{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# [Chapter 3](https://github.com/Ziaeemehr/netsci/blob/main/docs/examples/chap_03.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### **Random Networks**\n",
"\n",
"Code by : Abolfazl Ziaeemehr \n",
"- https://github.com/Ziaeemehr\n",
"\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# uncomment and run this line to install the package on colab\n",
"# !pip install \"git+https://github.com/Ziaeemehr/netsci.git\" -q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A random network consists of N nodes where each node pair is connected with probability p.\n",
"To construct a random network we follow these steps:\n",
"1) Start with N isolated nodes.\n",
"2) Select a node pair and generate a random number between 0 and 1. If the number exceeds p, connect the selected node pair with a link, otherwise leave them disconnected.\n",
"3) Repeat step (2) for each of the N(N-1)/2 node pairs.\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import random\n",
"import numpy as np\n",
"import networkx as nx\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"from netsci.plot import plot_graph"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"LABELSIZE = 13\n",
"plt.rc('axes', labelsize=LABELSIZE)\n",
"plt.rc('axes', titlesize=LABELSIZE)\n",
"plt.rc('figure', titlesize=LABELSIZE)\n",
"plt.rc('legend', fontsize=LABELSIZE)\n",
"plt.rc('xtick', labelsize=LABELSIZE)\n",
"plt.rc('ytick', labelsize=LABELSIZE)\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"def create_random_network(N, p):\n",
" G = nx.Graph() # Initialize an empty graph\n",
" G.add_nodes_from(range(N)) # Add N isolated nodes\n",
"\n",
" # Iterate through each possible node pair\n",
" for i in range(N):\n",
" for j in range(i + 1, N):\n",
" if random.random() <= p: # Generate a random number and compare it with p\n",
" G.add_edge(i, j) # Connect the nodes if the condition is met\n",
"\n",
" return G\n",
"\n",
"# Example usage:\n",
"N = 10 # Number of nodes\n",
"p = 0.3 # Probability of edge creation\n",
"\n",
"seed=2\n",
"random.seed(seed)\n",
"np.random.seed(seed)\n",
"\n",
"random_network = create_random_network(N, p)\n",
"plot_graph(random_network, seed=2, figsize=(5, 3), title=\"Random Network\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Other option would be to use the `nx.gnp_random_graph` function from NetworkX, which generates random graphs with a given number of nodes and a given probability of edge creation.\n",
"\n",
"```python\n",
"G = nx.gnp_random_graph(N, p)\n",
"```\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Binimial distribution\n",
"\n",
"Degree distribution in a random network follows a binomial distribution."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# make a random graph with N nodes and average degree of k\n",
"np.random.seed(2)\n",
"\n",
"num_nodes = [100, 1000, 10000]\n",
"average_degree = 50\n",
"lambd = 50\n",
"colors1 = plt.cm.Reds(np.linspace(0.2, 0.6, len(num_nodes)))\n",
"\n",
"for i in range(len(num_nodes)):\n",
" probability = average_degree / num_nodes[i]\n",
" graph_b = nx.gnp_random_graph(num_nodes[i], probability)\n",
" degrees = [d for n, d in graph_b.degree()]\n",
" sns.kdeplot(degrees, fill=False, label=f\"N.bino={num_nodes[i]}\", color=colors1[i])\n",
"\n",
"s = np.random.poisson(lambd, num_nodes[-1])\n",
"sns.kdeplot(s, fill=False, label=f\"N.pois={num_nodes[i]}\", color='b')\n",
"\n",
"plt.xlabel(\"k\")\n",
"plt.ylabel(\"P(k)\")\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### The evolution of a random network"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Connected Components:\n",
"Component 1: Size 1\n",
"Component 2: Size 1\n",
"Component 3: Size 18\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",
"# Step 1: Generate a random graph (Erdős-Rényi model)\n",
"n = 20 # number of nodes\n",
"p = 0.12 # probability of edge creation\n",
"G = nx.erdos_renyi_graph(n, p)\n",
"\n",
"# Step 2: Find all connected components\n",
"connected_components = list(nx.connected_components(G))\n",
"\n",
"# Step 3: Calculate the size of each connected component\n",
"component_sizes = [len(component) for component in connected_components]\n",
"\n",
"# Display the graph and component sizes\n",
"print(\"Connected Components:\")\n",
"for i, component in enumerate(connected_components):\n",
" print(f\"Component {i + 1}: Size {len(component)}\")\n",
"\n",
"# Optionally, visualize the graph\n",
"plot_graph(G, seed=2, figsize=(5, 3));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting the size of giant connected component vs average degree"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"N=10000, Ln(N)= 9.210340371976182\n",
"average k = 0.100, giant_component_size= 4\n",
"average k = 0.500, giant_component_size= 11\n",
"average k = 0.900, giant_component_size= 164\n",
"average k = 1.000, giant_component_size= 480\n",
"average k = 1.100, giant_component_size= 1682\n",
"average k = 2.001, giant_component_size= 8028\n",
"average k = 2.902, giant_component_size= 9363\n",
"average k = 3.803, giant_component_size= 9755\n",
"average k = 4.705, giant_component_size= 9909\n",
"average k = 5.606, giant_component_size= 9967\n",
"average k = 6.507, giant_component_size= 9989\n",
"average k = 7.408, giant_component_size= 9999\n",
"average k = 8.309, giant_component_size= 9997\n",
"average k = 9.210, giant_component_size= 9998\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = int(1e4)\n",
"print(f\"N={N}, Ln(N)= {np.log(N)}\")\n",
"k_avg = [.1, 0.5, 0.9, 1.0] + np.linspace(1.1, np.log(N), 10).tolist()\n",
"giant_component_sizes = []\n",
"for i in range(len(k_avg)):\n",
" p = k_avg[i] / N \n",
" G = nx.erdos_renyi_graph(N, p)\n",
" connected_components = list(nx.connected_components(G))\n",
" component_sizes = [len(component) for component in connected_components]\n",
" giant_component_size = max(component_sizes)\n",
" giant_component_sizes.append(giant_component_size)\n",
" \n",
" print(f\"average k = {k_avg[i]:10.3f}, giant_component_size={giant_component_size:10d}\")\n",
" \n",
"giant_component_sizes = np.array(giant_component_sizes)/N\n",
"plt.plot(k_avg, giant_component_sizes, marker='o', label='Giant Component Size')\n",
"plt.xlabel(r'Average Degree')\n",
"plt.ylabel(r'$N_G / N$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Degree distribution of real networks"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"dict_keys(['Collaboration', 'Internet', 'PowerGrid', 'Protein', 'PhoneCalls', 'Citation', 'Metabolic', 'Email', 'WWW', 'Actor'])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from netsci.utils import load_sample_graph, list_sample_graphs\n",
"from netsci.analysis import graph_info\n",
"\n",
"# on google colab: \n",
"nets = ['Collaboration', 'Internet', 'PowerGrid', 'Protein', 'PhoneCalls', 'Citation', 'Metabolic', 'Email', 'WWW', 'Actor']\n",
"\n",
"# on local:\n",
"graphs = list_sample_graphs()\n",
"graphs.keys()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### On Google Colab only:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from google.colab import drive\n",
"import os\n",
"\n",
"# URL of the zip file to be downloaded\n",
"url = \"https://networksciencebook.com/translations/en/resources/networks.zip\"\n",
"# Mount Google Drive\n",
"drive.mount('/content/drive')\n",
"# Create the 'network_science' directory in MyDrive if it doesn't exist\n",
"network_science_dir = '/content/drive/MyDrive/network_science'\n",
"os.makedirs(network_science_dir, exist_ok=True)\n",
"# empty the directory\n",
"!rm -rf /content/drive/MyDrive/network_science/*\n",
"# Change directory to 'network_science'\n",
"os.chdir(network_science_dir)\n",
"# Download the zip file to the 'network_science' directory\n",
"!wget $url -O networks.zip\n",
"# Unzip the downloaded file in the 'network_science' directory\n",
"!unzip networks.zip\n",
"\n",
"json_file = \"https://raw.githubusercontent.com/Ziaeemehr/netsci/main/netsci/datasets/sample_graphs.json\"\n",
"# download json file\n",
"!wget $json_file -O sample_graphs.json"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Successfully loaded Collaboration\n",
"================================\n",
"Scientific collaboration network based on the arXiv preprint archive's \n",
" Condense Matter Physics category covering the period from January 1993 to April 2003. \n",
" Each node represents an author, and two nodes are connected if they co-authored at \n",
" least one paper in the dataset. Ref: Leskovec, J., Kleinberg, J., & Faloutsos, C. (2007). \n",
" Graph evolution: Densification and shrinking diameters. \n",
" ACM Transactions on Knowledge Discovery from Data (TKDD), 1(1), 2.\n",
"Graph information\n",
"Directed : False\n",
"Number of nodes : 23133\n",
"Number of edges : 93439\n",
"Average degree : 8.0784\n",
"Connectivity : disconnected\n"
]
}
],
"source": [
"# on colab:\n",
"# G_collab = load_sample_graph('Collaboration', verbose=True, colab_path=network_science_dir)\n",
"\n",
"# on local:\n",
"G_collab = load_sample_graph('Collaboration', verbose=True)\n",
"graph_info(G_collab)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Figure 3.6"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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RKOjZsyd27NiB+fPno2XLllAoFBg+fLhNYyIiIvfm4+ODLVu24LHHHsPgwYPx8MMP46GHHkLDhg1x+fJlaLVabNu2Da+88goAoF69eliwYAHi4+PRo0cP81i4evVqZGVlISUlxaKxZWX4+/vj4Ycfxtq1a1G3bl2Eh4fj7NmzSElJQevWrcutSXrr1i306dMH//rXv3Djxg289957uHnzJpYtW2bep127dnj55ZexYMEC9O3bFzExMbhx4wZSU1ORm5uLjz76qNKlUJ588kmkpKQgJiYGDz74IC5evIj333/f3GelpPDwcCiVSsyZMwfXrl2Dr68vWrdujR49elh977Fjx+KDDz7A/PnzodPp0LdvX2RlZeGdd97BXXfdVanVAURERM5GpVJh+fLlGDJkCMLDwxEXFwd/f39s3LgRe/fuxYwZM8yzywHnO0cnckdMoBNRlUyePBlnzpzBJ598gvfeew9GoxFarRaNGzdGly5dcOjQIcydOxdffPEF3nvvPfj7+6NVq1YYO3ZsmWXrtvLaa6+hW7duWLZsGZYuXYq8vDw0btwYHTp0sEgIAMA777yD+Ph4zJkzxzwLkAl0IiKqqpCQEBw6dAgpKSnYtGkT5syZg9zcXDRo0ADdunXDBx98gBEjRpj3f/7559G0aVMsXLgQr7/+OgCgc+fO+PTTTzF48OBqxbB27VpMmzYNX375JT744AOEhoZizpw5qF27NsaNG2f1NR9++CHee+89zJs3D9evX0enTp2wevXqMjPg58+fj5CQELzzzjuYNm0a6tSpgx49emDdunXo06dPpWNcvHgx/P39kZ6ejs8//xwtWrRAXFwcwsPDyywnb9myJd5//33Mnz8fzz33HIqLizFmzJhyE+i1a9fGtm3bMHv2bGzcuBGbN29GvXr1EB0djdmzZ6NFixaVjpOIiMiZDBw4EDt37sTs2bOxcOFCFBUV4e6778bKlSsRGxtrsa8znqMTuRuFxIr/RERERERERERERERlsCggEREREREREREREZEVTKATEREREREREREREVnBBDoRERERERERERERkRVMoBMRERERERERERERWcEEOhERERERERERERGRFUygExERERERERERERFZUUvuANyR0WjEhQsX4O/vD4VCIXc4RETkYiRJwo0bN9CsWTMolbzWbU8cs4mIqLo4XjsWx2wiIqqumo7ZTKDbwYULF9CiRQu5wyAiIhd37tw5qNVqucNwaxyziYiopjheOwbHbCIiqqnqjtlMoNuBv78/APGPEhAQUK33+PDDDzFx4kRIkgSFQoFly5Zh9OjRtgzTLWIiInJHOTk5aNGihXk8IfuxxZjtqs6fP4/Tp0+jTZs2aN68udzhEBG5HI7XjmWrMZvjHxGR56npmK2QJEmycUweLycnB4GBgcjOzq7WwK7X66HRaGA0Gs3bVCoVdDqdbDMbnDEmIiJ3VdNxhCrPU7/rtLQ0xMXFwWg0QqlUIjU1FbGxsXKH5XqKioDjx4HcXCA///YtL8/y53vuAZ58EqjFuStE7sRTxxC52OL75vhHROSZajqG8CjeCWVmZlokqgHAYDAgKytLtmS1M8ZEREREVafX683JA0DUlJ0wYQKioqI4pldWURHw/vvAnDmAXl+51/z73+L2r38BKpV94yMiciPJyclITk6GwWCo0ftw/CMioupiAt0JhYaGQqlUlpntHRISwpiIiIioRhx9UVyv1yMzMxOhoaGun6AoLgY+/BB4803g7FmxLTAQaNQI8PEBfH3FfcnHtWoBmzYBmZnAqFHitf/+NzB8OBPpRESVEB8fj/j4ePPsweripDAiIqoutgp3Qmq1GqmpqVD9fVKlUqmQkpIi66DujDERERFR1Zkuipdkr4viaWlp0Gg0iIyMhEajQVpams0/wyEMBmDNGuDuu4FnnhHJ8yZNgGXLgD//FMnxI0eAn38GduwAvvgCWL8eSEsDUlIAnQ6YOxdo0AA4dQoYOVKUdVm3Trw3ERHZnSPHPyIici9MoNtQcnIywsLCEB4eXuP3io2NhU6ng1arhU6nc4q6bM4YExERebb09HQ88MAD8PPzQ6tWreQOxyU46qJ4eUvl9ZUteeIMjEZgwwaR7B49Gjh9Wsw2/89/gDNngBdfBLy97/w+fn7AtGkikT5nDlC/PvDrr8BTTwEdOgD79tn9VyEi8nScFEZERNXFJqJ2wGYyRERUExxHKm/79u3466+/cPHiRSxZsgQ6na5Kr/fk71qv1yMrKwshISF2SR5otVpERkZa3R4REWHzz7MpoxH49FPgtdeAY8fEtgYNgFdeAeLjRUK8JnJyxOz1//wHuH4dqFcP+PFHkagnIpfhyWOIHGz1fdt7/CMiIufDJqJERETksR566CEAwGeffSZvIC5IrVbbNXHgsv1TbtwAhg0DvvlG/FyvHpCYCEycCNgqQRYQALz6qpjBPmCAKP3yyCPivkUL23wGERFZZe/xj4iI3A9LuBAREVG1zZ07F9HR0QgODoZCoaiwjIrRaMSSJUvQvn17eHt7o0WLFkhMTEReXp7jAiaHccml8hcvAv37i+R53brAzJnAb7+JZLc9ZpcGBgJffilqq+v1Iol+9artP4eIiIiIiKqNCXQiIiKqthkzZmDXrl1o06YN6tevX+G+kydPRkJCAsLCwpCUlITo6GgsW7YMAwcOtJilDADDhw+HQqEo97Z79247/lZkKy7VPyUrC+jVCzh4UNQ5/+474I03xAx0e2rQQCTsmzcHjh8HBg0Cbt6072cSEREREVGlsYQLeTZJAi5dEo28Tp68fW80AgMHAkOHAk2ayB0lEZHTOn36NIKDgwEAHTp0QG5urtX9jh07hqSkJAwdOhSbNm0yb2/dujUmTpyIDRs2YMSIEebtK1aswPLly8v93MDAQBv9Brah1+uRmZmJ0NBQ555hLQOXWCqfkQE89hhw+TIQHAxs2wY4stRMy5Yiif7AA8BPPwH/+hfwySdALR6qExERERHJjUfl5Dlu3QK+/RY4etQyWX79uvX9v/lG1Cbt21fUQh06FLjrLoeGTETk7EzJ8ztZv349JEnCpEmTLLaPHz8e06ZNw9q1ay0S6P7+/vD397dlqHaTlpaGuLg4GI1GKJVKpKamOvdMaxdmlwsVX38NPPkkkJ8PdO0KbN0qz3jfoQPwxRfAww8Dn38umpW+9x6gUDg+FiIiJ5KcnIzk5GQYDAa5QyEiIg/FEi7k/iQJ2LIF6NxZzC6bPh344ANg716RPFcogNatgUcfBSZNEierCxcCPXqImei7dwPPPw80awZERgLvvitmrRMRUaVlZGRAqVSie/fuFtu9vb3RpUsXZGRkVOt9DQYDCgoKUFxcDEmSUFBQgMLCQluEXCl6vd6cPAdEnfcJEyZAr9c7LAZPkZaWBo1Gg8jISGg0GqSlpdX8TVevFivO8vNF4nr3bnkvlvftC6xbByiVQGqqKCFDROTh4uPjcfz48WofKxAREdUUE+jk3g4cEEnvgQNFXdEGDYCnnhInpOnpYjZ6Xh5w5oyYcbZkCTBhAjBlikiw63TAokVA9+4ima7VimR6y5bAxo1y/3ZERC7jwoULCAoKgpeXV5nnmjdvjitXrqCoqKjK77tmzRrUrVsXw4YNw++//466deuiXbt25e5fWFiInJwci1tNZGZmlqnfbjAYkJWVVaP3JUs2v1AhScBbbwHjxgEGAzBqlGjm6QyrHoYOBZKTxeNZs4ASJY+IiIiIiMjxmEAn9/Tbb8CIEUB4uJhN5uUFvPIKcPo0sHYtMHMmEB0NdOwI1K1b/vtoNEBiIrBvn3jPhQuBe+8FCgtFfdJlyxz2KxERubL8/HyryXNAzEI37VNVY8eOhSRJFjedTlfu/nPnzkVgYKD51qJFiyp/ZkmhoaFQKi0Pp1QqFUIcWT/bA9j0QoXBALzwAvB//yd+njpVrEyrU8cGkdrIs8+Ki/kAkJDApqJERERERDJiAt2K9PR0PPDAA/Dz80OrVq3kDsft6fV6aLVa2yx3v3pVJLzbtwfWrxflWUaNEvXO588H6tWr/nu3aiVOZjMyxIm3JAEvvSRKwkhSzWMnInJjPj4+5ZZWKSgoMO9jb9OnT0d2drb5du7cuRq9n1qtRmpqKlQqFQCRPE9JSXH+ppkuxmYXKgoKRF+Td94RxwjLlgHz5jlnnfHXXweaNwd+/x14+225oyEiIiIi8lhMoFtRv359vPDCC5gzZ47cobg9m9UzLSgQpVbatAEWLwaKioB//AM4eBD48EMxk9xWVCpxwm3672PePODpp4HiYtt9BhFVSqtWrRARESF3GFQJzZo1w5UrV6wm0c+fP4+goCDUccAMYC8vLwQEBFjcaio2NhY6nQ5arRY6nY4NRO3AJhcqrl0Tdc43bxazzTduFM3CnZWPDzB3rnj81lvAxYvyxkNUQxyziYiIXAPH7LKYQLfioYcewvDhw6GxZdKVyrBJPVOjUTTbat8eePll0RS0Y0fg66+B7dtFuRV7UCiAGTOAtDSRUF+9Ghg8WNRTJyKiMsLDw2E0GrF//36L7QUFBTh8+DC6desmU2S2oVarERERwZnndlSjCxXnzwN9+gA//AAEBgLbtolSbs7uqaeA++4DbtwAXntN7miIiIiIiDySUybQ586di+joaAQHB0OhUFRYRsVoNGLJkiVo3749vL290aJFCyQmJiKPiUynV+N6pno90Lu3OLk8e1Ysc37/feDQIeCRRxyzHPvpp4FPPwW8vUUT0n/8A/jrL/t/LhGRi4mJiYFCocDSpUsttq9YsQL5+fl46qmnHBpPcnIywsLCEB4e7tDPpZqp1oWKnBzg0UeBY8eAZs1EEt1VZtQolWJlHQCsWAH873/yxkNERERE5IFqyR2ANTNmzECDBg3QtWtXXL9+vcJ9J0+ejGXLlmHIkCFITEzEiRMnsGzZMhw6dAg7duywqJc5fPhwbNy4sdz30mq1XKLgQKZ6piWT6JWuZ7pvn5jx/eefgL8/MG0aMGmSWO7saAMHAjt3Ao8/LuJ64AHgxx+Bhg0dHwuRkzEYDCgsLHRIbWuSx5o1a3D27FkAwOXLl1FUVITZs2cDADQaDUaNGgUA6NixI+Lj47F8+XIMHToUAwYMMI/Z/fr1w4gRIxwad3x8POLj45GTk4PAwECHfjY50K1boun3f/+LwgYNcPWTT9C0Y0e5o6qavn2BoUNF6ZkpU4BvvpE7InJTHLOJiIhcA8dsx3PKGeinT5/GX3/9he3bt6NZs2bl7nfs2DEkJSVh6NCh2Lx5M8aPH4/Fixdj8eLF0Gq12LBhg8X+K1aswOXLl8u99e7d296/GpVQ7Xqma9cC/fqJ5HnHjsDRo6Kcipx/OHr1An76CWjRAjh5UiTziRzApk14a2j16tVQKBTYsWMH3nzzTbRp0wbe3t5IT0+HJEl49913cd9998HHxwd+fn7o378/tFptmfd555138PDDD6N58+aoU6cOmjZtipEjR0Kn0zn+l6I7SktLw8yZMzFz5kxcunQJ169fN/9cuq/F0qVLsWjRIhw7dgzx8fHYsGEDXnzxRWzZsqVMg0gim0hMBLZuRT6AB65ehfqBB6rfb0VOCxYAtWuL0jNMoLssjtlERESugWM2laaQJEmSO4iKdOjQAbm5uVb/QV999VXMmTMH33//Pfr06WPeXlBQgIYNG6Jfv37YunVrtT/7s88+w6RJk6r8H5NpNlt2drZNmpO5O71ej6ysLISEhFScPDcaRaJ8/nzx8xNPAGvWiBnozmL/fuD++0WsX30FDBggd0TkxtLS0sx9BJRKJVJTU2VtXrh69WqMGzcOnTt3RnFxMUaNGoWAgADce++9SE5Oxvr16/Hkk0+iT58+KCwsxEcffYSjR49i8+bNGDRokPl9goOD0bNnT3Tu3BkNGjTA//73P6xcuRKBgYH473//i4YlVne0atUKrVq1wu7du2X4je2H44jj8Lt2Y++8A8THAwCeBLDp780qlQo6nc716tVPmQL85z9AWBhw5AhQyykXklI5OGa755jNMcSx+H0TkSNwzOaYbZXk5O655x5Jo9FYfe7hhx+WlEqlVFBQUOa5Xr16SUFBQdX6zFu3bkk3b96U0tPTpZYtW0o3b960+hnlyc7OlgBI2dnZ1fp8siInR5IGDpQkQNxmzJAkg0HuqKxLSBAxqtWSxP8GyE7OnTsnKZVKCYD5plKppHPnzskW06pVqyQAUtu2baW8vDzz9s2bN0sApJSUFIv9i4uLpfvuu09q1aqVZDQazdtzc3PLvPeOHTskANL8+fMttms0Gqlfv362/UWcAMcR+1u+fLl09913S23btuV37Y6++UaSVCpJAqRpJf5Omm5arVbuCKvu2jVJathQHGO8+67c0VAVcMwW3HHM5njtWPy+icjeOGYLHLPLcun10hcuXEBQUBC8vLzKPNe8eXNcuXIFRUVFVX7fNWvWoG7duhg2bBh+//131K1bF+3atSt3/8LCQuTk5FjcyIZ++02USPnyS8DLC/joI2DOHNFYyxm9+SYQHCyanE6bJnc05KZq3ITXjp577jmLWmxr166Fv78/Bg8ejCtXrphv169fx8CBA6HT6ZCZmWne39fXF4BoEp2dnY0rV66gc+fOCAwMxL59+xz++5B7io+Px/Hjx5GRkSF3KGRrx44Bw4YBBgPynnwSC0o1Fa90vxVnU68eMGuWePzvfwPZ2XJGQ1XAMZuoZtj4m4gchWM2lcdJM5CVk5+fbzV5DgDe3t7mfapq7NixkCTJ4lZRGZe5c+ciMDDQfGvRokWVP5PK8d13QHg48L//AU2bAt9/D5RoNOdMdanMfHyAlSvF43ffFTET2ZipCW9JzpIUatu2rcXPJ06cwI0bN3DXXXehUaNGFrdZfyeDLl68aN5/165diIiIgK+vL+rVq2feNzs7G9euXXPkr0JErubSJdHUOycH6NsXvh99hNQVK6reb8VZTZgAtGsHXL4MLFokdzRUSRyziWqGF72JyFE4ZlN5XLp4oo+PDy5dumT1uYKCAvM+9jZ9+nQkJCSYf87JyWES3RZWrACefx64dQvo1g347DOgeXPz085Wl8pC//7A+PHid3jmGVGrtG5duaMiN2JqwjthwgQYDAanSgqV/rsrSRIaNWqEdevWlfuaDh06AAAyMjLw8MMPIyQkBPPmzUPr1q1Rt25dKBQKDB8+vMxsACIis4ICYPBgQKcDQkKAzZuBOnUQGxuLqKioyvVbcXa1awOzZwPR0UBqKjBzJlCnjtxR0R1wzCYiInINHLOpPC6dQG/WrBmOHz+OwsLCMjPRz58/j6CgINRxwEmFl5dXuTPhqRpu3QISE4Fly8TPw4cD779vkYDW6/Xm5DkglqBMmDABUVFRTvGHDQCwYIFoJJqZCbz+OjBvntwRkZtxlaRQaGgoTp06hZ49e8LPz6/CfdetWweDwYCvv/4arVu3Nm/Py8vjVXEiKp8kAU8/DezZI0qdbNkClGiEpFarq/Q3Uq/XIzMzE6Ghoc73t/WJJ4AmTYA//wS++AJ48km5I6JK4JhNRETkGjhmkzUuXcIlPDwcRqMR+/fvt9heUFCAw4cPo1u3bg6Nh7XZbODaNWDAgNvJ89mzgXXryszedua6VGb16okSLoBYZn3woKzhkHtSq9WIiIhw2kEdAEaPHg2j0Yjp06dbfb7ksjJTmQVJkiz2eeutt3hVnGyKY7abef11YP16oFYtMfO8gt41d5KWlgaNRoPIyEhoNBqkpaXZMFAbqF0bMK24S0mRNxaqEo7ZREREroFjNpXm0jPQY2Ji8NZbb2Hp0qXo06ePefuKFSuQn5+Pp556yqHxxMfHIz4+Hjk5OQgMDHToZ7uFX38FBg0CTp0CfH2BNWuAIUOs7mqqS1Xyf3RnqUtlYdAgICYG2LhRnOxmZIgTXyIP8uSTT2LcuHFYvnw5fvnlFzz++OMICgqCXq/Hnj17kJWVhTNnzgAAhgwZgiVLlmDAgAGIi4tDnTp1sH37dhw9ehRBQUEy/ybkTjhmu5F160QCHQDee0+UUasml1jhBojycG+9BezYAZw+DbRpI3dE5CY4ZhMREbkGjtmO5ZQz0NesWYPZs2dj9uzZuHz5MrKzs80/r1mzxrxfx44dER8fj82bN2Po0KFYuXIlEhMTkZCQgH79+mFEiWaT5OS+/Rbo0UMkz1u2BH76qdzkOXC7LpVLNAVbtkwsIz9yhDPFyGO9//77+PDDD6FUKjF37ly8+OKL+OCDD+Dn54e5c+ea9+vduzc2bdoEX19fzJw5E7NmzULdunXx3XffmbuGExGZ/fwzMG6cePzyy7dnZleTS6xwA4BWrYCoKPF4xQpZQyH3wzGbiIjINXDMdhyFVHr+vhOIiIjAd999Z/W5fv36Yffu3eafDQYDli5ditTUVOh0OgQFBSEmJgZvvPHGHWsA2VpycjKSk5NhMBhw6tQpZGdnIyAgwKExuKRly4DJkwGjEejdWyy9bty4Ui/V6/VOX5cKAPDOO0B8PBAcLC4S/J34JyKyxjQrmuOI/fG7dmG//SYuvl++LOqCb9pU4/FVr9dDo9GUWeGm0+mc7zjjs8/EZIPGjYFz59hMlEgGHEMci983ERFVV03HEKdMoLs6DuyVJEnAzJnAnDni53HjRM1wd2zImp8PtGgBXL0qTvCHDpU7IiJyYhxHHIfftYvKzgZ69QKOHwfuvRf44QdR/s0G0tLSMGHCBBgMBvMKt9gazmy3i+JiQKMB/vgDSE8HoqPljojI43AMcSx+30REVF01HUOcsoQLeQBJAhISbifP584F0tLcM3kOAD4+wHPPiceLF8sbCxERkSu7dQsYNkwkz5s1A7780mbJcwCIjY2FTqeDVquFTqerMHmu1+uh1Wqh1+tt9vmVxmaiRERkTX4+cOkSkJsrVnkTEVGNuXQTUWdTsoQLVcBgAJ59Fli5UvycnAw8/7y8MTlCfDywYIGo775vn1h2TkREsuCY7aIkCZg4UfRO8fERyfPmzW3+MWq1+o4lW9LS0swNR5VKJVJTUx0/U/2ZZ8RkhJ07gawswNmaqRMRkf0ZjcChQ8C2beL288/iYrOJt7e40OzjI+5LPr7TfWX2qcW0EhG5P5ZwsQMuLatAcTEwdiywbh2gVALvvw+MGSN3VI4zdizwwQdi5tzGjXJHQ0ROiuOI4/C7djFvvw1MmgQoFKJnyuDBsoThVLXSBwwAvv4aeOUVYP58x342kYfjGOJY/L5L+OMPcTF52zZg+3bgyhX5Yqldu2yy3ddXjE+TJwN168oXGxHR32o6hvBSITlOYSEwfLhoelWrlkiiO7hep16vR2ZmJkJDQ+VpBpaQIBLon3wC6HRAq1aOj4GIiMgV/fCDGEcBkSiWKXkOAJmZmRbJc0A0ts/KynL88UVcnEigr1oFvPkmm4kSEbmjggLgxx9vzzL/738tn/fzAyIjgagocWvdGrh5E8jLEyVdKrqv7j6muZjFxcD16+JW0k8/Ae+9J1Zhx8SIi99ERC6KCXRyjPx80Thz2zZR5/yTT4DHH3doCE6x1LpTJ+DBB4EdO4Bly1gPnYiIqDKuXAH+9S+xTH3kSGDKFFnDCQ0NhVKpLDMDPUSOEiqPPy5qwV+4ICYpDBvm+BiIiMi2JAk4efJ2wvy770RC3EShALp2vZ0w79nTfAFVr9cj87vv7DtpTJLEBLnykuxnz4oSY+fOifE7KQlYuhQID7dPPEREdsYmomR/OTnAo4+Kgd/HB/jqK4cnz/V6vTl5DgBGoxETJkyQp+mXafbcypVAdrbjP5+IiMiVGI3A6NHA+fNA+/bAu+/KPotNrVYjNTUVKpUKgEiep6SkyLO6rVYtNhMlInIH164BH38s+ltoNEBYmCiB8s03InnetKkof7puHXDxInDggEhS9+1rTp6npaVBo9EgMjISGo0GaWlp9olVoRC11Rs2BFq0EOPzffcBffoAjzwCTJggLgC88YbIAfz8M9C9u4j/wgX7xEREZEesgW5DJRuSnTp1irXZAODqVZE8378fCAgAtm4Fevd2eBharRaRkZFWt0dERDg2GKMR6NABOHEC+M9/bifUiYj+xhqfjsPv2gUsWABMnSpO1PfvBzp2lDsiM71ej6ysLISEhMiTPDc5e1Ys15ckIDOTzUSJHIRjiGO53fd965YY10yzzDMyxLmiiZeXSEibZpl36FDhBWSn6s9R0vnzwIwZwIcfip99fIDp04HERNZHJyKHqekYwhnoNhQfH4/jx48jIyND7lCcw8WLQP/+4qCgYUNAq5UleQ7cXmpdkmxLrZXK20nzt9+27JBOREQOkZycjLCwMIRzKbFz+/lncdINiNJnTpQ8B8RM9IiICHkTE4CYqfjgg+Lxp5/KGwsREZVPpwNSU4F//hMIChLnx2+8AezbJ5Lnd98tmmV//bWYjLZ9uyhb1rHjHVdfVdSfQ1bNm4s+YPv2AfffL8q8zJwpZq1v3Hi7ljoRkRNjAp3sQ68H+vUDjh4FmjQRNdu6dpUtHKdaag0ATz0FNGoE/P47sGmTPDEQEXkwXvR2AX/9JZqPGwyifuozz8gdUbXo9XpotVr7l40zNVX9/HP7fg4RkYO59EXv3FxRwnTiRKBdO7FaaMIEYPNmUc6zfn0gOlqU9/z9d+D4cWDJElEGxcenSh/lVJPGrOneXTQWXb9elH35/Xcxzj/wgJh9T0TkxFjCxQ7cbmlZVZ05A/zjH+LqesuWwM6dTrOU2GmWWgPArFnA66+LA4l9++SNhYicisePIw7E79pJSRLwxBPAl18CoaHAwYOAv7/cUVWZQxuYnzsnjrsUCrEKsFEj+3wOEZlxDHEsl/i+jUbgyBHg229FWZYffwSKi28/r1KJhp8PPyzKsnTrJrbZSFpaGiZMmACDwWCeNGa3cacm8vNFOdN588RjQNRHf+st0RibiMjGajqGMIFuBy4xsNvLyZNiCfH58yJpvnOnOJlzIXq9HpmZmfbtWg6Ik9vmzcXMulOnRIKAiAgePo44GL9rJ7V4saiN6uUF7N0LdOkid0RVJkst2vvuA375BXj/fWDcOPt8BhGZcQxxLKf9vi9eFKVWtm0TifNLlyyf12hu1zGPjATq1bNrOE41aexOStdH9/UV9dETElgfnYhsijXQnYhLLy2zhSNHRAfw8+eBe+4Bvv/e5ZLnDutaDgB33SVm6gOi2zoRWRUREYFWrVrJHQYROcq+faJpKCCWsbtg8hyQqRbtoEHi/osv7PcZRBXgmE0eobBQ9PeaNg24915RsnTUKGDtWpE89/UFHn9c9O749Vfgt9+AlBRg6FC7J88BJ+rPURml66Pn5QGvvsr66EQOwDG7aphAtyGPrqe6bx8QEQFcvixqne/eDTRtKndUVaLX683LrAHAaDRiwoQJ9q1ZOmyYuE9Pt99nEBERuYpr14CYGNFgOzoaePZZuSOqNllq0T7xhLj/9lvg5k37fQ4RkSeRJJEIT0oSifGGDcVM8vnzgcOHxT733isu/u7aJXp4fPkl8OKLQNu2d2z+SSi/PnqfPsCBA3JHR0TEBDrZwHffibIt168DvXqJg4agILmjqjJZZooNHixq3h05Isq4EFEZ3377LX799Ve5wyAie5Mk4OmngbNngeBgYMUKl046yNLAvHNnsfovP1+U0SNyMI7Z5DauXwc2bRINP1u3FjOiJ04UDUHz8oDGjYGRI4E1a4A//xTls+bNA/r3F+XHqOoUCpE0P3kSeOMN0UT1p5+A8HBRluzCBbkjJHIrHLOrhgl0qplvvhEdwnNzRTmSb78FAgPljqpaZJkp1rChuPgAsIwLUTnq1KkDL56IELm/pCTgs8+AOnXEyiwXPZ4oKTY2FjqdDlqtFjqdzv6N3BSK22VcPv/cvp9FZAXHbHJZBoPoufHGG0Dv3mJC2JNPAqmp4sJunTpi1vm8ecChQ8Aff4jk+ciRojQn2Y6PDzBzpphgNnq02LZ6tZjNP2cOV1gR2QjH7KphAp2q79NPxUlaQYFYyrZli6j35qJkmSkGiCXqABPo5PJWr14NhUKBHTt2YNasWdBoNPDy8kKnTp2wYcOGMvt/9tln6N27N3x9feHn54fevXvjcysJH2u12Y4dO4bo6Gg0b94cXl5eaNKkCfr374+vvvrKvE9BQQFmzZqFdu3awcfHB/Xq1UPHjh3x8ssvl/mMlStXomvXrqhbty4CAwPx8MMP48cffyyzn0KhwNixY7Fnzx7069cPvr6+aNiwIZ555hnk5uZW41sjuXh83xJnc+AAMGWKeLxokWiG6SbuVItWr9dDq9XarmScKYH+5ZdAqZV1RCYcszlmE4Bz54C0NFFWs1EjUYP7tdeAn38WCfV27cSs8y1bgKtXxcqeqVNFbw4lUyl2V1599LvvFhfciTwEx2znGLMVksSuDLbmtN3Bbemjj4AxY8SBxbBhomFK7dpyR2UTDu9a/tdfovHMrVuitl7btvb/TJKXJInl9c7Ix6faJRNWr16NcePGoWvXrsjLy8O4ceMAAKtWrcKvv/6KVatWYezYsQCAd955B/Hx8Wjfvr152+rVq3Hy5EmkpKQgLi7O/L4RERHQ6XTQ6XQAgL/++gthYWEAgGeffRYajQZXrlzBgQMH0L59e7zxxhsAxMzP999/H6NHj0avXr1w69YtZGZm4ocffsDBgwfN7z916lQsWLAA3bt3x/Dhw3Hjxg2kpqbi4sWL+PzzzzFgwADzvgqFAp07d8a5c+cwbtw4hIaGYvfu3diwYQPGjx+P1NTUan13pXnEOOIk+F07gexs0T/lzBnRYO2TT1y6dEtVpKWlmfuvKJVKpKam1nyWelGRSATl5AB79gA9e9omWE/FMZtjdgU4hjiW+fseORIBdepU/41u3QIyMoATJyy3BwaK1cFRUcDDDwMaTc0CJtuRJNFU9JVXxIUPhUI0zH78cbkjI2fCMZtjdgVqPGZLZDPLly+X7r77bqlt27YSACk7O1vukOwjJUWSFApJAiRp7FhJunVL7ogc6ty5c9KuXbukc+fO2e5No6LE9zl7tu3ek5xXbq7493bGW25utX+tVatWSQCkli1bStevXzdvv379utSyZUupfv36Un5+vnT16lXJ19dXatOmjcXfyezsbCk4OFjy8/OTrl27Zt7er18/SaPRmH/+/PPPJQDSxo0bK4ynfv360qOPPlrhPidPnpQUCoXUu3dvqbCw0Lz9/PnzUmBgoKTRaKRbJf7GAZAUCoW0d+9ei/cZMGCAVKtWLenGjRsVfl5lZWdnu/c44kT4XcvMaJSkJ58Uf39atZKkEv/vu7tz585JSqVSAmC+qVQq2xxfxMSI73T69Jq/l6fjmM0xuwIcQxzL/H3b6v8hpVKSevaUpNdek6SffpKk4mK5f0W6k7w8SRo3Tvz7BQRI0q+/yh0ROROO2RyzK1DTMZvrjmwoPj4ex48fR0ZGhtyh2M+SJaKRiiQB8fFiydvfJU88QVpaGjQaDSIjI6HRaJCWlmabNx42TNynp9vm/Yhk9NxzzyGwRO3iwMBAPPvss7h27Rp2796N7du3Iy8vDxMnTrS48hsQEICJEyciNzcXO3bsKPf9Te/99ddfIycnp8L9jh07hv/973/l7vP5559DkiS88sorqFNiJlOzZs0wbtw4nD17FocOHbJ4zf33348ePXpYbIuMjMStW7fMV++JqJLefVfMOK9dW8wsq1dP7ogcxq7Ny594QtyzDjrdAcdsckmvvQbMnVuzW3o6cPmyWKkzaxbQqxdQq5bcvxndiY8PkJIC9OkjVloNHizuiTwAx2x5cYSgyjEagf/7P9E0BRBLp+bN85gl1oAo7WJaZg0ARqMREyZMQFRUVM1LvQweLC5MHD0qyri0a1fzgMl5+fiIxrvOyMenxm9x9913l9lmWgp25swZcw2ze+65p8x+pm1nzpwp9/379euH0aNHY/Xq1fjoo48QHh6OBx98EDExMebPAYClS5di1KhR6NixI4KDg9G/f38MHDgQAwcONDcM/u233yoVS7du3czbg4ODy+zbsGFDAGLZGxFV0qFDwOTJ4vH8+UD37vLG42Cm5uUlk+g2a17+6KMiEXT8OJCVBdizIbq745gNgGM2OZmEBIAlczxX7dqif9h994kyPGPGAJs2sS49cczmmG1X/AtDd3bzJjB8+O3k+ezZHpc8B+w8U6xBA1FvD2AzUU+gUIiGu854c5H/rz/44AP897//xZw5c9CwYUP85z//QadOnbB8+XLzPk888QR0Oh3WrFmDyMhI7Ny5E4MHD0ZERASKioqq/dmqClbdSJJU7fcl8ig5OWL1VVGRaHo5aZLcETmcXZuX16sH9OsnHn/xRc3fz5NxzK4xjtlEZHN33QVs3gx4eYmGonPmyB0ROQOO2TXGMbt8TKBTxS5dAiIjRVK3dm1gzRoxE91F/ue3JdNMsZJsNlMMAKKjxT0T6OTiTpRuyATg+PHjAMRVZdOV5WPHjlW435106NABL7/8Mr744gvo9Xq0adMG06ZNsxhcGzRogJEjR2LFihU4c+YMXnnlFfzwww/mLuS2ioWIqkCSxKqrrCygZUtg1SqPPK4ARBMmnU4HrVYLnU5X8waiJQ0aJO6ZQKcKcMwmIpfVvbsoBQeIsj5btsgbD5GdccyWFxPoVL4TJ4CePYG9e4H69YHt24GRI+WOSjZ2nSkGiDIutWrdLuNC5KLeffddZGdnm3/Ozs7Ge++9h3r16qFfv3546KGH4Ovri6SkJNy4ccO8340bN5CUlAQ/Pz889NBD5b7/1atXy6wGqVevHlq3bo38/HwUFBTAYDDg+vXrFvsoFArce++95vcAgEGDBkGhUGDhwoUoLi427/vHH39g1apV0Gg05tcQkY2sWAFs2CDGvA0bxCosD6ZWqxEREWG74wkTUwL9hx8AJ1j2Ss6JYzYRubRx40RvNkkCnnoKOHVK7oiI7IZjtrxYA52s02qBoUOB69eB4GBg61bW5YaYKRYVFYWsrCyEhITY9mS3QQPgoYeAr78Ws9BffdV2703kQEFBQejRowfGjRsHAFi1ahV+//13rFy5Ej4+PvDx8cGCBQsQHx+PHj16YOzYsQCA1atXIysrCykpKRbNUUr78MMPsWTJEgwZMgQhISGoXbs2vvvuO2zbtg3Dhg1D3bp1cf36dTRt2hSDBg3Cvffei8aNG+O3337Du+++i/r162PgwIEAgHbt2uHll1/GggUL0LdvX8TExODGjRtITU1Fbm4uPvroowqXkhFRFR09Crz0knj81lvA/ffLG487a9UK6NRJfOdbtwKjRskdETkhjtlE5PIWLwaOHAF+/FFMStu7lzXyyS1xzJaZRDazfPly6e6775batm0rAZCys7PlDql6Vq+WpNq1JQmQpF69JOnSJbkjchnnzp2Tdu3aJZ07d656b/D+++J779jRtoEROcCqVaskANL27dulf//731KLFi2kOnXqSB06dJA++uijMvtv3rxZuv/++yUfHx/Jx8dHuv/++6VPP/20zH79+vWTNBqN+edDhw5Jo0ePltq0aSP5+PhI/v7+UqdOnaRFixZJBQUFkiRJUmFhoTRt2jQpPDxcatCggVSnTh1Jo9FI48aNk06dOlXmM1JTU6UuXbpIXl5ekr+/v/Tggw9K33//fZn9AEhjxowp93fXarWV/r4qkp2d7drjiAvhd+1AN25IUrt2Ypx79FFJMhjkjsip1fiYQpIkado08X2PHWu7wMgtcMy2zZjNMcSx+H1Tuf78U5KaNxdj3uDBPMYgt8Ix2znGbIUkOUEldjeTk5ODwMBAZGdnI8CVrnxKkqgd9uab4ueYGGD1asDbW9awXEVaWhri4uJgNBqhVCqRmppa9VqmV68CQUHi3+L8eaBZM/sES2QHq1evxrhx46DVahERESF3OC7NZccRF5KcnIzk5GQYDAacOnWK37W9SRIwejSwdi3QvDlw+LAY78gqmxxTAMA33wCPPgq0bg2cOWP7QMllccy2DY7XjsXvmyq0fz/Qp49oUP7GG8DMmXJHRGQTHLNto6ZjCGugk1BYKOqbm5LnM2YA69YxeV5Jer3efKILAEajERMmTIBer6/aGzVoANx3n3i8c6eNoyQiIpP4+HgcP34cGRkZcofiGVatEslzlQpYv57J8wrY7JgCAHr3Ft/5b78B587ZOFIiIiInwqaiRGRHTKATcOUK8OCDImFeqxaQlgbMmQMo+Z9HZWVmZpZptmAwGJCVlVX1N/vHP8Q9E+hEROQOjh0DXnhBPH7jDTE7jMpl02MKf3+ga1fx+PvvbRAdERGRE3v6aeD559lUlIhsjhlST5eZKRp4/fgjEBgolvo+/bTcUbmc0NBQKEtdcFCpVAgJCan6mz34oLjfsUMM/ERERK4qLw+IjgZu3gQefhiYNk3uiJyeTY8pAKBvX3H/3Xc1jIyIqPrS09PxwAMPwM/PD61atZI7HHJnS5YADzwA5OSIpqI5OXJHRERugAl0T/bDD0DPnkBWFqDRAD//fHv2M1WJWq1GamqquYuwSqVCSkoK1Gp11d+sd2/Ay0vUQOcVc3IhY8eOhSRJrMtGRLe98AJw4gTQtCmwZg1Xt1WCTY8pAKBfP3HPBDqVwDGbHK1+/fp44YUXMGfOHLlDIXdXpw7wySei58qJE8CYMUCplV1EroRjtnPgWYynWrdOzHS+elXUCtu3DwgLkzsqlxYbGwudTgetVgudTmfR7Euv10Or1VaufmnduiKJDohZ6ERERK7oww9FM3KlUhx3NG4sd0Quo6JjCqCKxxV9+gAKhbgo/8cfdoqYiKhiDz30EIYPHw6NRiN3KOQJ7roL2LRJJNM/+0yUqCUiqgEm0D2NJAGzZ4t6YEVFwNChgFYrBhiqMbVajYiICItZYmlpadBoNIiMjIRGo0FaWtqd34h10ImIyJWdOAE895x4/NprAGfMVJm1YwqgGscV9eoBnTuLx6yDTuSx5s6di+joaAQHB0OhUFRYRsVoNGLJkiVo3749vL290aJFCyQmJiIvL89xARPVVI8ebCpKRDbDBLonKSoCxo0DZs4UP0+ZAnz8MeDjI29cbkyv1yMuLs7cDMxoNGLChAl3njFmqoOu1QIGg52jJCIisqH8fGDYMHEfGQn83//JHZHbqPZxBcu4EHm8GTNmYNeuXWjTpg3q169f4b6TJ09GQkICwsLCkJSUhOjoaCxbtgwDBw4s0+R4+PDhUCgU5d52795tx9+K6A7YVJSIbKSW3AGQg1y7BvzznyIhq1IBy5cDzz4rd1RuLzMzs8xBpsFgQFZWVsW1TO+7TzR1vX4d+OUXIDzcvoESERHZyksvAf/7n1jd9tFH4riDbKKi4wrT86GhoWWPMfr1A95+mwl0Ig92+vRpBAcHAwA6dOiA3Nxcq/sdO3YMSUlJGDp0KDZt2mTe3rp1a0ycOBEbNmzAiBEjzNtXrFiB5cuXl/u5gYGBNvoNyJXo9fryxyRHW7IEOHoU+PFH0VR0714gIEDemIjI5XAGuic4cwbo1Uskz/39xdIlJs8dIjQ0FMpSDdNUKhVCQkIqfqFKdXu5O8u4EBGRq1i3Dli5UtTc/ugjoEkTuSNyK+UdV2RkZFRc1qVPH3F//Dhw+bKDoiUiZ2JKnt/J+vXrIUkSJk2aZLF9/Pjx8PHxwdq1ay22+/v7IygoqNxb7dq1bfUrkIuoVglTe6pTR6y8Z1NRIqoBJtBtKDk5GWFhYQh3ptnCe/cCPXsCJ08CarW46vrII3JH5THUajVSU1Oh+nv2nUqlQkpKSuWuwpvKuLCRKBERuYJTp4AJE8TjV1+93c+DbMbaccW8efMwbdq0isu6BAUB99wjHrMOOhFVICMjA0qlEt27d7fY7u3tjS5duiAjI6Na72swGFBQUIDi4mJIkoSCggIUFhbaImRyItUuNWZvTZqwqSgR1QgT6DYUHx+P48ePV/ugwuY+/hjo31/MNLr3XmDfPqBTJ7mj8jixsbHQ6XTQarXQ6XSIjY01P6fX66HVaq0fUJgSDz/+CNy86aBoiYiIqqGgQNQ9z80V5UJee03uiNxW6eOK++67r8KyLmamOuhMoBNRBS5cuICgoCB4eXmVea558+a4cuUKioqKqvy+a9asQd26dTFs2DD8/vvvqFu3Ltq1a1fhawoLC5GTk2NxI+d2p1JjsmJTUSKqASbQ3ZEkAQsWiBPZggJg4EBxstSsmdyReSy1Wo2IiAiLmed3XNrWvr34NyssBH7+2cERExERVcHkycCRI0CjRqKMC+ue21XJ44qKysVZXKhnI1EiqoT8/HyryXNAzEI37VNVY8eOhSRJFjedTlfha+bOnYvAwEDzrUWLFlX+XHKsapcwdZSnnwaee45NRYmoyphAdzfFxWL59NSp4ueJE4FPPwX8/OSNiyxUammbQnF7FjrroBMRkbNKTwfee088XrOGF+wdrLxycdu2bbO4UL/OdIxx9KhoLk9EZIWPj0+5pVUKCgrM+zjC9OnTkZ2dbb6dO3fOIZ9L1VejEqaOsnQp8MADQE6OaCrKUkJEVAlMoLuT7GzgsceAFSsApRJ4+21x4ywwp1PppW2sg05ERM4sKwt45hnxePp0ICpK3ng8VOmyLlFRUWUu1I9+5RUUt2kjZt398IPMERORs2rWrBmuXLliNYl+/vx5BAUFoU6dOg6JxcvLCwEBARY3cn4VlTB1Cqamok2aiKaiq1bJHRERuQAm0N3F77+Lq6jbtwM+PqIxxsSJckdF5aj00jbTDPSDBzlbjIjIhpyy8berKSwEYmKAGzfEMcgbb8gdkUcrWdalvAv1l+++W/zAMi5EVI7w8HAYjUbs37/fYntBQQEOHz6Mbt26yRQZuRJrJUydSpMmwP/9n3g8dy5Qjbr+RORZmEB3BwcOiIYY//sf0LSpmFU0cKDcUVEFKr20rXlzUQvdaAR273Z8oEREbsrpGn+7oilTgF9+ARo2BNavB2rVkjsi+lt5F+q9Hn5Y/MAEOhGVIyYmBgqFAkuXLrXYvmLFCuTn5+Opp55yeEy86E12ERsrEum//y5K0BERVUAhSZIkdxDuJicnB4GBgcjOzrb/MrPPPgNGjABu3gQ6dgS++gpgcxWXodfrkZWVhZCQEHPyXK/XIzMzE6GhoWJbfDzwzjvApEnAkiXyBkxEDuHQccTD8buupk2bgCefFI+/+goYMEDeeKiMtLQ0TJgwAQaDwXyhPjYqShwnKpXA1atAYKDcYRK5NFcaQ9asWYOzZ88CAJKSklBUVITExEQAgEajwahRo8z7vvjii1i+fDmGDBmCAQMG4MSJE1i2bBl69+6NXbt2lblA5yiu9H2Ti1i8GEhMBIKDgV9/5WQAIjdW0zGECXQ7cMjALkmi+UVionj8yCPAxo0ADyRcWlpamrlmqVKpRGpqKmK9vIBRo4D77wd+/lnuEInIAXiC6Dj8rqvhzBmga1fRe+Xll4EFC+SOiMph7UI92rQR/4bffMOa9UQ15EpjSEREBL4rZ/VJv379sLvEaleDwYClS5ciNTUVOp0OQUFBiImJwRtvvAE/Pz8HRVyWK33f5CLy8oBWrYArV4APPxTn3UTklphAd0J2H9hv3RKzkZOTxc8TJgDLl/NqqYvT6/XQaDQWNUtVKhX0Wi2a9O0LeHmJTuEOatpDRPLhCaLj8LuuoqIiUe88I0Nc2P3uO6B2bbmjoqoYMUKU3Jk9+3b9VyKqFo4hjsXvm+xi/nxg2jSgbVvg+HHg7zKrROReajqGsAZ6KYWFhRg/fjyCg4Ph7++Ptm3bIikpSe6wbrtxA3jiCZE8VyiARYuAd99l8twNlNfw6+StW0CDBqJZ29GjMkVHREQEYOpUkTyvXx/YsIHJc1dkagB44IC8cRARETmD558X59unTgEffyx3NETkpJhAL+XWrVto0qQJvv32W2RnZyM9PR2zZ89Genq63KEBej3Qpw+wdStQty7wySeihItCIXdkZAPlNfzy9fPDXyEhYsO+fTJERkREBODzz0X5OABYvRpo2VLOaKiaLv3973aLxxRE5CLYRJTsyt9frPAHxOqsUpPaiIgAJtDL8PX1xZtvvomQkBAolUp06dIFgwYNwo8//ihvYIcPAz16AEeOAI0bA7t3A0OHyhsT2ZRarUZqaipUfy8ZU6lUGDlyJHr27Imk/fsBAFlr18oZIhEReaqzZ4GxY8XjyZOBQYNkDYeqJy0tDaHDhsEIoNYff2Dd4sVyh0REdEfx8fE4fvw4MjIy5A6F3NWLL4p+cseOAZ99Jnc0ROSEnDKBPnfuXERHRyM4OBgKhQKtWrUqd1+j0YglS5agffv28Pb2RosWLZCYmIi8vDybxFJcXIwffvgBnTp1ssn7VctXX4l6oxcuAGFhYhZy9+7yxUN2ExsbC51OB61Wiz179mDNmjUwGo0wzREz7t0LvV4va4xERORhiouB4cOB69fF8ce8eXJHRNWg1+sRFxeHHEnCyb+3bXj5ZR5XEBER1asHvPSSePzmmwBbBRJRKU6ZQJ8xYwZ27dqFNm3aoH79+hXuO3nyZCQkJCAsLAxJSUmIjo7GsmXLMHDgwDL1pIcPHw6FQlHurWTncZMXXngB/v7+GD16dNV/kVu3Kr4VF9/5lpwsZnnl5QH/+Afw00+iSzS5LbVajYiICOTm5pr/G97/93NtAeh++UW22IiIyAPNmAHs3QsEBoq652xm7ZJK9loxVT+/12hEVlYW9Ho9tFotk+lEROS5Jk0C/PzE6v8tW+SOhoicjFN2njx9+jSCg4MBAB06dEBubq7V/Y4dO4akpCQMHToUmzZtMm9v3bo1Jk6ciA0bNmDEiBHm7StWrMDy5cvL/dzAwECLnxMSErBnzx7s2rULdapzstiwYdVfU56nnxbNQnnS6jFMNdGNRiOuAsgEEAqgXXY29Ho9MjMzERoaCrVaLXOkRETktr76SjQsB4BVq4DWreWNh6qt5HHFAQCjAYQDOHDgAP7xj3/AaDRCqVQiNTUVsbGxMkdLRERknd3OhRs0AOLjgfnzxSz0xx9nvzkiMnPKGeim5PmdrF+/HpIkYZKp4cPfxo8fDx8fH6wtVS/a398fQUFB5d5q165t3nfSpEnYvn07du7ciaCgoBr/TtVWpw7w1lvAypVMnnuY0jXR9/09eJ/75BNoNBpERkZCo9EgLS1NzjCJiMhdnTsHmFbgvfgiMGSIvPFQjZQ8rjDNQI/w98fUV14xz0w3Go2YMGECZ6ITEZFTSktLs++5cEICULcukJEBfPutbd+biFyaQpKcu7iTaQa6Tqcr81xUVBR27NiB/Px8eHl5WTzXu3dvnDp1CpcvX67yZ06cOBG7du2CVqtFo0aNqvz6nJwcBAYGIvu33xAQEFDxzne6ountLf6Ak8fS6/XIyspC5x9/RP2ZM/E1gAElnlepVNDpdJyJTuRGzONIdvadxxGqEX7X5SguBvr3F6Xj7rtP3Jc61iLXpNfrceZ//0Ofxx6DwmhEcwAXSu2j1WoREREhQ3REroVjiGMkJycjOTkZBoMBp06d4vftofR6PTQajUWpXrucCycmAosXA716AT/+yFnoRG6ipmO2U85Ar6wLFy4gKCioTPIcAJo3b44rV66gqKioSu959uxZJCUlISsrC61bt4afnx/8/Pzw6KOPlvuawsJC5OTkWNwAiCVAd7rVr1/xjclzj2eqiV4/KgqAWG5dksFgQFZWluMDIyIi9/Xvf4ukeUAAsHEjk+duRK1Wo+8jj0Bxzz0AgO6lEgMqlQohISFyhEZEZFV8fDyOHz+OjIwMuUMhGZXs5WFil3PhKVPEcc/PPwNarW3fm4hclksn0K3NPDfx9vY271MVGo0GkiShoKAAubm55tvXX39d7mvmzp2LwMBA861FixZV+kyiSuncGZKXF4IAtCmxWaVSwdfXl82/iIjINr75Bpg3TzxeuRJo06bi/ck1desGAPj3Y4+Zy8WpVCqkpKRwVRsRETkdUy+Pkuxy0bdpU2D8ePH4zTdt+95E5LJcOoHu4+ODwsJCq88VFBSY97G36dOnIzs723w7d+6c3T+TPFCdOlDcey8A4P6/Z4upVCqMHDkSPXv2ZE10IvI4hYWFGD9+PIKDg+Hv74+2bdsiKSlJ7rBc2/nzwKhR4vFzzwHR0fLGQ/bzdwL93lu3oNPpoNVqodPp2ECUiIicUukeYXa96Dt1quhBt3s38MMPtn9/InI5teQOoCaaNWuG48ePo7CwsMxM9PPnzyMoKAh1HNB408vLq9yZ8EQ21aMHsHcv3h0zBrFjxsDX1xc9e/Ys0/wrKiqKs8eIyO3dunULTZo0wbfffovg4GAcPXoUUVFRuOuuuzBs2DC5w3M9t24BI0YAV64AXbqI+p/kvsL/Lgp34ADUzZvzuIGIiJxebGwsoqKikJWVhZCQEPuNXWo1MG4ckJIiZqGzoSiRx3PpGejh4eEwGo3Yv3+/xfaCggIcPnwY3f6eWeMoycnJCAsLQ3h46SrVRDbSowcAwO/YMURERCA3N9dqHbiPP/6Y5VyIyO35+vrizTffREhICJRKJbp06YJBgwbhxx9/lDs01/T668D33wN+fkB6umhkTu6rUyegdm1xweT33+WOhoiIqFJMPcLsfuF32jSgVi1g+3Zg3z77fhYROT2XTqDHxMRAoVBg6dKlFttXrFiB/Px8PPXUUw6Nh81NyO7+TqDj8GGgoMBqHTgASEhIYDkXInKIuXPnIjo6GsHBwVAoFGjVqlW5+xqNRixZsgTt27eHt7c3WrRogcTEROTl5dkkluLiYvzwww/o1KmTTd7Po+zYAcyZIx6npgKhofLGQ/bn5QV07CgeHzhg8ZRer2dvFSJyGpyoRrJo1ep2WTvWQifyeE6ZQF+zZg1mz56N2bNn4/Lly8jOzjb/vGbNGvN+HTt2RHx8PDZv3oyhQ4di5cqVSExMREJCAvr164cRI0bI+FsQ2UHr1kCjRkBxMXD4cJk6cCWZyrnw5JeI7GnGjBnYtWsX2rRpg/r161e47+TJk5GQkICwsDAkJSUhOjoay5Ytw8CBA8usphk+fDgUCkW5t927d5d5/xdeeAH+/v4YPXq0LX9F9/fnn8DIkYAkiaZZ//qX3BGRo5hWa5ZIoKelpUGj0VTYW4UJdiJyJE5UI9nMmAEolcBXXwG//CJ3NEQkI4UkSZLcQZQWERGB7777zupz/fr1szhpNhgMWLp0KVJTU6HT6RAUFISYmBi88cYb8PPzc1DEQnJyMpKTk2EwGHDq1ClkZ2cjICDAoTGQBxg4ENiyBVi6FHjpJQDiRPbjjz9GQkJCmd21Wi0iIiIcGyMR1UhOTg4CAwNdYhw5c+YMgoODAQAdOnRAbm4udDpdmf2OHTuGjh07YsiQIdi0aZN5e1JSEiZOnIiPPvrI4sL3jRs3ym0UDgCBgYGoXbu2+eeEhATs2LEDu3btQlBQUKXjd6Xv2i4MBuDhh4Fdu8Rs5H37gLp15Y6KHGXFCiAuDnjwQWD7duj1emg0GosLWiqVCjqdzrxUPi0tDXFxcTAajVAqlUhNTWXjUfJYHj+GOBi/b5LFqFHA2rXA4MHAp5/KHQ0RVVNNxxCnTKC7Og7sZFezZwMzZ4pGbx99ZN5c3knvnj17kJubi9DQUDYII3IRrjqOVJRAf/XVVzFnzhx8//336NOnj3l7QUEBGjZsiH79+mHr1q3V+txJkyZh586d2LVrFxo1alSl17rqd20zb7wBvPYa4OsrZiG3by93RORIhw4BXbsC9eoBV69Cu3s3IiMjy+xmuhhfmQQ7kSfx+DHEwfh9kyxOngTCwsRKvSNHRA8RInI5NR1DnLKECxFVoGtXcX/4sMXm0uVcVCoVRo4ciZ49e1a4DJuIyBEyMjKgVCrRvXt3i+3e3t7o0qVLtZdlT5w40TzzvKrJc4+3e7doHAoA777L5LknuuceUQv9+nXgzBmrvVVUKhVCQkIAAJmZmVabl2dlZTkqYiIiIsdq3x6IjhaPTf1iiMjjMIFO5Go6dxb3v/4KFBRYPBUbGwudTgetVos9e/ZgzZo15hNd1kQnIjlduHABQUFB8PLyKvNc8+bNceXKFRQVFVXpPc+ePYukpCRkZWWhdevW8PPzg5+fHx599NFyX1NYWIicnByLm0c6cwYYPhwwGoFx4243ySLPUqfO7eOKAwesXoxPSUkxzy6/U4KdiIjILb36qrj/+GPgxAl5YyEiWTCBbkPsDk4O0awZ0KCBqFtrZfBWq9WIiIhAbm4uZ4kRkdPIz8+3mjwHxCx00z5VodFoIEkSCgoKkJuba759/fXX5b5m7ty5CAwMNN9atGhRpc90CxcvirrnFy+K5GlSktwRkZxKNRIteTFep9NZ1De/U4KdiIjILXXsCAwZIsq4cBY6kUdiAt2G2B2cHEKhuF137ejRcnezNktMqVTi0qVLnIVORA7n4+NTblPQgr9X0/j4+Ng9junTpyM7O9t8O3funN0/06ncuAEMGACcPg20agV8/bWof06ey5RAP3jQvMl0Md6UGNfr9dBqtdDr9RUm2ImIiNyWaRb6+vVAZqa8sRCRwzGBTuSKTMutjxwpd5fSs8QUCgUkSUJMTAzroRORwzVr1gxXrlyxmkQ/f/48goKCUKdOHbvH4eXlhYCAAIubxygqAoYOBX75BQgKArZtA5o2lTsqkpvpovz//mf16bS0NGg0Got+KqUT7ERE9sSV3uQUunYFHntMlL+bO1fuaIjIwZhAJ3JFlZiBDtxehp2enm5OoAOsh05EjhceHg6j0Yj9+/dbbC8oKMDhw4fRzTQLluzDaATGjAF27BAzzrduBdq2lTsqcgZ33y1Wt12+DFy6ZPGUXq9HXFxchf1USs5OJyKyB670Jqcxc6a4//BD4Lff5I2FiByKCXQb4pVxchhTAv3IEVGHrQJqtRpBQUGsh05EsoqJiYFCocDSpUsttq9YsQL5+fl46qmnHBqPR43ZkgQkJAAbNgC1agGbNwOe8HtT5fj4AG3aiMelZqFnZmZWePxgbXY6ERGR2+rRQ/SRMRiAefPkjoaIHEghSXfIvlGV5eTkIDAwENnZ2Z61NJwc5+ZNwM9PzCj84w+gSZMKd9fr9dBoNBYnwSqVCjqdjsuviZyQK40ja9aswdmzZwEASUlJKCoqQmJiIgDR5HPUqFHmfV988UUsX74cQ4YMwYABA3DixAksW7YMvXv3xq5du8r0bXAEV/quq23+fGDaNPF47VrAwRcryAUMGQJ89hnw9tvAxInmzRUdPwDgsQV5PI8YQ5wIv29yCj/8APTtC9StK1Zu+fnJHRERVUJNxxDOQCdyRXXr3l56X0EddJPS9dBVKhXmzZuHzMxMLrkmohpJS0vDzJkzMXPmTFy6dAnXr183/1x6NurSpUuxaNEiHDt2DPHx8diwYQNefPFFbNmyRZbkuUdYtep28nzxYibPyboOHcR9qRno1o4fUlJSoFar7zg7nYiIyC098IBYuXXzJrBli9zREJGD1JI7ACKqpk6dgJMnRR30qKg77h4bG4uoqChkZWUhIyMDU6dOhdFohFKpREJCAl566SXOGCOiKtu9e3el91WpVEhMTDTPUCc727IFGD9ePH7lFWDyZHnjIedVTgIdsDx+CAkJMR8rhIaGQqlUlpmBHhIS4pCQiYiIZKFQADExwFtvARs3AsOHyx0RETkAp3sRuapKNhItSa1WIyQkBNOmTbNoCLZo0SK0bNmStUuJyGO4fQ30PXuAYcNEjc7Ro1mnkypWMoFupbqjWq1GRESExYX2imanW8Nmo0RE5DZMSfOtW4HsbHljISKHYALdhtz+ZJycSzUS6ID1hmAAIEkSJkyYwBNbIvII8fHxOH78ODIyMuQOxfaOHwcee0wsLX70UWDlSjFbiqg8oaFA7drAjRvAuXOVfllsbCx0Oh20Wi10Oh1iY2Ot7sdmo0RE5FY6dADuvhsoKgI+/1zuaIjIAZhAtyG3Phkn59O5s7g/cUIM3JVkWnJtDWuXEhG5OL1elPW6dg3o0QP4+GORGCWqSJ06QLt24rGVMi4VsTY7vSS9Xo+4uDiLlW+8YE9ERC7NVMYFEGVciMjtMYFO5KpatAACA4HiYlELvZJKL7kuSalU4tKlSzypJSJyRVeviuS5Xi+SoVu2AL6+ckdFrqKCOug1wWajRFRTXOlNTsmUQP/2W+Cvv+SNhYjsjgl0IlelUFS7jItpyfWUKVPMs9EVCgUkSUJMTAyXVxMRuZr8fGDQIFG+pVkzYNs2IChI7qjIldgpgW5t5RubjRJRVXClNzml9u3FqvBbt4BPP5U7GiKyMybQiVyZKYF+5EiVX6pWq7Fw4UKcPXsW6enp5gQ6wOXVROT+3Go2261bopnVTz8B9eqJ5LlGI3dU5GpsnEA3NQ0FUKVmo0RERC6DZVyIPAYT6ESuzFQHvYoz0EtSq9UICgri8moi8ihuM5tNkoBnnwW+/BLw8gK++OJ2IpSoKkz/3Rw/DhgM1XoLU9J84cKFFk1DAVSq2SgREZFLMSXQd+0CLl6UNxYisism0G3IrWazkWuoZgmX0qwtr2Y9dCIiFzBzJpCWBiiVwIYNQJ8+ckdErqp1a6BuXaCwEDh9usovT0tLMyfNX3nllTJNQwFU2GyUiIjI5QQHA+HhgNEIbNokdzREZEdMoNuQ28xmI9dxzz2iFvqffwKXLlX7bUo3FmU9dCIiF5CUBMyZIx6/9x4weLCs4ZCLUyrFcQVQ5TIuer0ecXFxZVazmXBVGxERORvTqqkaTxgzzULfsKHmQRGR02ICnciV+fkBbdqIxzWchW5qLMp66ERELiA9HXjpJfH4jTeA8ePljYfcQzXroGdmZpabPAfYNJSIiJxLyVVTNZ4wNmyYuP/xR+D8edsESEROhwl0IldngzroJhXVQ9+zZ0+N35+IyFm4dNm1nTuBkSNF/fPnnwdefVXuiMhdVDOBbq0UnAmbhhIRkTMpvWqqxhPGWrQAevcWx2Uff2zDSInImTCBTuTqOnYU91U82S1PeSfBMTExLOVCRG7DZcuuHToEDBkCFBcDTz4JLFsmSnkR2YIpgf7f/1bpZaVLwalUKixcuJBNQ4mIyOlYWzVV41JjLONC5PaYQCdyde3bi/tff7XJ25U+CTaRJImlXIiI5HT6NPDoo8CNG0BEBLBmDVDqbzVRjZgS6JmZQEFBlV5qKgVnSppPmTKFTUOJiMjpWJswVuNSY9HRopfIvn2ATlezAInIKTGBTuTq2rUT9zZKoAPiJHjdunVltrOUCxGRTC5eBKKixH3nzsBnnwHe3nJHRe6mWTOgXj3AYKjWcYVarWbSnIiInJq1VVM1LjXWpAnQr594nJ5ugyiJyNkwgU7k6tq2Ffd//QVcuWKzt+3Vq5fVUi7Dhw9nKRciIke6cQMYMEDMQG/VCvj6ayAwUO6oyB0pFNWug05EROQqSq+askmpMZZxIXJrTKDbkEs3JCPX5eMDaDTi8cmTNntb05X50kl0o9GIuLg4pKenIyMjA1qtlmVdiIjspbBQ1Dz/5RegUSPg22+Bpk3ljorcGRPoRORkeJ5N9lCTVVN6vb7sefA//ylK6x06JEqhEZFbYQLdhly2IRm5PjuUcQHElfn169eX2W40GhETE4Pu3bsjMjISGo2Gs9KJiGzNaATGjAF27gR8fYGtW4HQULmjIncnUwLdajKCiAg8zybnkpaWBo1GU/Y8OCgIePBB8XjjRvkCJCK7YAKdyB2YGonacAa6SXmlXEoyGo1sMEpELsXpZ7NJEjB5sjgBq1UL2LwZ6NZN7qjIE9g5gV4yUW56vGjRIuvJCCIiIiei1+sRFxcHo9EIwMp5MMu4ELktJtCJ3IGdZqADZZuslMdgMCArK8vmn09EZA9OP5tt/nxg2TLx+IMPgIcfljce8hx33y3uz54Fbt606VuXnLXXsmVLtGzZEpGRkXj55ZfLT0YQERE5iczMTPN4ZWJxHjxkCFC7NnDsGEuhEbkZJtCJ3IEdZ6ADt5uspKenlzsbXalUwtfX1y6fT0TkUVatAqZPF4+XLAFGjJA3HvIsjRqJJrWSJBrX2kjpWXuSJEGSJKv78qI8ERE5o9DQ0DLnwyqVCiEhIeKHevWARx4Rj1nGhcitMIFO5A5MCfQzZ4CiIrt8hFqtRnR0dLmz0Y1GI3r27Mll10RENbFlCzB+vHj8yivApEmyhkMeSKEA2rYVj0+dstnbWpu1Vx6LZAQREZGTKL06W6VSISUlxbIRqamMy8aN4mI0EbkFJtCJ3EHTpoCfH2Aw2HS2mDWm2eharRZffvmlxRV4LrsmIqqBn38Ghg0Tf8vHjAHmzZM7IvJUdkigW5u1Z43VZAQREZGTKHk+rNPpEBsba7nDoEGAtzeQmQkcPixLjERke0ygE7kDhcLuZVxKUqvViIiIgK+vr9UacFu2bDE3CCMioko4fhx4/HFRc3rAAGDFCvG3nUgOdkigl561p1Qqofj7v3GVSoUFCxaUn4wgIiJyIqbzYasXe/39gcceE4/ZTJTIbdSSOwAispH27YEDBxySQDcxzSYrnUR/7rnnAIiT49TUVJ4IExFV5Nw5ICoKuHYN6NEDSE8XDaiI5GKHBDogZu1FRUUhKyvLXKLF9JgzzomIyG3ExACbNoljunnzOCmCyA1wBjqRu2jXTtz/+qvDPrL0bLLSWNKFiOgOrl4Vzab0enEh9KuvADZkJrnZKYEOWM7aq3AGH0TjUa5oIyIil/PYY+J4TqcD9u+XOxoisgEm0InchQNLuJQUGxuLdevWlfu8wWBAVlaWAyMiIrqz5ORkhIWFITw8XL4g8vOBgQNF+ZbmzYFt24CGDeWLh8gkNFTcX74sVkbIIC0tDRqNBpGRkdBoNGxSTkRErsPHR9RCB1jGhchNMIFuQ05xMk6eq+QMdAd3++7Vq1e5jcFUKpV5mTYRkbOIj4/H8ePHkZGRIU8At24Bw4eLxqH16gHffAO0bClPLESl+fsDzZqJx5mZDv94vV6PuLg4c4k4rmgjIiKXExMj7j/+GChV8pSIXA8T6DYk+8k4ebbQUFFb7fp14NIlh350eaVcVCoVnnnmGfz888886SUiMpEkYMIE4MsvAW9v4IsvgA4d5I6KyJIdy7jcSWZmptUm5VzRRkRELuORR4DAQOD8eeCnn+SOhohqiAl0Infh7Q20bi0eO7iMCyBKueh0Omi1Wuzfvx9TpkyBwWBASkoKYmJi0LJlSy6/JiICgJkzgfffB5RKsay3Tx+5IyIqS8YEuqlJeUlc0UZERC7FywsYPFg8ZhkXIpfHBDqRO5GhkWhJpmZgTZs2xX/+8x+L5yRJ4vJrIqKkJGDOHPE4JQV44gl54yEqj4wJ9NIr21QqFVJSUsptNkpEROSUTGVcPvlElO8jIpfFBDqRO5GpkWhpmZmZkKzUYefyayLyaOnpwEsvicdvvgk884y88RBVRMYEOmC5sm3Pnj0IDg7mRXgiInItDz4INGggSqzu3i13NERUA0ygE7kT0wx0mRPooaGhUCgUZbarVCr4+vpCq9XyJJiIPMvOncDIkaL+eXw88H//J3dERBUrmUB3YHNyvV5vPk5Qq9U4ffo0evbsicjISGg0GpaDIyIi11G7NvDPf4rHGzfKGwsR1QgT6ETuxDQDXaYSLiZqtRorVqywSKIrlUqMHDmSJ8FE5Hl++QUYMgQoLgaefBJ4+23R9JnImbVuDahUQF4e8McfDvnItLQ0aDQa83HCwoULERcXZ24oajQaERcXh4yMDIfEQ0TOITk5GWFhYQgPD5c7FKKqM5Vx2bwZKCqSNxYiqjaFZK3OAtVITk4OAgMDkZ2djYCAALnDIU9y8SLQpIlIzOTni8aiMtLr9dizZw8AoG7dunjiiSfMJ8GAmJGu0+lY05SoFI4jjmP37/r0aaBXL7F0t39/4OuvRVMpIlcQGgpkZQFaLRARYdeP0uv10Gg0FscJSqXS4mcThUKB+fPno1u3bggNDeVxBMmG47Vj8fsml2QwAM2bi3P1r78GHnlE7oiIPFJNx5AazUD/73//e8d91q9fX5OPIKKqaNwYCAwUS62doNa4Wq1GdHQ0cnJyMGjQoDInwayJTuQYHK9lcvEiEBUlkuedOwOffsrkObkWB9ZBz8zMLHOcYDQaoVSWPV2RJAmvvPIKV7SRW+KYTeRmVCpg4EDxePt2eWMhomqrUQL90UcfrbCOcXp6OsaMGVOTjyCiqlAogJAQ8fjMGXlj+Zter0dcXJzVpqKAOAFgPXQi++J4XZbdl4Pn5ACPPipmoLduLWYcBQba57OI7MWBCfTQ0NAyyXKVSoX58+dbTaKbGI1GTJgwgccS5DY4ZhO5n786dwYAFG3bdsd9S/YCISLnUaMEuq+vLx555BFcu3atzHObN2/GyJEj8Y9//KMmHyGL559/Hi1atEBAQACaN2+OSZMmoYi1qshVBAeL+9On5Y3jb9ZmlJWUmprK2WNEduau43VNxMfH4/jx4/appVxYCAwdChw6BDRqBGzbBjRtavvPIbI3BybQ1Wo1UlNToVKpAIjkeUpKCqZMmYK9e/dabU5uwhVt5E44ZhO5l7S0NHScOBEAUOvYMax9++0K9y3ZC4TnyETOo0YJ9G+++QZ//fUXBg0ahMLCQvP2L774Av/617/Qt29ffPbZZzWN0eFeeOEFnDx5Ejk5OThy5AiOHDmCt956S+6wiCqnTRtx7yQz0K3NKCuNs8eI7Mtdx2unZDQCY8YAO3cCvr7A1q2ijjSRK3JgAh0AYmNjodPpoNVqodPpEBsbCwAIDw/HihUrzMn10lQqFUJMK/CIXBzHbCL3YVqN/Yck4ThEAu6zhASr572mfUs2zuY5MpHzqFECvXXr1vjqq69w5MgR/Otf/4IkSdi6dSuGDRuGnj174ssvv4SXC9b6DAsLg6+vLwBRY1GpVCIzM1PmqIgqyclmoJeeUVYezh4jsh93Ha+djiQBkyYBGzcCtWuLmufduskdFVH1mRLop08Dt2455CPVajUiIiLKNAYtmVxfuHBhmZnqbCRK7oJjNpH7KLkae9ff2yKMRqvnvdZWbvMcmch51CiBDgBdu3bFpk2b8NVXX+Hxxx/Hk08+ifvuuw9bt25F3bp1q/Wec+fORXR0NIKDg6FQKNCqVaty9zUajViyZAnat28Pb29vtGjRAomJicjLy6vmbyTMmzcPfn5+aNy4MY4cOYJJkybV6P2IHMbJZqADZU96rc1I5+wxIvuyx3hNpcybByQliccffAA89JC88RDVVPPmQN26Inmu08kdjTm5PmXKFKsz1YncBcdsIvdQcjW2KYHeH7B63lteLxCeIxM5B4VUXme/Kvroo48wevRodO/eHdu3b4efn1/1g1Io0KBBA3Tt2hUHDx5EQEAAdOUctL/00ktYtmwZhgwZgkcffRQnTpxAUlIS+vTpgx07dlj8ARo+fDg2btxY7udqtVpERERYbDtx4gQ++ugjPPvss5We2ZKTk4PAwEBkZ2cjICCgUq8hshmdTjSsq1MHyM8XXb+djF6vx9tvv40lS5bAYDCYZ4/xBJhIsOc4Ysvx2h2Yv+vnn0dAeTP6KnOolJ0NrFolHi9ZImaiE7mDzp2Bo0eBr74CBgyQOxoip2Lv8z6O2ZZ4nk2uKC0tDRMmTECgwYDL+HsW6x9/AE2alLsvz5GJbK+mY0iVEuiRkZEVPn/gwAG0bdvWIhCFQoGdO3dWKagzZ84g+O8yFB06dEBubq7VBPqxY8fQsWNHDBkyBJs2bTJvT0pKwsSJE/HRRx9hxIgR5u03btywqCNXWmBgIGrXrl1m+8cff4x33nkHWq22UvFzYCdZGQyAt7eYLfb770CLFnJHVC69Xo+srCyEhIRArVZDr9cjMzMToaGhXIpNHq2m44ijxmt3YP6uAdhkxJ46VcxEJ3IX0dHAJ5/wwhCRFbY47+OYXXk8zyZXZTrv7fXCC6hz7Biwbh3wr39VuK/pHJmIbKOmY0itqux85swZKBSKcp9v2LAh/vrrL/z1119VDqQkU/L8TtavXw9JksqUVxk/fjymTZuGtWvXWiTQ/f394e/vX+V4iouLccpBzZOIakylAlq1ArKyRM1SJ06gq9Vq80HBokWLMHXqVBiNRiiVSqSmpvJqO1E1OWq8diuTJgHWZqCX9z1a2x4WBjz1lE3DIpKdgxuJVhcvwpOr4phN5P7M571RUcCxY4BWW24CveQ5MhE5jyol0MsroyKXjIwMKJVKdO/e3WK7t7c3unTpgoyMjCq/Z3Z2Nj799FMMHjwYgYGB+O9//4vZs2cjKiqq3NcUFhZazGzPycmp8ucS2VSbNiKBfuYMUKoskTNauHAhXnnlFfPPRqMRcXFx6NSpE8LDw2WMjMg1Odt47RJefx3gbDaislwggZ6Wloa4uDhehCeXxDGbyINERgKLFwO7dt15XyJyKlVKoJensLAQu3fvxpm/mxa2adMGffv2hbe3ty3evlwXLlxAUFCQ1S7kzZs3x88//4yioiLUqVOn0u+pUCiwdu1aJCQkoKioCI0bN8bQoUPx+uuvl/uauXPnVvg8kcOZVnGcPi1vHJWQkZFhkTw3MRqN6NGjB1asWMGTYCIbkWu8JiIXFhoq7jMz5Y2jHHq93pw8B8Txw4QJExAVFcUZfOTSOGYTuaE+fcSK8dOngbNnAY1G7oiIqJJqnED/8MMPkZCQgGvXrsFUTl2hUKBevXr4z3/+g7Fjx9b0I8qVn59vNXkOwHxgkZ+fX6UEekBAAHbs2FGlOKZPn46EhATzzzk5OWjhxGUzyAO0aSPu/z7gdlamGWPlkSSJJ8FENiLneE1ELsx0UV6vB4qLASv9guT0888/m5PnJgaDAVlZWTx2IJfFMZvITQUEAN26Afv2iTIu/H+ZyGXUKIG+ceNGjB07Fi1btsSUKVMQFhYGQDT3fO+99xAbG4u6desiJibGJsGW5uPjg0uXLll9rqCgwLyPvXl5eZWbyCeShQvMQC89Y6w8PAkmqjm5x2sicmF33QXUrQvcvCmak5su0juBtLQ0jB8/vsx2lUqFkJAQGSIiqjmO2URuLjKSCXQiF6SQTJe0q6Fz584oLi7G3r17y3Qwzc7ORo8ePeDl5YUjR45UO8AOHTogNzfXam24qKgo7Nixw+pM9N69e+PUqVO4fPlytT+7qpKTk5GcnAyDwYBTp06xOzjJ5+hRoHNnoGFD4MoVuaOxSqvVIjIyslL7Lly4EFOmTLFzRETOo6YdwktzxHjtqmz9XRO5pbAw4MQJ4NtvgYcekjsaAOJCvEajKXMhXqVSISUlxVz+jc1FyZ7sMYZwzC4fx2xyCzt2iLFUrRYXpitoIkxEtlPTMURZkw//9ddfMW7cOKsfHBgYiHHjxuGUHRsOhYeHw2g0Yv/+/RbbCwoKcPjwYXTr1s1un21NfHw8jh8/Xq3mpUQ21bq1uP/rLyA7W95YyhEaGgql0vJPkFKpxAsvvFBm36lTpyI9PR16vd5R4RG5FbnHayJycaaVbb/9Jm8cJWRmZlpdxbZ+/Xpz8jwtLQ0ajQaRkZHQaDRIS0tzdJhEVcYxm8jN9eolyqHp9UBWltzREFEl1SiB3qRJkwqfVygUuOuuu2ryERWKiYmBQqHA0qVLLbavWLEC+fn5eOqpp+z22UROzd8faNxYPHbSOuhqtRqpqalQqVQAxIyx1NRUDB06tMy+RqMRMTExPPklqia5x2tnlJycjLCwMISHh8sdCpHzM12Yd6IEurUL8SqVCvfffz+A8puL8mI8OTuO2URuzscH+HusglYrbyxEVGk1SqCPHTsWq1atQm5ubpnncnJysGrVKowbN67K77tmzRrMnj0bs2fPxuXLl5GdnW3+ec2aNeb9OnbsiPj4eGzevBlDhw7FypUrkZiYiISEBPTr1w8jRoyoya9XZTwZJ6fiAnXQY2NjodPpoNVqodPpEBsba/WE2IQnv0TVY6/x2pVx1RhRFThhAt3ahfiUlBRzmRZrM9RNfVWInBnHbCIPYCplumuXvHEQUaXVqIlonz59sGXLFnTs2BHPP/882rdvDwA4ceIE3n33XQQFBaFPnz74/vvvLV7Xt2/fCt83LS0N3333ncW2mTNnAgD69euHUaNGmbcvXboUrVq1QmpqKr766isEBQXhxRdfxBtvvFFuEs5e4uPjER8fb66rQySrNm2AvXuddga6iVqttqhJqlarMW/ePLzyyitW9zcYDPj4448RHR3NWqZElWSv8ZqIPIQpge5kxxSxsbGIiopCVlYWQkJCLI4LTBfkSybRVSoVLl26BL1ez2MIclruOGYXFhbihRdewM6dO3H58mU0bdoUL774Il588UW5QyOSR//+wKxZYga6JLEOOpELqFET0dIJasXf/9OXfEtFiT8EkiRBoVDAYDBU9yNdApubkFP497+BN98E4uKAlBS5o6mSyjQYVSgUSExMxEsvvcSTYHI7th5HOF6Xj2M2USUcOQJ06QIEBQGXL8sdTYVKNg3dtm0bJkyYAIPBAKVSCUmSIEkSlEolUlNTzbXSiarLHmOIO47ZeXl5mDdvHsaMGYPg4GAcPXoUUVFRSEpKwrBhwyr9PhyzyW0UFgL16wM3bwL/+x9wzz1yR0Tk9mo6htRoBvqqVatq8nIisqc2bcS9k80Wqwxrs8ZKkyQJixYtwuLFi3kSTHQHHK+JqEZMM9CvXAFu3BC9VpxQWlqaue65KUmu0+mwZ88exMTEmBOQppJwUVFRvAhPTscdx2xfX1+8+eab5p+7dOmCQYMG4ccff6xSAp3IbXh5AQ88AGzfLsq4MIFO5PRqlEAfM2aMreJwC8nJyUhOTnbqq//kQVygBnp5THVNTbPGKsKTYKI743hNRDUSEAA0aABcvSrqoHfqJHdEZVhrGhoXF4e9e/ciKCgIpRfdmuqh89iBnI29xuy5c+fil19+wcGDB/Hbb79Bo9FAp9NZ3ddoNOLtt99GSkoKdDodGjVqhGHDhuGNN96Ar69vjWMpLi7GDz/8gClTptT4vYhcVv/+txPoLGdE5PQcWyTczbEhGTkVUwL999+B4mJ5Y6kGU4PRxYsX33FfNgUjIiKyMydsJFqStaahRqMRPXr0wIEDB8qUxVCpVAgJCXFkiESymjFjBnbt2oU2bdqgfv36Fe47efJkJCQkICwsDElJSYiOjsayZcswcODAMv+fDR8+HAqFotzb7t27y7z/Cy+8AH9/f4wePdqWvyKRazGVLP3uO4CTMImcHhPoRO6qaVPA21sMxr//Lnc01aJWqxEdHW1R59EangQTERHZmenCvJMm0E3l30qTJAnTp0/H/PnzoVKpAIjjhpSUFM4+J49y+vRp/PXXX9i+fTuaNWtW7n7Hjh1DUlIShg4dis2bN2P8+PFYvHgxFi9eDK1Wiw0bNljsv2LFCly+fLncW+/evS32T0hIwJ49e/D111+jTp06dvldiVzCffeJkmjXroleI0Tk1JhAJ3JXSuXt2WIuWAfdRK1WY/78+eU+r1QqMXnyZAdGRERE5IGcfAa6qfybtSS6wWBAt27doNPpoNVqodPp2DuFPE6w6SLYHaxfvx6SJGHSpEkW28ePHw8fHx+sXbvWYru/vz+CgoLKvdWuXdu876RJk7B9+3bs3LkTQUFBNf6diFxarVpAv37i8a5d8sZCRHfEBLoNJScnIywsDOHh4XKHQiS4cCPRkl5++WUsXLjQfFKsUqmwcOFCc93ERYsWQaPRIC0tTc4wiYiI3JcLXJSPjY3F3r17y6xcM61UU6vViIiI4MxzogpkZGRAqVSie/fuFtu9vb3RpUuXapcrnThxInbs2IFdu3ahUaNGtgiVyPX17y/umUAncnpMoNsQa6CT03HhRqKlTZkyBWfPnjXPHBs+fDgWL15cpllYeno69Hq9zNESERG5GSefgW4SHh6OFStWsFwLUTVduHABQUFB8PLyKvNc8+bNceXKFRQVFVXpPc+ePYukpCRkZWWhdevW8PPzg5+fHx599NEKX1dYWIicnByLG5FbMdVB/+EHl+xbRuRJaskdABHZUatW4t5Fa6CXplarzSfAWq3WarOwmJgYKJVKpKamcnk2ERGRrZSsgS5JwB36k8gpNjYWUVFRyMrKMs88J6LKyc/Pt5o8B8QsdNM+ValfrtFoIElSlWOZO3cuXn/99Sq/jshldOoENGgAXL0KHDgA3H9/pV+q1+uRmZmJ0NBQjnNEDsAZ6ETurGVLcX/2rLxx2EF5zcIAkUifMGECZ6ITERHZSsuWImmenw9cuiR3NHdUslyLXq+HVqs1HxeU/pmIbvPx8UFhYaHV5woKCsz7OML06dORnZ1tvp07d84hn0vkMEolEBEhHlehjEtaWho0Gg0iIyNZypTIQZhAJ3JnGo24d5MZ6CVt27atwpksBoMBb7/9tgMjIiIicmNeXkDz5uKxk5dxKal0kmHs2LFMOhBVoFmzZrhy5YrVJPr58+cRFBRUpdnnNeHl5YWAgACLG5HbMZVx0Wortbter0dcXJxFKVNOHiOyPybQbYhNRMnpmGag//EHUMVahc7MdNBwp6Wgixcv5oEEERGRrbhIHXQTa0mGDz74gEkHogqEh4fDaDRi//79FtsLCgpw+PBhdOvWTabIiNyUKYH+00/A36s8KpKZmVmmlKnBYEBWVpY9oiOivzGBbkNsIkpOp1EjwNtb1Cp1o5NDawcN1hiNRh5IEBER2UrJOuguoDLHC0w6EFmKiYmBQqHA0qVLLbavWLEC+fn5eOqpp+QJjMhdtW8PNGkikud7995xd2ulTFUqFUJCQuwVIRGBCXQi96ZQ3J6F7kZlXCqqf14aL2gRubfnn38eLVq0QEBAAJo3b45JkyahyI1W3BA5FdMM9DNn5I2jkipzvMCkA3mKNWvWYPbs2Zg9ezYuX76M7Oxs889r1qwx79exY0fEx8dj8+bNGDp0KFauXInExEQkJCSgX79+GDFihMNj50pvcmsKBdC/v3hciTIuarUaqampUKlUAMQ4lpKSwkaiRHbGBDqRu3PDRqKmg4bKJNGnTZvGJDqRG3vhhRdw8uRJ5OTk4MiRIzhy5AjeeustucMick8uVsLFWpJhzJgxTDqQR0pLS8PMmTMxc+ZMXLp0CdevXzf/XLoXwNKlS7Fo0SIcO3YM8fHx2LBhA1588UVs2bKl0pNYbIkrvcntmcq4VLKRaGxsLHQ6HbRaLXQ6HWJjY+0YHBEBQC25AyAiO3PTRqKxsbHo1KkTevbsWeHybKPRiJ49eyI1NZUHFkRuKCwszPxYkiQolUpkZmbKGBGRG3OxBDogjheioqKQlZWFkJAQqNVqzJ492/wzAGi1WoSGhjKRTm5t9+7dld5XpVIhMTERiYmJ9guIiG4zJdD37QPy8gBf3zu+RK1Wc9wiciDOQCdyd244A90kPDy8zMwyhUJRZj82CSOyn7lz5yI6OhrBwcFQKBRo1apVufsajUYsWbIE7du3h7e3N1q0aIHExETk5eXVKIZ58+bBz88PjRs3xpEjRzBp0qQavR8RlcNUA/3334Fbt+SNpQrUajUiIiLMiQbTz9u2bYNGo0FkZCQ0Gk2ZWbhEREQO0bq1OG8vLhbNRInI6TCBbkOszUZOyU1noJuUXr42f/58q/uxSRiRfcyYMQO7du1CmzZtUL9+/Qr3nTx5MhISEhAWFoakpCRER0dj2bJlGDhwYJmVJMOHD4dCoSj3VnIm3bRp05Cbm4vjx4/j2WefRdOmTe3xqxJR06aAlxdgMADnzskdTY3o9XrExcWZ//bwYjsREclGoahyGRciciyWcLGh+Ph4xMfHIycnB4GBgXKHQyS4YRPR0kouX+vWrZvVfZRKJZuEEdnB6dOnEfz3rNQOHTogNzfX6n7Hjh1DUlIShg4dik2bNpm3t27dGhMnTsSGDRssGpOtWLECy5cvL/dzrY2zd999Nzp37oxRo0ZBW4kmTERURUqluDB/6pQo42Iq6eKCMjMzy1y4M11s55J4IueSnJyM5ORkGAwGuUMhsp/ISGD1aibQiZwUZ6ATubuSCXRJkjcWBwgNDbXa3Gj+/Pk8ISayA1Py/E7Wr18PSZLKlFcZP348fHx8sHbtWovt/v7+CAoKKvdWu3Ztq59TXFyMU6dOVet3IaJKcME66NZYO15QqVRlLrbr9XpotVrOTCeSEZuIkkfo31/cHzwIZGfLGwsRlcEEOpG7U6vFkrCbN4ErV+SOxu7UarVFXXSlUokFCxZgypQpMkdG5NkyMjKgVCrRvXt3i+3e3t7o0qVLtU6Ks7OzsXr1aly/fh2SJOHo0aOYPXs2oqKibBU2EZVmumh25oy8cdRQ6eMFlUqFlJQUi4vtaWlprJFORESOoVYDoaGA0Qh8/73c0RBRKUygE7k7Ly+gSRPx2A0biVpTsi763r170a1bN84cI5LZhQsXEBQUBC8vrzLPNW/eHFeuXEFRUVGV3lOhUGDt2rUIDg6Gv78/Bg8ejAEDBiApKanc1xQWFiInJ8fiRkRV4Ea9VaKiorBu3Tqkp6dDp9MhKirKPNs8IyODNdKJiMixWAedyGmxBjqRJ9BogD/+ECe75dQIdzdqtRrbtm0zn/wqlUqkpqYiKioKmZmZCA0NZUkXIgfKz8+3mjwHxCx00z516tSp9HsGBARgx44dVYpj7ty5eP3116v0GiIqoUULce/iTUTT0tIsjhFGjRqFNWvWwGg0QqFQQLJS9o410omIyK769wdSUphAJ3JCnIFO5AlMddA9ZAY6IGqWlp45Nn78eC7FJpKJj48PCgsLrT5XUFBg3sfepk+fjuzsbPPtnIsnAYkczg2ak1s7Rvjggw/MP1tLngPWa6QTkf0lJycjLCwM4eHhcodCZF8REeL+6FGPKL9K5EqYQCfyBG5wsltVmZmZ5hNhE0mSuBSbSCbNmjXDlStXrCbRz58/j6CgoCrNPq8uLy8vBAQEWNyIqApMM9D1elGn1QVZO0a4E6VSWaZGOhE5BpuIkse46y6gXTvxmP+9EzkVJtBtiFfGyWm5Ub3SygoNDYVCoahwH9NSbCKyv/DwcBiNRuzfv99ie0FBAQ4fPoxuHlJeisjlNWsGKJVAcTFw6ZLc0VRLaGgolMrKnwYplUrs3bsXsbGxdoyKiIgIgCmfdOCAvHEQkQUm0G2IV8bJaXlgCRe1Wo3ExMQK9+FSbCLHiYmJgUKhwNKlSy22r1ixAvn5+XjqqaccGg8vehNVU+3aQNOm4rGLXphXq9VITU2FSqUCII4HxowZY/5ZqVSaL8KrVCqkpqbybwURETmGaVIJE+hETkUhlVfkj6otJycHgYGByM7O5tJwcg5HjgBdugCNGrnsbLHq0Ov10Gg05S7TfvbZZzFs2DA2FCWn40rjyJo1a3D274tzSUlJKCoqMl+80mg0GDVqlHnfF198EcuXL8eQIUMwYMAAnDhxAsuWLUPv3r2xa9euKs0ItRVX+q6JnEavXsCePcAnnwD//Kfc0VSbXq9HVlYWQkJCoFarLX4GYPEckTUcQxyL3zd5hJ9+Ah54QKz4On++2m+j1+uRmZnJc12iv9V0DGEC3Q44sJPTuXYNaNBAPM7LAxzQqM9ZpKWlYfz48eU2BAPETLPU1FQuzSan4UrjSEREBL777jurz/Xr1w+7d+82/2wwGLB06VKkpqZCp9MhKCgIMTExeOONN+Dn5+egiC250ndN5DRiYoD0dGDxYmDyZLmjsQkmGqg6OIY4Fr9v8gh5eUBAgOgzcv68SKRXUVpamrlZNs91iYSajiEs4ULkCerVA/z9xeNz52QNxdGioqLuuE/phqJ6vR7p6elIT09nk1GiO9i9ezckSbJ6K5k8B0QphMTERPz6668oLCzE+fPnsXjxYtmS50RUTabScG5yTJGWlgaNRoPIyEhoNBqkpaXJHRIREXkqX18gLEw8Pniwyi/X6/Xm5DlQ9lyXiKqHCXQiT6BQeGQddADIzMyscPa5icFgwMcff4xFixahZcuWiImJQUxMDFq2bMkTaSI3xBroRDXQooW4d9Ea6CVVNdGg1+uh1WqZiCByII7Z5HFqUAc9MzOzTAlTg8GArKwsW0RG5LGYQCfyFKYEuhuc7FZFaGhopesqJyQk4OWXX7ZIuEuShLi4OJ4oE7kZNv4mqgE3moFelUQDZ6oTyYNjNnmcGiTQrZ3/qlQqc38PE14QJqoaJtCJPIVGI+49LIGuVquRmpoKlUoFAFAoFFV+D6PRiD179vAAg4iICHCrGejlJRouXbpkMeZzSTwRETnMffeJ+wMHgCq2LSx9/qtSqZCSkmLR34MXhImqjgl0Ik/hoSVcACA2NhY6nQ5arRb79u2rchJdoVAgJiaGBxhERETA7WOKP/8ECgvljaWGSicalEoljEYjYmJiLMb88maqv/322w6PmYiI3FznzoBKBVy6BFTjQm3J81+dTmfRQJQXhImqhwl0Ik/hoSVcTNRqNSIiIhAeHo4FCxZU+nWmZLuprAsPMIiIyOMFBQHe3uLx+fPyxmIDpkRDenq6uQkyYDnml1cSbvHixTwmICIi26pbF+jQQTyuRhkX4Pb5b8mZ5wBrpBNVFxPoRJ6ieXNx7wYnujWRlpaGqVOnmn8ubzb6u+++i/T0dGzYsKFME1KDwYA9e/bYNU4isi82JCOqAYXidhkXN6iDDohEQ1BQkNUxPysrC2q1GgkJCWVeZzQamXQgIiLbq0Ed9IpUpkY666MTlcUEug3xZJycWskEehXrqLmL0svVAJFAnzBhgjmRrlQqsWDBArRr1w73338/fHx8rL7X8OHDWcqFyIWxIRlRDblRHXSTOyUVXnrppTIX3q01ZiMiIqoxOyXQ71QjnfXRiaxjAt2GeDJOTs2UQM/PB7Kz5Y1FJtaWqxmNRgwfPhy///47tFot5s+fj2nTpiEyMhItW7bEwIEDrb4XS7kQEZFHM5WGc5MZ6MCdkwpqtRorVqywqJc+efJk2eIl8hScqEYeqWQC3cYT4Mqrkc766ETlYwKdyFP4+AD164vHHlrGpaKZZWq1GiEhIZg6dar5gKH0Mu7SWCuOiIg8lhvOQAcqbrxW8vkpU6YAABYtWsQZekR2xolq5JE6dgRq1wauXgV0Opu/vbUa6ayPTlQ+JtCJPImH10Evb2YZAGi1Wvz8889lDhgqolQquWybiIg8kxvOQDcpr/FaSYsXL+YMPSIish8vL6BTJ/H44EGHfGRl6qMTeSom0Ik8iYcn0IGyM8sAmGu8DR8+vNymotaMHz/eTlESkb1xOThRDbnpDHRrSjdT4ww9IiJyCDvVQS/PnUqZEXkyJtCJPAkT6ABuzywDYFHjzVSyxXTAUB6FQgGFQoGUlBQu2yZyUVwOTlRDbjwDvSRrzdQ4Q4+IiBzCwQl04M6lzIg8FRPoRJ6ECXQL1maQSZKEN998s8xMdKVSif379yM9PR0KhcKcbOeybSIi8kimGejZ2UBOjryx2El5zdQAWMzQUyqVmDdvHmfoERGRbdmxkWhFKlPKjMjTMIFO5EmYQLdgbQYZAMyYMaNMA1Gj0Yi8vDwEBQVx2TYREZGf3+3m5G46C72iUi2xsbGYO3cuFAoFjEYjpk6dyhVpRERkW/fcI2qhZ2cDp0/LHQ2RR2MCnciTMIFuoXSNt4qYlmZz2TYREdHf3LwOekVjvl6vx7Rp07gijYiI7Kd2baBLF/HYgWVciKgsJtCJPAkT6GXExsZi3bp1Vp8znTSrVCrMmzcPmZmZAIBRo0ZZ7NfNtLSOiIjIk7h5HfSKmqmxkSgRETnEffeJeybQiWRVS+4AnNnNmzfRsWNH/Pnnn8jNzZU7HKKaMyXQL14EioqAOnXkjcdJ9OrVC0ql0uJEWKVSYc+ePcjLy0NGRgamTp0Ko9FYpjY6AOzbtw8tWrTAypUr2WSFiIg8h2kGupsm0AFxoT0qKgpZWVkICQkx14M1zU4vfezAFWlEtpecnIzk5GQYDAa5QyFyPBkaiRJRWZyBXoF///vf0Gg0codBZDtBQWIZGAD88Ye8sTiR0jPMTM3AwsPDERISgmnTpplPkCVJKlMf3WT8+PFIT0/n8m0iF5CcnIywsDCEh4fLHQqR6zLNQHfTEi4m1pqpVTQ7nYhsKz4+HsePH0dGRobcoRA5nimBfvAgUGrlExE5DhPo5Th48CC++eYbTJ06Ve5QiGxHqQSaNROPWcbFQnnNwKwt0S6PJEmIiYmBRqNhIzEiJ8eTcSIb8IAZ6BWJjY2FTqeDVquFTqfjKjQiIrK9u+8G6tYFcnOBU6fkjobIYzllAn3u3LmIjo5GcHAwFAoFWrVqVe6+RqMRS5YsQfv27eHt7Y0WLVogMTEReXl51f78W7duYfz48UhOTkYdlrggd8M66FaV1wzMz8+vTNkWa2VcSjIajYiLi+NsdCIicm8eMgO9Imq1GiEhIcjMzERGRga0Wi3HfiIisp1atYB77xWPWcaFSDZOmUCfMWMGdu3ahTZt2qB+/foV7jt58mQkJCQgLCwMSUlJiI6OxrJlyzBw4MAys0aHDx8OhUJR7m337t0AgIULF+Lee+9F37597fUrEsnHtLSYCXQL5TUDS09Pt9imUCiwYsUKPPnkkxW+n9Fo5Gx0IiJyb6YZ6Hq9xy4rT0tLg0ajQWRkJLp3747IyEiO/UREZFusg04kO6dsInr69GkEBwcDADp06FBuA89jx44hKSkJQ4cOxaZNm8zbW7dujYkTJ2LDhg0YMWKEefuKFSuwfPnycj83MDAQWVlZeO+993Do0CEb/TZEToYz0K2y1gxMqVRi8eLFFjXPlUolOnXqhODgYAQGBt7xBNk0kz0qKop1UYmIyL00bw4oFEBhIXDlCtC4sdwROZRer0dcXFyZC/Ac+4mIyKaYQCeSnVPOQDclz+9k/fr1kCQJkyZNstg+fvx4+Pj4YO3atRbb/f39ERQUVO6tdu3a+PHHH3Hx4kW0bdsWQUFBeOKJJ5CXl4egoCB8//33tvoVieTDBLpV1pqBJSQkWJ2V3qNHD0RGRuL999+v1HsbDAZkZWXZPGYiIiJZ1a4NNGokHl+4IG8sMqioTwrHfiIishlTAv3QIcBgkDcWIg/llAn0ysrIyIBSqUT37t0ttnt7e6NLly7Vagw2bNgwZGVl4fDhwzh8+DBWrlwJHx8fHD58GD169LBV6ETyYQK9XKWbgb300ktQKsv+mTTNSJckqUw99H79+pV5jUqlQkhIiP0CJyIikovpuMIDEuh6vd6ixrlp9Zo1SqUSJ06cYF10IiKqubZtAT8/ID8fOHlS7miIPJJLJ9AvXLiAoKAgeHl5lXmuefPmuHLlCoqKiqr0nj4+PlCr1eZbo0aNoFAooFarrX4OABQWFiInJ8fiRuS0mECvkFqtRkREhPlvQMlZ6eUl0999910sWbIE+/fvx9q1a5GQkGDeV6lUIiUlhUu4iYjIPTVrJu7d/LiiZK1zU43z0scJJRmNRjz//POsi05ERDWnUgFdu4rHLONCJAuXTqDn5+eXm9T29vY271MTERER5dZgN5k7dy4CAwPNtxamhkpEzqhkAr1EbW+yruSs9L1795aZca5SqfD4449j0qRJOHr0KDQaDRYtWlRmSXfpWWtEJK/k5GSEhYUhPDxc7lCIXJsHzEAvXevcVONcr9dbHCd8+eWXZY4TTEq+hoiIqMpYB51IVi6dQPfx8UFhYaHV5woKCsz72Nv06dORnZ1tvp07d87un0lUbaaZYgUFwNWr8sbiIkyz0o8ePWqxXaFQmGeXV9RILC4uDi1btuQMNCInEh8fj+PHj1er3BsRleABM9Ct1TovWePcdJzg6+tr0Xi8NNZFJyKianPBBDonkZE7cekEerNmzXDlyhWrSfTz588jKCgIderUsXscXl5eCAgIsLgROS1vb6BhQ/HYjU92bc2UIC95YqxUKhEVFQWg4kZiRqPR/DrOQCMiIrdiSqC78Qx0a7XOrfU3qagmOiCOGy5dugS9Xg+9Xo/09HSkp6dX6piASQgiIg9nSqAfPgwUF8saSmVYK31G5MpcOoEeHh4Oo9GI/fv3W2wvKCjA4cOH0c30B8ZBuBycXAbroFfZnWaf+fn5lbtsuzTOQCMiIrfhASVcStc6V6lUVvubmPazlkRXKBSQJAkx/9/e/UdHVd/5H3/NDPIzEH8E5MdA+JGAYnFtIbRQFOrWxrJyttJFEA6G880CLvEHlt1K3eN2VRRr9ygC2W8N5LuygNR0bbuHcnZrXSJKoUuggpWgJGqQARSkkJCEBMjc7x/jHTPJnclMcmfuTOb5OCdnks/cH++ZezOf+3nP534+c+dqxIgRGj58uObOnRv8O1JigSQE0h3tbEDSmDHSgAGBO8krK52OJqJIQ58BqSqlE+hz586Vy+XSmjVrQso3bNigxsZGLViwIKHxcDs4UgYJ9JhF6n1WWlqqb3zjGxFv27ZaDwCAlJcGQ7hIoXOi1NTUqLCwMOxyx44dC/Yu37dvn8rKyoIJdEntrhcMwwibWCAJAdDOBiRJbrc0cWLg9yQfxqWjzmdAKurhdABWNm/erGPHjkmSzpw5o0uXLmnVqlWSpOzsbC1cuFCSNGHCBBUVFWn9+vWaPXu2Zs6cqSNHjmjt2rWaPn265s+f79hrAJIaCfSYmb3Kli5dqpaWlmDvM0mWY5+HE67XGgAAKcm8pjh9OnBL+VVXORtPHHm93qjqb6/Xqzlz5gT/rq+v7/A6wUwstN1+pCQE1xIAkGYmTZLKywMJ9DBf5CYDs/NZ6/qLTmRIdUmZQC8tLdWuXbtCyh5//HFJ0vTp04MJdElas2aNRo4cqZKSEu3YsUNZWVl68MEH9eSTT0YcgzAeiouLVVxcrJaWloTuF4iZ2eAigR6TwsJC5efnq7q6Wjk5OfJ6vSovL486ee5yufTss8+G7bUGAEDKue66QNL88mXp1ClpxAinI0o6VomEtsIlFkhCAACCUmQi0XCdz/jiF6nMZUQ75gCiVldXp8zMTNXW1jKhKJLTxo3S4sXSzJnSjh1OR5PSfD6fsrOzY+qBXlNTw8UDIqIeSRzea8AGI0dKx45Je/dK3/iG09E4yufzqaqqSrm5uZICPcgzMjJUVlam559/Xn6/PzhnitkMc7vdKikpCfsFe2lpabskBF/GJwfqkMTi/Uba++ijwFjoV10lXbgg9erldEQR+Xy+kM5ngJO6WockZQ90AHE2ZEjg8dNPnY2jG/B6vVq4cKE2bdoU1fItLS168cUX9dOf/jTOkQEAkCBDhwYS6N14ItFolJaWBod1a5sklwKJ8r//+7/Xww8/LEnau3evJGnKlCkREwtWd8ABANLQqFHSNddI585J77335ZjoSSraoc+AVJDSk4gmG2YHR8oYPDjwSAK9y3w+nzZv3hzTOs8//zyTfwEAuo80mUg0kraTfRqG0W6yUL/frxdeeEHSl+Okz5kzJ+px1WfMmEEiAgDSmcuVMsO4AN0NCXQbMTs4UoaZQP/sM4kx+7vEanKvjvj9fv3mN79ReXm5KioqVF5eLp/PJ5/PF/wdQHzxpTdgI3Mi0TTugR7t9YA5ASgAAJ1CAh1wBEO4AOlo0KDAt9ctLdLZs4G/0SnRTAxm5e/+7u9C/m59q3dHY6EC6LqioiIVFRUFx8ID0AX0QI/6eoAJQAEAXUICHXAEPdCBdHTVVVJWVuD3U6ecjSXFmTOMezweSYHxTc1keCxa3+rt9/u1ZMkSeqIDAFIDPdCjuh4wJwC1GoYl3F1o3J0GAAhhJtDfe09qanI2FiCNkEAH0hUTidqmsLBQNTU1Ki8v17Fjx/TJJ5/o+eef79I2/X6/XnzxRZsiBAAgjuiBLsn6eqC8vFz79u1TeXm5ampqLO8uKy0tVXZ2tm6//XZlZ2ertLQ0YjkAII0NHy4NHChduSK9+67T0QBpgyFcbFRcXKzi4mK1MKY0UsHgwYEKlwS6LVrPMO7z+dS7d+8ub/OFF17Qww8/zIRhAIDkZibQ07gHuqn19YD5dyRtJx/1+/1aunSpbr75Zsvy/Px8rgsAIJ2ZE4n+138FhnGZPNnpiIC0QA90GzGJKFKKOZEoQ7jYyuwttmzZsi5vi4nGAAApwRzCpa5Oqq93NpYUYzX5aEtLi3bv3m1ZznUBACA4jAu5JyBhSKAD6YohXGzXthdZLNxut9zu0I9kJhoDAKSE/v2ljIzA7/RCj4k5+WhrHo9H06ZN47oAAGDtllsCj3/6k6NhAOmEBDqQrswe6CTQbWPVi6yt6dOnWzaIS0pK2k0+9uyzz3KbNgAgNTCRaKe0nXzUnGg0Ly/PspzrAgCAbrop8HjkiNSJzlsAYscY6EC6YggX25m9yKyS6NOnT9dbb72lXbt2Bcsee+wx3XHHHcrJyQk2iP/85z/r0Ucfld/v16OPPqprrrnGcsIxAACSytCh0gcfpP1Eop1RWFio/Px8VVdXh1wThCsHAKS5MWOknj2lxkbp2DFp1KiE7Nbn86mqqkq5ubkhdVK48njsK577tCMudF/0QLdRcXGxxo8fr7y8PKdDATrGEC62a9uLrLVdu3bJMIyQsp/85CchDWKfz6eVK1cGlzMnDPP5fPEPHgCArmAi0S7xer2aMWOGZUKiX79+qqqq4noAABDQo4c0blzg98rKhOzSnOvr9ttvV3Z2tkpLSyOWx2Nf0T4fL07tF8mBBLqNmEQUKYUhXOKisLBQr7zySlTLtp0MLNxEYnv37lV5ebkqKipUXl5OAxoAkHwYwsVWrRvpkydPprGOtEZHNcDC+PGBx8OH476rtnN9mR29KioqLMu70l4Nty9zmx09Hy9O7RfJgwQ6kK7MBHpdXeDWL9hm6tSp7cY5t9J2MjCricRcLpfmzZtHAxoAkNzMHugM4dJl4SYlp7GOdEVHNcCCOQ56Anqgh+votXv3bsvy1p3E7NqXuc2Ono8Xp/aL5EECHUhXAwZIffoEfqcXuq2sJgSz0naS0Lbrmcl0GtAAgKRHD3TbRJqUnMY6AEBSQnugW3X08ng8mjZtmmV5605idu3L3GZHz8eLU/tF8iCBDqQrl4thXOKosLBQNTU1Ki8vDzuky6RJkyKut23btnbjpptoQAMAkgo90G1j1Ug30VgHAEj6sgf6kSNSmC9d7WLVQeyll15SXl6eZXlXJtcMty9zmx09Hy9O7RfJo4fTAQBw0JAh0scfS6dOOR1Jt+T1euX1euXz+eR2u0N6k3k8Hh05ckSnT5/WqFGjVF9fr4yMDH388ceSpFFfzKTedr3W69OABjqvuLhYxcXFamlpcToUoHtoPYmoYQS+qEenmI30pUuXhnxG0VgHAASNGSNddZXU0CB98ok0cmRcd1dYWKj8/HxVV1crJycnWBeFK4/HvqJ9Pl6c2i+Sg8sI170RMWvdGD969Khqa2s1YMAAp8MCwvv+96Vf/lJav14qKnI6mm6ttLQ02BAOlxS34nK55HK52iXfX3rpJRUWFsYrXDisrq5OmZmZ1CMJwHsN2KS5WerdO/D7mTNSVpaz8XQDPp9P1dXV6tevnxoaGmisJyHqkMTi/QbamDBBeu89accOaeZMp6MBklpX6xB6oNuoqKhIRUVFwYMCJD2GcEkY89vqvXv36p577ol6PcMw5HK5VFZWppEjR9KABgAkp169Aknzzz8P9EIngd5l5p1sAABYGj8+kEA/fJgEOhBnJNCBdDZkSOCRIVwSwuv1KqsTCQW/36+BAwcqLy8vDlEBAGCTYcO+TKDffLPT0aQEn8+nqqoq5ebmhiTLw5VHs37rMklRbQcAkILMiUQrK52NA0gDTCIKpDN6oCec2ZiNRdvxzn0+n8rLy+Xz+ewMDQCArmEi0ZiUlpYqOztbt99+u7Kzs1VaWhqxPJr1W5eNGDFCI0aM6HA7AIAUZU4keviws3EAaYAEOpDOzAQ6PdAT5re//a1cMUys1nbCsGgb1QAAJJx5XfHZZ87GkQJ8Pp+WLFkSnOPE7/dr6dKlqqiosCxv+6V5uPUXL14cLDMMQ+Z0V+G2AwBIYa17oDO9IRBXJNCBdGYO4UIP9IQwG7vRzN3sdrtVVlammpqa4GSh4RrLNIYBAEmBO9uiVlVV1W5C8ZaWFu3evduyvLq6Oqr1I11jWG0HAJDCcnOlHj2khgbpk0+cjsZR3KWNeCOBDqSz1j3F2jTCYD+rxm445rjnrccrDddYpjEMAEgKJNCjlpubK7c7tCnm8Xg0bdo0y/LWQ7lFWj/SXW5W2wEApLCrrpLGjg38nsbjoHOXNhKBBLqNiouLNX78eCb6Q+oYNEhyuaSWlsCkX4grq8ZuOLE0lmkMAwCSAkO4RM3r9aqkpEQej0fSl0O25eXlWZa3nQA03PobNmwIlrlcruB1Q7jtAABSnDkOepom0LlLG4nSw+kAupOioiIVFRWprq5OmZmZTocDdOyqq6SsLOnMmUBvsUGDnI6oWzMbu0uXLlVLS0uwl1jb2609Ho9Wr16tqqoqnTp1SvX19crNzW23vp2NYZ/Pp6qqquB+AACI2fXXBx7pgR6VwsJC5efnq7q6Wjk5OcH6N1x5tOu3LpPU4XYAACnMHAc9TScSjXSXNvUe7EQCHUh3gwd/mUC/+Wano+n2Wjd29+/fr3/4h38Ied7lcmn27NlauXJlyIWA2+1WSUlJ1I3qWJSWlga/tW+9HwAAYsIQLjHzer2WdXm48miWa1tGAgEAurE074Fu3qXduu3MXdqIB4ZwAdKdOZHoqVPOxpFGvF6vcnJy9MMf/rDdc4Zh6Be/+EW7b9Fb34rm9Xo1Y8YM23qec8sbAMAWZgK9rk5qbHQ2FgAA0oHZA72yUoowkXR3FW5IM748ht1IoAPpjt5ijqiqqmo3dEtH4jFhKBOTAgBsM2CA1Lt34HfGQQcAIP5yc6UePaQLF6Q07QRVWFiompoalZeXq6amhrupERcM4QKkOxLojsjNzZXL5YopiR6PW9G45Q0AYBuXK3BdUVMTuK4YNcrpiJJSR/OOhHveLM/IyAjOjyIp4rLRlgMAUlTPnoEk+pEjgXHQhw93OiJHRDv0GdBZ9EAH0p05cejp087GkWa8Xq82bNgQnEjU5HK5VFBQELwFzRSvW9G45Q0AYCvzi3l6oFsqLS1Vdna2br/9dmVnZ6u0tDSq51uXT548WbfffrtGjBihESNGRFw2mnIAQIpL83HQgURwGbGOIYAO1dXVKTMzU7W1tRowYIDT4QCRbd4s3Xef9O1vS7/7ndPRpB2fz6e9e/fq7Nmzuu666zRlyhR5vV5VVFRo9+7dys3N1cWLF1VVVaXTp09r0BdfeDQ1NWny5Mlq/GKM2alTp0pS1D3TrOKwc2JSdA31SOLwXgM2+973pP/8T+n//l/p/vudjiap+Hw+ZWdnt7vrq6amRl6vN+zze/fu1Te+8Y12Q661FW7ZSOXmvtE51CGJxfsNhPHjH0tPPin9n/8j8eUoYKmrdQhDuADpjh7ojvJ6vZozZ05IWWlpaXBiz1iGeWm7rNm73TAMud1ulZSUhB0PjlvekMouXryoCRMm6NNPP1V9fb3T4QDpjaHhwoo074jX6w37/O7duztMnkdaNlK5uW8g3pYtW6bt27ertrZW/fv315w5c/Tcc8+pZ8+eTocGpD56oANxxxAuQLq7/vrAIwn0pODz+YLJc0kxjZHedlnDMIJlfr9fS5culS9NJ5ZB9/ZP//RPys7OdjoMABIJ9AjMeUdaaz3vSLjnp02b1q7cSrhlI5Uz5wkS5YEHHtD777+vuro6HTp0SIcOHdIzzzzjdFhA9zB+fOCxslJikAkgLkigA+nO7IF+5owURe8mxJdV7zO7mD3NgO7kwIED+u///m89+uijTocCQCKBHkFH846Eez4vLy+k3ORyuYJJ8XDLdlRO73Mkyvjx49WvXz9JX94dWVVV5XBUQDcxdqzk8Uh1ddKJE05HA3RLJNBtVFxcrPHjxysvL8/pUIDoZWUFHltapHPnnI0Flr3P7EJPM9ht9erVmjNnjkaPHi2Xy6WRI0eGXdbv9+uFF17QDTfcoN69e2v48OFasWKFGhoaOr3/K1euaPHixSouLuYWcCBZkECPqLCwUDU1NSovL1dNTU27odXCPd+6fN++fSovL9cnn3yiY8eORVw2mnKkB6frbEl69tlnlZGRoUGDBunQoUNavnx5l7YH4As9e0pfzH+lw4edjQXopkig26ioqEiVlZWqqKhwOhQgej17StdcE/idYVwc17b3mTmOeTTaJt6teqbR0wx2euyxx7Rz506NGTNG15ifI2E88sgj+sEPfqDx48dr3bp1mjNnjtauXatZs2a1u+ti3rx5crlcYX/efPNNSdJPf/pTffWrX9Vtt90Wr5cIIFZmAv2zz5yNI4l5vV7NmDEjbJ0c7nmzPC8vL/h8R8tGW47uz+k6W5JWrlyp+vp6VVZW6v7779eQIUPi8VKB9MQ46EBcMYkogMAwLufOBRLoN97odDRpr7CwUPn5+aqurg72GP/Nb36jo0ePauDAgZKk5uZmTZo0SRcvXpQkTZkyRZJUXV2tfv36qaGhIbiuuR0ay7Dbhx9+qNGjR0uSvvKVr4SdwPPw4cNat26dZs+erddeey1YPmrUKD300EP6+c9/rvnz5wfLN2zYoPXr14fdb2Zmpqqrq/Wzn/1M77zzjk2vBoAtWvdANwwphi+CAcSPk3V2WzfeeKP+4i/+QgsXLlR5eXlnXxKA1saPl157jR7oQJyQQAcQSKB/8AE90JOI2avMdP/990e9XjRlgB3MhnhHtm3bJsMw2t2qvXjxYq1cuVJbtmwJaYz3799f/fv3j7jN3bt367PPPtPYsWMlSZcvX1ZDQ4OysrL0y1/+kl7pgFPMycmbmgJjsVokzwAknpN1tpXLly/r6NGjMa8HIAx6oNvC5/OpqqpKubm5tKMRggQ6gC8nEiWBnhTMSjsjI0P19fUhlXfb5zIyMvTxxx/r7Nmzuu666zR16lR5vV5VVFRo+/btGjJkiGbNmtVufS4IkEgVFRVyu92aPHlySHnv3r11yy23dGros3vuuUff/va3g3/v3btXixYt0sGDB4N3agBwQJ8+0oABgeT5p5+SQAdSTDzq7NraWv3qV7/S9773PWVmZupPf/qTVq1apfz8fLvCBjB+fODx8GHuAOuk0tJSLVmyRH6/X263WyUlJcwXgiAS6ABIoCeR1pW2yay8JbV7ri2Xy6UpU6Zoz549wbJly5Zp48aNIetzQYBEOnnypLKystSrV692zw0bNkx79uzRpUuXYpoItG/fvurbt2/w74EDB8rlcnX4xVBzc7Oam5uDf9fV1UW9TwBRGjz4ywT6uHFORwMgBvGos10ul7Zs2aIf/OAHunTpkgYNGqTZs2friSeeiLgedTYQg7FjJY8nUP+ePCkNG+Z0RCnF5/OFtLX9fr+WLl2q/Px8Op5BEgl0ABIJ9CTRttI2+f1+LVmyJPh7JIZhhCTPTYsXLw4+b26HCwIkSmNjo2VDXAr0aDOXiaUx3taMGTPCjufa2urVqztssAPoosGDpaNHAwl0ACklHnX2gAED9MYbb8QcC3U2EINevaScnMDQrIcPk0CPUVVVVbu2dktLi6qrq2kvQ5LkdjoAAEnATKB/9pmzcaQ5q0rb5Pf7O0yeR2IYRjB5bjIvCIB469u3b0gPstaampqCyyTCj370I9XW1gZ/jh8/npD9AmnFnEiU6wog5VBnAynMHMaFcdBjlpubK7c7NEXq8XiUk5PjUERINvRAB0AP9CRhVtpWiXKzMu9sEt31xRh4rZPoXBAgUYYOHarKyko1Nze369V24sQJZWVldan3eSx69eoVtmcdAJuYCXR6oEcl0twnkdYx7zibOnWqJGnPnj0hc6JICm53//79OnXqlGbNmqW8vLxOx8gcKt0fdTaQwm66SfrVrwI90BETr9erkpISLV26VC0tLfJ4PHrppZeo8xBEAh2AdP31gUcS6I5qW2mbzMpbUrvn2rIaA12SNmzYELI+FwRIpLy8PL3++uvat2+fbr311mB5U1OTDh48qNtuu83B6ADYzryuIIHeoUhzn4Sbp6S0tFSLFy8Ofinucrna3WUWrvypp55SQUGBXn755U7FyBwq3R91NpDC6IHeJYWFhcrPz1d1dbVycnJoKyMECXQLixYt0iuvvBLyzfp//Md/6M4773QwKiCO6IGeNFpX2v369VNDQ0NI5d32uX79+qmmpibY42zKlCnyer2qqKjQjh07NHjwYN11113t1ueCAIk0d+5cPfPMM1qzZk1IY3zDhg1qbGzUggULEh5TcXGxiouLI34hBaCT6IEelUhzn4Sbp8Tn84UkzyVZJs8jlW/atElFRUVR9URnUrX0Q50NpLCbbgo8Hj4sGYb0xV3IiJ7X66V+gyUS6GEsWbJE69evdzoMIDHMBHptrdTcHJiABI6JVGlbPWfVAM7Ly7Ms54IAdtq8ebOOHTsmSTpz5owuXbqkVatWSZKys7O1cOFCSdKECRNUVFSk9evXa/bs2Zo5c6aOHDmitWvXavr06Zo/f37CYy8qKlJRUZHq6uqUmZmZ8P0D3RoJ9KhEmvsk3MRlVVVVYRPjsfj9738fVQKdSdW6D+psIA2MHSu53YF2/alT0tChTkcEdBsk0AFIV18t9eghXbkinTkj0SACEIXS0lLt2rUrpOzxxx+XJE2fPj3YGJekNWvWaOTIkSopKdGOHTuUlZWlBx98UE8++WS7CXsApDgS6FGJNPdJuHlKcnNzww7ZEotvfvObnY6ROVRSE3U2kAZ695ZycqSjRwO90EmgA7ZJytpv9erVmjNnjkaPHi2Xy6WRI0eGXdbv9+uFF17QDTfcoN69e2v48OFasWKFGhoauhTD1q1bde211+rGG2/U008/rStXrnRpe0BSc7kYxgVAzN58800ZhmH58+abb4Ys6/F4tGLFCn3wwQdqbm7WiRMn9PzzzysjI8OZ4AHEj5lAP31a6uTk1+nAnPvE4/GElEeap8Tr9WrDhg3BycElhfzeWrhEZ0FBQdQTibaNkTlUUhd1NpAmGAcdiIuk7IH+2GOP6dprr9XXvvY1nT9/PuKyjzzyiNauXau7775bK1asCN5e9s477+iNN94IuXCcN2+eXn311bDbKi8v14wZM/TQQw/pueeeU1ZWlv74xz/q3nvvVVNTk5566im7XiKQfAYNkk6eJIEOIC0wnioQRwMHBr6cb2mRzp4N/A1LHc19EmmdvXv3SpKmTJkiSdq7d2/InCiSgts9cOCAPv30U/3VX/1V1MlzqxiZQwUAktxNN0m//nWgBzoA27gMOwbRs9lHH32k0aNHS5K+8pWvqL6+XjU1Ne2WO3z4sCZMmKC7775br732WrB83bp1euihh7R169aQMdouXLig5ubmsPvNzMzUVVdd1a78lVde0Y9//GNVVVVFFb85Nlttba0GDBgQ1TqA4/LzpddflzZtku67z+looMDEXVVVVcrIyFB9fb1yc3MlBcYjbWho0L59+zRkyBANHz5cb7zxhurr6zVx4kTNmjVLXq83ZP39+/frgw8+0Lhx4zRp0iR9/PHHOnv2rM6dO6fTp09r3LhxwfXi9Tpyc3O7vP1w27JzH8mAeiRxeK+BOBk0KDAs3LvvShMmOB0NEBfUIYnR+kvvo0eP8n4DkbzyirRggfTNb0q7dzsdDZA0ulpnJ2UPdDN53pFt27bJMAwtX748pHzx4sVauXKltmzZEpJA79+/v/r37x9zPG6325bJeoCkxhAuSaW0tFRLliwJGXPUvEU70udRaWmpli1bpoKCAm3evDns5GRWli1bpo0bN6qwsLDzgVvEY74Ot9utkpKSTm8/3Lbs3AcAwCbXXx9IoH/6KQl0AF3CJKJADG66KfBYWSkZRuCOMABdlpRjoEeroqJCbrdbkydPDinv3bu3brnlFlVUVHRqu6+++qpqa2tlGIbeffddPfHEE5ozZ44dIQPJiwR60vD5fO2S55KC41RGY9OmTTElz01LliyRz+eLeT0rbV+H3+/X0qVLO7X9cNuqqKiwbR8AABsxkSgAAIk3bpzkdkvnzlEHAzZK6QT6yZMnlZWVpV69erV7btiwYfr888916dKlmLf7r//6rxo5cqT69++v73//+7r33nv15JNPhl2+ublZdXV1IT9AyiGBnjSqqqo6lfy2g9/vV3V1tS3bsnodLS0tndp+uG3t3r3btn0AAGxEAh0AgMTr3VsaMybwOxOJArZJyiFcotXY2GiZPJcCvdDNZXr27BnTdnft2hXT8qtXr9YTTzwR0zpA0rn++sAjCXTH5ebmyu12O5JEd7vdysnJsWVbVq/D4/F0avvhtjVt2jTb9oH0wiSiQJyZ1xUk0AEASKzx46WqqsBEon/5l05HA3QLKd0DvW/fvmEnBW1qagouE28/+tGPVFtbG/w5fvx43PcJ2M7sgf7ZZ87GAXm9XpWUlMjj8YSUu1wuud0df2y7XC4VFBS0Wz+a9UpKSmybhLPt6/B4PHrppZc6tf1w28rLy7NtH0gvRUVFqqys7PRwbwA6YF5XnDnjbBwAAKSb1uOgA7BFSvdAHzp0qCorK9Xc3NyuJ/qJEyeUlZUVc+/zzujVq1fYnvBAymAIl6RSWFio/Px8VVdXq1+/fmpoaAj2qq6urlZ9fb3279+vwYMHy+v1aufOnbpw4YImTpyou+66S16vV6tWrQquf+DAAR09elRjx47VxIkTVVNTo7Nnz+rcuXM6c+aMxo4dG1wvXq8jJyenS9sPty079wEAsAkJdAA24a4xIEbjxwceDx92Ng6gG0npBHpeXp5ef/117du3T7feemuwvKmpSQcPHtRtt92W0Hio2JHSWifQma07KXi9XstksFl21113Bcta/261fl5eXshzbf+Op3Cvw85t2bkPAIAN+GIegE2KiopUVFSkuro6ZWZmOh0OkPzMHuiHD9O2B2yS0kO4zJ07Vy6XS2vWrAkp37BhgxobG7VgwYKExsPt4EhpAwcGHi9dkpgIFwAAdIV5XUECHQCAxBo3TnK7pXPnGKIVsElS9kDfvHmzjh07Jkk6c+aMLl26pFWrVkmSsrOztXDhQknShAkTVFRUpPXr12v27NmaOXOmjhw5orVr12r69OmaP3++Y68BSDl9+kj9+0sXLgQau/TuANCNcdcYEGeth3Ch9xsAAInTp480apT04YfSkSPS4MFORwSkvKRMoJeWlmrXrl0hZY8//rgkafr06cEEuiStWbNGI0eOVElJiXbs2KGsrCw9+OCDevLJJ6OabM9ONMaR8gYN+jKBnpvrdDQAEDfcDg7EmdkDvbk5cG0xYICz8QAAkE5ycwMJ9A8/lL71LaejAVJeUibQ33zzzaiX9Xg8WrFihVasWBG/gKJEYxwpLysrUMF+/rnTkQAAgFTWt6/Ur5/U0BD4Yp4EOgAAiTNmTOCxutrZOIBuIqXHQAdgs6yswCMJdAAA0FWth3EBgE4qLi7W+PHjlZeX53QoQOrIyQk8fvihs3EA3QQJdABfIoEOAADswkSiAGxQVFSkyspKVVRUOB0KkDrMBDo90AFbkEC3Ed+MI+WZDV0S6AAAoKvogQ4AgDPMIVw+/DAwmTeALiGBbiO+GUfKM3ug09AFAABdZSbQ6YEOAEBijRoluVyBibxp3wNdRgIdwJcYwgVAmuCuMSABGMIFAABn9O4tDR8e+J1hXIAuI4EO4Esk0AGkCe4aAxKAIVwAAHBOEk4k6vP5VF5eLp/PF7HM7v20/tuu/dnxWqJdvqPl7NpOIvl8PpWVlamsrCxiPMkScw9H997NFBcXq7i4WC0tLU6HAnQOCXQAAGAXhnBpx+fzqaqqSrm5ufJ6vZbP79mzR5I0derUdstUVFTo7bff1q233truDprW25bUbj/m8xkZGdq/f78++OADjRs3TrNmzdKpU6fabdfc19ixY9XY2ChJGjVqlPbv369Tp05p1qxZysvLaxdz2313FFdHsXf0nnXm/e7KNgEgZYwZI+3cmTQ90EtLS7VkyRL5/X653W6VlJRIUruywsJCW/ezcOFCbd68WX6/Xy6XS5JkGEaX9mfHa7HahtXyHS1n13YSqbS0VIsXL5bxxfj8LpdLGzZsaBdPMsXsMgxmE7BbXV2dMjMzVVtbqwEDBjgdDhC9Dz6QbrhBysyUzp93Opq0YtWQi7VxV1FRoa1bt6q+vl4TJ04MNoi3b9+u5uZmNTc3q1evXmpubta4ceM0adIkffzxxzpw4IDeffddXX311ZowYYJycnLU2NionTt3asiQIcrMzNTp06eD65iN7l69euns2bM6ffq0rly5omnTpum+++4LNna3b9+ut956S+fPn9ett96qO+64Q/X19SGN42PHjunVV19VXV2dbrjhBt1///3Bxnjb115RUaHt27erd+/ekqTTp09r0KBBysnJ0ahRo1RfX6+GhgYdPXo0mABoux2zkX/27Fldd9116tu3b3D5IUOGREwAdOYYdhb1SOLwXgNx9NvfSnfeKd18s3TokNPROC6aBnCkxuSiRYu0adOm4PIFBQV6+eWX223bKjkgfdmo70hBQYEkhewrnKlTp2rv3r1q3aR0uVzBfUeTtIgUe+v1Y204h3u/7WyMU4ckFu83EKPnnpMefVSaP1/autXRUHw+n7Kzs0PqIY/HI7/fH1KHeDwe1dTUdLo9ZbWfSDqzPzteS7httF2+o+Xs2k4ihTtGbrdbx44dC8mH2Blzl+sQA7arra01JBm1tbVOhwLE5uxZwwjM0W0Yzc1OR5M2Nm7caLjdbkOS4Xa7jY0bN1qWRVJQUGBISoqfjmJxuVyGy+UK+/zUqVPbvfbOvL622ykoKIi433AxRvP+x3q8OkI9kji810Ac/fGPgWuKIUOcjsRxx48fD9YT5o/H4zGOHz8e9nmzTjl+/Lixb98+y/pq3759YddtvZ9o679E/ng8HmPfvn0RY7dax3zPOvN+W+0v2m1aoQ5JjPXr1xs33nijMXbsWN5vIBavvRaoh7/+dacjMXbu3Bn1Z315eXlC9tPZ/dnxWsJto+3yHS1n13YSKdL71zoeu2Puap3NGOgAvnT11ZL7i4+Fs2cdDSVd+Hy+kB5hfr9fS5YsaVe2dOnSsGN+VVRURNVLLFE6isUwjJBv5tvas2dPu/ejM6+v7XY2bdoUcb/hYuzo/bc6hpGWB4C00XoM9Ch7gnVXVVVV7XpatbS0qPqL2+qtnpcCdUp1dbXefvtty+3+/ve/D7tu6/1EW/8lUktLi3bv3h11L0FzneoohiII935b7S/abcI5zFsCdNKYMYHHJPiMy83NldsdmoL0eDzBO49al+WYY7fbtJ9IOrM/O15LuG20Xb6j5ezaTiKFO0ZutzsknmSKWWISUQCtud3SddcFfmcc9ISwauD5/f6YGnfhGtXdRSwN63iJ9P53lBQBgLRlzq1y5UraDw3XmQaw9GVj8tZbb7Xc7je/+c0OkwVWjfpk4PF4NG3atLgkOsK931b7c7IxDgBxZSbQz551vB72er0qKSmRx+ORFPjsfemll7Rhw4Z2ZV0ZUsRqPwUFBcG/3W53sE7s7P7seC3httF2+Y6Ws2s7iWTG0ro+drlcKikpCYknmWKWJIZwsRG3lqFbuPHGwG1eO3c6HUlasLrF2O12x3R7cbjburvLTyy3dsfrJ9L739Ft+Z3BLeGJw3sNxFlmZuC64v33nY7EcRs3bjQ8Hk+wnmg73Ffr4cCkwHBirZdpO5xZQUGB5bZdLldwO+Z+Wj/f0U9BQUHUQ6e1Hi7N3Lc5XIzH4zEKCgqC+3W73SHPma8tUuyt17d6zzrzfnd0HGJBHZJYvN9AJwweHKiH9+93OhLDMAJtp/Ly8pC2klWZ3ftp/bdd+7PjtUS7fEfL2bWdRDp+/LhRVlZmlJWVRYzHrpi7WocwiWgc1NbW6uqrr9bx48eZ3ASp5847pb17pX/7N2n2bKejSQv//u//rocffjg4mdWLL74oSe3K7rvvvrDbuP/++7Vt27ZEhRzRvffeGzEWc3KxcCZPnqz9+/eHvPY9e/bE/Prabmfu3Ln6+c9/HvNt7NG8/1bHMNLyHamrq9Pw4cN1/vx5ZWZmdno7CK+4uFjFxcW6cuWKqqqqqLOBePnqV6WPPpL+67+kLyZoTmcnTpzQRx99pNGjR2vYsGGWz+/bt09SoB5ru8yBAwf0v//7v/r617+uiRMnht22pHb7MZ/v27evDh48qOrqauXk5OjOO+/Up59+2m675r5Gjx6tixcvSpJGjBihgwcP6vTp0/rOd76jiRMntou57b47iquj2Dt6zzrzfndlm61RXycW7WygE/LzpT/8Qfp//0/6/vedjgZwTFfrbBLoceDz+TR8+HCnwwAApLjjx487d4tamqDOBgB0FfV1YlBnAwC6qrN1Ngn0OPD7/Tp58qT69+9vOd5gXl6e5QQobcvNb0eS7Rv2cPE7tc1Y141m+Y6WifR8tMdXSs5jnA7HN5rl7DjGyXh8pfQ4xqn+P2wYhi5cuKChQ4fGNDYsYmdVZ3fm/EjW//eOxOPzIN776ey2nKpPolkmVa4RopGoc8rOfSVbHRbNcp19nvPK3v1QXyeW3+/X2LFjdeDAgYjj+nd0HFP1/yAWifwsdiKG7vz5H8uykZbjPE/9GFLxPI9lHbuWi/Zc72qd3SPmNdAht9sd8dsMj8djeVDDlQ8YMCCpPvDCxenUNmNdN5rlO1om0vOxHl8puY5xOhzfaJaz8xgn0/GV0uMYd4f/YW4FTwyrOrsz54cp2f7fOxKPz4N476ez23KqPolmmVS5RohGos4pO/eVbHVYNMt19XnOK/v2Q32dOG63Wz179uzwPY/2OKba/0EsEvlZ7EQM3fnzP5Zlo1mO8zx1Y0jF8zyWdexeLppzvSt1Nl+TO6CoqCim8mQTjzi7ss1Y141m+Y6WifQ8x9febcbj+EazHMc4cdvkfxjJpjPnR6pK1Ouxcz+d3ZZT9Uk0y3Sn8yqRr8WufSVbHRbNcul0Tkmp+VmF+LDjMzcdJMN7EM8YuvPnfyzLJsNxdlIyvH7O886vk2rnOUO4JLG6ujplZmaqtrbW8W/VEB8c4+6N49v9cYxh4lyA3TinEA+cVwD/B0gPnOdIF4k61+mBnsR69eqlH//4x+rVq5fToSBOOMbdG8e3++MYw8S5ALtxTiEeOK8A/g+QHjjPkS4Sda7TAx0AAAAAAAAAAAv0QAcAAAAAAAAAwAIJ9G7gypUrevjhh3Xttdfq6quvVmFhoZqampwOCzYqKyvTtGnTlJGRoZEjRzodDmzU3NysxYsXa/To0erfv7/Gjh2rdevWOR0WbLZs2TINHz5cAwYM0LBhw7R8+XJdunTJ6bDgAOps2I1rBNiNaxMggDob6YDrCKQDO65tSKB3A88884zKy8v1pz/9SVVVVaqsrNQPf/hDp8OCja655ho98MADevrpp50OBTa7cuWKBg8erNdff121tbUqKyvTqlWrVFZW5nRosNEDDzyg999/X3V1dTp06JAOHTqkZ555xumw4ADqbNiNawTYjWsTIIA6G+mA6wikAzuubRgDvRsYMWKEnnvuOc2bN0+S9Nvf/lZz5szRuXPn5PF4HI4Odvr1r3+t5cuXq6amxulQEEeLFy9Wnz59tHbtWqdDQRycOXNG8+bN0+DBg7V161anw0GCUWcjXrhGQDxxbYJ0RJ2NdMJ1BNJNrNc29EBPoNWrV2vOnDkaPXq0XC5XxNtj/H6/XnjhBd1www3q3bu3hg8frhUrVqihoSFkufPnz+v48eO65ZZbgmVf+9rXdOHCBT74HBCPY4zkkYjje/nyZb399tu6+eabbY4e0YjnMX722WeVkZGhQYMG6dChQ1q+fHl8XgRsQZ0Nu3GNgHjg2gSgzkZ64DoC6SJpr20MJIwk49prrzW+/e1vG9dcc42RnZ0ddtmHHnrIkGTcfffdRklJifHII48YPXr0ML7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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import poisson\n",
"from collections import Counter\n",
"\n",
"fig, ax = plt.subplots(1,3, figsize=(15,4))\n",
"\n",
"c = 0\n",
"for net in [\"Internet\", \"Collaboration\", \"Protein\"]:\n",
" G = load_sample_graph(net) # on colab: add colab_path=network_science_dir\n",
" degrees = [G.degree(n) for n in G.nodes()]\n",
" degree_count = Counter(degrees)\n",
" k, pk = zip(*degree_count.items())\n",
" k = np.array(k)\n",
" pk = np.array(pk)/sum(pk)\n",
"\n",
"\n",
" ax[c].loglog(k, pk, 'k.', label='real')\n",
" ax[c].set_xlabel(\"k\")\n",
" ax[c].set_ylabel(\"pk\");\n",
" ymin, ymax = np.min(pk)*0.9, np.max(pk)*1.1\n",
"\n",
" # add poisson distribution to graph\n",
"\n",
" k = np.arange(0, max(degrees)+1)\n",
" pk_poisson = poisson.pmf(k, np.mean(degrees))\n",
" ax[c].loglog(k, pk_poisson, 'r', label='poisson')\n",
" # plt.ylim([1e-5, 1])\n",
" ax[c].legend(frameon=False);\n",
" ax[c].set_ylim([ymin, ymax])\n",
" ax[c].set_title(net)\n",
" c += 1\n",
"\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Clustering coefficient\n",
"\n",
"The local clustering coefficient of a random network is\n",
"\n",
"$$\n",
"C_i = p= \\frac{⟨k⟩}{N}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To analyze the dependence of the average path length $d(p)$ and the clustering coefficient $\\langle C(p) \\rangle$ on the rewiring parameter $p$ for a small-world network, you can use the Watts-Strogatz model. This model begins with a regular lattice and introduces randomness by rewiring each edge with probability $p$. Here's a step-by-step guide on how to perform this analysis:\n",
"\n",
"1. **Generate a regular lattice**: Create a regular ring lattice with $N$ nodes where each node is connected to its $k$ nearest neighbors.\n",
"\n",
"2. **Rewire edges**: For each edge in the lattice, rewire it with probability $p$. This involves replacing the existing edge with a new edge that connects the node to a randomly chosen node in the network.\n",
"\n",
"3. **Compute $d(p)$ and $\\langle C(p) \\rangle$**:\n",
" - $d(p)$ is the average shortest path length between all pairs of nodes in the network.\n",
" - $\\langle C(p) \\rangle$ is the average clustering coefficient of all nodes in the network.\n",
"\n",
"4. **Normalize by $d(0)$ and $\\langle C(0) \\rangle$**:\n",
" - $d(0)$ is the average path length of the regular lattice (when $p=0$).\n",
" - $\\langle C(0) \\rangle$ is the average clustering coefficient of the regular lattice (when $p=0$).\n",
"\n",
"5. **Plot the results**: Plot $d(p)/d(0)$ and $\\langle C(p) \\rangle / \\langle C(0) \\rangle$ as functions of $p$ on a log scale to observe the small-world phenomenon."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import networkx as nx\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Parameters\n",
"N = 1000 # Number of nodes\n",
"k = 10 # Each node is connected to k nearest neighbors in ring topology\n",
"p_values = np.logspace(-4, 0, num=100) # Rewiring probabilities\n",
"\n",
"# Initialize lists to store results\n",
"average_path_lengths = []\n",
"clustering_coefficients = []\n",
"\n",
"# Generate the initial regular lattice\n",
"G0 = nx.watts_strogatz_graph(N, k, 0)\n",
"d0 = nx.average_shortest_path_length(G0)\n",
"C0 = nx.average_clustering(G0)\n",
"\n",
"for p in p_values:\n",
" G = nx.watts_strogatz_graph(N, k, p)\n",
" d = nx.average_shortest_path_length(G)\n",
" C = nx.average_clustering(G)\n",
" average_path_lengths.append(d / d0)\n",
" clustering_coefficients.append(C / C0)\n",
"\n",
"# Plotting\n",
"plt.figure(figsize=(5, 4))\n",
"\n",
"# Average path length plot\n",
"plt.plot(p_values, average_path_lengths, marker='o', linestyle='-', color='blue', label=r\"$d(p)/d(0)$\")\n",
"\n",
"# Clustering coefficient plot\n",
"plt.plot(p_values, clustering_coefficients, marker='o', linestyle='-', color='red', label=r\"$\\langle C(p) \\rangle / \\langle C(0) \\rangle$\")\n",
"plt.xscale('log')\n",
"plt.xlabel('Rewiring probability p')\n",
"plt.legend(frameon=False)\n",
"plt.tight_layout()\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 2
}