[Phase 1] Cleaning Data and Looking for Trends.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datascience import Table\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "import warnings\n",
    "warnings.simplefilter('ignore', FutureWarning)\n",
    "from matplotlib import patches\n",
    "from ipywidgets import interact, interactive, fixed #pip installed ipywdigets in Terminal\n",
    "import ipywidgets as widgets\n",
    "import plotly.plotly as py\n",
    "import plotly\n",
    "plotly.tools.set_credentials_file(username='KevinMiao', api_key='FZpVgpkGX9s8HNG6MbHJ')\n",
    "from __future__ import print_function\n",
    "import time\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.datasets import fetch_mldata\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.manifold import TSNE\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's clean it up 🧽"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We pulled the Dataset downloaded from Kaggle (https://www.kaggle.com/jboysen/mri-and-alzheimers). The Datasets have been released as part of OASIS and open-source project aiming to clarify and encourage new discoveries in Alzheimers. The data has been collected by HHMI (Hughes Howard's Medical Institute, University of Washington and Harvard University)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross-Sectional Data\n",
    "\n",
    "\n",
    "**Cross-Section**, in other words, the plane that consists of the Sagital and Frontal axes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1** : We pulled the data. The columns `hand` and `delay` have been removed since the former column only contains right handed people and the latter column does not contribute to the classification or analysis of Alzheimers. Delay is only a technical note about when the data has been processed after the scan."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>OAS1_0001_MR1</td>\n",
       "      <td>F</td>\n",
       "      <td>74</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1344</td>\n",
       "      <td>0.743</td>\n",
       "      <td>1.306</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>OAS1_0002_MR1</td>\n",
       "      <td>F</td>\n",
       "      <td>55</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1147</td>\n",
       "      <td>0.810</td>\n",
       "      <td>1.531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>OAS1_0003_MR1</td>\n",
       "      <td>F</td>\n",
       "      <td>73</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1454</td>\n",
       "      <td>0.708</td>\n",
       "      <td>1.207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OAS1_0004_MR1</td>\n",
       "      <td>M</td>\n",
       "      <td>28</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1588</td>\n",
       "      <td>0.803</td>\n",
       "      <td>1.105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OAS1_0005_MR1</td>\n",
       "      <td>M</td>\n",
       "      <td>18</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1737</td>\n",
       "      <td>0.848</td>\n",
       "      <td>1.010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "              ID M/F  Age  Educ  SES  MMSE  CDR  eTIV   nWBV    ASF\n",
       "0  OAS1_0001_MR1   F   74   2.0  3.0  29.0  0.0  1344  0.743  1.306\n",
       "1  OAS1_0002_MR1   F   55   4.0  1.0  29.0  0.0  1147  0.810  1.531\n",
       "2  OAS1_0003_MR1   F   73   4.0  3.0  27.0  0.5  1454  0.708  1.207\n",
       "3  OAS1_0004_MR1   M   28   NaN  NaN   NaN  NaN  1588  0.803  1.105\n",
       "4  OAS1_0005_MR1   M   18   NaN  NaN   NaN  NaN  1737  0.848  1.010"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#pull data\n",
    "cs = pd.read_csv('oasis_cross-sectional.csv')\n",
    "cs = cs.drop(['Hand', 'Delay'], axis=1)\n",
    "cs.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cleaning\n",
    "\n",
    "The Data have been cleaned, in other words, the redundant columns have been removed. Now we are replacing the `NaN` values by the median. This is very common practice and will help us to buffer for extreme variation, if applicable. The columns that have been cleaned are **`Educ`, `SES`, `MMSE` and `CDR`.** For more information, please read `Phase 0`. Additionally, we have made sure that all values are numerical now; this includes **`M/F`**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>OAS1_0001_MR1</td>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
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       "    <tr>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>OAS1_0003_MR1</td>\n",
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       "      <td>1.207</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OAS1_0004_MR1</td>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1588</td>\n",
       "      <td>0.803</td>\n",
       "      <td>1.105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OAS1_0005_MR1</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1737</td>\n",
       "      <td>0.848</td>\n",
       "      <td>1.010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "              ID  M/F  Age  Educ  SES  MMSE  CDR  eTIV   nWBV    ASF\n",
       "0  OAS1_0001_MR1    1   74   2.0  3.0  29.0  0.0  1344  0.743  1.306\n",
       "1  OAS1_0002_MR1    1   55   4.0  1.0  29.0  0.0  1147  0.810  1.531\n",
       "2  OAS1_0003_MR1    1   73   4.0  3.0  27.0  0.5  1454  0.708  1.207\n",
       "3  OAS1_0004_MR1    0   28   3.0  2.0  29.0  0.0  1588  0.803  1.105\n",
       "4  OAS1_0005_MR1    0   18   3.0  2.0  29.0  0.0  1737  0.848  1.010"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#fill NA values w median values\n",
    "cs[\"Educ\"] = cs[\"Educ\"].fillna(cs[\"Educ\"].median())\n",
    "cs[\"SES\"] = cs[\"SES\"].fillna(cs[\"SES\"].median())\n",
    "cs[\"MMSE\"] = cs[\"MMSE\"].fillna(cs[\"MMSE\"].median())\n",
    "cs[\"CDR\"] = cs[\"CDR\"].fillna(cs[\"CDR\"].median())\n",
    "\n",
    "#change categorical variable age to numercail\n",
    "# M --> 0, F --> 1\n",
    "cs[\"M/F\"] = cs[\"M/F\"].map(dict({\"M\": 0, \"F\": 1}))\n",
    "cs.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `0` = Male\n",
    "* `1` = Female"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
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       "      <th>0</th>\n",
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       "      <td>0.743</td>\n",
       "      <td>1.306</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>55</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>0.810</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>73</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1454</td>\n",
       "      <td>0.708</td>\n",
       "      <td>1.207</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1588</td>\n",
       "      <td>0.803</td>\n",
       "      <td>1.105</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1737</td>\n",
       "      <td>0.848</td>\n",
       "      <td>1.010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   M/F  Age  Educ  SES  MMSE  CDR  eTIV   nWBV    ASF\n",
       "0    1   74   2.0  3.0  29.0  0.0  1344  0.743  1.306\n",
       "1    1   55   4.0  1.0  29.0  0.0  1147  0.810  1.531\n",
       "2    1   73   4.0  3.0  27.0  0.5  1454  0.708  1.207\n",
       "3    0   28   3.0  2.0  29.0  0.0  1588  0.803  1.105\n",
       "4    0   18   3.0  2.0  29.0  0.0  1737  0.848  1.010"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CrossSectionCleaned = cs.drop(columns = ['ID'])\n",
    "CrossSectionCleaned.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M/F</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>48.148810</td>\n",
       "      <td>3.142857</td>\n",
       "      <td>2.172619</td>\n",
       "      <td>28.041667</td>\n",
       "      <td>0.157738</td>\n",
       "      <td>1592.410714</td>\n",
       "      <td>0.791452</td>\n",
       "      <td>1.109821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>53.369403</td>\n",
       "      <td>3.067164</td>\n",
       "      <td>2.287313</td>\n",
       "      <td>27.902985</td>\n",
       "      <td>0.151119</td>\n",
       "      <td>1412.656716</td>\n",
       "      <td>0.791806</td>\n",
       "      <td>1.254731</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "           Age      Educ       SES       MMSE       CDR         eTIV  \\\n",
       "M/F                                                                    \n",
       "0    48.148810  3.142857  2.172619  28.041667  0.157738  1592.410714   \n",
       "1    53.369403  3.067164  2.287313  27.902985  0.151119  1412.656716   \n",
       "\n",
       "         nWBV       ASF  \n",
       "M/F                      \n",
       "0    0.791452  1.109821  \n",
       "1    0.791806  1.254731  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csgroup1 = cs.groupby(\"M/F\").agg(np.mean)\n",
    "csgroup1.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bias?\n",
    "\n",
    "There does not seem to be a bias between men and female (except for `age`). All variables seem to lie close to each other. The dataset, therefore, is representative and can be used to analyze the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is data from 436 patients in this set.\n"
     ]
    }
   ],
   "source": [
    "print('There is data from ' + str(cs.shape[0]) + ' patients in this set.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Longitudinal Data\n",
    "\n",
    "\n",
    "**Longitudinal**, in other words, data collected in the saggital plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Subject ID</th>\n",
       "      <th>Group</th>\n",
       "      <th>Visit</th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>EDUC</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "      <th>Educ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>OAS2_0001</td>\n",
       "      <td>Nondemented</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>87</td>\n",
       "      <td>14</td>\n",
       "      <td>2.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0.696</td>\n",
       "      <td>0.883</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>OAS2_0001</td>\n",
       "      <td>Nondemented</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>88</td>\n",
       "      <td>14</td>\n",
       "      <td>2.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2004</td>\n",
       "      <td>0.681</td>\n",
       "      <td>0.876</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>OAS2_0002</td>\n",
       "      <td>Demented</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>75</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1678</td>\n",
       "      <td>0.736</td>\n",
       "      <td>1.046</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OAS2_0002</td>\n",
       "      <td>Demented</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>76</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1738</td>\n",
       "      <td>0.713</td>\n",
       "      <td>1.010</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OAS2_0002</td>\n",
       "      <td>Demented</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1698</td>\n",
       "      <td>0.701</td>\n",
       "      <td>1.034</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Subject ID        Group  Visit  M/F  Age  EDUC  SES  MMSE  CDR  eTIV   nWBV  \\\n",
       "0  OAS2_0001  Nondemented      1    0   87    14  2.0  27.0  0.0  1987  0.696   \n",
       "1  OAS2_0001  Nondemented      2    0   88    14  2.0  30.0  0.0  2004  0.681   \n",
       "2  OAS2_0002     Demented      1    0   75    12  2.0  23.0  0.5  1678  0.736   \n",
       "3  OAS2_0002     Demented      2    0   76    12  2.0  28.0  0.5  1738  0.713   \n",
       "4  OAS2_0002     Demented      3    0   80    12  2.0  22.0  0.5  1698  0.701   \n",
       "\n",
       "     ASF  Educ  \n",
       "0  0.883    14  \n",
       "1  0.876    14  \n",
       "2  1.046    12  \n",
       "3  1.010    12  \n",
       "4  1.034    12  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#pulling the data from csv... drop hand as redundant\n",
    "lg = pd.read_csv('oasis_longitudinal.csv')\n",
    "lg = lg.drop('Hand', axis=1)\n",
    "lg = lg.drop('MR Delay', axis=1)\n",
    "lg = lg.drop('MRI ID', axis=1)\n",
    "\n",
    "#going to fill in NA values with the median.. #of NA values too significant to get rid of \n",
    "lg[\"Educ\"] = lg[\"EDUC\"].fillna(lg[\"EDUC\"].median())\n",
    "lg[\"SES\"] = lg[\"SES\"].fillna(lg[\"SES\"].median())\n",
    "lg[\"MMSE\"] = lg[\"MMSE\"].fillna(lg[\"MMSE\"].median())\n",
    "lg[\"CDR\"] = lg[\"CDR\"].fillna(lg[\"CDR\"].median())\n",
    "#change gender M F values to integer values\n",
    "# M --> 0, F --> 1\n",
    "lg[\"M/F\"] = lg[\"M/F\"].map(dict({\"M\": 0, \"F\": 1}))\n",
    "\n",
    "lg.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same columns have been dropped and cleaned similar to what we did to the cross-sectional dataset. It is worht noting that this table is larger than the one before, since we have extra columns. In addition to this, this DataFrame has a time component to it (Visit) for the same people so we can track the development of the disease.\n",
    "\n",
    "`Group` \n",
    "- `Demented` : Alzheimers\n",
    "- `Nondemented` : No-Alzheimers\n",
    "- `Converted` : Developed Alzheimers during the study"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Visit</th>\n",
       "      <th>Age</th>\n",
       "      <th>EDUC</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "      <th>Educ</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M/F</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.956250</td>\n",
       "      <td>76.681250</td>\n",
       "      <td>14.893750</td>\n",
       "      <td>2.375000</td>\n",
       "      <td>26.637500</td>\n",
       "      <td>0.378125</td>\n",
       "      <td>1604.331250</td>\n",
       "      <td>0.718888</td>\n",
       "      <td>1.106094</td>\n",
       "      <td>14.893750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.826291</td>\n",
       "      <td>77.262911</td>\n",
       "      <td>14.375587</td>\n",
       "      <td>2.483568</td>\n",
       "      <td>27.887324</td>\n",
       "      <td>0.225352</td>\n",
       "      <td>1400.840376</td>\n",
       "      <td>0.737592</td>\n",
       "      <td>1.262592</td>\n",
       "      <td>14.375587</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Visit        Age       EDUC       SES       MMSE       CDR  \\\n",
       "M/F                                                                  \n",
       "0    1.956250  76.681250  14.893750  2.375000  26.637500  0.378125   \n",
       "1    1.826291  77.262911  14.375587  2.483568  27.887324  0.225352   \n",
       "\n",
       "            eTIV      nWBV       ASF       Educ  \n",
       "M/F                                              \n",
       "0    1604.331250  0.718888  1.106094  14.893750  \n",
       "1    1400.840376  0.737592  1.262592  14.375587  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lggroup2 = lg.groupby(\"M/F\").agg(np.mean)\n",
    "lggroup2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, no selection bias since all values lie pretty close to each other irrespective of whether they are sick or not or any other variables. :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Visit</th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>EDUC</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "      <th>Educ</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Group</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Converted</th>\n",
       "      <td>2.027027</td>\n",
       "      <td>0.648649</td>\n",
       "      <td>79.756757</td>\n",
       "      <td>15.459459</td>\n",
       "      <td>1.729730</td>\n",
       "      <td>28.675676</td>\n",
       "      <td>0.256757</td>\n",
       "      <td>1459.270270</td>\n",
       "      <td>0.723730</td>\n",
       "      <td>1.212405</td>\n",
       "      <td>15.459459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Demented</th>\n",
       "      <td>1.732877</td>\n",
       "      <td>0.410959</td>\n",
       "      <td>76.260274</td>\n",
       "      <td>13.671233</td>\n",
       "      <td>2.671233</td>\n",
       "      <td>24.575342</td>\n",
       "      <td>0.671233</td>\n",
       "      <td>1485.849315</td>\n",
       "      <td>0.716301</td>\n",
       "      <td>1.196890</td>\n",
       "      <td>13.671233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nondemented</th>\n",
       "      <td>1.968421</td>\n",
       "      <td>0.678947</td>\n",
       "      <td>77.057895</td>\n",
       "      <td>15.142105</td>\n",
       "      <td>2.394737</td>\n",
       "      <td>29.226316</td>\n",
       "      <td>0.005263</td>\n",
       "      <td>1495.500000</td>\n",
       "      <td>0.740900</td>\n",
       "      <td>1.191063</td>\n",
       "      <td>15.142105</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Visit       M/F        Age       EDUC       SES       MMSE  \\\n",
       "Group                                                                        \n",
       "Converted    2.027027  0.648649  79.756757  15.459459  1.729730  28.675676   \n",
       "Demented     1.732877  0.410959  76.260274  13.671233  2.671233  24.575342   \n",
       "Nondemented  1.968421  0.678947  77.057895  15.142105  2.394737  29.226316   \n",
       "\n",
       "                  CDR         eTIV      nWBV       ASF       Educ  \n",
       "Group                                                              \n",
       "Converted    0.256757  1459.270270  0.723730  1.212405  15.459459  \n",
       "Demented     0.671233  1485.849315  0.716301  1.196890  13.671233  \n",
       "Nondemented  0.005263  1495.500000  0.740900  1.191063  15.142105  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lggroup1 = lg.groupby(\"Group\").agg(np.mean)\n",
    "lggroup1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is data from 373 patients in this set.\n"
     ]
    }
   ],
   "source": [
    "print('There is data from ' + str(lg.shape[0]) + ' patients in this set.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standard_units(data):\n",
    "    avg = np.average(data)\n",
    "    stddev = np.std(data)\n",
    "    return (data - avg) / stdev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def correlation(x, y):\n",
    "    stdx = standard_units(x)\n",
    "    stdy = standard_units(y)\n",
    "    return np.mean(stdx * stdy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Age and CDR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a0bc6dfd0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lg.plot.scatter(x='CDR', y = 'MMSE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>OAS1_0001_MR1</td>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1344</td>\n",
       "      <td>0.743</td>\n",
       "      <td>1.306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>OAS1_0002_MR1</td>\n",
       "      <td>1</td>\n",
       "      <td>55</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1147</td>\n",
       "      <td>0.810</td>\n",
       "      <td>1.531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>OAS1_0003_MR1</td>\n",
       "      <td>1</td>\n",
       "      <td>73</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1454</td>\n",
       "      <td>0.708</td>\n",
       "      <td>1.207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OAS1_0004_MR1</td>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1588</td>\n",
       "      <td>0.803</td>\n",
       "      <td>1.105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OAS1_0005_MR1</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1737</td>\n",
       "      <td>0.848</td>\n",
       "      <td>1.010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              ID  M/F  Age  Educ  SES  MMSE  CDR  eTIV   nWBV    ASF\n",
       "0  OAS1_0001_MR1    1   74   2.0  3.0  29.0  0.0  1344  0.743  1.306\n",
       "1  OAS1_0002_MR1    1   55   4.0  1.0  29.0  0.0  1147  0.810  1.531\n",
       "2  OAS1_0003_MR1    1   73   4.0  3.0  27.0  0.5  1454  0.708  1.207\n",
       "3  OAS1_0004_MR1    0   28   3.0  2.0  29.0  0.0  1588  0.803  1.105\n",
       "4  OAS1_0005_MR1    0   18   3.0  2.0  29.0  0.0  1737  0.848  1.010"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cs.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA : Cross-sectional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.00000</td>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.000000</td>\n",
       "      <td>436.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.614679</td>\n",
       "      <td>51.357798</td>\n",
       "      <td>3.096330</td>\n",
       "      <td>2.243119</td>\n",
       "      <td>27.956422</td>\n",
       "      <td>0.15367</td>\n",
       "      <td>1481.919725</td>\n",
       "      <td>0.791670</td>\n",
       "      <td>1.198894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.487230</td>\n",
       "      <td>25.269862</td>\n",
       "      <td>0.966037</td>\n",
       "      <td>0.825219</td>\n",
       "      <td>2.878446</td>\n",
       "      <td>0.31515</td>\n",
       "      <td>158.740866</td>\n",
       "      <td>0.059937</td>\n",
       "      <td>0.128682</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1123.000000</td>\n",
       "      <td>0.644000</td>\n",
       "      <td>0.881000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1367.750000</td>\n",
       "      <td>0.742750</td>\n",
       "      <td>1.111750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>29.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1475.500000</td>\n",
       "      <td>0.809000</td>\n",
       "      <td>1.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>74.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>29.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1579.250000</td>\n",
       "      <td>0.842000</td>\n",
       "      <td>1.284250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>96.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>1992.000000</td>\n",
       "      <td>0.893000</td>\n",
       "      <td>1.563000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              M/F         Age        Educ         SES        MMSE        CDR  \\\n",
       "count  436.000000  436.000000  436.000000  436.000000  436.000000  436.00000   \n",
       "mean     0.614679   51.357798    3.096330    2.243119   27.956422    0.15367   \n",
       "std      0.487230   25.269862    0.966037    0.825219    2.878446    0.31515   \n",
       "min      0.000000   18.000000    1.000000    1.000000   14.000000    0.00000   \n",
       "25%      0.000000   23.000000    3.000000    2.000000   28.000000    0.00000   \n",
       "50%      1.000000   54.000000    3.000000    2.000000   29.000000    0.00000   \n",
       "75%      1.000000   74.000000    3.000000    2.000000   29.000000    0.00000   \n",
       "max      1.000000   96.000000    5.000000    5.000000   30.000000    2.00000   \n",
       "\n",
       "              eTIV        nWBV         ASF  \n",
       "count   436.000000  436.000000  436.000000  \n",
       "mean   1481.919725    0.791670    1.198894  \n",
       "std     158.740866    0.059937    0.128682  \n",
       "min    1123.000000    0.644000    0.881000  \n",
       "25%    1367.750000    0.742750    1.111750  \n",
       "50%    1475.500000    0.809000    1.190000  \n",
       "75%    1579.250000    0.842000    1.284250  \n",
       "max    1992.000000    0.893000    1.563000  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cs.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>Educ</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OAS1_0001_MR1</th>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1344</td>\n",
       "      <td>0.743</td>\n",
       "      <td>1.306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS1_0002_MR1</th>\n",
       "      <td>1</td>\n",
       "      <td>55</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1147</td>\n",
       "      <td>0.810</td>\n",
       "      <td>1.531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS1_0003_MR1</th>\n",
       "      <td>1</td>\n",
       "      <td>73</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1454</td>\n",
       "      <td>0.708</td>\n",
       "      <td>1.207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS1_0004_MR1</th>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1588</td>\n",
       "      <td>0.803</td>\n",
       "      <td>1.105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS1_0005_MR1</th>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1737</td>\n",
       "      <td>0.848</td>\n",
       "      <td>1.010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               M/F  Age  Educ  SES  MMSE  CDR  eTIV   nWBV    ASF\n",
       "ID                                                               \n",
       "OAS1_0001_MR1    1   74   2.0  3.0  29.0  0.0  1344  0.743  1.306\n",
       "OAS1_0002_MR1    1   55   4.0  1.0  29.0  0.0  1147  0.810  1.531\n",
       "OAS1_0003_MR1    1   73   4.0  3.0  27.0  0.5  1454  0.708  1.207\n",
       "OAS1_0004_MR1    0   28   3.0  2.0  29.0  0.0  1588  0.803  1.105\n",
       "OAS1_0005_MR1    0   18   3.0  2.0  29.0  0.0  1737  0.848  1.010"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = list(cs)\n",
    "features.pop(6)\n",
    "daf = cs.set_index('ID')\n",
    "daf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.79174849,  0.89704535, -1.13617746, ..., -0.86983375,\n",
       "        -0.81294769,  0.83328123],\n",
       "       [ 0.79174849,  0.14429781,  0.93651448, ..., -2.11227567,\n",
       "         0.30617709,  2.58378209],\n",
       "       [ 0.79174849,  0.85742706,  0.93651448, ..., -0.17608445,\n",
       "        -1.39756511,  0.06306086],\n",
       "       ...,\n",
       "       [-1.26302735, -1.1631058 , -0.09983149, ...,  0.61857384,\n",
       "         1.07453142, -0.68381951],\n",
       "       [ 0.79174849, -1.24234238, -0.09983149, ..., -1.38699231,\n",
       "         1.1580482 ,  1.48680156],\n",
       "       [ 0.79174849, -1.00463264, -0.09983149, ..., -1.25454927,\n",
       "         0.70705761,  1.31564147]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "x = daf.iloc[:, [0,1,2,3,4,6,7,8]].values\n",
    "y = daf.iloc[:, [5]]\n",
    "X_std = StandardScaler().fit_transform(x) #standardized data!\n",
    "X_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance matrix \n",
      "[[ 1.00229885  0.10089006 -0.03826424  0.06787411 -0.02352838 -0.55299501\n",
      "   0.00288095  0.54993415]\n",
      " [ 0.10089006  1.00229885  0.01066311  0.29867132 -0.38602492 -0.14130847\n",
      "  -0.87610949  0.13783036]\n",
      " [-0.03826424  0.01066311  1.00229885 -0.64803974  0.2484457   0.09475561\n",
      "   0.04293278 -0.07947059]\n",
      " [ 0.06787411  0.29867132 -0.64803974  1.00229885 -0.27294478 -0.16893676\n",
      "  -0.26744255  0.15492772]\n",
      " [-0.02352838 -0.38602492  0.2484457  -0.27294478  1.00229885  0.04743885\n",
      "   0.51839719 -0.04001703]\n",
      " [-0.55299501 -0.14130847  0.09475561 -0.16893676  0.04743885  1.00229885\n",
      "  -0.00970712 -0.97790905]\n",
      " [ 0.00288095 -0.87610949  0.04293278 -0.26744255  0.51839719 -0.00970712\n",
      "   1.00229885  0.01380295]\n",
      " [ 0.54993415  0.13783036 -0.07947059  0.15492772 -0.04001703 -0.97790905\n",
      "   0.01380295  1.00229885]]\n"
     ]
    }
   ],
   "source": [
    "mean_vec = np.mean(X_std, axis=0)\n",
    "cov_mat = (X_std - mean_vec).T.dot((X_std - mean_vec)) / (X_std.shape[0]-1)\n",
    "print('Covariance matrix \\n%s' %cov_mat)\n",
    "#CovarianceMatrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigendecomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvectors \n",
      "[[-0.3169669  -0.35472917  0.11123191  0.86147784  0.12904103  0.04617502\n",
      "  -0.01966582  0.00348349]\n",
      " [-0.39027651  0.35206113  0.3581489   0.02832108 -0.34746968 -0.10486529\n",
      "   0.68038896  0.00185377]\n",
      " [ 0.23169947 -0.10627577  0.69484365 -0.08155452 -0.02709473  0.66129475\n",
      "  -0.08636067 -0.00767725]\n",
      " [-0.34916311  0.18359042 -0.51611187  0.02701683 -0.34336285  0.67082569\n",
      "  -0.09670339  0.00464787]\n",
      " [ 0.30586641 -0.33424857  0.00500982  0.10991305 -0.85169394 -0.20386276\n",
      "  -0.12517899 -0.002301  ]\n",
      " [ 0.42660873  0.43754387 -0.06373909  0.34028922  0.00584084  0.04420329\n",
      "   0.04555416  0.70896946]\n",
      " [ 0.34439513 -0.45509079 -0.31713203 -0.03646379  0.13608589  0.23282553\n",
      "   0.70686102  0.00156252]\n",
      " [-0.42125934 -0.4415267   0.07427763 -0.3470815  -0.00670886 -0.04279718\n",
      "  -0.04976895  0.70516555]]\n",
      "\n",
      "Eigenvalues \n",
      "[2.72399823 2.20369394 1.44802584 0.56824281 0.66276907 0.29055859\n",
      " 0.09686119 0.02424112]\n"
     ]
    }
   ],
   "source": [
    "cov_mat = np.cov(X_std.T)\n",
    "\n",
    "eig_vals, eig_vecs = np.linalg.eig(cov_mat)\n",
    "\n",
    "print('Eigenvectors \\n%s' %eig_vecs)\n",
    "print('\\nEigenvalues \\n%s' %eig_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.3169669 ,  0.35472917,  0.11123191, -0.12904103, -0.86147784,\n",
       "        -0.04617502,  0.01966582,  0.00348349],\n",
       "       [-0.39027651, -0.35206113,  0.3581489 ,  0.34746968, -0.02832108,\n",
       "         0.10486529, -0.68038896,  0.00185377],\n",
       "       [ 0.23169947,  0.10627577,  0.69484365,  0.02709473,  0.08155452,\n",
       "        -0.66129475,  0.08636067, -0.00767725],\n",
       "       [-0.34916311, -0.18359042, -0.51611187,  0.34336285, -0.02701683,\n",
       "        -0.67082569,  0.09670339,  0.00464787],\n",
       "       [ 0.30586641,  0.33424857,  0.00500982,  0.85169394, -0.10991305,\n",
       "         0.20386276,  0.12517899, -0.002301  ],\n",
       "       [ 0.42660873, -0.43754387, -0.06373909, -0.00584084, -0.34028922,\n",
       "        -0.04420329, -0.04555416,  0.70896946],\n",
       "       [ 0.34439513,  0.45509079, -0.31713203, -0.13608589,  0.03646379,\n",
       "        -0.23282553, -0.70686102,  0.00156252],\n",
       "       [-0.42125934,  0.4415267 ,  0.07427763,  0.00670886,  0.3470815 ,\n",
       "         0.04279718,  0.04976895,  0.70516555]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u,s,v = np.linalg.svd(X_std.T)\n",
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Everything ok!\n"
     ]
    }
   ],
   "source": [
    "for ev in eig_vecs:\n",
    "    np.testing.assert_array_almost_equal(1.0, np.linalg.norm(ev))\n",
    "print('Everything ok!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in descending order:\n",
      "2.7239982318192277\n",
      "2.2036939419586097\n",
      "1.4480258373977113\n",
      "0.6627690731084468\n",
      "0.5682428144217616\n",
      "0.29055859201364154\n",
      "0.09686119362586446\n",
      "0.02424112025243185\n"
     ]
    }
   ],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eig_pairs.sort()\n",
    "eig_pairs.reverse()\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "print('Eigenvalues in descending order:')\n",
    "for i in eig_pairs:\n",
    "    print(i[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "High five! You successfully sent some data to your account on plotly. View your plot in your browser at https://plot.ly/~KevinMiao/0 or inside your plot.ly account where it is named 'selecting-principal-components'\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\" seamless=\"seamless\" src=\"https://plot.ly/~KevinMiao/0.embed\" height=\"525px\" width=\"100%\"></iframe>"
      ],
      "text/plain": [
       "<chart_studio.tools.PlotlyDisplay object>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tot = sum(eig_vals)\n",
    "var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)\n",
    "\n",
    "trace1 = dict(\n",
    "    type='bar',\n",
    "    x=['PC %s' %i for i in range(1,5)],\n",
    "    y=var_exp,\n",
    "    name='Individual'\n",
    ")\n",
    "\n",
    "trace2 = dict(\n",
    "    type='scatter',\n",
    "    x=['PC %s' %i for i in range(1,5)], \n",
    "    y=cum_var_exp,\n",
    "    name='Cumulative'\n",
    ")\n",
    "\n",
    "data = [trace1, trace2]\n",
    "\n",
    "layout=dict(\n",
    "    title='Explained variance by different principal components',\n",
    "    yaxis=dict(\n",
    "        title='Explained variance in percent'\n",
    "    ),\n",
    "    annotations=list([\n",
    "        dict(\n",
    "            x=1.16,\n",
    "            y=1.05,\n",
    "            xref='paper',\n",
    "            yref='paper',\n",
    "            text='Explained Variance',\n",
    "            showarrow=False,\n",
    "        )\n",
    "    ])\n",
    ")\n",
    "\n",
    "fig = dict(data=data, layout=layout)\n",
    "py.iplot(fig, filename='selecting-principal-components')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Variance Explained (%)</th> <th>Principal Component #</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>33.9719               </td> <td>1                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>27.483                </td> <td>2                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>18.0588               </td> <td>3                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>8.26561               </td> <td>4                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>7.08674               </td> <td>5                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3.62365               </td> <td>6                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1.20799               </td> <td>7                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>0.302319              </td> <td>8                    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Variance Explained (%) | Principal Component #\n",
       "33.9719                | 1\n",
       "27.483                 | 2\n",
       "18.0588                | 3\n",
       "8.26561                | 4\n",
       "7.08674                | 5\n",
       "3.62365                | 6\n",
       "1.20799                | 7\n",
       "0.302319               | 8"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tot = sum(eig_vals)\n",
    "var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)\n",
    "Table().with_column('Variance Explained (%)'\n",
    "                    , var_exp).with_column('Principal Component #', np.arange(1, 9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.3169669  -0.35472917]\n",
      " [-0.39027651  0.35206113]\n",
      " [ 0.23169947 -0.10627577]\n",
      " [-0.34916311  0.18359042]\n",
      " [ 0.30586641 -0.33424857]\n",
      " [ 0.42660873  0.43754387]\n",
      " [ 0.34439513 -0.45509079]\n",
      " [-0.42125934 -0.4415267 ]]\n"
     ]
    }
   ],
   "source": [
    "matrix_w = np.hstack((eig_pairs[0][1].reshape(8,1), \n",
    "                      eig_pairs[1][1].reshape(8,1)))\n",
    "\n",
    "print('Matrix W:\\n', matrix_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.0759838 , -0.17557517],\n",
       "       [-1.33678967, -2.93214484],\n",
       "       [-1.37396347,  0.73238161],\n",
       "       [ 1.61069307,  0.48651234],\n",
       "       [ 2.73642243,  0.74246137],\n",
       "       [-1.33065111, -3.53979993],\n",
       "       [ 1.51010294, -0.19367437],\n",
       "       [ 0.88995976, -1.09660172],\n",
       "       [ 1.0642932 ,  1.90054638],\n",
       "       [-0.61976055, -1.71256088],\n",
       "       [ 1.73367694,  0.14496439],\n",
       "       [ 0.38156544,  1.48440692],\n",
       "       [ 1.08317686, -1.10265351],\n",
       "       [ 0.75372853,  2.76120045],\n",
       "       [-1.46318731,  1.92289759],\n",
       "       [ 2.44858796,  0.57503654],\n",
       "       [ 0.77857227,  1.36801951],\n",
       "       [ 0.25903925,  0.44753682],\n",
       "       [-0.39254376, -1.51870266],\n",
       "       [-0.15464699,  2.69675235],\n",
       "       [-2.39811336,  1.1722122 ],\n",
       "       [-1.51708582,  1.59843639],\n",
       "       [-0.41332666, -3.00749072],\n",
       "       [-0.38186505, -2.57201378],\n",
       "       [-1.35052889, -2.60985322],\n",
       "       [-2.33279947,  1.10112942],\n",
       "       [ 2.3511315 ,  0.29786741],\n",
       "       [-1.53939243, -0.17370522],\n",
       "       [-2.58974622,  2.40214407],\n",
       "       [ 0.73952381,  2.25879267],\n",
       "       [-1.43298294, -0.60073287],\n",
       "       [ 2.0674663 , -0.11017086],\n",
       "       [-1.61635699,  0.45771104],\n",
       "       [ 0.35352677, -1.37626363],\n",
       "       [ 0.48987978, -1.36719476],\n",
       "       [-0.04819513,  0.74929959],\n",
       "       [-1.00285038, -2.26293306],\n",
       "       [-1.45112424, -0.5262832 ],\n",
       "       [ 1.73955817,  3.09298942],\n",
       "       [ 1.57230411, -0.34627199],\n",
       "       [-0.14162568, -1.75277807],\n",
       "       [ 1.75345587,  0.31177437],\n",
       "       [-1.29625854,  0.71377913],\n",
       "       [-0.54799003, -0.67794605],\n",
       "       [ 0.16154005, -2.44918012],\n",
       "       [-0.36622306, -1.53275554],\n",
       "       [ 1.09966488, -0.65089405],\n",
       "       [-3.46318346,  2.17275466],\n",
       "       [-3.75087861,  1.78824384],\n",
       "       [ 1.22083435, -0.79155829],\n",
       "       [ 0.42787566, -1.41293197],\n",
       "       [-3.84182392,  1.76361332],\n",
       "       [ 0.02613586, -2.22041514],\n",
       "       [ 1.75721507, -0.67214354],\n",
       "       [ 0.2064066 , -1.5883555 ],\n",
       "       [ 0.54503235,  1.4876069 ],\n",
       "       [ 0.62790929, -1.34512425],\n",
       "       [-0.59478032, -0.0662557 ],\n",
       "       [ 1.80862843,  1.08732702],\n",
       "       [-1.35606678,  1.35636855],\n",
       "       [-2.91798507,  1.72008501],\n",
       "       [-2.80471418, -0.22208084],\n",
       "       [ 0.12884895,  0.60814007],\n",
       "       [-0.78154914,  0.19217036],\n",
       "       [ 2.77538208,  0.85339519],\n",
       "       [-0.90360229, -1.32432458],\n",
       "       [ 1.00541732, -1.23935096],\n",
       "       [ 0.60766926, -1.52555623],\n",
       "       [-2.94067536,  2.44650315],\n",
       "       [ 1.77302119, -0.07788477],\n",
       "       [-1.62778003, -0.37664662],\n",
       "       [ 0.87727936, -1.11543493],\n",
       "       [ 1.10648764, -0.99426948],\n",
       "       [-0.47705621, -0.96026223],\n",
       "       [ 0.80320129, -0.80606753],\n",
       "       [ 1.51253275, -0.49157668],\n",
       "       [-0.09947121, -2.37292168],\n",
       "       [-1.64512397,  0.08029516],\n",
       "       [-2.80653386, -0.86192914],\n",
       "       [-1.45096966,  0.69088886],\n",
       "       [-2.1053346 , -0.97754632],\n",
       "       [ 0.10761329, -2.2379281 ],\n",
       "       [ 0.89466126, -1.08890265],\n",
       "       [ 0.97500088, -0.707412  ],\n",
       "       [ 2.74215475,  0.61848985],\n",
       "       [ 1.83562849, -0.05491996],\n",
       "       [ 1.12190708, -0.62044075],\n",
       "       [-1.09715616, -0.02016738],\n",
       "       [ 1.86573124,  0.03198993],\n",
       "       [-0.06056902, -1.52992573],\n",
       "       [ 1.66309231,  0.21467073],\n",
       "       [-1.37092586,  2.85378259],\n",
       "       [ 0.9945441 , -1.49294977],\n",
       "       [ 1.28455796, -0.32333243],\n",
       "       [ 1.80376494, -0.25053572],\n",
       "       [ 0.91643689, -1.19405794],\n",
       "       [ 0.50651716, -1.34710652],\n",
       "       [ 1.55346626, -0.30081466],\n",
       "       [-3.35429035, -0.50405135],\n",
       "       [ 2.71366666,  0.71100651],\n",
       "       [ 3.05678591,  1.20220895],\n",
       "       [-1.07067937, -1.41757163],\n",
       "       [-1.35668469,  2.07739792],\n",
       "       [ 2.58026481,  0.6357175 ],\n",
       "       [ 0.13856504,  0.36729758],\n",
       "       [-0.42620441,  0.80387252],\n",
       "       [-1.00910038,  0.23246437],\n",
       "       [ 2.55074965,  3.12154783],\n",
       "       [ 0.34050089, -1.51345338],\n",
       "       [ 2.35279248,  1.43612818],\n",
       "       [ 1.51005119, -0.36223688],\n",
       "       [ 0.62877252,  3.27938759],\n",
       "       [ 2.20417876,  0.81071265],\n",
       "       [-1.78326657,  0.62442321],\n",
       "       [-2.99319016, -0.15416073],\n",
       "       [-0.14725782,  3.00614887],\n",
       "       [ 0.96051238, -0.8143425 ],\n",
       "       [ 2.15810689, -0.26818305],\n",
       "       [ 1.66665617, -0.19572078],\n",
       "       [ 1.63659419, -0.36953241],\n",
       "       [-0.58230604,  0.94368751],\n",
       "       [ 2.03333575,  0.51966115],\n",
       "       [ 2.01502437,  0.08823799],\n",
       "       [-0.68117606, -1.92868983],\n",
       "       [-2.51428782,  3.3628653 ],\n",
       "       [-0.17968634,  1.41967136],\n",
       "       [-0.93771883, -3.28074516],\n",
       "       [-2.57062061,  2.25070045],\n",
       "       [-0.45698723,  3.12644011],\n",
       "       [-0.77699609,  0.49067294],\n",
       "       [ 0.29683592, -2.01523199],\n",
       "       [ 1.59097833, -0.23696293],\n",
       "       [ 0.75574506,  1.75644599],\n",
       "       [-0.80639907,  0.8340387 ],\n",
       "       [ 3.05389001,  0.96034458],\n",
       "       [ 1.99480539,  0.68443386],\n",
       "       [ 0.18895119,  0.25186779],\n",
       "       [ 1.61305122, -0.2247686 ],\n",
       "       [ 1.26959897, -0.12530575],\n",
       "       [ 1.1006038 , -1.31231324],\n",
       "       [ 0.53287726, -1.49330321],\n",
       "       [ 0.58882212, -1.14250785],\n",
       "       [ 2.31806616,  0.43202191],\n",
       "       [-0.4337968 ,  0.20162034],\n",
       "       [ 1.27604945, -0.57446024],\n",
       "       [-1.90448598, -0.7594739 ],\n",
       "       [ 0.55862785,  1.83078092],\n",
       "       [ 0.09094805, -1.0269824 ],\n",
       "       [ 1.9666955 ,  1.58830609],\n",
       "       [-1.84711696,  0.36995474],\n",
       "       [-0.61071829, -3.04747718],\n",
       "       [ 1.65555738, -0.58031342],\n",
       "       [-1.77385607,  1.33411824],\n",
       "       [-1.52833866, -0.2044244 ],\n",
       "       [-1.0642101 ,  0.46501349],\n",
       "       [-0.19078679, -1.66918546],\n",
       "       [-0.06519323, -1.22829437],\n",
       "       [-1.75989591,  0.68478409],\n",
       "       [-1.27905916,  1.52084081],\n",
       "       [ 1.06941479, -0.21729739],\n",
       "       [ 1.13347198, -0.99908912],\n",
       "       [-1.07102173,  0.02394896],\n",
       "       [ 1.04977621, -1.09131845],\n",
       "       [-0.75186432, -2.21593579],\n",
       "       [-4.64675984,  1.24318879],\n",
       "       [-0.30216871,  0.20995896],\n",
       "       [-0.40336106, -1.84230565],\n",
       "       [ 1.24131931,  0.52688029],\n",
       "       [ 2.90537484,  2.12939313],\n",
       "       [-2.34750114,  2.56055043],\n",
       "       [-4.04007825,  1.34257076],\n",
       "       [ 1.8070095 ,  1.96479006],\n",
       "       [ 0.9314693 , -0.02717575],\n",
       "       [ 2.18720473,  0.22587424],\n",
       "       [ 1.30137209,  0.47994462],\n",
       "       [ 0.37633125, -1.49066037],\n",
       "       [-0.49682084, -2.151123  ],\n",
       "       [ 0.9864544 , -0.74391178],\n",
       "       [-0.74160163, -0.85960822],\n",
       "       [-3.26062773, -1.36974728],\n",
       "       [-0.03408022, -2.14715922],\n",
       "       [ 1.94214872,  0.71033968],\n",
       "       [-1.68055235, -0.61802527],\n",
       "       [-0.5215407 ,  0.25461386],\n",
       "       [ 1.32292438, -0.85639646],\n",
       "       [-1.62391293, -0.51165117],\n",
       "       [ 1.10571015, -0.37686769],\n",
       "       [ 2.54894166,  2.79842176],\n",
       "       [-1.06002235, -1.68514817],\n",
       "       [ 2.43182502,  1.09135541],\n",
       "       [ 0.38551892, -1.67935265],\n",
       "       [-0.13093961, -2.08197408],\n",
       "       [ 0.78184239,  1.22646816],\n",
       "       [ 2.33541497,  0.3736765 ],\n",
       "       [-0.33906543,  1.45483091],\n",
       "       [-0.74821427, -1.38631798],\n",
       "       [ 3.38424807,  1.11449973],\n",
       "       [-0.28102063, -0.0136239 ],\n",
       "       [-1.88113994,  0.57335747],\n",
       "       [-0.414404  , -2.26985323],\n",
       "       [-0.58110688, -1.20997478],\n",
       "       [-0.35808143,  0.44198777],\n",
       "       [-1.81538289, -2.51903833],\n",
       "       [-0.77069956,  3.45066926],\n",
       "       [ 0.21515075, -1.85856543],\n",
       "       [-1.83940988,  4.32602202],\n",
       "       [-0.80869899, -1.78330007],\n",
       "       [-0.74310647,  0.40505732],\n",
       "       [-1.02517796, -1.44882664],\n",
       "       [ 1.32532141, -0.71611876],\n",
       "       [ 0.53405288, -1.58771305],\n",
       "       [ 1.98157329, -0.04139178],\n",
       "       [-3.79745011,  1.75948535],\n",
       "       [ 0.90702701,  0.88206215],\n",
       "       [ 0.74350527, -0.67166732],\n",
       "       [-0.59367601, -3.08407794],\n",
       "       [-1.84471514, -0.4896057 ],\n",
       "       [-1.19832   ,  0.46793804],\n",
       "       [ 0.28119462, -1.18666005],\n",
       "       [-3.1098008 , -1.13669592],\n",
       "       [-0.44126365, -0.59543584],\n",
       "       [ 0.23335587,  1.83308462],\n",
       "       [-1.3173323 , -0.50786849],\n",
       "       [ 0.93587586, -0.96193486],\n",
       "       [-3.05131968,  1.89123801],\n",
       "       [-0.75538083, -2.94411541],\n",
       "       [ 1.46471597, -0.33569331],\n",
       "       [ 2.14109931,  0.07717611],\n",
       "       [-1.38108831, -1.01160082],\n",
       "       [ 0.076265  , -0.58003004],\n",
       "       [ 1.95438218,  1.36313618],\n",
       "       [ 1.08563178, -1.2300601 ],\n",
       "       [-1.36121257, -0.7426438 ],\n",
       "       [ 0.05966504,  3.24189974],\n",
       "       [ 0.95632374, -0.7614937 ],\n",
       "       [ 0.74483764,  1.18055886],\n",
       "       [ 1.69388066,  2.12847591],\n",
       "       [ 1.95178534,  0.0961978 ],\n",
       "       [-0.32284381, -0.9278458 ],\n",
       "       [ 3.4081336 ,  1.01092706],\n",
       "       [ 0.04666064,  1.61456104],\n",
       "       [-1.46761177,  2.36824939],\n",
       "       [-3.09864117,  2.35191015],\n",
       "       [-2.26600677, -0.50850396],\n",
       "       [-3.04778207,  0.42220604],\n",
       "       [-1.6729975 , -0.09622983],\n",
       "       [-3.76807025,  2.94212057],\n",
       "       [-0.89810979, -0.99624034],\n",
       "       [ 1.49610677,  1.04059057],\n",
       "       [ 3.41263954,  1.6566    ],\n",
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       "       [ 2.62612916,  0.60182184],\n",
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       "       [ 2.00652588,  0.6830269 ],\n",
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       "       [ 0.36127405, -1.53340131],\n",
       "       [ 1.16768951, -0.96300397],\n",
       "       [ 1.30735829, -0.77541533],\n",
       "       [-0.58953707, -3.02545835],\n",
       "       [ 0.26947412, -1.1852531 ],\n",
       "       [-0.79855464, -2.90746025],\n",
       "       [ 1.37236185, -0.5970785 ],\n",
       "       [ 2.09345049,  0.98296669],\n",
       "       [ 1.96716225, -0.04274433],\n",
       "       [-0.39443316, -2.67344745],\n",
       "       [-0.51392051, -2.25099603]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = X_std.dot(matrix_w)\n",
    "Y #2-dimensional to make it more visually interesting!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
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       "        PC1       PC2\n",
       "0 -2.075984 -0.175575\n",
       "1 -1.336790 -2.932145\n",
       "2 -1.373963  0.732382\n",
       "3  1.610693  0.486512\n",
       "4  2.736422  0.742461"
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     "execution_count": 48,
     "metadata": {},
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   "source": [
    "PCCS = pd.DataFrame(Y, columns=['PC1', 'PC2'])\n",
    "PCCS.head()"
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  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
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       "        PC1       PC2             ID  M/F  Age  Educ  SES  MMSE  CDR  eTIV  \\\n",
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       "1 -1.336790 -2.932145  OAS1_0002_MR1    1   55   4.0  1.0  29.0  0.0  1147   \n",
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       "3  1.610693  0.486512  OAS1_0004_MR1    0   28   3.0  2.0  29.0  0.0  1588   \n",
       "4  2.736422  0.742461  OAS1_0005_MR1    0   18   3.0  2.0  29.0  0.0  1737   \n",
       "\n",
       "    nWBV    ASF  \n",
       "0  0.743  1.306  \n",
       "1  0.810  1.531  \n",
       "2  0.708  1.207  \n",
       "3  0.803  1.105  \n",
       "4  0.848  1.010  "
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     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "joinedcs = PCCS.join(cs)\n",
    "joinedcs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
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       "0 -2.075984 -0.175575  0.0\n",
       "1 -1.336790 -2.932145  0.0\n",
       "2 -1.373963  0.732382  0.5\n",
       "3  1.610693  0.486512  0.0\n",
       "4  2.736422  0.742461  0.0"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tabularcs = joinedcs[['PC1', 'PC2', 'CDR']]\n",
    "tabularcs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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f/uGHU35cIYQQQgghpkpFJhV1TXUTihdSQ0Mjc+bMo719KQCnn/4+Xn75xSk/rhBCTDWlFK6liCmDq0FrVewiCSGEOEQqMql43yfehxNzRsWcmMP7PvG+KT/28uVH09/fx/r1rwLwyCN/4Igj2qf8uEIIMZW0VsRVxAu3PsAD193C879+ANeEWJYkFkIIUQkqck7F3nkT9/zbPfT39FPXVMf7PvG+gsyn2J8vf/kKLr30Mtrbl3LNNX/L9773HbLZHC0tLVx99bem7LhCCHEoOEQ8/tPf0btpFwC7/rSRbN8QK/+fDxAWuWxCCCGmnjLGmGIXYiJ6e1NE0egid3Rsoa1tfpFKJPaybU0QRMUuxqRIXSpvzc01dHcPFbsYFSmuIn739ZvHxM/89mfIVUinuNQ/UWxSB0UhaK1obKye+OumoCxCiGlGxsaLA1KKWE1iVMhJxEDqjhBCVARJKoQQ++VqiEUBXmcvCW1w5Iwh9iNQmhWfeC/atgBQWnPCxacRKqk0QghRCSpyToUQ4sBcDdsfe4kX71wDgLY07/jCh4i1NZb9MDdReEFoqJrdzPv/76fID2WI1SQJUPhhWY2wFUIIcZCkCUkIsU+WMbz0P4+N/ByFEWt/tRorkmm3Yt/8CLKRIqqqIhspfMk9hRCiYkhSIYTYpzAIMG9aFCHTl0IjY+SFEEIIMZokFUKIfdKOQ1XTjFGxuSsOJ5Scoiy5tsZVEa6lUPI7FPsRczQ1seF/MZlEJYSYADljTIGf/exfuPjij3DxxR/hxhuv3+/zHn30YT784Q+M/Dw0NMRf/dVf8PGPX8Dll3+W3t4eAHzf59vfvpqPf/wC/vzPP86WLZsBMMbw4x//PR/72PlcfPGHef75Z0fe65ZbfsnHPnY+F154Hg89dP9I/N577+biiz/MhReey29/+x8j8SeffJxPfepCLrzwXP7lX24cia9fv45LLvkEF154Htdd922CIACgo6ODyy//LB/72Pl89atfIpPJlOxn2N/3Ld6arzTv+otzmXP8Eqpb6jj89ONZ9sGTZUhLmVEKkrZi8wPP8Ng/3smrd60hroys6CXGqIppshs2sem3v2PTb39HbsMmqly5TRBCjI+cLQrsyScf58knH+Pmm/+dn//8V6xb9woPPfTAmOft3t3LDTf8PW/cJuQnP7mRo48+jn//999wzjkf4vrr/w6AW2/9NfF4gn//999wxRV/yXe/+9cAPPjgarZs2cQvf3kr11zzt1xzzf8lCAJefvlF7r33Lm6++Vf84z/+lBtuuJ7BwQG6u7v4yU9u5MYbf8rNN/+KO+64nU2bNpLP57j22m9x7bV/xy9/eSuvvPISa9Y8AsC3vnU1V175v/n1r2/DGMOdd/4nAD/4wXWce+4F/OpXv6W9fSk///lPS/Yz7O/7Fm8tDCM8bXPUBadw8hfPZcFpJ5AJDPIVlhdHwXO/eYh19z7FwI4eNj38Io/+0504SHY4lVxXM6Paoa7GoSppl3wSZ1maoH+QnqdfIPIDIj+g++kXCAYHsSy5VRBCHFjFninu+90DXPRnn+H0t53DRX/2Ge773dgb/4PR2NjE5ZdfieM42LbN/PkL6OzsGPO86677Dp/5zGdHxdaseYQzzng/AKef/j4ee+xRgiBgzZqHOeOMMwE49tjj6e/vo6OjgzVrHuG0085Aa828efNpbW3jhReeZ82aRzjllPcQi8Wor2/guONO4JFH/shTTz3B8cevoLZ2BolEglNPPY0HH1zNSy+9yNy585g1aza2bXPGGWfywAP30dGxi3w+z7JlywE466xzeOCB+wiCgGeffYZ3v/s0AM4888944IHVJfkZ3ur7FgcWRQYvNHhofFnxqSxZGHasfW1UrH9bN4Ty+5wq8ZhFLMqT3vgKQ6++QNC5ldoqp6SHndm2ZmjTtjHx1Obt2HbF3ioIISagIs8U9/3uAX7w3R/T1dGNMYaujm5+8N0fFySxWLTosJGb8G3btnL//fexatXJo55z662/5ogj2jnqqOWj4j093TQ2NgFg2zZVVVX09/eNisNw4tLd3bnPeFdX136ev+/4wTy/v7+fqqoqbNseVZ5S/Axv9X0LUQkM4FaP3pROWxotrc9TJu5qMts2YsLh4aJBaoh89y7isdJdxT0MI5IzW8bEE20thJKACiHGoSKvKjfd8AvyufyoWD6X56YbflGwY2zcuIErr7ycyy//C+bOnfeG+Gs89ND9fOpTl4x5zZuH5hhjUEqN/PcNj6CUJoqiUXFjhsdJDz//ze8z/ucf+P2jN5UHtNYl+Rne6vsWohKE2uK4C0/ljYt2Lf2zlYSyiteU0FoRefkx8SA9RCnncUEQkZjZQs382SOxmgWzSbQ1y740QohxKd1mkynU3dkzofhEPf/8s3z961/hiiu+xOmnv2/UYw88sJqenh4uvfSTBIFPT083n//8pdx4409pbm5h9+5eWlpaCYKATCbDjBl1NDe30NPTw+zZcwDo7e2lqamZlpbWkYnQMDxvoKmpeeT5b4zPmzcfgOeee2Y/z+8diQ+/f9N+37++voFUKkUYhliWRW9vD42NzQAl9xne6vsWohL4QUTtgjbO/Nan6d/eQ21bA7gOntwnTokoMmg3NiZuJasIo9KekJTKhzSuPI6WlccBEJrhmBBCjEcJt5tMnebWpgnFJ6Kzs4Orrvoy3/zmd8YkFACXXPI5fv3r2/j5z3/F979/PU1NzSM3uCtXnszdd/8PAPff/3uOOeZYbNtm1arX48899yyuG6OtrY2VK0/m3nvvJgxDtm/fxrZtWznyyKWsXHkSDz10P7lcjr6+Pp5++klWrDiRFStO5Omnn6Svr49cLseDD97P29++iqVLl7Ft2xa2b99GGIb8/vf3sHLlybS1zcR13ZEVme6++y5WrjwJ27Y55phjWb3693vi/8PKlSeV5Gd4q+9biErhR5DDomp+G74jCcVUy/sRiVnzQQ1fYq1EknjLbHL50v7ijYGMZxja8y/jy8IMQojxq8ieiksu/yQ/+O6PRw2BisVjXHL5Jyf93rfc8kvyeY9/+IcfjsQ+9KHzePjhP3DppZfR3r50v6/97Gcv47vf/Wsuvvgj1NRU841vfAeA88//KN///jVcfPFHcF2Hq6/+FgCnnnoaL730Ap/61EUAfPWrVxOLxVm6dBlnnHEWl176ScIw4NJLL6O5uWXPMT7PFVd8Dt8POOecD7J06TIArrrqm3zta/8bz8uzatXJnHrq8CTsb3zjO3zve98hnU5z+OHtXHDBhQD85V9+le9855v84hc30dLSxl//9XdL9jMIIYaFYfnfIWqtSMYsbFthDGTzEZ5fWq3p2VxI3K2iZslSMBAaw2Dal9XnhNhDqeG9cywMIYq8rFU+LShTZme53t4U0Zu6kDs6ttDWNn9C73Pf7x7gpht+QXdnD82tTVxy+Sc5/cxTC1nUimPbuuzH3h5MXRKlo7m5hu7uoWIXQ0wRpWBGtUt2x2aC9BDKsknMnoev4+RKYJiO1D8xEXvnGxZSOdRBrRXVrqLn2ZfIdvZQNauVhuXtDOUjSbxLhNaKxsbqCb+uInsqAE4/81RJIoQQYgo4tsLas6hCoAq3HHE8ZpPr2kmQHr5pMmFAZutGag5fVhJJhRDjkXQVOgoJs3nsmiqyAWXfIDcRcRt2rH6UbNfwPMj87gG8gSEaT1pB1pOkopxVbFIhhBCi8GIaOp/bwIt3riEKIw4//Xjmn7SMXAGGXtkacumxrbCR56GUllZOUfKSrqL/uZfof2UjANpxmP+B0zCWPS2GJ46HBSMJxV6pbbtoVZXx+aezipyoLYQQovC0VngDKZ759QN46RxBzuOl/36Mga0dBdlALYiGV1Eac1zXlYRClAUdhSMJBUDk+3StWYtbSXdjCpRljQpZMRf5Cy5/06YaywVFTJbUISEmx7Ytdj6/cUx821Pr0QXYFiOXD4m3zsZKJIcDWpOYPZ+8LGclyoBSijA7dg8TbyhTUbvGeJGi5cSjR8VaVx2HF1XStzA9TYvhT7btkk4PUlVVO2ZTNiHGwxhDOj2IbbvFLooQZSsMIxoWto2JNx42E1OA2yZjDIPpgKrZC7GUAjW8+lN+CuZTxJzhlWkiFPnASKODmDRjDHZNFdpxiHx/JD5j8XxCpYHKmBeU9yMSc+ewaM5MvP5BYvUz8GQFqGmhKEnF9ddfzz333INSigsuuIDPfOYzk3q/+vpm+vq6SaX6C1RCcTC0Ht7xulzZtkt9fXOxiyFE2QrDiLq5Lcw+bjE7nnkNgObD5zD72MVkCrTsaxQZhtJBQd5rf2riFgOvvMbQ5h3EGutoXrGcTKAJw/I9v4nSkA0MCz5wGp1rnsEbSjNj8XxmtB/GUK4yEoq9sn4EKKwZdQz5BmTw07RwyJOKJ554gscee4w77riDIAg466yzOOWUU1i0aNFBv6dl2TQ1zSxgKcXBKIel7IQQUysXwfILTuHo89453LpvWWTL6H4p7mh6175A/7rhYVz5vgFyXb3MOetUUmX0OURpCgJD1rJpesfbUECIqriE4o0qZXJ6pTjkScWJJ57IL37xC2zbprOzkzAMSSaTh7oYokQpNTwuOwyjMfuRCCFKnzGQNwAaFBBBObVCOhoGXtsyKuYNpiAMoaJGvoupEobmDYl2+fxtCHEgRRn+5DgOP/rRj/jZz37G+9//flpbW8f92oPZjEMcOs3NNQf92iDvEWSypLftJN5UT6yuFjsRL2DpRCWYTB0Uws/kcKoSw4nEXkphOzbN9QduAJP6J4pN6qAolqLuqJ3NZrnssss466yz+OhHPzqu1+xrR21RGiYz/MlxNKari50PPj4Sm7FkAXXHLSPry+9bjI8MwROTZdsaOzXI1rv/MNztAjQecyTVRyzeMw58/6T+iWKTOigKoWx21N6wYQOe53HkkUeSSCQ444wzWLdu3aEuhigxMWXY+vhzo2ID6zfTdMKyIpVICFGKHEthmwgTGYzW+KiCNjQFQYSuruGwj55Nfnc/bm0NoWWRlWVrhRDiLR3ypGL79u386Ec/4pZbbgFg9erVnH/++Ye6GKLUKEUU7GNFF+mVEkLs4Wroeu41nr/tYUI/oGFhGys/ezY5NdKpUBBeYPAC0DV1+JHByGRSIYQ4oEO++d0pp5zCu9/9bj70oQ9x/vnnc9xxx3H22Wcf6mKIEuNHUH/k4lGxeHMDkZo2+zMKcUCWpUk6iipXEXOsA7+gwqgg4Jn/70FCf7gBYvemDl6+63GcQuystw9RZAqarAghxHRWlInaX/ziF/niF79YjEOLEpX3I2YcdThuXS1Dm7YRb26krn0RqbwMORCVwbEUbpin449P4w+lqV00j/rl7RW93OQbaa0Y2tU3Jt67YeeelZmkAUIIIYppWuyoLaaHVC7EaWujYWYrkVEMltPi9kJMUtxRbPqv+4n2tsK/8CpKa5LtS2SnWYZ7DWpnNgyv6vqG3oOWI+eBbUEgXQpCCFFM0rQjSorvh+S8CK9Au+8KUQ6UUgSpzEhCsdfgxm3Yso79iFBbnPiZ9+MmYwC0LVvAEe9dgScJBTC8x0/c0cRcjZItNUQJs21NlauoiWkSjkJP0RBGcWhJT4UQQhSZMQY7ERsTd2dUI30Ur/MjqFs8h9O+9nEwEClVVrt1T6WqmMbr7qF33Ubc2moajm4nE8iOxaL0uLbGyqTY/tAT+Kk0VbNbmfmuExnKD58LRfmSngohhCgBgbJoOPqIkZ+tmEvrquPJy03zKH5oyEWKnFF4kdyEADiORXb7LnasfpT09g76XnqNLXfcR9KZutbfuKupiSlqYoqEK7cSYvxiNmy9+w/4qTQA6R2ddD3+LDFbeivKnfRUCCFECch6ETXtS6g/cjFh3sNKxMkGEIXSVyHemkNEz4uvjooFmRxBKoNyEgVPvKpimoEXX6XvxfUYY5ixZAFNJyxjKCd1VRxYmM1jwtGtJekdnTS9TRoIyp0kFUIIUSL27h6vtIuRGzQxTgbQrjsmrh0bCjwnx7I0wcAgu//0+qa1A69uompWK3ZzC0EgXWvirdnxGKjRm8vEm+qRkXrlT/oshRCixMiInuLSWhF3NXFHY1mlf5n0jaKNvrDtAAAgAElEQVTl7cfwxtnZyVkt4LoFr0uWpcns6BwTT2/fhSVbq4hxyIcw610novZUGKemmraTT5ChntOA9FQIIYQQe7i2wgk8eh57EWMMTccuJYzHyfulm+kFQYSOJTjsI2eR3tGJU1uNU1tD2it8b1cYRiRnt9L7/Cuj4lVz2gjlplCMQz6IcFuaWfThszBRCMoiE0IUSe9suZOkQgghANfRxPTwjWMYQTaQScCVRilwidj4n78f6S5Kbd3JwvPeh68domhq64PWCqUU4UHMo/ECgwfYM2fiR4b8FG0cGoYR8Rm1NCw7nN0vrgdgxpL5xGe2kpKNGsU4eYHZsxS0AlnjbtqQpEIIUfHijibo6mLTo2uJPH/PEodvZygfylCkCuI4NoOvrh8z/qz/pdeoPnYZ+Xywn1dOjtaKmDKkuvoI8j51c5vx0AeVXATB1N+gpfMR1UuPoH7Z8GplQYQkFEIISSqEEMJREVsffHzk5/SOTnqfe4nqZUfKbtYVxBiDlYiPiVuJ+JQmlzFteOTH/8XAjp7hn6sTvOerFxIpXbJJbc6PyBW7EEKIklL6M9CEEGIKaa3I9w2OiWd2dmHJbtYVxfdDaubPxqlOjsSsRIy6IxbheVPTS2FZmt2bOkYSCoB8Ksv61WtxbLlECyHKh/RUCCGKzrY1jhoeX+tFHNSwj4MVRYZYXe2YeKKtiRBFoZfkFKUt7cO8c04j170bjCHR0kh6Cidpa63I9afGxLN9qYJVPaUUjqOJInNIhkcJISqTNIMIIQrOsjQxR+M6B15jMuYo7HSK7j8+Qc/Dj+Pm0sSmcCfgffHRtJ28AmUPlzfR2kjTcUfhyQ1YxQnDiKFcRFTXQFTfyGAuIpzCBfR9P2TmsoVoe/TfyuJ3H1uQdfsTcYvapMLO9pEgx4waB6Vk52IhROEpU2bLm/T2pqZ8BQ5xcJqba+juHip2MUSRuRpyvQNsfOh5kk21HPauo/G1tc8WUq0Vichj0+33joovPP/9ZIw94dWXJlMHXUcR08MbMoVALkDONWJCDrb+2Vph0hlevPNRgpzP4e89geo5zXiTnPvs2JqE8khv3TASs5LVxGYtYCjtT+7NRUmS67AoBK0VjY3VE36dDH8SQhSMbVsMbdnFo/9050hsy2Mv856vXMi+RqQ7jkX/cxvHxAdf3UTyqPYpW21nXzzf4MlQJ1EEQWSwqpMcfdFpYCDSuiC9ZDFXk9u+Y1QszKTQsoSnEGIKyPAnIUTB6DBg3b1PjYrlBtIMdexG67FDLowxoybF7mVXV0kvgagoYWjwQvCiwi0Lq9jPXivlNUBBCFEmJKkQQhSOUljO2A7QfcUAPC+kdvF8nOqqkZhTU03Ngjn4vqx7L8Rk5H1DrKltVEzH4hh94LlOQggxUTL8SQhRMKHSHPWBVXT/3XbMnp6GGbMaSTbWkt3PrNPh1Xbeg9c/CErhzqghLXtDCDFpnh/iJqupmr8Ev78HHU/g1DUymJL5FGLfnD2La0ijjjgYklQIUYK0VtgaMIZI6bJZBjIMI5y6Gs74xifZ+dxrJOtraFw8m7zZ/9KsYRgxFIJO1gCQz5XHZxWiHKQyAZZl4zTMwg8N6UGv2EUSJcixNVUJG3+wD4Cq2nrS2QC/TK49ojRIUiFEibG1QuXzvHTX4/iZPEveezzJlga8Mjm3+xEo22bm24/CGEM2iBjPgvsyh0KIqRGG0SHd+0WUn6qEReq1lzDRcA9FvmsX1YuPpH9I6o0YP0kqhCgxjom459pbCP3hlY86XtrCKVeej9PcMKU3BlortFYF6RUxRrrPhagkrq2IWQqiiEgpcqGSRKZMuK6N19c7klAAmCjE6+vFTTZM2W7yYvqRidpClBDbtuh8ectIQrHX+vufwZrC5U7jFkT9Q/S9soW4CXHkzCCEGKeYowi7utj4m7vY8B//w857/0DSMvtc8U2Uqn2vEib7JIqJkJ4KIUqIMQa3OjEmHqtJMnx2L3xiEdPwwm1/ZNtTrwKgtOKdX/gQsZnNBIH0NhSa42iUMRil8GVCupgGXA3b/vDkyFK1+b5BOtespXHlCWSnwbBGx7HQWuH74bQcpun7Acn6JvI9na8vN6wUbkMTAzKpX0yAtEcKMcWUUriWwiXCsd/6Ty4MI+oXtFI7s2Ek5sRdjjhjBf5+Vk+atCAYSSgATGR47jd/wAqly7uQlIKEreh+bgN/+vUDdD/7GklbSUugKGtKQZDJjdn7Ite9G13mm0lqrUja0P3Mq6z7r0cId/cTm4Z3TcZAJhdSs3gpbkMzbkMzNYuXksmHsqWJmBDpqRBiClmWwo0iXvivR+nb0knbUQs4/PQTyIZmvyfrfKR4xxXnMrC9Bz+bp+mwWXhKY6YoqXjzUCuAfDo3JceqZK6GF27/I1ufWAfAzuc20P3aDpad+07ycuEWZcoYcJIJlNaY6PWet+SsFkKmpnf1UHGV4dF/vJO+rV0AbHrkBVZ88r00LF0w7XoZPT/CDyLc2hYABtKBJBRiwqZhzi1E6XBMxMM3/CdbH3+FoY4+1q9+hud+89BbzlmIIkM2gMTsFmYsmUs2UoRT1UsBOIk4VU21o2KHvXM5xpINsgpJG8O2J18dFdv+9KsouXKLMpcLDXPOeAd2Mg5A1axWWk48hnxQ3nU7zHkjCcVer/zuCfQ0HRZqDOTzAfm8JBTi4EhPhRBTyAQhg7t2j4rtWPsaR5/3rgO+9lCtnOIpzSlXXsAr9zzF0K5e5r7tCNqWL9qzFKwoJGVpzBtuSLRlTdVUGSEOGS8wODUzmHfO6SgFYQQpz2Cm452pjFcUYr8kqRBiCmnbQlua6A0JQnxGEoMBSuPiFIYROaVYcuaJEEUYyyI7zbr2S0GoNEecsYKX73p8JHb4accRKo1kFaLc+UHEdJvSa8VdGha1sXtjx0hs6dlvJ7JsmKa9FUJMhiQVQkyhEMVRH1jFn25/BBheWen4i04jUBZQOjfuxgy3NiqlcJTGcZTsM1FgXmiY/45ltC2dT/f67TQtmU28oZb8FA5tE2IqJGIWrqsxBnJehOdNz3NFPlKs+uyf0fnyFga2dzN3xRE4M6rxJKEQYp+UKbP+yd7e1LRc0m06aG6uobt7qNjFKDmuBhUEpLr6qZ3ZQKA0pdgR4GiF8j22PPYysZokc45bTB5dVhtYlUMd1FphWcPfq5zLppdyqH+TVVvtEvR1ke/tRmlNvG02kVtNJjd9V4srpyVlK6EOiqmntaKxsXrCr5OeCiGmmBcB2iY2q3l4zfYSvCZprYjSGVZf9+uRFVxeve9pTv2rj5ItctmmmygyRJG0dIry49iaKDM4vJ8BYMKI7I4tVC8+EqXU9JxDARXVa+s4mmTMQgGRgXQumNKFQsT0Iqs/CXGIlHILl63g5bseH7UkZLYvxe7NHViWnCaEEGDbimCwf0w8SA1hH2APHlH6XEeTtELSm15haP0LZLeupyah5Rogxk1qiqg4tm3hOLJc6puZfSU9JZwICSEOrTACnagaE7fiybIaJin2LRG3SG/dgAmGh7JFXp7M9s0kpuOOf2JKSE0RFcOyNEkL+l7aRMeTLxMnwrZKYwWmYguB9jNPRL1hucR4bZKGRTPlZkEIAYDnhbh1jVjJ1xMLp64RY7sl3RMrxkcZgwlHD/UKsxm5TopxkzkVomLEiHjg724l0zsIwIt3PMpp/+dj6Fis4i+IYWhwaqs4/WsfY+Mf/0SsJsmCVUvxynxHXCFEYQ2mfapmLcBSgFL4gWEoPd0Wk61MBoWyrFGJhZVIEsicCjFOklSIimDbmt4NO0YSCoDQD3nl7ic58tx34lV4UgHgR6ATCZacvQpjIOsFSEIhhHijKDIMpafvSk9TwbYVCUthggBl23gh5Etwc9FMPqRq/mLS2zZifB8rFic5ZyFD2dIr60RprahO2GgiUIrQKFKZYNouLlAsklSIihF4Y1vTQs9HyY3ziCgy5PNywyCEEIVg2xrXz7H5jocI8x7K0sx814m4TU14QWlde3w/ImM0yQVHoIHQGIay0bQYAltb5ZDZtoEwmwHASlZTO2chA0NekUs2vcicClERgiCipX0uTiL2elDBEWesoMTO60Jg25pYzMaSscxClLWYNux66HHC/PDNqwkjdv3hSWIl+rftBxGDKZ/+lM9QOhiTUFiWwnEsVGkWf58cx8If6htJKADCTIook5JVywpMeipExfCM5vSrPsb6B57BS+VY8p7jsGqS+DJeVJSQ2moHk88QplLEquuIYg6pjPQeCVGOtFbk+wZHxUwY7pm3UEZ35gy39hPkCXMpktW1+CFkcqW/h4elFVFu7I5LYS6DrkoC5d8TUyokqRAVI4wMkdIcdsbbAEUQRvjjnEuhlELr4ecaoyp+YreYGlUJG69rB/5AHwD5ni7irbOIJ+rI5Uv/4i2EGC2IoGp2G+kdHSMxOxEHyxp+sExUJ/ecmwb7RmLJuYtwnTheiW8O6AcRVTMa8Pp6R8Wd2no5rxaY9PuIimIMeH6E54fjTgyUihjq38311/0jf/vtH7G7pxtp2RBTwbHVSEKxV667g5gjp2ohylE+MMx859uonjsTpTXxpnrmnfVuyqCBfxTbUqMSCoBcx3Zibun3toRhRGS5JGbNQzsu2o2RnLOAAC0NhAUmPRVCvAWlIJtO8+GzLsHbMyb27jtWc+vdNzOjvlFWjhBTT6qYEGUrigwpHxpXraBVD09+zoaKsIx6KYDhFrk3h6Jo1N5GpSyVCXDdauLzlwCQ9wxetswyuzJQlOavH//4x5x99tmcffbZfO973ytGEYQYF8ex+e/b7h1JKACCIOTX/3objrQeiwILQoNdM2NULNbUQt4vsxsQIcSIKDJk/YihfETGM2W5mlJkFFY8MSrmNrbgldG5yfNChtIBQ+mg5IdslatD3lPx6KOP8vDDD3P77bejlOLSSy/l97//Pe9973sPdVGEOCBjDFXVyTHx6pqqfTxbiMlJZwNqZ84jrB0kTKewa+vATZCRzcWEmPYcx8KxFKEx5EtsrH8qG1A7bzFefw9RNoMzox7i1XJuEqMc8qbW5uZmvvrVr+K6Lo7jcNhhh7Fz585DXQwhxsX3Q844+1QamupHYjW11Vzw8Q/geaV10hflzxgYGPLIW1WYujayxpXdioWoADVVDvEoQ9S9DT3UQ12Ni2WVTm94FBn6hzzCRD2qaTY5nZRzkxhDmSIOCt+8eTMXXXQRt9xyCwsWLChWMYR4S8YYerp28/BDjxP4Ae86bRWNTfXYtkxJEqISBZ6Pn/VQCmLVSZQuj3HlojSZKCLX20V21/aRmHZj1B7WjnacIpZMiIkpWlKxfv16Pve5z/HFL36Rc889d9yv6+1NyWz9EtXcXEN391CxizFlbHt4wx9fxmKWrFKvg46tiCvD4MatWPEY1XNnkvYpyzHWlSphK15bvZZND7+AWx3n2I+8m6rZzfhR6de/cqT3JGzT+bpfU2WT27KeyB+9u3P1YUcykJnYuUHqoCgErRWNjdUTf90UlOWAnn76aT796U/zl3/5lxNKKEqB7HBbuYIgLEhCYduapKOochQxxypAyUQ50FrhRgEbf/M7up/6Ex0PP8WWO+8nKQ2RZcNxNDvWrufV+9bi5zzSPYM88o93oENpaCg0y1LMqHGodkKqnZAZNc60vf4aA8oaey1QunSGPwkxHod8/MauXbu4/PLL+eEPf8iqVasO9eEPWtxROMqQ391Psq6WQGmy/vRtORFTw7U1tpel89G1+JksM5YsoO7IJQyV26LlYsJcS9H75AuY6PWWRz+VJte9G6uuQXoryoAKQnasXT86aKB3w07q2ucXp1DTVE3SIb35VSIvDwwPB6pZcDj9Q94BXll+8r4h0TaH9ObX65ZdM4NAbjFEmTnkScVNN91EPp/nuuuuG4ldeOGFXHTRRYe6KOPm2pqwp4et968ZibWuPJbYvLmy1KOYkLgFG/77fsyeG8jeZ1/GchzchQvKaok7x7HQaniX8qDc1lsvFsWohGIvE4aUyVLv42LbGqXU9BwmaFnUzW2mZ8PoxUVqZzYQhnIHWCiOY+EP9o0kFACRl8cf7MNxa6dd3fL9ECvmULPkKILUIDoWBycmE6FF2TnkScXXv/51vv71rx/qw06Ka8GWR54eFet68nkWLZhDfj+vEeLNtFbkdvePJBR7DWzYwsyF8yiH9jetFdWuZvC1zeR6+qhdPJ+qxnrSeUksDsQPofGYIxna8voNqRVzSbY1M5gr/+/PsjRJBzI7Owm9gJr5s8gF4E+jm20/jDj8vSfQ+fJWhjqHdxde9I5luLVV5Ar0OS1LE9MGBQSoKWu4UgpcR6ONIUCX1I261mrM/AKAyPfQ8WmUgb9BLh+S98Cya4j8iCgvCYUoP7J8zTgoIMyPPsGZMIJpPHFMFJ4xBqd67P4W7owaIhRv3jrZ2TPfopQu9glHsf33fyTXM3xDNbhpG80nHk18wXzptTuAMIyI4gkWnnsGu19cjx2PUb90McVujIzHLGKOxgB5LyJ/kEslJx3Yeudq/FQGgO4nn2fheWcQRHra7DxvDHha844rziPyfSzbIlSaQo1edGyN4+foXPMMQSbLjMMXUnv4IlIFHh5pWYoqW9H7/Mvke/upWTSXmgVzS2YYpu+H1NQ14vV2jYq7dY0HXUatFbatCcPS3XzOmOG5e0KUK0kqxiEwUDN/1qgWxnhzA5EaeyMoCqMUb6gnyxgwrkPdEYvoX7cRADsRp+VtR5N+QyunZSlcE7HrufWYyDDr6EX4ShOUQIuvCsORhGKv3c+vY/7CedJrNw4536C1S+3xyzEGBvMhxTyH1FY7BP09pHq6UFoRb5mFnaglnQ0m9D62rcns6hpJKACiIKD3+XXUHHPUQScqpSgMDSGA5Qz/6gr460tYsOG2+zF7Jn73PP0C2rZw588r6M7FCVux9XcP4g0MrxKU6ewhSGdJti8picaBKDJ4oaZqwRLy3bsAiDXPxAsV0T6GEB5IwlFoz2No0w7iTQ0kGupIexHTJNcVomRIUjEOOd/QetIKnNp1pLd3kGhtpOm4o0h5ckYqtL031NuffBmAOccvwVN62oxXzngRdccspfGYdkIvwIrHyASMulC6JuK+a36Fl84B8NKdazj9ax8noPjd/vtaj1/blqTWExBFpbFbrm1rTC5NvrsDABNCdtc2qhe1Dw8/mUBPrFKKyB+biESehzS8jM/rwyNH143B17bQOn9uYQ8WhiMJxV59r2xgxpGLS6ZxIJsP8W2bWOvwBPiMHx1UK77raLzOTnY99MRIrHr+LJpWnkDGK34CNR1YlsaxNZExsilshZOkYhyMMQzmQqqOPJzaI5cQohjKSyvHwbIshYvBS+dwEy7KsdEKFAYM3P93t5Hq6gfg5bue4L1f+zjZErihLpSMbwCF0g7mTXMRXNdiyyMvjCQUAF4mz6ZHX2Teu47F8ybWglxoIYrqebNIbX291655xXI8owG5mJQT29L4ff1j4n5qADtRP6GbA98PqZ07C+08Nyq5aDi6nZwsYTMuxhicquSYuFNbjdnH8MjJUPvYqdmKxSZ0BNvWuMqgFAToKemNCoJo0gtBOMrQ8dSfRsVSW3bSuvK4Sb2vGFadtNGhh9/fixNPkqytZzDtT+t9RcT+SVIxAa93C8sfy8GyLI3OZrnvB7/BS+dY/O6jWXjCIjrXPEOYy1M1u42TLj2TB37wW/ych5/Ns3nNi8wtgRvqQtt3UqrGzN8BCHJ+SawQlPUNLSedQF37YeR6+qiZP5vIcchOo2FqlSKKDE6iCn9g9HA2O1FF/iB6BrMhLDz3fez+0zpCz6NheTuh6xLJ0tvjYgzgutQuns/ga1sAsOIxmlccTabAPbWBUaOGYaIUbScdRz4aX/Li2Ao7n6FjzTMEmRx1hy+ktv2wgs/9KAQFmH31cBiz51FxsFzXgswQ6V1b90R24/f3Uj3nMAaLPVlMFIUkFeKQskzE07fcj5fOobRm8TuWse13D4zcYad3dGAn4yw8+SheXf0MAFEFTVzz/YAFJw1/9r2fW1uaxe9ajimBZNYYSOUjrNo64vX1ZPwIIzeNZcnzQ5K19fhDA4Tp4aEwzowGcOOEqYnfEPhBRKCg+uilAOSCSBKKCUp7EQ0nHE3TcUsJ8z52MjFmeGQhZL2I+mOPoq79MPL9gyRbm/CMHnevQNyCjf/9wMgSyT3PvIgVc3HmzcEvgTkZb+SjaVh+BN1v6K1INDcQKQsorbKWm5ijyO3sGBULc1m0fK8VS5IKcUgpYxjqHB5yEa9N4A2lxjTZZzt7aFi4CADLsVhw8jK8fYzXno6MgdC2ee/XPs6rq9dCZDj8PcdgMruxVRV21QzSmeJ/F2EYIZsIl7+BlE9V2zzsPTsV+4Fh8CASir2MYVpNyi6G4XH+GmXHxgyPLKS0F6GsGFZLC0N+xHhvsC1Lk+vZPWbPlYHXNtM6bzal1j6d90KqFy8gVj+DwQ1biDc1UHvYfFITnE+htSJugwWgFF5ESUxqLyoD++xCL4VudVEUklSIQ8pYmtnHLmLjH18gn8rh1lSPeU68pQHtOix+9zEsPvVYQtvGTJOJ2uMRROAkYhz9gRPx+noJBndigoBgqI/qRdUTnkQrxP4YY0iVQJIqxjoUc/aMMQQTnPMSRRGx/SyNXei5H4WSzkfYdfXUva2B0MDgQQzTqnY1Ox98jMyuLpRl0fK25STmzSFbwb1xed8Qb5lJZvvmkZhVVU1oJKmoVJJUiEPKDw1HnrUSY2DHM6/RvWEXM08+gY7HnsWEIfHGelpWHEMeRfWi2Xh+WFEJxV6W1vh9HWPGu/tDA9jJiU2iFUKIQjEGVCxG7ZL5DK4fnvthJ+I0r1hOqoRvsIMg4mDT55ij2f3COjK7hvfNMGFI52PPsmjOTJTSFbtoi+eH2PEqqg9rxx/ow4on0YlqmU8xCbatcWw10utbbnVLkgpxSBkD2dBw+FkraX//icO9p67NormzwEREKFK+KfgY4nITRQYnWQVvnkSbPLhJtEIIUShpL6Lh+KNpPu4oQs/HisfJBGbabHL4ZhpDpqN7TDy3ux/d0FSym+kdCplcMLyxYFUTXhQRpMYuNCLGpzrpoLwMfk8vyo0xo7GVoUxQVvVLkgpxyBkDXviGlTfyIa8voDo9L0oT5fkhyZo9k2hTb5hE68QJPWkFEqJUaa2IuRrLUoSRIpfzy661cTyG534olHandO5HKYiUpmpWK7nu3aPi8cZ60kW84XMca88QtuJ+/1Fkpt3qjIea61iQHSKzc8tILBjso3phOwND5ZOoSVIhRIkaSPlUtc7DnvWGSbTSrVx2HEdjMbzHx3TaIV6MZaKI2qQm17kTPwxw65qYkawim4/IF/nGb6pMx4TpzfJeSN3SJeR395Patgvt2LS8/VgCpYvSOxNzLRKuwh/sRzkOdk2N7A1R5lxH4XV2jopFvg++h1KqbHoBJakQokTJJNryVxO3SG3dwcC2XSRntVCzcB6pfPmNkxXjY8KAoQ2vwJ7hm0E6RaJtLrYVI7CcshrGIEZL5SMaV51A68nDP3uRIleE1Z+0ViRsw9BrL49kdDoWp27hErlelDFjQFnW2Ae0ppyWPpakQgghpkDC1fQ8/TwDr24GILV1J5ldXTStPGHP0BExnViWxk+nRhKKvfyhfoyJ4zY1kZWOqrJljCE7qqO4OC0Dcdci2719VBdRlM8NJ7BODGPk3FKO8n5EVetsUpteHYlZVdVEyiqr36kudgGEEGI6shUMrN8yKpbashNL5g1NS8YYtD22nU5ZNkE+j8wXEwWhgH0MczJRRLZzOyaQ3opyFAQReWNTs+Qo4jPnUjV/MfFZC0hlymvIsyQVQggxJQzKetMpVqlJbQxl25p4zB6e1CdKShQZrFgCK/GGPRy0xq1rxKmtxjdyuRWT5/kRsabWUTFl2djxBGE6VTZj78VYuXxIfyrAc2pIhzaDqfJb5EGGPwkhxBTwIkXTsUfR/dTzI7GG5YfjH+RkypoqB7wsQd9unHiS5IwGmZxZYrTjkJi7EHyPMJ/HiiUI8j66ppa8TNI/ZLRWuLbGMHwTPp1utIMgIrAdahYdQb63C2XbxOqbSO/cinZdlOxmXfbKeUEPSSqEEGIK5P2IqsPmUTW7lcyuLhKtTehkkvRBzKeIuRZRqo9cx47hwEAf/sBuquccJiuClZiBIR+tNW6smiAy+NohnMJN4YaXsLVQGLxgfMuL2rbGVQatIDDFmXA8VVxb4YQ+u9euQ1kWDcuPII/Gn+DO4aUskwvxHYvqtjnkd3czuHEdluNSNW8xynaAfLGLKCqUJBVCCDFFMp5B2zGcBfPJhxHRQU7QjjmKzI6uUbEwl0Wr6XOjNJ1EkSGXm/qx7a6jSbqKXNcOojAk2dRKmIiRzu7/2I6tcbwsHQ8/hZ/KUHvYPBqOWcpQrnxbR/fSWuFGARtvv3dkIvPA+s0suuBMJpt625amKjGcvKEUOS8ily/ed+b7/z97bx5jWXbf933OOXd/S+3VVdX7NkvPkENSXDQ0R6LEsSXFlExLph1AMmHCRgQZCgLEhgI4RBz/IRgRA9iyYcCy/zAgJYHFhBMj49gSxJCiZMq0JJKiyBnOdE/ve1XX8rb77nbOyR+vuqpr6e7aXi1d9/NPo3/v1bv3vbud3/b9aZrGEtZHqA2Noo2llRiGozJTUbJ3lE5FSUlJSR8xxmLM9hYfFnpa5TuzS4eCKHDwXAHWYhB0uvqZk3SNAkXr0ltLC+ii06Jy8hyO4z42YxE6cPmNr2F175ycf/s9hKOovPAc6QHPWLiOZO67F1coI1mtaV65gX/mFFm2tetQKUk1ELSvvostchCCcPIEoV+hu4eOhdaGdnywj1nJs0XZOVZSUlKyj3AdhScsnuwtZgDSzBIcmVrxPqda5xmq6BcLmSMAACAASURBVNhRqqEDrQe0Ln6f1qW36F6/RC1SG6o3l1Ig5f6P9jqOpOi01kyfy+Zm8Jz1H+1CCLJme8mheEjr6u1nQpXMIpCuu8YuXWdbDa+hL+neud5zKACspXvnBr53eAUTPE8yWPMYiHr/Bv7h/S1KlikzFSUlJSX7hEDB9FtXuPz738Wr+Lzvr76GW6+Q5RonrFA9+yJ5awEVRAg/pFX2U6xBCFDS0n2wPJ3WZCnJ9F2CoQm6jylLUkpQjVxsmgAW6Ye04mLfZjd6w7LWkbB1nPUURxf/xuJWwjV2f7D2DLgUkOcFQxfOs/DOld40YsAJA2onj9LcRnmXlIIi6a6yWuw2M5AHDSEE1chBCYsQoJMO8Z0bWK2Jjp7CeiHpFrNBJc8GpVNRUlJSsg9wXcXcpZt863/7ypLta//rl/iJ//lz5EjiboEQAjccItUW3S4divWQUmCyZI3dJDHuE3pQapFL59pFTNZrcpWuR+308yy0sr7t63bQ2iCjCBWE6MUFr5AKf2ySRvvxPRUFkpFXXmT2uz8Aeovu8R/+IPEzsBa0FroGTv/cT9K+cRuhFNVjE3S22ShfFAa3WidvLizZhFQIKYFn4IfbIPWqS/fWVXTcBsCJKlRPnKV15V3iO9epnbtQOhWHnNKpKCkpKXkMjiNxBVgBWWH7Kt8qtObqf/reCpspNA8u3WbwhZMURU8ac6t14Y/iOApHWrQVB1q+cD20tqgoWmN36kMUj/mqrqsoWgtLDgWAyTPyxixeMLgjv3k/aHVyasfPYvMUqzUqrNDpFiskVF1X4WCwCDJt6eaW6vNnGXzxLCYvkK5LXIAxW8vIPFSfAkgzvecSx0VhaRUW99gxrGVbGYqHdFPDwORxLJai2UQFAeHRk3T2uLldCIFSEq37L5vrugrdaS45FABF3KHodnAqtXVL8UoOH6VTUbJllJIYY58pDfCSg4frSEJfISWYouhFqndgYRO6AtNs8uB77yA9l7EPvUzquOQbkOzcElISjQwAt1aYo+Haji7Uqr4kuT/D/NWbhOMj1M6epJ0+W1r+SWqonDpP984NTJH3BtANjhA/JusghMDka18zeYYI929/hTGWRjtHSoUQDnrV96v4kvT+NDM/uIxTCRn90MskQtJditwrSLd+PvueInQhmbkD1lIbmyAzCiEkvicxRYGQijTTu97QvJPOsrWWRisnHD1GMNG7v3RSsyH53n5RCR0cYSjiFk5UQePQjvunOCalQLfjNXaTJkjXQ3o+xu7fa6VkdyidipJN40iBi2H+xl2igSr+QGU7z6WSki3juZJAFnSvX8bkGU6lRv3oKRrtfEuLZN+VvRIZKSkaTW7+zteXXmvfuMuZz/4UeZ+e27m2vPhTH+Xun18hbffKWcaeO0r9yCCJgZ24xHxX0vjBe0ulL61rt2hfv82RT75KJ3uGnIpMox2H4MQ5pBBkhaXxhDKmPNdEgyOkj/RhAHhDYwdCarXndK48fq4rSe7c5+4f/PGSrX3zLmd+7idp6u0fayEg9ASt995ejlALQXRkimT2PingD47QvXsbVakRBvU9VUraLtZa4idI9e4mgaeg26R99+aSzR+bIKwM922bea6pDQyRzc2ssLu1AbLGPJWT52h1D+7xLdkZSqeiZFMoJbCdmN/9tS+hF1dXk+8/zSt/48f3eM9KDiNR4NC69C7Y3pK76LRI7t0kHJki3uRisBpImu9c4c7blxh53/N0Z2ZXvG61pnPrHs7kFMXj6mi2gbUWr+rz+v/wWVrTDdzQw48csumbRMfO7MiQO0/C7bcurbDF9x8g7bMXFcgLs+GskrWWpIDq6ecXo+7gj02SabHlsqC9xsEy/YP3VthMlpPMNZDV+razX67rkC3MLTkUQimC0SM0Li07GencLPWzz9G8cpHaucED7VTsJ3xP0r55e4UtfXCf2tBo37ZpjKUQLuHRE6TT9wCLPz6JDCKkCmjGe1/6VrL3lE5FyaZQ1vKd/+sPlxwKgLt/fpWXfzqBkdoe7lnJoygl8SQILDnymaubf4jVxZJD8ZCi0yIa31wDpesqunfu8+A7bwGQd7oo31/zPhUGmD6WCUks6d0rBK6L7Rqydu877JTCqQWEkrA64CoFqyPdh40k1eRK4o8dRwiIc9sX53HXEAIVrHMO+x47MeDbWotwlmVE3doA2cLsyrp6a8gaC7jVOvaAOmf7ESGA1b/nLpQvdroFnlclOHkeQW8Se7u5P4UMSvaGck5FyeawlqS1tq4y7axVWynZGzxH4OddHvynP+b+1/4IHswQec/mpS6UAlauuFVYQW8yYqaEpXXlxtL/m1duMPTiWaS3rHnvDw0QjA71VWLUIBCui8nzpVkC0g/YgWoVADIDYx95/wpb/dxJ9rA0fF+htSFONJ2u3tN6+Z0gLSxjH31l8RrpEU2MoaJwR/pn8lzj1oYQD+dCWLu42l2FECAEQpZzDHaKrLC4A0MrbE61TrFTN4onbTvTtDoFzU6+bwUMSvYOYQ9Yd97sbLtMse0hriOZ/vZF/uz/XK419yKf17/wC1SHa8zMtPZw70oAah5c/tJ/WBG5Ov6TP0JRHdi3mvtbJfAVbhET37kBxiA9n8rJc5tOxXueIrl4eSlTARBNjnP0Rz9KPD2H9Fy8oTqdrL8KUI4jqXgQ3+j1iEjfp3L8LO3U7tgiN3QFMsto37pLMDaMO1CnXTZF7QhjY/vrHug6glAJutOzOFGAqlboZGbHgtpKSWqRg47bWMCrVHrlT4tRdKEUtTPPY62lk9I/kYNDhhBQr3oUzXmKdgMV1fAGR2i0c0ZHq/vqHCw5mEgpGBmpbvrvyvKnXUYIQeSKpRpmIyRxfnAUlPLCMPmh80hHce0/v0U0XOeln3mVnFL1YT/guor2jVtrUuELP7jM0Mc+hH7GAktJqrFeSO3cBbAW5TgstLJNL/yzTDP4wlnaN26TzPa06J0woEBghkcwWNKk/wuiojB0rCQ6+RxSgLaW9g6rzHRzi1Qe3pnTFMaQPgMORehJHGHB9oreurkt1S2BvLDkhUUNj5Bai9nhY621YaGV4TgBUgrSWFM7d4G8MYcQEm9wiLywxIl+5gIae4m10GhleF4dZ6yONuzbeSolh4vSqdhlqr7k7u9/k/juNNCLhk5+8mO0koPzBEwKy+j7zzH20qmeSo4Fswtp15KnY4zFra7V6HerEXa90oRngDQzpFlvwTI2FqL11krx2plh8vVPIIxBSIkGOnuw4C60odnp73aNsZhnZBpw1ZfMfuf7NN69CkDl6AQTP/LRA6HatFv0c0EfeRJZ5OTNmGBogE5XI4JBrIV2o1zo9pMs12TlDMySfUTpVOwirquIb99bcigA4rvTxHemccaPHKimwLzQgGDHir1LdgStDdHoEMHoEMmDeaAXcR963/O0y/rXJ2KMpZNBr0ejPK8PAkpJ8oXmkkMB0Ll9j/b1W7jHjpLnZXS8n0SuYOHP3mLh3StAr9zp5Kd/nNQNysxEyYEn9BX+Yj9iL+NWlBnQp1A6FbuIlIJ4enaNPZmepTo5QbE/JLBLDjjt1DL1+ifQcReT53iD9cUSu/5tUwiB6yqM2duBUCWHC6UE3fsP1ti7d2cYPH6MMojbHxxHEvoSRwn8wRoq8NFJb6r3/f/8bY588lXiMoZRcoCphA505mldvwvW4tQGGJg8UZaZPYVnUxJmn1IUmtrZE2vstbMnDlSWomR/Yxfr8BMnII9qtBKD7mNGKXAEETnJxUvwYIZaIBHPaKlVyf6iKAyV45Nr7NVTx0pFqz7huZKKa0luXqb57vfx6g6nPv1JlO8BPTnm8vIv2Q6hr6hXHKqRg1K7v0wVQuAIQ3L/zlJ/YtFqkC3M4nmlitmTKJ2KXURri6xWOfLqB1GhjxMGHPn4h5CVSl8XfSWHE2v7q1QEvZI+22hw9Y3f5cF33ubO177Jna98g4pXripK+o8xFhEGjH/sA0jXRSjF8PueJ5gYLQM1fSIKFO1rFzFpr3epaDXIm3MMv3wegIHzJylsubQo2RoDNQ+aM8RX3yW7c42qb/Hc3T2flBLouLPGrjstnPLUfiJl+dMuE2cG7/gxTp44CkCGJC5r3UsOKC6Ge9/63gpbd2YOm2UI4ZT1pyV9J84s/snjnD59HIDcQHsXlLoOK1brNYPXik6T6tGjICT186fLJvmSLRH4DtnsfbK5GQB0t6B99SK1cy+R5btXdqS1RUWVNXanWqNfbVpKSZSSFMXBnkxeOhV7QJYbli+P8uZbcrCx6zRkWmNwPIksNBYwyikjx4cA11UoLIbefW63SHNDumtbO9w8OkzvISoIceo1/LC6rx0KIcB1Hay15Pn+3c9ngV4J7OZ6+VwFSXNhpdEYbJ4hxK4MDQd6Wf7CKoKJoyT374I1OPVB3IEROn3oqahVXESeUHTaBNU6Rrm044PZZFs6FSUlJVsmRzLyyovc+fp/WbJ5AzWE59O8fJt3/uOfIKTgpZ9+lcrUKFkZQH5mqQaS5O4081dv4I8OM/jcGdqZOdBRt5K1pJkhnDxO915vHo5wXMKpE7S6el+X8fqeIvQE2cIsQjlU6kO04mLLKlVSCjxXYa0l3YFqAykFUaBwVK90NM0N3X3soD0OpSTVSEGegxRY6dDqFBuaxWUsSN/HrMpKCMfBJru7yO50C4JggOr5IQQ99adGe+cdiih0KObukc31BCfSB/fwxycJoiGS9OAd/3KidsmOsd+myZbsDqEnsK02jYtX8YYGGDh/iub9Bb72xS+teN9f/B9/Hh2GfR30WJ6De4PvSrqXLvPgO28v2YLRISY/9Qk6h8iTPCznX+ArAk+CtVgEna6m2McSslIK6qGgdfmdpXC3cFyqZ17YkppPGCg8YUjnZpCuizc0RjvOKbbhVA3WPLq3rlLEbRCCYHwSKkN0uptbTO/1OThYc+lcvbjkGKiwQnj8NI3W07XYpBTUI0n7ykWs7n1vf/QIoj666d/hoDBYc2ld/P5Ko5BUz1/Y0G/WL8qJ2iUlJXtCN7OoqEb9wx/AGEuqBVe/8f0177vxJ+9w6lMfJsuezYfDYcaVcPv7l1bYkgfzSLs4z6bkmSJJ9YGKovqeIpm5s6J+xhY5Om7jOMGGZLAdR+E6AgS4Nqd95eLSa9n8A6pnXtyy3GjgK7K5aUyegpRgespD1XODu1r2s1183yGbm1mRadDdDibpopT31KyQMZZOYqmcfQG0RihFlptn1qF4PPbA3jVLp6KkpGTbaG2WHhiep6hPjKx5T+3IcF+zFCV7iLVIV2HyVZE1ISkHCZbsC9a599gNnpu1igtph/zBHP7wGMns9IrXbVGgux2U8rdUTuU6AmdwGCeMkK6HTrrEd2+ikxgpwwMzSFAKMNna7iaTpUjPR2/AD80LQ6P18PsejO+9HfLC4tQHKR7pJfGGR0kP6ODOPRPHarfbfPrTn+bWrVt7tQslJSV9IMs0xz/yPLUjQ0u2gaOjHLlwomyOfEZJrWD8o6+ssNXPnmAfl9iXHCLSTOOPTaywCeXgRLWnZil8T2HaC8Q3r5K3GhTdzrpzeITcmgOtlERhaF5+l87Nq7SuvEvR7RBNHsMJKxhzcBaXWW7whkbX2N3aQCnU8RjipCCYOE44dYJw8jj1514iGBnHdeRSf81BYk8yFd/97nf5whe+wLVr1/Zi8yUlm8JRAtdaiiTFCTwKRN9k5Z4VEgOv/Xc/S9LoPYD9ekRiemogJc8eeW4Ix8c5/bM/QefWPYLRIZx6jXZaXigle0+vLFNRO3eBdG4GoRy8odENKex4jiC5u5yZyBbmqBw9Sd5q8vB+Jj0f6YfoLZQ/BZ6ke+c62OVrJZufJRg9QlpsTj3pSTiOwnME2lqyTPelpEprg/F9omOnSB/cR0hFcGSKJN+57/GsYS00WhlRWMMpujTf+wEYg3Q9qifP0UrsgclUwR45FV/60pf4h//wH/Irv/Ire7H5kpIN4zgS2+rwlX/6ZbI4RUjJB//rTzL60unSsXgCxli6gKhVsEBXQ+lQPNt0c4MQLu6pk+TGkJQORck+Ikk1aSbw6uNYC/EGHQALCLkso2uylHRhloHnLpAszCMdF6dapxVvralWStaoHQEYY+imO3PPXC7fmkV6AQMjR7alfPUk2nGB64b4U2ewQCc3BzpL4XkKa+l7lt1zBK2rV5fK9EyeEd++Tjh1inZ8cO6le1L+9Ku/+qt8+MMf3otNl5RsCqU1f/qbv0cW9+pErTH82W//Pk65QN4Q1va3yVApSb3qMlh1GKy5mI0U7Zb0jYf6/1uVFnUcSRg4eN7aWQglJdvFWkuaFpsSi0gySzBxbIXN5Dm5gSIcJHUqLLSyLZ/zeWFxB4dX2IRyEGpnhod6nsJ0GovlW02y2Wk6V9+lGvbvGstzQ7tb0OkWG2qC3494rmSw5uImC/h5m8Gah+pnOZIxax6Wuhv3d5t94MA1am9F4qpk9xgbq+31Luwo3UaH5r25FTajDbbQjD3SM1CyN+gspXXlXUzWi/QFYxOMjE0gnQN3azv0mKKg6LRIZ2fxwoja8BjSdfd6tzbNs3YPLAGjNQPPv0zeaqL8ABWESNcl2KnPj1yklKQLcyjPJ5o6jvR8xoKtbeHRc9DkOc27KxvLTZ4h0eW5+gR0mtC4+NayBPGMy+D5F5Gu15ftmTxHKNWbWL+IU63hOA5jYzt1pvWfA/fkLedU7F/2Wh+7H3gKJt93mtvfeW/J5tdChOM8c9/1oBEGCjt3d8mhAEhm7uEODDM73+3rtnvRI3Ggal33M76vcJIGyb3bAOTNBbLGPMGxszQ7e6fVvlmexXtgSQ8hwHGqmNygkwRIdvTz/WAQ/9gQxsJCu8CYrZ33q8/BauSsOwXdWFGeq48h8B1E494aCeK02SCRUV+yL64rqZw8T3zrKiZLcSpVwqkTzDeSPVnzlnMqSkr6QG4Er3z2RxFScO/716hPjfDhX3idXJRNx3uNEpAla50HnadI6fblRqyUpBY56KQLWFQUbXvoVQn4jiR+sDKaqpMuUpS/67OElAKlJEXRn0bhftLvuvo006Q7P7CZJDNER47SubY8R8ap1pFSUQkFaW4ObIlSvxCwvvy5tesqf+0EeW7oGEl44hxKCorC0uwUBy6IXjoVJSVPwFpLYgQv/dyP8L6ffQ1jQUtVRqj3AbkBpz6Inrn3iFWg/BCT9Se6XYscOteWy622M5W3ZBmLRUix1k3v0wO8ZPepVVyEztBJh0q1TlpYuknZA9VvisKQKZfa+Zco2r3yLel5dG5fRVhLND5Frly6B2iYYb9Jc01t5Aj5wnLps5AKpzpAu4/3+kIbWp2DvbbYU6fiq1/96l5uvqRkQ1hryTQsTQZe5VA4jiT0FUoKssLQTXQ55G0XSFPNwNAYtijIFuaQrkvl2Mm+PRxdV1G0GivKrWyRk80/wIuGyLLD9VAWQuAJ25t8KwVWSLYq+JRmluDIUeKbV5dsTq1eZoCeESqhQz5zh7zRW6QlQHT8DJ4bkPUp+u95Ct/pOappZsgPcTS+p3wFnl9DSU3z4ltLrxXXLlE7d4Ek64+ohhDgeQ5S9OZY7HRATkpB5CuUI9Da0k23LhTxkJ4EsaR67kWy2WmEUnjD44dwsvfmKTMVJSXbwHMloWOIb1zp1UHWBxiYOEGjnR249P5BpNHKCAfHqY5OYKzFCQPSB+2+bEsIgSnWRqlskSMPYUQ9VPDH/+Z3mbnYG2B6/IfO88pnf4TUyk2XU2S5xglCqudepGg1UH4EfkDrAPVTlDwe1xEkjZWCF8m9WwQnz9OPpGKt4mI7DZI79xFSEk4cw/G9Qx2Nt7Z3D8vmZta8ljXnccOdD4w4SlCNHLK5aUyeUxkeQ3sOne7ObKdXjqro3rpGN26jogq1o6dodbfvvCSpJssF3sAEBmi08/KZvgH2bKJ2ScmzQBQo2lcvYbKe5GzRbJBM3ybwS0nM3aKbaBrtnFan6Fu9K0CeF3iDI2vs3vBY36Kt+xXXVdz+zqUlhwLg5rcuMXf5Dr7JcZ3NP1riRNOMLZk/SMe4tOOC0FdUQoXrPv56elinX7KPWWc1Zo3uy/XqOBKymO7dm5g8Q6cJnevv4TtlNZ0xFuH6a+zK8zHG4nmKSuj0GpV34LeqRg7tK++QPpgmb8zTuXoRVaS9Y/QUeo3x8onnSBRI4huXKeJeIEnHHTo33qMS7Mzz1xhLkhakaVE6FBukvBOXlGwRIcAWxYpJqABFq4l7wLSlS56OtT3N+urZF3BrA7jVOtXTz5NpceCa6baLBGav3F1jn7s+zeyfvc1Wn+kP51woCfVQoB/cprh3ncB0qUYrE+tCQL3qUvMskUgZrHl4bvlI248YK1BBuMLWc8Z3/rpxHbmiFv4heauB4xzuYE+Wabyh0RWyqCoIUVGNSujgJg2Ke9cQzWkGqh5Sbv05JqXApEnvGfkI6YP7+E+5TqNQUY8Uge5QD8Waa39p34VYFM1YxqRpKfCwh5TlTyUlW8RaEOvMQ1BhuLrtoqSPSCkIHIESkMddHGfz5TcbJck0uRb4o8dAQDsz6EM4cE9by7EPnefmn15cYZ948QTz3/4uNs+BrS/gokDRurSsEV/EV4mOn8Fx/KVjW4tckjvX0Z1FWUwhqZ19geIQOnn7nXa3oH7yHNnsDCaJcQaGkFGNZnvna5+MsSh/ra6/8sPyvABacUH19HOQ5yAEVjlkhcEuTC+XRsUddKdF9fi57Uk6y7XOg5DyibqJvqeQ3RbtuzeXbWMThJXhNeVrhp5Yhi2W91EoB0sZ1NsryrBOSck2SDNDOHV8Ka8uXY9w8sShrt3dTaQUVF3B9B98k8v/9k2u/rvfw+12tlR+s1G0tsRJQdwtDq0KWFEYBk9NcOG/+hiO7+JVAl75uU9gk5gi7m5raJ3jSIpOe03JTDY/s5SJEEIgTLHsUABYQ/f+bQJvdx5rSgl839lQKcdhxxjLQjNDV4aRY8dJZdQXhwJ60qze0BjSXy7zUdUa+MGhvV4fRWtDo5XTTAXNBJrtHNcRZPMPVr4vTbYV8TfGIhxvVYZK4B+ZIs0efxwCT9K9f3uFLX1wH3+d67qbaCrHTyPkYgBDSqLjp8vn7x5SZipKSrZBN9UEfo3a+ZfAWgyCdvfgaUsfVHwH7v3Rt4jv9iJseTvm5u/8Aac/+1PkB1CoQ0qx6BBZ8sLu6/Mo0XDiR9/PmU+8RNZo0bpyndlvXWHiEx9mO890Y+y6TolwPOzi7yElGL12UWqL/vbVPKTiSXS7TevaLaKJMarjI3S2Kn11iEh3SSGtFedUTpxHLPZtaGTZ9L+KRxUKrQHpOJh81W+0zWupFRfUT5xDx21MkePWBuhmT26iFgIwq15fFWAIfNULHhgD0qN67gJYDUISp5osL6/FvaJ0KkpKtkmSapIyMrInKCC+u3JomikKTLq98pu9wHMEntXMfuv7WKMZeeUCheORFqYny+hKhLVoZF+HcG2GNDNoRxGODOIPVhn7yCtkxpJu46FujAXXR0UVdNwBQChFMDZBo9P73lr3Bg8KqbBm+bfwhkdJ+ywd6ruS9uXrzPzpnwMw/9YlaqePMfKRD/R1uyUbR2u7KhOyP66XnURKgeP0ZiZtW+koMwSTx4lvXFmyeSPj2+55Mcay0MpwnADhhXTaT4/0ZIXFHRgib8wv2VSltiQvHYUOLgXxrevouINQisqp5+hkUBSl47jXlE5FSUnJgUUDwejwCsdCSInyXUj2b7RKiJ6C0sMpvUKALyxXvvy72MUoXfPqLc787E+gHY9QGeb+/AdkjRYD509TmRjra2RcCAh8ByV7Y1mSJ6ifFIWhVQBI2KEFfatTUDt6GlHkGF2ggohOt1gRXe10C6pnXyCZvoPNc7zhUQiq5H2OSHsSbn/37ZX7e/UW4x8tnYqS3aEaOUidU7TnCSo1CIJt9T5kuUb5QW9AXtxBBSEaSTvemXTvZnrcuklB/cgxVBD1hvVVqniDozTaObWKiyxS8uY8/tAocnyS9o0rdG9fIzx6htYhnkWyXyidipKSkgNLWsDEJz7Mrd/9A7JmG+k6TL72EdItPguF6A3qcpQAa9EG2t2dHWboOQJfGJqXr6ICn9rxSXIUjXcvLTkUAFjL/NuXGPnABa79P1+l6MQAdG7f58irH8Q7fqwvaX4pBfWKSzJ9hzRu41SqDIxN0ezku1aOZW0v0iylQAgXvc4U27wwNGOLPzyJEoIkN313KJZ3cHc2U1KymsBXmNY83ek7QK/fwBsaYXB8CoFFpwlDdY9uokk2UW7WTTXdFJQKMV2LtXtTP2ptb/6QFwzgRIPoxWxH4Ct04wHxzL3Fdz7AGxgiPDJF9+6tUlZ6n1A6FSUlJQcWYyxdITn2U59EWINyXeLMbLkEpl51Se7coNtuAr20e/3oKRrrLGq3gpQCt8i4/O9+b6lO2K1VOPnTnyL1vDXvV2FIESdLDsVD5t+6xNTxo+zMXq0kChTdW1coFkuPsizFZBnRxIkdi1xulKc5McZYusnulrZkBobf/zwPvr08lbh6YgpdKs6U7AK+K2kvLax75K0G4fgk7euXexKrQhJNHUf4lU03LT8spfI9haN6csBJurOBlY2QZXrF/c33JO3rK0tds8Y8tdEjOLX6oZ6Yvp8oXbuSkpIDjdaWdmZp5QK3EpJt8eHiOBITtykWHQoA3Wmh240nDl/bDJ4jeovRRx7QeatD8mCe+tnjOOGyFKbyPQafO4VcR1tf+WsdkJ3CkWLJoXhI0Wn1sjclpLmh9twZjv3Eaww+d5rJH/koR/7Ch+mWzaElu0Cvd3rlAt8fHiO+d3t5ZoM1xLevr6uYtBEGqh5OskB+9xp2/i4DVaevmQClBKHv4Ptq073hQgjCyZOl4tM+ocxUlJSUlACeq9CNeI1ddzvIgdrObMSyssTpzSDvrgAAIABJREFUoVlrugWc+sxfpHNnGoyhcmyCuADfcakcm6BzazE6KQTjH/sAmRX0ow7HChbllZb3UyhVTpR9hE5qULVBah8axhhLa5ezJSWHlzS3vcGBs8tReyeqkM3PrnmvzTOEkJvKMgS+Ip+/T/qg9/m6G6M7baqnnqPR3nnHOQoUrtBks3eQjsvAyDjtWFOsaj7PMoM/Ok76SJbGHRgC5dDqlIqL+4XSqSgpKTn0+BLufvsiE89NrHnNHRims0Op9dzAyCsv0r65PI1aBT7B+AitpJfud8bHAWguNpprAUc+8RGKVpus0aIydYTUiv4N+EtNb9bK7WtLtnDyOMkTtOUPI1tR3VFK4lqNyQqkqzBCUv6sJZuhmxTUh8dxogpFq4FTqSH9AKdSJVsxSVwgXA+bbK7PyHMF8SoHxeQZwu78iaqUxLE57auXlmxFu0Ht1HNobdHG0k11r8wx1dQGRqlEVfLmAk61inJ94ns3qY1NEWeylJLdB5RORUlJyZboSRr2plcflCiRlAIpVy7IhRAUcZdv/x9f5SOfe53RExMUzQdgIRg7glEeequd36vQ2mCiiFOf+UvMv3URJwoZevEcnUekG1c7C9ZCOzXIoIKMqrRyQz87hdNMI/2I2nMvY9IU6fukmSEtywu2hRDgWc0f/NMv055pAHDmtffx3E9+lHLERclmaLZzHCfAGYxIjCWygmBsAlPkFO0WQjlER09uKRDQm1nhovWq611KNivN6zgSKQV5rtfNdPqeJJ2+v7wJ16N67DTduzcoOm1UVKE+eYJWrNHa0Ork+L5HMDxK9+7NJcnpVrNJ7fyF0qnYB5RORUlJyaapVRxEkVN0GgTVGka6u97EuxmEeDiwrEPW6lCbGCM1gqwwKCWYvdrLHPzJb36FEx99gbOfeAk38jBhjXiHv1eaW6TyqP/Q+7EWmhtcrBuze8PwekowGikVJnt8pNNxJKEvkUKQF5buE6RnDzuuFPzg//3mkkMBcOUPv8eZ196HiKJdb4QtOdgUhVkKQDQLTRg4REdPIUTvXhEnhmwLgYBuZqlMnVjMHvTOSW94lLzY+PkphKBedTFxG5OkRPVBkpw185ysZdFZ6RGMTxLfvbnU01W0msT5ZaJjZ2jHBmtBSUFy/86SQ9H7IEPRaeM4Yd8yuCUbo3QqSkpKNkUUOBTzM0s1venMXfyxCcLqCN1kfzoWkSuZ/safLpUdCSk58ekfw/EjtLYMn1oue7rxx+9w44/f4aWfeZWjr77cl/0xxh6IyP+TnBjfVQSqIL55FZNluANDDIxPsbBDSlnPHMbQuL227r11f57a2Qpal05FycYRAjzPQdDLLsbdgrgLY2M15mZaW/7cotAkUlF77iV0N0Z6/qZnVtQqDt2bV9Dd3sI/uX+HyqnzFI6zYtGfZpr6+CStVgOsRfnBGpEInXRxlaAeCITjUGgwztqlq3RdzDaH9ZVsn1L9qaSkZFN4riCbnVlhSx/cx3f3rzqQKPIVfQzWGKa/+Wd4wmKtxamEvPxXPo5aVHmaev8ZTr36UilT+ATCQNG+dgmTJmAN+cIs6ew9Ar+MVa2HVYpjP3R+hU1IwfCpiW1PRC5Ziecq6lWXwZpLFDqbVhTa77iOZKDqotoziOZ9BiKJ7y2rxEkpCHwH39u8mhJAmhkWWjmx9Wh2zaYcCiFAGL3kUDwkuX8H31255DTG0s0EtfMvEUwcQygHscphEFJhsoz2lXdoXXobZXOC8SmEXP6+KqwgXP/AlOE+y5R3/5KSki2w6ua9j0s3hACdr30o6nQ5op4amPrYBU589AWstVgh6ZaR48cihMBk6ZrjXrQaBIPjJHu0X/uZvDAc+/DzJI0OV//oLYJaxAf+xifRUkLpU+wYga9wTUJ89Qa2KHDrgwxMHH9iBs11JFGgEFgQgm5qSDcxOG63qYSK1ntvLym0ZXOz1M69SF4IjNbUAkE2dw+pFAPD47S7ektlQVvLnoleY8ZqrFnXwUlzTZprXK+OLiA6eorOjcu9e4sQRFPHSOdmlj4jvnWN6OR5qucuoJMOQjngeDQ7+zNLfth4qlPxxhtvcOfOHV5//XVeeOGFJftv/MZv8Iu/+It93bmSkpL9R15Y3IEh8sb8ks0dHNm3TXLWghOFOFFAES8vd4dePEfBsixrri05gt5DcW/29aBgrUW67hq78kMcRzJYc8kLS6dbPugfpVtYTn/qQ5z9sQ9gAS1VmQ3bYQJP0rp4Zen/eXMB6fkE1RF6gWxBni/3/iglqXjQvvoOtih6C9mjpxBeuKmJ1NAbGOe7AmvpTXjvwz3RdRV5a2GF5DNY0tn7+EMTmDShffkHS69k87NUz17YtbJEay04LtL1MPnyNv3RIyRP+D3yXJPnYD2P2vmXsTpHuS7J9F2yR541JksRQrDQylDKx2qL2aTCVUn/eGL50xe/+EXeeOMNZmdn+dznPsebb7659Nrv/M7v9H3nSkpK9h9xUuAfOUY4dQJ3YIjw6En88SnifazVHxeWkz/9OoPPnyGaHGfyRz9KdOrYjjhCQvQalveyxMJ1JRVPUPXlmhKD1TiOInQFoSu2NdAqK8Afn1r6v3Q9wiNTtK68Q+vi99Gzd6lX+zek76CSFZbECFLTP1ngw4qUYnkA3COYPCPyFW6ygBPPMlB18Ravk9CXxLev9RwKAGuJb18j8Dd3bdQqLk7aIL52keTmewQ2JQx2ZmjmaoRYZ9+ExFGS7vTdFWarNUWniePsXrV7O9ZUTj+PPzaBNzBE5dR5jF/ZkJOVZpqFVkYjthTakreaK1536gNLjrjWB0d58LDwxEzF17/+dd544w08z+Ozn/0sf/tv/23Gxsb44R/+4VKpoqTkkGItNFoZrltFDdVIjSXf5825WlvaBmqvvITEkltBZwd0PD0JZDlzl+4xeGwMFQUblgcVAsLAwXMExvbmQ2T55h2zwBWY+Xlu/efvoNOMwRfOMPTy8+sOZAtdiZ6fY/q7P0A6itEPvw/jR6RbWNzGSUFUGaL23DBYixDQuXkVm/eihnljDrdW3xNFFqUEjqMwxpJv4TfdDyglCTyJlL3s4GrlnJK1GGNRUbDSKAThkUma772NXZRJTR/cp3buAvmi+tsaR8Ta9Ut4HoPjSEhjknu3e38OxDevUD13gUSIHV0v5bmmUhtAOM6yIyQk/sg4aaERcq3zsK4T0ke0Niy0MvxoGFERdAqzJVnuuFtQPXWe7t0b6G4Xp1YnGD9Ko11mJvYrT3QqpJR4Xi/SdOHCBX7t136Nv/f3/h6//du/jXjWOp9KSnYRpeTSjIeD2qSZ55qDdGu3FtKlSNn2H/KuI5h9+xp/+ltfWbJd+Msf4/jHX97QQLOBqkdy/xatxjzCcQgnT6D8gO4mF4+uNVz+vf+09P+5772LW6vgHju2YkGtlMTGbW498t7Om1/lzF/7KTIhttQWEycFcQK+7yCb0+juyonkRaeFGqjsqlNRiRyUyckXZnCDiEptkGYnP1ARTdeVVFzo3r2GfqisNXKExj533vcDWWEJjhwlmb4D1uIPjZC3WksOBQDWks5O49XHKQqLU61TtJcj4kI5WDY+l8F1JPns3Bp70Wrg+AM77ti245zq2RfJmwtgNO7AMHGiKbRlcHyyVy60eEFL10VFVYodOHekFESBwlECSy8Q8qTek+32pRTa0ow14fgJfNkrUW20s/3cwnfoeaL7evLkSX7913+d2dmeDN5rr73G3/k7f4fPf/7zzM2tvYBKSkqeTq3iEskM2Zwmkhn1ytra9K2glMCXlkAYAmlxtlHaUvJ0lDF898t/uML2zu/8CWoDDovvK7K56aW+FFsUxDev4HubO2aOI4nvz6yxt67ewlnV/esqwcIPLq98o7W0rt3CdbdXplEUBrc2sMKmwgh/eBy5iwEoz1WIpE3n6kWy+Vm6d28S37xMNTxYmiSVwKF19V2KuIMtcrLZafK5aQK/P+U0zxJxojHhALXzL1E7/xLu6NRjMwWC3kyWcOokTrUOgApCqqfOb6qc0xiLDMI1dhWEfXFmC21ZaGZkbo08GGShlZPlvVIg6Xk9NaUjU4RTJ6iceYHWDszaEQLqFZf83nVaF79P+723cYtO30q8HmJMrzer2SnoJusP0SvZPzzxCfaP/tE/4tatW3z7299esn3+85/nb/2tv0WrtXUd5JKSw0pvxsN94huXyeZmiG9cJp+7RxRsb9EjpcDVmv/yG/+e//iFf8PX/pd/S3p/FkeWGcV+IYCiuzL6Z7TBmqdH5R3JisjoQ3Q3RqmNHzNjLP7QwBp7MDKIWXV7N4Bbrax5r1utbHvho7XBugH+2MRio+tJgrEJkpm7iNYMgzVvW/0bG8X3BOmqmnLdjZEHSF5JCIHNs1WNuJA35nE3cW4cZrqpZqGVs9AuaLRS3PrQCglShOiVC2UaYyzNTo4zfpzqcy/jHz1DO2NTDfRppvGGRlH+cumVU6uDF/Q1E53nmmxVNkBIxUIrJw8GSZ0qC83sqfuglKRWcRisutQr7rr9F76nSGfuUnTaPYMxdG9ff2oPV8nh4okrmeHhYb74xS+usf/8z/88f/2v//W+7VRJybOK5wpasw9W2LK5B9RGJ4i3ocPpYPnW//4V5m/0BtIlzZg/+pdv8pf+p7+5qHBU8iiOI/FEbyGd2a01zGohOPZD57n5pxeXbCNnJ7FSPVUiVJuetvrqWm7lB5h4cxFSEYQMPH+Gxrs9xRt/qM7w+56ntaqMKss0Qy+eo3HpGkXc264/PEA4MbZu/8VmaXVywsowteExdKdJ58YjCjyNeaqnn6PR6vPi3sK6HfP7rFzXcxWOI9DrDEG01q7R6geQvs8BquDaV3S6BdVzL5LNPwBr8IbGiFOzlMF4GA3fDkVhqJ46D9ZghaTQllZn7wpEVzsbj0MpQS2UxDevoJMu0vWoHD9DjFzhWDlKkMY9h8IbGsEfHAHZk49VSpTDG0uADUjK/rN/9s/4yEc+wquvvgrAr/zKr3DixAl++Zd/ue87V1JSsjEklgfv3VlhK9KcIs3BLRV4HiV0JcXcHHe//X2wMPqhlwhHhuluchprbuD9P/cj1CdHuPf2NUbPTnHuxz5AYpZlah9HmmkGxibR3U7PsRCCYHyS3Gy+t6GTGQZfeYnRD1zoZUmUop3ZdT+nU8DJv/I62UIL6SicSkRnIw0gG6SbapQSZDP3V9hNnkGR96LwfaxfSHNLMD5JfOvakk1FFbTdP07FQNWjaC9QzC6gwojBkXGa7ZU9H7nuSXCmD3q/o1CKcOI4zW7ZrL0V8sKw0DJ40QhCQKNT7GgZTa3iUMzepzHfCxipMCI6cfZAlOqEviK+dW0pwGHyjM7196iceYFGe/neUGiLU6miBodBSlrX3wNjcOuD1J4yB6Tk8PBEp+Jf/+t/zTe+8Q0+85nPLNl+4Rd+gV/91V+lUqnw+c9/vu87WFLyLJHlFm94hGxuOVvhDY2SFdt7+lgEI6cnmLl0e8mmXAfHd9mn4yP2BCkFIk24/ZVvLNlu/39/xKmfeR3pBpsqA7K2J1V79OMvc+xjL4JSxIVhI03g1kKzk1M5dgYlACFIM0N3i9HS7tJBFvCErIvWhpYGGVV7f7cDClirsRaQ69RZC0m/p7xlucYNK1TPvEDenEP6EapSo7lP1GLCwCGbvUe2OMyr6LQoOi0qR0/TemR4V6dbUKmPUhsew+oCoRw6XX2gms33I1m283NTpBRIXfSyIIvobkw2O4NfHV6TidpvOErQXTX92uqiNwjwEdJMMzA6CTqndfmdJXveXEAGEX44uK8HBpbsDk8shnvzzTf5V//qX3HixIkl2/vf/37+xb/4F7zxxht937mSkmeNOClwRyaITpzBGxohOn4Gd3SCeJup9xzBD/3N16lPDgPgVQJe/W/+MvmTL/FDh+sqGu9dW2NvXLq25WblvDBkVpBtsoTKGEurU7DQLlho5ZtWfdoOxti+LVDT3BBOHF1hU1EVK9SuRG473YJWCro6RiIjGq1s30ige65YsfiExT6adRIpnW7vvGh2ba9GvpxpsS+RUq47G0MnnXWP6/LfCaLAoRo5BP7eCQlobVGrmsyFUthVJYPWQifR6HRtna5uN1GlhkAJT8lUKKUYGFjbBDg6Oooqz6CSkqfiKIFjLbbQCEdSCEmzneM4Pmpggq42FDsQRTXGUjgeH//lz4A2CCXRQpKXda4reFxjszdU35dRYCHAdR2sPTjzForCkCqH2vmXyFsNpOcj/ZBmZ/emaxtjSbegi78ZKqGD6wiwFm3FhmryrV1csBWr3vuEno994g+VPAatNU6lusbu1odIH3P/VUpSixTJvVvkSRenNsDgyJE9kUuNU0Pt2Gk619/D5BlCOUTHT9Ndp8+qKDQyDBGuSzg2gQoirC7QRb6vSgxL9o6nusdZli3NqnjUVqy+KZaUlKxAKYGeb/GHv/EmSTMmGKjwF37pZ1D1KkVhdly7X2uDRoB42ChcrkZWk+ea2vEp/OFB0rkFAPyhAWonj9HcZxPBPUfgC0vj4ntIz6V+5jid3B6Ihsgk1aQZOF7PWdP7pPxop6hVXPIHd0gWetLqKgipnzj31L9LMkM4cWxFz4c3PEa2yX6ekv2DtZBqQXTsNN17t7Ba4w2PIit18sec95VQ0bl2CZOlAGSz01hdEA5NEie7u7bS2tBOBNHJ55DCYhF0HzOI01oorKR2+jni2zco7txEOC6V46dwXUGWywM7d6lkZxD2CXnhX//1X6fdbvMP/sE/WBp2Z63lH//jf4wxhi984Qu7tqMPmZ1t78uIYgmMjdWYmSmlhh8SSMvXfu23SRrL9arRSJ0f/e//2mIzb8lDhADPU0jRmx78OIfLcSS+tEgB2kKqWbHI3sg5KKUgcgU2TbEWZOAT5/0rB9oKQggqUnP1//5d7OJDWoU+pz/zl2gmh+ehLQQEfm/YltaWJDObPk5KSazdueMrpaDqGTpXL66w+2MTREemeDDbecxf9ogChaegiNuoIEJLRZoZXCUxtpycfVDxXEXgSYSALDdPLGccrDq0Lr210igE1fMv0WhtzwHv93M4ChzM7O3e4L2HCEH97AsUVu7ITIySvUdKwcjI2gzc03hipuKXfumX+Lt/9+/yqU99ildeeQVjDN/73vc4c+YM//yf//Mt72xJyWHAarPCoQCIZ5v0dCFLp+IhvVIAh3T2PjZLiYZGMVFAe9XDyXEkfpFx+6t/RNZoEY4NM/Xjr9KxYlMLRmMs7dQihAsCbB+albeL7wpmv/POkkMBoLspnVv3cCYmKYqdXXj6vkKJ3sTafJ909kspqFdckunbJJ0WMqxQnzhGKy42lK3xXEkUKHTcQXoeVrm04nzb5SVKSXSy1nEw3Rhrn/7bxYmmK0CpCia1VCOJX7TIZ+eRQcjgyJEDNwG8pCcSsF50f13WKXeTrrenx1wIgZQ89dpyFMQPZ1U8xFpMUaA8v497WHIQeKJT4Xkef//v/32+8pWv9CJni4pPH/jAB3Zr/0pKDixCSSojdTqzy0POakeGetre+2Pdti+oRQ7tK+9gi16ELm81CI+exHWjFQvcQMGNf/91im6vUbA7M8edr32TIz/2KvEW1Az3c626RbDeUAJre1maneLhwj2bm0YnMX59iLBa3xdqSaGv6N65RtHuRV1NvkCcpUTHzqxQSloPpSSha3vR4MUD7Vbr1KdO0txm3XpRaCqVGqvbVZ3VA9aegLW93pPAdygWZkhn7vVe6LQo2k2qx8/R3MMZByU7g1IC31W97EWx3BeV5obgyBTJ/UUZcCEIp070RY3taQgB1chF2gKT56goIk4KsscEF7QBJ4zIVwzvFEjHKXv4Sp4sDfPlL3+Zz33uc3z961/nN3/zNzl79mzpUJSUbJAcycd/6ad7jgRQnxzm1V/8NMUGFx6HASkFJk+XHIqHZLPT+Kunumq95FA8pDs9i9png812grwwDL/ywoqIpvI9qscmd7Rhuxo5xNcvkT64T9Fu0b1zg2LhwZbVaJSSBL6zZSWtR3EdseRQPEQn3SVFHaUEVU9Qc6Hmy17T9CKBJ0nu3VrhOebtJkLnDFQUgb/1/bOLZXfR8dNI1wUp8UePICu1pTLhjeK5Ykle9iEmTZCiXJwddHxXUfXBzNwkv3eNwHapRr3rqptobDRE7fxLVE6dp3b+JVLrbkvhSwhBFChMnlONnHWnYq9HNXLJpm/RvvwO8Y3LtC69ReT2rq/16KaacOoE8uH0cCmJjh4HqXZVwa5kf/LEJ8dv/dZv8eabb3LkyBG+853v8E/+yT/htdde2619Kyk50GhjcSoRf+G//asIwAoohEKX0pBLWGsRcu3DT0i1ps1cKIV0XUy+7ID4g3XMfk45bBFjLLnjcObnfpL5t99Deg5DL5xlE8O2N4TErpGIzOZmiAZHSdLNfVa14iDzlHxhDi+MqNSGtlXGYywIx1mplCQkCNHLRFBw8z/8IXmrjfI9jv74x6FaIy8MQrBWYQmweUbnzk0qJ86Sq603lXYTjeeGhCefR4je0L1mO2csDDb1OT01KAerVx3YZ9BRPmyEgaR16QdLjm0cX6Vy8hyO41IUhjgpiAEpFSbdXlZKCBiouiT3brLQaqD8gMrRk8RCPrGcUQiQGIpH+yOsoXv/FsH4iXUVzYyxNGNN9cQ5pAAhe5Phm7E+ECISJf3lqa7skSNHAPjgBz/I/Px833eopORZoigMqRUkVpAaUSpjrMJasNJBRZVHrIJg4ijJqknPiYajn/o40nMBcKKAqR97lfQZbXrPCkvHKKrvv0D0wnM008c3sG+ZdRavQqpNz3XwPYVtL9C5/h7ZwhzJ3VvEt65QCbeuv5+khujoKR7tPwqnjtNNDb6y3Pn9b5K3erXdOs249ZVvECwmILLC4g2PrfxeykG4LrbISWfu4LvbO2+yXNPs5DTaOckW5WuTVBNOHFthcweHyzKSA47jSIp2c02NZTY3g7cqg7BVp9txJKHv4LmK0HdI7t/qNU9bi066dK5eohKszcgJIQgDRTVUBL6zJksMYPL8iX6t1oZGO2e+lTPXyGi08vLZVgI8JVOxOpVbzqYoKSnZaVqdgvrR09g0QecpbrVOkln0quhtXhjcWp3TP/uTvciuUiSanV9o7yOs7e+8hVzb3iJ2URoVIPj/2XuTHzm2Pb/vc86JOTKz5plDkZfkvfe9J3X3g+TXathtyDDUfpYXAtwwGhAgQXtpoa3+AS0lQAstpb1hwXYvNLTbgBduCbD8umW94d7LS17OQxVryIzMmM85XkQxWVlVJKtYxSoO8QEIok5mRkRmRkac3/n9ft/vyqVDAd3b8F1J+vj5xJhOR6hTlPGUlUZ4Ht1bP8FUBdL1KEpDUWi6viR/MbnIZapqb8VfUJYaP54iWpOUO1tIzyOYWyR9+hDYm+t9ANmAqjY4vk/35o+pRwnKDzHKJWn7KT5qrG0arw8iHBdLI0mshAUhKCpLdkIZ2W7sQpFS7ezgBhH+zBxJlk4eg9GHMmBjf4yNJ5RZitOdwplfaoLtfRlgb2aesm4D25aTc6JlpJPWi7a0tLS8DWst/WGFUi7S9RgNmxusEI3BmKNeGozBMNUk9Z561iccTJwXo7SmO7+KP7OAzjOcTpeislTvUhv9Hu4PRakpSo0QApu/mvRoawmX5sieb43HlO8hlBqfF8mownUiOpd7FDsvSO59j9XNuRUsLDM8YeD0vsgKTV7uqUGVFmPagOJjR2uDCANUGKOzRilMKIdgcQUBmLqk2t0l39rAn18m7s4eyzwRGoll3d+i2HwKQNXfoUp2iVYvM7z3/cRzhVLsVwWJA8Xo/m1M0dQ26iLH1jXd61+RPX2IqUq86TlkZ4rRByDW0PLx8cag4ttvv+WnP/3p+O88z/npT3/a1EELwS9+8Yv3foAtHxeuq5BSUFW6lURsORFaG/YvrHVjl+LZQ7KkD4CKO0ytXWM3eQepp5bXkowqpBRIJ0aP6ndSRsorQ7C4Svb4/njM6fTOLO47eEx5Dav/9e/y+E//b/KtXdxOxOp/89fY71/40vHaWkMwM48QElPmeLOLlFocyoRdJC/VoFo+HQajmu6la4i6whqNCkKqpE/+/DHWGPzZeTpXv2D04Ac6M3MEvqIo9Vt/f74rGW1tTIzpdITygr3+nBoQhCuXKA4EzlLYcUDxkrK/jb+4ipxbQwlLWUPZBhQt78gbg4o/+ZM/Oa/jaPnIkVJQpRn1w4eUuwlTt65hfJ+8dYpteQccR2KLjHovoADQoyF1sovrds9UAeldkFLgOwJhLTXitfKLHwvGnM4criw1btihc/0rqsEOKoyRQfTeZFGNsaRCsvLf/pdIGu/43IjxxLxxvH5KvttkMlQUE1++TlYYklxjzMf9fbWcHUpJjLEn7iN6G9Y2zftSCoRw6dQ12ZMH48eLrU2UH9D74ivy7Q0kMDW7SJrrN15PLBwpS26FoHvja4Q1ICQWKA9mP47yx3Dc5vd0zk7eLZ8mbwwq1tbWzus4Wj5yYk9w74//T8p+IwG585vvufQ3/ivc6ZkLnwC2fHxIKdGjwwZjOhuh/B4XuY7mOILAajb+7C+oRinTt67TWb/M8DOXUxxlNVIKnHie0hjq97zaqbVhNPGRN5NCKQWiLql2X5VG6XREsbOFCafbDGoLAJ4niXyFzlJk6GHE++llMcbiupJ62D/0WJUMMGVF8aLJPBRbL+je/BFVbV6bschLQ7i0RrovK+j2prF1hTWG4b3bYC1CKuL1mxgrx8F2WVn8hZVx6RRAtHoZVOME/gkK6bWcM8cTMm5peQNCCOpRNg4oXvLiF7/EbV3eWt6Buta4valD405vhvqCVUZCR3Dvf/s/GD58SrHd5/l/+HOGPzzAc9vLqTEWrCXwJFHoIM/Sqe+YNI7X6aFxk42DCV2wAAAgAElEQVRQ7VfUwp45otOYI6YP7zK88w3VxuOxj8RZo7VBhfGhcRXF6HKfpLM1lDsvcN3J49jfz1qWGifu0r12k2BhmfjyNfyZOfLtTaTrNOOLK1gs6eMfCP1XJ32a17jTc/RufE18aZ3eF19RDvrkT+4TnUKpraXlJe0ltuVMOLJHU4hDXgMtLcfBGEuNQ7hypZECVYpgaRW88EJrz6UUlLvJhFcGQP+7H3A+grNdSkEcOnRjhzBwzry3utdxccsB5eO76M2H9EKJe87BVl0bnLh7aNzpTVN/3smklj0CT5I/PWCOONjBeU+mg8ZYrOPhzcyNx5yogzc1QzU4mMHYJ6EcOEx3Xbq+Ybrr4XuNAqe1luHDe+g8Jdt4SjUc4HV6JHdvk9y9jSkLuus3MWWJOhDYCwGDH74j23jC4O63lDsvqJM+7mvM7lpaTsKFhKZ//Md/zD//5/+cuq75u3/37/K3//bfvojDaDkjrLWoMMSf6VHsDMbjCz/9MZWVQHsnbzk5o6zG9zpE178CoKwMowuW2rTW4oT+oXEnDj/4kMJRgk6oyJ4+3FN66jG1uEp/WJ5J2YPnKnSy2zhZA+QZyegbujd+xO459pxYa6mMIly7Sv5sryl2bgEZ9aiGbZN/y15LwhH+DFbvKY29hzqgZFQRzyzTXVgBoDYWi9g7mL39SYk3M0eaVAS+QuYDkh8aGWSEIL56A+M4aAvSD6iSAQiBP73O4M43432Vu9tI1yVYXKU6IA1rLWAsRre/hZaz59yDiufPn/NP/sk/4V/9q3+F53n80R/9ET/72c+4cePGeR9KyxkyqixX/+Zfp//DI6rdhKlb62jXp277KVpOwUtJ0Q8FawHPo3vtEskPzeRZug6LP/ttsg/nMI+kE7mMfvhmnGWpdrfAGsK5VdJjylm+Cc8RlBtbk4PGYIocKZ1z7WVI8xrPi4muf4UQUJaGwbAk8BWeK7HWkpfmjW7DLZ8uZW3xZubJnz8ej43NEfPjLVx4nkJJqGtLdczs6UHZWNeRdG/8iKrf+MS4U7OM9i4kgSdJ7j969WRryR7fJ7x6iySt6K1exeQppq7Q1eEAoRomxFe+oH+gt6moDMHiMvnzJ6/ey+xC60vRciace1DxZ3/2Z/zu7/4u09PTAPzBH/wB/+bf/Bv+/t//++d9KC1niDEWNwpx1tbwLguySmPaG3bLJ8ioNMz/F7/D/O/8mDrN8Wd6ZDWYD1QSVEpBx5Ogq0NlW9Vgl87i2QhyGEC4LuTZxLhwXOwFXAvKUlPuC0h7HZd69wXp9guEkgTLl3D8gOwzb7A/b0Jf4XsSjMEKSZrrY0/Kz4qi1Pi9GUIpKXe3kJ5PsLjKMH37uSCEYKrjUvW30OkIvztF2OkxeAdhgqo27CYGL2jmQ6Nk3zasPdQ5baoSKZvh/rDCcXykF+B6Yp+cbIMKI/LSHArm80LT6czQibpUowFO1ME6fmu42HImnHtPxcbGBgsLC+O/FxcXef78+Rte0fIxUVWaoqhbhZWWT5pRaUhxqOIug9yc+6ToJESu4OG//b/QZaNfvx/p+ZgzKvXIC024dAnkq9uK053GCHnhqjKuIzFpQrH5DKtrTFmSPriL74oPwVj7syEM9kp6vvslyfe/ZnT3G2JfoC6gg34wrCjdLu7KNcTsCoNUH0sEohMq0kc/kD9/QpX0yZ48oNp+Thi8+xrtwQDYcSRIifQmSy2d3vRERsFzBLEn0NmIzvqNRskJUEGIP79CXhydgRymNUkpqMMZRrVqA4qWM+PcMxXGmAklg5dGesdlbq7zPg6r5YxYWDjcINnScp68z3PQWouta8AiHPdE166LIt/apdju0//uHp3LSxQvnjUPCEl8aR03Cgmis9mXtYbpL39CnedIx0G6LtJx37r9l5+rNRqkREiFVOpsDgowumZ4//GhcT1KmJ9fPLP9QHsNfBO6LOn/8Kqkx+rGu2F6/QbSuVj1oePOLHRZkKbDibFy+wXTiyt0uuGpj8Nojc5Sio0ndK5cJ3v+ZNwDFS2vIV2XuAPWGMr+NoMf7o1fGyws07v1E4SUKM9jPjjc/9XS8j4591/x8vIy//E//sfx35ubmywuHv+ivrU1bFfBP1AWFrpsbiZvf2JLy3vifZ6DYaBwddE44lqLP78I4RTD9MNd5RMCor00wYv/9A1C/ZipGzewxuDEMaOspnwPn5eUEltorNVA/sbnKiXpBoLhvdvYugIhCFcuo73OmZUm+b5CBSH1cDAxLvzgTO8p7TXwzUxFhzMSusioyprBTnbEKz48prvuoTEhJVVtGOye7LtvvDIk5fYLEAJvZh6MJrn7LdD4WARzC4Qrl8kry3Y/J/QrPKfJsKVPHk5sL998jtubxhjJdr84apctLcdCSvFOi/jnnnP8vd/7Pf79v//3bG9vk2UZ/+7f/Tt+//d//7wPo6WlpeXYCAG+gnrYJ1y9TLR6GZ2OkHXelCp8oFgLwvcI5pqa7c1f/Irv/+d/S94fkaT1e3MCbxyKj/fc0JNkT+43AcXeQWdPHjZ192dEUWi82UWUH4zH3KkZrPLaRapzRCgHISczUE53muqCvWdOQlUbvNn5ibFgaY2iPNl7EAIiT5Lc/jXFi+cUm88oNp81AcYetq7Inj+h2NrA2EZhTZZDktu/ajJ7+mDQbZt/1iDE3j4Ch17HJQ6dCykza/m8OPdMxdLSEv/wH/5D/s7f+TtUVcUf/uEf8pf/8l8+78NoaWlpOTauq5obteMyun8XBATzywiaev2L9M54G2llWfsbv8/o4ROKnT5TN9exnk/2gQgpSCWo84Or1BZrzvb4BqOKzpUbSCwIQV3btpb8nBnlNfG1m2RPHqCLHLc7RbAna/w+cB1JFCgEjXzrWTSFjzJNd3YZd2oWnaU4cZfaCooTyr95nkOxtTHRjG3rChUfXh0WXhP8Rr5k+LApH6uGA7zpWcrd7fHznCjGVCXCj4GaqY5L/vwRaTJABSHd1SsMc3nhBqItny7Cvg9B5vdIW/704dKm/t8dKQWu2zS0VpW+8MbWj5X3dQ7GsYdTpQzv35kY71y7Sa0CRqMPX/PddRVSCqpKf1DX0ChwMFuPqQa74zEhFZ0bX7ObfFyT/vYa+HaUkoS+RElBVVuyon4v1zvXkUSuZfTge2xdIxyH+MoN0kqcibCClE2DeV2bd/K18H0HmWxSbm3sGxX0bv2I4Q+3MXsysdLziddvsZuUTHddku9++fIA6K7foBom1MMEFUaNH4tS7CYVvicxLw78rhyH+NpXh2RmW1oO8q7lT60ve0vLBeM7AkdX7Pz5bZTvMv31TTIjPujV74tCSoHjSLS26HNebSv7u4fGqqQPU8ERz26O1XMVxtoJZZeLovpAPWOyQjO1fBmLpR70UX5AeGmdUf5hHm/L6dDaMEzf/283DBSje9/uCSuArWtGD+8QrX9JNTz9/o2xGPPu52hZ1kzNLTTlTrY5HiElViiia19iy6YXSXgByV7fVlVbnE6v6Q0yhuTubfyFJcJL69RGkBaa3pSH1gWe61DHHaTrUe5uYbVugqsP3qaz5WOmDSpaWi4QKQVOXfLD//on4zT4zjd3uf4//ncMTu9H9kkRhw4Ommq4QxDEEAbvpA3/LpSlJohiyt1Jczcn7JCWh7+oOHRwbE25+wzXC4imZxkMqw8qQ/ChYK2lP6wI5y4RLF/GGMuoMG1Q3XIqJGAP+LLYqjpVI6kQAs9T2BMsFLwuo2EtpLmhe/NHlDsvEFI25ndpRVUb5F7viSleZUHTXDO1epVye4N6OEDFXbyZBQajyWvLVNej6m9T9XdQfkh3/SbDR/cwZUGrodzyPmmDipaWC8RzBFv/z28m6mpNWTF89Izo8hre3i+01pZRpt8pzf4p4HsKkScMnzwAoADc3gzx/Oohl9r3QVVp4t5UUz89aspb3O4UIoypk8nSJ9eRyColffaYYGEZFYTYIqMbh/STD79M6iKw1pLm9duEolo+U6QUJw7Ijd3zYSlfqSBJz8cAncjBUc3kOi8N+TFUxgJfEThQ7mwiXI+oN0OS1m/MmHZjF6kr6mxAFHepTGP295Kyajxu3GgOmDS/O+r9WmvZTUqCeA63N4c2gv6wnCgfM0ZTbj2j3NoEQGcpdTpsxCXK4sQN5S0tJ6ENKlpa9tGU1yi0NudSXmOtQByhxx8tzkK6Q/L8Cdgm5T21epXdIyalgStxJYCltoLsE7xp+J4kffRkYqwa7BAsn40b9HHoJyXx8hWivclIpS2DIxpMfU9SPn9B58p10qePqNMh0vOIL13D8yTlJ/j9tLS8D+JQ4SqBLnOUHx47AABI85rOlS9IH95FFznKD4guX0dIQfH4Hlk6BCEJllaJwqkmqH0NSkl8qUm+/3Y8Vm5t0L12i93k1e858J2x3KsFqq1JNadw7Qq+16HYl+WwtimFOgn5m7IkWlPtbE8MmbJAej4lXusg3/JeaYOKlpY9Qk8gspzkzhPChVnCuRlGpXmvTdOVNsz91tcM7j7A7gUx/vwMTuBjSkG0dh1TFRQvnlLubOLHsxT7bgqxL9n9z79h59d3wFp6N66y8Fd/i+QTq0cXNMZqhzjHxI21jRPtcfCmZ0mfP6HeM8kyZcnw3vd0bnzdBhUtLccg9BWMdpuFlT3iqzfQrkt1DOWyWluS3BJd+gKlBFpbSgN2+9n4d4k15M8e0b05RfqGbfmuoNh4OjFmqhKdZyjlEXgSzxHU6ZD00WOs0fhzC3jdqYmgIn/2mOj61xNBxX5cV6GkoNanKf8TCMfBHtiHRZC9xmG7peWsaIOKlhbAcyX5w8c8/7NfjMe665eY+9lvk5bvb+ZqjKV0HK7/4c8Z3HmA9D2m1td4/h/+gv6dptQnXlti5fd+h2LrGU53lpfJfKUk9e6AnV99P97e4Pv7xGtLuEvLH2xj7rtQVBZ/bpFi89l4TEUd9AdYDpaXll7cJX30YGLcGg1nLJPa0vKp4nuS5N7kRD59cp/o6pfHCiqgaQpP9jWFx6F6FVDsf95ecKD1ya8noS8xyTa20yV9dG88Xmw+R616EyWT1pgjWxqEgF7HQw/76HRI2J1GdKJ36hkTjkO4eoXRvdvjMW92gao+/N6Uknhuk1YpKtP2fLWcmjaoaGkBPAlP/99fTowl9x6x+LPffu/7LmtDCfhfXEMIQbq5PQ4oAEaPnzN89JxobZ79cYJSkvTJ80PbSx89p7ey8t6P+zzJi5ru1DxREFEPdpBhjNub+SClEetao41ERRE6Hb16QEiQEvh0gr2WlveG3TNy2z9UVUj57o3G2oDT6aEP+KKoIEQPX7+KX1SWzuIK1T5Hdul6qCACLNloSH1EtFAlA5woHgcV3uw8ZXV44h6HDvnTB9RJH4Bydxt/fomwO0/2hrKsoxBCUOLSvfUTdDZCegEaeSjLGgYKD02x9RykpLewTFrY92aI2fJ50NortrTscaTZ1jmuhJdl40+RPX9x6LFsYxsn7k2kzbXWxJeWDz03vrLyTituHzrJqCLDx86sUnk9dpPyg21cH2aaaO0q0vWaASmJLq+39czvEaUkcejQiRx873CfUsvFoZQ8sZuzsQLpT8o1u1MzlKfIwOZ7zupOdwpo/FDCtasUR6zi70drQ2EUnRs/wptbJFhaI77+FdZahDWYqphwa3+JimJkEOF2pwhXr+DOLh0ZJDhKjAOKlxRbG00W4R3f525SkdqAQWYOBRRSCjyhGf7wLdVgl2p3m+T7b4iC9nfTcjraTEVLC1AZmP1LX/LiF78aj0UrCxghgfNbualrTefKKlv/6TcT491rlxhlk6vyWluCbpe53/qa7V9+izWW6S+vEywvMvzEeipeUtcfh9So1oZhJojWbyGxWCHIc/PaWuqW0+F5ktCx5M/uY+oKb2YevztzbpLDLUfjKEknctBZ0xStouitikkvGeU13as3yDeeYLIUpzuFN7v4Tu7bvt80fBsLSVoRLFwiXLmMtY36U3GM62VeaIpS4HUXEFJgy5z00T3iS+tYY7E0vVTlYBd/Zg4njFFxj1Feo+bXKGpLdZLz8WW39yl43efsu5Jia7K0DGuokj6u2/2kSmdbzpc2qGhpoakn7d66TjA3w+DuA8KleTpXLzEszncCa4xFRBFLP/ttNv/8V1hjmP3JLbz52SOPZVQa4i9vMP31DcBSWfHJBhQfG7W27aT2nIh8RXL7V+PMYv7sMaGUeG73VCvbLaejEymGd36D1c1KufQ8uutfHqlidxCtLf1hTTCzjDcLteFYrzvIVNej2tmk6O8gPZ/uyiVGuWGUvf3aHgXOXs+BxSAYZTVFUTfO1rdvg7Wkzx7TufoF+eYz3KkZwuU18o1n5FsbOHlGtBcIvSmpWtUWd3qWaveValOwsEzxnkqRLCDU4emfVM4Hm/1t+Thog4qWlj1GhcGZnmHqr8w2K1oXNDlPS4N/9Qrr1y4jgNLwxuAmr8w+ef/2htDyeaGURGfpoVLFcmcbd6VH2cZ1F4LvKcrtzXFAAY0KWj3s47qdY62GW2vJTnEdDnxFtb1B8eL53v4Lhne/pfPF1xNSsEfRiRz07ibJ1gYA0g/ord+kqgwC23heFDk6GzF6cAd/bhE37jC8fxedNb1UOksxZUE4v0b6Bj+dUVbTW1jF681Qp0Oc7hRGuuTHVJs7KUWpmZpfotrdbgQkaDw8VNQ55LvT0nIS2qCipWUfdW34EET3ikpTvP1pLReIUoIoUCghMEBW6GOr0rScHcZYZOgdGpeeh2lXXS8MIQSmPnw1tbpGuCffnucqAl8iRZMFTHP9VrUi1xFk/UnPBqs1tq6b6qLXvFwIUBiyvYACwBQ5xeZThOuRDhPi1SvkWxtUg11MVVENE9zu1DigeEk12KW7fOmNkrUAg2GFUh4qnicvNca8vzuRtTDKNJ0bP6IeDRBSocKYJG0j8JbT0QYVLS0tLSdESkE3ckgf3EHnGcJxiC5dQ3hO60NxzlhrMcLF6U1TD3aBprQjWFxlkLalTxdFWWm6cwtUu1uvBoXA7c2Qjk42YfY9hU9J+sM9bF2jopjepWsMRvUbAwtjQLk+dTU5WRZKYe3rj0FKiSkO27vXWYbnBdSjhOTekN71L6kGfaTnES6tNrP1A9GKUM6xFavOy3QVoKoNu0mJ40RYC7rNULScAa36U0tLS8sJCX1F9vj+WJrS1jWjB3eI/FY95SJIRhXe4iU6N35EfO0WnS++Ypi1uvsXiTGWUks617/E7U7h9qbpfvEVWWlPLKoX+orRgzvYvcyHTkdkTx8SvEXlKy8NwcrlPSnnBm92gbdVXmltUGF8aNzt9qhfZiKsRZcF3RtfEa1cokr6ICXB4qQiX7i8SjUa4X2gimR1fX6BTMunT5upaGlpadlH6CtcV2KNJSuPVptylCA/aKJlTGtud4Eko2Y1WgiJzdsyjg+BrNCUSuLPX8JiGWQG8w6/EavrQ7VKOh3ythhea0NWSbo3fowpC6TrUhkYHehVCHxF4MlxQ3aa1eSVIb7yBdnTh5i6xp+ZxY275BuvDDil6zG8fwcBxJfWGXz3K8LlNbrXv0QXGW7cpdh+gSVHdMITv++Wlo+NNqhoaWlp2WOq61FuPSPd3UY6blM3LZ1DUrC1tnumVvsCi9bc7oOgVa/5sNDakJ5yJVwo51BZkQpjjrPZsjKUVblX0nS45CnwFU41Irn/AKxFuh6d9ZsMUo1WHuHVWwghkNKS3PmWl2IYTqeHdZrnmrKg2Gn8hbJnj0FKpOthtaFOR4RrV+iP2utCy6dPG1S0tLR8lviuxMFigNIIHEdQ7WxSbm0Cjbng8N5tujd/fCioyApNb/Vq01NR5AjlEF1aJ8vbTEVLy1mTFZro8jWyx/exWqOCkHD1CoMT9Ga8LIVzHIkxdvx34EmSe/fHz3N70whrmIoVxgpGmabWBsdpSrlMWSCUgxGKwZ5nRhQGgNi/M0yRI6QkXLtCXrbBbsvnQRtUtLQcgePIpnmtrTX9aPA8halKurFDUVnKNxjNTUUOO7/8jv6d+7idmKXf+ynSCSj2Gn3HWIspcqR0JurzjbEkmSG6/AVKCCyQFab1RGhpOSOUEljb/NaKUmM9n/j61whAW0uSvrlJ+yCBrwhcQT1KkF4AjkeSVlj96jcbzC8hHIfB998AFuE4dNZvkeSCujaUlcDzfAB0/ao3JM1qphaWKfvb42yKcFyc7hT9YdX29rR8NrRBRUvLPlxXEgeKepQ0qh1RRDJqbwpnRegrfE+CMVgpSTNNdQYO2Z3IgSxh8P1TQOAvruCGHUZHaMP34iageLHnWl4NU+7/8Z9y44/+B2QQog+ovkjXwx4RLDRKLQLlCgTNJIiTGua+5bTyXEkUOI0Mp1IUpSEr2sCl5dPFdSRx6KDztDFjc1ySUU1ZmndWVnMciUfVGNa9HOtO0Vm6jJCiKVs0Bm96Zi+gaLB1TfbkAcHyVZQSVFvPSLabMid3epbewiqDYYW1lrQwdG/+mKq/jZAKpzvNoL13tHxmtEFFS8seQghiX5J8/+txw630A7pXb9Jv5fZOTegrVJGQ3HsINHXS8bVbDK08VUZIKYE0FaMnD8Zj2eP7dK59iZRi4qYuBAit6d95OLENU9VUgyHB0ho6HWGq5vv25hapjDhy8t/ruFQvnpHsvAAh8OeX6EzNMXxLSYZSgsgR1GmG8lysckgrc2gfriMJlSb5/tvx+RiuXSXwY/I2sGj5BBFCEIeK4Z1fjzMIKozpXrp2bHd6IcShUqPAk+SPH02M1UmfcPkSaa7prN8kfXwfe8R1SBcZgRLYIqPcCygAqt1t3E4Pxwn3shjNPy+YxloYtveMls+QNqhoadkj8CT55tMJBR9T5Jg8RSmvLYU6Jb4nxwEFNIou+ZP7hCvrDNN3/2wdR1H1XxwaL/vbuL1Fin3NmVJKrNV4vZgqmVRvkr7HMK2J128hrAEpqWpzZLbDdRUmHVLuNWdiLcXmM+K41zSEvmZ1UghBpOD+//4n1GmTEelcXWPhr/2U0QHX9MCXpA/uTpyP2ZMHdG/+uA0qaMpZfFciRNOMm57Cebnl/aNUkwWWovFyOCrrFniSfOPpREmSzkZQFUip3rjq/1LByVQl0vXISzP+nQjBxDZfYo0BIchqRXz1BlIKhFRjl2kApzOFoSmbOkg9SnCm4gmFuDeVXba0fOq0PhUtLS8RAo668ejGfbXldOy/Ub9E5/mxjaFehzEWFUSHxlUYofUBGUptkEHA0s9+C+m9svWd+dENrFLU2tIfVuyONLtJxSg7eoKglEAP+4fG69EAx3n9ZdVzBC/+/FfjgAJgeP8xJk0PfQ5KCkx5wFfd2rfXTH0GxJGDyvoMv/81yXe/xOw8Z6p72FX7Q0BKgeeppjzuM6Uxi1RkD2+T3P4Vye1fIfMBUTCpCSsE2PpwRsJU5RuvE76ncOuM5LtfMvrhO5LvfomrM3xPNb9HIfDnFiePyfWQSuGkO4SOAWtIH92nc/U6Kgj3jPqmCZfXyPIat9M7tF+nM0X9hsUmKQWuq059jWtp+VhoMxUtLXuUlSGeX2pMjF4iJU7cpU5a3fvTIqRqnGz3BW5Ot0ddn26SXFWauDuFimJ02hhTqaiDinvU+0oQxiuZ6Qg3Drj5P/2cfGeAE4VIz6OfHl9JRmuLH/egvzMx7sRdijf0iEgs1WB4aLxKRsj5aGIltqotTqdHPRy8er3rYfi8JyhSChw0w+ePx2PV7hZOFOO6MVX14WQU49DBQVMNdwmiGEL/2GU8nxKBp8ifPcIUe0GyteTPHtG99ZOJDFNZW8LZ+YlzHiHeeg0OPMnozoOJsezJAzo3foQpCoonDwkWVogurVPubqP8AH92ntH97/dKpSxup0c1SjC6JphfQroeusgpK01dG2wc4M8vUWxtgAVvdh4RRNSv+T47kYOymnrUx4k6aOkwPME1pqXlY6QNKlpa9tDaULtNnX/54jkoRbCwwqgtqzgTRpkmXr9F9uQ+Os9xe1MES5foD09fe9wfVnRWr+GqJnOhrZiYvLmOxLMlyXffj8f8hWX8uQWKypAd82avlEQpSV1rVKeHOzVD1d8BBN7cAtbx0cXrJz81gqmb66TPNsdjQkri5XkKI9h/FGmumVq9Sv78EfVwgAwiotUrDI8ox/qcUEpSj47IEiV9nPkO1QcyZ/d9hcgGDJ82JX8FTXNvPLtyZEndp4ySUGXpoXFTlo1Z4V72ra4NNgqJLl9rpJ2VIlxaPVTaplRTYvjydYLDmVCrNRJLcu87AIaj2zhxl3DtCkJIBrd/RbiwggoCyv4uOh3S++JLhg/vMXp0DwB/cWWcvE5GFWFnju7sAgBlZV8bIAa+wiQ7ZBtPxmP+/BJhd46svZ+0fMK0QUVLyz7SXKOUwptfw1roj3SrL35GVLVhaCXh6jWUFFS1pT8sz6Sax1pLMqpYWOiyvXm49jnwJdn9yZXMYvMZ3sw8Wf72CZ4Q0I1dbJGhRyPCXlP2oOZWCZbWgGaS8dLV+XVUlaGztszSz36Lnd/cQQU+S3/1L1FsbeDPzVM7alyfbW1TihXOrhItrKGNZZDqz15NxhiLG3XID4w7nS41gm7sjGV+00JfWOYicCWjh08mxqrdbYLF1Qs5nouk1han25todEYIpOdhDwThw7TGdUO85StYy54L956nxEtZ2HSECkM0imFaUxtLsHwJKQV1llLu7uCEIbqaXLCoRwnFi+cE88s4YYR0XYb374wfL3a2iC+tk/zwHd70HO70POm+bGdW6GOpr/meZHj/6cRYsbVBd3ahDSpaPmnaoKKl5QBaG15TSt9ySrQ2p2rKflekFJgjarWPG9FEgUP5/DHVoCl3Kl48I1y5TOV1T7zqPCwMM7euEa3MgtFUyTY6SzFVTrB6jeG+8ilrLekxgp7PiaZnRePPLVJsbQIWt7JZcN4AACAASURBVDvV/AOG9+80xmOOQ3TpGsJ1KC8osLCfeQD4krzUTM2vYOqaerCLdD3CtSuvnaBXlT6UcQoDF9dkJLdfBQHe7DydmWUcR1AUOVU2wom79G58BVJRDw8vMEjXx1jwZxfIXzyfeOxlD1Pn5o8pK/POqn8CDl9b2sWpls+AtlG7paXlk6esDN707MSY9H2MPV5/guuIcUDxknzjSeO5cUKEAGNq8mcPyTeeoPfKQqyuP/NuiUmEEDiOPCSSYK2lGg0RUtL94hbdL77C7fawdc3o0T3Mns+IrWvSB3cPNQO/b3xPMd11kVh6N76aaPBVcZdaf/yTSyEEYeAQhQrXffvna21Toqjm1uje+gnh1Vtk2qU4pu9EN3bxlSZ7MikFXW6/wHUF6f3vKXdeoPOMYmuD7PkTysqg4i7S98fPl66HOzXLYFSjog7iCAUOi2AwrE+VUShri3vgeuP0pqkO9I+5jiQKHQJftWIgLZ8EbaaipaXlkycvNL2FVYTjUSe7yCAiWFwhSd994mCtfacgwFpAOUjXxexbjvVmFyhP2bT+qdCJHBQGnac4cYeiZlymVpaaaGqO4d3fkG8+Axr34t6Nr8aN+i+xRp/rCrE1Gt8WJLd/AGsQStG5egMZhAjHxe3N0P/IG7VdRxIHknzjCaauCGYW8OPorf4sL7Nu6cG6tbftz1WQD7Gui9GH9yGsRefZxFg12CVcuYy1lu76Law16KpCuD5JWjflkmlNvLjK8N4rQzwVhFjlYO3pvqM0q5laXMOJOtTDASru4HRnGOzrH+t1XEyaUG1sI/2AqbklklS30uUtHzVtUNHS0vLJYy30kxI/nsHrzqIt9If1sftlamNRcRe9T6ven1uiqN5twjpMNd1rX1K8eIYpCtzpWUTYpXhLT8abEAK8vVXjWptDcrofC1GgMP0XZPtKU6JL63heNPYAGKYVnetfo9NGSUtFHara4EQx9b7AQkjFeS4BW61JH90Da8Z/jx79QLx+izQ3jI5RTqOUREpBdYSL+4dAHDoT5nT1aEi4dhXXjd6pf8X3FZ7TGEzmpZnwfABwFZRbW6gwxJ+eo9h+JXIg/QAQh+zpheOA0SR3vgFjcKIO4eVr9JOmh0spibVQ4tK58SOq/jbS83HiHoNT/Ab3009KXDfGmetSaTvx3fu+Qg+2yZ/v9dwME+qkT+fqLfrDNqho+Xhpg4qWlpbPhqLQFG9/2iFGqWZqbZ062UVnI5zeDHgh6TtOQLQ29IcGv7eEElDUhuoUkxnHkYTSsv2ff4POc2Z+cgsbROQfkLzqcfFcSXKg1j17+ojo+lfUtcFxFFprdpMSxwkAqJMSpQTdtXXSh3fReYZwXOLL115riidEU6okRVOucnAy+y5YYw+pEJmymUyWbwkSpBR0YxeTp9iqIu72yHJD8QEFF1IKTJEdMpIrtzfxVtZPrLzV67jU/W2ynU2kcohXLpNLNVEWZS0I16PY2qS7fgPpulRJHxVEePPLFJUhWFx5NUEHotUrZM+fjI0j63RI/vwJ4ewyniPR2RAQKC9mmNXIaA5j7IQE9VlQVebIQMtzBPn2pGGnKUs4wsunpeVjog0qWlpaWt6CtZbdpMR1uyi/R6YN9SlXNK2FvDhczhEGDr7brK4f1yk6cuDu//JvMWVzTIO7D7nyN/86KuycqpxCKYnrSIy15+cUfET2yBqNoyQd11CPdgniLjbwJ9S2tLYkmSG6dL0xDrSNmlt1RLDgKEknUhSbT9FVRTgzj43CsY9AFDp4TrP6baxgmNXHUt0SUjZeIvtUh5woPlYfRTdyyB58/6qU55mge/0rKi0+GMUva0EoB7fTQwUhOs+ohgOEcjhpMaDnKsywT7n1nGB+CSfuYnVNGPgU5avPLy8NU4sr1Emf5IfbuL1pvLkFVNSlqgyOtBB36d36MbrIkX4IWlMNdif2p9Mh4ZIgufMbbN18z9J16Vz7it0zDibeRvM5KjhwCRFSAh/fQkBLy0vaoKKlpeWTxvckoa/AWizitRPN41BV+uA84EzpRA5msNWs1FuLNzNHb351ohb7II4jSZ+9GAcUL9n+/75h9vf+ylEm8cc+FqlLqt1t3CAk6s0wGFXvfYKrrWjc0Pf5GkRrV8m3Nij2eiiKzWd4c4uEvYUJSWCtDcno7d9tJ3IY3vkNdq9Gvx4OiC6t4zohvifRu5skWxtAU2ffu3LjWPLHwnGI12+QPrrfZLTiLuHaVQZv6TeQUmDrcrI3wFqyjScE82vHCizPB4vy/MaUMR3idLoEC8ugFMkJj9H3JcqN6N34Gl0UjTeENURrVwkDf/y9WmsZpprOF19jqgIhFUYoskLjViOGj+83G5QSf34ZVIDnHG4ed+IOOs8RUmFF46Btqooq2cF1e+dabpaXlmj5EqN9/RxOb5ozSJa1tFwobVDR0tLyyeJ7Es8UJLfv7TXOOnTWbzJEnkm5y1kipUCaimxv4gxQ7myhou5evfrRkx5rQR2hwCPdd7+8e56CNGH09JW3R9XfprN2/cxqzl/HKKvpXfmCcmsDnY5wulO4nS7py8njHuXWJt25RbITNv42JTz5OKB4SbG1gb+6jsKQ7QUUQKMo9OIZfm/xyMzSfoQQJJklXF1HKUFdWwajt2c5hOBQSVGzc32kQtFFEQUO6dOHe4aPTUO0OzWDu7CG1sc/L3xPIsqM4aN7WK1RYUTn8jWS+3cY3rtD99ZPJr7XWht2kxIpJdYarDVMdVxGDx+9epIxFBtP6M3MUWtLdGmd7MnDJssVdxp/EKMJF1eQfkCV9Mk3nmLrGuGd72dc15pSuXRv/ph6NET6PlZ5DNOPu4m/paUNKlpaWj5ZQl+NAwpoZFvTx/cI166TfGBBheNI6uHuoXE97KNm49fWq2ttiOZm8Ka6lP2mkVwoyfzv/Jj0HdWkfFeQP3k2MaazFHkOpRnGWHYHJUFnDtWbo9LgGntEWdS7vbdx6ckBhHIAgS4OOz/rPMWdPt7+3sWLRWuLiqKmjGhfsOPNL5G9oxjA+8B1BHl/Ulq56u8QLK2hlGwkli0UlXlj2V3oOyS3vxl/pzpLyTaeEswtkD1/gtUV3cjBAkVpxpnF/cGZEAJrDu9DWIOsC1Tcxbn5I6y1GNs0lKePfnh1DMtr+LMLeNNzZG/JJJ0UpQQg3vgZ5IUmL8BxIkxpMaYNKFo+ftqgoqWl5dPF2nFA8RKdZyj14Vn0aG0I4u64xOclKu5SvKUmf1RaLv/3f53s2SY6z+lcWaMwAvOugZPlaNWkc1w1z/cZozlK4E7PUe1ujcfcqdlDuv/HwVqLVS4qil9J0ApBsLTGsDB0w/jQa9zuFO+7OmaY1nS++IrixXNsXeLNLKCVT31Cc8X3zgGlJYRACEHHM+QbjwFLZ2GF0nFea25ndXUoSKzTIf7sPMHiCtQ1xcYDsJZgcQU3CA+ZQBaVwZueo9x51fD8Uv1r9Oge0g/oXLlOpQWOEqT7sm4A2fOnTN36EaPcnJnqsFKCTuRiiwxrm0BxmFZv7Kn50DKmLS2noQ0qWlpaPlks4tDqr9PpvXNPxftEa4sNfLy5RcqXTtFTM6jOFNVbGkldV6IROMtLCG1ISs27ruQDFFUzmUsf3RuPqbiDPqZZ4FmTZjW9hVWcuNtkbjo9VNSj/4ZekzeRjGq6a9egKjBViRN3yXKD1pqiEkRXrpM9fYita7zpOZypuWPJwZ6GeqwItoAQMKosuvywAoqisvjzSxOBrz+/BNYyvPvteGw4TOh88TWFPLrJXDruoeDEiTrossDtTjVSsHukD+7Suf5VU7a2b1tZXjO1sIIMAuqkjxPGeL1pkvuN47YpcuphgtebbgLJg+Vl1mAsFGcoQNCNXEb3vhs7cwvHpXP9/BvBW1ouijaoaGn5yPFche8KLEfrvH/OpLmms36T9PE9dJ7hdHqEq1fe2jh7USSjiqi3QHduEYCqtm9s0pZS0Itdyu0NTJ7hTM3iRZ1TN52WlcYJYjpffEXV30EFETLqMDiBcVsYOHjuK/+B06pHDYYlrhuhZmMKbaneMaCAJlsxGFZIqZAyok5eva+s0HhuQHT1S4RsFLj65zQpbBTBPpSm7MNkeU2nN0enM0WdJjhRFxx3wjviJeXOJm5vieKIPhRtLPGlddInD8Y9FdHqZYRSZM+fHt7W7osjt9VPSjy3h788jR31Gdz9diJQMXUFQjQqUd0edTIYP6bC+Ex9EV1XUQ8H44ACwNYV5c4mfjR7psFLS8uHShtUtLR8xHRiB9IB+bMNhFJES2uUyv2gJybnSVUbhkjCtesoJalqc6zG2YvkJK7DncghvX8bXTQvqIYD/IUVgnjm1OdAmtdIKXDieUpjTqThP9XxKLeeMdx5gVCKcPkSThCdWsWoqvSJvRDehDH2yHOhrPRbfSU+V4Zpc14of5qsNCht8Fz30POk66PfMGsvB7t0rlwHKTFFQfLDbeL1m3uGdge25QXUr/nNlpWm1oZuFB8qqfKmZqgqTZprplauUvrPqZMBKooJZheohn3isMfoDErMhABTH/6N2Lr6oJrtW1reJx9eYXFLS8uxcByJKDKyJw8xZYHOUkb3bhO44jxL3z946tqQpDW7ScnomH4DHwsSOw4oXlJub+I5Z3NpN8ZSlvWJsl+eq6iTHcrtzUbGt65JH93Dc872vBQCurHDdMdhOlb0Oi5Stif+eWCMpar0+H+3O4N0vfHj0vVwp2Zfm52qqkaJLfnhNsmdbxk9uren6gROZwoVhK+25Qe4vZk3Zt+MsVRG0rl2Eyfu4nZ6dK9/CcphlNVYaylKjQpC/LlFhFQkP9wme/oQ94xM16tK403NwgG/Dm92oQ1QWz4b2kxFS8tHiusIqq2tQ+NV0sfxzld3veWCOGI2JJTCnqKf4rQ4SlAn/UPj9ShBqfjMyvO6sUvx9D71sFG8eukncbB+XYjGxE9riz3LepeWMUla0732JaZofDakH5Kkr1/9zwrN1PwyQimqwS7SDwiX1hqTQQudy18gTN20BSnnWDLGaa5xHIdg5QpSCPLKkg9enQtKCooXG5NeINAY5kkXfQyDwjdhLWSlpfPFlxQbT7HW4C+sUBqJaZ2yWz4T2qCipeUjxVhQXgBMTuCUH2BOeYNs+TiotW1WcQevZD6D5TXy8uL6arS1qDCiHiUT4yqIMMXZnJdKSWyRjQMKaFS9qv4Wnj89XhmOQwdHGHQ2QoUxtVVnUurSMoke+0g4CAH6GKVy/aTEj2fxe3MYA4NUj7OIg2E1jpetPX69W10bhq8JWmtjcTq9Q0GFCkJ08vp9OEoSBQopmnM7zV8vl1uUmloL/Pk1QDCqmub/lpbPhTaoaGn5SCkKzfTsIlV/B1M1N3EVd8EL0CdoqG35eBmmNd3FNby5BXSe4XZ6FJWlusCemqLQTM8tUo+SsSu2N7uAFgpjTjehl1IQeAqlBGaQHXrc5BkynAEg8BWkuwyfPR4/HiytEobTr5U6bTkdxy0tdByJ60iMsQxfk9E4blLJ8xRSCKr6zd4Y+d710lQlVX8H4TiEK1feGIC7jiTyLOmD25iyQAUh3cvXSTJeuy+tLWkbSLR8prRBRUvLR0yS1nTWb4GpQUgMkuQ9Ox6fN0pJAk8iBZTaUrQTwgmSUYWUEuV2SUf1mSravCuDYUW8do3GA0xQVq+fPB4Xz5OErqB48RQV93DiKaJLIVWyS9VvygDdqVnSvcme70mG9yeVhPKNp3RvzrZBxQXSjV0oUqqtbVQQMj0zz2BYnbjX6aXyWTXYwRQZ8dQc2ncZveE86w9LwrlVuktrGAt5YSjfcC6EgWL0w7fYurmm6jwjfXiX6NJ1klGrstfScpALCyr+6T/9pyil+Af/4B9c1CG0tHz06D1t+0byXQOf1mTJcxWRZ8me3sdUJe7ULFMzC+cm8fmx0KgYvb/vfhzYSahqyI+QCT14PMkZy/ZGviL5/tfEl67z7M/+guGjZ0jHYeGv/IRocbVREfIC6r39CjhkfPhBRFyfMb6nEFVGnSZNudpgl6q/Q+fKjbfKFTuOJPQlSgq0FSgJ6f3vx+VM5c4W4dpVPDd+bWO0tY3nyWHP9KOR2HFA8RKdZ6hWEKCl5UjOXf0pSRL+0T/6R/yLf/EvznvXLS2fLJ/qXCkKFMndb6lHQ0xZUmw+o9rdwvfURR/ameM6kl7HZbrj0ItdHPVhTFxcV9LxoX52j+zed4hkk6mu9/YXniGO03gAeN1pdr65x/BRY75m6prn/+EvkH5M7fcY7gtkqtri9KYnt9PtUV1Qv9HnrsjmKEkcKOphgtWaaPUywcIypsgRB4O/A7iOJPYs+eMfoC4x/RcIXR/qjyg2n+G7Z/dBvzTP3I/0A95QZdXS8llz7pmKP/3TP2V9fZ2/9/f+3nnvuqWl5SNCSoEpczCTd/Cqv4XfnaH4hJIVriOJXMvo3rfYqkJ6Hp0rNxgW9sLNDOPAIfn+V+PvodzaQAhB0Jk7Nz8Uay3CcRGuT/p049Dj2eYOdn5hYizNa6aWL1OFEfUwQcVdvOk5+ufcb+QoSSdyGr8CpagNpy4F+xjpRA6D738zdrcvd7fpXP0CFYRv9XGIAsXo7jcE84sU2y84KNs6Rrz+oXchLTTxleuMHtzF6hrpusSXrjFsy+daWo7k3IOKv/W3/hYA/+yf/bPz3nVLS8tHhDEW6RxtqmU+sZXCg7XbpiwZPbxLePkGyQUGFUIIbFUeEdjtEEzNc0yPvlOjtUFGITodEq0skG1uTzwezM8wOnCM1sJuUuIF0zjRDNrYQ3Kz7xspBZ1QMrzzajLtzszRmV3+qAKLl43V1kJRnrxvRymJzkbjz+AlxdYm/vwS2rw5EhBYrK5x4i7Z8yd0r91ClyVOFFOno/HzwqU1sjNUPqsqQ4oivv4VAotBMMwas72WlpbDvLeg4l//63/NP/7H/3hi7Pr16/zLf/kvT7XdubnOqV7f8n5ZWOhe9CG0fEKYusabnafcfgE0Hgzx6hVUEBC/5lT7GM9BXRSHardNkeM58sLfz0FzPQDp+3i+y0IcHvGK94ezsIw3NUe+3Wf06BnCUSz91d/Ci0NC/3xLsl7H/u/L6JrRw3sTk+lqZ4twYfnCv9fjYuqaOhtRvNhAuC4ziytI1zuxS3SZHBFESYnb7aFcjyA+7KQ9PoaqBCGx1iCUAilIH9ync/U6Os/RRY7Xm0L6AdOef9K3eCL88z3l34mP5dxq+fR4b0HFz3/+c37+85+f+Xa3toaflCPup8TCQpfNzeTtT2w5NkIIfEfgCIuxUBjxRtnET5HOzBLduf+fvXuLkTPJDjv/j4jvkvnlpbLuLF6aZJHd7O6ZFWRbNqS1vdoFBrKswWAgQQ/2k+AnWYJgAQbGGOtBgKCRxhAEjB5GgA3DwDxYhgwb1giCNQYMrdewIdgLzWoX0sz0vcnmtUgWWXn9rhGxD0kWmaxid90ri3V+bwxmZUZlZmXG+SLOOcv4qkKFIf3UUva3f5+d1PdguxmignAisNBxjaKy9LvH+/s06gHxwjL5wzVgHNjVz1zgcTc7ls9iYzRLf+uvo70fV5Zy8KiXA/mRz+VFL77/mnWDK7bOy+Y53aGd+u+yINDUVcHokw83x8ruY5pX3t7Vrk8cGRr1GjqKnz0fSlFbWmGjV+Dcs+do3Ck9RFUFviwxjSal9STnL42TsZfPYkcjgnpC/6P3CJIGKozI1h8QLJ5jcMx/L8ftpH4GiumitdrTRXwpKSvElFJK0YoV9//n/8vg5l3i2RlW/vZfJwvCYz9nv53AKOqBwluLMobceopq/4ump8dElFL47NUql/tUmlkaF68w+uQjXFmgo5jGhVX62fG/zsO0otFeoDW3iLcVygQM0+NbEFvrGG4eaZ/uRXlpIZyZnUwoVhod13HF9CcFxaGmWFubGPPWYrMRxkQ7usDRSAICVzC4cZ3GhUvYdIR3jqA9S5o73AvH1ppJSH7nxrPmiUrRWr0G9Tph0hh3i/eesD1Dtv6AathHByHx/PKOOm8LIQ6PBBVCHLIg0OMzxdbtKhioBYq1//Hn9D++BUB6f50bf/xfuPTln2C7kwTHKQg0cZVz/T/+V2yaowLDuf/jR4k6swcSWMA4WfdVVVaOIZrk4htoNe6WPsgq7JR0Rn/ahXpculgWbjuVF5a4PU/sHOXGI3QYUlu5wCibsj9gnr62k2PeA3prpTWlDX4H781abIgDTff9D8E5+h++S5A0MEmTqvLkxWTCs1JgvJ3sxu496dptkrOv0X3ve9RXzlOFTSrnCJoLhO15rFN0B8UrWwVPiJPi2IIK6U8hToNmrCnWH9P/5A6N82doLs4zyHcWWAQaBjfuTIzZNMdXFcdQDfpTxdpz5//6H9h0fIzBV5Y7/+V/cvln/+6BBRWvuqpy9KZoByoMDUZPdio+SYs2rRVKceyBWW9QEDfmqM3M4xwM8k/v/HzUPq06VVZY2stn6Q96my++qdVRYYTLPz24VEpRC5/kQzy3G1GNhlTpiNbc0ta5BGbcyPMFvqrwtsLEMem9WzSvvk3WL6dyx1aI00x2KoQ4JLVIs/EX7/Doe+8DsPHuR8y8cYnOX/lfdlShxHlP1GmTP9rYHFNao4OAaSuUrpUif9ybGHNVhbeWF2s8aq0wRlNV9kQtUk8LpRQzzZCq38WmAxozc/ha7cR0atda0W6G4By2yDFJnWFaUR7jAjTPLfnxp3xssVmd6qMfPLlYAWFnjub8CoNRhXOeUalovf45qkEPFYToOKE/+uz3QhQZivX7RLPzoPREI8IgaeC2+eNPYo3yGmWCieT2eG4BULiqBOdQ8rkhxFSarsudQrxCQgWPf/DhxFj3/RsEO/xGzJ3i7P/2N9DRk7KqSrH8Y3+FaSyRbp0nWZm88hjUa2Amj060GiHN0BEVPdqJIam9ek3sTrpmYhjd/pj07icUG48Y3vgA139MHE//axWFmplGQH7/LvmDuxijKR7epVFT6BPYBbkWGzrtiLl2xGw7on7Ar0EcGbK125sBBUC58QiD22zWVxSOjX5JZpqMXER3UOwsn8Z7MIb84RqNC5fGTeSUJp5fonFhlWG69egTtmJ05yatS1eJOnMEjRbJudcImm1cnuKriiBpUk15grsQp5XsVAgxparKQRhz+Wd+EleWmDCkcJ6snK5dCoDMwsqP/w3u/tf/m9Hd+8RzM5z933+U7Ll1QyMJKB/coew+6zGQnL9MFNYpyimMlE4poxV2OJgYyx/eI1mdJT/kiDYKDWGgxpXOit0ngyc1Q+/9729eFS82HtFafYP84RpxZ5k0Oznvs0YSwHCD/o274B1hu0N9+SxhGNI7oAZ+RkGxTXUqVxZoHU4cHauq3T13eWHpzC4w+PAdvHM0Ll3BBCH544dk9+/Qmlsiq8xkA0WlqEZD+tc/IOrMEcY1qnSESZpkD+8TzS0QL64c2O8vhDhYElQIcUhKB7Ofe51Hf/Hu5tjMG5eonGKnVWuqyj1Jyjaww1yM4+CcZ1gqlv7238BohfOezCrsc0dOQqPIupNNy9K1WyQXr0lQMe122ZNgL1qNED/qUjxYR4cR7eVzDDO342NLYWgou48njtkA5I/X0VHtwH4HYxS1yKAUlNskGx8EpRQBjsG925tjZW+DoJ6g602CwBxIPkFhPWFnDvvc46AUplbH9scL9zA0xKFCAXnpd/W3OhhZmlfeohr2MEFI74N3No815Y8e0rzyFoVWOOfxHrwymKSBHQ3J18ed0xuXXqfCUL9wBevHOSqvWvNLIV4VElQIcUiy0tH53BskZ5cY3rxL49wZovnZHSdqnzTOeUYOngVM25WSeYF1R7FeFbtQWU/QmqHqdzfHaosr5AfYqfhFUWRwgw2ye+NKZzYdUQ37u+6HoLatVKQJkgajA9jhi0JNEkF67xNcWRLNzhO3Zg/8ynkQaOxoa6+BajggCiOCoHEwQUVhqbVmia2j3FhHhSH1MxcYPdk9qMeG0Bdkt2/jvSdeWCZKmjvuBl5Zx0a/II6bqOFga0fth/eI586SZhWNukEbRfPiFWyeU40GhK0OXmkY9sg2xsFhe/HMuKu1JGkLMXUkqBDiEA1yh2l1aP7QHNa6Vzag2AnrFaaeYNPR5lg0v0heyvnoaVJZT3L2NWw6pBoNCdsdKhWQ73AhuRdRoCjuPZwY89biigytzY6OQZWlpdGaQT14romgHp/hLx2UB1DGNakF9D/43mY1o+zebWoooqh9oLtt1jpM0tgybpIGXmvsAV6q7w1K4sYstZk5vINBMa5OpRTEAfQ/+GDztuntGzQuXsWYcFcVrMa3fcnVA+9p1AMi4ym7j8bvuWabuDPPKLOY7BHZ052U4YBy0KVx+Rrd/un9LBViWklQIcQhs3a6Skgel2Fa0b5whWLjIS4dEczMoutNOR89JZSCmWZEvn6Pwe0uQbtDbWGZYVpRlIfbV8F7UGEIeTY5JxPgd7FDMhiVNFffpBr2xnkIrQ5p7sjy/c9fa4XNU148e1NurBOdm6E4wLexcx5LQG1phezBvXGzt9YMYbsDOqDcxe7NTmxXnSoMDWV/Y8tti411otmzpLv4TKsqh2k1J7vGK0VtcYVe6phpBqS3b1IOxhXkyt4GcZZSXzzD4M4LwWZZQlVt21dDCHG8JKgQQhwJ5/z4KER9Ft2YJbdQSkAxNWqxIbt/h3JjHYBi/T5V7zHJpWsUh1wcICssrTPn6X/47mZORNCawSmD97tYvNrxeywIGigFg97BLb699+gg3DKuomjP3cXHvTTUthcdBqOKemOW9uwCT7OwysoxPKK/GWs9cVzbMq6jGtUeVvP9UUlr9U3K3mO8rYg686TFOJdCwWZA8VT++CG1pTMos/2RNu8lD0uIaSNBhRDiSB1GYqvYvyjQDLqPJ8ZcWaLwRJEhChTeQ1Yc/M6btZ5RMe6HypcgPgAAIABJREFUYLMROgxxKmCwg34I29ltpaKd8B6c0oTtWcre+HlSxlBfPkdvtLvnQ2tFKwnwZY53DpMkDEYV1QvPa5rZY6tYZa1DJwkmaWJH42pgOoqJZhcY7WGnxD4J+MKojVKKdFg9t9OwzdEoNX6/1c+cZ/Dx+zzN0QpbMyhjMMbLDrAQU0aCCiGEEDjv0VGEe/EIktaExQb5vQdoE9A8c47MmgMPDovSUZQFxoS4FLyfvl2s/rCitXSOeGkFX5XoqMYwrXa9U9FqhKSffIDNUmB8zKt55U26A3doR3qUgigK0EBR2Zd2Gg8CTRQq8OMji/Wzl9C48Q6SDnbU+O7TlNvknpTWE80uUDx+dtSpvnSWNLeAYebNz+OtAzy2LBlcf5/Wxdd3lcQvhDh8ElQIsUvPOkI7vBzqFa+INHc0zl1k8PF7m4fVa0tncWVOdvcmAA4YfPwerdc/d2g7Ti9b7E6L/rBEKVDK4PLdL2qN0bh0uBlQAHhbka+vEbcWJ/s2HJAo1DTqAfnDNVxV0pxbogwNoxd2QZKaIXAF+doaSmsaSytkpSUv3JMchsMJ9PrDkvbCGaKZWap0QNCYwSpDnlZ0WhHp3VsUvQ10GJGsnCeo1amGfYKgLlWghJgiElQIsQutRoiqCmzaJ2m2Kb1mlMpxHnHyVZUjVZrW65/HlTk6CPEosjvXJ2/oPdVw8JkLuigyaKUoq1evUIH37PmCgtYKV25dnPuyRO2wvrJSikbdEGgFarzL82KA8FQ9NtRjQ++DH2yWdC27j2lcep0gCDZfQ2MUIZbBjWfVnspBj9bVtynKw9tBeao3KDHGYGqzpLnDuYpabMgf3KN4cizPFTmDTz6ivXqNYjRAGalHLcQ0kaBCiB1q1APKh3c3E1lZu0393EXiqHHq8gSUGp/BD/A4FLn1e05WFdPj6REkpTQ+q6jHBhXGwGSHbRPFuGL711trRbsRUvYe47IRjZl5XBztuLfBq+5p6dvs3q2J8kXR3CLDHSbEzzRDRrc/Jn3S+TyaX6LZWdzyHBujiY2jHAy37RERLb62GVSEgSF/dGfygbwfN92LZ7Y9tvSip43yAPJi540Ln7LWY+2zxwmNInuuX8rTObmyIGx1GPan74icEKeZBBVC7FAYKLKnAcUT2b3bJKtvnqqgQiloxoZH/9/36V+/Rdxps/y//jWy5656iukUBJp6pDFGUVnPKLPbBoNPr8JnhWNmaYVq0MVX40Vp0GzjTYhz2y/omvWA0c0PN/uRFBuPqK9cIIpaFK/w30lSD3BFQacZYL361FyLNHO0Vt8kvX8HnCVeWMbqCGs/O/CKI0Ox8RA7fBboFev3ac7MEQSapGbQ3oHWeD8OHsJma8v9KK0n/u09mDDacjsdRjvalUlqhsDmZHfugvfUFleI6nWG6d6DSetB1+q4cvKYmaknDGSHWIipI0GFEPvg3enrCB0Hmof/z1/QffdjAKpRxo3/+H9y6cs/QV8uRk+tMBh3gx7d+hCXZwSNJu1zlxik48DiZcHFYFTRXH0LXxZgDA79qcm6GjfR4BAgf7hG7WKb4hXNq20mAXbjARvr9wEw9QbtC6svTSTOS0tpFbWF8ygFo9JRFTv74zEa7Gi4ZbzKRrRaMww+fg9XjJtORJ05otl5FIqg0SKeW0BHEQoFxtAdPluYF2XFzNwixeP1zV0NHdcwSZPqMxKitVaE2jP4+MPNsdHNj2iuXhsf99rjLmaWW9pnzjPM0s3AorZ8jrz0h17mWAixexJUCLFD1nlM0pj4Qo/nFyl20ZzrVRAoT//jWxNjNs2fnBPfWlNeTIekZhh+/M7mjoMrCrAljRC8dei4Rn9Ubcl/eNr7YXze3352f4DtouxXOPLWWmG8JX0SUADYdEjx6AFxY+6lu5jOeUZ76PJdWQhbbaoX+jqEzTbZw3ubAQWMd4ni+UVG9+7QPH+JwSdPdpCUor68Qqs1R/dJ3wvvx70xmlfewmYjlNaoKKY3/OwjRkFgKLsPt4wXjx8Szpwh32PzQec8g9SSXHoDjQelyQtLuo/dDyHE4ZGgQogdGqaW9vlVyu46djQkaHfQSZve4BW9/PoSzkPUbpI9nOxpoMMAcsmrmFYKvxlQADQuXGZ06wb2SQlZFYS0Vq+x0d8+SN5pYrL1CtNoThzPqS2tkL8kB+Ok01phs607BzYdYlpzO7qPpBYQhQpvK5QJGabVS/MRitJSb80SZRnF43WU0dSWz437aGTZlttXWUbz/CXSB3ef7SB5T3rvDu3mDPXYkBWWIDB4Pw4gjYnw1uPyneUseO/R0TaN8uI6dp8Z3pX19KRJphAnggQVQuzQ047QUa2DSTpPOkKfroACoPCKM3/rR/jkP/4XXDlepC78tc8jpxGmnFKgNTg33nHLRpsBBYCvSorHD4mTl19d34nBqKJ97jJuNMBmKeFMh9IZij1clT8JrHUESXPLeNCeYQe5zSS1AAaP6D+4C4wb6jUuX2Pg9UurZnX7BUlnmdbiGbRSOOdQWlFbWmHwcX/zdiauETZb44W93TqZKh1Ra7WJQ0XZe4wOY3SrSX9Y7urI0jj5vI2p1TdL5eq4RtieZbiDXhJhqKnHBs04j2KU2VeuYpgQp4EEFULs0qucbLoTVeVQYczln/27VMOUoB5TeU0qUcVUSzNH4/xlhrc+RpsAV21d5LuyQOn9HVXy3tPtFwRBDd1IyDKLc4cfUIybtmnwkBXbJ6AfBu+hsJCcv0R69xbeWaLZeYLWzhbUUag2AwoAby3ZnU+onbnIMN36N6UU1GsBUahR3tH/6N0nRw8V9TPnaFy8yujWdaL5BaLmDKPbnzxJnF5GRzHZg3ub9xUkDXxR0P/o3c0xU09onV8lLRxV5Xb8PPaGJc0LV1DOAh50sKOjU1GoqemK0cfv46sKHddovXaFfuqnvmeJEGKSBBVCiF0rK09ZeVQQ4wsYt0UT0ywvLYQxratvg/coBdn9uxO3iWcXGOzk8voOjCuBHc37IqkZAl+S318jbHfotNo4r8hLR3rAOyRBoGnUDAoPSpFm4x4RUZQw88bbVNZRlI7uDgIKpZg4kvaULXIivc0PAO1mRL52C9tsoYKQxoVVbJ6SPVgjvXeL9rXPk1x+E6M9vfe+t/lzg2Gf1uobFBuP8M5RP3MObyvSe5NlZG06QrmKMOtTSxo4He6oHLBz42NKT9NndtooL6kZBh+8h3fj953LM9Lb16mvXJIyxEKcMBJUCCH2TBqKnyx5acfBBVCLDM3Va2T374DzxAvLlIQ7Kms6TTabtl1/n+T8RVye033/++A98fwSrc4i/R1cMd/ZY2maMQw+fhdflaA1jfOXIYzJC4ueSehu9D/7jp7wfpzLorTZXFQDhO0OZbX1jyuODOXG+rh619JZhreuj3M36o0nOTLXcUVJ7gPMcH3Lz+eP12muXsOXOVU6Gjc49FsDP18W5Ov38Wsl8eIZ6s35HQdnu/5M8G7idweoRkPq5iVRlRBiaslfrRBCnEJZYRkUGrN0geDMa4x8tKdqRMctCg35o/voKEZrMz7e4xx4T/5wDYqUIDiYr7qkphnduj4OKACcY3jrY+q1vd//MK1orr5BkDRRQUA0t0i8cIYs37pjFBiFHXTHuROffIhNxwniNh0yunWd2vJZVBjhnEdv23MipuxtYLMUVxQM794inl964TYRKgg3f8f84dpmQ7tDoTRKT1aNC5IGleRUCHHiyE6FEEKcUtY6Rulxz2J/nPfoICCoJ5TDrbsEVW+DoHPmQBozGq02E5GfTcDta8uurBx9r2mev4RRCs+4s7lSW+/WOo+uN9BBiMsnKz3ZPCOoJQzyirJ0NFoz6CjeLDGrwpBodh5X5CitMLUE8Kgwpnn5DYpHD9BRTDQzy/DW9Wd3fMjbkaPM0rh4heHNj/FViYlr1M9doi/N7YQ4cSSoEEIIcWIVhWVmfpn09nXi1gw5Dyb+3zSa5AeUtF1VnqDRpHquXK4yAZ79XclPaobi4T2KR+NeD0G7Q/vMhS15GVlu6cwvQ1WggmAiH0MFIRY2++b0hiWtS6/jixy8x9TqeEAHAaM7N6mGfVQY0rz4OiqqoaIYkzRIH65NBE5hZ55im6NYB6UoHR5Dcvnak+pPnn7qJElbiBNIggohxBZxZKhFGqWgqDxpVkn+hJhK46Ztlua5yygc0cwcRfcRMF6cm0abcgdJ0zsxyi3tc5dIb1+nGg7QcY3k/GVG2d6vqhujUWW2GVDAeHfFNtuEYZPyhcT53rCkmYQ0X1tlcP1DvLMobcY5Fc9d3XfO0+2XaG1oNkLy9fvjvhZBQLJ8ljKOyR89ZHT7OvG5VaLZBbIHd6nNLxImDcpBn6A5g2m0NhvkHZaydJRSPU6IE0+CCiHEhEY9QKU9Bjdvg3OEM7O0l8/vqJqNEMehsu5J0zZNfWGF1vJZAErrD7Q5pXOe3rAiOXORulFY5xnmbl9Hq4zRVKPBlnE77GPmWpQvrOefVlmKQkPj6lso7/FKkWZ224Z5gdHYQRc7GgAel2cMPvmI9pU3yR+vY9MRWkN3UFHrnKH04OI2KmqTO08pjeeEEDskQYUQYpNSEGjH4O7NzbGy+xhTbxBFbYoDKjcqDpcxmlqkMXq807Rd0u+ryFrHYLS3BX4Y6me7c+XLnzPn/IGWOq0qS63ZJn+ufwRA0OqQfkqwUpTj0rXwtK/h9sniSU1DWUO1O9TrDarRkHTtNlU6wsQ1VBBSVR7v/YGX3xVCnC4SVAghNhmjscOtV02rQZdgsU0hFy2nXhhqGiGkd6+TFzlhe5bOwhk2nuw0xZGhFmuUHyf+DrOjaxQ3reqxIXQ56Se38NYSzS3S7szTO4Kr9M55nA6Jl84+CSw80dwCqt6g2sHjN+oBgfa4LMU0E/LKkz45jlWvBRSPH04ELPWV80Sz8+NqWWFMbeU8vaEEE0KI/ZOgQgixyVqPSRpbxk3SRCo8ngyNmmHwwQ82a/8Xjx6AglprEQUE5YjBzU/AOUy9QfvCKt1BiT+mpJkgMISBwjlPfgzd6pWCOFT03/9wcyx/cBcdRYRBsu2RooM2GFXUkg7N1+dQQF66HQU09djgB48Z3H/WwC45d4k4SsgLO/69HqxN/Ey2dpfm6hsoE2AWz9EbVqc+qBRCHAzpUyGE2OS9x2KIF8/wtDWuabaIOgvHsuATu/O0Q/OLzcTK7gZhoIgjzej29XEZVMb9DbK129Ti4/kqaDVC6j7Fr9/CpI/ptCK0PsSeCNswxlANelvGy+5jwuDo5pLllm6/ZKNfbu40fJY40uQPJruip/duUptoxz0ZMHhnUSbgca9gmEpAIYQ4OLJTIYSYMBhV1JtztGYXAKisP/TqL+JgjDs0b/1YN3GM92z2LHieHQ2oLRztQh4gjg2u92jc0Rug16XqbdA8f4XeAXXA3gnnHLpW3zJuanXQhjhWFMWUVj/zbOkj4a19ej2AynpMo4V9rn9H2JmTCwRCiEMhOxVCiC3SzLLx5KrpYFQd29EYsXtl5cY7TU8oY6ivvEaaW3QUb7m9abQ4ghM+W8SBJl+/PzFmsxStjva95pzHm4hwZnZzTMc1agtLMHiEGTxgphEQh+ZT7uXJfVlLpxXSaYXjKmqHHKtZ5wleOK4Yzsxu9pUYpnZ8HGpphaDRonbmPPHSOdJTkrgvhDhaslMhhBCvkGFqSZrztGYX8LZCmYBharHWkxWO5MIq6Z0beGsJGk1qS2fp7qPsqjGaJNYYo6isJ83tjhqXeTxKa/yL69vDXolvoz8saS6cpbZ8DrxHG83gxgfYdNwELl9/QOvqWxSVemmA3UwCsgd3yR6sgfeEL2lgd5CGmaV9YZX84Rp2NCRotYk6C5uvp/eejX5BXJ/FNGYpLQylNLQQ4pBIUCGEEK+YUVYxyp7+69lRoiy3uCimsfoWSo2Px/SG5Z6P9gRG0awpRrc+wmYppt6gdf7Sk47In779kRee2plzjG5+/Oz+2h2qY+qk/LRMbBga4rK7GVAA4D35wzXimTNk+dZKSVorjKsY3H9WZansbWAaLaKwdWilmJ3zbPQKaq0FwpkFKstmla/nyXEnIcRRkKBCCCFOkaJwFMXBnHdKagHDG+/hyvFC1qZDRjc/Ijm/Sn/46Y9RlJagVqd59W2qfnecwxDV6B9hPsVBGTew624Zt8MeZr79fFx3KE5LHxIhxHSToEIIIcSeaOU3A4qnbJZidniEaZRZlFIE8QzOOuweCwJEkaEWjlME88qR72ORXZaWRnsGdd/g7ZP7UYp4YZnucPv7tdYRNJpbxoPmDLnUYhZCnBISVAghhNgTj0KZAG+fHQnSYcRuqpR67yn3cTyoUQ9Q+YDRnTvgPfHCMmGzw2AfDd0Gw4rmlbcpu+t464jm5kkz/9J8Cuc8VgXUls+S3b87zqmYmcM0Zyh3mMOgtSKpGQKt8Aqy3MmxJSHEiSJBhRBCiD1Jc0dy4TKjmx+NS5magOTCKsMjOo6jtSLAMrh9Y3Msu3ebxsU6xoSfmdfxMpV1bPQLoloHpRTdwWeXlB2MKuYXlgln5gAoKk9vhwnwSkG7EZLe+ph0NACtqa9cQMeNI6nUFIaapGZQ3oHSpBLQCCH2QIIKIYQQe1KUFsKAxpW3UN7jUYwyS3VENWqDwFD21reMl91HhJ2VPQcVTxW7XFhrY1h/NNr149TigOz+HarRYDzgHOntG7Te+PxnBhVajytS7TnZPtAkgWP44Xvj415K07hwGR9FB5Z7I4Q4HSSoEEIIsWdF6SjKnS8+g0DjnD+QTs7OOUw92TKu6wnlCeqtYjTkTwOK57g8Q+tg2+cqMIpmEuDKAqUNThkGo91X8kpiw+iTD5/lj3jH6NZ1GlffkqBCCLErElQIIYQ4dLXYUAsV1bCPjmoQRvT3Uc4WoKocupkQNNtUgx4AJmkQtmZPVD8G6yBoNCle6Hiu4xqu2Jq8rtS4L8bgo3fw1Th3xDRatM5epLfLZHetwRWTz5V3FnWCgjIhxHSQoEIIIcShCgJNrCr677/3bKzZpnnmAv19JFQD9IYljeUL1M8q8B7rx2MnSZZXzCyexRUF1bCP0ob62QvkL9kpiKOA/MG9zYACwA77UOZobXa1C1TZcVfuajTcHNNhhOPomxAKIU42CSqEEEIcqlqkSe/cmBirBj3q7P9quPfPGtedVP5JIJSceY26UXgPWfHy0rhaeWyZbxl3ZYHWya6CilFmaZ+/THr7BtWwj6knJOcvMUhP9nMqhDh6Rx5UfPe73+XrX/86ZVnS6XT4zd/8Tc6dO3fU0xBCCHFEFDw7s/8c7x1qvMFw6jnndxwcFRXUZxeoBv1ng0oRNFpU/d3t0jjn6Q0r6suvUQsU1vonHdHlRRFC7I4+6gf8yle+wte+9jX+8A//kC996Ut87WtfO+opCCGEOEJF5YnmFifGdBiBCV65gGKHff92JQg0rSRgphmS1AKstRA3qJ+9iKnVCRpNmpevkeZ7S6x2zjNMK7r9ksGo2nfVLCHE6XSkOxVFUfDLv/zLvPnmmwBcu3aNf/2v//VRTkEIIcQRywtL1OyQnA8oNh6h45h4fpn+6OT3QkhqAVGo0FpRDge0E41jb5WYthOFmnroSW9/hM0zwnaHmeXzdAcFYdAgOruKBwaFGwcbQghxTI40qIiiiC9/+cvAuBTgN7/5Tb7whS8c5RSEEEIcg/6wJAwTwsUE56E7OJhF93FqJAG+/wjVnqH30Yf4anz0KGi2aK3svhLTdpKaof/B98GNdw/K7mNQmtrsMmlm2aY4lBBCHAvl/eF8rH/nO9/h61//+sTY6uoq3/rWtyiKgq9+9at0u13++T//54RheBhTEEIIIQ5NlY3I1x/gnaN4PNmEr7V6jbDZ2v9jpCN6739/YkyZgJk33h4fIRNCiClxaEHFywyHQ37hF36BTqfDb//2bxNFu/tQXF8fHEjTJHHwFhdbPHjQ/+wbCnFI5D0oDkoYaBp1M+5/oTRBo0X/uXwDYzR1UigLymF/MmkaqJ+7SKaTfXcX77RC+u/95cRY0GgRLL/GUCo0iRfIZ6A4CFor5uebu/+5Q5jLp/rKV77CxYsX+Z3f+Z1dBxRCCCHEYVMKGnXD4IMfkN75hPT2dQYfv0Or8ezEsLWOoN6gHPSI2rNb7iBotPYdUADkpaN25jw86RuhgpD62QtkheRPCCGmy5HmVHz/+9/nT/7kT7h69So//dM/DcDS0hL/8l/+y6OchhBCCPFSURSQr9/Hu2cLd1+WVP0uYdikLMfjeemJZhdRWlE/c4788TraBNTOnCN9SY+J3UozS73WpvXGLHiHRzFIrZR8FUJMnSMNKt5++23efffdo3xIIYQQJ5xSinqsCYyispAV9lCPwSoAt01fDWs3vzW1VgRGYeImGvBJk6gzT1HYJ5WYDq4sa5rbAwtShBDisEhHbSGEOERRaJ4shj1FKQvD3dJa0W6EZPduMhoOMEmD9soFBmmF1gbwFAd8FKgoLa25pcnka6UJZ2YZ9kuUUrQbAaObH2HTEWhNcvY1oplZBunWTtdCCHEaSFAhhBCHQCmYaUaU3UdUwz5ho0UyM0d3UJz4UqpHKakZ0lsfU40GAFT9LkUc05pbIn/8EKUNycwcg1FJdUBHgpzz5FbTvPIW+cN7KK2JF84wysbBSz02ZGu3xwHF+AcY3bpO2GwfyOMLIcRJJEGFEEIcgqQWkN67SdXbAKAa9KjSIcnCuVNRtScMDcBm/sFeBUaRPgkoYJyoHM3M0nv/ezyNzvKHazSvvMVGv9jXYz0vyy2FVsSzK3gU3aHlabFEo6EcDbf8jCtzlFKAl8BRCHHqHHn1JyGEOA3CQG0GFE9VvQ3CQB3TjI5GYDSdVkRU9oiKHp1WSBjs/avGeVDBs+tfUbtD/ughz6/ava2oBl2CwOxr7lse23nS3JLlFc9XX6+cxyRbyy3qMGKmGdKOx6Vg6/HkfLRWGPNqv/5CiNNLdiqEEOKwKDWx+EW9+gvKZhIw+PAHeDvejcnu36F19W26A7enq/d54Wheep2y+5iy3x1nUb8kSfuont4st8wsn8OXBdVogDIBybnXcFVF/8N3Nl/z+rmL1OIGReloJgFUBd45TFJnMKqoDjCZWwghjpsEFUIIcQjywlFbWiFbu7M5VltaIS+mayGp1Pio1tMdlKxwZHusNBSGhrL3eDOgAMA5ikcPiBrz5LtMqA4DTT1W5A/W8FVF/cx5dFzDO0ux8RgYL96VMYStGbLR0Rwr8x56w5Jk5SJ1o8YxhFIMPnpnIohM79yk9frbxJEh/eQDbJY+mW9A88qbew60hBBiGklQIYQQhyDNLY3GLM0rbarRkCBpYL0hnbJ8iplmRHr3E7J+F5SitnSWRqOzp7wPpcC7rUGTd25P2wiNesDgg+9v9oso+10aF69S6pjW629TPHqAMoZoZpb84RpJs42tx0eSs+KcZ/BcENNphfiqnLyRHz8XLhttBhQwPq6VP1wjbi/uOYATQohpIzkVQghxSIZpRS+FImzRS2EwZQFFFBnK7jpVvzse8J5s7TaBck8SjnenKCxRZw7Uc18tShHPL+267KsxGjsaTDSgA8jX76MUdIeWeHEFW+T0PniHfP0+wxsfYGxOsI8cjr0qK7+l+pOOa3gUrtyaQO6r8jSchhNCnCISVAghxCHy3lOWdiLRd1oEWlEN+lvG7Wi454TiUWZpvf4W0dwi0dwCratvkRZ+D7+/R5mtidfKGLwHYxTVoEe58WhzRwDGQUcUHv1X2yizNC5cIuzMo4KQoD1D4+JVBqOKsDWzZacmml2gKKfvPSGEEHslx5+EEOKUqpwnbLaohpOBhUka2HRvC96idJSVI2ovoWCiFOtuWOtRSR1Tqz87OqQ0tcUVeqlFKT416Dhq3nt0GKE6y9QXzmAd9IbVuIJUpmiuvkl+/zbeOqKFJayJscV07VwJIcR+SFAhhBCnVFFYkpl5qnRI1euOF+1LK1Re4/3eF7zeQ57vf8HcH5a0XruKy0b4qiJothhlFvek+pNKapNBhx7Pvzc6nDwFYxT2MxrspbmFF5pq56Wlcop48QIKT1pCNWVH4YQQYr8kqBBCiFOsOyhIFs5TP3MBeFL9aUoWvM55uv0CYyKUiaj6k4nQ/WFF68JVfJHiqoqg0WSUuc2g46AktYAoAJulmGZCXrpx8LAL1npGU/K8CiHEYZCgQgghTjHvmfoO3/Yl/Ryc83QHBcYEKB1uCToOQi02qLRL/96tzbHk/CXiKNl1iVwhhHiVSaK2EEKIE81aT1UdTv+PWqTJ1m5PjKV3b1KL5OtTCCGeJ5+KQgghxMt4eDHz21t7IOVglYIg0FJaVgjxSpCgQgghhHiJynmCpDExFrRmKKv95W006gHtRFNzKTONgKS2tZKVEEKcJJJTIYQ4NEGgCQON855cOgeLE2iUWdrnV8kf3sOOBgTNNtHcEt3B3vM36rHB9x8xeHD32dg5ydMQQpxsslMhhDgUzSQgUQV+/TZmsE6nFWGMfOSIk+VpMrhvLxKevYxrzrPRL/bVzDCONPnDexNj2T3J0xBCnGyyUyGEOHBRaCAbMLx9Y3Os7D6mefka3X5xjDPbKo4NgQbrIC/ssTROE9PNe8gOcqftEPM0hBDiuMhlESHEgYtCRfFwbWLMlQWUBWpKVk5KMd49GTyivHsd1XvATDNC6+mYn3i5ODLU4uDE7nzZbfI0wplZin3maQghxHGSnQohxIHzHpTZJvFUa+BwSn/uVj0OyO7dpOxtAGDTETYd0Th7if5ouvs2HAalwBiDcwffPO6gGKNpJQHF44f4IqMxu4CNI4Yn7PUaPsnTKB7dx44GmOYMUWee7mC6dvGEEGI3JKgQQhy4vHQ0ls8x+Pi9zTGTNPHK4P10BBVRqOg/CSiesukQcwp3KmqxoRYqqkEfHdcgiOg0LqLrAAASOklEQVSPyqk7CtasG4bX38MVOQBF9zHJ+UuEYZ2q8iQ1QxgonIcsdxTldCY9O+fZ6BfUmvME7QUqO/63EEKcZBJUCCEOXFU5chPQev1zlP0uOorRcZ3ecHquKDsPygR4+9yclIJTFlOEoSGipP/++5tjQWuGxtJ5BlO0A6AUYKvNgOKp/OEa8blVGjVNevcTsn4XZQLqZ19Dx7WDzYU4YNM8NyGE2K2TeSBVCDH1stzSHVYUUZuRi+gOyn1VzDloWWGpr1yYGKstrZAXx7+TktQDOq2QTiukHh9u/4I4VGR3b06MVf0uwSF/O4SBZqYZ0mmOf9c42sHvuV0+jlIYrcjX16j6XQC8rRjd/EiqKQkhxBGSnQohxKHxHspjOoISGE2jblB4UIqscBNXhovCYeI6rdc/h81STFyjdIo0Pd6r8zPNiPzBHfob66AU8eIKzdbsoe0aKAXebX2NDvOYWhBokgiGH70z3ilSmuTCJYhqL+3T4D14bTD1BjYdbo7Xls/hgGrQ2/IzNk/ROpzaHBEhhHiVSFAhhHjlGKNp1hSDj9/FVyUoRXL2IsTJRGCR5pY0B2Ni3Oj4y8mGgcYOu5Qb6+MB78nv36HZbKG1OpTFcVF6orklsrXbm2M6ikEZDiupvh5rRjc/fHb0zDtGt67Tuvr2pzZ/6w8r2hdWcaMBtsiJ2h3yCqg8pt7A5dnE7U1UwxXTc4RLCCFeZRJUCCFeOfVYM7p9fRxQAHjP6M4NWq9/bttz7NYe/5EnGF/Br7pbr7hXwz4m7uC22VHYr7ywRK1ZkiCk7D5CxTXi+eVDrYBltNoSAODclt4NL/Le0+0XBEENXa+TPgkElYKZ5XOEjSYuz8i7j4jnl5Hm1EIIcXQkqBBCvHKMVtgsnRz0frxwnWLWeqJGa7PM7VMmaWIPMdejPywJw4RwMcF6Dr0SUVl5gkaTajjYHFNBiN9hlnxVTT4XzSSkGnQpH6+jw4j25WtklWd0zEfZhBDiNJEsNiHEK6e0nqDVmhhTxjzpkzG9itJiWh3Cdmc8oBTxwjLOHH5eQFlaRpklP4KKRGluqZ+7RNAYv0amVqd56SrDbPePHYUGP+qS3r5BNRpQdB/R+/AHRMEpK+MlhBDHTHYqhBCvnDSzzJx5jdTfoOr3MHGN+vlLe1q0HrXeoCBZOEftzHlg3PNjMEWleA+Cc57esKK+/Br1QGOto5+5PR1DiwJFcf/hxJi3FlfkaG0kSVsIIY6IBBVCiFeO957esKS+eIH6isY6xzB3W47NTCPvYXgKju045w/k9/SM+428SJkAPwXlgYUQ4rSY7rMAQgixR08XrRv9gv6wOhEBhdgDpUhWzk/0sAiabZwyx17NSwghThPZqRBCCHEi1WIDww3S0YD26jWqdISp1fFBRG9wuMnmQgghJklQIYQQ4kSqRZr+jdvgPWWvi6nV8N5Tf+2q7FIIIcQRk6BCCCHEyeT9c70t/GYZYS2Fn4QQ4shJToUQQogTyXqFqScTY0FrhrKSbQohhDhqElQIIYQ4kYZpRXLhCtHsPCauEc0vUV95jdEJKB0shBCvGjn+JIQQ4kRyztMdFNQ6Z4hmPZVTh94NXAghxPYkqBBCCLFvUWRQSlGW9kgbznkPafbq9/UQQohpJ8efhBBiSik10X5hKmmt6LQiwryH7t6jFXkadbleJYQQp4188gshxJTRWtFMApSrxi2jTUB/VB3pDsBONZOA0Y33sXkGQPF4neTCZRpJA2sdeWGlvKsQQpwCElQIIcSUaTdCRp988KxEalyjffH1qcsXUAqUs5sBxVP5/bvUz5zHDbrMzC8zSK10NBdCiFecHH8SQogpEoaGatDdDCgAXJ5R9h4TReYYZ7YLSuGqkmL9AYOP3qUpx6GEEOKVd+RBxZ/92Z/xMz/zM3zpS1/iH/7Df0i32z3qKQghxNTSWuGKbMu4yzPUlCVYeA9emy29ImoLyxQbj8a3qUpcmR/q3LVWGCPXyIQQ4jgd+afwP/2n/5Tf+q3f4o/+6I+4evUq/+pf/aujnoIQQkytsrSEM/NbxqPZecpy+vovDEbjXhH1sxeJF5Zprb6BLXKqYX/zNkobxskhny4INEGw890YpcZHxVqRJ1EZnVZIFElwIYQQx+HI96T/+I//mDAMKcuStbU1rl27dtRTEEKIqeWcp3SaxmtXyB7cBe+JF1coCXBu+kqnOufZ6BeEYYOg1sKriuz+vc3/N0kTrwzevzynwhhNqxFghwO8cwStFsPUUn5GHkYzCcnvfUI16I0HlKK5eg1rNdZKDocQQhylIw8qwjDk3Xff5R/8g39AEAT843/8j496CkIIMdVGmSUMY+Kzl8FDVjrKdPoCiueVpR33qIgMrdffphr00FEMUY3+8OVzb9QNcWTof/gurhwnoittaF59i+7AvbRylFKgvX0WUAB4T7Z2m9rSawxTCSqEEOIoKe8Pp9jfd77zHb7+9a9PjK2urvKtb31r89+///u/z7e//W1+//d//zCmIIQQYoo5W1F0H4N1jO7enPi/eH6JZOU8Sr/8OFM56NP/6N2JMVOr07r8BjoMD2XOQgghtndoQcV28jznv/23/8YXvvAFAEajEX/zb/5N/vzP/3zH97G+PpjKWu0CFhdbPHjQ/+wbCnFI5D14snRaIemdG4TNNum92xP/F3bmoLNClr98l6PTChl8+A7ePrtN/ewFiqBFcQz5J/L+E8dN3oPiIGitmJ9v7v7nDmEuLxUEAb/2a7/GX/7lXwLj3Yy/+lf/6lFOQQghxLTwHm8t0cwsqMmvo9rC8mcGBoPU0rzyJmFnjiBpUj93EZXMHEtAIYQQp92R5lQYY/jGN77Br/7qr2KtZXl5md/4jd84yikIIYSYEg5FPLdAtv6A1uob5OsP8N4Rzy2A0nj/6XkkVeXoDjy12RWMgrx0lMPyiGYvhBDieUeeqP0jP/Ij/If/8B+O+mGFEEJMmWFqaTfb5A8/oNhYJ5qZRauA0e1PqJ+7yHgz/dOPu3rvSbPpTmIXQojTQAp6CyGEOBbWOka5J5pfwlcV+foDsodreGfRYcQRpvwJIYTYpyPfqRBCCCGeyvOKqNEmOX+J4vE6OoqIF1cYjGT3QQghThIJKoQQQhyr/rAkDBPCpQbOe7qD8qX9KYQQQkwnCSqEEEIcu3HzvOOehRBCiL2SnAohhBBCCCHEvkhQIYQQQgghhNgXOf4khBAngNYKpRTWuiN5vEY9IAwUeI/1imFa4ZwkOgghhNieBBVCCDHFlFK0GgGUOd5aTKvBMK0oq8MLLtqNkOLBbbLuYwBMPaF94Qob/eLQHlMIIcTJJkGFEEJMsVYjIL31ES4djQe0pnXlLXojfyg7B8YoqHLKJwEFgE1H4+Z09Q5FYQ/8MYUQQpx8klMhhBBTSmsFZf4soABwjuz+HeLIHNJjauzzj/f0YbMhRqtDeUwhhBAnnwQVQggxpbRW+GprEzhvKw5reV9VjqDV3jIetmeprORUCCGE2J4EFUIIMaWqymGSBujJj+pobonikHIqvPeUVpGcv4QKQ5Q2xItnUPUmZSlHn4QQQmxPciqEEGKKjTJL68qbZGt38NYSzS3iwhrVaOsOxkE+ZhQmJBffAKUoSk9vIJ3phBBCvJwEFUIIMcWK0lFZRTx/Fq0gLTnUgOLZ41oKiSOEEELskAQVQggx5ZzzpJkcPRJCCDG9JKdCCCGEEEIIsS8SVAghhBBCCCH2RYIKIYQQQgghxL5IUCGEEEIIIYTYF0nUFkKIKRXHhkBD5SDPJVFbCCHE9JKdCiGEmDJKQacVYYaPqO7dwAzW6bQilDqsPtpCCCHE/shOhRBCTJmkFpDe/YSq3wWgGg2xWUpj+QKDI+hRIYQQQuyW7FQIIcSUCQO1GVA8VQ16BEZ2KoQQQkwnCSqEEGLKeAD9wsezko9rIYQQ00u+pYQQYsrkuaO+fG5irLa8Qla4Y5qREEII8ekkp0IIIaZMVliSWpvW1bep0hGmnlA5RZZKPoUQQojpJEGFEEJMoVFWkSrQuo4bWbw/7hkJIYQQLydBhRBCTCnvwVo58iSEEGL6SU6FEEIIIYQQYl8kqBBCCCGEEELsiwQVQgghhBBCiH2RoEIIIYQQQgixLxJUCCGEEEIIIfZFggohhBBCCCHEvkhQIYQQQgghhNgXCSqEEEIIIYQQ+yJBhRBCCCGEEGJfJKgQQgghhBBC7IsEFUIIIYQQQoh9kaBCCCGEEEIIsS8SVAghhBBCCCH2RYIKIYQQQgghxL4Exz2B3dJaHfcUxKeQ10ccN3kPiuMk7z9x3OQ9KPZrr+8h5b33BzwXIYQQQgghxCkix5+EEEIIIYQQ+yJBhRBCCCGEEGJfJKgQQgghhBBC7IsEFUIIIYQQQoh9kaBCCCGEEEIIsS8SVAghhBBCCCH2RYIKIYQQQgghxL5IUCGEEEIIIYTYFwkqhBBCCCGEEPsiQYU4cN///vf5/Oc/f9zTEKfQd7/7XX72Z3+WL3/5y/zcz/0ct2/fPu4piVPij/7oj/ipn/opfuInfoLf+73fO+7piFPmm9/8Jl/84hf54he/yG/91m8d93TEKSVBhThQaZry67/+65RledxTEafQV77yFb72ta/xh3/4h3zpS1/ia1/72nFPSZwCa2trfOMb3+Df/Jt/w7e//W3+7b/9t3zwwQfHPS1xSvzpn/4p//2//3f+4A/+gG9/+9t873vf4z//5/983NMSp5AEFeJA/bN/9s/4uZ/7ueOehjiFiqLgl3/5l3nzzTcBuHbtGnfv3j3mWYnT4E//9E/50R/9UTqdDkmS8Hf+zt/hP/2n/3Tc0xKnxOLiIl/96leJoogwDLly5Qp37tw57mmJU0iCCnFg/uRP/oQsy/jJn/zJ456KOIWiKOLLX/4yAM45vvnNb/KFL3zhmGclToP79++zuLi4+e+lpSXW1taOcUbiNHn99df54R/+YQCuX7/Od77zHX78x3/8mGclTqPguCcgTp7vfOc7fP3rX58YW11dZTAY8K1vfet4JiVOlZe9B7/1rW9RFAVf/epXqaqKn//5nz+mGYrTxDmHUmrz3977iX8LcRTef/99fv7nf55/8k/+CZcuXTru6YhTSHnv/XFPQpx8/+7f/Tv+xb/4FzQaDQDeeecd3nzzTX7v936PZrN5zLMTp8VwOOQXfuEX6HQ6/PZv/zZRFB33lMQp8Ad/8Af82Z/9Gb/xG78BwO/+7u/iveeXfumXjnlm4rT47ne/yz/6R/+IX/mVX+GLX/zicU9HnFISVIhDce3aNd59993jnoY4ZX7xF3+R+fl5fu3Xfg2t5XSnOBpra2v8/b//9/n3//7fU6/X+Xt/7+/x67/+6/zQD/3QcU9NnAJ3797lp3/6p/nGN77Bj/3Yjx33dMQp9v+3d/+u1LdxHMDfTwYmZTqLckgmnTL4E2zkRwYWC7Iy2hU5g5IyyCAWo50y2JVBLJQsStnk5Md5hrtHebbH99xO3c/rtX2va/lc47vP5/pexp+AP8Ll5WVOTk7S29ub8fHxJL9m23d2dppcGX+6UqmUpaWlzMzM5PX1NZOTkwIFP2Z3dze1Wi1ra2ufa1NTU5menm5iVfwf6VQAAACFmA8AAAAKESoAAIBChAoAAKAQoQIAAChEqAAAAArxS1kA/rP7+/sMDQ2lr6/vc61er2dmZiaTk5Op1WrZ3t7O6elp6vV6Pj4+MjIykvn5+S+vTV9dXWVubi5nZ2fNOAYADSJUAPAtbW1tOTo6+vx+eHjI8PBw+vv7U61W093dncPDw7S2tubp6SkLCwt5fn7O4uJi3t7ecnBwkJ2dnTw/PzfxFAA0gvEnABqiVCqlq6srx8fHubm5yfLyclpbW5MkHR0dWV9fz+DgYJJfjxVeX19na2urmSUD0CA6FQA0xPn5ee7u7pIklUolLS0tX/bL5XLK5fLnfqVSyf39/U+XCcBvIFQA8C0vLy8ZHR1Nkry/v6ejoyPVajW3t7ep1+tNrg6AnyRUAPAt/75T8Y/29vbs7e3l/f39S7fi4uIi+/v7qVarP1kmAD/AnQoAGmpgYCA9PT1ZXV1NrVZLkjw+PmZlZSWdnZ1Nrg6A30GnAoCG29zczMbGRiYmJtLS0pKPj4+MjY1ldna22aUB8Bv8VTf4CgAAFGD8CQAAKESoAAAAChEqAACAQoQKAACgEKECAAAoRKgAAAAKESoAAIBChAoAAKCQvwGnqPEvXoOF8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 842.4x595.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seaborn.set(rc={'figure.figsize':(11.7,8.27)})\n",
    "ax = seaborn.scatterplot(x=\"PC1\", y=\"PC2\", hue = 'CDR', data=tabularcs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA : LTD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Subject ID</th>\n",
       "      <th>Group</th>\n",
       "      <th>Visit</th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>EDUC</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "      <th>Educ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>OAS2_0001</td>\n",
       "      <td>Nondemented</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>87</td>\n",
       "      <td>14</td>\n",
       "      <td>2.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0.696</td>\n",
       "      <td>0.883</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>OAS2_0001</td>\n",
       "      <td>Nondemented</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>88</td>\n",
       "      <td>14</td>\n",
       "      <td>2.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2004</td>\n",
       "      <td>0.681</td>\n",
       "      <td>0.876</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>OAS2_0002</td>\n",
       "      <td>Demented</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>75</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1678</td>\n",
       "      <td>0.736</td>\n",
       "      <td>1.046</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OAS2_0002</td>\n",
       "      <td>Demented</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>76</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1738</td>\n",
       "      <td>0.713</td>\n",
       "      <td>1.010</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OAS2_0002</td>\n",
       "      <td>Demented</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1698</td>\n",
       "      <td>0.701</td>\n",
       "      <td>1.034</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Subject ID        Group  Visit  M/F  Age  EDUC  SES  MMSE  CDR  eTIV   nWBV  \\\n",
       "0  OAS2_0001  Nondemented      1    0   87    14  2.0  27.0  0.0  1987  0.696   \n",
       "1  OAS2_0001  Nondemented      2    0   88    14  2.0  30.0  0.0  2004  0.681   \n",
       "2  OAS2_0002     Demented      1    0   75    12  2.0  23.0  0.5  1678  0.736   \n",
       "3  OAS2_0002     Demented      2    0   76    12  2.0  28.0  0.5  1738  0.713   \n",
       "4  OAS2_0002     Demented      3    0   80    12  2.0  22.0  0.5  1698  0.701   \n",
       "\n",
       "     ASF  Educ  \n",
       "0  0.883    14  \n",
       "1  0.876    14  \n",
       "2  1.046    12  \n",
       "3  1.010    12  \n",
       "4  1.034    12  "
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lg.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Visit</th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>EDUC</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "      <th>Educ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "      <td>373.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.882038</td>\n",
       "      <td>0.571046</td>\n",
       "      <td>77.013405</td>\n",
       "      <td>14.597855</td>\n",
       "      <td>2.436997</td>\n",
       "      <td>27.351206</td>\n",
       "      <td>0.290885</td>\n",
       "      <td>1488.128686</td>\n",
       "      <td>0.729568</td>\n",
       "      <td>1.195461</td>\n",
       "      <td>14.597855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.922843</td>\n",
       "      <td>0.495592</td>\n",
       "      <td>7.640957</td>\n",
       "      <td>2.876339</td>\n",
       "      <td>1.109307</td>\n",
       "      <td>3.675329</td>\n",
       "      <td>0.374557</td>\n",
       "      <td>176.139286</td>\n",
       "      <td>0.037135</td>\n",
       "      <td>0.138092</td>\n",
       "      <td>2.876339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>60.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1106.000000</td>\n",
       "      <td>0.644000</td>\n",
       "      <td>0.876000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>71.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>27.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1357.000000</td>\n",
       "      <td>0.700000</td>\n",
       "      <td>1.099000</td>\n",
       "      <td>12.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>77.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>29.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1470.000000</td>\n",
       "      <td>0.729000</td>\n",
       "      <td>1.194000</td>\n",
       "      <td>15.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>82.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1597.000000</td>\n",
       "      <td>0.756000</td>\n",
       "      <td>1.293000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2004.000000</td>\n",
       "      <td>0.837000</td>\n",
       "      <td>1.587000</td>\n",
       "      <td>23.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Visit         M/F         Age        EDUC         SES        MMSE  \\\n",
       "count  373.000000  373.000000  373.000000  373.000000  373.000000  373.000000   \n",
       "mean     1.882038    0.571046   77.013405   14.597855    2.436997   27.351206   \n",
       "std      0.922843    0.495592    7.640957    2.876339    1.109307    3.675329   \n",
       "min      1.000000    0.000000   60.000000    6.000000    1.000000    4.000000   \n",
       "25%      1.000000    0.000000   71.000000   12.000000    2.000000   27.000000   \n",
       "50%      2.000000    1.000000   77.000000   15.000000    2.000000   29.000000   \n",
       "75%      2.000000    1.000000   82.000000   16.000000    3.000000   30.000000   \n",
       "max      5.000000    1.000000   98.000000   23.000000    5.000000   30.000000   \n",
       "\n",
       "              CDR         eTIV        nWBV         ASF        Educ  \n",
       "count  373.000000   373.000000  373.000000  373.000000  373.000000  \n",
       "mean     0.290885  1488.128686    0.729568    1.195461   14.597855  \n",
       "std      0.374557   176.139286    0.037135    0.138092    2.876339  \n",
       "min      0.000000  1106.000000    0.644000    0.876000    6.000000  \n",
       "25%      0.000000  1357.000000    0.700000    1.099000   12.000000  \n",
       "50%      0.000000  1470.000000    0.729000    1.194000   15.000000  \n",
       "75%      0.500000  1597.000000    0.756000    1.293000   16.000000  \n",
       "max      2.000000  2004.000000    0.837000    1.587000   23.000000  "
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lg.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M/F</th>\n",
       "      <th>Age</th>\n",
       "      <th>EDUC</th>\n",
       "      <th>SES</th>\n",
       "      <th>MMSE</th>\n",
       "      <th>CDR</th>\n",
       "      <th>eTIV</th>\n",
       "      <th>nWBV</th>\n",
       "      <th>ASF</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Subject ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OAS2_0001</th>\n",
       "      <td>0</td>\n",
       "      <td>87</td>\n",
       "      <td>14</td>\n",
       "      <td>2.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0.696</td>\n",
       "      <td>0.883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS2_0001</th>\n",
       "      <td>0</td>\n",
       "      <td>88</td>\n",
       "      <td>14</td>\n",
       "      <td>2.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2004</td>\n",
       "      <td>0.681</td>\n",
       "      <td>0.876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS2_0002</th>\n",
       "      <td>0</td>\n",
       "      <td>75</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1678</td>\n",
       "      <td>0.736</td>\n",
       "      <td>1.046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS2_0002</th>\n",
       "      <td>0</td>\n",
       "      <td>76</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1738</td>\n",
       "      <td>0.713</td>\n",
       "      <td>1.010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OAS2_0002</th>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1698</td>\n",
       "      <td>0.701</td>\n",
       "      <td>1.034</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            M/F  Age  EDUC  SES  MMSE  CDR  eTIV   nWBV    ASF\n",
       "Subject ID                                                    \n",
       "OAS2_0001     0   87    14  2.0  27.0  0.0  1987  0.696  0.883\n",
       "OAS2_0001     0   88    14  2.0  30.0  0.0  2004  0.681  0.876\n",
       "OAS2_0002     0   75    12  2.0  23.0  0.5  1678  0.736  1.046\n",
       "OAS2_0002     0   76    12  2.0  28.0  0.5  1738  0.713  1.010\n",
       "OAS2_0002     0   80    12  2.0  22.0  0.5  1698  0.701  1.034"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = list(lg)\n",
    "features.pop(6)\n",
    "longi = lg.set_index('Subject ID').drop(columns = ['Group', 'Visit', 'Educ'])\n",
    "longi.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.15379808,  1.30873772, -0.20813199, ...,  2.83605891,\n",
       "        -0.90516867, -2.2657425 ],\n",
       "       [-1.15379808,  1.43978716, -0.20813199, ...,  2.93270307,\n",
       "        -1.30964265, -2.31650145],\n",
       "       [-1.15379808, -0.26385558, -0.90439416, ...,  1.07940909,\n",
       "         0.17342861, -1.08378418],\n",
       "       ...,\n",
       "       [ 0.86670278, -2.09854775, -0.55626308, ..., -0.96148827,\n",
       "         1.92614919,  0.98283006],\n",
       "       [ 0.86670278, -1.83644887, -0.55626308, ..., -0.91600866,\n",
       "         1.79132453,  0.92481984],\n",
       "       [ 0.86670278, -1.57434999, -0.55626308, ..., -0.88189896,\n",
       "         1.92614919,  0.88131217]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "lx = longi.iloc[:, [0,1,2,3,4,6,7,8]].values\n",
    "ly = longi.iloc[:, [5]]\n",
    "lX_std = StandardScaler().fit_transform(x) #standardized data!\n",
    "lX_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# COVARIANCE MATRIX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance matrix \n",
      "[[ 1.00268817  0.03782786 -0.0895192   0.048634    0.16898277 -0.57408805\n",
      "   0.25028903  0.56315721]\n",
      " [ 0.03782786  1.00268817 -0.02796079 -0.04553242  0.05540365  0.04246226\n",
      "  -0.51975265 -0.03516099]\n",
      " [-0.0895192  -0.02796079  1.00268817 -0.69307976  0.19267487  0.25770596\n",
      "  -0.01223243 -0.24240188]\n",
      " [ 0.048634   -0.04553242 -0.69307976  1.00268817 -0.14031873 -0.24969899\n",
      "   0.09260902  0.24147833]\n",
      " [ 0.16898277  0.05540365  0.19267487 -0.14031873  1.00268817 -0.03633111\n",
      "   0.34310855  0.04508105]\n",
      " [-0.57408805  0.04246226  0.25770596 -0.24969899 -0.03633111  1.00268817\n",
      "  -0.21068667 -0.99153479]\n",
      " [ 0.25028903 -0.51975265 -0.01223243  0.09260902  0.34310855 -0.21068667\n",
      "   1.00268817  0.21405   ]\n",
      " [ 0.56315721 -0.03516099 -0.24240188  0.24147833  0.04508105 -0.99153479\n",
      "   0.21405     1.00268817]]\n"
     ]
    }
   ],
   "source": [
    "lmean_vec = np.mean(lX_std, axis=0)\n",
    "lcov_mat = (X_std - lmean_vec).T.dot((lX_std - mean_vec)) / (lX_std.shape[0]-1)\n",
    "print('Covariance matrix \\n%s' %lcov_mat)\n",
    "#CovarianceMatrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "High five! You successfully sent some data to your account on plotly. View your plot in your browser at https://plot.ly/~KevinMiao/0 or inside your plot.ly account where it is named 'selecting-principal-components'\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\" seamless=\"seamless\" src=\"https://plot.ly/~KevinMiao/0.embed\" height=\"525px\" width=\"100%\"></iframe>"
      ],
      "text/plain": [
       "<chart_studio.tools.PlotlyDisplay object>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tot = sum(eig_vals)\n",
    "var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)\n",
    "\n",
    "trace1 = dict(\n",
    "    type='bar',\n",
    "    x=['PC %s' %i for i in range(1,5)],\n",
    "    y=var_exp,\n",
    "    name='Individual'\n",
    ")\n",
    "\n",
    "trace2 = dict(\n",
    "    type='scatter',\n",
    "    x=['PC %s' %i for i in range(1,5)], \n",
    "    y=cum_var_exp,\n",
    "    name='Cumulative'\n",
    ")\n",
    "\n",
    "data = [trace1, trace2]\n",
    "\n",
    "layout=dict(\n",
    "    title='Explained variance by different principal components',\n",
    "    yaxis=dict(\n",
    "        title='Explained variance in percent'\n",
    "    ),\n",
    "    annotations=list([\n",
    "        dict(\n",
    "            x=1.16,\n",
    "            y=1.05,\n",
    "            xref='paper',\n",
    "            yref='paper',\n",
    "            text='Explained Variance',\n",
    "            showarrow=False,\n",
    "        )\n",
    "    ])\n",
    ")\n",
    "\n",
    "fig = dict(data=data, layout=layout)\n",
    "py.iplot(fig, filename='selecting-principal-components')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Variance Explained (%)</th> <th>Principal Component #</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>33.9719               </td> <td>1                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>27.483                </td> <td>2                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>18.0588               </td> <td>3                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>8.26561               </td> <td>4                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>7.08674               </td> <td>5                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3.62365               </td> <td>6                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1.20799               </td> <td>7                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>0.302319              </td> <td>8                    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Variance Explained (%) | Principal Component #\n",
       "33.9719                | 1\n",
       "27.483                 | 2\n",
       "18.0588                | 3\n",
       "8.26561                | 4\n",
       "7.08674                | 5\n",
       "3.62365                | 6\n",
       "1.20799                | 7\n",
       "0.302319               | 8"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tot = sum(eig_vals)\n",
    "var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)\n",
    "Table().with_column('Variance Explained (%)'\n",
    "                    , var_exp).with_column('Principal Component #', np.arange(1, 9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.3169669  -0.35472917]\n",
      " [-0.39027651  0.35206113]\n",
      " [ 0.23169947 -0.10627577]\n",
      " [-0.34916311  0.18359042]\n",
      " [ 0.30586641 -0.33424857]\n",
      " [ 0.42660873  0.43754387]\n",
      " [ 0.34439513 -0.45509079]\n",
      " [-0.42125934 -0.4415267 ]]\n"
     ]
    }
   ],
   "source": [
    "matrix_w = np.hstack((eig_pairs[0][1].reshape(8,1), \n",
    "                      eig_pairs[1][1].reshape(8,1)))\n",
    "\n",
    "print('Matrix W:\\n', matrix_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [-0.36584644, -1.17380672],\n",
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       "       [-0.63297668, -2.60757049],\n",
       "       [-2.43842974,  0.57517748],\n",
       "       [-2.19251905,  0.25122688],\n",
       "       [-1.32574736,  0.28712316],\n",
       "       [ 1.04232777, -1.082207  ],\n",
       "       [-2.26562673, -1.17738035],\n",
       "       [ 1.62481489, -0.81299636],\n",
       "       [ 0.80672608,  2.41572458],\n",
       "       [-1.09356586,  3.2754789 ],\n",
       "       [-2.94152411, -0.24004115],\n",
       "       [-1.05580326,  1.36713388],\n",
       "       [-1.87684977, -0.58273088],\n",
       "       [ 1.79475072,  1.03367578],\n",
       "       [-1.67333328, -0.1091488 ],\n",
       "       [ 2.12680688,  0.15724919],\n",
       "       [ 1.30944846, -0.48494684],\n",
       "       [ 1.20734654, -0.54542874],\n",
       "       [ 1.3354821 , -0.20271116],\n",
       "       [ 2.62612916,  0.60182184],\n",
       "       [ 2.32106449,  1.41686745],\n",
       "       [ 2.00652588,  0.6830269 ],\n",
       "       [ 1.08576199, -1.34125805],\n",
       "       [ 1.19410278, -0.63224104],\n",
       "       [ 0.36127405, -1.53340131],\n",
       "       [ 1.16768951, -0.96300397],\n",
       "       [ 1.30735829, -0.77541533],\n",
       "       [-0.58953707, -3.02545835],\n",
       "       [ 0.26947412, -1.1852531 ],\n",
       "       [-0.79855464, -2.90746025],\n",
       "       [ 1.37236185, -0.5970785 ],\n",
       "       [ 2.09345049,  0.98296669],\n",
       "       [ 1.96716225, -0.04274433],\n",
       "       [-0.39443316, -2.67344745],\n",
       "       [-0.51392051, -2.25099603]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = X_std.dot(matrix_w)\n",
    "Y #2-dimensional to make it more visually interesting!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
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       "        PC1       PC2\n",
       "0 -2.075984 -0.175575\n",
       "1 -1.336790 -2.932145\n",
       "2 -1.373963  0.732382\n",
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     "execution_count": 48,
     "metadata": {},
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   "source": [
    "PCCS = pd.DataFrame(Y, columns=['PC1', 'PC2'])\n",
    "PCCS.head()"
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  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
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       "        PC1       PC2             ID  M/F  Age  Educ  SES  MMSE  CDR  eTIV  \\\n",
       "0 -2.075984 -0.175575  OAS1_0001_MR1    1   74   2.0  3.0  29.0  0.0  1344   \n",
       "1 -1.336790 -2.932145  OAS1_0002_MR1    1   55   4.0  1.0  29.0  0.0  1147   \n",
       "2 -1.373963  0.732382  OAS1_0003_MR1    1   73   4.0  3.0  27.0  0.5  1454   \n",
       "3  1.610693  0.486512  OAS1_0004_MR1    0   28   3.0  2.0  29.0  0.0  1588   \n",
       "4  2.736422  0.742461  OAS1_0005_MR1    0   18   3.0  2.0  29.0  0.0  1737   \n",
       "\n",
       "    nWBV    ASF  \n",
       "0  0.743  1.306  \n",
       "1  0.810  1.531  \n",
       "2  0.708  1.207  \n",
       "3  0.803  1.105  \n",
       "4  0.848  1.010  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joinedcs = PCCS.join(cs)\n",
    "joinedcs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "        PC1       PC2  CDR\n",
       "0 -2.075984 -0.175575  0.0\n",
       "1 -1.336790 -2.932145  0.0\n",
       "2 -1.373963  0.732382  0.5\n",
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     "execution_count": 58,
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   ],
   "source": [
    "tabularcs = joinedcs[['PC1', 'PC2', 'CDR']]\n",
    "tabularcs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 842.4x595.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seaborn.set(rc={'figure.figsize':(11.7,8.27)})\n",
    "ax = seaborn.scatterplot(x=\"PC1\", y=\"PC2\", hue = 'CDR', data=tabularcs)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}