Predicting Activities from Accelerometer Data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using accelerometer data to identify activities\n",
    "\n",
    "This notebook has been adapated from [Charles Franzen](http://charlesfranzen.com/posts/predicting-activities-from-accelerometer-data/). In his work, he used this [data set](http://archive.ics.uci.edu/ml/datasets/Activity+Recognition+from+Single+Chest-Mounted+Accelerometer#), which consists of discrete samples of accelerometer data during various types of activities. \n",
    "\n",
    "The following code gives an example how to use supervised learning for the classification of activities on time series data. It uses scikit-learn, scipy, numpy, and pandas as the core technologies of this analysis.\n",
    "\n",
    "\n",
    "If you're new to the iPython notebook, you can learn [more here](http://opentechschool.github.io/python-data-intro/core/notebook.html)\n",
    "<!-- TEASER_END -->\n",
    "\n",
    "\n",
    "## Overview\n",
    "\n",
    "The task is to identify the wearers of activity given a sample of accelerometer data. The general approach that I took was that of Casale and Radeva in their [paper](https://www.researchgate.net/publication/221258784_Human_Activity_Recognition_from_Accelerometer_Data_Using_at_Wearable_Device?ev=prf_pub). It has been adapted to the dataset we are collecting in the HUNT4 study."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import libraries for matrix manipulation and data visualization\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import itertools\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas import HDFStore,DataFrame\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data set comes from synchronized and labelled data obtained from Axivity sensors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.io.pytables.HDFStore'>\n",
      "File path: /Users/kerstin/Documents/research/HUNT/hunt4training.h5\n",
      "/originial_data                       frame_table  (typ->appendable,nrows->10901356,ncols->8,indexers->[index],dc->[x_back,y_back,z_back,x_thigh,y_thigh,z_thigh,label,subject])\n",
      "/originial_data_textlabels            frame_table  (typ->appendable,nrows->10901356,ncols->8,indexers->[index],dc->[x_back,y_back,z_back,x_thigh,y_thigh,z_thigh,label,subject])\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_back</th>\n",
       "      <th>y_back</th>\n",
       "      <th>z_back</th>\n",
       "      <th>x_thigh</th>\n",
       "      <th>y_thigh</th>\n",
       "      <th>z_thigh</th>\n",
       "      <th>label</th>\n",
       "      <th>subject</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.001465</td>\n",
       "      <td>-0.140625</td>\n",
       "      <td>0.171875</td>\n",
       "      <td>-0.989990</td>\n",
       "      <td>-0.049072</td>\n",
       "      <td>-0.279785</td>\n",
       "      <td>6</td>\n",
       "      <td>009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.140625</td>\n",
       "      <td>0.171875</td>\n",
       "      <td>-1.003418</td>\n",
       "      <td>-0.048096</td>\n",
       "      <td>-0.287842</td>\n",
       "      <td>6</td>\n",
       "      <td>009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.140625</td>\n",
       "      <td>0.170410</td>\n",
       "      <td>-0.997070</td>\n",
       "      <td>-0.041504</td>\n",
       "      <td>-0.293945</td>\n",
       "      <td>6</td>\n",
       "      <td>009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.140625</td>\n",
       "      <td>0.155273</td>\n",
       "      <td>-0.972168</td>\n",
       "      <td>-0.027832</td>\n",
       "      <td>-0.277832</td>\n",
       "      <td>6</td>\n",
       "      <td>009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.140625</td>\n",
       "      <td>0.156250</td>\n",
       "      <td>-0.947510</td>\n",
       "      <td>-0.036621</td>\n",
       "      <td>-0.285645</td>\n",
       "      <td>6</td>\n",
       "      <td>009</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     x_back    y_back    z_back   x_thigh   y_thigh   z_thigh  label subject\n",
       "0 -1.001465 -0.140625  0.171875 -0.989990 -0.049072 -0.279785      6     009\n",
       "1 -1.000000 -0.140625  0.171875 -1.003418 -0.048096 -0.287842      6     009\n",
       "2 -1.000000 -0.140625  0.170410 -0.997070 -0.041504 -0.293945      6     009\n",
       "3 -1.000000 -0.140625  0.155273 -0.972168 -0.027832 -0.277832      6     009\n",
       "4 -1.000000 -0.140625  0.156250 -0.947510 -0.036621 -0.285645      6     009"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import data\n",
    "store = HDFStore('/Users/kerstin/Documents/research/HUNT/hunt4training.h5')\n",
    "print store\n",
    "data = store['originial_data']\n",
    "\n",
    "## use only one subject\n",
    "data = data[data[\"subject\"] == '009']\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploratory Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# filter data; remove subject id for the further processing\n",
    "data = data[['x_back' ,'y_back' ,'z_back', 'x_thigh' ,'y_thigh' ,'z_thigh', 'label']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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>x_back</th>\n",
       "      <th>y_back</th>\n",
       "      <th>z_back</th>\n",
       "      <th>x_thigh</th>\n",
       "      <th>y_thigh</th>\n",
       "      <th>z_thigh</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>310185.000000</td>\n",
       "      <td>310185.000000</td>\n",
       "      <td>310185.000000</td>\n",
       "      <td>310185.000000</td>\n",
       "      <td>310185.000000</td>\n",
       "      <td>310185.000000</td>\n",
       "      <td>310185.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.944251</td>\n",
       "      <td>-0.055900</td>\n",
       "      <td>0.312873</td>\n",
       "      <td>-0.957228</td>\n",
       "      <td>0.095314</td>\n",
       "      <td>0.310347</td>\n",
       "      <td>12.302793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.203294</td>\n",
       "      <td>0.172042</td>\n",
       "      <td>0.167103</td>\n",
       "      <td>0.658533</td>\n",
       "      <td>0.327879</td>\n",
       "      <td>0.851809</td>\n",
       "      <td>2.721524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-8.000000</td>\n",
       "      <td>-3.192139</td>\n",
       "      <td>-2.020752</td>\n",
       "      <td>-8.000000</td>\n",
       "      <td>-8.000000</td>\n",
       "      <td>-7.363770</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-1.040527</td>\n",
       "      <td>-0.145508</td>\n",
       "      <td>0.221680</td>\n",
       "      <td>-1.407227</td>\n",
       "      <td>-0.093018</td>\n",
       "      <td>-0.273682</td>\n",
       "      <td>13.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.953125</td>\n",
       "      <td>-0.052246</td>\n",
       "      <td>0.300049</td>\n",
       "      <td>-1.033203</td>\n",
       "      <td>0.083008</td>\n",
       "      <td>0.197021</td>\n",
       "      <td>13.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-0.844482</td>\n",
       "      <td>0.038086</td>\n",
       "      <td>0.389160</td>\n",
       "      <td>-0.618652</td>\n",
       "      <td>0.291016</td>\n",
       "      <td>0.814209</td>\n",
       "      <td>13.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.203857</td>\n",
       "      <td>3.057129</td>\n",
       "      <td>6.838135</td>\n",
       "      <td>4.279541</td>\n",
       "      <td>6.152832</td>\n",
       "      <td>7.999756</td>\n",
       "      <td>17.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              x_back         y_back         z_back        x_thigh  \\\n",
       "count  310185.000000  310185.000000  310185.000000  310185.000000   \n",
       "mean       -0.944251      -0.055900       0.312873      -0.957228   \n",
       "std         0.203294       0.172042       0.167103       0.658533   \n",
       "min        -8.000000      -3.192139      -2.020752      -8.000000   \n",
       "25%        -1.040527      -0.145508       0.221680      -1.407227   \n",
       "50%        -0.953125      -0.052246       0.300049      -1.033203   \n",
       "75%        -0.844482       0.038086       0.389160      -0.618652   \n",
       "max         3.203857       3.057129       6.838135       4.279541   \n",
       "\n",
       "             y_thigh        z_thigh         target  \n",
       "count  310185.000000  310185.000000  310185.000000  \n",
       "mean        0.095314       0.310347      12.302793  \n",
       "std         0.327879       0.851809       2.721524  \n",
       "min        -8.000000      -7.363770       1.000000  \n",
       "25%        -0.093018      -0.273682      13.000000  \n",
       "50%         0.083008       0.197021      13.000000  \n",
       "75%         0.291016       0.814209      13.000000  \n",
       "max         6.152832       7.999756      17.000000  "
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# renaming columns\n",
    "data.columns = ['x_back' ,'y_back' ,'z_back', 'x_thigh' ,'y_thigh' ,'z_thigh', 'target']\n",
    "#data.columns = ['x_back' ,'y_back' ,'z_back', 'target']\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# calculate and add norms for each data point\n",
    "data['m'] = np.sqrt(data['x_back']**2 + data['y_back']**2 + data['z_back']**2 + data['x_thigh']**2 + data['y_thigh']**2 + data['z_thigh']**2)\n",
    "#data['m'] = np.sqrt(data['x_back']**2 + data['y_back']**2 + data['z_back']**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Descriptive statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No missing values.\n"
     ]
    }
   ],
   "source": [
    "# check for missing data\n",
    "nan_flag = False\n",
    "for c in data.columns:\n",
    "    if any(data[c] == np.nan):\n",
    "        print c, 'contains NaNs'\n",
    "        nan_flag = True\n",
    "if not nan_flag:\n",
    "    print 'No missing values.'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13    0.841279\n",
       "14    0.071222\n",
       "6     0.039206\n",
       "1     0.036598\n",
       "5     0.003611\n",
       "17    0.003095\n",
       "4     0.002889\n",
       "3     0.001148\n",
       "12    0.000916\n",
       "15    0.000039\n",
       "Name: target, dtype: float64"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine class distribution\n",
    "data['target'].value_counts()/float(len(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAEWCAYAAAA3h9P4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVEREJLX/D+lasv7YajpgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x160722a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "for c in range(1, 8):\n",
    "    plt.plot(data[data['target'] == c]['m'], linewidth=.5)\n",
    "plt.xlim(0, len(data))\n",
    "plt.ylim(-1, 10)\n",
    "plt.ticklabel_format(style='sci', axis='y_thigh', scilimits=(0,0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives an idea of the shape of the signal. It's clear that there are large differences between the different activities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preprocessing\n",
    "\n",
    "As recommended in the paper cited above, I generated two new time series from each of the original series plus the norms by applying digital filters. For each series I applied a high and low pass filter, with the cutoff set to 2hz, resulting in 12 total series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x125ac3f90>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaQAAAE6CAYAAABZICYGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRAghJCT8ATuUgOOoDAWdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14c4fe7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.signal import butter, lfilter, freqz\n",
    "\n",
    "def butter_lowpass(cutoff, fs, order=5):\n",
    "    # helper function to return coefficients for scipy.lfilter\n",
    "    nyq = 0.5 * fs\n",
    "    normal_cutoff = cutoff / nyq\n",
    "    b, a = butter(order, normal_cutoff, btype='low', analog=False)\n",
    "    return b, a\n",
    "\n",
    "def butter_lowpass_filter(data, cutoff, fs, order=5):\n",
    "    # applies a lowpass filter\n",
    "    b, a = butter_lowpass(cutoff, fs, order=order)\n",
    "    y = lfilter(b, a, data)\n",
    "    return y\n",
    "\n",
    "def butter_highpass(cutoff, fs, order=5):\n",
    "    # helper function to return coefficients for scipy.lfilter\n",
    "    nyq = 0.5 * fs\n",
    "    normal_cutoff = cutoff / nyq\n",
    "    b, a = butter(order, normal_cutoff, btype='high', analog=False)\n",
    "    return b, a\n",
    "\n",
    "def butter_highpass_filter(data, cutoff, fs, order=5):\n",
    "    # applies a highpass filter\n",
    "    b, a = butter_highpass(cutoff, fs, order=order)\n",
    "    y = lfilter(b, a, data)\n",
    "    return y\n",
    "\n",
    "\n",
    "# Filter requirements.\n",
    "order = 6\n",
    "fs = 10.       # sample rate, Hz\n",
    "cutoff = 2.     # desired cutoff frequency of the filter, Hz\n",
    "\n",
    "# Get the filter coefficients so we can check its frequency response.\n",
    "b, a = butter_lowpass(cutoff, fs, order)\n",
    "\n",
    "# Plot the frequency response.\n",
    "w, h = freqz(b, a, worN=8000)\n",
    "plt.plot(0.5*fs*w/np.pi, np.abs(h))\n",
    "plt.plot(cutoff, 0.5*np.sqrt(2), 'ko')\n",
    "plt.axvline(cutoff, color='k')\n",
    "plt.xlim(0, 5)\n",
    "plt.title(\"Lowpass Filter Frequency Response\")\n",
    "plt.xlabel('Frequency [Hz]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500, 2650)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAawAAAEtCAYAAABUJFTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlcVPX++PHXmY1hFZBVBBcgF9wXxDQzbdFrapZe9baZ\nWbnUt/qZXvPmTc21zWvm0qIt96o3Lc1MKyu1NElNBHcdN3AFBYYdZju/P6gpBIFqEIb7fj4ePh7O\nOZ/Pmfd7gHnP53M+54xiNptVhBBCiDpOU9sBCCGEENUhBUsIIYRbkIIlhBDCLUjBEkII4RakYAkh\nhHALUrCEEEK4BSlYQggh3ILLC9brr79Onz59iIqKIiYmhhEjRnD06NEq+x05coQBAwYQHh5OXFwc\nL7/8sqtDE0II4cZcXrB27drFY489xpYtW9i4cSM6nY577rkHs9l83T55eXkMGTKEsLAwtm/fzty5\nc1m0aBGLFy92dXhCCCHclFLTd7ooKCggKiqKVatWcdddd1XYZvny5cyYMYOTJ09iMBgAePXVV3nv\nvfc4fPhwTYYnhBDCTdT4Oay8vDwcDgf+/v7XbbN37166d+/uLFYAffv25dKlS6SlpdV0iEIIIdxA\njResKVOm0L59e+Lj46/bJiMjg5CQkDLbgoODUVWVjIyMmg5RCCGEG9DV5MGnTp3Knj17+PLLL1EU\npSafSgghRD1XYwXr+eef59NPP+Xzzz8nKiqq0rYhISHlRlJXrlxBUZRyIy8hhBD/m2pkSvDvf/87\n69evZ+PGjURHR1fZPj4+nsTERCwWi3Pb1q1bCQ8Pr7LYCSGE+N/g8oL13HPPsXr1at555x38/PzI\nyMggIyODgoICZ5sZM2YwePBg5+OhQ4fi5eXF+PHjOXr0KJ999hkLFy5kwoQJrg6vTjGZTLUdgkvU\nlzyg/uQiedQtkodruHxKcPny5SiKUqYgQemo6+9//zsA6enppKamOvf5+fmxfv16nnvuOfr06YO/\nvz9PPfUU48ePd3V4Qggh3JTLC1Z2dnaVbZYsWVJuW6tWrdi0aZOrwxFCCFFPyL0EhRBCuAUpWEII\nIdyCFCwhhBBuQQpWLYqIiKjtEFyivuQB9SsXIeobKVi1yMvLq7ZDcIn6kgfUr1yEqG+kYAkhhHAL\nUrCEEEK4BSlYQggh3IIULCGEEG5BCpYQQgi3IAWrHpk7dy4BAQG1HYYQQtQIKVj1iKIof+iLMj/+\n+GOWLl1aAxEJIYTrSMESrF27lmXLltV2GEIIUSkpWEIIIdyCFCw3lZiYyG233UZYWBidOnXi/fff\nL9dm5cqV3HPPPbRo0YLQ0FA6d+7MggULUFXV2ebuu+9my5YtpKWlERAQQEBAAIGBgc79ixYton//\n/kRHRxMWFsbNN9/Mhx9+eCNSFEKIMlz+fVii5h05coT77ruPoKAgpk6dis1m4+WXXy5TaKD0yzRb\ntGjBnXfeidFo5LvvvmPmzJnk5eXxz3/+E4BJkyaRm5vLpUuXmDt3bpliBrBs2TL69evHkCFDUBSF\nzZs38/TTT+NwOBg1atSNSlkIIVDMZrNadbPfZ9euXSxatIiUlBQuXbrEkiVLGDly5HXbp6Wl0b59\n+7KBKQoff/wxffr0cXV4bu/+++9n69at7Nu3j0aNGgFw+vRpunXrht1uJysrC4Di4mKMRmOZvs88\n8wyffPIJp0+fRq/XAzB8+HCOHTtGSkpKueeq6Bj33nsvqamp7Nu3rybSEy5gMpmIjY2t7TD+NMmj\nbqntPGpkSrCgoIC4uDjmzZtX7ZuJKorC+vXrOXHiBCdOnOD48eP06tWrJsJzaw6Hg23bttG/f39n\nsQJo3rx5ueL+S6FxOByYzWaysrK4+eabKSgo4MSJE9V6vl+OYbPZnMfo2bMnZ86cIS8vz0VZCSFE\n1WpkSvCOO+7gjjvuAGD8+PHV6qOqKv7+/gQHB9dESJV671g+H5worLHjP3yTF4+09HHJsa5evUpR\nURHNmzcvty8mJoavv/7a+TgxMZGZM2eSlJSExWJxblcUhdzc3Go936ZNm3j11Vc5ePAgdru93DF8\nfX3/RDZCCFF9deoc1oMPPkhxcTHR0dGMGzeOwYMH35DnfaSlj8sKSl1x9uxZhgwZQkxMDPPmzSMi\nIgIPDw9SUlKYPn06DoejymMkJiby4IMPcvPNN7NgwQLCw8PR6/Vs2bKFpUuXVusYQgjhKnWiYPn4\n+DBr1iwSEhLQarVs3ryZ0aNHs2zZMoYNG1bb4dUpQUFBeHp6cvr06XL7Tp486fz/5s2bsVgsfPTR\nR2W+lPDs2bPl+l3vYuPPPvsMT09P1q9f7zzfBfD999//iQyEEOKPqRMFKzAwkAkTJjgfd+jQgezs\nbBYuXFhpwTKZTNfdFxERUS+/jE+j0dCnTx++/PJLLly44CxGJ0+eZOvWrc52Ol3pj/a3o6CSkhLe\nfvvtcsf09vYmJyen3HatVouiKNjtdmfBMpvNrFy50qU51XeFhYVcuHDhhj9vZX8f7kTyqFtqMo+q\nFnTUiYJVkU6dOlX5xlgfVt38Ec8//zzffvst/fr149FHH8Vut/Puu+/SsmVLDh8+DEDfvn3R6/UM\nHz6cUaNGUVJSwkcffeQsZL/VoUMH1q9fz5QpU+jSpQsajYZ7772Xfv36sXjxYu655x6GDx9OVlYW\nH374IaGhoWRkZNzotN2Wl5fXDf9dre3VXK4iedQttZ1Hnb1w+MCBA4SGhtZ2GHVSXFwc69atIzg4\nmHnz5rFy5UqmTJnCgAEDnG2io6NZtWoVer2e6dOn89Zbb9G/f39mzpxZ7nhjxoxhxIgRrF27liee\neIIxY8YA0LNnT5YtW4bZbGbq1KmsWrWKsWPH8vjjj9+wXIUQ4hc1ch1WQUEBp0+fRlVV+vXrx7PP\nPku/fv0ICAigcePGzJgxg6SkJDZs2ADA6tWr0ev1tGvXDo1GwxdffMGsWbOYMWMGY8eOdXV4QtR7\ntf1J2FUkj7qltvOokSnB/fv3M3DgQOfJ/Llz5zJ37lxGjhzJ4sWLSU9PJzU1tUyfV199lfPnz6PR\naIiJiWHx4sUMHTq0JsITQgjhhmpkhCWEqF21/UnYVSSPuqW286iz57CEEEKI35KCJYQQwi1IwRJC\nCOEWpGAJIYRwC1KwhBBCuAUpWEIIIdyCFCwhhBBuQQqWEEIItyAFSwghhFuQgiWEEMItSMFyQwcO\nHKB///40btyYwMBADh06xNy5cwkICCjTbsCAAQwcOLCWovxjAgICmD9//h/qm5aWRkBAAKtXr3Zx\nVEKIuqDOfh+WqJiqqjzyyCMAzJ49Gy8vLyIjI1EUBY2m7OePa79JuKioiIULF3LLLbfQo0ePGxaz\nOzh+/Djr16/n/vvvJzIysrbDEUJUQEZYbubSpUucPn2aJ554gocffphhw4bRoEEDJk+ezKVLlyrt\nW1RUxPz589m5c+cNitZ9HDt2jPnz55OWllbboQghrkMKlpv55Zt+fX19y2zXaDQYDIZK+6pqzdyY\n32q1Yrfba+TYN9K1I1IhRN0iBcuNjB8/nttuuw1FURg/fjwBAQHOc1QVncP6rbS0NGJiYlAUhXnz\n5hEQEEBAQAATJkxwtklPT+epp56iRYsWhIaG0q1bN1asWFHmODt37iQgIIC1a9cyd+5c2rRpQ3h4\nOBcvXgTAYrEwb948OnfuTGhoKK1bt2bq1KkUFRWVOY7FYuH5558nJiaGyMhI/va3vzmPUR05OTmM\nGzeOqKgomjRpwvjx48nJySnX7vDhw0yYMIGOHTsSFhZGdHQ0jz76KOfPn3e2WbVqFaNGjQLg7rvv\nJiAggMDAQOe5sMTEREaPHk3btm0JDQ2lZcuWPP3005jN5mrHK4T482rkHNauXbtYtGgRKSkpXLp0\niSVLljBy5MhK+xw5coRJkyaRlJREYGAgDz/8MJMnT66J8NzW6NGjad68ObNnz+aRRx6he/fuhISE\nAKWjg8pGCEFBQSxYsIBnn32WgQMHOgtds2bNALh69Sp9+/YFYMyYMQQHB/Pdd98xceJEsrOzmThx\nYpnjvf7662g0GsaNG4eqqvj4+ABw//33k5iYyMMPP0yLFi04fvw47777LsePH+eTTz5x9n/yySf5\n+OOPGTZsGPHx8ezcuZO//vWv1R7ljBw5kj179vDII4/QokULNm/ezLhx48r137ZtG6dOnWLkyJGE\nhYVx9uxZli9fTlJSEomJiRiNRnr06METTzzB22+/zXPPPcdNN90EQHx8PACffvopeXl5PPLIIwQF\nBXH48GE+/PBDjh07xldffVWteIUQf16NFKyCggLi4uIYOXIk48aNq7J9Xl4eQ4YMoWfPnmzfvp3j\nx48zYcIEvL29y4wAaorPw71r9Pj5H2x3yXG6dOmCTqdj9uzZdO3alWHDhlW7r5eXF4MGDeLZZ58l\nLi6uXN+XXnoJm81GYmKic6Q2atQo/Pz8eP3113nsscfw8/P7Naf8fPbu3YvRaHRuW7t2LVu3buXz\nzz+ne/fuzu0dO3bk8ccfZ/v27fTu3ZtDhw6xdu1axowZwyuvvALAo48+ytixYzly5EiVuWzatInE\nxERmzpzJU0895ew/aNCgcm3HjBnDk08+WWZb//79ufPOO9m4cSPDhg2jSZMmdO/enbfffpvevXuX\nW5AyY8aMMnkCdO3alccff5zdu3fTrVu3KmMWQvx5NTIleMcdd/DCCy8waNCgan1iXrNmDUVFRSxd\nupQWLVowaNAgnn76aZYsWVIT4YkKfPbZZ9x5552oqkpWVpbz32233UZhYSH79u0r037kyJHl3sQ/\n/fRTYmJiaNGiRZlj/FK8duzYAcCWLVtQFIXHHnusTP+xY8dW6zzbN998g1arZfTo0c5tiqIwZsyY\ncv1/G2NBQQHZ2dk0b96cBg0akJycXI1Xpuwx8vLyyMrKomvXrqiqWu1jCCH+vDqxrH3v3r107969\nzKKBvn37MmfOHNLS0oiKiqrR53fVCMhdXb16FbPZzH/+8x/+/e9/l9uvKApXrlwps61p06bl2p06\ndQqTyUR0dHSlxzh//jyKotC8efMybSrqV5Fz584RGhqKt7d3me0xMTHl2prNZqZPn85nn31GdnZ2\nmXhyc3Or9XwXLlxg2rRpfPPNN+Tl5f2hYwgh/rw6UbAyMjKIiIgosy04OBhVVcnIyKjxgvW/zuFw\nADB06FDuv//+Ctu0atWqzGNPT88Kj9OyZUvmzZtX4UgpPDzcBdH+PqNGjWLv3r08+eSTtG3b1rm6\ncvTo0c68K+NwOBgyZAhZWVlMnDiR2NhYvL29cTgc3HvvvdU6hhDCNepEwRI3xvWmZ4OCgvD19cVm\ns3Hrrbf+4eM3a9aMlJQUevXqVWm7yMhIVFXl9OnTzgUOACdPnqzW80RGRrJ9+3YKCgrKjLKu7W82\nm/nuu++YOnUqkyZNcm4vKSkpt8Lveq/N4cOHMZlMLFu2jOHDhzu3nz59ulqxCiFcp04UrJCQEOf1\nRb+4cuUKiqI4V8FVxGQyXXdfREQEXl5eLouxPvhlVHTtm7VGo2HQoEGsXbuWQ4cO0aZNmzL7MzMz\nadiwYZXHHzJkCFu2bGH58uU8+uijZfZZLBYsFgs+Pj7cfvvtzJw5k3feece56ALgrbfeqtY5zzvu\nuIP333+fFStWOBddqKrKO++8U6a/VqsFKDcKWrx4cblt3t7eqKpa7rW53jHeeOONaq9oLCws5MKF\nC9Vq60qV/X24E8mjbqnJPGJjYyvdXycKVnx8PNOnT8disTjPY23dupXw8PBKpwOrSk6UZTQaadWq\nFevWrSM6OprAwECaNGlC586dmT59Oj/88AN33nknDz30EK1atcJsNnPgwAE2b95c5V00AIYPH86G\nDRuYNGkSP/zwAwkJCaiqislk4tNPP+WDDz6gR48etG3blqFDh7J8+XJycnLo1q0bO3bs4NSpU9Va\ndNG/f38SEhKYMWMGqamptGzZkk2bNpW7DsvX15eePXvyxhtvYLFYiIyMJDExkV27dpUrwO3atUOr\n1bJgwQLMZjOenp506dKFm266iejoaP7xj39w4cIFAgIC+Prrr7l06VK1L8T28vK64b+rJpOpXvx9\nSB51S23nUSOrBAsKCjh48CAHDhzA4XBw/vx5Dh486LxYc8aMGQwePNjZfujQoXh5eTF+/HiOHj3K\nZ599xsKFC2/IknZ3dL1P9hVtv3bbm2++SVRUFNOmTWPMmDHOC4ODgoL49ttveeihh9i8eTOTJ09m\n6dKlXLlyhdmzZ1f7+VeuXMnMmTM5fvw4L774IvPmzWPfvn089thjxMXFOdsuXryYJ554gq1btzJ9\n+nSsVitr1qyp8nqyX55n9erVDBs2jLVr1zJr1izCw8NZunRpubbLly/nrrvu4v333+ef//wnubm5\nbNy4EW9v7zLPExwczBtvvIHZbOaZZ55hzJgx/PDDD+h0Oj766CM6d+7MokWLmD17Nn5+fnzyySfV\nilUI4TqK2Wx2+f16du7cycCBA8v9MY8cOZLFixczfvx4du3aVWZJ8NGjR3nuuedISkrC39+f0aNH\nlznvIISovtr+JOwqkkfdUtt51MiUYM+ePcssIb5WRddXtWrVik2bNtVEOEIIIeoBuZegEEIItyAF\nSwghhFuQgiWEEMItSMESQgjhFqRgCSGEcAtSsIQQQrgFKVhCCCHcghQsIYQQbkEKVi0qLCys7RBc\nor7kAfUrFyHqGylYtag27uBdE+pLHlC/chGivpGCJYQQwi1IwRJCCOEWpGAJIYRwC1KwhBBCuAUp\nWEIIIdyCFCwhhBBuocYK1rvvvkv79u0JCwujd+/eJCYmXrdtWloaAQEBZf4FBgaydevWmgpPCCGE\nm6mRbxxet24dzz//PK+//joJCQm88847DBs2jN27dxMREVFhH0VRWLduHXFxcc5tAQEBNRGeEEII\nN1QjI6wlS5bwwAMP8OCDDxIbG8vLL79MaGgoK1asuG4fVVXx9/cnODjY+U+nq5F6KoQQwg25vGBZ\nrVaSk5Pp3bt3me19+vRh9+7dlfb9pcD169ePDRs2uDo0IYQQbszlBSszMxO73U5ISEiZ7cHBwWRk\nZFTYx8fHh1mzZvH++++zdu1aevXqxejRo1m7dq2rwxNCCOGm6sScW2BgIBMmTHA+7tChA9nZ2Sxc\nuJBhw4Zdt5/JZLoR4dWo+pAD1J88oP7kInnULZJH1WJjYyvd7/KC1bBhQ7RabbnR1JUrV8qNuirT\nqVMnVq5cWWmbqpKr60wmk9vnAPUnD6g/uUgedYvk4RounxLU6/V06NCB7du3l9m+bds2EhISqn2c\nAwcOEBoa6uLohBBCuKsamRKcMGECY8eOpWPHjiQkJLB8+XLS09N55JFHAJgxYwZJSUnOhRWrV69G\nr9fTrl07NBoNX3zxBStWrGDGjBk1EZ4QQgg3VCMFa8iQIWRnZ/Paa6+Rnp5Oq1atWLt2rfMarPT0\ndFJTU8v0efXVVzl//jwajYaYmBgWL17M0KFDayI8IYQQbqjGFl2MHj2a0aNHV7hvyZIlZR6PHDmS\nkSNH1lQoQggh6gG5l6AQQgi3IAVLCCGEW5CCJYQQwi1IwRJCCOEWpGAJIYRwC1KwhBBCuAUpWFXI\nszhwqGqF+zRnjqP/eh1YLTc4KiGE+N9TJ25+W1el5dt4ckc2g5t58mhLn193qCr6r9dh+O8SFLsd\n7dH9FE94EbTycgohRE2REdZ1ZBbbmfyjmZExXmxOLSb56s+jKLsNj7dm47FyEYrdjmrwQLdvBx7v\nvgwOR+0GLYQQ9ZgUrAoU2hxM2Z3DXyI9GRnrzeQOvszZn0uuxYHux63oE79BNXpSNGE6RX9/HdXD\niH7XFgxr36nt0IUQot6SglWBTanFhHpqePAmLwC6hXrQK9yD1w/kof92PQAlIydgj++NIyaO4mfm\noCoa9F+tRclMr83QhRCi3pKCdQ2HqrLhbBHDo71QFMW5/bFWPjhOHkN76iiqty+27rc799lbd8KW\n0AfFbkO/aXVthC2EEPWeFKxrJF2x4qFVaBOoL7PdQ6vwXMbXABTf8hfwMJbZbxn4AKqioP9uE0rW\nlRsWrxBC/K+QgnWNT88Wck9TzzKjKwAlN5vwlO9woLA++o5y/dSIpti69kaxWdFv/u+NCleIP0RV\nVd47ls/+q3JJhnAfUrB+I6PIzoFMK30be5Tbp/tuE4rNSmHbBN7NasC5fFu5NtZBDwKg374RxZxZ\n4/EK8Uclplv46nwx8/bnMmtfDpnF9l93FhWiTdqJfvN/0W/5BN32z1EyLtZesEL8rMYK1rvvvkv7\n9u0JCwujd+/eJCYmVtr+yJEjDBgwgPDwcOLi4nj55ZdrKrTr2phaxO2NjXjprnlZHA702z8HQHvX\nEMa19uH/dmbz05Wyn04dkc2xdb4FxWpB/8VHNRZnrsXBvivyyVj8MVaHyuLD+Tzbzpf3b2tIsKeW\nx7dncWbXjxhffg7vCYPwXPgCHh8tw2PlIozvvYrX5AfwWPoSmnOnazt88T+sRgrWunXreP7553nu\nuefYsWMH8fHxDBs2jAsXLlTYPi8vjyFDhhAWFsb27duZO3cuixYtYvHixTURXoVK7Cqfny3inmae\n5fZpj6eguXoZR8NQ7HFd6B/lyYtdGjA7KZfPzhaVaWsZ/BAA+q0bUHKzXRqj/ecFIQ9vzeTFn3JI\nTC/5zROXoEk1lf5LOwklRdc/kPif9snpIiJ9tHQL8cBTpzDO4xwf7X6Jtm9NQXf4J3A4sMfEYbnz\nPiy3D8HWpRdoFPQ/fovnP8eg+3ZDbadQp1wutLP8WD42R/k74lgdKhvOFHK+WAOWktJVxCXFtRBl\n/VAjt2ZYsmQJDzzwAA8+WDpF9vLLL/Ptt9+yYsUKpk2bVq79mjVrKCoqYunSpRgMBlq0aMGJEydY\nsmQJEyZMqIkQy/kyrYjWgXqifMq/JLrvvwDA1vMu0JTW+A5BBhb18Gfsjmz6RHjgoy/d7mgSi63D\nzeiSd6H/cg2Wvz7hkvisDpUpP5qxOuDl7v4U2VRe3GPmg4YnCd73LbrkXSjFvxYp1dMba6+/YL19\nCGpII5fEINzLcbOVr88X0yZQT9tAPSV2OF9gY9XJAhb3DICSYgzrVqD/ai1eqordy5d1cYP5MKIP\nUeGB9I8y0rtR6eIi5eplDJ+vRL9tI8YPF2DJuIBl+BOg0dZylrUrq9jBc4lmtAqcz7fzQmc/tIqC\nqqokXshn/5bv6Hv2eyKvnMa7KBPl59u8qZ7eOBpFYY9ti71FO+xxXcot5BLlubxgWa1WkpOTeeqp\np8ps79OnD7t3766wz969e+nevTsGg8G5rW/fvsyZM4e0tDSioqJcHWYZdlXlo1OFTO3UoPzOogJ0\nP30HgLVnvzK7Gvvo6BpsYMu5Yu5t7uXcbhn8UGnB+mY9lv7Dwdf/T8WnqioLDuRh1Cm83LUBWkWB\nXDNvJ/+LRsd2Ods5wiNR9R4olhI0l89h+Got+q8/wXLfo1gH/A2uWUgi6q98m8LcvTn0Dvfgy3PF\nvJqSh7dOIcxLy2MtvGl6cg8eK99Ek3ERVaPB0n8EloH309/Lh+4lDpIzLSw6mI+nTqFbiAdqUBgl\noyZij26Nx3uvYfhyDZqrlyke+wLoDVUHVA/lWR1M+tFM3wgP/hbrzdTdZl5JziPBswDbprX0Pb6F\nO0vyne3tigbFPxAlPxelqADtqaNoTx2FL9egGozYOnTH1rMf9nbxNfe3qqpQUoRSkAclxaghEaBz\nn1vKuTzSzMxM7HY7ISEhZbYHBwfz3XffVdgnIyODiIiIcu1VVSUjI6PGC9aOSyUEGrXllrID6PZs\nR7GUYG/ZvsKRyuCmnrx+II8hzX5dWeho3hJbu27oDuzG8OVaLMMe+1Px/fdkISfMNt7o6Y9WUdAe\n3IvHW7NplmemWO/Jti5D6TGkH5rQX19DzdkT6L/6GP2uLXisfQft6WMUPzYFPL3/VCyianZVJTXP\nzvl8G91CPfDQKpCfi/bcKZTL51B9A1BDGuEIawyG8gt8/ixVVXn/kie9wz0Y38a3zD7NmeMY1r5T\nOvUH2COjKXl0Mo5mLZxt/D009G5kpKGHhml7c1jYI4AmvqVvFbZb+qMGhWF84wV0P32P8V//oPj/\nZoJH+an0+iyjyM4Le3LoEKRnVAtvFEVhdhsdye++S6/DX2CwlZ5jtkdFY+vZj+N+Ybxe0oJ2IV60\nCdCh5OfQLu8sAWcPoz20F+2po+j3bEO/Zxv2JrFYBj6AvUuv31W4bA6V5KtWjpqt9AjzoLnfr2/v\nGblFZH+9mWbb1xCY++vNDVS9AUezFthbtMfWNh5HTOs6fU/UuhvZDaKqKqtMhTzcouI3cv2O0ulA\n6y39K9zfvqEejQLJmVY6Bv36SdMy+CF0B3aj/2oN1h53ojZqUu14jufY2HmpBFOOjXP5NmwqvNkz\nAC+dBl3it3i8MwfFbsfWqiNFj0zmk5NGdl/WMjFExaZC0hULTUOiCX1iKrb43hjfno1u3w68Lp6l\n6KmXUCOa/r4XqZ745RyDTuP6T6+mHCu70y0kXbVwNNtGQ6OGhh4K+7/aylMnP8Xv/IlyfVRvP0qG\nPYbt1gHOqWZX+Ph0ETk2hcda/3zD5qICdD9+i37752jPlsahevlgGTIKa5/BoCv/QQ2gbUMDT7T2\nYeqeHOZ1a0Dkz9Pl9lYdKZryL4yvTkZ3aC+eL0+i+P9mojYIdFkOf1axTSXpqoU9GRZyrQ4mxPnQ\n0Pib6UubFc3ZE2hPHwUUHIHBqKGNcUQ2r/LYyVctzNyXy1+jPUtvMKCq6H74isCP3uL2n89b2zp0\nxzLwARwxcQDYTSZeiGjIokN5nM6zAR7My27O6E7tGDjkEbSZ6aU/oy2foE014fnmi9hvakfJQ89U\nK6Z1pwv54EQBjby0tAzQM/lHM0FGDf4eGoIP/sDYfStoXli6ctmiNVDo6YevhxZtZjraEwfRnjiI\nYeN/UL18sHW4GVu33qXTlHVs9KyYzeaKvzvjD7JarYSHh7N8+XIGDx7s3D5p0iSOHj3K559/Xq7P\n2LFjyc5Oona4AAAgAElEQVTO5qOPfl1Zt3//fvr27UtycvJ1R1gmk+lPx3usQMvKy57MaJ7Pte9j\nxvTztHpnBnaDB4eeeQ3HdT4Nb8sycLxQx9jGhWW2R218n4YpP5DfOBrTQ5OrfFNKLdKw9II3OkWl\nk6+VaE87oQYHQQYHOgWCftpG4y9Xo6CSnnAnF/veB4qGYju8nuaNUQPnSzQ01DvItGp4pFERbX1s\nGLIyaL52CZ5XLmDXe5A2cBTm1l3+1OtWlxTbQaOAoYKXt8imcv7UeXyOp9AidT8+1kJKAkPwCA3B\n2jCUksBQbEYvtJYSFLuVkoAQSgJDq11AVBU2Z3qwLdtAF18rrbxtxHjZaJh1gSYbVuB1OQ0ofZOw\nhkZQ3DAMXVE+xszLeGSXXmBeENGc1EGPUNIw7E+/Ft9lG9h41YO/N8knMvscwXu3EnB4D1pr6QId\nm9GLrPY9uNyjP3Yv3yqOVmprVukxu/pZuTuoBD9d6VuGR+ZlYlYuwJCbhdWnAWeGPE5Bk5v+dA5/\n1qlCLW9d8CLE4KCdZxG6/DxOZeQzwniJ2KzTeKadxPfyWbQ2a7m+uc1ac7HvfRSFlX3Pybcp7M/T\nkZSnJ7VYy5hGRbT2saHLz6HJhhX4nTlS2i4yhvN3jqAovOoPqBeKNfz7cunI9MGwIiKMDhSblYbJ\nOwnbsRF9QR6qouFKfF8u9RqE4zrnuA7m6/jwkifPNSkg1FB6A26HCsfNdjp+t5pWh0pntoqCI7h8\nywDSW3Tmg8vepJdoebjBFdpkncD3zFH8Th3GmHnZeVyrTwPSu/fjaqdeqDVcuOwqaBWIjY2ttJ3L\nCxbA7bffTtu2bVmwYIFzW5cuXbjnnnt44YUXyrVfsWIF06dP5+TJk87zWK+99horVqzg8OHDrg6v\njMk/mundyIO/RF0zpeFw4Dn7/9CePITljnuxPPB/1z1GgdXB8G8yef+2QIJ++ymuIA+vqaPQmDMp\nuf8prHfeV6afyWRy/oCySxyM/T6Lx1v50CfCo+yFy5YSPFa+iX77RgBK/voE1gEjyxwr1+Lg2wvF\nxIcYiPDWcSCz9FPggChj6ZSFpRiPFa+i//FbAGztumG5ZxSO6Fa/9yUr57d53EjbLxbz9fli9l+1\n4qlVGNPKm7sijdgccNRsZefJqyR8tpBbz1d87vR6VIMH9jZdKR79XKXnH0vsKq8k53KuwM7s+AbO\nn73mxEE8FzyPUpiPw78heXeN4CFu5tmuwXQJ/vkPX1XR7dmOYdWbaMyZOPwbUjR1IWpo4yrjc6gq\nh7KsJKZbSMm0cFMDPX0iPNh/1cpX54pY0NKK/0eLCDyY6DzJb2/RHmvvu0tX/P2BaUhziYN/mwrY\ncq6YOxob+Wu0F2FeWhRzJsYlM9EeT0FVNFjv/huWu/8GRq+qD1oNFf1u5VocrD1dyKEsK3c0NtKn\nkRGjTsF6PpUTP/xI5vET9Cg5h2/eFZRcs/M1uFZxaCTaFm1Bp0fJvor2eDJKYQEA1l5/oeRvE3AY\nvdh4togVxwvoFGSgV7gH3UINeOk0aA/uwePtuWhys1F9G1AycgK2m++ocBrven8jDlVlY2oxK47l\nM7CJJw/e5F06hVyQh+GT5ei3foaiOnD4B2EZOQ5btz5ljn+xwM6EHVnM7NqAtg1/LSqaYykY338V\nzaVzqDo9luFjsd4+xPlBTFVVtpwvZvmxAlo00PNEa28a++hQLp9Ht3c7usRv0F44Wxpjg0AsQ0Zh\nu3UAplOnXfK3nmtxkJJpJTnTQspVK2fybDTy0vLvvg0r7VcjBWv9+vWMHTuWV155hYSEBJYvX86q\nVav48ccfiYiIYMaMGSQlJbFhQ+ny2NzcXOLj4+nZsycTJ07EZDLx5JNPMmXKFMaPH+/q8JxO5diY\n/KOZ1bc3xKAt+0um27oB4wcLcDQIpHDuB+Bd+afRRQfz0Cgw4ZpzBtqknXgufAHVYKTon0vKDO9/\n+SW2OVQmJpppE6jnsVY+ZfprUk14LH8FbeoJVL2ekof/H7brTE9eK7PYzj/25BDbQMcz7XzRQun3\neH38DsrPS2vtN7XF1qkntk49qvVmWZHaKFjfXSxm2ZF8Hmnhzc1hHpzLt/PmoTwySxzklKjcmX+M\nZ3a+gW/uFVSjF9aed2Hv1ANHwzA06ec5fPg0V86c5TYlA721BNXoCRotjrRTGHKzAHAEhVH8zJwK\np2TO59uYsS+Xxt5a/t7BD6Ou9PdHm5yI8c0XUawWbJ16UDx2GngY2ZtRwispeSzvHYiv/jejt8J8\njAtfQHcsGUfDUIr+8QZqw9Dr5m2xq7y0L5e0fBu3hHvQIcjA0WwrWy8U428v4tWrX+D37ccolhJU\nrQ7rbQOx9r2n2lPSVckstvPx6SI2pRYxNs6n9IOe3YZh3XsYPl9Z+rr5B2EZ9ljpm/efnOr87e9W\noc3BRycLWX+2iFvCPOgaYmDniQya7/uSvmk/EG1OLddfVTSofv6o/kHYGwRij2gGLdqy3SeGhWc0\nLO4ZQKjXzx8y83MwbFyJ/pv1KDYrRQGhvHbzk5xq1Ib/186XZr+cEyrIw+OjZei/2wSArVVHSp74\nB2pAULXyqEhmsZ03DuZzJs/G1E5+tPQvnabVnD2Bx4cLShdnUHpOzHr3A+R27ElyloN3j+ZzdxNP\n56IvJTMdw4YPnbE5GjWheNw0HFExFT5viV1l3elCVp8q5O6o0oLpqVNAVdEmJ2JY/z7a1NJpZHvj\n5pxN6Edo/yHXnUauytk8G/P255KWbycuQE+HID0dGhqIaaAj43QqkbFNK+1fIwULSkdNCxcuJD09\nnVatWjF37lwSEhIAGD9+PLt27SI5OdnZ/ujRozz33HMkJSXh7+/P6NGjmTRp0u9/YrsNNFoOZlnZ\nednCQzd54a2v+I9mdlIOzXx1/C227PkrxZyJ1/MPoRQWUDRhOvb43lU+bWaxnVHbsljRO5Bgz7JL\nfT2WzSr9ShLfBhRNWYCjcekboMlkIiYmhoUH87lUaGdOtwZoASXjAroDe9Dt/NJ5zsERHE7xkzNw\nNP19Uy6FNgf/2JODv0HDlI5+pZ/e8szoNq9B/806tJZfrwlxNGqCrWMPbO0TSkde1filLLGrfHPo\nDIFhERTbVMi+SqP939Lo5D78CrLwzM9GURRUHz9UX38cDUNRg8NwRMZgi+sMfr9vBaXm/BlKDu3n\n+59OcIsxD59mzbHf1A5HoyY4DB6kpV0iesuHGJNLV0/ao1tRPHZahQtm/n2igG0XilnYIwDfn+cT\nTSYTNwX4YnzzRbRnjqN6GCl+ejb2uM7OflsvFLPwYB6PtPBm8G9u46U5eRjPuc+g2KxYbx1AycPP\nljmBveBAHsU2lec7+ZUNpKgQz1cnoT15GEdII4qmvlHhm1+xTeWfP+Vg1Cq80MnP+SFLybqCLvEb\n9F+uQfPzOZTsVp0xPPL/UEMjyh3HFc7l23h2l5nRLb2dsxOak4fx+M8itGeOAWBv3oqS+590nsf5\nvfIsDpJPnCGySROOZFtZcayADg31jG7pQ0RBOvov16Df8QWKpXS6U/X0xtahO47mrbBHRaOGNkb1\n87/uIoI1pwrZlFrEnG4NiPAubZNvdZCYdIJ2/32Z6KzSi6RtLdph6/UXVKMX2rMn0O34Ao05E1Wr\nKz0POGBklcv7q/uhbuuFYhYdzKNPhJEwLy16DcT6aml/6GsM699D8/MddLI8GnAqog1KbGvaBBpQ\nSorQHfoJ7YkDpa+FTv/zaPf+ap2Hyiy2s+xIPklXrPRq5EGPMA+KbCpfnyvCO2k741JW0qiwdArb\n7umDo0MCGD3BZkMpyEXJzMCWY0bj1wClYSiORk2wt+2KPSbO+fy700uYuz+Xx1r5cFekEZ3Dhubc\nKbQnj6A9sBvdgd3kf7C90jhrrGDdCLszSugUoMXzx6/RJf2A5sIZlIyLFAWGsTmoE+mte/CldwyT\nO/qXWRCBw475QAobtyXzsOdlDIW5OEIjUIMblb6AKYlocrKxtU+g+Nm51V6ps+xwPkV2lWfblY6y\nrA6VlEwru8/nMfCTWbQ+tx+HTwOKn52DIyYOk8nEbrURW88XsbhJJg12f4Nu3w40V3+dR1a9fbH2\nuBPLPaOqHOVdT4ldZX5yLrsuW7ipgY5QLw17Myw00ZYQk5pEj/N76XZpPx7Fvy7BVT2M2Fu0xx7X\nGXvrztgjmnIy30HSFSs2VUVV4USOjX1XLITorHQvSOWu5HW0St2HRq3+F1nam96Etc9g8rvdweE8\nOGG2cjbfjt2hogKNvLX0CPOgha4Yj3XLSy/Ivs4Uz2+pBiPWvwzHMvDB6y7bVdXSOz4cM9t4NcEf\no0759Y3FUoLHildKP2h4eVM4bQmO8ChWnSxkY2oRL3VtQGyDXwu6cvUynjPGocnNxnrboNJidc3v\nTZFN5YnvsxjU1JOhza+ZMivIw3P+RLSpJ3CER5VOD/oFOHdnFNl5aV8u4V5aJnfwRVdSiO6n79Ht\n+hrt0f2/Tv3FxFEyYhzH8ajxUe8vRetvMV7c08wTjaKAw4Fu19cY1r7tfHO1duuDZeiYqq8HtNtQ\ncrJwFBWxMc+Hd8868MSGh8FAiKeGR2M8iMs+iWHLJ2h/2oHy8++ZrV03rH0GY2/z+xcJrDQVsPZU\nIY28tTTx0bHzcgldgg0MjdLTYcdqDF+uRbGUv9DXHhNH8ehJ1V7A9HtmITKL7Xx6tohCm4rFrpJ0\n1YpGgVbeDoL3bOHRUxvxy75cYV/V4IGt481Y7hn1h0bVqXk2dlwq4Yf0EgwahTsaG+kV7oGvakX/\n7afkfr2RkKzz1T6eavDAHhbJGa8wTlkMdPWx4G/JQ7l6GSXzivNnCKDq9RS8+3Wlx3PrgvXB22sZ\ncegTGuZU/MMDKAwMZ01kb1q3akY7fw2ac6fQ7foaTfbVSo/tCI+iaNIrlU7PXMtc4uChrZm81SuQ\nI9lWlh3JJ8hTQ88wDxrp7UQvn07rtCQA8hrHcjS0JUWZWdxceBZ9xq93AVG9/bC17oS9c09snW9x\n2dLnQpuDI1k2Lhba6RpiINxLi6qqHM62sWB/Fo8rp7nl0k9oD+1De/Fs2dyMfhwIbUP+TR3IDY4i\np0EYzcmjS/YJdLu+wjft59VnWh32Dt2xdr8dR6MmlPj482pKHobCXJ5pYseYdRkl4yJa0yG0J1JQ\nrKUnvq94BfFl+8Fc7tafyEBvDBoFRYHT2SXoE7/m/n3/oWGxGbtGy/dNexDfJQ5tQCCaVBNa08HS\nX35rCagq1h53Yh34QLVWrTlUlfnJeZhLHMyKb8DZUyd/fWNxODC++SK6fTuwh0bw5rBX2JnvwSvd\n/cueqywqxHPWk2jPn8YW15ni/zf/ukUyvdDO//2QzagW3vS/9rxpfg6ec59Be/4M9shoiie/isPX\nn28vlPDmoTzua+7Fg/rzeGz5BN3e7SjW0qXTqk5f+prf0g97++6gKDdsmvZcfukUT7EdxrX2oUvI\nzwWjuBD7pyvx2rIGvd2KTaNjT5s7CezVh8YdO+DQaDh2Povc40e56dQeQk8mYci8hPKbb+22efth\n9fTGEBgMdhuaNJPz90XV6rB1vx1r/786Zyz+KJtDZd9VC2dybfSNMJadISkqQLd7G7rdW0unjJve\nhD26NfYOCb/rouk/8/P45W/0aLaVOyONNNArKJfPoT26H23aKVS9HvQeOCKaYuvUEzxdc/6wIiaT\nCb1dQ9L3e7hS7MCu0WIxenNzq8Z0jQ3FkWPmYtpFzqcc5Ka0/TTJTrt+XooGNTQCe0xr7NGtsXW5\ntcoZF7cuWD4P9wbAHNgIj0Ej+FQXzeo8f14JzaCZ6Ud0u7eiuc5XfVzyCcWnUzz6ZjGofgFo0i+g\nSb+AIyQce7uE0vMWf+DivRXH8ll3pogwTy1Pt/UpcyIUSwnqf9/G8MNXZUYzAKpvA6zd+mDrfjuO\n5i1v+B0EzuXbeHJnNvMT/Gnpr2fv8Ysc2PEjrS8cICHjIL75ld/MV/Xyxnr7vVjvuLfMyABK3xBe\nSc7jfIGNFzo1INz759wsJZi+/paAL1fRNLf0U5vDL6D0nEtgCNit6Ld+hjbtJAA5TePY+ZcJNG19\nk/O6IFewOVRe/CkHD63CMN8MWt30mzeWkiKMs55Cl3aSY2FxNJg6D98GvxnpFuTh+drf0Z46giM8\nksJpS6ocCafmlY5Mbg4zcLXYwcUCO7af36f9i83M/WoaEbkXKdYa2Nz0Nk5FteMBw0VCTqegNR1y\nHsfeoj3Wm+/A1vXWcs95I88rqqrKjkslvH20gAAPDQ/EemHQKsxOymWYXy6D9q4maN83zlFgkd4I\nKnjayo9c8rwCUIxGvHOvolSwis8RHomtU0+sd9xX6Tmjuqa2Fia52m/zUFUVs0XFS6eUnmr4DVVV\nSUy38PWxDIZ6ZdHeml76/uftC94+OILCSgcDv/NcmFsXLM/pT5DVazAPWzrT0FuPTlGY3sXv1+st\nHHa0h/eh272NK9l5mPJUQkICedc/nscGJ9DY94+dOKxMoc3BngwLt4R7lN6RoiKWEnT7dmJO2YN/\n6/Y4IqNxREbX+hXn239eyNDcV8e5AjtPtfGhS7ABDZR+ojuShNZ0CE3GRZQrl8DoiT22LZcahBA4\ncDh4+Vz32A5V5aOTpSd3/xbjTZBRwydnCsm1qPyzow+tT+/BsPHfznN2ZfoGhmAZOqb0SzNdeL3S\nb5XYVV7cm0N2fiHzbwnD30Pj3P6vbSd57pPJNCjMxtGoCUVPz0YNawy55tJzT6kmHEGhFP19QbVv\ng3Um18bujBIivHVEeGudS/JVQGe+Sviq1/E5vKdcP9XohfXWAVXecqs23iBtDpXvLpWw8kQBmSUO\n/tHJj/iQ0tkBTdopdD98hfbAbrQXSxdHqJ7eOMIaY28bX3ruqUnsr29gDgdKbjZphw/QNNAfVBV7\nk9g/PC1e2+pjwaoNbl2wfmHKsbLrsoX7Y70qvSj07SP5bE4rKnPlfm2q7R9+RVaaSpf1DmvuVW7l\n5PX8njwuFNhYdDAfi0Pl3mZedA8z/FrYVRXtob3o9mwHhx1QcERGY+0zqEbuCHEtu6ryyq5zJBd5\ncW8zLzKLHey/aiHKR8vUiHy83/gH2gtnUY1eqD5+KFkZKA4HjtDGFP39td81fVwdmvNn0G/5BOXq\nZRxNYrE3a4G9bddq3a2kNn+3VLX0Anb9df4WlZwsVJ2+WsWnLv6N/BGSh2vUi4JVXaqqUmRXy399\nSC2p7R++q9SXPKA0l0vekSRdtRLiqSHCW8st4R6lCwqKCjG+PQdd0k4AVEXBEduG4gnTUf0rv37k\nRqsvPxPJo26p7Txqf5hxAymKgpdObgArKterkZFejSq4q4CnF8VPzURz/gyqwVA6oqpjt64Roj77\nnypYQvxpGg2OqOjajkKI/0l1Y25MCCGEqIIULCGEEG5BCpYQQgi3IAVLCCGEW5CCJYQQwi1IwRJC\nCOEWpGAJIYRwC1KwhBBCuAUpWEIIIdyCywuWxWJh0qRJREdHExERwciRI7l48WKlfVatWkVAQACB\ngYEEBAQ4/2+xWFwdnhBCCDfl8oI1ZcoUNm3axIoVK/jiiy/Iy8tj+PDhqFV8S6y3tzcnTpxw/jt+\n/DgGg9ynTQghRCmX3kswNzeX//znPyxdupRbb70VgLfeeou2bduyfft2brvttuv2VRSFoCD3+UI2\nIYQQN5ZLR1jJycnYbLYyhSkiIoIWLVqwe/fuSvsWFRXRtm1b4uLiGD58OAcOHHBlaEIIIdycSwtW\nRkYGWq2WwMDAMtuDg4PJyMi4br/Y2FjefPNNVq9ezfLlyzEajfTr148zZ864MjwhhBBurFpTgrNm\nzeK111677n5FUdi4ceMfDqJr16507drV+Tg+Pp5bbrmFt956i3nz5v3h4wohhKg/qlWwJkyYwIgR\nIypt07hxY/bs2YPdbicrK6vMKOvKlSvcfPPN1Q5Ko9HQoUMHTp8+XWk7k8lU7WPWVfUhB6g/eUD9\nyUXyqFskj6pV9W3G1SpYvyw1r0qHDh3Q6XRs27aN++67D4ALFy5w/PhxEhISqvNUTocOHaJdu3aV\ntnH3r5yu7a+bdpX6kgfUn1wkj7pF8nANl64S9PPz48EHH+TFF18kKCgIf39/XnjhBdq2betcNQgw\naNAgunbtyrRp0wCYP38+Xbt2pXnz5uTl5bFs2TKOHj3KwoULXRmeEEIIN+bSggUwb948dDodo0eP\npri4mFtvvZW33noLRVGcbVJTU4mKinI+zsnJ4ZlnniEjIwM/Pz/atWvHF198QYcOHVwdnhBCCDfl\n8oKl1+uZP38+8+fPv26blJSUMo/nzJnDnDlzXB2KEEKIekTuJSiEEMItSMESQgjhFqRgCSGEcAtS\nsIQQQrgFKVhCCCHcghQsIYQQbkEKlhBCCLcgBUsIIYRbkIIlhBDCLUjBEkII4RakYAkhhHALUrCE\nEEK4BSlYQggh3IIULCGEEG5BCpYQQgi3IAVLCCGEW3B5wfrggw8YOHAgTZo0ISAggHPnzlWr34YN\nG0hISCA0NJTu3bvz+eefuzo0IYQQbszlBauwsJC+ffvy/PPPoyhKtfrs2bOHRx99lOHDh7Nz506G\nDh3KqFGjSEpKcnV4Qggh3JTO1QccN24cAMnJydXus2zZMnr16sWzzz4LwMSJE9mxYwdLly7lnXfe\ncXWIQggh3FCdOIe1Z88ebrvttjLb+vbty+7du2spIiGEEHVNnShYGRkZhISElNkWHBxMRkZGLUUk\nhBCirqnWlOCsWbN47bXXrrtfURQ2btxIjx49XBZYdZhMphv6fDWhPuQA9ScPqD+5SB51i+RRtdjY\n2Er3V6tgTZgwgREjRlTapnHjxtWP6hohISHlRlNXrlwpN+q6VlXJ1XUmk8ntc4D6kwfUn1wkj7pF\n8nCNahWsgIAAAgICaiyI+Ph4tm/fzlNPPeXctm3bNrp161ZjzymEEMK9uPwcVkZGBgcPHsRkMqGq\nKseOHePgwYOYzWZnm0GDBvHSSy85H48dO5bvv/+ef/3rX5hMJl5//XV27tzJ+PHjXR2eEEIIN+Xy\ngrVixQp69erFE088gaIoDB8+nFtvvZUvvvjC2SY1NZX09HTn4/j4eJYvX87q1avp2bMna9as4b33\n3qNjx46uDk8IIYSbcvl1WFOmTGHKlCmVtklJSSm3bdCgQQwaNMjV4QghhKgn6sSydiGEEKIqUrCE\nEEK4BSlYQggh3IIULCGEEG5BCpYQQgi3IAVLCCGEW5CCJYQQwi1IwRJCCOEWpGAJIYRwC1KwhBBC\nuAUpWEIIIdyCFCwhhBBuQQqWEEIItyAFSwghhFuQgiWEEMItuLxgffDBBwwcOJAmTZoQEBDAuXPn\nquyzatUqAgICCAwMJCAgwPl/i8Xi6vCEEEK4KZd/gWNhYSF9+/ZlwIABTJ06tdr9vL29SU5ORlVV\n5zaDweDq8IQQQrgplxescePGAZCcnPy7+imKQlBQkKvDEUIIUU/UmXNYRUVFtG3blri4OIYPH86B\nAwdqOyQhhBB1SJ0oWLGxsbz55pusXr2a5cuXYzQa6devH2fOnKnt0IQQQtQR1SpYs2bNci6GqOhf\nYGAgP/zwwx8OomvXrowYMYI2bdqQkJDAe++9R7NmzXjrrbf+8DGFEELUL4rZbFarapSdnU1mZmal\nbRo3bozRaHQ+Tk5Opk+fPqSkpBAZGfm7A5swYQJXrlxhzZo1121jMpl+93GFEELUTbGxsZXur9ai\ni19GUjfSoUOHaNeuXaVtqkqurjOZTG6fA9SfPKD+5CJ51C2Sh2u4fJVgRkYG6enpmEwmVFXl2LFj\nmM1mIiMj8ff3B2DQoEF07dqVadOmATB//ny6du1K8+bNycvLY9myZRw9epSFCxe6OjwhhBBuyuUF\na8WKFcyfPx9FUVAUheHDhwOwePFiRo4cCUBqaipRUVHOPjk5OTzzzDNkZGTg5+dHu3bt+OKLL+jQ\noYOrwxNCCOGmXF6wpkyZwpQpUyptk5KSUubxnDlzmDNnjqtDEUIIUY/UiWXtQgghRFWkYAkhhHAL\nUrCEEEK4BSlYQggh3IIULCGEEG5BCpYQQgi3IAVLCCGEW5CCJYQQwi1IwRJCCOEWpGAJIYRwC1Kw\nhBBCuAUpWEIIIdyCFCwhhBBuQQqWEEIItyAFSwghhFuQgiWEEMItuLRgmc1mJk+eTHx8POHh4bRp\n04aJEyeSnZ1dZd8NGzaQkJBAaGgo3bt35/PPP3dlaEIIIdycSwvWpUuXuHz5Mi+99BKJiYm8/fbb\n7Nq1izFjxlTab8+ePTz66KMMHz6cnTt3MnToUEaNGkVSUpIrwxNCCOHGdK48WKtWrfjwww+dj5s2\nbcrMmTMZMWIE+fn5+Pj4VNhv2bJl9OrVi2effRaAiRMnsmPHDpYuXco777zjyhCFEEK4qRo/h5Wb\nm4uHhwdeXl7XbbNnzx5uu+22Mtv69u3L7t27azo8IYQQbqJGC5bZbGbOnDk8/PDDaDTXf6qMjAxC\nQkLKbAsODiYjI6MmwxNCCOFGqjUlOGvWLF577bXr7lcUhY0bN9KjRw/ntoKCAkaOHElERAQzZsz4\n85FWwGQy1chxb6T6kAPUnzyg/uQiedQtkkfVYmNjK91frYI1YcIERowYUWmbxo0bO/9fUFDA0KFD\n0Wg0/Pe//8VgMFTaNyQkpNxo6sqVK+VGXdeqKrm6zmQyuX0OUH/ygPqTi+RRt0gerlGtghUQEEBA\nQEC1Dpifn8+wYcMAWLt2baXnrn4RHx/P9u3beeqpp5zbtm3bRrdu3ar1nEIIIeo/l64SzM/PZ8iQ\nIRQUFLBy5Ury8/PJz88HSoueXq8HYNCgQXTt2pVp06YBMHbsWAYMGMC//vUvBgwYwMaNG9m5cydf\nffWVK8MTQgjhxlxasJKTk9m3bx8AnTt3BkBV1XLnuFJTU4mKinL2i4+PZ/ny5cyePZu5c+fSrFkz\n3uKLgo4AAAzESURBVHvvPTp27OjK8IQQQrgxlxasnj17kpWVVWW7lJSUctsGDRrEoEGDXBmOEEKI\nekTuJSiEEMItSMESQgjhFqRgCSGEcAtSsIQQQrgFKVhCCCHcghQsIYQQbkEKlhBCCLcgBUsIIYRb\n+P/t3X9M1PUfB/Dn8dN5SPKjU/lxFj8igkMzQMuwwJHAGkXQwJY2N/Cs3KwoQyunkg6oXFCbpIZm\nyyhEHMgwXSsqQRCKMcqJVFIhDAgO7s6WJZ/vH45PHlx64nmfz6fv87F9Nrx7fz6+n/fxxQs/nw+f\nDxsWEREpAhsWEREpAhsWEREpAhsWEREpAhsWEREpAhsWEREpAhsWEREpgl0blsFgwPr16xEbG4s5\nc+YgMjISubm5GB4evup6Bw4cgJeXF7y9veHl5SV+ffHiRXtOj4iIFMyuD3Ds7e1FX18f8vPzERYW\nhvPnzyM3NxfZ2dmorKy86rpqtRptbW0QBEF8zc3NzZ7TIyIiBbNrwwoPD8f+/fvFP992223YunUr\nsrKyYDKZ4OHh8a/rqlQq+Pr62nM6RET0H3LTz2GNjo7C3d0d06dPv+q4P/74AzqdDhEREcjMzER7\ne/vNnhoRESnITW1YBoMB27dvx1NPPQUnp3//q0JDQ/Huu+/i448/xvvvv49p06YhKSkJP//8882c\nHhERKYjKYDAI1xr0+uuv46233vr3jahUqKmpweLFi8XXzGYzMjIy4OrqioMHD17X+aixsTHExcUh\nLi4OBQUFNq9HRET/XTY1rOHhYfz+++9XHRMQEIBp06YB+KdZOTk5oaKi4pqHA6159tlnMTAwgE8/\n/fS61yUiov8emy66GL/U3BYmkwmPP/44AEy5WQFAR0cHoqKiprQuERH999j1KkGTyYS0tDSYzWZ8\n9NFHMJlMMJlMAC43PVdXVwBAamoqYmJi8NprrwEACgsLERMTg6CgIBiNRpSWluL06dMoLi625/SI\niEjB7Nqw2tra0NraCgC45557AACCIEw6x9Xd3Q2tViuuNzIygueeew79/f3w9PREVFQU6urqMH/+\nfHtOj4iIFMymc1hERERSc/i9BHfs2IGEhARotVqEhIQgKysLp0+fthjzzDPPiOfNxpeHHnrIYszF\nixfx0ksvITg4GP7+/li+fDnOnz9vMcZgMGD16tXQarXQarXQ6/UYGRmRVRZbb2d1M7PYa59cKSMj\nA15eXqiurlZkjtbWVqSlpSEgIACBgYFISkqy2CdKyNHf34/Vq1cjLCwMfn5+uP/++1FRUWExRuoc\nANDV1YUVK1Zg7ty58PPzw4MPPoizZ8+K70td6/bIoZQ6v1aOiRxd5w5vWA0NDcjJycGxY8dQU1MD\nFxcXPProozAYDBbj4uPjcfbsWXR2dqKzs3PS1YJ5eXmora1FWVkZ6urqYDQakZmZaXFrp+zsbHR0\ndKCqqgqHDh1Ce3s71qxZI6ssV97OqrGxEbt27UJDQwOys7MttnEzs9hrn4x755134OzsDJVKNek9\nJeRoaWnBY489hiVLluDzzz9HfX091q5dCxeXf46gKyGHXq9HV1cXysvL0djYiKysLOj1ejQ2Nsom\nR3d3N5KSknD77bfjyJEjaGxsxKuvvgq1Wi2OkbrW7ZFDKXVuy/4YJ0WdS35I0Gw2Q6vV4sCBA1i2\nbBmAyz89Dg0Noby83Oo6o6OjCAkJwc6dO5Geng4A6OnpgU6nQ2VlJeLj43HmzBksWrQIx44dQ0xM\nDADg5MmTSE5ORktLC4KDg2WRxZrjx48jKysL3d3d8PDwQGdnJxYuXOiwLDeS49tvv8XKlStRX1+P\nkJAQfPDBB0hNTQUAxeRYtmwZlixZgldeecXq+0rJERAQgKKiIjzxxBPiazqdDnq9HmvXrnV4jVjL\nkZOTA5VKhV27dlldR461PpUc1sixzm3NIVWdS/54EaPRiLGxMcycOdPi9ZMnTyI0NBTR0dFYt24d\nBgcHxffa2trw999/Iz4+XnzN398fYWFhaGpqAgCcOnUKM2bMED8wAFi0aBHUarU4Rg5ZrJl4O6vm\n5maHZplqDqPRiJycHJSUlMDHx2fSdpWQY3BwEM3NzdBoNEhOTkZoaCiSk5NRX1+vqBwAcO+99+Lw\n4cMYHh6GIAiora3F0NCQWDeOrpGJOQRBwNGjR3HnnXciIyMDISEhSEhIQFVVlbiOHGt9KjmskVud\n25pDyjqXvGHl5eVh3rx5iI2NFV9LTExEaWkpqqursW3bNrS2tiI1NRV//fUXgMvH5p2dneHt7W2x\nrVtvvRX9/f3iGGsfpq+vrzhGDlkmsnY7K0dnmWqO3NxcJCYmIiEhwep2lZDj3LlzAICCggKsWLEC\nhw4dwn333Yf09HR8//33iskBAGVlZQCAoKAgaDQarFmzBnv27EFERIQscgwMDMBkMmHHjh1YunQp\nDh8+jPT0dOTk5OD48ePiHOVW61PJMZEc69zWHFLWuV0va79eGzduRHNzM44ePWpxHDQtLU38Ojw8\nHPPmzYNOp8Nnn32Ghx9+WIqpXpM9spjNZixfvhz+/v7YsmWLw+Z+panmKC8vR0dHB7788ksJZj3Z\nVHOMjY0BAFatWiUeStPpdPj666+xd+9evPnmm4rIAQD5+fkYGhpCdXU1vL29UVtbC71ej7q6OrFp\nSZlj/LNOSUnB008/DQCIjIxEW1sbdu/ejcTERIfO0Rb2yCHXOrclh9R1Ltn/sDZs2ICqqirU1NRY\n/E6WNbNnz4afnx9++uknAIBGo8GlS5cwNDRkMW5gYAAajUYcY+12UoODg+IYe7mRLOOuvJ1VeXm5\nxb0XHZXlRnJ89dVXOHPmDPz8/ODr6ys+KmbVqlVITk5WTI5Zs2YBAMLCwizGhYWF4ddffwWgjBzn\nzp3D7t27UVJSgri4OERERGD9+vVYsGCBeH5C6hw+Pj5wcXGZ9Fnfcccd+O2338Q5yqXWbyTHODnX\nuS05pK5zSRrWyy+/LH5gtpyAGxwcRG9vr/jNZP78+XBxccEXX3whjunp6RFPvgJAbGwsTCYTTp06\nJY5pamrChQsXsHDhQtlkAS7fISQjIwOA9dtZOSLLVHPMnj0bALBp0yacOHEC33zzjbgAwLZt21Ba\nWir7HOP7Y+7cuZgzZ86ky3i7urrE4lZCjgsXLkClUk16SoKzs7P4k7TUOVxdXbFgwQKrn3VgYCAA\n+dT6jeYA5F/ntuSQus6d8/LyNt/QFq7Tiy++iE8++QT79u2Dv78/zGYzzGYzgMtPGDabzcjPz8eM\nGTNw6dIltLe3Y926dRgbG8Mbb7wBNzc3uLu7o6+vTzwePzIyghdeeAEzZ87E5s2boVKp4OPjg5aW\nFlRUVCAqKgo9PT14/vnnER0djZycHNlkGb+dldFoFM85jG/Hzc0Nzs7ONz3LjeQoKiqCm5sbPDw8\nxJ+4xpfCwkKsXLlS/Ecq5xzj+wMAnJycUFxcjKCgILi7u6OsrAwVFRV4++23odFoFJHDy8sLBw8e\nRENDA8LDw/Hnn3/iww8/xL59+7Bx40YEBwdLngMAvL29UVhYCI1Gg1tuuQXV1dUoKSnB9u3bxc9f\n6lq3Rw4l1LktOSSvc4PBIDhyUalUgpOT06Rlw4YNgsFgEPr6+oSlS5cKGo1GcHd3F7RarfDkk08K\nP/zwg8V2BgYGBL1eL/j4+AhqtVpISUmZNKa7u1vIzMwUPD09BU9PTyErK0v45ZdfZJXlyJEjk9Yf\n325tba1Dsthrn0xcnJychP379ztsn9gzx9atW4XAwEDBw8NDiI6OFqqrqxWX47vvvhMeeeQRYdas\nWYKHh4eg0+mE9957TzY5xpedO3cKISEhwvTp04XIyEhh7969sqp1e+RQQp3buj8mLo6sc8l/D4uI\niMgWkl/WTkREZAs2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCKZ\nam5uRkFBAUZHR6WeCpEssGERyVRTUxOKioowMjIi9VSIZIENi4iIFIENi0iGCgoKsGnTJgBAVFQU\nvLy84O3tjRMnTkg8MyLpSPrEYSKyLjU1FT/++CMqKytRUFAgPiJ+4sP1iP6fsGERydBdd92FqKgo\nVFZWIiUlxeJBgET/r3hIkIiIFIENi4iIFIENi4iIFIENi0imVCqV1FMgkhU2LCKZUqvVAACDwSDx\nTIjkgVcJEsnU3XffDUEQsGXLFmRkZMDNzQ0PPPAAfHx8pJ4akSRUBoNBkHoSRGRdcXEx9uzZg97e\nXoyNjaGmpgaLFy+WelpEkmDDIiIiReA5LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIi\nUgQ2LCIiUgQ2LCIiUgQ2LCIiUgQ2LCIiUoT/ARHbtrCijWNeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b51ca50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# test the filter on a sample of the dataset\n",
    "filter_test_data = data[data['target'] == 13]['y_back']\n",
    "filter_test_x = xrange(len(filter_test_data))\n",
    "filter_test_y = butter_lowpass_filter(filter_test_data, cutoff, fs, order)\n",
    "plt.plot(filter_test_x, filter_test_data, linewidth=1, label='data')\n",
    "plt.plot(filter_test_x, filter_test_y, linewidth=2, label='filtered data')\n",
    "plt.xlabel('t')\n",
    "plt.legend(loc='upper left')\n",
    "plt.xlim(0, len(filter_test_data))\n",
    "#plt.ylim(1900, 2300)\n",
    "plt.xlim(2500, 2650)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The filter should describe the signal of the raw data well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply the filters\n",
    "for c in ['x_back' ,'y_back' ,'z_back', 'x_thigh' ,'y_thigh' ,'z_thigh', 'm']:\n",
    "#for c in ['x_back' ,'y_back' ,'z_back', 'm']:\n",
    "    data[c+'l'] = butter_lowpass_filter(data[c], cutoff, fs, order)\n",
    "    data[c+'h'] = butter_highpass_filter(data[c], cutoff, fs, order)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Extraction\n",
    "\n",
    "I extracted features by windowing the series, creating 250 windows, each of a quarter second of data. Windows overlap adjacent windows, sharing 50% of its data with each. \n",
    "The following features are extracted from each window, for each time-series: \n",
    " - root mean square value (RMS)\n",
    " - mean of the minmax sums\n",
    " - mean,  \n",
    " - standard deviation. \n",
    "This results in a dataset with 84 features for 6 incoming raw signals.\n",
    "\n",
    "### RMS\n",
    "\n",
    "This is calculated by taking the square root of the average of the squares of the series.\n",
    "\n",
    "### Minmax sums\n",
    "\n",
    "This is calculated by finding the differences between each min and max in the series, then averaging these values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.signal import argrelmin, argrelmax\n",
    "\n",
    "def rms(series):\n",
    "    # returns root mean square value of a series\n",
    "    return np.sqrt((series**2).mean())\n",
    "\n",
    "\n",
    "def min_max_mean(series):\n",
    "    # returns the average of the differences between local mins/maxs\n",
    "    mins = argrelmin(series)[0]    # indices of the local minima\n",
    "    maxs = argrelmax(series)[0]    # local maxima\n",
    "    min_max_sum = 0\n",
    "    # build the sums, then take the average\n",
    "    if len(mins) <= len(maxs):\n",
    "        for j, arg in enumerate(mins):\n",
    "            min_max_sum += series[maxs[j]] - series[arg]\n",
    "    else:\n",
    "        for j, arg in enumerate(maxs):\n",
    "            min_max_sum += series[arg] - series[mins[j]]\n",
    "    return min_max_sum/float(min(len(mins), len(maxs)))\n",
    "\n",
    "\n",
    "def extract_features(data, y, num_windows):\n",
    "    window_len = len(data)/(num_windows/2)\n",
    "    print 'window_len: ', window_len\n",
    "    num_windows = len(data)/window_len\n",
    "    print 'num_windows: ', num_windows\n",
    "    i = 0    # initialize index\n",
    "\n",
    "    print 'before: ', len(data)\n",
    "    data = data[:window_len*num_windows-1]\n",
    "    y = y[:window_len*num_windows]\n",
    "    print 'after: ', len(data)\n",
    "    \n",
    "    features = []\n",
    "    targets = []\n",
    "    \n",
    "    for n in range(num_windows):\n",
    "        # isolate window\n",
    "        win = data[i:i+window_len]\n",
    "        \n",
    "        # extract target\n",
    "        target = int(y[i:i+window_len].mode())\n",
    "        targets.append(target)\n",
    "        \n",
    "        for c in data.columns:\n",
    "            # extract features for each series\n",
    "            s = np.array(win[c])\n",
    "            rms_val = rms(s)\n",
    "            min_max = min_max_mean(s)\n",
    "            mean = s.mean()\n",
    "            std = s.std()\n",
    "            new_features = [rms_val, min_max, mean, std]\n",
    "            features.append(new_features)\n",
    "        # update index\n",
    "        i += window_len/2\n",
    "    features = np.array(features)\n",
    "    features.shape = num_windows, 84 #xyz --> 48; b+t xyz --> 84\n",
    "    targets = np.array(targets)\n",
    "    return features, targets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "window_len:  295\n",
      "num_windows:  1051\n",
      "before:  310185\n",
      "after:  310044\n",
      "features: 88284\n",
      "targets 1051\n"
     ]
    }
   ],
   "source": [
    "#features = data.drop(['sample', 'target'], axis=1)\n",
    "features = data.drop(['target'], axis=1)\n",
    "targets = data['target']\n",
    "\n",
    "num_windows = 2100\n",
    "X, y = extract_features(features, targets, num_windows)\n",
    "\n",
    "print 'features:', X.size #features 702 * 48\n",
    "print 'targets', y.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#create target label lists\n",
    "\n",
    "\n",
    "#column_names_num = sorted(data['target'].unique())\n",
    "#column_names_text = column_names_num.replace({'target': no_to_label_dict})\n",
    "#print column_names_num\n",
    "\n",
    "#print features.info()\n",
    "#print targets.size\n",
    "#print features.size / targets.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model building and evaluation\n",
    "\n",
    "The null classifier predicts the majority class for every data point. I used this as a starting point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split, cross_val_score\n",
    "\n",
    "# train-test split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = .2, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.848341232227\n"
     ]
    }
   ],
   "source": [
    "# majority class prediction\n",
    "from collections import Counter\n",
    "\n",
    "label_counts = Counter(y_test)\n",
    "null = label_counts.most_common()[0][1]/float(len(y_test))\n",
    "print null"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sklearn.metrics as met\n",
    "    \n",
    "# helper function to quickly build different models\n",
    "def model_build(model):\n",
    "    model.fit(X_train, y_train)\n",
    "    return model\n",
    "\n",
    "# helper function to handle evaluation\n",
    "def model_eval(model):\n",
    "    pred = model.predict(X_test)\n",
    "    print 'Accuracy:\\n-----------------------------'\n",
    "    print met.accuracy_score(y_test, pred)\n",
    "    print '\\nConfusion Matrix:\\n-----------------------------'\n",
    "    print met.confusion_matrix(y_test, pred)\n",
    "    print '\\nClassification Report:\\n-----------------------------'\n",
    "    print met.classification_report(y_test, pred)\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:\n",
      "-----------------------------\n",
      "0.9336492891\n",
      "\n",
      "Confusion Matrix:\n",
      "-----------------------------\n",
      "[[  7   0   0   0   0]\n",
      " [  4   0   0   0   0]\n",
      " [  0   0   5   0   0]\n",
      " [  0   0   0 178   1]\n",
      " [  1   0   0   8   7]]\n",
      "\n",
      "Classification Report:\n",
      "-----------------------------\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "          1       0.58      1.00      0.74         7\n",
      "          4       0.00      0.00      0.00         4\n",
      "          6       1.00      1.00      1.00         5\n",
      "         13       0.96      0.99      0.98       179\n",
      "         14       0.88      0.44      0.58        16\n",
      "\n",
      "avg / total       0.92      0.93      0.92       211\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# K-Nearest Neighbors\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "knn = model_build(KNeighborsClassifier())\n",
    "model_eval(knn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:\n",
      "-----------------------------\n",
      "0.952606635071\n",
      "\n",
      "Confusion Matrix:\n",
      "-----------------------------\n",
      "[[  6   0   0   0   1]\n",
      " [  3   1   0   0   0]\n",
      " [  0   0   5   0   0]\n",
      " [  0   0   0 176   3]\n",
      " [  1   0   0   2  13]]\n",
      "\n",
      "Classification Report:\n",
      "-----------------------------\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "          1       0.60      0.86      0.71         7\n",
      "          4       1.00      0.25      0.40         4\n",
      "          6       1.00      1.00      1.00         5\n",
      "         13       0.99      0.98      0.99       179\n",
      "         14       0.76      0.81      0.79        16\n",
      "\n",
      "avg / total       0.96      0.95      0.95       211\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Random Forest\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "rfc = model_build(RandomForestClassifier(n_estimators=20))\n",
    "model_eval(rfc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:\n",
      "-----------------------------\n",
      "0.9336492891\n",
      "\n",
      "Confusion Matrix:\n",
      "-----------------------------\n",
      "[[  7   0   0   0   0]\n",
      " [  4   0   0   0   0]\n",
      " [  0   0   5   0   0]\n",
      " [  0   0   0 178   1]\n",
      " [  1   0   0   8   7]]\n",
      "\n",
      "Classification Report:\n",
      "-----------------------------\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "          1       0.58      1.00      0.74         7\n",
      "          4       0.00      0.00      0.00         4\n",
      "          6       1.00      1.00      1.00         5\n",
      "         13       0.96      0.99      0.98       179\n",
      "         14       0.88      0.44      0.58        16\n",
      "\n",
      "avg / total       0.92      0.93      0.92       211\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Blending the models by voting\n",
    "from sklearn.ensemble import VotingClassifier\n",
    "\n",
    "vote = model_build(VotingClassifier(estimators=[('rf', rfc), ('knn', knn)]))\n",
    "model_eval(vote)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:\n",
      "-----------------------------\n",
      "0.947867298578\n",
      "\n",
      "Confusion Matrix:\n",
      "-----------------------------\n",
      "[[  6   0   0   1   0]\n",
      " [  4   0   0   0   0]\n",
      " [  0   0   5   0   0]\n",
      " [  0   0   0 178   1]\n",
      " [  0   0   0   5  11]]\n",
      "\n",
      "Classification Report:\n",
      "-----------------------------\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "          1       0.60      0.86      0.71         7\n",
      "          4       0.00      0.00      0.00         4\n",
      "          6       1.00      1.00      1.00         5\n",
      "         13       0.97      0.99      0.98       179\n",
      "         14       0.92      0.69      0.79        16\n",
      "\n",
      "avg / total       0.93      0.95      0.94       211\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Random Forest with weighted classes\n",
    "\n",
    "rfc_bal = model_build(RandomForestClassifier(n_estimators=50, class_weight='balanced'))\n",
    "model_eval(rfc_bal)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "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"
  },
  "nikola": {
   "category": "",
   "date": "2016-04-26 21:05:30 UTC+08:00",
   "description": "",
   "link": "",
   "slug": "predicting-activities-from-accelerometer-data",
   "tags": "",
   "title": "Predicting Activities from Accelerometer Data",
   "type": "text"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}