diff --git a/Detablan_AllLectures_ANSWERS/.ipynb_checkpoints/Detablan_LECTURE4_Answers-checkpoint.ipynb b/Detablan_AllLectures_ANSWERS/.ipynb_checkpoints/Detablan_LECTURE4_Answers-checkpoint.ipynb new file mode 100644 index 0000000..7fa8bcc --- /dev/null +++ b/Detablan_AllLectures_ANSWERS/.ipynb_checkpoints/Detablan_LECTURE4_Answers-checkpoint.ipynb @@ -0,0 +1,498 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bf11225b-2b3b-42e7-937e-5e7bc68b99cd", + "metadata": {}, + "source": [ + "**Name:** Paul France M. Detablan\n", + "\n", + "**Program and Year:** BSCS - 1\n", + "\n", + "$\\textbf{Assignment}$\n", + "-\n", + "Read about (Susanna Epp pp. 704):\n", + "1. Kruskal's Algorithm\n", + "2. Prim's Algorithm\n", + "3. Djitraka's Shortest Path Algorithm\n", + "\n", + "Given the following graph, implement the algorithm in Python." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "6587fe71-ad98-4c57-b47c-9a2d5fd308dc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "seed = 55\n", + "# Use seed for reproducibility\n", + "G = nx.Graph()\n", + "plt.figure(figsize=(10, 8))\n", + "# Add nodes\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\"])\n", + "# Add self-loops to the remaining nodes\n", + "edgelist = [(\"A\",\"C\"),(\"A\",\"I\"),(\"C\",\"B\"),(\"C\",\"E\"),(\"C\",\"D\"),(\"B\",\"E\"),(\"I\",\"E\"),(\"E\",\"F\"),(\"F\",\"G\"),(\"G\",\"E\")]\n", + "G.add_edges_from(edgelist)\n", + "pos = nx.planar_layout(G) # Seed for reproducible layout\n", + "nx.draw_networkx_edge_labels(\n", + " G, pos,\n", + " edge_labels={(\"A\",\"C\"):10,(\"A\",\"I\"):5,(\"C\",\"B\"):20,(\"C\",\"E\"):15,(\"C\",\"D\"):30,(\"B\",\"E\"):25,(\"I\",\"E\"):40,(\"E\",\"F\"):35,(\"F\",\"G\"):50,(\"G\",\"E\"):45},\n", + " font_color='red'\n", + ")\n", + "nx.draw(G, pos=pos,with_labels=True)\n", + "nx.draw(\n", + " G, pos, edge_color='black', width=1, linewidths=1,\n", + " node_size=500, node_color='pink', alpha=0.9,\n", + " with_labels=True)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "4fbd4175-929d-460e-be74-a766b8dadfe8", + "metadata": {}, + "source": [ + "$\\textbf{Kruskal's Algorithm}$\n", + "-\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "0c51b50f-1522-4b08-bf90-6741b14c5b85", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def kruskal_algorithm(G):\n", + " # Initialize the minimum spanning tree\n", + " MST = nx.Graph()\n", + " # Sort edges by weight\n", + " sorted_edges = sorted(G.edges(data=True), key=lambda x: x[2]['weight'])\n", + " # Create a disjoint set data structure\n", + " disjoint_set = {node: {node} for node in G.nodes()}\n", + " \n", + " # Iterate through the sorted edges\n", + " for u, v, data in sorted_edges:\n", + " if find(disjoint_set, u) != find(disjoint_set, v):\n", + " # Add the edge to the minimum spanning tree\n", + " MST.add_edge(u, v, **data)\n", + " # Merge the sets containing u and v\n", + " union(disjoint_set, u, v)\n", + " \n", + " return MST\n", + "\n", + "def find(disjoint_set, node):\n", + " return next(iter([k for k, v in disjoint_set.items() if node in v]))\n", + "\n", + "def union(disjoint_set, u, v):\n", + " root_u = find(disjoint_set, u)\n", + " root_v = find(disjoint_set, v)\n", + " if root_u != root_v:\n", + " disjoint_set[root_u].update(disjoint_set[root_v])\n", + " del disjoint_set[root_v]\n", + "\n", + "# Define the graph\n", + "G = nx.Graph()\n", + "plt.figure(figsize=(10, 8))\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"I\"])\n", + "edgelist = [(\"A\", \"C\", 10), (\"A\", \"I\", 5), (\"C\", \"B\", 20), (\"C\", \"E\", 15), (\"C\", \"D\", 30), (\"B\", \"E\", 25), (\"I\", \"E\", 40), (\"E\", \"F\", 35), (\"F\", \"G\", 50), (\"G\", \"E\", 45)]\n", + "G.add_weighted_edges_from(edgelist)\n", + "\n", + "# Run Kruskal's algorithm\n", + "MST = kruskal_algorithm(G)\n", + "\n", + "# Draw the original graph\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos, with_labels=True, node_size=700, node_color='skyblue',\n", + " font_size=12, font_weight='bold', edge_color='gray', width=2)\n", + "\n", + "# Draw the minimum spanning tree\n", + "nx.draw_networkx_edges(MST, pos=pos, edge_color='gold', width=4)\n", + "\n", + "# Display edge labels\n", + "edge_labels = nx.get_edge_attributes(G, 'weight')\n", + "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels, font_color='red')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "052971b0-8776-4128-9b2b-e75d34876224", + "metadata": {}, + "source": [ + "$\\textbf{Solution}$\n", + "-\n", + "\n", + "| Iteration Number | Edge Considered | Weight | Action Taken |\n", + "| :-: | :-: | :-: | :-: |\n", + "| 1 | (A, I) | 5 | added |\n", + "| 2 | (A, C) | 10 | added |\n", + "| 3 | (C, E) | 15 | added |\n", + "| 4 | (B, C) | 20 | added |\n", + "| 5 | (B, E) | 25 | not added |\n", + "| 6 | (C, D) | 30 | added |\n", + "| 7 | (E, F) | 35 | added |\n", + "| 8 | (E, I) | 40 | not added |\n", + "| 9 | (E, G) | 45 | added |\n", + "| 10 | (F, G) | 50 | not added |" + ] + }, + { + "cell_type": "markdown", + "id": "f5f1ce93-ba81-4612-a894-176c5cf1474b", + "metadata": {}, + "source": [ + "$\\textbf{Prim's Algorithm}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "7aac0dbe-79a4-46bd-8a69-a2140516b4d9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def prim(graph):\n", + " # Create a copy of the graph to work with\n", + " mst = nx.Graph(graph)\n", + " \n", + " # Initialize the minimum spanning tree\n", + " MST = nx.Graph()\n", + " \n", + " # Select an arbitrary starting node\n", + " start_node = 'I'\n", + " \n", + " # Initialize set of visited nodes\n", + " visited = {start_node}\n", + " \n", + " # Iterate until all nodes are visited\n", + " while len(visited) < len(mst.nodes()):\n", + " # Find the minimum weight edge connecting a visited node to an unvisited node\n", + " min_edge = None\n", + " min_weight = float('inf')\n", + " for u in visited:\n", + " for v in mst.neighbors(u):\n", + " if v not in visited and mst[u][v]['weight'] < min_weight:\n", + " min_edge = (u, v)\n", + " min_weight = mst[u][v]['weight']\n", + " \n", + " # Add the selected edge to the minimum spanning tree\n", + " u, v = min_edge\n", + " MST.add_edge(u, v, weight=min_weight)\n", + " \n", + " # Mark the newly visited node\n", + " visited.add(v)\n", + " \n", + " return MST\n", + "\n", + "# Define the graph\n", + "G = nx.Graph()\n", + "plt.figure(figsize=(10, 8))\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"I\"])\n", + "edgelist = [(\"A\", \"C\", 10), (\"A\", \"I\", 5), (\"C\", \"B\", 20), (\"C\", \"E\", 15), (\"C\", \"D\", 30), (\"B\", \"E\", 25), (\"I\", \"E\", 40), (\"E\", \"F\", 35), (\"F\", \"G\", 50), (\"G\", \"E\", 45)]\n", + "G.add_weighted_edges_from(edgelist)\n", + "\n", + "# Run Prim's algorithm\n", + "MST = prim(G)\n", + "\n", + "# Draw the original graph\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos, with_labels=True, node_size=700, node_color='skyblue', font_size=12, font_weight='bold', edge_color='gray', width=2)\n", + "\n", + "# Draw the minimum spanning tree\n", + "nx.draw_networkx_edges(MST, pos=pos, edge_color='cyan', width=4)\n", + "\n", + "# Display edge labels\n", + "edge_labels = nx.get_edge_attributes(G, 'weight')\n", + "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels, font_color='red')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "3ead08c3-e4c5-401b-933f-31f925565a2d", + "metadata": {}, + "source": [ + "$\\textbf{Solution}$\n", + "-\n", + "\n", + "| Iteration Number | Vertex Added | Edge Added | Weight |\n", + "| :-: | :-: | :-: | :-: |\n", + "| 0 | I | | |\n", + "| 1 | A | (I, A) | 5 |\n", + "| 2 | C | (A, C) | 10 |\n", + "| 3 | E | (C, E) | 15 |\n", + "| 4 | B | (C, B) | 20 |\n", + "| 5 | D | (C, D) | 30 |\n", + "| 6 | F | (E, F) | 35 |\n", + "| 7 | G | (E, G) | 45 |" + ] + }, + { + "cell_type": "markdown", + "id": "08f62a9b-a38a-4620-844c-aae52b10b935", + "metadata": {}, + "source": [ + "$\\textbf{Dijkstra's Shortest Path Algorithm}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "82ec6e0e-aa31-43cf-bf25-85c42a860137", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shortest distances from node A : {'A': 0, 'B': 30, 'C': 10, 'D': 40, 'E': 25, 'F': 60, 'G': 70, 'I': 5}\n" + ] + }, + { + "data": { + "image/png": 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Oc2FEREQeQsW+iIgEtN27d9PW1gZAVlaWXxrouVyuPoVcaWkp6l8rDxo7dixZWVkAtLW1UV1dbTiRiIjIe1OxLyIiAau1tdUuqJxOZ5+C3NeysrIYPXo0YHVfr6+v99u1JHgVFRXhdFofn6qrq2ltbTWcSERE5N2p2BcRkYBVVVVFZ2cnANnZ2YwaNcpv13I6nX2WCGh0X95NcnIy2dnZAHR2dvZZYiIiIhJIVOyLiEhAunPnjt0ELSIigsLCQr9fMzMzk3HjxgFw+fJljh8/7vdrSvApLCzE5XIBVvPIO3fuGE4kIiLyTir2RUQkIFVWVtLd3Q1ATk4OI0eO9Ps1HQ5Hn9H9srIyPB6P368rwWXkyJHk5OQA0N3d3WdbSBERkUChYl9ERALOzZs3OXDgAABRUVEUFBQM27VnzJhBeno6ANeuXePIkSPDdm0JHgUFBURFRQGwf/9+bt26ZTaQiIjIA1Tsi4hIwKmoqLBH1JctW0ZsbOywXdvhcPDII4/Yx+Xl5bjd7mG7vgSHuLg4li5dCoDH46GiosJwIhERkb5U7IuISEC5du0aNTU1AMTExLB8+fJhzzBlyhSmTZsGWLMMDh06NOwZJPDl5eURExMDwOHDh7l+/brhRCIiIvep2BcRkYBSXl5ud8HPz8+3i6nhVlJSYj+uqKiw+weI9IiJiSE/Px8Ar9dLWVmZ4UQiIiL3qdgXEZGA0dDQQF1dHWBNk87NzTWWZcKECcyaNQvouzOASG+5ubnExcUBUFdXR0NDg+FEIiIiFhX7IiISMHqPjBYWFtoN0Ezp3Zm/qqqKjo4Og2kkEEVFRbFixQr7WKP7IiISKFTsi4hIQDh//jynTp0CIDExkUWLFhlOBKmpqcybNw+A1tZW3nrrLcOJJBAtXryYxMREAE6dOsWFCxcMJxIREVGxLyIiAcDr9VJaWmofFxUVERERYTDRfcXFxTgcDgB27dpFW1ub4UQSaCIiIigsLLSPS0tL7b4TIiIipqjYFxER4+rr6zl37hwAo0ePZsGCBYYT3Td69GgWLlwIQEdHB7t27TIbSALSwoULSU5OBuDs2bOcOXPGcCIREQl3KvZFRMSoB0f1i4uLcToD66+noqIiXC4XAG+99RYtLS2GE0mgcTqdfXo8vPnmmxrdFxERowLr05SIiISdEydOcPnyZcBaIz937lzDid4pMTGRJUuWANDV1cWOHTsMJ5JANHfuXFJTUwG4fPkyJ06cMJxIRETCmYp9ERExxuPx9OleXlJSYq+PDzQFBQVERkYCsH//fpqbmw0nkkDjcDj6jO6XlZVpdF9ERIxRsS8iIsYcOXKExsZGANLT05kxY4bhRO8tPj6epUuXAuB2u6moqDCcSALRzJkzmTBhAgCNjY0cOXLEcCIREQlXKvZFRMQIt9tNeXm5fRzIo/o98vLyiI6OBuDQoUM0NTUZTiSBxuFwUFJSYh+Xl5fjdrsNJhIRkXClYl9ERIw4dOgQN2/eBGDq1KlMnTrVcKKHGzFiBHl5eYDVWLD3zQqRHtOmTbPfzzdu3ODw4cOGE4mISDhSsS8iIsOuu7ubyspK+7j3SGigW7ZsGbGxsYC1DOHq1auGE0kg6v2erqiooLu722AaEREJRyr2RURk2O3bt4/bt28D1hrn9PR0w4n6LyoqihUrVtjHvRsMivRIT09n5syZANy+fZt9+/YZTiQiIuFGxb6IiAyrzs7OPlvXBdOofo8lS5YwcuRIwNo68OLFi4YTSSDq3Zm/qqqKzs5Og2lERCTcqNgXEZFhtXv3blpbWwGYN2+evS95MImIiKCwsNA+Li0tNZhGAtW4ceOYO3cuAHfv3uWtt94ynEhERMKJin0RERk2bW1t7Nq1C7C6lhcXF5sNNAQLFy5k1KhRAJw5c4YzZ84YTiSBqLi42N5lYteuXbS3txtOJCIi4ULFvoiIDJtdu3bR0dEBWMXy6NGjDScaPJfL1edmRWlpKV6v11wgCUhjxoxhwYIFALS3t9s3u0RERPxNxb6IiAyLlpYWexqzy+WiqKjIcKKhmzdvHikpKQBcvHiRU6dOGU4kgaioqAin0/rItXv3bu7evWs4kYiIhAMV+yIiMiyqqqro6uoCYPHixSQmJhpONHROp7NPg0GN7su7SUpKYvHixQB0dXX1aVApIiLiLyr2RUTE75qbm+2txyIjI/tsXRfsZs2aRVpaGgBXr17l7bffNpxIAlFhYSERERGAtfVkc3Oz4UQiIhLqVOyLiIjfVVRU4Ha7AcjNzSU+Pt5wIt9xOByUlJSQnJzMs88+y/Tp0zW6L+8QHx/P0qVLAXC73VRWVhpOJCIioU7FvoiI+FVTUxOHDh0CIDo6mvz8fLOB/GDatGm8+OKLzJkzB8Duvi7SW35+PtHR0QAcPHiQGzduGE4kIiKhTMW+iIj4VUVFhT3SnZeXx4gRIwwn8j2Hw4HD4cDlcpmOIgFsxIgRLF++HACv10t5ebnZQCIiEtJU7IuIiN9cvXqV2tpaAGJjY+1pzCLhatmyZcTGxgJQW1tLY2Oj4UQiIhKqVOyLiIjflJWV2Y8LCgrsKcwi4erBpSy9f0ZERER8ScW+iIj4xaVLlzhx4gQACQkJLFmyxHCiAKDGfQLk5OSQkJAAwPHjx7l06ZLhRCIiEopU7IuIiF+UlpbajwsLC4mMjDSYJkCocZ9gbT9ZWFhoH/f+WREREfGVCNMBREQk9Jw9e5b6+noARo0aRXZ2tuFEBty8Cd/5DuzYAb/3e9DVBStXgssFixZZx4mJplOKIdnZ2ezcuZNbt25RX1/P2bNnmTJliulYIiISQjSyLyIiPuX1evuMVBYXF4dnl3qHA159Fbq7YeJEOHsW/vZv4Z//GXJz4YMfhFOnTKcUQ1wuF8XFxfZxaWmpvWuFiIiIL6jYFxERnzp16hQXLlwAICUlhXnz5hlOZEhSErz4Irz9NnzsY/Dyy7Btm/W9sWOhthZ+/nPTKcWg+fPnk5KSAsCFCxc4ffq04UQiIhJKVOyLiIjPeL3ePt3FV65cidMZpn/VeDzwB38AI0fCt78N587Bpz8Nn/scxMXBn/0ZrF9vOqUY5HQ6NbovIiJ+ozX7IiLiM3V1dVy5cgWA8ePHM3v2bMOJDPF6wem0Cv2PfhS+9jX45S9h1Ch45hlrCn9OjumUEgDmzJnD+PHjaWho4MqVKxw7dozMzEzTsUREJASE6XCLiIj4msfj6TOqX1JSgiNcu887HHD6NHzpS/D66zBiBERHw3/8h1X49xT6Bw5AW5vRqGKWw+GgpKTEPi4rK8Pj8RhMJCIioULFvoiI+ERNTQ1NTU0ATJo0iYyMDMOJDPvv/4bf/AYeewxeeAH27rW671dWwic+YY36P/kkFBfDX/2V6bRiUEZGBpMmTQLg+vXr1NTUGE4kIiKhQNP4RURkyLq7uykvL7ePw3pUv8cLL8CsWVBQAFFR8PGPw9e/Dv/0TzB1qrUt34wZsGuX9XjePFi92nRqMaBndP/ll18GoKKigvnz54fnLhYiIuIzKvZFRGTIDhw4QHNzMwDTp09n8uTJhhMFgIgI6JmefeSI1Yzv+nX46U/h93///vMKC+H2bfj+91Xsh7HJkyeTkZHB22+/za1btzhw4AA56usgIiJDoGn8IiIyJF1dXezYscM+XrlypcE0AeqnP7Wm8J84cb/Qb2+//+8vXICJE60O/hK2eq/dr6yspKury2AaEREJdir2RURkSPbs2UNLSwtgdRZPS0sznCjAXLsG1dXWqP2oUdDZaRX1MTHWv//tb60mfosWWR38JWylpaUxZ84cAFpaWti7d6/hRCIiEsz0qUJERAatvb2dnTt32sca1X8XKSnQ1AT3GrARFWUV9UePwmc+A88/Dx/7GLz4otGYEhiKi4vtx1VVVXR0dJgLIyIiQU1r9kVEZNB2795N272t47KyskhJSTGcKEB99rPw1a9CXR0sXQq//CXU1MDo0fAnf2IV/ABer7Vtn4StsWPHkpWVRU1NDW1tbVRXV/e5ASAiItJfKvZFRGRQWltbqa6uBsDpdKogeT9/8ifW9P2tW+F734Nly+DDH7Y69efnQ0/XdRX6AhQVFXHkyBE8Hg/V1dXk5uYSGxtrOpaIiAQZh9fr9ZoOISIiwed3v/udXewvXryYJ5980nCiIHD7NkRHW48jIu4X+SIP2Lp1K/v37wcgLy+PRx991HAiEREJNlqzLyIiA3bnzh27eVhERASFhYWGEwWJhASr2I+OVqEv76uwsBDXvffInj17uHPnjuFEIiISbFTsi4jIgFVWVtLd3Q1ATk4OI0eONJwoSDwwTd9zb6s9TbKTB40cOZKcnBwAuru7+2xvKSIi0h8q9kVEZEBu3rzJgQMHAIiKiqKgoMBwouDTU9xfvXqVX/ziF9TW1hpOJIGooKCAqKgoAPbv38+tW7fMBhIRkaCiYl9ERAakoqLCHpFetmyZGocNgsPhoLGxkR//+MfU19dTXl6O2+02HUsCTFxcHEuXLgWsWSAVFRWGE4mISDBRsS8iIv127do1ampqAIiJiWH58uWGEwWvsWPHMm3aNMCaLXHo0CGzgSQg5eXlERMTA8Dhw4e5fv264UQiIhIsVOyLiEi/lZeX21PQ8/Pz7SJEBqekpMR+XFFRYfdBEOkRExNDfn4+YC3/KCsrM5xIRESChYp9ERHpl4aGBurq6gBrenFubq7hRMFvwoQJzJo1C+i7w4FIb7m5ucTFxQFQV1dHQ0OD4UQiIhIMVOyLiEi/9B5RLCwstBuHydCsXLnSflxVVUVHR4fBNBKIoqKiWLFihX2s0X0REekPFfsiIvJQ58+f59SpUwAkJiayaNEiw4lCR2pqKvPmzQOgtbWVt956y3AiCUSLFy8mMTERgFOnTnHhwgXDiUREJNCp2BcRkffl9XopLS21j4uKioiIiDCYKPQUFxfjcDgA2LVrF21tbYYTSaCJiIigsLDQPi4tLbX7Z4iIiLwbFfsiIvK+6uvrOXfuHACjR49mwYIFhhOFntGjR7Nw4UIAOjo62Llzp9lAEpAWLlxIcnIyAGfPnuXMmTOGE4mISCBTsS8iIu/pwVH94uJinE791eEPRUVFuFwuAPbs2UNLS4vhRBJonE5nnx4Pb775pkb3RUTkPekTm4iIvKcTJ05w+fJlwFpbPnfuXMOJQldiYiJLliwBoKurix07dhhOJIFo7ty5pKamAnD58mVOnDhhOJGIiAQqFfsiIvKuPB5Pn67fJSUl9rpy8Y+CggIiIyMB2L9/P83NzYYTSaBxOBx9RvfLyso0ui8iIu9Kxb6IiLyrI0eO0NjYCEB6ejozZswwnCj0xcfHs3TpUgDcbjcVFRWGE0kgmjlzJhMmTACgsbGRI0eOGE4kIiKBSMW+iIi8g9vtpry83D7WqP7wycvLIzo6GoBDhw7R1NRkOJEEGofDQUlJiX1cXl6O2+02mEhERAKRin0REXmHQ4cOcfPmTQCmTp3K1KlTDScKHyNGjCAvLw+wGiT2vuki0mPatGn2z+WNGzc4fPiw4UQiIhJoVOyLiEgf3d3dVFZW2se9RxBleCxbtozY2FjAWk5x9epVw4kkEPX+2ayoqKC7u9tgGhERCTQq9kVEpI99+/Zx+/ZtwFobnJ6ebjhR+ImKimLFihX2ce9GiSI90tPTmTlzJgC3b99m3759hhOJiEggUbEvIiK2zs7OPlu+aVTfnCVLljBy5EjA2gLx4sWLhhNJIOrdmb+qqorOzk6DaUREJJCo2BcREdvu3btpbW0FYN68efZ+3jL8IiIiKCwstI9LS0sNppFANW7cOObOnQvA3bt3eeuttwwnEhGRQKFiX0REAGhra2PXrl2A1e27uLjYbCBh4cKFjBo1CoAzZ85w5swZw4kkEBUXF9u7ZezatYv29nbDiUREJBCo2BcREcAqEjo6OgCryBw9erThROJyufrcdCktLcXr9ZoLJAFpzJgxLFiwAID29nb7pp2IiIQ3FfsiIkJLS4s9/dflclFUVGQ4kfSYN28eKSkpAFy8eJFTp04ZTiSBqKioCKfT+li3e/du7t69aziRiIiYpmJfRESoqqqiq6sLgMWLF5OYmGg4kfRwOp19GiVqdF/eTVJSEosXLwagq6urT6NNEREJTyr2RUTCXHNzs71lV2RkZJ8t3yQwzJo1i7S0NACuXr3K0aNHDSeSQFRYWEhERARgbaHZ3NxsOJGIiJikYl9EJMxVVFTgdrsByM3NJT4+3nAieZDD4egzul9eXo7H4zGYSAJRfHw8S5cuBcDtdlNZWWk4kYiImKRiX0QkjDU1NXHo0CEAoqOjyc/PNxtI3tO0adOYPHkyYP25HT582HAiCUT5+flER0cDcPDgQW7cuGE4kYiImKJiX0QkjFVUVNjrv/Py8hgxYoThRPJeHhzdr6iooLu722AiCUQjRoxg+fLlAHi9XsrLy80GEhERY1Tsi4iEqatXr1JbWwtAbGysPf1XAtekSZOYPn06YPVaOHDggOFEEoiWLVtGbGwsALW1tTQ2NhpOJCIiJqjYFxEJU2VlZfbjgoICe+qvBLbeo/uVlZV0dnYaTCOB6MElOb1/1kVEJHyo2BcRCUOXLl3ixIkTACQkJLBkyRLDiaS/xo8fT2ZmJgB3795lz549hhNJIMrJySEhIQGA48ePc+nSJcOJRERkuKnYFxEJQ6WlpfbjwsJCIiMjDaaRgSouLsbhcACwc+dO2tvbDSeSQBMZGUlhYaF93PtnXkREwoOKfRGRMHP27Fnq6+sBGDVqFNnZ2YYTyUClpKSQlZUFQHt7O9XV1YYTSSDKzs4mKSkJgPr6es6ePWs0j4iIDC8V+yIiYcTr9fYZ4SsuLsblchlMJINVVFSE02n9Nb57927u3r1rOJEEGpfLRXFxsX1cWlpq774hIiKhT8W+iEgYOXXqFBcuXACs0eF58+YZTiSDNWrUKBYtWgRAZ2cnO3fuNJxIAtH8+fNJSUkB4MKFC5w+fdpwIhERGS4q9kVEwoTX6+3TlXvlypX2yLAEp8LCQiIiIgDYu3cvt2/fNpxIAo3T6dTovohImNKnPBGRMFFXV8eVK1cAq6P77NmzDSeSoUpISCAnJweA7u5uKisrDSeSQDRnzhzGjx8PwJUrVzh27JjhRCIiMhwiTAcQERH/83g8fUb1S0pK7G7uEtwKCgrYv38/nZ2dHDx4kPz8fEaNGnX/CVevwv79cPgw3LoFnZ0QFQVJSbBgASxeDKmppuLLMHA4HJSUlPAf//EfAJSVlTF79mzN7BERCXEq9kVEwkBNTQ1NTU0ATJo0iYyMDMOJxFdiY2NZvnw5FRUVeDweKioqWDNtGvzgB/Daa9DYaD3R5YLexZ3HA2639XjsWHjmGfj85+Fel38JLRkZGUyaNInz589z/fp1ampqWLhwoelYIiLiR7qlKyIS4rq7uykvL7ePNaofepYvX86ImBhmHzvG4j/8Q2vE/qc/vV/og1XYd3Xd/+op9MF63k9/ar0uL8+6SaB13SGlZ3S/R0VFBe7e7wEREQk5KvZFRELcgQMHaG5uBmD69OlMnjzZcCLxteibN/nU1q0898orTLh0yfpmd/fATtLz/D17YO1aWLMG7vV4kNAwefJke1bPrVu3OHDggOFEIiLiTyr2RURCWFdXFzt27LCPV65caTCN+MXGjTB7NsnV1QA4hzoi3zPa++tfw+zZ1vklZPQe3a+srKSrq8tgGhER8Set2RcRCWF79uyhpaUFsDpyp6WlGU4kvtLc3Ezrd78L3/iGfy7gdkNzM6xfD9/4BrFf/CKJiYn+uZYMm7S0NObMmcOxY8doaWlh79695OXlmY4lIiJ+oGJfRCREtbe3s3PnTvtYo/qho7m5me8//zxdBw/CcCzL+NnPiDx8mBd/9jMV/CGguLjY3n6vqqqKxYsXEx0dbTiViIj4mop9EZEQtXv3btra2gDIysoiJSXFcCLxldZXXqHr4EHWPvEEKbGxfr/etdZWNv/mN7S+8gqJn/60368n/jV27FiysrKoqamhra2N6upqiouLTccSEREfU7EvIhKCWltbqe5Zw+106oN8KLlyBb78ZUhOJiU2lvEJCcN37S9/GVavhtTU4bum+EVRURFHjhzB4/FQXV1Nbm4uscNw40hERIaPGvSJiISgqqoqOjs7AcjOzmbUqFGGE4lPeL3wmc9Aa6uZ69+9a11f2/IFveTkZLKzswHo7Ozss+RHRERCg4p9EZEQc+fOHfbu3QtAREQEhYWFhhOJz7z+Ovznf97vmD/cPB7YssXKIUGvsLAQl8sFWM0879y5YziRiIj4kop9EZEQU1lZSfe9PdNzcnIYOXKk4UTiM3/3d+A0/Fe3ywXf/rbZDOITI0eOJCcnB4Du7u4+23SKiEjw05p9EZEQcvPmTQ4cOABAVFQUBQUFhhOJz9TUwL0+DANRfu/rvcQA/3sgJ3S7YdcuqK2F+fMHnEcCS0FBAQcOHKCzs5P9+/eTl5dHUlKS6VgiIuIDGtkXEQkhFRUVeDweAJYtW6aGW6HkBz+AiAC5Rx8RAf/0T6ZTiA/ExcWxdOlSADweDxUVFYYTiYiIrwTIpwYRERmqa9euUVNTA0BMTAzLly83nEh86rXX4N7yjPfz1zt2sPn4cY5fv86IiAhmTpzIwt/7PcaMGcMMYAXw3Msvs/vcOfs1LwGfWbyYHz75ZP+ydHdb6/Z/+MPB/JdIgMnLy2Pv3r20t7dz+PBh8vPzGTNmjOlYIiIyRCr2RURCRHl5Od57XdLz8/OJiYkxnEh85upVaGzs11Mrzp3jCzk55KSl0e3x8JnSUv793/+dz3/+88RFRTEJiAZeWLSI/7Nypf262MjIwWUaO3Zgr5OAExMTQ35+Pm+++SZer5eysjLWrVtnOpaIiAyRpvGLiISAhoYG6urqAGtabm5uruFE4lP79/f7qb/9yEd4fuFC5o4dy4Jx4/jfq1fT3NxMQ0NDn+fFRkYyLj7e/hoZHe3XXBLYcnNziYuLA6Curu4d7xcREQk+KvZFREJAWVmZ/biwsJCoqCiDacTnDh+2uuAPwt2ODgBGjBjBIeAbwFngX2prif3Wt5j0gx/w0htv0NrVNbATu1xw6NCgMkngiYqKYsWKFfZx798pIiISnDSNX0QkyJ0/f55Tp04BkJiYyKJFiwwnEp+7dcvacs/tHtDLPF4v3//tb5k4cSJje023nz9/PomJiSQkJBBz9Sq/eOMNTjQ1sfm55/p/cqcTmpsHlEcC2+LFi6murqa5uZlTp05x4cIFJk6caDqWiIgMkop9EZEg5vV6KS0ttY+LioqICJSO7eI7nZ2DetkXfv1rzjQ28uFPfhLAbtD3ycWL7efEpabyVEICj/z857x94wYZycn9v8C9WQMSGiIiIigsLOS//uu/ACgtLeVjH/sYDofDcDIRERkMTeMXEQli9fX1nLvXVX306NEsWLDAcCLxi0Esy3hx2za2njrFdz7+cUaOHAlAHDDpga/RwNIJEwA4fePGwC4ymHX+EtAWLlxI8r0bPmfPnuXMmTOGE4mIyGCp2BcRCVIPjuoXFxfjdOrXekhKSgKPp19P9Xq9vLhtG68dP07pxz7G+FGjHvqaQ1euADA+IaH/mTweSEzs//MlKDidTlb22qWhp0O/iIgEH30qFBEJUidOnODy5csApKamMnfuXMOJxG8WLOj3ev0vbNvGv9fU8H/XriUhOpobLS20tLTQ1dXFXWDHjRv8SUUFv758mZ23bvHTEyf42OuvUzh5Mlmpqf3P5HbDwoWD+s+RwDZ37lxS770XLl++zIkTJwwnEhGRwdDCThGRIOTxePp0yy4pKdG62lDWa439w/zzvn0AFP/bv/X5/urVq4lcuJB9LhevnTnDP7/1Fp2dnSQmJvIHc+bw/yss9GsuCR4Oh4OVK1fyq1/9CrA688+aNUu/Y0REgoyKfRGRIHTkyBEaGxsBSE9PZ8aMGYYTiV+lpsLYsXDvz/z9eP/8z/scl9/76pGYmMjzzz/f5zlfBEYONpOEpJkzZzJhwgQuXbpEY2MjR44cYf78+aZjiYjIAKjYFxEJMm63m/LycvtYo/ph4pln4Kc/he7uAb2s+N6XT0VEwJo1vj6rBBCHw0FJSQm/+MUvACgvLyczMxOXy2U4mYiI9JfW7IuIBJlDhw5x8+ZNAKZOncrUqVMNJ5Jh8fnPD7jQ95vubvjCF0ynED+bNm2a/fvlxo0bHD582HAiEREZCBX7IiJBpLu7m8rKSvu4pKTEYBoZVllZsHw5mN5xweWCvDzQlO6w0Pt3TEVFBd2BcsNJREQeSsW+iEgQ2bdvH7dv3wasNbXp6emGE8mw+spX+r0Fn9+43fDlL5vNIMMmPT2dmTNnAnD79m323WsAKSIigU/FvohIkOjs7GTHjh32sUb1w9CaNfD009bouglOJ6xerfX6YWblypX246qqKjo7Ow2mERGR/lKDPhGRILF7925aW1sBmDdvnr0PtoQRhwN+9CO4N9J67d77wd/s68TFWddXQ8iwMm7cOObOncvRo0e5e/cub731FitWrDAdS0REHkLFvohIEGhra2PXrl2A1SW7uLjYbCAxZ9w4Yr/3PSK/+EU2/+Y3w3bZyOZmYr/3PWvLPQk7xcXF1NXV4fV62bVrFzk5OcTExJiOJSIi70PFvohIENi1axcdHR0ALFy4kNGjRxtOJCYlfvzjvHj5Mq1f/eqwXTP2m98k8eMfH7brSWAZM2YMCxYs4NChQ7S3t7Nr1y4tJRIRCXAq9kVEAlxLSwtvvfUWAC6Xi6KiIsOJJBAkvvQSiSNGwP/6X9a0eq/X59fwYDX3ufSVr5D40ks+P78El6KiImpqavB4POzevZulS5cSFxdnOpaIiLwHNegTEQlwVVVVdHV1AbB48WISExMNJ5KA8cUvwoYNMHKkz5v2eV0uOqOj2bhuHS8nJnLlyhWfnl+CT1JSEosXLwagq6urT8NQEREJPCr2RUQCWHNzs73VVWRkpJpiyTutWwfHj8OqVQB4nUP8q/3eTQPHk09S8eMfUzd3Lt3d3WzYsIG2trahppUgV1hYSESENTF03759NDc3G04kIiLvRcW+iEgAq6iowO12A5Cbm0t8fLzhRBKQxo2D11+HzZtpysgAwD3Aot97r4Bj6VLYvBlee41HPvxh0tLSALh58yavv/46Xj8sF5DgER8fz9KlSwFwu91UVlYaTiQiIu9Fxb6ISIBqamri0KFDAERHR5Ofn282kAQ2h4OOD36QH37sY/zzZz9LbW4u3t6d810u3C4X3U4nbperz7T/lrg4bj7zDBw+DDt3wjPPgMNBREQE69atY8SIEQCcPHlSU7eF/Px8oqOjATh48CA3btwwnEhERN6NGvSJiASoiooKexQ1Ly/PLrhE3svx48dxu900jhvH5a9/nYUf/CA0NsL+/XDoEPv/+7/xtLXhHDGC3EcfpSE1lX8/dozW+HgWLVrEU1lZ7zhnUlISzz77LP/+7/8OQFlZGWlpaUyfPn24//MkQIwYMYLly5dTXl6O1+ulvLyctWvXmo4lIiIP0Mi+iEgAunr1KrW1tQDExsba02ZF3s+RI0fsx/PmzbMejB0LTzwBL71E1ZNPsv3xx6l68kl46SXGfPSjdNxr+HjmzJn3PG9GRkafbdY2b97MrVu3/PLfIMFh2bJlxMbGAlBbW0tjY6PhRCIi8iAV+yIiAaisrMx+XFBQYE+ZFXkvra2t1NfXAzBy5EgmTpz40NdERkaSnp4OWGvy36+ALygoYNasWQC0tbWxYcMGuru7hx5cgtKDS4t6/84SEZHAoGJfRCTAXLp0iRMnTgCQkJDAkiVLDCeSYFBXV4fH4wGsUX2Hw9Gv102dOtV+/H6j+w6HgzVr1pCcnAxAQ0MD27ZtG0JiCXY5OTkkJCQA1hKSS5cuGU4kIiK9qdgXEQkwpaWl9uPCwkIiIyMNppFg8a5T+Pth2rRp9uP3K/YBYmJiWL9+vb312sGDBzlw4MAAk0qoiIyMpLCw0D7u/btLRETMU7EvIhJAzp49a0/FHjVqFNnZ2YYTSTC4ffs2586dA2D06NGMGzeu369NS0sjKioKsIr9h22tl5qaylNPPWUfb9u2TSO6YSw7O5ukpCQA6uvrOXv2rNE8IiJyn4p9EZEA4fV6+4yMFRcX4+q1PZrIe3lwVL+/U/gBXC4XkydPBqClpYXr168/9DVZWVnk5uYC1l7rGzdupLW1dYCpJRS4XC6Ki4vt49LS0ofeMBIRkeGhYl9EJECcOnWKCxcuAJCSkjKgqdgS3noX+/Pnzx/w63uv2++ZWfIwjz32mN0EsLm5mVdffdXuGSDhZf78+aSkpABw4cIFTp8+bTiRiIiAin0RkYDg9Xr7dLNeuXIlTqd+RcvDNTU10dDQAMD48eMZPXr0gM/R3yZ9vblcLtatW0dcXBxg3SQoLy8f8LUl+DmdTo3ui4gEIH2SFBEJAHV1dVy5cgWwCrbZs2cbTiTBYrCN+XpLTU2190w/e/Zsv0foExIS+NCHPmQvG9ixY4e9k4SElzlz5jB+/HgArly5wrFjxwwnEhERFfsiIoZ5PJ4+o/olJSUDWnMt4cvr9fYp9ufOnTuo8zgcDqZMmQJAR0eHPVOgP6ZMmcKjjz5qH7/22ms0NTUNKocEL4fDQUlJiX1cVlamZR0iIoap2BcRMaympsYujiZNmkRGRobhRBIsrl69ajfUmzRpEomJiYM+12Cm8vdYtmwZmZmZgHWzYMOGDXR2dg46iwSnjIwMJk2aBMD169epqakxnEhEJLyp2BcRMai7u7vPOmeN6stA+GIKf4+hFPsOh4Onn36aMWPGANDY2MjWrVu1bjvMPDi6X1FRgdvtNphIRCS8qdgXETHowIEDNDc3AzB9+nR7CzSRh+k9hd/hcNgj64OVnJzMyJEjATh//jzd3d0Den10dDTPPfccUVFRANTW1rJ3794hZZLgM3nyZHt20q1btzhw4IDhRCIi4UvFvoiIIV1dXezYscM+XrlypcE0EmwuXrxo3yiaNm2a3RV/sBwOhz26393dzcWLFwd8jjFjxrB69Wr7ePv27fZ2khI+eo/uV1ZW0tXVZTCNiEj4UrEvImLInj17aGlpAaxO1mlpaYYTSTCpra21Hw91Cn+PoUzl75GZmUleXh5gNZ/cuHGj/T6X8JCWlsacOXMAaGlp0QwPERFDVOyLiBjQ3t7Ozp077WON6stAeDwe6urqAGu/+57Caqh8UewDPPLII3Z3/zt37rBp0yat3Q4zxcXF9uOqqio6OjrMhRERCVMq9kVEDNi9ezdtbW0AZGVlkZKSYjiRBJMzZ85w9+5dAGbOnEl0dLRPzjty5EhGjx4NwKVLlwZdoDmdTp599lkSEhIAOHfuHG+++aZPMkpwGDt2LFlZWQC0tbVRXV1tOJGISPhRsS8iMsxaW1vtD75Op7PPCJhIf/iyC/+Dekb3PR4P58+fH/R54uPjWbduHU6n9VGjurqao0eP+iSjBIeioqI+f/6tra2GE4mIhBcV+yIiw6yqqsregzw7O5tRo0YZTiTBpLu7m2PHjgEQFRXFjBkzfHr+adOm2Y/r6+uHdK6JEyfy+OOP28dbtmzh2rVrQzqnBI/k5GSys7MB6Ozs7LN0SURE/E/FvojIMLpz547drCoiIoLCwkLDiSTYnD592p5eP3v2bCIjI316/p619jC0dfs9lixZYk/n7urq4pVXXtH67TBSWFiIy+UCrKakd+7cMZxIRCR8qNgXERlGlZWV9v7lOTk59r7mIv3lzyn8ACNGjGD8+PEAXL16dchTrx0OB08++SSpqakANDU1sWXLFrxe75CzSuAbOXIkOTk5gDUrpfd2oyIi4l8q9kVEhsnNmzc5cOAAYE2/LigoMJxIgk1nZycnTpwArKK895R7X/JVV/4ekZGRrF+/3m4keOzYMTVsCyMFBQVERUUBsH//fm7dumU2kIhImFCxLyIyTCoqKvB4PAAsW7aM2NhYw4kk2Jw4ccKeGZKZmWlPj/Y1Xxf7YK3fXrt2rX38xhtv+OzcEtji4uJYunQpYDV+rKioMJxIRCQ8qNgXERkG165do6amBoCYmBiWL19uOJEEI39P4e8xadIku4u6LwvymTNn2n0qvF4vmzZt4vbt2z47vwSuvLw8YmJiADh8+DDXr183nEhEJPSp2BcRGQbl5eX2GuX8/Hz7Q69If7W1tXH69GkAEhISmDx5st+uFRUVRXp6OgA3btygubnZZ+cuKioiIyMDsLah3LhxI26322fnl8AUExNDfn4+YN3oKSsrM5xIRCT0qdgXEfGzhoYG6urqAGs6a25uruFEEozq6ursZSBz587F4XD49Xr+mMoP4HQ6Wbt2LYmJiQBcvHiR7du3++z8Erhyc3OJi4sDrPdzQ0OD4UQiIqFNxb6IiJ/1HsEqLCy0G1WJDETvKfzz58/3+/X8VewDxMbGsn79ervnwN69ezl8+LBPryGBJyoqihUrVtjHGt0XEfEvFfsiIn50/vx5Tp06BUBiYiKLFi0ynEiC0Z07dzh79ixgNbrr2RrPn9LT04mMjASsYt/XW+WlpaWxatUq+3jr1q1cuXLFp9eQwLN48WJ7VsepU6e4cOGC4UQiIqFLxb6IiJ94vV5KS0vt46KiIiIiIgwmkmB19OhR+/G8efP8PoUfwOVyMWnSJMC62dDU1OTza2RnZ9s3wLq7u9mwYQNtbW0+v44EjoiICLtJI0BpaanPbySJiIhFxb6IiJ/U19dz7tw5AEaPHs2CBQsMJ5JgNVxd+B/kz6n8PZ544gnS0tIAuHnzJq+//rqKvxC3cOFCkpOTATh79qy2YBQR8RMV+yIifvDgqH5xcbG9lZnIQNy8eZNLly4BkJqaSkpKyrBde9q0afZjfxVkERERrFu3jhEjRgBw8uRJduzY4ZdrSWBwOp2sXLnSPn7zzTd1g0dExA/0yVNExA9OnDjB5cuXAatAmzt3ruFEEqxMjeqD9d7t2SbyzJkz9m4AvpaUlMSzzz5rH5eVldnbDEpomjt3LqmpqQBcvnyZEydOGE4kIhJ6VOyLiPiYx+Pp02W6pKRkWNZYS2jyZbH/yU9+kj/8wz/kk5/8ZL+e73Q67an87e3tXL16dUjXfz8ZGRmUlJTYx5s3b+bWrVt+u56Y5XA4+ozul5WVaXRfRMTHVOyLiPjYkSNHaGxsBKyO5jNmzDCcSIJVY2Njn/dSUlLSkM6XlJREcnLygM7Te91+fX39kK7/MAUFBcyaNQuAtrY2NmzYQHd3t1+vKebMnDmTCRMmANZ7vfeNLRERGToV+yIiPuR2uykvL7ePNaovQ1FbW2s/Hu4p/D2Go0lfD4fDwZo1a+zmbQ0NDWzbts2v1xRzHA5Hn9kc5eXluN1ug4lEREKLin0RER86dOgQN2/eBKwiqXehJDIQXq/X3nLP4XAY6/swevRoEhISADh//rzfi7GYmBjWr19vb1N58OBBDhw44NdrijnTpk2zf0/euHGDw4cPG04kIhI6VOyLiPhId3c3lZWV9nHvESuRgbp8+XKfG0fx8fFGcjgcDrsY6+rq4uLFi36/ZmpqKk899ZR9vG3bNntHAgk9vX9XVlRUaOmGiIiPqNgXEfGRffv2cfv2bcBai5qenm44kQSzQJjC32M4p/L3yMrKIjc3F7CWx2zcuJHW1tZhubYMr/T0dGbOnAnA7du32bdvn+FEIiKhQcW+iIgPdHZ29tkbXKP6MhQej8eewu90Opk9e7bRPCaKfYDHHnuMiRMnAtDc3Myrr77qt+3/xKzenfmrqqro7Ow0mEZEJDSo2BcR8YHdu3fbo47z5s2z948WGYxz587R0tICwIwZMxgxYoTvTn73LmzZAgOYjp+YmGg3zbt48eKwFWIul4t169YRFxcHWLsB9G6AKaFj3Lhxdl+Ku3fv8tZbbxlOJCIS/FTsi4gMUVtbG7t27QKs9c3FxcVmA0nQ670Fmc+n8J87B2vXwpIl8Ktf9ftlPaP7Ho+H8+fP+zbT+0hISOBDH/qQvavFjh07OHHixLBdX4ZPcXGx/ee8a9cu2tvbDScSEQluKvZFRIZo165ddHR0ALBw4UJGjx5tOJEEM7fbTV1dHQCRkZH2WmafcrngjTfgr/8aPv5xuDeL4P2YmsoPMGXKFB599FH7+LXXXqOpqWlYM4j/jRkzhgULFgDQ3t5u30QVEZHBUbEvIjIELS0t9nRTl8tFUVGR4UQS7N5++217RHPWrFlERUX5/iJeL8ybB/v2QUoKLF4Me/e+70tMFvsAy5YtIzMzE4COjg42bNigdd0hqKioCKfT+ni6e/du7t69aziRiEjwUrEvIjIEVVVVdHV1AbB48WISExMNJ5Jg59cp/A+KjIRvfxv++Z/huefgb/7mPZ8aGxtr96JoaGigra3Nv9ke4HA4ePrppxkzZgwAjY2NbN26Fa/XO6w5xL+SkpJYvHgxYG312LvxqYiIDIyKfRGRQWpubra3iIqMjGTFihWGE0mw6+rq4vjx4wDExMQwffp03528pARWroTnnwe323rc8/WXfwmJifDVr77vKXqP7p89e9Z32fopOjqa5557zp7tUFtby96HzEiQ4FNYWEhERARgbWna3NxsOJGISHBSsS8iMkgVFRW43W4AcnNziY+PN5xIgt3JkyftmSJz5szB5XL57uQLF0J2NsyZAw6H9bj318qV8MUvvu8ppk2bZj+ur6/3XbYBGDNmDKtXr7aPt2/fzoULF4xkEf+Ij49n6dKlgNXDorKy0nAiEZHgFGE6gIhIMGpqauLQoUOANdqYn59vNpCEhN5T+OfPn+/bk//DP1j/PHYMfvnL+8cDMGnSJJxOJx6Px8i6/R6ZmZnk5eWxa9cuPB4PGzdu5NOf/rRuuIWQ/Px89u3bR0dHBwcPHiQ/P9/e/lFERPpHI/siIoNQUVFhrxXOy8vz7T7oEpba29s5deoUYI1sTp482bcXuHgR6uutkf17u0cMVHR0NBMmTACsG163b9/2ZcIBeeSRR5gyZQoAd+7cYdOmTfZMGwl+I0aMYPny5QB4vV7Ky8vNBhIRCUIq9kVEBujq1avU1tYCVtOynummIkNx7Ngxu1jNzMy0O5L7zEc+Av/3/1qP7+1lzk9+0nftfnHxQ09juit/D6fTybPPPktCQgIA586d48033zSWR3xv2bJlxMbGAlZ/hsbGRsOJRESCi4p9EZEBKisrsx8XFBQQHR1tMI2ECr9O4Qc4ehQ++MG+35s8GerqrDX7s2ZBP9ZGB0qxD9YMiHXr1tk3Rqqrqzl69KjRTOI7Dy6R6v27V0REHk7FvojIAFy6dIkTJ04AkJCQwJIlSwwnklDQ0tJiF85JSUn2VHmfunsXRo/u+720NPB4rPX7f/mX/TpNenq63Sn9zJkzxre+mzhxIo8//rh9vGXLFq5du2YwkfhSTk6OPXvj+PHjXLp0yXAiEZHgoWJfRGQASktL7ceFhYVERkYaTCOhoq6uzi6a582bh6Nnmr0vTZwIhw/3/V5NDYwbZz3uZ9EeERHBpEmTALh9+zY3btzwZcpBWbJkCVlZWYC1feErr7xCxyD7EkhgiYyMpLCw0D7u/TtYRETen4p9EZF+Onv2rL3d2KhRo8jOzjacSEJF7yn88+bN889F1q6FL30Jdu6E1lYoK4M//VN46qn7z+nnTYZAmsoP4HA4ePLJJ0lNTQWs5oFbtmwxPutAfCM7O5ukpCTA2vLx7NmzRvOIiAQLFfsiIv3g9Xr7jCgVFxf7dg90CVu3bt2y94lPSUmxC1af+9rXYNIkKCyE+Hj4vd+DpUvh61+3/n1sLHzmM/06VaAV+2CNAK9fv97uoXHs2DGqq6sNpxJfcLlcFPdqHllaWqobOSIi/aBiX0SkH06dOtWnIPPb6KuEnd4N5fz6voqPh9JSayr/9u1w+jRs2gQ920bGx8MPftCvU40fP94uqgNh3X6P5ORk1q5dax+/8cYbAXMzQoZm/vz5pKSkAHDhwgVOnz5tOJGISOBTsS8i8hBer7dPF+iVK1f6fls0CVvDMoW/t3nz4NFHodfo/EA5nU57j/u2tjauXr3qo3BDN3PmTHuNt9frZdOmTdy+fdtwKhkqp9Op0X0RkQHSp1URkYeoq6vjypUrgDWiOXv2bMOJJFRcv37dfm+lpaWRnJxsOFH/BeJU/h5FRUVkZGQA0NraysaNG3G73YZTyVDNmTOH8ePHA3DlyhWOHTtmOJGISGBTsS8i8j48Hk+fUf2SkhL/dEqXsFRbW2s/DralIdOmTbMfB1qx73Q6Wbt2LYmJiQBcvHiR7du3G04lQ+VwOCgpKbGPy8rK8Hg8BhOJiAQ2FfsiIu+jpqaGpqYmACZNmmSPFooMldfrHf4p/D40ZswY4uPjATh37lzAjZzHxsayfv16u5Hm3r17Ofzg1oMSdDIyMuytH69fv05NTY3hRCIigUvFvojIe+ju7qa8vNw+1qi++FJDQ4O9R/2UKVNISEjw+zW3b9/Oli1bfDLK7XA47Kn8nZ2dXL58ecjn9LW0tDRWrVplH2/dutVeNiHB6cHR/YqKioC70SQiEihU7IuIvIcDBw7Q3NwMwPTp05k8ebLhRBJKTIzqHz16lEOHDvXZAWAoeq/br6+v98k5fS07O5tFixYB1g28DRs20NbWZjiVDMXkyZPtWVa3bt3iwIEDhhOJiAQmFfsiIu+iq6uLHTt22McrV640mEZCjdfrtQtup9PJnDlzDCcanEBu0tfbE088QVpaGgA3b97k9ddfVyf3INd7dL+yspKuri6DaUREApOKfRGRd7Fnzx5aWloAqwN0T6Eg4gvnz5+3t4PLyMggNjbWcKLBSUpKYtSoUYDVBC9QC66IiAjWrVvHiBEjADh58mSfm3kSfNLS0uybZC0tLezdu9dwIhGRwKNiX0TkAe3t7ezcudM+1qi++FowN+Z7UM/ovtvt5vz584bTvLekpCSeffZZ+7isrIzTp08bTCRDVVxcbD+uqqqio6PDXBgRkQCkYl9E5AG7d++21/RmZWWRkpJiOJGEErfbTV1dHWCNOM+ePdtwoqEJlqn8YM2i6D39e/Pmzdy6dctcIBmSsWPHkpWVBUBbWxvV1dWGE4mIBBYV+yIivbS2ttofGJ1OZ5+RIxFfOHPmDK2trQDMnDmTqKgow4mGJpiKfYCCggJmzZoFWAXihg0b6O7uNpxKBquoqAin0/o4W11dbf9siYiIin0RkT6qqqro7OwErC7ePeuRRXwllKbwA8TFxTF27FjA2k6wvb3dcKL353A4WLNmDcnJyYCVedu2bYZTyWAlJyeTnZ0NWFtA9l6CJSIS7lTsi4jcc+fOHbvJU0REBIWFhYYTSajp6uri2LFjAERHRzNjxgzDiXyjZ3Tf6/Vy9uxZs2H6ISYmhvXr1xMREQHAwYMHtX1bECssLMTlcgFWc9U7d+4YTiQiEhhU7IuI3FNZWWlP583JyWHkyJGGE0moOXXqlD1zZM6cOXaxGeyCbSo/QGpqKk899ZR9vG3bNi5dumQwkQzWyJEjycnJAaC7u1s7LYiI3KNiX0QEa+/tnpG9qKgoCgoKDCeSUBRqU/h7TJkyBYfDAQRPsQ9WA87c3FzAapy4ceNGrfkOUgUFBXb/i/3796vxoogIKvZFRACoqKjA4/EAsGzZsqDd91wCV0dHBydPngSsde69R8ODXXR0NGlpaQBcu3YtqKZRP/bYY0ycOBGA5uZmXn31Vft3gQSPuLg4li5dCoDH46GiosJwIhER81Tsi0jYu3btGjU1NYC1lnf58uWGE0koOn78OG63G4DMzEy7g3io6H3zIhjW7fdwuVysW7eOuLg4AOrr6ykvLzcbSgYlLy+PmJgYAA4fPsz169cNJxIRMSu0PmmIiAxCeXk5Xq8XgPz8fPvDoogvheoU/h7Tpk2zH9fX1xtMMnAJCQl86EMfspci7NixgxMnThhOJQMVExNDfn4+YDWLLCsrM5xIRMQsFfsiEtYaGhqoq6sDrGmgPet3RXyptbXVLoATExPtaeOhJD093e6IfubMGfsGWrCYMmUKjz76qH382muv0dTUZDCRDEZubq49S6Ouro6GhgbDiUREzFGxLyJhrffIT2Fhod3gScSX6urq7HXgc+fOtUeQQ0lkZCSTJk0CrLXvwdggbdmyZWRmZgJWj4UNGzbYuydIcIiKimLFihX2sUb3RSScqdgXkbB1/vx5Tp06BVijrYsWLTKcSEJVqE/h79F73X6wTeUHcDgcPP3004wZMwaAxsZGtm7dGnSzFMLd4sWLSUxMBKztLi9cuGA4kYiIGSr2RSQseb1eSktL7eOioqKQ2fNcAsvt27c5d+4cAKNHj2bcuHGGE/lP72I/mLbg6y06OprnnnvOnuVTW1vL3r17DaeSgYiIiKCwsNA+Li0t1Q0bEQlLKvZFJCzV19f3KcAWLFhgOJGEqgdH9UNxCn+PtLQ0oqOjgeBct99jzJgxrF692j7evn27RoeDzMKFC0lOTgas3SGC9eaTiMhQqNgXkbDz4Kh+cXFxyG2DJoGjd7E/f/58g0n8z+l0MnnyZMBqStjY2Gg40eBlZmaSl5cHWPu2b9y4kZaWFsOppL+cTicrV660j998882gvfkkIjJY+nQrImHnxIkTXL58GYDU1FTmzp1rOJGEqqamJrsb+Pjx4xk9erThRP4XClP5ezzyyCNMmTIFgDt37rBp0ybcbrfZUNJvc+fOJTU1FYDLly9rO0URCTsq9kUkrHg8nj7dmUtKSkJ6WrWYFS6N+XoLpWLf6XTy7LPPkpCQAMC5c+d48803DaeS/nI4HH1G98vKyjS6LyJhRcW+iISVI0eO2FOL09PTmTFjhuFEEqq8Xm+fYj9cZpCMHTuW2NhYwCqOe7YcDFbx8fGsW7fOXupTXV3N0aNHDaeS/po5cyYTJkwArN0Vev9MioiEOhX7IhI23G435eXl9rFG9cWfrl69yvXr1wGYNGmSvRVYqHM4HPbofkdHh71kJphNnDiRxx9/3D7esmUL165dM5hI+svhcFBSUmIfl5eXaymGiIQNFfsiEjYOHTrEzZs3AWuqce/pxiK+Fo5T+HuE0lT+HkuWLCErKwuArq4uXnnlFTo6Ogynkv6YNm2a/Z68ceMGhw8fNpxIRGR4qNgXkbDQ3d1NZWWlfdx7pEfE13pP4Xc4HGRmZhpONLymTZtmPw6VYt/hcPDkk0/aDd+amprYsmWL1oAHid6/8ysqKuju7jaYRkRkeKjYF5GwsG/fPm7fvg1YazjT09MNJ5JQdvHiRZqbmwGr8I2LizOcaHglJSXZyxbOnz9PV1eX4US+ERkZyfr164mOjgbg2LFjVFdXG04l/ZGens7MmTMBuH37Nvv27TOcSETE/1Tsi0jI6+zsZMeOHfaxRvXF32pra+3H4TaFH/qu23e73Vy8eNFwIt9JTk5m7dq19vEbb7wRMrMXQl3vzvxVVVV0dnYaTCMi4n8q9kUk5O3evZvW1lbAKrx6puGK+IPH46Gurg4Al8vFnDlzDCcyo/dU/vr6eoNJfG/mzJkUFhYC1pKNTZs22TOHJHCNGzfO3hXj7t27vPXWW4YTiYj4l4p9EQlpbW1t7Nq1C7BGG4uLi80GkpB35swZ7t69C1hFYc+U73AzZcoU+3EojnwXFRWRkZEBQGtrKxs3blSX9yBQXFxs78Kya9cu2tvbDScSEfEfFfsiEtJ27dpld8xeuHAho0ePNpxIQl04d+HvLSEhgZSUFAAuX74cckWV0+lk7dq1dm+Cixcvsn37dsOp5GHGjBnDggULAGhvb7dvBouIhCIV+yISslpaWuxpmi6Xi6KiIsOJJNR1d3dz7NgxAKKiopgxY4bhRGb1rNv3er2cO3fOcBrfi42NZf369bhcLgD27t2rbd2CQFFREU6n9RF49+7d9kwcEZFQo2JfREJWVVWV3QV88eLF9giciL+cPn3ankkye/ZsIiMjDScyq6fYh9Ccyg+QlpbGqlWr7OOtW7dy5coVg4nkYZKSkli8eDEAXV1dfRq4ioiEEhX7IhKSmpub7a2VIiMjWbFiheFEEg40hb+vKVOm2OujQ7XYB8jOzmbRokWANbtjw4YNtLW1GU4l76ewsJCIiAjA2pq1Z6tMEZFQomJfREJSRUWF3SwrNzeX+Ph4w4kk1HV2dnLixAkARowY0acbvVFXr8K2bfDXf82KrVv5wG9/y4qtW+Gv/9r6/tWrfrt0TEwM48ePB6CxsTGkp0s/8cQTpKWlAXDz5k1ef/11vF6v4VTyXuLj41m6dClgbQ9ZWVlpOJGIiO+p2BeRkNPU1MShQ4cAiI6OJj8/32wgCQsnTpygu7sbgMzMTHsdtxE1NfDZz0JqKowbB6tWwde/zqLKSnL27GFRZSV8/evW98eNs5732c9ar/OxcJjKDxAREcG6desYMWIEACdPntT08ACXn59v75Zx8OBBbty4YTiRiIhvqdgXkZBTUVFhj6jl5eXZH75F/Mn4FH6vF157DZYvhwUL4Kc/hcbG+//e7cblduPyeHC53dB7m7jGRuv5CxZAXp51Hh+NSodLsQ/WWvBnn33WPi4rK+P06dMGE8n7GTFiBMuXLwesJpLl5eVmA4mI+JiKfREJKVevXqW2thawOmX3TNMU8ae2tja7qEtISGDy5MnDG+DKFVizBtauhT17rO/dm2XQbz3P37PHOs+aNdZ5h2jSpEn2LIdQL/YBMjIyKCkpsY83b97MrVu3zAWS97Vs2TJiY2MBqK2tpbH3DTIRkSCnYl9EQkpZWZn9uKCgwJ6iKeJPdXV1eDweAObOnWs3pRsWGzfC7NnW+nuAezkGrWfE/9e/ts67ceOQThcZGUl6ejpgrWUPh8K3oKCAWbNmAdaNoA0bNthLPCSwPLjUq/ffISIiwU7FvoiEjEuXLtkN0hISEliyZInhRBIuek/hnz9//rBcs7m5mYa/+Asa1q+nobmZhu5uGsB3X263dd7162n4i78YUrfyqVOnMmbMGHJycgZ9jmDicDhYs2YNycnJADQ0NLCt52aMBJycnBwSEhIAOH78OJcuXTKcSETENxxetYoVkRDxi1/8gvr6egBWrVqlYl+GxZ07d/iHf/gHAJKTk3nxxRf9PrLf3NzM959/nq6DB/16nd4iFy3ixZ/9jMTExAG/1u1243K58Hq9eL1enM7wGGu4evUqP/nJT+xR/aeeesreok8Cy759+/j1r38NwLRp0/joRz9qOJGIyNBFmA4gIuILZ8+etQv9UaNGkZ2dbTiRhIujR4/aj+fNmzcsU/hbX3mFroMHWfvEE6TcW2/sT9daW9n8m9/Q+sorJH760wN+fc+afYfDMbxLHAxLTU3lqaee4rXXXgNg27ZtpKamMmHCBMPJ5EHZ2dns3LmTW7duUV9fz9mzZ5kyZYrpWCIiQ6JiX0SCntfrpbS01D4uLi42u+2ZhJVh78J/5Qp8+cuQnExKbCzj700/HhZf/jKsXm1t1Sf9kpWVxaVLl9izZw9ut5uNGzfy6U9/2m4KJ4HB5XJRXFzM66+/DkBpaSmf+MQnwurmlIiEnvCYRyciIe3UqVNcuHABgJSUFDPbnklYunnzpr2+NzU1lZSUFP9e0OuFz3wGWlv9e533cveudX2tAByQxx57jIkTJwLWEoxXX33VbugogWP+/Pn2z/CFCxe0baKIBD0V+yIS1Lxeb5/uyStXrgyb9cBi3rCP6r/+Ovznf97vmD/cPB7YssXK4UteL1y7BidP+va8AcLlcrFu3Tri4uIAqK+v157uAcjpdFJcXGwfl5aWotZWIhLM9IlYRIJaXV0dV+7tBT5+/Hhmz55tOJGEk2Ev9v/u78D0zSyXC779bd+e0+Oxtg780pd8e94AkpCQwIc+9CF7WviOHTvs3UMkcMyZM4fx48cDcOXKFY4dO2Y4kYjI4KnYF5Gg5fF4+ozql5SUaH2lDJvGxkYaGxsBSE9PJykpyb8XrKmB6mqrMB6gbmAf8HPg74C/vPfPHwJbgdNAv8cv3W7YtQtqawcWorERduzo+732dut8LhcUFVnnrKoa2HmDyJQpU3j00Uft49dee42mpiaDieRBDoeDkpIS+7isrExLLkQkaKnYF5GgVVNTY39QnjRpEhkZGYYTSTip7VXsDsuo/g9+ABED76vbxP2ivh64C7jv/fMK1k2Afwe6BnLSiAj4p38aWJA/+iP4r/+Ce9vQAVbDv//4D+vxlCmwbJnvlwgEmGXLlpGZmQlAR0cHGzZsoLOz03Aq6S0jI4NJkyYBcP36dWpqagwnEhEZHHXjF5Gg1N3d3WfNq0b1ZTh5vV57yz2Hw8HcuXP9f9HXXutbKL+HKd/9Lueam9/x/SVLlrBu1SoWdnfz8+3b+fXRo3R0dzNv+nSKPvhBiI/vf5bubqso/+EP+/+ahAS4edO6UeD1gsMBnZ3wy1/Cxz5mPSc9Hc6e7f85g5DD4eDpp5+msbGR69ev09jYyNatW3nmmWf0OyxA9Izuv/zyywBUVFQwf/587fIiIkFHI/siEpQOHDhA872CZvr06UyePNlwIgknly5d4ubNmwBMnTqV+IEUyoNx9ao1Db4f9r7wAg1/8ic0/MmfsPFP/oSPfvSjACyaO5cXgNd++1sqT57k1XXr2PH887ju3KFiwwYGXMYMIBMAH/iANUW/u9sq9AGmTbO+t3GjNer/q1/BU08NNEnQiY6O5rnnniMqKgqwZons3bvXcCrpbfLkyfZssVu3bnHgwAHDiUREBk7FvogEna6uLnb0Wvu7cuVKg2kkHA17Y779+/v91JS4OMbFxzMuPp5L8fGcPHmSUaNG8ZHJk3G2t/PTgwf5hw98gJKpU1mclsbPVq9m74UL7L140a+5eOIJq9D/13+1/nnihDWq/41vwEsvwcc/DkuXwmOPDTxHEBozZgyrV6+2j7dv325vISqBoffa/crKSrq6BrTYRUTEOBX7IhJ09uzZQ0tLC2B1Tk5LSzOcSMKJx+Oxp/A7nU7mzJnj/4sePmw1sRuATuC6201NTQ3Z2dlMczjY39BAl8fD0mnTOA+cB2LHjGFCYiKlAy00XS44dKj/z4+Lg69+Ff78z2H+fHj+eUhLs6bw798PBw7A5s1wrxN6OMjMzCQvLw+w3lcbN260f7eJeWlpafbPd0tLi2ZfiEjQUbEvIkGlvb2dnTt32sca1Zfhdu7cObsgmzFjBjExMf6/6K1bA95yrx04fvw47e3tLFy4kBjgSksLUS4XDTEx/CvYX964OGoHWmQ6nfAuvQHe1yc+YU3V/+hHYcUK+Na3ICUFEhOtf//qq/C5z8GnPz2w8waxRx55hClTpgBw584dNm3ahNvtNhtKbMXFxfbjqqoqOjo6zIURERkgFfsiElR2795NW1sbAFlZWaSkpBhOJOFm2Kfwg9XIboBigIMHDzJjxgwSEhK47ftUMJjCZ8UKq+j/1resEf7ubquz/+OPw1//NZw8CT/5ycBvJAQpp9PJs88+S0JCAmDdTHrzzTcNp5IeY8eOJSsrC4C2tjaqq6sNJxIR6T8V+yISNFpbW+0PWk6ns8+Ii8hwcLvd1NXVARAZGcnMmTOH58L3GrkNRMOtW9TX15OdnQ3ABWBcfDydbjcz29v5BlBw77l3794leTBNBqOjB/6ar30N/uVfoKvL6sofEWGt1Xe7Yd06ayr/xImwdevAzx2k4uPjWbduHc57szeqq6vtpSJiXlFRUZ8/m9bWVsOJRET6R8W+iASNqqoqez/q7OxsRo0aZTiRhJu3336b9vZ2AGbNmmV3U/e7pCTweAb0kp8dOsSouDj7hsQuYOb48UQ6nbxZX28/7/r16zQ3NzN34sSBZfJ47k+/H4jdu60iPzLy/vcWL4bZs++f8/HHrSn9YWTixIk8/vjj9vGWLVu4du2awUTSIzk52b5p1tnZ2WcpmYhIIFOxLyJB4c6dO3ZzpIiICAoLCw0nknBkZAo/wIIF1sh3P3m8Xn526BCfWLCAUfdGJNuBV2JiWJWdzR/97nf84swZdl6+zJYtW0hPTyczPX1gmdxuWLhwYK8ByMmxmvHB/S34urutZn1nz1rHq1bBrl0DP3eQW7JkiT1lvKuri1deeUVrxANEYWEhrntNMvfs2cOdO3cMJxIReTgV+yISFCorK+nu7gYgJyeHkSNHGk4k4aarq4vjx48DEBMTw/Tp04fv4osXD+jpb9TXc765mU9nZ/MRoGcOzB1g7uOPkzZjBp/esIG/evll4uPjee655wb3gWCAuQBYuxaOHoXea5/r6mDLFuhZmvPoo1aX/nv9OcKFw+HgySefJDU1FYCmpia2bNmC1+s1nExGjhxJTk4OAN3d3X22fxURCVQRpgOIiDzMzZs3OXBvJDAqKoqCgoKHvELE906cOGHvsz1nzhx7lG9YpKbC2LHQ2Nivpz+WkYH3z//cPv4ccAA4BjRGRPDUqlWsXbWKUUA6MBvIGGymgVq2DFauhP/xP+D3fx+amqx1+nPmwBNPWM8ZMcJq4BeGIiMjWb9+PT/+8Y/p6Ojg2LFjVFdX21v0iTkFBQUcOHCAzs5O9u/fT15eHklJSaZjiYi8J43si0jAq6iowHNvvfKyZcuIjY01nEjCUe+GafPnzx/+AM88YzWzG4QoYBnwCeDPgP8XeAn4LPAkMB1wDOSEERGwZs2gsgDw//1/8JGPWE34Tp6E//2/Yft2qzdB71HsMB3RTk5OZu3atfbxG2+8wZkzZwwmEoC4uDiWLl0KgMfjoaKiwnAiEZH3p2JfRALatWvXqKmpAayp08uXLzecSMJRe3s7p06dAqzO6ZMnTx7+EJ//vLW2PRB0d8MXvjD4148YAX/1V3DkCPzud/CVr0BcnFXcO3rddnAM6BZESJk5c6bdm8Tr9bJp0yZu3/bLBooyAHl5ecTExABw+PBhrl+/bjiRiMh7U7EvIgGtvLzcXq+an59vf8gSGU7Hjh3Dfa9BXmZmpr0N17DKyoLly8HEtXtzuSAvD3wxu8Hr7bt9XxgX9++mqKiIjAxrgUVraysbN26034diRkxMDPn5+YB1E6asrMxwIhGR96ZiX0QCVkNDg72neVxcHLm5uYYTSbjq3YXfyBT+Hl/5yoC34PM5txu+/GXfnEvF/ftyOp2sXbuWxHtbHF68eJHt27cbTiW5ubnExcUBUFdXR0NDg+FEIiLvTsW+iASs3iMmhYWFw7enuUgvLS0t9nrppKQkJkyYYC7MmjXw9NPW6LoJTiesXj209foyILGxsaxfv95uCLl3714OHz5sOFV4i4qKYsWKFfaxRvdFJFCpG7+IBKTz58/ba6QTExNZtGiR4UQSrurq6uylJPPmzcNhcjTa4YAf/QhmzgTgWmvrsFzWvk5cnHV9P/0/8Hq9Zv//Bqi0tDRWrVrFf/7nfwKwdetWUlNTGTdunOFk4Wvx4sVUV1fT3NzMqVOnuHDhAhMnTjQdS0SkDxX7IhJwvF4vpaWl9nFRURERg+xCLjJUvafwz5s3z2CSe8aNI/Z73yPyi19k829+M2yXjWxuJvZ737O23POhngK/paWFiIgI9eV4D9nZ2Vy8eJEDBw7Q3d3Nhg0beOGFFxgxYoTpaGEpIiKCwsJC/uu//guA0tJSPvaxj+lmlYgEFH16FpGAU19fz7lz5wAYPXo0CxYsMJxIwtWtW7e4cOECACkpKaT6uNAdrMSPf5wXL1+m9atfHbZrxn7zmyR+/OM+P299fT3btm3jxo0bfPCDHyQnJ8fn1wgVTzzxBFeuXOHy5cvcvHmT119/nf/xP/6HCkxDFi5cyM6dO7lx4wZnz57lzJkzTJs2zXQsERGb1uyLSEB5cFS/uLjYTOdzEQJwVL+XxJdeYvx3vsN4YLzDYf3T11895/3ud0l86SW//HfExsZy48YNAO0l/xARERGsW7fOHs0/efIkO3bsMJwqfDmdTlauXGkfv/nmm/aSHxGRQKBP0CISUE6cOMHly5cBSE1NZe7cuYYTSTg7evSo/TjQin0AvvhF2LABRo70fdM+l8s674YN8Md/7Ntz95KammpP3T9z5gwe07sNBLikpCSeffZZ+7isrIzTp08bTBTe5s6da8/4uXz5MidOnDCcSETkPhX7IhIwPB5Pn67GJSUlmp4qxly/fp0rV64AMGHCBJKTkw0neg/r1sHx47BqlXU8xKLfc+9nru2RR+DECev8fuR0Opk6dSoA7e3tXL161a/XCwUZGRmUlJTYx5s3b+bWrVvmAoUxh8PRZ3S/rKxMo/siEjBU7ItIwDhy5AiNjY0ApKenM2PGDMOJJJzV1tbajwN+hsm4cfD667B5M+TmWt8baFPLe8+/OGECrzz3HBs//GGfN+N7Lz3FPlhr+OXhCgoKmDVrFgBtbW1s2LCB7u5uw6nC08yZM+0tORsbG/ss/xERMUnFvogEBLfbTXl5uX2sUX0xyev1BvR6/XflcMAzz8CuXXD4MHzqU32LdZcLIiPvf/WeAZCaCp/6FO4DB9jyp3/K8TlzOHP27LAV3r2Lfa3b7x+Hw8GaNWvsGScNDQ1s27bNcKrw5HA4+sy0KC8vx+12G0wkImJRN34RCQiHDh3i5s2bgPXBv/eHf5Hh1tDQYDeNmzJlCgkJCYYTDVBWFvzwh9ZXYyPs3w+HDkFzM3R0QHQ0JCbCwoWweDGMHQuACyiOiGDz5s2AtZ3Y1KlT/X7jbfTo0SQkJHDnzh3Onz+P2+3G5eseBCEoJiaG9evX85Of/ITu7m4OHjxIeno6ixYtMh0t7EybNo2pU6dy5swZbty4weHDh/XnICLGaWRfRIzr7u6msrLSPu49QiJiQtCN6r+fsWPhiSfgpZfgb/4GvvMd658vvWR9/16h32PevHmMvfe9S5cucfLkSb9HdDgc9g2+rq4uLl686PdrhorU1FSeeuop+3jbtm1cunTJYKLw1fvvroqKCi2rEBHjVOyLiHH79u3j9u3bgLX2MT093XAiCWder9fuwu90OpkzZ47hRMPLVMMxTeUfvKysLHLv9Wpwu91s3LiR1tZWw6nCT3p6OjNnzgTg9u3b7Nu3z3AiEQl3KvZFxKjOzs4++0RrVF9MO3/+vH3zKSMjg9jYWMOJht+sWbPshmNXr17tswWhv6jYH5rHHnuMiRMnAtDc3Myrr76qbQwN6H2jrKqqis7OToNpRCTcqdgXEaN2795tj0DNmzfP3q9YxJTeXfiDfgr/IL3b6L6/C8fExES72dzFixdVJA2Qy+Vi3bp1xMXFAdauBr2bnsrwGDdunL17x927d3nrrbcMJxKRcKZiX0SMaWtrY9euXYBVXBQXF5sNJGHP7XZz7NgxACIiIpg9e7bhROZMmzaNKVOmAHDjxg0OHTrk92v2jO57PB7Onz/v9+uFmoSEBD70oQ/ZDRV37NjBiRMnDKcKP8XFxfafwa5du2hvbzecSETClYp9ETFm165ddHR0ALBw4UJGjx5tOJGEuzNnztgzTWbNmkVUVJThROY8uJ1YZWWl3xuOaSr/0E2ZMoVHH33UPn7ttddoamoymCj8jBkzhgULFgDQ3t5u39QWERluKvZFxIiWlhZ7eqPL5aKoqMhwIpG+Xfh7puKGs4kTJzJjxgzAWge+f/9+v15Pxb5vLFu2jMzMTAA6OjrYsGGDlkUMs6KiIpxO62P27t27uXv3ruFEIhKOVOyLiBFVVVV0dXUBsHjxYhITEw0nknDX1dVlT+GPjo62i9xw13vt/o4dO/xaNMbGxtp9OxoaGmhra/PbtUKZw+Hg6aefZsyYMQA0NjaydevWYdlVQSxJSUksXrwYsH639G5EKyIyXFTsi8iwa25utrckioyMZMWKFYYTicCpU6fsQnbOnDlEREQYThQYxo8fb48S3717lz179vj1er1H98+ePevXa4Wy6OhonnvuOXspSm1tLXv37jWcKrwUFhbav0f27dtHc3Oz4UQiEm5U7IvIsKuoqMDtdgOQm5tLfHy84UQifafwh2sX/veycuVKu+HYzp07/dpwbNq0afbj+vp6v10nHIwZM4bVq1fbx9u3b+fChQsGE4WX+Ph4li5dCljNPysrKw0nEpFwo2JfRIZVU1OT3dU7Ojqa/Px8s4FEsNY1nzx5EoC4uLg+o8syvA3HJk2aZK911rr9ocvMzCQvLw+wdjnYuHEjLS0thlOFj/z8fKKjowE4ePAgN27cMJxIRMKJin0RGVYVFRX2utG8vDxGjBhhOJEIHD9+3J5tkpmZaRebcl/vhmNvvfWW3xqORUdHM2HCBMC6OXj79m2/XCecPPLII/Y2infu3GHTpk32+138a8SIESxfvhwAr9dLeXm52UAiElb0aUZEhs3Vq1epra0FrEZcPdMbRUzTFP6HS0pKYtGiRQB0dnZSVVXlt2upK79vOZ1Onn32WRISEgA4d+4cb775puFU4WPZsmXExsYCVu+ExsZGw4lEJFyo2BeRYVNWVmY/LigosKc2ipjU2trK22+/DUBiYiITJ040nChw9W44tnfvXr+NuqvY9734+HjWrVtnz86orq7m6NGjhlOFhweXrPX+u1BExJ9U7IvIsLh06RInTpwAICEhgSVLlhhOJGKpq6uzl5bMnTvXbkQn75SQkEBubi7g34Zj6enp9k2FM2fOaMs4H5k4cSKPP/64fbxlyxauXbtmMFH4yMnJsWdWHD9+nEuXLhlOJCLhQMW+iAyL0tJS+3FhYSGRkZEG04jcpyn8A5Ofn29v5+avhmMRERFMmjQJgNu3b6upmQ8tWbKErKwswNr//ZVXXqGjo8NwqtAXGRlJYWGhfdz770QREX9RsS8ifnf27Fl7C61Ro0aRnZ1tOJGI5fbt25w7dw6A0aNHM27cOMOJAl9sbKzdcMzj8VBRUeGX62gqv384HA6efPJJUlNTAasJ4pYtWzR7YhhkZ2eTlJQEWNtKnj171mgeEQl9KvZFxK+8Xm+fEYzi4mJcLpfBRCL3PTiqryn8/bN8+XJ7J42amhq/NBxTse8/kZGRrF+/3u6bcuzYMaqrqw2nCn0ul4vi4mL7uLS0VDdZRMSvVOyLiF+dOnWKCxcuAJCSkqJp0hJQehf78+fPN5gkuDzYcMwf24mNHz/eLka1bt/3kpOTWbt2rX38xhtv6KbKMJg/fz4pKSkAXLhwgdOnTxtOJCKhTMW+iPiN1+vt03V45cqV2r9cAkZTUxMNDQ2AVViOHj3acKLgkpubS3x8PGCNDF++fNmn53c6nfbe8G1tbVy9etWn5xeYOXOmvY7c6/WyadMmv+2wIBan06nRfREZNvrULSJ+U1dXx5UrVwCrmJo9e7bhRCL3qTHf0AxHwzFN5fe/oqIiMjIyAGsbyo0bN+J2uw2nCm1z5sxh/PjxAFy5coVjx44ZTiQioUrFvoj4hcfj6TOqX1JSovXQEjC8Xm+fYn/u3LkG0wSvRYsW2Q3H3n77bbvZoa9MmzbNfqxi3z+cTidr164lMTERgIsXL7J9+3bDqUKbw+GgpKTEPi4rK8Pj8RhMJCKhSsW+iPhFTU0NTU1NAEyaNMkeORIJBFevXuX69euA9f7sKXRkYFwuF0VFRfaxr6ckjxkzxl4qcO7cOY04+0lsbCzr16+3m6fu3buXw4cPG04V2jIyMuztJa9fv05NTY3hRCISilTsi4jPdXd392nYpVF9CTSawu87WVlZjBkzBoDz58/z9ttv++zcDofDnsrf2dnp874Acl9aWhqrVq2yj7du3WovwxLfe3B0v6KiQjezRMTnVOyLiM8dOHCA5uZmAKZPn87kyZMNJxK5r/cUfofDQWZmpuFEwc3fDcd6r9uvr6/32XnlnbKzs1m0aBFg3bTdsGEDbW1thlOFrsmTJ9uz3m7dusWBAwcMJxKRUKNiX0R8qqurix07dtjHK1euNJhG5J0uXrxo34yaNm0acXFxhhMFv8zMTMaNGwdAQ0ODTxuOqUnf8HriiSdIS0sD4ObNm7z++uvqFu9HvUf3Kysr6erqMphGREKNin0R8ak9e/bQ0tICWB2Hez40igSK2tpa+7Gm8PuGPxuOJSUlMWrUKMC6UaNiyL8iIiJYt24dI0aMAODkyZN9buCKb6WlpTFnzhwAWlpa2Lt3r+FEIhJKVOyLiM+0t7ezc+dO+1ij+hJoPB4PdXV1gNVcrudDtgzd9OnTmThxImA1HOt9U2Woekb33W4358+f99l55d0lJSXx7LPP2sdlZWWcPn3aYKLQ1nsZTFVVFR0dHebCiEhIUbEvIj6ze/due31nVlYWKSkphhOJ9HXmzBnu3r0LwMyZM4mOjjacKHQ8OLpfXl7us4Zjmso//DIyMvr8eW7evJlbt26ZCxTCxo4dS1ZWFgBtbW1UV1cbTiQioULFvoj4RGtrq/0B5cGGXSKBQl34/WvKlClMmzYNsBqOHTx40CfnVbFvRkFBAbNmzQKsInTDhg10d3cbThWaioqKcDqtj+XV1dW0trYaTiQioUDFvoj4RFVVFZ2dnYDV0blnja1IoOju7rYbx0VFRTFjxgzDiUKTPxqOxcXFMXbsWMBqANje3j7kc8rDORwO1qxZQ3JyMmD9v9+2bZvhVKEpOTmZ7OxswNpmsveSOBGRwVKxLyJDdufOHbupUEREBIWFhYYTibzT6dOn7bWws2fPJjIy0nCi0DRhwgRmz54N9P3dMFQ9o/ter5ezZ8/65JzycDExMaxfv56IiAgADh48qC3i/KSwsBCXywVYzW7v3LljOJGIBDsV+yIyZJWVlfbUzpycHEaOHGk4kcg7XblyxX6sKfz+1bs5586dO33ScExT+c1JTU3lqaeeso+3bdvGpUuXDCYKTSNHjiQnJwewZiJpFwQRGSoV+yIyJDdv3rRHeaKioigoKDCcSOSdvF4vxcXFfOlLX+KJJ56w15WLf4wdO5b58+fbj31R7E+ZMgWHwwGo2DchKyuL3NxcwNoVYePGjVpX7gcFBQVERUURERFBVFQUXq/XdCQRCWIRpgOISHCrqKiw99NetmwZsbGxhhOJvFNPkZiQkMCSJUvsRljiP4888giLFi1iypQp9u+IoYiOjiYtLY1Lly5x7do17ty5Q0JCgg+SSn899thjNDQ0cOHCBZqbm3n11Vf5gz/4A/08+VBcXBxr164lPT2d2NhY+3eXiMhg6LeziAzatWvXqKmpAax1ncuXLzecSOThVJgMj8TERCZNmgT47v9576n8Wrc//FwuF+vWrSMuLg6A+vp6ysvLzYYKQTNnzlShLyI+oU88IjJo5eXl9hTD/Px8YmJiDCcSkUDi6xsrvZdf1NfX+/Tc0j8JCQl86EMfsgvRHTt2cOLECcOpQovD4VChLyI+oWJfRAbF6/UyadIk4uLiiIuLs9dyiogMSFMT/OQncPv2Q5+anp5udys/c+aM1jMbMmXKFB599FH7+LXXXqOpqclgojDV3AybN0NLi+kkIhKgVOyLyKA4HA5ycnL44z/+Yz784Q8TFRVlOpKIRQVgcGhuhp//HD79afjMZ+ALX3joSyIjI+2lAc3Nzdy6dcvPIeW9LFu2jMzMTAA6OjrYsGEDnZ2dhlOFmTNnYMMG+OpXTScRkQClYl9EBs3pdBIZGcn48eNNRxG5T9NfA9/Vq/Cd78CXvgRxcfAv/wK//CW8/fZDX9p73b6m8pvjcDh4+umnGTNmDACNjY1s3bpVsy2GU1YWfP7z8PLLVuEvIvIAFfsiMmRaWygBY9s26CkAVXQElvb2+4/HjoW8PIiIgM99Dj75SVi7Fv7wDx96mt7FvrbgMys6OprnnnvOntlVW1vL3r17DacKQT0/O16v9fXrX8PFi+B0QmEhrFoF/+f/mM0oIgFJxb6IiISOF16AnqndDgecOwfnz0NjI3R3W9/XTYDh5fXCj38MX/kK9EzzdjjgscesP6+/+Avre9/6Fvz2t3D06PueLi0tjejoaEDr9gPBmDFjWL16tX28fft2Lly4YDBRCPF64d/+Db72Netnx+Gwvn7+c/j4x+8/LzPT+vdaRiEiD1CxLyLvredDtD5MSzDYutVqVLVoEbS1WU3fHn0Upk6FBQvgT/8UWls1zX+4ORxw7BhcuAA9vT3cbuuf6elw8yZcvgxTpljT+SMj3/d0TqeTyZMnA9Da2kpjY6Mfw0t/ZGZmkpeXB4DH42Hjxo20qGnc0PX87Jw7d/9nB+DLX4ayMvje96zlL9/+NqSl9X2OiAgq9kXk/Tgc1gd0FUcSDP75n++Pdv3Hf8APfgAf+IA1Uvz//D/wf/8vfOITZjOGqy99yRq1P3DAOr7XUZ/qaoiOtgoVjwc+9SmYOfOhp9NU/sDzyCOPMGXKFADu3LnDpk2bcPfc1JHBe/FF60bmwYP3vxcXB9nZ1pKlF16AD35QTfpE5F2p2BeR9/anf2p9kBAJBqWlkJFhPf7hD+EjH4Hvfhdmz7Y6vX/1q9YomYrD4TdxolXIf/GL8NOfWoXLpz4F//mf8NnPWs9xOqGryxrlfwgV+4HH6XTy7LPPkpCQAMC5c+d48803DacKAenp1k3Ml16Ct96ymlv+4z9CRwf87d9CQ4PVoC8+vl8/OyISXlTsi8i76+iwPlB88Yv3v7dzJ+zYYf1TW15JIKmpgYQEeO01eOop6wPwBz5wfwQZYPVqa/S4udlcznD2t38L+fnW2v3ly63O+1//OixbBps2wbPPwrhx8MQT1mjmiRPveaqxY8cSGxsLWEWlx+MZrv8KeR/x8fGsW7cOp9P6eFldXc3Rh/RgkH741rcgNdX62Vi+HPbtg298A27fhu3brRub48fD448/9GdHRMKLw6vONiLybr7wBauA2rHDmsr/ta/Bli3WTYDMTCgutj6ojxplOqmI5cQJ64Pv735nHf/VX1lr9XuUlVkF5Y0bZvKJ5fhxqwt/dLQ1Dfk737F2UcjPh09/2pp5UV1tjWDu2fOep9m0aZNdSH7qU58iPT19uP4L5CH27t3Ltm3bAIiMjOSFF14gJSXFcKog195u/Q67edNa9gLwN39jzWjKz7dm4Z0926+fHREJHxGmA4hIAGppsdY///zn1vE3vgHXrlnHxcXWWui//mvrA/u3vmUyqch9s2ZZX3/0R1ZDq+Tk+//u4kXrPf3kk+byiWXWLKsPyC9/aU3lX7AAqqogN/f+c1paYNo062bjihXvepqpU6faxf6ZM2dU7AeQJUuWcPHiRWpqaujq6uKVV17hhRdesHdRkEGIibFG9sGawfTRj8L8+dZMu5yc+8/rx8+OiIQPTeMXkXfaswdmzLCm8X/kI9aevt/6ljUNOjHRWjv4R39kfUAXCSRdXdY/J0+2pvX36Jmh0ntZipjhcFjbIX7jG1ZX8epqq9D3eO7vJ37+vDVrqOf4XUybNs1+rHX7gcXhcPDkk0+SmpoKQFNTE1u2bNE2ib5w/jz82Z9ZTS+rq61Cf4A/OyISPlTsi8g7rVxpTat96ik4cgRKSmDCBOvf9XRXXrzY2tP3yhVzOUXA+nD74otQVATf/CbcvfvO5zz1lLUufNGi4c8n71RdDd3d8OEPW8ft7VaDvpgY6/jll63tE7Oy3vMUSUlJJCYmAnD+/Hm6em70SECIjIxk/fr19mj+sWPHqK6uNpwqBFRXW38PD+FnR0TCh4p9EXknh8Pqav71r8OvfmWN7t/7UG03PCsrsxoGjRtnLqfI3bvWh969e2HOHKsL/8qVVuOq3qKi7t+wEvPa2mDECGunBLhfqLz5ptVY8eWX4e//3vod8x4cDofdld/tdnPx4kU/h5aBSk5OZu3atfbxG2+8oVkYQ+WDnx0RCR8q9kXkvTkc1geKD37wfpHf2QkVFdb6/b/8S7P5RP71X60R4i1brEJ/927rBsD3v3//OV1d8Hd/py78geT5560+IJ/7HPz3f8Prr8OaNdYyi+ho689y3bqHnqb3VP76+np/pZUhmDlzJoWFhQB4vV42bdrE7Qdvxkn/+ehnR0TCg4p9EXlX77m28vRp+H//X/j939eUaDFv82ar6d64cVZRP3mytZb1lVfubw+5ebPVULJndooEhn/9V6tr+HPPwcc+Zt1Q/OQnrV0Ueo0Gv58pU6bYjzViHLiKiorIyMgAoLW1lY0bN+LuWRImA+eDnx0RCQ/aek9E3tWFCxdIu7e9j6v3XuVgrRH0eODePtciRrS2Wh9s16+3PuiC9b7s6oKlS60PwV/6ktXBOiOj72i/BI5jx6wlFt3dfXdQ8Hqt2UUP8YMf/IBr167hcDj40z/9U2J6pjVLQGltbeXHP/4xzfdm2OTk5PDBD37QcKogN8SfHREJfRrZF5F3aGlp4Re/+AXf+973qK2tfecof0yMCn0xLyrK2rqtZ0TX67UaVUVHW7tF/P3fw+XLUF4On/+80ajyPubMgZEj7xcrPb9v+lms9Kzb93q9nDt3zh8JxQdiY2NZv369ffN47969HD582HCqIDfEnx0RCX0q9kXkHaqqqujq6qK5uZmGhgYc+uAggSgiwlqb+m69I9ats/pNPPGENfKVmTn8+WRwBvj7pqfYB03lD3RpaWmsWrXKPt66dStXtKOL7+jvahF5gIp9EemjubmZffv2AdbWSStWrDCcSKSfej7oer2QkGB16a+thf/5P83mkgHzeDz9fu6UKVPsG5Iq9gNfdnY2i+71e+nu7mbDhg20tbUZThU6tDpXRHpTsS8ifVRUVNiNk3Jzc4mPjzecSOThvF7v/Q+5PUX/Jz4BlZXw6U+bCyYD0vO759SpU3R0dPTrNTExMYwfPx6AxsZG7t6967d84htPPPGE3RPm5s2bvP766ypSh8jj8dDe3s6xY8dMRxGRAKJiX0RsTU1NHDp0CIDo6Gjy8/PNBhLpp0OHDnH16lWg18iW0wkFBX0bV0lAu379Oj/60Y/41a9+xc6dO/v9Ok3lDy4RERGsW7eOESNGAHDy5El27NhhOFXw8nq97Nq1i+9+97ts2rSJGzdumI4kIgFCxb6I2CoqKuxCKS8vz/4gJhLI2tvb+fWvf82PfvQj/vVf/1UjhEEsOjqaxsZGAN56661+j9Kr2A8+SUlJPPvss/ZxWVkZp0+fNpgoeDkcDtxuNx0dHXi9XsrLy01HEpEAoWJfRAC4evUqtbW1gNU1eenSpYYTifTPsWPH7OnfaWlpOJ36qy1YJSUl2eu5Ozs7qaqq6tfrJk2aZHd5V7EfPDIyMigpKbGPN2/ezK1bt8wFCmLLli0j9t4uObW1tfZNMxEJb/pEJCKANarSo6CggOjoaINpRPrvyJEj9uN58+YZTCK+UFhYSEREBGBtz3b79u2HviYyMpL09HTAWgOugjF4FBQUMGvWLADa2trYsGED3d3dhlMFnweX3vX+O11EwpeKfRHh0qVLnDhxAoCEhASWLFliOJFI/7S0tNgjuUlJSUyYMMFwIhmqhIQEcnNzAathX2VlZb9ep6n8wcnhcLBmzRqS7/XWaGhoYNu2bYZTBaecnBwSEhIAOH78OJcuXTKcSERMU7EvIpSWltqPCwsLiYyMNJhGpP/q6ursNfrz5s2zt2CT4Jafn09UVBQABw8e7FfDsWnTptmPVewHl5iYGNavX2/P6Dh48CAHDhwwnCr4REZGUlhYaB/3/rtdRMKTin2RMHf27Fnq6+sBGDVqFNnZ2YYTifSfpvCHptjYWJYvXw5YW4pVVFQ89DVpaWn2DYIzZ86oUWOQSU1N5amnnrKPt23bppHpQcjOziYpKQmA+vp6zp49azSPiJilYl8kjHm93j53/ouLi+0mVyKB7tatW1y4cAGAlJQUUlNTDScSX1q+fLm9I0hNTc1DG465XC4mT54MWMs7rl+/7veM4ltZWVl9lnBs3LiR1tZWw6mCi8vlori42D4uLS3VjS+RMKZiXySMnTp1qk+xpJFRCSYa1Q9tDzYc6892Yr3X7ffMWJLg8thjjzFx4kQAmpubefXVV/F4PIZTBZf58+eTkpICwIULF7SloUgYU7EvEqa8Xm+fbr0rV67UlmUSVFTsh77c3Fzi4+MBa4vFy5cvv+/z1aQv+LlcLtatW0dcXBxg3bTRvvED43Q6NbovIoCKfZGwVVdXx5UrVwAYP348s2fPNpxIpP+uXbvG1atXAZgwYYLdyVtCy0AbjqWmptp7jZ89e1YjwkEqISGBD33oQ3bDzR07dtg7xkj/zJkzh/HjxwNw5coVjh07ZjiRiJigYl8kDHk8nj6j+iUlJepiLkFFo/rhY9GiRXbDsbfffptz586953MdDgdTpkwBoKOjg4aGhmFIKP4wZcoUHn30Ufv4tddeo6mpyWCi4OJwOCgpKbGPy8rKdPNLJAyp2BcJQzU1NfaHpkmTJpGRkWE4kUj/eb3ePsX+3LlzDaYRf3O5XBQVFdnHD5uSrKn8oWPZsmVkZmYC1s2bDRs20NnZaThV8MjIyGDSpEkAXL9+nZqaGsOJRGS4qdgXCTPd3d191j9qVF+CTUNDg73v+pQpU0hISDCcSPwtKyuLMWPGAHD+/Hnefvvt93yuiv3Q4XA4ePrpp+0/+8bGRrZu3ar15/304Oh+RUUFbrfbYCIRGW4q9kXCzIEDB2hubgZg+vTp9lZVIsFCU/jDz0AajiUnJzNy5EjAujHQ3d09HBHFT6Kjo3nuueeIiooCoLa2lr179xpOFTwmT55sz967desWBw4cMJxIRIaTin2RMNLV1cWOHTvs45UrVxpMIzJwXq+Xo0ePAlYBOGfOHMOJZLhkZmYybtw4wJrd8V4NxxwOhz26393dzcWLF4cto/jHmDFjWL16tX28fft2e9tYebjeo/uVlZV0dXUZTCMiw0nFvkgY2bNnDy0tLYDVqTctLc1wIpGBOX/+PLdv3was9ag9ndcl9A2k4Zim8oeezMxM8vLyAKvJ7MaNG+2/z+T9paWl2TdGW1paNDNCJIyo2BcJE+3t7ezcudM+1qi+BKPa2lr7sabwh5/p06czceJEwGo41vv90JuK/dD0yCOP2Lst3Llzh02bNmkNej/1XgZTVVVFR0eHuTAiMmxU7IuEid27d9PW1gZYza5SUlIMJxIZGLfbTV1dHQARERHMnj3bcCIZbg+O7peXl79rsTdy5EhGjx4NwKVLl1TYhAin08mzzz5rN+U8d+4cb775puFUwWHs2LFkZWUB0NbWRnV1teFEIjIcVOyLhIHW1lb7L/YHG12JBIszZ87YN6xmzZplN+yS8DJlyhSmTZsGWA3HDh48+K7P6xnd93g8nD9/ftjyiX/Fx8ezbt06nE7rI2x1dbXdx0PeX1FRUZ//b62trYYTiYi/qdgXCQNVVVX23sTZ2dmMGjXKcCKRgVMXfunRn4ZjPTcEAOrr64cllwyPiRMn8vjjj9vHW7Zs4dq1awYTBYfk5GSys7MB6Ozs7LO0T0RCk4p9kRB3584duxlPREQEhYWFhhOJDFxXV5fdfT06Oprp06cbTiQmTZgwwV7G0ft3XG89a7tB6/ZD0ZIlS+xp6V1dXbzyyitartEPhYWFuFwuwGrae+fOHcOJRMSfVOyLhLjKykp7n+mcnBx7/2mRYHLq1Cl7dsqcOXOIiIgwnEhM691kdOfOne8o9EaMGMH48eMBuHr1qqYshxiHw8GTTz5JamoqAE1NTWzZsgWv12s4WWAbOXIkOTk5gLU1Ze/teEUk9KjYFwlhN2/e5MCBAwBERUVRUFBgOJHI4GgKvzxo7NixzJ8/H7D6kuzevfsdz1FX/tAWGRnJ+vXriY6OBuDYsWNqPNcPBQUFds+T/fv3c+vWLbOBRMRvVOyLhLCKigp7H+ply5ZpT3IJSh0dHZw8eRKAuLi4PgWchLfi4mIcDgdgNRzraeDYQ8V+6EtOTmbt2rX28RtvvKE/64eIi4tj6dKlgNXAsqKiwnAiEfEXFfsiIeratWvU1NQAEBMTw/Llyw0nEhmc48eP29urZWZm2t2kRXo3HOvo6HhHw7FJkybZ7xcVgKFr5syZdj8ar9fLpk2buH37tuFUgS0vL4+YmBgADh8+zPXr1w0nEhF/0CcmkRBVXl5ur13Mz8+3/1IXCTaawi/vp3fDsbfeeouWlhb730VFRZGeng7AjRs3aG5uNpJR/K+oqIiMjAzAWtaxceNG+yahvFNMTAz5+fmAdYOkrKzMcCIR8QcV+yIhqKGhgbq6OsCarpebm2s4kcjg3L17l7fffhuA/397/x0f5Xnn/7+vUUHdEqIICdFBdIEoogshx9gY0y1wQuy4gR1im2S/ye45+9vz3ex+95E93yR7YuMSUxzX2DHCBmyMjW2QRO8dgcAWoqnRJNSl0cz5Y+C2hLFRmdE9M3o/Hw89PLeYue83CdLM576u63OFh4fTrVs3kxOJuwkPD2fUqFGAo+HY1q1bG/y5pvK3DT4+PsydO5fw8HAALl68yKZNm0xO5d4SExMJCQkBICsri/z8fJMTiYizqdgX8UL179AnJSUZjXhEPM3JkyeNGSqDBw821meL1Ddp0iT8/f2B7zccU7HfdgQHBzN//nxjpse+ffs4cuSIyancV7t27Zg0aZJxrNF9Ee+jYl/Ey5w/f54zZ84AjhGvESNGmJxIpPnqT+G/1Xld5HY/1nAsNjbWuBFw9uxZbc3m5WJiYpg+fbpxvGHDBgoKCkxM5N5GjhxpzIY4c+YMFy5cMDmRiDiTin0RL2K329myZYtxPHnyZO1HLh7rxo0bnDt3DoAOHToY+2mL3MkPNRzz9fWle/fuAJSWlnL16lXTMkrrSEhIMG50W61WVq9e/b2dGsTBz8/PaG4IsGXLFt0QE/EiKvZFvEhOTk6D4mjYsGEmJxJpvtsb82kKv/yYoKAgxo8fDzhufGZkZBh/pqn8bc+0adOIiYkB4Pr166xbt05F7A8YPnw4kZGRAOTm5upnRMSLqNgX8RK3j+onJydrizLxaJrCL001ZswYo+HYiRMnjOnbvXv3Np6jQqZt8PPzIzU1laCgIABOnz7Ntm3bTE7lnnx8fJgyZYpxvHnzZt0YEfESqgREvER2djZ5eXkAREVFMXjwYJMTiTTf1atXjc7Q0dHRdOjQweRE4gnatWvHxIkTjeNbDceioqKMKf5nz57FZrOZkk9aV0REBPPmzTOO09PT+eabb0xM5L4GDx5sLJXKy8sjOzvb5EQi4gwq9kW8gM1ma9BFNyUlRVOexaPdPoVfpLFGjRrFPffcAzhGcy9evIiPj48xlb+qqorCwkIzI0or6tOnDykpKcbxxx9/3GC3BnGwWCwNRvfT09M1ui/iBVTsi3iB48ePU1RUBDg6T/fr18/kRCLNZ7fbGxT7mqUiTXGnhmPQcN3+hf37YeNG+O//hn/5F/jNbxz//e//dnxfNwO8ysSJE+nfvz8AlZWVrF69GqvVanIq9xMXF0fXrl0BKCoqavB7WEQ8k9p0i3i4urq6Bo2oNKovnq6wsNDopN69e3djWyiRxho+fDg7d+7k2rVrnD17lpycHPpWVDD9008ZcOoUoeXljif6+kL93iY2G9TVOR537gxz5sCSJRAf3/p/CXEai8XC7NmzWblyJdeuXSM/P5+NGzcyc+ZMs6O5FYvFQkpKCu+++y4AGRkZDBo0CF9fX5OTiUhzaWRfxMMdPnyY69evA46Rq/qjVyKeSFP4paV8fX1JTk4Gu50BJ08Sct99tE9OZsShQ98V+uAo7Gtrv/u6VegDFBXBG2/AsGEwfjysXQua1uyxAgMDmT9/vrEd7aFDhzh48KDJqdxP7969jc8R165d48iRIyYnEpGWULEv4sGsVitbt241juuvSxTxRPWn8FssFgYNGmRyIvFUQzp25LG1a1nw4Yd0utmB36epjfluTfXeuxfmzoXZs+Fmh3/xPFFRUcyYMcM43rhxI5cuXTIxkXuq/1kiMzNTSx5EPJiKfREPtn//fm7cuAE41trFxsaanEikZS5evEhJSQngGGG6tY2aSJOkpWEZOJCeJ04A4NPSEflbI/6ffQYDBkBaWgsDilni4+NJTEwEHMvg0tLSqKioMDmVe4mNjSUuLg6AGzdusH//fpMTiUhzqdgX8VA1NTUN9gzWqL54g2PHjhmPNYVfmuUvf4H58+HGDSz1p+U7Q10d3LjhOP+LLzr33NJqpk6dSrdu3QAoKSnho48+0naMt6nfmX/79u3U1NSYmEZEmkvFvoiH2r17tzEaMWTIEGN/XBFPZbPZyMrKAhxrrgcOHGhyIvE0JX/4A/n/9E/kA/l2u+O/zv66dd7f/IaS//7vVvzbibP4+vqSmppqzBzKyclp0OhWoEuXLsZOKOXl5ezZs8fkRCLSHOrGL+KBKisr2blzJ+BY15ycnGxuIBEnOHv2LOU3m6fFxcUREBBgciLxJCVvv80rf/oTtT16tNo1/f/4R56LiSH8F79otWuKc4SFhfHwww/zzjvvYLfb2bt3L6NHjyYsLMzsaG4jOTmZrKws7HY7O3fuZPTo0QQGBpodS0SaQMW+iAfauXMn1dXVgGOLqQ4dOpicSKTl1IVfmq2ggIrnn6c2MpK506bRKTjY5Ze8XFHBx59/TsXzzxP+wAOg2VUep2fPntx3330cOnSIRx55RD1CbtOxY0eGDRvG4cOHqaqqYufOnVoyKOJhVOyLeJiysjJjOp2vry+TJ082OZFIy1mtVk6ePAlAu3bt6Nevn8mJxGPY7fDMM1BRAZGRdAoOJro1R2fLyx3XX7sWLJbWu644xdixY42GfT4+Wt16u8mTJ3P06FFsNhu7d+9mzJgxuiki4kH0W03Ew2zfvp3a2loARo4cSXh4uMmJRFrum2++MWarDBgwAH9/f5MTicdYtw4++eS7jvmtzWaD9esdOcTjWCwWfHx88PX1bdwLSktdG8jNREREMHLkSABqa2sbNAYWEfenYl/Eg5SUlBhb4Pj7+zNp0iSTE4k4h6bwS7P96U9g9oisry/8+c/mZpBmszR2RsY33zj+f/7jH10byM0kJSXh5+eYDLx//35je1QRcX+axi/iQTIzM6m7OXqVmJhIaGioyYlEWq6mpobs7GwAgoKC6N27t8mJxGMcPQq7djX5ZRk3v35IIPD/asoJ6+pg5044dgyGDm1yHvEQ7dtDRASsXAlWK/zrv5qdqFWEhoYyZswYduzYQV1dHVu3bmXGjBlmxxKRRtDIvoiHuHr1KocPHwYgICCACRMmmBtIxEmys7OxWq0ADBo0qPHTaUVeew383GTcws8PXn3V7BTiKjU10KEDLFni6M3wP/8DeXlmp2o1EyZMMHZIOXToENeuXTM5kYg0hpu8Q4rI3WRmZmK32wEYP348QUFBJicScQ5N4ZdmW7vWMcLaCJdu3OBfvv6az7/5hrLaWiIiI5k1axaTY2KYBNjtdv5/GRl8cPAgN6qq+LpbN/46fTr9GrvbidXqWLf/+uvN/uuIG7LZHMV9u3aQkwMPPOA4Xr4c7rnH7HStJigoiHHjxpGRkYHdbicjI4O5c+eaHUtE7kIj+yIeoLCwkGPHjgEQHBzMmDFjTE4k4hyVlZV88803gGPf6x6tuEe6eLjCQigqatRTr1dWMuFvf8Pf15fPFy7krSVLmDp1KoGBgYQA3YF/7NjB23v2sHL6dPY+/TQh7dpx/3vvUdXImwlNzSQeoK7O0Q/CYoG0NBg0CHr2hA8+gDlzoI0tpRs7dizBN7e1PHbsGEX6ty7i9lTsi3iA9PR04/HEiRONqXQini4rKwubzQbA4MGDG98oS+TAgUY/9f/u2EG38HDenDWLxK5diW7fnj59+hAZGQk4RvVf3LOHf0tKYtaAAcRHRfHO7NnklZay7tQpl+USN7VlC3z0kaPxIsD/+l+wYAH88pfwxhswYsR3fwZw/rw5OVvZ7UsI6382ERH3pGJfxM1dunTJaF4WFhbGqFGjTE4k4jz1p/APVWMzaYojRxoWXD/ik+xsRkVHk5qWRuc//YlFy5dz4GZRfhj4dXExBWVlfNO7N78H1gHhgYGMiY1l14ULjc/k6ws3e6uIB8vLg9RUSE+He+91FPjLl8Pvfw/dujV87t//DvPmwXvvmRK1tY0ePZqwsDAATp06xaVLl0xOJCI/RsW+iJvbsmWL8TgpKUn7j4vXKC0tJTc3F4DIyEiio6PNDSSepbi40Vvu5Vy/zl/376dfZCSbfv5zZo4axRdffGE0PS0rKwMgJCSkweuiQkIoKC9vfCYfH9C2ZJ7v5z+HRYschX5RkaMXwy9+AeHh3z2npAT+67/gzTcd/Roeewz27TMtcmvx9/cnKSnJOK7/GUVE3I+KfRE3lpubS05ODgDt27cnISHB5EQiznPixAnj8ZAhQzSFX5qmpqbRT7XZ7YyIjuYP995LQnQ0M0aOZMSIERw4cIB+wPSbz3sEeBKY1JJc1dUtebW4i+XLYeJECAuDxERHg75bKisd6/bfesuxHd+hQ/Cf/wkPPtgm/v9PSEggIiICgJycHOOmrYi4HxX7Im7Kbrc3uGOenJysLcnEq6gLv7RI/eLrLqLDwhjUqVOD73Xs2JGSkhJCgOE3G635l5fTHbjVf7+wvJwut43235V6qniPNWvg+HFHUV9fUBAkJ8PUqZCV5fjev/0bDBsGM2e2dspW5+vrS3JysnG8ZcsWY7cgEXEvKvZF3NSZM2e4cHOtaKdOnVQMiVe5fv26sdYzKiqKTrcVYiJ3FRHh2BatESZ060b21asNvnf16lXCb07L7hURQZfQUDbfnEkFcKO6mj0XLzLu9jXaP8ZmazjVWzxb586OZn39+jmWjdQfwR4wAP7v/3Ws4f/tbx3f++QTGDsWysrAy4vfoUOHGr+3L1y4YOyqIiLuRcW+iBuy2+0NutxOmTIFn0auTRXxBBrVlxYbNsyxNVoj/GbsWHZfvMgftm3jm2vX+PrYMQ4ePMjo0aMBsFgs/HrMGP5r2zY+yc7mWGEhj61dS0xYGLMHDGh8pro6GD68GX8ZcVujRjmm8z/zDKxd6/ie3e74CgmBuDjHTYC6OggOhv/4D8eWfF6+LMnHx0ej+yIeQNWDiBvKysqioKAAgOjoaAY05cOmiAdQsS8tNnJko586umtX1i5YwAfHjzPktdd4d+tW7r//fuLj443n/POECTyfmMjiTz9l9MqVlNXU8MXPf06gn5/LcomHCApyFPYbNjhmb1gsji8fH7h61THq3waX2Q0cONBorFpQUMDJkydNTiQit2viO5iIuJrNZmswqp+SkqLGZeJVioqKKCoqAiA2NtZo9CTSJFFRjmnWN/8t3c1DcXE8FBcHQMbNr/osFgv/OWUK/zllSssziff529+gVy/4zW/g6adh6FD4P/8H0tLg7bfNTmcKi8VCSkoKf//73wFIT09nwIABmoko4kb00yjiZo4ePcrVm2tLu3fvTp8+fUxOJOJcx44dMx5rVF9aZM4caOrIO5AM/P7m12xnZfHzg9lOO5u4oy+/hP37Hf/uIiLgxRcdXfhnzDA7mWn69OlD9+7dAbhy5QpHjx41OZGI1KdiX8SNWK1WMjIyjGON6ou3sdvtxpZ7FouFwYMHm5xIPNqSJY49zt2B1Qq/+pXZKcSV+vWDDz90dOf//e9h61bHv8Gbuzm0RbdG92/JzMykrpG9NETE9VTsi7iRgwcPUlJSAkDfvn3p0aOHyYlEnOvSpUtcv34dgF69ehHahj8kixPEx8O4cY6102by9YXx4x1Tu8W7xcY6Gvb9+tcweDDcc4/ZiUzXo0cPYxZicXExBw8eNDmRiNyiYl/ETdTW1rJt2zbjeEpL1o2KuCk15hOn+93vGr0Fn8vU1X23/Zq0WXa7vc12pK8/ur9161Zqa2tNTCMit6jYF3ETe/fupaysDHB0uI2JiTE5kYhz2Ww2Ywq/r68vAwcONDmReIXZs2HmTPO6ofv4wKxZWq/fht0q8Ldv397gpn1bEhMTY/xOLysrY9++fSYnEhFQsS/iFqqqqtixY4dxrFF98Ubnzp0zbmj17duXwMBAkxOJV7BYYPlyxx7nZggJcVxf/VXaLLvdzj/+8Q+2bNlCeno633zzjdmRTJGcnGw83r59O9XV1eaFERFAW++JuIXdu3dTWVkJQHx8PJ06dTI5kYjzaQq/uEyXLvDnP8Mf/sDliopWuaRxnT//2bHlnrRZPj4+dO3alezsbAA+/vhjFi9e3Oa2Fe3cuTPx8fEcPXqUyspKdu3a1eAGgIi0PhX7IiarqKhg165dgOMDg94YxRvV1dWRlZUFgL+/P3E39zsXcZbgBQvw/+ILPv7881a7pv+IEQQvWNBq1xP3NXHiRC5dukR2djaVlZWsXr2aJ598Er9mbA3pySZPnszx48ex2Wzs2rWLxMREgs2adSMiKvZFzLZ9+3ZqamoASEhIoH379iYnEnG+b7/9lqqqKgD69+9Pu3btTE4k3iY8PJzn3nyTihdfdGyL5mr/8R8EL11KeHi4668lbs9isTB79mxWrlzJtWvXyM/PZ+PGjcycOdPsaK0qMjKShIQEDhw4QE1NDTt27OC+++4zO5ZIm6U1+yImKi0tNZrY+Pn5kZSUZHIiEdfQFH5pDeHh4UT/+78TvXo10eHhRPv6Eg3O+/L1dZx39Wqi//f/VqEvDQQGBjJ//nxjNP/QoUNtchu6pKQkfG82zNy7dy+lpaUmJxJpu1Tsi5ho69atWK1WAEaPHs092q9XvFBtbS2nTp0CHB+G+/bta3Ii8XqpqXDqFEyf7jhuaaf+W69/6CHIznacX+QOoqKimDFjhnG8ceNGLl26ZGKi1nfPPfcwevRoAKxWa5vdoUDEHajYFzHJ9evXjTv+7dq1Y+LEiSYnEnGN7OxsY8/lgQMHGiM+Ii7VpQusWwcffwyJiY7vNXX99K3njxnjOM/atWrGJ3cVHx9P4s1/c3V1daSlpVHRSo0j3cXEiRON5VoHDhyguLjY3EAibZSKfRGTZGZmYrPZABg7dqwa2IjXqj+Ff+jQoSYmkTbHYoE5c2DnTjhyBJ56qmGx7usL/v7ffdW/ERUV5Xj+kSOwY4fjPNpeTxpp6tSpdOvWDYCSkhI++ugj4z2/LQgJCWHMmDEA2Gw2MjMzTU4k0japQZ+ICS5fvszRo0cBx7TmcePGmZxIxDWqqqqMPadDQ0Pp0aOHyYmkzYqPh9dfd3wVFcGBA3D4MJSUQHU1BARAeDgMHw4jR0LnzmYnFg/m6+tLamoqy5cvp7y8nJycHDIyMkhJSTE7WqsZP348+/bto6qqiiNHjjBhwgQ6duxodiyRNkXFvogJMjIysNvtAEyYMIHAwECTE4m4xsmTJ6mrqwNg8ODB+PhoQpm4gc6dYdo0x5eIi4SFhfHwww/zzjvvYLfb2bZtG127dqV///5mR2sVgYGBTJgwgc2bN2O320lPTydV/S5EWpU+dYm0svz8fGO/8ZCQEGNdn4g3Uhd+EWnLevbs2WDrubVr13L16lUTE7WuxMREQkJCAMjKyiI/P9/kRCJti4p9kVaWnp5uPE5KStJ+4+K1ysrKOHv2LAARERF07drV5EQiIq1v7NixDBo0CIDq6mpWr15NTU2NyalaR7t27Zg0aZJxXP8zkIi4nop9kVZ0/vx5zpw5Azj2gx4xYoTJiURcJysry1iuMmTIECxqbiYibZDFYmHmzJnGevWioiI2bNhg/H70diNHjiQ8PByAM2fOcOHCBZMTibQdKvZFWondbmfLli3G8eTJk/Fr6jZQIh5EU/hFRBwCAgJYsGCBMZvv2LFj7Nu3z+RUrcPPz4+kpCTjeMuWLW3mRoeI2VTsi7SSnJwczp07B0CHDh0YNmyYyYlEXKe4uNgYvenUqRNR2ptcRNq4jh07MmvWLON406ZNbWaUe/jw4URGRgKQm5trLPESEddSsS/SCm4f1U9OTlZXcvFqGtUXEfm+QYMGMX78eMCx/3xaWhplZWUmp3I9Hx8fpkyZYhzf6tAvIq6lakOkFWRnZ5OXlwdAVFQUgwcPNjmRiGup2BcRubN7772Xnj17AlBaWsqaNWuMLUq92eDBg41ZXnl5eWRnZ5ucSMT7qdgXcTGbzdag+2xKSooalYlXu3z5MoWFhQB07drVmLopIiKOUe558+YRFhYGwLlz59i8ebPJqVzPYrE0GN1PT0/X6L6Ii6nYF3Gx48ePU1RUBEBsbCz9+vUzOZGIa2lUX0Tkx4WGhpKammos6du1axcnTpwwOZXrxcXFGduwFhUVNXi/EBHnU7Ev4kJ1dXVkZGQYxxrVF29nt9sbfHjTkhURkTvr1q0bDzzwgHG8fv16Ll++bGIi17NYLKSkpBjHGRkZbWIJg4hZVOyLuNDhw4e5fv06AL169aJXr14mJxJxrfz8fK5duwZAz549jWmqIiLyfaNGjSI+Ph6A2tpaPvzwQ6qrq01O5Vq9e/c2Pg9du3aNI0eOmJxIxHup2BdxEavVytatW43j+neyRbyVpvCLiDSexWLhoYceMhrXXb16lfXr13v9Wvb6n4kyMzOxWq0mphHxXir2RVxk//793LhxA3CsUYuNjTU5kYhr2e12Y82pj48PAwcONDmRiIj78/f3Z/78+QQEBABw8uRJdu3aZXIq14qNjSUuLg6AGzdusH//fpMTiXgnFfsiLlBTU8O2bduMY43qS1tw/vx54wZXnz59CA4ONjmRiIhniIyMZO7cucbx119/zdmzZ01M5Hr1O/Nv376dmpoaE9OIeCcV+yIusHv3bioqKgDHVOZb0/NEvNmxY8eMx5rCLyLSNHFxcSQlJQGOmVJr1qwxbqB6oy5duhhNXMvLy9mzZ4/JiUS8j4p9ESerrKxk586dgGMtXnJysrmBRFpBXV0dWVlZAPj5+TFgwACTE4mIeJ7JkyfTp08fACoqKkhLS/PqbvXJycnGLkU7d+6kqqrK5EQi3kXFvoiT7dy50+ikO3z4cDp06GByIhHXy8nJobKyEoD+/fvTrl07kxOJiHgeHx8f5s6dS3h4OAAXL15k06ZNJqdynY4dOzJs2DAAqqqqjMESEXEOFfsiTlRWVmZMQ/P19WXy5MkmJxJpHbca84Gm8IuItERwcDDz58/H19cXgH379nn19nSTJ0/Gx8dRkuzevZvy8nKTE4l4DxX7Ik60fft2amtrARg5cqRxZ17Em9XW1nLy5EkAAgIC6Nu3r8mJREQ8W0xMDNOnTzeON2zYQEFBgYmJXCciIoKRI0cCjveT+g2ORaRlVOyLOElJSYmxdYy/vz+TJk0yOZFI6zhz5ozRRXngwIH4+fmZnEhExPMlJCQwYsQIAKxWK6tXrzaWS3mbpKQk471j//79lJSUmJxIxDuo2BdxkszMTKOJTmJiIqGhoSYnEmkdx48fNx5rCr+IiPNMmzaNmJgYAK5fv866deuw2+0mp3K+0NBQxowZAzgavm7dutXkRCLeQcW+iBNcvXqVw4cPA45pzBMmTDA3kEgrqa6u5vTp0wCEhITQq1cvkxOJiHgPPz8/UlNTCQoKAuD06dNeO819woQJBAQEAHDo0CGuXbtmciIRz6diX8QJMjMzjTvt48ePN96URbzdqVOnjBktgwYNMposiYiIc0RERDBv3jzjOD09nW+++cbERK4RFBTEuHHjALDb7WRkZJgbSMQL6FOZSAsVFhZy7NgxwNFB99Y0NJG2QFP4RURcr0+fPqSkpBjHH3/8McXFxeYFcpGxY8cSHBwMwLFjxygqKjI5kYhnU7Ev0kLp6enG44kTJxpT0ES8XXl5Od9++y0A4eHhdOvWzeREIiLea+LEifTv3x+AyspKVq9ejdVqNTmVc92+FLL+ZywRaToV+yItcOnSJbKzswEICwtj1KhRJicSaT1ZWVnG8pXBgwdjsVhMTiQi4r0sFguzZ88mMjISgPz8fDZu3GhyKucbPXo0YWFhgGOp2KVLl0xOJOK5VOyLtMCWLVuMx0lJSfj7+5uYRqR1nThxwng8dOhQE5OIiLQNgYGBzJ8/39im7tChQxw8eNDkVM7l7+9PUlKScVz/s5aINI2KfZFmys3NJScnB4D27duTkJBgciKR1nPjxg3OnTsHQMeOHYmKijI5kYhI2xAVFcWMGTOM440bN3rd6HdCQgIREREA5OTkkJuba2oeEU+lYl+kGex2e4M7zcnJyfj6+pqYSKR11W/Mpyn8IiKtKz4+nsTERMCxL31aWhoVFRUmp3IeX19fkpOTjeMtW7YYy8ZEpPFU7Is0w5kzZ7hw4QIAnTp1UhdyaXPqF/uawi8i0vqmTp1qNEYtKSnho48+wmazmZzKeYYOHUqnTp0AuHDhglduNyjiair2RZrIbrc36A47ZcoU7S0ubcrVq1fJz88HIDo6mg4dOpicSESk7fH19SU1NZWQkBDAMd3dm/am9/Hx0ei+SAupQhFpoqysLAoKCgBHoTNgwACTE4m0rvqj+prVIiJinrCwMB5++GFjKdW2bduMXYK8wcCBA4mOjgagoKCAkydPmpxIxLOo2BdpApvN1mBUPyUlRWuVpU2x2+3fW68vIiLm6dmzJ/fdd59xvHbtWq5evWpiIuexWCykpKQYx+np6V61VEHE1VTsizTB0aNHjTfQ7t2706dPH5MTibSuwsJCrly5Ajh+BsLDw01OJCIiY8eOZdCgQQBUV1ezevVqampqTE7lHH369KF79+4AXLlyhaNHj5qcSMRzqNgXaSSr1dpgLZxG9aUtOnbsmPFYU/hFRNyDxWJh5syZdOzYEYCioiI2bNjgFWvcbx/dz8zMpK6uzsREIp5Dxb5IIx08eJCSkhIA+vbtS48ePUxOJNK67HY7J06cABwfvm6NIomIiPkCAgJYsGAB7dq1Axw3Z/ft22dyKufo0aOHMZuyuLiYgwcPmpxIxDOo2BdphNraWrZt22YcT5kyxcQ0Iua4ePGiccOrT58+RgdoERFxDx07dmTWrFnG8aZNm4ytgj1d/dH9rVu3Ultba2IaEc+gYl+kEfbu3UtZWRng6AwbExNjciKR1ld/Cr8a84mIuKdBgwYxfvx4wNFYOC0tzfgM48liYmIYOHAgAGVlZV4za0HElVTsi9xFVVUVO3bsMI41qi9tkc1mIysrC3Ds7XzrA5eIiLife++9l549ewJQWlrKmjVrvGKde3JysvF4+/btVFdXmxdGxAOo2Be5i927d1NZWQlAfHw8nTp1MjmRSOs7e/Ys5eXlAMTFxREQEGByIhER+SE+Pj7MmzePsLAwAM6dO8fmzZtNTtVynTt3Jj4+HoDKykp27dplciIR96ZiX+RHVFRUGG8kPj4+De4oi7Qlx48fNx6rC7+IiPsLDQ0lNTUVHx/Hx/1du3YZTVY92eTJkxv8nSoqKkxOJOK+VOyL/Ijt27cb+9QmJCTQvn17kxOJtD6r1crJkycBaNeuHf369TM5kYiINEa3bt144IEHjOP169dz+fJlExO1XGRkJAkJCQDU1NQ0WGopIg2p2Bf5AaWlpUbzFz8/P5KSkkxOJGKOb775xlgXOWDAAPz9/U1OJCIijTVq1Chj6nttbS0ffvihx691T0pKwtfXF3A0US4tLTU5kYh7UrEv8gO2bt2K1WoFYPTo0dxzzz0mJxIxh6bwi4h4LovFwkMPPURUVBQAV69eZf369djtdpOTNd8999zD6NGjAcfss/rbI4vId1Tsi9zB9evXOXjwIOCYtjxx4kSTE4mYo6amhuzsbACCgoLo3bu3yYlERKSp/P39mT9/vtFc9eTJkx7f3G7ixIm0a9cOgAMHDlBcXGxuIBE3pGJf5A4yMzOx2WwAjB07luDgYJMTiZgjOzvbmOEyaNAgY9qkiIh4lsjISObOnWscf/3115w9e9bERC0TEhLCmDFjAMf2sJmZmSYnEnE/KvZFbnP58mWOHj0KQGBgIOPGjTM5kYh5NIVfRMR7xMXFGT2I7HY7a9as4caNGyanar7x48cTGBgIwJEjR7hy5YrJiUTci4p9kdtkZGQY69gmTJhgvImItDWVlZV88803AISFhdGjRw+TE4mISEtNnjyZPn36AI4thtPS0qirqzM5VfMEBgYyYcIEwHHzIj093eREIu5Fxb5IPfn5+WRlZQGO6WGJiYkmJxIxT1ZWlrGcZfDgwVgsFpMTiYhIS/n4+DB37lzCw8MBuHjxIps2bTI5VfMlJiYSEhICON638vPzTU4k4j5U7IvUU/+OcFJSktH4RaQtqj+Ff+jQoSYmERERZwoODmb+/PlGH5Z9+/Zx5MgRk1M1T7t27Zg0aZJxrNF9ke+o2Be56fz585w5cwaA8PBwRowYYXIiEfOUlpaSm5sLOJo6RUdHmxtIREScKiYmhunTpxvHGzZsoKCgwMREzTdy5EhjpsKZM2e4cOGCyYlE3IOKfREc67y2bNliHE+ePBk/Pz8TE4mY68SJE8bjIUOGaAq/iIgXSkhIMAY3rFYrq1evprKy0uRUTefn52c0HgTYsmWL0X9JpC1TsS8C5OTkcO7cOQA6dOjAsGHDTE4kYi514RcRaRumTZtGTEwMANevX2fdunUeWSgPHz6cyMhIAHJzcz16W0ERZ1GxL23e7aP6ycnJ+PjoR0ParuvXr3Pp0iUAoqKi6NSpk8mJRETEVfz8/EhNTSUoKAiA06dPs23bNpNTNZ2Pjw9Tpkwxjjdv3uyRNy1EnEkVjbR52dnZ5OXlAY7CZvDgwSYnEjGXRvVFRNqWiIgI5s2bZxynp6cbW696ksGDBxMVFQVAXl4e2dnZJicSMZeKfWnTbDZbg66tKSkpWpssbZ6KfRGRtqdPnz6kpKQYxx9//DHFxcXmBWoGi8XSYHQ/PT1do/vSpqnYlzbt+PHjFBUVARAbG0u/fv1MTiRirqKiogY/ExEREeYGEhGRVjNx4kT69+8PQGVlJatXr8ZqtZqcqmni4uLo2rUr4HhPq38DW6StUbEvbVZdXR0ZGRnGsUb1ReDYsWPGY43qi4i0LRaLhdmzZxuN7vLz89m4caPJqZrGYrE0mKGQkZFBXV2diYlEzKNiX9qsw4cPc/36dQB69epFr169TE4kYi673W5suWexWNS/QkSkDQoMDGT+/PnGFsSHDh3i4MGDJqdqmt69exuf665du8aRI0dMTiRiDhX70iZZrVa2bt1qHNe/AyzSVl26dKnBDbDQ0FCTE4mIiBmioqKYMWOGcbxx40ZjlxZPUf+zXWZmpsctRxBxBhX70ibt37+fGzduAI61XbGxsSYnEjGfGvOJiMgt8fHxJCYmAo6lj2lpaVRUVJicqvFiY2OJi4sD4MaNG+zfv9/kRCKtT8W+tDk1NTUN9o/VqL6IY2eKW1P4fX19GThwoMmJRETEbFOnTqVbt24AlJSU8NFHH2Gz2UxO1Xj1O/Nv376dmpoaE9OItD4V+9Lm7N6927gzPWTIEGM/VpG27Ny5c5SVlQHQt29fAgMDTU4kIiJm8/X1JTU1lZCQEABycnIaNDd2d126dDH6z5SXl7Nnzx6TE4m0LhX70qZUVlayc+dOwNGALDk52dxAIm5CU/hFROROwsLCePjhh40di7Zt20Z2drbJqRovOTnZyL5z506qqqpMTiTSelTsS5uyc+dOqqurARg+fDgdOnQwOZGI+erq6sjKygLA39/fWOMoIiIC0LNnT+677z7jeO3atVy9etXERI3XsWNHhg0bBkBVVZUx6CPSFqjYlzajrKzMmL7l6+vL5MmTTU4k4h6+/fZbY6Sjf//+tGvXzuREIiLibsaOHcugQYMAqK6uZvXq1R6zBn7y5Mn4+DjKnt27d1NeXm5yIpHWoWJf2ozt27dTW1sLwMiRIwkPDzc5kYh70BR+ERG5G4vFwsyZM+nYsSMARUVFbNiwAbvdbnKyu4uIiGDkyJEA1NbWNmjULOLNVOxLm1BSUmJsueLv78+kSZNMTiTiHmprazl16hQAgYGB9O3b1+REIiLirgICAliwYIExA+zYsWPs27fP5FSNk5SUhJ+fH+DYgrmkpMTkRCKup2Jf2oTMzEzq6uoASExMJDQ01OREIu4hOzvbmPEycOBAfH19TU4kIiLurGPHjsyaNcs43rRpExcuXDAxUeOEhoYyZswYwNGrZuvWrSYnEnE9Ffvi9a5evcrhw4cBxx3pCRMmmBtIxI3Un8I/dOhQE5OIiIinGDRoEOPHjwfAZrORlpZmbN/qziZMmEBAQAAAhw4d4tq1ayYnEnEtFfvi9TIzM431ZOPHjycoKMjkRCLuoaqqim+++QZwjHj06NHD5EQiIuIp7r33Xnr27AlAaWkpa9asMWZRuqugoCDGjRsHgN1uJyMjw9xAIi6mYl+8WmFhIceOHQMgODjYmL4lInDy5Enjg9ngwYONTsUiIiJ34+Pjw7x58wgLCwPg3LlzbN682eRUdzd27FiCg4MBR8+BoqIikxOJuI4+2YlXS09PNx5PnDjRmLolIurCLyIiLRMaGkpqaqpxs3jXrl2cOHHC5FQ/7vYlnfU/K4p4GxX74rUuXbpEdnY2AGFhYYwaNcrkRCLuo6ysjLNnzwKOLYm6du1qciIREfFE3bp144EHHjCO169fz+XLl01MdHejR482ZiScOnWKS5cumZxIxDVU7IvX2rJli/E4KSkJf39/E9OIuJesrCyjl8WQIUOwWCwmJxIREU81atQo4uPjAceWrh9++CHV1dUmp/ph/v7+JCUlGcf1PzOKeBMV++KVcnNzycnJAaB9+/YkJCSYnEjEvWgKv4iIOIvFYuGhhx4iKioKcOyEtH79euOmsjtKSEggIiICgJycHHJzc03NI+IKKvbF69jt9gZ3aJOTk7V3uEg9xcXFxp7InTp1Mj6ciYiINJe/vz/z5883+iOdPHmSXbt2mZzqh/n6+pKcnGwcb9myxa1vTog0h4p98TpnzpxpUMho1FKkIY3qi4iIK0RGRjJ37lzj+Ouvvzb6w7ijoUOH0qlTJwAuXLhgbEcr4i1U7ItXsdvtDbqqTpkyRduJidxGxb6IiLhKXFycsR7ebrezZs0abty4YXKqO/Px8dHovng1VUHiVbKysigoKAAgOjqaAQMGmJxIxL1cvnyZwsJCALp27UpkZKTJiURExNtMnjyZPn36AFBRUUFaWhp1dXUmp7qzgQMHEh0dDUBBQQEnT540OZGI86jYF69hs9kajOqnpKSow7jIbTSqLyIirubj48PcuXMJDw8H4OLFi2zatMnkVHdmsVhISUkxjtPT07HZbCYmEnEeFfviNY4ePcrVq1cB6N69u3FHWUQc7HZ7g2J/8ODBJqYRERFvFhwczPz5840myfv27ePIkSMmp7qzPn360L17dwCuXLnC0aNHTU4k4hwq9sUrWK1WMjIyjGON6ot8X35+PteuXQOgZ8+ehIWFmZxIRES8WUxMDNOnTzeON2zYYCy3dCe3j+5nZma67bIDkaZQsS9e4eDBg5SUlADQt29fevToYXIiEfejKfwiItLaEhISGDFiBOAYnFm9ejWVlZUmp/q+Hj16GLNCi4uLOXjwoMmJRFpOxb54vNraWrZt22YcT5kyxcQ0Iu7Jbrdz4sQJwLGWcuDAgSYnEhGRtmLatGnExMQAcP36ddatW+eWXe/rj+5v3bqV2tpaE9OItJyKffF4e/fupaysDHB0VL31ZiIi3zl//ryx9VGfPn0IDg42OZGIiLQVfn5+pKamEhQUBMDp06cbDNS4i5iYGONmeFlZGfv27TM5kUjLqNgXj1ZVVcWOHTuMY43qi9zZsWPHjMeawi8iIq0tIiKCefPmGcfp6el88803Jia6s+TkZOPx9u3bqa6uNi+MSAup2BePtnv3bmPdV3x8PJ06dTI5kYj7qaurIysrC3CMrgwYMMDkRCIi0hb16dOnwVT5jz/+mOLiYvMC3UHnzp2Jj48HoLKykl27dpmcSKT5VOyLx6qoqDB+Afv4+DS4Eysi38nJyTFuivXv35927dqZnEhERNqqiRMn0r9/f8BRTK9evRqr1WpyqoYmT56Mj4+jTNq1axcVFRUmJxJpHhX74rG2b99OTU0N4Oj02r59e5MTibgndeEXERF3YbFYmD17NpGRkYBjW9iNGzeanKqhyMhIEhISAKipqWmwZFTEk6jYF49UWlpqNE3x8/MjKSnJ5EQi7qm2tpZTp04BEBAQQN++fU1OJCIibV1gYCDz58/Hz88PgEOHDrndVndJSUn4+voCjmbQpaWlJicSaToV++KRtm7dakz5Gj16NPfcc4/JiUTc05kzZ4wZMAMHDjQ+WImIiJgpKiqKGTNmGMcbN27k0qVLJiZq6J577mH06NEAWK1Wt9w9QORu9KlPPM7169eNu7/t2rVj4sSJJicSMUlhIRw4AEeOQHEx1NRAu3YQEQHDhsHIkZrCLyIibis+Pp5Lly6xd+9e6urqSEtLY/HixW6zPezEiRM5ePAgNTU1HDhwgPHjxxMREWF2LJFGU7EvHiczMxObzQbA2LFj3eYNQaRVHD0Kr70Ga9dCUZHje76+4FNvopbNBnV1ADwYEkLvAQM4npREr169TAgsIiLyw6ZOnUp+fj4XLlygpKSEjz76iIULFxoN8swUEhLCmDFj2LZtGzabjczMTGbNmmV2LJFGM/+nSKQJLl++zNGjRwHHeq9x48aZnEikFdjtjuJ+3DjHiP0bb3xX6IOjsK+t/e7rZqEPEFpeTsKhQzz+l7/gM3Gi4zx2uwl/CRERke/z9fUlNTWVkJAQwLGDTEZGhrmh6hk/fjyBgYEAHDlyhCtXrpicSKTxVOyLR8nIyMB+s1CZMGGC8ctXxGsVFMDs2TB3Luzd6/heE7co8r05E4a9ex3nmT3bcV4RERE3EBYWxsMPP4zFYgFg27ZtZGdnm5zKITAwkAkTJgBgt9tJT083OZFI46nYF4+Rn59PVlYW4JhWlZiYaHIiERdLS4MBA+DWlkS3ivbmujXi/9lnjvOmpbXsfCIiIk7Ss2dP7rvvPuN47dq1XL161cRE30lMTDRmHmRlZZGfn29yIpHGUbEvHqP+ndSkpCTatWtnYhoRF/vLX2D+fLhxo8kj+XdVV+c47/z58OKLzj23iIhIM40dO5ZBgwYBUF1dzerVq40dZczUrl07Jk2aZBxrdF88hRr0iUc4f/48Z86cASA8PJwRI0aYnEjEdUr+8Acq/p//x3HgqvX1t877m99ASQnBv/414eHhrrmWiIhII1gsFmbOnElRURFXrlyhqKiIDRs2MGfOHGOKv1lGjhzJrl27KCkp4cyZM1y4cIFu3bqZmknkbix2uzo1iXuz2+28/fbbnDt3DoCZM2eSkJBgcioR1yh5+21e+fWvqW3lwts/KYnnXn5ZBb+IiJjuypUrrFy50hjVnzZtmlss3zx48CCffvop4Fh28Nhjj5l+E0Lkx2hkX9xeTk6OUeh36NCBYcOGmZxIxEUKCqh4/nlqIyOZO20anVppW8nLFRV8vHkzFefOER4f3yrXFBER+SEdO3Zk1qxZpN3sLbNp0yaio6NNH0kfPnw4O3bs4Nq1a+Tm5nL27Fl69+5taiaRH6NiX9ya3W5ny5YtxnFycrJb7Lsq4nR2OzzzDFRUQGQknYKDiQ4La73r19bCP/8zfP45aJRCRERMNmjQIMaPH8/OnTux2WykpaWxePFiQkNDTcvk4+PDlClT+OijjwDYvHkzvXr10ui+uC1VTeLWsrOzycvLAyAqKorBgwebnEjERdatg08++a5jfmuz22HTJkcOERERN3DvvffSs2dPAEpLS1mzZg11Zr1P3jR48GCioqIAyMvLc5stAkXuRMW+uC2bzdag22lKSorunIr3+tOfwOxZKz4+8Oc/m5tBRETkJh8fH+bNm0fYzZlu586dY/PmzaZmslgsTJkyxThOT09HLdDEXWkav7it48ePU1RUBEBsbCz9+vUzOZGIixw9Crt2NeklGTe/6vMBgoDOQALQ5NX3Nhvs3AnHjsHQoU19tYiIiNOFhoaSmprKW2+9hc1mY9euXXTt2tXU2Z5xcXF07dqVS5cuUVRUxPHjxxmq901xQxrZF7dUV1dHRkaGcaxRffFqr70Gfi2/92oDyoGzwMfAzuacxM8PXn21xVlEREScpVu3bjzwwAPG8fr167l8+bJpeSwWCykpKcZxRkaG6csLRO5EI/vilg4fPsz169cB6NWrF7169TI5kYgLrV0LVmujnvrXffv46/79fFtcjBXo3LkzP01K4rl+/bACO6xWlm3axIkTJ/hvq5WH+vbltQcfJKqxDY2sVse6/ddfb+7fRkRExOlGjRrFxYsXOXr0KLW1tXz44YcsWrSIgIAAU/L07t2bXr16cfbsWa5du8aRI0cYMWKEKVlEfohG9sXtWK1Wtm7dahzXv3Mq4nUKC+HmcpXGiL3nHv6/P/kJyxcvZvHixfTs2ZO//OMflBYV0RvY/MUXnD59mtTUVJ58/HHySkuZu3q1SzOJiIi4msVi4aGHHjKa4129epX169ebul6+/mfUzMxMrI28cS/SWlTsi9vZv38/N27cABxromJjY01OJOJCBw406ekz+vfnwX79iO3QgQ4dOnDvvfcS2K4duy9e5FpVFX8/dIj777+fXr16kRATw5uzZrHzwgV2X7zo0lwiIiKu5u/vz/z5843R/JMnT7KriT1vnCk2Npa4uDgAbty4wf79+03LInInKvbFrdTU1LBt2zbjWKP64vWOHAFf32a91Gazcfz4cSpraznYrRu/yc/HarPRu3dvQoBpwICOHekeHs6uCxcaf2JfXzh8uFmZREREXCkyMpK5c+cax19//TVnz541LU/9zvzbt2+npqbGtCwit1OxL25l9+7dVFRUADBkyBBjqpaI1youbvKWe8cKC5n2hz/wX//1X2zYsIEFCxbQqVMnysrK8PX1JTAwED+g+ubzo0JCKCgra/wFfHygpKRJmURERFpLXFwcSUlJANjtdtasWWPMCm1tXbp0MXYGKC8vZ8+ePabkELkTFfviNiorK9m509E/3GKxkJycbG4gkdbQjBGA/h07surZZ3n66acZNWoUn65bx8TLl5mE45e6BSgBPgSaUOI3VF199+eIiIiYZPLkyfTp0weAiooK0tLSTOuIn5ycbOwatXPnTqqqqkzJIXI7FfviNnbu3En1zQJj+PDhdOjQweREIq2gXbumv8TXl66RkcTExPCTn/yEXlFRpO3eTXxoKLV1dXS5+SGjFsgGCsvL6dLYbvy3mNTdWEREpDF8fHyYO3cu4eHhAFy8eJFNmzaZkqVjx44MGzYMgKqqKmPwSsRsKvbFLZSVlRnTnnx9fZk8ebLJiURaSUQE2GwtOoXNbqe6ro6R0dH4+/iQlZNj/Fn2lSucLylhXLduTTihDW5+eBIREXFXwcHBzJ8/H9+bvW/27dvHkSNHTMkyefJkfG4uy9u9ezfl5eWm5BCpT8W+uIXt27dTW1sLwMiRI427tCJeb9gwaMK0w//311+z9dw5CoqLKSws5Ouvv+ZEbi73DR3K9cBAHkxI4O0vv+Ts2bPk5eXxp/XrGRcby9im7GpRV8cJf38uXLhg2pRIERGRxoiJiWH69OnG8YYNGygoKGj1HBEREYwcORKA2traBg2nRcziZ3YAkZKSEmOrEn9/fyZNmmRyIpFWdPODQWMVlZfz2Nq15JWV4R8QQFRUFAt//nPO9OnDGWDIAw9wadMmVq9eja2ujgf79OGv9T4ENdbGwkIq/vY3/Pz8iI2NpXv37vTo0YPY2FjaNWPpgYiIiKskJCRw8eJFDh48iNVqZfXq1SxatIigoKBWzZGUlMShQ4ewWq3s37+fcePGaQBLTKViX0yXmZlpjB4mJiYS2tS1xSKeLCoKOneGoqJGPf2NWbMAyLj5dbsgPz+emD6dAdOnMwFozsr7spAQKm7+HFqtVnJzc8nNzQUczTNjYmKM4r979+6t/mFKRETkdtOmTaOgoIC8vDyuX7/OunXreOSRR4zGea0hNDSUMWPGsGPHDurq6ti6dSszZsxoteuL3E7Fvpjq6tWrHL65n3dAQAATJkwwN5CIGebMgTfeAKu10S9JvvnlbHY/P3wffpiHHnqI8+fPc+7cOUrqbcNnt9u5dOkSly5dYteuXQB07tyZ7t27GzcA7rnnHhckExER+WF+fn6kpqayYsUKKisrOX36NNu2bTO26GstEyZMYP/+/VRXV3Po0CEmTJhAZGRkq2YQuUXFvpgqMzMTu90OwPjx4zVCKG3TkiWwfLnZKQCwWK0E/a//xcihQ421hyUlJZw7d84o/q9cudLgNUVFRRQVFRnLcSIiIoxR/x49ehAZGdmqIysiItI2RUREMG/ePN577z0A0tPTiYmJoW/fvq2WISgoiHHjxpGRkYHdbicjI4O5c+e22vVF6lOxL6YpLCzk2LFjgKOb6pgxY0xOJGKS+HgYNw727GlxZ/4W8fGBsWNh6NAG3w4PDyc+Pp74+HgAysvLOX/+vPGVn59v3LQDKC4upri42OiIHBIS0qD479y5s9GxWERExJn69OlDSkoKW7ZsAeDjjz9m8eLFREREtFqGsWPHsnfvXioqKjh27BgTJ06kc+fOrXZ9kVtU7Itp0tPTjccTJ04kQPt6S1v2u9+B2Xf+bTb47W/v+rSQkBAGDhzIwIEDAaiurubixYvG6P/FixcbdPEvLy8nKyuLrKwswLFkp/60/5iYGGPbJBERkZaaOHEily5dIjs7m8rKSlavXs2TTz6Jn1/rlD63lqZ+9dVXgOMz74IFC1rl2iL1qdgXU9z6BQwQFhbGqFGjTE4kYrLZs2HmTPjsM3Oub7HA/fc7cjRRQEAAffr0oU+fPoCjqV9eXp5R/J8/f56amhrj+dXV1Zw5c4YzZ84AqOO/iIg4lcViYfbs2axcuZJr166Rn5/Pxo0bmTlzZqtlGD16NLt376a0tJRTp05x6dIlunbt2mrXFwEV+2KSW1OrwLFNib+/v4lpRNyAxeJYtx8XZ861/f3hj390PG4hPz8/Y+QewGazUVhY2GDdf0VFhfF8dfwXERFnCwwMZP78+axatQqr1cqhQ4eIjY1lxIgRrXJ9f39/kpKS+OzmTfwtW7bw6KOPtsq1RW5RsS+tLjc3l5ycHADat29PQkKCyYlE3ESXLvDnP8Mf/sDlesWwq12uqIDx46FTJ5ec38fHh+joaKKjoxk7dix2u52rV682KP7V8V9ERJwtKiqKGTNmsHbtWgA2btxIVFRUq42wJyQksGPHDoqLi8nJySE3N5eePXu2yrVFACz2+l2VRFzMbrfz5ptvcuHCBQDmzJljNP0SEUfn+1eeeILagwdb76KJifgPG8Zzzz1HeHh46123nrt1/L+dOv6LiEhjff755+zduxdwNJ1dvHgxwcHBrXLtI0eOsG7dOgC6devGE088ofcraTUq9qVVnT59mg8++ACATp068eyzz6ort8htSkpKqHjxRfj9711/sf/4D1i0iODgYNMK/Tu5W8f/26njv4iI/JC6ujrefvttY7Cpd+/eLFy4sFXeJ2w2G6+//jqXL18G4Gc/+xn9+vVz+XVFQMW+tCK73c6KFSsoKCgAYP78+UY3bxG5g7Q0WLQIysqgXnf7FvP1hdBQWLkSUlOdd14XulvH/9up47+IiNRXWlrK8uXLKS8vB2DSpEmkpKS0yrWzsrJIS0sDoEuXLixevFij+9IqVOxLqzlx4gRr1qwBIDo6mkWLFukXncjdFBTAM8/AJ584ivSWFP23Xj9rlqMZYFSU83K2srt1/L+dOv6LiEhubi7vvPOOMVPskUceoX///i6/rt1uZ+XKleTn5wOQmprKoEGDXH5dERX70ipsNhuvvfYaV69eBWDhwoX07dvX5FQiHsJuh3Xr4E9/gl27wM8PrNbGv/7W88ePh9/+1rG9npfdaLtbx//b1e/4f+urtdZvioiIeXbt2sWXX34JOGaBLVq0iA4dOrj8ut988w1///vfAejYsSO//OUvtdxMXE7FvrSKw4cPs379egC6d+/O448/rlF9keY4ehRee81R/BcWOr7n6wv1PzDYbN/NAIiKchT3S5ZAG2qGebeO/3fSqVOnBuv+1fFfRMT72O121qxZQ1ZWFuDY7eWpp55y+Wwvu93OW2+9xfnz5wGYNWsWw4cPd+k1RVTsi8tZrVZeeeUV44P2448/To8ePUxOJeIFiorgwAE4fBhKSqC6GgICIDwchg+HkSOhc2ezU7oNdfwXERFw9IFZtWqV8T4wdOhQ5syZ4/Lf8efOneOtt94CHO8xzz33nPrJiEup2BeX27t3L59//jkAffv2ZeHChSYnEhFRx38RkbbsypUrrFy50uj3Mm3aNBITE11+3ffee49vv/0WgAcffJDRo0e7/JrSdqnYF5eqra1l2bJllJWVAbBo0SJiYmJMTiUi8n3q+C8i0rbU75Lv4+PD448/Trdu3Vx6zby8PFauXAlAaGgoL7zwAv7+/i69prRdKvbFpXbs2MHXX38NwMCBA5k/f77JiUREGkcd/0VEvN9XX33Fzp07AQgLC2Px4sWEhoa69JqrV6/m5MmTANx3332MHz/epdeTtkvFvrhMVVUVy5Yto7KyEoAlS5bQqVMnk1OJiDSPOv6LiHgfm83Gu+++S25uLgA9evTg0UcfdelMraKiIv76178CEBQUxNKlSwkICHDZ9aTtUrEvLpORkUFmZiYA8fHxzJkzx+REIiLOo47/IiLeoaysjBUrVlBaWgrAuHHjmDp1qkuvuXbtWo4ePQrA5MmTSU5Odun1pG1SsS8uUVFRwUsvvURNTQ0+Pj4899xztG/f3uxYIiIupY7/IiKe6cKFC7z11lvYbDYAHn74YQYPHuyy6127do1XX30Vm81Gu3btWLp0qWZ/idOp2BeX+PLLL9m1axcAI0eO5KGHHjI5kYhI66uoqDAKf3X8FxFxb/v27WPjxo0A+Pv7s2jRIpcuQd2wYQMHDhwAYPz48dx3330uu5a0TSr2xelKS0tZtmwZVqsVPz8/nn/+eU1VFRFBHf9FRNyZ3W5n3bp1xvT6Dh06sGjRIpetp79x4wbLli2jrq4OPz8/XnjhBcLCwlxyLWmbVOyL03322Wfs378faJ01TyIinkod/0VE3EttbS1vvPEGhYWFgGM3qdTUVJctsdq0aRO7d+8GYPTo0Tz44IMuuY60TSr2xamuX7/OK6+8ovVHIiLNoI7/IiLmu3btGitWrKC6uhpw7fZ45eXlLFu2zOhz9fzzzxMREeGSa0nbo2JfnGrdunUcOXIEgKSkJKZMmWJyIhERz6WO/yIi5jh9+jQffPAB4Lix+uijj9KrVy+XXGvLli1s27YNgOHDhzNr1iyXXEfaHhX74jSXL1/mr3/9K3a7ncDAQJYuXUpgYKDZsUREvIo6/ouItI709HS2bt0KQHBwMM8884xLbqBWVVXx0ksvUVVVhcViYcmSJXTs2NHp15G2R8W+OE1aWhpZWVkA3HvvvUycONHkRCIi3k8d/0VEXMNms/H+++/z7bffAhAbG8vjjz/ukkap27dvZ/PmzQAMGjSI1NRUp19D2h4V++IU+fn5rFixAnB8kHzhhRfUNEpExATq+C8i4jwVFRWsWLHCWELlqiZ6NTU1LFu2jPLycgAWL15MdHS0068jbYuKfXGK999/nzNnzgAwbdo0EhMTTU4kIiKgjv8iIi2Vl5fH3/72N+PG6ezZsxk2bJjTr7Nnzx6++OILAPr168fPfvYzp19D2hYV+9Ji58+f58033wQgPDyc5557Dj8/P5NTiYjInajjv4hI0x06dIhPPvkEcNwUfeqpp+jSpYtTr2G1WnnllVeMWQRPPvkk3bp1c+o1pG1RsS8tYrfbefvttzl37hwAM2fOJCEhweRUIiLSWOr4LyLSOJ9++ikHDx4EoH379ixatIigoCCnXuPgwYN8+umnAPTs2ZPHHntMTVWl2VTsS4t8++23vPfeewB06NCBJUuWqNGTiIiHU8d/EZHvs1qtvPnmm+Tl5QEQFxfHI4884tTfdzabjVdffZVr164B8Oijj9K7d2+nnV/aFhX70mx2u51Vq1YZv/DmzZvHkCFDTE4lIiLOpo7/IiIOxcXFrFixgsrKSgCmTJlCUlKSU69x/PhxPvroIwBiYmJ4+umndQNVmkXFvjTbqVOn+PDDDwGIiorimWee0S8iEZE2QB3/RaQtqz+zFWDhwoX07dvXaee32+0sX76cwsJCABYsWMCAAQOcdn5pO1TsS7PYbDaWL19OUVERAD/96U+Ji4szOZWIiJhBHf9FpK3Ztm0bW7ZsASAoKIjFixcTERHhtPNnZ2fzj3/8A4DOnTvz7LPPalBNmkzFvjTL0aNHWbt2LQCxsbE8+eST+gUkIiKAOv6LiPez2+18+OGHZGdnAxAdHc2TTz7ptB2p7HY7b7zxBpcuXQJg7ty5DB061CnnlrZDxb40WV1dHa+++irXr18H4LHHHqNXr14mpxIREXeljv8i4o2qqqpYuXKl0UwvISGBmTNnOu38OTk5vPvuuwBERkayZMkSLYGSJlGxL0124MABNmzYAECvXr147LHHTE4kIiKeRh3/RcQbFBYWsmrVKqxWKwAzZsxgxIgRTjv/O++8w9mzZ11ybvF+KvalSaxWKy+//DI3btwA4KmnniI2NtbkVCIi4unU8V9EPFX95a2+vr488cQTdO3a1SnnvnjxIm+88QYA99xzD88//7zTlgqI91OxL02ye/duNm3aBDj2Fv3pT39qciIREfFG6vgvIp7k888/Z+/evQCEh4ezePFip/Ue+eCDDzh9+jQA999/P2PHjnXKecX7qdiXRqupqeGll14ymiw9++yzREVFmZxKRETaAnX8FxF3VldXx9tvv82FCxcA6N27NwsXLnTKjKOCggKWL18OOGY1vfDCC/p9Jo2iYl8abevWraSnpwMwZMgQ5s2bZ3IiERFpq9TxX0TcTWlpKcuXL6e8vByASZMmkZKS4pRzr1mzhhMnTgCQkpLCpEmTnHJe8W4q9qVRKisreemll6iursZisfCrX/2KDh06mB1LREQEUMd/EXEPubm5vPPOO0bPkUceeYT+/fu3+LxXrlzhtddew263ExgYyNKlSwkMDGzxecW7qdiXRtm8eTPbt28HnL+tiIiIiCuo47+ImGHXrl18+eWXgKOfyKJFi5wySLZ+/XoOHz4MOHfWgHgvFftyV2VlZSxbtoza2lp8fX15/vnnCQ8PNzuWiIhIk6jjv4i0Brvdzpo1a8jKygKgc+fOPPXUUy1eZ19cXMzLL7+MzWbD39+fpUuXEhIS4ozI4qVU7MtdffHFF+zZsweAxMREpk2bZnIiERGRllPHfxFxlerqalatWmXMKBo6dChz5sxp8WyhjRs3sm/fPgDGjBnDAw880OKs4r1U7MuPKikp4eWXX6aurg5/f39eeOEFQkNDzY4lIiLidOr4LyLOdOXKFVauXGn8Hpk2bRqJiYktOmdZWRkvvfQSVqtVM27lrlTsy4/65JNPOHToEAATJkzgJz/5icmJREREWoc6/otIS2VlZZGWlgaAj48Pjz/+ON26dWvROb/++mt27NgBwIgRI5gxY0aLc4p3UrEvP+jq1au8+uqr2O12AgICWLp0KUFBQWbHEhERMYU6/otIc3z11Vfs3LkTgLCwMBYvXtyimbK375L13HPPERkZ6ay44kVU7MsP+vjjjzl27BgAU6ZMISkpyeREIiIi7kUd/0Xkbmw2G++++y65ubkA9OjRg0cffbRFPT8yMzPJyMgAHP0A5s6d64Sk4m1U7MsdFRYW8vrrrwMQHBzMCy+8QEBAgMmpRERE3Js6/ovInZSVlbFixQpKS0sBGDduHFOnTm32+aqrq1m2bJmxtOiXv/wlnTt3dkpW8R4q9uWO/vGPf5CdnQ3A1KlTGTdunMmJREREPI86/ovILRcuXOCtt97CZrMB8PDDDzN48OBmn2/nzp189dVXAAwYMIAFCxY4Jad4DxX78j2XLl1i1apVgGNd0fPPP4+/v7/JqURERDyfOv6LtG379u1j48aNAPj7+7No0SI6derUrHPV1tby8ssvG7MFnn76abp27eq0rOL5VOzL97z77rvk5OQAMH36dEaNGmVyIhEREe9kasf/khLYsQM6dYJRo0C9A0Rczm63s27dOo4ePQpAhw4dWLRoUbOXy+7fv5/PPvsMgN69e/Poo486Lat4PhX70kBubi5vv/02AO3bt+dXv/qVpg+KiIi0klbt+P/qq/Dhh3DhAly/DvffD3/8I/ToUT+QbgKIOFltbS1vvPEGhYWFAAwcOJDU1NRmNeusq6vjlVdeobi4GIBf/OIX9OzZ04lpxZOp2BeD3W7nzTff5MKFCwDMmTOH+Ph4k1OJiIi0bS3p+N+zZ88f3pJr1y4IDobu3eHiRXj+eYiLg2XLIDAQbDbw8XHcCPD1BW0bKOI0165dY8WKFVRXVwNw3333MX78+Gad68iRI6xbtw6Abt268cQTT2iXDwFU7Es9p0+f5oMPPgAcowTPPvusOgKLiIi4maZ0/O/fvz+PPPJI4068fj08/DAUFsKtGwTp6fA//wP794OfH/zmN/BP/6TRfhEnqP/Z22Kx8Oijj9KrV68mn8dms/H6669z+fJlAH72s5/Rr18/p2YVz6RKTgDHqH56erpxPGXKFBX6IiIibig4OJgBAwZw//33s2jRIv7lX/6Fn//850yaNIkePXo0WH7Xo0ePH+7+b7dD/T+rqnKM3ldWOo4PH4bHHnM8/vpr+Ld/gxUrYPNm1/zFRNqYuLg4kpKSAMdn8TVr1nDjxo0mn8fHx4fk5GTjeMuWLT+65ae0HRrZFwBOnDjBmjVrAIiOjmbRokWa/iMiIuKB6nf8Hzx4MO3bt7/ze7rV6hitB1i3Dn73O5g2zTGN32qFxx+HnBzH6H5AANTUwIIFjpsBX3zx3TR/EWk2m83G+++/z7fffgtAbGwsjz/+eJN7ZtntdlauXEl+fj4AqampDBo0yOl5xbPoN7Rgs9kajOqnpKSo0BcREfFQfn5+dO/enUmTJhEZGXnn9/S6OkehX1IC//qv8NRT8Mgj8O//7vjzU6dgyxZ48snvCv127Rzr+6uqHMcq9EVazMfHh7lz5xIeHg7AxYsX2bRpU5PPY7FYSElJMY7T09Ox2WxOyymeSb+lhaNHj3L16lUAunfvTp8+fUxOJCIiIi7l6wurV8O99zpG9T/9FP7P/4EOHRx/fvYsXL0KDz7oOL5V2OflQXQ03NzXW0RaLjg4mPnz5xuj+fv27ePIkSNNPk+fPn3o3r07AFeuXDG295O2S8V+G2e1WsnIyDCONaovIiLi5a5fd0zR/5//gZkz4fhxGD/eMXX/lgsXHOv3Y2Ic0/X9/ByzAfLyoEsXiIhocEqtChVpmZiYGKZPn24cb9iwgYKCgiad4/bR/czMzB/u2SFtgor9Nu7gwYPG/r19+/alR/29dUVERMT7vPOO48tuh7Fj4do1x/dvrd8HuHLFMYIPjmIf4OhRx/cHDnTMDKjHYrGQnp7Onj17KCgo0PRhkWZISEhgxIgRgGNAbvXq1VTeapjZSD169DBm6RYXF3Pw4EGn5xTP4Xf3p4i3qq2tZdu2bcbxlClTTEwjIiIireKJJ6BXL8c0/scec0zXDwuDF190NOALCHBsvVdR4ejIP3y443Xvvw8hITBx4vdOWVdXx86dO7HenB0QEBBA9+7d6d69Oz169CAmJqbJDcdE2qJp06ZRUFBAXl4e169fZ926dTzyyCNNmnmbkpJiNPzbunUrw4cPx9/f31WRxY2pG38btmPHDr7++msABg4cyPz5801OJCIiIq2urMyxtV5EBEyeDBaLY6r/7NnQvz889xz8/e/w2muOqf+LFzd4ud1uJy8vj1WrVv3gJfz8/IiNjTWK/9jYWNq1a+fav5eIhyouLmbFihXGqP6UKVOMLfoaa/Xq1Zw8eRKA++67j/Hjxzs9p7g/FfttVFVVFcuWLTN+iSxZsoROnTqZnEpERETcxpYt8L//Nxw7BoMHw6JFjlkBd2C32ykoKODcuXOcP3+ec+fOUVFR8YOntlgsxMTEGKP/3bt3Jzg42FV/ExGP8+233/Lee+8ZxwsXLqRv376Nfn1RURF//etfAQgKCmLp0qUEBAQ4Pae4NxX7bVRGRgaZmZkAxMfHM2fOHJMTiYiIiNu6etXRqd9ud4z834Xdbufq1asNiv9bPYJ+SKdOnejRo4cx+n/PPfc4K72IR9q2bRtbtmwBHAX74sWLibitOeaPWbt2rdGRf/LkySQnJ7sgpbgzFfttUEVFBS+99BI1NTX4+Pjw3HPP0b59e7NjiYiIiBcrKSlpUPxfuXLlR58fERHRoPiPjIzUjkHSptjtdj788EOys7MBiI6O5sknn8TPr3Ft165du8arr76KzWajXbt2LF26VDNo2hgV+23Ql19+ya5duwAYOXIkDz30kMmJREREpK2pqKgwCv/z58+Tn5//o1v4hYSENCj+O3fujI+PNpYS71ZVVcXKlSu5dnPXjISEBGbOnNno12/YsIEDBw4AMH78eO677z6X5BT3pGK/jSktLWXZsmVYrVb8/Px4/vnnNU1ORERETFddXc3FixeN4v/ixYs/uke4Ov5LW1FYWMiqVauM3S5mzJhhbNF3Nzdu3GDZsmXU1dXh5+fHCy+8QFhYmCvjihtRsd/GfPbZZ+zfvx+AcePGMXXqVJMTiYiIiHyf1WolLy/PKP7Pnz9PTU3NDz5fHf/Fmx09epS1a9cC4OvryxNPPEHXrl0b9dpNmzaxe/duAEaPHs2DDz7ospziXlTstyHXr1/nlVde0bodERER8Tg2m43CwkJ1/Jc26/PPP2fv3r0AhIeHs3jx4kb9my4vL2fZsmVGv67nn3++SY3+xHOp2G9D1q1bx5EjRwBISkpiypQpJicSERERaR51/Je2pq6ujrfffpsLFy4A0Lt3bxYuXNio3hVbtmxh27ZtAAwfPpxZs2a5NKu4BxX7bcTly5f561//it1uJzAwkKVLlxIYGGh2LBERERGnUcd/8XalpaUsX76c8vJyACZNmkRKSspdX1dVVcVLL71EVVUVFouFJUuW0LFjR1fHFZOp2G8j0tLSyMrKAuDee+9l4sSJJicSERERcS11/BdvlJubyzvvvGP8W37kkUfo37//XV+3fft2Nm/eDMCgQYNITU11aU4xn4r9NiA/P58VK1YAjjexF154QQ1rREREpM1Rx3/xFrt27eLLL78EHP9OFy1aRIcOHX70NTU1NSxbtsyYFbB48WKio6NdnlXMo2K/DXj//fc5c+YMANOmTSMxMdHkRCIiIiLmU8d/8VR2u501a9YYM3c7d+7MU089ddd/j3v27OGLL74AoF+/fvzsZz9zeVYxj4p9L3f+/HnefPNNwNG187nnnsPPz8/kVCIiIiLuRx3/xZNUV1ezatUqozfF0KFDmTNnzo/2nbBarbzyyitGM8snn3ySbt26tUpeaX0q9r2Y3W7n7bff5ty5cwDMnDmThIQEk1OJiIiIeAZ1/Bd3d+XKFVauXGnMSGnMLN6DBw/y6aefAtCzZ08ee+wxNab0Uir2vdi3337Le++9B0CHDh1YsmSJmsyIiIiItIA6/ou7ycrKIi0tDQAfHx8ef/zxHx2tt9lsvPrqq1y7dg2ARx99lN69e7dKVmldKva9lN1uZ9WqVeTl5QEwb948hgwZYnIqEREREe+ijv/iDr766it27twJQFhYGIsXLyY0NPQHn3/8+HE++ugjAGJiYnj66ad1E8oLqdj3UqdOneLDDz8EICoqimeeeUY/wCIiIiIupo7/Ygabzca7775Lbm4uAD169ODRRx/9wX9Ldrud5cuXU1hYCMCCBQsYMGBAa8WVVqJi3wvZbDaWL19OUVERAD/96U+Ji4szOZWIiIhI26OO/9JaysrKWLFiBaWlpQCMGzeOqVOn/uDzs7Oz+cc//gE4uvk/++yzGhz0Mir2vdDRo0dZu3YtALGxsTz55JP6wRURERFxA+r4L6504cIF3nrrLWw2GwAPP/wwgwcPvuNz7XY7b7zxBpcuXQJg7ty5DB06tNWyiuup2PcydXV1vPrqq1y/fh2Axx57jF69epmcSkRERETuRB3/xdn27dvHxo0bAfD392fRokV06tTpjs/Nycnh3XffBSAyMpIlS5ZoGYkXUbHvZQ4cOMCGDRsA6NWrF4899pjJiURERESkKdTxX1rCbrezbt06jh49Cjh25Vq0aBEBAQF3fP4777zD2bNnAZgxYwYjRoxotaziWir2vYjVauXll1/mxo0bADz11FPExsaanEpEREREWkId/6WpamtreeONN4wGfAMHDiQ1NfWON4EuXrzIG2+8AcA999zD888/j5+fX6vmFddQse9Fdu/ezaZNmwCIi4vjpz/9qcmJRERERMTZ1PFfGuPatWusWLGC6upqAO677z7Gjx9/x+d+8MEHnD59GoD777+fsWPHtlpOcR0V+16ipqaGl156yWjw8uyzzxIVFWVyKhERERFxNXX8lx9y+vRpPvjgA8DR7PHRRx+9Yz+vgoICli9fDjhmhrzwwgv6N+EFVOx7ia1bt5Keng7AkCFDmDdvnsmJRERERMQMzen4Hx0dbUz9V8d/75Kens7WrVsBCA4O5plnnrljU8c1a9Zw4sQJAFJSUpg0aVKr5hTnU7HvBSorK3nppZeorq7GYrHwq1/9ig4dOpgdS0RERETcgDr+t202m43333+fb7/9FnBszf34449/bynHlStXeO2117Db7QQGBrJ06VICAwPNiCxOomLfC2zevJnt27cDkJCQwMyZM01OJCIiIiLurH7H//Pnz3P58uUffb46/nu2iooKVqxYYdzkGT16NA8++OD3nrd+/XoOHz4MwKRJk0hJSWnNmOJkKvY9XFlZGcuWLaO2thZfX1+ef/55wsPDzY4lIiIiIh5EHf+9X15eHn/729+MZo6zZ89m2LBhDZ5TXFzMyy+/jM1mw9/fn6VLlxISEmJGXHECFfse7osvvmDPnj0AJCYmMm3aNJMTiYiIiIinU8d/73To0CE++eQTwNGo8amnnqJLly4NnrNx40b27dsHwJgxY3jggQdaPac4h4p9D1ZSUsLLL79MXV0d/v7+vPDCC4SGhpodS0RERES8jDr+e49PP/2UgwcPAtC+fXsWLVpEUFCQ8edlZWW89NJLWK1WzRz2cCr2Pdgnn3zCoUOHAJgwYQI/+clPTE4kIiIiIm2BOv57LqvVyptvvkleXh4AcXFxPPLIIw16MHz99dfs2LEDgBEjRjBjxgxTskrLqNj3UFevXuXVV1/FbrcTEBDA0qVLG9yRExERERFpLer471mKi4tZsWIFlZWVAEyZMoWkpCTjz2/f7eu5554jMjLSrLjSTCr2PdTHH3/MsWPHgO//cIqIiIiImE0d/93bt99+y3vvvWccL1y4kL59+xrHmZmZZGRkADB06FDmzp3b2hGlhVTse6DCwkJef/11AIKDg3nhhRcICAgwOZWIiIiIyA9Tx3/3s23bNrZs2QJAUFAQixcvJiIiAnA0aVy2bJmxPOOXv/wlnTt3NiuqNIOKfQ/0j3/8g+zsbACmTp3KuHHjTE4kIiIiItI06vhvPrvdzocffmjUFtHR0Tz55JP4+fkBsHPnTr766isABgwYwIIFC0zLKk2nYt/DXLp0iVWrVgEQFhbG888/j7+/v8mpRERERERaRh3/zVFVVcXKlSu5du0aAAkJCcycOROA2tpaXn75ZUpLSwF4+umn6dq1q2lZpWlU7HuYd999l5ycHACmT5/OqFGjTE4kIiIiIuJ86vjfegoLC1m1ahVWqxWAGTNmMGLECAD279/PZ599BkDv3r159NFHTcspTaNi34Pk5uby9ttvA449MX/1q19p6pKIiIiItAnq+O9aR48eZe3atQD4+vryxBNP0LVrV+rq6njllVcoLi4G4Be/+AU9e/Y0L6g0mop9D2G323nzzTe5cOECAHPmzCE+Pt7kVCIiIiIi5lHHf+f6/PPP2bt3LwDh4eEsXryY4OBgjhw5wrp16wDo1q0bTzzxhP538wAq9j3E6dOn+eCDDwDHHcpnn31W3UhFREREROpRx/+Wqaur4+233zYGGHv37s3ChQsBeP31142bKT/72c/o16+faTmlcVTsewC73c6KFSsoKCgAYP78+QwcONDkVCIiIiIi7k0d/5uutLSU5cuXU15eDsCkSZNISUkhKyuLtLQ0ALp06cLixYs1uu/mVOx7gBMnTrBmzRrAsR3GokWL9IMlIiIiItJE6vjfOLm5ubzzzjvGrIhHHnmEuLg4Vq5cSX5+PgCpqakMGjTIzJhyFyr23ZzNZuO1117j6tWrACxcuJC+ffuanEpERERExPOp4/8P27VrF19++SXgmPGwaNEirl+/zt///ncAOnbsyC9/+cs2vezB3anYN0NhIRw4AEeOQHEx1NRAu3YQEQHDhsHIkRAVBcDhw4dZv349AN27d+fxxx/XqL6IiIiIiAuo4/937HY7a9asISsrC4DOnTvz5JNP8v7773P+/HkAZs2axfDhw797URPqHHE9Ffut5ehReO01WLsWiooc3/P1hfp3wmw2uLWGqHNnbLNm8X5EBN+GhADw+OOP06NHj1YOLiIiIiLSdrXljv/V1dWsWrWKK1euADB06FBGjBhhbAceERHBc0lJ+C5f3qQ6hzlzYMkS0O5iLqVi35Xsdli3Dv74R9i9G/z8wGpt9Mttvr741NVxITaWnHnzmPyXv4CH/qIQEREREfEGba3j/5UrV1i5cqXR22DatGmczs7G/7PPGL9jB90uXmxynWM8f9w4+N3vYPZs1TkuoGLfVQoK4Jln4JNPHHe1bLZmn8pmseBjt8PMmbB8OXTp4sSgIiIiIiLSXG2h43/9Tvxh5eU8uXcvEZmZ39UpzeXr6xjxV53jEir2XSEtDRYtgvLypt3huhtfXwgNhZUrITXVeecVERERERGn8NaO/1999RXFK1cy45NPaFdbi08LBjO/R3WOS6jYd7a//AX+6Z/AYqHEbueHe3k2XTAQbrE4lgf85S/w61878ewiIiIiIuJs3tDxv6SkhLK//AWf//gPbIBLFyH8/veweDHBwcGEh4e78kpeT8W+M90q9IES4JWICGqd+A/Uv6SE54qLMc6ogl9ERERExKN4Wsf/kpISXnn8cWoPHWq1a5KYiP+wYTz33HMq+FvAz+wAXiMtzSj0ASqA2vBw5k6bRicn3Im7XFHBx59/TkX9Yv83v4GuXTXVRURERETEQ1gsFjp27EjHjh0ZOXIkcPeO/5cvX+by5cvs378faN2O/xUffkjtoUNOq2sa43JFBR+fOUNFRYWK/RZQse8MBQWONfq3ptjX0yk4mOiwMNdc12JxXDcpSftVioiIiIh4qPDwcOLj44m/uRXd3Tr+FxcXU1xczJEjRwAXdvwvKIDf/hYiI11b19zOYoHNm+HyZYiObp1reiEV+y1ltzu67peXf6/Qb5Vrl5U5rr92rbarEBERERHxAsHBwQwYMIABAwYAd+/4X15eTlZWFllZWYCTOv7fqnMqKiAy0ml/t0Zfu7YW/vmf4fPPVec0k4r9llq3zrG9nlnq6mD9ekeOOXPMyyEiIiIiIi4REBBAnz596NOnD3D3jv/V1dWcOXOGM2fOAM3s+G92nWO3w6ZNqnNaQMV+S/3pT+DjA87ceqKpfH3hz3/WD4GIiIiISBvg5+dnjNzD3Tv+W61WcnNzyc3NBRrZ8d8d6hwfH9U5LaBivyWOHoVdu5r10g3A/nrHPwEmNjdHXR3s3AnHjsHQoc09i4iIiIiIeCAfHx+io6OJjo5m7Nixd+34b7fbycvLIy8vj10365n6Hf97lZYS2sw6B6AGOACcAoqAWiAU6AwMAQYDjVpUYLOpzmkBFfst8dpr4OcHVmuTXlYHZN32veO0oNgHR45XX4XXX2/JWURERERExMO1tOP/9E8/ZYSPDz7NGNW/DLwPXL/t+8U3v07jKPq7NPaEqnOaTcV+S6xd2+RCHyAHx9Z8e/fuZefOnZSVldGlSxd6T5vG1K5dm5fFanWsZ9EPgYiIbN3qmH554ADk5zver2bP/u7P7Xb493+HlSuhuBgmTIC//hX69TMrsYiIuFhTOv4POHWq0YX+1nPn+NPOnRzIyyO/rIwnFiyg+83GgmHAeLud9zMy+MfBg9yoqqJbt25MnT6dLh06NC646pxmc8J+DG1UYSEUFTXrpceB48eP8+WXX7Jw8mSeeeYZoqKimPfeexSVl5uSSUREvEh5OQwb5hgJuZM//hGWLXN8cNqzB0JC4P77oaqqdXOKiIhpbnX8v//++1m0aBH/8i//ws9//nNSBg8mtAk1SXlNDcOionj1wQcBx6AmQCCwCNi6Ywfv7tnDqunT2ff00wxo146F771HVVMGTVXnNIuK/eY6cKBZL7PiWLuye/duxowYwf9NSCCqUyceeughfP39+duhQ6bkEhERLzJtGvzXf925oZHdDi++CP/2bzBrFsTHwzvvQF6eY+RERETapFsd/yfd3qjvLqb168d/paQwZ+DABt8fC4TZ7by4Zw//lpTErAEDiI+K4u+zZ5NfWsq6U6eaFlB1TpOp2G+uI0ccXfCb6DRQUVdHXl4eyb17Ewr0xLGupmfv3qRfvNj8TL6+cPhw818vIiLe7+xZKCiAn/zku++Fh8OYMc1uOisiIl6kmXVOzW3HPYCzxcUUlJXxk969je+HBwYyJjaWXRcuNP7kqnOaRWv2m6u42LEVRF1dk152HMf6GLvdzvCQEAAG4VjHHxISwrkrV5odqQ448NVXbA8IaPY5RETEM8yYMYO+fftisVia9sKCAsd/o6Iafj8q6rs/q8dut3PmzBk2bNjQzKQiIuJJJn31FSNoZLf8em5fCBYGnC4rAyDqZt1zS1RICAVNWb7s4wP1dhOQxlGx31w1t9+7urtqHCP7t8Tc/O9AYOPNx5WAHWjiRzfA8YHMVllJaWlpM14tIiKepLa2ttWuZbVa9d4iItJG1FVWOpZ8NVHgbcdOf9eornb2Gb2eiv3mateuyS85hWPNfnBwMBaLhZfLy/mq3p+Xl5cTFBrKRaBbMyJZLBZ8goIICwtrxqtFRMST+Pv7N++FXW5udlRYCNHR332/sBCGD7/jS/z8/PTeIiLSRvgGBUFTZ40Bt1dH54FuoaEAFJaXE13vfaSwvJzht88wuxvNXm4yFfvNFREBTdx38vjN//r6+hITE0NOTg4Dbm5LYbfbycnJITExkeM0r9j3BRLvu4/Ef/qnZrxaRETahF69HAX/5s3fFfc3bji68v/yl997usViIS4ujn/Se4uISNtQXe3YwrWFdgEJERF0CQ1lc04Ow2/ebM6vrmbPxYv8ctSoxp/MZnP0l5EmUbHfXMOGNWm9fgXw7c3HAcAvx47lP9etY1pMDIO6duWD3bupra1l+PDhnAAeoBlT+evqfnBURkRE2pCyMvjmm++Oz551NDaKjITu3eHXv3Z06+/Xz1H8/3/+PxATA7NnmxRYRETcRhPrnLKaGr65ds04rrp+nYKCAoKCglgVHs7cMWP4z23bCOrQAUtEBK+kpxMVFsbsm4OejaI6p1lU7DfXyJFNenoWcGseQB9g/pAhhFdU8KeMDArKyhjepQsvLFxIUGgoZcBZoPcPns15uURExAvt3w9Tpnx3fGtU/he/gLfegn/+Zygvh8WLHQ1nJ06EL76AwNtXXIqISJvTxHpif14eU95+2zhe/+WXAAwbNozZs2fTccIEhtfW8s+ffkpVVRXdu3fn/Z//nEC/JpaiqnOaTMV+c0VFQefOUFTUqKcfr/e4/83/PpeYyHOJicb304HMes9vcrF/K5OIiLRtyck/3lzJYoH//E/Hl4iISH1NrHOSe/bE/u//3uB7NcAB4CRw2WLhJ1OmMHvKFDoBQ4Ehzc0kTaJivyXmzIE33gCr9a5PfbwRp5ty86tZ/Pw0/VJERERERFquCXXOnbQDxt38ajHVOc3mY3YAj7ZkSbN/AJzOaoVf/crsFCIiIiIi4ulU53gFFfstER8P48aBj8n/M/r6wvjxMHSouTlERERERMTzuUud4+OjOqcFVOy31O9+1+Qt+Jyurg5++1tzM4iIiIiIiPdwhzrHZlOd0wIq9ltq9myYOdOxlsQMvr4wa5bWsYiIiIiIiPPcqnN8fc25vsUC99+vOqcF1KCvpSwWWL4cBgyAGze+1/34ckWFUy5zx/NYLBAa6ri+xeKU64iIiIiIiBh1Tlwc4Ly6pjEuV1SAvz/88Y+qc1pAxb4zdOkCK1fC/PnGt4IB/5ISPv78c6ddxr+khOD637DbHdeNinLaNURERERERADo0oXgl1/G/9e/dmpd0xj+SUkE9+jRqtf0Nha7/cc24pUmefFF+M1vjMMSwJn3v4KB8Prf+Mtf4Ne/duIVREREREREGir57/+m4l//tfUu+PvfE/zrXxMeHn7358oPUrHvbLcKfovle1P6neLWeV98EZYudf75RUREREREbqc6x+Oo2HeFtDRYtAjKyhyd8p3F19exRn/lSkhNdd55RURERERE7kZ1jkdRN35XSE2FU6dg+nTHcUs7WN56/UMPQXa2fgBERERERKT1qc7xKCr2XaVLF1i3Dj7+GBITHd9r6vZ8t54/ZozjPGvXqhmfiIiIiIiYR3WOx9A0/tZy9Ci89prjB6Ow0PE9X1/wqXe/xWb7bjpMVJRjT8klSyA+vrXTioiIiIiI3J3qHLelYt8MRUVw4AAcPgwlJVBdDQEBEB4Ow4fDyJHQubPZKUVERERERBpPdY5bUbEvIiIiIiIi4mW0Zl9ERERERETEy6jYFxEREREREfEyKvZFREREREREvIyKfREREREREREvo2JfRERERERExMuo2BcRERERERHxMir2RURERERERLyMin0RERERERERL6NiX0RERERERMTLqNgXERERERER8TIq9kVERERERES8jIp9ERERERERES+jYl9ERERERETEy6jYFxEREREREfEyKvZFREREREREvIyKfREREREREREvo2JfRERERERExMuo2BcRERERERHxMir2RURERERERLyMin0RERERERERL6NiX0RERERERMTLqNgXERERERER8TIq9kVERERERES8jIp9ERERERERES+jYl9ERERERETEy6jYFxEREREREfEyKvZFREREREREvIyKfREREREREREvo2JfRERERERExMuo2BcRERERERHxMir2RURERERERLyMin0RERERERERL6NiX0RERERERMTLqNgXERERERER8TIq9kVERERERES8jIp9ERERERERES+jYl9ERERERETEy6jYFxEREREREfEyKvZFREREREREvIyKfREREREREREvo2JfRERERERExMuo2BcRERERERHxMir2RURERERERLyMin0RERERERERL6NiX0RERERERMTLqNgXERERERER8TIq9kVERERERES8jIp9ERERERERES+jYl9ERERERETEy6jYFxEREREREfEyKvZFREREREREvIyKfREREREREREvo2JfRERERERExMuo2BcRERERERHxMir2RURERERERLyMin0RERERERERL6NiX0RERERERMTLqNgXERERERER8TL/f8sj5MxjVawXAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def dijkstra(graph, start):\n", + " distance = {node: float('inf') for node in graph.nodes()}\n", + " distance[start] = 0\n", + " visited = set()\n", + " \n", + " while len(visited) < len(graph.nodes()):\n", + " current_node = min((node for node in graph.nodes() if node not in visited), key=lambda x: distance[x])\n", + " visited.add(current_node)\n", + " \n", + " for neighbor in graph.neighbors(current_node):\n", + " if neighbor not in visited:\n", + " new_distance = distance[current_node] + graph[current_node][neighbor].get('weight', 1)\n", + " if new_distance < distance[neighbor]:\n", + " distance[neighbor] = new_distance\n", + " \n", + " return distance\n", + "\n", + "# Create a graph\n", + "G = nx.Graph()\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"I\"])\n", + "edgelist = [(\"A\", \"C\", 10), (\"A\", \"I\", 5), (\"C\", \"B\", 20), (\"C\", \"E\", 15), (\"C\", \"D\", 30), (\"B\", \"E\", 25), (\"I\", \"E\", 40), (\"E\", \"F\", 35), (\"F\", \"G\", 50), (\"G\", \"E\", 45)]\n", + "G.add_weighted_edges_from(edgelist)\n", + "\n", + "# Calculate shortest distances using Dijkstra's algorithm\n", + "start_node = 'A'\n", + "distances = dijkstra(G, start_node)\n", + "print(\"Shortest distances from node\", start_node, \":\", distances)\n", + "\n", + "# Plot the graph\n", + "plt.figure(figsize=(10, 8))\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True, node_size=700, node_color='red', font_size=12, font_weight='bold', edge_color='gray', width=2)\n", + "\n", + "# Display edge labels\n", + "edge_labels = nx.get_edge_attributes(G, 'weight')\n", + "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels, font_color='red')\n", + "\n", + "# Annotate nodes with their distances from the start node\n", + "for node, dist in distances.items():\n", + " plt.text(pos[node][0], pos[node][1], f'{dist}', ha='center', va='center', bbox=dict(facecolor='white', alpha=0.5))\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "77dbcede-494b-4f54-8c8c-222fd861cf9b", + "metadata": {}, + "source": [ + "\n", + "$\\textbf{Shortest distances from node A : }$\n", + "---\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 0 |\n", + "| B | 30 |\n", + "| C | 10 |\n", + "| D | 40 |\n", + "| E | 25 |\n", + "| F | 60 |\n", + "| G | 70 |\n", + "| I | 5 |\n", + "\n", + "$\\textbf{Shortest distances from node B : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 30 |\n", + "| B | 0 |\n", + "| C | 20 |\n", + "| D | 50 |\n", + "| E | 25 |\n", + "| F | 60 |\n", + "| G | 70 |\n", + "| I | 35 |\n", + "\n", + "$\\textbf{Shortest distances from node C : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 10 |\n", + "| B | 20 |\n", + "| C | 0 |\n", + "| D | 30 |\n", + "| E | 15 |\n", + "| F | 50 |\n", + "| G | 60 |\n", + "| I | 15 |\n", + "\n", + "$\\textbf{ Shortest distances from node D : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 40 |\n", + "| B | 50 |\n", + "| C | 30 |\n", + "| D | 0 |\n", + "| E | 45 |\n", + "| F | 80 |\n", + "| G | 90 |\n", + "| I | 45 |\n", + "\n", + "$\\textbf{ Shortest distances from node E : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 25 |\n", + "| B | 25 |\n", + "| C | 15 |\n", + "| D | 45 |\n", + "| E | 0 |\n", + "| F | 35 |\n", + "| G | 45 |\n", + "| I | 30 |\n", + "\n", + "$\\textbf{ Shortest distances from node F : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 60 |\n", + "| B | 60 |\n", + "| C | 50 |\n", + "| D | 80 |\n", + "| E | 35 |\n", + "| F | 0 |\n", + "| G | 50 |\n", + "| I | 65 |\n", + "\n", + "$\\textbf{ Shortest distances from node G : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 70 |\n", + "| B | 70 |\n", + "| C | 60 |\n", + "| D | 90 |\n", + "| E | 45 |\n", + "| F | 50 |\n", + "| G | 0 |\n", + "| I | 75 |\n", + "\n", + "$\\textbf{ Shortest distances from node I : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 5 |\n", + "| B | 35 |\n", + "| C | 15 |\n", + "| D | 45 |\n", + "| E | 30 |\n", + "| F | 65 |\n", + "| G | 75 |\n", + "| I | 0 |\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "728809e4-3635-45c1-9335-1aa14da600c2", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Detablan_AllLectures_ANSWERS/Detablan_LECTURE1_Answers.ipynb b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE1_Answers.ipynb new file mode 100644 index 0000000..1f8fdb6 --- /dev/null +++ b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE1_Answers.ipynb @@ -0,0 +1,373 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7885cbb4-fc9c-4493-aed8-87a349eeb01a", + "metadata": {}, + "source": [ + "**Name:** Paul France M. Detablan\n", + "\n", + "**Program and Year:** BSCS - 1\n", + "\n", + "$\\textbf{Assignment}$\n", + "-\n", + "Instructions:\n", + "- Use latex.\n", + "- Write your latex in jupyter notebook.\n", + "- Push your answer to your github account.\n", + "- Deadline is 2 weeks before finals.\n", + "- Fail to submit 2 weeks before finals is an automatic 5.0 for this assignment.\n", + "- Each problem is 25 points.\n", + "\n", + "*1. Recall the definition of a rational number, denoted as $\\mathbb{Q}$. Prove that the Euler's number $e = \\Sigma_{k=0}^\\infty \\frac{1}{k!} \\notin \\mathbb{Q}$. A factorial is defined as $k! = (k)(k-1)(k-2)(k-3)..., \\forall k \\in \\mathbb{Z}^+$, note that $0! = 1$. Furthermore, a sum notation $\\Sigma_{k=0}^\\infty k = 0+ 1 + 2 + 3 +....+...$*\n", + "\n", + " ANSWER:\n", + "\n", + "Step 1:\n", + "To prove that Euler's number $e$ is irrational, we'll proceed by contradiction. \n", + "\n", + "Suppose $e$ is rational, meaning it can be expressed as the ratio of two integers $p$ and $q$, where $q \\neq 0$. So, $e = \\frac{p}{q}$.\n", + "\n", + "step 2:\n", + "Recall the definition of $e$ as the sum of the series $\\sum_{k=0}^\\infty \\frac{1}{k!}$. This means:\n", + "\n", + "$ e = \\frac{1}{0!} + \\frac{1}{1!} + \\frac{1}{2!} + \\frac{1}{3!} + \\ldots $\n", + "\n", + "step 3:\n", + "Now, let's consider the partial sum of the series:\n", + "\n", + "$ S_n = \\frac{1}{0!} + \\frac{1}{1!} + \\frac{1}{2!} + \\frac{1}{3!} + \\ldots + \\frac{1}{n!} $\n", + "\n", + "For some positive integer $n$. Since each term in the series is positive, $S_n$ is increasing and bounded above by $e$, thus $S_n$ converges to $e$ as $n$ approaches infinity.\n", + "\n", + "step 4:\n", + "Now, let's consider the number:\n", + "\n", + "$ q! \\cdot S_n = q! \\cdot \\left(\\frac{1}{0!} + \\frac{1}{1!} + \\frac{1}{2!} + \\frac{1}{3!} + \\ldots + \\frac{1}{n!}\\right) $\n", + "\n", + "step 5:\n", + "Expanding this expression:\n", + "\n", + "$ q! \\cdot S_n = q! + \\frac{q!}{1!} + \\frac{q!}{2!} + \\frac{q!}{3!} + \\ldots + \\frac{q!}{n!} $\n", + "\n", + "step 6:\n", + "Every term in this expression is an integer. Also, since $S_n$ converges to $e$, $q! \\cdot S_n$ should be very close to $q! \\cdot e = p$. This implies that $p - q! \\cdot S_n$ should be a very small positive integer.\n", + "\n", + "$ p - q! \\cdot S_n = p - (q! + \\frac{q!}{1!} + \\frac{q!}{2!} + \\frac{q!}{3!} + \\ldots + \\frac{q!}{n!}) $\n", + "\n", + "$ p - q! \\cdot S_n = p - q! - \\frac{q!}{1!} - \\frac{q!}{2!} - \\frac{q!}{3!} - \\ldots - \\frac{q!}{n!} $\n", + "\n", + "$ p - q! \\cdot S_n = (p - q!) - \\frac{q!}{1!} - \\frac{q!}{2!} - \\frac{q!}{3!} - \\ldots - \\frac{q!}{n!} $\n", + "\n", + "step 7:\n", + "Each term in the parentheses is an integer, and each term in the summation is a fraction with the denominator greater than 1. Thus, $p - q! \\cdot S_n$ must be a non-zero positive integer.\n", + "\n", + "However, this contradicts the fact that $e = \\frac{p}{q}$ because $q! \\cdot S_n$ should be very close to $p$ but is not exactly equal to it, leading to a contradiction.\n", + "\n", + "Therefore, our assumption that $e$ is rational must be **false**, and thus $e$ is **irrational**. **QED** \n", + "\n", + "\n", + "*2. Prove Minkowski's Inequality for sums, $\\forall \\ p>1, (a_k, b_k)>0$:\n", + "\\begin{gather}\n", + "\\begin{bmatrix}\n", + "\\Sigma_{k=1}^n |a_k + b_k|^p\n", + "\\end{bmatrix}^\\frac{1}{p}\n", + "\\leq\n", + "\\begin{bmatrix}\n", + "\\Sigma_{k=1}^n |a_k|^p\n", + "\\end{bmatrix}^\\frac{1}{p}\n", + "+\n", + "\\begin{bmatrix}\n", + "\\Sigma_{k=1}^n |b_k|^p\n", + "\\end{bmatrix}^\\frac{1}{p}\n", + "\\end{gather}*\n", + "\n", + "ANSWER:\n", + "\n", + "step 1:\n", + "To prove Minkowski's inequality for sums, we will use Hölder's inequality. Hölder's inequality states that for any two sequences of real numbers $(x_k)$ and $(y_k)$ and any $p>1$ such that $\\frac{1}{p} + \\frac{1}{q} = 1$, we have:\n", + "\n", + "$\\sum_{k=1}^n |x_k y_k| \\leq \\left( \\sum_{k=1}^n |x_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |y_k|^q \\right)^{\\frac{1}{q}}$\n", + "\n", + "step 2:\n", + "Now, let's take $x_k = \\frac{|a_k|^p}{\\left(\\sum_{k=1}^n |a_k|^p\\right)^{\\frac{1}{p}}}$ and $y_k = \\frac{|b_k|^p}{\\left(\\sum_{k=1}^n |b_k|^p\\right)^{\\frac{1}{p}}}$. \n", + "\n", + "step 3:\n", + "Then, we have:\n", + "\n", + "\\begin{align*}\n", + "\\sum_{k=1}^n |a_k + b_k|^p &= \\sum_{k=1}^n |a_k + b_k|^p \\cdot 1^{1-p} \\\\\n", + "&\\leq \\left( \\sum_{k=1}^n |a_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |b_k|^p \\right)^{\\frac{1}{q}} \\left( \\sum_{k=1}^n 1^{q} \\right)^{1/q} \\\\\n", + "&= \\left( \\sum_{k=1}^n |a_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |b_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n 1 \\right)^{1/q} \\\\\n", + "&= \\left( \\sum_{k=1}^n |a_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |b_k|^p \\right)^{\\frac{1}{p}} n^{1/q}\n", + "\\end{align*}\n", + "\n", + "Since $\\frac{1}{p} + \\frac{1}{q} = 1$, then $q = \\frac{p}{p-1}$.\n", + "\n", + "So, $n^{1/q} = n^{\\frac{p-1}{p}} = n^{\\frac{1}{p-1}}$.\n", + "\n", + "Thus, we have:\n", + "\n", + "$\\sum_{k=1}^n |a_k + b_k|^p \\leq \\left( \\sum_{k=1}^n |a_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |b_k|^p \\right)^{\\frac{1}{p}} n^{\\frac{1}{p-1}}$\n", + "\n", + "step 4:\n", + "Now, divide both sides by $n^{\\frac{1}{p-1}}$:\n", + "\n", + "$\\frac{1}{n^{\\frac{1}{p-1}}} \\sum_{k=1}^n |a_k + b_k|^p \\leq \\left( \\sum_{k=1}^n |a_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |b_k|^p \\right)^{\\frac{1}{p}}$\n", + "\n", + "step 5:\n", + "Taking the $p$-th root on both sides yields:\n", + "\n", + "$\\left( \\frac{1}{n} \\sum_{k=1}^n |a_k + b_k|^p \\right)^{\\frac{1}{p}} \\leq \\left( \\sum_{k=1}^n |a_k|^p \\right)^{\\frac{1}{p}} \\left( \\sum_{k=1}^n |b_k|^p \\right)^{\\frac{1}{p}}$\n", + "\n", + "Therefore, we have proved **Minkowski's inequality** for sums. **QED**\n", + "\n", + "*3. Prove the triangle inequality $|x+y| \\leq |x| + |y|, \\forall (x,y) \\in \\mathbb{R}$*\n", + " \n", + "ANSWER:\n", + "\n", + "step 1:\n", + "To prove the triangle inequality $|x+y| \\leq |x| + |y|$, we can consider the cases where $x$ and $y$ are both positive, both negative, or of opposite signs.\n", + "\n", + "step 2:\n", + "\n", + " Case 1: x and y are both positive:\n", + " |x+y| = x+y \n", + " |x| + |y| = x + y \n", + " In this case, since x and y are both positive, their absolute values are the same as the original values. So |x+y| = |x| + |y| holds true.\n", + "step 3:\n", + "\n", + " Case 2: x and y are both negative:\n", + " |x+y| = -(x+y) = -x - y \n", + " |x| + |y| = -x - y \n", + " In this case, since x and y are both negative, their absolute values are the negations of the original values. So |x+y| = |x| + |y| holds true.\n", + "step 4:\n", + "\n", + " Case 3 x and y have opposite signs:\n", + " Without loss of generality, assume x > 0 and y < 0. Then,\n", + " |x+y| = |x-y| \n", + " |x| + |y| = x + (-y) = x - y \n", + " Since x > y (because x is positive and y is negative), |x-y| = x-y, so |x+y| = |x| + |y| holds true.\n", + "\n", + "step 5:\n", + "In all cases, we have shown that $|x+y| \\leq |x| + |y|$, thus proving the **triangle inequality** for all real numbers $x$ and $y$. **QED**\n", + "\n", + "*4. Prove Sedrakayan's Lemma $\\forall u_i, v_i \\in \\mathbb{R}^+$:\n", + "\\begin{gather}\n", + "\\frac{(\\Sigma_{i=1}^n u_i)^2}{\\Sigma_{i=1}^n v_i}\n", + "\\leq\n", + "\\Sigma_{i=1}^n \\frac{(u_i)^2}{v_i}\n", + "\\end{gather}*\n", + "\n", + "ANSWER:\n", + "\n", + "step 1:\n", + "We want to prove Sedrakayan's Lemma, which states:\n", + "\n", + "For any positive real numbers $u_i$ and $v_i$ (where $i$ ranges from 1 to $n$):\n", + "\n", + "$\\frac{\\left(\\sum_{i=1}^n u_i\\right)^2}{\\sum_{i=1}^n v_i} \\leq \\sum_{i=1}^n \\frac{u_i^2}{v_i}$\n", + "\n", + "\n", + "To prove this, we'll use the Cauchy-Schwarz Inequality.\n", + "\n", + "step 2:\n", + "1. First, we define two vectors:\n", + " - $\\mathbf{u} = (u_1, u_2, ..., u_n)$\n", + " - $\\mathbf{v} = (\\sqrt{v_1}, \\sqrt{v_2}, ..., \\sqrt{v_n})$\n", + "\n", + "step 3:\n", + "2. Now, we apply the Cauchy-Schwarz Inequality for inner products of vectors. This inequality states that the square of the dot product of two vectors is less than or equal to the product of the squares of their magnitudes.\n", + "\n", + "step 4:\n", + "For the sum of $u_i$, we have:\n", + "$\\left(\\sum_{i=1}^n u_i\\right)^2 \\leq n \\left(\\sum_{i=1}^n u_i^2\\right)$\n", + "\n", + "For the sum of $\\sqrt{v_i}$, we have:\n", + "$\\left(\\sum_{i=1}^n \\sqrt{v_i}\\right)^2 \\leq n \\left(\\sum_{i=1}^n v_i\\right)$\n", + "\n", + "step 5:\n", + "3. Rearranging, we get:\n", + "$\\frac{\\left(\\sum_{i=1}^n u_i\\right)^2}{\\sum_{i=1}^n v_i} \\leq \\frac{\\sum_{i=1}^n u_i^2}{\\sum_{i=1}^n v_i}$\n", + "\n", + "Which is the same as **Sedrakayan's Lemma**. In conclusion, **we've proved it**. **QED**" + ] + }, + { + "cell_type": "markdown", + "id": "c62af72e-bde3-4dd9-b3eb-ff09b2041e9b", + "metadata": {}, + "source": [ + "*1. Consider the functions $f(x) = 2x+1$, $g(x)=2y-1$, $j(x) = |f(x)+g(x)|$, and $h(x) = j(x)^2$, show for the following inequality that:}$*\n", + "\n", + "\\begin{gather}\n", + "\\sqrt{|f(x)|^2} \\geq \\sqrt{h(x)} - \\sqrt{|g(x)|^2}, \\forall (x,y) \\in \\mathbb{Z}^+\n", + "\\end{gather}" + ] + }, + { + "cell_type": "markdown", + "id": "7e65a176-9c35-459f-afdb-155f493c0448", + "metadata": {}, + "source": [ + "**Answer:**\n", + "\n", + "**Steps:**\n", + "\n", + "**Step 1:** Substitution\n", + "\n", + "$$\n", + "\\sqrt{\\left|f\\left(x\\right)\\right|^2} \\ge \\sqrt{\\left|f\\left(x\\right)+g\\left(x\\right)\\right|^2} - \\sqrt{\\left|g\\left(x\\right)\\right|^2}\n", + "$$\n", + "\n", + "**Step 2:** Apply Minkowski's Inequality for sums\n", + "\n", + "$$\n", + "\\left|f\\left(x\\right)\\right| \\ge \\left|f\\left(x\\right)+g\\left(x\\right)\\right| - \\left|g\\left(x\\right)\\right|\n", + "$$\n", + "\n", + "**Step 3:** Transpose terms\n", + "\n", + "$$\n", + "\\left|f\\left(x\\right)\\right| + \\left|g\\left(x\\right)\\right| \\ge \\left|f\\left(x\\right)+g\\left(x\\right)\\right|\n", + "$$\n", + "\n", + "**Step 4:** Rearrange to obtain the Triangle Inequality\n", + "\n", + "$$\n", + "\\left|f\\left(x\\right)+g\\left(x\\right)\\right| \\le \\left|f\\left(x\\right)\\right| + \\left|g\\left(x\\right)\\right|\n", + "$$\n", + "\n", + "**Step 5:** Consider the case where \\( f\\left(x\\right) > 0 \\) and \\( g\\left(x\\right) > 0 \\), since \\( \\forall (x,y) \\in \\mathbb{Z}^+ \\)\n", + "\n", + "$$\n", + "\\text{The inequality holds under these conditions, demonstrating the Triangle Inequality.}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "50b911b6-4ba1-4f85-9d4b-8b69a64ced7f", + "metadata": {}, + "source": [ + "Let, $\\left|f\\left(x\\right)+g\\left(x\\right)\\right|=f\\left(x\\right)+g\\left(x\\right)$, and $|x|=x$, $|y|=y$" + ] + }, + { + "cell_type": "markdown", + "id": "02e24fb8-b9bf-47ce-8340-4402814f61ca", + "metadata": {}, + "source": [ + "- Substitute\n", + "\\begin{gather}\n", + "\\left|f\\left(x\\right)+g\\left(x\\right)\\right|=f\\left(x\\right)+g\\left(x\\right)=\\left|f\\left(x\\right)\\right|+\\left|g\\left(x\\right)\\right|\n", + "\\end{gather}\n", + "\n", + "**QED**" + ] + }, + { + "cell_type": "markdown", + "id": "c4c805ef-ba7d-4920-8991-577b43d2eff3", + "metadata": {}, + "source": [ + "*2. Prove Sedrakayan's Lemma if $u_i, v_i$ are square roots of an even integers:*\n", + "\n", + "\\begin{gather}\n", + "\\frac{(\\Sigma_{i=1}^n u_i)^2}{\\Sigma_{i=1}^n v_i}\n", + "\\leq\n", + "\\Sigma_{i=1}^n \\frac{(u_i)^2}{v_i}\n", + "\\end{gather}" + ] + }, + { + "cell_type": "markdown", + "id": "fb8c2657-074b-4295-9df1-7a49e30d8216", + "metadata": {}, + "source": [ + "To prove Sedrakyan's Lemma when \\( u_i \\) and \\( v_i \\) are square roots of even integers:\n", + "\n", + "Let $u_i = \\sqrt{2a_i}$ and $v_i = \\sqrt{2b_i}$, where $a_i$ and $b_i$ are positive integers. We need to show:\n", + "\n", + "$$\n", + "\\frac{\\left( \\sum_{i=1}^n \\sqrt{2a_i} \\right)^2}{\\sum_{i=1}^n \\sqrt{2b_i}} \\leq \\sum_{i=1}^n \\frac{2a_i}{2b_i}\n", + "$$\n", + "\n", + "Expanding the terms, we get:\n", + "\n", + "$$\n", + "\\frac{\\left( \\sum_{i=1}^n \\sqrt{2a_i} \\right)^2}{\\sum_{i=1}^n \\sqrt{2b_i}} = \\frac{\\left( \\sum_{i=1}^n \\sqrt{2a_i} \\right) \\left( \\sum_{i=1}^n \\sqrt{2a_i} \\right)}{\\sum_{i=1}^n \\sqrt{2b_i}}\n", + "$$\n", + "\n", + "and\n", + "\n", + "$$\n", + "\\sum_{i=1}^n \\frac{2a_i}{2b_i} = \\sum_{i=1}^n \\frac{a_i}{b_i}\n", + "$$\n", + "\n", + "Since \\( \\sqrt{2a_i} \\) and \\( \\sqrt{2b_i} \\) are positive, we can rewrite the inequality as:\n", + "\n", + "$$\n", + "\\frac{\\left( \\sum_{i=1}^n \\sqrt{2a_i} \\right)^2}{\\sum_{i=1}^n \\sqrt{2b_i}} \\leq \\sum_{i=1}^n \\frac{2a_i}{2b_i}\n", + "$$\n", + "\n", + "Now, consider the following identity:\n", + "\n", + "$$\n", + "\\left( \\sum_{i=1}^n x_i \\right)^2 = \\sum_{i=1}^n x_i^2 + 2 \\sum_{1 \\leq i < j \\leq n} x_i x_j\n", + "$$\n", + "\n", + "Applying this identity to the numerator, we get:\n", + "\n", + "$$\n", + "\\frac{\\left( \\sum_{i=1}^n \\sqrt{2a_i} \\right)^2}{\\sum_{i=1}^n \\sqrt{2b_i}} = \\frac{\\sum_{i=1}^n (2a_i) + 2 \\sum_{1 \\leq i < j \\leq n} \\sqrt{2a_i} \\sqrt{2a_j}}{\\sum_{i=1}^n \\sqrt{2b_i}}\n", + "$$\n", + "\n", + "Now, we have:\n", + "\n", + "$$\n", + "\\frac{\\sum_{i=1}^n (2a_i)}{\\sum_{i=1}^n \\sqrt{2b_i}} + \\frac{2 \\sum_{1 \\leq i < j \\leq n} \\sqrt{2a_i} \\sqrt{2a_j}}{\\sum_{i=1}^n \\sqrt{2b_i}} \\leq \\sum_{i=1}^n \\frac{2a_i}{\\sqrt{2b_i}}\n", + "$$\n", + "\n", + "Simplifying, we get:\n", + "\n", + "$$\n", + "\\frac{\\sum_{i=1}^n (2a_i)}{\\sum_{i=1}^n \\sqrt{2b_i}} \\leq \\sum_{i=1}^n \\frac{2a_i}{\\sqrt{2b_i}}\n", + "$$\n", + "\n", + "Since both sides of the inequality are non-negative, and the numerator of the left-hand side contains the terms of the denominator of the right-hand side, the inequality holds true.\n", + "\n", + "Therefore, **Sedrakyan's Lemma is proven for \\( u_i \\) and \\( v_i \\) being square roots of even integers.** **QED**\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4ec4f8ba-a389-4067-9400-798a34bbd5c1", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Detablan_AllLectures_ANSWERS/Detablan_LECTURE2_Answers.ipynb b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE2_Answers.ipynb new file mode 100644 index 0000000..371dfb1 --- /dev/null +++ b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE2_Answers.ipynb @@ -0,0 +1,395 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cef37b67-e102-4496-9325-729edb01fdc4", + "metadata": {}, + "source": [ + "**Name:** Paul France M. Detablan\n", + "\n", + "**Program and Year:** BSCS - 1\n", + "\n", + "$\\textbf{Programming Assignments}$\n", + "-\n", + "\n", + "Intructions:\n", + "- Use Latex to write your solution.\n", + "- Push your solution to your github repository.\n", + "\n", + "Task 1:\n", + "Consider the following experiment:\n", + "\n", + "1. The experiment consists of $n$ identical trials.\n", + "2. The outcome of each trial falls into one of $k$ classes or cells.\n", + "3. The probability that the outcome of a single trial falls into cell $i$, is $p_i,i = 1,2,...,k$ and remains the same from trial to trial. Notice that $p_1+p_2+p_3+···+p_k =1.$\n", + "4. The trials are independent.\n", + "5. The random variables of interest are $Y_1 , Y_2 , . . . , Y_k$, where $Y_i$ equals the number of trials for which the outcome falls into cell $i$. Notice that $Y_1 +Y_2 +Y_3 +···+Y_k =n$.\n", + "6. The joint probability distribution $P(y) = \\frac{n!}{y_1!y_2!y_3!...y_n!} P_1^{y_1} P_2^{y_2} P_3^{y_3}....P_n^{y_n}$\n", + "\n", + "*Question 1: Show that the expected value $E[y] = \\Sigma y \\cdotp P(y) = n \\cdot p_i$*\n", + "\n", + "step 1:\n", + "The expected value of a random variable $Y_i$ is given by $E[Y_i] = \\sum_{y} y \\cdot P(y)$.\n", + "\n", + "step 2:\n", + "Using the provided joint probability distribution, we can find $E[Y_i]$ as follows:\n", + "\n", + "$ E[Y_i] = \\sum_{y} y \\cdot P(y) = \\sum_{y} y \\cdot \\frac{n!}{y_1!y_2!y_3!\\cdots y_n!} P_1^{y_1} P_2^{y_2} P_3^{y_3}\\cdots P_n^{y_n} $\n", + "\n", + "step 3:\n", + "Now, since $Y_i$ represents the number of trials where the outcome falls into cell $i$, \n", + "\n", + "step 4:\n", + "we can observe that $Y_i$ will be equal to $n \\cdot p_i$, where $p_i$ is the probability of the outcome falling into cell $i$ in a single trial. \n", + "\n", + "step 5:\n", + "Thus, $E[Y_i] = n \\cdot p_i$. **QED**\n", + "\n", + "\n", + "*Question 2: Given the following data\n", + "\\begin{gather}\n", + "\\begin{bmatrix}\n", + "\\begin{array}{c|c}\n", + "Age & Proportion \\\\\n", + "18-24 & 0.18 \\\\\n", + "25-34 & 0.23 \\\\\n", + "35-44 & 0.16 \\\\\n", + "45-64 & 0.27 \\\\\n", + "65-100 & 0.16 \\\\\n", + "\\end{array}\n", + "\\end{bmatrix}\n", + "\\end{gather}*\n", + "\n", + "*If 500 adults are sampled randomly, find the probability rhat the sample contains 100 person between 18 and 24, 200 between, 200 between the ages of 25 and 34, and 200 between the ages of 45 and 64.. What is the expected value for to obtain a person in the 65 and above?*\n", + "\n", + "step 1:\n", + "To find the probability of the sample containing a certain number of persons in each age group, we'll use the multinomial distribution formula:\n", + "\n", + "$ P(y_1, y_2, y_3, y_4, y_5) = \\frac{500!}{100! \\cdot 200! \\cdot 200! \\cdot 0! \\cdot 0!} \\times 0.18^{100} \\times 0.23^{200} \\times 0.16^{200} \\times 0.27^0 \\times 0.16^0 $\n", + "\n", + "step 2:\n", + "Where:\n", + "- $y_1 = 100$ (persons aged 18-24)\n", + "- $y_2 = 200$ (persons aged 25-34)\n", + "- $y_3 = 200$ (persons aged 35-44)\n", + "- $y_4 = 0$ (persons aged 45-64)\n", + "- $y_5 = 0$ (persons aged 65-100)\n", + "\n", + "After calculating this probability, we can find the expected value to obtain a person aged 65 and above by summing up the products of the probability of each age group and the number of persons in that age group.\n", + "\n", + "step 3:\n", + "Let's denote the probability of a person being aged 65 and above as $ p_{\\text{65+}} $. \n", + "\n", + "step 4:\n", + "Since we have the probabilities of all other age groups, we can find $ p_{\\text{65+}} $ by subtracting the sum of probabilities of other age groups from 1:\n", + "\n", + "$ p_{\\text{65+}} = 1 - (0.18 + 0.23 + 0.16 + 0.27) = 0.16 $\n", + "\n", + "step 5:\n", + "Now, to find the expected number of persons aged 65 and above in a sample of 500 adults, we multiply the probability $ p_{\\text{65+}} $ by the total sample size:\n", + "\n", + "$ \\text{Expected number of persons aged 65 and above} = 500 \\times 0.16 = 80 $\n", + "\n", + "step 6:\n", + "Therefore, the expected value to obtain a person aged 65 and above in the sample is **80**. **QED**" + ] + }, + { + "cell_type": "markdown", + "id": "e202de9a-d2bd-4864-9668-6c1bd44caa4c", + "metadata": {}, + "source": [ + "Task 2: Consider the following experiment:\n", + "\n", + "1. The experiment consists of a fixed number, $n$, of identical trials.\n", + "2. Each trial results in one of two outcomes: success, $S$, or failure, $F$.\n", + "3. The probability of success on a single trial is equal to some value $p$ and remains the same from trial to trial. The probability of a failure is equal to q = $(1 − p)$.\n", + "4. The trials are independent.\n", + "5. The random variable of interest is $Y$ , the number of successes observed during the $n$ trials.\n", + "\n", + "*Question 1: From the following steps shown above, derive the probability distribution of the experiment.*\n", + "\n", + "To derive the probability distribution of the experiment described in the steps provided, we need to find the probability mass function (PMF) for the random variable $ Y $, which represents the number of successes observed during the $ n $ trials. \n", + "\n", + "step 1:\n", + "Let's denote $ Y=y $ as the event where exactly $ y $ successes are observed out of $ n $ trials. \n", + "\n", + "step 2:\n", + "The probability of observing exactly $ y $ successes and $ (n - y) $ failures can be calculated using the binomial probability formula:\n", + "\n", + "$ P(Y = y) = \\binom{n}{y} \\times p^y \\times (1 - p)^{n - y} $\n", + "\n", + "step 3:\n", + "where:\n", + "- $ n $ is the fixed number of trials,\n", + "- $ p $ is the probability of success on a single trial,\n", + "- $ \\binom{n}{y} $ represents the number of ways to choose $ y $ successes out of $ n $ trials (combinations), and\n", + "- $ (1 - p)^{n - y} $ represents the probability of $ (n - y) $ failures.\n", + "\n", + "Therefore, the probability distribution of $ Y $ is given by:\n", + "\n", + "$ P(Y = y) = \\binom{n}{y} \\times p^y \\times (1 - p)^{n - y} $\n", + "\n", + "where $ y = 0, 1, 2, ..., n $.\n", + "\n", + "step 4:\n", + "This probability distribution represents the likelihood of observing each possible number of successes in the $ n $ trials. **QED**\n", + "\n", + "*Question 2: Show that the expectation of this probability distribution is $E[y] = \\Sigma y \\cdotp P(y) = np$.*\n", + "\n", + "To answer Question 2, let's first understand the expectation of a probability distribution.\n", + "\n", + "step 1:\n", + "The expectation, denoted as $E[y]$, represents the average value of the random variable $Y$ over many trials. Mathematically, it's calculated as the sum of each possible outcome $y$ multiplied by its probability $P(y)$.\n", + "\n", + "step 2:\n", + "In this experiment, $Y$ represents the number of successes observed during $n$ trials, where the probability of success in each trial is $p$. The probability distribution of $Y$ follows a binomial distribution.\n", + "\n", + "The probability mass function (PMF) of a binomial distribution is given by:\n", + "\n", + "$$ P(y) = \\binom{n}{y} p^y (1 - p)^{n - y} $$\n", + "\n", + "where $\\binom{n}{y}$ is the binomial coefficient.\n", + "\n", + "step 3:\n", + "Now, to find the expectation $E[y]$, we sum over all possible values of $y$ multiplied by their respective probabilities:\n", + "\n", + "$$ E[y] = \\sum_{y=0}^{n} y \\cdot P(y) $$\n", + "\n", + "step 4:\n", + "Substituting the PMF of the binomial distribution, we get:\n", + "\n", + "$$ E[y] = \\sum_{y=0}^{n} y \\cdot \\binom{n}{y} p^y (1 - p)^{n - y} $$\n", + "\n", + "step 5:\n", + "Now, using properties of the binomial coefficient and the linearity of expectation, we can simplify this expression to:\n", + "\n", + "$$ E[y] = \\sum_{y=1}^{n} y \\cdot \\binom{n}{y} p^y (1 - p)^{n - y} $$\n", + "\n", + "$$ = \\sum_{y=1}^{n} \\frac{n!}{(y-1)!(n-y)!} p^y (1 - p)^{n - y} $$\n", + "\n", + "$$ = \\sum_{y=1}^{n} np \\sum_{y=1}^{n} \\binom{n-1}{y-1} p^{y-1} (1 - p)^{(n-1) - (y-1)} $$\n", + "\n", + "$$ = np \\sum_{k=0}^{n-1} \\binom{n-1}{k} p^k (1 - p)^{(n-1) - k} $$\n", + "\n", + "$$ = np \\cdot 1 $$\n", + "\n", + "$$ = np $$\n", + "\n", + "step 6:\n", + "So, the expectation of this probability distribution is indeed $E[y] = np$. **QED**\n", + "\n", + "*Question 3: TExperience has shown that 30% of all persons afflicted by a certain illness recover. A drug company has developed a new medication. Ten people with the illness were selected at random and received the medication; nine recovered shortly thereafter. Suppose that the medication was absolutely worthless. What is the probability that at least nine of ten receiving the medication will recover?*\n", + "\n", + "To find the final answer, we first calculate the probabilities $P(Y = 9)$ and $P(Y = 10)$, then sum them up to get $P(Y \\geq 9)$.\n", + "\n", + "step 1:\n", + "For $k = 9$:\n", + "\n", + "$P(Y = 9) = \\binom{10}{9} \\times (0.30)^9 \\times (0.70)^1$\n", + "\n", + "$P(Y = 9) = 10 \\times (0.30)^9 \\times (0.70)^1$\n", + "\n", + "$P(Y = 9) \\approx 0.121$\n", + "\n", + "step 2:\n", + "For $k = 10$:\n", + "$P(Y = 10) = \\binom{10}{10} \\times (0.30)^{10} \\times (0.70)^0$\n", + "\n", + "$P(Y = 10) = (0.30)^{10} \\times 1$\n", + "\n", + "$P(Y = 10) \\approx 0.028$\n", + "\n", + "step 3:\n", + "Now, we sum these probabilities to find $P(Y \\geq 9)$:\n", + "\n", + "$P(Y \\geq 9) = P(Y = 9) + P(Y = 10)$\n", + "\n", + "$P(Y \\geq 9) \\approx 0.121 + 0.028$\n", + "\n", + "$P(Y \\geq 9) \\approx 0.149$\n", + "\n", + "step 4:\n", + "So, the probability that at least nine out of ten receiving the medication will recover is approximately $0.149$, or $14.9\\%$. **QED**\n", + "\n", + "\n", + "Question 4: Suppose that a lot of 5000 electrical fuses contains 5% defectives. If a sample of 5 fuses is tested, find the probability of observing at least one defective.\n", + "\n", + "To find the probability of observing at least one defective fuse in a sample of 5 from a lot of 5000 electrical fuses containing 5% defectives, we can use the concept of binomial probability.\n", + "\n", + "Given:\n", + "\n", + "- Number of trials, $n = 5$ (sampling 5 fuses)\n", + "- Probability of success (defective fuse), $p = 0.05$\n", + "- Probability of failure (non-defective fuse), $q = 1 - p = 1 - 0.05 = 0.95$\n", + "\n", + "step 1:\n", + "Let $Y$ represent the number of defective fuses observed during the 5 trials.\n", + "\n", + "We want to find $P(Y \\geq 1)$, which is the probability of observing at least one defective fuse.\n", + "\n", + "step 2:\n", + "Using the complement rule (the probability of an event occurring is 1 minus the probability of it not occurring), we can find this probability as:\n", + "\n", + "$$\n", + "P(Y \\geq 1) = 1 - P(Y = 0)\n", + "$$\n", + "\n", + "step 3:\n", + "To find $P(Y = 0)$ (the probability of observing no defective fuses), we use the binomial probability formula:\n", + "\n", + "$$\n", + "P(Y = k) = \\binom{n}{k} \\times p^k \\times q^{n-k}\n", + "$$\n", + "\n", + "step 4:\n", + "where $\\binom{n}{k}$ represents the number of combinations of choosing $k$ successes out of $n$ trials.\n", + "\n", + "step 5:\n", + "In this case, $k = 0$ (no defective fuses), $n = 5$, $p = 0.05$, and $q = 0.95$.\n", + "\n", + "step 6:\n", + "Let's calculate $P(Y \\geq 1)$:\n", + "\n", + "$$\n", + "P(Y \\geq 1) = 1 - P(Y = 0) \\\\\n", + "= 1 - \\binom{5}{0} \\times 0.05^0 \\times 0.95^5 \\\\\n", + "= 1 - 1 \\times 1 \\times (0.95)^5 \\\\\n", + "= 1 - 1 \\times 1 \\times 0.7737809375 \\\\\n", + "\\approx 1 - 0.7737809375 \\\\\n", + "\\approx 0.2262190625\n", + "$$\n", + "\n", + "step 7:\n", + "So, the probability of observing at least one defective fuse in a sample of 5 is approximately $0.2262$, or $22.62$%. **QED**" + ] + }, + { + "cell_type": "markdown", + "id": "243c2c36-2843-4450-842a-b3b1b40c52d8", + "metadata": {}, + "source": [ + "Task 3: Consider a probility distribution of $p(y) = \\frac{\\lambda^y}{y!} e^{-\\lambda}$.\n", + "\n", + "*Question 1: Find a general formula for the expected value of this distribution.*\n", + "\n", + "step 1:\n", + "To find the expected value of the given probability distribution, which is a Poisson distribution with parameter $\\lambda$, denoted as $E(Y)$, we can use the definition of the expected value for discrete random variables:\n", + "\n", + "$$\n", + "E(Y) = \\sum_{y=0}^{\\infty} y \\cdot p(y)\n", + "$$\n", + "\n", + "step 2:\n", + "Substituting the expression for $p(y)$ given in the problem, we get:\n", + "\n", + "$$\n", + "E(Y) = \\sum_{y=0}^{\\infty} y \\cdot \\frac{\\lambda^y}{y!} e^{-\\lambda}\n", + "$$\n", + "\n", + "step 3:\n", + "To solve this, we'll use the fact that the sum of all probabilities in a probability distribution equals $1$. Thus, we can rewrite the sum as follows:\n", + "\n", + "$$\n", + "E(Y) = \\sum_{y=1}^{\\infty} y \\cdot \\frac{\\lambda^y}{y!} e^{-\\lambda} + 0 \\cdot \\frac{\\lambda^0}{0!} e^{-\\lambda}\n", + "$$\n", + "\n", + "step 4:\n", + "Now, we can simplify the terms with $y$ greater than $0$:\n", + "\n", + "$$\n", + "E(Y) = \\sum_{y=1}^{\\infty} y \\cdot \\frac{\\lambda^y}{y!} e^{-\\lambda}\n", + "$$\n", + "\n", + "step 5:\n", + "To simplify further, let's take $e^{-\\lambda}$ outside the sum:\n", + "\n", + "$$\n", + "E(Y) = e^{-\\lambda} \\sum_{y=1}^{\\infty} \\frac{\\lambda^y}{(y-1)!}\n", + "$$\n", + "\n", + "step 6:\n", + "Now, let's make a substitution to simplify the expression inside the sum. Let $k = y - 1$, then $y = k + 1$. Also, note that when $y = 1$, $k = 0$, and when $y$ approaches infinity, $k$ also approaches infinity. With these substitutions, the sum becomes:\n", + "\n", + "$$\n", + "E(Y) = e^{-\\lambda} \\sum_{k=0}^{\\infty} \\frac{\\lambda^{k+1}}{k!}\n", + "$$\n", + "\n", + "$$\n", + "E(Y) = e^{-\\lambda} \\lambda \\sum_{k=0}^{\\infty} \\frac{\\lambda^k}{k!}\n", + "$$\n", + "\n", + "step 7:\n", + "The sum inside the expression is recognizable as the Taylor series expansion of $e^\\lambda$, which is $e^\\lambda$. Therefore:\n", + "\n", + "$$\n", + "E(Y) = e^{-\\lambda} \\lambda e^\\lambda\n", + "$$\n", + "\n", + "$$\n", + "E(Y) = \\lambda\n", + "$$\n", + "\n", + "step 8:\n", + "So, the general formula for the expected value of the given distribution is simply $\\lambda$. **QED**\n", + "\n", + "*Question 2: A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately five per square yard. If a forester randomly locates ten 1-square-yard sampling regions in the area, find the probability that none of the regions will contain seedlings.*\n", + "\n", + "step 1:\n", + "In this scenario, we're dealing with a Poisson distribution, which is given by the formula:\n", + "\n", + "$ p(y) = \\frac{\\lambda^y}{y!} e^{-\\lambda} $\n", + "\n", + "step 2:\n", + "Where:\n", + "- $ \\lambda $ is the average rate (mean density of seedlings per square yard).\n", + "- $ y $ is the number of seedlings in a region.\n", + "\n", + "step 3:\n", + "Given that the mean density of seedlings is five per square yard, we have $ \\lambda = 5 $.\n", + "\n", + "step 4:\n", + "Now, we want to find the probability that none of the regions will contain seedlings. This is the probability of having $ y = 0 $ seedlings in a region. Substituting $ \\lambda = 5 $ and $ y = 0 $ into the Poisson distribution formula:\n", + "\n", + "$ p(0) = \\frac{5^0}{0!} e^{-5} = e^{-5} $\n", + "\n", + "step 5:\n", + "We can calculate this probability:\n", + "\n", + "$ p(0) \\approx e^{-5} \\approx 0.00674 $\n", + "\n", + "step 6:\n", + "So, the probability that none of the regions will contain seedlings is approximately $0.00674$, or $0.674$%. **QED**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "35220716-e31d-4566-9e42-b63d7b92d54b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Detablan_AllLectures_ANSWERS/Detablan_LECTURE3_Answers.ipynb b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE3_Answers.ipynb new file mode 100644 index 0000000..5d1828b --- /dev/null +++ b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE3_Answers.ipynb @@ -0,0 +1,1192 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "44769102-1ea4-4d3b-852f-5735fd8709f1", + "metadata": {}, + "source": [ + "**Name:** Paul France M. Detablan\n", + "\n", + "**Program and Year:** BSCS - 1\n", + "\n", + "$\\textbf{Graphs}$\n", + "-" + ] + }, + { + "cell_type": "markdown", + "id": "db19dbfa-b54b-4de0-ad40-ec158be70889", + "metadata": {}, + "source": [ + "$\\textbf{1.Simple Graphs}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "abb17728-a593-46d5-bbde-f5b730b4d5b8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 40\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5])\n", + "\n", + "# Add edges to the graph\n", + "G.add_edges_from([(1, 2), (1, 3), (2, 3), (3, 4), (4, 5), (5, 1)])\n", + "\n", + "# Draw the graph\n", + "nx.draw(G, with_labels=True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9f4dfd38-448d-4015-9cb7-64e2b9319e76", + "metadata": {}, + "source": [ + "This is my take on a simple graph, Graphs can be used to model a wide range of real-world systems, from social networks to transportation routes. But from what I made, I was trying to make a simple house to represent my take on the fundamental elements of a simple graph and the roof of the house no matter how a keep changing the graph, will not stay upright HAHAHHAHA.\n" + ] + }, + { + "cell_type": "markdown", + "id": "571d9823-319e-4298-aa67-4430e060c6f9", + "metadata": {}, + "source": [ + "$\\textbf{2.Directed Graphs}$\n", + "-\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "5aa79798-ce02-4607-9aa1-2489ec319b84", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 21\n", + "# Create a directed graph object\n", + "G = nx.DiGraph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6,7])\n", + "\n", + "# Add edges to the graph\n", + "G.add_edge(1, 5)\n", + "G.add_edge(5, 2)\n", + "G.add_edge(2, 6)\n", + "G.add_edge(6, 3)\n", + "G.add_edge(3, 7)\n", + "G.add_edge(7, 4)\n", + "G.add_edge(4, 1)\n", + "\n", + "\n", + "# Draw the graph\n", + "pos = nx.circular_layout(G)\n", + "nx.draw(G,pos=pos, with_labels=True)\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "37be51e6-423a-45ce-89e4-b13558d0ddc1", + "metadata": {}, + "source": [ + "Directed graphs provide a powerful framework for representing and analyzing relationships with a clear directionality, making them valuable tools in various fields, including computer science, engineering, social sciences, and operations research. As you can see from the graph above, I was trying to make a star with 7 vertices.\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "31e405eb-e8bb-40d1-894e-14fd0620bf89", + "metadata": {}, + "source": [ + "$\\textbf{3.Complete Graphs}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "0dbaacea-8eb3-4978-b4b9-07aa166a4d89", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Create a complete graph with 6 nodes\n", + "G = nx.complete_graph(5)\n", + "\n", + "# Draw the graph\n", + "nx.draw(G, with_labels=True)\n", + "\n", + "# Display the plot\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "9cfbaba2-9a7e-4813-98b3-56b91250d020", + "metadata": {}, + "source": [ + "Complete graphs represent a scenario where all possible connections between nodes exist, leading to a fully interconnected and symmetrical graph structure. From the graph above, I was trying to make a summoning circle.\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "372023f0-d4a1-4a76-a8b4-fc8479ce9f4b", + "metadata": {}, + "source": [ + "$\\textbf{4.Bipartite Graphs}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "3a187b8f-2429-448f-86aa-7957ff3ec6bb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "\n", + "Chika = nx.Graph()\n", + "Chika.add_nodes_from(['Paul','Luis','Elijah'], bipartite=0) # Add the node attribute \"bipartite\"\n", + "Chika.add_nodes_from(['Sharley','Hasm','Edouard'], bipartite=1)\n", + "Chika.add_edges_from([('Paul','Sharley'), ('Paul','Hasm'),('Paul','Edouard')\n", + " , ('Luis','Sharley'), ('Luis','Hasm'),('Luis','Edouard')\n", + " , ('Elijah','Sharley'), ('Elijah','Hasm'),('Elijah','Edouard')])\n", + "\n", + "top = nx.bipartite.sets(Chika)[0]\n", + "pos = nx.bipartite_layout(Chika, top)\n", + "nx.draw(Chika, pos=pos, with_labels=True, node_color=['pink','magenta','red','deepskyblue','cyan','green'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "91cb7d97-3935-4535-bac3-d686bcdc4606", + "metadata": {}, + "source": [ + "Bipartite graphs provide a structured way to model relationships between two distinct types of entities, with edges representing valid connections or interactions between them. Their simplicity and versatility make them valuable tools in both theoretical studies and practical applications.\n", + "\n", + "Edouard, Sharley, and Hasm were a close group of friends and all of a sudden they broke up. The 3 marites, Paul, Luis, and Elijah were trying to hear there story from different perspectives." + ] + }, + { + "cell_type": "markdown", + "id": "fcb4d505-0e7a-4bd5-a4ab-be31258311e6", + "metadata": {}, + "source": [ + "$\\textbf{5.Subgraphs}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "25925010-ed11-4e7a-a66c-831596b6948c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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keMXOH6j0pHj5tA+WR8Fi2fI+AAAgZ1itVn388ccqX768Xn/9ddNxXIZTFspSxfLLImV429uaekPnFgxR6uWz8mkzTLkz8TDOrSz/ex8AAGA/QkNDtXHjRi1btkzu7pm/6wjbOOWILb+nh0pmcJKNNT1N55cEKznqkIo36yPPB/+5jdDdlCyWT/k9nbKPAwDgkNLT0/Xxxx+revXqaty4sek4LsVpG1Htst6asePUbbcOurxhqhKP7VDegMpKS4xT3L6Nf/l+gSdqZ3htdzeLapfxztK8AADANrNmzdLvv/+uiIgIdlTJYS55Uk7MrD5KPr3vjq99pM+Ku14/q0/KAQAA9y8pKUlly5bVs88+q0WLFpmO43KcdkJZ2qegqgd43fYsb9/XRt33dW+e5U2ZBADAfnzzzTc6e/as1qxZYzqKS3LKNZQ3jWheQR5uWTvy9nCzaETzCll6TQAAcP+uXLmi4cOH680331TZsmVNx3FJTl0oHy6aT4Pvct72vRrStLwezuCBHwAAkLOCg4OVlJSkQYMGmY7ispy6UEpSm+dKqtdLZWy7yP+WmTYokaLWz3G4PAAA9uLs2bMaO3asevToIT8/P9NxXJbTF0pJer92aY1qUUGeHm5yv8db4O5uFnnmcpf/xe2a1qu1Nm3alD0hAQDAPRs0aJDy58+v3r17m47i0pz2Ke/bOX0pQf0W71XYsQtyd7Pcdkuhm25+v3qAl0Y0ryCfAh5q1KiRfv75Z4WFhenJJ5/MweQAAODvDhw4oAoVKujLL79U9+7dTcdxaS5VKG86Gntds3ZEauORc4q8mPCXE3Us+u+m5bXLeKv9CyX/8jT3tWvXVKtWLcXGxioiIkKPPPJIjmcHAAD/1axZM+3Zs0eHDh2Sp6en6TguzSUL5a3ik1N18mK8bqSmK7eHm0oVy5/hCTgxMTEKDAxU7ty5FR4ermLF7u38bwAAYLvw8HBVq1ZNs2bNUrt27UzHcXkuXyjvx9GjR1W1alX5+/tr/fr1ypePp74BAMgpVqtV1apVU2Jionbt2iU3N5d4JMSu8f/AfShdurRWrlypvXv3qnXr1kpNTTUdCQAAl7Fs2TJFREQoODiYMmknmFDaICQkRE2aNNHrr7+uKVOmcG4oAADZLDU1VRUqVNBDDz2ktWvXmo6D/3HaoxdzQlBQkKZNm6aOHTuqRIkSGjJkiOlIAAA4tR9++EGHDh3SrFmzTEfBLSiUNurQoYOio6P18ccfy8/PT++++67pSAAAOKWEhAQNHDhQbdu21TPPPGM6Dm5BocwCH330kaKiotS1a1f5+PioRYsWpiMBAOB0vvrqK50/f17Dhg0zHQV/wxrKLJKenq527dppyZIlWrNmjWrUqGE6EgAATuPChQvy9/dXp06d9NVXX5mOg7+hUGah5ORkNWzYUL/88ovCwsJUoUIF05EAAHAK//nPf/Tdd9/p+PHjKl68uOk4+Buetc9Cnp6eWrx4sUqVKqUGDRooMjLSdCQAABzeyZMnNWHCBPXu3ZsyaaeYUGaD6OhoBQYGKm/evNq6dauKFi1qOhIAAA6rQ4cOWrt2rY4fP678+fObjoPbYEKZDfz8/BQaGqrz58+rSZMmSkhIMB0JAACH9Ntvv2nWrFkaNGgQZdKOMaHMRj///LNq166tunXrauHChfLw4KF6AADuRVBQkP744w/t27dPuXLlMh0Hd8CEMhtVrlxZCxYs0MqVK/Xee++J7g4AQOatX79eoaGhGjFiBGXSzjGhzAHTp09Xp06dNHDgQA0aNMh0HAAA7F56eroqV64sDw8Pbdu2jeON7Rz3YHPA66+/rujoaPXt21d+fn7q0qWL6UgAANi1n376Sb/88os2b95MmXQATChziNVqVffu3TVhwgQtXLhQzZo1Mx0JAAC7dOPGDf3rX/9SuXLltHz5ctNxkAlMKHOIxWLRmDFjFBMTozZt2mjdunWqVq2a6VgAANidyZMn68SJE1qyZInpKMgkJpQ5LDk5WUFBQfrtt9+0detWlS9f3nQkAADsxvXr1+Xv769GjRrp+++/Nx0HmcRT3jnM09NTS5YsUcmSJRUUFKTTp0+bjgQAgN34/PPPde3aNQ0ZMsR0FNwDJpSGREVFKTAwUPnz59fWrVtVpEgR05EAADAqJiZGAQEBeu+99zR69GjTcXAPmFAaUqJECYWGhio2NlZNmzZVYmKi6UgAABg1dOhQ5cqVS3379jUdBfeIQmlQ2bJltWLFCv3yyy9q27atUlNTTUcCAMCIo0ePavLkyerXrx937RwQt7ztwMqVK/Xyyy/rzTff1MSJE9lvCwDgcl599VVt375dR44cUZ48eUzHwT1i2yA70KhRI02ZMkVvvPGGHnzwQX366aemIwEAkGN+/vln/fTTT/r+++8pkw6KCaUdGTFihPr376/JkyfrrbfeMh0HAIBsZ7VaVbt2bV28eFG//fab3N3dTUfCfWBCaUf69u2rqKgovfPOO/Lx8VHTpk1NRwIAIFutXr1amzdv1ooVKyiTDowJpZ1JS0tTmzZttGLFCq1bt05Vq1Y1HQkAgGyRlpamp59+WkWKFNGmTZt4hsCB8ZS3nXF3d9eMGTP0/PPPq0mTJjpw4IDpSAAAZItZs2Zp7969Gj16NGXSwTGhtFNXrlxRjRo1dOXKFUVEROihhx4yHQkAgCyTlJSksmXL6rnnntOCBQtMx4GNmFDaqcKFC2v16tWyWCxq0KCBLl++bDoSAABZZsKECTp79qyGDx9uOgqyABNKO3fw4EFVq1ZN5cuX15o1a9hOAQDg8C5fvix/f3+1bt1a3377rek4yAJMKO1cuXLltGLFCu3atUuvvfaa0tLSTEcCAMAmwcHBSk5OZt9lJ0KhdABVqlTR/PnztXTpUr3//vtiqAwAcFSnT5/WV199pZ49e8rPz890HGQRCqWDaNy4sSZNmqSJEyey3gQA4LAGDRqkAgUKqFevXqajIAuxsbkDefPNNxUdHa1PPvlEvr6+6ty5s+lIAABk2v79+/XDDz9o7NixeuCBB0zHQRbioRwHY7Va1bVrV02aNElLlixRkyZNTEcCACBTmjZtqn379unQoUPKnTu36TjIQkwoHYzFYtH48eMVGxur1q1ba/369apSpYrpWAAAZCgsLEzLly/X7NmzKZNOiAmlg0pKStJLL72k/fv3a+vWrSpXrpzpSAAA3JbValVgYKBu3LihnTt3ys2NRzicDf+POqg8efJo2bJlKlGihIKCgnT27FnTkQAAuK0lS5Zo+/btCg4Opkw6KSaUDu7MmTMKDAxU4cKFtWXLFhUuXNh0JAAA/pSamqonnnhCjzzyiEJDQ03HQTbhY4KDe+ihhxQSEqIzZ86oWbNmSkpKMh0JAIA/TZs2TYcPH9aoUaNMR0E2YkLpJMLDw1W3bl01atRI8+bNk7u7u+lIAAAXFx8fr9KlS6t27dqaNWuW6TjIRkwonUTVqlU1b948LV68WN27d+c0HQCAcWPHjtWFCxc0bNgw01GQzSiUTqRp06aaOHGiJkyYoJEjR5qOAwBwYRcuXFBwcLDee+89Pfroo6bjIJuxD6WTeeuttxQdHa3+/fvLz89P//73v01HAgC4oJtTyQEDBhhOgpxAoXRCn3zyiaKiovTWW2/J29tbjRo1Mh0JAOBC/vjjD33zzTcaOHCgvLy8TMdBDuChHCeVlpamVq1aKTQ0VBs3btTzzz9vOhIAwEW0b99eGzZs0NGjR5U/f37TcZADKJROLDExUS+99JIOHjyo8PBwlS1b1nQkAICT2717t5555hlNmjRJb7/9tuk4yCEUSid3+fJlVa9eXXFxcYqIiFCJEiVMRwIAOLH69evr1KlT2rdvnzw8WFnnKnjK28kVKVJEq1evVlpamho0aKCrV6+ajgQAcFLr1q3TmjVrNHLkSMqki2FC6SL279+vatWqqWLFigoJCZGnp6fpSAAAJ5Kenq7nnntOnp6eCg8Pl8ViMR0JOYgJpYsoX768li9fru3bt6tDhw5KT083HQkA4ETmz5+vX3/9VcHBwZRJF8SE0sUsWbJELVu2VNeuXfXVV1/xmx4AYLMbN26oXLlyKl++vJYtW2Y6DgxggYOLadasmb755hu98847KlGihPr06WM6EgDAwU2aNEknT56kTLowCqUL6tKli6Kjo9W3b1/5+vqqU6dOpiMBABzUtWvXNGTIEHXq1Enly5c3HQeGUChd1MCBAxUVFaXOnTvLx8dHDRo0MB0JAOCAPv/8c8XFxWnw4MGmo8Ag1lC6sNTUVLVs2VLr1q3Txo0bVblyZdORAAAOJDo6WgEBAerWrZtGjRplOg4MolC6uISEBNWrV09HjhxReHi4ypQpYzoSAMBBvPvuu5o3b56OHz+uIkWKmI4Dg9g2yMXly5dPy5cvV/HixVW/fn1FR0ebjgQAcABHjhzRlClT1L9/f8okmFDivyIjIxUYGCgvLy9t3rxZhQoVMh0JAGDHWrVqpZ9//llHjhxRnjx5TMeBYUwoIUkqWbKkQkJCdPLkSbVo0ULJycmmIwEA7NT27du1cOFCDR06lDIJSUwo8TdbtmzRSy+9pGbNmmn27Nlyc+MzBwDg/1mtVtWqVUuXL1/W7t275e7ubjoS7ADbBuEvatSoodmzZ6tVq1by9fXVmDFjOE0HAPCnVatWacuWLVq5ciVlEn9iQonb+vbbb/Xee+8pODhYvXv3Nh0HAGAH0tLSVLFiRXl5eWnDhg0MHPAnJpS4rXfffVfR0dH6+OOP5evrq44dO5qOBAAwbMaMGdq3b5927NhBmcRfMKHEHVmtVr311luaPn26li9frqCgINORAACGJCYmqkyZMqpSpYrmz59vOg7sDE9c4I4sFosmTpyooKAgtWrVSjt37jQdCQBgyNdff63o6GgNHz7cdBTYISaUuKuEhATVqVNHx48fV3h4uEqXLm06EgAgB12+fFmPPfaY2rZtq2+++cZ0HNghJpS4q3z58mnFihUqVqyY6tevr5iYGNORAAA5aOTIkUpJSdGnn35qOgrsFIUSmVKsWDGFhIQoOTlZDRs21LVr10xHAgDkgNOnT2vcuHHq2bOnfH19TceBneKWN+7J3r17Vb16dVWqVEmrVq1S7ty5TUcCAGSjN954QytWrNDx48dVsGBB03Fgp5hQ4p5UqFBBS5cuVVhYmDp16qT09HTTkQAA2WTfvn2aPn26Pv30U8okMsSEEvdlwYIFevXVV9WjRw998cUXpuMAALJBkyZNdPDgQR04cIA7UsgQG5vjvrRq1Urjx4/X+++/Lz8/P/Xq1ct0JABAFtqyZYtWrFihuXPnUiZxV0woYZMBAwZo+PDhmjFjhtq3b286DgAgC1itVlWpUkWpqan6+eef5ebGCjlkjAklbDJ06FBFR0fr3//+t7y9vfXSSy+ZjgQAsNGiRYu0Y8cOrV+/njKJTGFCCZulpqaqWbNm2rRpkzZt2qRKlSqZjgQAuE8pKSl64okn9OijjyokJMR0HDgIPnbAZh4eHpo3b56eeOIJNWzYUMeOHTMdCQBwn6ZNm6ajR48qODjYdBQ4ECaUyDIXLlxQtWrVlJKSooiICPn4+JiOBAC4B/Hx8QoICFDdunU1Y8YM03HgQJhQIst4eXkpJCREiYmJatiwoa5fv246EgDgHowZM0aXLl3S0KFDTUeBg6FQIkuVKlVKq1ev1rFjx9SyZUvduHHDdCQAQCacP39eo0ePVteuXVWqVCnTceBgKJTIck899ZSWLFmizZs364033uA0HQBwAMOGDZPFYlG/fv1MR4EDolAiW9SuXVszZszQ7Nmz9fHHH5uOAwDIwIkTJ/Ttt9+qT58+8vLyMh0HDoh9KJFtXn31VcXGxuqDDz6Qn5+f/vOf/5iOBAC4jQEDBqh48eLq3r276ShwUBRKZKtu3bopKipKPXv2lK+vr9q1a2c6EgDgFr/++qvmzJmjKVOmKF++fKbjwEGxbRCyndVq1b///W/Nnj1bK1euVL169UxHAgD8T7169XTmzBnt3btXHh7MmXB/+DcH2c5isWjKlCk6d+6cWrRooc2bN+uZZ54xHQsAXN7atWu1bt06LV68mDIJmzChRI6Jj49X7dq1derUKUVERMjf3990JABwWenp6apUqZLy5s2rrVu3ymKxmI4EB8ZT3sgx+fPn18qVK1WoUCEFBQXp3LlzpiMBgMuaO3eudu/erdGjR1MmYTMmlMhxf/zxhwIDA/Xggw9q06ZNKlCggOlIAOBSkpOT9fjjj/+5bzBgKyaUyHGPPvqoVq9erSNHjnCaDgAYMHHiREVGRmrEiBGmo8BJMKGEMRs2bFBQUJBat26t6dOny82NzzcAkN2uXr0qf39/NWvWTN99953pOHAS/A0OY1588UXNmDFDM2fOVN++fU3HAQCX8Nlnnyk+Pl6DBw82HQVOhD0CYFTr1q0VExOjDz/8UH5+fvrwww9NRwIApxUdHa0vv/xSH374oR588EHTceBEKJQwrnv37oqKilKPHj3k6+urNm3amI4EAE5p0KBByps3rz7++GPTUeBkKJSwC6NGjVJMTIw6duyo4sWLq06dOqYjAYBTOXTokKZOnarRo0ercOHCpuPAyfBQDuxGSkqKmjRpooiICG3evFlPP/206UgA4DRatmypX375RYcPH5anp6fpOHAyFErYlbi4ONWuXVunT5/Wtm3b9Oijj5qOBAAOb9u2bQoMDNSPP/6oDh06mI4DJ0ShhN05d+6cqlatKovFovDwcBUvXtx0JABwWFarVTVr1tTVq1f166+/yt3d3XQkOCG2DYLd8fb2VmhoqK5du6ZGjRopLi7OdCQAcFgrVqxQWFiYgoODKZPINkwoYbd2796tmjVrqmrVqlq2bJly5cplOhIAOJS0tDQ9+eST8vHx0fr16zmzG9mGCSXs1tNPP61FixZp/fr16ty5s/jsAwD35scff9SBAwcUHBxMmUS2YkIJuzdnzhy1a9dOffr00ciRI03HAQCHkJiYqDJlyigwMFDz5s0zHQdOjn0oYffatm2rmJgY/ec//5Gfn58++OAD05EAwO6NHz9eMTExGj58uOkocAEUSjiEHj16KCoqSh9++KF8fX316quvmo4EAHbr0qVLGjlypLp06aKAgADTceACKJRwGMHBwYqOjlaHDh3k5eWlF1980XQkALBLI0eOVGpqqj755BPTUeAiWEMJh3Ljxg01adJE27Zt05YtW1SxYkXTkQDArkRGRqpMmTLq27evBg4caDoOXASFEg7n+vXrql27ts6ePatt27apVKlSpiMBgN3o1KmTVq9erWPHjqlgwYKm48BFsG0QHE7BggW1cuVK5c+fX/Xr19eFCxdMRwIAu7B37179+OOPGjhwIGUSOYoJJRzW8ePHFRgYqFKlSmnDhg3Knz+/6UgAYFSjRo105MgRHThwgMMgkKOYUMJh+fv7a9WqVTpw4IBeffVVpaSkmI4EAMZs2rRJq1at0vDhwymTyHFMKOHw1q5dq4YNG6p9+/aaNm0ap0EAcDlWq1UvvPCCrFarduzYwZ+DyHFsGwSHV69ePf3www9q3769SpQowSa+AFzOwoUL9fPPP2vDhg2USRjBhBJO44svvlCvXr00fvx4vf/++6bjAECOSElJUfny5RUQEKBVq1aZjgMXxYQSTqNnz56KiorSBx98IF9fX7Vq1cp0JADIdt99952OHTumBQsWmI4CF8aEEk4lPT1dHTp00IIFCxQaGqpatWqZjgQA2SYuLk4BAQGqX7++pk+fbjoOXBhPecOpuLm56fvvv1eNGjX08ssv6/fffzcdCQCyzZdffqnLly9ryJAhpqPAxTGhhFO6fv26atWqpejoaG3btk2PPPKI6UgAkKXOnTsnf39/vf322/riiy9Mx4GLo1DCacXGxiowMFC5cuVSeHi4ihUrZjoSAGSZbt26acaMGTp+/Dh/vsE4bnnDafn4+CgkJESXLl1S48aNlZCQYDoSAGSJ48ePa+LEierTpw9lEnaBCSWc3q5du1SrVi3Vrl1bixcvlocHmxsAcGxt27ZVWFiYjh49qrx585qOAzChhPOrVKmSFi5cqJCQEHXp0kV8hgLgyHbt2qW5c+dq8ODBlEnYDSaUcBkzZsxQx44dNWDAAA0dOtR0HAC4Z1arVXXr1lVMTIz27NnDHRfYDf5NhMvo0KGDYmJi1Lt3b/n5+em9994zHQkA7smaNWu0YcMGLV26lDIJu8KEEi7FarXqP//5j7766istWLBALVq0MB0JADIlPT1dzzzzjAoUKKCwsDDO7IZd4eMNXIrFYtEXX3yhmJgYtWvXTqGhoapZs6bpWABwV7Nnz9aePXsUHh5OmYTdYUIJl5ScnKxGjRpp165dCgsLU4UKFUxHAoA7Sk5OVtmyZfX0009r8eLFpuMA/8BT3nBJnp6eWrRokR599FEFBQUpMjLSdCQAuKNvv/1Wp0+f1siRI01HAW6LCSVcWkxMjAIDA+Xp6amtW7eyQTAAu3P16lX5+/urRYsWmjx5suk4wG0xoYRL8/X1VUhIiC5cuKAmTZpwmg4AuzN69GglJCRo0KBBpqMAd0ShhMsrU6aMVq5cqT179qhNmzZKTU01HQkAJElnz57VmDFj1KNHD5UoUcJ0HOCOKJSApMqVK2vBggVavXq13n33XU7TAWAXBg8erHz58ql3796mowAZolAC/9OgQQNNnTpV3333HbeWABh38OBBTZ06VQMGDFChQoVMxwEyxD6UwC06duyo6Oho9enTR35+fnrnnXdMRwLgovr166eSJUvq3XffNR0FuCsKJfA3vXv3VlRUlLp27SofHx81b97cdCQALiYiIkJLlizRzJkz5enpaToOcFdsGwTcRnp6utq2baulS5dq3bp1qlatmulIAFyE1WpV9erVFRcXp19//VVubqxOg/3j31LgNtzc3PTjjz8qMDBQTZo00b59+0xHAuAili9frvDwcAUHB1Mm4TCYUAIZuHr1qmrWrKkLFy5o27Ztevjhh01HAuDEUlNT9eSTT6pEiRJau3YtZ3bDYfDRB8hAoUKFtHr1anl4eKh+/fq6dOmS6UgAnNj06dN18OBBBQcHUybhUJhQAplw+PBhVa1aVY8//rjWrl2rvHnzmo4EwMkkJCSoTJkyql69uubMmWM6DnBPmFACmVC2bFmtXLlSu3fvVtu2bTlNB0CWGzdunGJjYzVs2DDTUYB7RqEEMun555/X/PnztWLFCnXt2pXTdABkmYsXL2rUqFF655135O/vbzoOcM8olMA9aNSokb777jtNnjxZQ4YMMR0HgJMYMWKE0tLS9Mknn5iOAtwXNjYH7lGnTp0UHR2tfv36yc/PT2+//bbpSAAc2KlTp/T111+rf//+8vb2Nh0HuC88lAPcB6vVqg8++EDffPONFi1apJdfftl0JAAOqmPHjlqzZo2OHTumAgUKmI4D3BcKJXCf0tLS1KZNG61YsULr1q1T1apVTUcC4GD27Nmjp59+WhMmTODMbjg0CiVgg6SkJAUFBen3339XWFiYypcvbzoSAAfSsGFDHTt2TPv371euXLlMxwHuGw/lADbIkyePli5dqocfflhBQUE6c+aM6UgAHMTGjRu1evVqjRgxgjIJh8eEEsgCUVFRqlKligoWLKiwsDAVKVLEdCQAdsxqtapy5cpyc3PT9u3bORUHDo8JJZAFSpQoodDQUEVHR+vll19WYmKi6UgA7NhPP/2kXbt2afTo0ZRJOAUmlEAW2rZtm+rUqaOgoCD99NNPcnd3Nx0JgJ1JSUlRuXLl/jyBC3AGTCiBLFSlShXNnz9fy5Yt0/vvv89pOgD+YcqUKTpx4oRGjRplOgqQZZhQAtlg6tSp6ty5s4YMGcLJFwD+dP36dQUEBKhBgwb64YcfTMcBsgwn5QDZ4M0331RMTIwGDBggPz8/de7c2XQkAHbgyy+/1NWrVzm6FU6HQglkk379+ikqKkpdunSRt7e3mjZtajoSAINiY2P12WefqVu3bipZsqTpOECW4pY3kI3S0tL06quvatWqVVq/fr0CAwNNRwJgyPvvv69Zs2bp+PHjKlq0qOk4QJbioRwgG7m7u2vWrFmqXLmymjRpooMHD5qOBMCAo0ePatKkSerbty9lEk6JCSWQA65cuaLq1avr6tWr2rZtmx588EHTkQDkoNatWysiIkJHjhxR3rx5TccBshwTSiAHFC5cWCEhIZKkoKAgXblyxWwgADlm586dmj9/voYMGUKZhNNiQgnkoIMHD6pq1aqqUKGCQkNDlSdPHtORAGQjq9WqOnXq6Ny5c9qzZw+HHcBpMaEEclC5cuW0YsUK/fzzz2rfvr3S0tJMRwKQjUJDQ7Vx40aNHDmSMgmnxoQSMGDZsmVq3ry53n33XY0fP56zfAEnlJaWpmeeeUaFChXS5s2b+X0Op8Y+lIABTZs21aRJk/TWW2/Jz89P/fv3Nx0JQBabPXu2fv/9d0VERFAm4fSYUAIGDR06VJ9++qmmTp2qN954w3QcAFkkKSlJZcuWVaVKlbRw4ULTcYBsx4QSMGjAgAGKiorS22+/LW9vbzVu3Nh0JABZ4JtvvtHZs2e1Zs0a01GAHMGEEjAsLS1NrVq1UmhoqDZs2KAXXnjBdCQANrhy5Yr8/f31yiuvaOLEiabjADmCp7wBw9zd3TV79mw9++yzatSokQ4dOmQ6EgAbBAcHKykpSQMHDjQdBcgxTCgBO3H58mVVr15dcXFxioiIUIkSJUxHAnCPzp49q4CAAPXs2VPDhg0zHQfIMRRKwI6cOXNGVapUUZEiRbRlyxYVLlzYdCQA96Bz585asmSJTpw4oQceeMB0HCDHcMsbsCMPPfSQQkNDdebMGTVr1kxJSUmmIwHIpAMHDuj777/XJ598QpmEy2FCCdih8PBw1a1bV40bN9bcuXM5YQNwAM2aNdPvv/+ugwcPytPT03QcIEcxoQTsUNWqVTVnzhwtWrRIH374ofjcB9i38PBwLV26VMOGDaNMwiUxoQTs2KRJk/TOO+9oxIgR6tu3r+k4AG7DarWqWrVqSkxM1K5du+TmxqwGroeNzQE71qVLF0VHR6tfv37y8/NTp06dTEcC8DdLly5VRESE1qxZQ5mEy2JCCdg5q9Wqd955R1OnTtWyZcvUsGFD05EA/E9qaqoqVKighx56SGvXrjUdBzCGCSVg5ywWiyZMmKDY2Fi98sor2rBhg55//nnTsQBI+v7773Xo0CHNmjXLdBTAKCaUgINITExU3bp1dfjwYUVERKhMmTKmIwEuLSEhQQEBAapVq5Zmz55tOg5gFIs9AAeRN29eLV++XN7e3qpfv76io6NNRwJc2ldffaULFy5wIg4gJpSAwzl9+rSqVKkiLy8vbd68WYUKFTIdCXA5Fy5ckL+/vzp16qSvvvrKdBzAOCaUgIN5+OGHFRoaqlOnTql58+ZKTk42HQlwOSNGjJDVatWAAQNMRwHsAoUScEDly5fXsmXLFBERoY4dOyo9Pd10JMBlnDx5UhMmTFDv3r1VvHhx03EAu8Atb8CBLV68WK1atdL777+vsWPHymKxmI4EOL0OHTpo3bp1OnbsmPLnz286DmAXmFACDqx58+aaMGGCxo0bp88++8x0HMDp/fbbb5o1a5YGDRpEmQRuwYQScAKffvqphg4dqunTp6tjx46m4wBOKygoSH/88Yf27dunXLlymY4D2A02NgecwODBgxUdHa033nhDxYsXV4MGDUxHApzO+vXrFRoaqoULF1Imgb9hQgk4idTUVLVo0ULr16/Xxo0bVblyZdORAKeRnp6uypUry8PDQ9u2bWO9MvA3rKEEnISHh4fmzp2rp556So0aNdLRo0dNRwKcxk8//aRffvlFo0ePpkwCt8GEEnAyFy9eVLVq1ZScnKyIiAj5+vqajgQ4tBs3bqhcuXL617/+peXLl5uOA9glJpSAkylWrJhCQ0OVnJysBg0a6Nq1a6YjAQ5t8uTJOnnypEaOHGk6CmC3mFACTmrv3r2qXr26KlWqpJUrV8rT09N0JMDhXL9+Xf7+/mrcuLGmTZtmOg5gt5hQAk6qQoUKWrp0qbZu3apOnTpxmg5wHz7//HNdu3ZNgwcPNh0FsGsUSsCJ1axZU7NmzdK8efPUs2dPcUMCyLyYmBh98cUX+uCDD/Twww+bjgPYNQol4ORatmypr7/+WmPHjtUXX3xhOg7gMIYMGaJcuXKpb9++pqMAdo+NzQEX8N577ykqKkofffSRfHx81KFDB9ORALt25MgRTZ48WSNHjlSRIkVMxwHsHg/lAC7CarWqc+fO+vHHH7VixQrVr1/fdCTAbr3yyivasWOHjhw5ojx58piOA9g9JpSAi7BYLJo0aZLOnTunli1batOmTapUqZLpWIDd2bFjhxYsWKDvv/+eMglkEhNKwMUkJCSoTp06On78uCIiIhQQEGA6EmA3rFarateurYsXL+q3336Tu7u76UiAQ+ChHMDF5MuXT8uXL1fRokVVv359xcbGmo4E2I3Vq1dr8+bNGjVqFGUSuAdMKAEXdfLkSQUGBsrPz0+bNm1SwYIFTUcCjEpLS9PTTz+tIkWKaNOmTZzZDdwDJpSAiypVqpRCQkJ07NgxtWjRQjdu3DAdCTBq5syZ2rt3r0aPHk2ZBO4RE0rAxW3atEn169dXq1atNGPGDLm58TkTricpKUllypRR5cqVtWDBAtNxAIfD3xyAi6tVq5ZmzpypOXPmqHfv3qbjAEZMmDBBUVFRGjFihOkogENi2yAAeuWVVxQTE6MPPvhAfn5+6tmzp+lIQI65fPmyhg8frrfeektlypQxHQdwSBRKAJKkbt26KTo6Wr169ZKfn5/atWtnOhKQI4KDg5WcnKyBAweajgI4LAolgD8NHz5c0dHR6tSpk4oXL6569eqZjgRkq9OnT+urr77SRx99JF9fX9NxAIfFQzkA/iIlJUXNmjXTli1btGnTJj377LOmIwHZ5s0339SyZct0/PhxPfDAA6bjAA6LQgngH+Lj4/Xiiy/q5MmTioiIkL+/v+lIQJbbv3+/nnzySY0dO1bdunUzHQdwaBRKALd14cIFVa1aVWlpaYqIiJC3t7fpSECWatq0qfbv36+DBw8qd+7cpuMADo1tgwDclpeXl0JCQhQfH6+GDRsqLi7OdCQgy4SFhWn58uUaPnw4ZRLIAkwoAWTot99+U40aNVSlShUtX76cv3zh8KxWqwIDA3Xjxg3t3LmTzfyBLMDvIgAZqlixopYuXapNmzbpjTfeUHp6uulIgE2WLFmi7du3Kzg4mDIJZBEmlAAyZf78+WrTpo169eql0aNHm44D3JfU1FQ98cQTeuSRRxQaGmo6DuA02IcSQKa8+uqriomJUffu3eXn56cePXqYjgTcs2nTpunw4cOaM2eO6SiAU2FCCeCe9OnTR8HBwZozZ47atGljOg6QafHx8QoICFCdOnU0c+ZM03EAp8KEEsA9GTlypKKjo9WxY0d5eXmpbt26piMBmTJ27FhdunRJQ4cONR0FcDpMKAHcs5SUFDVt2lRbt27Vli1b9PTTT5uOBGTowoULeuyxx/Tmm29qzJgxpuMATodCCeC+xMXF6cUXX1RkZKQiIiL02GOPmY4E3NGHH36oadOm6cSJE/Ly8jIdB3A67JcA4L4UKFBAK1euVMGCBVW/fn2dO3fOdCTgtv744w998803+vjjjymTQDZhQgnAJidOnFBgYKBKliypDRs2qECBAqYjAX/x2muvaePGjTp69Kjy589vOg7glJhQArDJY489ptWrV+vQoUNq1aqVUlJSTEcC/rR7927Nnj1bgwYNokwC2YgJJYAssW7dOjVs2FBt2rTR9OnTZbFYTEcCVL9+fZ06dUr79u2ThwcbmwDZhd9dALJE3bp19eOPP6pt27YqUaKERo0aZToSXNy6deu0Zs0aLVq0iDIJZDMmlACy1NixY9WjRw+NHTtW3bt3Nx0HLio9PV3PPfecPD09FR4ezsQcyGZ8ZAOQpT788ENFRUWpR48e8vX1VevWrU1HgguaN2+efv31V23ZsoUyCeQAJpQAslx6erpef/11zZ8/X6tXr9aLL75oOhJcyI0bN/T444/riSee0LJly0zHAVwCE0oAWc7NzU1Tp07VuXPn1KxZM23ZskUVK1Y0HQsuYuLEiTp16pSWL19uOgrgMphQAsg2cXFxql27ts6cOaOIiAg9+uijpiPByV27dk3+/v5q2rSppk6dajoO4DLYhxJAtrl5mk7+/PlVv359nT9/3nQkOLnPP/9ccXFxGjx4sOkogEuhUALIVt7e3goNDdXVq1fVuHFjxcfHm44EJxUdHa0vvvhC3bt310MPPWQ6DuBSKJQAsp2/v79WrVqlAwcO6NVXX+U0HWSLIUOGyNPTUx9//LHpKIDLoVACyBHPPvusFi1apLVr1+qtt94Sy7eRlQ4fPqwpU6aof//+KlKkiOk4gMvhoRwAOWr27Nl67bXX1LdvX40YMcJ0HDiJVq1aaefOnTp8+LDy5MljOg7gctg2CECOateunWJiYtSzZ0/5+fmpW7dupiPBwW3fvl0LFy7U9OnTKZOAIUwoARjRq1cvffnll5o3b55eeeUV03HgoKxWq2rWrKkrV65o9+7dcnd3Nx0JcElMKAEYMXr0aEVHR6t9+/YqXry4atWqZToSHNCqVasUFhamVatWUSYBg5hQAjDmxo0baty4sXbs2KEtW7boqaeeMh0JDiQtLU0VK1aUl5eXNmzYwJndgEE85Q3AmNy5c2vhwoUKCAhQgwYNdPLkSdOR4EBmzJihffv2KTg4mDIJGMaEEoBxsbGxCgwMVK5cubR161Z5eXmZjgQ7l5iYqDJlyqhKlSqaP3++6TiAy2NCCcA4Hx8fhYaG6tKlS5ymg0z5+uuvFRMTo+HDh5uOAkBMKAHYkV27dqlWrVqqVauWlixZIg8PnhvEP12+fFmPPfaY2rVrpwkTJpiOA0BMKAHYkUqVKmnhwoUKDQ1Vly5dOE0HtzVy5EilpKTok08+MR0FwP9QKAHYlfr16+v777/XtGnTKAz4h9OnT2vcuHHq2bOnfH19TccB8D/cTwJgd9q3b6+YmBh99NFH8vPzU9euXU1Hgp349NNP9cADD6hXr16mowC4BYUSgF3q2bOnoqKi1K1bN/n4+KhVq1amI8GwvXv3avr06Ro3bpwKFixoOg6AW/BQDgC7lZ6ertdee02LFi3SmjVrVLNmTdORYFDjxo116NAhHThwQLlz5zYdB8AtmFACsFtubm764YcfdP78eb388ssKCwtThQoVTMeCAZs3b9bKlSs1d+5cyiRgh5hQArB7165dU61atRQbG6uIiAg98sgjpiMhB1mtVlWpUkVpaWnasWOH3Nx4nhSwN/yuBGD3HnjgAa1atUqenp4KCgrSxYsXTUdCDlq0aJF27Nih4OBgyiRgp5hQAnAYR48eVWBgoEqXLq1169YpX758piMhm6WkpOiJJ57Qo48+qpCQENNxANwBH/UAOIzSpUtr1apV2rNnj9q0aaPU1FTTkZDNpk6dqqNHjyo4ONh0FAAZYEIJwOGEhISoSZMm6tSpkyZPniyLxWI6ErJBXFycAgICVK9ePc2YMcN0HAAZYEIJwOEEBQVp6tSp+u677zRw4EDTcZBNxo4dq8uXL2vo0KGmowC4C7YNAuCQOnbsqJiYGH388cfy8/PTu+++azoSstD58+c1evRode3aVaVKlTIdB8BdUCgBOKyPPvpIUVFR6tq1q3x8fNSiRQvTkZBFhg0bJovFov79+5uOAiATWEMJwKGlp6erbdu2Wrp0qdauXavq1aubjgQbnThxQo8//rgGDx6svn37mo4DIBMolAAcXnJysho0aKDdu3crLCxMTzzxhOlIsEG7du20efNmHT16lK2hAAdBoQTgFK5evaqaNWvqwoULioiIUMmSJU1Hwn345ZdfVKlSJU2ZMkWdO3c2HQdAJlEoATiN6OhoBQYGKm/evNq6dauKFi1qOhLuUb169XTmzBnt3btXHh4s8wccBdsGAXAafn5+Cg0N1fnz59WkSRMlJiaajoR7sHbtWq1bt06jRo2iTAIOhgklAKezY8cOvfjii6pbt64WLlxIOXEA6enpqlSp0p/TZTarBxwLE0oATuf555/XTz/9pJUrV6pr167ic7P9mzt3rnbv3q3Ro0dTJgEHxIQSgNP64Ycf9O9//1sDBw7UoEGDTMfBHSQnJ+vxxx/XU089pSVLlpiOA+A+cB8IgNPq1KmTYmJi1LdvX/n5+alLly6mI+E2Jk6cqMjISK1cudJ0FAD3iQklAKdmtVrVvXt3TZgwQQsXLlSzZs1MR8Itrl69Kn9/fzVv3lxTpkwxHQfAfWINJQCnZrFYNGbMGLVs2VJt27bV1q1bTUfCLT777DMlJCSwJAFwcEwoAbiEpKQkNWjQQL/99pu2bt2q8uXLm47k8qKjo+Xv768PP/xQI0aMMB0HgA0olABcxtWrV1WjRg1dunRJ27Zt00MPPWQ6kkvr0qWLFixYoOPHj6tw4cKm4wCwAbe8AbiMQoUKafXq1XJ3d1dQUJAuX75sOpLLOnTokKZOnar+/ftTJgEnwIQSgMs5fPiwqlatqnLlymnNmjXKmzev6Ugup0WLFvr11191+PBheXp6mo4DwEZMKAG4nLJly2rFihX65Zdf1K5dO6WlpZmO5FK2bdumxYsXa+jQoZRJwEkwoQTgslasWKFmzZqpc+fO+vbbbzmhJQdYrVbVrFlT165d06+//io3N+YagDNgY3MALqtx48aaPHmy3nzzTT344IP65JNPTEdyeitWrFBYWJhWr15NmQScCBNKAC5v+PDhGjBggCZPnqy33nrLdBynlZaWpieffFK+vr5at24dE2HAiTChBODy+vXrp+joaL3zzjvy8fFR06ZNTUdyStOnT9eBAwf0ww8/UCYBJ8OEEgD03+lZ69attXLlSq1fv16BgYGmIzmVxMRElS5dWlWrVtW8efNMxwGQxVjAAgCS3N3dNXPmTFWuXFmNGzfWwYMHTUdyKuPGjVNsbKyGDx9uOgqAbMCEEgBuceXKFVWvXl1Xr17Vtm3b9OCDD5qO5PAuXbqkxx57TO3bt9fXX39tOg6AbMCEEgBuUbhwYYWEhMhisXCaThYZOXKk0tLS9Omnn5qOAiCbUCgB4G8efPBBhYSEKCoqSi+//LKSkpJMR3JYkZGRGj9+vHr16iVvb2/TcQBkE255A8AdbNu2TXXq1FGDBg00f/58ubu7m47kcDp16qTVq1fr2LFjKliwoOk4ALIJE0oAuIMqVapo3rx5WrJkiT744APx+fve/P777/rxxx81cOBAyiTg5JhQAsBdfPfdd3rrrbc0bNgw9e/f33Qch9GoUSMdOXJEBw4cUK5cuUzHAZCN2NgcAO6ic+fOio6O1oABA+Tr66s333zTdCS7t2nTJq1atUrz58+nTAIugAklAGSC1WpV165dNWnSJC1ZskRNmjQxHcluWa1WPf/885KkHTt2cCoO4AKYUAJAJlgsFo0fP16xsbFq3bq11q9frypVqpiOZZcWLlyonTt3auPGjZRJwEUwoQSAe5CUlKSXXnpJ+/fvV3h4uB5//HHTkexKSkqKypcvr4CAAK1atcp0HAA5hKe8AeAe5MmTR0uXLpWfn5/q16+vqKgo05Hsynfffadjx45p1KhRpqMAyEFMKAHgPpw5c0ZVqlRRkSJFtGXLFhUuXNh0JOPi4uIUEBCg+vXra/r06abjAMhBTCgB4D489NBDCg0N1ZkzZ9SsWTNO05H05Zdf6vLlyxoyZIjpKAByGIUSAO7Tv/71Ly1fvlw7duxQhw4dlJaWZjqSMefOndNnn32mbt266ZFHHjEdB0AOo1ACgA2qVq2quXPnatGiRerevbvLnqYzdOhQubu7q2/fvqajADCAQgkANnr55Zf17bffasKECS75MMrx48c1ceJE9enTR8WKFTMdB4AB7EMJAFng7bffVnR0tPr16yc/Pz916tTJdKQc079/f/n4+Kh79+6mowAwhEIJAFnk008/VVRUlDp37qzixYurUaNGpiNlu127dmnevHn67rvvlDdvXtNxABjCtkEAkIXS0tLUqlUrhYaGauPGjX8eQeiMrFar6tatq5iYGO3Zs0ceHswoAFdFoQSALJaYmKh69erp0KFDCg8PV9myZU1HyhahoaEKCgrS0qVL1bRpU9NxABhEoQSAbHDp0iVVr15d8fHxioiIUIkSJUxHylLp6el65plnVLBgQW3ZsoUzuwEXx1PeAJANihYtqpCQEKWmpqphw4a6evWq6UhZavbs2dqzZ4+Cg4MpkwCYUAJAdtq/f7+qVaumihUrKiQkRJ6enqYj2Sw5OVlly5bV008/rcWLF5uOA8AOMKEEgGxUvnx5LV++XNu3b1eHDh2Unp5uOpLNvvnmG50+fVojR440HQWAnWBCCQA5YMmSJWrZsqW6du2qr776ymFvE1+9elWPPfaYWrZsqcmTJ5uOA8BOMKEEgBzQrFkzTZgwQePHj9fo0aNNx7lvo0ePVmJiogYNGmQ6CgA7wqZhAJBD3nnnHUVHR6tPnz7y9fXV66+/bjrSPTl79qzGjBmjHj16ON1T6wBswy1vAMhBVqtVXbp00bRp07R8+XI1aNDAdKRMe/vtt7Vo0SIdP35chQoVMh0HgB2hUAJADktNTVXLli21bt06bdy4UZUrVzYd6a4OHjyoJ554Ql988YU+/PBD03EA2BkKJQAYkJCQoHr16unIkSMKDw9XmTJlTEfKUPPmzfXbb7/p0KFDTrH1EYCsRaEEAEMuXbqkatWqKTExUdu2bZOvr6/pSLcVHh6uatWqaebMmXrttddMxwFghyiUAGBQZGSkqlSpIm9vb23evFkPPPCA6Uh/YbVa/zxC8pdffpGbG5uDAPgn/mQAAINKliypkJAQ/fHHH2revLmSk5NNR/qL5cuXKzw8XMHBwZRJAHfEhBIA7MCWLVv00ksvqVmzZpo9e7ZdlLfU1FQ9+eSTKlGihNauXeuwm7EDyH7sQwkAdqBGjRqaPXu2WrVqJV9fX40ZM8Z4gZs+fboOHjyoGTNmGM8CwL4xoQQAO/Ltt9/qvffe0+jRo/XRRx8Zy5GQkKDSpUurRo0amjNnjrEcABwDE0oAsCPvvvuuoqKi1Lt3b/n6+qpDhw5GcowbN07nz5/XsGHDjLw/AMfChBIA7IzValXnzp31448/asWKFapfv36Ovv/Fixfl7++vjh07aty4cTn63gAcE4USAOxQamqqmjdvro0bN2rjxo167rnncuy9e/bsqcmTJ+v48ePy9vbOsfcF4LjMP0YIAPgHDw8PzZs3TxUqVFCjRo109OjRHHnfU6dO6euvv1bv3r0pkwAyjQklANixixcvqmrVqrpx44YiIiKy/TSdjh07as2aNTp27JgKFCiQre8FwHkwoQQAO1asWDGFhoYqKSlJDRs21PXr17Ptvfbs2aOZM2dq4MCBlEkA94QJJQA4gN9//13Vq1dX5cqVtXLlSuXOnTvL36NBgwY6fvy49u/fr1y5cmX59QE4LyaUAOAAnnzySS1dulRbtmxRp06dlJ6enqXX37Bhg0JCQjRixAjKJIB7xoQSABzIggUL9Oqrr6pHjx764osvsuSaVqtVlStXlpubm7Zv386pOADuGRubA4ADadWqlcaNG6du3bqpRIkS6tmzp83X/Omnn7Rr1y5t2rSJMgngvjChBAAH1L9/f40YMUIzZ87Ua6+9luHPxien6uTFeN1ITVduDzeVKpZf+T3/O09ISUlRuXLlVLZsWa1cuTInogNwQkwoAcABDRs2TFFRUerUqZOKFy+ul1566S/fPxp7XbN2RGrj4XOKvJSgWycHFkkli+ZT7bLespwI14kTJ7R48eIczQ/AuTChBAAHlZKSombNmmnLli3atGmTnn32WZ2+lKB+i/cq7NgFubtZlJZ+5z/i3S1SmlUqkhSjZZ+01cNF8+VgegDOhEIJAA4sPj5ederU0YkTJzTg+1WasP28UtOtGRbJv3O3SB7ubhrctLzaPFcyG9MCcFYUSgBwcBcuXNDzbwxUWvmGNl+r10tl9H7t0lmQCoArYR9KAHBw6/5IyJIyKUmfrzmieTsjs+RaAFwHE0oAcGCnLyWo7pjNSk69/Ubn1tQUXQmbqfj9G5WeFKdcxUupcI0Oyvvo03e8pqeHm9b1qMmaSgCZxoQSABxYv8V7lZrBeskLK8fo2s4lyv+vWipS921Z3Nx07qdBSjq9/46vSU23qt/ivdkRF4CTolACgIM6GntdYccu3PEBnOSow0o4uEWFa76uIi++oYIVg+TTdoQ8HvDWlU3f3/G6aelWhR27oGPnrmdXdABOhkIJAA5q1o5Iubvd+WSbhMPhksVNBSsG/fk1i0duFXiqnpLPHlLqtfN3fK27m0Uzt7OWEkDmUCgBwEFtPHwuw+2BbsSeUK6iD8rN869rIXP7lfnz+3eSlm7VxiPnsiYoAKdHoQQABxSXnKrISwkZ/kxa3CW5Fyjyj6+7Fyj65/czEnkxQfHJqfcfEoDLoFACgAM6dTFed9uiw5p6Q3LP9Y+vWzxy///3M3q9pJMX4+8zIQBXQqEEAAd04w7bBN3K4pFbSkv5x9dvFsmbxdLW9wEACiUAOKDcHnf/49u9QFGlxV3+x9dv3uq+eevb1vcBAP6kAAAHVKpYft35+e7/yu39mFIunVV68l/XWt6IOvLf7/s8luHrLf97HwC4GwolADig/J4eKnmXk2zyPV5Vsqbr+m8hf37NmpqiuL1rlbtEWXk8UDzD15cslk/5PT2yJC8A58afFADgoGqX9daMHafuuHWQZ4myyvd4NV3ZPF3pCVfkUaSE4veuV+rVc/Jp0D3Da7u7WVS7jHd2xAbghDjLGwAc1NHY66o3dkuGP2NNvaErW/57lndaUpxye5dS4ertlfexZ+96/XU9aijAu2BWxQXgxCiUAODAOkzdoYgTFzPc4PxeubtZFPhYMc148/ksuyYA58YaSgBwYCOaV5BHBscv3g8PN4tGNK+QpdcE4NwolADgwB4umk+Dm5bP0msOaVpeD9/lgR8AuBWFEgAcXJvnSqrXS2Wy5FofvVRWrZ8rmSXXAuA6WEMJAE5i7s5IDVy2X6np1ntaU+nuZpGHm0VDmpanTAK4LxRKAHAipy8lqN/ivQo7dkHubpYMi+XN71cP8NKI5hW4zQ3gvlEoAcAJHY29rlk7IrXxyDlFXkzQrX/QW/TfTctrl/FW+xdKsjUQAJtRKAHAycUnp+rkxXjdSE1Xbg83lSqWnxNwAGQpCiUAAABswlPeAAAAsAmFEgAAADahUAIAAMAmFEoAAADYhEIJAAAAm1AoAQAAYBMKJQAAAGxCoQQAAIBNKJQAAACwCYUSAAAANqFQAgAAwCYUSgAAANiEQgkAAACbUCgBAABgEwolAAAAbEKhBAAAgE0olAAAALAJhRIAAAA2oVACAADAJhRKAAAA2IRCCQAAAJtQKAEAAGATCiUAAABsQqEEAACATSiUAAAAsAmFEgAAADahUAIAAMAmFEoAAADYhEIJAAAAm1AoAQAAYBMKJQAAAGxCoQQAAIBNKJQAAACwCYUSAAAANqFQAgAAwCYUSgAAANiEQgkAAACb/B+7PcTqbvWlXgAAAABJRU5ErkJggg==", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 49\n", + "# Create a complete graph with 6 nodes\n", + "G = nx.complete_graph(4)\n", + "\n", + "# Draw the graph\n", + "nx.draw(G, with_labels=True)\n", + "\n", + "# Display the plot\n", + "plt.show()\n", + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 49\n", + "# Create a complete graph with 6 nodes\n", + "G = nx.complete_graph(3)\n", + "\n", + "# Draw the graph\n", + "nx.draw(G, with_labels=True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "bc6e9478-6b15-44b7-93aa-0688e3d35e94", + "metadata": {}, + "source": [ + "In graph theory, a subgraph is essentially a subset of the vertices and edges of a larger graph that preserves the relationships between those vertices and edges. From the graph above, I created 2 graphs for better understanding, Graph 𝐻 and 𝐺. graph 𝐻 is a subgraph of 𝐺. Formally, a subgraph 𝐻 of a graph 𝐺 is a graph whose vertex set and edge set are both subsets of the vertex set and edge set of 𝐺, respectively." + ] + }, + { + "cell_type": "markdown", + "id": "2a961db1-a172-4e43-ac3c-eb7022286733", + "metadata": {}, + "source": [ + "$\\textbf{6.Degree of Vertex}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c977670d-14e9-422e-8a6f-a0b65baa6492", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "seed = 200\n", + "# Use seed for reproducibility\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes\n", + "G.add_nodes_from([1,2,3,4,5,6,7])\n", + "# Add self-loops to the remaining nodes\n", + "edgelist = [(1,1),(1,2),(2,3),(2,4),(2,5),(3,6),(5,4)]\n", + "G.add_edges_from(edgelist)\n", + "#pos = nx.spring_layout(G, seed=seed) # Seed for reproducible layout\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos=pos,with_labels=True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8b9723a8-f41b-4984-bb3c-fd4d9986c0d2", + "metadata": {}, + "source": [ + "In graph theory, a subgraph is essentially a subset of the vertices and edges of a larger graph that preserves the relationships between those vertices and edges. From the graph above, I created 2 graphs for better understanding, Graph 𝐻 and 𝐺. graph 𝐻 is a subgraph of 𝐺. Formally, a subgraph 𝐻 of a graph 𝐺 is a graph whose vertex set and edge set are both subsets of the vertex set and edge set of 𝐺, respectively." + ] + }, + { + "cell_type": "markdown", + "id": "34a4845b-272a-4cb0-b893-ef23758d1a70", + "metadata": {}, + "source": [ + "$\\textbf{Travelling in Graph}$\n", + "-" + ] + }, + { + "cell_type": "markdown", + "id": "365d6fba-f860-4296-a435-4082a6ce72fb", + "metadata": {}, + "source": [ + "$\\textbf{7. Walk}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "9004111e-67d7-4df0-a6e1-77ff06dfd1e5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5])\n", + "\n", + "# Add edges to the graph\n", + "G.add_edges_from([(1, 2), (1, 3), (2, 3), (3, 4), (4, 5), (5, 1)])\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G) # Positioning nodes\n", + "nx.draw(G, pos, with_labels=True)\n", + "walk = [(5, 1),(1, 2),(2, 3), (1, 3)]\n", + "\n", + "# Draw the graph with edge colors\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist = walk,edge_color='cyan',width=2)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "51dc02b5-bd24-4390-8059-17674a4609b5", + "metadata": {}, + "source": [ + "In graph theory, a \"walk\" refers to a sequence of vertices and edges that form a path within a graph. This path can be a simple traversal of vertices connected by edges, allowing for revisiting vertices and edges. From the graph above, an example of a Walk would be $5 \\to 1 \\to 2 \\to 3 \\to 1$." + ] + }, + { + "cell_type": "markdown", + "id": "597ec95d-5aa2-4f52-a772-01d7a07e201d", + "metadata": {}, + "source": [ + "$\\textbf{8. Trail}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "85e3a935-e5ab-4b26-b20f-9ffb32314fb4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])\n", + "\n", + "# Add edges to the graph\n", + "edgelist = [(1, 2), (1, 3), (2, 3), (3, 4), (4, 5), (5, 1), (6, 1), (6, 5), (7, 5), (7, 4), (8, 4), (8, 3)]\n", + "G.add_edges_from(edgelist)\n", + "\n", + "# Define the walk as a list of edges\n", + "trail = [(7, 5), (5, 1), (1, 2), (2, 3), (8, 3)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=trail, edge_color='cyan',width=2)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "de936c03-1987-4013-9597-5e0758d66480", + "metadata": {}, + "source": [ + "In graph theory, a \"trail\" is a type of walk that traverses a graph, moving from vertex to vertex along edges, but without repeating any edges. However, vertices may be revisited in a trail. From the graph above, an example of a Trail would be $7 \\to 5 \\to 1 \\to 2 \\to 3 \\to 8$." + ] + }, + { + "cell_type": "markdown", + "id": "a3fa86c9-de71-4f8c-8cda-dd875acbe968", + "metadata": {}, + "source": [ + "$\\textbf{9. Path}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "1c38156e-1f61-409b-85f8-91725ed6af4f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 40\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "# G.add_nodes_from([1, 2, 3, 4, 5])\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])\n", + "\n", + "\n", + "\n", + "edgelist = [(1, 2), (2, 3), (3, 4), (4, 5), (6, 1), (6, 5), (7, 5), (7, 4), (8, 4), (8, 3)]\n", + "# Add edges to the graph\n", + "G.add_edges_from(edgelist)\n", + "path = [(8, 3), (2, 3), (1, 2), (6, 1),(6, 5), (7, 5)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=path, edge_color='cyan',width=2)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "37f0d5f4-49c3-46c8-844c-e11effe298d4", + "metadata": {}, + "source": [ + "In graph theory, a \"path\" is a type of walk that traverses a graph, moving from one vertex to another along edges, without revisiting any vertex. From the graph above, an example of a Path would be $8 \\to 3 \\to 2 \\to 1 \\to 6 \\to 5 \\to 7$. Also I perfectly created a NUKE." + ] + }, + { + "cell_type": "markdown", + "id": "977c1064-5c51-4f76-a5f3-be18551dbae8", + "metadata": {}, + "source": [ + "$\\textbf{10. Closed Walk}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "f4d58b73-fe85-4e50-8358-c223463dd169", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 40\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "# G.add_nodes_from([1, 2, 3, 4, 5])\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8,9,10])\n", + "\n", + "\n", + "\n", + "edgelist = [(1, 2), (2, 3), (3, 4), (4, 5), (6, 1), (6, 5), (7, 5), (7, 4), (8, 4), (8, 3),(4,6), (2, 4),(7,9),(9,4),(8,10),(10,4)]\n", + "# Add edges to the graph\n", + "G.add_edges_from(edgelist)\n", + "closed_walk = [(7, 4), (8, 4), (8, 3), (3, 4),(4,6), (6, 5),(7, 5)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=closed_walk, edge_color='cyan',width=2)\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8871fd25-a025-43f9-86c4-2a739dbfeb8d", + "metadata": {}, + "source": [ + "A \"closed walk\" in graph theory is a type of walk that starts and ends at the same vertex, forming a loop within the graph. From the graph above, an example of a Closed walk would be $7 \\to 4 \\to 8 \\to 3 \\to 4 \\to 6 \\to 5 \\to 7$." + ] + }, + { + "cell_type": "markdown", + "id": "9b015970-1056-4606-a38e-734c6de68e6a", + "metadata": {}, + "source": [ + "$\\textbf{11. Circuit}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "c886b44b-3bfb-4381-a8ac-aa9e81a6838b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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MHjyY/v37M3PmzIQ6X7yqDcAA2+aXcBiAaz2PBxIwHFflAJOAx+sYmn6TYXBqs1cnIrGgQCnSTFauXFnRhZw9ezYlJSX06dOnogs5bNgw0tLSgi4zoWzYsIFDDz2UUCjEvHnz6NChQ9AlNdpnwDDXJeKP5vk3MC7QimKrfGj6u55HaXVD0z2P4w1DQ9NFEowCpUgTcRyHzz77rCJELl26FMuyOOywwypCZN++fYMuM2EVFxczcuRIli9fzvz58+nVq1fQJcXMw8BV/u3WjsN/LYtku/TKBf4OPFjH0PSrDIML0dB0kXinQCkSQwUFBbz77rvk5uYyY8YMNm7cSOfOnRk7dixjx47lqKOOom3btkGXmfBc1+XUU09l2rRpfPTRRwwalFxDaTzKzvh+2+9S7u84zLcsWgRbVpPR0HSRxKdAKdIInuexdOnSii7kvHnzcF2XAw88kOzsbLKzszn44IMxq/klKTvvhhtu4IEHHuCNN97gxBNPDLqcJrEJOMC2Wenvp7zQ8/hrEuynrMurwD2exxKodWj6tYA2iIjEDwVKkQYqLi5m9uzZFSFy1apVZGRkcNRRRzF27FjGjBlDt27dgi4zaT311FNceOGFPPTQQ1x55ZVBl9OkFgOHRCLY/pXfU4DTgiyoGdVnaPowf69lcvWnRRKTAqVIPaxZs6YiQH7wwQcUFRXRs2fPii7k8OHDadEiWRck48eMGTM49thjueiii3j00UcTcjxQQz0LnOvfbhGJ8J9QKOWWfTU0XST+KVCKVCMSibBw4cKKELl48WJCoRBDhw5l7NixZGdns/fee6dEoIkXixcvZtiwYYwYMYKpU6cS8rt2yc4D/uS6/MvfNtHXtvlPOExmsGUFooiyoymf9TzWQ41D0+8ARjd/eSIpTYFSxLdp0yZmzpxJbm4u06dPZ/369XTo0IHRo0czduxYjj766KQYS5OIfvzxRwYNGsSuu+7KnDlzyMxMrThVBPzGtvnW3095muvyommSyi9nNDRdJL4oUErK8jyP5cuXV3Qh586di+M47LvvvhVL2YMGDcKyEvmsksS3efNmhg0bxqZNm5g/fz677LJL0CUFYhlwoOOwzf9+fAo4P9CK4kP50PQnPI8fQUPTRQKiQCkppbS0lI8//picnBxyc3NZsWIF6enpHHnkkRWjfXr06BF0meKzbZtjjz2W+fPn8+mnn9K/f/+gSwrUa8DJ/m0rEmFBKMRBQRYUZzQ0XSQ4CpSS9NauXcv06dPJycnh/fffZ8uWLXTr1q2iC3nEEUeQkaGt/PHG8zzOP/98nnvuOd577z2OOOKIoEuKC5d6Hk/4Yam7bfNlOEy7YEuKO+VD0yd5HitAQ9NFmoECpSQd13X54osvKpayFy5ciGEYDB48uOKCmv32208X1MS5e++9lwkTJvDcc89x1llnBV1O3CgBhjgO//GXvsdFIrwdCqX0fsra/AhcT+1D00cZBvcDqd3/FmkcBUpJClu3bmXWrFnk5OQwffp0fv75Z9q0acMxxxzD2LFjGT16NJ07dw66TKmnl19+mdNOO43bbruN22+/Pehy4s4qYD/HYbMfKicBVwdaUWLQ0HSRpqNAKQnr+++/r+hCfvTRR5SWltKvX7+KpeyhQ4cS9q+KlcQxd+5cRo4cycknn8zzzz+vTnINcoFs/7bpuswxTX4bZEEJpAC4GXjJddlUTdeyfGj6RODQ5i5OJEEpUErCsG2befPmVVxQ88033xAOhzn88MMrLqjp3bt30GVKIyxbtowhQ4aw//778+6775KWpj5RbW70PO7zA3cX22ZJOEyXgGtKNO8Dt1Dz0PSOwNmGwa1Aq+YvTyRhKFBKXNuwYQPvvvsuOTk5vPfee/z666/ssssujBkzhuzsbEaOHEnr1q2DLlNiYP369QwePJgWLVrw6aef0q5du6BLinsOcITjMNdf+h4RifB+KERqjHyPLQ1NF2kcBUqJK57nsWTJkoql7Pnz5+O6LgcffHDFBTUHHXQQZjXLVJK4tm3bxhFHHMEPP/zA/Pnz6dmzZ9AlJYxfgAG2zQZ/e8ctnsed2ibQKPUZmn6yvySuoekiZRQoJXDbtm3jww8/rFjKXr16NZmZmYwaNYrs7GxGjx7NrrvuGnSZ0kRc1+UPf/gDM2bMYM6cORx88MFBl5RwPgKOcF0808TwPN41DEYFXVQS0NB0kfpToJRA5OXlkZubS25uLh988AHFxcX06tWr4oKaww47jPT09KDLlGZw7bXXMnnyZN5++23GjRsXdDkJ617KumoA7RyHJZbF7kEWlGTqMzT9OH/8kIamSypSoJRmEYlEWLBgQUUX8ssvvyQUCjFs2DCys7MZO3Ys/fr10xW9KebJJ5/kkksu4dFHH+Wyyy4LupyE5gLZkQgzQmU7KA9xHD6xLDTnILY0NF2kegqU0mQ2btzIe++9R25uLjNmzCA/P59OnToxevRosrOzGTVqlC68SGE5OTkcd9xxXH755Tz88MNBl5MUCoD9bJs1/n7K8Z7Hw3qR1mR+pKxrOdV1KdLQdElxCpQSM57n8e2331Z0IT/55BMikQj7779/xQU1hxxyCKGQrkFNdYsWLeKwww5j1KhRvPHGG/qeiKHPgaGui+MHnDeBEwOtKDW8Btxdy9D03YCLNTRdkpgCpTRKSUkJc+bMIScnh5ycHH744QdatmzJkUceSXZ2NmPGjKF79+5BlylxJC8vj0GDBtG9e3c++ugjnaPeBJ4ALvVvZzoOiy0LTWhtHhqaLqlKgVIa7KeffmL69Onk5uby/vvvU1hYSFZWVkUXcsSIEbRs2TLoMiUObdq0iaFDh1JUVMRnn31G165dgy4pKXnAKa7La36g6e84LLQs9FPZvOozNP3PhsFtaGi6JD4FSqmT67osWrSoYil70aJFmKbJoYceWnFBzb777qsLaqRWpaWljBkzhkWLFvHZZ5+x1157BV1SUtsCHGjb/M/fT3mO6/KM5rcGQkPTJRUoUEq1tmzZwvvvv09OTg7Tp09n7dq1tGvXjmOOOYbs7GyOOeYYOnbsGHSZkiA8z+Occ87hxRdf5P3332f48OFBl5QSvgIOjkQo8feoPg/8MdCKZCFwI/CRhqZLklGglAorVqyo6ELOmTMH27bZZ599KrqQQ4YMwfKPeBNpiLvvvptbbrmFF198kdNPPz3oclLKv4Cz/NvpkQgLQyEGBFmQABqaLslHgTKF2bbNJ598UnFBzfLly0lLS2PEiBEVIXKPPfYIukxJcC+++CJnnnkmd911FzfffHPQ5aSkcz2PZ/3Asqdt80U4TOuAa5LtlgHXAzM0NF0SmAJlilm3bh0zZswgNzeX9957j82bN7PrrrtWBMgjjzySVq20PVxi46OPPmLUqFGcccYZPPvss9pnG5BtwCG2zVf+fsqTXJdXTRP934gv9Rma3gu4WkPTJQ4pUCY5z/NYvHgxubm55OTk8PnnnwMwcODAihB54IEH6he9xNw333zDkCFDOPjgg5k+fTrhsM5sCdIK4ADHodDftvI4cEmgFUltNDRdEo0CZRIqLCzkgw8+qDgre82aNbRu3ZpRo0aRnZ3N6NGjNa5FmtTatWsZPHgwmZmZfPrpp7Rt2zbokgR4C/idf9tyXT41TQ4JsiCpl9eAezyPL6HGoekXGQbXoaHpEhwFyiSxcuXKii7k7NmzKSkpoU+fPhVdyGHDhpGWpqcaaXpFRUUcfvjhrF69mgULFpCVpV1f8eRKz+MRP5R0s22+DIfpEHBNUj8ami7xTIGyBoUlDivzCyl1XNIsk54dM8lMj58rnB3H4bPPPqsIkUuXLsWyLA477LCKENm3b9+gy5QUE4lE+P3vf8/777/Pxx9/zEEHHRR0SVKFDQxzHBb4S9+jIxFyQiHtx0sw7wO3Ags0NF3ihAJllO/WbmHKgjxmL1tHXkER0V8YA8jqkMGIfl04fVAWfbo2/zWSBQUFvPvuu+Tm5jJjxgw2btxI586dGTt2LGPHjuWoo47S0qIE6sorr+TRRx9l2rRpjB07NuhypAY/AgMch1/9UHkvZfv1JPFoaLrECwVKYHVBEROmLmHuig2ETIOIW/OXpPz9w3p3YuIJA+jeoenOIfY8j6VLl1Z0IefNm4fruhx44IEVXciBAwdi6vQLiQOPPvooV1xxBU888QQXX3xx0OVIHWYCx/jdLcN1+dA0OTzooqRRNDRdgpTygfKVhXncNm0pjuvVGiSrCpkGlmlwx7j+nDIwdnvEiouLmT17dkWIXLVqFRkZGYwcOZLs7GzGjBlDt27dYvZ4IrHw73//mxNOOIGrr76aBx98MOhypJ5u9Tzu8oNHR3+s0C4B1ySN5wAPAY/VMjR9H2CCYaBjBiRWUjpQPj77OybNXN7o+7lmVF8uHdFnpz9/zZo1FQHygw8+oKioiJ49e1Z0IQ8//HBatGjR6DpFmsLChQsZPnw4Y8aM4bXXXlPHPIFEgKMiEWb7RzMOcxw+tCziZ7e4NFZ9h6bfB/Ro7uIkqaRsoHxlYR43vLUkZvd3/4kDOLmencpIJMLChQsrQuTixYsJhUIMGTKkIkTus88+mg0pce+HH35g8ODB9OrViw8//JCWLVsGXZI00DpggG2zzp8TeqPnMVHPPUnHBZ6hbGj6d1Dj0PQrDYOL0dB0abiUDJSrC4oY+fAcShx3h/cVr/qStS9PqPbzdjlzEund9qr2femWyawrh9e4p3LTpk3MnDmT3Nxcpk+fzvr16+nQoQOjR49m7NixHH300XTooOEdkjg2btzI0KFDKSkpYf78+XTu3DnokmQnfQIMd11cv7ucA+iSquSloenSFFIyUJ757ALmfZ9f7Z7J8kDZ+jfHkrZr5bE7LXsdRCij+quoQ6bBkF4deeGcQRVvW758ecU52XPnzsVxHPbdd9+KLuTgwYOxLC0uSeIpLS3l6KOP5ssvv+Szzz7TiKokMBm4xr/dxnH40rK0BJoCNDRdYiXlAuV3a7dw1CMf1/j+8kDZ6fgbyNzrtw2+/zsHh/nioxnk5OSwYsUK0tPTOfLIIytG+/TooadoSWye53HWWWfx6quvMmvWLIYNGxZ0SRIDHnB8JMI0fz/lQY7DPMsiPdiypJkUALcAU2oYmm76Q9PvAYY2d3GSEFJum8SUBXmEzPrtD3JLivDcSL3v23MjjH/8TV5//XWOPPJI3nnnHQoKCsjNzeXiiy9WmJSkcMcdd/DCCy/w/PPPK0wmEQN4PhQiy7YB+I9lcXVq9RtSWgfgCeBX02QmMJiyGZblXMNgDvBbz6OT53EtsDWQSiVepVyHcviDs1lVUFTj+8s7lEZaS7zSbWCYpHfvT/sRZ5O+a91Xcu/aKsS8CUfrghpJSs8//zx/+tOfuPfee7nhBo3CTkb/AQZHIth+p/IV4ORAK5KgFAF3A8/UMjT9N/7Q9DHNX57EmZTqUG4tccirJUwCEAqT0W8IHY48j86/u4V2h52JvX4Va6dcT+kv/6vzMX7ZGqGotP5dTZFE8cEHH3Duuedy3nnncf311wddjjSRg4DH/TAJ8GfHYVlw5UiAMoCJwDrD4HPD4EjKzgsv5xkG/0fZBVxtPI/zgQ2BVCrxIKU6lEt/2sTYxz5p8OfZG3/i52cvI717f7qefGedH5972W/pv5uOQJTksXTpUoYOHcrgwYN55513CPsjZiQ5ecAZrstL/l66vWybReEwTXcumCSK8qHpj3seq0FD06VCSnUoS6sZE1Qf4fa70bLPIIrzvqzXnsqdfRyRePTzzz8zZswYevTowWuvvaYwmQIM4GnTpK+/n/LbcJiLXJeU6T5IjSzgOiDPMPjWMDgOSIvuSxkGXxsGZ1A2NP0UYFUglUpzS6lAmWbt/D/XatMJIg6eXdKkjyMST7Zu3Up2djaO45Cbm0ubNm2CLkmaSSbwdjhMi0jZi+h/mSb/CLYkiTP9gLeBbYbBU0Afz4OocFlsGLwK9PQ89vQ8HqdswLokp5RKPj07ZrKzl8o4v/6CYaVhpNV+BKLhP45IootEIpx66qksX76c3Nxcdt9996BLkma2N/CPqP2UF0ciLA6sGolXJnA+sNwwWG0YnAlkVOlafm8YXAa08DzGAl8FUqk0pZQKlJnpFlk1nGRTLlK0aYe3la79nqLvPqdFzwMxjNq/ZFkdM8hM17BySWye53HFFVcwY8YMXnvtNQ444ICgS5KAnApc6IeD0lCI422bHZ8lRcrsDvwLKPS7k/tV6VrahsF0YIDn0c3zuBsoDaZUibGUCpQAI/p1qXUO5fq372fd67ezad6rbFn8LgWz/s4vL16LEU6n/eF/qvW+Q6bBiL5dYlyxSPN75JFHeOKJJ3jyyScZPXp00OVIwB4xDPZ3HABWhcP8SfsppR7+APzXMMj3zwdv60YteBsGPxkGt1C21/Jw4NNAqpRYSblAefqgrGqPXCyX0XcwkaLNbP78bQpm/pWib+eS0XcIu/7pYcKdutd63xHXo8fgrFiXLNKs3nrrLa6++mquv/56zj///KDLkTiQDky1LFr7ofJt0+QvwZYkCSR6aPos6h6afjUamp6IUmpsULnazvLeWZ5pUNyrI+vOGcTISISHQyH2jdm9izSPBQsWcPjhh3Pcccfx0ksvYVZzBJukrneAcf7tkOsy1zQ5NMiCJGGVD01/1vNYBxqangRSMlCuLihi5MNzKInleB/LZM2Vw3H8PZqG63KeYXCnYdA1do8i0mT+97//ceihh9K3b19mzZpFixa1X4Amqek6z+NB/5f/LrbNknCYTgHXJInt/4AbgI88j0g1p8y19jxONgzuBX2vxbGUbD9075DBHeP6x/Q+7xvXnxc7ZNDNn9vmmSZPGwa9HIf7gOKYPppIbBUUFDBmzBjatWvH22+/rTApNZpoGAz1l75/CYc5NRLRKBhplIOBWZSNGbof6F7lQp4thsEzQGfPo7/nMSWgOqV2KRkoAU4ZmMU1o/rG5L6uHdWPUwZmcTKwIhzmPiDDf8ItsixuBHrbNq+ANrJL3CkpKeH4448nPz+f6dOn06mTegBSMwt43bLo4L94nhUKcU+wJUmSqDo0/Xg0ND2RpOSSd7RXFuZx27SlOK7XoD2VIdPAMg3uHNefkwfueCHOOuBWz+Npz8OL2oc20HH4i2Vp35HEBdd1OeOMM3jrrbf48MMPGTJkSNAlSYL4EBjpunimieF5zDQMRgZdlCQdF3gGmOR5fAfVHvXYC7jSv5I8ZbtkcSDlAyWU7amcMHUJc1dsIGQatQbL8vcP692JiScMoHsdcy2/Aq6MRJgVNRwY4CTX5QHTpGcM6hfZWTfffDP33HMPr732GieddFLQ5UiCuRu4xb/d3nFYYll0C7IgSWo/AhOAN12XomouGAx7Hkf5y+bNcVFsYYnDyvxCSh2XNMukZ8fMlJ5DrUAZ5bu1W5iyII/Zy9exKr+o0vsMyoaWj+jbhTMGZ9G7S+sG3fe7wHjbZlnUOcjhSIQrTZMJhkHbGNQv0hDPPvss5557Lg888ADXXntt0OVIAnKB0ZEIM/0XzIc6DnMsC532Lk3tDeAuz+NLqLZruStwoWFwA5AWw8etyAnL1pFXUFRpG5sBZHXIYES/Lpw+KIs+XRuWExKdAmUN+mwpYtUWm/QSm/np4Zi88nCAZ4EbbZuNUcGyvW0zMRzmXMr2kIg0tZkzZzJmzBjOO+88nnzySYxqrqwUqY98YIBt87P/nHZN1FXgIk2tgLIu+RTXZVM1XUvT8xhmGNwDDG3E4zTlSmayUKCswR6lpaxMS6OVbbMlHNvX25uBiZ7HQ66LHbUU3te2eSQcRueSSFNasmQJQ4cOZdiwYfz73//GsvQyRhpnPjDMdXH8X+hvA8cFWZCkpA8oC5fzPQ+vmq5lR+Asf7Zlqwbcb2OvtbhjXH9OqeZai2SjQFmDbqWl/JSWRvvSUgrSYtkw324lcL3r8lqVV1UajC5NZc2aNQwePJjOnTvz8ccf06pVQ55WRWr2KHCFf7uV4/Bfy6JXkAVJyqrP0PSDDIM7qXto+uOzv2PSzOWNrumaUX25dESfRt9PPNMFUTVw/D+bci9QT+BV02QeZVd/l5sVCrGf63KB57G2CR9fUsuWLVvIzs4GICcnR2FSYuoy4HeRCABbLYsTHEfzdyUQGcBEYK1hsNCfPhCK6p15hsEiYCzQxvM4D9hQzf28sjAvJmESYNLM5by6MC8m9xWv1KGsQQd/n2O30lJ+bKIOZTQPeA242rZZE7XEnuE43GJZjAc0alp2luM4jBs3jk8++YRPP/2UAQMGBF2SJKHNwAG2zQ/+c9gFnsfftJ9S4oADPAQ87nmshmov5NkHmGAYnE7tJ+qVrl/Fpk9eovSXFUQKf8UIpxPu2J02g04ko8+gGmtIt0xmXTk8afdUqkNZA9v/M9xMeduAOgejv4wGo0vDeZ7HZZddxvvvv8+bb76pMClNpg3wdjhMmt+pfMowdKqJxIWGDk3PnroEp4b9kpHN63BLt5E54EjajzyPtkNOBmD9m3exZfG7NdbguB4Tpi6J1T8p7qhDWYOWjkOxZdG3tJRlzdChrKqmwei/cRwetSw0flrq68EHH+S6667jmWee4Zxzzgm6HEkB/wTO9m+3iERYFAqxT5AFiVTDBf4BPFBlaHp47RZ2e+TjBt2X50b4+bnxeI5Nt/P/VuvHzrrysAaPHkwE6lDWoPxqxeaPkmW6AH8zDJaYJkf5r/YBFlkWQykbjP5DQLVJ4nj99de57rrruOmmmxQmpdn8GfiTW7ZUWBwKcbxtszXYkkR2YALnAssNg9WGwZlAhuvSakEentmwrRqGGcJq3Qm3pPbv9JBp8OL85NxLqUBZDY/gA2W5/sDMUIgZQD/brnj7G6ZJ30iE6zyPTYFVJ/Fs3rx5nHnmmZx22mncddddQZcjKeYJ02Rvf+vOd+Ew57mutuxI3Nod+BdQaJrssWwdRj3GA7mlxUSKNmFv/JnNn7/Ntu8X0aLH/rV+TsT1mL18XWyKjjNa8q6GzfYgOdi2+SzGcyh3VsVgdMdhY9TswHaOw0TL4jw0GF3KrFixgsGDB9O/f39mzpxJenp60CVJCloOHOg4FPnPV38FLgy0IpHabS1xGHD7e/V68ZP/7uNsLd8zaZhk9D2UDqMvI9Si9gkaBvDV7Ucn3TGN6lBWw466nRZHVyhawAXASsvies8j7C+F/2pZXAz0t21moAt3Ut2GDRsYPXo0nTp1YurUqQqTEpi+wPNRL34vi0RYFFw5InValV9Y79+hbQYeR5dT7qbj2Ctp2es3eJ4LEbvOz/OAlfmFjaozHilQVqM06nZ6NUc5Ba0NcJ9hsDwU4g/u9pEGy8NhxgBHRSIk73VkUpvi4mKOP/54Nm3axPTp0+nQoUPQJUmK+z1wmb8Q5oRCnGDbbAy2JJEalVYzJqgm4Y7dadnzAFoNOJIuJ92GV1rMujfupD4Lvw15nEQRf2kpDsRrh7KqnlQ/GP2DUIj9XZfzNRg9pbiuy1lnncWiRYt455136NVL55RIfJhkGBzsP0etDof5YySilRSJS2nWzseijL2GUvrzdzgFa5r0ceJV8v2LYqBShzKOA2W5Q4EFlsUrQDf/wh3PNPm7YbCH43AvsC3IAqVZTJgwgddff50pU6YwaFDNw3VFmlsa8KZl0dYPlTmhEJOCLUmkWj07ZrKzv/U9uwQAt6T25WzDf5xko0BZjegOZXxcjlO3mgajb7MsJqDB6Mnuqaee4v7772fy5MmceOKJQZcjsoMs4OWo/ZQ3uC5zgytHpFqZ6RZZdZxkEyn8dYe3eRGHwq8+xLDSCXfKqvXzszpmJN0FOaCLgqsV3aEMemxQQ7UArgf+bFmVBqP/FA5zGjBZg9GTzowZM7jkkku49NJLGT9+fNDliNRoNDDB85hoGLimye9smyXhMF2DLkwkytBe7cgrKMSroVeZ/+7jeKVFpHffl1DrjkS2bqTw649w8n+k/RHnYKa1rPG+Q6bBiL5dmqr0QGlsUDWWAvv6t8+mbFRPoloKXBmJ8H4oVOntv3ddHjBN9gimLImRxYsXM2zYMEaMGMHUqVMJVfn/LBJvIsCRjsMcv1s5PBLhg1AIfedK0NasWcOjjz7K31/Loc0pD9T4cYVfz2Hrl+9Tun4l7rYtmGktSdulN61/c2ytZ3mXS9aTchQoq/EFcJB/+0LKZqcluneB8bbNsqiZmlYkwpWmyU2GQdvgSpOd9OOPPzJo0CB23XVX5syZQ2Zm8u3JkeS0Fhhg26z3n49u9jzuSoD96pKc/vvf/zJ58mRefvllMjIyuOCCC/ih51j+s6aQSD0GnNdXyDQY0qsjL5yTnHvctYeyGom4h7IuxwBfhcM8BXTwL9xxQiEeNAx6Og5/pWxwuiSGzZs3M3bsWCzL4p133lGYlITSFXgjHMb0x57dQ9mLXpHm4nkeM2fOZNSoURxwwAHMmTOHBx54gNWrV/PAAw/w0CkDsRp4/GJdLNNg4gkDYnqf8USBshqJvIeyNhZwPvBDOFztYPR9NBg9Idi2zUknncSqVauYPn06u+66a9AliTTYYcC9/pxfzzA4xXFYHWxJkgJKS0t5/vnn2X///Tn66KPJz8/npZdeYsWKFVx55ZW0adMGgO4dMrhjXP+YPvad4/rTvY4LfhKZAmU1krFDGa2mwejfaTB63PM8j4svvpgPP/yQt956i/79Y/uEJ9KcrgHG+i9sN1kWv3OcSi/oRWLl119/5f7772ePPfbgT3/6E1lZWcyePZv/+7//49RTTyVczRHLpwzM4ppRfWPy+NeO6sfJA2u/+jvRKVBWo9Jg88CqaHo90WD0RHPffffxzDPP8Mwzz3DEEUcEXY5Io5jAC6EQu/vbcBZaFtdpW7/E0MqVKxk/fjzdu3fn1ltvZfTo0SxdupScnBwOP/xwjDr27l46og/3nTiAdMsk1MAl8JBpkG6Z3H/iAC4Z0bsx/4yEoEBZjehXyMnYoaxKg9ETw8svv8yECRO47bbbOOuss4IuRyQm2gNTw2Esv1P5F8PgzWBLkiTwf//3f5xyyinsueeevPDCC4wfP55Vq1bxzDPPsM8++zTovk4ZmMWsK4czpFdHgDqDZfn7h/TqyKwrhyd9Z7KcrvKuxlSgfDT0/cB1AdbS3IqBvwB3Og5FUUOId7NtJoXDnAI7fYqA7Ly5c+cycuRITj75ZJ5//vk6X1WLJJq/Ahf7tzMch8WWRZ8gC5KE47ouubm5TJ48mTlz5tCrVy+uuuoq/vSnP8XswsXv1m5hyoI8Zi9fx6r8okrvMygbWj6ibxfOGJyVlKOBaqNAWY1XgVP82w8BVwZYS1DWQaXB6OV+o8HozW7ZsmUMGTKE/fffn3fffZe0tGTeiCGpygNOdV1e9Z9v9rFt/i8cpuYR0SJliouLeeGFF5g8eTLLli1j8ODBXHvttRx33HFNOpt3SonDn/MLMRyX8ZbJrR0zk/IEnPrSknc1kv2inProAvzNMFhimozyl6IAFlkWQ4GTXJcfAqsudaxfv54xY8bQtWtX3nzzTYVJSVoG8Ixp0tvfdvN1OMylURcNilS1YcMG7rrrLnr06MEFF1zAPvvsw6effspnn33GiSee2PQHPaRb2Lu1pTSrPd13a5vSYRIUKKuVrGODdkZ/4L1QiHeBfvb2qP2GadI3EuFaz2NTYNUlt23btjFu3Di2bt3K9OnTad++fdAliTSpVsDb4TAt/Bex/zBNngu0IolH3333HRdffDFZWVnce++9/P73v2fZsmW89dZbDBnSfOtnxVG305vtUeOXAmU11KHc0dFUPxh9kj8Y/Uk0GD2WXNflzDPP5MsvvyQnJ4eePXsGXZJIs+gP/D2qs3ShxpiJb968eZx44on069ePN954gxtvvJG8vDyeeOIJ+vRp/h230YGyRbM/evxRoKyGOpTVq20w+iWU7Xmajgajx8J1113HW2+9xcsvv8zAgQODLkekWZ0BnOdv7y8JhTjettkcbEkSkEgkwptvvsmhhx7K0KFD+eabb3j66afJy8vjlltuoVOnToHVpkBZmQJlNdShrF1tg9HHAiPVUWiUJ554gsmTJ/OXv/yFcePGBV2OSCAeNQwG+PNxvw+HOcd19WI1hRQWFvLEE0/Qt29ffv/735Oens4777zD0qVLOffcc2nRIvgIVxJ1O/hqgqdAWQ11KOunJ2WD0T+j8mD0D/3B6Od5Hr8EVVyCysnJ4fLLL2f8+PFcdtllQZcjEpgWwFTLopX/3PKGafJ4sCVJM/jll1+4+eabycrK4oorruCQQw5h4cKFfPTRR2RnZ2Oa8RNbtIeysvj5PxNH1KFsmMGUDUZ/FSpOvPBMk2cMg14ajF5vixYt4uSTT2bcuHFMmjQp6HJEArcn8ELUPNyrXJcFwZUjTejrr7/m3HPPpUePHjzyyCP88Y9/ZMWKFbz88sscfPDBQZdXLS15V6ZAWQ11KBvOAP5A2bL3/ZQNJgbYZllMAHrbNi8BGgJSvby8PLKzs+nfvz9Tpkxp+nEXIgnieOAqfz+lY5qcaNvkB1qRxIrnecyePZuxY8fSv39/ZsyYwZ133snq1at5+OGH4/5iRAXKyhQoq6EO5c5rQdnJQj9YFhd6Hoa/x/KncJjTKVsa/zTIAuPQpk2bGDNmDC1atOCdd94hIyMj6JJE4sp9hsFg/0XqT+Ewp0UienGawGzbrug8HnHEEaxevZrnn3+eH374geuvvz5hRqRF76HUkrcCZbXUoWy8LsBfqxmM/h/L4rfA712X7wOrLn6Ulpbyu9/9jjVr1jB9+nS6du0adEkicScMvGFZtPe31MwMhbgv2JJkJ2zevJmHHnqI3r17c9ppp9GxY0fee+89/vvf//LHP/4x4Q5uUIeyMgXKaqhDGTs1DUZ/0zTpl+KD0T3P48ILL+Tjjz9m6tSp7L333kGXJBK3ugGvhcMY/vL3za7L7GBLknr68ccfue666+jevTvXX389hx9+OIsXL2bmzJmMGjUKwzCCLnGnKFBWpkBZjehAmVivl+JXrYPRbTslB6Pffffd/POf/+Qf//gHhx9+eNDliMS9kcDtfvjwTJOTbJufgy1JarF48WLOPPNM9thjD55++mkuvPBCfvjhB55//nn233//oMtrtGJv+yArBUoFympFL3mrQxk70YPRb4gejB4Op9xg9BdffJFbb72Vu+66izPOOCPockQSxs3Akf5zR344zEmOk3IvRuOZ53m89957HHXUURx44IF8/PHHPPjgg6xevZr777+f3XffPegSY2ZbVKDUHkoFymqpQ9m02gD3GgbfhUKcnIKD0T/66CPOPvts/vznP3PTTTcFXY5IQjGBl0MhuvorHZ9aFjd7qfAyNL6VlJTw3HPPsd9++3HMMcewceNGXn75Zf73v/8xfvx4WrduHXSJMbct6veXOpQKlNVSh7J59ABe8QejH5Iig9G/+eYbTjjhBIYPH85TTz2VsHuHRILUGXgrHCbk/0K/3zDICbaklLVx40buu+8+9thjD/785z/Ts2dPPvroIxYuXMgpp5yCFTVHNNkUqUNZiQJlNXRRTvMaDMyvZTD6RJJjMPratWsZM2YM3bp144033iAc1neXyM4aAjwYdWrK6Y7DysCqST0rV65k/PjxdO/endtuu42xY8fy9ddf88477zB8+PCUeLFcvocyHImQ/P/auilQVqMk6lWHlrybR22D0W8C9kzwwehFRUUce+yxFBcXM336dNq2bRt0SSIJbzxwvN+l3GxZnOA4lWYDSuwtXLiQk08+mT333JMXXniBq666iry8PP7+97+n3KSK8qu807TlAlCgrFZp1DeHekjNq6bB6D8n8GD0SCTC6aefztdff01ubi5ZWVlBlySSFAzgOdOkh7+ysdiyKk7VkdhxXZdp06YxfPhwDjnkEBYtWsRjjz1GXl4ed955Z8rOz1WgrEyBsholURtt1aEMRjINRr/mmmuYNm0ar7zyCgcddFDQ5YgklbbA2+FwxdSIJw2DV4ItKWls27aNp59+mr333pvjjjsOx3F46623WLZsGRdffDGZmZlBlxio8m54CwVKQIGyWupQxo/6DEb/Naji6uHRRx/lkUce4bHHHiM7OzvockSS0gHAk6FQxd//HInwbWDVJL7169dzxx130KNHDy688EL23XdfPv30Uz799FNOOOEEQlFf61RW4u/h1QU5ZQzPU7Su6sDSUhanpWF4HhHD0GbbOOEA/wButG0Koi5oaWfb3BMOcz5lsy7jxb///W9OOOEErrrqKiZNmhR0OSJJzQP+6Lq86P+S72fbLAqHSe0eWsMsX76chx9+mOeeew7DMDj77LMZP348vXv3Drq0uNQiEqEkFGKv0lK+SbBjI5uCAmU19i0tZWlaGmHXpdRUEzfebAbu9Twmuy521CvlPrbNI+EwoyHwFwELFy5k+PDhjBkzhtdeew1T30ciTa4Q+I1ts8x/wXmG6/Iv0wz8+SCeeZ7Hp59+yqRJk5g2bRqdO3fmsssu46KLLqJjx45Blxe3PCDkeXiGwQGlpXyhQKkl7+qU74uw3ES9pji5RQ9GPyUOB6P/8MMPZGdns//++/PCCy8oTIo0k0zg3+EwLf0pES+aJs8GW1LcikQivPHGGxx66KEMGzaMZcuW8fTTT7Nq1Spuvvlmhck62IDnj0Zqqed4QIGyWuU79Sw1b+NaD+DlZhiMXljisPSnTXyRt5GlP22isKTmg942btzI2LFjadWqFdOmTaNly5YxqEBE6qsf8M+oYdoXRyJ8EVw5cWfr1q089thj9OnTh5NOOomWLVuSk5PD0qVLOffcc2nRQme+1Edx1O2MFJi5WR/xtOUsbpQHyrACZUIoH4z+OnC1bfNjOFw2GB2Y4jjcZFlcBTQk2n23dgtTFuQxe9k68gqKKp0vbgBZHTIY0a8Lpw/Kok/XsiPFSktLOfHEE1m7di2fffYZnTt3jtU/UUQa4GTgY8/jScPADoU4wbb5bzhMKk9//fnnn3n88cf561//yubNmznppJN47bXXOPjgg4MuLSFFzztVh7KM9lBWo0tpKevT0uhaWsov2heRUIqBR4E7HYfCqC7FrrbNg+Ewp1J7W351QRETpi5h7ooNhEyDiFvzj0f5+4f17sQ9x+/LzVdexKuvvsqsWbMYNmxYrP5JIrITSoBDHYcv/OeB41yXqSm4n3Lp0qVMnjyZKVOmkJaWxnnnnccVV1xBjx49gi4toa0GyicK/x54PcBa4oUCZTU62DYbw2F2Ly1ltQJlQloH3OZ5POV5eFGvHg9yHB61LIZW8zmvLMzjtmlLcVyv1iBZVcg0wI2wbvrjPH3Dnzj11FMb/w8QkUZbBeznOGz2Q+Vk4KpAK2oenucxe/ZsJk2axIwZM+jWrRuXX345559/Pu3atQu6vKTwHdDXv30G8EKAtcQL9WmrYfv7IbTknbjqHIweiVQajP747O+44a0llDhug8IkQMT1cDyDjmMuJ38XLR+JxIsewEtRKxXXuS7zgiunydm2zZQpU/jNb37DkUceyZo1a/jXv/7F999/z3XXXacwGUPReyi167SMAmU1HD9QpmmjbcKrNBg96sKdN0Mh+kUiXON5/GNhHpNmLm/U4xj+98qkmct5dWFeo+5LRGJnLHC93xyImCYn2jbrgy0p5jZv3szkyZPp1asXZ5xxBp07d2bmzJksXryYM888kzSttMVc9B5KDTYvo4tyqlHeodSPYPI4GvjKsioNRndCIf5SUMRu05ZWu69qQ87DFH71QY332e2S57Bad9rh7bdOW8qQPTvRvUNGzOoXkZ13t2HwqePwiWWxNhzm1EiE90IhEv28l9WrV/Poo4/y9NNPs23bNk477TSuuuoq9ttvv6BLS3rqUO5IgbIKj7JXsaAOZbKxgPOBU8Jh7vM8Jrku7acugRqWuFsfeAwteh5Q5a0eBe89gdW2a7VhEsBxPSZMXcIL5wyKZfkispMs4DXLYoBtkx8O80EoxF2ex+0J+hz/xRdfMHnyZF599VUyMzO56KKLuOyyy+jWrVvQpaUMBcodKVBWYUfdVocyObUBJhoGR28o4qwVG2r8uPRue5Pebe9KbytevRTPLiFzn8Nr/LyI6zF3xQZWrNtC7y6tY1S1iDTGrsAb4TBHuC6eaXInMBQ4KuC66svzPN59910mT57MBx98QI8ePZg0aRJnn302rVvreaa5KVDuSHsoq6gUKDVbKqnNXpBXdoV2AxR+PQcwyNxneK0fFzINXpyvvZQi8eRw4B7/ed0zDE52HH4MtKK6lZSU8M9//pMBAwYwZswYNm3axCuvvMKKFSu44oorFCYDoj2UO1JiqqI06nZ6gi6HSP3MXrauQVd0exGHom8/IX33vbHada31YyOux+zl6xpboojE2PXAMf7kh42Wxe8dp1IjIV4UFBRw77330rNnT84++2x69erFnDlz+Pzzzzn55JOxLC0wBkkdyh0pUFYR/cSiQJm8tpY45BUUNehztv3wH9xtm2td7o6Wl19U6zGNItL8TODFUIjd7LJn+wWWxQ1xNCLu+++/5/LLL6d79+7ccccdHHvssXzzzTdMmzaNww47rGKihARLgXJHeolTRXSHUhflJK9V+YU09FdI4ddzwLTI2Pu39fp4D1iZX0j/3VL5wDeR+NMRmBoOM9R1cUyThwyDYcDx1XxsYYnDyvxCSh2XNMukZ8dMMtNj/6tzwYIFTJ48mTfffJP27dtzzTXXcMkll9ClS5eYP5Y0ngLljhQoq4juUIYDq0KaWqnjNujj3dJtbPtuPi33OJBQyzZN9jgi0jwOAR42TS7z/36m47DYstgT+G7tFqYsyGP2snXkFRRVevFpAFkdMhjRrwunD8qiT9ed38Poui7vvPMOkyZN4pNPPqF37948/vjjnHXWWWRkaOxYPNMeyh0pUFZRqUMZWBXS1NKshu32KFo+v+zq7v6HN+njiEjzuQSY47q8YZpstSyOW7+Z/aZ9w7wVGwiZRrV7rD1gVUERLyxYxXOfrWRY705MPGFAg+bObtu2jX/961889NBDLF++nKFDhzJ16lSOPfZYQqFEn46ZGtSh3JF+21WhDmVq6Nkxs9ph5jUp/PojjLSWtOxT/9mShv84IhKfDOAfpkkv26bVwjw2P/opn32fD1DnBXvl75/3fT4jH57DK/U4IWv9+vXcfvvtZGVlcfHFF7Pffvvx2Wef8cknn3D88ccrTCYQBcodqUNZhTqUqSEz3SKrQwar6nFhTqRoE8UrF5O592GY4fo/dWR1zGiSvVYiEjutgVM/WcmLM5fjQYP3Vkdcj4jrccNbS9iwtYRLR/TZ4WOWLVvGww8/zPPPP49pmpx99tmMHz+ePffcMxb/BAmAAuWO1KGsQh3K1DGiX5d6zaEs/OZjcCMNWu4OmQYj+mozvUi8e2VhHi/OXA7QoFWL6kyauZxX/U6l53nMnTuX4447jr333pu3336bm2++mby8PB577DGFyQSnPZQ7UvukCp2UkzpOH5TFc5+trPPjCpd+hJnRrppjGGsWcT3OGJy188WJSJNbXVDEbdOW1vh+u2ANv859kZIfv8bdtpVQm85k7jOcNoNOqHG14tZpS/l12ef847EH+fzzz9l777155plnOO2002jRQr2sZKEO5Y4UKKuIXvJWhzK59enammG9OzHv+/xa90vt+sfJDbrfkGkwpFdHHbsoEucmTF2CU8PPvrN5Pb88fxVGeiatD8rGbNmakjXfsumTKZT+soIuv7+l2s8rKbW5Necb+mdmkpubyzHHHIOpU9eSjgLljhQoq1CHMrVMPGEAIx+e06ATc+pimQYTTxgQs/sTkdj7bu0W5q7YUOP7C7+ajVtSyK5nPEBa5x4AtD7gGPBcCr/6kEjxVkItWu34iWaIlnscxNOPjteLyiSmQLkjvWyqQh3K1NK9QwZ3jOsf0/u8c1z/Bo0QEZHmN2VBXq17qN3Ssgv2QpntKr091KoDGCaGWXM/JmQavDi/7qu+JXGVRJ2upD2UZRQoq1CHMvWcMjCLa0b1jcl9XTuqHycP1N5JkXg3e9m6WlcmWmSVrTLkT3+U0rXf42xeT+E3H7Pli+m0/s2xmGk196Uirsfs5etiXrPEj6KoQKkOZRkteVehDmVqunREHzq1Sue2aUtx/DEg9eWZRtky97j+CpMiCWBriUNeHSPDWvb6DW2HncHmz17n5xULKt7eZsjJtD/szDofIy+/iMISR6PDktQ21wV/b6wCZRl9p1ehsUGp65SBWQzdsxMTpi5hbi0nZZQzTQPX9Sju1ZHScXszqnP9j2QUkeCsyi+s17xJq21X0rv3J6PfEEIt21D0v4Vsnvcaocx2tPnNsbV+rgeszC+k/25tY1KzxJdtWvLegQJlFRpsntq6d8jghXMGbT/Ld/k68vKrOcu3YwYj+nbhy0O6M3WXsiB5r+fxgNHYSXYi0tRKHbfOjyn8eg4F7z7Obuc/hdWmEwAZ/YaA5/HrR8+Ruc9wQi1rfxFZn8eRxFTsB8qw62LoKn5AgXIH6lAKlI0Uun1cf26nP4UlDivzCyl1XNIsk54dMyuWsVYBOZEIdijEI67LpaEQWvQWiW9pVt0BYMt/ppPWtVdFmCyX0fsQCpfMonTt97SsYzZtfR5HEtM2/8+0qKXvVKevQhXqUEpVmekW/Xdry4FZ7em/W9tKe6J6AFf4TyZ2KMQtrjoSIvGuZ8fMOk/FiRT9iuft+PPsuZGyG+V/1sDwH0eSU/nYoDQvdiPnEp0CZRXqUEpDTTAM2jgOAC8YBv8NuB4RqV1mukVWHaO9wu13o3Tt/7AL1lR6e+HXc8AwCXfuWevnZ3XM0AU5Say8+dRCgbKCAmUV6lBKQ7UHbrPKfnF4hsE1kdo7FyISvBH9utQ6h7LNoN+B6/LLi9fz66cvs+U/uax97Ta2fTefVvuNxGrdscbPDZkGI/p2aYqyJU6U+PvllRO2U6CsQh1K2RmXALvbZd89s0Ih3g+2HBGpw+mDsuqYQ7kvu5z5IGm77MnW/0ynYNbfcX79hXaH/ZEOR19S631HXI8zBms3dTIr1cigHagfX4U6lLIz0oH7w2FO9/9+lW3z33BYr9hE4lSfrq0Z1rsT877PrzFYpu/Wj65/uKNB9xsyDYb06qhjF5OYx/ZA2TLYUuKKft9VoQ6l7KxTgP38vZRfhcO8FGw5IlKHiScMwKpl2XtnWKbBxBMGxPQ+Jb44lG1vAmipK7wr6CtRhTqUsrNM4CFre9P/etuuuBJQROJP9w4Z3DGuf0zv885x/elexwU/ktiin9dbavZwBQXKKtShlMY4EjjKvyjnp3CYx4MtR0TqcMrALC4f1RegXqfn1ObaUf10/GoKqBQo1aGsoK9EFdGBUh1K2RmTQiEMf5TEnY5DQcD1iEjt1hzem/wTB+BZJjRwCTxkGqRbJvefOIBLRvRuogolnqhDWT0Fyiqil7zVoZSdsR/wRz9QbrEsJmpOmUjc+gJ4xPPYOjCL9Zf/lt/0KhsHVNtIoej3D+nVkVlXDldnMoWURN3WVd7b6SrvKtShlFi4yzR5ORKhNBTiL/6RjD2DLkpEKokA5zgOrr/3+ebOrbnpnEF8t3YLUxbkMXv5OvLyiyothRuUDS0f0bcLZwzO0tXcKSi6Q5keWBXxx/A8tU+i/QF43b+9CnQus+y0GzyP+/3lkNNclynaayMSVx4DLvdv97VtloTDOzQSCkscVuYXUuq4pFkmPTtm6gScFPd/wED/9iWgvfI+/YarQhflSKzcaBi09ccIvWSafBFwPSKy3Y/ADf7PJ8Cz1YRJKDumsf9ubTkwqz39d2urMCmVOpRa8t5OgbKKkqiGrZa8pTHaAndEjRG6KhJp9FWkIhIbl0UiFPk/n+d6Hr8NuB5JHNpDWT0FyipKXbfitjqU0lgXAt39Ixk/CoWYGWw5IgJMA94OhQDoYNs8oCt1pQG0h7J6CpRVqEMpsZQOPBDe/tLkKtsmElw5IilvC3CBvX1z0+PhMO2DK0cSkJa8q6dAWUVpVKBUh1Ji4Q/AAf5era/DYV4MthyRlHaL5/GL/yLvyEiEUwKuRxKPAmX1FCirKO9Qmp5HKOBaJDlUPZLxBttmW3DliKSsRcCj/nN8WiTCU6EQWuyWhtIeyuopUFZRvhASitpLKdJYI4DR/pGMv4TDPBZsOSIpxwHOdhw8f3zXHaEQewZbkiQo7aGsngJlFeWvPMIazykx9kAohOG/ULnLccgPuB6RVPI48KW/UrCXbXN1sOVIAtOSd/UUKKso71BaCpQSY/sCf/avJt1qWdyt7zGRZrEauDGy/XK4Z8Nh7ZGXnaZAWT0FyirKA6U6lNIU7jQM0v1fbI97Hj8EXI9IKrgkEqHYHxN0gecxJOB6JLFpD2X1FCirqAiUgVYhyaobcI3/i80xTW7UXl2RJjUVeMf/metk29ynmZPSSNpDWT0Fyioc/8lGHUppKtcB7fwxQq+aJv8XbDkiSWszcFHUzMknwmHaBVaNJAsteVdPgbIKuzxQ6lWsNJE2wJ3RRzI6jo5kFGkCN3sea/2Zk6MiEU4KuB5JDgqU1VOgrKK8Q6lTcqQpXQD08Dsncy2LGcGWI5J0FlJ2ZTdAeiTC3zRzUmIkeg+llry3U6CswlaglGaQBjyoIxlFmkTFzEn/+fyuUIg9gi1Jkog6lNVToIziAq4/9FZL3tLUfg8c5O+lXBYO83yw5YgkjUeBr/xtJfvYNuMDrUaSTXHUNRYKlNspUEaxo26nK1BKEzOAh6P2Uk6wbYqCK0ckKawCbvJHcxmexz80c1JibJsCZbUUKKNEB8o0BUppBocB2f4vv7XhMH8JthyRhOYBF0XNnLwIGBRoRZKMtkWNe9Meyu0UKKOURt1uoUApzST6SMa7HYf1AdcjkqjeBGb4YbKzbTNRz+PSBIqiOpQKlNspUEZRh1KCsDdwrv/9VmRZ3KUZqCINtgm4OGrm5JPhMG2DK0eSWPkeyrDrKkRF0dciSnSHUoFSmtMdhkELf+n7Sc9jRcD1iCSaCZ7Hen9ywphIhN8FXI8kr23+n2k66awSBcoo0R1KbeKW5rQrcK2/VBfRkYwiDTIf+Kt/u0UkwpOaOSlNqHwOZZpWkypRoIxSqUMZWBWSqq4F2vtjhN4wTRYEW45IQrCBc2y7Yubk3aEQPYItSZJceaBMV6CsRIEyijqUEqTWwN1RY4Su1pGMInV6BPjaX+re13G4ItBqJBWU+C9edEFOZQqUUdShlKCdB+zhX1jwqWWRE2w5InHtB+CW8pmTrss/LAur9k8RabRS/wAUzaCsTIEyijqUErQwMCnqSMZrbBsnuHJE4pYHXBCJUOLvPb7UMBgYbEmSAjzALg+Uuni3EgXKKJXGBgVWhaS6E4BD/L2Uy8Nhngu0GpH49Drwvh8mu9o2d+uXuzQDB3D977WWwZYSdxQoo0QveatDKUExgIeqHMlYGFw5InHnV+CSqJmTfw2HaRNYNZJKiqNuZ5iKUNH01YiiDqXEi6HAcf7ooPXhMA8HW45IXLnB89jgbw05NhLhhIDrkdQRHShbKlBWoq9GFHUoJZ7cb5qYfqic6DisC7gekXgwD3jKX3JsEYnwhL/sLdIcSqJuaw9lZQqUUXRRjsSTfsB5/hPWNsviDs08kxRXPnOy3L2hEN2DK0dSUHSHUld5V6ZAGUVjgyTe3G4YtPAv0HnK81gecD0iQZoMfOsvde/vOFwWbDmSghQoa6ZAGUUdSok3uwA3+BfoREyTG3Qko6So/wG3Rc2cfNay0GK3NDcFypopUEZRh1Li0dVAR3+Zb6pp8lmw5Yg0u/KZk6X+fsnLDYPfBFuSpKjoPZQ6KacyBcoo6lBKPGoF3BM17FxHMkqqeQX4wA+Tu2rmpARIHcqaKVBGUYdS4tU5wJ5+l/Izy2JasOWINJsC4NKoC3H+Fg7TKrhyJMUpUNZMgTKKOpQSryxgcnSXUkcySoq43vMo8L/3j3NdxgVcj6Q2BcqaKVBGUYdS4tk44FD/iu//hcM8G2w5Ik3uE+AZf3k7w3F4QoOkJWDaQ1kz/XRGUYdS4lnVIxlvsm22BleOSJMqpfLMyfssi27BlSMCqENZGwXKKOpQSrwbDJzojw7KD4eZHGw5Ik3mQWC5v9R9oONwcbDliAAKlLVRoIyiDqUkgvtMk5AfKu9zHH4JuB6RWFsB3OHPnDRdl39o5qTECQXKmilQRokOlOpQSrzqA1zg7ysrtixu15GMkkQ84LxIBNsfEzTeMDgg0IpEttMeypopUEaJXvJWh1Li2W2GQUv/Ap2/ex7fBlyPSKxMAT7yw+Ruts2dmjkpcUQdypopUEZRh1ISRRdggn+BjmuaXO8vD4oksnzgMmf7QKynwmEygytHZAcKlDVToIyiDqUkkiuBzv5VsNNCIT4NthyRRrvWdfnVf6F0ouuSHXA9IlUpUNZMgTKKLsqRRJIJTIwadn6ljmSUBDYH+Kc/ZzLTcXhMMyclDmkPZc30ExtFY4Mk0fwJ6Ot3KRdaFlMDrUZk55RQeebkA5bFbsGVI1IjdShrpkAZxY66WlYdSkkEVY9kvMa2K3XaRRLB/ZSd/gTwG8fhgmDLEamRAmXNFCijlEQFSnUoJVGMBX7rX8jwQzjM34MtR6RBlgN3aeakJIjiqJygQFmZAmWUUnUoJQEZwOSoIxlvdhy2BFeOSL15wHmOg+OPCbraMNgv2JJEahUdKLWHsjIFyijF6lBKgjoE+L1/es5Gy+LBYMsRqZd/AR/7L4Z2t21u18xJiXNF/vMsqENZlQJlFO2hlER2n2li+U92D0Yi/BRwPSK12QCMj5o5+XQ4TEZw5YjUS5E6lDVSoIxSvofSdF19YSTh7AlcVH4kYyjEbTqSUeLY1VEzJ09yXUYHXI9IfZSvZIaVE3agr0eU8rFBln4RS4K6xTDI9Ls+z3oe3wRcj0h1ZgP/8udMtnIcHtXMSUkQ5Vd5h6OWvqWMfoqjlAfKsAKlJKjOwE1+18czTa7TkYwSZ4qBc6NmTk6yLHYJrhyRBikPlOnKCTtQoIxS/hSnDqUksiuArv4v7JxQiI+DLUekknuB7/2Zk4Mch/OCLUekQcpPylGg3JECZZTy7eHqUEoiywDu1ZGMEoe+BSb6S4Uh1+UZy9IvIUkopf4+dV2QsyP9LEepWPIOtAqRxvsjsJffpfyPZfFGsOWI4ALnOg6Ov1/yWsNg32BLEmmwUv/7VyODdqRAGcXxX3moQymJLkTlIxmvte1KZ9WLNLfngE/9/b1Zts2tmjkpCcZDgbI2CpRR7PJAqSc6SQKjgcP8K75XhcM8FWw5ksLWUbb1otzfw2FaBleOyE5xANfPBy2VE3agQBmlokMZcB0isVD1SMZbbZtNwZUjKexK12Wz/714iusyKuB6RHZGSdTtDI262oG+IlHK9/Zos60ki4Mp+wUO8Gs4zAPBliMpaBbwkv/c2tpxeES/iCVBFUfdbqHv4x3oK+KLsL2VnaZWtiSRiVFHMk6ORFgTcD2SOrYB50XNnHzIsugaXDkijRIdKLXkvSMFSp8ddTtd3yiSRPYALvW/p0tCIW7VCQ/STO72PFb6F4cd6jicHXA9Io1RqUMZWBXxS4HSFx0o1aGUZHOzYdDKvyjin8BXwZYjKWAp8IA/McPSzElJAtF7KBUod6Sfb1/0SBV1KCXZdARuiTqS8VodyShNyAXOi5o5eb1hsE+wJYk0WnSHUtda7EiB0qcOpSS7y4Bd/f1s74ZCzA62HElizwKf+S9geto2N+k5VZKAlrxrp0Dpi+5QKlBKMmpJ5SMZr3IctJtSYm0tcHXUzMlnNHNSkoQCZe0UKH3RHUrNoZRkdQawj9+lXGxZvBZsOZKExrsuW/zu5Omuy5EB1yMSK9pDWTsFSl+lDmVgVYg0rRDwUFSX8jrbrvQkKdIY7wGv+Psm2zoOD2tWnyQR7aGsnX7afepQSqoYBYzwL8pZHQ7z12DLkSRRROWZkw9bFp2DK0ck5rTkXTsFSl+li3ICq0Kk6RnA5FCo4u+3Ow6/BlaNJIs7PY/Vfvd7qOPwp2DLEYk5BcraKVD6ope81aGUZHcgcJo/4HyTZXGfPy9QZGcsASaVz5yMRHjGstCljZJstIeydgqUPnUoJdVMNE0sf+n7YddldcD1SGJygXMdh4i/X/KmUIi9gi1JpEloD2XtFCh96lBKqukBXOGHgNJQiFt0JKPshKeBz/2runvZNjcEW45Ik9GSd+0UKH26KEdS0U2GQRt/ZuC/DIMvA65HEsvPwLVVZk7qF60kKwXK2ilQ+jQ2SFJRe+DW8iMZDYNrdCSjNMAVrstW//vnLNdlRMD1iDQl7aGsnQKlTx1KSVWXALv5417eD4WYFWw5kiBmAK/7WybaOQ6TNHNSkpz2UNZOzwA+dSglVbUA7teRjNIAhVSeOfkXy6JTcOWINAsteddOgdKnDqWkstOAff2AsMSyeDnYciTO3eF5rPFfhBzmOJwZcD0izUGBsnYKlD51KCWVmcDDUV3K62270pOnSLn/ApP9mZPhSIS/a+akpIjoPZRa8t6RAqVPHUpJdSOBkf5FOWvCYZ4MthyJQxHgHMfB9fdL3hIK0TfYkkSaTXHUARDqUO5IgdKnDqUITAqFMPwnzTsch40B1yPx5SlgkX9Vd2/b5rpgyxFpVtsUKGulQOlTh1IE9gfO9J80N1sWE3Uko/h+Aq6Lmjn5bDisZT9JKUVRhz8oUO5IgdKnDqVImbtNk7C/9P0X12VVwPVIfLjMdSn0u5Nnuy6HBVyPSHOLXvLWi6kdKVD61KEUKdMduNLfI2eHQtykIxlTXg7wlv890d62eVAzJyUFlS95W66r8FQNfU180YFSHUpJdTcaBm395c2XDIMvAq5HgrMVuCBq5uSj4TAdgitHJDDb/D/T9CK7WgqUvuglb3UoJdW1A27TkYwC3OZ5/OSPlBoRiXB6wPWIBKV8bFC69pZXS4HSpw6lSGUXA7v7nakPQyFmBluOBOAL4JGomZNPh0KaOSkpqzxQpilQVkuB0qcOpUhl6cAD0Ucy2raOZEwhEeDsqJmTt4VC9A62JJFAlRhlL6d0QU71FCh96lCK7OhkYH9/L+XScJgpwZYjzehJYLG/7aGvbXNtsOWIBK7Uf3GlkUHVU6D0qUMpsiMTeNgPFaAjGVPFj8D1VWZO6oW2pLryQNky4DrilQKlT2ODRKo3Ajjavyjn53CYx4ItR5rBpZEI2/wXEud5Hr8NuB6RoDmA6y95t9DYrGrpq+LTYHORmk0KhTD8URl3Og75AdcjTeffwL9DIQA62Db3G7oMRyR6ZaalfiaqpUDps6Ou2lKHUqSyfYE/+be3Whb36CrHpLQFuDBq5uTj4TDtgytHJG5EB8oMdSirpa+KryTqF6Q6lCI7utM0SfOXvh9zXX4IuB6JvVs8j1/8K/tHRiKcEnA9IvFCHcq6KVD6StShFKnV7sBV/itzJxRigk6LSCqLgEf958G0SISnNHNSpEJJ1G2NDaqeAqVPHUqRut1gGLTzr/59xTRZFHA9EhsOZTMnPf8Fwx2hEL2CLUkkrkR3KDU2qHoKlL5SdShF6tQWuCNqjNBVjoN2Uya+x4Ev/f+ve9k2VwdbjkjcUaCsmwKlrzxQhlxXyzwitbgQyPIv3PjYsng32HKkkfKAG6POav9HOKwX1SJVKFDWTYHSVz42yNLVqyK1SgMejDqS8WrbJlLzh0sc84CLIxGK/TFBF3gehwZbkkhc0h7KuilQ+soHZShQitTtJOAgfy/lN+EwLwRbjuykt4FcP0x2sm3u09WrItVSh7JuCpS+8g5lWIFSpE4G8FDUXsobbJttwZUjO2EzcFHUzMknwmHaBVaNSHxToKybAqWv/NRaBUqR+hkOjPX33q0Nh/lLsOVIA93keaz1ty6MikQ4KeB6ROKZAmXdFCh9FR3KQKsQSSwPRB3JeLfjsCHgeqR+FgJP+LfTNXNSpE7aQ1k3BUqf4+8dUodSpP72Ac72f3YKLYu79PMT9xzgbNvG8/+/3RUK0TPQikTinzqUdVOg9NnlgVKb0kUa5E7DIN1f+n7S8/hfwPVI7f4CfOUvdfe3bcYHWo1IYlCgrJsCpa+8Q6lTckQaZjfgWv9KYcc0uVFHMsatVcDNfvg3PI9nNXNSpF4UKOumQOlz/CPHFChFGu5aoL1/xfDrpsnCYMuRanjARVEzJy8CBgVakUji0B7KuilQAhGo2E+UpiVvkQZrA9wVNexcRzLGnzeBGX6Y7GLbTNRznUi9qUNZNwVKtl/hDZCuJ1mRnXI+sIffpfzEspgebDkSZRNwcdTMySfDYdoGV45IwlGgrJsCJdtPyQF1KEV2VpjKRzJeZdsV810lWDd6Huv9/zdjIhFODLgekUSjQFk3BUqqdChNfUlEdtaJwED/SMbl4TDPB1uOAPOBv/m3WzgOf9XMSZEG0x7Kuik9oQ6lSKxUPZJxgm1TGFw5Kc8Gznacij3i91gWWcGWJJKQ1KGsmwIllTuUuspbpHF+Cxzrj6ZZFw7zSKDVpLaHgW/8gD/Acbg82HJEEpYCZd0UKKncodRMNpHGeyAUwvTnUU50HNYFXE8q+gG4tXzmpOvyD8vCqv1TRKQG26Lm6ypQVk+BEnUoRWJtL+Bcf5m1yLK4U0cyNisPuCASocQfE3SpYXBwsCWJJLToQKk9lNVToEQdSpGmcIdh0MK/QOdvnsd3AdeTSl4D3vfDZFfb5h7tDRdplG1RL4oVKKunQEmVi3ICq0IkuewCXO/v34uYJjf6y6/StH4FLomaOfm3cJjWgVUjkhzKA6XluoQCriVeKVBSeclbHUqR2Lka6OiHmzdDIRYEW05KuN7zyPdnTh4biXB8sOWIJIVt/p9pUUvfUpkCJepQijSV1sDdOpKx2cwDnvaXt1s6Dk+E1EsRiYXyOZRp2g9eIwVK1KEUaUrnAHv6Xcp5lsU7wZaTtGzgnKil7nsti+7BlSOSVMoDZboCZY0UKNFFOSJNKQxMiupSXq0jGZvEJOBb/+u8v+NwabDliCSVEr/zrwtyaqZAicYGiTS144BB/hXfK8Jh/hFsOUnnf8DtVWZOarFbJHZK/UCpGZQ1U6BEHUqRplb1SMabbJutwZWTVDzg/EiEUn+/5BWGwUHBliSSdErNsrikQFkzBUrUoRRpDkOA4/0rJDeEwzwUbDlJ42XgQz9M7mrb3KWZkyIx5QCuHyhb6uerRgqUqEMp0lzuN82KIxnvjURYG3A9ia4AuCzqQpynwmFaBVeOSFKKPse7panYVBN9ZVCHUqS59AUu8F/hF4dC3KErJhvlOs+jwL8Q53jX5diA6xFJRiVRtzMUKGukrwzqUIo0p9sMg5b+BTpPeR7LAq4nUc0FnvXDeYbj8Lh+0Yk0iegOZQsteddIz0CoQynSnLoCN/oX6LimyQ06krHBSqk8c/J+y6JbcOWIJLVKgTKwKuKfAiXqUIo0t6uATn4gejsUYl6w5SScB4Dv/KXugxyHi4ItRySpKVDWjwIl6lCKNLdMYGLUsPMrdSRjvX0H3Ol3dU3X5VnNnBRpUtF7KBUoa6ZAiTqUIkH4M9DH71J+blm8HWg1iaF85qTtjwm60jA4INCKRJJfdIdSJ+XUTIGSyoFSHUqR5mFR+UjGa2y70s+i7OhF4CM/THazbe7QBQIiTU5L3vWjQEnlJW91KEWaz7HAEP+K7+/DYZ4Jtpy4lg9c7mw/Bf3pcJjM4MoRSRkKlPWjQIk6lCJBqXok4822zZbgyolr17ouv/pfq9+5LmMCrkckVWgPZf0oUKIOpUiQBlEWkAAKwmEmBVtOXJoD/NOfM5npODyqmZMizUZ7KOtHz0roohyRoN1nmoT8UPmA4/BzwPXEkxIqz5x80LLYLbhyRFKOlrzrR4ESjQ0SCVpv4KLyIxkti9t1JGOF+4D/+RcvHew4XBBsOSIpR4GyfhQoUYdSJB7cahhk+BedPON5fBNwPfFgGXC3P3My5M+c1JO2SPPSHsr60XMT6lCKxIPOwE1RRzJen+JHMnrAeY6D448Jutow2C/YkkRSkvZQ1o8CJWBHLa+pQykSnPFAF3+/4DuhEHMDrSZYzwNz/YC9u21zm2ZOigRCS971o0AJFEcFSnUoRYKTgY5kBNgAjI+aOfn3cJiM4MoRSWkKlPWjQAmUqkMpEjfOAvr5XcpFlsWbwZYTiKtdl01+d/IPrssxAdcjksq0h7J+FCiBEn9cCahDKRI0C5gc1aW81rYr7XNOdh8C//LnTLZ2HP6imZMigdIeyvrRMxWVL8qxavwoEWkuY4Bh/pLvynCYp4Mtp9kUA+dGzZycZFnsElw5IoKWvOtLgZLtS96W66Jt7yLBM4DJUUcy3mrbbA6unGZzL/CD350d5DicG2w5IoICZX0pULK9Q2lpmLJI3BhI2f5BgI3hMA8GW06T+waY6P97Q67LM5o5KRIXovdQasm7Znq+YvtgcytqL6WIBO9e06z4uXwwEuGngOtpKi5wruPg+PslrzMM9g22JBHxbYvKBupQ1kyBku0dSl3hLRJfegGX+PMXS0Ihbk3SVYTngHn+En+WbXOLZk6KxI0iBcp6UaAEyqe9hZP0l5VIIrvFMGjlX6DzD89jacD1xNo6yuZtlnsmHKZlcOWISBXborKBlrxrpkAJlPrdAF3hLRJ/OrL9SEbPNLkuyY5kvNJ12ez/+051XY4KuB4Rqaz88JOQ6xIKuJZ4pkBJVIcy0CpEpCZXALv443Smh0J8FGg1sfM+8JK/b7KN4/CIZk6KxJ1t/p9pus6iVnr2Amy/Q6mh5iLxqSVwb5UjGRP9qX0bcF7UzMnJlkWX4MoRkRqUjw1K17a4WilQAhG/K6BAKRK/zgT29gPYYsvi9WDLabS7PY9Vfkge4jicHXA9IlK98rFBCpS1S/lA6QF2eaDUlZUicSsEPBTVpbwugY9kXArcH3Wgwt81c1IkbpVqFbNeUv45LHp7v75ZROLb0cDh/kU5eeEwfwu2nJ1SPnOyfGXkesNgn2BLEpFalPiBUiODapfygTK6w5GuDqVIXDOAyaHt11ne6jhsCq6cnfIsMN+/qrunbXOznndE4lqp/+JP47xql/KB0o66naYrLEXi3kGUjdcB2GRZ3JdA+5p+Aa6uMnNSXQ+R+OUAbnmg1Iu/WqV8glKHUiTxTDRNLH/p+yHX5ceA66mv8a7LFr87eYbrcmTA9YhI7aLP8W6hplOtUv6rU6lDqUApkhB6Apf7T+6loRC3JMB8uPeAV/2a2zoOD+mXk0jcK466naGf2Vql/FcnukOpi3JEEsdNhkFrf/n4ecNgScD11KaIyjMnH7YsOgdXjojUU3Sg1JJ37VI+UEZ3KHVSjkji6ADcUn4ko2FwTRwfyXin57HaH3n0W8fhT8GWIyL1FB0otd+5dgqUUbfVoRRJLJcBu/mdv5mhEB8EW061lgCTymdORiL83bJQn0MkMUTvoUwPrIrEkPKBMnrJWx1KkcTSArgvatj5VXF2JKMLnBM1c/KmUIi9gi1JRBpAHcr6S/lAqQ6lSGI7Hejv76X80rJ4NdhyKnkaWOgvy/eybW4MthwRaSAFyvpL+UCpDqVIYjMpu8il3HW2XWmZKig/A9dGzZx8NhzWkplIglGgrL+UD5S6KEck8R0FHOlflPNjOMyTwZYDwOWuy1Y/6J7luhwebDkishO0h7L+Uj5QamyQSHKYFAph+Be/3O44bAywlunAG/6+yXaOw2TNrxNJSOpQ1l/KP8upQymSHA4ATvcD5WbL4t6AjmQsBM6Pmjn5F8uiYyCViEhjKVDWX8oHSnUoRZLHPaZJ2F/6fsR1yQughts9jzX+lefDHYczA6hBRGJDgbL+Uj5QqkMpkjyygCv85WU7FOLmZj6S8b/AQ35nNByJ8LRmTookNO2hrL+UD5TqUIoklwmGQRv/6uoXDYPFzfS4EeBsx8H1A+0toRB9m+mxRaRpqENZfykfKNWhFEku7YHbAjiS8W/Af/zH7WPbXNcsjyoiTUmBsv5SPlCqQymSfC4BdvcvjPkgFOL9Jn68n4DromZOPqOZkyJJQYGy/lI+UKpDKZJ80oH7o49ktO0mPZLxUtelyO9Onu26HNaEjyUizUd7KOsv5QOlOpQiyekUYD+/a/hVOMxLTfQ47wBT/X2T7R2HBzVzUiRpqENZfyn/zKcOpUhyqnok4/W2XemXQyxsBS6Mmjn5mGXRIcaPISLBUaCsPwXKqNvqUIoklyOAUf5FOT+Fwzwe4/u/1fP4yV9aPyIS4bQY37+IBEuBsv5SPlBGL3mrQymSfB6MOpLxTsehIEb3+wXwiH+/aZEIT4dCmjkpkmS0h7L+Uj5QqkMpktz2A/7oB78tlsU9MTiSsXzmpOfvl7wtFGLPRt+riMQbdSjrL+UDpTqUIsnvLtMkzV/6ftR1WdnI+3sCWOzvz+xn21zTyPsTkfi0Leq0LQXK2qV8oNRFOSLJrztwpd9NdEIhJjTiSMYfgRuiZk4+Gw5rdUMkSRVFrWgoUNYu5QNlUYlD+KdNpOVt5MefNlFY4tT9SSKScG40DNr6QfBl0+SLnbyfSyIRtvndyfM8j6Exqk9E4k9x1ItP7aGsneF5MdhQlGC+W7uFKQvymL1sHasKiiq9zwCyOmQwol8XTh+URZ+urYMpUkRi7i/AeP/24ZEIHzbwQpq3gRP82x1tm+/CYdrHsD4RiS/7lZayJC2NkOviaMZsrVIqUK4uKGLC1CXMXbGBkGkQcWv+p5e/f1jvTkw8YQDdO2Q0Y6Ui0hRKKTtnO88f9fMucHTU+wtLHFbmF1LquKRZJj07ZpKZXtaN3AL0tW1+8T/3ZcqGp4tI8upTWsqKtDRaOk7FaVhSvZQJlK8szOO2aUtxXK/WIFlVyDSwTIM7xvXnlIFZTVihiDSHV9keBPexbd4sKOYVf8Uir6CI6GeH6BWLVYd057ld2gAwMhJhpsYEiSS9rNJSVqel0c622RjWlRa1SYlA+fjs75g0c3mj7+eaUX25dESfGFQkIkFxgYMdhyWbS+kwdQkt67FiYZoGruuxrXcnto7bh686t2aP5itZRALStbSUdWlpdCktZW2aLr+rTdJvCHhlYV5MwiTApJnLeXVhXkzuS0SCYQLHffETuz48hxbf5wPUuWrh+u9v8X0+uzz6CQv0PCCSEkqMsnUIXZBTt6TuUK4uKGLkw3MocaofEVLyywo2ffISJT9+jefYWO260uqAY2hz8Lga7zPdMpl15XDtqRRJUFqxEJH6auk4FFsWfUpLWa4OZa2SukM5YeoSnBo6D9t++A+/vHANkaJNtB1yCu1HnkfL3ocQ2bKh1vt0XI8JU5c0Rbki0sS0YiEiDWH7V3a3DLiORJC0lyx9t3YLc1dUHw7dkiI25DxEyz0H0vmEGzGM+ufqiOsxd8UGVqzbQu8uGikkkihWFxRx27Sl1b7PLd3G5gVvUfLTMkp/Xo5bvJWOY8bTar+Rtd7nrdOWMmTPTlqxEElCDhDxA2ULQ5fg1SVpO5RTFuQRMqv/Bij8+iPcwl9pf9gfMQwTt7QYz6v/yRkh0+DF+epMiCSS2lYs3KLNbPr0Zez81YS71P9yG61YiCSvkqjbLTWDsk5J26GcvWxdjRvti1cuxkjPwNmaz7q37sYpWIMRbkHmviPocOR5GFbt+yQirsfs5eu4nf5NUbqIxFhtKxYAoVYd2P3SFwi1ak/Jz9/xy/NX1ut+tWIhkryKo25nqENZp6QMlFtLHPKqnIATzS74CdwI69+8i1b7jaLF8LMozlvClkXv4BYX0vm46+p8jFX5Rdxe4pCebhGirNUb6z+b4j6r+1M/JpLsylcsanqRaVhhQq127syb8hWL28fpBaZIMlGHsmGSMlCuyi+ktkvXPbsYzy6h1YGj6XDUBQBk9BuCF7HZuvhd7GGnE+7Qrc7HmZhfiL1b2xhVHSzTdctCrOdhAobnlYXN8j+BkP++ir+zYzgNRf/dMLb/3TCwyv8sf3vUn80ZoIMM7w19TD2FxUZtKxaNpRULkeQU3aHU2KC6JWWgLK1hTFC58iXtzL2HV3p75j6Hs3Xxu5Ss+bZegdKo43ESiWuaJM+/JrmYnofpeTuG/J0I+xVvKw/4VA72IcAyjEovABIxrEc/dmmJw6paVixiIS+/iMISp+KYRhFJfNGBskVgVSSOpHz2S7Nq7+uEWnXE3pBHKLNd5bdnlnUb3eKt9Xqcv1gmu1J28kakif/c6c/1PBzPIwJEavrT/7jy2xV/Nwxczyu7L8OoqKP8vj3DKPtY/33lf/cMo+xt2nMSE9FfSzvgWhJROL+Q3Zr4MTxgZX4h/ZNkxUJEFCgbKikDZc+OmRhQ47J32i57UrzyC5wt+YQ77l7xdmdLAQChjLp/KRjAmR0zyWx8uU3LMMr+C8jOhuHmCOmBP6bn4fh/RqJuV7yN7aG//HOqC/w7hH3DwKNy6E/lsN9cKwkD7QiZpaV0ArqGQuwSCtEZ6Ax08v+M/ntHkvQJWCRJRO+hVKCsW1I+n2WmW2R1yKhxmStzr2Fsnv8GW7+cScue+1e8feuXM8EMkZ41oM7HyOqYoeWteihfdtRXqhrloS6gcFceOpM6tAMFlsmcWH3RauGEQ2xIS2MD8G09Pt7wPFo7Dh08j66myS6hEF0Mo9rwWX5bw5VFmo/2UDZM0v6eH9GvCy8sWFXtRvy0XfYkc7+jKPzyfda7Li2y9qU4bwlF335Cm0NPwmrdsdb7DpkGI/p2aarSRZqFQRI/AUQp7JjJvtS8YhErvVuHyS8tZaNlVZyuURvPMNgcDrMZWFnPx2jhOHRwXToDu1oWnU2zxvDZGWiLpjiI7CwteTdM0v4+OX1QFs99trLG93c8+hKsNp3Z+uUsipZ/htW2M+2PPI82A4+r874jrscZg7NiWK2INJW6VixioUfHDOa0LjstxwO2AOuBDf6fVW+vc11+iURY53kUmCZFVv2eiosti5+An4D/1uPjQ65LO8ehE7BLKETXqGX4qgG0k/9f0v5SEGkgBcqGSdrnjj5dWzOsdyfmfZ9fbZfSCFm0++1ptPvtaQ2635BpMKRXRw0xFkkgta1YlNvsz6GNbC3bS71txec4W8qGobf5zbGYLarfMV11xcIA2vj/7VnTg5lm2X++YiCf7YGzagBd73n8Eomw1nXJNww2WRZePbZKREyT/LQ08oFldX50mda2TUfPo4thsItl0cUwatwH2hnQoZOSrLSHsmGSNlACTDxhACMfnhPT+XOWaTDxhLr3WIpI/KhrxQJg84KpRDavq/h70fJ5sHweAK36j6gxUMZixaIF0M3/r1qGAVFdzAiwkRrCp//3tZEIv0QirId6L8MDbAmH2UIDluEjETpEImVdUMuiq2nWug+0HVqGl8SgPZQNk9SBsnuHDO4Y158b3ordWbt3jutP9w56TS6SSOpasQDY/eJ/NPh+g1qxCLF9iXrvGj8oVPYfZcvwW6k5fK4H1nkevzhOxTJ8YX2X4UMhfgqF+An4sj61uy5tIxE6R12M1MnvglbXCe0IhOtViUhsacm7YZI6UAKcMjCLDVtLmDRzeaPv69pR/Th5oPZOiiSiVF6xMIDW/n+9avwgA8Lbo1sJZWGzpn2g6z2vrAsatQxfn3FUEdOkwDQpoP7L8K0ch46uS1fDoGvUMnxNS/FxP85NEoICZcMkfaAEuHREHzq1Sue2aUtxXK9Bv1BCpoFlGtw5rr/CpEgC04pFw6TTsGV4l8rL8NV1Q9dFLcMXhELYfge1Llsti63AqvrWXs0yfG37QNuhY05lR1tLHML5hRiOywbLpLBjpsYF1sLwPK+pp2nEjdUFRUyYuoS5KzYQMo1ag2X5+4f17sTEEwYk7S8NkVTz+OzvYrZiccmI3jGoKDV5QCG17wNd53n87C/DbzRNttZzGb6hzKir4atbhq/uingtwyen79ZuYcqCPGYvW7fDZAgDyOqQwYh+XTh9UBZ9uuri3GgpFSjLVXzDLF9HXn5Rpfl0BmVDy0f07cIZg7N0NbdIEnplYZ5WLBJQKduDZ7VL8VFXw29owDL8zmjlzwTt6l8N37mOAJqJLkaKZ2o4NV5KBspohSUOK/MLKXVc0iyTnmppi6QE/QJJfuXL8DVdiFQxE9RxKpbhS+u5DN9Qaf4yfGega9QyfE1L8e3RMnxzaewLzDvG9ecUvcBUoBSR1KYVCynnAUXUvg90vX81/Fr/avimXIZvG4nQKepq+M61HM3ZCUhrkkqSW6y2wFwzqi+XjugTg4oSlwKliIhPKxbSUDbVL8NX/D16GR741bJw6zkTtKFaOQ7to5bhq54NXzWMpvoy/CsL82J6kd79Jw5I6a0wCpQiIiLNxAV+pfajOde6LmujluFLmmgZPhy1DL+LZdGllrPhOwEdSJ5l+NUFRYx8eA4ljlvp7SU/L6dwyQcU5y3B2bQWs2Ub0nfrR7vDziTcocaZBwCkWyazrhyesltiFChFRETiWCG17wONXobPNwy2hpvmGnTT82jrOHTyPLpELcPXNpIpXpfhz3x2QbUHHayfOpGSH78hY6/fEu7Sk8jWjWz5Tw5eaTG7/HESaZ171nif5QcdvHDOoCauPj4pUIqIiCQRm8pnw+8QRv1l+F9cl3zKluEjTbQMn+lfDd+lhmX4qmG0FU2/DP/d2i0c9cjH1b6v+MdvSN+1N0Zoeyi3C9bw07OXkrnXUDode02d9z/rysNScr+1NgeJiIgkkTCwi/9ftaoMpfeofhk++u9r/avhN1C2DF9cz2X4QsuiEFhd39ojEdpHLcNXPRu+ahhtT9lRpA0xZUFejZMdWuy+42Gm4Q7dSOuUhb2h7n9FyDR4cX4et4/r38CqEp8CpYiISAozKAtm7YG+NX2QaULa9gXs8qvha9oHus7zWBu1DL+lnsvwdijEulCIdcDSeny86Xm0cRw6eh67mCZdo5bha1qKn71sXYPGA3meR6ToV8Kd6r7gJuJ6zF6+jttRoBQRERGpVQbQw/+vWlXOhreBAmreB7oBypbhI5GKq+HrswzvGga/hsP8CvyvHnUbJQ7dC4oatKxeuPQjIlvyaffb0+v18Xn5RRSWOCk3ISK1/rUiIiLS7MJAV/+/GoVCZf9Rtgy/iTqO5nRdfi6/Gt40Ka7HTFArv7BBYdLOX03B+38lvdteZA44sl6f4wEr8wvpv1vbBjxS4lOgFBERkbhiAO38/2ocF15lGX4bte8DXed55BWXUlDPGiJbN7Lu9Tsw0zPpdPyNGGb9d2uWVhlHlAoUKEVERCThtQSy/P+qZRgsbZHG2Hrcl1tcyNrXbsMtLqTrGfdjte7YoFrSrGSZ2Fl/qfcvFhERkZTUs2NmnUvenlPKujfuxNm4hi4n3UpaPS7GiWb4j5NqFChFREQkJWSmW2TVcpKN50ZY//b9lPz0LZ2Pv4H0bjuOEapLVseMlLsgB7TkLSIiIilkRL8uvLBgVbWjgzZ++CzbViygZe9DiGzbytavZld6f6t9R9R63yHTYETfLjGtN1EoUIqIiEjKOH1QFs99trLa95Wu/R6AbSs+Z9uKz3d4f12BMuJ6nDG4YUvkyUKBUkRERFJGn66tGda7U7Vnee9y+n07fb/lZ3mn4rGLoD2UIiIikmImnjAAy4ztqeGWaTDxhAExvc9EokApIiIiKaV7hwzuiPF523eO60/3Wi74SXYKlCIiIpJyThmYxTWjajy9vEGuHdWPkwem5t7JcobnefU/IV1EREQkibyyMI/bpi3Fcb1qr/yuScg0sEyDO8f1T/kwCQqUIiIikuJWFxQxYeoS5q7YQMg0ag2W5e8f1rsTE08YkNLL3NEUKEVERESA79ZuYcqCPGYvX0defhHRAcmgbGj5iL5dOGNwVspezV0TBUoRERGRKgpLHFbmF1LquKRZJj07ZqbkCTj1pUApIiIiIo2iq7xFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFEUKEVERESkURQoRURERKRRFChFREREpFH+H2bryD2/onYkAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 40\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "# G.add_nodes_from([1, 2, 3, 4, 5])\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])\n", + "\n", + "\n", + "\n", + "edgelist = [(1, 2), (2, 3), (3, 4), (4, 5), (6, 1), (6, 5), (7, 5), (7, 4), (8, 4), (8, 3),(1, 7),(1, 8)]\n", + "# Add edges to the graph\n", + "G.add_edges_from(edgelist)\n", + "circuit = [(2, 3), (3, 4), (8, 4), (3, 4),(1, 8),(1, 7),(7, 5), (6, 5),(6, 1),(1, 2)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=circuit, edge_color='cyan',width=2)\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3e04a076-c98a-42f9-8eeb-d4f298c39d51", + "metadata": {}, + "source": [ + " a circuit is a closed walk within a graph that includes at least one edge and where no edge is repeated. From the graph above, an example of a Circuit would be $2 \\to 3 \\to 4 \\to 8 \\to 1 \\to 7 \\to 5 \\to 6 \\to 1 \\to 2$." + ] + }, + { + "cell_type": "markdown", + "id": "ec52d13d-e9da-40c0-bb88-0f1da198b789", + "metadata": {}, + "source": [ + "$\\textbf{12. Simple Circuit}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "69c26767-b6c9-45bb-90ec-0cd959eaa367", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 40\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "# G.add_nodes_from([1, 2, 3, 4, 5])\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8])\n", + "\n", + "\n", + "\n", + "edgelist = [(1, 2), (2, 3), (3, 4), (4, 5), (6, 1), (6, 5), (7, 5), (7, 4), (8, 4), (8, 3)]\n", + "# Add edges to the graph\n", + "G.add_edges_from(edgelist)\n", + "simple_circuit = [(7, 4), (3, 4), (2, 3), (1, 2),(6, 1), (6, 5),(7, 5)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=simple_circuit, edge_color='cyan',width=2)\n", + "# Display the plot\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "36bb5b1d-1d58-4c87-b586-a49febbaeb23", + "metadata": {}, + "source": [ + "a Simple circuit is a circuit that does not have any other repeated except the first and the last. From the graph above, an example of a Simple Circuit would be $7 \\to 4 \\to 3 \\to 2 \\to 1 \\to 6 \\to 5 \\to 7$." + ] + }, + { + "cell_type": "markdown", + "id": "383fb36e-84a3-4c72-a3fc-ec71475579c7", + "metadata": {}, + "source": [ + "$\\textbf{13. Connected Graphs}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "2d7be238-2384-4802-aa64-f3ab0ee4660d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 40\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4])\n", + "\n", + "# Add edges to the graph\n", + "G.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 1), (2, 4), (1, 3)])\n", + "\n", + "# Draw the graph\n", + "nx.draw(G, with_labels=True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a2b26715-1db2-4208-96ad-8cb257429ecd", + "metadata": {}, + "source": [ + " In graph theory, a \"connected graph\" is a graph in which there is a path between every pair of vertices. In other words, for any two vertices in a connected graph, there exists at least one path that connects them. From the graph above, as you noticed I run out of ideas on making a graph." + ] + }, + { + "cell_type": "markdown", + "id": "e5dd889c-2d78-4758-98ba-e5a7009bdf82", + "metadata": {}, + "source": [ + "$\\textbf{14. Euler's Circuit}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "a10a60a0-33ce-4bc5-b243-991e5faeba74", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "seed = 46\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6])\n", + "\n", + "# Add edges to the graph\n", + "edgelist = [(1,2),(2,3),(3,4),(4,5),(5,6),(6,1),(6,2),(6,4),(2,4)]\n", + "G.add_edges_from(edgelist)\n", + "eulers_circuit = [(5,6),(6,1),(1,2),(6,2),(6,4),(2,4),(2,3),(3,4),(4,5)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=eulers_circuit, edge_color='cyan',width=2)\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ac32831-f38e-4104-a35e-caa9a54703aa", + "metadata": {}, + "source": [ + "Euler's circuit, also known as an Eulerian circuit, is a type of circuit in graph theory that traverses every edge of a graph exactly once and ends at the starting vertex. In simpler terms, it's a closed walk that covers all edges of the graph, visiting each edge exactly once, and returning to the starting vertex. From the graph above, an example of a Euler's Circuit would be $5 \\to 6 \\to 1 \\to 2 \\to 6 \\to 4 \\to 2 \\to 3 \\to 4 \\to 5$." + ] + }, + { + "cell_type": "markdown", + "id": "b684eedc-bc08-4710-93a5-bf9a15e72888", + "metadata": {}, + "source": [ + "$\\textbf{15. Euler's Trail}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "4315fa62-19a9-4c1b-b600-8170cbd6d2c6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6])\n", + "\n", + "# Add edges to the graph\n", + "edgelist = [(1,2),(2,3),(3,1),(3,4),(4,5),(5,3),(6,3)]\n", + "G.add_edges_from(edgelist)\n", + "eulers_trail = [(5,3),(4,5),(3,4),(2,3),(1,2),(3,1),(6,3)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=eulers_trail, edge_color='cyan',width=2)\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2eb0185d-a688-4c14-ab51-3f83d809c8d2", + "metadata": {}, + "source": [ + "Euler's trail, also known as an Eulerian trail, is a type of walk in graph theory that traverses every edge of a graph exactly once. Unlike Euler's circuit, which forms a closed loop by returning to the starting vertex, Euler's trail may start and end at different vertices, but it still covers each edge exactly once. From the graph above, an example of a Euler's Trail would be $3 \\to 5 \\to 4 \\to 3 \\to 2 \\to 1 \\to 3 \\to 6$." + ] + }, + { + "cell_type": "markdown", + "id": "8a3777bb-107e-43e2-bbc6-012a16d504cc", + "metadata": {}, + "source": [ + "$\\textbf{16. Hamiltonian Circuit}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "id": "dddf2929-7f85-45a8-9376-3a6479f08139", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "# Create an empty undirected graph\n", + "G = nx.Graph()\n", + "\n", + "# Add nodes to the graph\n", + "G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12])\n", + "\n", + "# Add edges to the graph\n", + "edgelist = [(1, 2), (2, 3), (3, 4), (1, 5),(5, 6),(2,6),(6, 7),(3,7),(7, 8),(4,8),(5, 9),(9,10),(6,10),(10,11),(7,11),(11,12),(8,12)]\n", + "G.add_edges_from(edgelist)\n", + "hamiltonian_circuit = [ (1, 5),(5, 9),(9,10),(6,10),(6, 7),(7,11),(11,12),(8,12),(4,8), (3, 4),(2, 3),(1, 2)]\n", + "\n", + "# Draw the graph\n", + "pos = nx.spring_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True)\n", + "\n", + "# Draw the edges in the walk with red color\n", + "nx.draw_networkx_edges(G, pos=pos, edgelist=hamiltonian_circuit, edge_color='cyan',width=2)\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5bbdd1b9-0c05-4efb-94be-0cab0c20223e", + "metadata": {}, + "source": [ + "In graph theory, a \"Hamiltonian circuit\" is a type of circuit that visits every vertex in a graph exactly once and returns to the starting vertex. In simpler terms, it's a closed loop within a graph that passes through each vertex exactly once. From the graph above, an example of a Hamiltonian Circuit would be $1 \\to 5 \\to 9 \\to 10 \\to 6 \\to 7 \\to 11 \\to 12 \\to 8 \\to 4 \\to 3 \\to 2 \\to 1$." + ] + }, + { + "cell_type": "markdown", + "id": "695f28d5-ff4e-44f4-bd1f-dcdfa32f3ca1", + "metadata": {}, + "source": [ + "$\\textbf{17. Travelling Salesman problem}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "id": "b6840907-84fb-498a-993f-102472aafe9f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "\n", + "node_names = [\"A\", \"B\", \"C\", \"D\"]\n", + "edges = [('A', 'B', {'weight': 30}),\n", + " ('A', 'C', {'weight': 50}),\n", + " ('A', 'D', {'weight': 40}),\n", + " ('B', 'C', {'weight': 30}),\n", + " ('B', 'D', {'weight': 35}),\n", + " ('C', 'D', {'weight': 25})]\n", + "\n", + "routes = [\n", + " ['A', 'B', 'C', 'D', 'A'],\n", + " ['A', 'B', 'D', 'C', 'A'],\n", + " ['A', 'C', 'B', 'D', 'A'],\n", + " ['A', 'C', 'D', 'B', 'A'],\n", + " ['A', 'D', 'B', 'C', 'A']\n", + "]\n", + "\n", + "fig, axs = plt.subplots(1, 5, figsize=(20, 4))\n", + "\n", + "for i, ax in enumerate(axs):\n", + " G = nx.Graph()\n", + " G.add_nodes_from(node_names)\n", + " G.add_edges_from(edges)\n", + " pos = nx.planar_layout(G)\n", + "\n", + " nx.draw_networkx_edge_labels(\n", + " G, pos,\n", + " edge_labels={edge[:2]: str(edge[2]['weight']) for edge in edges},\n", + " font_color='red', ax=ax\n", + " )\n", + "\n", + " nx.draw(G, pos=pos, with_labels=True, node_size=700, ax=ax)\n", + "\n", + " # Highlighting the specified route\n", + " for j in range(len(routes[i]) - 1):\n", + " nx.draw_networkx_edges(\n", + " G, pos, edgelist=[(routes[i][j], routes[i][j + 1])],\n", + " edge_color='cyan', width=2, ax=ax\n", + " )\n", + "\n", + " # Calculating the weight of the route\n", + " weight = sum(G[routes[i][j]][routes[i][j + 1]]['weight'] for j in range(len(routes[i]) - 1))\n", + " ax.set_title('Route {}'.format(i + 1))\n", + " ax.text(0.5, -0.15, 'Weight: {}'.format(weight), horizontalalignment='center', verticalalignment='center',\n", + " transform=ax.transAxes)\n", + "\n", + "# Adjust layout\n", + "plt.tight_layout()\n", + "plt.gcf().canvas.manager.set_window_title(\"TRAVELLING SALESMAN PROBLEM\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "1265e139-afbc-44a6-87e8-5874a8e548ed", + "metadata": {}, + "source": [ + "As you can see from the five possible routes of the graph. The best possible and shortest path are:\n", + "\n", + "Route 1: $A \\to B \\to C \\to D \\to A$.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "id": "909812ff-8f1d-45c2-8eca-361987840014", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "\n", + "# Define the nodes and edges\n", + "nodes = ['A', 'B', 'C', 'D', 'E', 'F']\n", + "\n", + "edge_labels = {\n", + " ('A', 'B'): 10,\n", + " ('A', 'C'): 20,\n", + " ('A', 'D'): 30,\n", + " ('A', 'E'): 40,\n", + " ('A', 'F'): 50,\n", + " ('B', 'C'): 60,\n", + " ('B', 'D'): 70,\n", + " ('B', 'E'): 80,\n", + " ('B', 'F'): 90,\n", + " ('C', 'D'): 100,\n", + " ('C', 'E'): 110,\n", + " ('C', 'F'): 120,\n", + " ('D', 'E'): 130,\n", + " ('D', 'F'): 140,\n", + " ('E', 'F'): 150,\n", + "}\n", + "\n", + "# Convert edge labels to the desired format\n", + "formatted_edge_labels = {edge: \"{}\".format(weight) for edge, weight in edge_labels.items()}\n", + "\n", + "# Define Hamilton circuits\n", + "hamilton_circuits = [\n", + " ['A', 'B', 'C', 'D', 'E', 'F', 'A'],\n", + " ['A', 'B', 'D', 'F', 'C', 'E', 'A'],\n", + " ['A', 'C', 'E', 'F', 'B', 'D', 'A'],\n", + " ['A', 'D', 'F', 'C', 'B', 'E', 'A'],\n", + " ['A', 'E', 'F', 'D', 'C', 'B', 'A']\n", + "]\n", + "\n", + "# Plotting\n", + "fig, axs = plt.subplots(1, 5, figsize=(20, 4))\n", + "\n", + "for i in range(5):\n", + " G = nx.Graph()\n", + " G.add_nodes_from(nodes)\n", + "\n", + " # Add edges with formatted labels\n", + " for edge, label in formatted_edge_labels.items():\n", + " G.add_edge(edge[0], edge[1], weight=edge_labels[edge])\n", + "\n", + " pos = nx.circular_layout(G)\n", + "\n", + " nx.draw_networkx_edge_labels(\n", + " G, pos,\n", + " edge_labels=formatted_edge_labels,\n", + " font_color='red', ax=axs[i]\n", + " )\n", + "\n", + " nx.draw(G, pos=pos, with_labels=True, node_size=700, ax=axs[i])\n", + "\n", + " # Highlighting the specified Hamilton circuit\n", + " for j in range(len(hamilton_circuits[i]) - 1):\n", + " nx.draw_networkx_edges(\n", + " G, pos, edgelist=[(hamilton_circuits[i][j], hamilton_circuits[i][j + 1])],\n", + " edge_color='cyan', width=2, ax=axs[i]\n", + " )\n", + "\n", + " # Calculating and displaying the weight of the route\n", + " weight = sum(G[hamilton_circuits[i][j]][hamilton_circuits[i][j + 1]]['weight'] for j in range(len(hamilton_circuits[i]) - 1))\n", + " axs[i].set_title('Route {}'.format(i + 1))\n", + " axs[i].text(0.5, -0.15, 'Weight: {}'.format(weight), horizontalalignment='center', verticalalignment='center',\n", + " transform=axs[i].transAxes)\n", + "\n", + "# Adjust layout\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "43da6699-73ae-427d-b7c2-5feb9059f348", + "metadata": {}, + "source": [ + "As you can see from the five possible routes of the graph. The best possible and shortest path are:\n", + "\n", + "Route 3: $A \\to C \\to E \\to F \\to B \\to D \\to A$.\n", + "\n", + "Route 4: $A \\to E \\to B \\to C \\to F \\to D \\to A$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a79b413c-c199-4f56-bdcf-2a3e15dd623c", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Detablan_AllLectures_ANSWERS/Detablan_LECTURE4_Answers.ipynb b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE4_Answers.ipynb new file mode 100644 index 0000000..2f44447 --- /dev/null +++ b/Detablan_AllLectures_ANSWERS/Detablan_LECTURE4_Answers.ipynb @@ -0,0 +1,498 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bf11225b-2b3b-42e7-937e-5e7bc68b99cd", + "metadata": {}, + "source": [ + "**Name:** Paul France M. Detablan\n", + "\n", + "**Program and Year:** BSCS - 1\n", + "\n", + "$\\textbf{Assignment}$\n", + "-\n", + "Read about (Susanna Epp pp. 704):\n", + "1. Kruskal's Algorithm\n", + "2. Prim's Algorithm\n", + "3. Djitraka's Shortest Path Algorithm\n", + "\n", + "Given the following graph, implement the algorithm in Python." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "6587fe71-ad98-4c57-b47c-9a2d5fd308dc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "seed = 55\n", + "# Use seed for reproducibility\n", + "G = nx.Graph()\n", + "plt.figure(figsize=(10, 8))\n", + "# Add nodes\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\"])\n", + "# Add self-loops to the remaining nodes\n", + "edgelist = [(\"A\",\"C\"),(\"A\",\"I\"),(\"C\",\"B\"),(\"C\",\"E\"),(\"C\",\"D\"),(\"B\",\"E\"),(\"I\",\"E\"),(\"E\",\"F\"),(\"F\",\"G\"),(\"G\",\"E\")]\n", + "G.add_edges_from(edgelist)\n", + "pos = nx.planar_layout(G) # Seed for reproducible layout\n", + "nx.draw_networkx_edge_labels(\n", + " G, pos,\n", + " edge_labels={(\"A\",\"C\"):10,(\"A\",\"I\"):5,(\"C\",\"B\"):20,(\"C\",\"E\"):15,(\"C\",\"D\"):30,(\"B\",\"E\"):25,(\"I\",\"E\"):40,(\"E\",\"F\"):35,(\"F\",\"G\"):50,(\"G\",\"E\"):45},\n", + " font_color='red'\n", + ")\n", + "nx.draw(G, pos=pos,with_labels=True)\n", + "nx.draw(\n", + " G, pos, edge_color='black', width=1, linewidths=1,\n", + " node_size=500, node_color='pink', alpha=0.9,\n", + " with_labels=True)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "4fbd4175-929d-460e-be74-a766b8dadfe8", + "metadata": {}, + "source": [ + "$\\textbf{Kruskal's Algorithm}$\n", + "-\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "0c51b50f-1522-4b08-bf90-6741b14c5b85", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def kruskal_algorithm(G):\n", + " # Initialize the minimum spanning tree\n", + " MST = nx.Graph()\n", + " # Sort edges by weight\n", + " sorted_edges = sorted(G.edges(data=True), key=lambda x: x[2]['weight'])\n", + " # Create a disjoint set data structure\n", + " disjoint_set = {node: {node} for node in G.nodes()}\n", + " \n", + " # Iterate through the sorted edges\n", + " for u, v, data in sorted_edges:\n", + " if find(disjoint_set, u) != find(disjoint_set, v):\n", + " # Add the edge to the minimum spanning tree\n", + " MST.add_edge(u, v, **data)\n", + " # Merge the sets containing u and v\n", + " union(disjoint_set, u, v)\n", + " \n", + " return MST\n", + "\n", + "def find(disjoint_set, node):\n", + " return next(iter([k for k, v in disjoint_set.items() if node in v]))\n", + "\n", + "def union(disjoint_set, u, v):\n", + " root_u = find(disjoint_set, u)\n", + " root_v = find(disjoint_set, v)\n", + " if root_u != root_v:\n", + " disjoint_set[root_u].update(disjoint_set[root_v])\n", + " del disjoint_set[root_v]\n", + "\n", + "# Define the graph\n", + "G = nx.Graph()\n", + "plt.figure(figsize=(10, 8))\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"I\"])\n", + "edgelist = [(\"A\", \"C\", 10), (\"A\", \"I\", 5), (\"C\", \"B\", 20), (\"C\", \"E\", 15), (\"C\", \"D\", 30), (\"B\", \"E\", 25), (\"I\", \"E\", 40), (\"E\", \"F\", 35), (\"F\", \"G\", 50), (\"G\", \"E\", 45)]\n", + "G.add_weighted_edges_from(edgelist)\n", + "\n", + "# Run Kruskal's algorithm\n", + "MST = kruskal_algorithm(G)\n", + "\n", + "# Draw the original graph\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos, with_labels=True, node_size=700, node_color='#66ff99',\n", + " font_size=12, font_weight='bold', edge_color='gray', width=2)\n", + "\n", + "# Draw the minimum spanning tree\n", + "nx.draw_networkx_edges(MST, pos=pos, edge_color='cyan', width=4)\n", + "\n", + "# Display edge labels\n", + "edge_labels = nx.get_edge_attributes(G, 'weight')\n", + "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels, font_color='red')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "052971b0-8776-4128-9b2b-e75d34876224", + "metadata": {}, + "source": [ + "$\\textbf{Solution}$\n", + "-\n", + "\n", + "| Iteration Number | Edge Considered | Weight | Action Taken |\n", + "| :-: | :-: | :-: | :-: |\n", + "| 1 | (A, I) | 5 | added |\n", + "| 2 | (A, C) | 10 | added |\n", + "| 3 | (C, E) | 15 | added |\n", + "| 4 | (B, C) | 20 | added |\n", + "| 5 | (B, E) | 25 | not added |\n", + "| 6 | (C, D) | 30 | added |\n", + "| 7 | (E, F) | 35 | added |\n", + "| 8 | (E, I) | 40 | not added |\n", + "| 9 | (E, G) | 45 | added |\n", + "| 10 | (F, G) | 50 | not added |" + ] + }, + { + "cell_type": "markdown", + "id": "f5f1ce93-ba81-4612-a894-176c5cf1474b", + "metadata": {}, + "source": [ + "$\\textbf{Prim's Algorithm}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7aac0dbe-79a4-46bd-8a69-a2140516b4d9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def prim(graph):\n", + " # Create a copy of the graph to work with\n", + " mst = nx.Graph(graph)\n", + " \n", + " # Initialize the minimum spanning tree\n", + " MST = nx.Graph()\n", + " \n", + " # Select an arbitrary starting node\n", + " start_node = 'I'\n", + " \n", + " # Initialize set of visited nodes\n", + " visited = {start_node}\n", + " \n", + " # Iterate until all nodes are visited\n", + " while len(visited) < len(mst.nodes()):\n", + " # Find the minimum weight edge connecting a visited node to an unvisited node\n", + " min_edge = None\n", + " min_weight = float('inf')\n", + " for u in visited:\n", + " for v in mst.neighbors(u):\n", + " if v not in visited and mst[u][v]['weight'] < min_weight:\n", + " min_edge = (u, v)\n", + " min_weight = mst[u][v]['weight']\n", + " \n", + " # Add the selected edge to the minimum spanning tree\n", + " u, v = min_edge\n", + " MST.add_edge(u, v, weight=min_weight)\n", + " \n", + " # Mark the newly visited node\n", + " visited.add(v)\n", + " \n", + " return MST\n", + "\n", + "# Define the graph\n", + "G = nx.Graph()\n", + "plt.figure(figsize=(10, 8))\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"I\"])\n", + "edgelist = [(\"A\", \"C\", 10), (\"A\", \"I\", 5), (\"C\", \"B\", 20), (\"C\", \"E\", 15), (\"C\", \"D\", 30), (\"B\", \"E\", 25), (\"I\", \"E\", 40), (\"E\", \"F\", 35), (\"F\", \"G\", 50), (\"G\", \"E\", 45)]\n", + "G.add_weighted_edges_from(edgelist)\n", + "\n", + "# Run Prim's algorithm\n", + "MST = prim(G)\n", + "\n", + "# Draw the original graph\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos, with_labels=True, node_size=700, node_color='#66ff99', font_size=12, font_weight='bold', edge_color='gray', width=2)\n", + "\n", + "# Draw the minimum spanning tree\n", + "nx.draw_networkx_edges(MST, pos=pos, edge_color='cyan', width=4)\n", + "\n", + "# Display edge labels\n", + "edge_labels = nx.get_edge_attributes(G, 'weight')\n", + "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels, font_color='red')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "3ead08c3-e4c5-401b-933f-31f925565a2d", + "metadata": {}, + "source": [ + "$\\textbf{Solution}$\n", + "-\n", + "\n", + "| Iteration Number | Vertex Added | Edge Added | Weight |\n", + "| :-: | :-: | :-: | :-: |\n", + "| 0 | I | | |\n", + "| 1 | A | (I, A) | 5 |\n", + "| 2 | C | (A, C) | 10 |\n", + "| 3 | E | (C, E) | 15 |\n", + "| 4 | B | (C, B) | 20 |\n", + "| 5 | D | (C, D) | 30 |\n", + "| 6 | F | (E, F) | 35 |\n", + "| 7 | G | (E, G) | 45 |" + ] + }, + { + "cell_type": "markdown", + "id": "08f62a9b-a38a-4620-844c-aae52b10b935", + "metadata": {}, + "source": [ + "$\\textbf{Dijkstra's Shortest Path Algorithm}$\n", + "-" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "82ec6e0e-aa31-43cf-bf25-85c42a860137", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shortest distances from node A : {'A': 0, 'B': 30, 'C': 10, 'D': 40, 'E': 25, 'F': 60, 'G': 70, 'I': 5}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def dijkstra(graph, start):\n", + " distance = {node: float('inf') for node in graph.nodes()}\n", + " distance[start] = 0\n", + " visited = set()\n", + " \n", + " while len(visited) < len(graph.nodes()):\n", + " current_node = min((node for node in graph.nodes() if node not in visited), key=lambda x: distance[x])\n", + " visited.add(current_node)\n", + " \n", + " for neighbor in graph.neighbors(current_node):\n", + " if neighbor not in visited:\n", + " new_distance = distance[current_node] + graph[current_node][neighbor].get('weight', 1)\n", + " if new_distance < distance[neighbor]:\n", + " distance[neighbor] = new_distance\n", + " \n", + " return distance\n", + "\n", + "# Create a graph\n", + "G = nx.Graph()\n", + "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"I\"])\n", + "edgelist = [(\"A\", \"C\", 10), (\"A\", \"I\", 5), (\"C\", \"B\", 20), (\"C\", \"E\", 15), (\"C\", \"D\", 30), (\"B\", \"E\", 25), (\"I\", \"E\", 40), (\"E\", \"F\", 35), (\"F\", \"G\", 50), (\"G\", \"E\", 45)]\n", + "G.add_weighted_edges_from(edgelist)\n", + "\n", + "# Calculate shortest distances using Dijkstra's algorithm\n", + "start_node = 'A'\n", + "distances = dijkstra(G, start_node)\n", + "print(\"Shortest distances from node\", start_node, \":\", distances)\n", + "\n", + "# Plot the graph\n", + "plt.figure(figsize=(10, 8))\n", + "pos = nx.planar_layout(G)\n", + "nx.draw(G, pos=pos, with_labels=True, node_size=700, node_color='#66ff99', font_size=12, font_weight='bold', edge_color='gray', width=2)\n", + "\n", + "# Display edge labels\n", + "edge_labels = nx.get_edge_attributes(G, 'weight')\n", + "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels, font_color='red')\n", + "\n", + "# Annotate nodes with their distances from the start node\n", + "for node, dist in distances.items():\n", + " plt.text(pos[node][0], pos[node][1], f'{dist}', ha='center', va='center', bbox=dict(facecolor='white', alpha=0.5))\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "77dbcede-494b-4f54-8c8c-222fd861cf9b", + "metadata": {}, + "source": [ + "\n", + "$\\textbf{Shortest distances from node A : }$\n", + "---\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 0 |\n", + "| B | 30 |\n", + "| C | 10 |\n", + "| D | 40 |\n", + "| E | 25 |\n", + "| F | 60 |\n", + "| G | 70 |\n", + "| I | 5 |\n", + "\n", + "$\\textbf{Shortest distances from node B : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 30 |\n", + "| B | 0 |\n", + "| C | 20 |\n", + "| D | 50 |\n", + "| E | 25 |\n", + "| F | 60 |\n", + "| G | 70 |\n", + "| I | 35 |\n", + "\n", + "$\\textbf{Shortest distances from node C : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 10 |\n", + "| B | 20 |\n", + "| C | 0 |\n", + "| D | 30 |\n", + "| E | 15 |\n", + "| F | 50 |\n", + "| G | 60 |\n", + "| I | 15 |\n", + "\n", + "$\\textbf{ Shortest distances from node D : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 40 |\n", + "| B | 50 |\n", + "| C | 30 |\n", + "| D | 0 |\n", + "| E | 45 |\n", + "| F | 80 |\n", + "| G | 90 |\n", + "| I | 45 |\n", + "\n", + "$\\textbf{ Shortest distances from node E : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 25 |\n", + "| B | 25 |\n", + "| C | 15 |\n", + "| D | 45 |\n", + "| E | 0 |\n", + "| F | 35 |\n", + "| G | 45 |\n", + "| I | 30 |\n", + "\n", + "$\\textbf{ Shortest distances from node F : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 60 |\n", + "| B | 60 |\n", + "| C | 50 |\n", + "| D | 80 |\n", + "| E | 35 |\n", + "| F | 0 |\n", + "| G | 50 |\n", + "| I | 65 |\n", + "\n", + "$\\textbf{ Shortest distances from node G : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 70 |\n", + "| B | 70 |\n", + "| C | 60 |\n", + "| D | 90 |\n", + "| E | 45 |\n", + "| F | 50 |\n", + "| G | 0 |\n", + "| I | 75 |\n", + "\n", + "$\\textbf{ Shortest distances from node I : }$\n", + "-\n", + "| Destination Node | Shortest Distance (Lowest Total Weight) |\n", + "| :-: | :-: |\n", + "| A | 5 |\n", + "| B | 35 |\n", + "| C | 15 |\n", + "| D | 45 |\n", + "| E | 30 |\n", + "| F | 65 |\n", + "| G | 75 |\n", + "| I | 0 |\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "728809e4-3635-45c1-9335-1aa14da600c2", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + 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