12_ds08_1 Cluestering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7b727a48",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Sklearn으로-k-means-클러스터링\" data-toc-modified-id=\"Sklearn으로-k-means-클러스터링-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Sklearn으로 k-means 클러스터링</a></span><ul class=\"toc-item\"><li><span><a href=\"#데이터\" data-toc-modified-id=\"데이터-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>데이터</a></span></li><li><span><a href=\"#클러스터-할당\" data-toc-modified-id=\"클러스터-할당-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>클러스터 할당</a></span></li><li><span><a href=\"#예측\" data-toc-modified-id=\"예측-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>예측</a></span></li></ul></li><li><span><a href=\"#Spark-Clustering\" data-toc-modified-id=\"Spark-Clustering-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Spark Clustering</a></span><ul class=\"toc-item\"><li><span><a href=\"#DataFrame-생성\" data-toc-modified-id=\"DataFrame-생성-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>DataFrame 생성</a></span></li><li><span><a href=\"#Features-설정\" data-toc-modified-id=\"Features-설정-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Features 설정</a></span></li><li><span><a href=\"#k-means-클러스터링\" data-toc-modified-id=\"k-means-클러스터링-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>k-means 클러스터링</a></span></li><li><span><a href=\"#클러스터-중심점\" data-toc-modified-id=\"클러스터-중심점-2.4\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span>클러스터 중심점</a></span></li></ul></li><li><span><a href=\"#Iris-데이터-클러스터링(군집화)\" data-toc-modified-id=\"Iris-데이터-클러스터링(군집화)-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Iris 데이터 클러스터링(군집화)</a></span><ul class=\"toc-item\"><li><span><a href=\"#데이터\" data-toc-modified-id=\"데이터-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>데이터</a></span></li><li><span><a href=\"#그래프\" data-toc-modified-id=\"그래프-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>그래프</a></span></li><li><span><a href=\"#RDD-생성\" data-toc-modified-id=\"RDD-생성-3.3\"><span class=\"toc-item-num\">3.3&nbsp;&nbsp;</span>RDD 생성</a></span></li><li><span><a href=\"#형변환\" data-toc-modified-id=\"형변환-3.4\"><span class=\"toc-item-num\">3.4&nbsp;&nbsp;</span>형변환</a></span></li><li><span><a href=\"#k-Means-모델링\" data-toc-modified-id=\"k-Means-모델링-3.5\"><span class=\"toc-item-num\">3.5&nbsp;&nbsp;</span>k-Means 모델링</a></span></li><li><span><a href=\"#DataFrame-생성\" data-toc-modified-id=\"DataFrame-생성-3.6\"><span class=\"toc-item-num\">3.6&nbsp;&nbsp;</span>DataFrame 생성</a></span></li><li><span><a href=\"#통계량\" data-toc-modified-id=\"통계량-3.7\"><span class=\"toc-item-num\">3.7&nbsp;&nbsp;</span>통계량</a></span></li><li><span><a href=\"#features-생성\" data-toc-modified-id=\"features-생성-3.8\"><span class=\"toc-item-num\">3.8&nbsp;&nbsp;</span>features 생성</a></span></li><li><span><a href=\"#k-Means\" data-toc-modified-id=\"k-Means-3.9\"><span class=\"toc-item-num\">3.9&nbsp;&nbsp;</span>k-Means</a></span></li><li><span><a href=\"#최적의-클러스터-개수-구하기\" data-toc-modified-id=\"최적의-클러스터-개수-구하기-3.10\"><span class=\"toc-item-num\">3.10&nbsp;&nbsp;</span>최적의 클러스터 개수 구하기</a></span></li><li><span><a href=\"#클러스터-개수에-따른-오류-그래프\" data-toc-modified-id=\"클러스터-개수에-따른-오류-그래프-3.11\"><span class=\"toc-item-num\">3.11&nbsp;&nbsp;</span>클러스터 개수에 따른 오류 그래프</a></span></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "38042db7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# SparkSession 생성\n",
    "import pyspark\n",
    "import os\n",
    "\n",
    "myConf=pyspark.SparkConf()\n",
    "spark = pyspark.sql.SparkSession\\\n",
    "    .builder\\\n",
    "    .master(\"local\")\\\n",
    "    .appName(\"myApp\")\\\n",
    "    .config(conf=myConf)\\\n",
    "    .getOrCreate()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "970df33d",
   "metadata": {},
   "source": [
    "## Sklearn으로 k-means 클러스터링"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f61a299",
   "metadata": {},
   "source": [
    "### 데이터"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7784ddea",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = np.array([[2,5],[3,6],[2,4],[5,7],[7,2],[8,3],[9,4],[8,4],[7,3]], dtype = float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dfae309f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "kmeans = KMeans(n_clusters=2, init='random', random_state=2).fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6679f487",
   "metadata": {},
   "source": [
    "### 클러스터 할당"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6bd1a371",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster label:  [1 1 1 1 0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "print (\"Cluster label: \", kmeans.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3b04f68d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Centroid:  [[7.8 3.2]\n",
      " [3.  5.5]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Centroid: \", kmeans.cluster_centers_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a66fa25",
   "metadata": {},
   "source": [
    "### 예측\n",
    "두 점을 입력하면 예측 가능"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d8d5e332",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictions:  [1 0]\n"
     ]
    }
   ],
   "source": [
    "print (\"Predictions: \", kmeans.predict([[0, 0], [7, 4]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece5f195",
   "metadata": {},
   "source": [
    "## Spark Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "753383cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.array([[2,5],[3,6],[2,4],[5,7],[7,2],[8,3],[9,4],[8,4],[7,3]], dtype = float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e027e05e",
   "metadata": {},
   "source": [
    "### DataFrame 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1418d002",
   "metadata": {},
   "outputs": [],
   "source": [
    "_xRdd = spark.sparkContext.parallelize(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0002e72a",
   "metadata": {},
   "outputs": [],
   "source": [
    "xRdd = _xRdd.map(lambda x: [int(i) for i in x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5b5604dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2, 5], [3, 6], [2, 4], [5, 7], [7, 2], [8, 3], [9, 4], [8, 4], [7, 3]]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xRdd.collect()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fae3fd62",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---+---+\n",
      "|  x|  y|\n",
      "+---+---+\n",
      "|  2|  5|\n",
      "|  3|  6|\n",
      "|  2|  4|\n",
      "|  5|  7|\n",
      "|  7|  2|\n",
      "|  8|  3|\n",
      "|  9|  4|\n",
      "|  8|  4|\n",
      "|  7|  3|\n",
      "+---+---+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xDf = xRdd.toDF([\"x\", \"y\"])\n",
    "xDf.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0caff152",
   "metadata": {},
   "source": [
    "### Features 설정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "17946dc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#from pyspark.ml.linalg import Vectors\n",
    "from pyspark.ml.feature import VectorAssembler\n",
    "\n",
    "va = VectorAssembler(inputCols=[\"x\",\"y\"],outputCol=\"features\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bff606fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "xxDf = va.transform(xDf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f1d96a35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root\n",
      " |-- x: long (nullable = true)\n",
      " |-- y: long (nullable = true)\n",
      " |-- features: vector (nullable = true)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xxDf.printSchema()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fc9a2ad4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---+---+---------+\n",
      "|  x|  y| features|\n",
      "+---+---+---------+\n",
      "|  2|  5|[2.0,5.0]|\n",
      "|  3|  6|[3.0,6.0]|\n",
      "|  2|  4|[2.0,4.0]|\n",
      "|  5|  7|[5.0,7.0]|\n",
      "|  7|  2|[7.0,2.0]|\n",
      "+---+---+---------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xxDf.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4769615",
   "metadata": {},
   "source": [
    "### k-means 클러스터링"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "fa706b97",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyspark.ml.clustering import KMeans\n",
    "\n",
    "kmeans = KMeans(k=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e7f84357",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = kmeans.fit(xxDf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87377108",
   "metadata": {},
   "source": [
    "### 클러스터 중심점"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "02a9de81",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([7.8, 3.2]), array([3. , 5.5])]\n"
     ]
    }
   ],
   "source": [
    "print (model.clusterCenters())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "234cf277",
   "metadata": {},
   "source": [
    "## Iris 데이터 클러스터링(군집화)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08b53b2a",
   "metadata": {},
   "source": [
    "### 데이터"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5f4105c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "dataset = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "486c4561",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dataset['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9d5705d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.9, 3. , 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[1:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "671e45fe",
   "metadata": {},
   "source": [
    "### 그래프"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "1e912b6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Public\\Documents\\ESTsoft\\CreatorTemp/ipykernel_24792/2284455069.py:4: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
      "  ax = plt.figure().gca(projection='3d')\n"
     ]
    },
    {
     "data": {
      "image/png": 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uF9XV1aMG7ySrsISIq9HU1ERhYSHLly9PeLvom15Vfba1tWnNdyfaZroQK5jas2cPhYWFMxbfSGVgMTZtqdaotLa2jsiowOTJaSqIR1CBQCDV/UAuBt6RUnanctFkMGeJYjxXo729nebmZtauXTtqpoZer0+YKNR2d/39/VRWVo4oGU8E0SMFDx8+DDCi+W48qHqNmbyohRAzGt+YTsFVbI2KmlHp6urC5/Ph9/s1EpyJMv9wODyKKNxu95gPikniI8yi2wFzkCjUgGVzczNms5nCwkLtolMH70DkhoxnQut0OsLh8IT7UXUW2dnZbN26lb6+Pq3wJ1EIIQiFQrz99ttagVki28x2UVii8Y3J3mwzpcyMDiIaDAaNJOx2O7W1tSnLqIwHVWwVDZfLlTKiEEJkABcAn0rJgpPEnCKKaFcjVh8RPXintLR0zDUScT1U3z1aZzGZG7i3txen08nJJ5/8rhwpqCLV+o3ZOD9VlTtWRqW1tXVEBWlubu64ll+y+41GKlWZUko3MH7vgiQghMgH9EBw+McvpQxNtN2cIYrYFnVq70MpJc3NzXR2do7r+6tQt4uHaFcjNquRTGxDURTq6uo0EzPZkYLqsczEDTWZ0vlU6DfmQq1HvIyKWkHa0NCQcCHYeIhnUUyD6zFlDFsmFwKnADpAAcxANfCYEELIcS6WWSeKsVrU6fV6PB4P+/fvx2q1cvLJJ086EwGRAFNVVRVZWVlxsxrJqCwPHjxIUVERy5Yt4+23307kNEccn9/vZ9++fSPKt/Pz86fFNFb3OVlMRr8xW0VhE1kIsRWkakZFPReTyaSdS2w9x1gYiyjmSp2HEEIvpQwD5wDfBR4FBgATkAl0JrLOrBLFeC3qPB4PLS0trFmzZtTgnfEQ78uN52rEIhGiUIVYatPcyVgFTqeTjo4O1q9fr0l91fLt6GrSuTopLJH4htfrJRgMzmiJ9WTSo/EyKgMDA7S0tOByubSMSn5+PlarNe61Nd0xiqlimCQAQsAfpJQ/GuN9417Is0YUY2kj1PqKrq4u5s2blxRJxEJ1NcYb4qNiPKIYy2VJ5qkZXcm6YMEC8vLyCAaDWju3xYsXEwqFRlRhqk/ruTzwJ15849ChQ9TX1xMOh2esPiUVOgqLxcKCBQu0c1EzKvX19SO6gEcHed8FFsU6YDOwCFgmhLgGOAL4hn/6pZS+cZYAZoEoxtNGRJdyr1q1ip6enknvJxAIUF1dTWZm5rhDfFSM57Ko6yQqxIpFKBSipqYGk8nE0qVLcTqdcd9nMBhG9EiIbk/n9XrJysrSTOPZnNsxFtT4htlsZs2aNej1+hmrT0l1rcd4NSqHDx/WSB4YpeBVWwmm4BhygZ8CawEJ/JuU8o0kl1kIfBxoArKAu4F+InGK+cD9wANRLkpczChRjKeNUGdhqMVTDocjoTRnPIRCIfbs2cOyZcs0s3IixLMoHA4HNTU1Sa0TC5fLRVVVFRUVFSxYsIDe3t6E3RWr1Uppaak2IEftMtXe3o6iKHPaTVED0jOl35huZeZYNSrNzc0MDAzQ29tLbm4uiqJgt9sTSpUngAeAP0spPzCszky6HFVK+SfgT0KICsAnpewSQqimdS7gGn7fuDfbjBFF7Pi+aOmtmkGIblCbjHBKhVqI5ff7OeOMM5LykaOJQkpJa2sr7e3tEza8GQ/d3d0cP358hDBssulRIcQoN2VwcJDe3t4RbspcLgqbTv2GShRSSg53uXB4Q1QW2piXPT2iKzWj4nA4mD9/PgUFBQwODvL000/z+OOPY7VaaWtr44YbbqC8vDzp9YUQOcBZwCcApJQBIDCFQ74OaACelFJ6h/fxOaAN+M2sZz3GczU8Hg9VVVWUlJSwYsWKERdXosIpFdEugs1mm3T1qCrq0ul0E6osx4KUkrq6OlwuF9u2bRuRzUhVViA2gh9706luitq+biaR6PmlUr+hWqk/fKmRV+sH0AmBEHDH+5eyaVFOqk4t7n7VDuCFhYV88pOfpK2tTbt2AoFJ39uLgV7g50KIDcA+4AvDuoqEIYRYAqwDLgPeEULUE0mLqiXsqixcEHFv4mJaiULNwasR4+iLRx28s2bNmrgX83h6iFiofqPqItjt9qRvRnXq1549exJWWcZDIBDg4MGD5OXlxZ06NlNFYU6nU7vpXC4X9fX1mpuSCqHReJgMEU5Vv6EoCrU9Xl6pHyDXakAnBN5gmPv/3sgvrt8wbRZWvGCmx+OhtLSUs846aypLG4gEIT8npXxLCPEA8HXgm0muk0lEP7GASIziTMBKxO3YDfxj+H0zn/VQtRGBQIADBw5w+umna6/FDt4ZSzuQCFGomYSenp4RWQ3VGknGZ+3u7sbtdnPKKadMuoWZGtMYLw07U0Vhqj9dVlbGvn37yM3N1TpOq1PC8vPzp8VNSYXFlGx8Q1EUhvwKOiHQDe/bYtDR7wkRlmCYJk9sGgVXbUCblPKt4f/vIEIUSUFKeRC4RQhxDvDmWBmOGU+PRmsjYqcqxRu8MxYm0jWorkZGRsaorEayKsujR4/i9Xqx2WyTJonW1lba2tqmFNOYLgghRrgpql4g1k3Jz89PWTYl1eQzUXwjGAySk5+BlBJ/SMGkFwx6Q6wozsCgm754zXSlR4eDjq1CiBXDna7OBw4nu44QQielVIgIrG4TQjiAQSLKzDagTko5oegqpUQxnjZCLcGOHbwzFsZrdqu231+6dGlcnUWigVBVZVlcXMzKlSt5441kM0+Rc6upqUFRlIRiGnOh1iNWL6C6KTU1NYTD4RHZlOl2UyaLWFdr7969FFjgqgqF3x31EkLHkkIbXzo3+UBiMhhLcJWixrqfA349nPFoAG6cwlr/RiQ4epCIfuI0IoSRIYT4PvDIeDUfKSMKNfUJIyeFSyk5ePAgBoNh0sHB6LVUV2O8J3cigVB1iM/q1asn3QXK6/Xi8XhYtGgRixYtSugpOheIIhrRbkpFRYWWTZkpNyUVUIPkZWVlVFZW8pHzQvQODOJxOmirP0y7EGRm53LYocerGFg1PytlAc6xYhSpIAop5QFg61SXGf6tB7ZJKbX2b0KIJ4GvAr8BdhEho7hIGVHEBish8uR3u93jDt5JFIFAgJqaGqxW64QCqolUlmpn7UTnhcaDSjRmszlhkoATRBEKhfB4PNN+8yVLSrHZlFg3JRUjBKYD0ToKg8HA/OJCKI6cg8fn545naznS40YJK+h0gmvX5/PBbWVT/vzjxcI8Hs9cnBC2BFgihOglIrYKEBFy9RIhE+94G6fU9VBvUFXP0NPTQ2ZmZsIt88fCRK7GWMcRC7UwTO1BMZkLRD23vr4+tm7dyjvvvJNU8E4IQSAQYM+ePZhMJvx+P1lZWRQUFExbz4Sp3AixborL5aK/v19LYar9LFNVtj0VjPXwqO3x0TwUYn5exvDnH+KZ2iG2FDbijRrIPBnyi6cIlVLO+mehIipI+VPgs8AGIi7HucABQDW9x027pjyYGTt455133iEcDk9K56+6Gl1dXUkFCeMRhUo2U1FZhkIhqqursVqtmpxb3VeiGZb+/n7sdjsnnXSSFjh0Op309/fT2toKoF202dnZ02JtKFKyt9nBgCdAeb6NVfMSC7xFpzArKioIh8MjyrYNBgP5+flae4CJjl1Kyd+O9vNcVRcC2L5hHucvL0j5OftDyrCuIrKu0ahHBCWrVq/BoBNT7r8RfbyzUTmbCKSUDwshaoikSiuB3VLKX4vIwV6oirDGQkqJoq+vb1SVpsFgmJQUOxgMajGARCZ9RSM6tSqlpKWlhc7OzillJFQp9uLFi0e4UYnGHKSUHDt2jMHBQa0xbCAQQKfTaYpLiJz3wMAAHR0dHDlyhIyMDI04UjEsR0rJAy818kaDHQkIATeesoiL1yRPnnq9fkQjXL/fz8DAAIFAgLfffnvCJ/VrDXYefbWZTJMeCTzySjM2o47TKvOneJYjsbIkA7NBh8MbwmrU4fSH2FaWi1EfuaZSPT9lLpLFsGy7H3iciJuhCCGKpZQ9TOB2QIqJIhQKjWoIk4xwSoX69LdYLCxbtixpDX+0ylKdYL5t27ZJm4NdXV00NDTEzdgkQhTBYFBzedasWUNdXZ22bSyMRiMlJSWUlJQgpdTK0I8cOUIwGJyyqX+s18ObjYMUZJgQQhAMK/zirTbet7JQu3EmC7PZzPz582lra9OGOEc/qWOP/bX6AcwGHVZT5DyCYYVXjw9MiijG+w7yM0x89/IVPPpqM33uAOeXF3Lz6WVx35usfiOZ45gtCCEMwJeI9KTIJSK4MgMeIq7IhEgpUcyfP38UKUQPDZ4Iajcr1dWora0lHA4n7bfrdDo8Hg/Hjx+fsHVevGOIrUPxeDyjpNjR+xovFatqR5YsWUJJSQlerzfhi0kIQWZmJpmZmZSVlY0y9dWMREFBQcJl6J5AGJ04QVIGHQQVid0TpDgrdcHJeErLWDcl6BX4gyGkxYAAQookwzQ9YuHKQhv3XLUq6e0m0m/4/X46Ozs1q8nv96dsTKIQoglwEokjhKSUk82AFAK3ACuklK6o9RN+Mkx7rUeiFkUwGKSmpgaz2ay5GpNpvQ8RN8Fut7N58+ak0lTRdRjqSMH8/Hw2bdo05k04nkWhWiLr16/XBDhTSY/GmvpqRiK6DH2ioOjiAitmox6HN4jFpOdYT2Qi+3/sOMTFa4r56LbSaTGb47kpiq2Lg53tNHf70Ot1ZFqMXLJycqnqmTL1o/UboVBI61R2+PBhbYwgRFS6qjs5RZwrpexLwTovAyEhhJFIExuGhVgJIaVEEe/LSiRGoUqflyxZMmJoTrJui6IoHDlyBJfLRVlZWdK5bJWYhoaGOHTo0IQjBSH+ja/GI5xO55iWSCoQnZFQFCVuUDQ3N3fE8eVYjfznRUv54d8bOdLtQiBZV5qFQafjhUO9VBbaUh4jiAez2cyWFeU8OK+ENxrt+Hx+VmSHcXQ0sKcluWzKZDqNpQKKomAymSgvL6e8vByfz0draysPPvggF198Maeccgr333//jB9XHAgiLscviOglPERIoyvR/hYzYlGM5XpMFGhMhii8Xi8HDx5k3rx5ZGdnJ+zuREMIQUtLy6jakYm2ibZ6ouMRExWFpTLoNVZQtLOzE5fLRU1NTcQ8zszh13vacflDBMIKmSY9Rr0OnRAYdIJjvZ4ZIQoV83MsXL1xpMYmnpuSl5dHQUFB3F6WqW5akyhixVYWi4XNmzezceNGfvOb30zqGoyBBF4UQkjg/6SUP57kOnqgkUivzDOJFIflEJGEvxEl8x4Ts+Z6xHM1Et02FmrTG1Vl2dXVlXR5bzgcxu12YzKZkgp8RkvNY+MR8RBNFNNpLqtB0cLCQjweDxUVFQwMDPDzv9ZwsCtAUaaJLJOgzx2k1xWgONNESJHMGyNOoSgKASVSaDXdGCubok4Hi80EzfRAJRXxGvqqIjogFa3/zpBStgshioG/CiGOSClfSWaB4T4TbcCtQogyoCNWqp2ICzLtroderx81WGcsVyPetuPFKKSU1NfX43A4tNmjkHwvC4/Hw8GDBzGZTKxYsSKpbIJ648eLR4z3/pm8sKODooEqLyX5AYwiTIniZ8AdpGPARTBgYs2CbM5ZNtqa+N2+Du7523ECIYnFqOOuS5Zxydr4RDgdLoCaTVGng8VmgjIzMwmHw4RCoRmZq6pirDqPFM70aB/+3SOEeAY4CUiKKKSUUghRBHwAuAn4J/B5IcQHASGl/N1ETWtgBiwKg8GA2+1WD5qWlhY6OjrYuHHjhKW4493wqsoyJyeHLVu2jGp6k2gQVLVG1qxZQ1NTU9LBUyEEzc3NBAKBhOIRs13rUZ5vo7HfQ3GWmXyTicXSxHnLc1mdBxlhJwf37xsRFD3W5+N7L9YTViKOrjeocMcfj7KiJJMlRfHTg4mQYH2vm+N9HuZnm1lfmtxclNhMUF9fH3a7nQMHDqDT6TRrIysra1oJeTo7cIvIHA6dlNIpTszk+HaSa6guxYVEmtT8fPg3RFyPM4DfEZF0z24rPNV9CAaDHDp0CKPRmHBx2Fiuh9qoZqy+D4kQRXTNh2qNJJtlCQaD9PX1kZ+fHzceEQ8zTRSx+/rQlvm02L00DUTStKdW5nLDqeWahiI2KPrnxoBGEkIHeglhBV6s7eUz4xDFvhYHv97TTigsuXRtMReuOjEa8pkDnfzwpSaEACnhqo3z+OK5iyd1fup0sKysLNatW0cgENDGH8RzU1KJae7AXQI8M/yZGYDfSCn/PMm1iojEI44QUWVCpP/mQKILzIjr4fV62bNnzyhV40SIJQpVZ9Hd3T1usHEil0UNOGZmZrJlyxYtPpIMUahKzaysrAl7a0RDJYrBwUHa29tnpJV9NOp73SwpsrG8OIMzluSzKM8yyhqLDop2Gjt56uixSAmijNzYAIFgkAF3gPyMkf0rpJQ0OhR+/tZRTa/xwEuNCAEXrirCEwhrJKHXCRQpeeZAF1esK6GycHKq2WgJvclkYt68ecybN2+UmxIIBEZkU6b6mY81oDgVRCGlbCBBMVQCqAfWExl2HB6OVawD9qu7m2iBab06pZT09vYyMDDAKaeckrRJFt1zMLrlfSLVo2O5LGrAsbKyclR8ZLweGNFQm+auX79e64idKFSNxpEjRygrK2NoaIjm5mZNEVhQUJDyilJ1rWcPdvHgP5oIKRKzQce+Fgf/78qVGPVj7+uStSU89kYb9X1ejSRMevhjVRcvVHdxWlkGt5xVRn5eHnq9Hikl7/SEUKSOLEvEDfMEwuyq6eHCVUU4vEGNJIBIDYYO+t2BlBBF7HnHuikOh0Orhp2qmzKWRZGMwG86oQYppZTPCyFswPuJaCieI2KhPBz9vvEwbUSh3tiqVn4yfpt6w6s3t9ryPpHt4t28HR0dNDU1jRlwjE11xkINng4NDWnxiGRcCbWbVigU4vTTT0dRFM11UiP7TU1NWj+DVFaU+kNh7vnrcQKhSIbA4QnyD3eQW56s4cvnV7JyuDBMSkmr3YfTF6Is30qWxcDOf9/Cw680s7fFwZAviDeoUJRpQkp4q8PPkuoO9KF62tw6FuRngFSQnLiBpJSaazPgiYyOdPpCZJh0hCUYdbpJkwQk3qo/Vp4dz02JngyWyH7Hy3rMNkSkk7cNCA4HLZ8nMsujVUoZSCSIqWJaiEKdPF5RUUFhYSEHDx6c1Dp6vZ7BwUG6u7snzCZEI5Yo1BvU7/dz0kknjWlyjud6jKWPSJQogsGg1nTXarViMBhGpHBjI/tDQ0NanEAIoVkb483EDCuSpn4PIUVSWWgbUbvxZuMgvqCCySAIhiVhCUpYodvp5zt/Osb3r1pJaY6FR19r4c+He9ELgdmo4zuXLWdpUQa3nhOJIXzyN1UM+dRJ82Aw6HmrV0dNhyQYDqI7PsgCWxgZCNMb0KHT6zEZ9Fy3bQHPV3dz91/qCctIRWcwLCnKNHL39pUUZEy+Bd9kZ3rEuikej4eBgQHq6urw+/3k5ORodR3xrplQKDSKUFLY3SoVuAQ4FbAPazF8RArAQsNds55jnGY10Ug5UbS0tNDe3q5NHlcUZVLVo+FwmJaWFtxuN6eddlpS/mR0jMLn81FVVUVRURErV66cVJ9ONR4xlrsykeuhbr906VKKi4vp7u4e9/1CiBFxAvXJp87EVK2NnNw8BnwKOgG5ViN3vXCM2k4nCEFpjoXvbV9BhjFyvp5AGKtRh2/4BgVAQnGmGYcvSE2Hkz5XgD8f7iXbokcnBE5fiHv/1sCjH1mnHVtZnpW3mwdx+0P0uYMEwwpdQ36yLQZMBgOKotDuVrjtgqX8dk8bHQ4/xeYw9tY6vvOaD0WCXqfDYtCh1wnuunQ5W8tyx/08JkIqhv8IcWIy2KJFi7QBPwMDAzQ3N2tzPKLL/8eyKObKOEGgA6gb/rd1+CebiACrBPg7aFqLmUuPKopCMBgckdWYyJyPB3XeR15eHmazOemgk+qyqNkRdfpYItvFHmt0PGIsd2W8z7inp4f6+vqEe4XGQ1jo2XHUx9tNQTLNNj6yMRcx5OL/vXicVqeCwWjAZjbR7QqRZ4u4KS12L//7ciNLCqy0twc4bb2BDLMedyCsRa4sBh1GfSSg2OsKYB92C9Qu1hlmPZ1DvhEpz0+fWc6+VgdN/ZHKZJNeJR8FvU4fsTSQ/OLtDpoHfPhDEmdA8P19YUJhiU4wPJQapNTR4/AAU1OCTseUMJUY1DaJgUAAu92ulf/bbDZCodAoNXGKOnADkUnkwF6gXUp5WbLbSyn/wYl2/OO9b2aDmXq9nqVLl464cZINEKkDetXZlY2NjUkfhxACr9dLXV3dqLL38RAdzIwXjxhrX/E+Zykjg40HBgbYunXrlLpbP/bPVv5R30+BzYQ3qPDIG92cXpnLgGKjosSAPxDgQLsbiUQvA4SkHgXB34/2016cgdMZomlPOyAwGXSEFUlYkYSkpKHPgzcY5vnqHrzBMIPeEJkmPQa9wOkLU1kwMrBamGmiNMfCkC+E1ajHoIPmAR8OX5jgMBHohKCx36NZLiFFMuQLsyDXQpczEEnaS4kOsHp6+M2LbQxKK0vm5XL+mtKkHwwzocw0mUwjyv89Hg+1tbW0t7fT0tJCTk4O/f39WlfzFOELQC0RKyBpDFeH6hiZ1VD/LRONT8AsTjOPhVpIpd6YJpMJj8eTtNui9qAIh8MJDSeOhmr9TFSvEW+baITDYaqrqyOFT1Hp18liT/MgBVYjBp3AYIpYBYc6XdjMenR6PVarlfysMK0DXhx+hUgndsgygBU/OrNAUSS+UJiVJRmEFeh2+hnyhQgpCgtyLRRkmFCkxBNw0zQQucltJj3Xbomks1vtXh77Zyu9rgDdQ370QmDUCwIhBUWRIMAdCKPXCW5YZ+WJ6tG9UG49u4Jf7emgtstFjsXIty9bztEeN7843EY47IJqJy9WtfHxdSe0D4lkgOK5ANMJ1U2xWq1UVFRgtVpxOBw8/fTT7Nu3j4997GNcfPHF3HbbbZO2LoQQC4FLgf8m0ksiaQxnM5Ivv46DlBPFZARFakl3Xl7eCJVlstWjbrebqqoqFi1ahNvtnlTDG4/Hw549e+LGI8baJvp81eK0hQsXjjltLN7nc7zXTfugj+IsM8uKMzjS7SIYliwvziDLbMAdCGPQDwuagIW5Fo72uMk0R24QoxCEhi8JdTacKwRS6FHCYVyuIWw66HZ4GfIrhKREIBjyhciyRC4DnRCEwhKDTgwTB/zP3xq4+4oV3PXCMTz+ECaDDocviNsfJqzI4cBmpLjLFwzjDYQ51BPklIpc9jQ78IUUjHpBYaaJc5YX8v7VxZorM+gJcscfjmLUCUwmA4qU7OuX/HtxOQa8IzJAKnHEs+xmq9ZD1VGobsrtt9/OSy+9xJNPPsnbb789VYHXD4l0yJ60eSKEUHX2IYZ7Wgz/VgBFShlMdK0ZsyjGkvaqcYR4Jd3JEIXqsqxdu5acnBxaWlqSPkaXy0VPTw9btmxJ2HyMJkb1XMYaAfD68X5++loT7b0+zh48yq1nl2E1GXi+upufv9mGTkTMdINO4PJHGszkWI3cfNpCfvrPNtyBMAJYVpzBZ84q55FXmjnY7sQdCJFpMqDXCU2fIKUkEJb0+0Gv6MnIzOKCNZk8+Fo7/lDkeOdlCKTOQOeQnwW5VsJhBac/RGmuhSxz5NJweIP86VAPHn+IHGvkJjUbdPSJAJeuK+blugEG3AG6nX7CikRK2Nul8L8fWsDKeZnsbx1icYGVL5y7GPNwQZl6HTj9IfQ6gS5KU2HQgV/qWVB6oqGvOsW9ra0NQKskzcrK0oh6LlSPQuRBsXDhwkkNJlYhhLgM6JFS7hORCV+TxS1EApheIiQRJNJ92xfZjfiplNI/zvYaZoQo1Bs+2vdUG+eOV9KdqBQ7XmFYMlDXUMfVJ9vsJhwOa9PPx4qJHO12cc9f6uhw+AmHJDsOdHC818nHTlrII69GekWa9Hq8gSBNDh+L8qyY9Dr63QH+XtfP/9u+kqM9keZEbzcN8pkna/CHwngDChajHlcgRFg5ESNQAINOsLIkA+egn4+eVc59u5soyTbT5wqg18FQEMqyJC6vwvHOQUJSYDPqR7XEMxl0keaaw1AUidWk59azKlg9L4tv/vGoFqhEgF7Ao6+28KtPbBr3s5uXbSbXaqDPFcBs0OEPKWSYDSwuOBEgjM4ALV68WGtN19HRgdPp1K6b2RjGPJbLkwLSOh24QghxCWABsoUQv5JSfizJdY4QiW9YicQqTEQslKLh33MrRqE2r1GJQi0xt1gs48YRJlJKjlcYlijUeERWVhaVlZV4vRP2GR0BIQRdXV3avJGxfOWjXUO0DfowGfToJEgheL3RwVvNQ4SGb3CrUYciAYSmgjTrdbTZfZTlWynLt/I/fztOVbuTggwD+9si9RqrcixYDDqGvCGGfCEUEXE/bj27nBtOWkBVlZulxZnYvUEKMkwMeUMEFYkE/Bg5Z0UeB9uHkOEwSihEc3+IPKsendBRmmfjQ5vns6/FQV2PG0VGsiWfOqMMIQTnLS/gmUU5vHo8MkHcYtShkwruwMSWoFGv44EPruE//3iUhj4PC3IsfPuy5WRbxr4so1vTqUHF+vp6Ojs76erqmtHxAbES7lRVBUspbwduBxi2KG6bBEkgpfxt9P+Hsyh6KWXSI9anJUYRi2gXYjwJdTJQRV2qNmEyiNVHdHd3J5XKDQQCNDY2YrFYWL9+/bgXic1kIKxI9EKiAC7/iS7hAIqMNJdFRv7tCYYJhMIowOr5J9KHB9uGKMgwEj1O0+0PoRdG5ueYufWcCrLMBtbOz2RRvo1gMOKGWgw6CjOMDPlClBfY6B7y4w2GuWbjPJ6t6ibXZsSoN0dK5of8bJhvZaFNYUOOj7ojtbg9fnRCaulPdf9CCG4+fRFVHc7hQhBJKAzvWzF+ZzAVi/KsPHH9xkQ/8hFQg4pZWVmUlpaSl5cXt6fodE45i9dEZzbiJfEwnPUQwCbgYiJDgJxCiEwirs3XEl1rxlyPUCikpZKSUVnGg7qOKuoaC+N9aao+IlrfkExRmNPppKqqiuLi4lHDmOPhzKUFFGeZ6XP5kWEIRxlKOiLRpVA4YlWgSPrdAQSCHIuBT5xyIiiaazXiCYTIMBvItRroGPRztNuttd5XlIgA65dvtzM/x8JV6yIScSEE37hoGf/1Qh1OXwh/SKEgw8T+tiFc/jCeQBh3IIxJr8Nm0nP5xkWctTRCUH+u7mAo0EyxBRQlDDo9v93bxlUbStDr9WxcmMNdlyzjoVea8fiDnLzAwqfOnN6Zn9FQdRRj9RRVG+FmZ2ePGxSdKqajKlhK+TKRfpeT2VYZLlH/PpE+FucDdwHXE4lTJIwZIQqdTsexY8cwGo1s27Zt0lV7iqJQW1tLKBSacB31po81P8fTRyRKFGqTmg0bNuDxeHA4HBNuYzbq+dn1m7n9mRoauyPxAEWCQR/xzQVQaAF3SCHbrKck24wQEXfiraZBLl8XCWB/+sxyvvunY7QPunAFwyNzXxK+92IDmWYDEolOCF6s7eWL6yMvVxba+Ml167l3dwMH2xwUZ5lxB8IMeoMEwxKDDtz+ME5/iLK8E3EWo9FEGB0dHklY0WEzQoYxxDvvvIPRaKSgoICTF+Zz7s2bsdvtDAwMTOsE8ViMJbiKnXI2UVA0WcQ+HLxe75ybZE8kRmGTUv6XEGK7lPIxIcRvgRchMVUmzIDr4fF46OnpYd68eRNKqMeDOnm8pKSE8vLyCddRZdzRRBEdj9i8eTMA3UM+PIEwpbnWCWMiag8LNXBqNBrHbb/v9ofodQUoyDCRZTGQYwjx6RUB3BVGyldv5oYn3sHtj6gUTXrBgoIMOocCGIVkyO3DpJMEwzo6+gYJhwvR6/XMyzZj0AsQAu9wHEAwbE0Ml4GHwgqZFgNSSjqH/NT2Gzh5+JhMBh1Hu13My7ZoWZKwIskw6yOpUT2EwwpffaaWy9eV8OGtCyjMNDHgDqIQsX4GvQqVhTls27ae/c39/OlYNyLYw8rsENk2Czqdbka7TSWizEwkKKrW0ySS1oz3nadSlZlCGIG24QKxLiHEmUAekcAmnMimj4tp/SbVlGVxcTF5eXmTIgkhhDYQeNWqVVrl30RQZdyqxRAbj5BS8ugrTfztSC96HRRkmPjyWQvGtCjUcYI2m22ECGssK2R/6yB3/fEIQUVBIPj3bUUUh3vYsGFDZAxAholtZbkc7nKhSIWSTCM2ixHpCNDrjaQN9UJHjkVPeUaYv7y2l7+2KjQOgcMv0et1hIbjhZLIt33iMzvx2SElIWXkdZBpNuAPKdhMes09K8owYTbqaOzzoCAIS3imqhtJRI1ZlGnEH5aEwhFScfqDvFTXz4P/aEIZvmlqCzL59EYbzsEBDhw4MK2l89GYjIQ7XlA0ur1eTk4OBQUFYwZF42k3UtXdKsUYIKLJ8AE/ITK5vAP47vDrs1c9qigKx44dw+VysW3bNjo6OiZVGCalJBAIUF9fn5QUG0bewPHiEW822nmxtoeiDBM6naDPFeBnb3fxkWWjL2a1p2Z5efmoMvd4AjNfMMxdzx9BErkpnR4f//tKC7+66SQtNvM/L9bT4fBRkGGkodeD0xcmyxLE5QuSZzXiDoRRJJy+JJ8NK8r4+BP76XMHUSLxTtQolbpnlQvMBoFepyMUVggrkGHSsyxv5IV+4ykLeeDlJpy+EBJYUWxjyBdmyBkgqEgyTXrybEZCiuSV+gGu27oAk0HPvJwI6XoDYWwmPY+/2UqmSY/ZGLHEmgd81DtsrMrPZ/HixWOWzufn56fU2piq4Cq2IEztW9Hf3691AVePWyW8eG7tHLUoTETKzP3AM0S6Zqnt+xOq84BpGlK8b98+CgoKtCfvZMYKqv0sADZs2JC0yk21KKJl4dHxiC6HDySa2CfLbKB10IeijOxC3d/fz5EjRzQhVyziEUW/O0AwFDH/vR4vBkBYrPR7FRYQEVUd63FRYBveJxJfQMEXDA8fu+CMpfnYPUHyM0z8+LVmepzBaCkDCiOtiEwDbC7N4HPnLeb5w3bebh6kJMvMF84uw9lxfMTxbS3P5TuXLae+14PNpGdLWTav1A/w3MFuDnU6qSzKQK8T+IJhciwmTq3M47mqbq19nkEn+MK5i7n/741kmU8U/wnAHz5h30SXzke32GtpadGaxkxUOp8IUl0UFtu3wu/309/fPyIoGq/RTSoqR4UQFiKBRzOR+3OHlPJbk1hH7Zd5FvB54DwhhE1K6QGuAG4FLhBC6KWUE96cKSeKUCjEkiVLRlRrGgwGfL7Eg6yqm1BRUTHp4S5CCA4fPkxeXl7ceo0FuRaEiPRw0OsiUuY182woSiSdqDYC7urqGteaied65NtM6HRgd7jIsBgRBiPhoEJJdiT9qBdgMYjhmwq8AQWdLqJ49AQUBj1BAsEw/qDCugXZ/ODvDQgiXaGklJpUG8CoAxB8/cLFbC6UDPS2cnZOgCvPzhseNWjmcMfo464osFERJWy6YGURp1TkcevvajjS5UJKSbbFwJfOW4zVqOf/XbmS144P4PaHWTM/i2XFGZxROcjLx/rJskRcGZNBx/ICM0KMVgZHt9irrKwcs3R+MhmJ6VZmms3mUUHRrq4unE4n+/btIy8vj8zMTBwORyosCj9wnpTSJSJTvV4TQvxJSvlmkuvkCiEuAD4M5AkhbgAsQoheIoKu+mQWSzlRZGZmjppcncz80Vg3oa+vL2lrxOVy0dfXR3l5OUuWLIn7npMq8rh03Tz+VNOFTgjm5Zj55BlldDfXoygKhw8fRko5YWFZtEXRZvfyw78fp6nXiTnkxa83EcSADEo+f94SijJNKIrC4sWLuczVzK8OuQiEdRE143Bg0WrSISXYPUEuX1vEKeVZFGeaON7nIRwTazAaIk9xo05H/YCfi9ct1kxnu91OT08Pg4ODBAIBOjo6KCgo4LUmJ0/u7SCkSE6uyGVFSQaFGSbWLsjC7gniCyrkWPRA5Hha7F42LMzBatRzwcqRjYw/dWY5FqOOPc0OSrLM3HTaInKki0ACYqvYpjGqtaFmJFRrI5EWddNRZj4W1KCo+r0vWbIEu93OK6+8wn/9139hs9lYuXIll19+eVL9YVUMuwLqfFDj8M9k8q4KEcm2F2gh0lR3PhGXo4pI3IJErAmYBcHVWJBSUldXp8U11KdKsm6LSjSFhYXjynqFENx0ejnbN8zDN/y0V0JB2kMh9u7dS3FxcULZFfWC8QXDfPMPtfQ7vehCPqTRSlmWhf9431LMBsE7zQ5+/noTJy/OZUVJMR9+Xwm58zp5/mAH3nYnmQaJxQhmk4n8TCsPXrsWKSXtg14GPEF0IpKdEIBORFwlq0mHyxfCH1bYfaSf1gEfd16yjPwME/kFBdQN6WjV2wh4OigLBtnxykGeOOQnw2TApwh+/JoDmynSpGZ9aTanVeYSViTlBTZCYUn3kJ9fvh0pTz+9Mo+imOFAZoOOT55RzifPOPG3zk5n0m6EEILs7Gyys7O1jER0i7rMzEzN2ogn0Z9JolCh1nmoQdEPfOAD+P1+jh07hsfj4dChQ5MiCtAUlPuApcBDUsq3kl1DSjkIPA08LYRYDriklJptKZL8kmZUwj0WAoGA1iYu1k1IVNsQq49obGxMaLvCzBMX/4DDjcPhYNOmTePOHO10+Hjo5Qaa+j3MzzJywYIQlgEPfQ4XZp1Cdl4uQqfD7g4Akv/+0zEcnkiM4YVDPdz+/mV0Dfn52ZvtGHSCTIsZpz9EXrYFIyEuKQ2wb98+snPz+ebLA3QOBbAYBEFFkGHS8V+XLOHR19rocQUJhCV5ViNl+VY6h/z88q02Pn/uYu7563FerO0jrCgYCBPIEgzpC8mw9mM1QGuPl7ACQ74wRj283jCgNamBSG9LBbCZ9JgNOl45PsCla4qxGCeWRU81u6FOOVN7P7hcLvr7+6mpqUFRFC1+kJ2drV0fs0EUsfv0er0sWbKEW265ZUprDz/lNwohcokEH9dKKWuSWUPVRwghFhNpiXeLEOJhKeUPhRCfBI4Du2dNRxEP41kF6tSwsWZ0JGJRxOoj1ABqMnLszs5OGhsbsdls45JEIKTwvT/XMTgcaOxy+nmiysPHOEYwrFCYnYXQRZrDKBL2NNmxewKUZFkQRJrKPrmvne4hP7lWI2aDjoIMEx0OHx/aupCLVhdjM0VctYPHO2jo96Ba8gLwhwQlORn8+Lp13L+7gXfahijJMuHwBvAEwrzTNsSe5kF27u/SUp9SkezY38XFa4oiregMRoTOhxyuMTHoBMGQpMfhoSjDSOegF3dQYtQJzqjMx2rU4/SH8ATCExJFqtWJQgiysrLIysqioqKCUCjEwMAAXV1d1NXVYbPZCAQCBAKBUS7vdGKsDtyJdFJLFFLKQSHES8BFQFJEwYmhPjcRcWWeJRIgBVgBFAC7o943LmbM9YgXo2htbaWtrS3ugOLobccjirH6WSY6VlBtmKO6PHv27Bn3/T1OP3ZPQLNEcix6mgaDZGdlcuWWPP5U063pGq7eNC+SWUFoGYpINkEZLgRT6HYGh28uSWGGCZtJr533EYfAHzohqALwBsPsqTpMxsp5nFyeRXWnmwFPiFBYIRBSsBl1/PyfLShSamXdARkhqHOWFbCn2cGAO0Bkj2DUCyQCvR4yrSY+eUoR1a12qrs8LC+0UGwO4gsEkJKErInprnUwGAwj9A9ut5uDBw9y+PBhQqGQprbMycmZVitjLKKYajBTRMb/BYdJwgpcQESCPVkUEiGEDZyIfZg5Mfxn9nQUsYi92cPhMLW1tSiKMuHUsPGIIp4+QkUiLksoFOLgwYNkZ2ezadOmhC7wDLMeZVj9KJUw/XY7QuhYvric0zJNbC3PpdPhY0G2mdIcE/f/vZG2QS9DviDzsy24A2E+sGUBNW0OfrO3QxMrWY16rd8lQK8rQEu/F7NBRyCsaN9mhknPljUrMBt8LBS9LLX5eKtbYjbqWZhr47K1JTxzsBO9iHTb1kdKRzAZBKvmZfLvpy3ihUM9LAlY2dM8hC+kYNBF+l4syrNy/voKLtpUSafDy+7DXXQ5XLjae1mVr6e73U9hYeG46cyZ7A0hhud2GI1GNm3aRCgUYnBwUBP6WSwWrfYj1VPCxtJRpKAN3nzgieE4hQ74nZTy+ckc4vDvt4C1wOXA34UQm4mUmTcns9i0EEWstiA6RqF2gFqwYAGLFi2a8OaMZxkk0s9yIqJQn0TJVrHm2Uxcs2kBv3mzCb/Pi9WWwRklIS3Qt6UsNzIZ3R/ihl8coMfpRycEva4geqHj1nMX876VhfzktSZ0ItKRWsWfDnWzbngOZyCkkGUzsCDHTLczUhXsH5Zivnh0gJtPL2fjggUsXRHksVfrIeDFPuRi39EGcgxmirKMDPnCeAMhTHrBv5+2kF6Hl4Y+N+cuy0enE5xckcfbzQ6CiqQi38onTy/TelHMz7FyzdYy3P5I926TTo6YKJ6VlUVhYeGouSOzWT1pMBgoLCyksLAwrtoyNzdXU1tOlcyiVb8qUmFRSCmriFR7TnUdOfz750KIW4g0rNkGbAfuk8PjCWUCw39gBovCFEXRpNhjdYCKB71er5VKQyQeUV1dTWZm5rj9LKOnjMVCPY5169aRnZ1c31IpJRtzfLBCT878NZF2961HOd7rxqQXzMuKXDz724YYcAc1VyLDLHEGQrxvZSF9rkgrOZNBaDLssCI1QgDIyzBi0us4qSKXvS0OWu0+jHodFQU23mi002r38j/XrCHTYuS0ZSX8dm8HbplD2B8my6hw3gJ4uz2IPtPI5evnce2WUloH/ZE6ESSKIsmz6jmlIodrtyyIe+NYjXqsUe5GdIDR6XTS19enzR1Rn9yz1ZYuFvHUloODg/T19VFfX4/ZbNaOOZFhP7GY5rmjKYWU8mEhxBtE2p2/LaV0JrvGjBCFlBK/309DQwNbt25NKuik1+s1sdZ48zViMZYl0tzcTE9PT9LHAZGL49ChQxgMBq48J6Kv6Bny8t0/eAlW1RBWFE5dnM+X3reEsW6VNruPh//RRL87gD8U6UStFnQVZZ5I/VmNenIsBt5u9GIz6jHpBWX5VnKH3ZNOh5+WAS9LizLIzzBRlGlmqc2A1agnHPDT3d3FTz6+SZv2vXfvXgI6M0NDRvIsuVjMZgacPuZlmwmHw4TD4YgYTB9puT+RdkRNZ0Ika6UqFwcHB8nIyECv18/oTNWJEFuC7vV66e/v14b9RFsbiTS8GYso5tDwHwCEEGuJlJWXEQl3fUQI8aiUcm8y60y766EWU0kp2bp1a9ImnxqjGC8eEQ+xrod6k+v1+kkdh9/v58CBA8yfP5+ysjLt7z95rZl+r8Kioki15msNA6yrzaQiP4MMsx6HJ4hOB1IKzl1WwLdfqMPtj7S694dCWuAzz2bA5T8R8O13BTjc6cJmNmAy6Gjsj4iw8mwmQKIgtVLusALZVgMLciw4nS56eroomrdAs9qiTXGOtfPG8VbCYYXSgizWVC7UTOhwOKx9ZpHZG0JrHjseTCaTJtVWxytEz1RVb1CbzZZya2Oyro7VatUaICuKwuDgoFbboZbO5+fnj3nM8YhiLg3/iZJw/w8RgdV/A0PAZcBDQogPSSkTjlNMK92rFsDixYvxer2T8gt1Oh39/f04nc5x52vE2y56WtjBgwdH3eSJYmhoiOrq6lGDhKSMjPCzGXU4HA4MBiM9QyG++cc6bCY9y4oiqkebWc9J5bmsXZDN//vLMXJtRtyBEL5gGEkkyCiRkd6UgCIlrYNeGvs9lBfYEEjmZ1toc3gZcAcIS8mWslzK8iMmc0m2GaNeR1NnH363E0v+PDaWjayyVU3xszcu59R1S/H5g3iG7PT3dNFUX0dmZiaFhYUUFBRoMSV1yptqmakNeib6HjMzM0fMVFVvQK/Xq1Vl5g0PNZ4qUhETiR5WDJHrJfaYY0cLxtNRuFyuOUMURM3vAL4b5W48JIS4lohqM2FMG1GozV1UC6CxsTHpLzUYDFJfH5FUTzRfIxaqjmJwcJBDhw4lVaIe7zw2btw4IlAlpURRFCoLI23lsm0GmvrduPxhrHrQKZKj3U62lefy0ZMXsaUsl9ou53DPCElBhpl+V5CgIvGHFAw6wQc2LSAQUvhLbQ9VbUP0uSKdrRfmWViUZyHLouekijwqi2xcsKpYm+iVbTGwLsvL37vdZOeVsGFRDluGx/S12b38/Wgf7kCIFfMyOXNJASa9DpPNTLZtpIS6r69PmxOrBgXVtHW0tREKhcZ0UWK/4+g6CXVMX39/P42NjdqTW7U2JoPpEFtZLBZKS0spLS0dNVpQtZACgcCo/fr9/ilpOYQQi4BfEBn3J4EfSykfmMq5EOm+fb8Q4lmgD1gF9AJmIYRFSplQEda0EMXx48ex2+1xpdiJ+qyqNTJ//nyczuRlwTqdjqGhIQYHB8fVacSD6jY1NDSMOA9PIMyOfe002z2sLM5gy6Ic3reyiLZBH+2DPhw+hQyznhyrER0Spy9IW28/79S4KZTzWVhQyMZF2expGiSkSHJtRlbNy2D9whzOWlrAsuJM/tkwQHO/l8oiGx0OL91DAbyBMAWZRlbOz+SMJfnkWE0Yh90ORVGoOXSIwz1h8gpL0Ot0HOtxs7wkE5Nex453OsgwG8g0G3inOdKJ67zlI4Vt0TEHtWBLvZndbjc5OTkUFhaSn5+vxX4URRkxV1a1DsZ7GMSO6VOf3PX19fh8vqTjBOr5T2c6NvaYVQtJvT5VC0l9iEzxWELAl6WU7wghsoB9Qoi/SikPJ7tQlNqylcig4nVE7vcyIqrMnUCmEGJ9ImQxLURRWlpKRUXFiAsmthP3eIiOR6gTzZOBGrT0er2cccYZSQXUhBCEQiEOHz6MyWRi8+bN6HQ6gmGF2585xJFuJwad4PmDXQgdzMu2kGMx8M1LlvPY6y3U97rxBxWEkCjoyMnJ4pS1i9DrvByrO8o2m496o6TbAzazkQyjnhVFmYTCMjLw1+Ej06LHbNCzpSyPt5vsZFoMWIx6hnxhXjk2gDcUJsdiZGGOCV9fKwuKCgiY9SzMjbgiTl+I1+oHWD0/C0WiDfiZl22mttM1iihib+7omIP6RO3r66OxsXFECtJqtY4gDCkloVBIs7Ymumlin9zRcQKTyZRQVmKm5duqhdTZ2cmGDRtwu9309/fz0Y9+lO7ubu6++24uvfRSNm7cmPTaUspOoHP4304hRC1QCiRNFFFrflb993B9hyAyAkAPmGfVorBaraMyDqo6czzTLJ4+wu/3JyXFDgaDHDx4kIyMDHJyckaRhJSS144P8HJdLxaDnqs2zmdp8Ui/ct++fZSWlrJo0SLtb8e6XRzrdZFnNeDyK3iCIUIK+IMejAYdP361mS+et5g7njvCgDtAIKxgMegpyDBhMpn44etdNA8oBMN6AsEQg94gnUMBGnrdNPcOsXlxIZ6gwl9re/EEIy7N5etLWDUvk1MW5/Fmo5152RYk8HaTnQMtgywy+cjMyUHm2tCJE6lVi1E3nH7VEY7Ss/iGu1qpCCkKbzbYOdzlwqATnFaZx8p5o4VrsVZAX18fx44dw+fzkZeXR2FhITk5OQwMDOBwOCgrK9NiG4kGRGPjBKoGoq6ujkAgMKYGYjbqPNT96vV6rXT+xRdf5NRTT6W8vJxnnnlmUkQRDSFEBRE9RdIFYWNBqhJg8Az/KeE06YzlriaSYo+lj0imelQ1B5csWUJOTg6HD48m4n8c6+fhfzRgM+oJKZKD7Q7u3r6asnwbDocDl8vFhg0bRowAkFISVpRhKbUOTyCo1V8Ewwr+kMLbzXa6naV8aMt8/nSoB50QlOZasBj13Pn8UXUl2uw+vMHImD2G06K1fX4WWLvY3Roi06TDYtDR0Ofh6Xc6+ew5i1lWnMnbTYPodYJ+dwCHx4/ic1O+eD65WZk09LnJsRpwB0JYDHp6nAHWlWZRnm+losBGU78HnRDoBFyz6USHrgOtDqrah1iQayEUlvz9aB9ZFiOluWOrGC0Wi5YtUMvZe3t7NQl1ZWUlBoMBk8k0pYCozWbDZrNp+4nWQET3t5wtooCR5QqKomAymfjYx5IevxFv3UwirsEXpZRDU14wBZi29Ggsxrvhx9NHJFqz0dPTQ319vRY8DQQCcbf7U003mcM+O0Sa6/7z+ACmwBANDQ1kZ2eP6GSlmtGLC6yRzMOgT1NI6ojUbqiFE/tbHTh9IXQ6QYHNhMMbom3Qy6A3IrxyeCPpTwnaoB9BpBHNEaeRkBLGGwIdYcxCYnd52VgoyDLrKc4y0zXkx+120zfoZPG8PPKzMyIDeYx6Lllbwuv1duyeIGsXZHFSRR5GvY4rN8yjqd9LIBQppS+M0mo09nvJzzChEwKTITLpvGvINy5RREOv11NYWIjH48Fms7Fs2TLsdjuHDh0iFApRUFBAYWGhls6ebPo1OsWqpnn7+/upra3F7/ej0+kYHBzUqklnA16vNyVt8Iab1ewEfi2lfHrKC6YIM2ZRGAyGuIVhsTd4LBLpjN3Y2Eh/fz9bt27V+hWMJeHW6yI9HwfcgeHtob+vl3adwrZt26iurkZRFAbcAfpcfvKsenKtRixGPd+/ejWPv9HCS3V9DHqChCSElEj1ZWGWmZCiEAwrGIcvVpNBh8+pIAT0Ov14ggqh4fZU0Q1vdUjaBn2EFYlBp0Ov0+MNhjEZ9Ty9r5Uycx0VWTaGfCF6hrysXFhIYZaFIV8Ypy/EaZV5LMqz8eFtowO2Rr2OZcXxL+Aci4F2h09zRwKhSL/MRCGlpKGhAbfbzaZNm9DpdGRnZ1NeXq5Veba3tzM0NBQ3/SqlJBwOa9dFomIvVXFZVlamNbuJriZVNRAzWU3qcrmm3Kp/OIbwGFArpbw/JQeWIsya65FIvcZECIfD1NTUYDKZ2LJly4gLbCyiOK0ynz8f6om02AOElBSttmjujk6n47mDXfx6Xxc6EWmO+9mzF3Py4jz0QnBKRR79zoDW2CUUVjAbdKydn0l5vg27O0B+hommfg8CWDU/i5IsMw/9owkY7i2p7puIdWE26Mg06RkihC8kMeiUyCTzkkz6pA17IJNzdH7WZHvYWGDBG3TTrYAw6TllcSFrFyQnQ1dx0uI8/nCwi06HD0WBRXkWKosSeypKKTly5AgA69atG2VFxlZ5xqZfCwoKKCoqGjP9qloaibThz8jIYOnSpVo1aX9/P4cOHdJ6VxQUFJCdnZ0ysddYrfpToKE4Hfg4UC2EODD8tzuklC9MdeGpYlZcj0TrNcaDWlym+suxGMsSaR7wMj/HEinLDviwmU20BE+0kj/SH+Shd1qwmgzohMAfDHD/7uN89KRSjnS5aej34PQGed+qItoGvDQNeCmwGbls3TxOrczjSJeLtxrtbFyYg90T5ECbg3daHeiHe2KCwOULodOBQS/QD5+6ySDIxhDptCUhrCiUF9jIsxk50txFmzWDq884FSEEwWCQvr4++vr6cLV0ccSRQ1FREfn5+UmJmHKtRj6weYE2tLgk24whAdNdURRqamrIyMigsrIyoS5g8dKvTU1NuFyuMdOvicQ2omtL1GrSzMzMEVZNR0cHR44cmbBTVqKIlwJOhdhKSvkajKn+n1XMqOsRDoeTqtcYC3a7ncOHDydVXKbCH1SwGkCPn8yibDxh8AUjTzIpJXs7g+iI9HUIKdDjDGD3Bvm/15rZWJrDvCwTXQ4ffz3cS2GmieIsE+9fXcw5yyPNbtaXZpNrNdLt9PGD3Y202L0oiiQYloSUMPOyzfiCIcxGA0WZRloGvOgE+EMKbr/CqgwjDm+IUBiq2hx4PB5ybWbKy05U2hqNxlHpy97eXo4fP47ZbKawsJCioqKESqttJr2m8EwEoVCIqqoqCgsLJ6VyhdHp16GhIXp7e+OmX1X3JDq2EU0a45W1x1o1aqes6upqILm+nNEYS749B1v1pwwz6nrY7Xba2toSrteIh7a2Ntra2ti8efOY+fWWAQ/NA146nKNdj7UF8JcqD/k5mfilwB8Mc/6KQi1oWVKQi66rhyG3B1dAEpICq8lAttlA84CHVfOy6HMFcPtDDPmDmPU6zlxyQtYthKC8wIbJoKNzyIeiKBgNenJ0RhzeIGFFkmk2YtQLDEJgMerJMOvJs5nYVm6lMMuEQQj+cawfn8eNyWTGGdah1wma+j387Ugv3kCYNQuyOWtZPoaY9KXH46Gvr29EQLGoqCglprfasnDhwoWT7gcZC51OR25urtbfNDr96vV6ycvLo6ioSDu/WLFXIBDQ5mxMFNuI7pQV25czmS7g8Yhijg7/SRlmxPWQUtLd3c3Q0BCnnnpq0vEIVQRVV1dHMBhk27ZtY5rYf6vt4Qe7jyMEuNx+XBlN3HRGhRYTKZBDfPPydTxXHYlTXHhyCRUFVoY8fmwmPWcsL6ZjKEhNp5OgP4BBByvzJN0uF3qDgabeSIl2YaaJkmwzdk+A/3utibeb7Vy4sohL1kWsJItRRzCsTv+ONMS1mfSctbSAD28rpbbLxeEOJ11OH5vLctELQSCk4AmECYeClFl86G3Z2CwWzAZBx6CPF2v7yDLrsZn0vNEwgF4HZy8b2bbPZrNRVlZGWVkZoVBIC/YNDQ2RnZ09IqCYDNR6mSVLlozbKnCqiE6/KoqC3W7XiMNisWjWhslkIhAI0NXVpZWRx1ob4yG2L2d0F3AhxLgzR95NJeapwrRbFGo8Qq/XU1RUNOkp0u+88w6FhYWsWrVqzCejPxjmgb8fx2rUYzLoUPywc38H5ywvwNlxHIslErQMhBTKCjPpdPh46Wgvbzb0oxOwfcN8tpXnYtLrONQ1xFuNg+RYDVQWZtDQ66KqzUH/kBclHKLAJPAHAnQ4/OiFoH3QFxmvh+SydfPJs5k4fUkeLx3tJ6SE0YlIDGBrRR4rSrJYUZLF2csK+Nk/WxnyhrAYdPS4AmwoMnCkqZf580oozctAyoj2IhBSkFJqKsuSbDM1Hc5RRBENg8Ew4mZQTfympiYMBgNFRUUj6jnGgtvtpqqqilWrVo3b2TzV0Ol0I0rD3W63Zi0Fg0ECgQALFy6kqKhIsyrUmEYy6dfYLuBqDKW5uVkb+BM94SxNFClGdDzCarVqMxuSgdPpxOVysXr1akpLS8d/rz803PYtcmHoRETU9Ma+Ks5ZV87ChQtxeIM88o8GWga81Pe6WZRr5uSKfIKKwh+quijLX8zGRTlsXJTDpWvnsfOdTjoGfWRZTHzrspW0D/r49dttKIpCx6CXYEiiN0i6Br0YDHqer+7hsnXzcftDfObMcnQIWu1esiwG1i/M5sylJwrT8mwmPrKtlJeO9uEJhFmfD8VKH6deuJnfH+gZdl0kG8uyqSzIoLbbpW3rD4axmZOTpqsqwqVLl+Lz+ejt7eXo0aP4/X7y8/MpKioa1WvS4XBw+PBh1q1bN+s3gpoWnT9/Pvv372f+/Pn4fD727Nkzbvo1WbFXbAxFzdi0tLSg1+s16Xp0UDNF/TJ/RqQMvEdKuXZKi6UY0+Z6xOojXC5XwkOAVKg1H7m5uQkFLfNsJvIzTAy4A+RYjfjDCjLs5bT161hYGlFaPrmnjTcb7Rj1ApcvSH1vZJJ5WYENxRNkyBfSxFi5ViP/dtoivEGF7iEv3/nTMbocftyBEMWZJmwmI65AgEyLEZ1UcPoCHO8a4KV9h3m1Q2IwGsmyGPjEqYtYWpTJ/BzzqAa1C3IsXLetlIaGBlwuL2vXbkGv13PT6WX0uQIYdYLCTBPBsORAm5U2uzfSZVwIrtgwumt5orBYLCxatEgz2wcGBujs7NSyA4WFheh0OhobG9m4ceOkukBNB9S+IEuXLtUsDTVQ2dvbOyL9WlhYqN28kxV7RU84U/ff3NzM4OAge/bs0f7ucDgoKSmZ6uk9DjxIpIJ0TmFaiEJtNDPZQT5SSo4fP87g4CDbtm2jtrY2oW31OsF/b1/Ft54/Qmu/C52UfHv7GipLT8ix9zYPYjXqyDAZsJuCuAMhupx+irLM6HWCHMvIj0QIgc2k554Xj9PrDDA/x0K/20/TwLCC0RUclmTrMOhhYUEmL7cEIeRDcQXQmcy8etTHSeUr4naxVqeSGY1G1q9frz2hTHodC3JOZC1MBsG1W0tp6PUQCCssyLGMUFlOBapbWFRUpPnrTU1N9PX1kZmZSXd3t3bTzWabO5/Px4EDB1ixYsWIB0d0oDI6/drc3IzL5SI7O1tLH6vp12hrI9HOXhApCsvNzcVkMlFWVobD4eDpp5/ml7/8Jbm5uVqB2GTiOFLKV4ZrPOYcpoUo9Ho969evH7PB7nhQO2JZrVa2bNmifXmJFoYtyrNy+ymZ9A1K9NLMpoqRjWYyzToG3AqZZpiXY+ZYTwh/UMHlD3HNxvlkxDHnFUWh2e6lJMtEWJE4vGH0ukjrOl9IweULMj/HzMJcCzlWEyaDYH5OHsiI3qOp18Hrb+9jQa5NiwuYzWYtflNQUEB5efmE52bS61g5b3rNfyEEDoeDYDDIWWedpbXSO378OB6Ph/z8fK2p7kzKpVXdzMqVKyeMk0S7DlLKMatf1fRxsmIvNUahFszddNNNHD9+nFNPPRWXy4XX603puc8FzGh6dCLXw+PxcPDgQcrKykbEIxK1RlSSsdlsnLptM++88452AahPkMvXlfDYP1uwe4IoUrJxYTZfOHcJFYVWzIb4mRSdTkeu1YjTH8Zq0KMM+6aFmSYMOkFTv2RhrpUMs54Pbp7Pi7V9OH0hsiwGpMFEUX4+Z59WAUE/vb29VFdXEw6H8fv9lJeXT1qPkGqocnin08nGjRvR6/UYDIYRpeBqEZgql1aJbyoCpongdruprq5m9erVSTdDFkJo6Vc1NhNd/Zqbm6sRnxAiIbHXWOnRxYsXc+qpp6bmpOcYZowoJqrZGBgYoLa2ljVr1ox6YiRCFF6vlwMHDowgGdUSUb98IQRnLC3EoNexr8WBxajnwlVFI6Z6j4X/OK+Su/98jH5/AF8wTFm+lfJ8GwUZITJMej64pZTFhTaKs8zk2kz8/p0OOh1+THodH9g8nwyTAUwGMjIyKCgooLq6mgULFuBwOHjzzTdH6AVmo7BJSsnRo0dRFGWECxSN6CyEKpeOJ8seb+5HsnC5XFRXV7N27dqUNK4dK/2qduaOJj5VrxEr9gqFQqNiNumsxyQRO9tjPLS0tNDZ2cmWLVviqgknIgq13V2sUlOn0xEMBjEajRE9g4hIpk9fUsDpUSKpRLCtIo9HrltPfa8bbyDMnmYHHUM+zHodnzm7giVFJy6S0lwLnz27AncgjM2kx6Q/ceP39/dz7NgxNmzYoAXaYp/UGRkZ2gU72XRyMlAUhUOHDmGxWFixYkVCN3m0XLqiomJUVyz1SZ2srDwaTqeTmpoa1q9fPy1ipnjp1/7+fg4fPkwwGNTcrKysLC22EQ6HcTqd2Gw2gsGg5oLMxQ7cqcSs9lJXFEULVG7dunXMC2q8OaIdHR00NzePUmpKKTEYDLS1tVFaWpoStp+XbWFedoTIzl5WiMsfyZCo6dhoGPU6cq0j/97e3k5HRwebN28eYarHPqnVCP7+/fu1Uu7oAqpUIhwOU1VVRX5+fkJxkrEQm1JU+0eosnKV+BKd2OVwOKitrWXDhg3Tct7xEF2VqtaJqJmgjIwMCgsLGRoawmQyUVhYOMJFaWlpmbL7JYT4LXAOUCiEaAO+JaV8LAWnNmXMGlH4/X4OHjxIcXEx5eXl4z7FxprRET0zNFppqMYjKisr6evr07op5+XlUVxcTG5u7pRNY5NBR74hsQtDLcd2uVxs3rx53CdsbARf9alVvYNq3ufk5Ez5HILBIAcOHKC0tJQFCxZMvEGCiO1WFS2USkRWbrfbOXr0KBs2bJi1tGy86te6ujrcbjdWq5XW1lYtbfrzn/8ck8mUdPwkFlLKj6To8FMOMYF7MOnR1KFQaNTN/cYbb3DKKafgdDqprq5mxYoVCaWR2tvbCQaDVFRUaGtXV1eTkZHBsmXLRlxsKkmoYhj1NVUr0Nvbi8Ph0FJmBQUFKWkbPxZUq0mv1yds1o+FcDhMf38/vb29miR7suegSrIrKyvjTpGfLqg1Fr29vTidzhGpS4PBwMDAgOaapXpe6FRw/PhxfD4fq1evJhgM0t/fz5///GfuueceFEXhnnvu4bLLLpus+zEnK0ajMaMWhU6n01yF2Pb34yF6WpgatCwvLx/1FIyW8MYGBGO1AmrFZUNDAxaLRXstldF7tdIy0fTnRNDr9SOectHnkIx5r2YRYvUIM4HYGovo1KWUkmAwyPr16+cUSagW6Zo1axBCaG6W2WymsrKSO++8k927d7NgwQLOPvvs2T7cacGMWRRSSl599VWsViubNm1Kqiipt7eXwcFBCgsLOXz48KjMiFr5qWY2kn1qu91uent76e3tjaQ9CwspLi6ekm+sPrErKipSodibEGrVaG9vL+FwmIKCAoqLi0dlIIaGhjh06FDKsgipQk9PDw0NDZSUlGC32wkEApq6MlZWPpNobGzE5XKxdu3aEZ/jjh07eOyxx9i1a1cq4l9z3qKYNqKIbnGmPlnVlmnJfrBqND0YDI6SE0+VJGLh9/s10vD7/VogMZkybTVaP9NFVCpGNLZxubTUq1pBu379+hkLECaCrq4uWltb2bhx44jxhv39/fT19eFwOLTpYwUFBTOSCQJoampiaGiItWvXjiCq5557jocffpjnn39+RH/VKSBNFKqIqqKigr6+PsrLy5MK+kgpqa6uxm63c/rpp48KWqaSJGKhlmmr/nRubu4IKXA8qOnPdevWzYn+BGoGorm5mYGBAfLz8ykpKZl2kVSi6Ojo0GZkjGVlqsHE3t5e+vv70el0IzJB0yErb2lpwW63s27duhHf9QsvvMB9993HCy+8kEq37b1NFF1dXRw9epS1a9eSk5NDbW0t8+bNS/gDVi0RtfX7hg0bThzYGEHL6YJ6w/X29jIwMBBX69DR0UF7ezsbNmyYEzehivb2djo7O1m/fj2BQIDe3l76+vo0N6uoqGhWSK2trY2enh42bNiQVDDW7/drbpbX69UqX2NnfkwWra2t9Pf3s379+hHr/fWvf+Xuu+9m165dqe7J8d4liq6uLi16rXZDrqur08zgiRAdtMzNzeXo0aNs2rQpclBRE6mO9njoHvJRkGlm3YLkWppNFqrWoaenh/7+fq2gSEqpSZ/nAqSUNDU14XA4tKlr0Yi+4Xw+35il5tOBlpYWBgYG4h5XMlBni/T19WG32zW9w2Qtpra2Nnp7e9mwYcOIz+Cll17irrvuYteuXSNmvqQI712iCAaDWoGNiuPHj5ORkTFhr0y1J6YatPT5fBw6dIjNmzePcDX+WN3NrppudMM36TnLC7l2y4IZrXBUFIXq6mptaG04HNae0qmUMicLVWcSDAZZtWrVhDd+bPo4KytLiwkk2w1rIqj1JLG+/1ShyspViwlODFtO5Ltob2/XLJzo43r11Ve54447eP7551PWAjAGc54opi09Gk9NmUjNhtoTM1rOrW4XTRJOf4g/H+5hXrYFg06gKJJXjvVz3opCirNmZp5DdPqzrKxsRIfsxsZGPB6PZkGlyixOBGrpuslkYvXq1QmRVWz6OLobltFo1NysqQigVOGZ1+tNOUnASFm52qlK/S5UWblaTxNrxXR0dNDd3T2KJN58802+/vWv88c//nG6SOJdgRnVUYxXaq4WJfl8vlE9MXU6HT6fD4/Hg9VqRQgRGQRMZPhO5D0CnU7gDyU+p3Qq8Pl8VFVVUV5ePiL9Gdshe2BgQIvVZGVlUVxcPK0iL1WSnZeXpwnUkkVsNyyv10tvby+1tbUEg0HtKZ1MJkjNuASDQU2PMN0wmUwsWLCABQsWjIgx1dfXj+i/abfb6ezsHOU27t27ly996Us899xzcUdCvJcwba6HlJJAIDDib52dnXi9XiorK0f8PRQKcfDgQbKzs1m6dGlcpWVHRwddXV2aaZ9fWMRDr3fSOeQjz2rC4QuSazXyjYuXjVkuniqo6c+VK1cmHJhVn9JqXMNsNlNcXJxSkZc6oHn+/PkTtg2cLGIzQTk5E88UUR8CwJTVqamCKitvb2/H5/OxaNEiiouLNfI7cOAAn/nMZ3jmmWdGXa/TgNn/QCbAjBJFT08PDoeDZcuWaX+LTp/GmnZq0BJOKC1V076np4deh4c3+kwMBPVUFGVz3UmlFGVOr9uRqvRntMgL0Mz+ya6p1s5UVFRMR7AtLqJnigwMDMRVuEopqa2txWAwjJLbzza6u7tpbW1lzZo1mkJ09+7dvPLKK9TV1bFz584pTyVPEHPnQxkDM0oU6pNo5cqVwIkeFGr6NHrbRPQRqiinp6cHp9M57T0dpiv9qWYfenp6tMKv6KfbRPB4PFRVVbF8+XKtEGs2EEt+BQUFWmB0yZIlc4okenp6aG5uHqUSrq6u5otf/CJr1qzh4MGD3HnnnVx++eXTfThz54MZA9NGFBC5AaLhcDhobW1l7dq1WtBy48aNI3T9kxVRRfd0sNvtKY0HqJ2fhoaGppzOmwix5DeRyEt1g9asWTPl6sVUQpWwq81eZiOoOxZUkohWgkIkfX/99dfzq1/9ivXr1wNMOFhoPKjtE0pLS3n++edHvPb444/zla98hdLSUg5GOv88KKX86aRPapoxo0Thcrm0QJLP5xt106VKaRkbD7BarRQXF0+qEUwqqz+TxUQiL7Uce66oQFUoiqIFVMvLyzWtg1qzMxtybBXq6MJNmzaN2HdjYyPXXXcdP//5z9m8eXNK9nX//fezd+9ehoaG4hLF3r17efDBB+FdYFFMa9YjtsuVlJKBgQHKysrYsGFDQuXhk91vdNTe7XbT09PD/v37tcE3xcXFmhBsLKjpT7Wpy0ybztF9HWIb2iiKolVaziWSCIfDHDx4kKKiIhYtWgSgNd8pLCwcIcdW52SocY3p7j2hpkpjSaKlpYXrrruOn/70pykjiba2Nnbt2sU3vvEN7r///pSsOZuYsfSo6kebTCaWLl064rV4QctUITq3XllZqaX6qqurkVJqpBFbJKWmP8vKyiY9TDmViG5oY7FYaG1tZdGiRdTX188ZkZeavZo/f/6YjXCip3ItWbJEG0RUW1tLIBCYVBFeIujv76ehoWGUu9He3s6HP/xhHn74YbZt25ay/X3xi1/knnvuwel0jvmenTt38sorr1BdXb0D+A8pZWvKDiDFmBGiiG6cW1tbO+K16Ma3M3GBW61WbTanWvdw9OhRraxZ1UQcOnRoVvo1TISmpibsdrvWOlAduBstLEp17UMiUFOzCxcuTIpYowcRqe3nomelpqK50MDAAPX19WzatGlEELqrq4trr72WBx54gNNPP33S68fi+eefp7i4mC1btvDyyy/Hfc/ll1/ORz7yEcxmM0KIvwJPAOel7CBSjGmNUQSDQZqbm2lvb9eClv/85z857bTTpr3yM1mo+oDW1lZt6lNpaWlK2ualAqpgye/3s3r16jEJQBV5qfGAmRB5qS31ysvLU5aajW7Mo+pOVBdlIpcxGna7nbq6OjZu3Dhiu56eHq655hq+//3v8773vS8lx6zi9ttv55e//CUGgwGfz8fQ0BBXX301v/rVr+K+XwhhAAaklCmpWZ8OTCtR1NTU4PF4WLt2rXaR/vOf/+TUU0/VulGpMxPmAtT059q1a7W4hsPh0ERFBQUFsxKxVwOqBoOB5cuXJ6WGVKXYfX190yLyCgQCHDhwgMWLF09rSz1VINXb24uiKAm5WoODgxw5coRNmzaNIIm+vj6uueYavvOd73DRRRdN2zEDvPzyy9x7772jgpmdnZ2abkgIcTXwNSnlKdN6MFPAtLoepaWlmuQ6GmrQcq6QRHT6U21+a7VateDb4OCgNks1IyNDy6CkulgqHsLhMDU1NWRlZbF48eKkPq94Qd3e3l6qqqq0+MxURF5qCjR6Duh0Qe2QXV5ePsrViqefUUki1pKw2+188IMf5M4775x2kojFnXfeydatW7niiiv43//9X/7whz+o19DngU/M6MEkiWm1KOK1w3vrrbfIzMxk3rx5c8KsVxSFI0eOIIRg5cqV4x5PdHl5X18fJpMp5U/oaKjBwZKSkpTXGqjxGbXEPFmRlzrib7bjOLH6GZVQenp62LRp0wiNjsPh4JprruG2227j6quvnrVjjoPZf1pOgBkjCjVoKaXEbrePMOtLSkpmZULWVNOfHo8nIiUf7rWpkkYq0nyqSR9bdDYdiBV55eTkUFxcPKbIS81grVq1KlWt4FICKSXd3d0cPXoUs9mspcItFgs2m40PfOAD3HrrrVx77bWzfaixSBNFKBQaM2ipCop6enqw2+1kZ2drgbfpJo1Upz/9fr9GGqFQSGvQO5kJ4OrTetmyZdNu0sdCrd/o6emJK/Jyu91UVVXNOSUonFCpqkOD1P6n3/zmN3nllVfYsmULt99+O6eeeuqsq0NjkCaKQCCQUGZDjXJ3d3czMDBAZmamFgtIdbRenWeZTPVnMoguXPN6vUmZ9eqxrV69etaf1tEiL7URjNpLYqYJbCLEkoQKr9fLtddey9VXX82iRYt44YUX+OEPf5hU5mQG8N4mii9+8YvMnz+f7du3s2jRoqSi9U6nU4sFqBLsoqKiKQcQBwYGqKurY+3atTMyVDZe7UZxcXFcV2twcJDa2to5p7aESJv/6upqSkpKGBoa0iZ+xRsJMNNQyTX2c/P5fFx33XVceeWVfOpTn0rZMY5Xw+H3+7n++uvZt28fBQUFPPXUU4n0BXlvE0VbWxtPP/00zzzzDD6fj8suu4zt27cnFb1X25t1d3dPOYDY2dlJa2vriD6eM4lYVyta42C32zl+/Picm5AFJ+aARrf5V62m3t7eWRN5AZorFEsSgUCAj3/847zvfe/j85//fEqJbLwajocffpiqqioeffRRnnzySZ555hmeeuqpiZZ8bxOFtoiU9PT08PTTT/P000/jcDi45JJL2L59e1K6AEDTN/T29o6YnDXeja+mPx0OB+vXr58TzW+jC9fUhjxLlixh3rx5M14oNR7UwrPYKt9oxBN5qXGN6fysVZJYt27dCOswGAxy4403cuqpp3LbbbellCTa2tq44YYbtBqOWKJ4//vfz1133cWpp55KKBRi3rx5WrB7HKSJIh76+vp47rnn2LlzJ93d3Vx88cVceeWVrFq1Kqkv1ev1aqQBxM06RKc/V6xYMdeCWLS0tNDX18eSJUu0m00lQDViP1vo7++nvr5+lBZhPESLvPr7+zGZTJNSVE4EteFR7MSzUCjEzTffzIYNG7jjjjtS7hJ94AMf4Pbbb8fpdMYVUq1du5Y///nPWjp7yZIlvPXWWxO195/zRDEr08wLCwu56aabuOmmmxgcHOQPf/gD3/nOd2hpaeGCCy7gqquuGjV4JR6sVivl5eWUl5drWYfDhw8TDoc1JeXx48e1cufZ1mxEQ0rJ8ePH8Xg8bNy4EZ1OR05ODosXL9YK1w4dOoSiKFMWRk0G0eXYybh4sSIvNYUcXYQ31XPxer1UVVWNIolwOMwtt9zCqlWrpoUkEqnh+FfFrFgUY2FoaIhdu3axc+dOjh07xvnnn8/27dvZsmVLUpZAIBCgs7OThoYGrdltSUnJpFKV0wEpJUeOHAGYUOSlCqN6enq0wrXi4mKysqZvhslYjV2mingiL3WOSKLnoqaOV69ePSI9Gw6H+fznP09JSQnf+973puWzSaSGI+16zDA8Hg8vvPACO3fupKamhnPOOYft27dz8sknT+j3ulwuampqWLFiBZmZmSNSlaq+YTpvtPGgKAo1NTVkZGRQWVmZ1DGohWs9PT24XC7y8/MpLi5OqcK1s7NTa/c3nbESNRvU29vL0NBQQk16fT4fBw4cGCX0UhSFL33pS2RmZnLvvffOiHs5Vg3HQw89RHV1tRbMfPrpp/nd73430XJpokgFfD4fL774Ijt27OCdd97h9NNP56qrruK0004blS4dL/0ZDofp6+uju7sbt9utPZ2TeaJNBaoSNLqpy2ShBhBVhWsqxGqJzAGdDkSLvOx2e9yOZCpJrFy5csTgZ0VR+PrXvw7A//7v/85YDCqaKKJrOHw+Hx//+MfZv38/+fn5PPnkk4l08U4TRaoRCATYvXs3O3fu5I033uCUU07hyiuv5Mwzz2T37t3k5+cnFHxTJ2P19PQwNDREXl6epm+YDtJQJdnT0QgnunBNVVMmW7jW2tqqjdKbzayQmg5XNTR6vZ68vDy6urpYvXr1KJL41re+hdPp5NFHH51zgeokkCaK6UQwGOSVV17hd7/7Hbt27SIvL49vfOMbvP/9708qwq4WFnV3d2v1J+PVOiQL1a9eunRpqofbjkK8wjW1i9dYQcnm5mbsdvuoobxzAUNDQxw8eFA79sLCQrKysigoKODuu++ms7OTxx57bE6kvKeANFHMBO688066u7v50Ic+xLPPPstLL73EunXruPLKK3nf+96XVJGW+nTu7u5OSTdvVTW4atWqEU/DmUJs4ZpKGupnMl1zQFOBQCDA/v37WbZsGfn5+QSDQfr7+/nFL37Bz3/+cywWCw8++CDnnHPOnNKeTAJpopgJ9Pb2UlhYqLkMiqLw5ptvsmPHDv72t7+xfPlyrrzySi688MKkZNuqJqC7u5v+/v6kTXqHw8Hhw4dHCYJmC2qRVE9PD8FgEJ1Oh8FgmDMitGiortqSJUtG1JVIKXnggQfYt28fN910E7t27eLaa6/lrLPOmsWjTR5qE+lhpIlitqEoCu+88w6///3v+ctf/kJFRQVXXHEFF198cVJFV6pJr0rJLRaLJoqK9zRTJ4pt2LBh2rtLJwt1xJ/L5cJoNOL1erUMykwFdsdDMBhk//79VFZWjnDVpJQ88sgjvPbaa/zud79LSQ8Qn8/HWWedhd/vJxQK8YEPfID/+q//GvGe6BkcALfeeis333zzpPYXDofR6/V0d3dTUlKizg1JE8VcgqIoVFdXs2PHDl544QVKSkrYvn07l156adITtqLjAAaDQZOSm0wmurq6aGlpYePGjdPS0GYqiDcHNDZVOV7h2nRDJYnY1npSSh577DFefPFFdu7cmTKVpxo8zczMJBgMcsYZZ/DAAw9wyiknutLFzOCYFDo7Ozl8+DDnn38+L7zwAl/72tc4/fTTOf3007n++uszpZTuVJzPdGFWlJmzBZ1Ox4YNG9iwYQPf/va3qa2tZceOHVx99dXk5uayfft2LrvssoR6P0aPAFDjAAcPHtTGKM5Vkjh8+LA2MkG1HKJrZqIL1+rq6masbgNONOmtqKgY9R088cQT7Nq1i+eeey6lUnB1nIO6/2AwOC0W1d69e/nUpz7FN7/5Td544w3uu+8+6uvrOXDgAMDNQoifSSnH7u0/y3hPWRRjQe1wvWPHDv7whz9gtVq54ooruOKKKygpKUnowpFS0tDQgMPhoKCggN7eXqSU2g042+6HoigcOnQIm82WsNArduLaRO7WVBAKhdi/fz9lZWWjOnr9+te/5sknn+SPf/zjqPkrqUA4HGbLli3U19fz2c9+lu9///sjXn/88ce5/fbbKSoqYvny5fzgBz+YlA7mhRde4Bvf+AZr167ll7/8JcFgkGeeeYZrr732PqAPeFRKOZiSk0ox0kQRAyklTU1N7Ny5k2effRadTsfll1/OlVdeyYIFC+LeYKo5ryjKiMK2QCBAT08PPT09hEIhLeMw070mVJcrOzubxYsXT3qdeJW7qShcC4VCHDhwIO5MkN///vf87Gc/Y9euXdMeEB4cHOSqq67iRz/6EWvXrtX+3t/fT2ZmJmazmf/7v//jqaee4u9///uE6wWDQV599VXOO+88amtraWtrw+fz8bGPfYxHHnmE6667DgAhxHXAycD9UsqWaTq9KSFNFONASkl7ezs7d+7kmWeeIRAIaD01KioqEEJoT2qr1TruxO5gMEhvby/d3d3aRKyZaPoSDoeprq4mPz+fsrKylK3r8/k00lCL8CZDguFwmAMHDrBgwQKtfb2KZ599lkceeYTnn39+xrp9ffvb38Zms3HbbbfFfT0cDpOfn4/D4ZhwLUVR+MQnPkFDQwPBYJB7772XM888k127dnHHHXdw22238fGPfxxACCFKpJTdqT2b1CFNFAlCbdyq9tQYGhriwgsv5JVXXuHuu+9OamZlKBTSpOTJtspLBuoc0OLi4pR38Y5GIBDQ6ml8Pl/C9TQqScQbQbhr1y5+8IMfaEK66UJvby9Go5Hc3Fy8Xi8XXnghX/va17jsssu090TP4HjmmWf4/ve/z5tvvjnmmj6fjyeeeIJPfepTtLS0cNJJJ7Fo0SL27NmjvefFF1/k1ltv5T/+4z/4zGc+k856/Kvi2LFjXHrppRQXF+Pz+bj44ovZvn170j011IxDd3d3Sgu9EpkDOh2IV7imztyIPh+VxNSJbNF48cUX+d73vscLL7ww7b05q6qquOGGG7Qu8R/60Ie48847R9Rv3H777doMjvz8fB555BFWrlw55potLS1ce+21XHrppVx22WUEAgG++tWvYrPZeOGFF4ATPT69Xi/nnXdemij+VfHUU0+RmZnJpZdeit1u5w9/+AM7d+6ktbWVCy+8kCuvvDKhnhrRUBRFu8mmkqZUsweLFi2a1QHLYxWu5ebmUlNTQ1FR0ShL56WXXuKuu+5i165dKRtPOJMIBoMYjUbefvttPve5z3HGGWdw3333AXDuuedisVh44IEHuOWWW/jpT3+q9tNME8V7DWofxZ07d1JfX8/73vc+tm/fzubNm5MmDVVKPjg4mHB1qKporKiomFM3WnSX9fb2dmw2GxUVFSNUrq+++ip33HEHu3btmhMT5JOFKqY6fvw4t9xyCxs2bOAXv/gFH/rQh7j33nsxmUx88IMfZGBggI9+9KP827/9m7ppmijey3C73bzwwgvs2LGDw4cPc+6557J9+3ZOOumkpDQJ8UYZlJSUjKo/UWsjlixZMu3FZ5OBoihUVVWRl5dHfn6+Jlj7y1/+gtfrZffu3fzlL38Z5Yq8GxAKhTAYDCiKwqc//WnmzZvHt7/9bTo6OvjkJz9JQUEBP/nJTzCZTPT29mo6kWEpd5oo0ojA5/Pxl7/8hR07drB//37OOOMMrrzyyrg9NcZDrLbBarVSUlJCZmYmNTU1LF++PGmV6UxATdHm5uZSXl4+4rVnnnmG//mf/8FisWCxWHjsscdYsmTJLB1p8nj44YfJy8vjIx/5CAD33nsvLpdLi0u0tLSwevVqPvGJT3DPPfdoWpCoeo80UaQxGn6/n927d7Njxw7eeustTj31VK2nRjJCJrX+pL29nfb2drKysli4cOG0CKKmArWrV3Z29qgZFwcOHOAzn/kMzz77LIsXL6arq4vc3NxJazMSqd2Y5OyNMaEOuLr55pv5wQ9+wIEDB3jwwQe54447tKrca665huuuu44PfvCD8ZZIE0Ua4yMYDPKPf/yDHTt28Oqrr7J161a2b9/Oueeem5BUOXoOqMFg0LQNav1JqrtfJwspJTU1NWRmZo4Se9XU1PDv//7v/P73v2f58uUp299EtRuTnL0Rd19CCILBIE6nk6985St0dnbyzDPP8Pjjj7N7925MJhPV1dXcfPPNfO5znxtrqTRRpAoVFRVkZWWh1+sxGAzs3bt3tg8p5QiFQrz22mvs2LGDl19+mfXr13PllVdy/vnnx5WAq3MtYrtRw4lRBj09PdoA5eLi4hlt/y+lHCEbj0ZtbS033ngjTz31FKtWrZqW/Xs8Hs444wweeeQRTj75ZO3vk2yAGxeKonD//fezYcMGLrjgAm699VaOHTvG008/zcDAAEePHsXr9XL55ZcDo8rLVaSJIlWoqKhg7969czJINx0Ih8NaT43du3ezYsUKradGRkYGXV1dNDY2JtTrwufzaX0o1Pb/xcXF01I3oUItQDObzSxdunTEa3V1dVx//fX8+te/Zt26dSnf90S1G5OcvTFifb1er9306uSw3/zmNwDcdtttvPXWW/z2t78dkf4dLimPt+ScJ4q51dIoDQ16vZ7TTz9d83m/+tWvcvDgQS644AK2b9/OhRdeSGlpaUL1DxaLhUWLFrFlyxatu/aRI0d46623aGhowOVypfTYpZTU1tZiMplGBSUbGxu54YYbeOKJJ6aFJCDy2R04cIC2tjbefvttampqUr5+OBzmc5/7HI8++ihf+tKXMBgMmmtx7733snHjxlEduudaB7Fk8K6xKBYvXqyp+z71qU/xyU9+crYPaVbw+uuvc9NNN3HBBRfw+uuva0OgL7300qSlzur80O7ubk16rWZQJpuxU2eW6PV6li1bNmIdVbH405/+lG3btk1q/WQRr3Zjsq5HtEVgt9u54IILaG9v55prruEjH/kIDz74IJ/73Oc47bTTkj3MOW9RvGv6Ubz22muUlpbS09PDBRdcwMqVK9917c9SAbfbzV//+lcWLVqkmfc7duzgyiuvJD8/X+upkYgZrQ5Hmj9/via9bmxs1EYZlJSUJFV/olbR6nS6USTR3t7Ohz/8YR599NFpJYnY2o2//vWvfO1rXxvxniuuuIInnniCU089lR07dnDeeecldI4qSezevZuzzz6bp59+mt///vc0NjbyzDPP8M9//hNgBFGMEZN41+FdY1FE46677iIzM3PMCr/3IqSUHDt2TOupYbPZku6poUKtP+np6cHpdCY0ykBKSV1dHVJKrXOWiq6uLj7wgQ/wwx/+cNrJPZHajUnO3gCgurqa22+/nY0bN2Kz2SgrK2PFihWsWbOGp556igMHDvDAAw8ke9hznkneFUThdrtRFIWsrCzcbjcXXHABd955JxdddNFsH9qchDq9Xe2podfrJ+ypMRZi6zVycnIoKSkZUX+iNv4JhUKjRiT29PRwzTXXcM8993D++een/FynG+o5R7sd7e3tHDlyhMcee4x//OMfLFy4kCeeeGJEoViSlkSaKFKBhoYGrrrqKiCSQrzuuuv4xje+MctH9e6AlJK2tjatp0YoFNJ6aiQ7uFlKid1u1yZ6qaMMBgcHCYVCoypn+/r6uPrqq/nud7/7riT1l156ibvvvpv/+7//o7KyknA4jE6nG3GO3/rWt/j1r3/NZz7zGb785S9Pdldpokhj7kBKSVdXl9ZTw+Vycemll7J9+/YRPTQTXcvhcFBXVzcipqH21rTb7Vx99dV885vfHNHb4d2E5uZmHn/8cQ4dOsR///d/s2zZMs2yUFOkEHF31q9fP5VdpYkijbmL3t5enn32WXbu3El/fz8XX3wxV1xxRcI9NRoaGvB4PKxevVrrSl5VVcWPf/xjhoaGuO222/jYxz42A2eSWkS7De3t7fz85z9n37593H333axatUp7PVYXMY5OYiKkieLdjMHBQW6++WZqamoQQvCzn/2MU089dbYPa1owMDCg9dRoa2vj/e9/P1deeeWYE8QaGxtxuVysXbt2BKkMDQ1x3XXXUVhYSHNzM+ecc84owdNcRryb3ePxaKKq73znO6xbty7V2Yw0UbybccMNN3DmmWdy8803EwgE8Hg8szIWcKbhcDi0nhrHjx/XRF6bNm1Cp9Nx+PBhQqHQKBJxu9188IMf5Oabb9YsCbfbPaVmwq2trVx//fV0d3cjhOCTn/wkX/jCF0a85+WXX2b79u1aLcnVV1/NnXfemfS+okniC1/4Arm5uQwODvL9738fvV7Pfffdx1tvvcXtt9/OSSedNOlzioM5TxRIKcf7ec9icHBQVlRUSEVRZvtQZhVOp1M+9dRT8oMf/KBct26dvOiii+Tll18uBwcHpdvt1n76+vrkeeedJx977LGU7r+jo0Pu27dPSinl0NCQXLZsmTx06NCI97z00kvy0ksvTdk+P/3pT8vrr79eVlVVycrKSnnhhRdKh8Mhw+Gw/OY3vym/+c1vpmxfw5joPpz1n3evpnSa0djYSFFRETfeeCObNm3i5ptvxu2e08OcpgWZmZl86EMf4ne/+x033ngj/f39ZGVlcfrpp/PlL3+ZV199FbfbzUc/+lE+9KEPceONN6Z0//Pnz9caF2dlZbFq1Sra29tTuo9oNDQ0kJOTwxNPPMF9993HNddcQ0VFBVdddRUOh4Nvf/vbfPvb3562/c9ZTMAk71ns2bNH6vV6+eabb0oppfz85z8v//M//3OWj2r2oCiKfOihh6TP55NSSunz+eTzzz8vP/GJT8j8/Hx51113Tbv11djYKBctWiQdDseIv7/00ksyPz9frl+/Xl500UWypqYm4TXD4fCovzkcDrlz5055ySWXSCmlfOWVV2RZWZn893//d+09KT7XWbcYJvpJE8UY6OzslOXl5dr/X3nlFe3CSWMknE7ntJOE0+mUmzdvljt37hz1msPhkE6nU0op5a5du+TSpUsTWjP6mB9++GH58MMPy1/+8pdSSilffPFFeeutt0qPxyP/8z//Uz700EMyFAql4EziYtaJYKKfd4XroSgK4XB4Rvc5b948Fi1apA303b17N6tXr57RY3i3YLqHGAWDQa655ho++tGPcvXVV496PTs7W6uiveSSS7Rit/Eg5YmsxUMPPcSjjz6KEII777yT7373u6xbt47GxkY+8YlP8Nxzz3HjjTei1+tRFCX1J/guwJwuCgsGg+j1+lkrz/3Rj37ERz/6UQKBAJWVlfz85z+fleN4L0NKyU033cSqVav40pe+FPc9XV1dWj3L22+/jaIoE84DUUniqaeeYu/evTz55JOsWrWKK6+8knPPPZd58+bx9NNP09PTQ2FhIRaLZYTI6j2HCUyOWYPL5ZL33Xef3Lx5s7z88svlX/7yl1HvCYfDcX3MNP518Oqrr0pArlu3Tm7YsEFu2LBB7tq1Sz7yyCPykUcekVJK+aMf/UiuXr1arl+/Xp588sny9ddfH3M91d1Qf3/lK1+RS5culU888YR0uVxSSilff/11+W//9m8jtpvm62zWXYuJfuasRdHc3Myrr77Kb37zGw4fPsyBAwfYunUr+fn5VFVVsWTJklH5+Sko49KYozjjjDMiwbRxcOutt3LrrbdOuJaMcjeOHDlCeXk599xzD2VlZTz99NOUl5dz8skn8+qrr9Ld3T3CgnivX1dzlihycnJoaWnhxRdfHNGU9I477sDn8/GPf/yDFStW8MADD2gzEtQvU/Uj341f7tGjR7n22mu1/zc0NPDtb3+bL37xi7N3UP8iUEni0Ucf5be//S3btm2jq6uLX/3qV/T29vLlL3+ZFStWEA6H+fGPfzyi3d17HhOYHLOCQCAgpYxEsz/1qU/Ju+66S/r9fvnkk0/KrKwsWVtbK4PBoLz33nvl3//+dymllF//+tflG2+8Ie12+6j1FEV5VwqnQqGQLCkpkU1NTbN9KP8y+Nvf/ibPOOMM2d/fL2+55RZ51VVXaa89+OCD8uyzz5Yvv/yylDLlKdDxMOuuxUQ/c9KiqKur44033uCjH/0on/70p/nKV77CwYMHef311zn33HP5yle+Qnd3N8FgkMHBQVatWsVTTz1FZ2cne/fuZdWqVfzqV7/S2tSrTwQ5bMK+W54Qu3fvZsmSJaMG5qQxeVgsFj796U/z7LPPcvToUXbt2gVExhl+9rOfxe12c/vtt/Poo49OtSL0XwsTMMmsoLGxUX7kIx+RmzZtkhdddJH82te+JkOhkFy3bp08fvy4lFLK5uZm+dhjj8n29nb54x//WG7fvl0ePHhQSinlJz7xCfnnP/9ZShnJq993332ytbV1xD72798vf/SjH0m/3z+zJ5cEbrzxRvmjH/1otg/jXwKHDh2SPT098tChQ7KwsFCuXbtWe+2xxx6TH/zgB7Vr4Ze//OV0aibiYdYthol+5iRRROOdd97RIs4//OEP5Ve/+lXZ3t4+4j2XXXaZfO6556Tb7ZZSSnnuuefKn/zkJ1JKKauqquR//ud/yk2bNsnvfe97Ukop/X6/fPTRR+X27dtn7kSShN/vlwUFBbKrq2u2DyWlaGlpkeecc45ctWqVXL16tfzhD3846j2KosjPfe5zcsmSJXLdunVarcdk8etf/1qedtpp8vDhw1JKKX/xi1/I0047Tf7kJz+RP/rRj+TmzZtlVVXVlPYxRcw6EUz0MyeJIhwOx2X0trY2+alPfUquWbNGbt++Xb7zzjuyqalJbt68Wf7mN7+RUkb8+srKStna2irdbrd8/PHH5VtvvSWPHj0qP//5z8uenh7Z19cnb7nlFvnTn/5U20bKyM35s5/9TD766KMzd7Jj4Nlnn5UXXHDBbB9GypFIkdeuXbvkRRddJBVFkW+88YY86aSTJr2/119/XW7cuFG2tLRIKaVsb2+X77zzjty7d6+84YYb5Fe/+lV54MABKeW0p0DHw6wTwUQ/czJGMVa2orS0lEcffRQ40VXo0UcfJSsri5qaGpqbm/nFL36hjdf75Cc/SWZmJk8//TQNDQ0IIbj33nupra2lubmZr3zlK8CJmMXg4CCvv/66VoQUDoe112Y6g/Lb3/5WG3r7rwS16zeMLPKKVr0+99xzXH/99QghOOWUUxgcHKSzs1PbLhmEw2E2bdrEq6++SmNjI7t370an03H33Xfz+OOPa+9Lp9bHx7vqk4mWcquBpl27dnHDDTdgtVo5//zz8fl8PPDAAxw4cACDwcCjjz7Kc889x3XXXcfKlSsxGo3s2bOHvLw8bTCteoG0trbS3d3NpZdeCqCpQmf6AlJb8seTK/8roampif37948Y9weRrlKLFi3S/r9w4cJJV4yuXr2ayspK7r//flatWsVDDz3ERRddREdHx4j3pUliAsy2STOVH6AU+BuwOOpv+uHfC4B/AvcCnwIagQ8Mv/YocEvM+43AzcBjw/+vBB4E/h9wUpx96wDdbH8G79YfIBPYB1wd57XngTOi/r8b2DrF/VmHf58OHIr3naZ/xv55V9OolLIduAhoE0Lohv8WHv7dAXwWcAAZQB7wJyHEWiIE86K6zPDvXGDb8Hu2AncAzwBVwNeFEMuFEDohRPHw+oqU8r1ZITRFCCGMwE7g11LKp+O8pR1YFPX/hcN/mwqCQoiTgR8B/yGlfFu8W/LkcwBzMkaRDKSUoXFe2w/sBxBC/E5K6RZCrAAUKWX98HvUm30hkYvzL8D/AmcBJUQsEj8RQvoF8N9CCCvQBTwtpfxn9D6FEPrIsu9OEhFC/AcRy0oC1cCNUkpfCtcXwGNArZTy/jHe9gfgViHEk8DJgENK2TmV/UopQ0KIWiJWZYMQQshhEyONifGutigmwrAFIACklG3Dv3cC16uvD/82AluBbsANLAbeT+Tp83EilsZRYBlwCvA2UAP8QAixZXgNdT/haJIYPoZ3BSELIUqBzxMx89cCeuDDKd7N6UQ+0/OEEAeGfy4RQnxaCPHp4fe8ADQA9cBPgFtSsWMp5ZCUsmH432mSSALvigt4shjrqS6ldMS8rgcKgCoppSKE2A+cLaV8jGEXRQiRBXwEeFlK+b/Df7uNiFsD8G9CiA8QcXXuAQ4Mr78GWC6EeEVK2SuE0Kvu0RyFAbAKIYKADeiY4P1JQUr5GhM0kx2+iT+byv2mMTX8SxNFohg2rf9f1JP/JeAbw7GKKuD3gBmoAI4ACCHWAXVArxDifcDtwBVELI7vAM1CiB8A/wE0DVsyEIl3hIAfSCkDM3F+iUJK2S6EuBdoAbzAi1LKFyfYLI33AP6lXY9kocY7pJR/ALYDh4GziTwBlxIhir3Dbz+PiHlsAU4FfiSlPEwkAJoHtAJB4ALgBiHEU0IIM3AS0KCSxFwKqAkh8oic92IiWaMMIcS7b4JPGilHmijiYDjQ1SWl/JGU8sNSyl4i8Yu3gHeG33Y+kWBfIxErQiWQMuAA8DoRt+QPwI1E4h0riLg4RUKIa4UQtjnmK78PaJRS9kopg8DTwGmzfExpzAGkiSIOpJRSRKCP+tsRKeUDUsrgcLyimggh+IhYEGr67hoiGoH9wMVAH1Az7JufAZiGf24Efj2cQZkraAFOEULYhi2d84HaWT6mNOYA0kQxBmQEWtBRzZAMv+aUUn5DSnlwOL7xEPAPIcRvgXOJZEjcwHrg4PC/IeKGPCal/KGU8iIiKchNM3NGE0NK+Rawg4jVVE3k+vjxrB5UGnMC6WBmgohNeap/E0KcC+yTUpYLIb4OuIA9RD7bISKaDb8QYjGQDfx9+GmdB6wlQipzBlLKbwHfmu3jSGNuIU0Uk0BM2jUL+OZwILCdiCjrNSllQAjRBDwuhLiGiE6jEegadm0uATqklP0zfPhppJE0JhpSnEaCEEIsAgqklAdi/i6IkMmNQC/wu2GV4B+Av6majDTSmMtIE8U0YixxlRDCQiSDcslwvUoaacxppIlihiCE0L1b6z/SSCOd9ZghxAuGppHGuwVpiyKNNNKYEOknWxpppDEh0kSRRhppTIg0UaSRRhoTIk0UaaSRxoRIE0UaaaQxIdJEkUYaaUyI/w9au/ghfNWOXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "ax = plt.figure().gca(projection='3d')\n",
    "ax.scatter(data[:,0], data[:,1], data[:,2])\n",
    "ax.set_xlabel('sepal length')\n",
    "ax.set_ylabel('sepal width')\n",
    "ax.set_zlabel('petal length')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef186e17",
   "metadata": {},
   "source": [
    "### RDD 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "738fbea7",
   "metadata": {},
   "outputs": [],
   "source": [
    "_xRdd = spark.sparkContext.parallelize(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "22bb24a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([5.1, 3.5, 1.4, 0.2])]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_xRdd.take(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3391e0b8",
   "metadata": {},
   "source": [
    "### 형변환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5bc659a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "xRdd = _xRdd.map(lambda x: [float(i) for i in x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3757c320",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[5.1, 3.5, 1.4, 0.2]]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xRdd.take(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "111bcaa8",
   "metadata": {},
   "source": [
    "### k-Means 모델링"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "667c7677",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyspark.mllib.clustering import KMeans\n",
    "\n",
    "model = KMeans.train(xRdd, k = 2, maxIterations = 10) # maxiterations=반복횟수 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d171d3e",
   "metadata": {},
   "source": [
    "중심값 출력"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cfd26e7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([5.00566038, 3.36981132, 1.56037736, 0.29056604]),\n",
       " array([6.30103093, 2.88659794, 4.95876289, 1.69587629])]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.clusterCenters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6288f0e",
   "metadata": {},
   "source": [
    "오류 계산"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "64fe67a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "152.34795176035803"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.computeCost(xRdd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57469c78",
   "metadata": {},
   "source": [
    "### DataFrame 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b420c514",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "48a5cf1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "iris = pd.read_csv(file_name, names=[\"sepal_length\",\"sepal_width\",\"petal_length\", \"petal_width\",\"species\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "b844072a",
   "metadata": {},
   "outputs": [],
   "source": [
    "irisDf = spark.createDataFrame(iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb8aa361",
   "metadata": {},
   "source": [
    "### 통계량"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c2ac6781",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+------------------+-------------------+------------------+------------------+--------------+\n",
      "|summary|      sepal_length|        sepal_width|      petal_length|       petal_width|       species|\n",
      "+-------+------------------+-------------------+------------------+------------------+--------------+\n",
      "|  count|               150|                150|               150|               150|           150|\n",
      "|   mean| 5.843333333333335| 3.0540000000000007|3.7586666666666693|1.1986666666666672|          null|\n",
      "| stddev|0.8280661279778637|0.43359431136217375| 1.764420419952262|0.7631607417008414|          null|\n",
      "|    min|               4.3|                2.0|               1.0|               0.1|   Iris-setosa|\n",
      "|    max|               7.9|                4.4|               6.9|               2.5|Iris-virginica|\n",
      "+-------+------------------+-------------------+------------------+------------------+--------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "irisDf.describe().show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e3e46de",
   "metadata": {},
   "source": [
    "### features 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "cc3bcf85",
   "metadata": {},
   "outputs": [],
   "source": [
    "#from pyspark.ml.linalg import Vectors\n",
    "from pyspark.ml.feature import VectorAssembler\n",
    "\n",
    "va = VectorAssembler(inputCols=[\"sepal_length\", \"sepal_width\", \"petal_length\", \"petal_width\"], outputCol=\"features\")\n",
    "xxDf = va.transform(irisDf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d8a53474",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root\n",
      " |-- sepal_length: double (nullable = true)\n",
      " |-- sepal_width: double (nullable = true)\n",
      " |-- petal_length: double (nullable = true)\n",
      " |-- petal_width: double (nullable = true)\n",
      " |-- species: string (nullable = true)\n",
      " |-- features: vector (nullable = true)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xxDf.printSchema()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "362e3a92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------------+-----------+------------+-----------+-----------+-----------------+\n",
      "|sepal_length|sepal_width|petal_length|petal_width|    species|         features|\n",
      "+------------+-----------+------------+-----------+-----------+-----------------+\n",
      "|         5.1|        3.5|         1.4|        0.2|Iris-setosa|[5.1,3.5,1.4,0.2]|\n",
      "|         4.9|        3.0|         1.4|        0.2|Iris-setosa|[4.9,3.0,1.4,0.2]|\n",
      "|         4.7|        3.2|         1.3|        0.2|Iris-setosa|[4.7,3.2,1.3,0.2]|\n",
      "+------------+-----------+------------+-----------+-----------+-----------------+\n",
      "only showing top 3 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xxDf.show(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ba08966",
   "metadata": {},
   "source": [
    "입력데이터가 명목변수이면??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "60af0f5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyspark.ml.feature import VectorIndexer\n",
    "\n",
    "featureIndexer = VectorIndexer(inputCol=\"features\", \\\n",
    "                               outputCol=\"featuresIndexed\",\\\n",
    "                               maxCategories=4).fit(xxDf)\n",
    "xxxDf = featureIndexer.transform(xxDf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "e94a4002",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root\n",
      " |-- sepal_length: double (nullable = true)\n",
      " |-- sepal_width: double (nullable = true)\n",
      " |-- petal_length: double (nullable = true)\n",
      " |-- petal_width: double (nullable = true)\n",
      " |-- species: string (nullable = true)\n",
      " |-- features: vector (nullable = true)\n",
      " |-- featuresIndexed: vector (nullable = true)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xxxDf.printSchema()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "b4d4d415",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------------+-----------+------------+-----------+-----------+-----------------+-----------------+\n",
      "|sepal_length|sepal_width|petal_length|petal_width|    species|         features|  featuresIndexed|\n",
      "+------------+-----------+------------+-----------+-----------+-----------------+-----------------+\n",
      "|         5.1|        3.5|         1.4|        0.2|Iris-setosa|[5.1,3.5,1.4,0.2]|[5.1,3.5,1.4,0.2]|\n",
      "|         4.9|        3.0|         1.4|        0.2|Iris-setosa|[4.9,3.0,1.4,0.2]|[4.9,3.0,1.4,0.2]|\n",
      "|         4.7|        3.2|         1.3|        0.2|Iris-setosa|[4.7,3.2,1.3,0.2]|[4.7,3.2,1.3,0.2]|\n",
      "|         4.6|        3.1|         1.5|        0.2|Iris-setosa|[4.6,3.1,1.5,0.2]|[4.6,3.1,1.5,0.2]|\n",
      "|         5.0|        3.6|         1.4|        0.2|Iris-setosa|[5.0,3.6,1.4,0.2]|[5.0,3.6,1.4,0.2]|\n",
      "+------------+-----------+------------+-----------+-----------+-----------------+-----------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "xxxDf.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed935d9c",
   "metadata": {},
   "source": [
    "### k-Means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "8188744d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyspark.ml.clustering import KMeans\n",
    "\n",
    "kmeans = KMeans(k=2) \\\n",
    "            .setFeaturesCol(\"features\") \\\n",
    "            .setPredictionCol(\"cluster\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "736967e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = kmeans.fit(xxDf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "b16d2084",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([6.30103093, 2.88659794, 4.95876289, 1.69587629]), array([5.00566038, 3.36037736, 1.56226415, 0.28867925])]\n"
     ]
    }
   ],
   "source": [
    "print (model.clusterCenters())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "191fd8f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------------+-----------+------------+-----------+-----------+-----------------+-------+\n",
      "|sepal_length|sepal_width|petal_length|petal_width|    species|         features|cluster|\n",
      "+------------+-----------+------------+-----------+-----------+-----------------+-------+\n",
      "|         5.1|        3.5|         1.4|        0.2|Iris-setosa|[5.1,3.5,1.4,0.2]|      1|\n",
      "|         4.9|        3.0|         1.4|        0.2|Iris-setosa|[4.9,3.0,1.4,0.2]|      1|\n",
      "|         4.7|        3.2|         1.3|        0.2|Iris-setosa|[4.7,3.2,1.3,0.2]|      1|\n",
      "|         4.6|        3.1|         1.5|        0.2|Iris-setosa|[4.6,3.1,1.5,0.2]|      1|\n",
      "|         5.0|        3.6|         1.4|        0.2|Iris-setosa|[5.0,3.6,1.4,0.2]|      1|\n",
      "|         5.4|        3.9|         1.7|        0.4|Iris-setosa|[5.4,3.9,1.7,0.4]|      1|\n",
      "|         4.6|        3.4|         1.4|        0.3|Iris-setosa|[4.6,3.4,1.4,0.3]|      1|\n",
      "|         5.0|        3.4|         1.5|        0.2|Iris-setosa|[5.0,3.4,1.5,0.2]|      1|\n",
      "|         4.4|        2.9|         1.4|        0.2|Iris-setosa|[4.4,2.9,1.4,0.2]|      1|\n",
      "|         4.9|        3.1|         1.5|        0.1|Iris-setosa|[4.9,3.1,1.5,0.1]|      1|\n",
      "|         5.4|        3.7|         1.5|        0.2|Iris-setosa|[5.4,3.7,1.5,0.2]|      1|\n",
      "|         4.8|        3.4|         1.6|        0.2|Iris-setosa|[4.8,3.4,1.6,0.2]|      1|\n",
      "|         4.8|        3.0|         1.4|        0.1|Iris-setosa|[4.8,3.0,1.4,0.1]|      1|\n",
      "|         4.3|        3.0|         1.1|        0.1|Iris-setosa|[4.3,3.0,1.1,0.1]|      1|\n",
      "|         5.8|        4.0|         1.2|        0.2|Iris-setosa|[5.8,4.0,1.2,0.2]|      1|\n",
      "|         5.7|        4.4|         1.5|        0.4|Iris-setosa|[5.7,4.4,1.5,0.4]|      1|\n",
      "|         5.4|        3.9|         1.3|        0.4|Iris-setosa|[5.4,3.9,1.3,0.4]|      1|\n",
      "|         5.1|        3.5|         1.4|        0.3|Iris-setosa|[5.1,3.5,1.4,0.3]|      1|\n",
      "|         5.7|        3.8|         1.7|        0.3|Iris-setosa|[5.7,3.8,1.7,0.3]|      1|\n",
      "|         5.1|        3.8|         1.5|        0.3|Iris-setosa|[5.1,3.8,1.5,0.3]|      1|\n",
      "+------------+-----------+------------+-----------+-----------+-----------------+-------+\n",
      "only showing top 20 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "model.transform(xxDf).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "709e29ed",
   "metadata": {},
   "source": [
    "### 최적의 클러스터 개수 구하기\n",
    "Silhouette : 1에 가까울수록 좋다"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "89846736",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...2 Within Set Sum of Squared Errors 0.8501515983265806\n",
      "...3 Within Set Sum of Squared Errors 0.7342113066202725\n",
      "...4 Within Set Sum of Squared Errors 0.6711848003790326\n",
      "...5 Within Set Sum of Squared Errors 0.6693502650358714\n",
      "...6 Within Set Sum of Squared Errors 0.6438928241588121\n",
      "...7 Within Set Sum of Squared Errors 0.5348738274527646\n",
      "...8 Within Set Sum of Squared Errors 0.6172586649457701\n",
      "...9 Within Set Sum of Squared Errors 0.494507403994743\n",
      "...10 Within Set Sum of Squared Errors 0.4888408569527127\n",
      "...11 Within Set Sum of Squared Errors 0.4600942552619037\n",
      "...12 Within Set Sum of Squared Errors 0.4038335912317261\n",
      "...13 Within Set Sum of Squared Errors 0.3875002302551008\n",
      "...14 Within Set Sum of Squared Errors 0.3786055185887995\n",
      "...15 Within Set Sum of Squared Errors 0.4123630985764056\n",
      "...16 Within Set Sum of Squared Errors 0.4230354994650789\n"
     ]
    }
   ],
   "source": [
    "from pyspark.ml.evaluation import ClusteringEvaluator\n",
    "#silhouette = np.zeros(15)\n",
    "silhouetteList = list()\n",
    "for i in range(2, 17):\n",
    "    # Trains a k-means model.\n",
    "    kmeans = KMeans().setK(i).setFeaturesCol(\"features\")\n",
    "    model = kmeans.fit(xxDf)\n",
    "    # Evaluate clustering by computing Within Set Sum of Squared Errors\n",
    "    predictions = model.transform(xxxDf)\n",
    "    # Evaluate clustering by computing Silhouette score\n",
    "    evaluator = ClusteringEvaluator().setMetricName(\"silhouette\")\n",
    "    silhouette = evaluator.evaluate(predictions)\n",
    "    #silh_val.append(silhouette)\n",
    "    print(\"...{} Within Set Sum of Squared Errors {}\".format(i, silhouette))\n",
    "    silhouetteList.append(silhouette)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "621f297f",
   "metadata": {},
   "source": [
    "### 클러스터 개수에 따른 오류 그래프"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "5b6fdc2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x21dcfb3e1f0>]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(np.arange(14), silhouetteList[0:14], color='blue')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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