nilmtk_matlab.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this post, I'll show how to interface an NILM algorithm written in Matlab with nilmtk. I'll be using the code provided by the authors of the [Infinite Factorial Dynamical Model](http://papers.nips.cc/paper/5667-infinite-factorial-dynamical-model.pdf) paper presented at [NIPS 2015](https://nips.cc/). The authors have kindly made their [code](https://github.com/franrruiz/iFDM) available on Github. I had a conversation with them and they modified the code so that it can be easily interfaced with nilmk.\n",
    "\n",
    "Since the code is written in Matlab, we need to install some package that allows communication between Python and Matlab. The Matlab engine for Python would have been a perfect choice given that it is supported by Matlab. However, I had tough luck getting it to work on my system. Instead, I ended up using [pymatbridge](https://arokem.github.io/python-matlab-bridge/). Not only does pymatbridge provide the ability to communicate between the two languages, it also comes with a handy IPython extension that I'll be using in this post."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Vendor:  Continuum Analytics, Inc.\n",
      "Package: mkl\n",
      "Message: trial mode expires in 26 days\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pymatbridge as pymat\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting MATLAB on ZMQ socket ipc:///tmp/pymatbridge-29b8b57b-f052-42a1-8ffa-e824dcbec50a\n",
      "Send 'exit' command to kill the server\n",
      "...........MATLAB started and connected!\n"
     ]
    }
   ],
   "source": [
    "%load_ext pymatbridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, I have a Matlab session started."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "I'll be using the REDD data set for illustration. I'll disaggregate the first day from House #1. Also, we'll be disaggregating the lights, fridge, dish washer, microwave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from nilmtk import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nipunbatra/anaconda/lib/python2.7/site-packages/tables/__init__.py:82: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility\n",
      "  from tables.utilsextension import (\n",
      "/Users/nipunbatra/anaconda/lib/python2.7/site-packages/tables/file.py:35: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility\n",
      "  from tables import hdf5extension\n",
      "/Users/nipunbatra/anaconda/lib/python2.7/site-packages/tables/link.py:32: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility\n",
      "  from tables import linkextension\n",
      "/Users/nipunbatra/anaconda/lib/python2.7/site-packages/tables/table.py:25: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility\n",
      "  from tables import tableextension\n",
      "/Users/nipunbatra/anaconda/lib/python2.7/site-packages/tables/index.py:30: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility\n",
      "  from tables import indexesextension\n"
     ]
    }
   ],
   "source": [
    "ds = DataSet(\"/data/REDD/redd.h5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Getting the `elec` for the first house."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "elec = ds.buildings[1].elec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting the time window for our analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ds.set_window(\"2011-04-19\", \"2011-04-20\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating a Pandas dataframe of the appliances we are interested in, along with the mains. We will be summing up all the lights instances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "appliances = {'mains':elec.mains(),\n",
    "             'fridge':elec['fridge'],\n",
    "             'dish washer':elec['dish washer'],\n",
    "             'microwave':elec['microwave'],\n",
    "             'light':MeterGroup([elec['light',1], elec['light',2], elec['light',3]])}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll  be downsampling the data to 30 seconds by median filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dish washer\n",
      "mains\n",
      "Loading data for meter ElecMeterID(instance=2, building=1, dataset='REDD')     \n",
      "Done loading data all meters for this chunk.\n",
      "fridge\n",
      "microwave\n",
      "light\n",
      "Loading data for meter ElecMeterID(instance=18, building=1, dataset='REDD')     \n",
      "Done loading data all meters for this chunk.\n"
     ]
    }
   ],
   "source": [
    "data = {}\n",
    "for appliance_name, appliance_el  in appliances.iteritems():\n",
    "    print appliance_name\n",
    "    data[appliance_name] = next(appliance_el.load(sample_period=30, resample_kwargs = {\"how\":\"median\"}))\n",
    "    if appliance_name ==\"mains\":\n",
    "           data[appliance_name] = data[appliance_name][('power','apparent')]\n",
    "    else:\n",
    "        data[appliance_name] = data[appliance_name][('power','active')]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating the dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_df = pd.DataFrame(data)[[\"mains\",\"fridge\",\"light\",\"dish washer\", \"microwave\"]].dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mains</th>\n",
       "      <th>fridge</th>\n",
       "      <th>light</th>\n",
       "      <th>dish washer</th>\n",
       "      <th>microwave</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:00:00-04:00</th>\n",
       "      <td>190.699997</td>\n",
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       "    <tr>\n",
       "      <th>2011-04-19 00:00:30-04:00</th>\n",
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       "      <td>83</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2011-04-19 00:01:00-04:00</th>\n",
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       "      <td>6</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2011-04-19 00:01:30-04:00</th>\n",
       "      <td>191.619995</td>\n",
       "      <td>7</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:02:00-04:00</th>\n",
       "      <td>192.069992</td>\n",
       "      <td>7</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                mains  fridge  light  dish washer  microwave\n",
       "2011-04-19 00:00:00-04:00  190.699997       7     82            0          4\n",
       "2011-04-19 00:00:30-04:00  191.434998       7     83            0          4\n",
       "2011-04-19 00:01:00-04:00  190.529999       6     83            0          4\n",
       "2011-04-19 00:01:30-04:00  191.619995       7     83            0          4\n",
       "2011-04-19 00:02:00-04:00  192.069992       7     83            0          4"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mains</th>\n",
       "      <th>fridge</th>\n",
       "      <th>light</th>\n",
       "      <th>dish washer</th>\n",
       "      <th>microwave</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2692.000000</td>\n",
       "      <td>2692.000000</td>\n",
       "      <td>2692.000000</td>\n",
       "      <td>2692.000000</td>\n",
       "      <td>2692.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>295.715698</td>\n",
       "      <td>47.881500</td>\n",
       "      <td>111.082466</td>\n",
       "      <td>0.013930</td>\n",
       "      <td>20.370171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>252.303360</td>\n",
       "      <td>77.789963</td>\n",
       "      <td>51.122974</td>\n",
       "      <td>0.116826</td>\n",
       "      <td>156.773621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>168.059998</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>66.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>175.342499</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>83.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>246.055000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>353.608734</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>122.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3388.339844</td>\n",
       "      <td>233.000000</td>\n",
       "      <td>408.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1586.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mains       fridge        light  dish washer    microwave\n",
       "count  2692.000000  2692.000000  2692.000000  2692.000000  2692.000000\n",
       "mean    295.715698    47.881500   111.082466     0.013930    20.370171\n",
       "std     252.303360    77.789963    51.122974     0.116826   156.773621\n",
       "min     168.059998     6.000000    66.000000     0.000000     2.000000\n",
       "25%     175.342499     6.000000    83.000000     0.000000     4.000000\n",
       "50%     246.055000     6.000000    84.000000     0.000000     4.000000\n",
       "75%     353.608734     7.000000   122.000000     0.000000     4.000000\n",
       "max    3388.339844   233.000000   408.000000     1.000000  1586.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10e8412d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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I7nPW3I8MlbOryKljhafSW0kA9wBNSqlbXeETlFJrnNNTgTed48eAh6SUt2DMRlOBpUop\nLaVsllLOBpZiNmK/LVVyWizxoLXewzlsiAq/H7MHNEKIYoxCWOVcuzYq7nLAi9N61GZzH7vBjyUr\nSKVZ6XDgXOANKeW/nbAfAWdJKQ/E2Fs/BuYCKKWapJQKaALagUsdTyWASzGurIUYV1Y7GJ3dDBlb\nuxDiROB5zCD7TcAbWusVmZXKYkk9qfRW+gexJ9U92Uua6zG+4tHhrwEzUyWbJeNk6yS4WJyE8aAT\nmLkOZ2ZWHIslPVj/OoslAbTWXwe+nmk5LJZ0Y5fPsFgsFks3rHKwWCwWSzescrBYLBZLN6xysFgs\nFks3rHKwWCwWSzescrBY4kQIcZ8Q4mfO8ZeEEO/Gkab2C1/4wqnpl65vhBCVQohQpuWwZAfWldVi\niR/tfNBavwjsG2caiyXrsD0HiyUxEp3QN5QmAO5ECGEblkMcqxwslh4QQhwkhPiXs+XnnzA7E0au\ndTHRCCF+KIRY5cR91711aHt7uzfW1qExyrtWCHGbc5wrhPhcCPFL57xQCNEihBjhnP9ZCLFGCLFJ\nCPGCs0tdJJ/jhRBvO+WtEkJcGVXO94QQa4UQ/xVCXBgJb25u9gohbnK2Qf1ECHGXEKLA9XtXCSF+\nIIRYg1lHzTKEscrBYomBECIPeBSzyN5I4M/AacQwEwkh9gEuA/xa61Lgy8DyyOXXX399H2ARMByz\n8N4dPRS7mM5l6CuANXQu7/0F4B2t9SbnvB7YGxgD/Av4oyufe4BvOLLMoOvigeOBUsx+KpcAvxZC\nDAc444wzjnHyPMD5ngT8xJV2nPNfTMZZI80ydLFdQ8ug5qqrrur3NqE33HBDMqadQ4EcrfWvnPP/\nE0I09hC3A8gHZgghNmitV7ov7r333ivfeeed6K1DY/EKMFUIMQr4EqaSv1QIMQw4EnghElFrfV/k\nWAhxLXCFEKJEa70FaHVkeVNrvRn4t6uMNuCnWusw8KQQYiuwjxCiMS8vbxawb0QBCSF+gVE6P3LS\nhoH5Wus2Jx/LEMYqB8ugpo+KvZb0baYyEbMLoZuYq69qrZcJIb7ryDJDCPE0Zr+GNQAjRozY6oq+\nDSgQQnicCtqdz3YhRBCjCI4Afg4ciFnx+AicpeuFEF7n2umYnkMY06MpA7ZgejjXADcIId4ArtJa\nR3Zd3BBV7jagGBjT1taWC7wmxM6/XNDVurBOa90a6z+wDD2sWcliic0aum9PO6WnyFrrRVrrLzlx\nNHBjkuW+AByN2Wa30Tk/DjgEWOLEORuzOuzRWuvhwB6Yilw4sgS11qdgFMejgIqj3PU5OTltQLnW\neqTzGeGYpnb+zCR/kyULscrBYonNS0C7EOJyZ3B4DmYcoBtCiGlCiCohRD6wA2jBmJqS4QXgfOBt\nx3yzGPga8JHWeoMTp9gpZ6Njctq57L0j6zlCiOFa6w5MT6JPWbTW4aqqqn8Btwohxjh5TRJCfDnJ\n32HJcqxysKSTrG1pOhXzHOBCYAMggf+LjuZ85wO/ANZhehxlwNWROC4zTXS6WLyM8YqK9BLeAba7\nzsHsJ7ECY/Z6y0njzvNc4GMhxGbgG8A58ZStlHoWWAa84qR9FpgWp9yWIYYdc7Ckk6z28ddavwYc\n3MO1xRivHbTWbwKze4h3La7/wbV1aE9lbgXyXOca4yXkjvM5cEpU0gddx1/tS2ZXWGQ7VEpLSzu0\n1j8G/ieetJahje05WCyWQUUo4P9DKOD/dabl2NWxysGSTqwZwpIM52DMYZYMYpWDJZ1ktVnJkjG2\nYE3eGSdlN0BK6cMMlI3FtBh/q5S6TUo5CngY4+K3HJBKqU1OmquBizHeFJcrpZ5xwmcB92EG5p5Q\nSl2RKjktFsugZwWwX6aF2NVJZc+hDZinlJqBmV16mZRyOnAV8KxSahrwvHOOlLIcOAMox/hx3yml\njLQ07wIuUUpNBaZKKY9LoZyWgcOalSzJsCbTAlhSqByUUp8opV53jrdiXPAmYSbr3O9Eu59OL4uT\ngUVKqTal1HKMC91sKeUEoEQptdSJ9wDdPTMs2UFGzUqhgP+OUMA/KpMyWJIi2TkilhSSljEHKeXu\nmBmerwLjlFJrnUtr6XTLmwisciVbhVEm0eGr6T5T1WKJh8uAYzMthMWSjaR80EdKWYyZLHSFUmqL\nlHLnNaWUllKmxNQgpaykcwVLlFKQvnV2Ukklg1/OSlIgY9ExJxy27bm/UVR53NG4fPdTWE6f6UvP\n+trpwPR+lJEKKhn89xwG4H7EQ87kPfZuX/kxveSVknIGgEqyQ06klLWu08VKqcUpVQ5SylyMYnhQ\nKfWoE7xWSjleKfWJYzL61AlfDfhcyXfD9BhWO8fu8OgF0FBKLcYsLRBhPtlxI2oZ/HLWkgIZtz33\ntxrg2G2Ln3p+dM1118eI0t9y+ko/v3nR3U3Ni+7+ja8++Ek/yukRIcRk4G2g1JmwFotaBv89h/Tf\nj7hoX/nxbMyS4T3llZJyBoBaskPO+Uqp2ujAlJmVnMHke4AmpdStrkuPARc4xxdgFgKLhJ8ppcyT\nUu4BTAWWKqU+AZqllLOdPM9zpbFYEuUnwDPpylxrvVJrXdKLYrBYspJU9hwOx6zp8oaUMrJ+/NXA\nDYCSUl6C48oKoJRqklIqoAloBy5VSkVesEsxrqyFGFfWp1Iop2XgGCwVZlmmBYhGCJGjtW7PtBwW\nS0+kTDkopf5Bzz2RY3pIcz2uFSVd4a8BM1MlmyVjZO0kOCHEcsyObedjlsRWmE1v7gMOA5YC1cAI\n4CPMxkBhZ6OemzG7wRUCL2it/yOEqAT+gNmTYR7wjBDi68AvnXxwyvih1rpVCPEC8Cut9SNCiMOB\nF4ETtNZPCCGOBm7SWh8khNgL+B2wP0YZPw1cprXeLIT4IWZ3ukj+CCF+BaC1vsLZAe4WzFpM4Tlz\n5nz4yCOPRDYCsuzi2BnSFktsNGZV1qOBfYATgCcx83TGYt6dy2OkexAzebPciXeL61r0NpvXYPZp\nOMD5HOKEQdctQ4/EKKAjXOeLXfn+HJiAGXj30WnnXgQcL4Qohp2bBFXTuaXofZhd4/YCDgoGg3th\nlge3JEgo4D8uFPCPyLQcqcROUbekk36bldqXXJD0NqETfjgDgDU3vp1s8bdrrdcBCCFeBNZqrf/j\nnP8Fozgic3gQQkzATOgc5WzPCabFf7Rz3GWbTSHE2cC3tdbrnfTXAgsx4yRL6FQsX8IsCR6puI8E\nFgBorT8EPnTC1wshFjjp0VqvFEL8CzgVo7SqgG1a66VCiHGYHsMIrXULsP2aa6555ec///mZwG+T\n/cPSSSjgzwGm+OqDmRYlFk9iJu9eGglo/aCpdO13zz/YVx/8V+bESh6rHCzppItZKRTwC0xr+3Zf\nfTAu00XOEfcnvU1oKODvr3Ja6zreHnXegtl0x40P2OhSDNFEb7M5ka5bj650wsDs0TBNCDEWs1Xo\nScC1QojRmE2HlgA4lfyvgC8CJZgezUZXng8BZ2GUw9l09hqmALnAmsh+E/n5+YXABz3IPhj4NkYp\nXptpQXog132y4aafnIwxIWaledWalSzpJKIAIi/HeOBWjA0fgFDAXxsK+N8LBfzZ8Cz29ZKHgFGO\nLT8W0crqv8DurvPJThha623Aa8B3gTed3sZLwJXAMq11RAFcj5lRvJ+zZeh5dH2v/xeoFEJMwqw0\n8JBL1h3A6Mi2oC0tLTdorQfzWF9WmW08JcO3ZFqG/pANL6Qle/mK8z3M+Y5Urj4A3dbqxZiFptHL\nBjjZgtZ6Dca8cKcQYoSzZecRvSRZBFwjhCgTQpRhzEHuTXtewMzyfsE5X4xpPb/gilMMfA40Owqg\nJkqmdU66+zBbjb7nkvUZ4BYhRIkQwrNkyZKRfchrSQBv2djPMi1Df7DKwTIQxH7OtBaY1mu2uHTq\nqGMdI/w8zCKU72LMUJdHpXFzHRAE3nA+QScswguYyj+yRegSjKJ1bxl6LWa3us3A45hJqNHlPIQZ\n93goKvx8zMz1JmDj2WefLTG9O0sK8JYO3wYQCvhHZlqWZLBjDpZ0EsSs0BvpMfRmlhlUdln39pnO\n+XlR5/dgJn2Cq9ejtf4Ms++0m9oetujcAVzhfGLJ8ExU3m8R1cPSWjcB/qikt0TF+QPGjTY6/2bM\nAGpkELUW4047WBlUz0gCTASyrhdhew6WdBNrUFhEXRksk+UslnSQlfVsVgptyRoEpuLvrcVnFYNl\nSJLtK6pY5WBJN+43pDfzUraaDCwDR7Y+I1kpt1UOlnTS60uh0WLnocViGVRY5WBJN9asZNk10Tor\newwRrHKwpBtrVrKkimx9RrJSbuvKakknvQ9Ia03pud/MRWtRevr515D4fIdKelk+o/TsbxghcnNL\neos3AFRmuPx4qSQ75LQMAFY5WNJNj2aj1ad96XrM8hDe5j8uvM5XH2xJMO9aeqnMmh/6bWRRvi2l\n8qIe4w0AtWRHpVtLdsiZHXQ++VnZc7BmJUs6ie45xDMZzmLpCfvcDCBWOVjSTW8DzqKHY4vFkmGs\ncrCkk556Dm7caxRZLDBknged1T1lqxws6abn5TPSjKfYDqllIzll+UWekpj3Lisr2WwlZW+PlPJe\nIAB8qpSa6YTVYnavWudE+5FS6knn2tXAxZi16C9XSj3jhM/CLC9cADyhlIq5KJklKxAiV6DbevT3\nTqtZadxl+7D+/g9p+yTRcW5LJim7cK8jOra2ZVqMhBj+1Ym0vN9clmk5Ukkqew6/x2yR6EYDtyil\nDnI+EcVQDpyB2Wf3OOBOKWWkcrgLuEQpNRWYKqWMztOSJRQdNHL38d8rdy8BPeBmJe/wvHRlbUkX\nHkROlt23ov1HUnTwqOnusLyyjZOGHz8RsrTHkzLloJR6kdjL0sb6Y04GFiml2pRSy4FlwGwp5QSg\nRCm11In3AGb3KksWkju2YAxA3u7DTIvKK8ibMgwG8GXJHV+AtzTXmk+ziPDW9m09XMqqSjan9POx\nRTOzcisHYGDmOXxHSnk+Zm3/K5VSmzDrm7/iirMKmITZJGWVK3y1E27JYgqmlU4BGFYxemzpkePY\n9OTqyD1Nu7dS8aFjyN+7dHQ68rakh/Dn7S3ektyi6PDCGcN3847Mnh5FeEfuVkq2j8u0HMmS7hbV\nXZj9gg8E1gA3p7k8y+BCAAiPMBvUaHOeMzrfXVmn3VvJU+i1PYcsQnfojljhhfuP3L/k8LEDLU7S\nhNtyWgFyJxYWZ1qWZEhrz0Ep9WnkWEp5N2YbQzA9Ap8r6m6YHsNq59gdvjpW3lLKSsx0/0hZkB2z\nOysZ/HJWkgIZxfAJU2AHntJxPqB22Ck1k9j0AHnlR38ZKJ7wwBP5ay45OZ+wFhMffPJHmJ5jOuQU\nccZLF5UZLj9eKhkMcubkR/Ycr3UHi8KR46EVBoucUYiC4aNxySXyS8pgI8PP+8Z3gKqMCRYHjvNQ\nhMVKqcVpVQ5SyglKqTXO6anAm87xY8BDUspbMGajqcBSpZSWUjZLKWcDSzH78d4WK2+l1GLMxukR\n5jMIH5gY1DL45awlBTLqzWuqYNTkcPPaEFD7+V/rDi09ctzXWpuef7bo+O/VrTn/+OHAZYD3v2cf\n+wtffXBriuWMLJ+h+4iXbmozXH681DIY5GzfcRkUFREli97+2akwbBzmva/tnjCjzNctmzfgkkvv\n2FINjNnx8qL/LTzivIczJlnfzFdK1UYHptKVdRFwJFAmpQxhXsxKKeWBmJfzY2AugFKqSUqpMBub\ntwOXKqUipoVLMa6shRhX1qdSJaMlw2g7Cc4SF0PleRAAOvZzP+hJmXJQSp0VI/jeXuJfD1wfI/w1\nYGaq5LJkDh01M1p47NpKll0PIbLzebcDdZZMEEtJZOULZLHEQVbWs1kptCXr6K17bc1KliGJiDzW\nWdrsscrBMmC4utdZ+rpYMoptQgwoVjlY0kffA3HWrGTZBRBZWc9mpdCW7ETH3hnLmpUsQxPtLDhp\nB6Qtlt7JVq8Ny6DBPj8DiFUOlvQTbV6KPfZgX3zLUCUrn22rHCzppMtLsdNbSVuzkmUXIkt7zFY5\nWAYAU/e7JsFZLEMenaU9hghWOVgGHhHjKMtfJIulF7Kyns1KoS1ZR1dzkjUrWXYlsrTZY5WDJZ1E\nDUSLLH3zNzN+AAAgAElEQVRNLIODHvcit6QBqxwsaadbt6BTSVizkmVXICvr2awU2pKlRCYFdVUX\n1qxkGSrEfI4F2dljtsrBkj6iZ0Rn5ztiyRChgD/bHpgoebPbDGaVg2XAcbWkrFnJEouh9SzYeQ4W\nSze6vhSOWUl3bVFZs5JlqNDTc2yVg8USC9FpVjI7wln7kiU+su05iTYrRQ6ysp7NSqEtWYPTU+j9\neoxji8WSYaxysKSfqIFp3f2qNStZhgKxn+MsbfbkpCojKeW9QAD4VCk10wkbBTwMTAGWA1Iptcm5\ndjVwMdABXK6UesYJnwXcBxQATyilrkiVjJYMERmQc77t0t2WOIl+Tgb7c9OTvFnZCE+l0L8HjosK\nuwp4Vik1DXjeOUdKWQ6cAZQ7ae6UUkb+yLuAS5RSU4GpUsroPC1DB2tWsnTH9iMHBSlTDkqpF4HP\nooJPAu53ju8HTnGOTwYWKaXalFLLgWXAbCnlBKBEKbXUifeAK40l+4ispYTzbddWsvRN9jYTejAr\nZacDRrq7O+OUUmud47XAOOd4IrDKFW8VMClG+Gon3DIU6DQvWSzxEOUKnSEp4qcnebPyiR8wW5hS\nyrYQdzl23u6eXg5rVrJ0x9YSg4KUDUj3wFop5Xil1CeOyehTJ3w14HPF2w3TY1jtHLvDV8fKWEpZ\nCVRGzpVSALUpkjudVDL45awkBTJ6isdMgjCiePQEoLbw6K/vzY6/krPXF44Easf/+uHitVdeNAwd\nFuNu+2MNsC1Ncoo446WLygyXHy+VDAY5c/KLAHb7yz9/AoQjwaJwxFhoh8EiZxSiYPhoXHKJ/GGj\noZnc/b78VWB0xgSLAyllret0sVJqcbqVw2PABcCNzvejrvCHpJS3YMxGU4GlSiktpWyWUs4GlgLn\nAbfFylgptRhY7AqazyB8YGJQy+CXs5YUyBjesu54GD1Jb92wBqjd/vzvvlryxbHntH/48otA7SeX\nnTEeOBfwfjL3tDpffXBdiuWc73zrPuKlm9oMlx8vtQwGOdt3XAZFRatOPfxnvvpgWyRYb99UDcVj\nMO99babE64H5umXzBlxy6dat5wCj2t5+5hmO+c6tGZOsb+YrpWqjA1PpyroIOBIok1KGgJ8ANwBK\nSnkJjisrgFKqSUqpgCZMU+BSx+wEcCnGlbUQ48r6VKpktAxqrFnJEsE+C4OAlCkHpdRZPVw6pof4\n1wPXxwh/DZiZKrksgwjdox+4tTJbhgJD6jnOyskZlqyjyyQ46ObKarHEItt6ED15K2VlPZuVQluy\nhni8lPqKa7FkN1m6IoBVDpb007O/tzUrWYYSQ+o5tsrBkn46jUnWrGRJhGxrcYuuJ9pZoj7rfgdg\nlYNlYIjn5cjKF8hi6RO7fIbF0o3IWkq6y3n0ddt7sMTHYK9kYz/HOjsfb6scLOmjp7EGYc1KlrgY\n7Mogmi7ydi4eY3sOFktstPZ2PbfeSpZdiqx8tq1ysKSdjq3tkUmN0c+bNStZhhI9PcdWOVgsURhv\njRzR3D10J1YxWHoiKyvVTnRWy2+VgyV9aLzOd7Q6yOqXxmJJCDsJzmLpitY61znsaS9du5+DJQY9\ntLiztVGRpXJb5WBJH2EdWdix63PW3VvJmpYsscjKSrUbtudgsUShyXW+7XNmsWQZ9qW1pA2tI0vC\nO2aC7v7e1qxk2RXIymfbKgdL+thpVupVKVizkiUK83h4Cr1ZWal2w5qVLJZuOGYl3dtAtMUyVIm1\n0GTWYJWDJX2EjbeS1tZbyZIQiewDspNQwF8cCvjz0yBPf8nKZ9sqB0vKCQX8OhTwD+8cc8AbCvgb\neohuzUqWmIgCb6L103vAX9Mhy65IyvaQtliiqN7prWQ4qnXF1o0cNgaytCVlyTh9NSImAhNDAf9Y\noN1XH9w4ADL1ws7FiLPyeR8Q5SClXA40Ax1Am1LqECnlKOBhYAqwHJBKqU1O/KuBi534lyulnhkI\nOS0p5Vq0zgMomjliweevrJ8X3tZxGtDTpj9Z+QJZBpS+npGPgT2AtQChgP9MX33w4bRL1Rd2QLpX\nNFCplDpIKXWIE3YV8KxSahrwvHOOlLIcOAMoB44D7pRSWvNXdhEGdi8+tOzHADmj8tcDFSLX83qM\nuNasZOmKU5WKXE+i7/3zwEvAXOf8T6kTKimyUilEGMhKN/qPOgm43zm+HzjFOT4ZWKSUalNKLQeW\nAYdgySY8QLunMGdHJMBXHwwiaAesKrCkCwH83lcf/C2mHqkfyMLDW9r37eFSViqJgew5PCelDEop\nv+6EjVNKrXWO1wLjnOOJwCpX2lXApIER09JfQgG/ALSvPthdBQjC5luk3azkyGEZQEIB/6xQwF/b\nzzzydWt4JED7upYNoYA/kYahF5xnDNqd84FDa0IB/+gYV7LyWRwo5XC4Uuog4KvAZVLKL7kvKqX6\nMi3Ytmb24H5Bo++bCdddFlazZqWhwyXA/H7m4W4IeoEHE0jrwYxT4nwPrHIwbZ7nQwH/DaGA/ww6\nwlltDh+QAWml1Brne52U8i8YM9FaKeV4pdQnUsoJwKdO9NWAz5V8NyesC1LKSqDSVQZAbRrETzWV\nDH45K0lSxkn/u8S7WlYKoFaMO/wwvfafiDFfOBrI846esBtAzpSDZwO1Y+vuGbHu2nkj0GHPmOt+\nPQ/YnCo5d3t8KR3/uChyKnqKN0BUZrj8eKmkH3IWfvGY6dv/8Rw6HK4VCQ8XGMp+fPM4/fFdbUDu\nyG9fff/mBxcev1OmgtIyp30RU868fWcemL/fwSXAHiO+9YM9tz72p71jxUsnI77+vbdaXn/1iJb/\nBK9o37DRy+QicvaYfeRAy5EoUspa1+lipdTitCsHKWUR4FVKbZFSDgO+DFwLPAZcANzofD/qJHkM\neEhKeQumFTEVWBqdr1JqMbDYFTSfQX4DHGoZ/HLWkqSMq08/ohD4PlCr1/6zBjhWr3v5eaZ/8/qO\njZ8cC3vs1r7y368CtZ/WXLInxjbs/XTeBbf66oMr3HmFAv4vABt99cH3EpVz1YmH5Ez44YxIK1Yn\n83tCAX8hIHz1wW2Jpo2iNpny+4tjWivy1Qc/jzNJLf2Qc/s/nrsQqFx14iFzgEeAf/rqg88mksf6\nn12pR8kpQD6b7627Lfx5+6ydMrU0nwnFozHvfTc5W999c1rru2/Wj7joO3/cdNcvjwIm9+f3JMh8\ntKbklLPPLTnlbEIB/x16+/a5UETH8ldfHEA5kmG+Uqo2OnAguj3jgBellK8DrwJ/c1xTbwCOlVK+\nD1Q55yilmgAFNAFPApc6ZidLduChB7OS2Bket1npJWBJogKEAv4ioC3RdDGoB95KQT6Z4mhga6KJ\nQgH/3FDAf3YS5bVj3t0rgfFAci7onSNSiZqGMmtW6kprlPk060h7z0Ep9TFwYIzwjcAxPaS5Hrg+\nzaJZ0oNbOUS/HIkq+bXAuFDA/xPgAV99cHmc6XKjzpNtXIwC9ggF/LOAN331wdYk88kUbQChgP8K\nzP/3WZzpbgUKQgH/e8C/ffXBcF8JHLzADl998NlQwP8KcG7CEsNz3pF5E4AZSSqHiKyZVg4drkZQ\nVo49ZKXQiRAK+GeEAv59Mi1HJggF/LmhgD+6okw3XjpbbwB8uHHfIxcuaLoQEamk4/ZWqseYEHYH\n3goF/E+EAv54XviuccLaGwr4T48jXTTPOd//CzSHAv6nnF5JtiAwinEOsDEU8K8OBfw9uVu6eQL4\nCHgIWBcK+M+Mszx3yz1Zb6Gw8IpWAOH1hLvk4azRteHm+YeHAv5jQwH/t0IB/wGhgH+GE8PtDBEm\ns/Vbx86eQ5b2H3aF5TP+CQwniVvkdK0P89UHv51s4aGA/wRgX1998KYE0wngh8CNMd1C46MeGA3M\nSiRRx2cb8v577lfW++qDZUmUuS9Oy33LjtLhJfnNbG0dvh9wa3PRpPdj+Pn1ZlbyYFq8v3dav6sx\n41Ar+5DBC6wHygBErudzjIJJlFbgGl998OehgH8ksAYYi5nRHxehgP+wkZdfM6X4K6f0Hbl72irg\nNV99MNGB+gheYLGvPlgVCvjzMBX+ZODdPtK1Aj/21QcfclxT9ye+CWXuyrmD5OoXD0Jo5yhm639b\nQ/0xRFkdQgF/5FC5yh8XCvgPc+RI5acG+JuvPnhiL7+jvXN70L6XzwgF/AXAt3z1wQV9xY2RVgA3\nA1f2o67oxpDvOQD/BggF/LOT8H0/G7jMebGS5QqgLhTwD08wXQ7wC0xlmyy7Awcn+rvDmzflAaND\nAX9CyiEU8HuAl4FXAEKb9zoWoHzMv34HfPL6tG9UJJIfrsrGVx/cgjEzFcSRzm1eiDQLkmnF7mwJ\nOyaZ/yaRz5Of3XbdhUmUDWbG7y+STAtd5W/FjJ/E2/OK9AC2E38lnwqb/840QoiYeYjCoq0Yx5bb\nMK6uL7ouf+B8v+t8bgKuA67BOEp8G/gaxuR1OnACRtF8EfAD+wF7Y7wky4BizO9vx4zfrHfyPwEg\nFPAvCgX8seZhdXQ2R+Mae5gK3BJnzzgaLzAPGJNE2h7ZFXoO/8K4xj4EFDurg/7AVx8MxZH2JSAA\nrAkF/M8Aj/vqgw8lWP4LmIdvZSjg/zh3z2n5bR+9f52vPtjeR7qI4n4lFPC/Cjztqw/enGDZizEP\n3bpQwP8+8Od4WiZa76xX3wkF/I8ADXGuUeMFOnz1waMBtrcNmwaQ621rnTuvfN8l1z+1EnMv4jUr\nuSsbMC9oPM9stGlLk3xF5ba3J1PhLQZOCgX8fwbuBV5NcEG4b4UC/hXA34CmBFuGycqfbCUfbdYR\noYBfJCizp3P5DNHVrBShoyMH+FdvnlC++mAzZl5VygkF/C8BNziNxjOdTzcpOw/japttd74fcZ6V\n53z1wU/iFCnyH90dCvgfBl7w1QdX9ZYgHnaFnoMX+LWvPrgXMBvTmvb3mqKTbcCvgAMwpow7kih/\nB6b1sjtwadtH7+8LlMSRzgu0YBYm/A1wUyjgT1SZbwD+B+MQcCemO9w34bDAtJKPwJhy4l2jpkul\nrPFEv9hhAN0edtvtezMr9adyix5ETbbn0F/l8F7hF456EWPevAn4RwJpXwbqMGadt4BzEiw7WrnG\nK3+0eSje3+zuqWgnj0T/Ly+R58Er2jGrrC4JBfyPdmxtmwagW3cUYN6rTLEdY56L6VDj0Nn4i2/h\nPS+wEXgWs5TQe6GAP96eQKQefxozvrQsFPBPjDNtn5kOZdwP7HISMw14gLCjhX8HxOvt4cbr5PGZ\nrz74ksjL3x5n+R5MK3yTrz74CMbzJNEXLZLHKkwLNr4WXLhDODK/g7Flbu8jRYToFnsXebU3ZytA\n25rtF4UC/l/Rd5OqPz2HVCmHZCrXLnmIYcNafPXBWzGmiEQGtAXwF1998BxgIfE1Ktwkq1zd97Fb\nmlDAXxQK+M8JBfzVoYD/tFDAf1Yo4D8Zo7xGuKJ2G5QOBfxTnbjuMPcGPZ6IhX7YQaMiJpwvYebD\nGOHGTlgFxDt3Ix18jJm0G1m7KdYz2dlI6tDxOIV4gE999cE7fPXB04F1dP0v+0q7zVcf/LWvPnga\nZsmhYXGm7TXToU5/Wn/JtqCiy++sYDyeeE0cqWi1JiW/bm9P1iWwa89Biy7pto/ZLQhEVMLlmNZX\nhFiKIhVmEcisWckjhCeilBNN39/nL1nl1pdZ6UjgD8A3MeNy1ZhVlQvpHBCOpI2uOL9P54RXQgF/\nOdASCvgjm/Ts7DkUzhgRBg4GKoDcwhkj7gOY+PvH70nlwGui+OqDG331QT/GZFvtqw92AOSMzndP\n1m3ImTD+E4COz1pnxpFtquqpRNP2yK4w5tCfPy4VA2xRg6MiXhe7lFRMdMofv2ufMSsl/LtXj//C\nsA2jZuQ9saDpOeD9/caJrls2Ck8HQPGhY77d8k7zFZjKpC9vpWzvOXh3et8knr6/z19/eg69KaWx\nwIO++uD5feTTAjzjKACBMc3OBAgF/E9jBoT3c+Iu7yy7s53gqw/+O3LcvuSCeOdbDAi++uAyzKrR\nAOT5hv3Hda2xo+mO9/T6xvG6PRyvGTn6XsXbeE/Fc9qNXUE59OePS8Wkmq433VQUybR+k1UOifcc\nHLNSb+mcga9hwJzI5LC1Yw4e/8nYijzg/4CCscPWPErnUuyA1gC5Yws2YNwl+/I8SrY11fW/S95b\nKTUK2uNN9hnq7/PXnzGH3uYrjMWYPfriSGA65l57MY2BNsxvUpjnZKwT94hQwF8D+BEE48h7qBF9\nrxIZr0mFlaEbu4pySFYjp96sJDzx3vRU3PDkKhfTc4i4kIZDAT+hgN8TNVO2CuPqNxGn1Se0zi1s\n2RA+/0dH3gXQvuTGHFzKQTjKAVNdzwD+jNkhMAczAPcPzLyMUow7bAXGwydCPnBYKOD/HCga9f2f\nTdp4048PxlRgw53rWzADuLu50mngS6GA/ywnbotT5hqM99QKJ327I9t057+aAfzHlc9Y4PxQwJ/r\nqw++FNd/CR48Sfcc3M9fO5AbCviPxtiic+nc52Q1xs1yo/NbizEV8vF0LoUfKb/acasuxtjOt2B+\nu7f0rK/PaF70uznAnnR9bipDAf/xmBnjfox79m/6Et5XH3wTeDPWtVDA/3XMni7vYWz304FDgcdF\nrifi9p2l08e6ke73vT+9jh7ZFZRDps1KXrp4LsTdc+h3q/XT/BFFLd78Ql+C6XVHu7vn4E7rDmsG\nRuJq/QvdkSt02G0iir1kt+GrmEpttZP3ZIxiaMUoh2s25w7bvCF/+GrXEr0PYpaFPhco2LTwpjGY\nyioXU2GuxjzTPsyaTF8BEB7RhhkI/gam5VrqfLyYyvNjTAXZ4pRf6Ag/LYxwe6i9gPGT/zbxV1ze\nfow5RD9/P8MMhH6KMdEUYZwF9nKuD8PcDw0UaNhjXf7I37v+v6XAtzD/zxZMZb8D+ATI37bk6b2B\nPMxcgXecNJFFD38OvI+5hztwjRskg68+eDdwd6xr7UsuaEgmz4q6hjwg3FhT1ZebeFpobs8bNir2\npbjMyDo19VSiaXtkyCuH+/c8vnx9wcjcW+EeJyjuP+7PU6pmLCvxTboTfpJIOjdLR5ePXzlsfME8\n51wIoXUc+ezw5HpeLdsv99a6BtFYU6WTKf+ag751yqa8ksKXzcq3caff1NKRd+7h1+79QmdQJK17\nMbtcnAqm05dd54LWFXUNGhj+8uyuFaj56QZfffCpqGKjzRSPzalr+Ay4qRGOctLciln3J0ItMVa7\nrKhrKAS2vexsNChyPK2++mC39b36oqKu4WHgikZnkNVXHzwvFPCfD3SEAn5vZCCyNxZMP2t27o7J\nw280pwndw28cevU+47ZvPOY+0/ruwPznJ/vqg6/FKf/JwKONzha8vvrg7cDtvSSpBWor6hqOASY3\nwiqnh7R3nOXtBlzXWFN1YTzxe8hjxf8dUNw6sSDh9QLBTHh9Hzg12fLjYeGCpjGYxo0XWDR3XnkL\nQMPGKWffWNdwYWNNlfOeOJPfdN/3/OmJh05aOG3OrMbOoLiflR2eXM+Fh88fs6OuwdtYU9WRSNre\nGFLKIdaEm+cmzN7/89zC2RV1DQ8CLz2SwB/3StnMAz4umbRPRV3DAQ/mFCwf1t6S8B/+4J7HH7N6\n2NgpD9U13NRYU/W6MyDdZz7r80fk3Vp+1kjg1Iq6hscSkduFaPfkFFXUNUx7xLQ040q/tTWcuy23\n0FtR13AG8H89lJ2LURb/BAgF/H+cNGq/HZtL99JOo/qKLe25uiSnU58Ids6ui7fVXQxUVtQ1nAL8\nLYEWYX9mtLvZC5hVUdcwC/hXY02V9tUHdSjg34ExYfW5lPcbI/fea3N7SUlFXcOs+3KK3itt3xb3\nPVxfMDJ3fcHIWyrqGu57pLNl+GmvibqyA6CiruF0oL6xpipel+RHgWEVdQ3TG2uq+lpqw81M4IKK\nuobfAEsba6qSGUCevKa1GEc5xHxO/v7U6sPff2fzfc5pxKFBf8lTOh0ov+2Wt/6YLzzb6Ors0Ndx\nvPHArDoLpsf59YULmj64ZBaMJ49TvKMX33nL2x95heg4ap+cffYsBuLoObQLTx5ARV3DccBzibzv\n6/NH5O/w5gngItezYpVDFC2hgH8NZvJQG7DtiL1PLnx24uyt7Z6c+cDM7/m/u7nm7QcnE/AvxfyB\nEVufxpgV2jEv/vBDpxxd9nHJJIDHzjv82oIvr3m15JsB/zQnbiumgoz+5GPMLW8B4RnT5qxdPWzs\nFODxirqG/BnTzi39WfCOy0MBf2TQLYSZezESYxpZAWwsyispd65fD9z785kXlV715n3+UMC/mxNv\nLZ0DfOMxlf9/MRXjSEDvt6/ctHi8fxSwZM6RN3acufzZPBnw+zAPz0hH1hCdg8P5QG7beVeWOqbq\ny4Hf3jDj/Lyr3n5gH2embgHG/DMKOMwpbz1wlvbk+Fpzi9fB5xOBL9y3ev+vfmfKazz26dST5pjf\nkaj74Z8wg5q/BzwVdQ1/B+bEUel0eTHWtRZOOKmu4ejGmqrnEyz/GaAc+AuQU1HX8Apw1iPmP6hy\n/g+NeY9aMHbzdkyPagtQ6t/n9B3PTzikBFh64eHz27+w7s28moB/D4xiEZh7ON0pbxWmQh8HtI85\n9CrW5Y9sQ4jl35r9w89+8PYD7LF1TSKzq1uc70uB+yvqGt4AzmqsqVreR7oG4ETgnYq6ho+BeY01\nVX/tIw3AJuf7MWBMRV3DksaaqiMTkBfg5TzRcSBQeFTj2W+1vNrw28aaqhvcEVZ8tMWPuTfrcc22\n36o7Zm4jXLFet53iQWwrE7n1Uz2FLztx3LPyezuOJ95PMYsxbsKMkxQD5+8gzLLw9tFt6APzEB9V\nesNtAKvKDp3Qg7nJTeSZvRXY638O/NaWb3zwl2G+3lI47PDmRurxucAvf3zAXH3xsseK40nbG0NN\nOYzCzAbeC8euvKJ4wnNh4Xmqsabq5oq6hknr84e/8l7plP0mbN9wN0YpdNBZMRbQ2X3fkhNuz9u7\neeWTy0onB/LCbWe8PGbmH7/5/iPPO/G2Yypm96cd83K3Y2ZE61E7Ng+f2rzyrx+UTp4DzH67ePJL\nmEp1rJPHIU6ZmzAVzZ6ALmxvETnhdv3yD7+8b0Vdw+TXRk9foYW4C603YxTaDucTeXAjcwbCmAlC\norT183F7NYcWfljqu1Sgqx/zfel+ueK5l+n0JV9P54J0LU7anNaHfze6xD9vR8P/nHh4RV3DzKVj\n9nsDeM2RsQBY++GU4/M+2PPU6rA3/8dz55W3AT99YkHTQUAF7Z+PB068aNIbVwM/W9dauC90MSvF\n23NoA2oba6rurahrKMMMIOfS9+xYD2Z2+GiAXBFuxQxuJ6ocNMbW/gvMM/UfYAKm8fFHzKTIMOY+\n5mL+n3WYwfAiYENeuM17Sllr8NH1eYfn6I5TXh67/8M0sdSJH2nheTHPXzNGWRQBH43csUWPaN16\n6gelk1/c7s1f2jR8zy17bF2TyMZDHuDvjTVVVRV1DUXO759K3wsHbsVMaPsLphI8AohHOXiAlxpr\nqg6vqGv4Il3XPIqX5kkFW5YBM4u87Te1hHO/hbPXS4SwMdM8NHdeeZcdIivqGmZjxjEeAG5Es/dN\nV85amIQMiRACaF/CvVtF6/bff//QfSvqGiYC923OaS0EaKVgVCjg/xTzPO/A3PthmAbEdqDtgKIx\nM8Zs39iyrnDUdGDKspLdPswLtz0dCvjfxDTeijDPSItzHHGeaJ3oyS3KDbfpl374lYqKuoa9VxaP\nfztXd9wdCvib6XROKMI05CLm4eJIfr762M5hQ0o5ODte/dP5ANBU1zAOp0veWFO1uqKu4dXbpp/5\n8Hn3/vbPfeX3YF3DlcCkxpoqXVHX0NjqzVvhqw/umYhMf6pruAoY2VhTFa6oa3gjxyPa47F/V9Q1\nFGMGCmmsqVpZUdfQKo+8YY/GmqqWPpLu5LG6hl8CG5yy/7ktp3CDrz64W1/pmtc0L9jyh2BkiesP\nMQ9QoTvOE7e8vRkhfgjchentQGcvzAOEi3PanEpcON1qnaiZYacHR2NN1fqKuoZ4l4HuMkCXI8IR\n98lE8WAGOMPABxV1DZ8AXl998LB4M3iyruHmE8aPn9l4UXlrRV3Dq0DIVx+c3GdC4H3TU9nQWFPV\nXFHX0HDP1JPf/uZvf5XU2kqNNVXbKuoamknAGaKxpmp7RV3Di5heZkLlAa8Th9ktBp6IV9uY3G2v\nbWwr7PZ7dVh7MRVet7QYuVsq6hqewyj0Aaexpuq/FXUNb0XKbx9Z9h/gOIxSGEmnhSKyymtucPT0\n/TfmD/+xM764/NAbn13xStl+Pzg19MIaJ24bnQ3ByP/aAeSuKho7vE3kPOuUvWz2L59d9dKYmd+T\nK55fSec4YaTxF7F6NDvhZZjVersxpJRDD8TyH05mckkqXFk7wvHvDpXqSXBxu7d1GBl7/91CrMcs\n5+Ce6ObVWncAurGmSrcvuV8DRAYhIjvBvbvugMP/uaBpFqYH9T6mRwDmAf4c80D/Zxiewjw8RQsX\nNI0GyEd0HOIpGbNwQdNWgEu+s6/nntvfLcR5wXDKmSmKyj7Q27tUKqV4SyL5xEsx3mEeaI2kK8Cj\nJ4m80QsXNH0yd155vMs3eDxmnAlSMM9h4YKmQ5yw4XT2WrZgKowOOnvD4dHklGwj7Fm4oGk6kD+S\nnLxRImfSwgVNPkyF047pYXuAz0+qnjLysT+v8BXjKSzCW7xwQdOEMnKGhWH4wgVNk514o4AfY5aT\n3+AWdjy5IzbTIRYuaBp9rGdEwZLwZm+i/3khnny0WZNrtC4sLsCTF8nj/ANz83O9bYQ1OcTuPabC\n9bw/uJ+5jnCkh+zxCF99cK0THnNBvAeME8fOAboOj3fHg3sFmi7/zc1NfRU6p66hFJdHZFh42/60\nx1c+uPLOG/tMi3l2YrKrKIf+uIilchJch9YDOusxKfnDYd3nJDhMF3UrXQd/I+V1GXjWjlIaXxJ6\nBbSsebEAABfISURBVLiiecfIg00wf8GYZiIusfmYZYdLgB+c7i0b5UEcj3HhpNo7pigf8W8nbf49\nt787DPgBnSa9MMAhnhLPgRSXRoQS4byiOd6yKzG297g5zTu6SCDCGNdVqr1lI3IRzzi/K94l2D2e\n/s2Q3rnK6dGeEV/GLMTXhDFhCcz/NsL59tBppvKcmlM2pt0o6xeA/JO8owoFYj+MV1IuxrTZjDE5\nbHny0VAecO4cb1mxB3EE8LOAd1RR2OR7PM7/jhkTOQUzr2InX/WOyulAFwHvTxb5VHvH5GOUf9xU\ne8tKd+wYJchbzX7tk/5vL29ucSSP5ZumFU8d/TZC7FSKsf6v/jbmkkZEKYfIfg7xeCfS/0asnQSX\nBP1pgad6ElyHjt/enrG1ldq7KwdPRadLbYSIcjht4YKm3TC7pkXKizbhCIB9yt74COCQ3RbfcdjZ\nF/2hDzG+WVHXsAh4rLGmahFARV3DRmBqY03VhoULmsTXr5he6/GI+dEJK+oaJgP/uNT484O39fP7\nOtbe1FhTdW08v9+VzwIg1FhTdYtz3uSB6otzxr+xcEFTztx55fF4T3nFzh3wEp6c5J6p3OET+UcB\nB86dV/5OL2nc8p8AfKuxpirgnP8V+H1jTVVPcxRqMa6sjwL3NdZUPVpR13AFsFdjTdXlcZR3LPDD\nxpqqYyrqGrxAW2NNVUI9h4q6hhfOLlg/HDhgacE7R72+ZfzDjTVV0wDal9x4L3DR174z/UZi7xGe\n4Z6D7qIcdGSzn6g1xnogVfVUJK2dBOdm4YKmdzB/ys7Pud6xZV7EmQsXNN0AtJ3nHVsEVC1c0HQ1\nnTY8D129FQTgOc87dgQgFi5oOvcS77iCbYRHLVzQFHIV2duELw3g5KEXLmg6/2s549mi2/nNLW9/\nJLpuDtUtn4u947xb6RixcEHTBwDSW1ZSjLdx4YKmcA/puuVztnfMOA+ideGCprkXe8eJZpNfU1S8\nbnb83ALPhGpvWfHCBU1vfS1nPBt1GyPJeXPhgi691NEY76hazMO4EvhMmxZdpEJzzEoi2Qe1RwU5\nd155X2syRSuoZGTo1nsLm/K3YQaOe+ySu/PwdvYcEl3CukvPz2MU8scJpk92+YxkKtnotbxEjEZF\n32U7jgteoaPL7iufQdVziJy0duTvsXBB0z9jpYlwvnfssGY69o7EO8U7es9SvPcvXNDUp/nyIu+4\nnA20lSSTFmDuvPKY4YNWOUgpj8O4dXmBu5VSN8aRbA6dLdcwEH6iY+MvchHBE3NG3w3kPt6x4fZR\nIvftKu+IRzA3MzJI4/6EAf10x2ff0eA9OWf0ze/p7aWvh7cuOTNnbGQwsreNanaeP9Xx2ZUeaD0x\nZ/QdAE92fPbh8d5RxxXjbY+Rdufxh7ql7PXw1serc8YcD/BMx2evHOQpPm8vUbiht3Tu84aOTT/O\nF55lx3pH/mkD7UVLOja/cFpOWXVU3G5r4+92cOmP1JJlh56aU3YmwN87Nv/7OO/Ic4d1ygymglzn\nlFWCmSiVu5H29XQ6BEQmAUVv7pPucZco5aCTXZW1J+W0CXhn4YKm6Elw3ZT1Od6xo/Pf7chZ+FbT\nxxd7x4nPjYL+qKf47pMzvGN8RXgeW7igqfUc79hICzyRfQxSsTZVUmZYx4kjogwTmbHsEc7z4RXh\n6LLjWeI9cz0HEa0czPjinqPeufXd9Qf9rbeky3TL9BW65Xtf9Y76AUBjeMvdu4uC26eLoj7nmayj\nbWSwY8sDJ+SMTjitQ8w9RgalcpBSejEb6xyDWRKhUUr5mFKq1+50rO723XUN24GNc+eVb3LOt2zS\nHWsfnlf+dl9y3F3XsAXQc+eVr6yoaxgJiLnzykN9pYvKYyuwZe688o8B7r2pIfynjnUr+/I6qjBy\nt82dV/6Bk0/r38ObV/zyyln/TaDsZjRr5s4rb3JcGcXcOH73Pz5cv2kD7dvnzit/y8mnY1HHuvd6\nmUTVjLlPVJjBsS6tdp18FzcVC8e5wxKlJ+V0AF33VuixcfB0x8ZfHDtt3JhhH3R8fY1uLf5nuPkl\nmTPm2HjSPtPx2ZN7egq+c5Ao/rAhvGneDh1ufrrmiKS8laLkTyRdf80biSqHiJs1BZ6ORHtaGTUr\ndes5OI2iCSWhj+fOK++15+Ao0uZIvLvrGppX69a3b/3/9s48vKrq3MNvEpIwRARBEFFERVGoXuex\nKg5PcQLrkE9b51qLOOKIorfVSrGI1qF6axWHx5mf2qvXKrb2anACFa4DUitVVAqRoYpMQhhy7h/f\nOnBMAglwhn10vc+Th+yz9+K82WedvaZvrXXpHhOae98QOlu3PmnXRiILBzz2/2NJnwGY2eP4Zh8t\n6mttwIauypoOmcvGmAOlJSWp+lRqfQaoshGt1LIB6W9HK63re2e+Z/iyNL/B+lr+rw1uOYQ33+DP\nLv3+gy7u8xUNBmPXxOhRLy2mbWmbQRf3nrbnqJfaAaWDLu7zSQvTrphUv+jTuy7da+roUS/NpXGB\nt17+65gu32v8rAplbdW45ZDobqU1jjm0rKW8oc+pDb3vjShJpdalIpIfzOwEoL+ks8PxKcDeki5Y\nS7LUbQ/ecn/DF2vrNjqwV5uvnj1u0w9rAO6q3WNQXX1Zh07lS5ptcs1Z1m73TuXfTD59s/ee+HpF\n68rbZ+z9yDZt5j20Ln/L7GXt9uxSsXjiqV3ffxrgus8OerpH6/mPl5fUr3Upg2X1ZVWzllX1G7bV\nq2cDjPj8gHu6ViyqqSxd2eJFZ2rrqvbv2Xr+i9ZlyovLU2WlIz7/4VPbtpn3QHPpqtp33e+jud9U\nDO3x+sVp5y1bzx9TUVLfbNz6ilRp5Yy69gOu2eqVU6sq6y8qK+Xgdxd04b35ne/u2XZBt4M6zRjw\n/oLOr01Z2PnjlDfEU/Wrep8I/5aQgtTnSzoctlPVnDGHbTJtEilSI6fv/8fNKha93K502VygpEuX\nLXf7Ys6Md1KUlNSHCOF6SkqWrmzVYe7ydnuO6P3Kqjkdv5y6/wddKxa/DaTSDx8fKE6lSiBVkgpv\nX7JqQZzUv5ZufFCP1vNrrMuUvwKMmr7fyI7lSz/YqKxuTspTezRKCSUeaOARu6kUJSkvEEtq66oO\nOGDrjb/cd+XYGxbXV5TfNH3fJ3Zs++//avbDA6Yu6XTywM4fXbVzu9m198/a5aT5y1v32rxy4VvN\np3S+XN6m1/JUWbsLt3hzFMAdM/casry+tH33yoVN1ii7b9Zjj5mzpk+ctqTjwD3a1959WMdp7z85\nt88h05Z0OHLzykXNTmibv6Kyx4pUWdVFW0y4ATzfbNtm3n0VJStbPDfn4yWbVF+73WuL2pSt3Hrq\ngvbn3127242923z5AMDAzT7p37Xym22frzvqrZmzpjeaufXp0g5H9G03d8zRnaZOeGPBlr1q5vW8\nolebr55s6XtvCGdvNfncvy/stGTL8nmnA6VPzO1zzK4dvx64a9WMdu8t6DzurXnd1tpiX7CystvX\ny1v3vqzHG8MAbpq+34gO5Us/al9W98Xa0gEsTbWqmrG0/ZHDtnr15+uaFmDwqZedSxMFWFILh+OB\nw9dWOJhZP6Bf+lhSo6iVSCQSiTSPmWVG8tVIqiGVSiXup7q6ep/q6uoXMo6vqq6uHtpMmmsL7d3C\nvy3xnsXgGD2jZ9J/isVzTT9JHXOYCGxnZj3xcMkTgZ8U1CgSiUS+R2zwRIlcIGkFPiv1L/hs0DHN\nRSpFIpFIJHskteWApLHA2HVIUpMjlWxTU2iBFlBTaIEWUlNogRZSU2iBFlJTaIEWUlNogRZSU2iB\nDSGRA9KRSCQSKSyJ7FaKRCKRSGGJhUMkEolEGlF0hYOZFYVz9MwuxeIZ+f7xXc2biR2QzsTMqoAz\ngefxjWG+MbMSSYkaMIme2aWIPCskNbUzWaKIntmjWPLmhpD4AWkzOwTfivIDfM/jZc0so1EQomd2\nKSLPIcAZ+B7Lb0v6cxIfEtEzexRL3txQiqE5tDnwmKTj8e0J9zezsyBxzbnomV0S72lmh+KTM88E\nPgKuM7O9JaWS4gjRMwckPm9mg8T9IWbWw8x2y3hpB3xfYSTNwfeuvT4cr8+m8VkhemaXIvIszzjs\nDDwv6R1JjwIPAndBYR0hemaTYsmb2SZRhYOZDcc3ihlpZqPMrAM+EW5w+hpJLwITzew/C6QZPbNM\nMXiaWbmZ/Q4YFWq44PsU9EtfI+k2oNzMzgxp1nep8uiZHM/E581ckZjCwcw6A9vjO4oZnlF+Jel1\n4EMzG5Fx+X1A1wa1jugZPXPlWArcidds/w+4yswGSXoK6GJmJ2dcfg1wAkC++8mjZ9Y9E583c0li\nCgd8w/B9gE0lzQMEYGanAr8ATjazA8O1vYGZkpraZDx6Rs9sszGwMzBI0oPAzcAuZnYQcB4wwswq\nw7W1+IOjrAD9z9EzuxRD3swZBSsc0k3E8KGXSJqP3/x0rWEyMB7YF5gNXAf81MxeCde8HT2jZ678\nMo5Lw4Phc3ygFLybYSJwkqQa4K/A7WZWjfc/V0lamcv+5+iZO9ek5s18k/fCwczOMbNdCHvwhg89\n3Vx8FdjezHYKK7NOwyMDqiTdB1wMjJS0s6S/Rc/omQNWfSfCg6w+1FifAXY3sy6SFgDvAyvMbGvg\nCuDPeKTNFEnn5NgxemaRIsqbeSVv8xzMrC/wCDAj/LSWdEY49xBwO96EPB3YVlI6NOxV4GxJzW7r\nGT2j5wZ4/hS4FH8YjJc0Jrw+APgn8A1wITBX0shwbjxwsaQJ4bg8190K0TOrjkWRNwtFPlsOXfBM\ncjRwGdDZzEaFc1dIelvSTOBefKOfu83sTXz2YYv2Qo2e0XN9MLMd8QfZJcD/AueGhxtAB3x/3Vq8\nNjvQzI41s174A25F+v/JwwM3emaXxOfNQpKzloN5yNf2wDuSlpvZOUAfSReG81sD7wB9Jc1MNznD\nuU2BXYBuYcAqZ0TP761n5vv2A47LcDwCGC2pexPpBgLHAvsBt0r6Q/QsDs9iyZtJISeFg5n9AhiO\nD9D8G7g6nJqI3/gvw3W3AJtIOj0c/xx4QdKMrEtFz+i52vNXQFfgZUlPmNnu+MNr14xrXgDelXRl\nxmvpPvNKYLlyP0AaPbPnWBR5M0lkvVvJzNrgo/kHSDoKmA5cBSwEHgXuzrj8IaAslOgAdXj4WM6J\nnt9bz2vwWuoLwAVmdpmkSUCt+YSnNJcDB5rZxiHdb4GTACTV5eGBGz2z51gUeTNpZL1wkLQE/yC6\nhJceAr7EZxReAfyHeYgawLbAPElfh7QPSZqdbafoGT0BzKwVcABwuaT/wdfF2dx80tVgYLCZbREu\n/wqPoEkzQr6kQ86JntmlGPJmEsla4WDfnqRyH3AMgKSpwBtAT6ATcAFwqJn9DV+P5M1sObTQs1VS\nPcOXLf17sdzPYvFsJQ9FnIKHSILH178BHArMA24FbgqDp1cD3fFBUuThltGziDzNrLQY8mZSWe/C\nwcxOM7OD0s0vfXuSymtABzM7LBxPxUvtjpLG4h/GKGB3SQ+vv36LPM8ws6PMrEfwXJFQzyHAY2a2\nc/BM6v08xcz2T3cPJNizdcbvZeFBBt790d3M+obXJuO12p2AEcADwI+AenxSVq4je/Yws43Sxwn2\n7GZmZeH3Vkn0NLPemceS6pOYN4uFdRqQNp9B2A3vp6sHPgaqgIskzTUPA3sLn+F4Ct7kPEXSCjN7\nHrhJ0ktZ/hvW5PpD4Lf46olTgC2BsyQtMLMb8DVdkuBZgc+03AO4MvTXps8lyXMbvDk+H4/o6I53\nJyTtc+8PDMHj1l9NR5aY2T5Aa2ASHmbZRtLQcO4ZYEy6m8PyMw/gMOBa/GF6maTF4fW9gLYJ9JyD\nz0kYFF5PzP00n8D2DLAM+JGkTzPOJeY7VGy0uOUQPuAUPotwpqRDgHPxWkJ6QGekpCfk084fBVLA\n42Y2Fi9EpmbVvmnPMvPFr44AbpHUH1/29wtgabhsVAI80wt0leG1rJMkTUrXyAM3JcizDzBO0pGS\nrsYrB7eFcwX93M2sJHQXDsVrq3cALwOHm9mPw2UbASWSFuLx9T8ws0vMrCNQjhd6QO7i64NnmZmd\nBzwM3CFpcLpgCGxcaM8M3z54BetWvH++h61eQTUJ97Ms/LoTcAMwATjGVq/LBHBjob9DxUqzLYfw\nAYwEKoCn8Eksx0j6Wcb5WsAkjctscoZa8T7ADpLubvINskSGZ2tgDPCWpLpw7l48ouL68PrHCfCs\nAJ4F3gWG4QXYmcDewKd4KOAb9u1Y60J4VuIPsiOBXpJODueH4jXKQySNL+D9LMUfUitD3/ZESVND\nV80v8d3EZA12Ewu1zSHAbsAzknK63HIDzzPwhedGSpptZkfia/YsavggLZAn8hDT04B9JQ02s/Z4\nv/0QYI4abOOZT8+QN4fj2xw/B/xD0iwz2xevHFwi6Z01pM1b3ix21lo42OqlddvjfYsnAuPwEf5D\nJb0frhsMnCipXzg+FqiVlJeBnQaeY/Hp7s/gLZpqYC98pmY/YEdJRyTE82TgRXwS0EtAO+A3wNn4\nJKJ9EuD5F+B4fABvGB6SWIFveLIS2EbSgAJ5/gy/X/dLGmZmbfHWYZl8ktNjwIvyNXAy07UP3YsV\n4dolefbsApwP7IovB/0RHjL5T0nXJMhzB+AWvIuuP/AZ8C8gJemUQniar9x6G16YTsJXR71c0rhw\n/ha8VTtc0rx0pSDfefO7QHPdShvhswLPkfQQ8Ee8WTYLX2Y3XYr/NzDXzHqGdCkgL1ETTXg+HNx2\nAAZKekTSRfJQu+H45iE/SIjnnXhLZzFeQHwkaZ6kG4Eq89mjhfZ8EBgdXv8TsAQ4GB9/uBP4PGNA\nNW+e5hu8H4O3bo4ws16SvgmDkMvDg6qSBitlmtkF+LLQSFqWhwduQ8/t5buHvY6vTPoTST/G8+YA\nM9sppDuvwJ695WsHHYe3ZIdLOhA4C++u2y+kOz+fnngeuzl0x43Gu5IOzzh/Mz5+1yccp7tpS8nv\nd6joWWvhEPrpPmP10rrj8IGpscDO5rMO64EtgBWSPgvpnpb0YY6cW+L5Gl6rOMTMNsu4tDdeC/ow\nIZ6vBJ8p+IScdmbW3TzS5kPg7wnxHIcvUbwEGCvp+FAD2xWoC/3OefWUtAi4QNKteOvm17AqaAKg\nI9BW0uRwT08Ir4+WdEM+HNfmibcYh0l6Nxz/Ax/oT/vfV2DPa8Op5cDRePAJkpYCjwObhPP35tMT\nL+yfyBhvGI+P26WjqGYA9wBDzew5fLwESU/l8zv0XaAlA9J/wjfi6CaPTZ6KxzD/Eq9dPgs8hkcE\nFJJMz0X4hJs6PMxuazO7GvgDMEnSyoR4LsC7FL7Ga+HleDP+TWCqpI8Lp9nIczJ+P3uaWSczux4f\nBBxfKEFJ08Ovt+ILo/XPGFfYGg9dHIL3S28W0uS6Ztuc57bBs56wD3HgCjyibkZIU2jPXmZ2ZBhH\neg64xcx2MLNheMRPuuKSV09JSyQtzfgO92f1PUuH1/bFA1LeU1hlNbLutKRweA1fi+QMAPlyugPw\nh+y5eDPuYEmj1vg/5IeGnpPwsYYUHme9HTBA0u8LJRho6PkmnpE/CfdwJNBfHhFUSNZ0P0vxWaSt\n8MHoJwslmEbSLLzrK/Oe7YN3L6S7F+8ohFsmDT3D4PTR5pvF9AVOk/RVIR2DV9rzqnD8Gzwi6Uo8\nMuhoSdMKZ7hqMmsZvqbT8+G1Hc3XdVoMbCdpWCEdi50WzXMI/Ysjgd/jzbp78SbxhNzqrRtNeN6P\nrxn/gXK8xsy60ITnaOAaSQWrhTdFE573AZdKKnQr8VtkDDo+hY+HfQnMBD6U9Eph7VbTwPMLYBEe\nrTY1Sfe0gedsfJD/MWBy6FZKBKH79R58zPMs/LO/PAkF7HeBFk+CC+F21fgaJXckoSbWFNEzuxSR\nZ1u8r3xH4HpJtzWTpCAUqeevJd1eYKVGhNDV9JId90u6t8BK3ynWdYZ0BbCywH32zRI9s0sxeJrZ\npUAPfJOWukL7rInomT3MF/U7DZ8suqy56yPrRt62CY1EcknmZMEkEz0jxUIsHCKRSCTSiHzuIR2J\nRCKRIiEWDpFIJBJpRCwcIpFIJNKIWDhEIpFIpBGxcIhEIpFII2LhEIlEIpFGxMIhEolEIo34fze2\nAWtRyOb/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112047990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_df.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating a dataframe with mains as sum of appliances. \n",
    "\n",
    "We do this because the algorithm in this NIPS paper assumes that the signal to be disaggregated is the sum of the the appliances we are trying to disaggregate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_df_artificial_aggregate = data_df.copy()\n",
    "data_df_artificial_aggregate[\"mains\"] = data_df_artificial_aggregate[[\"fridge\",\"light\",\"dish washer\", \"microwave\"]].sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mains</th>\n",
       "      <th>fridge</th>\n",
       "      <th>light</th>\n",
       "      <th>dish washer</th>\n",
       "      <th>microwave</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:00:00-04:00</th>\n",
       "      <td>93</td>\n",
       "      <td>7</td>\n",
       "      <td>82</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:00:30-04:00</th>\n",
       "      <td>94</td>\n",
       "      <td>7</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:01:00-04:00</th>\n",
       "      <td>93</td>\n",
       "      <td>6</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:01:30-04:00</th>\n",
       "      <td>94</td>\n",
       "      <td>7</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-19 00:02:00-04:00</th>\n",
       "      <td>94</td>\n",
       "      <td>7</td>\n",
       "      <td>83</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           mains  fridge  light  dish washer  microwave\n",
       "2011-04-19 00:00:00-04:00     93       7     82            0          4\n",
       "2011-04-19 00:00:30-04:00     94       7     83            0          4\n",
       "2011-04-19 00:01:00-04:00     93       6     83            0          4\n",
       "2011-04-19 00:01:30-04:00     94       7     83            0          4\n",
       "2011-04-19 00:02:00-04:00     94       7     83            0          4"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_df_artificial_aggregate.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interface requirements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reason we chose to create a dataframe in this format is that we tried to keep a simple interface between Matlab and Python. We chose the following interface:\n",
    "\n",
    "1. The input to the Matlab method should be a .mat where the rows correpond to different appliances and the columns correpsond to time. The first row should correspond to the mains (aggregate).\n",
    "2. The output from the Matlab method should be a .mat where the rows correspond to the disaggregated time series data with columns correpsonding to time.\n",
    "3. Any additional arguments to the Matlab disaggregation method should be a JSON file.\n",
    "\n",
    "So, based on these requirements, the Matlab function had the following signature\n",
    "\n",
    "```Matlab\n",
    "function power_disaggregation(input_file, output_file, config_file)\n",
    "%\n",
    "% This function applies the iFDM model [1] for power disaggregation.\n",
    "% \n",
    "% Usage:\n",
    "%     power_disaggregation(input_file, output_file [, config_file])\n",
    "% \n",
    "%  +input_file: Path to the input file. It should contain a matrix in which\n",
    "%   the first row corresponds to the observations (aggregated signal),\n",
    "%   while the rest of the rows correspond to the individual consuption of\n",
    "%   the devices. The number of columns of the matrix corresponds to the\n",
    "%   number of time steps.\n",
    "% \n",
    "%  +output_file: Path to the output file. Two variables are saved in the\n",
    "%   output file, detailed below. Warning: These results correspond to the\n",
    "%   last iteration of the sampler, they have not been averaged over several\n",
    "%   iterations.\n",
    "%   -acc: The resulting accuracy.\n",
    "%   -output: The inferred disaggregated signals, sorted to match the input.\n",
    "% \n",
    "%  +config_file: Path to a JSON configuration file (optional). \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we are all set. We'll have a look at the first few lines of the parameters passed to the disaggregation method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " {\r\n",
      "     \"Q\": 4,\r\n",
      "     \"Niter\": 1000,\r\n",
      "     \"verboseCycle\": 10,\r\n",
      "     \"pgas\":\r\n",
      "     {\r\n",
      "         \"N_PG\": 1000,\r\n",
      "         \"Niter\": 1,\r\n",
      "         \"maxM\": 40\r\n",
      "     },\r\n"
     ]
    }
   ],
   "source": [
    "!head /Users/nipunbatra/git/iFDM/PowerDisaggregation/parameters.json"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The authors suggested that the data should be scaled such that the aggregate power is in 10s. So, they suggested a scaling down factor of 100, which I'll do next."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scaled_data_df = data_df_artificial_aggregate.div(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we'll get the matrix representation from the dataframe and store in a .mat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.io as sio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sio.savemat(\"/Users/nipunbatra/git/iFDM/PowerDisaggregation/redd_data_nilmtk_1.mat\",{\"X\":scaled_data_df.T.values})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/nipunbatra/git/iFDM/PowerDisaggregation\n"
     ]
    }
   ],
   "source": [
    "cd ~/git/iFDM/PowerDisaggregation/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, I'll call the Matlab method for disaggregation on the data we've produced using nilmtk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[\bWarning: Function isrow has the same name as a MATLAB builtin. We suggest you\n",
       "rename the function to avoid a potential name conflict.]\b \n",
       "[\b> In path (line 109)\n",
       "  In addpath (line 88)\n",
       "  In power_disaggregation (line 69)\n",
       "  In pymat_eval (line 31)\n",
       "  In matlabserver (line 24)]\b \n",
       "[\bWarning: Function isrow has the same name as a MATLAB builtin. We suggest you\n",
       "rename the function to avoid a potential name conflict.]\b \n",
       "[\b> In path (line 109)\n",
       "  In addpath (line 88)\n",
       "  In power_disaggregation (line 70)\n",
       "  In pymat_eval (line 31)\n",
       "  In matlabserver (line 24)]\b \n",
       "Initializing inference...\r",
       "Iteration 10 out of 1000 completed\r",
       "Iteration 20 out of 1000 completed\r",
       "Iteration 30 out of 1000 completed\r",
       "Iteration 40 out of 1000 completed\r",
       "Iteration 50 out of 1000 completed\r",
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       "Iteration 190 out of 1000 completed\r",
       "Iteration 200 out of 1000 completed\r",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%matlab\n",
    "cd('/Users/nipunbatra/git/iFDM/PowerDisaggregation/');\n",
    "pwd;\n",
    "power_disaggregation('redd_data_nilmtk_1.mat','output_nilmtk.mat', 'parameters.json' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "out = sio.loadmat(\"/Users/nipunbatra/git/iFDM/PowerDisaggregation/output_nilmtk.mat\")\n",
    "disag_df = out['output']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "disag_df = pd.DataFrame(disag_df).T\n",
    "disag_df.columns = data_df.columns[1:]\n",
    "disag_df.index = data_df.index\n",
    "\n",
    "# Scaling back up by a factor of 100\n",
    "disag_df = disag_df.mul(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating dataframes for appliances to compare the ground truth and the disaggregated streams."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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yT4phtJ4khK1gqh1pA9QFLHIuqCb/5azGh4xFguIXLx1/LdqhYBvjdu17cJ+uJV8D3QOS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\nInlE4xCJRCKRPKJxiEQikUge/wMZJMINYcj4lAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113103890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3B44VkaOAHkBfEbkbWC4iO6rqMhEZBqwI/C8BSmPCjwzctkFEKoCK6L2qAkTS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\nZxr44psICrLmoMb6ALCPiAxR1TXAf4A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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118822f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uzMcVD/85/snr7Whz/Pv2Wx5dZ/e97syPi6ddAVxdMO2kwmX1L11yxYJP7XHGxj+/dzM3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\nbO6JMpP1Un6/R8C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CFePpZvanePgxQkd/Pv4rGxxnb/zSCuBjhOITzOw/wHXAxPj1K5KM\nk5Dsbyjob7iP0G+Xr6KaD1wOnOq9zxL6SzCzG5P8H1obVNIhfRPhizgmW6hNfoJQw/xNwqfLW4Fr\nCRUBjVQY5yuEG25eI5TZbe69PwO4GHjIzN5ISZxLCE0KLxE+hXcQLuMfAJ4ws6caF2ZJnH8lbM/N\nvPfreu/PInQC3teoAM3s3/GfMwgPRvtoQb/C5oTSxS8R2qU3jOcZ6k+2a4rz7XGc/cTfQxybRqio\nmx/P0+g4t/De7x33I2WB73vvt/Hen06o+Ml/cEk0TjNbbmb/Kfgf/ihvbbN8ee32hIKUP1v8lFWp\nXiXJ4feEZ5EcCWDhcbr7EE6yJxAu43Y3s/MGXEIyiuN8iNDXEBHqrLcE9jGzHzQqwFhxnA8QDuR/\nxNtwOvBRCxVBjTTQ9mwj3EU6jNAZ/bNGBZhnZk8Tmr4Kt9kuhOaFfPPiRY2IrVBxnHHn9Md8+LKY\n7YEjzOyFRsYYx5WP82vx8DmEiqTTCJVBHzOzuY2L8M2bWdsJz3S6LR63rQ/PdXoV2NLMTm9kjM2u\novsc4vbF6cAPCJd1VxAuie8f2vCqUybOqwjPjP+bDfEzZqpRJs6ZwNfNrGGfwsspE+eVwFfNrNFX\niaso6HS8kdAf9jywAHjUzH7X2OjeUhTnIuAVQrXaE2napkVxPkPo5L8W+GvcrJQKcfPr5YQ+z6MJ\n+/6UNCTYtUHFN8HF5XYHEp5RclEaPomVozjrq4niHE1oK98WOMvMLljDLA3RpHH+t5ld2OCQSsSl\nq/lHdlxlZlc0OKS1SrV3SA8H3mhwm/0aKc76aoY4vfdfBTYhfEnLa42OZyCKs358eKjfEYSbRV9f\n0/RSncS+JlRkKBXeLJhmilOahZKDiIiUSPI7pEVEpEkoOYiISAklBxERKaHkICIiJZQcRESkhJKD\niIiUUHIQEZES/x/Jb6FPDOvGyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118947790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/zaSTMOdgVI2szk5ppIPMRSutJpPl3pyDUQ2Kb45M3ixGdRmwqsXKSQ0x52AY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\nb3N1cz1uRYnfsCL0qW/A40Y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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118997e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "appliance_dfs = {}\n",
    "for appliance in ['fridge', 'light', 'dish washer','microwave']:\n",
    "    appliance_dfs[appliance] = pd.DataFrame({\"GT\":data_df[appliance],\"Predicted\":disag_df[appliance]})\n",
    "    appliance_dfs[appliance].plot(title=appliance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There you go! We have a working interface to the Matlab iFDM NILM algorithm. It should be noted that the program over 1000 iterations took several hours to run. I think that speedups upto 2 orders of magnitude should be possible by compiling it using `mex-setup`. I'll get onto that in a while. Another thing to note is that the disaggregated fridge power signal matches the state changes observed in the ground truth signal. However, the predicted seems to have a higher magniutde than the ground truth. This can possibly be due to the fact that the aggregate measures apparent power and the appliance meters measure active power.\n",
    "\n",
    "I think that this small demo shows that it is straight forward to interface a Matlab NILM algorithm with nilmtk. Hope to get more such state-of-the-art algorithms interfaced with nilmtk soon."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}