python-pour-finance/08-Analyse-Time-Series/.ipynb_checkpoints/4-ARIMA-et-ARIMA-Saisonnier...

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"___\n",
"\n",
"<a href='http://www.pieriandata.com'> <img src='../Pierian_Data_Logo.png' /></a>\n",
"___\n",
"<center>*Copyright Pierian Data 2017*</center>\n",
"<center>*For more information, visit us at www.pieriandata.com*</center>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Warning! This is a complicated topic! Remember that this is an optional notebook to go through and that to fully understand it you should read the supplemental links and watch the full explanatory walkthrough video. This notebook and the video lectures are not meant to be a full comprehensive overview of ARIMA, but instead a walkthrough of what you can use it for, so you can later understand why it may or may not be a good choice for Financial Stock Data.\n",
"____\n",
"\n",
"\n",
"# ARIMA and Seasonal ARIMA\n",
"\n",
"\n",
"## Autoregressive Integrated Moving Averages\n",
"\n",
"The general process for ARIMA models is the following:\n",
"* Visualize the Time Series Data\n",
"* Make the time series data stationary\n",
"* Plot the Correlation and AutoCorrelation Charts\n",
"* Construct the ARIMA Model\n",
"* Use the model to make predictions\n",
"\n",
"Let's go through these steps!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step 1: Get the Data (and format it)\n",
"\n",
"We will be using some data about monthly milk production, full details on it can be found [here](https://datamarket.com/data/set/22ox/monthly-milk-production-pounds-per-cow-jan-62-dec-75#!ds=22ox&display=line).\n",
"\n",
"Its saved as a csv for you already, let's load it up:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\Marcial\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
" from pandas.core import datetools\n"
]
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df = pd.read_csv('monthly-milk-production-pounds-p.csv')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Month</th>\n",
" <th>Monthly milk production: pounds per cow. Jan 62 ? Dec 75</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1962-01</td>\n",
" <td>589.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1962-02</td>\n",
" <td>561.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1962-03</td>\n",
" <td>640.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1962-04</td>\n",
" <td>656.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1962-05</td>\n",
" <td>727.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Month Monthly milk production: pounds per cow. Jan 62 ? Dec 75\n",
"0 1962-01 589.0 \n",
"1 1962-02 561.0 \n",
"2 1962-03 640.0 \n",
"3 1962-04 656.0 \n",
"4 1962-05 727.0 "
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Month</th>\n",
" <th>Monthly milk production: pounds per cow. Jan 62 ? Dec 75</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>164</th>\n",
" <td>1975-09</td>\n",
" <td>817.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>165</th>\n",
" <td>1975-10</td>\n",
" <td>827.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>166</th>\n",
" <td>1975-11</td>\n",
" <td>797.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>167</th>\n",
" <td>1975-12</td>\n",
" <td>843.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>168</th>\n",
" <td>Monthly milk production: pounds per cow. Jan 6...</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Month \\\n",
"164 1975-09 \n",
"165 1975-10 \n",
"166 1975-11 \n",
"167 1975-12 \n",
"168 Monthly milk production: pounds per cow. Jan 6... \n",
"\n",
" Monthly milk production: pounds per cow. Jan 62 ? Dec 75 \n",
"164 817.0 \n",
"165 827.0 \n",
"166 797.0 \n",
"167 843.0 \n",
"168 NaN "
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.tail()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Clean Up**\n",
"\n",
"Let's clean this up just a little!"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Month</th>\n",
" <th>Milk in pounds per cow</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1962-01</td>\n",
" <td>589.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1962-02</td>\n",
" <td>561.0</td>\n",
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" <tr>\n",
" <th>2</th>\n",
" <td>1962-03</td>\n",
" <td>640.0</td>\n",
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" <tr>\n",
" <th>3</th>\n",
" <td>1962-04</td>\n",
" <td>656.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1962-05</td>\n",
" <td>727.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Month Milk in pounds per cow\n",
"0 1962-01 589.0\n",
"1 1962-02 561.0\n",
"2 1962-03 640.0\n",
"3 1962-04 656.0\n",
"4 1962-05 727.0"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.columns = ['Month','Milk in pounds per cow']\n",
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Weird last value at bottom causing issues\n",
"df.drop(168,axis=0,inplace=True)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df['Month'] = pd.to_datetime(df['Month'])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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" <th></th>\n",
" <th>Month</th>\n",
" <th>Milk in pounds per cow</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1962-01-01</td>\n",
" <td>589.0</td>\n",
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" <td>1962-02-01</td>\n",
" <td>561.0</td>\n",
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" <th>2</th>\n",
" <td>1962-03-01</td>\n",
" <td>640.0</td>\n",
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" <th>3</th>\n",
" <td>1962-04-01</td>\n",
" <td>656.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1962-05-01</td>\n",
" <td>727.0</td>\n",
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"text/plain": [
" Month Milk in pounds per cow\n",
"0 1962-01-01 589.0\n",
"1 1962-02-01 561.0\n",
"2 1962-03-01 640.0\n",
"3 1962-04-01 656.0\n",
"4 1962-05-01 727.0"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df.set_index('Month',inplace=True)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"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>Milk in pounds per cow</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Month</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1962-01-01</th>\n",
" <td>589.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-02-01</th>\n",
" <td>561.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-03-01</th>\n",
" <td>640.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-04-01</th>\n",
" <td>656.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-05-01</th>\n",
" <td>727.0</td>\n",
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"</table>\n",
"</div>"
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"text/plain": [
" Milk in pounds per cow\n",
"Month \n",
"1962-01-01 589.0\n",
"1962-02-01 561.0\n",
"1962-03-01 640.0\n",
"1962-04-01 656.0\n",
"1962-05-01 727.0"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>count</th>\n",
" <th>mean</th>\n",
" <th>std</th>\n",
" <th>min</th>\n",
" <th>25%</th>\n",
" <th>50%</th>\n",
" <th>75%</th>\n",
" <th>max</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Milk in pounds per cow</th>\n",
" <td>168.0</td>\n",
" <td>754.708333</td>\n",
" <td>102.204524</td>\n",
" <td>553.0</td>\n",
" <td>677.75</td>\n",
" <td>761.0</td>\n",
" <td>824.5</td>\n",
" <td>969.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" count mean std min 25% 50% \\\n",
"Milk in pounds per cow 168.0 754.708333 102.204524 553.0 677.75 761.0 \n",
"\n",
" 75% max \n",
"Milk in pounds per cow 824.5 969.0 "
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.describe().transpose()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step 2: Visualize the Data\n",
"\n",
"Let's visualize this data with a few methods."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11e1831d0>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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t0mlFMi8gLOvzDCPdpGq0Vq3YbQQDIX0DqrNFNhhcuwbd63fpkiD0SB96N0oB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\nAym7s8vopLMWAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11e169d68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df.plot()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"timeseries = df['Milk in pounds per cow']"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1a11e5d8438>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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7gmy/WP0iwapgrs2+dtLxqOAo4kLiqDT6LgIbjm3A5rRx++Lbpz2frE3GEGTw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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11e5d8b00>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"timeseries.rolling(12).mean().plot(label='12 Month Rolling Mean')\n",
"timeseries.rolling(12).std().plot(label='12 Month Rolling Std')\n",
"timeseries.plot()\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1a11e548978>"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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LEn2l6CljBr3O8LINiGBkam4EWSsGpY/0wsgqiV0G0ytBSDdAZ3Mtf9/ey/Nf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\nO8wpLeK+jWtZd14N/HaTvaCnzZNH7yOk5F0dG6u0rhufdxt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JEOESekgtZbG6wW7f2W67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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11e5575c0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"timeseries.rolling(12).mean().plot(label='12 Month Rolling Mean')\n",
"timeseries.plot()\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Decomposition\n",
"\n",
"ETS decomposition allows us to see the individual parts!"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11e63c898>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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l26JkU50Gd7Zn+ezerHm8P0deGcFr4wIIcLZEkiQCnC359ZG+5JVW88Dy41eq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8MS2f9zcd48ZxITxwcQRXxQVy28c7uGnhNv529XDmxrf/3WAsDHZ2bZknZ8SwLjWf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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11e63cb70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from statsmodels.tsa.seasonal import seasonal_decompose\n",
"decomposition = seasonal_decompose(df['Milk in pounds per cow'], freq=12) \n",
"fig = plt.figure() \n",
"fig = decomposition.plot() \n",
"fig.set_size_inches(15, 8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Testing for Stationarity\n",
"\n",
"We can use the Augmented [Dickey-Fuller](https://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test) [unit root test](https://en.wikipedia.org/wiki/Unit_root_test).\n",
"\n",
"In statistics and econometrics, an augmented DickeyFuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity.\n",
"\n",
"Basically, we are trying to whether to accept the Null Hypothesis **H0** (that the time series has a unit root, indicating it is non-stationary) or reject **H0** and go with the Alternative Hypothesis (that the time series has no unit root and is stationary).\n",
"\n",
"We end up deciding this based on the p-value return.\n",
"\n",
"* A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.\n",
"\n",
"* A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.\n",
"\n",
"Let's run the Augmented Dickey-Fuller test on our data:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Milk in pounds per cow</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Month</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1962-01-01</th>\n",
" <td>589.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-02-01</th>\n",
" <td>561.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-03-01</th>\n",
" <td>640.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-04-01</th>\n",
" <td>656.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-05-01</th>\n",
" <td>727.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Milk in pounds per cow\n",
"Month \n",
"1962-01-01 589.0\n",
"1962-02-01 561.0\n",
"1962-03-01 640.0\n",
"1962-04-01 656.0\n",
"1962-05-01 727.0"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from statsmodels.tsa.stattools import adfuller"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"result = adfuller(df['Milk in pounds per cow'])"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Augmented Dickey-Fuller Test:\n",
"ADF Test Statistic : -1.30381158742\n",
"p-value : 0.627426708603\n",
"#Lags Used : 13\n",
"Number of Observations Used : 154\n",
"weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \n"
]
}
],
"source": [
"print('Augmented Dickey-Fuller Test:')\n",
"labels = ['ADF Test Statistic','p-value','#Lags Used','Number of Observations Used']\n",
"\n",
"for value,label in zip(result,labels):\n",
" print(label+' : '+str(value) )\n",
" \n",
"if result[1] <= 0.05:\n",
" print(\"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\")\n",
"else:\n",
" print(\"weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \")"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Store in a function for later use!\n",
"def adf_check(time_series):\n",
" \"\"\"\n",
" Pass in a time series, returns ADF report\n",
" \"\"\"\n",
" result = adfuller(time_series)\n",
" print('Augmented Dickey-Fuller Test:')\n",
" labels = ['ADF Test Statistic','p-value','#Lags Used','Number of Observations Used']\n",
"\n",
" for value,label in zip(result,labels):\n",
" print(label+' : '+str(value) )\n",
" \n",
" if result[1] <= 0.05:\n",
" print(\"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\")\n",
" else:\n",
" print(\"weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"___________\n",
"\n",
"## Important Note!\n",
"\n",
"** We have now realized that our data is seasonal (it is also pretty obvious from the plot itself). This means we need to use Seasonal ARIMA on our model. If our data was not seasonal, it means we could use just ARIMA on it. We will take this into account when differencing our data! Typically financial stock data won't be seasonal, but that is kind of the point of this section, to show you common methods, that won't work well on stock finance data!**\n",
"\n",
"_____"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Differencing\n",
"\n",
"The first difference of a time series is the series of changes from one period to the next. We can do this easily with pandas. You can continue to take the second difference, third difference, and so on until your data is stationary."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** First Difference **"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df['Milk First Difference'] = df['Milk in pounds per cow'] - df['Milk in pounds per cow'].shift(1)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Augmented Dickey-Fuller Test:\n",
"ADF Test Statistic : -3.05499555865\n",
"p-value : 0.0300680040018\n",
"#Lags Used : 14\n",
"Number of Observations Used : 152\n",
"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\n"
]
}
],
"source": [
"adf_check(df['Milk First Difference'].dropna())"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11ea04160>"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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fzlETJdK1tQLtGp7dKSBYTemofuZ7Omk7lEoq00lbXwGXrg+hs62cwutyD+hh\n5Q4LMA55XKjkVe/p9h2euL6Pe27bQBSIQtIW3iiLhFRMYVDKEQyRp+EqI8DQskD3+T954wAPPm0f\n7KMLuwKDwElRM1Q//FAIvUOxdfgdOfwO1/NYOnxalBsMgY9CgUkUDpOQScmhBRiHqnlRFAhMR8Pk\nCOghJgdADodOz+liV3cX+OaffJ+15ac6hVEYIArEIHUKD+QnWcWZBE2RON6DhTk6ruv4dKj6s7tz\n63XiSGkHoSmdAVVACuEHOiFKjeCGGp8jTMAE+C6fQTJUrhQDmEMuyDKB7knPJ64f4EXn1pUEU1fa\nmhwKUHBogyVVoVs3WAeIDLSLDplDPgyls0wlLm3PrZ1TxuYPKJ28Cejdrs/P/dkT+Le//UnrNQpY\no4qkcNf5n3yEr2WThtKZRKF6YAfh8NUFitiCn47CPIE1gEIhv2FFDr9PjuChSzv4g09dwwcev6Ff\n0wg8dziWrLRnwKI+6UmaMYSvrhFvPdHVIdOD/uxuBUedtw5YJBn2lsNy+HGWaQ7/Ru7wT00jDweI\nmEeIkvRd7sFSI/xqSmeUH/Cxv0jZgT3dvsPOLMG5jbGF8FNNWZQD1tAIv6TS6XiPf/EDT+G3Hrhs\nvVbOQfSndOJEBaQbXFxRCCj7i0SrBrte/3c/dAW/9MGnrNekRA3C70rpnHAOn77wBkvaTqIgX7DD\ncfhh7hAAYDpS4w/hEOgh3iwg/M1JdxUQqRsubxuErOefn6m6e0iFQppJPHRpR7+fxqdeOjctWWk/\nSudqlcPPHdr2geHY+8z/P//JY+Wkp07ahjq/cWptNHidwpjpvQkBdnE4NJ/tIsJnKhpAHdBNAKIP\nxzsKBcLA7GAphxKx+Z/qiWCrLCMOX5+Za+vwu9hP/eFnSsVFRLkMkbSl5/XS9syaP6eM4lT2vv7L\nNMPV3YW1gygGrMMUdp18hF+QZc7jTDn8fPEc1gjBRgyhTUchwiAYZHy6AbRAdpjD74rwCSFfYg6f\nghLtUOyEVff5P3J1z+qHzgPiKBD6d1EgOiN8+vsrOzalk0mTI+CovqtDvrq7wL/41QfxKx962no9\nzlU0tIMDgFPT0bCyzKCa0unyGZrDn8UlhxCFxiFY43dWcWQYhYFuJUzz5w5Hjd8PwX70qZta+kmW\n0HkBVQi/M4LNdOEYGc+hAAWVS8+k56WbZo0Wk7aAqQvqc/0XiekIC5jmkDxHQPeiT0Bpa8fS4acF\nSgdQDjmG2sXNAAAgAElEQVQKgmFaK+QLOihROmKQpC2Nrzn8nFLYnEadHyZy+JcZ+rAQeBhodKPq\nFLrP/wGWsEoYwo8KDu3M+rjz/GkxHizTUs9vziGTdW2tQI6kagehCq+Yw18bTnarK1Uj7vC7Uzp0\nPcttwKsoF3LI7e+xlOr4vFEY6FbCNP/AkYPoGhT/8S98GG9+x8et1/gRkJSDEJqS6qgzz6Qlbabx\nuU6e39fODplAFQMldN5BxCm7npQOXU++RilgcUpHj98joLS1Y+nwdaVtjvABpaiJBnLI3KGNQ0bp\nhMMEFHJy9IBuz2IIob5Pd4SvnMAzFZQOPVBEB2xNo14I9oGnd/TCi1OpGzsFhQV/Zn3UW6UDKE0+\n/w50RCDZ6bVRZw6f/r7o8ONUIUw6phFQCH/IfvXFgHgYSgewpZkagVsBq88OQv3tKDTOl49fGVA6\nXqODZYpPXtm1XtM6/LDCoXUFDUmG6wdLO6mad8vk65P8RXeErMa9XKR0mIoJwKEoNcBeo8Wkf5pJ\ns4PoOn4HkHQ8HX7+hdeYw5+MwsE4di471Ag/ClUZ+AAOgW7wNE80Z1L9TIdZdDHqs37ZonTUa2EY\nKEpnZpLCfTjqB57Zxivu3FJzzwzCDwsO+ex6dw7ccvh8wbNuk2TnNsa9KaOrBQ4/SaVWdpGdmo4g\n5UCl9ymdGMUokUkfhM8cfqE9QMgqSYF+HDuNbxA+qXSgT4wi2+wxf/qMx68fWPeumNTeWyS9rg+g\nvi+vltbjFygXo5Lqh5AvFUBVMcexMckLHbvKJvP5WEq7XHYbVgaUWwzh6/bFo1BvA1XSdqDWChoh\nB3pBro1Da8t7GEs0qgowPWRS2FA6RjZGzzshBPqbrWnUOWBlmcRDz+zgtXefAaDQgqaMSgi/h0NO\nHQ6/ghI5tzEeOClcpnSAbg9Imkn8lR/5Xfz6R56xX5dlWaZ+YHsjfOPwKWlYLfvsHlBGYaAlnjS+\nkh1WqIw6rqFlokDCY8+Z4jqqdObti7XKpacK5QarZzG9nso5iK4BndYQ5/CrVEzUbrtv6wOL0snM\nIezF+Xe9Pieew6dFOQoN5TKJAoQs6XSo8TWHb3pZTDQC77ZYHrm6h7/9439kJa3oBoyiQPesn47C\nXpQRUTpLlriyZKUWwuyelHz8+gH2Fgle88LTCIQaOyvIPsnOrvegXCooHWocRXUQZvweDj//+6JK\nJ86UMqWYtAW6cbwHywSPXt3HH37qmvV6mmGQpO2SbccthE+ywAqH0Ef2OYpswFGdtO3H4dMz8+ln\n9/RrxFHT+txfpr1kq2p89R1u7POAWF6ffR0mjX+ZUY4mx2Guj3qGu4O2SkpH2oVXAEsK36oIPwwC\nO6k6FKXDED6XZY7C7rLPj1/awYeeuIl/9RsP6dc0qgqERvhr+fw7UzrMYdKW01LRFBZ814B1fV8t\nwjtPr+mAl1jjmwV5Zn2MNJOdghbNPxBmwXOdP0f4t230SArn4z+3v9RIigrTwsBQOkKYB6rLucU0\n/qev7lmvZ8ThVyVteyL8basiuCqgqPG7BF26nuNQaNGDlLIyadtXlknfgTv8JE+aVyU9uyPkMsI3\nOYjDBawsM+v90vbM7KILSVVAgc5R0J2WpXtQQviF+7sx7psjOOEcPl1QKpwBcoQ/FKXDOXwmy+xD\nGRHH/q6HruD3P3kVAKN0GMKfjBRl1Bnhx10cfneOncafRoEOSJlj/NNr3StJyWFePL2mKR1OGREC\nFEIlhfvuIKSE3gERwhuFJqCv5yos/vtW4zNnxpOGSZ4U5vPvk5R0Jm3zwjHbIZND6+DwE0bp5M4r\nyaTDYXafP3eY3OFXFabR/LveY43wucPXKp2qpHaH65Ovhds3J5jH5uwKam3B5z8ZBbq3URfTwoK9\nskqHX//JiKSz7cfvCsCOpcPXCNyidEJLR3y48U1A0Rx+vl3ruh2kszpv2xjje3/9QcRpVhmw1nIV\nUHdZpqmwJBWB5fALCLMrOqD5T0ahOrDcqrQ1lML6ONTfpcsDu8yLfi6cmuj2CjwpTNd/cxJhkh8Y\n06U5GN8B0QNlFdaNKEcTabTZjXJR42/PYlzb4xwyLIRMSfmu4/P1sFPo+VNMGvbR4dscvlGE1LWG\n6EMZAUWEn5V2iH2SktSIEIClxacDaKoory5JVbr+95xbA2BAFbW24Aif7nFXH0TPJKcdUwmrkhdg\noLPH/W1rx9LhFwuLABX9+iDkZZLhw0/aJ8LQgrNUOpRU7Ynwv+MNL8WjV/fx8OVdw5uGBQ6/R6Xw\nIslwYWuKKBB6MVrXJ1/wo1BgOgo7KwioqEp9/wAxQwyBMAF3YxLpa9UlcRsnGcZhgAtbE91Ardic\nDVDoj37usuC5w6EtMz3EXHa7nifl1e+771CAKgRrVEZr49BUZfZN2jIOnwLKuILS6dSrhwkIOMKv\nohQOk3SOAoFHr+3p3WGa1rSe6DS+WQs3CudKBM4cR/f7e8+5dQDA5R0DqlThoY3wR4Gw8i5dvkOR\n0hGFgGWKS/utnzZ2LB0+5/CJg51GoT5soou988HL+Lof+yM8zhQEHAHyHEGU65T7IMx7b1cLZn+R\n6KAxjrhKJ+y3HUwyrI1D3HFqWqJ0+AM7jfoVjlFSeBqF6rCTJDMqILbl3BiH2vl0cpipOurxwtZU\nV9tmFdd/cxLp3Upfh3y1QBlFgdABd31sKJ0uAYXvIDiPryiRwNohknPoLcucFQvTUEm59Bl/HBnn\nSLs4V1K4GyWl/valFzYxjzM8fVM5zCQr1yn0obx4cLixX6Z0uEM+dYhKZ3L4+hnLz8Xl12ca5bvg\nniqaa3tLExCzco5A9/PquUNsY4d2+EKIu4UQ7xVCPCSEeFAI8Y/y179XCPG0EOLD+X9f3XbMIRE+\n9bH5xGVTGMJbKxSTwkA3WRc5zDPrYwCqCMWidHKHs9azjmCRpJhEAS6enupeH1WVsNOx2g5mstv8\nCeFPcsqJ+F3ATqqujyP9WV0Q/jIhhz/BzjzBPE7tgJuPuTU143cpJFlWUDoU9KhbJpAj8IAojfbz\n5w7/kQqET2ezTnN+l39+G+NtOIoqnaBE2RGl0338EodPSeGKwqsu14fGf+XFUwDMLqh4gAgfv1sO\nwqyF6wdFSscRsLrkaPL7+4KzawgDoaWZskJFM+nJAiRphq28cSLlIfiJaWRUt9M36d/GhkD4CYB/\nIqV8JYDXA/gOIcQr89/9Wynla/P/frP1gPqBZQ4/l5X1bT5W3I4D5aRt2BMBjqNAZ9i5w+c6fONQ\nu1M6kyjAxTNruvjKVtHYOQig2yKg1gSKnxR58zRS1hiHsDEJ9b3oisDHUYA7Tk0BKBROAYUv+M0p\no4w6jW+Kca7tkmyVIXwdsFjStgeHD1RQOpzDt5LCXSgp9be3bY4tlY5u3VDZWqGHLJNx+EleTc3b\n/wLA5qS7zp+uz58vOHxC+ONDInzuvG8e2DkUV6VwH4Q/HYW4sDWxdtFFSmqiWYb26zPN1Olxd51W\nOQLKA8k8ILJ4opSCQbd+YV3rYg7t8KWUl6SUH8x/3gXwcQAvOMyYSYVDnuQOqW/zMY7OXBw+PVxd\nHeYkCnSjt4NlYqRwTKVjZJkdKaM4wyQKc4Sviq9sSsogTLpWXQKW4fAVZaMcvvpdFAQYRZS0NQi8\nS3uFRao4/POnJgBUX3xbZaTG35qOdD6ia1IYAM5vTRjCp6S/oQTXRpF2Dn2Skvfetm7QawWltjYK\n2fjdVTS3bYwthK8pEXZ/TY6jH4cfaoSflQLWJDIS6D47lAunJrhtY4xHctpLcfiBRUltHrL1xPX9\ncmGahfAnPc4j0LLVAHeenhoOX5pKWCr+pF1cn6TqXWcM4AFMQBFM6684/G79sJ5XDl8IcS+AvwDg\nfflL/1AI8VEhxE8JIc62HYfr5DnCD4PuHDsh2CL/ChQQfmQQcled+SQKtcOfxTalwzn8MHcIXWLW\nIkkxGQW489QUi0TJxqp2KBzhd1kwRElRwihJeaWt6ea3MTEqna4IZBwp9ASok68slQ7n8DWl031L\nfteZNVzdpR2Quf5jhvDDHklVGv9Vd53G5Z05dudxZbdVnrTtgzBv35xoDp8HFLr+RAmq93QYP5//\nOO+WSfOjSlV6zZp/D5XLKAysXUpCSe2ojPC7XB8dvANhc/ik0qnKcXTZYTHZ6uYk0m2KSaVDnw1Q\npW03hL9MzfoEgKt7lCMARB5J6B5PtVLwGHP4ZEKITQC/BOB/lVLuAPj3AF4C4LUALgH4Ecf73iSE\nuF8Icf/Vq7mOncvqDs2xG4RPgaKqtQIlbYFuF3GRt26m83f3F4zSiQIjC+xJuSxylcvF0wohPLM9\nq5z/hM2/C0Kex2p8ci7LtLrSduOQHD4l1HYXiZUUpoB1inP4PZK2d52eavSkKZ2wQOn0Qfj5+K+8\nS1EWj1zdt5Lm1vrsscOi73rb5kQjfH7ADQ/oevw+rRUioQGHVukI0/pA9ZLqvv45fTmJQv28UWsL\nTkltTCII0W8HcfvmBDdYAzVK2grWT4d0+F38A69Eph2umb/tkCdRrpPvEbC0w8/XaFVAmeaJ/2OP\n8IUQIyhn/zNSyl8GACnlFSllKqXMAPxHAK+req+U8q1SyvuklPedP38egFkQowKH34djJ4S/v0xL\nskbeWmFtzJNa3RDyZBRgOlLn4844pRMGmJLKaGTG77yDGAU4t6GSwjcPYtM8jSGoNRYQuyzIeZzq\noDTOFQJVlEtfWeYyyTBm9zEu6PzpdZ607RKwiDK6sDUxDp+hwqnW4XME230HxJOSVXUEHIH3oVzO\nbYx0T3y7l1HuDHrO3+LwOaVTKPyxdyh9xlfXmp433U00KqhcculvW6Prc+HUBIvEnO1LAQswWvl+\nslUzf87PZ7lKB7AdstLJdx//9NoI01FQonQAk0fhu+yu47e1IVQ6AsBPAvi4lPLfsNcvsj/72wAe\naDumxeGzpOco6I6g+MELxMGmmnJhrRsi9sB2QfhJhmkUQgiB9VFYodIp7yC6jZ9iEoU6F7BMGAIv\nygJ7jZ9pnjvKC9t0UpVRFnbSs7ssk9M1VbJSKrxS43eljAKcz1VAiyRllI7h8C1ZZg+E/5LzGwCA\nSzeLh7wzlU5PhDwOA5xeGyGTCphk1vhl2Wcf2eSYO/xUnVscFJLOmjLq4pAZZaROF0t10ComPYkD\n70LZ6RxBTglS8RXJSgFYu9BA9JSthgFGkZF9Z2z8okPuk1SlNUpJWzpgBYDeeZGPOO6UzhcB+GYA\nf6UgwXyLEOJjQoiPAngDgH/cdsCqXjd0pi3QrRfKIsl05NcOP3+7HVD6bck5Ql4bR9hfpkjSDCKv\n0jMIvx8CJMqItvaLJLMQ7Jg7nB4c9SJONQpWp09Jc8g7k71xhN8labvMKSmuwOEI+dzGGBvjEC+7\nY6sXZRSnxuEDSgWhAYNF6bCkbQ+EvD5WdMSy2HqC7bD6yjKjUGjKa2cWF3YQ4tDjA6ZbJsBbK0Ar\nRdZGAUQuQ+wiy+SUyHSkOrdasuFSJWm/pOf5LUVp6tYHuawUMA5Z7VKCXknhcU7XLC1Kisa3abs+\nCH8cBji/aXah3OHrpG2u0ukji21rUfOf1JuU8g8BiIpftZZhFk1TLgLWASV9eqHM4xR3nV7DlWCu\nE7e8tUKVw+yW9Mwsnni2TLBMVdWoEDbCJ3qgq+xzwnIBiyTV18RCgGMTsDqpjJIU03z3QIVbVUnt\n9b6FV0mmHyb1Xk4Zqa3ux773KxEEAu979Ll+44cBbt9UDv/q7sL0MgoCbE4jTPOkNz/kpcv4gHoY\nx6HKcVSpyKaHSHqOwkDzz9uzWEt8+YlLViVvT8qC1yGQSgdQDo3OnuiqMy9y+PM4tQIup3QmUWDR\nJm2MxioifJkHLDVnRadO8n5QfXZwo9Dm8DPJAopO2nbX4fN80m2bE91VN80kJpFNSU20NLp7DqKt\nDarSGcqocZQQnMM3KpeuHPh0FOCl5zctjTCgLjQhq9Nro14qCE6JrI8NpUN8OjlTqxKzY2HXZGSc\n7TLJKlsTkEYY6EjpxCZgUfM4jmDJ4fTm8FOl0qHvXqSkAPNgjdguoPX4iY3wr+4uWI5DYH0c4Xf/\n6Rvwta+9qzflBUDvUpaJQfhEiUyiAGfWxr1kvarXUKAb0+3MYmv+HOH3oXToXkWM0qHWAPq6BwJr\nOuh3q2anscahAiUc4Rd7xdAuulNAyedPdRy8cClkHPvaKMwrY7slPakOQp35W0jaUlKVI/COAYsH\nlElkzm9OWUAxtFqQX5/ust62diwdfpJKxpvl3SajoBfCUTr5EC+9sMk4fOPQ/uor78Db/v4X4oVn\n13tt+Re5Dh8wDj9JM+28ePtlrYNuOX8pZQXCz+ykanQ4BGgh/CgoJVWJ7tliDr8PAicJoEXpFFaf\n3kF0DigFh68fYnU97jw9VQ6vT9LT4qiDUsANA4Ff/Pa/jP/u9fcgyOmRrg5tzCmdeWLnUAJzf0kX\n3icpPGaFV7TT1Bw4qxehPE778YkSETnCr94BAYzD7zJ+AeGTNJNUOjTnNbZL7ZuD4MGIUy5GpdO9\nHz6ndMYR20GwgBIycNid8nqeZJlDGvXSBmAlbQ+jcnnphU1c31/i+v7Skr2NwgCve/E5AOi1JVc7\nCEL4EQ6WCZapmT9H+FHYbQehag5U0JiEJmlbxeH33UHM48xw+IGwjjgMhMDL79jCW77+NXjDKy70\nU9HkCBzI0SNzmPRAkRlKqmPSNgx024G9hV2nYI3fQ5a5SFS3T0owLwsBFwBe/cLT+vP7cMijKNCn\nce3MYutEM3Ly5ND6Uy6mTQAFMY4wzfjdEL5VVT4KsEhSvQOKmMpICONUO/XS0bLVMYQAruccfpbZ\nSdspm3+vHEek6Kclc8ic0qHrFwVBJ0DCKZ1xvn4A03qCxgdM4VXf9tpt7NAcvg/jCZPiiVRAN4cw\njzPcthFqBHjjYJl32jMLnqwfJWIQ/to4xLW9Ra68MDcRoDN5u1FSRCcolQ5D+BWtCaykbYcFOY9T\nTScoBYW0VCJCCLzxvrsBGEffTZZprg9th10Ouc8OggIKOaxiawtufRE+oVRCaJyyKFpXDjnOcg5f\nI/zY6mUEkLy0H+USMwEB7XhoXdH1/86vfDleemEzH79bA76SDp8j/JDVueRKtq5HBPLWB6fXRgbh\nS9shh3kOousxpRYC55SOtHMcJL7ou4MYFYJdmhnZZ1Ep1UcW29aOpcNPcg4fsJO2/RC+UqGQ06Gk\nUtHZAOhMuajxM+2MNyoonb/4onP4mtdcxCvu3NL9sNs6NOoDRAlDABbC5L2GuCyzy4KkHAcArUDQ\nrScKDk3PoYcsE1AOs6jS4UYOqU9hF9FPs2VqUQrc+uRolmlq5h8W5l+xhjqXxieKwycl2c4ssXIE\nAPCtX/RifOnLbs/H70a5UI6AFDiAub50/b8hD+hm/C7Xx3Dg05G6PlyWzGWravyuAcvQc2fXx5rD\nJ1kpYKvtujpkPf88oZxJOi/ATtpO+DPSq04h0DtcwJZ9WpRO6Lcf/vF0+IzDf+09Z/C6F5/DuY1x\nr37mi1hRLsRRzuMsP8C5Ap31aH7Fk7Zr4yhHmFI7l/NbE/zof/v5ANA5YBmEbzhwpTOvSNqOuM68\nG8I36EU9jBrhh0WHTBx7d8oFyB1mYieFufUNKFSyvz6OsL9MrDORuZk6iG4Bhe6vTtoyjr1onRFg\nvhuMcodZRUl91994hfkOHSmXJJX6uhYpuar5dz6Ao6DDB1Q/KZo/oXp9DXvmCNQuKMLOXI2dMpWO\nRel0dcgFDp8+M+MqoNDMv3thlMmhcMqIsxi8l07XY1C7Jm2Pp8NnHP7n33MWb/v7XwjAXJiuCH8S\nmS0ZOUyuHiDr0/yKdhAAl2VmJToBYA6n5YLnlA4AzQFmDCFbvXR6qDjmcWYSdgF1y4QenxslKZdp\nWhym0pI0QyZhIfxiUphb39YK43VzDWiHpcZ3UTodAxajpFTSPB/P4TC71InEqdTrYhKFKkdTs4Po\nQ7nQc0Pj0c4xLA/fm3IZRSbBT/1obI7dIPxevXS0SiqvtGUI+XPu2MLmhOU4eiBkhcDzHVDu8LVO\nPggshN8lR8M7/04YZSSZSoeeK6qV8NkP/1g6/NRJuXRX0cxzhE8LbhFnzvG7OoQ0k4hTqR3yxjjE\nQd48jZyENb6mjNoifNPYDFAofsEcAu+lszbqVwm74Bx7lLdW0Ai2/Pc88dRkhGb4dptTUqUcyiHa\nLwMUcFN2fRxJ2447uGLAovVXTDoD6KxCWTKHPIlUQMkcAZHG7+rQaI1oaawOiNWU1GF66QDAfo7w\n6XmKQsGSqqLzDk6Nr2ib2VJV8nKH+SNv/Dz9951ljWmGQNi0EFWDc8pII/yuOv8CpaMpIyl1a2Te\nRr1rC/XPCh0+tYYtWp9eMeTQ6IYpDj+rXuwdVRxFh7w2jiAlsDdPHOivW0BZsMNJAONsqXAsDAXO\nrKtk39mNMasU7k55AUalw3cQRRt1KAzh22X13vqkpyns6vZAaYc/iXKEb3Ic3Hr1imGUFMkyefO3\nonU/scg45MmooAKqTAp31YFLPT5RdLSuXJRUH9kq71ukET7Lw01Y0rnL9dd9tYKgnENxBNyuR2TS\n+uE7ZE77nl4b4dyGUWF16dhrUzp2Ho5z+NYzeKupdJK02iGHHR0mIXAL4edb8nqE3zapajh2ALpF\n8vYs1s3O7PG7IVhT9JPXIuSyN065fO4LTuPX/8EX43NfcEofL9d2waSZxDK1k7ZSsqRexTUas46I\nTcb7iNC/dUnPooqk7WfoauBRiINlwiqpC5ROr6RtZiVtb1iUVPnv+5xYxHMci5odENCHQ2aUFCVt\nCeFXOczOCFblCIQQJQ6frncUCoZg++nMSaDA6yAqA1bHgBizgMh3yCmTTX7f171K35MR80HFHFGV\ncUqH51Bs2acRlURh0ImyjtOsEly67Pgi/FoOvDsCn44Mwk+z6ovUtZJRc+yktc8d/s1ZXEvptE/a\nGpUOwB2C7ZBf/cLT+UEK3XYoy0KOgK4vNZyreqDGYfuk0qLg8EnH7qIs6DCIw1A6lDRXn1cev6tD\n5q0zyjr86nvcrV+9cTiqvXBqtacuj9+9l0uJw0/cCD8KOzpMFlAIOOwtKGlrrltvWWlmKJFxnuOg\nr++i1LoFLNOqhPd74iqgC1tTXMxPrOraAJFTXuNiQBEkPReYjk1SuOsBLlX5QpcdS4SfOigdw4G3\nuyD8NKc2skxzAEpbh5YfD6hlmaZ4pnL+HQuvijsI2vK7OGqDYNteH3v+RYRd9R0IZbUxQpIThpAV\nAle/d1EiXQ9A4ZTObJk6dxBADwTLmu+N826KtZRLVw45Y1XZxdYELhVQT8qIdjxFWWZxfHpuXPYT\nv/cIXnL7Bv76q+60AopG+Dmlw6XVfI11o3SM7FNTmjU7rCgMsL9sJyoAigjfVulUAWfez2sNYeP4\nS07pWOObgPs/fclL8FzeRXPUQiX1rgcv49Fr+/j2L/tzWCZZq50G2bFF+H2Tqld3F/ix9346b0tQ\ngfCTmqRtxy2/PgCc9dIBqDrTrQLqU3hF/y54L5dDJj3nOmAZ9KU+N0f4DofWdvwih68pHUelbdfx\ngbwfPjn8UYj9ZWKhwqrxu6p0JpySsiiX8t/3S6oax9jk8Lsi8CVDgJEO6DbHzi1s4XD+0x8/hl/7\nyDNs/tUIn9bnt37Rvfj6v6i0/p1ln4WkKqcEK9dPD5URNXjjsmNO6XDrKrzgKiaTFKYDaNTffP49\nZ/HXXnmHGj9Ux7jW5Qh+7SPP4Kf/+DE9fhWb4LJjivCrKZc2DvNdD13GD73zYXzNay7qowQ5wq9X\n6XSTZZaTtibij6oona45gsL4hHDcSe2OlFdhB0Hzo0BWzeG3R/i89SyQo9NEliip0vgtHyYppcXh\nr+WUDu+VVLSoI8JcJKlFSVkqmgGSqnEi9X2bjEJsz9ytIYAerRXY9WlD6bRxmPMk07tDnhSejqo5\n/G/+wnvN/FkL4lbzt2SrgQV43Pe3W46myOEv01SpgCopo24+QnP4TFG3TFNnQOHtRcZR+feAej4P\n8l0MD7ht7Fgi/JgVXnFr0xyMtpO7+WEYgOlREQUC8yR1U0YdZZlFBE6UDmCSO9b4LdCBlBLvf+y6\ndmaA4fBN0rZhB9QX4Qc2wq9yaISy2lgxaWtUOnCP3wHBcgUEYGSZsYPyUq91O2BimdoqHa4ycq3R\nziqdyCB8KynpuP5Nss9PXdnVLQiqEOyihtJpM/9FnGpQwBEmAQeiVCodWo8cREklVSdbDZqvz1M3\nDvDUjYPS+PrMiRrA07U4c8nySea8B2nJPu35N4PCRZLqoOrylS47lg4/dRZGNSc9KfLtLRKLw6d/\nDYdfsd3vi5DZMXp6rJ6FV+9/7Aa+4Sf+BB95aruy8GrRgpJqQsiX86MezfXJHXJkI/xq2V4zwr+y\nM7cCFqd0LIRWsVBHLRDgsztzZLnCiMYFVAvnJJOYx6mu8ixa514lBR2+Rek4EGDXgMJlmar5mPpd\nX4T/zT/5Z/jx3/00ABsB0nBGhVV+b5vmb/yoQU5JaYS/sBE+t1HU9UzYTDu0NpRgm4D1PW9/AP/8\n7eoAPquwjvJ8NZSXlm522OWOQmr1bgCrq9q/zZkNizhDnErEaeYs8nTZsXT4bg6/OUN+EKvFtr9I\nTC8apiIgh+OS1KnxOyY9Cxw+nys3LulyGR3wcHl7Xll4RZRO1fUhlUvd/B+9uofX/5/vwQcev67n\nb4pKTGK7anyaSx0Cv7w9x1/+gd/B733yKhYFh0zoPa2jRBoQ/vYsxpe85b14x8culXYQ1EDNlTQH\nemz5eWuFog68JyXCrYhgF3FzUrJpB3TjYInr+6qrJOfwaX1oSqdH87ckzXRQpfmP2PwBYG9R7zC7\n5iB059wWsuE23TJvzmJc36e+VuWkLQG5isvTmZZNLMrITtrWUTp134EC0sEytSi7NnYsHb6bw292\nmAQeFWoAACAASURBVETp7C0SzAuySX4iTyXC76qiKVAu3OGPK9CrCSju8Wd5wLp5sCxx7BzhOx1a\nQ1Lsyo5a6E9cP9Dz5zp8+l4uhz8K6ymdq7sLpJnEkzdm1uEPQLnbZFXSs9HhH8RYJBmeuTkrOXy6\n/jtzt8NvStrGaYa/9K/frZOSxdYKqrbD7TAp6dbWuMOhAzKKzdPs+dcnhekMBe6QuUMIA6HbE/Rp\n/kZrhhA+FyhMShx+9TPWJWmbpKbzLN0HLRt2qGiaxl/EqfYTvNKZ/p3XUJpdW3jzvlq8V1QqZUNA\ncY9P3/8g7xt18hF+2tDNsia6EqWzO08YgmVb5tjtMNvotD91ZRdf9e9+XznkAgJf5xx+DaVTm4PI\n538jd2z81CmS7bkQvvqMeh0vXZObB3EJ4esFH6eVix1obq1AjmBnFjOdv3GYTZWkTUlbGn9vkZQo\no/W8idruPKncYQHUa8U9/715gis7C31YTrG1AmAcQjWH3x7BZpnici0dfmxkpa5+T20csuF4M2ue\no8Dcvz7N32j8BefwCwifOPxqFVN3nX8U2td/tqwPuE0Of5lmuv0D36HQ96gTLXSudUnLlBH1w3Il\n/WleLqP56dP1TjqH74pabQ6wIIS8t0gYgs05/LywxdVaAWhuvvTAM9v4xOVdPHJ1r8yxR6aFc2Xh\nWIscxCx/WG7OllafG4Ccberk/4BmhDyrcPi8sRXQgPCj+sIZcjQ789iRtJW1lMi4QYdP89+dJyUO\nf70VpVM/fx1Q5qpNcZJJKwcBGIfj7IffEsFq+WjO7RLCT2p2QE1nntI91Rx7QSIcMkqnav7qEPMO\n46fSmj+g6FTAgfDzwrTWrQlYRau+/vHhKKNFnGmEH6d2YR3/jq6AoubVksNPygElTmtkn1p40eIe\nLNNch3+MEL4Q4quEEA8LIT4thPiuNu9xNk9rwZ8RQt5flBH+dBTk7ZGrFzvQnBSjPiHbs1jnCMhh\nAiZxW0XptNmuaYe/H1tVnoCN8KseJoAKW5qT2tuzuBSweOGVq1q7EeEvCeGXHXJTawUAVgvZKqN7\nus8QfrG1xc48cSoXmpK2Mz5+xfz537gqVdtrtG2VkU5q16hQmlQuhP7oPnAOH1AOsYkDr3OYmtJh\nskCav2qvEOikbR1Cbkt7JRUIvM7hN61/wCB8EhZojl1TRjUIv2O/LdU1wFZJLZOsWfZZe48Zh99R\nh+/V4QshQgA/BuBvAHglgG8SQryy6X3JABy+kmXaCN9w+JnbITRwmIRgbx7EJkcQGe6epJl1hVf1\nSWeidJb5AeNm7IlOGmaV6I8+ow2CVTkCR+FVTdJ23OCQKaBYCF8/sBRQ6h7YdjuUvQqHTJSOQvgO\nSqdhy0+ObG+ZsIBoz39G/d4dKqDWstJCRfMkUknJOllsU9K5iMCTLLPARxQ0JG0bxqe5zZO05DAB\ntZb2alQ6bdqj/PEj1/Cxp7YB2DkOs8OqQ+DNss9FnCKTKnjZSVtDaarxy+/tKn2u0vnXFja28HHk\nd/aXSefWCr4R/usAfFpK+aiUcgng5wF8bdObUgeH30bHfsApHXZiFJAj/BodO9DMYdoI33Y4gEGZ\nVZSOkgrWR2+N8A9iRemw3cNkFEJKhUBqEX4dOtCUUWwqhYnSCRiH73L4PTj8cWnLXOdw6sdfcIdf\naC5nJW0dAX0U1CNwTukUdxCtKIUOSUlThWk4fMAETZcstpbfZQoOoEzp8MInZ9K2xQ5CaoeZWUWG\nkyjQn12rY6/5Dt//Gx/H//WeT+q/o3vJ26M4x29BGRFQOChQIlqH35DjANrr8LmKZlzaQZT/vkmJ\nyOXOs2PI4b8AwJPs/5/KX9MmhHiTEOJ+IcT9V69eBaAupsthAg0In1E6GuFHRodPZ266KZ36AywI\n4StKJAU/HBowlI7rJjTlCGZLhvALkiv6+aDGITclxQ4KAQWAdeIV0KzSqUXgS+bwGygRV6Vta4Tv\nkGXGDsAAkENunn8lpROaU9Nc8+8iO+S90vnn0Byc3SxrOfYs/5dz7JzSEWyHVX5/k8OkgKt+Vgh5\nXED4/ODuqvnTvFx2sEw0sIrTTNMoJUqthhJxUUakYgLUPVaUiE256IDiaF4HdKi0ZfnIcWF8VzdU\nwB0QeSfZg2V68nT4Usq3Sinvk1Led/78eQDu5mltDkG2ZJlxCiGM851EzQg/DOoPsNi3HKZNuQCG\n0nHxak0qC0PpxNZ5uYBB4rNl4gxYTd0I6WHZzhF+wK4PX/BOlU5DawVD6ZiAWzxib1bzQI2b5p8n\nTPfmiT55qyjLBAzXWrTWSVu2Q+wSsFpxyLlKo8jhE4KtQ8hNOQLO70opSw4hYjuoPg5zzu79LC4j\nTJ5zqqakmh3mLE4NJcWSwhRwDaVTfm9Tnkz1slc/aw68qMNP2jjk9ru4Iodft/6bij/nLOAeLJOS\n7LbJfDv8pwHczf7/hflrtebqhw8065wJgROHP41CXXGpKm1zWaZry9+U9Mz5yZ0c4fOELWAQfh2H\nXO/QmA4/Sa2AohH+0o3wmwqvjCxziXmsxqfrY5prZZWLHVBOL8nMubRFI0qNKB3qlc7nT4HYtWWu\nCyjzSkpHjbsxMbJY5/VpkGXqpPCSIfzQ3rUdhkOWUuLLf+i9+M9/+rjVOhcwAb2JEomzzInAOYdv\nAko1h9/nzAmO8I3DtxF+cSxuWqnSsMvldQSRA+HXN0BsRsj7y8RO2hZ7SdXo8NsWXlUlheuufxPC\n551MVeHV8eLw3w/gZUKIFwshxgC+EcCvNb2pqbCoDUIjlQ53yIrSIYTvRoBtVECEkIsIf70FpdOm\nNUSSSVzfj0sqHfqbWhVKC8poexZjVrg+49CgizpKB3AfrTYvJG35Tod+XsRZww6lHaVT7Lc/iQJd\nzOK6/mGDCku35piXKaMi5eI6la2OElmmGZ7ZnuMz1/aZwy8iWLfKJQpUYteJwBnHTsnTIoevZZ+O\npC1Q4/CZw5zHZVngxKKPKoQLLZKec6t1QzlpW0uJNAgjeMA6WKQW5UUMQl2OoE0e8d+862F85y9+\nJJ8/30EIaw5VrT/09XeMbyP81OqV1Ma8OnwpZQLgHwB4J4CPA3iblPLBpvfFmazsswIQwq9eLMs8\n6w7QlrygcokC1R5ZysoDnIFmWeYBS3oWZZMAk2W6KJ2WAQVQPWlsHb6pZKx6WGn8WsolXzCZBK7t\nLSxExoOIyyHTfFxO2XTxk9guHATDt7SuHURTJe+iwuFP2ANLWvy6gNUmIO4v0pLD10nD2i1/PSVC\nlOPOPNZrdVQYv56jbnLIZv3szFR7BUuHz5xwdfOuesplXkD4vLAIKCB8R2Ea4KZE0kwlJWca+Njt\no4H6HAfvV19lfG2R0otfH+qIClS3VuDtEVz2oSdv4v7HbuTzN3UERNeYHEH5vU3nds8THrDK828y\n7+2RpZS/CeA3u7wnzaSbgw3cKhpaCEIohDYvUC7UiyZOshqEX4+Q91nS9raNccmxE4fvpHQaAso8\nTjVKv76/LAUsIEf4NSqaGXsoizZjAeXyzsIKKHzh1DlkAM6gcsA++9rewk46M4RclyNog/ClNA7N\nUklNIuwvU3elbQPlReMv00wjZCPLtDnkpjMbCps/AGb97M0T0z66A6UzZg6HO1c9f3Z/t8nhF5K2\nZPUqmnYIXyHwag6/7lxqN+Viy0orZZm1KqkmhG8+d2eerx9eiRzypHY/Dn8Rm0reZWIqhYNA9TKq\nT/rXj29ROnF67Dj8zialrE2q1qloiD++bWOCvWWiOWoycv4HsdthNqksCKHppO2oI6XTEFAOlinu\nPD3V/1+dtK1T6bTj8AHgyvbccho8yDoDCpWHOz6DO5xre4sCws850qRe9tmGsgOA5/JGc3zBa1ls\nT0qQXx9qZGdK44U1hz5nEvDWH0UdflHF4dLhA+22/FUOzXb45fc3Ff5YHPgitVpDADbCr+8nXw/a\nLA6/JMusSTo3VLPzdbt9UN4BjaOglsOPGhA4oNY3VxmNCzuIusK9ptYN1g5rmeK46fA7m+kjUsPB\nNjxMd5yaQErgxn5sI3x2BJuLMmpK2lLk3pmp1gRTB6XjuglNzc0Olinuys/PVHPuxrG3yXGQfPHq\n3sIKWJzScVFG/FSgyvFrHD7fktdRLmkmGzlqALrnO/8M+m4uhN9Up8ApteuFgFKkFGopF0dApF3D\n7sLIVs0Rh0Udfvn9mhJxbvmZQ6ugdJrucRNHzR3O7ry8w2pE+A2UC0f2cZpZssxWOvwGyoUj/Juz\n8voZhUFtjqBNg8XZMtWVvMUdkKKMWgT0FgF3d57UClCq7Ng5fHKGdRy+62IQ+r6wNQEAXNtfVCL8\nZepOGjb1EqGHcZlm2J7FJYRfV2kLtCjtXya4eIYhfE7pNCggAFUJ26TDp/HTTDopHff4dA2raaOD\nOMWp/AzY5/aWlZROfa+e+i1/FcIfdUD4TUlbPv6NAzV+sfCqtl96A0etZcPzxCnL3NdJ4fIaGnVw\nyDuziqRtUH+PGx1mweHw+QNmjbpVWE0I1qaMLFlmKcdRfn9TjoOv25sVCJ87/L6yUlWFrOaZsOZv\nZvyawsOgfv3Q3MZRUJmjabJj6/DrOHw3wlcL8Hzu8J/bW1qUyDRqdpijsP4AiP1Fog+1LiZVgRaF\nVzVJQyklZnGKiw0IH6inLJpaq15klJFF6XD056Rc1OtLJ8JP9PyTTFYnbZepcwfBW8hWzr8CgfN5\nkzSzb3vkqvHLKh16YCvGD+oR2j6TDRdlmTqgtED4bRxmJcJnk666B42yzIak8LRQtV2avw5Y7ZPC\nJVlmTSWyPqCkFcInysumHU2lbc38WxS/7S/SUi+jcShqdxAUsFzCFHrvbRtjfX9PNIdfdx4pUF+4\nRAnDO04ph7Y9iwsIuY3DdCPANFNVekS53DiISw6/rrWCGd+NnjIJbE0jbOWOq4rDB2quT0N75Nky\n1dcHgEVJUXtooFpBADRz+AfLFHewgOJS6bjWqKGM3CoFom1u7C8xjgJL3mYonbr725HS0UlbQym4\nTtRqOvNA14ksuMO3OWrKRfVRoVRy+Ey2ZymxaiiLuqQnvW23QvZJz1tdJThQkwNi858vMySpLF3/\n2sKlpvlXcfjs+jQi8BYqHd7gT3H4ZpxxrhQEXDmUhqR5Prez62MW0E80pZMnsmplmfX8MVE6gN3J\n0kL4NQjcLTlUC/yuM9UIGQBOr40A2FWfxfm70AHNf30c4syGGqeq8AqoKyyqr8Q8WCY4NR1hUwcU\ne560eJp0+O7CkBR3sOtv7VAYB1un0lHju6/R7VtjAIrSmYSOgFtXaVsny4xTPQY5fN7+mv6mro5A\nzd+B8OngjSTTP/N++PQdgfoj9pwOjSHwaoRfv4aakpKLJNVrfKfC4RiE786h1M3f0pnHSV54pd4T\nhQECUc/hNyadKzj8YtJ2UTN+GAgEol374v1lYnX7pM+a1+SARk2y2Pz+ntsYm/kfl26ZfayudS6Q\nyzIdF5v6cJ+3HA7n8JnDr2mP7NRQ5zfq4plqygUAvvRzzuPH/+7n4xV3bjnHd6K/2Dj8s+vj0vj2\nDsXxQDVw+PM4w9o41A9tMelMC66RcnHJMpfKIdCDX9ULaJFkNUnzpoCS4fZNdX+LOn/AdMx0UzrN\nskwa/zkHwk8z6e5W2sAh0xoFoI/ZqyrsEqK6MKdNJSaNU0W5NCZtGxDmPM6wOY0QBoLtIMoI33H5\nGytVedL/YJmWzsYYR0FtnYKRfdardEah0Bx+UUVTd+IVQKChev4pa5mxnxd2FTn8um6ZTeuHgsnZ\njbHeiZxoDj9uUOlEuYqjymghnN/iCLzMLzaN3/Sw3nW6OqkKqIv/1a++WPmwqs91F17RYp+OjEO2\nHqaQSd56yEqTVB16vDYKcWZ9pD/Lmn/+ea4dVh2lQzmI9XGIU9Py/PnW2Y2Q1esLF6UTpzi/aQJ6\nyeE3UDphIJBJOFtDzONUA4YbBZUOIcy6+TdxyPsWZRTn7ylSOnU7iGaHcC4HCzvzxHoPYAOpPmeq\nLpIU0yjE2ijUSdtKDr9GJQXUBBR23/cq5j/mSdW61hANlbZn1scmaVuQDtPcnLUoNaCN71CoAZ+l\n8+eyz9qkeX2O5lz+/AKfJRy+C8GGgRvBHlRQOnbhEk/aOhZki/GtpOqo2yVsR+lEDOF3y0HUnelJ\nDxN3+MUdCo3bJMusQvjzWB3ssDaOcKoiYPGF6U4K1zvMWax2EMVTkMiIjnHe3wZZ48Eyxe2b6trf\nrKAs6P11vYyAGg6/AuEXK22lrM9hqfHdAZHubRXC52IIVzdOoK6XjmroNx1Vq0QaOfymStJlOQcR\nWQg/ZJRXxfgN95eAyrn1sZbIFhE+WV01e5ukM82/lLStQ/gNSe1FXsNCz1dx/CY7dg6/icMf1XD4\nBxWUjhPh18k+GyijC6cmGukVHWaT1VI6eY5AUTplh9yGw2+Tg1gbhzizppxaCeE3ODSaTxUCpx3W\n2ijQOxTL2TR0UuR/X5cjWBuHWo1TRDdE6dT1MgLchTmzZYrNiaKkpEQpKUwBpikp6VbpMIRfoBSE\nEPrnuqQ8UI8At6YRokBUt1awlFju+Tuvf97QbzoKK3cQjSqdhvnzpG3VDmLCEHKfXjTE4Z9Zr3aY\n9jNWOQTqzszg86cdhB2w2u1QXOPP4wzTKNBqQJpPWzt2Dr+Jww8Dd9LtYKkUHNNRyLTN1Ry+K3qH\nNbJGQvibk8hw4BXl7XVWRxkRh782DnGGED4LUlSaDdQ7TFfzrvnSIPzTmtIpcPgN49P35UhGz18H\nrEhr8V0Iv0nnX4fw10ahTjq7EX69Q67TOa+NA5PULow/aXD4TTp5ukYAQ/gFhwYcIiAmKaajEGvj\nsBJhjti8+zQHW8QZpqNAOfwKWWATwm8T0MmqksJ0TCbQr1+9RvgbYzan8g4OqEH4NUpBqzDwoCwb\n5iqgqoDS1AJeNYQMNXUJnPCkbawpHfcD5dKoHsQpNibqQtC/dqVtW0qkXkO9wRx+P4Rfv521KRc7\noGgE6NoB1SDYGQ8oa9Xj874fVUYBaFHh8GmrvTYODaXj2C43duOs0PlLKVWH0hqHT7JM1zbXIMB2\nAaV4f+n71G33gbqkbarHvrEfIxD2taDr687REOXidjiTnGOv0mk3Nk9r0S2Txq9K2jYh/KbCqyaE\n3wQaGrt9aoRvHL6dZ2qzi27H4euksKO40Znnq6NlY9VDaZ21Aj/ZHL5O2ro5/Lo+HLTV2ZyWH9g2\nlapRjayRqiTXmcql6DCbrBbhM1lmlUoHMN+hLukMVC94Q7nwpG01h9+M8MsOh8+fkraTwgOkdf41\nlcJAdVJ4wXIQmy5KJ690rjvgBqi+PpR0XhtHTspIJ7UbKQuXLDPBhVOKcry+vywFpiZKpympt8hb\nXq+PQ9aNkyPMlknbGp3/dBRgbcTGr0D4zoDVod+75vDZWNx51nUrrZOVRoHQO1CgXHilx6/bRbco\nTKuSxVoByzV+jfBinh97ah32c5IdPt2oOtlenYpmfaRu5OakTLm04fBHNYVLtB3fGEc47XDITaYq\nhesLx9bGoU48b03thqZNCJMWbJXDtDh8TRkVdhBEKTiuz1oNpcMDyqm1agTePP/coVXlCLSKKdAB\nvSzLzBF+TZ0CUO1wFkmedB6xHIFr/g3j11E6d+aFb7M4LQUUuh9N16cOYU5zWrP4HqCg0unRS4cQ\nPqcau1TatjnRiYK5bt1QUcvRNH+nLDM/o4GAQXH+lrCgRrrtLAzkOv+c0uHXoingAvU7iEWsVFLr\nn20cfn0vFPd2nB74zfxfvjDV6UvqZzeH704KU8JtfcIQfleVTu0OxXDgr3/Jbfh/v/UL8Nq7z1h/\nUzxwvGh1DmHOEb4jB9GE8EdhgDAQVl9uM39G6UzLlI56fz3Cr+N46TPrKBfTD7/6vpjS9Yod0NIk\nnbdcDr8xaVtPuewvlYqG5l3kXw3Cr3x74/jzJNMIn6x4xCFZXa+bOo59EgU68AN2Ja/h8Ouvv/MZ\nXipadhwGujkb3+3bSq/y+5sCIp1hQZQvUJRltqF0mqXVgKrEB9yUTq0KqIbSUQi/OmA12bFz+ElD\n0ra+l46pkiSHwKtrhRD6QWvS4VclPQ+WCaJAKSm0w+xM6dTJMg1lEQQCb3j5hRLP18Th1z1QenyO\n8IuFVw2UAqCKteopnaiyjoD/f1OlbdUOhQcUd9I2L7yqqaQGqhEg32E5EX5jUrUeYR4sEmyMI71z\nK65DE9AdOYgWzbWmUWipOKp6MDUHLLfDrNtBtO2ls3Tq8El4EbDmb9WUTp9uk4TwXSoXu/VE5RCW\nVr9q/oAqPKukdFrkCEZNSdsCwncdtlRlx8/hN+jw67Y7SqWTUzrTagQ+1QiwQWVRseD3FypHIIQ4\nBMKv6wWUYBwFtc6WPq+O/wOqZV2a0hmFeM0LT+PbvvjFeP1LbrPf30C5AHQ2cJ1KJ6zU4QPNHPW4\nxiETZTSJajh8onQaktpVDsEEFMPhVxXW1c2/SWe+v0yxMYmwNS3LVtXnEWVU+fbagK6S2rlKZ8QR\nYJlGaCocq9OBFxF+Fx2+EKK22nm2rFcZWRx+j26TdE70xriaw29L6dQlzYG89cFBuXWDjfArh6hF\n+IuGHVyTHT+H36DDr5dNJrUIH2iW1dV1IzxYJnqh9E3a1vXzn7Edisvo8xqThpWFUQbBTkch/sXX\nvFJ/j+L769YQHQbvGn86qq60Bcz22anz14e8JKXf0WeujUM3h99QeFV3fznlRQi8xLE3zF/rqCvG\nl1KqPFPNDqVpB6Hvb8UailOJTCqUTQhWFFRA5PydAaVh/koFVETI7RG++l0NZZHvIHglb+RA+HXd\nJutkmYrDr0bIbSmdpvbFt21MNMLvMn/6+zpKTQVEE7DqrnXRjp3Db+LwVeGVu0pyo8Th2w60CeHX\nyd72lyZHcNpRqdpkdQesHCxTS19bZQYhO7b8NSoFnlR1z6+Z0pmMgkoO31LprDlULg1JTwoUVNTD\nTQeUKHA6zNs2JvgL95zBq+46VTm+cWj114cCe9+kc9U9XqYZkkzmCL+6QKxJ5VLXXIvuCddpj0K7\ncIzWTVNAqcpxEM02GYWl3Fjb+dNnOB0aq6WpQvhF1Zdr/rWVwlGgd3DF8dtw7OOwudL2ts0xaAou\nFVDdLt2ZlM/rLDZ6UjqHOtNWCPFDAP4mgCWARwB8q5TyphDiXqhDyx/O//RPpZTf3mbMJg6/UZZZ\nUOkUHfJUI+SmpFIFwl8YhP/yO7awNgqtw0raWG0vICYrdZmmdGr4RcBBieQcfl2xWFNSFVDXsEqH\nf8DqCF54dh0b4xD33r5h/Y0OWI7hJ1GAUSg0uuPGdyiG0imrjN7+v3yRc+51Dk3Pf2ySekMmbbms\n1zh8xw6iwSHX7VAmI8Phu5LmTWcWV7Um4IfGW5QOT9q2QPij0O3QVPO6MdbGoW594Dozt67wyhVQ\nqhC+paJh38V1jaajANf2qg8AMg7fVPu7AkqtSqeGMuI7uOKYTXbYQ8x/G8B3SykTIcQPAvhuAP9b\n/rtHpJSv7TpgE4fvkmVKKbHPKZ38gSo6t+mo6YF1L/h9Rrl83t1n8PF/9VWN36c0fiBqj3drcvhN\nCL+ufW6bHEHUgAABdQ2rKJ1ZrtEOAoFzG2M8+H3l69NE6QghsDUdaYVGcXwgV+k4KJ0mi2o4XqPS\niZw7iMZeOjXj88I9AiQlHX5TJW+dQ87vCS+9L+4gmuog6mSZnLLjz2BlpXDtGqunLNbGoZbIFsdv\nUumocwrqK4U5wh8XdkBtdPLnt6b40BM3HfNX5wWcYVSpi9JxPWJNlNEkUiomUhQemSxTSvkuKSVB\nsT8F8MLDjAe04fCrox8tEKJcbt8cQwhYBRZAi9LvmgU/yxNuh7EoUD1aqhGmqSNwWXPhFakgKrb8\nLXIETZQL4E7azpZpLV0EQHcOrHMIW9OoEuHzbqIG4bdf7ACvxKzPcejCvY4Oue7EItpBcJVO1xxB\nW4fMKR1uo4aAbrpNugMKR/hC2GuRlHBNCL+ulw514ySzZJlt+jEF7vbFizTDmKlcis5y1BBQAHVm\n9nP7S0cDwZxycVTCtjvTwo3wF3mlrRCCfYfnJ2n7PwL4r+z/XyyE+LAQ4veEEF/SdpBGDt+R9NT8\ncb5QvvrVF/FL//NfxoVTNuXStOWkm1DlkPkOoq/VbfnbUDpNhT/6oHMHR93kkJt66QC5w3dw+Fwf\nXDm/FghQOfwywqdun5bD74rwazh2i8OvOHHMmn9TUrVifKIo1ieM0onscZoASZ1Dpl3XlFE6RWdA\n73etH1LRVCWFNaUzMg65mCOgz3ftQNV76iiLFNNxiKnFUVcj5LqgmzoRvlIZuXI0oxYInwrnnt2d\nl+efy0o3HJRLm/FVR+Dy/NNMYplmGhT0cfiNcFUI8W4Ad1b86nuklL+a/833AEgA/Ez+u0sA7pFS\nPieE+IsAfkUI8Sop5U7F+G8C8CYAuOeee1pw+AYh87/hjbsAdRE+/56zpfc3yjLzi1dZqbpILTlX\nH+MIrbhZOFimuOtMOw6/qbVCtawxa3T4URsO30npJI0Bq43sc2syqubwl2UE3p3ScSdteQ7CJfs0\nAbd6/LpKXuLwbR1+dUBxXR9yyFU6dpO0NZRO8fpELQK6SzrMk+ZUp1LVx6UJ4dd1dJ3na5SjZ7vw\nyuws3GdOuJVw5DCNfLc6xwG47wEd4XllZ44Xnl23fjdbZiWE72zOVuODDipUaksGeADl68JgWfus\nFq3Re0kp/2rd74UQ/wOArwHwFTJfBVLKBYBF/vMHhBCPAPgcAPdXjP9WAG8FgPvuu0+20eEDCiGH\ngXEuGuFPGhxmQ+EVPSi8Yo5sf9ns0JqsrpdLGwTepGOnqF+1YGbLpLG7ZytKJ3Lp8A8/f0Ah/Mef\nOyi9XqnS6YBugPqkbWVS2JG0da3PIBDYnES6cRa3fVan0KTDb8qz1DpkC4GL0nubx69GmBzhXnAE\nrAAAIABJREFUk1Xxxwrhu8c/uz7Cc3vLyt9RHmiZMEqnggOvAwyjmoCyyE8EG4cqKLlyKID7Gbhj\nixz+ovQ76nVjVfJ2VOm4ijPN/VXjrY3CTvw9cHiVzlcB+E4AXyalPGCvnwdwXUqZCiFeAuBlAB5t\nMyZxn204TI6QuSSwzsjhuW4mIa+dAqUgpbRkn32t7kShLiodV8DS541WceBxew6/DqFNHDr8NvMf\nNVAiAGqTtqNQIAoDXDy9hm/8grvxxS87X/t5RdNJW0drhTBQCNrp8FsExAtbE1zdLTsDCsKbE54U\ndlA6Ndfn7PpIn7fLTVM6jKMuBiZynjWMi/PcaFJmTaIANLsqOuGbX/8i3H1urfQ62QvOrOEDT9wo\nvR6nGdJMWo3ZgAIH3mL91BVnKoRvOPBaSsdxj+/MEf7l7TKlQ71uXLLPpsIxgAJ63Q7OdATuQucA\nh1fp/CiACYDfzrdXJL/8UgDfJ4SIAWQAvl1Keb3NgJMoxO2bEydyc3WDNFWk9V+pqTCEdOBFSmGR\nqMXYxFE3WZMssLHwqq2OfVbhMFsknbVsr0GlU9keOU6tPuNV1hbhVyZt84eJ3v8Df+c1tZ9VZXXt\nkWmHIoRgKg5Hc7kaYHXh1KSS36VDyy0O34Ew6xzy3efW8cT1mh1Q3q8eKPfqaeqVBLh7xSwYpUD3\nr8rh/L0vfYl78gDuOrOGd3zsUomWnbEdCqesigeIAA0Bqy5pm3P4gFJL1SVtXdfo7PoI4zDAlSoO\nP5dNboyrKZ0mlRH9fbWogK5/jvDHUfcdbqe/LpiU8qWO138JwC/1GfONX3A33vgFdzt/7zoCjGuc\n66wpKUYPYtHhGIXFIZO2xCEXHH6Wmda8ddak0tl07FAA9R24Prh6fs0OuS5p+8Kzh6d0Tq2NsLtI\nSg5hHmdWMq+PNSVtaYdyahrhJec38LI7Nq2/aVOYdmFrio88VZbt0YlpnMPvQ+m86LZ1vPfhq6XX\nLZUOJSWLlE6LHcraKMTeonx/qfUv5+i75lAA5fDjVOLa3gJ3MFHFnKmwOMK3dPi6jqOO0qnpNpmY\npOdaJcJnHL7jqwkhcOHUBFcqED6tIQ6sioeYk7lp2WrAYyjNnMMfdUf4Q6p0jsRcSVVqfNVEuRiE\nX/3VtzTCtx3mvlZYHF6WCZQDFu/1XmdNDjMMBLYmkS7r5jZvRem0SNpG6oEs7lKoD0rt+FG9SgQw\nUtq9hb3o5y1yHE1mAm41B07jR2GA3/knX46vfvVF62/aqIwubE3w7M6i1IBvnyWFnRy+rhNxP5ov\num0DV3cXpTzNXHPsgaWi4dYG4V88PcXl7Vnpda4CoueoK4cMKEoHAJ6+aX+Gbp0xCrHmaL9sEH73\nHYqUUhdeASrwus4jAOqv0R2nptUcflVzM+7wW8hK771tHZe256U8Ig/oAHD3uTVNL7W1E+fwqWS/\nGAGJwmiiLKa69Lv69y6ET9vNQ6t0HKXfvPFYnU0aCscAhZCp0yC3drLM5qQYPezFxG2XHEE9h0/3\nwA5aKqAcbsnWnWnbqo6gjcM/NcEsTksB6yDvo0OJXaCMwJsqkQFF6QAo0ToLnrR1SPaaDqkHlEN+\n5mYFP80Q/tQRUNrYXbnDf6bg8GcV8y9+Rpvr70o6q6M/zS7q/NbEKpACbIdcd43uPDXFlZ0qSie1\nZMNq/qLyZ5fKiKrTH7++XxjbBHQA+Gdf+Qr87N/7S845VtnJc/g5Mioi2E8/u4f1cagz6C5rbD8b\nBpiOghqEf1iEWU0pHDDJYZ2RQ6hLqp5aG1VSOm0QeKR3EO6/cZ1rq5rXDaHDr86jkMb5MEYP9KKq\nvXOuAa+zSYuAeGGLdNo2AtxnORQnpdMgGwaAF5HDLyiZ+Jbf6fAbWisAyiFf3pk7d6G88Kqfw1fX\np+jwjUrKBJRi87dxC8AQObpxEitAa/AH/s6r8YOFPFAb2SSgEP7lnXlpF0f96uk+u+YPuO/xi3OH\n/5mrBYevA66R3HbNKZ44h08qlO2C7O3hy7v4nDu2am8S0KzDB0gl4uLwD4fwjSzTXpCEbtojfPet\nOzWNqpO2LVo3GErHPb5G+EwrnWVSa6jrrG3SFqjYZS3TUjO8rrY1ibA1iaqTni2a1xEl1UTpAMCz\nhS2/6raaKyzGEQJR5sB1e+Qah/ai26oRPpX1j0Khv0dRBWRyNM7h8YKza0gziSuFgMUphenIOJ2u\ntjUdYWsa4ekbNQifAoqjTsGFjgF3Ja9RGamxL2xNS4WZbShNQFXbHizLuziiBTcmZv5W64YWlA45\n/Eev2Q5/UUja9rET6/A5gpVS4uEru3jFnVuN7582JG0B5TCLzkYj/EMmDY1KpMx/A204fJq/+28U\nwrfnH6cZ4lQ2O7QWlEIVwucHpLcavxXCt4PWPGkOKE0mhMCfu7CJTz+7V/pdu15GzeuHzqwtKnVU\na2QVzIJA4Ie/4fPwDffZAoU2O6DTa6PKWgWiE4QQjZW2dQjZRbnw1gra4fdA+ICijZ4u0EZVlE4x\nR2Cuj3vsi6enePJGOaAXEX6VtdlBAEaaWaR1zHkEIYTo17phYxLhwtYEjxUdfkGW2cdOrMPnlM7V\nvQWu7y/x8hYO/0s+53b891/4Itx91q0T3pqWKRF6uC52TJIUjRby/rJ6B9Gow4/aIPxRCeHPWzrk\nphOR1BzcDr8pILYpnHEh/HkLjr2NvfTCJj591eHw23L4NfM/T5ROAeHvL+w6jv/m81+o0RzZpEVS\nUgiBF91WlmZS61waRzmc7pTOCwqUy9ve/yTe9+hzWCQZwkDVQYSBOvmtT9IWUEGlHFAM6NF1BK5e\nRjXX/+V3nMIT1w80SDPjm4DlMqNiqp//BUfxFR0xKYRQSeEeOn9AofzPXCty+LegwydnwB3+Jy7t\nAkArh3/x9Bq+72s/t7SQip9RdDYPPLONu05PG2WNTXY2P1qwWIn5h5++CiGUAqPO2rSfPbUWlQLW\nrOViaaOCoKDBi6/a7lBGLXIEzqRtfPikLaAc/tXdRSkP1CbH0QaBn5pGmERBCeG3yXE0HXBD9qJz\nG9rhv+vBy/jMtX0lW2WUx1qFbK9NN9SLp42KJs0k/uWvPYgf+91HcgWKGW86Cnpx+IDi8Z/ZrqZ0\n1hhl5FLR1K3PV1zcgpTAJ6/sWq+3Qfht6lCA6uIrKhwjFqGqMKrNiVoA8JLzVQ7fdEPtayfO4Ueh\nKqvnD+vDl9WNfcWd1YdedLVTFZWeDzy9jVe94PShxyaHf+PAVErOlil+5n1P4K/9+Tu0ZM1lLzm/\nibvPrWke9/9v79yj47jKA/779qX307L8kC2/H7EVP+LEsYPJy5BAQgmBQ2MacoCkvFJK6elpCjnk\nNDk0hVJSoOUUSCEUCiXQAIUQaBJeDdAEEsfBr9jxI7Zj+SHJlmS9tZJu/5i5u6OVtDO7O7vSZO/v\nnD3anZl795vRzjff/e73fXcyqu05CGckileF7Kk8cmLi0+pTKcVnn3zJli/9AyvmcYQCE7OFBz24\nXLywfLYVW5/q1vEWZeRuIes4bT1pu/P4eTr7hukbHh0XvTEZbvXwNc2zyjnZ2c+xjj4+8M2dPPDE\nwYQ7QXP5kvoJC8EkonTSyF9REqG2PMqprgGOtvcyEB9lX2u3XTYg2X9ZLDzBgvVKU205Xf3xcVa4\nc72GqUpDeMlT0K5drRc0SQt/6v+xV5fOHNtt50y+Sh1FV8Qiieq7mnH19tN8x+JZFZzrGx6n5/yw\n8HPNtJ0WalLCDg+c6WF2VYlrlqdXUi38vqERjnb08eb1TTn3XWuvlOW08H+wq5Wu/jh3bFvi2r6p\ntoxf33Vt2mP0erK9gyOJlbm8uly8DPkTPnzbp/jAEy/x/V2t/NXrV7JpUX3a/hPlkdP82KdaBGXA\nrgWeK8sbLYV/pK2XTYuSBfY8lbZwqcWkaawqpe3CEBcG49zy5WdY3lhJZ9+wh8RAdwsWoLm+nPio\n4pM/fZExBc8cPc+GhTXjFPLX3rN5QjsvxdMA5tdYoZl7T3UDcK5vmOPn+sdZl4vqK1iQxjWatn/b\nbXS6e4DljZaCdi4xqbCMlYmJae6lJxbWlVMeC3PgTKqFb/Wf3sL3dv3L7eQ5Z/JVYs3lROmDCKMp\nUTxeonQgOXF7rKOP1fOqGBgeTYZl5mDhB1LhV5dFx1v4Zy94mrD1SlXpeJfI/tMXUAouXpD7CEJb\nL512LRSlFA/99mVamqrZvCS9svRKtSPbVit8rTzdEse8hH1qhT8wPMYr5/v5wi8P8/ZNC/jQtZMm\nXo/Di0tnqkVQhuJjvlj4C+vLiUVC4/z4OtPZ1aVjT9q6Dfkbq0p46WwPz758npExlVA+bnkiXhQa\nJEMzH993lpqyKB29Q+w7dcE1EcdLJjVYPvaTnf3sOZkscLvrRBezq5IuzW+993LX6zAVyeSrQZrr\nK4iExKEwQyi0D3/ySdt0CjkUElbMqUpj4adR+B5GEJq5dmhmav/6oVgeCyfOKbV/mHoRc3BG6vTy\nqZ8e4Eh7L9etnUPEnkPJlsC5dGB82OHomOLQ2V6fFX6UwfhYouLe3lbLymmZn7tLB6xaHF22/M+f\n6ORwWy/vuWJJ2lCzTJhsYlvH9C5O4woC7+WRwbLI9A/+zRvme5Lfyw0LE0dZI6NjDI/mHqUD1rkt\nbajgkMPH29FnuV8qXfIsvPjwwc627Rni6SPniEVC3H9zC5Acfbn172rhO/6Puu/T3YMJ//FUeBnB\ngTVx29o1wN5T3ayeW0VIrMxnp7KMhtOvnpYOHQm0t7WbN3z+Ke763m6G4qOIpCR2TVk+On3/q+dU\nceDMhXFx8kM++vAB5tWWsftkN122ezbV5VJfEZvwgE+uiZw+tLR5Vjki8OX/PcrTR8/R1jPEd587\nmZM7BwKq8GscFv6xc30MjYyxyif/PUyMEtnbeoHZVSUTYnazpaY8lviR6Im3jc21vvQNSaXiHKUc\naushFglNqN+dirYA02faJl062jVVW+bNneYl0xYmLoKSXPzEn59saqTOw79/BYBrV89J285rnHZj\ndSk9gyP88mAblzTXcuvli/j2e7fw7isWp22X9FGnl39eTRmxcIjLFtdx48XzmG9b9m7XJ1laIX3/\n82vL6Bkc4Q+vdLF5ST3L7HmPXPMgNI1VJYRDwgNPHORoex+/ONBGn6N4XSLKKDKFhe/y+1k1t4rO\n/vi4qqWeLPyQtwcKwIeuWc653mHe+43nGIwnXS76/rj7hot44O2TJ3a5yV8SCbOgrowDZ3poaarm\nlksXMmxHAOVCYBW+VmbJCVt/LXxIRonsO9VNy3z/Hih15VE6bUWpf5DOoXKuJCtmJi3kw229LG2o\ncFVUMQ+JRaWJsMyxxOSznptww0viFUxcBKXfntzL1cLRLG+s5GTnAIPxUYZGRvnG08e5etXshH9/\nKrxa+Pr/eaS9jy1LZwGwddks13kmt0xwTTgkfG7HBj751nWISOI7vGdSu7t0wMqubZlfQ4sdsJCL\n/zhVjrnVpSjgxovncb5vmD0nux0ZtlaU0YQFYjzKv3qepQ+cfnwdpZPuHEIhIRISTyOXzUvq+adb\n1vPssU7ue3TfuCgjsFyHen5CEw4JIXEfYYE1cQtw35tbuOsNq+zorxwz/XNqPU04LXxtIS9uSB8d\nkglOC38wPsqhtl5evya95ZcJdeUxXjxj+Ubbe4YojYZcozcyQdcbclr4h9t7Wb/AfRThxcIvcbh0\nxuxIoBqvCt+jwkxNLHpsz2kA1nk4By8sb6xEKTjS3suLp3vo6B3i9te4T5p7iQOHZLYtwFZbGXsh\n5tECBMYVdtuybBbf39XqrvA91NIBK9tWs7apmguDcX6wq9U3hQ/woWuXU1ESYePCWh7bc5qdJzoT\nyweCpThTE7u8jrB0xN7BMz1cudJaMyE103YqouGQ57mJN62bz5P7z/LzF9t4Y4v1/3CzwmOREIJ7\n/3/62qVsX92YCCz43I4NnJ6kQmcmBFLhV5dF6R8eJT46xpnuQapKI74qTOciKC+evsDomGKtT/57\nsKzhLoeF31BZ4pv/HhwuHfuhOBgf5WTnAG+7xH2N+eWNlVy/dg4bFk6tWPVweyg+Sv/wSKJCpxe8\nZNrC+EVQRscU//5/x7ikuTatXJmgLfnPPnmIl872sHJOJa9d0eDarkRP2nqI0gHrWm3IwF2nk5oy\nnZfbmrDwPbp0XH34lsKPhUOsaKxKjLb8GmEBvGNzc+L9groyTnYOjJO/NBqeMGkrIsQi7gq5viLG\n7KoSnj12nju2LSEUkkQtILdyENGwNwtfc9G8an74wqnEaN3LqnJq8urN47hq5WyuWplc4MfN3eiF\nwLp0wFJop7oGcs5+TcW5CIpO3rhonn8uozrbhz82pmjvHfLVnQNQGYsgklT4R9p7UQpXdwVYUSRf\nvu3StNEe2sc6ODJGV3+cmrKo5weW10kx56Ttz188y/Fz/dyxbamn7/DC0oZKVs2p4pmj5+jqH+bD\n21d4OodELR03C9+O0960qC7jYfg1q2azPsMH28L6cravbpx0HWcnbouYa2ZXlhANC6vmVhGLhFhj\nuzT9tPCdTOaSKotNXu+9xONk8XVr5vDE/rP80Rd+w97W7sSasG7nEItkNhmt8zr2nbpgn4NL/2HL\nYJoOAmnhO6NQzlwYZG5NdrHAU+F06Zw4308kJK4JUZlQWx5lTEHP0AgdPcNpk6iyIWRb3DpxSScY\neVH4XimNWuvadg3EJ5SYTYdXl051aYTe4RHGxhRf/c3LNNWWcf1a/9xqsUiIx//yyozblUbCNNWm\nT3wDqC+P0VRbxhta5mb8HV9512UZtwH46rvd24nYPmoXjRMKCesW1LJlqRUqXF0aZdOiOpb66Dp1\nsnXpLB7ZeXJcFNaKxspxC6RoYpGQq/wAf/eWFjYvqecTP97PPT/cy3Vr5ibapyOaoULW95WO5vNi\n4afG5xeKwCv8092DrJnn34QqjJ+0PX6un6a6spxiX1OpTZRXGKa9d4hLF6e3yrLBqolvW/htvYSE\nCXVbckEvZN7dH/fsv4cMJm1LoygFu17p4ncvn+fuG1b7+j/IllBI+O1H0ye+6eN+8zfXFECizAl7\nnJR85ANbJ3z20/XoZMuyiRb+F9+5adJjYxFvCllEuGlDE3tbu/n608fZttxy2bkVfIuGvT1QNDqv\nY98pjwo/IsRHp8fEn/47KAv0pGRH7zAdvUMZr/riRqqF31zvrwVeZyvI9h6r6JvfLh0YH8l0uL2X\n5vpyX7JUNaXREIPxMboGhjOy8PXD1G3ORf8PvvnMcUICN290n3+YaYhI3hRkLnidlEyVP5/n0lRb\nxtKGCk/GQ6Yul5amGoZHxth/6oKnxKVMffg6r6Nv2Fvpg2g45ClKJx/kpPBF5F4RaRWRF+zXDY59\nHxORwyJyUESuz13UJNrCP9TWg1K5V7BMJRq2FnjQFr7fCl9b+NrVkg+Fb1XMTLp0/HTngMOl0x9P\nnI8X5taU8oM7r3CNetIPhsf2nOY1yxvyco2KlWwmhQvB195zGffcuMb1uFiGCV864OL5E52e6vdn\nEqWjWea4v9yKm8UyHEH4iR8unc8qpT7j3CAia4AdwFpgPvAzEVmplJq4MnIW6CgUHYPvtw8fLAuz\ntWuA7oG47z52beEfshV+Q44VOCejuizCsY5+RkbHeLmjj2tWN/raf0k0zODIGN39cc8x+JqNLhOL\nkBzFDY+McdOG3GsYGZJYGbIzT+O7VYrVlEQzU/hLGiooj4Xp7I8n7r10xCLeomic6IlbLyMIK8oo\ns/79Il8+/JuAh5VSQ8DLInIY2Aw87UfnOopGK/z5Plv4YCl8PeveXO/vRJWumHko3xb+YJzj5/uJ\nj6rED9IvSiMh+oZG6Bka8Zxlmwnawi+JhHydrDXA3TesZkWjf1FnheYj21dmtBBROCSsnV/Ns8e8\nW/iTLZGYDj2C9lL6I7AuHZs/F5HdIvKQiGjTrQl4xXHMSXubL5RGw5REQhyxU+P99uGDpXB04o/f\nLp3qsigiJGq5zM6LhW9N2v7yQBsAlyzyd2K4NBpOrPaTqYXvBe3Df91FcxLK3+APb71kARcv8C+v\npNC8bs0crljunjPhRLt1vMxjRcOSsULWCt9L6YlM5wj8xFXhi8jPRGTvJK+bgC8CS4ENwGnggUwF\nEJH3ichzIvJce3u753Y1ZVHio4rKkkheFIJWODC+UJUfhENCdWk0kTWXLwu/b3iU7z/fSktTdaIW\nil+URkOJFZ3yofCbasu4bHEdt29b7HvfhuJDl4bwYuFftbJxXMKTF5Y0VBASb7WeMo0C8hNXl45S\n6nVeOhKRfwN+bH9sBZyLdS6wt03W/4PAgwCXXnqpZ89ZTVmUth7/I3Q02m3UUBnzNYtXU1dulYeo\nKo34mr2o0T7w/acv8PEbL/K9/9JoOFGbpCaDKJ1M+v+vD1zhe7+G4qSlyXvi2AevXpZx/6XRMAvr\nyz2tAFYSCahLR0TmOT7eDOy13/8I2CEiJSKyBFgB/D6X70pFKxm/I3Q02sL3252j0ZEt+XDnQPKB\nJWLV+/AbZxneTKJ0DIbpYPnsSkoiIU8WfrZsaq7zlKA5r6YssWJWocnVdP20iGwAFHAMeD+AUmqf\niHwX2A+MAH/mV4SOpjrgCl9HCzTkKdxQX58tS2blZRTkHLpmEodvMEwHkXCI9QtqqSzNX67p37/1\nYk/H3fOmNYwFMdNWKXVbmn33A/fn0n86tIWfj5BMSEaJNHsMFcsUHamTr/hyXYb3pg3+W/cApTGn\nhW8UvmHm84U/2YiHIpVZ49U1m89RhhuBLK0ASYWfj5BMSFr4iwLq0tm4sJZ/vfUSrvOxrLMT7dIR\nwUTRGAKBXwsYBZnAKvzqhIWfL4WvLfx8KXyr/3xZ+KGQjKuX7jfamqkujU5biJnBYMiMmZdu5xG9\nUPe8PLl0rlzRwG1bFrEuT/HK2oefLws/32gfvnHnGAzBIbAW/tZls9i+upHFDfmxwBurS/nEW1ry\n0jc4XDoBrRGjLXwzYWswBIfAKvy182s81f+eqbQ01dBcX85FPpd2LhRJC9+EZBoMQSGwCj/oLGmo\n4Km7Zma9dC/oSVvj0jEYgkNgffiG6cW4dAyG4GEUviErSmyXTo1x6RgMgcEofENWGAvfYAgeRuEb\nskL78PNROM1gMOQHo/ANWbFyTiXvv2op1/q8kpbBYMgfJkrHkBWRcIiPvdH/sssGgyF/GAvfYDAY\nigSj8A0Gg6FIMArfYDAYigSj8A0Gg6FIMArfYDAYigSj8A0Gg6FIMArfYDAYigSj8A0Gg6FIEDVN\nq6dPhoh0A4fy+BXNwIk89l8DdOex/3zLD8E/ByN/eoz86Qmq/IuUUrPdDpppCv9BpdT78th/u5eL\nkkP/gZbf/o5An4OR37V/I3/6/gMtvxszzaXzaJ7778pz/0GXH4J/Dkb+9Bj50xN0+dMyoxS+Uirf\nFzufQ7XAyw/BPwcjvytG/jQEXX43ZpTCLwAPTrcAORJ0+SH452Dkn16M/Dkwo3z4BoPBYMgfxWbh\nGwwGQ9ESeIUvIg+JSJuI7HVsWy8iT4vIHhF5VESqHfvW2fv22ftL7e3/IyJ/sLd/SUTCAZP/VyJy\nUEResF8FWZnED/lFpMoh9wsi0iEinwuK/Pb2W0Rkt739Hwohe6byi8itKdd5TEQ22PvuF5FXRKS3\nULL7LP+Mv39d5C/M/auUCvQLuBK4BNjr2PYscJX9/nbgE/b7CLAbWG9/ngWE7ffV9l8BvgfsCJj8\nvwIuDer1T+lzJ3BlUOS3/54AZtvbvw5sn2nyp7S7GDji+LwFmAf0ztTfj4v8M/7+dZG/IPdv4C18\npdRTwPmUzSuBp+z3TwJvs99fB+xWSv3BbntOKTVqv79gHxMBYkBBJjf8kn+68Ft+EVkJNAK/zpvQ\nDnySfylwSCnVbh/3M0ebvJKh/E7eATzs6OcZpdTpvAiZBh/lD8L962Sc/IUi8Ap/CvYBN9nv3w4s\ntN+vBJSIPC4iz4vIXc5GIvI40Ab0AI8USthJyEp+4Ov2cPAeEZFCCTsJ2coPsAP4jrLNnmkiU/kP\nA6tEZLGIRIC3ONpMB1PJ7+QW4NsFkygzspI/APevk8muf97v31erwr8duFNEdgJVwLC9PQJsA261\n/94sItt1I6XU9VjD2hLg2oJKPJ5s5L9VKbUWeK39uq2wIo8jq+tvs4PpV0QZya+U6gQ+CHwHa2Ry\nDJjOkddU8gMgIpcD/UqpvZM1ngFkJX8A7l9gSvkLcv++KhW+UuqAUuo6pdQmLOVxxN51EnhKKdWh\nlOoHfoLlf3O2HQR+SPIJXXCykV8p1Wr/7QH+E9hceMktsr3+IrIeiCildhZcaAdZXv9HlVKXK6W2\nAgeBl6ZDdluWqeTXzISH6pTkIv8Mv381E+Qv1P37qlT4eoZbRELAx4Ev2bseBy4WkXJ76H0VsF9E\nKkVknt0mAtwIHCi85BZZyB8RkQa7TRR4EzBt1lum8juavoMZoIiykd/Rpg64E/hKoeXWpJFfb/tj\npsF/7JVM5Q/Q/TuV/IW7f/M9K5zvF5aCOA3EsSywO4C/wLKwXgI+hZ1gZh//Tiwf217g0/a2OVgz\n67vt7f+CZWkGRf4KrMiW3fa+zzNJ9MtMld+x7yiwOmi/H0c/++1XQSJEspT/auCZSfr5tN1+zP57\nb1DkD9j9O5n8Bbt/TaatwWAwFAmvSpeOwWAwGCZiFL7BYDAUCUbhGwwGQ5FgFL7BYDAUCUbhGwwG\nQ5FgFL6hqBARJSLfdHyOiEi7iPw4y/5qReROx+ers+3LYMg3RuEbio0+oEVEyuzPrwdac+ivFivR\nymCY8RiFbyhGfoKVjQkp2b0iUi8i/y1WbftnRGSdvf1eu/b5r0TkqIh82G7yKWCZXfTqH+1tlSLy\niIgcEJFvTXMhO4MhgVH4hmLkYWCHWIuXrAN+59h3H7BLKbUOuBv4hmPfauB6rDonf2t/TXoUAAAB\nC0lEQVSnwX8Uq675BqXUX9vHbQQ+AqzBKp38mnyejMHgFaPwDUWHUmo3sBjLuv9Jyu5twH/Yx/0C\nmCXJFa8eU0oNKaU6sMrwzpniK36vlDqplBoDXrC/y2CYdiLTLYDBME38CPgMVm2TWR7bDDnejzL1\n/eP1OIOhoBgL31CsPATcp5Tak7L911j17hGRq4EOlVxNaTJ6sGqeGwwzHmN5GIoSpdRJ4J8n2XUv\n8JCI7Ab6gXe59HNORH4r1iLWPwUe81tWg8EvTLVMg8FgKBKMS8dgMBiKBKPwDQaDoUgwCt9gMBiK\nBKPwDQaDoUgwCt9gMBiKBKPwDQaDoUgwCt9gMBiKBKPwDQaDoUj4f8haSDkVU1bNAAAAAElFTkSu\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11ea87198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df['Milk First Difference'].plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Second Difference **"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Sometimes it would be necessary to do a second difference \n",
"# This is just for show, we didn't need to do a second difference in our case\n",
"df['Milk Second Difference'] = df['Milk First Difference'] - df['Milk First Difference'].shift(1)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Augmented Dickey-Fuller Test:\n",
"ADF Test Statistic : -14.3278736456\n",
"p-value : 1.11269893321e-26\n",
"#Lags Used : 11\n",
"Number of Observations Used : 154\n",
"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\n"
]
}
],
"source": [
"adf_check(df['Milk Second Difference'].dropna())"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11ea602b0>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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b2fzxpx7FL73r7rk6CbKc5sYZ9OLI33TGBqVtDjNsT/K5sFGtNNNDIPszAzJ2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NAAAF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\n/w8OqL2IDnb+ygAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11eabed30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df['Milk Second Difference'].plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Seasonal Difference **"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11ed76828>"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Uos3CKj61jKSkukf4AbcNPqd6kDFuGLsdVgx3uvWWE+vRbB7+9FIcW7s8YIxh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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11ec03dd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df['Seasonal Difference'] = df['Milk in pounds per cow'] - df['Milk in pounds per cow'].shift(12)\n",
"df['Seasonal Difference'].plot()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Augmented Dickey-Fuller Test:\n",
"ADF Test Statistic : -2.33541931436\n",
"p-value : 0.160798805277\n",
"#Lags Used : 12\n",
"Number of Observations Used : 143\n",
"weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \n"
]
}
],
"source": [
"# Seasonal Difference by itself was not enough!\n",
"adf_check(df['Seasonal Difference'].dropna())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Seasonal First Difference **"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11eb66f28>"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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OQVSopROv9/Dz7sV86UQWNneSPs0QzOFTIoGIczgVw2rJFIQ0koqLvyNLZyQd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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11ecaa9e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# You can also do seasonal first difference\n",
"df['Seasonal First Difference'] = df['Milk First Difference'] - df['Milk First Difference'].shift(12)\n",
"df['Seasonal First Difference'].plot()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Augmented Dickey-Fuller Test:\n",
"ADF Test Statistic : -5.03800227492\n",
"p-value : 1.86542343188e-05\n",
"#Lags Used : 11\n",
"Number of Observations Used : 143\n",
"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\n"
]
}
],
"source": [
"adf_check(df['Seasonal First Difference'].dropna())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Autocorrelation and Partial Autocorrelation Plots\n",
"\n",
"An autocorrelation plot (also known as a [Correlogram](https://en.wikipedia.org/wiki/Correlogram) ) shows the correlation of the series with itself, lagged by x time units. So the y axis is the correlation and the x axis is the number of time units of lag.\n",
"\n",
"So imagine taking your time series of length T, copying it, and deleting the first observation of copy #1 and the last observation of copy #2. Now you have two series of length T1 for which you calculate a correlation coefficient. This is the value of of the vertical axis at x=1x=1 in your plots. It represents the correlation of the series lagged by one time unit. You go on and do this for all possible time lags x and this defines the plot.\n",
"\n",
"You will run these plots on your differenced/stationary data. There is a lot of great information for identifying and interpreting ACF and PACF [here](http://people.duke.edu/~rnau/arimrule.htm) and [here](https://people.duke.edu/~rnau/411arim3.htm).\n",
"\n",
"### Autocorrelation Interpretation\n",
"\n",
"The actual interpretation and how it relates to ARIMA models can get a bit complicated, but there are some basic common methods we can use for the ARIMA model. Our main priority here is to try to figure out whether we will use the AR or MA components for the ARIMA model (or both!) as well as how many lags we should use. In general you would use either AR or MA, using both is less common.\n",
"\n",
"* If the autocorrelation plot shows positive autocorrelation at the first lag (lag-1), then it suggests to use the AR terms in relation to the lag\n",
"\n",
"* If the autocorrelation plot shows negative autocorrelation at the first lag, then it suggests using MA terms."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_____\n",
"### <font color='red'> Important Note! </font> \n",
"\n",
"Here we will be showing running the ACF and PACF on multiple differenced data sets that have been made stationary in different ways, typically you would just choose a single stationary data set and continue all the way through with that.\n",
"\n",
"The reason we use two here is to show you the two typical types of behaviour you would see when using ACF.\n",
"_____"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from statsmodels.graphics.tsaplots import plot_acf,plot_pacf"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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DS41aY53ALU7Mcc35Nwmpw0uV9OGlhlENAhEAEbleRA6IyKCI3JXnuJeKSFxE3hbEdY3C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\nPnPiEJ+hq7uXmVg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7lzJn4gzxzjCTKZ8XW1vN11mb+LyRa+rV6qy1WL1hBEdbCUC2Wj7A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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11ebfee48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Duplicate plots\n",
"# Check out: https://stackoverflow.com/questions/21788593/statsmodels-duplicate-charts\n",
"# https://github.com/statsmodels/statsmodels/issues/1265\n",
"fig_first = plot_acf(df[\"Milk First Difference\"].dropna())"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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rq+CcFnpp5wv5STxYx3/d4s5ZDGddhrMuZ4fyu1+LClR1OXX8ML2TpuXF3x6K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\nMQn3fwDUsmwsxWROpQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11eb052b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig_seasonal_first = plot_acf(df[\"Seasonal First Difference\"].dropna())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pandas also has this functionality built in, but only for ACF, not PACF. So I recommend using statsmodels, as ACF and PACF is more core to its functionality than it is to pandas' functionality."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a121adf390>"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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L/BZYrapPOK93AwuAcf2t25PU1FQdc+v/4olJpGDb4zRnTub45Oso2PIocS0n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\nREQMRApKREQMxH8Ac2tyk6KpuD0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a121af3390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pandas.plotting import autocorrelation_plot\n",
"autocorrelation_plot(df['Seasonal First Difference'].dropna())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Partial Autocorrelation\n",
"\n",
"In general, a partial correlation is a conditional correlation.\n",
"\n",
"It is the correlation between two variables under the assumption that we know and take into account the values of some other set of variables.\n",
"\n",
"For instance, consider a regression context in which y = response variable and x1, x2, and x3 are predictor variables. The partial correlation between y and x3 is the correlation between the variables determined taking into account how both y and x3 are related to x1 and x2.\n",
"\n",
"Formally, this is relationship is defined as:\n",
"\n",
"## $\\frac{\\text{Covariance}(y, x_3|x_1, x_2)}{\\sqrt{\\text{Variance}(y|x_1, x_2)\\text{Variance}(x_3| x_1, x_2)}}$\n",
"\n",
"Check out this [link](http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4463.htm) for full details on this."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can then plot this relationship:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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3b3m3vv/zgTF/+AvfZvvBblIKERFmTcycP/C4cJMaEmXk7lXUdWxNx+/dn5Ex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\ncpYIjDEm5CwRGGNMyP1/HvgNQL+oGcYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a121b44cc0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"result = plot_pacf(df[\"Seasonal First Difference\"].dropna())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Interpretation\n",
"\n",
"Typically a sharp drop after lag \"k\" suggests an AR-k model should be used. If there is a gradual decline, it suggests an MA model."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### Final Thoughts on Autocorrelation and Partial Autocorrelation\n",
"\n",
"* Identification of an AR model is often best done with the PACF.\n",
" * For an AR model, the theoretical PACF “shuts off” past the order of the model. The phrase “shuts off” means that in theory the partial autocorrelations are equal to 0 beyond that point. Put another way, the number of non-zero partial autocorrelations gives the order of the AR model. By the “order of the model” we mean the most extreme lag of x that is used as a predictor.\n",
" \n",
" \n",
"* Identification of an MA model is often best done with the ACF rather than the PACF.\n",
" * For an MA model, the theoretical PACF does not shut off, but instead tapers toward 0 in some manner. A clearer pattern for an MA model is in the ACF. The ACF will have non-zero autocorrelations only at lags involved in the model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_____\n",
"### Final ACF and PACF Plots\n",
"\n",
"We've run quite a few plots, so let's just quickly get our \"final\" ACF and PACF plots. These are the ones we will be referencing in the rest of the notebook below.\n",
"_____"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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kSZJKMDhLkiRJJRicJUmSpBIMzpIkSVIJlYJzRJwaEX8bEQ8V/58ySdn+iPhq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\n3alVh258nergLwfWrBN+IY05AxB9PfG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"text/plain": [
"<matplotlib.figure.Figure at 0x1a11fc60048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12,8))\n",
"ax1 = fig.add_subplot(211)\n",
"fig = sm.graphics.tsa.plot_acf(df['Seasonal First Difference'].iloc[13:], lags=40, ax=ax1)\n",
"ax2 = fig.add_subplot(212)\n",
"fig = sm.graphics.tsa.plot_pacf(df['Seasonal First Difference'].iloc[13:], lags=40, ax=ax2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using the Seasonal ARIMA model\n",
"\n",
"Finally we can use our ARIMA model now that we have an understanding of our data!"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# For non-seasonal data\n",
"from statsmodels.tsa.arima_model import ARIMA"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Help on class ARIMA in module statsmodels.tsa.arima_model:\n",
"\n",
"class ARIMA(ARMA)\n",
" | Autoregressive Integrated Moving Average ARIMA(p,d,q) Model\n",
" | \n",
" | Parameters\n",
" | ----------\n",
" | endog : array-like\n",
" | The endogenous variable.\n",
" | order : iterable\n",
" | The (p,d,q) order of the model for the number of AR parameters,\n",
" | differences, and MA parameters to use.\n",
" | exog : array-like, optional\n",
" | An optional array of exogenous variables. This should *not* include a\n",
" | constant or trend. You can specify this in the `fit` method.\n",
" | dates : array-like of datetime, optional\n",
" | An array-like object of datetime objects. If a pandas object is given\n",
" | for endog or exog, it is assumed to have a DateIndex.\n",
" | freq : str, optional\n",
" | The frequency of the time-series. A Pandas offset or 'B', 'D', 'W',\n",
" | 'M', 'A', or 'Q'. This is optional if dates are given.\n",
" | \n",
" | \n",
" | Notes\n",
" | -----\n",
" | If exogenous variables are given, then the model that is fit is\n",
" | \n",
" | .. math::\n",
" | \n",
" | \\phi(L)(y_t - X_t\\beta) = \\theta(L)\\epsilon_t\n",
" | \n",
" | where :math:`\\phi` and :math:`\\theta` are polynomials in the lag\n",
" | operator, :math:`L`. This is the regression model with ARMA errors,\n",
" | or ARMAX model. This specification is used, whether or not the model\n",
" | is fit using conditional sum of square or maximum-likelihood, using\n",
" | the `method` argument in\n",
" | :meth:`statsmodels.tsa.arima_model.ARIMA.fit`. Therefore, for\n",
" | now, `css` and `mle` refer to estimation methods only. This may\n",
" | change for the case of the `css` model in future versions.\n",
" | \n",
" | Method resolution order:\n",
" | ARIMA\n",
" | ARMA\n",
" | statsmodels.tsa.base.tsa_model.TimeSeriesModel\n",
" | statsmodels.base.model.LikelihoodModel\n",
" | statsmodels.base.model.Model\n",
" | builtins.object\n",
" | \n",
" | Methods defined here:\n",
" | \n",
" | __getnewargs__(self)\n",
" | \n",
" | __init__(self, endog, order, exog=None, dates=None, freq=None, missing='none')\n",
" | Initialize self. See help(type(self)) for accurate signature.\n",
" | \n",
" | fit(self, start_params=None, trend='c', method='css-mle', transparams=True, solver='lbfgs', maxiter=50, full_output=1, disp=5, callback=None, start_ar_lags=None, **kwargs)\n",
" | Fits ARIMA(p,d,q) model by exact maximum likelihood via Kalman filter.\n",
" | \n",
" | Parameters\n",
" | ----------\n",
" | start_params : array-like, optional\n",
" | Starting parameters for ARMA(p,q). If None, the default is given\n",
" | by ARMA._fit_start_params. See there for more information.\n",
" | transparams : bool, optional\n",
" | Whehter or not to transform the parameters to ensure stationarity.\n",
" | Uses the transformation suggested in Jones (1980). If False,\n",
" | no checking for stationarity or invertibility is done.\n",
" | method : str {'css-mle','mle','css'}\n",
" | This is the loglikelihood to maximize. If \"css-mle\", the\n",
" | conditional sum of squares likelihood is maximized and its values\n",
" | are used as starting values for the computation of the exact\n",
" | likelihood via the Kalman filter. If \"mle\", the exact likelihood\n",
" | is maximized via the Kalman Filter. If \"css\" the conditional sum\n",
" | of squares likelihood is maximized. All three methods use\n",
" | `start_params` as starting parameters. See above for more\n",
" | information.\n",
" | trend : str {'c','nc'}\n",
" | Whether to include a constant or not. 'c' includes constant,\n",
" | 'nc' no constant.\n",
" | solver : str or None, optional\n",
" | Solver to be used. The default is 'lbfgs' (limited memory\n",
" | Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs',\n",
" | 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' -\n",
" | (conjugate gradient), 'ncg' (non-conjugate gradient), and\n",
" | 'powell'. By default, the limited memory BFGS uses m=12 to\n",
" | approximate the Hessian, projected gradient tolerance of 1e-8 and\n",
" | factr = 1e2. You can change these by using kwargs.\n",
" | maxiter : int, optional\n",
" | The maximum number of function evaluations. Default is 50.\n",
" | tol : float\n",
" | The convergence tolerance. Default is 1e-08.\n",
" | full_output : bool, optional\n",
" | If True, all output from solver will be available in\n",
" | the Results object's mle_retvals attribute. Output is dependent\n",
" | on the solver. See Notes for more information.\n",
" | disp : int, optional\n",
" | If True, convergence information is printed. For the default\n",
" | l_bfgs_b solver, disp controls the frequency of the output during\n",
" | the iterations. disp < 0 means no output in this case.\n",
" | callback : function, optional\n",
" | Called after each iteration as callback(xk) where xk is the current\n",
" | parameter vector.\n",
" | start_ar_lags : int, optional\n",
" | Parameter for fitting start_params. When fitting start_params,\n",
" | residuals are obtained from an AR fit, then an ARMA(p,q) model is\n",
" | fit via OLS using these residuals. If start_ar_lags is None, fit\n",
" | an AR process according to best BIC. If start_ar_lags is not None,\n",
" | fits an AR process with a lag length equal to start_ar_lags.\n",
" | See ARMA._fit_start_params_hr for more information.\n",
" | kwargs\n",
" | See Notes for keyword arguments that can be passed to fit.\n",
" | \n",
" | Returns\n",
" | -------\n",
" | `statsmodels.tsa.arima.ARIMAResults` class\n",
" | \n",
" | See also\n",
" | --------\n",
" | statsmodels.base.model.LikelihoodModel.fit : for more information\n",
" | on using the solvers.\n",
" | ARIMAResults : results class returned by fit\n",
" | \n",
" | Notes\n",
" | ------\n",
" | If fit by 'mle', it is assumed for the Kalman Filter that the initial\n",
" | unkown state is zero, and that the inital variance is\n",
" | P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r,\n",
" | r, order = 'F')\n",
" | \n",
" | predict(self, params, start=None, end=None, exog=None, typ='linear', dynamic=False)\n",
" | ARIMA model in-sample and out-of-sample prediction\n",
" | \n",
" | Parameters\n",
" | ----------\n",
" | params : array-like\n",
" | The fitted parameters of the model.\n",
" | start : int, str, or datetime\n",
" | Zero-indexed observation number at which to start forecasting, ie.,\n",
" | the first forecast is start. Can also be a date string to\n",
" | parse or a datetime type.\n",
" | end : int, str, or datetime\n",
" | Zero-indexed observation number at which to end forecasting, ie.,\n",
" | the first forecast is start. Can also be a date string to\n",
" | parse or a datetime type. However, if the dates index does not\n",
" | have a fixed frequency, end must be an integer index if you\n",
" | want out of sample prediction.\n",
" | exog : array-like, optional\n",
" | If the model is an ARMAX and out-of-sample forecasting is\n",
" | requested, exog must be given. Note that you'll need to pass\n",
" | `k_ar` additional lags for any exogenous variables. E.g., if you\n",
" | fit an ARMAX(2, q) model and want to predict 5 steps, you need 7\n",
" | observations to do this.\n",
" | dynamic : bool, optional\n",
" | The `dynamic` keyword affects in-sample prediction. If dynamic\n",
" | is False, then the in-sample lagged values are used for\n",
" | prediction. If `dynamic` is True, then in-sample forecasts are\n",
" | used in place of lagged dependent variables. The first forecasted\n",
" | value is `start`.\n",
" | typ : str {'linear', 'levels'}\n",
" | \n",
" | - 'linear' : Linear prediction in terms of the differenced\n",
" | endogenous variables.\n",
" | - 'levels' : Predict the levels of the original endogenous\n",
" | variables.\n",
" | \n",
" | \n",
" | Returns\n",
" | -------\n",
" | predict : array\n",
" | The predicted values.\n",
" | \n",
" | \n",
" | \n",
" | Notes\n",
" | -----\n",
" | Use the results predict method instead.\n",
" | \n",
" | ----------------------------------------------------------------------\n",
" | Static methods defined here:\n",
" | \n",
" | __new__(cls, endog, order, exog=None, dates=None, freq=None, missing='none')\n",
" | Create and return a new object. See help(type) for accurate signature.\n",
" | \n",
" | ----------------------------------------------------------------------\n",
" | Methods inherited from ARMA:\n",
" | \n",
" | geterrors(self, params)\n",
" | Get the errors of the ARMA process.\n",
" | \n",
" | Parameters\n",
" | ----------\n",
" | params : array-like\n",
" | The fitted ARMA parameters\n",
" | order : array-like\n",
" | 3 item iterable, with the number of AR, MA, and exogenous\n",
" | parameters, including the trend\n",
" | \n",
" | hessian(self, params)\n",
" | Compute the Hessian at params,\n",
" | \n",
" | Notes\n",
" | -----\n",
" | This is a numerical approximation.\n",
" | \n",
" | loglike(self, params, set_sigma2=True)\n",
" | Compute the log-likelihood for ARMA(p,q) model\n",
" | \n",
" | Notes\n",
" | -----\n",
" | Likelihood used depends on the method set in fit\n",
" | \n",
" | loglike_css(self, params, set_sigma2=True)\n",
" | Conditional Sum of Squares likelihood function.\n",
" | \n",
" | loglike_kalman(self, params, set_sigma2=True)\n",
" | Compute exact loglikelihood for ARMA(p,q) model by the Kalman Filter.\n",
" | \n",
" | score(self, params)\n",
" | Compute the score function at params.\n",
" | \n",
" | Notes\n",
" | -----\n",
" | This is a numerical approximation.\n",
" | \n",
" | ----------------------------------------------------------------------\n",
" | Data descriptors inherited from statsmodels.tsa.base.tsa_model.TimeSeriesModel:\n",
" | \n",
" | exog_names\n",
" | \n",
" | ----------------------------------------------------------------------\n",
" | Methods inherited from statsmodels.base.model.LikelihoodModel:\n",
" | \n",
" | information(self, params)\n",
" | Fisher information matrix of model\n",
" | \n",
" | Returns -Hessian of loglike evaluated at params.\n",
" | \n",
" | initialize(self)\n",
" | Initialize (possibly re-initialize) a Model instance. For\n",
" | instance, the design matrix of a linear model may change\n",
" | and some things must be recomputed.\n",
" | \n",
" | ----------------------------------------------------------------------\n",
" | Class methods inherited from statsmodels.base.model.Model:\n",
" | \n",
" | from_formula(formula, data, subset=None, drop_cols=None, *args, **kwargs) from builtins.type\n",
" | Create a Model from a formula and dataframe.\n",
" | \n",
" | Parameters\n",
" | ----------\n",
" | formula : str or generic Formula object\n",
" | The formula specifying the model\n",
" | data : array-like\n",
" | The data for the model. See Notes.\n",
" | subset : array-like\n",
" | An array-like object of booleans, integers, or index values that\n",
" | indicate the subset of df to use in the model. Assumes df is a\n",
" | `pandas.DataFrame`\n",
" | drop_cols : array-like\n",
" | Columns to drop from the design matrix. Cannot be used to\n",
" | drop terms involving categoricals.\n",
" | args : extra arguments\n",
" | These are passed to the model\n",
" | kwargs : extra keyword arguments\n",
" | These are passed to the model with one exception. The\n",
" | ``eval_env`` keyword is passed to patsy. It can be either a\n",
" | :class:`patsy:patsy.EvalEnvironment` object or an integer\n",
" | indicating the depth of the namespace to use. For example, the\n",
" | default ``eval_env=0`` uses the calling namespace. If you wish\n",
" | to use a \"clean\" environment set ``eval_env=-1``.\n",
" | \n",
" | Returns\n",
" | -------\n",
" | model : Model instance\n",
" | \n",
" | Notes\n",
" | ------\n",
" | data must define __getitem__ with the keys in the formula terms\n",
" | args and kwargs are passed on to the model instantiation. E.g.,\n",
" | a numpy structured or rec array, a dictionary, or a pandas DataFrame.\n",
" | \n",
" | ----------------------------------------------------------------------\n",
" | Data descriptors inherited from statsmodels.base.model.Model:\n",
" | \n",
" | __dict__\n",
" | dictionary for instance variables (if defined)\n",
" | \n",
" | __weakref__\n",
" | list of weak references to the object (if defined)\n",
" | \n",
" | endog_names\n",
" | Names of endogenous variables\n",
"\n"
]
}
],
"source": [
"# I recommend you glance over this!\n",
"\n",
"# \n",
"help(ARIMA)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### p,d,q parameters\n",
"\n",
"* p: The number of lag observations included in the model.\n",
"* d: The number of times that the raw observations are differenced, also called the degree of differencing.\n",
"* q: The size of the moving average window, also called the order of moving average."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Statespace Model Results \n",
"==========================================================================================\n",
"Dep. Variable: Milk in pounds per cow No. Observations: 168\n",
"Model: SARIMAX(0, 1, 0)x(1, 1, 1, 12) Log Likelihood -534.065\n",
"Date: Thu, 13 Jul 2017 AIC 1074.131\n",
"Time: 00:16:10 BIC 1083.503\n",
"Sample: 01-01-1962 HQIC 1077.934\n",
" - 12-01-1975 \n",
"Covariance Type: opg \n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"ar.S.L12 -0.0449 0.106 -0.422 0.673 -0.253 0.163\n",
"ma.S.L12 -0.5860 0.102 -5.761 0.000 -0.785 -0.387\n",
"sigma2 55.5118 5.356 10.365 0.000 45.015 66.009\n",
"===================================================================================\n",
"Ljung-Box (Q): 33.48 Jarque-Bera (JB): 32.04\n",
"Prob(Q): 0.76 Prob(JB): 0.00\n",
"Heteroskedasticity (H): 0.69 Skew: 0.77\n",
"Prob(H) (two-sided): 0.18 Kurtosis: 4.60\n",
"===================================================================================\n",
"\n",
"Warnings:\n",
"[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
]
}
],
"source": [
"# We have seasonal data!\n",
"model = sm.tsa.statespace.SARIMAX(df['Milk in pounds per cow'],order=(0,1,0), seasonal_order=(1,1,1,12))\n",
"results = model.fit()\n",
"print(results.summary())"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11fc47fd0>"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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+8w0PXz2a757Wv24fpZU1fL4ujw9X7CRrdyn/PmU4Zw3uylNzNvL4Zxvruoqv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\n/x+HKeyT5n5qBwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11ff65b70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"results.resid.plot()"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11fd9da20>"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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tqV/SHXW2S9Kd6fbHJa1u1VbSxZIekvR0+u/CzLYPp/V3S3p7ka/NprddPznK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\nTjBmZlYIJxgzMyuEE4yZmRXi/wM/2Lz7Gx2axwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11fcca160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"results.resid.plot(kind='kde')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Prediction of Future Values\n",
"\n",
"Firts we can get an idea of how well our model performs by just predicting for values that we actually already know:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11ea87588>"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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JfWEOTauO7r8FSGXyy/avwsIhMKdO4liphcCqnjv5IGGtAXo47pBlKgcfhlwK\nTn8lYPzsr/QOBhh99COpDHo5QB9r9lVWJQFaCCGEcBBrC2Glk/siFEq64+cQz6jasiPsYMkhMAea\nSS/fw90T9uF2KY5u4Zito4UjXygx1e7RiM/9DDxBOOkqwGwBWuX6B+MBslqJOe+AcYMEaCGEEEIk\n1eOriOVRdg5v40hWWUJSyToENubQAD1dZY23xbh2v+NbOGoK0AlrlF0b+6B13eh/PuWl4DNWpScz\nWnmB0HKsdzGOFULg9kkLhxBCCCHMNojQ0gBtjLJz8kFCXddrqiAOme0DTpRcpYe73xzD51S1BmhH\nzIIe2WGE39OuK9+UUlduAQLj5wdgdDZvTOKQCrQQQgghjBaOxSEuHvQSD3o54uBNePO5AoWSXnWG\ncqUBB28jnFHzVQ8QWgaifsYdWoHWiiXUfLHGCrS10a+NP097fgUoxgFCU0090JUHUWPrICUVaCGE\nEOLP3nKj4AZifkcfYCtPD1klAA3FjDFkbT/AVkUtY/jGHPo9mK1hC6GlJ+zD53G1952A9DgE4hDu\nAaBU0qv2/y/VH/WjKOY679iwtHAIIYQQf+50XTf6QKuEiIFYwNH9t1aAXq0CPRgPkNGKzJpb55xk\nOp1f8foHYn6SqkZWK7bwqmpTyxpvi6IoxizodvZA51Xwhcu/ncsW0HVW7YH2ul30RvzmOu9ho4Wj\nDS/GJEALIYQQDpHVSuQLpapV3P5ogHGHtj7Awgzl1d+CN9sHZp3VjlIs6cxmtWUPEYKztxHWE6DB\nAb3omgreUPm3yYz581PjFJERq4WjmAN1ummXuRwJ0EIIIYRDlNd4B6ss8oj5GZ/LUSo5r/UBjP5V\nqL4Gu1L5EJjDDhKmMhq6Dl0r9UDHrGUqzrp2WPjZqWUONBgHCUfaWYHW1PL0DVh5BvdSA7GKbYTQ\nljYOCdBCCCGEQ1hVuKotHFE/hZJervQ6TbJcgV7lEKFD13lbf68rt3A4dxthvRXowXiA8bkcxXa9\nIMunl1Sgaw/QQ+VthOuMG9owiUMCtBBCCOEQtWzCc2J4g+oryKvpjwYWDoE5SLKGFpSBmB9wZgW6\nnkOEYITQQklnar5NP09LWzhU68Xjyi/AwAj/qYxGJmgtU5EKtBBCCPFna6UqYr8VoB06BWJGzRP1\ne/C6V44WPo+LnrDfcSF0Or36Ich40IvP43Lk96DeCvT5Mz/n/Z672vdCJr+4hSNVRwV60HoXoxgD\nl0cq0EJyyANAAAAgAElEQVQIIcSfs9SKFWij+unUg4QpVVt1hJ2l7QfYqqilhUNRFGOcoAPfBUhl\nNIJeNz5PbdFuaO5p3uC+r30zuTUVvAtTOGp9BwMqDqLOtW+ZSkMBWlGUf1AUZaeiKE8rivKP5m3d\niqLcqyjKHvPXror7f0BRlL2KojynKMo1jV68EEIIcSJZqQe6L2q1DzgvvIERQFcbYWcZjDtvo5/V\nQtAVXjnADUSdd+1Q+xZCi79nAwklzeRU6ydYAMcdIvzdvkk29YRWfQcDYGjRMpVhmD3StMtczpoD\ntKIoZwPvBC4CzgVepSjKKcD7gV/rur4V+LX5exRFORN4A3AWcC3wGUVR3I1dvhBCCHHiSKoabpdC\nxO857nN+j5uukNexy1RmVllCUmkw5sQKtIZnmb/7SgMx521S1HWdPxycYetApObHhHo3ADA/2frw\nCRgtHGYP9L6JeX6/f5rXv3BDTQ8tt3BUzoJusUYq0GcAj+q6ruq6XgAeBF4LvBr4inmfrwB/aX78\nauBbuq7ndF0/AOzFCN9CCCGEgPImNkVRqn7eqctUdF1nYi636gQOS/kQWN45C0mSap5EyLfs372l\n34EtHE8fm+XAZJpXnjNU82Nc8fUAFJOHm3VZy9P1RYcI73r0EB6Xwl+9oLYAHfS5iQe9C+u827BM\npZEAvRO4XFGUHkVRQsB1wAZgQNf1EfM+o4B5RJJ1QOV36Yh523EURfkbRVG2K4qyfWJiooFLFEII\nITrHclsILf0xZy5TeezANEeTGV50Uk9N9y/PgnbQn8XYQljbDOL5XIH5nHM2Kf74qWN4XArXnj1Y\n+4PaOEMZLQPo4AuR1Yp874kjXHPWYLlNqRYLy1SGjTCeTTbveqtYc4DWdf0Z4JPAL4GfAzuA4pL7\n6EDdLwl0Xb9D1/ULdV2/sK+vb62XKIQQQnSU1Q7i9Uf9jqxA/8/DB+gKeXntBVXrYsex3oIfSTln\nG+HYbI7uFZaoWJx2mFPXdX761Agv3tpb8zsAQDlA+9KjTbqyFWjm990b5uc7R0mqGn998ca6nsJ4\nN6ZymUpr2zgaOkSo6/oXdV1/ga7rVwAzwG5gTFGUIQDz13Hz7kcxKtSW9eZtQgghhGChhWM5AzE/\nE/PO2kZ4cDLNr54Z402XbCLgre1o06DDthGmVI0/HU3xws3dq953IOqsedw7Dic5MpPhVduG63ug\nN4jqiRPOjaG3uP0BLW386gvxzUcPsbknVPO7F5ZF67yhswK0oij95q8bMfqfvwn8CHireZe3Aneb\nH/8IeIOiKH5FUbYAW4HHGvn6QgghxIkkmcmvWEUciAUolnSm0s7ZRnjn7w7icSm8+ZJNNT9m0GEt\nHA/umaBY0rnq9P5V72vN43bKYc6fPDWCz+3i5WcNrH7nJdTAIH36VHkGc8vkVQBGVIXHDk5z40Ub\ncblW7j1fajAeYHI+Rz5ktq20uBVl5aOmq/u+oig9gAa8W9f1pKIonwC+oyjK24HngRsAdF1/WlGU\n7wC7gIJ5f+ecHhBCCCHaLKmu0gNdrn5m6+oXbZZURuM72w9z/bnrysGyFiGfh1jA45gK9P3PjtMd\n9nHehsSq93XSNsJSyWjfuPK0PmKB2kfYWYqRIYZnDzCSytbX/tEoswJ9//40Pnc3r3vB+rqfYjge\nRNdhTE+wQXG1vALdUIDWdf3yKrdNAS9d5v4fBz7eyNcUQgghTkTFks5ctrDKIUKz/3YuC8RbdGXL\n+9Zjh1DzRd7+4i11P3YoHuRYsv0htFjSeeC5ca46rR93DVXQiN9DyOd2RAvH9udnGJ3N8oFtp6/p\n8a74OgZHtvPkbJYzhmI2X90KzAr0r/fNcc3Zg/RE6n8xOJwwZkEfm9XYEBmEVGsr0LKJUAghhHCA\n2RpWGQ9Y7QMOCG9ascSdvzvIpSf3cOZw/eFrKBFgdLb9hwh3HJ5hRtW4+ozV2zfA2kbojGUqP3nq\nGAGvi784o/72DQBfzwa6lXkmpls7wcI6RDiZ8/DXF9V3eNAynDD+WziWypizoCVACyGEEH92kjUE\n6L6Ic7YR3rNzlJFUdk3VZ3BOBfrXz4zjdilcvrX2qV/90fbPgi6WdH72p1GuPr2f8CrLX5YT7jX6\n1ucnWjwL2mzh0L0hLjlp9YOb1ZQr0Mn2LFORAC2EEEI4gLVKeqUWDp/HRU/Yx5gDDrB99XcHOak3\nzFWn1Va5XWo4HmA6nSertfc41H3PjvPCzV11rcEeiAXa/j14dP8Uk/O5+qdvVPAkjAkW2nSLA7TZ\nwoE3tOrimuUEvG56wj6OJjMLy1RaSAK0EEII4QDWJIR4cOXDXH1RvyNmEB+YTPOik3vqnp5gGTIr\niO1c6X00meHZ0TmurmH6RqWBmJ+x2Wzrx79V+PnTo4R87jW/gAHKI+D0uRZPFdbMAO0LNfQ0Q4kA\nx5JmC0d+DrKzNlxcbSRACyGEEA6QqqGFA5yzzjudLxBZY+sAGBVogJFk+/qg73vWWFVx9en19RAP\nxAJktRKz2fZtIxxNZdnYHSLoq232dlXWMpX5kVXuaLO8OQfaG27oaYbjwYUADS2tQkuAFkIIcUI6\nPK1SdNDCkdUkVasCvVqA9rd9BnGhWCKrldbcewsLFehjbaxA3//sOBu7Q5zcV1+QWzjM2b5rz2jF\nxsIzgC+E6o4Ryo3Zc1G1Mg8RunzBhp5mOBFkJFm5TKV1lXQJ0EIIIU44STXPS//Pg3z/iSPtvpSa\nLbRwrF6BnpjLtfXFgWr2LYcaCHBDba5AZ/JFfrt3kqtP76+7D9cK0O18JyCTLxKscfPjStTAAD3F\nSdK5FlbTtTRZxU/QV//s6krrEkHmcgXm/GYbi1SghRBCiLUbn8uRL5b405FUuy+lZklVI+L34HWv\n/E9zf9RPSYep+faFNytsNdLCEfC66Q772laBfmT/JLlCqe7+Z3DGMpWMZk+ALoSHGFKmW7sVMq+S\nw99wBd2axHG0aM5Elwq0EEIIsXZWO8Se8bk2X0ntkpl8TZMg+h1Q/UznzAp0AwEajCr0SKo9Fehf\nPzNOyOfm4jWMUStvhGxjK01GKxJotIUDID7MoDLNWCtfyGgqGQINvwAoz4KeK0K4XwK0EEII0Qhr\nJNze8fk2X0ntUqus8baU+2/bGN4WKtCNVxBH2jQLetfILOdtSOD31P9nCPrcxAKets6CztrUwuHv\n3kivMsvYdAvfrcmnydhZgU5mId7aUXYSoIUQQpxwrAr05HyemXS+zVdTm1RGW3UCB1S2D7SxAp03\nAnTI11gFejgeMDbJtUEmX2yoBWUgFmC0jQcgM1qxoR50S7jP2AQ4P3mo4eeqmZYhrfsbfgHQF/Hj\ndSvmJA4J0EIIIURDkpmF0Lx3ojOq0MkaA3RvxI+itLf/1mrhCDcYoIcSQeayBeZbeYDN1GgAbfcy\nFdWmCrSvaz0A+ekWHrjVVNK6r+EKtMulMBgPGAdRW7zOWwK0EEKIE45VgQbYM9YhAbrGFg6v29hG\n2M4WDtWsQIcbbOFo5yQONd/YGLj+WPvWeZdKOrlCiYANAdoaAVdKtS586vk06ZLPlhcAw9ZK+OgQ\nZFMLM6abTAK0EEKIE86MqtET9hH2uTviIGGxpJPK5FfdQmjpjwba2n9rVYwbmQMNlT2srQ/Q2Xyx\noQA6EAswPpel1IZxgtmC8Q5Aw3OgobyExJtu3TIVPZ9GtaEHGoxRdkeTGYiYy3Dmxxt+zlpIgBZC\nCHHCSWXyJEJeTumPdMRBwl3HZtGKOmcMRWu6/0DM3972AauFw4YpHNCedd4Nt3BE/WhFnRm19T32\nmbwZoO2oQPsjZFwRQpnRxp+rRnpeJWNDDzQY67xHZ7MUw+Y4QgnQQgghxNokVY1EyMcp/dGOaOF4\n9MAUABdv6anp/v3R9q7zLh8ibDAADcQCKErrWzjyhRKFkt5QgGvnMhU1b2MFGkgHBkgUJsgXSrY8\n36o01ahA29HCkQhSLOlMKwnjhrQEaCGEEGJNkqpGV8jL1oEIo7NZZrPa6g9qo9/vn2ZTT4hBsyK7\nmoGYn8n5HIViiwLPEulcgZDPjctV3wa/pbxuF/1Rf8uXqWTMTYqNtHCU53G34Z2ArGZjBRrIhwcZ\nVKZb1levWHOgbXgBYLUBHSvEjBvmW7OWXAK0EEKIE05SNfqJt/ZHAGfPgy6VdP5wcJqLt9S+0KM/\nFkDXjTF97ZDOFxseYWcZigdbvkylHEAbmsJhjBMcb8M0lIzNAZrYemMbYSteyJSKuIo5Mro9hwjX\nmQH6+VwIFJe0cAghhBBrZY2E29pv9BTvdXAbx7Ojc6QyWs3tG9D+ZSrpXKHhJSqW4USg5ctUrBaI\nRnqg+6Ltm8edsbmFw9u1nj4lxejMrC3PtyJNBbDtEOFCH30eQr1SgRZCCNE+Wa3Ix3+6i5Tq7NaH\nanKFImq+SFfIy7quIAGvy9GTOMr9z3WslO5vY3gDYw60nRXoY6kMut66aRZ2HMLze9x0h31tmcdt\nRwtKpXCvuUxl4rAtz7eivBGg7dhECBANeIkFPMYylciAVKCFEEK0z5OHk3zhoQPc+0xrqjl2SmWM\n0B8P+XC7FE7ui7DHwS0cj+6fZl0iyPquUM2PWTjA1r4KdKMzoC3DiSBZrbRodnez2RVA+6P+tlag\n7dhECBDs3QBAdqoFAdqqQNs0hQOMn6GjySxE+qUCLYQQon2sELp7zLmV2+VYQSxhLiXZ2h9x7CQO\nXdd57OB0XdVngN6Ir63bCNV8oeERdpZh8y34Vq70Xgigjf0ZrFnQrWZ3D7QSN7YRtmSZSrmFI2Br\ngDYq0P1SgRZCCNE+VoB+brSDA7S5FnvrQJSjyQzpNqyLXs3e8Xmm03kuqaP/GcDjdjEQDRgb2Npg\nPldoeI23Zcg8BNbKPmi7AuhAzN/WFg67eqCtZSqe+RYsUzFbOLL4bKugDycCxgswqwLdgnYgCdBC\nCCGOYwXoPR1ZgTYmU3SFjK1+p5iTOPZNOK8K/fsD00B9/c+WDd1Bjsyodl9STdR80b4WjvIhsBZW\noMsBtLEYNBgLMDGXo9jibYRWBd2uHmj8UTKuMMFWLFPRjFXbqu4nYFuADpJUNfLBPijmIZu05XlX\nIgFaCCHEcawAfSzl/BnKS1kV6HhFCwfgyDaOR/dPMRgLsLG79v5ny/quEEdmWr8CG4wKtF2HCHsj\nfrxupaWzoLPlKRaN/Rn6YwFKOkzNt7YP2u450ADz/n7i2njzD3PmK6Zw2HT91ii7aaXLuKEFbRwS\noIUQQhzHCtDgzOC5kmTGqEBbLRwbu0P43C7HHSTUdZ1HDxj9z4pS/0KS9V3G/GStxctUdF1HzReJ\n2NQD7XIpDMQCLd1GqJqbFBtv4WjPNkI1X8TjUvB57Itx2eAg/UyRNl9cNI3ZA51XAnjd9lz/UNwI\n0GOl1i1TkQAthBDiOKmMht/8x7nTDhImVQ2PSykHPI/bxZbeMHsdNsruwGSaiblcXfOfK23oClHS\nW9s7DJArlCiWdEI2tXAADMeDLe3nzmjGiw47eqCh9Yc5M1rR1uozQCE8xJAy3fxquhmgS77633VZ\nznDCeCFzVLMCtFSghRBCtEEqo7F1IELI5+64g4TWEpXKqu4pA84bZfdoA/3PYFSggZb3QVuHMe2q\nQAMMWYfAWmRhjF1jMWigTeu8s1rRtv5hixIboIdZJmeb/H0wWzgUj30BeiAWwKXAgWzYuEEq0EII\nIdohldFIBH1sHYg6eglJNcYab++i27b2Rzg0rZZ7R53g0f1T9Eb8nNQbXtPjrbnRre6DTufsGQFX\naSgeZGw2S6lFh/Ey+QJBr3tNrTOVesI+XErrWzgyefsr0N7YIB6lxNx0k8OneYgQGyvQXreLgViA\n/XNecPskQAshhGiPVEYjHvRyan+E50adVbldTVLVSJgTOCxb+6PourMmcTTS/wxG1dalwOFWV6DN\n/uGwjRXQ4UQAragz2aLDeBmtaMsIOI/bRW/Ez1gLD0CCcf12jYCzBLrXGc89c8zW5z1OXqWEC7c3\nYOvTDieCxkHUFm0jlAAthBDiOClVIx7yctpglMn5HNPpfLsvqWZJVaMrtKQCPeCsSRxascRIKstp\nA9E1P4fX7WIoHmx5Bdo6gGfXIhVYOATWqkkcmXzJtgruQCzQ8hYONV+0b4SdKdJjzILWUk0eZadl\nyCkBgjb+/IAVoDMt20YoAVoIIZpg/8Q8/9dnf1eeSdxJdF0vV6C3mgGvkw4SGi0ciyvQ1pi4ds1N\nXkq1aRXz+q7Wz4KeN1s47JoDDTBkzYJu0SSOjFawbQmJsUyl9WPs7G7h8CeGACjONb+FI6vYN8LO\nMhwPMJLMoodbs41QArQQQjTBE4eSPP78DE8dSbX7Uuqm5osUSjrxoLdcIe2oAG0eIqwU8LrpDvta\nOmt4JXatkl7fFeLwdIsr0Dn7K9DWHN/WVaDtC6D9sQDj7ZjCYXMLB+F+AFzNDp95lSx+21tQhuIB\n8sUS2UCvVKCFEKJTWZXn56fSbb6S+lkzoONBLwMxP9GAp2MCdK5QRM0Xj2vhAOMf2FGHBGirDcKO\nCvTYXJZcoXWHI+etAG3jIcJEyEvA62phBdq+AD0QDTCVzpMvtG4edzMOEeKPkFGC+LJNDtCaiorf\n9haUQbMNaM7TDeoUlJr734QEaCGEaAJrG97zU85oGahHZYBWFIXTBqLs7pCDhOVrX3KIEIwAPeKY\nAG3PKuYN3SF0nZbOULau3c4KtKIoDMeDLfv+ZPL2VXCtWdATLdxGaOf1V5p1dxPMTdn+vIvk02R0\n+1s4Bs02oCm6QC9BetLW519KArQQQjSBtQ3vYIcHaIBTB6M8NzbX/BW/NrBeuCSCx1egB+MBRlo4\na3gl1hxiOyrQ0NrebqsCbfdb8H1RP+MtOoxnawW6vI2wlYtgmlCBBlRfD5FCkwO0lmFe99v+AsDq\nox/T48YNTW7jkAAthBBNMGMGuUPTndfCYYXQcoDuj5DKaEzMtfag1FqUA3TVFo4gSVUr9x+3k52H\nCKG1s6DVfAGPSylvqrRLfyzQsp8xO3uI+80KdCv7oJvSAw3kA70kSjP2zOPOqzBbZSSeliZd8tl+\n/b0RP26XwlHNnGzT5F5uCdBCCNEEqXKAVlu2HMIus1Uq0ADPdUAftNV73rVMCwfAaIsPfFWTMXug\nGw0Rg7EAHpfC4enWVaDTOWMGcaNLSJbqi/gZb1WAzpdsbOGwKtCtufZSSSerlWzvIQYohvrpI1l+\nF6ohD34S7njJcTfreZW07rO9gu52KfRH/RzMGiMrpQIthBAdyGrhyGqlloUCuyz0EZsBujyJw/l9\n0Eur55UGWzwqbSULLRyN9RF73C6GEoGWVqDTuYKta7wt/TE/ar5YbhFpJmsToR26Qz48LqVlLRw5\n87BiM1o4lGg/cUVlOmXD9KCjjxshNrf4hbeeT6M2oQcajP/G96nGuzISoIUQogMlVY3eiPHWbqdN\n4khlNFwKRMxw1xvx0xP2sXu0AyrQ5guXai0cw+YpfSccJLSrhQNgQ1eopT3Q6XyBUDMCdNQ8jNfk\nF5y6rtvaQ+wyK5+tqkDbNcGlGk/MmAWdmhxp7Il0HcaeNj5eOldaU8k0YYwdGO8yPT8H+KLSwiGE\nEJ0oqWqct8E4zNJpkzhSGY1Y0IvLtfAW/akD0Q5p4dDwuJSqFdJBR7VwGAHajjaC9V1BDre0Al20\ndY23pS/aml7ifLFESbfn797SHwu09AAkNKcCHegyAnTD67znxyAzbX68eLOhomWaMsYOjHaakVQW\nvQXbCCVACyGEzbRiiflcgTOHYnhcCs932EHCVEY7borFqQMR9nTAJA5riUq1/tyA101XyMsxB7Rw\nlCvQNoSI9V0hJuZyZLXWHI5M5wq2jrCz9EeNFzjNHgdXfvFiY4AzthG2JkBb3+dAE17EhHuNdd75\nZIMVaKv6DDBXEaCLGkpJQ9UDTTkEORQPoOaLFEN9UoEWQohOY/UQ90T8rOsKdlwFOmmu8a506mCU\ndL7IUQeEz5UYa7yPb9+wDMWDjlimouaL+NwuPO7G/xne0G20prTqe5POFxvu3a6mv1yBbnKA1uyr\n/lsGY4GWtXBk8s3rgY71rAOgONtg9XZ818LHlQE6bxQTsvia0sJhLVPJ+Ju/jVACtBBC2KxylNqm\nnnDHBWirhaOSdZBwz7izDxImVY1ElQkcFqcsU8nkC7YFuPVdIYCWTeIwDhHaH34SIS9et9L0Q7cZ\nG/vPLf2xAKmM1pJ3AZrZwuGJDVBCQUk3GD7HnobIIHgCMFdRzdaMn9FmtXAMmhNRZt3dUoEWQohO\nY41SS4R8bOoOcXAq7fjWh0qzVSrQwwmjsuOE6u1KkqpWdY23xSnLVFQbVzG3eha02qRDhIqi0Bfx\nN/0QoV1bICtZo+yaXT2HhUOEzWiBwO0lpcTwqhONPc/Y0zBwJkQHF1eC82aAbtIUDmtU5bSSgFwK\ntNr/mzgwWV+rnQRoIYSwWeU2vE09IeayhfJtnSBVJUD3RVrz9nqjjBaO5SvQw4kgM2prKoUrUbWi\nbRXQgWgAr1vhcIsmcaRzxaaMsQPoa8FhvGwTKrjWOu+xFhwkbMb1V5p1dxFoZJ13sQATz0H/mUYV\nurKFw6xAG1M4mjMKEWCsZG0jrL0K/fy9n6vra0mAFkIImyXNHuiukI9NPWEAnm/hootG6LpeNUD7\nPC56wr6WBIRGWIcIl2O9xdvuSnomb98mOZdLYV0i2JIKdLFkjIBrRv8q0JIKdDN6oFu5zrsZ119J\n9fUQ0RoI0NP7oZiDgbOMCnSVAK0SaMoLAL/HTU/YxxEtZtxQR4D2pA7W9bUkQAshhM2sFo54yKhA\nQ+fMgk7nixRLetUQ2h8LtHRdcb1yhSJqvrhiC4f1Fu+xNrdxqPmCrSF0Q3eoJQHaah9oVgW6P9a6\nFg5bK9DR1r0wa+YhQoCcv49EaXrtTzBuTuDoP/P4AG0eIszoPgK+5kTQwXiAg1mjcFHPQUJfur7J\nIxKghRDCZknVWEQS9XvY2G0F6M6oQJfDf5VJFq1cFrEWCxsUVzhE6JBe7oxWImjjW9jru4IcacG7\nHOmcPRsUl9MX8TOVzqMVS015fqhogbDxBUws6MHvcbVk62gzDxECFEJ99OhJtMIa25zGdoHigr7T\njACdn4Ocefi4ooWjWdc/FA+wJ1N/gA7n6js4KQFaCCFslswYo9RcLoWA181gLNAxAbocQqsE6FbO\nul2Lyt7z5VgtHO2exJHJF2yZAW1Z3xViKp0vV4ibJW0+f7gJUzhgoYd1aj7flOeH5syBVhSFgVig\nNS0czTxECBAZwK9oJKcn1/b48V3QfTJ4g0YPNCwE2fzCFI5mBeiBWIDdsz5AWdzCMX0A/vj1ZR8X\n1+o7OCkBWgjhSH84OM1bvvQYubVWQdrImASxUAXd2BPqmBYOK0AvHWMHxj9Mk/M5iiVnThSpHB+4\nnKDPTSLkbfskDjVvbx+xNYnjaJPbONI5M0A3qQJtLVNp5kFCq4Jrdx93q15gZrQibpeC1338siA7\neGIDAMxOHl3bE1gTOMCoQMPCKDuzAl1wBW2ZgV7NUDzAREZHD/UsBHd1Gr72Grj73cbHS+k6vaX6\nXjBIgBZCONJv907ym90T7Dw62+5LqVtS1YhXhLjNPaGOOUQ4u0IFuj8WoKTDVJM3xa2V1X7StUIL\nBzhjmYqdhwihYhZ0kydxlFs4mlSB7mvBMpVmjLED6I34mWxi5dySyZcIet1Vt23awZ8w1nmr02tY\n552bh5mDMHC28ftygDb7oM0AXfKGGrzK5VkHOrVgH6QnjKkg370JZg4Yd0geOu4xamqcgFLfpCQJ\n0EIIR5pOG/8Q/fHQTJuvpH7JTH5RG8GmnjATc7ly9c7JVmrhsDbFObUPOrnCtVdywjIVuyvQG1o0\nC9r6GW7aIULzZ6yZ67yzWhFFAb/H3gjUE/GV/3+rmTJasSlLSCwhcxthbi3rvCeeBXToP5NCsUTa\n12fcbgVos4VDaWKAHjK3Eao+swL9yw/CgQfh4r817lAlQCdHD9b9dSRACyEcaaocoJNtvpL6LW3h\nsCZxHOqAKrQVoKtt82vlqK61WFhgs3KAHmxzgC6Zo+DsPETYF/Xj87iaH6DN/ttmHSLsbcG88Uy+\nSKgJFdzusJ8ZNd/0FqeMzRNclkr0GQG6MDu6yj2rGDMncAycyafu28u1n38S3H6YtyrQaQp48Pn9\nNl3t8QbNSTtz7i449kd49HNwybvhJe837lAlQM9PPF/315EALYRwJKtN4IkOrECnlrRwbOo2Z0F3\nQB90UtVwuxTCVf6BtpZFtGLSwFokVQ2PS1m1OjocDzCdzrdtmUq2YH8PrqIoDLbgEJvVwtGsCrTP\n46Ir5G1qD7Sq2ds+Y+kJ+9B1mFGbW4XOaPZtsawmmugjr7vXtgp7fBd4w5DYzG/3TnJ4JoteOcou\nr5JzBZpaQbcC9JSSgFIBTr4aXnYbBLvAH68aoPNTR+r+OhKghRCOZL0VOpLKtv3AVz20Yom5XIFE\ncPEhQuiMUXbWEpVq1bneiB9FcXAF2lyislplcdB8i7ddf45mzCGG1hxis6Z8NKsHGoyDhM2cBZ3N\nN6cFoidi/Dff7DaOjFYi0MQKtMvtYlrpwquuIUCPPQ39p6PpsPNYCgAtNLCoBzqnBJpaQY/4PUT9\nHp7yXwinvAxe9yVwmy/4EhurBuhi6ggFvb5ILAFaCOFIU/N5zho2tkl1UhvHQgvEQgU6HvTSFfJ2\nxEHCalsILV63sY2w2auW18pY471y+wZULFNJtufPUR6jZnOI6I8Gmr5qfb7JUzjAaEdp5rsczdqk\n2B02AvRkkw/ZZvNFgt7mxreUuwt/veu8dd2oQPefye6xObKaMcs74+9dFKCbOQPaMhgP8Fv9bHjT\n94zKsyWxEZLHt2u450YYo7uuryEBWgjhOKWSzoya58Vbe/F5XDzxfOe0cSw3Sm1jT7gjWjhSGa3q\nCCTpIPoAACAASURBVDtLfzTg3EOEqla1d3spK0CPzrbnnY1mjVHrb0kFukjA68Ltas4ECDAOEjaz\nAq3mm9MC0RM2WpyaX4FubgsHwLy3l3C967znx0GdgoGzePJwqnzznLdv0RzoLP6mtnCAEaBHq/3/\nlFWB1hf3qQcyI0y5eur6GhKghRCOk8xolHQYigU4Z12cPx7unAr0wkG2xUFuU3eoI1o4ZjPaiotI\nBmJ+B1egtRXXeFusHsl2HSS0Wjjsn0McIJ0vlqvEzZDOFZpafQboM9d563pzDuM1a4qF3S0cP985\nwlcfOXjc7cYa+OZ+D7KBXmKFOtd5V6zwfvJwEus1VtLdBblZY423lkbV/c1bAmMajAUYrdb6l9gI\n+XnILC7KRHLjpLz9dX0NCdBCCMexDhB2R/ycvyHBn46myBeat9rXTsttw9vcE+JYMuP4P8dKLRyA\nuW3NmRVo49pXr0CHfB7iQS8jbWrhsPqIg157Q1D5kGcTq9DpXIFwkw4QWvoifvLFUrkdym7ZJrVw\ndIV8KAq2zYL+n4cO8PkH9x93e1YrNb2CWwj2kdBTUKrjoO3YLuPXgbN48kiS8zcarROTVmvE3Cjk\nVdK639YtnNUMxY0++kLFSvjf7p3k80+ZLy4r2zh0nURhEjUwWNfXkAAthHAca4RdT9jHBZu6yBdK\nPH0stcqjnMGaRbx0mcfGnjAlHY40edFFo5KrBOh+cxth5T9MTjGj5lcdYWdp5yzoTJMq0NYWP7te\n4Lz3rj9y12OLD1ylbZ5fXU2/OS6xWW0cqs1LbCxul0JXyMd0uvHr1nWd58bmmJw/vhJvjEBsbnzT\nI/24FZ1saqz2B03tgWA3aU+C3WNzXHZKLz63ixE9bnx+bhS0DGnd1/QK9EDcWPpkzRPXdZ3/955n\nuPug+XUrDxJmZgiQQwtLgBZCdLgps4LTE/FxgVnF6JSDhFYLR3xJkFuXMCY/tHuBx0pKJZ3Z1QJ0\n1I+u21dls0uuUETNF2tq4QAjQLerB7p5LRzWmMHGf8Yy+SI/fuoY9+xcPAs4nSs0bYSdxVqm0qyD\nhJkmTeEA4yDhlA3/bYzN5pjLFsgVSse15GSa1MNdyW1uEJydqGO8W+ooxNez82iKkg7nb0jQE/Fx\nREsYn58fBS3NfMnX9Ar60JI2rccOTLPz6CxHdHOxS0WALswcBkCPDtf1NSRACyEcx6rgdId9DMYD\nDMUDHTMPOqlquBSILgkZVrhx6gg4gPl8gZK+8iY/a5mK0/qgrUBfyyFCgKFEsG0tHE2bwmF9b2yo\nQO8dn0fXYe/Y3KLb0/kioWa3cFjbCJsUoLNNPITXHfaV30FrxHMVf++VgVzX9ZYcIrTWeaenjtb+\noNljEF/Pk0eMYse29XF6Ij4O5aPG5+dG0fMq6ZKv6e9iDMaMgsWoGaC/+PABQj43s4TJeaKLAvTc\nhPGxp3tDXV9DArQQwnGsf4C6zTB0wcauzqlAZ4xRaq4lUwoWtvg5s38YjAUwsFqAduY67+0HjQNP\n565P1HT/oViAqTYtU1GbtM0v6vcQ9LpteZG22wxwx1JZ5rILvchGBbrJLRxR+yrp1TRrjB1Ar03r\nvPdUBOjKsXjWaDg7t1hWE+oxqrHZmYp13slDcPC3yz9o9ijEhnnycIoN3UF6In56wn4OqT5jG+Gc\nUYFWWzTGDowA/fxUmnufGeNtl20m7HMz7R2EmYUeaNXcQhjs3VjX15AALYRwnKl5o5fV4zb+L+r8\njQmOJjNNPRxll6VrvC1hc7i/kyvQ1qGtpe0nlZy6zvu3eyeJBTycac4OX431D2yz5yZXozZpjJ2i\nKMYyFRsqt7srAty+iYXxi2qu+RMgIuYLgUa/N3vH5zm0ZPJNsyu4RgtH43//z41WBuiFQG6NQGz2\nHOi4GaDL67znJ+DL18G3bjxuBBxgTNjIJiG2jh2Hk+UXsj1hH5NpDaIDMDcCeRUVf1MXwQB0hbz4\nPC5GZ7N8+bcH8bgU3vKizWzuDXOM/kUVaG3GWKIS611X19eQAC2EcJzpdL68lADggk1GH3QntHGk\nMtqyAbQVc3obMZtZvQLdEzYmDTjpxYyu6/x27xQvOrmn5vnEw2ZP+rE2bLnM5IsoCvg99v8TbMzp\nbvx789zYHNGAEZQrq6HzLeiBVhSFvqi/fABsrf7mq9v51x/tXHRbrlBC12lagOsO+0lmtIYP2e4e\nm+OU/giwuAJdDtBNDqDdXQlm9aAx27mQg2+/CVKHIZsygvJSs8eMX3z9HE1mOG+DGaAjPqbSOfTo\nEMw8j4JORg80fQqHoigMxQPsHpvjO9sP87+2DTMQC7ClN8w+rXvRLGh99ijjJOiPh+r6GhKghRCO\nMzmfo9dcSgBw1nAMn9vVEW0cM2p+2TnKxgg45wTPpZI1BGiP20VvxO+oFo7D0xmOJjNcdkpvzY+p\nfIu31axFHqutHF+L/pg9S0j2jM1z5al9+Dwu9k7MA8YLFbUFUzjAaONopAJ9aEpl/2T6uO9veQJK\nkwJcb8SHrsOMuvYRfKWSzp7xeS45yRj/tihAm9ff7EN4IZ+bKRJ41HH48T/C4d/D2a8zPlllFTYp\n47DhnqzxDtC55QDtJ6uVKIb6YdoYyafS/DnQYPz/7QPPTaDmi9z84i0AnNQb5tlsArQ0qEbbl2du\nhBG9p9x7XysJ0EIIx1lagfZ73Jy1LtYRFejlWjjAGO7vpOC5VKqGAA3OW6by232TAFx6cu0B2jql\nfzTZhgp0E3twrRdpjSwhmctqHE1mOGMoxkm9YfaOGQE6VyhRKOlNnwMN1jrvtf+MPbhnAjj+IKLa\n5Aqu9f9bjfRBH01mUPNFzhqOkwh5Fx0izJZbOJpfwU26ujhl5iF48ptw5fvh0vcYn6wWoM0K9I5U\nGLdL4SyzlarH/PvIBPpBNf47zeBr+vXDwn/jl5zUzdnrjFF6W/rCHC5ZkzjM3ufsKJOuXvye+q5J\nArQQwnGm0/nyVi/LBRu7eOpICs2B84crpdSVWjgCjM9lKZWas2GtUTUHaIet8/7t3kn6o35O7gvX\n/JiQz0N32NeeAN2kOcRgvLhRG9xGuGfcCMynDkTZOhAt/94avxduUQW6kUr6b3YbAXpazS9qp2h2\nBdda5z3VwCxoq//81IEovRH/ogr0wgjE5r+Imff24NXzcOZfwpX/YmzxgxUD9O8m/Jw6EC1fX2/E\n+PuY83SX75ppwSZCWHiX6e0vPql82+aeMId1c+Og2cYRzU8w56tvCyFIgBZCOEyxpDOt5suVC8vW\n/gi5QsnRLRBascRcrkBimW14AzE/WtH48zlRKqPhcSmrVkf7HVSB1nWdR/ZNcdkpvXW3RKzvCnJk\npvUBWs0XCNm8hdBixzKV3eYBttMGomztj3B4RiWTL5I2Q3mzx9iB8WJzNltY05QUrVjikX1TBL1u\ndH1xNTirNTeAWi/8G5kFbY2w2zoQMQ7hVe2Bbn58ey56MY95Xwh/+VlwuSDYBb7oMgH6CHqoh+1H\nVM7bEC/fbFXkZ9w95dtaMYUD4JXnDHHTpZt56ekL4XhLb5ijuvlOVfIQZJP49SyZYH1LVEACtBDC\nYZJqHl1nUQsHLFQynLbAo5JVwV1uG96gQydYWFIZjUTIu2oQ7Y8GmJzPO+LdgOfG5phK57n05J7V\n77zEukSQo23YDNmsTXhgvLiBxg55Pjc2R9DrZn1XkK39EXQd9k3MkzbH7zX7ECEY67xhbbOg/3go\nyXyuwLVnG6GociGLVcFt5hQOaKyFY8/YPMPxALGAl96of1EYb1UPNMBzg9dzc/4WHh8x//4UxahC\nL1OBzoeHSGW0RaMkrRcUE3SVb1MJtKQCvW19gluvP2vRSNFEyIc3nEB1R40WjpQx57oQHqr7+SVA\nCyEcpbzGO7L4QEevecDDjhFRzZJUVw7Qdi66aIZURiO2SvsGLIyym3TA9+K3e6cAuLSOA4SW9V1B\njiYzDfULr0WmiQfxFhbdrP17s2dsnq3/P3tvHuRIfl93vl/iSNxXAYW6+p7uHs7N4ZDLeyyLCl2k\npNVaJmXLoh22Dlsbsh0bq5VW4XV4tbIlx66lCHm5MmOtFS1ZUkiyLMpcHZa4Cg45Q1Kcg3PPdPf0\nVV33gTsBJDLzt39k/hIJFG7kherfJ4LBHjSqOlFAAS+/+b7vFRMQBILLRT0J4sZ+vTuBdkH8FFKz\ntxE+c+0AAYHge57Qo9jcnOBmY3pKzTzvU2/v1nBlRS8fKSR600jc8kADwN/90HmkoyH8wK8+h1/4\nk7fQVtSRAvo4oHuLH7MKaMPSsqN1b2tSdybQw7iQj2NP0KPsaFUX0EJ6ugg7gAtoDofjM8wa774J\nNPtvP4i2YVSao9vwzOQHv06gpdE13gw/lal89Z1DnF+KmVXp07CeiaLV0WxpjpsGJ5Ms7Mjpfnuv\nhitFXcCdW4ojKBBc36+h0dbFmxsT6GWzjXD6x/HM9QO8+0wGl/IJ43ucTLGIOmShCQgE2djsbYSq\nRnHjoG7+/JfiYdQsVpamwxYUKw+vpfGn/+Qj+IH3nMGvfukdfM+vPIujULEnAs6kcg9bahZiUMAV\n46QL0Jc14+EA7nW6to4mwq5MoIdxfimO20oeKN9F80iv8Q5N2UIIcAHN4ZxaKlKnJ791UWCXPnN9\nS4QsYsjPFo5Sw5hADxGh7LK0ny0ckwjors/W28ehqBq+fvN4pukzAGxk9dxXt33QzY7qWJNcQgwi\nHg7MfHJTasg4qLVNERQKCLiQj+P6Xt2xBsVBzFrnfdyQ8epWBR+9UkA+adgHeibQ+mNwUsAtxWdv\nI7xz1ICsaKaAZlfe2Pdz2oLSTzISwi/+jcfwa3/3KRxLMv7j2wDa1d4saKNE5Z6aw0Y2ahZgMZYS\nIrZaIhDQnw+3PNDDuFjQs6Bp+S5ah3ehUoKEURwzDVxAczinlM986Qa+598+21PDuwiw7fWleK+F\nIxIKICEGfT2BZjnKw2LswkEBS/GwLya3g5hUQBdt8NnawStbFdTaCj40RXydlfWsPrXecllA60uE\nzgmI5VQEezMueVoTIBiXiwnc2K+j7uIEeikuQiC6hYNSis1jCX/08jZuGpnUw/jy9QNQCnz0SgGx\nsH4ycVizeoiNKmwHf/56G+FsArr789dPYLq7H/p7BptER1xYIrTy1x8s4tMfOIfXJcOKYbVxVPW6\n79udtFlQZCUXD+NI6gAJ3ZPepBFXPNzDuJCP4x4tgHQkYPcV7COLfHryBB8GF9Aczillt9JCs6Pi\nL97c8/pQpoJ98GQH+IiXEmFfT6DLRrrGuCpsrye3w6g0O0On51aWEl1x4yVffUf3P7PCiWlhAvqe\ny4uETi4RAkYE3IwnaUzAXV3pCugHlpO4fdQwX98x0XnxExAI8gkRv/f8PbzvX34RH/nXf4mf/O2X\n8C//+M2RX/fMtUNkYiE8auT+9jcaNl3wELP2vVm4tlcHITBbCNkSHhPQTVmFQIBwwH35tpqO4h5l\nGcpWAa2XqFxrps1FaSt59r6d1AW0GoxO3BjqBBfycWwajyOx/wJ2aM68qjYNXEBzOKcUdsnvCy/v\neHwk03HUaCMbC524DAjo05hDj0XbKCrNDgQCJEdM6Io+rfPWNIpqa7IJdEDQq5a9fhzP3jjEu1ZT\nJxZOJyUVCSEVCbqeBe1kDjRgnKTNPIGuIykGe4TQ5eUENAq8ulUB4M4EGgA+/EAe4aCADz+Qx899\n3yN48mwG2+Xhj4tSii9fP8CHHsibAq3/PaPlQhX2Ulyc2QP99l4NZ3Mx0yZT6Esfanaca7Ecx2om\nMkRA6xnQbzYSZnmJlaW4qC9VJov6DaHp9xXs5PxS3Hwc4U4VOzQ3dQshALjzW8DhcFynZEyLnrl+\nMLLcw2/0txBaySfCuHXYcPmIJqckyUhHQz2xSf0UUxG8ulV18agmo9ZWQCkmSuEAdB+0l1aUVkfF\n83dK+OH3n5vr+2xkY656oDuq3ubnpIWDnaRRSqcWWm/v6QkQ1q9jSRwvb5YhEEAMujN7+zeffKLn\nv9/YruDP3xh+Re2t3Rr2a208fblg3lZIimYRDKDbZwICQSjgnADNxcMoSx0oqjZwEDCKa7s1XF7u\nTv/7J9D61QtvpNt6JooK4ugE4wj1CGg9yWKb5rA6wMKxlNA94TS1jrYQQyTk7WdRNByAktwAjHOc\nA7KEVGT6nymfQHM4p5RSo4PLywl0VIo/e2PX68OZmKO6fML/zNBbufxs4Rhe480opiI4arR9kaFs\npSJN1kLI8HqSvl9tQ1Y0PLiamuv7rGejrnqgzSUwhyfQrY6Gamu6NkJKKa5bEjgYF/JxCAS4fSQh\nHg56Mv0ExuePs/bBj1zpeuILfY2GTVlzfILLRG9Jmm7/RFY03Dps4OpKN8UiFg4iZvFxtzqqKyUq\ng9BThAgq4ZXeCXRlCx0xhzbCZtKQlaWECEWjqD35E/js2s95msDBKBYKqBH9dV4XizO9HriA5nBO\nKUeNNp6+UsDZXAz/5eVtrw9nYo4G1HgzlhIiSn3VvH6i0hw/6S+mIqB0toIIJykbEXyTCujlVMTT\nx8BKPeatldbbCCXXsqCbLlQxF2aMgDuot1GSOj0xZAAgBgM4v6QvWcVdsm8MgpXEDFsk/sqNQ1xe\nTmA13Z2C5hMiKs2OnmEMloDirICbtc771mEDikZPnMDkE6L5vZqy6lmChRgMIJ8I4yBQPGHhkCK6\nPWOwhcNIQxFyeCX0uKcJHAzdB62faLVmaCEEuIDmcE4lTVlFq6Mhlwjj44+t4rl3jnxdQGJllIWj\nkAjr1bw+rcIuSfLYJbyVtD+j7N7a0ZfHLhYSY+6pU0xGcNSQISvenMywSe68tdLrmSgasmq2SNqF\nqlF8/Fe+jD9+tXcHoRsF5+wEGpg+p/varm51uNon4IDuUpsbC4TDKI6pKb950MAj6+me2wpmAZPh\nIZYVxwWc2UY45dWyQQkoAFvCMwR0xzsBDVgWCa1Z0NVtlEMF8+/7sdabe338jAv5OO6ouoDWktNH\n2AFzCmhCyD8lhLxOCHmNEPLbhJAIISRHCPlzQsh14/+zlvv/DCHkBiHkbULIt8/zb3M4nOEwgZmL\nhfHxx9agahR/+rr/bRyqRlGS5KFLYWakU82fAnoSC4dfMpT7efFuCeloCBfzk8U5sSi7A49OzLqT\n3Hkn0M5kQZclGa9tVfHCnVLP7W5ZOIDpX2NMwF0eIKCZD9qtBcJBjHpcqkaxV22dmIDm+yrB3RBw\neSYYp1wkvLZXQ0AguFjo/R1cSojme16zo3oaAbeajuCmkuvNgq7ewwHJIxYODPQSmxP5etvxBJpJ\nYVF2ACBkNmb6HjMLaELIOoCfBPAUpfQRAAEAnwLw0wC+SCm9DOCLxn+DEPKQ8fcPA/gOAJ8hhHj/\nU+RwTiElVkYSD+Ndq0lcLMQXIo2jJMmg9GQLIWMpMfoSrtdMsqw563TQaV66W8YTZzIjFyCtLKe8\nnaQzC8e8YmjDjLKzV0CzFJx+m0u3Sc7ZGDtghgn0Xg25eNgUgFbYYpsbNd7DGJU/flBrQ9HoiSW2\nbgETE9Ca4wKOTaCnvep3Y7+Oc0sxiMHe4+u3cHj5HKxloniracxFy3cBWQKaJWxpWaykIwO9xOz1\ndNiQPbWgWLmQj+MvtSfwjPooIlkPJtDQUzyihJAggBiAbQDfC+Bzxt9/DsD3GX/+XgC/QyltU0pv\nAbgB4H1z/vscDmcARxYBTQjBxx9bw9duHXlefDGOY8txD6I72fGX+AT0dIVaW0EmOnoCvRQPIygQ\nX9V5V1sdXNuv4cmz2fF3NjAn6RVvHgebQM/ryd1wKAuaLbv2n+xJNk3ORxEXg0iIQez3eaBf26qM\nFHXX9mq4UkwMFEHMwuHlBHpU/vh2RT8BWuubQPc3Grph4cjEwiAEU7cRbldaAyvpC0aKhapRVzzc\no1hNR3BdNnLXy3fNCLtbcgZrA+wbAJC1WFpaHh8/40wuhq/jUfxw52dQmKFEBZhDQFNKtwD87wDu\nAtgBUKGU/lcARUopG3XtAjCC/7AOYNPyLe4Zt52AEPKjhJDnCSHPHxwczHqIHM59C5tAszeuTzy2\nCkpxwo/pN5jYGLZEyGpt/WjhYB7azJgJtCAQLPsgQ9nKy5tlUAo8eS4z8dewD3q3M5QZdgnRdDSE\neDhg++MYOoE2J+fOCtHllIh9ywT6oNbG9/9fz+FX/r8bQ7/mnYOGKZT7uVRIgBB3aryHwcpVBv3u\n7Bj50P0eXHY1q8dD7LCACwgEuVgYh1MK6L1Ka3ARSVKERvXXVFP22MKR6StTMSLsrjVTAxM4AL0O\nPh0N4ahhWDh8MIEOBQScMU6eZ8mABuazcGShT5UvAFgDECeE/JD1PlRfa556tZlS+llK6VOU0qcK\nhcL4L+BwOD2Yk1zDj3u5mMTVYhJfeMXfApod97AYu6QYRDgg+NLCUZYmE9CAnmCx7yMLx0t3yyAE\nePzM5AI6Ewsh5oDwnBS2jDevGCKEYD0btd3Cwa6SeDGBBvSFO6vQ/M2v3YGsaLh9NDhHvdbqoNLs\nmJ7wfqLhAD54aQkPr80XGzgvepPnyd+dHTaBzvSKuEhI9+V2J9DuTEBz8fBUS4SqRnFQbw+OgbOk\nerQ8XsJbS0dQRgJKMN4zgX6zkRyYwMFYSoS7S4Q+mEADuo0DwEwthMB8Fo6PAbhFKT2glHYA/AGA\nDwLYI4SsAoDx//vG/bcAnLF8/YZxG4fDsZmSJEMgvZFkT18t4JubZdfiumaBbcoPs3AQQrq1sD6j\nYsTAZcYsEQLASiriKwvHi3dLuLycQCoyecEBIQTrmSi2vZ5A2yAmNrIx27Og2Wu5JHV6kkqaLjTh\nAUZOt2HhaHVU/ObX7gDA0MfJGv4GWQgY//EfvB8/9vQlm490Ooblj2+XW4iGAgNjGK113m55cFl5\nyKQc1ttQNWruSFgxPcQ171MsdI85QT2yaghovcZ7m+YGJnAw8nERh3XvTwCsXMjrV1uW3Z5AQ7du\nvJ8QEiO6YepbAbwJ4I8AfNq4z6cBfN748x8B+BQhRCSEXABwGcBfzfHvczicIRw1ZGRj4Z6FsKV4\nGIpG0TCEhx85asggBMiOmOLmk6IvJ9ClhjGBniBH2esSEiuaRvHS3fJU/mfGWibqqYUjHBSmbnob\nxHomarsH2iqerJ79pgspHEB3Ukspxee/uYWjhoyHVlPYLjcHnkRvlfXHv571tmZ5HMPyx3cqTaxm\nhi2x9aZYuCKg4yIOp9jV2DV2CYZZOADgoN5Cs+PtEmExqfvQj0Ir5gRaEbNoIzx2Ar1XbaGjUt8I\n6O98dAXf/djq0NSncczjgf46gN8H8CKAV43v9VkAvwDg2wgh16FPqX/BuP/rAH4XwBsA/hTAT1BK\n/ftJzuEsMKWGbPqfGcxaUPZphjIAHDfayERDI0XRUjzsSwF981DP0N2YQIAspyKotRTThuAlt44a\nqDQ7Mwno9WzUnFy6jSQrtgmJjWwU1ZaCasu+LGiraLZ69u2cnI+ikBQhKxoqzQ7+/Vdu4cGVJL7/\nyfWhmddbE0yg/cByUhyYP75daQ1dYuuZQLskQHPx6SbQ7IrUIAtH3rBwbJdboBSIeCiggwEBy8kI\ndsiyLqArW2hE9CKSYR5oQBfQ7L3CLxaO957P4f/8W08iMGHyUD9znbpTSv85pfRBSukjlNK/YyRs\nHFFKv5VSeplS+jFK6bHl/j9PKb1EKb1KKf2Tef5tDocznOOGbPqfGWkjHaI8Zb2smxzVh2dAM/IJ\n0bw87ide3qzgTC460TRjxUdRdi8aOcXvPju5/5mxnoniuCF7ciIgySriNi20samrnTaOo7qMSEj/\niD2od08yJFlFOGDP5HwUzArw+y/cw7W9Ov7BRy6a4niQ33ur1EQ4IKAw4zTOLdjj6s8f3yk3T/if\nGfoEug1No2h1NFeW8JYSYZSlztDa8X7YFalBFo5UVN/92DzWrxJ4PcFdzURwR13Ss6D330DFKFEZ\ndgIDALm4CNn4WfhFQM8LbyLkcE4hJUlGNt5rJWATaLsb1+zkaEQLISOf1DNR/ebl/uZmGY9vTCZC\nZy26cIIX75aRigRxacIGQitMkHnhg7ZzGYwtztkqoBuy2ShntRw0ZcUVAcFeY//2L28gnxDxicdX\nzROFQc/XVlm3QEyaA+4VxQH547Ki4aDeHurBLSRF1NoKysZ7nxs/f5b+UZrwit9upYVQgAzMwCeE\nYCkRNk98vBbQa+korrWNKLvKJvbJEqKhAFLR4Se01mxxr4/fLriA5nBOIXoddu8kqWvh8LGArreH\nlqgwluJhdFTqqxOBg1obW+UmnpgwxcJPdd4v3S3hibPZmYSTObn1wMbRsNHC0Z3M2ueDPm7IZiW2\ndelVcqkIgwnNstTBpz9wDmIwMDJ6cLvcHDlB9AssMcGaYrNX1a0NwybQLKbsrosTXPb+a7Vx1Fod\nM2K0n91qC8vJ4ScwS4kwNo3Xp9cT3NV0BK81upXp21oOq0NKVBjWZCUvPdx2wgU0h3PK0DSKktRB\nrn8CzSwcTf/ZHxjHDXloBjSj2yzmn8fxyj290nbSGLhln0yg620F1/ZqePcU8XVW1jL2Wx8mxU4h\nmk+EIQYF2xYiWSX9ajqCpCVCDQAkl2K8mNAUgwL+9vvPAdB9uZGQMPD52io1fb9ACHQbMK0lMTuV\nwRnQDGZLMS0QbkygWemT8T7VUTV86rNfw4/8h+cH3n+v2jJPegaRT4jm8+b1BHc1E8U7nSXzv2/J\nGawOOXlhWN/XvcyxthMuoDmcU0atpUDVKLKxYUuE/pncWlFUDeVm58TkvJ+8D+u8X94sIyCQiTNy\nk2IQ0VDAcw/0y5tlaBR48tz0C4SAvpEfEIiZ4OAmeqWxPR5ou7OgzUr6hNizwAa4V8UcDesT50+9\n94xpiyKEYC0TNVv7GLKiYa82uAXPbyzF9dec9eRzWAY0w4sJNLuSxlphf+0rt/D6dhVv7dYGbqqf\n2gAAIABJREFU2s92K62RS3j5hAhF07/O6wk0y4JWQ3qO8rVWCiup0a8dbuHgcDi+51ganKUcCQUg\nBgVfWR+slKQOKO19ox0Em2T4SUB/814FV4rJiQUdIQQrae+zoF+6qy8QTmo96ScYELCSiniSxNGw\n2Uu8kY3ZNoG2VtIXEmLvBFpWEHO4hZDxx//4I/hnH3+o57b1TPTEBJpZIBZBQAcEgkJC7Dn53B7S\nQsjI90+gXVkiNMpP6m3cPZLwS39xDbFwAPW2MvDq2V61PXCBsPv9/CNAWRZ0M7oGAHhrTIkKgJ7B\niNcnAHbBBTSHc8qwfnj3k4mFfBtjN+q4reTNDyZ/PA5KKV7eLOOJM+nxd7awnBSx77GAfvFuGQ8s\nJwaWT0zKIEHmBk1ZRdzGD2I9C9qex8Fem0vxsJ5bXuudQLslINIDIiHXM9ETnnX2uBfBwgGczFHf\nqTSRigQRFwefmDDxySbQblwByERDEIj+vvazf/gqAoSYJzP9bZD1toJ6WxmYAc2wpqN4bYFgk/6y\nqMfXbWnZsRYO9vMAuAeaw+H4lJECOhr2rYWD5eaOE9DZWBgC8c8E+s6RhEqzM3ECB2NYJbFbUErx\n0t0Snpwhvs7KetabMpVGW7HNwgHoWdB2RfKx1/JSQtQn0FYLh8dNbOuZqNkIx2CpHGsLMIEGTpap\nbJdbI489FBCQi4dNAe1GjrIgEGRjYfz+C/fw5euH+KnveBAfuKj7hm8f9gpoVqIyagKdT/hnCS8f\nFxEKENwJPYBW8hxaEMdOoAWBmFNor08A7IILaA7nlMG2vPs90ACQjoXMKCe/waZ2+TE5tAHjjdgv\nAvrlKRcIGczC4VUc3+0jCSVptgIVK+uZKHarLSgT5t3aRdPmZbwNG7OgeywcSRG1lmIKVrdSOIax\nNiB6kJ0AjRNBfmE5eXICPe7Y84mw+ZjdOoFZSoSxU2nhiTMZ/ND7z2EjG0VQICcm0KMyoK3fi+G1\nBUIQdAvaf0r+LTzzLb8PAGM90EDXnue1BcUuuIDmcE4ZwzzQgH4ZreLXCXR9sgk0oL8R+yWF45ub\nZURDAVxeni5HednSFOcFbPHq3FJ8ru+zlolC1Sj2BtQrO4WsaOio1FYLBxPQ92yYph/Wu5X07NI7\nm5i6aeEYRDcLuitAt0pNFJLiwkwGi6kISlIHbUU/KdmptAxf7nAKSRHGDp5rJzBLcRFBgeBfff+j\nCAgEwYCAjWwUt496l27NGu8xS4QMPwjQ1XQU9yoq7jb0q0DDFjitsJMAO68ceQkX0BzOCPxW1jEJ\npYYMMSgM/JDIxEK+jbG7tl9HMhI80aA4iHzCRxPozTIeXU9P3SxX9LiNUGrr4iMxxDc6KaPKOZyi\nadRhR238IF7P6GUqdvigrZX03dhF/Xn2egLdzYLuirjtSnNh7BtAN+N6v9pGU1Zx3JCxNmYCXfBA\ngP6jb7mEX/rkE3jXajed53w+ftLCwWq8J7Rw+OFEZy0dwXalid1KC5GQMNEeBbNwiMHTIT1Px6Pg\ncBzg5//fN/DDv/ZXXh/G1LA2v0Gh9pmYfz3Qr21V8Oh6eqJCD30C7b2A7qgaXtuu4vEpFwiB7rTJ\nqySOhuH1jYnzfRive5AFLXWMY7dRiBaMSL69yvzPx7GlUTNvmUBrGjWsJ95N4FbSEQik9/naKjWx\nsUACmuWo79fa5pWUYQkcjB4B6tIJzEcuF/CJx9d6bju/FMedI6lnOLNXbSEVCY68MqG/pwOE+EOA\nrmai2Ku29AbLdHRkiQpjJSUiGQn6vu1yUrx/Fjgcn/LGThVfv3nsurdzXkoNeaD/GdC38tuK1rNA\n5Afaioo3d6p4dGMyIbqUEH2RwvH2bg2yok3tfwaAYtLbMhXJmOLG5xRz7NKtm4uE7NjtFNAsHs2O\nE5rDumzGmLEJ9EG9jZZi/3FPSyggoJiKmEkclFJslRejRIWxnGQT6Fa3RGWMhYA9D4C3FojzS7ET\nUXbjMqABY/cjFkYsFJhIrDrNWjqCjkrx6lZlYu/8j370En79773P4SNzDy6gOZwhlBodyKp2wq/m\nd44leaiP2K9lKtd26+ioFI+uTyag8wkRkqzakpgwD9/cNBYIp0zgACyNal5NoNv2TKBj4SBy8bC7\nArrNhKi9k9z+eLRZOW7IZpGGmVtekx0R/rOwlomaFo6jhoy2oo21QPiJoqXJ00wQmXACHQoQhKa0\nW9nJuby+c2BdJNRbCMf//PMJ0fMFQgab+N8rNceKf0YhKeI9M5Y2+REuoDmcIbDlrut7NY+PZDpK\njREC2qd13q9uVQAAj61PJkTzFlHiJS9vlrEUD5sLaNMQCQWQiYU8s3CYYs6GaZzbWdDsxMluIbqc\nimDfBk/6Ub1tCudQQEA2FsJBvdX1bnvsYdWzoPXna8vMgI55eUhTkYuFERQI9mptcwI9TsSxCbTX\n/uELxtKu1Qe9W22N9D8z8smw58fPsE78FyW9xW64gOZwhlAy0izeXjABfTRKQPt0Av3qVhnpaAhn\ncpMJUbPOu+FxFfa9Mh4/k5n5kmox6V0WdENWEA4KUy8/DmItE3F1iVDqODPJXUnN3w6pavREJX0h\nKfZNoL1NIVjPRrFbaUHVqPm8LUILIUMQiFFEpHug84nxwpIJaM9PXrJRBCxRdoqq4aDWnmiK+8SZ\nDB6yLCR6iXXiP85/flo5HVkiHI7NtBXV/LC7vlf3+Ggmp6NqqLWUkR5owI8CWl8gnFSImgLaxei0\nfuptBdf36/juR9fG33kIxXTEOw90274mv/VMDF++fghKqSv+TCctHJVmB62OOvOkryTJoBSmhQPQ\nX68H9bZjk/NpWctE0VEpDmptcxK9SAIaMK4W1FoQCJlIwLH3DK9/9qGAgDOWKLvDugyNjs6AZvyP\n3/6g04c3MZlYCJGQgFZH4xNoDofTxSowF2kCXTIzoAdHCrEJdMVHFo62ouLt3RoemdD/DOiXMgF4\nmgX96r0KKMVMCRyMYtIez+0sNGT7mvzWs1FIsuraiZlTQpSJmHlsHGaNt6X4opAUcVBro9lh8Xve\nirgNS5TdvVITCTGIVHSx5mmsTGWSEhVAT7EQiPcWDkDPXmcWjkki7PwIIcScQk/qgT5tcAHN4QyA\nCdGL+ThuHTbMwH6/U2roAsZ6+dhKxphM+2kC/fZuDR2V4rEJEziAbtnKkYdRdmxydyE/exFJ0agk\nVjX388altor4nAuEjHWXkziaDlk4mICex8YxqJKe5Zb7xgPNWhfL+hLeWibii2SHaSimdPvTzpga\nbwZrMPX65AXQ3zNuHzZAKZ2oRMWvMB/0uAXO0woX0BzOAJgQ/W8u5qBqFLf6gu/9Cvvwzg6ZQMfD\nAQQF4qs671fu6QuEkyZwAIAYDCAVCXqaBV1r6T/DZGR8gcAwiukINApPHoetE2ijhMQtAd1wzMIx\nf7Qgq/G25g4XknpqDHuevbYRrFmyu7fKzYWzbwBdu02trUxsIVhOinPHNtrBuaUYGrKKw7o8UY23\nX1lLRyEGBfPK5v0GF9AczgDKxgT6fRdyAPQp6SLQnUAP9kATQvQ2Qh9NoF/bqiATC02dZJFPip5a\nOOot3UYwT5Nf0Vhs8sLGIck2TqCz7papNGUFhACRkL0fYSs2CGhm4eifQAPA3WPd9+r1FDQhBpGO\nhrBdbi5cBjRj2SI4x9V4M372u9+Ff/yxy04d0sSct0TZ7VZbCAVIj2d+UfiRj17E//E3H1+4qxd2\n4f2pGOfUUmt1IBCC+JxVwV5QMgTme87mEBDIwiwSHjMP9Ig67HQ05CsP9Cv3plsgZOTj3tZ519sK\nxKCA8BytYOyyrRdJHI22glzcnuiyrLFQ5FYShySrjhRKpKJBiEFhPgHdkEEIehZ5WQLEHWNxzOsU\nDkCfQl/fr6EsdRaqxpuxbClGmTTD+kMP5J06nKmwRtntVVpYTkYWsp3vSjGJK8Wk14fhGXwCzXGM\nn/itl/BTv/+K14cxE8wDvZwScSEfX5hFwpJx+Tg7YprhpzrvVkfFtb3aVPYNRj7pbZ13taUgGZlP\nCNnhuZ0VSbYvhYMQ0pMt7DQN2Zk6bEKI6a2dlaN6G9lYGAGLICoYE+jNYyagvffhrmeieOlu2fzz\nolGcYQLtF6xRdrvVFoqpwTsrHH/DBTTHMTaPJby5U/X6MGaiLMkQgwIioQCuFpMLU6Zy3JCRjARH\nNm1lov6xcLy1W4OiTbdAyNAXszy0cLSVufzPgB51JhBv2gglWUXMxqtDa5moaxPopqw4JkJXUvNF\nCx4PyGFnqTF3jiUQAohzXLWwi41sFG1FM/+8aDABLZCuFWpRsEbZ7VbH13hz/In3v8WcU0tZknGv\n1ITmQcLAvJSljnkJ9nIxgTvHkrlB72cGfXj3k46FzJZFr2ENhNNE2DGW4voSkWyIALeptzpz+Z8B\nIBgQUPAoyk6SFdsm0IAuwtyaQEuy6piAXp6zzvvIUuPNWIqLEIj+vuKE9WQW1ixNcoto4cjGQggF\nCJaTEVvKgNyGRdntVSar8eb4j8V71XEWAk2jurhRNezVvMm5nYeS1DE3i68Wk6AUuLHvfx90SZKH\nlqgwMtGwuSTpNa/eKyMXD890CZn5So88aiOstZS5BTSgT9J2XfZAaxo1RKh9E+j1TBSHdRmtjvMn\nmk4KaGbhoHS2E39rjTdDj1DTb3PCejILLDklKOgidNEgRD9ua6X0InEhH8f1/ToasrpwGdAcHS6g\nOY5QlxWwwfPmsXsVv3ZRtgjRy8aSxLUFsHFMMoHOxEJoyKpnk1srr25V8cgMC4RAd4lontKLedAt\nHPOLoeVkxHULB8tRtiuFA+hOMd2wcUg2RvD1s5KKoNlRUWsrM339sN9BvzThMVjyxmom0uPXXiS+\n69EVfPvDK14fxkycW4qZ78HcwrGYcAHNcYSKxWPLFmcWiZIkm1nK55diCAeEhRDQpQkFNADPbRxs\ngfCxGewbgH6pHQD2ParzrrUUJGwQ0Ctp9y0cDbPJz94JNOBOFrTTFg4A2KtM/5woqoaS1MHSgCIj\ndsXELwJ67RSUYPzsdz+EH3/6kteHMRPnLQVM3MKxmHABzXEEqzi7u4ACuix1zNa+YEDApeWE7wU0\npRRHk3igo/6o835zpwpVozP5nwGYl533PbII1VodJO2wcCQjKEkdV6wPDKm96BNoZy0cwGzRgiz+\nst/CAXSTOPxQJQ3oMZDhoLCQGdCngfNLXQHNLRyLiT/MWJxTh1VAb5YWS0BTSlFudpC1tCtdKSbw\n/O2Sh0c1nmZHRVvRxnugfVLn/dq2ntDy6AwJHACQT4RBiDcZypRSW1I4gK5gO6i1cSZnTy7zONgE\nOhqy7yNgJR0BIcB22fkTGsmhGDtgvjIV1kK4CBNoQSD4ue99GA+tzvb7x5mPDSPKTtUot3AsKHwC\nzXEEJqDT0RDuLZgHutpSoGq0R4heKSaxVW6a9c1+hH1454bUeDMyxgTaawF9bETQzTp9CQYELMVF\nHHgwgW52VGgUtlg4imn3s6Al2f4JdCggoJAQsVNx/ve9aXOCiJV5srmPjFzyRfBAA8An33t25hNY\nznyEAgI2slGkoyHfXJXgTAcX0BxHYOLskfXUwlk4WEJFpk9AA8B1HydxdGu8R2eiMg902WMPtCQr\niISEuRaYlpOiJ0uENaPG244lQlai4KYPutG23wMN6IUWOzN4h6eBUgqp45yFIxoOIBUJzrTYecQm\n0IMsHMYE2i8pHBzvuVJM4tySO1edOPbDf5M5jsAm0I+sp/HcO0doKyrE4GKcZTMfo9XCcZUlcezW\n8OTZrCfHNQ4W5zZ+As0sHN56oBuygvicYmI5JXqyRMgEtB0xditzeG5nxYkJNKBXKju9K9DqaKDU\nWSE6axth18IxXEDH+LSRY/Dz3/eIWWbDWTz4BJrjCOWmjHBAMDOUt0qLY+MoDZhAb2SjiIYCuLbn\n4wm0cdzjPNDJSBCEeJ/CIbVVxOYUcMtJ0ZMlwnrbvgl0OhpCOCh4MoGe9wSmn9W0PoGeNUN5EiTD\nv223+LeiZ3PPZuEgpPe9g8EsHFEfWTg43rKciri298CxHy6gOY5QbXaQiobMN4dFsnGwCL6MZQIt\nCASXi/5O4jg2LRyjBbQgEKR9UOdtywQ6GcFBrQ3V5bZL5oW3Y4mQEILinO1308Im0HbbINYyEUiy\nimpztgzlSWDHHnVwkltMzZbNfdTQ8+MH2ZL8tkTI4XDmgwtojiOUjSa/s4aA3lzACXT/JPdCPo47\nxw0vDmkiSg0ZAYEgNYGoy0RDPvBAz+9jLaZEaNT9NsK6jRYOQLdxuDqBNqe49k+gAWDbwUXCrvh3\n0sKhW4O0KU/Mjuona7wZmWgI7z2fxeNnMnYcIofD8RguoDmOUGl2kI6GUEjoWaP3FmgCXZI6IKSb\nl8xYiotmcoQfeeegjrVMBMIES3npmPd13o32/G1yBZYF7fIiIWups0tAL8/ouZ0Vqa1CIIAYtPcj\ngNUqO5nEwSwc89p/RlFMRaBo1FwKnJRRTaCCQPB7P/7BhW3O43A4vXABzXGEstRBJhqCIBBsZKML\nZeEoSzJSkdCJy7BLiTAasupq4cWkUErxjdslPHUuN9H9M9GQ9x5oGybQrDXuwOVFQrZEOMm0fxKK\nSX0C7aR32Aqzz8xSoT4K1mrnZBa0OYF22MIBTJ+MctRom15nDodzuuECmuMIbAINAGdzsYUqUylJ\nvSUqDDZZOp5yKuUGd48lHNbbeOr8ZAkhmZhPPNBzTnCXk6zO291FQmbhsGuRbSUtQpJVcznRaZry\n/AucgygkRQQF4vAE2h0LBzD962qSJlAOh3M64AKa4whsiRAAzmRj2FygMpWyJA/covezgP6G0ZL4\n3vOTT6C9tnBI7fkn0Gwxy+02wnq7g2gogGDAnrfQWSees9KQVdsTOAAgIBAUUxHs2DSBVtSTEV9u\nWTgAYLcy+etKUTWUpQ4X0BzOfQIX0BzbUVQNtbZiplicyUVRaXY8twxMSkmSB06g2XLQtL5IN3j+\n9jFSkSAeKCQmun86FjYbF73Cjgm0GAwgEwu5PoGutRRbIuwYy0l3s6CltuKYAF3LRLBVnv+EebfS\nwmP/4r/imWsHPbc7lSBipZAUjZr4yV9XLI+c1zJzOPcHXEBzbKdqXN62WjgAYHNBfNClRmdglnJ3\nAu1+ccc4nr9TwlPncxMtEALdOu+qRyc1qkbR6mi2iKBiMuLJEqEdNd4MJrp2HW7xYzTk+Rc4h8Gy\noOflL9/ehySreGOn2nN71wPtnIUjZNTET3NixmwrXEBzOPcHXEBzbKdbha2LtI2sLqDvLYgPepiF\nY8moyD7yWRLHcUPGjf063nNu8oZEr+u8zTIMG0ScF22E9ZaCpI0RcGadt0uTdElWEXdogruaiWC3\n0po6Aq4fNnnunwI3jdeO04UkxZR44oTm6zePUG0N/p1hJw2rXEBzOPcFXEBzbIdZNdgEepHKVGRF\nQ0NWB1o4UtEgggLxnQf6hTvT+Z8Bi4D2yAdtThFtsBEUkuJMpRfzUGt1bClRYcTCQSQjQdcm6Y22\ngpjNGdCMtXQUsqrNZXVSVA1fuXEI4KSAbsgqQgGCsM0RfP2s9EULPnPtAJ/87NfwW1+/O/D+u6aA\njjp6XBwOxx9wAc2xnbIpoMPG/4eQjoYWYpGw3OydnlshhCAbD/tOQD9/5xjhgIDHNtITfw17bryb\nQOsC2pYJdDKCg3rbtQg4QK/ytisDmlFMRVyzcDg6gU7PnwX98r0yai0FAYGc8IU3ZdXRFkLGcipi\nWjiasoqf/cNXAQB3jgYPArbLLcTCAaRstPZwOBz/wgU0x3aqfRNoQF8kXIQou7JZ4z14k34pHvbd\nEuHzt0t4ZD2FyBSigp0gVDyKsmsYcW12eKCXkyI6KkXJxcdSa9nrgQZ0y4BbFg47SmyGsZaZPwv6\nS9cOIRDg6SuFEycVkg3Lp5NQTIk4rMuQFQ2//MVr2DxuIhMLDbWi7VabWElHbM/W5nA4/oQLaI7t\nMAuHdYp7JhtbCAtHqTG4xpuR89kEutVR8eq9ylT2DaC7ROi1hcMOIcQix9xM4qjbnMIB6I/DDQsH\npdSWEpth2DGBfubaAR4/k8HlYgL7td6CmYasOu5/BnQLBwB86doB/u8v38InnzqDD13KD00Y2am0\nzCIZDodz+uEC2sf888+/hj98acvrw5gaNsW1TqDP5mK4V2rOvVjkNCXppPi34jcB/epWBbKq4akp\nBTR7bryycDRkGyfQrPTCJf+wplHUZXuXCAFdQO9V51++G4esalA06tgUNxcPQwwKMydxlCUZr9wr\n4yOXC1hJRU5cXWg6KP6tsBOz/+k/vYJsLISf+a4HsZ6NYqvUHGgX2im3eAIHh3MfwQW0j/mDF7fw\nBwsooCvNDmLhAEKWkomNXAyyouGg7r8IOCtsIpsdUoawFA/jyEeP4Ru3jwFgqgQOAAgGBCTFoGdt\nhFLbvgn0slmm4l4EHKWwdYkQAIpJEYpGcezwVQH2s3dKhBJCsJqOYHvGLOiv3DiERoGnr+QthSbd\n51ZyMILPCvu3jxsy/pdPPIxMLIz1TBRtRcNhXxKPomrYr7V4AgeHcx/BBbRPUTWKWlvB9b2a14cy\nNWWpY1oEGGey+qVNv9s42KRrUAoHAOTiIqotBZ0BDWle8PztEi4V4jO1n6VjIc/KbdgE2o5lMFZC\n4laUHavbttsD7VYWdMPGCMFhzJMF/cy1AyQjQTy+kRkY7+ek/cQKE8NPXyngE4+tAgA2jPexfh/0\nQb0NjfIEDg7nfoILaJ9SN8pIdiqthWnwY1QsNd6MMwtSplKWZISDwlBhl0voQrXkAxuHplG8cKc0\ntf+ZkYl5V+ctGSLUjgl0NBxAUgziwC0Bbfxu2p3CsWKIL6cFtJ0RgsNYzUSwM8MEmlKKL18/xIcf\nyCMYELr+9qr7AjobD+Pf/Z334Jc++YS5GLhuCOh+HzRbmOQTaA7n/oELaJ9iFc039hdrCl1pyic8\nxOuZKAiB76PsWI33sE16P9V53zioo9LsTG3fYGSiYQ890PbaCPQyFXcsHKxp0+4lwjUblu8mgSWg\nODmBXktHsVdrT10Vf2O/jp1KCx+9UgCgZ3wDwG6le3Kke6DdiYr79odXeq7urGfYBLr3OTIzoDNc\nQHM49wtcQPsUa9vV27t1D49keirNTs8CIQBEQgEUk5GFsHAMS+AArHXe3gto5n+edQKdjoU8i7GT\nZD3jV7SpDGPZxTpvZuGwW0DnEyJCAYKtOeLfJkGy+eRlEKuZCFSNTn1S8yWjffAjl/MAADEYQC4e\n7rFw6DXkzk+gB5GM6Jn2W30Cmp30rKa4hYPDuV/gAtqnWCfQ1xbMB11pdpCJnhSh69nozItFbqHX\neA9fDvPTBPrt3RqSYhDnlmIzfX0mGvJuAt3WL8PblZm77GKGctfCYe8SoSAQFFMRxyfQdkYIDoPF\nuU2bBf3M9UNcLMSxke2+pvV4v14LhxsxdsPYyEZPeKB3Ki1EQwGkorxEhcO5X+AC2qewMpJYOLBw\nArosdZAeIEJz8TBKHnluJ6U86QTaB0kcjbaKVHS43WQcS/EwypLsyUKkJCu2WgiWkyL2q+60EdaM\nq0N2T6ABXXju2DSBbnVU/PJfXEOro/bcLtkYITgMZmWY5mSg1VHx9ZtH+OjlQs/txZSIXUNAK6oG\nWdEctZ+MYz0TPeGB3q20sJrhJSoczv0EF9A+hU2gnzybXSgB3eqoaCvaCQsHoCdb+F1Al6TOyAl0\nJhYGIf6wcEiyMtckbjUThUbdi3+z0pBVW5fYlpMRtBXN9Cc7iVMpHIAuPLdtmkB/8c19/PJfXMdz\n7xz23N6wMUJwGCyNYpqTgZsHDbQVDU+d7/X0F5MRs85b6jhvPxnHRlbPtLeerG1XmnyBkMO5z+AC\n2qcwD/RT57M4rMu+yh4eRWVAjTcjGw+jJHVcmRLOAqXUsHAMn0AHBIJszB913pKsIj6HkGCVy7PG\njc2D1LZ5Am3EnR24YOOotZxbwltNR20rU3l9uwIApvhkuDGBTkWCiIcDQ1v7BsEsOP1CtJiO4LDe\nhqJqaBr2Ey8tHOvZKCRZ7clQ3620sML9zxzOfQUX0D6l2tSXrN59Vp/GXNtbjEXCkQI6FoasaKYH\n02/U2woUjQ7NgGb4pY2wOacXdN24zO6FL71hcxSZmQXtwiJhraUgIQYREOy/XL+W0Zv3Dm04YX59\nuwrg5M+kYRapODeBJoRgNROdysJxYBwney4ZxZQISvWsZdO/7aGFo5sFrT82vUSljTWewMHh3Fdw\nAe1TKs0OUpEgrhaTABZnkbA8ogo7Z0x2/Wrj6B776FKSXNwnE+jOfI1s7DL7NFNCu5BkxVYLwfKA\nwg2nqLc7tmdAM9hzsj3nVQFKaXcC3fczkWQFkZDgyAmAldV0ZKqrG8xKxKLrGEVDUO9V22YEn6cT\n6Az7vdEXCQ/qelwfr/HmcO4vuID2KdWWXkZSTIlIRYILI6DHWTgAoNTwZzEME/ajlggBffnODxNo\nqT3fBDouBpGJhTyZQNtdhsHqvN2YQNfbiiP+ZwDmFHOWEhIr+7W2WTe93+dxb9i8wDmM9Ux0qhSO\nvVoLmVgIkb4SI2tDY9MHHugzRkIIm0CzkwTugeZw7i9OtYDePJbQVvxpFxiHPoHWExauriQXRkCz\nZrtBMXbMGuHXCfS4Gm+GXywckqwiNmcV9mp6OpFjF1JbtVXEJcQgoqGAK3XetZbiSAIHYIl/m3MC\nzabPqUjwpAe6be8C5zBW01Ec1tsTvwfvVdvmtNkKu7qwX2tZMqy9s3CkokEkxKApoM0SFV7jzeHc\nV5xaAd1RNXzHLz+D/+fZ214fykxULWUkl4tJXNur+3b5zspEE2ifCmhT/E8wgS5J8tQta3Zjhw1i\nPRPxyAOt2CriCCEopkTXBLRTFg59AivMPYF+bUv3P3/kSuFEmUlDVhALOS9AWZTdXmXksRwFAAAg\nAElEQVSy52S/1jbFspV8XERAINirtswKeC8n0IQQIwtaf47Y7w+fQHM49xenVkBXmx00ZBVv7lS9\nPpSZqDQ7Zij/1WISlWbHFXEwL9VmB4QMzshl1gg/TG8HUWowC8f4CTSlXcHtFc3O/IUSaxn3y20o\npbZbOAB9+cyNSL5627kJNCFEz4K2YQJ9IR/HpXwcB32V2pLNEYLDYNP0Sa+e7VdbKKZOilBBIFhO\nitittF1pUZwEaxb0bqWFSEgYODTgcDinl9MroI2oqVuHDY+PZDaqLcUygU4AWIxFwrJhPREGLCil\noyEQ0rVK+A12XOM+CHMJfUrm5YmArGjoqHRuC8daJopqSzHLQdygrWhQNWr7ZfhCSsSBKxPoDpI2\ntxBasSML+vXtKh5aS6GQikCj6InBbNgcITiMqytJJMUgfuQ3nsc//M0X8OLd0tD7ahrVJ9DJkxNo\nAFhORXQLR8d7CwfQ20a4U2lhLR3lJSoczn3G6RXQhpXg1kFjIawP/VQNIQrATOJ4e9f/ArrSHF5E\nEhAI0tGQOen1Gyz5JBgY/Wvhhzpvu/JwvciC7kaR2T2BFk8szDlBveXcEiGge2nnaSOsSB3cKzXx\nyFoaRUOQWn3QTkz/B1FIiviL/+Fp/MOnL+HZG4f4/s88hx/41ecGnngeNXRL1KAJNACspETfWDgA\nPQu61lJQaXawU2nyBA4O5z7k1ApoVnZQayvmNvqiwNr8UsYkdCkhIp8IL8YEWuqMnODmYv6t8z5u\njC5RYZh13h4KaKljlHnM6cVdMz743YyyY1FkMZt9xMvJCBqyajYFOoGqUTRk1TELB6A/J3u11swV\n62yB8OG1lClIrT7ohs0RgqMopiL4qe94EF/9mW/F//xdD+Ibt0v4k9d2TtyPHV9xgAeafZ/dSneJ\nMDrnlZd52TCSOLZKTb1EhQtoDue+49QK6KrlkvTto8WycbBjT1mE6OXl5EKUqVSaowV0xqd13ppG\n8Y3bx7hi2GVG4YcJtF1eUDaBdtMH7VQZxkqaTVudm0KbNd5O1mBnoqBzVKyzAhWrgO6ZQLfdmUBb\niYtB/P0PX0Q4IODusXTi71n84PKQCXQxFUG1peC4ISMaCgy0iLkJy4K+eyxhr9Y2/d4cDuf+4fQK\n6GZXQN86WDABbRx7yjLlurqSxPW9mu/tKOMEdC4e9mUO9At3S9iptPDdj62OvS9LEzn28MpG06ZJ\n3HJSTzhwU0A3WJW0zYtsrEp5z0E7ChPQTk6gWZrDrLaa17crWE1HzCtXhPSKcTcn0FYCgp5ecffo\npIBmxzfMA81OBG4fNTy3bwDdNsKXNku8RIXDuU85vQLamOIKBLi5YIuElab+IW0VopeLCTRk1ZPW\nuGkYJ6CzPrVwfOHlbYhBAR97V3HsfUMBAalIEMcN71JRTBvEnFPcYEDASioyl+d2WqS2UxPo+YTn\nJNRbTEA7t0Q471WB17areHgtBUB/fpfiommRUDWKVkfzTISeXYoNnECzCXl/CyGDWTtuHTY8bSFk\n5OJhREICXritL0byCDsO5/7j9AropgKBABfycdw69L/1wYo5gbYI0UWo9KaUjlwiBPTprd8EtKpR\n/PFru/iWq8sTC6OlhOithYOlEdgwxV3LRNz1QMvOLIKtGFPKXZssHJTSEyKWpZU4auGY40SgKau4\neVDHQ2tp87ZiSjQFKmvycyOFYxBnczHcPZJOXEnbr7WQi4chBge/JtgEeqvc9OzYrehZ0DG8ck/3\nm/MSFQ7n/uP0CmijCvtiIbFwUXZset47gWYC2r8nA/W2AlWjYyfQrY5mWhD8wNdvHeGg1sbHHx9v\n32B43UbYtDEPdy0TnTs2bRok2Z4FyH6i4QDS0ZDZDDcvX3hlBx/513+JTcvEtMY80A5aOJKREJJi\ncKYylTd3q9Ao8IgxgQZ08ckm0GaKhQs50IM4m4uh1lZQ7ouy3KsOj7ADugKa0vmTZ+xiPROFbCx6\n8gk0h3P/cXoFtBEDdzEfx+0jCZrHrXHTUDE90F0hmo6GsJwUcfPAvwKaHfegGm8GKyk59tEU+guv\n7CAaCuCvP7g88dd4LaDNJUIbGuVW01HsVlquNSs22s7E2AG6kLHLwvGV64dQNYrn7xybtzELR8pB\nAQ2wk5rpH8frW0YCx/rgCXTDoQXOSTmb09Mr+m0c+7XW0AVCQP95R0L6x5UfPNBA1wctBoWRV904\nHM7p5PQK6JaCVDSI8/k4ZEVzdcI2L10LR++HXD4h+rbFD4A5VUqNmkCzOm+fPI6OquFPX9vFxx4q\nTuUnXoqHPU7h0IWcHdO49UwEHZXisO6Op1uSnYmxA3QftF0pHEw4v7xZMW9j8ZgJB4tUAL1MZWeG\n96zXt6vIxEJmPCEAFJIRHNbbUFTN4p33zgMNnBTQe9WWmVk9CL2qXX9MXpeoMNYNAb2W4SUqHM79\nyOkV0MYE+kI+DmCxGgmrLQWRkHDCD5jzWLSNgwn/kR5oI2fZLz7o5945wnFDxscnSN+woqeJyJ6l\nothZacyW1uz2Qd89kvAbX7194nYns3xXUvZMoI/qbbxjpPd8c7Ns3l5vGx5ohyfQs5apvL5dxSNr\n6R5BV0yJoBQ4rMvdCEEPUjgA4Ez2pIBWNYrDujy0RIXRFdB+mUDrj2VlzHFzOJzTyekV0K2uhQNY\nLAFdkTo99g0GE21+pdwcX4Wdi+t/55c67y+8vI2kGMTTVwpTfV0uHoaiUVSbzpV2jMJOEWq2Edqc\nxPEfvnob/+zzr/dksgP6sUdDAQQcyPJdSevTVlmZrYSE8cIdPV3hybMZvLFdNb9fvaWAEGfsJ1bW\n0hEcNWS0OpPvCnRUDW/v1swEDkYx2S1TcWqBc1LiYhD5hNgTZXfUaBsthMMn0ID/BDTLgub+Zw7n\n/uT0CuimbuEoJEXEw4GFEtDV1uAoOK99t+OoTCCgWdOfH04EZEXDn72+i297qIjIlEJ0KcHKVLyJ\nsmvKim2FEk6VqbxlVM/vV3t/Ro224pgIYmLG2rw3Cy/cKSEcEPBD7z8HWdXw1q5eTlJtKUiIQccv\n2a8az8k0C5HX9+qQVQ0P9QtoS5mKGSHo0QQaAM7moj0T6H0zwm60EF0xBLZfLBxnDAvHaoYLaA7n\nfuT0CmhjAk0Iwfl8fKEEdKXZGegjzsbCqLaUmSt+naYygYUjE2UTaO8F9JevH6DaUqZK32Dk4vqH\nuVcnNJJsX5tcKhJEQgzabuFgAvqg1iugJVl1LAWCicV5kzi+cfsYj22k8b4LOQDAy4aNo95WkHRB\nfDIP8zS7GzeNuM4rRmIPYznVbWhkE2gvq7DP5nqzoJlnfdEm0IWkiB9/+hI+8fia14fC4XA84FQK\n6I6qQZJVU4ReWDABPXwC7R/xOYiy1EEoQEZ+OAcDAtLRkC8m0H/2+i5SkSA+/MB09g3A+zpvSVZt\ni/MihGA1HbF1An1Yb5tLif3T4EZbcSwFguXxzuODbnVUvLpVwXvOZ7GeiSKfCOObxiJhvaU4WqLC\nWJ3BVrN5rD9/Z4ykC8ZSPAyBAPvVlhlj5+kEeimO7UrTtMXsGydY4zzQLKXDLzF2hBD89Hc+iAdX\nUuPvzOFwTh2nUkDX+qKmLubj2DyW5vZFukWl2RkYk8Wmnn6swgZYC2F47OXtbCzkCw/0TqWFS8sJ\nhIPT/xrkWJ23ZwLaXhFqdxb027vdwp+BE2iHRNCKaVeYXUC/vFlGR6V477kcCCF4fCODl+/pE+ha\nu+P4AiHQtaJMc1KzWZKQi4dPlLwEAwLyCRH7tbYZY+flFPdsLgZKgXslfQrNnqthLYQM9tw67T/n\ncDicSTiVArq/ye9CIQ6N6h8wi4Du3x5g4TAm0H71QVeaMtLR8eLCL22E9bYyc6Oc9wLavgk0YAho\nG5cImX1DICcFdENWHJuApqJBREOBuSbQzxsLhO85lwUAPH4mg3cO6qi2Oqi3Zn/NTEMkFEAuHu7J\ngqaU4sb+8CbSzWPJ9OX2U0zp8X6SrCAgEIgznDTaRX8W9F61jXwijFBg9DFtZKMgBMglRgttDofD\ncYPTKaBbvUUkF/IJAMCtA//bODSNojZiiRDwr4VDr/EeXqLCyMb8sQw5j5UgEgogHg7gqO7N42ja\nPMVdz0RwPGXqwyje3q0inwhjLRM1L9EzpLZzE2hmR5mnzvv528d4YDlhZpY/fiYDSoHX7lVQaytI\nujCBBlgpTHcC/Qt/8hY+9m+eMf3Y/WweS9jos28wlpN6mUrD+Nl7mVt8zsiCZg2PB7XW2AVCQD/J\n+6Of+DC+85EVR4+Pw+FwJuF0CmgjWsycQC8tTpRdXVagUQyOsYt567sdx1apiXxiMgHdX+XrBY22\nOtckNJcI49ijFI6GzQLa7iSOt3ZruLqSxHJSPOmBttl+0k8xFZl5iVDTKF64U8J7z2fN2x7f0Fv9\nvnmvjFrLTQHdzYL+9Wdv4d89cxMA8OZO9cR9VY1iq9w0p7v9LBt13nZbf2ahkBAhBgXcOepOoMct\nEDIe3UiPnVRzOByOG5zKdyJzAm3YCdKxEHLxMG4ugICujoiC81uLn5WdShO3jyS893xu7H2zsZAv\nJtC6hWN2EZqLi56dzDRlBVGbPdAAbLFxqBrFtb0arhZTKCRFV1M4AH1yO6uAvr5fR7Wl4Klz3ddx\nJhbG+aUYXt4su7ZECABrmQi2K0386Wu7+BdfeAMfe1cR4aAw8H1st9pCR6VmUUk/xZT+Wq02FUd/\n9pMgCARnLEkcegshj4LjcDiLxcwCmhBylRDyTcv/qoSQf0IIyRFC/pwQct34/6zla36GEHKDEPI2\nIeTb7XkIJzE90JYPOj2Jo+7UP2kblSE13gAQCghIRoK+EJ/9PHfjCADwwUv5sffNxsNodlTb7AKz\nQCnVLRxzTKCX4mHPLBySrNq6TLWWtm8CffdYQquj4cHVJJaTkRMWDidTOIBunbemTd8S+Y3ben33\nU5YJNKDbOF64U0azo7rigQb0CXStpeAnf+clPHEmg1/5wXfj/FIMNw9Ovo8xO8SZ3HAPNKXAnWPJ\n8wk0AJwzBLTeQjj5BJrD4XD8wswCmlL6NqX0CUrpEwDeA0AC8J8B/DSAL1JKLwP4ovHfIIQ8BOBT\nAB4G8B0APkMIcWQUwibQ1kutF/Jx3D70/xJhv/2kn5xPFvD6efadQ+TiYTy4khx7Xz/UebcVDYpG\n5xfQnhWp2LtEWEyLIMSeOu+3DIvBg4aFoyx10Fb0kyVF1dBWNEfLMFbSESgaxeEMz83zt49RSIon\nrBCPb2TMWD63BPSaUdCxnoni33/6vYiGA7iYT+DmgF0OJqCHWjiMhIvbhw1f5CizCfRhvQ2NAgVe\nh83hcBYMuywc3wrgHUrpHQDfC+Bzxu2fA/B9xp+/F8DvUErblNJbAG4AeJ9N/34P1aYCgaBn0nIh\nH8dutYVG25vq5UmpDJieW/HLAp4VSim++s4RPnBxaaJmPDPP2sM4PvY6mEcM5ZMijuryTJPOeaCU\nQurY64EWgwEUEqItE+i3dmsgBLi8nDSjyQ6NSb3UYU14zom4lTnKVJ6/U8JT57InluweP5Mx/+yW\nB/r9F5fwXY+u4HN/733mAvGl5TjuHksnypQ2jyUIpGvF6YdlLDc78/n+7eJsLgZJVvGGcbJVHBNh\nx+FwOH7DLgH9KQC/bfy5SCndMf68C6Bo/HkdwKbla+4Zt52AEPKjhJDnCSHPHxwcTH0w1VYHyUio\nR8xdyOuLhLeP/O2DZtPzYXXYfqzzvnXYwE6lhQ8+sDTR/f0wgW7YUGmcT4hQNGqe9LhFW9GgatT2\nKe5aJjpX/Bvj7d0aLizFEQ0HzBa8fSMVg1VJOzmBZmUq0wronUoT90pNPDXAx//wWgpB4/3ELQFd\nTEXwmb/9Hpxd6k6VL+YTUDTa0+QHAJulJlbT0aELdssWi4QfJtAsieN5wzIzrkSFw+Fw/MbcApoQ\nEgbwPQB+r//vKKUUwNTjOUrpZymlT1FKnyoUpm+JqzY7JzzETED7PYmjP8O6n1w87Lslwmff0f3P\nH5rA/wxYliE9FNB1cwI9u5hgiSPs0r5bNB0qw1jPRG2aQFdx1bDyLBvLYcwHLcmsCc85EVdM62Jx\n2ii7l+7q8XBPncue+LtIKIAHV/XHlBDdWSIcxMWC/j7Wb+O4eywN9T8DwFJcRMA4AfCDB5pZTb5x\nW8/c5gKaw+EsGnZMoL8TwIuU0j3jv/cIIasAYPz/vnH7FoAzlq/bMG6znWpLOWGBOG9E2bHoJL9S\nbXZACJAcMhnNxcM49pkH+rkbh1hLR8yp0jjMCbSHJwINef5K44JR6HDgsoBmNgi7BfRaJoKtchP6\nee9sSLKCO8eSKaCZhePAFND6sY+qe5+XfFxEUCBTT6DZe8MDy4mBf//4hm7jcGsCPYiLBf3Y+hcJ\n9RKV4b9/AYGYr1evUziAbt34y5tlEIKJ4i85HA7HT9ghoH8QXfsGAPwRgE8bf/40gM9bbv8UIUQk\nhFwAcBnAX9nw75+g2uycENDRcADJSND1aeG0VFsKkmJwqJc4Gwuj1dHMSZ7XaBrFV28e4YMP5Ccu\nZ8jEWKOidx5oNoGey8LR5+91i6bx3NsZYwfoFo62os31eK7v1UEp8OBKCoC+aElIdwLdsOHnPg5B\nIDNlQW+Xm0hHQ0OP7X0XcrrY89Cvm46GkE+EeybQrY6K/VrbFKXDYDYOP0ygI6EAiikRbUXDUlxE\nkGc7czicBWOud1JCSBzAtwH4McvNvwDgdwkhfx/AHQB/EwAopa8TQn4XwBsAFAA/QSl1JMes2uqY\nlg0rfrQ/9FNpdobaN4DuAt5xQ3bURzopb+xUUZY6+NCE/megG8fnrQfahiVCY6J3WHP3pIz5t2M2\nT3E3jAnmVrlpTo6n5W2jwpulsQQDApbiIg6MMhXJIftJPyvpyNR+7u1yc+gSHgB84rE1XF1JYn3E\nfdzgYj6Bm5ZIznul0QkcDN1OU/HFBBrQj3eaEhUOh8PxE3Od9lNKG5TSJUppxXLbEaX0Wymllyml\nH6OUHlv+7ucppZcopVcppX8yz789imrzpIUDMBIsfNCAN4pqc3CNNyMX1z9svEywsPLcO4cAJst/\ntpKNeRvHZ8ckNBMNISgQ169qmCLUZiHEhCETZLPw5m4V0VCgR8xZy1TssM5MAsuCnobtSgvrmeFe\nXEEg5mTdSy4W4j0T6M1j3bc+ygMNwBSqfphAA10bB/c/czicReRUXjertQZPcbOx0GJMoEc0nZkT\naJ/4oJ975wiXCvGpPwSz8TBKHp7M1I0pbmIOMSEIBEuJsPtLhB1dhNp9BWI9qwuwrdLsi4Rv79Zw\nZSXZY0HS67wND3TbpQl0Sp9AT+PnHjeB9gsXC3EcNWSUjfeATeOEZ5QHGugKVTvzw+fhXE6/Ssgn\n0BwOZxE5dQJaUTU0ZHXwBNqHEXD9VFsnE0SssAW8Y48KPKzIioa/unWMDz0w3fQZ8P5kpjuBnk9M\n5BMnq6qdxikbRDoaQjISxL0ZBTSlFG/t1vBgsbdMp5AUsV/tm0A7PAVdTUfQ7KhmMdE46m0FlWZn\nMQR0Xl8kfMeYQt89kiAGhbG2G1am4pcJ9Nkl/Wdd4DXeHA5nATl1ArrWYk1+Jz8kch7bBiahMtbC\nwQS09xaOl++VIckqPnhpcv8zw+vnotFWIAaFuZeX8gnR9SVCNsV1IsliIxubuY3woN7GcUM2494Y\ny0lRb5zTqGP2k35W0kaZyoQ2jh3jMa+m/S/mLi33JnFsliScycXGLvGyCbSfPNAAn0BzOJzF5NQJ\naFZEMmwCLckqWh1HdhdtYZh/m5GKhBAQiC+sKM/dOAIhemPatGQ9XuistxVbKpl1Ae32BJpZOJwQ\n0NGZLRxsgfDqykkBrWgUJUlGo60gKBCEHU5dYG2EO5XJHgs7afB6QXASzmSjCAUIbhqZ9pvHTZzJ\njj/up85n8cmnzuDJsydzrr3gkfU0fvB9Z/EtV5e9PhQOh8OZmtMnoJtsAn1ShOZ8UOAxClnR0Oyo\nIyfQgkCQjYV84YH+2s0jPLyWQiY2fYZrNhZCQ1bRVrw5mWm0FVsW2fLJMI7q8lzZydPSrcO2/1L8\neiaKeyVppsfTTeDoXbRjl+gP6m1Isl5BPmnk4ayYE+i+JI5htevbZf1+i2DhCAYEnM3FcPOgDkqp\nngE9JoEDAJKREH7xbzw28v3FTcRgAP/q+x9diJ85h8Ph9HP6BLQ5gT4pLroFHt7bHwZhHvuYD7hs\nLIxjl20Dg9ittnAhP7h0YhysjbDs0SJhva3aIkALCRGyqk3stbWDpqyCEEAM2v/ru5GNoiGrM9WT\nb5WbSIhB80SV0a3zbtt24jKO5WQEhPRaOH7ja3fw5P/256gMeM3tVJoICMT0Cfudi4UEbh40UGl2\nUGsrYyPsOBwOh2Mvp09Aj6jC9vsEunvsowVG1idthHphzWxiqLsM6c3jaLSVuWq8GWbTnos2DklW\nEQs5M8XdyLIou+ltHPtDMn2ZKN2vdSfQThMO6vnTbAL92lYFP/df3kBZ6uCNneqJ+2+Vm1hJRRam\n0ONiIY47RxJuG+2JG2MSODgcDodjL4vxaTEFo6a41hISP8KmfuMusS75oBCGUmokhsx2Odi8GuDR\niUDdLgsHK1NxVUArtrcQMpgQm0VA71ZbA+MMrXXeDdmdCTSgLwTuVluotxX897/1IhLGyd6N/dqJ\n+26XmwuxQMi4lE9AVjV89Z0jAOMzoDkcDodjL6dPQDMP9CgLhw+mt4OosgSREUuEgD/i+FodDR2V\nzuynzBonM17ZaWzzQHsioNW54/eGMU+Zyt4QAR0LB5EQg9ivtSC13ZlAA3rqxE65hZ/9z6/i7rGE\nX/2h9yApBnF9v37ivtvl1kJ5cS8W9AzlL13bB4CJPNAcDofDsY/TJ6BbHQhkcNYpE3tei89hTDqB\nZhFwwxai3IAd6zixP4ycDybQ85SoMPIJ/XG4mQUtyaojEXYAkImFEA8Hpo6yo5QaFo7BU1xWpiJ1\nFNcq6FfTEby9V8Pnv7mNf/qxK3jfhRweKCZwfa9XQGsaxU5lMUpUGBcL+u7B87dLyMRCM/8ecjgc\nDmc2Tp+AbnaQjIR6mtAYwYCAdNS/bYSj/NtWsvEwNNq1q3hB1yozmxjKmAud3nmg7ZhAZ2NhBFyu\n82466CMmhGA9G53awlGSOpBVbWimb96o83ZzAs2SOD54aQn/6FseAABcXk6cmEAf1tvoqHRkjbff\nyMXDyMRCUDQ6toGQw+FwOPZz+gR0Sxkp6nLxMI49rJAexTQeaMDbSXp1zgl0OCggIQY9qfPWNIqG\nrNqyRCgIBLl4GIc1956LhuzsFHcjG5s6C3rPSLsYNYE2PdAuTaA/cGkJ77uQwy9/8gkEjBPqy8tJ\nHNbbPSdubNq+SBNoALhkTKF5AgeHw+G4z+kT0M3OSFHndYX0KKqtDsIBYWw8WdYPAnrCyL1RZOMh\nTywcducou12m0pRVRB2c4rIs6GnYHSugI9ivGh5ol5rwnjybxe/+2AewbDmmB4q66Lxx0J1C71QW\nJwPaysW87oPe4AuEHA6H4zqnT0C3RgvonA8W8IZRberT83HxZDmPI+CA0cuak5KNefNcNNr6sdsl\noAtJdwW0JKuIOyigN7JRVFvKVBahfVNAD7ZwFJIiGrKKWtu9CfQgLhs12FYf9DabQKcXS4gyHzS3\ncHA4HI77nD4B3Rxt4cjGwij7NYWjOVksnJlg4eHjmNRuMorlpGhe+neTuiGg7ajyBvRFwkMHim1+\n/dlb+OFf+6sTt0uy6liMHQCsG1nQ09g49qr6CcRycriFg+HWBHoQa+koYuEArlui7LbKTcTDgZn9\n/F7xgHEycG6JC2gOh8Nxm9MnoCeZQPtVQI85dsZSXBcjxx42KjIPdHKO7f/VdNS8fO4mtk+gEyIO\n6m3b67y/dvMYz944hNqXtiLJiqOLeCwLehoBvVttYSkeRniI/WjZMpn2cgItCAQPLCdwY793Ar2W\niTpeL243f+1qAb/43z2KD17Ke30oHA6Hc99x+gT0mCluNh5Gq6OhKasuHtVkVJqdiSa60XAAkZCA\n44Z7toF+qq0OoqHAUME0CauZCCrNDiTZvRpsoDuBtitLOZ8QISuameNtF7vVFlSN4shiD6GUotlx\nNslilizo/Wqrx2vcT8E6gXYphWMYDywn+iwci5UBzQgFBHzyvWfNBUkOh8PhuMepEtCKqqEhq6Mn\n0Mw/7MMp9KQWDkB/HN5OoEdbZSaBeU63y+5OoRtt/eTJNgtHUn9N2e2DZvaWXYvNpdXRQCkcTeHI\nJ8IQg8JUWdC71RZWhvifgV5rh1tNhMO4vJzEbrVlerzZBJrD4XA4nEk5VQK6xpr8Rgi7TIw14PlL\nQKsaxX6tbUbUjSMbD3vqgZ7UbjIKVp28U5m+NnoeGrZ7oI02QhvLVNjrAQB2LTYXNq13coo7Sxb0\n3ogSFQDIREMIBfRJqdcTaLZIeGO/jlZHxVFDXqgMaA6Hw+F4z6kS0Ga02hgPNOC/NsJrezVIsorH\nz6Qnur/XaSKT2k1GwaZ+Oy5PoO1fImR13vY9H0f1tul9ti5aSob1yMkYO8DIgp5wAq2oGg7r7ZEW\nDkEg5s/J8wk0i7Lbq5se/NUFS+DgcDgcjrecLgHNotXGeKABbxMsBvHS3TIAPbt2ErwW0NXW5HaT\nYRRTERACbHs0gbYzBxqw18JhtW3sDhDQTk9x1zPRiZcI9QVKYGWEgAa6SRxeT6A3sjGIQQHX92vd\nCDtu4eBwOBzOFJwuAW1OoEc0EfogQ3kQL94tIRcPT9wqlo2FPbWhVJvKXBnQgN5GmE+Ipohxi0Zb\nASH2CblcPAyB2CygLbaN3Ur3+zILh9NJFhvZKI4a8kQLnizCblgGNKNg+KC9TOEAgIBAcKmgV3qz\nKfs6F9AcDofDmYLTJaCb49vxUtEQBOI/D/SLd0t48mxm4iitXDyMWluBrGgOHxlIDs8AACAASURB\nVNlg7JhAA8BaOuJ6lF29rSIeHl9YMykBgSAXt7dMhdk21jPRHgtH0zULB1vwHH9yM67Gm1HwyQQa\n0G0c1/fq2C43QQhQTI8W/xwOh8PhWDldAnqCeumAQJCJ+SsLuizJuHnQwLsntG8AXS+3F6UwlNKx\nlemTspaJejKBtivCjpFPhHFQs++52K22EBAIHl5LeWLhYAJ602Lj+Nxzt/HffuZZaH251JMKaDah\njnnsgQb0RcKtchM39usoJESIQe9FPYfD4XAWB+8/yWxk0nrpbCyEkuRdBFw/L23q/ud3n81M/DVM\nQB815JHLW05QbyvQ6HwthIzVdBRfunYASqlrRRZ1WbF9ka2Q1MtU7GK30sZyUsRaJoqvvnNk3t5w\nIYUDANYzvWUqL9wp4X/9whtQNYrbRw2zRhrQBXRQIGMTZD713rM4k43Ztrw5Dw8sJwEAz944xLml\nuMdHw+FwOP9/e3ceJdl91Qf8e2uv6q6q7up9m1UaaUaeEVpsybKQHAS2ExMvGIGMwxHYOYY4JyTh\nHHwISzCHY0xCIMFhizF2HEJsfAwBgR2MMTYS2NZmySNpZjSapae7Z3rfauvaf/njvVdLT/d0var3\n6tXr+X7O6TPVr5Z+9Su16tbt+7uX3GbfZaA9sneNZaLH2frh7V64sg6PAHdONh9A9+u13E48j2QT\n7QKbNd4XQrZQrn746YRMvmR5EDfYG7S0jd1iMoeRWAgjsRBS+VJ142OthMPeIHQ4GoTfK5hb38Jm\ntoif+uwL6NGD9peubjbc1gj2PXsM9BiNh/CeeyZtO2czjE4c69kixtnCjoiITNpfAfRWEdGQf883\n8r6Isx0stnthdgO3j8ZMZUWr7fgcKOGo1ppbUMJhtA/rZCeOTL5k+Ua2wd4AViwc560NJglhVK/N\nNco4jBKOHpsz0B6PYLwvjLn1LD78p9/BYjKHT//46xH0efDSXGMAvZS68RTCbnQwEan2pR5nCzsi\nIjJpXwXQqVxz0/ESEWeHkNSrVBRenNkwVb4B1AJoRzLQTWzWbNZYX+eHqaTzZctLOAZ7g8iXKtUe\n0+1a3MxhNB6q1hUv6hstt4qd2UQIaHXQf3NmEV9+ZREfftttuOdgAsfHYji9LQOtZcvdtQnP5/Xg\n8KBWusEWdkREZNa+CqCbnY7X3xPAeqZoWbawHa8tpZHKl5ru/2wwJiquOlnCYcUmQgfGeWslHNYG\noEaHCSuGqWTyJaTyJYzEQtXeyrUMdAlejyDgtf9Xd6IvjEKpgjffNoR/+eARAMCpyTheubrZsJFw\nYTO3Zw/obnSrXgfNAJqIiMzaXwH0VqmpoC7R40ehXEFG/3O4k16YWQcA3H3QXADt93oQC/kcyUBv\n6hloKzYRDkWD8HmkoxlorQuH9RlowJpe0EawPBoPYjTeGEBn8mVE/N6ObLi87/AAjo304jcevbNa\nFnVyIo5MoYxLKxkAWk12MldyXQkHANyij/RmD2giIjJrfwXQuWJTJRxObsDb7tsz6+iP+HFooLkB\nKvUGe4OWjo9uVq2Eo/0g1OsRjMRCHR3nnbZpEyEASzYSGuUaI7EQIgEfoiFfrYSjUEbE4uz5bt5z\nzyT+5t8/jIHeWnnGyUlt1PzLehlHsy3sutH3Hh/BGw4ncHSYXTiIiMic/RVAN9mbuLoBrysC6A3c\ndaC/pYzicCzYMGSjU4x+21YFoWPxkC2bCD/3zAw+8eTFhmOlcgX5UsX6DHRU+2/K0gy0HpSOxkK1\nEo5iGREHJ/ndMtSLkN+D03ONAbQbSzhOTsbx+Z94o6PrSURE7rS/AuhcqamNbf0OdrCot7lVxIWl\nNO42uYHQUB9YdVJyS8vg+iyqwx3rC9syjfB/fmMaf/StKw3HMnm9i4XFAXQiEoAIsGxBBrpWwhGq\n/rugj8veKpQQ9js39MPn9eDEWKyWgU41N8abiIhoP9k3AXS+VEY6X0J0jyEqgBbsAM5M8av3YnWA\nirn6Z8NILISlpHWt05qlbda0LgA1xnlb+TzypTIuLKUxv5FDuW7DW1ofRGL1JkKf14NEJIBlC0pq\nFjdziIZ81czoSCxULeHI5MuOj8I+NdmHl69tolxRtXKTuPsy0ERERK3aNwH089PaZrw7xuN73raa\ngc44O43w28YAlanWMtDDsRAK5Qo2OjxVcXOraEkLO8NYPIRCqWJpR5ELS2mUKgqlimooczEGklid\ngQaMmnRrMtD1JRGjsRCW03mUKwrZYrkjLexu5HUTcWQLZVxaTmMxmUPY70W0C6YLEhERdcq+CaD/\n/rVl+DyCNx4d2PO2sZAPXo84vonwhdkNHBuJtlxLvL3FWackrQ6g+4xWdtbVQZ+5lqxevlr3uGkb\nA+ihqFUBdL5avgFo2d1yRWElncdWwfohMGad0jcSvnR1E4upPEZiwY6NYSciIuoG+yaAfur8Cu45\n2N9UMCoi6I/4Ha+BPnMtWQ1GWmHUnXZ6I2Ey11y7wGbZ0Qv67HyqenluPVu9bGSgre7CAWgB9FLS\nmi4cI9sy0IDWbzlbcL6E4+hQL8J+L07PbV53rkRERDeDfRFAL6fyODOfxEPHhpq+T38k4HgGOrlV\nRKKn9c1XRuBiRdBmhpaBti4AtWMa4dn5JG4f1QZlXF2vPW61hMOGLO5oPISlVGPNtVnlisJyOn9d\nCQeg/aUhW3C+hMPrEdwxrm0kXEwxgCYiopvPvgign3ptGQDw0K0mAuiegKNt7AqlCgrlSlub2Yb1\nDHTHSzianPjYrIGeAAI+j2WdOJRSOLuQxF0H+jDYG8Tcen0Jh9aFw44M9HhfGMWyaquMY0WvdR5p\nKOGo/aUhWyg5noEGtDroV64lsbDpvjHeRERE7doXAfST55cx0BPAHeOxpu+TiASw7mAJhxWb2YI+\nL/oj/o6WcFQqCul8c+0CmyUiGI+HLKuBnt/MYSNbxPGxGCb6ww010LV1tz4IndAz6VfbeB4Lm9f3\nVR7s0aY1XtvIIVesdEXf4lOTcWwVy8iXKsxAExHRTcf1AXSlovDUayt48NbB6rjhZmgZaOe6cFi1\nmW0kFsJiB0s4UrkSlLJmjHe9sbh1vaDPzmsbCE+MxTDZH96WgbZvE+G4BZshtw9RAQCPRzAcDeLK\nqjY+uxsy0CcnarX7DKCJiOhm4/oA+sx8EquZgqnyDQBI9PixkS10vIeyIVOwZjObFkB3LgNtTCG0\nsg80oNVBz1uUgTYC6NvHYpjs0zLQFb0uOZMvwecRBH3W/6dvRQBdHY0dbyyLGImHcGm5ewLoI0O9\n1fMYZQ9oIiK6ybg+gH5Sr3/+7mODpu7XHwmgVFFI6RnJTrOqH/FIh8d5b27pAbTFGejxeBiLqXxb\nG/AMZ+dTOJCIoDfow2R/GIVSpVqXnM6X0BP02dJ2LRbyozfoa6ubyMJmDj6PYHDb5tLRWAjTegY6\n3AUlHMZGQgAYiTKAJiKim4v7A+jzyzg+FsOwyTfxhD5MxalOHLXNbO1lE0djIayk8yiVK1ac1p5q\nGWiLSzj6tF7HS6n2PwycmU/i+JjWgWOiX8sKz+lZ4XS+ZMsGQsN4X3u13AvJHIajwevKkUZiIeRL\n2mvc0wUZaECbSOiR2mZWIiKim4WrA+hMvoTnr6zjIZPZZ0DLQANwrBOHVRno4VgIFQWsWDBCuhnJ\nLe28rWxjB1jXCzpbKGF6NYMTY1qN7kRfBACqddCZfMmWDYSG8b4wrrXRjm8xmdtxLHZ9mYTTbewM\nP/nwUXzy8XsR8nfH+RAREXWKqwPob15cRbGsTNc/A7Vx3k514khb1I/Y2MDVqTKOpF7CYfkmQot6\nQZ9bSEEpXJeBvloNoMu2bCA0jPeF2y7hGN1hU179sW7owgFog2O+5/YRp0+DiIio41wdQD/52jLC\nfi/uPdRv+r6JagbamU4cVk3E6/Q472oJhw1dOABgvs0MtLGB8PiYVp/bG/ShL+KvTiO0u4Rjoi+M\ntUwBW4VyS/dfTOZ37GpRXybRDZsIiYiIbmbuDqDPL+P+IwkEfeYDiv4eLQB0qgbayk2EALDUwQy0\nCNBrcRY0FvKhJ+Btq/wB0MajR0Pa5kHDZF0v6Ey+ZMsUQsO4nklv5Xmk8yWk86Udu1rUZ6C7pYSD\niIjoZuXaADqTL2F6NYt7DyVaun9v0IeAz9PW1Lh2pPNlBLweBNpspzbQG4TXIx3rBZ3MlRAN+kz1\n3G6GiGCsL2xJBvr4WKyhy8ZEX3hbDbR9AXQ7mfSdhqgY6oNqOz8AEBER0d5cG0CncloGty/SWimB\niGA0Fur4GGyDVZvZvB7BUG+wcyUcW0XLyzcME33htqb4VSoK5xZSODHWOJFysj+Cq+tbUErpJRz2\nZXAn2ugFXe0BvUMAHQn4ENV7bzMDTURE5CzXBtDpvFaLG22jndpoLGTZ9DuzrMyEdrIX9OZW0fIW\ndgZtamC25fvPrGWRLZSrGwgNE31hbBXLWMsUkCnYu4lwJBaCSGvjvKsZ6F0GkxiZadZAExEROcu1\nAXRSz0BH2wiGRuOdneJXz8rNbCOxEJY6VsJRtLwDh2GyP4L1bLHaocSsM9UR3vGG40Y99MXlDMoV\nZWsAHfB5MBwNtpSB3mmMd73ReAh+r8Dvde2vLRER0b7g2nfitBFAtzFSeiyuZaCdGOedKViZge5c\nKUpyq2R5D2jDVEIfetJiFvrsfBJej+DWkd6G40Yru1cXUwDa73yyl1Z7QS8mc4iFfLuWaIzFQ7YG\n/0RERNQc9wbQRhu4NgLokVgIhVIF69nOt7JLW9iPeCQWxOZWEblia63TzEjm7Czh0IeerLVWB31u\nIYXDgz3XDfYwHvfVBS1DbXsAHW+tF/Tc+lb1XHfykw8fxW88emc7p0ZEREQWcG0AndL7EbcTDI3p\ntaYLDtRBZyzczNbJYSp2biI0Si1mW8xAz61v4WDi+gA0HvYjGvTh/EIaQPutA/dijPM2+5eNK6sZ\nHNjh/A1HhnrxyHEOLiEiInKaiwNoo4SjjU2ERgCdbK/3cCus7EdcC6DtrYMulivIFMq2ZaAHegII\n+73VlnNmLWxuVScabjfRH8a5TmWg+8LIlyqmxsRXKgqz61s4OLB7AE1ERETdwbUBdNqCSX5GAO1E\nJ460pV04OpOBNj60xG2qgRaRljtxbBXKWM8Wq32Yt5vsD1c3nlrRPvBGxqut7Jp/PRZTORRKFUzd\nIANNRERE3cG1AXQqV0Ik4IW3jYEeQ71BeARY7HAArZTSSzisCURHOxRAJ7fsGeNdb7I/jNkWaqD3\n6mBh9GcG7M9AGz/LTCu7mVXtQ8ONSjiIiIioO7g2gE7nSm114AAAn9eD4Wjne0HnihVUlHW1uLGw\nD0Gfx/IA+onvXMPXX12qfp/U687tKuEAgKlEpKUM9Lze9WK3Eo76zXl210AbtfVmWtnNrGnPmSUc\nRERE3c+9AbRFGdyReOenEabyxgZIa0oJRAQjsZDlNdAf+9JZfPgLp1EoVQBoLewA+zPQyVwJm1vm\nOqMYo7N3K+EwWtkB9gfQiZ4Agj6P6QDaI7XyDyIiIuperg2gk7kiei3IhI7FQh3vwpHJa+3mrAzk\nrB5Lni2UML+Zw1Iqjy++dA0AqkGtXX2ggbpWdiaz0HuVcEzWB9A2T/ITEUz0hU39ZWNmLYvxvjCH\npBAREbmAa9+t0/kSYm2WcADaRsLOB9DGZjbrAtHhWBBLFgbQ0ytaAOsR4JNPXYZSqlrCYdckQgCY\nqgbQ5uqg5ze30B/x7zqExKhLDvk98HUgSB3vC5urgV7LsnyDiIjIJVwbQKdy1pRwjMZDSOVLLY+P\nboUVHUS2MzLQVk1VnF7NAAB+5L4DeOVaEk9fXqttIrSxBrraC3rNXAZ6fiOH0V3KNwCtrCLs99q+\ngdBg9IJu1sxqlhsIiYiIXMK1AXTaogDaiWEqGRsC6JFYCLlipdqqrV2XV7QA+qe/7zb0R/z4w3+4\njGSuCK9HELGxBKIv4kdv0NdCBjpXfS13IiKY6A93bBT2WDyMpVQe+dLe0yHT+RJWMwUcSPR04MyI\niIioXe4NoPOltoaoGIya2U4G0GmbSjgAWFbGcWk5g9FYCImeAP7F/Qfxt2cXcXpuE7GQDyKttw7c\nS60XtLkAeiF54wAaAG4Z6sVwNNjO6TXNKBlZ3Kxt7NzMFqvt6uoZ2XZmoImIiNzBlQF0uaK0LhwW\n1UADtTZonWBsIrS6hAOAZRsJL6+kcWhQC+h+9P6D8HkET722YmsHDoPZYSq5YhlrmcKeAfRH3/06\n/Pf33t3u6TVlfFsv6FyxjPf+wbfw6P/4xnVlNlfYA5qIiMhVXBlAZwp6OzULAuhOTfGrV9tEaF0p\nhNXjvC+vZHB4sBcAMBwL4R13TgCwdwOhYbI/grn1rabruY2/HtyoBhoABnqD1Q9Mdhvva/xg9rEv\nncWZ+SQWk3lMb8tCVzPQ3ERIRETkCq4MoNM562qIQ34v+iP+jg5TqZZwBKytgQas+SCwkS1gPVvE\nkcFaTe4HHjwMwN4NhIbJ/jDS+eZ7QRuv3XiHguNm1MZ5b+HLryzgM9+8gkduHwYAPDu91nDbK2sZ\nxMP+jnw4ISIiova5MoBOGQG0BRloQMtcdjoDHQl44WljDPl24YAXsZDPkudhbCA8XBdAnxiP4dF7\nJvHALQNtP/5ejF7QzY70NrK8ncouNyPk9yLRE8Cz0+v48BdO4+REHL/zvrsRD/vx/PR6w21n1rZY\nvkFEROQinWlJYLG0PsnPik2EgNaJo5MZ6EyhZEs3iLF42FTrtN0YAfShwcauEL/+6J1tP3YzphJa\n9nZuPYuTk/E9b2+8drtNIXTKeF8If39+Gb1BH377R+5CyO/FvQf78eyVxgz07FoWJ8ZjDp0lERER\nmeXuDLRFQehIh6cRpvNlW/oRTyUiTWdtb+TySgYecW5TWzUD3eRGwoXNHPpuMETFKeN6QP+rP3AS\nBwe0DyP3Hkrg0nIGq2mtVr1cUZhbZw9oIiIiN3F1AB21qIRjLB7CaqbQVM9eK2TyJUs3EBqmEmHM\nrmfbHqZyaSWDqUQEAZ8z/3nEw37EQs33gp7f3Np1hLeT3v/gYfzyO+7AO+4crx6791A/AOD5K1oZ\nx/zmFoplxQCaiIjIRVwZQBub8KwKoI3a2SWLOljsJZ0vWbqB0DDVH0G2UMZqptDW40yvZBrqn51g\ndOJoxvxmrrppr5vcf2QAjz9wqOHYyYk4Al4PntMD6Bm9A8dBBtBERESu4c4A2uISDiN72ak66Eze\nmimK2xlZTLNjsOsppfQWdk4H0OHrnsdmtoj1HT4cLGzmumoD4Y2E/F6cmozjOb0ThzFYZYoBNBER\nkWu4MoBO5YoQsa4NXHWcd4c6cWglHPbUQAPArMkpfvWWUnlkC2XHA+ipRGMv6HypjPf8/jfwwT96\nruF2uaKWcR/rwhKO3dxzqB8vXd1ErljGzFoWPo/sOQSGiIiIuoc7A+h8Cb0Bn2Vt4Izs5UKHphGm\n82VbAujJfq2MoZ0M9KXl61vYOWGyP4wtfcIgAPze1y/iwlIaz19Zb+gPbbTtG+vCEo7dvP5gAsWy\nwndmNzCzlsVkfxg+ryt/FYmIiG5KrnzXTuesGeNtiIb86Al4O1zCYf0mwp6gD4O9gbYC6J16QDuh\n1oljCxeWUvjdr13EsZFeVBTw9KXV6u1qLezck8G956C2kfC5K+uYWcuyfIOIiMhlXBlAp3IlyzYQ\nGkbjoY4MUylXFLaK9mSgAS3wbLb9206mVzMI+DzVFmxOMXpBz6xl8XN/9jLCAS8+8/43IOT34BsX\n6wPo7huispf+ngBuGe7Fc9NrmFnL4iBHeBMREbmKKwPotA2b8Mbi4Y5koDMFazdAbjeViFQ7O7Ti\n0nIGhwYilk5JbIWRgf7dr13AM9Nr+Pm3H8dYPIzXH0rgGxdXqrdzYwYaAF5/qB9PX17DRrbIFnZE\nREQu48oAOpUvodeiKYSGTg1Tyegt+OzKQB9IhHFtI4dSudLS/S+vpB0v3wC0Dxj9ET/OLaRw/5EE\nHr1nEgDwplsGcX4xjaWU9lrNb+QQD/sRsaEtoJ3uPZhAtqD1HWcATURE5C7uDKBzRctLOMbiISyl\n8ihX2htCshe7A+ip/gjKFdVSNr1UrmBmLYvDg702nJl5k/3aMJdfffdJiGgZ8QeODgAAvqmXccxv\n5lyXfQZqA1UA4EDC+Q8sRERE1Ly2AmgR6RORL4jIORE5KyJvFJGEiHxFRF7T/+2vu/1/EJELIvKq\niLy11Z+bzpUQtTgAHYmHUK4orKTtHaaSzmtZRzs2EQL1rezMl3Fc3dCm4h3pggw0APz0W47h44/d\nhSNDtYD+jvE4YiEfvnFBC6AXkluuDKAPJCIYigYB1Oq9iYiIyB3azUD/FoC/VkrdDuBOAGcB/CyA\nryqlbgXwVf17iMgJAI8BuAPA2wD8roi0FEXaUgPdoWEq1Qy0TSUH7QxTMTpwHOqSAPqf3DaMt71u\ntOGY1yN449EB/KNeBz2/kcOowxseWyEieMPhBIaiQUQtLkciIiIie7UcQItIHMBDAP4QAJRSBaXU\nBoB3AviMfrPPAHiXfvmdAD6nlMorpS4DuADgDWZ/bqlcQbZQtjzoqPWCti6AvrqxVQ2YDWmbSzjG\n4iF4PYLZNfM9rbulhd1eHjg6iDm9vd1qpuDKDDQA/MLbj+MPH7/X6dMgIiIik9rJQB8GsAzg0yLy\ngoh8UkR6AIwopeb12ywAGNEvTwCYrbv/nH7sOiLyQRF5TkSeW15ebrguY5RA2NDGDrBumEqxXMHb\nP/4UPv53rzUcNwJqu7pw+LwejMVDLZVwXF7JIKr3ku5mb7pFq4P+s29fBeC+DhyGsXgYpyb7nD4N\nIiIiMqmdANoH4G4Av6eUugtABnq5hkFpc5hN78pTSn1CKXWvUureoaGhhutSeW0KndU10IlIAAGf\nB1c3rAmgX766iY1sEa8tphuO272JENDKOFppZXd5JYPDQz3VDXvd6uhQL4ajQfzfF4wA2n0lHERE\nRORe7QTQcwDmlFJP699/AVpAvSgiYwCg/7ukX38VwFTd/Sf1Y6akcloAanUXDo9HcDARwZXV1nso\n13v68hoAXBfIpmzOQANaJ45WSzgODnR3+Qag1Q8/cHSgWq/upiEqRERE5H4tB9BKqQUAsyJym37o\nEQBnADwB4HH92OMA/kK//ASAx0QkKCKHAdwK4BmzP9eoIba6hAMADg70YHo1Y8ljGeOm59az0BLx\nmky+BI8AIb99HQQPDESwks5jS+8z3IxiuYJrG1s46JKexA/cMli97NYSDiIiInKndqPQfwPgj0Uk\nAOASgB+HFpR/XkQ+AOAKgB8CAKXUKyLyeWhBdgnAv1ZKNR/h6dI5+zK4hwcjeOq1ZVQqqq1JfOWK\nwnPT6wj5PcgVK1hO5zEc1YK8TF4b421nmcRkv1bSMLuexbGRaFP3ubaxhYrSgm83MPpBx0I+W8th\niIiIiLZrK/JQSr0IYKc2Ao/scvuPAvhoOz8zmdNroG1o/XVosAf5UgULyRzG+1qvqz1zLYlUvoR3\nfdc4/vzFa5hdy1YDaDta8G03VdfKrtkA2ihdcctUvMn+CA4ORBDy2dNPm4iIiGg3rptEaJRwWF0D\nDQCH9Prfdss4nr6slW/84D1ayXd9PXImX7I9Y9pKL2ijVvugSzLQAPDz/+w4/u333ur0aRAREdFN\nxnV/+07btIkQqA0QmV7J4oGjrT/O05fXcHAgUh3XXB/IpjsQQA/0BBD2ezFjYiPh7FoWAa8HI1H3\n1BO/5Y7RvW9EREREZDHXZaBTOW0TXthv/Z/ux2IhBHyetjLQlYrCs9NruO9wAiG/F0PRYEMnjky+\nZNsYb4OIYCoRNtUL+spqFpOJcFu130REREQ3g64PoPOlSsP3Rg2xHZvwjFZ20yutB9CvLqawkS3i\nvsPaJrcDiUhDIJvJl20b413vQCJiuoTDLR04iIiIiJzU9QF0cqvY8H0qV7JlA6Gh3VZ2Rvu6+44k\nAABT/eGGGuhObCIEtE12s2uNLfR2o5TC7FrWNRsIiYiIiJzU9QF0rtTY6S6VK9pS/2w4PKgNU6lU\nTA9QBKDVP0/0hTHZrwWjU4kI5je3UCxrmfRMwf4aaOPnZgplrGdrH0C+/uoSLiylrrvteraIVL5U\n7d5BRERERLvr+gA6X9y5hMMu9a3szFJK4ZnLa9XsM6AFshWl9VkGOtOFA2jsxKGUwm9+5Tx+7NPP\n4lf+6ux1t6114Oj+KYRERERETuv6Lhz5UgVKqWrNczpfwkBPwLafV9/Kzmwv6AtLaaxmCrhfr38G\ntLHagNbKbjQeQrGsbN9ECABTCe3cp1cz+Nyzs/jsMzOIhnx46epmw3oCtQCaJRxEREREe+v6DHRF\nKSyl8tXvU7kSem2sga5vZWfWty6vAUBDBtqY7De7nkUmr5WjdKSEQw/cf+mJV/DZZ2bwoTcfxc+8\n9TasZQq4ttmYXZ/Ra74ZQBMRERHtresDaEDL7BpSOXtLOIxWdlda2Ej49KVVjMZCDYHoaCwEv1cw\ns5ZFRh8C04kAuifow0BPAJtbRXzkn5/Ah992O05N9gEAXprbaLjtzFoWQ9EgwgFO9SMiIiLaS9eX\ncADAxeU03nTLIAAgnS8iZuMmQqOV3eUWWtk9O72G+48MNJRHeD2C8b4wZtey1SmKnejCAQA/+09v\nR38kgO89MQIAuH00Cp9HcHpuE2973Vj1djPswEFERETUtK4PoD0i1Qx0sVxBrlixPQBtpZXdRraA\nxWQed4zHrrtO6wW91dEMNAA8eu9Uw/chvxfHRqJ46epmw/GZ1SzuPzIAIiIiItpb15dwBH0eXFzW\nAmhjjHevjRlooLVWdheXtYD7yGDvddcZPZlrGWjnSiVOTsSrGwkBIF8qYz6ZYws7IiIioiZ1fwDt\n91Qz0EYAaucgFaC1VnaX9CD/yND1reCmEmGsZQrVzZCdykDv5ORkHBvZEJnFhwAADHBJREFUIubW\ntbZ6c+tbUIobCImIiIia1fUBdMjnxWIyj1SuiGROGwpidwlHfSu7ek+eX8biLkH1pZUMfB7ZMZNr\nBKfn5rUhJp0Y5b2bkxNxAKiWcdR6QDOAJiIiImpG1wfQQZ92iheXM9USDjs3EQI7t7K7sJTC459+\nBr/ztQs73ufSchoHBiLwe69fUqOl3LmFJIDObSLcye1jUfi9Ug2gZ9kDmoiIiMiU7g+g/Vq98MWl\ndK2G2OYAeqdWdr/9dxegFPDKteSO97m0nNmx/hmoBadn57X7OlnCEfTpGwnntAD6ymoWIb8HQ9Gg\nY+dERERE5CZdH0AHfB74PIILy2mkcp1pA7e9ld2l5TSe+M41BH0enJtPXre5sFxRuLKaxdEd6p8B\noC/iR2/Qh/VsEQGvBwGfs8t+arK2kdBoYVffeo+IiIiIdtf1AbRAK6m4uJRGqkObCIHGVna/87WL\nCPg8+KlHbkWmUMbseuOUwrn1LArlyo4bCAFARDDZr43W7nGwA4fhdRNxbG4VMbu2hVn2gCYiIiIy\npesDaAA4OtSDC8vpag101OYSDqDWym56JYM/f/Eq3nffQXz3rdowlzPbyjguGS3shnYu4QBqZRxO\nlm8YTk1oEwlPX93QM9A7B/5EREREdD2XBNC9mFnNYj1bgM8j1Y2FdjJa2f3HJ16B1yP4iYeO4NhI\nFB6p1TIbjD7VR28QQBvdOZzcQGg4NtqLgNeDr51bRrZQxoFE2OlTIiIiInIN56O5Jtwy3ItSReHl\nq5uIhnwdqdc1Wtk9eX4ZP/bAIQzHQgC0LPMZvR2d4dJKBn0RPxI9gV0fb0ov4eiGADro8+K20Sj+\n5swCAOAAW9gRERERNc01GWgAOD23aXsHDoPRyi7g9eAnHj5SPX58LHZ9BnopjSODNy6DMILUbijh\nALSBKsamTJZwEBERETXPHQH0sBZAp/Ml9Abt30AIaK3s+iN+/Mh9BzAWr5U4nBiL4erGFjazxeqx\nSyuZG9Y/A7Ve0N2QgQZqA1VEUN3gSERERER7645obg+9QR9GYyEsJHMd2UAIaK3svvLTD6Mv3Biw\nHx+LAgDOLiRx/5EBpHJFLKfyu3bgMEz2Gxlo57twALUAejQWQsjfHedERERE5AauyEADWh00AEQ7\nmMEd7A3Ct22y4ImxGIDaRsJqB45dhqgYwgEv3nhkoBq4Ou3YSBQBr2fH0eNEREREtDtXZKABrZXd\nP1xY6VgN9G6GokEM9ARqAfSK0YFj7zriz37wflvPzYyAz4P33DNZ/WBCRERERM1xTQBdzUA7HECL\nCE6Mx3CmLgPtEXd2svjYD5x0+hSIiIiIXMc1JRxGJ45ObSK8keNjMZxfTKNUruDScgZTiQiCPtYR\nExEREd0MXBNAGxnoWNj5pPnxsSgKpQourWRwcXnvFnZEREREtH+4JoAejoXwX3/4Tvzg3ZNOnwqO\n6xsJX7m2ienVvVvYEREREdH+4Xw614R33+V88Axo5SQBrwdfPbuEXLGyZws7IiIiIto/XJOB7iZ+\nrwe3jvTiq2eXANTqs4mIiIho/2MA3aLjYzFsFcsAwAw0ERER0U2EAXSLjDroaNCHod6gw2dDRERE\nRJ3CALpFxkjvI0M9EBGHz4aIiIiIOoUBdIuMkd7swEFERER0c3FVF45u0hcJ4AMPHsabbxty+lSI\niIiIqIMYQLfhF7//hNOnQEREREQdxhIOIiIiIiITGEATEREREZnAAJqIiIiIyAQG0EREREREJjCA\nJiIiIiIygQE0EREREZEJDKCJiIiIiExgAE1EREREZAIDaCIiIiIiExhAExERERGZwACaiIiIiMgE\nBtBERERERCYwgCYiIiIiMoEBNBERERGRCQygiYiIiIhMYABNRERERGQCA2giIiIiIhMYQBMRERER\nmSBKKafP4YZEZBPAa06fRxsOAJhx+iTaEAew6fRJtIHr7yyuv/P4GjiL6+8srr+z3Lb+B5VSQ83c\n0A0B9CeUUh90+jxaJSLLzb4Y3Yjr7yyuv7Pcvv4AXwOncf2dxfV3ltvX/0bcUMLxl06fQJs2nD6B\nNnH9ncX1d5bb1x/ga+A0rr+zuP7Ocvv676rrA2illNv/43Hzn164/g7j+jtrH6w/wNfAaVx/Z3H9\nneXq9b+Rrg+g94FPOH0CNzmuv7O4/s7ja+Asrr+zuP7O2rfr3/U10ERERERE3YQZaCIiIiIiExhA\nExERERGZwADaJBH5lIgsicjLdcfuFJFvishLIvKXIhKru+6Uft0r+vUh/fhfi8h39OO/LyJeJ56P\n21i4/l8XkVdF5EX9a9iJ5+NGVrwGIhKtW/sXRWRFRP6bM8/IXSz8HfhhETmtH/9PTjwXNzKz/iLy\nvm3/nVdE5Lv06z4qIrMiknbqubiRhevP9+AWWfgauPt9WCnFLxNfAB4CcDeAl+uOPQvgYf3y+wH8\nin7ZB+A0gDv17wcAePXLMf1fAfCnAB5z+rm54cvC9f86gHudfj5u/LLqNdj2mM8DeMjp5+aGLyvW\nX/93BsCQfvwzAB5x+rm54cvM+m+730kAF+u+vx/AGIC008/JTV8Wrj/fg51/DVz9PswMtElKqScB\nrG07fAzAk/rlrwB4j375LQBOK6W+o993VSlV1i8n9dv4AAQAcDdnE6xaf2qd1a+BiBwDMAzgKdtO\neh+xaP2PAHhNKbWs3+5v6+5DN2By/eu9F8Dn6h7nW0qpeVtOch+zcP35Htwiq14Dt2MAbY1XALxT\nv/wogCn98jEASkS+LCLfFpEP199JRL4MYAlACsAXOnWy+1BL6w/gM/qfjX5RRKRTJ7tPtfoaAMBj\nAP5E6SkJaonZ9b8A4DYROSQiPgDvqrsPmbfb+tf7YQCf7dgZ3VxaWn++B1uq1d8B174PM4C2xvsB\nfEhEngcQBVDQj/sAPAjgffq/7xaRR4w7KaXeCu1PeEEA39PRM95fWln/9yml7gDw3frXj3b2lPed\nln4HdI+BgUW7TK2/UmodwL8C8CfQMv/TAPjXmdbttv4AABG5D0BWKfXyTnemtrW0/nwPtlQrr4Gr\n34cZQFtAKXVOKfUWpdQ90AKBi/pVcwCeVEqtKKWyAL4ErW6o/r45AH+B2ic3MqmV9VdKXdX/TQH4\nPwDe0Pkz3z9a/R0QkTsB+JRSz3f8pPeRFn8H/lIpdZ9S6o0AXgVw3olz3w9usP4Gfki0UTvrz/dg\na7TyGrj9fZgBtAWMnaMi4gHwCwB+X7/qywBOikhE/zPpwwDOiEiviIzp9/EBeDuAc50/8/2hhfX3\nicigfh8/gO8HwMxQG8y+BnV3fS8YWLStlfWvu08/gA8B+GSnz3u/uMH6G8d+CPuo9rPbmF1/vgdb\nr4XXwPXvwwygTRKRzwL4JrT6wTkR+QCA94rIeWi/gNcAfBoA9D+T/ia03akvAvi2UuqLAHoAPCEi\np/XjS6j7j412Z9H6BwF8uW79rwL4g44/GZey6DUw/BAYQJti4fr/loicAfCPAH5NKcUMdBPMrL/u\nIQCzSqlL2x7nP4vIHICI/jgf6cwzcDeL1p/vwW2w6DVw/fswR3kTEREREZnADDQRERERkQkMoImI\niIiITGAATURERERkAgNoIiIiIiITGEATEREREZnAAJqIqEuJiBKR/133vU9ElkXkr1p8vD4R+VDd\n929u9bGIiG5mDKCJiLpXBsDrRCSsf/990PqltqoP2tAUIiJqAwNoIqLu9iVok9KAbZMbRSQhIn8u\nIqdF5Fsicko//hER+ZSIfF1ELonIT+l3+TUAR0XkRRH5df1Yr4h8QUTOicgfi4h06okREbkVA2gi\nou72OQCPiUgIwCkAT9dd98sAXlBKnQLwcwD+V911twN4K4A3APglfVzuzwK4qJT6LqXUz+i3uwvA\nvwNwAsARAG+y88kQEe0HDKCJiLqYUuo0gEPQss9f2nb1gwD+SL/d3wEYEJGYft0XlVJ5pdQKtFHF\nI7v8iGeUUnNKqQq0kbqHrH0GRET7j8/pEyAioj09AeC/AHgzgIEm75Ovu1zG7v+/b/Z2RESkYwaa\niKj7fQrALyulXtp2/CkA7wO0jhoAVpRSyRs8TgpA1JYzJCK6iTDTQETU5ZRScwA+vsNVHwHwKRE5\nDSAL4PE9HmdVRP5RRF4G8P8AfNHqcyUiuhmIUsrpcyAiIiIicg2WcBARERERmcAAmoiIiIjIBAbQ\nREREREQmMIAmIiIiIjKBATQRERERkQkMoImIiIiITGAATURERERkwv8HFf61U9F63rkAAAAASUVO\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11e9f2160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df['forecast'] = results.predict(start = 150, end= 168, dynamic= True) \n",
"df[['Milk in pounds per cow','forecast']].plot(figsize=(12,8))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Forecasting\n",
"This requires more time periods, so let's create them with pandas onto our original dataframe!"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Milk in pounds per cow</th>\n",
" <th>Milk First Difference</th>\n",
" <th>Milk Second Difference</th>\n",
" <th>Seasonal Difference</th>\n",
" <th>Seasonal First Difference</th>\n",
" <th>forecast</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Month</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>1975-08-01</th>\n",
" <td>858.0</td>\n",
" <td>-38.0</td>\n",
" <td>3.0</td>\n",
" <td>-9.0</td>\n",
" <td>3.0</td>\n",
" <td>879.668789</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1975-09-01</th>\n",
" <td>817.0</td>\n",
" <td>-41.0</td>\n",
" <td>-3.0</td>\n",
" <td>2.0</td>\n",
" <td>11.0</td>\n",
" <td>832.328247</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1975-10-01</th>\n",
" <td>827.0</td>\n",
" <td>10.0</td>\n",
" <td>51.0</td>\n",
" <td>15.0</td>\n",
" <td>13.0</td>\n",
" <td>837.721945</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1975-11-01</th>\n",
" <td>797.0</td>\n",
" <td>-30.0</td>\n",
" <td>-40.0</td>\n",
" <td>24.0</td>\n",
" <td>9.0</td>\n",
" <td>802.452364</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1975-12-01</th>\n",
" <td>843.0</td>\n",
" <td>46.0</td>\n",
" <td>76.0</td>\n",
" <td>30.0</td>\n",
" <td>6.0</td>\n",
" <td>842.499524</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Milk in pounds per cow Milk First Difference \\\n",
"Month \n",
"1975-08-01 858.0 -38.0 \n",
"1975-09-01 817.0 -41.0 \n",
"1975-10-01 827.0 10.0 \n",
"1975-11-01 797.0 -30.0 \n",
"1975-12-01 843.0 46.0 \n",
"\n",
" Milk Second Difference Seasonal Difference \\\n",
"Month \n",
"1975-08-01 3.0 -9.0 \n",
"1975-09-01 -3.0 2.0 \n",
"1975-10-01 51.0 15.0 \n",
"1975-11-01 -40.0 24.0 \n",
"1975-12-01 76.0 30.0 \n",
"\n",
" Seasonal First Difference forecast \n",
"Month \n",
"1975-08-01 3.0 879.668789 \n",
"1975-09-01 11.0 832.328247 \n",
"1975-10-01 13.0 837.721945 \n",
"1975-11-01 9.0 802.452364 \n",
"1975-12-01 6.0 842.499524 "
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.tail()"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# https://pandas.pydata.org/pandas-docs/stable/timeseries.html\n",
"# Alternatives \n",
"# pd.date_range(df.index[-1],periods=12,freq='M')"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from pandas.tseries.offsets import DateOffset"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"future_dates = [df.index[-1] + DateOffset(months=x) for x in range(0,24) ]"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Timestamp('1975-12-01 00:00:00'),\n",
" Timestamp('1976-01-01 00:00:00'),\n",
" Timestamp('1976-02-01 00:00:00'),\n",
" Timestamp('1976-03-01 00:00:00'),\n",
" Timestamp('1976-04-01 00:00:00'),\n",
" Timestamp('1976-05-01 00:00:00'),\n",
" Timestamp('1976-06-01 00:00:00'),\n",
" Timestamp('1976-07-01 00:00:00'),\n",
" Timestamp('1976-08-01 00:00:00'),\n",
" Timestamp('1976-09-01 00:00:00'),\n",
" Timestamp('1976-10-01 00:00:00'),\n",
" Timestamp('1976-11-01 00:00:00'),\n",
" Timestamp('1976-12-01 00:00:00'),\n",
" Timestamp('1977-01-01 00:00:00'),\n",
" Timestamp('1977-02-01 00:00:00'),\n",
" Timestamp('1977-03-01 00:00:00'),\n",
" Timestamp('1977-04-01 00:00:00'),\n",
" Timestamp('1977-05-01 00:00:00'),\n",
" Timestamp('1977-06-01 00:00:00'),\n",
" Timestamp('1977-07-01 00:00:00'),\n",
" Timestamp('1977-08-01 00:00:00'),\n",
" Timestamp('1977-09-01 00:00:00'),\n",
" Timestamp('1977-10-01 00:00:00'),\n",
" Timestamp('1977-11-01 00:00:00')]"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"future_dates"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"future_dates_df = pd.DataFrame(index=future_dates[1:],columns=df.columns)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"future_df = pd.concat([df,future_dates_df])"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Milk in pounds per cow</th>\n",
" <th>Milk First Difference</th>\n",
" <th>Milk Second Difference</th>\n",
" <th>Seasonal Difference</th>\n",
" <th>Seasonal First Difference</th>\n",
" <th>forecast</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1962-01-01</th>\n",
" <td>589.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-02-01</th>\n",
" <td>561.0</td>\n",
" <td>-28.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-03-01</th>\n",
" <td>640.0</td>\n",
" <td>79.0</td>\n",
" <td>107.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-04-01</th>\n",
" <td>656.0</td>\n",
" <td>16.0</td>\n",
" <td>-63.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1962-05-01</th>\n",
" <td>727.0</td>\n",
" <td>71.0</td>\n",
" <td>55.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Milk in pounds per cow Milk First Difference \\\n",
"1962-01-01 589.0 NaN \n",
"1962-02-01 561.0 -28.0 \n",
"1962-03-01 640.0 79.0 \n",
"1962-04-01 656.0 16.0 \n",
"1962-05-01 727.0 71.0 \n",
"\n",
" Milk Second Difference Seasonal Difference \\\n",
"1962-01-01 NaN NaN \n",
"1962-02-01 NaN NaN \n",
"1962-03-01 107.0 NaN \n",
"1962-04-01 -63.0 NaN \n",
"1962-05-01 55.0 NaN \n",
"\n",
" Seasonal First Difference forecast \n",
"1962-01-01 NaN NaN \n",
"1962-02-01 NaN NaN \n",
"1962-03-01 NaN NaN \n",
"1962-04-01 NaN NaN \n",
"1962-05-01 NaN NaN "
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"future_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Milk in pounds per cow</th>\n",
" <th>Milk First Difference</th>\n",
" <th>Milk Second Difference</th>\n",
" <th>Seasonal Difference</th>\n",
" <th>Seasonal First Difference</th>\n",
" <th>forecast</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1977-07-01</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1977-08-01</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1977-09-01</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1977-10-01</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1977-11-01</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Milk in pounds per cow Milk First Difference \\\n",
"1977-07-01 NaN NaN \n",
"1977-08-01 NaN NaN \n",
"1977-09-01 NaN NaN \n",
"1977-10-01 NaN NaN \n",
"1977-11-01 NaN NaN \n",
"\n",
" Milk Second Difference Seasonal Difference \\\n",
"1977-07-01 NaN NaN \n",
"1977-08-01 NaN NaN \n",
"1977-09-01 NaN NaN \n",
"1977-10-01 NaN NaN \n",
"1977-11-01 NaN NaN \n",
"\n",
" Seasonal First Difference forecast \n",
"1977-07-01 NaN NaN \n",
"1977-08-01 NaN NaN \n",
"1977-09-01 NaN NaN \n",
"1977-10-01 NaN NaN \n",
"1977-11-01 NaN NaN "
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"future_df.tail()"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a11ed43fd0>"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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bwJtqrv+BpmkFTdOeBfYAFymKMgKkNE37reE6f6fmPoIgCIIgCILbjO+Bg79z+xTNyach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k7mp1czcTQkBd2e85ntWbjpQOeTMSRjEWxXl3egrQ0cwOCw22FTNnPaTruqJ7GWS2Cv3oWmaXNv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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a11eace390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"future_df['forecast'] = results.predict(start = 168, end = 188, dynamic= True) \n",
"future_df[['Milk in pounds per cow', 'forecast']].plot(figsize=(12, 8)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not bad! Pretty cool in fact! I hope this helped you see the potential for ARIMA models, unfortunately a lot of financial data won't follow this sort of behaviour, in fact it will often follow something indicating brownian motion, what is that you ask? Well head on over to the next video section and we'll find out!\n",
"\n",
"# Great Job!"
]
}
],
"metadata": {
"anaconda-cloud": {},
"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": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 1
}