k_means_clustering/k_means_clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c73fbdd7",
   "metadata": {},
   "source": [
    "# $k$-means Clustering\n",
    "\n",
    "## Introduction\n",
    "\n",
    "$k$-means clustering is a classical problem in data science. It consists in finding a partition of a given set of observations into a given number of clusters.\n",
    "\n",
    "![Example](data.png \"Before k_means\")\n",
    "\n",
    "<div style=\"text-align: center;\">\n",
    "    <img src=\"arrow.png\" alt=\"Arrow\" style=\"width: 100px; height: auto; margin-left: -150px;\">\n",
    "</div>\n",
    "\n",
    "![Example](clusterdata.png \"After k_means\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c96fc362-2f45-4e54-849f-6af78c7025ca",
   "metadata": {},
   "source": [
    "## Notebook installation requirements "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c583ea2a-ef36-4560-879e-31dac075b864",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All packages have been successfully installed.\n"
     ]
    }
   ],
   "source": [
    "import subprocess\n",
    "import sys\n",
    "\n",
    "def install_requirements():\n",
    "    try:\n",
    "        with open('requirements.txt') as f:\n",
    "            packages = f.read().splitlines()\n",
    "        subprocess.check_call([sys.executable, '-m', 'pip', 'install', '-r', 'requirements.txt'])\n",
    "        print(\"All packages have been successfully installed.\")\n",
    "    except Exception as e:\n",
    "        print(f\"An error occurred while installing the packages: {e}\")\n",
    "\n",
    "install_requirements()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10883432",
   "metadata": {},
   "source": [
    "## Problem description\n",
    "\n",
    "**Inputs**\n",
    "* $N$ observations with their coordinates $X_i$, $i = 1, \\dots, N$ in the considered space\n",
    "* A number of clusters to build $K$.\n",
    "\n",
    "**Problem**: partition the $N$ observations into $K$ clusters such that each observations belongs to exactly one cluster.\n",
    "\n",
    "**Objective**: minimize the total sum of euclidean distances between each observation and the center of its cluster\n",
    "\n",
    "$$\n",
    "\\min \\sum_{k=1}^K \\sum_{i \\in \\mathrm{cluster_k}} \\| X_i - c_k \\|^2_2\n",
    "$$\n",
    "with $c_k$ the coordinates of the center of cluster $k$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7eb3d5e",
   "metadata": {},
   "source": [
    "## Resolution with Scikit-learn\n",
    "\n",
    "$k$-means clustering being a classical problem in data science, algorithms to solve it are already available. For example, in Python, Scikit-learn offers an algorithm to solve $k$-means clustering problems.\n",
    "\n",
    "First, let's generate some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7b73b5c3-dc20-42c2-b0db-924c9a15625e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "module was compiled against NumPy C-API version 0x10 (NumPy 1.23) but the running NumPy has C-API version 0xf. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[1;31mRuntimeError\u001b[0m: module was compiled against NumPy C-API version 0x10 (NumPy 1.23) but the running NumPy has C-API version 0xf. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem."
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             X          Y\n",
      "0     2.072345  -3.241693\n",
      "1    17.936710  15.784810\n",
      "2     1.083576   7.319176\n",
      "3    11.120670  14.406780\n",
      "4    23.711550   2.557729\n",
      "..         ...        ...\n",
      "295  12.731310   7.050802\n",
      "296   8.388222  23.453470\n",
      "297  23.427080   4.598641\n",
      "298   4.046104   7.634936\n",
      "299   7.667025   3.193633\n",
      "\n",
      "[300 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "\n",
    "data = pd.read_csv('kmeans.csv')\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "13d9f1da-057d-4c1a-ad76-314f5b7fcdbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data['X'].values\n",
    "Y = data['Y'].values \n",
    "observations_positions = np.array(list(zip(X,Y)))\n",
    "nb_observations = len(observations_positions)\n",
    "nb_clusters = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "837c07ca",
   "metadata": {},
   "source": [
    "Let's plot this data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "68edd5f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aGcOc4zjNmy0vwIQFt+vXPSMpCirh/eL5p9PJM6e7ZwsK7/4D8k/k+RzRxAlF+m1Jvm8BZE3bxcTxBRoYKtPg0Jie8qLjx0yLhRwd6B8CV0Gy7lwdLNNgGXNVCmshR9Q2vkC/Pdj4tIHHfujQ5h9W39nJJ+Xo0i9K3W16/RwyoUD9A5irksQL+RxNGJen9wJz9bCJRcnTjLm+xrzwcnT3H9Y9WjPwvDjtuv/x3+iWv/7HuhHe/e8NiE+afD5H/AcPwiuLduIElgiHBofKsh2P4d74wcwV3oODEF7BeVCZq3g4E0RK/HuVhfe9jAQSnvsZ0b/9nOjAAaJPfIzotM9K3m16ffHvgP7BIRpCIEEMuiu8irl62CHjxM4xFjsa88IbHHR/hJerNCCHt3W+FkhpkB9LpDTIM+Ue3blaGqTSAB7OpAhnKaVB6p6y0A9yeOVHASkN8ky5RwhvgGtQeFGlwc7Ea0SvEF556hBeeaYQXjtMIbx2uEJ45blCeOWZQngVTIPCy4egDq+dyZd2rxBeeeIQXnmmEF47TCG8drhCeOW5QnjlmUJ4BZiiLJkAxJS6gPDKg4bwyjOF8NphCuG1wxXCK88VwivPFMIrwBTCKwAxpS4gvPKgIbzyTCG8dphCeO1whfDKc4XwyjOF8AowhfAKQEypCwivPGgIrzxTCK8dphBeO1whvPJcIbzyTCG8AkwhvAIQU+oCwisPGsIrzxTCa4cphNcOVwivPFcIrzxTCK8AUwivAMSUuoDwyoOG8MozhfDaYQrhtcMVwivPFcIrzxTCK8AUwisAMaUuILzyoCG88kwhvHaYQnjtcIXwynOF8MozhfAKMIXwCkBMqQsIrzxoCK88UwivHaYQXjtcIbzyXCG88kwhvAJMIbwCEFPqAsIrDxrCK88UwmuHKYTXDlcIrzxXCK88UwivAFMIrwDElLqA8MqDhvDKM4Xw2mEK4bXDFcIrzxXCK88UwivAFMIrADGlLiC88qAhvPJMIbx2mEJ47XCF8MpzhfDKM4XwCjCF8ApATKkLCK88aAivPFMIrx2mEF47XCG88lwhvPJMIbwCTCG8AhBT6gLCKw8awivPFMJrhymE1w5XCK88VwivPFMIrwBTCK8AxJS6gPDKg4bwyjOF8NphCuG1wxXCK88VwivPFMIrwBTCKwAxpS4gvPKgIbzyTCG8dphCeO1whfDKc4XwyjOF8AowhfAKQEypCwivPOhmEd6HNhZox86cC6CtjeiiC8p04vSyPBChHt25Whqk0kB2r1HoVlPrBsJrBzWEV54rhFeeKYRXgCmEVwBiSl1AeOVBN4PwPrs1T489nq+6eZbe5csGaWKbPBOJHiG8EhSr+4DwyjPlHiG88lwhvPJMIbwCTCG8AhBT6gLCKw+6GYT3wfV52rW7WniZxMLLhuj4TkceikCPEF4BiIEuILzyTCG8dphCeO1wzTmOk83f+HbuV7xXCK84UmsdQnjl0TaD8PrTGfwEILzy8yHLPUJ47YwOIrzyXCG88kwR4RVgCuEVgJhSFxBeedDNILzbd+To4UcKVTffPsmhFVcNyQMR6hERXiGQvm4gvPJMEeG1wxTCa4crIryGXCG8hgBTbA7hlYfdDMLLd815vLt25+hAKUeT28t0xmllOqpDnodUjxBeKZKj/UB45ZlCeO0whfDa4QrhNeQK4TUEmGJzCK887GYRXvk7t9sjhFeeL4RXnimE1w5TCK8drhBeQ64QXkOAKTaH8MrDhvDKM+UeIbzyXCG88kwhvHaYQnjtcIXwGnKF8BoCTLE5hFceNoRXnimE1w5TCK8drli0Js8VwivPlHuE8BpyhfAaAkyxOYRXHjaEV54phNcOUwivHa4QXnmuEF55phBeAaYQXgGIKXUB4ZUHDeGVZwrhrWZ6oES0aXPBXXRYKhGdOK1MpydYdAjhtTNXIbzyXCG88kwhvAJMIbwCEFPqAsIrDxrCK88UwlvNdNPmPG3ZVr1xSHu7QyuWxSsrB+G1M1chvPJcIbzyTCG8AkwhvAIQU+oCwisPGsIrzxTCW830vvsL1NWdqwG98pp4W0NDeO3MVQivPFcIrzxTCK8AUwivAMSUuoDwyoOG8MozhfBCeO3MKju9QnjluUJ45ZlCeAWYQngFIKbUBYRXHjSEV54phLea6RNP5+mpp6tTGqZMIbpyyWAs+IjwxsKlfTCEVxuV9oEQXm1UsQ5ElYZYuGoPhvAaAkyxOYRXHjaEV54phLeaKS9aY+HdviNPpYNE06cl2ykPwmtnrkJ45blCeOWZIsIrwBTCKwAxpS4gvPKgIbzyTCG8dphCeO1whfDKc4XwyjOF8AowhfAKQEypCwivPGgIrzxTCK8dphBeO1whvPJcIbzyTCG8AkwhvAIQU+oCwisPGsIrz9SW8G7fkaO+fTlqayOaOaNME9vsXHtWe4Xw2hkZCK88VwivPFMIrwBTCK8AxJS6gPDKg4bwyjO1IbzfWlOk3t7Ra2XpXb4sXlkvO3eaXq8QXjusIbzyXCG88kwhvAJMIbwCEFPqAsIrDxrCK89UWnhf6crR2gcKNRfKu5WdeVrZzg1ksFcIr51BgfDKc4XwyjOF8AowhfAKQEypCwivPGgIrzxTaeH97iN5emFHdVkvPgeE187YRfXqbZXc1V05snMq0by5Q02bYgLhjRrx+D+H8MZnptMCZcl0KNU5BsJrCDDF5hBeedgQXnmmksLr1rB9Kk9Uu1EZnXN2mU6ZgwivnREM71W1c9zMGQ5dfGG8rZLTvu6w80F45UcCwivPFBFeAaYQXgGIKXUB4ZUHDeGVZyopvDfcVHQv0KFq522f5NDSJc0bVUxCPSspDd6Y+O+hvd2hFcsgvEnGtRXbQHjtjCoivIZcIbyGAFNsDuGVhw3hlWdqQ3g963VyROOLRH+2YmwtWOP7z7TwTnJoxVUQXjvfpubrFcJrZ8wgvIZcIbyGAFNsDuGVhw3hlWcqKbw3f6Po7k7m/3ROdWjR5c0pVya0syK8SGkwGcWx0RbCa2ecIbyGXCG8hgBTbA7hlYcN4ZVnKim8L+3K07oNowvW2iYQLZg/RMd3cpLD2PpkRXj39BBt2lygru5KYjU/gPCYNGtdZOTwyn+PILzyTLlHCK8hVwivIcAUm0N45WFDeOWZSgov97W3L0d9fZXr7OhwmlasTElnRXhN7yNr7SG88iMC4ZVnCuEVYArhFYCYUhcQXnnQEF55ptLCa+cKm69XCK+dMYPwynOF8MozhfAKMIXwCkBMqQsIrzxoCK88UwivHaYQXjtcIbzyXCG88kwhvMNM71izgf5h3aMjhL/9zevo5JnTR/77oUefoa/eep/73+edNYdu/Moimtg23v1vCK+diWmjVwivPFUIrzxTCK8dphBeO1whvPJcIbzyTCG8nN+2bz+t/c4mWnr5F1yJfbn7dfrzVffS11d+mU6YejQ9v2MX3b5mA62+ZTlNnnQYsRzzZ8WSSyC8duaktV4hvPJoIbzyTCG8dphCeO1whfDKc4XwyjOF8CqYsgAvve5OunrJJW6UlwW387gOuvjcU92jgwKMCK+diWmjVwivPFUIrzxTCK8dphBeO1whvPJcIbzyTCG8CqYstCtX3Utrbr2ajp5yJH3ttvtozkkfGxHeYAQYwmtnYtroNevCy6vpu7srdz51KtHk9uyXjoLw2pipRO5cLQ1SaWDsbP1rh+RorxBeO4QhvPJcIbzyTCG8PqYsskuuuZ329L5NXg7vgVK/K7xfPP/0kZzeoPD2D1go4J7LubsCDQzij53ktC8W8jTkOOSUsyeSW5536H+tr76uJZfnacYnJAnI91Us5imfy9HgYJnKTva4yt9xsMdKLVXpT7GQo3LZoQxOVelbTdTfeweI/vN1h449OkeHTPS6qD//crkcFQqVuYqPHAH392rZIWdMfv/lOPp7Cpur48cV7JxwjPSKOryBgfanNHx8+ocjI7xv7gtsYyQwcYp5osMOGU973+0X6A1deATef0iRDvaX6WAG/+DdeHOeSqXqsTq+k2jxomz/cX7/IeNowrg8/ea9ATo4JqORdiSfuZb6h6g/g3O10b9R/te6PP38pdEHjbPOKNPnz+BxqP/w4f5enTiO9v52oNG30FLnn/S+cXTg4CD1D9r5LrQULM2b4YDX+9qK1BeYqx+YNEGzBxymIgDhVVDx5+0ih7d1vjhZTmm44aaiEvRNNwxmegCQ0qA/PLzr2abHeROIHLW3OzRrhkNnnKZ+oEFKg5rr9h05eviR2ijX0sWDdFSHus2BEtHWbXnq7s4RRyM//vFBmjkDcqY/c+sfiZQGKZKj/SClQZ4p9zjmhZdTFH70Lz+jxf/tfJewl9qwauWX3TQGVGmwM/Ea0WuWhffmbxSpFHhZwFuOLrrcQsqMIHwIrx5Mzs++8+5aUVt4mXqbXwivmusTT+fpqadHt0r2jrrogiGaNVMtsQ+uz9Ou3dVtTj+tTGeGPGzojSiO8ghAeOXnAoRXnimEl4i8PN3v/2jrCGHU4bUz2Rrda5aFV/WHfMElZWprc+j4zuxGoyC8erOao7vrNtSKWph4QXjjCW/YgwP3onp70gwPk3ozq/FHQXjlxwDCK88UwivAFFUaBCCm1EWWhZcRvNKVo1e6K3mIb7yRq8pT/PTsMs2bm718Xgiv3uSF8OpxijpqTw/R6nuq03/aJhAtv2qQJrapW6uEt32SQyuuyvbbkygWWfk5hFd+JCC88kwhvAJMIbwCEFPqIuvC62FQ/VHnn9V7bZsSwprTQHj1yJukNHAO6nfWF0Yeho6f6tA5c4dCc1b1rqh5j+IHw+0789TXR9TeTm4edL0SfnfcVaC+fdUL2qZPK9Ol87P3ANmMowLhlR81CK88UwivAFMIrwDElLpoFuF9dmueHntc//V3SviUp4Hw1mJhQe3pyVFPb446p5ZHxJSjvJy60ttLNGUK0awZZTplTvSitYc2FmjHzmphY+ldmPH87kbOS/+5WZDXrS+M5MhzdHfh5fUlOSvX3gzXAeGVHyUIrzxTCK8AUwivAMSUumgW4Y37+jslfBBeDdAcyV37AEcfRwU1STqKP4dXtaCRLyXrFTw0cKV6yJtv5uiDh48npyBfSjLVG8nYySC88gMC4ZVnCuEVYArhFYCYUhfNIrwcIbzzrtqqDcuXDWVu9zVEeKsnb1gVgbhj5xde1St5CG/8XxrYaS0+M50WEF4dSvGOgfDG46V79JgvS6YLKuw4CK8pwfTaN4vwMhHO433yad6MIudWavj07GxWa4DwVs/f++4vUNfwwkP/T+pVEVB9A/zCq0pp4DqyF1+IRVdxfntAeOPQ0j8WwqvPSvdICK8uqXjHQXjj8ao5GsJrCDDF5s0kvCliMToVhLca36bNedqyrTb/ut7GCFHCyxH/TZsL1NVVObKzk2je3KHQqgRGA9rCjSG8dgYXwivPFcIrz5R7hPAacoXwGgJMsTmENxlsXvTDUWbVTlYQ3mqmqgobSWq+2q7Dy7nGvBCO/y9XOOCIcb1KB8lmTrZaQXjtjAeEV54rhFeeKYRXgCmEVwBiSl1AeOOB5m1cNz1eoFKp0q6jg2jhZdX1TpnpG2/mactPB+k/Xyu7x8yZXR7T0UeWyO3DVRW4RmxYJYZ6o2FTeN0c8buLI+PK19HWRrR8WXgt23gzJ5tH+4WXH+Iq961+kMvmHWTzqiC88uMC4ZVnCuEVYArhFYCYUhcQ3nigVdUBghUHnIHx9LVV1aW12tsdWroYr9zj0a4c7ZU0GzxYpMOPGKIjjpSvFcsPMg8/UrvNcRbrPCdhGNaGhXd8YTzd9jdD1NMzehS2GTajHFd4+WGD6ye3+hsFE6oQXhN64W2R0mDIFcJrCDDF5lkQXn7l3bcvT20THOrocMQioSxKO3bmaU9P5RU1F9ZXpSDo4uY/SmsfqJWi4Ov5LVvG0aYf1G59HHeRlu51tfJxPDfWPlAdeRQKf4UAACAASURBVD3n7PBavUlZhFWSyJL4cS1qrmPMc5nnnMT22iy8P3thHP3vjbUPEXFzrJOyb8V2usKr88aoFfkkuScIbxJq0W0gvNGM6h4B4TUEmGLzRgtvcEMJfo3MKQImYurh+9aaoruhgf9j8kc8bGew4A5VYcK74JIynThdPjqZ4nRJ/VQPrs/Trt21C96k6+2G1XnOypipKl1IPECx8H7nn4u080U8oElObl3hVb0xQrUR9UhAeCVn6GhfEF5DrhBeQ4ApNm+08N5wU7HmbiW2OA2LxppG7FTiEZSiHTvG0UOP1AqEiWynOCUydaqwkmZxa/jq3FTwXEkW1umcJ+4xug9acfvl41l4f/yTIn3/cQhvEn5hbXSEN2y79KzMO0keEn1BeCUo1vYB4TXkCuE1BJhi80YKr81f+GHCayrTnCaxfQdHHStVGmbNoJqobVtxPP39/Q794uVRiUiys1iK0yCzpwoTXukIrweA56RX51niLYMEWN1UmiTnYuHdv28c3XxH9ZsH3ub5yiWDSbpEGyLSEV7+XbLq1toHfggvIrxpfokgvIa0IbyGAFNs3kjh5dtURXglfuGHybSN/M/gcHllyZ7f2U/9g2WsejeYzyrZG4sPD6rviQQHr0rDv+4+SC/trmz/3DHFoVkzx3ZVEYMp6zbVEV4+TueNkem1tEp7RHjtjCSE15ArhNcQYIrNGy28qh2zJHITGWFwIVL7JIeWLrFfKQF1eGUnMD+8sIxNHF+gww4tU2GcQ08+k3erCnDJt1kzysTy18qfYK47z+WFl5eNV/WjDq+dWaMrvBzl5U1ZuobreqveGNm5wubrFcJrZ8wgvIZcIbyGAFNs3mjh5Vvllcp791VqgJ5oWEkhiM57Rc3/LrGqXWdoILw6lOIfw1z/c88Q3XJHZa74P1IPSfGvKr0WnMvb11c5n1Q1EwivnfHTFd64Z+cHn927R+slnzO39TdH8RhBeOPOFr3jIbx6nEKPgvAaAkyxeRaEN8XbTeVUEF47mJnrM88O0YaHa4XXdDGinSvOfq8QXjtjZEN4VbWiub73imVDdm4iY71CeO0MCITXkCuE1xBgis0hvPKwIbzyTLlHCK88VwivPFPu0YbwplmxxA4Vs14hvGb8wlpDeA25QngNAabYHMIrD7uZhJcXhUWlevCrdK5KwdspS214kIR6GikNzKOrOyd6n8xvh7etchvRzBnZWRAG4U0yE6PbpCm8Y6XcIYQ3et4lOQLCm4Sarw2E1xBgis0hvPKwm0F4N23Ou4tlvE/Yin/VTmcS1QGSUHfnammQtv8b0abNOerblyNevDVzpkNnnma2aI0XD/GObv7tdXlB3BWLzUpzseyuvqfgPix4H4l+k/BTtYHwSpGs7seG8Kp2A2ybQHT9tWZz1A4B+V4hvPJMuUcIryFXCK8hwBSbQ3jlYT/5xDh68seVGry8c9xFF9jfYY0jkxyF7enJUWenQ3Nmh0cRw0q2qRZ+qapo8H2tvGZQbAto3RHwhLc0YCa3qvMFqyB4x5guhgvbsti0X11mUcdBeKMIJfu5DeHlh7KHN47uPMiyu2D+UOQbmmR3kL1WEF47YwLhNeQK4TUEmGJzCK8sbNXCEpbepYuHjEtIhV2pqlZtvcUsYRKmWvgVljfYCGGzKbxxmMSZMcFIupRIx7mGesemIbz8gLVjJ5eRi34Yk7qvRvdjQ3gbfU+NPj+E184IQHgNuUJ4DQGm2LwZhZcjHRPbUoQU41RhEVGbghg3iqiScr5F1aYciPCaRdDCIsc28y5f2pWnnt7K24Xp0+qXrbItvKq3Cfwwxg+AWf0Ox/i6hx4K4ZWgWN0HhFeeKfcI4TXkCuE1BJhi82YSXo5kPvxIZTco/hw/1aE/nJ+tP5y2InqcC/rk0ywyOZo4wXHTFs4YzluNK9luXumaApUOjk40fj3Km3JMbh/dDpl/6ubw3l+sOrbRObw2Uhr4IerOu6rvU2J7Xe6XWXO+sfcx2d6aZXbHzsr2x9OnOzUL4ILzj6V34WWDFLZNsm3hjfswluKvPqungvDK44XwyjOF8AowhfAKQEypi2YS3jvuqhYHRjRzhkMXX5idOpQsJOs2jC4G42tkmVx+lVnOqyq1wEtBSBJFZJFlgWZxamtz6NOzndBcQBbkri5yNweR3hgkzjS3mdLA18Fyun1H3pV7HjPJ7XX5YY1Zt7eXQ+UzioUqMs8PfQsvr8x/vv5VtxZruqn3HYHwRlFP9nMIbzJu9VpBeOWZQngFmEJ4BSCm1EWzCG/YH3Muk7Vo+A9+SsgiT7Njxzh68d+JXn3Noc6pZTcSGxZhi+xs+IAbbqoVGe/emc269QW3nJb3abaNGPgetg5XjeAoM0ta8GNbeHXHolHHheVT33RDZZW+Kpeb/73ed8S28CZ5GGsUX8nzQnglaVb6gvDKM4XwCjCF8ApATKmLZhFexlFP+lLCpXUa6bJkurLvbaPc3k7WFshpAahzEEcpuZqEK2KdRJweoSrd5Y9cet0FhdfbajeqjrDpNWelfdTGA1mM8DK74HU3KiUmzXGE8MrThvDKM4XwCjCF8ApATKmLZhLeeq/1U8KldRpp4eWTNkM6RxQcVT4ny8+ENqKnnq5OA+G+ggv9POHdu79M31lfoFeGI9qcpzrv7CGaNbM2Khx1TfyQYBp9jzqH1M9VudrBOqw1ObwTiBZe3rgcXu/em+FhTGqcuB8IryTNSl8QXnmmEF4BphBeAYgpddFMwust3Orrq8DhhVumGw7YwGxDeFkYOG3BW/zEr6m5BmczrXRXSfuECUQnTndGdiLzj0eY8D7xL0SPPV4ryHFqAwdftTdD1JHn/4PrC9TbW6HEsjtvbq3o81x5aXeeJk9y3IVt9eaI7ZQGG9+vZugTwis/ShBeeaYQXgGmEF4BiCl10UzCmxIS49PYEF7Ti+LX3VwHlT+NSnlQpaTw9cye7dC2baP5x969Bkt3eRHev/37yva/wY9u6bewjTcuuiBZlNh0bOK296KlEqkcEN649PWOh/DqcYpzFIQ3Di39Y1GWTJ+V8kgIryHAFJtDeOVhZ014eTHTug3V29suuMTO7m+ejHHlh2CqwN+vLdCrv64WVcch+txny/Tii5Wtgr2PqnSXJ7wP/u+cMiKsW9s2rA5xsy30k5i5EF4JirV9QHjluUJ45ZlyjxBeQ64QXkOAKTaH8MrDzprwqnKfOe/1+msqq/ulPg+uH932lPsMLjz76Qs5euR7BSLPax0iJ0duqbOLLixTV1ee9vZxTq26RJonvC/90qG1DxSqLjtOzVyvdJw/4zfnEJ1+ejmTKTJS46PqB8Jrhy6EV54rhFeeKYRXgCmEVwBiSl1AeOVBZ014b/5G9YYK3h37y1mZbugRVhLLH0keSSXwTHNYfHUjq/4qDSyt24c3YGBB5j5085k5veOv7ijSQMD3P/nxMv3Xi8vyE8Jij8yBx65UqpyEHx6+cKE+CwivncGB8MpzhfDKM4XwCjCF8ApATKkLCK886KwJb1T9VtVisriLuMJ21ArKbLDSQPskx93hTUdWJevw/t29BXp9T20esPcQID8r7PSoephRbREddna/8Hpl3tzofGf8ihd27rA5e4Xwyo8bhFeeKYRXgCmEVwBiSl1AeOVBZ014VcX/PRFlybnz7gIFgq51NytQEQvLi1XJF0d6+/ry7g5vccRKUnjDHgLiVHqQnznxekyy0UTwDJ7wrn9koKo0XHu7Q0sX6z2IxLvqsXF0UHj5rcKOnaOReN5YJbiN99ggk/wuIbzJ2dVriRxeQ64QXkOAKTaH8MrDzprw8h2yHHl1a7lclVezdvcvcvSP3yn402pdIJx/G2cHO/6Dfudd1akTElsq+0dHUniD+cZ8nmBNW/mZIdtjWLUJ1YK/ehHe8YXxdPX/rN2eWzfVRPauWqO3oPCqHrB0F1m2BhHzu4DwmjNU9QDhNeQK4TUEmGJzCK887CwKb9hdqtIZONrL2yFH1ThmifbKg3FdYC53tn1njrq6cm6N5FnCUSxJ4XUrV6wvUOngKJk4qQDysya6R87X3bqt8uDCDyRzZju0aXN1dQvuJU55NY7wvtEzju5cXZu7nMVtu6MpZeMIv/CGPZjETRvKxp017iogvHbYQ3gNuUJ4DQGm2BzCaw6b5Yl3CmMR6egg+szsHM07s0jv7O+nUn9t5Mz8jHI9qGrjHnoo0TUr6ldw8Cod+K/EdkRQUnj5ujmdg2sTl0oOdXTUllGTo2zek5d6EuyJF9m9+O9EpVIlH3n6NIdOmaO/8I6Fd/++cXTzHbVt+LX7xRdme/6ak7XTg194JVJP7Fxlc/UK4bUzXhBeQ64QXkOAKTaH8JrBZhFZfU91jVvu8St/WqQPdAw0pfCGRfb4D/eu3RVJ3PebHL29d7TCGN+zjVJn/tGRFl6zkU+3ta3awV4O7zfuHqzZzEN3I490STTH2XQivLYfEJuDlP5VQnj1WcU5EsIbh5biWAivIcAUm0N4zWCHRW/OPydPn/vsUOaFV5XLqvpDrHoty6kPwToHNqscQHiraw/zzDWVJk94X+09SNt35KmnN0e8YI1TJuIsKDT7FrVe62AO76bNedqybXQ77DjVSVqPTrI7gvAm4xbVCsIbRSji5xBeQ4ApNofwmsFuduHlxWacjrFneNvhsFfiYWXH3PIOw9Zre9HXWBbesJQG0ygs6vCaff/DWqvKknm7EHIbPEzE5w7hjc9MpwWEV4dSnWMgvIYAU2wO4TWDHSYiV36pSFOPz35Kg+7dqyLBbluf8MZZLKV7Xv9xY1l4mQOnNWzaXFloxw8Xc+ZELyyM4gzhjSKU7Oeow5uMW71WEF55ptwjhNeQK4TXEGCKzSG85rB5AZe3Wp5F5IxTc/T//EFzLFrTvXtVLV9ue8ZpQ9Q+iaizk6zXFR3rwqs7VnGOg/DGoaV/LIRXn5XukRBeXVLxjhvzwnug1E9fu+0++v6Pto6Q+/Y3r6OTZ04f+e+HHn2Gvnrrfe5/n3fWHLrxK4toYtt4978hvPEmXCOPHivCy6kH23fmaV8fuSvyuaSTrcLvzVSWTHfucerDffcXqbd3tIVp/qjuub3jILxxiUUfD+GNZpTkCAhvEmr120B45Zlyj2NeePfu209rv7OJll7+BVdin9+xi1auupfW3Ho1nTD1aPe/b1+zgVbfspwmTzqM7lizwR2JFUsugfDamZPWeh0LwqtacMUVBZYvG9Ta0jYu/FYUXo+Bl4fINXf9DwwsxLt35+hAKUedU8t0VEdcatHHQ3ijGcU9AsIbl5je8RBePU5xjoLwxqGlf+yYF94gKhbgpdfdSVcvucSN8rLgdh7XQRefe6p7aFCAEeHVn2yNPnIsCG/YgivTBT9hY6cSXhbFru68uzkDC+HEtkaPvN75+brXbShQX19lZdqJ08r0hQurr5+PWftAkUql0T5tFNWH8NaOGeeQ8xbNSecThFfvexD3KAhvXGLRx0N4oxklOQLCG6D2cvfr9Oer7qWvr/wyHT3lSDfdYc5JHxsRXv/POQK8550DSbjXbVPM52jyYRPozX2+v6riZxl7HU4+dDwdODhEpYHWLTD/xFN5evLp0ZJA3ihfdOEQ/d5MXnUl+2GmbeMLtPfdysYTjz5WXZKIo8tXLBmyllIheTe3f7NAffuqi4+xzJ57zuhGBf+0Pk+7dtXy/cuv1d+8Iu51unO1NEilQf2NFeKeo1mOf50fRNaPPohwRH3B/Phzalw+R5MOHU9v/ca35VwGIbDYb3osR3t6czSZHxo7ncidABt5G4cfNoF+e2CADmKuig3D+EKeDnvfOHo7MFePOnyi2DnGYkcQXt+oe/m8nuB6//3F808fyekNCq8j7xBu6SP+s2ul77E4y4fvOZerLLSv/H+t+fnJtjJ9e12t0H/1K0X60DHBSrLmDJipi9QheusdopU3DdR0+vnT8jT/otq6quZnl+vhvQNEV62svfajO3J043XFkRPd9teD9IuXayfQn11ZpGkfleM7Fuaq7uhdd+OAu/GH/zPzEzni6iCxPk3ye1V1v3+8oECfmV37oBXr/i0djLlqAWzIXPV+31o445joEsI7PMye3HZ88PCR/NygAPOhQeFFSkPzfE/GQkoDj0awrJbNBVf+lIaXflGmtQ/Uim3YbmZZmjmcl7vq1lqBYpFfdPnQSC3RsJJl0ptQIKVhdHaotoTmDSNWLIv3pqYZUhrCSv9l+TuElAb532RIaZBnyj1CeIlIJbsebuTw2pl4jeh1rAgvs+U/nH3DVRqS5jzqjJFfePe8UaY7764VXhs5rjrXFveYO/+6SHsDkUSO5Z4yu0zz5lZSC1Sbb9i4PwhvfeFNIoDNILyqRadMIsn9xp3/SY+H8CYlF94OwivPFMLrk11/nq4fNao02Jl4jeh1LAlvWnyDi9buu79AXd2jr/a5Vu/CywetVDKQvsd/fTFP//xQnnLOcNbL8G3w4rVL54/m0vLDxPadlR8eNYXoxOnRebbeLm89PZWFV1wqrt4OVK0svCx1j20u0CvD84S39v3D+UOhi9F0t4SOmg/NILx8Dzd/o+huuOH/2HxLE8Ut6ucQ3ihC8X8O4Y3PTKfFmI/wcorCkmtupz29b1fx+tKCc0dSG1CHV2cqZf8YCK/8GKmqNPAuWXuHF3/NmmGvBrD03YS9Tj7n7DKdMidaautdz7fWVNf15WPrVc5oZeENPhQxi5kzHLr4QnWKQnBL6KSLuJpFePktwsMb8yMLKKdPK9NFgWoh0nPfpD8Irwk9dVsIrzxTRHgFmCKHVwBiSl1AeOVBt1odXpb1hx8ZTcvgV8lcEcAkLUSVBsEjUS8VopWFVyonN+5sbhbhjXtfjT4ewis/AhBeeaYQXgGmEF4BiCl1AeGVB93swsvRw++sH329zouhFlwyRKVSzt2lzkR0PdphwsuRO3+qhH90xprwTplCdOUS2dJuwdkO4ZX//nOPEF55rhBeeaYQXgGmEF4BiCl1AeGVB93swvvQxgLtGM7H9egkqQBQj2ySVIlmE17Oy33q6Ty9MrzhCOc9n3GaOg3k9ruKtG9fNbF6KQ1SsxbCK0Wyuh8IrzxXCK88UwivAFMIrwDElLqA8MqDbnbhVeXWMiXpMmNxUyWaTXjvuKt2046LLhiiWYHNTngnQN4YxV3yN1zOeNIkoiv+u52tr/0zHsIr//1HhNcOUwivHa5jftGaKVYIrynB9NpDeOVZN7vwqhZQ2RBejzynN/CWy5Pb6+9+0kzCGydlI23epsL70q48dXVz6cocfbiz7C6uwwcRXttzAMJrhzCE15ArhNcQYIrNIbzysJtdeDniyK/i/Z8s1DxtVeFVRYJtPmCYCK9qbmS5PJj8t1uvx7CUBk7l2botR1yKb1I70awZ5bql+PTONjaOgvDaGWcIryFXCK8hwBSbQ3jlYTe78PKitS3b8tTVlXOjeEd1ODRvrllVBgnKpsLLstbN93QwRx1THDefNiqqbHLdqtqxqnJuqpq67ZMcWnFVvF3Tklxr3JQGVbpLWxvR9dfYXVyX5N4a2UYlvPy9Wn1Pgfr6qrfbrleKr5H3kLVzQ3jtjAiE15ArhNcQYIrNIbzysJtdeOWJyPRoIryqyGRHB9EVi+2JGr/637Q5N1I7NmwRGkf9HlxfoN7eCieWXS77dlRHPG7cD+cC7+urtJs+3XHLvNX7xBVeVfk07l86vzvenWfvaJXwhqW5IEKuN34QXj1OcY+C8MYlFjgewqsPkH8Jep96u0zp9xjvSAhvLS8WB65SUCoRcfRqzuxyrFJcEN54c1D3aBPhDcuTXXlNsoVhXIFh1+68Oz+mT5PZSIQjgPyJW/aNf4dwhYenflygd6r3CiLVIjk/77jCq+KYVjRad55k4bg4wptGNY4sMDG9BgivKUF1ewivIVcIrx7A4B8P3k504eX2X2P6rw7CWz1WLB133l10Zdf7cEmupYv1X+lDePXmf9yjbAjv8mVDsdMaVNHiBZeUtbZTjnvP9Y5XviLn9WO+N+ZRuddxhZflet36wsg2v7xNNu94prOVtOS9Z70vlfAmKcWX9ftM8/ogvHZoQ3gNuUJ4owHy6851G6oXBnGrtP9wQnirx+rZrXl67HGzcUlDeL03A/7qBt6/tbU5I6/DvVqwL/mikVnIx43+htQeYSK8mzbn3bxk/ydpZFL1Wj9KLJPcb1SbsLnqd96o64orvHxNLNq86Io/OtU1ou6jFX8etmgtOGZR49OKbJLeE4Q3Kbn67SC8hlwhvNEAVVEibpV2PheEt3qsJMbFpvCybKx9oEg9PaPXfd68IfrJlnzVYhhvi17VIqN62/dGz9zGHWEivMyNI5Nd3cOiNslxI5NJ0oiU2wCntMjMTz9srrq1fIejvFG/T5IIb+NmQPOcud7GE94DAx4W4o0nhDceL92jIby6pEKOg/BGAwwW3fdaROXcRfcc7wgIbzWvsHGJs5LapvCqIpWBt9gjN7R08SCtvqdYMyGaNaoUFF6OXq/bMLrq3WYuJEfPvVJt3a/mqBwoPdsIplHCy9fEi9/q5QRDeOP9vtQ9Gjut6ZLSPw7Cq88qzpEQ3ji0FMdCeKMBurmidxVHcuG4BefDLb8q2SKa6DOqj4Dw1nIJ5lZPn1amS+fXX+3u78Wm8KoWDYUJL0v62gcKLSu8umW/kn43vHbB3EvHIcpVV5aiOA9Eptfjv67Va0bzafnfp0whunKJfuUJCK/UaFT3A+GV5wrhlWfKPUJ4DblCePUAevVOvaP5VXPcFdp6Zwo/CsKrZqPKh9VlbVN4H9pYcCtI+D/1hPfRzaPlrvzzbN5cfYHXvW/bx/kjvGElnmxEWlW5ssycz3XiNIdOnC5TpSEOP45ul0o52v9ujt4arszAD8yzZsb7HZJUeDm6XKlkkqPjp5bdVKy4ZdTi3G+zHQvhlR8xCK88UwivAFMIrwDElLqA8MqDtim8KtE76iiH9uyplmBP/FiMuDarW0JrQqU2ayssWuP7UqVrxI3G64x+2OKwqPxYnb6THBNMZeB6wgsvG30zxBHp727M0yvD+cpc/eWcueq6vkmEV5VKwZVMVixLt8JMEna22nDwYvfuHDF7Ho/PnjyO3j0wQAcHmu/B0hYj034hvKYE1e0R4TXkCuE1BGihOf8i7hsuSO9fqAPhlYdtU3j5all6d7l/XDnKWInqcaRt+84cHSwRTZoUP9InT0GmR5633d1cGSBHn/xYgY44fIhKwxKh2pJ39skO8SI+yU+YXHOOdNpRzbBr8e/gptq5LexBIInwhtU0TlLiTXKcGtWXqpThR0/I0Z/88RCEV3BQILyCMH1dQXgNuUJ4DQEKNw8uxOJozMLLKtuqQniFYRO5TNvGF+i1N/pp608d2rUrR1wqbOYMQr3SGLhVpfsuucihj3+iIrQ/fSFHG/9PgXIOuYUJuDIBx7ltiFcwqtmo6G5YKod/wV6c3dAgvDEmZMihYYsHlyx06JjjZB++zK+2eXuA8NoZOwivIVcIryFA4eaqxT3eH0gIrzBsn/DefOcA/aqruv+0q3DI3116PaoiiW0Tia7/SmVRVpho1GPMD38cHZ/QlqMPd5aJvweSH+7/yWcqJeL4wfKMU8s0a6bcOXS2p1V93zmd5fpraxezJRFeZUpDymXZvBxi5swpBMy5UZtfZFV4VbW6Jed62n1BeO0Qh/AacoXwGgIUbB61uAfCKwh7uCtmWh4q0LLrBmo6t7GoSv4O5Hv0/vjGqXsbFamMK7yqkm6Skdq0Uh9UqRz+9ArVwsawkm1JhJdf4W/aPLp4kitDXHxheukdYZv22Ijs63wTsia8nAa09oHqutyt8KAN4dWZjfGPgfDGZ1bVAsJrCFCwOf9xWnVrbS1WL6cPwquGzdw4L5bTPrwV8f4dzOoNETN948083XRrbUStlYXXyxPv6HBGqo24W9FuKIxs1cxRzwWXqBdQBZkqI7xtRNdfU+Ea9jAXJj6qyCdHB69YrF/Gq964B8XHjev6SpjVWzwW5yvPc3P7jjx1dZMb3TxxWnWFBE9I9wzvhnZUR/hCxSTCG+dabRwbJphp71Lp3ZuqxORHP5yjP1nYmBxe1QNPm+97Y2NM0ugTwmuHMoTXkCuE1xCgcHOVOHh/HCC81bCDK9wLBaIhXxqezuYGXg7vn147MCJ63ll02gsPfyrdBeeYFzlVRSPDFlCxOPjL8qkieZ8/w6FTPzc6IO6r7R056tuXI94qeN5cLhOmXhkfFTE2BRW6EYSvYynB9i9C9T9gxL0HCG9cYuEPyJyrv3dfjo6aQvTZ/9K4Kg1hiwobUStahm6lFwivJM3RviC8hlwhvIYAhZv7I0KT24mmT3NGtlSF8FbD9kdHVBsM8NFRq/M94X386X565Pu5kc1F+NXvpfOH3KixrQ+LUKnkpFo9IKxsV9hOb8Fokz/VgH92+qllOmVORVr5frj6BH9mTC/SMccOjlRpCDJk4dy6Le8+ZHAked7Z1fKrku8PHevQ4UcQ7evjaKlDc2Ynr6mrs0EFX/NNN5hFlIOLUJkZlyVLUjGiGYVXFdnnHOWlS+x+t+J8ZxtZhzdMeFdek+6mRnF46RwL4dWhFP8YCG98ZlUtILyGAFNsDuGthu3/YxG2oUNUPlywLBn/gdZNh/Cuhh9SeCvbnh69Cg8sW5w60NNT6YEliFMH4uTMJp12qtxY7itspzf/bmBhWzmr0hKCWwv7r1cnr5OPeXhjfuQBZNx4ooH+6rtmUV66uP52vPU48TlYvHt7iYJvB7x2psKrSs1IWn+4GYWXOfJD1tZtlcg+z6czT2vcojXVfGik8Kq+C62QSgXhTfobun47CK8h11YTXpYPFo+KSKQbPTMcisjmEN74whv1alCiDu+31hRdafJ/6p23kXl7Ya/y+Xq5IsKWbfmq+/AvGloCggAAIABJREFUFIuTj1lPeMP6mXd22b2GAwdzNHGCQ783y6H3v78SYeeNGfihIviJGt/IL9XwAavvKZCXR+u1OfIIh5ZdqV+qisWONzTgT2cnR6DLypz8uFsKe9eTRHj5IWXHzjzt6a3sssZR8TQerHS5p3Ec5/U/trngziF+uJw1o7LbnJeS00jhdee2olZ32rt4So8DhFeaaKU/CK8h11YSXpZd/sPF5W+8j+TKbkPUxs2zIrz8C5ojNrxQbFI70RmnVeoEp/3xi5Mqwst5ovzqtN4fD1PhDVvtXy//t5GbAaiu18+JpY0XWPGHt+L1l+mqJ8tBiYorvDx+E8YT9QeiuJ7Qxjl3knn41ZuKbl3gSpFgIidHdOwxDi35kp7wqq6P50Bwa2lXhqc6tOhyvX799+IXXv5dxyLLKSEscTNn1G5TrEwnaOPax839ujzu+KrSY/x/FxotvHHvpxmOh/DaGSUIryHXVhLesD+KjSqBYzg0Nc2zILyqP6Kmr5ZNOPGYd3VVHnDGTyD64Acc+s//zLkRtlkzonM8TYU3qpSc6t7ChNf09bn/XMHvAj+U8P/jD1/z9p1cComIqwLo5sKG5WMuv6pWoOoJr6qfcUWiAUW6rCcmXu6x92DDOdtsqFy1IUk+bHBcVIvk4kRiVVF+PsenZ5drouZRaTZh3wdPeF/tPUh33l2sWmSpWmBn+yHB5HubVttgrrZ3Xv9DB4RXfjQgvPJMuUcIryHXVhLeVl3x6g1xFoQ37I/o1GMd+tjv8g5ltZEmwylqtbmp8IaVkvNvHxu8AdXCsY4pDl2xJH7UTwXHZo1Zzjncsm00ZYglWiWczPXtvYO09WdcMq42CskMWLo5FYTlg6OpP362NmXBH4m786+LtHfv6B0XikSLF8kIr2murao9Xyk/xHBaQU8vb6BBxOXOkqYUeMK7/pEBrfQOG8LLAslpJ/zpnKoee6tf2JidQ3hjAhM6HMIrBDLQDYTXkGsrCW/YgpyolfqGCFNrnmXhdV8F5yq1RqVqpaYB1kR4OVLZ1Z1zcz9/9asc9Q/vXcECt2B+/VQKlqDHflCg996rcOMPp4WYLMLyeIWJTr30HpbkXbt54R3nn9a+IvfSWPbuy7v5tRwVrrdbFnP9+u1lty6y9+FX72Gv08PExF+vVRWFTboALDi3aqopTCBaeLm+TD+4Pu/y8384VWTFVZWHGL4/07SfKOENPmTFWWSo811TLbBKGq2udz6pMm7eOZDSoDO6ssdAeGV5er1BeA25tpLwql6VJs2XM8RqpXkWhDesrJU/h1ZqIZEViIFOkwqv6o//zE86dMbpevnMYVHYepFhXR5hY+T17S1k4v449aPz+DKt/Xb1hiecprJiWUXW3GL9gVfo/O/1xvnX3ePp3vtra+xGRb55YVrpYOVO/YIexkvy+20iWnx969YX3EoE/GHZ5YcezrP1LwTkFId5c9W1h6PG1xPejZsH6LHH9RbwVZWRm0A0b+5Q4u2TozYXibp+nZ8HH9Z4Hi68TO87FdY/j82TT1ceSHhcTpzuGC1a43nC/XF5PO875KUL6dzjWDgGwmtnlCG8hlxbSXgZBf9ye2k40sL1Hr0aoYaYMtE8C8LLIILRrGAN3LEgvKqczTg7JIWV5pJYZBkWLeVcdq6TG6x2wNUI3np7dKGnN9m9cQzLU653rVu2jKNNP6hdyGhyf6oIr6TwSnzJ/bWVpVNL/Dm8991fXRkkDQ62NwMJSw8yeUjQGdO4Obyq777Eg6rOtTbLMRBeOyMF4TXk2mrCa4gj082zIrxe1O9HTxTouZ/WilIzLRJMGuE1/eOfRCLjTE7un6NQ3ocjUJw7GpbnrurbE94kcv5273i6a01tJPO8eUM0++RkFT1U5dyy/HCVJLWk3hgHy5LxGHOpLZO84DhzShnhnUB0/bVmm3N415BkAWic6w87No7whkl5Gg8cEveaVh8QXjukIbyGXCG8hgBTbJ4l4fWkNxhpMongpYhy5FRJhVf1x9+fs6lzL8FIUdgOVBL5n971qPIZo3apC4sY18vfVOXwepUVPjatTAvmJ3utz+kYvCUsf06cprdoyls0xm06p1Ld3GOdcdM9Jiq1RLcf77gkdXjjnqPe8aoHH8nve9g8s73Fdxzh1VkEJ8m8WfuC8NoZOQivIVcIryHAFJtnTXj9kRn+3+3tlYVXzfTxhPe1N/pp608dt6IAL7xjmYr7x9+/wEqHgbeNtJezGiyjFlyEKfHaVLW4ijd3mDgxV7V5RlBkWBo3bS6M5Nf6XzPzfXx3Y340laiN6I/m5+mjHxmkn2xz6LvfK1TW5fleBkjciw5jVZRVUtLqXUO91JIk35NGCy/fqz9lTPeBQ2ecvGNUD5K2o/hxhJevU1WRw3baRRyGWTgWwmtnFCC8hlwhvIYAU2yeVeFNEYH4qZjpu+8W6C9uHaDSgdHu+TXxwojNAVhouroqbbiyQRKJCbuhsDSCJBVHvFJSLPNHH+3Q9x/Njyyu4qgyL67idAd+pcyfuDsUqiKZEycSffELDj3+BLkluYIbg6QlnSo5SbOSCDPlMm68SQtz/bTBTmdZEF7xL6CiQ55PPGd4wVoa6RpxhZfHlLe99hYo6lRlSYNbls4B4bUzGhBeQ64QXkOAKTaH8MrDZqabf0T0vcdqI7pJ5FLqCsPyP+NGRlXizH3wSvVSSWbr7dC8YNX2d8P/lpbwmuZaS42nRD9jRXglWMXpI67wxul7rB4L4bUz8hBeQ64QXkOAKTaH8OrB9iKVOgX+memD/0z07HO1wmv7VWq9uwkT3rhpE2mUklKlSfC91fFdSuthQpWznHSBEb/O7+rO08Q2h6ZOlY3o68xsCK8OpfjHQHjjM4tqAeGNIpTs5xDeZNxGWkF4DQGm2BzCWx+2Wwt1Q4H6+rxX80QXXcDRzPB83KxGeFX5n2GL2upRSSPCqdrg4LD3Ee3/be2VHXGEQxecV6kYYfvDDw0///c8vfU2UXn4dP4UjjjnD+ZTcwm6hZfpb0wR51xhx7aK8HLONz848NbWWditDcIrMTur+4DwyjPlHiG8hlwhvIYAU2yeJeHlP1pbt+Wpazjvc9bMMvFq6kZ+lLtd+TZQUF3bSA7vNwbcBWveR2oHLxMe/tJiSfM/bZeS8u6P8y69LWf5Ws85q0jf/NvaB424Eeqk/PwRcjfS7BBNPc6hSy+tvwNe2Pls7vKme4+tILz8ILf6nkLVd63RC74gvLozUP84CK8+qzhHQnjj0FIcC+E1BJhi8ywJr0qk4uaXSqNTvb7mc9x0Q3idUH+Vhh3/VnZLXqWxUCbJvfujjLygZ97Z9bf35XM8/7MCfe/7lUVjboSAiNIYJ+b63AtD9Mij5C7u4cjqnDllOvO0ZOXI4vJSbQ4QNRfCztGo+rDB69m/P08//3mRfr5ryN0hjx8wJRdKxmWc5Piw7d9XXjNIE9uS9GjeBsJrzjDYA4RXnqn7+9tx3OqO+CQkAOFNCK4BzbIkvFnc9Sps8ZSO8L6zv59K/ZWtdLP4UaUN8Gv15cvCRYFFjVM8/JHrT51UdlMKbH/cuVoapNKA/XOp7iXJw089Jo2O8Kq2d44af9tjnKT/sO9oI/PlIbxJRrJ+GwivPFMIrwBTCK8AxJS6yIrwZnW3IdVCr6ii9Uk3nkhpyEdOo9pljH9YTxRUKR4cHVh02RBR3iEq57RyaXm8e3oqedG6tZaTCi+fiz+m0T5lesskh1ZcleyhRhWZTFPSVA88zCmNaL3kXA+bx43cnRHCKznClb4gvPJMIbwCTCG8AhBT6iIrwsu3q6pvGiWXaWBiMXhpd0XOeFetU+bUjzC2svAGo2k1O6oNl1Gol0MZjBJzVDFqISCzjyu8vODw4UeK1NNTmSWcsrHgkiE6qiPZrOFc0QfXF0Y20+Bd8LjecNL++Cq4xNue3sr1BDcJSXaV+q2ktynWP7PskTzOq+8pjnTKU/ADRzr0id91iKtnRC1m5Pa7dle2zOZ0Dol1AxBe2TGG8Mrz9HpESoOP7R1rNlDncR108bmnVhF/6NFn6Ku33uf+23lnzaEbv7KIJraNd/8bwmtvckr3nCXhdUVo/ejOW1OmEF06f6jpcgqbRXiVKQ0TiJZfFZ7SUCW8qhphPEGH/z2sTFi9smbBnGIWYU9Y4gqvKiLr3/yDReeppyu7ubF0z5pRJq7lGxUJ5ogxb/rQbLmuwd8dYRuRpLUIUPJ3GT+MbN+Zo7fezNGLP/dtv0fkjmlYnrcql5p3e0u6TbV3TxBeydGt9IUIrzxT7hHCS0R+of3LaxZVCe/zO3bR7Ws20OpbltPkSYcRSzF/Viy5BMJrZ05a6zVLwuvdJItIW1v2hIL/OOq8fo8jvEl3IpOaEBzlY/HZx+WcOst0xmnluhFLvyBE+G7oq3FVJJ/vh1+lP/Z4JdLmfVhEr7+mskAwrvCGncfLv1bl5Ka1eYXU+Jn2891HCvTCjlFBzEIlEZN7iptzH1bv2XTBG4TXZBTVbSG88kwhvAGmqghv8N+CAowIr52JaaPXLAqvjfs06TMYCeUo4R/ODy9FpSO8HCVc+8Do63a+vmaRLY6mvbQrR798OUcvv1wdTeP78NIcwiKFYVLCsuW9WvaPl5fXGld46y0yU9Uk5nMm3UDCZH41si2XJdu/bxzteWsg9vbPjbzusHPHraRha8EbhFd+dkB45ZlCeCOE90Cpn752230056SPjUR9X+5+nf581b309ZVfphOmHo2UBjvz0kqvEN76WMPEqN7CHh3h5RqzwWgmX0lau4VJTCZ3lf9dRSod9PXmEDk5ool1UiNU986yz7m2ksKrWhTm5YRDeCtjplOHl1nxpxlSOOLWiA5b8FavCovOdwfCq0Mp3jEQ3ni8dI9GSoOPVDCa6wnvF88/nU6eOd09Mii8XI5J+lPI5+iwieOo77fyfUtfazP1d9jEIh0cKFP/oFmpp8efIHrlFW83MofOP5fo8MnNREJ9rS//imjNfbVRzN890aEPH5+jHzxJVDpA1DaR6HOfJvr9Mx06dGLRzTd798BgKNdHvk/04y21/S5Z5NAJH24ebu/sJfrpdqL/eJnot7+tpKJ88AMVDvXGn/MsX+9xXHZHH0X0qd8j+ukLRBseqmYyuZ1o5Z9VqkRW5uoQ9Q/qVY08cIDoX7YQ/epXlT6PPsqh3z+TaOLECt9Vf5WjvX3VrD9/pkNnn9kc/Hlu/mp4k5YPdyabN8V8jt43sUj7fjtQc9Ov7SF64MEc7d1b+dHkyUSXXerQMUdllw8zuf/BXFXZPP5d9LlT1HOG5+83v1V9vMQcOOyQcVTqH6QBzbmaXaLZubJiIUeHtBXpN4G5ygEGfJITgPBqCG+9CK+N2qO5HNG4Yp76G1SDM/l0ynZLZjpUdqjs7ZOa4HK3Pu/QP26o/oNy7NE5um55rdAl6L6hTX75H0R3ral9GPjUrIroBT/XLs/RCR8qUD6fc2U3jOv3H3do0w9q/whftSRPH/2InVv+9euV8x13dLxx4XYsph89IV67JHfBXP71RaJ39jr00ROI5p2dG7led64OOVQWKpPO97WJz/fvlZJlcz6Vc893yLAQJ7n+tNrsfJHo3vur5+W838/ReWfHGyP392ohr3wwu+fbZZeN/8NjctV/r86zTuuedc/z9jtEv3zZofdKPGej5/t7B4hee43o7b0OHXNM9PE618EPvIOCc1XnnK1+TD6XI5beYHCmbXyh1W/d6v1BeOsIL/8IObxW51+qnUukNITlwTWyDqYkRFVe4MwZZdqxM/CH3yHqPN6h3z+9QJ+YXqDSYPjGE8FSSny9XJXiyiXhO7glvSc+F28W0Tf8apoXgi28bDCynFYwz5jbzTt7iGbNrBV1r64ubwFsUqbLu0deTNc9HL2c1E40b+4QHfOBxm48kZS/jXb1Kl3EOV+9lAbVxhjct+nr/jjX16zHIqVBfuSQ0iDPlHuE8EYIL6o02Jl4jejVpvA2Uz5qPfYsc1y+ak9Pzl3Y8+nZjvu//Tm4wYoFRxxOtGypQ7lC+KYELKJcEotzV7m+76yZ0SWxkswR1Ur0jg6iKxbXl2tVfqO/aoJ3Lbyob9Pjo7uvcd9c79af88nVHbq6K9HHqO1rVfVheaHg1X9aiNxpjfODDw7nFPMiOAn5TsI82IbHmj9S1yMlo/WEV7Xoj7dzvv5a+YcyCcZZ6gPCKz8aEF55phDeYab+smTuL+opR9CaW692F6XxB3V47Uy+tHuVEF6VoLT6H8aqRU8h9bk4d/DkTzVeDpLKUVjkPvggE7VhSNwdxcLO+ze35esKr6pdmjuXqb67wU02TDe/8M6h2gCkkCea+iGHvIh4VD1h7que8NZb9Jf276lmOx+EV37EILzyTCG8AkxRlkwAYkpdSAgvR0Af3pgfWWHPO1BddOHohgEp3YrIafheurq9qGv9XZq4fu2WbVzsnujd92pzJ3nxy6mfTbbtbNybYbHauo0X31Si0HNmj1570khdmHj6a5SqCvfztfvLe6mEu175r7Dz3npTnig3SCVFHn9Y1QXbO/VxdHvX7gr36dN5l67qKL2KvUStW/+mETW73RGRTgQ/Snj5u7BlW566hlNLOjv57YadtxBx53vWj4fwyo8QhFeeKYRXgCmEVwBiSl1ICG9Kl2r9NCxNq+8ZfTXPJ9TZdSlM+iSFlwWnp7ciMnxN/o/qujn1YOniSlqBKgJfb+tfr2/VTlxBUWUpWnXr6LauXltP6sJElCXtzNMrG10EP6pUCn6I+v//Z3hKg454S08gVXm14HxRyT5HeVcsM38QYrZdXURbn6uk2wQ/Ojn0OmXJdLnxPNuyNe9WSDj0UIfOPJ3o5JPM71P3/Fk6DsIrPxoQXnmmEF4BphBeAYgpdQHhHQWtEkP+qU4ucnBhG79Ovu7q+jm8ukMc7DsYvQur6euvFcyRyO3Di+ymT3PolDl6ZehYerfvrGyly+1UecaqiKx/0wmV9HlZICq2LHL8xoBzft3j2OUcosMPJ/qDuQ595KO1EhUm3jpirzsOweN0dvVS3bv04kSTzROkhJfnyYMbKos4PfXmsbvgvDKdfJLeXEs6DllsB+GVHxUIrzxTCK8AUwivAETNLrzFQCwJR3XUvlKN6gbCO0oorAi9bh4oS+XefTk6fFKBTj+lWLdKQ9S4eD8P7vLm/TsLJW8FzJUieNczb0GYv9+0dm5j2dy+g1NaKlsvz5pRnc5S8yDhFXnI1d9dLixqGxa5DJ6Ho8ILLy+7UW4WMk752LuPaPKkynmP79Sr5xs2VjrCq5pTYePiLY58aThF4vipZTpnrhO54YNJDr2U8PI1PPl0fkR2PWbve59D11499qK8EF7d33D6x0F49VnFORJVGuLQUhwL4TUEqNlcJQS8mn3h5fp/YJpdeP0VAvg1Pkf0VK/JdZCaRHj9/evstKZzPXxM2DXNmV2RXX59HLJmTisyrXsdpsdt+kGenn12uIxbbjQKWG/HOu/eR/x4eBe3P5g3RLNPVssqV0PgaDR/Ojoct76u6nviT/lIem+q6hfBxZr+hwE+Dz8MqMq68c9Ui8R0cnH5HOvWF0YeevgauIxb2Hn89yspvE89xTnWtTT9ZcxsPHgkHT+b7SC88nQhvPJMuUcIryFXCK8hQM3mYRFJndw97xTNLLyqWrZ8X7oR2SBmNxd2TaFqq9x6i6vChklSeMMivNOmObR7d/gmAyz+vHCtb3gnMU/+NKeW+GFhubz15qoXNXR/KfuuiKOGy64ccmVW5xP20JB0nnjn5Htae3+e+vYN7zA4gdzFmidOT/YKXydiXO9+WXx5vOOUPpMSXn6o4Ot3008CH094bT146MyBtI+B8MoTh/DKM4XwCjCF8ApA1OjCJHevFYQ3LHfV5FW+F5ErHeRX35yzGv+1t6Tw8vXcd3+RentHJwTngH7kI2X6yU9qd7yad3aZPj2n7L7Cf/iRSgSYP7qbTQSnHUvKvn1EkyaRcQoA98Wvvb0PR+LrpRW4EvVAQRU0jPVQEya8/jxjja9b6CFeVFk3RYKP57rOr3Tn3Yoas2Y47lsJU+FNcg9Swsvnvv+fCvTyy9XG68+htj0OSe7fVhsIrzxZCK88UwivAFMIrwBEjS5Ur0C5mb9sVFQ3zRzhDYt+mghvFC+dn3vC+x+v9tPOFx1XOv2bILDEbt1WKX3Gr6yjNmLg43ftquQHs4Rz+SsuF8XSFPx4i8BUtXGPPNKhP7q07K7s7+mtiAkvRAsTtaCA6bxe1+ET5xiVRHH7eqkQwf5V1Sb4mDhvQuJcc9Sxqp37eM4eHC4D5m8vvcAteG2Swst9M+uubqIDpRxxDrL/gTFMeC+6QC/9Ioprln4O4ZUfDQivPFMIrwBTCK8ARI0ugq9UuUlc2Wtm4U3ymlwDq/EhzLS7O0+3/U31phM8Nhzx4tJn3ja/fLIk+aQswZx+4b1Or8hrmS6dX3mdHlYZoVggGgqkeKuEI0wSpaKiupDDovinnFKmcz6vnzrgly1VjmvcKK3u9QePC6smwakzC+YP0abNBdqxs/Iwwv/GubhxUhT85+MIOUf5vbnGJdO+cGF1HV1p4a3HJWsPHknHUKcdhFeHUrxjILzxeOkejRxeXVIhx0F4DQHGbM5/2PjDK+T927nqdNPMwsv3523+0NOTcxcp8ba/SXModXjpHMNM7/47h37xcm06BOeNrn2gUNNN3AcV7sDdJKMrT3t6iXixoj9SqxReZ7jEV+DsqjzlsGhckuvUYVbvGOWrfofo5JPLdP65+tKrOof70PjAqBTyw8e8s+1FHMMe0jqmsPBWKkqYfPitB6dKHCw59MuX8zQY2OgvOH5pCi/fV/DBg69Ht0SeCZe020J45YlDeOWZco8QXkOuEF5DgCk2b3bhTRGV9qnqCS9HUx9+REZ4613Qd/65QD9/qTqfUrUjF/ehem0eli4S9/UzCw5HLDnKyFJ+TsKI5Q03Vja3KA9XePDuLGlussdOWWmhjej6a+xtCa3afc27nrh8/XMg7CHFf0zw4SZt4dX+EjX5gRBe+QGE8MozhfAKMIXwCkBMqQsIrzzoesLLObar76ndmSxOTqrOFXN+N6cDjKya92qXKWqYqba65ejxnXcVqypWcCrA8qsGtasjqKSZBXX5Mv0++F79UVGTbXRV3MIWitnM7+X0iYc2Vi9E9IaF+bBsewvb9vTyVtE5d3e9qHJ7YfcC4dX5xsgeA+GV5cm9QXjlmUJ4BZhCeAUgptRFFoSXhea7G3nVupea4dCCS5LnLoah8173TmxzqHMqWUt9GMnh/evBkRq5LDRz5jh03twhCpaTC0bdOEVFd8V/2L16kcug377//Q795jejkV+W2IWXDyrzRP0VK/g8nH+sWwqMjzfdyMN/b395S5EGDlZv4+X46vn6a73G+eqkVRmBWXLdZF4wyKlHvFiQK1aoNgzhe1FFgaOiv/Uix2ERZER448wW/WMhvPqsdI+E8OqSinccUhri8ao5GsJrCDDF5lkQXpUYtbc7tGKZ/gYaUchUFS2ko6reNTDTN97M0023Vr8W90c3/RskeHIbvEaTbXH9i71c6R1ODV1+VYWpRH1ezp/mXcE4X7Szk6tNVAuxpPD+7ZrCSGUJj7Mn87yj2orh+4qaB8Gfq6LQqoh33H6Dx6vEmvN2vWoZ/uM5unzn3bVpL1E1oVXpGeOKRFy3mCW7s9OhM0+rznlutPDyw663SM/bOMaUdRbaQ3jlRwHCK8+Ue4TwGnKF8BoCTLF5FoRXVaaJEXBEy1uAw0LFApj0o1rEFSUQwXO5i8S6R8uJ8Wtm1YeZbv4R0fceq/152GYHYZtoeGXG4t63qn6v5IIzlSgyD1545X2UKQ0x0yK8vsKqTnCs2vS+WNy376zs0MaR11kz40Wyo8YmbKHaccc59OtfV+dZc4m6WbOGaO23a9Nejj3GocVfCn8I5DnEO67F2QijkcKrmvNxd4qMYt+on0N45clDeOWZQngFmEJ4BSCm1EUWhFcV/VJtl2sS8VQJU5zIoFsGLFBOLOyPcz3hDXstbasqgkkFD9UUZA6c1qCbCsD3tXVr3s0F5sVxF1+oTp+Imu6q8ePo5R+ca6+iQtQ16f5ctcMYt+UHLs7L3bU7V1W31n1Q2Fio2aZ36lSHvqSxbbg35jq76zVSeMPqiCd9yNMdjzSOg/DKU4bwyjOF8AowhfAKQEypiywIr0r2xo0jGhiohZA0V1O1EUOcV9dh9WBVEVtm+rPtOVr7YG00LuyPeVj/ttIu4k6vmp3bJhAdOFjjZNY2c1ClR3A09OIL5dJe4jLRPT6s9m7YAxzPhU2P5ytpKL4A8Gc+U6a5ZyV/y6G6XhPh5ch1dzfRhLYccXpG3JJqEjtF6o5B2sdBeOWJQ3jlmUJ4BZhCeAUgptRFFoSXhYB3DuvqqkS6jupw6KVdOTrIi5QCn6TC6wrbxkqkkT/1Fmup0MfZJcrbae3Ov+unf/eVBqv36p3lgTeS8K7Pu8alS4bchU5bniuM7Mx2xqllawvuwqad6oEhGIVnptdfa6ecF8+RJ54YR7/4D4fGTyB3jvCmDHEW0aX0lVKeJvhAw28XeGxV1x+W3hKWDmNyX0mFN5iuwvm3vNA0zmLLsO8Uczlqilk9YhMmEm0hvBIUq/uA8MozhfAKMIXwCkBMqYssCK/qVlULcOKkIKj6ZKlMulgr7I9zWIS3bXyB3tnfT3veKLvn1Hm9zK+it2zLubmkbW2VTTT4o9qowmbZrCC7MAEr+HZtU+1eJj2F3blaGqTSgGyUU/o6w/rzz78oMTRZwMjzSHcTmqTCq3oASpITH9wt0GPH6UK8K1zcqHFaYxl1HghvFKH4P4fwxmem0wKL1nQo1TkGwmsIMMXmYcLLEdGe3sqF8B+yqD/Q0pecZAFOkmtgOXjq6bzblCWTo7BukJIFAAAgAElEQVSqrVxVdWlVGzZwP16El4W31F955c6yk+SPd5zIcpL712kTtujKy0HlPnSEXudc9Y5pFuHlufvwI0U3Is+Rz1kzyjRvbjJJj1OijqOumx4vUKlUocjS+Ifz60fBkwqvKqfaqyEcZ5z5e8W7JP7TgwU6OFidItMsKSuq+4XwxpkFesdCePU4xT0KwhuXWOB4CK8hwBSbq4RXJVmNyiWNswAnLjZV5DJfIDr2aIcK+UoZJ3+xf/7jvGtXjvbuy9HkSbyaX/3a1S+8W54rV0lI3D/iWRBe5qqqpBFVFzbueEQdn0R4ecz4k2bqg6oeru3vT1iecNR5kwhvvUV4izQW1QXHud4DVZL+ouZRGj+H8MpThvDKM+UeIbyGXCG8hgBTbK4SXtXryo4OoisW28nPTPF2q04VuhWrLzk1SckrT3j/49V+uuX26rJTfAFxRDFMLjilgT+cLmEz+u5FwAcGid57L0eHHOJQsVjZOOGUOcmilknHO47w+qOsfD6u62xjM5PgvYSlf8R93R+XUVIJjSu8bq75PQViwQ7O7AWX6OWWq2pQS5QNjMvM5vEQXnm6EF55phBeAaYQXgGIKXWhEl7VHx++nKQLxlK6ldinCRNe//a1SUTFE97nd/bTmvtqhTdueTVe8LR1W86tr8p5zGed4dAL23MjO9Pxq+R5Z8uX51JJFIvj0sWNWSwWR3hVOeCqMnIsbps2F9zSYPxhkTdZDJeW8HL6gldvl6uN8Ee1ZbX3RsGrqMCLQjunjqbtxBXeqsVqDhHvdsefWZ906OIvRFfMCFbb8MZEVbEhKjod+wufYgMIrzxsCK88UwivAFMIrwDElLpQCa/qlWwS8UvpFhKfRrUxAnfmrz4Qlqdb76RRwpskauw/n6p+aZL8yShwcRbqRfUl8fM4wqt6S6F6aFOVO4tTrk51X7ZTGlTjz4snH91coN7hvHvvuvjfeRHkug2VPHXv48lkXOENK5+nM6fDHgb4WnizD37w8BaVNuINgsQc9fqA8ErSrPQF4ZVnCuEVYArhFYCYUhcq4eUFa/4/kLwC/6IL9V5XpnTZYqcJCo8/ussnicq55Qjhjp15N7d3UntlgdJJnxhHXKXhtTf6adVf5apKjXGfpuWl0qpfKrk1sMSAxRFelXSqhFdXjONcP4vdk0/nadfuvBuRnzmzdkvfOP0Fj1W9gWFJ5+8oL8Dc01Op8jFrBrnl61TzxXtAiiu8JiXTgr9XvPvSkWUTXo1oqyO8HHV/bHOlKgt/pk/nyizppgk1gk3Sc0J4k5Kr3w45vIZcIbyGAFNsHlalgX8Z8+pp/vAK/CQVBqJuw3sty398OaJj4xxR1+D9nP+Q88e/NStHtVki6l2XajHXVUvy9ImPVcqSvfLqkCs/3h81LjXGEmLyUb2u5/7iliqLep0fFs2Lex6Te/W3DQqvt+ubqn9VFFT18GJDeKXuV9VPklzdevLvCe8vuvu15YvnBYu1VzNaV1jDrl23vU2u0n3rCK9qXOLk90tfc9b7g/DaGSEIryFXCK8hwBSbN6oObzDqxNLLuaGNlF4Pez2R8g9NWLRr9qdy9OU/KrrC65UlkxxSVaQsScqJzuv8oFw3Mq+S5+rbewfp2/9Unb+s2vDAv5kJs+eNKlisgtUadBhIjp1EX2ER3kvnqx+klBHe4U1CPOFdedPgSE6wd43S8uVuz72mUHUefnvEG01k4XsvMTZeH1HCG/a7wzSdRvIestYXhNfOiEB4DblCeA0Bpti8EcIb9su+2SI9YRGrj3w4R9ddZU94eXqw9G7fSW7kOEzmoqaR7mt/FhXOrVTVJ446h+TPea5+99Eh+uGT1QsBTfKX+d54Bz5OP+CPlxqQZhmzuIyCudVRuwaqHpC87xoL7/594+jmO2plmVlMbq/sgsgficWR3oMI1yjmyi+zZjT2zU5c9rrHRwlvkki97rlb9TgIr52RhfAacoXwGgJMsXkjhLdVftmH1T69+IIcnXuWXeHVnSLeBiIsFycOr+b32kq/zudx7equyCinD0hH7Xiu3vGtMv2qq/buly4ebLiQe1fFD3Sc180pQZwONGe2GQsv13NPL9d/rtSHZhnl/tvactTZWRu5DhLiPrbvrIwNV0bwStmx8L7RM47uXF0rvEcc4dDbb9dWGWlUSovunM/CcVHCy9eo+v418g1KFrjVuwYIr50RgvAacoXwGgJMsXkjhLdVIrw8TMFKD1zV4eor83T4pEoOr42UBt3pEcwvDtZSVr3OT5Iawdfjz5l1q1w4RIce5tChh+Zc0Z4zO1rKou6rnvAGJczbsKRejWIvh3mHTwTPmTtkJM5enVpvtzMvMrp82WDizS9s5np6KQ3Lrx+qWVx5wgkOvfxyrfDq1tuNGs9W/rmO8PLDKL9d8HKhm+HtQiPHDMJrhz6E15ArhNcQYIrNGyG8fHtB2WrmXD5ve1ReGc+v/VVbC6c4pO6pwlbE+/MyVa/zeWe5JKkL/rzSYKULvh6JdBXm+syzQ7Th4WoJ85eO44eptQ8UR7bXrbfhhEr4TTdYCSvlllQSbe9C5gnvM9sGauTryCOJfvyT6nJmPJamVUbS/i404nw6wtuI62rmc0J47YwehNeQK4TXEGCKzRslvHyLHIV7pTtHR03h17TmEcAUsdU9VRaEN0y8JMQzePNhqR3+45JGjv19eFUanvgXGtkoor2d3O2fvfQJVdWMsIVAqmP5fCYbrIRxT/qq2vZGFvXKkqlSj/jBdPlVyaPVWfmO2r4OCK88YQivPFPuEcJryBXCawgwxeaNFN4UbzPVU/26ezz99AWHfvOuQ7/zO2WaOSN9mdeJ8EpC8SK8/k07bAlvaSC8rFucXQLD6hmbCG/YZiYmOcaqXE+pB5eoOrx8P9t35ol3aJvcXiYuqye1lbU/55sfiKT6lZzXSfuC8CYlF94OwivPFMIrwBTCKwAxpS4gvLKgVcKj2tJW9qzq3oIRTH71v+hyO9G5qsimwnqjNvDQ4aGz8YRKDnnzhxVX1W57q6rVKxGJDqZKxN1KOsiCxZBzPf1bCXN9aIlKElHCqzMuSY5R1XiWkvgk1yPdBsIrTRQ7rckTrfSICK8hWQivIcAUm0N4ZWGHRQ1XXmNHNOtdPaca8A5we/fx6n7H3clJQpJU5+Rc0zfeJHdV/8GDDv3shTz9Zv/wDlLDu4CZnltHeFUSGyZS3qK1rq5KeTdOq5k316yigseGeXApN065kK5WITljGyW8qnQSk/Jykkwk+oLwSlCs7gMRXnmmEF4BphBeAYgpdQHhlQUdJrwmr7Rlr1C2N84xXbehQH19Fbmtt0jM9Mw6wsvn4OhhV3flbCdOc2jWTA4546Mi0CjhjZN60owjB+GVHzUIrzxTCK8AUwivAMSUuoDwyoJWrfz3FvpwbVavXJVEmS7ZK0/Wm2qbY1u7RekKb7I7GZutGiW8qgfDsNSTZhwZCK/8qEF45ZlCeAWYQngFIKbURasJL79K9uqq8qtkzh2V+nh9e7tEqaSVj9nwz0V6bU/lvCy7Z505RD/Zkh+Jgrr/3kZkUptV6p5M+0kzUjcWhdcrecfjxJtYmKaFBMe7UcKrWlSZtHSb6Ry20R7CK08VwivPFMIrwBTCKwAxpS5aSXhVZZRMFwx5w6DaUIBf3y9dPFQjIcz0jTfz1PvWAB1z7FBoTdykpapSmhpap1EtEmPJv/7aQa32cQ4aa8IbrCnMD0kXXVCmE6eHV6mIw5OPbZTw8rn5O8W7xZVKDnV2ZjvXOS5XCG9cYtHHQ3ijGSU5AovWklDztYHwGgJMsXkrCa/q9TqjlFgwFlZf1SvCzz/fum00ZeGCeQX67GcG3Z3WbNfE5Sigly6h2kLY5nRSLRKTesgIXvdYE17VfOaHrBXLaitOJB3jRgpv0mtuhnYQXvlRgvDKM0WEV4AphFcAYkpdpCG8LGQsg/zhKFVYXVqO+Oza7a3sj79a/t61BXr11RyRtxHXcHmsRZcNGdf4rLehwPGdZVp9T7FmxK660qEjjhhyN9hY+0Ch5uf+Xc+SDrcq8pxmGTQe2y3b8tTVVYHe2ekQC6/0q3fuW1d4OTK6a3dlvnE+cZKd45KOh2Q7VfSc+zepExy8Pgiv5IiN9gXhlecK4ZVnCuEVYArhFYCYUhe2hVclZKrtW1X1a+Pm9N3+zSLt+001OHbev7zB/PW6qm4on4mrL7y0O09PPV27Bevnz3To1M9WonHBRTr+7XBNhjpMxFuxKoSO8KpyQ00eLLyHNRb6Se1Es2aUjR+edMfbxsYYEF5d+mbHQXjN+KlaQ3jlmUJ4BZg2Qnj5D11PbyWCOH1a/OigwG03ZRe2hTcqFcCDdsddhZHC+t6/qcS4HuTb7ijQ/ne98O7okVIRsaCAeJsphMnw+ecSnfypUdnmSK/3kdpVSlUVgs/hpVo05aQMuWgd4VXVdzVJA1D1lxZb1XdHOl0EEV473xAIrzxXCK88UwivANO0hTf4R5+ld+Flg037KlNgCLS7aJTwBqO3Eqv903gF7ElrW5szMr84in3n3bUpC9dd7dAh75PLt1QNKiK81VQk5pHXY1gqirR01vuy8puPV7orbw+On1oWrykM4dX+VRnrQAhvLFxaB0N4tTDFPgiL1jSQPfToM/TVW+9zjzzvrDl041cW0cS28e5/pym8YbIhsZWpBoamP8S28NZLBfDnVqpkNe5rf1W0U2KrWJ1BZjl68mkuPUZ05BF5mntGgaYeP+AuWrP5cVNG1hSodHD0LLbq4Erch0meduIIb8jWwlH3Eya8WeYbdU/Bn0N44xLTOx7Cq8cpzlEQ3ji09I+F8Eawen7HLrp9zQZafctymjzpMLpjzQa3xYoll6QuvGF/lNISHf1pJXskL8x5+JEicU1YjmhzbuG8ufHLFdkWXs6BZCHr2zf6Ol8lDBI5vHyuhzfmRxYs8RyYN3co9Ug/M20bX6B39vdbF16eVf4thHnBmlS6hOyMJTIdYx3hlczhDXuYboVyct7YQnilZ3mlPwivPFcIrzxT7hHCG8GVBbfzuA66+NxT3SODApyFCG+arx3tTMP6vaoiokn+ENsWXu8u+MFkT0+OjuoIFzKWeF4Axp8Tm3h1fdrC24j5l+ScpnnaOsLL18Wi+tKuygPWidPN8vmDks4PUQvm19ZeTsIjC20gvHZGAcIrzxXCK88UwhvB9ECpn752230056SPjQjvy92v05+vupe+vvLLdMLUo1NNaeDLDdYC5cL3S5cMEe+01YofFkNVGawkUe20hLcVxyHsniSF1yuxxRL3oePK9Knfa945bZpfqyu80nPN2+3Mn7ctfY5G9QfhtUMewivPFcIrzxTCqym8Xzz/dDp55nT36KDw2hmW+r2++ppD2/+1TEcenqNZn8zTIRMbcRXpnJPv9aZba0tt/c4JObpmWW092HSuCmeRJvCTbWVa+2B1DvBhhxItv6JIHzqmthqF9Pml+/sf1w646Rf+z7FH5+gvrsWclWadVn9vvUP0w6eG6NevOXTcMTn6/OkFOvLwtM6O84AACJgSQEpDHYI6EV7TAUD7aALX/sUAvb23+riFlxboM7Nr68FG94YjskSAJeLZ58r0wyeH6L2AIHJ8d9YncvSnf9J8kqgS+Cu/VKRZn2w+ec/SfGnUtbx3gOjaGwfowIHRK5g4kegbXxvX0gGHRvHGeUHABgEIbwTVLOXw2pgAzdAnv+rmqgC8o1T7JIdmznTozNOyt2itGVhKX6NJSgNHQO+8u0ilgOj6r5EXKV5/jflmGtL3rdOfSZ52o1IadO6rWY8xSWkIq8BistFHs3IMXjdSGuRHEikN8ky5RwhvBNcsVWmwMwXGTq/I4ZUfaxPhrZKI4a2R/VfoOORWYVh0ud1yZ/JUzHuE8CZnyA8aqi2WTYQ3rAb06aeVEz18J7+77LWE8MqPCYRXnimEV5NpVurwal4uDgshAOGVnxomwuuXCJbbXPBtv0N0+uljUyg84d3zpkPd3ZVxmzqVWnZxqsTMDEZhg9VrTIRXVQKOr1l6JzqWdd66myu48K55s2Y4dEaCt1kSPHX7GCvC69XV5jdSvDMmV9ex9YHw2iGLCK8h1zTLkhle6phvDuGVnwImwhsUFLcmg0M0eTLR4Yc7NOPj8rttyROw0yNzfe6FIXpgXfVTQHDXPjtnT6dXFojHNudoT2+O2tpyrkAklbuwai7+lAMT4WUiwc1ebGz4oyrBmPW0ibEgvDy/1j5QnX5lY/y9bx6E187vIAivIVcIryHAFJtDeOVhmwgvX8231hSpt9f1XMo5RIcc4tDUDzl0zlyzmrLyd5puj8z1q18v096+6vNyZOmKxc2Z0+zdCUdLH34kP5K77Y/uJ00RCMux9ffnF16W7a3bctTTk6NJ7ZXNbHQ2MeF2vMNge7t8tL1Zd7sbC8Kr2tmS5/PyZXZKgkJ47fy+hfAacoXwGgJMsTmEVxY2/4HuPGYcHdNhttPa4z/M04+fra640QpiZ0Kb5+qffkX9yvSmG5pXeMMWKnrSm6S+NnMOSzlQCe+rvQdp9T0F6uurjp4vXTyY+k6F/jkC4TX5xthte9/9Berqrq2wIp3Sggiv3XGE8BryhfAaAkyxOYRXBnZwR65pH8nRpfPLlCskW1wW9sdEJ3rCEbcdOyt/iFiWdKJ0MhTs9hIW4Z0yhejKJc0rvGFS59FMKryuSN9VpNLB6nHxzyEvwvvczn5a+0ChZgCTRpclZwJSGiRpyvUVFuFdec0gTWyTOw+EV56lv0cIryFfCK8hwBSbQ3jNYbNYrLq1ti7u+ecSnfypZCKWVHhVUb0sSIs5ZSKeq5ufGKLvbaqOKiXZUlviergPfrjgj8mujlHCa7JNule+sFSqXCfnA/sfgJpBePkeHtpYSfPhXTRnzSzTvLn2FkdJzI2xkNLAc3/1mkLVA5XJXI3ijpSGKELJfg7hTcZtpBWE1xBgis0hvOaww4Tlw51Ef3xZMuFVlXziP/bXX1u/P5UoN3PdXv/oeFUaXvqlQ68Mv0o9XjOCzQ8lnGeqKs2VZAawhK3bMJoCwNUDFlwylKj/sEgspzScOL1MF11YthIx4/v2hPdfd3NKQ+1DWyMfJpKMS1bajAXhZdY8d3ftytHefZUFllLfL9U4QnjtzG4IryFXCK8hwBSbQ3jNYYethj9pFtGF5ycTXv5D8vDGysYi/OHNRVh8otIT7rirQH37avPqmjnH1RuhJHV4meN31hdGBJnlf97ZQzRrplv/IvHnwfWjY+N1YpJj7UViu7ry1NHh0PRpDp0yx34U079oLfiQlTSVIjHUFmo4VoQ3zSGD8NqhDeE15ArhNQSYYnMIrwxsr7KCv7clixw65thkObxJr0oZ4dWIDCc9X5rtkgivMlIusFOdKq+UWTTbg0WwLBk/IHCVBhsVF9KcK40+l5Tw8tqAHTsrD72dnQ7NmW0v2t9oZlHnh/BGEUr2cwhvMm4jrSC8hgBTbA7hlYHNosDF8ff05Oj9h+Zo7hlF+kDHAJX60xVeVQ5vq7yWTiK8tlaSt0ok3bQOr8y3p/V6kRBe1cMapw0smG8/8p/FEYHw2hkVCK8hVwivIcAUm0N45WGb1uE1vSJeTNLVxfl1OTq+025enem1xmmfRHhVqQd8Tp1qF/WuTSUjNovu+6+FH67qrYLn8e/praS1dEypX7sZwhtnBuofKyG8YQ9rzfYWQZ9a/SMhvFIkq/uB8BpyhfAaAkyxOYRXHrap8LLQbNpcoF27K9Jy/NQyfcHiwiV5ApUeOdrc01upYDBtmmO88CqJ8AbLxfF1SZUxY+nt6hou/9bpEK9Qt1GOia+ZJfa7G/Mjuci8SO6iC2pzunkBJS+m461evU+9XckgvHZmv4TwtspbBCnCEF4pkhBeUZIQXlGcVjuD8MrjNRVeVX1Lrkaw8PJ00yNMyASjUyxoSxcPGQlhEuHle2Dp3T6cB8m5qfPmml2HCZekbVVzgpmuWFY9J+JW6YDwJh2R+u0khPf/tnf3MXJd5R3Hn5ndmHWA2oGC14nAG1CFQ4tsFyEspBJepKqFUl5E4hpV0KQilvuSNE4JJIhQQJAQRCithJVEJA1CBFwpUUKbQCpowh/gCFVxKG0cVMARInFoCXYD9drZ3ameWc/uzN07O/fld86emfnuH4h473nmzufcnfnNmXPPyft2wm9e3XfZ8LwOKHUJvErN5VqM8NZ0JfDWBIzYnMCrx64beId9ZKffMm115xJXDbz6Ho5fMe+mSD+L7NfbZW+mI/CG6UtF4PVR/Vtvay6tuuLLEu7eNT9wpZbOM/Jvih59tNH+dmBr4CXDwij2ViXwhlEm8NZ0JfDWBIzYnMCrxx73wJs3jcCV626AMc6Bt+h8zqLHda56Aq/+798rKgJv58w8sM7OtkqtcevL3N36hcmeqS0hN4UIo0jgjeFK4K2pTOCtCRixOYG3OLbP2fR1cf3N5NnrWzY337Azz2zZjm2t9g5WnZ+6gTfv6+thWhO13wjvMAZeDxu+YYWvjRtqfm6RKzDvJrm8ayLvw8Zq7qkFXh+VPPhgsz0q6XO//UbAOrvYFbENcYwy8FY5v9jb/lY5x7JtGOEtK1bseAJvMae+RxF4awJGbD6qgddD19RUuVGR1dh7lvvyPQsyezt0f11fN/B2blo79PDig/jXkSF32wpxuWW/gvevYy+/bK5WaIw9wpsdLa0b2Os6d98kt9pcZL/2OzvRbd60uFtbv5+UAq9f9/tvWt69zs/ZNwq5/NJ6101d9yrt1zrwhlqOr4qFqg2BVyXZW4fAW9OVwFsTMGLzUQu82a/y6mz52t0N9369ad95sGk5Wbd9WPdoW93Aq+x+Hynz4LwWI2b+IeEJX6VhQ8u2bq0/Qhoz8H77YNO+dt/igv/dP3svmSv11bKyL0PUSinw5q0h7c95rT9oVHFf68DLCG+VXhvPNgTemv1O4K0JGLH5qAXevBu+fIT0XTUXa48deD24z86eXpZspto2uD5i9pm/653HN4wjZh2LFz5/0p7/vHmbfSb8wvt5Uwj8z/Kidxe/aSjin3Hlh0op8Pb7kEHgLd+97Q/+t03a7MnltszhLe84Di0IvDV7mcBbEzBi81ELvNd8dHKFnoe8q6+cq6XaMzey5JSGzkYAJ2dbtmXL4rq0q/1klyOanvagVf5r3X4BYrV1WWshBWic/Wr2N89r2a4Lwi/LROAN0JkDSoZa3SP+M9HetFb1/P1155HDjXboHTS1pepjxGzHlIYw2gTemq4E3pqAEZuPQ+BVbjRw8GDTTpw0m2iaLZweaMzusNU9peGRHyyU2gjAR2b237QytFdZ0qtfaAs9Yta58cgvY/+wsX1btQ0Z+q324KOsPj/bbyDsPIaPXil/8vrB10Ddu2f41vBdzSWlEV4/z+yHvWG6WbPbea2nNCj/FlKpReAN0xME3pquBN6agBGbj1rg7Uw96CYMHfCy3dUdeD93s9mRx3rvcFttxFk5j7FfrZBfy+dNo8jbIKHIJd4vsHuAPnR6I4lOnfNetmC7a05byZ6Tjzj6hhW+SsPm6ZbtfPVwrhgwTIHXz1UxnafI9RXyGAKvXpfAqzf1igTemq4E3pqAEZuPWuB1Ov8q37fl9VHA817Wsh3bq82BrdoN3YH3mo8tfqWY/cluGND5vXpJr+yUAMV85tVclFMB+k3JOOfslv308cwyGWZ21ZXlp31U7eNRaZfaCO+ouBJ49T1J4NWbEngFpgReAWKkEqMYeCPR9X2YQSO83rBf4PXfZW+88yW9/Kv0QXN/+51QZ8RMuUxbv8fqF3irTMlojxZ/tvfGGx8df8ELWvaTn6wMvCFHrtf6mgr1+ATeMLIEXr0rgVdvSuAVmBJ4BYiRShB49dDdgfeh77Xs9gO9y1sNmmLhQe+hQ007ftzsWVPW3tiiatjVP7vVK/Ybla0aRv3Gm4cebtjRo2bnvnjCtr1iwb72DWsvtVZ01Dy2wTA9HoE3TG8RePWuBF69KYFXYErgFSBGKkHg1UNn1+EtsxGA/mziVvSwfsttk/bkk8uPq5pG0VmH94n/btmttzXt2PHl0DvoQ0RcheF5NAJvmL4i8OpdCbx6UwKvwJTAK0CMVGJYA6/fwe+Bp84qAKGIU9p4ItRzHFTXQ77f7OU7gp1bcR3h7GN0bzzhwfro0cXAG2OqxqDnO6y/J/CG6TkCr96VwKs3JfAKTAm8AsRIJYYx8K7Ytjax7UcJvGEu3pg7rYV5BulVJfCG6RMCr96VwKs3JfAKTAm8AsRIJYYt8KpXMQjBTOANoWpG4NW7Enj1pl6RwKt3JfDqTQm8AlMCrwAxUolhC7z9NiNIZQ6nf9X+zW+eYd/7j5adOGHm68P6uW2ejtShfR7GV2q48+7J9s1f/nPulpa97a0LQ3MznJ8zgVd/DRF49aYE3jCmBN4wrqzDW9OVwFsTMGLzYQu8qW8/mrfxhW8N/GeX1NvauO4lkV2P1+upbiare25F2xN4i0oVP47AW9yqzJGM8JbRKnYsgbeYU9mjCLxlxTLHE3hrAkZsPmyB12my4S2lLV/zgqWf82rr7sbo7ms+unK74tV2fItxTmUfg8BbVmzw8QTewUZVjiDwVlFbvQ2BV2/qFQm8NV0JvDUBIzYfxsDrPJ2lvjZvMpuZWbD1UxHRVnmoQYHX15XNrqnr0zQ6W+XOzPgWtvrnkxd4/YPCvsvm04ArcBYE3gJIJQ8h8JYEK3g4gbcgVInDCLwlsEocSuAtgZV3KIG3JmDE5sMaeCMSlXqovCkNmzaZvebV83bvfRM2O7tYzufQ/tGuefvOg027/4HejSl83u/uXQulHnfQwXfcNbFis4bt21r2jrcSeAfZDfvvfV75vV+faG+37ddf97xyAm+Y3iXw6l0JvHpTr0jgrelK4K0JGLE5gbcc9qCbv5ZuWjCipWkAABU4SURBVPt+y/z/+zzZ15+/YLfe1rtFrj+qb7frIeTIY+F3DeuEnidOr137kpnFm+lSGRkv0guM8BZRWnnMavPKCbzVTAe1IvAOEir/ewJvebMiLQi8RZRWOYbAWxMwYnMCbznsvCkL2ZHSvJ3Wbv3CxIoHmtniobjRsytZ56C1nvNbTiXO0QTeas6rTbMh8FYzHdSKwDtIqPzvCbzlzYq0IPAWUSLw1lRKozmBt1w/5M6F3diyfZcuTw3IBl4fFd5/08qbxnz0138OP9o7pWHY5taWE6x+NIG3mh2Bt5pbnVYE3jp6+W0JvHpTr0jgrenKCG9NwIjNCbzlsPMC73PObNkF71xY2uI2b+OJ7O5w/qhv/8N5m5kx+9JXJpZGeaeeZbZ717xsO95yzy7towm81fqn37zyP98zZ4zwVjMd1IrAO0io/O8JvOXNirQg8BZRYoS3plIazQm85fqhe7Ssdbpp9wxcnxf7zj+YtKl1E/bU06ds9tTiyK+vzvCvDzTt2LHFRju2LdiO7Z0Ki7+fnW2t+QYV5TTiHk3grea9dNPa4YbNnlyeV+6boRB4q5kOakXgHSRU/vcE3vJmRVoQeIsoEXhrKqXRnMBbrh+6b/765S/NfvWrle0/clXTzpnuDbzlHoWj8wQIvPrrgsCrN/WKBF69K4FXb+oVCbw1XZnSUBMwYnMCb3XsfnMjL9vTtFe8nMBbXTa/JYFXLcoIr150sSKBVy9L4NWbEngFpgReAWKkEgTe6tB5cyO92vsvb9hvzEz2TGmo/ii07AgQePXXAiO8elMCbxhTAm8YV0Z4a7oSeGsCRmxO4K2Onbf6gi819td/MbFiDm/1R6ElgTfcNUDg7W+bXXN7etpvNJ0rNM+eEV79NUvg1ZsywiswJfAKECOVIPDWg/Y3xUcebdrJWbMNG8x2bF+wc16wjsBbjzW3NSO8elQCb3/TL32luWLJQF9K8F0FdkEk8OqvVQKv3pTAKzAl8AoQI5Ug8Oqh85Yl0z/K+FVUBV6/8fDo0YYdP262adN4r4xB4O3/d5S3BKEfXWRTGAKv/vWJwKs3JfBmTG+48YDNvGja3vGm1/b85o57vmUfuv6W9r+9+Y077SPvu9jWT61r/zeBN8yFGaIqgVevSuDVm3pFReD15d/23zRhs7PL5+hLyb3h/MVNQMbth8Dbv8c/8cmV24H7OtlXv39u4GVC4B1IVPoAAm9pskINmMNrZt2B9mNXXtwTeL976LB9+sYDtv+6y+2sDc81D8X+s2/PhQTeQpdYOgcRePV90R147/mXVvtrUV9/99wtC+bhytc/5ae8gCLw3nHXhB16uHvl5MXzuOrKOVs/Vf6chr0Fgbd/D+ZdK9ltxPu1JvDq/zIIvHpTr0jg7XLNG+HN/ls2ADPCG+bCDFGVwKtX7QTe+x44ZQfu6A1XU1Mt233hAjupVWBXBN5+S8ld9O7x3N2OwNv/QvSpL/c/0LQnji7+DW+ebrU/sBb5YETgrfAHPqAJgVdvSuDNmGbD7YnZU/bhT91iO1/58qVR3x8+9rh98Nqb7eNXvddeuuVspjSEuS6DVCXw6lk7gfcTn3nGfnRkZX3fX+33f3fBXrNzPL9GryquCLz9Rngvv3Teztq4vPNd1XMctnYE3jA9RuDVuxJ49aYE3oKB94K3vM5etX1r++hs4J2bD/NGPtFs2PzC+L0phbnMF6s2mw1rtcxa/j/8SAQmmk1rNMyu/7s5+8EPV7r6v7z4nIZ98Iqm5PHGpYj//fuff51r9Qf/1bIbPtf7+rTttxq29+Lx7Asfu/TXAF5XtX9FimtVe0bDX61hDWs2bcW1Ojkxnn+7qh4d6SkNPmL7+dvvybXKztX1g6qM8D75i647QkS9MjnRsA3PXmc//9+TooqUcYGNzz7DTpyat5PPhPmQMo7KG5+zzp51RtPu/vozdnf2T83T7ulZDh//m/lx5Kn8nNvX6sk5OzlX78PZ476U3OHFTjhrg9lv76hXr/ITSqChv67+2plntDdJ4Ucn4K8B/zf7jJ2qea3qzmj4K50x2bDnrD/DfpG5VjedNYaT74XdOdKBt6wTc3jLig3X8Uxp0PdXZ0rDT392yu78J1u+SaqTqxpmvkHFxe8h8JbRV0xpKPN443DsMExp8B0NH3q42V5Zo8zmD2vZf0xp0OszpUFv6hUJvF2ueYGXVRrCXHhrUZXAq1fPLkv2yOGm3X5g+Ws3X9ro7W9dsPO2MqpeRp/AW0ar2LGpB96HDjXszrsnep7M1JTZ1VcOXhqsmECYowi8elcCr96UwHvatHtZMv+nzZuebzdef0X7pjT/YR3eMBdf7KoEXr143jq8vv6rb3bgP9PTrbG8QaquNIG3ruDK9qkH3rzdzvxZpL6qBoFXf60SePWmBF6BKcuSCRAjlSDw6qHZeEJv6hUJvHpXAq/e1CsSePWuBF69KYFXYErgFSBGKkHg1UOPS+B94qjZ1FQj2mg1gVd/raYeePOmNGzc0LJ9l6U9/53Aq79WCbx6UwKvwJTAK0CMVILAq4ce9cD74yMNu/3A8va8Gze27KJ3LwQPvgRe/bWaeuD1Z/zNB5p26FDDjh1v2NaXLdjrh2C3QgKv/lol8OpNCbwCUwKvADFSiVEOvD469OPHmrZ+qmUzWyzaTWKjHnhv+OxEO3x0/3gQedeusDfhEXj1LwrDEHj1zzp8RQKv3pjAqzcl8ApMCbwCxEglRjXw+lJG33mwd0Hy34u0u9moB95rPjq54ur0Ud59l4b9mpnAq39RIPDqTb0igVfvSuDVmxJ4BaYEXgFipBKjGnjzQlmstW/HMfDGsCXw6l8UCLx6UwJvGFMCbxhX1uGt6UrgrQkYsfk4BV5f//bq94dfv3PUA2/eUlGvO3/B3nA+Uxoi/ulKHorAK2FcUYQRXr0rgVdvygivwJTAK0CMVGJUA+8nPjlps5ldqGPMM/VuG/XAe2LW2tNFjhxZnMe7Y9uC7dgefnvetRrh9ZumDj/atGPHzM7dsmAe7jdPR/oDDfwwMQKv3+ToO6UdP7a4BvXOV4/+OtQEXv2FS+DVmxJ4BaYEXgFipBKjGnh9d7M772ouhV4f3b3oPXNRgsqoB95Il+aKh1mLwPvtg0372n29c8FjzFeOZRw68PrSdftv6p3z7X57L5m39VOxnmX8xyHw6s0JvHpTAq/AlMArQIxUYlQDr/P57mY+Kuc/PrIU6w2WwBvm4l2LwHvLbRN25LHeFSn82e29JM6HpzCSy1VDB14fHb//gd4PDP7oqe+UVtedwFtXcGV7Aq/elMArMCXwChAjlRjlwBuJMHckcmrdhD319CmbPRV25YK1eo5r8bgEXr06gVdv6hUJvHpXAq/elMArMCXwChAjlSDw6qEZ4dWbesW1CLy5UxqGYKevoj0QOvDm+Y3SCHk/ZwJv0Suw+HEE3uJWZY5klYYyWjnHEnhrAkZsTuDVYxN49aZrFXj9ce+4a8IOPbw4rcG3td29az7KXPAwir1VQwdef7TstJAYK3rEsFvtMQi8+h4g8OpNGeEVmBJ4BYiRShB49dAEXr3pWgbeMM8mjaoxAq8/0858+phz6ddSmMCr1yfw6k0JvAJTAq8AMVIJAq8emsCrNyXwhjGNFXjDnH26VQm8+r4h8OpNCbwCUwKvADFSCQKvHprAqzcl8IYxJfCGcSXw6l0JvHpTAq/AlMArQIxUgsCrhybw6k0JvGFMCbxhXAm8elcCr96UwCswJfAKECOVIPDqoQm8elMCbxhTAm8YVwKv3pXAqzcl8ApMCbwCxEglCLx6aAKv3pTAG8aUwBvGlcCrdyXw6k0JvAJTAq8AMVIJAq8emsCrNyXwhjEl8IZxJfDqXQm8elMCr8CUwCtAjFSCwKuHJvDqTQm8YUwJvGFcCbx6VwKv3pTAKzAl8AoQI5Ug8OqhCbx6UwJvGFMCbxhXAq/elcCrNyXwCkwJvALESCUIvHpoAq/elMAbxpTAG8aVwKt3JfDqTQm8AlMCrwAxUgkCrx6awKs3JfCGMSXwhnEl8OpdCbx6UwKvwJTAK0CMVILAq4cm8OpNCbxhTAm8YVwJvHpXAq/elMArMCXwChAjlSDw6qEJvHpTAm8YUwJvGFcCr96VwKs3JfAKTAm8AsRIJQi8emgCr96UwBvGlMAbxpXAq3cl8OpNCbwCUwKvADFSCQKvHprAqzcl8IYxJfCGcSXw6l0JvHpTAq/AlMArQIxUgsCrhybw6k0JvGFMCbxhXAm8elcCr96UwCswJfAKECOVIPDqoQm8elMCbxhTAm8YVwKv3pXAqzcl8IYxpSoCCCCAAAIIIIBAQgKNVqvVSuh8OBUEEEAAAQQQQAABBKQCBF4pJ8UQQAABBBBAAAEEUhMg8KbWI5wPAggggAACCCCAgFSAwCvlrF/sxOwp+/CnbrF//sbBpWL/8LcfsFdt37r033fc8y370PW3tP/7zW/caR9538W2fmpd/Qcfgwpud+QnR23fngt7nu0vjj9tez/wGfv3R37U/ves+RjQlH6K3z102P7kr65rt3vFeS+x/dddbmdteG7pOjQw++Fjj9unPvdlu/bq9/YYcl2Wvzp4DS1vVqSFX6N7rvy0PfHkz3Pfe7hWiyj2P6Zz3foR3e/pvN/Xc+1uTeDVWUoq+YvGrV++1/a+523tEOuh4qprb7Ybr7/CXrrl7PZ/f/rGA0vh4oYbD7QfNxvgJCczQkW6w9mf7n5Tj1fnhWbnK19u73jTa9vh44PX3mwfv+q9bXN+VgpkjfxF+eC//ScfvkpeLN0hIfuhgeuyJObpw3kNreY2qJX/jb/o7BcuDb50v/dwrQ7SW/333R/SugexeL+v55ptTeDVesqrdd4Qr9hzYfuFxl9kZl403Q5m/pP9g5CfwIgVzBvhzY6uZV+8R4xA8nSyjnxIqMeaN8LLdVnPtNOa11CNY7ZK94fcx5/8n55vKHgNLWfeeV/3Vt0DB7zfl3McdDSBd5DQGv++O0icvenX29MdOiORfmoEjXIdlBd48z40MHK+umvWJxsqyvUKR+cFXq5LzXXBa6jGsbtKJ9BOv/B57W/LuFarG3e/lnZ/iPCKvN9Xd81rSeDVekqrZT8ld/77gre8bulrJQJvOfJ+gfcfv3p/z9fxBN7Bgbf7mwYCb7nrMHt0v8DLdVnPldfQen55rf218fO339Nz/4gHXq7V8tbZ96O8wMv7fXnXfi0IvDrLVSvl3UjR3SB7k1T2E7Qfm/c10bgH3u65udkOyLuhjxFezQXPCK/GsVOFEV6tZ/frZWcUktdQrXF3OPv+4R/13Fvij8SgwWDvzoeHvPeuD/zlH9t1f/9FvtEdzFj4CAJvYap4B+aF3c6jM6enXj8wh7eeX6c1c3g1jqsFXubwVjfmNbS6XdGW3dfnU8eeZg5vUbhVjsve/Mv7vQC1qwSBV+tZu9qgyf7ctVmPOC/wcodxeVNWaShvtlqLvBFerstqxryGVnMb1OqmL37V3vg7r1xaucbD2NGfPdWeCuY/3fNNx/2bx0GW/X6fDby831eVzG9H4NV61q6WXeuwU7B7KS3W5SvPnDf1oXsaCWtI1jNlHd7yft4ie935v3X/rXNdlnflNbS8WZEW2dfQ7JQxrtUiiqsfk7e8I+/39V07FQi8OksqIYAAAggggAACCCQoQOBNsFM4JQQQQAABBBBAAAGdAIFXZ0klBBBAAAEEEEAAgQQFCLwJdgqnhAACCCCAAAIIIKATIPDqLKmEAAIIIIAAAgggkKAAgTfBTuGUEEAAAQQQQAABBHQCBF6dJZUQQAABBBBAAAEEEhQg8CbYKZwSAggggAACCCCAgE6AwKuzpBICCCCAAAIIIIBAggIE3gQ7hVNCAAEEEEAAAQQQ0AkQeHWWVEIAAQQQQAABBBBIUIDAm2CncEoIIIAAAggggAACOgECr86SSggggAACCCCAAAIJChB4E+wUTgkBBBBAAAEEEEBAJ0Dg1VlSCQEEEEAAAQQQQCBBAQJvgp3CKSGAAAIIIIAAAgjoBAi8OksqIYAAAggggAACCCQoQOBNsFM4JQQQQAABBBBAAAGdAIFXZ0klBBBAAAEEEEAAgQQFCLwJdgqnhAACCCCAAAIIIKATIPDqLKmEAAIIIIAAAgggkKAAgTfBTuGUEEAAAQQQQAABBHQCBF6dJZUQQAABBBBAAAEEEhQg8CbYKZwSAggggAACCCCAgE6AwKuzpBICCCCAAAIIIIBAggIE3gQ7hVNCAAEEEEAAAQQQ0AkQeHWWVEIAAQQQQAABBBBIUIDAm2CncEoIIIAAAggggAACOgECr86SSggggAACCCCAAAIJChB4E+wUTgkBBBBAAAEEEEBAJ0Dg1VlSCQEEEEAAAQQQQCBBAQJvgp3CKSGAAAIIIIAAAgjoBAi8OksqIYAAAggggAACCCQoQOBNsFM4JQQQQAABBBBAAAGdAIFXZ0klBBBAAAEEEEAAgQQFCLwJdgqnhAACCCCAAAIIIKATIPDqLKmEAAIIIIAAAgggkKAAgTfBTuGUEEAAAQQQQAABBHQCBF6dJZUQQAABBBBAAAEEEhQg8CbYKZwSAggggAACCCCAgE6AwKuzpBICCCCAAAIIIIBAggIE3gQ7hVNCAAEEEEAAAQQQ0AkQeHWWVEIAAQQQQAABBBBIUIDAm2CncEoIIIAAAggggAACOgECr86SSggggAACCCCAAAIJChB4E+wUTgkBBBBAAAEEEEBAJ0Dg1VlSCQEEEEAAAQQQQCBBAQJvgp3CKSGAAAIIIIAAAgjoBAi8OksqIYAAAggggAACCCQoQOBNsFM4JQQQQAABBBBAAAGdAIFXZ0klBBBAAAEEEEAAgQQFCLwJdgqnhAACCCCAAAIIIKATIPDqLKmEAAIIIIAAAgggkKAAgTfBTuGUEEAAAQQQQAABBHQCBF6dJZUQQAABBBBAAAEEEhQg8CbYKZwSAggggAACCCCAgE6AwKuzpBICCCCAAAIIIIBAggIE3gQ7hVNCAAEEEEAAAQQQ0AkQeHWWVEIAAQQQQAABBBBIUIDAm2CncEoIIIAAAggggAACOgECr86SSggggAACCCCAAAIJChB4E+wUTgkBBBBAAAEEEEBAJ0Dg1VlSCQEEEEAAAQQQQCBBAQJvgp3CKSGAAAIIIIAAAgjoBAi8OksqIYAAAggggAACCCQoQOBNsFM4JQQQQAABBBBAAAGdAIFXZ0klBBBAAAEEEEAAgQQF/h+5bKQBYlnDFwAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.graph_objects as go\n",
    "\n",
    "def draw_data(observations_positions,name):\n",
    "    nb_observations = len(observations_positions)\n",
    "    fig = go.Figure()\n",
    "    fig.add_scatter(x = [observations_positions[i][0] for i in range(nb_observations)], y =  [observations_positions[i][1] for i in range(nb_observations)], mode ='markers', name=\"Observations\")\n",
    "    fig.update_layout(\n",
    "        title = name,\n",
    "                )\n",
    "    fig.show(\"png\")\n",
    "\n",
    "draw_data(observations_positions, \"Example\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "686b440e",
   "metadata": {},
   "source": [
    "Now, let's, solve the problem using the algorithm from Scikit-learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ee9062ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "kmeans = KMeans(n_clusters=3, random_state=0).fit(observations_positions)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42f098e2",
   "metadata": {},
   "source": [
    "Let's visualize the solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d96ef3ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total cost (which is the total sum of euclidean distances between each observation and the center of its cluster): 26236.67493465098\n"
     ]
    }
   ],
   "source": [
    "fig_sk = go.Figure()\n",
    "for j in range(nb_clusters):\n",
    "    fig_sk.add_scatter(x = [observations_positions[i][0] for i in range(nb_observations) if (kmeans.labels_[i] == j)], y =  [observations_positions[i][1] for i in range(nb_observations) if (kmeans.labels_[i] == j)], mode ='markers', name=f\"Cluster{j}\")\n",
    "\n",
    "fig_sk.update_layout(\n",
    "        title = \"Kmeans Solution\",\n",
    "                )\n",
    "\n",
    "fig_sk.show(\"png\")\n",
    "print(f\"Total cost (which is the total sum of euclidean distances between each observation and the center of its cluster): {kmeans.inertia_}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d183a6d1-6be3-4a72-b3ba-8dcf1cc0774b",
   "metadata": {},
   "source": [
    "## Mathematical model\n",
    "Now, we show how to model the $k$-means clustering problem using nonlinear programming.\n",
    "\n",
    "Variables:\n",
    "\n",
    "* $a^k_i \\in \\{ 0 , 1\\}$,  $i = 1, \\dots, N$, $k = 1, \\dots, K$: a boolean variable which is 1 if the observation $i$ is in cluster $k$: else 0 .\n",
    "* $d^k_i \\in \\mathbb{R^+}$, $i = 1, \\dots, N$, $k = 1, \\dots, K$: a positive variable which represents the euclidian squared distance between observation i and cluster k.\n",
    "* $c^k \\in \\mathbb{R^2}$,  $k = 1, \\dots, K$: position of the barycenter of the cluster k. \n",
    "\n",
    "Objective:\n",
    "$$\n",
    "\\min \\sum_{i=1}^N{\\sum_{k=1}^K}{a^k_id^k_i}\n",
    "$$\n",
    "\n",
    "Constraints:\n",
    "* Each observation has to be in one cluster\n",
    "$$\n",
    "\\forall i = 1, \\dots, N \\qquad\\sum_{k=1}^K{a^k_i}= 1\n",
    "$$\n",
    "\n",
    "* Coordinates of the barycenter of the clusters\n",
    "$$\n",
    "\\forall k = 1, \\dots, K \\qquad c_k\\sum_{i=1}^N{a^k_i} = \\sum_{i=1}^N{X_i}a^k_i \n",
    "$$\n",
    "\n",
    "* Square distance formula\n",
    "$$\n",
    "\\forall i = 1, \\dots, N, \\forall k = 1, \\dots, K, \\qquad d^k_i = \\| X_i - c_k \\|^2_2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4df14003-16a2-4ce1-b1f6-314027d8739c",
   "metadata": {},
   "source": [
    "# Implementation with Pyomo\n",
    "\n",
    "Now, let's write the model with the modeler Pyomo.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6ce0532b-f096-4e61-a114-98263ee25754",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Artelys Knitro 14.1.0: \n",
      "=======================================\n",
      "          Commercial License\n",
      "         Artelys Knitro 14.1.0\n",
      "=======================================\n",
      "\n",
      "No start point provided -- Knitro computing one.\n",
      "\n",
      "WARNING: Problem appears to have nonlinear equalities and be non-convex.\n",
      "         The Knitro mixed integer solver is designed for convex problems.\n",
      "         For non-convex problems it is only a heuristic, and the reported\n",
      "         bounds and optimality claims cannot be verified.\n",
      "\n",
      "concurrent_evals         0\n",
      "datacheck                0\n",
      "hessian_no_f             1\n",
      "hessopt                  1\n",
      "The problem is identified as a MIQCQP.\n",
      "Knitro changing mip_method from AUTO to 1.\n",
      "Knitro changing mip_rootalg from AUTO to 1.\n",
      "Knitro changing mip_lpalg from AUTO to 3.\n",
      "Knitro changing mip_branchrule from AUTO to 2.\n",
      "Knitro changing mip_selectrule from AUTO to 2.\n",
      "Knitro changing mip_mir from AUTO to 2.\n",
      "Knitro changing mip_clique from AUTO to 0.\n",
      "Knitro changing mip_zerohalf from AUTO to 0.\n",
      "Knitro changing mip_liftproject from AUTO to 0.\n",
      "Knitro changing mip_knapsack from AUTO to 2.\n",
      "Knitro changing mip_gomory from AUTO to 0.\n",
      "Knitro changing mip_cut_flowcover from AUTO to 2.\n",
      "Knitro changing mip_cut_probing from AUTO to 1.\n",
      "Knitro changing mip_rounding from AUTO to 3.\n",
      "Knitro changing mip_heuristic_strategy from AUTO to 1.\n",
      "Knitro changing mip_heuristic_feaspump from AUTO to 1.\n",
      "Knitro changing mip_heuristic_misqp from AUTO to 0.\n",
      "Knitro changing mip_heuristic_mpec from AUTO to 1.\n",
      "Knitro changing mip_heuristic_diving from AUTO to 0.\n",
      "Knitro changing mip_heuristic_lns from AUTO to 0.\n",
      "Knitro changing mip_heuristic_localsearch from AUTO to 1.\n",
      "Knitro changing mip_pseudoinit from AUTO to 1.\n",
      "\n",
      "Problem Characteristics                                 (   Presolved)\n",
      "-----------------------\n",
      "Objective goal:  Minimize\n",
      "Objective type:  quadratic\n",
      "Number of variables:                               1806 (        1806)\n",
      "    bounded below only:                             900 (         900)\n",
      "    bounded above only:                               0 (           0)\n",
      "    bounded below and above:                        900 (         900)\n",
      "    fixed:                                            0 (           0)\n",
      "    free:                                             6 (           6)\n",
      "Number of binary variables:                         900 (         900)\n",
      "Number of integer variables:                          0 (           0)\n",
      "Number of constraints:                             1206 (        1206)\n",
      "    linear equalities:                              300 (         300)\n",
      "    quadratic equalities:                           906 (         906)\n",
      "    gen. nonlinear equalities:                        0 (           0)\n",
      "    linear one-sided inequalities:                    0 (           0)\n",
      "    quadratic one-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear one-sided inequalities:            0 (           0)\n",
      "    linear two-sided inequalities:                    0 (           0)\n",
      "    quadratic two-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear two-sided inequalities:            0 (           0)\n",
      "Number of nonzeros in Jacobian:                    5406 (        5406)\n",
      "Number of nonzeros in Hessian:                     2706 (        2706)\n",
      "\n",
      "Knitro using Branch and Bound method with 8 threads.\n",
      "\n",
      "Initial points\n",
      "--------------\n",
      "No initial point provided for the root node relaxation.\n",
      "No primal point provided for the MIP.\n",
      "\n",
      "Root node relaxation\n",
      "--------------------\n",
      "\n",
      " Iter      Objective      Feasibility        Optimality       Time \n",
      "                             error              error        (secs)\n",
      " ----      ---------      -----------        ----------      ------\n",
      "    1        61428.9         0.810476           238.200       0.094\n",
      "    2        61429.7      2.05045e-02           5.27634       0.119\n",
      "    3        61426.8          1.74886           2.31499       0.141\n",
      "    4        61424.4         0.367875           1.73485       0.162\n",
      "    5        61424.2      3.06875e-02          0.148464       0.181\n",
      "    6        61424.0      9.15910e-02           4.40846       0.194\n",
      "    7        61423.6      7.27635e-02           2.95712       0.228\n",
      "    8        61423.4      8.19242e-02           1.95240       0.253\n",
      "    9        61423.1      6.27545e-02           1.63373       0.275\n",
      "   10        61422.9      6.96193e-02           3.58004       0.306\n",
      "   11        61422.7      5.19901e-02           3.07080       0.335\n",
      "   12        61422.5      5.36730e-02           1.71777       0.355\n",
      "   13        61418.7         0.178290           12.7171       0.384\n",
      "   14        61418.4         0.155242           9.87655       0.407\n",
      "   15        61418.2         0.151578           9.26114       0.423\n",
      "   16        61418.0         0.147415           9.34574       0.442\n",
      "   17        61411.6         0.222589           17.2914       0.469\n",
      "   18        61401.6         0.233460           35.7393       0.504\n",
      "   19        61350.3          1.23100           58.9136       0.521\n",
      "   20        61318.7         0.146373           6.77668       0.535\n",
      "   21        61174.2         0.645375           45.1732       0.560\n",
      "   22        61089.4      3.23234e-02          0.751102       0.579\n",
      "   23        60730.9         0.325199           18.8005       0.593\n",
      "   24        60251.8         0.178161           9.03847       0.617\n",
      "   25        59977.7         0.184861           24.1317       0.634\n",
      "   26        59694.7         0.223110           56.3279       0.655\n",
      "   27        59117.4          4.88173           258.794       0.676\n",
      "   28        59003.4          3.42678           262.958       0.700\n",
      "   29        58906.9         0.427151           284.057       0.727\n",
      "   30        57867.3          20.2928           477.241       0.746\n",
      "   31        57500.1          5.91232           747.826       0.773\n",
      "   32        57000.9          2.23216           917.785       0.802\n",
      "   33        56715.7          2.48070           825.070       0.838\n",
      "   34        56908.9         0.494999           882.983       0.855\n",
      "   35        56024.4          4.97512           895.760       0.867\n",
      "   36        56039.6          4.76675           1084.21       0.894\n",
      "   37        55921.7          2.81874           1160.53       0.912\n",
      "   38        54874.6          2.56431           993.516       0.938\n",
      "   39        54856.7         0.171953           58.6680       0.966\n",
      "   40        54817.5      5.30973e-03           11.2848       0.990\n",
      "   41        54747.6      1.98257e-02           29.9037       1.007\n",
      "   42        53781.7          1.63794           241.128       1.029\n",
      "   43        53615.1          1.18810           199.137       1.051\n",
      "   44        52243.3          3.18649           45.1509       1.060\n",
      "   45        51823.2          3.09242           121.651       1.074\n",
      "   46        51015.0          1.08160           288.243       1.098\n",
      "   47        49008.9          5.03136           646.187       1.116\n",
      "   48        49500.2          2.15847           402.344       1.130\n",
      "   49        48684.4          2.39426           485.818       1.157\n",
      "   50        44998.0          10.8322           958.593       1.198\n",
      "   51        44102.9          10.8202           327.245       1.222\n",
      "   52        43607.6          10.1535           298.890       1.254\n",
      "   53        43039.9          9.97624           316.792       1.271\n",
      "   54        43014.2          2.72229           19.9685       1.286\n",
      "   55        42910.2      2.99875e-03           22.1009       1.324\n",
      "   56        42809.4      1.11763e-02           39.8467       1.336\n",
      "   57        42724.7      4.03831e-03           41.3761       1.357\n",
      "   58        42720.8      1.65855e-04           41.3761       1.383\n",
      "   59        42715.9      3.57639e-05           41.3761       1.408\n",
      "   60        42700.7      1.81839e-03           41.3760       1.432\n",
      "   61        42633.1      3.26420e-02           41.3755       1.457\n",
      "   62        42559.7      2.21437e-02           60.1505       1.473\n",
      "   63        42551.9      6.34403e-04           60.8803       1.495\n",
      "   64        42493.3      2.37254e-02           60.8798       1.509\n",
      "   65        42473.3      4.53074e-03           59.3727       1.536\n",
      "   66        42416.1      1.96119e-02           59.3727       1.550\n",
      "   67        42376.3      3.31522e-02           59.3734       1.576\n",
      "   68        42375.3      4.00246e-05           59.3745       1.605\n",
      "   69        42372.7      1.69221e-04           59.3930       1.630\n",
      "   70        42368.8      4.10997e-04           59.4761       1.656\n",
      "   71        42337.8         0.178153           61.2252       1.675\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   72        42308.1      5.15268e-03           66.8564       1.708\n",
      "   73        42281.0      2.85893e-03           66.8602       1.736\n",
      "   74        42216.0      5.82716e-02           66.8672       1.758\n",
      "   75        42186.6      1.23702e-02           69.4217       1.778\n",
      "   76        42117.4      6.39415e-02           74.7473       1.808\n",
      "   77        42102.6      3.01014e-03           74.7487       1.831\n",
      "   78        42082.7      4.20294e-03           74.7352       1.853\n",
      "   79        41966.7         0.106213           77.8061       1.872\n",
      "   80        41909.7      2.09260e-02           38.0348       1.891\n",
      "   81        41844.5      2.84104e-02           19.8907       1.910\n",
      "   82        41842.3      2.84037e-02           20.5224       1.933\n",
      "   83        41821.4      8.34499e-03           28.5178       1.960\n",
      "   84        41736.3      5.99638e-02           55.1520       1.974\n",
      "   85        41658.7      9.02260e-02           75.8501       1.987\n",
      "   86        41616.7      1.43234e-02           16.2091       2.009\n",
      "   87        41586.6      5.39667e-03           21.8006       2.036\n",
      "   88        41566.9      2.08529e-03           21.7928       2.069\n",
      "   89        41528.1      7.79916e-03           22.9721       2.095\n",
      "   90        41467.0      2.75994e-02           32.6511       2.113\n",
      "   91        41414.8      1.53945e-02           14.3672       2.136\n",
      "   92        41357.9      1.57707e-02           28.8939       2.165\n",
      "   93        41330.0      9.10366e-03           39.9454       2.193\n",
      "   94        41302.0      7.55334e-03           50.0373       2.212\n",
      "   95        41271.3      3.60244e-03           55.6501       2.241\n",
      "   96        41180.3      4.13452e-02           63.5053       2.283\n",
      "   97        41071.5      7.14036e-02           32.1562       2.307\n",
      "   98        41052.0      1.79079e-03           31.8860       2.338\n",
      "   99        41038.7      1.43988e-03           31.8405       2.357\n",
      "  100        41008.2      7.27781e-03           31.7144       2.386\n",
      "  101        41007.1      7.28050e-03           31.7078       2.402\n",
      "  102        40952.8      2.55798e-02           32.5626       2.428\n",
      "  103        40941.8      2.49334e-03           35.2241       2.473\n",
      "  104        40931.3      8.89722e-04           36.9970       2.508\n",
      "  105        40913.1      1.87487e-03           40.7366       2.545\n",
      "  106        40840.5      3.29115e-02           59.9093       2.573\n",
      "  107        40821.2      2.70306e-03           65.3438       2.600\n",
      "  108        40781.2      2.24370e-02           79.0458       2.618\n",
      "  109        40750.5      5.36505e-03           23.5382       2.640\n",
      "  110        40677.3      1.40953e-02           23.8328       2.661\n",
      "  111        40627.8      2.49309e-02           36.9165       2.692\n",
      "  112        40559.9      3.44218e-02           22.4391       2.713\n",
      "  113        40495.8      2.45648e-02           15.5767       2.752\n",
      "  114        40438.8      1.73279e-02           15.2287       2.787\n",
      "  115        40301.0         0.103464           30.8797       2.817\n",
      "  116        40226.7      3.35949e-02           18.7700       2.850\n",
      "  117        40214.7      1.02018e-03           22.0755       2.892\n",
      "  118        40154.2      1.87406e-02           30.2906       2.920\n",
      "  119        40146.6      1.88624e-02           30.3426       2.934\n",
      "  120        40129.9      9.58476e-03           30.4403       2.954\n",
      "  121        40113.5      3.66657e-03           30.9556       2.977\n",
      "  122        40047.5      2.13012e-02           32.6832       2.991\n",
      "  123        40016.6      1.55937e-02           41.5142       3.016\n",
      "  124        39985.1      2.51012e-02           52.8062       3.029\n",
      "  125        39940.8      4.18155e-02           65.7642       3.046\n",
      "  126        39845.5      6.01631e-02           91.3020       3.061\n",
      "  127        39766.1      3.57071e-02           18.3427       3.079\n",
      "  128        39650.2      8.24433e-02           41.7799       3.099\n",
      "  129        39643.5      7.09070e-04           24.1849       3.126\n",
      "  130        39636.1      4.77599e-04           24.1169       3.146\n",
      "  131        39605.0      7.37326e-03           24.0065       3.173\n",
      "  132        39527.1      4.64383e-02           20.2264       3.196\n",
      "  133        39514.2      5.08705e-02           30.4093       3.212\n",
      "  134        39440.9      7.97555e-02           42.3717       3.232\n",
      "  135        39402.4      8.23036e-02           51.4694       3.249\n",
      "  136        39313.9         0.232696           63.9922       3.263\n",
      "  137        39304.3         0.228021           65.1909       3.279\n",
      "  138        39283.8      4.83872e-03           8.44380       3.305\n",
      "  139        39278.6      1.79640e-04           8.29812       3.341\n",
      "  140        39261.4      3.13253e-03           11.1100       3.372\n",
      "  141        39249.8      9.81766e-04           14.0803       3.395\n",
      "  142        39240.9      1.90009e-03           16.8185       3.409\n",
      "  143        39165.0      8.81416e-02           16.6492       3.435\n",
      "  144        39122.8      9.86511e-02           26.5756       3.451\n",
      "  145        39107.0      3.50493e-03           19.4675       3.476\n",
      "  146        39039.5      9.73326e-02           31.4255       3.491\n",
      "  147        39023.2      2.55529e-03           33.7993       3.513\n",
      "  148        38853.1         0.135539           38.0843       3.536\n",
      "  149        38765.0         0.132996           55.9579       3.553\n",
      "  150        38698.0         0.135763           70.0920       3.588\n",
      "  151        38649.1         0.139844           79.8419       3.608\n",
      "  152        38615.0         0.130161           79.7744       3.624\n",
      "  153        38582.3         0.127730           59.4783       3.644\n",
      "  154        38555.7         0.132212           58.8645       3.666\n",
      "  155        38549.5      8.01656e-04           11.8114       3.686\n",
      "  156        38439.9      7.64318e-02           35.4204       3.709\n",
      "  157        38438.8      7.07056e-02           33.2966       3.752\n",
      "  158        38363.3      8.36043e-02           47.8069       3.780\n",
      "  159        38348.9      1.74729e-03           21.7913       3.837\n",
      "  160        38299.4      5.82082e-02           19.4041       3.866\n",
      "  161        38264.5      2.64440e-02           22.4095       3.892\n",
      "  162        38236.6      3.44254e-02           25.1869       3.911\n",
      "  163        38210.2      4.01151e-02           31.8913       3.937\n",
      "  164        38130.5      9.89671e-02           51.5108       3.955\n",
      "  165        38104.8      4.43971e-03           6.23365       3.999\n",
      "  166        38049.9      1.94918e-02           19.7067       4.031\n",
      "  167        38032.8      1.94462e-02           21.5601       4.052\n",
      "  168        38002.5      2.33425e-02           28.3055       4.076\n",
      "  169        37900.0      5.91781e-02           56.1120       4.087\n",
      "  170        37865.5      5.78190e-02           50.2075       4.110\n",
      "  171        37768.1      8.00102e-02           40.4758       4.125\n",
      "  172        37744.0      7.93845e-02           36.3424       4.138\n",
      "  173        37697.1      8.92758e-02           36.2952       4.152\n",
      "  174        37683.9      8.41042e-02           35.1472       4.169\n",
      "  175        37672.3      8.05501e-02           32.6650       4.193\n",
      "  176        37619.3      9.01271e-02           33.1040       4.218\n",
      "  177        37541.9         0.128805           31.9207       4.258\n",
      "  178        37459.1         0.107006           31.2397       4.275\n",
      "  179        37329.0         0.154476           56.2035       4.296\n",
      "  180        37256.0      5.34435e-02           39.4243       4.325\n",
      "  181        37244.0      1.59331e-03           39.0186       4.344\n",
      "  182        37220.5      8.91449e-03           38.2388       4.357\n",
      "  183        37144.1      6.92762e-02           52.2202       4.375\n",
      "  184        37133.9      9.68014e-04           10.1079       4.394\n",
      "  185        37112.5      9.85975e-03           10.7812       4.411\n",
      "  186        37043.9      2.71928e-02           28.0090       4.435\n",
      "  187        36962.0      6.13058e-02           50.0759       4.452\n",
      "  188        36919.8      6.44532e-02           49.2045       4.472\n",
      "  189        36823.2         0.120119           65.2617       4.481\n",
      "  190        36770.6      1.59286e-02           13.0821       4.509\n",
      "  191        36723.7      1.69143e-02           27.0993       4.530\n",
      "  192        36654.4      5.68446e-02           38.2661       4.539\n",
      "  193        36639.3      5.08174e-02           41.9907       4.554\n",
      "  194        36503.5         0.237296           38.8426       4.574\n",
      "  195        36470.5         0.227024           28.8230       4.603\n",
      "  196        36460.5         0.218133           26.2026       4.624\n",
      "  197        36438.3      4.59142e-03           28.8599       4.651\n",
      "  198        36395.8      1.59829e-02           25.3592       4.675\n",
      "  199        36363.4      1.04146e-02           25.5879       4.692\n",
      "  200        36348.8      8.31857e-03           24.6720       4.710\n",
      "  201        36316.3      1.25581e-02           19.1963       4.737\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  202        36250.5      4.91984e-02           18.8379       4.755\n",
      "  203        36154.3         0.137069           24.6958       4.769\n",
      "  204        36102.1         0.142825           25.4574       4.784\n",
      "  205        36006.1         0.223825           30.4542       4.796\n",
      "  206        36000.6      6.16379e-04           9.43916       4.814\n",
      "  207        35991.2      2.42597e-03           9.73727       4.824\n",
      "  208        35966.2      5.58148e-03           11.5607       4.839\n",
      "  209        35843.9      5.51052e-02           26.8087       4.860\n",
      "  210        35740.3      2.43877e-02           38.9111       4.878\n",
      "  211        35573.4      7.79036e-02           23.3486       4.892\n",
      "  212        35506.3      9.24492e-02           12.4898       4.901\n",
      "  213        35511.5      8.36733e-02           10.6179       4.921\n",
      "  214        35481.3      8.44871e-02           10.2502       4.942\n",
      "  215        35464.0      2.55938e-03           6.03578       4.958\n",
      "  216        35431.7      9.53404e-03           11.0688       4.977\n",
      "  217        35365.1      2.83970e-02           12.5052       5.000\n",
      "  218        35357.7      2.98861e-04           12.6738       5.041\n",
      "  219        35060.3         0.325169           72.2010       5.072\n",
      "  220        35043.6         0.318019           14.2125       5.096\n",
      "  221        35038.5         0.313103           13.0680       5.112\n",
      "  222        35037.2      2.99404e-04           16.9197       5.128\n",
      "  223        34979.2      1.27309e-02           20.6928       5.155\n",
      "  224        34872.6      3.81220e-02           26.3773       5.172\n",
      "  225        34817.9      1.82708e-02           15.2985       5.190\n",
      "  226        34813.4      1.23889e-04           16.6299       5.214\n",
      "  227        34777.4      1.73307e-03           23.8964       5.235\n",
      "  228        34752.6      1.82109e-03           29.8787       5.249\n",
      "  229        34710.4      6.58891e-03           41.0452       5.264\n",
      "  230        34639.1      9.05574e-03           53.5095       5.286\n",
      "  231        34497.1      1.45513e-02           11.1706       5.301\n",
      "  232        34494.0      4.90375e-05           11.1404       5.331\n",
      "  233        34487.0      8.62079e-05           10.8765       5.358\n",
      "  234        34383.8      3.57439e-02           27.5020       5.385\n",
      "  235        34319.1      4.31261e-02           11.3571       5.402\n",
      "  236        34259.3      5.04283e-02           12.4769       5.434\n",
      "  237        34156.2         0.106706           16.1374       5.451\n",
      "  238        34132.5      8.86084e-02           15.1626       5.474\n",
      "  239        34064.2         0.137955           24.1129       5.495\n",
      "  240        34042.9      2.95288e-03           7.73249       5.530\n",
      "  241        34029.5      3.57714e-03           8.58665       5.568\n",
      "  242        33936.4         0.108468           30.5669       5.591\n",
      "  243        33911.7         0.102478           28.7806       5.618\n",
      "  244        33833.9      8.59540e-02           21.9968       5.632\n",
      "  245        33805.7      7.91643e-02           13.4578       5.648\n",
      "  246        33625.5      4.83926e-02           37.5375       5.663\n",
      "  247        33475.1      4.59715e-02           33.4518       5.680\n",
      "  248        33390.4      4.86196e-02           36.9857       5.694\n",
      "  249        33339.9      5.23055e-02           30.1054       5.704\n",
      "  250        33315.9      5.13183e-02           28.6609       5.719\n",
      "  251        33213.9         0.138082           42.5979       5.743\n",
      "  252        33192.1      3.92615e-03           30.0028       5.766\n",
      "  253        33100.4      2.33184e-02           33.6036       5.782\n",
      "  254        32996.3      3.30657e-02           46.2701       5.798\n",
      "  255        32917.7      3.67574e-02           40.9601       5.818\n",
      "  256        32741.9      7.01995e-02           42.8845       5.841\n",
      "  257        32674.7      8.00083e-02           40.9184       5.859\n",
      "  258        32542.8      4.25933e-02           60.6767       5.888\n",
      "  259        32490.2      4.25895e-02           46.4167       5.909\n",
      "  260        32455.3      4.07087e-02           45.2483       5.937\n",
      "  261        32400.8      4.08727e-02           42.5363       5.953\n",
      "  262        32381.5      3.86833e-02           39.4131       5.980\n",
      "  263        32267.9      5.36393e-02           53.0580       5.992\n",
      "  264        32187.5      6.04454e-02           53.6840       6.004\n",
      "  265        32142.7      5.46802e-03           37.0232       6.035\n",
      "  266        32118.1      1.15091e-02           36.8959       6.061\n",
      "  267        32076.1      2.40757e-03           6.45057       6.088\n",
      "  268        32012.7      7.65372e-03           16.0921       6.112\n",
      "  269        31921.1      6.59989e-02           28.9301       6.128\n",
      "  270        31892.6      6.19569e-02           31.1388       6.154\n",
      "  271        31878.9      1.47654e-03           31.7659       6.172\n",
      "  272        31703.4      4.85733e-02           60.5470       6.199\n",
      "  273        31624.5      6.31788e-02           72.1287       6.219\n",
      "  274        31530.9      1.37163e-02           20.8121       6.235\n",
      "  275        31502.5      1.45386e-02           20.4449       6.248\n",
      "  276        31346.6      3.88425e-02           43.4212       6.262\n",
      "  277        31300.6      3.68570e-02           48.3887       6.282\n",
      "  278        31202.6      2.87722e-02           62.3439       6.296\n",
      "  279        31183.6      2.36096e-03           64.8876       6.321\n",
      "  280        31169.8      3.00633e-04           62.1341       6.338\n",
      "  281        31033.3      2.64801e-02           60.9686       6.358\n",
      "  282        30929.9      4.41288e-02           60.2348       6.368\n",
      "  283        30904.2      7.89497e-04           19.0533       6.396\n",
      "  284        30796.5      2.07114e-02           26.9524       6.414\n",
      "  285        30674.1      2.21376e-02           21.1028       6.431\n",
      "  286        30507.2      5.69481e-02           49.7767       6.442\n",
      "  287        30489.3      3.78268e-04           34.1839       6.460\n",
      "  288        30411.2      7.00574e-03           35.7095       6.472\n",
      "  289        30213.1      3.41463e-02           44.0003       6.488\n",
      "  290        30029.4      4.81050e-02           28.9081       6.501\n",
      "  291        30019.3      1.15245e-04           29.8780       6.518\n",
      "  292        29963.7      5.95860e-03           32.8718       6.537\n",
      "  293        29780.6      6.63809e-02           59.8977       6.556\n",
      "  294        29767.3      3.74776e-04           63.7768       6.575\n",
      "  295        29698.2      6.01961e-03           77.8085       6.595\n",
      "  296        29588.8      2.76707e-02           75.7890       6.620\n",
      "  297        29515.3      3.83970e-02           68.5149       6.644\n",
      "  298        29283.5      3.66235e-02           74.2496       6.673\n",
      "  299        29253.0         0.262172           78.1270       6.689\n",
      "  300        29144.5         0.230551           81.9785       6.701\n",
      "  301        28989.5         0.183136           100.236       6.727\n",
      "  302        28828.1         0.154533           86.2503       6.755\n",
      "  303        28796.7      2.88556e-03           41.4976       6.779\n",
      "  304        28773.9      4.65411e-03           42.8388       6.808\n",
      "  305        28514.2         0.113715           46.3860       6.827\n",
      "  306        28451.9      6.38356e-03           45.2332       6.850\n",
      "  307        28382.3      1.37489e-02           52.5229       6.860\n",
      "  308        28319.3      3.55762e-02           65.5765       6.875\n",
      "  309        28310.6      1.52219e-02           39.6910       6.906\n",
      "  310        28241.1      2.44641e-02           39.3723       6.921\n",
      "  311        28172.9      4.47339e-02           38.9277       6.939\n",
      "  312        28163.7      2.15211e-02           38.9099       6.960\n",
      "  313        28046.3      3.08257e-02           51.6958       6.982\n",
      "  314        28009.2      1.46723e-02           47.1181       7.011\n",
      "  315        27982.9      7.22947e-03           47.2273       7.052\n",
      "  316        27935.3      3.99651e-03           47.3417       7.084\n",
      "  317        27908.7      3.83130e-03           47.6015       7.106\n",
      "  318        27825.9      4.28040e-03           60.0206       7.133\n",
      "  319        27811.5      1.94535e-04           29.2399       7.169\n",
      "  320        27764.6      1.56602e-02           30.5173       7.190\n",
      "  321        27753.4      1.59482e-02           30.6825       7.204\n",
      "  322        27745.6      1.74780e-02           30.0351       7.222\n",
      "  323        27741.5      1.65863e-02           29.9105       7.239\n",
      "  324        27675.9      2.16813e-02           29.8748       7.255\n",
      "  325        27660.3      8.71135e-03           30.1702       7.278\n",
      "  326        27572.2      9.91533e-02           47.8807       7.294\n",
      "  327        27443.0      2.55671e-02           57.9727       7.325\n",
      "  328        27355.9      3.19978e-02           40.1902       7.350\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  329        27293.2      4.00342e-02           39.9067       7.370\n",
      "  330        27280.9      2.12192e-04           40.8199       7.391\n",
      "  331        27255.8      1.88208e-03           41.6686       7.420\n",
      "  332        27198.1      5.76435e-02           34.5775       7.432\n",
      "  333        27175.7         0.104525           34.6551       7.441\n",
      "  334        27154.0         0.247583           36.2329       7.456\n",
      "  335        27111.4         0.385519           30.1540       7.469\n",
      "  336        27093.0         0.311454           26.6558       7.499\n",
      "  337        27061.3         0.285492           32.1937       7.512\n",
      "  338        27061.0         0.235199           31.7516       7.526\n",
      "  339        27023.6         0.200182           27.4785       7.538\n",
      "  340        26996.0         0.194666           24.2706       7.567\n",
      "  341        26984.8         0.174783           19.2917       7.590\n",
      "  342        26921.6         0.159100           15.1068       7.606\n",
      "  343        26920.4         0.117677           15.1972       7.630\n",
      "  344        26917.0         0.111162           11.0092       7.650\n",
      "  345        26922.0      8.22444e-02           11.0987       7.666\n",
      "  346        26907.4      7.64869e-02           9.48815       7.684\n",
      "  347        26888.8      3.79170e-02           13.6003       7.710\n",
      "  348        26846.4      1.87308e-02           20.8906       7.731\n",
      "  349        26830.7      9.03772e-03           23.4717       7.760\n",
      "  350        26823.0      4.15743e-03           26.1632       7.784\n",
      "  351        26806.7      6.56384e-03           28.2788       7.798\n",
      "  352        26792.9      4.71374e-03           8.33393       7.816\n",
      "  353        26777.5      6.51213e-03           11.4404       7.840\n",
      "  354        26769.8      3.64777e-04           13.7330       7.857\n",
      "  355        26725.0      1.80172e-02           11.2194       7.878\n",
      "  356        26703.0      3.24982e-02           10.6024       7.890\n",
      "  357        26696.4      1.50162e-03           4.05289       7.907\n",
      "  358        26686.1      2.74448e-03           8.40935       7.924\n",
      "  359        26622.4      4.01603e-02           27.8989       7.940\n",
      "  360        26606.8      3.58851e-02           23.1343       7.959\n",
      "  361        26602.5      6.41860e-04           23.9986       7.988\n",
      "  362        26598.5      5.75641e-04           19.9665       8.016\n",
      "  363        26594.3      3.81696e-04           19.9685       8.038\n",
      "  364        26593.0      3.52317e-04           18.7060       8.053\n",
      "  365        26587.6      9.18098e-03           16.2522       8.064\n",
      "  366        26578.5      3.81809e-02           20.6885       8.077\n",
      "  367        26545.4      8.46445e-02           18.6856       8.098\n",
      "  368        26521.7         0.121236           19.9175       8.117\n",
      "  369        26520.6         0.105103           16.8008       8.133\n",
      "  370        26478.4         0.185938           23.2401       8.157\n",
      "  371        26477.5         0.182720           19.3691       8.168\n",
      "  372        26467.1         0.152107           26.2725       8.177\n",
      "  373        26449.4      7.07639e-02           4.25104       8.189\n",
      "  374        26447.3      6.88398e-02           2.65842       8.200\n",
      "  375        26446.8      5.66668e-02           2.29070       8.207\n",
      "  376        26435.9      6.35583e-02           10.1517       8.221\n",
      "  377        26407.8      5.24120e-02           22.6919       8.241\n",
      "  378        26409.3      5.21399e-02           21.6861       8.257\n",
      "  379        26406.6      5.15872e-02           25.0645       8.272\n",
      "  380        26405.1      2.41042e-02           23.3202       8.290\n",
      "  381        26404.0      1.44788e-02           20.5204       8.300\n",
      "  382        26402.0      6.01760e-03           12.6197       8.321\n",
      "  383        26381.6         0.184185           13.4712       8.337\n",
      "  384        26379.9         0.177367           16.0814       8.368\n",
      "  385        26381.6      4.63741e-04           2.54192       8.399\n",
      "  386        26381.6      4.25008e-04           2.54284       8.421\n",
      "  387        26381.5      1.78633e-04           2.55887       8.435\n",
      "  388        26378.3      7.63311e-03           8.11215       8.448\n",
      "  389        26359.4      7.83443e-02           1.26132       8.465\n",
      "  390        26352.6      7.02411e-02           7.86615       8.483\n",
      "  391        26352.3      9.06439e-04           2.31982       8.500\n",
      "  392        26352.3      1.32824e-07           2.32116       8.517\n",
      "  393        26352.2      1.58732e-07           2.32156       8.523\n",
      "  394        26352.2      2.41912e-07           2.32255       8.529\n",
      "  395        26351.9      2.55025e-04           3.32244       8.539\n",
      "  396        26347.0      2.47161e-02           3.06172       8.564\n",
      "  397        26342.2      3.53526e-02           1.26377       8.576\n",
      "  398        26338.4      4.38192e-02           6.59663       8.586\n",
      "  399        26338.9      4.16255e-02           5.67892       8.598\n",
      "  400        26338.9      4.15938e-02           5.68740       8.604\n",
      "  401        26338.3      2.70648e-02           6.75602       8.616\n",
      "  402        26338.4      1.82399e-02           6.92758       8.627\n",
      "  403        26338.2      4.54988e-03           8.25965       8.636\n",
      "  404        26337.6      1.94026e-03           9.92861       8.649\n",
      "  405        26330.2      2.94035e-02           18.5505       8.659\n",
      "  406        26324.4      5.05987e-02           20.4353       8.668\n",
      "  407        26322.2      4.96297e-02           18.5281       8.678\n",
      "  408        26321.3      2.10421e-02           16.7303       8.695\n",
      "  409        26321.3      2.10416e-02           16.7212       8.702\n",
      "  410        26320.7      1.40837e-02           6.17819       8.722\n",
      "  411        26313.5      3.43209e-02           5.46722       8.734\n",
      "  412        26309.3      4.08115e-02           3.42201       8.755\n",
      "  413        26309.3      4.07185e-02           3.38913       8.773\n",
      "  414        26309.4      3.04628e-02           3.43874       8.787\n",
      "  415        26298.3         0.103749           16.5133       8.801\n",
      "  416        26299.1      6.54222e-02           15.1360       8.819\n",
      "  417        26296.6      1.42908e-02           9.23645       8.837\n",
      "  418        26279.5         0.104999           17.4799       8.858\n",
      "  419        26276.5      3.49289e-02          0.247077       8.870\n",
      "  420        26273.4      3.30937e-02           6.24290       8.890\n",
      "  421        26272.1      1.34369e-03           2.47299       8.920\n",
      "  422        26272.1      4.93283e-04           2.45883       8.938\n",
      "  423        26272.1      2.28063e-04           2.53759       8.954\n",
      "  424        26270.6      6.14124e-03           7.67956       8.970\n",
      "  425        26269.1      4.06404e-03           12.5091       9.001\n",
      "  426        26261.0      7.61764e-02           3.94178       9.032\n",
      "  427        26260.6      7.51814e-02           4.68964       9.056\n",
      "  428        26261.1      6.29715e-02           4.68700       9.078\n",
      "  429        26258.6      1.38172e-02           11.7284       9.121\n",
      "  430        26257.5      1.45500e-03           2.50664       9.164\n",
      "  431        26257.6      6.62059e-04           2.43348       9.188\n",
      "  432        26257.6      4.37183e-04           2.56598       9.205\n",
      "  433        26250.8      5.56886e-02           12.3611       9.217\n",
      "  434        26249.5      5.82949e-03          0.390496       9.235\n",
      "  435        26248.9      5.68060e-03           1.71432       9.249\n",
      "  436        26248.9      5.68035e-03           1.71432       9.257\n",
      "  437        26248.9      5.66816e-03           1.72097       9.270\n",
      "  438        26248.9      4.18573e-03           1.72615       9.279\n",
      "  439        26249.0      1.88159e-03           1.76850       9.291\n",
      "  440        26246.2      7.74859e-03           2.61259       9.316\n",
      "  441        26238.4      3.74735e-02           2.34165       9.330\n",
      "  442        26239.0      1.02164e-02           2.46762       9.344\n",
      "  443        26239.0      1.02076e-02           2.46803       9.356\n",
      "  444        26239.0      1.01739e-02           2.47034       9.367\n",
      "  445        26239.0      9.87683e-03           2.46537       9.376\n",
      "  446        26239.0      9.52168e-03           2.47312       9.385\n",
      "  447        26239.1      2.00271e-07           2.49712       9.395\n",
      "  448        26239.1      5.67461e-07           2.52534       9.403\n",
      "  449        26238.8      1.22551e-03           3.75380       9.409\n",
      "  450        26238.6      4.37160e-04          0.458011       9.428\n",
      "  451        26237.7      4.17462e-03       1.21375e-02       9.436\n",
      "  452        26234.4      2.98468e-02           1.08350       9.449\n",
      "  453        26234.9      8.91904e-03           1.15581       9.469\n",
      "  454        26235.0      1.57771e-07           1.16798       9.474\n",
      "  455        26235.0      1.01881e-09       5.11096e-03       9.488\n",
      "  456        26235.0      1.56481e-09       2.35345e-07       9.499\n",
      "  457        26235.0      1.30496e-12       7.42620e-13       9.504\n",
      "  458        26235.0      1.30496e-12       7.42620e-13       9.527\n",
      "\n",
      "Tree search\n",
      "-----------\n",
      "\n",
      "       Nodes        Best solution   Best bound      Gap       Time \n",
      "   Expl  |  Unexpl      value         value                  (secs)\n",
      "   ---------------  -------------   ----------      ---      ------\n",
      "      1       0      26235.0 LEAF      26235.0      0.00%     9.532\n",
      "\n",
      "EXIT: Optimal solution found (assuming convexity).\n",
      "\n",
      "HINT: The problem may be a non-convex mixed-integer problem.  Set\n",
      "      mip_multistart=1 to enable a mixed-integer multistart heuristic,\n",
      "      which may improve the chances of finding the global solution.\n",
      "\n",
      "Final Statistics for MIP\n",
      "------------------------\n",
      "Final objective value               =  2.62350112223449e+04\n",
      "Final bound value                   =  2.62350112223449e+04\n",
      "Final optimality gap (abs / rel)    =  0.00e+00 / 0.00e+00 (0.00%)\n",
      "# of root cutting plane rounds      =  0\n",
      "# of restarts                       =  0\n",
      "# of nodes processed                =  1 (9.516s)\n",
      "# of strong branching evaluations   =  0 (0.000s)\n",
      "# of function evaluations           =  0 (0.000s)\n",
      "# of gradient evaluations           =  0 (0.000s)\n",
      "# of hessian evaluations            =  0 (0.000s)\n",
      "# of hessian-vector evaluations     =  0\n",
      "# of subproblems processed          =  1 (9.516s)\n",
      "Total program time (secs)           =  9.532 (10.656 CPU time)\n",
      "Time spent in evaluations (secs)    =  0.000\n",
      "\n",
      "Cuts statistics (gen / add)\n",
      "---------------------------\n",
      "Knapsack cuts                       =  0 / 0\n",
      "Mixed-integer rounding cuts         =  0 / 0\n",
      "Flow-cover cuts                     =  0 / 0\n",
      "Probing cuts                        =  0 / 0\n",
      "\n",
      "Heuristics statistics (calls / successes / time)\n",
      "------------------------------------------------\n",
      "Feasibility pump                    =  0 / 0 / 0.000s\n",
      "Rounding heuristic                  =  0 / 0 / 0.000s\n",
      "MPEC heuristic                      =  0 / 0 / 0.000s\n",
      "Local search heuristic              =  4 / 0 / 2.169s\n",
      "\n",
      "===========================================================================\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b"
     ]
    }
   ],
   "source": [
    "import pyomo.environ as pyo\n",
    "\n",
    "def build_model(nb_observations, nb_clusters):\n",
    "\n",
    "    ####################\n",
    "    # Create variables #\n",
    "    ####################\n",
    "    \n",
    "    model.N = pyo.RangeSet(0, nb_observations - 1)\n",
    "    model.K = pyo.RangeSet(0, nb_clusters - 1)\n",
    "    model.a = pyo.Var(model.N, model.K, within = pyo.Binary)\n",
    "    model.d = pyo.Var(model.N, model.K, within = pyo.NonNegativeReals)\n",
    "    # cx & cy (abcissa and ordinate)\n",
    "    model.cx = pyo.Var(model.K, within = pyo.Reals)\n",
    "    model.cy = pyo.Var(model.K, within = pyo.Reals)\n",
    "    \n",
    "    #############\n",
    "    # Objective #\n",
    "    #############\n",
    "    \n",
    "    model.objective = pyo.Objective(\n",
    "                expr= pyo.quicksum(model.a[s,t]* model.d[s,t]\n",
    "                                   for s in model.N\n",
    "                                   for t in model.K),\n",
    "                sense=pyo.minimize)\n",
    "    \n",
    "    ###############\n",
    "    # Constraints #\n",
    "    ###############\n",
    "    \n",
    "    \n",
    "    def one_cluster_rule(model,i):\n",
    "        total = 0\n",
    "        for j in range(nb_clusters):\n",
    "            total += model.a[i,j]\n",
    "        return (total == 1)\n",
    "    model.constraints_one_cluster = pyo.Constraint(model.N, rule=one_cluster_rule)\n",
    "    \n",
    "    def barycenter_x_position_rule(model, j):\n",
    "        total_a = 0 \n",
    "        total_pa_x = 0\n",
    "        for i in range(nb_observations):\n",
    "             total_a += model.a[i,j]\n",
    "             total_pa_x += model.a[i,j] * observations_positions[i][0]\n",
    "        return (model.cx[j] * total_a == total_pa_x)\n",
    "    model.constraints_barycenter_x_position_rule = pyo.Constraint(model.K,rule=barycenter_x_position_rule)\n",
    "    \n",
    "    def barycenter_y_position_rule(model, j):\n",
    "        total_a = 0 \n",
    "        total_pa_y = 0\n",
    "        for i in range(nb_observations):\n",
    "             total_a += model.a[i,j]\n",
    "             total_pa_y += model.a[i,j] * observations_positions[i][1]\n",
    "        return (total_a * model.cy[j] == total_pa_y)\n",
    "    model.constraints_barycenter_y_position_rule = pyo.Constraint(model.K,rule=barycenter_y_position_rule)\n",
    "\n",
    "    def dist_rule(model,s,t):\n",
    "        return (model.d[s,t] == (((observations_positions[s][0]-model.cx[t])**2)  +\n",
    "                                                         ((observations_positions[s][1]-model.cy[t])**2)))\n",
    "\n",
    "    model.constraints_dist_rule = pyo.Constraint(model.N,model.K,rule=dist_rule)\n",
    "\n",
    "# Let's build the model and run it \n",
    "model = pyo.ConcreteModel()\n",
    "build_model(nb_observations,nb_clusters)\n",
    "solver = pyo.SolverFactory('knitroampl')\n",
    "results = solver.solve(model, tee=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ac88b7a-b72f-4e78-a902-c8ee39baca69",
   "metadata": {},
   "source": [
    "# Comparison with Scikit-learn\n",
    "\n",
    "Let's visualize the solution and compare it with the classic Kmeans Algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "30cd2f54-321d-4ee7-b4b2-96b6dde1339f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster 0 contains 88 observations\n",
      "Cluster 1 contains 117 observations\n",
      "Cluster 2 contains 95 observations\n",
      "Total cost is 26235.011222344914\n"
     ]
    }
   ],
   "source": [
    "def draw_figure(nb_observations,nb_clusters,model,name):\n",
    "    fig = go.Figure()\n",
    "    for k in range(nb_clusters):\n",
    "        fig.add_scatter(x = [observations_positions[i][0] for i in range(nb_observations) if (model.a[i,k]() > 0.99)], y =  [observations_positions[i][1] for i in range(nb_observations) if (model.a[i,k]() > 0.99)], mode ='markers', name=f\"Cluster{k}\")\n",
    "    fig.update_layout(\n",
    "        title = name,\n",
    "                )\n",
    "    fig.show(\"png\")\n",
    "    \n",
    "    for k in range(nb_clusters):\n",
    "        total = 0\n",
    "        for i in range(nb_observations):\n",
    "            if (model.a[i,k]() > 0.99):\n",
    "                total += 1\n",
    "        print(f\"Cluster {k} contains {total} observations\") \n",
    "    \n",
    "    print(f\"Total cost is {model.objective()}\")\n",
    "\n",
    "draw_figure(nb_observations,nb_clusters,model, \"Knitro Solution\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "585035da",
   "metadata": {},
   "source": [
    "Nonlinear programming is significantly slower than the algorithm implemented in Sciki-learn. However, it finds a better solution ($26235.01 < 26243.6$) on the considered instance.\n",
    "\n",
    "In the next section, we will see that another advantage of nonlinear programming is when additional constraints need to be taken into account."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d6c6b0f-4a14-4213-b6ad-d5b728731205",
   "metadata": {},
   "source": [
    "# Model Extensions\n",
    "\n",
    "In some cases, additional constraints must be taken into account. These extensions are usually not supported by the algorithms available in the data science libraries. Here we illustrate 3 of these additional constraints and how to model them with nonlinear programming:\n",
    "* Force some pairs of observations to be in the same cluster\n",
    "* Force some pairs of observations to be in different clusters\n",
    "* Impose a minimum and maximum sizes for clusters\n",
    "\n",
    "## Cannot-link and must-link observations\n",
    "\n",
    "### Problem description\n",
    "\n",
    "In some cases, some pairs of observations might be known to belong to the same cluster or to different clusters. These are called \"must-link\" and \"cannot-link\" constraints.\n",
    "\n",
    "Let $P^\\text{must}$ be the set of set of observations that must belong to the same cluster.\n",
    "\n",
    "Let $P^\\text{cannot}$ be the set of pairs of observations that must belong to different clusters.\n",
    "\n",
    "### Input data\n",
    "\n",
    "The input data of observations is the same as for the previous example. We just need to specify must-link observations or cannot-link observations (between two observations which should not be linked)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18352887-c3aa-440f-a403-7b7c8cda4368",
   "metadata": {},
   "source": [
    "#### Must-link observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5fd2fbfe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[22, 247]\n"
     ]
    }
   ],
   "source": [
    "must_link_g1 = []\n",
    "must_link_g2 = []\n",
    "cannot_link = []\n",
    "\n",
    "for k in range(nb_observations):\n",
    "    if(0 < observations_positions[k][0] < 10 and observations_positions[k][1] >= 20):\n",
    "        must_link_g1.append(k)\n",
    "    if (10 < observations_positions[k][0] < 20 and observations_positions[k][1] >= 20):\n",
    "        must_link_g2.append(k)\n",
    "    if( observations_positions[k][0] == 8.9204 or observations_positions[k][0] == 10.61132):\n",
    "        cannot_link.append(k)\n",
    "print(cannot_link)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d0ea6ddd-aa6d-427b-941e-45085900e297",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure()\n",
    "fig.add_scatter(x = [observations_positions[i][0] for i in range(nb_observations)], y =  [observations_positions[i][1] for i in range(nb_observations)], mode ='markers', name=\"Observations\")\n",
    "fig.add_scatter(x = [observations_positions[i][0] for i in must_link_g1], y =  [observations_positions[i][1] for i in must_link_g1], mode ='markers', name=\"Must_link observations (Group 1)\")\n",
    "fig.add_scatter(x = [observations_positions[i][0] for i in must_link_g2], y =  [observations_positions[i][1] for i in must_link_g2], mode ='markers', name=\"Must-link observations (Group 2)\")\n",
    "fig.add_scatter(x = [observations_positions[i][0] for i in cannot_link], y =  [observations_positions[i][1] for i in cannot_link], mode ='lines', name=\"Cannot-link observations\")\n",
    "fig.update_layout(\n",
    "    title = \"Affected observations\",\n",
    "            )\n",
    "fig.show(\"png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "238173dc-d47d-4dbb-a7c4-9646a117a236",
   "metadata": {},
   "source": [
    "All red/green elements should be in the same cluster. Moreover, the linked observations should not be in the same cluster."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d8aa217",
   "metadata": {},
   "source": [
    "### Mathematical model\n",
    "\n",
    "We add the two following set of constraints to the previous mathematical model.\n",
    "\n",
    "* Must-link constraints\n",
    "\n",
    "$$\n",
    "\\forall k = 1, \\dots, K, \\quad \\forall S \\in P^\\text{must}, \\quad \\forall i \\in S, \\qquad a^k_{i} = a^k_{S[0]} \n",
    "$$\n",
    "\n",
    "* Cannot-link constraints\n",
    "\n",
    "$$\n",
    "\\forall k = 1, \\dots, K, \\quad \\forall i_1, i_2 \\in P^\\text{cannot}, \\qquad a^k_{i_1} + a^k_{i_2} \\leq 1\n",
    "$$\n",
    "\n",
    "### Implementation with Pyomo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fdee7c43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Artelys Knitro 14.1.0: WARNING: 12 constraints are constant or undefined and will be ignored.\n",
      "\n",
      "=======================================\n",
      "          Commercial License\n",
      "         Artelys Knitro 14.1.0\n",
      "=======================================\n",
      "\n",
      "MINLP solver shifted start point to satisfy bounds (157 variables).\n",
      "WARNING: Problem appears to have nonlinear equalities and be non-convex.\n",
      "         The Knitro mixed integer solver is designed for convex problems.\n",
      "         For non-convex problems it is only a heuristic, and the reported\n",
      "         bounds and optimality claims cannot be verified.\n",
      "\n",
      "concurrent_evals         0\n",
      "datacheck                0\n",
      "hessian_no_f             1\n",
      "hessopt                  1\n",
      "The problem is identified as a MIQCQP.\n",
      "Knitro changing mip_method from AUTO to 1.\n",
      "Knitro changing mip_rootalg from AUTO to 1.\n",
      "Knitro changing mip_lpalg from AUTO to 3.\n",
      "Knitro changing mip_branchrule from AUTO to 2.\n",
      "Knitro changing mip_selectrule from AUTO to 2.\n",
      "Knitro changing mip_mir from AUTO to 2.\n",
      "Knitro changing mip_clique from AUTO to 0.\n",
      "Knitro changing mip_zerohalf from AUTO to 0.\n",
      "Knitro changing mip_liftproject from AUTO to 0.\n",
      "Knitro changing mip_knapsack from AUTO to 2.\n",
      "Knitro changing mip_gomory from AUTO to 0.\n",
      "Knitro changing mip_cut_flowcover from AUTO to 2.\n",
      "Knitro changing mip_cut_probing from AUTO to 1.\n",
      "Knitro changing mip_rounding from AUTO to 3.\n",
      "Knitro changing mip_heuristic_strategy from AUTO to 1.\n",
      "Knitro changing mip_heuristic_feaspump from AUTO to 1.\n",
      "Knitro changing mip_heuristic_misqp from AUTO to 0.\n",
      "Knitro changing mip_heuristic_mpec from AUTO to 1.\n",
      "Knitro changing mip_heuristic_diving from AUTO to 0.\n",
      "Knitro changing mip_heuristic_lns from AUTO to 0.\n",
      "Knitro changing mip_heuristic_localsearch from AUTO to 1.\n",
      "Knitro changing mip_pseudoinit from AUTO to 1.\n",
      "\n",
      "Problem Characteristics                                 (   Presolved)\n",
      "-----------------------\n",
      "Objective goal:  Minimize\n",
      "Objective type:  quadratic\n",
      "Number of variables:                               1806 (        1806)\n",
      "    bounded below only:                             900 (         900)\n",
      "    bounded above only:                               0 (           0)\n",
      "    bounded below and above:                        900 (         900)\n",
      "    fixed:                                            0 (           0)\n",
      "    free:                                             6 (           6)\n",
      "Number of binary variables:                         900 (         900)\n",
      "Number of integer variables:                          0 (           0)\n",
      "Number of constraints:                             1329 (        1329)\n",
      "    linear equalities:                              417 (         417)\n",
      "    quadratic equalities:                           906 (         906)\n",
      "    gen. nonlinear equalities:                        0 (           0)\n",
      "    linear one-sided inequalities:                    6 (           6)\n",
      "    quadratic one-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear one-sided inequalities:            0 (           0)\n",
      "    linear two-sided inequalities:                    0 (           0)\n",
      "    quadratic two-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear two-sided inequalities:            0 (           0)\n",
      "Number of nonzeros in Jacobian:                    5628 (        5628)\n",
      "Number of nonzeros in Hessian:                     2706 (        2706)\n",
      "\n",
      "Knitro using Branch and Bound method with 8 threads.\n",
      "\n",
      "Initial points\n",
      "--------------\n",
      "The initial point provided for the root node relaxation is not feasible for the MIP.\n",
      "No primal point provided for the MIP.\n",
      "\n",
      "Root node relaxation\n",
      "--------------------\n",
      "\n",
      " Iter      Objective      Feasibility        Optimality       Time \n",
      "                             error              error        (secs)\n",
      " ----      ---------      -----------        ----------      ------\n",
      "    1        26441.5         0.991009          0.660535       0.157\n",
      "    2        27071.8         0.970923           2.77077       0.171\n",
      "    3        27483.9         0.689300           1.58162       0.204\n",
      "    4        28218.3         0.650284           3.87968       0.264\n",
      "    5        28311.0         0.519688           3.81007       0.305\n",
      "    6        28318.9          2.12618           13.2873       0.316\n",
      "    7        31050.2         0.684933           7.49180       0.330\n",
      "    8        30987.5         0.836845           2.13084       0.356\n",
      "    9        31315.1         0.540418           5.22607       0.374\n",
      "   10        31435.8         0.480237           6.69924       0.392\n",
      "   11        31546.2         0.428675           8.07227       0.403\n",
      "   12        31898.2         0.863099           7.83054       0.415\n",
      "   13        31892.8         0.717183           2.18969       0.441\n",
      "   14        32074.5         0.565557           4.59930       0.461\n",
      "   15        32222.5         0.412926           6.02034       0.474\n",
      "   16        32226.9         0.240810           6.34894       0.500\n",
      "   17        32230.4         0.228699           4.84201       0.518\n",
      "   18        32235.9         0.167960           2.94440       0.545\n",
      "   19        32242.7         0.167841           3.01893       0.558\n",
      "   20        32247.6         0.123728           1.69755       0.582\n",
      "   21        32241.5         0.121448           1.74491       0.596\n",
      "   22        32246.1         0.118268           2.82326       0.616\n",
      "   23        32251.9      8.26558e-02           4.67923       0.632\n",
      "   24        32272.2      5.80659e-02           4.86296       0.664\n",
      "   25        32307.3      6.21579e-02           3.67851       0.674\n",
      "   26        32372.4         0.110871           3.71560       0.687\n",
      "   27        32394.6         0.119461           3.74003       0.713\n",
      "   28        32410.6         0.128266           3.78799       0.725\n",
      "   29        32423.5         0.138688           3.86231       0.737\n",
      "   30        32424.9         0.150311           3.94225       0.749\n",
      "   31        32637.8         0.195366           3.70329       0.761\n",
      "   32        32582.4         0.206705           3.67127       0.773\n",
      "   33        32553.7         0.156663           2.33956       0.798\n",
      "   34        32441.2      3.41520e-03           3.91283       0.820\n",
      "   35        30386.6          4.16698           7.71041       0.836\n",
      "   36        30333.1          3.69747           7.21772       0.844\n",
      "   37        30331.8          1.71384           6.54953       0.856\n",
      "   38        30307.3         0.806349           6.73433       0.865\n",
      "   39        30328.9         0.598840           4.79456       0.874\n",
      "   40        30253.5         0.501309           6.76944       0.886\n",
      "   41        30203.0         0.408596           6.10483       0.897\n",
      "   42        30120.9         0.298498           6.14818       0.908\n",
      "   43        30152.7         0.213519           5.77272       0.926\n",
      "   44        29658.2         0.162373          0.681592       0.943\n",
      "   45        29641.9         0.181313          0.650918       0.955\n",
      "   46        29591.3         0.128079          0.699252       0.971\n",
      "   47        29510.7         0.118611          0.265432       0.987\n",
      "   48        29490.3      8.22302e-02          0.535993       1.000\n",
      "   49        29470.9      5.89645e-02          0.452643       1.010\n",
      "   50        29449.8         0.137745           1.34928       1.020\n",
      "   51        29347.6      4.43963e-03          0.495085       1.030\n",
      "   52        29320.5         0.195552           2.85828       1.047\n",
      "   53        29322.0      9.02929e-02           2.43020       1.055\n",
      "   54        29312.3      7.74707e-02           1.86588       1.064\n",
      "   55        29306.8         0.103575           1.72867       1.071\n",
      "   56        29307.9      7.91935e-02          0.707297       1.078\n",
      "   57        29304.2      2.85740e-02          0.844138       1.085\n",
      "   58        29307.6      2.00264e-02          0.339985       1.099\n",
      "   59        29301.3      5.30692e-03          0.522223       1.106\n",
      "   60        29290.2      5.41023e-02          0.955953       1.121\n",
      "   61        29288.9      8.40026e-03          0.635099       1.130\n",
      "   62        29288.4      4.21488e-03       2.14238e-03       1.137\n",
      "   63        29287.9      6.30070e-04       1.68469e-04       1.150\n",
      "   64        29286.5      1.49767e-02       9.09968e-04       1.165\n",
      "   65        29286.2      2.00415e-03       3.90476e-04       1.183\n",
      "   66        29286.0      2.07670e-03       5.72888e-02       1.202\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   67        29286.1      2.67501e-09       5.71801e-02       1.232\n",
      "   68        29286.1      7.03882e-11       5.71801e-02       1.266\n",
      "   69        29286.1      3.37764e-10       3.82668e-07       1.274\n",
      "   70        29286.1      3.37764e-10       3.82668e-07       1.297\n",
      "   71        29286.1      3.37764e-10       3.82668e-07       1.339\n",
      "\n",
      "Tree search\n",
      "-----------\n",
      "\n",
      "       Nodes        Best solution   Best bound      Gap       Time \n",
      "   Expl  |  Unexpl      value         value                  (secs)\n",
      "   ---------------  -------------   ----------      ---      ------\n",
      "      1       2      29286.1 FCRD         -inf                1.473\n",
      "      3       0      29286.1           29286.1     -0.00%     1.600\n",
      "\n",
      "EXIT: Optimal solution found (assuming convexity).\n",
      "\n",
      "HINT: The problem may be a non-convex mixed-integer problem.  Set\n",
      "      mip_multistart=1 to enable a mixed-integer multistart heuristic,\n",
      "      which may improve the chances of finding the global solution.\n",
      "\n",
      "Final Statistics for MIP\n",
      "------------------------\n",
      "Final objective value               =  2.92860809191001e+04\n",
      "Final bound value                   =  2.92860811010834e+04\n",
      "Final optimality gap (abs / rel)    =  -1.82e-04 / -6.21e-09 (-0.00%)\n",
      "# of root cutting plane rounds      =  1\n",
      "# of restarts                       =  0\n",
      "# of nodes processed                =  3 (1.319s)\n",
      "# of strong branching evaluations   =  0 (0.000s)\n",
      "# of function evaluations           =  0 (0.000s)\n",
      "# of gradient evaluations           =  0 (0.000s)\n",
      "# of hessian evaluations            =  0 (0.000s)\n",
      "# of hessian-vector evaluations     =  0\n",
      "# of subproblems processed          =  2 (1.362s)\n",
      "Total program time (secs)           =  2.212 (3.922 CPU time)\n",
      "Time spent in evaluations (secs)    =  0.000\n",
      "\n",
      "Cuts statistics (gen / add)\n",
      "---------------------------\n",
      "Knapsack cuts                       =  0 / 0\n",
      "Mixed-integer rounding cuts         =  0 / 0\n",
      "Flow-cover cuts                     =  0 / 0\n",
      "Probing cuts                        =  1944 / 0\n",
      "\n",
      "Heuristics statistics (calls / successes / time)\n",
      "------------------------------------------------\n",
      "Feasibility pump                    =  0 / 0 / 0.000s\n",
      "Rounding heuristic                  =  1 / 1 / 0.050s\n",
      "MPEC heuristic                      =  0 / 0 / 0.000s\n",
      "Local search heuristic              =  5 / 0 / 1.718s\n",
      "\n",
      "===========================================================================\n",
      "\n",
      "\b"
     ]
    }
   ],
   "source": [
    "model.MLG1 = pyo.Set(initialize = must_link_g1)\n",
    "model.MLG2 =pyo.Set(initialize = must_link_g2)\n",
    "model.CL = pyo.Set(initialize = cannot_link)\n",
    "\n",
    "def cannot_link_rule(model,i,p,j):\n",
    "    if (i != p):\n",
    "        return(model.a[i,j] + model.a[p,j] <= 1)\n",
    "    else:\n",
    "        return(model.a[i,j] == model.a[p,j])\n",
    "model.constraints_cannot_link = pyo.Constraint(model.CL,model.CL,model.K,rule=cannot_link_rule)\n",
    "\n",
    "def must_link_rule_g1(model,i,j):\n",
    "    return(model.a[i,j] == model.a[must_link_g1[0],j])\n",
    "model.constraints_must_link_g1 = pyo.Constraint(model.MLG1,model.K,rule=must_link_rule_g1)\n",
    "\n",
    "def must_link_rule_g2(model,i,j):\n",
    "    return(model.a[i,j] == model.a[must_link_g2[0],j])\n",
    "model.constraints_must_link_g2 = pyo.Constraint(model.MLG2,model.K,rule=must_link_rule_g2)\n",
    "\n",
    "    \n",
    "#Run with new constraints \n",
    "solver = pyo.SolverFactory('knitroampl')\n",
    "results = solver.solve(model, tee=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1408511",
   "metadata": {},
   "source": [
    "### Output visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e67665c0-905d-4c7f-b85a-85aff95bed6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster 0 contains 111 observations\n",
      "Cluster 1 contains 109 observations\n",
      "Cluster 2 contains 80 observations\n",
      "Total cost is 29286.08091910009\n"
     ]
    }
   ],
   "source": [
    "draw_figure(nb_observations,nb_clusters,model, \"Knitro solution\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51b1ac72-625a-4119-ad48-01ec10cb3aec",
   "metadata": {},
   "source": [
    "## Constrained clustering\n",
    "\n",
    "### Problem description\n",
    "\n",
    "Another common case in clustering is to have lower and/or upper bounds on the cluster sizes. This is known as \"constrained clustering\".\n",
    "\n",
    "Let $u_{limit} \\in \\mathbb{R^+}$ be the maximum number of observations in a cluster.\n",
    "\n",
    "Let $l_{limit} \\in \\mathbb{R^+}$ be the minimum number of observations in a cluster.\n",
    "\n",
    "### Input data\n",
    "To illustrate this, we are going to use some new observations from the `kmeans2.csv` file.\n",
    "We look to partition these observations into 10 clusters such that the size of each cluster lies between 8 and 12. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "898b29aa-dc3e-4fa1-9397-2b3c3f5fa4c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            X          Y\n",
      "0    2.072345  -3.241693\n",
      "1   17.936710  15.784810\n",
      "2    1.083576   7.319176\n",
      "3   11.120670  14.406780\n",
      "4   23.711550   2.557729\n",
      "..        ...        ...\n",
      "85   5.987025   7.456533\n",
      "86  12.639020  14.350810\n",
      "87   7.392535  22.613040\n",
      "88  10.372120  -1.258270\n",
      "89 -19.017910   0.650730\n",
      "\n",
      "[90 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('kmeans2.csv')\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "41b1eadc-4157-4d90-bd9b-3abdda7e54ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = data['X'].values\n",
    "Y = data['Y'].values \n",
    "observations_positions = np.array(list(zip(X,Y)))\n",
    "nb_observations = len(observations_positions)\n",
    "nb_clusters = 10\n",
    "draw_data(observations_positions, \"Example\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9488ed4b",
   "metadata": {},
   "source": [
    "### Resolution without bounds on cluster sizes\n",
    "\n",
    "Let's solve the problem using the model defined in the previous section. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "53b2b49a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Artelys Knitro 14.1.0: \n",
      "=======================================\n",
      "          Commercial License\n",
      "         Artelys Knitro 14.1.0\n",
      "=======================================\n",
      "\n",
      "No start point provided -- Knitro computing one.\n",
      "\n",
      "WARNING: Problem appears to have nonlinear equalities and be non-convex.\n",
      "         The Knitro mixed integer solver is designed for convex problems.\n",
      "         For non-convex problems it is only a heuristic, and the reported\n",
      "         bounds and optimality claims cannot be verified.\n",
      "\n",
      "concurrent_evals         0\n",
      "datacheck                0\n",
      "hessian_no_f             1\n",
      "hessopt                  1\n",
      "The problem is identified as a MIQCQP.\n",
      "Knitro changing mip_method from AUTO to 1.\n",
      "Knitro changing mip_rootalg from AUTO to 1.\n",
      "Knitro changing mip_lpalg from AUTO to 3.\n",
      "Knitro changing mip_branchrule from AUTO to 2.\n",
      "Knitro changing mip_selectrule from AUTO to 2.\n",
      "Knitro changing mip_mir from AUTO to 2.\n",
      "Knitro changing mip_clique from AUTO to 0.\n",
      "Knitro changing mip_zerohalf from AUTO to 0.\n",
      "Knitro changing mip_liftproject from AUTO to 0.\n",
      "Knitro changing mip_knapsack from AUTO to 2.\n",
      "Knitro changing mip_gomory from AUTO to 0.\n",
      "Knitro changing mip_cut_flowcover from AUTO to 2.\n",
      "Knitro changing mip_cut_probing from AUTO to 1.\n",
      "Knitro changing mip_rounding from AUTO to 3.\n",
      "Knitro changing mip_heuristic_strategy from AUTO to 1.\n",
      "Knitro changing mip_heuristic_feaspump from AUTO to 1.\n",
      "Knitro changing mip_heuristic_misqp from AUTO to 0.\n",
      "Knitro changing mip_heuristic_mpec from AUTO to 1.\n",
      "Knitro changing mip_heuristic_diving from AUTO to 0.\n",
      "Knitro changing mip_heuristic_lns from AUTO to 0.\n",
      "Knitro changing mip_heuristic_localsearch from AUTO to 1.\n",
      "Knitro changing mip_pseudoinit from AUTO to 1.\n",
      "\n",
      "Problem Characteristics                                 (   Presolved)\n",
      "-----------------------\n",
      "Objective goal:  Minimize\n",
      "Objective type:  quadratic\n",
      "Number of variables:                               1820 (        1820)\n",
      "    bounded below only:                             900 (         900)\n",
      "    bounded above only:                               0 (           0)\n",
      "    bounded below and above:                        900 (         900)\n",
      "    fixed:                                            0 (           0)\n",
      "    free:                                            20 (          20)\n",
      "Number of binary variables:                         900 (         900)\n",
      "Number of integer variables:                          0 (           0)\n",
      "Number of constraints:                             1010 (        1010)\n",
      "    linear equalities:                               90 (          90)\n",
      "    quadratic equalities:                           920 (         920)\n",
      "    gen. nonlinear equalities:                        0 (           0)\n",
      "    linear one-sided inequalities:                    0 (           0)\n",
      "    quadratic one-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear one-sided inequalities:            0 (           0)\n",
      "    linear two-sided inequalities:                    0 (           0)\n",
      "    quadratic two-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear two-sided inequalities:            0 (           0)\n",
      "Number of nonzeros in Jacobian:                    5420 (        5420)\n",
      "Number of nonzeros in Hessian:                     2720 (        2720)\n",
      "\n",
      "Knitro using Branch and Bound method with 8 threads.\n",
      "\n",
      "Initial points\n",
      "--------------\n",
      "No initial point provided for the root node relaxation.\n",
      "No primal point provided for the MIP.\n",
      "\n",
      "Root node relaxation\n",
      "--------------------\n",
      "\n",
      " Iter      Objective      Feasibility        Optimality       Time \n",
      "                             error              error        (secs)\n",
      " ----      ---------      -----------        ----------      ------\n",
      "    1        1489.96          1101.54           3.28216       0.124\n",
      "    2        2482.99          1044.72           3.82035       0.140\n",
      "    3        6271.23          815.034           4.63892       0.163\n",
      "    4        7965.46          702.519           18.5155       0.191\n",
      "    5        12424.0          410.141           27.0727       0.225\n",
      "    6        17871.9         0.231274           12.8653       0.262\n",
      "    7        17736.2          3.52975           8.48360       0.300\n",
      "    8        17578.9          3.72570           12.2615       0.346\n",
      "    9        17464.5          1.40190           30.7010       0.386\n",
      "   10        17381.0          1.29736           5.58370       0.405\n",
      "   11        17188.5         0.416642           5.57479       0.426\n",
      "   12        16911.7         0.744502           46.2014       0.446\n",
      "   13        16473.6          1.33078           58.2969       0.486\n",
      "   14        16463.3          1.30617           56.5002       0.510\n",
      "   15        16446.1          1.22791           7.31768       0.539\n",
      "   16        16098.2         0.559629           14.5196       0.578\n",
      "   17        14763.1          3.60201           78.6022       0.619\n",
      "   18        14365.2          2.41139           169.711       0.661\n",
      "   19        14351.8          3.20843           185.274       0.693\n",
      "   20        14429.4          2.30497           185.259       0.730\n",
      "   21        14542.4          2.24456           185.274       0.752\n",
      "   22        14188.4          1.17612           50.8083       0.779\n",
      "   23        13384.4         0.946353           111.146       0.810\n",
      "   24        13042.5         0.318150           105.294       0.832\n",
      "   25        12855.7         0.287074           58.4667       0.857\n",
      "   26        12446.7         0.338125           40.3254       0.871\n",
      "   27        12230.5         0.368240           36.4192       0.891\n",
      "   28        12142.3         0.359540           37.0595       0.921\n",
      "   29        12008.2         0.364175           36.5870       0.947\n",
      "   30        11951.2         0.355127           37.0224       0.987\n",
      "   31        11878.3         0.353497           37.1777       1.007\n",
      "   32        11856.8         0.348571           37.3519       1.029\n",
      "   33        11867.6      4.24031e-02           37.5511       1.047\n",
      "   34        11861.0      6.96911e-05           38.0918       1.078\n",
      "   35        11844.8      3.26920e-04           39.2155       1.101\n",
      "   36        11837.6      6.40843e-04           41.1954       1.135\n",
      "   37        11836.1      4.34746e-05           41.5221       1.164\n",
      "   38        11834.6      3.78373e-04           41.5357       1.194\n",
      "   39        11825.7      1.56731e-02           41.1890       1.224\n",
      "   40        11821.5      1.89520e-02           41.0023       1.244\n",
      "   41        11818.8      2.01761e-02           43.7812       1.272\n",
      "   42        11819.0      9.45522e-07           43.8565       1.297\n",
      "   43        11818.1      5.62474e-05           43.3360       1.339\n",
      "   44        11812.6      2.96524e-03           44.7207       1.366\n",
      "   45        11788.7      3.47412e-02           57.1067       1.382\n",
      "   46        11778.2      3.53798e-02           60.3223       1.407\n",
      "   47        11770.5      3.76476e-02           61.1950       1.429\n",
      "   48        11768.8      3.65803e-02           60.1286       1.457\n",
      "   49        11762.2      3.74282e-02           60.6307       1.474\n",
      "   50        11728.9      5.02712e-02           72.0284       1.491\n",
      "   51        11726.7      8.09304e-04           73.3469       1.516\n",
      "   52        11726.2      7.63831e-05           73.0338       1.541\n",
      "   53        11723.1      2.09619e-03           63.5331       1.557\n",
      "   54        11720.1      3.00491e-04           62.5618       1.586\n",
      "   55        11714.1      2.15672e-03           60.0065       1.608\n",
      "   56        11647.6         0.141426           42.3000       1.636\n",
      "   57        11633.3      3.89063e-03           41.2549       1.669\n",
      "   58        11613.2      7.42841e-03           40.0120       1.699\n",
      "   59        11608.6      4.83366e-04           39.6924       1.730\n",
      "   60        11573.1      3.65696e-02           37.8700       1.751\n",
      "   61        11520.8      7.85215e-02           35.2025       1.776\n",
      "   62        11489.0      1.25082e-02           31.1300       1.805\n",
      "   63        11467.0      3.84008e-03           19.9889       1.825\n",
      "   64        11466.3      3.83700e-03           19.9889       1.841\n",
      "   65        11448.8      6.01568e-03           19.9886       1.867\n",
      "   66        11438.3      6.69374e-03           19.9882       1.881\n",
      "   67        11431.1      3.92442e-04           19.9883       1.899\n",
      "   68        11425.0      5.70812e-04           19.9882       1.923\n",
      "   69        11420.3      1.76943e-04           19.9883       1.944\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   70        11397.5      6.26694e-03           19.9887       1.966\n",
      "   71        11381.2      4.42987e-03           19.9892       1.989\n",
      "   72        11360.8      5.20498e-03           22.6700       2.013\n",
      "   73        11348.6      1.86841e-03           25.0612       2.034\n",
      "   74        11336.4      5.92938e-03           25.2675       2.064\n",
      "   75        11304.6      4.32419e-02           32.1321       2.101\n",
      "   76        11281.2      2.87446e-02           41.4445       2.126\n",
      "   77        11244.5      6.21144e-02           55.1569       2.151\n",
      "   78        11227.2      3.94910e-03           56.2608       2.167\n",
      "   79        11225.2      4.01805e-03           50.9597       2.196\n",
      "   80        11140.1      8.79540e-02           55.0379       2.211\n",
      "   81        11119.0      4.55821e-02           55.7404       2.230\n",
      "   82        11118.5      1.34220e-02           55.9759       2.266\n",
      "   83        11117.0      4.28332e-03           56.1908       2.286\n",
      "   84        11098.6      3.83726e-02           59.0834       2.304\n",
      "   85        11019.5      7.59419e-02           74.9174       2.335\n",
      "   86        10968.2      2.55007e-02           84.1725       2.362\n",
      "   87        10905.6      3.47228e-02           92.1686       2.381\n",
      "   88        10904.2      3.43014e-02           65.8186       2.398\n",
      "   89        10895.1      3.11090e-02           66.5394       2.409\n",
      "   90        10885.5      3.01389e-02           64.0775       2.424\n",
      "   91        10882.5      3.41936e-04           64.9076       2.455\n",
      "   92        10873.6      3.70424e-03           68.2986       2.488\n",
      "   93        10872.3      7.66304e-05           68.3409       2.515\n",
      "   94        10861.7      5.08627e-03           66.1719       2.545\n",
      "   95        10856.9      1.36198e-03           66.1520       2.575\n",
      "   96        10828.1      1.19091e-02           69.3369       2.611\n",
      "   97        10794.4      1.17539e-02           74.0551       2.641\n",
      "   98        10757.4      1.32850e-02           79.0653       2.673\n",
      "   99        10737.0      5.58005e-03           81.9008       2.701\n",
      "  100        10706.6      9.36373e-03           86.4570       2.735\n",
      "  101        10706.4      9.35902e-03           82.9746       2.761\n",
      "  102        10702.3      1.00542e-03           83.0204       2.783\n",
      "  103        10697.2      1.13324e-03           80.2964       2.809\n",
      "  104        10673.7      2.52600e-02           79.1070       2.834\n",
      "  105        10617.0      4.03440e-02           85.4201       2.865\n",
      "  106        10592.5      3.91661e-02           81.5711       2.893\n",
      "  107        10581.1      1.24606e-03           83.1531       2.921\n",
      "  108        10575.8      2.93929e-04           84.0578       2.958\n",
      "  109        10568.4      2.24614e-03           74.3148       2.977\n",
      "  110        10554.2      2.83464e-03           72.1612       3.006\n",
      "  111        10499.6      2.24449e-02           70.9392       3.024\n",
      "  112        10472.2      1.83493e-02           71.7967       3.049\n",
      "  113        10467.3      1.19347e-03           72.8153       3.078\n",
      "  114        10445.0      5.64651e-03           72.3177       3.102\n",
      "  115        10419.2      7.75763e-03           75.9182       3.132\n",
      "  116        10400.4      3.94651e-03           78.8750       3.161\n",
      "  117        10390.6      3.82291e-03           70.2931       3.187\n",
      "  118        10369.1      8.18881e-03           70.3956       3.218\n",
      "  119        10361.7      8.48929e-03           68.1316       3.245\n",
      "  120        10347.7      1.00426e-02           66.8607       3.263\n",
      "  121        10335.6      1.93525e-03           69.2117       3.289\n",
      "  122        10328.1      9.80329e-04           70.9095       3.314\n",
      "  123        10313.8      3.02786e-03           73.8400       3.347\n",
      "  124        10293.7      4.32931e-03           62.2713       3.403\n",
      "  125        10249.3      1.61286e-02           36.5968       3.457\n",
      "  126        10219.7      2.39815e-02           36.1681       3.493\n",
      "  127        10172.2      5.93895e-02           32.7025       3.523\n",
      "  128        10171.0      5.81407e-02           32.5998       3.549\n",
      "  129        10146.4      5.44524e-02           32.1710       3.577\n",
      "  130        10122.2      2.94162e-02           31.6933       3.624\n",
      "  131        10080.3      3.26401e-02           37.6011       3.651\n",
      "  132        10049.2      3.10202e-02           44.0708       3.687\n",
      "  133        10031.9      3.07795e-02           36.8014       3.710\n",
      "  134        10001.2      4.43892e-02           35.6035       3.732\n",
      "  135        9953.15      5.37340e-02           35.1678       3.760\n",
      "  136        9911.82      6.88839e-02           32.1824       3.781\n",
      "  137        9909.33      6.72913e-02           26.5321       3.815\n",
      "  138        9909.82      1.56611e-04           27.1871       3.844\n",
      "  139        9901.61      2.74824e-03           29.5277       3.869\n",
      "  140        9894.45      2.54609e-03           32.0211       3.893\n",
      "  141        9853.53      6.89554e-02           45.1352       3.913\n",
      "  142        9811.04      5.23071e-02           56.6399       3.936\n",
      "  143        9801.41      5.42178e-02           48.9296       3.947\n",
      "  144        9798.57      5.32338e-02           47.3920       3.964\n",
      "  145        9753.42         0.174887           52.4695       3.978\n",
      "  146        9744.55         0.159296           49.4517       3.991\n",
      "  147        9724.95         0.155484           49.3220       4.000\n",
      "  148        9705.55         0.133485           51.0453       4.025\n",
      "  149        9683.26         0.142192           54.5766       4.049\n",
      "  150        9661.91         0.126126           44.9030       4.069\n",
      "  151        9648.63         0.127884           39.4558       4.085\n",
      "  152        9628.77      1.07067e-02           43.7200       4.113\n",
      "  153        9618.88      2.41565e-03           43.8997       4.138\n",
      "  154        9591.56      1.56125e-02           44.6749       4.153\n",
      "  155        9536.97      2.02397e-02           42.1135       4.182\n",
      "  156        9461.32      5.79797e-02           37.5958       4.204\n",
      "  157        9411.61      6.51808e-02           32.7959       4.222\n",
      "  158        9403.86      6.13030e-02           32.8390       4.245\n",
      "  159        9396.31      5.66657e-02           32.5581       4.276\n",
      "  160        9380.45      6.24056e-02           33.0062       4.289\n",
      "  161        9359.73      5.72921e-02           25.8921       4.319\n",
      "  162        9345.30      5.99903e-02           18.6215       4.342\n",
      "  163        9332.01      8.82832e-03           21.1367       4.364\n",
      "  164        9315.37      1.38164e-02           16.8238       4.394\n",
      "  165        9290.37      3.20584e-02           21.8388       4.427\n",
      "  166        9262.90      3.32723e-02           20.6855       4.476\n",
      "  167        9256.65      3.37975e-02           18.7267       4.503\n",
      "  168        9243.93      3.20329e-02           19.1481       4.525\n",
      "  169        9218.60      4.11652e-02           17.2313       4.549\n",
      "  170        9185.76      5.47151e-02           13.9419       4.570\n",
      "  171        9142.70         0.106862           11.3992       4.585\n",
      "  172        9131.42      9.31488e-02           3.97282       4.619\n",
      "  173        9129.10      9.18297e-02           3.46072       4.638\n",
      "  174        9125.04      3.13673e-04           4.02190       4.664\n",
      "  175        9118.37      1.08446e-03           4.10463       4.701\n",
      "  176        9110.83      2.69033e-03           4.18618       4.724\n",
      "  177        9101.15      2.39034e-03           6.10538       4.762\n",
      "  178        9065.00      2.43103e-02           4.56648       4.784\n",
      "  179        9053.62      2.41001e-02           5.63037       4.806\n",
      "  180        9048.39      2.41037e-02           5.44062       4.818\n",
      "  181        9014.23      2.23172e-02           4.93828       4.837\n",
      "  182        9001.95      1.92068e-03           6.35493       4.857\n",
      "  183        8916.80         0.102669           4.26265       4.885\n",
      "  184        8847.54      5.26958e-02           8.57450       4.923\n",
      "  185        8800.21      6.99167e-02           10.0662       4.944\n",
      "  186        8780.03      7.12152e-02           9.78998       4.963\n",
      "  187        8767.48      6.80838e-02           9.07468       4.989\n",
      "  188        8762.64      8.62586e-04           9.14992       5.019\n",
      "  189        8722.84      5.00226e-02           16.4220       5.044\n",
      "  190        8716.24      2.32115e-03           17.1190       5.064\n",
      "  191        8688.47      3.13820e-02           19.0994       5.087\n",
      "  192        8683.25      3.10789e-02           11.1368       5.112\n",
      "  193        8640.95      1.75242e-02           15.3846       5.136\n",
      "  194        8621.66      2.02247e-02           12.0362       5.154\n",
      "  195        8603.80      3.56413e-03           14.5594       5.180\n",
      "  196        8600.55      3.62686e-03           11.3277       5.196\n",
      "  197        8518.62         0.133639           17.9226       5.213\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  198        8468.91         0.179778           20.6151       5.226\n",
      "  199        8471.05      1.34727e-04           21.1623       5.255\n",
      "  200        8442.81      7.68367e-03           23.1447       5.282\n",
      "  201        8193.70         0.435082           38.4497       5.304\n",
      "  202        8134.05      3.39424e-02           26.5251       5.328\n",
      "  203        8100.75      7.25874e-03           24.9267       5.355\n",
      "  204        8085.31      1.26062e-03           24.1893       5.376\n",
      "  205        7993.69      6.24085e-02           20.1974       5.394\n",
      "  206        7866.89      9.78713e-02           28.6568       5.412\n",
      "  207        7828.76      8.67174e-03           33.1280       5.431\n",
      "  208        7754.67      3.23255e-02           34.3197       5.447\n",
      "  209        7722.87      4.21594e-02           33.3427       5.457\n",
      "  210        7649.47      6.71864e-02           39.4089       5.479\n",
      "  211        7519.35         0.102346           36.2029       5.499\n",
      "  212        7538.40         0.103964           32.4448       5.514\n",
      "  213        7523.80         0.102595           34.6261       5.526\n",
      "  214        7470.61         0.163303           32.7013       5.544\n",
      "  215        7469.01      5.79347e-04           33.5435       5.567\n",
      "  216        7404.30      2.51330e-02           42.1330       5.589\n",
      "  217        7405.12      2.49050e-02           41.7986       5.621\n",
      "  218        7343.91      4.47885e-02           44.1860       5.639\n",
      "  219        7298.78      4.96550e-02           38.1458       5.658\n",
      "  220        7202.07      7.02689e-02           31.7569       5.674\n",
      "  221        7178.77      6.88803e-02           31.6436       5.698\n",
      "  222        7142.21      7.45690e-02           32.5881       5.714\n",
      "  223        7078.05      2.54525e-02           38.1792       5.731\n",
      "  224        7049.31      5.37484e-03           42.0182       5.761\n",
      "  225        6942.73      7.42393e-02           55.2803       5.786\n",
      "  226        6938.41      2.39625e-04           55.5135       5.809\n",
      "  227        6931.61      3.14716e-04           55.7640       5.827\n",
      "  228        6908.73      6.37690e-03           55.6194       5.841\n",
      "  229        6773.94         0.149067           54.5401       5.858\n",
      "  230        6721.94         0.141701           47.1782       5.877\n",
      "  231        6662.23         0.156650           45.5232       5.889\n",
      "  232        6647.87      2.96175e-03           45.8180       5.907\n",
      "  233        6607.97      1.96279e-02           37.3039       5.929\n",
      "  234        6582.19      7.20427e-03           39.4706       5.955\n",
      "  235        6470.03         0.114919           48.3942       5.984\n",
      "  236        6421.52      1.21406e-02           51.7354       6.001\n",
      "  237        6416.92      9.37256e-05           52.0295       6.025\n",
      "  238        6322.75      5.64380e-02           41.5617       6.044\n",
      "  239        6317.54      3.05855e-04           42.8098       6.059\n",
      "  240        6280.14      1.49620e-02           36.8455       6.077\n",
      "  241        6254.14      3.00764e-03           39.3329       6.098\n",
      "  242        6188.03      2.14308e-02           42.5489       6.119\n",
      "  243        6126.64      1.65131e-02           51.8867       6.137\n",
      "  244        6118.96      1.63945e-02           37.1601       6.163\n",
      "  245        6101.96      1.57018e-02           36.4923       6.188\n",
      "  246        6095.83      5.51846e-04           33.5538       6.206\n",
      "  247        6088.31      8.39627e-04           33.8365       6.229\n",
      "  248        6070.82      4.14717e-03           34.4013       6.255\n",
      "  249        6060.38      5.22396e-03           34.6945       6.272\n",
      "  250        6050.19      1.28850e-03           35.0002       6.296\n",
      "  251        6033.95      2.74007e-03           35.3257       6.326\n",
      "  252        5991.74      1.80643e-02           36.3151       6.341\n",
      "  253        5982.42      1.22129e-03           36.5969       6.359\n",
      "  254        5925.36      3.80674e-02           38.1361       6.381\n",
      "  255        5917.71      1.07457e-03           31.2254       6.398\n",
      "  256        5875.17      2.06483e-02           31.4914       6.414\n",
      "  257        5858.95      7.29744e-02           31.6391       6.439\n",
      "  258        5852.84      7.07494e-02           31.7342       6.460\n",
      "  259        5833.80      2.27387e-02           32.1797       6.473\n",
      "  260        5828.51      2.21381e-02           32.2844       6.494\n",
      "  261        5804.01      2.13075e-02           32.7009       6.507\n",
      "  262        5786.31      2.32992e-02           33.1645       6.522\n",
      "  263        5777.30      2.29506e-02           33.5098       6.535\n",
      "  264        5761.84      5.29077e-03           34.2144       6.550\n",
      "  265        5744.90      1.23018e-02           35.7465       6.568\n",
      "  266        5680.81      9.91220e-02           32.9060       6.589\n",
      "  267        5652.61         0.105450           32.6361       6.605\n",
      "  268        5636.31      9.08846e-02           32.4342       6.626\n",
      "  269        5619.45      8.82491e-02           32.2077       6.649\n",
      "  270        5600.19      8.41470e-02           34.6709       6.662\n",
      "  271        5583.72      7.51783e-02           38.5024       6.681\n",
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      "  276        5482.17      4.96842e-02           27.4844       6.774\n",
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      "  279        5405.72      4.11649e-02           33.8648       6.825\n",
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      "  281        5378.54      4.60771e-02           31.0350       6.859\n",
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      "  284        5322.78      8.51128e-03           13.1309       6.918\n",
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      "  320        4985.47      4.48506e-02           2.31038       7.601\n",
      "  321        4972.72      4.81392e-02           7.36663       7.620\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  322        4973.18      1.92967e-04           7.40674       7.646\n",
      "  323        4964.07      3.20782e-02           8.38636       7.660\n",
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      "  420        4131.64         0.199730           6.59407       9.570\n",
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      "  422        4087.96         0.128541           6.76314       9.608\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  443        3942.36      9.85628e-02           7.03173      10.036\n",
      "  444        3938.22      8.60847e-02           4.97706      10.064\n",
      "  445        3853.96         0.362296           12.2012      10.082\n",
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      "  493        3395.31         0.355653           12.3620      11.104\n",
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      "  508        3299.43         0.116229           2.52477      11.361\n",
      "  509        3302.21         0.110253           4.99347      11.382\n",
      "  510        3295.02         0.119735           4.71227      11.399\n",
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      "  518        3274.48      4.96657e-03          0.989710      11.555\n",
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      "  520        3266.91      3.51366e-02           2.32074      11.625\n",
      "  521        3251.59         0.224473           6.10272      11.670\n",
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      "  524        3227.37         0.147680          0.861438      11.771\n",
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      "  530        3202.70         0.172147           4.98352      11.918\n",
      "  531        3188.80         0.617026           4.88307      11.944\n",
      "  532        3187.65         0.565918           4.10089      11.971\n",
      "  533        3184.53         0.254290           5.43168      11.996\n",
      "  534        3174.73         0.196573           6.94316      12.012\n",
      "  535        3175.18      1.08529e-03           4.90419      12.030\n",
      "  536        3173.13      2.64231e-03           5.06872      12.069\n",
      "  537        3158.52      7.27153e-02           7.14664      12.087\n",
      "  538        3144.99         0.146628           12.3846      12.115\n",
      "  539        3141.19         0.136454           12.4612      12.136\n",
      "  540        3138.23         0.118696           13.3705      12.159\n",
      "  541        3119.48         0.253338           17.8454      12.174\n",
      "  542        3114.75         0.188249           14.0061      12.203\n",
      "  543        3089.55         0.260442           20.6820      12.222\n",
      "  544        3090.08      1.60633e-03           10.0346      12.244\n",
      "  545        3054.02         0.209070           10.5650      12.266\n",
      "  546        3048.14         0.212173           12.6018      12.282\n",
      "  547        3044.87         0.174883           6.76985      12.296\n",
      "  548        3008.05         0.316034           6.09104      12.310\n",
      "  549        3006.48         0.285343           5.65725      12.344\n",
      "  550        3006.82         0.231201           5.64788      12.373\n",
      "  551        3008.54         0.121206           5.64386      12.415\n",
      "  552        3007.52         0.110023           3.44549      12.450\n",
      "  553        3004.64      2.66321e-02           3.25658      12.509\n",
      "  554        2993.67      7.02675e-02           5.94830      12.544\n",
      "  555        2967.21         0.296392           9.50364      12.587\n",
      "  556        2949.25         0.313470           9.60519      12.637\n",
      "  557        2888.94          1.06678           8.10268      12.660\n",
      "  558        2897.72          1.07522           7.09286      12.697\n",
      "  559        2892.87         0.898081           8.10189      12.709\n",
      "  560        2893.09         0.870838           7.93724      12.727\n",
      "  561        2892.74         0.292397           6.00617      12.749\n",
      "  562        2876.97         0.186492           7.20690      12.776\n",
      "  563        2873.80         0.193102           4.98204      12.799\n",
      "  564        2873.35      3.77208e-03           5.39077      12.824\n",
      "  565        2857.52      8.23695e-02           5.50417      12.846\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  566        2849.57      2.38948e-02           8.74892      12.884\n",
      "  567        2836.31      8.85068e-02           9.67932      12.915\n",
      "  568        2823.44      5.05111e-02           5.41154      12.939\n",
      "  569        2820.39      5.09183e-02           5.62313      12.956\n",
      "  570        2814.26      7.91706e-03           6.97197      12.989\n",
      "  571        2803.86      2.51283e-02           3.53592      13.012\n",
      "  572        2799.72      2.39008e-02           3.34088      13.029\n",
      "  573        2792.42      1.79283e-02           2.82522      13.056\n",
      "  574        2790.99      1.76080e-02           2.35273      13.070\n",
      "  575        2789.15      3.18059e-03           2.11872      13.093\n",
      "  576        2788.75      3.26752e-03           2.07434      13.125\n",
      "  577        2773.34         0.152716           8.52316      13.145\n",
      "  578        2774.30         0.151488           5.94244      13.178\n",
      "  579        2762.26      9.81306e-02           1.85258      13.211\n",
      "  580        2754.64      9.78885e-02           1.90377      13.241\n",
      "  581        2754.77      7.20119e-02           2.54180      13.267\n",
      "  582        2748.31         0.158029           4.52366      13.283\n",
      "  583        2749.24      8.33514e-04           4.31555      13.312\n",
      "  584        2749.26      7.11341e-05       2.77925e-02      13.322\n",
      "  585        2748.98      4.95665e-07       6.85121e-04      13.332\n",
      "  586        2748.98      4.95665e-07       6.85121e-04      13.346\n",
      "\n",
      "Tree search\n",
      "-----------\n",
      "\n",
      "       Nodes        Best solution   Best bound      Gap       Time \n",
      "   Expl  |  Unexpl      value         value                  (secs)\n",
      "   ---------------  -------------   ----------      ---      ------\n",
      "      1       2      2748.98 FCRD         -inf               13.409\n",
      "      3       0      2748.98           2748.98     -0.00%    13.550\n",
      "\n",
      "EXIT: Optimal solution found (assuming convexity).\n",
      "\n",
      "HINT: The problem may be a non-convex mixed-integer problem.  Set\n",
      "      mip_multistart=1 to enable a mixed-integer multistart heuristic,\n",
      "      which may improve the chances of finding the global solution.\n",
      "\n",
      "Final Statistics for MIP\n",
      "------------------------\n",
      "Final objective value               =  2.74898309722742e+03\n",
      "Final bound value                   =  2.74898448038897e+03\n",
      "Final optimality gap (abs / rel)    =  -1.38e-03 / -5.03e-07 (-0.00%)\n",
      "# of root cutting plane rounds      =  1\n",
      "# of restarts                       =  0\n",
      "# of nodes processed                =  3 (13.319s)\n",
      "# of strong branching evaluations   =  0 (0.000s)\n",
      "# of function evaluations           =  0 (0.000s)\n",
      "# of gradient evaluations           =  0 (0.000s)\n",
      "# of hessian evaluations            =  0 (0.000s)\n",
      "# of hessian-vector evaluations     =  0\n",
      "# of subproblems processed          =  2 (13.355s)\n",
      "Total program time (secs)           =  13.983 (14.797 CPU time)\n",
      "Time spent in evaluations (secs)    =  0.000\n",
      "\n",
      "Cuts statistics (gen / add)\n",
      "---------------------------\n",
      "Knapsack cuts                       =  0 / 0\n",
      "Mixed-integer rounding cuts         =  0 / 0\n",
      "Flow-cover cuts                     =  0 / 0\n",
      "Probing cuts                        =  0 / 0\n",
      "\n",
      "Heuristics statistics (calls / successes / time)\n",
      "------------------------------------------------\n",
      "Feasibility pump                    =  0 / 0 / 0.000s\n",
      "Rounding heuristic                  =  1 / 1 / 0.041s\n",
      "MPEC heuristic                      =  0 / 0 / 0.000s\n",
      "Local search heuristic              =  5 / 0 / 1.861s\n",
      "\n",
      "===========================================================================\n",
      "\n",
      "\b"
     ]
    }
   ],
   "source": [
    "model = pyo.ConcreteModel()\n",
    "build_model(nb_observations,nb_clusters)\n",
    "solver = pyo.SolverFactory('knitroampl')\n",
    "results = solver.solve(model, tee=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1e45f9ea-7064-4722-92fe-4b7660831582",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster 0 contains 15 observations\n",
      "Cluster 1 contains 8 observations\n",
      "Cluster 2 contains 12 observations\n",
      "Cluster 3 contains 5 observations\n",
      "Cluster 4 contains 7 observations\n",
      "Cluster 5 contains 12 observations\n",
      "Cluster 6 contains 9 observations\n",
      "Cluster 7 contains 6 observations\n",
      "Cluster 8 contains 5 observations\n",
      "Cluster 9 contains 11 observations\n",
      "Total cost is 2748.983097227423\n"
     ]
    }
   ],
   "source": [
    "draw_figure(nb_observations,nb_clusters,model, \"Clusters with various number of elements\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f72faa0-6fc8-425d-a5d3-9d4a0aa45c0a",
   "metadata": {},
   "source": [
    "In this case, some clusters have less observations (or more observations) than required. We need to add new constraints to the model in order to take into account the limits on the number of observations in each cluster."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93b73aba",
   "metadata": {},
   "source": [
    "### Mathematical formulation\n",
    "\n",
    "We add the two following set of constraints to the previous mathematical model.\n",
    "\n",
    "* Cluster size upper bound\n",
    "\n",
    "$$\n",
    "\\forall k = 1, \\dots, K, \\qquad \\sum_{i=1}^N {a^k_i} \\leq u_{limit}\n",
    "$$\n",
    "\n",
    "* Cluster size lower bound\n",
    "\n",
    "$$\n",
    "\\forall k = 1, \\dots, K, \\qquad \\sum_{i=1}^N {a^k_i} \\geq l_{limit}\n",
    "$$\n",
    "\n",
    "### Implementation with Pyomo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "971f0e70-842d-4e68-b78d-8dc3efdd0824",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Artelys Knitro 14.1.0: \n",
      "=======================================\n",
      "          Commercial License\n",
      "         Artelys Knitro 14.1.0\n",
      "=======================================\n",
      "\n",
      "WARNING: Problem appears to have nonlinear equalities and be non-convex.\n",
      "         The Knitro mixed integer solver is designed for convex problems.\n",
      "         For non-convex problems it is only a heuristic, and the reported\n",
      "         bounds and optimality claims cannot be verified.\n",
      "\n",
      "concurrent_evals         0\n",
      "datacheck                0\n",
      "hessian_no_f             1\n",
      "hessopt                  1\n",
      "The problem is identified as a MIQCQP.\n",
      "Knitro changing mip_method from AUTO to 1.\n",
      "Knitro changing mip_rootalg from AUTO to 1.\n",
      "Knitro changing mip_lpalg from AUTO to 3.\n",
      "Knitro changing mip_branchrule from AUTO to 2.\n",
      "Knitro changing mip_selectrule from AUTO to 2.\n",
      "Knitro changing mip_mir from AUTO to 2.\n",
      "Knitro changing mip_clique from AUTO to 0.\n",
      "Knitro changing mip_zerohalf from AUTO to 0.\n",
      "Knitro changing mip_liftproject from AUTO to 0.\n",
      "Knitro changing mip_knapsack from AUTO to 2.\n",
      "Knitro changing mip_gomory from AUTO to 0.\n",
      "Knitro changing mip_cut_flowcover from AUTO to 2.\n",
      "Knitro changing mip_cut_probing from AUTO to 1.\n",
      "Knitro changing mip_rounding from AUTO to 3.\n",
      "Knitro changing mip_heuristic_strategy from AUTO to 1.\n",
      "Knitro changing mip_heuristic_feaspump from AUTO to 1.\n",
      "Knitro changing mip_heuristic_misqp from AUTO to 0.\n",
      "Knitro changing mip_heuristic_mpec from AUTO to 1.\n",
      "Knitro changing mip_heuristic_diving from AUTO to 0.\n",
      "Knitro changing mip_heuristic_lns from AUTO to 0.\n",
      "Knitro changing mip_heuristic_localsearch from AUTO to 1.\n",
      "Knitro changing mip_pseudoinit from AUTO to 1.\n",
      "\n",
      "Problem Characteristics                                 (   Presolved)\n",
      "-----------------------\n",
      "Objective goal:  Minimize\n",
      "Objective type:  quadratic\n",
      "Number of variables:                               1820 (        1820)\n",
      "    bounded below only:                             900 (         900)\n",
      "    bounded above only:                               0 (           0)\n",
      "    bounded below and above:                        900 (         900)\n",
      "    fixed:                                            0 (           0)\n",
      "    free:                                            20 (          20)\n",
      "Number of binary variables:                         900 (         900)\n",
      "Number of integer variables:                          0 (           0)\n",
      "Number of constraints:                             1030 (        1030)\n",
      "    linear equalities:                               90 (          90)\n",
      "    quadratic equalities:                           920 (         920)\n",
      "    gen. nonlinear equalities:                        0 (           0)\n",
      "    linear one-sided inequalities:                   20 (          20)\n",
      "    quadratic one-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear one-sided inequalities:            0 (           0)\n",
      "    linear two-sided inequalities:                    0 (           0)\n",
      "    quadratic two-sided inequalities:                 0 (           0)\n",
      "    gen. nonlinear two-sided inequalities:            0 (           0)\n",
      "Number of nonzeros in Jacobian:                    7220 (        7220)\n",
      "Number of nonzeros in Hessian:                     2720 (        2720)\n",
      "\n",
      "Knitro using Branch and Bound method with 8 threads.\n",
      "\n",
      "Initial points\n",
      "--------------\n",
      "The initial point provided for the root node relaxation is not feasible for the MIP.\n",
      "No primal point provided for the MIP.\n",
      "\n",
      "Root node relaxation\n",
      "--------------------\n",
      "\n",
      " Iter      Objective      Feasibility        Optimality       Time \n",
      "                             error              error        (secs)\n",
      " ----      ---------      -----------        ----------      ------\n",
      "    1        2695.90          2.94303           2.94303       0.088\n",
      "    2        2793.83          2.79221           2.79221       0.109\n",
      "    3        3295.37          2.29836           2.22278       0.130\n",
      "    4        3441.65          2.11919           1.83729       0.152\n",
      "    5        3557.45          1.94809           2.07454       0.175\n",
      "    6        3633.34          1.90113           2.82013       0.204\n",
      "    7        3717.14          1.86173           3.31044       0.246\n",
      "    8        3856.81          1.68199           2.32504       0.286\n",
      "    9        3644.97          1.31551           3.00732       0.350\n",
      "   10        3597.72          1.23722           2.87426       0.403\n",
      "   11        3683.70          1.22785           3.56681       0.433\n",
      "   12        3699.34          1.22720           4.55511       0.462\n",
      "   13        3649.45          1.17673           3.51884       0.520\n",
      "   14        3647.10          1.15131           3.50544       0.584\n",
      "   15        3689.13         0.960206           3.38711       0.626\n",
      "   16        3813.65         0.855158           3.26395       0.652\n",
      "   17        3778.06         0.834936           3.27014       0.686\n",
      "   18        3716.28         0.820414           3.26445       0.726\n",
      "   19        3694.68         0.793182           3.26736       0.750\n",
      "   20        3695.81         0.784115           3.26704       0.784\n",
      "   21        3700.87         0.773072           3.26211       0.814\n",
      "   22        3647.66         0.761226           3.26475       0.855\n",
      "   23        3644.67         0.748625           3.26875       0.890\n",
      "   24        3721.26         0.718586           3.42744       0.932\n",
      "   25        3802.95         0.696144           3.53255       0.979\n",
      "   26        3869.74         0.617545           3.78332       1.015\n",
      "   27        3761.89         0.565161           3.73962       1.054\n",
      "   28        3783.01         0.507987           1.50466       1.091\n",
      "   29        3697.57         0.497452           1.48325       1.120\n",
      "   30        3775.88         0.401107          0.996207       1.143\n",
      "   31        3640.38         0.394257          0.990349       1.177\n",
      "   32        3667.97         0.315883          0.972671       1.207\n",
      "   33        3701.52         0.293319          0.968941       1.232\n",
      "   34        3625.99         0.285180          0.968364       1.260\n",
      "   35        3676.28         0.249638           1.24105       1.300\n",
      "   36        3683.63         0.222175           1.24936       1.327\n",
      "   37        3672.10         0.221363           1.30237       1.371\n",
      "   38        3666.25         0.214850           1.31968       1.411\n",
      "   39        3633.47         0.210764           1.41425       1.452\n",
      "   40        3648.83         0.195690           1.14268       1.487\n",
      "   41        3579.95         0.194245           1.10971       1.512\n",
      "   42        3575.30         0.193636          0.982727       1.561\n",
      "   43        3561.42         0.187809          0.984412       1.605\n",
      "   44        3572.84         0.174756          0.859023       1.699\n",
      "   45        3570.85         0.172922          0.861948       1.758\n",
      "   46        3571.06         0.170747          0.863755       1.822\n",
      "   47        3580.17         0.154101          0.738684       1.873\n",
      "   48        3553.54         0.142253          0.816383       1.905\n",
      "   49        3540.22         0.130504          0.806186       1.948\n",
      "   50        3360.60         0.129077          0.810911       1.999\n",
      "   51        3372.06         0.122931          0.492277       2.035\n",
      "   52        3363.59         0.119910          0.523369       2.069\n",
      "   53        3367.87         0.112790          0.335162       2.119\n",
      "   54        3358.19         0.107645          0.323854       2.158\n",
      "   55        3355.26      9.83740e-02          0.232146       2.194\n",
      "   56        3335.94      9.13586e-02          0.187115       2.246\n",
      "   57        3314.07         0.102563          0.234915       2.300\n",
      "   58        3297.54      9.11240e-02          0.253833       2.337\n",
      "   59        3283.28      8.79085e-02          0.221003       2.374\n",
      "   60        3190.91      4.98832e-02       9.61242e-02       2.414\n",
      "   61        3186.22      4.77857e-02       9.00464e-02       2.458\n",
      "   62        3176.62      5.58245e-02       9.02274e-02       2.507\n",
      "   63        3172.71      5.29323e-02          0.208487       2.558\n",
      "   64        3174.19      2.76942e-02          0.294615       2.595\n",
      "   65        3167.98      2.69612e-02          0.218159       2.632\n",
      "   66        3163.21      2.81406e-02          0.183589       2.668\n",
      "   67        3155.49      2.31871e-02          0.189378       2.717\n",
      "   68        3146.70      2.03662e-02          0.189029       2.757\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   69        3143.17      1.97046e-02          0.197977       2.802\n",
      "   70        3125.90      1.49504e-02          0.204929       2.845\n",
      "   71        3123.35      1.47054e-02          0.215685       2.895\n",
      "   72        3087.87      2.06704e-02          0.179008       2.940\n",
      "   73        3084.04      2.07386e-02          0.164460       2.967\n",
      "   74        3079.91      1.67127e-02          0.150466       3.009\n",
      "   75        3080.95      6.19903e-03          0.148613       3.065\n",
      "   76        3074.09      6.89759e-03          0.158361       3.101\n",
      "   77        3066.05      9.69863e-03          0.167435       3.144\n",
      "   78        3060.56      1.13810e-02          0.204393       3.187\n",
      "   79        3048.16      1.20553e-02          0.186139       3.239\n",
      "   80        3036.95      1.59141e-02          0.166813       3.287\n",
      "   81        3014.60      1.74148e-02       6.87101e-02       3.336\n",
      "   82        3009.97      1.64190e-02       4.75957e-02       3.366\n",
      "   83        3001.95      1.38726e-02       3.62140e-02       3.410\n",
      "   84        2994.74      1.21344e-02       3.13347e-02       3.441\n",
      "   85        2990.24      9.65764e-04       4.48838e-02       3.492\n",
      "   86        2978.61      1.43674e-02          0.182614       3.526\n",
      "   87        2977.87      1.44516e-02          0.159534       3.565\n",
      "   88        2974.52      1.83866e-02          0.116294       3.592\n",
      "   89        2973.07      2.03630e-02          0.112029       3.614\n",
      "   90        2966.47      2.40604e-02       6.08700e-02       3.649\n",
      "   91        2961.92      3.11816e-02       3.44882e-02       3.675\n",
      "   92        2948.34      3.82688e-02       5.31521e-02       3.713\n",
      "   93        2942.20      4.70722e-02       4.88137e-02       3.743\n",
      "   94        2938.89      5.34211e-02       4.44047e-02       3.779\n",
      "   95        2935.48      5.18809e-02       7.54313e-02       3.814\n",
      "   96        2934.01      4.71830e-02       8.15180e-02       3.847\n",
      "   97        2932.18      3.89193e-02       6.43215e-02       3.893\n",
      "   98        2924.64      4.46156e-02       6.73247e-02       3.945\n",
      "   99        2917.22      2.85401e-02       3.24359e-02       3.992\n",
      "  100        2899.14      6.11714e-02          0.183652       4.027\n",
      "  101        2899.11      7.12501e-04          0.182823       4.065\n",
      "  102        2894.56      7.68333e-03          0.183079       4.106\n",
      "  103        2891.01      1.27795e-02          0.177047       4.130\n",
      "  104        2881.96      2.57750e-02          0.141622       4.173\n",
      "  105        2882.38      2.57238e-02          0.140335       4.209\n",
      "  106        2880.93      2.35258e-02          0.124069       4.245\n",
      "  107        2877.10      2.85684e-02       8.73044e-02       4.271\n",
      "  108        2876.14      1.04394e-03       7.36294e-02       4.313\n",
      "  109        2875.83      7.29762e-04       7.08761e-02       4.329\n",
      "  110        2875.75      5.75377e-04       7.04596e-02       4.347\n",
      "  111        2875.06      8.33108e-04       6.17770e-02       4.366\n",
      "  112        2871.54      1.11737e-02       7.85474e-02       4.398\n",
      "  113        2865.22      3.45922e-02          0.220618       4.428\n",
      "  114        2860.23      5.62126e-02          0.328978       4.452\n",
      "  115        2854.81      6.13670e-02          0.285713       4.479\n",
      "  116        2855.40      6.43103e-05          0.188237       4.512\n",
      "  117        2854.99      1.15535e-03       7.94103e-02       4.547\n",
      "  118        2838.12         0.385631          0.210341       4.569\n",
      "  119        2837.39         0.282557       3.14414e-02       4.597\n",
      "  120        2837.38         0.282212       3.15125e-02       4.610\n",
      "  121        2838.80         0.150938       2.32991e-02       4.628\n",
      "  122        2839.91      4.91540e-02       2.04538e-02       4.642\n",
      "  123        2834.47         0.132846          0.181423       4.656\n",
      "  124        2832.72      2.52719e-02       5.87738e-02       4.680\n",
      "  125        2820.82         0.109064       3.16521e-02       4.700\n",
      "  126        2821.91      2.30356e-03       4.78563e-02       4.723\n",
      "  127        2805.37         0.249655          0.335767       4.763\n",
      "  128        2808.16      2.27977e-04          0.337207       4.784\n",
      "  129        2808.26      4.00846e-07          0.336846       4.801\n",
      "  130        2808.25      1.20151e-06          0.336575       4.816\n",
      "  131        2808.19      1.72055e-06          0.299171       4.832\n",
      "  132        2808.06      2.70282e-04          0.249993       4.852\n",
      "  133        2807.17      6.49032e-03          0.216811       4.883\n",
      "  134        2786.75         0.411874          0.271666       4.916\n",
      "  135        2789.73         0.350341          0.251920       4.957\n",
      "  136        2782.90         0.218898          0.410537       4.990\n",
      "  137        2784.97         0.206843          0.334721       5.007\n",
      "  138        2785.53      1.37838e-02          0.171998       5.036\n",
      "  139        2785.37      1.35313e-02          0.165188       5.071\n",
      "  140        2785.22      1.53270e-04          0.166324       5.111\n",
      "  141        2785.22      1.52356e-04          0.117654       5.124\n",
      "  142        2785.21      7.13390e-05          0.114787       5.143\n",
      "  143        2784.93      1.36286e-03       8.86167e-03       5.182\n",
      "  144        2783.75      1.67316e-02       8.02273e-03       5.203\n",
      "  145        2770.80         0.380958          0.217099       5.226\n",
      "  146        2773.35         0.375622          0.135121       5.259\n",
      "  147        2774.59      8.44547e-03       3.06909e-03       5.272\n",
      "  148        2774.66      3.96378e-05       5.09209e-06       5.282\n",
      "  149        2774.66      3.68190e-10       8.39316e-11       5.301\n",
      "  150        2774.66      3.68190e-10       8.39316e-11       5.318\n",
      "  151        2774.66      3.68190e-10       8.39316e-11       5.339\n",
      "\n",
      "Tree search\n",
      "-----------\n",
      "\n",
      "       Nodes        Best solution   Best bound      Gap       Time \n",
      "   Expl  |  Unexpl      value         value                  (secs)\n",
      "   ---------------  -------------   ----------      ---      ------\n",
      "      1       0      2774.66 LEAF      2774.66      0.00%     5.343\n",
      "\n",
      "EXIT: Optimal solution found (assuming convexity).\n",
      "\n",
      "HINT: The problem may be a non-convex mixed-integer problem.  Set\n",
      "      mip_multistart=1 to enable a mixed-integer multistart heuristic,\n",
      "      which may improve the chances of finding the global solution.\n",
      "\n",
      "Final Statistics for MIP\n",
      "------------------------\n",
      "Final objective value               =  2.77465725625193e+03\n",
      "Final bound value                   =  2.77465725625193e+03\n",
      "Final optimality gap (abs / rel)    =  0.00e+00 / 0.00e+00 (0.00%)\n",
      "# of root cutting plane rounds      =  0\n",
      "# of restarts                       =  0\n",
      "# of nodes processed                =  1 (5.326s)\n",
      "# of strong branching evaluations   =  0 (0.000s)\n",
      "# of function evaluations           =  0 (0.000s)\n",
      "# of gradient evaluations           =  0 (0.000s)\n",
      "# of hessian evaluations            =  0 (0.000s)\n",
      "# of hessian-vector evaluations     =  0\n",
      "# of subproblems processed          =  1 (5.326s)\n",
      "Total program time (secs)           =  5.343 (5.906 CPU time)\n",
      "Time spent in evaluations (secs)    =  0.000\n",
      "\n",
      "Cuts statistics (gen / add)\n",
      "---------------------------\n",
      "Knapsack cuts                       =  0 / 0\n",
      "Mixed-integer rounding cuts         =  0 / 0\n",
      "Flow-cover cuts                     =  0 / 0\n",
      "Probing cuts                        =  0 / 0\n",
      "\n",
      "Heuristics statistics (calls / successes / time)\n",
      "------------------------------------------------\n",
      "Feasibility pump                    =  0 / 0 / 0.000s\n",
      "Rounding heuristic                  =  0 / 0 / 0.000s\n",
      "MPEC heuristic                      =  0 / 0 / 0.000s\n",
      "Local search heuristic              =  4 / 0 / 1.530s\n",
      "\n",
      "===========================================================================\n",
      "\n",
      "\b"
     ]
    }
   ],
   "source": [
    "def size_upper_clusters_rule(model,j):\n",
    "    total = sum(model.a[i,j] for i in range(nb_observations))\n",
    "    return (total <= 12)\n",
    "model.constraints_size_upper_clusters = pyo.Constraint(model.K,rule=size_upper_clusters_rule)\n",
    "\n",
    "def size_lower_clusters_rule(model,j):\n",
    "    total = sum(model.a[i,j] for i in range(nb_observations))\n",
    "    return (total >= 8)\n",
    "model.constraints_size_lower_clusters = pyo.Constraint(model.K,rule=size_lower_clusters_rule)\n",
    "\n",
    "results = solver.solve(model, tee=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8adb8ac3",
   "metadata": {},
   "source": [
    "### Output visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1232a56e-0686-4658-bcff-c705ad20ab43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fCC8vXwgvL19Et0YAwmuNk2krCK8kQBe7Q3j5YEN4+dhCeHnZiugQXl7GEF5evohujQCE1xonCK8kJy90h/Dy7QKEl48thJeXLYSXny+El58xRkhPAMKbnlHKFsjwSgJ0sTuElw82hJePLYSXly2El58vhJefMUZITwDCm54RhFeSkVe6Q3j5dgLCy8cWwsvLFsLLzxfCy88YI6QnAOFNzwjCK8nIK90hvHw7AeHlYwvh5WUL4eXnC+HlZ4wR0hOA8KZnBOGVZOSV7hBevp2A8PKxhfDysoXw8vOF8PIzxgjpCUB40zOC8Eoy8kp3CC/fTkB4+dhCeHnZQnj5+UJ4+RljhPQEILzpGUF4JRl5pTuEl28nILx8bCG8vGwhvPx8Ibz8jDMd4cH69UrXu+pmZRoiZ/pBeCW3Cqc0SAJ0sTuElw82hJePLYSXly2El58vhJefcaoRPvjoENUtWEmHj56IN3vsoYV0ycRx5ITwPr35ZWrYuZuW3D2bikPBjBf7p1176LY7lyn9Lxg/mlYvm0eVFeUZx9N3hPBKooTwSgJ0sTuElw82hJePLYSXly2El58vhDc148Ymol1/iVJ7B9HEC3w0fKjPsU1RJVIVXBH4ZEsrPbpuC8299Xpa/fgzylgyGV4nhFdI+T1L19ADi+bQmBG15ERMCK9jt1FvIAivw0AZw0F4+eBCePnYQnh52UJ4+flCeM0Zv/nnGP3bI90JDb7xDwG6/G/80hvTEY7QfSvW0uRJE2jm1CsN42kzvHrpVPvfOH2Kkg3WZ4pvv3kqzbjuioTssTYzK6T13uVrlXGnXTM5ngFWZbasrISefHYbiTgjh9XQ/gNH4uKtn4s0DCJChleSIoRXEqCL3SG8fLAhvHxsIby8bCG8/HwhvOaMl/+0m977IJbQoLiY6GfLCqU3xoo0WhXe88eNVuRZlV8hw09teolumHYVbdnWkFTSIKR2/cbt8bIEMY6QWiHeqghrs8760gqRhZ67cBXNr5ulyLYTF4RXkiKEVxKgi90hvHywIbx8bCG8vGwhvPx8IbzmjO/4Xpfhhz//iTPCu+LhdbR08RzTWlirwjt21FBFQGdNn5KULdaXHxhllkVpxYaN25Usr5Ega4VYAIHw8n9f2h4BwmsbWdY6QHj50EN4+dhCeHnZQnj5+UJ4bWZ4Q0Q/+1dnhFdbF2s0C6vCa1TSoGZozYR309aGhCHVsgYz4RWN1VpiCC//96XtESC8tpFlrQOElw89hJePLYSXl62XhTd43E+xghh1VSb+yZufiLMjQHjNeeZSDa92FSJju7J+vVKy8OKONxNKGvS1v/rVGz2QJr6GGl5nv+9SRlM3STTSHq9hVngt2kF4XdwgyaEgvJIAU3SH8PKxhfDysvWi8JbsD1DFriD5Pvlrd1f/GDVOCVNMPunHD9NgBAhvauzilIY3/yxOaYjRpz/lz9opDfqsqvaEB1HSsHlrA90y81plMVrhfX/fwbj8qseI6Wt409X84pQGF781VdkVKXjt04TaTRUbqS+shvC6uEmSQ0F4JQFCePkApolcEPDRgPIiOtYcztoc8nngsuIC8vt8dKrduJ7S7bUPeaY4Lrvq2KfP7qaWid6Yn10eEF67xJxtb+ccXu1ZuDfNuJra2tqVB9XUh9bUMoUh1QOpfvl85QgxrT+ZndIgVnT/gtnxh9aMzu3FObzO7rtpNLVgWjTQboS+kFovwBBelzbIgWEgvA5ANAmBDC8fW2R4edl6LcMryhiqthclLToyKEqNUzr5YTCMAOFlgIqQtgnglAaihKyttrZE0NSfYadPu0N4bd9zWesA4eVDD+HlYwvh5WXrNeENnPZR9eZQ0qLDtT3UdHmEHwbDCBBeBqgIaZtAnxdefaG0kfCq584JunrhbW1PPDDa9g5oOgQCPioq9FN7uEcmDPqaEAgF/dQTI+rqioKRwwQKAz4KFQWoqztG4QjuX4fxkt9PVFxUQKc7nPt54/QcczlesNBPPh9RZ8QbPxtKng9Q4Gji27Y6pvRQ9/DcfHitJBSgzq4o9YgfwDlwlZcU5MAsMUW7BPq88IqShUee2JzETdTxLvynr9Kyn/0q4S0lScLb4VxNVYHfR4UFAeqI4D9qdm9kK+2LCgMUi8Yo0uON/6hZmXOutCkM+CkUDFBXTxTCy7Bpor60OBig05342cCAl4IFfvKRjzq7PfLLWoQo+L6fCj72UyxI1DU2d2VX7FdJsEBh2xPNEeEtztGnAzm+OfIoZp8XXv1e6o/LQA1v/tztKGng20uUNPCxFZHx0BovX689tMa7Wvejo6TBfeYYMZkAhFfHRC+8OKUhf75tILx8ewnh5WML4eVlK6JDeHkZQ3h5+SK6NQIQ3jTCKz7GObzWbiavt4Lw8u0QhJePLYSXly2El58vhJefMUZITwDCm55RyhY4pUESoIvdIbx8sCG8fGwhvLxsIbz8fCG8/IwxQnoCEN70jCC8koy80h3Cy7cTEF4+thBeXrYQXn6+EF5+xhghPQEIb3pGEF5JRl7pDuHl2wkILx9bCC8vWwgvP18ILz/jTEfQvz020zi50A/CK7lLKGmQBOhidwgvH2wILx9bCC8vWwgvP18ILz/jVCPYebVwJjPVP+yfSQy1z8mWVlr0ozV097e+ory22MkLwitJE8IrCdDF7hBePtgQXj62EF5ethBefr4Q3tSMo8cOU9frv6fY6TYqvORvKTDybMc2RZw0ddudy+ixhxbSJRPHKXGFVD66bgvNvfV6Wv34M8rX7qqblfGYTghvRziivNl209YGGlI9kOqXz4fwZrwjTB0hvExgGcJCeBmgfhISwsvHFsLLyxbCy88XwmvOuOuPL9PpHy9OaFDyrcUUnDJVemNUiZw8aQLNnHqlYTxtSYP+xVpqf/Vts/pM8e03T6UZ111BdQtW0uGjJ5T4F4wfTauXzaPKinLTE65UQS4rK6Enn91GIo4q3MjwSm87XwAILx9bpyNDeJ0meiYehJePLYSXly2El58vhNeccdsPvkPdu3clNPCVlFHFY89Jb4xeYI0CWhXe88eNVjKwqvwKGX5q00t0w7SraMu2BmrYuZuW3D2bikNBZRghtes3bo/Lr/YlXupRr9qsszo3CK/0tvMFgPDysXU6MoTXaaIQXj6iiZHxpjVe0njxBC9fCK853+ZZVxh+2H/9K9KbIoR3xcPraOniOUrGVUZ4x44aSnMXrqJZ06ckZYv1JQ1GmWVRWrFh43ZFio0EGcIrvd38ASC8/IydGgHC6xTJ5DjI8PKxFZEhvLx8Iby8fCG85nyNMrxUUkr9H3teelOczPCK+l99SYOaoTUTXlGPq72mXTMZwiu9q1kMAOHNInybQ0N4bQKz0RzCawNWBk0hvBlAs9EFwmsDVgZNIbzm0HKphle7CpGxXVm/XilZeHHHmwklDfraX/3qUz3khpKGDL7B3OoC4XWLtPw4EF55hmYRILx8bJHh5WUrokN4eRlDeFPzVU5p+JM4paGVCj9zZdZOaRCyKcoW5tfNUk500J7wIEoaNm9toFtmXqssRiu87+87GJdftXRCX8ObruZXJQTh5f1elIoO4ZXC52pnCC8fbggvH1sILy9bCC8/XwgvP+NUI9g5h1eVXBHvphlXU1tbu/KgmvrQmlqmoD06THukmNkpDSLe/QtmK/W/RhlebQx1LWoJhPognCxFnMMrSRDCKwnQxe4QXj7YEF4+thBeXrYQXn6+EF5+xhghPQEIb3pGKVtAeCUButgdwssHG8LLxxbCy8sWwsvPF8LLzxgjpCcA4U3PCMIrycgr3SG8fDsB4eVjC+HlZQvh5ecL4eVnjBHSE4DwpmcE4ZVk5JXuEF6+nYDw8rGF8PKyhfDy84Xw8jPGCOkJQHjTM4LwSjLySncIL99OQHj52EJ4edlCePn5Qnj5GWOE9AQgvOkZQXglGXmlO4SXbycgvHxsIby8bCG8/HwhvPyMMUJ6AhDe9IwgvJKMvNIdwsu3ExBePrYQXl62EF5+vhBefsYYIT0BCG96RhBeSUZe6Q7h5dsJCC8fWwgvL1sILz9fCC8/Y4yQngCENz0jCK8kI690h/Dy7QSEl48thJeXLYSXny+El58xRkhPAMKbnhGEV5KRV7pDePl2AsLLxxbCy8sWwsvPF8LLzzjTER6sX690vatuVqYhcqYfhFdyq/DiCUmALnaH8PLBhvDysYXw8rKF8PLzhfDyM041gp1XC2cyU6NXBduNo5+j9hXFdmOZtYfwSpKE8EoCdLE7hJcPNoSXjy2El5cthJefL4Q3NeP9kVZ6tnkfNfdEaEb/kTSxuMqxTfnTrj10253L6LGHFtIlE8cpcU+2tNKj67bQ3Fuvp9WPPyOd4XVCeMU8Dxw6RjOnXqnMR2SejxxroiV3z6biUNARHhBeSYwQXkmALnaH8PLBhvDysYXw8rKF8PLzhfCaM36meR996YPnEho8OvKzdNvAXjmVuTrCEbpvxVqaPGlCXCT18bQlDSLLes/SNfTAojk0ZkQtqf1vnD5FkWV9Fvb2m6fSjOuuoLoFK+nw0RNKaG1mVojwvcvXKl+fds3kuLyqglxWVkJPPruNRBx9SYUQ4JX162n1snlUWVEugyHeF8IriRHCKwnQxe4QXj7YEF4+thBeXrYQXn6+EF5zxlPefZZeajuU0KB/IEgnJ94uvTF6gTUKaFV4zx83WpFnVX6FDD+16SW6YdpVtGVbAzXs3J2QjRVSu37j9riwinFGDqtRxFsVYW3WWT83J7LG+pgQXslbCsIrCdDF7hBePtgQXj62EF5ethBefr4QXnPGvp2rDT+MTZorvTFCeFc8vI6WLp5jmiW1KrxjRw2luQtX0azpU5KyxXo5Ncosi4ztho3bFSk2EmTtYq2IeiZwILyZUNP0gfBKAnSxO4SXDzaEl48thJeXLYSXny+E116GtyIQpGaPZXiNShrUDK2Z8G7a2pCwcLWsIZXwqmUTSxfNidccO3WHQnglSUJ4JQG62B3CywcbwsvHFsLLyxbCy88XwmvOOJdqeLWr0NbYvrjjzYSSBn3tr371ZuUKnLIr5gDhlfxeh/BKAnSxO4SXDzaEl48thJeXLYSXny+ENzVjcUqDEN/m7k66vnJU1k5pEKc3iLKF+XWzlOyq9oQHUdKweWsD3TLzWmUxWuF9f9/BpAfM9DW86Wp+ucoYtOQhvJLf6xBeSYAudofw8sGG8PKxhfDysoXw8vOF8PIzTjWCnXN4VckV8W6acTW1tbUrD6qpD62pZQpDqgdS/fL5Cac5iM/MTmkQ8e5fMDv+0JrRQ27qiQ7ataR6sM0uVQivXWK69hBeSYAudofw8sGG8PKxhfDysoXw8vOF8PIzxgjpCUB40zNK2QLCKwnQxe4QXj7YEF4+thBeXrYQXn6+EF5+xhghPQEIb3pGEF5JRl7pDuHl2wkILx9bCC8vWwgvP18ILz9jjJCeAIQ3PSMIryQjr3SH8PLtBISXjy2El5cthJefL4SXnzFGSE8AwpueEYRXkpFXukN4+XYCwsvHFsLLy9aLwlt40ke+Lp+y8MjgKD8A5hEgvMyAEd4SAQivJUzmjVDDKwnQxe4QXj7YEF4+thBeXrZeE96KXYVUurcgvujIoCiduLyTYoX8HLhGgPBykUVcOwQgvHZoGbSF8EoCdLE7hJcPNoSXjy2El5etl4RXZHYH/U8oacEtF3bR6XO6+UEwjQDhZQKLsLYIQHht4UpuDOGVBOhidwgvH2wILx9bCC8vWy8Jb+hggAa8GkxacOt53dQ6oYsfBNMIEF4msAhriwCE1xYuCK8krqx2h/Dy4Yfw8rGF8PKy9ZLwBo/7qWp7EYSXf8tTjlA7sDjLM8DwHAQgvJJUkeGVBOhidwgvH2wILx9bCC8vWy8Jr5hL9aYQBdp7H1hTr6NTw9RTGuMHwTQCMrxMYB0I+2D9eiXKXXWzHIjm7RAQXsn9gfBKAnSxOwnNMA8AACAASURBVISXDzaEl48thJeXrdeE19dFVLa3kEQ9b1dljMJDupX/n8sXhDe7u2fn1cKZzPTpzS+T/lXBduOcbGmluQtX0V/e+VDpqn1Fsd1YZu0hvJIkIbySAF3sDuHlgw3h5WML4eVl6zXh5V+t+yNAeFMzb28kOrgrSl3tRLUTfdR/eGKGX2bH/rRrD9125zJ67KGFdMnEcUooIZePrttCc2+9nlY//ozyNZkMrxPCK+Z54NAxmjn1SmU+TsTUc4PwytxJRAThlQToYncILx9sCC8fWwgvL1sILz9fCK8540NvxujVf0s8gePibwRo5OV+6Y3pCEfovhVrafKkCXGR1AfVljSITPA9S9fQA4vm0JgRtaT2v3H6FEWW9Zni22+eSjOuu4LqFqykw0dPKKG1mVkhrfcuX6t8fdo1k2nJ3bOpOBSMy2xZWQk9+ew2EnH0wi0EeGX9elq9bB5VVpRLsxABILySGCG8kgBd7A7h5YMN4eVjC+HlZQvh5ecL4TVnvH15NzW+l1iyUlhMNONn8gcv6wXWaBZWhff8caMVeVblV8jwU5teohumXUVbtjUklTQI2V2/cXtcWMU4I4fVKOKtirA262wk4keONcUl2Ym7FMJLRGIjHnlic5ynfhPMfksRHSC8TtyG7sSA8PJxhvDysYXw8rKF8PLzhfCaM/6vO4yPm/vyz50R3hUPr6Oli+eYZkmtCu/YUUOVGttZ06ckZYv15QdGmWWRsd2wcbsisEaCrBJSfQs1vAzfl9paFpFq1/9GpE+r659ohPAybApTSAgvE1gigvDysYXw8rKF8PLzhfDay/AWFBNd77EMr1FJg5ocNBPeTVsbEhauljWkEl61A0oa+L8vlWJu8VvM/LpZSs2KNg0vhtdvAoTXhU1xaAgIr0MgDcJAePnYQnh52UJ4+flCeM0Z51INr3YVWhd6ccebCSUN+tpf/eqtPJAmXGzRj9bQ3d/6ilJP7MSFkgYdRbGJi5auofrl86m2uiqp4FufAYbwOnEbuhMDwsvHGcLLxxbCy8sWwsvPF8KbmrFySsOb4pSGGNV+2p+1Uxr0CT/tCQ+ipGHz1ga6Zea1ymK0wvv+voNJD5jpa3it1PwOqx0cP0lC39+JuxTC+wlF7dOHapre6LcUK0XgTmwMYoAACIAACIAACICALAE75/CqkivGvGnG1dTW1q48qKY+tKaWKQypHqgkBrWnOYjPzE5pEPHuXzA7/tCa/txe/RxRwyu76xb6a3/DUTdYe6QHMrwWIHq0CTK8fBuDDC8fW2R4edkiw8vPFxlefsYYIT0BZHgNGGnrdlHDm/4mypUWEF6+nYLw8rGF8PKyhfDy84Xw8jPGCOkJ9HnhFRnbrb/fSd/86nSFlppWX7pojlJLglMa0t9EudICwsu3UxBePrYQXl62EF5+vhBefsYYIT2BPi+8ap2u9vgMnMOb/sbJxRYQXr5dg/DysYXw8rKF8PLzhfDyM8YI6Qn0eeFNjyh1C5zSIEvQvf4QXj7WEF4+tqmEN9B9nHoKBvEO3geilxUXkN/no1Ptxi8B6AMIWJcI4WXFi+AWCUB4LYIyawbhlQToYncILx9sCC8fWyPhLWl9mfo1/Yp80XZl4HDJJDpZPY93EnkcHcLLu7kQXl6+iG6NAITXGifTVhBeSYAudofw8sGG8Jqz9UVPU3H7Tgp0NVJX0QhFTu1eBQEfDSgvomPNYRJZ3UEH74nLrhrr1ICv0umK6+yGRnsigvDy3gYQXl6+iG6NAITXGicIryQnL3SH8PLtAoTXmK2QXSGnge7GeIOu4AhqHPqArc3QCm8wvJsGHv5RUv9wyUV0svouW3HRuJcAhJf3ToDw8vJFdGsEILzWOEF4JTl5oTuEl28XILzGbEtbnlNKD/TXiSGLKRKaYHlDrAjv6X5foFMDv2Y5JhqeIQDh5b0bILy8fBHdGgEIrzVOEF5JTl7oDuHl2wUIrzHbsuanqfzk00kftlR9k9rLr7S8IVrhFZ0GH7gzIWssvnay+k4Kl1xsOSYaQnjdugcgvG6Rtj+OeNeAuO6qm2W/c471gPBKbhhqeCUButgdwssHG8JrzJYjwytGEnW8/U78kvyx3ofWOkqvtCXQfHdCbkZGhpd33yC8vHzTRbfzauF0sYw+f3rzy6R/VXAmcdQ+6ny/desM5VXETl0QXkmSEF5JgC52h/DywYbwGrM1ruEdTo1Dk2twU+2OPsPLt5N9MzKEl3ffIbxp+LYdJzqwkyjSTjRsEtGAEY5tiHh51m13LiPt+wVOtrTSo+u20Nxbr6fVjz+jjCWT4XVSeLVyfv+C2RBex+4EBwJBeB2A6FIICC8faAivOVvllIbTO8nf00jdweEZlR1AePnuXREZwsvLF8Kbgu/HrxNtX5XY4PI6ojHymU31xVqTJ00wFUdtSYOQzXuWrqEHFs2hMSNqSe1/4/Qpyptn9Zni22+eSjOuu4LqFqykw0dPKGu4YPxoWr1sHlVWlJMQ4XuXr1W+Pu2aybTk7tlUHAoqXxcZ4bKyEnry2W0k4gjhFiK+6Edr6Duzv0S/WP88pZp3JncsMryZUNP0gfBKAnSxO4SXDzaEl4+tiAzh5eUL4eXlC+FNwff5+4mO7klsUFhCdPMa6U3RC6xRQKvCe/640XTfirWkyq+Q4ac2vUQ3TLuKtmxrSCppEFK7fuP2uPyKcUYOq1HEWxVhfdZ57sJVNL9uFqljQXilbwFnA0B4neXJGQ3Cy0cXwsvHFsLLyxYZXn6+EN4UjH9xi/GHX/+19MYI4V3x8DpauniOknGVEd6xo4aSENJZ06ckZYv1JQ1GmWVRWrFh43Yly6sXZH0m2UpmOhM4yPBmQg0ZXklq2ekO4eXjDuHlYwvh5WUL4eXnC+G1m+EtJrr559Ib42SG16ikQc3Qmgnvpq0NCWtQyxr0witKGYRM/+WdD5PW7GQdL4RX8pZChlcSoIvdIbx8sCG8fGwhvLxsIbz8fCG8KRjnUA2vdhUiY7uyfr1SsvDijjcTShr0GVv96tM95IYML//3ZEYjQHgzwpaVThBePuwQXj62EF5ethBefr4Q3jSMlVMaXv/klIaLs3ZKg5ppFXW0IqOrPeFBlDRs3tpAt8y8VlmMVnjf33cwLr9q6YS+hjddza+WEISX/3syoxEgvBlhy0onCC8fdggvH1sILy9bCC8/XwgvP+NUI9g5h1eVXBHvphlXU1tbu/KgmvogmVqmMKR6INUvn59wmoP4zOyUBhFPLU9Ahje790PGo0N4M0bnekcILx9yCC8fWwgvL1sILz9fCC8/Y4yQngBqeNMzStkCwisJ0MXuEF4+2BBePrYQXl62EF5+vhBefsYYIT0BCG96RhBeSUZe6Q7h5dsJCC8fWwgvL1sILz9fCC8/Y4yQngCENz0jCK8kI690h/Dy7QSEl48thJeXLYSXny+El58xRkhPAMKbnhGEV5KRV7pDePl2Il+FN9B9nAJdjQq4rqLhFPOX8kFMERlvWuPFjjet8fKF8PLyRXRrBCC81jiZtkINryRAF7tDePlg56Pwhtpfp8qjD8Whxfwl1FR9J0VCE/hAmkSG8PIih/Dy8oXw8vJFdGsEILzWOEF4JTl5oTuEl28X8lF4az76Jvmi7QnQwiUX0cnqu/hAQnhdZysGhPDyYofw8vJFdGsEILzWOEF4JTl5oTuEl28X8lF4h+z7ahIwkeU9MuI/+EBCeF1nC+HlRw7h5WeMEdITgPCmZ5SyBUoaJAG62B3Cywe7rwhvpHgcnaj5v3wgIbyOsQ0e9xPFiHpKY8r/Ul3I8DqG3TAQhJeXL6JbIwDhtcYJGV5JTl7oDuHl24V8FN5+J35JpaeeT4B2asBX6XTFdXwgIbxp2fq6iIoPBihw2qeIbPvInoQ+4vPBvwspn6tX8yWRpHbaThDetNilGkB4pfCxdn6wfr0S/666WazjeCE4hFdyF5DhlQToYncILx/sfBReQauk9WUqiHxE0UApRULjsvLAmpgHHlrrvXeFzNZsKlb+v3p19Y/R8WvD8X+v2FVIpXsLkm72w9d3UKzQ+HsAwsv3s0FEhvDy8k0X3c6rhdPFMvo83auCrcQ82dJKcxeuor+882G8ufb1xVZipGsD4U1HKM3nEF5JgC52h/Dywc5X4eUjlhhZPf4s5i+mrqKRScNCeHuRlL5XQBVvJVtr45ROigyKKm2qtheRUs6gu7Rt9J9BeHnvdAhvar4HumL03KluOtUToy/0K6DzQ8n3b6Y79Kdde+i2O5fRYw8tpEsmjlPCCLl8dN0Wmnvr9bT68WeUr8lkeJ0U3vl1s+LzzHTNZv0gvJJEIbySAF3sDuHlgw3hzZxtWfPTVH7y6XiAruAIOjFkccKZvxDeXjzluwup/O3k7K22ZKH/H4NU8lEgaUOOTg2b1vJCeDO/f630hPCaU9pyqptu//jMXyhEy1VDQ3RTZfJ9boW1tk1HOEL3rVhLkydNoJlTrzTsri1pEJnge5auoQcWzaExI2pJ7X/j9CmKhOozxbffPJVmXHcF1S1YSYePnlDiXzB+NK1eNo8qK8pJiPC9y9cqX592zWRacvdsKg4Fla837NxNZWUl9OSz20jE+cZX/k7J8EJ47e6yi+0hvC7ClhwKwisJMEV3CG9mbEVmd/CBeUmd9bXCEN5eRFYyvCK7K7K82ktkf0WG1+yC8GZ2/1rtBeE1JzVzXwc1nE6sQ+/nJ9ozocwqXtN2eoE1amhVeM8fN1qRZ1V+hQw/teklumHaVbRlW4MisKrQinGE1K7fuD0uv2KckcNqFPFWRVifddaWNDhdziDmhAyv5C0F4ZUE6GJ3CC8fbAhvZmyD4d008PCPkjrrz/uF8PYiUh5IeyFEgfYzD6Tpa3hFOyG96oNtnYOi1D6q27R+V7SH8GZ2/1rtBeE1J1X71zbDDw+d74zwrnh4HS1dPEfJuMoI79hRQ5UM7KzpU5KyxfqSBqPMsiit2LBxuyLFRoKsn5temK3ea6naQXglKUJ4JQG62B3CywcbwpsZWzPhba2cSW39Z8aDQnjP8BXSW3QsQIUtfuqqiFJ4aGJ2LJOdgPBmQs16HwivOSujDG+5n+hdj2V4jUoa1AytmfBu2tqQsHC1rMGK8Io640U/WkN3f+srSnmFExeEV5IihFcSoIvdIbx8sL0qvNr6WPHSiOZB36RwycV8IDKIXHVwMRVGPk7oKWp4ta8whvBmANZGFwivDVgZNIXwmkPLpRpe7SpExnZl/XqlZOHFHW8mlDToa3+Nsrf6Egh9GwhvBt9o3F0gvNyEnYsP4XWOpT6SF4VXHClW0Zj4VjQhvceHPkA9BYMchRFqf53KTv6GCiMfkXjorK3yS5bF2hc9TSWtv6dQx+vUVTiCwqWTko4/4xJe9XSISPF4R3nkWjAIL++OQXhT81VPaWjpidF1WTylQT0aTH1wTHvCgyhp2Ly1gW6Zea2yGK3wvr/vYFx+1dIJfUlCuppfEU9c6kkSTpz8oKeODK/k9zmEVxKgi90hvHywvSi8Ri+OEAT02VNZKoWd+6nqUPLb144NW+WYWDstvEKyBxx9iILhd5Tli18ExINy7eXGT3LLMvJ6fwgv7w5BeHn5potu5xxeVXJFzJtmXE1tbe3Kg2rqQ2tqmYL2oTI1oys+MzulQcS7f8Hs+ENr+gyvfo7aOOnWZ/VzCK9VUibtILySAF3sDuHlg+1F4dUf96Wu3mnhNRvHybeyOS28Rr8MCOk9MiIxI853x3grMoSXdz8gvLx8Ed0aAQivNU6mrSC8kgBd7A7h5YPtReEVZQaVRx9KWLSQuqPDViWccStLJReFd+CRf6FgR++fELVXY+2/GL74QpaR1/tDeHl3yEx4xWkasYIYdVXGeCdgM3rtwGKbPdA8FwhAeCV3CcIrCdDF7hBePtheFF6x2tKW55Ta2MLOj6mraDi19p8Zr48VJySUtjxP/mg7dRcMUupuM6ntNTtpwcslDWbC6+Sc+e425yNDeJ1nqo2oF96S/QGq2BWMvyJaHC3XdFmn6YtBeGeXHB3C6zZxd8aD8EpyhvBKAnSxO4SXD7ZXhddsxUaS2lNQpTzQFvOX2gYlHpATmd5AdyOJOOJIMSfrYZ0uaTDKfkeKx9GJmuRaZNswcrADhJd30/TCO+SZ4rjsqiO3j+ih5s9EeCdiMTqE1yKoHGsG4ZXcMAivJEAXu0N4+WDnmvC6Vd/rFHGnhVfMS0hvcevL5I+1K6dDiLN/M5F9p9aYzTgQXl76WuEtPOmjQf8TShow3dvweGeYGB3C6yZt98aC8EqyhvBKAnSxO4SXDzaEl4+tiMwhvLwzzq3oEF7e/dIKr3hxiMjw6i8IL+8eIDpeLSx9D0B4pRG6FgDCy4c614RX1Pb2a/pVEhCv1rBCePnuXREZwsvLV1/SULW9SHn9s/ZqviRC7SPl35rnxEqQ4XWCovdiIMMruScQXkmALnaH8PLBzjXhFSQqjz5IofY34lCcPEbMadIQXqeJJsaD8PLy1QuvyPKW7Cug4kMBihbGFNF14hXRTq0CwusUSW/FgfBK7geEVxKgi90hvHywc1F4BQ3xAgbxdjTta3z5KGUeGcKbOTsrPSG8Vihl3gbn8GbODj2dIwDhlWQJ4ZUE6GJ3CC8f7FwVXj4izkaG8DrLUx8NwsvLF8LLy1cm+oP165Xud9XNkgmTE337vPBqX4mn7thjDy2Mv89ZfE280/ne5WuVj6ddM5mW3D2bikNB5d8hvDlxnyuThPDy7RWEl4+tiAzh5eUL4eXlC+Hl5Zsuup1XC6eLZfS5cCT9q4IziSP6CAF/5InNSvfbb57qqIj3eeE92dJKj67bQnNvvV6RWPEe6UVL11D98vk0ZkSt8u8r69fT6mXzqLKiXNkM7W9DEN5Mb2v3+0F4+ZhDePnYQnh52YroEF5exhDeNHxPnCLa9SFRR4TowlFEwwY5tiHCYW67cxlpE3la71n9+DMJTpPJwE4JL3e2uc8Lr35zxY0wd+Eqml83S8nyig0YOayGZk69UmmqF2AIbybfHtnpA+Hl456Pwivqe4vbd1Kgq5F6Cquoo2RS0jm1ok15828o2PEO+aOnqSs4gk4N/GpGb2xLtTvI8PLduxBeXrYiOoQ3BWMhuqs3JTa49XNEl42X3hj1L9iTJ02IO4w+qFYyRSb4nqVr6IFFc5SEn9r/xulTFB/SZ4pFBnbGdVdQ3YKVdPjoCSX0BeNHxxOEZn8dVwW5rKyEnnx2m5LJ/du/+RRt2Lg94S/o0gB0ASC8OiDaDa+trqL7Vqwl7c2ivyEgvE7fknzxILx8bPNReKsOLqbCyMdxaEJmTwxZnCC9Ri+wiITG04kh9zgKG8JrjFO8xCB0KKB8GA0SnT67OyPuyPBmhM1yJwhvClQ/fppo78HEBsVBoofqLPM1a6j3FaN2VoX3/HGjFR9S5VfI8FObXqIbpl1FW7Y1JJU0CKldv3F7wl/H1eShKsLarLNWjtV56stLZYFAeDUE9b8N6X+7EU31N1Bre5fsHsT7BwI+ChYEqKMzsx/ajk0kTwMVBQMUjcaoqzuapyvM3rIKA34KFQUUtuGIN87SlKFR0PpHCh14MClEZ+1c6up/VfzrxR8tocDpd5LatU1YJzN8Ul+/30fFwQCdDuNngwoncMRHJS8UJLDqqYlR++ftMwoW+slHPursyv1719Ebz6FgJUUF1NndQz09MYci8oYpLynkHUAbve5nxmPV/5P0HISvrHh4HS1dPEcpyZQR3rGjhip//Z41fUpStlhf0mCUWRZ/HVczuEaCbPTXdG15qTQMcSpPLBbLjTvQidWmiKFuUM3gAfEiaaNNSxLeDvs/XM2mUeD3kfjB296JH7oc2x0q9FM0RhSB8DqOtzDgo1AwQF09sbwQ3uDxDRQ89l9JnHrKLqSOEYvPCO/+HxgL73lPOsrY7yMqLiqA8Gqohl4JUOEHvuRfNm7opliZPfzBAj/5fESdXfhl2B45a61LigIK2x7xAzgHrvLixF+kWKecIxleo5IGNQNrJrybtjYkoFMf+rcivFbKMezuC4SXKF6nopVdFSRqeO3eUt5tj5IGvr3Jt5KGUPvrVHn0oWRgMaLGof9CXUUjlc8qjtdTSdvvE9r1FFTRsWEGfSXwo6QhGZ7R27pEq8YpnSReU2vnQkmDHVr226KkIQWzHKrh1a5C+zzTizveTChpMPrruLav0UNu4mv7DxxJSjiqJRT277rkHn1eeNP9FoFTGpy4zbwRA8LLtw/5JryCVPXH3yJ/zykNtN7s1MnqeRQuuVj5Z/HQWv/j9fE3tnUFh1NL1TfjQuwUcQhvMsmKXYVUujc5E3f4+g6K2fyLNITXqTvVOA6ENw1f9ZSG9k6iiaOzdkqD/qF97QkPoqRh89YGumXmtcpitG70/r6DCadZic/1Nbzpan7VB+KWLpqjPCCndy8n7tA+L7xG59MJsNrz33AOrxO3WvZjQHj59iAfhbf3gbSnhNYSkZDd3j+fiwfX3H4zG4Q3+d4NnPaRyPIG2s+UNbSe102tE+w/VwHh5fvZICJDeHn5potu5xxeVXJFzJtmXE1tbe3Kg2rqQ2tqmcKQ6oHx41u17zMwO6VBxLt/wWyl/tfsGDPt2Nr46dZn9fM+L7xWQZm1wykNsgTd6w/h5WOdj8Jb2Lmfqg793wRoMX8JHR22Kul4Mj6yvZEhvMaEfV1Ehc1+5cNYQYy6KjOrEYXw8t7BEF5evohujQCE1xon01YQXkmALnaH8PLBzkfhFbSC4d1U2vIc+WPt1B0YRG2VMx0/Y9fKrkB4rVDKvA2EN3N2VnpCeK1QQhtuAhBeScIQXkmALnaH8PLBzlfh5SNmLzKE1x4vu60hvHaJ2WsP4bXHC615CEB4JblCeCUButgdwssHG8LLx1ZEhvDy8oXw8vKF8PLyRXRrBCC81jiZtoLwSgJ0sTuElw82hJePLYSXl62IDuHlZQzh5eWL6NYIQHitcYLwSnLyQncIL98uQHj52EJ4edlCePn5Qnj5GWOE9AQgvOkZpWyBDK8kQBe7Q3j5YEN4+dhCeHnZQnj5+ZoJb+FJHw14rYjEEXPiah/ZQy0TI7bPUXZ6BbUDi50OiXgeIADhldwECK8kQBe7Q3j5YEN4+dhCeHnZQnj5+ZoJb/WmUMI5ymImmZ6l7OQqILxO0vROLAiv5F5AeCUButgdwssHG8LLxxbCa51tdwfR+xv81PR279m8BSGisbOiNOC81K8aRg2vdcaZtDQSXpHVrd4cSgonXgstXg+dzQvCm036fGNDeCXZQnglAbrYHcJrDvvFcIzWnY5Ra4yoNkD0lVIfXRw88wardNsE4U1HSO5zr53S0PKhj4697qfISaLS2hgNuTxGRQMye+mDHJnE3od+76f9/90ru+olpPczS7pTDgPhdXIXkmNBeHn5ykR/sH690v2uulkyYXKiL4RXcpsgvJIAXewO4TWG/XokRv94IjEDVu4jerY6QP0sOi+El/dG9pLwnj5I9NZPCxIWXFQZowu/10MFWS59/Gt9gE59mHzTnlfXQxWjzYUcwst7/6KkgZdvuuh2Xi2cLpbR52avCrYTS8S4d/napC7q64jtxDJrC+GVpAjhlQToYncIrzHs+rYYrWlN/pPvvw/0W87yZkt4fV2nqWzfVmVh0cISaj/rUooVlrp4V7kzlJeE98Dv/HTgfxKzqIJCOql0g9Sex/3UtDt5bhd+t5tKh5rPAMLLuzupHlor311IRccD1F0ao/DQHmqd0MU7GQvR3S5p6OhppqOd71J3LEyDi86lfgU1FmZprcmfdu2h2+5cRo89tJAumThO6XSypZUeXbeF5t56Pa1+/BnlazIZXieEV78aMcdFP1pDd3/rKzRmRK21xaZpBeGVxAjhlQToYncIrz3hXVHpp8+GrKV4syG8QnZrti0iX3d7fGFd/YbT8b/9vot3lTtDeUl492300+FXvCm8x1730fsbAgmbIrLPkxb2pNwoCC/vfYxjycz5Hu3cQ280P5nQ4IJ+M+is4onSm9IRjtB9K9bS5EkTaObUKw3jaUsaRCb4nqVr6IFFcxTJVPvfOH2KIsv6TPHtN0+lGdddQXULVtLhoyeU+BeMH02rl82jyopy0mZtp10zmZbcPZuKQ0Hl6w07d1NZWQk9+ew2EnH0wi3a7D9wRErE9QuG8EreUhBeSYAudofwGsPe2B6jJS3JGd7fDg4o9bxWrmwIb/ne31L5e79Nml7j5P9DkYG9mYx8ubwkvEZ1soJzuiyqW3sh5te0u/cXtYJQjEZNT19fDOHl3R0IrznfPzQ9Rk1dHyU0KPCF6NrB/yy9KXqBNQpoVXjPHzdakWdVfoUMP7XpJbph2lW0ZVuDIrCq0IpxhLCu37g9Lr9inJHDahTxVkVYm3XWzo0juyviQ3glbykIryRAF7tDeM1hrzwVpSdO99Y4lvmI5vfz0/QSa9ld0cdLwtt84Teo/azLXbyz+IfykvCK1eprZYd9LkrDrk19EgI/pcxHgPBmzs5KTwivOaUtR5cYfvh31fdZQZuyjRDeFQ+vo6WL5ygZVxnhHTtqKM1duIpmTZ+SlC3WlzQYZZZFacWGjdsVKTYSZO3cOLK7EF7p24kIwusARJdCQHj5QGdDeEv3/Y4qdif+KVCsEBlevn3WRu5s8lG4mah0SCwrD6uJh+da9vWWVgyckD6Lm4oKhJf3noHwmvM1zvAW0bWDF0pvipMZXqOSBjVDaya8m7Y2JKxBLWtIJbxW5pwpGGR4MyX3ST8IryRAF7tDePlgZ0N4RQ1vVcOPqfDUgfjCwtUTqeni7/AtNEuRvZbhzRKG+LBGtbrjvp7+vF2zeUN4eXcUwmvON5dqeLWrEBnblfXrlZKFF3e8mVDSoK/91a8+1UNunMekQXglv88hvJIAXewO4eWD6xRkhAAAIABJREFUnQ3hVVcTPLFHkd6ufsPyrnZXXSOEN/He/cN9BdQTTvxav9ExOr8u9cNpEF6+nwGpIkN4U3PvPaVhD3VFw1QdGpe1UxpE7awoW5hfN0t5SE17woMoadi8tYFumXmtshit8L6/72BcftXSCX0Nb7qaXxGTM7sr4kN4Jb//IbySAF3sDuHlg60V3n872kkvhXvrgYcEiL5Z7rf88BvfDHM7MoQ3cf9e/efEc4DVTy/719QvmIDwZuf7AMKbHe7qqHbO4VUlV/S9acbV1NbWrjyopj60ppYpDKkeSPXL5yec5iA+MzulQcRTz9Q1yvBaOVFCliKEV5IghFcSoIvdIbx8sFXh/eXxCP3z0UjCQOcU+ug/q5KPseKbTf5FhvAm7ikyvLl1j0N4c2u/8nW2EF7JnYXwSgJ0sTuElw+2KrzXf9hBf2xP/rOynSPO+GaZu5EhvIl7Z/TyC9Twevf+hvB6d2/60swgvJK7DeGVBOhidwgvH+x0wvvrKj+dW2j9mDO+mfJEFnXERD7qKR5IPSVVjg8C4U1GKk5pUN+qNngSTmlw/KZzMCCE10GYCJUxAQhvxuh6O0J4JQG62B3CywdbFd5lhzvppycSXw0qzvXdXmPxDRZ8U2SJLE6KGPz7H1Kgo/ctQ+JqPeeL1Hr2Fx0dD8LrKM6kYDilgZcvhJeXL6JbIwDhtcbJtBWEVxKgi90hvHywVeE90tFDd/xvmN7oPPMSix8P8NPFQd7sbqC9UZHOrn5nUaywlG+hushmb3s7+tlljmZ60wlvdwfRu78IUMuHvZzF63THzopSxejefTC7RPvDr/iop8NHgeIYDbsmSqVDXcPnmYEgvLxbAeHl5Yvo1ghAeK1xgvBKcvJCdwgv3y44dSxZYcvHJCTS39VB0cJiahv1uZRHjYkM68DXH6Zg07vxxbn5prWqhuUUPPFeElinX36RTnj3bfTT4VcSHwwU0jtpofkxXeLFEW/9JEDdmuO9CkJEF36vh4oGpBZlvjspO5EhvLzcIby8fBHdGgEIrzVOEF5JTl7oDuHl2wUnhFfIa822ReTrbk+YaKpsqdnb1g5//ieuZHordj9Bpfu2JoE9fsX3qatiuGPA0wmv/lW/6sBjvhSlxrd8SuZXZHuHXBGjAef1vgL40O/9tP+/k0/PGHtjDw2+GMLr2Ob1gUChgwGqeKuQAqd9FCskaju7i1rPO3NEHIS3D9wEObBECK/kJqGkQRKgi90hvHywnRDekv/dQf3fejRpkqlqYt3KsJqREw+ribe9aa/IwHOocfICR2FnJLzCWQ0qSSb9c28G1+ikAzHpYZ+L0rBre6W4r1zaDK/IfB/b2QsuNCBGgyb1Lfm3u+dCcgf/LkS+xNJ9ar4kQu0je//CAOG1SxXtOQhAeCWpQnglAbrYHcLLB9sJ4TXL1qYS3v5vraWS/301aWFOZ1hTkRPSW9T0Hok6YvG2t/azLnM8u5xOeI3ktbCMqKsteeYj/z5KtX8bVbK+b9cnP0x44Xe7+1wdryq8h/d20dv/UZBQ5iEy4+dl+AY3vu8470QOHvdT1fai5F9Uz+um1gm9Fgzh9c5+9eWZQHgldx/CKwnQxe4QXj7YTgivqN8d9MoPkybZNOnbFK75tOHkjTKsQjqP/+19fIvNQuR0wiumJKRXSGx3h49Ka2NUGIrRoR3JJQuq8Io++trfIVdEadT0vpXdFRxU4X3ryZ6kWmjxeV/8JcDqbQ7htUrKm+0erF+vTOyuulnenKCDs4LwSsKE8EoCdLE7hJcPtqzwho68SYWnDlDRiXco2LQ3PtHTo66hlgk3p5y4kF6R5S3o6M2wnjr7i45nWO2SE9leMSd/dzt1F1dR+1mXSs3JivDq5yjOqX3rp8mv4DWSN7XG1+4686W9KryvrorSqU9OutCuTWR40514kS8s7K5DlDLUbCpOKmlouixC4aEoabDLk6O9nVcLZzK+0auCM41z7/K1Slftq4sziWXUB8IrSRLCKwnQxe4QXj7YMsKrf/ArVlBCLeO+TO0jruSbMGNkIbvibF7tw3fihRRHr/7XjEfNRHjFYCLre+gVP/WEiQKh3vpcUc6AK5FAugyvWvcMbsYERJa339uFJP5/V/8YtY/optPnyD20tubUbnqh/WNlwLMKyugHAy6hCn9y6QTHntQOLOYIax6zlYj2E1EnEY0UNSDODf+nXXvotjuX0WMPLaRLJo5TAp9saaVH122hubdeT6sff0b5mkyG1wnhFfNcWb+eVi+bR5UV5aT/dyeIQHglKUJ4JQG62B3Cywc7U+EVJzMMeeF7SRMTdbDNF87mmzBjZLOzeWWOKstUeBmXmVehVeE9/r/dtOsnAeUXBPXqq2UeTm6w3RpeIbs/aPpjwhQuC9XQhprrnJyWaSxXhXcfET2vm8pniehc+aV2hCN034q1NHnSBJo51TiBoC1pEJnge5auoQcWzaExI2pJ7X/j9CmKLOszxbffPJVmXHcF1S1YSYeP9r5854Lxo+PSKkRYzdhOu2YyLbl7NhWHgqQKcllZCT357DYScUYOq6GGnbvjbfRzkadBBOGVpAjhlQToYncILx/sTIXXqAZXzJLjpAO+1SdGNhPeVLXI6eZmJrzihRMFLiej0s01Fz/XntIgmJ760E/hJqKK0X3zRRxO76Fd4f3ykefotfCRpGkcHHmb01MzjOeq8D5LRId10wgSkQO/71uRRqvCe/640Yo8q/IrZPipTS/RDdOuoi3bGhJkVaxGSO36jdvj8ivGEVIrxFsVYX3Wee7CVTS8drAivSLm/gNHpDLP+s2F8Ep++0B4JQG62B3Cywc7U+HNxwyv2WkTMidHaIVXCNn7G/zU9HbvA2niZREjp7t7dq6Yg/qii0Ax0eBJ0ZwWb7x4gu9ng4jslPDuHn6zK2UNrgrvv5uw/0f5PRHCu+LhdbR08RylTMDosiq8Y0cNJSGks6ZPScoW60sajDLLokRhw8btcZnVZnPVeYm5vPvBAXrlj39BDa/89jsfAcLrPFOuiBBeLrJEmQqvmFFyDW8xNU6+29EXN4gTIAbs/Dfl9cPiaj/rcmqZMEvqQTIzmkLixdm84iE89ZIt0dAKr9ELI4T0XrSw2xXpFLL7xrLEo7tKaokmfu9MzSbfncYTGcLLw1WNald472x8hTa0vZ8wqX7+IL0z/B94J/pJdFeFN0cyvEYlDWqG1kx4N21tSNgvtazBLCOszegKQV60dA3VL5+vlFc4cSHDK0kRwisJ0MXuEF4+2DLCK2YlhDR0bBeJh7s6qic6LqLV2/45LrsqhVTn+zpBSpRriEs8hCf71jWt8O553E9Nu5OPG3PrJAGzN7S5Nb4Te6OPAeHloHompl3hPdDdRvMaX4mXNQjZfWTw1STqeN24XBXeHKrh1bLXPlT24o43E0oa9LW/+j0zeshNW/Ig2osH60RGeX7drPjDdrJ7D+GVJAjhlQToYncILx9sWeHlmxkpL4SofnFh0hC5VCesFd696wN0/JM3gWkX5ZZw5uMb2iC8nN+B9ksa1Nm0RDvpVLSLhhWU8U5QF91V4RVji1MahPhGsntKg14ytSc8iJKGzVsb6JaZ1yq0tML7/r6DCScsiM/1Nbx2a36R4XX1lrc2GITXGicvtILw8u0ChJePrYisFV5Ru7vnF4kZ3qLKGE1a2HvmKfeFDC834fyLbzfDm20Crgsv84LtnMOrSq6Y0k0zrqa2tnblQTX1oTW1TEF7Tq6a0RWfmZ3SIOLdv2B2/KE1sxreR57YrNDAObzMN0Um4SG8mVDLTh8ILx93LwuvWHU2ShqcpK0/peHY6z46tlN9aC1Go6bHqGhAzMkhTWOJGt6/1hdQu+bJ8n6jY3R+Dr9+Fxle3lsHwsvLF9GtEUBJgzVOpq0gvJIAXewO4eWD7XXhFTXC4riwohPvUndJlfKq4tazv8gHxOHIXjyHV7yd7fRBH5UOjeX8W8ggvA7fsLpwEF5evohujQCE1xonCK8kJy90h/Dy7YLXhVe/clHXW7F7Hfm7OpSPOmo+TadHfY4PkGRkLwqv5JI81T0U6qbj3X+l9shpCvmqqcI31lPzy/XJQHhzfQfzY/4QXsl9RIZXEqCL3SG8fLBzTXiNShyaL/yGclyZFy8IL9+uRGIttDf6OHXHzrxerdJ/AQ33/x3foH0sMoS3j224R5cL4ZXcGAivJEAXu0N4+WDnkvCK8oZBr/wwCYaXT22A8PLdu4eiW+l4dGfSAOcEbqViXzXfwH0oMoS3D222h5cK4ZXcHAivJEAXu0N4+WDnkvDm4uuMIbx89+4HPU9QW+zMS0LUkcYEvkJlvuF8A3s08tuRE8pRYOK61KFzbyG8Ht3sPjYtCK/khkN4JQG62B3Cywc7l4RXUBjy/D+RTxw3oLm4X0QhQx/CK0Mvdd8j0R10NLoDGV4i0r/h7LzgANpQ8wXp1/lCePnuX0S2TgDCq2Glf9OH+pE4QPne5WuVf1VfjVccCir/DuG1frNluyWEl28Hck14Q0fepMq31salN1w9kU5e+A3H3/DmFHEIr1Mkk+P01vA+Rt2xzviHlb7zaXhgKt+gHowsMrufP7QxaWY/GPAZmtNvgtSMIbxS+NDZIQIQ3k/eCKIKrXowsspX+zaRyopyElIsrrvqZkF4HboJ3QoD4eUjnWvCy0eCJzKEl4erGlWc0tDU/R6dipykMt+wPlnK8Gr4CN145Lkk0DeWjaWHqq6Q2gAIrxQ+dHaIAIRXA9Iow6v/ml6AkeF16E50IQyElw8yhJePrYgM4eXli3N4icyE967+E2l+/4lSGwDhlcLH2lmfxGMdLMvBIbwphFd9Xd7kSROU1+GJS7yi756la+iBRXNozIhaOtyUWAcos59FBX4qLS6kptYzf1qTiYe+iQT6lRRSd0+M2ju7gSZDAod6iP7jVJQORXsD3Fzio88W+6g4GKD+ZUHqiPRQc5t4ITwuJwkU+H1UWV5Ex1vOHJ3lZPxcjiVKEiJ0iop9gyhAoYyWUhoqIL/PR60dvQ9r9dXr2oO/pbcjTQnLf2HodDo/OFAKycDyIoVtpPuTHxxS0fg7DxlQzD+IiyPYebVwJtMSZZ9Grwq2G0tbPqp9RbHdOGbtIbwaMvpsriq84j3Sl0wcp7TUC2/Mybd5+oh8RORoTKfulDyI4xNwwVdqJz/z3mk62JV4028YWUyXlQYIfKXQpu6Mnw2GfP548jFq6voo/tnY0qtobOkU2xuBe7cXWXNPJz124l16q6ORRgbL6daB45T/L3sJvspPDSf/eyk7qRT91fuBcYjE0JFjRCf/SNTTTtT/EqKSUY4NLf4qfdudy+ixhxbGPeZkSys9um4Lzb31elr9+DPKWGqZZiYDOyG8RuWjR4410ZK7Z5P6zFQmc9P2gfBaEN5UGV6UNMjegu71R0mDHOvXIzH6xxPJGZqZpT66f1AhVYoMb2cPnUSGVw60QW+UNCRDOR59nQ5FtyV9kMn5uShpcPyWTQiIkoYUfJv/QLH3lyc08I38DlHVZ6U3xeiv1Pqg2pIGfUJPn/TTZ4pvv3kqzbjuCqpbsJIOHz2hhNZmZs0e+FcFuayshJ58dht9/cYv0ImmFkrlWtIwiAjCm0J4xUeo4XXiNvNGDAiv3D7ohVdN1nySOKdLSwO0bHAhlYb79p+F5Sgb94bwJnMxO04sk/NzIbwcd+2ZmBBec76xd+8lat2d2CBQQr5P/1J6U/QCaxTQqvCeP2403bdiLal/8RYy/NSml+iGaVfRlm0NSSUNQmrXb9xOq5fNI/WB/5HDapTyUFWE1ayzkZiLLPTchatoft2seGZaFgiEN43w4pQG2VvMO/0hvHJ7Iep3v3isJx5ECK8qu+oXZ/YL0OJSuXHQO5kAhNe68A70X0T9fefaqumF8PJ+10F4Uwjv6zcYfui7+CnpTRHCu+LhdbR08RxFOmWEd+yooYqAzpo+Jf5MkxpPX9JgJLDCpTZs3K6UKJgJsrYOGMIrvf3GAbRpd9FiSPVAql8+X3koTVw4h5cJvMthIbzywDe2x2jlqSi1mdTiTSjy0y8G6DVYfty+HsHLwtsRO0o91PugojjSy61LjPtez+Omv4AFfRUkyhusPMgG4eXdNQhvCuHNkQyveI5JX9KgZmjNhHfT1oaEhavvMTASXlWStX30LiZ7lyLDK0kQNbySAF3sDuFNhn0qRvTD5ihtD/ca7JAA0X39/XRxMLW0vtsVo1sak+t5P1MSoIcrXNzUPjKUV4X3457NdDL21/gu2JFMJ7auLfYxNUX/SmE6TkKA9Ve1/3Kq8V+edigIb1pEUg0gvCnw5VANr3YV2r9+v7jjzYSSBqMH/rV9rTzkJuT610//D9099yt4aE3qu8/BzhBeB2Eyh4LwJgOub4vRmtZEcS33Eb1YE0i7G99sitIbnYmp3u8OLKSvB3Pj6KG0C/RAg5Kd71HhkSaikiIKnTecjg6WOx7KySXpM6xq7Fr/1TTIf7GTQ6WNJcT3g551Se0G+SdRrf+atP2dFl7xQN2p2PvUETumZL2r/ZdRsa867TzytQGEN83OfnJKQ6znNPn6fyZrpzToywi0JzyIkobNWxvolpnXKovRCu/7+w7Syvr18Xpd8bm+hjddza+WEEc5g4iPDK/kTxgIryRAm91FZlFc5xba/7M5hDcZtpG0ila/rvKnZSyywytbonQ4SsoZplf2K6BvVwRwSoPNe9qsecV/v0alr76d8HHzDVdS+6RzbI/g6+ik4nc+osDJNuoaMpDCE0bYjqHvICuZ0hPQBDCbSzYyvC2xvbS/5zcJyxNlFeMLvmmpvMJJLl6JBeHN7k7YOYdXlVwx45tmXE1tbe3Kg2rqQ2tqyYG23EBbjmB2SoOIp77J1ijDq0ruX975MKms1Cl6EF5JkhBeSYAWuwvR/T8no3T4k2emxJ/ef1yZXsq04SG81oX3t4MDVJs+yRsPiDetWbyRbTSrXfzzM60/OcQ0MrqWGudMsxGFSMhuzYonyRc+80KQyKghtuNYFV6rkmlrERYav9vzGIVjx+ItA1RE5wRuI1Fmke5yMsN7KLqVjkd3Jg2pPz3i7cgJei18lCr8QZocqqFhBWXpppmzn0N4c3br8mriEF7J7YTwSgK02P3mxijt1b3w4KoiH60c4LcYgQjCm4xKPIS2pCWxBEFUM/z3YBu2S0QQXsu3oeWGivCqb6FRT8L3ER3/9vXUVVtlOU751jdI/E9/Nd4xjSKjh1iOY9RQL5mizfhAnSXJlBrYpLMoJeih3jdVinIGKw+sibZuC+/6tr00r3FHwioeGXw1XVcynANL1mNCeLO+BZgAShrk7wEIrzxDKxEuVlO7usavi1SvxQvCawxK1PHujMToUHeMzi3w0fwKv63srogK4bV4E9poNuSHvyBfRyTp7Lfw+OHU9LXPW47EKbw9FFYeGuuiFvJTiAb4zrcsu+JP/yIjKzKw/XxjLcup5YXbaOik8DZF/0IHolsSRtdnm8d//J90Kpr4Cu5LQzX0XzXX2Zh17jSF8ObOXuXzTJHhldxdCK8kQIvdjYTXbiYSwmsRdgbNrAqvqPtti5Jtoc5gSoZdxJ/3C062psyQijZlr75Nod0fkT/cqdS8tkybTD2V8q9YtbMO8cBa/6deTuoSCwXp8Pe/bjkUp/BanoSu4b6ep5WHutRLZGLFEWJWyg8yHTNVPyeFV4yjLWsQsjssMJUqfGfHpzB0/2OG0zk48jaO5WU9JoQ361uACSDDK38PQHjlGVqJIM5+feJ04okAc8r9VFdm/eE1CK8V0pm1SSe84qUVogb7vU/KUsRJECsGpD/+LLPZJPcSEjvwV/9DwX2HlQ+FNAqJNXoAzEgQhfQe/6cvOTUdy3ES6ng/6WV3Llw1vJYXoWtodrpDtmp/xfScFt50bJDhTUcou5/XDizO7gQwOgsBZHglsUJ4JQHa6P6fp2O0/ZNjsKYU+egfSq3LrhgGwmsDts2m6YT3vuYobepI/IXF6vFnNqcSbx788HC8RrV0x1+pYlPiIehmmdKqNZviYqwd+9CP7sh0Khn3MzqpofWai0j8z86lnNKw+yMKNDt3SoOd8bVtzU5UEMd3jQncnGlYqX5uC+/K5l30YPOuhDmjhldqCx3tDOF1FKdngkF4JbcCwisJ0MXuEF4+2OmE1+z4s201Aepn7/eWtIvQS+Lpy8+nwkMnDCXW6MEtM+E9fO/XKFZclHZ8pxsIWS/Z/REVlIeo5exhGR1L5vScZOIhw9tL79XwEXotfET551llY3FKg8xN5XBfCK/DQD0SDsIruREQXkmALnaH8PLBzlR47Tx0aGX2hYcaadD/eyapqSgDKDx8Iunrx7+TfOKBUVa1p38ZHV3wFStTYGnj1TetZbrY5Bpe60eIZTpmqn5uZ3g51uDlmKjh9fLu9J25QXgl9xrCKwnQxe4QXj7Y6YTX6I1uFxX56D9sHCtnZfZGpQuiX8enRlPxnz9MCGFWCyv+/F/5Xy9R6J2PlfZCdpu++jlbR4FZmaudNoWRCA348CC1HzxJ0VCQ2i86OyvZZjtzTtdWnNIg3kQWpH5U4T87b05pSLfuvvg5hLcv7rr31gzhldwTCK8kQBe7Q3j5YKcTXjGytgb73AIi8dCh0+UM4mSFAb/6XdJCRc2rENeSN/Yqn3VXlil1sG6fvJDpDgz+2W+oQJOhFvXHR+6+KeelN1MeTvdDhtdpoonxILy8fBHdGgEIrzVOpq0gvJIAXeyeK8IrTjSw85YzFxGaDmVFeN2Yp9GJBGLco3fflDNyq+dkJvHilAlRn4xLnkC2hVe8dU28iOLtSJOymMtCNfTzwZ+lCr/7NePyNJMjQHg5qCKmXQIQXrvEdO0hvJIAXezuZeEV59Pe3RRVXgAhLreP7ZLdBq8Ir1iHqOMVR4v5w10UDRVS2+UXSL9RTJaPTH+zc3QzOa1BZh753Dfbwnvtod/S7k9kV+V8Y9lYeqjqirzADuHNi23M+UVAeCW3EMIrCdDF7l4WXqNzhrmP7XISvZeE18l1eSGWOF6t6uebkqbSfMOVOX9igxf4ijlkW3iNXkRxXnAAvVD7Ra8gkpoHhFcKHzo7RADCKwkSwisJ0MXuXhZes2O7fl3lp3MLHT63i4E5hJcBqiakvoZXPHDXeMdU1PA6hN2LwptPrxqG8Dp0oyKMFAEIrxQ+IgivJEAXu+ei8HKcU8uBHMLLQfVMTHEs2cDDjdT+l4+UVx2HJ4zgHbCPRc+28H75yHPxM3lV9Hf0G09LBvxNXuwEhDcvtjHnFwHhldxCCK8kQBe7e1l4N7bHaElLNIHG2YU+eqLK7yKhzIeC8GbOzkrPfDuH18qaM20jXmxxKva+0j3oq6BKX/oH+7ItvAe62+i+pj8oD6318xfRZaFquqv/RDy0lulNINkPL56QBOjR7hBeyY2B8EoCdLG7l4VXYNAe2zXET1RX7s+Z0xogvLw3MoTXGl+j1xYP8k+iWv81KQPICK8Ys9g3OKvnCFujk71WyPBmjz1GPkMAwit5N0B4JQG62N3rwusiCseHgvA6jjQhIITXGt8Pep6gttiBpMYXFixwXHiPR1+nQ9Ft8bhlvuE0JpC9t/FZI5SdVhDe7HDHqIkEILySdwSEVxKgi90hvHywIbx8bEVkCK81vmbCe07gVir2VZsGsZvhjcRa6J2e+qR4tf6raZD/YmuT7UOtILx9aLM9vFQIr+TmQHglAbrYHcLLBxvCy8cWwmud7b6ep+P1u9peTmd4jUonxHhWyiesryZ/WkJ482cvc3klEF7J3YPwSgJ0sTuElw82hJePLYTXOlvxwNoHPeuohzrjnaxkXe1meM2Et9p/OdX4L7c+4T7S0o7wtkR79y6bb5nDQ2v5eWNCeCX3FcIrCdDF7hBePtgQXj62EF57bHsoTB2xYyTKDsTDZKlKGdTIdoVXjPFu92PURacSJidqeEUtL65EAlaEV/965WEFZfTI4M/SecGBruOE8LqO3JUBIbySmCG8kgBd7A7h5YMN4eVjC+HlZSui2xVe0UcI9ZHoDuqiFvJTkVK7C9k13isrwjv72FZ6vj3xgcMvlAyjtYNTn7DBcXdAeDmoZj8mhFdyDyC8kgBd7A7h5YMN4eVjC+HlZZup8PLPKn9GsCK8Rq9XFgQOjrzNdRAQXteRuzIghFcSM4RXEqCL3SG8fLAhvHxsIby8bCG8/HytCO/4j/+TTkUjCZPp5w/SO8P/gX+CuhEgvK4jd2VACK8kZgivJEAXu0N4+WB7SXh9HZ1U8sZeKtp3mHoqy6lj/AiKjB7Ctnh1vOLdH1G0OEjtF53j+Kt/OY8l8zUeIV/TUYqecyEbI68HzqSkwetr8tL8rAjvnY2v0Ia23jfkqdeNZWPpoaorXF8KhNd15K4MCOGVxAzhlQToYncILx9sLwlv1ZpNFNx3OGGxjXdMY5Neo/Gavnqto9LLIrztrRT69yXk3/tWL6viMorc+I/UfekX+G4Uj0aG8PJujBXhFacz/PzUO/Ra+IgymfOClVl7vTKEl/d+yFZ0CK8keQivJEAXu0N4+WB7RXgDJ1upesWTSQttv+hsav7yVY4DENndIff/MiluZNQQapwzzbHxOIQ3uOFhKtj2m8Q5FpdR+4O6rzm2Cu8GgvDy7o0V4eWdgb3oEF57vHKlNYRXcqcgvJIAXewO4eWD7RXhDX54mKp+voldQNUBCg810qD/9wz7eBzCG1o1n/zv/Tlp7uF5Kyh6zkS+m8WDkSG8vJsC4eXli+jWCEB4rXEybQXhlQToYncILx9srwivWcb19GXnUcvfX8oCYMgPf0G+cOLDNk5nlN0U3o77f0mxqhoWVl4Nmk3hPdDdRo+c2k1vR5rovOAAurFsTFbOnuXcGwgvJ13EtkoAwmuVlEk7CK8kQBe7Q3j5YHtFeMUKS3aPf4w6AAAgAElEQVS+R/2fejm+2K4hA6nxjqkUKy5iASDGq9jUEJdejvE4hDewawcV1f8ggUn0nE9ReN5KFk5eDpot4RV1q184tJGE9GqvhrO+TOLFC/lyQXjzZSdzex0QXsn9g/BKAnSxO4SXD7aXhFesUtTyBk72SgTnCQ1aoqKcIhYqpK7aKsdBcwivwmnXDip47XnyhU9T9KwxFJn2NaKScsfn7/WA2RLeV8NH6MYjzyXhuav/RJrfP3/KSiC8Xv8O6Bvzg/BK7jOEVxKgi90hvHywvSa8fCvNTmQu4c3Oarw3araEd33bXprXuAPC67FbAg+teWxDHJoOhFcSJIRXEqCL3SG8fLDNhPfNXT7a865PGXj8uBhNvDDGN4k8jgzh5d3cbAnv25ET9PlDG5MW94MBn6E5/SbwLtrF6MjwuggbQ5kSgPBK3hwQXkmALnaH8PLBNhLebS/5aftL/oRBp1wVpauvivJNJE8jQ3h5NzZbwitWdV/TH5TzZ9Xr0lAN/VfNdbwLdjk6hNdl4BjOkACEV/LGgPBKAnSxO4SXB/bJZh/VVvupsixIHZ09dLKt98SCB38SoOaW3uyueoVCRIsXdPNMJI+jQnh5NzebwitWJh5aE/8TD6rl08Nq6q5BeHnvX0S3RgDCa42TaSsIryRAF7tDeJ2FLcoVtrwQoHC4N+65Y300+2s+6uzpFd7v/7DAcMAfft8Z4RUPpolXCIsrGhKv9D2b7SQGZ8nZjwbhtc/MTo9sC6+dueZiWwhvLu5a/s0Zwiu5pxBeSYAudvea8O7b76P9H/VmQEeOiNGokfbrW4V0vviyn5qbfdS/f4w+e2WUPj3RfpxMtuFH/1pA4c7Enn93rY8uvbRL+eLaxwPx9amtqquJvl0nL7xCdgf/7DcJ59+K48CO/9OXMlmK5/tAeHm3CMLLyxfCy8sX0a0RgPBa42TaCsIrCdDF7l4SXiGqv/ltIGH1X/pijy1ZFaUEq36aGEMEnPvNbhrC/N6Aw0eIVv9HcgZ37Ggfff2rvcIr2jz6+BkpDhURfeNWZ+ZWvvUNEv/TX413THPtGDIXb12C8PLShvDy8oXw8vJFdGsEILzWOHlCeLUZQfG0e2V/dzJ5kog8091LwmtU3yoytHd9t8cyr1cb/PTcC4kPhYnObjwYZibbWuFVFyLuW3FlksE2g2EmvE1fvZbCE0ZYZpgrDSG8vDsF4eXlC+Hl5Yvo1ghAeK1xyrrwbnneT6/9IVFuvvH1HkclQhKF57t7SXidqG/NpvCKzf63+gI6ejRx22+Z5aNzx/VmeDmv0h1/Vd5upr+Of+d6lhc/cK7FSmwIrxVKmbeB8GbOzkpPCK8VSmjDTQDCa4Hw05tfpnuXr1VaTrtmMi25ezYVh4LKv7tV0mAkSKLuc/at1jOCFpaa1028JLxGsmi3vjWbJQ3iRhHjv/iSqB8m8vt8dNVlAbpoYix+SgPnzeTr6FRqeAPNZ17JGh4/nJq+9nnOYaVi+xqPUGDvn4k62ih69qcoOmys5XgQXsuoMmoI4c0Im+VOEF7LqNCQkQCENw3cP+3aQyvr19PqZfOosqKcHqxfr/S4q26Wa8JrJjYQXnvfGV4S3nf2+OmJ9YkZ+5tnRWn8OHtn1Io44rxbkWkVwizOuLUbwx5F49bZetOaeJ1v4eETFBlV4+nMrv+9XRT69yWK7KpX17SvUdfff90SfgivJUwZN4LwZozOUkcIryVMaMRMAMKbBrAQ3JHDamjm1CuVlnoBzmaGd9y5UfqHm+wJEvP95OnwXhJeAUr8IrN/fy+ykSMpp2uysyW8nr7hNJMrWv19Cvz5taTptq/+naUlQHgtYcq4EYQ3Y3SWOkJ4LWFCI2YCEN4UgDvCEbpvxVqaPGlCXHg/+OgQ3bN0DT2waA6NGVHrWkmDvl5TPPF+802o4bXz/eE14bUzd6+3dVp4xQkPe971k88Xo5EjfTRyeG7/YhdaNZ/87/0ZwuvRGxnCy7sxEF5evohujQCE14Lw3jh9Cl0ycZzSUi+81jA70+rjgzF6d2+MSoqJzj3bT1UDnImLKCDgJQLrnu6h322PEvmU/1OukcN8dNe3C5R7Pxevth98h7p370qaev/1r+TicjBnEAABEMg5AhBeC8KbKsObczuOCYOAxwnc8b0uInHiXuJbielzV/npKzOTzx32+HKU6XW//Qa1LfluwlSLpt5Ixbd9LxemjzmCAAiAQM4TgPCm2UKv1PDm/J3mgQWgpIFvE5wqaRBn9j76eCBJdpUsb46fSiJOaShoeEHZhJ5zPkXRcyZa3hDU8FpGlVFDlDRkhM1yJ5Q0WEaFhowEILxp4HrhlAbG/e9ToSG8fNvtlPCKGd77wwJ9cleZeF9+SBPCy3fvisgQXl6+EF5evohujQCE1wInL5zDa2GaaJKGAISX7xZxUnjFS1bEQ5o+XUlDJse28a3Y3cha4fUfeJ+o47Qygeg5F7o7kVwcrb2Vin7xYwq89Wovs2FjKPK1/5NwDnKuCO+r4SP0yKnddCoaUdZye78JdF3JcM/vCoTX81vUJyYI4ZXcZreOJZOcJroTEYSX7zZwUnjFLPe856OXf++n0+0+Ki2J0SWTovTpiX33Vdqq8Db/5P54WYQib2dfSOF/vI+opJxvc3M8cvDxFQnMxHJiA6up419+FV9ZLghvS7STLv3fp6jlE9lVJ/9C7XQ6LzjQ07sE4fX09vSZyUF4JbcawisJ0MXuEF4+2E4LL99MczOyEN6KEx9Tx6LZSQuIfHkudV8zMzcX5sKsrRwJlwvC+1z7x3T7sW1JxO7qP5Hm97deD+4C8qQhILzZoI4x9QQgvJL3BIRXEqCL3SG8fLAhvHxsRWQhvP32/IHCD96TNJCdN7bxztKb0fNFeNe37aV5jTsgvC7cZrUDc/T8QxfY5PIQEF7J3YPwSgJ0sTuElw82hJePrSq8FQfepo77k48xg/CmZl/437+gwk2/TGgUPedTFJ63Mv61XMjwvh05QZ8/tDFpsauqLqdZZWfz3oCS0ZHhlQSI7o4QgPBKYoTwSgJ0sTuElw82hJePrSq8A8qLqPXbN5Cv6VjCYB33/5JiVTW8E8jl6O2tFNz0S+VNd772VoqeNYYiN34rgVkuCK/YgjWndtODzbviD63d0W88LRnwN57fHQiv57eoT0wQwiu5zRBeSYAudofw8sGG8PKx1QrvsUPHqXDbb0ic1BAdNpa6J38esusA+lwRXnWp4gG2Cn+RAyt3JwSE1x3OGCU1AQiv5B0C4ZUE6GJ3CC8fbAgvH9sE4W0O2xtIyW7+igJv7SDfiaPUc+FlJEoghCzjOkMg14Q31/YOwptrO5af84XwSu4rhFcSoIvdIbx8sCG8fGxlhNewfnXYGAov/nfeCedYdAgv74ZBeHn5Iro1AhBea5xMW0F4JQG62B3CywcbwsvHVkZ4TU8oWPk0zu7VbBmEl/f+hfDy8kV0awQgvNY4QXglOXmhO4SXbxcgvHxsIby8bEV0CC8vYwgvL19Et0YAwmuNE4RXkpMXukN4+XbBCeHtCBPtestP+/cTFYV8NP7cGI0fF+WbNHNk/3u7lBMBnHgLmvbVwnamHdzwMBVs+01Cl9iAwdTxwK/thPFM24LXnqeC135HFG6j2IBqx+qRIby8W/z/27u/GDuq+4DjZ9ebZTf8s6ESBhVBkyoBqraOogjnBVxQE4WUtEEySh4Kwi04plIlsECBCEUoBVIooU9xDAop5IHIVPRPFAJIIMgDcRVVcVoVUNQQEJVZKGADCjZmvVvNpV7v3r3rmXvP/K7PLp99CvacM7OfczP73fHcuYI31tfszQQEbzMnwZvpVMJwwRu3Cm0E7733rUovvDiy4CC/fOnMsovesccfSuP/uG3u+6jeKPbuV27Owh80eFP1prUHv/P+m9b2/SZVz5+tPpltOb5prfoFYuKu6xY6Th6X3vmb+7N/qRC8WS/P2sGCt5bIBkMQELyZyO7hzQQc4nDBG4edG7zV1d3bbh9bdIBnnjGbNl1+MO7AW565elzYxK1bFs2a+/G/Awdvy9/f0Zyu19Xq6nj2X3NHmvlY3kfrCt7YlRW8sb5mbyYgeJs5ucKb6VTCcMEbtwq5wfvyVErb7l4BwdvrKmRKnX96f+9PLht4AQRvSoJ34JfPUR8oeI/6EjiAlJLgzXwZuMKbCTjE4YI3Djs3eKsju/Vvx9L+dxce47o/nE2X/OkyusIreMNeZNX9u+P3/92i+dv4pDlXeMOWrTOx4I31NXszAcHbzMkV3kynEoYL3rhVaCN4f75rJP340VVz0bv6xNl0xeUzac3q2bgDb3vmd95Ok7d8ZdHH/+6/cVvWfbOu8L6/UOP33ZHGdj7W+d+zk8em9zZuSdOf/mz2KgrebMIjTiB4Y33N3kxA8DZzEryZTiUMF7xxq9BG8FZHV93LOzX1/hvXfufMvNDds3ck7d37/vecO1c/ciOvTaUP/ej7afSNqTQ7cWx678JLsu8xFbz9rED/2wre/s36GSF4+9GybZSA4M2UdUtDJuAQhwveOOy2gretI3x652h65LHRuenWrk3pisum0+REW3sY7jyCN9Zb8Mb6Ct5YX7M3ExC8zZxc4c10KmG44I1bhTaC94mnRtOuX1RXZUdSFah/dN5gjyRb6okPG86fSRecvzyf6yt441671cyCN9ZX8Mb6mr2ZgOBt5iR4M51KGC5441YhN3iffW40PbDj8BXZ6kgnJlLactXBvu/h/fULI+l7969a9M0ut0eczf8GBG/ca1fwxtpWswveeGN7qBcQvPVGR9zCLQ2ZgEMcLnjjsHODt7q6++RTC4O3OtorLjvY9/23Sz3ibLk98UHwxr1eu2d2hTfWWvDG+pq9mYDgbebkCm+mUwnDBW/cKpQUvNV32etT2waJ5zix/mZ2hbc/r363Frz9ivW3veDtz8vWMQKCN9PVFd5MwCEOF7xx2LnB2/OWhmNS2rK5/1saqu+yuo/357tG0wsvprRmdUpnfXy27yvFcVr9zyx4+zfrZ4Tg7Uer/20Fb/9mRrQvIHgzTQVvJuAQhwveOOzc4K2OrPOmtV0jae+bI+mUU1LnDWZnn7U832TWtrTgbVt04XyCN9ZX8Mb6mr2ZgOBt5rTkVoI3E3CIwwVvHHYbwRt3dMt/ZsEbu4aCN9ZX8Mb6mr2ZgOBt5iR4M51KGC5441ZB8MbZVjML3lhfwRvrK3hjfc3eTEDwNnMSvJlOJQwXvHGrIHjjbAVvrG01u+CNNRa8sb5mbyYgeJs5Cd5MpxKGC964VRC8cbaCN9ZW8Mb7Ct54Y3uoFxC89UZH3MI9vJmAQxwueAOxZ1alV6Y+lJ5/8WBafdLBdPbHvdmsTW23NLSpuXguV3hjfQVvrK/ZmwkI3mZOrvBmOpUwXPDGrEL1CLD7vj+Wdr98eP7qo4Gvvmo6ZocfwFkFb+yiC95YX8Eb62v2ZgKCt5mT4M10KmG44I1Zhad3jqZHHmvnU9JijnD5zyp4Y9dQ8Mb6Ct5YX7M3ExC8zZwEb6ZTCcMFb8wqLPWxwBvOn+k8S9dXvoDgzTc80gyCN9ZX8Mb6mr2ZgOBt5iR4M51KGC54Y1bBFd4Y1/mzCt52jEdf+u80+j/Pp5mTT0kzv/2RlD58fGdiwduO71KzCN5YX7M3ExC8zZwEb6ZTCcMFb8wqVPfwfufusbRn7+H5q09K+6vN7uFtS1zw5kuOP/jtNPbEPx2eaPK4tO/GbWn2t9YK3nzeI84geIOBTd9IQPA2Ylp6I09pyAQc4nDBG4g9syr9+vmxNPW/M2licjp9Yt1s4M4+eFML3rw1H3ltKk3e9OeLJpm+4IvpwMarBW8eb+1owVtLZIMhCAjeTGTBmwk4xOGCNw7bc3jjbKuZBW+e7+gvd6WJu65bNMnMx/4g7b/mTsGbx1s7WvDWEtlgCAKCNxNZ8GYCDnG44I3DFrxxtoI339YV3nzDnBkEb46esW0JCN5MScGbCTjE4YI3DlvwxtkK3nZsJ+7amkZ/+R8LJtt/47Y0c/rvusLbDvGSswjeYGDTNxIQvI2Ylt5I8GYCDnG44I3DFrxxtoK3Pduxnz6aRl5/pTPh9PrPdN6wVn15SkN7xr1mEryxvmZvJiB4mzktuZXgzQQc4nDBG4cteONsBW+sreCN9xW88cb2UC8geOuNjriF4M0EHOJwwRuHLXjjbAVvrK3gjfcVvPHG9lAvIHjrjQRvplEpwwVv3EoI3jhbwRtrK3ib+z69fyo9c+CN9HvjJ6VzxtekE0ePaTRY8DZislGwgODNBHaFNxNwiMMFbxy24I2zFbyxtoK3me+mVx9Pj77z0tzGp48dlx497eJG0St4mxnbKlZA8Gb6Ct5MwCEOF7xx2II3zlbwxtoK3nrf/zrwevrM7h8u2vDa1evS1tXraicQvLVENhiCgODNRBa8mYBDHC5447AFb5yt4I21Fbz1vtWtDBunHlm04V+ecHa6+aRzaycQvLVENhiCgOCdh/yt7TvSmaevTZdcdN4C+oce/km66fZ7O3/2+QvXp5uv25QmJ8Y7/y14h/AqbWkXgrclyB7TCN44W8Ebayt4632XCl5XeOvtbFGOgOBNKc0P2m9cv2lB8P5s13Ppzu070rZvXpPWnHh8qqK4+rp286WCt5zXcaMjEbyNmAbaSPAOxNZ4kI8Wbkw10Iaew1vP9se7/7XzhrVDXyeMjqfHTvtCqu7lrftyhbdOyN8PQ0DwzlPudYW3+8+6A9gV3mG8TNvZh+Btx7HXLII3ztYV3lhbV3ib+97z1jPprZkDnQHV7Qye0tDczpZHX0DwHiF49+0/kL5+x71p/SfPmbvq+6sXd6ev3XZPuuWGK9NHzzgtTe3Z39oqHjM2mo6dHEtvvP3+CcVXuwInfHgsTR9M6Z13p9ud2GxpcnxVqn6h2HfgYHrzN+8RaVmgusK7+tjx9Npb77Y8s+kqgWMnxtLoSEpv73NuiHhFnHz8eMf2wPRMxPStz7l2zUTrc5rw6AsI3gbBu/HiDelT687qbNkdvDMzs+2t4khKI2kkzc62OGd7R7fsZxoZGUkpzSa87S9lRVv5VrZev+37VjOOjo6kVs83MYe5LGftnBqce8PWrnNuSNXJIWwXrU5c/X/N18oTWNHBW92O8N0HHu65at336lYbdd++0OQKr1sals//KdzSELdWbmmIs61mdg9vrK97eGN93cMb62v2ZgIrOnibERzeyj28/Yotr+0Fb9x6Cd44W8Eba1vNLnhjjQVvrK/ZmwkI3nlOvYLXUxqavZCWw1aCN26VBG+creCNtRW88b6CN97YHuoFBG/XY8kqslNPOTltv31r501p1Zfn8Na/kJbDFoI3bpUEb5yt4I21FbzxvoI33tge6gUEb73REbdwD28m4BCHC944bMEbZyt4Y20Fb7yv4I03tod6AcFbbyR4M41KGS5441ZC8MbZCt5YW8Eb7yt4443toV5A8NYbCd5Mo1KGC964lRC8cbaCN9ZW8Mb7Ct54Y3uoFxC89UaCN9OolOErPXhfnkrpp/+2Kr25N6W1a2fT+nNn05rVw3nwpeCNfZV7LFmsr6c0xPoK3lhfszcTELzNnJbcyj28mYBDHL6Sg3fP3pG07e5Vaf+8D/6bmEjpmr+eTpND+NAgwRv7Qha8sb6CN9ZX8Mb6mr2ZgOBt5iR4M51KGL6Sg/fpnaPpkcdGFzF/8QsH0yfWxV/lFbyxr3DBG+sreGN9BW+sr9mbCQjeZk6CN9OphOErOXifeGo0PfnU4uDdcP5MuuD8+M+vF7yxr3DBG+sreGN9BW+sr9mbCQjeZk6CN9OphOErOXiffW40PbBjcfBuuWo6nbo2Xl/wxhoL3lhfwRvrK3hjfc3eTEDwNnMSvJlOJQxfycFb+T70L6vSrl+MzFF/+tyZ9LnPxl/drXYoeGNf4YI31lfwxvoK3lhfszcTELzNnARvplMJw1d68FbG1ZvX9v7/UxqG8Wa1Q+sqeGNf4YI31lfwxvoK3lhfszcTELzNnARvplMJwz8IwXu0nAVvrLzgjfUVvLG+gjfW1+zNBARvMyfBm+lUwnDBG7cKgjfOtppZ8Mb6Ct5YX8Eb62v2ZgKCt5mT4M10KmG44I1bBcEbZyt4Y22r2QVvrLHgjfU1ezMBwdvMSfBmOpUwXPDGrYLgjbMVvLG2gjfeV/DGG9tDvYDgrTc64hY+aS0TcIjDBW8ctuCNsxW8sbaCN95X8MYb20O9gOCtNxK8mUalDBe8cSsheONsBW+sreCN9xW88cb2UC8geOuNBG+mUSnDBW/cSgjeOFvBG2sreON9BW+8sT3UCwjeeiPBm2lUynDBG7cSgjfOVvDG2greeF/BG29sD/UCgrfeSPBmGpUyXPDGrYTgjbMVvLG2gjfeV/DGG9tDvYDgrTcSvJlGpQwXvHErIXjjbAVvrK3gjfcVvPHG9lAvIHjrjQRvplEpwwVv3EoI3jhbwRtrK3jjfQVvvLE91AsI3nojwZtpVMpwwRu3EoI3zlbwxtoK3nhfwRtvbA/1AoK33kjwZhqVMlzwxq2E4I2zFbyxtoI33lfwxhvbQ72A4K03EryZRqUMF7xxKyF442wFb6yt4I33FbzxxvZQLyB4640Eb6ZRKcMFb9xKCN44W8Ebayt4430Fb7yxPdQLCN56I8GbaVTKcMEbtxKCN85W8MbaCt54X8Ebb2wP9QKCt97IFgQIECBAgAABAstYQPAu48Vz6AQIECBAgAABAvUCgrfeyBYECBAgQIAAAQLLWEDwLuPFc+gECBAgQIAAAQL1AoK33mgoW/zqxd1p8/V3ppdfeb2zv98/+yNp2zevSWtOPH5u/w89/JN00+33dv778xeuTzdftylNTowP5fhWyk4q5zu+/YN0241XLrDd8+bbactX70r/+ezznW/1H/7+q+lT685aKd926PfBLob3W9t3pDNPX5suuei8BTtwHhjcu+48u2//gfT1O+5NP3p8Z2cn37h+0yL/wfe+8kfOf2328nOuWPmvgZK/Q8FbyOr8bNdz6aXdr86dXKsfdlOvvjEXtdXf37l9x1wEV39ffV27+dJCvoOyD2P+ibb7l4lDP+TWf/Kcjn/1Q/Frt92TbrnhyvTRM04r+xs7ykfHrv0FmB8N3cHlPJDnXXeenX9ePXTO2Lr5Ur/8NmCvzgXb7vvndMWXPte5mNDt51zRANEmoQKCN5R38Ml7/WCbf7Wn++8H39MHa2SvK7zdf9Z9Yv5gCfX33bLrz6ufrXtd4e3+M+eBfkQXbzvfr/rbG269J1139ZfmftF1YWFw316BO/9f15xnB7c1cjABwTuYW/io6irPzn9/pnOFt/qq/pnt0BXI6r9dhRxsCXoFb69o8IOumS+7Zk6DbNUdt70CwXlgENnDY+afZ3e/8tqif9mZ//duH+vP+tDtI7fdcGXnCrlzRX9+tm5fQPC2b5o9Y/cPsUM/6DZevGHun9b8oBuMeangffCHTy64J1rwNvOtfoixa2bV71ZLBa/zQL+SvbfvPof2OjcI3v6t598+Nv+WHOeK/i2NaFdA8LbruWi27jdBdG/Q/eao7t+Kq+1d2Vl6kbrfhDJ/y15v/HOFt90XvKs27XrOn80V3jjbXufZXhcRBO/ga9D9c8u5YnBLI9sRELztOLYyS6+T8KGJ3bvXCnHnVpDupzS4D3VwW3aD29WNdA9vndBgf7/Ueba6Muke3sFMlxpV/cLwwktTnTdXO1e0a2u2/gUEb/9mISPqblHw7ux22HsFr3cPD27LbnC7upG9gtd5oE7tyH9fd571lIbBfatfGL73gx+nLZf/WedxmYdubbj04g2dp984Vwxua2Q7AoK3HcfsWbqfX3howvm3PHj+5uDM3c9/rGb6iy9fNPdYN8+HbM/WM4wHt6xGdp8LTj3l5LT99q1zTw5wHhjct+486zm8g9tWI6tfGL77wMNzk3Q/Vs95Ns/X6DwBwZvnZzQBAgQIECBAgEDhAoK38AVyeAQIECBAgAABAnkCgjfPz2gCBAgQIECAAIHCBQRv4Qvk8AgQIECAAAECBPIEBG+en9EECBAgQIAAAQKFCwjewhfI4REgQIAAAQIECOQJCN48P6MJECBAgAABAgQKFxC8hS+QwyNAgAABAgQIEMgTELx5fkYTIECAAAECBAgULiB4C18gh0eAAAECBAgQIJAnIHjz/IwmQIAAAQIECBAoXEDwFr5ADo8AAQIECBAgQCBPQPDm+RlNgAABAgQIECBQuIDgLXyBHB4BAgQIECBAgECegODN8zOaAAECBAgQIECgcAHBW/gCOTwCBAgQIECAAIE8AcGb52c0AQIECBAgQIBA4QKCt/AFcngECBAgQIAAAQJ5AoI3z89oAgQIECBAgACBwgUEb+EL5PAIECBAgAABAgTyBARvnp/RBAgQIECAAAEChQsI3sIXyOERIECAAAECBAjkCQjePD+jCRAgQIAAAQIEChcQvIUvkMMjQIAAAQIECBDIExC8eX5GEyBAgAABAgQIFC4geAtfIIdHgAABAgQIECCQJyB48/yMJkCAAAECBAgQKFxA8Ba+QA6PAAECBAgQIEAgT0Dw5vkZTYAAAQIECBAgULiA4C18gRweAQIECBAgQIBAnoDgzfMzmgABAgQIECBAoHABwVv4Ajk8AgQIECBAgACBPAHBm+dnNAECBAgQIECAQOECgrfwBXJ4BAgQIECAAAECeQKCN8/PaAIECBAgQIAAgcIFBG/hC+TwCBAgQIAAAQIE8gQEb56f0QQIECBAgAABAoULCN7CF8jhESBAgAABAgQI5AkI3jw/owkQIECAAAECBAoXELyFL5DDI0CAAAECBAgQyBMQvHl+RhMgQIAAAQIECBQuIHgLXyCHR4AAAQIECBAgkCcgePP8jCZAgAABAgQIEChcQPAWvkAOj6C8q1gAAAGNSURBVAABAgQIECBAIE9A8Ob5GU2AAAECBAgQIFC4gOAtfIEcHgECBAgQIECAQJ6A4M3zM5oAAQIECBAgQKBwAcFb+AI5PAIECBAgQIAAgTwBwZvnZzQBAgQIECBAgEDhAoK38AVyeAQIECBAgAABAnkCgjfPz2gCBAgQIECAAIHCBQRv4Qvk8AgQIECAAAECBPIEBG+en9EECBAgQIAAAQKFCwjewhfI4REgQIAAAQIECOQJCN48P6MJECBAgAABAgQKFxC8hS+QwyNAgAABAgQIEMgTELx5fkYTIECAAAECBAgULiB4C18gh0eAAAECBAgQIJAnIHjz/IwmQIAAAQIECBAoXEDwFr5ADo8AAQIECBAgQCBPQPDm+RlNgAABAgQIECBQuIDgLXyBHB4BAgQIECBAgECegODN8zOaAAECBAgQIECgcAHBW/gCOTwCBAgQIECAAIE8AcGb52c0AQIECBAgQIBA4QKCt/AFcngECBAgQIAAAQJ5AoI3z89oAgQIECBAgACBwgX+D3FB+YntRUZ2AAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster 0 contains 12 observations\n",
      "Cluster 1 contains 8 observations\n",
      "Cluster 2 contains 8 observations\n",
      "Cluster 3 contains 9 observations\n",
      "Cluster 4 contains 8 observations\n",
      "Cluster 5 contains 8 observations\n",
      "Cluster 6 contains 10 observations\n",
      "Cluster 7 contains 8 observations\n",
      "Cluster 8 contains 8 observations\n",
      "Cluster 9 contains 11 observations\n",
      "Total cost is 2774.6572562519264\n"
     ]
    }
   ],
   "source": [
    "draw_figure(nb_observations,nb_clusters,model,\"Clusters with restricted sizes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f60d8c3-e0ef-4a8f-95d8-2a87c2b68991",
   "metadata": {},
   "source": [
    "The constraints are satisfied, we can observe that each cluster has a number of observations between 8 and 12. "
   ]
  }
 ],
 "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",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}