/0UcXFxaN26Nex2O3rv2AHvoUOBfX4P+VZaAPgD5P4CwF0AeiHC+11WBnz8cZQzbGj1bb8qcF68eDFuvfXWwO9VAOZDPsTLIR9QPIAJABaZ9ssEsATAEIhAKId8BIMBbAZwAYB1ANqp7cvdbrRv1Qp+vx+xsbGIiYmBYRg4evQoXnvtNTRq1AilpaU4cuQIysvLYbfbERcXh4yMDMTHxyM2NhZxcXHwegUybTYbvvzySwwfPhxutxuPPvooUlNT8d1338HtdiM5ORl+vx/ffvstvF4vHA4HysvLsX//fuzcuTOgKOi/gHz0paWluDchAXtiYnDbyZNwVldHBc0qABUQYFoIEUxmUD+ulq9T9+e3AM6z2K5cLTOiPi3rVg0BgxIALQFcCXkurSCCpBLA5xABnQtgvNrvAQDPA9iqxh0AIB/A5HqOfxLAKIjCURhhm/4AOgL4sA7HawPUELr/AtAE8m6uhLx/CyBgotsuCHAfBZAC4M4oYyQBeMz0e446fl3B+WeLZa9CQPJNCDBafQfmNhwCmATwHUSJA+Raz4coSneoZakAZgDIUL+Pqr/vA+gGeQa9IM/gPgAfm7b9EcAlAG6EPAfdGPa/fvduhihBurkg8gCIrkBWQN7jLyDvnFnZvxDAbADPQN7NhZDnXAh5f1eoc/QB2ARgOYDjJEqPHAnIgbS0NHg8Hhw5cgSHDx9G2jffYPvJk5bnshPynf0FooxatQKIcnC/zYacnBwcOnQI33//PY4dOwYeORLY7g7It+QC8A/Is9mifi+HPOeIzQTwDe30268KnBcsWIAFCxYAmzYBffoAx48H1n1Uy77XqP4/AN4FMFQt7wSgC0RYtYMA1MYTJ/DFF18ENNOvvvoKO3bsQHJyMuLi4lBUVIRzzz0XLVu2hM1mw4UXXoi1a9fCbrfj559/xqFDhwJ/nU4nHnnkETRv3hwHDx7EwYMHQRIrVqwAABw7dgwejweJiYkAgN27d8Pn8+Grr77Chg0bEBMTg+rqalRUVIAk3G434uLicPToURw4cADdu3dHwYwZ2JuUhI8vvxyDIQLEw6A4Ow4RZp9DPtw2sBZcGoCHQQSUturCW4z6q0eoD0h3hFhoSRAgeApAGkTRWgN5NmkA3BBheR3EG7IOwEwA7wH4M0Sg3YD6gXM1gDEQQfXXKNtlQEBrJoAHTAqRVbOySvcC+AQCxt9CQGkIgOYQIVsFAddXAOyGWKI+yPUCAhwnIPfZgCidPtVfgSgqQyHAWJf2EWo+xy0QgOyofod/B+GtUo25MWx5R4iStUZd41p13mbrbA5E0dOerDshAD8eYmGbIasTgD9BwMqqVeLMCL2PAfRzOHDY5BXTyv4CCDBPATAacl/+Ydr3OYh1WgHxKPw2Lg6ftWsHp9OJzz//HHv37sXu3bsBiBJtGAZ+rK62PI+vIUrILZB3M1qrBLCrvBx73n8/ZPlPpv+7mP4fB/FevAR5n+cBSIw2gN8fbW1Dq2/7b/rU/6utlpw+M2GBObr4TYRSU2rKSZ1CUgYw3RTspRm+hg8fzlWrVnHo0KH87W9/y6uuuoo9e/YMzCd36dKF48aN42233cbnn3+e27ZtY0VFBa+++mpmZGRw2bJlgVNPT0+nw+Gg3W7n8OHDuWvXLm7dupUAeNVVV7FLly40DIMtW7YMYQnT+dEpKSmh856KLMXlcrFpQgJvjonhY3Y730xI4CMAb7DZuCwn54wVqA/v1UANKtFSWOdFvwoJELsQMtc6GTK/OAoyr3eFuiZdtlLvlwAJYloPmZOcBElrqc85jofMg0YqaBHe60L6YTWf+yd1jeYI86GQSNzw/edDguSscox3q32fhASOeSAlQFejfkFrKZA5z/p8B9Vq20/VMY5D5o6tAsGiVSbbpM55BoJzpwMRNt9p6k1gHaWt0/m2hi2vb+S77j/a7dyQm8vvZ8xg5UsvsdrjOaV3/xgkWt9ms9Hr9TImJoYAAqyAsbGxtNvtlpkOeyHxA0sjHHsFgjEUn0Lm83WcSExMDJs0acILLriAL/frx3K73fIYgyBc5okQRjydYqnfi8f0tg1zzme8/XrBmYxalWo+rAUhEUpNqSknCakks6t9e7Zs2ZKFhYVs3759IGhLd5vNJiQgK1fyrbfeYnZ2Nr/++mu+8847XLFiBWfOnMkhQ4YwPz8/EEzWvXt3+nw+PvTQQ1y7di2dTmeAtKS8vDxwOQCYnp5Ol8vFpUuX0ufzBYLK4uLiWFhYSMMwuGHDBk6ZMiUQfJabmxuIJr/uuus4depUajAHwCuKi3lc5VhmKCFZgGDgyKfqo/ep3k8t+wKhVa1ehwBoIkSQD1MChhDB/QKCkd6/U4IzXCBVqHvfC8LuNRYS3DRd3V9Ny6nzs3ValA2hudOL1XbmqN3jiBzFezUk2OYoBAwLIQFM+ZCo/kg5p7UFzlkF+mgFJByc/wzrc1uJID95bT1aupdVARWrXtt3QARJRcy9CWqC4XrUrGCWAQH9KghH95thxzTfl9r6SYTWrX4xbP01kHfDKiPBC4vAp7B+HEoJcblqFC+prWvlTadRejweOp3OAOd+fHw8fT5fSBS3+RksQPBdN3d9/PEQQPWqe/87gG2zs9moUSNeddVVnD59Ort06cJWKSmssNt5COA/EfzWVql9t0FA3pxiCcg7H1BUG6K1z3j7dYMzKcnzw4fLy3WK2q/u1R4PuWkTq6uruW7dOg4cOJAZGRmcOnUqBw8eHKgiZe6pqalcsGABDx48GHJa77zzDtPS0rh27Vo++eSTzMnJYbdu3RgfH09tkfv9fvbq1Yt//etf+cADDxCQPMYVK1YwLi4uYDXn5eWxadOmdDqdbNWqFTt37hxC+QmAGTYbv7z6ar7RqBFfcbu5EuBcl4spAF9yu1kFoTfVdJafQzToDyFpSLshwFYJ0bSLUbOq1fcIcpafADgbwjJVG2iYBdIqiHUVXhzhdxBA+yRsuQ+SipOA0HSimyGW2km1j079Woua0eRfqWPFQADfUH8fhSgXexE557S267KySrUCslD9fgcCgFq5CLeIWqFuxCwaEMKVhUgVrVJN25xOZL+5h4OzVQWz36rlh9S91taatvbTIQpRbWNVQCKYzV6CTxGqgOVBACwcnDdAIrlrA2fdKyHv9AnUnZTnujAufKfTSa/Xy9jYWEul/jnDqFemg7lXGQZfT0qi1+tlSkoKnU4nExMTmZiYyIkTJ/L77t25H5HJV8J7yH1pyHM+K60BnHX74Qdxy4wZQxYVkRHcPJH6CYeDi7Kz+e2334Yc9uOPP+bEiRPp8/l41VVX8Z577gkUtggX1MnJyRw/fjxfe+01ZmZmct26dYHjrF69mk2aNKHT6aTH42G7du147733Mi4ujj169Agcw0w+cs4559DlcgVypzMzM9m6deuAe9vpdHKAz8dnIRpwuLtWk4hYWZPbIBbOk2HLT0Jyxp2IXtXqBGTKoKVpmVWO8BhYux21kB+KIOGDE2JNFEAAsy8EnHU5yAdM+4+DeACIYOpbXUCoG8QNW9v7YM45rU/u83y1zyeQsos6vehZ07HDLaJZqFly0qqHu9nrW9GqLkU8IlGMboWwzMWo59RHLTO7xzerbQABh7sQaq1tVOv2ouY0SF2u9QUE3+WT6rkXQhTJSxG0yI9BXOlpat9PUPe8aDMNa6R7+qxhsItJMdZdV5QzA3JcXByTk5Ol/rvTydJaas9H6ifsdv4mPp69evXixIkTef755zMhIYEdO3bk0KFDOap5c0vGwDr1Boaws9IawDlSi+LyNvdKgJUxMay+914uWrSI+fn5IXWdddu/fz8XLFjAtLQ02u12ZmVlcdGiRezXr18AqM1uRYfDwb59+/Lpp59mVVUVt2/fTkC4s1evXs34+HhWVlayqKiIADhlypQAKLvdbv7+97/nzJkzLXMnfT4fAfD23FyeqAMRiblfg+D8ZnuE1rJNRJCnOhnWVa2+VtsZEHf0Q2HCy5wjbEW8EB4LkANx6Wprs5M6hrY271DH+hNEEO+FWO+ZEBAnxJVuvj+RQKgSAiy3qbGyIRWSrOagzTmnteU+n45Vqr0Vtb2j4WB1qhWtattPk8dcHfbcbrS47jQEAT0X8k6kQohDrIrL7Ebtbu1o11pl2u4mi/OZr9ZZVVHbXY9ncgwytWMm5XkU4E0OB1Mh3i2PxxP4Np1OJx0OB+Pi4hgbG0u3280WLVqwc+fObNu2LVNTU+n3+9mjRw9eYxhSrrae5zMrLo4TJkzg6tWrefjwYZJkWVkZX3rpJU6ePJnZ2dm8OTmZZTZb/YG5gVv7rLQGcI7Worm8Vem0H3r2ZH+fj08++SRJ8t5772VWVha3bNlieciysjImJyfT7XazdevWfPDBB/nzzz/zH//4RyCQS4Oz2RLWLurs7GySZE5ODtu2bUu73c64uDi2bduWANioUSOWlZUFxvP7/QEBo+eqvV5vvUsZ9kYorZ8PUqTABWEMyoFYcn3VWA61nROh86G65GKc6tPCxjFbsVbzsfMtBGehWvcJZE7bBiGceAISOAaIi3Q2ZE7YD3E597IYM5pA1wVRSiBz1m0hgFIcdg1b1Rhm16vVGHVRCGoTuktQN/rUkjMwlga82op4VKAmo5i5a++Kx7SsLsVlKiHK1Zm41kiV1xZC3nNt+Wv37W71v3lud6HpeAchxCnJqvc21WLXLmRddc4wDNrtdjqdTubl5bFHjx5s1qwZc3NzWVBQQK/Xy06dOnHy5Ml84IEHuHnzZm7YsIEej4c+n4935OXVuSpVldvNqr/+lR9++CFvv/129u/fn3FxcezevTvnzZvHt99+m+Xl5ayurubmzZu5dsgQHq+L+7yhKtVZbw3gXJdmdnkPHSp/ly4NBEBs2bKFWVlZ/Otf/0qSfPLJJ5mamsq33367xqGOHDlCj8fDm2++ma+88goHDRrE9PR0LliwgAsXLmRxcTH//Oc/s6ioKFCJJlyQ6488JiaGGzZsoNfrpXaLLVmyJDDWc889F1LjOTk5mRdffDE7KmEWKcCLkKCkFgiWvOsStv4ZSNRsewgQvwWxonshONe7HzUt55sg89A/qX1sCI3O1exDgHUks1nAzwPYGKHzta8BHKz2t6vzOMe0X6Xa9j6IUnEQwWCy8F6CUKv4J7X8YQQtxIGQgCa9zQ6I0vJo2PmGW+fRAPpULOG60qearfTdAM9T9ygd4gXQVulr6tnGQ+Zll6PmfHWkMZ+M8ty0d8WAVGzSy3+D0OIyQyFelnAFoaQe12qg5pRKKWS6xY4gLap+Rw+pY3ggMQVtUROcI1nt10BiLA5DKEd/g9AI+sTERBYVFfH888+n2+3msmXLuHTpUo4ePZrFxcV0Op2Mj4/npZdeygULFvCPf/wjb731Vo4ZM4YtWrQIfN+jR4/m8uXL+dHf/873s7NZbrOxLMySPmG3s9LpZPnQoZbu5uPHj3P9+vW88cYbWVJSwoSEBA4ZMoR33XUXP/74Y1Zv3MjSQYN40uHgiTBLuhTgCcPgjjZt+N3atWdJ4DY0sgGcz1j78ssv2axZM95yyy2srq7mK6+8wpSUFK5ZsyZku3nz5rFdu3acNWtWYNmnn37KIUOG0DAMXnLJJfzkk09Iku+9916gZrP+OK3mqg3DYFJSEp1OJxcvXsyvv/6aF1xwAZs2bRoIQjMMg40bN2arVq34DBA1wOtHJbieggDZLCWkw2n9JkLcw3mmZdeZzisZNataZSGYbrNHbXehaf8KBAEgWoGE+agJbvMhHMZeJRjTlYA1V9R6yGK/SDzTqRbCuBEEDPTvixAE568gc8D3WZxvbZazWSGoryVcn26mTz1P3dsyyJxuESSYr0I9//shbvON6jluRt0Ke9RW2OIYwHsQqpQVIFhcpgzgVNSsVlafWtQul4vnoiZn+SjI++CBuNWTEHxHkyCKZipCgw5TIJHy0cB5kLom/ftPAAtUuuOIESO4ePFizpkzh+PHjw/wZWdkZLBfv36cOnUq586dy7S0NN5zzz2cMWMG+/Xrx5SUFCYlJQU4+a+88krOnj2bl19+OZs0aRJ4RxclJvLdpk35bceO/KpXL77Ypw9/2717IENj/PjxXL58Obdu3crKysoasuvAgQN86qmnOGnSJObn5zMjI4OjR4/mE8uW8dDcuay49FJ+W1LCd/LzOc/rZYny2iUmJrKkpIRLlizhtm3bzq6A/RW2BnA+g+37779nhw4dOGnSJFZWVvJf//oX09PT+cgjj5Ak9+3bx6SkJC5fvpxDhgwJ7Ldr1y6mp6fzueee46JFi5iRkcGePXsyLS2NQ4YMYUpKCq+88kp27drVEpjNQWAej4dut5s9e/YMpEdpcL/nnns45txzLedIzQFeyyEWjFkw6oIQSWrdHRAQzFKC9d9K6OugHUMJOAfEOi6C5KoCMsfoRdCC0kLwQ4jSoAEgmuWsyz4eCVveGuDzpt+H1LF+tDhGJSQ4J5KAn4WagUe3QKzP/RBLujHEbR8t57Qc9ePbro8lXJ8eXomsEKGpRbMg+d+66IRZOegI4cCOFtymFcFoz033Ksi7pKPO2yBYXIYQ3npAPBv1BWZ9reFTIpqX/TtYV15LgqQSfQdJyStSx3oforwCketNr4UoOz+p/huAc5o0YUJCAt1uN7t27crMzEx6vV7m5+fT7/dz2rRpnD17Nq+//npefvnlNAyD8fHxzMjIYN++fXnNNdcwLy+PTqeTI0eO5KBBg5iUlERA3OUul4sTJkzgtddey5EjR7JNmzaBYNGJEyfy7rvv5sqVK7ls2TKOGzeOzZs3Z3x8PPv27cs5c+Zw7dq1/MEi/enLL7/k8uXLOWLECCYnJ7OwsJBTp07l6tWrefDgQb7zzju84YYbWFhYyOTkZLZq1YpJSUksLCzkzTffzH//+9+srq7+xeTu/6vNIEk0tDPWjhw5guHDhyMhIQGPP/44du/ejXPPPRfTp0/Htm3bkJiYiIkTJ2Lo0KHYuXMnSktL0b17d1x55ZWYOnUqAODTTz9Fr1694HQ68cMPPyA9PR2tW7fGG2+8gSVLlmDRokUoLRV25UaNGuHo0aMgiSMmGj7DMGCz2VBVVQWbzQbDMNC2bVsM2LIFC0i41WO/FkKlWAagPYC3AcyFsBfdZ7quJgA8EGamCtUXQqgIXRAGqb0QZq4jEBanryE0nsfUdsMhbE4eCPVkHwhr1HQI89BOCKNVGYDGEMYjO4R3egWE2UmzO02CsGA9Gnb/J6jx/w5hLPsjgHsA7LN4VqUAeiMyJeGjqMm6dBLCJ/64utbGEFrGZhBmqHBu6WMQZqZMhHKO/zfaLAC3Isjkdj+EMe1+AIcAnAuhrb0QQmd7DoRBbSOEoWszhCr0NbV9JE71WQjyhT8c4VwqIVS570HeuzEQDu2/q/UH1ViPQLjBo9JGRrjW8HN4FPI+9EcoLerHkHfvnxA2rM4QWs+XAPwHwkudAWAbhP3sIIR57iiAl9Wxv4Vwgr+ufvcD8Gz//kh5+20sXLgQa9aswVtvvYXjx4/j888/x5AhQzB8+HAcPnwY27dvx44dO1BRUYG2bduiZcuW8Hg8eO211/DNN9/A6/Xi2LFjAICcnBx07doV+/btQ1lZGUpKSrB9+3Zs3boVTqcTxcXFSE9Ph8PhwJEjR7Br1y7s2LEDBQUFKCkpQWFhYUCubN68GRs3bkRqaiq6du2Krl27olu3biguLg5w+1dXV2PLli1Yv349Xn31VXzwwQcoLi5G//79MWDAACQlJeHll1/GmjVrsGnTJmRlZeHnn3+G1+vFiBEjMHz4cHTt2hU2mxVXYEOL1hrA+Sy08vJyjB07Fvv378fq1atx+PBh9OnTB/v378eePXsQHx+P+Ph4HDp0COPGjUNsbCz+/ve/wzAMbNu2Df3798e8efPw2GOP4f3334fNZkN5eTn69++Pt956C1VVVXA6nYiNjcVNN92Eu+++G3v27AmM73Q6kVRZibEkihEUont9PjT9+WdcEna+VRCKyDchnMSTIfzGt5u2OQfAVQhyVQ+C0C0ugoBcJaSwwcMQofsmhDZyLkTwtVDb7YUIzHUQofs5BGS7AXgLAr7HIQI0lGQwSI14AiIsn4EIQXM7CClQsh6iQBRB6Bw7h21XCqHXXI7IbQ2EWzha09zMD0fZ5lsA2ahZBCRSsZCz1cKVjc8h9JJbIe/AOAAPQRSktRDe8v+Pve8Oj6Ja///MbN9kUzbZTYMUQoBAKIEkkoQmTZo0AUUsKFzEggXEgnixgNhAv1dFsVzBXhEURTGIiBRFBUSEgJAAgUASSCBlk2x2398f78xkdrObArbrL+/znCfZqefMnDmft7+npWOfB79/gBkUneo6cnrXdeAc9EfA8+Qk6pmqjWCw7QZ+9vMBfADOEW4Eg9pl0nFdwOD6EhoWpWjJWHPh+W4eAc/HBeCUoHJa1B3gFKJXSWNZCf4OXkd9Dm1vOgkG97NgRjMbQHcw+JPU/50AdggCunTpgqKiIrRr1w5XXXUVEhIS8Nlnn8HpdGL5cp6BbrcbEyZMQGJiIux2u8c3LYoi4uLi0LFjRwQHB0MQBKxbtw4RERE4efIkjEYjOnfujPj4eJhMJjidThQXFyM3NxdHjhxBUlISYmJiYDabUVVVhWPHjuHQoUNo3749evbsiZiYGLjdbhQWFuKHH35Afn4+evbsiczMTAW0o6KiAAAOhwNbt25FTk4OvvzySxw4cAB9+/bF4MGDkZGRgby8PHzyySdYt24dgoKC4HQ64XK5MHHiRFx22WXo37+/Avyt1Di1gvMfRC6XC7fddhu+/fZbrFu3DlOnTsW+fftwySWX4IUXXkBKSgqGDh2K7du3Y9OmTTAajfjll18wdOhQPPLII9Dr9Zg2bRpcLhdiYmKQkpKCtWvXAgAGDRqEwMBAbNu2DbW1tUhJScEvv/yCs2fPohcR5gEYLghwEzUoTGGA/4T+M8G5sw+BF+Blqn1d4Vl8YbjUloGlqPHghfTfYElyj3TOCnChiOUAbgBXRXobDNgp4EpEz0n/TwFXwwF4cb0WDMBjGulzS0kuUNAUMMt9aCpfcXPAuQT8PHqDF27vdyID22I0XSzDYDCgpsYXXDRNambDDS4McgMYSCoAXA9moq4HF7P4CFwg5CBYw/E0GMz8kQuc43mx1/YFYMC9H/ysTOAc2I/CM4f28+CqY1UAEtFyaVlNH4Nzh6vfzXhw8RMd6hnJS8GMYAAYvI+BJe4AAG3AjMRMMGAfATMYN4Gl5EgwgxUMrn61BQzQAPCTTodMpxMxCQm4++67IQgC7rzzTlx88cWoqanBwYMHcfjwYdjtdrRr1w5xcXH49ddfcerUKZRKBSTatWuHHTt2QBRFHDx4ELm5ucjNzcVPP/2EtWvXwmg0wmw2Iz4+HlarFTqdDtXV1SgpKcGhQ4dgMpnQqVMn2O12GAwGVFVV4eTJk/j1119hNpsRFxeHoKAg1NXV4eTJkzh8+DASExPRtWtXhIaGora2FseOHcMPP/wAi8XiIV336NEDBoMBp0+fxsaNGxWwrqysxODBgzFgwACYzWZs374dq1atgsPhgE6nQ1VVFcaOHYsJEyZgyJAhSpW9VmpIreD8BxIRYdGiRXjuueeg1Wqxc+dOTJ48GUFBQSgoKMDBgwexZ88exMTEYPfu3Rg2bBiWLFmC4cOHIyoqCjU1NRg4cCAOHTqEgoICWCwWvPPOO1i/fj2eeeYZOJ1OBAYGIioqCmVlZZh4+jSWAE1Wl/JH08GLklzybou0/Ti4gtP30r53wVLUdrD0uxJcZYfASfRF8EI8GsBAsKSsla43AcBR8CJ5CrxIJ4AlrY1giQ3gxXUMuDDC1/BfirC5JIPgZ2DwaM7C/wF4QfdVmKNOag+CAcBb7a4m+QNrrMBHS5iG8yU1s1ECluRlcAH4ncwHM2GLwJKfTLeDx9tYwQ+ZKsHz4lac33trytzQHPIlOT8ABv9pYGl4BRic48FzeiN4Lt4OVnEHgZnVnmApOQ08t4eCgdsonQNw+dQUAI9Lv2eLIr7v0gW5hw/j0ksvxdtvv43PP/8c//rXv7Br1y6EhYVhxIgRSEpKQkFBAdavXw+TyYSKigo4pepTgiAgKioK8fFDkFZtAAAgAElEQVTxSEhIUNrOnTtx9OhRvPvuuygqKlJAW92OHz+OmJgY2O12GI1G1NXVobS0FEeOHIHBYEBSUhKsVitEUUR5eTmOHTuGwsJCxMbGIiwsDESE06dP4+jRo2jXrh3at2+PgIAAVFVV4fDhwzh06BC6d+/uAdht2rRBXl4eNmzYgJycHGzYsAE2mw2DBg1CUlISSkpKsHbtWuTm5sJisaC8vBxDhw7F5MmTMWLECFgslgt44/88agXnP5jcbjfatWuHs2fPIicnBykpKbhm2DDEff01xrZrh6zOnXHa5cJzmzej+9NPY/T11yMuLg7Hjh3DJZdcgg0bNiAkJAQmkwlr167FmjVr8NRTTykfKRHBbDbj2ZQUTPr++2YvhkVgVeIosCSTAwaitwBkgW2o/wVLSnNRr+7UgCXjJHAVHjUJYPthCbh0X510rSAwwJ8Cq3HvBAOfCQxKT4Bt051Qr0qXJWeApbslaNlCXwdmFNzgxX6fdN/GauKqKQ1cwelO8LM5AwZ4PfgZ1MKzGhLA9ucKaf8AMEBFtaDPQPPU7edLdwsCHiKCXvrdDmy7lyXn68BS/UNgCfBjMOgcBtuj70a9arspcgP4FMycteS9tWT8oijCLVVrUpsMLGAzwgdgk4LMOBFYfR0D9qG4AWyemQiei7Ol+z7hdZ8FYI3CPPB3A/C7/hr1pSrzwMzIVuk+cQDix45FmzZt8M4772DGjBlYuHAh5s6di927dyM7OxvLly9HWVkZ5s2bhylTpmDz5s247rrrYLVa8e233yIxMVGpUJWfn4+8vDzk5eVh7dq1EAQBDocDbdu2RUJCQgMAj4qKwrlz53DgwIEGwO12uxEdHY3AwEAQEcrLy3H8+HEYDAbExsYiKCgIRIQzZ84gPz8fAQEBsNvtih37+PHjaNu2LeLi4mAwGFBWVob9+/fDYDAoQN27d2+kpqYiNzcXOTk5yMnJwbZt29C1a1dcdNFF0Ol02LVrFzZv3oyAgABUVFQgKysLV199NUaPHo2wsLBmzph/LrWC8x9Mb7/9NpYuXYq7774by6dPx8pOnRD2/fcNyjLW6fXQCAK+EEXc73CgOC4OR44cQbdu3UBE+Pe//4377rsPBoNB+WB0Oh2OHz+OK5OS8EJuLgLAoLAd9RJcDBiQCsGL0Q/S/z+AF6Pd4IU0Dry4yItvDrjk3RFwGbkVYAnDH/lS774MLrNZB1783oenWnQLWAp5Eiyp7QKrDavA6nF1jWIZoI1oXMXtBjMJtagvTQm0XH38IVjduRQs1X8CBtvfwKr9JeDncRP4ee8BMxp9pX3PgYFBlO4J8DsxgBmUbdKY1P12SP3qhAuXHH3RELAD0xGp35vBEqQIVsteDAY0M+prd2vB4GoAMyhXwrcK/0GwZPol+LnJM/t7sETZ1Hs7H82BIAjobzZjVmWlR93wB6T+qEn2V9gLZjROgktwLgLwLfjZDwBLzaVSX+Rz1ERgSfoG+C836hBFDNHpsM3phMlkQkZGBoqLi2G1WlFdXY2ffvoJ2dnZeOSRRzBhwgR89c47ML33Hr578UWYnE5079cPsSNHAtddB9hsHtc+e/Ys2rZtixMnTkCr1eLIkSMKaKsBPC8vDw6HwwO04+PjER8fj9DQUNTU1ODEiRMeoJ2fnw+r1YqQkBBoNBpFDa7VatGmTRuYzWY4nU4UFRWhtLQUkZGRMJlMcDgcKCwsREREBGJiYiCKIoqLi3Hs2DF06dJFAezU1FQcP35ckaxzc3ORlZWFmJgYFBcX45tvvoHb7UZNTQ26du2Ka6+9FuPHj0dMTEwzZ8Q/i1rB+Q+kmpoadOrUCa+++ioG7NsH1x13ADU1zVqk7tFq8UufPqipqUFcXBy++uoraLVaVFdXw2QyYcaMGdiyZQvWr1+PLwICMKiyUpHYrgKrqNV0Cgw4qWBpNg+Ng21LyRucc8BSeXuwNJELVnOvQ3293xngYvX7pOO7StsdAGLBErigqofcC1wHdwQa2m5rwbZEgu8a0jI1BwRsYABTW8NWSdedBpbO4sG280KwU1C41OaAgXwFGGBHgIGgszSuFX7uuQLsXPcbGKhXg00AvigmJgaVlZUoKyvzP1Af9CG41vYocM3rF8Bq7SFgpuxWMANzEPzeZJLH/oWfMRySrnsarPEYrNpHYBVxFXy/t/MxN8h0s0aDx1yuJoHfm7zn6gYAl4M1SUlggH4JwJtg27SaFoDfzffwZP5kqgPwK4BDAQH4mQjPVlUpzn6CICgq5dzcXNyWlYURu3cjs6wMbiKP+UYmEwQiYPhw4N57gfR0AMA777yD119/HZ9++mmT4ywvL28A2OrfGo3GA7xjY2NhMBhQV1eHs2fPIi8vD7m5udi3bx8cDgfCwsKg1+tRW1uLkpISaDQaRW1eVVWFwsJCmM1mBAcHw+l0oqSkBCEhIYiMjITb7caJEycgCAKysrLQu3dvdO7cGefOncOWLVuQk5OD8vJypKamQhAE7NmzByUlJSAixMfH45prrsEVV1yBxMTEJsfdYioqAlasAH7+GTh7FggOBrp188kc/ZnUCs5/IC1duhQbN27EJyNGAHfeCVRVNftchyjiqZgYLK2qgtVqRUFBAXQ6HaZNm4Zdu3bhxx9/hE6ng/bMGeSpPuwB8A3OMtWBQex8wZng23bqveDdB3awkUk+5wppe4JqnxGsMrwfDEwfwT8wAQyCaq9nO5jp8LVY+qPG1KfeIUcynQJrIi4FS7gR8JTAu4C9zt8Cj/EdsNr0N/Czbsxx7GLwu1sg/VYzKL5Iq9Wirq7Oz96GpGY4ksHS/Qhp31xw+Nly+AZnmfTg+QPUS8aXgtX7VvC4ZdKAGaEfwJLmNWCQ9uWtvrKRcfqj8zF1yORLy/Mc2OHtLIA7wOaVtWBNiEzPSvfcDLY5q8mXX4G3tiY/PByhoaEQRRF3mEy4etcuGNE0M1kriliZkoKfLroIW7ZsQdeuXTFmzBjY7XbYbDbY7XaEh4dDq/Xl8eCbZLW1L4k7Ly8PR44cQVBQkCJxR0VFwWAwwOVyoby8HKdOncK+ffuQl5cHs9mMgIAA1NXVoaysDIIgKA5qZWVlqKqqQkhICERRRGlpKQICAmC1WuF0OnHq1Cm0b98effv2RWJiIhwOB/bs2YOvvvoKQUFBiI6ORmFhIY4dOwZBEGC323H55Zdj6tSp6NKlCwShMU+OJmjHDmDxYmCdpNuqrq7fZ5KSy3oxR38mtYLzH0SlpaXo0KEDvnv2WbS7/voWAbNMVYKAwVotdmo0GD9+PPbt24e9e/eCiGCz2XD27FnMNxhw25kzHuC8F7xYdASr7Qaornkh4OwAx3omg0HUjHrHqPnwjEfeApamvgCHMa0CA+4zYNV2AnhB/whAP9U9CCzJbWhmnwSwqlW2f78J/+riXqrtcphVPgDSamE2m5U4cX/xzcPBqt1EsBQ6Ayx9Agw2Z6X+3AQGqjXSOJ5CvZp9MVjVr6YjYPvvb6hnWnyp9ltCanss4MlwNBbfLIDt5G6whmUp6ufJXWA7/Gqw171dOq4f2ERyDdiUMUS65o9gJghgFb83oJ0veTsJHgRrXSaA58Ej8GQMXWD1fRGYsWvKw/4AmNkrABAqbfsv+H18A35XMjXX2a8G9TbtO0wmLHQ4GjB/jVGNVov3MjIwbccOjBgxAm63G2fPnkVJSQlKSkpw+vRpBAcHewC291/1/1arFRqNf32D2+3GqVOn/Erdx48fh91uR3x8PGw2G0wmE4gIFRUVKCwsxOHDh1FRUQGLxaJsB6DYuc+dOweDwQC9Xo+KigoYjUZYLBZUVVXB7XYjPT0dHTp0gNPpxKFDh7Bjxw5ERUXB5XKhoKAAAGCxWDB69GjMnDkTGRkZLQPq559ngckh1XPzR4LAQP3kk8CN3l/uH0ut4PwH0dy5c3H27Fm8WFICWr2aVVRgaepBsMdyJHiB6AtexG+Wtss23jYAvgkNxdVmM06cOAGj0QgiwogRI5CamgoASF26FCOl0AuAw0c6g6Wcd8B2411gQAHOD5zVquAXBQFhRIoEtE66j5pkW92zYGnkFOrB62UwWCeApSuj6ry+YECbh+aD0lDwc1zpZ/8K1KuL1Z/uIrAklyuKSB08GLt27UJREbv7eMc3u8EMwDmwo9QX0pjGwDPcrIvUNkjjvhqs4gwBP4tdYA/opfBUlz4snfO1V9/VTnEXSmqGo7H45m/AIV9VYBD7Wuq3Fp6gthL8jo+Dx3oTeD69DFZrp4Ht8HLQl+yM1VyHvMbIO7xuKJgJOAVmos6AJf9HwAzVA+A56gSbGCLA4PumNK468PzoAg6lugbMmMgA/yZ47m+UxlAHZlK7iCIEFQPUFFUCeF6jwY0uFwLgey04Cv/MZWdRxDCjEaWJiThz5gzOnDkDl8sFq9UKq9UKi8UCs9kMg8GgSNFutxu1tbWorq5GZWUlzp07hzNnzuDs2bMICwvzCdy+tsmSr0x1dXUoKCjwqzYvLi5GdHQ07HY7zGYzBEHA2bNncerUKRQVFUGj0ShmOgDQ6/Woq6uDy+VSVOc6nQ4GgwGVlZWIiopChw4doNfrceTIERw+fBihoaEoKytDbW0tjEYjBg0ahJtvvhkDBw5sXIsgA3NLBCaz+U8H6FZw/gMoPz8fvXr1wq9ffw17ejoEKS71S7C6+V0wQBVKxxvA4PkyGBTuB6vOtoM/zARRRHT37oqKZ//+/ejcuTN69+6Nf338MbodPeq3L3KykFnSb3/gLHP3/uyBS/V6bK2thSAISvYxb7Xqp6hXlcrkKwNZCRico6XrDwF7yIZL58igFBQUhKqqKhARXC6Xx3U1Gg2sLheuQ+OZqLzVxZDGPgIMktMBaIxGnJCSJcj3l4GMwHG/+dJzWAR2DBsHXtDlcLNKsDRpBYP4YbBkKZMMbJ3ASS8+VO1LAjMk13n1XQ4n8ya1Hb65JDMcjcU3P+51jgvsab8dLJmqwXkgeJy7wSDcCfXgnAR+v93AwA7wc1wL9ju4kLF4+wO8A9bKtJeu/zHYHPAZmAH6GUAfcDavq+CZ9Q7geXE7WPo/BPb0vg4cciWDf4I0bhH8/bil+x2U9jelrXkAPG/UZpdl4O/cey3wdn1agXrmkgAc6NIFnX75RdnvcDhQWlqqgLXcfG1Tt8rKSgQHB8NiscBkMimALggC3G43nE6nB6A7HA5YrVZEREQgIiKiSQndYDDg6NGjftXmFRUVsNlssFgscLvdKC8vV1TgOp1OWVvUWQ7dbje0Wq3yf0xMDCwWCwoLC1FZWal4sGu1WmRmZuLGG2/EuHHjYDConvyOHcCAAeelyYTZDGzaBKSltfzc86DmGylaqdk0f/58zJo1C+Gffopap1P5KBeAVWO9pd/yh/gimGufKP1+AAxU+8ELzUyTCbvj4pCZmYnMzExYLBa89dZbWLFiBbLOnPFI5OBNAupVb43RF4GB+M7tRp+gIIjnzqHQ4cDhwEB8k5CAnQUF6NmzJ5CTo4Q9EFGDhdXl47rLwKpsOQOZQRrbDnimQpyC+lSIIdJfdTpSb3K5XE1KlUfAzMB/vbbPAktF8gI/qbraQ1L/GcyYmMEqaNlhzQRepKvA76gHGGTlcDOAnaoeBEuUanCWyft9bAGrfH3Z2P25e50PPy1f6wxYOrwF/C4MYDCaj4bg7Ku/AEt3m1DvgT1A2l4MjnfvKG1/xus6nX1cX6PRtMh2fq2qP+fA39MGAK+g3lEPYKe3BLCauxjscb9ManLGtt9Qr1H6uZF75kl/V4HNE2+hXt0N8Nydovq9AgyoPVXbLpf6IvtsZMH3WuBNK8GSvCC1DgcPAsXFiqOSyWSCyWRCdHR0IyNoSE6nE2VlZU2CuAz0p0+fxunTp7Fv3z4cPnxYkdB1Op0HoNfU1KCyshJ1dXUICQlBWFgYIiIiEBUVhZiYGKSmpiqg7HQ6UVVVhdLSUhQWFiI/Px+HDh1SnNVklbjD4VDSFatjwPPz85X/AU7QY7Vace7cOWzbtg2bN2+GIGVomz59OqZNm4aAxYtZlQ3+rm8Gm19sYAFhHPgdXwlmro6ANSYDAD5v8WLgQzVr/cdRKzj/zvTjjz/iq6++wgsvvIBdGRnoJam9ZOeY0WCuuxpsk30CbCPurrpGAHjR2AuWSKZlZGD9qFHIycnBk08+idLSUhARYmNjUWwwoKqgAGbwAvwd2EtYC+bKvwGrHSHdUwbQGum3EQw2X1VUMECpOcrycvZgBJCTkwMAiu0IaAgS/sBEA5Ze3gBLLreC1Z4AqxifBds5z4EltTLUx62miiKCiXCGqEGqy25oXE36GlhVrnY++wgs/YwDMwsCgB6C4GF3WgmO9T2AeocxC+qByib1916wg1sdGORqwNKQC5zOUU5zGQi2bxvANtuFqv6sBIdmeadfqELjgNEUyYyT/FdmOMLBz+N5MLOxQrpPHHi+OcFS8mmwetoBfoZdpb8u6ZnIzmEm8Ht4DDy37wI7VF0HT2cqgOe1VqtFREQESktLUV1d3eKcy91Qr925H+w939bHcafA728XWJJXL3Tym/4F9eDcHBoGYLHBgOSaGpxq5Dg1oHqTgMbXArXHti/mUtBo2LN47lxcCOl0OthsNtha6I0sS7n+QFz+v7i4GEVFRSgpKcEvv/yCrVu3AgCMRqOH9FtXV6eoti0WC0JCQtCpUyeEhoYiMDAQer0eRITKykqcOnUKhYWFKCoqUjR4TqdT8a2orq5WrqU8L8nz+7bbbsPC227DUfCaVwfWSs0EazQ3gTVLO8EMXh+wRmWi+mJEwGefeTBHfyS1gvPvSESEuXPnYsGCBVizZg0ijxxR9sn2sA/AKmsdeHIsBKsWvV91MFgVBwC7Nm7E9I2ci0ij0SjSRl5eHhbCM+fxfLDELScLWQ2WZADPD7+T3GcAGkHAm6IIqFTHoiiCuGpZg3EmJCSgW7duWLNmDUaOHIlx48ZhxowZ2ON2K4Dvi+rAqkNvkhcxAi9UqeCFiQCYVTa9KjBoyt6vIWicXgOri2WqBIPHZ17HBXmNsVi6x2CwtmMq2Cb7kGq/CQy2s8Dq1HzwxzQE7On7Njh+9jSYQ5czSQEseUIa63vwVHHLJMC/Hb05JL83+a/McAAsAd4O1l5owItROniO3gjWDrjAQL4VbK54GPUqfEjn/Qa2lf5L2k/g56UBmwy8qRJQnIDat2+P/fv3e5grvJ3YZJIlIyJS3vkusDZjZ4Oj+TuQpdn3pT4tBi/ESdJzEMDzqTmk9rmw1NQ06l3tT1vzCdjkEQVWr/tbCxapzvHFXAoOB7BnTzN7/vuTKIoIDg5GcHAwEhISmj5BIlkC9qdyP3XqFE6cOIFTp06hpKQEubm5KC8vR2VlJZxOpwLoRIS6ujoIgqCkL9VqtSAi1NTUwOFweGhi1PPpWrDJAeA18gSYkRTAZppscD71h8HfB+AjRE8QfhfmqDnUCs7nQ37i4ja0bYvCwkKkpqZi5MiRyElMVD4kGRhnoT5r1GzwB9kPLDWq6RzqpalSQEnBJ09MjUYDk8mEzmlp+H7PHvQ5cwY28ILrj3wpQ10A1mu1OA1AJFIms69FUibZjiSnJN2+fTtzsqi3q/nKQPY2WCX4HRhYk6Sx3QpWGwVLfewM33GrssQ0BuwN/IuPY2TypS4+CAZRWaKrBTupXePj/MXSPR6Qfj8otW7gxf40WOpcKrVKMJgtBTM+w8GAPlQ6/37p/mrnOSN8axtcYAZC1hDINrgLcQ+RGY4xYHX816p9si15IFgTkQsG61/BmoyLUA/sY8FOezNQr0K+AvwODWD1bEc01ASQdL3Kykrk5eXBF/mbc+pxy8/ra/C7jJV+V4Cf26/g5CJ68He1AfydGcEaCjlUygJP7/E68Hzw5XOxAcxUZoN9GF6Af/IFqJPAzysCPPfHS9t9rQXe4KxmLmXa8OGHmCkVxNFoNBBFUWkt+X0h5/6e95Il5uTkZJ/73W63otqurKxERUWFomo/c+YMysrKUF5ejoqKCmg0GlRXV6O2trbBfFJrXXx9SYTG1xQArNr+k5ijVnBuCTUSF0erVqFvdTU+79kTt4wejXHjxmH1W28hCTwhQsGLgS9Vl5zLWqZK8GLQBfXqTVldIycy0Gg0cDgcyM/Px38jIpB+5kyLQjNkqgGwf9w4WHJyUFtbq6itve3JajWpHNOYnJyMgwcPoqKiAjeAbWjy+ASw6nQm6jOQPQ0Gh7dRnwoxCCxtvo16e1xTCSU0YCDoBJY6ZclGndval7o4BWxvlWkr2OY0FrzgqiW3H8CS0rOqa8qq0i7S2PyZIiLAjIF6f3ewFqM5VA3P4hGyne1CSWY4mooN/g78vhbAs7RiGhiYBbBqe4X0f3ew5uc7sCPcz2DpHGDQlEkta/iTkpsiWT0/A8wUyPQkGKx1YI/sz8BzTVYv3yw1gN/hQvB8gHS9x6S/chW3Co0G50QRsU4nBoGrnzWnRIMvQFXb2rPAUpksvfujxnwRHAYDAgIC4Ha7Fe2WzLzJTb3PexuABvua0+TzvM9v7Levc2Tytd97X1PkK3xK3uZtMglRzbdOYJ+QJ8DM2kawavvi5txUFR3zR1IrODeXmoiLExwOGAC0+fFHvC+KmPfGG3jO4cBdqmOuAzvJDAMvIk+DJctx4IVLdi56CMzldQIv1Pn9+iFs716UlpYqYQayw8TJkyexWavF52AbVkteaJUg4NuxY/HwunUoLy/3iHs0mUyYPHkyduzYgZ9//hmiKEKv16OmpkYB8J07WamYhoYJIWzgye6LJqNh5qWW0kJ4pmh8A54lJX2pi7Woz4UMsJpRBKsXgYaS23Kwt3k31KtKrwW/l8ZMERWq3977miI5OYq/TFnh4eE4ffr0eUnRMsPRVPKOArAEcRkYINSlFQms1bkBrAXQgO3SG8DP0xeRdB21f4Db7VYAWqPRNPDG90eyet4ETyk3EOw5Hob6XOhfgR3AquEZKjUDXJNbduoSpOPOiCLsdjuKiooww+XCEper0Spu3tQYoKpJAEv8vtYC9Th9+SK4DAakXHklnp8yRbG7nk8D8D93/oVS5fjxwEcfAdIzXw3WXjwGXsMmoZmJjEJDmz7m9yBqpaZp2TIis5mIYblZrQKgmQCtAqhO2lYL0I0ABQMUAdAsgCSopy8B6giQEaD+AOUB5BYE+tRopGeeeYbcbjfdeeed1K5dO5o/fz717duXsvV6WqvXkwOgyhb0rU7q320GA4HXzgbNIO0zGAyk1WpJFEUSBMHjGPm3FqBrvO6RI43HBNAAgPJV+zoDFKBqGqmpt4kA3aI6512AOgEUCFAyQB9J211Sa8m7UT+HD/yMX26vSde/HKDh0jskgG6V3qX6einS9c5I555S7Xtf2t/UO7mhif6cT7MDdKc0lo8B2g5QNern5X0AXavqy1KAdAA5VdtGAfS09P+VAI0F6LR0nYcAymhkbG6ArmpmX73nGACyefX/iI93ni8da4DnPHoDoFKAugJkBn9396jG7msO3CC9C+9xOMHf6z3SeBxez+hfAF3t47zV4DnhBug7gKIBehn+1wKHtD3H1/M0GomKiv7qFfFvT7W1tbR161aaPXs2de/enUwmE80FqKqReZoJ0Ate22IA2qjeZjIRPf74nzKGVnD2Qc888wz16tWL9Ho9XTtypALM2wAaDFAoQOEATQDohOrFDfNaGHTSsdUazXmBB5nNVLB6NSUlJdH8+fPJ7XbT448/TnFxcVS4YAG5zWZyCUKzr+eQJucHAPVCw0UxICBA+S2KIgUGBja5mAYBNB2ei3uxtP09gFYCZAWDbTuAvvHq0wLpOneptlVIz2+T9LtAepafSQvcWjDoy+DnPp9nK93H+zl4tznghXgAPD/s5QBleV3LBNA+6XcUQOtRDwA3S/PFm4mqlK77sU7XZF9a2tIA+lC6vvd9HVK/nADd6/X+ctA4OHcBA468r1S6X7GPZ+wGA2Rj4OvdQkJCKCgoiLL1er/9P9937m8OREREkMFgoAxBoAqApgAUCZAFoCSAXkL9XFW3ZPAa0BigXgH+BgLADOvTfvrSZBMEovHj/+rl8W9JJ0+epPfee48mT55McXFxpNFoSBRFCg0NpYEDB9LSpUvpxK5dzNxIz3O39N4qAXoCoHgws0nSXwcYnL+Q/nfjz2WOWsHZB3344Yf00Ucf0cyZM+na2Fj+KMDg8B5AZ6UXeh1AlzTyMfUDaIpG45cTb7SZzSyxE9GRI0coJSWFRo8eTe+++y69kpbW4uu5wYvtnCYWRl9Nr9eTVqttsF0URbpLEOgueC7uy8Fc6HqAYgH6CqwR+BoMtPJxvwGUAJAAlojk7Suk7fICvB0sPanHEw7QVtWHVNPC5yFrNkRRbHTsRoDSASr3Or8IzIB8IH24dwF0kWr/3dL7PwPQTmmMQdLzXwnQGunvHGksv7e0LM85WUL01ZzSMXeBwUiWBGsBSgRLxE6AvgVrLGTGYypA4wEqk45dBJYGveebG6A3W9BneY7p9Xq6JySkyf5faPPWVAiCQJ8ZjVQH0C+oX6j3gaXbH9DyNcC7ueDJ9LSomc1EO3b8xavjX09Op5N+/PFHevLJJ2ngwIEUEhJCGo2GNBoNRUdH02WXXUZvvfUWlZSUNDx53DhlPb8ToBAw0zQMoIOqZx3nY37mAX8qc9QKzo3QfbffTteKot+P5Udp0fK1Lw8sLf4KUIQo0kNRUVSr15O7CUnXBZa0n0hMpHbt2pHFYiGtVksmk4kEQSABLMnJx+8Fc/4hUhskbZP3V0sLkB0sxQ+Xzpev6wt01YuVwWCgzMxMGjZsGAUHBxMAstvtBIASEhLo4+DgBmrRW8HAlwlW3xFY2vrAa6zDABoifRxfqrZfDJZS5N91YKBbI/3/EZijVTMo29A0GMnXqgBontXqE5h9bdOhoaqU4NsUof4iex8AACAASURBVH7u14Elr2DpOvLz8/WcvX8bjUa/76W5wNzUYr/Ax7nyc/8FoN5gVXAy2Dwjn1cCVm3bpLFlg9W1hHpQLoCnKttbNf2a9NsXY3KLVttyZrYFzZ8JwQbfas/9YCn6XR/7GlsDfDWHKNIbbdu2yAxFgAez/v8bFRUV0Zo1a+j222+nlJQU0ul0ZDKZSKvVUlJSEs2YMYM+++wzOnv2bNMX+/77FpsoPd7Bn8gctYJzI3TfwIGNgvNT8JSW1O1B8IJdq9XSx3370sSJE2la9+70eUCATxtxJVhy+RCgizQaslqt1L59e8rMzKSxY8fSoEGDKCUlhYLBoH+tdF4pQLlgSSZWWmTaqa77GNjedrW0+OjBUkBXH4ui3KKjoykuLo5koNDpdKTRaHwe+wka2iyvB2guGNQWg6UwPUADVYvfewCNAINXBOrB+Yg0vsNez+dl1NunTWDVtnr/GjCTIkuy3pJ0jbTdl0pfDZC9e/dWtsmMSxrOQ/MhtSpB8Lif0Wj0uMfv0UwmkzKG9Avo6/mqit3Ss/0NDLwdVX1rTLUuq/Q/lI5TP+s8MCMZIs2Pm8ES5zfwZJQCpPM+8NH/Br+NRlZLjh9PD48Zo8zpwMBA0mg0dKdXH28EzzUAlIqG2hNC42uAr7kwx2ym7OxseiQ2liqBJpn1OoDcJtP/N8DsdDpp586dtGzZMpowYQJFRkaSXq+nwMBA0uv1lJqaSvPmzaOvv/6aqqqqzu8m5+FD9FcwR63g3Ajd16WLB+io226wJOptQ5VbIkCvSv+/o9dTQkIC9erVi4YPH063Tp5Mnw8eTLkXXUTHe/WiE0OG0PHbb6fju3ZRZWUlud1un/358L//pQmiSB3gCYY10iKxEQx2BtW+mWAmoRtAJ8ESkAXswKPRaEin0zW5+AuC4NdW+BoagvOtYAcxgIHwBFj66gjQPGmRaw92PIoDMxUyOD8MlpLVz/JLsM1uB1iz8D1YktmpOmYlPIHAFzh7A4EsKavBUv08Bg0apIx/UZs2LQY9WToLDg5WHOz+qObPOa8pP4mvwPb0IOldtGjBUo2zFxpqAJqjWpcBSH5WH0q/h4PnlAOgQrAz3f/5OHcjWHKtgAR0bdsSjRpFB1NTaVebNkQTJ1JxZia9azDQk5GRdPTHH6mmpoaCg4NJp9ORIAjUoUMHevXVV+nYgAE++7YZPC9rvfY1tQbIzQUG/ZtEkUaOHEmRkZGUlpZGl8XF0Sd6Pbn0+gZ+KTLj8pXV+o9WZZeUlNDatWvpvvvuo6ysLDIajRQcHEzBwcFkMpmoX79+tHjxYtq2bRvV1tb+fjeWAbopnx1B+Mu0Fq2hVI1RTY3Pzb+Bk0z8HxqmKAQ4M9RJ1IdUtA8Px6hRo5Tk8DabDQF2O8hmg9Fma1DxxR+NLy7GT4KAA17b9eAQIjkRw/WqfdPAIRrjwWEZ74Nj+fYBCHW5UCKFsKgTXXjHOPvKfyyHwRw0GOD0ek5dwLmOAQ5VCALHoD4KTsxRDS4s8Rk4DvU11bmvAbjHa3y7wAkl5JSf6eDEGDnghBpV4NCgr1Gf79mb9NJfOYGJXMvZ7XZj+/btynHqmOING7hwJRHhwaIiHAWHIfm7h0zeVby055Nkv4VERAgCh4Ooo6JLwaFDl4BDyW4Bh/R9Lu0PAM+XyeB844TG42+9ySP0SzVnWlJvWSMdtwT8njTgfNa3gJ91JDjkaK+Pc1eCv7MA6f51hYV4bPx4/BIYiC/y8zFcp0NxYCC+AWAVBNyVng4iz3jbQ4cOYfbs2XjX4WhQ1tJX6lmg6TUAAJxaLVx1dfg1Ph75kyfjxSeeQNTPP0Or1aK8vBy/GI240W5HcG0tbjAYMKFjR0QZjUBoKF5bvx6lZ85gsM0GPPigkugI1133p6SO/CPI5XLh119/xbZt27BlyxZ88803KCwsRGhoKBxSvushQ4Zg8ODB6NevH7p27dpoWcsLohtv5BrNixdzSk5BUHJuA6iv5zxiBNdz/pOKXaipFZwbI3U1E4mOgNM63o+GNX9lWgkGw0Dpd2hCAhISElBcXIwffvgBRUVFKC4uVlplZSXCw8MV4FaDuPr/bt9+65FiU01l4IUyBpyvV6YO4CQRz6O+wEZ7cOKPQEHA4xIYq0FJp9PB5XIhKChIKZ4uCAIGDRqE7du347LLLsPOnTtx6NAhPF9ZianwTAQix21bwUAhx23Lyf03SM+xDJx+sRQMKleAC0Z45LMFg/GjYJDuIZ2zGRyDDOmew4FmJWFRAwFQnzvbm5TSe6WlXB6zthYhYAYgFpzdTK5pLZO6itdi1APWhSQRaUnVphnguG113ufhXsfcAs69LlOG1HLk+0l/mwJpNQOifoYajQapLheWgGOjt6N+kYkBxzpvBIPcMfD76AdO9hIj3RfgOOR3wJnjSsHZzR726kMVOEb9E9U2N4CL9u2DfvBgrFq1Cj179sTu3btRU1MDl8uFQYMGYdOmTejQoQMqKipQUlKC6OhoFBQU4KRXXmY1qVPPNrUGHJPGuF8QQNOmoS40FK+88ALcbjcmTpyIF198EWVlZYiLi4PL5cJJlwt3nDiBiz74AFGCACxejGklJXC6XDDn5gK5UoT4qlXAggXA8OEMGOnpfvv7d6DS0lJ899132Lp1K7Zu3Yrt27fDbDbDbDajtLQUJpMJl112Gfr3749+/fqhY8eOv0s8c7MpLY2LWBQXc8bHPXs4wUhoKNC1KzB16l/LCP3psvr/ADmdTnI4HHTPgAF0lSgqXqwFYHvu442oQarATjIb5G3NiIurrq6mgoIC2rlzJ33xxRf0xhtv0FNPPUXz5s2j6dOn05gxYygrK4s2mM10H1hFfa2f+0dLKko5zOhKcBjMOEnVKICdfE6DVdIAKD4+nvr370+iKFLnzp3pvffeo8jISHI6nXTHHXdQRkYGTZw4kZKTkykhIYHMZjPp9Xqfqu4FqFdFh0n3ywJoF0B9AJoPdii6F6xaLwSoDdgGfR08nd3U7RmwqSAQ7Mk9FqxK1aNhbGkl2F4YJj2Lvl77f5S2BYDVwABowIABHnb1DEGgj7XaRm2lu8G2b2/Pa38mgOaEEflqaie1xhyrfJkYvJs/G+mX8K3W9rbbymP3Z7sH6lXT/cEhSN7XPAnQcen/arB/wqVex5jAvgfq696s2p8DNm0I0n3yVftqJ0+mN998k4KDgykwMJAuvfRSMplMdM0111Dnzp199tloNNKSyEiq1WrpFEBvg80vdQB9Dv5mVqPpNaAKoHs0GjKbzR7vu3PnzhQQEEDBwcE0depUSk1NpaCgIIqKilJCFhdERLB9+W+savVHLpeL9u7dSy+99BJdf/311KlTJzKZTJSYmEhJSUlksVioXbt2NG3aNFq5ciXl5eX5Nd+1ElMrOPugBQsW+ASdB6T/vR1S1B/OW2AbqrKo/Z5xcVOmNAuc9QD9JP3uArbhykkjTqLeweUTUSStVksWi4XMZrNPAJFtsDabjfR6PV1++eV09913U0hICOn1egL8O0w1lnRF3eLg6a3dnPYh2Gv7BjRMgDIFnDSkSFpcf1DtKwYD3BtgoHndx0J9kxTr2hJbaVhYGM2YMYNCQkIoIiJCuZa/MDQAFB4eTsOHD/fYpo41V7c+BgN9JAh+nQmrwLbkxsC5MRupP3CWmxNsv75LFOnilBSy2+0kSvNHzXyk2O1ULYFLf/gGZ3WrBif1SFZtcwHUFqCF0v4jYEfAK1TvMAjs1DgPzJyoGY61okh2u12x88vzVN1MJpPC9BQXF/P3deoUkdFIReBvJhjsn5EC0IvStZtaA5w6HX370UcUGBhI6enpZDabFYc9+XtKTU2l0NBQGjp0KJlMJtLpdBccbvlnU1lZGX3xxRf0wAMP0CWXXELBwcEUFRVF3bt3p+TkZAoICKCUlBS6+eab6d1336UTJ078Jf38X6ZWcG6KVHFxLW6/Y9IAp9NJjoUL6R6NhlLAEqYTHEv8ExgozkoLRRjqQXCqtMC8ifqY1ChpoXgW7JEcFhZGNpuNACjSo06nI7PZ7OEg1Zjkd16LywW2amlxVoPRfmm8Z/2ccy88pfMqeIbznM84qkSR5oeFeYQ/aTQa6tq1q09g1uv1FBoa6rFN/Wy7d+/u8S6a61jlgn9wPghm3F7zc25T4ExSH9KkuWEwGGjRokWUmZlJoiiSzWYjURQ9PJ77S882DKw92ai61hEw+Alg7cWrqn3F0nMok36vAIcCdpF+LweoJxiwf5P6ZUR9HPZ7Xs/bYrFQcHAwTZ8+na666ipavHgxZWdnU0BAAAUEBFC3bt0oPz9f+d7PN+OcSxDoy6Agcrvd1LNnT9qwYQMdO3aM/vOf/1BmZmaD70dmEAQwQ6m+VmMZ9tRhehEALbn99t9ljfFHbreb9u3bR//973/pX//6F6WkpJDZbKaUlBTKysqiLl26kNlsprS0NJo9ezatXr3ad4xxK7WIWsG5KfqbxMX5kubvA6vfOoJBORzsqf086jPalIDVcAawtJEF9uCOBuhenY6Cg4M91KbywnvTTTfR66+/TmFhYZSVlUV6vZ7mzZtHgwYNIqPRSEajscFiM0uKT72QxBFuNJ2Os05aoJxoCEYrwZLO7WBQkFNqyvsvBnuTZ4Il6OHgtIuNaQCa0xyiSAMCAxWg8sfECIJAer2e9Hq9ksVIlpbVGdkMBgMJgkA3azQt6pMvcM4HA+/zXtv7oz7dpREMkgQGUQGekuEK6bmvlvqsHpPMROj1eg/w3w7QOeldrQCbJH7z6sNpgB4FS+Xq7QngMDwn2BzSCWyiIen9ZcDTXCHH0bsB+kwU6corr6QXXniBEhISiIjouuuuo+XLl5PdbqfffvuNIiIiFG/gpUuXUlRUFG3ZsoX2rlhBlefJjLvNZrosLo6+/vprWrx4Mc2cOdPjG547dy6NGDGCMjIyPL6dofDU/qgz7DnQUDNwj/RMzkDKo2Aw0Lp1636XdYaI6Ny5c5STk0MPP/wwjRgxgqxWK7Vp04b69eunhHQGBARQnz59aN68efT555/TuXPnfrf7txJTKzg3h/4mcXH+1O2ERjLawHfSiO06HcUHBJDT6SS3203PPPOMItH5Al6tVksjRoygwMBA6tGjB8XGxtLll19O4eHhZDabKTk5mbKysujq5GT6IjCQnILQ4rjZCrBk/wEaj4vdgPp4aW8wWqR6LjXgrGQB0iJG4FSMweBwLAdY1d4e9bbSSnCcdiwYTHqAs0Kp++DLnu0rR3NgYCANHTqUIiIiqE+fPhQQEEA2m43S09M9QquMRqNiVlC3ljAL/vI+N2Yj7Q+WQh3SGGOl/9eDk7z4uo+saTAajRQUFERBQUEeTMXHfs4jcCat//jYXgiWjNWZs3ZK/QuSrjsc9X4U14ND615WHZ+Feul7tcFAYWFhtGTJErJYLFRSUkLz58+nqVOnUs+ePamyspL0ej3FxcXR1KlTiYjo008/pfDwcEpLS6OcCRNa/L07NBr6cvx4WrZsGY0bN45+++03stvtVFdXp3y/K1asoClTphAR0ZkzZ+iVV16h7KQkvxn21N+FWjMQDU4pKe+fr9HQ5WPHntea4na76cCBA7Ry5UqaOXMmdevWjcxmM6Wnp9Oll15KI0aMoM6dO1NgYCANHjyYHnrooQuLMW6lZlMrODeX/i5xcRciyav6eLx3bxo6dKhy2SeffJI0Gg2FhITQ8ePHqa6ujhISEqhDhw5ksVgaSEuCIFDbtm0VkBk/fjzpdDrav38/Wa1W6mi10ukBA4g0miZBWrbdPtGunXL9CFH0SHV5FVgdrwHH6srS9T1gxiROOu8meOaF/goMpAbpmG5gVb987xLpvDAw8FSAgT1PuscnYJDOk45vzJ7trSKXUwpefPHFZDabafjw4ZSWlkZarbZZzmED4KmFeAnsFBcABrrjqn3/9nH+v9G4jbQ/WCrzPq87/INzJdjxTR6bIAjKX0EQ/KrNCZwRzles8jHpvqd97PMV995Y0RGS5ovBYKDExEQyGo10//3303PPPUedO3emxYsX0969eykyMpJSUlLogQceUL6BTz75hERRpNmzZ9PRe+8lhyg2qQVyS9/78fnzyW630/HjxyksLIzy8vKoZ8+e9NVXXynX37RpE2VnZ3t+z489RnfDd4Y99X1kzYBcVOWkat/7ej2lREY2a/moqKigjRs30qJFi2jUqFEUHh5Obdu2pZEjR9KUKVNozJgx1KFDBwoJCaFRo0bR448/Ttu3b/99Y4xbqVnUGkrVXPq7xMWlpwNPPgnMnu1RT7olRCYT3ktMRL/kZGXbgQMHoNfrkZ6ejujoaHz66acwm804ceIE9uzZg9mzZ2PVqlUwmUxK6ciCggLodDoAwKpVq6TupaO8vBw9Bw/GuqlTcdxmQ8dVqzDU5YJWq4VOFS/tEASIANZrtXjQ6cTPx44hKCgIbrcbTr0eT5WVwe12Iw3AmMBAjKqoQA44PEsdFW4HsBQcgtXOa6wBANqCQ8q+A4d0qYM15P8ng1e9AHDMuEyjACSAw6JqAHwMLqkYJO3vpX6uAKYCWCKFP8llEDdu3AgAWCfXAZfIbDZDEARUVlbCm4zg+t9ylOcmcJ3gjeAwrtukPstlOaOlMW6QxjQEXId5JriUpj9aAS6z2BHAInDo0tcAhoLrUpvB9a4Xgp+NGfwM5bHJYXbt27eHw+HAzwUFqAJQC37e/cGhVO8C+AZcGnEVOKQvCcBpALMBpMJ3yUlfce+N1T8HAIdej8zMTGzfvh11dXV46qmnEBsbi4MHD2LixInYt28fzGYzRFFEfHy8cp3Vq1fj5ptvxjvvvINnS0rw6m234fK8PFSvXg290QhR9b05BAE6rRYYPhzVd9wBfUoK+u3fj8cffxxjx47FQw89hD59+uC5556DyWSC0+lEQUEB9u/fj08++QROpxNOpxPpa9Y0iGdtcTnS2lqUlzcsSEpEyMvLw9atW7Ft2zZs27YNubm56Nq1K5KTk9GmTRsMGDAAO3bswI4dO9CvXz8MGjQIDz74IFJSUv64GONWah791dzB/yQVFXF41NVXE40axX8ff/zPLeW2bBmRXt9iqbkCoC1XX03p6en0zTffKJcbPHgwBQQE0GuvvUZERP369aPs7GyaP38+Pfvss9SmTRvSarUUHR1N5eXl9NBDD1GfPn3oiSeeUNSaoaGhDUpLyvbI7tHR9E6vXvS6KNLGwEB632Si+/R6Sg4Pp4iICAoICKBbbrmFIiMjSavVKnmovT2nZTW2LzVuNNixyVfRhlfAkvMGcErInWAHuVmSlOhP4jsJlrr3oWl7NknHyF7MLQ2dUmsnesPTSWgOWCsg/z4uHSfbcDPB6lB5/8toOq2kP5twITg/uwucRrUvQDNU560VRVq8eDFNnz6d2rRp0yDUqwqsWUiTrhks9UWu0vUfcAUguYTj5fB0eJLbFumYc17bGys6Ui2K9G+zmXr37k3Tpk0jq9Xq8WwTExMVm2lgYCD17t2bBg8eTBdddBGJokgaKXVucHAw6fV6stlsFCGKdLdGQ68LAn0iCErYnA0soQcGBpLVaqXw8HASRZGio6NJFEVq3749abVaSk9Pp+zsbOrfvz8JgkDDhg2jsWPH0qRJk+jHmBifGfZaUo70A4BSLBaqrKykTZs20aOPPkpjxowhu91O0dHRNH78eJozZw7NmTOHLrvsMoqMjKQ2bdrQlClTaPny5bRv377WsKa/IbWC8/8y7dhB1KNHs0C5DqAanY6Wp6YqDl0Oh0O5lLyQlJeX07Zt2ygqKoqioqJow4YNSiq9+Ph4io6Opr1791JYWBjl5+fTyy+/TF26dCGtVkvJyckKOIuiqMQ3durUiTp16tTAc9loNHqEGk2YMIF2795NBw4coNDQUJql0zWwucoL2QIf4GYBOzP9gvoYWQEMroK0nwBaBgbyEHAMeD+AtlitDZ5ZLbiQiAxMTdmzCWxzVfdJp9ORVqslq9VK/fv3V2pjNwXUo70W7NleC3aBdJxcujEIDLby/h1gYGyJ3d+fTXgb2MarZkAA/977cpxzc++rbur+zoD/uHd/RUccYJOI0Wikhx9+mO69914ymUyKJ73JZCKNRkMGg4GCgoLolVdeoaeffppCQ0MpLCyMVq5cST/99BP9/PPPdM8995DZbKYOHTpQr1696OjRo3TVVVdR165dSafT0bx58xp8krfeeivdeuutNHbsWHr++ecpNTXVQ7WdkJBABw8eVH7XXn55A3BuSTlSAuh+gPrq9YqteNasWbRo0SK67777aPTo0WS1WikpKak1xvh/jFrB+Z9A69cTpaRQnSA0XBRNJiKjkX5NTqY0gN5//32yWCyk1+vp2I8/Ej32GNGUKfSpKNJqi4Xoscdo6siRlJCQQE8//TRFRESQ0Wik2NhYKioqouzsbEpJSaGlS5fSb7/9RuHh4bR582YKCwsjANSrVy8KCwujWbNmUffu3SkhIYFCQkII4LjeyMhIZVGXpWO9Xq+AusFgoG7dutHYmBifzlCNxfE2KIyuWtyM4KQV3vtcAOWnpdEHJlOD7ZeDHZHknMpL0XidYzVwXWibhIY1lsPAscpVEnAJ4Lh6AjMj+1THH5Cu0xJw9mcT3g6OjybU25zVfdXr9ZSRkUEJCQkkiuIFFd9womlvfX+tDqC8Xr2oS5cuJAgCDR48mHbv3k02m43CwsJIo9FQQkKCR9+zs7MVzc3Ro0cbfFqyNmjZsmX0+OOPU48ePai8vJzmzp1LOp1O0TTJdOrUKbJarfTWW29RcnIyLVq0iG688UZl/8UXX0zr168nIg6PPDxrFt0JTye+lpQj3Qee109mZtKCBQto6NChZLFYqGvXrq0xxv/j1ArO/yBaeu+99F5GBn1ksfhUt8+YMYO0Wi1dk5xMa/V6cgDkMhg8QcloJAdAX1osNL17dzIajWSz2aigoICIiGbOnEmBgYHkcDgoIyODBg8erCQkSUxMpNGjR1N0dLQiEWdnZ9OkSZMoNTWVAgICPKpdDR06lCIjI2nmzJlks9koPj5ekaJl6asant7TEeBCDnJ/3wWH2QSCQ4Ee9rFor5AWsDg/i3oVWBqukpz93GCnsQHwLCGYg8bB2QmW2hsrh9icptPpGkjOBI5Lbw9Wpz4iLeByQpEgcNnGZ8CZu7SoD40icNIVtUOYXG1pi9Tvq1AfPhUG0DQwU3JUeg5TVc/K37hk6VQURbrfZjuvQiHvJyYq76GlrQKgwSEhtHfvXgoMDKTOnTtTVFQUBQUFUWRkJEVGRlJBQQFFRUUpfTYYDGSz2WjYsGENv6elS0kURfriiy8oIiKCAgMD6ciRI0TEXs6yE+TmzZs9zrv//vvp2muvpa5du9Krr75KERERitf29ddfTy+++CIREc2aNavBM1wgjaW55Ujt4FC0IT160Jw5c2jNmjWtMcb/EGoF538QPfroozR16lRKSUnxud/tdtNjCQnNTmhRAdDtBgMdPnyYiLiuqt1uJ6vVqngdT58+nQYMGEAjR46k4OBgRWUIgGJjY6lNmzZ0880305dffkk1NTW0d+9eMhgMpNPpqG/fvh5pQDt06EBt27alHtHRShIVb+/pSRLo5IFVuzpwGJBbAhU9PO1xBI5tvhr+wblSuocMxDeAJRXvEoG18G3P3ufnmlUAbQwNpTHR0X5Lbvpr3jZn75YLtseekX5ngrNYyZnTBoBB1N/5/0F9jHMw2ENbrtn8sPQcteDUqreA7b5ynHNTtaaNRiONHDmSvrnySqpsxlyrA6hGq6X7bTbq0KED/dtuJ/d5hC4+JIHu4sWLadCgQWQymejkyZOUkJBAgYGBZDAYaNKkSSQIgsIoWiwWktXdI0aMoAMHDhAR0bp168hisdDo0aNp586dZLVaKTU1lcaMGUPl5eVExJJveno6mUwmOnTokPKdlZWVkd1upwceeIBGjRrlodp+6KGHaOrUqTRkyBAl3v2rkJAmS0f6/U4FgWovvfSPXFZa6S+iVnD+B9ETTzxBU6ZModTUVN8HLFtGLqOxZR+/0aiEhU2aNIkyMjLIYDCQRqOh1atX0yWXXEJms5nCwsJIq9V6ZBR74IEH6NixY/TBBx/QnDlzKDs72yPn8CuvvEL/+c9/KCMjg3r27ElLly6lkJAQmouGMc5qB7AQsDr3W7AUWS3tiwFLkBtRr87NA0uE/0V9HK93OUkC6HVBoNWiSIekvsvAJbc3pON+AQOnGZxycpWPa3kvnpUA3eojhaTsgBQZGdkgztkE0GTUqzodAO2RxnUELE3dq7rP82ANQgHYWSxc6qe/fg0Ah1n52lcCtrV7OyXJpSFlxis1NbXBmDIyMuiWW26hpKQkEgSBemu1ShnPKq/ryQzMKqnmdVJSEqWlpZHRaKRt117bLCbSrQpdLCgoIEEQSKvV0ptvvkkhISH0zDPPUEhICKWmppLValVSecbGxtKECRNoyZIl1LlzZzIajaSRGI+JEydSWFgYZWRk0EsvvURt27al9957j2pqamjatGkeGcUqKiooNjaWwsLCqLS0VPnUlixZQqNGjSKbzUZz5syhmTNn0meffUbt2rVT7iOr1HtrNOetLfg9Ex210t+LWsH5H0RLly6lSZMm0UUXXdRw5wXER7tNJpo3dCiJokhXXHEFhYWFKZmu5IVmwIABlJSURCaTiex2u7IvLCyMRo0aRQsXLqQNGzbQ6dOnFXAuKiqi06dPk8lkoo4dO1J4eDgtX76czowc2aAPC9BQQrsfbHuz+9iXJ513vY99/X2McQ0uLENYU03OwR0TE6MkHbn44ospJSWlSa/uBQCVgnNJyx7O93gBlxtcQCJUar3RMOe43PLBNurDXtvfBKtKAQb3XV7XrwXoI1GkvirJWWbMDAaDojGRGY60tDQl01k4oMStf4yGhUJCQkIoNDSUlzMjzgAAIABJREFUwsPDldjpTJ2OSvr35/z0Xj4BNRqNUoBjdHQ03XnnnbRp0ya64YYbCAANHTqUoqKiKDY2liIiIkgQBOrZsyfdcccdFBYWpsTom81mWrFiBZWXl9Mdd9yhmFUMBgPp9XpKTU2lhx9+WPmM3G63klFs69atRMR25uDgYOrYsSPV1NQQEZHD4aC2bdvS5MmTqUePHh55yEVRpEsuuYQWLlxIWVlZ9PTTT9PHw4c3YEibBcx/o+IXrfT7Uis4/4Po//7v/2jcuHHUp0+fhju9coQfAEuHsup0I3ynbCQJBD4SRerevTtpNBrFgUuj0dDo0aNpxowZlJycrCzWo0ePJr1eT+3ataMVK1Y06Iqc1GTZsmVUW1tLQUFBpNfr6YcffuADRo3yuRh5e08TOGQoAJycxASuEqU+JwkcRtXUQrcSILvd/ofmCK8AKEuvp/79+1NKSoritR0cHExt27YlgMPRQkJCyGAwXJBjVWOOcw/BN4OinhvzwSFV3vvkhDG3qrzsRVEkq9VKERERHjnDdTodmUwmioyM9GA2DAaDUl3rfaORPhVFeh2guwSBksPDFenWYrHQkiVLqOzgQSV00T1qFL1rMNCdAN125ZVK/nJZYxQaGqqYEIYMGUIA6KKEBFoYHEzfdehA30dE0PtGI72QmEg3TphA7du3p7Zt21Lfvn3p5ZdfptjYWMrKylIYJqPRSB999FED7+ZPP/2UbDab4hC2f/9+MhgM1K9fP/rwww/ptttuo/DwcI9xZ2dn09q1a8lms9FLL71EV199Nel0OrJardShQwf6v06dyGU0Nq3i/htWpWql359awfkfRM8++yxdeumlNHDgQM8dUrUd9Qc+BJyfVw3O/rJCEVj9GKPXK1V15KxQ48aNo7vvvlsJQ7FYLHTu3DmKj4+nzMxMSkxMJKfT6dGd2NhYMpvN1KdPH8rKyqKIiAglBzIREU2Z0uD+vrynvwSH+OyQ9n8PdvzaKe33Fyfr3SoloOit0dCH0vXVXs6yk5XeC/D8OVnJWcOGee3XgVXrMnCNGjWKHnzwQQWQ7Xa7AiyypHU+zIKvnOPq1h6s5m/sGm+Dy4w2xmjcAE5RKse5yxKv7MEtCAJ1796d7Ha7AnZpYDu8r/SsVYJAVWC7eRpAKSkplJ2dTSEhIXTTTTfRvn37iIhozpw5CgOYkJBAw4YNI1EU6cknn6Rjx47RhAkTlHt9CFC1IFC1KHrcyyFV+DqVnU3Orf+PveuOr+n8/5+7kntv7h7Jzd57kQRBFoIgVsxEgxhNldojdimKWjVam2oRNWpXtUGp3dqbUmo3KSGSyLjv3x/n3iM3O7q+/O779Tovzn7Oc27O53k+4/0+ghUrVkAkEkGpVGLevHnw8vKCSCRi3eRBQUE4ffq0ye/49OnTsLe3R2xsLBITE1k1MplMxg5KOBwOdDodfH194e7uzh6TmJiIJUuWQCQS4cmTJ/D29saJEycYF3VCQrneAmPlBRISzK7s/wcwG+e3CJ9//jni4uLKZp7OmGFinNcToRMx7tLqGucXRBjF5SIhIQEtWrRAbGwsAgMDsWnTJnh5eWHRokUAgKZNm2LLli2YOHEihEIhIiMjsXLlSpPmBAUFQS6Xg8PhYPz48RgzZgw0Go1Je0vG4CrKnv6EGCnMku1sa9gOqrxOtvTAYxhVrPxkTLJ6rxKDB2K4nd2o4vKlaGJmpHYCQYUJYnw+H8HBwUhOTkbHjh2hUqkwUiqtXhIfh4NcDgffcDhlKCGNy0/EDFg+ofIHHMblS2Lc50Smcp53ianBVhp+L0EG4RSVSmUSN7e0tGQ9AwKBAFwuF8PE4hpJcQ60sEC9evWgVCoRFhYGlUqF5s2bIy0tDW3atMGRI0cgl8thZWWFZs2agcPhwNfXF2q1GsMlkmrHrPUiEWZ5eGDgwIE4fPgw6tatCyJCUlIS9u/fz86keTweG1OPjo6GlZUVvL29WeObkJDAJsvxeDx4eHjAysoKAoEAEokEMpkMv/76K9zd3XH16lU8fvwYSqUSV65cgZ2dHYqLi1/9DfwvEB2Z8Z/CbJzfIixduhSxsbFoXTp7s8RMNJsYV+8dKmucBcTEb12IYcEqPWM74eOD9PR0uLm54c8//8SiRYugVCoxatQo9lZz585F7969cfjwYajVavTo0QOurq4sN29xcTFcXFzANbjJv/rqK6xZswZ8Pv8Vf++jRya6zxVlTx8gJkPbOFM+RcxM+juq/INc2hCcq6byU2WzUVDlSVa3iInzXqSydcJGd3aPHj0wfvx4DBgwAP7+/mzckwyGtCJBEOOMM0OpRLREAm+VqkztrPHYvsRkrpcecCyjV1nuF4mZXauJIbwoaZxjiDCIGO/CL8RkqyuVSsjlcri4uOCDDz6Ap6cniAgKhYJ1fb+OB8A4O3d0dERcXBycnJxgb28PGxsb8Hg8zJ8/H+fPn4e3tzdUKhVbKz/J1rbGiY95PB6KFy3CkSNHoFAo4OTkhOTkZDarW6vVsrN/LpeL9u3b4969ezh06BCioqJYhTFj5jeHw0FaWhru3buHsLAwuLq6ws3NDfv370eTJk3w3Xff4fjx4wgJCcGMGTPKKFiZYYbZOL9FWLFiBWJiYtChQwfTHSViuAOJqYsEmRrnqigbQYRDSiUsLCzQqlUrvPvuu3B3dwePx8PIkSMxf/58LF++HHPmzIFSqcTmzZshFoshk8kQFhaGmTNn4tatWyYSdJMmTUK7du3w9ddfQy6Xswk2ALDF0JbfqPLs6QXElDdJiJEZnFXNj3FJV3Xp2XVFWrpG4/w9EWoTMwN1IKbWuqIkK+MyiV7FeddbWGDIkCEIDw8Hl8tF3759MXLkSERGRrIJVmKx2GR2bW1tDbFYDH9ra5xKSsK5WrXwnaUl1vH5GGFIuKosoQzEGGq54flKDzh6EjMwExNTcuZCjPF2plfG+bnheo9LnN+LCEqRiNVzLpkoaGx/uGHwU1F4oLI+zyFCvzp12Gv6+vqiXr16ICJotVo2AVEikcDFxQUxVlavHafP5/HQ0FD3bGFhAR8fH7zzzjvo0qULHBwcUK9ePYwYMYKlBDUuEokEFhYW8PPzg1arxZEjR9C5c2cIBAJcuHAB33//PWxsbODu7o6RPXvi67AwXKtbF3dDQnDA0RELnZ3xw/r1//LXwoz/dZiN81uE1atXIyIiAomJiaY7DDPn00Two1elRCWNc+mlNGUjiLBJLMZ7772HVatWISYmBu7u7ggPD0e9evUwYMAA9OrVC126dIGVlRXq1q3L0laKxWL2w11y9mGc7Tg4OEAoFMLd3R2tW7dGhw4dEEb0+uUl1Vg2E+Pe70jV19IdS4zbXEtMbXUhMWVHN6jqJCt3eiVpuJ0Y97WVlRWmT5+OvLw8HDp0CGPHjjVJIhIIBOBwOJBKpWjatCmb6W1nZwepVAp/f3+2z2QyGRo3bgwOhwOJRFLtzPPyvAFfE+O6Bpka52eGdpWsI+9p6I+S7mypVAoej8carW8MzHUVhQcq63PjeTExMejVqxc0Bi52Y5WAMSZsLOPjl3qfL4nQgV6plu0v9axziRnUSYnxEsQb3k2XLl1w9OhRZGZmYseOHRg2bBg8PDzY33BJt71QKMTatWsBvEoU++KLL1C3bl1IJBI8fvwY74WGYhuPhzwiFPD5Jm14QQS9pSWTtHnixH/w5TDjfxFm4/wW4csvv0R4eDi6d+9uumPGDOiFQsylV6U4NsTMQIXEzAJLf7RLUjaCmASa9NBQ6PV6zJ49G/7+/njy5AlL4VlS33Xw4MH46KOPEBkZia1bt0IikUAgEKBPnz4AGP5hNzc3rF+/Hg0bNkSXLl1Qu3ZthISEYNu2bfjkk09ARJju4oI8Hq9GRldPVdM/GmOaI4hqpKU71vAhH1fONStLsjpk6GujW36dwZjw+Xy2/EgkErEffB6Ph8aNG0MikaB+/fqsqIKLiws7uAkODmZriQcMGIAHDx4gMzMTEokELVq0ABFhiEhUZXlOaeP83PAsRg9ASeMMYrTABxiM6C+G34iTQIDY2Fg28atkaZhRCKOye1alX1ySlYzL5bIZ4Xw+HzExMXBzc4NQKISaz0efUtd+SYwBPkRMsmBp43yDmDI1ECNZ2YjDgVIgQEhICGv8dTodateuDa1Wi4YNG6JFixYsgUhJbW4vLy9cuXIFFy5cgKurK0aMGAFHR0eMkstRZGlZNd+4OQvbjBIoqbxnxhsOHo9HRUVFZGFhYbqjZ0+CXk/vEiOtd8awvEdErYjoO2JkAu8Q8wX8nRiZvrYlLgGAXnTqRBs3bqS5c+fS7t27SaFQkLu7O9WtW5fS09PZY1u1akW7du0iDw8PmjZtGllZWVFQUBDt2bOH8vPzSaPREJfLJbFYTN27d6ebN2+Sr68vXbt2jeLi4sja2pqEQiHt9/am/a1aUR6Xy0h0VoJiIsrn8WiRREI3AgLoJYdDEApNjing8SiPiHZwuRQnFBLKuc5FIgousW5FRO6G7UREfxj+DSRGkvEdIvqWiO4TUccK2vYFESUQkYQYqcHTxcVUVFREWq2WBAIBubm50cuXL6mwsJD0ej0VFxfTvn37qLi4mPLy8qhLly40b9482rFjByUmJpKFhQXduHGDnJycyMLCglavXk3BwcHk7u5OeXl59PTpU+Lz+RSTnk40eza9MPRPdTCRiJKJkcksD2uJ6BYxMpz9iKgbEan1erp69So9ffqUZDIZubm5kb+/Pzk7O1NfPr/cfi6JqvocxEhxcjgc0uv19OTJEyIiKioqoh9//JFu3bpFSqWSJtjYlJGdtCCiwUQUQa/kN0vCnYgUJe5DAHlyOJSYmEhbtmyh1NRUev78Od29e5eePHlCJ06coCdPntAPP/xAN2/epNjYWJJIJOTh4UE3btwgHx8fGjBgAO3du5eOHTtGI2UympCdTbyXL8u9vwkAotxcouHDiT7/vKqjzXjLYTbObxGMxtmosczC2ppu+fiQkIh0JRYJMbrBWiI6RUT1ifkwNiCiACKabzi9mIiuuLnR6DlzqHfv3rRz505ycnJiLz9gwABasGABAcxnODIyks6fP0+7du2i7OxsunjxImVmZpKjoyMtX76clEolAaDc3Fxq164dnT9/nkQiEXl6etLPP/9Mp06dIpVKRXfu3KEt1ta0umdPovbtiYRCyi31zLlElEdEW4nofT8/Ota2Lc2oW5dWTJxInMmTKa9jR/qWz6cviWiKhQW1rVWLdvfuTceKiqixWk2leopyyFQrl4jRbv7T0A8viNEY3kBE1w33/oCIOhCRtJx3kkdEG4kxLkSM1vJ6Cwvy8PCgx48fU05ODt28eZP0ej3p9Xri8Xisjm5RURFdv36dvvzyS+rTpw8FBQXRunXrqKCggHJzc+nhw4estjaPxyOdTkcikYhOnDhBRUVFNG7cOAr+/HOKJqLDGg3lE1EBv3IJ9wxi3rvxN/I7EXUmohmG/c5EtJOYQcpxYvSY7YqLqVatWnT79m369ddfaevWrTRv3jz66KOPKCkwkMSV3rH8PjfqFxMxGtK1uFwSCoVkb29PFhYWxDc8BxjvHz18+JCU9+6VeZ/VwTpi3rGGiM4T0UQHB7px4wYlJSVRcXEx9e/fnzgcDrVr145mzpxJHh4e1L59e4qPjyc+n0/ffPMNDRkyhNzd3UmlUtGBAwfIy8uLGkkk1PfKlSqfvwyMBvrnn1/jacx4a/CfztvN+FuxadMmBAYGYtCgQWX2jWrcGIWvof8MIhRYWKC1rS2EQiF0Oh1mzZplcu3i4mK4u7uzCV2bNm2ChYUFYmNj0axZMwCMyz0gIAC2trZYsWIFXF1d2RIrDw8PtGzZEkOGDMHUqVPRtGlThISEQCKRIDQ0FPv37wcAXD54EMOIodrcTozAxCgeDxpiSlf4fD5u3boFhUKB5cuXo02bNix38sCBA6FUKjFx4kTweDxMnToV28txsZanpVsypmpcJhr2HTas/1BB360jprZZT4w7fRO90gC2tbVl4/Fubm6QSqWQyWTYtm0b9Ho9cnNzsXr1agQFBcHNzQ2TJk3Cnj17EBcXx8pyOgmFGMnhYB2Phz0CATYIBBhOBBcrKwQGBrLt5XA4sDPsW0MM7ehhYlz7JbO6M4lJDjQuDsTEgo0u+UvExJ5fElNupTb0l/E+MpkMvr6+CAgIQJxajfvl9ElN9IuN69voVWJcQEAAK6BScnnX4LrmUvlZ9fbExMiJTF31PYipVBAb/hURYcSIEZg8eTJ0Oh06duyICxcumPzmCwsLcfDgQYwYMQI+Pj6wtbVF7969MX78eLi7uzOxcDKNfx8lRrRFSYybviNRuf3zkpjkOHuh8O/+RJjxBsFsnN8ifPPNN/D19cWIESNMtuv1elhbWyNzypQaCwq85PPxdPp0ODo6wtXVFYmJifD09DShNAQY6tDExEQMHToULi4uGDt2LOLj4+Hk5ASAMeC1atVCnTp10LdvXzg5OWHhwoUAgPbt28PX1xfbtm1D06ZN4eHhgbZt20IqlUIikeDChQtITU1l9Z/j4+NZKT9jfFNLhFEcDg44OmInh4NvNRoc79gR9dzcIBaLkZKSgvbt24PH42HMmDEIDg7GVqm0xlq6EcRkXhv3/0wM13d1+jKHGGIMuVzOJjUZGdUsLS1hZ2eHTz/9FB4eHggODoabmxvq1KmDLVu2oKCgAN988w2io6NhZ2eHWLkcOy0sUGxhUS5ndR69IvOIjY3F5MmTMXnyZBNVsIoGHCUX51KGbK7BsIiJiT8fovJVqoylU+XF/2va56DqSXF+YDB4XlS+cbYhJmegdHlYD0ObQEySYDsiBOp0aNu2Lc6cOVOtv73r169jzpw5iImJgVAoRJinJ/qWasduYgY62YZ3lEKMhnbpdk4hplrCnshc1/z/GGbj/BZh+/bt8PLyKiMCf/nyZTg7OwMArg4ZgtzydJ9LLcVEyONy8WL2bISEhOCjjz7Cs2fP0LRpU8TFxcHX1xdjx45laQ0vXrzIJjJlZWXh3r17UCqVEAqFyMnJAQB8//33cHR0hEqlgk6nw8yZMwEAY8aMgVAoxMOHDyGRSCAWi5GamgobGxtYW1tDo9Fg/PjxcHFxQfPmzRETE8MmT9XlcFhhhdLJT8VCIXKJcMbdHY0kEvB4PCQnJ2PVqlXgcDi4NXAg0ni8GmnpriCmzOhXw/06UfWITnKI0J/Hw8CBAxEQEMBmG/v5+YHD4SAsLAz9+vWDlZUVpFIp3NzcIJPJMHjwYHz88cdwdXVFvXr1sG7dOhQuWFCtBKMiwzvc1bo1wsLCWIPM5/PZbOodAkHViUoVLHoOB/tVKrRu3RpeXl6skXyPys+0LyleUpM+NzK4Ga9vTKYrbZyHG64dSOUbZ0sifExlBxwljfOXhvMvpqQgKysLeXl5Zag7q8Kff/6JU4mJGMXhVFoXb6wTL7ntJjECJrvJYJwNfyNm/P+D2Ti/Rdi1axfc3d3x4YcfmmxfsmQJkpOTAQB9+vTBJ126YLdIBH05FIG5HA4K+HzsEgrxYMcOxMXFoU+fPuwH6uXLl0hMTES9evUQEBCAoUOHIiMjA7a2tggLC8OkSZPY+9auXRtubm44deoUu6158+bw8fGBWCxm2zllyhTY2dlhz549CAoKAofDgb29PXg8Htq2bYucnBzcvHkTlpaWWLp0KVxcXKDVajGAz6+R/OVcb288fPgQYrEYfn5+ZT7uEw3HV6alCyJMIGa2qDEYmT8rubcxM3ywpSWsra1N7sfn89kynPbt20MgEMDS0pIl2zBmBYtEIkycOBF6vR7FixZBX5rWsYolhwj9OByo1Wr07dsXo0ePRr9+/aBWq9HG1vYv6SdHW1mBx+MhICAAkZGRiLC0rLCEayKVne1Wp8/ziOBvbY1JkybB0dERSUlJAIATO3fiU3t7FHbtipzYWNyLisIoYlzi79Ar8pV8YurihcQQ1DgRYa9h3zJiaGGVxAwQhMSUU200UHkaeeQlEgmsra3h6uoKf39/1KlTBzExMWjZsiU6deqEHj16oF+/fhg+fDgmTJiAC7VrV0laM5dMByEgQitiQg77jcbZ8Hdrxv8/mI3zW4Q9e/bAxcUFU6dONdnerVs3LFu2DHl5eVCpVOjUqROmT5/OUgQ+a9cO3woE2OfggLW1a8NPq8X+/fvRu3dvtGzZsgw3dnFxMQYOHAhfX182bvrdd9/h7NmzsLe3Z5m+xo0bB29vb6xbt44998yZM2wpzODBgwEAEydOROPGjREVFQWpVAoOh4MWLVpALpfjl19+AQBMmDABMpkMw4cPB4fDwfscTo3JJvRiMeb5+MDS0hLNmjWDg4MDbgQFofg1jVMREe5xOHjJ45WZtedzuUy5kYsL2tjZITMzE6tWrYJYLGZ5tI11skSMYEi3bt3Qr18/EyOu1WoREhICkUjEknm8TltzORwMjYpCdHQ0goKC4OjoyHJi9+fx8KKGfWCk1+RyuRAIBBCLxfjiiy+QFR2NYqqYcKS6cdeSffyLiwuUSiU8PDxQv359xFhZ4Y/ISOgtLVmXfmWG37GcfV8a9vU0tEVkMNoJxMxmf2rQgP3NFhYW4tmzZ3jw4AF+/fVXnDt3DseOHcO+ffuwdetWLF26FFOmTMHgwYPRvXt3tG7dGj+pVJUa57OG+x4ssW0LvXJzs8Y5Pv4f+VaY8b8Ps3F+i2B0G3/yySfsNr1eDwcHB1y9ehVff/01oqKioFAokJmZye5v1qwZunXrBg8PD4SFhWHGjBmYPHkyQkNDWWH50sjKyoKPjw8sLCwQEBCA3r17o6ioCFFRUdi4cSMA4MiRI7C2tsaECRNMzu3WrRuICPXr18eTJ0/QqFEjloO4RYsW4HK5SEpKgkgkQkFBAXbs2MFyFqtUKnDIlDylKqIJEONCjKRXAhSRkZHo3r17pTO96hioSa1b4+KBA5ih1SKrVSsct7HBRpEIh9u1w/6vv4ZSqcSSJUvQtWtXCAQCaDQaqFQqiEQi8Hg8iESiMobDSNDi4uLC7hcIBBCQaYLRRYMBVBiWJoZtxv0zieBvMDYuRBjr6IiMjAycPn0av/32G7Kzs5GdnY3o6GisrFuXyUeowkgbPQHvlxhYGAcZJWuaKyIcqW7c1bjkcbmoLxBgwYIFEIlEGFENnvHSRnEomeYJOJOpW7v0kkqEVCcnbNq0CUuWLMHUqVMxdOhQdO/eHa1atUK9evXg4eEBhUIBHo8HjUYDb29vNGzYEG3atEGvXr3ws69vhcb5OhHsiEnMK/lb8iBGEczEOJtnzv9vYTbObxH27dsHe3t7fPrpp+y2W7duwcbGBnq9Hq1bt0bHjh2RkpLC7v/qq6/g5+cHa2trdOrUCW3btsXKlSvh4uKCBw8elHufX375Ba6urhg0aBAWL14Ma2trhIWFoVu3bli3bh2io6MBAEVFRZBIJIgvNfq/ffs2+1FXKBTw9/fHwIEDERISgmbNmoGI2MxuBwcHeHt7w9raGh4eHli2bBmaUVkWqMqIJv4wGI6vDAZhPZ/PylQSMWQdNTXQeQaBiZ1KJQ6rVFjH42EUlwt/Q4zcqNqlUCigUCjA4XAgEonYJDatVgtnZ2fWU0DEME1xuVwIhUJIJBLW6PH5fMiJyhBsPCHG/WvMBP+UmHipcf8MYgYlhUS4QszMcP2SJWXe54sXLxAbG4uBDRrgUUQECgWCclmsconwrViMEY0aISUlBb6+vrCzs4O/vz/EYjGGU9m4f1Wu3fLiriUNViq9GgCM12pfi/UsmJisciP5DpeYWev0Cs7vQ4TGMhnat2+PPn36IC0tDZ988glWrVqF7du348iRI7h69SqysrJMxSpKYsYMjOXxyjz7b8QMDj4vtf00Efgl2qg0tNNGIsGtW7dq9iEw461A5UWPZrxR4PF4VFxcbFLnfPDgQYqKiqLMzEz68ccfSSaT0fbt24mIKCsri4YNG0YuLi7k4+NDp06dopkzZ9L7779PBw4cIJ1OZ3J9ALR8+XIaM2YMLVq0iDp37kxERDqdjvr06UNERHl5eXTt2jU6f/48BQYGUmRkJJ0+fZq9xrlz52jWrFlERMTlcqlv375UVFRE9vb21KZNG5ozZw4REV28eJFq1apFX3zxBU2bNo3y8/PJycmJpHl5VIuIHpVol5Fogqh8ook5RNScGMIMIqK2RUU06Plz0ltZ0YABA6hhw4b0y6ZNFLZ+PVlWcA0jiomxFjyAmhGR2ECI0YAY0pYPHz+m/UIhzbC0pJtqNQGg+/fvk1gsptzcXAoODqb4+Hg6fPgw/fzzz9SuXTv64IMPKDQ0lLhcLuXk5NDUqVNp2bJlNGnSJGratCmtWrWKbL/6ijL/+MPkuRVkSqDBI6IbJfaPLPF/byJqw+PRrk8/pRc8Ht2+fZtdfvvtN3rw4AH9xOXSlyIRJbRoQQnPnpFHXh4piChfKKQVJ07QYU9POnTlCi1MTCTr7GzKysqib7/9lp4/f07NmzendqdPk/i33yrpvbI4SET+pbbpiakPX+LpSdmhocTZsIFIr6ebf/xBVoZjjhHReCL6xfDcMcS8Z63hHRUQUR8i2m74fx0imkkMcUwdw7EtDNfaRERxxNRT/0BE6US044svKKZduxo9ixFFRUVU1LUrFY8Zw5DjEBGfmN9sYyLqTwwBUEkEEFNTbsQRIhpARKeOHiWto+NrtcOMNxz/9ejAjL8PP/30E7RaLZYvX85u6927NxYsWIAFCxYgMjISDRs2ZPelpKQgKioKgYGBUKvVSE9Ph1arxaFDh8pc+8WLF+jRowf8/f1ZXd2SOHjwIBsf9fb2Zqk6V61aBS6Xi71796J58+awtbXFxx9/DBsbG/D5fCgUCiQkJCAiIgJyuRxETB0wh8NBRkYGsrKyIJfL0b59e6xZswbpoaFlKDdLLvYLk5s4AAAgAElEQVTlzJwbEVNLW98wg25BTIKUkZ7ROHOtw+FUqPz0gpgZeiFVLwEtj8vFZFtbcDgciMViSCQSpKWlITw8HC4uLpg9ezaePHlS4bu8cuUKmjVrBj8/P+zbtw/o1q3CWaicCDwicIjwUQVt0hOhFhE+kErRo0cPTJgwAStXrkRGRgZu3LiBly9foqCgAF26dEFsbCybYX/nzh1s2LABHTp0MNGaTkxMxIwZMzBr1ixIpVL07NkTpx0dq5zFllzKi7uCCA+5XNQpVerVnEy9JeW5x92pbGx5GDEJZe/QK31qZzJ1a0cQkwwmJUIQEdbXqfPaf4MAk0NRuh0TiVEsIzIVcLGqoG/2k7nO+f87zMb5LcLRo0ehVquxZs0adpunpyfOnTuHunXrIigoCOnp6QCA/fv3Q6fTQalUws3NDZ988gns7e3ZeHFJXLt2DUFBQejWrRv70S4P586dg729Pfz9/cHn83H79m0sX74cRARXV1esWLEC+fn5AAAvLy8oFAoIBAJW6ergwYPg8XhsQlReXh4WLlyIrl27wt3dHZcuXcI2mazSD355xtnTYMBOGD7UHxAh2JAB7eHhgfDwcHz44YeQyWSQSCSI9vPDHDs77NJosE8iwW9RUdhdDZ7q8tyyH9nbQ61Ww8bGBtHR0diyZQuKioqq9T71ej22bNkCZ2dn/GxrW+lz5xBhERF2VrB/gsHw7Fcq0apVK3Tu3BkpKSkYMGAARo0ahcmTJ2PGjBkYPnw4nJ2dIRaLIZVKIRKJ4OzsjMDAQFbq02hwXF1d0aBBA9StWxcikQgHnZ2rbZzLi7sal3V8Pvz8/NC0aVM0adIEjpaWlQ7IQGXd4+8RQ7BiXN9JTP1zle9NLAZOnqzBX10lOHGCuV4Nfzd/ezvMeCNhNs5vEU6cOAGlUon1Bvm5+/fvQ6VS4dKlS1Cr1bCzs0NBQQHy8vLg6ekJd3d3hIaG4p133oGfnx/mzJlT5pqbN2+GVqvFZ599Vq16z1u3bsHDwwNCoRB8Ph/169eHlZUVJk2ahOLiYnz//ffo2rUreDwepFIpNBoNBAIB5s2bh2+++Qa2trbsDDo/Px8hISHYvHkzpFIpXrx4gR0cTo2NcxAxWbnG9UyDcVGpVJg/fz4mT57MZp3LZDI0adIEWq0W8+fPR2FhITK//Rb5pWKwNTHQY5o1w+nTp1/7vb548QJnAgKqjN8WE6Mk9qjU9gXEJIT9ToTfGzXCZ599hrFjx7KCIzY2Nmz83bgYPQoikYglf+Hz+WXIS3g8Hqs7PYrLrVLkAlRx3BVEKLKwwO5GjRij7OgICwsLDKeyAiWll9JlSSeJITa5R8zMOpEYHeoqDeLfLTrx2Wc1N9Bm8QszYI45v1Xg8Xik1+tZ4YtDhw5RREQErV27luzs7Khjx44kEAjoo48+Ii6XSwKBgAoKCuj27dvUrFkzGjJkCHutwsJCGj16NG3atIl27dpFderUqfL+jx8/ppUrV9Kff/5JfD6fioqKiIjIw8ODVqxYQStXriSlUkm9e/emx48f082bN2nq1KnUq1cv2rdvH4WGhpK7uzsdOXKELCwsaO3atZSZmUkCgYBcXV0pNTWVmgE17pcgYjitjTD+f+vWrbRixQo6ePAgZWVlkUajocLCQvL09KT09HRasWIFOTg4UNajR5REjICFEblENJyIviaiQmKEGw4a9n1IRFOJyNJ4cEYG9ZbJatxuI8RiMQUlJ1N6Whrz+a4AekO77hGRtWHbSiKabmibiogm7t9Pcw8eJL1eTwCIy+USALK0tCQ7OzvS6XRkY2NDGo2GLl26RHfv3qVhw4aRq6srqdVq0mg0tGzZMvr222/pt99+oyZNmtDcuXPp+fPnNKZPH+JdvEik11MRERURE/+tbtyViKigoIB67N9PuVZWZGVlRfb29hSZlUUnnj2r8LnPEdFkItpWYpsXETkRkT0xMelAIlpYSb9xxWKiWbOI+vWr8D6vBeP1hg8nysur9P0Rh0MkEv0z7TDjzcN/PTow4+/DmTNnIJVKsX37dgBA//79MXPmTDg4OEAqleLBgwe4ePEi5HI5FAoFVCoV4uPj0aFDB5Os03v37iEiIgItWrRgS64qw7Vr15CamgqlUonU1FRcvXoVf/zxBzujMmru/vzzz+w5SUlJsLGxQXFxMeRyOSwtLdlsciKGQ9nJyQnu7u6wtLSETqeDv78/BhPDBFWSYQrEEE3kGWbO3xn+rzfsyyCm1Og0EQqI0J8IrgIBHB0doVaroVQqYWlpiYiICJw+fRpPnjzB+PHjIZFI0DYmBqlcbplZWzdiyCseExOD/rnEvolUSidbKHwtGsbCwkI8evQIGzduRISXV5nn3kuEU4b7ZxPjrrc17Acx2ek2xPBhw7A93qC9/dVXX+H8+fN4+PAhW5deGnq9HhMmTICPjw/u3r1rsr1Xr14IDAyEQCDA6NGjAQCPHj3CbqEQxRxOhXXHH1LFcdciIjxt0gSFhYXIzs7G/fv3cf36dTyNiqqxezyJGBrOLMNvYzIR6pY+XyTCSx4P14OD/3kX8smTQEIC81soTSIjEjHbExLMrmwzWJiN81uE8+fPw8rKCnv27AEABAYGYvHixdDpdEhKSkJxcTHCw8OhUqmgVquRkJCAhg0bmmgx79+/H7a2tpg8eXLFZSIGHDt2DAkJCdBoNBg3bhwePnyIs2fPYuDAgWztp0KhgFqtBofDwU8//cSe+8EHH0AulwMAoqKiYGlpCbFYDJ1OByJiXaifffYZWrdujdWrV7MJSaU/+KBXNc4ll1slPoCfGT7iCiK04nDgaBCcMLppO3fujJs3b2LKlCnQaDTo2bMnbt68WW5JzBVikoeyK3BLljHOIhEKP/4Y9+/fx/nz57F//35s2rQJixcvxtSpUzFo0CAkJCSgfv368PDwgFqtZpPiyuPANj7318SwalkRQ+jRgpgkK+N9XYgpz2GNII+H1NTUGv+upk+fDnd3d5OSnsLCQsTHxyMwMBB8Ph+rV68GAJxZtqzGsXnj8lIgwIxOnco2oIJkuN+oYve4PxG2llh/Yui3Pzp1Yog9kpNRPH06fNRq/PbbbzXuk9eGgfgHyclsOzBzpplD24wyMBvntwiXLl2CSCTCvn37kJWVxWbRqlQqHD16FEuWLIFWq4WtrS2aNm0Kb29vdmZcXFyMjz/+GDqdDnv37q3wHsXFxdixYwciIyPh7OyM+fPn4969e/j8888RFhYGBwcHjBs3Dr/++ityc3OhVqvZ2bBGo8H9+/cBAGlpabCwsED//v1Nanp1Oh20Wi2kUim4XC7y8/Ph7OyMgQMHgsvlQiaT4VuR6LX5oIsNXNw2NjaQyWSQy+UYNGgQatWqBQ6HA1tbW8ycORPPnj1jHrgcw/AFMRSRg4mpny2toDSRmOxfJRH8DAODNfRK8MLe3h52dnbQarXssysUCnh7eyMmJgY9evRAhw4doFAo0KZNG5w7d45JIvsLCUYvOBx8GB+Pp0+fvtZva/78+XBycsK1a9fYbS9evEB4eDi8vb0hEAjYLP/vO3RALpdb4zjrn1OnQqlU4vnz59Dr9fj5558xZswYTLexKeM1uEsEN2KIVsq7Xk9i2L6eEuMt+ZAIdjKZyTMdPnwYgYGBr9UfZpjxT8NsnN8iXL16FUKhEIcOHcK2bdvQpEkTSCQSBAUF4d69e5DJZJBKpazE3c2bNwEwRP2tW7dGeHg47ty5U+618/PzsWLFCvj6+qJ27dpYt24dMjIykJycDLlcjo4dO2L37t1lMpFHjBiBoUOHgs/ng8vlQi6XIyQkhJ0ZzpgxAxERERg6dCg4HA4sLCzg6+sLgUAAe3t7bN++HVKpFFKpFCqVChqNBvW43L/E6hVtZYWOHTuiadOmiIqKgq2tLTp06IDjx49j7dq1iI+Ph0wmQ6tWrXDO2bmMcZ5Kr2avL4lwgJiZqdF9fJGYRKQiYmQZdUQYLxIhISEBgwYNwieffIL09HQcPnwYt2/fNnErnzt3DpGRkQgJCcHRo0dRWFiI06dP47PPPsM777yDcRpNjWem+TweMqdMQWpqKpycnJCRkfFav6/ly5fDzs7ORD4xMzMT3t7ecHJygkgkwq+//gq9Xo/FtWohn8+HvipaUA6HTYB6+fIlwsPDERMTAwcHB3h5eaFBgwbleg0qc4+DmKS/JGJK5+TEJIcdN3iUjBg9enQZkRgzzPhfgdk4v0W4ceMGLCwscPz4cQwdOhRdu3aFSqXC6tWr0aZNGwiFQjbWfNIQ2zp16hTc3NwwcOBAvHz5ssw1nzx5gunTp8PW1hbNmzdHeno6pkyZAnd3d/j7+2POnDl4XI5LTq/X48KFCxg/fjwEAgE7MxYIBFCr1Zg7dy6ICHq9Hs2bN8fgwYPh4OAAIoKLiwsEAgHq1auH5ORkaLVaNGnSBCqVCmKxGBwOB/15vBoLNuQQYZxGg71796JTp04QCASoW7cuJk6ciAkTJqB79+6IioqCk5MTq3y0hspmHM8hhgK0sMS2eCLMq+C+HxMhwSCdWRGys7MxZMgQaDQa9OvXD2lpaWjUqBE7mEpJScGyZctw4cIFFC9axBi0Kp5fz+FALxJhQ0wMdDod0tPTsWvXLtjb22PgwIF48eJFjX9ja9euhU6nMxEzuX37Nuzs7KBWq6HRaPDkyRM8ffoU7RwccDssDMUlOLDZxRBnfdm6NfZMmYKuXbtCoVDAx8cH9vb2ZWvp27cvV36yut6SM+7uZZ4lICCA1SA3w4z/NZiN81uEW7duQSAQ4NSpUwgLC0Pt2rUhk8mwefNmtiRGpVJh165d0Ov1WLZsGTQaDVv7XBJ37tzB0KFDoVKpkJSUhDlz5qBVq1ZQKBTo27cvjh07Vqa06t69e/jiiy+QnJwMW1tbuLi4oG/fvggJCUFoaCgCAgIwcuRISCQSKBQKEDHlUo0bN0ZCQgISExNhjDc3a9YMLi4u0Ol0kMvliIyMhFgsZmdPCoUC05ycUGhhUS3pRGPNsaenJztQMFKH1q1bl63XdXFxYcuK+Hw+RlDZMp4famicp/P5aB8QUKaPi4qKcObMGaSkpEAkEkEmk8HKygpNmjTB+PHjsXv3bmRlZZX/sitJMCoWCvGSy8VukQj7Zs6EXq/HkSNH4OvrizZt2uD8+fNITEyEl5cXjh07VuPf2ebNm2FtbY2jR4+y286dOwe1Wg2xWAxfX1+8fPkSZ86cgUajwZVDh3Cic2dsUyhQ1LIlchIScLhdO3SKiYFUKkXLli2xdOlSPHjwAEVFRXBxcWEHjyxOnMBLgeC1jHM+n49NaWkml7t16xasra2rXXNuhhn/NszG+W3Ao0fAjBnIad8eOzgc/BEXhzF8PuwEAgwcOBAqlQoWFhZQqVRYunQpXrx4gZ49e8LPz6/MDOXcuXNITk6GUqlE9+7d0bdvX1hbWyMyMhKrV682ISF59uwZdu7ciUGDBsHPzw9KpRIdOnTA4sWLcePGDfa4PXv2QKfTITY2Fj179sTBgwdhZWUFIsKRI0cQGRmJ2rVro0OHDqzx3bZtG2xsbEBEGDRoEIRCIRo3bswmSA0ePBgqlQo9AwIYHWAOp1xWr1wibOFw0FythkAgYHWAraysEBQUhFatWuHdd99F165d4ezsDGtra7i4uMDOzg5Tp07F/bNny2g+FxDDRjXZsP4TMQQYlw333UqMjKSeCMeJSURbPX8+/vzzT+zevRvjx49HbGwsrKysIBKJoFKpMHLkSJw9e7bmxqKSBKOMjAz4+fmhWbNmuHLlCvLz8zFhwgRoNBosXrwY69evh7W1NcaNG1eu16Qy7Nq1C1qtFgcOHGC3/fjjjyyxTFxcHPR6PVauXAlvb28cPXoUvr6+0Ol0UKlUSE5OxqZNm8oVVpk2bRrLMFcSlwcNeq1Y9iwPjzKu/Pnz56Nnz541emYzzPg3YTbObzJOnADat2dmT0KhyUcpl8NBLhGO2dujLocDmUyGsWPH4vr16wgKCkJSUhL7YdTr9cjIyEBcXBxsbGyQkJCAOnXqQKfTYdSoUbh69SoAJkP3yJEjmDRpEiIjIyGRSNCoUSNMmzYNJ06cqNCwFBcXQ6fToU6dOmz51HfffQcigkQiQWBgIORyOXx9fVmj3bVrV9SqVQtExLrktVqtSezRaGh5PB40RBjJ5WINEbYRk7Q1nBgdYK1WCzc3N0yfPh1xcXHo3bs3AEabesWKFfDw8ICTkxO0Wi3q16+PDRs2oKCgoEIaRhDhAhHCiSAmgi8xcn/Gvu9KDBmIFTHZ1MOVSvj6+rL9NWzYMLRr1w5qtRoLFy78R2dvBQUFmD17NtRqNUaNGoXnz5/j/PnzqFu3LqKjo3Ho0CG0atUKtWvXxvnz52t07YyMDGi1WrY6AGBm1UqlElwuFx06dMCQIUMglUohFovRt29fqFQqho60Ejx48AAKhaJM8lpOTg4+EAiqpZ5VMpat0+nw+++/m1yradOm2Lx5c42e1wwz/k2YjfObCiPzUDUl/paFhmLLli3QarVYtGgR9Ho9CgsLkZ6ejpCQEDg5OSEiIgIKhQJt27bF9u3bUVBQgMuXL2PBggVo27Yt5HI5goODMXz4cOzZs6dGMctRo0ZBKpXC19cXJ0+exB9//MG6ljkcDng8Hng8nkl5k3EpzV5FRKyOMJfLBY/Hg7e3N4KDg8HlciGRSCCRSGBvb4/atWtj586d0Ov1+PzzzxEcHIzMzEzMnTsXOp0Ojo6OsLKyQlJSEk6cOFF+40+cYAzC67hUeTx8PXIkTp06hYKCAqxduxZ2dnZISUnBo0eP/qYfQ9W4f/8+3nnnHTg4OGDDhg0oLCzE3LlzoVarMW3aNCxZsgQajQYzZ86s0WDh8OHDsLa2xtatW5GTk4MtW7YgPDycfYfx8fE4duwYgoKCsGjRImzfvh2urq6vsuErQKdOnbBo0aIy20NDQ3F62bJq1wxnZ2fDysrKpCzw2bNnkEgkVbbBDDP+S5iN85uI16AEfMnnY7RSiePHjyMnJwcLFiyAk5MTXFxc2MzYGTNm4Ny5c1i7di169uwJBwcHODo6olevXli3bl2NjEleXh6uXr2K7777DkuWLMF7773HGmOhUMjWLEskkjKGV61Ws/usiZDG42ENEX4QibCWw8FIDgd2AgE4HA6srKwglUpZikmJRAIejwcnJyds2bKFjYufPn0aKpWKra+2sbGBQqHAuHHjcO/evUqfJTs7G/P9/JBXQ5fqCyLM9/PDmjVrcPz4cURHR6NWrVo4fPjwX3r9fwUHDx5EUFAQGjdujIsXL+LmzZto2rQpateuje3btyMqKgoREREmYYnK8OjRI4wbNw4WFhYQiUSIjY3FggULMGjQIGi1WvB4PHz//fe4fv06tFotjh8/jt69e7Pei4qQkZGBwMDAMnkNAwcOxPTp05mVEi79vUIhnrdvX6Zm+OTJk6hVq5bJNTZt2oRmzZpV6/nMMOO/gtk4vyFYsGABQkNDYSEQoAeP98roEqEDvSLh2F/KQOiJSWhSGZbYgABIpVLY2tpCKpUiOTkZs2bNwpAhQxAUFASFQoF27dph4cKFuHr1aoV82rm5ubhy5Qr27NmD+fPn491330WjRo3g7u7O1iiLxWJYWVmxsd6S+sajR48Gl8vFpEmT2Ji4kcu5W7duaCKTYTMxcd6KYsmbiVDHMLOuX78+W641bdo0k5nStWvXoFAoYGFhAblcDk9PT6xYscKEfKUi3Lp1C35+foiPj8eOVq2Qx+VWXWNtcKnmz5uHFStWwM3NDRwOB7Vr18amTZtY8Y//CoWFhZg/fz40Gg2GDh2Kp0+fYvXq1bC2tsbIkSMxffp0qNVqfP755+W+/6tXr2LmzJlo0KAB5HI5OnfuzCqNrVq1CgATKunTpw/7bq9cucKKeNy6dQuurq7Ytm1bhW3U6/Xw8vIqM5DZsGEDWrduXeZ4f39/nDt3rsz2tWvXonPnzibbevTogQULFlSnq8ww4z+D2Ti/Idi8eTO++eYbvOfqapI5/JIY0v9DxNTTljbOi4lR4/mdCLeJ4EAErVaLdu3aISIiAhKJBFFRUZg8eTJbVwswxvfy5cvYunUrJk2ahMTERNSrVw+Ojo4QG9i1jGIIXC4XKpUKPj4+aNasGfr374+FCxdi+/btOH36NDIzM6HX6xEdHQ2lUgmFQoGHDx9CJBJh9erVkMlkUKlUEAgEICIMEYlQaGlZrSzsF0SY6ugIS0tLWFpamrBY3bhxA0lJSazru2nTpti3b1+lAh56vR5Xr17F6tWr0bZtW/D5fFhYWKBBgwYYMWIE9s2cibyWLat0qepPnMD69ethb2+Pnj174tKlS1iyZAliYmKgVCrRq1cvfP/99/9ptvCjR4/Qq1cv2NnZ4csvv8SDBw/QqVMneHp6YvXq1QgNDUVcXBzu3LmDo0ePIi0tDT4+PrCzs8N7772Hb7/91mSgceXKFTg4OLDuaCOLmJHsJTMzE8OGDUOLFi1w4MAB6HS6csvwjJg9ezaSk5NNtt29exdqtbrMO6xfv74JA50REydOxLhx49j1oqIiaLXaf5cVzAwzXgNm4/wm4dGjMlSSJZfyFJnqE2FJifXPiSAVCtG/f38sWLAAixYtwpAhQxAfH4+goCDY2NiwBCHG+K9EIoGzszPq16+Pbt264aOPPsKWLVvwyy+/4PHjx9VSqwKA4cOHw9XVFXEhITjZqRPSBQLc8PXFVxwOxlpYwFEoRH8er8YEI7mGuueDBw8CYDjGY2Nj2cGDUqmsMNnp+fPn2LdvH6ZOnYr4+HhoNBo4OjoiPDwcVlZWmD17dvmZzJVkSV+8eBGNGjVCcHBwuQbj7t27mD17NkJDQ6HT6TBo0KByS9P+LRw9ehQhISGIiIjAmTNnsHXrVtjZ2aF58+aoVasWuFwuHBwcMHr0aBw/frxSWtebN2/C1dUVs2bNAsAM8urVqweRSAQ3Nzfk5OQgIiICU6ZMwYgRI9CuXbsKnzszMxNyubxMOZmzs3OZKoO4uDjs2rWrzDUSExNNJFTNrGBmvCkwG+c3CeXwPFdlnGVEOFZi/RAxNbrG+K5QKISNjQ0CAwPRqlUrDB48GMuXL8fx48fx4MGDKvm1a4KtY8fiR7Ua+RwO8kvFb3M5HOSTae1wTROvfl68GLVq1YJAIIBKpcLgwYOhVqtx6dIlAMys+MaNG/jyyy/x/vvvo3bt2hCLxahfvz6GDh2KjRs34vfff8eHH34IZ2dnnD17tkbP9+zZMwwfPhwajYaVm6wKV69exYcffggvLy+4ublh7NixuHjx4mv1719BUVERZs+eDZlMxoYmdDodZDIZ0tLS4Ovri06dOuGPP/6o8lq///47vLy8MHnyZOj1emRlZcHT0xN8Ph9RUVG4e/cubG1tsXv3bgQGBrKu8PLwzjvvlJEy7datG5YvX26yrXPnzqxUakmEhITg+PHj7HpaWpqZFcyMNwJm4/wmoQIBgMqMM5de1d+CCNcMRvnOnTv/rkv1s89QVIGregERQolgUerZjhIhlhiOag0ROhLhfon9E8lU2EFIBFdXV2zcuBHZ2dnw8fHB6NGjMX36dLRt2xbW1tawt7dHx44dMXv2bBw5csTELZuXl8e67x88eFDtR9Pr9UhPT4e9vT26d++Ohw8f1rh79Ho9fvnlFwwbNgz29vYICgrC9OnT/3H362+//YZPP/0UjRo1gkwmQ4sWLRAdHQ1ra2usXLkS+/btg4eHBxISEpCamgpbW1vs2LGjyus+ePAAAQEBSEtLg16vx507d2BtbQ0ul4vevXvjhx9+gK2tLfbu3QuNRmMSjiiJn376CV5eXiaz688++wwpKSkmx/Xt2xeLFy822abX6yGRSPDnn3+y28ysYGa8KTAb5zcJ8fE1Ns4yYogwjOs/E0HC4/277a4iu3wzEb4hwnulnm03McpL2cTEllOI0LyUcS6p/lQkEGDz4sUYMGAA1Go1eDwe6tati0GDBiE9Pb1C3nAAePjwIcLDw9GlS5dqJYoZcenSJTRu3BhBQUGs8MNfRXFxMQ4cOIB3330XarUaDRs2xKJFiyqNz1YXer0ep06dwoQJExAcHAytVouUlBRs3brVpDTu5MmTqFevHsLDw/HTTz9h1KhR0Gq1GDVqFFxcXNC7d29kZ2dXeq/MzEyEhIRg4MCBKC4uxoULFyCTycDlcjFr1ixMmTIFDRs2xNSpUxEdHV2ul0av1yMgIMCkNvrs2bPw8vIyOW7YsGGYOXOmybb79+9Dq9Wy62ZWMDPeJHBrpv5sxn8KubzGp/gT0dkS62eJyF+p/LtaVDVOnmSE5nNzTTa/Q0S2RCQjojQiyiQidalTWxBRJ8MxYiIaQESHK7lVQWEhPV+wgB4/fkxSqZQePnxIx48fp3nz5lGXLl3I0dGx3PMuXLhA4eHh1KxZM1q3bh2JRKIqHysnJ4dGjhxJUVFR1LZtW/rll18oIiKiyvOqAy6XS9HR0bRkyRK6f/8+paWl0eHDh8nT05NatGhBa9asoWfPnlX7eoWFhZSRkUEffPABubi4UOfOnenFixe0cOFCevDgAa1cuZLatm1LYrGYPScsLIyOHDlCffv2pQ4dOlB2djalp6fT3r17ydXVlXJycig4OJgOHDhQ4X3VajVlZGTQyZMnKTU1lXx8fGj37t0kFApp5MiRFBAQQDKZjDIzM6m4uJjmzZtX5hocDodSU1NpyZIl7DZ/f3969OgR/fHHH+w2uVxepk+uXbtGXl5e7PqOHTuoZcuWxOPxqt13Zpjxn+G/Hh2YUT0UFhYib8qUMlSSIEZMPs8wc/7O8H89vUoA8yFGYu8eEfw4HHzevv2/1/D27cslSrlgaDcMbncbIvSqxCsAYrLS65WaOZeWZnzSujU0Gk212a6MNJRfffVVtY7X6/XYsGEDHBwckLKyZyUAABcfSURBVJycXCP3919FTk4O1q9fj9atW0Mmk6Fjx47YsmUL8vLyyhz77NkzfP3110hKSoJSqUTdunUxdepUXLx4scaJZ3/++ScGDBgAa2trLFq0CNOmTYNarUafPn1gZ2eHwYMHV+pteP78OWJiYpCUlITCwkJs3boVQqEQfD4fP/74I5ydnbFo0SJoNBoTxSsjnj59ymb4G9G8eXNs3bqVXZ83bx4++OADk/OWLFmCXr16setmVjAz3iSYjfMbgsqoJJ1LbSci3DLs0xNhhMGAKYkwgseD/t9ipnr0qAytaHnLFWLKwNpXYpzPGtp/sMS28qQZx1lalkkWKg96vR6ffvopdDpdtUlBLl++jCZNmiAwMBA//vjjX+2dv4SsrCwsXbqULc1KSUnB+vXrsWjRIsTFxUEqlSIuLg6LFy+ukmSlujh9+jQaNmyI0NBQbNy4EdHR0QgJCUHz5s3h4+NTVqyiBHJzcxEXF4eEhAS8fPkSixcvhqWlJcRiMfbs2QOtVoupU6eiVq1a5WbH9+7dGx9//DG7PnnyZAwfPpxdX7VqFXr06GFyzrBhw1jCkuzsbEil0nK5vM0w438RZuP8pqGCmWi1Fg6HoTX8tzBjRqXGuR8RRIbBRG3DIKI843ydGPGINVU838dEiBKLq5wZFhYW4v3334efnx+raV0Znj9/jlGjRkGtVmPevHnVysL+N6DX63Hx4kWMGjUKTk5O4PF4EAqFaNGiBX744Yd/pDRLr9djzZo1sLW1RUpKCmbNmgWNRoOEhARotVpMnDjRRJ+6JPLz89G+fXu0bNkSubm5rJyora0t5s2bh6CgILRo0aLcbOqTJ0/C1dWVjUtnZGSgfv367P7NmzejXbt2Jue0bt0aW7ZsAcCwgjVv3vzv6gYzzPjHYY45v2kYPZqoGjHRciESMef/Wzh3jig/v8LdnxHRcyI6REQJRFReJPA2EcUS0XgiSq7idkVEpHB2Jg6HU+ExT58+pVatWtHNmzfpyJEj5OrqWuGxAGjjxo3k6+tL9+7do/Pnz9OgQYOIz+dX0ZJ/DsXFxXTo0CEaPnw4eXl5UVxcHOXm5tLKlSspLy+Pzp49S+Hh4dS/f3/y8PCgsWPH0sWLF/+2+3M4HEpOTqYrV66QQqGg6dOn06BBg6igoIDkcjl99913VL9+fbp06VKZcy0tLWnDhg0kl8spPj6eRowYQUlJSfT48WNas2YN+fn5kVwupxUrVtCRI0dMzg0LCyOlUknff/89ERHVq1ePzp49S/mG35dMJqs05rxjxw6Kj4//2/rBDDP+cfzXowMzXgOvwa1tVOj5VxEfX622FRKhNzFlUyXj6XeJ4EaEmRWcV5E0Y0X49ddf4evriwEDBlQ5+718+TJiY2MREBDwn7uwX7x4ga1btyIlJQVarRbBwcGYOHEiTp06VeHs2FiaNXz4cNjb2yMwMBAff/xxhSVLr4sLFy4gJiYGwcHBmDRpEmxsbNCoUSOoVCrMmjWr3MzooqIi9OrVCw0aNEBWVhZiY2PB4XDQoUMH+Pr64v3334e7u3sZF/TSpUtNZsehoaFshvyJEycQGhrK7isoKIClpSXy8/PNrGBmvJEwG+c3FdVUpSopnfevo1u3ahnniVQ2Zj6RCB8a/m9VajGeV1qa8dOgoAqbcujQIeh0uio5lXNycpCWlga1Wo05c+ZU6KL9p/H48WOsXLkSbdu2hVQqRaNGjfDpp5++lnEtLi7Gjz/+iNTUVGg0GjRo0AALFy7821SxjHXeDg4O6Ny5Mzp16gQ7Ozv4+/sjKiqq3NBBcXExBgwYgNDQUNy9excBAQHgcDjo168fNBoN4uPjkZqaanLO8+fPoVQqWfnHkiIYV65cgaenJ3vstWvX4OrqCsDMCmbGmwmzcX6TcfJktaXz/hNUEHN+RIT1RHhuSObaQ4wu8tbXiaMbFr1YXOFzrlmzBlqtFt9++22FTdXr9di4cSMcHR3RrVs33L9//5/qlQpx/fp1zJo1C5GRkWw29pdfflmGvvKv4OXLl9i5cye6desGuVyO5s2b44svvqiyZrk6eP78OUaOHAm1Wo3U1FQ4OTkhJCQEarUaS5cuLTPL1+v1GDlyJAIDA3H16lXY2tqCw+FgwIABcHV1hYODQxlKzvfffx8ffvghAODrr79mRTAePHgAGxsb9ridO3eyMWYzK5gZbyLMxvltQCU8z/8pKsjWfkyEKCLIiSAlQgARlv4VwywSlesZKC4uxtixY+Hi4lJuiY4RV65cQdOmTeHv748DBw78kz1Spn3Hjx/HmDFj4OfnB51Oh3fffRe7du0qtzzq74axNKtNmzbsYGDz5s1/+d6XL19G06ZN4evriw4dOvxfe/ceFWW9rwH8GQYQkJsOzNAgCF7BE1ourKjNUgkkSFO00mO6wG2pZam1NQNpr4O11LxgKuo+2UVP5sHykqRS6vG2Vmpq5mUXW0ktRVupiRU3UeY5f0zOBi95HRjq+azFWjDv+xvelzWLZ37f+V1oMpkYERHB1NTUK9702Gw25uTksH379ty5cyd9fX3p5ubGfv36MT4+nlartc6Sofv27WNoaCgvXLjAEydOODbBKC8vp5eXl+O83Nxcjho1iqR9x6rt27ff1j2J1DeFszjXbYwut13n+EWAF728rhrM5eXlfOKJJ/jggw9es3xbVlbGzMxMmkwmzpgxo15K2FVVVSwsLOSIESNotVoZHR3NV155hdu3b7+j65jfrJ9++okLFixg9+7d2axZM2ZkZHDdunW3PDLdZrNx+fLlDA8PZ1JSEtu0acO2bdsyKCiIS5cuveL8adOmsVWrVly3bh09PT3p4eHBmJgYdu3alY8//nidXndcXJxju8mIiAgWFRXRZrPR3d3dMQ1r+PDhzMvL45EjRxgcHKxVwaTRUTiLc+3cefOD1y6Fs5sb6el5Rcne5u3NKoOBxR07XrWUffLkSXbp0oVPPfXUVXuBtYNj4MCBd2we8LWUlpY69hUOCAjgQw89xKlTp/LgwYNO/b23qqSkhLm5uYyNjaXFYuELL7zA7du339LUrPLycmZnZ9NkMjExMZF+fn60WCzs37//FeX6vLw8hoWFccmSJTQajfT393f0umsvErNo0SKmpKSQrLsJRvPmzR297O7du3PdunWcPXs2MzIybvVPIdJgFM7ifLcwurzcYKBt3jzy1CmWZmUx39OTFYmJ5ODBXPngg8x49NGrhsXevXsZHh7u2BHpcgcPHmRycjI7dOjATZs2Oe2Wv//+e86ZM4cPP/ww/fz82KtXL7799tu3tClGQzp06JCj7BwZGcmsrKwbXn2ttuLiYqampjIyMpLt2rWj1WqlxWLh2rVr65z3zjvv0Gq1cvr06TQYDLzrrrsYHBxMk8nkWBu9oqKCJpOJR44cqbMJRmRkJA8fPkySDA0N5XfffadVwaTRUjhL/bjB0eUXAZYB/DAhwdF0yJAhzMzMJGlfbCIyMpKlpaVX/IqCggIGBQUxPz//imNlZWXMysqiyWTi9OnT73gJ22azce/evczJyeG9997LoKAgpqenc8WKFSwrK7ujv6shXNowY+zYsWzRogVjYmI4adKkmx49XlBQwMjISHbs2JG+vr4MDAzk0KFD+csvvzjOWbJkCS0WC0ePHk0AjIiIYKtWrZiQkOAo/Y8ZM4aZmZl1NsHo1KkT9+zZw19//ZXe3t4sLS3VqmDSaCmcpf7UGl1ecXlPGWC10chVHh78i5eXY2DWgQMHaDabee7cOcfnh7X35yXtwTFjxgxarVbu2LHjimMrVqxgeHg4BwwYwJKSkjt2OxcuXODGjRs5atQoR4C8+OKL3LJli8usIuYMl6ZmjRgxgkFBQYyLi+OcOXNuuCpQWVnJnJwcBgYGMjIykoGBgbRardy6davjnJUrV9JsNvOxxx4jAFqtVoaGhnLWrFkk7YPOLBYLKyoqGBAQwB9//JHx8fHcvHkz9+zZw5iYGH700UdaFUwaLYWz1L9Tp/iPNm14vHt3rgK40s+PrxiNHN63L41GI318fBzh1rNnT86cOZPnz5/nfffdx9zc3DpPVV1dzWHDhjEmJuaKRSYOHTrERx55hNHR0XW2HLwdv/76K5ctW8ZBgwaxefPmjI2N5WuvvcYDBw44ZblMV1ddXc01a9Y4pmb16NGD7733Hs+dO3fdtkePHmWfPn1oNpvp4+PDpk2bcvTo0Y5xAoWFhQwODmbnzp0JgL6+vvT39+c333xDkuzWrRs//PBDJicnc+XKlezZsycLCgqYn5/Pfv36MT09nXl5eU69fxFnUThLgxg5ciTffPNNAmDr1q3p4eHBTp06EQDTfts1a8uWLYyIiGBVVRVfeukl9urVq04Anj17lgkJCXz00UfrlEXLy8s5YcIEmkwmTps27aobKdyMH374gW+99RZTU1Pp5+fHHj16cO7cuY7FMMSuvLyc+fn5jqlZ/fr147Jly647NauwsJCtWrViSEgIvb29GRERwS+//JIkuWnTJgYHBzMsLIwA6OXlxZiYGFZXVzM/P58JCQmOTTAGDhzI999/nxMnTnTsP61VwaSxUjhLg5gzZw5HjBhBAAwPD6ebmxs9PDxoNBq5dOlS2mw23n///Vy8eDELCgoYHh5eZ3RvcXEx27VrxxdffNExTcZms3HlypVs2bIl+/fvf1vhWVRUxMmTJ/OBBx5gYGAgBwwYwPz8/BvqEYr9jdOCBQuYkJDAwMBApqen87PPPrtmub+qqoqTJk2in58fvby82KRJE2ZlZfHChQvctm0bzWYz/f39aTAY2LRpU2ZlZfH8+fM0m81ctGgR4+Li+Oyzz3Lu3LkcNGgQJ0yYoFXBpFFTOEuDWL9+Pbt160Y3NzdaLBb6+vo6wvncuXNctmwZ77nnHh49epRms7nOto6bN2+mxWLh/PnzHY8VFxczJSWFUVFR3LBhw01fz8WLF/n5559z3LhxbNeuHUNDQ/ncc89x3bp1t93z/rM7ceIEZ86cyS5dutBisfD555/ntm3brvoxwLFjx5iWlsamTZvS3d2drVu3ZlFREb/88ksGBwfTw8ODBoOBTZo04RdffMHx48cz6+mnmeXhwd3R0TzUvj3Xmkz833vv5eujRzfA3YrcGQpnaRDHjx9nSEgI3d3dGRgYyKCgIBoMBkZFRbG6uppt27blmjVrGBcXxzfeeMPR7t1332VwcDDXr19P0l5KffXVV2kymTh16tSbCtKKigoWFBRw6NChNJvNjImJYXZ2Nnfv3v2n/Py4PhQXF3PixImMiopiREQEMzMzuX///ivO27BhA1u2bOlYkCQnJ4f79u2j2WymwWCgwWBgcvPm/Pnhh1kJsPKyWQAVBgNrPD3ti+Ds3NkAdypyexTO0iBsNpujt+zj48OgoCAC4JQpUzhv3jwmJiby5ZdfZkpKCmtqalhTU8Px48c7elI2m40ff/wxIyIi+OSTT95wCfvMmTNcuHAh09LS6O/vz65du3LmzJmO+bFSP2w2G7/66iuOGzeOYWFhvPvuuzlp0qQ6m2ScP3+ekydPppeXFw0GA9u2bcsNGzbQbDZz+G9T7mquN2e+ITd+EbkNCmdpGD/+yDdDQ/mBwcDVBgM/cHPjOIBFW7cyJCSEs2bNYosWLXj69GmWlZUxLS2N8fHxPH36NL/99lumpqayffv2jh707zl8+DBzc3PZtWtX+vv7My0tjYsWLeKZM2fq4Ublempqarh161bHjlRxcXGcPXu2Y2rWiRMnmJKSQqPRSKPRyOVJSSy/2RXnFNDSyCicpX7t3GkvNXp5scpovHKus7s7t911F5ObN+eWLVtYUlLCzp07Mz09naWlpfz73/9Ok8nEKVOmXLOEbbPZuGvXLmZnZzMmJoZms5lPP/00P/nkE1ZUVNTzDcvNuDQ1a9CgQQwICGBSUpJjatbGjRuZGBDAst9eL0cBpgAMBGgBOBL2fcAPAnwMYBDAZgB7APzXpYBuqB3aRG6SgSQhUh/mzwfGjgUqK+3/Xq+hBkCNhwd++Nvf8JfFizFy5Eh06NABY8aMQWxsLGbMmIGwsLA6baqrq7F582asWrUKBQUF8PHxQZ8+fdC7d2/cf//9MBqNTr45udMqKiqwevVqLFmyBJs2bUJiYiJmHT8O665dcAOQCsAM4B8AzgFIAvAMgAcAHACQBsAPwEQAHwH4l8EApKUBy5c3yP2I3AyFs9SPS8FcUXHDTSoA7OzfH9PLylBcXIy8vDwkJSU5jv/8888oLCzEqlWr8OmnnyI6Ohq9e/dG7969ERUV5YSbkIZSWlqKtQsX4vGxY9HEZgMARAOYAXtIA8A4AL8A+O/L2p4FYAJwBoDJyws4dgwIDq6fCxe5RW4NfQHyx5WXl4fY2Fg08fRExgsvOIJ5B+y9nOYAggE8AeCHWu2mAbgbgAVAxtKlaHr2LPbv34+kpCSUlJRg3rx5SE5ORlhYGBYvXoyEhAQUFRVh27ZtGD9+vIL5D6hZs2Z46sIFNPH0dDw2GkA+7G/iTgAoBPDIVdpuBRACe0DDYAAWLnT25YrcNoWzOI3VakV2djb+2qIFUFPjeLwUwDAA3wH4HvbS45Ba7Qjgf34771MA2776CoMHD0ZsbCw6deqEHTt2YNiwYTh58iRWr16NZ555BiEhIfV1W9JQ9u8HqqocP3YF8DUAfwAtAMQC6HNZkxIAIwHkXnqgshI4cMDplypyu9wb+gLkj6tv377AqVPYfewYSmo9nnLZec/D/o/2kpdrfR8FoFdVFXZ+/TWm5eUhPj4e7u562f4p/fyz41sbgGQAwwFsA1AG4K8AxgOY+ts5pwH0APAcgP+s/Tylpc6/VpHbpJ6zONcNlBC3AviPaxwjgO0GA55u3x7du3dXMP+ZBQQ4vj0L4Djsb+yawF6yHgJg7W/HS2EP5scATLj8eZo1c/KFitw+hbM41/79dUraVxyGfTTttGsc/y8ANhJDvL3v/LVJ49KxI+DlBQAIAhAJYD6Ai7CP1l4EoBPsg8KSATwEYMrlz+HtDcTE1NMFi9w6hbM4V61S5OW+hb3EPQtA/FWO58H+2fMaAE1++cUZVyeNSUZGnR9XwD4mIRhAG9g/o5sJYCWAXQDeA+Bb6+sYYJ/Cd9nziLgihbM4V61SZG3fA0gE8CqAwVc5/i7svZ7/g32wj0qRArMZSEmxj7gGcA+AzbCXsM/APpfZDCAd9o9DymH/LPrSV7jBAKSmahqVNAoKZ3Gaixcvoio6GjVGI2oAVMFegjwBIAH2UbQjrtLuAwBZANYDaAWoFCn/lplpfz3cCm9ve3uRRkDhLE7z+uuvwzs7G1NqarAYgDeA1wG8DeAIgBzULTtekg3gJwBdLh2rrMSIf/6zXq9dXFSXLsD06YCPz8218/Gxt4uNdc51idxhWiFMnK9vX+Djj393yc5r0pKLcjU3uBQsDAZ7j3n6dODZZ+vv+kRuk8JZnG/XLqBbt5tautPBxwfYskU9HrnS7t3A5MnA2rX2EK6s/Pcxb297aKem2kvZev1II6NwlvpxC2trO0qR6vHI7zl92j6f/sAB+wIjzZrZxyhkZGjwlzRaCmepPypFiojcEIWz1C+VIkVErkvhLA1DpUgRkWtSOIuIiLgYzXMWERFxMQpnERERF6NwFhERcTEKZxERERejcBYREXExCmcREREXo3AWERFxMQpnERERF6NwFhERcTEKZxERERejcBYREXExCmcREREXo3AWERFxMQpnERERF6NwFhERcTEKZxERERejcBYREXExCmcREREXo3AWERFxMQpnERERF6NwFhERcTEKZxERERejcBYREXExCmcREREXo3AWERFxMQpnERERF6NwFhERcTEKZxERERejcBYREXExCmcREREXo3AWERFxMf8P+nJK4wr0mHYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111cda750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "dest_verts = [7,37,59,82,99,115,133,165,188,197]\n",
    "undirected_djikstra_naive(testcase(), 1 , dest_verts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ans:  2599,2610,2947,2052,2367,2399,2029,2442,2505,3068"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br>\n",
    "***\n",
    "# Dijkstra's Algorithm using Heaps\n",
    "Recall that in Djikstra's algorithm the crux was to pick the next vertex with lowest Djikstra score greedily. In absence of datastructure like Heap, we have to look at all edges where one vertex has its Djikstra's score calculated and another one lies outside the frontier. This is an expensive operation and the algorithm in absence of heap runs in polynomial time in worst case. Lets implement heap using heapq package in the following code snippet. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex s\n",
      "Vertex s is at distance 0\n",
      "Vertex v is at distance 1\n",
      "Vertex w is at distance 3\n",
      "Vertex t is at distance 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "import heapq\n",
    "import numpy as np\n",
    "\n",
    "def djikstra_heap(DG, source, destination):\n",
    "    #Heap implementation which does the following\n",
    "    #\n",
    "    # 1. For vertices in X, find all edges originating from them to all vertices not in X\n",
    "    # 2. Keep track of minimum value of len(w) + lwv\n",
    "    # 3. Return w, v and lwv\n",
    "    X = [source]\n",
    "    minHeap = []\n",
    "    heapq.heappush(minHeap, [0, source])\n",
    "    all_nodes = list(DG.nodes)\n",
    "    for node in all_nodes:\n",
    "        DG.nodes[node]['shortest_dist'] = float('inf')\n",
    "    while len(minHeap) != 0:\n",
    "        w = heapq.heappop(minHeap)\n",
    "        X.append(w[1])\n",
    "        DG.nodes[w[1]]['shortest_dist'] = w[0]\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] == w[1]) and (edge[1] not in X):  # node that has just been popped should be the tail\n",
    "                dji_greedy = w[0] + DG.edges[edge[0], edge[1]]['weight'] #djikstra's greedy criterion\n",
    "                doublenp = np.array(minHeap)\n",
    "                singlenp = []\n",
    "                if len(doublenp) == 0:\n",
    "                    heapq.heappush(minHeap, [dji_greedy, edge[1]])\n",
    "                    continue\n",
    "                else:\n",
    "                    singlenp = doublenp[:,1]\n",
    "                if edge[1] not in singlenp:\n",
    "                    heapq.heappush(minHeap, [dji_greedy, edge[1]])\n",
    "                else:\n",
    "                    dest_idx = np.where(singlenp == edge[1])\n",
    "                    if dji_greedy < int(doublenp[dest_idx][0][0]):\n",
    "                        minHeap[dest_idx[0][0]] = minHeap[0]\n",
    "                        heapq.heapify(minHeap)\n",
    "                        heapq.heappop(minHeap)\n",
    "                        heapq.heappush(minHeap, [dji_greedy, edge[1]])\n",
    "    print(\"Printing minimum distances from starting vertex {}\".format(source))\n",
    "    for node in all_nodes:\n",
    "        if node in destination:\n",
    "            print(\"Vertex {} is at distance {}\".format(node, DG.nodes[node]['shortest_dist']))\n",
    "\n",
    "        \n",
    "\n",
    "g = nx.DiGraph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('v', pos = (5, 0))\n",
    "g.add_node('w', pos = (5, 5))\n",
    "g.add_node('t', pos = (10, 5))\n",
    "g.add_edge('s', 'v', weight = 1)\n",
    "g.add_edge('v', 't', weight = 6)\n",
    "g.add_edge('s', 'w', weight = 4)\n",
    "g.add_edge('v', 'w', weight = 2)\n",
    "g.add_edge('w', 't', weight = 3)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "dest_verts = ['s', 'v', 'w', 't']\n",
    "djikstra_heap(g, start_vert, dest_verts)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aorCMg8S0gmrio9JCE20GfAW1NkZgMFTQsksfqOkagZP7QqwcIcDlZwUoKms+myYk9RkAWhi2B0NN/f8/McAAA/x3OWJlZO2zg4MDhg4dWqPgApUuaIaGhvDz88Phw4exdOnSBrVDURxUdCkieDweoqKiMH/+fABATFKWVOcJyt+BV/wWLQwtqh1jAIi5J109ykBdfS46F4WMzeOQvdcPqq31q02pALL3ua7YvFpaWhg4cCASExORkpKCnJycWstTlAs1RRtAUR5OnDiBjh07wsHBAQCQmssUc5GqCSLgo/DkZrTuPhTqBubVjrP5QqTmlDaKvY1BXX02GBEA/eHfgfM2FeyMx2Coqlcr0xh9FgqFUFGpHCNV/bt3714UFxfT7BXNDCq6FBHh4eFYuHCh6DOTza+1PCFCFJ7eAqiqQX+4n8RyTHbzSeZYV58BgKGiCk1zO5QnX0bp/Xjo9BpTQz3y7XNGRgZ4PB7S0tKQlJSEoqIi/Pvvv1i6dCn18W1mUNGlAKjMgpCRkYGxY8cCqFywEbDKJJYnhKAoPhyC8hK0m7AaDFXJl5KOZvXRoLKiTuohlkJhtTndKuTVZ0IItm/fjsWLF2PatGnQ0dEBg8GAi4sLFi5ciI4dO8qlHUrTQUWXAqBylDtr1iycOXMG8fHxiI+Ph2p3DzC6jwJRqX6ZFJ+LBK8oE0aT10FFXfI2WMLn4NShaGjcbwNvb284OzuLXo+VAUIInj59iri4OMTFxeG1Zhe0dJ5Qrc+C8hKw0x9Cq0sfMNRagP3mAcqfJqLt6MXV6tRUU4G1ibZc7GMwGJgxY0bl30NVFeHh4eJ2/X/YSFVVVbm0R2l8qMvYZwwhBM+fP8cff/yBtWvXQkNDAy4uLvD09ISJiQkO/hmL5M6TwVATf33lv8/H210zAVV1MFT+u9n1PQLR2m6wWFkNNRVEuuvh8tlTiIuLQ2FhIUaPHg1vb28MHToUWlpaTdLXDxEIBLh58ybi4uIQGxsLNpsNb29veHt7o5tTXwzadq3avK6g4j0KTvwMbv5rgAihptsO2k6jod3To4YGeFjrJMS0CWPl+oCZMmUK2Gw2jh07BnV1dRBCUF5eDjc3N/zwww+YPHkyTZDZDKCi+5nBZrORmJgoGtGyWCwYGxvDwMAAf/75J65evYrQ0FBkZ2fjhx9+wL2WTkhIK6x1G6wkavJZffnypWhU+eDBAwwbNgze3t7w8vJq1AWhiooKXLhwAXFxcTh9+jRMTExEQuvo6CgmVpL8dKWBwQC6tREg//h6lJSUYPHixZg+fTo0NOQTCOjQoUMYPHgwvvjiC9F3N2/ehJ+fH4yMjBAZGQlLS0u5tEVpHKjofgakp6eLpgwSExPRo0cPeHl5wdPTE9bW1ujYsSMCAgJw5MgRaGhoYMmSJRg/fjzU1NQk7s6Shrp2ZxUWFuL06dOIi4tDQkICHB0dRUIoj+hbBQUFovovXboEJycnjB07FmPGjKl1LlQefe7+hS4SExMRGhqKhw8fYsGCBfDz82u0XWR8Ph87duzAzz//jPnz5yM4OFhuQk+RL1R0P0F4PB6uX7+O+Ph4nDlzBvn5+Rg5ciQ8PT3h7u4OfX19AJVbT/39/RETE4P+/fsjODgYw4YNq/aK2hRxCCoqKnDx4kXExcXh1KlTMDY2Fgmwk5OT1K/Nz58/F42kHz16hOHDh4tG0lX9lgZ59vnhw4cICwvD33//jVmzZmHhwoUwMTGRut76kJGRgQULFiAlJQW7du3CkCFDGqUdSsOhovuJkJOTg7Nnz+LMmTO4ePEiLC0t4enpCU9PT/Tq1UtsoSU/Px/h4eHYvXs3hEIhli1bhkWLFtVaf1NGGRMIBLh165ZIPMvLyzFmzBiMHTsWgwYNEnOREgqFuHv3rqhscXExRo8ejbFjx2LIkCESd3ZJg7R9BhFCq4V6nX1+8+YNtm7dikOHDmHcuHH44YcfYGVl1WD7auPkyZOYN28eBg4ciM2bN8PIyKjukyhNAhXdZopAIMCdO3dE0wavXr3C8OHD4enpiZEjR9Z4k718+RKbN2/G0aNHMXnyZAwdOhRLlizB8+fPpVr9fpRVgqgrL3D5WQEYqNwEUEVVbNnBVoYIGNRFrkFuUlNTERsbi7i4OKSmpmLYsGHo2LEj8vPzcf78ebRp00Y0Ku7Tp49cF6+k6TP7VRLWT3PDtJEDpKqzsLAQkZGRiIyMFL1hODs713oOl8uFqqpqvbwUysrKsHbtWuzfvx8//fQTZs+erVSeI58thKIw3r59S4KCgoi7uzu5dOkSKS0trbV8YWEhOXz4MPnqq6+IgYEB6datGwkODiaJiYmEy+VKPO/ff/8lEydOJAYGBiQkJITk5uYSQgiZOnUq2bJlS73tLixlk+jEF2Th0fvEcNwKsvDofRKd+IIUlrLrXZe0FBcXk4MHD5JRo0YRLS0toqenRzQ0NEi/fv3Izp07SUZGRqO1TYh4n2fuvyPW53379pEBAwYQoVBYrzrLyspIeHg4ad++PdmxYwfh8XgSy2ZmZpKvv/6aODs7k9TU1Hq18/DhQ9K3b1/i4uJCHjx4UK9zKfKHiq4CmTdvHvn222/JX3/9RWbPnk2WL19OCCFEIBCIynA4HLJu3TrSr18/oq2tTcaMGUOio6NJenp6rXULhUJy/vx5MnToUGJmZka2bt1KmEym6Pjbt2+Jnp4eeffunUx9aMzn9uvXr8n27dvJ4MGDRX3/9ddfSV5eHiGEkNLSUnL8+HEyffp0oq+vTxwdHcmaNWvIgwcP6i2AssDn84mdnR05depUg87ncrm1Cu6HLF26lGzdurXebQgEArJnzx5iaGhIFi1aVOcDntJ4UNFtIrKyssiSJUvInDlzSFxcHCkoKCCzZs0iz58/J4QQ8uLFC2JkZEQqKirEzisrKyM7duwg586dIywWq852eDweOXLkCHFwcCC2trZk//79hMPhVCu3YsUKEhAQIHO/5Cm6QqGQJCUlkZUrVxJ7e3vStm1b8s0335DY2FhSXl5e67k8Ho9cvnyZLFy4kHTs2JF06NCBzJ8/nyQkJNT6FiAvTp06Rezs7Aifz5d73RcvXiTTpk0jOTk5pFevXuTYsWMkPT2dHDt2jJw/f75edeXl5ZHp06cTCwsLEhsbK3dbKXVDRbcJSEhIIN26dSOLFi0isbGxxM7Ojly6dIl069ZNJLqEEOLu7k42btxICBEf7UpDRUUFiYyMJJ06dSL9+/cnp06dklgHi8Ui7dq1IykpKQ3v1P8jq+hyOBxy/vx5EhgYSMzNzUmXLl3IokWLyNWrVxssYEKhkDx69IisXbuWODk5EX19fTJt2jTy559/io325YlQKCQDBgwg+/btk0t9H7/tjB49mri5uZHIyEhy4MAB0r9/f7Jw4UJia2tLli1bRoRCYb1G9wkJCaRr165kzJgx5M2bN3KxmSIdVHSbgPT0dPLvv/+KPs+dO5f8/vvvJDAwkAQGBoq+P3v2LHFwcKhX3UVFRWTt2rWkXbt2ZMyYMeT69et1nrN//37i7u5er3Yk0RDRff/+PTl69CiZMmUK0dPTI3369CEbNmwgycnJjTItkJmZSSIjI4m7uzvR1tYmI0eOJNHR0SQ7O1uu7dy4cYOYm5tXe1tpCOnp6WIj9Pv375Np06aR4uJiYmdnRw4dOkQIISQ5OZmMHz++QW2w2Wyydu1aYmBgQMLCwprkjYBCRbdJqBqxVV3UmzZtImvWrCFpaWnE2NhYVC4jI4N4e3uTt2/f1llneno6WbhwIdHT0yO+vr5Sj1qFQiFxcHAgZ86caUBPqiOt6EoSPmn6Kk9KSkrI0aNHyeTJk0mbNm2Is7OzXAXfx8eHhIWFyVSHUCgkERERxM3NTbRAuHXrVhIZGUkCAgLI1KlTCSGVUyq3b98mc+bMIQUFBQ1u7/nz52T48OGke/fu5MaNGzLZTqkbKrqNRG03sIuLC0lMTCSEEOLp6Ul++uknwmKxyP79+0lQUFCt5z9+/Fi0cPTDDz+QzMzMetl17do1YmlpWe/pC0lIEt2qV/yffvqJ9OrVi+jp6TX6K359+XBqw8zMTC5TG0+fPiWGhoakuLhYZvt27txJbGxsiI+PD5kxYwYJDg4mpqam5P3796Iy69atI998843MbQmFQnLkyBFiYmJC5syZIxf7KTVDRVeOZGZmkj179pCAgACJXgE3btwgY8aMEY16Hz16RDZu3Eh69OhB7O3tyR9//FHjeRwOh3h5eRFjY2OyYcOGBnsdTJgwgYSHhzfo3Jr4UHR5PB65cuWKaDGrffv2TbqYJQsfLuL16NGDGBoaEl9fX6kW8T5m9uzZJDg4WC52ZWdnk3PnzpHi4mKyefNmsnbtWkJI5e/67t27xM7Ojjx9+lTUB1l59+4dCQgIIMbGxuTgwYNN6gXyuUBFVwZ4PB65du0aWbp0KbG3tycDBgwgL168IDwer9rFWvU5OjqabNy4kWRmZpLvv/9e9Jr/5MkTie2w2WwSERFBdu/eLZUHgyQyMjKInp6e2EhJVgCQ48ePkxkzZhADAwPi4OCgELctefPq1atq7mq//fYbyc/Pr/PcrKwsoq+vX++3kLqIjY0Vzd+eO3eOTJgwgWzevJkQUrnwxmazycuXL2W6Rqq4ffs26dmzJxk8eHC9/YIptUNFt57k5+eTAwcOkEmTJhE9PT3Ss2dPsmLFCpKZmSmVyFhaWhIzMzMycOBAEhISUqcAslgswmaz5eKK9OOPP5L58+fLXE9ubi7Zu3cv8fLyIgDIsGHDyM6dO+v0HW6uFBUVkYMHD5Jx48YRHR0d0r9/fxIWFkbS0tIknrN06VLy7bffytUOJpNJfHx8iIODA5k5cyaJjIwUO87j8cjUqVOJsbExWb9+vcxTBDwej2zbto0YGBiQlStXykXMKYQ0u23AhWUcxCRlITWXCSabDx1NNVgb62CCkxkMWss/qpJQKERSUpJou21qaiqGDh0q2m77YYi9umCz2fjpp5/g4uKC0aNH11q2oqICampqUFdXl0uMVBaLBQsLC9y8eRNdunSp+4SPSE1NFcU3SElJgYeHB7y9vTF16lQ0s0tIJthsNi5duoS4uDicPHkSenp6GDt2LLy9vdG7d2/RNtuSkhJ07doVV65cga2trVxtuH//PqytrUWxiAkhYtfIkydPEBYWhtOnT8PX1xfff/99va7TKqrutXuvcnH73iMwi/Lw5RBnLJs8pFHutc+FZiO6DzNLEHnlBRLTCgBALMh01R74QVaGCHDrAntz2fb9l5SU4Pz584iPj8fff/8NfX19eHp6wsvLC/3792+0nFRsNhsqKirgcDjQ1pZP5oEqfvnlF8TGxuL06dNSlRcIBLh9+7Yo5kFV0Blvb28MGjRIFDaQwWB8VqL7IR8G24mNjUVJSYkoQPuQIUMQFRWFq1evIjY2tlHa/1hsPyYjIwPbt2/H/v374e3tjSVLlsDGxqbOemu718DngqGiioGWBggaYSfzvfY50ixEt7EjXBFC8OTJE9Fo9v79+xgwYIBoNCuP2K61UVpaClVVVXC5XLRpI/+LmBACe3t7bNmyBcOHD5dYjsViiYVXNDIyqjO84ucsuh/zcVjJIUOG4Nq1azh48CBGjhypMLuKi4sRFRWFiIgIODs7Izg4GP369auxrLT3GhEKoa4KrBzVDTP60Txt9UHpRbexYrmWlZXh0qVLogwKampqosDegwcPbvQ0MjweDwKBAPn5+dDV1ZU5uHVto57Lly8jMDAQycnJ1cp8GEj80qVLcHBwqFcgcSq6NVMVQH3nzp149OgRBgwYIJqG6NChg0JsYrFY2L9/PzZv3gwTExMEBwfDy8tLNCXSkHsNAi6+622IpRP6N5LVnx5KLbqSIvgzk06h/HECuAVv0MrGDW1HfV/t3JqyFjx//lwksjdv3kSfPn1EQmtlZSXz3GlaWhq6du0q8TghBGw2GwKBAM+fP4eVlRVatmwpU5tApYCrq0vOPuvj4wN3d3f4+/sDkG/KHCq6tSMQCGBvbw9vb2/k5OSIpQoaO3YsHBwc6nXd1TWlIA18Ph/Hjx9HaGgoOBwOlixZAruBnpi+L0litgxe8Vtk/zoXraxd0XYA5nrYAAAgAElEQVT0D+I28TgYLHyAnWsWy31a7FNEqUVXUq6qimc3AAYDrNf3QHjcGkWXwQCGWRlivPE70bRBRUWFKLD30KFDoaOjIxc7CwoKMHv2bLx9+xbDhg1Dnz594OPjA6FQWC1+KYfDgYqKSq0iKS1paWkICwvD69ev8c0332DEiBEwNDQUK/P69Wv06tULJ06cwPnz5xEXF4eCggK5JYekols38fHxWLx4MR4+fAgGgyGWFJPD4Yjmyt3c3KRaLyCEoKSkBLm5ubC0tISaWsOSehNCkJCQgNDQUDxr5wYVi54Aahb0vKMrQPgcqOm2qya6DAAG7CzkxazDjh074OPjQxNk1oLSim5hGQeuoZeqZWX9kHdXD0LALKxRdAGA8Lkw/TcKo4cPhqenJ+zt7RvlYli3bh3S09MRHh6OM2fOYMmSJTh37hwsLS3lMjKpiYyMDAQGBsLNzQ02NjaIiopCUFAQhg4dKiojEAgwYMAAPHr0CObm5qJpA3mmQaeiWzeEEAwePBgzZszAzJkzxb7/MP37s2fP4OHhgd27d0scEBw4cAC3b9/G/fv3YWVlhX379slsX2EZB31/vghJswrlKYmoSLsJdQNz8EtyqokuUJn1efNALQQvCECnTp0QERGhsGkUZadhj8gmICYpS+Y6NDU18M2aaHw3sLMcLBKHxWJBS0sLfD4fDAYDQ4YMgZaWFsaPH4/k5GRMnz4dt27darQnfnFxMdLS0nDq1CkAwP79+2FqaipWhsvlol+/fvjpp5/ExJjStDAYDISGhmL8+PGYMmWK6M2CwWDA1tYWtra2WLp0KXJycnDnzp0a34IKCwsxf/58WFpaYvTo0WCz2Zg4cSIA1PhGVR9ikrIqzxdWV10hpwIl1w7DaMp6lD08L7mPALI1zPHgwQNs2bIFvXr1wuLFixEUFCSXt7pPCaXN3ZGay6x1lCsNHD5Bak6pnCz6j7Vr18LV1RV5eXlQU1MDn8/HiRMnRMdXrVoFHo+H6OhoAGiUkWCPHj2gq6uLwMBAWFlZ4dmzZzh48CAePnwoKqOlpYVly5ZRwVUCnJ2d4ezsjJ07d0osUzXX+/F0z9u3b/Hjjz/Czc0Na9asQVlZGYqLi+Hu7g4AMr+11HavlVw9iNb27lDTMazxeBVsvhCpOaVo0aIFli5dijt37uDKlStwcHDAP//8I5N9nxpKK7pMNl8u9dxMeoCwsDAcPnwYly9fxrNnz1Ba2nAhPnLkCC5dugRra2sEBQUBqBTZGzdu4Pjx46JyK1euxK1bt8DlchtltKuioiLy/wwODkZSUhJUVFSwa9cuFBQUiMrJa96aIjvr169HWFgYiouL63Uek8lEVlYWtm/fjq1btyI+Ph4TJ05s0NSOUCgUjahjYmKwdetW3Ep6WGNZbt4rsNMfQqe3t3R2snmi/3fq1Anx8fFYvXo1Jk+ejFmzZqGoqKhetn6qKO30go6mfExr07IF8vLycP/+fWRnZ4t+AMDU1FTsx8TEpNp3rVq1Eqtv3LhxsLe3h7m5Odzd3XHo0CFMmzYN27Ztw6JFi+Dq6gpjY2OoqqrC1NRULhspeDwerl69io4dO4q5cZmamuLVq1eiVzgfHx+Eh4ejoKBAtKDW0EUWivyxsrLCuHHjsHHjRmzatEnq82xsbHD27FlcvnwZK1aswP3798Wug/Lycpw/fx7Dhw+HUChEZmYmMjIyRP9W/WRmZiIrKwtt2rSBhYUFzM3NYWFhAd02xsjlVG+XnfEY/Pd5yIryBQAQLhsgQuQULoCJ745q5XU0xacRGAwGxo8fD3d3d6xYsQJ2dnbYuHEjvv766896oU1pF9KiE19i28W0Gl97iFAACAUo+ed3CEqLYDByHqCiCoaKeKZUTTUVfD+8a41zuqWlpWIinJOTI/a56kddXR379u2Dl5eXaBdWFX/99RfWrVuHhIQE6OnpISgoCIWFhdDT08PFixcxY8YMBAcHN6j/paWlOHv2LOLi4hAfH48uXbogKCgIEyZMEGWELS8vx6pVq9C6dWusXr0aR48eRUxMDGJiYhrUZkOgC2n1IycnB926dcODBw9gbm4u1Tl8Pl/08Fy5ciXKysrg6emJYcOGgcPhYO/evVi6dCnKysqgqqoKQ0NDWFlZwdLSUkxcLSwsYGZmVi0tvaR7Tchjg3BYos/MO3+B/z4P+iMCodpS3K+8tnutiqSkJPj5+aFly5aIjo6Wanfcp4jSim5t3gsl1w7j/fUjYt/puk5BmwFfiX2noaaCG8EN3ydOCAGTyUR6ejo6d+5cbdQLAHPmzIFAIMCvv/6K8vJyvHjxAmfPnoWzszMGDRpUr/ays7Nx8uRJxMXF4fr163B1dYW3tzdGjx4tce/89evXsWzZMnA4lUOV5cuXY9SoUY3mNfExVHTrz/Lly5GdnY3ffvtN9F3V77C2v1lubi5WrFiBxYsXi/zB+Xw+EhISYGRkBF1dXdy8eRMnT57EuXPnYGNjI/JYsba2llivNJ5CQOV9J8l7QRVCnA/sg85mRrXWIRAIsGvXLqxZswZz5sxBSEiIXHzVmxNKK7qAZD9daWAwgBG2Roie1qvB7ZeUlGDXrl0IDw+Hn58fli9fLhplVsFkMjFy5EhYWlqCy+Viy5YtMDExqVYXi8VCaWkp/P39kZaWBhMTE5iYmKBFixbIzc3Fs2fPkJubiyFDhmDixIkYNWqU1POxb968QWlpKbp3797gvjYUKrrSUVFRIXrdT01NxY8//gh3d3eUlpYiMzMTmZmZSExMRO/eveXSHpfLxZUrV0TuaK1atRIJsIuLS7XrWKZ7DUBb9lu8/N+PmDFjBoKCgmBhYVHrOdnZ2QgKCsLdu3cRGRkJDw+P+jfcTFFq0ZW0I00aatqRJi1v377F9u3b8dtvv8HLywuLFy+WKGgFBQXo27cvWrdujejoaLi4uEislxCC/Px8xMfH4/Tp0/jnn3/A4XBgYWEBHR0dcLlc5ObmIjc3F7q6ujXONZubm8PT07PaTaMo9u7di9mzZyvaDIUiEAiQk5MjNnf68f/Ly8thbm4uetXPzs5Gbm4uwsLCRFMANb1JyQNCCJKSkkQCnJeXJ9ocM2zYMGhpacnlXjNglEt931Rx9uxZBAYGwsnJCdu3b6/m9vgpotSiCzRe7IWaSE1NRVhYGE6cOCH1Ezs4OBitWrXCypUrJZZhs9mi+dnTp0/DzMxMtA20pg0bQqEQhYWF1eaai4uL4erqCh8fH6ioqEh8FRUKhRAKheDz+aioqICOjg5dUGsgVbu/JIlpRkYGcnNz0bZtW7G504//b2hoKPb34nA4sLKywsGDBzFgwIAm7dOrV69E01j37t3DkCFD4O3tDbZZb+y4miHzvVZSUoLo6Gjs2LEDjo6OCA4OxoABAyRerywWCxs2bEB0dDTWrFkDf3//T3qhTelFF2j8KGM3b95EaGgobt68iblz5yIgIEDqGAQCgaDGUSchBI8fP8aaNWtw4cIF9OnTB97e3hgzZgzat28vtW31QSAQgMfjISUlBceOHcOFCxeQk5ODwsJCGBgY1OmpYWhoqDQj6KaCEILs7GykpaVJHKmqqKhIFFMLCwt88cUXDfJSOXjwIHbt2oXr168rTGSKiopw5swZxMXF4eLFi+jk/jVKuwyHAJXhUiUhzb3GZrNx4MABhIWFoW3btliyZAm8vb0l+hU/ffoUT548wahRoxo94JQiaRaiCwCPskoQdeUFLj8rAAOVzthVVMXTHWxliIBBXaSaUhAKhYiPj8emTZuQlZWFRYsWwdfXV+ZJfS6Xi5ycHEybNk3k7O7p6Qk9PT2Z6pWGqtHtx4HP+Xw+8vPz6/TUePfuHQwNDdG+fXv8+eefMDExkdt2YWWGyWTC29sbZmZm1QTV3Nxc5ghwkhAIBHB0dMSaNWswduzYRmmjPrDZbCQkJODA6UTcKGkNVfMeUFVVgQD/PYgbcq8JBALExsYiNDQUTCYTixcvxrRp06p5AwHyCeij7DQb0a2iqIyDmHtZSM0pBZPNg46mOqxNtDHeUbrMETweD0eOHMGmTZugrq6O4OBgjB8/XubXb4FAAC6Xi/Pnz0NTU1Ms0HdzgcfjIS8vD2VlZejcuXOd2zerbpDnz58jNTUVdnZ26NSpU5PdOKWlpdVGp/r6+pgzZw5at24tVnbhwoVgs9no3LkzPD09YWdn1+j2ScPff/+NoKAgPH78WKmmgIRCIS5cvYmos/fwJLMYPIY6zNrpw8XGAovHDYCJfv2jiRFCcOXKFYSGhuLx48dYsGABvvvuO6keap+SGDc70W0oZWVl2Lt3L7Zt24auXbsiODgYw4YNq/cfsmo08PjxY0yePFnkysVisdC6detPdmQoEAjw9OlT3Lt3DwDg7u4OY2NjHDhwAKGhoTA2NoatrS3mzJmD7t27i90kp06dEsWGqGl6Q09Pr9rfgcfj4e3btxLnUTMzM8HlckUj06pRqYeHB5ycnKpNk1y6dAmpqalIS0tDbm4uoqOjGyVgfH0hhGDIkCH46quvMGvWLEWbI5G0tDRRZLTk5GS4u7vL9Bb38OFDbNq0CWfPnsXs2bMREhJSa1jIjRs3gslkYsOGDbJ0Qyn45EU3Pz8fO3fuRHR0NAYPHowlS5agV6/6uZF9PO/Vs2dPkftN587yD6YjDbIGOakvx44dw6ZNm2BrawtVVVWoq6sjJCQE69evx8yZM+Hi4oJt27bh7t27+P3338XsKysrw9mzZ8WmMtLT05GZmYm8vDxwOBy0bt0aampqIISAw+GAzWZDV1cXJiYmsLCwgKWlJSwtLdG+fXvRq39NYi0NdnZ22LdvH/r06SPvX1ODuHPnDr788kukpaU1C5/VvLw8UeD7K1euiNYrvL2961x4/pg3b97g999/x8KFC2vte3p6OpYtW4aXL1/if//7H6ysrGTthsL4ZEX31atX2Lx5M44ePYpJkyZh0aJF9UrI+Pr1a5GLzYcrvKNGjULbtm0b0fK6KSkpwalTpzB27FjR6EDSgp68ePPmDVq1agVDQ0MUFxdj+vTpmD17NtasWYP79+8DqNxt5eTkJNpmXQWHw4G/v79ohJqZmQktLS3R6NTU1BS6urrQ0tKCiooKBAIBysvLkZubKzb/zOPxal0INDExQZcuXWp8TX/z5g1Wr14NAwMDZGZmIjIyslrsYUUyYcIEODk54ccff1S0KfWivLwcFy5cqOaZ4+3tjZ49e0r9UJR2+iAkJAQGBgaiuCfNkU9OdO/du4dNmzbh4sWL+O677zB//nwYGdW+Swao/KPfu3dPlIixJl9GZWHr1q24ceMGYmJiUFhYiFu3buHMmTNQU1PDt99+i549ezZa21XibmVlhatXr8LW1hY5OTmi1XtDQ0M8e/YM+vr6onP4fD6OHDkCIyMjmXxSy8rKkJOTU+NCYNV3V69erfHvnZ+fj7179+L69euYOHEivvnmmwb/DhqDtLQ09OvXD8+ePat39g5lgc/n48aNG6LBCo/HEwnwwIEDGxziMSEhQZRmaMyYMfj2228xZ84csNlscLncZhfU6ZMQ3Q8j4KempuL777/H7Nmz60wd8uGunZMnT6Jly5a17tpRFiZMmIAvv/wSU6ZMQVBQEHJycjBixAhkZmaCw+Fg1apVUFNTq/erd5VPamZmJtq1awdjY+NqxxkMBn755RdcuXIFhw4dgqWlJY4dOwYHBwcAgJOTE8LDw+Hq6iq3/sqT+Ph4xMXFITw8HBoaGqioqEBERAQePXokcfTcVK/8/v7+aNWqFTZv3twk7TUmhBCkpKSI5oFfvHiBkSNHwtvbGx4eHnUK5YfTU1wuF+PGjUNFRQVcXV0xb948tG3bFq9fv4aLiws2bNiAmTNnNpv1FOVZLm0AVbmeNm3aBBaLhSVLlmDq1Km1+ky+f/8ef//9N2JjY8X2p1+4cKHW/enKhJubG96+fQug8pU+IiICBgYGKCsrg5eXF27fvo3+/asnCuRwOMjKyqp15xSDwUD79u1Fv8sPHzwMBgM5OTn4/fffsXjxYgCAo6Mjrl69CgcHBwgEAnTt2hUsFqta24qCzWZDXV1d1A8mkwl1dXVUVFRAQ0MDGhoaGDp0KExNTUVzzTdv3hQbQWtoaNQZkc7ExKRaIJn6snLlSnTr1g3z5s1rNF/upoLBYMDOzg52dnZYtmyZKK7Ivn37MGvWLLi6umLr1q2wtraucXCQlZUFExMTqKuro0WLFli/fj02bNiAtWvXisp06tQJ586dg5+fH/bv34/o6Gh069atKbvZIJrlSLeurKYfk5mZKdqBc+vWLQwcOFAUSObj0VxzoKCgANOnT0dpaSnU1dURGBiICRMmAACsra3x8OFDMXc1LpcLKysrZGdn44svvqh155Qk952qUW5ISAiMjIwwf/58AMC5c+dw/Phx9O7dG+np6SgvL8fPP/8sswDJi+LiYgQEBIDP58POzg53797F+PHj4evrK9WbQNXov66IdDk5OWjVqlU1cf5YoI2NjWt1JVyxYgUyMzOxf/9+Of4WlAsmk4lz586hd+/eNab0IYQgKioKf/75Jw4cOAALCwuEh4ejqKgIq1evRkVFBa5evYrevXujbdu2EAgE2LNnD1auXImZM2di5cqVjbalWh40K9EtLi5GVFQUIiIi4OzsjCVLltT4Glu1G6xqfjY9PR1eXl7w9vaGu7t7NR/O5kBNCw0xMTE4ceIE4uPj0aFDB7i4uMDAwADr1q0TK8dkMlFWVgYjIyOZpkzOnDmDgIAATJw4ERwOB3w+H0uWLEF+fj5Wr14NExMTzJw5U+mmFtLS0pCSkoKUlBRYW1vjyy+/lHsbhBAUFxdLnGuu+qmKq1HTVIapqSl0dHQwadIknDt3Do6OjnK3U9mobQEtIiICUVFRsLOzA5fLxdy5czF8+HCw2WwsWLAAf/75J7766issWrQIHTp0QG5uLhYtWoTr168jIiICo0aNauLeSEezEN3MzExs27YN+/fvh7e3NxYvXgxbW1uxMnw+H9euXRNN4jMYDNH8bP/+/ZXK8fxjeDwesrOzqwWcrvq/hoYGwsPDRfOmH44iuVwuKioq8ObNG2hoaDRqjNK9e/ciKioK3t7eaNeuHfr06QMHBwelnftWRoRCIYqKimrcEVgl0GlpaWAymTA0NKzVU8PU1BRGRkZKfW3LSk5ODh4/foxevXqJLc5WHduxYwf27t0LDw8PLFmyBPb29rhw4QICAgLQvXt3hIeHw8zMTEHW14zcRbewjIOYpCyk5jLBZPOho6kGa2MdTHCSbsfYhyQnJ2PTpk04ffo0fH19sXDhQrFfYFlZGc6dO4fY2FjEx8ejU6dOIqHt1q2bUuxgIYSgqKio1nnU/Px8GBsbS9zbX5NPKiEEZWVldS4WUpofHA4H1tbW2LJlCzp27FijOFdUVCA3NxdpaWlicTUkCXS7du2a/cORzWbjyZMnsLCwQLt27UTfM5lM7N69G9u3b0f37t0RHBwMFxcXhIaGIiIiAiEhIZg3b16dDyd5aldtyE10H2aWIPLKCySmVebn4tQQG2GQlSEC3LrA3rz2nUD//PMPQkNDcffuXcyfPx/+/v6iXS85OTk4deoU4uLicO3aNfTt21cUSEYRT7QP46TWJKhVPqm1zaOamprWe7Syfft2aGhowN/fv5F6RlEkhw8fxs6dO3Hz5s1aBw9CoRAFBQXIzMys1ZWuuLhYNHKWJM6mpqZo27atUnoBEEJQWloKPz8/xMfHw87OTjTAqtooweFwcOjQIYSFhUFHRwdLliyBra0t5s2bh+LiYuzevbvGDTHy1C5pkIvoyiMKmFAoxKlTp7Bp0ybk5eVh8eLFmDFjBjQ1NZGamiqan01LS4OHh4fI9aSxgpEA/8VJlbQVtSpOak2BUqr+b25uLvc5ZD6fj06dOuHEiRNwcnKSa90U5UAoFMLR0RGrVq2Cj4+PzPVVxdWoLeBRTk4OSkpKYGRkVGdEOgMDA4W9SXI4HFy+fFnk6qmjoyMSYGdnZwDAyZMnERoaiqKiIixatAgtWrTAsmXL4OPjgw0bNoi2gDd2BMMa65JVdGWNd8vlcnH48GGEhYWhZcuWCA4Ohre3N+7cuSOan2WxWKJfqpubm1ySPX7okyrp1T8nJwcGBga1vvZ/HCe1KTh+/Di2bdumFKmt4+Li4O0tXbZYSv14/fo19PX1oaOj02TXWFUg/bo8NUpLS2FsbFynK11Dt2pLi1AoFAvQXlBQgNGjR2Ps2LEYMmQI7t69i02bNiEpKQmzZ89GZmYmzp07hy1btoDfoS82/N00sbo/RCbRlSXavKaaCka3eokjERthZ2eHBQsWgMfjibYTmpqaioTWwcGh3n+4D31SJQlrlU+qJEFtaJzUxmbgwIGYO3cuJk6cqGhTaLqeRkSZI2ux2ew6xTk7OxssFqvWhcCqH11dXbn09eXLlyIBfvDgAYYNGwZvb2907NgRe/fuxZkzZzBixAgkvSkEt38AiGr9d8nJkpUGkFF05xz8F8cP/oKyxwngFrxBKxs3tB31PQCA8zYVJdcOgZv7AmCoQNOiO/SGfwe11pUrkEQoRJvydPi0LcSDBw9w+fJlODk5iYS2Jv+9KoRCIfLz82sV1Hfv3sHU1LTW4NONOTXRWNy/fx9jxozBq1evGrytUp5Q0aXUBovFqibINQl0VVyNugRaW1tbanEuLCwUBapKSEiAg4MDBg4ciKysLJwtt0CLDk5ADfPXuYd/BCf7mSi7uKq2Ab6Ys1t0XNb8iw0W3aoMou+S/wEYDLBe3wPhcUWiy3r5L4Q8NrQ6OgIqKig+Hw1BWTGMJv23o4TwuXDIOI7xoz3g6ekpcgmpStYnaR717du30NHRqVVQZfVJVVZ8fX3RtWtXLF26VNGmAKCiqwwo84hYWsrLy2tdCMzOzhbtwpRGnD9eR2GxWLh48SLi4uJw6sIVaE3aDEgY5eYe/hGtug2Gtv0IifbKkmm8wQ5+MUlZAICWVv0AAJzcFxDwCkXHtTqLPwW0nUYh73dxoVBXV4OmzSDcuHEDR48eFYlrVZzUD8V08ODBos9mZmZKFYCmqcjPz0dsbCyeP3+uaFMoCqK0tBSpqam4ePEiKioqMGPGDHTs2LHZ++q2atUKXbp0qTMSYGlpaTVxfvv2Lf7991+x71RVVWsU4+HDh0PfdSL+es4FX4axAgNAzL0sfDew/qFdG/yXSs1lirlW1AUnMxnqbcVjbfKJCnLYKuhvawsPDw+R0Orr6zf7J3djsHfvXowbN07hoSUpiuHIkSP4+eefoaqqCktLSwwfPhyLFy+Gh4cH/Pz8FG1ek6CtrQ1tbW107dpVYhlCCJhMZrWRclVcjSfaTuC3qz1GQ8mV/6Hkyv+grv8F2gycDs32PcSOs/lCpOaUNqgPDRZdJpsvdVlu/mu8v34EhuOWVzvWxaY75n7du6FmfDbweDxERUXh77//VrQpFAUQEhKCxMREjBs3DkKhEO3atcPs2bNhY2OD77777rMRXWlgMBjQ1dWFrq5ujTs0Z/7vLi6l5ks8X2+wL9QNzMFQVUf506vIP/4TTHzDoa5nIlaOyeY1yL4Gi66OpnSn8t5lI//YKugNmwNN8+pPFx1NxS8GNQeOHz+Orl27okePHnUXpnxSvHz5Es+ePRO5CHK5XDg7O8PX1xf9+/eHo6MjsrOzYWpqqmBLmwd1aZeG6X9ZKVp3H4rylESwXv4L9V6jP6qnYdrV4K0n1sY60FCr/XT++3zkHVkOXdfJaN1tSLXjmmoqsDah21ilYceOHaLIXpTPi86dOyMlJQWvX79GWVkZjh8/jp49e6KiogIAsHnzZrFtsZTakUa7xGAwgI8S0suiXQ0W3fFOlVtuiVAAwucCQgFAhCB8LohQAH5pIfKOLIO2kxe0HTxrrIMAGO+oXMEolJE7d+4gJycHY8aMUbQpFAUxadIkBAUFYfXq1Th27BjGjh0rmtv/1IPeyJsq7aoJIbsMrFdJIh0rS74MTuaTSi+sD5BFuxr8l2rbWgNuXQ1xbM9WvP/niOj78uTL0HWdAjAY4Jfk4v0/R8SOWyyKAVC5+jfYylCugSQ+VXbu3Im5c+d+ki5wFOkIDg5GdnY2Lly4AB8fH6ULn9mcaNtaA/076yEhtQBgiI87iVCAkquHwCvOAhgqUDcwg+GXy6Fu8J/AMhiyaZfCdqQRHgfz7QRY5Duhoc1/FuTk5MDW1havXr1qUKrrxob66TY9AoEAfD4fLVq0oF4+DeDmzZv4bukGcAb4g9MAvzFZd6TJFE7I3rwNQjytoaVev2q01FUwp3db7A1dga+++grv3r2TxYxPmt27d2Py5MlKKbgUxaCiooIvv/wSf/31l6JNaVbweDysWLECPj4++PtwNH4c0bVB2hXiad1gwQVkFF0AmObSASGeNtBSV0VdD10Go/IpEeJpg5BJA3Hv3j0YGBjA3t4eCQkJspryycHhcLB7927MmzdP0aZIZMaMGYo24bODwWBg4cKFWLZsGXi8hrktfW6kpqaib9++uHfvHqKjo9GuXTv49u/SIO1SeJSxKh5llSDqygtcflYABiqdh6uoikk52MoQAYO6VHtKnD9/HjNnzsSECROwYcOGz3K3WU0cPHgQBw8exPnz5xVtikRKS0tpIHUFMXz4cIwfPx7fffedok1RWgghiIyMxJo1a7Bu3Tp88cUX8Pf3FwW8AmTTroYg98wRRWUcxNzLQmpOKZhsHnQ01WFtoo3xjrVHXy8uLoafnx+Sk5Nx6NAhUWqazxVCCHr37o3Vq1crba4nimJJSkrC6NGj8fz5c6VOxKgosrOz4evri/fv3+PgwYO4e/cugoKCcPLkyRqDmTdUu+oNUSKEQiE5dOgQMTQ0JBs2bCB8Pl/RJimM69evk86dOxOBQKBoUyhKzOTJk8m6desUbes/uLsAACAASURBVIbScezYMdKuXTuydu1awuPxSEREBDEzMyNPnjyp89xHjx6RgoKCGo+x2WyZbVMq0a0iPT2dDB48mLi6upKXL18q2hyFMGnSJLJ9+3ZFm0FRcl68eEEMDAwkisTnxrt378i0adNI165dyZ07d4hQKCRr164lnTt3Jq9evZKqDgcHB1JSUiL6XDXwKS8vJ3369JHZRuVLhgTAwsICFy9exLhx4+Ds7Ixff/31s3JLysrKwvnz5/HNN98o2hSKktO5c2dMmTIF69evV7QpCufy5cuwt7eHrq4u7t+/DycnJ3z//feIiYnBP//8g44dO0pVj1AoFIu1XZUSq2XLluByubIbKrNsNzKPHz8m9vb2xNvbm+Tl5SnanCZh2bJlZN68eYo2o04a+zWMIh15eXnEwMBA6pHcpwaLxSJBQUHkiy++IH///TchhBAej0dmzJhBXF1dybt37+pVX/fu3UlFRQUhhJD3798TbW1tUl5eTvh8PunWrZvM9irlSPdDunXrhtu3b8Pa2hr29vY4deqUok1qVFgsFvbu3Yu5c+cq2pQ6+frrr8WyVwiFlau+FRUVGDhwoKLM+uxo164d5s2bh5UrVyralCbnwYMH6NWrF9LT0/Hw4UN4eHiAzWZj3LhxKCgowPnz50VJKKVl0qRJGDFiBNauXQsfHx8EBgZi4MCBcHV1xfjx42U3WmbZbkKuXr1KOnToQGbPnk1KS0sVbU6j8Ouvv5KRI0cq2gypsLe3F/vcs2fPGv9PaXyYTCYxNjYm9+/fV7QpTQKfzycbN24kbdu2JQcOHCBCoZAQUjkyHTRoEJk8eTLhcDgNrv/MmTMkLCyMXLt2jRQWFpLbt2+TW7duycX2ZiW6hFT+Un19fUnnzp3J9evXFW2OXBEKhcTe3p6cPXtW0aZIRWO/hlHqR0REBPHw8FC0GY3Oq1evSP/+/Ymbmxt58+aN6Pv8/Hzi5ORE/P39ZfJ8evXqFZk4cSIxNDQklpaWxNLSkhgaGpKJEyeS169fy2x/sxPdKv766y9iZGREQkJCZHqiKROJiYnEysqq2biJrVu3jgwYMICsWbOGDB48mPz444/EycmJODs7k9WrVyvavM8ODodDOnfuTBISEhRtSqMgFArJb7/9Rtq2bUs2b94sdp9kZGQQKysrsnz5ctGot6H06dOHHD16VKx+gUBAjh07RpydnWWqm5BmLLqEEJKTk0O8vLyIo6MjSUlJUbQ5MvPll1+SyMhIRZtRL86cOUO2bNlCkpOTCSGE3Llzh9y+fVvBVn2+HD16lPTq1Utm4VE28vPziY+PD+nRowd59OiR2LHU1FRiYWFBtmzZIpe2LC0tJR7r2rWrzPXLfUdaYRkHMUlZSM1lgsnmQ0dTDdbGOpjgJOddHf8PIQR79uxBSEgIVq5ciblz50KlhrTKyk56ejocHR2Rnp5eLZMphSItQqEQffr0QXBwMCZM+DQi+J05cwazZ8/G9OnTsXbtWmho/Kcj9+7dg5eXFzZs2ABfX1+Z2qnSrr1/noGKZmtYdTRHd3MDeNroo7woF//73/9QUlKCI0eO1F1ZLchNdB9mliDyygskphUAgFjSyqr9y4OsDBHg1gX25rLvX/6Y58+fY/r06dDW1sa+fftgZta8gqMvWbIEfD4fW7duVbQp9aKwsJAmylQyEhIS4Ofnh5SUFDHvkuYGIQTPnj3DpEmTsHPnzmoeMYmJiZgwYQJ2794NHx+fBrdTm3aBzwUYDLQuTcc4G22sCJghc8B4uYjuoVtvsD4+FWy+ALXVxmAAmmqqCPG0ljlST03w+Xz8/PPP2LlzJ3bu3IlJkybJvY3GoLy8HO3bt8edO3fQqVMnRZtTL2g8XeVkxIgRGDt2LPz9/RVtikzweDyoqqpWe3s9efIkvv32Wxw9ehRDhw5tcP2K0C6ZRbfS6Kdg8aRPx14Zk1L2EGmSuHv3LqZPnw4nJydEREQofSzaPXv24MyZM4iLi1O0KfWGiq5ycv/+fXh5eSEtLe3/2jvzuCir/Y+/Z4ZdBBTHHa8aKlrmSmlmSqm4tboGKPe6pl4X1LBr5qtuZmqIiktFWhqaaZhWmIkbelNRUST9qXhVZDHZJMARZn9+f3CZnGBYhxmW5/168XqN85w5z/fI4TPnOee71LvtqoiICN5++21++uknvL2rXkncWtpVrc3PhNRcPvr5RqWMBijU6Pno5xv8lpZbndubxNvbm0uXLtG0adNan6tXEATCwsKYP3++tU0RqUf06tULHx8f1q1bZ21TzMrNmzf597//zfHjx6sluNbUrmqtdGdExLEvYiuKK8dQZ92lUddBNBsdBICg05D94yeo7t9Cl59JizdX4vC3P8uHSyTg260FnwX0rbLxFeHw4cNMnTq11ubqPXbsGPPnz+fKlSt1svSKpVe6qampTJ48mfT0dKRSKTNmzBC/sExw584dnnnmGa5fv45cLre2OSYRBMEw99VqNVKpFJlMVurfQ2FhITY2NtXeq54REceR6xkmtxQeXTtJ7und6PKzkDVqgvuoBTh4PAVUX7uqvNLNVqg4eTMLmbM7rs9NwPnpoSXa2Ld9kmYvL0LWqOTjvSDAicQsHihUVTWhQvj6+pKQkMC9e/fo27cv8fHxNXq/yhIWFsa8efPqpOBaAxsbG9auXcv169eJjY1l8+bNXLt2zdpm1Uo6duyIv78/K1assLYpJtHr9UZzf/78+fj5+bFixQpDifnHcXR0rLbgFmuXKcEtTIrnj5jtNBu5AI+F39HCfxU2bi0N16urXVUW3ciLaQA4dXkOp879kTq6GF2XyGxx8X4VB48nwYQLlwSIvJRWVRMqjLu7O3v27GHp0qX4+vry8ccfo9NVvpimubl9+zZnzpwhICDA2qbUGVq1akXv3kXlsBs3bkzXrl25d++ela2qvSxbtoxdu3Zx584da5tSAq1Wa3RAtnDhQgoKCliyZAlRUVGcO3cO+DOnh7ko1i5T5P26C9cBb2LfxguJRIpN42bYNDb20KmOdlVZdG+k5xu7VlQBpVbPjfsPq9VHRZFIJPj7+xMXF8eRI0cYNGiQ1Sfi5s2bmTJlCk5OTla1o65y9+5d4uPjefbZZ61tSq1FLpczf/583nvvPWubYiA3N5eVK1dSWFhoeO/kyZMcO3aM8PBw+vTpg4eHBxs2bODNN99k3bp1KBQKs92/LO0S9DpU92+hL8jj3mfTSdscSE70p+g1xqva6mhXlR3O8pXaqn7UiF3ffc/6idYpzfPEE09Y5b5/Zc2aNdY2oVrU1NaIXC7n7t27pX4pKRQKxowZw/r163Fx+fMpKzc3Fz8/Pw4dOlQjNtVlvvnmG2ubYKB9+/ZGe/GDBg0iKioKe3t7Dh8+zJkzZ7h27Rpnz57lyy+/pEOHDrzxxhsl+snPz2fWrFmVGpt8zHs4dSr9i1r3KBf0WgoST9MiYDUSqYysfSvIO7OHJoOMi7DmK6tWFLTKK10Xh+o5CBfjP+4NhKJwZIv/XLlyhR49evDqq6+SkZFh0Xtv2rSJMWPGWG3s5voBaqzvzMzMUgVXo9EwZswY/P39S/whurm58fPPP1v9/6W2/WzZsoVhw4ZZ7f6FhYUsXLiQ1q1bc+jQIZKSkkrUdfPw8ACKzmHi4uJwc3NjxIgRvPjii8TFxZW6zeDi4sKuXbsQBAG9Xk9mZiZxcXHs37+fDRs2sGjRIsaPH0+/fv1o3bo1tra2OJYhXRLbomi3xn1exsa5KTInVxp7v0bh7biS93ao2t5ylUXXq6UL9jbVC7d1sJHi1cp6lWStlatXr9ezceNG5s2bZ5H71ScEQWDq1Kl07dqVhQsXWtucOsO0adO4c+cOR48etfi9H895+9tvvzF8+HCTbYu/yFu2/PPg6vvvv6djx46lhverVCrGjx9P586dcXJyokuXLkydOpUvv/ySxMRE5HI5r732GiEhIZw9e5aCggL+NSvQpHbJHJyRNS4/wrI62lXl5erYPm1Zd/Qmgl4HxT+CHkGrBqkMiVSGoNUA/1sN6bVF12S2hsdRnSAwtrd1w3Xt7e1ZtWoVo0aNYvLkyfz000+EhobWqEN5dHQ0jo6ODBw4sMbuUV85ffo0ERERdO/enZ49ewKwcuVKRo4caWXLaje2trasXLmSd955h/Pnz1skP4lOpyMkJISQkBBCQ0MJCAgwuRUlCEVuY8XXpVIpOp2OadOm0bZtW6ZNm1biM2q1mvPnzzN16lTatWuHh4dHhf5ui7XLFM7dh/DwYhSOHfuAzIaHcT/g5GnsEyxAlbWr2n66e8NDyfvVOAGE64A3cRvoT9qWKejyM42utXlrGzZuLQABbdJFvFWXWbJkCf369auqGWYjPz+fBQsWcOrUKb7++muee+65GrnPyJEjGTduXLUTdNQGxIi0uoMgCDz77LMsWrSoxkPkk5KSmDx5MjKZjO3bt+Pq6kpKSgopKSmkpqaWeD1q1ChCQkJwcHAwfCHk5ORw4MAB/vGPf5j93KAsP11BpyXnaDiPrp1EYmNLI6+BNPH5BxIbO6D6frrVEt2E1FwmfhFLoaby7leOtjK2T+rBhcP7WLt2Le3atSM4OJiRI0da3Wd1//79zJo1i2nTprF8+XLs7OzM1ndiYiIvvPACycnJODg4mK1fayGKbt3ixIkTTJ8+nWvXrpltXiuVStLS0khNTSU5OZkffviBQ4cO0b59e6RSKSkpKUilUtq1a2f48fDwMLxOTU1lwYIF7Nu3j0GDBpnFpvKornbtmdGPp9tWLXFXrci9oNVq2bt3L2vWrEGn0xEcHMzEiROtmiEpPT2dadOmcf/+fXbu3EnXrl3N0u/cuXNxdXWt1Q7rlUEU3brHiBEjGD16NHPmzKlQ++JDqjNnznDhwoUSK9WcnBzatGlDq1atSEtLQ6lUMnPmTPr3728Q18er6z7OgQMHmDFjBnv37mXw4MFmHGX5WCv3Qq3KMiYIAtHR0axevZpbt26xcOFCpk2bZrWEHYJg3ly9eXl5dOjQgStXrtCmTRszWmo9RNGtexQXcLx58yaCIBhENDU1FXd3d0aPHm2Us7YYpVLJ1q1bUalURivVFi1a8Msvv5jMeWuKr776iqVLlxIVFWUoc25p6mSWsWJ+S8tlS8wtTiRmIaHIebiY4ny6Pl3kzB7sWaFl+YULF1izZg0xMTHMmjWLuXPnWi1+vDhXr4uLC1999VWVBXP9+vWcO3eu2kmQaxOi6NZeNBoN9+7dK3Uf9fTp0xQWFiKTyQwC6u/vz5tvvlmpbQeFQsHixYs5fPgwO3bsqHAV6NDQUDZs2MDhw4fx8vKq6hDNgrm1qzzMXjnigUJF5KU0btx/SL5Sg4uDLV6tGjO2d9UqR/z3v/8lJCSEvXv34ufnx6JFiyqVc7b4VLS6FOfq3bRpE2FhYeUeRPz1vnq9ns6dOxMREUH//v2rbU9tQRRd6yAIAtnZ2SYPplJSUsjKyqJFixal7qPKZDImTZrEtWvXjNyzKkNsbCyTJk1iwIABhIWFGQWplGX3e++9R2RkJNHR0bRr165K964JzK1dpjC76NYU6enphIWFER4eztChQwkODqZXr/Ij2VJTUw1O1+bgwoULvPvuu+zbtw9nZ2eTgr5r1y5cXFx4+eWXgSLRjo6OZsSIEVY/KDQnDUl0k5OTiYmJISMjAx8fH7y9vc32pf5XCgoKTIppamoqqampODg4lCqoxa9bt25dZpWDoKAgtFotGzduLNOW0saoUql45ZVXmDFjBmPGjKnQmHQ6Hf/85z85f/48v/zyS63OfFaT1BnRLSY/P5/w8HC++uorYmNjady4dAflU6dOsXPnTnJycsjMzOSDDz7Ax8fHLDYUR9mUtb979uxZpkyZwscff8xrr70GFD3u1eXyKaXRUEQ3KSmJt99+G0dHRxo1akRhYSFBQUEGX+HKoNPpuH//fpkuVAqFAg8Pj1LFtDI+qWWRnZ3NhAkTOHLkSIm5fOnSJf7zn/8YQnVLE169Xl/hMw61Wm1Iyfnjjz9WaFVcXzFPLK8FcXFxYfHixQQFBZn8Y7958yZBQUG88847jBkzhj179vDRRx/Rvn17OnToUG0bHnfi/ivFgty/f3+OHDmCr68vGo2GcePG1TvBbUgkJiaSmJjIlStXABg+fDh5eXkl2gmCQG5ubpmP/ffv38fd3d3IheqJJ57Ax8fHIKhyubzGAxiaNWtmqM1XvI9b7KmwaNEikpKSePToEUuXLkUikZQQ2YraV1BQwJgxY7Czs+PQoUO1Lqe1palzK93yUKvVTJo0ieTkZObMmWNwPcvKysLZ2dliv/D09HRUKhXe3t706NGDnTt30qJFC4vc25I0lJXu7du3GTduHG+99RY3btwgPT2diIgIZDIZULTq2759O/Pnz0cikZT52N+mTZsKne5bApVKhSAIJXzGw8PDycnJISUlBblczgcffFCl/v/44w9Gjx6Np6cn27Ztq3ZRx/pAvRPdgwcPMmnSJHbs2EFsbCzx8fHs2LEDd3f3Gls5/PXR65tvvuH48eOkpKQwZMgQZs2aZXIbpK5Tn0S3OGFKSkoKnp6eNG3a1Oj6119/zaeffoq3tzd3795l/PjxjBs3ziCgCoUCnU5n0ie1tqLVakuI4c6dOzl69CjTp08nPDycpk2bIpPJWLVqFVKptEJ/S+np6fj6+uLj40NoaKhFQo/rAvXua2fz5s1s3LiRl19+mZdeeokpU6ag0Whq9BdeLLi7du3i8uXLfPvtt3zyySd4eXlVac9PpGZ4+PBhmfuoaWlpuLq64uHhwUcffVQiMcvBgwcJCwvD29ubn3/+mf379/Pkk08aDnTragFIiURCQUGBUUa3IUOGkJiYyIABA0hMTGTu3Lm8/vrrFV6pJiUlMXToUAIDA1m2bFm9OjyuLvVOdPv160fnzp2BotNmrVZLcnIyLVq0QKVS1VjC8HHjxpGRkcHrr7/OyZMnjdzadDqd4TFUpGYo9kkt68RfrVaXeNx/fB/Vw8PD5PZTVlYWbm5upKenA0W5ftVqdb1Y5ctkMoOXT/Hfh7OzM/fu3ePzzz8nNDSUBQsWcP36ddavX8+CBQvK7O/q1asMHz6cf/3rXxWOemtI1DvR9fT0ZNKkSYYMXnK5nP79+6PRaBg8eDAtW7ZkyZIlDBgwwKz3DQsLo1WrVoZ/Fx86KJVKZDKZKLrVoNgntSxBzczMNPikFgtrt27d8PX1NYhs06ZNq7zicnd3p2XLlmzbto2cnBx+/PFHunbtSu/evWvMbcySdO7cmT179vDqq6/i6OiIs7MznTp1YuXKlYSEhDBu3DhiYmKM5nhpxMbG8uqrr7Ju3Tr8/PwsZH3dot7t6QLcu3ePb775hmHDhuHh4WHYmyssLGT79u2EhIQYxHf06NFm3Xp4/IRXrVaTnp7O0KFDCQkJMfjs1ifMsadbGZ9UUy5U5fmkmoO8vDy++OILEhMT6d+/P8OHD6d169Y1ek9LcfnyZV5//XXeffddpkyZglQqJTMzk9TUVEOIbnkuYkeOHMHPz4/t27czatQoS5le56iXolseOp2Offv2sXr1apRKJW+//TZ+fn5mzSam1+u5e/cuHh4exMbGMnnyZIYOHVrjuXotTXmi+7hPqilhVSgUtG3b1mQWKnP4pIqUzl9z3u7evZuQkBC6detm1K681XxkZCSzZ89m3759Yp7ocmiQoluMIAgcO3aMNWvWcO3aNYKCgpgxY0alPA2yFSoiL6ZxIz2ffKUWFwcbvFq68GJ7R6L2fWuobvB4rt76EgpcHCCSkJBQqpiW5pNa2krVEj6pIiV5POftjh07+Nvf/sZvv/2Gr68vycnJ5KuFUuf2uD7GYbFbt25l+fLlHDx4sEJRog2dBi26j3Pp0iXWrFnD0aNHmTlzJvPmzSvTrzYhNZfNMbc4eTMLwKi6qIONFKVKxeAuzQka1o0eHn8mySjO1Tt9+nSWL19eqwMmVCoVaWlp5UZOPfnkk0ZiWlt9UkWKEASB7du3ExwczDvvvENQUJDRl97r0xbwoEVfMqTuQMm5LQCDu8iZPciTw7vD+fTTT4mOjqZTp06WHkqdRBTdv3Dnzh3Wrl3L7t27GT9+PIsXL8bT09OoTXXTwRXn6i12sDdXrt7K8LhPqilBLc6TWlYoapMmTerFCX5DISsri5kzZ3L79m127txJ9+7dja7vjL3LhwevoVTrkJTx9CGRgFSvQ/rbAU6E/5u2ba1bdqsuIYquCTIzM9m4cSOfffYZgwcPZsmSJfTt29dsiY+Lc/UuW7aM5cuXM2fOHLM+Yhf7pJraR01LS8PFxaXMfdSWLVuW63VRn4Ij6jsHDx4sM+dtVea2g42UZaOql9S7oSGKbjkoFAq2bt1KaGgoHj2fJ6u7P9kXfuLRlWOos+7SqOsgmo0OMrQvvHuZnOjP0OVnYde6M81GBWHj2txkiY+q5OrVaDT8/vvvRnunfxVXlUpV5j5q27ZtzeKzLIpu7aciOW9LK1+TsnasURtBq6Zxr5E0HfaW0fvVLV/T0BBFt4JoNBpeWfMT1/NtKfhvLEgkFCZdQtCoDaKrK8jj3ufTcR8xDyfPZ8g9tRNl2v/RavLaMovZPZ6rd8OGDQwZMqTMx/7SfFL/+ro6PqmVQRTd2k1Fc96WVagRQK9WkrYxgObj3seh3VNG16pbqLGhUe+CI2qKPJWeO0pHkOpx6lJUJViVfgudJtvQpuDmWeyataOR1/MAuD7vx8MwPzQPUrF19+BEYhZpWbk8yskoVVAdHBzw8/PD1tYWT09POnbsaBDTXr16GV63bt26Vh/AiVgfjUbDhx9+SHh4OJs3by4z5222QsXJm1llnk8UJJ5G5uSKvceTJa4JApxIzOKBQmXWZN/1FVF0K0jkxbRy22iykrFt/mfqSKmdAzZuLVFnpWDr7oFSWcjTr82gacYlo9Vp//79mTBhAh4eHri7u7NixQp++OEHFixYwEsvvVSTwxKph9y4cYOAgACaN29OfHx8uVFkFZnbiivHaPTUiyafniRA5KU0Zr7wRFVMblCIoltBbqTnG7nOlIZeo0TmZJxhSmrfCEFdCIDExp7J8/7F+gll+zJu3LiR0aNHExgYyPjx41m5cmW9KNcuUrMIgsDmzZt5//33WbFiBTNnzqzQFlN5c1ubl4kq9SruI+eZbKPU6rlx/2GV7G5oiB7pFSRfqS23jdTWAb2qwOg9vboAid2fSVQeVqAfAF9fXxISEkhLS6NPnz7Ex8dXzmCRBsXvv//O8OHDiYiI4MyZM7z11lsV3tMvb24rrh7Hvm03bN3KrqWWr9RU2N6GjCi6FcTFofyHAlv539BkJhn+rVcr0f6Rjp38z+J7Lg4V34t1d3dnz549LF26FF9fX1atWoVOpyv/gyINiu+++45evXoxYMAATp8+bciyV1HKm9uPrh7H+akXK9CPeM5QEUTRrSBeLV2wtyn67xL0OgStGvQ6EPQIWjWCXodT5/6os5N5dOM0glZN3und2DZvj617UWFMBxspXq0ql8xcIpHg7+9PXFwc0dHRDBo0iDt37ph9fCJ1j9zcXCZNmsSyZcuIiopi+fLlVUr646jKQaIvfbWrTLuOTvEAp/8dDpuiKnO7oSKKbgUZ2+fPiJu809+SEvIG+bGRPPq/E6SEvEHe6W+RObkif30puaciSF0/EdXvichfCTZ8TgDG9q5a5E67du04evQob7zxBs8++yxffvml6KrVgImJiaFHjx64uroSHx+Pt7d3pT6v1+uJiopi4MCBfPtxEFJp6UEwj64ew6nzc0jty/bprs7cbmiIfrqVoDxfxrIwpy/j1atXCQgIoH379oSHh9O8efNq91lVRD9dy6LValm7di1hYWFs27atRHWL8lCr1ezevZtPPvkEOzs7goODGTt2LLN3X64Vc7shIK50K8GcwZ442FQtGbmDjYzZgz3Lb1gBnnrqKc6dO2coB/TTTz+ZpV+R2o9UKmX27NmG6gwV5eHDh4SGhvLEE08QERHBunXruHjxIhMnTsTGxqbWzO2GgCi6laCHhxvvjvTC0bZy/21FuRe8zBomaW9vz6pVq9izZw/z5s1jxowZKBQKs/UvUjuRSqU4OzvTpEmTCrXPzMxk2bJldOzYkXPnznHgwAGOHj3K0KFDjbwbatPcru+IoltJAvq1592RXXG0lVGeR45EUhSX/tdkN+Zk4MCBJCQkoNVq6dmzJ2fPnq2R+4jUHiriCnb79m1mzZpFly5dePDgAWfPnmXPnj2GKhClUdvmdn1F3NOtIr+l5bIl5hYnErOQUOQcXkxxzlGfLnJmD/a02Crg+++/Z/bs2RbN1Svu6dYuLl68yJo1azh27BhvvfUWc+fOLTMvdGnUxrldnxBFt5o8UKiIvJTGjfsPyVdqcHGwxatVY8b2bmuVOPT09HSmTp1KRkaGRXL1iqJrGfLy8nB1dS31miAIHD16lNWrV5OYmMjChQuZNm1apSqglEZtm9v1BkGk3qHX64XPPvtMcHd3F8LCwgSdTldj9xKnUM1y+/Zt4cUXXxSCg4NLva7RaIT58+cL3bp1E7Zv3y6oVCoLWyhSWcSVbj2mKrl6K4u40jUPGo0GmUxmlMh+3bp17Nixg+nTpzNnzhyTn1Wr1djY2Ih15uoI4m+pHtOpUyd+/fVXBg4cSO/evdm7d6+1TRIphXPnzvH3v/8dtVpt9P6vv/5Kt27dDIKbmJhIYWFhic/b2dmJgluHEFe6DYQLFy4QEBCAt7c3mzZtws3NPAcg4kq36mg0GlasWMHnn39eas7brKwsXnjhBWbPns2BAwdwcXFBqVQSHByMj4+PlawWqS7i12MDwdvbm/j4eNzc3Hj66ac5fvy4tU1q0CQmJvLcc89x4cIF4uPjS00yLpfLWbRoEatXr2bmzJns37+fIUOGsH//frKzX4kizQAABtdJREFUs0vpVaROYM0NZRHrcOjQIaFNmzZCUFCQUFhYWK2+xClUOfR6vbBp0ybB3d1d2LJli6DX60tc12q1Ru8lJycbXufm5gr9+vUTkpKSLGGuSA0grnQbIMOHDychIYHU1FT69u3L5cuXrW1Sg+D3339nxIgR7NixgzNnzjBr1ixDoINer+fAgQM8//zzXL16Fb3+T9/Ydu3+TA16+PBh3NzcsLOzs7j9ImbC2qovYj30er0QEREhyOVyYdWqVSVWWBVBnEIVY+/evULz5s2F999/X1Cr1Yb3lUqlsG3bNsHLy0vo27ev8N1335X4Peh0OiE1NVUYNmyYMGTIECEuLs7S5ouYEfEgTYSUlBQCAwPRarV8/fXXdOjQofwP/Q/xIK1scnNzmTt3LufPnyciIoJnnnkGgPz8fD7//HPWr19P9+7dDYdjpkJ8Hzx4QFRUFIGBgZY0X6QGkL3//vvvW9sIEevi6urK5MmTycvLIzAwELlcTs+ePU0KQLZCxddnk9l5Lpk7QnPuCW7cfVBAh2aNcLKrn2X3Hh/z3otpnEjMLHfMMTEx+Pr60r17dyIjI+nQoQP3799n5cqVBAYG0qhRI7Zs2cLixYvp0KFDmTkVnJyc6NmzZ00NT8SCiCtdESOuXLlCQEAAHTt2JDw8HLlcbriWkJrL5phbnLyZBWBUzLA4Jn9wFzmzB3nSw6N+xORXZcxKpZJly5axe/dutm7dyogRI7h58yYhISFERkbi7+/PwoULK/VEIVJ/EA/SRIzo3r0758+fp3PnzvTo0YOoqCgAdsbeZeIXsRy5noFKqy9RPVb5v/eir2Uw8YtYdsbetYL15qUqY05ISMDb25u7d4teu7u7M3bsWJ5//nlatWpFYmIiGzduFAW3ASOudEVMcurUKQIDA/F6eTpJrr2Msk2VR1Ge1bqb9m9n7F0++vk6hZqKj9kGPY9+jWD19NHI5XLWrFnDnTt3WLRoEVOnTqVRo0Y1aLFIXUEUXZEyOXPjHgFfxaGXGu9barJTeRD9KeqMW8gcXWni8w+cujxn1MbRVsaeGf3qXPq/hNRcJn4RS6HGuPKyNjeDB9FbUN+7ATa2NOoygCZDZiB5rL6YDXrsT3+KLDeN4OBgJkyYYJEUmyJ1B3F7QaRMtl+4jyAzFlxBryNz34c4eXrjMX83TYf/k+yotWhy7hm1U2p1bIm5ZUlzzcLmmFsotSVL3T+I3oLMyY22cyNo/Y+NKFOv8vDSQaM2WgE6vTKHhIQEAgICRMEVKYEouiImyVaoOHkzq0SxQs2DVHSKHBp7v4ZEKsOxfQ/s23Tj0VXj0GJBgBOJWTxQqCxodfUwNWYAbV4Gjbo+j8TGDplzExw79EGTnWLcSCLlep6UnEfqkh2IiCCKrkgZRF5MK/1CqRtSAuqs5BLvSoDISyb6qYWYHDPg0vcVHl07hV6jRPswm8I7cTh26F2iXV0bs4hlEUVXxCQ30vNLnNgD2Lq3RebkSv65fQg6LYVJl1CmXEXQllzRKrV6btx/aAlzzYKpMQM4eHRHk51Cauh47m3+O3YtO+HYuX+JdnVtzCKWRRRdEZPkK7Wlvi+R2SAfs4zC23GkbZxE/vn9NOr6PLLGzUz0o6lJM82KqTELgp6Mvctx6vIc7Rbto+38b9ArFeTGfGWin7ozZhHLIoquiElcHExHl9k170BL/1V4LNhNiwkfos1Nx75VZxP91J3DJFNj1hc+RJefRePeo5HY2CJzdMH56SEU3o4z0U/dGbOIZRFFV8QkXi1dsLcpfYqoM5MQtGr0GiV5575Hq/gD5+5DSrRzsJHi1ap6BRItiakxy5xcsXFtwcP4nxH0OvRKBYorx7BtXjLIoa6NWcSyiH66IibJVqgYsPp4qXucfxz/EkXCYQS9DnuPJ2k6dCa2TVqXaGdvI+XMkhfrTPXYssaszrhDztFwNJlJIJXh0K47TYfNQtbI2A+5ro1ZxLKIoitSJjMi4jhyPaNUF6rykEjAt1sLPgvoa37DapCGOGYRyyFuL4iUyZzBnjjYyMpvWAoONjJmD/Y0s0U1T0Mcs4jlEEVXpEx6eLjx7kgvHG0rN1WKci941bkQYGiYYxaxHPUz+amIWSlOWvPRzzdQanVlPnZLJEWrvXdHetXZZDfQMMcsYhnEPV2RCvNbWi5bYm5xIjELCRhlHSvOLevTRc7swZ71ZrXXEMcsUrOIoitSaR4oVEReSuPG/YfkKzW4ONji1aoxY3u3rbcn9g1xzCI1gyi6IiIiIhZEPEgTERERsSCi6IqIiIhYEFF0RURERCyIKLoiIiIiFkQUXRERERELIoquiIiIiAX5fymojHnFRr2yAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "import heapq\n",
    "import numpy as np\n",
    "\n",
    "def undirected_djikstra_heap(DG, source, destination):\n",
    "    #Heap implementation which does the following\n",
    "    #\n",
    "    # 1. For vertices in X, find all edges originating from them to all vertices not in X\n",
    "    # 2. Keep track of minimum value of len(w) + lwv\n",
    "    # 3. Return w, v and lwv\n",
    "    X = [source]\n",
    "    minHeap = []\n",
    "    heapq.heappush(minHeap, [0, source])\n",
    "    all_nodes = list(DG.nodes)\n",
    "    for node in all_nodes:\n",
    "        DG.nodes[node]['shortest_dist'] = float('inf') \n",
    "    while len(minHeap) != 0:\n",
    "        w = heapq.heappop(minHeap)\n",
    "        X.append(w[1])\n",
    "        DG.nodes[w[1]]['shortest_dist'] = w[0]\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] == w[1]) and (edge[1] not in X):\n",
    "                edge_tail = edge[0]\n",
    "                edge_head = edge[1]\n",
    "            elif (edge[1] == w[1]) and (edge[0] not in X):\n",
    "                edge_tail = edge[1]\n",
    "                edge_head = edge[0]\n",
    "            else:\n",
    "                continue\n",
    "            if ((edge_tail == w[1]) and (edge_head not in X)) : # node that has just been popped should be the tail\n",
    "                dji_greedy = w[0] + DG.edges[edge_tail, edge_head]['weight'] #djikstra's greedy criterion\n",
    "                if len(minHeap) == 0:\n",
    "                    heapq.heappush(minHeap, [dji_greedy, edge_head])\n",
    "                    continue\n",
    "                singlenp = [i[1] for i in minHeap]\n",
    "                if edge_head not in singlenp:\n",
    "                    heapq.heappush(minHeap, [dji_greedy, edge_head])\n",
    "                else:\n",
    "                    dest_idx = singlenp.index(edge_head)\n",
    "                    if dji_greedy < minHeap[dest_idx][0]:\n",
    "                        minHeap[dest_idx] = minHeap[0]\n",
    "                        heapq.heapify(minHeap)\n",
    "                        heapq.heappop(minHeap)\n",
    "                        heapq.heappush(minHeap, [dji_greedy, edge_head])\n",
    "    #print(\"Printing minimum distances from starting vertex \\'{}\\'\".format(source))\n",
    "    B = []\n",
    "    for node in all_nodes:\n",
    "        if node in destination:\n",
    "            #print(\"Vertex {} is at distance {}\".format(node, DG.nodes[node]['shortest_dist']))\n",
    "            B.append([node, DG.nodes[node]['shortest_dist']])\n",
    "    B = sorted(B)\n",
    "    return B\n",
    "\n",
    "            \n",
    "def undirected_djikstra_naive(DG, source, destination):\n",
    "    X = [source]\n",
    "    A = {}\n",
    "    A[source] = 0\n",
    "    all_nodes = list(DG.nodes)\n",
    "    minimum_2nd_overall = float('inf')\n",
    "    w_overall = float('inf')\n",
    "    while len(X) != len(all_nodes):\n",
    "        for edge in list(DG.edges):\n",
    "            if (edge[0] in X) and (edge[1] not in X):\n",
    "                edge_tail = edge[0]\n",
    "                edge_head = edge[1]\n",
    "            elif (edge[1] in X) and (edge[0] not in X):\n",
    "                edge_tail = edge[1]\n",
    "                edge_head = edge[0]\n",
    "            if ((edge_tail in X) and (edge_head not in X)) :\n",
    "                dji_greedy = A[edge_tail] + DG.edges[edge_tail, edge_head]['weight'] #djikstra's greedy criterion\n",
    "                if edge_head not in A:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                elif dji_greedy < A[edge_head]:\n",
    "                    A[edge_head] = dji_greedy\n",
    "                if dji_greedy < minimum_2nd_overall:\n",
    "                    minimum_2nd_overall = dji_greedy\n",
    "                    w_overall = edge_head  \n",
    "        minimum_2nd_overall = float('inf')\n",
    "        X.append(w_overall)\n",
    "    #print(\"Printing minimum distances from starting vertex {}\".format(source))\n",
    "    B = []\n",
    "    for node in A:\n",
    "        if node in destination:\n",
    "            #print(\"Vertex {} is at distance {}\".format(node, A[node]))\n",
    "            B.append([node, A[node]])\n",
    "    B = sorted(B)\n",
    "    return B\n",
    "        \n",
    "\n",
    "    \n",
    "from heapq import heappush, heappop\n",
    "\n",
    "\n",
    "g = nx.Graph()\n",
    "g.add_node(1, pos = (-3, 20))\n",
    "g.add_node(2, pos = (5, 25))\n",
    "g.add_node(3, pos = (10, 25))\n",
    "g.add_node(4, pos = (15, 20))\n",
    "g.add_node(5, pos = (20, 15))\n",
    "g.add_node(6, pos = (20, 10))\n",
    "g.add_node(7, pos = (15, 5))\n",
    "g.add_node(8, pos = (10, 0))\n",
    "g.add_node(9, pos = (5, 0))\n",
    "g.add_node(10, pos = (0, 5))\n",
    "g.add_node(11, pos = (-5, 10))\n",
    "g.add_node(12, pos = (-5, 15))\n",
    "g.add_node(13, pos = (5, 30))\n",
    "g.add_node(14, pos = (5, 35))\n",
    "\n",
    "\n",
    "edges = [(4,5,6),(7,3,6),(10,13,6),(4,5,3),(14,13,6),(14,5,2),(5,2,1), (1,2,20), (1,5,3), (2,5,4), (13, 2,1), (12,2,10), (12,3,8), (9,2,3), (4,3,30), (4,12,20), (12,9,7), (11,6,2), (11,10,6), (6,10,8), (8,7,5), (8,5,4), (7,5,3), (5,6,30)]\n",
    "g.add_weighted_edges_from(edges)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 1\n",
    "dest_verts = g.nodes\n",
    "heap_dji = undirected_djikstra_heap(g, start_vert, dest_verts)\n",
    "naive_dji = undirected_djikstra_naive(g, start_vert , dest_verts)\n",
    "\n",
    "for a in range(len(dest_verts)):\n",
    "    assert heap_dji[a][1] == naive_dji[a][1]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/aishwaya/anaconda2/envs/python_3_6/lib/python3.6/site-packages/urllib3/connectionpool.py:847: InsecureRequestWarning: Unverified HTTPS request is being made. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#ssl-warnings\n",
      "  InsecureRequestWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "challenge_graph_g = testcase()\n",
    "start_vert = 1\n",
    "dest_verts = challenge_graph_g.nodes\n",
    "heap_dji = undirected_djikstra_heap(challenge_graph_g, start_vert, dest_verts)\n",
    "naive_dji = undirected_djikstra_naive(challenge_graph_g, start_vert , dest_verts)\n",
    "\n",
    "for a in range(len(dest_verts)):\n",
    "    assert heap_dji[a][1] == naive_dji[a][1], \"Dist Mismatch at Vertex {} dist heap {}, Vertex {} dist naive {}\".format(heap_dji[a][0], heap_dji[a][1], naive_dji[a][0], naive_dji[a][1])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above assert did not fail when comparing naive implementation and heap implementation of Djikstra Algorithm so they give same result on challenge dataset. <br>\n",
    "Note : Naive implementation was previously implemented correctly on challenge dataset\n",
    "\n",
    "Ans:  2599,2610,2947,2052,2367,2399,2029,2442,2505,3068"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex 's'\n",
      "Vertex s is at distance 0\n",
      "Vertex v is at distance 1\n",
      "Vertex w is at distance 3\n",
      "Vertex t is at distance 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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CjRs34OrqitWrV6N3796ix9E8brpiGQoQsbGxcHV1FT2OYjB0Kyk5ORm9e/dmcUIGGLriZGVlwc3NDRMnTsTw4cNFj6MoDN0qYHFCHhi6YrAAYRqGbhVIkoT3338fOp0O4eHhPHSCMHTFYAHCNAzdKrp//z7c3d0xevRojB49WvQ4msTQtT5DASI5ORmtWrUSPY4iMXRNYChO7NixA25ubqLH0RyGrnVdu3YNrq6uCAoKQs+ePUWPo1i8ZMwETzzxBIKDg+Hj44P09HTR4xBZjKEAMXToUAauibjpmgGLE2Jw07WeyZMnIzU1lQUIM+CmawZz5syBJEksTpAqRUdHIyoqigUIM+Gmaybp6elwcXHBqlWr0KdPH9HjaAI3XctLS0tDly5dEBcXBxcXF9HjqAI3XTNp2LAhIiMjMXz4cFy8eFH0OEQmy8rKgoeHB+bPn8/ANSNuuma2Zs0aBAYGsjhhBdx0LUeSJPTv3x+Ojo4ICQkRPY6qMHTNjMUJ62HoWs6KFSsQHh7OAoQFMHQtgMUJ62DoWsbhw4fh6enJAoSFMHQt5OLFi+jYsSO2b98Od3d30eOoEkPX/AwFiODgYLz11luix1ElPpFmIW3btsXatWtZnCDFyM/PR9++fTFs2DAGrgVx07WwadOmISUlBXv27OE1jmbGTde8PvnkE5w5cwa7du1CtWrcxyyF31kLmzNnDgDgiy++EDwJUfmioqIQHR2N9evXM3AtjJuuFbA4YRncdM2DBQjr4o80K/h7ceLChQuixyEqYShALFiwgIFrJdx0rcjf3x/+/v5ISkqCo6Oj6HEUj5uuaSRJQr9+/VCrVi2sXbtW9DiawdC1IkmSMHjwYEiShK+//prFCRMxdE2zfPlyfPPNN0hMTISDg4PocTSDv16wIp1Oh4CAAJw6dQoBAQGix1G8DRs2iB5BsZKTkzF//nxERUUxcK2MoWtlNWvWRHR0NNLT01FYWCh6HEXr37+/6BEUSZIk3L59G2FhYWycCcBfLwhSUFAAW1vbUh8vLCyEXq/H448/LmAqUqO0tDS0adMGdnZ2JR/Ly8tD9erVBU6lXdx0BSkrcAHgwIED6NmzJ6ZMmWLliUhtfvvtN3Tp0gULFizAn3/++cDnGLjicNOVmZycHOzYsQOjRo1CamoqmjZtKnokUqC8vDz4+PjA3d0dU6dOLfm4JEl8AlcwbroyU1RUhI0bN2Ly5Mlo2rQpioqKRI9ECmP4nW3jxo1LAnfHjh24cuUKsrKyBE9HZf8/LgkTGBiIzMzMkr8s3EqKpaWl4ffff4ebmxucnJxKPh4XF4f/+7//EziZ/Oh0Otjb2+PQoUPYv38/1q1bh4yMDNSrVw/16tXDqlWreK4E4qYrIz/99BNCQ0OxYMECAMVPqvEvB7By5Ur06dMHq1atQrt27bBt27aSz02bNk3gZPJVp04dDB8+HFOmTEHXrl0RFxeHadOm4d69e4iIiBA9nqYxdAWTJAm7d+8GACxbtgzvvPMOXF1dIUkSX5Xsf4KDg3Hs2DFs3boV8fHxmDNnDlasWAEALEcY4enpifv37+Pnn38GALRr1w6PPPIIGjduLHgybWPoCpaVlYWVK1fisccew/HjxzFv3jwADJO/KywsLPmVQsuWLREfH4/du3dj0qRJ/D4Z8fjjj8Pf3x87d+7EDz/8gE2bNiE+Pp5vvyMYQ1ewWrVqYffu3Zg6dSouX76M7du3Q5Ikvrze3zRp0gQnTpwo+XcnJyfs3LkTN2/eRGpqqsDJ5K9bt26YP38+4uLiEBwcjODgYHTu3Fn0WJrGS8ZkRK/X4+zZs3jjjTeg0+lQVFTE8EXx98XW1hZNmjQp9bnExER06tRJwFTyJUkSf3DLGP9UZKRZs2bo0aMHdDod8vLyMG/ePBQUFIgeS7hmzZqVGbgAGLhlWLJkCfLz80WPQeVg6MqUnZ0dDh06hM8//1z0KLJ1+vRp0SPIzubNm+Hv78/ru2WMv16QsZs3b8LFxQUrVqzAu+++K3oc2eFLOz7o7NmzePXVV7Fnzx689NJLosehcnDTlbEGDRogMjISI0aM4DtOkFF3796Fh4cHFi5cyMCVOW66ChAQEAA/Pz8kJyfzHSf+hptuMUmS0LdvX9SpUwfBwcGix6GHYOgqgCRJ+PDDD5Gfn4/169ezpfY/DN1iy5Ytw4YNG3D48GG+ILkCMHQV4v79++jYsSOGDRuGcePGiR5HFhi6wKFDh+Dj44OjR4/yNZgVgqGrIL/88gs6duyIrVu34pVXXhE9jnBaD92rV6/C1dUV69atw7/+9S/R41AF8Yk0BWnTpg1CQkLg4+ODGzduiB6HBMrPz4ePjw9GjhzJwFUYbroK9Pnnn+PIkSP47rvvyn0HCi3Q8qY7adIknDt3Djt27GDzTGH4p6VAs2fPhq2tLaZPny56FBJg8+bN2Lp1K7755hsGrgJx01UoQ3Fi+fLleO+990SPI4QWN92ff/4ZXbt2xXfffYcXX3xR9DhUBfwxqVANGjRAVFQURo4cifPnz4seh6zg7t278PT0xKJFixi4CsZNV+ECAwOxevVqTRYntLTpSpIEHx8fPPLIIwgKChI9DpmAoatwWi5OaCl0WYBQD4auCmRnZ6Njx44YMmQIPvroI9HjWI1WQpcFCHVh6KrEr7/+ildeeQUxMTHo2LGj6HGsQguh+8cff6BDhw4IDQ3Fm2++KXocMgM+kaYSrVu3RkhICPr27Yvr16+LHofMwFCAGDVqFANXRbjpqswXX3yBw4cPY+/evaovTqh90/34449x4cIFbN++ndfjqgj/JFVm1qxZqF69OosTCvftt99i27ZtLECoEDddFbp58yZcXV2xbNkyeHh4iB7HYtS66bIAoW78EapChnecGDVqFM6dOyd6HKqEzMxMeHh4YPHixQxcleKmq2JBQUFYuXIljh49qsrihNo2XUmS4O3tjfr16yMwMFD0OGQhDF0VkyQJQ4YMQW5uLiIiIlRXnFBb6C5duhSbNm3C999/zwKEijF0VU7NxQk1hW5CQgL69u3LAoQGMHQ1wFCc2LJlCzp16iR6HLNRS+j+8ccfcHV1RVhYGK/H1QA+kaYBrVu3xrp161ickCFDAWLMmDEMXI3gpqshM2bMwPfff6+a4oQaNt2JEyfil19+wbZt23g9rkbwT1lDZs6cierVq2PatGmiRyEAmzZtwo4dO/D1118zcDWEm67GZGRkwMXFBUuXLoWnp6focUyi5E33zJkz6NatG/bu3YsXXnhB9DhkRfzxqjH169dHVFQUixMCGQoQS5YsYeBqEDddjQoODsby5ctx9OhRODk5iR6nSpS46UqSBC8vLzRs2BABAQGixyEBGLoaJUkShg4diuzsbGzYsEGRxQklhu6SJUuwefNmfP/997C3txc9DgnA0NWw7OxsdOrUCR988AHGjx8vepxKU1roGgoQKSkpaNGihehxSBCGrsYpuTihpND9/fff0aFDBxYgiE+kaV3r1q0RGhqKvn374tq1a6LHUaW8vDz4+Phg7NixDFzipkvFZs6ciYSEBOzbt08xxQmlbLoTJkzAb7/9hq1bt/J6XOKmS8VmzJgBBwcHfPbZZ6JHUZWNGzdi165dLEBQCW66VCIjIwOurq5YsmSJIooTct90WYCgsvBHL5WoX78+IiMjMXr0aKSlpYkeR9FYgKDycNOlUtauXYtly5YhJSVF1sUJuW66hgJEo0aN4O/vL3ockhmGLpVp6NChuHfvHjZu3Cjb4oRcQ3fx4sWIiorCoUOHWICgUhi6VCZDcWLw4MGYMGGC6HHKJMfQjY+PR79+/ViAoHIxdKlcv/32G9zd3WVbnJBb6BoKEOHh4ejRo4focUim+EQalatVq1YsTlTQ3wsQDFwyhpsuPdSsWbNw8OBB7Nu3D3Z2dqLHKSGnTXf8+PG4dOkSCxD0UDwd9FAzZsxAzZo1WZwox8aNGxEbG8sCBFUIN12qEENxYvHixfDy8hI9DgB5bLqnT59G9+7dsW/fPrRv317oLKQM/LFMFWJ4xwkWJ/6SmZkJT09PLF26lIFLFcZNlypFTsUJkZuuJEnw9PRE48aNWYCgSmHoUqUNGzYMd+/exaZNm4QWJ0SG7qJFixAdHc0CBFUaQ5cqLScnB506dcKgQYMwceJEYXOICt2DBw9iwIABSElJQfPmza3++KRsDF2qEkNxIjo6Gp07dxYyg4jQNRQgvv76a7zxxhtWfWxSBz6RRlXSqlUrhIWFoV+/fpopTuTl5cHb2xvjxo1j4FKVcdMlk4gsTlh702UBgsyBJ4dMMmPGDDg6OmLq1KmiR7GoiIgIFiDILLjpkslu3boFFxcXLFq0CN7e3lZ7XGttuoYCxP79+/H8889b/PFI3fgjm0xWr149REdHY8yYMTh79qzocczqzp078PDwwLJlyxi4ZBbcdMlsQkJCsHTpUqsVJyy96RoKEE2aNMGaNWss9jikLQxdMitrFicsHbosQJAlMHTJrHJyctC5c2f4+vpavDhhydA9cOAABg4cyAIEmR1Dl8zu0qVLcHNzQ1RUFLp06WKxx7FU6Or1enTo0AHr16/H66+/bvb7J23jE2lkdi1btkR4eDj69euHq1evih6nUgwFiPHjxzNwySK46ZLFzJ49G/v378f+/fstUpywxKb70Ucf4fLly4iJieH1uGQRPFVkMV988QWcnJwUU5yIiIhAXFwcwsPDGbhkMdx0yaJu3boFV1dXLFy40OzFCXNuuqmpqXjttddYgCCL449zsqh69eohKipK1sWJO3fuwNPTE1999RUDlyyOmy5Zxbp167B48WKkpKSgVq1aZrlPc2y6kiTBw8MDTZs2hZ+fn1nmIjKGoUtWM3z4cNy5cwfffvutWYoT5gjdhQsXIiYmBgkJCSxAkFUwdMlqDMWJgQMH4uOPPzb5/kwNXRYgSASGLlnVpUuX4O7ujsjISJOLE6aELgsQJAqfSCOrkkNxwlCAmDBhAgOXrI6bLgnx5ZdfYu/evThw4ECVixNV3XTHjRsHvV6PmJgYoe9mTNrETZeE+Pzzz1G7dm18+umnVn3ciIgI7NmzB+Hh4QxcEoKbLgljKE4sWLAAPj4+lf76ym66LECQHHDTJWEMxYmxY8davDhheAcIFiBING66JFxoaCgWLVpU6eJERTfdoqIieHh4oFmzZli9erUpoxKZjKFLsjBixAj8+eef2Lx5c4V/11rR0F2wYAG2bduGhIQEVK9e3dRRiUzC0CVZMBQnBgwYgEmTJlXoayoSuvv374evry9++OEHNGvWzByjEpmEoUuy8d///hdubm7YvHkzXn311Yfe/mGhayhARERE4LXXXjPnqERVxifSSDYef/xxhIeHo3///iYXJ3Jzc+Hl5YUJEyYwcElWuOmS7MyZMwd79uzBwYMHjRYnjG26Y8eOxR9//IEtW7bwelySFW66JDvTp09H3bp1MWXKlCp9/fr167F3716EhYUxcEl2uOmSLP35559wcXEpVZy4mZWLqGN6pF3LxIbIGAzwfg/OTWrD26UZ6jvZ49SpU3j99ddx4MABPPfccwL/C4jKxtAl2frpp5/w5ptvIiEhAfm1msIv/iISzqcDAHILikpu52BbDRKATq3qIiFgOr6cMBQDBw4UNDWRcQxdkrXQ0FDM/fYQbDv4ILewCEZPq1QEGxRh9rvt4eve0lojElWKregBiIyxe7o7il6oh5y/bbbl0lVDIaphbmxxpZjBS3LEJ9JItk5euY25sWko0lVuN8jOL8Lc2DSc0t+20GREVcfQJdnyi7+InILCKn1tTkEh1sRfNPNERKZj6JIs3czKRcL5dOO/wzVCkoCD59KRkZVr3sGITMTQJVmKOqYv9bE7SZFIj5n3wMdu7Q3Erb2BZd6HDkDU8dL3QyQSQ5dkKe1a5gOXhQGA4zNdkf3LMRTl3gcASEWFuJ92GI7PdC3zPnIKipB29a7FZyWqDIYuyVJmTkGpj9nWaYTqTdrg/vkkAEDOf09BZ2cP+8ecjdxPvsVmJKoKhi7JUm2Hsq9YcHymK+6dPQQAuPdzQrlb7l/3U7U3vSSyFIYuyZJzk9qwty19PGs6d0bu5VQUZN7E/fNJcHz5fw3EAAABO0lEQVSmW7n34WBbDc6PVvydKIisgaFLsuTlUvYLjtvUrAP7Fs8hI3Y5bOs0hl2D5uXehwTA6yW+cDnJC0OXZKmBkz26PtkQZb1ImOMzXZFz6QQcny3/Vws6HdD9qYao72RvwSmJKo+vvUCydfLKbfQLTkZ2fuULEjXsbPDtCHc836yuBSYjqjpuuiRb7ZvXxfSezqhhV7ljWsOuGqb3dGbgkizxBW9I1gwvWjM3Ng05BYVGG2o6HeBga4PpPZ35YjckW/z1AinCKf1trIm/iIPn0qEDHnjVMcPr6XZ/qiHGdGvLDZdkjaFLipKRlYuo43qkXb2LzJx81Hawg/OjteD1UjM+aUaKwNAlIrIiPpFGRGRFDF0iIiti6BIRWRFDl4jIihi6RERWxNAlIrIihi4RkRUxdImIrOj/Afg3yHcQPF5BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = nx.Graph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('v', pos = (5, 0))\n",
    "g.add_node('w', pos = (5, 5))\n",
    "g.add_node('t', pos = (10, 5))\n",
    "g.add_edge('s', 'v', weight = 1)\n",
    "g.add_edge('v', 't', weight = 6)\n",
    "g.add_edge('s', 'w', weight = 4)\n",
    "g.add_edge('v', 'w', weight = 2)\n",
    "g.add_edge('w', 't', weight = 3)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "dest_verts = ['s', 'v', 'w', 't']\n",
    "undirected_djikstra_heap(g, start_vert, dest_verts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing minimum distances from starting vertex 's'\n",
      "Vertex s is at distance 0\n",
      "Vertex a is at distance 5\n",
      "Vertex b is at distance 5\n",
      "Vertex c is at distance 8\n",
      "Vertex d is at distance 8\n",
      "Vertex e is at distance 16\n",
      "Vertex f is at distance 6\n",
      "Vertex g is at distance 4\n",
      "Vertex h is at distance 7\n",
      "Vertex i is at distance 9\n",
      "Vertex t is at distance 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = nx.Graph()\n",
    "g.add_node('s', pos = (0, 5))\n",
    "g.add_node('a', pos = (5, 10))\n",
    "g.add_node('b', pos = (10, 10))\n",
    "g.add_node('c', pos = (15, 10))\n",
    "g.add_node('d', pos = (5, 5))\n",
    "g.add_node('e', pos = (10, 5))\n",
    "g.add_node('f', pos = (15, 5))\n",
    "g.add_node('g', pos = (5, 0))\n",
    "g.add_node('h', pos = (10, 0))\n",
    "g.add_node('i', pos = (15, 0))\n",
    "g.add_node('t', pos = (20, 5))\n",
    "g.add_edge('s', 'a', weight = 5)\n",
    "g.add_edge('a', 'b', weight = 5)\n",
    "g.add_edge('b', 'c', weight = 3)\n",
    "g.add_edge('c', 't', weight = 4)\n",
    "g.add_edge('s', 'd', weight = 8)\n",
    "g.add_edge('d', 'e', weight = 9)\n",
    "g.add_edge('e', 'f', weight = 10)\n",
    "g.add_edge('f', 't', weight = 2)\n",
    "g.add_edge('s', 'g', weight = 4)\n",
    "g.add_edge('g', 'h', weight = 20)\n",
    "g.add_edge('h', 'i', weight = 2)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "g.add_edge('a', 'f', weight = 1)\n",
    "g.add_edge('b', 'f', weight = 1)\n",
    "g.add_edge('b', 'g', weight = 1)\n",
    "g.add_edge('h', 'f', weight = 1)\n",
    "g.add_edge('i', 't', weight = 1)\n",
    "pos = nx.get_node_attributes(g, 'pos')\n",
    "weights = nx.get_edge_attributes(g, 'weight')\n",
    "nx.draw_networkx_edge_labels(g, pos, edge_labels = weights)\n",
    "nx.draw(g, pos, with_labels = True)\n",
    "\n",
    "start_vert = 's'\n",
    "dest_verts = g.nodes\n",
    "undirected_djikstra_heap(g, start_vert, dest_verts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}