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nelson-yao/gist:fdef3bf4d6d8796a54d5eb9045548c76

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## MIDS UC Berkeley, Machine Learning at Scale \n",
" \n",
"__W261-1__ Summer 2016 \n",
"__Week 9__: PageRank \n",
"\n",
"__Name__ : Xin (Nelson) Yao \n",
"nelson.yao@ischool.berkeley.edu \n",
"\n",
"July 10, 2016 \n",
"\n",
"***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** INSTRUCTIONS for SUBMISSIONS ** \n",
"\n",
"Follow the instructions for submissions carefully.\n",
"\n",
"Submit your homework via the following form by:\n",
"\n",
"https://docs.google.com/forms/d/1ZOr9RnIe_A06AcZDB6K1mJN4vrLeSmS2PD6Xm3eOiis/viewform?usp=send_form \n",
"\n",
"Note that all referenced files life in the enclosing directory (checkout the Data subdirectory on Dropbox). \n",
"\n",
"***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Table of Contents <a id=\"TOC\"></a>\n",
"* [HW9.0](#HW9.0)\n",
"* [HW9.1](#HW9.1)\n",
" * [Script for Basic PageRank, Preprocessing](#pagerankpre)\n",
" * [Script for Basic PageRrank, Step 1](#pagerank1)\n",
" * [Script for Basic PageRrank, Step 2](#pagerank2)\n",
"* [HW9.2](#HW9.2)\n",
"* [HW9.3](#HW9.3)\n",
"* [HW9.4](#HW9.4)\n",
"* [HW9.5](#HW9.5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"HW9.0\"></a>\n",
"[Back to Top](#TOC)\n",
"<h1 style=\"color:#021353;\">HW 9.0: Short Answer Questions</h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"What is PageRank and what is it used for in the context of web search?\n",
"What modifications have to be made to the webgraph in order to leverage the machinery of Markov Chains to \n",
"compute the steady stade distibuton?\n",
"OPTIONAL: In topic-specific pagerank, how can we insure that the irreducible property is satified? (HINT: see HW9.4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"PageRank is a way of ranking the importance of web pages depending on the number in-links and the pages they are linked to. It is used to order search engine results \n",
"\n",
"Markov Chains have a steady state distribution with non-negative values. But a stochastic system needs to be irreducible to be a Markov Chain, i.e., evey node should be reachable from any other node. This can be a problem because in the web graph available, some nodes have no out-links to other nodes. This is caused by the fact that some webpages have no links to other webipages or their out-links have not been crawled. The existence of these dangling nodes in the graph prevents the system from being Markov Chain. To solve this problem, we can imagine a random web surfer at a particualar node having a certain probability to go to another webpage randomly. This way, the user can go to other nodes in the graph given they started from a dangling node. This probability is called teleportaion factor. \n",
"\n",
"In topic-specific pagerank, irreducibility can be achived when calculating PageRank for a specific topic by deleting nodes that can not be reached from any in-topic nodes. However, this is difficult to achieve. An alternative approach is to use biased damping vectors, which have different damping factors for in-topic nodes and out-topic nodes. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"HW9.1\"></a>\n",
"[Back to Top](#TOC)\n",
"\n",
"<h1 style=\"color:#021353;\">HW 9.1: MRJob implementation of basic PageRank</h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"Write a basic MRJob implementation of the iterative PageRank algorithm\n",
"that takes sparse adjacency lists as input (as explored in HW 7).\n",
"Make sure that you implementation utilizes teleportation (1-damping/the number of nodes in the network), \n",
"and further, distributes the mass of dangling nodes with each iteration\n",
"so that the output of each iteration is correctly normalized (sums to 1).\n",
"[NOTE: The PageRank algorithm assumes that a random surfer (walker), starting from a random web page,\n",
"chooses the next page to which it will move by clicking at random, with probability d,\n",
"one of the hyperlinks in the current page. This probability is represented by a so-called\n",
"‘damping factor’ d, where d ∈ (0, 1). Otherwise, with probability (1 − d), the surfer\n",
"jumps to any web page in the network. If a page is a dangling end, meaning it has no\n",
"outgoing hyperlinks, the random surfer selects an arbitrary web page from a uniform\n",
"distribution and “teleports” to that page]\n",
"\n",
"\n",
"As you build your code, use the test data\n",
"\n",
"s3://ucb-mids-mls-networks/PageRank-test.txt\n",
"Or under the Data Subfolder for HW7 on Dropbox with the same file name. \n",
"(On Dropbox https://www.dropbox.com/sh/2c0k5adwz36lkcw/AAAAKsjQfF9uHfv-X9mCqr9wa?dl=0)\n",
"\n",
"with teleportation parameter set to 0.15 (1-d, where d, the damping factor is set to 0.85), and crosscheck\n",
"your work with the true result, displayed in the first image\n",
"in the Wikipedia article:\n",
"\n",
"https://en.wikipedia.org/wiki/PageRank\n",
"\n",
"and here for reference are the corresponding PageRank probabilities:\n",
"\n",
"A,0.033\n",
"B,0.384\n",
"C,0.343\n",
"D,0.039\n",
"E,0.081\n",
"F,0.039\n",
"G,0.016\n",
"H,0.016\n",
"I,0.016\n",
"J,0.016\n",
"K,0.016\n",
"\n",
"</pre>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"B\t{'C': 1}\n",
"C\t{'B': 1}\n",
"D\t{'A': 1, 'B': 1}\n",
"E\t{'D': 1, 'B': 1, 'F': 1}\n",
"F\t{'B': 1, 'E': 1}\n",
"G\t{'B': 1, 'E': 1}\n",
"H\t{'B': 1, 'E': 1}\n",
"I\t{'B': 1, 'E': 1}\n",
"J\t{'E': 1}\n",
"K\t{'E': 1}\n",
"10 /data/hw9/PageRank-test.txt\n"
]
}
],
"source": [
"#downloaded from dropbox\n",
"!head /data/hw9/PageRank-test.txt\n",
"!wc -l /data/hw9/PageRank-test.txt"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting /data/hw9/testanswer.csv\n"
]
}
],
"source": [
"%%writefile /data/hw9/testanswer.csv\n",
"\"A\",0.033\n",
"\"B\",0.384\n",
"\"C\",0.343\n",
"\"D\",0.039\n",
"\"E\",0.081\n",
"\"F\",0.039\n",
"\"G\",0.016\n",
"\"H\",0.016\n",
"\"I\",0.016\n",
"\"J\",0.016\n",
"\"K\",0.016"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"pagerankpre\"></a>\n",
"## PageRank preprocessing\n"
]
},
{
"cell_type": "code",
"execution_count": 304,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting Preprocess.py\n"
]
}
],
"source": [
"%%writefile Preprocess.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"# Description: Preprocess the web graph by iterating through all the nodes and the nodes they are connected to.\n",
"# During this process, create new records for all the dangling nodes which have empty stripes for edges \n",
"# The total number of nodes is also counted during this process\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import json\n",
"\n",
"class Preproc(MRJob):\n",
" \n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" \n",
" def __init__(self, *args, **kargs):\n",
" super(Preproc, self).__init__(*args, **kargs)\n",
" self.totalnode=0\n",
" def mapper(self, _, line):\n",
" inputlist=line.split('\\t')\n",
" node=inputlist[0]\n",
" edges=eval(inputlist[1])\n",
" degree=len(edges)\n",
" for item in edges:\n",
" yield item, None # iterate through all the destination nodes\n",
" \n",
" yield node, edges\n",
" \n",
" def reducer(self, node, info):\n",
" edges={}\n",
" self.totalnode+=1\n",
" for edge in info:\n",
" if edge is not None:\n",
" edges=edge\n",
" yield node, str(edges)\n",
" \n",
" def reducer_final(self):\n",
" self.increment_counter(\"Total\", \"Node\", self.totalnode) # output total node using a counter\n",
" \n",
"if __name__ == '__main__':\n",
" Preproc.run()\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 424,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Running step 1 of 1...\n",
"Creating temp directory /tmp/Preprocess.root.20160713.221800.997424\n",
"Counters: 1\n",
"\tTotal\n",
"\t\tNode=11\n",
"Removing temp directory /tmp/Preprocess.root.20160713.221800.997424...\n"
]
}
],
"source": [
"# test the preprocessing code\n",
"!python Preprocess.py /data/hw9/PageRank-test.txt --output-dir /data/hw9/PRTEST/Init --no-output"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A\t{}\r\n",
"B\t{'C': 1}\r\n",
"C\t{'B': 1}\r\n",
"D\t{'A': 1, 'B': 1}\r\n",
"E\t{'B': 1, 'D': 1, 'F': 1}\r\n",
"F\t{'B': 1, 'E': 1}\r\n",
"G\t{'B': 1, 'E': 1}\r\n",
"H\t{'B': 1, 'E': 1}\r\n",
"I\t{'B': 1, 'E': 1}\r\n",
"J\t{'E': 1}\r\n",
"K\t{'E': 1}\r\n"
]
}
],
"source": [
"!cat /data/hw9/PRTEST/Init/part-*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[back to top](#TOC)\n",
"## PageRank Step 1 <a id=\"pagerank1\"></a> "
]
},
{
"cell_type": "code",
"execution_count": 306,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting PageRank1.py\n"
]
}
],
"source": [
"%%writefile PageRank1.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"# Mapper: Divide the PageRank of each node by the number if its neighbours, emit the mass to each of the neighbors\n",
"# along with their ids. If a node is a dangling node (empty edges), add the dangling mass to the \n",
"# Reducer: collect the mass received by each node, as well as the edges of each node. Emit each node with their new \n",
"# PageRank score and edges\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import json\n",
"\n",
"\n",
"class PR_step1(MRJob):\n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" #log_to_stream(level='ERROR')\n",
"\n",
" def __init__(self, *args, **kargs):\n",
" super(PR_step1, self).__init__(*args, **kargs)\n",
" self.missing=0\n",
"\n",
" def configure_options(self):\n",
" super(PR_step1, self).configure_options()\n",
" self.add_passthrough_option(\n",
" '--total-node', dest=\"totalnode\",type='int', default=1, help=\"Specify total number of nodes\")\n",
"\n",
"\n",
"\n",
" def mapper_init(self):\n",
" self.totalnode=self.options.totalnode\n",
" \n",
" def mapper1(self, _, line ):\n",
"\n",
" inputlist=line.split('\\t')\n",
" node=inputlist[0]\n",
"\n",
" if len(inputlist)==2:\n",
"\n",
" pagerank=float(1)/float(self.totalnode)\n",
" edges=eval(inputlist[1])\n",
" degree=len(edges)\n",
" elif len(inputlist)==3:\n",
" \n",
" pagerank=eval(inputlist[1])\n",
" edges=eval(inputlist[2])\n",
" \n",
" degree=len(edges)\n",
" #print \"New node\"\n",
" #print node, pagerank\n",
" for item in edges:\n",
" newrank=pagerank*float(1)/float(degree)\n",
" yield item, \"{:01.10f}\\t{}\".format(newrank, None) #\n",
" #print item, newrank\n",
" \n",
" if len(edges)!=0:\n",
" yield node, \"%s\\t%s\" %(0, edges)\n",
" \n",
" else:\n",
" yield node, \"%s\\t%s\" %(0, edges)\n",
" yield \"*Dangling\", \"%s\\t%s\\t%s\" %(node, pagerank, edges)\n",
" \n",
" def reducer1(self, node, mass):\n",
"\n",
" if node==\"*Dangling\":\n",
" self.missing=sum([eval(item.split('\\t')[1]) for item in mass])\n",
" #yield \"*Dangling\", missing\n",
" #print \"missing mass\", missing\n",
" \n",
" else:\n",
" totalscore=0\n",
" edges=None\n",
" \n",
" for info in mass:\n",
" number=info.split('\\t')\n",
" PR=eval(number[0])\n",
" #self.allmass+=PR\n",
" totalscore+=PR\n",
"\n",
" edges=eval(number[1])\n",
" \n",
" yield \"{}\\t{}\\t{}\".format(node, totalscore, edges), None\n",
" \n",
" def reducer_final(self):\n",
" missingmass=self.missing\n",
" self.increment_counter(\"Dangling\", \"Mass\", int(self.missing*1000000000))\n",
" \n",
" def steps(self):\n",
" JOBCONF1={\n",
" #'mapreduce.job.output.key.comparator.class': 'org.apache.hadoop.mapred.lib.KeyFieldBasedComparator',\n",
" #'stream.num.map.output.key.field': 5,\n",
" 'stream.map.output.field.separator':'\\t',\n",
" #'mapreduce.partition.keycomparator.options': '-k1,1 -k5,5' ,\n",
" 'reduce.output.key.value.fields.spec': \"1:1-\"\n",
" #'mapred.reduce.tasks': 1,\n",
" #'mapred.map.tasks': 1\n",
" }\n",
" return[\n",
" MRStep(\n",
" #jobconf=JOBCONF1,\n",
" mapper_init=self.mapper_init,\n",
" mapper=self.mapper1,\n",
" reducer=self.reducer1,\n",
" reducer_final=self.reducer_final\n",
" )\n",
" ]\n",
"\n",
"if __name__ == '__main__':\n",
" PR_step1.run()\n"
]
},
{
"cell_type": "code",
"execution_count": 297,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A\t{}\r\n",
"B\t{'C': 1}\r\n",
"C\t{'B': 1}\r\n",
"D\t{'A': 1, 'B': 1}\r\n",
"E\t{'B': 1, 'D': 1, 'F': 1}\r\n",
"F\t{'B': 1, 'E': 1}\r\n",
"G\t{'B': 1, 'E': 1}\r\n",
"H\t{'B': 1, 'E': 1}\r\n",
"I\t{'B': 1, 'E': 1}\r\n",
"J\t{'E': 1}\r\n",
"K\t{'E': 1}\r\n"
]
}
],
"source": [
"!cat /data/hw9/PRTEST/Init/part-*"
]
},
{
"cell_type": "code",
"execution_count": 307,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Running step 1 of 1...\n",
"Creating temp directory /tmp/PageRank1.root.20160718.005805.066074\n",
"Counters: 1\n",
"\tDangling\n",
"\t\tMass=90909090\n",
"Streaming final output from /data/hw9/PRTEST/Iter1/Step1...\n",
"E\t0.3636363638\t{'B': 1, 'D': 1, 'F': 1}\n",
"F\t0.0303030303\t{'B': 1, 'E': 1}\n",
"G\t0\t{'B': 1, 'E': 1}\n",
"H\t0\t{'B': 1, 'E': 1}\n",
"I\t0\t{'B': 1, 'E': 1}\n",
"J\t0\t{'E': 1}\n",
"K\t0\t{'E': 1}\n",
"A\t0.0454545455\t{}\n",
"B\t0.3484848487\t{'C': 1}\n",
"C\t0.0909090909\t{'B': 1}\n",
"D\t0.0303030303\t{'A': 1, 'B': 1}\n",
"Removing temp directory /tmp/PageRank1.root.20160718.005805.066074...\n"
]
}
],
"source": [
"!python PageRank1.py /data/hw9/PRTEST/Init/part-* --total-node 11 --output-dir /data/hw9/PRTEST/Iter1/Step1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PageRank Step2 <a id='pagerank2'></a>"
]
},
{
"cell_type": "code",
"execution_count": 300,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting PageRank2.py\n"
]
}
],
"source": [
"%%writefile PageRank2.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"#Mapper only job: apply teleportation factor and emit the dangling mass to all nodes in the graph\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import json\n",
"\n",
"\n",
"class PR_step2(MRJob):\n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" #log_to_stream(level='ERROR')\n",
"\n",
" def __init__(self, *args, **kargs):\n",
" super(PR_step2, self).__init__(*args, **kargs)\n",
" self.missingmass=0\n",
" self.alpha=0\n",
" self.totalnode=1\n",
"\n",
" def configure_options(self):\n",
" super(PR_step2, self).configure_options()\n",
" self.add_passthrough_option('--total-node', dest=\"totalnode\",type='str', default=1)\n",
" self.add_passthrough_option('--teleportation', dest=\"alpha\",type='float', default=0)\n",
" self.add_passthrough_option('--missing-mass', dest=\"missing\",type='int', default=0)\n",
" \n",
" def mapper2_init(self):\n",
" self.alpha=self.options.alpha\n",
" self.totalnode=self.options.totalnode\n",
" self.missing=float(self.options.missing)/float(1000000000)\n",
" #print \"missing mass: \", self.missing\n",
" \n",
" def mapper2(self, _, line ):\n",
" #if text==\"*Dangling\":\n",
" #self.missing=info \n",
" \n",
" inputlist=line.split('\\t')\n",
"\n",
" node=inputlist[0]\n",
"\n",
" if len(inputlist)!=3:\n",
" print \"Step 2, Input in wrong format\"\n",
"\n",
" pagerank=eval(inputlist[1])\n",
" edges=eval(inputlist[2])\n",
" alpha=float(self.alpha)\n",
" totalnode=int(self.totalnode)\n",
"\n",
" #print \"total node number:\",totalnode\n",
" \n",
" if self.missing==0: \n",
" self.increment_counter(\"MissingMass\", \"Zeros\", 1)\n",
" \n",
" newrank=alpha/totalnode+(1.00-alpha)*(self.missing/totalnode+pagerank)\n",
"\n",
" yield None, \"{}\\t{}\\t{}\".format(node, newrank, edges)\n",
" #print \"{}\\t{}\\t{}\".format(node, newrank, edges)\n",
" \n",
" #def reducer2(self, node, info):\n",
" #for item in info:\n",
" #yield None, \"{}\\t{}\".format(node, item)\n",
" \n",
" def steps(self):\n",
" JOBCONF1={\n",
" #'mapreduce.job.output.key.comparator.class': 'org.apache.hadoop.mapred.lib.KeyFieldBasedComparator',\n",
" #'stream.num.map.output.key.field': 5,\n",
" 'stream.map.output.field.separator':'\\t',\n",
" #'mapreduce.partition.keycomparator.options': '-k1,1 -k5,5' ,\n",
" 'reduce.output.key.value.fields.spec': \"1:1-\"\n",
" #'mapred.reduce.tasks': 1,\n",
" #'mapred.map.tasks': 1\n",
" }\n",
" return[\n",
" MRStep(\n",
" #jobconf=JOBCONF1,\n",
" mapper_init=self.mapper2_init,\n",
" mapper=self.mapper2,\n",
" #reducer=self.reducer1,\n",
" #reducer_final=self.reducer_final\n",
" )\n",
" ]\n",
"\n",
"if __name__ == '__main__':\n",
" PR_step2.run()\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 301,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/PageRank2.root.20160718.003319.533839\n",
"Running step 1 of 1...\n",
"Streaming final output from /tmp/PageRank2.root.20160718.003319.533839/output...\n",
"E\t0.329752066185\t{'B': 1, 'D': 1, 'F': 1}\n",
"F\t0.0464187327095\t{'B': 1, 'E': 1}\n",
"G\t0.0206611569545\t{'B': 1, 'E': 1}\n",
"H\t0.0206611569545\t{'B': 1, 'E': 1}\n",
"I\t0.0206611569545\t{'B': 1, 'E': 1}\n",
"A\t0.0592975206295\t{}\n",
"B\t0.31687327835\t{'C': 1}\n",
"C\t0.0979338842195\t{'B': 1}\n",
"D\t0.0464187327095\t{'A': 1, 'B': 1}\n",
"J\t0.0206611569545\t{'E': 1}\n",
"K\t0.0206611569545\t{'E': 1}\n",
"Removing temp directory /tmp/PageRank2.root.20160718.003319.533839...\n"
]
}
],
"source": [
"!python PageRank2.py /data/hw9/PRTEST/Iter1/Step1/part-* --missing-mass 90909090 --total-node 11 --teleportation 0.15"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%reload_ext autoreload\n",
"%autoreload 2\n",
"\n",
"# A driver cdoe for the calculation of PageRank\n",
"\n",
"from PageRank1 import PR_step1\n",
"from PageRank2 import PR_step2\n",
"\n",
"\n",
"def PageRank(Input=None, TotalNode=1, Teleport=0, maxIter=10, OutDir=\"/data/hw9/PR-test\"):\n",
" iternum=1\n",
" \n",
" while iternum<=maxIter:\n",
" if iternum==1:\n",
" Step1Input=Input\n",
" else:\n",
" Step1Input=Step2Output+\"/part-*\" # in subsequent steps, the output of the previous steps becomes the \n",
" # input for the preceeding step\n",
" \n",
" dangling=0\n",
" Step1Output=OutDir+\"/Iter%s/Step1\" %iternum\n",
"\n",
" Step1=PR_step1(args=[Step1Input, \"--total-node\", str(TotalNode), \"--output-dir\", Step1Output, \"--no-output\"])\n",
"\n",
" #print \"Step 1: %s\" %Step1Indicator\n",
" #print \"Step 1 Input: %s \" %Step1Input\n",
" #print \"Step 1 Output: %s \" %Step1Output\n",
"\n",
" with Step1.make_runner() as runner1:\n",
" runner1.run()\n",
" counter1=runner1.counters()\n",
" if \"Dangling\" in counter1[0]:\n",
"\n",
" danglingmass=counter1[0][\"Dangling\"][\"Mass\"]\n",
" dangling=danglingmass\n",
" #print \"mass sent %s\" %dangling\n",
"\n",
" Step2Input=Step1Output+\"/part-*\"\n",
" Step2Output=OutDir+\"/Iter%s/Step2\" %iternum\n",
" \n",
" Step2=PR_step2(args=[Step2Input, \"--total-node\", str(TotalNode), \"--teleportation\", str(Teleport), \"--missing-mass\", str(dangling), \"--output-dir\", Step2Output, \"--no-output\"])\n",
"\n",
" #print \"Step 2 Input: %s \" %Step2Input\n",
" #print \"Step 2 Output: %s \" %Step2Output\n",
"\n",
" with Step2.make_runner() as runner2:\n",
" runner2.run()\n",
" iternum+=1\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 303,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"E\t0.0811452572818\t{'B': 1, 'D': 1, 'F': 1}\r\n",
"F\t0.0393846632718\t{'B': 1, 'E': 1}\r\n",
"G\t0.0162071272818\t{'B': 1, 'E': 1}\r\n",
"H\t0.0162071272818\t{'B': 1, 'E': 1}\r\n",
"I\t0.0162071272818\t{'B': 1, 'E': 1}\r\n",
"J\t0.0162071272818\t{'E': 1}\r\n",
"K\t0.0162071272818\t{'E': 1}\r\n",
"A\t0.0329301016568\t{}\r\n",
"B\t0.363235948047\t{'C': 1}\r\n",
"C\t0.362883727342\t{'B': 1}\r\n",
"D\t0.0393846632718\t{'A': 1, 'B': 1}\r\n"
]
}
],
"source": [
"PageRank(Input=\"/data/hw9/PRTEST/Init/part-*\", TotalNode=11, Teleport=0.15, maxIter=10, OutDir=\"/data/hw9/PRtest1\")\n",
"!cat /data/hw9/PRtest1/Iter10/Step2/part-*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"HW9.2\"></a>\n",
"[Back to Top](#TOC)\n",
"\n",
"<h1 style=\"color:#021353;\">HW 9.2: Exploring PageRank teleportation and network plots</h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"In order to overcome problems such as disconnected components, the damping factor (a typical value for d is 0.85) can be varied. \n",
"Using the graph in HW1, plot the test graph (using networkx, https://networkx.github.io/) for several values of the damping parameter alpha,\n",
"so that each nodes radius is proportional to its PageRank score. In particular you should\n",
"do this for the following damping factors: [0,0.25,0.5,0.75, 0.85, 1]. Note your plots should look like the following:\n",
"\n",
"https://en.wikipedia.org/wiki/PageRank#/media/File:PageRanks-Example.svg\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 313,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"PageRank(Input=\"/data/hw9/PRTEST/Init/part-*\", TotalNode=11, Teleport=0.15, maxIter=30, OutDir=\"/data/hw9/PRToys/First\")"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import glob\n",
"import networkx as nx\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from copy import deepcopy\n",
"\n",
"# Description: Collect node, edge and labels for plotting\n",
"# plot the nodes in circular layouts, and adjust their size to be proportional with their PageRank\n",
"\n",
"def plot(inputDir, sep=\"\\t\"):\n",
" \n",
" scores=[]\n",
" nodes=[]\n",
" edges=[]\n",
" labellist_node={}\n",
" labellist_score={}\n",
" g = nx.DiGraph()\n",
" for inputfile in glob.glob(inputDir):\n",
" #print inputfile\n",
" with open(inputfile, \"r\") as f:\n",
" for line in f.readlines():\n",
" line=line.strip()\n",
" line=line.split('\\t')\n",
" node=line[0]\n",
" nodes.append(node)\n",
" scores.append(eval(line[1]))\n",
" edge=eval(line[2])\n",
" for key in edge:\n",
" edges.append((node, key))\n",
" labellist_score[node]='{:01.3f}' .format(eval(line[1]))\n",
" labellist_node[node]=node\n",
"\n",
" #print \"Total Score: %s\" %(sum(scores))\n",
" g.add_nodes_from(nodes)\n",
" g.add_edges_from(edges)\n",
" nodesize=np.array(scores)*12000\n",
"\n",
"\n",
" position=nx.circular_layout(g)\n",
"\n",
" position_label=deepcopy(position)\n",
" for key in position_label:\n",
" position_label[key][0]+=0.2\n",
" position_label[key][1]+=0.2\n",
" #print position\n",
" #print position_label\n",
"\n",
" #position=nx.graphviz_layout(g,prog='circo')\n",
"\n",
" #nx.draw(g, nodelist=nodes, node_size = np.array(scores)*5000, labels=labellist, with_labels=True) \n",
" nx.draw_networkx_nodes(g, position, nodelist=nodes, node_size=nodesize, node_color=\"y\")\n",
" nx.draw_networkx_edges(g, position, edgelist=edges, arrows=True)\n",
" nx.draw_networkx_labels(g, position, labellist_node, fontsize=8) \n",
" nx.draw_networkx_labels(g, position_label, labellist_score, fontsize=8) \n",
"\n",
" #plt.figure(figsize=(5,5))\n",
" #x,y=position[1]\n",
" #plt.text(x,y+0.1,s='some text', bbox=dict(facecolor='red', alpha=0.5),horizontalalignment='center')\n",
" fig = plt.gcf()\n",
" fig.set_size_inches(10, 7)\n",
" plt.axis('off')\n",
" plt.show()\n",
"\n",
"#plot(\"/data/hw9/PRToys/Run0/Iter30/Step2/part-*\")\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Damping factor: 0\n"
]
},
{
"data": {
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5lSWTrPsNSz8/BrwQ7SiQxJr9gKuAUQmGvIE9lymR+xbD0prRE5ZXYanwWIRs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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x580dbd0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Damping factor: 0.25\n"
]
},
{
"data": {
"image/png": 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NrDWT/PgjnHsuFT/+yONVVRwczwcQETkSi+zVAAer6hOZXaXjdAxcgDlLNCKy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Akzi8fjmhKL6aoTT5TOPVeJ1tadXp6WpPfek+bN02Hz5+ugdNoOzWY1zt03B5t0nTEzi8V0xODB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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x582e250>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Damping factor: 0.5\n"
]
},
{
"data": {
"image/png": 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ish/mVxZeuzYSE5FXNGc9QVo05NG1J9EtPSJZCbyMPT9eVdXlccy3J9YmavMo\np2uw3a2Xl5XR7ZZb+LBXLwpS1TS7uUyaRM133zGvooLLAILnU08ROQWL7B0lIsep6osZXajjpAkX\nYE5roG+PHsScXhKBa66BbbaxPpDffAM33QTTp8P5kXvpGmDzzaGmhjKswHoetWLqxKAWKlJgrQ8s\noX7q72vg1bDv58UTNQuc6W/GGoufoqpvxnpvlLF2xeqowj2oKoGDVbWpZskjIr5/OB6h0QS3Aw+E\nfX+SiFzWUAsfVZ0vIntjjv2dwk6NEZEFqnpnPJOLSBdMYA7G+mXGsudwMZZ+fg54I7KjQAxzdgZu\nBIY2cMmHwHBV/Sb4/uvsbBk+ahR33HUXBRts0MBdGWLyZPTOO1lWUcHekd0cVPWeINX8KPCCiHyK\nPefSumHFcdLNarZ52XHq06YN2265JXGV3ocSHdnZsO228K9/WXHwnDmx3d+pE9TUUIBFpqYCD2FF\n7jthzuVTMNEwEtgBKFbVjqq6jarur6p/V9XLVPUuVX1BVT9T1V9jFV8ikiciFwOfY7v9tm6m+Por\nFmELd12vAY5U1bebuHdr6hfr357oWqLwJFZPF2Jt4IjGbggsPvbBRG+ddYlIQ6KmDiIyNBADP2Ei\ndzcaf838DXvcA4GOqnqSqr4Yj/gSkTYicjYwg+jiayG223OXMPEFQE0NT61YwR8jRthu3ZbCu++i\nY8dSUlHBbg053qtqhaoeDvTBPqz8KiLXScI9LFovIrK2iEwUkeUiMltEjmzgut1EZLKILBWR2Q1c\nMzoYY4WIzAi86UL3ficiy4J53g5eI5wk4gLMWe3JzWX99u2bV/uy8caw0Ubw7bexXS8CBQWUAr1V\ndT1V7aOq+wVvupeo6h2q+ryqfqqqPydzF56I7IUVL/cH+qrq1ZFRhTjH2xQzWm0Xcep0VZ0YwxCR\n0a+3VXVaouuJRFXLgPsiDo9s6s1ZVb8DDsC8x0II8GgQIWuK9bAWUY3xP2AsJrK7qOpIVZ2cyK5X\nEdkF80K7Aep9oFCsCXsPVb0/ihVHG+Cpmhq6LVkCp50W+4eJVPLKK9Rccw3LKirYVVWb/OtS1Smq\nugmWYh4NzBeRPVK+0NWLO4Dl1PoM3iEiW0S5biX2dxM1XS8iZwJHA7uraltsE0moJnEqsJeqtsfq\nTT+l/t+g00xcgDmtgaR8Tm7fHlbE0SFQhBqsRU5aEJHOIvIk9kZ8jqoe3FwzVxHZECsK7xhx6iJV\nvSeG+9epQtXbAAAgAElEQVQCjok4nMzoV4i7MBESYhtg+6ZuUtUPsTepcEHUBpgoIvXc50UkR0R2\nF5FbgYsaGPZb4J+Yqepmqnq+qn4cKYpiRUTWF5EHgf8S1kEgjC+B7VX19AbsP7KwN8dBYNHd5cvh\njDOoeeEFajJR1l5SAlddRdmttzK/ooK/qerX8dyvqjdR+8b/poi8IyKx7Cxt1QT+b0OAS1W1WlW/\nAp6h7kYVAIKo+mOYkW/kOFnAJcBZqjo3uP5nVV0a/H+Bqv4eXJ6Fvc7NTcVjWpNxAeas9lRVsaw0\najVQfCxbBm3bxn59RQU5WLF5SgnSUudg5qczMWuHl5Iw7lpY5Cty+8J4zLw1Fk6grvnsL1jtU1JR\n1R+ByMc8MsZ7X8XWGU4R8IqIbBGkcweJyH1Yfd644N89MQ81gn/PwwRXH1UdE0RrEpY3IpItIsOx\n3+nxUS5ZhkUX+6vqpw2MIVgrpsg34G/Ly9np7ruZMWoUK9OZkvzkEzj6aEo/+IB/l5ezeRObNxpE\nVVcGliPbY9Yq80XksqQudvVjc6A0wrbjW2DLOMfpiUV4/yYic0XkVxG5LvwCEekiIkuw17hBwN+b\nsW4nCi7AnNWeykq+njmTZrmdz50Lv/xifkqxsGgRVFdTjRXgp4ywtNTewA5B3VhZE7fFMm4hVvO1\ndcSpRzDfsiaFRfApenjE4QmJpN9iJDKydriIREbuohJEAkZHHF4Hq6Gbj7UymgL0U9V+QVp3Ovb4\nNlLVHVV1XEM1TPEiItthO1ZvB9aKcsnDWLrxjiZsRC4A/i/i2GxgX1X9uLSUPjNncs2JJ1L2/PPU\nVFUlY/XRWbIErr6asn/+k/nLl3NQaamepKpxxJSjE6TxN8KijpcEYqHJ6GcrpRjqvdaVAHF8dATs\nuQ9W19gT6AscLCJ/lhMEEbG1sVTnZ9TdCOMkARdgTmvgi2nTYt8FGU51NXz5JVx2Gey9N8RqZTFr\nFuTnMzVVvkUi0lFEHsIaXo/B3lC/T9LYbbDC9p0jTr0MnBxHKm0v6lo9VGH+Y6niDSD8Z9CG+D6V\nP4b5ToVTiAmwIap6UygdE0JVv07U0iMaIrJO4Hn1CfamF8l3WKeB45vaBRjYN1wdcXge5tf2O4Cq\nrqqs1KvKy+l3zz1MOeQQuOsumJekjw2qMGUKXHYZpUccQfn77/NweTndVfWt5MwQPpdehUVtZgAf\nisirIhKL91prooT6fnPFmFVMvOMAjFPVMlX9A7gb87Org6qWYB9QDgy875wk4TYUTmtg6pIltFm4\nMPZ2LBdfbDsgs7OhSxc49FDzAYuVzz6DlStZV0ROJYk9HgO/sNMw0fUg5unV7ChC2PhZmM/XARGn\n3geGqmo8MZLI4vunU2kdoNak+w4sRRridBG5rqGoW2DncAhWN9MPeBN4C9upGKI7lo4cmMyfdcQ6\nsrA041jM6y2SEizCc0ssvwMRGYLVxYWzHBPq0Uxqp4nI+0CfZ5+F556D3r2pPvhgsnv2tL+bWOso\nq6vhp5/gm2/Qp5+mZOlSVpSXM66mhoc0yR0fojyOZcBAEdkd+xCxWEQuUNXxTdzaWpgFFIhIl7A0\n5NZY0Xw8zMQsZsJp7MNkThPnnQTwVkROq6CwUB4YOpRjTjgh9R8qKipg8GDKy8o4D7Od2Berwwj1\n8UuoWFVE+mM7nFZiHk/xvqg2NX6oXujsiFNTsKjL0jjG6obtAAx/294pKHqP5f6YWhFFuW8trNtA\neN3ZoeG7NYOt9IMx0dUDqx2bCLyuqqWByP03cFjE8G8CBzRnR2kDa+6D/V53bOCSp4CzY420BbsC\nX6WuCWw5sI+q/reBe9phP7fw3ZX3tGvHVuXl9G7ThuzNNqOqd2+K//IXsvLyIDfXIlyVlbY5ZeZM\nKr/7jrK5cynMzWWRCB+tXMntwORURYIbI3g+Xw38A6s9PFgjrDnSuJYsrD5rW8xGIx/72yjHdhZ+\nBcxIRnpeRB4Pxj0N27TxFva3Nz3iOsGeI3sAd2J/CzUhgR9s/GgPHIXtgH4buFVV7xSRA4Cpqvpj\n8Dd3C7Chqu7V3PU7tbgAc1oFIrJ127Z8NHEihTkplmCvvQa33877K1boLsHc+VhEJdQHcC61Ymx6\nwyMZItIBeyM5CCv0fjQVb2gicgFwTcThH7EX79+j3NLYWNdhaw3xFWaJEdO6ExVgwb0TgFPDDk3G\n6qCGYMKrI/A89jt4R6NYgIi193kJK7QP52nM+6zZu1sD0TMGOJO65rYhvgdGqOobcYzZF2uoHi6k\nqrEUamR6Nfy+EVhbpxB/ABuramXwRt0F6JuTw98KCugjQhHW9qgaKK2pYWlJCR9ivndfxSPWU41Y\nd4IXsGL954Cjki2iG5i3R24up+blMbCsjJ7Fxazq0YOaDTYgr6DAft/l5VQvWEDljBmwbBm5BQX8\nUFnJOxUV3BPvztCwedcG7sdecxYBF6jqkyKyM9YrtV1w3QBMVIX/rb2rqnsE59tiacf9MEF3r6pe\nEpwbhX1Q64DZuLwG/J+qhvvxOc3EBZjTaigulneHDWPHY49NXRSspASOOYbSZcs4QKMYlIo1yd6F\nWjGwAhMCE4EvwwVK8Kn5REx8PYVtLU/JG5uI/J369VnzgJ3jLSwXazz9M/biHOLvqhqzT1AzBdjW\n2I7QcH7FUlITgY9jEVDBG9Bb1Pf6uguLQCb04hgImiMwP68No1xSDlwJXB+PUBDrnfg+VgcVzomq\n+mAT65kKhHtFXaGqlzdwy2qJWAuqxzDhOFpV707BHDnAQcXFnFdTw9YHHkhOv3602Wwzs7FpjJIS\n+OEH+Oorqp9/noqaGmaXlHAt8Ew6BKPT8nAB5rQaRKRrXh7T7ryToliL6ePl2msp/+9/eaq0VKPZ\nBkSuJwurOxqCeVHlUtuouwSLSGQDZ6jql6lZ8Z/1Qk9Td9PNcmBAIp/CxZp1h++IWoLtFIzZDCQR\nARZsHtgV+3n+nbopuNtVNSZbiogx18VETY+IU/9S1bgtDwJDzNuwtE80JmHiYE6c43bG2g9Fdnr8\nh6pe38S9e2BCM0Q1Fv1K2uaClkIgNm/CLEr+BxykqjOSNPZe+fk8stFGFA4bRttdd7U0bSJUV8NH\nH8GTT7Li+++prqjgFFV9JhnrdFYfXIA5rYrsbDllgw0Yf9ddFMXj6RULb7yB3ngjC8rL2Uzj7HMY\nvDFsCRwJnIJFjz7AUoJvRUuTJQMxl/tp1BUrFVi90LsJjvkZtc2xAW5Q1ahu242MEZMAC9K7e2Gi\n60DMYmEiFkUKL7wuATrH+3sJ5uiK/S42ijg1WlVviXGMIuBSLG3TJsolc4BRmkCjaRFZB3gP6BVx\n6jpVvSCG+5/Ffn4hnlbVmNoxra4EgvVF4K/YTuIT49xgEj5Wu4ICbs3N5bCLLqKwf/9krhSmToUr\nrmBlSQmTS0s5WVUXJHcGp6XiAsxpVYiI5OdzS6dOnDh+PEXtkrRp+u230euuY0VFBTsmUhwfCLAj\nMZPPV7Gi2N2wN8ZewCuYsHhNVZvlaRZl7oeA44Jva7B6oYTMUoONAp+EHVLMnLTezrsmxmlQgAW1\nU/tjP5u9sYblE4HnVfWn4JpcrNYuvO30SFVNyIU/iFy9T60/UoijVfXxRu4TbJflTdSPToHtNBsL\nXBNPhDBs/CJsc0Ck79V9WPP1Rl/AxRqJz6Fu9HO3RMX36oaIHIrVS2UDp6n5wcVz/075+Tw/YADF\nI0eSXxxXx9nYqaiAe++l8sUXKauo4GhVfTk1MzktCRdgTqsjEGE3tW/PyWPGUNQjMrkUB1VV8Mgj\nrHrqKVYEzYRj7BZZZz1bYIaba2O1RR9FnO8EHIwJjr9h6aKJwEvN3dYvZuT6Nla4vRv2pp2woaKI\nPExd1/VXVbWed1AM40S+8KyHbUIYgqUZ38N+BpMaigiIyD+B8Dqm6ViXgERrt0I/+3CfpVVYGuvV\nKNdvCtyKFTFH43XgTE3QCT4QmS9gu2zDeR44PJYddSJyJXBx2KGpWP/SNeaFP9j1OgGrt5wGHBhL\nClhEBhUU8NSll1K4ww4pXmTAlClw4YWUlZVxenW1PpyeWZ1M4QLMaZWIiIhwRG4uEwYPJu+448gt\nKIhvjJkz4corWbl4MZ+VlnJMvDUzYWmpk4F/AXc09aYZpJsOwITIHlgLnOew6E9cDWVEZEtsd+Lz\nqjpURDaNN1IVMd562Hb/8HTmIFV9JYGxIl94lmOCZSK2k2tZDGN0wqJg4ZsuBqrq5HjXEzbm3tju\nyPA0Ylkw7kfBNfmYMeWFQF6UYX7FdmU+0wwxmAU8ikVNw3kH2E9Vy2MYIw/bLBFetH+Gqkb6h60R\niMgmWA3eFlgE8bSGfj8ickBhIU+NG0dBr8jEb4qZOxdGjaJs5UpGrFqV+Iclp+XjAsxp1YhIx6Ii\n7q6uZu+990YOPpi8bt0aNp0sK4MPP7Ti2J9+YlVVFefU1PBgPG+kQVpqMFaj9B5WKB2XzUMwTjEW\n/RiMpeSmUmtvUa/BbsS9XTCzxU9Vdbd4525gzAup67w+G0s/xtyFINjJN5j6vSYLNYEWSyLyFHB4\n2KGJqnpovONEjDkMeIK6HmdLsN2tXbGo16ZRbq3GfudXaDMMXYPnz82YfUU4X2Hpw5jq3ETkaEzE\nhViO1cmlvH9pS0ZEjsd82VZhtWETI87vmp/PqzfeSOEWW0QdIuX89BMMH05ZaSlH1dTo85lZhZNq\nXIA5awQi0iU3l+HZ2fy9upp2m2xC2WabkV9URM6qVejChVRMn07NwoXkFxTwZUkJY4EX4y3cDUtL\n/QXzeKpnVZHg+vOwiNgQLF35CxYZmwhMi7C3aI9Fhn4Gtk5GuilI48ymbp3Tuap6QxP3CdAnWPcQ\nrMbqOSJ6SMZjQxEx/q5AeD1TNdBN6zYrTmTc4dTvPVmOGWxG4z0svfxdc+YN5r4UuCLi8A+YZUjM\nnQZE5EMgPHl2i6pG9sNcIwl21D6E2YV8iW3wmAeMzMvj8iuuYJ1kF9vHy4wZcNZZlFRU0LM17lh1\nXIA5ayAisj7mWN0Dc1RfBSzGXoinJrIjMUhLXYBtfx8L3JTCnY3ZWB/HkNdYGbVeY99iRdeVQPdE\nd35FmfNgrPYoRDkWTVkc5dosrGg8JLo0bH2fqLUUStgHLGIuwR7zVmGHrwoZSjYHEbkcaw/UGPOB\nc0mSea6InIFFZ8L5HdgxHusKEdkWM00Np6eqzmzeClsXItILq7PrBrydm8ueAwei551HQs/HZPPA\nA1Q98wwflpay+5pUt7em4ALMcZpJYAB5K7Zb7/+aG32Jc27BmjqHvMY2wQTlYODNWAq1Y5znDeq6\nxt+vqieHnW9D7a7OQ4AF1Ebovo1880iWAAvGOh3bVRpiPtC1ueaWIrIbtv61o5yuCea8RJNknisi\nQ7EWSeE/i6XALvFG1kTkPuCksENvqreRaRARORcYt9Za8PjjEG+9aKpYtQpOOomVv/7KqOpqvT/T\n63GSiwswx0mQwD/qJqwZ7khVfS3D6/kY6I31bdsbay8zCRMRbyUqSESkJ7bDMJy+wbG9MdF1ANZa\nJ1Sj9n0TYyZTgBVjhe/hpiPHxGs5EDFmG6zx8V8auOQzrH9mk8XwMc63F/Ay9Yv/99QY+2uGjbUO\n9vMIT5cekqj1yJqAiNyal8fIq6+GbbfN9Grq8sMPMHIkKysq6Bot4uysvmQ1fYnjOOGISK6InI+l\nLL8GtmoB4utFYBtgG1W9UFX7Av2xwv0LgT9E5HEROTwQLPEwPOL774GLsH6CozAx0kdVt1fVsU2J\nr2QTFJU/GHF4RDOHzQY+buKawibOx0TgrfYcdcXXKuCweMVXwEnUFV8/YTs7nYaZsummVLU08QXQ\nvTvssAOSnV0noum0AlyAOU4ciMjumOjaFfibql6RrChIM9Z0L+ZFtUu455SqzlHV8aq6C7b1/l3M\nEuM3EXlBRI4PoiWNjV0MnBBxuASL1myqqgNV9TZV/SWJDykRIuumdgjqoOImSCl/h9lthFr4PERt\nTdVSTHw3y6MtmGsLzJi3KOLUCQnae2QDZ0QcvkuT0Fy8NVNczMgjj4zawaBFcNhhFObmcnZQX+m0\nEvyX6TgxICIbishjWKTlIuCA5nhqJYvAaPNEzFzy04auU9U/VHWCqu4LbIz1hjwYmCMib4rI8MBX\nKzRuVxEZjQmN8KZOC4AdVPUBVV2YiseUCEFx+RsRh+OKggWPeSJWzzcysLP4O7CTqp4A7INtsOiB\nbTK4tDlrDlLYr1Pfff+sZqRP98XqAENUAvcmONYagYj8NSuLTdNltpoIvXpBhw4UU7cO01nNcQHm\nOI0gIjmBEPkWS+X0UtXnW8KOJBEZiYnBk6I5tTeEqi5R1UdVdQiwIRY92hGYJiJzReRnLMrXh/pG\no3c3t7g9hUTaRhzVVIQP6qWUvyEspRxEET8M/r9IVc9X1fmY0Dk+2LUYN2JNwF+nfv/Jq1T15kTG\nDIgUnU+q9xZslIICzhg8mNzs7EyvpGFEYOhQiouLOSvTa3GShwswx2kAEdkB+BxrkbNLUFuV1D6N\niRKYhd4CnK+qDyU4hmDRnG2x+rGVmPD6GqjC0qzhvl/VWEuXlspLmEgOkY9FBxskSkp5TCwp5aAr\nwV7AJcHuxZgRkbZY78/IJlkTaEZUTUS6U79t0W2JjremkJ3NHv371+mm0CLp1w9ZtYoWHKdz4sUF\nmONEICLrBdv4n8Ec2/dU1RkZXtafBKLhceBGVR0X573ZIrKziNwI/Ag8iRV/nwR0UdWDVfVAoBNm\n5BrO/4BOLbUOJahzujPi8PBo641IKV9MAillVZ2N1d7dFrQwapLAUHcisF3EqWcw497mRFbPoK6F\nxeeNpaUd+32UlbHxptH6GrQwNrC28wUiskETlzqrCS3yhdRxMoGIZInIadjOweXAFqr675aQbgwh\nIn2w1NUTqnpujPfkisg+IjIBsye4DSskPxDYPEirfRLRUmgDrPVOOJ8CDwA/ichtIrKHiLS0yMF9\nQHiKdBPCokINpJSfS/R3rNac/VDgMbFm3g0SFMg/Qv06nrcw24yEC+VFpBDq7ZKLTMk69em9/vqU\n5UXr6Jkgb74Jp58OgwbBQQfBuefC1183f1wR2HRTyjELGKcV0NJePB0nI4hIX2r7w+2lqt9keEn1\nEJGNMWuEd1T1mCauLcSKxocAg4AZWORlpxgjPXtQ9wPadOA4VdXAF2wwcB3QTURCXmNvZnpHqKou\nEJEngePCDo8EXglSyndiXQ92VdVIb7NE53xPRE4EXhCR3aONG6R7b6Nu30qwFPfgJNTVHQmsFfb9\nIiy66TRO3169kvc++NRT8PTTcP750Lcv1NTAZ5/Bp5/CX//a/PF796Zo+nT6Y7uQndUcj4A5azQi\nsraI3I69oN2F1Xq1RPHVAYvazMDMT6Nds5aIHCMiz2Lta4YDH2JF5Tuq6vWxptlU9RHgFMzrazFw\neyhKpKozVPUaVd0O+zT+DfAPzGvsSREZFtQ5ZYrIyM++Yk27n8FE48Bkia8QqvoScB7wn2B3YyRj\ngNMjjs0E9tdmNO6GP8XdyIjD92kCzc3XQDbo1Ck5fm4rV8KDD8I//gH9+lnEKjsbtt8eTj01GTNA\nx47k5OcT7fnlrIa4AHPWSMQ4DpiGmW72CqwVapq4Ne2ISAGWFl0E9AtPl4lIRxE5VURewxpwH465\n33dT1b1U9U5V/S3BqQ/D+ltuBERtg6Kqc1X1ZlUdgBWVvwkcD/wqIi+KyInBjr+0EdQ9fRZ2SIBN\nsd/xE6lKKavqw1hnhP+EP2YRGUX94vpfgb2TtENxByA8vqLYhwmnCXJyKE5W+nHqVPs3lU28c3Mh\nK6ueZ5yzmuIpSGeNQ0S2wtKNhcBBqvpZE7dkjKBuaAr2YWlLVa0Wkb9gKcAhWBPqVzGvp8MCV/hk\nzLsZFt0aHGtaUVXnAfcA94hIeyz1OQS4SUQ+x9zen0+TaevL1C103wTb2ZlSVPVGEVkPS3kOxOrs\nIm0lFmPi66d6AyRGZPTrJVX9MUljt2pEsPhhEli+HNq1a/q65pCVBSIeOGkt+C/SWWMQkbYicj3w\nNvAEZjvQksWXAJ8A62MNrs8WkS+w6M6WwDXABqp6lKo+kyzxFXAG1nA7oZouVV2mqo+r6mGY19gt\nmCD6RqxnZUoI0rC3YesP/3mshdVJpYOLsLTsu5iDfjilwCBVnZaMiUSkIxapDMeL72OkqoqVlZXJ\nGatdOxNhqaSyEmpqaBFWOE7zcQHmtHqCdONQLN24LhZJurMlt2cJxNf7WGppAVZQvT5wDrChqv5d\nVV9JhSmqiBRhRexJSWOpaqmqvqCqx2O7K+t5XYlIH2lGLCIspTwdi+z3or4Q2SfR8eMhSHE+hDVp\nD88yVAFDVDWZAvQU6vaQ/J76HQGchlm8cCFJ+Rvackv799MUGn8sWUJNZSXzUjeDk05cgDkZISh+\nnygiy0Vktog0GJ0QketEZIGIzBeRaxu45jgRqRGRk8KO5QY74iqwiNevwKWBk3mLI/Do2lVEbgJW\nYO70jwBHAF1VdbSqvqOqq1K8lKOAD1R1TrIHVtUqVY0mEJ4HfhCRcSKyQzxeY0FK+R2sMfhBqnq6\nqi7GBGQVJrxfBoY1+wHEtp4tsTq8cG91xXaR/ieJ8+RQv7D/jpZYx9iC+XraNJKyc7eoCE44Aa6/\nHj7/HFShuho++QTuvjsZM8B331FSVfVnT1JnNcdrwJxMcQfmtbU2FimYLCJfR+5OC3y59sUKvAV4\nS0Rmq+rdYdesBVyINVAOHSsEXgQGAP8EbsQsCO4EDkjdw4qPwJhzD6xW6iBMJJYABZgdxptpXo9g\n7WzOS+e8WI1WH+zncA+wjog8j9lbvKuq9eq3gp2Wl2PRusuxNkl/RjVVdY6IbIi9zs3A0pDNbqDd\nGFLb33HtiFOvqeq/kzzdwUDnsO9LMWNZJ3a++vlnCqurbcdicxk6FDp0gHvvhcsvtzF79IBjGjWN\niZ1Zs8jBrEucVoC0II9JZw0hEEdLgO6q+nNw7B5ggapeFHHtB8CEYIcZInI05hi+Y9g1d2I1N8Ow\niNECrOaoBnhVVUcG1+0PjFfVyBYwaSVI8e2LiY39sR2OE7Ei9UOAGzBjzsczsLadMTPTLVIZSRGR\nOi88qioR5zendqNBd0xMT8TSa+VY3dONmInpeU1FNUXkceAzVR2frMfQwDzFWPRr97DD47Df622q\neksS55ocMc/dqnpassZfUygqkl9vvZVOm2zS9LWZZMkSGDaMsqoqilqSObSTOJ6CdDLB5kBpSHwF\nfIsVlkeyJSauol4nIv2Bvqp6F9b770zsDe8ULIqzi1jbmULgaKxfYNoJUq7HBVGd34FTgf9iQmdn\nVb0RsxO4ATgnE+IrYARpSGOpqoREV6T4Co7NUtXrVPVvWB3cF8D/AfOxn98NwN9V9YQYU8q30UBb\noiSj2O7amWHzno95t/1DRI5KxiRBmnP3iMNefJ8AInz87be0eEHz7beQn88UF1+tBxdgTiYohno7\neUqAaOadkdeWBMcI3kxvB84SkYsx24TZQB9VfVNVnwW+wtJ6S4GewL+S+DgaJRB+p4vI65hH12Dg\nWWBjVd1HVSeoNXVGrJfgI8DYVEdpGlsvFplLqLl3qgiE+n3AB0AlVu81BXhaRF4WkZMD64fG+Ah7\n7uyVqnWKSC5m9joD+5BwIjBajTlY38jxIrJfEqYbHvH9e2ptkZw4WbmSCc8+S0lLlzUTJ7JixQoX\n2a0JF2BOJiiBemaCxVjheVPXFlNrLzACSzc+gFkcfAG8HNoZGFhOtMPqcYqwN8fXkvMQoiMim4jI\nOUHqdBqwM1YMvqGqDlbVR1R1ScQ9fbEi8UdU9YJUrq8JTgGeVNWlGVxDPUTkQCxN2x3YWlWPUNVB\nmEHsI9juxh9E5B0RGSUiXSLHCKIGt1HfMytZa8zC6q+qsMhctao+GB5JVNXvMBH+sFhbpETnakfd\nVkvg0a/m8OaiRZRMS4oxSGr49VeYaTHVpzK8FCeJuABzMsEsoCDijXJr7E02kqnBuRB9gKki0hlL\n7ewDrAf8DdgWuEFEQnU2g4AHAk+qKswQs38M0ZKYCewPthSRS0XkKyzS0gOLtHVU1WNUdaKqRvXu\nEZFNsMjOm6p6QrLWFS8i0gY4jRb0Ri4i3cT6TF4PnBIIr19D51V1uVqz9KGYvcWNwDbA1yLyqYhc\nENSShXgC2EFEuiV5nYI54G8EDGtsl6qqfoiJp+eDNGIiHEcQBQ74A6sfdBJAVWsqKrjhmWcozfRa\nGuK556gE7k3Ul89pmbgAc9KOqpZiBdVjRKSNiGwDHIpFMyJ5GDMgXVesvcs5wC9YXdijQDcstdgH\n2x00Brg4uHcGcJyItAsExplYDdGi5qw/EF39A0uMmcArwDqYDUInVT1VVV9T1UYtHgMh+DW2e3P/\n5qwpCRwC/E9Vp2R4HYhIXpBS/hxrPr51U7tBVbVMVSep6omYGLsQ6AK8IyLfici/MGH8EPWtG5rL\nJcCumAVGk/0XVfVV4GzgNbGuBjETtks1nAlNPdecxqmp4YEPP4Rf0tGjIU4WL4aXX6a6ooLbMr0W\nJ7m4DYWTKUZg/QUXBV9nqOr0YBfeK6raDkBVJwQRixnY87USE1E7qOr34QOKSAWwXGubG4/A0n8/\nY55M3wGHJFJgHngu7YKlkAZj6dLnMHf1L+MtjJXa/o7zMUf+TFegjIDMv8CLyF7BOmZgmyvmxDtG\nEO18C7MsORPoj+2mfAbIBTqI9c58t7mbDUTkDOAEYKd4Ureq+phYg/XXRWTnOLzp9sA+cIRYBSTJ\nZWrNRVUX5+TIxVdcwZV33klRMiwpkoEqjB1LqSp3qOrsTK/HSS5uQ+G0eMTarYzF3nz+D3g2HYIl\n8Ojak1qPrrkEdhGRfmVxjpsN/IB5fXWLJWqSSgIj09exzQEp75cYMbeqqgQp5RsxsTRKVV9MwVwC\n9NaqSw0AACAASURBVMY2QuRjDvIhr7F34o0iiXVXGA/skuibYxCZ2x/YXVWbbGQjIhOxDwAhng5S\nsE4zEZGswkI+O/54+gwdSouQYG+9hd5wA3PLyuipKeh64WQWT0E6LRYxZ/gRWORqPtBLredhysSX\niBSLyOEi8gRWW3M+tuOun6r2U9Wrmym+BEutrYNZUGRUfAWMwNJYaRVfIUTkHCylPAtrE5V08QVW\niB/sFDwLmIdtkPgflrb+Q0QeFpFDAsuSpta8Nxap26+ZkYnLsN6eL4hIfgzX34+1GwqR8ahla0FV\na0pLGXb//VT8lKw26c1g0SK48UbKy8o43MVX68QjYE6LRET+hrnllwDDVTVagX6y5uoAHIhFugYA\nH2JRkUmqmtS+ayLyBvbG31NV5yZz7ATX0x6Yg4nb39M89y6YF9rrwJmqOitN82ZjYu8oVf0kONYZ\nq4MbAvQD3sSeAy9HphaD5+ZLWF/H95K0nn9jafKhjRXxB6nw/wGjsX6X17SA9HWrok0bObV9e8ZP\nmEBhhw6ZWUNJCQwfzsr587m+vFz/mZlVOKnGBZjTogjE0NVYyu884NFUvMGISCdq33C3wxzWnyPK\nG24S53wMGIpF075p6vp0ICKjsPqltPRJDOYMTylvBGSlW0SIyLlYcX+knUOkIN8N26U6EXgB6AC8\njVlNJM3UN0h3v4SluU9p6OchIocA56tqwjYWTtPk5cnlHTpw3m23UbjOOumdu6QEzj6blb/8wmNl\nZZzuArv14ilIp0UgIlkicjLmnVWJpeceSeaLj4h0F5F/iMhHWFpzeyyFs6GqHqaqj6VQfN2ANdXe\nuwWJL8EMPdOSxgpSysMJSynDnx5d6eZ+4EARWT/yhKouCjy8DsJ6LT4ADMRSf19h0bGk7hYNUkxD\nMMuVqxu5tEVslmjtVFZyxaJFXH/aaZT+nsa48OLFMGIEK3/+mcfLyjjDxVfrxiNgTsYRkb9i6cYs\nLN34ZZLGFWAr7I1tCNARi3I9RwJF181Yxz+A64AjVfXJdMwZCyKyJ1b43ifVL/RiLaPuwBpGDw9M\nSf8swk/l3I2s6T7gB1W9JoZr1wXeB97DnqdJ25TRwDx3q7WnCj/XE+sCsLHXBKWH3FwZmZ3N2BEj\nyB80CHtFSRHvvgvjxlFWXc0N5eVc5uKr9eMCzMkYQf3RFVhk6BLgviTYAmRRazswBKurmRh8fayq\n1c1adPzrOR6LoIxS1RYVuRDrS/mKqqbMxkBE1gGuoYGUcoYF2LbYLshNmqi7aktga6GqFwbHQrYk\nQ6i1JQk9z+K2JYmYrysmwi7RoAl9cPwWzGblkkTHduJHRHoXFvJ09+5sdNFFFHXsmNzxly6F66+n\n9MsvWVRWxjBV/Si5MzgtFRdgTtoJIlNHYk2zXwEuVNWFzRgvBzPCDL0ZLsGiXBOBrzP1SVKs599L\nWKF0i3rTDN7kvwK6agMu/c0cPwvzx7oa89+6JFp6N5MCLJj/Q6z/5vMNnA/VZs0BTo32XAoe63bY\nc+9QzGssJMY+TET0i8gWWK3ZKar6oogUYxG3v2rdJvZOGvh/9s4zSqoqa8PP20AnEETMOSCgqIgB\nc8IREwZQ+VAUMUsYcx51zI6OjqMSVEZhzIMKoo4C5jGNOSCSVHTMigHo3ND7+3EO0rYdqrtv1a1w\nnrV6sbrq3nN30dVd791n73dLapefz0V5eZx/wAG0GTCA/HXXbd2a338Pjz3G0ilTqK6pYXxFBRek\nSVd0IEUEARZIKf6DZQxuPuOIlt7t+Zb9fXCi6yDcEO7l20FzIwq3xfgtt1eBiWZ2Ytzx1EXSNUCx\nmZ2RhLV74bYb2+IMdhvcUk4DATYEGGZmvxvS7bsTH8C9jka7E2udI9wg7uUZ2LVwxfuTgeeas+1d\nu9vSr9nPzAYmen4geiRtVFDAKOCkbt3giCNYqXdv6NChyVMBKC+HmTPh4Ycpef992rRpwz3l5fw9\nqi3sQGYRBFjgV/yHx/bATh06sHteHusCMuOnkhJeNuMNWlg7Jak9cAlwAm7bcVwiH2h11lgJZ1o5\nEDcD8l1cputRM0sD5x6HpK44l/sZZnZQ3PHUxYvXz3EGopFZP8gNib4Cl91MaEs5DQRYAe7/Yk8z\nm1PrceFEZHfgAGvhDD65WZ8DcO/ZzXFD1ycD0xPJPHq/sXuBxbgM3HMtiSMQLf536PCVVuKM8nK2\n7NSJqh49YMstad+lCyoocMdVVcHPP8OsWZR+9BE1P/5IYVER80pLucWM+82sJNYXEoiVIMACSGqX\nl8dJhYWcX1zMKn360HbzzSlc3feHLVoE8+ZR/dZblH/9NWbG2KoqbjCznxJYW7gPoJtwBcznmNm3\nzYhtVVz90EDcNuNLrPDo+qG5rzXZeIuFT4CZ6WoVIOkY4Ggz2zei9YSr47sBeAq4INEt5bgFmI/h\nKqCjmZ1W67ErcMPcE3KoT/A6awOH4N7LO+DqyiYDT5jZz42cdxluvml3C+No0g6fKe0BbFtYyE75\n+awLFAMCyqqr+ba8nNeAt4FZFpPhcSD9CAIsx5G0dXExk7p2Ze3jjqN9r17QWKfPggUwaRKVL7xA\neUUFx5rZY42svQlwK7ABMNLMXkgwpnVZ4dG1Dc6oczKuYDySD8Nk4LN8nwMLcTYaafnLJel14OrG\nfnbNWKtVW8ppIsDWwznxb2BmS7w32iigOTMam3vNVYD+uPd4X+A1VmRzv61z7ENADbCtjynhG5hA\nIJC+BAGWw+TlaVBhIRNOO42iffdtXov1Bx/AFVdQVlLCuMpKzq3T2VYIXID7ELse+HtT25aSNmVF\n3UxX4HGc6Ho6EwpTJbXDzXdsh5vvmJY2AZK2wxXFb9KajtA6W8pXAmObu6Xs14ldgPk4HsH5ey3C\nWYbsZi0YBN7Ca3cA9sO99w/A+aRNxgmyKpzn2Ia4EUoDcdulSfGrCwQCqSMIsBwlL08Diou57+ab\nKdpkk5atsWgRnHYapd99x9iKCjsPfu38uxV4DzizoY4tv23VixX1MV1Y4dH1Yial6f1r+QDn6r6h\nmS2KOaQGkTQBmGNm17XwfOGyk3/HbQefa60YYZRGAqwvzpy1CNh7uU9ZDHEU4DJiA3HblctwWdXj\ngdnALbjfm30z4cYkEAg0TBBgOYikDQoKmHXzzbTv3r11ay1aBMOGUfbLLwzHfTBvBYwys2n1XDcP\n5z6/PNNlrGjXf721HmBxIekFnPfYpmb2VczhNIivp5uPi7PZth+1tpQ3xG0pPx9BTOkiwHbCCcrT\nzWxM3PEASCoCvsRZteyJM7GdDPQGKoHDWpJ1DAQC6UEYRZRjSFJxMQ8cfTQFrRVfAJ06wcUXU1xQ\nwETcHfoWtcWXpHaS/iBpLO7D5DbcgO0BQFczO9fMXstg8TUJ2BnYPp3Fl+d4YGpzxZekQkl/Bl7H\nObFvHYX4Shck9cQZst6OEzrpwiHA+2Z2DLA+MAR307IR0A94X9Ke3gcvEAhkGOEXN/fYvX17tjzy\nyOh+9ttuCzvuSOXLL7Nk6VKr8Hfu/XBZrv64rMtkYA8zmx/VdeNG0q2sqMmZFXc8jeE7tUYARzTz\nvOVbyu8D26ST3UcUSNoQmAachas7/EzSOmkipkfhuoeXz8t8C3hL0p9wzSlTgH/h7qsew/2OPZuu\n9YeBQOC3BAGWY7RvzzmDB9O+TZvGj3vuOXj4Yfj8c9cVuc46sPfeMGhQ/ccPHkzh669zoaRtcQap\nb+M+EC5Kkw+zSJF0EU7QHGZmL8cdTwIcAHxnZm8mcrB3yv87jWwpZzpyg7hnAH81s/v8Y/cDpwCX\nxhxbL1z38NS6z3kx9rbcDNWXgMdww80vBO6T9BROnD0VfKYCgfQlbEHmEJIKKivZt18/Gq25mTQJ\nxo2DYcPgscfgiSfg3HPh449haQMVJz16QKdOFANzcFuLe5vZmCwVXycAV+Fc3usdYZOGjMTZRTSK\npHxJ5wPv4LJeW2Sp+OqI8yz7l5ndUuupscBJkvLjiexXRgK3N1bj5X349sUZ3y4ys92AzYAXgROB\nryVNlXSst70IBAJpRBBgucWWq61GeWNjM0pLYcIEOP986NMHlmfKunaFiy6Cto3kTHv1ohr4tiUF\n3pmCpIOBO4DLLIlDrKNEUjdc4fakJo7bC9e9ujuwg5ld3lIH+HTG26Q8CrxJnUyXmX2Eq2U8LIbQ\nAJDUGbdVPL6pY83sS9x2/9WSDjWzb83sdm+yuwHwEK6WbIGkpyUNl7RWMuMPBAKJEQRYbtGre3ca\n3XycNcttOW63XfMX32wzitq3Z8eWBpfuSNoZt616m5ldEXc8zWA4cFdDYkrSWpLuAybiHNf7m9kn\nKYwvZfhauPuAH3GdnPW1gY/GZaDiYhjOdPi7RA7246T6A3dI2rPW4z+b2b3m5keuDYwDdgFmSXpV\n0jm+szUQCMRAEGC5RafOnWnX2AGLFkHHjr99bNQoOOgg2G8/N0i2ITp2hDZt6BJFoOmGpB64DsCp\nZhbnh3Oz8IapQ3Hdp3WfayvpdJyH2f+Azc1sSro6+LcW72F2G9ARN4qpISPax4ANfI1VSvFWLSNI\nYLu4Nmb2Nm4c1CRJvet5vtTMJpvZ0cCawOXApsCrkt6T9GdJW6pZdsyBQKA1BAGWWyxbtoxGP1w7\ndYLFdYb9jB4Njz/unqtpxCximfs4a7G7errit2zexnmVxbY11UKGAC+Z2ee1H/S+V2/htqd2N7ML\nLYHh0BnO1TgT04GNdQr6uqvbiCcL1g9YghtN1CzMDeoeDvzbT5Zo6LgqM5tuZqfgMmN/BFYGngDm\nSbpO0g5eDAYCgSQRfsFyi6++/JJGW9Q339z9+2Y9vXJN5UW+/RarqCCrtq4kdQJmAZ/haqMyBp/N\n+E3xvaRVJd2JG0d0Hc71fXZMIaYMSWfiR/2Y2ZIETvkHcLivx0olI4ExLc1CmtkjwJ+B6X74d1PH\nLzOzl8zsTJzB7v8B1cAE4H+SbpW0V/AaCwSiJwiw3OLtefMatx7p0AGGDoXrr4c33vg1q8WCBVDZ\nhLvQzJmUVFXx36iCjRs/3/EjoBRnPpppW3O7AoXAs5LyJJ2Mez1LcNuND2Tga2o2koYCZwL9Em0Q\n8fVXT+LqsVKCpI2AnYAHWrOOmY3HCcjpzRGQ5njHzC42s81xdjLf4Oa5fivpLkn9fRNDIBBoJWEU\nUQ4hSQUF/DRuHCtvtFHjxz777AofsLZtYc01oV8/GDBgRWdkbaqq4NBDKS8vZ7O6212ZiM8efQSs\njpvvmEjWJK2Q9CDwKvAKzl5hKTDCzN6PNbBaJHsUkaT+ODGyV3MzfX6b9h6gWyomNUi6Hsgzs3Mi\nWEvA34DtccKzrJXrbYAbNTYQt407Dec19mQm/m4EAulAEGA5RkGBrtl3X8486ywivYt9+mm45RZe\nXbLEdoly3biQ9DLOuqFra4ZNx4WvW5uNs544GGfS+c90G/mUTAEmaVecSOhvZq+34Hzhav8uSrYX\nmp8e8T9gx6g6UH0N1z+BVYBDLaIB95LWwL2nBuK6Kl/EdQc/ns0WNIFA1IQtyByjqoqxM2ZgP/wQ\n3ZrV1TBxIiUlJVwX3arxIWkKLnOwbYaKL+HqvtoBNbjtxgnpJr6SiaStcKJgSEvEF/zqOD8GNxIo\n2QwG3ojS/sP/vI/HzY+8K6qiejP7zszGm9n+wHq4LdMDgU8kPStplKR1o7hWIJDNBAGWY5jZl2bc\ncM01lEaV/LznHqp/+YU3cbP0MhpJtwEH4eZWzok7nuYiaQtcRqI/cLyZneod03MGSRvjXO7/aGYz\nWrncA8COvj4rKXjBPIpmWk8kgs96DcIN8L4xapsJM1tkZveb2eHAWri5oX2ADyT9V9J5krpGec1A\nPEjqLGmypMWSPpV0ZCPHXifpB0nfS/pLnefyJF0l6Uu/1nt+MgWSxkla4h9fLKlC0qJkv7a4CAIs\nB6mq4sq5c/ni3ntpcMxJorzxBkyaREVZGcdkekG3pMuAk4ABZpZRzQSSVpJ0A/AcMBd4zcz+FXNY\nKUfSmrj5jldH8fp97dREnL1DstgBZwORlG1O/xoOAvbGbUUnBTMrM7NHzWwosAZwCU74vSTpA0mX\nSeoVvMYylrHAYqAzblLEWEmb1T1I0inAfkB33Gis/XwD0HL+iivv2NrMOuI6bysAzGy4ma1kZh39\ncw/gpjlkJaEGLEeRtHZhIW8NHsyqQ4fSriV/El95Ba68ktLKSvqZ2avRR5k6JJ2KnwNoZnfGHU+i\n+A+zw3EF188C5+H+YI02s7T/wxVlDZi3DHkRmGJml0expl93E+C/wPpmVh7VurXWvwd4z8xujHrt\nOtdZG3gZ+Esqx2j56QM74mrGBuK2xSf7r9dzaWs8U5FUDPyMq4n9wj82HvjBzC6qc+wruDmmd/vv\nhwCjzGwnSV2Ar4CNzezrJq7ZHteFe4CZvRz5i0oDQgYsRzGzrysq2HbSJOaddhql336b+LllZXD9\n9VRcdRULKyvpmwXiayBu++fiDBNf3YDpuHmGR5nZMFzmoStu1mHO4IvYHwNeAiIdE+Xrst7A1WlF\niqTVcdvFE6Jeuy7+A68fcJmklBkKe6+xV8zsbGBjXPakHDfr8ktJYyX9wdu+/IaQLUsbugFly8WX\n5wOgZz3H9gTer3Ocd5hkB5yQO1nS15I+k3R2A9c8DPg+W8UXBAGW05jZN2VlbD13LlcfeyzlV19N\n+ezZ9bvdm8FXX8Ftt1F9xBGUv/ACj1RU0NXM3kh95NEhaTdcp+BoM7sm7ngSQVKxpCtxFhPTgG3M\n7CX/9Ejc3WckHW+ZgDcJfRD4Gjg9SVvhY4BRSRAEJwKPpKpOz8w+xhXMj5PUNxXXrHN9M7P3zOxS\nM9sC2AvX/Xk1zmtsoqSDJRX5n+tMSXdI2k9SfqrjDfxKB5wfYm1KgJUSOLbEPwauI3cN/7UesC9w\nvqQD61lnKHB3K2JOe8IWZAAASau1bcuJ+fmMqq5m1Q03pHzNNcnLy0M//cSyTz4hf9kyqiXuqajg\nZjObH3fMrUVST+Bd3JbV/8UdTyJIOgi4BXgdONvMvqr1XCecY//mmdK92dotSC+I7sIVgB9sZlWR\nBffb6+QB83FdlZHUB3qB8SlwiJm9G8Wazbj2Hrit6gPM7K1UXrshJK3HCq+xbYB3gD1rHbIINy5p\nMjDdsn90VtogNxf1eTPrXOuxPwJ/MLND6hz7C66J6X3//ZbAy2bWSdKhwCPABmb2pX/+FqCN1Zqx\nK2l93O9GVzP7LLmvLj7CeIkAAGb2A3AtcK2kLvPns838+ayBy5L+DLwHfJnphfbL8X/s3wRezQTx\nJWlD4GagB65O7Zl6DjsW98GUEeIrIq7HFfrunSzxBc7SQdJYXIYxqgaN/rjfqZSKLwAze9EXRj8u\naU8zm5vqGOqJ6QtcF+Wtklbj9xMBOuFmmw4ByiVNx4mxJ8zs55QGm3vMA4okrVdrG3Ir3Ji2uszy\nzy3fhuxV67gP6jm+vs+Uo3Gi7bMWR5wBhAxYIOfwmaLPcVsfvdJZVEoqAM7BjdL5G3Cj1TNI2mdo\nZgMnZFLNRGsyYJLOw40K2s3Mfow0sPqvtwrwCdDdzL6PYL1ngLvM7P5WB9fyGI7H1RDuujwjkS5I\nmglskcChS3Hdv1OAR82sGRWtgUSRdD+uW/EU3M/lWWAXqzNhwndBnoobZQXwNDDW3IgsJL0AfAic\ngZs/+gowzMyeqrXGHOBaM/tnEl9S7IQasEBO4QXNHNx2Ru80F1/74O4Y+wDbmdk19Ykvz964P46v\npCq+OPHCYQRuzE7SxReAr9N6BFe31Sp8+/4Wfr3YMLO7cN2/M3yHWjqxLc7O4A6gMcHbFtdcMA74\nWtLLks5SEr3bcpSROAuKH3GZx+FmNlvSrpIWLz/IzG7HNQfNwd0UTlsuvjxHApsAP+GE81V1xNeO\nwDrAw0l+PbETMmCBnMHXC80BuuBqENKyhkTSOrhsVx/gNDNr0uBW0lTg36m0F4iClmTAfB3Jbbg6\nk5RunUnqDUzFtdG32EdP0q3AIjO7OLLgWoGkvwK74Wp6SuKOpy7eymJnVlhZrJ/gqe/iMmOTgY/S\n+YYrkHsEARbIGST9F9ci3dXMvos7nrr4NvzTcGaZ43Ap+CaHKMsNSn4H51OVlqKyIZorwCTtiSse\n3z+u4nHvc3SDmU1p4fkr4bbAe9Vp64+NWs0MawMHJbOerrX4WHuzQoz9zgy0Aeaxwn/srSDGAnET\nBFggJ5D0OG6boqdvxU8rvB3GWJyVwh/NbF4zzr0WKDSzM5MVX7JojgDz2afpwJFm9mxyI2s0jqNw\nY57+0MLzh+MyTSnz4koE35X5CFCG6/bMCINUv507wH9tl+BpX+KE2BRcsXerp4IEAs0lCLBA1iPp\nH7hi7R3TpeV+OZLWwHXy9QXOAh5uzp25pEJcM8EumWgNkqgAk7QpzuX+j2YWa92UryP8HNirbgFy\nAucKV4A8ysyeT0Z8rcEb2k4DZuL+rzPqA8Jng5dbWewGJCLuF+K2lScDzzZSZxkIREoowg9kNZKu\nAo4D+qeT+JLURtII3Ifx9zjvroda8IE3CHgnE8VXosiN0JkO/Dlu8QXgP6DH45oAmsse/t8XIgso\nQsyNWjoY2BXXHZlRmNnnZnazme2B84Y7GScoGzMmXhU4Afg38IOk+yUdIalDI+cEAq0mZMACWYuk\nUTjT0mPN7J6441mOpD647cYyYISZfdiKtd4ArkykUD8daSoDJqkz8B/gAUujSQWS1sV1qG5gZkua\ncd7DOEPLMUkLLgLkhpq/DPzNzMbGHU9r8dYzB+IyY/sDxQmcVokT/pOBxy1F0woCuUMQYIGsRNL/\n4YwczzOzG+KOB371kboWl2E4D7i3NVs8krbHjVHqambLookytTQmwOQGAM/AGeaelW7bYV5MPZeo\nQGmpaIsLSRvjxO85ZvZg3PFEhX9f9cOJsYOAlRM4bRkuazkZ5zXW6CDpVOO3xdcDCoAq4Jt07GYN\n/JYgwAJZh6S9gGeAm8zsnDSIJw9Xg3YNroPvEjP7JYJ1J+Ja669v7Vpx0ZAA8x2hj+K8go5Nx4Jw\n/z4bDWyRiDiUdAWwipmNSnpwESFpK9zv0tFmNiPueKLGv8/2xImxAbgZhYnwGr6I39yw9pTiawl3\nKS7mxLw8di0vZ/2VVqKyXTts2TK0aBGFhYV8C7xeWsoEnBdXRt6kZTNBgAWyCkm9gLeAB83smDSJ\nZyzOLHK4mb0T0bqr4mYTdk2VEWkyqE+AecH6T5zp4wBL08HitQrqR5rZC00cm48r3O/b3ML9uJG0\nK65bsL+ZvR53PMnCe43tyAp7iw0TPPUDVthbfJjMTK0kSRxZXMxVRUWsPnAgRb16kbfJJlBQsOK4\npUvhs89g1ix49FGWfPcdFdXVXLt0KbeGjs/0IQiwQNbgO6DmAC+ZWb+YY+kIXIFzfb4YuDPKLI6k\n84EeZnZcVGvGQV0B5kXN34DtcS73TfqgxYlvpOhrZoc3cdyRwIlmtndqIosWSQcCd+Je60dxx5Ns\n/PuwFyvEWM8ET/2YFWLszYh/59cuLuaezp3Z4YwzaL/NNpCXYBvdnDkwejSlCxbwWVkZR2TaTUC2\nEgRYICvwY1Q+9V/bxFUv5P9wDwZuAJ4CLjCzhRFfow1uJuHh6dTZ2RLqEWAX4f7/9rAMGLBcy1R1\nK2tklqKk5QXtk1MWXMRIOga4Gjc38n9xx5NKJHXHbVEOxN0cJMJXuG30ycB/WpN5ktSnoICnjziC\noqFDadeuXfPXMIPHHqPmttuoqKhgiJk92tJ4AtEQBFgg4/HeRQtwXYWbxlXr4A0hx+C2zkaY2WtJ\nus7BwEVmtmMy1k8ltQWYpJOBC3Af8GlV5NwYkkYDP5vZJQ08vzXwOLBRpm//SDoTN4x5NzP7Ie54\n4kDSeqzwGtudxOycfgQew4mxZ8ysohnX276ggOf+/Gc67LRTSyL+LXPnwtlnU15ayhBr4TSHQDQE\nARbIaHw2aC7QEdddVh5DDO2BS3BeQlcCY5P5QStpOq6DMm2sNVrKcgEm6TDgVmB3S8NJBY3hhfdz\nuPff70b4SBoPfGZmV6c8uCQg6RpgH9x2ZNp3cyYTSavhupoHAn8A8hM4rQR4EifGnmzs/1DSGgUF\nzL30UjrtvHMUETvmzYPTT6esooKdzOyD6FYONIcgwAIZi9/uexPohssupLQY3V//UODvwEvAuWb2\nTZKv2c1fa4Pm3EWnK5IM2Bt4ENjXzN6NOaQWIelZ4B9m9kCdxzvjtsV7WBrOH20J/n1/O7AxcKAF\n53jg17rPA3Bi7ACgfQKnVQJPs8Jr7NdyBUkqLubJ/v3pO3x4QsKuWTz5JDZ6NPPLy9kiXRtdsp0g\nwAIZi6SngL1wH26fpfjam+AyNhviuuBSMlZG0t+BMjO7KBXXSzZegP0AHGFmL8YdT0uRNADnl7VL\nncfPwtUkHh1PZMnBZ54nATXA4GBx8Ft8WcQ+ODF2MK4soSlqcOO2JuNqx7ZfYw3uuftu2udHLr9c\nTdiZZ1I2ezbXVFZmR3Y20wgCLJBRSDoAt91zGzAE6JPKrImfvXg+8EfcDMe/17ftlKRrd8AVfPfO\nhiJoX9g8B2c1kdEFwXKDrD8FDln+fvR2GvOAY5JVDxgn/nfhSdxrHJ5uRrnpgvca24MVA8PXSuS8\n4mLKL7yQol13TV5sCxbA8OH8UlnJ6iELlnrCLMhAxuBb+f+N+9A+Btg/xeJrf5zv01a4rMb1qRJf\nniG4bqpsEF/r4sa8kOniC8DX/N0OjKz18L7AIuC/sQSVZPwW+KG4rsArYg4nbTGzajN7xsxGAusC\nO+O6pD9t7Ly2bSmKoui+MTbaCDbckDa4n2MgxQQBFsgIJO0H3O2/3QD4DGeAmIprryfpEdyW4ygz\nOyzVIsjX3YzEdVlmNN4yZDrOoDabGA8c5uu+wP+8sjkzZGaLcbMVB0k6Le540h0zqzGz18zsHUF4\niQAAIABJREFUXKArsDVwOTCz9nFt2kD//u7f5nDGGXDwwc6INVEOO4yVVlqJU5t3pUAUBAEWSHsk\n7QQ8gnOTX856wBZJvm6+Nzx9Fyf2tjCzacm8ZiPshuuwejam60eC7xh9Atf9lbEjlOrDzL7HZWiP\n83MUd8Q1F2Q1/nX3A86VNCTueDIFc7xvZpeZ2Va4ZqLzgdcLC6FXr+at9+23znB15ZXhlVcSP2+L\nLaC6mt7Nu1ogCto2fUggEB+SeuI+1IprPWzAUDN7LonX3QuXbVoA7BDHvLc6ZHw2xY/jeQS3hXxe\nzOEki9HAvbg6nwnp7uQfFWb2uc9SPyfpJzN7Ku6YMg0zmw9cL+mGqipKu3WjsDnnz5gB224Lm20G\n06fDHnskdt6aawJQJGlNM/u2uXEHWk7IgAXSFj9aaDq/7yD6o5klJbMgaS1J9wETgT/h5t/FKr4k\nrY3rqLq7qWPTFV+QPhHXdn9SJgvJJngdWAycBIyLOZaUYmazcLVEd0uK0LUq5+gkkbfyys07acYM\n2Gsv2HNPePNN+OWXxM6TYLXVqMSVdgRSSBBggbTEGxzOANap89TlZhZ5HZSktpJOx201/g/Y3Mym\npIlQOBk3XHxR3IG0BF+/djPuZzk4093gG8O/X94DKs2s0SLrbMR3ex4DTJGU1BKBLCa/bVuaZesx\ncyYsXAi77ALrrgsbbgjPPNOMCzqbiySYXQQaIwiwQNrh5+s9hauJqM0YXMFq1NfbCXgLOATnxH6h\nmZVGfZ2W4LftTiazi+8vwdWwHRzHpIJU4sXm1kCBrwPLOXyd5JnAU5I2jDeajKRq6VKaVX4/fTps\ntx0UFbnv99jDZcQSvqDr5U5lR3eAUAMWSDO8t9CjwLZ1nvoXcFqUGSlJqwLXAfsB5+CyTOmQ8arN\nAGCe397JOCQNB4bi5jtmZAavmeyAG4s1HhgOnBtvOPFgZvf7btcZknb1hfqBxFhkxrJffnEF9U1R\nVQUvvOCMVQ87zD22dCmUlMCnn8LGTdwGmMEPP1CI8xgMpJCQAQukDd5d+z6gb52nZuCK7msiuk6e\nH/z8EbAEt934QBqKL3DF96PjDqIlSBoEXAz0y6Hi3lE4e41xuG7I4iaOz1rM7FZcF+g0P6YnkABm\nVlNYyOx58xI7/qWXnF3FxInwj3+4r4kTYcstXWasKb51v5llOfQ7mjYEARZIC/zWzTjc6I7avA4c\nFpXhqaRtgdeAY4F9zOyMdM3MSNoKN29vatyxNBdJ/XDCcf9cqYWStAZwIK778VOcAevgeKOKnT/j\nfoen+ux2IAEqK/nPzJmJ1YHNmAH77w+rrQadO6/4OvRQePZZqGnitvXDD6FdOzJyBmumE0YRBdIC\nSVcDdecbzgZ2i2LItqSVgauAw4ELgX9GlVFLFpJuB740syvjjqU5SNoB5/U10MxeauJYMzOlJrLk\nIulPuKHwJ/rv9weuBrZN0+xqSvCZ7fuBdsCgbG7CiApJW3fqxCuPPEJxc81Ym8upp7Jk7lxOMLOH\nknulQF1CBiwQO5LO4Pfi6wtg39aKLzmG4sRcW9x244QMEF8rA4NwtUQZg6TNcBm745oSX9mEnwV5\nCr9tlpiOqwfbMZag0gQ/qHsosBJwm892BxrBzN5btoxPX0vyBNEFC+Czz1iGq7sNpJggwAKxIKmz\npMmSyoGb6jz9I65u6At/7HWSfpD0vaS/1FpjV0lLJC32X0sk1Uga4J/fAngBOA0n6E4GEnTHiZ1j\ngWmZVJchaX2c6DjPzJ6IO54UcxDwRe3ZpF7kj+W38yFzEjOrxDWUbAVcE3M4GUFJCZeOHk1pVZJ6\nE83g5pspM+OGMIg7HoIAC8TFWFx2oF2dx0txdUNzACSdgutS7A5sBuznC+gxs5fNbCUz62hmHYH+\nuKL6lyXdADyHKwK+CSjHOeinPd60NKOK72v5tv3dzDLWMLYVjKL+n9cE4EBfH5bTmFkJcABwqKSz\n4o4nA3h0yRJeuvPO5NhDPPUUNn8+X1RVkVUjwTKJIMACKcd3hh0G7Aq/8btZBhxqZm/WemwocKOZ\n/eS3I/8KDGtg6WE4P693gFVxsyLvw/lQZZIdwB+AMuDVuANJBO/b9iQwxcz+Fnc8qcZvu26OG7P0\nG8zsZ+Bh4MRUx5WOmNlCYF/gdF8aEGgAM7OyMoZNnUr5qxH/JZg3D269lfKyMgaF7Fd8BAEWiIMD\ncfVYBbUeM+AdM6vr39wTeL/W9x/4x36D7xg8BtgQOMrMhnnvoWtw2bbvIos++YwiQ+Y+SioApuDc\n3+vW8eUKI4F/NNKpOwY41deJ5Txm9j9cVvt6SQfFHU86Y2bfVVayzxVXUBJVPdjcuXDWWZRXVHC0\nmX0QzaqBlhAEWCCleHfwcUDdQty7gZJ6TumA25ZcTol/bPl6xZKuBF7B1Xf1WF78LWk7YGfg1she\nQJLxzuE747rG0hrf3XYvbvbh8EwQjFHjs39HAbc3dIyZvYczuTw4VXGlO2Y2G/f/cZek3eKOJ50x\nszcrK9n78stZ/I9/UF3dwnxVTQ08+ig1Z5xBWWkpR5nZlGgjDTSXIMACKUPSmrg6oS51nroEeBtX\nv1WXEqB9re87+Mfwd8+zgE2Bd4Fbl6fTfafVGOB0LwwypfPqVODudBmF1BC1/n+74DKOuWotcAzw\nnJl92cRxYwjF+L/BzN7AiddHJPWKO550xszeqKykx5Qp/Oe44yh9882m/b1qM2cOnHYapePHM7ui\ngu3MLHQ9pgHBByyQEiR1Al4E6v6hvQU4A7gD+MHMLqpz3ivAbWZ2j//+aNycuS+BHrgPtTnAAqCb\nmS2odb0fge9x4qsNri7sW+AIM3slCS+zVXijyv8BO5vZx3HH0xg+63gAsJeZLW7FOhnrA+ZF6Cxg\nhJm90MSx+bgsWF+f/Ql4/MSEm3BzWD+JO550xrnqMLi4mKuKilhj4ECKttqKvE02gcJaNrfV1fDZ\nZ/DRRzBlCku+/56K6mquWbqU0Tl8s5R2BAEWSDqSioBpwO51nvoEV7zcE3gW2KXuh5PvgjwV2AfI\nxxXZrwRciyvOr5R0Ec62Ys86565e69v1gTeAtYGF6fhHSNKxwGAz2z/uWBpD0mm4OrVWz/jLcAG2\nF257e8tEtl8lXQGsYmajkh5chuFnhp6De099E3c86Y4X/zsXF3NSXh67lJezQYcOVOXnU7N0KVq8\nmMLCQr4BXi8tZQIw3fuxBdKIUBQaSCq+8PhBfi++nsZ1+i3EZaqGm9lsSbsCT3pbCczsdkkb4cRa\ne+BTXIbos1prHQ2/b6WuLQ68CDTg+zQ2YR0FXB53EI0haQiuo3S3MGCZkcDYZtS+3Q7MlHRRa7KG\n2YiZjZO0Km5u5B5mlil+fbHg33Ov+C8kFSxaxLq4xqYq4NuSEquvpjaQRoQMWCBp+Lu0O4Hj6jz1\nGm4OY5N1TpLWAf4G9AFOM7PHIw80DZDUBydUN03XO1U/WmcisLeZfRjRmhmZAZO0Lq4jdwMzq692\nsaHzHgaeN7MxTR6cY/i/FzcDW+OmYJTHHFIgkFRCEX4gmVzH78XXLKB/U+JLUjtv1vg+MA/oma3i\nyzMSGJfG4mtnXKfqgKjEV4ZzCnBfc8SXZzQwMozj+T0+q3MGbmrFv4JtRyDbCRmwQFKQdC6/3xb8\nHFfn9VUT5+6G8+76Gvijmc1LTpTpgXeRnwd0be3sy2TgRzo9Cwwzs6ciXjvjMmDe++xzXANCswrq\nvfCaiXtfP5+M+DId37AwFefdd3walwwEAq0iZMACkSPpOH4vvn7AbTs2KL4krSHpnzgPrCuA/bJd\nfHlOwLnIp6P42hDXQHFW1OIrgzkM+LAl3Yw+yzMGV+8XqAdvaHs40A1n1ppRAj0QSJQgwAKRIukQ\n4B91Hl6CE1PzGzinjaQRwIc424jNzeyhXDD29Gamw3EfymmF7yKdAVxvZvfFHU8aMZLW/bzuBfaS\ntF5E8WQdvkShP84x/7yYwwkEkkLYYw/8Dn/HuT6wMs5DqxRY0JR1g6Q9gH/xW2FfBRxiZu80cE4f\n3HZjGW5LJ9fqi/oDX5vZ23EHUhtJHXGZrwfN7Ja440kXJPUG1gNaXI9oZksk3YerI7s4qtiyDTP7\nSdK+wMuSFprZnXHHFAhESagBCwCuq6tdO04qKuKA8nJ6FhRgHTqwVILycvKWLKGguJiPq6t5vqKC\nO8zs/Trn9wZeADrWergGOLy+kReSVsF5eR2Mu8O9NxcyXnWRNAPnfH9v3LEsxxvCPoUzuB2RzJ9L\nptWASfoH8KmZXdPKdXrgfl82MLPKKGLLViR1w5k4jwjjcwLZRBBgOY6k3u3b85elS9m9Xz+0yy4U\ndOsGnTv/9riyMpg/H955h6WPPkpVTQ2flJRwsZk9Jqkrzo9m9TrLn2Rmv9mOlJQHDMMNyX4IuCRX\nPX8kdQf+A6yfLh/CvvNsElCNGzGU1K7MTBJg/qbhE6B7FB5okp4B7jKztJ/7GTeStsXdFAxqaupA\nIJApBAGWo0jKLyjgirw8TjvpJAr32w8VFSV27rJl8OqrcOutlJaU8HJ5OT2ADeocdqGZ/aXONXvh\nthvb4oxX692WzBUk3QyUmNmf4o4Fft16Ho/7WfZPhSjMMAF2NrC1mR0T0XqHAueZ2c5RrJft+MkD\n/8LVk+b0345AdhAEWA4iac2iIl7o2ZP1LriA4i51R2MnSEUF3H479uSTqKrqN0/9DThn+daVrye6\nAjgSV/NyZ663lkvqgLMy6G1m/4s7HgBJ1wJ74+YVpsRFO1MEmM/czgeGmNl/I1qzLW6ywyFm9m4U\na2Y7kgbivNT2aKipJxDIFEIXZI4haa3CQt4aNIiNr7++5eIL3PDX009Hl1wCBQW/Pnw3cK6ZmRsc\nqyOB2UAHnJnq+FwXX56jgRfTSHydBRwKHJAq8ZVh7Af8DLwe1YK+qeU2XFdlIAHMbDLwZ2CGpLXj\njicQaA0hA5ZDSCosKuKDQYPYcNgw2kW59muvweWXs7Syks3NbL6kzXCt+p1xxbOvRXm9TMZv9X0A\nnGFmz6ZBPEOBK3HzHVMqCDMoA/Zv4GEzmxDxuqsDc4FNzOynKNfOZiRdCBwF7G5mP8cdTyDQEkIG\nLIcoLOSaXr1Y59hjoxVfADvtBEOHouJiHpD0F1xx+aPA9kF8/Y7dcXVwz8UdiKSDcKa5+6VLNi7d\nkLQJbhbpg1Gv7Yv5n+D3I7sCjfMX4GngCUnFcQcTCLSEkAHLEST1ad+eF+6+m6JVVknONZYtg5NO\nwj77jLfMOMTMvknOlTIbSZOA/5jZ6Jjj2A2YDBxoZm/EFEPaZ8Ak3QDUmFlSDEEl7QjchxvEHrbn\nE8TX5U0EVsXV0VXHG1Eg0DxCBixH6NCBm4YPT574AmjTBi6+GOXn0x0I2yn1IGkd4A+4Wrk44+gF\nPIKzmohFfGUCPrsyDBiXxMu8jqsv2y+J18g6vFg9Aec3OMELskAgYwhv2BxA0qY1NWyzzz7Jv9bG\nG0PXrgg3Ly/we04GHjCzxXEFIGlj4ElglJk9HVccGcKRwH/NbEGyLlBrPmQoxm8mPus1CGed8rcw\nNzKQSQQBlgMUFDDywANpk5+fmusNGsRKHTpwbmquljlIygdOwnmhxRXDmrj5jleZ2aS44sgE/If5\nSJztQbJ5EOjj680CzcDMyoCDgL7ARTGHEwgkTJgFmQPk57P/brs1r/B+8GD45Re3rWgGEtxzDySy\nhbnDDlBeTk9JhWZW0dK4s5ABwFwzmxXHxSWtjJvveLeZJXNLLVvYEVgJJ1iTipmVS5qAG8x+TrKv\nl22Y2S915kbeHndMgUBTBAGW5UjKb9OGjbp2be55cO210Lt3869ZUACrr075N9+wJfBm81fIWkYB\nf4/jwpKKgMeAl3CWE4GmGQWMTWFh/DjgTUmX+qxOoBmY2TdehP1H0o9m9nDcMQUCjRG2ILOfzbp0\noSLRMUO1aU2D7Oab0xZogXzLTnzR+0bA1Biu3Ra3xfUlcHouDj1vLpLWAA7AddmlBF9n9hqu7izQ\nAszsY9zPbaykveOOJxBojCDAsp/OnTqR8tb2Ll3Ix5mwBhwjgdu9+3nKqDXfsQAYFmwOEuZEnPFq\nqk0+xwCjQjF5yzGz94AjgAckbRd3PIFAQ4QtyOynTV4LZfYll7gaMICtt4Yrrkj83Lw8BLRp2ZWz\nC197dQSwWQyXvx7oAfzBzKqaOjjwa8bwVFxhd6qZAdwK7AS8GsP1swIze1HSScDjkvYyszlxxxQI\n1CUIsOynrLy8ZSdedVXLasAAyspYCrTwylnHMOApM/s2lReVdB5uO2Y3MytN5bUznIOBz30mJaWY\nWY2ksbiMaRBgrcDMpkpaBZguaRcz+zLumAKB2oQtyOxn7jffUFTTgo2n1lQKzZtHBW4Id07jzSFT\nZWVQ+7rHAyOAfcOMwWYzCrcVGBcTgQN8HVqgFfjZnaNxw7u7xB1PIFCbIMCyHDP7qW1bfvkyhfd+\nZvDppxQBb6fuqmnLPkAJrrg6JUg6FLga6Bfu+puHpM1xW8WPxBWDrzt7COcZF2glZvZX3LzNf0vq\nEHc8rUVSZ0mTJS2W9KmkBps2JF0n6QdJ3/sZvfUdM1RSjb9pW/5YvqQ7JP3orzNN0nrJeD25TBBg\nOUCbNrz+XjM3U1pTAvzJJ9CmDYvM7IeWr5I1jALGpKrzUNKeuKL7/mY2LxXXzDJGAOPToF5uDHCK\nr0cLtJ7zgY+AR7whciYzFliMa3I6DNfx+bv6Ukmn4MZbdcfdVOwn6eQ6x6wMXAh8WOf0M4Ht/bmr\nAt+R3HFcOUkQYDlASQnjHn6YJc2RAPffD9ts07LrTZ1KxdKl3NGys7MHSRvhiqnvT9H1tgEmAf9n\nZiH72EwkdQSOAmI38TSz94HPgUPijiUb8DdAJ+PqUv+ZqXMj/WzSgcAlZrbMzN4FHgaOqefwocCN\nZvaTmf0I/BVXj1qba4GbgR/rPN4VmG5mC/3NyL+ATaN7JQEIAixXmL5wIeWzU1CRVVYGTz8N1dXh\nbgnXSffPVJhqStoUt80y3MyeS/b1spRjgGfN7Ku4A/GMJsyHjAxvAXMksDZwS4ZafXQDyszsi1qP\nfQD0rOfYnsD7DR0nqQ+wrZndVs+504D9Ja3lRd8Q3N+XQIQEAZYDmFlNdTVX3XILpS0pxm8Od95J\nVdu2PJFGH2Kx4J3njycFaXtJa+PsC/5sZrHVLmUyteY+xll8X5fJwGa+Li0QAWZWjuty3QW4NOZw\nWkIHoG5HcwluZFZTx5b4x5Y3BzU4AN7/HXkX+Ar4BWdlEyZoREwQYDnC0qWM/eIL5k+ZkjxT1g8/\nhH//m/LSUoYn6xoZxP8Bb3pn7qQhqTMwHVe3ND6Z18py9gJqgBfjDmQ5fuvnDkIWLFLMbBGuNupo\nSSPijqeZlADt6zzWAViSwLEd/GPg3lPvm1m9o+Ik3QB0xNWZtcdtc05rediB+ggCLEcws2VlZQwa\nP56KuXOjX//nn+GyyyirrOQEM1sY/RUyB59NSbqVgd8aeAJ4BlfLEWg5I0lhs0QzuAM40tenBSLC\nzL4D+gEXSRocdzzNYB5QVKcjcStgVj3HzvLPLadXreP6AgMkfSPpG2Bn4EZJt/jnDwQmmNkiM6vG\n1Yn1kbRahK8l5wkCLIcws/mVlRx19tmUz58f3bo//wynnUZpSQm3hC0wAPrg7hyTdscoqR3urvRT\n4Ow0FA4Zg/8w2xO4J+ZQfoffyn8WV1AdiBA/e3N/4GY/xDvt8fWkk4HLJbWT1BvXCVnfe/du4CxJ\nq0paFTgbmOCfOxbXGdnLf70FXA78yT8/BxgqqaP/W/NH4Ht+X6wfaAVBgOUYZja1rIyjTz+dsuef\nb/16c+bAKadQ9sMPjK6s5KLWr5gVjATGmdmyZCzu6zcm4LbMjg/zHVvNKcB9ZlbS5JHxMBoYkaFF\n42mNmc3EdRXeK2nHuONJkJG4G7wfcWJsuJnNlrSrpMXLDzKz23HlCXNwptjTlpcpmNliM/t++RdQ\nCSw2syW1rlEAfAH8DAwADg1/a6JF4cY5N5G0Q1ERD/XuTZezz6Z4lVWad35lJUycSNWUKVRWVXFK\nTY09kJxIMwtJqwNzgU2S4UDvP4RvArbDGa0mvcMymUgyM4tNWEgqwNk97Jmu8wL9z3wmcFrocE0O\nkg4E7gT6mtlHcccTyA2CAMthJBUWFnJtTQ2n7rILNYcfTvFmmzVuwvrVVzB1KlVPPEFNXh7PlpZy\ngq+nCACSLgS6mtkJSVr/T7gC/z28Y3pGkwYCbAgwzMz2iSuGRJB0Kk5wD4w7lmxF0tHANbjZqZ/H\nHU8g+wkCLICkLm3acEJ+PmeYscomm1CxxRa079SJtnl5UFaGffQRS+bNo01FBSZxZ2Ult5rZJ3HH\nnk541/JPgAFm9k4S1j8F5+i9q5l9HfX6cZAGAuxV4HozezSuGBLBj9D5HNi6jgdUIEIknQEMx/2O\nhUkegaQSBFjgN0haC9gW6JWfz6oSbaqrWVRTw4e4Qs1PQ8F3/fgZjOeZ2c5JWPtw4BZg92RbW6SS\nOAWYnxzwKLCxN+lMa3yH2mIzuzjuWLIZSVfjOiT71qqJCgQiJwiwQCAiJD0NTDSz+yJed2/gAWBf\nP3oka4hZgN0JfGxmGWHhIakH8AKwgZlVxhxO1uJr7m7DjeM5IPxfB5JFEGCBQAT4D8cXgfWj/IMt\naTvgKeBwM0sbk9CoiEuASVoFt13cLZO2mpIl8gO/RVIb3PxDcLNVk9LRHMhtgg1FIBANI3Bu9FGK\nrx44o9WTslF8xczxwOOZJL48Y3Amv4Ek4gXXEJzdw9hgARJIBiEDFgi0Ekkr4Qqke0VVIC1pXeAV\n4HIzuyuKNdORODJgPrsxDzjKzF5P5bVbS7IbPQK/xf9uP4/z0Aq1d4FICRmwQKD1HA08H6H46oIb\nrj0mm8VXjOyHM5d8I+5AmotvFriNMB8yJfgi/P2BIySdHnc8gewiZMACgVYQtUmmtxt4BnjJzM5t\n7XrpTkwZsCeBSWY2MZXXjQo/j28ezm8ujIZJAZI2AF4GLjSzexs4pgewQ2EhO+Xnsx6g6mq+KS/n\nNZzYnxk6yAO1CQIsEGgFkvYExgI9W/vHVVI+8DjwNW7EUNb/cqZagEnqCryGa5YoT9V1o0bS3cAH\nZnZD3LHkCpJ6As8Bx5nZk/6xtsBRHTpwfl4eG261FTVbbkmHLl2cofVPP8FHH1H6/vtQUcEP5eVc\nb8YEM6uI9cUE0oIgwAKBViDpIeAFMxvTynXygPuAYuCwTPClioIYBNiNwFIzOz9V10wGknbAWZNs\nGjr0UoefF/k4cCjwc3Exk9Zbjw2GDqXDDjtAmzb1n2cG77wD995L6dy5LCwv5wgzezOFoQfSkCDA\nAoEWImkd3Pbjhma2uKnjG1lHwK3AlsB+mZyZaS6pFGCSioH/Adub2YJUXDNZ+PfMG8BlZvbvuOPJ\nJSTtBzxYWEjBqaeSf/DB5CXaI2kGzz+P3XgjFVVVnFVdbbclNdhAWhOK8AOBlnMKcH9rxJfnUmAX\n4OBcEl8xcCTwWqaLLwC/PT2GUIwfB4Xt21N0yy0UHnJI4uIL3LZk377ojjso6tCBG9u10ynJCzOQ\n7oQMWCDQAny91ufA3mb2USvWGQGcBeySi0PNU5UB8xmjd4ALzGx6sq+XCiQV4d6DO2fTeKp0RtJG\nBQV8ePPNFHfv3rq1vvoKTjqJ8vJydg2WIrlJyIAFAi1jIDC7leJrMHAR0C8XxVeK2QnoADwddyBR\n4bOlE3DDowNJRlJecTEPHnssBa0VXwDrrAOnn05hURGT/A1dIMcIAiwQaBmjgNEtPVlSP9xw7QPM\n7NPIogo0xChgrJnVxB1IxNwGHOvr2wLJ5Q8rr8zmgwbRQKl98+nXD220EWvitscDOUYQYIFAM5G0\nNbAB8FgLz98B1/E40Mw+iDK2wO+RtAbOTHNizKFEjq9nexU4Ku5Ysp0OHTj/qKNo31CnY13OPBOe\nfLLxYyQYMoT27duT0V25gZYRBFgg0HxGAre3xCpC0ubAVGCYmb0ceWSB+jgJeMjMfo47kCQxBhgZ\n5hUmD0kdKyvZtW9fIv8/3mEHADaUtEnUawfSmyDAAoFmIKkzcDgwPpFjJU2WtFjSp5JGAdOAc+ta\nB0i6TtIPkr6X9JcG1hsqqUbS8bUey5d0h6Qf/XWmSVqvda8ye/BGmafiREq28jSuvm3nuAPJYnqv\nuy7lRUXRL9ymDWy2GUuB7aJfPZDOBAEWCDSPYcCTCRbNjwUWA52BE4CbgfvM7J7aB0k6BTefsDuw\nGbCfpJPrHLMycCHwYZ1rnAls789dFfgOGNe8l5TVHAIsMLP34w4kWfi6tmBJkVx69+xJYbIW32IL\n2rdrFwRYrhEEWCCQIN6tfiQJFN/7ouiBwCU4d/vrgQ+A+nxfhgI3mtlPfrbfX3FCrzbX4gRc3dl/\nXYHpZrbQzKqAfwGbJvqacoBRZHf2azkTgf0lrRl3IFlK51VWoSBpi3cmLz+fNZK1fiA9CQIsEEic\nfriM1n8TOLYbUAZ8D0wB3gXuAnrWc2xPoHaG5oPax0nqA2xrVq9r9jTcB+9aXvQNAZ5IIL6sx8/u\n6w5MjjuWZGNmvwCTcPVugeipof6bp2gWrwEzsq1DN9AEQYAFAokzChiT4JDsDkApcC+wCOfVVAKs\n1Mixyynxjy3PujW4vWRmj+DE3VfAL0AP4MoE4ssFRgDjfWYwFxgDnCKpXdyBZCHffvUVSZtS8d13\nLK2o4H/JWj+QngQBFggkgKSNgB1xA5AToQRYDegCDPEDkzsASxo4tn2t7zv4x8AJr/cbGtwr6Qag\nI67OrD3wMC4rltNI6ojzVro97lhShbc0WYCrewtEy9sffUSzu54TZeZMSmtqeCNZ6wfSkyDAAoHE\nGA5MNLOyBI//P6AdMNLMKvxjWwGz6jl2ln9uOb1qHdcXGCDpG0nf4DrdbpR0i3/+QGB3VhemAAAW\nlUlEQVSCmS0ys2pcnVgfSasl+sKylKHAM2b2ddyBpJjRhGL8ZDBz4ULyf/qpeSclYgxSXg4ff0wh\nUO9NViB7CQIsEGgCP3PvOBLsLpR0Oq4AfwpwrqR2knoDhwH31HPK3cBZklaVtCpwNm7EDMCxuM7I\nXv7rLeBy4E/++TnAUEkd/dbTH3F1Z3WL9XMG74c1ktwovq/LFKC7r38LRISZVbZty0NPPMGyRM+p\nqIBEbCueew7atuWVMI4s9wgCLBBomsHAG2b2SVMHSjoaOAdXsH8ibmvwR1wh+HAzmy1pV0mLl59j\nZrcD03FiajYwzczG++cWm9n3y7+ASmCxmS3fyhwJFABfAD8DA4BDs3DkTnPoCywF/hN3IKnG17vd\nQciCRU55OTc+9BCVJSVNH7tgAXz2GWzaRD9yVRXccw+lpaVcH0mQgYxCidUTBwK5ic+mvAVcYmaN\nDhaRdAAuc9XXzOrbagzUQZKZWaTu4pImAzMa6BrNeiStjfOL29DMFjd1fCBxiov1zz32YND55zfs\nCXbHHW4E0eDB7qsxxo+n+tFHebGsjH4JNvcEsoggwAKBRpC0I25u46aNZZUk7QI8ChxsZq+lKr5M\nJ2oBJml94D1gfTNLIFeRnUiaBPzHzFo8MD7weyR1LCxk/llnsdo++7RuLNEbb8Cll7KkspLuZvZN\nVDEGMoewBRkINM5IYGwT4mtL3BbjMUF8xc4pwD25LL48ownzISPHzBZXVLD3jTeyZMaMlvuC/fe/\ncOmllFVWsn8QX7lLyIAFAg0gaXVgLrCJmdXb/+TtKV4CzjOz+1MZXzYQZQZMUgHwP2B3M5sbxZqZ\nihdeHwBnmNmzcceTbUjavLCQ53bemY5nnEHRSvW5+9VDeTncfjuV06ZRVlnJgeGGLbcJAiwQaABJ\nFwEbm9mJDTy/BvAycIuZ3ZrS4LKEiAXY0cBQM+sXxXqZjqRTgX3NbEDcsWQjkjoUFXGTxJCDD6bt\nIYfQbs0GBkH99BM88QTLHnmEyqVLmVZWxkkN3dQFcocgwAKBepDUFvgUOMTM3q3n+U7A88ATZnZp\nquPLFiIWYK8BfzGzqVGsl+lI6gB8DvQ2s+CyniQk9Sgs5PRlyxjavj3WvTs1a6xBvoQWLqRqzhxY\ntIh2+flMKivjpvr+ngRykyDAAoF6kDQAOMfMdqnnuUKc2/xsYEToXmo5UQkwSdvi6vA29lMHAoCk\nm4ESM/tTkwcHWoUfG7YpsA2wOq7GeiFuVNgcM0uak34gMwkCLBCoB0nPAHfVrevymbGHgCrgqPBh\n3zoiFGB3AfPM7C8RhJU1SOqO80Nb38wq444nEAisIAiwQKAOkjbDbS9uUPtDyxc2jwc2APqHD7TW\nE4UAk9QF+BjoZmY/RBNZ9iBpBnC3md0bdyyBQGAFbeMOIBBIJZLaANsD27Vvzw5t2rCKGUsrKphf\nXc3rwKvACGB8PQLrWtzMxr5BfKUVxwOPBfHVIGOAC4EgwAKBNCJkwAI5gaRV2rZlZNu2nNa5MwVb\nbUXbHj1c+/iyZfDNN9TMnEnJrFkUSLQpL+fY2tuPks7GjRbazcwWxvdKsovWZsC8oJ4PDDazN6KL\nLHvw/0efAgPN7O244wkEAo4gwAJZj6RDCgqYuNtuFBxxBEXdujV8bEWFG447cSKlpaW8UFbG8cD+\nwJXArqGbLFoiEGAHApeZ2fYRhpV1SLoAt0V7fNyxAEjqDNwJ/AFXqP4nM3uggWOvw2U5DVeXeUE9\nxwwFJgInmtld/rF8nCHtYUA7XHb7JDP7IvIXFAi0gCDAAlmLpLyiIm4tLmbYpZdSvNVWiZ9bVQV3\n3knV1KlUV1ZSgct8zU5asDlKBALsKeBBM/tnhGFlHZJWA+YBXc3sxzSI5wHcYPkTcNv6zwE71/0d\nk3QKriRgL0DAs7jJFHfUOmZl4DWgGvh7LQF2PjAY2AdYjKvf7GJm/ZP76gKBxAijiAJZiSQVFjJm\nnXU4duLE5okvgPx8GD6c/AsuoH1BAUWEesm0Q1JXYFvgX3HHku74+rjHcJmkWJFUDAzEDbhf5n2x\nHgaOqefwocCNZvaTF45/BYbVOeZa4GagrrDsCkw3s4VmVoV7n2wa3SsJBFpHEGCBrETiyJVX5pib\nbqJ9hw4tX2fPPeHssykqLGSa/+AIpA8jgAlmVhF3IBnCGGC4rwmLk25AWZ2twA+AnvUc2xN4v6Hj\nJPUBtjWz2+o5dxqwv6S1/O/uEOCJ1gYfCERFEGCBrEPSmvn53HbZZa0TX8vZZx/Upw+dCwu5ofWr\nBaLAf6AOBcbFHUum4JsUFuJqGuOkA1Ba57ESoL6JinWPLfGPLTc+HQOMrO8iZvYIzgT1K+AXoAeu\nljMQSAuCAAtkHYWF/OmAAyjo3j26Nc86iyIzjpO0bnSrBlrBUfx/e/ceZHdZ33H8/d3NbvZKsuEy\ngBoLNoiCSgKJitihogXtTIoyoQYR66WoJcWC40iLOtzsBClRbpILlxodZlKRlFhqooLVaJQabiYK\nJAYSEyEJhGKSvZ89T//4nWiMSfZk9+zvJGffr5nzx57z/J7zZLIz+znPeX7fL6xIKa2v9kIOMfsM\nLDnaCbTu8VwbsKOMsW2l5yD7dzyRUvr53t4kIv4NOAzoKM1xL9mumHRQMICppkRES7HIh2fMoLGc\n8TNnwqOPDj5u3LhsJ6yhgU8Md40anlJB3Flkd7jpwCwCTo2Iap6FWgM0R8SrdnvujcAv9zL2l6XX\ndnnTbuPeAbw3Ip6PiOeB04EbI+Lm0ut/TfYV9e9SSv1k58SmlW5IkKrOAKZac/akSQwcc0zlJ54+\nnbFjxvDRys+sA3Q60AJ8v9oLOdSUzsvdBXyyimvoIuvbeXVENETEZLJSEV/fy/CFwOURcUREHAF8\nGri79NqHgNeRhbI3ASuBq4FdfS+fAi6KiMMiogH4R2Arf3pYX6oKA5hqSkMDbzntNCpw8utPHX88\nFAocXqphpOqZRVaKoFjthRyi5pIFkz2/BszTJWRfDW4jC2OfTCk9GRFnRMT2XYNSSvOAZWRh6klg\naUppQem17SmlrbseZGUttqeUduz2HmOBjcD/Ae8FzvX3RgcLb61XTWlu5oxJk0bmg0V9PUycSNe6\ndZxC1itSOYuIo4FzqOIOzqEupbQ+In5Cdo5uQZXWsCsQ7fn8j8nObe3+3BXAnxRf3cu179jj5+eA\n6cNbqTRy3AFTTUmJCePGjdz8HR0E2Sd3VcffA/+RUnq52gs5xN0GXFI6TyepCgxgqikRjOjXC8Ui\nCUb2PbR3pXM8HycLD4ON7YiI+yJie0Q8ExEz9zP2+oh4ISK2RsTsfYy5KCKKEfGR3Z5rjIj5EbGt\n9D5L9zhYfjD7Ptk5urdVeyHSaGUAU615buvWkZt8yxYC2DJy76D9+BvgmZTSL8oY+1Wy9jMdZAe8\nvxoRr9tzUKnVzTnAa8kOdJ8TERfvMWY88M/A6j0uvwyYWrr2CLLfi0OiLlnpHNTBUJJCGrUMYKop\nO3fyo6eeon8k5u7rg82baeGPK3MrP5dQ3u6XrW7K8zWywDkC9wxLGowBTDWlWGTFww9TdmuaAzkB\ns3o1NDWxvnQbvXIUESeT7TQtLmO4rW7KUDpHt4jsXJ2knBnAVGv+Z+tWep5+urzB99wDU6aUN/Zb\n36Kzu5ubBx+pEfAPwPzSTtNgbHVTvtuAi0vn6yTlyACmmpJSGigUmLNwIRXdpfrNb2DlSqJY5GuV\nnFeDi4hxwExgfpmX2OqmTCmlVcAzZOfrJOXIAKaaUyhw02OP8dKPflSZ+QYG4Npr6SwWuSKltH3w\nK1RhFwHfLdV1Koetbg7MrWTFbSXlKFJK1V6DVHERcXpLC9+bO5eWVw2zMMDcufR9+9s80dXFW6yi\nXVkRkVJK+zyJV6pT9SRwcUqp7EgdEfcAPWRlK04GHgTellJ6co9xHwc+Abyr9NT3yKrsL4iIw4Cm\n3YYvBr4J3JlS2hERi4EC8FGgG7ic7M7IYw+l35PS148bgL8CEnDa2LFMbWjgSGCgp4dnCgV+Djyc\nUtpczbVKtcRK+KpJKaUVY8bEpbNmcctXvkLzcccd+BzFItx5J/1LlvB8dzfvOZT+qNaQs4A+YPkB\nXncJWc/DbaXH71vdAP+dUjoMslY3EXEcWaubBNyxe6sbslIWAETE3lrdzCVrdVNPVqbiUGx10wA8\n1tLCisZG6k4+mXTSSbS1t0NKsHkzA6tW0fn00zS2tcWKzk6uB76X/PQuDYs7YKpp9fXxwYYG5n3s\nYzS+733U15X5pfvmzXDddXQ++yzPdHVxVkrphZFd6ehUxg7YYrL+f/NyXNaoERFnNDWx6KSTGH/B\nBbRMnrzvO4O7u+Ghh2DhQjp37uTHXV18KKVkTTxpiAxgqnkRMamlhUXjxzPp/e+n9Z3vJJqb9z52\n3Tq47z56HnyQVCxybX8/N6SUCvmuePTYXwCLiIlkdxm+OqW0c29jNHRjx8YVjY184bOfpfmMM8q/\nrq8P7r6bvsWL6e7t5eyU0sMjt0qpdhnANCqUSgqc1drKZ3p6OPPoo+k+8UTGjBtHQ6FAceNGeteu\nZUx/Pz3FIrf19zP3AA59a4gGCWD/CrSklP4p52XVvLFj41/Gj+fKW2+l5cgh3jLw05/C1Vezs7eX\nv0wprazsCqXaZwDTqBMRzWR3vr2JrIxAgewczyPABs+25GdfASwimsgOhr89pbQm/5XVrog4q72d\nJXfeOfTwtcvy5fDFL/Jiby9/nlL6XWVWKI0OBjBJVbOfAPZB4MKU0tlVWFbNioj2pibWXXUVR775\nzZWZ8/rr6fnhD7m3qyvtrdWTpH2wDpikg1FZfR91YMaMYdbUqbRVKnwBzJpFUwTnRcRrKzerVPsM\nYJIOKhFxGnA08EC111JLIqK+oYHLLriAfdyCkpk5Ex599A8/P/QQTJ8Ov/jF3se3tsL06YxpauLS\nSq5XqnUGMEkHm0uA21NKA9VeSI05vaODphNPLP+CpUvh5pth9mx44xv3PW76dBqKRS4qFc6VVAYL\nsUrKXUQcQbbLRUS8EvhtSilFxOHAucCkaq6vRk099VQayx28ZAncfTfccANMGuR/45hjoLGRur4+\nXg2sH94ypdHBACZpxJXKgLyrrY1ZAwO8tbGR9vHj6UkJOjtZUygwcNhh8QTZ3aj/lVJ6scpLrjlt\nbZxx4omMLWfs/ffD6tUwZw6U20Vi0iQKjz3GFAxgUlkMYJJGVESc3dzMXYcfTvuMGbRNmUIceyzU\n1f1+N6b5xRdh9Wredu+9pLVr6W5oiIcLBb56CLb1OWjV1XFUR0d5Yx95BCZPLj98ARx+OPXAhCEt\nThqFPAMmaURERFNra3x9/Hjuu+oqjl24kPbp04lXvhL2bAl1xBFw5plw663E3Lm0TJzI7JYWfhoR\nx1Zl8TUogrJrDl12GWzcCF/6UvnzlyoaWddIKpMBTFLFRURzSws/mDyZ877xDVqmTdt3j8E9HXcc\nzJ9P63nnMaWpiUdKLYk0TIUCm14os6NpR0f29eOqVfDlL5d3zZYtFAB7Q0plMoBJqqiIiJYW7ps6\nlVOuvprm1tYDn6O+Hj7yEcZ8+MMc2dTE8ogYwizaXWcnP/nVr+gud/yECXDjjbByJdw2SEW2lGDd\nOsYCj+5/pKRdDGCSKiqCCzs6ePuVV9JUXz+8uc4/n/q3vpUjm5oocx9G+/GzlSsZGKz5ye47lUcd\nlYWw5cvhjjv2fc369ZASnfZPlcpnKyJJFRMR48eOZeMtt9A2WOmCcu3YAR/4AF07dnBmSunnlZl1\n9CntTD5zzTX82amnVnbuOXPoWbaMOb296crKzizVLnfAJFVMBH83bRp1lQpfAO3tcOGFNLW2ckXl\nZh19Ukqpu5vrFy6ks5Kfu196Cb77Xejr4/bKzSrVPgOYpIppbubTM2bQsr8xe7a6gazi+qX7aWTz\n7ndT19/Pe0qFWjVEKXHX2rU8v2xZZe5WTAlmz6YLuDmltKkSc0qjhQFMUkVExDHFIkeefPJQr9/3\na+3tcMIJ9AGnD212AaSU+rq7mXHTTfQ8++zw51u8mIHVq9nc28sXhj+bNLoYwCRVypTjj6dnpLoB\nvuENtNbVMXVkZh89UkqP9/XxsUsvpfvXvx76PIsXU5w/n5e7u3lnSqm3ciuURgcDmKRKec1rXlNe\nq5uhmDiR+tZWhri/pt0NDKR7Ojv50KxZdC1axMDAAbQ9f/ll+Nzn6FqwgE29vUxLKVVgL00afWxF\nJKlSGhoayvtQ9/nPZ7W+dunvhxNO2P81jY0QQdNwFqg/KBbTNyPi0YULWbRkCa+dOZO2s86C5ua9\nj9+8Ge6/n/7776eQEnf09HBFSqnsumKS/pgBTFKldHV2UtZeynXXZb0Gd1m6FL7znUEm74Jike3D\nWaD+WEppXURM6+riXfPm8ZmbbuIvXvEKul7/esZ2dNBYLJI2baL7ySdh+3bq6uv5954ebk4pPV3t\ntUuHOgOYpEr51Zo19AH72EP5g6GUQVi7lt6dO7EOWIWVGp4vA5ZFRPuGDZyyYQOnAOOAAeA54BHg\nqb6+VKjiUqWaYgCTVCmPbdxIS38/NDRUfvJVq+glCwIaISmlHcDy0kPSCPIQvqSKSCltb2riieWD\n/Okeyl2Sv/0tPPccdcDPhrQ4STrI2IpIUsVExIxJk7hr3jzaKlmO4pZb6HvgAW7r6UmXV25WSaoe\nd8AkVdJ/btrESz/4QeUmXL8eHniA/t5eG3JLqh0GMEkVk1Lq7+5mxpw5dG/bNvz5+vvhmmvoLBT4\nTEpp4/BnlKSDgwFMUkWllP63UGD2pz5F18svD32eQgGuuoruLVtYPjDA3MqtUJKqzwAmqeJ6e7l2\n2zZuvfhiup4eQsWoF16Ayy+n6/HHWdHVxXuTh1Ul1RgP4UsaMXV18YHGRm4/91yazj+fhgkT9j++\nuxuWLiUtWEDPwAA39vVxTUqpP5/VSlJ+DGCSRlREHNPSwg2FAudNm0Zx2jRaTjgBjjoK6uqy3oJr\n1sATT9D74IOk+npWdHby6ZTS49VeuySNFAOYpFxERAfwt21tvCMl3tzfzwSgbswYdtTX8/iOHTwE\nLEopbajyUiVpxBnAJEmScuYhfEmSpJwZwCRJknJmAJMkScqZAUySJClnBjBJkqScGcAkSZJyZgCT\nJEnKmQFMkiQpZwYwSZKknBnAJEmScmYAkyRJypkBTJIkKWcGMEmSpJwZwCRJknJmAJMkScqZAUyS\nJClnBjBJkqScGcAkSZJyZgCTJEnKmQFMkiQpZwYwSZKknBnAJEmScmYAkyRJypkBTJIkKWcGMEmS\npJwZwCRJknJmAJMkScqZAUySJClnBjBJkqScGcAkSZJyZgCTJEnKmQFMkiQpZwYwSZKknBnAJEmS\ncmYAkyRJypkBTJIkKWcGMEmSpJwZwCRJknJmAJMkScqZAUySJClnBjBJkqScGcAkSZJyZgCTJEnK\nmQFMkiQpZwYwSZKknBnAJEmScmYAkyRJypkBTJIkKWcGMEmSpJwZwCRJknJmAJMkScqZAUySJCln\nBjBJkqScGcAkSZJyZgCTJEnKmQFMkiQpZwYwSZKknBnAJEmScmYAkyRJypkBTJIkKWcGMEmSpJwZ\nwCRJknJmAJMkScqZAUySJClnBjBJkqScGcAkSZJyZgCTJEnKmQFMkiQpZwYwSZKknBnAJEmScmYA\nkyRJypkBTJIkKWcGMEmSpJwZwCRJknL2/0FzzAX6nBUCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x57367d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Damping factor: 0.75\n"
]
},
{
"data": {
"image/png": 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ilU/kek2Okw08AuZ0JzZecUVqKipa/1CU4NJLYbPNgpB67z247jr46CM4++zW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\nTudxAeZ0WySpuJi/5OVx1qm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IfCCnm2Cc1HAB5uQESb0ljZc0X9KXklqMTki6XNIsST9J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"text/plain": [
"<matplotlib.figure.Figure at 0x317c5d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Damping factor: 0.85\n"
]
},
{
"data": {
"image/png": 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isjcm3sIsB4bXJb4CRlBTfBUBDzRnDWFUdbqIfARsGV0iVs92Vh3jlwWGrO9Q\ns3btZExE/rsl6wnSouH0czxLj1iKgeex348XVbUpjaW3UKXsllvIveiiJi+3zVFUBHfcQUlRERen\ney11EYitTYEtCwoYIsLfMzNZa/XVKeneHc3JQXJzLUJeVkZ1JIL+9hv89BMFhYWySIQPi4qYiv1N\nz3BR1nFxAea0RwatvjrVPeqovBGBq66CzTc3r6GZM2H8eJg9G86N3UsXMGwYvPUWFK94q5yBRbme\nxFJ8UTF1VFALFSuwugO/Uzv1NwPz14o+/qUpUbPAmf4moC9wnKpOaey1cebaHqujCrclKgf2UdWG\nzDBPinn8QBOFRn3cSs2I3NEicnFsC58oqrpYRHbBrC16hk5dJiJLwqaxjUFE1sIE5gisX2Zj0s9L\nsfTzk8CrsR0FGnHPXsANwKiKCqtFnDYNtt66KbO0PW66CUpLKcF2sbYqRGRAXh6nZWdzyGqrUbnR\nRmQNGEB+376w/vqQnV3D+64WFRWwYAFrzZvHWl9+ye6ff05k0SJyCgrkqZISrlfVj1L1XJzWgacg\nnXaHiJwyfDjjzjnnr1Y1NTj4YDj7bNgilKT67js4+mi45x6IVzNWVAQjRkBlJe9h0Z2VMHG1BvAn\ndff8ix77JZGF4IGn2FnYrsPrgetb0qZIRDbD6pHCHyLVwAGqOrmBazfFdkWGGaCqdX6INjYFGYzN\nw9ztVwkdPkZV721gXRtj/mPheqwaPSsbuH4U9jP+W0NjA37CBNdk4K3mbLwICvjHAJcBheFznTvD\nI4/U9K9rT0yfDpdcwu9lZfwJrIX9Xp+XaFPiphCk1vctLORcoP+IEXTaay+yVlstMfP/8Qe88AJV\nkyZRVl7OD8XFjMN2J9e581NEugH3YBHYX4ELVPXROONOxzberIp9kXoRS8PHeuntgKXtr1DVi4Nj\nA7Cf/yBgZVWN1yvWaSEeAXPaHdnZrLfWWvHFV12ssw6suSZ89ll8AVZYCFlZVFVW8iw1C9l/TuUO\nOwARGYbVNM3BGlwvaOF8G2BGq7Hf4E9oSHwFxEa/3qhPfDUVVS0VkXswF/8oJ4vIffV9OKvq54EJ\n7RRWbEgQ4CER+UNVX6nr2oDVaFh8fY2ln58Eprek0D/oBnAbNU1so2gkwtybbmLdCy5o2u92W6Co\nCK68kpKyMg5U1VdF5DTMPuVoETkw3k7aZCIimZ06cUZODhesvz4ZBx5I5223tbKFRLLSSnDIIWQe\neCAF06fkU/ySAAAgAElEQVTTb+JEbvnyS27JzZWbIxH+XceXqtuAZdgXi02B10VkRhwz5yeBe4K0\n/ErY7+kFwJmh55mF+flNi7m2AngMiz4/lYjn6tTGBZjTHpHm+CZ17QrL6+kQKEIFcK+qLm72ylpA\nKC31N+yb7HMJmLMHVhS+esyp81X17kZcvxJwWMzhW1u6rjjcAZzNCi+zzYGtMYuNOlHV90RkP+AZ\nVrzfdQImi0gtf7fgA2kIK3y74vEZQQcD4POWRmgCW5NrgCPqGPIJcGJ5OV++8w7zp00jt72lIidM\noKy8nEmq+iqAqo4XkbuxlPgUEXkLGJHo3cTxEJF++flMXGcd1j/7bArWi7UVTgKZmTB4MAweTOFP\nP8H48Zz2+eccLCIHhNP/QUuxkUDvoAb0UxGZhO0UPj88Z8wXs0wsov1dzK3PxKxausdcOw+YF3w5\nc5JEY2oZHKdNUV7OoiVLqGjqdX/+aWmeeEQiUF5OJpZuTCki0ilouTMTmIul9xIhvlbCIl+xHzE3\nYtGHxnAkNc1nf8RqnxKKqn4LxD7nkxt57YvYOsMUAC+ISH8RyRGRPYIo2yLMfmMRluKJCrz3sQjc\nhqo6UFUvU9VZLRFfIpIpIqOx1zSe+PoTiy5uparTVbWorIyDr7ySksVp+QqQHN58E506leWlpYwJ\nH1fV4sByZGvMWmWxiCStOF9EMrOz5dycHD459lgGTJiQGvEVS8+eMG4c+aefzrr5+bydmyvjgpID\ngD5Aiar+ELrkM2BAvLlE5GAR+RNYjG3cuTl0bh3gKGxjSgez+m0duABz2iOfzppF3ALtuvjuO+sF\nuUkdzWG+/hry8vixJXVWzSFIS32CtTgarKoXJ8IZPPgm/SyWwgjzIOZb1qCwCFzeR8ccvjOJprOx\nkbUDRCQ2chcXVX0YazYeZmXgI+zD6VysTdSWqrqlql4ZpHRGYz0ot1HVa1V1fsuegiEif8N2rN6K\n1RPG8gDQV1VvC+92VdU3IhEuHTOGkt+THgtKPh9+CFdfTXFZGbvWtWkjEJ9rApcCF4rIQhFJaAxQ\nRPrm5/NJ795cdO+95I0YQUZGGj8dRWDYMOTBB8nbdFNOzstjtogMwuoCY3dNFgFxvzqq6qOq2hXr\nA9snSO1GuQm4sK7NLE7ycQHmtEemf/cdOX82IlZVVQWffAIXXwy77AJ1feN9/300EqGXiDwhIocG\n0aOkISKri8j9WMPry4DdVPWrBM3dCavv2C7m1PNYcXtj65iGUdPqoQJrCZQsXgXCP4NOwLFNuP5h\nLBUZJh8TYCNVdbyq1kjRqOqM5lp6xENEVhaROzDxNSjOkM+xTgNHaB1tqyIRvfbPP7n51FMpLypK\n1MpSz+efw8UXUxKJsJuqftrQeFUdi9XlzQHeE5EXRaSJDcZqIyLb5+Tw0bHHsvGECRT07NnwNali\n5ZVXRMNyc3kL+52Jfc6FmFVMnQQRs6uBw+Ev25rOqjopCct2GokLMKfdoap/dOrEcy+9RJ1C4oIL\nYM89YeRIuPde2G8/OOec+GMrK+HppymtqGAoFjU6EPg++AA4vrFRmMYQSkt9jgmDjVR1UqJ2ggVR\nq/8Ae8acegcYpapNSd3GFt8/XpdoSASBMLwt5vAJQd1WXESkl4icJCKvYb0kK4HXYob1xtKRdSSg\nW46IZIjIUVi68Z/UTvkUYTsut1DVtxuaLxLhw59/ptOJJ8LSWk2hWj8ffwxnn01JWRkjVPXdxl6n\nqn+q6lBgKCZGlga7/ZqFiOyem8uLY8dSmO6oV11Eo2Hjx5Ofn89VQEFgjRJlU6xFWEOE/052AgaJ\nyCIRWYS9p50mIk8mbuVOQ7gNhdMuEZHNCwp456GHyG+pg/ijj1L58MNMKypa4cwdfFgPxwpid2NF\nYfaTsVGUJqx5K0xgFAOjVbUxb6pNmV+A6zDrijCzsKjLH02Yaz1sB2BYSGyrqu818vpG21DEXLcS\n1m0gXHe2X3i3poj0xjy7RmL+aM9hr80rqloSmOL+D9g/ZvopwJ6JTjOLyEDsdd2mjiETgTMaG2kT\nkZ0wS4HszEzo1g0mTIDVE/Y1ILm8/TaMHUtRJMIeqvpWc+cJfp+vxDZn/Ij51cXaodR3/e75+Tx+\n7bXkt5VemwsWwHHHURXY4QzFdsy+hv3t1dgFKSKHAc+p6h9BMf0kYJKqjg0ih+FI2s3Y39Xl0feB\noO5sA+zLYB6gqd7x3d5phXrfcVqOqn5aWcld48ZRUod7faP49lu4/34ixcUWug/Nv1xVJ6rqQZgX\n2DisFclHIvKRiJwvIv0bcw8RWUVE7sSK128C/pFo8RVwLrXF17fArk0RXwEnUFN8fUoDOxITQbDO\nh2IOnyQim4rIpSIyE4vmbYD1pVxDVQ9X1aeitS5BTdVhmOAKszPwYCDQWoyIdBGRGzHH83ji6ytg\nF1U9sAniaxD2e5INlkJfupTqY46hfOrURKw6eZSXw+23Uz52LH9EIvyjJeILTA2o6r8wP76fsB2B\nT4QK1utERLbPzW1b4gvMIuemm8jMzGQbbJPGZOBEVZ0tItuJSLiObhi2k3EZ8Dr2e3Ml/LXBYXH0\nH9YyqTgkvtYJjs3CvPNKsdSvk0A8Aua0W0QkNy+PaTvvTL/TTiOnqemF77+HMWMoKSri+KoqfbiR\n9wzbGIzAajOilgWfhFOJQTrwKOxNcSJwUTOEUKMQkWOpXZ/1C9bfsUmF5RLfGPVYVb2nCXM0KwIW\nXBvP+HUhVtc2GZimjeh/GUQxX6O219cdWASyWW+OQWTmIMzIMl4/hjLgCuC6pkTbRKQPJi5jbUCP\nAubl5TFxyy3pduaZ5Hft2pyVJ4/Zs+Gyyyhevpy3Sko4MhlWLmItqB7GojWnqupddYzbKCeHD8aO\npXBQvCq8NsDcuXD66ZSUlrJLU1K4TuvCBZjTrhGRlfLzea1PH/qdfz75jXGwVoXXXkNvvJGySIST\nKyvrd1yv594ZWA/DkcB+WNQi2qi7CDNTzcS+wX7SnHs0ch0jgcepGfFeBuygqjOaMd+R1GwN9Du2\nU7DRu6maI8CCzQPbYz/PY6nZh/FWVW2ULUXMnKtioqZvzKnLNXAFb+J8/bHXdac6hjyDiYMFTZy3\nF/AesHbMqbNV9bpgTF5uLtdkZnLMOeeQt/32TVt7Migvh3vuofzppymLRDhOG9GBoCUE4nc8ZlHy\nNbC3qs4Jnc/Kz+ezf/6Tvnvv3bYzQO+8A2PHsqisjA3V+0m2SVyAOe0eEemUnc3FGRmcuc8+ZO27\nL53WWKP2uKoq67f36KMUffMNv5aWcoAmqD9b8MEwADgYOA6LHr0LXAW8lqzaiqD240tqipUIlnZs\nVtJKRD5kRXNssDZIcZtj1zNHowSYWOPjYZjo2gsrpJ+MRZFuDA0tAnrVZWXQwFrWxl6LNWNOnRr2\nTWpgjgLgIizFG68J/ALMPPfZZqxvZeBtIDZZNk5Vz4szftu8PB4bNIiVTz6ZvHTUhqnCjBlwzTUU\nL1uWvKhXXQSC9VlgM2wn8VGqWpGTIxf17cu5N91EQXPMmlsbl15K6QcfcH9pqZ6Y7rU4TccFmNNh\nEJENc3M5tbqaIwsL0b590ZVXplNlJfrtt5R/+y152dnMD/VjS1gxdiDADsZMPl8Ebgf+gQmLjYAX\nMGHxUqK/zQZ2FtEatmrMcqFZZqnBRoGwe7xi5qRfN3GeOgWYiHQBdsd+NrtgDcsnA0+p6vfBmGzM\n1TsspU9W1Wa58AeRq3cwb7Awh6rqI/VcJ8C+WNQlNjoF1oPvGuCq5vgtBcJuCmZGGuYerPl63Ddw\nEcnPzeXy6mpOHDCAvIMOgi23hGTv8ispgVdfRR97jOI//uDP0lLOBCYmahdvUxHrgnAvFmm+PDeX\nS+67j7x4X8DaIsuWwWGHUbJ8OcNbWlPnpB4XYE6HIyiy7ou1s+mGWRN8g9Vo/ZqE+/XHDDe7YbVF\n78ec7wnsgwmOv2N1SZOxHUwtstsUM3J9A3gTE3zHqep99V3TwHwPYG1Poryoqrs3Y57YN57VgL2x\nn8H2WMRnMvCMqi6pY45LsUL7KLOxLgHNrd2K/uzDu8MqsTTWi3HGbwDcgu2GjccrwBi1ti7NWU82\nVji9W8ypp7Am6Q0a3orIOOCcvDzIy4MDDoDdd4cusV0/W8i338LkyURefRXNymJqcTHXAq+nS3iF\nCf7e78rN5egTToB99kn3ihLLu+/CFVd4KrIt4gLMcZJEKC11DHA5cFtDH5pBumlPTIjshO0sfBKL\n/vzcxPsPwHYnPqWqo0Rkg6ZGqmLmWw3b7h9OZ+6hqi80Y67YN55lmGCZDLygqg3a6AbC9Ttq+hsN\n1RY0bhaRXTDbinAasTSY9/1gTC62o/RfQLwddwuB07Et/80VgxnYbs+DY069CQxX1bJGzJGDbZb4\nq/IxN5dPq6vZqF8/IptsQkG/fmT26QOrrWZ+U42hqso6R8ydC7NnE5k5k8gvv1BdXc2tFRXcoao/\nNvJppoycHLmgTx8uuPlm8tpD6jGWyy6jdNo0T0W2NVyAOU6CCdJSI7AapbexQulFzZinEIt+jMBS\ncl+wwmvs2wauXQsz/Zyuqv9o6r3rmPNfBNvYA77B0o+NNvoIdvKNoHavyXxtRoslEZkIHBA6NFlV\n92vqPDFzHgg8Sk2bjd+x3a1rY1GveE2Kq7DX/N+qWq8zeQP3F8yOZEzMqU8xi5JG1bmJyKHUtOxY\nBvQCcoFts7LYKj+fHSIRNs3MpFPv3kQ22ojCggIyc3IgOxuqq62Qvrwcliwh8vnnlP3wA/nZ2SzJ\nyOCjoiKmYjYb72nTTHxThojkZWez+J57KFwztsqvnfDnnzBqFGXl5axdV8TYaX24AHOcBBJKS60L\nnKSqbyRo3hwsIjYSS1f+iEXGJgNfxthbdMUiQz8AmyYiDRSkcb6hZp3TWap6fQPXCTAwWPdIrMbq\nSWJ6SDbFhiJm/u2B8GaCKmA9rdmsuDnzjqZ278kyTLzE420svfx5S+4b3PsirEFymPmYZUijOw2I\nyHvA4NChm1U1th9m9DXqhTnLb5yZSZdOnSjMzKRQlcqqKoorKlheXc2vWF/ST5uz2SFdiMgRm23G\nhBtvpDDda0kmY8dS+uabXF5RoVeley1O43AB5jgJIEhLnYdtf78GGJ/EnY2ZWB/HqNdYKSu8xj7D\ndtyVA70TFZUQkX2w2qMoZdiuw1qNcIL02dasEF0aWt8HqlrdEh+wmHsJ9pw3Dh0eq6oXNme+mLkv\nwRpA18dirIXQQwkSuidSu93SImCbplhXiMgWWGQqTD9VnduyFbY9OneWL88/n/6DBzc8ti0TeIMt\nKS2lR2N88Jz006Z9UBynNRAYQH6OiYDNVfWaZIkvMCd3VZ0aRDPWAQ7FRM5DmB3DSli/wUR+u4r1\n2HokLL5EpJOIDBOR27EaqDuwlkojMCF4tqq+35R0ZWMIRE9spOq4xrihN4KpWOoxHtXBffuq6oMJ\nEl+jqP1c/sDc8hc0cbrYPp1TOqL4EpEts7JYZ6ut0r2S5NO3L3TvTi61N204rRSPgDlOMwn8o8Zj\nzXBPVtWX0ryeaVg7pJsx+4a1MOPPyZjXWLNsNUSkH7bDMMyg4NguWJRrT6y1TrRG7asG5kxIBCyY\nqxATfeG9fYepNq57QR1zdgLmYankeHyI9c9ssBi+kfcbBjxP7eL/nbWR/TVDc62M/TzC6dJ9m2s9\n0pYpKJBHDjmEUYceSkLaS7V2XnoJbr2Vt5Yv1x3SvRanYTwC5jhNRESyReRcrB5mBrBxKxBfz2K2\nGpur6r9UdRCwFVa4/y/gZxF5REQOCARLUxgd8/gr4HzgZ+AUTIwMVNWtg+hfveIr0ahqEfDfmMOx\nEaCmkglMa2BMfgPnG0XgrfYkNcVXJbB/U8VXwNHUFF/fYzs7OxQi0qWykhG7794xxBfAjjtCVRVb\nBV8OnVaOCzDHaQIisiMmurYH/q6q/05UFKQFa/oP5kU1JOw5paoLVPVGVR0C9MdSascAP4nI0yJy\nRBAtqW/uQuDImMNFWLRmA1UdqqoTWoH1QGzd1OCgDqrJhFLK2ZgvGMD9rKip+gMT3y3yaAvu1R8z\n5i2IOXVkM+09MoFYK4I7OmhN0N/WXptIt27pXkbqyMmBgQOpwGpEnVaOCzDHaQQi0kNEHsYiLecD\ne7bEUytRiMgVWDPmvVR1el3jVPVnVb1TVXfD6sYex3ZTLhCRKSIyOvDVis67toicigmNzqGplgCD\nVfW+ZJjWNpegvunVmMNNioIFz3kytov15MDO4lhgW1U9EtgV22DRF9tkcFFL1hxEKV6htvv+aS1I\nn+4GrB96XA78p5lztXUGbbwxeeleRKrZZBMKc3Jo51sO2gcuwBynHkQkKxAin2GpnI1U9alW4vB9\nMiYGj47n1F4Xqvq7qj6kqiOBHlj0aBvgSxH5TkR+wKJ8A6ltNHpXc2vJUkBsAfshDUX4oFZKeSah\nlHIQRXwv+P/fVPVctZ6GuwFHBLsWm4xYE/BXqN1/cqyq3tScOQNiRedjHdUXqnNndujfv4ZpcIeg\nTx8kO5sh6V6H0zBZDQ9xnI6JiAzGejb+hqX35qR5SX8RmIXeDJyrqvc3cw7BojlbYPVjxZjwysDq\nx7anpu9XFXBnC5adbJ7DRHJ0zblYdLBOr7IgpXwr8C2WUm5UVFNVfw4K598Wkd9UdWJjFykinbHe\nn31jTt1JC6JqItKb2jvgJjR3vrZOVRWD+vRJ9ypSz4YbQmkp/UQkI9G7jp3E4hEwx4lBRFYTkXuA\nSZhj+86tTHztCDwC3KCq1zbx2kwR2U5EbsBEx2NY8ffRwFqquo+q7gX0xIxcw3wN9Ax8vlodQZ3T\n7TGHR8dbb0xK+QKakVJW1W+w2rsJQQujBgnsMSYDf4s5NQkz7m1JZPVEarr3f1RfWro9IyLdKipY\nea210r2S1NO1K3TuTAWwYbrX4tRPq3wjdZx0ICIZIvJPbOfgMqC/qv6vNaQbo4jIQCx19aiqntXI\na7JFZFcRuROzJ5iAFZLvBfQJ0mofxHxbXgNqpTGmA/cB34vIBBHZSURaWxT9HiCcIl2fUFSojpTy\nk819jVX1M2A/4GGxZt51EhTIPwjsHHPqNcw2o9mF8iKSj4noMLEp2Y7E5uusQ0lmGvY/TpkCJ5wA\ne+wBe+8NZ50FM2akdg19+6KYVYzTimltb56OkxZEZBBWC1UJDFPVmWleUi1EZB3MGuFNVT2sgbH5\nWNH4SGAPYA4Wedm2kZGenaj5BW02cLiqauALNgIYB6wnIlGvsSnp3hGqqktE5DHg8NDhk4EXQinl\npZiHV6y3WXPv+baIHAU8LSI7xps3SPdOoGbfSoCPgBEJqKs7GDPgjfIbFt3sqPTs0SP1AYaJE+Hx\nx+Hcc2HQIOul+eGHMH06bLZZ6tbRqxe5WH2n04rxCJjToRGRbiJyK2arcAdW69UaxdcqWNRmDmZ+\nGm/MSiJymIg8gbWvGQ28hxWVb6Oq1zWhxulB4DjM62spcGs0SqSqc1T1KlX9G/YteyZwNuY19piI\nHBjUOaWL2MjPbmJNuydhonFoosRXFFV9DjgHeLkOD6bLgBNijs0FdtcWNO6Gv8RdbKeCe7QZzc3b\nEbk5Oan1/youhv/+F84+G7bcEkQgMxO23hqOPz6VK4HcXLKg4+0AbWu4AHM6JGIcDnyJmW5uFFgr\ntLqiVRHJw9KivwFbhtNlIrK6iBwvIi9hDbgPwNzv11PVYap6u6r+1Mxb74/1t1wTuDfeAFX9TlVv\nUtUdsKLyKcARwEIReVZEjgp2/KWMoO7pw9AhATbAXuNHk5VSVtUHsM4IL4efs4icQu3i+oVYi6FE\n7FAcDITjK4p9mejI5OXmpvbz7Ysv7L+toe1RdjaSkZEYo2AneXgK0ulwiMjGWLoxH9hbVT9s4JK0\nEdQNzcK+LA1Q1SoRWRdLAY7E+k++iHk97R+4wifivhti0a0RjU0rquovwN3A3SLSFUt9jgTGi8hH\nmNv7UykybX2emoXu6wMJaUxeH6p6g4ishqU8h2J1drG2Eksx8fV9gm4bG/16TlW/TdDcbRWLC6aQ\nZcugS5eGx6WCjAwQ6TgdANoqHgFzOgwi0llErgPeAB7FbAdas/gS4AOgO7AvcIaIfIxFdwYAVwFr\nqOohqjopUeIr4ETg3ubWdKnqn6r6iKruj9Wi3IwJopliPSuTQpCGnYCtP/zzWAmrk0oF52Np2amY\ng36YEmAPVf0yETcSkdWxSGWYjlx8H6UsEiGl0ewuXUyEtQYiEbSqiuJ0r8OpHxdgTrsnSDeOwtKN\nq2KRpNtbc3uWQHy9g6WWlmAF1d2BM4Eeqnqsqr6QDFNUESnAitgTksZS1RJVfVpVj8B2V9byuhKR\ngdKCmEUopTwbi+xvRG0hsmtz528KQYrzfqxJezjLUAGMVNVECtDjqNlD8itqdwToiJSWlaVWgA0Y\nYP+d3gqMP8rKqMKauTutGBdgTloIit8ni8gyEflGROqMTojIOBFZIiKLReTqmHN3isgcEakKPoBj\nr90J+AWLeHUGFgdO5q2OwKNrexEZDyzH3OkfBA4C1lbVU1X1TVWtTPJSDgHeVdUFiZ5YVStUNZ5A\neAqYLyLXisjgpniNBSnlN7HG4Hur6gmquhQTkBWY8H4eOLDFT6Bx6xmA1eGFU0CK7SJ9OYH3yaJ2\nYf9trbGOMQ0sXbqUlH7BKiiAI4+E666Djz4CVaiqgg8+gLvuSuVK4LffiJCAXqVOcvEaMCdd3IZ5\nbXXDIgWvi8iM2N1pgS/XbliBtwCvicg3qhp9S5sB/A/b3Ra+Lh+4BDgLeAI4DPsQ3CBpz6gZBMac\nO2G1UntjxdlF2A6mYao6JcXrEaydzTmpvC9WozUQ+zncDawsIk9h9hZTVbVW/Vaw0/ISLFp3CdYm\n6a8PXVVdICI9sPe5OVgaMqkfSrKiv2NsC+iXVPV/Cb7dPkCv0OMSzFjWgRlff02Oqu1GTBWjRsEq\nq8B//gOXXGK7IPv2hcPqNY1JPLNnU4W11nJaMdKKPCadDkIgjn4HeqvqD8Gxu4Elqnp+zNh3gTuD\nHWaIyKGYY/g2MePeBu5W1QdEZC+s5mgpUBTs0Gs1BCm+3TCxsTu2w3EyVqS+L9Y65zBVfSQNa9sO\nMzPtn8xIiojUeONRVYk534cVGw16A89iP6NXgTKs7ukGzMT0nIaimiLyCPChqt6YqOdQx30KsejX\njqHD12Kv6wRVvTmB93o95j53qeo/EzV/W0ZEJCeHP+6/ny6rr57u1aSWsjLYay8qKispVNXydK/H\nqRtPQTrpoA9QEhVfAZ9hheWxDMAKmhsaB7BqYAp6LVYb8zXwnYi8LCK/ich7IrJFy5ffdIKU6+FB\nVGcRcDzwFiZ0tlPVGzA7geuBM9MhvgJOIgVpLFWVqOiKFV/BsXmqOk5V/47VwX0MnA4sxn5+1wPH\nquqRjUwpT6COtkQJRrHdtXND9z0X8247W0QOScRNgjTnjjGHvfg+QFU1J4fP5s5teGx7Y/58yM1l\ngYuv1o8LMCcdFEKtHTpFWI1WQ2OLgmN/EaTx1sLMLqcBA4PU3cpY3c/VqroKMBF4VkTCRctJQ6zf\n4Aki8grm0TUCS4euo6q7quqdqvpzMHYXrN7rmmRHaepbLxaZa1Zz72QRCPV7gHeBcqzeaxbwuIg8\nLyLHBNYP9fE+9rszLFnrFJFszOx1DvYl4SjgVDUWYH0jbxSR4Qm43eiYx2+rtUVyAoqLmTp3bmrr\nwFoD8+ZBdTXvp3sdTsO4AHPSQRFQEHOsECs8b2hsISF7AREZhkXFCoFLVPXK0M7AIuAdVX0DQFXH\nB3MlrSmIiKwvImcGqdMvge2wYvAeqjpCVR9U1d9jrhmEFYk/qKrnJWttjeA44DFV/SONa6hFkFL+\nAktFbqqqB6nqHphB7IPY7sb5IvKmiJwiIrVaMAc7EydQ2zMrUWvMwOqvKrDIXJWq/jccSVTVzzER\n/oBYW6Tm3qsLNVstgUe/alFVxfRZszqeFcMXX1BSUsK76V6H0zAuwJx0MA/Ii/mg3BT7kI3li+Bc\nlIHAFyLSS6zn352YNcNs4NeYaz/DUkJJI7A/GCAiF4nIp1ikpS9wObC6qh6mqpNVNe4HgYisj0V2\npqjqkclca30EUcF/0oo+yEVkvSClfB1wXCC8FkbPq+oytWbpozB7ixuAzYEZIjJdRM4LasmiPAoM\nFpH1ErxOwRzw1wQOrG+Xqqq+h4mnp4I0YnM4nJpR4J+x+kGnJtPnzSO7LK3dSVNLdTV88gmKZQKc\nVo4LMCflqGoJVlB9mYh0EpHNgf2waEYsD2AGpKuKtXc5E/gRqwubiwmyKdgOyWwRyQn5ST0EbC0i\nQwBEZAwWZZvRkvUHomurwBJjLvAClu48Beipqser6ksN1WAEabMZwOdYMX462Rf4WlVnpXkdBK/h\nBVij6mlY1Kve3aCqWqqqz6jqUZgY+xeWln5TRD4XkcsxYXw/ta0bWsqFwPaYBUaD3kuq+iJwBvCS\nWFeDRhPapRrmTq/3qY2q/typEx+88Ua6V5I6PvwQKipYiKXonVaO21A46eIkrL/gb8G/E1V1drAL\n7wVV7QKgqncGEYs52O9rOVaIPVhVvxKRN4AdsEjXYCwitiPwlqrOE5HDgHtFpDsWTdsjnqVBQwSe\nS0OwFNIITMg9ibmrf6JN3E4sK/o7LsYc+dO9HfkkLEWXVoKU8gTs9R7UHC+y4PV9DbMsGQNshe2m\nnARkA6uI9c6c2tLNBiJyInAksG1TUreq+rBYg/VXRGS7JnjT7QT0Cz2uBFLsMtV2KCrimsceY4vh\nw+PWl7Y7Jk6kqLiYca3g/cRpBG5D4bR6xNqtXIN9+JwOPJGKN5iguH9nVnh0fUdgFxHrV9bEeTOB\n+ZjX13qNiZokk8DI9BVsc0DS+yXG3FtVVUSkF5ZC3Ao4RVWfTcK9BNgE2wiRiznIR73G3mxqFEms\nu9DQihgAACAASURBVMKNwBBV/aaZa7oci37uqKoNNrIRkcnYF4AojwcpWCcOIpKZl8dPN9xA9379\nGh7flvn5ZzjiCIrLy+keZBmcVo6nIJ1Wi5gz/ElYim4xsJFaz8OkiS8RKRSRA0TkUay25lwsnL+l\nqm4ZFPm3RHwJllpbGbOgaA3tQk7C0lgpFV9RRORMLKU8D2sTlXDxBVaIH+wUPA3rjrAdZlVyGfCz\niDwgIvuK+dQ1tOZdsEjd8OaKr4CLsd6eT4tIbiPG34u1G4qS9qhla0ZVqyoquHHSpPbfluepp6jI\nyOC/Lr7aDh4Bc1olIvJ3zC2/CBitqvEK9BN1r1WAvbBI1w7Ae1hU5BlV/SXB93oV++Dvp6rfJXLu\nZq6nK7AAE7eLUnzvIZgX2ivAGFWdl6L7ZmJi7xBV/SA41gurgxsJbInVFU4Gno9NLQa/m89hfR3f\nTtB6/oe1LhpVXxF/kAr/GjgV63d5laeb6kdEVs3O5oeJE8nt2jXdq0kO5eUwYgSlJSVslqq/I6fl\neATMaVWIyCoicieWGhoP/CMZ4ktEeorIaBGZAnwD7Ik1vF5HVYer6t1JEF8PA/8Atm4N4ivgCOCV\nVIovEVldRO4Homazu6XyQ0OtXdHthIrZVXWhqt6qqkOxtkjPYh5y34vIiyJynIh0F5H+wNPAUYkQ\nX6H1HIb54N0R2kQSjz2Bn1T1qSAa6+KrAVT116wsHrvrLtrtfshHHqFChHddfLUtXIA5rQIRyRCR\nYzDvrHIsPfdgIj9gRKS3iJwtIu9jac2tsRROD1XdX1UfTpYHlohcjzXV3kVVZzY0PhUEH/SjSVEa\nK0gpjyaUUoa/PLpSzb3AXsHmjBqo6m+Bh9feWK/F+4ChWOrvUyw6ltBdZmredSMxy5Ur6xnaKjZL\ntDVKSjjt9dcp+fjjdK8k8cyfD//7H5HiYo5M91qcpuEpSCftiMhmWLoxA0s3JqSJbCAwNsY+2EYC\nq2M7F5+kGUXXLVjH2Viz8INV9bFU3LMxiMjOWOH7wGSLIBHZCnuNS7DX+PPguGqcVkSpQETuAear\n6lWNGLsq8A7wNvZ7mrBNGXXc5y619lThc/2wLgDr6AqzYaeRiMjwbt2Y9NBD5Oc3WOXXNqishKOP\npnjhQk6pqtJ7070ep2l4BMxJGyLSVURu+n/2zjs8yjJ7w/cDJIEQ7KvYxbW7ioquFQULYlfUVSy4\ndinWFd217W8ta123KCqi2LCsBQsWQLHrrl1RFJG1u2sBKwkJkJzfH+eNhJAySWbmm/Le18Wlme/9\nvu9Myswz5z3nOcAkPMuwTUfFV8ikbSXpMjxj8RCwBJ7pWdnMhprZ5CyKryNw8XVSLomvwAh8QHQm\nmxqWCVvKDwJ/B3aoF185wChgaKirahZJPXCvt/vN7FgzOxpYERgZ/vu4pPckXSSpTytbiC1iZrPw\nuZGnSGrsdj8MuCGKr/ZhZo/V1PDgqFGFsxU5bhzzZ8/mlbo6bko6lkjbiRmwSNYJb1CD8aHZjwJ/\nCG887b1eF9wIcxDeov8dnuUaD7yZVJ2MfObfw3ih9DlJxNAcklbDt9NWs2Zc+jt4/U64P9afcf+t\nc5ra3k0yAxbu/yI+f/OBZo6X4T/Dj4HjmvpdCs91C/x3b3/ca2x8+PdiqPFqa1zrA0/hEwAmSKrA\nM26b2KJD7CNtQNJSXbvynwsvZJk+fZKOpmPMnAkjRjCnpob1rMGEiEj+EAVYJKuEN5ZRwNL4VlS7\nhsaGlv1dcNG1F15IX78d9H6awm03YcvtReBmMzsm6XgaI+nPQLmZnZKBa/fGtxu74Aa7zWY1c0CA\nHQr81swWG9IduhPvxJ9Hi92JDc4RPoi7ftt7RTz7Nx54si2Z14bdluGaA8xsUKrnR5pG0sAePbjv\nuusoX2mlpKNpH99+CyecQNXs2QyrrbVbko4n0j6iAItkBUndgXOBo4HzgWtTeUNrdI0euGnlIHwA\n8xt4pusBM/s0vRG3H0lr4S73k81sr6TjaUwQr5/gBqJp65qSD4k+H89ungPcaK04zeeAACvDvxf9\nzGx6g8eFi8h1gd3NrF3bVvJZn/vhv7Mb4EPXxwOTUsk8Br+xccCPeAbuyfbEEVmUkhKNWHJJLr3u\nOsqXWy7paNrGnDkwdCiV33zD36ur7eyk44m0n1gDFskocgbh3Y2rABuZ2VWpii/5DMijJD0MfIEP\nIp4MrG1m/c3sHzkmvlbA5zu+noviK3AgvjWbFvEVfsaD8YHoFbiZ6pjWxFcuEOqpbsDrqxryJ9yV\nf9/2iq9w/Q/N7C9mti2exXoBGAr8T9L9kg6XtHQL50/GheDq+DZoJA3Mn29X//QTl5x4IpWzZycd\nTerMmQOnnkrlrFncVlNDTpU1RNpOzIBFMoakXwJX4W8ew83s6RTPW4WFppib4YJrPD4jstVxLUkR\nsnyfALNwG42c/OOS9BJwkZk9lIZrdWhLOekMWIhhVdyJf3Uz+0nSSXiDQltmNLb1nsvgnl6D8BFb\n/2JhNvfLRmvvAeqAPiGmL4l0GEkqLeW8Hj044+qrKe/ZM+mIWua77+Dkk6n85hvGVVczLB8+4ERa\nJgqwSNoJW1y/x9/ELgP+1lrti6S1WVg3sxZuhDkeeNxyY1xPi0gqwec7luDzHXOyU03S5nhR/C/b\nUxze4DoNt5QvAK5p65ZyuE7iAizEcR/u7/UD3rXa19oxCLyd964ABuK/+7vjPmnjcUE2D/ccWwMf\noTQI3y7NiF9dMVJaqhO7deOSiy+mfIMNko6maT76CM48k6off+TvNTWcnasf7iJtIwqwSFoJnX9X\n4dtwpzbXsRVqbHqzsD5mWRZ6dD1jCc0lbA/huUzFt1jXMLMfEg6pWSTdBEw3s0vbeb7w7OTfcE+s\nkdYBF/0cEmA74uas3YCdkrLKCDVpO+J/E/sAtXhW9Sh8i/cf+N/NrvnwwSRfkLRfWRk377MPXY8+\nmtLS0qQjcmpr4c47WTBuHDULFnDyggV2Y9IxRdJHFGCRxZC0cpcuHNm1KxsAXWpq+GT+fG4zH2Tc\n3Dmr4W/KGwMjzGxiE2s64e7z9ZkuY2G7/kv5mlKX9DReL7R2LreDB5PPD/A422z70WBLeQ18S/mp\nNMSUKwJsa1xQnmxmo5KOB0BSN+Bz3KqlH25iOx7YFKgB9m9P1jHSNJKWLy9nbI8e9DvvPLonnQ37\n6CM4/3wqv/6aN6uqOCSXal0j6SEKsMjPSFqze3dGLVhAv513RuutR1mnTvDf/1L70EPUmPHBnDmc\nbGbPNDinFDgVN6X8B+6pVN3geAk+4HoQnjmZxcLtlan5nkqXdDf+vDa1DA4MTweSzsCHbv+2jed1\nBc4ETiTFLeU2XDtxASZpQ+BJfGt2eTM7MMl46pF0MN75uGPIPPbB/472B1bDrVeGA89HIZY+JB1Y\nVsYNe+/t2bCysuzef8ECuOuun7Nep9XWMibfXycjTRMFWATwcUBlZTw9ZAg99t2XTo1HddTWwrPP\nwhVXMLe6mqNqa+0uSf3xAuyPcKf3/4RrdcPdvAfhhcYfsNCj64MsPq2MIukqvKOtn5k9n3Q8LRE8\nrf4DHGhmr7ThvPot5bfwLeW0fgpPWoBJWgPPfP0erzv8GO/UTTyTKel54K9mdl+jx4U3p9wPlAHC\nJz6MB6bkav1hPhGyYTcCO++1F5332YeSFVfM7D1nzYKHH2bB+PHMq6vjtcpKDotZr8ImCrAIklYo\nK+PdM89k6f79EcCTT8K998Inn4AEK68MO+0Em28OI0ZQPXcuzwLrASfjRpNLsNCjaxfgNfwN4YFc\neDNLN5LOwovP92/ORT2XkLQX7ka/ZYrrW91STlNciQkw+SDu5/FxTP8Ij10NfGtm5yURU4PYeuMm\nrL2ay26FTsrncPH1Nf639yvgMVycPWZmc7ITcWEiae2uXTmpro4jN9wQ+81vqNhiC+jcOT3XN4O3\n3oJ77qHy1Vfp1Lkz/5w7l7+2VO4RKRyiAItQWqoLd9mF00eOpAzg7rvhnntg5Ejo08dfbGbO9MfP\nOAOeeAKuuorPq6roC+yMv/BvBzyDi64J7akxyhckHQ2MAU4ws+uTjicVJE0E7jCzW1tZ13BL+Srg\n0o74YKUQVyICLJjGPoVbm5zb4PENgCm4JUVW5oU2E9/1wKdmdmEr61bBReT5ZjZWUk+8eH8QsDX+\nHOv/Jr/NcNgFi6Ry4KDu3fl9SQkrb7UVnTbYgG7rrgu9ekFJSWrXqa2Fjz+GGTPgvfeoeekl5s+Z\nw7fV1VxeV8etuWyzE0k/UYAVOZJKysr4+tprWapXL6ishAMOgAsu8GxXU8ybB/vuS93cuVQShhTj\nb2Q/ZTH0RJC0N/58/2Rm5ycdTypIWgfPlKzekphqbks5w7FlXYCFmrZHgRn4qCRrdPxJYIyZ3ZnN\nuBrcf2m8vms9M/sqhfXr4B9+hjbMxobr7IGLsZ2Al1mYlW5352qxI2lToG/37vQFfl1dzUorrUTV\nhhtS2rMnXcvKoLTUdw7mzYOaGpg1i5p33qH6s88oLy3lm06deHXOHJ7B/d/+HWu8ipMuSQcQSZzt\nevakU69e/sW0af7C0Zz4An9x2Xln6iZM4LLWPqEXEpK2wd/ArssX8RUYCoxtTnxJWhG4As9inoK/\nQRfkG0KohbsdmI13cjb1PK8GTsPnQCbBb/EPNK2KLwAzmyFpT+AxSd/XGx6b2Xf4GKNxwbdtV1yM\nXSRpOgvrMjMutAsJM3sDH4NWv23d/bPP6P3ZZ/Tp1IkVunShoksXKgDV1jJn/nzm1NUxC3gdeGP+\n/JjlijhRgEV+0dAB+ocfYIklFl0wYoTXgs2fD5dfDhttBCuvTJfSUlbIbqjJIWk94GngQTMbnnA4\nKRPeeIfgRduNj3XBu+jOwcfxbGApzCfMV0Lx+nV4veKeLRjRPgT8XdImZvZm1gLkZ6uWYcARbTnP\nzF4LXZN3S9o1iISGxysJli9hm7k/LsZelPQ/PKs7HninUMV3pgjf2xfDv0gkZeIsyMi8+Q0sT5dc\nEn5s9Pns6qthwgQ/VhecuubPh9paqrIXZnKEDNFruFfZ/knH00YOBZ4zs08aPhh8r17F64W2N7M/\nFLL4ClyEm5gOaqlTMBS9X4eL02wzAPgJ35pqE+aDuocCj4TJEs2tm2dmk8zseGAl3F5kKbzof4ak\nSyVtGcRgJBLJEPEPLDLjgw/oUhtyAfXmg680YVTQ8HPxW28xp7aW6ZkPL1kkLQlMw+0Jtk82mrYR\nMj7D8bqu+seWk3Qj7nl1Ke76/l5CIWYNSacSRv2kWKt4A3CAWhiUnSGGA6Pam4UKlhV/BCZJWimF\n9bVm9pyZnYob7B4EzAduAj6VdJWk/iFbGolE0kgUYEWOmb1rxswXQ/K8ogKGDIHLLoOXX/auHXBX\n5pqQM/jqK5g6lU7A3YkEnSWCiey7QCWwSR5uzWwHdAWmSOok6Tj8+fyEbzfemYfPqc1IGoJ3dg5I\ntTs31F89itdjZQVJvfDOxQ7VnpnZGFxATmqLgDTndTM7x8w2wO1k/oeb734paaykPUMTQyQS6SCx\nCzKCpEN69eL60aPpXt9OPWXKQh+wLl2gZ08YMAD22w/++lfmTZnC2LlzbWiykWeOkD16F1gen++Y\ndx2eku7C61JeAK4BFgDDzOytRANrQKa7IENx+g1A/7Zm+sI27W3AOpaFMVmSLgM6mdnpabiWgCuB\nLXDh2aFyAUmr4xMfBuHbuBMpou7nSCQTRAEWQVLnbt14tE8f+p53Ht2a87Qxg9tvZ8Htt/O/6mo2\nKWRfoeBCvimwVj627Ie6tffwLOXewB+AW7IhJNpCJgWYpO1wkbCnmb3UjvOF1/6dlSkj2gb36gZ8\nCmyVrq7EUMN1C7AMsK+lacC9pBXw36lBwLYUif9fJJJuogCLAP4G0K0b45dbju0OP5yKHXZwuwnw\nwvvXX4c776Tyvff4cu5c+pnZ58lGnDkk3Y+7+vc2s7yrcwvC4T7cduA2XEDkpFjOlACTtDHwBHCY\nmU3uwHWOBvYzsz3TFlzT9zkSOMDM9kjzdUtwEfodcES6BXiokaz3GtsFb+y4H7cyKdjXiEgkHUQB\nFvmZ8Il5r4oKRtbW0mellajp3Bm+/pou8+fzZVUVl5pxe0e3M3IZSdcBxwDbmdm/k46nrUj6Fb7d\nuBVwuJn9M+GQWiQTAkzSmrjx7Gkdff7BAf1TYAsz+ygd8TVxD+HC5VwzezQD1y8HJgOv4N+TjLzo\nh/s0nAE7g2B9YWYzM3HPSPYI9YQ34tNPZgFnN2dWLOlS4CjAcA/C34fHl8Vnrq4HlOKmzxeY2d3h\n+MHA+UBPoA7/Ox7RuIu7UIgCLNIkYRbgGrhX3JfAe4VesC3p/4Bz8e2aCQmH0yYk9cC734bgsznX\nMbMdko2qddItwMIonueBK83smjRd8wqgzszOSMf1mrj+Vrg57NqZ2iIOb57PAHeZ2Z8zcY9G9ysB\n+uFibF/gG4LxKzC10F9LChFJdwI1wNH4jNgngW0a11ZKOh73suuPD4qfAlxjZtdLKgNWA2aamUna\nB+/I/oWZfS9pZaDGzGYFQX890C0P7X9SInZBRprEzD41s2fN7EnvlCzsF0xJJwDnAcflk/iScyDe\nMLAcPox5HdzNvagI22ETgdvSJb4C1wJHhjqtTDAcf4PKWH1ecMUfCBwTumEzipnNN7PHzWwosAru\nT9YDeACYKelySVtHr7H8IIihQXiWtjYY/d4LHN7E8iHAX8zsWzObDVxO6CY2sxoz+yCIL+FZrm/A\nPSXN7IsGdYSdgFqgILNfEAVYJIKkQbhX1jlmdmPS8aRKmAE4CReOh5jZb4EVgLXwN7qiIYijh/At\ni7SOiQpF8S8DB6fzugCSlse3625K97UbY2b/xbcI/09S1jIK4Q37BTP7HbAmsD8wFx9o/7mkayTt\nHLJmixDepCPJsw5QZWafNXhsKrBhE2s3BN5qaZ2kt4Bq/Pd+P2sw+F7StpK+A34AVgXOTMszyEGi\nAIsUNZL64p2CV2djayYdSCqXdAFuMTER2MzMnguHhwOj09Xxlg8Ek9C7gP8CJ2coWzsKGJEBQXAM\ncF+2miRCLdYewLWSdszGPRvd38zsTTM7z8x+hW9TfYpPKfhS0s2S9pbULfxc35Z0vaSB8hFKkWSo\nwP0QGzIHz2q2tnZOeOxnzKw30A04C7hPPjKt/tgLZrY0bgE0F59TW5BEARYpWiRtiNcn3GdmJycd\nTypI2gt35l8b79K8sl5shS24g/DMQlEQBNEYoIwMdPk1YCI+rmfLdF0wCIwTaDCpIBuE7aMDgbsk\nbZ7NezcRy/tmdomZbQlsgtt+nIrXnT6OZ06OBR4DvpY0TtKghm/YkawwB2j8Pa/ATZ1bW1sRHlsE\nM6szs+vxDt2dmjg+G8/uD2lnzDlPFGCRokTSqnhX2ItmdlDS8bSGpDUkPYh/GjzWzA42sy8aLTsC\nmJSPvmUd4DJgfWD/htsY6SYIu2tI73zIPYHPrdHg7GxgZs8AxwETJK2b7fs3hZl9ZmZXmVl/fBu9\n8bD0JfHZpvcB30i6X9LhbXH7j7SbGUC38LpZz8b4h8HGTAvH6undzLp6OrdwrAveSVmQRAEWKTpC\npuhtYCa+BZKzSCqTdDZuU/ASsLGZPdHEuk64OCia4ntJZ+DbaXtYdgaJ3wTsGeq20sEIEvx5mdkD\nwNn4yKJVkoqjKczsG7yesTm64d2Vt+KZsUmSTghdsJE0E6yHxgN/klQiaVO8lu+2JpbfCpwmnzu7\nHPA7Qo2jpC3CP4XrnAT8Ang6HD+w/mcoN5O+ABfcBUkUYJGiIrRBT8cLPDfN5e5OSbvgBay/BjY3\nsz+bWU0zy3fCi1pfyFZ8SSLpKLzVfUDYqsg4oU7rPrxuq0NIWh/vWE30zcXMxuKZvcnBoymX6IN3\nbl4PfN3Cui54c8G1wH8lPS/pNPlszUj6GA4sDczGxdhQM3tP0naSfqxfZGaj8eag6fg0jonm80kB\nyoGx+OvvN/hEhQFmVn/+ZsDr4XqvhWuclPFnlhDRByxSNIR6oenAssDqWcqatJnghXMlLrxOSsUW\nI2xPPhJqKvKG9viASdoXuA7Ywczez0xkzd57U9xnbU0zW9CB61wF/GBm56QtuA4g6XKgL7CzmS1W\nr5M0kjoD2+BWCINwL6lUeAP3HhsPFLydTiS/iAIsUjRI+jde1LuWmX2VdDyNCW34J+FzG68FLrYU\npg7IByW/DqyWq6KyOdoqwCT1A+4BdjOzVzMWWMsxvABcYWb3t/P8Hri3Ue9Gbf2JET6cjAVWAvbK\nZD1dRwmxbspCMbZ+iqf+7MwPvBrFWCRpogCLFAWSJuDbFBtaDo5FCXYY1+BWCiea2Yw2nHsx0NXM\nTs1UfJmiLQIsZJ8mAYPNbEpmI2sxjkOAo8xs53aePxTPNOWUu3foyrwPN8U8NJPGsOkkbOfuF/6l\n2tX5OQud+Z/vSDYzEmkvUYBFCh5JN+BOzFsllTVpDkkr4J18OwKnAfe25ZO5pK64j9K2ZvZBZqLM\nHKkKMElr46N0TjSzROumQh3hJ0B/azSGJYVzBbyDz7d7KhPxdYRgaDsRb1I5Md+yRCEbvC+eGeuL\nj8JpjVn4tvJ4YEoLdZaRSFqJRfiRgkbShcCRwJ65JL4kdZY0DH8z/hrYwMzuaccb3m+A1/NRfKWK\npJXwzNcfkxZf4ONUcO+xYe04vX4+59NpCyiNmNlcvDB6O9yDKa8ws0/M7O/mc1BXxK02JgItGRMv\nh883fAS3t7gjdONVtHBOJNJhYgYsUrBIGgH8AzfobKpdOhEk/RrfbqwChpnZOx241svABakU6uci\nrWXAgsfTs8CduTSpINg2TMWbOZoyo2zuvHuBp8wsq+arbUUZGGqeJMF6Zg88M7Yb3o3XGjW48B8P\nTMjWtIJI8RAFWKQgkXQQcCdwhpnlxCgLScsAF+MZhjOAcR3Z4pG0BT5GaS0za2xamRe0JMDkA4An\n44a5p+XadlgQU0+mKlDaK9qSQtKauPg93czuSjqedBF+rwbgYmwvfMJBa9TiWcvxwAPmczUjkQ4R\nBVik4JDUH3gC+KuZnZ4D8XTCa9D+jHfwnWtm36fhujfjrfWXdfRaSdGcAAsdoQ8A35LZEUPtJvye\nXQ38KhVxKOl8YBkzG5Hx4NKEpI3xv6XDzGxy0vGkm/B71g8XY/vRsvlrQ/5FKOI3H9YeibSZKMAi\nBYWk3rhr/F1mdniOxHMNbhY51MxeT9N1lwM+wLNfWTEizQRNCbAgWG/BTR/3sxwdLN6goH64mT3d\nytpSvHB/x7YW7ieNpO3wbsE9zeylpOPJFMFrbCsW2luskeKpU1lob/FOrmVqI7lLFGCRgiF0QE0H\nnjOzAQnHsgRwPjAYOAe4MZ1ZHElnAuuZ2ZHpumYSNBZgQdRcCWyBO2S36oOWJKGRYkczO6CVdYOB\nY8xssaHD+YCkPYAb8ef6btLxZJrwe9ibhWJswxRPnclCMfZKLmZuI7lDFGCRgiCMUfkw/NssqU+h\n4YX7YHxo9mPA781sVprv0Rn4D3BALnV2tocmBNhZ+PdvBzP7LrnIUqOBqerGZvZ5C+vqC9rHZy24\nNCPpcOAiYDsz+zTpeLKJfGD5frgY2yLF077At9HHA89Gr7FIY6IAi+Q9wbvoI7yrcO2kCtKDIeQo\nfOtsmJn9K0P32Rs4y8y2ysT1s0lDASbpOOD3+Bt83hQ5S7oa+M7Mzm3m+CbABKBXvr8JSzoVOB7o\naz4wu+iQtCoLvca2JzU7p9nAQ7gYe8LMqtMUyy8khlRUMLC2lo1qaynv1Il5JSW8V1XFkwsWcLOZ\nfZSOe0XSTxRgkbwmZIPeB5bAu8vmJhBDd+Bc3EvoAuCaTL7RSpqEd1DmjLVGe6kXYJL2B64Ctrcc\nnFTQEkF4P4n//i02wkfSGOBjM7so68FlAEl/BnbBtyNzvpszk0j6Bd7VPAjYGShN4bQ5wKO4GHu0\nPd9DSUt068bfamsZvP322NZb022ttaCiAqqr4cMP4bXXmDdxInWdO/NkZSXH5tOHmmIhCrBI3hK2\n+14B1sGzC1ktRg/33xf4G/AcMNLM/pfhe64T7rV6uj5FJ4kkA3YC7gJ2NbM3Eg6pXUiaAtxgZnc2\nenxpfFt8PcvB+aPtIfzejwbWBPaIzvFOqPvcHRdjuwPdUzitBnichV5jrZYrSOrTtSuP9etHj6FD\n6brEEs2vra6G229n/j33UFNTw2AzeziV5xLJDlGARfIWSY8B/fE3t4+zfO9f4hmbNfAuuKyMlZH0\nN6DKzM7Kxv0yTRBg3wAHmtkzScfTXiTth/tlbdvo8dPwmsTDkoksM4TM891AHXBwvvrQZYpQFrEL\nLsb2xssSWqMOH7dV7zW2WE2hpM3KynjmrLOo2H771ON5910YOZKqqioGm9lDqZ8ZySRRgEXyCkm7\n49s91wGHAr/OZtYkzF48EzgRn+H4t6a2nTJ07wq84HvTQiiCDoXN03GriQeSjqcjhEHWHwL71P8+\nBjuNGcDhmaoHTJLwt/Ao/hyHRvuFpgleYzuwcGD4iime+hILvcY+kFTRtSszzzyTFfr1a3sc06fD\nKadQWVPDBoXw+lEIxFmQkbwhtPI/gr9pHw7slmXxtRvu+7QxntW4LFviK3Ao3k2V9y+ewRV+EkC+\niy+AUPM3Ghje4OFdgR+AfycSVIYJW+D74l2B5yccTs5iZvPN7AkzGw6sAmyDd0l/2MqpWwKXAjMk\nvV1aypNbb81S7RFfAOutB4ccQln37tzSvitE0k3MgEXyAkkD8U6yLuGhD4GtzezrLNx7VbzOqzcw\nwswmZvqeTcQg4C18JM8T2b5/OgmWIc/iZquXNuWEn49IWh5vCFnTzL6T9DAw3szGJhxaRgnP+zlg\nlJn9I+l48oXwN70xC+0tNmppfUkJ3HUXLLNM82tOOcUL8MePhy5dFj8+fz7stx9zKyvpk2+GCtRV\npAAAIABJREFUwIVIzIBFch5JWwP3sVB8AawK/CrD9y0Nhqdv4G7Xv0pCfAX64h1WUxK6f1oIHaMP\n491feTtCqSnCh4FHgCPDHMWt8OaCgiY87wHASEmHJh1PvmDOW2b2f2a2Md5MdCa+9bgYm23Wsvj6\n8kvfZlxqKXjhhabXlJTA3ntTUlbG8R1+ApEOEwVYJKeRtCH+plbe4GEDhpjZkxm8b3/gTdznZ0sz\n+1PCXYfD8QxD3qaswzie+/At5DMSDidTXA0MA4YCN+W6k3+6MLNPgIHAlWGrPtJGzOyDUNawFf4B\n80S83rW2rAy22abl8ydPhj59YMAAmDSp+XWbb06X0lLyciJDoREFWCRnCaOFJrF4B9GJZpaRzIKk\nFSXdDtwMnI3Pv0t02K6klfCOqluTjKMjhIL0m/G2+2PzWUi2wkvAj8CxwLUJx5JVzGwaXhN2q6RW\n5EKkJczsczO7Ooyu6llSwldrrdXyOZMnQ//+0K8fvPIKfP990+vWWguqq2nlapFsEAVYJCcJBoeT\ngZUbHfqTmY3KwP26SDoZ32r8FNjAzO7PEaFwHD5c/IekA2kPodbl7/jP8uB8d4NvifD78iZQY2at\nFVkXHKHb83DgfkkZLREoFsxslhkLunVrfs3bb8OsWbDttrDKKrDGGvBEM5Wi5eWwYEFKhrGRDBMF\nWCTnCPP1HsNrIhoyCvhTBu63NfAqsA/uxP4HM6tM933aQ9i2Ow5/7vnKuXgN295JTCrIJkFsbgKU\nhTqwoiPUSZ4KPCZpjWSjKQw6daJqbgt/OZMmweabQ71I22EHz4g1RVUVdOlCNru3I83QRJ9EJJIc\nwVvoAaBPo0P/BE5KZ0ZK0nJ4m/dA4HQ8y5QLGa+G7AfMCNs7eYekocAQfL5jXmbw2siW+FisMXgd\n2Mhkw0kGM7sjdLtOlrRdNrqVC5m6Ot6YOZO1N9hg8WPz5sHTT4MZ7L+/P7ZgAcyZ4x2Razb6GDBz\nJnTtSl6N+ypUYgYskjMEd+3bgR0bHZqMF93Xpek+ncLg53eBn/DtxjtzUHyBF99fnXQQ7UHSb4Bz\ngAFm9mXS8WSJEcA1eP3XkZLKW1lfsJjZVXgX6MQwpifSTioreeKll2gyK//cc9C5M9x8M9xwg/+7\n+WbYaKOmi/FffZUF8+bldzd1oRAFWCQnCFs31+J+OA15Cdg/XYankvoA/wKOAHYxs1NyNTMjaWN8\n3t6DScfSViQNwIXjbsVSCyVpBWAPvPvxQ9yA9eBko0qcP+J/ww+G7Hakfdz96qt0mt3EtNvJk2G3\n3eAXv4Cll174b999YcoUqGvwsXX+fHjoIebX1DA6e6FHmiMasUZyAkkXAY3nG74H9E3HkG1JSwEX\nAgcAfwBuSVdGLVNIGg18bmYXJB1LW5C0Je71NcjMnmtlrRWQEevZ+FD4Y8LXuwEXAX1yNLuaFUJm\n+w6gBPhNITdhZJLyco3aemuOPPdcWijHb5lbb2XB3Xfz/Jw51j+dsUXaR8yARRJH0iksLr4+A3bt\nqPiSMwQXc13w7cab8kB8LQX8Bq8lyhskrY9n7I5sTXwVEmEW5PEs2iwxCa8H2yqRoHKEMKh7CNAD\nuC5kuyNtZO5cznzxRX546qn2nT99OtxxBzWVlQxJb2SR9hIFWCQRJC0tabykucBfGx2ejdcNfRbW\nXirpG0lfS7qkwTWWlfSipG8lzZH0dqg7qj++KfAFcCPQDViAz+bLB44AJuZT7ZSk1XDRcYaZPZx0\nPFlmL+CzhrNJg8i/hkXnQxYlZlaDN5RsDPw54XDyEjObU13NHpdeypxnnmnbue++C7/7HVU1NQyu\nf12NJE/cgowkgqQ7gV8A/YDODQ5VAv3N7JWw7njcWbw/IHwUzzVmdr2kMmA1YKaZmaR9gHuBXsAp\neBfa5/iwYOHWFpPMLO1WFukkmJZOx7NIzQwVyS2Cb9tzwPVmdmUbziuILUhJU4AbzOzORo8vjc8t\nXc/MvkokuBwidB4/B4xpy+9JZCGS+nTtymM77ECPYcPoukQL7Q3V1XD77cy/5x5qgvgqtg9GOU0U\nYJGsEzrDvgfqgLIGh2qBgQ2HTUt6ARhtZreGrw8FhpvZIk7bYVtjT3zAcyUu1LYA/mhm94Y1g4FL\nzGz1TD23dBAK2C8DNs2H2qHg2/Yk8ISZ/aGN5+a9AAvbrk8CqzfVLCJpDPCxmV2U9eBykJApfQ44\nt/7vOtI2JC3RrRt/q61lcN++2NZb023ttaGiAubOdfuJ115j3qRJ1HXuzJOVlRxrZv9NOu7IokQf\nsEgS7IH/7jV84zXg9YbiK7Ah8FaDr6eGx35G0lvA+uHLTwn1R5LebnStTsAqknqY2U8dfA6ZZAR5\nMvcxZCHvx93fG9fxFQvD8exXc526o4AJki6NBehgZp9KGgg8Jek7M5uQdEz5hpn9CBwl6cwnn2TI\nyy+za20tG9fWUt6pEzUlJbxXWcmU2lpuMbOPk4430jQxAxbJKsEd/GVg2UaHbgFWM7MdG61fgG/f\nzAxf98K3HDuHr8vxrsaheBZiG2BdM6uUdDnwa9zhvjPemfdrYNVc/TQYnMNfxbMpOeHG3xyhu+0u\n/Hvbru62fM+AhezfJ8DGZvZ5C+ueB640s/FZCy7HkfRr4BFS6JaNRAqRWIQfyRqSeuKmqo3F17nA\na7gpamPmAN0bfF0RHkPSXsA0YG2gt5n9BvgO2CmsPQ/4AJiBezI9jGfavkvD08kUJwC35oH4Ep7Z\nWRY4pIgzO4cDT7YkvgKjiMX4i2BmLwOHAPdJ6p10PJFItokCLJIVJC0JTAR+2ejQP3CvpI1xMdWY\naeFYPb2BmZIeBK4AjjWzg83si3D854J+M5trZseY2fJmtjZubfFmrs4jDEaVR+Gdc7nO+XiN3b5m\nVp10MEkQROgIUptUcB+wQagXiwTM7HH8e/iopMavDZFIQRMFWCTjSOoGPISLp4b8B5+VtwmwP3Bb\nE6ffCpwmaTlJK+HF6evg7tpHAj8Er68SSSfhnZVPh/uuKGn58P+98UHe56f56aWTg4DX6rdbc5Xw\nfT4Id7n/Mel4EqQf3kjSqilAqA8bQ8yCLYaZ3Y2bJE+WtGLS8UQi2SIW4UcySjCovAvYvtGhx4Eq\nYBbu+zXUzN6TtB3wqJktAWBmo0Pd13/wrcgPgW3M7GNJOwCjgdXxN8JX8fFC9aJgLWBcsAL4AviD\nmT2UwafbUUbgIjFnCV2oI/EJBcU+YHk4bomSaiHtaOBtSWcVuXBdDDO7NlhUTJS0g5l9n3RMkUim\niUX4kYwRtmhuxDNVDfkXLpRarXOStDJwJV48f1KhdkyFguS7gLWDc3jOEUbr3AzsZGbvpOmaeVmE\nL2kVvCN39bZ01Eq6F3jKzEa1urjICK8Xf8cz4rvmaqlAJJIu4hZkJJNcyuLiaxqwZ2viK2wpnoZb\nUMwANixU8RUYDlybw+JrG3w7eL90ia8853jg9nbYmVwNDI/jeBYnZBJPwWs1/xmy55FIwRIzYJGM\nIGkkXq/VkE+AbRsUzDd3bl+8EP2/wIlmNiMzUeYGwUV+BrBWR2dfZgJJv8KNbX9rZo+l+dp5lwEL\n3mef4BMb3mvjuQLexn+v2znVr7CRVIrPE/0KOCrX57ZGIu0lZsAiaUfSkSwuvr7Btx2bFV+SVpB0\nC3AHXiw/sNDFV+Bo4P4cFV9r4N2rp6VbfOUx+wPvtFV8wc9ZnlF4vV+kCULDwgF4s81lMVsYKVSi\nAIuklTCP8YZGD/+Ei6kPmjmns6RhwDvA18AGZnZPPjjBd5RgZjoUf1POKUIH6WTgMjO7Pel4cojh\ndOznNQ7oL2nVNMVTcIQShT2BgcAZCYcTiWSEuMceSRuhK/GfLCrs5wH7mNnrzZzza3y7sQrf0im2\n+qI9gf+a2WtJB9IQSUvgma+7zOwfSceTK0jaFFgVaHc9opn9JOl2vI7snHTFVmiY2beSdgWelzTL\nzG5MOqZIJJ3EGrBIWghvTE8DSzR4uA44wMzub2L9MsDFwN74J9xxxZDxaoykybjz/bikY6knGMI+\nBkwHhmXy55JvNWCSbgA+NLM/d/A66+F/L6ubWU06YitUJK2De60Na+q1JBLJV+IWZKTDSFoLz5Ys\n0ejQ8Y1fMCV1knQU8C6eHVvfzG4rUvG1Lm5Oe0/SsdQTOs/uwLeCRxTjz6U5woeG/Vl8i73NmNl0\nfMt9/45eq9AJdaB7AqMl9Us4nEgkbUQBFukQwbl6MrB8o0N/MLMbGq3tDTyHb73sbmYnFrnh4jDg\nhlzJgIRi5+uAHsCQXLXESJAjgYfTaEB7NbEYPyXCFv1BwN2SNks6nkgkHcQtyEiThPFBPXGRPsvM\nfmhizdL41sBGjQ5dCZxenz0J9UTnA4Pxmpcbi721XFIFbmWwqZl9mnQ8AJIuxgeZ72hmc7J0z7zY\ngpTUCR/sfqiZ/TtN1+yCT3bYx8zeSMc1Cx1Jg3DhukNzTT2RSL4QM2CRn5G0drdu+kdFhT7u3Jkf\nl1ySt5daijdLSvime3d91b27/ilpmzB7sRwvRG4svm4FRpqZhXWDgfeACtxMdUyxi6/AYcAzOSS+\nTgP2xTOTWRFfecZA4Dt8BmlaMLMFeMYxzodMETMbD/wRnxu5UtLxRCIdIWbAIkharrycMcCue+1F\n5379KF1zTSgt9eO1tfD55/DSS9Tdcw9VVVV8VFXFt8AOjS71MDDIzOZLWh9v1V8aL579VxafUk4T\ntvqmAqeY2ZQciGcIcAE+3zGrgjCPMmCPAPea2U1pvu7ywPvAL83s23Reu5CR9AfgEGB7M/su6Xgi\nkfYQBViRI2mHsjIe3HNPuh5zDGVdu7a8vq4OJkzArrsO1dRAg1+f54EBeFb1XNxc9AJ8WPGCjD2B\nPCTYdVyH+50l+gcoaS9gDO1wdU/T/XNegEn6JfBvYLVMzCeUdBvwppn9Jd3XLlTCh5i/AFviBs9V\nCYcUibSZKMCKGEn9unblkQsvpLxPn7ad+8UXcNJJ8P33UFfHVDwb1h/4G15oP9LM/pf2oAsASXcD\nz5rZ1QnH0RcYD+xhZi8nFEM+CLArgDozy4ghqKStgNvxQexxez5FQl3ezcByeB3d/GQjikTaRhRg\nRYqknmVlzLjoInq0VXzV8+WXcMwxWGUlw3A/rzWA4XHGXfNIWhmfBbiGmf2YYBy9gcfxovLHE4wj\npwVYqHX8FNjCzD7K0D0EvAKcZ2aPZuIehYqkEuB+4Hu8czcK2EjeEIvwi5Tycm7ad1/K2iu+AHr2\nhN//HpWVMQp4Adgkiq9WOQ64M2HxtSbwKO7zlZj4yhMGA//OlPiCReZDxmL8NhKyXr8BVgeujHMj\nI/lEFGBFiKTenTuz/VFHUdrRa223HWywAdUSX4chupFmkFQKHIuPXkoqhp64b9uFZnZ3UnHkA+HN\nfDhue5Bp7gJ+HerNIm0g1H/tBewInJVwOJFIysRZkEVIeTmnDhpEaWkL8uvgg72+q3NnL7SX4Lbb\nYJllmlxbPmMGZ+LF3JHm2Q9438ymJXFzSUvhEwtuNbNrk4ghz9gKN6WdnOkbmdlcSTfhg9lPz/T9\nCg0z+77R3MjRSccUibRGFGBFiBl77Lhjyz97CS6+GDbdtPXrbb45LFjAKpJ6mtmX6YqzABmBNylk\nnWCs+xDeIHFBEjHkISPwLt5s1RVdC7wi6bzY1dd2zOx/QYQ9K2m2md2bdEyRSEvELcgiQ9JytbUs\nscoqra9NtT+jUydYc02qgQ5UlBU2oei9F/BgAvfugm9xfQ6cnLT1RT4gaQVgd7zLLiuEOrN/4XVn\nkXZgZjPxn9s1knZKOp5IpCWiACs+Vl9uOao7pfkn36sXpXgXZKRphgOjs+2JFuqYxgBlwG9jl1jK\nHIMbr2bb5HMUMCIWk7cfM3sTOBC4U9LmSccTiTRH3IIsPjp37kxKGZBzz/UaMIBNNoHzz29+badO\niCjomyTUXh0IrJ/A7S8D1gN2jk0SqREyhifghd3ZZjJwFbA18GIC9y8IzOwZSccCEyT1N7PpSccU\niTQmCrDi49sffkjt537hhanVgAHMns18II5SaZrfAo9luz5O0hn4dkxfM6vM5r3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8AAAQ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\nJkmSlJkBJkmSlJkBJkmSlNl/AeKxVgcfbdZVAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x5ef3f90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Damping factor: 1\n"
]
},
{
"data": {
"image/png": 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WxXuezsA3ExhwoZmdm63nPT8SNWDB/E5rFgUz8Df/D/Dm1OkCa3Iud9gBSNoS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\nM7OKOQEzMzMzq5gTMDMzM7OK/X+tWBvyNE8EYAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x4b12510>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dampingfactor=[0,0.25,0.5,0.75, 0.85, 1]\n",
"def plotmany(dampingfactorlist=[]):\n",
" \n",
" for i in range(len(dampingfactorlist)):\n",
" print \"Damping factor: %s\" %(dampingfactorlist[i])\n",
" outputdir=\"/data/hw9/PRToys/Run%s\" %i\n",
" PageRank(Input=\"/data/hw9/PRTEST/Init/part-*\", TotalNode=11, Teleport=1-dampingfactorlist[i], maxIter=25, OutDir=outputdir)\n",
" plot(outputdir+\"/Iter25/Step2/part-*\")\n",
"\n",
"plotmany(dampingfactor)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"B\t{'C': 1}\r\n",
"C\t{'B': 1}\r\n",
"D\t{'A': 1, 'B': 1}\r\n",
"E\t{'D': 1, 'B': 1, 'F': 1}\r\n",
"F\t{'B': 1, 'E': 1}\r\n",
"G\t{'B': 1, 'E': 1}\r\n",
"H\t{'B': 1, 'E': 1}\r\n",
"I\t{'B': 1, 'E': 1}\r\n",
"J\t{'E': 1}\r\n",
"K\t{'E': 1}\r\n"
]
}
],
"source": [
"!cat /data/hw9/PageRank-test.txt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As the graphs show, when the damping factor is 0, all the nodes end up with equal PageRank. This shows what happens when the user does not follow the links and only jump to other pages randomly with uniform probability distributions. As the damping factors increases, page B, which has many in-links, has its PageRank increase since the mass emited by other nodes are weighted more, while nodes with no in-links such as J and K gets lower in PageRank, since random surfing is weighted less. Interestingly, page C which only has link to and from node B, also increase in PageRank. When damping factor inreases to 1, the user is trapped between B and C, since many nodes has link that point to B but B only has out-links that point to C. Furthermore, the probability of randomly going to another page is 0. These graphs show that choosing an appropriate dangling factor is import for balancing the PageRank scores for the pages in the graph. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"HW9.3\"></a>\n",
"[Back to Top](#TOC)\n",
"\n",
"<h1 style=\"color:#021353;\">HW 9.3: Applying PageRank to the Wikipedia hyperlinks network</h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"Run your PageRank implementation on the Wikipedia dataset for 5 iterations,\n",
"and display the top 100 ranked nodes (with alpha = 0.85).\n",
"\n",
"Run your PageRank implementation on the Wikipedia dataset for 10 iterations,\n",
"and display the top 100 ranked nodes (with teleportation factor of 0.15). \n",
"Have the top 100 ranked pages changed? Comment on your findings. Plot the pagerank values for the top 100 pages resulting from the 5 iterations run. Then plot the pagerank values for the same 100 pages that resulted from the 10 iterations run. \n",
"\n",
"</pre>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"make_bucket: s3://nyaohw9/\r\n"
]
}
],
"source": [
"!aws s3 mb s3://nyaohw9"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"Using s3://mrjob-f4c6818345514ca1/tmp/ as our temp dir on S3\n",
"Creating persistent cluster to run several jobs in...\n",
"Creating temp directory /tmp/no_script.root.20160714.163056.796805\n",
"Copying local files to s3://mrjob-f4c6818345514ca1/tmp/no_script.root.20160714.163056.796805/files/...\n",
"Can't access IAM API, trying default instance profile: EMR_EC2_DefaultRole\n",
"Can't access IAM API, trying default service role: EMR_DefaultRole\n",
"j-14S45E32BL3OK\n"
]
}
],
"source": [
"!mrjob create-cluster --num-ec2-instances=10 --max-hours-idle 0.4"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initialization finished, Total time taken: 543.758561134 s\n",
"Total Number of Nodes: 15192277\n"
]
}
],
"source": [
"# Preprocess the graph and put it in S3\n",
"inputdir=\"s3://ucb-mids-mls-networks/wikipedia/all-pages-indexed-out.txt\"\n",
"initdir=\"s3://nyaohw9/WikiPR/iter5_init\"\n",
"clusterid=\"j-3UN2RZT5DAV4N\"\n",
"\n",
"preprocess=Preproc(args=[inputdir, \"--output-dir\", initdir, \"--no-output\", \"-r\",\"emr\", \"--cluster-id=%s\" %clusterid, \"--no-output\"])\n",
"with preprocess.make_runner() as runner1:\n",
" initstart=time()\n",
" runner1.run()\n",
" initend=time()\n",
" print \"Initialization finished, Total time taken: %s s\" %(initend-initstart)\n",
" if \"Total\" in runner1.counters()[0]:\n",
" totalnode=runner1.counters()[0][\"Total\"][\"Node\"]\n",
" print \"Total Number of Nodes:\", totalnode"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%reload_ext autoreload\n",
"%autoreload 2\n",
"#Description: modify the driver code for EMR. It is very similar to the original, with added EMR options in \n",
"#class instantiation\n",
"\n",
"from PageRank1 import PR_step1\n",
"from PageRank2 import PR_step2\n",
"from time import time\n",
"\n",
"\n",
"def PageRankEMR(Input=None, TotalNode=1, Teleport=0, maxIter=10, OutDir=\"/data/hw9/PR-test\", clusterID=None):\n",
" iternum=1\n",
" \n",
" allstart=time()\n",
" while iternum<=maxIter:\n",
" start=time()\n",
" print \"Starting Iteration %s\" %iternum\n",
" if iternum==1:\n",
" Step1Input=Input\n",
" else:\n",
" Step1Input=Step2Output+\"/part-*\"\n",
" \n",
" dangling=0\n",
" Step1Output=OutDir+\"/Iter%s/Step1\" %iternum\n",
" \n",
" Step1=PR_step1(args=[Step1Input, \"-r\", \"emr\", \"--cluster-id=%s\"%clusterID ,\"--total-node\", str(TotalNode), \"--output-dir\", Step1Output, \"--no-output\", ])\n",
"\n",
" #print \"Step 1: %s\" %Step1Indicator\n",
" #print \"Step 1 Input: %s \" %Step1Input\n",
" #print \"Step 1 Output: %s \" %Step1Output\n",
" \n",
" with Step1.make_runner() as runner1:\n",
" \n",
" runner1.run()\n",
" print \"Step 1 Finished\"\n",
" counter1=runner1.counters()\n",
" if \"Dangling\" in counter1[0]:\n",
"\n",
" danglingmass=counter1[0][\"Dangling\"][\"Mass\"]\n",
" dangling=danglingmass\n",
" #print \"mass sent %s\" %dangling\n",
" else: \n",
" print \"no Dangling mass sent\"\n",
"\n",
" Step2Input=Step1Output+\"/part-*\"\n",
" Step2Output=OutDir+\"/Iter%s/Step2\" %iternum\n",
" \n",
" Step2=PR_step2(args=[Step2Input, \"-r\", \"emr\", \"--cluster-id=%s\"%clusterID, \"--total-node\", str(TotalNode), \"--teleportation\", str(Teleport), \"--missing-mass\", str(dangling), \"--output-dir\", Step2Output, \"--no-output\"])\n",
"\n",
" #print \"Step 2 Input: %s \" %Step2Input\n",
" #print \"Step 2 Output: %s \" %Step2Output\n",
"\n",
" with Step2.make_runner() as runner2:\n",
" runner2.run()\n",
" print \"Step 2 Finished\"\n",
" \n",
" \n",
" end=time()\n",
" totalseconds=(end-start)\n",
" minutes=totalseconds//60.0\n",
" seconds=totalseconds%60.0\n",
" print \"Iteration {} Finished in: {:1.0f} min, {:1.0f}sec\".format(iternum, minutes, seconds) \n",
" \n",
" iternum+=1\n",
" \n",
"\n",
" else:\n",
" allend=time()\n",
" allseconds=(allend-allstart)\n",
" allminutes=allseconds//60.0\n",
" leftseconds=allseconds%60.0\n",
" print \"Page Rank calculation time: {:1.0f} min, {:1.0f}sec\".format(allminutes, leftseconds) "
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Starting Iteration 1\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 1 Finished in: 23 min, 25sec\n",
"Starting Iteration 2\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 2 Finished in: 18 min, 44sec\n",
"Starting Iteration 3\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 3 Finished in: 19 min, 9sec\n",
"Starting Iteration 4\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 4 Finished in: 19 min, 9sec\n",
"Starting Iteration 5\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 5 Finished in: 19 min, 45sec\n",
"Starting Iteration 6\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 6 Finished in: 18 min, 44sec\n",
"Starting Iteration 7\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 7 Finished in: 18 min, 49sec\n",
"Starting Iteration 8\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 8 Finished in: 18 min, 22sec\n",
"Starting Iteration 9\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 9 Finished in: 18 min, 8sec\n",
"Starting Iteration 10\n",
"Step 1 Finished\n",
"Step 2 Finished\n",
"Iteration 10 Finished in: 18 min, 14sec\n",
"Page Rank calculation time: 192 min, 30sec\n"
]
}
],
"source": [
"inputdir=\"s3://nyaohw9/WikiPR/iter5_init/part-*\"\n",
"outputdir=\"s3://nyaohw9/WikiPR/Run2/Results\"\n",
"clusterid=\"j-14S45E32BL3OK\"\n",
"# started at 12:30PM\n",
"PageRankEMR(Input=inputdir, TotalNode=15192277, Teleport=0.15, maxIter=10, OutDir=outputdir, clusterID=clusterid)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sort PageRank results"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#!mkdir /data/hw9/wikiPRiter5\n",
"!aws s3 sync s3://nyaohw9/WikiPR/Run2/Results/Iter5/Step2 /data/hw9/wikiPRiter5"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting multipleReducerSort.py\n"
]
}
],
"source": [
"%%writefile multipleReducerSort.py\n",
"#/usr/bin/python\n",
"# -*- coding: utf-8 -*-\n",
"#Description: TotalSort using multiple reducers\n",
"# Adapted from script that originally written by Kyle Hamilton \n",
"# http://nbviewer.jupyter.org/urls/dl.dropbox.com/s/24tcqzbhsca22iy/mrjob-total-order-sort-voodoo.ipynb\n",
"\n",
"import mrjob\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawValueProtocol\n",
"from mrjob.protocol import RawProtocol\n",
"from operator import itemgetter\n",
"import numpy as np\n",
"\n",
"\n",
"class multipleReducerSort(MRJob):\n",
" \n",
" # The following three settings are your sorting best friends:\n",
" MRJob.SORT_VALUES = True \n",
" INTERNAL_PROTOCOL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" \n",
" def mapper_partitioner_init(self):\n",
" \n",
" def makeKeyHash(key, num_reducers):\n",
" byteof = lambda char: int(format(ord(char), 'b'), 2)\n",
" current_hash = 0\n",
" for c in key:\n",
" current_hash = (current_hash * 31 + byteof(c))\n",
" return current_hash % num_reducers\n",
" \n",
"\n",
" keys = [str(unichr(i)) for i in range(65,65+55)]\n",
" partitions = []\n",
" \n",
" for key in keys:\n",
" partitions.append([key, makeKeyHash(key, 55)])\n",
"\n",
" parts = sorted(partitions,key=itemgetter(1))\n",
" self.ascii55 = list(np.array(parts)[:,0])\n",
" \n",
" self.i55 = np.arange(0,0.0016*1000000000,np.floor(0.0016*1000000000/54))[::-1]\n",
" \n",
" def mapper_partition(self, _, line):\n",
" line = line.strip()\n",
" node,rank,edges = line.split('\\t')\n",
" key=float(rank)*1000000000 # make the page rank into integers \n",
" # Prepend the approriate key by finding the bucket, and using the index to fetch the key.\n",
" for idx in xrange(55):\n",
" if float(key) > self.i55[idx]:\n",
" yield str(self.ascii55[idx]), \"%s\\t%s\"%(node, rank)\n",
" break\n",
" \n",
" \n",
" \n",
" def reducer(self,key,value):\n",
" for v in value:\n",
" yield key,v\n",
" \n",
" def reducer_step_two(self,key,value):\n",
" for v in value:\n",
" yield key,v \n",
" # if you want to omit the partition key, specify 'None'\n",
" # I am keeping it for debugging purposes\n",
" \n",
" def steps(self):\n",
" JOBCONF_STEP1 = {\n",
" 'mapred.reduce.tasks': 55\n",
" }\n",
" JOBCONF_STEP2 = {\n",
" 'stream.num.map.output.key.field':2,\n",
" 'stream.map.output.field.separator':\"\\t\",\n",
" 'mapreduce.partition.keypartitioner.options':'-k1,1',\n",
" 'mapreduce.job.output.key.comparator.class': 'org.apache.hadoop.mapred.lib.KeyFieldBasedComparator',\n",
" 'mapreduce.partition.keycomparator.options':'-k2,2nr',\n",
" 'mapred.reduce.tasks': 55,\n",
" 'partitioner':'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
" }\n",
" return [\n",
" self.mr(jobconf=JOBCONF_STEP1,\n",
" mapper_init=self.mapper_partitioner_init,\n",
" mapper=self.mapper_partition,\n",
" reducer=self.reducer)\n",
" ,self.mr(jobconf=JOBCONF_STEP2,\n",
" mapper=None, # None specifies identity mapper\n",
" reducer=self.reducer_step_two)\n",
" ]\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" multipleReducerSort.run()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"Using s3://mrjob-f4c6818345514ca1/tmp/ as our temp dir on S3\n",
"Creating persistent cluster to run several jobs in...\n",
"Creating temp directory /tmp/no_script.root.20160715.025842.258149\n",
"Copying local files to s3://mrjob-f4c6818345514ca1/tmp/no_script.root.20160715.025842.258149/files/...\n",
"Can't access IAM API, trying default instance profile: EMR_EC2_DefaultRole\n",
"Can't access IAM API, trying default service role: EMR_DefaultRole\n",
"j-3C3XMVBFLGC9Z\n"
]
}
],
"source": [
"!mrjob create-cluster --num-ec2-instances=8 --max-hours-idle 0.4"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from multipleReducerSort import multipleReducerSort\n",
"inputdir=\"s3://nyaohw9/WikiPR/Run2/Results/Iter5/Step2/part-*\"\n",
"outputdir=\"s3://nyaohw9/WikiPR5_sorted\"\n",
"clusterid=\"j-3C3XMVBFLGC9Z\"\n",
"sortjob=multipleReducerSort(args=[inputdir, \"-r\", \"emr\", \"--no-output\", \"--output-dir\", outputdir, \"--cluster-id=%s\"%clusterid])\n",
"with sortjob.make_runner() as sortrunner:\n",
" sortrunner.run()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from multipleReducerSort import multipleReducerSort\n",
"inputdir=\"s3://nyaohw9/WikiPR/Run2/Results/Iter10/Step2/part-*\"\n",
"outputdir=\"s3://nyaohw9/WikiPR10_sorted\"\n",
"clusterid=\"j-3MJ0Z5GTDTK8X\"\n",
"sortjob=multipleReducerSort(args=[inputdir, \"-r\", \"emr\", \"--no-output\", \"--output-dir\", outputdir, \"--cluster-id=%s\"%clusterid])\n",
"with sortjob.make_runner() as sortrunner:\n",
" sortrunner.run()"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"download: s3://nyaohw9/WikiPR5_sorted/part-00000 to ../../data/WikiPR5_sorted/part-00000\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00005 to ../../data/WikiPR5_sorted/part-00005\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00003 to ../../data/WikiPR5_sorted/part-00003\n",
"download: s3://nyaohw9/WikiPR5_sorted/_SUCCESS to ../../data/WikiPR5_sorted/_SUCCESS\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00001 to ../../data/WikiPR5_sorted/part-00001\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00008 to ../../data/WikiPR5_sorted/part-00008\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00006 to ../../data/WikiPR5_sorted/part-00006\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00007 to ../../data/WikiPR5_sorted/part-00007\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00004 to ../../data/WikiPR5_sorted/part-00004\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00010 to ../../data/WikiPR5_sorted/part-00010\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00009 to ../../data/WikiPR5_sorted/part-00009\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00011 to ../../data/WikiPR5_sorted/part-00011\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00012 to ../../data/WikiPR5_sorted/part-00012\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00013 to ../../data/WikiPR5_sorted/part-00013\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00002 to ../../data/WikiPR5_sorted/part-00002\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00014 to ../../data/WikiPR5_sorted/part-00014\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00015 to ../../data/WikiPR5_sorted/part-00015\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00019 to ../../data/WikiPR5_sorted/part-00019\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00018 to ../../data/WikiPR5_sorted/part-00018\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00017 to ../../data/WikiPR5_sorted/part-00017\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00020 to ../../data/WikiPR5_sorted/part-00020\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00016 to ../../data/WikiPR5_sorted/part-00016\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00021 to ../../data/WikiPR5_sorted/part-00021\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00022 to ../../data/WikiPR5_sorted/part-00022\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00026 to ../../data/WikiPR5_sorted/part-00026\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00025 to ../../data/WikiPR5_sorted/part-00025\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00027 to ../../data/WikiPR5_sorted/part-00027\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00024 to ../../data/WikiPR5_sorted/part-00024\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00028 to ../../data/WikiPR5_sorted/part-00028\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00029 to ../../data/WikiPR5_sorted/part-00029\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00031 to ../../data/WikiPR5_sorted/part-00031\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00030 to ../../data/WikiPR5_sorted/part-00030\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00032 to ../../data/WikiPR5_sorted/part-00032\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00033 to ../../data/WikiPR5_sorted/part-00033\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00034 to ../../data/WikiPR5_sorted/part-00034\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00035 to ../../data/WikiPR5_sorted/part-00035\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00037 to ../../data/WikiPR5_sorted/part-00037\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00036 to ../../data/WikiPR5_sorted/part-00036\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00038 to ../../data/WikiPR5_sorted/part-00038\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00039 to ../../data/WikiPR5_sorted/part-00039\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00042 to ../../data/WikiPR5_sorted/part-00042\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00041 to ../../data/WikiPR5_sorted/part-00041\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00040 to ../../data/WikiPR5_sorted/part-00040\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00044 to ../../data/WikiPR5_sorted/part-00044\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00045 to ../../data/WikiPR5_sorted/part-00045\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00043 to ../../data/WikiPR5_sorted/part-00043\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00046 to ../../data/WikiPR5_sorted/part-00046\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00047 to ../../data/WikiPR5_sorted/part-00047\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00049 to ../../data/WikiPR5_sorted/part-00049\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00048 to ../../data/WikiPR5_sorted/part-00048\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00051 to ../../data/WikiPR5_sorted/part-00051\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00050 to ../../data/WikiPR5_sorted/part-00050\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00052 to ../../data/WikiPR5_sorted/part-00052\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00053 to ../../data/WikiPR5_sorted/part-00053\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00023 to ../../data/WikiPR5_sorted/part-00023\n",
"download: s3://nyaohw9/WikiPR5_sorted/part-00054 to ../../data/WikiPR5_sorted/part-00054\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00006 to ../../data/WikiPR10_sorted/part-00006\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00007 to ../../data/WikiPR10_sorted/part-00007\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00001 to ../../data/WikiPR10_sorted/part-00001\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00008 to ../../data/WikiPR10_sorted/part-00008\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00002 to ../../data/WikiPR10_sorted/part-00002\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00000 to ../../data/WikiPR10_sorted/part-00000\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00004 to ../../data/WikiPR10_sorted/part-00004\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00003 to ../../data/WikiPR10_sorted/part-00003\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00005 to ../../data/WikiPR10_sorted/part-00005\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00009 to ../../data/WikiPR10_sorted/part-00009\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00011 to ../../data/WikiPR10_sorted/part-00011\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00012 to ../../data/WikiPR10_sorted/part-00012\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00010 to ../../data/WikiPR10_sorted/part-00010\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00013 to ../../data/WikiPR10_sorted/part-00013\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00014 to ../../data/WikiPR10_sorted/part-00014\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00015 to ../../data/WikiPR10_sorted/part-00015\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00016 to ../../data/WikiPR10_sorted/part-00016\n",
"download: s3://nyaohw9/WikiPR10_sorted/_SUCCESS to ../../data/WikiPR10_sorted/_SUCCESS\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00017 to ../../data/WikiPR10_sorted/part-00017\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00018 to ../../data/WikiPR10_sorted/part-00018\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00019 to ../../data/WikiPR10_sorted/part-00019\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00020 to ../../data/WikiPR10_sorted/part-00020\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00021 to ../../data/WikiPR10_sorted/part-00021\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00022 to ../../data/WikiPR10_sorted/part-00022\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00023 to ../../data/WikiPR10_sorted/part-00023\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00025 to ../../data/WikiPR10_sorted/part-00025\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00024 to ../../data/WikiPR10_sorted/part-00024\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00026 to ../../data/WikiPR10_sorted/part-00026\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00028 to ../../data/WikiPR10_sorted/part-00028\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00027 to ../../data/WikiPR10_sorted/part-00027\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00029 to ../../data/WikiPR10_sorted/part-00029\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00030 to ../../data/WikiPR10_sorted/part-00030\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00031 to ../../data/WikiPR10_sorted/part-00031\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00032 to ../../data/WikiPR10_sorted/part-00032\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00033 to ../../data/WikiPR10_sorted/part-00033\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00037 to ../../data/WikiPR10_sorted/part-00037\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00034 to ../../data/WikiPR10_sorted/part-00034\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00036 to ../../data/WikiPR10_sorted/part-00036\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00035 to ../../data/WikiPR10_sorted/part-00035\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00038 to ../../data/WikiPR10_sorted/part-00038\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00039 to ../../data/WikiPR10_sorted/part-00039\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00041 to ../../data/WikiPR10_sorted/part-00041\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00040 to ../../data/WikiPR10_sorted/part-00040\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00042 to ../../data/WikiPR10_sorted/part-00042\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00044 to ../../data/WikiPR10_sorted/part-00044\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00045 to ../../data/WikiPR10_sorted/part-00045\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00043 to ../../data/WikiPR10_sorted/part-00043\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00046 to ../../data/WikiPR10_sorted/part-00046\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00047 to ../../data/WikiPR10_sorted/part-00047\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00048 to ../../data/WikiPR10_sorted/part-00048\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00049 to ../../data/WikiPR10_sorted/part-00049\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00051 to ../../data/WikiPR10_sorted/part-00051\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00050 to ../../data/WikiPR10_sorted/part-00050\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00052 to ../../data/WikiPR10_sorted/part-00052\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00053 to ../../data/WikiPR10_sorted/part-00053\n",
"download: s3://nyaohw9/WikiPR10_sorted/part-00054 to ../../data/WikiPR10_sorted/part-00054\n"
]
}
],
"source": [
"!mkdir /data/WikiPR5_sorted\n",
"!aws s3 sync s3://nyaohw9/WikiPR5_sorted /data/WikiPR5_sorted\n",
"!mkdir /data/WikiPR10_sorted\n",
"!aws s3 sync s3://nyaohw9/WikiPR10_sorted /data/WikiPR10_sorted"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# clean up the results, cut out the edges information\n",
"\n",
"!cut -f2- -d$'\\t' /data/WikiPR5_sorted/part-* > /data/hw9/WikiPR5Sorted.txt\n",
"!cut -f2- -d$'\\t' /data/WikiPR10_sorted/part-* > /data/hw9/WikiPR10Sorted.txt"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"13455888\t0.00146123974689\r\n",
"1184351\t0.00066601136689\r\n",
"4695850\t0.00063966757189\r\n",
"5051368\t0.00057476335689\r\n",
"6113490\t0.00044455933689\r\n",
"2437837\t0.00044654051689\r\n",
"1384888\t0.00045003087189\r\n",
"13425865\t0.00043291544189\r\n",
"7902219\t0.00044435746189\r\n",
"6076759\t0.00042773928189\r\n"
]
}
],
"source": [
"!head /data/hw9/WikiPR10Sorted.txt"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"!head -100 /data/hw9/WikiPR5Sorted.txt > /data/hw9/WikiPR5_top100.txt"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"13455888\t0.0014606514274\r\n",
"1184351\t0.000682656202401\r\n",
"4695850\t0.000642996562401\r\n",
"5051368\t0.000576320522401\r\n",
"7902219\t0.000458580732401\r\n",
"6113490\t0.000454596867401\r\n",
"2437837\t0.000445627497401\r\n",
"1384888\t0.000459896532401\r\n",
"13425865\t0.000428620357401\r\n",
"6076759\t0.000430410967401\r\n"
]
}
],
"source": [
"!head -10 /data/hw9/WikiPR5_top100.txt"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import glob\n",
"# Description:for each of top 100 pages after iteration 5, find the corresponding PageRank after iteration 10\n",
"# First, read the top 100 results from 5th iteration and put them into a dictionary with the node as keys and \n",
"# PageRank as Values\n",
"\n",
"iter5={}\n",
"keys=set()\n",
"with open(\"/data/hw9/WikiPR5_top100.txt\", \"r\") as f:\n",
" for line in f.readlines():\n",
" line=line.strip()\n",
" inputlist=line.split('\\t')\n",
" iter5[inputlist[0]]=inputlist[1]\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
" \n",
"# Then, read all of the result from the 10th iteration and put them into a dictionary, with the node as keys\n",
"iter10={}\n",
"\n",
"with open(\"/data/hw9/WikiPR10Sorted.txt\", \"r\") as f:\n",
" for line in f.readlines():\n",
" line=line.strip()\n",
" if line.split('\\t')[0] in keys:\n",
" iter10[line.split('\\t')[0]]=line.split('\\t')[1]\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# write the pagerank of top 100 nodes at 10th iteration\n",
"with open(\"/data/hw9/WikiPR10_top100.txt\", \"w\") as f:\n",
" for key in iter10:\n",
" f.write(\"%s\\t%s\\n\" %(key, iter10[key]))"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3191491\t0.00033830984689\r\n",
"4624519\t0.00013778099189\r\n",
"6113490\t0.00044455933689\r\n",
"2437837\t0.00044654051689\r\n",
"13853369\t0.00012080343189\r\n",
"9997298\t0.00016063885189\r\n",
"6076759\t0.00042773928189\r\n",
"6416278\t0.00032926338189\r\n",
"5490435\t0.00017836041689\r\n",
"12038331\t0.00014129667689\r\n"
]
}
],
"source": [
"!head /data/hw9/WikiPR10_top100.txt"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# join the results at the 5th and 10th iteration by the node index\n",
"\n",
"with open(\"/data/hw9/WikiPRtop100merge.txt\", \"w\") as f:\n",
" for key in iter5:\n",
" f.write(\"%s\\t%3.6f\\t%3.6f\\n\" %(key, float(iter5[key]), float(iter10[key])))"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3191491\t0.000345\t0.000338\r\n",
"4624519\t0.000144\t0.000138\r\n",
"6113490\t0.000455\t0.000445\r\n",
"2437837\t0.000446\t0.000447\r\n",
"13853369\t0.000117\t0.000121\r\n",
"9997298\t0.000159\t0.000161\r\n",
"6076759\t0.000430\t0.000428\r\n",
"6416278\t0.000331\t0.000329\r\n",
"5490435\t0.000180\t0.000178\r\n",
"12038331\t0.000142\t0.000141\r\n"
]
}
],
"source": [
"!head /data/hw9/WikiPRtop100merge.txt"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[('0.000344826677401', '0.00033830984689'), ('0.000143999557401', '0.00013778099189'), ('0.000454596867401', '0.00044455933689'), ('0.000445627497401', '0.00044654051689'), ('0.000117397872401', '0.00012080343189')]\n"
]
}
],
"source": [
"# putting PageRanks of the same page into a tuple\n",
"def mergevalue(list1, lookup):\n",
" resultlist=[]\n",
" for key in list1:\n",
" resultlist.append((list1[key], lookup[key]))\n",
" return resultlist\n",
"\n",
"pairs100=mergevalue(iter5, iter10) \n",
"print pairs100[0:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Visualize results"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11803d50>]"
]
},
"execution_count": 97,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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SJG2V0rZHjIjPVJ+uAH4RETcDz284n5nfKCqUJElSIRYuhKYmuP12WLYMdtih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\nEREREanw/40oO+ZKUGLPAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x117f2390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"# Description: To compare the pagerank of each page at iteration 5 and 10, plot the PageRanks at 5th iteration \n",
"# on the x-axis and the PageRanks at 10th iteration on the y-axis. If the two PageRanks are similar, the point should\n",
"# lie on the line y=x, otherwise the poitn will lie far away from this line\n",
"\n",
"fig = plt.figure()\n",
"ax = plt.axes()\n",
"x = np.linspace(0, 10, 1000)\n",
"for item in pairs100:\n",
" ax.plot(item[0], item[1], \"o\")\n",
"plt.xlabel('Page Rank at 5th Iteration')\n",
"plt.ylabel('Page Rank at 10th Iteration') \n",
"fig = plt.gcf()\n",
"fig.set_size_inches(17, 7)\n",
"plt.plot(np.linspace(0, 0.0016, 50), np.linspace(0, 0.0016, 50), linestyle=\"dashed\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Most of the poitns lie very close to the line y=x, which indicatest that the PageRank of the top 100 pages at the 5th iteration stayed about the same compared to their PageRank at 10th iteration. This indicates that for these 100 pages their PageRank more or less converged at teh 5th iteration. "
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting GraphJoin.py\n"
]
}
],
"source": [
"%%writefile GraphJoin.py \n",
"#!/usr/bin/python\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from mrjob.util import log_to_stream\n",
"import numpy as np\n",
"from boto.s3.connection import S3Connection\n",
"from boto.s3.key import Key\n",
"\n",
"# Author : Xin Yao\n",
"# Description: This takes the result path from SSSP and inner join with the indices\n",
"# The path information is held in memory\n",
"# Since the indices are divided into different partitions, it's possible that each mapper can not join the all the \n",
"# nodes in the path with the documents name on their own \n",
"# so the partial results from each mapper is emmitted and the union is obtained in the reducer \n",
"# only a single reducer can be used \n",
"# but even, the job did not take more than a few minutes in local mode on the wikipedia data\n",
"\n",
"class Join(MRJob):\n",
" \n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" #log_to_stream(level='ERROR')\n",
" \n",
" def __init__(self, *args, **kargs):\n",
" super(Join, self).__init__(*args, **kargs)\n",
" self.Pagerank={}\n",
" \n",
" def configure_options(self):\n",
" super(Join, self).configure_options()\n",
" self.add_passthrough_option('--PRfile', dest=\"PRfile\",type='str', default=None)\n",
" \n",
" def mapper1_init(self):\n",
" \n",
" with open(self.options.PRfile, 'r') as f:\n",
" for line in f.readlines():\n",
" line=line.strip()\n",
" index=line.split('\\t')[0]\n",
" PR=\"\\t\".join(line.split('\\t')[1::])\n",
" self.Pagerank[index]=PR\n",
" \n",
" def mapper(self, _, line ):\n",
" line=line.strip()\n",
" inputlist=line.split('\\t')\n",
" name=inputlist[0]\n",
" index=inputlist[1]\n",
" if index in self.Pagerank:\n",
" yield \"*join\", \"%s\\t%s\" %(name, index)\n",
" \n",
" def reducer_init(self):\n",
" with open(self.options.PRfile, 'r') as f:\n",
" for line in f.readlines():\n",
" line=line.strip()\n",
" index=line.split('\\t')[0]\n",
" PR=\"\\t\".join(line.split('\\t')[1::])\n",
" self.Pagerank[index]=PR\n",
" \n",
" def reducer(self, key, items):\n",
" if key==\"*join\":\n",
" for inputline in items:\n",
" item=inputline.split('\\t')\n",
" name=item[0]\n",
" index=item[1]\n",
" self.Pagerank[name]=self.Pagerank[index]\n",
" del self.Pagerank[index]\n",
" \n",
" def reducer_final(self):\n",
" for name in self.Pagerank:\n",
" yield name, self.Pagerank[name]\n",
" \n",
" def steps(self):\n",
" JOBCONF2={'mapred.reduce.tasks': 1,\n",
" 'reduce.output.key.value.fields.spec': \"1:1-\"\n",
" }\n",
"\n",
" return[\n",
" MRStep(\n",
" #jobconf=JOBCONF2,\n",
" mapper_init=self.mapper1_init,\n",
" mapper=self.mapper,\n",
" reducer_init=self.reducer_init,\n",
" reducer=self.reducer,\n",
" reducer_final=self.reducer_final\n",
" )\n",
" ]\n",
" \n",
"if __name__ == '__main__':\n",
" Join.run()\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"download: s3://ucb-mids-mls-networks/wikipedia/indices.txt to ../../data/hw9/indices.txt\n"
]
}
],
"source": [
"!aws s3 cp s3://ucb-mids-mls-networks/wikipedia/indices.txt /data/hw9"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/GraphJoin.root.20160719.034152.856114\n",
"Running step 1 of 1...\n",
"Streaming final output from /tmp/GraphJoin.root.20160719.034152.856114/output...\n",
"Removing temp directory /tmp/GraphJoin.root.20160719.034152.856114...\n"
]
}
],
"source": [
"!python GraphJoin.py /data/hw9/indices.txt --file /data/hw9/WikiPRtop100merge.txt \\\n",
"--PRfile \"/data/hw9/WikiPRtop100merge.txt\" > /data/hw9/WikiPRtop100labeled.txt"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Canada\t0.000446\t0.000447\r\n",
"Allmusic\t0.000168\t0.000165\r\n",
"United States Census Bureau\t0.000150\t0.000148\r\n",
"Paris\t0.000159\t0.000161\r\n",
"Hangul\t0.000180\t0.000178\r\n",
"Romanize\t0.000151\t0.000149\r\n",
"Argentina\t0.000132\t0.000131\r\n",
"Rural Districts of Iran\t0.000206\t0.000203\r\n",
"Voivodeships of Poland\t0.000321\t0.000313\r\n",
"Spain\t0.000251\t0.000251\r\n"
]
}
],
"source": [
"!head /data/hw9/WikiPRtop100labeled.txt"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Article</th>\n",
" <th>Iter 5 PageRank</th>\n",
" <th>Iter 10 PageRank</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Article</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Canada</th>\n",
" <td>Canada</td>\n",
" <td>0.000446</td>\n",
" <td>0.000447</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Allmusic</th>\n",
" <td>Allmusic</td>\n",
" <td>0.000168</td>\n",
" <td>0.000165</td>\n",
" </tr>\n",
" <tr>\n",
" <th>United States Census Bureau</th>\n",
" <td>United States Census Bureau</td>\n",
" <td>0.000150</td>\n",
" <td>0.000148</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Paris</th>\n",
" <td>Paris</td>\n",
" <td>0.000159</td>\n",
" <td>0.000161</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Hangul</th>\n",
" <td>Hangul</td>\n",
" <td>0.000180</td>\n",
" <td>0.000178</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Article Iter 5 PageRank \\\n",
"Article \n",
"Canada Canada 0.000446 \n",
"Allmusic Allmusic 0.000168 \n",
"United States Census Bureau United States Census Bureau 0.000150 \n",
"Paris Paris 0.000159 \n",
"Hangul Hangul 0.000180 \n",
"\n",
" Iter 10 PageRank \n",
"Article \n",
"Canada 0.000447 \n",
"Allmusic 0.000165 \n",
"United States Census Bureau 0.000148 \n",
"Paris 0.000161 \n",
"Hangul 0.000178 "
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"Top100=pd.read_table(\"/data/hw9/WikiPRtop100labeled.txt\", header=None, names=[\"Article\", \"Iter 5 PageRank\", \\\n",
" \"Iter 10 PageRank\"])\n",
"Top100=Top100.set_index(Top100['Article'])\n",
"Top100.head()"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0xd746150>"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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NNR85MhWCCdn/mON4w+FRVenuWjhvq+6EAnW2GoH6gdkO67gd+BzZCPvN5rNN\nYXUCdY6UtQJ1Q98BAABgQrZ8oO5aXQAAAI4mW37ou6FcbBWGvh+Y7bCO24HPkY2w32w+2xRWZ+g7\nR4qh7wAAALBFCNThKDZ/aYjLQgAAYPoE6nAUGx7F0198zT+aBwAAuNlU7oEmUIeJ0QsOAABHxnxH\n15Hq7FoqUK+qM6pqb1VdUVXPWTD/+Kp6xZjmkqo6ZWbeOVX1/qq6rKoedgB5/lJV3bDRFYOtSi84\nAABsb+sG6lV1fJLzkzw8yf2SPKaq7j+X7OlJrunu+yR5QZIXjss+KMnZSe6d5BFJXlxVx62X57jc\nHbL/7UkBAADgqLZMj/qDk1ze3R/v7s8nuSjJWXNpzkpy4fj/a5M8pIbnHJyZ5KLuvqm7r05yeZLT\n18qzqo5J8r+SPPvgVg0AAAC2nmUC9Z1Jrpx5f9U4bWGaHh46eH2SExcse/U4ba08n57k97r72iQL\nnykHALCVTeVmRQBM07GHKN8NBdhV9eVJHpvkoZtbHQCA6bj5fiSz0/RPADBYJlC/KskpM+93jtNm\nXZnk5CTXjUPeT0jyiTHdyQuWPWaVPB+Q5O5J/mbM5zZV9Vfdfdqiiu3evXvlvyS7xhcAAABMy549\ne7Jnz56l0tYwUn2NBFW3TPLBJF+fIfh+W5KndvelM2melWRndz+zqs5O8uTufuR4U7jzk3xdkh1J\n3prktAyB+pp5jvne0N23W6Ve3d0Z4vn5daist15wuC27r+6fbpk0G89rqny3jw4+RzZiO+w3h3sd\nt8M2hY3ayu0lNt/hPF5WVbp74XCqdXvUu/vGqnpakjdlGNJ+YXdfWlXnJXlXd78+yYuSXFhVe5Pc\nkOQJ47LvrqrXJLksyRcyBOOfGyu1X56Lij/AdQUAAIAtbd0e9anSo85Wo0f9wPhuHx18jmzEdthv\n9KjDdGzl9hKbbyo96svc9R0AAAA21fwTMDz94mZ61OEw0aN+YHy3jw4+RzZiO+w3etRhOrZye2mr\nm+K216MOAAAA7EegDgAAABMiUAcAYNLmr2N1LStwtFv38WwAAHAkXXvtRzN/zei11y68rBPgqKBH\nHQAAACZEoA4AAAATIlAHALYkz98F4GglUAcAtqSbr1seXsN7AOY5sbn1uJkcAADAUWz+hoxuxjh9\netQBAABgQgTqAAAAE2O4+vYmUAeAidAoY9b8/mCfgO3FfTi2t+ru9VNNUFV1d6eqMnu9xTg3W3W9\nOHotu69tmFeTAAAgAElEQVTun26ZNBvPa6p8t48OPscDs5W/s5tpqx/jduw4dZ8G9Ukn3S3XXPOR\nfdIss46b+f3Z6t/FrV5/pm2qx5LNrNd2WMfNcjiPN1WV7l54wwA96tuMs/MAcGjpBQPgYLnr+zYz\nf8fHYZq7PgIAAEyFHnUAjhpGDR05tj0AbB6BOkAEGUeL+SHHhh0fPrY9AGwegTpANjfIEPQDAHAw\nXKMOsMncCwIAgIOhRx0AAAAmRKAOAAAAEyJQBwAAgAkRqAMAAMCECNSBdbmLOQAAHD4CdWBdno8M\nAMBWt5U6nzyeDQAAgKPeVnqErh51AAC2ja3UowZsXwJ1gAnToATYXC7nArYCgTrAhGlQ3sxJiwMz\nv71sKwDYOgTqAEeB7RDEOmlxYOa3l20FAFuHQJ2F9MTAobeZwbUgFoAV2+HkLRztqrvXTzVBVdXd\nnarK/J37kspWXa9DbdnttX862/Rgbea2P9yf45H4nh3uMjezvI1/Pvun28y8joTDvV2nuh2WtZnH\n3mXy2rHj1P1O6Jx00t1yzTUf2YTyFpe5mXlN9bdqs47jR2KbTpVtcWC2wzpupq18LDkSeW2mw12v\nqbUlqirdvfC28x7PBgDb1FZ6TA0AbCeGvgMARy1DgAHYigTqAMBRy/0bYPtyoo6tzNB3AADgqOPy\nHrYyPeoAAAAwIQJ1AAAAmJClAvWqOqOq9lbVFVX1nAXzj6+qV4xpLqmqU2bmnVNV76+qy6rqYevl\nWVW/M6b/QFX9VlUdf7ArCQCHyvw1kK5/ZCtzTS8s5rvB4bZuoD4GyucneXiS+yV5TFXdfy7Z05Nc\n0933SfKCJC8cl31QkrOT3DvJI5K8uKqOWyfPl3T3V3f3PTNcQ/8DB7mOALCPzQyu529W5kZlbGVu\nvgeLLfvdcPKWzbJMj/qDk1ze3R/v7s8nuSjJWXNpzkpy4fj/a5M8pIYnxZ+Z5KLuvqm7r05yeZLT\n18qzu988k+/bktx1Y6sGwEZsh14DwTUAh4LfFzbLMoH6ziRXzry/apy2ME13d5Lrk5y4YNmrx2nr\n5llVxyZ5cpLfX6KOxBk8YHPoUQMAOLIO1c3kNuO5B7+c5C3d/eebkNe24AwesBVthx58AIADscxz\n1K9KcsrM+53jtFlXJjk5yXXjkPcTknxiTHfygmWPWSvPqnpukjt391PXqtju3btX/kuya3wBsJV4\nzi0AsB3s2bMne/bsWSptDSPV10hQdcskH0zy9RmC77cleWp3XzqT5llJdnb3M6vq7CRP7u5HjjeT\nOz/J1yXZkeStSU7LEKgvzLOqvi/DkPdv7u4b16hXd3eG8wLz61BZb72ORvtvi/23w7Lba5m8lrVj\nx6n79O6fdNLdcs01H9lQXlvZZm77w/05Honv2eEuczPL2/jns3+6zcxrWYc7r2lsr43vW1s5r628\n3yxOd2jXcVmbVa9pbNONl7mZprqvTtV2WMdl2pdbue015bw20+Gu1+E+9i5Tn+5e2Dux7tD3MVh+\nWpI3JXlvklePAfV5VfVtY7IXJblrVe1N8uwkzxiXfXeS1yS5LMnFGYLxz62W55jX+Rmub39HVV1a\nVf9zQ2vNIbfscNXDPSR/M4fRGpILwAq/CTAdLvncPrbrsXfdHvWp0qO+v8N9NvBInFlcxlTPum/l\nbT+NHqlDW+Y0Puv90+lRP1x5TaOXQo/6geU11XXUo775prqvbqb5HuJk46MQp7qOm2k7tHunmtdm\nmuJxfMv0qLMx2/XMD7A9OMYBbC5P3ABmLXMzOTbAzZGAo5ljHADAoaNHHQBY0/wICqMnAFiLkXcH\nb9sE6nYW2L58/+HguGkTAAfCpRwHb9sE6nYW2L58/wEA1qZjY1q2TaAOh5JhoQMHeADgYGhLHDk6\nNqZFoL4BDiDMMyx04AAPrMeJTWAt2hIwEKhvgAPI5nPyA2B7cGKTrUC7BDjSBOozjsRBWc/CwMkP\nAGAqtEuAI02gPuNIHJT1LADAkefEORtxuDt59PTD9iFQB4AFNIi3FyfO2YhlOnk281iipx+2D4E6\nACywmQ3izWyoO4EAW8t2CK4dl2DzCdS3AAc/DiX7Fxx6m9lQ3w6NfmBrcVw6MFu97eVSocPj2CNd\nAdZ388Fvdlodmcpw1LF/AQAcPlu97TVf/61U961EjzoAAEubam/gVOsFh5L9/uglUGdLMdQGAPZ1\nuBvqUx3mPNV6waFkvz96CdTZUtyVFwD2paHOobSZnSQ6XNhuDuZEqkAd4AAYYgbAdrKZnSQ6XDhU\npto+O5gTqW4mB3AAtvoNYAAAjjZHY/tMjzoAAABMiEAdAAAAJkSgDhxWU72GCAC2E7/HMG0CdbYt\ndx49Mjbz7sQaGQDTtcwx2nH8yPG0ADg4h/r45WZybFvzN53Y6jec2I6OxhuHHEo7dpy6XyPspJPu\nlmuu+ciRqRBwVFvmGO04DmxVh/r4JVAH2CY0iAEAtgZD3wEAAGBCBOoAAAAwIQJ1AAAAmBCBOgAA\nAEyIQB0AAAAmRKAOAAAAEyJQBwAAgAkRqAMAAMCECNQBAABgQgTqAAAAMCECdQAAAJgQgToAAABM\niEAdAAAAJkSgDgAAABMiUAcAAIAJWSpQr6ozqmpvVV1RVc9ZMP/4qnrFmOaSqjplZt45VfX+qrqs\nqh62Xp5VdWpVvW1M/ztVdezyq7Nnk9LI6+jI63CXJy95yUte8tradZeXvOQlr8OZ1+EuT17Tz+tm\n6wbqVXV8kvOTPDzJ/ZI8pqruP5fs6Umu6e77JHlBkheOyz4oydlJ7p3kEUleXFXHrZPnLyX5me6+\nb5Jrx7yXtGeT0sjr6MjrcJcnL3nJS17y2tp1l5e85CWvw5nX4S5PXtPP62bL9Kg/OMnl3f3x7v58\nkouSnDWX5qwkF47/vzbJQ6qqkpyZ5KLuvqm7r05yeZLTV8uzqm6R5CHd/doxr5cl+bYDWiMAAADY\nwpYJ1HcmuXLm/VXjtIVpuruTXJ/kxAXLXj1OWy3PE5N8Ym76XZeoIwAAABwVaoir10hQ9Z1J/n13\n/+D4/juSPLS7nzaT5kNjmuvG9x9M8tAkz0vy5u5+5Tj9V5L8aYYTBPvlOab/k+6+5zh9R5I/XXk/\nV6+1Kw4AAAAT1t21aPoyN2q7KskpM+93jtNmXZnk5CTXjUPeT8jQM37VOH1+2WNWyfO6JF+2TllJ\nVl8hAAAA2MqWGfr+ziT3qqq7VNVxSR6f5OK5NBcneeL4/6OTvKO7b0ryhiSPr6pjq2pnknuN+S3K\n8w3d/YUkb6+qR415PXFBWQAAAHDUWnfoezI8Si3D3dwryYXd/dNVdV6Sd3X366vqlhluJnfPJDck\neUJ3f2Rc9pwkT0ryhSTP6u43rZbnOP3fJHl5ki9J8v4kT+ruz23eKgMAAMB0LRWoAwAAAIfHMkPf\nAdhEVbWtjr1VdUxVnXCk6wGwlY0jWNedBhwd9KiPquobF03v7j873HXZiKp6aIYb930xAOju3zoE\n5bwwyao7TXc/YwN53jbJZ7v7pqo6Lcm9k/xBd9+4gby+Jcm/6e6XVNWXJbldd//dgaarqlsk+S9J\nTunuc8d7LNylu995oHXaTFX1DUku7e7PVtWTknxNkv/d3X+7gbx+KMnLuvtTm1Cvv0jy60l+p7s/\ns07ar0xy9+5+Y1XdKslx3X3DwdbhUKuqn0vy6919xSbk9bdJXpnkgu7+q4PMa6l9taru1N3XH0xZ\nM3l9dZJfTXKn7r7n+P6x3X3eTJpXJPneDJc3vSvJ7ZL8cnc/fzPqsEq9fiTJi5N8NslLk/y7JP+j\nu99wiMrbkeSp2f/Y+z2HoryxzGW2/V2S/GySE7v7YVX1bzM8reVXD1W9llFVd8qwr85vrwP+3dgu\nquo+3b33SNfjUFlmf14yn1snuW13f2Ju+p2T3NDd/zK+v22S/5HhGPk9VXX3JF/d3a/bjPVZo353\nTvJVmbmJ82z7sqru393vnVvmEd198dy0S7v7getNW7JO787wu/3yzWgHbKaquuV8G3B22vh7/Nwk\nn0vyh0kekOSZ3f0b4/w1Twx39yc3WK9TM9zoevb49WdzaTaljbNs23gz2/9Lrt9Bt9nH3+pVdffP\nH0C1Z/P9kgzbopNc1d3/NDf/GRnaBp/N0Fb4d0nO6e43zqU7Psm3Z//t+vNz6e6R5NSxvI929wc3\nUu+1bPlAfbzL/Jdn34Pfx2bmPyPJb6wED1V1+wzXvb9oLp/Zg/Stkpye5N3d/c1z6dZsCI75rBXI\nPnImr2Ub2Osd4F+Z4Yv13gz3AhiTDI2fqtq7Tp3uu9q8eVX13WvN7+7fnEu/bmBZVZcmeUiSE5Nc\nkuFmg5/v7u+cy+s2SR6b/b84zxvn/1SS+yT5t919WlWdmOT3u/tr5/JZN11VvTTJvyT55rHxcLsk\ne7r7QeP8pbbpZv9YVNVl3X3fqnpgkpdk2Acf190PXZB2R5IfT/Jvs+++883j/J9M8h1JLs3wY/3G\nXuWAUFX3SvLs7H8AX8nrHkmenOHzeVuGAPTNC/L5oQz7/B26++7jj8JvdPeuBWnXPemyTEBSVd+e\n4UfkpkXrNpPuwu5+0mrTqur7xnU8NskFGU5KfHqtPNco6w5JvnPM718zbP9Xdvc/zqVb8zMc06y5\nr86k++sMx4gLkly82me9ZP3fkeQZSV7c3Q8Yp13e3feeSfOe7n7A+L2/X5JzMhxT7zuX15rf6wOs\n1/u6+35VdWaGkwTPzXAPlP0asUv8dqzbGBmPXX+U5N25+dib7n71XFlfkiGgv8dced8zk+abkpyb\nm79jNSTpr5jLa5lt/ydJfiXJj4/b4xZJ3tvd95lJs+6x6UAaU0vuq+9O8pYke5PcNJNmn9+NZaz1\n+7nG8Xllm+73m7fe7/EBtCXW/azHdEud5Kmqtya5ZZLfSPLbqx1zqupxSf79+PbPuvtVC9KseYw7\nUFX1oAX1/92Z+f+tu//33DL7TFtmf16yLr+Z5LWz5Y/Tz07yyO5+8vj+9zL8Rn1Xd9+7ht7od3b3\n/cb5/3GtcubWb6kT5+Pv3tMyHG/em+Rrk7x97rtxaZIndvf7x/ePTfKj3f014/sdSe6a5GVJnpBh\nX06G+zld0N1fueSmmq3XV2b4DXp8kr/M8NvwpvnfhvWC4jHNmm2EmXRLnUxd74TEzO/Lf0pyRpL/\nnmG/X/kc/y7DMWDRE6IWHVfXPRFfVb+Y5OwkV2TftvZsu/5A2jhrBvTLtI03s/2/zPotW6+ZtAvb\ncVV17mp1Ggvd70RdVZ2efY9x7xqn3zbJUzK0Z++U4QlileSkJP+Q4b5nv9bd/zjTRjgjw/F3d4bP\nfb699MdJPpP9f6vOGz/TH0lyZoYnk/39WN6XZ/iO/kGSX+jxXm2LVNWvdvdT1toGsxtjy76SPCbJ\n3yX5p/HvTUmumEvz3gXLvWeJvO+a5FULpr9v/HtmkldnuJP9pTPzH7rWay6vlyb55SQfGN/fLkND\ndjbND2W4qd6nMjyD/p8zPGt+Ns1frbMudxtfP5tkJUi9T5KfTPLTC9J/Z5KPZLgx4GdW/m7wM7ps\n/PvADAHhf03ylrk0l45/n5Hk2bPbeS7dnya5KMmPJnnWymtm/vszfFneMzNt0ee/brokl8/vK3P/\nL7VNx/3yw+PfL2Q4aFw//v93M+n2JrlstdeCbfXcJN8zO23Ber4lQ7DygXH/e0mSn5lLU0kenuQV\nSf5mXJevXJDXBzM0NE5P8qCV14J0t8hwoL96XOdzk5wwt+2Pn9uWiz7rn0ryupV9O8MPwjsWpPuT\nJI/Lzd/LWyTZO5fmZUn+dvys7rHGvnrpgnXZ77uVIRD56SQfzfAD8C1z8++5Uvfxs/9wkg+vUe6u\ncXvdkKGh9JUz85b5DNfcV+c+629N8jszn/VpC9J9U5I9Y5qVfffDc2neu6DM982luSLJcRm+sw9d\no15rfq8PZLvm5uPN/05y9hplLvPbcWmGAOnk8bN+VYaTMwf0WzKm+/0kPzHuh9+d5I0ZGvSzaT6c\n5BHjvn6nldeCvJbZ9u9bkOY9c2lmj03zrw+Pac4dXy9P8tdJfm58/VWG0TgHerz5y3W202rHwb2Z\nOQ6OaVf9/czNx+eFr1XKXvP3OEu2JZb5rGf2r5/JcPz6TyuvVer2VUmen+E7+fIk3zo3/xcynDD6\nnvH1xgwNxQM+xiX5xnGb/0uGk4hfyILf/yS/nSG4+80Mx60LMjR4Vy1v9ju67P68xj4x/9t4+Rr7\n1WXz/2f13/aVdfmDDO2uV4+vTyZ5/aJ8s0b7Zpz/oQwdQCvr+lVJXj2X5ivHPE7LEDz/eZI7zsz/\n7gzHyhvGvyuvNyT5zgVlLt2OyxBYPzLD79DHxv33y+a3z7iP/lqS22f/Y86ybYT12tA7xmU/kOGE\nwAPH179P8jfzn3eG48wZq30fl30l+b5xm/9Fkh9IcvsFaf42yS3XyWfZNs4PZTjB+7fj+1MznGDf\n7/uTNdrG2cT2/zLrt2y9xmlLteOW/Hyek+TyJM8bX3tnyn7z+PmdtGC5k5J8f5I/ntv/fjHJf1xt\nv8nccWpu3iuT/Ickxy6Yd2yGdtZF66zPft+NVdNudKeewmv8It8pNx9EvjHJS+bTzL2vJB9cIu9K\n8qHVPrys0xBcsv7rNrCz3AH+FRl6FNcr750Lpv3FgmkfTXLPTfqM1g0sk7wnw5notye51+x2XrS9\n1ijrsrkyb5Xk/RtJl+R9GRoxK2nuuKj8A9imv5rkYTPvvzXJr8y8X+pgmqEx/OwMDeUd4366d768\nufXcOzNtUbB7vwwHrQ8mOT9DY+Hn1lvPBfl8dZL/Nebzf5J8/VjX/Rq7ufk7e0zmvqPj9GVPuqwb\nkIzTvjTD2dN3jPvZUzKc2U2Gnt4bknw+Q4NmpVHzqcw1dsd94lFJfi/Dj+xzkrw2Q2/4Spq/TPIt\nGRqSd0vy/yV53lw+x2RoqLxq3Nd+NMPJwcfN7ovLfIbL7qtzy3xThkbZp5O8Nck3zMxbN2DM0EC8\n+0yZ35bkT+fSPHMs4w3jZ7kzyZ8f6Pf6ALfrb43lfSjJbTL0Ni3aH5b57VimkfQTSR6+RN0vn11+\n/Lz+fC7N25bcDsts+7eP67eS5gFZcFxa9jWWeZuZ97dZUOYy++qzMgSSX57khJXXzPy7rfVaZZuu\n+d0/gHVc7+TsUm2JZT7rjdR1zOc/jd+pD2T4DXjsOO+KjCMkx/fHZN/jyIEc4/ZmCBrfM5b5pCTP\nX1CfVdtRGYLE1435//7M64+TvPVA9ucs/9u43+/DonkZjtu3ninvlEXLZng08Ikz7++c4THCi44R\na544z/CEpJVte9z4/6K2yT0y/Pb9UWa+b3NpFp7MWZBuqXZckvtmONHzoSS/lOTBGY7ds8HzukFx\nlmgjjOnWbENnyRMSGdoal2dorxyX4Vjyrpn5D1zrtUb9Vj0Rn+T1SW69zvodSBtnzYA+S7SNs4nt\n/2XWb9l6zazjwnbcuK+t+lolr1vNvN+n3T6Ws3OJuv92hmPRX2X4HbvN/L48s3/9h2X26TXKunWS\nOy+YfufZdVnv9cVhWVvUP3X39TU8iz3d/WdV9Utzad5cw7WSvza+//4MvXD7qH2vvT4myf0zNAjn\nvbeq3pDhh+WccZjbfmaG3eyj9x1u84VxuF2Py9wxwwFn1me6+1+q6hZVdVx3/3VV3XMuzUlJPlRV\n70zyxWGZPTdcJcltq+pru/sdY3kPztBrMO+j3f2BReu1ATdU1bOT/OckDx2Hm86v43/PMPzk97r7\niqq6W5JF9wa4pKru1asPTXpVVb04yR2q6skZzkovGlK5TLoXZgjATqzhUYSPy9CjMW/Zbfo1PTPM\npbv/qKp+dub9R8fld3X36TPL7a3h+u8VTxhf39vd14zDM1+woLxkGH2RJP9QVY9Ick2GBnLGsv5b\nku/K0Mv/kgzByOfGz+iDGRrVK95QVU/NcICb3cc+Oeb1zgxD2X49yXO7e6XsP6+qr5/J561V9WNJ\nbj0O9X1qhh/geZ/v7q6qle/GrTL8qM37bA3Xva6ke0CGXqB9dPdnqur/Zjhw/nCGXv/nVNULe7hm\n+vlV9fzuPmdBGSvb6xcyXLP05iQ/1TOXqFTV7D55bHe/uaqOGT/Xnxi3z3Nn0vx1hiFjL+x9r/96\nZQ3Xm61Y8zMcLbWvjtvpiRka3tdmOKP/+xkaahdlOAmYJNf03HWRCzw1w3fmnlX10SSfyDDs7Iu6\n+xcyNABXXDW3bivW+16vWGa7PjlDQ+yvexiOekKGYYjzlvntqKr6mgxBx/etTJtL88NJfryqbsww\nLHRlaPWXzqX77MrfGq7BvS5DT/2sP6uqn87wWc5+xy6dS7do2z9+Ls2PZOhVvXtVvSVDMPLYuZW7\nR3d/sIbLaPYzV+7J2fd79bkF9V9mX70xwz7x3Nz8+9hJvuL/p+67w/YoqvbvO4GQ0BUCiBAIXbEg\nEHoVEUFQJHQQVBCkCIgogtJEqeKHgkqRjoJUQYrUSA8tlEDoTfkEQQVBCR8l5/fHfeZ9Zmdnd+d5\n8/LDnOt6rvfd3bOzs7uzM6fex6/5XK4vDdS4fpJ8Hflwz6b309qeU5EsgbJ3DQBXkNzAktzIWofJ\nT0Dj+vOQAreJmU0i+SHIyHah39eckOEN0Bo0MFZL5zint83sSZIjzOxdAOeQvAdS9mO6neTSZvZY\npo3boXDQeaEIjEBToRDdmFrnkj7WxldJfsLMKnIbyY9BholAh0Jz+MJUuPy6kOE2pbFm9lLUj5dJ\nLpbwBPlmewBrNcg3APAClZJ0BTSOXoFCZkHyPlTH6tz+91aSsHraztVUCmJXqlCnHEelorwKRZN8\nz3ppPXcm6/bVJB+C5oDdfF59J2muVUaIqFWGNqXBnEVyvCUpRAnfd1yG+qeZvUvyTSgqINBxDacC\net6fTnf697+M//4OGcH3IrmrmW3p9zWZ5A3JPcYYG6Uyzltm9paGDEABzKYyTqNszF6a7RwYOvm/\n5P5a+5VQmxx3b4a/jYgovcz/j+c4I3kFpLu10Y6QkeExlxHmgSLBUroDwOX+TWfXdnZjPJwEreeX\nJPvXgMbqVzv6quu4dj9DEskJkFfqeGiRegnA6ma2YsQzHPKIrOe7rgNwoi9AcVs7RpvToEn0T5Y8\nIG8vCIKv+oS1sJk9kPDNE22OBLAZZFk5OOLZGcCm0MA6DRKwj7IoX4/k5ZCSeyDkoXwFsnh9NuLJ\nCb8ws5uSPq0KhXSNhAbdfyAr8MSE72eQNy2dcC/x48MA7GVmx+eum7T1YUixnGhmt7hiuZ5lchJJ\nzmEtgBskp0CW/me8X7V8Qyof+bN+7BprAIgp4XMBaX3nuS59x85T+kxvhiz05/murQFsZGZrJXxT\n4vN9Mj3DzD4a8cR5TaMgBab23Pwe/+TP7ETv44/M7FI/fhgUqlgTjkl+JF7kKcNTShYMTySXsgJQ\nNP9+dkf07CGAsWkJ30GQB3Z9yGv5VSg/+OiEb1VIUV0SEgDHQF6meyKeMCEuAXlczzKzl/zZTbYo\nt48teBCUUecCS8BJ/Nhc5rmjJO8ws1V90bgKEliPi410JNeyOkDLKplxE97hkn6flXcY8ZWM1ccB\nnAONp+eTY/tDcyOgeQjoVhjDPEcz+3vmWBGgWcl37Xwlz7UU96Nk7VgPUnhvNrOjXRj5jpntmd5r\nF5HcBfr2V4FyjUcAONTMfpH0KSWzeo7nWFOO38CzD/sSvpkhIwwhb8dbyfFTzGyXkuuS/CEUSRLG\n3aZQPvAhEU/rfOM8TwNYKTdekr6t5W0sBSkjwyHjSiwk5dbPI23wIEqt7fUhS3S+a+d7HYr4aDXy\nUIaW06BUvKnJsS+b2Tk+Nx0OeawJKZ8HW5RD7PzjoRzk1317Tmg9jt/RLX7+uZBX8UUAu5jZR5K2\n1oFkhBfQ/t2WrleNc4kfb10bqfzV30HRa0EJWAEyqGxjZndGbc0HhVIT8vD/LXO9U6Eopwt81xYA\n/mpmX494iuWb6Jz1IYPxH11RW7yJFwCsnu8+AZqvUlyM4/x4yLFfGy1ynPMuZmZPt10/4h2NnlI8\nKxQa/kJ0vFVGiPhKZehO7BLKyJhiQQz2+48N8adZYog3s2XZgNGUyOylMs4J0LezA5QysCuA/zWz\n2EESeGuycZPcH/Wpb/m/5P66+pUcz8lxV5jZMU3ntLT1fWhOjteg31kETkvyTMgbX5NVIp5hkLNi\njJkd7t/wh2KZ0fmegda8yWZ5RZkdGA9swdqg40113/mMr6jPBuVRzQQN9lEQ2MqQIBsn1+rH+9DU\nxl1WtQgXCdgRb2WC7+sGqu2MVpcbF8QzMrvNqsBHt5vZaoPtQ3K9tSCr1AgzG0OBkuxtCdCCC8q5\njj2X8M2N6sSeBWzr4vPn9OGEJ/ueC57pvFCo3pqQFfRWAAdZHaG2dTJlH0AlXcQhBBaigG6OgpSy\njVwpW93MTu+3rajNUqNLl0JyFrTw1iy+JNczB71jB+APyZkga2yXEjgOCtMaDeDH0Df7EzO7PeIZ\nSuTeVaHF5N++PTuAjyUL8DAAx+aEgIgnp7AFShW3TvRuFgCaOV/pd13yXEuB9YZs7WAH2OdQU8nY\nYSHwWZ/XXRXyBBiAWzPjq9N4S/JqAJtaBzowBYD0JchbvCKkDH3UEm9wyfpJtoMGNrQHKKexcT3+\nbyOSC0NzFqB56/kMz/1mtlyy7z5zEDffXgSKuJkViqoaBeBXZvZEct6TkCErBVt6LuLpXK9KFDLn\nK1E0xkIKTxCAJ0MpZs9EPLk5diqU//x2xEfIoD4w5iHFoCY0F8gSrXO0fz8PpHNjjtqEfz+ek9+i\nrlXkuFJj6g4NjfWtFLM/Y2qbQeJIaLx/FDLcbgjNS5tnrtmp0LPQED9U1KDQnxiPrxLZ2Mf8C9ar\najAKytV+tuG6XbLqLBBwKqCUh9pcXSqzO2+RHFdC0RoE6F3fkRx/FDIUPwfNDzln3qnQfLWWywhz\nQnDeh6MAACAASURBVKk2qYwwwczWLezXMChl51fQWD0LSu24Pp1vo3Nqc3Fj+zOyot5GJC8wsy3Z\ngHiYWjKocPJjUEesDR7DYu+D88eLwTBI2PiWmS0d8ZwGhb7eH+071MwOTdoaAVlG44UgRifu9D44\n31CiK/+Pt3ER9EGEtib58abQw8AXe0bug8JALrce6uvk3KLVJnS5UHCw92caeh9patHt5CN5NBTO\n9kR0H7n33NczdYXduhSCpsmU8iosB+UWhWf1gDnSqW9/18yOYUMpPeuhgabC/XAol2qpTH9GQGG+\nAXHzJshy+ZYfvx6auPePlLL7rId+31flAV98XjT3IKWLD/tA5i0lko9B+foTzWw5kktCES7j/XiR\nEthxjZUgtNT9oByoQLMB2NHMlkn4O5Gh0wnfv5F7M8rcrWa2BoaAWIDezR666n3RWK0oBRFvUVnF\ngn49ZEJyjq9ZvCAmbU1A/vuJDRZdxp3tzexcNqCnWxU1nZBymgqUoarFMhDw0jEQ9kOg2SDv6ZJR\nW50KWbT/KciIc1K07woz2zjh61qHOo23JC/1e5iAltDKMDfRPVm+7x6rRjzkUOvfNLM3Ip4t4IoI\nJPQvAs1xyzb0bxX0FLPbzGxiqSzRz7uOrtcWwVOMXN+H8vlweu8kp1gUsVVKJfNJ4XrVqpBl2mxV\nNAr6PRHy6D4IPcuPQTn+owHsYWaX99FWLEvEckIqc3TO0RQa/TfM7MWOa54EyY2tqUIkVzez29r2\nsdyYekK0ORKKKplkZpuT/LSZ3di0Jqdrcek6ym6DxGMQwOgkX6/nhQAuP5fw9aPQL4qW0mRdeoLz\nfAnyHqfVO1J5vKQiQqdsTCGwjzOP7KEcChPDXNk0H0V9j9egDaAooMe930tAcsl18Tn9yOxDRSxz\nSHQa/UtlBMo7PxaqchCvVWl5tpCatBFkbPkNgNUgr/1rkAE7l47zS0siaptohsxRL1QC9/bNjZv4\nEjoHAoYK4S87IMo1Minpw6AJ7fZ8ExWKF5kQSj8+4dkAwIokj7Oede8LUO4HAIDkflDY+wvoCcSG\nnsUYEFJtzfuQ6dOVyCyI0bWKFDynMKjjfgzk/ZjZHN7m4QD+gmrI90Lppc3sL2Sa/lnrX1boggQ/\nQNb9jxQs4CV84yHFoStyofWZRn1fHgolnM23/w2VYrkv4aso/uGZRIp/SV5TCFm/BxkieQA0pkaR\nDLl7hHLOzmy4hdOh/LSQc7wN5N3YzrdHm9lvqXw9mMLj4ucRvsM9/DrxeBieud7FUB5RoLcho1AQ\n1Ddp6CegcRiH9xUZstCNB7FymOD9Hl/3518hyrq8H+rK9aeh9z8vNPeOjk6bivr8AEiwuA7AtWge\nX5XnZ2ZGz71OaLIrSpegalxLBam4fM6vofeQls8xM2sVAFCIH8CoXKJfbxh6ocMgebyZ7cOG0pdW\nzcXL5RkPrHNBucisITlhar/o/5HQHJuW+NsTPePOunTjTnQ85F/mcCtSOh16l+tCz2FzqOxNoKWh\n72huVMf/VPRy6APNEm+4YjCq4bpvA1iXCiXe1ee8Dyfnx+tQyA1M16E7qbSprPHW6ff+66L/uMA5\nmTKavojesww0CfrGXvH+zA3gb1T+704uwP0QmjOuN5VyWgta22tE8sfQcw2hlSf7mCuVJfp5141G\nHvRyZ0tlF0DgnVnlk2SsfD5I8lhIOQOEbj3Z+9OXc8PbOhdaA7Oh1Shbr0Zbgeeqa22k8AAOgHLc\nfwphCawFyR9fi+S2vwD4inm9Y8qL/EPoe7sSChUHyW0grI8wh+XmiFKZo2SOngvA4yTvQPX7SRXg\ntQB8jQrNbUw5gFKlUgPOiRCwZKB5zOwClwnCup3mnsPMvhlvu3L9O99cG8JqyK3JlbXYKbeO5mSA\nLuySf5lKZ9KVtn9Aee8pbYaeQv/VoNCnTJTzaTMkpclQzb1u1ROcjvdjjSHTTjtCXteYdkr2lcjG\nwy1KvzGzdyijaqCi+cjpWABrmtmTAEClZVyK6jxf2q/Ob4h9pNFCUT2xMv0f9OY9QA0/x4zRP2nn\nXb9ukBHmQl4XfsZ/I5DHRwoOizaMh2MAXEYym45TcM8DNzbD/iCr1S7+Iub0mz8s4ZkdwDD/fyno\nQ6yVH0APifChaF8OJfHuoei7tzUJmpz/ACnbM6GOpPksMiV60nb878PRvloZHHQjQW/if3fM/QZ5\nj7l+3JNsXwFZoCZBC9qeUP5jel4rUjOk1JSUlujkg4TN1ude8kzje4ZCbcL2mkhK8fn+CWgvQXcC\nJDA/Cgn05yNBaO/j3dSQfPu5z+RbmQihroax+MmG76cUJT9X6iOHKjq2ax/KUYwvh+aSI6HF+TIo\n32igTyirBNBZpgbAYoXPvaSU5NVQCN3M/tsTCjFL+c7I/E7P8MXlcy5BUj7Hj7WidzvPqj7u/wV5\n35+BLP/p9VoR/sOzQ1nJy52h+eR5AIdBc8YOg/k+Gp71Hcl2J5ozZHjYp6DtUBYsPP9RSMr1hOda\n0NaJ0Nywnv/Ohyz4Od4wnr8LlSYak3nfz6J7HZqQ+d2Y4ZsdCmNva2sRyDjyQSjN4acAlkx4TkGE\nyuv3eTKk8IZneI//jeeqLDo4FD01ItoeAeXRxv3ulCX6GEudFV36aOtCRKUnIaPO7yCQvkei/bND\nisBDPmZ/CmB2P/ah6NnXfplrds4nKFivIKPBsgX32LU23gXJg/tByPhb+PNdH9X5JDdnT/a/cRm3\n59CBmo5ymaNzjkbvW638Gr6NxvcDzbvfhgwS+0a/g1CvXDCo6hB+D08NcqyWrqNTIMPuY8iUaPRx\nMweEUP8ktL6fk2nnrui6s0NrzRMZvqe73iUK9AQAN3S00VQR4QbUKyJ0ysYQoORG0fbGqFcUKV2D\nHi7cVyqzl3xDpdVOatWN0n0oKAcHRShe5t/HQdBc+NWW62bLpPqxTjkOKrt3FDRXXAWV5KzJrW2/\nGdKjHtGGFoXCATiVQic9JNp3M4BVKfCQ66DJfAvUrRkBpOVZkrujh1ia0k0kA5CONXWsIdxkKqSc\nBS8JTXkvm5A8FALimSs550mofmcblXgfgA4LpXnuiLUAoQRyD01jmGZEw0huDQkSBoFBpF7InSDL\n2OKQVfR61D1EQDdS8w8A3EWFtrUhVpbwHQ09z8loR9IsRayexaIQKhPwTM7r2eVd2Ada8J+AFuNr\nIKF8gJo8jxF91+RNuJCZkEnL5+EbyUWsh8C7SHKN/SCv72IUYugSqCNRA+Uo+a+R3Mjci0tyY6hc\nS0oXo+41SPcVoRhH7/YARngQEUtpJYDXzOxXmf3w6JlvAziOjoSa9CH1npQgQ38VElqOgjy+N0LG\ntbTtIoRRYABJdQNI8HmYddN5K3q30yRIaBzAD4jajqkV4d/M7vW/A+A47ikfm45VkxX9LvTylre2\nhjxjdodyx6HVwyCDywJJM41ozlGb00huCXla2ihEt7xDpTy8Ai3yKT3o60s6934t4tkbAj77lm9f\nh2SeiIh+/jFUGOW1kIIcU+c61DFv6ULk5tA4HQ5grEefHGNmn0/aCqGKbwL4fkNzaSWNG0j+xMx2\njSJdXqfSZm4neR4U/VTzGDo9B0UihKiPWSADRaBWWYL1qgEVyqxDJRVdSiOCPuJzerjWYyQ/amZP\nk3w72v9vAHuTnNMcvyA69oL/rYGLNtxPyXzSuV6h3EPctTaOMs+tJvkNM7vQ91/HauTT0yRPhGQS\nQJ70Z30+iCN+SqrflMocnXO0j9/50cMZmGgZkDuT17CWAhjRCEghnQnVtXUqZFyKKVcdYsuEJ5Up\nhkHG28sSnqJ8d5Svoxtm9g2QmX3D//0fkldC5a5ylZom+Rx9JhS58jrkWEhpCuqyaUolesKBJP8I\nGadzIdP9VEQokY2/DuB8qpIRoIiSin7Txxr0gLcTIh63Qr76Va5fOeT0km+oJBILUNWY3dGrurEr\ngL8mPJvCHQvexksuTwyQmZ1M8m70ZIQdg4wRExUB+BtIlyIVhZdGwW6aiSqo6HmmdM3vNd9+N83Q\nOeouVByDqhL4Xavm/YRct70gZelYJjlSzpcCFY2ELL+3J3wBqfUdSIhoyj/5LRRyF4ATPg9ZBMcC\n+IOZHUbyMKuj5n7LqjmQp0EL9FVoyJNwpSko523gL6XoygtAwlGahxP36wxkwjTNbKekrYBWvRr0\njm6HQl0qfSshdiA1+8d3C1ryZkv5/FmdlOFJkTRLn2mYuMMEuA2Adcxsg4SvNf+MZXlNa/u/m0Hj\nOZ50XwYwm/WBt+BtbgSF5j7q97gkFF56dcQzC5QSQci6bVYHditFyV8G8r7M43wvAdjWeuGK/eTr\ntqIYB6GV+ZxXWAQMxDLwqkOhhbhWpobkSmZ2FxWelbvWDUlbRcjQJUQBqO2KdgUPJM+GhIjFIQ8L\noZy+GHCqE72bhYB5LESGpSonbAjNb/dC73Gime0d8XTmsfn+bEqRVfN+n0EvXG8aZIH/oZnlSnKB\nLWCf7MD0cJ5DIA/nJtAc9y6Ean1g0tblkHdoWyhkd1uopvXeGASR3MQigB+SY6DQ4BhduWQd6hTU\nqRJPq0ORAiE/sIZ+y4I8T/+uL0NV4doUirS41xTqPhskOM2MDtBAKkd4HKSEGzQe70LP8LJGmyzB\nBsTk6Fml61BnRRfn6wTW87b+nDyLRaF0mtujNXJtKEyzDZyqJOQ7yAA5Y2OMn7FCKgST3NjMroi2\nF2l4XimYZNfaODC3pPNMcmxWyIAQyo/dDn1vU6G1MSDit1a/cZ4imaOESG4HhR5PgJ752gD2M7Pz\nEr4i3AW6YZ1egahhzBNaCyrGVEsAxFhFGJ8G4HmrV5koynd33iIQ5ZxBwnqYREWgdEl7S6FBoSd5\nMRQJ2FiarERPIHktgH+jPiYOa+rXYIkyQI03swupMG80rcmFa9BIyLgbsCduAXC8OVBdxNeJf+D7\nSr6hIjnU9ZKToNSgYOza3SJMh7CWRHrfSChy46NJWx9AHSg6zSO/B8C+1sMMWdOfxQoRT6eel7m3\ncO6hluCRNfLajK2odyqBVB7MLgB+DmBnk3eoERafHeUG+ujbBCgcJQbDuhJ6kQ+ZWWtJjqidQ3L7\nwwDwD/UsK0Dq7mNBvAkqY7UflMP2ZQD/MLP9I55HTEAgATBqFICrrQ/0cTbkwkf9SgGGckLXudar\n5V0BG2q5bicfyYlmtkobj/OVPtN5oLCceAL8frp4din+DYpOdjzn7qH0vnLk7ziAu0yOJ2+Sp1q1\nbM2sUNTJ+sgQCwGBmhYfkl+EhPIvwHMKnaZCyLyx97XVkEUHzkoUs1hADYCSPwdwvnVgVLClTI3f\nzzyW1B52peYfXc+j4XqdgHPOV6TgsaB8DlvQu70/H4YMI9sCA1702SDFc4nMOSXlEsPiuwsUpntY\nOvZZDqz3LBRSP+gKIT73Tk4F5AbeYqOY888GlbGqIQ2zB4YT5t7hUAm51SOedaHIshQYabG0Pedv\nRa7vWoecp1NQD++HVSCfGpgZVU+7Nc+T8mz/CFWF6yDI8z/GenmWC0FeSoPCemto6M7XqmhDyl2x\nLNEPsd3IUwKsV6p8loBTPQfgc9ZdgzvG1BgJzccvJIrNJCj15CHf3hpyRqzMPgykfm7X2vgGFPlB\nyMj4ZDgVClHNRRm23d8Z+W5VDBGtsgT7wP0h+TBk2Pq7b88L4KZ0fiH5CCRHVHAXzGznhK/iEYQ8\nyRWPIMnTk/uZDRobWUNyG7EDPHQQ77vVIME+wF193MUgkedneLLfv7nRxef7o8zsux3PoWhOYEuk\nTJ/jplRW7WsN6mgrJ4fWwEpLvqGhJBaU9aUwcb4K4ClE0YBWL5VcA8fLyBuD1vOYGMjbaIYOfXdB\n+3MdbPtB4Gy/94V1EVTBIQAMfDSnQ2FDXeUGSsrxLIRqGNXbkLA7lQpvAgsAjazDCmcKaVmYZAVQ\nooH3ORdcm0KmAn3AzE4juY8rPDdRoV0xFYVpdigRWbCzFjrYZCz4P3j4CxXqHwwI11C1cFNwmzRk\ns4Tvdgpc6Aq01JIufaauEOzqY2dai4KQDfeivBzbAhjrCleg2aAc4BzNw2q4+hjISxLa3BKaxP7j\nE9w4AIeb2d0RTxO6+sIkY8voyyRPMLNvUqVqrkAGmI6yZP4Yjh5PGYUOMrNXEr5W4CAzuwwC6VjV\nkhIdGVoCwEv+fmthtObo1mY2tqOdewH8gFKqL4WU9toY7mjnZGhxfizZvwCkdGwBAOyvHGQJ4Bwg\nYfULJL9gZmdRQFC1udAEKPQygI8xA5bn9CaUGjIBde/DBpCnYyHIQxxoKqRI5e7nD+hZpZtoZv9+\nxkMhp0BdiCkF1usM5W74Pn5kvZC2aSQfJ7mgmaUheCntZEm9YpIpMvQoKGR9QKAk+TNLamdDIH+A\nwPo+CgmxCyc8p0HAja0gl37dLlCzUm9QCTDVFJLbAhhOVXbYHcDdaUMQWnku5HKAzOwlSHHOUVDS\n94BSXEJ98eNJHmGZ1BT/JhpLE5F8HmWyRElEWsXIYwmqckKdqW0mpPsjGs6PHQ8lIFAl4aows4vj\nbcq7lD6PzQFc5O98TcjAHiIGfgvl096LnmF0oHlU02iAjlBoCDCsk1iA3O3bJaH9XbJEK7Br2jWL\nDLVm9nfmX1RXCmCgUyEU+dgj+GsohSfQ/5L8pZnt7mvzleiFFvc6VhZl0QUemr7vgeaRf99dQJCl\n4K6nA1gQPfC7HUiub0n0p3VEQfh8v3obj9PVJD9jZtd38LWBQPczbv5E8luoe8or65u1pI2wvLLF\nqpBjdDSr6b2zQca69LzOb8jHeFu1k2Kjhaku+ibQuFsBqmaSyhVbAljUOkqEQt/GAahGwb6Q8LTp\nea+hhUqVdGAGV9RZEMppCiW9Idp+DgI+SOlnUHjs5c73sA/K9JqdQo3TBVDuUlCqNoFygkdF12hE\nY2R/SMd/BjDRrxV/qGkZgS7U9EBBMPw7yQ0hweBDCc9VlAXzOChc6l0opDmlRiUinRjZHc2wPnpK\neaCNo33b+t9YGcstACV8wTK4WsKThuMUPVOf4E+HozGTfBMCsKgomS2Kfz95TYH2g8bFY8BAuPo3\nouM/cMF6Lb+vn0BK5MoRT0Bync+fxQ3e1rrep0u83weS/CmV+zcOCge7INOn30D5YV/07e2gBTwV\nworQ9AH8i+StkJLwEVdctkgUix0A/IrkP6FIhpuhUO7UOHCOH7vFonzPQD5ez6I8AuMBHE1yjHmY\nPcvK1CxlZjXLtpndxGoJnH0hJSRXoigdh7Qo2qWFShQ8kDweWjjb0G8b0buj5zQ+FeaT6xSXcHQ6\nAsLxuMnM7nZF6emEpySPDVAKxM0kG0O5kf8+TkD1+5gHwGNUXnw896ZYFhehjqWQ7rsA+sbDO98K\nEuJS9O9f+9x7MDS3jkAVlwVQacOrUUZdyPVB+TwQ9bU2HoclKP9fhwRwQuvgNajOSYG68jxL+/Qt\nKPXhVT9nbmhOqSnqzJQmIrljUKL7kCV+B0WkfQZRRFrM0KeRZ3vIALU7FBG0MBKE7VLlE/o+VgNg\nVMTDbqh/Q/dR+fyN4aoNtBSU4zxAphz5raG54s8APhsMT30YSENbTWvjwPF0nxv2XrWoRB3KkLuL\n5Et0yBJm9gdXHpe1Dk8sgAku7wWFcksoDD6lgLtwG9txFzpxcczsIJLHUGkFK0Ae49ycfRS6oyxa\n8937fd/oNkjkKnzkjLKrW7Us8plQCl+FCr+hB9ldOWV3AN8h2ZWu1oid0+e4CVhAcQRqTe5l4iSB\n1vMfuBxUWtmiH/wDuJxxCtrls65qJ8VGC8r4e31QgkmOIrmoVWvKPwBgVkRzWwNtB8kcV/r2zeh9\n74Ha9LxHvA/rAvgmNK7C/ZxoZn/qup8Bsj6Q5/7bftBCcjgUwrAjNEn8LOGZAOUyVH6ZtgKaY4w8\nnEMZLEZqhcLQvuO/1Rt4RkBWmTHh5/v7QTo+JPfLXKsVNT3i2wT6CJcHcBsk2Hyp5T3MBmCuhmMl\nqNVrQR6QP/v2sgBOiY7vBuV9vAEZBcLvyaZn//9xDJY+00cArBZtrwqFHad8W0Chff/xv9OQQd3s\no38jIcV5RSg3Kzfmj4Tyv4EE7TnivRrKPQ3boyEjzBei3xcho8HJYV+mnRxyew7hvRRNfyKErn5f\n17mQVX0vSGB8J3N8XfSUn6chULq9M3wrQcrUk1AeUth/mP89I/M7vele255D4TM4HMAGBXyhQsb6\nECryy1COV8r3FKYDzTpqh9DifaA/14OhqJhc/1urd/RxzQUgpeA1qGzKJQAWyPB1zpkl3wc65mdI\nyB/vz3Sz6PdlJMjDuXHbsK+k0sFR/lsVmseXB7B8wzMrQa6/CQILesTv8dcAjk54OlH+ISEtvX5u\n37X+7g5reT8lfboFKl8UtmdCgqwcHXsQwBLR9uKookyXyhIPhucZ7ZuY4bsZ8nbfgAj9OcOXm4P2\nTrbvgVDCH4SMxQdBeArpefND89q/oO/jIgikLeZpnL8Svteh7+x1KCf3WfS+k8mortUvoofeHZ7P\n8m2/3DhBy9oIKSC3+rj5FITm/CJkJNk08113VfhplS+hCMHV0vMaxtatBTyE5oWT/bc9ZIRN+WaD\nFJtZoLlyL2RQqSEg1AOgSMdF/f9r/Fg8F42H1u1Twr7cWC3o/yyQorwCJG+MQL7C0ngAc0TbcyIj\nX0Lf2yh/FudBzrR7ouNfR0GFD3+PC0XbC0FRMSlf5zeEwm+jcEzcAs1H50Pgxd9CHZW/c9z0cb2r\noDV4Mf8dBKWrDqatRQr5OuUzlFc7GZnZN2+yPQn1+T6tMrWij5krobniEgCXTMdzXQ3S8fZDoudB\nIfBPQN74pSF5YFtoLtyo9Bozeo56Sa5eHOYzUAvXEisVySsg60nwCO4GYH0z+2LCd7eZjfMQkeXN\n7G1mcuyctwtVuATQqBM8rJTo+VThufm+Sk5nQRsPQMr7bRBIzTMd/IdDk00jajU78uaoOocfgATm\nGD1xqgnVscSTGV9vBJTPFyyLNwH4uane6/Zmdi7zqP2wepRC0TMleZeZrZTsu9PMVk72teafsbwm\neGhvbdTTDs72Y1dCwtUG0OT1HyifN5fv/qiZLZPuQz5sNbqUVWoWUzmLe5hHEpBcBSobleY7tQIH\nRXy5nNcKWCTJ7aF3/XEAf4eEuVssEzLvc8g4SGn/BjTGlvFjx0Dzx1PQ4vp7c09dKbkH92irgxKu\nBeBAM6ul8rS9Qz9eBDhHcmz6vTbsuwJSntKQ6+IQOec9A2WAk7U8z4Z9x0GCxtuQEPopKN/1zLQf\nQ0H9fB8tbfSDpXA2NObv9u0VAXzTzHZM2uwE6WN/QJGdoGbsgfTE83IlN5IKG5+GFmCqhr7n5svO\nPM+2PkXz93LQd38ZNF6/ACnQX8m0N5ADntvXhyxxpykHewLkoXsRmisWSfjWzt1XZm7oxCWJ5sF4\nHaqtOV3E/uoat7WzSNtxk3c8N0YjlhqYVNfa+CAkLM8FKZ0bmtlECnj04ug93mFmq/o8dxU8isWS\n6INC+fJuMxtX8Dx+BRkRa55YP7a/JSj800vs4eKE/gZcnH8ynzscdauGb1ICClYKHpr73nP5zbNB\nKVYzoQEIki2gdOxFo84Frel3+fbK0Dq0Tq5fg/2G2F+6WvhG/gZ5d7Mg0G3jJuKpyFgRz9nxdm5O\nzchKpUCSJdFMpfJZmC/vhRTbVwA8ZmaLpv2HQIBDxaDxUJndpZruJ3ffFBbEaaiD/d3gx1urJlkS\nLUdyJchBZ9D8EKeO/gnArlbHJFoKckau03SdmGbo0HcUhHJaHXb/NpK5nNbSEmGd5XiAmhL+LjCQ\nhxN/KHtCtWHbAI12hCyJaV9/1u+AQmHIlA+iEyAPiUGh/XuZ2eOQQLcaNDke4pPpHegp7ncmze0D\n4PtsDwNqzZszASr9i+QPoJDO/yO5DoDlSZ4FfSQ3IgkHDKfDw7MjOh0Kyfwf394GsoxuB02aQL5k\nWI5Kw9BuJ/lLKFTGIKXltjCpR5N4V7hXW15ThUheAFmP70c1hDlM4FtDGA/Hm0DDFoAEnRzd4kpm\nCGffAlJ2v+7C3R5mdkLDuTF9A8DZ7JXMmIpq3lmg0pI9r5BcHL3wt41Rzz0+HlKuTwIwwaphUANE\nlZUL4/kWyBv4kh8j5D1a1boB8OaBcrRT5XovKDzwKgqMLcxNK0Dv4fNIqOAdwlpSaBJqLWXHXg7Y\n/0H5sDn029IQOQBYxXqAk4dRho5cOHZJCUdAoEHf9gX6Keg7uBkRFgLLke1LBI3G74PNYfuV+c36\nw1IYB6Wq/MW3x0Bh9cEosiUUbTQXq0bJ2ZDMV1ZQKi3iDetEU1lCoCwd6g4XygfWXMowt7yfsxGA\nDyfzWRPAV0meZ1ufwvN4yn+BLkfzmtlamqgPWeJHLiPsCxlVR0LrYIVShTwl9odLUlRelh3GLiso\n41SikFgPFyVbhQHKgy8eo06dudlmdq1f54dBoPe+xmvyXj5P7AmFAo+CvNcplaQK3cSCcr3QGHgV\n1ZSlIJs8DeBekoeY2W+bGsjMOSnoaWqsXwoC9XwXmk/XgFKHPmHlpToDzQkpzXFFAgNwCXvgoaOo\ndJcYPDTnQMiFp8+S7jCzoJi+iyRvnlWMhyYsi5807G+ixm+IZcDH/aSrwcpKULaNm0DjEv71IM9y\nRVGH8KQG1iHKSZKmFZakOAC99J710ZDe41Qin5Wm0W4H4HRXfheEjAmp4bmkrO+/LXG4JRTGTVPV\npAEiuT907xdD4/50kmeb2bHOMleqpAOAmT1OOSCLaEb3qO8CPcRVIGFtBIBDzewXEU+MMBlq4Z5k\nUZ4MB2lFZjtS67PoQBUmeT3kta+9hGiRXgNSGgLNCoUTrckGi3ygVBBggYXS+e6HPAGxUrZ/agV1\n3nkhgXYfAGPNbHjK00Usj2Z4ABIsloSApy6DBNdfW3f+XNzOgMU03UdyTzNrqjeca6v0mRZ5h1gD\n1gAAIABJREFUD9hdgq4TATi65uOxtbGh/61RHxEfofccgK5uhTyCYQK+3cxWS89rue5ov9bLDcez\nHhmro+kvBRleVoCe1ctQ7ewnE75lIeV/DWj8PGZJpQSqfMkKkHJ6G6QE3mE9RM+i6BPKMnwTGkr2\nUHmy26NntJsMVS94JWmq6B06XyPAJQtL2bGgvBTJay0pH9XSp1JLeVEJx+gb/TWAi8zsj0w8MSxH\ntu+sbOF8Rd9HwbPojAZoGvMRLYdy73wrQE/EV4RcTwH0/AkCZgzK54/M7FIWoPyT/KT3/4f+HOK+\nT0jnARZEibT1KeLZwnr1tBv3+f7W0kRDJUuUGnl8PIxFJpIMCt8ekDlYXl72PpM3ejyEC/JtyAsU\ne7hayziRPMUKy3umc6aPy1oVhhIqXRvT/3PbhdcrkS/DOH0Xei/pOzzazPZvGnNROx+GgDfnhfAT\n4nWjWLZJ2nwaMqw+lLT3XMRzDmRkf82354KiC1vXguQ6O0KG6RVRzSOeCuAcq5eXOw9ybp3ku74B\npXxu5cfD9xHmkfCtpM/2Uu97K8ZDeAcF+9JvaBSAn5jZ7YVr4yqWlAFt6E82Gi1qK/b+FpVBS47P\nAa0HGyX7V4LWvFAa9w0AX7YIEJfkzZagnzdcozPCyvfl5LOtzOypWqMYkKez1U78+KYQxsTrANbK\nyHkfgb7ZAJr8MqKyvs5zHJSqkwJFp+XZOqsmUZUolo/WiEo5OJL3WqYKQdexGu+MrKiXEAtr4XYp\nGpQleA8ot2MKFK77dgt/oxIe8TTWpu1nkR5qyil+7IV4D4eEzNWgkKrFoXzXOyClpuYlaFMi/Pj8\nUDTDZ6B3dT2A3TLCW1BS94es6ydSYfPWzyLsE+XG1rP6LwLVbf74YBb0oaQuxZ8dNcGTts6HhMaX\nGq7VmXrRR79/Cr27VLhLJ7+jAByRCAb7W1Ir2o/VgIOalCTKi11BzY2OzQmN1bWhEPh5oZzR7OLr\nC91XICVuATMLAIBnQkLMpNx50flFZQJLqOsdOk8W4NJ6xp/i8Gvnb6x9nCrGHX0/BPW64GdaVP+5\nHyJ5LKRcvAWFL84B5VyOi3g6w1WdrySUeyi/j04Fyfk6xzwLvPMsTDtw3iKBt+VaxYI6yZnDukmB\nG43t+p6mh3Lzeao8+r7OMqdDJUu8n8QyY1dx2kTB9XIljmr7CtvqWhvfhdYe+rHgESeU3zqz801A\nPm2n7/sr6PMUyEjaaZygQph/DEUHxvNNrZQV5Q0dMJpbPZKxSOlq+D5y+zpBwdgBHhrxze73uZ73\n/zrIYPzvrnOTdm6GZNFWIM+G+6mluUwvlcqO7Blk94CiL8P8uDWUX/29iLeoDFpyfGbIOJ0tDcYW\nJwkLUhycrzS9J6QgEb15cyoUdXUq+kujPQ3SN74K6U0/g1LFfpHhbawp7zJ0SpZ+KySfAPAZq1ZN\nusHcseH7HoEiVMKaNjOEwfER334Vmcog0LNYw8w+0HbPgWbo0HcmJZzCfou8BlaOMHmnD9KsFRlS\njP4NWdk3hEqB5NBqA5WgCv/ZfyP8h4jvOW+jhjzfL7H/kKkbSH4HvVDUzQFcR3kUnocMFb8A8L2C\nj6uk9M/fIICRLnqbQlnfDj3U8Jkgj0s/tD/0vh8FBtDQawJsG2We6cAh5HN62hA3B8hawr2cOhGA\nI5ofPUTqeAyGhawk9SL0vyt3KShLcT6XQV7smDaIFyIz+xfJz0EKUXy9UjT9BQOfmX2WKp22tpmd\nErHdGv1OtOY6yntC72cFKDf5dFSjWVYBsD1VZzgIhDnF7TySX4PCvNvKBDYSe2ktc6D9HQIdqN3W\nX/g1AJxKMq59vA0UMXMF6mHXFUoW9KNM+cm/JXkZ9K2+mbnXEmRYmNl3qPD5f5pKf70JGR9iKkK2\nR1kod/H3UUAh3HNDSEH6F8lpMUPpmAewOZWv15arX5p2ALQg17Mg5NMKUf6dbvDnPQoS1l50A8ne\n/gw6w6pL+sQ+Q+2toMzpEMoSRdTPGkOlqXzJqgbQi8xs/eTcq0k+BBm7dvM1vZKqZYUh6Q3zQHAk\nhDJGpVUYOqlrbbTyaL44vWsAayDsYAM+TXSduPLAcHiak5kdSnIhAAual3CEvrlXAMzOarmmgXdI\nRXv9CnouK0XPLktU2dhNoBKhAHAKyT+Y2Q8S1sNJngop/k1K10hG1XZ83IzKXPZ0CLTuZG9jis9X\n8Rw9gUrv65Jx/g1gb3pd9cz9xU6xh6G87ZyMly31GbWzGyQnLebzZaBZoairlH9VKAR9IVT1ib4N\ns20UKX7rWDX/fTLJO6O+FJVBYzUFdhi0XlyWXpfkUxC42y3+y0UzNqY4JHy59J69UacV/Xc5NOY/\nD0UQ7gTJYw+gPI12MoCdzcwAPENyZVTLv8aOoL/7ds0RZGZrooy6qiYB0gvvoYzdgBwiccrBF9FM\nxakZM7RH3a05tRJOZnZcxDMCmtRSZT59wa1WZEZgWlRN0/varMKUNynX4GG5/S3tFIE7DCVRngOg\nrtwDmuR+Bykz70JgYsGb/r+Zth5DT4lYLigRZjY+4vl5eh56VrcL/cMEBRyyK2RBPs8tXNtBE/aT\nmTaaFClQeeUh/H2y9UJX3kFP2M+1Najn7gabidCHDe/3ama2oR8vDYcsBhdkB1gRC6I+oraeQ1nu\nUlc7jwD4uJm949sjIAtkClTXChwU8d0IhdB933oe1Put5yUdBoG3xSHfTX3bD1rA7g39S46XhuOH\n3MdX0HunZvVSSW192RUKwUutv2sC+JuZnRrxFgFcUl7WnCcpzd9eDFIy4trHG7ty+Q9ICMgBSljc\nFsu9NRPhQqD1AGdy6SmdoDksCFd1vhA2HcLuc2HTbalJs1h3HdaYvyQaoHTMl4Qv32VmK7Ej7cB5\nG+cJFoR8Ru2MhlCyB+rAQ56ylyKeEBW1C4APuRFhAOyHBWHVJX1in6H2fu2zIQN8pcwpZLRru17q\nbRoyj3QplX5rvn80esauWaE8yhei40VGZQpscVX0SoitA63ZS0LC8qlUWsRJkGF+GqQ07m5mL0bt\nXAKBO11tZhXjlR/v19HQN9EB5vz/rOwWyKpe5NMgxebTJsPYHBBidSWkleRllqTyRccegVD8ry3s\n6xNQ2a63fHsEhH6/ZML3Gwhp+mE0eOh9ndkXSnMk5Pg6zqqGbrAMFKxVxon41obe9wgzG+OGir3N\nbBc//ntUnWIvmlmbUyy0uwaAbcxsD99uBSHOnP80ZJBOU9ZqZf8art/kPQ3tpJ7+KQC+Zj1wtJWh\nVKGP+jNaB1IMT4pOmwpVmnkkaieev6cBeN4yDjQK7HNl6LteHRobD5rZl0ruL2mrKCTf58KNrJc+\nOApCW/88hP6+eMTbmUbrRpwxZjaloV85UMKw5mzjesNeuXPNrKaHUKHsH4fmm4eCnpDwrIpeutSt\nVuYM6YtmaI86VFaky/p7FQQCVfn4UipoZ0B5M7N3SLZ6cUsUcpYBGjWCO5A8x8y+3KSoNVxzJURo\n51bNT1kJAnkZ69s7Q57uvwA4yOT5jtuaFfKgrgbgSKoeZKrMvGZmb5IcToU9PkHlkcQ0Epo0LvLt\nzSDhaHsodHM3YCCMeo9wkikk9EgK1bvJq5x7BntBIbgBXXkukjubctMnpx96QXslIdoLWTU/9HAq\n5z7wlwKCNYILpozWAVaEsqiPAd42JZ1kLXTd2zoi2XU+ZHk/07e/AtVRT6kTOMhpHlOt6wOc711G\nwEEmT1lRVIqZ/cS/gb31SqsInmjx4iW0L4DFrQV0juRyZnZ/sm9D69W+3hzAvmY2OeH5BwS6EnuU\nigAu/XigkZD1t+a9sZbax9A4qIViJn3sF1xopJndxSqYZM6r2QmaEwmY13kfsmReZ9XPX72Bre37\nuAMCSTvHWsKlo3NKogFKx3yndx7AlSwD6KnME0zqTlsPVyGb6500dSm03oa5eGvfFz/fmf0a4wEE\nD+DAdxWE9bb1ODYOtPA8AIHD/RYy0Aejz0PWbGAJwHPDUAXnuwiKBgvfazxQc96mncysUpucMn69\nlzQTo5rslGd3RAPvRwEsTBkxA8VeoN9ACldQLLeD5uiKwgU9h6Ws572a19tZAcCdAE51hXzTjr7/\nEgpn/TnJCyFlZQCAqY+1sYiYxxpYILreYSzHLVrZlEpwn5/7evJcQ5sp3k6sVC7XMiZz9BwEvhbS\nH2dB3pi0giUG8Ey/TqYiaUIY+tZmdl+GtQQUrFXGieh4SK673PvwcLJGL2M9p9hpAHL9gR//FGRQ\nDqX7BiJ6zEGIAWyTyL03Qw6+lJ43s8sz+8EyrIGXkQeSa6KvATiTPWDdN3xfmJNvInlml6GgQM4L\n9C4UhfUupAu95D+wHqVkkLFkguUBPU9AHZj2RCi6K6aF0Bun8OsvbGZTSb5GVTZJ02h/Da2vFSK5\nOaQPDQcw1g08x5hZDMI7kuRMVnUEBYDouf3v6Mz91Ij1iKExJKdC60D8vT7mv3DeB62P6MkSmtEV\n9VtJLmvtJZzmM7PPdDVE8uDc/mji+SR7oUuEhNDX0GDVLVTCS5AT2xSklajQ369R3oCKpJsOFvYQ\nCoNgcQarCIWnwEOVSa4HeSO+CXkmfg0XwKgQlZXR+8DGQcp8DuCiRIn4KIA1zQY857+EwLjWBvA4\nm0tCBcv6W6VWT6evxdYzF3R3giaavojl4aoliJupEBHoTUhoKkIAZnnIZGPqRYbuo0BgmnKX4nsZ\nCVlMa9+lC0EPQHgEgMBaamFaKEfTf4PKTw9j51OoLgyAQsouRUuJEz/3u5D3OOxPETyvRM+TMxLA\nWGiCTt/1Y6gjjaZ0OlUKcIpfewsA30UvPHm+VEn3Pj9EYTrE+0pQu2FJWLIrMTFWRPp9fRBaFO8k\nGUIA86UZqrQBZIBZCBJcwjlTkQ9XLBECYWbfTPo/BzSHgn2Eqzr/ElCoXhppFSvPbd/HbCS3BbBa\nZkHPja0dov/jQ7GCFMb87R1jvjV82RWFa03hrANpB5YA9JBcE/I2vQR5ws+B8BtmJrmTmf0+Yj8A\nSoWK6fvJvtkTw9yRFIJ4TEdAkQw3mdndVJTK08gQG8oSsr9qJ+sCOAvA49A4XILkjmZ2Xea8rHHd\n56utIfDHywCcZwmIUUIXoS7E5vYNJR0MIYdfD93nulDYb4VYUEUC5QrXYrEx0sz+TnIxU/mv2fx6\n2TQFE0p2+P96ANdTHtBt/P+/QF7Xc6wKmtfoaOiD7kVvHg9YA5XUNytAv3d6l4riCnPXB5BHNc8p\nlZf4tfpR0gEpUI+SvM6vuz6Au4JRL3q2t5Fc2jKo0wnF/W3SCXaFvqOPUNF1L0Mo2DEVyThAe5Uf\ndDjFKICybaBv8iVoDmKTca9gXQ/UliqwCcnvIT8PBnq9VGn2OXphM1uGMlxag2F/dioSLp0HY8DG\n0qjb4LD8KWREi3WN3Hc0J4CDSY4zsyP9WsUh+U4XQGMzyKybALjQ17mPQ9ECRWm0AA6FjGp/AgYM\nPGlaW6cjyMxaUyYi2gmKGLoReqbroBcxNAf0PLORhVDaxpDRjB76PgVCfH0GDSWcqJDDaxqsQnFb\n3442g6LxqHV4j1ra60QVZhmgUSO4A8lvQeUgFoMsURVLv9XrgnYhFA6EMlH1G/9mZof69iOm0K77\noEnjHgid+XYorL0TCIQNKPkkn4SsynEJl/tNaMGTAHzezF5gMyryd8xsz67rR9d7xCLwNWrFeMQn\nzQOt7gVubQtl4arjIEE4LktWQdx0vmeh5/sK9D7nhmpt/hsSGr6MIQYXZJSj1sKT88ZZ0/dBWTKv\nNrP1Btmn2aB7mxntaPqrQtbdJaB8pzFQfnMcKVLU967vI9PH5SAQrq8n+y+FlPcJqJc3CzxLQIvY\n1pCxa2covPwVP14L/Y7Ojeu8FqF2N7SzNKTQLeLbrajjptrHHzPPXS9ovxRcaGlIKC9Cho3OGwDN\nYR/hqn7uo5AnLw1zzIFh1r4PV3K3hUqmpV6Y3NiKSxcORAOY2eYRz6zogWXt6Hy/SQ2uzhuHL88G\nYE6rhi931ndmQd1p9nK9t4QbRZxmgzx2MaL3cZAnNrzzL0HlDPeLeOZJv+GGvmUVSlP+eTZUHz2m\nOELgQQCbBcXaDUKXWj4dqhVkzJ/zFyEFZR4o3Sa+VlF1hfeKKOfAAGK9JRFwzlNSCWQSNK/FCtcv\nrR5afzpk2AnvezPI0bAHBFz4cTakKVgSFUEZW7eH1re/Ql791SC5YG3nSR0NXwKQU7iGhNiBfu88\nO0MRA8tBc9iWUG3ns/14Tqn8jtUjD/vpV1E6issmi6NdPk7LS2WfKVtAwczz8fuQcVqr/LAHChiu\nF4ABg2Nmdsjxs4eZ/cXPeTqVd6PrFa3rbEkV8LltJ7923JcYa+ASM2vEb8n0q4YqnuF5FIqWTNN7\n4xKYRWmJFKjsGlAU7FuQ7H6zef3whnNGQM8qyBvFIflRG8GhByj3/Dbfvw2kCJem0ebSL3Ipfpsi\nAqY2dwSxT6BoKpJuB6tHDG0P4M73ej6vkJnNsD/Ie1n7JTybQR/WVMgC8joUjt3V9swQwt9g+/ag\n/50c7ZuY8NzpfydAYWWfgjzoMc8Zmd/pCc+vCvv0CICZk3t8JNp+DPK8AAKMWzdzP5+AG3g6rvXB\ntl/CuzvkuToDyit9FlrsQ3mMwLdh5jrfGMS7ORGyvK3nv/MhQWQw7/ke//tQtO/+hGcYpDwCCrsZ\n3dLeKRDSZNheDwJwWQVSRGcHMMyPLeXje5ZB9n0tKLf/z769LIBTBjvmk7bnSsdyH+cOK/32fIwc\nBHm7r/D/Rw3yuq3fR8M5kzP7dvTfDtFvxwzfMv6dXQdg1uTYeQC2y5yzLYTUHu+7FAIw6rq/19Gb\nA//t39m2DbyEapWOCb8+nuMXIG9B2D7c7/NaKFS26bx5AMzbcvwPkFJ8ub/rZwD8LDo+E5SCMqyg\nj3cU8HR+H1CY82DG2hwArkreS/x73X+vQOH5n++z/Z9ACkTjXA2f08PYT4494H8/6WP5uWhc7wgp\nJKOTc16HBNx3/Dctuo/XnOcJSFnZqKNvjw/muWbaebhkn+9fIfqt7s/wmOj4cMiAfw5kQNggOf+L\n0Br2D1TX619CAJfTfT+ZPi/jf5fP/TL850PROm1tjgPwKDQ/PAvNiytm+IZBYfG/8N928bfnx48p\nuIdLofnhAAi3ID42Mfp/CpQmE7ZHApgyiGe2Wea3YebaEzK/GzPtfQLCifg2gE8mx6ZB81U8Hz7d\n0K/1MMi1q6G9Evm46JlCXsnH/Zs4zsfHhZDD5hD0J+PMDxkGQmj6RW38mfM39XH8DHr4B8+08Bet\n65DRt+valw3h+zkKKge5MJpl47sK2rm5z+su49d9DsrX7+J/IDe2ov/ng/AGpudZzAoZAA6E1oia\n7OhjcFsolWssgGOhSh0p34JQ6uB4RHIRZHDop0+18RD2IZLxobXwBP9tXtj2ERCo9Twl/DO0Rx0Y\n8IY25gdTwGhfhATq4pulQpjut0FaPllQvoAFgEZ9XK8zJIzk96FBFSMU/s56YS2HQ5Pey5Al9pOm\nELBFnK/V+pdc6xn0LI6BwrZZ3ds/BgqnB2TAyNXyvh0CtbnRt78LGRPS3Lmuvg2HwKuCt/c6CA08\ni/bb0dYESOj8GSR8V2q7Rnyd1lPny4FhBPCoyVCOz6rQ5HgrVJrkHTPbZhB9vw9esst6Fsps6Rwf\nAydBXg74tfeA8rre8bbC9zUcyg8+1syO7rdffr1rAIy3jkgNKgz2r9DCDcjbtZCZbdzVdzN7Nmmr\n6/uIQ71CbuOHzGwdP745gPnNgcuo3L/R0HM52MzOTZ4ToNzIV+Fo6NarAzw/FL4ewDLh15sfsp7H\nYExFZWpKye/jWCTpHFbotfdxOs6ETfElAEdDXqVPAdg+PK+Iv4JGaw2pTGwBzfE+nwoZZIdDuZYT\nWvq4PbTYX49q1EPsLev8PiiAnr1RzX/8mXVEuHg0wGPpPJjhI5RffbF1eEKT80J953egsZVDCi+u\nO+39Lc317rqfz0C5mOOgqJIzzezxhK+xLCE7UqGs6jH8LWQoCCWQtgIwd+l8SfIOKMR/a8gTdT2A\n83Pra3ROaXWF6Sb2UdPc+SdA3t9aFQk61g0dFIotZZz66N+tZrZGB89GZnZVsq8G1siOUkh99KkT\nBK/P9uJSabdZVEvbvXtbQ7LNNdB4P80yFQRInuX9+ic0F94MgVO9kvIOFZU+UxaAgpXKOEPY9xDh\nsg0kt54NRctcm/DF6zr9nIF1PeI7DTIstaYKUOmmIaf+dutA6W9p55nM7opsTPJQCEcmjaj9J3sp\nV2ujrKTaxZDh9Sn42IJk7RpAmvMPg+bLnczTh70/vzFhTY2CjO/LQmN/RzO7ItdWE7EljdaSKFnn\n/SGESE/oezrIzN6IeHaA0gDiFKADXPZ6BzKC17oBPfdK2inbI4b+aGZrkzze7z9eX6aY2bc67ntT\n9HSsLEhuhX9GVtTZkB8cC5QkJ1hBuZFk0R8OCcRHmVkxhH7SXlDCl0CvfEHfSjjL6lemOTiNIWHs\nQCh0YXg+KF0glHpZEsAc1n95GUJK018KeBdFvSzGzQnPvJAn7TsAPgdZBrfpEor7JZ+gxlszaEjM\nWxqifRQUwp6G0aU4ArdAeZDh2ptDCuPa8Nw6E4LlXpAn/Vgm6Kt93GculKhJUb8FUoRCvs82UN7a\nrN6fuGbnNCht4o2kjZWhNI0pJrCntr5dBil216H6vPZK+HLo4JV9TX3PCZBt3wer4dXTIKyFC8zL\nBrliPt564Xj3QwLErAB+a2ZrJc+pRhaFe/s4/CzksQEUpn1talBiB7p/wrs1qvV3f5fh6UznYEv1\nAVZTaE6HFNKjfbtWv5bTgUZLcisz+x0VIripqbTXypCy3Cg0+vf4ZchjHoc5xrl/nd8HyXOhMMKA\ndLwN9E1sl1wvzqseDuFyXGZm+3Tdo5+/q5mdXMJbSiysO+28n0WS6w0JZtclbW6JqsH4IjQQyXWh\n5zY75CU5wMxu9WM5hdLM7IskP2RKhfo2ZOCpYJ5YhFdChbl+C1FIOIDjc8Ip8yBjJ0FyxYOQYGtI\nwuMzc9JxUM54W/m894Xa5oowtlMjTaaNfsrG/QoyRjbig+Su17Cv1ZBaSiwMaWVB6U/WS6VtCoUA\nV0qllSqV0XU3h9JSFjSz9wxLqvSZUkjzy4S1h6p89IiZLcmeI6FUxlkKckyF+fkOyChXMdb1eR8f\ngHL/t7JMul20rgdjSg6srCRV4MuQJ7ymCA62723Upswzn9IX86TpVytC1apy2Ei5b/odCHdq90im\nGVi/qbKLW0IOr6Ug7I7lUEicjjTaljYfhvCu/unbH4SM/8v69VZsOjcjVw2Dvtfg4Lkduse4lOPD\nAD5mrkj7OQ9ZQ7rkYGlGV9RLBMozAYyFFsxGZGtW8zOnAXjJBuEx6IdYAGjEgtJF7M49j+tSToHC\nvPutPT4oCsJuB8/xkHHhIVSF5ppHkOR80CR5LwQKZ2yp6+wNpZbFdaFwrdQwEFsyi63D/h4XN7Nr\nKCvjTFbPae20nkb39yNEOT1QOPc/oRDkCyFcgp9DNSUfZlTeqB9iR65Ywlt7jxTA0DQrQMkneSQU\ninQvZI0+zsxOaOHfMbff6rmNZwM4wXoI/isC+KaZ7RjxZPseKZN9fx/+nl61KtZC5TokTzS3CjPK\nGfbJ/AFrKe9YQiRXsch7U8B/OhQWFpTzLQC8YGY7JXz3mNmKrObCp/eWE6QD5saj0IL4HwgobBvr\nlaCpGYJc6BsHGaPWgELgHzSzXf34nFB6zCKQseIkyNN9BIAnXHmrRKKk25lnUSlx1MDT+X2kc3HL\nvjQaAJDXfw8MIZHc01S9AuwGWu2n3c5cbxZ4F1jNRf4blNd7OWSM+l2kJMXPi5Dyv7VVjfCHQILi\nP6ExfaHl87JnQbXETnZdZzUKLICM/RCadxsFpcyc1Fk+770gNoDv9XH+BZBRYUHI6zZwCInC0keb\nOWXCTHm/oTrEuVBIa1wd4gwzWyLT3nSXQmJUajfdF89z7Cj96TxFpdKSa2WVSirKZ01orP4dMgzd\nMph77IdYzSHOPlM3SHwOPTyOTSBv6uFQhMC20fdToYyMcz9kALnAd20B1bouVvL6JSridC3vX1rN\nJfBko2etavhrVASTthZFt+NpBFSKbMCwCeDnbWvS+02J3HQx5Dg42bf7kkOpcsudkc6sgifXKNGX\nKjnrJAmtQR/pkgkGQ657rWoO1EoBYk60ekTKApBjK52fizDQZnTU95JyNs/4rxXZOnyMFKDPshC4\nwV/77RAbUE6j68TW9yug/LVL0Fw6rqR0EZN97wKVkPNzUa1LuQy85Fm/1K9SDOB+kstbuzd+Eyh3\ntUmASq19IyClanOShl5oynyQ9etG314XUnTTPp0GKWYVgI6E/kSB9XVZh78JIUvODVlj54fy7NeJ\n+SwT6pYjU6jnLg2Hn6S8SIdCaRQP++LSWLuzg3aCxt/iUEjP9RCoWY7+Q3ljg6d/S2hMLcIWxO3I\nILY5FOYTUNpvhKzqFSI5xsz+nAq/Gb4QATMzhEr+Z99eBMqfK+l7oNbvgy3hXhSCdAj3qsynVg3d\nmjXaP43kUyQXsCiEfRD0SziSNKM6wC20upktHTbciJk+K6AFcZ8CgMlVH5gVveoDJ0B4Cv+CcgeD\nkr4sMmjuaEejBRQJ8XfI87I+lCP9BpRfH0pmpSi0lW2rlxx8EEpVaQM2y30fOyU8RnKRaP1YBHlh\n9Sa2lBKaXooMJ19Dr3rFORg6pPHhFiGdm9lTrrjEtD6q3oUzIeNrTHd4vzY1s9gTPonkr6P2c88r\nBi+CKarsMBf4toLKGT1vUZUXkhtA83EJ6nvRHF1AJeXzhpTYgeaeWUMHToV7wU3pBAtAIaVFaTNU\ndZixZvZrn9fntCp680xQmlGIzpsLMjIDzdUh3kBUHYJ1Q+rxXYbUDrrd5644pPV2n/NsfyO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ICW8DgXYDaDACIWh4DExprZQg1tveDnXAGBerwCr6Hr9/4OydmtuQ7jbP635B297R9h6PcYVI05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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xc386450>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.display import display\n",
"plt.figure()\n",
"fig = plt.gcf()\n",
"fig.set_size_inches(17, 7)\n",
"Top100['Iter 5 PageRank'].plot.bar(title='PageRank at 5th Iteration')\n"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0xfabe050>"
]
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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UAQAAYEIE6gAAADAhAnUAAACYEIE6AAAATIhAHQAAACZEoA4AAAATIlAHAACACRGoAwAA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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xe28ac10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"fig = plt.gcf()\n",
"fig.set_size_inches(17, 7)\n",
"Top100['Iter 10 PageRank'].plot.bar(title='PageRank at 10th Iteration', color='r')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"HW9.4\"></a>\n",
"[Back to Top](#TOC)\n",
"<h1 style=\"color:#021353;\">HW 9.4: Topic-specific PageRank implementation using MRJob</h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"Modify your PageRank implementation to produce a topic specific PageRank implementation,\n",
"as described in:\n",
"\n",
"http://www-cs-students.stanford.edu/~taherh/papers/topic-sensitive-pagerank.pdf\n",
"\n",
"Note in this article that there is a special caveat to ensure that the transition matrix is irreducible.\n",
"This caveat lies in footnote 3 on page 3:\n",
"\n",
"\tA minor caveat: to ensure that M is irreducible when p\n",
"\tcontains any 0 entries, nodes not reachable from nonzero\n",
"\tnodes in p should be removed. In practice this is not problematic.\n",
"\n",
"and must be adhered to for convergence to be guaranteed.\n",
"\n",
"Run topic specific PageRank on the following randomly generated network of 100 nodes:\n",
"\n",
"s3://ucb-mids-mls-networks/randNet.txt (also available on Dropbox)\n",
"\n",
"which are organized into ten topics, as described in the file:\n",
"\n",
"s3://ucb-mids-mls-networks/randNet_topics.txt (also available on Dropbox)\n",
"\n",
"Since there are 10 topics, your result should be 11 PageRank vectors\n",
"(one for the vanilla PageRank implementation in 9.1, and one for each topic\n",
"with the topic specific implementation). Print out the top ten ranking nodes \n",
"and their topics for each of the 11 versions, and comment on your result. \n",
"Assume a teleportation factor of 0.15 in all your analyses.\n",
"\n",
"One final and important comment here: please consider the \n",
"requirements for irreducibility with topic-specific PageRank.\n",
"In particular, the literature ensures irreducibility by requiring that\n",
"nodes not reachable from in-topic nodes be removed from the network.\n",
"\n",
"This is not a small task, especially as it it must be performed\n",
"separately for each of the (10) topics.\n",
"\n",
"So, instead of using this method for irreducibility, \n",
"please comment on why the literature's method is difficult to implement,\n",
"and what what extra computation it will require.\n",
"Then for your code, please use the alternative, \n",
"non-uniform damping vector:\n",
"\n",
"vji = beta*(1/|Tj|); if node i lies in topic Tj\n",
"\n",
"vji = (1-beta)*(1/(N - |Tj|)); if node i lies outside of topic Tj\n",
"\n",
"for beta in (0,1) close to 1. \n",
"\n",
"With this approach, you will not have to delete any nodes.\n",
"If beta > 0.5, PageRank is topic-sensitive, \n",
"and if beta < 0.5, the PageRank is anti-topic-sensitive. \n",
"For any value of beta irreducibility should hold,\n",
"so please try beta=0.99, and perhaps some other values locally,\n",
"on the smaller networks.\n",
"\n",
"</pre>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting ReduceJoin.py\n"
]
}
],
"source": [
"%%writefile ReduceJoin.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"# Description: use reducer-side join to join the randNet graph information with the topics\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import json\n",
"\n",
"\n",
"class ReduceJoin(MRJob):\n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" #log_to_stream(level='ERROR')\n",
"\n",
" def __init__(self, *args, **kargs):\n",
" super(ReduceJoin, self).__init__(*args, **kargs)\n",
"\n",
" def mapper(self, _, line ):\n",
"\n",
" inputlist=line.split('\\t')\n",
" node=inputlist[0]\n",
"\n",
" yield node, \"\\t\".join(inputlist[1::])\n",
" \n",
" def reducer(self, node, info):\n",
" \n",
" combine=[]\n",
" for items in info:\n",
" \n",
" combine.append(items)\n",
"\n",
" yield node, \"\\t\".join(combine)\n",
" \n",
" def steps(self):\n",
" return[\n",
" MRStep(\n",
"\n",
" mapper=self.mapper,\n",
" reducer=self.reducer,\n",
" )\n",
" ]\n",
"\n",
"if __name__ == '__main__':\n",
" ReduceJoin.run()\n"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/ReduceJoin.root.20160716.185415.354546\n",
"Running step 1 of 1...\n",
"Streaming final output from /tmp/ReduceJoin.root.20160716.185415.354546/output...\n",
"Removing temp directory /tmp/ReduceJoin.root.20160716.185415.354546...\n"
]
}
],
"source": [
"!python ReduceJoin.py /data/hw9/randnet/randNet_topics.txt /data/hw9/randnet/randNet.txt > /data/hw9/randnet/randNetLabeled.txt"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"54\t8\t{'24': 1, '16': 1, '86': 1, '23': 1, '28': 1, '35': 1, '42': 1, '98': 1, '67': 1, '90': 1, '92': 1, '95': 1}\r\n",
"55\t7\t{'77': 1, '12': 1, '32': 1, '34': 1, '1': 1, '3': 1, '47': 1, '84': 1}\r\n",
"56\t6\t{'27': 1, '15': 1, '46': 1, '32': 1, '31': 1, '52': 1, '68': 1, '84': 1}\r\n",
"57\t9\t{'43': 1, '52': 1, '61': 1, '63': 1, '80': 1, '78': 1}\r\n",
"58\t2\t{'21': 1, '33': 1, '56': 1, '28': 1, '43': 1, '52': 1, '2': 1, '6': 1, '83': 1, '94': 1, '74': 1}\r\n",
"59\t2\t{'25': 1, '17': 1, '23': 1, '55': 1, '44': 1, '50': 1, '40': 1, '52': 1, '73': 1, '35': 1, '70': 1, '69': 1, '93': 1}\r\n",
"6\t8\t{'21': 1, '19': 1, '30': 1, '76': 1, '2': 1, '100': 1, '81': 1}\r\n",
"60\t10\t{'14': 1, '17': 1, '76': 1, '29': 1, '1': 1, '98': 1, '62': 1, '63': 1, '6': 1, '94': 1}\r\n",
"61\t8\t{'25': 1, '14': 1, '35': 1, '63': 1, '72': 1, '9': 1, '86': 1}\r\n",
"62\t8\t{'11': 1, '14': 1, '16': 1, '28': 1, '43': 1, '52': 1, '99': 1, '89': 1, '72': 1, '67': 1, '100': 1, '81': 1, '95': 1, '97': 1, '96': 1}\r\n"
]
}
],
"source": [
"!head -10 /data/hw9/randnet/randNetLabeled.txt"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100 /data/hw9/randnet/randNetLabeled.txt\r\n"
]
}
],
"source": [
"!wc -l /data/hw9/randnet/randNetLabeled.txt\n",
"# This shows that there is no dangling nodes in the graph"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting Preprocess94.py\n"
]
}
],
"source": [
"%%writefile Preprocess94.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"# Description: same as the preprocessing used in 9.1, except for adapting to the layout of the labeled\n",
"# randNet graph. The script also counts the number of articles in each topic\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import json\n",
"\n",
"class Preproc(MRJob):\n",
" \n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" \n",
" def __init__(self, *args, **kargs):\n",
" super(Preproc, self).__init__(*args, **kargs)\n",
" self.topicfreq={}\n",
" def mapper(self, _, line):\n",
" inputlist=line.split('\\t')\n",
" node=inputlist[0]\n",
" topic=inputlist[1]\n",
" edges=eval(inputlist[2])\n",
" degree=len(edges)\n",
" for item in edges:\n",
" yield item, None\n",
" \n",
" yield node, \"\\t\".join(inputlist[1::])\n",
" \n",
" def reducer(self, node, info):\n",
" edges={}\n",
" topic=None\n",
" \n",
" for edge in info:\n",
" if edge is not None:\n",
" infolist=edge.split('\\t')\n",
" edges=infolist[1]\n",
" topic=infolist[0]\n",
" self.topicfreq.setdefault(topic, 0)\n",
" self.topicfreq[topic]+=1 \n",
" yield node, \"\\t\".join([topic, edges])\n",
" \n",
" def reducer_final(self):\n",
" for key in self.topicfreq:\n",
" self.increment_counter(\"Total\", key, self.topicfreq[key])\n",
" \n",
"if __name__ == '__main__':\n",
" Preproc.run()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/Preprocess94.root.20160717.022853.270174\n",
"Running step 1 of 1...\n",
"Counters: 10\n",
"\tTotal\n",
"\t\t1=17\n",
"\t\t10=12\n",
"\t\t2=8\n",
"\t\t3=9\n",
"\t\t4=13\n",
"\t\t5=9\n",
"\t\t6=6\n",
"\t\t7=10\n",
"\t\t8=9\n",
"\t\t9=7\n",
"Streaming final output from /tmp/Preprocess94.root.20160717.022853.270174/output...\n",
"Removing temp directory /tmp/Preprocess94.root.20160717.022853.270174...\n"
]
}
],
"source": [
"!python Preprocess94.py /data/hw9/randnet/randNetLabeled.txt >/data/hw9/randnet/randnet_Init.txt"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'10': 12, '1': 17, '3': 9, '2': 8, '5': 9, '4': 13, '7': 10, '6': 6, '9': 7, '8': 9}\n"
]
}
],
"source": [
"from Preprocess94 import Preproc\n",
"procjob=Preproc(args=[\"/data/hw9/randnet/randNetLabeled.txt\"])\n",
"with procjob.make_runner() as runner:\n",
" runner.run()\n",
" topiccounter=runner.counters()\n",
" print topiccounter[0]['Total']\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"55\t7\t{'77': 1, '12': 1, '32': 1, '34': 1, '1': 1, '3': 1, '47': 1, '84': 1}\r\n",
"56\t6\t{'27': 1, '15': 1, '46': 1, '32': 1, '31': 1, '52': 1, '68': 1, '84': 1}\r\n",
"57\t9\t{'43': 1, '52': 1, '61': 1, '63': 1, '80': 1, '78': 1}\r\n",
"58\t2\t{'21': 1, '33': 1, '56': 1, '28': 1, '43': 1, '52': 1, '2': 1, '6': 1, '83': 1, '94': 1, '74': 1}\r\n",
"59\t2\t{'25': 1, '17': 1, '23': 1, '55': 1, '44': 1, '50': 1, '40': 1, '52': 1, '73': 1, '35': 1, '70': 1, '69': 1, '93': 1}\r\n",
"6\t8\t{'21': 1, '19': 1, '30': 1, '76': 1, '2': 1, '100': 1, '81': 1}\r\n",
"60\t10\t{'14': 1, '17': 1, '76': 1, '29': 1, '1': 1, '98': 1, '62': 1, '63': 1, '6': 1, '94': 1}\r\n",
"61\t8\t{'25': 1, '14': 1, '35': 1, '63': 1, '72': 1, '9': 1, '86': 1}\r\n",
"62\t8\t{'11': 1, '14': 1, '16': 1, '28': 1, '43': 1, '52': 1, '99': 1, '89': 1, '72': 1, '67': 1, '100': 1, '81': 1, '95': 1, '97': 1, '96': 1}\r\n",
"63\t4\t{'11': 1, '25': 1, '27': 1, '21': 1, '17': 1, '54': 1, '44': 1, '28': 1, '36': 1, '37': 1, '7': 1}\r\n"
]
}
],
"source": [
"!head -10 /data/hw9/randnet/randNet_init.txt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Topic PageRank Step 1\n",
"The PageRank for each page is now a vector with 11 elements. The 1st is for vanilla PageRank. The other 10 are for each of the 10 topics. "
]
},
{
"cell_type": "code",
"execution_count": 155,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting TopicPageRank1.py\n"
]
}
],
"source": [
"%%writefile TopicPageRank1.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"# Description: same as the Step 1 script for basic PageRank, but adpated to the file strcture of randNet file\n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import json\n",
"import numpy as np\n",
"\n",
"\n",
"class TPR_step1(MRJob):\n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" #log_to_stream(level='ERROR')\n",
"\n",
" def __init__(self, *args, **kargs):\n",
" super(TPR_step1, self).__init__(*args, **kargs)\n",
" self.missing=np.array([0.0]*11)\n",
" \n",
" def configure_options(self):\n",
" super(TPR_step1, self).configure_options()\n",
" self.add_passthrough_option('--total-node', dest=\"totalnode\",type='str', default=1)\n",
"\n",
" \n",
" def mapper_init(self):\n",
" self.totalnode=self.options.totalnode\n",
"\n",
" \n",
" def mapper1(self, _, line ):\n",
"\n",
" inputlist=line.split('\\t')\n",
" node=inputlist[0]\n",
"\n",
" if len(inputlist)==3:\n",
" topic=inputlist[1] \n",
" pagerank=np.array([float(1)/float(self.totalnode)]*11)\n",
" edges=eval(inputlist[2])\n",
" degree=len(edges)\n",
" \n",
" elif len(inputlist)>3:\n",
" topic=inputlist[1] \n",
" pagerank=eval(inputlist[3])\n",
" edges=eval(inputlist[2])\n",
" degree=len(edges)\n",
" \n",
" #print \"New node\"\n",
" #print node, pagerank\n",
" newrank=np.array(pagerank)/float(degree)\n",
" \n",
" for item in edges:\n",
" \n",
" yield item, \"{}\\t{}\\t{}\".format(\"empty\", \"empty\", newrank.tolist())\n",
" #print item, newrank\n",
" \n",
" yield node, \"%s\\t%s\\t%s\" %(topic,edges, str([0.0]*11))\n",
" if len(edges)==0:\n",
" yield \"*Dangling\", \"%s\" %(pagerank)\n",
" \n",
" \n",
" \n",
" def reducer1(self, node, mass):\n",
" \n",
" if node==\"*Dangling\":\n",
" for item in info:\n",
" self.missing=self.missing+eval(item)\n",
"\n",
" else:\n",
" totalscore=np.array([0.0]*11, dtype=\"float64\")\n",
" edges={}\n",
" topic=None\n",
" \n",
" for info in mass:\n",
" \n",
" infolist=info.split('\\t')\n",
" \n",
" PR=eval(infolist[2])\n",
" \n",
" totalscore+=PR\n",
" if infolist[0]!=\"empty\":\n",
" topic=infolist[0]\n",
" if infolist[1]!=\"empty\":\n",
" edges=eval(infolist[1])\n",
" \n",
" yield \"{}\\t{}\\t{}\\t{}\".format(node, topic, edges, totalscore.tolist()), None\n",
" \n",
" def reducer_final(self):\n",
" missingmass=sum([self.missing[key] for key in self.missing])\n",
" \n",
" self.increment_counter(\"Dangling\", \"Mass\", 0)\n",
" self.increment_counter(\"Dangling\", \"Mass\", int(missingmass))\n",
"\n",
" def steps(self):\n",
" return[\n",
" MRStep(\n",
" mapper_init=self.mapper_init,\n",
" mapper=self.mapper1,\n",
" reducer=self.reducer1,\n",
" reducer_final=self.reducer_final\n",
" )\n",
" ]\n",
"\n",
"if __name__ == '__main__':\n",
" TPR_step1.run()\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/TopicPageRank1.root.20160717.155103.880079\n",
"Running step 1 of 1...\n",
"TopicPageRank1.py:93: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
" missingmass=sum([self.missing[key] for key in self.missing])\n",
"Counters: 1\n",
"\tDangling\n",
"\t\tMass=0\n",
"Streaming final output from /tmp/TopicPageRank1.root.20160717.155103.880079/output...\n",
"Removing temp directory /tmp/TopicPageRank1.root.20160717.155103.880079...\n"
]
}
],
"source": [
"!python TopicPageRank1.py /data/hw9/randnet/randNet_init.txt --total-node 100 > /data/hw9/randnet/Step1_1.txt"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting TopicPageRank2.py\n"
]
}
],
"source": [
"%%writefile TopicPageRank2.py\n",
"#!/usr/bin/python\n",
"# Author : Xin Yao\n",
"# Description: The same as the script for PageRank step 2, but the damping array is adjusted according to the \n",
"# instruction given \n",
"\n",
"from mrjob.job import MRJob\n",
"from mrjob.step import MRStep\n",
"from mrjob.protocol import RawProtocol, ReprProtocol\n",
"import sys\n",
"from copy import deepcopy\n",
"from numpy import argmin\n",
"from mrjob.util import log_to_stream\n",
"from operator import itemgetter\n",
"import numpy as np\n",
"import json\n",
"\n",
"\n",
"class TPR_step2(MRJob):\n",
" SORT_VALUES = True\n",
" INPUT_PROTOCL = RawProtocol\n",
" OUTPUT_PROTOCOL = RawProtocol\n",
" #log_to_stream(level='ERROR')\n",
"\n",
" def __init__(self, *args, **kargs):\n",
" super(TPR_step2, self).__init__(*args, **kargs)\n",
" self.missingmass=0\n",
" self.alpha=0\n",
" self.totalnode=1\n",
"\n",
" def configure_options(self):\n",
" super(TPR_step2, self).configure_options()\n",
" self.add_passthrough_option('--total-node', dest=\"totalnode\",type='str', default=1)\n",
" self.add_passthrough_option('--beta', dest=\"beta\",type='str', default=\"0\")\n",
" self.add_passthrough_option('--missing-mass', dest=\"missing\",type='int', default=0)\n",
" self.add_passthrough_option('--topicfreq', dest=\"topicfreq\",type='str')\n",
" self.add_passthrough_option('--teleport', dest=\"teleport\",type='str')\n",
" \n",
" \n",
" def mapper2_init(self):\n",
" self.beta=float(self.options.beta)\n",
" self.totalnode=float(self.options.totalnode)\n",
" self.missing=float(self.options.missing)/float(1000000000)\n",
" self.topicfreq=eval(self.options.topicfreq.strip('\"'))\n",
" self.teleport=float(self.options.teleport)\n",
" \n",
" def mapper2(self, _, line ):\n",
" \n",
" inputlist=line.split('\\t')\n",
" \n",
" node=inputlist[0]\n",
"\n",
"\n",
" pagerank=np.array(eval(inputlist[3]))\n",
" edges=eval(inputlist[2])\n",
" topic=inputlist[1]\n",
" beta=self.beta\n",
" totalnode=self.totalnode\n",
" # set the probability of teleportation for basic PageRank\n",
" damping=[1/self.totalnode] \n",
" # set the probability of teleportation for other topics\n",
" damping.extend([(1.0-beta)/(totalnode-self.topicfreq[topic])]*10) \n",
" # set the probability of teleportation for the topic of the page\n",
" index=int(topic)\n",
" damping[index]=beta/float(self.topicfreq[topic])\n",
" \n",
" dampingarray=np.array(damping)\n",
" \n",
" newrank=self.teleport*dampingarray+self.teleport*(self.missing/totalnode+pagerank)\n",
" \n",
" yield None, \"{}\\t{}\\t{}\\t{}\".format(node, topic, edges, newrank.tolist())\n",
" \n",
"\n",
" \n",
" def steps(self):\n",
" JOBCONF1={\n",
" #'mapreduce.job.output.key.comparator.class': 'org.apache.hadoop.mapred.lib.KeyFieldBasedComparator',\n",
" #'stream.num.map.output.key.field': 5,\n",
" 'stream.map.output.field.separator':'\\t',\n",
" #'mapreduce.partition.keycomparator.options': '-k1,1 -k5,5' ,\n",
" 'reduce.output.key.value.fields.spec': \"1:1-\"\n",
" #'mapred.reduce.tasks': 1,\n",
" #'mapred.map.tasks': 1\n",
" }\n",
" return[\n",
" MRStep(\n",
" #jobconf=JOBCONF1,\n",
" mapper_init=self.mapper2_init,\n",
" mapper=self.mapper2,\n",
" #reducer=self.reducer1,\n",
" #reducer_final=self.reducer_final\n",
" )\n",
" ]\n",
"\n",
"if __name__ == '__main__':\n",
" TPR_step2.run()\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/TopicPageRank2.root.20160718.144110.520794\n",
"Running step 1 of 1...\n",
"Streaming final output from /tmp/TopicPageRank2.root.20160718.144110.520794/output...\n",
"Removing temp directory /tmp/TopicPageRank2.root.20160718.144110.520794...\n"
]
}
],
"source": [
" \n",
"!python TopicPageRank2.py /data/hw9/randnet/Step1_1.txt --total-node 100 --beta 0.99 --missing-mass 0 --teleport 0.15 \\\n",
"--topicfreq \"{'10': 12, '1': 17, '3': 9, '2': 8, '5': 9, '4': 13, '7': 10, '6': 6, '9': 7, '8': 9}\" > /data/hw9/randnet/Step1_2.txt"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using configs in /etc/mrjob.conf\n",
"ignoring partitioner keyword arg (requires real Hadoop): 'org.apache.hadoop.mapred.lib.KeyFieldBasedPartitioner'\n",
"Creating temp directory /tmp/TopicPageRank1.root.20160718.144115.073994\n",
"Running step 1 of 1...\n",
"TopicPageRank1.py:93: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
" missingmass=sum([self.missing[key] for key in self.missing])\n",
"Counters: 1\n",
"\tDangling\n",
"\t\tMass=0\n",
"Streaming final output from /tmp/TopicPageRank1.root.20160718.144115.073994/output...\n",
"Removing temp directory /tmp/TopicPageRank1.root.20160718.144115.073994...\n"
]
}
],
"source": [
"!python TopicPageRank1.py /data/hw9/randnet/Step1_2.txt --total-node 100 > /data/hw9/randnet/Step2_1.txt"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%reload_ext autoreload\n",
"%autoreload 2\n",
"\n",
"# Author: Xin Yao\n",
"# Description: Driver code for Topic Page rank\n",
"# Very similar to the driver code for basic PageRank\n",
"\n",
"from Preprocess94 import Preproc\n",
"from TopicPageRank1 import TPR_step1\n",
"from TopicPageRank2 import TPR_step2\n",
"\n",
"def TopicPageRank(Input=None, Teleport=0, maxIter=10, beta=0.5, OutDir=\"/data/hw9/TPR-test\"):\n",
" iternum=1\n",
" procjob=Preproc(args=[\"/data/hw9/randnet/randNetLabeled.txt\"])\n",
" with procjob.make_runner() as runner:\n",
" runner.run()\n",
" # extract the counter that contains the nubmer of pages for each topic \n",
" topiccounter=runner.counters()[0]['Total']\n",
" print topiccounter\n",
" # calculate total nubmer of pages\n",
" TotalNode=sum([topiccounter[key] for key in topiccounter])\n",
"\n",
" while iternum<=maxIter:\n",
" if iternum==1:\n",
" Step1Input=Input\n",
" else:\n",
" Step1Input=Step2Output+\"/part-*\"\n",
" \n",
" dangling=0\n",
" Step1Output=OutDir+\"/Iter%s/Step1\" %iternum\n",
"\n",
" Step1=TPR_step1(args=[Step1Input, \"--total-node\", str(TotalNode), \"--output-dir\", Step1Output, \"--no-output\"])\n",
"\n",
"\n",
" with Step1.make_runner() as runner1:\n",
" runner1.run()\n",
" counter1=runner1.counters()\n",
" if \"Dangling\" in counter1[0]:\n",
"\n",
" danglingmass=counter1[0][\"Dangling\"][\"Mass\"]\n",
" dangling=danglingmass\n",
" \n",
"\n",
" Step2Input=Step1Output+\"/part-*\"\n",
" Step2Output=OutDir+\"/Iter%s/Step2\"%iternum\n",
" \n",
" Step2=TPR_step2(args=[Step2Input, \"--total-node\", str(TotalNode), \"--teleport\", str(Teleport), \"--missing-mass\", str(dangling), \"--beta\", str(beta), \"--output-dir\", Step2Output,\"--topicfreq\",str(topiccounter), \"--no-output\", ])\n",
"\n",
" #print \"Step 2 Input: %s \" %Step2Input\n",
" #print \"Step 2 Output: %s \" %Step2Output\n",
"\n",
" with Step2.make_runner() as runner2:\n",
" runner2.run()\n",
" \n",
" iternum+=1\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'10': 12, '1': 17, '3': 9, '2': 8, '5': 9, '4': 13, '7': 10, '6': 6, '9': 7, '8': 9}\n"
]
}
],
"source": [
"TopicPageRank(Input=\"/data/hw9/randnet/randNetLabeled.txt\", Teleport=0.15, maxIter=30, beta=0.99, OutDir=\"/data/hw9/randnet/test\")"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"56\t6\t[0.0017905673247578912, 0.0003396433232175579, 0.00031689561619489067, 0.000364795646513211, 0.0004579707156527016, 0.0002761196192724166, 0.02478419535021654, 0.00023403116139108056, 0.00027317274606900916, 5.6963340603104765e-05, 0.00042691604516023965]\r\n",
"57\t9\t[0.0017613210158030545, 0.0004307737928552389, 4.549140109189481e-05, 0.00033228357294343196, 5.446068593693204e-05, 5.771394912070073e-05, 0.00042755762406016255, 0.00022458769005162537, 0.0006642079765997394, 0.021247509836482478, 0.00039211549896847354]\r\n",
"58\t2\t[0.0019053681678558325, 0.0006483929528830438, 0.01865303978395912, 0.0003888273342928079, 0.00024580117816067103, 0.0009946173829869858, 0.00035251973750406864, 0.0007545245260201114, 0.000402937682813292, 6.360220069664702e-05, 7.594852565583224e-05]\r\n",
"59\t2\t[0.0017104499066233625, 0.0001662226223182504, 0.018876166046668374, 0.00023552815896097935, 0.00032785987622848686, 0.00016919597554228947, 3.911337736105933e-05, 0.0003074674517234511, 6.690994519197863e-05, 5.5231568358067966e-05, 0.00041725140345367416]\r\n",
"6\t8\t[0.0017486342306182612, 0.0006576255860875197, 0.00030325353817999825, 0.0002660892180752208, 6.996989190011039e-05, 0.00019030875758186801, 7.906844414107568e-05, 5.472610084200454e-05, 0.016539029667147806, 0.0005059844091602746, 0.00023547832296369966]\r\n"
]
}
],
"source": [
"# show the results\n",
"!cut -f1,2,4- -d$'\\t' /data/hw9/randnet/test/Iter30/Step2/part-* > /data/hw9/randnet/randnet_result.txt\n",
"!head -5 /data/hw9/randnet/randnet_result.txt"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#Put the result into a better format\n",
"resulttext=[]\n",
"with open(\"/data/hw9/randnet/randnet_result.txt\", \"r\") as f:\n",
" for line in f.readlines():\n",
" line=line.strip()\n",
" inputlist=line.split('\\t')\n",
" ranks=eval(inputlist[2])\n",
" ranks=[\"{:1.5f}\".format(x) for x in ranks]\n",
" result=inputlist[0:2]\n",
" result.extend(ranks)\n",
" resulttext.append('\\t'.join(str(x) for x in result))\n",
" \n",
"with open(\"/data/hw9/randnet/randnet_prettyresult.txt\", 'w') as f:\n",
" for line in resulttext:\n",
" f.write(line+\"\\n\")\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import pandas as pd\n",
"titles=[\"PageID\", \"Topic\", \"Vanilla PR\"]\n",
"titles.extend([\"Topic %s\" %i for i in range(1,11)])\n",
"# read the results into a pandas dataFrame\n",
"RandNetPR=pd.read_table(\"/data/hw9/randnet/randnet_prettyresult.txt\", header=None, names=titles)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As the result shows, the PageRank score for a particular page is much higher for its own topic than for other topics. For example, Page 56 has a score 0.024784 for Topic 6. But the scores under other topics for this page less than one-tenth of the score for topic 6. At Query time, a user whos searches about Topic 6 will be more likely to see page 56 than other pages "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>PageID</th>\n",
" <th>Topic</th>\n",
" <th>Vanilla PR</th>\n",
" <th>Topic 1</th>\n",
" <th>Topic 2</th>\n",
" <th>Topic 3</th>\n",
" <th>Topic 4</th>\n",
" <th>Topic 5</th>\n",
" <th>Topic 6</th>\n",
" <th>Topic 7</th>\n",
" <th>Topic 8</th>\n",
" <th>Topic 9</th>\n",
" <th>Topic 10</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>56</td>\n",
" <td>6</td>\n",
" <td>0.00179</td>\n",
" <td>0.00034</td>\n",
" <td>0.00032</td>\n",
" <td>0.00036</td>\n",
" <td>0.00046</td>\n",
" <td>0.00028</td>\n",
" <td>0.02478</td>\n",
" <td>0.00023</td>\n",
" <td>0.00027</td>\n",
" <td>0.00006</td>\n",
" <td>0.00043</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>57</td>\n",
" <td>9</td>\n",
" <td>0.00176</td>\n",
" <td>0.00043</td>\n",
" <td>0.00005</td>\n",
" <td>0.00033</td>\n",
" <td>0.00005</td>\n",
" <td>0.00006</td>\n",
" <td>0.00043</td>\n",
" <td>0.00022</td>\n",
" <td>0.00066</td>\n",
" <td>0.02125</td>\n",
" <td>0.00039</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>58</td>\n",
" <td>2</td>\n",
" <td>0.00191</td>\n",
" <td>0.00065</td>\n",
" <td>0.01865</td>\n",
" <td>0.00039</td>\n",
" <td>0.00025</td>\n",
" <td>0.00099</td>\n",
" <td>0.00035</td>\n",
" <td>0.00075</td>\n",
" <td>0.00040</td>\n",
" <td>0.00006</td>\n",
" <td>0.00008</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>59</td>\n",
" <td>2</td>\n",
" <td>0.00171</td>\n",
" <td>0.00017</td>\n",
" <td>0.01888</td>\n",
" <td>0.00024</td>\n",
" <td>0.00033</td>\n",
" <td>0.00017</td>\n",
" <td>0.00004</td>\n",
" <td>0.00031</td>\n",
" <td>0.00007</td>\n",
" <td>0.00006</td>\n",
" <td>0.00042</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>6</td>\n",
" <td>8</td>\n",
" <td>0.00175</td>\n",
" <td>0.00066</td>\n",
" <td>0.00030</td>\n",
" <td>0.00027</td>\n",
" <td>0.00007</td>\n",
" <td>0.00019</td>\n",
" <td>0.00008</td>\n",
" <td>0.00005</td>\n",
" <td>0.01654</td>\n",
" <td>0.00051</td>\n",
" <td>0.00024</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" PageID Topic Vanilla PR Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 \\\n",
"0 56 6 0.00179 0.00034 0.00032 0.00036 0.00046 0.00028 \n",
"1 57 9 0.00176 0.00043 0.00005 0.00033 0.00005 0.00006 \n",
"2 58 2 0.00191 0.00065 0.01865 0.00039 0.00025 0.00099 \n",
"3 59 2 0.00171 0.00017 0.01888 0.00024 0.00033 0.00017 \n",
"4 6 8 0.00175 0.00066 0.00030 0.00027 0.00007 0.00019 \n",
"\n",
" Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 \n",
"0 0.02478 0.00023 0.00027 0.00006 0.00043 \n",
"1 0.00043 0.00022 0.00066 0.02125 0.00039 \n",
"2 0.00035 0.00075 0.00040 0.00006 0.00008 \n",
"3 0.00004 0.00031 0.00007 0.00006 0.00042 \n",
"4 0.00008 0.00005 0.01654 0.00051 0.00024 "
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"RandNetPR.head(5)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Top 10 pages in Topic 1\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>PageID</th>\n",
" <th>Topic</th>\n",
" <th>Vanilla PR</th>\n",
" <th>Topic 1</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>46</th>\n",
" <td>98</td>\n",
" <td>1</td>\n",
" <td>0.00178</td>\n",
" <td>0.00926</td>\n",
" </tr>\n",
" <tr>\n",
" <th>68</th>\n",
" <td>27</td>\n",
" <td>1</td>\n",
" <td>0.00179</td>\n",
" <td>0.00910</td>\n",
" </tr>\n",
" <tr>\n",
" <th>74</th>\n",
" <td>32</td>\n",
" <td>1</td>\n",
" <td>0.00186</td>\n",
" <td>0.00904</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75</th>\n",
" <td>33</td>\n",
" <td>1</td>\n",
" <td>0.00167</td>\n",
" <td>0.00902</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td>77</td>\n",
" <td>1</td>\n",
" <td>0.00187</td>\n",
" <td>0.00899</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49</th>\n",
" <td>10</td>\n",
" <td>1</td>\n",
" <td>0.00177</td>\n",
" <td>0.00898</td>\n",
" </tr>\n",
" <tr>\n",
" <th>56</th>\n",
" <td>16</td>\n",
" <td>1</td>\n",
" <td>0.00172</td>\n",
" <td>0.00895</td>\n",
" </tr>\n",
" <tr>\n",
" <th>87</th>\n",
" <td>44</td>\n",
" <td>1</td>\n",
" <td>0.00173</td>\n",
" <td>0.00895</td>\n",
" </tr>\n",
" <tr>\n",
" <th>89</th>\n",
" <td>46</td>\n",
" <td>1</td>\n",
" <td>0.00177</td>\n",
" <td>0.00891</td>\n",
" </tr>\n",
" <tr>\n",
" <th>40</th>\n",
" <td>92</td>\n",
" <td>1</td>\n",
" <td>0.00188</td>\n",
" <td>0.00890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>59</th>\n",
" <td>19</td>\n",
" <td>1</td>\n",
" <td>0.00162</td>\n",
" <td>0.00887</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" PageID Topic Vanilla PR Topic 1\n",
"46 98 1 0.00178 0.00926\n",
"68 27 1 0.00179 0.00910\n",
"74 32 1 0.00186 0.00904\n",
"75 33 1 0.00167 0.00902\n",
"23 77 1 0.00187 0.00899\n",
"49 10 1 0.00177 0.00898\n",
"56 16 1 0.00172 0.00895\n",
"87 44 1 0.00173 0.00895\n",
"89 46 1 0.00177 0.00891\n",
"40 92 1 0.00188 0.00890\n",
"59 19 1 0.00162 0.00887"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"Top 10 pages in Topic 2\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>PageID</th>\n",
" <th>Topic</th>\n",
" <th>Vanilla PR</th>\n",
" <th>Topic 2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>52</th>\n",
" <td>12</td>\n",
" <td>2</td>\n",
" <td>0.00177</td>\n",
" <td>0.01890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>82</td>\n",
" <td>2</td>\n",
" <td>0.00161</td>\n",
" <td>0.01889</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>59</td>\n",
" <td>2</td>\n",
" <td>0.00171</td>\n",
" <td>0.01888</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>73</td>\n",
" <td>2</td>\n",
" <td>0.00184</td>\n",
" <td>0.01885</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>58</td>\n",
" <td>2</td>\n",
" <td>0.00191</td>\n",
" <td>0.01865</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>71</td>\n",
" <td>2</td>\n",
" <td>0.00189</td>\n",
" <td>0.01863</td>\n",
" </tr>\n",
" <tr>\n",
" <th>37</th>\n",
" <td>9</td>\n",
" <td>2</td>\n",
" <td>0.00193</td>\n",
" <td>0.01861</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>75</td>\n",
" <td>2</td>\n",
" <td>0.00176</td>\n",
" <td>0.01861</td>\n",
" </tr>\n",
" <tr>\n",
" <th>57</th>\n",
" <td>17</td>\n",
" <td>10</td>\n",
" <td>0.00185</td>\n",
" <td>0.00100</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>62</td>\n",
" <td>8</td>\n",
" <td>0.00177</td>\n",
" <td>0.00097</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>52</td>\n",
" <td>1</td>\n",
" <td>0.00187</td>\n",
" <td>0.00095</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" PageID Topic Vanilla PR Topic 2\n",
"52 12 2 0.00177 0.01890\n",
"29 82 2 0.00161 0.01889\n",
"3 59 2 0.00171 0.01888\n",
"19 73 2 0.00184 0.01885\n",
"2 58 2 0.00191 0.01865\n",
"17 71 2 0.00189 0.01863\n",
"37 9 2 0.00193 0.01861\n",
"21 75 2 0.00176 0.01861\n",
"57 17 10 0.00185 0.00100\n",
"7 62 8 0.00177 0.00097\n",
"96 52 1 0.00187 0.00095"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"Top 10 pages in Topic 3\n"
]
},
{
"data": {
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"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>PageID</th>\n",
" <th>Topic</th>\n",
" <th>Vanilla PR</th>\n",
" <th>Topic 3</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>33</th>\n",
" <td>86</td>\n",
" <td>3</td>\n",
" <td>0.00178</td>\n",
" <td>0.01702</td>\n",
" </tr>\n",
" <tr>\n",
" <th>55</th>\n",
" <td>15</td>\n",
" <td>3</td>\n",
" <td>0.00195</td>\n",
" <td>0.01700</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>66</td>\n",
" <td>3</td>\n",
" <td>0.00171</td>\n",
" <td>0.01678</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>70</td>\n",
" <td>3</td>\n",
" <td>0.00182</td>\n",
" <td>0.01657</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39</th>\n",
" <td>91</td>\n",
" <td>3</td>\n",
" <td>0.00180</td>\n",
" <td>0.01654</td>\n",
" </tr>\n",
" <tr>\n",
" <th>60</th>\n",
" <td>2</td>\n",
" <td>3</td>\n",
" <td>0.00179</td>\n",
" <td>0.01654</td>\n",
" </tr>\n",
" <tr>\n",
" <th>83</th>\n",
" <td>40</td>\n",
" <td>3</td>\n",
" <td>0.00173</td>\n",
" <td>0.01653</td>\n",
" </tr>\n",
" <tr>\n",
" <th>73</th>\n",
" <td>31</td>\n",
" <td>3</td>\n",
" <td>0.00173</td>\n",
" <td>0.01653</td>\n",
" </tr>\n",
" <tr>\n",
" <th>61</th>\n",
" <td>20</td>\n",
" <td>3</td>\n",
" <td>0.00160</td>\n",
" <td>0.01652</td>\n",
" </tr>\n",
" <tr>\n",
" <th>38</th>\n",
" <td>90</td>\n",
" <td>5</td>\n",
" <td>0.00185</td>\n",
" <td>0.00101</td>\n",
" </tr>\n",
" <tr>\n",
" <th>89</th>\n",
" <td>46</td>\n",
" <td>1</td>\n",
" <td>0.00177</td>\n",
" <td>0.00092</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" PageID Topic Vanilla PR Topic 3\n",
"33 86 3 0.00178 0.01702\n",
"55 15 3 0.00195 0.01700\n",
"11 66 3 0.00171 0.01678\n",
"16 70 3 0.00182 0.01657\n",
"39 91 3 0.00180 0.01654\n",
"60 2 3 0.00179 0.01654\n",
"83 40 3 0.00173 0.01653\n",
"73 31 3 0.00173 0.01653\n",
"61 20 3 0.00160 0.01652\n",
"38 90 5 0.00185 0.00101\n",
"89 46 1 0.00177 0.00092"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
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"text": [
"\n",
"\n",
"Top 10 pages in Topic 4\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
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" <th>PageID</th>\n",
" <th>Topic</th>\n",
" <th>Vanilla PR</th>\n",
" <th>Topic 4</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>30</th>\n",
" <td>83</td>\n",
" <td>4</td>\n",
" <td>0.00179</td>\n",
" <td>0.01200</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>63</td>\n",
" <td>4</td>\n",
" <td>0.00195</td>\n",
" <td>0.01197</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>78</td>\n",
" <td>4</td>\n",
" <td>0.00176</td>\n",
" <td>0.01174</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>65</td>\n",
" <td>4</td>\n",
" <td>0.00178</td>\n",
" <td>0.01171</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td>79</td>\n",
" <td>4</td>\n",
" <td>0.00172</td>\n",
" <td>0.01171</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>76</td>\n",
" <td>4</td>\n",
" <td>0.00166</td>\n",
" <td>0.01164</td>\n",
" </tr>\n",
" <tr>\n",
" <th>80</th>\n",
" <td>38</td>\n",
" <td>4</td>\n",
" <td>0.00166</td>\n",
" <td>0.01159</td>\n",
" </tr>\n",
" <tr>\n",
" <th>31</th>\n",
" <td>84</td>\n",
" <td>4</td>\n",
" <td>0.00178</td>\n",
" <td>0.01148</td>\n",
" </tr>\n",
" <tr>\n",
" <th>84</th>\n",
" <td>41</td>\n",
" <td>4</td>\n",
" <td>0.00178</td>\n",
" <td>0.01148</td>\n",
" </tr>\n",
" <tr>\n",
" <th>41</th>\n",
" <td>93</td>\n",
" <td>4</td>\n",
" <td>0.00169</td>\n",
" <td>0.01145</td>\n",
" </tr>\n",
" <tr>\n",
" <th>36</th>\n",
" <td>89</td>\n",
" <td>4</td>\n",
" <td>0.00171</td>\n",
" <td>0.01145</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
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" PageID Topic Vanilla PR Topic 4\n",
"30 83 4 0.00179 0.01200\n",
"8 63 4 0.00195 0.01197\n",
"24 78 4 0.00176 0.01174\n",
"10 65 4 0.00178 0.01171\n",
"25 79 4 0.00172 0.01171\n",
"22 76 4 0.00166 0.01164\n",
"80 38 4 0.00166 0.01159\n",
"31 84 4 0.00178 0.01148\n",
"84 41 4 0.00178 0.01148\n",
"41 93 4 0.00169 0.01145\n",
"36 89 4 0.00171 0.01145"
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" <th>47</th>\n",
" <td>99</td>\n",
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" <td>0.01679</td>\n",
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" <th>76</th>\n",
" <td>34</td>\n",
" <td>5</td>\n",
" <td>0.00173</td>\n",
" <td>0.01675</td>\n",
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" <tr>\n",
" <th>95</th>\n",
" <td>51</td>\n",
" <td>5</td>\n",
" <td>0.00182</td>\n",
" <td>0.01675</td>\n",
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" <tr>\n",
" <th>88</th>\n",
" <td>45</td>\n",
" <td>5</td>\n",
" <td>0.00186</td>\n",
" <td>0.01674</td>\n",
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" <tr>\n",
" <th>82</th>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>0.00174</td>\n",
" <td>0.01655</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>80</td>\n",
" <td>5</td>\n",
" <td>0.00171</td>\n",
" <td>0.01653</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50</th>\n",
" <td>100</td>\n",
" <td>8</td>\n",
" <td>0.00195</td>\n",
" <td>0.00099</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>58</td>\n",
" <td>2</td>\n",
" <td>0.00191</td>\n",
" <td>0.00099</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
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" PageID Topic Vanilla PR Topic 5\n",
"47 99 5 0.00177 0.01717\n",
"93 5 5 0.00167 0.01696\n",
"38 90 5 0.00185 0.01683\n",
"35 88 5 0.00188 0.01679\n",
"76 34 5 0.00173 0.01675\n",
"95 51 5 0.00182 0.01675\n",
"88 45 5 0.00186 0.01674\n",
"82 4 5 0.00174 0.01655\n",
"27 80 5 0.00171 0.01653\n",
"50 100 8 0.00195 0.00099\n",
"2 58 2 0.00191 0.00099"
]
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" <th>Topic 6</th>\n",
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" <tr>\n",
" <th>53</th>\n",
" <td>13</td>\n",
" <td>6</td>\n",
" <td>0.00186</td>\n",
" <td>0.02481</td>\n",
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" <tr>\n",
" <th>79</th>\n",
" <td>37</td>\n",
" <td>6</td>\n",
" <td>0.00170</td>\n",
" <td>0.02480</td>\n",
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" <th>0</th>\n",
" <td>56</td>\n",
" <td>6</td>\n",
" <td>0.00179</td>\n",
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" <tr>\n",
" <th>14</th>\n",
" <td>69</td>\n",
" <td>6</td>\n",
" <td>0.00170</td>\n",
" <td>0.02478</td>\n",
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" <tr>\n",
" <th>51</th>\n",
" <td>11</td>\n",
" <td>6</td>\n",
" <td>0.00174</td>\n",
" <td>0.02478</td>\n",
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" <tr>\n",
" <th>64</th>\n",
" <td>23</td>\n",
" <td>6</td>\n",
" <td>0.00162</td>\n",
" <td>0.02477</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>52</td>\n",
" <td>1</td>\n",
" <td>0.00187</td>\n",
" <td>0.00115</td>\n",
" </tr>\n",
" <tr>\n",
" <th>55</th>\n",
" <td>15</td>\n",
" <td>3</td>\n",
" <td>0.00195</td>\n",
" <td>0.00114</td>\n",
" </tr>\n",
" <tr>\n",
" <th>99</th>\n",
" <td>55</td>\n",
" <td>7</td>\n",
" <td>0.00180</td>\n",
" <td>0.00112</td>\n",
" </tr>\n",
" <tr>\n",
" <th>74</th>\n",
" <td>32</td>\n",
" <td>1</td>\n",
" <td>0.00186</td>\n",
" <td>0.00100</td>\n",
" </tr>\n",
" <tr>\n",
" <th>32</th>\n",
" <td>85</td>\n",
" <td>7</td>\n",
" <td>0.00191</td>\n",
" <td>0.00098</td>\n",
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" </tbody>\n",
"</table>\n",
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" PageID Topic Vanilla PR Topic 6\n",
"53 13 6 0.00186 0.02481\n",
"79 37 6 0.00170 0.02480\n",
"0 56 6 0.00179 0.02478\n",
"14 69 6 0.00170 0.02478\n",
"51 11 6 0.00174 0.02478\n",
"64 23 6 0.00162 0.02477\n",
"96 52 1 0.00187 0.00115\n",
"55 15 3 0.00195 0.00114\n",
"99 55 7 0.00180 0.00112\n",
"74 32 1 0.00186 0.00100\n",
"32 85 7 0.00191 0.00098"
]
},
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" <th>90</th>\n",
" <td>47</td>\n",
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" <td>0.00170</td>\n",
" <td>0.01533</td>\n",
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" <tr>\n",
" <th>66</th>\n",
" <td>25</td>\n",
" <td>7</td>\n",
" <td>0.00182</td>\n",
" <td>0.01516</td>\n",
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" <tr>\n",
" <th>72</th>\n",
" <td>30</td>\n",
" <td>7</td>\n",
" <td>0.00172</td>\n",
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" <th>69</th>\n",
" <td>28</td>\n",
" <td>7</td>\n",
" <td>0.00181</td>\n",
" <td>0.01511</td>\n",
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" <tr>\n",
" <th>45</th>\n",
" <td>97</td>\n",
" <td>7</td>\n",
" <td>0.00177</td>\n",
" <td>0.01510</td>\n",
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" <tr>\n",
" <th>97</th>\n",
" <td>53</td>\n",
" <td>7</td>\n",
" <td>0.00184</td>\n",
" <td>0.01506</td>\n",
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" <tr>\n",
" <th>94</th>\n",
" <td>50</td>\n",
" <td>7</td>\n",
" <td>0.00167</td>\n",
" <td>0.01504</td>\n",
" </tr>\n",
" <tr>\n",
" <th>77</th>\n",
" <td>35</td>\n",
" <td>7</td>\n",
" <td>0.00180</td>\n",
" <td>0.01492</td>\n",
" </tr>\n",
" <tr>\n",
" <th>32</th>\n",
" <td>85</td>\n",
" <td>7</td>\n",
" <td>0.00191</td>\n",
" <td>0.01492</td>\n",
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" <tr>\n",
" <th>99</th>\n",
" <td>55</td>\n",
" <td>7</td>\n",
" <td>0.00180</td>\n",
" <td>0.01488</td>\n",
" </tr>\n",
" <tr>\n",
" <th>57</th>\n",
" <td>17</td>\n",
" <td>10</td>\n",
" <td>0.00185</td>\n",
" <td>0.00108</td>\n",
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" </tbody>\n",
"</table>\n",
"</div>"
],
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" PageID Topic Vanilla PR Topic 7\n",
"90 47 7 0.00170 0.01533\n",
"66 25 7 0.00182 0.01516\n",
"72 30 7 0.00172 0.01515\n",
"69 28 7 0.00181 0.01511\n",
"45 97 7 0.00177 0.01510\n",
"97 53 7 0.00184 0.01506\n",
"94 50 7 0.00167 0.01504\n",
"77 35 7 0.00180 0.01492\n",
"32 85 7 0.00191 0.01492\n",
"99 55 7 0.00180 0.01488\n",
"57 17 10 0.00185 0.00108"
]
},
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" <th>50</th>\n",
" <td>100</td>\n",
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" <td>0.00195</td>\n",
" <td>0.01751</td>\n",
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" <tr>\n",
" <th>26</th>\n",
" <td>8</td>\n",
" <td>8</td>\n",
" <td>0.00181</td>\n",
" <td>0.01716</td>\n",
" </tr>\n",
" <tr>\n",
" <th>34</th>\n",
" <td>87</td>\n",
" <td>8</td>\n",
" <td>0.00171</td>\n",
" <td>0.01699</td>\n",
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" <tr>\n",
" <th>81</th>\n",
" <td>39</td>\n",
" <td>8</td>\n",
" <td>0.00180</td>\n",
" <td>0.01686</td>\n",
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" <tr>\n",
" <th>7</th>\n",
" <td>62</td>\n",
" <td>8</td>\n",
" <td>0.00177</td>\n",
" <td>0.01678</td>\n",
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" <tr>\n",
" <th>6</th>\n",
" <td>61</td>\n",
" <td>8</td>\n",
" <td>0.00190</td>\n",
" <td>0.01657</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>6</td>\n",
" <td>8</td>\n",
" <td>0.00175</td>\n",
" <td>0.01654</td>\n",
" </tr>\n",
" <tr>\n",
" <th>98</th>\n",
" <td>54</td>\n",
" <td>8</td>\n",
" <td>0.00172</td>\n",
" <td>0.01653</td>\n",
" </tr>\n",
" <tr>\n",
" <th>58</th>\n",
" <td>18</td>\n",
" <td>8</td>\n",
" <td>0.00165</td>\n",
" <td>0.01652</td>\n",
" </tr>\n",
" <tr>\n",
" <th>60</th>\n",
" <td>2</td>\n",
" <td>3</td>\n",
" <td>0.00179</td>\n",
" <td>0.00102</td>\n",
" </tr>\n",
" <tr>\n",
" <th>33</th>\n",
" <td>86</td>\n",
" <td>3</td>\n",
" <td>0.00178</td>\n",
" <td>0.00083</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
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" PageID Topic Vanilla PR Topic 8\n",
"50 100 8 0.00195 0.01751\n",
"26 8 8 0.00181 0.01716\n",
"34 87 8 0.00171 0.01699\n",
"81 39 8 0.00180 0.01686\n",
"7 62 8 0.00177 0.01678\n",
"6 61 8 0.00190 0.01657\n",
"4 6 8 0.00175 0.01654\n",
"98 54 8 0.00172 0.01653\n",
"58 18 8 0.00165 0.01652\n",
"60 2 3 0.00179 0.00102\n",
"33 86 3 0.00178 0.00083"
]
},
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},
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"Top 10 pages in Topic 9\n"
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" <th>Topic 9</th>\n",
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" <tr>\n",
" <th>85</th>\n",
" <td>42</td>\n",
" <td>9</td>\n",
" <td>0.00179</td>\n",
" <td>0.02149</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42</th>\n",
" <td>94</td>\n",
" <td>9</td>\n",
" <td>0.00183</td>\n",
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" <tr>\n",
" <th>54</th>\n",
" <td>14</td>\n",
" <td>9</td>\n",
" <td>0.00176</td>\n",
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" <tr>\n",
" <th>44</th>\n",
" <td>96</td>\n",
" <td>9</td>\n",
" <td>0.00163</td>\n",
" <td>0.02146</td>\n",
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" <tr>\n",
" <th>62</th>\n",
" <td>21</td>\n",
" <td>9</td>\n",
" <td>0.00175</td>\n",
" <td>0.02126</td>\n",
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" <tr>\n",
" <th>1</th>\n",
" <td>57</td>\n",
" <td>9</td>\n",
" <td>0.00176</td>\n",
" <td>0.02125</td>\n",
" </tr>\n",
" <tr>\n",
" <th>65</th>\n",
" <td>24</td>\n",
" <td>9</td>\n",
" <td>0.00171</td>\n",
" <td>0.02124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>61</td>\n",
" <td>8</td>\n",
" <td>0.00190</td>\n",
" <td>0.00106</td>\n",
" </tr>\n",
" <tr>\n",
" <th>86</th>\n",
" <td>43</td>\n",
" <td>10</td>\n",
" <td>0.00176</td>\n",
" <td>0.00104</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>63</td>\n",
" <td>4</td>\n",
" <td>0.00195</td>\n",
" <td>0.00092</td>\n",
" </tr>\n",
" <tr>\n",
" <th>35</th>\n",
" <td>88</td>\n",
" <td>5</td>\n",
" <td>0.00188</td>\n",
" <td>0.00081</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
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" PageID Topic Vanilla PR Topic 9\n",
"85 42 9 0.00179 0.02149\n",
"42 94 9 0.00183 0.02148\n",
"54 14 9 0.00176 0.02148\n",
"44 96 9 0.00163 0.02146\n",
"62 21 9 0.00175 0.02126\n",
"1 57 9 0.00176 0.02125\n",
"65 24 9 0.00171 0.02124\n",
"6 61 8 0.00190 0.00106\n",
"86 43 10 0.00176 0.00104\n",
"8 63 4 0.00195 0.00092\n",
"35 88 5 0.00188 0.00081"
]
},
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},
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"\n",
"Top 10 pages in Topic 10\n"
]
},
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" <th>Topic</th>\n",
" <th>Vanilla PR</th>\n",
" <th>Topic 10</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>74</td>\n",
" <td>10</td>\n",
" <td>0.00192</td>\n",
" <td>0.01275</td>\n",
" </tr>\n",
" <tr>\n",
" <th>92</th>\n",
" <td>49</td>\n",
" <td>10</td>\n",
" <td>0.00184</td>\n",
" <td>0.01268</td>\n",
" </tr>\n",
" <tr>\n",
" <th>57</th>\n",
" <td>17</td>\n",
" <td>10</td>\n",
" <td>0.00185</td>\n",
" <td>0.01262</td>\n",
" </tr>\n",
" <tr>\n",
" <th>91</th>\n",
" <td>48</td>\n",
" <td>10</td>\n",
" <td>0.00170</td>\n",
" <td>0.01261</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>7</td>\n",
" <td>10</td>\n",
" <td>0.00172</td>\n",
" <td>0.01260</td>\n",
" </tr>\n",
" <tr>\n",
" <th>48</th>\n",
" <td>1</td>\n",
" <td>10</td>\n",
" <td>0.00171</td>\n",
" <td>0.01260</td>\n",
" </tr>\n",
" <tr>\n",
" <th>71</th>\n",
" <td>3</td>\n",
" <td>10</td>\n",
" <td>0.00171</td>\n",
" <td>0.01254</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>60</td>\n",
" <td>10</td>\n",
" <td>0.00165</td>\n",
" <td>0.01253</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43</th>\n",
" <td>95</td>\n",
" <td>10</td>\n",
" <td>0.00181</td>\n",
" <td>0.01242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>68</td>\n",
" <td>10</td>\n",
" <td>0.00175</td>\n",
" <td>0.01242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>86</th>\n",
" <td>43</td>\n",
" <td>10</td>\n",
" <td>0.00176</td>\n",
" <td>0.01240</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" PageID Topic Vanilla PR Topic 10\n",
"20 74 10 0.00192 0.01275\n",
"92 49 10 0.00184 0.01268\n",
"57 17 10 0.00185 0.01262\n",
"91 48 10 0.00170 0.01261\n",
"15 7 10 0.00172 0.01260\n",
"48 1 10 0.00171 0.01260\n",
"71 3 10 0.00171 0.01254\n",
"5 60 10 0.00165 0.01253\n",
"43 95 10 0.00181 0.01242\n",
"13 68 10 0.00175 0.01242\n",
"86 43 10 0.00176 0.01240"
]
},
"metadata": {},
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},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n"
]
}
],
"source": [
"from IPython.display import display, HTML\n",
"# Display the top 10 ranked pages in each topic\n",
"for i in range(1,11):\n",
" print \"Top 10 pages in Topic %s\" %i\n",
" topicPR=RandNetPR.sort_values(\"Topic %s\" %i, ascending=False)\n",
" selectcolumn=topicPR[[\"PageID\", \"Topic\", \"Vanilla PR\", \"Topic %s\" %i]].copy()\n",
" selectrow=selectcolumn.iloc[0:11,:]\n",
" display(selectrow)\n",
" print \"\\n\"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"HW9.5\"></a>\n",
"[Back to Top](#TOC)\n",
"\n",
"\n",
"<h1 style=\"color:#021353;\">HW 9.5: (OPTIONAL) Applying topic-specific PageRank to Wikipedia</h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"Here you will apply your topic-specific PageRank implementation to Wikipedia,\n",
"defining topics (very arbitrarily) for each page by the length (number of \n",
"characters) of the name of the article mod 10, so that there are \n",
"10 topics. Once again, print out the top ten ranking nodes \n",
"and their topics for each of the 11 versions, and comment on your result.\n",
"Assume a teleportation factor of 0.15 in all your analyses. Run for 10 iterations.\n",
"\n",
"Plot the pagerank values for the top 100 pages resulting from the 5 iterations run in HW9.3. \n",
"Then plot the pagerank values for the same 100 pages that result from the \n",
"topic specific pagerank after 10 iterations run. Comment on your findings. \n",
"\n",
"\n",
"</pre>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1 style=\"color:#021353;\">HW 9.6: (OPTIONAL) TextRank </h1>\n",
"<div style=\"margin:10px;border-left:5px solid #eee;\">\n",
"<pre style=\"font-family:sans-serif;background-color:transparent\">\n",
"What is TextRank. Describe the main steps in the algorithm. Why does TextRank work?\n",
"Implement TextRank in MrJob for keyword phrases (not just unigrams) extraction using co-occurrence based similarity measure with with sizes of N = 2 and 3. And evaluate your code using the following example using precision, recall, and FBeta (Beta=1):\n",
"\n",
"\"Compatibility of systems of linear constraints over the set of natural numbers\n",
"Criteria of compatibility of a system of linear Diophantine equations, strict \n",
"inequations, and nonstrict inequations are considered. Upper bounds for\n",
"components of a minimal set of solutions and algorithms of construction of \n",
"minimal generating sets of solutions for all types of systems are given. \n",
"These criteria and the corresponding algorithms for constructing a minimal \n",
"supporting set of solutions can be used in solving all the considered types of \n",
"systems and systems of mixed types.\" \n",
"\n",
"The extracted keywords should in the following set:\n",
"\n",
"linear constraints, linear diophantine equations, natural numbers, non-strict inequations, strict inequations, upper bounds\n",
"\n",
"\n",
"</pre>\n",
"</div>\n",
"\n",
"***"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"==================END HW 7=================="
]
}
],
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