{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# %load ../../preconfig.py\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "plt.rcParams['axes.grid'] = False\n", "\n", "import numpy as np\n", "import pandas as pd\n", "#import itertools\n", "\n", "import networkx as nx\n", "\n", "import string\n", "\n", "import logging\n", "logger = logging.getLogger()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "10 Mining Social-Network Graphs\n", "=================\n", "1. how to identify \"communities\"? \n", " communities: strong connections, usually overlap.\n", " \n", "2. explore efficient algorithms for discovering other properities of graphs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.1 Social Networks as Graphs\n", "#### 10.1.1 What is a Social Network?\n", "The essential characteristics of a social network are:\n", "\n", "1. There is a collection of entities that participate in the network.\n", "\n", "2. There is at least one relationship between entities of the network.\n", "\n", " + all-or-nothing: friends of Facebook.\n", " \n", " + discrete degree: friends, family as in Google plus.\n", " \n", " + real number: the times of talking.\n", " \n", "3. There is an assumption of nonrandomness or locality. \n", " If A is related to both B and C, then there is a higher probability than average that B and C are related." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.1.2 Social Networks as Graphs\n", "social graph: The entities are the nodes, and an edge connects two nodes if the nodes are realted by the relationship that characterizes the network." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DjBo1ihEjRuDj4+OQHpVC3ViuAXq9noyMDFavXk1mZiaJiYn079+/VisxWeYZ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\nXsqcOI7H9XdbxgrOCxVAQScpBad1/oXEGZ+UtEhIbPliKXPshwixaPP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_1.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is Fig 10.1 typical of a social network, in the sense that it exhibits locality of relationships?\n", "\n", "Suppose X, Y and Z are nodes of Fig 10.1, with edges between X and Y and also between X and Z.\n", "\n", "1. What would we *expect* the probability of an edge between Y and Z to be? \n", " The graph has 9 edges out of the $C_7^2 = 21$ pairs of nodes. \n", " \n", " Since we already have (X,Y) and (X,Z), the probability of an edge (Y,Z) is $(9-2)/(21-2) = 0.368$. If the graph were large enough, that probability would be very close to the fraction of the pairs of nodes that have edges between them, i.e., $9/21 = 0.429$.\n", " \n", "2. Then, we must compute the probability that $(Y,Z)$ exists in Fig 10.1, given that edges $(X,Y)$ and $(Y,Z)$ exist. \n", " We count the pairs of nodes that could be $Y$ and $Z$, without worrying about which node is $Y$ and which is $Z$.\n", " \n", " If $X$ is $A$, $(B,C)$ contributes one positive example. All details are in the table following. In all, the fraction of times the third edge exists in thus $9 / 16 = 0.563 > 0.368$. \n", " \n", "| node | pos | neg |\n", "|------|-----|-----|\n", "| A | 1 | 0|\n", "| C | 1 | 0|\n", "| E | 1 | 0|\n", "| G | 1 | 0|\n", "| F | 2 | 1|\n", "| B | 1 | 2|\n", "| D | 2 | 4|\n", "|sum| 9 | 7| 16 |\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.1.3 Varieties of Social Networks\n", "1. Telephone Networks\n", "\n", "2. Email Networks\n", "\n", "3. Collaboration Networks \n", " + Wikipedia: articles and editors. \n", " + published research papers and authors. \n", " \n", "4. Other example \n", " + information networks (patents) \n", " + infrastruture networks (roads) \n", " + biological networks (genes) \n", " + product co-purchasing networks (Groupon) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.1.4 Graphs with Several Node Types\n", "There are other social phenomena that involve entities of different types. The natural way to represent such information is as a $K$-partite graph for some $k > 1$. In general, a $k$-partite graph consists of $k$ disjoint sets of nodes, with no edges between nodes of the same set.\n", "\n", "Eg: \n", "deli.cio.cu: there are three different kinds of entites: users, tags and pages." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OnTq5tQYhLkfCWrQLGo0Gg8GAyWRq9IIWVquVd999lzFjxhAaGnrdtdTU1LBz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_2.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.2 Clustering of Social-Network Graphs\n", "clustering of the graph as a way to identify communities.\n", "\n", "\n", "#### 10.2.1 Distance Measures for Social-Network Graphs\n", "distance measure:\n", "\\begin{align}\n", " d(x,y) = \n", " \\begin{cases}\n", " 0 \\text{ or } 1 \\text{ or } 1 & \\text{if edge} (x,y) {exists} \\\\\n", " 1 \\text{ or } \\infty \\text{ or } 1.5 & \\text{otherwise}\n", " \\end{cases}\n", "\\end{align}\n", "\n", "\n", "#### 10.2.2 Applying Standard Clustering Methods\n", "They are generally unsuitable for the problem of clustering social-network graphs.\n", "\n", "\n", "#### 10.2.3 Betweenness: define\n", "*betweenness* of an edge $(a,b)$: \n", "the number of pairs of nodes $x$ and $y$ such that $(a,b)$ lies on the shortest path between $x$ and $y$. And it's credicted with the fraction of all shortest paths between $x$ and $y$ if existed.\n", "\n", "A high score indicates that $(a,b)$ runs between two different communities, namely, $a$ and $b$ do no belong to the same community.\n", "\n", "\n", "#### 10.2.4 The Girvan-Newman Algorithm: calculate betweenness\n", "The algorithm is aimed to calculate the number of shortest paths going through each eage.\n", "\n", "1) Starting at a node $X$, perform a breadth-first search (BFS) of the graph to label levels of each node. \n", " + DAG edges: edges between levels.\n", " \n", " + If there is a DAG edge $(Y,Z)$, where $Y$ is at the level about $Z$, then we shall call $Y$ a *parent* of $Z$ and $Z$ a *child* of $Y$.\n", " \n", "2) to label each node by the number of shortest paths that reach it from the root. \n", " + Start by labeling the root 1. \n", " + Then, from the top down, label each node $Y$ by the sum of the labes of its parents." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hEEePHmVubo7JyUmsViuJiYnExcVhGAYmk4lwOIzP52NmZobU1FSysrIealPj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\nj/D86Aq+uLHuyGW+hk4imkATs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_4.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3) to calculate for each edge $e$ the sum over all nodes $Y$ of the fraction of shortest paths from the root $X$ to $Y$ that go through $e$. \n", " + from the bottom up.\n", " \n", " 1. Each leaf in the DAG gets a credit of 1.\n", " \n", " 2. Each node that is not a leaf gets a credit = 1 + the sum of the credits of the DAG edges from that node to its child nodes.\n", " \n", " 3. credit for $(Y_i, Z)$ is: \n", " $$\\text{credit}(Y_i, Z) = \\text{credit}(Z) \\frac{p_i}{\\sum_{j=1}^k p_i}$$\n", " where $Y_1, Y_2, \\dotsc, Y_k$ are the parents of $Z$, and $p_i$ is the number of the shorest paths from the root to $Y_i$, namely, the labels in Step 2)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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n2bVr16pvnRBiLXFtKODjv/Ei8RsuL8oq3fUUcVUm4o1h0isHCUUtJKXnUlKY\niWWeIazVasXlcs3ehzWZ5nv7argSM/k3v/kVHgorLBYjuh7GEZtKTk428bF2DAuE4uDgIE6nc96g\nut127txJW1sbGzduXLBcpi12Aw8/+1tUH/DhSsokdp6V6dfSdZ3a2lqKi4vnbHkC0IxWkrLK+d3/\n8meo2CSyk2MxaBpaTA7PPP8icUmJTG/MZ3B0Apc7lcycPDYkxS77FLm4Oy0ayDk5OXzrW9/iy1/+\nMgANDQ1s27YNgD179nD06FEMBgPV1dWYTCZcLhe5ubm0tLTMmd4S4m5mccSRXxg3++eUnE0kK9A0\nyCq+fA/yeqNQg8FAcXExb7/9NhMTEyQmJs7zXA1XUgb3JmXcVNtmToDasmXL0heNLaOKigrOnDnD\n4ODgvAU8NE3D7k6mYkvyDb/mzAlZly5d4oEHHpi34IhmtJKcmU9yZv7VH2uNp3pL3OV/rOwsypUO\nGD7891pSF4WYY9F5locffviqN8OVixecTiderxefz3fV1abD4WBqamqZmyrEnUXTNAwG7cP/GzAY\nDIuuKs7Ly8NqtVJTU7PoveQbpes6NTU16LpOTk7OLdWMXi4Oh4Pi4mIaGhrw+/3L8prRaJTa2lqS\nkpLIzs6+qROfNO3y1rGZCyaDwfjhv92yNE0IYAn7kK/8Jvb5fMTGxuJyufB6vXP+XgixvEwmE488\n8ggnT56kra2NSCRySyt8dV2nu7ubY8eOsX37dtxu96rXsYbLAVheXo7P56OlpeWW+6mUoqenh56e\nHsrLy+Xnk1iTbjqQy8rKqKmpAeC9996jurqayspKTp8+TSgUYmpqio6ODoqKipa9sUIIyMzMZP/+\n/Rw/fpzu7u45249uhFIKXdcZHBzk/fffp7KyksLCwgXuS99+M5XDNm7cSENDAxcvXlxyKOu6ztjY\nGDU1NaSnp5Obm7v8DRZiGdz0u+8P//AP+epXv0o4HKagoIADBw6gaRqf+cxneOGFF1BK8dJLL62J\n+1BC3Ik0TeOee+7B5/Nx9OhR4PKq5JsJ05kwPnbs2OzRhAsd4rBaZg6DmJiY4MiRI4RCIQoKCrBa\nrVeflLXA1qiZi46BgQGOHj2KpmlUVVWtuX4KMUNTsqNdiHXJ6/Vy5MgRLl68yJYtW9i0aRN2u/26\n90Z1XScUCtHa2kpNTQ1ut5s9e/YseIjDapspqXn48GE6OzspKSmhqqrqqq1Z09PTaJp21epwXdcJ\nBAK0tLReQ879AAAgAElEQVRw9uxZrFYrDz/88JrtpxAggSzEuub3+zl79iz19fW4XC6qqqqIi4vD\nZDJhsVgwGo1Eo1FCoRDRaBSfz0d9fT0DAwMUFBSwbdu2q8pXrlWRSITa2lpaWlrQNI1NmzYRFxeH\npmnU19eTkJBAbm7ubLWvUCjE+fPnmZiYIDMzk23btsl9Y7HmSSALsY4ppRgdHeXgwYMkJSXh9/uZ\nmJjAaDQSExODzWYjGAwyNTVFOBwmNjaWmJgYBgYG2Lt3L+np6Te12ng1RaNRhoaG6OzsZGxsjNHR\nUYaHh+np6aGqqoqEhAT8fj/BYBC32z171GJmZiZWq3XxTyDEKpNAFmIdm56e5uDBg+i6zoMPPkgo\nFJrdiujz+QgEAlgsFlwuF06nE4fDQUxMDD/96U9JTk5mx44d2O321e7GTQmHw0xNTTEwMMChQ4cw\nGo0UFxfjdDpn++l0OmcvSNb66F+IGWtjSaUQ4qYppbh48SJ9fX08+eSTuFwuNE0jISFh9vGZ6+2Z\n/bMz4bRjxw4OHjxIQUEBGRkZ62aUDJdPa4qPj6e7u5vk5GR2795NamoqMLefQqwn6+ddKIS4ytjY\nGA0NDVRVVZGSknJVveiZYiNGo3H2IIUrQyorK4vExETa29uXrcDI7aKUwuv10tTURF5eHsnJyQv2\nU4j1RAJZiHVopiazpmmUlJQsqbpWWVkZQ0NDjIyMrEALV044HObYsWPY7XYKCgrWzN5pIW6VBLIQ\n64xSiq6uLrq6uti0adOSVg9rmkZaWhp2u53Ozk7C4fAKtHT5zUzTt7S0UFpaOrvSWog7gQSyEOvM\nxMQEP/7xjyksLCQvL2/J07ROp5O8vDy6u7sZHx9fgZYuP4/Hw+nTp6mqqiInJ2dd3fsWYjHy3SzE\nOjFTJKOmpobY2Fg2bdqEyWRa8ghR0zTy8vIwGo20tLQQDAaXucXLRylFJBKhqakJg8FAeXm5rKAW\ndxwJZCFutytWP98MXddpbW1lYGCARx55hJiYmFsOJKfTSXl5OY2NjQwPD6Pr+sJP/rDdN9L2mect\n557KgYEBent7KSsrIy4ubt7n3Gj7VqqNQtwKCWQhbhuFrkeY9nuZmJhgOhhGv4lg9ng81NXVUVhY\nSFpa2rJN1xYVFeFwOGhra1twlKyUIhIO4ff58AeCRPS57b78nDDBQIBQKIDXO01U15cl8HRdp6Gh\nAafTSW5u7txFbEqhohGCAT9er49gaP6DKJSuEw6FCAYCTE9P458O3tS/gRArSZYnCnGbKBVlsP0Y\nv/jle7Rf8pGSuZdnP72X1FgLhkVGukop6uvrsVgslJaWLuuZxVarlT179nDo0CEKCwvn3ZesR33U\nHPoXGvr8+HQ39z/yGJWZCViMH7U7Mu3h5K/f5tj5dkKRCHGbD/Ab+ypJdN5alayZhVwDAwPs2bMH\nl8s19zkohtvP8/6xWsbHfdgKt/Do3m0kuqxXnFmsCIz18ItfvU1T5yC6zU3Frkd4tLoAh3n1z4AW\nQkbIQtwmwakRztSeZcrsJsUV4s3vfZcTF4aIXmeWGD4KpIaGBjZv3rwiZxZnZ2cTHx9PR0fH3H3J\nKsyFX/8f/u+PzqE74tB7jvM3r/yUzhEvMwNlpRTDHc2898YxuvsGGR2ZwGq3YTLcWtAppfB4PBw8\neJDc3NwFZwai3j5e/+73+eBSgMRkK+/9y//kVyeb8YWisyN0FQ3S/N5JThw+z+DIKF7vNFarddGL\nISFuFwlkIW4TpYxkFe7huec/x2df/BT5Np3IImmslGJiYoLDhw9TUlJCZmbmii1kKi8vZ3BwcM6+\nZBUa4dXv/ZBI7i7+zYFP8sLH7+fC269R2zFAaHbqWqf55Ls0DUTIK67gsU89zye2FxJrM3IrrQ2F\nQpw7dw6Xy0VpaemCx7pOdBzj1y0DbHvoYR579nkOlE5x6NcnGZic5vKMtCI4OcixEx8wEYmhomob\nH//4k9y/MR2rUQJZrA0SyELcJlZXPBuLCwn2nubNH73GBX0DaW4718vXYDA4WwSjurp6zlnAy+XK\nfcldXV1EIpHZx6LeId7vGCarJA2X3UJcej4J0xe52DtEMDxzQRHFaNaIS/Jy6LXv8/ff/wHtl8aI\nLDL6vx6lFL29vXR1dbFjxw4SExMXvG8+3t3EtJZCZkIMJrOT4qKNjLd0MuENzI6Qo5Eo8RtsGOjh\nX//3/+BHP/kVA+NebqGJQiwrCWQhbhOD0YTZpDE12kdHVy8TQ/WcPNbCdCQ678Knmanqnp4e9uzZ\nsyyrqq9nZsFUV1cXY2Njs38fDXjxR0JYLEYMmobJ6iLJpDE56btihG/m3k/9Hn/8X/6IL376Y0y8\n+y/84lgj3kBk/k+2CKUUPp+PpqYmMjMzycrKuu5982goCMqCEQOgYdSMEAihRz/6yjoSc/jkv/1P\n/PF/fokXn9jNhXd+ygeNPYQjsqhLrA0SyELcJkopMNop3vkpXvrKn/Ibj2TRcL4FX1hnvkQeHx+f\nvW+cmpq64kUwNE0jPz8fg8FAa2vrRyuuTRYcBiN6+PI2IT3kYzQaIcbtxGjUZlczm21OUrKKePwz\nv8PnHstg1OcjuNgN8utob29ncnKSjRs3YrPZrt92gwUIoysdUOjRKJjNaAYNlLp8r1szYHXGklm4\nmed/7/d5YIubcf800XlWjAuxGiSQhbhN9HCIkZFh/KEozqQcNm3JJSU9EbNh7qh3pla1UoqNGzcu\n66rq67lyX/LIyAi6rmNyZ7C/II3BC4NM+gJ4RnqZiEkmJy0Opidov9iDZ2qCgYFBJrx+whFF2B5P\nYpILk3FpP2I8Hg+tra3k5eWRlJS06PPj88pwGYe5ND5BKOilq2uQpKJ84l1Wpsf6aGnvY3x8lIGh\nEbzTQcJRDWNMPLFuB4Z5vv5CrAbZ9iTEbTI9OcjBH7/KqJZAcV46o0EHDz1YRYzFeNV9ZKUU3d3d\ndHZ2ct999y2pVvWtKC4u5uzZs7S2tpKQkIDdlsLHf+tZ/vcbdfzypyGC4zUUPPQ8m/PTmeo8ySs/\nbOChJ7dw8lgNRncqmfFOGrV9PFxeQqz15n/ERCIRjh8/jtFopKSkZMGFXFeKL7qf+4tPcua993EO\nWzl6wcS+T20j1W2l+52f8M1f6jx+IIPz9ReIy8gixQx+9/3szUvHLIu6xBohI2QhbhOj2YI7xoFn\n+BL9/RNUPPIiuzdlzxkhezwe3njjDQoKCm6pVvVSzexL7uzsZHR0FF0ZKHjwRZ55qpKQZ5BA3Fb+\n/fNPU5DixuaMJz89g1inG6fDimdsiEuTGp/8rU9zb0n6VfuUb8TMxUhbWxvl5eXExsbeUN9NjjQ+\n+VsvsiXJzMjwFNWf/DyP7CzFaTHijEtjY2YasTFurCbF4NAlRkMxPPXME2zMSMAo257EGqGppdTw\nE0IsidJ1olEdzWScEwQz9ZoPHz5MZ2cnzz777A0H0rK3UyneeOMNEhIS2L59OzabDaV0IpEoBoMR\n44dT0UrXieoKg9EAepRIVMdoNM0+frOf0+Px8POf/5z09HR27ty56L3ja14BPRolqmsYTUZmrnOU\nHiWic/l+d/Ty780mk0xVizVHRshC3EaawYDJbJp3VDZTq/rSpUs8+uijK76qejFlZWUMDAwwOjoK\ngKYZMJvNV4WtZjBgMl1efW0wmrBYLEsO40gkQmtrK0ajkfLycqzWm63wdbkNZvNHYXy5jUbMJiMG\nzYDRZMZqMUsYizVJAlmINWJycpK6ujry8/NJT09f1aMFNU0jPT199rzkK/clr5TBwUE6OjooLS0l\nISFBTnISdx0JZCHWAKUUDQ0NmM1mysrKbtuq6utZaF/yStB1naamJux2Ozk5OWui/0LcbhLIQqwy\npRRdXV3U1dWxadMm4uLi1sTocOa8ZE3TrnsS1K1SStHR0UF/fz+bNm0iJiZmRT6PEGudBLIQq2hm\nIdO7775LUVERWVlZayKMZ7hcLsrLy2loaJjdl7yclFJMTk5y/PhxcnJy2LBhw6pO1QuxmuQ7X4hV\nFAwGOX78OFarlW3btq1YrepbUVJSgs1mW5FRcjgcpqamBpPJtMSFXELcOSSQhVglM1PV3d3d7N69\ne9W2OC3GarWye/fuj/YlL9MoWSlFf38/Fy9epKqqioSEBBkdi7uafPcLsUomJiaoq6ujsrJywXN+\n14rc3Fzcbvf85yUvwczhEQ0NDeTn55Ofny8LucRdb+3+BBDiDqbrOufPn0fX9dtaq/pWXLsv+VZ1\ndnYyNTVFcXHxTRYAEeLOJIEsxG2mlKKnp4eOjg4qKytve63qpdA0jYyMDGw225zzkpfC4/HQ2NhI\nXl4eKSkpy9RKIdY3CWQhbjOPx8Obb75JXl4eBQUFGI3GNXnv+FpX7kseHx9f8uvouk5NTQ26rlNU\nVHRDh0cIcTe4oUCura3lM5/5DABNTU3s2bOHz372s3z2s5/lF7/4BQCvvvoqTz/9NM899xyHDx9e\nsQYLsV4ppQiHw5w6dQqr1UpVVRVms3ldhDF8dF4ysOQV17qu09HRQVtbG1u2bMHtdq+b/gux0hY9\nG+273/0ub7zxBk6nE4D6+np++7d/m8997nOzzxkZGeGVV17h9ddfJxAI8Pzzz7Nr1y7MZvOKNVyI\n9UbXdS5cuEB/fz+PPvroml1VfT0ul4uysjJOnjxJbm7uTe0bntlzXFNTQ2FhIVlZWevi3rkQt8ui\n76ScnBy+9a1vzf65oaGBw4cP8+KLL/Inf/In+Hw+zp8/T3V1NSaTCZfLRW5uLi0tLSvacCHWOqUU\nuq4TjUaJRCJMTExw9uxZsrOzSUtLW3dhPGPmjOK2trbZFddX9jMcDhOJRIhGo+i6zsyBcpFIhJaW\nFkwmE1VVVbKQS4hrLDpCfvjhh+nr65v98+bNm3n22WcpKyvj29/+Nt/85jcpLS29qtydw+Fgampq\nZVosxDoQiUQIBoOMj48zNjbG2NgYLS0t9Pb2kpaWxsDAAPHx8dhsNkwm07oKZ5vNxu7duzl69ChF\nRUXExsYyOTnJ2NgYo6OjTE1NYbVaSUxMJCEhgfj4eBwOB6Ojo7S3t1NRUUFSUtKa3uYlxGpYNJCv\ntX///tnw3b9/P3/xF3/B9u3b8Xq9s8/x+XzrYuWoEMtp5gjByclJmpubqaurQ9d1HA4HdrsduDzj\n1NXVRXNzM0opSktLKS0tJSkpad0s7lJKkZ2dzYULFzh//jw9PT2EQqHZflqtVvx+P5cuXcLv9xON\nRikoKMDv92O328nOzpYwFmIeNx3In//85/nqV79KZWUlx48fp7y8nMrKSv7mb/6GUChEMBiko6OD\noqKilWivEGuSUgqv10tbWxvNzc2YTCZKS0txuVzExcURHx+PyWQiHA4zOTnJxMQEHo+H0dFRDh06\nRGFhISUlJcTExKzpsFJK4ff76ejoYHR0dHahV2xsLPHx8cTFxeF0OgkGg3g8HiYmJpiamqKvr4/z\n589TVVVFKBRC1/U13U8hVsNNB/LXvvY1/vzP/xyz2UxycjJ/9md/htPp5DOf+QwvvPACSileeukl\n2cog7hCKD2+BXnf06vf7OXLkCKOjoxQVFZGfn7/gtGxiYiJw+b7r+Pg4Fy9epLa2loGBAXbu3Llm\np3NnFmWdOnWKzs5OiouLKSwsJCkpac4CTrvdTlxcHDk5OSilGBkZITU1ld7eXt5//33uv//+NdtP\nIVaLpmZWXAghrqKUIhycxufzoxutxLqcmEwGro3lUCjET37yE8bHx3nooYfIzMy8qfvCkUgEj8fD\nz372M2JjY3nwwQeJiYlZc9PX09PTHD9+nM7OTh544AGysrJueNuWUopoNMrw8DCHDx8mGo3y2GOP\nkZCQsOb6KcRqkctTIRYwPTHEL370z3zjv/41f/rH/4m3T3cSiuhceQUbjUb54IMP6Ojo4LHHHiMn\nJ+em9xabTCYSExN57LHHGB0dpa6ujmg0uvwdugVKKdra2ujs7GT37t0UFBRgsVhuuJ+apmEymUhL\nS+PRRx/F6/Vy8uRJfD4fMiYQ4jIJZCEW0N/eRFu/g81bN+PofYdXXjvDVOCjkpFKKbq7u2loaOCJ\nJ5645bN8ExMT2blzJ+fPn6e/v3/Zzx6+FRMTE5w+fZrS0lJycnIWfb5SasGgTUhI4IknnqCvr4/2\n9vY1d/EhxGqRQBZiAc64VJ741AGeOPAI23OysDssXDkgDAaD1NbWXlUC81pK14l8uNgxGAwRCgYJ\nhcPo+tywMhgMFBUVkZmZyTvvvEMgEFjJ7t0wXdc5dOgQsbGxbNy4ceGCP0qh61GCwWm8Pj++6WkC\nwQDBcIRrry0yMjIoLS2lubkZj8ez8p0QYh246UVdQtwtUvOKcI1f4q033+Aff1zP1v83FpPxo0Qe\nHh5meHiYxx57bIGQUnhH+zjx9kHOdQ9isSZj17w4NmSzecceNubEY75mRG2xWNi9ezdf+9rX2Lt3\nLzk5Oau+8Gl4eJj6+nqee+65hUtdKoUeCdLXfp4jx0/RHXUSr0/BlE76pu3s3r2dONvV/SgpKaGz\ns5Pu7u7ZhW5C3M1khCzEAgxGIyhFRFfEFcVw/Oc/oGPUh/7hVGxfXx8Oh4Pk5OQF76VqmgFf12n+\n+i9f5myfF1SIutf+D//ly9+mY9TPPANl4uLi2LVrF2fOnCEcDq9kF2/IqVOn2Lhx43XPbFbotJ9+\nl2/993/k/YZBbK4YYuwm2k+9xw9/9msGJ6+ue61pGvHx8cTHx9Pf379gP2emvpVSyJ1mcaeTQBZi\nAUopHPHpPPnMb/LyX3wFU1cjQ57A7Daojo4O8vLyrlOPWcOVlEH19nLsNgv3ffxxXvjiF/nEg/mc\nePv/o214iugC91n37dtHY2PjLR9zeKt0Xaerq4u8vLzZevbzPi9widf/6R+56E/kuc99gd979hM8\n9/xv86U/+DyVmwtRus61XTUajaSlpTE1NTVvZT+ldELTk7Q2tTE44ScqiSzucBLIQixgauQSPf0j\nhLCSmJZN7IaNxDsss9ue+vv7SU9PX3RKeSZHmk+do+boMU62dZBcWUmS0zZnC9WMhIQEAoHAqi94\nmqlV7XA4rnsQRHC4kYOtgxTcu4vK/FRMGkRCfozuLHaV5aCHAoSjcxeppaSk4Pf75wlkRSTgo6Pu\nKH/7je/xflMfEQlkcYeTe8hCLKDz/Dv80y9byC8txm0OsOPZ36QwNQbDh9PTPp8Pp9N5w1t/elta\nqPMF+PlbtRg2/Sb26+xVNhgMmM1mIpEISqlV26sbDAYxmUyLntymh/z4NROxiXFYjJcvUML+CU4f\nOcS7H4yz99PPkbMhjmvLBdnt9tkDKea8ph4lGpzkUm8fnqngnBG2EHcaCWQhFhCfXkhJgReT2Uhy\n4W6eqi7GZTEtOKpdzN6nH+epjTEUxis+99f/yusnPkbRxypwWBYeea6FPbqapi16QaBhxBiO4pv0\nEdF1FAZsMXEYpoaoa/PydFICVtMC95/n7aOG1RnHxspNpCa/B3IHWdwFJJCFWEDWxnv5neIdKE3D\noBm4NpPsdjvT09PXHcEqpZgZ2pmtLuJTsti6vQRH6Ft09AwRnW9VFx8dVGEyre5bdGaUvti9bGtK\nMdviHLS8f5SmHWVsLUnBZDRis1qIK0gkPt6GyTD3a7TYCPyKL58Qdzy5hyzEQjQNg9GI0TA3jAGS\nkpIYGRm5zihWEQl4GRkaR6HRd6GF+tqz/LqmltjkLDYVpM4bUgCBQABN01b9BCibzUY0GiUQCFx3\ntG505fHkc4/h623mzR+/w6nGVlqbG+kdnsBot2Fa4D77xMQEVqt19jQsIe5mMkIWYolmjlKsqKhY\nYMGTYmqki9MNg2zaupOGX/0zHe8aCcen8sWv/i2feqAYq3n+oKqtrSUrK+u6C6luh5ntSUNDQwSD\nQWw22wJPNLPjYy/w1cQkfvzzQ/yP754n3TBMSLl58sD9ZMRZ53yIUor+/n5iYmLkuFYhkEAWYsly\ncnJ455138Hq9xMfHzzOSNZCQVcEX/vK/84UbfE2l1OxhFc8+++yqn5qmaRrbt2/ntddeo7y8nMzM\nzHlH7JqmYXMlsPOR59i+7xNMTwdQmhmb3YbROHeGYeYYx9HRUdLT0+cNeqV0wqEQ0WiYcCRMJKqj\nDIvfzxZivZIpayGWKCUlBZfLRWtr67LVndZ1nfPnz2Oz2RbZ43z75Ofn43A4aG1tnb1nfj0GsxVn\nrBtXjOPy6VgL5GdnZyfBYJD8/Px5HlWEAz7amhoJhkboaG2iZ9iz4D13Ie4EEshCLJHL5aK0tJSG\nhgaGh4dveUW0UoqhoSFOnDjBJz7xiesW4ridjEYjH/vYx2hra6O7u3tZ9kZ7vd7ZafmFymYajCbi\nMyv4t//+d3nivgoSHDd+upQQ65EEshBLZDAYqKiowG638+677zI1NXVLoez3+zl69CjZ2dkUFhau\nidHxjOzsbIqLizl9+jRjY2NL7qdSimAwyJEjRwiFQlRUVCwwLa9hstjJLtrEnn2PsGdHFRvinRgX\nWAQnxJ1AAlmIW2CxWHjyySdpb2/nyJEjeDwedF2/4cCaqdMcDAb54IMPmJiYYMeOHVitcxdBrSaD\nwUB1dTVGo5ETJ07g8XiIRqPXPWbxSkopdF3H7/dz8uRJzp49y759+0hMTJRRrxAf0tRaqDwgxDo3\nNDTEG2+8QWpqKps2bWLDhg1YLB9NsV4ZOjNvuZkFXKOjo5w9e5aBgQF2795NUVHRqp/wtJCenh7e\ne+89zGYzW7duJS0tDZvNNtvehfoZiUQYGRmhsbGRjo4OHnjggTU3CyDEapNAFmKZDAwMcPLkSQYH\nBykpKSEjIwO3201MTMxVBT4ikQher5fJyUn6+vpoamoiPj6ee+65h6ysrDUbxvDRfe4zZ87Q399P\nTk4O2dnZxMXFERMTc9X0czQane3n0NAQzc3NOJ1OtmzZQk5OjoSxENeQQBZimSilGB8fp66ujnPn\nzuH1eikoKKCgoACHw0E0GsVoNDI9PU1nZyft7e3YbDZKSkq49957iY2NXTfTt8FgkL6+Po4cOUJ/\nfz+ZmZkUFBQQGxuLrusYDAZCoRBdXV20trZiNpvZu3cvhYWFuFyuNX3RIcRqkUAWYplEo1FOnz5N\nb28vBw4cwOv10tHRwcWLFxkZGWF6ehqbzUZCQgK5ubmz24l+8YtfUFZWRnl5+apX5rpZ0WiU8fFx\nOjs7uXjxIsPDw/h8PiwWC/Hx8eTk5JCfn09aWtqqlwEVYq2TQBZimQwMDPDWW29RXl5OVVXVDU/J\n1tbW8tZbb/HMM8+QnZ0to0ch7lLyzhdiGYRCIU6fPk1SUhIlJSU3FaqlpaXk5eVx6tSpW946JYRY\nvySQhbhFSilaWlpoa2tj06ZNOByOm5p2tlgsPP744/j9furq6giHwxLKQtyFJJCFuAVKKUZGRnj7\n7bfZvXs3aWlpS5pyttvtbNu2jcbGRgYHB1egpUKItU4CWYglUkrh8/l49913yc7Onl2UtVT5+fnk\n5ORw/vx5/H6/jJKFuMtIIAuxRNFodPbAhT179txydS2bzUZVVRW9vb00NDQQiUSWqaVCiPVAAlmI\nJRoeHqa+vp4tW7aQlJS0LNuVkpOT2b59O8eOHWNwcHDZTpESQqx9EsjirqKUQo9GmPb5ieg6S50U\njkajnDlzBqvVSn5+/rLtHTYYDLOVrA4fPnxTq64v14uOEpieJnwLfRNCrA4JZHEXUURD0/RdOMN/\n+9sf0DURYCm3aaPRKI2NjQwMDHDffffd9KrqG/Hwww/j9/tpamq64VXXKhpmpKeZ7//Da7QMe5Gj\ng4VYXySQxV1E4R0fpPnsQf7bf3+NPk/gpkNrppbzL3/5SyorK5e8qnoxLpeL3bt3097eTn9//w19\nTHB6kgvnj/BPf/86F0f9EshCrDMSyOIuouFKSKO6qgKnzbCkb/5AIMCJEycoLCykoqJiRQ9IyMvL\nIyYmhrNnzxIMBhd9vsXupnxTJSmJTtZP8U0hxIzr/kyKRCJ8+ctf5tOf/jTPPvsshw4doru7mxde\neIEXX3yRP/3TP5197quvvsrTTz/Nc889x+HDh1e63UIsgYbJYsPhdLGUQW00GqWhoYHR0VEeeuih\nFZmqvpLNZmPHjh2MjIzQ2tpKJBK57tS10WTG7ozBZJLrbCHWo+tWe3/zzTeJj4/nr//6r5mcnOSp\np55i48aNvPTSS2zbto2XX36ZgwcPUlVVxSuvvMLrr79OIBDg+eefZ9euXZjN5tvVDyFW3MjICE1N\nTWzevBmn03lbPmdqairbtm3jrbfewu12k5WVta4OnxBC3LjrBvJjjz3GgQMHAGaPjmtsbGTbtm0A\n7Nmzh6NHj2IwGKiursZkMuFyucjNzaWlpYWKioqV74EQt0E4HOb06dPEx8dTWlp6Ww+AKC8vp62t\njdOnTxMXF7f4MY1y71iIdem6P1XsdjsOhwOv18vv//7v8wd/8AdXTZk5nU68Xi8+n4+YmJjZv3c4\nHExNTa1cq4VYosvbnqKATlRFUTeQXjO1qltbW5dUq/pWWSwWnnjiCbxeL/X19YTD4QXbqUd1lNLR\n9ahU+hJinVn0Mv/S/8/efQfJcd4Hn//25Jx2Z2dzxGKxEVgABAECYIREEqQkKlASRSXLesuns++V\n7Tq7/J5kl1+beqte+d5zvSq/liWHk0+kzBzAAIJEzmGxCyywCZuwARtnJ4fumenu+2OBRQ4UQXJB\n9adqiuDOTM/zdHh+T+qnJyf5zne+wxe/+EUee+yxy1oGyWQSl8uFw+EgkUhc9XeNZnFRkZJhzvSd\nQVUjDA2NEE1lbhi4VFVlbm6O9957jw0bNlBcXPyJPB7RZrOxcuVKTp8+zczMzDXTnMukGBnqJ5ma\n4cyZAYLxNIo21VqjuWPcsGQJBoP8/u//Pn/2Z3/GF7/4RWD+UXHHjh0DYO/evaxatYrm5maOHz9O\nJiaHGG4AACAASURBVJMhHo8zNDREbW3tR596jeYDykopgmkr3/+DRzCmEkgZ+bptZFVVSaVS7N69\nm9LSUpqamjAYbjjK85GqqalZWOs6nU5fFZSVXJZwEh7+/Ebs6RgpKaf1Xms0dxBBvUHz4Cc/+Qlb\nt26luroaVVURBIEf/ehHPPPMM2SzWWpqanjmmWcQBIGXXnqJF154AVVV+cEPfsCmTZs+znxoNLed\nLMt0dnZy8uRJHn30Ufx+/yfSOr7U1NQUb7zxBqtWrWL58uXaxEmN5lPkhgFZo/ldNjU1xfvvv09L\nSwvNzc2feDAGUBSFEydOsG/fPp588kkKCwsXRbo0Gs2Hp13JGs01KIpCR0cHBoPhtq5V/WHpdDpW\nrlxJaWkpu3btIpFIaJO3NJpPCS0gazRXUBSFnp4eJiYm2LBhA3a7fdEE5AsefvhhEokEvb291511\nrdFo7ixaQNZoLnFhreqtW7fS1NT0ka1V/WE5HA42bNjAwMAAk5OTWitZo/kUWHwljUbzCRJFkSNH\njlBVVfWRr1X9YdXU1GC32295rWuNRrO4aQFZoznvwmMVZ2Zm2LRp06Lsqr7UhbWuZ2ZmGBwcRJa1\nxUA0mjuZFpA1mvPm5ubo7u5m+fLlOByOTzo5t6SwsJDVq1ezdetWzp07pwVkjeYOpgVkjYb5tarb\n29vxeDwf+1rVH1ZTUxOlpaUcP35cm3Wt0dzB7pxSR6P5iKiqSn9/P729vbS0tCz6ruormUwmPve5\nzxGPxxfWutaCskZz59ECsuZ3mqqqhMNhtm3bxvr16ykpKbmjWscX2O12WltbOXXqFLOzs590cjQa\nzW/hzit5NJrb5MJa1bt27aK4uJjm5uZPdK3qD2vJkiWUlZXR2dmJKIpaK1mjucNoAVnzO0tRFAYG\nBojFYtx3332YTKZPOkkfitVqpbW1ldHRUbq7u5Fl+ZNOkkaj+QC0gKz5nRUMBjl16hStra2L4sER\nt0MgEGDVqlXs37+fmZkZFEX5pJOk0Whu0Z1fAmk0t0BV1ctesizT3t6OTqejpqbmUxGMLzyRbdWq\nVRQXF7N79+6FWddXvjQazeJz55dCGs0NqKqKoihks1mSySSRSITp6WmOHTvGqVOnaGxsRFEUMpkM\niqLcscHqQqDNZDIkk0nWrl3L2bNnOXz4MJOTk0QiERKJxB2fT43m00x7/KLmU0tRFNLpNHNzc4RC\nIWZnZwmFQkiSxPDwMLlcjrq6Ovx+P/n5+eTl5ZGXl4fNZkOn090xtz4pioIoiszOzhIOh5mdnWVu\nbo7+/n4EQaC4uBiLxUJeXh75+fl4vV7y8/Ox2+13VD41mk87LSBrPpVkWWZ6epquri7OnDlDYWEh\nzc3NWCwWAHK5HHq9HkEQyGQy9PT0MDQ0xJIlS2hubqa4uHjRz7i+0PU+PT1Nd3c3fX19FBcX09jY\niNVqXRg/vtAdn8lk6OvrY2RkhJKSkoUFRUwmkxaUNZpFQAvImk+VC13U/f397NmzB0VReOKJJygs\nLLxp0AmFQrz++uskk0nuu+8+6uvrMRqNH1PKP7hsNsvg4CDbt28nk8nw1FNP3VI+o9Eor776KpFI\nhPXr19PU1ITNZvuYUq3RaK5HC8iaTw1VVcnlcnR2drJ//34aGhrYuHHjQqv4VmSzWQ4dOkR7eztr\n165lxYoVmM3mRdeCVBSF06dPc/DgQRobG1m7du0HqjyoqsqJEydoa2ujvr6eu+66S2spazSfsMXd\nJ6fRfACqqjI0NERbWxsbN26kpaXlA3c7G41GNm7ciM/nY8+ePdhsNhoaGha6txcDVVUZHx9n//79\nrF69mhUrVnzgfAqCQEtLCyaTiQMHDmC322lqalrUPQIazaedFpA1nxqxWIwjR45QV1f3oVbdEgSB\nxsZGUqkUx44dIxAIUFBQcJtT+9tLJBI8//zzrFq1ipaWFoxG429VWdDr9dTV1ZFMJtm5cyder5fy\n8vJPxS1gGs2dSLvyNHeM+UlMOTLZLMo1Rlq6u7vJZrOsWrXqFoKxipyVkJVr35d7oQVpt9vp7Oxc\nNKteKYrCvn37sNlsrFu3DovFcs1grKoqipxDEtOkkkmSKQkpkyGTuXzfGQwG1qxZQ15eHu3t7aRS\nqev+tqqqyLkcOVlGG+jSaG4/rYWsuWNkUhHOtB+gM+Zk8/334LVf7F7NZDIcPnyYz372s9hstpu2\nGFUlQ8f7v0HX+DlayvLQC3DlNywWCytWrGD37t20traSn5//EeTqg5mdnaW7u5unnnoKq9V67Q+p\nKjkxQV/HUdo7ejF4vEQTKTImIwFvNZs+s4Z8u/myr3zpS1/iV7/6FefOnWPJkiXo9forNqmSDE9y\n5Egnen8Va1fWYVkcPfgazaeG1kLW3DGCZ7vY8uoL/Mvr+4ims5e919XVhcFgoLKy8qpgcjUVKXia\nn//dz3hxWxtxKcf1mnw1NTXIsszo6Ogn3kpWVZWuri6qqqrIz8+/bqVDyaU59v5z/N0vnuVMSMLp\n85LnNTNwZAfb3jpGNJW96jtOp5O6ujoGBgbIZq9+H3KM953g9ZdeYdfhPrJaC1mjue20gKy5Y/hK\nq6kqKsKs6LkyFm3bto01a9bc2oxqReLEllcZjKsc3/UOQ7Px637UaDTS3NxMW1sbkiR9yBx8OLlc\njmAwSGFh4Q0fhJGebOe//Nf/m2n/Or77B99n8yOP8NWvfoP//PTv8XB1EVb91Ze9IAhUVFQQDAav\nk089xVVLqCrNx6AXrupN0Gg0H54WkDV3DKvTQ57dOj/OckVE7u7uprq6+hZax5CN9PHzX6v86V/8\nKfrJYQ51Dt+wxdfY2MipU6eQJOm660HfbK3oG71/s7WmL/wtkUiQy+Xw+Xw3yJ3CePu7nBka44nN\nD1Dqc6ATBEBP1Zp72Py/PUK+69qVFofDgcFgIJFIXPWeIOiwu71YrdarKkMajeb20MaQNXeYa0dO\nVVVv6dYkVZHoevU1Zh9spaK6gvpAit27DvGljY0UuS3XbPl5PB5mZ2eZmppCkiT0ej15eXkLv5XJ\nZIhEIgsrY1ksFtxu98L7iUSCZDK5EGidTufCOLeqqkSjUURRBOZX1XK73Qv3BOdyOaLRKNlslmAw\nSDwev8ljImVmzg2Ry2ZwOea3cSFPBrMZl9l83W8ajUYMBsNCWjQazcdLC8iaT4Vbu+1HRYqM8Pbh\nPsq9FvbtmyWts9D23i7avvUEj7SUYNJdvR1FUUgkEnR3d+NwOLDb7axevXqhezwej9Pd3b3Q1Vtc\nXIzdbl+4p3dmZoahoaGFMej6+vqFlbEURWFkZISpqSkAzGYzTU1N5OXlASCKIoODg4TDYSKRCDMz\nMzcZy9aTV1yH0WRhIhglpyiY9HoEQFUUFFVB0OnPt5qvvQ+1RzZqNJ8MLSBr7hgqoKjz/1KVq7t1\nb/p9JcfA8f1kG+/mOw88Qp7VwPrlBUz/+Kc899Ix1lT7CTjNV3XJqqqKx+OhqakJr9eLXq+/bAEN\np9NJU1PTQiAzm82XdZ0HAgGcTudCGh0Ox8J7Op2OyspKioqKFv7f5XItvG+xWKitrSWbzTI3N0c0\nGr3JfcI6KlY+QOPSZ3ln6042NRaxrNiLQVCJzU4wG0lRWLUEt+XqBUAuPAXqWt3+qqqiKsr8CxVF\nUUGv9V1rNLeTFpA1dwwxPsfETIhUysbI1BwlXivG80HBbDYjiuLCM4GvJTU7xMuvHSVVez/1y5bg\nsehJF0BToYef/Y9fsePhOr6wrg674fJJY7OzsxQXF1NYWIjb7b5quyaT6Ya3RNntdux2+zXfEwTh\nmtu8wGAw4PV6AbBarTidTtLp9HU/D2ArX8//+L++z3/5+dv84y9VvvBgC4ZchuH+HmKSiSe/U3LN\ngCxJEtls9jrrWqsEJ8eYnhpjVvIzHoxRW+DEeI0JYhqN5rejBWTNHUOMRzEV1bLWYyYaiZFVZAx6\nAwKwevVqenp68Pv91x1jTcViBAoKyOU7UWQZFT1SWqHygYf5wZJZpifnkHIKdsPFFqKqqpw8eZKV\nK1divsH468fBarViMpkIhUI3rHgIgp6Wz/+f/J23mTfe3s3RgyHiCYnSlY/x9CN3U+i6Oh+qqhKL\nxYDLW/AXKURCYQJV5Vj1RiKROLLfibbQpkZz+2gPl9B8KgwNDfHKK6/w/e9/H4/Hc9vWnU6lUvzy\nl7/kkUceYenSpZ/4spKHDh1ieHiYL3zhC9dtdS9QVXK5LJlsDsFgwmI0XHeGtKIobNmyBafTyYYN\nGz7xyodG87tI62/SfCpUVFTgcDg4c+bMbVvAQ1EUenp6cDqdFBcXf+LBGKChoYGZmRlGRkZunk9B\nwGA0YbPZsJquH4xVVWVqaorR0VGWLFmiPWBCo/mE3LCEyeVy/Pmf/zlPP/00X/3qV9m5cyc9PT3c\ne++9fPvb3+bb3/42W7duBeDFF1/ky1/+Ml//+tfZvXv3x5F2jWaBXq/n3nvvpb29nXA4fEuTvG4m\nHo9z8uRJGhoacDqdtyGVH57L5eKuu+5iy5YtC13XH1Y6nebVV19l2bJlFBQULJqnWmk0v2tuOIa8\nZcsWvF4vP/3pT4lGozzxxBP84R/+Id/73vf47ne/u/C5YDDIr3/9a1577TVEUeSpp55i/fr1Wk1b\n87Gqqqqip6eHo0ePcv/999/SmtbXoqoq2WyWY8eOYTabqa+v/whS+9sRBIG7776bEydOcODAAR58\n8MGFysIHzauqqoiiyOHDh1FVldbW1uuvj63RaD5yN2whP/roo/zwhz8E5rvvDAYDXV1d7Nq1i29+\n85v8+Mc/JplM0tnZufCEHYfDQWVlJX19fR9LBjSaC2w2G2vXrmVycpLjx48Tj8cXbuW5FRdWxEql\nUnR0dNDf38+6detwuVyLqtVoMBh4+umnCQaDtLW1EY9ff+nP67kQjDs7OxkaGmLz5s03WQFMo9F8\n1G7YQr5QW04kEvzwhz/kj//4j8lkMjz55JM0NDTwi1/8gn/4h3+gvr7+si49m832WxUSGs2HVVxc\nzAMPPMAbb7xBMplk+fLl+P1+DAbDTYOqLMuEQiFOnjxJZ2cnmzdvXrTPB/Z4PDz00EPs3LkTSZJY\nuXIleXl5N12t7EKlIxKJcPr0ac6cOcNdd91FRUXFLS07qtFoPjo3ve1pcnKSP/qjP+Kb3/wmjz32\nGPF4fCH4btq0iWeeeYY1a9Zctv5tMpm8bHEDjebjotPpqK6u5vvf/z7PPfcc4+PjrFq1ivr6+oUh\nFEEQFpatvNB6zuVy9Pf3c/z4cZLJJN/61rfw+/2fZFZuqrKyks2bN/PKK68wMTHBypUrqampwWq1\notPpLgvMF/IqSRKjo6N0dHQwMzPD5s2bqa6uvoXnR2s0mo/aDW97CgaDfPvb3+av/uqvWLt2LQBf\n/epX+cu//Euam5t59tlnmZqa4rvf/S7f+973ePnll5Ekia997Wu8/vrrN1lzV6P5aF0YHx0cHKS4\nuBhVVbHb7bhcLpxOJ6lUikgkQiKRQK/XMzY2RllZGffccw8Oh2NRdVPfSCaTYf/+/QwMDBAIBDAa\njdjtdtxuN1arFVEUicViCw+nmJmZwe/3s3Hjxtt6i5hGo/lwbhiQf/KTn7B161aqq6sXFiL4kz/5\nE376059iNBrx+/38zd/8DXa7nZdeeokXXngBVVX5wQ9+wKZNmz7OfGg016SqKnNzc5w5c4bZ2Vlk\nWV4YV77QUtbr9fh8PpYuXUpBQcGi7KK+FaFQiL6+PmZnZ8nlcpflU6fTodfr8Xq9LFmyhMLCwjs2\nnxrNp5W2MIjmd4Ysy4iiiCiKZDIZjEYjFosFi8VyS0+KulNcms9sNovBYPhU5lOj+bTRArJGo9Fo\nNIuA1mel0Wg0Gs0ioAVkjUaj0WgWAS0gazQajUazCGgBWaPRaDSaRUALyBqNRqPRLAJaQNZoNBqN\nZhHQArJGo9FoNIuAFpA1Go1Go1kEtICs0Wg0Gs0ioAVkjUaj0WgWAS0gazQajUazCGgBWaPRaDSa\nRUALyBqNRqPRLAJaQNZoNBqNZhHQArJGo9FoNIuA4ZNOwOVUbvR0Zu3B6tfzcew3FVU5/0+dwJ10\nJFRVOb9/BHS6W0v5/GPCVUC4beedqqoLLwQB3SXbXQzn9qWPRr+YnivPLYFFkNQPZf58EBAuPY9V\nlQtHHLjs2Hz06VHnf/gOu65uJ/WKAmwxXA/Xc+3r5PZYVAFZVRRS8RCRuIiigsFgQKcTUBQZOatg\n8QXwWQUSiQRGqwOL0fjJFQ6qiqIqZEQJ9EbMJsP8wVFV5FyGRDyJIggYTBZsVgs64eqCTFVVclKa\nlJRBlVVMdidWk/6DHWRVRUzGCMfi5GQVncGAXtAhoJDNyphtdrxeN0oiTFK14XZZfqvCRpESjE/M\nkNNZKCwqxGrUfeB0KoDAx3mxqSg5iZmJMabmIpjsBdRUl2Iy6K8q+FRFAeF88FWzhCYnmUuIuPyl\nFHisH7KAVlEVmUQ0xNTkJKF4GoPFSUGgAFlMYXP58Hsd5DIiSTGH3W7HoL99FYFbSqGqko7NEY6n\nyCp6fHl5OGxm1JxENBwmIeYQ9AZcbi9Ou/ljDVi3laoSH+uhO2ajcUkZDosBgfl4mAhNMz2XwJlf\nQL7Xhf42ZFFVZRKJJIrOhMNqRq8TLhboggA5iVAwSDCcxF9WjttuRn+n7tsPQcmmmZ0JkswK5BcW\n4rYar/vZC/tv/vpQkaU0yXQWk82B2ai/zTHhYoVUEATkrEg4OE0oDgVFBbid1ttaidL/9V//9V/f\nxu19KGouy3DnXl558RXe3HEM1SgQnJrkbFc7e7e/x2lDLc3OGFtefJaQvYoKv+sTKxiUbJKxoREO\n79jDpGiktMSPXhBQ5Awjp4+wZdtORkf76T0TxlcUwGUzXVXAZhIhThzczd62U3TtfJOzcoAlFX70\nH6imnGOs/xSHt7/Ef7y5m8lkjlRkjplzQ+x4/31GpmaprKtl4PWf8eohlaaVlZj1ug98EmVj47y3\ndQu72oeoWNaIz2b8QAFDzcWYnMthtxk/vmOmqswOtfHSW3uZHtrF4VOT1LW24jRdXZETZ8dIGeyY\n9HoENcvIyX386vk3EP3LqCv2oL/FlvU1k6FkmRs6zVsvvsjJoTFkvR4pNs3RPbvZsasda341VWVe\nJs4c5tl328kvqSDfaf7YWwkzgyd5d9u7vPr620R1AcrLApjkJL1tu3jlpTfpm06SFyjB77bdck/D\nYqMqKY688i/8rzf6aVzZhN9lRScAqsrY6f28+OwbRC2++Yrb7QjIUph3XnuZveOwtDyAzaQnEw0S\nlwWMBiNkYnQf38Ozv34RfXkj5QUejHfovv0wsolZjux9j/cPdeIqr6PUa7vOJxVSiRSSJGMyGxFQ\nmek5wJaX96B6SikscHJ7d59KKp5CyiiYzEZkMUrP/m28+NppXCWVlBa5buu476IaQxb0BgKVVagT\nw7x/UqSusYmWlhZa19zDyjo7p0+OIYlJJsaGCKfFhZqLqqooirLwX0W52DWoqCoqF/9f5ULXoXL5\nfxf+fnFbN5KLDvP6c2/y4m9e5kT/OWRlvsMrMdHLcy/sxF6+jKaGemL9R9m2txMxp1y+ATVH18E3\n+PWOTvzlS/HEjvLy828xJ+Xmu89u8vsX6cgrrqSl2sGho8fwVjbS0txCU3Mr61YvJT07yFw8Q2x2\nkLMTERRVPb995ZL8XvF7C/tRWdjHBkeAmup8ZoaHSGVyN0jP/LYvfn9+29LEYV4+eBYxc3HfqqqK\nesnx4tLjdCEN54/NzV3Y1qXbz9J7/BgjKQvrH9hE49JaLNdqHasyg1t/zpGREFlZRRVMlNWvwDTR\nx2RMRFHO76Mrfk+54veul670XD//79/+Nw5061l136N8dtNneeC++2ip9DFyaohIQgIgmwgze24K\nMStf3D/n99Gl++WaL1jY7+rCPrviMwv7+top9ZVU4DAKDJ86zr/+z+c40jVOzmCjqqEJd9LCsrpa\niv0udOdbeRePLzdJ16V/u/S8U66Z9ovH5erz8FrnyK1fK5CJTLC/Z4iOve/QNTyFdOG6FAQKSssx\n60UmZsIo6oXfunh+Kpfsv6vP3Qt/u/yYoWSJTY4xMxubP7dUham2N9nXNUg8oyAY7VQ31JAa7Wcq\nGCUnz5dZl+6Dy/J7xfG8eKxvrwvH6laOyVXn2CXnxGXfv+r8uHj+GKxuAoVekjOTRFPixc9feU0r\nIoMne+nuHCF7vmyXkiHOnZsglpK4lfPjqnhxg/NHlUUGTvbQc2qUrKqiNzuorCkhl5AITqcvHufL\nf+AWy4arLaoua0Gnx+svIuByorf7KSorxyenSbs9lH3xaxz729Oojkae+oO/wJZXhF4HipwlGYsR\nT2cw222I4RA5k5NCr5l4PA1GCx6nmWQ8STan4vC6UaUUiWQSwWhDzaTA4iLPZUPNSoTm5khmFJy+\nfDx2K/rrVFmMecv4/R/6cf5bmIjuwgknM9R+lO6EjW+tvZsKn4ncwCl+cfQ4mzetwubWL3xfSY/y\n/C9+TcFXnuGe1gZmlW/Q11uEzaBDyYkkRRWb3YrhZtU9QY/LF8BQUYLRZKKopJSyMiczgzOsWvcg\ngslJJi1R/+Rf82eCA4dRh5iKE08m0Zuc6JU0aVHB4fFit5rQoSCl4syGQiiCBa/PN/93k4MCfx4G\n3Y3qcCpKLks0HCKWzGAwGzGbndiNEkd2vseA9BiReCkGvROTQUdWTBCcC5NTjfgK8rEZdaQTMVKi\nis1mIBFLojNbcTovdEVdZ1+oCjkpxezsHFnBiNvrw2k1o8oSM6EoGJzYi9fzeKMbs1HPpRFZVXLE\ngiNs374DW/k3aA3Y8Ths2PMKyLfp0KsSoeAMAgbcPi9WkwEBhUw6xmwwiqq34M3zYjNfp8dAydDx\n9kv85uQU//XfvsHdLaUYdQKC4ODuBx+moyuC8XynaUHNWv73799Nnt9JTkoSS0gYTEbSySQ6kwu3\nHTIZGRk9TocNJZsmLWbRmaxYDQrh2SCpnIrTm4fbYQVVJpWIk8rqcDv1ROdiKEYLLqcLq/nyS18Q\nBGxOD0VlLXz9m072bP0PXnrtbapLnqa2qILKuiaal9bgc1kRFJlkLEw4lsZgtuPxONHL0nxFQtAh\nCCqyoqLT6zCbTOSyWeScitFiQEomyKpGbGaBeDyFwWLHYTeTjkSQFAG7y4XdakYAcmKKcCiEqOhw\n+fJw2cwgZ0km4oiyCbtZIZFIIZjtuJ0OTIabtC9UmYm+IXAGKLL1cOxYHw+uqMLqtiAIAnavH4/f\nQ0InIKCi5HIk4zGSkozZYiIVi4DFhd/nRsiJzM2FyKgGXG4PTrsZJZsmHkujNxvJJJNgsuGwOnn0\nqe/zkMmDz6YnFZ3m2KGDDC4ppLmqDKvbgS/fj9VsQs1KhOdmSRiNeN1uzEYBKZUknspgcdjJJWOI\nsg6n04lJzRCJp9CZbLhcdkwG/Y3z/oGoKDmRcChMKqNid3pwuWwYkEkn4oSjMRS9BY/Hg82iJyum\nSCSzGM1G5GwaKafD4XBgIEs8nkZntuJyONALOZKJBFlFh8EokEmJYLTgcjgwGS14PN75oT/mg6ac\nyxCLhImns9jsblxOK1JohCMHjqL4W6hdnsJuNuCr28B3/ngtrjwfSlYiHo+RxYBZr0MSJXRmG26X\nA6MO5FyWZCJGSlQwGHVIqSSYXQQC3quCoaLIJGfOcuTAUYSC5SxpKcVhteAJFOD22cll0oSCQVSd\nEbfbidloAFUhk04SCkfJqQZcXg9O260P8SyqgAxcnFUhpYhFo0T6T3ION+vWNfLVbxuIjJ/mna37\nqdj0TR5fUcpkbzt72gZwuE0Mn5smORPCWL2cJ1cWsH3rLihZzlc2r6B99w7aeqbZ/N3vYZnq5P23\ntxMyF+DWx5FL1/Pdx1YyfGArJ0ayOBwKUxGBR5/8CjX51x4/FHTG8wFTdzHRao65WASL3Y7FaEAQ\n9Dh9ZqanBoiJGYrdloVYkB47xvtjST4fm6D9cIxQxMeXPrcGp1HH7Mn9vHRgjC//3rcotBlvqQtG\nBRRZJhmNEpyc5Ff/eJjv/e1XqV22gkx0hu1vbmU8V8Lv/eAJQj1tvPn2+2Qc1SyrKYD4NFNyLV9/\ncj1OJcjOrW8SFNzoxSS4ynjg3o0Ueiw3T4MiM9bdzvGus5icTpLBYbCtpLkizr/9agfRZUUcqzLR\nuryRIluCHW/sZgoTRilM2lnH459ZztiR99l+eIi8kmpKiqzEwnO4ypu5b+1yHOZrzBlQFZLBEd7b\nuZc0NkyCRDrnYs2D91MgTDAwMsaZSIqjbd3c/8BazKbLhwOyyShdB9/l5fYwzc1tVOlFWpobKfCA\nmo3T17afQ5lKlOl+coUP8Phnm1BCw7y7bQeiyUdOSmMrrudz963EbjFe3frOznHwUC/R/Edorsyb\nHxtmvsAxOn20rluHxe8EZLoP72TPqMJjn3uMIrGH37y2g4zNQzo8h2JZx5MPWGg7cpIZcxlPfe0R\ndFNdbN12mMCKDZScPc3+UQV/mUw07eTBLz5GqS1H175t7DgxTWNzCaoCsViUwNJVbFy9HMslZfiF\nyoScVCkoupv//O0IP/2Xt3l3+zLyv7QaBB2qAChZJs+0sWtXN6rbgSymKGpYSYUxzMHjpxHsfiqL\nXAz2nSFnK+OBe5czfKKNgXMqd9/fwEj7IbrG4lRUVeCyQDSaxOX2otfrENMRBEcx9268h4BDT8dr\n79AdlLC4UsRyBWx6/CEKzQna3t/Kvt4EDY2FmHQqU3Nxlt/7CCtqSjDfYOBXycbpHknRctcXqYpO\n88bxg4x98R78TvPVQxKKwmjvEY50j2LSqwSng4yHkxRVNvDZ9fV0n2gjljFgJkMq52blxvV4skO8\n/84u5nQ+nPIkorWcta2N9B3Zx1TBWr71wDJCPQd588gAicgplnptyE0tVPlVjLJMb9sB3JlJL0Lx\nNgAAIABJREFUgrMzFNRt4KGV5cwMtbP1vaOojjxKCjxI8RiKxYnPYEZWU4RjEo3rHmRFfSnGq7J+\n48melx73S7+TiQc5euQg3eMRjCqIop27N91HoWGato4u0ooevZxEZy2hpbUeee4M27YfQ7F4KCny\nISXjSIoZv9sN2SiheIYlKx+gsdLAid17aD9zDnN5NQUWyM6J5FU3s2bdssta+ko2RX/7YU70ToIZ\npLRCdfNyhLEj7Nn9Np4VUHPSRm1FPjNdh9ndPsm6xx6lJl/gwLZtdJ9LUFpVhcesEIsJ1K97gNYa\nB8Onj9HWN4bZZCQcnGZsOk7JkuV86SuP4TfrLtsPOSlB99F97Nn9Dr6VAlWddhobl+JTQSZET+9R\nTIKHUChCUe1q1q9uQgmf5ciew4wndZiMWUyuYu7ZeA8l1+2Cv9yi6rK+zNwwO3e8xzvbdnFuJglY\nqK4rx+12cO70MTrHgmSlJIfffYO2EZH6lgbCHe8wnMpneWMZNnce5uQoh490IWEmUGjg4NtbGI9l\nsbl9RNu38fbbXVhdLjLpFJGBvfyvn/8TGXcFK5prmXrrl/z7rkGy8gfrclAEKPDbMRnnSzsVUFMZ\n5Cu2E5udIR1LM9Izi9VmYebEm/zjL15nOpUlMTfBwaNniGVkPshgr5RIcGzH+7z28svsHIqBzkRB\nYTH+Ah9+/Szvvr2bSBocHh+htnd4/a1DWIqqqS+F//jn3zAYTpEMDrLn/d04ypZSU2xn75YXaO+b\nPN+FdxNymhMHD3H6bJKq2qXku6wkgynMnhJWFZqxOH3k+7xYTQK97/wTv3q2nbzKOpoqrTz/83+g\n/VwcvRzl6J6DjEQMVNc3EjBHeP3Zf+fYcIjcNdKgygkOvfE8r7ZNUrnibu5ZXU/o6Dv8z1eOEs/q\ncDrsOFxu8vLzsRiuHpsXdHoCtfWUWe248/Lx+s63ogFFTBAcC1JUU0edb5YXf/MmU+FZdr38LP9+\ncIKy+hZq8jO888KbDMwlrtl1qEhpohkJxWy8ZJKQihgNMRNMUN1QTlGBBVkBoyDT2X6Uc9E0ZqeX\neP8BdhzswOayEQ+lwKBnqu8I23afIC7mkGJRRgbOopBk13PPcnzayrK6EjreeYWdPVPk0OOyw5Gd\nb7KjN0Z5QwNCqI99h48TFiUykoQoioiiRE5WFtIvo6P+0d9j0z1NHN75Lke7z3Lh9M1Ex3nrhX/l\n0NkENfUNuFPjvP3WHoI5EzO9R9l/pAfMJob2vsY7u0+TkkSGDp1iMpjCaLIhJGfYu2UrAxEdS+rK\nCfYf4vXtbZhLllDuNXBk9066z4VRcmH2vLuLc5KLpUt87P2PX3G4Z4yszozbkmH32y9y4lyG8rpK\nJtq2s+vEAMmsco0jcGGXq6RCM4SyIUxFflo/swJRHODUwASSfPX3FDnNwXdf5cRkluqaIgbeep1z\nio+qYicntr7MG4fOUrhsJXevaiDSsY1fvryfcEZHbLKfNw92o8/zgZRCNlpIDZ1g9+lBYhkVd3E5\n5fl+3B4v3nwfdut8JU5QVEbnMgQqavFnz/Dcc7uZCGWwO61MnjzAC/9xHJO7glJHirdffJH2qRxV\nS8uZ6e3gaGc/mWudfKpKLpMmMhdkdnb2ileIlJi9+rpWMgwf28uvf72dlL2ChhIfQ/uOcOxIN/u2\nbeXEWIL6VetY3VDG0OHtvLO3C9VsYra/g+1bT6K3l1HmSLH7zRdpH0lQWlXIbG87u/d1ktFb0Wfj\ntB3cR/esSlVtLY7UJK//+4vsP32OS4vI2GQXW996hXNJHc3N9chDbby/4ygpo4uCogBOu5v8PA8O\nmw2HRWWws43ewUkEkw01Psm+t7YyElaprvIzdvoQ2/efJDg3wZ4d2zgxq2NpVQETnacJqy5qKwq5\n1hQyQWfA4/fjLyzA5fDg97mxGg0Igg5ZHCGUSlBYUUZm/CS7du9nOhrh5IG32LLzIK6yOqrzTHTu\nfp/9XVO3PKyw+FrIF7hLaGloIme3IPrmaxeCzkBBaQ2lAT9JHaDIxFJxHHk+fPlFNJR4yPoauXfF\ncqwGPevubWL/myKC2UPTqpW49Hp0OiNFVctYmm+ldM1XePJra1EVgZkdz3BqIsMDTginddRWl3K4\ne5zcEw2YuPW4KADJuIQsK4AOVBCuUe8RdAJOj4fHvvI4a9eXUe8Y4nN/8hqDc1/irrsf58cVm6h0\nmT7Q5CujxUJNUwutgRrGhkcXAoDFW8LGTSv56Ru70ekMlNTUs9xnomv157m3tQFjMIJZeA8pJ2Nw\nlrByzb2kZqaYlUVyyRTBUIJbqpcIerx5Hib37+Ffgr2UVDXQtKyQ4uoaSpwWAo3LaG5cgl0f4dfP\n7yKc93msagLJ4qY0IJDK6impLCG/qpknvnw/ddV5VDse4vW3dtM2NM3aJX6MV3SZy4lZdhw6RvXj\nP6KlqhSHqYSNq538f78+hPTVVipKCpn2ltO6vBan6erT3Wj3UFO3BLvZSH1jE421ZfNdn4KMavZR\nf+8mltfWIJhWoHvhMOnYFHvbTpIp/jxCOoLOoCNPN0NUyiCrXNWbIZjt+MxW9Kk02YXST2G0Yx+7\nes4RDIYxFS3nu099ltLqJVQ4TmDUCdgKltJcV0okfS/f+OZmkA3k+yw88eVNnPrZcWajaXxShroN\nX+be1kbc3/oCSjzHVDgNapSZRAoMVmqaGwkUVnDPww/TUO0h6C+kbwoy8QmO9g6TSGdAMFCzYhVV\nfjPn58GDOZ+Hv/wFBv7+73nvrTcoMVfTpEJqdpTTPWex3b2eTCqJyeFDjaSw+Jbymc0PMb59DJ3H\ni8Nfhnk6TjKZwFy9gi/et5HGWj/moXKKlq/h4c9spL5UoD1QTG1VC2ta6sgNxXDrT5FOZxH0Tloe\nW8N4VmI2CXpCxMQUgsVN0+omfPkVrFy3lmW1HvJdbkKZ3A0rjSoqsxMjjA+MkbOeJpcVUcUkXSd7\nia5bhs2ov+LzCmIyirs6n4LiMgqsdjyV9bQuC/APL3biv+c/0VJbRb5NYOMqD2+9eBzx861U1tSy\nyhdg02NfwqnI2JxWsiU+DqZ1GM1WSgJV5Pvc2GpraWpowGsSEJQQGaOBdQ89xPKGBmKxcp7dmSKT\n1VFUVUOxP5+Nqx5j7V0t6EfHcbkrWLt+NfUNTvoqK4kIyrXzruaIzo5w/GgnIenySoei2mm5+y7q\nqoswXfr3TJQTXe0kXAHuv2c1dfYUVmcR2VyILW+NUHrvBpaUFmFSXCwt2c2B/lHsjzxMTUUZxpoW\n1tzdimV8iuLCcpY1tdC03M/QsU6GsyJGm4fKinKqa+poXLue1U0BZnVRjrX/M50dfVTefbEXLjLW\nx/D4FBUVEEtkceYFMEYFvF4vBf4AjspmGusq0QGu5kYqqo4hCDpcvkLqK8uobFzOXRs20FAjczjg\nYkqKkpFEMpKEtyRAIFBEwJVHXl0La+5aicN8ZRktYDTbKSopJuAvwFXRRMP535PToDc6qWtupWHZ\nUiYOFjA0IyPGw4yc6SWsGDAbsmQkM3a9hdhUGAW4lUGFxRuQ7R6ql9XjKitkTlIuzjw8PykJQG80\n4SsrZlf3EKeP6+mYymPN5ipM5wvty07BC7VgAUBFkVWcBV6sNgdmg46gImEwFFJY6MfvMrPhD3/E\nKsWD+WbjUpfVfQRMgoHpmQRSTgZVjyIrmDzz41uqIpPNyuiNRlz+IkxWA85CBwhgsTtR1DjpjIzJ\n6qSm3IVZ98FmQxvMZsqXLmV5tQ1T2ndZIXP5BauiyFBYUYZJJyx0awkoRGZmONrRSchv4Pc2L6G4\n0AuZFNF0BkWd71K5fpp0lDav4BFZT+eJg7TteJvJCYEVa8tRmJ/wkg4FiakhwikBe10+fr8flznA\nX/z4RzhK8jFMAYoeowCCoGIwmtEbdaSV7DVrmaqaI6XmMOnn7yJBFbA7vRiiCTLy/IQNRVW4YRVV\nmb8lS1UVQlNBTFYLeX4TBqOZfH8eBp2w0DoXFAVJVSj255Gf78cWuJf/9IeryQu4r3nB6UwumivK\ncGzvZmgqSrnHhk6vo3zV/azObOFvnt3N43/2CG6LkSgKAiq684lVdDqcvmIcdhcOswFQqWxeT6Xn\nLd481E6r1E/xfU9jkmP0neng1JyXpQ1PsMLlIaYXEBMxkFVUdLgtei4ZXEGOT7B75zbOTUcA2OAo\npMhbCfr5gywIAoGaVj73yCP897//Z97hIR586lG8igyKA3+enwK/H5P/M5S0qlQU2skZmvBuO847\nr7xFwdrHadixjf07D1C4rJnCUh96Yf4c8BT4cdmsCIig6nFYzJj0AjkBdLr5Sk0uMUv/mXYG5RKq\n6+5lld2JVc0hptPoFBXQYTfM50lRb6HCLMtMT4yR17Ke5bWF2MxL+MLwELvGTjIa3ESR6/IhGZ1g\npjDfyKmh4xw9OMVUaTmfaS7FasyQVuXzczsEUOfH3o3JObJZGUVVsZv0GA1WfA4DkAXUi9eNqqIw\nP0kwFYuRkbLkBxQEwGMzotcJ6ARl/hic/7ysqngLrRhMF+Y/OLAIRnR6PUajGcP1ci8Y8RYu4b5H\nKriyD0BFwGQyXRUAVDmHlBUx2dyYTQYsbj/LVjgInj1AWpVRzv+UIOixWuzoMgq5nIIqqNi9Zoxm\nHYIOdNgwYUavN2I0mjFm539VVVX0Oh0Ggw4BAZPFjNWiJyNlkLk4pKcqMka9k/z8AgryCvA/+mWa\nBQtueRRUBVWQSSVCiLIFl8IlXfMqKCruPB8upx0dsfONIrBY7eQ7svSeOcxhRyUJn4OV9SU3LuNV\nFVVQQVBIx0OkFQuu840ss0GHTuDipDBVRVUMOOwFFATyyDfk4a+sx+7Ov+VyfFF1WauqgphOksrm\nEHJp4tE4elceZcWF5wOHSkYSUXIyYiJFVlYxm/Op9ZgZHg5z/ze+x13lNrI5GVR1fnxEyZJKJQlN\njpNSckSjccRUAjEHiXiMZDqDoqq4y+opsNuRjVbyCwtw6GY5PhRGVtRr7kxVyZGIxUiLKRKJCJF4\nClkwUFxcjFeKMxOKk0rFGJmcpay2Gq/NQjo6wdbXt9F/LorJt5RlXjPnxqdJJBNMjZ3Dbi/HZzEQ\nGjzE8795k6CYvekYEKqClEoSjadQZZVkOIqYEWhcvxzb+RnFSk4iGovP718pQ0ZKIcoQT0RJiSKp\nZGp+LDYepev4EQbkUv70e19gic+FlDESGu9hf+8UkWgKJZdFlDLXrJGr2QTHj7cT97Xyx3/5//AX\n/8eXsQtTpDMyZoeZeCzKud5uhkbj3HNvA/r4HAarm4KCfHK9nUxFUiiqAVUaY2Byhlg8wUhPP/GY\ng4o85zUnuOksHpaVBZjuHWIqFCUanuLgiRHK7lmK26iSkbJI6TTxtHTD2ZRms4FUPM6pjlP0D88i\npWOkszKxZBJRSpOIp1DkHJJgo64ygDkkYnX4KMjzcG5ogmAyc1WhB4Bg465vfInPrg2y5Y0t9Jyd\nJJFIoxr0GE0mcNnwuB0Y9CpiKoWYzZIUJeSMSDqZRYokSWcunAcCRm85n1/fwnvP/owdU0XUFTkR\nx9v41evHeOjrv8+6ZQGiZpVkPMjpQweZCEfJZjMk42kkSUISMySTIrJnFT/6m//OP/3yl/zTL3/J\n0xuaMCsisViIcCxCSsohGGy0PvAIjz+yEodOQFDB4s6jwF9ITtFj9+Xjc+kYnZkjnMziKiinvtDE\n9nd6qFqymnseqGTH4X4w5uF3GFDlHJmMRCKZIpqSEMU0UiaDlBYRxQxiMokoZkimRcIDezk6EOH+\nRz9PS7mTGaPCzOQYfV2nmA5FkeUs6XQaMSWSzcnEYylEKXfNY6zIWcJT/Rw73seSulqampqoW7qM\n1tXriJ2dovPkANF0BklMI4oSUlpCyioY3KXYXD6CcSsPP/UH1BW60ZmcLC0rIDYyxvRciEh4ksMn\nR/A0VeCx6VGkDPFYimhSQlYUcpJIOptDktKkpPkuYqNBj5iSGBk8Q8eJYaKRJCgqUjqNJKVJJCWU\nnEhaEkmn0qg5BTGZQpREUikJOSuRFEXEVIpYao5oMowo5a4uKwQBvcGIxWbDdsXLbrNiNFx9z67e\n4qG2phrT7Bj9vWeJxMJ0t5+iayiJz+UkNj3NXDRGeHaM3nNzOEp8mAWZrJQlI84PgaRS88MhUkYk\nlUwQS84REyOIYgYEyEQiBMdnCMciDA4NM5UxU14aQCeJyJkskihi8RTh9frRm2x4An5clgzjMyGS\nshGzSSCZmGKkv5Oe0Sli8SRSRiKTyZLJSIgZiURaJJFKkxZFMhkJSZIQsyrGvArsHh/JlIHWDY+x\npDDvfG/mtemNViwmgWRikrODnfSOTROPp5AkEUnKzJ9/mSypdJaMosfrL8VisqCzucjLd5JKhjk7\nm7zlLutFdR+ykhXpOrKd/R39ZBQRJZvE7C0h4HPMT6xSsvSfOsKeI6cJxWRqG2sYOrqb9qEgZqPM\ncO8pTpweBFcB5YUeVDFMd1c3kpxlaGCYiYlhJJMPU2KC4x2DzCo58t0llJfm4S6sRBcbpePkKKnU\nDB1tPZjrVtNS4rrmPZdqapy3nn+L0wMjBMMRghEDS5ZVkZfvJDHYwYlpiVx8gsM9o6y7/zM0VhaS\nmu3hX3+5BW/jSpbWVJEnzbCvbQhJnGD/rmPUb3yah9YtIdj5Fj/75zbWP/EZ8iyGG9/orkr07dvD\n+22dTM7EyaQyWNz5lATyFiaqJCZ6ee3t7ZwLJQhUN6APnWLPgX4mcgLFARdnT7dxZmQEndFNUcBN\neHIMnVFguGOAqWCISChNYaWHrrZjjE8GsQYqWFpRdNWsVlWW6Gs/wOFTQ5iMWc52D1NQvZyW5hrM\nuSC7Tw6SU7IUVzaxcv0K4qOnODMRIjzVR+fJWWrvXoVDmmL7e28xKxmQ01GOHjiJvWoDX3p0NV7r\n1ZOmdEYrpT4rg8cPMT4VY3L0ND0RE1/5+hMUM83u3YcYmw0jWopYVlGA0XCtXgeV+HgXfaNxVHLU\nNNUSOv0+u48OEzK5KHXlOLTvICPTc7iLl7Jx1RKmDx9gNBwheG6E3okcy1vr8FpN1zxWFk8RDZX5\njPWc4ETPJIl4gqmR4xzvCJJx+VixopnqQtj32tt0jE6ScxZTY5pl+54jzMREvGXllBdeOJ56PAEr\nR97Zzt3f/APWVfjQyQnOnuoio9qJhiaYk5KcHRknK5uRE+foGxggnnBR4Mxw+lAbgzMhLIEqqot8\nl7UOxk4f5L2d+xkcGyevuoaA14XZ5qIsYCEY0nPX2kYChQV4bCqnD3YwEYkxebafadVJw9IqvHYL\nSnSOtKOUBx9YS4EFguEsq+/bQHW+nVRsgqP79tIxMIniKcSaGqH9xElmghKF5QWMHDhIx5lxJLuf\nhjIXE/0jSBmFyckpoorIxFwSo17P7PgQQ6NjGK0FmNMhTnX1MhGJU1RRS0m+C+MVt0akQ8O8/cYr\nvH9qlIKiemqrCzEJSTr3H2Soe4hQLIylsJzsVDdH2juYDSkUVRYzemIHgxNxhFyCob4uuvuGETyV\n3LW0kMnek4xNhBgf7qE3auDRJx6nSBdk/8E2RqaC6B3FVJd4CA2eZu+h4wyHkwTKqqkq9JINj9F1\nZpJMPEReWRGTw12c7D1LzmTFY8lyuuM4Z0dD2Px+xOgYHZ19hNMS+T4Hoz3t9I2MItkDOIUwx4/u\nZ3QmSKC6gUKf6+Z3ZdyMTo/bbUMJjXBmYJjJmSn6hkIEappoLrMx1neGiakgZwdPEcTLvRtXI04P\nsu9wJ0lZh9thYLy3g1NDE+i8+ZjkCO3H9jMRi1JYXos9F+LItm0MRVXIzXGqbwh3wz185u4KejuO\ncrp/FGwe6ppacZCk9/QgM5EgY4P9JGwB6qpLkKdG6e4eIJK1ku9zMXf2JMc6+xAcAQo8Kn3Hj3By\nJILJ60WJjnGi8xSxVA6v28bkmQ7OTsTQ5+IMnemie3ACwVFAeaH7mg0vvV4gNjJMd88AkYyVgN/N\n3NAJjnb2oehd2BWR3hOdjERTBCqXUr+kjMTYEF39k4TnxhmZSeCvrKUyz35Lu19QP+iNUh8hRc4y\nNTrAVCiFoJPJyQaKKmspzpsPyKoiMzs1wvhUGDmnw+vN8OzPnmXJ5idZVuAgJyY4vn0rYf8q/uh7\nT+AQ0gyd6SUmgtHpw5yaImFw47XoiUZFMMg4vBVUledj0AlI0f+/vTuPrqo8Fz/+3XufeUhOTuZ5\nIhBmMThVoVgZROmgYq1e7eoq666Fv/ZXV1n2J1padWmVVtvb9i57reO9hQ54r97awQmqMorECESI\nhJAAScg8n/ns4f39EYggY3BItO/nn+Tsk7P3e569z3ly3rP383Sxf38LhqagOjOYVFmA6zRFNERy\ngL27DxBHAwwsW4Cp08rx2GGo7QA793ehqQLFm86MKRX4XTaMxBBNB9sJFpSQ4XOSDPfw3u79hPQ4\niiOV6TNnEPTaifW3UX8wxsQZpXjsJ183e+JAdDobm2gJRVGFwNAtMgpKKM79ICEnBjupO9CCUBVS\n0gtJUQdoaY9gqpCenYUx1Es0EUNR/eTnZ9HX3kzUUlF0F34/9PcnKSzLoK21HcsSeNJzKS88VUJO\n0tF6kObuEB6HHT1hkVdeQWaaFyvaQ21dA4bDR3lpBel+F/0dBznY3o+CwJtVQnlukMH6V/h/D73E\n4n/5OmU5KRiWRkFpKTlp3tNfOmDpdLc00NweQdjAl55LeVHe8LRn0xHihoktNZ+pZTk4TpmQLUId\nTdQ1dOJJy6R0QhHhI/W09prg9pCb7qG7owsLC09qDsWF2UTaD3C4PYxidxHMLaAwJ3iW4iEW3UcO\nsb+xDdO0MLUkKf4SgkEPqWlppHkFjbX19Jsmdn8mZQFB45FuLEshmFdyXEIGrBi179RSOG0WqW4H\nqkjQur+Otn4dm9dDMMVNV0cX/qxi3NYA/UNhdMNPQb6fgc4uIqaJL7uEstx0nPbhfSiEYKDjEIfa\netANi5zSieRlBIbf4K04Lc2DpOcEcbvsCD1Ka/0BOmMGdqeL7PxCstP9qAiiPR10JwSZ2TlosSF6\nugdIzc/H57SRjA3RcvAQfeEkWloOmc4EfX0D6LpGdlEeiY5OBuJJNH86FcXp9DQfpDeUAHcKGal2\nevvCpAbSMGODhGNRbLYgAY/KQGiIuGGSVTThlAlZj/RS39hMVLdICxZQVJiJQ0nS3NBAXySBaZgE\n8svwiSE6e/rQDQcBWxtPPbuVqkXzKMlJwUzEeOeN9YQDl7Lsm1eiDLTS0hHCVATeYA5lhbnooR6a\nWjrQkzrOtHzKCzNI9ndxuL2buGkSzCmhOCcNPdRJfX0zQnVTWF7AUG8ng6EYqsNJesBLqL+PeMzE\nGcjEbR+e1TNNQUZ2Fka4j1AsjuXKIidVo7+7m7hukF06idxg6kdPyMdeDz1tHG5uJWra8aZmUVqa\nh8OK0d7cTM9AFEtTCGTmk5+ZykBPO60dfdjsDgKBFIxIPwMxHacvnRS3xmBvD7oQZOYVoTdV89Ta\nFwl88WYWTEoDzUl+YTFBp8mh5hYGQ8MnNBYVFeHQh2g51MZQUsflSSEnP5+g306oo43GQ22Y7gyK\nCoIkhjrp6g/h9KWTmeZmqLuTgaiFOy0Nr2YwODCAZSmEOg+yeXsT0+deRmHQTWyoi7c21qBnXML3\nvnM1vlOFzjIY7DjCgUMdmJ50SguDxAc76ewL4XCkkOp1EB4cIAoEswrIz0wh0tXO4fY+sNtJTc+m\nIC/zHL76HDauEvJoDbS/x3+sfpbyxV9n1sQciPez8dW/EcmYxbe/vhi/Uxu5QPzDp/ef7prW4//+\n/CslCayj31+qqnZ0Xafc2PBF9JZA0YZLUY6LGj1Hx3WuMTv+cWLk1w8ef+znSTVgjxWFYPg7HmEk\neX/zOu5b/Q8WLlvODV+eTcBtO+dym0IcK855fuU5j5XPPNd6zaPe3vHFClDQNHW4XOeoR/pBLI/f\n7vHjOeaTqvYljp3Lcbp9fHT/fpRxfHgbH2VdoxVt2cLD//4mM6+ay/TyAkSsk7de20g0bTY3f2Mu\naW47Hxy5ox/TRz1WP2mnqy19fI330dU1FyRjA+x86b95+q9vUfqV5fzrghkEfS6UM6zn+GPg1PXV\nz/G1ahk07tzI/7xcy+TLL2VKYRbxvsNseWMnZlYV3/7WPDynXc95bE+IkTCNZv+O35O6zkFK5kS+\n/NUv8to71ZjhAsyBDgZchXxt/hX4HMP/kYw2sX60RDyyFlRNO/sX9McaDIyrb/I5qfHBaB6njPx6\nimu3P7zs6N8fW2roMTr6k1TOzqOxpoHBBRcQ8Jw8TX36zX+0QCpnLHryMWzv6LGljXI7p17VqeL7\n6R1IiqKclChHln9w4xPZxqfBlX8xX1vUxdY9O4n3daAP7CPinsiChVWkuo4VgTn/sX2a++p8nO49\n8Lyft4BEpJ/uoTDZuVlYXYfoHJhI8Cy1oE99DIy+wYmiahRWzmJOdx87du1gqC2HxGArtqwyFl1T\ndYZkfJ7bU5TzCtNn+hPyMIGeSBCJxVE1Bx6vG+10n0ilcU6cUNpRVVW5H6WxIyz0ZIJYPAmqHa/X\n9bH8M/VP6+gVD0fndlAU9WOuO30uYzi6T2MJVLsTt8s5PFM1TnwOEvIZfKjO6yc/NXQ0mZzHVMXI\nGo5bwXicypIkSZI+GWedsrYsi1WrVnHw4EFUVeX+++/H4XCwcuVKVFWloqKCe++9F4DnnnuOdevW\nYbfbWb58OfPmzfukx39GQgiioUEiSUEgLYBdA9M0ABVNG2X7wHPcXiIWJhSK40gNkOI89Vm3Z1gD\neiJGKBRG2H2kBzyjmvUYrv9qgKqiqR//85MkSZI+OWf9rP7666+jKAp//OMfueOOO/jFL37Bww8/\nzIoVK1i7di2WZbFhwwZ6enpYs2YN69at46mnnuLnP/85uq5/Gs/htCwjwf631/PM42sZbUjBAAAQ\na0lEQVQ40D2Iqcepe3s9b723n+TRzivD10KaZ7/e99w2yJEDu/jDfz7FG/u6MUe7UmHS397Ai2uf\n5ek360me4fo4GP7nIhZLjJyAYelR9mx/jbf3NHKmKoKSJEnS+HPWhDx//nweeOABANra2khNTaWu\nro7Zs2cDMHfuXLZt20ZtbS1VVVXYbDZ8Ph8lJSXU19ef36hOaNEFxyq8iLMs//A6UFT8Ho3aLZto\n6A5h6DFqt/yNLbvqSJgCYcbZV/8eDW0hztjE7KTtHlt8YgsxFBVfipvDu7fzXks3lnXc3x1ryzby\nuJOfA6g4PX4iB3by0p4jGObxbd0+3GpNEBnoYO+7TehH120mIuzc9Fe21n6QzE/12NO1ypMkSZLG\nzjmdZa2qKitXrmTDhg386le/YuvWrSP3eb1ewuEwkUgEv98/stzj8RAKhUY9ICEERiLG0FAIU7Hh\n86fg1Cyi0TjC5kA1E+iWjZQUL4qwiIVDRGJJbC4vqX4PmqogLItkPEI4ppNeOpHsggxUQNXszF50\nGzN9ebhsEO4+wvbt2yiYlUVxphuvx3nSSQbHxjM4FMI6Oh6304aCIBYeJBxLYnf58Pvc2FQb2YXl\nFGalk1CHz7ITljlcSSscw+Z04fN5wUwSjyewufy47RCPRUnoCv5UP4HsImYUZ7BeDF9/LCyTeDhM\nKBpFc/rwp3ixaypWMkbju5vZUhugZFohKX4Pqt3Fpdd8EzO1EKemIIRFMj48BW4pdvypKTjtKnoi\nTiweR7N5UESCpC5weX24HLZP/yQLSZIkCRjFZU+rV6+mt7eXpUuXkkgkRpZHIhFSUlLw+XyEw+GT\nlo+KEOiRft6r2cr+IxE0u8CVOYFZpSns2LyZIS0dFwP0hbO58cYrsYUP8daOWsJJGDAczLnySipz\nfQy2N/BO9X6iNic2s4+2ngigEOlvYe/7+3EWuZlQlE7tplf4ywsbme8owUeSSy8sx3V8X1EhSIb7\nhsfTFkWzCzxZFVxx8Uw8sUOsX7+JmOLGVDzMumwulflBVHF8g3GLUM9hdmzdRVfMwqkMkDv5EtII\nsX37btIv/grzy2zUvrOZnfUW1337erLdw7VutaMnhkU7jrBtwzsMOhKYlkLZzMuZUZnH4OE9PP/k\n4zRnfJnKmiAzLr4A91ALe99vwFPqp6Ion0S4h5q3qjnSHwFV4M8s4qLZ0xlorGXL9hqUQBm5AZXo\n4CBKcCpXzZmC13mWQiSSJEnSJ+KsU9YvvvgiTzzxBABOpxNVVZk2bRo7duwAYNOmTVRVVTF9+nRq\nampIJpOEQiGampqoqKgY1WCEpfP+jpd5fM3/4iyqZGphnGf+63fsbeujaeuf+ekD9/LKznre3vge\nfX1tvPD4v/GX2g4mzZxEe/XvefTJ1+nqOsyfn/41f359H3llZZgDLbS39SOEgjAS7NuxgVc21xCN\nR0kKD0GRIDwQJhpOnHI8ddv/zuNr/4y3ZCqTc6M887u17O0M07HjSR575iVKp1XSsu33PLp2MxHd\nPGHi24yH2PjcUzz3ah0TLroUV8s61vz+T3QODbL5D7/h9++2ohsmkbad/Me/P0Vz6EM1ooXJgU3r\n+fVjbzNx+kUo3dt59rfP0xlOEA4lcGf60KMhItE4KgKhx9j71qu8um0XMd1g72vP8l9/2k6wsoqL\nJnh5+dmHeGnjHsLxMG/+6XF+/sjjNCfdZKpNPHzvEzT0hs+tzaIkSZL0sTvrJ+SFCxdy9913c+ut\nt2IYBqtWraKsrIxVq1ah6zrl5eVcffXVKIrCbbfdxi233IIQghUrVuBwOM62+hOYyQjVmzeSPmMx\nX7poOrZICjcuDFJSNp2JCyv53/dzuPP7d+KLxwmKvax9eRdfXHEzmnCw6AtFPPLcDhrqdF59V/C9\nR79NVXkmyYxr+MfrDSiKIDV/CpdeUsU/WlUUexqz51zBpjff5pKFC7lqYhqqdmK/HiM+xPbNm8ma\ntYQrq6aghDwsXZBJpseOPTCJi2dlEosYlGZ7+MOb7xP53mJ8xz3l2GA7W7fv56Kb7uGC8nw65v9f\nYm1Opl80h6tLfbxss+EM5DB3/gJ8v96LxoevJRd4ygq54CsJhkJ9ePMq0Pc2MRQXTJ11BbMnZhKO\nzeOaRVfg0FQ07zQunn0BWwcUVNHPq3/8G8XX/htXTC3FaSvnpi+9zjP/2MSV9/8fFpd66UpZyvUL\nr8Dbq+H95a8IJY8WqJcfkSVJkj51Z03IbrebX/7ylyctX7NmzUnLbrzxRm688cbzHoxlGsSGwqQW\neLFrCp5AMV9dkoHqcNJqhHBkzCY3kEq6O4N4fTWDisBpU7AsC1fRVSz7poY92UlCdeJ12FGU4RaN\nml3jWOM5yzSPO4HLOtqaz2KgtQklr4Kg44NiFJZpEB+MECjzYtMU3MFivnptJppdpTHkoL2vg70H\neyhKTUXTNIx4hLhqjeQz09CJJFXcXi+qAgUzFhGsSOJ0KAhVYBfDnaQM8zQBEQJBEjPUSG1zMZNc\nKWSoCmYiRsJyYxkGQgUrPkBb0kN+YLj8owAw+mjstDEtxz9cKAWBJ5hBLNlLPGlgJgVZ0yvxauoH\nhTjOe89JkiRJH9W4eg9WbQ7SM4N0dnUyFE1gmgmam5s41NaPrhuQtI1UcrIH8ikNOsnwZ1FaNoHJ\nU6uwGwKb249bxOkfjGAYOpH+XiKDYQzDxLIssCyEaQ2fAa2AhSCR0Gl87a8cGjpxylizOUjPDNDR\n1UkolsQ0Ehw63MTh1kZ+94uniU68ihuuuoycjGxUm52Oxl3s74yiWBbCMlA0Fyka9HR0kEgaJGNh\nWg/U0RcRpOa4SAxG0A2DgcOdmAkLwzSxrOFxGoZOIjrItjf+TjS9ki9fNYeSPB8mJu17d9EaiqE5\nvRhWiHBrDRv2dWEYFoppYRkWli2TKaV+2g4dIpLQMZIRWhu68AWycNsEphhO3oZpDl+7LMAwzDOf\nbS5JkiR9YsZV+0VVs+G2KWx9vZohSyHR38jmPYdxu9w0vLORPQ0xiipzyMnOxJ2aTXrkfaq3teJI\ntXFk91u8/J7FoiWXIPr3Ut3Yg8cFe7a8ypbNu1BTiinKhk1vbOZgZ4JJs2aR5VGo3bmdtmiM7rYk\n075wMUH3B+0OVZsdtyrY/EY1YaER62tgy94WMvKK6H+/miF3NvmuBNVbamlqHyDFniSMxb6aGvoN\nG5OmziA7JczW2gYsu4OO93fQ0NxB0eQLyHC28MrfW8nKc7Lzv/9CdWM3OeW5eElSs3kTOzviTCgu\nRu+oo3PQSU5Qpa72XXZ3dNHVlWDChTMJGoNs37qHWMLEVlBJgdrOaxs2cahHp/LCL1CRr/Deu7vR\nbXa691Xz0qutXHHzv1BoHeKNVzaz10xhanGQI/veYUv1HgI5JZSWFuJxaLKoiCRJ0qdsXCVkFJVA\nTgETAnbaegZBSVAw8QvMyrfREvYwY1Y6TnsqhUUFuGx2CqdeiE/tZzCSZCji4brbrqEgI4OJE8oJ\nd7eSUGzYHF7KZk7EjZPsPD+RhJ2S3Gxyi8vIywySnuYnNNhJ+gVf4pIJ2dg05YTxpOUWMCHVRmvP\nAIqiU1R5GRdPLmHihAKsWB+G4WTCzFlcmG/HljqBklw77mAu2W6FzNLpXDhtGj6idEcSqKbJ1DlL\nKM3w4s+owGf2EDIhpbyEyTNKcasWKX4/uivI5HwfroxyLr6gAhGJY4k4SnAml1bm4c2fzGVTykgP\nZqAmIvQrucy9bCquRBddMTtFWZnklpYzacoMMtwm/UMhQt0RKr/2dRZfUkK4rYlw6hSm5nnxpwVI\nRBJMmlaG1+ahsLQUv8smE7IkSdKnbNzWsjYNHUuAzWY/Y/lJYVmYhoFis5/Yj9YySZoWmmYDhuen\nVfUUvXDF8LStqtnO2OHI1HUsThyPsEwMU6DZNLAsFO00lwwJC90wUVRtuGTnyGID3RBoNhuKGG79\np56ieL1lmhiGic1h/1A3paNtHlHQ1NPUvhYCwzQQaNhO2QtYkiRJGg/GNCEbGGhojJMuwJIkSZI0\nZsbtJ2RJkiRJ+mcyrs6yliRJkqR/VjIhS5IkSdI4IBOyJEmSJI0DMiFLkiRJ0jggE7IkSZIkjQMy\nIUuSJEnSOHDO/ZA/TkII7rvvPurr63E4HPzkJz+hsLBwLIbymbB7924effRR1qxZQ3NzMytXrkRV\nVSoqKrj33nsBeO6551i3bh12u53ly5czb968sR30OGAYBvfccw9HjhxB13WWL1/OhAkTZPzOkWVZ\nrFq1ioMHD6KqKvfffz8Oh0PGb5R6e3u54YYbePbZZ9E0TcZvFK6//np8Ph8ABQUFLF++/PMdPzEG\nXnvtNbFy5UohhBC7du0St99++1gM4zPhySefFEuWLBE33XSTEEKI5cuXi+rqaiGEED/+8Y/F+vXr\nRXd3t1iyZInQdV2EQiGxZMkSkUwmx3LY48Lzzz8vHnroISGEEIODg2LevHkyfqOwfv16cc899wgh\nhHj77bfF7bffLuM3Srqui+985zti0aJFoqmpScZvFBKJhLjuuutOWPZ5j9+YTFnX1NQwZ84cAGbO\nnMmePXvGYhifCcXFxTz22GMjt/fu3cvs2bMBmDt3Ltu2baO2tpaqqipsNhs+n4+SkhLq6+vHasjj\nxuLFi7njjjsAME0TTdOoq6uT8TtH8+fP54EHHgCgra2N1NRUGb9R+ulPf8rNN99MVlYWQggZv1HY\nt28f0WiUZcuW8a1vfYvdu3d/7uM3Jgk5HA7j9/tHbttstuHWiNJJFixYgKZpI7fFcYXVvF4v4XCY\nSCRyQjw9Hg+hUOhTHed45Ha78Xg8hMNh7rjjDr7//e/L+I2SqqqsXLmSBx98kCVLlsj4jcILL7xA\ne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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_6.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4) After performing the credit calculation with *each node* as the root, \n", " 1. we sum the credits for each edge. \n", " \n", " 2. And then divive the credit for each edge by 2, as each shortest path will have been discovered twice.\n", " \n", " 3. Then we get the the true betweenness." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.2.5 Using Betweenness to Find Communities\n", "It's a process of edge removal:\n", "\n", "1. Start with the graph and all its edges;\n", "\n", "2. then remove edges with the highest betweenness, until the graph has broken into a suitable number of connected components." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Tm8yuxCmvbcXYiBNenmEp1EGJW//IoW7DMNjZ2WFjY4OSkhI5ATwjmqbR2NjI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1z7Fl43o8ukZsPJP77/s5/8+RPRyte5TszWV4nFcOnGlqaqK4uFimJwBFRUVcuHBh0b5G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\nN1zc4GjDVCy6+xvcNDMOf+NJWnxBvP4gKlUAZqU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_7.png'))\n", "plt.figure()\n", "plt.imshow(plt.imread('./res/fig10_8.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Speeding up the Betweenness Calculation: \n", "If the large is large, we can pick a subset of the nodes at random and use these as the root of breadth-first searches, we can get an approximation to the betweenness of each edge that will serve in most applications." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**cons**: \n", "It is not possible to place an individual in two different communities, and everyone is assigned to a community." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Exercises for Section 10.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.3 Direct Discovery of Communities\n", "#### 10.3.1 Finding Cliques\n", "NP-complete: finding a large *clique* (a sef of nodes with edges between any two of them)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.3.2 Complete Bipartite Graphs\n", "A *complete bipartite graph* $K_{s,t}$ consists of $s$ nodes on one side and $t$ nodes on the other side, with all $st$ possible edges between the nodes of one side and the other present.\n", "\n", "**Idea**: \n", "\n", "1. While it is not possible to guarantee that a graph with many edges necessarily has a large clique, it is possible to guarantee that a bipartite graph with many edges has a large complete bipartite subgraph.\n", "\n", "2. We can regard a complete bipartite subgraph as the nucleus of a community, and add to it nodes with many edges to existing members of the community.\n", "\n", " + If its nodes is consisted of two or more types, construct bipartite graphs directly.\n", " \n", " + If all nodes have the same type, divide the node into two equal groups at random." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.3.3 Finding Complete Bipartite Subgraphs\n", "It's possible to view the problem of finding instance of $K_{s,t}$ within $G$ as one of finding frequent itemsets.\n", "\n", "1. \"items\" - left side. \n", "\n", "2. \"baskets\" - right side. \n", " The members of the basket for node $v$ are the nodes of the left side to which $v$ is connected.\n", "\n", "3. Let the support threshold be $s$, the number of nodes that the instance of $K_{s,t}$ has on the right side.\n", "\n", "the problem of find $K_{s,t}$ $\\to$ finding frequent itemsets $F$ of size $t$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.3.4 Why Complete Bipartite Graphs Must Exist\n", "Assume:\n", "\n", "1. the graph $G$ has $n$ nodes on the left and another $n$ nodes on the right.\n", "\n", "2. let $d$ be the average degree of all nodes.\n", "\n", "3. the degree of the $i$th node on the right is $d_i$.\n", "\n", "Proof:\n", "\n", "1. The total contribution of the $n$ nodes on the right is $\\sum_i \\binom{d_i}{t} \\geq n \\binom{d}{t}$ .\n", "\n", "2. The number of itemsets of size $t$ is $\\binom{n}{t}$.\n", "\n", "3. Thus, the average count of an itemset of size $t$ is $n \\binom{d}{t} / \\binom{n}{t}$ ???\n", "\n", "\\begin{align}\n", " n \\binom{d}{t} / \\binom{n}{t} &= n \\frac{d!}{(d-t)! t!} \\frac{t! (n-t)!}{n!} \\\\\n", " &= n \\frac{d (d-1) \\dotso (d-t+1)}{n (n-1) \\dotso (n-t+1)} \\\\\n", " &\\approx n \\frac{d^t}{n^t} \\quad \\text{when } n >> d >> t\n", "\\end{align}\n", "\n", "That is, if there is a community with $n$ nodes on each side, the average degree of the nodes is $d$, and $n(d/n)^t \\geq s$, then this community is guaranteed to have a complete bipartite subgraph $K_{s,t}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Exercises for Section 10.3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.4 Partitioning of Graphs\n", "tools from matrix theory $\\to$ minimizing the \"cut\" size." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.4.1 What Makes a Good Partition?\n", "1. divide the nodes into two sets so that the *cut* (sets of edges between two groups) is minimized.\n", "\n", "2. two sets are approximately equal in size." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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T0xkZGVG6qs02QpAF0yxqLxMavMpf/KCL3zqZht7npLAsxPH3TvEbX9hNaZZl0p+Ox+Pc\nvn07Zb2xVKCrq2tmZx6t43TcbSPQcwVvMES2U82D3iGiFcvQ6iY2HskKR1evXk3JGtdut5v+/n4S\nicS8ecnRaJSuri7y8vKm/bOfHrFWrweVihjqSWNKgUCAmzdv0t/fP+3fuVRoa2sjPz9/2vfFvav3\nac8MER/sRhr0ok3Aw6XT5O9jNpsJhUIzHu/TEIIsAJji/qGMnAjR/I//RHhHCSM3mrga7cGRYWTo\n+Pu8f/nXWXWk7DN7Yo+SrHUtmBi3243X6yUajU7vB9fu5eu/+TtkGlUM3DzB737zX/OHf/ITvrRn\nLSvsmgn390OhEKOjo9y/f3/ansbzoKysjPHxcbxe77yNIR6P43a7Z+Styp/8V5ZBTsToedCFSmVg\nRUkOevUEmdqSRCQSob29nZGRkWca+2Kmv7+f9PT0aR3bUwFv/MFv8xtbs9GrY1QW/xxNphr3kJ/c\nTCvqSeyXJElzuigUgrzEUalUSo/dpxdfl/D33+TvPxzhf/7Dt9mWaUZiKxXL02ht+RP+5m+O8yt7\nV5JrfnIBB1mWMZvNvPDCC6xduzYlE4hSgfb2dmpra6e0jSDLMrIkkZBlCAUJReMktFqszgysdjum\n1jGCkjTp2t9gMLB161a+8IUvYLFMHuFYqsRisamHRmUZWU6QSMiARDwWJx6PkYiEGe5p4a/eOUVG\nzk5eryzGqJk4TJqZmckXv/hFcnJyZvOjLCqysrIIBoNTcyY+Oc8uIxOLhEgk4sQkFauPVdF/9xz/\n35UA//r1dRgmiSYFAoE5fUaEIC9xjEajshqfvPuPTDQ4TPMv3uWqKp/fKSmhJNsKyARdMltWFPAX\np/87x8/v5419m3CYPntrJT2+VK+dPN8k+0hPxSOU4hGGe3sZDEVRt7dz/epNhs1xem6cZjAss+3Y\nTnJME3vHsiwzNDSE0+lMyeM1ycXifDdb0Gq1aLXaKVVqkuU448O9dA8FQe2n7eYNTANaxof7aKg7\nT323lV//3d/hwOrMCaNJw8PDSucowcSkpaUxNDREKBSafLEkywS9w3T1u5FkFR23bnDd7EEjywTH\n+vngv/03RqvfRp4kZC1JEiMjI7hcrjm7H8VsL3GS4Z7h4eGn7sUEBu9z7V43OdZCHvR4qfhEkP2j\nXky5Jeze2Mflkz9jz/o1TxTkwcFBjEYjVqt1Dj/RwsfhcKDVahkeHn5q8kgiNM7N+sv4MpaxQxvm\no5+9i1EtIUkSe179OlVHq3HqP1vsIEkyFFtRUfFc+75OlXA4TCgUmvdewSqVCpfLhcfjIRwOT+4l\nxcN03WriTsjFpp02mn7xHq160OiMOLNX82/efotdOytIMzx5ofToEauF0iJzvsjLy6OpqYnx8fGn\nnNmPM9R9m4a7o6zZuJ2hyyd5974BFTLxSJDu8Tx+p2oFWs3E9i9Zi38uC9QIQV7iJEvNdXd3k5eX\nN+mN5sjfxK/9/l/wZkKNyeb45KsqXEXr+Vd/8l/4ZuLh/orN+VkjIkkS9+/fx2azTfOI1dJDr9eT\nnp6O2+1+qvHXWdLZ+fKbbDj8+mMJQiq1BqPRjMlk+KRK1GdJeseJRGLejxVNRGdnJz09Pezfv3/e\nveTi4mJu376Nx+OZXJB1Fsp2HON/W/cC0iOTolJrMBhNmIwGNJOEqqPRKA8ePKCoqCgl9/RTiays\nLKVT3eSd0HTklWznX357Lb8uPSnCocPhsk8YsUiWTV22bJkIWQvmDovFQkFBAffv32fDhg2T3Gwq\nNDoTDtenxVaFVm8kzTWx4ZBlGb/fT0dHB0VFRWKf8imoVCrWrVvHu+++S39/P6tWrZpQLFUaLRa7\nk5lc0UQiQUtLCzabLWX3KR88eIDf70+Jms55eXnodDru3LlDXl7ehJELlUqNwWzHMIOE9WTZ1HA4\nTF5e3rwvQlIdrVbL5s2baW5uZt26dcp2z2dQqdAZzKTNYFJkWSYYDNLS0kJxcfGcnkQQsy1g69at\nDA8P09bWNidF/GVZpq2tjVAoREVFRUp6YqlGTk6OEo4LBAKzLkhJ77ijo4Pi4mKsVmtKzovb7SYn\nJyclhEmj0VBVVcXly5fp6+ubk2clFApx/fp1srKyWLZs2ay//2Jk48aNhEIhrly5MifHKSVJ4s6d\nO0iSxMqVK+e0Dv/83+WCecflcrF9+3Zqampwu92zavwlSWJoaIjGxsaU6Wm7EEj2Yu3t7eXq1atE\no9FZnZdIJEJzczMGg4HVq1enpBjDw6pl2dnZKTO+4uJiCgsLOXXq1Kz395Ykibt37zIwMMC6desm\n7iYleAyTycSLL75ITU0NHR0ds9q5TJZlhoeHuXHjBqtWrSI7O3vW3vtJCEEWAA+95OzsbD744ANG\nR0dnZfUvSRJer5cPPvgAp9PJli1bhIGZBpmZmVRXV3Pu3Dnu3r1LPB5Hkh4mbM1UCGRZJhqNcu3a\nNe7du8fu3btT1jsGKCgomKSl3vNHq9Vy5MgRxsbGaGhomLVwuiRJ9Pf3U1tbS1lZGYWFhSnzmRcC\n5eXlbNq0iTNnzjAwMDAropwMVdfX16NSqdi4cSNarXZO50Xz9ttvvz1n7y5YMGi1WlasWEFTUxMj\nIyNkZ2c/0wpdkiTGxsaoqanh3Llz/OZv/qZoKDEDMjIykGWZhoYGMjIylONQE+6VTYIsy0QiEVpa\nWnj//fc5evQoJSUlKd0KMz8/H6vVmhIh6yQmk4mCggLOnj2r1IGfSUlNeDgniUSC/v5+fvaznxGL\nxXjppZcwm81CkKeBWq2moKCAjo4OOjs7ycrKwmQyTbMK4S+RJAm/309DQwMtLS28/PLLZGVlzfmc\nCEEWKCTDl2fOnGF8fByHw4HRaJyWwZZlmXg8zuDgIBcuXODGjRtkZmZSXFw87/1sFyJqtZq8vDxG\nRkZobGzk7t27DA4OUlxcPOUzqsmCCD6fj5s3b3LixAmqq6vZuHFjyp8JNxgMKTk+m82Gw+GgtrZW\naQSi0+mmtXBILpA6Ojo4ffo0Pp8Pm81GdnY2DocjpRYhC4Fk17obN24oTSfMZjNq9Wf7Tk9EcoE0\nNDREQ0MD586d41d/9VdnVJ5zJghBFjyGwWCgqKiI27dv09nZSTwex2QyPVac4dEQXbJwQ7K4yPj4\nOK2trUoy0ptvvkk4HOby5cssX758Rp7dUketVpOTk8OtW7f44IMPSE9Pp6ioCLVarRibT4dNk/MS\njUYJBAL09PTQ3NxMW1sbVVVVbN26NeXFOPmZUnGMyXPJNpuNGzdu0N/fj1qtRqvVKvOSHP+jfyYN\nfjAYxOPxcO3aNS5fvkxaWhpf/epX8Xq9tLS0YLVasdvt0xKTpY5KpcJsNpOXl8eDBw+4f/8+4XBY\nifQlr+On5yP5Stqvu3fv0tzcjNvt5qtf/epzE2MAlZwK5wkEKcfY2BhNTU243W40Gg0rV65UjmGo\nVCqliERyX1OWZXp6eujo6CAWi5GTk8O2bdtwOBz4/X5+9KMfkZuby4EDB4QoTxNJkujt7eXs2bPE\n43F0Oh2yLJOVlcWKFSuwWq3IsoxWq0Wj0RCPx0kkEqjVakZGRnjw4AHj4+OYTCY2btzI8uXLUzpM\nnSQYDJJIJFJ6jzt5TKmpqQmfz4fVamXlypVkZmYCDzOzE4kEGo1GycuIRCJ0dnbS19cHQElJCWvX\nrsVgMBAOh7lw4QLDw8Ns2bKFoqKilCzYkur4/X4uXbpET08PWq2WgoIC8vPz0ev1yrMSj8eVhVPy\nLHNHRwehUIjMzEy2bds29Raos4QQZMGEJBIJent7uX//PvF4nHA4jM/nA1Cqbfn9fuBhCM9gMKDX\n61mxYgX5+fmK0U9WHqqtrWXTpk2sW7duzpMjFguyLDM6OsqZM2fQarVUVVWhUqlobW3F5/MRi8Xw\n+/2Ew2HMZjMGg4FgMEg0GsVisWAymdDpdGRmZrJq1aoFtTd58+ZN/H4/W7duTfkSktFolPv379Pf\n308sFiMUCuH3+9Fqtbjdblwul7KQtdls6HQ6rFYrq1atIiMj47HwtM/no7GxkcHBQbZt20ZRUVHK\nf/5URJZlBgYGuHfvHuFwmEgkgs/nUxZIbrebzMxMVCoVVqsVo9GIXq+noKCAgoICdLon1+SfS4Qg\nC55Kcv8x2Z81FAoRCAQAFKNvNBqx2WxYrdYnel+xWIympiZu3bpFdXW1yCKdIsFgkFOnTtHX18ex\nY8ceC58Fgw+brCfnJBgMEolEMBqNWCwW5U+bzTbjpKP55IMPPkClUnH48OEFI0ixWAyfz0cgECAc\nDhMIBPjRj37Ezp07KS0txWw2YzKZsNlsyv7mk/D7/dTV1dHd3c2+ffuEKD8DiUSCQCDwmP3q6Ojg\nwoULvP7669hsNqWkr9VqnVdnQcyw4Kmo1WocDgcOh+OxPePkv00lk1Gn01FRUUFLSwsNDQ3k5ORg\nMBiex/AXLIlEghs3bnDlyhVef/31zxSKMJvNStWg5JxIkvTY3vJCxuPxUFJSsqA+h06nw+Vy4XK5\nlGelpqaG8vJySktLpzwvVquVqqoqTp8+zcmTJzl8+LAQ5Rmi0Wiw2+3Y7XZlTiwWC+3t7VRUVKTU\nYlWk8QmmhUqlUpJXkgksU72ZHQ4Hhw8fpre3l1u3bhGPx1OiJGKqkUz86ezspK6ujqNHj1JWVjZp\nEpZKpUKj0aDT6VI+WWuq+Hw+0tPTF2y2cfJZUavVypxMZ170ej1Hjx5lxYoV1NbWKvkZ4pmZOck5\n0Wg0KblwnfFy6wtf+IKyj5ifn89v/dZv8Qd/8Aeo1WpKSkr4zne+M2uDFCweCgsLqays5MMPP1T2\n0BZCgtHzJJnEVVtbS3l5uZIRvdQoKChI2aYXz5ODBw9y9uxZmpqaAFi+fLlI9FqkzEiQk31tf/jD\nHypf++3f/m2+9a1vsXXrVr7zne9w6tQpXnjhhdkZ5QImVfq5phIbNmygvb2dmpoa0tLSlIIXgl8m\ncTU0NKDX69m+ffuSFGOAyspKbDbbfA9j3tHr9ezatYv6+nqam5sBRPh6kTIjlWhtbSUYDPL1r3+d\nX/u1X+PatWvcvn2brVu3ArBv3z7q6upmdaALlWAwyOjo6HwPI6UwGAwcPXoUvV5PY2MjwWBQhOE+\nIRqNcvPmTbxeL9u3b1/S1c1cLpfwBD/BarWyY8cOXC4XdXV1So0AweJiRoJsNBr5+te/zg9+8APe\nfvttfu/3fu8xg2qxWJTjMUudvr4+Tp48OSedYRYyDoeDF154gfb2dm7evDmrBeEXKolEggcPHnD3\n7l22bt3K8uXLl2xk5dGCDYKH2Gw2KisryczM5NSpU0KUFyEzetqLiop49dVXlf93Op14PB7l3wOB\nwJJe2T+K3W5XuigJHic7O5vVq1fT2NjI0NDQkja+kiQxMDDAiRMnKC4uZu3atfNyDjJVCIfDKdMH\nOZUwm80cOXKE/Px8Tp06RVdXlxDlRcSMBPmnP/0p3/ve94CH/Ur9fj+VlZU0NjYCUFtby5YtW2Zv\nlAuY7OxsKisrOX36tHhwPoVOp2Pbtm1kZmZy+fLlJRu6TvYmPn78OC6Xi23bti3ZfeMk3d3dtLW1\nzUl/24WOSqXi6NGjLF++XAlfi+u0OJiRIH/pS1/C5/Px5ptv8u1vf5vvfe97/NEf/RF//ud/zhtv\nvEE8Hufo0aOzPdYFS3V1NW63G6/XO99DSTkcDgc7duygo6ODa9euLbnQtSzL+P1+GhsbicfjHDly\nBIvFMt/Dmnd6enqWfNRkMjQaDXv37iUzM5Pm5mbhKS8SZpSmp9Pp+LM/+7PPfP2dd9555gEtRrKz\ns9m9e7cwLhNQUFDAhg0bqKurIzc3d8nsncqyTDgc5saNGwwPD3Ps2DGllN9Sx+fzYbfbRSbxJFgs\nFnbu3El9fT0NDQ1KC0JxzRYui9/qpQibN2/G4XDM9zBSEq1Wy9atW1m5ciUnT55kdHR0SSxe4vE4\nd+/epaWlhS1btlBYWLgkFiJTIRQKodfrxfV4Cna7nd27d+NyuUSi1yJA3O3PCb1ej1arFZmjE2A0\nGnnppZcIh8PU1NQQDofne0hzjtvtpr6+ntzcXIqLi4X4PEJOTs5z77SzULFarRw6dIjc3Fw+/vhj\nEb5ewAiRXe9PAAAgAElEQVQL8ByRZZlQKCTK302AwWDgpZdeoq2tjTt37pBIJBbldUqGquvr69Hp\ndGzfvh2TySTE5xH27t3L6tWrxTWZIjqdjpdffpn8/HzOnz+viPJifH4WM0KQnyOyLNPW1kZ7e7t4\nUCagqKiIPXv2cPXqVfr7+xfddUouyhoaGhgdHeXQoUOiPOQTSNYaFkyP/fv3k52dTVNTE11dXUsu\nSXKhI+7454hKpcLv99PQ0EAkEpnv4aQkWq2WDRs2YDQaaWxsVPotLwZkWSYSiXDt2jWam5vZs2fP\nY+0UBQ8RRUFmjtlsZteuXTidTpqamuju7hbh6wWEEOTniEqloqysjL6+Pnp6euZ7OCmLzWZjy5Yt\nDAwM0NraumiqnCUrcdXV1bFt2zZKSkqEF/gEIpEI4+Pji2benzd2u51du3bhcDiora0VoryAENbg\nOZORkcG6deu4ePHifA8lZVGr1RQVFbFlyxbq6uro6+tb8N6SLMsMDw/T2NhISUnJku3gNBXcbjfX\nr18nHA4v+HmfL+x2O1VVVWRkZIhErwWEEOTnjFqtZufOncIYPwWtVsuOHTvIzMzkH/7hH/B6vQvW\nOCeLfzQ3N2M0Gtm7dy9Go1GEqifA4/HQ19cnrs8zYjKZOHbsGNnZ2dTU1NDT0yP2lFMcIcjzQHp6\nOp///OfnexgLgiNHjuD1eqmvrycajS5IUY5EIly9epWBgQF27NiBw+EQYjMJkUiERCKxpGt5zybV\n1dXk5uZSX18vPOUURwjyPGGxWETyyhRIT0/nq1/9Kvfu3aOlpWXBHeVIJBLcvXuXK1euUFFRQV5e\nnhCZSZBlGZVKJcR4FjEYDFRWVuJ0Orl06ZLwlFMYIcjzTNIbEEzMypUrqaiooLGxcUHtJyc7OJ0/\nf55Vq1axbt060d93CmRkZLBy5UqR8DaL2O12du7cidVq5eLFiyLRK0URd/w8kkgk6OzsxO12LxiR\nmQ9UKhUbNmzAarVy9erVBdEVSpZlRkdHOXPmDBkZGezbtw+z2Sy8vilQUFBARUWFuFazjNPpZM+e\nPTgcDj7++GMhyimIEOR5RJIkHjx4QHNzs3gwJkGlUuF0OqmsrFSOQqWyICeTuM6fP08wGOTYsWNY\nrVYhMFNApVJhMBhE5bI5wmazceTIETIzMzl9+rQIX6cYQpDnEb1eT1FREX19faLV3FNQqVQsX76c\ntWvXcvbs2ZSt4iXLMtFolOvXr9PR0cGBAweEuEwDkVcx92i1Wl566SWys7MfC1+Laz7/CEGeZ/Ly\n8rBarXR1dYlCCFNgw4YNuFwuPv74Y/x+f8oZEUmS6OrqorW1la1bt7J8+XIhxtMgkUgwMjKScvO6\n2NBqtVRVVSkVvXp6eoT9SQGEIM8zNptNKaIvHoinY7VaOXbsGOPj49TV1aVU8QhZlhkcHOTy5csU\nFBSwfv16kcQ1TZKh/kgkkjLzulix2Wzs3r0bi8VCQ0MDvb29YutsnhGCPM+oVCrWrFlDeXm5KBYy\nRbKysjh69ChXrlyhpaUlJfbAZFnG6/Vy9uxZJEliy5YtYt94BoRCIVpbW8V1e04kczOsVisff/wx\nPT09QpTnESHIKYDJZMJms4ljHtNg1apVbNu2jYaGhpTYf49EItTX13P//n127dolevnOkEQiQSQS\nQa1Wi+v3nHA4HBw8eBCXy6UkeglRnh+EAqQAKpUKlUqFLMuiV/IUUavV7NixA5fLRUNDA4FAYF6u\nmyzLxONx2traaGpq4nOf+xwFBQVicTVDZFkmLS1tvoex5DCZTHzuc58jIyOD2tpa+vr6Fm0/8lRG\nWI0UIpFIcPv2baLR6HwPZUFgsVjYuXMnvb293Lx587mHrmVZVs6SNzU1ceDAAbH18IxotVrWr18v\nruE8kezP3dDQIBK95gEhyClGfX099+7dEyvTKZKbm0t5eTnXr19/7gVWZFlmYGCA+vp6srOz2bJl\nixCSZ8TlcrFlyxYRYZgnLBYLlZWVmM1mGhsb6e3tTYkcjaWCuOtTCK1Wy/Lly5XsYcHT0ev1bN++\nnfT0dGpqap5rV6hAIKAUddmyZQsGg+G5/N7FjMFgEMlw84zT6WT37t2YTCZqa2vFnvJzRAhyirFj\nxw68Xi+dnZ3zPZQFg9VqZe/evfT09HDx4kVisdic/85EIkFLSwtut5sdO3aQlZU1579zKSBCpKlB\nWloa+/fvx263c+bMGXEk6jkhBDnFsNlsbN68WdS3niaZmZm8+uqr1NXV8eDBgzk17JIk0dnZSV1d\nHZs3b6akpASNRiO8ullgcHBQiHKKkDzzn5aWxpkzZ+jv7xfh6zlGCHKKodVq2bZtG6WlpUKQp4FK\npaK8vJwDBw5w9uxZBgYG5sSwS5JEd3c3x48fp7i4mI0bNwoxnkX++Z//+blEOARTQ6PRcOTIEVwu\nFxcvXhR7ynOMEOQUxGKxkJubKxJbZsCuXbswGo1cvHhx1ktryrKMx+Ph9OnTSvKLSOKaPWRZpqmp\nSSxEUwyj0ci+ffuwWCw0NTUpR6IEs4+w+CmMLMsifDdN9Ho9u3btYmRkhLt3706675W8vsnXZEIg\nyzLBYJDm5mYkSeLYsWM4HA7hGc8ikUgEi8Uy38MQPIFkopfBYODixYv09fWJPeU5QAhyChMMBnG7\n3fM9jAWFWq1mxYoVrFu3jqtXr9LX1/eY0EqSRDweJxaLEQqFGBsbY2hoiJGREQKBAJFIhHg8/phA\nJzs43bhxg/7+fg4cOEB2drYQ41lmbGyMZcuWichQiuJyudizZw9Go5HTp0+LRK85QDvfAxBMjMfj\n4dSpU3zta18TTQqmgU6nY/369dy7d4+zZ8/y+uuvYzQaicVi+Hw+hoeHGRsbw+/3EwqFiEajaDQa\nzGYzJpMJh8NBeno6TqcTg8GASqWivb2d5uZmtm/fTmFhoRCNOUCSJGVPXpCaOJ1Ojhw5wocffkhN\nTQ0HDhwgLy9PzNksIQQ5hXG5XHR3d3P37l3Ky8uFRzYNLBYLhw4d4oc//CFNTU2UlZVx//59hoaG\nCIVCDA4Oolaryc7OxuVyEQwG6ezsZHx8nIyMDOx2OzabjVWrVmEymaipqSEjI4OKigq0WvHYzAXL\nli0jJydHLHZSHKPRyLFjx3j//fc5f/48+/btIzc3V4jyLCAsSwpjtVo5cOAA//iP/0hxcTF6vX6+\nh7SgyMnJYd++ffzd3/0dpaWlWK1WCgsLqaqqmnT/NxwOc/v2bW7fvs3du3cJhUJEIhFee+01TCbT\nc/4USwshxgsDnU7HwYMHOXv2LA0NDWzfvp28vDwxf8+IuHopzqZNm0gkEoyOjs73UBYUkiTh8XgY\nHR1FrVbT0tLC3r17eeGFF3A6nZNGG4xGI5s3b+YLX/gCsViM1tZWtFotPp+PeDwusoDnCJG5u7Cw\n2+1UVlai1+tpaGgQ55RnASHIKY7NZuO1114T3vE0kGWZ8fFxzp49y9DQEN/4xjd49dVXsdvt0wr7\n63Q61qxZwze+8Q3Ky8upra2lq6tLZL7PEd3d3eLaLjBcLpciyiLR69kRgrwAqKiowOFwzPcwFgSy\nLBOJRGhqamJsbIzq6mrWrl3LgQMHSE9Pn9Z7aTQatm/fzqZNm9i/fz+ZmZmcP3+esbEx4SXPAe+8\n844oCrIAcblcHDx4EIvFQk1NjTin/AxMSZCvXbvG1772NQC6urp48803eeutt/jjP/5j5Xveffdd\nvvjFL/LGG29QU1MzJ4Ndqmg0GtRqNbIsCyF4CrIs09HRwe3bt9m7dy+5ubmoVCpMJtO0M9XVajU2\nmw2NRoPFYmH//v0EAgEuXbokvIBZJtlTWhjyhYnVauW1117DarXOaaW8xc5TBfn73/8+//bf/ltl\n5frd736Xb33rW/zt3/4tkiRx6tQphoeHeeedd/jJT37C97//ff7zf/7PYqU7B4RCIXw+nxDlSQgG\ng9TV1VFWVkZxcfFTQtQPFzhSIkE8FicWjxNPSCQSiU+as6P8vEqlwm63c+TIEZqamujo6BAGZxYZ\nHx8nJydHnCRYwKjVaqqrq7Hb7dTV1QlPeQY8VZCXL1/OX/7lXyp/v3XrFlu3bgVg3759XLx4kevX\nr7Nlyxa0Wi1Wq5WioiLa2trmbtRLEFmW6enp4dq1a6I14yS0tbUxOjrKrl27nnoMQ5YSBL1DdN5v\n4caNVu603qSt7S53W+/Q0zdM/AnrnpUrV7J27Vp+8YtfiHmYRcbGxsjPzxdHZxY4yc5rer2exsZG\nBgYGhChPg6cK8uHDhx97SB71ziwWC36/n0AggM1mU75uNpvx+XyzPFQBQEtLC4ODg8JLfgKSJHHi\nxAl27tyJ0+l82ncz7u7g1D//iO//1/+XH/3kI2pO/A/+7r//V7777/8D//BBM6EnOMAqlYpDhw7R\n0dFBZ2en8JJnCb1ez+bNm4UgLwKSiV4ajYZz584JT3kaTDup69FzZoFAALvdjtVqxe/3f+brgtlD\npVKRn5+PXq/nzp07QgiewNDQEJ2dnWzevPmp3yvFvJz64f/Dn/75eyRcG3ntSy9y5OVf4eUXtmMY\n7eTBAzcT7RLbbDZeeOEFamtrhaGZJbKzs9myZYs4x7pISE9Pp6qqCr1ez9mzZ4UoT5Fp3/1r1qyh\nqakJgNraWrZs2cK6detobm4mGo3i8/l48OABJSUlsz7YpY7JZGLDhg10dXWJpKInUF9fz7Zt2zAa\njU/9Xn/HGf7L9/4b9nV7+I1vvMWuraspLlvHzgOv8i+//btU5JsnfTj279/PzZs3xTzMEnq9HovF\nIvaQFxFOp5Njx45hNps5e/asOKc8BaZdqev3f//3+Xf/7t8Ri8VYtWoVR48eRaVS8bWvfY0333wT\nWZb51re+Jc7NzgEqlYrVq1eLYzcT0NTUxJe//OUpfKfEvVN/T5PWxjePvMmKDJMivmqtiYrdh8mt\n8GOaRJHNZjMGgwG/34/RaBRC8oxIkoRKpRLXcZFhMBh48cUX+fDDD7l48SJ79uwhOztbbE1MwJQE\nOS8vjx//+McAFBUV8c4773zme15//XVef/312R2d4DOYTCb27dsnQntPoLe3l8LCwil8Z5zee/ew\n6HWsWZbGp02DOS0Nc1raU9/F5XIxNjZGenq6EJJnQJZl3G43mZmZok74IsRkMrF//36lzOaOHTuE\nKE+AsOoLEI1Gg0qlEueSP0U4HJ5SuBpU6PRaJEnCH44ifeoaJq/r0y6tXq8XIetZQJIkTp8+TSgU\nmu+hCOaItLQ09uzZg0ql4uLFiyL7egKEIC9gAoGAOHrzCFqtdooPuY7SnfvRRUJcar7CWCj2SO9j\niXgkhN8fIC5NrsiJREJEKmaBYDBId3e3MNCLnIyMDCW6Jyp6PRlhTRYw7e3t3LlzR3jJn+ByuRga\nGprS9xbs/gpHVqVx6xc/4HTjdUZ9AUKhEAGvh9YrjTRevkvwKc6vz+cTiUizwPj4ODabTSxulgAu\nl4vq6mpMJhO1tbUi0etTiCdgARMMBjl//jzBYFCIMg9PANy4cWNK36vL3MQf/tkfkk8/P/y//xM/\n+h//yPGf/5x/+qd3+Yf3T9DWE0KjmVho4/E4Y2Njk7ZxFEwNn8+Hw+EQ+8dLBKvVyssvv4zBYODc\nuXMMDg6KY5yfIAR5AbN69WpUKpXwkj+hsrKSCxcuTHlft7zydf7y//wu1dtKuH/9MnUX67jdPsaO\nz3+df/HGbqwT6IMsy9y9e5esrCwMBsMsfoKlidlsprS0dNq1xgULF71ez+HDhzEajdTX14va158g\nlqQLGIvFQnl5OZ2dnZSXl08xoWnxkVyMlJSUEAgElGzrp3muaq2Boo1H+O2KA4TCUWRU6M0WDE9J\n/ozFYrz//vtKkkry9wtPeWbk5uaSlZUlPOQlhsPhYM+ePZw/f576+np27dpFVlbWks6+Fh7yAkar\n1VJWVkZ2dvaS3IeRpIeNIKLRKOPj4wwNDVFZWcnZs2eJRqNTfh+NTo/VZsVme7oYS5LEnTt3cLvd\n5OXl4fF48Pl8xGIx4vH4J00pRLRiOuj1ekwmk1jQLEEyMzPZs2cPADU1NUt+T1ksSRc4WVlZpKWl\nLYlCLLIsI0mS8vJ6vYyPjzM+Ps7IyAjDw8OsXbuWjz76iHv37lFeXj6riUKyLOP1ejlx4gQvvfQS\nPT09tLS04HA4sNlsWCwWrFYrNpsNk8mEWq1GpVKhVqtFwtIkiKIgS5vMzEwOHjzIqVOnqK2tZd++\nfeTm5i5JT1kI8gJHq9Uu6lBfUoQTiQSxWIzx8XE8Hg9jY2MMDw8zPDxMNBolNzeXtWvXUlZWhsfj\n4fz58+Tk5OByuWbN0EejUerr6zGZTGzfvp1AIEB7ezudnZ1cvXoVg8GA0+nE6XRit9ux2WzYbDYc\nDgdWq/UxcRYC9BBZlhkfH8dkMmEwGMQ1WaI4nU5effVVjh8/zrlz56iqqiInJ2fJLWQXryVfYsiy\nTCQSWbBG7dEwryzLxONxYrEYkUiEkZERPB4Po6OjeL1efD4f4XCY4uJiDh48SH5+/mPJVRs2bKCz\ns5P6+nqqqqqe+WhScjytra3cvn2bz3/+85jNZiwWC1lZWezYsQOA4eFhuru76ezspKWlBbVajdls\nxmq1YjKZsFqtOJ1OHA4HZrNZWUxptdrPGJ6FOIczIRqNcuXKFUpKSsjPz5/v4QjmEb1eT3V1NR99\n9BF1dXVUVlaSlZW1pERZCPIiIZFIcOXKFdatW4fVap3v4UyJRyuNJRIJIpEIkUiEYDCIx+PB4/Hg\n9XqVfVm9Xs/y5cspKCggNzd3QtFKS0ujsrKSU6dO0dzczPr165XjSdMVOkmSiEajPHjwgMbGRrZv\n305+fv4T3ycjI4OMjAw2bdpEIpFgfHwct9tNf38/IyMjjI2N0dfXp4wjKc5OpxOTyYRer8dgMKDT\n6ZRqbMnfs1gFOhgM0tvbS0FBwXwPRZAC2Gw2qqqqqK2tpb6+np07d5KZmblkwtdCkBcJyeNPoVCI\n/fv3p+yq8pdlKR96nYFAgGAwiM/nUzxhn8+H2WzGbDaTmZmpvBwOx5QfzJUrV7J7927q6+vx+Xys\nW7eOzMxMpRHE0wQuOb7R0VElJL1ixQo2bdo0peM5Go0Gl8uFy+WivLycRCKBz+djdHSU0dFRfD4f\nkUiE7u5u7t69iyzL2Gw20tLSsNvtmM1mTCaTEsrVarXKuBdTuDsYDKLRaMTxMYFCRkaGkn197tw5\nKisrl0ztayHIiwSNRsPGjRt577332LJlCw6HY76HpJDcB06G1X0+Hz6fD6/Xq+wDx+Nx0tLSyMzM\npKysDLvdrgjTTMRHrVazdu1arFYrTU1NnDx5koqKCoqKinC5XI/t4z5aFzz5CgaDStLW0NAQ27dv\nZ82aNZjN5hldA41Go+wvr1ixAnhY+tTv9yuLkmRy2r1794hGo6SlpT0W4rZYLMor6UEv9P3oSCSC\n0Whcskf2BE8mKyuLqqoqTp8+TW1tLXv37iUnJ2fRi7IQ5EXEmjVr+Pjjj7l69SpVVVXzOpZHk7HC\n4TBjY2OMjY0xOjqqiLAkSRQVFbF582aysrIwGo3o9fpZKxChVqtZsWIFWVlZ3Llzh4aGBvr6+li2\nbBlqtVoRN5PJRCwWIxgM4vf7icfjeL1eWltbWbVqFQcPHsTpdM66MUj+fngYGk/um8diMQKBAIOD\ng/T29vLgwQOi0agS3k5LS8NkMimJYxaLBZ1OpySMpWp05EkYjUaKioqU6yAQJElPT+ell17iww8/\n5Ny5c+zbt2/Re8pCkBcROp2Oo0eP0traiizLc+41ffq8bTLMm0gkCAaDSgh6ZGSE0dFRPB4PBoOB\n0tJSdu/eTW5u7pyODx6G8q1WK5s3b2b16tVcvXqVxsZGfD7fY154LBbD6/Xi9XqRZZny8nK+8pWv\nPLfWimq1Gr1erxxfczqd5OXlsWnTJmRZJhQK0dHRQXt7O5cvX0aSJGX8yWxuu92uZHgnE8U0Gs0T\nBTpVPOply5axbNmy+R6GIEWxWCy8+OKLvP/++1y4cIF9+/aRmZm5oBad00EI8iJj9erVZGVlzenv\n+GVnpIcCHI1GiUaj+P1+JRnL7/cTiUSIRqOYzWZWr16thIvnSwzMZjO7d+9m9+7dn0kcMxqNuFwu\n0tPTsdvtKbUKV6lUmM1m1qxZw5o1a4CH4e6+vj56e3sZGBhgYGBASQjT6/WYzWbFo04KtE6nW1IJ\nY4LFgdls5uDBg9TU1DyW6LUYRVkI8iJDrVaTkZExq+/5qADLskw0GiUUChEKhZR9YI/HQywWUwx/\nWloaubm55ObmYrPZZnU8s0EyaWyhZvdaLBZKSkooKSkBHgq0x+NhaGiIkZERJVGuo6ODRCKB2WxW\n9rAtFouyb5sU8flIGHs0wiIWBYLJSE9PVxK9Ll68yK5duxZl9rUQ5EWKLMskEgnFG5oJyUQsSZII\nh8P4/X78fj9jY2NKKBoehlezsrJwOBykpaUpe5yC50dyP7qwsBBJkohEIkoI3uv1EgqF8Pl89PX1\nEQwGHzsTbbPZMBqNyn66Xq//TNLbXCDLMj6fD61WO+PkPcHSITs7m71793L27FnOnj3L3r17F92e\nshDkR3j0XOxCD4dEIhEGBgbIycmZVgZrsixlch94fHxcSchKesJms5n8/HwlmzvpbT6L+AtmD7Va\nrRyZys7ORpZlYrEY4XCYcDhMNBplZGQEt9tNW1sbgUAAs9lMWloaDodDEXe73Y7FYsFgMDxWBnS2\n5jgWi3H79m0cDofSuWyxkbQpopPR7JCVlaUUDzl37twzi3Kq1Z1f0oL8aF3kZAGIcDiMTqfDaDQq\nGasTJcakMl6vl48++ogjR46wfPnyCb8vaTASiYRSHzpZFWtkZIShoSE8Hg8ZGRmUlpayf/9+HA7H\nYyUgBamNSqVSEsbsdjvwMJlqzZo1ylE0t9tNZ2cnd+7cwePxKOHttLQ0Jdxtt9txOByKB/2s90Ak\nEqG/v39RnUF+9FlK2pTk9kEwGFSy4ReiTUkVHA4HL7/8MsePH+f8+fNUVVVNuqf86Rr48Xic8fFx\ngsEggUBASYBNzsl82rQlJ8jJyQmFQvj9fqWCks/nIxqNEo/H0Wg06HQ6JTHG5XI9Vu4QUn/PKy0t\nDa1Wy40bNygsLHzs35JGI1maMinCyWQsv99POBwmPT2dzZs3U1xcPOPzt4LU5NHjUTqdDqvVyqpV\nq4CH5SwHBgbo6uqiu7sbn8+H0WhUIiHJI1dJkU4WLkm+Hn02JntOYrEY0Wh0wVSWm4hPb+ski78k\nnyOPx8O1a9cYHBzEYrEoWztOpxOz2awc80t1m5JKmEwmDh8+zKlTp6irq2P37t1kZGQo93TS841G\nowQCAUZHRxkbG1O2b4aGhhgcHOTcuXNKUxiXy4XT6cRqtSoliJ/3nKjkVPPZ54ikJxgKhRgeHubO\nnTsMDQ1hs9nQ6XSEQiH0ej02m41IJEIgEECv16NSqfD7/Wi1WkpLS8nLy8NqtS6I8Gxrayvvvfce\nv/u7v4vBYFAiAOFwWPGAR0dHicViyvXJyspSSlOKfWABQDweZ3BwkIGBAdxuN6FQCEApqGIwGJSM\nbqfTqXjjyVfSSH46q3twcJAzZ86wd+/eSUuhpirJZyYpuvfv36e/v185Fx6JRJQFvFqtJhqNKh6y\n3+9Ho9FQXFxMfn6+ktm/0K7BfON2uzl37hw6nY5du3aRnp6OWq1WvOCuri7u37+PRqNRjjcmkxzD\n4bDyPgaDQbGNeXl5rFixgoyMDEUDnhdLRpAlSWJ0dJTW1lbu3buHzWYjOzuboqIisrOzn9gxSZZl\nxsbG6OzspK+vj+HhYTIyMqioqCAvLy8luyw9Wm0qFArx13/91+zZswen06kU5RgbG1OOxlitVqVC\nVkZGRkp+JkFqkew/nfQ6AoEAkUiEUCikbPkkvUCHw4HBYMBoNCplQJPeebL4ytq1a5+5AcjzJvmM\njY2NcffuXdra2jCbzeTk5FBYWEhOTo6Svf5pkkLR29vL0NAQTqeTNWvWUFhYOGtFcZYSAwMDnDt3\nDoA9e/Zgt9vp7u7m5s2bhEIhcnNzycvLo6CgYML7LBqN0tPTQ1dXF263G1mWKSsro7i4WOnU9jxY\nMoI8ODjI+fPnGR8fZ/369axatQqn0znlnw+Hw3R1dXH16lUCgQC7du2ipKQkJTL8Hk0cSdZMTmbX\n3r59m2g0SiKRwOFwkJWVRUZGxmNVnoQIC56FWCxGKBQiEAgor2QEZmRkBL1er+xHW61WJUSYFOdP\nlwJdCMiyjMfjoa6ujuHhYdasWUNxcfGUz9knjw/29PRw7do1RkdH2b59O6tXrxaiPAM8Hg+nTp1C\nlmWWLVvGnTt3KCgoYPXq1SxbtmzK1zSRSDA8PExbWxu3bt2iuLiY7du3Y7fbn4soLwlBDgaDHD9+\nHK/Xy8svv6y09JpJ559QKERNTQ3Xr1/njTfeYPny5fNmRJLJI9FoFK/Xq5Sm9Hg8DA8PEwqFyMrK\nYtWqVRQUFGAymZTiEAvJGxEsHJILw3g8rrzGxsbo7e2lp6eHwcFBRaCTe9DJjO7kAvHTGd2peK+G\nQiE+/PBDhoeHOXz4MPn5+TNa2CZD3hcvXuTixYt88YtfpLS0VCySZ4DP5+Ov//qvCYfDHDp0iA0b\nNsyoHW2y4FF3dzd///d/z+bNm6mqqnoueTSLWpCTF/bkyZNcvXqVb37zm9Pyiifjvffeo729nV/9\n1V8lIyNjTs9qPvr/iUSCRCKhHF0ZHh5WQofJLkJlZWWUlZVRWFioZLAmvehUNXCCpcPg4KBSBnRw\ncFAJcdtsNiVhLBnuTh6nS74+fe/Ox70cj8c5f/48TU1NvPXWW+Tk5MzKOD7++GOuXLnCr/zKr5CX\nl7dgogWpgCzLdHd389Of/pQdO3awc+fOWbl+Q0ND/NVf/RUvvPACW7du/UzS4myzqAU5kUhw/fp1\n3husLw0AACAASURBVH33Xb75zW/OalWmRCLB3/zN32Cz2Xj55ZdntbDBo5Wxkh5w8vhEUoS9Xq/y\nda1Wy7Jly5RewU8iHA4zMjKy6A7SCxYmyaIgiUSCeDxOf38/fX19igedrPim1WpxOByP9Y1ORnmS\nZUCB57bQlCSJ1tZWfvKTn/CVr3yF0tLSKRn+T1clm6jW/I9//GNkWebFF19UengLJkeWZbxeLz/8\n4Q/Jz8/n5ZdfntWw//Xr16mtreXo0aOsXLlyThdKizYuIssyIyMjnDp1is9//vMTi7Esk5ASSAkJ\nmYcPi1qjRc0n5wk/eZBUag1arYbk46HRaPjc5z7Hj3/8Y27fvs3mzZufSegeTcZKJBKEQiGl+9Cj\nR5IerVW8YsUKcnJylCNOk7231+ulvr6effv2PbeGCQLBZLS0tGA0GpVe1evXr0eSJKUSXLI3drI8\nazweR6VSfaZv9KNJY49uRc2FSI+Pj/PRRx+xb98+SkpKnmqcZUkikYgTiyeQZT7x9FXEY2Aw6vj0\n8A4dOsTPfvYzbt++zbZt2+bcI1sMJBIJzp07RyKR4PDhwxPYQvmTuZAUm/4YKg063S/t+6OUlZXR\n1dXFlStXyMrKwmazzdmcLFpBliSJhoYGsrOz2bx584TfJ0sxRvvaedA1QDAmozM4WLmmnDRViPv3\n7zE8HgC1lvS8YkpW5GB45PlzuVxs2rSJGzduUFJSMu1w+KN9gpPn5ZIGKGmQIpGIEsIrKCh4LDlm\nqjeFSqVCp9Ph9Xq5d+8eaWlpwksWzCuyLNPe3k5RUdFj3qNarcblcuFyuSgpKUGSJAKBAF6vF5/P\np/SQHhgY4M6dO0qyYvK5ePS8dLJuwGzV6ZYkiUuXLmGxWNi9e/dTnyFZSuAfHeDBnQcMBiKoVFoM\nOg1Wh8yQO4d9B4sxah8XdJfLRUVFBW1tbZSUlMx6XfrFSH9/P9euXeOtt96aJFtfJuQd5t6DDka8\nITRaHWrVL/8tZshh56aV/z979x1fVX0/fvx1zrkzew8yySBkQRgyRBS/AoKzrn6r1tbW/iqt/dbW\nVqu2fqXW7la7tKXa9qu4QBRRcYKiICvsECCLkL3Xvbn7jN8fIZEREkAwAT/Px4OHJrnjc8793M/7\nfMZ5f7Apx19gWSwWioqKeOutt6ipqSE/P18E5FPV3d1NVVUVl19++ZBfHEPz0Vi2mWee/AdrS3xM\nX3AL37snHZvSwro3XuCpFe9BwkQWffd/SEtP4MicQoqiMH78ePbt28ehQ4eYOHHisB/UkVljfD7f\nQFrK/l5Bf08gOTmZ8ePHExsbO5AG8bPcExcWFkZGRgaVlZXk5+ePyg0fhC+W7u5uIiIihqzTsiwP\nbC8JDEzh+Hy+gXwB7e3ttLS0UF5ejq7rAwvG+oe4Q0JCBnrT/dtSns6+0b29vZSWlnLZZZcNm47W\nMDS6mip5740VrHh9J2GZqUQHBaN21NHl3Elx4yLWXTQWq0k+qlfW36aUlJRQW1srRrOG0d/xys3N\nZcyYMUOcK53u1mrefO6vvPDWVsZOmUNqlA0ZUH3dFDsnserpuxgTbD2ulyxJEomJicTGxnLw4EGy\ns7NPKR3xqThvA3JFRcXAjkNDVWjJHELBpV/mmq2v8vK77XzroR8wJVZBIpxv3nYVT7/4CtYLv8W3\nrp7OIBdPREdHExERQUNDAwUFBSe8n7l/RXT/tn/9t4T054e2WCxkZmYyf/58EhMTjxt6+6z6kxDU\n1tbS09Pzud5bJwjHMgyD3t7eU54nlWV5YKeq/tfpTw3b/5q1tbVUV1ezefNmDMMYyLbXH9jDw8MH\n9pI+crHYcHdeVFZWEh4ePkzD30d1tvDms4/xk2d3c/ndD/Hz/76U+BALvvaDPPvz+3i7TeNEi3ci\nIiKIjY2lsbGRgoKC8yq16JnmdrupqanhqquuGmZlukJi1jRunj+Jp154g8u+9SDfvjAJsyzhbt/H\nTx4vQR7iM1UUhaKiIl577bWBzHVnw3kbkFtbWwdWbg5FkiQkRcGiSEjYCLKDrmkA6BIYEsRFh2Ia\nLBoffn5WVhY7d+7E7XYTGhp61GKsQCAwsDVe/967brcbt9uN1WolKyuL+fPnD2SYOZvi4+OZOnWq\nSIMpjDhJkgameT7LheGxw9Dh4eEUFhZSWFgI9N0KU19fP/BP07SBgG632wfydPe3Ff0LyUwm03Gr\numtra4mNjR1+dMlQadj5Hk8//w5p8x7m97fPJ8ZmRjIMTHGZ3P7Qj9j/ixYUDPoWrhx/TLm5uXzw\nwQd4PB4RkIdQX18/sCJ/6HokIckSsmxFkmRkswQG6JqHuhYL375+MpHWoacgkpOT6enpweVyERsb\ne2YP5LDzNiD3r9Q8tSDnperAfiy2vu+Jv/EgXq8ftKGflZyczNq1a3E4HAM5bZ1O50Dv1+v1DjQc\noaGhZGVlkZSURHh4+Gc5xFPWPxwmCCNNkqSTGvr9rEJDQ8nNzSU3NxfoG3ZubW2ltbWV9vZ2Ojs7\n6ejoAPpuZ+pfMHbkvtH9bYnH4yE2Nnb4e4R1LweKd9JSK3Hn1TMJP7xYyND9dLU30doTxg036PR0\n9xJmi8Q8SCBJTk6mvb0dr9eLpg3TAH2BNTU1ERoaesr50BvKK6mIcKI56lj66iFu/fYNWJXBF3X1\nM5vNhIWF0dPTc8JV8p/VeRuQ+7P/nJpm3n15GXssgCShdh+k2+E+qffq7Oxk//79AHR2dqLrOiEh\nIYSGhpKUlER0dDQxMTGjpnfav5BGDFsLI0GSpBHZVCIkJISQkBAyMjIGEv0cuY7D7/fT3t5ObW0t\ngUBgYDOIkJAQ2traiI+PH/5NjACOTi8eTwJJ0WGfbngQcFO7/0NefGE1Za1BXHPnD/lyXAQmWTou\nENjtdnp7e6mvr8fn8535E3GeqKmpISQk5JRuc5KA3R9tI0dKwNNcyY49Ktf7T+7u36ioKLq6utB1\n/awsjD2pgLx7927+8Ic/sHTpUvbv38+dd95Jeno6ADfffDMLFy5k+fLlLFu2DLPZzKJFi5gzZ84Z\nL+yp6J8bOjUxzL3uRnIP76ngb93Ga299MOyz+tOtVVRUMG7cOHJzcwd2DemvLKMt8DmdzoH5NUH4\nvPXvDzySyS/603YGBweTlJQE9N2v73a7B/Jy9+8DXltbS1lZGTk5OcO/sKRgC7ZgtnTT0tGLrgMK\nSOZg0nKnk+j8DUvWpPDd3yZilQdvF3Rdp7e3l+Li4jOWzOh8tHfvXgoKCk5pX2MDmDr/Ui6+MAHJ\nV4jmqSTacnJ9U4vFQiAQOM3SDm/YUjz99NOsWrWK4OBgoO8EfPOb3+T2228feEx7eztLly5l5cqV\neL1ebr75ZmbNmjWiOVl1XT+NIBjC+IIiig5PEXnru7FbLSdcfNHPYrEQHx/PggULBlLojfYsOzU1\nNdTV1bFgwYJRX1bh/ONwOJBleWB/5tHi2AVj/WlA3W43uq6f3BC7bCejIJPEpOW89dpmbpiWRkKo\nFUWxEBU3lrGxdmQ5jJjocBTp+N4x9HUoQkNDueSSS06uV/4F1r93/alIyEgiNTUJi5zC7d/PwhJ6\nciOX/dvzni3DBuS0tDSeeOIJ7rvvPgBKS0s5dOgQa9asIT09nQceeIA9e/YwZcoUTCYTISEhpKen\nU1ZWRkFBwVkr+HA8Hg8mk2nYsX7D0FF9LnrdAQyctLV34bOHY5Y03L0udF2np7uDHrefULuFwS5o\nPR7PwDyGxWI5i0d15kRERLBs2TKmTp1KbGzsqOvBC+e3HTt2EBERQVFR0ai9IOzftL7/n91uP7n5\nXMlM9oULWbBwC088/yLPXpjETXMmEB1swfB309IqERRsQoHjEoP08/v92Gw2oqKiiI6OPqPHdT6J\ni4ujp6dn+M/FMFBVHy6PG8PQ6WrvwuuPx2wzERZzcqOE/QmWzmZikGG/CfPmzTvqimDixIncd999\nPPfcc6SkpPC3v/2N3t7eo1YeBgUF4XQ6z0qBT1b/ZuHDDmVoPuoPFLOj1k9MosYHK1+mqsWNt7uV\njVv2YguOxLP3PVbvOIR/kKcbhkFDQwORkZHn1GrIlJQUMjMzKS4uHhg+FITPS2lp6cA+3OcCk8mE\nxWLB4/GcVFC2xmbzrUX/ww8X5bD15X/zzDNLee6553j++efZE8jlS7deRoztxIuIGhsbiYqKOmcu\n8EdKXFwcDoeD3t7eYR6p0l53gI17DhEencD+daspqWhBPYXqp2kaXV1dZ/WOmFNe1DV37tyB4Dt3\n7lweffRRpk2bdtQJcblcIz4UFRERQW1tLW63e5jFIxImSygTr/gG2fNAVkxYTDKSYiI0MZ+7f3Q/\nAGE2C9IgtygYhsHBgweJj4/HbrefteM5G2bNmsX69etHxeclfLE0NTWd1U1ZzoaEhASqqqpwuVwn\nMa8rk5B7Id/7YRqXbFnPviYnAR1MIcnM/95/UZRfwJgg86ABWdd1KioqSEpKOufalM9bUlISH330\nEZ2dncPciiShmC0kTbiM+zJnIysmgmymIVdVH8kwDFpaWrDb7QPTt2fDKQfkO+64g4ceeojCwkI2\nbdpEfn4+hYWFPP744wMZdPqzmYykzMxM9uzZQ3NzM5mZmSf84ksmGyl5M0nJm3nMX4K4ZP5VQ75H\nf4L81tZWJk6ceM7tY5qSksLEiRPPmV6KcP5wOp0nvXfwaJGdnc22bdtobm4+6YQmQdFJTFv430xR\nA+gGyIqCMkQCEsMwcLlc1NfXU1BQIHrIw+hP8lJdXU1mZuaJb0mTTMSm5LEwJe+03kfXdfbu3Utq\naupZvTvglAPy4sWL+cUvfoHZbCY2NpZHHnmE4OBgbrvtNm655RYMw+Cee+4Z8YoUHx9PZGQkpaWl\njB079qxMxBuGQWVlJYZhkJ6efk41LtC3GGLChAkir7XwuZs4ceIZ3SHt8xAVFUViYiK7d+9m7Nix\nJz1FJUkSJvPJtYeGYVBVVYVhGKSkpIza+fXRQlEUZsyYwSuvvMLkyZPPynoYwzDo6uqitraWSZMm\nndVRi/N6+8XGxkb+8Y9/8K1vfYvU1NQz/voOh4MVK1aQkpLC3Llzz6nGRRBG0rl6H3xnZyePPfYY\nt956K+PGjTvjF7MOh4NVq1YRGxvL3LlzB90DWjiaYRgsWbKEqKgorrnmmjOebEZVVdavX09tbS3X\nXHPNZ84uN5Tz+vJrzJgxTJs2jVdeeYWOjo4zNjTbvztTcXExHo+H6dOnn9Nfmv4cwKqqjnRRhC+I\nz2v/4jMtKiqKuXPn8uabb9Lc3IymaWekXelvU3bt2oXH4xnYzvVcPEefN0mSuPHGG9m1axclJSX4\n/f4z1tbruk5tbS3l5eUUFhae9T2qz+uADH0LzywWC2vWrKG7u3tgu8PTZRgGPp+PkpISduzYwbx5\n8875BVG6rrN7926amppGuijCF0D/vt/nqlmzZhEXF8e6detob28/I21KIBCgvLycXbt2MX369HNu\nwdtIi4mJ4YYbbmDTpk1UVlZ+5hX8/RsCtbW18dFHH5GYmEheXt5Z/0zO+4Bss9n4yle+Qnd3Nxs2\nbKCjo+O0rmr7kwT09vayb98+PvzwQ2bPnj3ii9fOBEmS6OnpYcOGDeIWKOGs6+7uPonbVEYvs9nM\ntddei6qqbNq0idbWVlRVPe02xe12c+DAAd577z0mTpxIXl6emDs+DUVFReTk5LBlyxaqqqrwer2n\nFZT7L5AaGxt5//33MZlMzJ49G6vVetYDsrJ48eLFZ/UdRoGgoCDi4uLYt28fjY2N2Gw2goODh91u\n7UiBQID29nZ2797N9u3bmTVrFlOmTDkvFkRJkoTdbmf16tUUFhaOSI5h4Yvj448/JhAIEBcXd872\nAq1WKzExMVRUVFBXV4fFYhlIGHEywbS/0e/o6KCkpIQtW7YwefJkZsyYMSpT7Z4LJEkiISGBrq4u\n9u/fj67rhIaGYjKZTmqK5MhOV1VVFevXr8dsNrNgwYLP7Y6AL0RAhr5dX5KTk6moqODAgQP4fD7s\ndjsmkwld1wd6hpIkDfysqiqBQAC/309paSnFxcXU19czb968E+59fK4KCQmhubmZ2traEc2wJpz/\n3n77bdLT08/pgNy/c1tSUhKHDh2itLR0YKtEi8Vy3CjcsW1KIBCgrKyM4uJiqqurufTSS5k0aZII\nxp+BJEmYzWZSUlLw+/1s3bp1YGem4ODggYDb/7n0/6xpGqqqoqoqTU1N7Nixg+LiYrKyspg3b95Z\nnzc+6hjO51XWg9E0je3bt7NhwwZSUlIICQnBbrcP3M8WGhqK1+vF4XDQ09ODw+FAUZSBG/UvvfTS\n83ZDhqamJtatW8fNN9880kURzmMPPfQQd911F/Hx8edF8NF1nZKSEtauXUtiYuJA1r6wsLCBnaIC\ngcBRbYokSVRXVxMXF8cll1xyzt2TfS5oaWlh9erVqKpKSkoKiqIM7HsdFhaGoig4nc6Bz8Tv99PZ\n2YnX6+Xiiy8mIyPjcx8B/cIF5H4ej2fg6tQwDMxm88Dm5P1XTP1XstHR0UydOpXk5OSRLvZZ53A4\nzvlFasLodt999/Hwww+f1YxHI8Hv97Njxw4qKytRVXXQNkVVVfx+P5GRkUyePJnU1FQxX3yWVVRU\nsHv3bpxOJyaTaeAzkSRpoJ3v3zQiLy+P/Pz8s75P94l8YQMyfLqSrre3F4fDgdPpxOl0YrPZBnrL\nYWFhWCyWL9TV65FV4ot03MLn4+WXX+aaa645p3K/n4r+NqW/PXE6nZjN5oH2JCwsbMQa/C8qXdfx\ner04nc6Btr5/z/r+tr5/XdFI+kIHZGFwuq4TCAQwmUznxaI1YXTp6ekhNDR0xBs/QRhtxDdCOI7f\n7+fQoUN0d3ef0/eLCqNTeHi4CMaCMAjxrRCOo6oqO3fuHLh1QBDOlHM9KYggnE0iIAvHCQ4OJikp\niYqKihHf11o4v3R1dZ3cPuWC8AUkArJwHEmSyMnJobe3l9bW1pEujnAeKSkpoa6uTgRkQRiECMjC\noKKjo8nNzcXn8410UYTzSGVlJV6vV6zeF4RBnD+ppoQzSlEUpk+fLhbfCGeUw+HAZrOJgCwIgxAB\nWTghkdNaOJMMw0CSJHErnSCcgOj+CCfUn5C9PxG+mPcTPgvDMJgwYQIREREjXRRBGJVEYhBhWIFA\ngIqKCrKysrBYLCNdHOEcZRgGfr9fJJwRhBMQPWThpGzevJna2lrRSxZOmyRJWK1WEYwF4QREQBaG\npSgKkZGR7Nq1i0AgMNLFEc5Rx25/JwjC0URAFoYlSRKTJk2ipaWFlpaWkS6OcI7q32hBBGRBGJwI\nyMKwJEkiNjaWjIwMOjs7RYMqnJaysjIOHDgg0rEKwgmI256EkxIUFMT06dNRVXWkiyKco5qamr5w\nW5kKwqkQAVk4KZIkERUVNdLFEM5R/XuP999KJwjC8cSQtXDK+hfnCMLJ0nUdm80mks0IwhBED1k4\nZb29vfT29pKYmDjSRRHOEYZhkJKSQkhIiOghC8IJiB6ycMqampp444030DRtpIsinCMURSEvL4/U\n1NSRLoogjFoiIAunLDY2lrKyMqqrq8WKa+GkSJKELMvIsix6yIJwAiIgC6csMjKSSy+9lLVr14pV\n18JJEesOBGF4IiALp+Wiiy7C6/XS3d090kURzgFer5euri4xoiIIQxABWTgtERERzJs3D7PZPNJF\nEc4BDQ0NbNy4UfSSBWEIYpW1cNpycnLEfKAwLMMwcDqd1NfXo+u62FxCEE5ABGThtPU3rEcOQ4oA\nLQzGMAyCg4NF/RCEIYgha+EzMQwDh8OB2+0e6aIIo5Su6/j9fqKjo0VAFoQhDNlDVlWVBx98kIaG\nBgKBAIsWLSIrK4v7778fWZbJzs7m4YcfBmD58uUsW7YMs9nMokWLmDNnzudRfmEUqKioAKCoqAiT\nSQy6CEeTJIno6GgiIiJEQBaEIQzZer7++utERkbyu9/9DofDwbXXXsv48eO55557mDp1Kg8//DBr\n1qyhqKiIpUuXsnLlSrxeLzfffDOzZs0SC36+ICRJYtu2bWRlZRERETHSxRFGGUmSBhKCiIAsCCc2\n5JD1woULufvuuwHQNA1FUdi3bx9Tp04F4OKLL2bjxo3s2bOHKVOmYDKZCAkJIT09nbKysrNfemHE\nSZJEdnY2TqeT6urqkS6OMApJkoTVasVqtYqALAhDGDIg2+12goKC6O3t5e677+aHP/zhUQt4goOD\n6e3txeVyERoaOvD7oKAgnE7n2Su1MKqEhoYyffp0tm7dOtJFEUYhkRREEE7OsIu6mpqa+PrXv851\n113HlVdeiSx/+hSXy0VYWBghISH09vYe93vhi0GSJCZOnEhKSspIF0UYhXRdp7m5WSQFEYRhDBmQ\n29vbueOOO7j33nu57rrrAMjNzaW4uBiAjz/+mClTplBYWMj27dvx+/04nU4OHjxIdnb22S+9MGqE\nhYVx2WWXjXQxhFHI5/PxwQcfiDSrgjCMIRd1LVmyBIfDwZNPPskTTzyBJEn89Kc/5dFHHyUQCJCZ\nmcmCBQuQJInbbruNW265BcMwuOeee7BYLJ/XMQijhNVqHegFiblCoZ/H46GyslL0kAVhGJIhviXC\nGWQYBn6/H0VRxC1QAgCVlZW8/fbb3HnnneJCXRCGIBKDCGeUpmlUVVXR2NgoekQC0Df1FRMTc9T6\nE0EQjie6MMIZV1dXh8PhICEhQfSIBKxWK1lZWSIgC8IwxDdEOKNMJhPjxo2jvb1d9JIFACZMmEBR\nUZEIyIIwDPENEc64uLg4oqOjOXToEJqmjXRxhBGmKIrI2icIJ0EEZOGMCwoKIj8/H5vNJhJCCIIg\nnCSxylo4KwKBAKqqYrVaxVClIAjCSRABWRAEQRBGAdF1EQRBEIRRQARkQRAEQRgFREAWBEEQhFFA\nBGRBEARBGAVEpi5BEAYYhoGmqWja0berSbKMoijIkozYN0QQzg4RkAVBGGBoKi0HS9i9v4KuXgOr\n3YIiSVgsNuKSx5KZkUZEiA35VKKyYWAYBrpuICvyGdkJzDA0NF1CkSWxs5hw3hABWRCETxk6zraD\nvPGvx3npEzdX/fdlpIRZ6G6spr3XxJX/7y5uuGwGIRaZvhsmDQxDOtxrlpAwOP4+SgNHezNtXV7G\nZKZjV47fntMwjL7AjXQSPXADb2c11T2RjEuLPByUz8zhC8JIUhYvXrx4pAshCMLoICkmYpKT0Ksq\n+Lg+jl//5RFuu+4KCpPD2fDKv6m2pTB72hRCrQpawENPVzc9vR4MWcFiVgADv8tJV08PLrebgKEg\n+Xv4YNVy3ttaw9j8cYTbrMhyfwQ1MHQdr9tBZ0cnTrcXSVbQA16cDgdeQ8FmNnB0deHyBlBMZjRX\nKx8tfYhVbekUpUZitVqQZQkRk4VzneghC4JwtMM9XyQJzefD4/Wgm62YoyNRTba+h6huDu7YyOY9\nFdS19pKcO5XL588i2uSl9MO32VzThowHPWM+C2IqePLpp+mxZpE2pYjoiyYRGXx4FzBDp7e9hq3F\n29lbWoVD1cmaeCHZkbBn8yb8eddw28XRbHjrNSodVi6edyUhB1fw68dX4Lg8i2kxErMvvoCYIDMi\nIgvnOrHKWhCEwVXUsXv7DjaseZ0lTy3hzWoLmeMLCLGacDds5m8P/BU1IZsUYx9P/Oxelm2vxdFS\nzVtPLYfM6Uwc08pbB5uwRKczeWwMUbE5jB0Th9X0abOj+btZ99xTLFnfyKwb/pvJkc08s+RpGgwr\nNZ+s4/UtVaCEk5kcysZXX2N7eSshKRlYOxTSUnPIyRlLmE0ZwZMkCGeOCMhfAMbhRTWGARyeqzvj\nr33Mz8J5wNZFacl21r77Itv2VZMYbcPn9eD1+9jxwm9Y40sl3CwRmhhJUqrGh7vqUWWNVqOW9Vv2\nIGfexF2TxhGTkE1uaiwx8WMZl5WC3dI/MGfgqNnNq+vbuWbuPCZmpHPRwlu5qTCbtDER2NHxBVSQ\nzETERGEL9qNKBjGZ2USbTKSl5pCVGo9VESu/hfODGLI+z/UFSA1dB0mSkTBAkpHgMzdihtE3/6fD\nwAYShq6hGxKKSREjiOe67Cl887vfZ3JqBM7GPfzxpz/mj795ipmFaTQVF0P2JdhNYM/+Ej/+32vQ\ngrMJDjO4YEY2f3nhH/xsZxHXf/PbBIwYNE1CMkxI/cPhSIBOV1M1HV2dmBUzkmEQlnYBX3t4Erra\nyntImD690jv8XwmMvi09vap++E+GWGktnBdEQD6fGQYBj4OGxiZ6PWC1WzAZEhEJCUSG2D/zy/tc\nPTS1tBBQgkhOSkB3tNHc2o5PiWf8uHhOeSDxpFfZCmfLwGpnw8AI+PAFVHRdxxoUSdyYRKydXXi8\nGmGJ4UhVB4lMuZ2ClAj83TV8sLEZd1IE8ZO+zf0p+3jz+af4zaNhzJn+ILphQsJEwOsmYAnGYlIA\nCbMtFKurnl27dzF7Qhwhip/qg4eQrBYwQHO6cHt9uF1uPF4DLaCDoSBJoKl+PF4vktWG2STqjXDu\nEwH5PGZoXnave4U/r9hKRFACitxORzP89733cMXUjFMPmMeo37uO3y15iYiCy/j+t27g0Nv/5KmV\nxYRP/zG/v+9UA7KB6nHgUUIItYo5wRFj6PR2tdPS5UStb6d8XwXR/nCaK4vZdaCS9AvnkBYXRcTC\nW1Hue4W//vlprp1XQNuuzXSlXMuU9h7WrtzE9d+7ni/3lrP9SQ9eHWQTtLftZ+umFKbOmEJKdBgy\nEtGpuYyfGs9bL/6FEIuX9KAe9tb1cs0N1xETHUnduvV8tCUZd8knlB10kt/UjU9NIDwyiH37drBl\np4nx48aTEheMWGctnOvEbU/nMa1rH4t+8CDahK/x49vmMj4tnF3rN2EfP5Wp2YlIHDEHrOvoxuFh\nbMNA13X6hhUlJKk/sYOOrusYhx9nNiuU7XyfHW1mFvzXpSQlhLDp349SGnk1t16egwkwdB1NCQ3O\n/gAAIABJREFU0wYGKSVJAsNA0/WBeW1J6lu1u3/NcvZbshkbYRFDkCNED/jYu+5NXl+7DZ/ipqm+\njOItm9hRWkVsziV86/YvMzU7iZj0CQT72vl441bKyw9gz5jO7TfPI0zrZM2Lq6jq7qasrokpV1/H\nwmnZuDoOsW7LVqSoFC4oyiPcbkFCwhQUQXJCLG17Sygu2UtDczuXXf81Zk3IJiYCtu7YyIHKfWjm\nGEIlhZTJE5mQk0lYoJoNO8qRTHFMmppHhN0k6oxwzhP7IZ/HfLXrmDb/q+Tc8jseu+sa4iOs7H/p\nD3wSOZs7Lr8Qzd1NZ08vktmK29GNT7eRkpaA2t1KS7sTe2Q8SQmRmGQJX28HdfXNdPb4iUhIIjM1\nDjnQw/N/u5dlB+P5668eZmy4j79cnchrOS/y9h+uwqIHcHS0UlffihwUTnxiIpGhNgyvg9pD9biR\nsdlDiImOoGf/Or5/7TeZ8e913DYlhcS4MLHicAQYhoGmBggE1GMSfEgoJhNmU1/gkyQD1efF6XSg\nSRaCg0OwWU0Yho7X5UXVAmiSQlBQEBaTjBbw4/b6MVlt2CymozJ9GbpGwOumx+XFYg8mJKgvE5ih\na3hcLlQDrBYbhqahWC2YTQq66qHXo2Kx2rFaDpfp8z5ZgnCGiSHr85gSGsvEzEhe+fU3COMxvnzV\nPCbNuYXLzZGY8LHl3X/xwjulROYUYXYcYmtJD5dftwBrdwP7t2zHG3UBP/rZHYyLs7Ft5T9Y+lEb\nXnc3vvAUfvbIg+SFH/uORzSJhkbrwQ2seHcXdVWHcHj9pEyZz23Xz8Wz9iX++nElcclheP0BLrz8\nBtpeXMbazm6CP3iDTeZruHZungjII0CSJExmCyazZbhHYrLaibQevRZBkhSCQoOPe7TJYiXMYh38\nlWQFS1AosUGhR/9eMREcdlwlA0AxBxFuHqaIgnCOEW3eeUyJyOK+H97BrVdezOtLfsO9Dy3mxQ93\nYVFkJPy01exgzesfUue0cOn8eUTUv8EDP38WV+wE5s/OYsfK1eyp68IwvGx651UYfxX/+6MvUfHx\ns7xX1T3ke+veDl75z+95vRJuXfRtCqM7eeqpZ9m0v4bi5/7NxvBp3HLT9eSNC8GjRDP3a1djD7Fz\nwZXXc9kF6Z95flsQBOFcI3rI5y2DgFcn+9Lv8kjyhRS8+hKrV77IX397AF9QHD+4dgYzr7iFnGeb\nWXjlNcyZHk1Dno13W6/mzlvm4t3lJCF5F7phIEkWpl1/O5ZAN++t2Uxrlwt0fch397QdZO3WdlLm\nBNFUVUN41iyu1nxEWc1oM8fQ/vp/+E3PxSz40sVMSgwn2h+GLMuERscTGR70OZ0jQRCE0UME5POW\nTn3JVpyJORTmXMC3/yeVKfnJ/PTnj/H6lnK+d9U0MHQMSUaX+/qjZjNIVutRlUICDM1H/cGDlHV1\ns2BKDuGhQRhIR+QXOX72ztfbQ8AdQlJ6FvkTxiNJE7nwIg+K3U7v/Lu437WCv7+6gsqaAyz68UNc\nkazTt1EBGIdXl4k1OoIgfJGIIevzWG/FKp5atoqmbjeKLZoJUy8mIyMNSZZBMtA1DcMAXevbGk83\n+ra10zV9IKFIQNPQOnbxz6fXEFEwl8njEgm2KnicLtxeFV0zMFQDQzPQNR+e7r7XsEYnEB+lsv6j\nrfSoMhazQc2uDWzc8iGvvNfJgjt/zv/96W6i63ezZWM5Hq2vMnrcvfR0d+BRh+6BC4IgnG9ED/m8\npRCbPp6Pf/s4MaYwLslPxl23BafPyhUXZKKoTg6V78etBnC0ttHR3MvBbgWzs4KK2kbkxjb8vg5K\nyypoi5Fol3x8su5dUps82D1+il9/ni3B82mqaaejCapqGpBNe9i+04w6rg6nPI1rpl3AA4//lrv0\nHq7Iktnf6OTar36Nzj89youJsSzISyFvxiTC4sKwWP2k2uysf3slEQ1pXHjZAjIjxPWiIAhfHOI+\n5POYooAjLIvIqmI2722ks7mJvAU389UrZhOstfPJhx+gxWSRGBtPpNLOzvYgcuPBHJGA3tOFZjbj\n0iwUXDyXaWF+HF1uUvMvZE56Kt2eTtLS42mp7iYyMprIxHj8VetoSswje4ydxIxJXHTZFKIkE25X\nJx7CueIr32HBpDEEetoo3VdLQHYSCEnhyzdeTkJMJHHdbhqd3YRNnMulefHialEQhC8UcR/y+UzX\n0CQZGQO/z48sKygmM/JpdDz7E4PIioKka6jImOSTmOTVVTy+AIrZcjhdYt96MAkVv1/DZLGi9JdH\nD+DTJKxmEYoFQfjiEQFZEARBEEYBMUknCIIgCKOACMiCIAiCMAoMOVmnqioPPvggDQ0NBAIBFi1a\nRGJiInfeeSfp6ekA3HzzzSxcuJDly5ezbNkyzGYzixYtYs6cOZ9D8QVBEATh/DDkHPKrr75KWVkZ\nDzzwAD09PXzpS1/irrvuore3l9tvv33gce3t7XzjG99g5cqVeL1ebr75Zl599VXMZpFsVhAEQRBO\nxpA95IULF7JgwQIAdF3HZDJRWlrKwYMHWbNmDenp6TzwwAPs2bOHKVOmYDKZCAkJIT09nbKyMgoK\nCj6XgxBGg/6tFEV6LUEQhNMxZEC22/t2cunt7eXuu+/mBz/4AX6/n5tuuom8vDyWLFnC3/72N3Jz\ncwkN/XSnlqCgIJxO59ktuTCqGJqPrl6dKJGHWhAE4bQMu6irqamJr3/961x33XVceeWVzJ07l7y8\nPADmzp3LgQMHCA0Npbe3d+A5LpeLsLCws1dq4awzDB1NU1FVDV03Dv+soel9aTV1TUPTDv9N1+iu\n3czLH5SjHU7HKQiCIJyaIQNye3s7d9xxB/feey/XXXcdAHfccQclJSUAbNq0ifz8fAoLC9m+fTt+\nvx+n08nBgwfJzs4++6UXzjzDQNf89LQ3UrprB1u2bmX/oWaczi4O7t3D/uoGPAEvtWWl7N27h7pW\nJ73t1Sz/w0/4yydbObC/ih6/yEMtCIJwqoYcsl6yZAkOh4Mnn3ySJ554AkmSeOCBB/jVr36F2Wwm\nNjaWRx55hODgYG677TZuueUWDMPgnnvuwWIZboNzYTQyMOiqK2XVm2tpdkv4OsrY3xTM7f/zVRpW\nPcsWYxz3/+AmGvZv49WXVxA1fzHfmNjIuxua6cgqYUtxNJelZBBhFXfUCYIgnAqRqUs4ih7w8P6/\nf8Uz22z86JHvMda5njsW/oArn3uP5O3/4g/rVB7/y0MUxvn437m57Jn1LEt/Mo7fXH8Ln8z4ESt+\nvJDIiBCUkT4QQRCEc4zoxghHUf09bF//AeFjZ5CXEE5U5hx++fcnmZ8TgazInwZak5XgEJDMMla7\nDavZjMUWRowIxoIgCKdFBGThKIbuw1HXirutA48vgC4FkX3RFHB5MQCTYSAZBoauowEYn97mpOnG\n4U0oxKCLIAjCqRIBWTiKYgojrTCG0r0vsXFnBe1tjWx85xmefWMfEia83b109bhwtNTS4DCBO0BA\nM5AVBT3gpdfVTafTN9KHIQiCcM4RAVk4imIJ4cIv301RWhRV+3ZzqOoAz79TxtU3zWJs3hQuGpuE\nx9FNS8U2fONu4MJkO56AjaK5C8lNtNLZ1URdi3ukD0MQBOGcIxZ1CYIgCMIoIHrIgiAIgjAKiIAs\nCIIgCKOACMiCIAiCMAqIgCwIgiAIo4AIyIIgCIIwCoiALAiCIAijgAjIgiAIgjAKiIAsCIIgCKOA\nCMiCIAiCMAqIgCwIgiAIo4AIyIIgCIIwCoiALAiCIAijgAjIgiAIgjAKiIAsCIIgCKOACMiCIAiC\nMAqIgCwIgiAIo4AIyIIgCIIwCoiALAiCIAijgAjIgiAIgjAKmEa6AKOdoWvoxtCPkWUZSQJdN0CS\nkCXp8yncSTMwBo5B4tPiffp7w+gruwRIQ5TfOPwEwwBZPv5xxqdvNOTrnKic+nAnu++FkTDQNL3v\nR1lBlvvKPqoZBrqho+s6BgomRcIwjMM/S5gU+TTO2ZEvb3ym548kw9AxjL66OeQxGAaarmMYOkgy\niqww6MMNAwMG6vRZc/h9hiuzruvohoEky8iSdGY+p0GO0dA1tMPtkCJ/tvrUd641DN1AUhRkSR78\nXJ/2y38O9dUwMM52HTiDREAehs/RQnVzD5qqIkkKJkXp+4NkoKt+dHMwCUmpRNkMWppaITiGhEjb\nqKkAhmFg6Bp+rwe3XyU4LAKrcrh0Buiqj16HE6+qoRoy4RGRBFvNg3zx+oK3rmkEfE46e2QSx4Qf\ncZwGhm6gaQHcvS4MOYiw8FM9Dzrt1RV0qDIWswkJg4A/gIGMxWoGQ0P1q1ijk0iNgvI9++hwG4wZ\nm8PYpMhRc85PLEBbQx119fX0WlKZOTEFn6OVg1XVOIhi8oRsgq2m0zyOvgsURTlBgDoj+t6jP6ic\nydcNODtp6vIRm5SI3TREA2r4qK+qorG1BTk0i0kFyZgV+bjHG4aBzuEhwLPY6B/5PicKLrqu0VZX\nRlW9k9j0TMaOicF0JuIxYOg6HBF4uxqrqKhpxRyRyLisdIItnyEoG15qyspp7XQQOXYC2YlhZyyA\nGoaOrhnIZ7W+Hu5QyQrKOXKhqixevHjxSBdiNHO3VrFx81beeOEFdpTXowFd7W20tzeyZ/1brN1Z\njT05nwxbC08+8RQb22KYPXEMykgX/DDN46C2vpGSrWtYu72SMVl5RNj6Zip0I0Bj+Wbee+t9apta\nKN66mVpvEBlJcVhNx8xmGAY+l4OW+iq2fbiCl1Z7mH1Z9qdXdIZKd3MTdbWlvPfamzR74snOjjnF\nORE/7/z2Id4ub6bX66ezoYw3Vqzkw80HsQZJNFftZeO6d9nhiuOinBA+XrWSF5a9j5xQQOG4uFFz\nzk/I8FNbtpNXn17Csp1Wrp6fh6e9mrdfWMpL61qYdckkIoIspxeQdRcVZZ2ERQejDDJycUYYfpoa\nOpFNZqyWM3ktr1P94Yv888U3iZ5wIYmhlhMHfN3NvuINLPv7kxR3JDPnomxsgwRkf08rHS4Vu912\nVkesVFcXnQ4XZqsd0wnOu64FqNn9Ac+/8CbusGRys5KxnIHPSPe76e5ox7AE912USNBYup6XX3qe\nnW0GhYX5hNtMpx9EdRe7P1nHy/9+jo4x05iSEXXG6pau9lBb5yI0Iuisfj6uxjK6pHBCLGc38J8p\nYg55GMGxY5k+YzragfXUtGjkT5vGtGnTmDrlAmbMuohwvYdDtT3ogV4qS0vYfqiDowddjb5eKod7\nq4f/MfDzEY/sH4I68nkD/44u14l+fyxX4x6eeeYVVq94ltXrNtLtUwf+5nO08O7ypexvUUjLziE/\nPZjlS37Hml3N6Me9kk7bwT28+/pzvLD0GV5cX4565J8NDzvfXMYrq5/nuZdWDnIeToaP+t27SZ4w\nnSmTiiiaOJaO4s28XylTOHECRZMvYMLYEMoPNaNL4RRdMBlTRx2dzkDf0NQJTsbJnqujH3v853b0\nZ8LRPw/xOgMkCynjCkkzO6ms6kAzZCLj08mKC6K9vhW/qh/5Asc//5jfH1kO1XmIP/31Ixw+9aTO\n+2DnZPCf+39hoHs7eOO1zVQ19AxSP4569UHO2TF/O+bxjvZaSvdsp9MdGPSxA+WVg8idMoNE9yEa\nWt0YxrHl7Ot9te35kA079+DyD11SjjgPg57vY47nyLIbhkFX5TY2bd5Ih0c9Yf2TFRMp2blEBek4\nHa4T1pn+1zyZ+moYBu7WGorXvUltj5/+V4vPyCMp1kRLVyfqEdNLQ73PCcnBFM68iChnHc0edehz\ndIr11dm0l6Uv7cSjasPW18HPyeCfx9H1V6X81T/ySa0T7WS+/KOAGLIehmIPJy3TxJgwhY7gOJLT\n0og3a3TWNhE9awFul0RZYydqSA73PfwovrAUzEDfEK5OwO/Hr2koZiuy6sftDWAPDUY2tL7hP8mC\n1aagBQIEAiqYrNjMEmogQEDVMVtMqF4fhmLCZrMiA5rmx+P2oSFhsdiwWk0nvMoMSsznllvHULW+\nlX3rvUddJXbX72bt9h6u/9l1TJ+ShFSUzYE3nuDVZz7hsgu+TNhRXU6ZmPR8Lr8+FnPDDj7ae8zQ\nqhTEhMuvY0xvM22bf4J0TA/bMHQ0VUNSTCee7zUceGKu4JYr5pBqkSFgIt5iQYpMJiMzAzuQFuVh\n3UsONMzEjUkkKgQMdPxeL35dRzFbsJjNyBJg6GhqAI/biyYpWK02rBblBD0GAy0QwOPx9g1ByjIm\nixWzAoFAX2OkKAqaGkBHxmK1okgGfp8XzZAxWywDvRTDMAj4fXh9AZBN2O22w/PDCqGR0STGWJGr\nZCQkbMFhJMSFYTM7+ubv6Xu+6vfh8wXQJAmbzY7FpAA6qt+P1+dHR8ZkkpAVKxbZT93uLWw90InH\nHyBgljGZTAzemTHQNQ2v24VqSJjMVqxWM4amElBVDEzY7GYMVe07bsWMzayArtJec4Cde/aRM2sS\nAb8fk8mCctxAioGm9tVlyWRG0QP4NANFMWGxmDHUAD5VBcmEzWpGkWUMHTLnfpNf5t9IcnIYitQ3\nFKsGfARUDUxWFCOAx+PHbA8iIi6BMVESkgIBvx+PaiArZqxWMxIQ8HZTunkX5SEKs6f7CVIsmM3H\njp/0zeuqfj+qLmE2y/j9AZAkzGYLZtOn9UTXNPw+D37VQDFbsFosKLKE6ndSsbOE0iYbBTP8BGx9\nUy3HkmSFkMg4wiPCUSWDgM+L2w+yydxXV/u/D4aO6vfh8fqRDn/fTcrg9VXX/DRUlrJjYyWRM70E\nAmYsZoWg8FiioiOQGkEL+HG7dSRZwWK19M0p0zeE7vd48KkGitmMzWpFkaXje5CSmejEMcSGyjQa\nBn6/F9UAk7nvfPa3OYauE/B58Pg1ZMWEzdZX3zF0Al4P3oAGsoysKFgtFiTNRdnGtZTWjsPrD2BT\nZEzyiean++qT1+NBlxSsFitmiwk0FX8ggCEpWCwWJEPr+xkZq9WCZOi4e2pZs2wLIVM9+AMBJJMJ\n5dgKO8qIgHxS+q70dUNH1VRUw8Hrv/gTU//0WzLGjycowk99eRWH6usIBIeSlxaJomt0N9ew70AZ\nqtmGJyBj8XdwsMFJ0ZzZmBpqaHR6CI+fwPQpcdTuL6GyphEj8QLmFIRQW7abAzVOUrOSady/DzUk\nnqkzZxJj9lK5by/76nqwB4HZHkvRxAJiQu2DVmhzcBTZ4yLp3hcGeI/6W1f9XtpsQYxNi+5rvE1h\nTCoq4PU1n9DiuoGwIyOyJGMPiyYlLIQ4mw3p2I6HZCImLZOQHjOh/ads4PQZeJ3t7N9VQ3RWDimJ\nYYN/+XSImzaTGIv86Wk//D/9/2uOSSdT3o0XkNFBUnG0H2J7sRvN14Vhi2Pi1ClE2xX87h7K9u6h\nrNGFPUgiKDyRiQW5RAZbj3t/3e+kfOdOajr9mC06XqebxPypZAQ5KS49RECTiYqNQXX00O3VCMvI\nJcPupbqyDrehExSXztTcsdhNEu7OZnaXlNHj8eHy6iRm5lOUm0zwcUHhyPp1xLlytVNZWkJjhw9N\n9WKLzmXy5Exsag/lpWU0O71IioTX5yUmpZAEqlnyh5fo8eSwY9t2UuISyMrJJNSqHHPhY6D5XNQf\nOMDuA7VYwuwoRghZBVkEOus51NSEZh7HpXMy6Kmv5sD+SpyhOcydkY6v7SCvPfsKO3e0MmFfPibX\nGMZPLiIm+OgLM0Pz01S1m9KqFiyxCYS6e3AaCj7DQmpGKlpbM11uJz1unYyCSeQmRaE6Wig/WE1T\ni5Pg9BwibBKuzgbK9pfjMsAdMGPVu6lr6CS96CKmF44BwO/voHzvDvwuF7pkJnvSdMYEQ8Xm1by8\ncT2uzBD2FMcSm55LQXocJkU68lTgdbayu3gXrS4zqUl22nt8mAwPQdFpjM/NIcxqBiNAW91+9pcf\nwmuYkUx2UrLGkz0mippdH/Dq2tUctE8if/sWOsfmUpSViFk5vnIf7qvS2VLHjuJd2C0qLtVKenYW\nafFRmBUJv6ONXTtLaO71IysKCWnZFGan9V0QHUWjrXILq1Y+ywd1oSTvLEbqHUdRTiqmw9+WgMdB\n9Z6dNJgMXD5IyytkfHI0JgK015VTUlKOTw5CVqyMHT+BjOSoQcsNBkgqXTVV7N7Rher3IJnDGZub\nT1JUMLKk0dNWy76SUnpUO6g+4sZOJHdcAlpXPbt2VeKWJTACuAljcl463VUbefyRZXQW3cq24h1k\nZGQxNjkOy3Hvb6C6uynbUUJ1WxeKyYwtKJGJM/KR28so3l+LKTyRwgmF2Hur2br3IKoUQtGMadhc\n9Xyy8u882+zk6tJt7DKlkpqRzZjokFG46PZTYg75pPj55LknOKAmkpocSt3+Yl78+wZmf+cWxiXE\nMCbJyuY3V/Kv3z/K0q1j+ObXpiD1NvDKkkd54YO9pKZH8tJff8OqT3agm3RC4uIpf+t1/v33JykP\nTOLK/0pkyxsrefoPj7J0dxq3XZnI1jf+zW//9Ax7Kjqoqd7GytfWEDfxYozytTz0+Eu0x+SQF9bK\n0v97lp6gFPIyUwep0J9qOPAR6w64mDv/chKC+67DDm1Zxfv7XVx2xVUkhZgBifqNr/BWeRcXLvgS\nqaGDXa9pVH6wnNUNWXz3a9OwHPNX1dfD+pWvII2bzyVTkgfmdRv2reP+236PllpI0YSkwRe1yOFM\nmp51eIQB0LpZ++zL7A2dwl03TcYMSEooky7Ixq7I+Hpb+OjVZ9nT2I7bYsfcsZmnFv8FZcb1TIyD\n7e8u5yePr8CbOoFUqnjuhRUYMZnkpCUcN9/nrHyH79z1d8InXUh6sIN3//Mc3thsxmgHWLLkn/z9\nmVeobXZjsxjs/uQ1frlqN0ZDEzXNHTSVfciSN3YzbfZM4oJl9qx5gUeefIeYnAzat73N75/dSPaF\nMxkbZUeWNCo/XME7Denc8ZVpBJklmks2sKbEzxXXXkyEVWXH2//H08+9ipyQhq15G0/84jWUgsnI\ndR/z9DPvEppRQEpQBy+89DItIRnoTXvZtGUj9S0ONF8XDpeZcQU5hB4zb2boPg5ufp8//+wflDpD\nSEuUeOOxP1OuBuGqLWHp479idXkqN35pPDXb1/OfP/6Wf6wxuPnLU2mv2sIrqz+gtr4Rt6eH2uoe\ncmdeQEzQ0QsANZ+LXWuW8se/PsXqj3fS2uQiIlpixbKlvL21hoaqJixWD+8v/T1v1YRy2axCjJa9\nrHrpXzz6xyeJn/tVCiN8fLj8r/zfa+sIiw3h/eef5Lk31qCHmLGEJjB+bBJlq5ewrqIHr9RLwN3C\n2399jL3hM5iZbmbr6uf5YHcNbZ1OulobcEfkMSkr9rjPvLOxlH/9+jH++fRKDrQcxBWUiPfA67y8\n7GNiJ13M2Bg7XVVbWfLnv7CzJUBaUjSlG97gtfUHSMkeR826pazdeYjG1h4cHa10h2QzLSce8yC9\nMN3voHjTW7yxbjutrmDGRPp489UVbC7vITkzg1iLi/ee/Ru/eHErERnp9FZ8xLJ3tzJ24hQSw4OP\nGe1Q2bPqSd7edoiDDR24erroNicwLT8NM3727fyYd9fupr3ZSVS8hXdW/Iv3q2UumVGA2rSLf/1u\nMe+Wd5OdlcD2Zcv46IBG/uRsIuzmQXrjAYqXPcE7H9egB1lQfLW8++IL7GhSyRw/HqurnlX/+SPL\n15WQPXkyjR8u5+XXqxgzIZP9r/6JJe+2UzQ9H3dtMS9sKCd1TDgff/gxleW7aHEEcPV0Y49JJiMt\n4bj2y1Cd7FjxDH/45XI8kUlYWnfyxB9XEDfrYoLqP+QvT/yDjw92MWXmRVjq1/Ovp//Js6vWMn7O\n1djqN/P+ug1sPVCHqup0druISc0hJWZ0B2TRQz5pBl0dLezbU4KvoYQy9YgvnRLBlf9vEa4tL1HS\nZkIGXM2VfFxcz+U/fIwbL84lqXc/v37fyR13PcT4hDCC5kzDVfoepTYFWYngqm8vwrX5RRZ3qlgi\nk7nyK9/gg+ID1IRP49+PzmDZix+QYWlj1fJleLKu4qc3XoTV8NK2fwdrNqzniktmEBJhPmHpB9Nd\nXwPYj/u9LEmYz/DCoNDYVBbefjX5ufEMcd1wUvoXuhsS6CgkFV3Dd++4iTEhLlpfmsGGTdVcP8bC\nC0tfwjztTv73hpmo7nE0lGxn8+ZtzJ8xAVvw0VW/p+EATcFxjI2xE5mayLxrbkSPjSRxxqU8YnJw\n6R3PMXvhl7njxhn49kfz1nUP0jHlX/zy3tmolW+z90f/oaHHQ36sBZ/PTcLYdArzJ5E3PY4tV93J\nml2NzBkbiTLMN87TdYiVz6xGmXQrC+ZeToxtNg3rb+X1FZsImdyCzxZCeJidsKQL+MaNvVTZUrh2\n9nQiajay970CHvn9j4gLMh++fe3o11YdDbz+wovUpl/M3/94J5H+dtTa7ZSHhnL5rddj3r2cfwRM\nyLKdqQuuo3fPGnas1TAkE+OmXc0Pb2/hob/s5Lv3/S8XFSQO+h4mezgXXfsNtu2v5r3KWL7z0x+T\nGx9EfKCSny9tYs7ib3P5zBRmh5fznSXb6PTdyrjMi/jOt7t57o3NmABfZyPF28vJX/BtbrpxLpfE\nOfnuk8Xc9LX7mJoSSYgVDAXsERlc89V7mJVmJe3ALn6+Zj8P3jiZa++8n6rOh2hMuprFd1xPhE05\nvqCSRHzGVL76tS9RVreUzCu+ywM3zMTflE/NXY9QVtnKJdkW1iz5M28cKuT5//sxGZE25s/M4d6v\n/D/+/NJ0/vb9n9IR+CUfu8bz0Pe/RUq4ddgV3bET5vLgvd9gbJSdmdmJPPzzP/POJxlE5/Tw+7+8\nwPh7/83XLi9Ab49kz/2PsG5fM5NTYlCO+tJYmHn7r9HDf81j7/dwz/8uZmJiSN90ie/w5xCUyle+\ndxcXF6QwNaqZ+/6zmabuK2l79SWWbbbyu+d+wqQ4M0m+Nn71rx0crJ9LWnTQ4FNJiom4oWB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_11.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.4.2 Normalized Cuts\n", "A proper definition of a \"good\" cut must belance the size of the cut itself against the difference in the sizes of the sets that the cut creates.\n", "\n", "The *normalized cut* value for $S$ and $T$ is\n", "\$$\n", " \\frac{\\operatorname{Cut}(S,T)}{\\operatorname{Vol}(S)} + \\frac{\\operatorname{Cut}(S,T)}{\\operatorname{Vol}(T)}\n", "\$$\n", "where $\\operatorname{Vol}(S)$ is the number of edges with at least one end in $S$, and $\\operatorname{Cut}(S,T)$ is the number of edges connected between $S$ and $T$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.4.3 Some Matrices That Describe Graphs\n", "1. adjacent matrix:\n", " \$$\n", " A_{i,j} = \\begin{cases}\n", " 1, & \\text{if node i and j is connected} \\\\\n", " 0, & \\text{otherwise}\n", " \\end{cases}\n", " \$$\n", " \n", "2. degree matrix:\n", " $D_{i,i}$ is the degree of the $i$th node.\n", " \n", "3. Laplacian matrix:\n", " $L = D - A$\n", " Notice that each row and column sums to zero." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.4.4 Eigenvalues of the Laplacian Matrix\n", "The smallest eignevalues and their eigenvectors reveal the information we desire.\n", "\n", "1. The smallest eignevalues for every Laplacian matrix is 0, and its corresponding eigenvectors is $\\mathbf{1}$ ones matrix.\n", "\n", "2. the second-smallest eigenvalues of $L$ is the minimum of $x^T L x$, and the minimum is taken under the constraints:\n", " + $\\displaystyle \\sum_{i=1}^n x_i^2 = 1$\n", " + $x$ is orthogonal to the eigenvector associated with the smallest eigenvalue.\n", " $$x^T \\mathbf{1} = \\displaystyle \\sum_{i=1}^n x_i = 0$$\n", " \n", "In all:\n", "$x^T L x = \\sum_{i,j} (x_i - x_j)^2$\n", " \n", "As a consequence, $x$ must have some positive and some negative components $\\to$ two sets/groups." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.4.5 Alternative Partitioning Methods\n", "1. We could set the threshold at some point other than zero.\n", "\n", "2. We may also want to a partition into more than two components:\n", " + split repeatedly as far as desired.\n", " + use several of the eigenvectors to partition the graph.\n", " \n", "Attention: \n", "while each eigenvector tries to produce a minimum-sized cut, the fact that successive eigenvectors have to satisfy more and more constraints generally causes the cuts they describe to be progressively worse." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Exercises for Section 10.4\n", "## Ex 10.4.1 \n", "### (a)\n", "\n", "edges = [\n", " ('A', 'B'), ('A', 'C'), ('B', 'C'), \n", " ('B', 'H'), ('C', 'D'), ('H', 'I'),\n", " ('H', 'G'), ('D', 'E'), ('D', 'F'),\n", " ('I', 'G'), ('G', 'E'), ('E', 'F')\n", "]\n", "\n", "G = nx.Graph()\n", "G.add_edges_from(edges)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RESZPnoyLFy8iMjISTZo0ER2pTMnJyejduzfOnz+v8XnIRPpGqVDgRufO6JOb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\nTEREJMD/AbmZi+fNUrhzAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nx.draw(G)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "matrix([[0, 0, 0, 0, 0, 0, 0, 1, 1],\n", " [0, 0, 1, 0, 0, 1, 0, 0, 0],\n", " [0, 1, 0, 1, 0, 1, 0, 0, 0],\n", " [0, 0, 1, 0, 1, 0, 1, 0, 0],\n", " [0, 0, 0, 1, 0, 0, 1, 0, 0],\n", " [0, 1, 1, 0, 0, 0, 0, 0, 1],\n", " [0, 0, 0, 1, 1, 0, 0, 1, 0],\n", " [1, 0, 0, 0, 0, 0, 1, 0, 1],\n", " [1, 0, 0, 0, 0, 1, 0, 1, 0]], dtype=int64)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = nx.adjacency_matrix(G).todense()\n", "A" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[2, 0, 0, 0, 0, 0, 0, 0, 0],\n", " [0, 2, 0, 0, 0, 0, 0, 0, 0],\n", " [0, 0, 3, 0, 0, 0, 0, 0, 0],\n", " [0, 0, 0, 3, 0, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 2, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 0, 3, 0, 0, 0],\n", " [0, 0, 0, 0, 0, 0, 3, 0, 0],\n", " [0, 0, 0, 0, 0, 0, 0, 3, 0],\n", " [0, 0, 0, 0, 0, 0, 0, 0, 3]], dtype=int64)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D = np.diag(np.ravel(A.sum(axis=1)))\n", "D" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "matrix([[ 2, 0, 0, 0, 0, 0, 0, -1, -1],\n", " [ 0, 2, -1, 0, 0, -1, 0, 0, 0],\n", " [ 0, -1, 3, -1, 0, -1, 0, 0, 0],\n", " [ 0, 0, -1, 3, -1, 0, -1, 0, 0],\n", " [ 0, 0, 0, -1, 2, 0, -1, 0, 0],\n", " [ 0, -1, -1, 0, 0, 3, 0, 0, -1],\n", " [ 0, 0, 0, -1, -1, 0, 3, -1, 0],\n", " [-1, 0, 0, 0, 0, 0, -1, 3, -1],\n", " [-1, 0, 0, 0, 0, -1, 0, -1, 3]], dtype=int64)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = D - A\n", "L" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [], "source": [ "### Ex 10.4.2 \n", "w, v = np.linalg.eig(L)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false }, "outputs": [], "source": [ "eig_min = np.argmin(w)\n", "w = np.delete(w, eig_min)\n", "v =np.delete(v, eig_min, axis=0)\n", "\n", "eig_2nd_min = np.argmin(w)\n", "eigv_2nd_min = np.ravel(v[eig_2nd_min])" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'B', 'F', 'D', 'C', 'A', 'E'} {'I', 'H', 'G'}\n" ] } ], "source": [ "setA = set([n for v, n in zip(eigv_2nd_min, G.nodes()) if v >= 0])\n", "setB = set(G.nodes()) - setA\n", "print(setA, setB)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.5 Finding Overlapping Communities\n", "Communities are in practice rarely disjoint.\n", "\n", "Assume: \n", "the probability that two individuals are connected by an edge increases as they become members of more communities in common." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.5.1 The Nature of Communities\n", "We expect edges to be dense with any community, but we expect edges to be even denser in the intersection of two communities, three communities, and so on." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3uoX6ycvg4CBvvvkmjz76KMHBwZ42Z9QRBIH8/Hx8fHw4c+bMqA+W5h4jZmUY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\nnK5UMtOttDfWMOAOo7e5KCjIw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_19.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.5.2 Maximum-Likelihood Estimation\n", "We assume that the value of the parameters that gives the largest value of the likelihood is the correct model for the observed artifact.\n", "$$\\operatorname{argmax}_{\\theta} P[f(\\theta)])$$\n", "\n", "prior probabilities:\n", "$$\\operatorname{argmax}_{\\theta} P[f(\\theta)]) = \\operatorname{argmax}_{\\theta} P[f(\\theta) | \\theta] \\, P[\\theta]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.5.3 The Affiliation-Graph Model\n", "affiliation-graph model: generate social graphs from communities.\n", "\n", "community-affiliation graphs:\n", "\n", "+ Given: $C$ communities, $N$ nodes(individuals).\n", "\n", "+ Question: $n_i \\in C_k$ ?\n", "\n", "+ Model:\n", " - Parameter: the memberships in the communities, $C_k = {n_i}$. \n", " - Parameter: $P_{ck}$ is the probability that two members of community $C_k$ are connected by an edge, $P_{ck} = P[(u,v) \\in E \\, | \\, u \\in C_k, v \\in C_k]$.\n", " \n", " \n", "we compute the likelihood that a given graph with the proper number of nodes is generated by this mechanism.\n", "\n", "##### membership: Y/N\n", "1. Parameter: membership\n", " define membership: $n_i \\in C_k$. \n", " 0 / 1, Yes / No, decrete variable $\\to$ brute search\n", "\n", "2. Parameter: $P_{ck}$ \n", "\\begin{align}\n", " &P_{u,v} = 1 - \\displaystyle \\prod_{C_k in M} (1 - P_{ck}) \\quad \\text{where } M = {C_i: u \\in C_i, v \\in C_i}\\\\\n", " &P[f(P_{ck}, C_k, E)] = \\displaystyle \\prod_{(u,v) \\in E} P_{u,v} \\, \\prod_{(u,v) \\notin E} (1 - P_{u,v}) \n", "\\end{align}\n", "\n", "3. Goal:\n", " find $\\operatorname{argmax}_{C_k} P[f(P_{ck}, C_k, E)]$. \n", " \n", "##### membership: \"strength\"\n", "avoiding the use of discrete membership changes. This improvement allows us to use standard methods.\n", "\n", "\"strenght of membership\": \n", "the stronger the membership of two individuals in the same community, the more likely it is that this community will cause them to have an edge between them.\n", "\n", "In the improved model,\n", "\n", "1. Parameter: membership\n", " define membership: strength, $F_{xC} \\in \\mathbb{R}_{\\ge 0}$\n", " \n", "2. Parameter: $P_{ck}$\n", " $$P_C(u,v) = 1 - e^{- F_{u,C} F_{v,C}}$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.6 Simrank\n", "The purpose of simrank is to measure the similarity between nodes of the same type, and it does so by seeing where random walkers on the graph wind up when starting at a particular node $\\to$ limited in the size of graphs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.6.1 Random Walkers on a Social Graph\n", "Random walkers:\n", "\n", "A walker at a node $N$ of an undirected graph will move with equal probability to any of the *neighbors* of $N$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.6.2 Random Walks with Restart\n", "Let $M$ be the *transition matrix* of the graph $G$: the entry in row $i$ and column $j$ of $M$ is $1/k$ if node $j$ of $G$ has degree $k$, and one of the adjacent nodes is $i$.\n", "\n", "$\\beta$ is the probability that the walker continues at random, so $1 - \\beta$ is the probability the walker will teleport to the initial node $N$. \n", "\n", "$v'$ is the probability the walker is at each of the nodes at the next round:\n", "$$v' = \\beta M v + (1 - \\beta) e_N$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IMOBFTEYYfGuEbKlWpxeJSjHNxWP/yDeOR+g59Em2B01EJ28yeHmUVKnG/bgF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\nDAYDGzduZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig10_22.png'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LXB1iI0zgAKCJrFq1Svfee6/69+9vOgpQDetT++FXCgCaiMPh0Jw5c0zHAGpgfWo/FDgA\naAL79+9Xfn6+Jk+ebDoKUM2+fft0/vx5PfTQQ6ajoA4ocADQBObPn68f/ehHatGihekoQDVpaWma\nMmUK61Ob4V2oANDIKioqFBUVpR07dujuu+82HQeoZuDAgXI4HBoxYoTpKKgD6jYANLLU1FQNHz6c\n8gafs3//fpWWlvJWEBuiwAFAI7Is68abFwBfw/rUvvgVA4BGtG3bNp0/f15jxowxHQWogdOn9kWB\nA4BGNG/ePM2ePZsJB3zOgQMHVFJSouHDh5uOgnrgdxQAaCRnz57VqlWr9MILL5iOAtTA+tTe+FUD\ngEby7rvvasKECQoLCzMdBaiB9am98S5UAGgEbrdb8+fP15IlS0xHAWr46quvdObMGdanNsYEDgAa\nwYYNGxQSEsLLweGTrq9PmzVrZjoK6okCBwCN4Pp7T4OCgkxHAWpgfWp/vIkBALzs+PHjGjx4sI4e\nPaqQkBDTcYBqCgoKNHLkSBUVFTGBszEmcADgZQsXLtSzzz5LeYNPSktL0+TJkylvNschBgDwoqtX\nr2rRokX6+OOPTUcBbiotLU1/+tOfTMdAAzGBAwAvWrlypfr06aN+/fqZjgLUcPDgQblcLj388MOm\no6CBKHAA4EUOh4P3nsJnsT71HxQ4APCSvXv3av/+/Zo4caLpKMBNcfrUf1DgAMBL5s+fr5deekkt\nWrQwHQWo4dChQzpx4oRGjhxpOgq8gEMMAOAF5eXlSklJkdPpNB0FuCnWp/6FCRwAeMEHH3ygkSNH\n6gc/+IHpKMBNsT71LxQ4AGggy7I0b948zZkzx3QU4KYOHz6soqIi1qd+hAIHAA30xRdfqKysTI88\n8ojpKMBNpaWladKkSWrenE9O+QsKHAA00Lx58zR79mwFB/NbKnwT61P/w7tQAaABSkpK1KtXLx08\neFAdO3Y0HQeo4fDhw3rwwQd18uRJJnB+hL8uAkADLF68WI8//jjlDT4rPT2d9akfosABQD253W7N\nnz+fNy/Ap7E+9U8UOACop/Xr1+uuu+7S0KFDTUcBburIkSMqLCxUXFyc6SjwMgocANTT9feeBgUF\nmY4C3BTrU/9FgQOAejh27Jg2bdqkadOmmY4C3BLrU/9FgQOAeli4cKGSk5N15513mo4C3FRhYaGO\nHDmi+Ph401HQCJipAkAdXb16VYsWLVJOTo7pKMAtpaena+LEiaxP/RQTOACooxUrVqhfv37q27ev\n6SjALbE+9W8UOACoI957Cl939OhRHTp0iPWpH6PAAUAd5Ofnq6CgQBMnTjQdBbil6+vTO+64w3QU\nNBIKHADUgcPh0Msvv8wfjPBprE/9H+9CBQAPlZeXKyoqSnl5eYqMjDQdB7ipY8eOKSYmRi6Xi79o\n+DEmcADgoffff19xcXGUN/i09PR0PfHEE5Q3P0eBAwAPWJbF4QXYAuvTwECBAwAPfP7557p8+bJG\njx5tOgpwS8ePH9dXX33Ff6cBgAIHAB6YN2+eZs+ereBgftuE72J9Gjj4nQgAbqO4uFhZWVl6/vnn\nTUcBasX6NHBQ4ADgNt555x1NnDhRoaGhpqMAt3T8+HEdOHCA9WmA4AVpAFCLqqoqLViwQB9++KHp\nKECtMjIy9Pjjj6tFixamo6AJMIEDgFr87W9/U2hoqIYMGWI6ClAr1qeBhQIHALVwOByaO3eu6RhA\nrYqKirRv3z4lJiaajoImwgoVAG6hsLBQmzdvZn0Kn8f6NPAwgQOAW1i4cKFmzJihNm3amI4C1Ir1\naeDhXagAcBNXrlxRVFSUPv30U/Xp08d0HOCWTpw4oYEDB+rUqVNM4AIIEzgAuInly5dr4MCBlDf4\nvIyMDE2YMIHyFmAocABwE7z3FHbB+jQwsUIFgO/ZvXu3xo4dq8LCQl5JBJ928uRJDRgwQC6XSy1b\ntjQdB02ICRwAfI/D4dDLL79MeYPPy8jI0Pjx4ylvAYhrRADgO8rKypSamqrdu3ebjgLcVlpaml57\n7TXTMWAAEzgA+I6UlBTFx8erW7dupqMAtXK5XNq9e7fGjBljOgoMoMABwLcsy+LNC7CN5cuXsz4N\nYBQ4APjWZ599pitXrighIcF0FOC2OH0a2ChwAPAth8OhOXPmKCgoyHQUoFanTp2S0+lkfRrAKHAA\nIOnMmTPKysrSzJkzTUcBbmv58uVKSkpSq1atTEeBIRQ4AJD0zjvvaMqUKerQoYPpKMBtsT4FF/kC\nCHhVVVXq2bOn0tPTFRsbazoOUKvTp0/rvvvuk8vlYgIXwJjAAQh469atU6dOnShvsIXly5frscce\no7wFOAocgIDHe09hJ6xPIbFCBRDgjhw5oiFDhujYsWNq06aN6ThArc6cOaPevXvL5XKpdevWpuPA\nICZwAALaggULNGPGDMobbOH6+pTyBt6FCiBgXblyRYsXL9bGjRtNRwE8kpaWpn/4h38wHQM+gAkc\ngICVnp6uQYMGqXfv3qajALd15swZffnllxo7dqzpKPABFDgAAYv3nsJOVqxYoXHjxrE+hSQKHIAA\n5XQ6VVhYqAkTJpiOAniE06f4Lk6hAghIs2fPVteuXfWLX/zCdBTgtoqLi9WrVy9On+IGDjEACDgX\nL17Uhx9+qPz8fNNRAI+sWLFCY8eOpbzhBlaoAALO0qVLlZiYqK5du5qOAniE9Sm+jxUqgIBiWZYG\nDhyot956SwkJCabjALdVUlKie++9VydPnuS+QtzABA5AQNm4caOuXbum+Ph401EAj6xYsUKPPvoo\n5Q3VUOAABBSHw6E5c+YoKCjIdBTAI6xPcTOsUAEEjNOnT6tPnz4qLCxU+/btTccBbov1KW6FCRyA\ngPG///u/evLJJylvsI2VK1dqzJgxlDfUwDUiAAJCVVWVFixYoBUrVpiOAngsLS1NL730kukY8EFM\n4AAEhDVr1igiIkIxMTGmowAeOXv2rLZs2aLHHnvMdBT4IAocgIAwb948zZkzx3QMwGPX16d33nmn\n6SjwQRQ4AH7v0KFD2r59u55++mnTUQCPcfoUteEUKgC/9/rrr8vtduvNN980HQXwSGlpqXr06KGT\nJ08ygcNNcYgBgF/7+uuv9e6772rz5s2mowAeW7lypR555BHKG26JFSoAv5aWlqb7779f9957r+ko\ngMdYn+J2WKEC8GvDhg3TP//zP+uJJ54wHQXwyPX16YkTJxQSEmI6DnwUEzgAfmvXrl06fvy4kpKS\nTEcBPLZq1SolJiZS3lArChwAv+VwODRr1iw1b87HfWEfrE/hCVaoAPzShQsX1L17d+3bt09dunQx\nHQfwyLlz59S9e3cVFRWpbdu2puPAhzGBA+CXli5dqjFjxlDeYCurVq1SQkIC5Q23RYED4Hcsy+LN\nC7Al1qfwFAUOgN/59NNPJUmjRo0ynATw3Pnz57Vx40ZNmDDBdBTYAAUOgN+5Pn0LCgoyHQXwGOtT\n1AUFDoBfOXXqlNavX68ZM2aYjgLUCetT1AWnUAH4ld/+9rc6duyYFi5caDoK4LHz588rKipKRUVF\nateunek4sAEuRwLgN65du6aFCxdq9erVpqMAdbJ69WrFx8dT3uAxVqgA/EZWVpa6deumwYMHm44C\n1AnrU9QVK1QAfmPs2LF67rnnNH36dNNRAI9duHBBP/jBD3T8+HHdddddpuPAJlihAvALBw8e1Jdf\nfqmVK1eajgLUyerVqxUXF0d5Q52wQgXgF+bPn68XXnhBrVq1Mh0FqBPWp6gPVqgAbO/y5cuKiorS\nli1b1LNnT9NxAI+xPkV9MYEDYHt//etfFRsbS3mD7Xz00UcaNWoU5Q11RoEDYHsOh4P3nsKWWJ+i\nvlihArC1HTt2aNKkSTp8+LCaNWtmOg7gsYsXLyoyMlLHjh1T+/btTceBzTCBA2BrDodDr7zyCuUN\ntvPRRx9p5MiRlDfUC9eIALCt8+fPKz09Xfv27TMdBagz1qdoCFaoAGzrrbfe0ubNm5Wammo6ClAn\nrE/RUEzgANiSZVlyOBxasGCB6ShAnWVmZurhhx+mvKHe+AwcAFvKzc1Vs2bN9PDDD5uOAtQZ61M0\nFCtUALb01FNPKS4uTj/+8Y9NRwHqpKysTN26ddPRo0fVoUMH03FgU0zgANjOyZMntWHDBl5aD1vK\nzMzUiBEjKG9oEAocANtZtGiRnnnmGbVr1850FKDOWJ/CG1ihArCVa9euqXv37srKylJ0dLTpOECd\nlJeXq1u3bjpy5IhCQ0NNx4GNcQoVgE9zFRXpq61bVV5SopCwMB08e1Z333035Q22lJmZqWHDhlHe\n0GAUOAA+x7IsbcrI0JnUVEVkZ+v+c+cUIqlc0qXmzTXl/vu1MSNDIyZPVlBQkOm4gMdYn8JbWKEC\n8CnFLpeykpM1LjdXnd3uW36708HBWhsXp6SUFIVHRDRhQqB+WJ/CmzjEAMBnFLtc2pCUpJnZ2bWW\nN0nq7HZrZna2Nowfr2KXq4kSAvWXlZWlhx56iPIGr6DAAfAJlmVpTXKypu7cKU+XokGSpu7YoTXT\np4tlAnwd61N4EytUAD5hY3q6ej/zzG0nbzdzKjhYB9PSNGLy5EZIBjRcRUWFunbtqsOHD6tjx46m\n48APMIED4BPOpKbWq7xJUhe3W6eXLfNyIsB7srKy9OCDD1Le4DUUOADGuYqKFJGd3aBnROTkyFVU\n5KVEgHexPoW3UeAAGPfV1q0acO5cg57Rv7RUBdu3eykR4D0VFRVav369Jk6caDoK/Aj3wAEwrryk\nRCENfEaIpC25uWp7990KDw9XeHi4WrZs6Y14QIOsWbNGP/zhDxUWFmY6CvwIBQ6AcSFhYSqX1JA3\nm5ZLWpOTo2W5uTp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" ], "text/plain": [ " e_0\n", "Picture 1 1\n", "Picture 2 0\n", "Picture 3 0\n", "Sky 0\n", "Tree 0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta = 0.8\n", "e_0 = np.identity(M.shape[0])[0]\n", "e_0 = pd.DataFrame({'e_0': e_0}, index=nodelist)\n", "e_0" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def random_walk(v: pd.DataFrame, beta: float, M: pd.DataFrame, e_n: pd.DataFrame) -> pd.DataFrame:\n", " return beta * (M.dot(v)) + (1 - beta) * e_n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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If we wanted to know what node were most similar to another node, we would have to start the analsis over for that node.\n", "\n", "2. notice that convergence takes time, since there is an initial oscillation." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.7 Counting Triangles\n", "#### 10.7.1 Why Count Triangles?\n", "1. to measure the extent to which a graph looks like a social network.\n", "\n", " If we start with $n$ nodes and add $m$ edges to a graph at random:\n", " + sets of three nodes: $\\binom{n}{3}$.\n", " + The probability of an edge between any two given nodes being added is $m / \\binom{n}{2} \\approx 2 m / n^2$.\n", " + The probability that any set of three nodes has edges between each pair (independently chosen) is $(2m / n^2)^3 = 8 m^3 / n^6$.\n", " + expected number of triangles of random graph is $(8 m^3 / n^6) (n^3 / 6) = \\frac{4}{3} (m / n)^3$.\n", " \n", " We expect the number of triangles to be much greater than the value for a random graph.\n", " \n", "2. It has been demonstrated that the age of a community is related to the density of triangles." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.7.2 An Algorithm for Finding Triangles\n", "Suppose we have a graph of $n$ nodes and $m \\geq n$ edges.\n", "\n", "nouns:\n", "+ heavy hitter: the node whose degree is at least $\\sqrt{m}$.\n", " note, the number of heavy-hitter nodes is nore more than $2\\sqrt{m}$, since otherwise the sum of degree of nodes would be more than $2m$.\n", " \n", "+ heavy-hitter triangle: the triangle all three of whose nodes are heavy hitter.\n", "\n", "Assuming the graph is represented by its edges, we preprocess the graph as follows:\n", "\n", "1. Compute the degree of each node. $O(m)$\n", "\n", "2. Create an index on edges, with the pair of nodes at its ends as the key. constructed in $O(m)$. Query the existence of an edge $O(1)$.\n", "\n", "3. Create another index of edges, this one with key equal to a single node. to retrieve the nodes adjacent to given node. $O(\\sqrt{m})$\n", "\n", "\n", "order the nodes: nodes.sort_values(by=['degree', 'id'])\n", "\n", "\n", "##### Finding triangles:\n", "1. Heavy-Hitter Triangles:\n", " Find in all heavy-hitter nodes which is only $O(\\sqrt{m})$.\n", " time: $O(\\sqrt{m}^3) = O(m^{3/2})$\n", " \n", "2. Other Triangles:\n", " Consider each edge $(v_1, v_2)$:\n", " + if both $v_1$ and $v_2$ are heavy hitters, ignore the dege. (use $v_3$ since the computation is less).\n", " \n", " + if $v_1 < v_2$, query whether $(v_1.\\text{adjacent nodes}), v_2)$ exits. $O(\\sqrt{m} * m) = O(m^{3/2})$.\n", " \n", "The total time of the algorithm is $O(m^{3/2})$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.7.3 Optimality of the Triangle-Finding Algorithm\n", "It turns out the algorithm described above is, to within an order of magnitude the best possible.\n", "\n", "For a complete graph on $n$ nodes, it has $m = \\binom{n}{2}$ edges and the number of triangles is $\\binom{n}{3}$. Since we cannot enumerate triangles in less time than the number of those triangles $O(n^3) = O((\\sqrt{m})^3) = O(m^{3/2})$.\n", "\n", "For sparse graphs, we can add to the complete graph a chain of nodes with any length up to $n^2$ to convert." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.7.4 Finding Triangles Using MapReduce\n", "multiway join technique:\n", "$E(X, Y) \\bowtie E(X, Z) \\bowtie E(Y, Z)$\n", "\n", "if we hash nodes to $b$ buckets, then there will be $b^3$ reducers, since $(h(u), h(v), z)$, $(h(u), y, h(v))$ and $(x, h(u), h(v)$ are mapped. \n", "$\\to$ The total communication required is thus $3b$ key-value pairs for each of the $m$ tuples of the edge relation $E$, namely $O(mb)$ if we use $b^3$ Reduce tasks. \n", "$\\to$ each Reduce task receives $O(mb) / b^3 = O(m / b^2)$ edges. \n", "$\\to$ If we use the algorithm of Section 10.7.2, the computation cost of each Reduce is $O((m / b^2)^{3/2})$. Thus, the total computation cost of $b^3$ Reduce is $O((m / b^2)^{3/2} * b^3) = O(m^{3/2})$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.7.5 Using Fewer Reduce Tasks\n", "By a judicious ordering of the nodes, we can lower the number of reduce tasks by approximately a factor of 6.\n", "\n", "Order by \"name\", $(h(i), i)$. The Reduce task corresponding to list of bucket $(i, j, k)$ will be needed only if $i \\leq j \\leq k$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.7.6 Exercises for Section 10.7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.8 Neighborhood Properties of Graphs\n", "#### 10.8.1 Directed Graphs and Neighborhoods\n", "all undirected graphs can be represented by directed graphs.\n", "\n", "**path**: a sequence of nodes in a directed graph. Its *length* is the number of arcs, instead of nodes, along the path.\n", "\n", "The *neighborhood of radius* $d$ for $v$ is: $\\{u : \\operatorname{len}(u, v) \\leq d\\}$, denote this neighborhood by $N(v, d)$.\n", "\n", "The *neighborhood profile* of a node $v$ is the sequence of sizes of its neighborhoods $|N(v, 1)|, |N(v, 2)|, \\dotso$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.8.2 The Diameter of a Graph\n", "The *diameter* $d$ of a directed graph: $\\max (\\operatorname{len}(u, v)): u \\in G, v \\in G$.\n", "\n", "for each node $v$, we can find the smallest $d$ such that $|N(v, d)| = |N(v, d+1)|$, and call it $d(v)$. $\\to$ the $d$ of $G$ is: $\\max_{v} d(v)$.\n", "\n", "A graph is *strongly connected* if there is a paht from any node to any other node. If $G$ is strongly connected, the $d = \\max_{v} d(v)$.\n", "\n", "\"six degrees of separation\": the diameter of social graph is six. Unfortunately, not all important graphs exhibit such tight connections." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.8.3 Transitive Closure and Reachability\n", "The *transitive closure* of a graph is: $\\{(u, v) : \\operatorname{len of Path}(u, v) \\geq 0 \\}$. denoted $\\operatorname{Path}(u, v)$.\n", "\n", "*reachability*: we say node $u$ reaches node $v$ if $\\operatorname{Path}(u, v)$.\n", "\n", "$\\operatorname{Path}(u, v)$ is true if and only if $v$ is in $N(u, \\infty) = \\cup_{i \\geq 0} N(u, i)$.\n", "\n", "The two problems - transtive closure and reachability - are related, but there are many examples of graphs where reachability is feasible and transitive closure is not." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.8.4 Transitive Closure Via MapReduce\n", "transitive closure is actually more readily parallelizable than is reachability.\n", "\n", "##### calculate reachability\n", "$\\operatorname{Arc}(X, Y) = \\{(x, y) \\text{ where } x \\to y\\}$.\n", "\n", "\n", "SELECT DISTINCT Arc.Y\n", "FROM Reach, Arc\n", "WHERE Arc.X = Reach.X\n", "\n", "\n", "how many rounds this process requires depends on how far from $v$ is the furthest node that $v$ can reach.\n", "\n", "\n", "##### calculate transitive closure\n", "recursive-doubling method\n", "\n", "\n", "SELECT DISTINCT p1.X, p2.Y\n", "FROM Path p1, Path p2\n", "WHERE p1.Y = p2.X\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.8.5 Smart Transitive Closure\n", "The above recursive-doubling method does a lot of redundant work, since there may exist many paths between two nodes.\n", "\n", "_smart_ transitive closure: \n", "Every path of length greater than 1 can be broken into a _head_ whose length is a power of 2, followed by a _tail_ whose length is no greater than the length of the head.\n", "\n", "$Q(X, Y)$ holds all pairs of nodes $(x, y)$ such that the shortest path from $x$ to $y$ is of length exactly $2^i$ after the $i$th round.\n", "\n", "Intitally, set both $Q$ and _Path_ to be copies of the relation _Arc_.\n", "\n", "On the $(i + 1)$st round, we do the following:\n", "\n", "1. Compute a new value for $Q$ by joining it with itself: \n", " \n", " SELECT DISTINCT q1.X, q2.Y\n", " FROM Q q1, Q q2\n", " WHERE q1.Y = q2.X\n", " \n", " \n", "2. Subtract _Path_ from the relation _Q_ computed in step 1.\n", "\n", "3. Join _Path_ with the nw value of _Q_ computed in 2: \n", " \n", " SELECT DISTINCT Q.X, Path.Y\n", " FROM Q, Path\n", " WHERE Q.Y = Path.X\n", " \n", " \n", "4. Set the new value of _Path_ to be the union of the relation computed in step 3, the new value of _Q_ computed in step 1, and the old value of _Path_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.8.6 Transitive Closure by Graph Reduction\n", "collapse an SCC (Stronly connected components) to a single node when computing the transitive closure.\n", "\n", "to find most of the SCC's in a graph by some random node selections followed by two breadth-first searches.\n", "\n", "Let $G$ be the graph to be reduced, and let $G'$ be $G$ with all the arcs reversed.\n", "\n", "1. Pick a node $v$ from $G$ at random.\n", "\n", "2. Find $N_G(v, \\infty)$, the set of nodes reachable from $v$ in $G$.\n", "\n", "3. Find $N_{G'} (v, \\infty)$, the set of nodes that $v$ reaches in the graph $G'$ that has the arcs of $G$ reversed.\n", "\n", "4. Construct the SCC S containing $v$, which is $N_G(v, \\infty) \\cap N_{G'}(v, \\infty)$.\n", "\n", "5. Replace SCC S by a single node $s$ in $G$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.8.7 Approximating the Sizes of Neighborhoods\n", "approximation:\n", "\n", "1. apply hash function $h$ to nodes $\\{v\\}$, find the longest \"tail length\" $R$.\n", "\n", "2. estimate the size of the set is $2^R$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Exercise 10.8.8" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }