{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import pandas as pd\n", "\n", "import numpy as np\n", "from __future__ import division\n", "import itertools\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "plt.rcParams['axes.grid'] = False\n", "\n", "import logging\n", "logger = logging.getLogger()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5 Link Analysis\n", "========\n", "\n", "### 5.1 PageRank\n", "#### 5.1.1 Eearly Search Engines and Term Spam\n", "**inverted index**: \n", "a data structure that makes it easy to find all the palces where that a term given occurs.\n", "\n", "**term spam**: \n", "techniques for fooling search engines.\n", "\n", "To combat term spam, Google introduced two innovations:\n", "\n", "1. PageRank was used to simulate where Web surfers. $\\gets$ random surfer.\n", "\n", "2. Use those links that links to the page. $\\gets$ \"vote with their feet.\"\n", "\n", "\n", "#### 5.1.2 Definiton of PageRank\n", "intent: the higher the PageRank of a page, the more \"important\" it is.\n", "\n", "**transition matrix**: \n", "to describe what happens to random surfers after one stop. \n", "$m_{ij} = \\frac{1}{k}$ if page $j$ has $k$ arcs out, and one of them is to page $i$. \n", "Otherwise, $m_{ij} = 0$." ] }, { "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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ku7vbd05yYGAgRqPxhu99VVUZHR2lubnZN1Hr3LlzrFmzhkceeQSz2XxLm9JY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig_5_1.png'))" ] }, { "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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HpLTxPy0E/QGuNcpKlaPEIiFkUyqlJTI2s4GzySHVeBj/cD8dnT14IwJmVwp2UcWamo7L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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/eg_5_1.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PageRank $v$ simulate random surfers: \n", "\n", "1. start at a random page of all $n$. \n", " $v_i^0 = \\frac{1}{n} \\quad i = 1, 2, \\dotsc, n$.\n", " \n", "2. randomly choose next page linked. \n", " $v^{k+1} = M v^{k}$ \n", " give us the distribution of the surfer after $k+1$ stpes." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5 , 1. , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0.5 , 0. , 0. ]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# eg. 5.1\n", "matrix_5_1 = np.array([\n", " [0, 1/3, 1/3, 1/3],\n", " [1/2, 0, 0, 1/2],\n", " [1, 0, 0, 0],\n", " [0, 1/2, 1/2, 0]\n", " ]).T\n", "\n", "matrix_5_1" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.25],\n", " [ 0.25],\n", " [ 0.25],\n", " [ 0.25]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = matrix_5_1.shape[1]\n", "\n", "v = np.ones((n,1)) / n\n", "v" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.375 ],\n", " [ 0.20833333],\n", " [ 0.20833333],\n", " [ 0.20833333]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def dist_after_surfing(M, v=None, steps=1):\n", " if v is None:\n", " n = M.shape[1]\n", " v = np.ones((n,1)) / n\n", " \n", " for __ in xrange(steps):\n", " v = M.dot(v)\n", " \n", " return v\n", "\n", "steps = 1\n", "v_ = dist_after_surfing(matrix_5_1, v, steps)\n", "v_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Markov processes**: \n", "It is known that the distribution of the surfer approaches a limiting distribution $v$ that satisfies $v = Mv$, provided two conditions are met: \n", "\n", "1. The graph is trongly connnected. \n", " namely, it is possible to get from any node to any other node.\n", " \n", "2. There are no dead ends.\n", "\n", "eigenvalue and eigenvector: $Mx = \\lambda x$ \n", "$v = x : \\lambda = 1 \\text{ and } \\sum_j x_{ij} = 1 \\text{ for every } i$.\n", "\n", "$v$ is a [stochastic vector](http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/lecture33.pdf), and $M$ is a [stochastic/Markov matrix](https://en.wikipedia.org/wiki/Stochastic_matrix).\n", "\n", "**Iteration** $O(M^2)$ is better than **Gaussian elimination** $O(M^3)$.\n", "\n", "in practice, for the Web itself, 50-75 itreations are sufficient to converge to within the error limits of double-precision arithmetic." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.33325195],\n", " [ 0.22224935],\n", " [ 0.22224935],\n", " [ 0.22224935]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# eg 5.2\n", "v_ = dist_after_surfing(matrix_5_1, v, 10)\n", "v_" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.33333333],\n", " [ 0.22222222],\n", " [ 0.22222222],\n", " [ 0.22222222]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v_ = dist_after_surfing(matrix_5_1, v, 50)\n", "v_" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.33333333],\n", " [ 0.22222222],\n", " [ 0.22222222],\n", " [ 0.22222222]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v_ = dist_after_surfing(matrix_5_1, v, 75)\n", "v_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.1.3 Structure of the Web\n", "Some structures in reality violate the assumptions needed for the Markov-process iteration to converge to a limit." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fs1qtKIri8akTWZZ58sknvT4j39nZSWpqqggfgnCJm+6ZD4DIyEhGRkambXxh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37Ee3xBisKEdOggogEIpGQrc+PPHmh4xqd+QT/C6qGvzYbKdRcHsKqvJdz4lA4G6o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\nfIiIiIhRaj5ERETEKDUfIiIiYtQfrkksczlYDDoAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (10,10))\n", "plt.imshow(plt.imread('./res/fig_5_2.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Two problems** we need to avoid by modifing PageRank:\n", "\n", "1. the dead end.\n", "\n", "2. spider traps. \n", " the groups of pages that all have outlinks but they never link to any other pages." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.1.4 Avoiding Dead Ends\n", "Dead Ends $\\to$ $M$ is no longer stochastic, since some of the columns will sum to 0 rather than 1.\n", "\n", "If we compute $M^iv$ and $M$ is substochastic, then some or all of the components of the vector go to 0." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sy1gsFi5evEhNTQ01NTXU1dXR29uLyWRClmXPozni4+OZPn06WVlZpKenk5CQ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\niJB0BLR3onhlpKNpMeGsqyFz4Sfkdhw5ZpdyOkyDAc2R1iAF0jcqhEG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# eg 5.3\n", "plt.imshow(plt.imread('./res/fig_5_3.png'))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5 , 0. , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0.5 , 0. , 0. ]])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = np.array([\n", " [0, 1/3, 1/3, 1/3],\n", " [1/2, 0, 0, 1/2],\n", " [0, 0, 0, 0],\n", " [0, 1/2, 1/2, 0]\n", " ]).T\n", "\n", "M" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 2.55407417e-08],\n", " [ 3.72237693e-08],\n", " [ 3.72237693e-08],\n", " [ 3.72237693e-08]])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist_after_surfing(M, v, 50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Two Solutions\n", "###### 1. Drop the dead end \n", " recursive deletion of dead ends, and solve the remaining graph $G'$. \n", " then we restore $G$ from $G'$, recursivly. \n", " $$e = \\sum \\frac{v_p}{k_p}$$ \n", " where $e \\in (G - G')$, $p \\in G'$ and is the predecessor of $e$, $k$ is the number of successors of $p$ in $G$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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1z0rCWQgr8PT05KWXXkKr1UqT0AFcD2eTyWTrUm5LwlkIK5o5c6Y0CR2AQqFA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\n2f8h5I3vmT2qBwJBJQ5KTFbK7dcUSHsx2+PPcmBTOL2XKhC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# eg 5.4\n", "plt.imshow(plt.imread('./res/fig_5_4.png'))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5 , 0. , 0. , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 , 0. ],\n", " [ 0.33333333, 0.5 , 0. , 0. , 0. ],\n", " [ 0. , 0. , 1. , 0. , 0. ]])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M_G = np.array([\n", " [0, 1/3, 1/3, 1/3, 0],\n", " [1/2, 0, 0, 1/2, 0],\n", " [0, 0, 0, 0, 1],\n", " [0, 1/2, 1/2, 0, 0],\n", " [0, 0, 0, 0, 0]\n", " ]).T\n", "M_G" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5, 0. ],\n", " [ 0.5, 0. , 1. ],\n", " [ 0.5, 0.5, 0. ]])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.preprocessing import normalize \n", "\n", "index = [0, 1, 3]\n", "M = M_G.take(index, axis=0).take(index, axis=1)\n", "M = normalize(M, norm='l1', axis=0) \n", "M" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.22222222],\n", " [ 0.44444444],\n", " [ 0.33333333]])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = M.shape[1]\n", "v = np.ones((n,1)) / n\n", "\n", "v_ = dist_after_surfing(M, v, 50)\n", "v_" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.24074074])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# the PageRank of C, whose predecessors are A and D.\n", "1/3 * v_[0] + 1/2 * v_[2]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.24074074])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# the PageRank of D, which is the only one successor of C.\n", "# hence, it is the same with C.\n", "_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###### 2. modify the process of moving\n", "\"taxation\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.1.5 Spider Traps and Taxation\n", "**spider traps**: \n", "a set of nodes with no dead ends but no arcs out. \n", "they cause the PageRank calculation to place all the weights within the spider traps." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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reNasWRQXF7N582aZlSmGRFRUFGFhYRQXFzu7FHENJFSF+Dvd61jnzZvH8ePH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\n40nj7kcYTJw4Ufa409FkIarnENwvTuXth65hTkQA5Y4obnvwPvrF+Z2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig_5_6.png'))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5 , 0. , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0. , 1. , 0.5 ],\n", " [ 0.33333333, 0.5 , 0. , 0. ]])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = np.array([\n", " [0, 1/3, 1/3, 1/3],\n", " [1/2, 0, 0, 1/2],\n", " [0, 0, 1, 0],\n", " [0, 1/2, 1/2, 0]\n", " ]).T\n", "M" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.],\n", " [ 0.],\n", " [ 1.],\n", " [ 0.]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.round(dist_after_surfing(M, steps=50), 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution**: \n", "allow each random surfer a small probability of teleporting to a random page. \n", "$$v = \\beta M v + (1 - \\beta) \\frac{e}{n}$$ \n", "where $n$ is the number of nodes in $G$, and $e$ is a vector of all 1's." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.10135136],\n", " [ 0.12837839],\n", " [ 0.64189186],\n", " [ 0.12837839]])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def dist_using_taxation(M, v=None, beta=1, steps=1):\n", " n = M.shape[1]\n", " \n", " if v is None:\n", " v = np.ones((n,1)) / n\n", " \n", " e = np.ones(v.shape) \n", " for __ in xrange(steps):\n", " v = beta * M.dot(v) + (1-beta) * e / n\n", "\n", " return v\n", "\n", "dist_using_taxation(M, beta=0.8, steps=30) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although C gets more than half of the PageRank for itself, the effect has been limited.\n", "\n", "**Note** that for a random surfer, there are **three path** to move:\n", "\n", "1. follow a link.\n", "\n", "2. teleport to a random page. $\\gets$ taxation\n", "\n", "3. goes nowhere. $\\gets$ dead ends\n", "\n", "Since there will always be some fraction of a surfer operating on the Web, so even if there are dead ends, the sum of the ocmponents of $v$ may be less than 1, but it will never reacher 0." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.1.6 Using PageRank in a Search Engine\n", "1. find the qualified pages, which have at least one of the search terms in the query.\n", "\n", "2. calculate a score for those pages, including PageRank." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.1.7 Exercises\n", "\n", "###### 5.1.1 \n", "略\n", "\n", "###### 5.1.2 \n", "略\n", "\n", "###### 5.1.3\n", "$n$ nodes: 1/n \n", "the additional node: n * 1/n * 1/n = 1/n\n", "\n", "###### 5.1.4\n", "todo\n", "\n", "###### 5.1.5\n", "略\n", "\n", "###### 5.1.6\n", "the first node: 1 \n", "the left nodes: 1/2\n", "\n", "###### 5.1.7\n", "root: 1 \n", "height = 1: 1/3 \n", "height = 2: 1/3 * 1/2 \n", "height = k: $\\frac{1}{3} \\times (\\frac{1}{2})^{k-1}, k > 1$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Efficient Computation of PageRank \n", "PageRank: matrix-vector multiplicaton $\\to$ MapReduce. \n", "However, we must deal with two issues:\n", "\n", "1. $M$ is very sparse. \n", " list its nonzero elements.\n", "\n", "2. we may wish to use a combiner to reduce the amount of data (Map $\\to$ Reduce). \n", " striping approach." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.2.1 Representing Transition Matrices\n", "The proper way to represent any sparse matrix is to list the **locations** and **values** of the nonzero entries. \n", "The space needed is linear in the number of nonzero entries.\n", "\n", "Represent a column by: \n", " 1. one integer for the out-degree, \n", " 2. one integer for rowname per nonzero entry." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5 , 1. , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0.5 , 0. , 0. ]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix_5_1" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " A B C D\n", "A 0.000000 0.5 1 0.0\n", "B 0.333333 0.0 0 0.5\n", "C 0.333333 0.0 0 0.5\n", "D 0.333333 0.5 0 0.0" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import string\n", "\n", "df_M = pd.DataFrame(matrix_5_1, index=list(string.uppercase[0:4]), columns=list(string.uppercase[0:4]))\n", "df_M" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
DegreeDestinations
A3[1, 2, 3]
B2[0, 3]
C1[0]
D2[1, 2]
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" ], "text/plain": [ " Degree Destinations\n", "A 3 [1, 2, 3]\n", "B 2 [0, 3]\n", "C 1 [0]\n", "D 2 [1, 2]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def compact_representation_of_sparse_matrix(df):\n", " \"\"\"It is introduced in Example 5.7\"\"\"\n", " \n", " degree = df.apply(np.count_nonzero, axis=0) \n", " \n", " dest = df.apply(np.nonzero, axis=0) \n", " dest = dest.apply(lambda x: x[0])\n", " \n", " return pd.concat([degree, dest], axis=1, keys=['Degree', 'Destinations']) \n", " \n", " \n", "compact_representation_of_sparse_matrix(df_M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.2.2 PageRank Iteration Using MapReduce\n", "estimate: $$v' = \\beta M v + (1 - \\beta) \\frac{e}{n}$$\n", "\n", "if $v$ is much too large to fit in main memory, we could use the method of triping: \n", "break $M$into stripes and break $v$ into corresponding horizontal stripes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.2.3 Use of Combiners to Consolidate the Result Vector\n", "There are two reasons the method of Section 5.2.2 might not be adequate: \n", "\n", "1. We might wish to add term for $v'_i$.\n", " \n", "2. We might execute the iteration step at a single machine or a collection of machines instead.\n", "\n", "Hence, we need to implement a combiner in conjunction with a Map task.\n", "\n", "**thrashing**: \n", "repeatly read some components of $v'$. \n", "An alternative strategy is based on partitioning $M$ into $k^2$ blocks." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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nFe5sn0h4UkfqWjBSpmnHUqN/r+r7FDnG6JZvMe3j13gw+PytD+NLJIcFP2/C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\n7psCEPDx4fM2ctjbKtC+D+v4XuwaP2dNjcE6qBKqLucBHBA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig_5_12.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each task gets $M_{ij}$ and $v_j$. \n", "Thus, $v$ is transmitted over the network $k$ times, but $M$ is sent only once.\n", "\n", "The advantage of this approach is: \n", "We can keep both the $v_j$ and $v'_i$ in main memory as we process $M_{ij}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.2.4 Representing Blocks of the Transition Matrix\n", "for each columns of $M_{ij}$, we need list its out-degree and rows of nonzero entry. \n", "And it might lead to that the out-degree will be repeated as many times as the out-degree itself." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jCzX/yB9VTNaQE+DtAUYgnI6Bbd9/0ZGiGDCbD9pj1UxcXDile/ZTWBiLOjCN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\nw6K/PMZ766qQxDIO5tcQnRzMqpdnsSyvnubWAzR7RJIzBxB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VbGLmW7P5651L6JT/e/bn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fDNB33BQjTsWs7Tf51JZUs9h6qPMvGJD3n5niFIpztk1UPp8tm8+sEiqlweOkJFPPXsbxhfmMTJ\nualKZ+thZr3wLLOXH8QYbSZt0DV8777vMDg94hIdWw+hBulw+DBbzBj1X15Z/vb9vPyXd7ENupP7\nb+3HpUqlVDlIe+Nhtq5eytzP1lLR4iY+KYGg14Ndk8F3bxvCocf/hO3lz/jVJU4Kyj97jh//fQEB\nazJPz5zLhGTjOfdRgrW8/qMfslyjRysHMYRbsBnNSKqHTn8Qky2fSVddw9WThpAcHXbmOhKQAz68\ngRA6kwXT+SQkX1PI28bG+W/x94VN3PbYf3dPUiA3M/uZP/D+4mVUD3qM0pkPEH6uhoziYO3MZ3lr\nw0EcngDacDNxYVYURUZR22kPxVM8cDw3TZ9KcX4ChkuZGKiXDUW1ly1S73/wO+q/Fm9RnUFFlQNu\ntXL5c2pyUpL6yp72s+/uPqL+vx9MU3/+0mdqqzt4lg1l1e9zq02V69Rf3nutmjngIfWjdQfVtg67\n2lBzQF3y+k/VSQNz1H73/1Hd1uj6Ro/w28pesV1duXKJeqDVf8H7tuxbqy5du06t6gic8KpP/fC+\nq9T83gPV1/d2fnOB/ieCTerrP7pXnfLDF9UtpRvUH33/fvV77+1SFeVMOyiq3+9Rqze/qd41bZCa\n3GuU+uaqMtUbOnmrkM+hLp/9RzW5Vy918NW3q6+uPKC2uzxqIHTGN75y+evUd15drJZWtqjyCS+3\n7XpDHd5/sHrbA3NU9yUKRQ761aP71qhPPvqQOnLEjepTz32kHm5xHovLr5avekG9aVCBmpZxvbqu\n0XeJovpSwN2qrn3nd2rJuCnqvArnee4VUttbatU5f75d7TNsvPrXRXvVNkeHam9rU2vLtqov//4n\n6pCiCerPX1yiNroCZ32n9sod6qoVi9X9X6NOOG9yQD28/TP14WsHqUWT7lHfWFl5Urm4dGTV46hV\nX3tgmJo76W9qa+h8opBVr9ells79g1pSlKM+9NJKtcPZoba1taltzTXq4nf+rA4vLFBve/BZtdwR\nOvfbfYMunzkFoU7WLl2CL34gJQX5WHUSGn0YvZK+aG2d41DD0njo5kFsn/cpZY0OzjxkrMFgDCM+\nPYeC6HgibRaiosKJtEWRmJrP5Pv+ys+mpOLa+D4fb6z/Bg/w20qm/Ug5lXtLcQUvdEwvRHP5Xg6X\nVeAJnfi6kRE//hn33/8TRiZf2hbWGakh2lWZAb0TSUkdzP888TR/uq7w9L0EAEgYDHqctU7io+OI\niGzmqL2DoHzCOVJl2mp2s2rJWlLjIkhLyaWkfy6RFjP6C+xxuRIEHEfZuKaKljY/J5a0iOxx/Oq/\n7uauB/tzSfqUVJn2ml28+OyzfLzZz+2/eZwf/+AmMmOtx2oZA7njvsNtA9OxFI0kO/LSDwPpjFbi\nYsMvcC8tZiM0llYQHZnBqMG9iY6wERUdTXLvEh742X9x3dhIFnwwj7K6duQzvk9XnVCxtxRn4GKN\n86t4246yZdki9tmNqM2dNDZ0EDr3jheBBnNENJEWHRrpfLvfNZhMBtqqKggForl6dD9sVhvR0dFE\nx6UwaNgYJmV1YPccpK4jcJHjP9ll07sdaKtgywEoKikmK/HLi+GLqYM6grTXVdHoDGKNiiM+Lgrj\nKXlCcsltFPgfZsOBRkrSo0/ozj4NVen6d8JndNETFReJqrbh9p182SgBD831NdQ1d6KxxJGdnUy4\nyUDIZael000gZCChVxSuhhravArWqDjiYqIwakH2ueno7MTpCRGdEIOvqY62oJ6ktDRsRg2qIuNq\nq6e6pgGfZCEpLZXE2Ai0gOJzUltTTYPdiyEimgitTERaLnFmDaAS9Dmpqz5Cc4ePiLgkUlN6YTHI\nODs6cbnd+NQwUnqFUX/4CE5ZS2RsIslxEaCEcDQcYO2K5ezqiCfPacdusGAJt2DUawEVt72WQxUN\nBDUmEtIzSY0LR6Kr67Xt6C5WrlhHZcQgBnW2YZfCCI+wQsCJNqGYW28OYgv7skJVlSBOexNHjjbh\nUQwkpqTSK86GQSMR8nZi73DjdXuxpqRj6jxKVbMPiy2S+MSEM84nOZHsbedwZTWtLgVbXCJpaUlY\n9RJywI+n00EgEMTlddPR0U5afCyWc80bCXVQeshE8dAplLXNpa7JSTAkg6Frv4CniXXvLyKQNZHe\nlYvQ9+pPiu3i3EBUVaWjrorq+jYwhdMrLYX4yC9uYioeRwu1NfU4vCEiElLJTo1Hp5FQZS9tzR34\nQjJaUzjhhgANDa2oxggSE2IJDzMiqUEcbR24fV58qpWMZBM1h6pxYyA6NpHEGOsJY9AyzrZmamrq\ncId0JKZnkxxrRXusu1WVZex11RxptKMx20hKSyY2wkygs4lNCxZT3u6lw9eJvc2E2RqJ1ajQ6TFS\nctV1SMZItCj4vW4c7Z34ZA0RNishdzstHR6M4TGkJMZg0H154cshLy31dXT4wBYdjc7fxv6yOiwp\nuRTlJJ12OCzos7N61nN8tKmZGx/+KXdfM4CIr3xtEeQPjyTHNYiosw4KqwTc7dTW1GF3BglPSCYj\nORajrusNAy47bR1eQrJKeGw0ofYGmjplbLFxxMVEYjwpvhD2hgYa253ozFGnJNrnQyXgqGLLNjfW\nYcPJij55foY2PJkRGTYWL9/B0bZOQkr8V8a71S/qhJXL2dUWQ67Tjt1owRIednzIR/F3cuRwFQ3t\nASzRcWRmpRNhuLAkWAl6qdy1nu1lOu64YQoLXt2K7PMjq3DWCQ+qgtdp50hVDZ1BHXFJySTFR2PU\nSaAG6bQ7cHs9+FQLaUlmjlZU41L1RMcm0is2/KS3lgNu7C0tXd9brIWgRjn7Z58q2MzW7bV44sZQ\nmBh2wrH5aKgqZVdDBLb0TBJsl3aezGWSFKi0Vpdid2jpE59C+EkFTAeqyup3nqc9tzcpFh91BysI\nLxzL1KnjSQr/8oRrrGmMyzExc/Mhvn9VPgbt+VfQXflwiNbK7Xyy4jBGfR9KCuKO/93fUc+65QtZ\nX24nKSkRx4GFLEgayN33TsZ6dDN/+fdCfEE9KRlJhIXHEKXxUXewnvQxVzFl8iisHZXM+fBTtu13\nMHRkDuUHtlPfLJE6+of8z92FHN2+lFkLN2JMzCHS52ChXcfom69jZI6GRXM+od5lIDExkdCB9axe\nu4fJv32RG/NMuFsOs+TNd9nTYSY9J4LWVQuJzh/LtIn9qd84n09XbaPRE83Q3hrspjySzc1sOuBm\n4q0PMDHVz/p57zJ/0wbq9flEf/QO+xJymDh5LLkp0bTtfoVXZu8iqf9VGNtreOPj+QyZfgffGZGB\nq/Ewqz+ZxaJdO3DFaIiZrRIVX8j0GWMxHF3PszOX0en0MeO3f2NqVhhKwM3+bav5aPVuLPEZJGpa\nWbm0nbwRM5g0tC+Bik38852lNLc4SBo5Dl1lC8mF0dj3l2IpupabbhpDzFmGVd21u3ju9dl0RubS\nL95A67pPUOOLmT59OrHeKpYt+ZBNZYeob1pLjL+FMTfdwej8hLNOggx11HHUaCU3N40syxKO1LcR\nCMnHy2TV+rf43JPF5OE+npxrZkLf3tguSt+dl50LX2fu6oPE9h6MCSf7F2q5esaNTOkTRf2eFSxY\nsImALZ1e0VrKP5yLpu9V/OCusZgDdla/+09WV7qwWOPIzbASMkXiaGlASRjAbdPGkRUbYt+KD5i3\ncT/twUTG9lFo0ucSrWmktF7HlJvvYlJhLCg+qrasZP78LciJqUQbWvlkXoAJtz7IhKJeaFQ3W+e/\nzqKN1cTl9UcTclCx2ML0q8cS3bCMt96dR+XRKFaviKZ6q5n+M+5iTIaPxa/+mU31GhLyb+IXPxxG\n+9F9fPr+R+xu1JCRaMUan4jVrLC/vIH00bdy/8RCTHoNQXctn736BtubjKRn2mgpq6Qj2kRtWQMZ\nQyYTk3QDmeGnVpEq9so1vPb+BhJTr+O624ecJiHoEpk1iXsj89Frzvyluuq3sHTBHOpCacRZTOyY\n+ynhA6bwoxlDiDLqqN+1mGff24CiMRCX1xer20+kzU9znZuiyTcxfkQ+Fh0onnqWvf0hq/cH6Dc+\nF7mlls2bNwEX8IiZCh01u9mjhjF4SH9izlj9BfCF5NM8VaHibq9n/fz3mL9xA7XaPKI+fofShBwm\nTB5LXko0/sYDvDLzA6p1qQxNi6R90xwWGXO4/tY7KIgPO92HnYaCq62S1QvWkHztzxhl3sx6bQeu\nNjseBcxniltVaG84wKtvzKXTlkausYUVC+rJHH49k8eOINro48Caj/l03R5a/XGMLlBpMvYmQdfI\nzmqFq265h6l94wAFR91BVi79jHKHiZTEWLxV5WwttRO4gPt3oKmCHfVuNP3yidQreL1eQp529mxc\nwHsfLiSQM507b7yeLNulvU1fJsMHMq1VjcgmCVti+CkTjbpKbl2nnryiYkpKBpMZK7N59ovMWbCN\nzpMa82HkDUmldncNnvN9PLFpO3Nm/Zvnn3uOxx97nP9+4ikWSpN4/ImfM70opiuCYCdb1i3i7x+v\nxx9XyPiJExg/OI6Vn77FR5sOIUWmMjAVFi34hCUH/eQXD2LokP7Eqi3MfeZfzFu6G785hpxkK4f2\nreff75WRnN8P3a7lfF7VjKtxF08++zKb3AmMnTCRCSMLcdd9zjufLmXX1uXMW7gbc0Ifxk0Yx+hh\nQ7HVrKWyw0/I52TLR//g3YV7SBkylomTJpAb4WDVrHdYv70BW1oOUYHDbFj6Hstr9fQvGcLQQf3w\nbX+XmR/sJmQIIzW3L7n5vbFGxpCWU0BudioRFiMSPnZ8NJOZszaRPmIMY8eNIMH1OW+8+m/K2mV0\npnAyC4tJz8ogIjaB9NwC8rKTsRh1mGNS6J8fybpFC6hxBkAJ0lC+mbde+5AWfSpjx41h4vgxZFtd\nzJ/5Guv2VYEtmX5ZFjavXMp7/1pFTPEgRpT0JUpTz5y5c6i0n6ULzlvNS394mrWNFkaOHsukiWMZ\nlJ/MkQ1zeX/OUhy6CFKzs0mIspGbnkFeQQGJNjOaM48dANB+pBx9ZJD4vGwK9Cbayupx+7uab6Hm\nz/nHy61MuWcyoerdBOLC6dsn+aJMkmva8i5/+r8XsMcPYMLE0fRO0LHxjXdZ9Nl2jlZ8zkdvzOaA\n3UK/kWMZO2E8IwfG8/lLz/LM4oNo9OGkZmXiP7yMJWvWUG9IY8jQEtINzaz9ZBG7y1uQJRNJ2flE\nOHezbP7brGiJYvDQoQzIT6V542zmLCwjgErb4a189OYblNp19B89nomTJhDRsIjn//wxDT6Zuo1v\n838vvIGz1wAmTBxFZkSQta+9y7LVB9AnFVDcO5mYiFjSUrPond+bhHAjSGFkFPRD17yJtbuaUCQt\nlsgEEiK11OyYx5Jd1RiT8xk6dAhRzWt567XV2H3BrvOyZwH/mvkxuuxBDOnfG8V5mJW76uk77mrG\nDcjBovtq9aiqKnXbV7I/YCN75FSK408/eRkgYdDNTC5IOMvs8RC1uzcxd+Y82rWxDJ0wjv6x7Xz8\n2rOsr+pABazxGeTGK6yY9xlrVlSQOmAww/pnYq/ewqK1m2l2h0BxsPpf/+Lvs3cR06eIoSUlDCzK\nwqY4L6icqKpC9fb1BKwmhgzO+mqLUXZS3+jD47MSZtCfdqKhVh9Gam4Rufl5J9UJtjAjkq+Od5/7\nB4sPyQwfMZpJk8YycnBfnPs+49XXZ9PgO786Vwn6KF0/i82Wodw6tTfhFjM2m5eg4iF0lrdQlQAN\nZat49ZMVNEf3YeKE4UQ665n95qd8XtGCIhlJzMzD5tnP6kWzWNYYzuChQxnUN4eOLe/zwdx9+AG/\nvYqlc15l/uZDRGf2YXDJQIryEvA2aVGC53u2obF8J00uB8bOfXz8/ru88847vDXzNf78vy+xpdLA\ngz/+PjPG5nHuKaLfrMskKVAJ+hT01nDMVuMpPTgySBJT7ryPacMKycgpYuKNt9E3U8uSlcsorXef\nsK2G8Egrms7Q+T9brI0nM7eI4uJiBham4Dq8G197O9mjivgiwfO2VrNz7QK8pmoXabUAACAASURB\nVHgmjx1ORq9EiidPZKipg027j6CNLeDWaYPQGYzMuPs+rhnZnz4Dh3LDfbeQl9jOktWrqPZHMXLE\nABLjjMQPGMYtN9zL7/72Ak/dM5Cj695mc1kTV107g5KcXqT16cvIvil0Vhyi4mgLsreBrVs2s2V3\nOYGI3tx2/w/o38uEp+MQ77+9Hk/ueK6ePIheCRkMHjqSKKWdyiP1xBaO4urxRdisBUy5/V4mDMgh\nPW8o04am46jpxBARR9GQ4eSlJxCVnEbJuMlcNXYwvaIsSIAhbiCFY24gMz6amIRsxpXk4j28kyMd\nQawxSRSXDCUjKZa49GyGjp/CVWP6E2M1YUst5o47p5MGaDUQ8nayb9XH7G7yMnX6tQzJSSEpsz9T\np16F1HGQD1fsJmjL4+Y7biBLpyN30o3cfdsYcnN603/0aGLkNlyBM/el1m+aw8zFm5l4x/1cOyCL\nuLgUBo++hoE5VpYuX0mp3UzJiPHkpyaTW9SHCVOvojDZxtmH/QPU7GrE5tfSKyaOpGQ9gfomXIEQ\nKk7m/vz39LrlYQZG+Ti4cS8xEXnkp544BizjOLqPNdsq6PR8WdOoioc9Kz7ilRdfZuZ7SzjU0HmO\nAtrB0n++zE7nGB548C6KslLJzevLzdOG0C/NxMF161iyU6HP+GkM7ZdNXEIaY2+9g0lx5bz/l9ep\nkyPoP+Faxg/KIj5lFNOun8HAPkWMGFxMssmAzxlAxUDm4ElMH5+HXlfIdfc9xJjiHPIKhjC2qBfO\nBiey4qJ0y2aW7/GRO24i/fPTScgYyLUTh1GzfQ21nlaWPP8qZcFx3HvvbRRmplJY2J+bppZQmJlC\nVp8RDC7MxBaTQvGQUUyeNpn8RAuSLpKh0+5iysBkCGmQ0BARn8XICWPok5lL36HTmDJhJPn5A7hm\ndCFKS1dXPED9zpU06wuZfvN4igb0Z+jYISSE9GT0HcbYYf2INZ2melQD1OwvxRIRxrDJxYSdpQzo\nrDas55g2rrMmk1J8Nbl5BcTGpjB62ACsrQc42NSJqkJs7lBuueUa0sOjKJk6gxlTSigYMISiwiz0\nwU78IQVP3XbeWbQM84hruOfuq8hKTia/ZAI3ThsGnDq8eWaq2s6uz/YQZixkQG7kV/7ub65gW20b\ndmMOieFhp0l2JMwRsRSVDKd3RiJRSakMHnusToi20LJrGR8uXcfg6bdy09A8YiJjKRw6jSnDM1m7\nbBGr9rWeV5zuhq08/+4GBl0zAbPXjsvnQta3Y3c24fCceaYDSJhMVob378/4gmQSUvIp7FdA0N5C\nbV0HMgbSB4xn2vgCzMYCpt/zIOOKs8nJH8qk/il01jlRCFK7eyvLPtxLfN5VzJgyit7ZOQy74WbG\n9bZhOO+lbrwc3LEXlyONe2+YxKDiYoqLiykZNpY7bphOhr2BXZu24uyGpXMuk+EDQMtZU5yoKOux\n/5IwWaOJ7hVPc2UzjS1uSD3xMRYZLJrzz5aiUhlYMoKxRb1QAwPpbTrK1J99yt/e3cqsR0ejB4Je\nHz5HJw07VzHzOTerE+Ig6KdZ1RNvMqMBZFVGo5HolRBxLKnREZOSTnrfZNaWN9Pc5kWJ7KrM+vRL\nwmyykDhuKqgqG+c34etoYdmLj+HYmIPqC9FRU01UVD+SCkYyrmgjry1+k32bFhIZEY6u37X8/QYj\nSquDlho7VepCHv99C+lGlZCnnSZtNAWRXV15RgNIUYMoSbF1TaqTtIRHmZDQdM0NUFUUVUVVFRT1\nxBJsYPBtD3GrcSl//O4ddFozCCtfBVI0KF3bqap67J+CyilZmP7Lfjg5GMTRXE/IYMVq/bJlZo1N\nItliZnezE39AhggjIDHy+mGYATRatKawrslnZ6m8O+tr6EQlJubLRwD1ZgsJCUnoXEdp6/ADKjIq\n8uliPZ1gO2XNYaixKcRarKQVJWFaWUN7wE/Dyn/zZswNvH5DNv4jq9h+QCFi+mBSrF39BLKjmmWL\nl7H60yXUF97Gk5nJRIR1nY+t/7yP2ZHf4+5hKezauILf/2UD9/3wp0zMjT59HL4m1mxpRNN3ANnR\nXdPw4jKLueeXaWhNsOb1JbQG9JgtJo43jLXR5A1Kx/dyBR0hSJTAaA4nKr6YvJiu9zCFGTCY9EhI\nx0+tyQBSzAhGpnaVHY1WizXCiNShQaMGcbe7cDVUMvfj16jduwSbTsLf3kF0RgLaQBNrPm9BN6qY\nzCgDoNKrdwn3/7I3+vAYTJKKBhUJBemU8y9JYDBInDjLTKcFXXgaSb0yiQvrquasNhMarfbLeCNi\nCAYrqG500jfFi8PRSshsIDw8rOvZ8dNRPdSVHkGnSyE26syPv9WtmclWyyimFGcSdsb5LFpS+49i\nmjvEZ5+8zIKZRqwtZdjbnEiyfMLBGbFGWug3urCr1ajXozcY0QUACdoO7uaoy8HwQdmEH4tbkiRM\n4Rf2SKvacYjV5QFMY0aRFX7q8ctUblnJ4ZpKiq+7i8x42xl7tVToqhO+eOb+GFdzPZ3BAFFRXya/\nWr2B+ORMrL79NLZ6ziNKL8ue+wPbanWY3n+eP2hVXO3VlHb4yAq4CQYVOENkkkZPYv4E7prgZuWr\nv2alrOBzNlHpSUCRlOOlymQAKXoYw1Otx/bTYo00ITk0SLKXozW1HHJamZGWTqTp2GdpTETHa9B0\nnMchAPia2FHagiO1hPHDR9E3yXasXKrkJ4dzaPFrrN24jKvvuoGEXpd2svXlkxScg+6EBy0kSYNW\nY8AvB/F+ZZjADL4LmC2i5fgMdK0hnILxMyiQ36dywyGcj44mmq7FaRQ5SPagUdx83/cojDF1XTn3\nKBhtCViMWrouh66b5Bc0Oi1agxafrOA/IU7NKU3UUDCAJTKG6d//FVdnR3Q1DVQVnSkcjauJ6Jt/\nSeFkB9XVVexaM5cP5v6Lv/QbzZ+GQtAQQdqgG/n5QxOxHjtFKjpsMTFYtWBXZNCHYdIcSwIAzjLv\nuHnvNjqikkmNg/m//TOv7nEy49EfcdWAdJo/h1+9thMFDSrKV1ow9ds24EwtJCs+Cv1Jn6Ig40NR\nwwgpX+4lB710yEG+HBjounGHnzCoqKKeJdpj74MXgEDoy7uKKofwBDwcb4df4MMAgfYG2iP1xGSl\nYdFoiIqJRk8NtYfW8/5Tdn710aPE6UMcqN3HHn0E1w3KJ/zYZ2gsiZSMm0aUr4znmhQCXxyyXMcn\n/95M/W9+T9/+OcToOzm47RlWLL6aUbkjztDNGMTpB0yG41Wl3mghIckCwdaupA6Zk9uTQdyOZiDj\npNncWr35hDUWFDg1OVJlMFg5uYF97H1VCCkQii7gumm3c9OYHL6Y+vMQRnpFNOMMgGTUH4tTwmAO\nJ8H8xQ0kgATH/+GrYuFGmanjso/9/ZSeIFUFjR69zsCXj8nLJ8WcPHwamt/9kGd/cgef5dg4cDjA\nsFseYWCm7bRnsissK6nFOUgr/GdOHJRGPnpnHxkPjEJ7tu4k2UXpvLm88eJ8rOOm8uB3JtDLs5nS\nXxwlhA6QkZG6zqFGIuyEmdEKX35jcrBrBUWz/j979qK9Yjv70DN29ICvzG0JthxgzqqdlIZG8dSM\nESRFn/+NqnnfdjpsSfgUH6ASlL+8IlVFwed303GeF1j7tld5buUo3nnvbqKPnX7n0R3MeqWVCq8P\njy8AnH5gXw762Lv0df531g76TLqdByb1p2P7Rzg/rkAjAyEFVSOBIoPBcko5/iJmhYAcxKfTozXq\nT2o8Shcw9udtqORAWwcZw4uItZhOOnpVC16/QsjowRs4V+31zbtMhg9AawC7pxOHx3fadlxH8MuT\nG/S4cTU3kBRnJTXh5Gza5WhFNZ3PF6HhdKdPE2YlTFWQj+6k0avic7tot7swxMSiMUYQl5BBZkYm\nmZmZpFlamL2yDK//i8+T0Gu/zNM6m5poOlRBWmIESXHW46+r6smlLyI1HbR6LNEZZKZ3vXd6rIYD\nB8vYsvID5u6txZI3ihtvv5fH/jaLZ6/tZF+DF53ZRooMhpCZ1Oyu/TIz0wkePsj+fQfpDAKYTzlO\nCR0ntJBUQAGtRoNWo6GzvpbG9k46j3zOW6V7SfruT3jwxgn0ycskuVcCGo2Kq2Y/a2Z/xBHPsX21\nWjSSho6jVTR1egipwPFP0aHR6bBGxYIqceJTtGrQT0AJYQ03oNNJx/aRQPflOdSiw6TRcLZlwSJi\nE756XhWZUNCPzqjDEqYDNBjRoNWekAWehf3IUcJMXlJz45CA2OxCDGF1/OnRx8l/7HuMjA9DCQap\n3bkNs83EsH7JxysGSWciJiGJhIQotDrNl0NZ2liu+tkvuWtIEhqNFpPZgkELPs1ZLmRjKhMHSig7\n13Po+BCzSlPZftYvXY1bMRLuD0HwxDKv4Gj3gRqL5Xg3y8mTwDQY0Hyl8rVwYvYkoUEjHevZ0RqI\nNJiJ9IHNFkt61hflLY2a+R+yz5PMxGKF4J7NVLq+jLNuzy42rFhLcxBCPlD0dDUEA23sLG86fm60\nnNpq18MpDyhqMSOdcKb87dWYb36afz//DI889Dj/fuFFHrttDPGnGzb44pgkHRkDBuLx+Nm9q/o0\nW4TY+8EzlKbmkp8Rf9ZFZ0KOOjaVbeFo7gCm33U7Ywb3ISs9Bb1eT5jRz4o//g/bHF1XXJgEaL4o\nn8fOvkYDGom43DwMFiullS3IJzQetFo9Xd/H+d2tytcuAYOWMUMzTipPfnsFb7zwIh8ucHPfIw8y\naXAmxrMtzqMA8ql1ggODLRaNTodyUv2lIAc8oNcQYT3HLD25ij/c/zx3v/QTBvfOISen61/f4n5k\n5ebQ3OahvcN7xt2DnibWvTkXVTOKRx6+iZKiPFKibYQZDIScB3lz3kYq6510lfUTy7GE9ovyr7WQ\n0iuWHG0DjoYmPMdvNhc2G6jp0G7a21sY0TcV6wmrcCpBH/tXz2ZOZQyx1gkU9TrfyZffnMskKdDT\nKzuTGL8Jf5Pnq2Noqsobj79PowxKoJPdq5fw/mIPfYffwKDUE0+6j8PbG4gcVYD1NJOMTuRsPMpO\nezMtXi/tLj+eYOiEZEQm6N/CwXoPB3dvZ+ZbrQwbOQHLlgV8NGsBDU4Z5FZm/vhpDju8KMduMn63\nn38+/A5NMgSdDSxZ/Amv7Ytm0LBpFPUy4/MECYUUjtS04PX6uz5Kksib/DA3hDXy1mO/Z1djEFQ3\nW2d/zLKP1xCw2Kh4bwGf7z6KrDMTERmGrwEiwg1YovO5548zOLTjTZ6fu4cg4Dyymbdnr2RvtR8d\n7ZTv24OvZjfVrS6CoRDBQDMHSrfjb6qm3hVAazChD4ugvslFY0sre5ceoO1IO8gBvKqKqjcRZtQS\n8DYx77G/Ewr6aayqpK68Ho05DJ3ZypFaB23trWz/ZC/OVhcS0Fa1l+2As60NjSWKAeNvJ//wfmb9\n77scdSvga2Tu399hz/okbhs3jPhIE/aynexQZMp3H8ZPiIDXQ0N9Nbs7PdTVtp3Uy3CilKse5pEk\nLf+487fsscsge6nYsIJ3/7KL/jnTGN03Fm97K+XuTirqW3C6PYTOMOlEVRTcrVUsX76S3XvqsWi6\nWnF6kw2NRiV28m+4d3QWqs+H017BuoVrMeg1xER8tUJUObUtbmT8Pd9nam4Eqt9B2c6VrLMncNWk\nPmdoGwGSjdueeAKfazU/+ttCnEDI1cCa5Z/x4fog426ewuD+7bw3fz77j3b1fZbN/zv/u8HDnf/6\nBbk6BY+jlvKd23A3VdLYGSAUclPfcIjWqn00tdnxBBXkQCulO3Yg1+2mstVHKBTE7amncv9O3M21\nNHmN/5+9+w6Tor4fOP6e7f36HdwByzV6772qgIoNe0ls0RgTjSYm/qJGTTRWTIwae4mKBQUVVERE\nQJAqnQMOrnBc72V3b9vMfn9/HBJADpB23N339Tz3PDAzu/vZmdmZz3wrg88/m+ETFN6dO4dV2eVE\ngPI1r/F/bxQRZXdx+V/vo7bqW/74wtd4gXB9AV8v/Jov1tRi1BtwJesxl++hrM5HdfYyvveoTU/M\noQp27NiIGqmhLqAhtADlRbsp3bmBqopS6hrDqGo9u3dvJViUTX5tU7mcPaoLfPUkT/13Lgu+nMfH\nH7zDJ59/y+6S6uZLlxQdGZNv5YbMYr58/s/MXV+8f5XqKWXBw7/j7llw/gXTSEtyHPH5VwiNkBYm\nZDBiMhnR6xpZ9NTL1JdWUFu1l+wV2WiKRln2JjY2BtmbW0xIqPhrq8ivqWBbWS3VNR4saRO5dVg8\nWS+8yrKcpmMYqNvJc7/6NxEtTMhXf8R2BVpQI1i3k0+e34RBP5geiUbCgQCNvlp2rpnLvXfdzmOL\nqrj26b/xm2tGEWs58g1QbzJjtLsoKfdQWlHJtkU7qN5TS8cxl/PL1Djevvkh1pYHm8Z72L2a5+6a\nR9cOlzJ9ZHJzEdJYu5uXfn0xc403cP7QuANuXIJGr4f62loCDV4aPF5C4vAVfBGh4G30oygGDHoz\nam0Oi9evZ0VJI1WVOewsrqLBV8WOzZsIF20mr8qPqqr4/WXs2r4Bf/leynyQMXQs/Sem8fXKb1if\nXYYAKla/wbMrq/CFPU2NP5sRUVVCnmLWLdtMRUkqXRMS0EfCBAMBvFV5zHnmN1x33xySuk3hT09e\nR4ef2VXzpDitQyWdQuGK9eL+39wmnnhrkag5YLAt747XRNq0Z8SHL90levcaIy695lwxcNy5Yub8\nH8Sh4w1GArnigbPGi5kLs0RIa2ZEOa1BLP3PP8Q0t1sM6N9fjBrZXXTv5hbX/+srUdfYNBLi+nfu\nFqlp3cTA8ZeJ3//2XPGPT3YKofnE9qWvil+cO0iMmjZNjBsyRNzw4NuiuNYvhBDCs+0VkdKpk3BP\nniL69xohLpoyUAw56xLxn683C58QonzDx+Kmi0eLwQMHilGZmSLTfaH4tvjHb6CJhrIN4snbJoi+\ngweLyeeeKy66/Dfiy43FomDpc+LaKeNEqrubOP8XvxBjevQQadf/U+Tte2m4sU4sfesxMdbdR4we\nMkmcNfZi8X9PLBRlnnLx9i3XimHuQWLokAyRkTZMfLp1k/j78K4iI22YGDrELSZMv1wszK8XhZu/\nFL+/aoxIdbvFgGseEt/urBCaWiW+/PfvRJ/uGSJ16mVibPee4v7XPhCP3zxY9Bg+Rdz33joREKrI\nWfW+uOnC4SLV7RaDb35GbCyqE9kf3iH6dE8XI0eMEJk9+4lbZu0QQguIwk2fiz9cPlIMHj5cDBk5\nUvSffpt4b02eaNSEyPnkz2JYv25ixPDhIi0tQ0x79AvxxZv3iO7duolBAweK1AEXiYffWCv8zZ1A\n/kLx+t1TRLfMTDHpvPNF9yETxO9fWywqQ0JUbJwr7rpihBjYv7/o2b27SHVfIxZuLxfhn5wimij8\n4Svx+1Fukdqrl0jt00eMvOkRsWRXjRDBXPGX8x8Wy3dVClV4xSuXu0WqO1VkuoeKIW63GDj5UvGf\nxQUHvVvegr+La2fOFtnljQefp2Gf2PT1f8Tocy4S87ZWi0jzwyruV7TqbXGR2y16ZrjF+IEDxRU3\n/Efs2vdDqc1bJ/523UWi78Ax4twRPUTP9KHi3/M3iYgQorF6k/iNO110yxwsBg/sLi6/8S7x3+f/\nIS7t00f079dL9OrhFve89qa4f/JZoo97qBgxPFWkp44Sn679Xvx5aLronjlYDBroFtNv+J34vrhR\nNBRuEU/cfIXo5x4tLp46RvTtdZOYt7FSqBEhIhFV7F78ipjudovemW4xZsBQcf1v3xC5tU2/K606\nSzx57YWin9stUt2TxMebSoXm3yQudaeKDPcwMdTdS1x45X1izoeviRnuXqJvnz6iT6++4q/Pvype\n+PVlYkTmYDFsaLpIT3WLFzZUiR3zHxJdUjNErzHTxLlnnSVG9+8vUrt0EZ0nXS9eXLJTND9mnyY8\n1Vni33+cIVLdvcXY8ZeJG66aJkb1dotf3POUyCqqF8c0HqXmE9uXvSN+ed4IkTpyohjYZ4C49e8v\niFcfuED07Z4qRv7xI/HdC5eKjLQ0MXTIENFj5DRx53Mfiif/cu2+79ZLpI66Q8xbu1eE1UrxxbPX\ni97d0sTlv71RZKYPFxde6BapbrfoO/ES8fSigmaCaBQf3jBa9Ehr2vbQv15DJog7npgldhTW/ozR\nAlVRtGWBuPvqfdeEqx8Ui3dUNL0+WCo+evgKkZHaVUyZMUNk9Owvrn7iU1FyhIEP8xY8KkYP6ilS\n3U3XiYE3fdg0cqXWKDZ/9aY4z+0WfXo1He9Ut1v85bU5orTxp9FqYb/YMu/f4ly3Wwwc4BaTJk4Q\nt97ymPjTr68Wvd39xP0vvyX+Pn26GOAeIoYPSxNpXUeIeVvWi/uHpYluGUPE4EFuMeWqm8TSQp/w\nlWwXz/32OjGg/0RxweQBYuC0c8Wwbj1EutstUt1TxQ+HHcw2JDa895S4fODh93Wq2y169rxYvPDh\nClF5CgeCPBpFiLYytVQdCx57lE8qUvj13TcysLPr4CxdCILeGuqDBuxRDuzGQ7PdCPlfPcMtj5fw\n6DsPMKRzzPEXowiBr6aQ3L2VGJwdyMxI2f8kFwkFaPB4iRhsRDmt+wdt8WW9Rr+LnuLRBT8wo2OI\nuoABu8uJzXjsUYiIRsBTj0/VYXe6sJp0qH4fmsGIkQi19R4wWImNsqMcVAQuCIf8eDyNGKwOHDbL\nz/7uWtCPpzGA2WbHajYdsLyRujoPmjGaxFgzIiJQQyrGA4rMVL+PBn8Iu9N50Jj2h/2Oagif10NQ\nGHA6HZiaq9c9HkIQ8tVT51exO6NO/+Q6h9jz1SPcn9WNB66bTvd9Xd+E2siOZe/x5NO53PnmgyT4\nK6iuCdB7cLejNhCKRMLU13gQejPRMfZDjnEEn6ceXwgc0VFY9bpTOOlNhMZ9n+WKcu0fqOdHmhai\nodYLBgtR0bZD4gzTUNNAxBJFlNVwLDU5hxfYyNS+VzHt1W+4c0KnHz+Z6rxVPPnY61gHX8jvbr6I\nuCPs1Ija1AC2qLQG1WgjsXMySTHOn91QK6KG8Hk8+DUz0dE2TAYdwcYgZtvP74ymNTZQ5fFjjU7C\nYYzg93rRWa2YjcbTXizc3DUBQPPVU+UNYnNF47SezrlNBJoawtvgQTWYcLpcmFQVVSjoDPojzufw\nUxH83ga8wQjRUS6MSpiGYASzyYzZ0Hqb67XeyH8imtGXTWbRA1+yYVMO3ToOOLgKQFEwO+NIbGbk\nz7Avj3mv/sDAa39Nt4RjmeXqCBQFe1wX+sV1+ckqnclCdNzBjXTUxoami7UQVJTV0tghkfg4y8++\nKCs6PdaoWA7sOW2w2vcf5LhmJ2VRMJpsxMYdf/2V3mwl2vzTPtt6s424pP+9r6JTDkoIfowx1nps\nE5koBhOO6DgcR9/051MUTI5oEk/Jm/8MWoi62lrKK7xUFBWzN38viY40om0K+cvf5ILbnmPG7+4j\nd/F7LCiqxpI6hd6Dj/62Op2RmPhmeimgw+6M+UnN/Kmhw+aMobmzTa83HSFOI67YuBMPIaLDEmNC\nDdRSVR+Ny2ZCqEGCwTB6uxWTVX+ULqegMxiJSXYTk+w+oVB0BhPOmDgOvDQdT0IAoLe5SLL9b2h3\nu6vlJtVq7poAoLdH0RJzF4GC3mAmKvaA/WswHOeNUIfVEY11//XCgOv0NwE46fQPPfTQQy0dxMli\njk0hrnYz837YS2yXdDrFO9Afw6OE2ljDmk9fY0F+JjffOAV3ou20Tg1avW0x//1oPnUhG0U19Tit\nCWSkJZ222d6kM0uksYLvv17AN2uKCJeXUZi7F1t6H1ITQnzx2HM0uBKpLcgma+dufIYYRp41mV5J\nbeBqdDoZY0nW5fLpx59RJ+yEGmvYk72RufMWkkNXzj9/Gj2SHG2l0ZUkHbM2VH2wT7CMj599gaKu\nU7h++giirUfPAetzlvPiu9/T99zLmTw4jaO0oznpghV5bMyrweEwEw4E0NtT6NUzuS0V40jSGUdE\nNKoKd7B+YxaFlQ0YLE66ZPZlYO8MYp2nexw5SToztL2kACBYS0FlhI5J0Zh+0nbgp/zV5TQIC9Ex\nrkMmGJEkSZKk9qNtJgWSJEmSJP1ssspMkiRJkiRAJgWSJEmSJO0jkwJJkiRJkgCZFEiSJEmStI9M\nCiRJkiRJAmRSIEmSJEnSPjIpkCRJkiQJkEmBJEmSJEn7yKRAkiRJkiRAJgWSJEmSJO1z1Dl3NE3j\n/vvvZ8+ePSiKwsMPP4zJZOLee+9Fp9ORmZnJgw8+iKIozJ49mw8//BCDwcBtt93GhAkTTsNXkCRJ\nkiTpZDhqUrBkyRJ0Oh3vv/8+a9eu5ZlnngHg7rvvZujQoTz44IMsXryY/v3788477zB37lyCwSBX\nXXUVo0aNwmQynfIvIUmSJEnSiTtqUnDWWWcxceJEAIqLi4mKimLlypUMHToUgHHjxvH999+j0+kY\nNGgQRqMRo9GI2+0mOzubvn37ntpvIEmSJEnSSXFMbQr0ej333nsvjz76KNOnT+fAiRXtdjsejwev\n14vT6TxoudfrPfkRS5IkSZJ0Shy1pOBHjz/+OFVVVVx22WWEQqH9y71eLy6XC4fDgc/n27/c5/Ph\ncrlObrSSJEmSJJ0yR00KPv30U8rLy7n11luxWCzodDr69OnD2rVrGTZsGN999x0jR46kX79+/POf\n/yQUChEMBsnNzSUzM/N0fAephaiqisfjIaJpLR2KJEmnmN3hwGKxtHQY0immiAPrAg4jEAhw7733\nUlVVhaqq3HLLLaSlpfHAAw8QDodJT0/nkUceQVEUPvroIz788EMikQi33XYbZ5999un6HtJppqoq\nWVlZfPbpp2iq2tLhnBGEEITCYSKahtVqbelwzijhcJiwqmI2m9HrZE/o1iYcDjN8xAgmTZ58UDWx\n1PYcNSmQpMPx+/18u3gxubm5nHveeS0dzhkhGAiwdu1aqqqrufjii1s6KCO9QwAAIABJREFUnDNK\n1rZt7Nixg/Hjx5OQmNjS4Ug/U/bOnZQUF3POlCm4u3Zt6XCkU+iY2xRI0oGEEGiaRlRUFBkZGS0d\nzhnB7/eTv2cPkUhE7pND1NbUUFZWRhe3m5SUlJYOR/qZPB4PpaWlqLKqsM2T5XiSJEmSJAEyKZAk\nSZKOQmnpAKTTRlYfSKeNGmykprKMinIPwmojrkMSTs1PWGfCHh2DWd/SEZ5GQsNXV0dQMaDXKRCJ\nEBECEAgUDEYTFosFo0Hf7i7IES2Er8FLWNGjVwAhDtg3OowmMxaLGaP+VD/TCMLBIBp6zCYjymk5\nEIJQIEBEZ8RiOnMuz7LhWftx5px1Upum+mv4ZvaLPPbcIuJS0ugQX09N2Ea8L0B0v4lcd8ev6B5j\nbOkwTxuh7uXZG67j82AsFqFhE0YMVgUFH15NIbbjQKadP41JowaREutoShzaBY2agrU8fdf9LA85\nsUYEFp0Bg1lBoYFa1ULXtOFMv+Q8xg3uQ4LTfBI+UxAOhwiFwWYz70/CRLiCr979gN3hnlx/zXhi\nT8pn/ShCKBhCEzosFtP/PjNUytwX36LYNY47bhiNsd0cd+lMIasPpNOibP0s/vCv5fzq5VnM/ewN\n/vPSW/x5+mgq83dQgkZ7exZRjCn8+vU5PH7zMEp2lWPrdRUvvPFf3nzjA95+9gnOSQnz/gO38thz\nr7KrvJ5Iu9k9OmLcQ/jDi69w25Q0CvaE6D3ldl564y3efGM27868n96RfP5166U89fYnlPtOQnfY\nSICC7K18+eVWQgcsDlfuYsHiL/nvqyspbwie3DNU87Ft/UaWfreb8AGLQ6VbmPPVfN5+aQ0N7eeg\nS2cQWVIgnRYFaxbisIxn4qB9Lc+NTgZOv4QZubtZp0L76xhrIjYujszeg+hh/BxzYjTxsS7MQHRs\nLDf9pQuZiWYeePFFno/vzt9uPoc4a3soSVHQ6y0kdEyhR1oPulrzsMVHERsbhQmIjh3JPc+k0eOR\nP/Gnp/+EIakPf7+0DydS8xRR/ezdsZM1q+I5/9L/LTcl9OTKGTMYRA8SYywntRpHCzaQvXEXe30Z\nTDrnf8vNHQdy8zWXsydqDA79mVNKcOZEIp1qMimQTguD2U5jYCsrNxdwfu/OWI06sMTTv+cAQg0W\nDPsHtBH4asooKq4iKHTEdOxMpwQXCiC0MH6vB09jCL3VTpTLiS7sw+NpxB8IYopOJNZhQvXWUuML\nEhF6XFFWGioqidiiiY+NxqxXQAtSU15KeZUHzeIkOSWZWHvTbJ5CRPDXVVBUUkEAC4kdk0mMdZya\nIjUBNNfFyxjLmCuvYejSdXzy3ntcPm04Y9Pj0SkQ0YJUFhVSXuvD4oonObkDDsuPt0UNX30NVbUe\nFLOL+GgzlXnbySozMGxUT3SeBkIRBbPNgRKqoz6gIzYuDoe1qQhb8zdQUlxEtUfFFtuRNHfC/ouE\n0MI0VJdTWl6DanTSMaUDMU7rKdo3AiLN7BtTEuf97nbe/mot7zz7PL885wW6u/SIiIqvtoLi0ipC\nOhtJyR2Jj7ajAyJBL6XFRVQ1hDA6o3HqNBzJbqL0QYp3bmbFkiXUxV5IQ10dqsmM1WIiFDTSa8x0\nMrDgMhtAhKitqiekhRF6BzEOKC+tRDVYiYuLw2U/oOpBC1JZXERpjQ+TI5pOXTrjNCmAQAv6yNu0\nlrUb1mDt24n6ujpsZitWi55AwMSgKVfQFxvGAxoxaGqQmvJiKqp96G1Okjp0INphQREq3gYvfr+f\nIBY6JFgp31tEY8SAKyaBxFj7vpgEQW89pSUlNDQK7FF29EY7HRJjjqntQrvL2dsxmRRIp0V01x7U\n187i348+ScGEQaR0SqV7ZipJfUYyzmwnxq4HguStmsf8b7KxdUojyuAjZ3YNXSdN5+KJvdB5qln3\nzTy+XLWbrsMnc/60s4ltyGf2x1+yK7+EYdf+kUsGpVCXs5x/vr8CvSGWPv1jWb9mI5HoAZx3wUWM\nzdCxbuk3LF5XRGxSEjZ1O2WhDlz5q9tJdegoyVrORwuWE7Z3wKUGqPVZGXXBNEb2SeF0P6frYrow\nqrODb9cuYcPeOkanxUO4huWz3ua73QE6ZMQTrKvA3Gkw086ZSCeXSs6apSxakoWhYzyhvWUEbREq\nlAhZczfS8NLfYNHbbK63k+ROh+Jt5FSrjDn/UqaMG46pdhfz539BjteMO85G7pocOk65lOsuGIg5\n6CX7hyUsWJmFwRmPUltP0NqJKZecTe8usSf0pH5c+yahG1O6GFm7ah5ri/5JZjcdezYv49PF68CZ\niMXnwyNimXDRFAakRFg0fz4l9Tpc0TFovkLWrtnJlHtmMt66i/nvvcBHC7JJHhnL3I+rSUntzfBh\nmexd/hmLV22jSj+Mu+6cTnKUn7VzX2VJTg06czL9M4zURlyojdUE7BmcN3USPTs6QK3nm8/msXRP\ngMwEC97C9fhcvZhx3Q1kuAS1hRuYM+t1Fi4to5c+jjmzC+jaZxgj+ndk68L3Wboxn3rLeB6+fzoO\nnULYX8m6L95nZXaIhM4dCNVW49EnMW7aZAakWtm18nMWrtxCRSCeUb30lKgdiTNVs6NYYdLFVzG5\nZywNJTv5bslS8j12kqLN1OZms8vj5pbfXUS3lChZEiDtJ9sUSKdFl2GXcf35w6j7/hP+9fijPPL3\nv/OPR//BG19vwIMNh1GhcttCXnn2PfaqCQwdP5FJk8bitlbz4dPPMWdDCTqDEbtdT0neDyxbv5na\ngIrB5iI+BtYsWcSuygYEYHLF41SL+eDDuXz2bSl2k0rOiiXsKiph6+L5PPeveZSJJIZPnEB/RxEf\nvPwM76wuIVizgyefeZZ5+ToGj53EhGGZVGV/xxsfLyC/JtACe02PAQVFgdIqL0JoZC98nmefnYPi\nHsiksybRLSHMig9e4ctvd1JXuYtP332V5Tn1dOnRj54xjbz+8uvkxIzipktHEWux47TryF76Dp8v\n+oYGnYny7CzWbirA6y3jo/fe4LlFu0noMYyzz5nEoMRqnn78aZburqR49xqeevldfmiIYsT4SYzt\nl8TmZZ/x3terqfSFj/5VTjoDhn13spKKOuqKN/PUc6+wpMzC0LGTGDe4C3vWf83b85awff1C3v1w\nFcak3kw+ZzKjB/QkuGk+u2uD6Ex2kjqlk5pgxGKKIT42lmiHDaPOgCMqFlG9mYXLtlPnD4POSkLH\nJGq3fc6cOe+ztsJAz/796WSpZ9nc2Sz7oQgVUGuzeeetN5hbaGL4+HGMHJjEsqf+wXOfb0dDwWBx\nkdypC51izdgsMSTExRJlt2LQGXBFx6OVrOKzxbsIRgRCC7Nj0Ru8+uYyDJ37MnbSREYM6ErVhiW8\nOetLdlYEiY6LRy39gQVzXueTzbWk9R3EoF5d2Lv4Vd6YvYVQJEDOxuUs+HY9rl4jmXz2WAakO9iy\nei+VtYFjKgWQSUP7IUsKpNPCmtCLu//0FwYMnkB+aSl78razafMK/pu1HdVi47ZLh7P8vbksKk3n\nhccup19qDDo6cvEtv2DHV5cx57+DmTrzZgZPOJep23ewrBIUBcwxXbjksul88/ZnmPY9rkalDufa\ni9by369z6T7+Uu4ab2HXzr04OoRZ8OpifEk9ueOa8xjcLY6G4IUMH2gg3mak8Pt3+HJtPjf862km\n9O6CGnQwfthK3vh+O7tLPXSLPd2TwSjo9tUrGwyAWsTbz8wiN+kKnrruLLoYIjiHT2LNtxvYvnUb\nxSkKu4r8DLr6LIYPGUR0XwN9Xp+LokYz/fbfohnMeIwzWPn5fHYnDuTq26/GOzmHsKMz+qKVLFi0\nlM4T7+GiUb2Jthk59zfX8crbN/Dl6l0YvLPZXBzkd7+ZzpBuSWidxjDq2yUsztpNed1YOthPf3sH\n3b7jrVPC5K14j++2V3LrUzMY3TMFtauFMSuXM2fnTnYnmFADtWRt20rXZAcZXYZx4403UpdoxRqf\nybgpF7Nu0Wrqe4xi+iUT+PEox46+AH3lahbu/bGKxMrA869nxvbZ/FDXhfOuuZ7xKRbKDEWsWl6C\nt6qRCKBogi5d0ogflE5yQhLGcZczxP0SX3y7k8C1/Ynu1I9xE89m9coikvqP5YIZQzHt+8wBZ1+J\nofxb5rxpQg+EfQXMfn4uhZ1+zZNXTSHBCCRH483dzFPvzGPN0P5cPWUql+xZwPzVZs7+xe1MH9QR\n1Z/E9CHJvJVfi4pGoydIxY4y8jZvYrerH11HT+LKhiqSY6zHdMOX1Qfth0wKpNOieNsWDD0GcNEv\nu+NraKCmupycLct5861ZrFi3maljupCTV02jJROX1bD/QmWwdSCtVyxrcvNo0CDeZMZitnHQ7Vlv\nxIbuoGIvLaJhs5voO7Az0ckuhiWnU71tASVlBXToM4kOCS50gKv7ZP5wXz/iMhLZ88Zewo0NrH33\nCWZuzyASUKnJKyQmKpWT28zsWAmEToACdocVtDoKsr14k9by5MxnSDcJ1GADe8KxdIq3oTcJdAaN\nitp6giGNYF0FtRGNdJcdvdmCHgEigqKLwhnXnY4xCdhHJgBQtPQLVH8jJd+8w0vswKKY0WleolNS\ncKoanrJSfKX5LH77SapWd0IEQxSXNhCbasfYUvtmX1Jgt1tpKCkiUFvG8neeJLixKyIYpjyngpiY\nznToMZix3Zbz/qcvs2nFfOJjojH0PItH4i3sa9ixv979UCaTDkVTDlpls1uwxY9gYMemSa/MFjM2\npxUFBQUwxPbkissv5LsVX3Df3f8lOTOa7+pBCBVt/+dEUBCIw3ym2axD2Vf4ooUr2bbbi75/Ao4f\n8y6dlfguyTiV76mrriMcAatFjxI9gtFdowFQdAai4h1QrkPRWUnv1Y/UTl8x59WZrF3YkdgoC0PO\nvQGXyyxLAaSDyKRAOi1KVsyiMrY356YYcUbH4YyOIyUlEU9WDrN2h/H71X0dE8MceAUWIkSwsX7f\npXufQ69iYY2AEEQOWawoCnrD/1KFiKoRUTUMJt3+J3CdJZYe/WIByA2HMdvsjL74OqZ2i276QCEw\n2qLpmBx18nbGsfIUsWaPj4bgaIZ0jUUvSggrOmyp47l2+lSi990UBUai4hNJtFeRmBTHl2/OJFCw\niOrd2VT1vZSHJ7gPeludokNnMB70449oKiIi6DPpPM4+exhOox4ETJt2KRaHkw05KtEdOjHugisZ\n2dkJEWDqdMxRSXROaIEZIevyWJyrEhFTGJFuperrMPaYOMZedDUT06Kajt206ZgccdhC1diuuode\nZ1WRX1DA1u+/4JMPX+KlAWN5fHpXFJrqURVAUevYlVeDyRZP104uOFx32YiGzuLEsv/Uiuz72xda\n7mpmffA+u5V0LjnvKvqmRxFaNpv5YdALQUSLNH3Wj3/hKjZnN5CU1IEOCTbggG6WmkBFHLyMCFrY\nhxYOoAERBYioYHZgO6jHwr7XRMIQ1YGpN9/NWF85BdlZfDd/ER8//y59+vViQp9OGI+SGcjEof2Q\nSYF0Wmih3by8OJtzf9Fn/zKDxUqc1Y4BhbDBQqyix+gPH9Q/UURUGmpD6HRRmPedrUbAiI4fm8SE\na/ZSoAZIPuR0FoAQ/0sKXEnJuJKS2ZZbQXW1j66uphu9VrGa55ZEcXanTuj0+SS4+9G3V9M64S1i\nxZZC6lUbw3vEn/wd02wTvUbWz3+Vdbt2M+72ZxiYEo3O6qMzkKO66DWgL3H7vmXx1i3sydqGvruJ\nxtQx3DgxncGdowhiIzGlM2kdjn7TtsbGYbBacSRm0KNHX2KtTXH58r/l9bVe0pOSMFh8JKf2o293\nBwCRumw++6EQg9lBWkfHydgZB1Boft94WPLmo2yq9DDjkd/R22lkQ3IKeqOXpK796NvL1RRfQz7f\nbCpC3fU5PzhGcOWkaYyaIPBdfClDHhnDrL3epu00UMOABdB8FJaUYI+x0bWTCz0WlJ80vbIf9D8d\nBpT9FQABshbOZ/WyMDe9dDUXjuyBwxhgnRmEQUfR7mWs2NWBSdGgRQAToDaQU1CK0RpNhwQbemz7\nyhxAZ7STJARF/gNHUBD4G4ME/CbMBnPTqI9YObiJmIIe277Ng+zYsIn1eQrX33EJEydN5aLzxvC7\nP31Alc/fNAbGUe76svqg/ZANDaXTQlFs7H7x97y6LHf/YC2ewt0sy8sirlsCmcnpXHzHDDqwhH9+\nvIpASAMh2DD3n3xcHs15d15OigEQEdSIxs6CKopK64AgK59/l4rCctav24FHiyAE+DwhQiGVwqJq\nIpGmpzhzUg/OGdED65bXWbDsO6oaVaCezx74E9sEpJ19C5dE1zDroUfZUh4G4Wfz55/z1ftf4zWc\n/DrziKZSmJvFFk1DbWzEFw4TDAapr8jns3/8mb8+MYfYc+7kT9dPJN5mBF1nbn/xFup3v8Vj760j\njI9g3VI2bXiRnKpVRMcUk+xZyqpln7F4xSpWfbeIhZ9/ycqNuwnStO8ioUb8jT4ChXupC0TYt2uI\n6zOZGQPc/PDc0yzaUEg4IkAt5rmr7qU6piP9x1/KgPosPnr+dXJqVIh4+PbF/7JyZRYB/cnvexBq\n9JBblEeOGiYUCODft29qirfz3ztu5P6XVzPsN//kwav6YTYY6T7pOiYrhXzwxLNsrwyD8LH6vY/4\n9ouV+I1mtr39KRt2VWGwuUhMTsJQA3a7EVAwWk1EuTz48osorywguziP4rACES8Fe3bi95dS6w8j\nBKjBcnZs3ESofDcl9SFUNUB1TSHledupra7CE4rg9fgIh3U47FGYDTrqt3/EzPUCTVSTk7ONXRUh\nzE4jDkMtnqJyKkp3sa28hGpNAa2BnJwsVLWCqkYVozOTmx48j5L1b/LWtzkA1OSuZ97Xy4iMGMeI\n4T2xanXs3p5FqDiLgmo/qqoSClWye+cWghWFlDeq6AIlbF6zgvU7PTiiYkmIdWIyWjHrdadp+Gap\ntVCEaH/DxkgnrrGxkW8WLaK2tpZfXn/9Ubdf8eRofpU9ngl577M+2JEB/bpSuHkljgFX86d7/siQ\ntFiIaBRtmM+9v36YdcYODNZls7Uulf97+WWuGJWOQacAKmXbv+Pxx2aytDJCUn0dnYcOoWHZd2yo\nrUN0upsPfpvD1ffPJ9oVjVYn6H72L3ns+bvpaoaIVs+6uS/z92ffZ4cxGqWsjD7XPswb98wg1qTQ\nULqRFx++i3fXNZLcKQWLLp5f/ukBLhjRdX9r9+b4/X4WL15MeVkZN9188xG3jYRy+EOPc/hMUwmF\nNXR6A0Zj0zwHQggSe43k6ptu54rJg0lwWfZfuIUaYuvCV/j3v5+m09BoEhME1oQhnHfhUKICecz9\n9Es2FAQIeuIo2AhZeyrQAOflT/Hlr5O4f/KNfK9EYbWHMWWO5s57/8p1wzoAoAXLWPjqgzz4ylLi\nB43E8913jPjLLB65cQRmghRuW8S/H3uUpcVmok0G4rqO5s57fsvwbokcbZyddWvXsmHDBs6fPv0o\nUyerlG1fxn3n38y3qkpYE+gNBgx63b59E6HTsHO59bbfcuHIbth/LD4SYSrzVvL8I/fx2Q6NxNho\nnNHdueWeP5JZ+R5/eORTNu2tYsBZ46hesYLC4bfw9XN3kelSEMFa1s55mT//+UUKDXFM++Xv+OMd\nk5j/1wd4fd4m0Lz4TP15bcWjfDH2PD5Wo4mKrSe+01huum4CXz/2BKv9Corez9jrH+BXk9x8dN/f\nmZ+9lx6DFbZuupAnnurK3+/4F+aMEfztrdeZnFDPV6/+i0ef+YAyfRJX3/MAt1/dk5d/dScfrinG\notVRbx7BR1s/oK9Sx/IPnuehxz8gkBCDw1tNx9FX88c/3Ub/zhpv/+pOnv9mO1psPR5PR5798jXW\nX38Bb5c6cUTVEJ82kGHDB7PyzVepju1KeoqdmuIC+l9yP//3qxkkRx+9Ae3GjRtZ/8MPTJw0ifT0\n9KNuL7VeMimQjsvPTQpq9+RA1wycQT/Febsorg/iSuiIu3MKTtOhBVYa9dWVNAoLsfHRHG7E+UjI\nR0ODF3/ETGyME0VtJKwZMFusTS31j0IL+PA0eFEtUcQ6LRw4xLyIaAQ8dXhCCg5XNDbzsRWo/Zyk\n4PgFgCVEInn4GwNgMGG1mNFFGlj+xZcUhBOZfNYYOrpMQAowki2f/ptL/riejzfPZ4D9KG8PaI0N\nVDU0YnbEE+04pEpGDeH1NBAQJlxOB2bjse2bY08KTozQVBo99TRqepxOFxaTjnCjB81oxiQ0qusa\nwGgjIcZ5yCsjBP1evH6wu1xYTrhiVcPvaaDeF8CR1AGHoiCCQcIG8/5eMqDh93rwq0YcTvsByw/7\nzVDDfurrvSgWBy6H7djrfkWEYFBFFQaMwofH40fviMJpMx81mfuRTAraD9mmQDotYrpmNP3DbMXd\nsz/uI26tJyquA0dq2qcz2YmOtxP94wKjc3+t7rHQW+xEWw5/h1R0eqxRcbRA87mjCAELgXJ0OiN2\nxwFVGgIwKOgBVVVRNT06ZS8RNURihzj0tgiGY6ws1NtcJNlch12nGEw4Y+I59JZ6plD0BuzRcQfV\n+httzv0DTyUkNndUdZitLswn7aDrsTpjsB6woxSz+ZBzVI/VEX2M55mCwWgjLt7280NRdJgtpn3J\ntZM425l69KQzgUwKJKnV2AaUH36V3kHvnhlUfLeKlctD9OyRQbRFoabkG2b+J5fRtz9P+pmX5UiS\ndIaRSYEktQoqkHOE9Tpiuw7mgqQMigv3UlhWRGVYw+JK5rFnptIpYeTpClRqg2RbxPZDJgWS1CrU\nAJ6jbmW0RtG1W1+6djtwqQCqgcRTE5rU5smGZ+2H7JIoSa1C3Qm+vuikRCFJUtsmkwJJahUOM7Le\nz1J8sgKR2iFZfdB+yOoD6bgoioLBYKCsvJzvV6xo6XDOCMFQiPy8POrq6k76PjGaSomJyUFRDh3M\n+dgIUUh1lRNNa5mffE5ODqUlJWxYv549+fktEoN0/PLz81FVFeOx9PeVWjV5hKXjotPpsNnthIJB\ndu3a1dLhnBE0TaOurg6/33/S94nRGKJr10p0OvXoGx+GEDqKijbQ2Bh99I1PgaqqKgLBIHv37qWq\nqqpFYpCOX01NDXHx8ZjMhxs1RGpLZFIgHZdIJELA7ycpKYlzzjmnpcM5IwSCQdatXUt1dfXJ3ycK\n2GwWlOa6JB6FQEd6Rm80tffJjesYZWVlsWPHDkaNGkViomzw2NpkZ2dTUFBAMBhs6VCkU0wmBdJx\nEUIQCoUwm82kdOrU0uGcEfx+Pw6nE5/Pd4r2SS+aBjA6HgpNP/eWOVYlJSVYLBYSk5JO6YiG0qlR\nUVlJXl4eqnp8JVVS6yEbGkpSq5F0Aq8VNHVrlJ3LJElqnkwKJKnVONFi9xDgOxmBSJLURsmkQGpT\n6nasYmXeifbpP1NZAccJvF4DGk5SLC0gEqahupyCPbvJ3VuGpjX1xBCBOmoatRYOTpLaBtmmQGoz\nNM8W/jD9GrJ/+yErfj+0pcM5RWIBb/OrhUbAU0NhQQFltV4M1jjcaWkkxtgw6CIcy6iIZxIhIoQ8\n5Wxa+hkzX/qALbllxHd101BWRiD9Gj5+9lzmT5iBffY6fj/48JM4NcdfvYF7x/6CZYmd6exS8Ac8\nqEEd4KUhYiGj3zRuuv4aRvd34/jJTJ6S1DbJM11qGzQ/X780k6XhEPFqkOPrzd8axB5xrbdkG+++\n/SbrC70kdYyj8vuveP6Jh1m6oxKB4IgJxRkmooUo372WJ++7l9vvm0vfaXeyaM1Gvlu4kC2bV/P2\nBflcM2oqbxkHMCb95yUEAJbYfjzwzaf8+ZxY8moinPW7Z5n9ySd8/NECPvrXQ3Tzb+Kuy2/mtQWb\n8Ybb7hklSQeSSYHUBmhUrv+Umd8UYlMFW5Zlt6Jb3891pAmlVUqyduKpqKJj18640/tywS0XE6fX\nsWxhNgEitJo2BZEwZbtW868nHufjrXpufmomd91+MZ2jrfsuWlZGXP83bky2oMscT9pxDL+gKAZs\nZgN1+bl0SEhh3LA+JMbGEp+YSPrgs3no6Yc4a5SBf784h9wqb7tuoilHNGw/ZFIgtXrh+lzemjmf\nC3/9K8abTRD2o7XZK/iRnogVLK4EOnZOw6AzIYQgIvbVETpMKAig8fSEeUIEjTV7+PL91/hkbYir\nrv0V15zdF8dPrlYJjL48gcSzhx+l/KQ5Gv66Paxf5SMqYQSpcaaD1hpiM5jeI4qEvBXkV/uItNlz\n6uja8Vdvd2RSILVuws/Gz95he6cLuXjccJISdYiduVSGWzqwU+VIDQ31pAwaybmXX8OQ9I4YI40U\nrN9EmXCRmpmEkQgQ4Ey/xAvNT/7W7/jsk5X0GD6cs6YPwKk//LaujsO5bnT68X1QRKOueDubcZE0\noB/xzbaw8uIJhM/wvSZJJ4dsaCi1anV5S5m1poFLbhxOYkwCaekKlJXiCwOmo768FbICepp6EvyU\n3mTFZQxQsGUrRZVFbF62CZEyhunDO9N0X9UAFTCeroB/NrWxgdyNK8jSunBFv/H0TLQ2u617yp+5\n3Hl8Qzdrapi9W1cTjLIxcHDqT/dIpJGqapVQ2InN3L4vlbL6oP2QJQVS6xUoZ95HH+PrOYyMJDtB\nXwOqCYQoorS2rRYV6ICjjD8vBFo4RBgzKb26gLGOrTllNI1FF+H4R0U8PUIBH2W5ucR3TaTfmJ7Y\nj3BHMsd1JPo4kz8tXEfWt1uJsqcyIPOnFRChqhzW7qmnQd+VRLsZXTu+M8pSkvajfae/UiumsmfV\nfD5fkYvSxcWchr2Y9Bo7y8MIiqiqC0GnM/dp+MSYOWLbAJ2VtCHDSUPgr8ml4vnX+HaRj9S060l1\nCOBMHqpWEA40UJZXhNORSlK8s9ktS5bPYkvyhUxNP76xG8J1eXyfFcA2dhRp0YdeCjX2rPmWXeVF\nZE79BV1j7PIJSmoX5HkutUrBiiw+/byQgeOu54YZ0xk9YjhDh47IVoYSAAAgAElEQVRi3JB+ANR7\nWkODuuN1+EfjSLCWjSsWM3vhD5TWBxAoWGNT6BarEKnJp8Kr0vTMdyYnBaA32ohKikdRFPS6Zi5R\nkTJmPfsNanPrj0Htni1kYSV1eH9iDnkbtWY3c79ZS77an2uvGEWCq33PDtiOC0naHVlSILU+wsPq\nL77C40ziwitn0LeLc/9Fq86+mb++tYWcghoYmdCiYZ46h//ZikAdebk72JDroEf3NBKjLOjRY9yX\nQ4TUCE1JwZnc517BbIuiU99e1H3lY+/eKvjJ5FIqW97/O2tTJ3NTsuV/S4M+yoqK0RwdcCcdfdyC\nvDVL0GxGRgxN5cB2jKG6Pcx+/TU++SbEhbf9hrMGujHr2/dtUVYftB+ypEBqRQRqqJ4tX7/LO/O2\nEtNtAGmdHAc8xWjU1TYghKCyuJKApp3Rt7/jd/ifrWIwEdEbEClJ2GxmdECoOoflxQKdkkmXuB+f\nds/svWJ0xDJw3HQG6zYxf9bL/JBfu3+d2lDM5w/dwf99Hs2tt04l5seRBkWYkl3L+PONN/OPZ/7J\n9rrmS0O0kEaoIZev39qM2diTXh0tqKEQ/sY6cjYs4PGH72PmwlLOu/v33H7tGBIdJvmkLLUbsqRA\najW8pTuY/co/eP6jLOo9KquDn5HavQtTB3dCHyrg0UtvY15+DvFxcax99XYuW9WTe194h9FJba1t\nweFvUTpbByaOHUXjgu/4YoGH7h0MZG3eQY2xO1fecBGdLK3jGUDRmXAPOIe7HlZ5+T9v8asZV9C3\nf0/i9EXs2LmHXlNv5dFHLqJXahzKAbtCj0BXlUNOQSZl3jC9ftJOAMDPZ3deyFPrq6iuaiRoWMFt\n543HpGsaUtkY1YHBEy7g2ZmTGdC9M06LUSYEUrsikwKp1bAndeeaP7/MZXfve9JVDFis5qaiX1Nn\n/vDebO4QAkVREEKgKDostraWEECzNbyKnrgufbj6+lSqq6rxNAbJ6DGCpKR47GZTq2o9rzc66T5s\nBo/0mETJ3kLKq71gc9KxSwodYmOwmYwHJQQoRpJ7T2HmR3NYtXoJEdFcgbeF82fO5ezmRrdSdBiN\nJkwmAzqlFe0wSTpJZFIgtRqKTo/ZYsdsOdxaHRaHg8OuanOaL/5XFB1Gi5MOnZx0aHar1lJiYMAe\nnUBmdAKZx7S9Rm1lLfmr4KJrbM1thcnmaJtDWEjSSdA6rg6SJB3gRHoPKEAzwwO2agJv6S6WLn+N\n4vMvpEv77iwgScdNlhRIUqtzoklB2/zZG1xdOPvSJ/hFj0z5tHOSyYqU9qNtXh0kqU0LnsBrdZzJ\nQxwfPwWLPYq0HkeaRVI6XrJLYvshE2pJalUEJzZMsULbTAokSToZZFIgSa2OrD6QTi9ZfdB+yKRA\nOm56gwGzWbboOpDhtOyTw8+QeGxappGh3mDAaDKhyG5+rZJOp8NgMKA7gWGlpdZBHmFJalV+HKr4\neLTVngeSJJ0sMimQjpumqgSDJ9Lore1RT/k+OdHJjFomKdBUlXAohGh2UCHpTBaJRFBVlUjkzB4i\nWzpxsnJRan2Ejy1ffcInS7YQccViwovXG6LpelVLva4LEyZM4axxQ4i3tbW89+hJgQj7KC8po8YT\nwuyMoUOnJOx6hVbXnkD42fXdIj76eCm++AQcBj9eXwBNBWigniSGj5rCBVNHEdc+Rq1qMTKVaz9a\n0RVCkvZRTCR2H8DQ8iJe+/ALvCljufHCCcSaDej1QfI2LuXph+9n8eBr+dvMX9CxTTV7CB9xbai+\niG+WLCdgSSLRGmDDkm/QG2I46/LL6B5no1X95BUjcek9GTZsD+/Nm88uXSbXXHIOGbFO9MJHUfZ6\n3nviL3zx4dk88vK99HDJqhFJOlGt6AohST8ykti1Fz3zl2EI1jBwxGgmTphMnFUPCIYP6EfVmlHM\nXv8h6wpncEGGvaUDPomOlBT42bRyDWW6jowbNIBku460Dk7eenMB895ezi13TiFK15punAZiU9Lp\n0b0DVrWazMGXMmnyOaRHm1CEIDxiNMN6JnLOTf/h3hdH8cGfJ7aTYa4l6dRpa2WrUjuh0wXYk51H\nTXlXeru74rKbMRgMGAxGrC4rlpBA4CUs2top3nxSoHqq2FtZQW5WGaEQWOwukjMHM6KDoK7qe3Kr\nw7S25wBFCVK+ew9l2Q66depGUrQNo8GAwWjE6oqjx8Qr+X2fBvbO+5Qif0tH23bJPiPtR1u7Ykrt\nhb+SrJxqStN7k9IpDvMBZ3LBN6/y7EYbrs5XMjbD2nIxnhLND1yk1xtAr0et9RMOa031wLoIoQoQ\nhAkEIrS6gYsCdeQVl5HnyiC5UwrOQ3IaRW/GaYygBvIo9Z5IV03pSGSbgvajdT02SNI+jeUF5FWX\noYvNAC1AVWUFYU8lS97/G//34mrGXvkA//jbzSS2uUec5hsaKraOXHDJdUy9WIfVYkIPiEgjAQF6\nYyc6xlppbT95f20p+eX52Hv0o0uXxMNEL4hEFHREYW1dX02SzkjyZyS1QoLS/GyqSkpxWn7go9eq\n+FKvBxpZtXwXTn03fvHL6aS0tUIC4GgNDU1W6/+mBY6EyV+zhDUGCz3OmkKqvZX1PkBQW1xE+e4C\negyeTOckx0+2iDRksfgHBV3nOOyW1tReonVpc7m11KzWdIWQpCbCy55deyipTOWWx/7GldP6/a+B\nWV0W9408h3uuvZXXl81hWHRbu1Ec4zgFIkxV3nreXVZI4shLuGJs6r4VregnLxopzc8nLyeKAef2\nIMFxaOyComWfsVpvoGef8XRpk0ngmUFWH7Qfsk2B1OpEvFXs3ltBbZdMEpLj//dkDBCdTrehgrC2\nh5xSX0uFeAodQ1IgVGr2bOfLrzaRNOAcbp3aB12jl2AEWtOIhhF/A3tLiymMc9MxtQvOQ0LXvIW8\n++Z7GGMyuP7OibSlPiaS1FJkUiC1Or6KQgrL9uDumULnpOiDTmJf6SaW71TQ67qQ6GxljeqOydGS\nAo3aPTv5bslmbAPGc+3k3th0guJNqynxC1pTUuCvq2Lv3t240hJJS006KPKwt5TF77/EK+uSGHfl\nfVzUL6bF4mwPZPVB+9GKyhKldk8IImqA4t3ZFOfUkdE3mXiHCU3TiIT9lOduYu67L/B1STLTf3kb\nQ5PbYnnykVrYR/BU7GLlgoXk2FMZafSRuyMLtdHDrrX5DOrfSuY+EBDRQlTm55H7w166DBtD53gL\nmqahqX4qC7az5OvPeHbWFs69/E7u+8MEbC0dcxsnqw/aD5kUSK2EoL54Fys+n8M3369hW0GAzutW\n8N9wIWZFEAn72LttB3s1Fzf+9o/88jdnE9Umy8GaTwpEuIFt69eQVV1DbW2Axflb0On1hD0eIonj\nmWrVceYnBQJ/XRkrP36br9dsYc0uDy7nFma/+hwOPaiqj5qaaqr9Fi769V3cetUk4k1Hf1dJko6N\nTAqkVkPRG7G64uk19jx6jT10rYu+43tx9bDB9O2bhv1Mv/cdt+YnpFEwEN91EONieqBpGuKAyWt0\nMek4ddAaagwVnR6LK4aMYePJGDb+kLUukrsNp1//gfRMTcSokwXbknQyyaRAaiUUXB3TmHT1LUxq\n6VBa1BFmqTM6yOzZj8xmN/hxUqQzmYIlKpHRV9zC6JYORZLaoTP/sUGSpAOc6NS18icvSVLz5BVC\nklqVE00KzvSSAkmSWpJMCiSpVTnRn2ybbWwhnUIylWw/ZFIgSa2K6wReqwM5xI90HGSXxPZDEULI\n4y39bKqqsmrlSp6ZOROfry2OHPjzCSEIqyqRSASL2XxKPiM6OsSo0ZXH8UqF8jIz69fHnfSYjoWq\nqqiahsloRKeTzyKtjaqqXHrZZVxz7bVERUW1dDjSKSSTAum4RSIRAoEAkciJ1nNLxy6CwbAYna4Y\naEpEFEXZ/28ARVEO828TmjaJSKRji0QttX5msxmjsS2OEiodSCYFktTqVAILgcZj3F4BegJjTllE\nkiS1DbIcT5JanVhgMHAswzjrgQ7AsFMakSRJbYMcvEiSWh09kE5T98Q9NJUY+IHQvmVGwEJT0hAD\n9AfkWMCSJB2drD6QpFZL0JQM1ADVQB1NcyPYgbh9f1HIAkFJko6VTAokqc3QaEoU9Mie5ZIkHQ9Z\nfSBJbYYcmEiSpBMjyxUlSZIkSQJkUiBJkiRJ0j4yKZAkSZIkCZBJgSRJkiRJ+8ikQJIkSZIkQCYF\nkiRJkiTtI5MCSZIkSZKAY0wKqqurGT9+PPn5+RQUFHDVVVdxzTXX8NBDD+2fjW327NnMmDGDK664\ngqVLl57KmCVJkiRJOgWOmhSEw2H++te/YrVaEULw2GOPcffddzNr1iyEECxevJjKykreeecdPvjg\nA15//XVmzpxJKBQ6HfFLkiRJknSSHDUpePLJJ7nqqqtISEgAYPv27QwdOhSAcePGsXLlSrZu3cqg\nQYMwGo04HA7cbjfZ2dmnNnJJkiRJkk6qIyYFc+fOJTY2ljFjmuZhF0Jw4FQJdrsdj8eD1+vF6XQe\ntNzr9Z6ikCVJkiRJOhWOOPfB3LlzURSFlStXsnPnTu69915qa2v3r/d6vbhcLhwOBz6fb/9yn8+H\ny+U6dVEfVYSKncvZEEpnUu8UTPrmJ4dprNjNhiIfndzdcMfZ5DQyUvOERsAfQFUM2CwmdIo8W6SD\nqY0NNIR1OOw2TAbZjvtUEBGVgD9AOBLBYPx/9s4zsI7iXMPPnl7Ve++SJVkucscFMGDA9BKKqTEB\nJyGES25ooSaBJKb33jHY4IJ7r3KXrGKr9967jk4/u/eHhJHBNiYBm0v2+WUfbflmduabd2a+mdFh\n0GlA8uD2SAgKJUqFXC//E04qCj799NOj/7755pt58sknWbhwIQcPHmTSpEns2rWLqVOnkpGRwQsv\nvIDT6cThcFBVVUViYuJPbvyJ6Kvew0cvL8Nx4W84OzWMk50Y57F3kbNuDXtiz+HWS6cT4qU98YMl\nBw1F+ezeV4TDyxuzUsJht+P2WLBatYTFJ5OekUZciPePn6j/IuydNRyuHSQhPRU/3c/DsXqsHWRv\n386Bw5UMChoyL7yWc0dHoT6e4JScNJfksTe7GIfOgEIbyIQpmcSFeH/nyCLR7aClPJc9ubXYRSsK\n72imTJtGQqDhtKTrl4CltYySVkhKTcJbcwYbBHGQw5tXs2sgiMsvmk6sv/702+Dp4Ks3v6BZqcY7\n/Xyunx77/cdkif3sXbyYfJc3oV5qHI4BnA4ANy7A6B/L2IzRxIYHoD1JB+snx9VHed4BNu8vxmqz\nIRiMeEQzGdNmkiq0UtvpIXbaNKK8TtM5f6KF3G07yS+rxR45gV/NHkeAUXPyeyQbFbt3c7C8BaWX\nCaVkxW73MDQAb8GmDGH06PGMSYvFeIaOK/xBrxUEgQcffJBHH30Ul8tFfHw8F154IYIgcMstt3Dj\njTciiiL33XcfGs33ZM5PhGRtYPEnH9DgP4c/zUhE+z1q3RyVydUz6/jr51+xNSqEq6amoledqOBL\neNwO+toq2br5MNUNWqafM4nESCUDnR20Vu1k9ZpAEs+/kbsvHcd/g1t3DvTQ3tOLJiCKIMMPO6XP\n3ttO+4ADU2AYfrqv73Vx6ONXeT6rmRsWvss1icYf3+gfimSjeNNq3lh6CL9QgT1bd7BPPZqpKRGo\nlcdPs9vjpK+1iA37cylpCOPh58KJDPJGeUxxFOnqKOepp54ip8pGyrRpTJscgtsjn2Z+PCxtdbSL\nRkIC/DCov85IJ7te+jsft3hxx1+f5byoM9AQD9NTk8+KLz9lj/kCzp41Gc6EKEDENtDO5qWLaD8r\niCunx56CHxKx2600Hcnio/3VxE07nxmJQUgeJ7bBTnZn7WHd6gRuuu0GZk6O5UQ63eOw0d5chycg\ngQjzj9uiWVoK+eyDz9lzoALjqDGkxQZgNBnpbKpjy5JXWFHTil/KTG6bctaP+t6TI+Ky95G//lM2\nC92clZmCv1HzPaPNEi6Xk86aHDYePIw9OJU5E1MwKtQo6aOmuohtqzYz+dzLmXfbhQTrTr8IO+Uv\n98knnxz3319z7bXXcu211/44Vv3beKjavYw19V787o9TCffRncJ0gJrIqRdyYe56Vq3eQWZCNMmh\npuPfJ2iJHD2Vm6KC8SxcSEmNxOTzL+eyqdFIdgutVft496+P8MaztYSEvcItmSE/egp/blg7qikq\nOILP5Ot/sCiwNBZzuLaL6EmXjhAFApJCpKN1AI/449v7b+GxkJ+ThyswhRvuuogpGeOxxsajOZF4\nFNSEp07lQkcjOQd30NvcTlNbOw53EroRPVmPw0b+V6+wansuERnTuOjG33LF6EA0avlE8+PRU7qL\nbHc8MydPGiEKBETBQ0er5YyWF8neweaNG9iYX44lOpOBQTsiXqd/IxhlEFfd81ua93zK8j4HpyQv\nFd5Mv2kBxndu4cv1fZx91XxumRCA5JHwOPrYtew1XnrtU9YlJTAqPYpI8/HruWuwm4r9q7FN/v2P\nKgp6Knby/Kvvsny/h/m/u52rLppOZJAZJRL2/gY2vvsizy5rZuasWIJPYNtPgsJM5gUX03loNdl7\nHUinIuYFPUkzL0DlrmTrrm3ET57DvHmz8dOqUOCmu7GUrxa9z6vvvYMnMo575yaj/ulTcgw/j7HZ\nHwt7M8u3HCQyYxrp0SGcsMP/bdTenH/RXAYrt5Nb3YTzhM5FQKlUY/L2JchoxqjToDdo0ev0mH0C\nScy8hGvPG4VYe4j9xd0/UqJ+zrjorK2h7EA57h88v+6kubScqoJa3MfcqmLsDX9g4fNPMfsM9vqO\nQZBwKSRiwnwIDIzmsquu4/rJsScZhRJQKkXaqhzERI4hNslMh2UQp3uk05DortzM57kSZ6WGEuib\nztiUEPRatTwnelysVOwroKWxC/EYya5m+u8e5x9/e4BJISeZ+vtJcVOzZwvlVS1EBUah6rdgd7rP\nkC0CWoMJzXBLcmoOXkCjcVK45zBq9QSmpoej1+oxGAyYfQOICQ0kQNtLv70Ph/tEDZ/IYE8zBZvy\ncf2IsTburiKee+l1Fq+ysuCRP/Obmy4iJsg8PCUioPMKZ/xZZ5F5QRK+cTF4nUZNAAIqjR6NVoUg\nnGyS+lv3qFy0FNdg6QxgUloifl5GDAYdOoOJsMRxXDPvOqbqyjmwbjtdrp84CcfhF9UlGWwsoao2\nlpnnjibQfOz0hehxU394P9mFdSi8Q0ifMJaEMP+j823muLOYpvqYguJGLs5MQKs7SemSJIYngfDA\nCDWuQHI7kQDLMZXHQ197PXkHc2nocROTNoGxqTGYdUrsXY1Ut3TSa9WQPi6BrsKDVHQ58Q+PJSk+\nFrMG3IM9NLe00NrtICw+AntdObUDSpLGjCfKR4MkeuipL2LfwQK6Pd6MGjeBMSlhqAG3pZOivGwK\nqztRB0YQqpUIHjedJD8Nkuimu66I/QcP0y35kDp+AhlJoahFB52tbbR3dDIgepGa5Edlbj6NgyKh\nMWmMSwlFIbpor9jHiiXvsn8gkpjGWupdZnz8/TEbtQiI9DQWsnt3Ib0uLUmTpjEhORQlQ/PoTYVb\nWbZyMRXGiaQ21lJnM+Mf6I/K0U1Llw2l5MQ6Ig8lj5OuxgoOHiqkw64lMWMsGcnRmNQCjv52Gps6\n6Onsxy8jE//OfLJKevEJCiUlPY0Aw/e7Ro+lmX1Z+yhrdRAUk8zkKeMI0itw2wfpaWuiu8dC7WAL\ntTXVmOIi8VMpT+4EnD1UdWjxj5lEVEcbtXVdWO0uMAw1XJLYxMd/+Yop8y5g9z+LUE7NJML402n0\n5sL97M2rRDQEkDphPCnRQcOVX6KvrYaCQ4dp7LIRkJjBtHFJmLRq8AxQXdbAgMMG+hCi/F0cyS/H\nZQggOSmR8EAzgmintaGZrp4e+iU/MtN8yM86QIeoIzIulfT4oBENk5uuxkoOZRfQNqggadw0xiSF\nojva65dw9jZyIOsAdb0QnJxGZnoi3io7ZVlLWLJ9J4pZibQ21OAyehEWHoCnt5HmbgdKRBwiiC47\n3W1NNLX0ovQOIMgLaiuq6XVqiEsbTUyQF0e1nCQy0FJBfkk9mIOJDjNTu28T+e06zrn0ckZH+ZxS\n3jo6y9l6oBZN9Dmc4xSpX9eLxeLEI8HJ9J3kttNcVUJOfhlWlQ+jJ0wgKcJ/KDDaY6GmvIEBuwWX\nJoSkcAUF2YXYtH4kJCUSHeJzTIPv6GumtKSS1j6JuLGxKH+onrZUszHbguqcc4k1f/NkW2cte3IO\nkz+Qyq3RyQQetycuMdBaxup3/8maOivzmmtpUJoxePnh5zMUvC3auinKO0R+RTsqn1CmnTOT6O+d\n+7ey+/N32Lb9IBPveJEbZo/mu69XojfqSR4dRlBMyEnjJ+x9LWTv2kNVr0R0cjrjMpLx0Slg2N91\ndHTSL3qRmuRLVV4BjRaRkGF/N/K5bvsAzbWVVDf24hUejA0Xwg8RI7YOjlS20eE7hoRgv2PjNAQF\nOpM/sYZB9nZW0mkTCVGf3r678oknnnjitL7xJ0OkZv8S1ub1MXX2LJIivUdUmj6WP30Lf31/CxET\npuPqLOCJN1bj8B/FhFhfBEBQarBWr+LzUi8unDEaH/1JBm3EQYqzsthb7WHGBdNJifBFgYv67JU8\n8vfP6HDN4e9P30iUWQWinerdq3j2T/+kxBlISqSN5R+/wZEBH1ITY3BVb+TO+/7KihXLWPblUnJ7\nTfi7W/nyyX+yvbqb2LHjMQ2U8dZrL/DC68toqDjEpxu+4KsvV7KqOIh5l4yifP2rzH/0TVyxk4l2\n1vH+s59Qpw1ndOQgr7/wL/bWQ+bkTJQNm/nnC2+jGnc5kyIMFK59hTuffBdP3GQirVW8//xnNOkj\nGJPmT8n6j3j22Rf59IutFGxeRJEillhVMQ899ixV5klMCbay5oNXWZ1bRFVTH511ZeSXtOIbHktk\niDcNm/7APX95g4iZVxAr1fA/f3manZ545mZG0FdfwupP3mZ9QRm1zb10VBdyqLyXqIR4pNrN/M/D\nT/PFshV4zbiezBAdHoeFA+s+4Pf/WoQrahzppma++uhFDjRJJCYl4yjfyAOP/5NFXyxjT2kxH79d\nTPpkf/a//leW7hkk4+zJ+J4kxKW3ZCNX3PxHsg1juSQzhLINz/H20j2EjJ6On62aLz95iUUb91DZ\n0E9jYQlCaBKJEQEnXdXi7Kwgq7Yd75RktJX5VIhhnD8tHf/hQKTD79zG9sS7uTyyire2VHHWdbdx\nwSj/n2D1ywAbnrud+579gtBJ5+MlVvHQwo9oMaUyM9lMxY73eebJl2hURZOR5M3WV17gpR09TJs1\nBj+dleV//x1PvrmUbWu3UXJkL706Pyr3r+C9LZWExKYSGyRwYMlLPPX8GyxdvoPCLR9RpB9LsG0/\nTz7zAe1+E5ie6DcUhLfyI/71l7fo9IojzruR915/hQZdEmPiQ9EoBbqKV3P7LQ+xqzucs9KVFKz4\nC+vzu9ArXWxbvZhtxXU0t/bRUnqQfZUSkyaNonv/R9z2P0+zfd8BQs66nFhFB2s+eZFHF77B1v17\nWbm2GJegwlrwJa+/tgX/CdOICTSiEKBw9XPM/8sb9BrDsBxewd+f+ZTWtkZamgdR6uNITz95IwOA\nZCV/yxryyvqYfcs8/Dr3czCvisTzZ5MaE4T6RB/UM8DWlYt44M3NGOJH4de8irdefZm+gAxSokLR\nqAZZ/697eOS1JWxeu5OSnE206cLoKFzL6ytyMEWNJiXUBLip2vEx//uXp8i3B5Hg72TpH+9nWbUF\nddJsbpmbfkrDzwOFq3n8k12EXnw7N04IxDYwQFPpPt5/fSHLDgww97a7ufnKGQQZ1d8po6K7nw1v\nLGRpdh6l9f30NNdTXFSBxxxJUmwg9sY8Hnv8ST4pE5k+JR2x+EMeevxljOMvIS3kxBEPtoY9PPvW\nYvKrErj/b3cwOtz7uCJLoTISFJpAXFQE5hMEmnr6C7nx6t+SZc7k/Mh+Nn/wKOsLOokfN4UAg4sj\n6z/imZH+jhhiVKU8/OgzVJonc35aICDSW1/AB88/zjtbSjEH+lOx9FM+W72XOlM6118xjWCv75+y\ntrbks3j1BvrjZ3H9nIkEmY51To6BDg6sXEKjLoM5l51LoPb0ioJf0EiBm55yC+bQMPyDvI6pzBVf\nPMrfvijh1y+s5PZpgRRv70C/bwUVaTl0z4wlQAWgIWZUCuLOXqxONxKnMBxUu4lnH6nlMz9vmmpr\nsQ700jvpfnYuvJ6IQC0g0dNQyIqP3qAj+nz+9975JPtI+PQWsfC9L8jJSGd2xmV89A8Lk656nOjz\nX+H5By7AqHIwOljHv/70Me+Zorn/z5dx94KbqWtcyKq8IN554S4O//V3HEowI7Ts4IaH3iPmlmd4\n+KZZaGzNDPTWs3jTcmKFSCorVMy4/lymZo5CyEiif8dqqtweHE3buOmxj0m4dSEPzpuB2tpIb289\nyzetYOKEBCZdehd39dXx6GtrGZz5HI/dej5BBjv1q99h0ZJcpKuv5+oFf0bl/SqL8gXuePhRxgfr\n0BsMKBkkf0sN5aVq7kobw9SgyTzXe5i7P3ySrAvXMjtiFDf+7k841C+S1RvDgj/8jlEBegxGA8rI\nq3jvlQCumvt7HJIIkpu28q28+OIqzv3937h7bgY6hYe4AC+eeXUpy0PDueWiS3jtH3rm3fAA+Wtt\nrMx+jmSjSKK7lHve2UFF23ziTCdwPgNHeGDB4/hf8giv/vY8vHQK0iKDUL7+T9567iUef/p+5t39\nMK7+hdR7T+Kmm64iPsRrxJz28emuq8JAN1HxZyMotKzMqaWnz4YUZESsX8stz2Wy7mA6Ze+8hsZb\nz4TRYT/Jctia1f/i/rd2c/1Lm7jz7Ehaitz45r5LxYYsiqPq+OL9regzb2X+b+YSblKQOSqUp6//\nE79/PYH1D5zPNQ+/huOxy3n9sJWY657njqlhVG0dpPrN/UkNLrsAACAASURBVJQXtzBjVBrTb3oQ\nt6WG+9/ah23BIp67bgLC4BiqNlzD/jVHGLw4joGiXSxZ/AWaqTdwyx3XE2VyoW7cz9NPf8SsSclM\nCGjjsV89RHXor/nyn/MJsFTTtsuL5bnVTJhzMwv+cA8NXQth/A384drzCDIb8DJqCDj7N3z+Rii3\nzH8OlySi94vgylt/i8Ph5pm3irj+T/O5845zMTQGs/63/+BQdQtnpwSgUjXzxcMfMjD7YR6463IG\nyyNozH8ZZ9i13Pu7mQSbvU7JOfbVFbCzohDhnAVkRprI1ihQKl14JPGk8/luSyeNlTnUWbWEJY3j\niivS6M79Ex9+uIMZY5IZFerDFY++i/vR8/jbtmYCrv2Ue2dF0ZSjovrZLyg+VM9F44KxFq7mqZfe\nI2D2Pdxz3RxCvNRMHxtG+1m3U2079XJSenAzDknEnvcBDz+wHCQPHa11ZB+sZdaVv+HmX51HpJ/2\nuGVUoTIz586HCIrz40/v5HLLA09zdoQOrV6Pyt7Au6+8Tp0ynSd/ezNjY/yRJqQRqL2f/7ljPvGb\nlpPpe3zp1VNTRUdnD2GX3cCYMJ8TTgdrfUOI9QlBEE5cJy1Vu8ipa2RCWDIz50Ti7Xbyj2e28NWE\nMv58ZRrjLr2LBf0NPPrqagZnPMcjt55HiNFB4+q3+XjxIQZ+NQpNdx0bFr/ElkYdC/70Z6YnBiBd\nkA5/aKe5ETjFmJb2ynK62loZf3Y4fmbdsX+URGwDDRwuUaKcbkKrOa3zIcAvLKZA1IBCr0RxjJxs\nZelzy3EH3savzk3AoDcTkzaROx69lYsunIjf0ZovoFS5EEQFKukU3XPQedzzyCt8smgRG1a8yXVp\natj6Dof6FEMFWLLTWF3E2j0efJLHEeGjRhI0xKVPxmDopdM6gKgyYPbSIiBw+7zzCfQ2YTD6k37W\nOcy5Loyckl3k1g6iN+pRqwVmXJ5BclIGf/xqLx/eex5la17Handx6cwMjGoJyeBFUmgE/l09tFqV\nKJw5vPrGM7zyyWoO13Qy7q5nuWRUAGVr38TucDN3ejpGtQRGb5JDIvDp7KW524ZGbyYmIRKD8Ryu\nP3cSIX4mtPoAJk+fhNuuQKVQoTOZ0GgUCColerMJH28zWrUSUBMz7Xxm3vRr4vxNeOwu9P5ReGz9\n9FgdKFRqdCYjarUShVqFwcsLH28TGpUCpcZAQFQk0QoFAkPBeEfWfka9Usn4Cel46bVotAZikxPx\n9fGwakchTT0e/ONHEa3WMOuh3zImyBu9wURQUiYpgguPcOLaWrnpCw60tjF99lT8TTrUKg2+gaEk\np0ZwuKSI7XkdmAxeqNUaBK0as48XRq2ak0+bOmgs7IMmLRGBAQQmaNBIA9hcbkS6eXnun7l//f/i\nL/STtz0HL/0URkV+vcrCRX3+Fl567D7uuuN+3llxgD7rNxOLkmilePsSPtlaewoFtIM1b6ymz3w7\nt16YglFvIDh6DHc8eitXXDmG1kN57CpVEZ42inA/PWqNFq/wdCaNEal5603yLQImvwASkpMI8rmA\nK6YnYTaYiIyNJzw8AtwCAgJaozcJyVGoNRdwx9zx+Bh1GM3BjJ0wBtEhoBT7KT1SxM5iA8FJqQQa\nlUgKPaMyZ6KQ6uiwOmk+uIp1A4Pc8tgtxPsYMQdEkHnBb7jt4kuZOioEvUGPSqVAoVVj9vbB18uA\nUhBQ6cwER0cRASCAoFBi8A8lLCSCMTMmMfn8qQSbDJjjMsgwGFApPEONtaWJgzYX46ZkEmgyEhAc\nRmy8CaeyB6+wMPz8TxBsPBJnN9kHtpNVZGd6oomOlgb6PYOIqgrKmtqwOk5c7pQaEwnJk7j93ClM\nijAjetQEJioR+/qwOj1IKDB4B5CSFo+X4UKuPzcFs9FIaHgMMXFxSG4BBRYOLNtIRUE4M6dOJCzQ\nC61Wj0/UODKT4dSiDAG6ObAxH6Xycj7++D2ef+55nn/+JT754AM+fugG2r78gPc/XknnCee3FehM\nXmh1SgSFAq3RiI+PF3qtmvbD+8gpKiAsLZGosEC0ajU6oy9TZk6ip7OY91efaOdbN21NNVgtA8yc\nnoyX6STxIoICFIqT1kldQBK/mn0xt2aGoZAENF5avAPsDHYO4kJAozcTnRCB0XQO1507kTB/85C/\nmzERj11AiZv2mlJ2flJCSPC5TBgdgVGvwxQYR1qSN+ZTnq6xUJNfRkddGKMiozDpj230JY+LliN7\n2KfwwhQ4mhDdCR7zE/ILGik4AYPt5DRICHOC8RIAFAREZ3DDnRnfvVYCzMKpSyWDAq1OhUalQh82\njnuf/DMfXPwoDy5cy9x3foVOAqUkoe2vZPXHT3B47ydEDJdtMTiZQD8vFMI3AtPl8Rx9tNbkhU9E\nFIMlVvr77TA8vRkc6IVGq0KhUqIAJNGAzdLHC/MvYMfkDLABLhf+KRPJyDyXUe5Sat5Zw1t/383r\nbheuSb9mzRtTEEUD1r4unp8/h22TRh+9LzB5ChHGYSPdNvCLI8KkP6rSBcWInSqlY/2OJHqQEBAU\nalLnXMdlAx/zm8njafQbS0LTHgSf4BMOZUoeD5KgGBZ0Al9vhSUB0te9rhGVXm3yJ1zvTalLGgrv\nENwMIpGZGXn0MlHwYANOpvG+frYwwqMo1Fp8fcMJo3ZoB0+FBIof4GMdPVRadfSbogjWa3EkxWLy\n7KdrsI/Sz19mw2/eZmOchv7GCvaW6jHOm0i4Zii1NZvf5929NUy+4UHmacr43R/vZ3v1n3jltxdh\nat7EPY8tovlwIaEPf8HN32eHtZOCJg9ifAg+wlAGmgNjufqu+8DTw8YPN2EfTvs3qTcQlpqIYl0/\nosTwB3CjC07hmzg+FwjfOtvEZYWgVGKOLq6WEIRBvv5oKklC3ZXPe688zM5VEQQNj5j6p4zB16Sl\noygPSRAI9B0a0VHofBk351eMG36a8+te73Asj+h2g1I1NJwsfFNehhBx4SEg3IuQYK+jv1mROLqD\niCmMqcFu1q3dSv3l4biaqqgo7cD3rFi8T2U1teShpTyfzR8vptkRw4v/ezcIAtaBeuoHYLwknVxU\n6PzJmHI2nQ3vcf81C3H5+9Dd0kGbb/Ix/kdwW1GFpBP+9dI0wY0g2If+7eilos1CT0wkAWbDiNFR\nAd0P2DtO6qlgU5EH1YXnEKlSfdMoqPwJGx1L1Kh26tprae9zEBRwasGckigiSRKiOLQL7pB8/AZ9\nUAJJSIjSiWqVi/7GbhwWB8KwTzgevZU57Ny1A9O5v2d2zIlbZnXIWdx+fTuvPXgxT7TaCY7wprjJ\nzM0jk+OygV8sESbDN/5OGPZ3oou+3nZKMTE+PhTzUXME1AZQnGqHfrCD4uYuWiLTiQwJQP+ttsZh\n7WDL5x8QGD2OS2+fwZlYkP2LEgWCAB5RPLagqdTotRKSw45L5GiFczuduN0e1Ho9X08Ni5IWLMIp\neP/jF1BDTCaZgoJDRbV0SxAqSbicIi7fVK6+83H+8duzjjaKDosFSaNDI4D76FO/ea7oceF2WpEU\nCqQRi9td7q83uhi+TnRg8PLhkWUHuSFxWFaKbmxOF11VxbRNns8bF/+JvqYqcrYv5/3PP+G+jy5k\noc6B0TeQR5ft57qEEfc5XKD82it+tzIK30679M1VLXn7adP5Exul4aMb7uTDagP3v7mC62ck0VPw\nFrPmf4DTI2Id6EUUOZrPAtCwbzudoUkkx0RhPPpWAZAQFQ4kScI9Ys2Z29pHk8OCRSUM9xCGLXMf\nG/UtHCcNIxEVDiQknK5v7hPdLnr722mG4V0Lv+8px2LvbsNusuEVHY0OMJm90GgESvevZMVX4bz2\n1QSQoKs8myMmPTdNTUEHIA3S0GSjrc2MTqkhIH4GD14ZzN2f59B+0zn4JczlzU8uYN871/PKqZw3\nplKh14LgsOEU4es4Ro/bhXPQiugRUEgekDwjbrLRUVeB6AnCM8LxfZvvlIPjXjP8QknAIypwB0/h\n7j8/wj3XjDnqeOz9/WAwUW8OGPq/Z0R3VPLgcLgQBfU3Dd6weKtcv5SBqZcxPmBYRBxjw7B1ogjS\nN2VGMeJ+CGP6HF+Wr13ErdfuJtjRjCH1cn7967MwfScl38U50MrBTVvoT3qGnS/M4evmqD17Efc9\n9gItnf1DZUp/PIUhMVCfx1sLn2B5Uxh3P7OMKyfFkvPafP6yWUDpstPRMUhwoJHj91CG06BUotEo\nUHqceETxu38/RbpLDlLm8XDhheMZ2UZKHhudHV20tmvwUmpRfd/GRSP8Uk9VKfXd/UgeF5LgxuXx\nHOOX7d0NlANJJ4zE1BOVmY7Xml1I7m8Cu0ciuvooLiomv8iHu246WVdd5MjH93LFP7K5/OHn2Hjj\n2diL1/PcP15HsLsZ7B9EUmsZyutv2zOc/4KAUq1EqxARXe5TnSn4DgPtjdR0thI6JpOwIO9jvq7o\ntFC8+QNeKYhgxrx7uGys77/5lv+MX9D0gYDeW0t3bx/9Fvs35VMbw7Vzw3HlbWZ7Vd/QagGPg4r9\ne1i3civtR9sCkd62ViR/JUrld13eSES3G6vbg1MU8XhGqN1hzyW27aWuT2RwoJ+64gHiTdDVUEPz\nwNC6Ybetm/VvfcSekkZGjjB21/fgkoa28WyrqyYvp5y4mEhSonyQhhW30yUhjlgPGzxmKn5KD1UF\n5Qy6JEBksLmEdSvXsHn7Wpat30hxt560CWfz6/tf5OlrAnAJEJwxBT+li6rDFUfvszQVsmbVWrKK\nO4ccsk1CdDhwuocqtCS5cVoFJJcDp0cCFChQ4vFIeDwifc3tdHX1Y2kuZqu9n7Tf/ZFLJ8cjCB46\nypsRELG1lLHlvY+osSkQUAzdK4p0N7TQ02tFBNxOF0jgcYOgVBEUk4bJ7aKzqRuHRwLJTV9bB4M9\nElHBfpj0Kjx2J0gSDpcHkaG8Ep1Ddjs9J57f9Y9OJVivpq2qZXi1g4TL2k9HfQ/epgDCAvWIHhHR\nI+IWJTySdFLNKLqdNFfV4OjtIDbeHwCf6CS05i7ef/MLznvqOqIMGkSPnbJduzHqVEwZFTRchI2k\nnnsJv11wJWPCTUiuPmqanRjigzCqVUfLpONUDyDVRHLJ+REoCjayoaxnqOyLLhqL8ln5+QZcXgGE\naz30dHQyaB+qCPa+dmrb3XhHjCJQN3S9bXAoqt/lkZAkEY9bxG1343a7hvJDcmO3geS043CLw2ek\nuHHaJESXA5egISggmBi1nZbGejqtQyt03NZ2li58nezmfqKmXkCwwcPWVdvpcwyt6bF3VbFj01q2\n5LcPVS5JwOOWkCQPreW19NuHxIzbMVReRPfwwIbHg8flxuORcHlEJCQ8Lg+SJOFwf91psFCT7cXd\nT73Gmwsf4NGX3+bvf7mJGG8VbvFkX1jC7eij5OAGNmxvZv4jsxnZHJmDQtGavGhs7MVmd5+grHjo\nrK+m8kAv0ydeysVTE9CJvbR12bGr1Fiat/H4hzm43U6sgyA5bTjdI/NexONy4VH6MzEzitCBCorr\nW7G5h5yJs6+NlsGh95wsLZIkIXkcFO/ZhejWc96YCCRRRBRFXLYBag/v5au1Wyj1TGFSynSifE4+\nhKJAhSSBxyNi6e6ho7kLrV8EwX4B2Nq66R90Do0+eWw0ltahVASSHH3iIY2A2FQiQvzJ2bGb2pae\nEaJCwmXtpSRrEzv3ZxF57VxCTmraAHs+X4vJcAn33nYO/honlv4uumwKnLYaVmzewb7iNhx2Ec+3\n/Z1t2N+JagJDY5kS76ajrJCGAQcwtK11p8Ux1BacrNwM+/WW0lLaa1oYHR+Ev7cOSRTxuB30ttez\nd80bzP/LWqZNn89TD11wRkYJ4Be1+kCJ2t3G7h3NxKSmkRjtNzwCoCZ6VAy79m9jx+FeIv08tFcW\nsn1XEb26OKZNiEYjANIAWR9+RnPqbC6fkozxuAEeHvpaGsnbuYVVWbspbbcRHOSNydefAC8TKsFG\n7ob1HO6swSdpBurWvazfruLim8LYtecArT1gFAYp27eJVQcdZM4cR3SgCXfnYV77eCsF+5zEp5mx\ntZSwdt1XrG8M4qrrbuWcBBWlh/ayaWcOHVYtfho9geFBGDQqTBHJmCv3sH7DXtx+wUiDbRxct5GS\nahtxKb4UrNpOba+I2VtFe00JO7bnY554BdeePw1D+W42btyP2y8Iz2ArB9ZspKzBxZhZmQiNhWxc\ntoQDBXXog4OJigmi8/AOli75lLJmNeGpQQQFBzHYWc/unEokhZqG7HLUAZEkxmrI3ZdNm9NMqJ+W\nrpoCNr21hHbRikfrh2BVk3H2eAYaK9h/pBGVQqJsVxm+SSmEGfrYv20Vi3YUYAyMIiImnqS4GOz7\n97DrYDVKfyMDLeWs+nQlZQ2R3DT/apL9+jmwcSWf7cpnEF8iY6PRW+vYuPYr1ubXo/WKIDzAjwCf\n755tYQiLxa+2mGWf7kCIDESydJKzbT3LllQxde58rpwdSG1eFsu2ZFHR5cZL401QaAAm3XejsJ2W\nHkr3bGTZmjXsLmgjKDaJsEB/jEIvm9flE3HR3fzhknH0luwl50gOy9/5jBanmsRxE/Dz9sfXqMbg\n7UdYcCBGwUrh3q94d2sDF1w3j2nJoUNbKksitdlLOaSdzTVjA76nTqiISIokJ287q/Z3EBcEXXVl\n7N6RTbUrjquvnojKXc2u7GLsogosrexf+QErSj1c9+hDnBero3DTGlYsXUpdr4rI5HCMWMjd8hXb\nduZi05gIiw9msKqQjUs/J7ekE5/oMCKj/GjYv4Gvli+ntltLWEo4CalJ6HStbNlTQL9Nic7Tx5Ht\nq1mRq+OiSzMJDk8gYmAvuzZvoNcrBo+1g8N7dlBY0UrCtOnE+igoPpJHXs0gXiobu5cVMfrSWfgM\nlLNx3QqWHaggICqR0ABvLFX7+Wr9ZrLrLfgERxNs8lB+cBuLt+2n020mwCuY2Cg/ara+x1Nv7qHH\n2kTewb1k7cymqqUTpcGMv6/vcbewHmg+zJZN6/jg+Vco9zqP889OI9RHjyC5aKutYP+2Dew8cJgu\nu4FQXwU+oRF4H6esDHa3cuRADh2iAb8AkabDB1h9oIzKThfeQgc9pmQSBo6wfMnnVLQLRKRE4K11\nUbhjFZu27KFPMBCWEEVyagKtbcXsOtyM2aDH3VPDvvXv8OzyMhReISTHhxIaFsh3g/JFOkrzyc/b\nzZfvLaekM4YJ06Lor6+murqSwgM7+OKzL8lpNHLNbbdw3fVn4ac5cR9SEGCwv51tu3KwYsJSWU23\nRU/mRbMIt/ZwYNUu2kQBldJFfeFOnn/sS0Im/pEH7516wh0Xtb5hhCmaKcpaRU6bEhMKHK4BmsoL\nyd+9mXXL96Ka/nt+c1Hi966wqNq3juwqichUf+ytpWTt3MuOqj4E0YZCb8TotlOetZoD+bXoQoKI\nig6k68hOli3+hNJmDeGpwUTGJOLlJZJ1KI/uQSV6qY+yg6t4e9kuqnpURESEEJ8YiVH97bZDYrCr\nldLsXaxfvoGsvR0EJsZjVlhprKuhvDSXrSsX8dbKIkZd/UeeffpGws/Ulhv8okQBaPUS+Vu30OsT\nRXpy9NEIcbVvPOeOi2DgYBYH8nKpqWnHO3Y6N8ybebSg2zsO89kn+xl30VwmJoWhPt6wluSisSCb\nDSu24vYNZWyyD5a2GgYNMaTFhaLX+ZOcYKSp101HfSuCu5GEy27ispmTiNU5KNp7iIrqciqbtVx4\n41VMHR2ORiHgGhYFKVdNoj83j+aWCppdgdxy551cPSsJT1sZ27MO4tIEEi4MUlHWRcyksYSadSgE\nPcmzZuEv1JG1N4fqxlb6RC/OnzePsf5Oui2DNDfU0trVxpG92XSNuor7r52Gj85I8owZ+FHL7n25\nVDW0YBH8uODGG5gQraZo01ZyaiAi3ZuupjYiRidRt+wzipTjSUt10tLQQdjYmaSF+2OwNpCXnYcl\nOo2Z500nPiKcaF8dreUF5NS0ULk7m+QFD3B2hJ3yejvR513J9JQIgn3NKHqqyT2Yjzt9CuedPQFN\nw3aWbCohOXUMzuYyBoInMCs9jlHTMhD6ith7MJ/iygb6vOO48X9uZdbYSGzl21i6rYjohDTU/fU0\na5OIF0pYnVXLqIQYLB3dCKZo0pICj7PETEfSrJnEeTexaeNOalrbKarrZfLtC5g/bzLqzgp279hK\nl8uLAI2HhgoLsRkphPoZv7U8SmKws4GspZ9RaDNg8jNjcSqJiI0nMtiMu8OXS66cQWSwjsMrXmfp\nriqUoRMZFeFPe3sHuvDRpIQah4tZP2V7d/LxmhzGX/prLkqNxMdbP7Sp0Q8SBaDyjmHOtCRcObvY\nnZtLXXUdHp+J/HrBxYT6+pOQmIx5oJmDhwqoKsmlokPL1Qv+zHXT4lFKPWx48ROa/McQF+eiv8eJ\nl06k+EAFQng4SncLkrcf3QdyKR/wJ3msnoayJhImZVC25HNqDKOJjR6kq9tO1LizmZqRRpC7i/y9\n+dQ1lFLa6MvN995ARqQvSkFF/NQ5hKts7MraS25lLa2DOmZcfQtnJwWg1JiJ9NfSX1tETs5hDBdc\nyxWTExgo+IJPtjaTkZ6GtbsNtykQd81uyjrVRPob6XNp8Dc4yck+jJd/BEZ7O2Ud/mRGlPD+49lE\nXTiKyKAgdEo17r52ig5spqBxgJiMSYR7fbf72XpoOR+uLUIdmEZQgIhbF824lCCUkpWiHdvYklWM\nT3QSYUYn9ZWlBI2ZRqyf8VtBcAIGb298fDW0VBRQWZtLca2B2XMuIE7TTV2TgmvnzaDi48VUeY8n\nLVWko8VCQKCRkh252IOjMao7cGoDiE+bzDnjk3FVFJB1uIau6t3kuZPIDPbC1+RgoA/Spow7zvp+\nN+VblrJqey5Wv2gSk31oLS+iuKSEkpJSqhv78I+Zzp333sXlczLx/b5lcYICg9mfYKGDgoM5tOsC\nmDD3IkaH+hGenkFiFBRk76GstpH9OaWEXL6AJx+7jMCTzsUrCU2dSGpMEKW5B8jaWUqvrYX8nZsp\n61Vw8e8f5qZzE/j+EBAVEakJOJqLOVycS0NrE6JuGlecG0V3TRtx6Wn49jZS0iAQke5Nd1MbkaOT\nqVv+OYWKcaSnDfm78PHnMHFUCrFaBwUHc6moLKSqTyLAJ4yYQIm2+h5Spk8h+DtbHUv01BSydcUy\nSuxqQlMiwNZFRWkJJSUllFfU4QmZxN1/vI8Fl2ViOv0LDo5BkKQTRnr8P8RC1uv/4J0CP+596HbG\nxvgdMz8iiW6sg3ZQqDEYRy6vcZD70UKe3Srwx8cXMDE+4D+aV3EOdtPW0Qsab8KObpAk4XI6sDvd\naLQ6NCOGg+1li0ie/QBPbinnljgRi0OB1qBDq/wBVkgiLrsNmxt0egMalYDocuIRBJQC2Gx2REGF\nyaA7Jqju6/vsbtAO3/dDEd0u7A4nSo0W7YgtekW3E5vVjluhx9ukRpKGhnFVmhHXuJzYnC40Wi1q\n1clDXCTRg9Nuwykp0Ol0qH9I/pwCHoeVQYcbjc6ATnNmwm0kZz+H9qzly2WFpJ0zl7PGeLFrbzuX\nXjmNALMOyeNi52vX86L+Sb76TfoPeLCHQYsNUVBhNOm+Vb4lnHYbdreEVq9Ho1T8hKeFSjgdNhwu\ncfhd3/KAkoTbYcXuklDpDCM2NhrC47BjdYkYDDqUin//+x9+YxbXv3c5O/bfR9Dwpxbdg+R+8Rov\n7mzl4gUPcOO44H/7+aeGhMflxG53IGh16DQaFG43bkH5/fP330HEbh3EISrxNhmQPA7sHgG1SoXq\nP8inH4rk8eCw25FUavTab20g57IzaHOi1AyfbPgDcNsH6GzvZtAloTP7EBjkcwpi4Fu2SR4cVisu\nSUBnMqEWRURRAqXypJtMHedJR325VqtDo5Swu0WUStUJz0L5/8QvKtAQTGReeRk7dr/NpoNlxIdO\nwls7IiZXocJo/m4YkaUph7XrW8mcewOJ4b7/caCFxuhHpNHvW78KqDU61N8qyYMtFRw6mIeExK4d\n2xmnGEd6Utj3b5rybQQFar3xmGE0hVpzNC1G0wkG2I5z3w9FoVJjUH33CQqVBuOI3pYgCMcIgq9t\nNH47U06AoFCiNZj4qUbWlFoDJzsk86fHReORLD54+U1yLWb6BSt5mzuoD7iCC0UBsb+O9ev3kZvf\nS6NjFSvDe8icMfXU9pkXlMct+8N/RKMz/GAn++8hoNEa0JwonwUBlc6I6QRLsZRaHeYf4Rv5xk7G\n7C7gy5V7mHvWKHy1El11hzl0pAitVwIhPqdji20BpVqLUT0iQSOj/38QCnQGM19nm6DUoj8D7ZOg\nVKIzHn82XKHWYVb/e2vsVDozIVHm/8Q0BEGJzvhNHqFQ8O/ppe/68h+ocX7W/KKmDwDU5iAiTX2s\nW7kFZ0gyKeG+J91L3tFVxYpPF1NvGMM1V59NpL/+J+wlfRdbcyl7jzQRFjsKg8qDXhtIYsIp7KQm\n8wtEwtY/iN4cSHJKCmHBgQSFxTB15jTSo/xReaw0NXdjDk9nTHQAfgEBhESEYj7JXK/M8TEFJuGr\n66WusZWOhgrKysspr6zBpQ/lrHMuZHJKJLp/Y9RMRub/O7+w6YNh3P3kbVxDhX4cV8xMRnOS45MH\n6gvZeaiGkLSJZCSEcLr9q3uwh9ZuKyq1EtHtQlJ5ERri/UtaFiIj87NE8thob2yktaMHhzi0CVNI\nWDj+PsZTP0xNRuYXxi9TFAC4bfRawdv8rTn0b19mt+IQFWh1Ok6iHWRkZGRkZH7x/HJFgYyMjIyM\njMwPQu4by8jIyMjIyACyKJCRkZGRkZEZRhYFMjIyMjIyMoAsCmRkZGRkZGSGkUWBjIyMjIyMDCCL\nAhkZGRkZGZlhZFEgIyMjIyMjA8iiQEZGRkZGRmYYWRTIyMjIyMjIALIokJGRkZGRkRlGFgUyMjIy\nMjIygCwKZGRkZGRkZIaRRYGMjIyMjIwMIIsCGRkZ3yv1CAAAIABJREFUGRkZmWFkUSAjIyMjIyMD\ngOpMGyDz/5fBwUFqampwOBxn2hQZGZmfmMjISAIDAxEE4UybIvMTIosCmX8Lp9PJwQMHWLJ4MUaT\n6Uyb87PA4/HQ19eH0+kkJCTkTJvzs2JgYIBBiwVfPz+0Wu2ZNkfmB2KxWBg7dixXX3MNQUFBZ9oc\nmZ8QWRTI/Fu43W4GBgaYOm0at95225k252eBzWZj69attLW2Mv+OO860OT8rsg8eJDc3l0suvZTw\n8PAzbY7MDyQvL49DOTkMDAzIouAXjhxTICMjIyMjIwPIokBGRkZGRkZmGHn6QOY0IiF63NhtTiSl\nCq1Oi1L0IAIKpRI5fElGRkbmzCKLApnTgiSJ9DQUs2XLQfrtCvTeCvQBYYQKIoJXEEljM/DT/fcM\nXEmePg6sWkutwgdvvQocDuxuN+DChRKfwBhGpSQR6mdG9d+TLYCErbeJ7O17aFN5YdYo8DgcOD0e\nwIEDHcFh8aSmJhFk0vLTBsK7aK2pYUDwJiYiEPVp+RBOmsorseqCSYj0/4nTd+r8TMyQOQ3IokDm\ntGDvKObVV1+moj+QSaPi0Ni6KNh4gOU5hQTN/hV3Jaf9V4kCsNFQXsTOunqy85oIDx/NpEmRaCQb\nFls/LQ1b8AoKZc611zN9dAJ69X9L3ki4nAPUFB9ia0UNJeUWkpJHk54SiEqw0tM/QNuK9QQnxHPZ\nvNuYHBf0nzeckpv+vh66+iAqOhDl8M/uvkqWfPg2h9vH8OTff0WEv+E/TdyId7ro6uzG5lITGub3\nzTu7i3n3tdeo91zAyy9dg1H582iOpTNtgMxpQxYFMqeF2qyPWL5N4sXlf+bsKB/w2GnI2caLNeUM\nIPLf5nYEZQBzf38/Sdmfk7fpPQznnM2Cuy9CL3lw2Xoo3LuNL956m7dqqxAf+ivnpEWh+Zk0ED8t\nCkwBCVz9+z/iv/xtHss+SMzkuSy4eRJaQcQx0EbO5nV8+vobPFffyIN/+yeZof9hYy05qSstIeug\nwK/v+UYU4HbQ391Ec1c0Do+IxI/YYxYHKcoupLHHh6vn+Y14p53ezgaaxH5cP+4bZWROCVkUyJwW\neuvL0ajHEhvhM/SDUkdk5nTmzNrHXit4xDNr3+lHhcFkJCgkghClEpXZgMmgQwtgNHLW3GsI0Tn4\nw5Ov8/yHW0l/4kbCvXRn2ujTgkKhxuTlTYh/MP5qFRqTHqNRjwYwGOI4/4ZbCdX0c/0j7/K3d+ey\n5NE5/Cc7H3js/TSUFlDWlHLM7yqfROb95j4uIIhQH/2P2jy7BjqpKi2mmQnHPFfln8aC/3mYHl0s\nJsXPZ3RIlib/PciiQOa0oNAZ6O3P4sOl+7jnson46lSgMpMy4Sw8Fi1m7dd9JZGOmkIO5VUw4FES\nM2YymUmhKADRaaenvYXWLgta30DCwkNQD3bS0t5FT58FY2QKcYFGHJ11VLf34xY1hEf60lRSjugb\nSUJcFGaNAK4BqouOUFzRgss7hLHjxxETYEAAJNFNT0Mph/JK6MOH5IwxjIoL+mkqigSIJxghURqI\nmzmH2YkreG/Tu+y7eQ5Xjg1HKYDH1U9pTjbFtV14h8czZkwGwd7q4RtddDRWU1nbisIrnMRII+W7\nVvPVER3zf38JqrZmLG4FZr9AFJZGGvuVxMfHE+RrRACcvc0UHDpEZZsdv5gxzJqWxNdSRHRaaaku\npqC4BocuhIzxo4kJ8fmml/uj588JlKLSTNol1zDntUV8ueSfHJh/LjPD1IhuBx11JeQdrmBQ5U/a\n2DEkRPqjAtwDHRzJzaG82YIhNJIQhZOgsWcRoRngSNZGPl+8EUVmAA0NDZgNZny8DVi7e3CrDGhR\nIAgSeAapq2pi0GHDow0kOlCi+HAFTp0vcXFxhAeajzaeonOAsrwcjtR0YQiMYuKUTIKNSkDCaWnn\nwMZ1rNmYRcwF0dQ3NGA2+eDrpaGvrRv03ugECUaMFLjsA9QU5VFS3YHaL5S0jHSiAr0QRAftzW30\n9PVgEX1IT/ah+EAunR4N4dFJpMQGDi8xExnoaORIXgFN3SKBYQGoDQGkj4rB2/j9kuq/axzvvxvl\nE0888cSZNkLm/x8ul4vq6mrsdjtjx4793usFdwdvfrqKivxsdmzbTlZBPTaXQFh8MikpcfgYtCgF\nC/s+eJDHn9tC4LhJxJh6+eCxf7Gu048ZkxOgp4F1n73GUy+9T4NTT0LqaAw9xfxj4XN8tOgLFGnn\nMiHal878L7jzz8+RtfMQdbX7eGfxIjZm1SP4JDDKv4ePXn6BF74sJighHn3Nmzz36udEnX0VEXoo\n2vgO9z3zCfaQVHy7y1j09ko6zRGkJgaj/p40ut1uampqGLRYGD9+/Cnkooilo5K1S7LQjj2Hy2Yk\nHCM+BJWanuxV7MkvJHT2TUyN9Uey1fHOgrv4aFcfoyZEUZX1GSv2VhGePIYQ4yC7PnyZZ59dicvH\nQPGH7/LW4sXsMccxuOg9rJMmUPjm//Lm6n3klZSz7YvFfLlyFT1qXxJTRuGq2s6jf/0He/v9mZTs\nzZpHH+ezSiOzZ6eitHSy7cvX+eei7ejC43EWZPHxkv3oY+OJCf1+YdDc1ERLSwtJycl4eXl9f9ZI\nTprL8tm6o4qoabOYkfF/7N13fBRl/sDxz/bdbHbTe++FBJJAEnoNEFQQUVCPs9ypd+p5nqenV36n\nnv701PvpWRDL2U5RFESK9N6LQOiQhIT03stuts7M748AAtK8UxCY9+vFy7g7u/vMM888852nTdhp\nv6HQaGle9xHrCqtJv/k39PN2sWvxuzz51gIITURbsY9Z/16DMzCKWK9G/vHCS5T0eJHWJx578dc8\n+/IH+A27hRj7Ht57/TmW76rHYe+mrqKYhk4FYVE+7J8/g9fefI+vNkqMGNMPX08Hy17+A8+/P591\nK7dQemgz9Qovqvct4+PVRfhGJhMb4AHOel55+lneOiQxND2QymX/yz8/XErEsElEGQUaCtfy3luv\nsfFAIw57J5VFh+nAi8hQPZs+fJ5X3/mURdsM3HRLFgYl2DqP8cVzv+HTDe0kZCbQsmc9H362AWdA\nFAkRBvYteJeXZ/yLrxZt4ejmORxUJODbs4sX35hNi28mg+K8aDy4lg/f+5AiIZq+CZ7s+3I2Hy+s\np9/QvgT7elywJaChoYH6ujpiYmLw9fW98PGTXbF+Ou1TsqtaUL9pvP+3X2KuP8a+HZtYMecdnvvT\nQ/z2hffYUWFBrYTyVe/yyr/ryHvg90weN5TsERN57H9uwzL7FV78+gg6nzDGTr6ZUVnB1Le24BJF\njGHpPPbIz/ASrFidTgACMybzzP3D2F9YRFHXUP50xzRSFS0YDBY2fPops7+qJ//mm7ll0hgyIiI4\nduQQ768+hrV2I796fhZkT+fBqRO4YcoEMvqILF3+NQeruy9DrknYu0AUoKa2DVFyseXth/l4n8T0\nvz7CdXnjyB8zAuW+lXz91U7qKw+wZON6jEOGc92kKfz68SmUV5QTGDWMv3/yJpP69OXGex4m2bGL\nuuYWrn/wVwxKiMdmMaDsKeXFN95jMxncd+skhg3L4/G/TWHn1y/zxbZyju5bwdOzthM67DbuujGf\naXdej7++lHmrNlHTZr8MeQM97b3/rapqoqFkLY/OWIznoJ9x35QJ3HTrBOLD2li4ciXb1izhQLEH\nOdnDyOmfyZibf8s0rwpanOAZPoDpv/4f8lMCSMqZyiO/f5hbbxhGiJcfg29+iLvGR2FzWXCLIii8\nyX/oeW6Kb6G8sQLjmIe4Z9qNjM9JwVBawMF9NTgBR2Mhu/YXUK/2o1/WEH72+N8I3L2T5z/cgkup\nJTBpNHfc/RuGJUXSf+Tt/P6x3zF5VCa+pgDy7voLd43wpKHbChKILgfbP/pf5uyN4s7Hf8e4ESOY\nctftjI10sODjuWwvtdF/4r3cNtiX9tpdNA94gEem5zNm/M0MVOxnw6ID9Ag9HC0s5FibjiHjRpOd\nPYTpv56ITtRjs7ovKq/l7oNrh9x9ILsk1B5+jPn542Tm30HZ0WL27trI8lUr2bf8I+ZFhxAbNI7l\ns7dSpO3H05nx+HoaUGAgqu9A0n2fZN2seVTnP0VUZAJJ0XE01PV+r1LrQXhcHDF6PZrjNZfG6EdY\nsBmTr55Rt4xkdK4fg6+7G0fbEV6fs5egvLGMGp5BoNmAKXcKU/K9yR0UTsnK52jrsvPLEQPwN2pw\nagNJCw9nW3EjtW1WiDBd4lxTYfRRoFJDYKAnCmcx7769D1vGYwxICUAjiARGpRAZ5U9VWzn1NdDa\nomVAcjJhQX54BmQwWKulosZO9LRcQEFrYBgeqiACwvIYMeY6rhs8Gkmlo3PPR5QXH2bwbXeQEGJG\nVKgJyR7C8J7X2L6/lJDWuSjUGkbmpGI2aBBDoxjg58WCqiY6rA7wvdTjHVSYA3r/CgjQUbr2E3qc\nImOH9MPHQ4NbE0a/oAAOFjbTkmJG0bOV12ZK1Nx8Hbl9Uxnz+Ezs0UZUOhX+wcF4GtQIZh+CwsMw\nHP8FrX8YSXGxGEQ9iL2/6RMaQ9/0eLyLUrk5L5NAoxJ1TAJREcWIDgkFoPLwZ1D/4QwbmISvhwa3\nIoi4TNhb1IRdocTkYcYv0B+DXo3B25fgiLCTYyK8gyNJjY9FvVLd253TXcgn7+7Fnf8M2cnBeCoA\njzjS04JYvGoF+/eMoP/UofRJi0Gv9+COScMI8zMj2CPJyU5jZ7GIQqlEI6moWrmR94VXaZ8ylszk\nWH77eBTJkaaLuuDL3QfXDjkokF0SxetWohkyntiwOAJCY8kdkc9tU6fw8kt/Z1VRNZWNLXTYXbiV\nalTKb6spldaHiPQ4xEI7AoBSiVKlPKOJS4ESxWmVm4SETqsmItwXtVaPp1aP9VgjnU11eEcZMRp6\nOwMMkUN58tUhKJRKdq9QY2lt4OW7R7Equy/YJCS7A5/EYQTqtD9+Jn2HgN0uIYigVGlAsqHucdGy\n6zXGTN5CuidIkoRTNDOofxhe/hJ6k4U9JeXc0N0fZcNBdrhdjE8ORaFQAhIKJDRqPXqTP15qDTpT\nbz50uJVIooKFz/6KinWZGCQDSBKkJJNl9kRoUFF1YAfP/GI8nyUlgENC7OkhdOBQTOrLUY24sfb0\n/qVUahGcKloqj/LC3Xks7JcKdgnJZieg73UkDxrDbZU7eHHWHJ7ZMLf3KX95T7D1bQ0gokRCTW+z\n6ZlNpwqFHaTTAx6l5EQX1JcoY+/WCqWASvXtHbfKL527fmHnk38+Tfbv9pMyJJFde8E/Xzp5cT31\nN8+8KCsUtt68ByTJRotdQKHW8O3kEy0+4eGYfU243W4kCZSCDQLSSfQ6Xk4VoFLbe/9QeJA2dCQj\np2zljS/eY9vyD1AoYOoTr5LaP1luBZCdRg4KZJdEa8EsSsOGEZvk0VspKxT4xPQlP6E/dQckEFX0\njq1ycup9iSh00VxZiqgYwIlq9zuVmN2JRRQ5c1iaKIHL/W1lrVbrUKt12BQiouLEbyhQImB3Sgiu\nHrwCQ3l2/lZujj1+7yaJuAURFD/acLpzkHA3HWZFYTvdTCU/LQi1VEmPUk1g3gts/+DWk3eXoiAg\nihJKqZ7gsHjmvPs0DxV8RNXRRkzj/8Rv8iK++/VnTO4XBSeiJHD363N5bOIgvLW970uii+7WJlYc\nsROfPZynZn7M6LDjFx5JwOmWUKt+rLw51+VKwlWzizmHnaj1v2JiPyOFq2wEx6fyzKylXB95In0i\nLkGkubAA5e2vsPgXIlVlxWxb9jFvff4CD38ygvm/Sjv951xN7Npfj8EcTlqi37nTpThX6iTqtnzE\nr/8yE0fWXczZ8gVpwRpm3RnH6xZQuF30OITTv81Ry4adLUTFxBATbj79e90KlEiA85QXXVja6rB2\ntCGgQFScSPzpKToZJos9NNsUjJj+LHf8XqB4z06+/ugzlv3jXXKyM5mcE4dW7kiWHScXBdklodJ1\n8/b8TXTaXCcv+aLbTo/LjkOrAoOJGD9vPHo66eiynbhRwtbdTlOXFi/fCMzH63o1gEui93ov0VV2\ngFK7BYtdPDmYXxQlkMDt/rai9A6PJSQmlqP7i6msakaQJECk89A8/vrhQQLSsvDATVVJDQ6hd/S3\nreEIi75exsZDTT9KvrhdAg4kJElElCQkSUIUXFjaKln8/iuUNDfz85duI8nPE4UxgAEBZtyVR6no\ntiMBkuCgcON6Fs9bSXV9FR0h/Xninc946akZfP7lShb89WZ8cR/PcwkkCVESkVyu0yY+mMNj8PXx\norGslm6rs3d7yU31pk946esyAhJSUdh6qK9qwiX05pulbBsfzFtHUe0PP95CEiVcbhEXvXly4p/g\ndtLVdJRP/+9/aNboeeTj+whXqghI6YfO7aTmWB3O4+nrqd7DFwtWsWXdbP719QYaCCJ72AQeeeFz\nZt6qoNt9IvBRILhFRJUbwWWlsa2FVqsTEBHdahClb/NKEnA6NEhuF27xeLpEBaJLgSAIiJKNw+s3\n016fzKP33kJKsAHJ2UJjG4gGKNn/Na/OL0ISFIiigKhy43Z2Ud3SRpfNBYgILjVIIoIooTL4kOzj\ngbutha4eFwCCy057ew8udQA+JjMahYjTqUJyu3AJJ/JKRHCqkQQ3guCk+JttfDV3Ne6AeEZMuoOX\nP3qRjOxoBASki2gqkFsTrh3y7APZf+T7zj6o2T6fL+avwaX3x6wVsFu7KN+ziUVbtxOWPYz8IYNJ\n7+vD4b3L2FjqIirQE1tbLas/eYVlbcHc++TjZAcZQLRTWXyQ1QU1GAICMblb2fzOB2zbd5R6AoiP\nisZP3cbW9WtYt7sC76AEIr0NePqY0Hh440MTZZvncaxHi8FkoqullK9fnYF7xM1MGp6Neu9Klq3a\niz4qBrWzhR0LlnCgpJu0kYMIM5+/C+F7zT6Q7FTs3c/mjYuZvb0Ub/8IYkK1NNfWUnF0H0vensHC\n7bVk3vkkD980DB8PDWAidaA3y1d+xZ5aPbH+OlrK97J06XY6PZMZmuVHwZcfsWDNViqqKti3fSMb\nt+6hts2CyicQP52Lo9s3sX7dFtpdPkQkh2M0eGLUqdD7h+LbXsbauUvp8AzGx1NFa2UBHzzxIVF3\n3sPoPhF0bVvOlr2VeISEIlqqWf3+l9QpA+mfk4qP4fyNjhc/+0DCZevmWMEuVq5fzopDjYSEhxPg\nKdBYV8exIzuZ+48XWVqiYOITb/DI2CSUKhXmoHBcO1ewZkshhohIlD0NbJq9gJJWNbGRSjZ+tpEe\nTx98zWpaa0tYu2gjxqE/Jz/JF9HVQeX+1RRXaPHx6eJQVTs+kfGYeypZ//WnbCu0EJ4YR0yML/V7\nNrHg0w852mQgISsOs8bOkS1LWL1yKza9P1HJ4dgqD7J7XyN+ydF4ay2UbFrMjPXlOJQmQk1dWD0z\nGBLrpHjXZuo6PDGqa9nTKBIXH42iuZhVX33EjjIlSf0SiYqOIyFZYvWqJVTZfAjxFCjfvZZ5yzbg\nMfRGpk0airLuCKvmfsKOAy2E9IkjMtSHpsObWTTnU461mInPDMJeX8T6tTtwmkPw0dioKd7D9gNd\nDBo9lNhALy60Lla9PPvgmiEHBbL/yPcNClqOrqEmbiKRRfNZsHYHpWWFbNuyBZ++1zP9lslEeuvQ\n+sQwJCOeuo3LWLjjAFXfLOVgZySPPPUs+an+vV+k1OHn54Wz5SjfHNrP/o3bID2HGE8TjrZj7Dri\nRabvbt5bUkJKbBTWogNUdmpJzemDp0pJQGw6SVEhHNmxhZUFe9m4Zise1z3Knyemo9N4kjpqBEbr\nQZat2siBwlKa3V5MuOsOcmO8L3i39H2CAsndyOwnnmV9rZXo8ED0jloKtm9nx44d7N5zCHtIOtMe\n/CN3jM/Fx/jtZEh9UB9GpAZyaMkiNu44xLGKajyiR3PnnQNpO7iZtQUluHT++Hvq0QsuGptrOLh5\nEe/sEJk0xJclr31Gk38SZo9WDlW24huVQlyAAdAS1X8giSE21i1fxv7qWrYtWEPq7//BvcMi8fAK\nIjU3DVvtbtZu3cnegkM4w7K49bbriQ80XjBvLj4oEOmsLWT2CzM50CkSHWLG2VrGruN5U7C/EFXa\naH712F+5dUgialVvs7nW4EPq0ByU7XtZuW4r+w8W022MYvL0W4jXt1Dd2kHRvm8ob65n01dLqMl+\nkOduH4inGrR6T7y9vDj6zTo2FtQRmzqIcYND2DpnDusOiYT7uik61ETq6CQ2/u0VDujTiI7upLq8\nFS+Tgp2Lt9DpHYBoL8WqDSZ35FBM9iq2b1nHsfINrN6ZyNNPTaR99xaaHEHc/vMJxAT5Y9SqOLx9\nLZv2dZAzZBRD0z1Z/u6/2VrjTaK/hYJdDWRNGk1cdBqZoTq+WbKIDQUFFB08SnD/yfz651OI93Oz\n5cNP2VCuJSpVQdHuYuKGZrL3zdfZJyUTFtJIZWUj+qBonA0llFcfo+jwHrYXHCbrhlvJz0nFqL1w\n9488JfHaoZAkSR5YKvveenp6WLN6Ne3t7dx1990X3N7a3IAUEIzB5aStqZ42qwsPsw8B/r7o1Wde\nUkR6urtwSBo8zcazrg8guR302Ow4RTUmowFEB4KoQq3RcjFd3KLLjq3HgaD1wKTXnN7FLok4bVZs\nbgUGgxGt5uIaT202G2vXrqWxoYF77r33oj7znxJFFz2WHtDo8TDoULobePe559gnpPLIw78kKeDE\n4DgXFeteJ+9Xa5i3fwUZxov4boeNLpsDjd6EUX96ZkqCG7utBxdqDAYDmotcennXzp3s2bOHGyZO\nJCws7Hvu7cWTRAGnrQeHqERv8ECrViA4bIhqDWpJpNvaA2o9ZuOZsyUkXE47DqeEzuCB5r8eJiHi\ntPXQ43Cj9/JCr1AguVwIKs0pD7gScdptOEUVer3+gg++EtxOenpsKLQGDHrtxS8aJUm4XAICKtSS\nHZvdiVLngUGnQXmR/QL79u5l9+7djBo9mri4uIv9ZdkVSB5oKLskjAHBvX9otASERRFw3q2VeJi8\nOd+K9gq1DqNJx7fXOMP3KsxKjR6j1zmm0SmUaD1MXI75BhfrxFLAJyn0BIf44j5QyJ69+zBlJWLW\nKemoL2XdrjKMySl4X2j1pRPfrTPgrTOc9T2FSo3B08zZ3738FEoVOqPptGWPVTrDyQuo2etcR1WB\nRmtA84MddCVagyfaUzJKodGcUUaVaPXGiy5nKrUW0wW6sM5KoUCjVR8Prg2YznFsz0e+c7x2yEGB\nTHY1UJkZOm4iVnElNYe2sbyxFA+ViLWrjcKOYH73+O2E/ZSjHJlM9pMgBwUy2VVBiV9MNlPvTqKu\npoqaxjZcbhFdUn9umBZDsO8P+Nhf2TVHnn1w7ZCDApnsKqIxmIlKSCMq4XKnRHY1kbsPrh3yOgUy\nmUwmk8kAOSiQyWQymUx2nNx9IPuPqFQqvLy8KC8rY/WqVZc7OT8JLpeLiooKrBaLnCdnqKutpa2t\njR3bt1/co5NlPykNDQ3oDQY8POSxKVc7OSiQ/cecTifVNTWnPV/gWiYIAk1NTdhsNlQ/2vMArkxt\nbW20t7XhdrsxGH6qExpl59LR3k5YePjlTobsEpCDAtl/RBAEbDYb6enpF7V40bXgUi5edKW5VIsX\nyX4ce/fupWD3bnp6ei53UmQ/MnlMgUwmk8nOS56SeO2QgwKZTCaTnZc8JfHaIXcfyGSyK4MkIQhu\n3G43kkKFTqvtfWaF6MaNCvXFLuQvk8nOSQ4KZFccl7WV0qNHae4W0OvVuJwuhOMPvHfY7Zh8w4lJ\niCXoXM82uMpJbjvtra102dxoDSZ8/X3RX8njHkUXXa31HC0po6a+CSfgcCoIiMlkWP9Q6teswZI1\nnowg3QW/SvafkcOta4ccFMiuOK6uRvZtW86KJbtp6LTjl5pMuL8JtUJJW1M1jh4F4TmjmXjjJHJi\n/S53ci8pV3cD27as51h9D4Kji/IGO1HxfRg/MZ9o7yvv4Qduexcl+3ewetlqCspa0Jk8CQoLxt7Z\nSu2GPZQVRbDnfz9i+NKxZARd7tReveTug2uHHBTIrjiGwESmTL8ba3E1b63tZPq0+7hhUBw6pRJX\nTwt7Vs/l/Y9e5f/q2vm/Jx8m2nytFHMbe1Yv5P01hQwaO5EBIW5aFn/Fa3/+hMPVep770zjMV9Ao\nIpe1lYKNi5j571V0qyKY/ouHGDM0HR8PLQpcHNv8Hg9Pf4GjvhN5NFKe5iiT/RCuoCpCJuulUKlR\nuLuodXai79uf5NgofExmjEZPvAOiGXXbw9x/c38K189n1eGWy53cS0aw1LJq7SaOtQaS0S+LAQPz\neeKJR8kLsbL0wxnsa3Fd7iReNMll4cjOFbz82pe0qvvw4F8eYdLY/vh6aI83ZWuIG3YH04d6ocwa\nTpS8ps6PSu4+uHbIQYHsitReWUpdQw2J6REE+BpPq7QUCg2RKWn02F0cKW28bGm81CSHjXaXg6qd\npbS2WhAAlVcIcS4FklhIZZP9cifxIom01xay5N/vUe7y4pa7bmVEWhi671yZTMRnmkgfmYHxciTz\nGiJ3H1w7rpV2VdlVxU5NYQlNFVpypkXiZfpuX7kIgASicKkTd9mozFHcfueD5IzRkhHjR+/YQitd\n7aBQhxPkfWUMvBSd3Rzds4aFW1tJGT+N4YNjzhIQ9ArJfYAHI6MvafpksquZHBTIrjyOdkor6qnR\nxnNLaBie6tOvGJIk0VxcjEqpxHgNrdWu0JjJGjiCDBSoVSoUQO2W+SyTRGIm3UdukOZyJ/GiuHqs\nVB/eR6dvBCnDBhHlee50h2TfTKD2ygh2ZLIrgdx9ILvi2NvrKW2uRZMcS3iIH5oz7iJFoZUtSzeg\n12tJjL+2hqSr1Go0ahUKBbgadvDQM59SO/Rh/vnnyXhdETGBhMveRX35MYLDfMnoH/ud43sqhcGI\n7kqebimT/cTIQYHsitNeU0VTVTnJiUGEBpqjJ2MVAAAgAElEQVS+Mwiqp3Qj/zog4h15E3lp3pcl\njZedtYTnH3iKA0HTWP7GA6QFXim97hIuezfNpQ1o1CoMunNHMkWf/IG3v2m7hGmTya5+clAgu8LY\nqTtaTk2hJ7HB8fibz7xodPD504+jMBq57+m7CT3fbebVylXHG794lA3Rt7B6xgP08fekYvNijnRd\nCeMrlOg8A4nOTkKpUKI+19MmhWO8+nozOfGmS5s8mewqJwcFsiuK5GinrLGWYz5xBEdGYFIBSEii\ngNPeyJdPXM9Le3RMe/Zz7kz3ueamUonuZr741aNsjLyOfz1+C2EeKhy2DtbNfJ9jlsuduoujNXgQ\nktCHlsY2DuwvO7laJQCShNvZzarn7qP97l+Q5SMPi7oUrrXz6Fomn1GyK4MkYLW0UXZwN7v3HUAK\njEWttFBTWYEkOmgt288n//NPtjld/PmjNdw7LPJyp/jSE7vZ9MnTfLB/C0Vejfxi8kdoDQa6Skvp\n8r6ZJf5XRue72uhH9thpTNn0AMs//gfBnn9gREowSoWbnuZyVrzyEl+4p/Lu7wfKzzu4ROQpidcO\nOSiQXRFEewe7V37C8+8sByCIUma/+ASzT27hw4g7/8yXt00gxvfKW873hyB2N1JQY8ArJpe+PT24\njje9+6WkEJY9hsgrJluUBMQN5IEXPsD0r/eY+dc/sTguBh91AxU1reRM+wNzpo3B33jF7JBMdsWQ\ngwLZFUFp8GPELY8x4pbHLndSfrKUXvE89tQrlzsZPxA1/lE5PPy3vtzZ3ExzuwX0ngSGBuJl0Mn9\nnpeY3B5z7ZCDAplM9pOl1OjxDY3AN/Ryp+TaJncfXDvkgFsmk8lkMhkgBwUymUwmuwC5++DaIQcF\nMplMJjsvufvg2iEHBTKZTCaTyQA5KJDJZDKZTHacPPtA9h9RqVR4+/hQWFjIvC+/vNzJ+Ulwu91U\nV1djtVrlPDlDY0MDTU1NrF61Ck9Pz8udHNn31NzcjNlslo/dNUAhSZLcXST73iRJoqGhgS2bN+Nw\nOC53cn4SJEAUBCRJQq2W4+1TiaKIKAio1GoUCnnY2pVGFEUyMjNJTU2Vy/ZV7qKCgptuuulkhBgR\nEcGvf/1r/vSnP6FUKklISODpp59GoVAwd+5c5syZg1qt5oEHHmDkyJE/dvpll5EoirjdbuS4Uia7\n+qnValTnekCV7KpxwZDvxF3grFmzTr52//338+ijj5Kdnc3TTz/N2rVr6devH7NmzWL+/Pk4HA5u\nv/12Bg8ejFYrL0V6tVIqlfLxlclksqvIBYOCoqIibDYb99xzD263m9///vccOXKE7OxsAIYPH87W\nrVtRKpVkZWWh0WjQaDRERUVRXFxMenr6j74TMplMJpPJ/nsXDAoMBgP33HMPU6dOpaKignvvvfe0\n941GI93d3VgsFkwm02mvWyxXyLNaZTKZTCaTXTgoiI6OJioq6uTf3t7eFBYWnnzfYrGcHJVqtVpP\nvm61WjGbzT9CkmUymUwmk/0YLrhOwfz583nxxRcBaGxsxGq1MmTIEHbu3AnApk2bGDBgAH379mX3\n7t04nU66u7s5duwYCQkJP27qZTKZTCaT/WAuOPvA7Xbz5z//mbq6OgAef/xxvL29efLJJ3G5XMTF\nxfHcc8+hUCj48ssvmTNnDqIo8sADDzB27NhLshMymUwmk8n+e/I6BTKZTCaTyQB5mWOZTCaTyWTH\nyUGBTCaTyWQyQA4KZDKZTCaTHScHBTKZTCaTyQA5KJDJZDKZTHacHBTIZDKZTCYD5KBAJpPJZDLZ\ncXJQIJPJZDKZDJCDAplMJpPJZMddZUGBhKOridqWThxu8aI+4bZ1UN/cQpfd/SOnTXY1kEQBl8uF\nIC8EKjuFJIkIbhdOpxO3IHKidIhuAbmk/DhEwY3L6cTlciMez2RRFJEX6f3vXPApiVcSZ1cd6z6Z\nyXJFLr+7bTxxfvpT3pVw9rRz9GAJPVojfqHRxAZ50lm+lZnzdhE18CZuHdEHs+48WSK56WxuoLKq\nCUGnQ6fsfTaEKDpxuVSYfP0JDA7E11N/7u+QXZC7p52Gdhd+QQEY1IrLnZzjRCwttRwtLqa2pQej\nbzLZuXGYtKqzbCvQ3VxPVU0Tbo0GhcpIWEQovp56ztwbSXTT3VpPVV07bsmFQu9NREQkvkbNpdip\nq4LT0kJzN/gF+qFXXdryIriddDTWUFNVQ1ObFYfLidrkRVxqOmFGJ3t2ttJ/VCoG1SW8/xItHNl1\nGItKgzE4ltRw7++Uu++QbJTtPECrzohRq0RwOxAEABEBBXqjHyEhQXh76lFe5lOyp72B6rJy6ls6\nsfS4UBk0BEYnEhfqTd2xZsxBQYSGel+6O17JTkVhCS3dPYi+0fSPD+KCxVBy0nC0lDqrC51egyQ6\ncbt6gxkJN5LGTHBwCIG+ZtSX+Nb9qgkKJFc3u1d9yqI9Zm773UCi/M68MItYWkv499+fYn2jwKBf\nPsc/fzUQv9Q8bksu5dXFcwkL/BVj+0ahOddBkBxUHdzGxx8t5GBXF/YuFRFRwfiY7XS0KPAL8iI4\noT/Zw0czPD0c7Y+90z8BbkcPFqsNlacPJu33K70uWzcWuxudpxceJzNd4Oiyj5m5oZ5b/vgMoyJ+\nGgGWq7uWVZ+9zMKdVbRVFlFYlcOn38xkUIjndzeWnNQc3s7sz+axt76FJmssf3z+j0waFI/utMpC\nwtJRzYev/Z2v1h3DOyqY+L7DuO32n5Eb43Wpdu2K4ehqoxstZqMR7cla182+L2bwWYmOnz/6B7KD\nLtVZJ+GwtHD4mw2sWrGGQ2XNKD2DCTJLWC2NeMQOpY+pijeXxrByaPKlDQqERua88gIri8vwm/Iy\nXz09jgueRWIbq2e8wUqnjY52C6aQUCK8TShEOxa7FbvgT0bWcG6YNIrECL9z15H8d3XCeUl2qg7s\nYNXK5WzafBDBJxQfgxG9sgm7PoSEaF92FghMuXM6k0O9f7jfvRChg41zPubzhQsoTP0jBz+9D/OF\nogLJwt6vv2LengNUNrej9AskMcgPRAlRaKXZ4kFUdBbXT8onJzMW46W8OZKuCqLUWrhCevi390iv\nzt8odTnFs24lCHapbOdi6aH8EdIDL62TbCfesDVIM576mfSbF2dJ5a026eyfliRJEiSX0ya1VhdI\nLzxyu5SQcaf075UHpdauDqm5rkzauuBFadqQRCl28u+ltWUdP/xu/gR1VhyU1i+fJ+1psH/vz7YW\nbZdWrV4uHWlxnPKqQ1r+x+lS//RB0nsHun64hP6Xmgo+l345caL01oL10p4Fz0uP/eYp6UCz9Rxb\ni5LLZZeqC+ZID0zNlcJCsqXX5+/4TrkUXDZp2/znpLCQEClz1CTpnbVFUofVJjld5y6B17La7Quk\nhVsKpAaL+5RX7dJnd42WBg2fJM0vsVyilIiSrb1aWvbWk9LdE4dIdz3xD2n5nnLJ6hQkSZIkZ2e5\n9PFf75X6xkdLE19eKdldwiVK1wmC1Fq9X3pqQpo04aEF0sXliiBZujukVa/9TErKyJH+vuyQ1N7d\nJXW0d0iN5YeleTOflcbkjpXufma2VNrSc546UpI6Kw9JG5Z9KRXUf/864Zzc3dK+xR9Iv70uRZow\n/SHpXyv2SW02V+9btjZp65zXpEm5adLQe5+VtpS2/XC/e1EEydZdJ3107yApIe+fUqv7Yo63INnt\nVunggr9JA9LipLvfXS+1W7uk9vYuqb2pVvpm6SfSLyddL42a8oS0/HCTdClL0NUxpsDdybYtm+gw\nRDOgXz9MmrNHVUqlBqPZCw8tKODbJjV9EFNvGEzNznUcKG/g3MMRlKg1enxDIojzDcTH04DZy4iX\nyQv/kBgGT36Mh65Pwr13IQu21/3w+/mTI9BRW05JwQEs7u/bj+empayYskPF2E4bzqGl/y8e5KFH\nHmdUhOEHTOt/x2XrwK1NItQnirQJv+GPf3uUFN9zpU+BWq2iu86Gv1cIgaEO6jvbcZyWRxJdNQUs\nWrmXpHAfggISyMmMx8tDj+Yn02XyU+Kkem8B1ZX1uMRT81HH8Ef+zAO/eoDsoEvTqiQ4u9m58FVm\nfrAQTdZ0/vi7B8jPjD7Z2qUxR3PLL24iMsiHUZlRqC55e7sSo7cfnroT/3dxn/HwgOrdhZg8Yhk2\nIBFvTxNe3l4ERqdy092/ZNq4cPauWsGhskbOfboLdNSVc7TgANbvXSec+zuPbf2Yl55+jgNe4/jT\nk89w3/h++Oh7G7pVeh8GjM5j6NB0+sUEEOJ/lta7H5USvac3Zg8VSgWcrUPxbJ/R6ZQ0Hj6K2x7A\n+KFpeHuY8PY24R0QSva4KTxw/0So/YbVawqwCD/yLpziqug+cLZXcajITXRkFilh5u++39VIeWUD\ndrRo3DY4S3dtYFo+fRVL2VNYzci0SDS685xKkgjHB7OIcMpAIjWeXgYkCbodp0cWgtNKY1UZZdUt\nYAwkKSUWf5MBd3cL9W1dWB0aomJD6K46Sl2XC5NfMGEhQRjUINgttLW30d7twjckAFdTLU02BaEx\n8QQY1SCJdDdXUVxcTrfkQURsAtHhvscPrkBnfRXFJZVY3ToCQswIeJOeEoYSCbfTQkVREdXNFsyB\nEcTFxeBtEOlq66Czq4se0YPIME/qj5XT4pDwDYwgNtwXhSjQWXeE9SsWsr1cS0R7M81aI0aTCYNe\ngwIRS0sVR45UYhU0hCWmEB/mgxKQBBetlXtZvXIFB4U4ktubaFIaMXuZULm6cXmEM2RwAOZTj4Ho\npqu1jqMllXS5NIRExxIddnzMgeigtakNS48Fm+RFQrQHpQePYlHoCQwJJzzQfOE+VURaKosoLmtE\n1BoJj08kOsgbBQK2Hgtt3T04RQsdnc00dfkS6GtCfb7K3t1JSaWKiMQRJFic1DZ0YXe4waA9XoRa\nWT5jLvr0ccQcqccSPoAor4urTv4TbZXFFJbVI+pMRCbEER7gfbzykujpaKS8tIKWbgfm0BiSY8Mw\naHrftXc20dRqxSWAd3AAzuYq6joEfINDCAn0Q69W4OrppLWtk+6uHkxR8Zi7yzhUbcVo9iEiOvK0\n4yjYu6gpP0ZFfQcar1D69InFrNecPD5uawvFh4tptoJXWCTxUaEYVU5qD69n8drt2AbG0dnahMZu\nxM/PjGhtQfSOZ1COhFGrQHQ7sXS00tpuRelhxtsDGusasLrVBEdGE+jt8W1/ryRia6unrKYZDN4E\n+hloLNxLeaeG9JyBRAcYz5KTEs1F63j9/YV0RdzCX+75OSmh370IeQRFYdL2JSPKF+V5yokkOGmp\nraCkvAG31kRsYiIhPkZUSkC00VDbjM3pBJ0PAWaByrJa3FozYWEh+Hl5nFauXZYWqqrq6LQr8QvW\n8H37LyXLMTbt6kSfMZxE39MrSaVHAOlh3gR3bqa2pQ2HEI3mjKuHJAp01heyYflCth9TE97RTLPu\n1DoBRHsHx4qPUt5oxegbRHJaMn7684cttvp9vDXzA7bb0vjHX59keJLvd7bRmn0xe6cT7x+Or+d5\nxuNIItaOJkqKSml3qgmJiiEqPLC3HpGctDe30W2x0COZSIg2cuzQUbokLQHBEUQEe50WYAn2bhrr\n62nucOAV4o1LJXIRFc237PXs2lNHj89g0oNPL2sKtZ7gwDD6ahvprCml3SlhNlya4PIqCAok2mqO\n0tTSTdyACMynddq6Kds8lxlfrCMwYzyJHlYOrFjGzkZIPaPcKAwh5CZ58M6+Y3TdkI1Zd/F3HYrj\nv9V0dAefLC5Gpcpm/IDQk+87OuvZsGweqw61Ep+UgO3wahZo47n7gSmEtO/kxTfm0dYlEBwWiDk4\nnlgvgeItB/AfnMctt00ioKeShbM/Z/3uRvpnx1JZfYTaWif+uQ/y5mPDqdu5iNdnr8E7KZdoOlj2\nxQoG3HobN45IoGn7V8zeUIFfZCJRvhJLXvkXBYpxfPTe7Wg6Kpj/yhvs6vAjc1A4jduWsjY4l6lT\nxtC5aylzvt5ARaeZrBhwhgwgyauFN2aWMeKuJ5jeV8XmRbNZsmMHx3pCMM/+gIPBsYzOH0dGYjAt\nBW8x87NviB40Bf+eGp7+7HPSp9zPH65LwdZcyfqFn7Ni3z6a1FbMn73HN0EpTJw8Du+W7bz83iIa\nWrq56Zn3mJrsieiyUbxzFe9+vR3f+AySDe1sWTOH4KwbmDx2OIFGBwdX/JsvNh6iwxnMsGQXXQED\nCVZUsKNU5Prp9zEpI+g8R9DKjk+eZdZGgdwJwzF0H2HxF4tJnngrt4+JonTPBj6bu4mioiqUS7VU\n1uRx7/QxhJxRKZ/K3dVAvUaJMSWNxJJt7GnuxO50c6KmLlv+f+ww5PDzPj080q1hSFYfvH6Udjsb\nu756jY+XHiZ+yPX4aQp5/6tljJn6C+4YGETt/lXMn7sWh38KCZFGtixcxOyo4Tx6//WEeGio2v01\nz3+0ATR6/OLS8HGpCA2wUXG0lfSJP2fCqHTsZTuZ8eFCKqpbCBo4BLGwiwHj42nYvApb1A3c++AU\nQgzQ01zO0oVfsqNGIC0piob5i5kXnMsjv7uRCJOe7qrtvPrKZ9RrExiR4cm+Tf9ic9R4hveLYdei\nOWysqEDFRrysZWiDcrnvrrHYDqzgqXdWoTZ4cetf/sEw7w62Lp3F5yv2YwgJw0MTSEyEP9q2gxxt\nCeT2R+8nK8oblQIqdnzFm3M24R2fib+jkr3FbfipO2hxBmMljPDrk79TQUpiF2vfnMH+Nh9uvPtm\n+keYzp7tWh9uvOMu0gJN575TFyxsX7OMzzeVE58Ug2fTQhbOdZL/yycY1ScCDT1s/fRlFh5qQ6cP\nIj3BA/xicbSW0aiKZ/q0yWRFeQECNbuX8cGXK1FEDSIzRM2qt1eysQoUERdfUrrKdrPHpaXvkP74\nnjM+FY7PrpA4/QooYetqZMui2SzZvp0SazCm2R9wKDiGUePHkZkUgqP+EDP+NYtyXRz5fSOo3vAO\n8xYG8LNfP0L2ufIRG7tn/5v1e9tImvxXrkvxO/tmKg8yh+WhMgfhea60SwIt1Qf454w5uKP6kmmo\nZ8Pi94kYPI0b88cQYHBwZO3nfLFmD832AIYkuegKGEyUtoq3D1rI//mDTB0QAoi0Vx7g6wXzKbH5\nkhwbSufcArbubsZxrt042541HGVvuxX/wdmEGM4VyIgIkoAgnpnfP56roPtApKO6DbdCgW+k92kn\ncdvBBTz94hu440aRP2owg4cOJCsrEZrpvcU/jZ7YftF0lDZhcbgvbhpRwy7mfvBPnnnmGR584Dc8\n8vjfWKq7gdfffoqJqT5A7wDIPdtX8Or8b1DH5DJhXB7Xj0+nbO8SvtiwH8EniclDwtm2eQ1b2wPJ\nyxvFyNEj6J/qy9a33ufzuVuwGkPIyUzA0V7CrMX1pOWMJbqpkNqOLsTWfTz+3AwOatOZfN04xo4Z\nhL++lrkLFnKkqoYtqzdQ7fQkc8hwhgwdxnX5iezdXIdTdLLj87/z6Zpy+k28kXFjx5Ed70PR0jms\nXl+GX3IOqUEuju1dzi5XJMOGD2PYiDGE1S9h9qwC3HozqTkjGJiTiXdQGFnD8hgxdADhASaU2Dmw\nbAVLFh8huF82w8ddx6iQRua98zL7mgT0nn70GzySzH6p+IfH0H/YWEYOySDIywNzWCoTx/aldPcO\n6q0ukATaKnfy7pufIQRnMXncKEbnjWdwchA7F33Kyh0HsAh6EnPHkGKo4ptNC9nvkcOEvGHkZvSB\nIytYsaIIx3kOY9nKGfzvG4dIvX4KY0YNZ+SYUfSPUrL2gw9ZvK+VkOg+DB/Uh9CIdPpnjSBvSCpm\nvfa8p2hHdRkqdRehSXEkaAx0FdXRabEjAULTdv70kpPb7huPo2g3Dm8P+veLuMhmx++nftsnPPPK\nhygybuSG/JH0jfWhfMEi1i7aSnnpHhZ8Mp9yZziDx45jxKgxTJyYTdvXH/LclwVIEgTED2Bs/yB2\nr93KkX2dDLwuj9FD+uLqPsr6nbtpsbjxDEkkf3gyNYX7WfzhbvrfPIGRg3NJT9CzYsU8iprsSI42\n1q1awNtrSgjsM5hxeXlMyk9h16qP+WLbMQRHFe88+gyLCnTccOsNDMvug6alhK+WbaTYYmbQyDHE\nREUQnphO7ohxjBqUgodGhVfMACbnJXF45w6abW40Bi+S+2YQ7SOwadEOnEo/huSNZPSQRA7uXsqW\nonrcogS0sOjZGWxoC2f8uFH0T43GVnKYNtUAbpl+MxnxvmetHCVHDavWHMXsFcuE8enozpXx6gBu\nmDoIP+M5t0CwNLB3+yrWlLQSmDyA8RPz0Rzaw+sfb6Ld5gKlJ31HTiDcsZdtBd/QFpzLuDEjyAzX\nU7FpLXsO1OMGukrW8uqMmTQYk8gbMZSBg4cwdFRfaAC+R7Nz2fb12LRqhg6K++7dotBFXV0Pnd1G\nDDotSsWZpV+BRm8mJWcEA3Oz8A4KJWtoHiOHDiA80IzSXsNnb7zJN81mbhg7mlHDh5I3fjKh1v28\n+c+3qeg5R5+tu5UtWwuxWv2YOm0QxnOddEpP+uWmk94n7Jx3upLoorF4A/PW78IS2Ie88XnE6GDx\nZ8v55mgjokJPXP8RpJob2bdtEQXqDCbkDWdQTn8MJcv4etFh7IC9+ShL5vyLDSVdpOUOY/jQwYwY\n2x+jRQ/Oi81tqC/cT0t3F4MGxWM4c+Sm5KK7s42aBi0alRHtJexSvAqCAglBEFEaDOiNp075srDx\n3X+z42Asd94zlcz4MEKiEsgZM4o+AZzlZFFiMGpR2SUU4kX2hRliyB6Sz42TJ3PrjSPws9dgLzuE\nMTX2ZLRqb6+jcMvXONQmRg3pT5ifDzHZ2Qz0EiksrMHtEcaw3EQUKLj5rp8zLCOR6LgU8qbexMAs\nFRu2ruVIq4aUlESCAgxE5WSQlzeZP7z5b165fyjV6z+goLiecddNIC3cF5/IGHLS41BUV3CsqQu3\nRaJ0xTqWL17B/uIWggaP54lHB6KzlfLp+1voih3F6OEp+JgDSO6bQ6hZorKmCkN4KkMGpuLr1Zf8\nGyaTmxpNUEQ61w1PxlJvRaU3EZ3al+hQf4w+viRmDCAnK5UgHyMKFJgiB5CedwuxQX54eAaSnZmC\nq/YIVZ0OdJ4+xKakERboiykgiJTMHHIyk/E16TEGxDBq3HBiNGqUShCcdgrXzqWgoZvR+ePoGxWE\nf3AsQ4YPw6xoYcHavdS2uglNyWH04DhUqiym/mwqGfERxMSlk9sngp5W+7mDPFctc19fyCHvMUyd\nNJgwP28CIhIZPHIAvg1b2LJ8J4qgeLLSowj0jyAutT+5/eLwPN/UVZzUFbagaoaIoECCwrXQ2YrV\n4UKki3kPPUPmY78jw9fJoY07MXuk0yf6RLeXm8aS3Xz5/gz+78W3WLzpMJZT1tBoOryBma++yj9f\nn8nqnSXYzrscRwdr3/uMg5Yx3Hf3ZOLDgoiMSef228cwuF8g1QU7WbWzh8icUfRPjcLHN4i+o/MZ\nFdPChpkfUdIj4ROZzpixI4nx8SN38o2MzE0hJjWDlLgoDG4rLlHE4BfFsLF5xBs9SJ00lWkT+hMe\nGk7K0NGEi51Y3W4sDSUc3LYSg38YI7LTCfDxJnHYUAapO9lxsJamAyv5bGcR+b+5j/wBcQSHxtJ3\n2O2MzBxIckIsSSnJ+HoZ8YuIJn3AQHL7xWJQqzCFpjB+wnDCAKUSVDojMWnZ5PbrQ3xyGmMm5ZGR\nHEPCwJGkequxu+y9c9pt1WwsbqDP8Hz6J8aQ1CeDzGRfFJ6e9BmYTWK8/1krR3dTGTtdWjyiR9Mv\n9DxjXiQVRqPuvF0HCqWW8PB4Juakkxbuj19YKikpZqoLq+l2CoCO2AEjGT4gFh+/wUyaNJ6U2Bj6\npqUR4++Nw+JCooddXy5g2w4j+TfeSE5qFAFB4Qy4biLZYcBFL7/Sxs5Fu9GqMxmQ+N2R+46mCvbV\n1tOoiyfIZOZskwo0ek+iU/oSHeaP0cePxMwBZGf1IdjHSNO+9Szf+g0pw0Yzum8sXp4mIlOHMmFU\nGgVb17BsV/1ZUyV21LPfYscWNpqBMeebUaBEp9OhPesU4RMUGE2BjM7JZmxKKN7+EcQkRSFZ22ho\n6EZAQ3BiFiMGJaLTZXHLz6aRlRBGRHRfhmXE0NNsQ8JF1b5drJ9fQmjCaPKGZhIZFk7ayPEMSTaj\nuehhFBaKtx3C0h5JTlIwmjNmpwi2LqqOHeKgyx+zdyRe2ksXFFwF3Qf0hjZnFlJ7I1v3N+JOHkmC\n14nONQVqnRaTN3Sd9YsEMILiYgcGmfyJTUolo18Mij5JxGhrWPqLd/jbOxsZ9nw+WkBwCTgsPVQX\nbODtZx5iRUQouNy0d7kI9TKhUSoQj49P8PM50RytxOQfTGR6DK0bW2lq6UEKlwCJuIRAjEYjQWlZ\nhAAHWztx9VhY8L/3UpfbB8kmYmttxisoGW+dP7k35rFs/xt89vYLLJ7liUGv5Nb/+RCd2EVXQze1\nzi+4/5EKEvQSostGg92HgYHeKBWgVokofNLoE+SDRtU7NNNoVgHK3nRKEr0NiYrjzYknaMm46S6m\nKRfx3G03Ue+ZSHD5esAD5cmASzr+GemMzwIq9cmYTZJErG1NuFVKPDy+7dLRewcSZjJztLMHh7N3\na61KQOE/iAHBvXdnCqUSg1EFFsW57+rFbsrrLUjRXhhPnA0KNR4+wQSHe1HR3oFTAoUkIknixTXg\nubo41qrBogwn2NMDR1I4nksO0m63UrvmXT5NvJNPr4tCaN3O9v1uPCbkEmXsLcB13yxgzvZiInIm\nk08Z/3jzGTZX/oa/Th2C4tgsbr+/nVc+noxQtI1Zf/gz625/jCcfGITH2dJhb2bHwTakyD5Em3ub\nJ72CE5j+2ONIaoFvvtxGq0OJ1qD7di600ovofjEIG5tODm6SNCo8vI2k58T3DsdRq1Cq1ShEvm3R\n1KgQFZCbn3H87lmBQqvjeLFBcDhx9tvgwKsAACAASURBVNgp+eYrXrWWEuLvDy4XLRojEZ4eNO7b\nRqdSQVKf8N5KyehH9nV30sepwNNbj9QknSwP33FKeendByWSSkVYQgiRsUG9LTCa3rvbkze4Oi9i\nvQUK9h2hk3QclhYaatvQ+/vhqVedcy6+va2abqWSAH9fjOe6/rireOv5XeTdPYr4qLO3OAAojSEM\nGXMd9kVzeek309AEminbX0Wnj4iokI7nImi1aoyBWST69B5DjVaFVtd7DiqcbewrqqczJIVof/PJ\n8RIKtR6vc7S0n1VHCSsLbagHjyLBdOaOCZTv2URp8UH6TfojidGBnPvGVUKSev9xyiJCjs42elxO\nPDwNKI4fBIVSiV9YAkHudbR02M76bc7uZixuB6KfH+ZzXRjFDjYt2U2nK4DxN/c751AKhUpLSGoe\nPxvVyfx/3MNnThHR1U1hdxQTld8uOKVVCSj8BtA/yHAynQZPFbQqUAg2amrqKHWZ6RsRgflEdKTU\n4uWnQNlyrnw5g7WePWVtdIZnk+BvOmNdA4mu5mr2rP0a3z4DyR3TD89LOFb16ggKzkYhYHNLSAbt\n6TupAMW5zlKFB/SouLi+A0DJyUpGqdYTMWAsmcqZHNhWSicQAEiSgOBykjhoNL/9y5NkBWp7v1+S\nUOs98fTQcuJ0EE85iRRKBSqNAockYRdPrQhPT5zLaUNnNPHLlz5kSrzx5NtKlRYPnZOiomT++spb\n2NprOXpgJ1/M+IQZv3+eIWt+i13tQfjQB/nXc9fz7RgWJTqDBwYVWCQRVFo0ylMvqqek5YyC2nSo\ngBadDxERBr7+7Z94a2c7tz77JNNG9sF6MJIbH5+HGyUSwncaaup3b6Xt/9m778Au6vvx48+7z975\nZO8BCSNskL037jrrrK21fq2jiq2KravWatW6AEUEB4gKOED23nuTECAQMshOPpmfve5+fyQCQYKz\n1vq7xz/R8Lm7993nPV73XonNoENyIoY2V5EJ4UGSZYLhs689Yb8bR9CHp82wpgQaPW0Xn3zDzpZh\nuXU3tHP7/SRC/ibcjbVI8S2dSmfihYufDYBgUw1NpiDa9A6YRQGrzYpWJVN+YitL3vTyxIIrsGmg\nrPgAe1UGrhjcvaXQyy5O5pxi3yEPWRMT6ZaVxd3D5vK3TzZTObEfwS2vUVT6f3TMyEAfbWDCTXm8\nv28TtYHBpF2oJhRC+EIga9VnhiZElRZrZDSEGpCllq1p2nabBXA6ypCliLY9oQKc+xImc35ObHmO\nhvNqlK+evhQOI4WC9Ln0Bh667//obNecLQcGC6WfzAFA/VXFL6jQm21n1tef3ytbtH4Z7r5j6WY3\ntLnOV2mRkVGraLPxS5vPiGlM/JWVT+e+wJWXLiHeVUAocSyTbxmK9SJfsjG1Gz0Q8IjtDx9V7FjC\nMVsCEw36i3bFOstymfvWS3xZEsHtd/+DSf1S2T3tTp7bD2oZQv4wotjyjAS19pyG+JynL4Txh2Uk\nnQbVeV367dZzF1B/8gCHwgLDxl3ytfsPOvJZsnk/u73DeWbiSDJiDd96dLs27wC1WhvBsA+ZMMHw\nOUOzsozXXc+F+wha6GLT6KIzckzU0F5o31x8lGMVhzH1vOlCc8jPCPs97P38JR75IIfhN/2J568a\nQN2Oubw+LxdVCOSghKwSWuoRtf68vRjO5GRCcpigqEbUqNqk6Ls8b1dlIUebGkke3IPY8zY1k/xO\nTuxbxfs50Yy85UbG94n9iWYTtPgFDB+ASgsN3mYcza6zGU6XzJg+WjSH9lFypi0RQG6/e8nVVEtY\nH/gWNX/L2/L5BJ0GDQJS6S7KPRDweqipqEOXkEBYUqPWWIi0RxIZGYkteJJ3l+yltvHsaLdOfTZL\nOx11nM7JJSXWQoeks91m8nnpj8zshAyEJPOZc9s1Lvbv38nGgwWs+vhLDhQ1kT1sPDff8zhfbJpB\nOFCHxxBJR0lCaPCij2o5LjIygrrcg+zYtINaP4CB8xfYqDlnJo0EhEAliqhFFW5HDbUNTTSVHODT\n8iIy7n2EO64YTHxMJBaTBVGQCdYWsHrmO5xwAuGWY1WiiLOmAkeTm6DUchUTAqBBEEVs0Ym0fCnn\ntDjhIOFwCItFi/ZM6TVz7pcnIKK68Dv0WTozyYIIzrazDkIhCY9bg1ZtoWWkQM+3nc7dWFGFJlhP\nZvd4BCCqQ1f01hpefORJsp+4ld6xFmRZ5vTuXWiNWkb2SW5JtWAka8Sl/P73v6JnogVRrYaQgN+i\nQSMKJA1/iafeGIFBEBDVKjTqMFI4QLujXbpUxvVVIe5dT27jV7+UcRSeZN3CxdRJeiL8YQicGxTI\nOJtDyFI01tYWWUSNURBAdSa0QIeIVqVq6bMHQI1JEEB99jsSUWMQBFCp0VmtGKNjCEladHrb2XLg\nPcy/5+8nud8wJElmy5aTZ1PirWLX9k2s3FXZktckUKvVCIJAQ2kRDm/47LVbf351ZQ0qtKJ4TvpU\nGBEQ1JrWLOLk5KYIpq9Yw6JZL/DG/BUsmPccI7rEXLT4i7YM+kb68R3YRIHz6/8edBzi2Vl59O3Z\ngYToi+W9IOV5+8lZ72DcyBu4YeIlJMfaMMkqBIMRf8Uq7ntjV+tn265uENAgfpUXNXH0zzZhLz5C\nudt3TuDz3WaonNiyhrAA44ZktLn/QGMRc2dM54OPa7jzD3dyxYjO6C7WkypztlyrVLgdtdTWN6G1\nxaDW6JBldZsPy0EvglrEbr3w3AvBFE+3OB36I5vIq/v6gL3kqWLVmq3klhkY0z/xot9dwFPF1jkr\nibRfyeS7L6dTUhRWrQa1WkvQmcfbn24iv6wZMNG2HhFQteYwVGbSkmPpoiqnoawC95myp+LbvTK0\nqDh2mOa6Wgb3TcZ8ziRDORzg2OYPuW/yArr2vInHJ08i4ideovwLCArUxKalk6SJIFDmPGcIzcil\nDz+OLWI/T01dRbPHh8tRyrZlb/PhsQBuTyN1Tv85bzteig9WYevfGauxvbcAmXAoiKOkgH2VpVR4\nXdQ4Gqlz+Vr3whfRatVI0k4OnWykMH8X018vof/oq8k4tYVPZnzA8SoXXlc586ZMpazOiaA9W0he\nuG4ap5o9uOpLWb9qPtMP2ugz/Cb6JmppbvTg84UoKaqgtqaBULil+KdNeoj7Oob4YPJDbC5oxOtp\nYM+XS1kzbx2i3UaEXMiqVTs4XuggEAzQVF2NRhNJhD6De9+7B8eJD3h29haaPF4cBbtYuGgtB08L\naEI1HD10EGfhPk6ersbt8+Nxnmbv/t2EKo9zoqYJSa1DHxGNo7aZk6eKObzhOFUn6lCpRFRqFT6X\nG5/fh8ddzid/+heiHKS04AQVRY1oTUb0VjvlFQ0Ul5Swd/lRGsubQQpQnr+ffVKYutJivIKe7hPv\nYrSzgvf+No28GheehtMsnv4Re9bZuH7kKNLjjfiaStm3ay9S+T6OnG7AF/DR4DjF0dx9OCtOcbrB\nRfhCjacqhQdmP4jl9DQmz9yKx+OlvryAFQtmkRPbiyt/N5GIYDOnT+fRWJxHWXk19U5vm16dr0jh\nEI3l+axdu5KN24tR+T0EQzJqrRm1SkvmDc9yy4COyK5G6qqPsGrRRlSCjF4dJBCSAJHEzr0YM3wA\nqVYVrqINTF9fz/hrRhJjMWDvPonfXt0DlRyk8uQBFsw6RNz4K0ludy6biaumPI3ZeIjfPjmPSrcb\nV10ZO9Yv4ZOdIiOunMC4SVoWL1vI5pxSvB4POYte540dTm6YOpmuGoGQz0Xh4d3sd3s5ebQQp99H\nU1UZx2orOVhaTVm5A7/fR2XuPvb7feTuyaMh4MfncVJyMo/9bh8F+SXIUVlMGjkW/bbPWTDvS4od\nbrzOEt78/fO49DoMPa7jHxPV7J5xJ4tyq3B7mzm+Yy3rPv8Mn1WH2mRDZzKTf6KS6ppSNn14GDkY\nRAr6KM7bw8GwRENlBZ5gCFdNOceLT3KwrJbS0io8fi+1Rfkc9nrIyTuFo9GNjI30gSoevfpBXn/v\nA95553VeevktFq3fR0Wjt91AS1SlcM9bf6O+djOPPPoBJ2td+Px+fF4np/Yv4b4HpmAdOppJA7pj\nvGjtKiAJGmQxjNfjxeXyUHt0Ne/sr8PhdnAi/wgVXglnbQEHdu3GV5HLqapmfL5mykqPUXbiIBUV\npTjcAkNvv5vEjg6mzV1FdYMTn9dN7qJ/8NrBMIFAPdWN3nb7y/xOFw0Vh/ji7VwEBpBuCtBUX4+j\ntoKcHZ/zt4fv5YXVtfxm6gs8eNdIIr9hbFvU6NDbonE4nJwsKCJn03GqTjiIG3gNv+vZkeUP/5P1\nR8rxeH3UF2zl2Ts/JD3xd9w0ur1lElHc9PSfSUit5P9+928OljXh9fvx+zzUluUx899/45O9Zdx+\n7x0ktrM/zdlHriGkEpFCHpqavDSV57JqzwG2V3qoLD9BsaOJ5sZyDu7dR7B0H3kl9fgCfprqi8g9\nvBd3xUmK67ykXTKSvpd2Y/3OtWw/VITH66F441u8vLUGl7+e4hpXu/kn5PPTXFPA1i8PUVmSSIpJ\nj9/ZSH19PeUlB3n/n3dy1UPvk/TbJ5j54f10MP30TbQgy//7fz0i3HicaS/NpDZ6MA/88XriDWcf\nZEPuSh648ylOxXajp/Ukef4MjKeP04CV8TfeyZ8m30a8BsLuk7zwm0cw3v44d1/eH/OF9vGUPRxa\nvIDXn3+L02YzJlOYpkYv3W98iqd/O5E4q5YTy17gtmc+Rx3bh7HZVRiG/Zu/Xp1G8aGVzJg2kxyn\nGZ3bS8rgG3j4nhtIjzHhOf4h2eMexzxoOFEVjXRKD1Hkiua6+x/jjgm9CeRv4LU33mTniSb0Ph/1\n/gye/uhVxmbFoBIg4Crko5ce4/2tDuJSUtATwa8feozLugt88OKrLN20mVpdR3qnejl8pIqbnp7L\nfeM7IwV95K6Zx9+fnoPbGktkhJEOA27h/vsGcuCNl3nny3347B5cTgt/nvYPKp/7Ex9WRBIZVQPG\njjz4yiz6Snm8N/UlPttagqXP1Tz60N1MyNazY/6b/HP2SmqjMoktzGPYY/8k9uBrvL9Xy+jfP8GT\nN/fDcWQ9M6ZOZfX+CmyDb+Off76DuBMzeeDl5UhaKw6Hg74Pz2XGrzOpK9rD7FdeZM1JD1qDEZ8x\nnd8/cD/XDsrCKFcz6zcP8NEJJ+bYOuobEnlq+hT2/nUyq50WjMYGEnteygOP/pV+7WxwU7H/C/7y\nx39RHJVKRrgMf+wwHnrqMYZl6dn13iymv72MamsQn99Hlxue5fk7xxFjObezUqbu1AHe+fM9LK7T\ng0ZDZJexTH7gj0zI9DB18pf0vutXDO4VyZcPX8bL21yIxBBBLf6ELK578F/cNza15VRSkKaS/Tzx\n/HTsQ3/DH68aRpzd0DLjWw5RfWoHbz/1AuUTnmXqrb3QqrUX3Y++/uhSHrvj7xxBJiHCjCnt1zz5\n8h/oZNfgrDjGx29MZeHe00TpnNQ06bnh0ee464pL0KlFDrx3F/e/cwSrzYZbF8uYa64numINi9Yd\nRZIkvLaR3D82yNK1O3CFjdTX1RF748s82XUPDz73BVarlYZABBNumszf/tCToq0LeOOteZRrEhAq\nq8i86k888YdLiTRqkELVfPr847yy6hhSTCx2fQy3Pfg4tw7piJoQJzbP44WpH5Jb3EjMZY/ywZRr\naFo6md+8upfIqChcgolRv/49mUXv896GKkSVCiFzDL+/NIPNX35OSZWH5qYmwul/YNmsAbzW9Xo2\npESR2SGDkNtNXVkpNW4nfa+6g7/85S90i7lwtCWHAxRu+YwXHnmFE9ZIOvXogq+qmHxvPL+//wFu\nHd2j3Q3UzuVvKGHFrLd4d+E6tCkyzc5B3HbbJWz6bAHHq1Q8NvdlDt/xO1arorDZmohKGsR1l/Zi\n44x3yZNUSLKLwbc+xn03/wpr5U6efvg5doYSGRiRw276YC84hAM9PQZdxdOvPEra127Hx6on7uKV\nDfk0B7+ePl1EPAMn3cLvbpxElxT7t3yDlKgt3Mv7017k0y0lmHtfyaMP3cPEHvGIQQdrZj/PC/O2\nE9elO4VHjtH1+sf414NXk/ANnXDOoh28eOcUVjU0kzlsLIlUsSWnnr7X/pG/330FCRePwFpSFvKT\nv3Eezz0+g2qrhDUijY4dx2ATj7F2/XEue/AetOuWseJoDZroBurronl2zr84+PBdLGm0Y7bUEdlx\nBH968jl6q8r4ZOpUPt5ZTmJkIxXaBDQlJdT7fch0YvaWj+n5tY6iEEcWzWLaW+9xqPFCKYTUITdw\n/123MaxH4n9kNdK38YsICsDF9tnT+GhvgOsfvJdR2THnZeAwzQ0NhFR6Ii1GQiEffkmFTqNBLYpA\nmFMrpzPl7XLufWEyI7ITftAX4muqpKi0BvQxZGYmnhnnkoJ+3G43YVGP2WRA3Tq7xJM/j65jp/D3\n9ce5PS1Ig0eF0WI+5+8BfAuyhN/txBWQMZqtGLQiSGE8fgm1Wo3sb8blC6O3RWBqc16ZcMiP0+lG\n1JkwGy8+Dnoh4YAfj9eHWmfAoD9busNBH84mF0GVhRi7DlmWCflDaPRnG9Ow34fL60dvNKLTXvyP\nAMnhEF63C58kYDKZ0Wl+3GIjyyGaGxsJqwxYrKaLjk/+p8hhP1WndvPe1FXEDb2Cy8dnkrPzFAPG\n9MFuVFF1dBtvvfQcab+dwdUdNVQWlRMzZBjx35DYlntzEkZLhN103ncs4XW78AQkDBYLBrXqPzqG\nKQV8ON1uZLUJi0nXdsc/WSbgbsYdkNCabJjO20Qs5HXh9EtYLGbUP+DvCeTOHMOv35zIun2Pkaj9\nKl1N7P5kOtO21HHV/Y9xU5+L7W0hE/S5qC6toNETwGCLJi4+FrP+u+ZJiaDfi8vtQ20yY9LpEINB\nAoL6eyxDC+NsbMAna4mxW5BCXjwhEZ1Wi0b8ad84w0E/Ho8Plc6AUd+2xQ97ndS7fOjNNiyG77LD\nUoDa4lKqG52IegtxSalEWb57KZXCftxONyGVBrPFgiYcJiSDqGp/gmk7ZzpTbqwWCxohiDMgodXq\n0Kn+W036D/cLmWhopvekUWzZv5ADu3Lo2WEU0W0KpwqrPfrM/6k1xjY3Hmg6ycoFR+g84Vq6pkb/\n4AhNb0ugqy3ha78XNTosEW3D9YDTQWVZNTIyRQXF1ESmEhdj/e7jOoKIzmxru25aVGE0tN6Nxobu\ngrt/CqjUeiLs33+LWJVWh0X79bcqlUZPRPTZ8wqC0CYgAFDp9Ni+5UZRgkqN0RrxTbMEvjdBUGM7\nJ5/89MI0lhzk9Zde5aAzkvG1OSx+fymbGvrQfXhvtGU7efHm37Cqyx1MLtrAu9sc+IKJ3Dlk2Dee\nueXe7O38q4jBZMVwoQ38/gNErR6btp3vXBDQmm3tzt5QG8zYf4Tdr3XWWPTGJgryi9Gnx2JUg7uh\nlkanC73NgL7dzWTOJBSN3kJyVmeSf1BKRDQ6E3bdOQ9fo/mef0xNhSUi+sysH1FtxPxfquFVGh0W\n24V7WlQGCzGG77DLzxlaYtI7EvPDkoaoOq8eVqm+Z0N4frlRYfn57Mz+vameeeaZZ/7bifgxaK2x\nRIfK2Lw7l7A9hfSEr5bRXVzQXcv2Lz9ma3kS1/96IlnJF9mB7D+gqWA3i1dtIqiJpM7ZjFETTees\nH9ZTofhfFaI8L4fTBZUIGhWNtVVUN/joPGwsw7OTacxdxsamCDIMHirLq2gM6OgwYDwjesQp+eU7\nssZm4Ti2kU3HHAghJ9VlxeTu2cT+Y+V0GXgpEwZkY/4x/8KfQvE/4hcyfNAqUM/GTz4iX9+day8d\nSqz1m+NtZ8l+Fny5i4T+4xk9oBPGn7h2DTSUk1/agE6vJeT3IGvj6Nw54ZfShaNQ/GxJwSYKcnI4\nUVSOK6zCZI+jS3Z30hIjL7g5j0Lx/4NfVlAAEHBS1RDCbreiu+juVi38TQ24wiImqxW98tfpFAqF\nQvH/sV9eUKBQKBQKheJ7UTrJFAqFQqFQAEpQoFAoFAqFopUSFCgUCoVCoQCUoEChUCgUCkUrJShQ\nKBQKhUIBKEGBQqFQKBSKVkpQoFAoFAqFAlCCAoVCoVAoFK2UoEChUCgUCgWgBAUKhUKhUChaKUGB\nQqFQKBQKQAkKFAqFQqFQtFKCAoVCoVAoFIASFCgUCoVCoWilBAUKhUKhUCgAJShQKBQKhULRSgkK\nFAqFQqFQAEpQoFAoFAqFopUSFCgUCoVCoQCUoEChUCgUCkUrJShQKBQKhUIBKEGBQqFQKBSKVkpQ\noFAoFAqFAlCCAoVCoVAoFK2UoEChUCgUCgWgBAUKhUKhUChaKUGBQqFQKBQKQAkKFAqFQqFQtFKC\nAoVCoVAoFIASFCgUCoVCoWilBAUKhUKhUCgAJShQKBQKhULRSgkKFAqFQqFQAEpQoFAoFAqFopUS\nFCh+JDJSOEwoGCIsycgAkoQs/7fTpVC0TwqHCIXCKNn0v0+WJEKhMJJSafxXqf/bCfjB5DDOhloc\ntY3IGh2iKBMKScjnZiyVCrUsEpWcikUj4XU58UkarFYz6p9xWBQK+PH7g2gMBjRqFXI4iMflRWU0\nodeoEC52sBzG6/EiqzTo9bp2oz8pFMTV1IBgicai/X4PQwr5cVSWUlRYiTcYQjRbSEpJRlVRjJDZ\nhzS77nudV/FLIBP0e3E5fejMVoz6n0uVI1FfeoLjp07jDhpJ7tCVrA5RqC9aqFrIUpjmmhJO17jQ\nmy0kpKRj1nyLA78Ff1MVxeV1BEIiyZ06Y9d/vUyGfE6qKyuod/qxxSUTH21Hq/qB15e9nMo9iUdU\noYtKISvBevH65cckhXE1VFGQf4pad4iY1A5kpqdg1ql+qhT8pKSAlyaXF7XBjEmvRfzJHvS383Mp\nod+f7KVg/xo++2QZRc4wzpCG2LhoLHo1AgLIAeobqqirkvi/GfMYa6tj/fwPOKrpwvU3XUtH28/1\nEUg4io6yfdNOpPgORNt0hL1NnCz2M+iK8fRIjrxABSYTCvhwNjVSVV7Avt35xPQYwLBBPTFfqL2X\nJepLj/DZwsVk3jSFcWmG757MsJ/Tx3by3vvzyT0Vpkd2FHWOEjTWJGpWrOCSGSuZPDIN4WeW8RXt\nkPxU1biJio1AI37HIFHyUVHlJi4xiq+qczns5dThdSxcdJxLJt3ApJEZP4vuSV9tLjOevJctdXbc\nhcXE9LqPN+f+kcQLVAe+plpcahtRRi2CAFLQz7E1s3l8xnLExB48M202wxP1P0q66vPW8e/X5rBu\ndzXPrtzG7d2sX/uMp+okS9+byjuLdjL4d0/w2B9uJtX6A+uxUAUfPP04q08UYLz6NVY9fxk/zh19\nExlvQynLZk5n9qrDBEIO1J0n8sTjjzGmk/0nScEPIgeoq/NgtJgw6DTf4gCJ6pwtzF++g4TRN3D5\noOzv/TL2n/LzSs33IRrJHn4df3zoTqKNbg6W6Bhz3R94/Ikn+dsTT/G3vz7K7y8fhkVVwimHB29j\nHYfXrGHPgcPUuEP/7dRfhIyr/Dgr33mOyX+8k9tvuZXJT73CllI/eo3mwtGlHKKh8hQbl3/JnPdm\n8err77E3r5SAdOErBLy1rJk7gznrDxKUwt8rlf7GYlZ9/hknQpn8fearPPvCv3hz2huMj5AoDPkJ\n8f3Oq/gvCZYz750t1HuD3/3YwGlmvr4R9zm/koMeqgoPsXbTXvKO1fI9zvofUbZ+Gh/utvPcW9OZ\n8ttB9OplQmyn17py12I25FcTklo+oNIZ6POr+3nk7ivQSTL+0I+Xx+MGXM9TD92MxeSl3uO/4Gcs\nqT24+e77uWJoT1RISD/G4Icmg0dnvcZVqTJyjZufrGaUQ9QU57Bk+TGG/uUFpjx6L507ZaLW/I80\nTcFaln22k8LyJtqpZs8jUXX8KHvWruFwURXe0M9vqOTn+pr8HYjo9CbiEuKwWExgsGCPjCQ6+qu3\nFTsjfv0QJn8ub+Y7sFyXwWUPTSHbG0VmxLeJ7P5bZGR0pHQayHVju2BSQWrPYVw2cSQpkeZ2u/YE\nUY01Jo3Rw2Xqi12oUF/ws7IsUbRrMTNmLkPofsn37ir0NtTQWFZPeualpMZZWn6pj+Xyyfezdct2\nZU7B/xhfbT7rN5Zx4wMSmL7bsd6qPFauqeThl87+TtRayR54OY8+0p2kXhn8XEqcu/40qshr6Zyc\nQs97XmRwSE/kBRPno2DzRsrHDD+n0hfQWSJJz8omjuIfNV2iWk9MrAVRFGjvnU0QNdgSUkiNjvkR\nG28Rsz0Be2tn4U/XcS8TlIKobUYGdO3K6MQuDBolYbJYfrIU/BD+hhJ2bS+mQ/9e3/IINR1GT+Jm\nTRrR3Tpj/Zn1EsAvIihoIcut8wiCcKb0esvZdlRkWL8EMgZeRdLeEMFggJgOPYjR6DGeE42Gfc1U\nlFfQ6IXopESM3kq2b9yGqdflDEhS4WjygFpHZHw8+rCH5sbGlnEhazSxkVYEbwM1jU7cHpmkDvHU\nnzyJSxtBckoyFq0ASLgbaigqLKHBKxOflkVaQiTadgcxZWTMdB1wNUPvuY1YVRhBrUEliu034IKG\n6JQujEvpQn3eStab2/96AzWHmTXzMNmXDSTndLhtlCuH8DjdyGoDBsPFx7wElQZB7eJYwQEOnezL\nkI7xLeOb5jSuGD2UoggTyD5qyh14QgH09njM4UZKK+oQjRHEx8VhM2nPnE8KeigrOEFRtQtjZCxZ\nnTKJaB1XlUIBnI111Dv9GKxW1AEXjkYvtvhkYm0m8NaRf+w41S4ZS3QsEVqByNRMIvUCUsBLbXkx\nxeUOZGMMmVlpRFkMFw6YwiHcjQ4cTh8agwmDGMThaMYYk0hcpAWNKBB0OSg4cYKqpjCRSZlkd0pA\nHQ7ianRQ5wqiM1oxa0LUVlfjRUdsQjKRFj0qAQLNDqoaXQSCInFJkdQVFRMwRpGUGI9JIwBhmmsr\nKSw8jTOkJrlDF1LjLKhEAVkOYD9OWQAAIABJREFUUnnyGKcqGtEabdgirVgskSTG2RAI01RbQWFh\nKa6QmuSOXUiNtaDCT01lHd5gALQ2oi0SpcUVhLQWEhLiibQaEOQQLkcJK+csokJMor6xHn1Qg9Ee\njVkjghzG3VDLqVPFNIc0JKSmkRwXhU4tgByiubqQL2d9Sp2tB/UOBwHAaLOjlYPI2lh69IvFbDOe\n87xlnI5yCgvLcPplIlMz6ZIWg4hMKODGUdOALySjN1vRSW4qqusRjZGkJMVi1l88tJDDARprKygs\nrsQj60jO6EBSrA2tKABBGuubaAyAJDbhqGvErjEQaTd+LS+Eg26K9y/j803Hie9TR2NdLaLKQFSU\n5UxzLQoCBD1UFZZR65awxycSG2ltM8YfaK4m//gJ6n1qYpI70qlD7EUr3q/KolYVorGsgNMNPkwR\nsSQmxmI401rLBJG/1g8n+RopyD9JRUMAc3Q8WVkZ2HRtGx5vo4OSomLqXCHsSSl0SItHr1Kdc+UW\noaAfj9vb0hMhaDAYjahDTkoKCyh3eNDaY4gQQ0R0yCbO2H7jJgfdVJwuoaSiAfQ2OnbtTJxZA7KM\nr7mBhkYngWCA2gYHgbhIzBZLu3MkpICTU0ePUdEcxh6fRIf0FMzai1RQkh9HVR2egJegKoLkaBXF\np04TUBmJj48nyq6jqbqSiuomVOYoUpNiMerOfjthXzOnjh2n0ikRlZBEelpyy/XkMN7GSjYvWkF+\nfYB6TyO1tRoMVjtWTYiaiho8wRBaSyxGyUF5fYjY+ETsRghrIuh5SR/0kXbUokDQ3URzQEINhAUN\nEREmpIAfl8uHLIBKo8VkMvJDp418W6pnnnnmmZ/mUv9ZYXclmzZv5XCFhSsvH0Zmko26g/N5fZeO\nKwemoDVGkWBUUbp/Ma+/8wnHK5tI7NKbOJMKZ9kRFnw0hzW5lQRr81m0dCWbVu/BW7+ZhWvNdLHk\n8OrbH5NXUk1cdj+ighUs+2IBH3z0KQ3GJDLTkpFKt/Pi1NmsWr2PYPA0c+fPZf3WY9SpMuiXZabi\n4Bbmz/yY3EovkreItWvW0ahLICMhGs0Fv22ZumNH2fjZMjYXl5KzZyNbNuQRtsSREGtD/Q2zUzzV\n+WzbcgBDh37075OJoU2ZbWbZ449R1PMubh0Cq3efZsSV19HJ3tI4O0v28OlHc1h7WkXHtESsF5kc\nJoQ9HD26ly9Wb6Po5AnyjhVSXtuMLOrp0LMnqSlJWNUNLJn+NB8s2sj2nfs5euQEDS4HB3auZ92h\nCizxiSTYTYhBBx/NnMmHh+qJN4c4vm4WK3bkk9hjILFGFUFnDdtXL+CtdxdTVHiC3Qc2sHjJCnYV\n6chO9PDuzJlUBEyYdCIlh1bw2YrtRPYeSZLQwNaVC/lo9R7cskDxti2s21dJfFYaURb9197Hwr5m\nDm3+jFff/pT8Y8fJPbadzxYvYceJMBkZaejrc3hrxjvsrJCI0XtZ/c7HHPLY6Z5lIW/jZ7z2zids\n376D/cdOUdPYxImN61izdhdCfDrJMTZcJ9bx1MvvsG1rDs3NJ/ho4cds3F1C0JRO9zQ9p7au4MNZ\nX1Dskgg15LFkxTpC0Z3pGGfk0MfP8PZ2N9E2LU2nj7Ls47VUk0TvbhGc2ryMebMXc9ojE6rP4ctl\n65Hju9IxVmbtOy8z+/PV7NqRQ1XxQQocbk4c3sL63BpiktKI1zazc9k7THt3BaWNXnR6L8d2HUSX\ndQkpFqgsOsQbMz4mr1lA7TjM5jVfUi3ZSEpOxhCsZtNnb/D6u+up84fQ6z0c33sEY8fu6Bty+eTN\n1/h03UlC2iSyO8eiwk/B1vl88P5SakI6NKFaVs9ZwLZ6C/16phCsL2Lp7KnM/XITh/fup7i0kKq6\nGrZtWse+KpHMtEQs7eTJsK+JA1tXMPPz9dSGNEi1R9iwbjUOIYrUhFh01LD8gznMW7mdkqJSwnoZ\nh8tEdqf4896OQ5Ts38yihe+xLKcId1iLrzSHg2V6+vVOQ02I2tJjrFm2gUpvgJITlTiK97Nh1W7C\n9lSS4u1oRKjP38JLr8/gcJMeS8jB6nlLKJSjye6S0G6vSbA+n3fnr6O5roaSBgmNv4bdiz9md2Ez\nCZmdsOtVILnYt2kzjYZk+vfrQYROhacih3+/Np115RJxRomC3V+wbm8B0R26E2vWACEqjm1l4dzZ\n7DlVj1rt58slS9leH8HQrgmohQB7P51FnmEst1yZRXXebua8+hbLNm/ieK2fmAiRdV/O51BRA1qD\nnvqCrbw/ZyH6PpeRHa294L0EGkpZtPBjFuwsQKXV0HBiHZ8v24g+vS9pEWoKtn/KO/MXcTC/itrm\nAGI4RGRKxpkXgbYnq+CVp19gaYWaBJWDfWvmsq+wkaRO3YnQtROUyE42z32DmfOXsmVrHrVFuzha\nG6Ts+HaW78jFUVlA7r79nK6tYdO6tRxy6MjukIBRqwJ/Of/++4usrFQTK1Sxd808Dp52kZSZjU10\ncmTLAmbOWkBuSQNqnZ+i3CPIidlk2N0snf4Uc5fv4EhFHUdWL+LT5Wuo8UGkBdZ+/hEfLVxCszWN\nrLRYyrcvZup7n7Bxw0Z27vHQZ3QWjiPrefH1d9m8OZcGv42OXZO40CP5T/j59V38UPV7effVp3no\ngQd45J9zqAq3jGKqjDF0yYojqWNXOsSK5OXk0OgPAx5yly3hk5WFxHTsydARw4l17GTRCicjfvcI\nN43LIj6jM5nRfnYeOEi9N4TGFEl2j46EmsopLK8iIMnoYzMZ1TOSLZtXMHuxixGjhqI6uoPSRhfN\n5UdZNm82B6qg75jxjBs/kQw5j4/fWMCJ6uZ2xqIEJL+HsrpmvJYEevTqhql5Bx+8+m+2H68k+O0G\nsC7o9PppTG3oxwO/7YNR+HoHpLe+lJ1bVrPxQD7N3ot3UOoiUhhz+U1c1S2a/PVL+HD2W7zx8vM8\n87cpvLXD0fKWorLQdcAQVPnr2LH9IBHZgxg6bASDuiZSvm8xb81fTX61h0BtHl8s+oLtLjtDho9k\n/KXDKPhwLtMW5xACVHozGR0yMEoVzF+aS8iURXrQQUVZKWW7P2XB6mb6DRnBqJHDGHLJAOzV+6ls\nbCJn7xpeXbAZf1wvxo8bx8SRWRzfvYQFmw7T7Pv6/YlaPUnpHUkwNvL58n1U+5PpbAjhKDmFq76A\n6TPeZkGBmhEjRzN6zFhG9TUwb9Y0Nhb6SM7IJFbbwJo9x3Cb0xk8ZCijx/cnnLOF6U/P5khFM/qE\nLozvaWXtulUs3ioxqE820vG9VDV7cJzcxadz5lIUsjNw7HjGTZhEUvNm3np+IeVNxbw7dR7qrkMY\nNXokI4b3JdGuI/+Ig6r87Syc8yElUhSDxo5n3IRLSWzawLTnPqUqZKDLgGFENOxi0/bNVFi6MWLE\nULrFihxbt4q9hysIqU2k9hjN8OwojJZ0+vbqy8AhA0m2qJFDPsrzNjB/3R488T0YO34kMd56Fn64\nkkNFDmSNmYy+ExnVxYTamMnAvn25ZEA/EsxajLYkunTtQKA2j/yylrxee2QtH8xagdPWmSGjRzNi\n9FgmjunIganP8/qaAvTmGLK6ZCGd3sSWnHzkxF4MHz6MTHUZGz7fQGFFO2VG8lGSu4W5c5dDXHcm\njh3F2HHj6RErsfSDd9h2/DQBzHTuM5AhXSJRR13CsEv60j0z7gLd5SLWuHSGjRqFzWYltWsvevcf\nwoCeqWfe8lWAt7Se8gInPYYPZVj/TCoLtrNh/xGafGGk5pP886XXWFwdw+UTxzN2zAh6pPqZN/c9\ndhY1XaRUtYy51YSjGThwAAMHDaJvr1SKVs9kztyN1F9oYob3NO+99Co76iK4fNwYxoweyYghg5EL\nNzN79seUeyXcFXks/XgmW08H6DZkDKNH9SR4aAcLX1tAieu8k4b9VJ88xL59eRiSu9G3R2dUlbtZ\nte4Ukam9GTlyOCOGjyGldhfFze3MFAnWs/nLBSzdUUxmjwGMHz2CseMnkSkU8MITz5Hvhqj07lzS\ntzvJEREMHDyY7E4dvtaz8RV/+W7emTufPE0mY8aMok+nJHZ+uJDPt51qf+aSaKTTgJEkevaxceNS\n8rVdGTliKD3T7ZRteJd5K/cSTurF8OEj6aQrYPXnW6mo8yAD/vKdzProc/L1mYwZO4oe6bFs+/Az\nluwqIizqicsawOCeGUTbE8nu2puBgwaSHqVHEC1kDxyOWLiKjWtXoOnchyStj9zcGjDH0bNXFj5H\nEQVlVQTCYE/ryvB+GRR8+ilLlxygKRCiviqf7QdyiM/uRbdO8bQX8/wn/GKGD84wJtJ76Fj6ZZop\n3lDA6vDZpymqdaRk92fs0GMULshBEIFQM0cLixASshnStycd061cNiKb2evr0KWP5tpMCa06wISx\n+ew/tQ1BAJUhgl79B9AvYwk1AggC6KM6MG54d1Tih3Qefyk3XZvO4MwBiKkplBxayorttXS97Tf0\n656OVS0zctggFqzfR2mTm+7JERfoohdJ6D+Me1/qTFS3bFIjNAxI8LL90beZt+YwvdJjiDZ/9xFa\nqW4fj/6riD9Me5kMs8AhuaV6Fc6pFiMyR3DvlHgClhTSIr9hDrLaQFavkTzyjwQuO3aCoqJC8nK2\nsXHHDo6VVJLVYx43904ke+gksuJepCjuen595QiitQKZSWYqc4/x9oI17LukPyk9dWR36UXP/h2J\nstqwdhtF1/R/s3lvCf7fX4JJZyGjczZdM6PJDccxeuJ1dLt8GA7Rjvro28jefD5btBLX6AF0iO/F\nNbfeSUDTwNFtX9IkRzBm5CDS4+3I1kEM+vBz9hwtwXnpQOznvXWKaj2JHbPp2y2B9afdDJ14DaNj\nxlHt16CpXMO2nfvoe8drjOiWjFolMujqSWTNfpRdp5xcNTabPt2SOeAVuerKifTpaIPOqagqjnLf\ny0v4bNe1PH1Nby4b3Y0pU1fTfcLl3HZZDKMGXYE+JZqjq5axIS/EpIdH0L1jAkZNIhNGD+bDp7dT\n4ZuAq1yi8PNPWW8eS8+MeEbddBld6zUc27WajcdkrnxkBNkZ8Rg1CUwaPZg5T2+h3Hc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "plt.imshow(plt.imread('./res/fig_5_14.png'))\n", "\n", "#todo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.2.5 Other Efficient Approaches to PageRank Iteration\n", "We can assign all the blocks of one row of blocks to a single Map task, \n", "namely, use blocks $M_{i1}$ through $M_{ik}$ and all of $v$ to compute $v'i$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.2.6 Exercise\n", "\n", "###### ex 5.2.1\n", "the fraction of 1's should be less than $\\frac{log_2 n}{n}$.\n", "\n", "###### ex 5.2.2\n", "略\n", "\n", "###### ex 5.2.3\n", "略\n", "\n", "###### ex 5.2.4\n", "k = n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.3 Topic-Sensitive PageRank\n", "###### improvement \n", "we can weight certain pages more heavily because of their topic.\n", "\n", "###### motivation \n", "1. Different people have different interests, and sometimes distinct interests are expressed using the same term in a query.\n", "\n", "2. It is not feasible to build a private PageRank vector for each user.\n", "\n", "**solution**: \n", "create one vector for each of some small number of topics, biasing the PageRank to favor pages of that topic, \n", "and classif users accroding to the degree of their interests in each of the selected topics. \n", "\n", "pons: only store a short vector for each user. \n", "cons: lose some accuracy.\n", "\n", "_note_: One useful topic set is the 16 top-level categories of the Open Directory ([DMOZ](www.dmoz.org))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.3.2 Biased Random Walks\n", "**Intuition**: \n", "Pages linked to by sports pages are themselves likely to be about sports. \n", "\n", "The only difference is how we add the new surfers: \n", "$$v' = \\beta M v + (1 - \\beta) \\frac{e_s}{|S|}$$\n", "where $S$ is the teleport set (the pages identified as belonging to certain topic), and $e_s$ is a vector that has 1 in the components in $S$ and 0 in other components." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LlnDzzTdjs9k4e/YsPT09xMfHf+ZyrRDXIi4ujqSkJOrr66mqqsJut49//U52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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig_5_15.png'))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "A 0\n", "B 1\n", "C 0\n", "D 1\n", "dtype: float64" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta = 0.8\n", "M = matrix_5_1\n", "S = ['B', 'D'] \n", "\n", "e_s = pd.Series(np.zeros(4), index=list(string.uppercase[0:4]))\n", "for s in S:\n", " e_s[s] = 1\n", "\n", "e_s" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.5 , 1. , 0. ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0. , 0. , 0.5 ],\n", " [ 0.33333333, 0.5 , 0. , 0. ]])" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v = \n", "[[ 0. 0.4 0.8 0. ]\n", " [ 0.26666667 0. 0. 0.4 ]\n", " [ 0.26666667 0. 0. 0.4 ]\n", " [ 0.26666667 0.4 0. 0. ]] v \n", "+ \n", "A 0.0\n", "B 0.1\n", "C 0.0\n", "D 0.1\n", "dtype: float64\n" ] } ], "source": [ "print('v = \\n{} v \\n+ \\n{}'.format(beta*M, (1-beta)*e_s/np.sum(e_s)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.3.3 Using Topic-Sensitive PageRank\n", "###### Integrate topic-sensitive PageRank into a search engine\n", "1. Select topics\n", "\n", "2. Pick a teleport set for each topic, and compute the topic-sensitive PageRank vector.\n", "\n", "3. Find a way of determining the topic of a particular search query.\n", "\n", "4. Use the corresponding topic-sensitive PageRank to respond.\n", "\n", "###### How to select topics\n", "+ use the top-level topics of the Open Directory.\n", "\n", "+ Allow the user to select a topic from a menu.\n", "\n", "+ Infer the topics by the words in search query recently.\n", "\n", "+ Infer the topics by information about the user." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.3.4 Inferring Topics from Words\n", "**Idea**: \n", "Topics are characterized by words that appear surprisingly often in documents on that topic.\n", "\n", "Be **careful**: \n", "avoid some extremely rare word (eg: misspell) $gets$ put a floor on the number of times a word appears.\n", "\n", "It is important to pick reasonably large set $S$ to make sure that we cover all aspects of the topic represented by the set.\n", "\n", "We could also blend the topic-sensitive PageRank vectors to reflect user's hybird interests." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.4 Link Spam\n", "**link spam**: the techniques for artificially increasing the PageRank of a page.\n", "\n", "**spam farm**: a collection of pages whose purpose is to increase the PageRank of a certain page or pages.\n", "\n", "#### 5.4.1 Architecture of a Spam Farm" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7MhgM2Lx5MyIiIjBnzhybnUpmGAbLli1DfX09MjIyEBoaCkdHR6xevdouF2tH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5lnniElJeW6unHfc889vP322/z000+Eh4fzzTffcOedd9KpU6cWSGu5CgoKyMnJYcKECXJHaV0j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\nQU0ufft04ZdWzvAHT8z8iohLwBBppq7OCcKI+/sTHBdGYscM2Pv9332cu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "plt.imshow(plt.imread('./res/fig_5_16.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Links from Accessible Pages: comments contained spam link in blog or news sites." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.4.2 Analysis of a Spam Farm\n", "Given: $n$ pages in total, $m$ support pages, $y$ is the PageRank of target page $t$.\n", "\n", "then: \n", "the PageRank of each support page:\n", "$$\\frac{\\beta y}{m} + \\frac{1 - \\beta}{n}$$\n", "\n", "support $x$ is the contribute of all accessible pages for target page. \n", "we can get the PageRank $p$ of targe page: \n", "\n", "\\begin{align}\n", " p &= x + \\beta (\\frac{\\beta y}{m} + \\frac{1 - \\beta}{n}) m + \\frac{1 - \\beta}{n} \\\\\n", " &\\approx x + \\beta (\\frac{\\beta y}{m} + \\frac{1 - \\beta}{n}) m \\\\\n", " &= x + \\beta^2 y + \\beta (1-\\beta) \\frac{m}{n}\n", "\\end{align}\n", "\n", "so we can solve $y$: \n", "$$y = \\frac{x}{1-\\beta^2} + c \\frac{m}{n}$$ \n", "where $c = \\frac{\\beta}{1+\\beta}$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "y = 3.6036036036 x + 0.459459459459 m/n\n" ] } ], "source": [ "beta = 0.85\n", "x_coe = 1 / (1 - beta**2)\n", "c = beta / (1+beta)\n", "\n", "print('y = {} x + {} m/n'.format(x_coe, c))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\beta = 0.85$ 时，放大 3.6 倍 $x$，同时吸收了 46% 的 $m/n$。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.4.3 Combating Link Spam\n", "Two Solutions:\n", "\n", "1. Identify the structure of spam farm. \n", " cons: spammer can modify and develop new spam farm. The war is no end.\n", " \n", "2. Use infomation (trustyworthy pages) to help judge. \n", " + TrustRank \n", " + Spam mass\n", " \n", "##### TrustRank\n", "topic-sensitive PageRank, and the topic is a set of pages believed to be trustworthy (not spam).\n", "\n", "**theory**: \n", "while a spam page might easily be mad to link to a trustworthy page, it is unlikely that a trustworthy page would link to a spam page.\n", "\n", "**develop teleport set of trustworthy pages**: \n", "exclude blog, news sites\n", "\n", "+ Let human examine and decide. \n", " eg: pick the pages of highest PageRank to examine.\n", " \n", "+ Pick a domain whose membership is controlled. \n", " eg: .edu, .gov, .edu.cn \n", " \n", "\n", "##### Spam Mass\n", "**idea**: we measure for each page that fraction of its PageRank that comes from spam.\n", "\n", "Suppose page $p$ has PageRank $r$ and TrustRank $t$, then the spam mass of $p$ is $$sm(p) = \\frac{r-t}{r}$$.\n", "\n", "if $sm(p)$ is close to 1, then $p$ is probably spam. \n", "if $sm(p)$ is negative or small positive, then $p$ might not spam. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.4.6 Exercise for Section 5.4\n", "###### 5.4.1\n", "(a) \n", "targe page $y$: $y = x + \\frac{1-\\beta}{n}$ \n", "support page $z$: \n", "\n", "\\begin{align}\n", " z &= \\beta(\\frac{y}{m} + z) + \\frac{1-\\beta}{n} \\\\\n", " &= \\frac{\\beta}{(1-\\beta) m} y + \\frac{1}{n}\n", "\\end{align}\n", "\n", "(b) \n", "targe page $y$: $y = x + \\frac{1-\\beta}{n}$ \n", "support page $z$: $$z = \\beta(\\frac{y}{m}) + \\frac{1-\\beta}{n}$$\n", "\n", "(c) \n", "targe page $y$: $$y = x + \\beta (\\frac{z}{2}) m + \\frac{1-\\beta}{n}$$ \n", "support page $z$: $$z = \\beta(\\frac{y}{m} + \\frac{z}{2}) + \\frac{1-\\beta}{n}$$\n", "\n", "then solve $y$ and $z$. 略\n", "\n", "###### 5.4.2\n", "略\n", "\n", "###### 5.4.3\n", "#todo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.5 Hubs and Authorities (HITS, hyperlink-induced topic search)\n", "used by the Ask search eigine.\n", "\n", "#### 5.5.1 The Intuition behind HITS\n", "Two flavors of importances:\n", "\n", "1. authorities: provide information about a topic.\n", "\n", "2. hubs: tell you where to go to find out about that topic.\n", "\n", "PageRank: a page is important if important pages link to it. \n", "HITS: a page is a good hub if it links to good authorities, and a page is a good authority if it is linked to by good hubs.\n", "\n", "#### Formalizing Hubbiness and Authority\n", "$h$ - hubbiness vector, $a$ - authority vector.\n", "\n", "In case of growing beyond bounds, we normally scale the values of $h$ and $a$: force either its largest component is 1 or the sum of components is 1.\n", "\n", "**link matrix**: $L_{ij} = 1$ if page $i$ links page $j$.\n", "\n", "We have: $$h = \\lambda L a$$\n", "then: $$a = u L^T h$$\n", "\n", "By substituting:\n", "\\begin{align}\n", " h &= \\lambda u L L^T h \\\\\n", " a &= \\lambda u L^T L a\n", "\\end{align}\n", "Since $L L^T$ and $L^T L$ are not as sparse as $L$ and $L^T$, for web-sized graphs, the only way of computing the solution is **iteratively**: \n", "1. start with $h$ a vector of all 1's. \n", "2. Compute $a = L^T h$ and then scale so the largest component is 1. \n", "3. Next, compute $h = L a$ and scale again. \n", "4. Repeat step 2-3 until statisfication." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.5.3 Exercises for Section 5.5\n", "略" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }