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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# A practical guide to time series - Store sales\n",
"Today we are going to talk about time series and forecasting! Forecasting is the use of a predictive model to predict future values based on previously observed values and meaningful characteristics of the time series data. It has application in various industries and use cases such as finance, retail, marketing and even anomaly detection for system outage."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Importing Libraries and dataset\n",
"We'll talk about individual libraries down the road as it's not obvious how they are helpful at this point of time."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"//anaconda3/lib/python3.7/site-packages/statsmodels/compat/pandas.py:23: FutureWarning: The Panel class is removed from pandas. Accessing it from the top-level namespace will also be removed in the next version\n",
" data_klasses = (pandas.Series, pandas.DataFrame, pandas.Panel)\n"
]
}
],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import statsmodels.api as sm\n",
"import itertools\n",
"import numpy as np\n",
"from pmdarima import auto_arima\n",
"from tsfresh.utilities.dataframe_functions import roll_time_series\n",
"from tsfresh.utilities.dataframe_functions import make_forecasting_frame\n",
"\n",
"from tsfresh.utilities.dataframe_functions import impute\n",
"from pylab import rcParams\n",
"\n",
"from statsmodels.tsa.stattools import adfuller\n",
"\n",
"from random import seed\n",
"from random import random\n",
"from sklearn.metrics import mean_squared_error\n",
"from statsmodels.graphics import tsaplots\n",
"from tbats import BATS, TBATS\n",
"from tsfresh import extract_features\n",
"\n",
"from pmdarima.arima import auto_arima"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"plt.style.use('fivethirtyeight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll use a small dataset, the Superstore sales data that can be downloaded from here."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"df = pd.read_excel('Sample - Superstore.xls')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Each row represents a sales transaction with pretty rich information such as customer demographics and profit. These would be helpful for feature engineering if we are going down the machine learning approach. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Row ID</th>\n",
" <th>Order ID</th>\n",
" <th>Order Date</th>\n",
" <th>Ship Date</th>\n",
" <th>Ship Mode</th>\n",
" <th>Customer ID</th>\n",
" <th>Customer Name</th>\n",
" <th>Segment</th>\n",
" <th>Country</th>\n",
" <th>City</th>\n",
" <th>...</th>\n",
" <th>Postal Code</th>\n",
" <th>Region</th>\n",
" <th>Product ID</th>\n",
" <th>Category</th>\n",
" <th>Sub-Category</th>\n",
" <th>Product Name</th>\n",
" <th>Sales</th>\n",
" <th>Quantity</th>\n",
" <th>Discount</th>\n",
" <th>Profit</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1</td>\n",
" <td>CA-2016-152156</td>\n",
" <td>2016-11-08</td>\n",
" <td>2016-11-11</td>\n",
" <td>Second Class</td>\n",
" <td>CG-12520</td>\n",
" <td>Claire Gute</td>\n",
" <td>Consumer</td>\n",
" <td>United States</td>\n",
" <td>Henderson</td>\n",
" <td>...</td>\n",
" <td>42420</td>\n",
" <td>South</td>\n",
" <td>FUR-BO-10001798</td>\n",
" <td>Furniture</td>\n",
" <td>Bookcases</td>\n",
" <td>Bush Somerset Collection Bookcase</td>\n",
" <td>261.9600</td>\n",
" <td>2</td>\n",
" <td>0.00</td>\n",
" <td>41.9136</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2</td>\n",
" <td>CA-2016-152156</td>\n",
" <td>2016-11-08</td>\n",
" <td>2016-11-11</td>\n",
" <td>Second Class</td>\n",
" <td>CG-12520</td>\n",
" <td>Claire Gute</td>\n",
" <td>Consumer</td>\n",
" <td>United States</td>\n",
" <td>Henderson</td>\n",
" <td>...</td>\n",
" <td>42420</td>\n",
" <td>South</td>\n",
" <td>FUR-CH-10000454</td>\n",
" <td>Furniture</td>\n",
" <td>Chairs</td>\n",
" <td>Hon Deluxe Fabric Upholstered Stacking Chairs,...</td>\n",
" <td>731.9400</td>\n",
" <td>3</td>\n",
" <td>0.00</td>\n",
" <td>219.5820</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>3</td>\n",
" <td>CA-2016-138688</td>\n",
" <td>2016-06-12</td>\n",
" <td>2016-06-16</td>\n",
" <td>Second Class</td>\n",
" <td>DV-13045</td>\n",
" <td>Darrin Van Huff</td>\n",
" <td>Corporate</td>\n",
" <td>United States</td>\n",
" <td>Los Angeles</td>\n",
" <td>...</td>\n",
" <td>90036</td>\n",
" <td>West</td>\n",
" <td>OFF-LA-10000240</td>\n",
" <td>Office Supplies</td>\n",
" <td>Labels</td>\n",
" <td>Self-Adhesive Address Labels for Typewriters b...</td>\n",
" <td>14.6200</td>\n",
" <td>2</td>\n",
" <td>0.00</td>\n",
" <td>6.8714</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4</td>\n",
" <td>US-2015-108966</td>\n",
" <td>2015-10-11</td>\n",
" <td>2015-10-18</td>\n",
" <td>Standard Class</td>\n",
" <td>SO-20335</td>\n",
" <td>Sean O'Donnell</td>\n",
" <td>Consumer</td>\n",
" <td>United States</td>\n",
" <td>Fort Lauderdale</td>\n",
" <td>...</td>\n",
" <td>33311</td>\n",
" <td>South</td>\n",
" <td>FUR-TA-10000577</td>\n",
" <td>Furniture</td>\n",
" <td>Tables</td>\n",
" <td>Bretford CR4500 Series Slim Rectangular Table</td>\n",
" <td>957.5775</td>\n",
" <td>5</td>\n",
" <td>0.45</td>\n",
" <td>-383.0310</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5</td>\n",
" <td>US-2015-108966</td>\n",
" <td>2015-10-11</td>\n",
" <td>2015-10-18</td>\n",
" <td>Standard Class</td>\n",
" <td>SO-20335</td>\n",
" <td>Sean O'Donnell</td>\n",
" <td>Consumer</td>\n",
" <td>United States</td>\n",
" <td>Fort Lauderdale</td>\n",
" <td>...</td>\n",
" <td>33311</td>\n",
" <td>South</td>\n",
" <td>OFF-ST-10000760</td>\n",
" <td>Office Supplies</td>\n",
" <td>Storage</td>\n",
" <td>Eldon Fold 'N Roll Cart System</td>\n",
" <td>22.3680</td>\n",
" <td>2</td>\n",
" <td>0.20</td>\n",
" <td>2.5164</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 21 columns</p>\n",
"</div>"
],
"text/plain": [
" Row ID Order ID Order Date Ship Date Ship Mode Customer ID \\\n",
"0 1 CA-2016-152156 2016-11-08 2016-11-11 Second Class CG-12520 \n",
"1 2 CA-2016-152156 2016-11-08 2016-11-11 Second Class CG-12520 \n",
"2 3 CA-2016-138688 2016-06-12 2016-06-16 Second Class DV-13045 \n",
"3 4 US-2015-108966 2015-10-11 2015-10-18 Standard Class SO-20335 \n",
"4 5 US-2015-108966 2015-10-11 2015-10-18 Standard Class SO-20335 \n",
"\n",
" Customer Name Segment Country City ... \\\n",
"0 Claire Gute Consumer United States Henderson ... \n",
"1 Claire Gute Consumer United States Henderson ... \n",
"2 Darrin Van Huff Corporate United States Los Angeles ... \n",
"3 Sean O'Donnell Consumer United States Fort Lauderdale ... \n",
"4 Sean O'Donnell Consumer United States Fort Lauderdale ... \n",
"\n",
" Postal Code Region Product ID Category Sub-Category \\\n",
"0 42420 South FUR-BO-10001798 Furniture Bookcases \n",
"1 42420 South FUR-CH-10000454 Furniture Chairs \n",
"2 90036 West OFF-LA-10000240 Office Supplies Labels \n",
"3 33311 South FUR-TA-10000577 Furniture Tables \n",
"4 33311 South OFF-ST-10000760 Office Supplies Storage \n",
"\n",
" Product Name Sales Quantity \\\n",
"0 Bush Somerset Collection Bookcase 261.9600 2 \n",
"1 Hon Deluxe Fabric Upholstered Stacking Chairs,... 731.9400 3 \n",
"2 Self-Adhesive Address Labels for Typewriters b... 14.6200 2 \n",
"3 Bretford CR4500 Series Slim Rectangular Table 957.5775 5 \n",
"4 Eldon Fold 'N Roll Cart System 22.3680 2 \n",
"\n",
" Discount Profit \n",
"0 0.00 41.9136 \n",
"1 0.00 219.5820 \n",
"2 0.00 6.8714 \n",
"3 0.45 -383.0310 \n",
"4 0.20 2.5164 \n",
"\n",
"[5 rows x 21 columns]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head(5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are tons of products with different categories over here. For now, let's just look at \"Furniture\"."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Office Supplies 6026\n",
"Furniture 2121\n",
"Technology 1847\n",
"Name: Category, dtype: int64"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['Category'].value_counts()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"sales_df = df.loc[df['Category'] == 'Furniture']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A quick look at the available period of the time series."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(Timestamp('2014-01-06 00:00:00'), Timestamp('2017-12-30 00:00:00'))"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sales_df['Order Date'].min(), sales_df['Order Date'].max()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have 4 years of data to play with!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Data preprocessing\n",
"Let's transform the data to univariate time series data by using only the main variable that we are most interssted in: sales. When we model univariate time series, we are modeling time series changes in a single variable over time.\n",
"\n",
"As a side benefit, we don't need to check and clean the data for all features. So let's just check for empty values for this particular variable."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"sales_df = sales_df[['Order Date','Sales']]\n",
"sales_df = sales_df.sort_values('Order Date')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
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" }\n",
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" text-align: right;\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Order Date</th>\n",
" <th>Sales</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>7474</th>\n",
" <td>2014-01-06</td>\n",
" <td>2573.820</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7660</th>\n",
" <td>2014-01-07</td>\n",
" <td>76.728</td>\n",
" </tr>\n",
" <tr>\n",
" <th>866</th>\n",
" <td>2014-01-10</td>\n",
" <td>51.940</td>\n",
" </tr>\n",
" <tr>\n",
" <th>716</th>\n",
" <td>2014-01-11</td>\n",
" <td>9.940</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2978</th>\n",
" <td>2014-01-13</td>\n",
" <td>545.940</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Order Date Sales\n",
"7474 2014-01-06 2573.820\n",
"7660 2014-01-07 76.728\n",
"866 2014-01-10 51.940\n",
"716 2014-01-11 9.940\n",
"2978 2014-01-13 545.940"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sales_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Order Date 0\n",
"Sales 0\n",
"dtype: int64"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sales_df.isnull().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are very lucky that this is a clean dataset; no empty value 😂\n",
"\n",
"Recall that each row of the dataset is a sales transaction so there will be multiple sales for each date(day). We want to summarize the data into a sales per day format. We are using summation to summarize, you could use other statistics as well."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"#the reset_index is here is to regenerate the index on the grouped panda series\n",
"sales_df = sales_df.groupby('Order Date')['Sales'].sum().reset_index()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Data Wrangling\n",
"We are going to make the order date as the index so that moving forward, the data manipulation can be easier."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Sales</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Order Date</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2014-01-06</th>\n",
" <td>2573.820</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-01-07</th>\n",
" <td>76.728</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-01-10</th>\n",
" <td>51.940</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-01-11</th>\n",
" <td>9.940</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-01-13</th>\n",
" <td>879.939</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Sales\n",
"Order Date \n",
"2014-01-06 2573.820\n",
"2014-01-07 76.728\n",
"2014-01-10 51.940\n",
"2014-01-11 9.940\n",
"2014-01-13 879.939"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sales_df = sales_df.set_index('Order Date')\n",
"sales_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3.1 Unevenly space time series\n",
"Notice that there are missing values for 8th, 9th and 12th in the time series data.\n",
"\n",
"We have met our first problem, the infamous \"unevenly space time series\" problem that is well studied in the field.\n",
"\n",
"1) If your eventual output allows you to forecast at monthly level, you are in luck: you could just resample at a higher level(roll up days to month and aggregate the values). There's a handly function to do it quickly: DataFrame.resample\n",
"\n",
"2) Interpolate the data "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Naive way: Downsample to monthly frequency"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"monthly_sales_df = sales_df.resample('MS').mean()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
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"<style scoped>\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Sales</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Order Date</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2014-01-01</th>\n",
" <td>480.194231</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-02-01</th>\n",
" <td>367.931600</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-03-01</th>\n",
" <td>857.291529</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-04-01</th>\n",
" <td>567.488357</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2014-05-01</th>\n",
" <td>432.049188</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Sales\n",
"Order Date \n",
"2014-01-01 480.194231\n",
"2014-02-01 367.931600\n",
"2014-03-01 857.291529\n",
"2014-04-01 567.488357\n",
"2014-05-01 432.049188"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"monthly_sales_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll talk about interpolation of time series later..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Visualizing the time series\n",
"Just like our usual data analysis work, we first plot the data before any modelling work(if any), in an attempt to identify some distinguishable patterns."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 936x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"monthly_sales_df.plot(figsize=(13, 5))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4.1 Describing Patterns - Seasonality"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first obvious pattern we observe in the plot is the yearly seasonality(12 months=a cycle). Sales are relatively lower at the start of the year and end higher at the end of the year, and this pattern repeats itself every year. The sales are also trending slightly downwards over the years.\n",
"\n",
"A time series process could be decomposed into several components: \n",
"Level: The average value in the series.\n",
"Trend: The increasing or decreasing value in the series.\n",
"Seasonality: The repeating short-term cycle in the series.\n",
"Noise: The random variation in the series.\n",
"\n",
"Instead of guesstimating the components, We could use scipy's seasonal_decompose function automatically decompose a time series and plot it out to have a better inspection of each component.\n",
"\n",
"Note that there's a model parameter, which means whether the time series is an additive and multiplicative model. The difference is how the compoenents are being combined together.\n",
"\n",
"Additive Model = y(t) = Level + Trend + Seasonality + Noise\n",
"\n",
"Multiplicative Model = y(t) = Level * Trend * Seasonality * Noise\n",
"\n",
"A easy rule of thumb: If you observe increasing variance over time, it's likely to be Multiplicative."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ZsmVYvXo1rl+/DgDg8/l4+OGH8e2333r68oQQUics+VcDg61schop4eHlTiFee/1ICR/zXF5vVboelzXUmY6Qmvg+g9vcY2LLIAQJSqZFUgGDx1vLOI+vOc8N9AeqFWe0FT5mdQCvHldj+oFi6Kx3nkQSQoi/pBdb8ec1bhOOZsF8fNhbjnMTG+DN7nKvB/+AkjRgZztzTLA6Kq45SAghFTlww4z3TmnufGIt8jgAuGzZMuzcuRPLly/HiRMnwLJlA6NEIsFDDz2ExMREr1wkIYQEolSlBT9lclMIX+8aglAv14p5LiEYsU7d66wOYPHJwPowIaQuuaq1IekGdzX2dvrvbdPiuQHAEwVWpCi5DUMCzRWtDZsuGznHRsSK3c7beNmIYdsLkKEqv3smIYT426cuixldFEL8OyEGMxKCIRP6rgxKrygRIpzKrKgtLI7lBfbYTwgJPLkGO6YfKILz+kGEmIe9D0Rh3wNR2DhCgdWDwvFRHzkWdg3BrPYyPNY6CPc1kaBPtAjxcgFipDx4e7jzOEdtw4YNeOqpp/DMM8+gqKjI7fG4uDhs27atRhdHCCGBimVZvHlCA+c14Xi5AE+2kVX4HE9JBQwWdQ/FDKfOpFuuGHE8z4zeMe4394SQyv2QaeC8d7tGCtFJwa2N10ouwJBGYk6gcM15PT7rH7g19D4/o+NMNNuGCfDLcAX+vGbC7EPF0FjLHsxQ2zB0ewE+7x+GCS0pvY0QEjiuaG3YeIm7mDG/c0itdDPn8xiMiBXjl4tl3z8x24gBDWm+RUhtyzPYUWByoH24oE6VLrE5WDy9vwgFTqVmGACrBoWje1T15pEsy8JgY1FsdqDYcutvswMqswMqi6P069t/7sTjAGBBQQE6duxY4eNisRh6vb7CxwkhpC7bnWPGgVzuDqJ3esoh8NHk9OGWUqxM0+FUYdmOnTdOqLFrdFSd+kAkxN9sDhbrM7nzk4oC90+3lXECgBsuGfFOT3lAdoTMM9ixPov7c73UMQQ8hsGDzaRICBNiSpISacVl5QP0NhbPHCjGsXwL3usph4hPYwkhxP8+P6ODc+m/eLkAo5tWXtjem0Y1lXIDgNdMeK8nS/MtQmrR5ssGzD6sgsHGYnAjMX4cGoFgH+7+9aZ3T2pw1GXn8CtdQjCscfXHMYZhIBMykAl5iPXCtXn8G4yJicGVK1cqfPzkyZNo1qyZpy9PCCEBy+Zg8eYJNefYwIbiclPtvIXHMHi3p5xz7ESBFVuvmCp4BiGkPLtzTJwiyjIBgwktpeWeO6qJBI2CyqZKBhuLX106BweKlWk6mJ2ayjUJ5nN+rlZyAfY8EIVJrdx/1lXpeoxOLECOjmqLEkL866bBjh9dFmle7lSymFFbhjYWw3md57LWjgtqGh8JqS0Hc82YcbC4tM76/htmTNlXBHMFHcEDyZ9XjfjMpUHkkEZivNLZezXia8LjAOCYMWOwdu1aZGVllR67vSqSmJiIDRs2YPz48TW/QkIICTDrLhiQ4TQRZAAs6Rnq85XhexqIcb/LCvhb/6jrxIchIYHi+wvcAN74FlKEVLCiLOAxmOqyO3BNhp5T9zgQqMwOrD7PvWF+sX0whC47koMEPKwcEI4V/cLguonxRIEVg7YVIOk6LSoQQvznq3M6WJyy2FwXM2pDiJCHgS4pv4nXaGwkpDakF1vxxD4lXHuVJd0w47mDxbAHcFOeK1obnj9czDnWKIiHVYPCa6WEQVV4HAB89dVX0aRJEwwaNAjTp08HwzD45JNPMHz4cDz++OPo0qUL5s6d681rJYQQv9NYHFjq0s3psdZBbvXDfGVxj1A4Z+ld1dmxKr1udCclxN9u6O3YlcO9iXsyvvK6nVPbyDjvufMqG44EWEH4NRl6aK3cbuRPtCm/rh/DMHgqXoZdo6PQNJjbQVNpdmD8LiU+PK2BI8CCnISQ+q/Y7MAal8WMuR3cFzNqg2s34MRsCgAS4mu5Bjse2a2ExlL+HGTzFSP+c0wVcAuxAGCysZi6r4hz7QIGWDM4ApES73cs95THAcCQkBDs2rUL8+bNQ0FBASQSCY4dOwa9Xo/XX38d27dvh0RSe7UaCCGkNnx2RotCp4KuUj6DN7qF1tr3j5ML8bRLwGJ5irZKRV8Judutz9RzmmQkhAvQPVJY6XMayfhutadcb1D9yWhjsfIcdxHguYRgBAkqn+J1iRThwJhojHQpXcACWHpKi0d3K1Fkspf/ZEII8YFv0nTQ28oG6WgpD4/Heb+5WlWMjOWO+8n5FhQYaUwkxFe0Vgce3a1Ejp77PpOLuAsAazMMeO8Ut0t4IHjtuAqpRVbOscU95egTYA0ba1RFUSKRYP78+Th06BBu3LiBmzdv4ujRo1iwYAEF/wgh9U6OzoavXG60X+gQjEay2l3VebVrCEKFZR+GaguL5SmaSp5BCHGwLH7I5Kb/PtlGVqXU/Wfacm9At101Ij9AbgR/zNRzusyFCBlMb1u1G+ZwMQ8/D1fgzW6hcN1gs/u6GYO2F+BUYWDtdiSE3JnFzkJjcQTkLpmK6KwO/DeNO8ea3T4YUoF/0uZigwXoFFG2QMQC2JlDuwAJ8QWrg8W0pCK3ANrT8TIcHBPNqccMAB+laN0WP/3p5ywD/udSYubBZhLMSvDPAkZlPA4A/vjjj1Cr1Xc+kRBC6ol3/tXAeUNMjJSHuR2Da/06IiV8zOvELSS7Kl2PSxoqUE1IRfbfMOOaruwNLOEDj7YqP03W1cCGYrQOFZR+bXUAP1zwfzMQq4PF5y6FpqfFyxAmrvr0jscwmN85BJtHKBAp4T4vW2fHyD8LsOZ84NU9JISUL63Yir5b8tB0fS6e3l8MSx2pE/y/DD1UTqlzchGDaXco0eBrbmnAVAeQEK9jWRbzj6qw57qZc3xkrBgf9pGjWYgAm0ZGIlzMXQx4PVmNXy/6fy6WVmzFvCMqzrGWIXx8eU94QHYO9zgA+OKLL6JNmzZ47LHHsHHjRhgM/v/lE0KIr5wqtOC3i0bOsYXdQv3Wjv65hGDEOu08tDqAxSdpUYaQinx/gZu2O6a5tMqBMoZhMM1lV93aDL3fC1FvumxEtlNQU8wHZrX3bFFiUCMJDoyJRq8obj1TiwOYd1SFmYeKoXetyE0ICSgqswOT9ypxUVMyLmy+YsSXAbRLpiJmO4svXRYzZrQLRqhrt6JaNqoJNwCYdMMMk61uBFQJqSs+TtVhncuiaheFEKsHR0BwKz2hbZgQG+6NhMxlR/CsQ8XY6cf6nFqrA08mFcHotNAi4QPfD1VA7ufxqyIeX9W+ffvw7LPP4syZM5g+fTri4uLw9NNP448//oDFQukihJD6g2VZLEzmBtcSwgV4vHXVdg/5gkTA4K3u3NqDW6+YcDzPXMEzCLl7FRjt+Mtl58aTbaq3s2Ry6yA413DO0dux248dcx0sixWp3Bo4k1sHoUGQ5yUJGsv4+GNUJJ4rJ2Xlt4tG3PtHAbLU1nKeSQjxN5ZlMetwMa5oueUJlp/WIlsX2BkCP2cZcNNYtsAQJGDKHYdqW2eFkJN6aLCxOJhL8yxCvOXXiwYs+ZdbxqhpMB+/Dle4bbLoESXCD0Mj4HzYzgJPJilx5Gbtvy9ZlsWcwypkqrnj60d9w9AxovL60v7kcQCwa9euWLJkCc6ePYvExERMnjwZR44cwZQpU9C6dWs899xz2L17tzevlRBC/OKvaya3rp9Lesr93s59Qkspuro0MHjjhJpS9Qhx8XOWAc6b1+LkAvSLqV7n7nAxD+NbcIP+/mwGsjPbhHRV2aSTxwBzOoRU8oyqEfEZvN87DGsHhyPYZaU9TWXDkO0F2HrFWMGzCSH+8sVZndtCBwAY7Sz+LzlwMwRsDhYrznAXM56KD4IiALpmMgyDUU2lnGOJ2TT+EeINB26Y8cLhYs6xMBGDDfcqEFPBYubQxhJ8OzAczrMTkx2YtFeJM0W1u0C5Kl2PzS7zoSfigvCEnxoXVZVX9iX26dMHy5cvR3p6OrZs2YLx48fjzz//xKRJk7zx8oQQ4jdWB4u3/uGuTA1rLMbQxv5vdMRjGCzpKeccO1FgxRa6OSekFMuybqklU+OCPKrL4toMZHeOGVe0tb+zhmVZfJrKTZcb11yKFk51CmtqXIsg7HswCm3DuK+ptbJ4MqkIC5PVsPo5BZoQUuLvm2YsPllxM7DtV03YE6ANLDZfNnJ2LQp5wAvta76Y4S33uaQB78g2wUELrYTUSFqxFVP2KTmLsyIesH6YAvFhle+eG9ciCB/3DeMc01hYTNhViMu1VA/9nwILFp7gLqy0DxdgeZ+wCp4ROLyamHzz5k2cO3cO586dg06nC8iih4QQUh1rzuuRpeHusnnXJejmT/0biDHapUj12/9oYK4jRb8J8bW/8yyc97CQBzwW51n6frdIIboouF0hv8+o/V2AR/IsSC7g7kr2RUOiNmFC7HkgCo+0lLo99tU5HcbsKESuITC6IRNyt8oz2PH0/iI4f+yHiRh0cElBW3BMFXD16xwsi0/LKWXQSOb/3X+3DWgg5tQdyzU4kKKkUgiEeOqG3o5HdimhsXLHo5UDwtG/gbhKr/F0WxkWduUuFOQbHXhoZyFu+nheUmSy46mkIk7wMkTIYN0Qhd+6lldHjQOASqUSa9aswejRo9GhQwcsXLgQLMvivffew9mzZ71xjYQQ4hcqswMfnOZOTKfEBSEhPLDqOizuEQrnz5urOju+TQ/8ot+E1IZ1LgG60U2liPQwtYxhGDztsgtw3QVDrQfcXW+Y720sRidF9VKaqypYyMO3A8PxUR85XHseHc2zYODWfKqJRYif2BwsnjlQhDwjt0HPtwMj8GX/ME6a3GWtHV+c5Y4d/rYj24Q0l1IGczsGzu4/oKTm8tDG3KBEoh+bDhBSl2mtDkzco8R1lyDd4h6hmNCyeouz/+kc4lYr9KrOjvG7CqEy+6ZpmYNlMeNgMXL03Ov/8p5wtJJ7LwvDlzwOAP74448YP3482rZti/nz56O4uBgLFy7EqVOnsGfPHsyaNQsNGjTw5rUSQkit+iRViyKnDxCZgMH/dQ2t5Bn+0VoudOtQ+lGKFkUm2plD7m7FZge2XuWmxD/ZpmbNeya0kCJUVHZbrTQ7sK0W0+5TlRbsuc4NuL3cybc3zAzDYHq7YCTeH8XpPg4ABaaSFffV52nRgZDatvSUBodvcncD/6dTCEY0kaBLpMhtweLjVC2u+qFsQXlYlsXHKdyA5PgWUrT0YikDb3HtBpxYTq1FQkjlrA4WTyUV4axLrb5n2sowp0P1sxgYhsHSXnJMbMXNUkgrtmHSHiUMNu8HAT9O0brNwWa1l2Fsc/dMiUDlcQDwxRdfxNWrV/HSSy/h2LFjOHLkCObNm4fmzZt78fIIIcQ/rmht+G8a94Z2bsfgCovS+turXUIQKiwLSqgtLJanBNZKPyG17deLBpid4uDNgvkY1Khq6SUVkQl5eKyVSzOQWkwDXnGGOy71jhahbzUbmniqR5QIB8ZEYajL79DBAguOqd0m9YQQ39mRbcQnLrVABzYU43WntLg3uoVCIS673TPZgdeOB0ZDkIO5Fpws5I4ZLwXY7r/bRjSRwLnv25kia8B3ViYkkLAsi3lHVNjrEjy7r4kEH/SWe1w6jscw+OqecIyM5c5LjuVbbqXpei9D48ANE5ae4t5b9Y4WYXGPwCkNVRUeBwCTkpJw8uRJLFy4EPHx8TW+kL///huTJk1Cu3btEBYWhvXr13MeZ1kWy5YtQ9u2bdGgQQOMHj0a6enpnHNUKhVmzJiBpk2bomnTppgxYwZUKhXnnHPnzuH+++9HgwYN0K5dO3zwwQfUMZMQ4uadkxpYnBaOGgXx8IIHq1O1JVLCx/zO3Inzd+f1uFRLxXAJCTQsy7ql/05pIwPPC/WJXXfVHM2z4FwtBL8uaWxuTX5e7hRcqzWXFRI+NtyrwKtdQjjphQ4WWJhMXcgJqQ1XtDbMPMjtntlAysN3g8LBd4pUhYt5WNyTm7mQmG3CjgDoZPuJSymD+5pI3OoWBopICR+9o7kLLTsoDZiQKlueosUPmdyGbF0jhVg9KBwCXs3mMEIeg7VDItwWQ3flmDH7ULFXmvbc0Nsx/UAxnH+nI6oAACAASURBVF9JIeZhzeAICGt4/bXNowCg0WjE0KFD8fHHH3vtQvR6PRISEvD+++9DKnXfQvnZZ5/hq6++wgcffIB9+/YhKioK48aNg1Zb9uExffp0pKamYsOGDfj999+RmpqKmTNnlj6u0Wgwbtw4REdHY9++fXj//ffxxRdf4Msvv/Taz0EIqftO5Fuw6TJ3cvxGt1AECbzaN8nrZrYL5qTnWR3A2/8Exko/IbXtnwIrp7YUnwEe97D5h6v4MCHuacCdaK6thV2An5/RwnkxOyFMgBGxtd+RnM9j8HrXUKwaFM45fiDXTLWxCPExk62kE7faUjYY8Blg7ZAIREvdsxQmtw5CryjuePXqMTWMfmwI8k+BBQdcaofO93Epg5py7QZMacCEVM1PmXq3nXNNg/n4dbgCMtfiwh4KEvDw8zAF2odzSwj8dsmI147XbHHSeqvWaoGpbGcIA+C7QeFoHEANi6rKo9+4VCpFVFQUQkK8N1CPGDECixYtwtixY8HjcS+LZVmsXLkSL730EsaOHYuEhASsXLkSOp0Ov//+OwAgIyMDe/bswYoVK9C7d2/06tULn376KXbu3InMzEwAwIYNG2A0GrFy5UokJCRg7NixmDt3Lr7++mtasSakBqwOFudVVq9us/YXlmWxMJkbNOsUIcSk1t4JHPiSRMDgre7clf5tV01I0QR24JIQX/j+AjcgNyJWgoZeTOF/xmUX4K8XDdBZfVN0GgByDXb8lMVdPX+pU4hXdjR6akILKQa7pAO/kayGhbqQE+Iz/5esdutC+3aPUPSNKb+8AY9hsLyvnJPCelVnx2dn/FcmxHX334AGIvSMrp1SBp5yrQN46KYZGovvxnxC6oMDN0yY8zc3IzNMxOD3exXlLljURJiYh00jItEihPu636bra1QW6Z2TGhzN49Zafa1rCIY0rv0FWG/w+K5w3Lhx2Lx5MxwO3w98V69eRV5eHoYOHVp6TCqVol+/fjh+/DgAIDk5GcHBwejdu3fpOX369IFMJuOc07dvX84Ow2HDhiE3NxdXr171+c9BSH2kNNkxaGs++mzOR/vfbgZEWklNbLtqQnIBd5B/t6fcrzfZ1TGhpRTdIrkpNCsuC2mRg9xVNBaH2y7eJ+O9G8Qf3VSKGGnZNEprZbHhou/Gv5XndJyyBE2D+Rjfwr9FpxmGwXs9uYGFS1o7Vp2vvZqIhNxNfr1ocKs5+kBTCV5oX3mJks4KkduixadntLjih4YgacVW/OWye861hEkgipML0CqUm2WRdIM6oBNSkXNFVkzZVwTnzcZiPvDTMAXahPkm3T8miI/NIyM58zMAWHpKi+/Sq9+sbPtVI744y33esMZiLKgDY1ZFPG6zNHr0aBw8eBD33Xcfpk6diubNm5ebutu9e/caXSAA5OXlAQCioqI4x6OiopCbmwsAyM/Ph0Kh4NTBYRgGkZGRyM/PLz2nUaNGbq9x+7GKGpjc3kFICHH3bqYIaaqSoSTf6MCkPUV4tKEVL7awQlzHNp5l6hm8miaG89rIPeF2NNJfQ10aBmY25GFmYdmq1FktH18fvYwRUdQVmNwdNuUKYLCV7SaJFjnQzJjj9ffx6Egh1mSXTWK/TilCf94NeHu9QGMDvkuXAk5V9ybFGHH5YpZ3v5EHRADGxQix8WbZ72HZSRV6Mbnwxfye5mTkbnVRz2BuigTO40CsxIH5jYqQlVV0x+c/Jgc2CqUospY832wHXth7A58kmL0+ZlXmnQwRnG9BE4LtaKTLrhPzrD4hQlzUlA1sv57NR4LVUskzKkZjGanP8s0MpqWIobFybwbfam1GlPYaMn28AfnTtgxmpkqgtZcNbguOqWAuzq/y/VCOkcFzp7ljbrTIgddii3Exq7jiJ/pZXFxcpY97HAAcM2ZM6X+fOHHCrQA1y7JgGAZFRXf+QKqqir5HRY9X5Zzbu2IqK6B9p18iIXer04UWbM8rcDv+a64QZ01SrBkcgXgfrfB4k93B4ouzOryXooFzBh+fAT4Z3BBxdeBncBYHYJtaiT+dVtg/vybF5O4xCK9rUVlCPJCYng+gLEXuyXZytGvTxOvfZ15DG/6Xk1daly/TwEOxvCl6V5CK56nlpzUw2Mtmy1ESHl7u1xxSQWDsTP6giR27f8+Dxlryi9DZGfyqjsJHfcO8+n0yMzNpTkbuSlqrA5O3F8DkKNuxJ+EDP42IQSdF1VNn3xMa8PyhshvXw8V8ZElicX/T2tlNfEVrw66/8zjH/q9XFNo08+9u5qqaHGLG+uuFpV8f1QjRolXTajcxoLGM1GcaiwPTEguRb+GWKni3Ryhm1VKn7zgAGxqaMW6nEsZbZUlYMHjrghjxTRUYfof6yUYbi6f/LIDeXvYzCBjgx3uj0TPau3O82uZxAPCrr77y5nVUKiYmBkDJLr3Y2NjS44WFhaU7+KKjo1FYWMgJ+LEsC6VSyTnn9m5A59cA3HcXEkIqx7JsSVHVCh4/V2zD4G0FeL+3HFPbBNVql8rquKSx4flDxTie776C+0xbmc+2qPva4h6h2JltKt12n2d04JVjKqwaFOHfCyPEx1KUFpx2qo/FAJjSxjc1PGODBRgZK+E0vlidofdqANBgc+C/adyUv+fbBwdM8A8o6ZC5oHMI3vxHU3psbYYez7SVoV143RxDCQkULMtizmEVMtXcdN3lfcKqFfwDgEmtpFh3Qc+pZ/XqcTUGNxLXSqOzz1waGbUNE+D+pnWnjlbvaBHCRAxUtxqwFJtZHM+3oH+Duh0QIMRbrI6SJkVni7jBv2fbyvBCh8pLFXhbnxgxvh8Sgcl7laX3QzYWmJpUhC0jFehVSSDv1eMqnHH5Gd7tKa/0OXWFxyP95MmTq/THG5o1a4aYmBgkJSWVHjOZTDh69Ghpzb9evXpBp9MhOTm59Jzk5GTo9XrOOUePHoXJVDZRT0pKQsOGDdGsWTOvXCshd4vNl4045hI0i3apt2C0s5h7RIWn9hdBZQ6sQsksy2LNeT3u2ZpfbvBvYisp3u0p98OVeUdruRAvu3TU23DJiG1X6naNRkLuZN0FbqOMoY3FaBrs8XrnHbnW1dpy2QilyXvp9j9cMEDpNH6GChm37xkIZiQEcwpv21lgYXLNOu8RQkoK2G92+ex+PC4IU9pUfxxgGAbL+4SB77R+kK2z49PU6tfGqq5cgx3rM7nj88t+bmRUXQIegxHUDZiQcrEsi5eOqNxqY45qIsH7veV+2QwyookEKweEc44ZbCwm7lYivdha7nN+ytS7zSXHNpfguYTAm3t5witLPTk5OTh9+jR0Os8/PHQ6HVJTU5GamgqHw4GcnBykpqYiOzsbDMPg+eefx4oVK7Bt2zakpaVh1qxZkMlkePjhhwEA8fHxGD58OF5++WWcOHECycnJePnllzFy5MjSLdYPP/wwpFIpZs2ahbS0NGzbtg0rVqzArFmzAnZ3EiGByGBzYJHTTg8AGBkrxonxMZhQTlH6rVdMuGdrPo7lBUax5Bt6Ox7ercS8oyoYbNyb0wgxD98PicC3AyMg5tftcWFB5xB0iODuvpl3VIVCLwYnCAkkeqsDGy5yJ21TPbhJro6hjcVo7hT4sjjgdpPrKeut8gTOnmkrg1wUeKn8Yj6Dd1wWTfbdMGN3TmCM+4TURSfyLXjjhJpzrH24AB/18Ty9vkOEEDPaccfFz85ocVHt24YgX511b2RU3pwx0N3fhHvNiXW8+R0h3vJhitZt/tM9UojVg8PBr2aavDc90ioIH/Tmzk9UFhbjdxXiqksjpHNFVsw/yh1zW4Xy8UX/8HoTL6rRDPKPP/5At27d0KlTJwwdOhQnT54EACiVSvTr1w/bt2+v8mudOnUKAwcOxMCBA2E0GrFs2TIMHDgQS5cuBQDMnTsXs2bNwoIFCzBkyBDcvHkTmzZtQkhI2Q6XVatWoUOHDhg/fjwmTJiADh064Jtvvil9XC6XY/PmzcjNzcWQIUOwYMECzJ49Gy+88EJNfg2E3HW+OKtDjr4siCRggCW95JCLePhuUDi+uicMMpf0tBy9HfcnFuKD0xrYHf7ZEcKyLDZcNKDvljzsve5+UzqyiQRHH4rG2OZ1b0JaHhGfwcoB4RAwZb/vQpMD846oaFcOqZe2XDGW1qEDSmrljWri2/QyHsNgWjz3Znpthh4OL7zHfr9k5Iy1Yj7wXELtptBUxwNNJbinATcl8Y0Talj9NOYTUpcpTXZM21/EqU0cKmSwboiixiUAXusayumSaXEArxz33dygyGTHWpfuxXM7Ble7dl4gGNpYDKHTHfRFjR2Z6vJ3EhFyt/gpU49lp7idPZoF8/HLcEWtlBe4k5kJwXi1CzczKtfgwLidhcg3lsyzNBYHpiaV1QwEACm/ZMwNDcCFV08xKpXKo5F+586deOyxx9CjRw8MGzYM77//PrZs2YJBgwYBACZOnAg+n4+ff/7ZqxdMCPGvHJ0NPTflcwbH2e2D8V4v7spKltqKp/cXI7XIfVLUL0aEbweGI9aHaXmulCY75h9VY0s5KbDBAgbLesvxRFzg1iqsidf2XsZ/r3Fvyr8bFI6HW/qmLhoh/jLyzwJOSv/cDsFYXAup/EqTHQm/3YTZaXPtxhEKDGvsefDRwbLouzkfGU67cp5pK8PHXm6s4W2pSgsGbSvg1If9oLccM70QuKTC+eRuYXewmLhH6bZYuW5IBMZ4aZHyt4sGzDjI7WT5w9AIPOiDhhzLTmnwwemy4EC0lIfUhxtAEkC1TKtj/M5C7HNKc3ynRyjmVKO5AY1lpD7Zf8OEh3eV1dkDgHAxg12joxAnD5w6wCzL4pVjaqw6z12M6BQhxPZRkZj7t8rtPvHre8IwOa5+pP7e5nEo88MPP0Tv3r2xa9cuPPvss26P9+zZE2fOnKnRxRFCAs/ikxpO8E8h5mFBZ/dJT2u5ELsfiMLs9u43fUfyLLhna36t1aPbmW1Cvy355Qb/+jcQ4fBD0ZjSRlYvg38A8GQTG7pGcj+A/3NUhZsGSgUm9Ud6sdWtnqev039vU0j4bjuHv0vXV3B21SReM3GCfzwGeLGWC2h7opNChCfiuIsLy05pUBxgdWAJCWQfpWrdgn8vtA/2WvAPAB5pKUV/lx27rx9XQ2/17ntVa3XgmzRuKYMX2gfX2eAfAIxyaVzi3AiKkLvJ2SIrpuwr4gT/xHzgp2GKgAr+ASU1UD/oI3crPZBaZEX/cu4Tp7YJqnfBP6AGAcC0tDSMHz++wsdjYmJKO+wSQuqH5HwzNlziDo5vdg9FmLj8oUTMZ/BeLzl+v1eBKAn3HJWFxdSkIrx8pBgGm29uDLVWB+b8XYxH9yiRZ+R+DzEfeK+XHNvvi0TzkNrbiegPAgZYOSAc4rIyZVBZShq0UCowqS/WXeAG3O5pIEIree29t59xSQPemWNCts6zmlosy+LTM9xUmgktpHVmrHqjWyiCnW7uVRYWH5zWVPIMQshtSddNeN8lla5PtAhv9Qj16vdhGAYfuTQEydHb8XGqtuIneeB/5/WlXXMBQC5iMC0AGxlVx0iX0hLH8y1UX5ncda7r7Zi4uxBap9IrDIBvBkSgb0xgdsvlMSXlkYY15l6fc7kVAOgYIcQHvQM748JTHgcARSIRzOaKCztnZ2cjNNS7H1SEEP9xsCxeO84titohQogpcXdOIx0eK8HhsdEY2sj9w2BthgFDtxfgXDmpwjVx+KYZ/bfku3VxAoAuCiEOjInG7PbBdar7XE20DRNiYVfumLwz24SfsrzTrIAQfzLZWPzi0vzjyVra/Xdbr2gR2oeXBegcLPB9OeNPVRy+acE/Bdwx8aVqpJf5W0wQH/NddoZ/l67HBRXVySKkMtf1dkw/UMxJoY+U8LBmcASEPqiX1y5ciOdd0vO/OKvzWk07k43Fl+e4u/9mJgQjRFi362k1DRZwmqw5WGAX7QIkdxG1xYFHdhfihoG7weLdnqF4KMCb+4j4DNYNiUDPqPJ3KJbUWo2oca3VQOXx6NunTx9s3ry53Mc0Gg3Wr1+PAQMGeHxhxDv+LbCg56Y8xP+Si/9l1Cwdidzdfsky4N9C7oRwWS95lbs6xQTx8fsIBd7tEQrXed95lQ1D/8jHqnRdjXekmWwsFiar8WBiIa7puKs5fAZ4tUsIdj8QhbZhgbUtvTbMbh+M3tHu6T45Hu5SIiRQ/HHNiGJz2dgRLmZ8UseqMgzD4Jm23BvpHy7oPWqA8anLDpyRsWK0j6hbY9bzCcFoGly27djGAm+6dDMlhJSx2FlMSyqC0ildnscAqweFo5GMX8kza+bVriFoGFQ2MbM6gFeOqb2SIfBTloGTgSETMHiuXd3e/Xeba4OpHRQAJHcJo43Fk0lFSCvm3j/MaCcrt/RTIJIJefjt3ki0C3PPrPhqQDhahNaNjAtPeBwAfO2113Du3Dk89NBDSExMBACkpqZizZo1GDRoEDQaDV555RWvXSipPpXZgcf2KpGptiHP6MBLR1R4718NpfyRatNaHXjnJDd9a0wzCQY0rN72bh7D4MWOIdg1OgotQ7iTWbMdWHBMjcl7i1DkYRrF6UILBm/Px1fndHD9V95GLsDu0VF4vWuoT1bR6wI+j8HX94RD6pTvo7GymPM3pQKTuu17lwWuR1sF+aW+1COtpJzU1zyjA39erd5N4elCC6e4PAC83Knu7P67TSJg8E4PbgOWnTlm7LtON8mElOetf9RILuDWMf2/rqEY1Mi3ncxDhDy859IsKemGGduqOXa5sjlYfOZSyuCpeBkiJL4LZtam+13qAO69bobJRnMpUr/prA48ukeJ/S7zlPubSrCsl7xO1VMPF/OwaWQkWjjdk87vFFzrC8i1zeMAYNeuXfH777/j+vXreOGFFwAAixYtwvz588Hn8/H7778jPj7eaxdKqm/xSbVb3bPlKVq8dlwNB93sk2r4NFWLm07/lsR84J0adNbsGinCgbHRmNTKfYBNzDbhnq35OJRbcYkBV1ZHSX2p4X8U4LzKfTfb8wkyHBgTjW5RonKefXdpJRe41RHad8PscaoiIf52SWPDoZvcm+baTv+9LUTIw6OtuWURVp/XVXB2+Vac4Z7fN0aEPgFaS+dOxjaXoG8Md9xdmKyGzYNdkYTUZ1uvGLEyjbuQcW9jMeZ1qp3dNONaSDHQZVH39eMq6GrQEGTTZSOuOmViiHioM7uDqqKzQsjZOam3sTh8s+pzV3L3OVdkxboLelzR1s3MG7XFgQm7lDjoco/WPVKI7waFVzkrLJA0DOLj8NhofHlPGDaNUODN7p7f39YVNdrbeM899+DEiRM4c+YMLl68CIfDgRYtWqBLly51KvpbHx3NM2NtRvk39N+k66G1svi8fxgEdfCNSmrXFa0NX7nUb5ndPrjGxehDhDz8d2AEhjY2YP5RFaeA7A2DA2N2FGJ+pxC82jWk0h17F1RWzDxUjFOF7vVqYmV8fD0g3G1Se7eb0U6GP64acdgpaPJGshpDGonRrI40GSDkNtfmH72iRGgX7r902afjZVh9vuyaDt20IENlRXwVyg5kqa3Y6tKF7uU6VPvPFcMwWNpLjiHbC0qPpats+P6C3i1dmpDymGwsNl8xIjnfDAmfQXyYEHFyAdrIBYiU8OrF/UaW2ooXDhdzjsXK+PhmYHit1SlmGAbL+8jRf0t+aTfPGwYHlp/WYrEHC74OlnUrZTC5dZBPU5lrG49hMDJWgv85LaAmZpswPNa3OzZJ3XM0z4yPU7TYc6uzt4ABPukXhql+Wqz0RJHJjvG7lDit5N5vJYQJ8MtwBYIEdbeup0zIwxP1sNtvRbxyp9exY0d07NjRGy9FvMBiZ/HyEVWl5/yUZYDO6sCqQREQ8+v+5In4zqITapidMnIbSHleTUeb2CoIPaNEmH6gCCedgngsgI9StTiYa8aqQeFugSkHy+KbND0Wn1SjvIzhx+OCsKyXHKGiuvuB5Cs8hsGX94Sj/5Z86G/N9HU2FrMPF2PbfZH1ujGKycZCaXag0GRHkcmBQpMDSrMDStOtP2Y7zPaSXVfT28ogq+OFyus7q4N1a2QzNf7OjYl8qX2EEH1jRDiaVxZgX3Nejw/63Lmb3OdnueUL2ocLcG9s3V7A6BopwmOtg/Cz0/+npf9qMaFFUIUd5Am5prNhzXk91l0woMhc/i60MBGDNnIh4sJKAoK3A4PNQwR1ZoHbYHNg6r4iziKokAd8PySi1lNl48OEmN0+GJ+dLVv0/eqcDpPjgqq0gOEs8ZoJ6U4ZGTwGmFuHFzMqMqqplBsAvGbER33qVhok8Q2WZZF0w4yPUrQ4ksfNUrCxwJy/VbiksWFR99CAn3fnG+14aEch0lyyrLoohNg0QlFv0vrvFh4HAP/++2+cOXMGzz33XOmxDRs24IMPPoBKpcKECROwbNky8Hg0uattn53RuqVBLu8jx/IULfKd0ji3XTVBv1eJH4ZG1OmoPfGdQ7nuNWAWdQ/1eve2FqEC7BgdhaX/arDiDPcGOLnAggFb87GiXxjGtyy5sb+ms2H2oWK3tD8AiJLw8Fn/MNzftH7Xb6ip5iECvNtTjnlHyxYLDt+0YFW6HjMT6sbOHAfLQmV23AroOQfxSv4uDfLd+rrI5ICuivV5dmSb8E2aDu/2lGN8CylN5gNU4jUT53MtVMhgXHP/v/efjpdxAoA/XzRgUffQSgPKN/R2TpAMKKn9Vx/+7S3qHoqtV4ww3Hr/Kc0OfJSixZJe9T/VhlQdy7I4kGvGt+l67Mg24U6Z4ioLi+QCi1vdPCEPaBlyKyAYJkAbuRBt5AK0lgsCalGQZVnMO6Jyu6le1kuO7n4qWbKgSwh+v2TEdUPJyqqNLanPvHWkospjEcuy+MRl99+EFtJ6WVR/YEMxggRM6dh2w+BAitKKLpFUcuZu5WBZJF4z4eNUrVvzRFcrzuhwWWvDfwcEbsfZ63o7xu4oRJaGO071jhbht3sVkAfQmEqqhlGpVB4VYhkzZgwUCgXWrl0LALhw4QL69++PFi1aoFmzZti7dy+WLFmCWbNmefWCSeWy1Fb035rP2bE1uXUQvh4QjksaG8buLES2S2fUvjEi/DKc3sCEy+5gMWh7Ac4WlX14dYsUYs8DUT5dqdp/w4SZB4vd6lcCwBNxJbsF3zih5qyW3/ZgMwk+7ReGSFqJ4sjMzERcXJzbcZZlMX6XEklOhXylfAaHx0ajlTywJurXdDasPKdDitJaGuQrMjvueIPoDX1jRPiwTxg61rEurHeDh3cVlqbUACWBt0/63Xmnna+Z7Sza/3YThaaycezz/pWn+yxMVnPKLTQP4eOf8TF1ZifTnXx4WoOlp8qCAkIecOyhmGqNNRWNZaRu01gc+CXLgO/O63FB7dvaWA2DeIi7FRC8vWMwTi5AYxm/1oPt32foMdclY+fhllKsGhju18D/1itGPJlUxDm2ZlB46SLsnRy4YcLYnUrOsb/HRte5TuZV9fheJf68VrZY/lqXELzWNbSSZ9BYVh/ZHSXlCj5J0boF9Z3xGLjNXXtECfHTMAWipYF1/3JFa8PYHYWcWp5ASeD7p2ERCKYsmTrJ4wBgmzZtMGfOnNIGIEuWLMG3336Ls2fPIjQ0FM8//zxSUlJw5MgRr14wqRjLshizo5CzK0oh5uHE+OjSrbk5OhvG7SrpDOyss0KIjSMUFDghpf6XocdLLhPTXaMj0Sva9+lohSY7Zh8qxs6cqhVTDhUxWN4nDBNb0k6t8lQ20czR2dBvSz40TgHV3tEi/DUqMmCK+R6+acaUfUoUm/3XOIDHlASX/q9rCKU6BIhrOhs6b8jj7Bje/2BUwOy8ePsfNaehRxeFEPvHRJd7brHZgQ6/3SxNyQeAT/qG4em29acmjcHmQK9N+cjRl91IjG4qwfphiiq/Bt001y/nVVZ8l67HL1mGSndny0UMJrcOglzEQ6bahgtqG7LUNhjt3vtMkAkYtJYL0DpUgFgZH41lfDSS8Uv/29v1Bk8XWjDyrwLOgn28XIC9D0b5/aa6vMXBhkE8JI+PqVIGyJgdhZwmAaOaSPDz8Kq/z+uaHzP1eOFw2Xy5s0KIAxWM9bfRWFZ/WOwsfrlowIpULS5py6lJdMuQRmLM7xyCID6DSXuVnOwFAGgazMdv9yrQtprp9r6SqbZi7I5C3DBwr3NErBjfD1EE7I5Fcmceb/HQaDQICytbZd+7dy+GDBmC0NCSFY++ffti+/btNb9CUmU/ZxncUiKX9pZzblZjgwX4a1Qkxu9S4ozTzq4UpRX3/1WILSMj61WBXuIZldmBd09qOMceaSmtleAfAERK+PhluALfpOux6IQalkqa0A1uJMaX/cMQGxxYO9bqithgAZb2lnMmr8fzLfj6nA4vBkC9nh8u6DHvqAo1aETIIWAAhYQHhZhX8rek5MYuQsJD5K1jqUorvk7Tcb6ngwW+O6/HxssGvNEtFE+1kQVMgPRu9WOmgRP866wQBkzwDwCeipfhM6eSBqeVVvxbYCm3G/m36TpO8C9GysPk1v6tZehtQQIe3u4RiukHypod/HnNhAM3zBjUqG7XOSRVZ3OwSMw2YVW63q2TpKv24QLMaBeMh1tK3dLnHSyLHL29JCCost0KDFqRqbaVm0FwJ3obixSlFSnK8lP2RDyg0a1gYOOgsgBhY6c/CnHVgoQqswNPJhVxgn8yAYN1QwNjRw3DMPiwjxz9tuSXfg7mGhz44NSd0/ZP5Fvc/r/O82Ld6EA0MlYCBigd61OUVlzX29GY7qfqNaONxQ8X9Pj8rI6zsOVqVBMJ/tM5hJPWv+eBKEzareTsFLyms2PEHwVYNzQCgxv5t5HMuSIrHtpZiAITdyx9sJkEqwdFQET9A+o0j++YY2JikJGRAQDIzc1FamoqnnrqqdLHNRoN+Hwa+GqL0mTHGye4AZshjcSY2NK9FlKUlI/t90Xi0T1KHM8vCxheUNtwop/UsAAAIABJREFU318F2Doysl7W6SBVtzxFC6VT0e0gAYO3e9RurSaGYfBcQjD6xYgw/UCxW1qQlM/gnZ6heKatLOCL5wa6x1sHYftVE3Zml6WwLDmlwb1NJH5bibQ7WLx9UoMvzuoqPS9UyNwK5N0O6vGhkPBKgnrikr9LvuYjQsyDXMTc8QZtQktgahsZXk9WYZfLLtRiM4v5R9VYm2HAh73l6NeAAhf+YHewWH+BWy/vyQDrptc8RIDhjcXY7ZSivDpD7xYA1Fsd+CaN28l4VvtgSOrh6vqEFlJ8k6bDiYKyIMv/JatwcEw0BdTruQKjHesuGLA2Q1/pzbKAAcY0l+LZdjL0iRZVOF7zGAZNgwVoGizAsMbcx1RmB7I0NlxQWUt3DGaqbbiksaGKZWDdWBzAFa0dVyrZ4SPhA42CygKDsZwgoQCNg3gIE/Pw/KFit5S6Ff3Cqt1ow5fi5ELM6RCMj1PLPoNXppU0BEmopMu6a+2/gQ3F6BkdOAszvhAl5aNnlIhTi3JHtpE6nddTWqsDa87r8dU5ndsuvtt4DDCuuRTzOoWUm/reNFiAxNFRmJZUhH1OO201VhYP71L6tUPwqUILxu8qdMu6eaSlFCsHhNebsiR3M4+jPA8++CBWrVoFs9mMf//9F2KxGKNGjSp9/OzZs2jevLk3rpFUwcJkNadLmoRfkj5U0cQpTMzDphEKPLGviLPF/5rOjlF/FWDTyMhKP+BJ/ZWptuKbNG7QZW7HYL+tZHZSiJD0YBReT1Zj3a0b/p5RQqwcEI7Wcvo36g0Mw+CzfmHoszkPKkvJB77ZDsw6VIxdo6Nq/cNeZ3Xg2QPFSMw2uT32apcQPNhMWhrw89UqZCu5AL/dG4md2Sa8flzlltZxtsiK+xML8XBLKd7pIaed07Vsz3VzaZF6oGSR4uFyFrz87em2Mk4AcOMlA5b0lCPcqfuta5fTUBGDafGBFcz0FoZhsLRXGO79s6D02LliG9ZnGfx2s0N862SBBd+m67D5srHS3fwxUh6eipfhqXgZGgbVbDwNE/PQI0qEHi7BdquDxRWt847Bkl2DF9Q2aCw1Tyc22YFLWnulaYBiPjg7/wBgelsZHmkVeDt+53UKwa8XjaUBWzsLLDimwh/3RZZ7f3GuyOr2uT2/090RBBvVVMIJACZeM1EAsJ4pNjvwTZoO/03Tlc6VXQkYYFLrILzcMeSO9W3lIh5+vVeBV46psDajbEHTnx2Cj+eZ8chuJacsEABMbROET/uG0UJdPeFxAPD1119Hfn4+fvvtN4SEhODLL79EdHRJvQONRoPt27fj2Wef9dqFkooduGHCLxeNnGOvdAm94y4+mZCHX4Yr8Mz+IvzhVLz2ptGB0YkF2HhvZLmpSqR+eyNZzVkhj5Xx8WIH/05iZEIePu8fjgWdQ1BsdqBjhJBq/XlZgyA+lvcJw7MHy9Lz/i20YsUZHf7TufbSd7J1Nkzao8S5YvcdnysHhOOhFrUb5BnZRILBjWKw8pwOy1O0nDRNAPj9khGJ10yY3zkEs9sHQ3yXpUU4WBabLhuRobKhd7QIQxqJa2WC+P0F7o65cS2kAdXd87YRsRLEyvilN9AmO/BTlgGz25eMqRY7iy9ddrk+21YWkD+Lt/SMFmFiSyl+u1Q2b3n3pAYPNQ/M/4ek+kw2FpsuG7DqvB6n7tAFs2+MCM+2leGBZlKfp5UJeQzi5ELEuSwesiyLfKMDF9Q2XNXZcF1vx3W9HTdu/X3dYPdKgBBwD/51ixTivQDthi0T8rCstxxT9pU1BPn7pgUbLhkxsZyA5Yoz3N1/3SOFGNjw7tglP6qpBIudSucczDVDZ3UEREo3qZl8ox1fndVh9Xl9hbVKJXxgShsZ5nQIRpNqlCQS8hh80jcMLUMFWHRCwylrUtsdgg/cMGPyXqXbPHdGOxne7y2nbKt6xOMmIJVxOBzQarUICgqCUEg7dHzJaGPRf0seZ7UxIUyAA2OjIaziTZjNweKFw8VuQcRgAYOfhysw4C758CbAnhwTHt7N7dxWnc5vJDBVtdg0y7KYmlSE7VfLFgSEPGDfg9G10gH3nwILJpdTGLmBlIefhyvQ1c/13W7o7Xj7HzUncOGsRQgfy3rLS+oB3QUTJauDxaxDxdjg9PtoHMTHpNZSPB4nQ0sflZK4abCj/W834Vz/v7YaFHni4xQt3v237MawdagAJ8ZHg2EYrM/UY7ZT/U0JHzjzSANEBVgnQG/L0dnQc1M+p4nDSx2D71hqggrnB7ZrOhvWntfje5ddra6kfAYTW0kxvV1wnemurrU6SoOCOc7BQb0dNwwlf2ut1bulChMxODg2Gk0DuIYxy7KYuFvJ2ckcIy1pCCJ3Cthf1tjQfVMep7vp+qERGN0s8HZm+wLLsui2MQ+Xne7H1g2JwJjm5f/8NJYFvmydDZ+f1eGHC3qYKtjUGyxg8HRbGWa3D0ZMDXcub79qxIwDxW7NjbpHCvHzcN92CN6dY8KUfUq3n/PljsFY1D30rpjT3k28FgDUaktWfUJC6neh10Dz7kk1pz4HA2CnBzdCDpbFq8fVWJXO3VUh4QPfD1FgZBP/FiOtTXkGO369aECQgMHwWAmahwTuxMybrA4W/bfkc2rt9Y0p6QZLA3/dVp2JZoHRjj6b8zk1IDtECLHvgSif7s7YeMmAWYeL3XZHdIoomfgEUjHto3lmvHJMzWmk5OzexmIs6y2v1ynqJhuLafuLyk3Tvq1fjAiPxwVhbHOpV3dBuAbU2oUJcOSh6IAdp/KNJQFL56YyW0eWLK712cwdc59tK8PyvmHlvEr9s/SUBh+eLtsxJOIByeNjKv3MpZvmqrmht2PvdRPSiq3gMQzE/JKdJmI+AxEPt/5mIOIzEPMA0a2vxXzcOsZA6PTY7eeVPsZD6fuNZVkcyDXj23Q9dmSbOAEgV81D+JjeVoYn4mQIE9e/nVEai4MTFMxx3Umot5furgkVMfhhiKJONMC5pLGhz+Y8Tgr38wkyLPt/9u48LKp6/wP4+8y+si+CiKaiuFuaopX7ftXMTG2zbLktlm1m3Vu/bouVmZZWtlqa1U1bTKubWq65a5ZpooiYGyLIMsDs2/n9MQoMA4g4A8zwfj1Pj3HmzHBG4cz3fM5n6V1+rnp0WxGWVOjL2iFChm3j4ppU1tC/dxvw7sHy66ib22rw3nWRVe7Lc1njlVXsxJsHSrE8y1ztALoIhYD7Oupwf0edV0uPy/X7OXuVE4Jb6KT4OkATgr8/bsHdmwt93uszV+oxo5u+0a6tqO4uKwB47NgxzJ49G7/88guKi4sBAOHh4Rg6dChmzpyJtm3b+u1AyVd6kQP9VuV5lWvenarFvDpePIiiiJd/L8XcSg18ZQLwQb9I3NgEssB25dpwy/pCr+BHxwgZRiarMDJZjati5CG7mHk/3YindxWXfS0A2DgmtlFN1aS6udSF5qrjFtyxsdBr25Pd9HjmqjB/HxpEUcTsfaV4bV+pz2Ojk1X4oF+kz/THxsDlFrH0iBkv/V5SZaaLXAI82FGHGd310DfC478cRocbt64vxOaLTPC8QCcTMO4KNW5L0aB3DU39a8Mtirjym1yvBvqv9grHA50ad6+luzYVYsXf5ZmSY1uqcFMbjVdpnVQAfr8xHi2byE0nk8ONnitykWMu//25vpUKnw6MrvY5vGiumtUpYkeuDeuzbVifbcUhg/PiT7pMFwKJgoAay2MFAEOTlLi3gw6DmytDdg1VG6IootguIt/qQoJG2ig/26rz8u8leP3P8s9pqQBsHhuHzlFynDG50P2bs14Bwg/7RVZZJhzKtuTYMGZNftnXUUoJMic3q7ItBs9ljU96kQNv7C/Fir8t1d7IiFVJ8FBnHe5K1QZsbXfS6PSZEAx4ht75e0Lw11lm3L+lCJWSDjHr6jA81JlJXaGqzgHAvXv34oYbboDFYsGgQYPQtm1biKKIrKwsbNiwASqVCt999x169uzp72MmeC6CRv6U7zXFt5lagl2VUvLr4q0DpXjuN++JwgKAN/tG4M4QbUwOAN8cM2NaFRlIFcWpJRjRQoWRLVTon6iERhY8i7eaFFhduOrbXBRXWMTflqLBO9dWfeeSgktdFpr3bC7ENxVKO6UCsH60fwPCFqeIaVuLvAIjFzzeVYdnr6rf5sd1UWRz45XfS/BxhqnKBWO8WoIXeoZjYht1o38vtWGwuTHxlwKvZueA532WOkSYLzJis22YDLemaDC5raZOjf43nbFi3NryNgVKKXB4UoJf78AHwtazNoxeXX5hKBU8fxcZFbL/JrZR48N+UQ1xeA3my6NmPLClyGvb/0bG4JpqpmvzotlDFEVkFjuxPtuGDdlWbD1r9ykba2jhCgG3pWhxd2rg2gFQ/TE73Uj7Lg8nK9x8uVAl8uyeEiw8WF6N1FInxd4b45vctFCHW0TbL3O81tKrR8WgT7zv+YznssbD4hTxf3uKseiwqdp9LvRDn9JOWy/9+Irtbp8JwYAnKcdfE4KXHjHhkW0GVP7kmNcnnANsQlydA4BDhw5FdnY2fvjhB7Rp08brsaNHj2LMmDFo0aIFfv75Z78cKHn75LAJj+8weG37dGAUrq+m18SlWnz+9Sv/cLzUMwwPdwmtOwKiKOL1P0vxyh++GUg1UUsFDEhUYmSyCiNaqALamyHQZuwweH3w6eUCfhsff9n9LKhxqMtCs9DqQp+VecitUIbQIUKGTWPj/DLoItfswi3rC7C3UoN4uQRY0DcCt6QE182GvwodeGqXAdvO2qt8vFesAnPSwoM6o/acxYXxPxf4lD6nRsjw3fAY6OQCvvvbgi8yzV43p6oiEYAhzZW4NUWLES1Utf6ZmrqxEN8dLw8Y39RajY/6N/6gmSiK6LMyD4dryMzaMS4OHSJDt2y8Km5RxOAfz3kNiugWLcfGMbFVBsyb8kVzsd2NzWc8Ab912baywTKNTecoOf7ZQYsJrdUhc5OUPFaftODm9d7VAS/3CsfLv5d43fx5s08EpqYG12e4v9y7udCrL+70zjq8eLVvb9OmfC5rTA4bHLhrUyHSi6r+bG6tl+LRrnpMbqMJ+JCiypxuEU9WmhB8wSOddfhPz7rfJK9c9QV41mXvXBN862+6dHUOACYkJODJJ5/E448/XuXj8+bNw9y5c5GTk3NZB0i+zppd6PVdrlfJxfAWKiwbHOXXOv1vjplx36++acEzuunxzJWh0RPA5hIxfVsRlmf5ZiB1i5bjQKGjxn42FwgAesbKMSpZjZHJKrQPlwXN38/BQgeu+z7P632+0DMMj4RYoLcpq+tCs6rFfm0a9V/MgUIHbl5X4HMBG62U4PPBUVXeLQ8Goijiu78t+L89Jcg2+16cCwCmtNPg/3qEIUYVXMH1bJML49bmI7PYe5HcPVqOb4dFI7rS+8ksduCLTDOWHTXjrKX6YQCAp0zqptZq3NZOW+NAgHyrCx2We/fS+2FETNAMqvog3YinKi24LxjZQoUvh1Rf+hrKdubaMOKnfK9tC6+NwK1VXIQ0pYtmtyjizwIH1p22YsMZG3bn2X3WY9WRCMDVsQr0S1AiTC7A5vasdxxuETaXCPv5r+1uEXbXRR5zi7BX2rdyoq9cAoxpqca9HbRIu8wyf2rcJq0rwNoaer82U0uwb0IzqOohS6oxWnHMjLs2l2c1twuXYff4eJ/9mtK5rDESRU8bl6d3FVeZPd0xQobHu+kxrpW6QTNZRVHEOweNPhOCAU8rkQ/6XfqE4Df3l3pNrAY8mYUf9Y/EDVc0rbL9pqrOOflxcXGQSKq/syeVShEf73vCo8v39K5ir+CfViZgblq43xdcE1proJUJuHNToVdZ7Nw/S1Fidwf9SPBCqwu3bSjE9lzvTBW5BHj7mkhMbqtBodWFX7JtWH3SinWnrdWOfxcB7DnnwJ5zDrywtwRX6KWevoEt1OgTr2i0ZRCiKOLfu4u9gn9X6KW4vyNTvwkYmazGzW01+PJo+d3Ht/4y4h/JalwdV7dMtp9OWnDv5qKyRugXpEbIsGxIdFAP3REEAeNbazC8hQpvHjDi7b9Kvc6dIoBPj5ix8rgF/74yDHenahvtuaGiv0ucGLs2H6eM3kHNPvEKLBsSXWXbiZRwOZ7vGY5nrwrD+mwbvsg0YfUpa5UNtQttbnxwyIQPDpnQNUqO21I0uKmNxqes98uj3g2524RJcW2z4MmonNxWgxf2llRZJv1Y16Z7zk2LV+KGVmqvzM4X95b4fXhMMMg1u7DhjKeP38Zsm1c/4otprpFicJISg5ur0D9BGdAhG27ROzgYppD4JTOcGr/Xeodj0xlrte1ypnXSNdngHwAMTlJBJqAsSH6k2ImjxY6QHgoWbAw2Nx7dbsDK477JH1fopZh1dThGJqsaxTWuIAh4uLMerfQynwnB35+wInv1uVpPCBZFEa/8UerVyxPw9HNdMjAKo5KbxsRuAqRPP/3083V6olSK9957D2PHjkVYmHdj+JMnT+KJJ57Aww8/jB49evjjOOm8taesmPW7d9T+hZ7hGJIUmCm9KeFy9I5T4ofjFq/mvnvzHThldGF4i8ZxgrxUR4sdGLMmH/sLvbNZIpUCvhoaU3YSVMsk6Bwlx7gr1JjWWYe+8QqEySXIs7hR4qj+VrzBLmLPOQe+PGrGh4eMSC9ywCmKSNRKoWpEi+SfTlrxxgGj17aF10Y2uTK0UFdYWIjo6LplF13bTImvsswoPf/zLgLYkWvHbe00kF9C8EoURbz9lxEPbzN4nUsATyno18Ni0CxESs4VUgH9EpS4qbUGJ40un6w5mwtYl23DjycsSI2UI1nXeIOeh4o858ozZu9/tMHNlVg2JPqiTbAlgoC24TLccIUGd6dqkaCR4qzZhXPWqgMbuRY3fsm24b2DRqQXOaGTC2ipk0IA8NA2g9fAlUe76JEWRNmiKqmAk0Yn/izwLqG+ppkCM7v7f8BOMLkyRo7FGaayDDeTU4RE8PweVXQ557LGyO4SsS3Xjk8Om/B/v5Xgud9K8L+TVqQXOS/a008pBfonKHFPBx1e6RWO53qEYVSyGqkR8oAHYARBgEwiQCUVoJVLguJGBvlHhFIClxvYWkW7iwiFgA/7RzXpYLBKKmB7rh3HS8sjpC10UvSOC+1zWbDYnWfDDT8XVNmmZGJrNb4cEo0u0Y0vi7l9hByDEpVYc8rqdQM9x+zGyuMWDExUIraGIKAoinh2TwnmV7rmU0sFfDkkGsNaMPjXlNS6BHjBggU+27766itkZWVh1KhRaN26NQAgKysLa9asQZs2bTBx4kRMnz7dv0fchBkdnga8FcvmukfLsX50bJUTpvzpt3N2TPg5H4ZKk97GtlThoyD7sN921obbNhSgyOb9XtqESfHVkBi0Cb/4xbgoijhQ6MDqU1asPmnFvkoXdNWRSzwBlZEtVBiRrGrQC3+bS0Tad7n4u8IipX+CEiuHRze6Dz66PJdbarI+24obfy7w2vZARy1e7V27ieN2l4jHdxjweaZvH5P7Omjxcq/wkL6AXJ9txdO7in0CgRfc2U6D53uGBzRjpy7+yLdj/M/5PufKMS1VWHQZ533xfGnjF5lmfH3M7PO5UllzjRQDmivxRYWfH5kApE9qFnS9V/8ssKP/9+e8tn0zNDpgN/GCyUt7izFvf/nFiUoK7B4f7/U5GQplcxaniGVHzVh72ootOTafbOiatA+XYVBzJYYkqdA3XlkvzeiJKrM6RaStzPUKcgHAU931+NeVTftmBuDbX61vvAI/jYr12icUzmXBxC2KmH/AiJd/L/FppaCVCZjbJwI3t2385a81TQj+dGAUBjb3XUu4RRFP7izGx5WGnOhkApYPja526BaFrloHACMjL30aqCAIKCwsvPiOVCvP7C72mrIlEYANfp7KWZODhQ7c8HM+8ir1cxqUqMRng6KgDYJSnS+PmjF9W5FPGVrfeAU+HxSFqDr25co2ubD2lBWrT1qwOcfmk+FUnc5RctzcVoMp7TQBGydfnQUHSvGfCtOeJQKw9fo4dGT2X8jxx0Lz0W1FWHKkPAAjAPixhmmdFxRaXbh9Y6HPcAypAMxJazqTxuwuER8cMmLOvtKybMqKmqklmJMWgbF+GuR0ubaftWHSugKfY53cRo13ro30W8DW6hTx00kLvjhqxoZsm0+Pm+qMbanC0kHBmT0x6Zd8rD3tmex3bTMFfhgRw5suAEodbvT8Ntdr8NCNV6jx8YDyIS/BftGcVezEzesLcKSamwGVhSkEDEjwlPUOaq5Ei0acLUxNy9pTVkxaV35jUCsTcOCm+Dqvo0PJ8VInun+TW/a1RACOTm7m9XcT7OeyYHLW7MJ9vxZhc47N57GuUXJ8MiAyqEq0q5sQLBWAN/pE4I725f1zXW4RD28z4L9HvW/AhysEfDssBj1jg6eNCvlPrQOAJ0+erNM3SE5OrtPzyNu+fDsG/XjOq1fbtE46vNzr8prxX6pjJU5cX0UvqLQ4BZYPrboXVGNQXd8DwHNBu+CaSL9lMZY63NiYbcPqU1asPWX1KlmrToRCwD0ddLi/o7ZehgPkml3ouSLX6+L+nlQt5vapXUYXBRd/LDRLHW5cszIPJyv87rfUSbFtXFy1fbqOGByYtK7AK8sU8FzUfjqg6juVoS7X7MILe0t8FmMX/CNZhdfTIpCobbiLqHWnrbh9Q6FPCeK9qVq8lha43q+njU4sy7Lgi0yTz89MZd8Oi8bgIP35Kba78WmGCW4RuLO9ttFlfjakz46Y8PA2g9e2taNi0Pt8qXcwXzRvzLbizk2FKK4h41WApxx6cHMVBjdXomds4+0hTDRjhwGLzmcVvdEnAnc10cm/Vem7Mtdrsuz713l6i18QzOeyYPLLaSse2FKE/CrajtzfUYsXeoYHVRXbBbWZEOwSgft+LcKKv717HUYrJfhueDS6RjP411TVeQow1R+nW8TgH8959Q1K0kqx84bqL7wD6bTRiRt+LvApZ+saJceK4dGNbrql1Sli2tYifPu3b7PXZ68KwxNddQHLvnC5Rew+Z8fqk1b8dNKKoyU13/VXSYHbU7SY1lkX0GEID20t8irHDFcI+P3GeJ9JnhQa/LXQ/DXHhrFrvKd13p2qxbwqAscbs624Y1Oh18AiwNNgefmQaLSLCJ67rYGw/awNj2w3VFkWHCYX8J+eYZjaXlvvPVZXHbfgns2FPlnSj3fV4f+uCquXTDVRFLE9144vMj0DUyoPzUjWSbFvQnxQ9p+lmrncIgb+cA77C8vXOz1i5PhldCwkghCUF82iKOL9dBOe2eM9cOuCeLUEg5qrMKS5EgMSlfwcpqAhiiIyip1QSwW0DOIBXoEwa28J5u4vTzoY10qNJQNDJ5u5sbO7RLywt8Srcu6CKKUE714XgRFB3vfuYhOCHW5gdaWJ3c3UEqwcEYPUJr4Gb+ouKwB4/PhxZGRkoLS0FDqdDqmpqWjVqpUfD48AYOFBI57ZXey1bfmQaAxv0XDZD+csLoz/uQAHCr1737UJk+LZq8IwpmXDjk2/IN/qwq3rC32avSqlwLvXRuLG1vXb7yGz2IHVJ61YfcqKXXn2Ki8GAE8a9/gr1Hikix6do/x7kt6Xb8fAH855fVjM7h3Oyb8hzJ8LzZk7DfjwkHcfkZXDozEgsfx8tOiQEU/tKvbps3K5pfahxuoUMW9/KeYfKK1yOm5anALzr4mot4XafzNNeGibwee89FyPMDzeVV8vx1BZqcONlX9b8EWmGTvz7AhTCFgyIAqDgjT7jy5u61kbRq/2vtHwQb9ITGqjCbqLZptLxBPV9D+d0FqNR7vo0SlSxhJwohCz95wdg38s7/eqlws4enNCWbZZsJ3LgsmxEifu2lRYZX/2a5sp8GG/qAatsvC3H05YfCYEVyVJK8X3I2LQOozB+qauTgHAVatWYfbs2cjIyPB5LDU1FU899RSuv/56vxxgU3fK6ETad3leTaIr30VqKAabG5PWVT1JKUkrxT87aDGlXcOVN2UYHJj4SwFOVCpXjlZK8N/BUWUlRQ0lz+LCosMmfHTI6NNkv6KhzZV4pKse18Rf/lQqURQxanU+duSW/5u1D5dh67i4S5roSsHFnwtNk8ON61bl4ViFEs0kracUWCsT8O/dxT4BQgC4LUWDN/pEQBGEpRaBdqjIgenbirDnnO9iVS4Bnuiqx2Nd9QEtU/nokBFP7iz22f56Wjju7dA4bg6U2N2QSQCNjCWzoe72DQX44UR55kKiRoI94+Nx5nhW0Fw051lcuH2D7w1IAcDzPcMwvXPgqg+IqGG5RREdlp/16mm6Ylh02c2rUAgAiqIIi0uEWio0mnPZ8iwznthugLFS5YBUAP51ZRge66IL+ODMhvD7OTtuXl/g9fNW0RV6KVaNiGnQ4ZPUeFxyAHDWrFl44403oNfrMWrUKHTp0gU6nQ5GoxEHDhzA6tWrUVJSgscffxzPPvtsoI67SRBFEZPXF2JthfTdMIWA3TfEo5mmcdy5MDncuG1DITae8W2sCniaAt/SVoP7O+pqNV3XXzafseL2jb7lh+3CZfhqaHRAy2svldHhxtIjZrx70Og14bmyq2PleKSLHqOSVXUufVtxzIy7Nhd5beMEytDn74XmzlwbRv6U75VFelNrNQptbqzP9j4XCABe7BmGh3ixWyOXW8THh014cW+Jz8IV8ATqF1wTgbQA3Lh4Y38pXtxb4rVNIgDvXBOBW1LY04nq398lTvT+LtdroNbT3fW4UZcbFBfN+/LtuHV9IbLN3p/permARf2jGrSCg4jqx/RtRVhaYXjavalavH6+ZUpDBgBtLhGlDjdK7SJKHG4YHeVflzpEGB1ulDhElNrdMDo9f5ae38foEM/v59kmAohUChjaXIURLVQY1FzVIIkfRocbM3YYsCzLt91TklaKRf0jA7J+akxOGZ2YVMWE4PbhMqwcEYNQidPDAAAgAElEQVSERhI7oIZ3SQHA9evXY8KECRg7dizeeusthIf7DqAoKSnBI488glWrVuGbb77BoEGD/HKgr776Kl577TWvbXFxcThy5AgAT7Bs9uzZ+PTTT2EwGNCjRw/MnTsXHTp0KNvfYDBg5syZWLNmDQBgxIgRmDNnDiIiGufgg1XHLbhjo/cU5cbYZNfmEvHYdt8JQxUJAIa1UOHBjjr0S7j8TLaaLD1iwuPbDah8Dd0/QYlPB0Y12obrdpeIb46Z8dZfRhw2VN8rsF24DNO76DCxteaSsqksThFXr8j1CjIOT1Ji+dCYyzpuavwCsdB8dncx3qmit0pFWpmAj/pHYlRycPdZqU+njU7M2FmMNZX6tlxwd6oW/+kRhjA/DFwSRREv7i3Bmwe8/x3lEmBR/yhc30gmElPT9J89xVjwV/nPploq4OurzLi2c9sGPKqL++5vMx7cYvApx2qtl+LLIdFoz95LRE3C6pMW3Ly+/DouSSvFgZviIQS4n2lWsROfZ5pwsMiBUoeIEvuFIJ8ncFdVyxF/kQpAn3gFhrfwBATbhgW+xcG+fDvu3lyIrBLfJIoxLVV4+5rIRnvt528ldjembiosuxnfJUqO7xphf35qWJcUAJw4cSLOnDmDX3/9FRJJ9b9Ibrcb/fr1Q0JCAr7++mu/HOirr76KFStW4McffyzbJpVKERPjCV7Mnz8fc+fOxcKFC5GSkoI5c+Zg586d2LNnD/R6T++iCRMm4PTp01iwYAEEQcD06dPRsmVLLF++3C/H6E/Fdjd6r8jF2QqpvL3jFFg9KqbRNj4/bHDg/YNGLMsyw1rDAMdOkTI80EmHCVdooJL57724z1/Mzj/gG5S4PUWDN/pGBEWZq1sUseaUFQsOGKssr74gUSPBg510uKO9FvpaDIOZs68Er/xR3pBYJgA7bohDSjgvRkJdIBaaFqeI/t/n4UgVQywAz0L3yyHR6OLnHpZNgSiKWHXcipm7DMiropwjUSPB62kR+EfLugfo3KKImTuLyyY4XqCWCvh8cFTQTtil0FFid+Oqb3O9pjeOinXiv6NbNuBRVc8tinjlj1LM/bPU57EBiUosHhCFyCZyEUpEgNnpRpv/nvW6GbDl+jh0iZL7fV3mFkWsO23DR4eM+CW76qqshtBaL8Ww88HAvvFKv7aBEUUR76Wb8PxvxV7Z4oBnqOIrvSIwtb2myVWfXLiONDlEjG2lDsopxxRYlxQAbNOmDR555BFMnz79ovu+9dZbWLBgAbKysi7rAC949dVX8f3332PHjh0+j4miiNTUVNx7772YMWMGAMBisSAlJQUvvfQSpk6dioyMDPTu3Rtr1qxBWloaAGDHjh0YOXIk9uzZ0+hKSp7YYcDHFS7M5BLg17Fx6BDZ+C+mC6wuLMkw46NDRq8AZmWxKgnuTtXirlQt4tSXd2fC7HTj/l+L8P0J36yZF3uG4eEgLT/ckWvD/P2lWHu6+g/zcIWAezvocF8HLWKr+XvMNrlw9Ypcr2ma0zrp8HIv3yxeCj2ButO895wdQ/93zmdoRI8YOf47OBrxLDe4LAabG/+3pxifVTFAAPBMeZuTFnHJLSGcbs9k9OWVSmX0cgHLh0Sjb7PQLpOh4LEkw4RHtxu8ts1NC8eUdtpG1U+01OHGfb8W4aeTvmuQ+ztqMevq8EYxGI2I6tfN6wq8JrH++0o9ZnYP89u6zGBz44ujZiw6ZMTfpTVkXwSIVIDPwLfq6OUCBiYqMbyFCsOSVNVes9RGvtWFaVuKqrw+So2Q4ZMBUegYBNfMRA3hkhqhmUwmREXVbvhEZGQkTCbfRvCX4/jx4+jQoQPkcjl69uyJ5557Dq1atcKJEyeQm5vrVW6sVqvRt29f7Nq1C1OnTsXu3buh0+nQu3fvsn3S0tKg1Wqxa9euRhUA3J1nwyeVsjIe6awPiuAfAESrpHiimx4Pd9Zh5XEL3j1orHIS0zmrG7P3leKN/aW4qY0GD3TU1Wniba7ZhVvWF2Bvvvf3UEmBD/oFdxlbn3gl+gxV4mChAwv+KsW3xyw+H7TFdhFz/yzFO3+V4rYULR7qrPPpcfjCb8Vewb9opQRPdmuYqZ4UOnrEKvB4Fz3m7i/PeLnxCjXeuTYSaj9m9zZVEUoJ3r42Eje10eDRbUVeg1cA4PsTVmzKycVLPcNxeztNrbLDbS4R92wu9BqwAABRSgm+HRaNK2MUfn0PRJfj9hQNPjpkxMGi8kzjGTuLMf+AEY911eG2FG2DZzccL3XilnW+fZfkEmBenwhMade42rYQUf0ZmazyCgCuPmXFzO5hl/266UUOfHTIiOVZFq/1fW3IJYBeLoFeLkAnFxCmuPD/nj/1cgn0ivKvw+QS6OSC5zFF+T46uefcuzvPjrWnrFh72lpjC6NSh4jvT1jx/QkrBAA9YuUYnqTC8BYqdImS1zpR49ccG/65ubDKJJM722nwSu9wDgsjqsElBQATEhKQnp5eq33T09PRrFmzOh1UVXr27Il3330XKSkpyM/Px+uvv45hw4Zh586dyM3NBQDExsZ6PSc2NhY5OTkAgLy8PERHR3udXARBQExMDPLy8mr83i63WG8TgxxuEY9uM3g112+t9wTUgo1CKmBiGw1uaq3Gzjw73j1oxP9OWn2yhexu4ItMM77INKNfghIPdtJiWFLtBl2kFzkwaV0BTlWa9BunluDLwdHoERsaF7OdouT4sF8Unr3KiYV/GbH0iNmnv5DVBSw6bMLiDBNuuEKNR7ro0SVKjt15Nnx1zDvT59mrwppMPwwKrH9fpYdaJmB7rg1jWqpxR7umV24RaP0SlNg2Lh6v/1mCtw4YvfqblthFPLLdgOVZZiy4JqLGkn6z043bNxT6DGppppbgu+ExQXOTiZoOqUTAK73Ccf3aAq/tp00uPLGjGPP+LMX0Lnrc0U7bIDcdtuTYcMfGQhTavC9EY1USfDYoKuSbzhNRzYZXGrL3R74DZ2oY+FcTp1vETyet+PCQEVvPVt8iCPBUYtzZXovWYTJPkO98UE8vl/j9pknfZkr0babEC1eH43ip0xMMPGXF1rM2n9LcC0QAv51z4LdzDrz8Rymaa6QY1sKTHdgvQVllAM/pFjF7Xynm/VmKyiHPMIWAt/pGYtwVwZv0QVRfLqkE+Mknn8SyZcuwefNmtG7dutr9jh07hv79+2Py5Ml4/fXX/XKglRmNRnTv3h2PPvoorr76agwfPhx//fUXkpKSyvZ58MEHkZubi2+//Rbz5s3DZ599hn379nm9TteuXTF16lQ89thj1X6vlC9OYUSsC6PinGirvbS7LJdq8SkZ3j3hHbRa2NmKXhEB7Nhaj7KtAr46I8OqXBlMruo/gJJVbkxKdGJ0vBPVVbftKJLgX4eVPq/TRuPGmx1tSFAF9t+qIRkcwFdn5PgqR4ZiZ/V/j30iXci3C8g0lX+Qpmjc+OxKKxpR9RQR1dIRo4CXjyqQbvQ9MSoEEXcnO3B7cycqtwU1OoHH0pXYV+L9vASlG+92tiFJHbrnSwp+y87IsOBvOZxi1R9cUXIRU5IcGN/MicvsKFJr3+TIMPeYHK5Kx9RO68a8DjY0C+E1CBHV3tQ/lfirtPzE9K82doxPqD5TrrIiB7DyrAzfnpUh11b9zXu5IGJojAsTE53opG/460aTE9htkGJrkRRbC6UodNTuwkMpEXF1uBvXRrlwTZQLzZQicqwCns1QYH+p7wm+i96FWe3tSOQ5lwgALlrZekkBwJycHPTp0wcKhQIvvvgixo8fD4WiPFhlt9uxYsUKPP/887Bardi+fTsSExPrfvQXMXr0aLRr1w7Tp09H9+7dsWHDBlx11VVlj0+cOBFRUVF4//338dlnn+Ff//oXTp06VZadIooikpKS8Nprr+G2226r9vtELM4u+//OUXJMaqPGTa01l9x36WKOlTjRZ2UubBVuDE1uo8b7/WpXdh1MSuxufJFpxvvpRpwwVn8nLFwh4I52WtzbQYsWuvKE1U8Om/DkToNPOeyQ5kp8MiDKLxMyg4HJ4cbSI2YsPGj0mu5bkx9GxOC6BGYlNCWBnDZH9c/lFvHBIRNe/r0EpipKfzpGyPDWtZHoeT4DusDqwvifC/BnpVYMKeEyrBweg+Za9mqkxu+00YkXt57Gqjy51zqpohiVBA910uHuDrUbjlUXDreIp3YW45MM3zY341qpsfDaCGgD9L2JKPjM+7MUL/1eUvb1sCQlXm5VdNF12R/5dnx4yIQVf5urPecBnsFgd6XqcEc7zWX11QsktyhiX74Da057sgMrr0dq0jlKjlNGJ4rt3usdAcDjXXV4+sqwoBjySNRYXFIAEAD27NmDKVOmIDc3F0qlEm3btoVer0dpaSmOHj0Km82GuLg4LF26FL169QrUccNqtaJbt2646667MHPmTKSmpuKf//wnnnjiibLHU1JS8OKLL3oNAVm7dm1ZH8Bdu3Zh+PDhFx0CUjEAeIFEAAYmKjGpjQb/SFZd9mJPFEWMW1uAzTnlpVlRSgn2jI9DdAiP7na5Raw+ZcV76UZsqyGdXSoAY1uqcX9HLb4/YcXCg76Tfu9O1eK13k2z0bbDLeKbYxa8daAUh2rovzG2pQpLB0XX45FRY8AAYGg6aXTiie2GKif+CQDu7eC5eXL7hkKfvjxdouRYMSy60V4sEFUlMzMTuuat8daBUizJ8G2FcUGkUsC0Tnrc20GLcD/eECywujBlY2GV65VnrtRjRjc9WyAQkZf0Igf6rixvN6WUAr/0MqNrqu+6zO4SsfK4BR8dMmLPuZqDZH3jFbivow6jklVBFwDLMbvwy2krVp+0YnOO7ZL7GMarJfiwXyT6J6ouvjMRebnkACAAFBcXY/HixVizZg0OHz4Mo9EInU6H9u3bY8SIEZg6dSoiIiL8eqDPPvssRowYgaSkpLIegNu3b8e2bduQnJyM+fPnY968eVi4cCHatm2LuXPnYvv27dizZw/0ek//vAkTJuDMmTNYsGABRFHEo48+ihYtWmD58uU1fu+qAoAV6WQCxrRSY3IbDa5LUNSqd11ly46acf+WIq9t714bgVtSmk7z6H35dryXbsSKvy1wXELmugDg5V7heKCjtskvvN2iiLWnrFhwwIided4XKEopsOuGeJ8BIRT6GAAMXaLoCf4/vasYBbbanTh7xSrw1dBo9gGloFPxXJZnceGdv4xYdNhU7cVjuELAAx11uL+j7rJ/3v8qdOCW9QU4WalqQSsT8H6/SIxpyd5TRORLFEV0/ybXq+Lp9Q423JtW3k4rx+zCJ4dN+PSICXlVDLe4QC0VMLGNGvd2qNvgxMbI4hSx9awNP5+yYvUp60UrmoYlKfHudZGICeEEGaJAqlMAsCHcdddd2L59OwoKChATE4OePXvimWeeQWpqKgDPyXX27NlYsmQJDAYDevTogblz56Jjx45lr1FUVISnnnoKq1evBgCMHDkSc+bMuWiw8qssM5YdNWNTjs1ngEVlzTVS3NRGjUltNLVuqF5gdaHXijyvi7d+CUqsGh7dJANaZ80uzzCLw6aLXtBqZAIW9Y/EqGQuvCvbkWvD/ANGrD1lhUzwTCO8o33TCShTOQYAQ1+h1YVn9pTgy6PmGvfrn6DEF4OjoGOJIgWhqs5l+VYX3j1oxIfpJhirCQSGyQX8s4MOD3bSIqoOF40/nrDgvl+LfEruk3VSfDk4Gp1C5EKciALj6V0GvJ9e3jZgTJwTS0clY2eeHR+mm/DDCQtqSoJrqZPing5a3J6iDembd6Io4pChfJDI7nP2smtvuQR4vqcn4aMuyTZE5BE0AcDGIMfswjfHPMHAg0UXb97aLVqOSW00mNBajbgayqwe3FKE/1a4aFNKge3Xx6NNeNPO1LI4RXx9zIz3DhqrLGtN0Hgm/XaPCY1Jv4FiOB9EDeUFA9WMAcCmY2O2FY9uN1TZW3VkCxUWD4iCqgGmpRL5Q03nsiKbG++lG/F+uhEl9qqXtjqZgHs6aDGtk65W5e+iKGLun6V4+Y9Sn8euaabA0oFRId2mhYj8Y/MZq9c0c71URKtwBQ4U1lzmO7i5Evd20GJocxWkQVbm6w8FVhfWZdtwxuTCP5JVaBfBmy1El4sBwDr6q9CB5VlmfJ1lxtkaUrUBT/+6wc09/QJHJauhrnDx9WuODWPX5Hvt/8yVejzZPSwgxx2MRFHEpjM2vJduxM+nPb2uroyR4/NB0WxeT1QLDAA2LWanG7P/KMU7B41ld85vaq3Gu9dFBl2fIKKKanMuM9jc+PCQEe8eNMJQTSBQIxMwtb0W0zvrEF/NQDeTw41pWw1Yedzi89hd7bV4LS2cv09EVCsOt4g2X+ZUe3OiIr1cwC1tNbingxYp4Qx4EZF/MQB4mVxuEZtzbFiWZcaPJ6wXbWKqlwu4vpWnRLhnrALXrspFVkl5pkZqhAy/jo2DQspFZVWyTS7kml3oHiNn+jdRLTEA2DQdKnJg9SkrUiNkGNFCxXMmBb1LOZeV2N34+LAJb/9lRGE17URUUuCOdlo80kWPxAo3FE8Znbh1fSH2V8rOkQnAa2nhuDtVV/c3QURN0t2bCvHt3743FC5oFy7DvR20mNxWE7Ap5kREDAD6kdHhxg8nrFieZcbmMzZc7C82TC6gxOG915pRMUiLVwbuIImoyWEAkIhCQV3OZUaHG4sPm/DWX0acs1YdCFRIgCnttHikiw7ZJhdu31Dos2+UUoIlA6PQL4FrNCK6dN/9bcbUTd4DHyUCMKKFCv/soEX/BGWT7P1ORPWLAcAAyTZ5+gUuP2pGehX966oytb0Gb/aNDPCREVFTwwAgEYWCyzmXmZ1uLMkw460DpdW2brmQdOOo9HDHCBn+OyQarfRNuzczEdWdyy3itg2FWH3KinCZiDtT9bgrVYuWPK8QUT1iADDARFHEgUIHlmWZ8c0xS7Wj3ePVEuy6IZ6DGojI7xgAJKJQ4I9zmdUp4rNME+bvNyLb7Dssp7JRySp80C+SJXlE5Bf5VhfyTx5Dajuuy4io/nE1E2CCIKBrtAKv9IpA+sRm+GZoNCa0VkNdocefRABeT4tg8I+IiIgogFQyAfd20OH3CfF4s08EkmoYJjajmx6fD4pi8I+I/CZGJQVbvRNRQ2HOcT2SSQQMSVJhSJIKJXY3fjxhwXGjC9c2U7KnDBEREVE9UUoFTE3V4tYUDZZlmfHG/lIcL/VkBKqlAhZeG4HxrTUNfJRERERE/sMAYAMJU0hwS4q2oQ+DiIiIqMlSSAVMaafFLW01WH3Kir9LnBjbSs1+f0RERBRyuLohIiIioiZNJhEwpqW6oQ+DiIiIKGA4BISIiIiIiIiIiCiEsasxERERERERERFRCGMAkIiIiIiIiIiIKIQxAEhERERERERERBTCGAAkIiIiIiIiIiIKYQwAEhERERERERERhTAGAImIiIiIiIiIiEIYA4BEREREREREREQhjAFAIiIiIiIiIiKiEMYAIBERERERERERUQhjAJCIiIiIiIiIiCiEMQBIREREREREREQUwhgAJCIiIiIiIiIiCmEMABIREREREREREYUwBgCJiIiIiIiIiIhCGAOAREREREREREREIYwBQCIiIiIiIiIiohDGACAREREREREREVEIC5oAoMvlwqxZs9C1a1fEx8eja9eumDVrFpxOZ9k+DzzwACIiIrz+GzJkiNfr2Gw2PPnkk2jdujUSExMxefJkZGdn1/fbISIiIiIiIiIiqheyhj6A2po/fz4WLVqE9957Dx07dsTBgwfxwAMPQKFQYObMmWX7DRgwAB988EHZ1wqFwut1/vWvf+Gnn37Cxx9/jMjISDzzzDOYNGkSNm/eDKlUWm/vh4iIiIiIiIiIqD4ETQBw9+7dGDFiBEaOHAkAaNmyJUaOHIm9e/d67adUKhEfH1/laxQXF+Ozzz7DwoULMXDgQADABx98gC5dumDTpk0YPHhwYN8EERERERERERFRPQuaEuC0tDRs3boVR44cAQAcPnwYW7ZswdChQ73227FjB9q2bYsePXpg+vTpOHfuXNlj+/btg8PhwKBBg8q2JSUloX379ti1a1f9vBEiIiIiIiIiIqJ6FDQZgI8++iiMRiN69+4NqVQKp9OJGTNm4J577inbZ8iQIRgzZgxatmyJkydPYtasWRg7diw2bdoEpVKJvLw8SKVSREdHe712bGws8vLy6vstERERERERERERBVzQBABXrFiBZcuWYdGiRUhNTcWBAwfw9NNPIzk5GVOmTAEA3HjjjWX7d+rUCd27d0eXLl2wdu1ajB07ttrXFkURgiAE/D0QERERERERERHVt6ApAX7uuefw0EMP4cYbb0SnTp0wefJkTJs2DW+++Wa1z0lISEBiYiKOHTsGAIiLi4PL5UJBQYHXfvn5+YiNjQ3o8RMRNZTMzMyGPgQ6TxRFZBY7sPiwCe8eNGJ3ng0ut9jQh0UUFHguI6JQwHMZETWUoMkANJvNPlN6pVIp3G53tc8pKChATk5O2VCQ7t27Qy6XY+PGjbjpppsAANnZ2cjIyEDv3r0Dd/BERNRk5Vlc2HzGho1nbNh8xoZss8vr8XCFgAGJSgxursKgRCWSdEHz0UxEREREREEiaK4yRowYgfnz56Nly5ZITU3F/v37sXDhQkyePBkAYDQaMXv2bIwdOxbx8fE4efIkXnzxRcTGxmL06NEAgPDwcNx+++147rnnEBsbi8jISDzzzDPo1KkTBgwY0IDvjoiIQoXJ4caOXDs2nrFh0xkrDhY5a9y/2C5i1XErVh23AgDah8swqLkSg5qrcE0zBTSyoEnWJyIiIiKiRipoAoBz5szByy+/jCeeeAL5+fmIj4/HHXfcgZkzZwLwZAOmp6dj2bJlKC4uRnx8PK677josXrwYer2+7HVeeeUVSKVSTJ06FVarFf369cP777/vk11IRERUGy63iD8KHNh0PuC3O88Oe/XJ6ReVUexERrET76WboJQCfeKVGJzoCQh2jJSxZy0REREREV0ywWAwsPkQEVEIy8zMREpKSkMfRsgQRRHHSlzYlGPFxmwbtpy1odhe+49SlRToG69EuEKCTTlWFNlq/9xmagkGNldhcHMlBiYqEa3izStqOnguI6JQwHMZETWUoMkAJCIiaij5Vhd+Pd/Hb1OODaeMros/6TwBQPcYOQYkKDEgUYXecQqoZJ4sPpdbxL4CBzZkW7HhjA278+xw1RAPPGtx48ujZnx51Fz2uoMTVRjUXImr4xSQS5gdSEREREREvhgAJCIiqsTiFLEz93zA74wN+wsdl/T8VnopBiZ6An7XNVMgqppMPalEQI9YBXrEKvBkd6DY7savOTZsyLZifbYNJ2sINIoA/sh34I98B+buL4VeLuC6BCUGN/cMFGml50c8ERERERF58OqAiIgInuDbN8fM+P64FTvzbLDVPskPkUoB/RNUGJCoxIBEZZ2Db+EKCca0VGNMSzVEUURWiRPrsz0BwS1n7TA7q08PLHWI+OmkFT+dtAIoRmu9FIObqzDuCjWuaaas0/EQEREREVFoYACQiIiaLFEUsTffgSUZJqz421JjgK0ipRRIi/ME+wYmKtElSg6pn8tvBUFA23A52obLcV9HHWwuETtz7dh4xpMdeOAiWYnHSl04dtiEjw6b8NY1EZjSTuvX4yMiIiIiouDBACARETU5xXY3vs4yY8kRM/6qZXlv1yh5WcAvLV4Jtax+++0ppQL6JyrRP1GJ53sCuWYXNp6xlfUPzLdWP3r46V3F6JdQ98xEIiIiIiIKbrwSICKiJkEURfx2zoElR0z4rhbZfi105/v4JSjRL1GJmEY2cTdeI8XkthpMbquBWxSxv8CBDecDgrvy7HBUiAeanSKmbS3CDyNiIBE4KISIiIiIqKlhAJCIiEKawebG18fMWJJhwsEiZ437JmokuL2dFje1VqNNmAxCkATLJIKA7jEKdI9R4PGuepQ63PjokAkv7i0p22fbWTsWHTLhnx11DXikRERERETUEBgAJCKikCOKIvacs2NJhhnf/W2BxVV9tp9EAIYmqXBnOw2GJqkg83Mvv4agl0vwWBcdtubYsOGMrWz783tLMDRJhSvC+PFPRERERNSU8AqAiIhChsHmxldZZiw5YkL6RbL9mmukuL2dBrelaJCkC72PQ0EQsOCaCPRdmYdShycAeqEU+MeRLAUmIiIiImpKQu+Kh4iImpQL2X6LM8xYWYtsv+FJKtzZXoshzZV+n9zb2LTQyfByr3BM32Yo27Y9144PD5lwP0uBiYiIiIiaDAYAiYgoKBlsbizPMuPTDBPSDTVn+yVpL2T7adFc27iGeQTa7SkarDpuwfrs8lLgF34rwbAkFVqzFJiIiIiIqEngyp+IiIKGKIrYlWfHkgwTVh63wOqqfl+pAAxvocKd7bQY3ASy/aojCAIW9PWUApecLwW2uDylwP9jKTARERERUZPAACARETV6NpeITzNMWJxhwqFaZPtNOZ/tl9jEsv2qk3S+FPjhCqXAO3Lt+CDdhAc6sRSYiIiIiCjUMQBIRESNWo7ZhVvWF+CPfEe1+0gFYEQLT2+/QYlNN9uvJrelaPD9cQt+qVAK/OJeTylwm3AuB4iIiIiIQhlX/ERE1Gjty7fjlvUFOGN2V/l4C50Ud7TT4tYUDRI0zPariSAImH9NJPqszEWJ3bcUmEFTIiIiIqLQJWnoAyAiIqrK98ctGLU63yf4JxWA0ckqfDM0GvtujMeMbnoG/2qpuVaKV3qFe23bmWfH+4dMDXRERERERERUHxgAJCKiRkUURbyxvxRTNhbC7BS9HhuepMRfE5vh88HRGJKkYtZaHdzaVoNhSUqvbS/tLcbR4upLrImIiIiIKLgxAEhERI2GzSXigS1FeHFvic9jD3bS4r+Do5ntd5kEQcD8vpEIU5QHT60uYNpWA1xusYZnEhEREcwOOQgAACAASURBVBFRsGIAkIiIGoV8qwvXr8nHsiyL13aZACzoG4FXekUw489PErVSzK5UCrwrz4730o0NdERERERERBRIDAASEVGDO1TkwKAfzmFnnt1re4RCwIrhMbijvbaBjix03dxWg+GVSoFn/V6CTJYCExERERGFHAYAiYioQf1y2oph/zuHk0aX1/a2YTKsHx2HfgnKap5Jl+PCVODwyqXAW1gKTEREREQUahgAJCKiBiGKIt47aMSkdQUodXgHnPolKLFudCzahMsa6OiahgSNFK/1jvDatvucHe8eZCkwEREREVEoYQCQiIjqncMt4okdxfjX7mJUTjab2l6Db4dFI0LJj6j6MKmNGiNaqLy2zfqjBEcMLAUmIiIiIgoVvLoiIqJ6ZbC5MeHnAnySYfLaLhGAV3uF440+EZBz2Ee98UwFjkBEhVJgmwuYtrWIpcBERERERCHCb7VVCxYsuOTnCIKA6dOn++sQiIiokcsqdmLSugIcLXF6bdfLBXzcPwrDKmWiUf1oppHitbQI3PdrUdm2PeccWHjQiOld9A14ZERERERE5A+CwWDwy+39yMhI3xcXPNkEoij6bBdFEYIgoLCw0B/fnoiIqpGZmYmUlJSGPgz8mmPDlA0FMNi9PxOSdVIsGxKNjpHyBjoyAjyf1bduKMRPJ61l25RS4NexcWgfwX8baniN5VxGRHQ5eC4joobitxLgs2fPev134MABdOrUCaNHj8ZPP/2EzMxMHDlyBP/73/8wevRodOnSBfv37/fXtyciokZs6RETxq/N9wn+pcUpsH50LIN/jYAgCHizTwQild6lwA9uKYKTpcBEREREREHNbwFApVLp9d9zzz2HpKQkLF26FH369EFMTAxiY2PRt29fLF26FImJifjPf/7jr29PRESNkMst4pndxZi+zQBnpRjSpDZqrBoRg1i1tGEOjnzEa6SYU2kq8N58B975i1OBiYiIiIiCWcCGgKxbtw5Dhgyp9vGhQ4di3bp1gfr2RETUwEodbtyyoRALD/oGj/7vqjC8f10klFIO+2hsJrRW4x/J3r0YX/mjBIc5FZiIiIiIKGgFLAAokUhw6NChah9PT08P1LcmIqIGdtLoxPD/ncPaU1av7WqpgE8HRuGJbvqyPrHUuAiCgDf7RiBKWb5EsLtZCkxEREREFMwCFgAcNWoUFi9ejHfeeQcWi6Vsu8Viwdtvv40lS5bgH//4R6C+PRERNZDdeTYM/uEc0ou8J/0maCRYPSoG17dSN9CRUW3FqaV4PS3ca9vv+Q68xVJgIiIiIqKg5LcpwJUZDAZMnjwZu3btglKpREJCAgRBwJkzZ2Cz2XD11Vfjq6++QkRExMVfjIiI6qw+p819lWXGw9uKYHN5b+8eLcd/B0cjUct+f8FCFEVM2ViIH06UZ3EqJMCmsXEc2kINgpMziSgU8FxGRA1FFqgXjoiIwOrVq7Fq1SqsXbsWp06dgiiK6N27N4YPH46xY8dCIglYAiIREdUjtyjilT9KMffPUp/HxrZU4f1+kdDIeM4PJoIgYF6fCGw7m4dCmxuApxR42tYi/PKPWMgkLOEmIiIiIgoWAQsAAp6Lh3HjxmHcuHGB/DZERNSAzE43HthShFXHrT6Pzeiqx7+v0kPCfn9BKU4txdy0cNy1uahs2x/5Diw4YMQT3fQNeGRERERERHQpmI5BRER1YnWKWHbUjCE/nPMJ/ikkwAf9IvFsjzAG/4LcDVeocX0r76nAs/eVIL2IU4GJiIiIiIJFQDMAly9fjk8//RQnTpxAUVERRNG73eCFnoBERI2FzSViZ64dSimQpJWimUbKUsdKjpc6sfiwCZ9lmstKQyuKUUnwxaAo9I5XNsDRkb8JgoC5aRHYmpOHgvP/3o7zU4F/GR0LOX8/iIgaXLHdjQyDA4cNThw2OOB0A9c2U2J0SxVvxBEREYAABgBfffVVvP7660hJScGwYcM47IOIGr0tOTZM21qEk8byCRZSAUjQSNFcK0WSttKfOs//RyklEEJ8ce1yi1iXbcPHh4345bQN1U2P6hghw5dDotFSH9D7S1TPYtVSzOsTgTs3FZZt21fgwPz9pXiye1gDHhkRUdNSYncjw+DEIYMDhw0OZBicOFzkRLbZ5bPvh4dMaB8uw2Nd9ZjQWs0bmkRETVzApgC3b98eV155JZYtW+aX13O5XHj11Vfx1VdfITc3F/Hx8Zg4cSKefvppyGSeC01RFDF79mx8+umnMBgM6NGjB+bOnYsOHTqUvY7BYMDMmTOxZs0aAMCIESMwZ84cBiiJmjCz040XfivBB4dMdXq+WiogSecbJEw6HyRsrpU26ACMy5k2d87iwueZZnySYcIpo+/FRUXjr1Bjft8IhCnYXSJU3bmxECuPW8q+lkuAjWPi0DmKU4Ep8Dg5k5qSioG+jPNZfdUF+mqjpU6Kx7rqcXNbDZRSBgIbEs9ljYvLLeKvIgccbqBzpBwqGX8/KHQFLEWjtLQUI0aM8NvrzZ8/H4sWLcJ7772Hjh074uDBg3jggQegUCgwc+ZMAMCCBQuwcOFCLFy4ECkpKZgzZw5uuOEG7NmzB3q9p1n5Pffcg9OnT+Prr7+GIAiYPn067rvvPixfvtxvx0pEwWNXrg0Pbi1CVkndFtQAYHGJyCx2IrPYWe0+UUqJT2AwWSfFVTEKJOukjSqDUBRF7M6z4+PDJqw8boHdt8q3TLhCwG0pWtzVXos24cz6C3Vz+4Rj61kb8q3epcDrx7AUmIioLkrsbhwpduJQUXn5bobBidOmuq9LqnLC6MKj2w2Ys68ED3XW4872mga9OUnU0M6YXPgs04TPjpjLft/kEuDKaAV6xyuQFuf5M0YlbeAjJfKfgGUAjhs3DqmpqZg9e7ZfXm/SpEmIjIzE+++/X7bt/vvvR1FREZYvXw5RFJGamop7770XM2bMAABYLBakpKTgpZdewtSpU5GRkYHevXtjzZo1SEtLAwDs2LEDI0eOxJ49e3gnhqgJsTpFvPpHCd4+aIS7irNgp0gZci3uskBHICVoJOgdp0Ta+cVG5yi5X8t0anun2ehw4+ssCxYdNuJgUfXBTADoHi3HPR20GH+FmhcQTcyq4xbcsbHQa9u/r9RjJkuBKcCYNUPByOUWkW9146zFhTyLGzlmF45cyOjzY6BPKgBtw2RoHyFDaqQcx0ud+PaYBa5qrvRiVBI82EmHu1O1CGfmfr3iuazhuEURG7JtWJxhwppT1mp/PypqGyZDWrwCveMU6BOvQJswWaO6cU90KQKWrjFnzhyMHz8ePXv2xIQJEy779dLS0vDxxx/jyJEjaNeuHQ4fPowtW7bgscceAwCcOHECubm5GDRoUNlz1Go1+vbti127dmHq1KnYvXs3dDodevfu7fW6Wq0Wu3bt4omYqInYl2/H/VuKcNjgG+RK1kmx8NpIXJfgGWBhcYo4Y3LhtMmzSD9tciHb5MJp4/k/TS6YnJd3HyXH7MbK45ay0kqtTEDPWEVZQLBnnAJ6eeAW54cNDnx82IRlR80odVT/XlRSYPwVGtyTqsVVsYqAHQ81bte3UmP8FWqs+Lu8FPj1P0sxMlmNLiwFJqImwuhwI9fsRu75wJ4nwOfCWbMbeRYXci2ex/Kt7ipvNNaVVADahMmQej7Qlxru+bNtmAyKSqW9/77Sifn7S/HFUTMcle5n5lvdeHFvCeYfKMV9HXR4oKMWUcx0ohCVa/a0tPn0iMmr13dtHC1x4miJE59nmgF4gue94zxr9LR4JbpFy31+94gaq4BlAPbr1w+FhYU4c+YM9Ho9kpKSIJV6f6gIgoDNmzfX6vVEUcSsWbPwxhtvQCqVwul0YsaMGXj22WcBALt27cLw4cNx4MABtGjRoux506ZNQ05ODlasWIF58+Zh6dKl+PPPP71eu1u3brjjjjvw+OOPV/m9MzMzL+WtE1Ej5XADn5ySY/EpGVzw/aAe38yB6a0c0F7CrRFRBEpdwFmrgFy7gLM2CXJtAs7aBORV+LOq71dbEohI0YroFuZCtzA3uoW5Ea+8vFO3ww1sKpDimxwZfi+pecHfQuXGjQlOjI5zIpzxHQJgcACTflej0FH+c52iceOjrtZL+v0hImpMXCJQ5AAK7ALy7QIKHAIK7ILP1/l2ARZ3YC/4pRDRQi2itcaNKzSeP1tr3EhWi7jUhL1cm4DPs2X47qwMtmqOWy0RMT7BiduaOxDDe3wUAtwisKdYgu9yZNhUKIVLrP53VikRESUXkWO79BvuSomIjjr3+TW6C13D3AjjWogayMWS2gL2o6lQKJCQkICEhAS/vN6KFSuwbNkyLFq0CKmpqThw4ACefvppJCcnY8qUKWX7VU7HFUXRa1tV6bqV96mMmYFEwe9goQP3bynCgUKHz2PNNVK8fW0EBjVXBeR7u9wici1unDY5y7IHT5lcOFjkwO/nHLBcpP7ADQEZJgEZJgm+yvFsa6GTenqTnL/72CFCBmk1ZcMVS02yTS4syTBh6RETci3VlzdLBGBECxXuSdViQKISEpY6UCXzNRZMqVAKnGmW4KljEfhmWHRAM1ap6WLZHAVCgdWFL4+asSzLgvQih1+z9WrjQkZf+wgZUiPk6BAhQ/v/Z+++46Ou7z+Av763L3dJLmQxMlgJU2TJEsSFCAgqOFsVBz8XKmpbR7WttXVDHRWw2jorakUQQUFZIiJb9gwjgyRkX3J7fn9/XNaNLMjlRl7Px4MHyd3l7nuBfPL5vr/voZOjb7ys3YZ1ZAEYPxj4m8WFxYeNeO+IyS/j3+IW8GmhHEvPynF7lgaPXKBFhpZRjGDgWhZc5VYXPs0x48NjJpw2NJ/tN1Anw539NLipTwx0SgmKzS5sL7Fja4kN20vtOFDpaLFM2OYWsKdGij01UgCeK+UDdHVlw54WP5lh1u+bOq+grerr1q1r1+f785//jIceegizZs0CAAwaNAgFBQV4/fXXcccddyA1NRUAUFpairS0tPqvKy8vR3JyMgAgJSUF5eXlXgE/URRRUVFR/xgiii5Ot4i3Dhrx0p4av/IXALi1bwxeGhUPnTJ4AQupREB3jRTdNf6ZdnaXiP2VDmyr3WhsK7GjrBV9BwuMLhQYLfjylKcMM04uYFSjgOCIZHl9bz63CGwstOLfR01YXWBt9uQmRS3BHdkazM6OQTo3/tSMGT3VuKG3GktPNZQCby+144YfKvDlpEROgyaisOUWRWwutuGj42asymt+2FV7SFAK6KqWIkUtRWqMBBlaGQbUBvzaM9DXkmS1FH8eEY9HBsfi3SNGLD5sRJXNe1NgcwH/PmrCh8dMuKlPDB4fokVfpv9TmBNFET+ftePDYyZ8k2cJuOevo5QC1/VU4+5+GoxKUXgF5rrFSHFdLzWu66UG4Cn1311mx9YSO7aX2rGz1A5jK1r/HNE7cUTvxAfHPGXDXdUSjE5V4JJuStzTX3t+b5boPETM2Z3ZbPYrIZZKpXC7PT/dmZmZSE1NxcaNGzF8+HAAgNVqxdatW/H8888DAEaNGgWj0YgdO3bU9wHcsWMHTCaTV19AIooOx/UOPLC5CrvL/bP+UtQSvDFOh6kZ6hAcWQOF1NPvb2SyAg/Bs4E5bXDVX3ncXmLHsWamC9epcYhYV2jDukIbAANkAjAkUY6hiQqsy1Mh31rR7NePS1VgTn8NrslUs48Jtdo/xupwusbp9TNWFwRcehWDgEQUXs6aPZlBn+SYkNtCZlBLFBIgRS1F1xiJ52+1FClqCVJrg3ypailS1RIkq6UdFuBrLZ1SgieGxuHBQVp8cMyEtw8a/aoCnCKw5IQZn50w4/peajw+JBaD2eeVwkyVzY0lJzzZfjkt7Jez4z3Zfrf2jUFCKy/8a+USTOyuwsTuniohp1vEoSoHtpfYsa12n15obnktOWtxY0WuFcUmNwOAFFJB6wEIACaTCe+//z42b96MsrIyLFiwAMOHD6+f3Hv11VejZ8+erXquBx54AJs2bcLrr7+O/v37Y//+/Xj00Udxyy234IUXXgAAvPHGG1iwYAEWLlyIvn37Yv78+fjll1+wc+dOxMbGAgBuuOEGFBUV4c0334Qoinj00UeRnp6OL774IljfBiLqYC63iMWHjfj7rzWwBvidPKuXGq+NiY+YZteVVld9duD2Ujt+Lbe3S7ZCrFzALX1icFd/DQYmcFNP56ba7sasH8qxq8w70D4qWcEgILUrls3RuXC6RawrtOKjY2b8cKblqZ8JSqE2eOcJ4KV4BfQaPtYphKgp6bM6Rfw3x4Q3DhibnUp8dboKv78wFiM5COy8cC07P6IoYlupHR8cM2FFrgW2ZuJvComnYuGufhqMS1UE5We2wOis36NvLbHhcJUTTS0zjwzW4vmL4tv9GIhaK2gBwJKSEkybNg2nT59Geno68vPzsXz5ckycOBGiKGLYsGGYOnUqXnzxxVY9n8FgwAsvvIBVq1ahvLwcqampmDVrFp544gmoVJ6IvCiKePnll/Hhhx9Cr9djxIgRmD9/PgYOHFj/PFVVVXjyySexevVqAMCUKVPw6quvQqfTtf83gYg63OkaJx78uQpbS+x+93VRSvCPsbr6tP5IZXWK2FtRt9GwY3upza+EpzkDE2SY01+LG/uo2auN2kVTQcCLkuX46qokBgGpXfCkmdoiz+CZ2vlpjglF5uavmvWOleKObE9mUGpMZFwcDAaHW8QXJ814fb8BJ2uajqpc2l2J318Yi4uDFFCJdlzLzo3e5sYXJz3Zfkf0zWf79YmT4s5sDX6TFYPEDr7gX213Y2dpXYagDbsa9fteckWXkFcfUecWtADg/fffjzVr1uDrr79Geno6+vbti6+//hoTJ04EADz77LNYv349tm7dGoyXJ6JOxi2KeP+oCX/eVQNzgN4c0zJUeH2cDinq6NvYu0UROdXO+izBbSU2nPIpbZJLavud9NdgTAo37NT+qu1u3PBDOXYGCAIuvSoJ8QwC0nniSTO1xO4SsbrAio+OmbCxyNZkFg7g6QM2I1ONO7I1GN+Vvxcbc7lFrMi1YP5+Aw5XNR1oGZOiwONDYnFlGoeFtQXXstYTRRG7yhz44JgJy09bmh2cJxOAazI92X4TuinC5v+kwy3iQIUDW0vt+E0byo+JgiFoPQDXrl2L++67D0OHDkVlZaXf/b169UJhYWGwXp6IOpECoxMPb9HjxyKb333xCgGvjtHhpt7qqN3cSwQB/XRy9NPJcUe2BgBQanFhW4ndM9HQUIE5F2VEZfCTwke8QoKvrkrCLJ8g4M4yB2b9UI6vGAQkoiDJqXbg4+OefnXlLQzSGqiT4Y5+GtzchyfiTZFKBMzsHYPreqmxpsCKBfsMAfspbyu146Z1FcjUSnF7tga/zYpBt06cQUntRxRFrCmw4pW9Buyt8P+/11imVoo7+3n+/4XjXlcuETA8WYHhLJ2nMBC0AKDJZEL37t2bvN9qtcLlOr/mu0TUuYmiiP/mmPHMjmrUOPyvCF7ZQ4m3Lk4IOH032qWopZjRU40ZPdXIySkJyw0RRZ+4JoKAuxgEJKJ2ZnGK+CbPgo+OmfBLgLYfjWlkAmb28mT7jUyWR+0FwfYmEQRMzVBjSroKm4pteG2fAVvO+n+v84wu/P3XGry0pwZXpakwu18MruyhgkzC7zO1jSh6htq9uKcGewIEnetIBWBKugp399fg0u7MQCVqraAFAHv37o09e/Zg9uzZAe/fuHEjBgwYEKyXJ6IoV2x2Yd6WKvxwxj/rL1Yu4IVR8bg9K4abfKIOVhcEvOGHCuwoazhRZBCQwlWZxYX1hTZsKLSi2OxCZqwMgxLkGNRFjsEJsogZGNVZHKx04KPjJvzvpBnV9uY7GQ1P8mTGz+ylZi/S8yAIAi7trsKl3VXYVmLDgn0GrC3033+5RGB1gRWrC6zoHiPBb7M0uC0rBpmxQTvlpCghiiJ+LPIE/nxbiTSWppFidnYMbsvWMNuU6BwEbTW+7bbb8Nxzz+HSSy/FhAkTAHh+edjtdrzyyivYsGED3nrrrWC9PBFFKVEUsfSUBX/Ypoc+wMb/km5KvD1ehwwtN5tEoRKnkGDpVYm4cW0Ftpd6BwFnfu8JAupYekch4nKL2FVmx9pCG9YXWv2yTDb7ZDh1i5FgcG1AsC4wmBUvg5zZTR3G4HBj2SkLPjpuwq/NZAUBQJxCwM29Y3BHPw0u6MIJ9+1tTKoSX16lxN5yOxYdMmJFXuAprEVmN17bZ8D8fQZc1l2J2f00mJKugkLKnxvytrnYE/gLNMCvzuR0Fe7up8GVPZSQcu0lOmdBGwIiiiLmzp2Lzz77DAkJCaiqqkK3bt1QUVEBu92OO++8E6+//nowXpqIolSZxYXHt+qxMs/qd1+MTMBfR8bhnv4algH4YLNpCpUau9svCAgAI5LkDAJSm53PWlZidmFdoRXrztiwscga8AJSWygkQLbOkyHoyRT0BAbZbqF9lVtdmL/PgE+Om2EKMOCrsbGpCszO1uDanmqoZdwHdJSq2smsHx8z4XALk1mTVBL8pm8M7siOQd/4zhuc5b7MY2uJDS/+WuN30aWxazJUeGpYHAYzmE/ULoIWAKyzadMmrFixAidOnIDb7UavXr0wa9YsXHrppcF8WSKKAqIo4lSNC5vP2vBTsSdTI1C5z5gUBRZNSEDvOGb9BcKNJoWSweHGDT/4BwGHJ8mxjEFAaoO2rGVOt4gdpXasK7Ri7RkbDlQ2nzXWXpJVEgxulCk4KEGGfjo5lMx6ahOTw41Fh4x466ARhgA9fuskKiX4TVYMbs+KQbaOAYJQEkURu8sd+OiYCctOW1oM2I5LVWB2Pw1mZHa+gG1n35ftLLXjxT012BhgeF+dq9NVeGpoLIYmcXAGUXsKSgDQ4XBg//79SExMRM+ePdv76YkoiuUZnPip2IbNZ234udiGInPT0/yUUuDZ4XF4cKCW5QDN6OwbTQo9g8ONG3+owDYGAek8tLSWFZnqsvys+LHYhpo2ZPldmCjHpB4qDE2S43SNEwerHDhU5cQxvQOO5ofKtkgmAFnxMq/A4LAkOZLYW9CP0+0Z7vXynhqctQT+xgsALuuuxB3ZGkzNYElpOKqxu7HstKdku7lBDgAQrxBwc58YzM7WYFAnyfLqrPuyPeV2vLSnJmD/7jqTeijx9LA4TswlCpKgBABdLhe6du2Kv//977jvvvva++mJKIoUmlzYXBvw21xsQ76xddPBhyfJsXhCAvrxin+LOutGk8JLU0HAYUlyLGcQkFrBdy2zu0RsL7Vj3Rkr1hZacbiq+fLDxhKUAi7vrsKVaSpc3l2J1CaayTvcInKqnThU6cDBSgcOVXn+FDdzcao1JAJwVZoKd7GnFQBP9ti3+VY8v7sGx6sD/zt2azRUoieHSkSM/RV2fHLcjC9OmVsMyo9IkmN2P8/QFq08en8ndLZ92f4KO17aY8DqAv8WPnUu667E08NiMSpF2YFHRtT5BK0EePjw4Zg9ezbmzZsXjKcnoghVYnbh59pg30/FNpwytC7gVydOIWDe4FjMu0ALWSc/YWqtzrbRpPBlcLhx09oKv0bfDAJSa+Tk5EDVrRfWF9qw9owVPxXbmi0PbUyA5//ZlWkqTOqhwvAk+XkF3SqsLhyqqg0MVjlwqNKBo3oHrG37lQbAM9XytqwY3J6tQQ9N58sK3F5iw5931fi1CaiToBTw+wvjMKe/hqXUEczsdGNFrhUfHzc1O+wBALQyAbN6qzE7W4NhSXIIUdbbubPsyw5VOvDy3pqAvbvrXNxVgT8Oi8PFXRn4I+oIQQsAvvPOO3j33Xexfv16JCQkBOMliCgCVFhd+Pms3ZPlV2zDsSau7DdFLRUwOlWBCV2VmNBNgWFJCk5ebKPOstGkyNBUEHBoohxfT2YQkPzlGpz4z1ETVp2qwWlz6/9/JColuKKH0pPl10MZ9JJbp1vEqRqnJ0uw0lNGfLDSgTOm1kUFO1tW4HG9A3/dXYNv8wMHB1RS4IGBWsy7IJbrQpQ5pnfg4+NmfHbCjEpb89m0g7vIcXtWDPrGe2d9ij5nsL4ntC3e73cL0EUp6ZB9ZrTvy47pHXh5jwHLcy1NPmZMigJ/HB6HS7ox8EfUkYIaAPz4449RWFiI66+/Hj179oRKpfJ+cUFgiTBRlNHb3NhytqGk91AbSrIAz2TFi1IUuKSbEhO6KjEiWcEr/ucp2jeaFHmMDs90YAYBqTluUcR7R0x4blcNLK6Wt6sSARiZpMAVacr6fn7hMBVeb3PjcG3p8KFKB7aX2nGkhWmp0ZwVeNbswst7avBJjhmB/lklAvCbvjF4elhc1L138mZzifg2z4KPc8z4sZmBEB1JpxBwVZoKUzPUuCJNidgglCJH677sRLUDr+414MtTlgDhVY+RyXI8MywOl3ZXRl1mJ1EkCFoAsDVZf4IgoLKyMhgvT0RB5nCLKDS5kG90Id/oxDG9E5uLbdhX4Wjyl34gMgEYmazA+NqA36gURaebBhds0brRpMjGICA154zRibk/67GpuPmgQIpagit6qHBlDyUu665ElwgYrFE3LfWDYyYsO2VpNrgZTVmBNXY33jpoxKJDRpibmBA7OV2Fv4yIw8AE9vftbHINTnxy3IRPc8xNDoDpaAoJcEk3JaZmqDElQ4VuTfQKbato25edrnHi1X0GfHHSDHcTy9nQRDn+OCwOk9IY+CMKpaAFAHNyclr1uGha/IiiidUp4ozJiQKjJ8hXUBvoKzC5kG9wodjiavKXfHMkAjAsUY4J3ZSY0E2J0SmKqG70HA6ibaNJ0cNYWw78i08Q8MLaIGACg4CdjiiK+PykBU9u06MmQH8/qQCMSlHgyh4qXNFDiSGJ4ZHld66q7W7876QZHxwztTjEJFKzAu0uER8cM+G1fQaUWwMHdkYkyfHXi+Ixnn3AOj2nW8T3BZ5egWsLbee01wyW4UlyZZ3vdwAAIABJREFUTM1QY2qGCgN0snMOZEXLvizP4MSC/QZ82kQ2L+Ap4f7jsFhMSVcx8EcUBto1APjZZ59h3LhxyMzMbK+nJKIgMTncKDA1CuzVB/qcyDe6UNJOV18FABd08QT8LummxNhUBeIUPKnvSNGy0aToxCAg1Sm3uvDoFj1WBegJFycX8GCGDfePzozK7NBozAoURRHLT1vwt19rcLqJgV+9Y6X484h4XNuTwQHyV2hyYUmOCbvK7HD4bEt9/7sE+t/je1tzX+MSgV/LHS32JKzTM1aKqRmeUuExKYo2DaaL5H1ZqcWFNQVWfJtvxYZCq9+/S50BOhmeGhaH6ZmqiL5IQxRt2jUA2KVLF/zrX//CjTfe2F5PSUTnaU+5HTtK7X4ZfBWt3OCci4EJstqhHUpc3FXJE/gQi+SNJnUOTQUBh3SRY8XVDAJ2Bt/mWTDvF33ADLFLuimxcLwO1uLTnWIti4aswJ+KbfjLrmrsKXcEvD9JJcFTQ2Mxu5+Gg70obLjcIraX2vFdvhXf5luaDFz7SlAKmFzbN/DyHsoWK1sibV+WU+3Ad/lWfJdvxY5Se7OtfrLjZXhqaCyu66Vm4I8oDLVrADAhIQHvvvsuA4BEYcDhFjF3cxX+d6rpCVznq6tagnStFBlaGdK1UgxNVGB8N0XQJy1S20TaRpM6J5PDjZvWVWDLWQYBO5NquxtPb6/GkhNmv/tUUuC5kfG4d4AGEkHodGtZJGYFHqp04Lld1VhbGLh3o0Ym4KHBWjw0WBuU4QpE7UUURRzVO2sDXxbsbiKY7UspBS6t7Rt4dboKqQH6Bob7WuYWRewqqwuEWpFT3fJAvz5xUjw5NA6zeqnDNiuZiBgAJIpKTreIe3+qwrLT5x78kwhA9xgp0rWePxkaGTJipUjXeAJ+PTRSqDisIyKE+0aTqA6DgJ3LT8U2PLi5CmdM/lk2w5PkeGdCArJ1DcMgOvNaFu5ZgQVGJ17cY8DnJ8wBs4OkAnBnPw2euDA2YECEKNwVm11YUxsM3FRsg70VhTQCPFNv6/oGZsd7+gaG41pmcYrYVOzJ8ltTYEVpK1sB9YmT4vEhsbi5T0ybyqCJKDTaPQD43nvv4YYbbmivpySiNnK5RTzwcxX+d7L54J9MAHpopMjQSpFem8FX93GGVooeGinLcqJEOG40iZpicrhx87oK/OwTBLygixwrJidGxJRXap7FKeKvu6vxzmGT330yAXhiaCweHxLrdzLJtaztWYEJCgnUMgFqmQCVVEBM7d9qmQB13d+Bbmt0n1oqQNXEfU63iH8eNOJfR4ywNVEtOSNThT+NiENWPCf7UnQwONzYUGjDt/kW/FBghd7eutPpPnFSTElXI9NdgTHZ6cjUSkPaF7vS6sL3Z2z4Lt+C9YW2Jqdz+xrSRY5pmZ6S58EJ5z4MhYg6XrsHABUKBSSS1i1kgiCgqKiovV6eqNNziyIe3qLHpznepVSZWiluz9Y0BPk0UnSLkTJFv5PgSTNFGpPDjVvWVWBzgCDgkiu6IF0rC9GR0fn6tcyO+zdX4XiAkrL+OhnemZCAoUmKgF/LtcxbW7ICQ2FsqgJ/HRmHUSmc7EvRy+EWsbXEju/yLfgu34p8Y+v6BtZJUArI1MrQM1aGTK0UmbEyZMZKkVl7UV4pbd+9eq7BiW9rMxm3ldibnN7bmEwAxndTYmq6ClMyVPwdTBTB2j0AOHbsWPTs2bPVX7No0aL2enmiTk0URTz2ix4fHvcO/mVopfh2ShJ/WXdiPGmmSNRUEFAhAe7pr8HvLoxlv9EI4nCLeG2fAQv2GfxOOAUAcwdp8ezwuGZbS3AtC6wtWYEdoV+8DH8ZGYcp6ZzsS52LKIo4VOWsDwburWhd38CmCPC048moDQhm1gYJe8bKkBkrQ7cYSYuDNkRRxN4KR33Qr7UXC2LlAq7socLUDBUmpamicvo6UWfEHoBEUUAURTyxvRrvHfEup+oRI8W3U5PQM5bBv86MJ80UqcxON25e6x8EBACtTMDcwVrMHaQNaQkVteyo3oH7fqrCvgAnwxlaKRZNSMD4ri1niXEta1ldVuBHx804WHl+wYe26hYjwdPD4vCbvuwFRgQAhSYXVtcGAzeftcHRurZ6raaQAOlaaUMGYazn48xYKSptbnyXb8XqfAuKzK174W4xkvp+heO7Kts9+5CIQo8BQKIIJ4ointlZjUWHvIN/XdUSfDc1Gb3jGPzr7HjSTJHM7HTjt+srsbEo8FTRRKUEj18Yi3v6aTiYKMy4RRGLDhnxt19rAvaHuyM7Bi+Mim/1NFiuZW1jcrhhdoowO0VYXSIsThEWlwhro9vq/rY6RZh97vN6fO3fdbc1/rtbjBR3ZGvwwCANYmQMxhMFUm13Y/0ZK34+a8fhkhqUuRXIN7raPSjYVgN1svqg39AkeYsZhUQU2RgZIIpgoijir7tr/IJ/KWoJvrk6icE/Iop4MTIJlk5KxGcnzXh5j8FvYmyFzY1ndlRj8SEjnhwai1uZfRQW8gxOPPhzld9EZ8DzO+qti3W4Ol0dgiPrPDRyCTScu0EUFuIVEszsHYOZvWOQk1OGrKwMuNwiis0u5BldyDM4/f4uNrsDTtU+HxIBGJOiwLRMNaamq9CL5wpEnQp/4oki2Et7DXjjgNHrtkSlBCsmJyFbx10/EUUHqUTAbVka3NArBu8fM2HBPgMqbN5pE2dMLjy8RY9/HjTimeFxmJHJ/mOhIIoiPskx44/bq2EMMFHy2p4q/GOsDons30hEnZxUIiBNK0OaVoaLA7RBsLlEFBg9AcFcgxN5BhfyjA1/V9laFx6MkQm4vLsSUzNUmJyu4vpL1Im1awCwqqqqPZ+OiJrx2t4avLrX4HVbglLA11cnYUACg39EFH1UMgEPDtLitqwYLDpkxNsHjX5BpuPVTszeWIlhSXL8ZUQcLu2uCtHRdj4lZhce2VKF78/4l2vHKwTMH6PDDb3VDMwSEbWCUiqgb7wcfeMD7+ur7e6AmYN5BhdcomcS99QMFS7troKaLTKICO3cA5CIOsabBwz4y64ar9viFQJWTE7C0CRFiI6KwhX7ZlG0Kre68I/9Bvz7iAn2JvooXdJNib+MiMOIZK6NwbQi14LHftGj0ub/D3FZdyXeHp+AHprzyzrhWkZE0YBrGRGFCjv1EkWYhYeMfsG/WLmAZVcx+EdEnUuSSooXR+mwe1YqbsuKQaDWfz8V23DFqjLctr4CR/UdOxW1M9Db3Pi/TZWYvbHSL/gXIxOwYGw8ll2VeN7BPyIiIiI6PwwAEkWQ944Y8cyOaq/bNDIBSyclMruFiDqtdK0Mb49PwNbrUjAjM3DJ76p8K8Z9XYoHN1ch3+js4COMTj8WWTHu6xJ8ecrid9+oZAU2z0jBPf21LPklIiIiCgMMABJFiA+PmfCHbd7BP7VUwP8mJWJ0qn/jYCKizqafTo6PL0/EhmuScWl3/3XRLQJLTpgx8qsSPLVdjzKLK8CzUEusThF/3KHHdd9XoMjsnfUnlwB/GRGH1VOT0Cees+aIiIiIwgUDgEQR4L85Jjz6i97rNpUU+PzKLgGnhhERdWbDkxX4enISVkxOxPAk/+bpdjfwzmEThi0twYt7alDTVANB8nO4yoHLV5Vi0SGT330DE2TYMD0Fjw2JhTRQPTYRERERhQwDgERh7ouTZjz8s3fwTyEBPr0iERM53ZKIqEkTu6uw/ppkfHJ5F/QLkI1mdIp4da8BQ5eW4O2DBlidnIvWFLcoYvEhIy5bWYrDVd4l1AKAeYO12Dg9BRd04RR6IiIionDEACBRGFt+2owHNleh8SmpXAJ8fHkXXNGDwT8iopYIgoDpmWr8cl0KFo7XIS3AMIpKmxvP7qzBiK9K8PFxE5xuBgIbO2t24ca1FXh6RzVsPlXTaRopVk1Jwl8viodSyqw/IiIionDFACBRmFqZZ8GcTVVofB4qE4APLu2Cq9PVoTswIqIIJJUI+G2WBrtnpeKlUfFIUvlvgQrNLjyyRY+Ry0qw+JARBgdLg1flWTDu61KsL7T53XdjbzV+vjaFrSiIiIiIIgADgERhaHW+BXf/WAlXo+CfRAD+PbELrslk8I+I6FwppQIeGKTFnhtS8fSwWMTK/bPWcg0uPL2jGoO+OItnd1R3yqnBJocb87ZU4bYNlai0eQdC4+QC3r0kAe9N7AKdkltJIiIiokjAXRtRmFl3xorZGyvROPFEAPCvCQm4rheDf0RE7SFWLsGTQ+Ow94ZUPDRIC6V/ZTBqHCLePmTEsKUluGtjJXaW2jv+QEPg1zI7LvmmFB8dN/vdNzZVgc3XpuCmPjEhODIiIiIiOlcMABKFkR+LrPjthgrYfYJ/C8frcCNPtoiI2l2iSoq/j4rH7pmpmJ0dA0WAnZFLBJbnWjDp2zJMWlWKr09borJPoMstYv4+A676tgwna7yb/ckE4E/D47Dq6iRkxvoPVCEiIiKi8MYdHFGY+PmsDbeuq/RrsP7GOB1+k6UJzUEREXUSaVoZ3rw4Ac8Mj8N/jprwn6MmlFv9ewDuLHPgzh8rka6V4t4BGtyRrUF8oKhhhMkzOHH/5ipsLfHPcuwbJ8N7ExMwLEkRgiMjIiIiovYQMTvWCy64ADqdzu/PTTfdBAB46aWX/O7Lzs72eg5RFPHSSy+hf//+6Nq1K6ZNm4YjR46E4u0QedlWYsPNaytgcXlnlMwfE4/Z/Rj8IyLqKClqKZ4eFoeDN3bFWxfrMEAX+FppgdGFP+2swaAvzuKp7XrkGiKzT6AoivjipBkTVpQGDP7dmR2DTTOSGfwjIiIiinARkwG4ceNGuFwNqVFnz57FpZdeiuuuu67+tqysLKxatar+c6nUu6HPm2++iYULF2LhwoXIysrCq6++iuuvvx47d+5EbGxs8N8EUQC7yuy4cW0FTE7v4N+Lo+IxZ4A2REdFRNS5qWQC7sjW4PasGPxYZMPCQ0asCzAJ1+gU8c5hE949YsLUdBXmDtZiTIoCguA/XCTc6G1u/G6rHl+dtvjdl6iU4J/jdZiawd6zRERERNEgYgKASUlJXp9/8skniI2N9QoAymQypKamBvx6URSxePFiPProo7j22msBAIsXL0ZWVhaWLl2Ku+66K3gHT9SEveV2zPyhHAaHd/Dv+ZFxeHAQg39ERKEmCAIu66HCZT1UOKp34J1DRnx+0gyrT7sGtwisyrdiVb4Vw5LkmDtIi2t7qiGXhGcg8OezNtz/UxXOmFx+913ZQ4mF4xOQGhNgMgoRERERRaSIKQFuTBRFfPLJJ7j55psRE9MwGCE3NxcDBgzAkCFDcPfddyM3N7f+vry8PJSUlODyyy+vv02tVmPcuHHYvn17Rx4+EQDgQKUD131fjhq7d/Dv2eFxeOQCZqQSEYWb/jo53rg4AYdu6opnhsUiVR14G7Wn3IE5m6ow9MsSvLHfAL3Nv5dgqNhdIp7bVY3pq8v9gn8qKfDq6Hh8OSmRwT8iIiKiKCPo9fqIG2O3YcMGzJw5Ez/99BOGDBkCAFi7di2MRiOysrJQXl6O1157DTk5Odi2bRu6dOmC7du3Y/LkyThw4ADS09Prn2vu3LkoLi7GsmXLmny9nJycoL8n6lxEEbhnvxIHDN4nWHPSHbgv0xGioyIiorawu4EfyqRYUiRHjqnpa6oqiYjpqU7c0t2JDHXotl25ZgF/OqbE0QDHmqVx42/ZNvTRRNy2kIiIiIjgaYvXnIgpAW7so48+wvDhw+uDfwAwadIkr8eMHDkSQ4cOxZIlS/DQQw/V3+7bk0cUxRb79LT0TSQ6F1/0cGH6mjKcrPFkYDx2gRZ/HhEXEX2jKLLk5ORwHSMKkkH9gEdFEZvP2rHwkBHfF1j9HmN1C/iyWI6lxXJMTldh7iAtxnftuD6Boiji/WMmPLuvxm/YFAA8PFiLZ4fHQSkN798/XMuIKBpwLSOiUIm4AGBZWRm+++47zJ8/v9nHabVa9O/fH6dOnQKA+t6ApaWlSEtLq39ceXk5kpOTg3fARE3orpHi2ynJmLGmHJPSVAz+ERFFKEEQcEk3JS7ppkROtQPvHDZhSY7ZL9gmAlhTYMWaAiv6xEmRrpUhUSlBF6UECSpJ/cddaj9OqP1YKxPO+fdDmcWFh7boAwYmu8dIsHhCF0zsrjyn5yYiIiKiyBFxAcAlS5ZAqVRi5syZzT7OarUiJycHEyZMAABkZmYiNTUVGzduxPDhw+sfs3XrVjz//PNBP26iQLrGSLH2mmTEyc/95I6IiMJHVrwcC8bq8OzwOHx4zIR3jxhRbPbvAXiyxlWfAd4ShQSewGBtQLDu40RVbZBQKUGiSup1e5xCwLozNsz9uQplVv/Xv66nGq+P0yFBGZHtoImIiIiojSIqACiKIj7++GPMnDkTsbHeQxKeffZZXH311UhLS6vvAWg2m3HrrbcC8Fydf+CBB7BgwQJkZWWhb9++mD9/PjQaDW644YZQvB0iAEC8gidfRETRJkEpwWNDYjF3kBZf51qw6JAReyvOrcer3Q2ctbhx1tL6YSISwTOZ2JdWJuDVMfG4tW8MLzwRERERdSIRFQDcvHkzTp48iXfffdfvvqKiIsyZMwcVFRVISkrCyJEjsXbtWmRkZNQ/Zt68ebBYLPjDH/4AvV6PESNGYNmyZX7BRCIiIqL2oJAKuKlPDG7srcbWEk+fwO/yrQj2qI1Awb9RyQr865IE9IqLqO0fEREREbWDiJwCTERErcdm00ThpdLqQq7BhUqbGxU2Nyqtnr+rGn1caXOjyupGhc0Fa+sqhZskFYAnhsbid0NiIZNEbtYf1zIiigZcy4goVHgJmIiIiKgDdVFJ0UUlbfXjzc6mg4QV1trbaj+urH2MweG5vtsvXoa3xyfgohRFsN4OEREREUUABgCJiIiIwliMTIIYrQRp2tZ/jc0lwuRwQ6eUQMJef0RERESdHgOARERERFFGKRWglLY+y5CIiIiIoht7ABIREREREREREUUxSagPgIiIiIiIiIiIiIKHAUAiIiIiIiIiIqIoxgAgERERERERERFRFGMAkIiIiIiIiIiIKIoxAEhERERERERERBTFGAAkIiIiIiIiIiKKYgwAEhERERERERERRTEGAImIiIiIiIiIiKIYA4BERERERERERERRjAFAIiIiIiIiIiKiKMYAIBERERERERERURRjAJCIiIiIiIiIiCiKMQBIREREREREREQUxRgAJCIiIiIiIiIiimIMABIREREREREREUUxBgCJiIiIiIiIiIiiGAOAREREREREREREUYwBQCIiIiIiIiIioijGACAREREREREREVEUYwCQiIiIiIiIiIgoijEASEREREREREREFMUYACQiIiIiIiIiIopiDAASEUW5nJycUB8CEdF541pGRNGAaxkRhQoDgEREHWx3mR0zvy/HhV+exXtHjKE+HCKic7Kx0Iqp35VhxFdn8dUpc6gPh4iozURRxNenLbhiZSnGLS/BhkJrqA+JiKjN3KKIT46bWnycrAOOhYiIAJgcbvz91xq8c9gEsfa2J7ZVY1yqEoO6yEN6bERErVVpdeGZnTX47ERD0G/uz1W4uKsSXWOkITwyIqLWKzK58LuteqwuaAj6zdlUhYM3pSJGxjwZIooMJ6odeGSLHr+U2HF7tqbZx3JlIyLqAOsLrRj7dSkWNwr+AYAI4KvTzJwhovAniiKWnTJj9PJSr+AfAFhdwMo8S4iOjIio9dyiiPePmjBmeYlX8A8AKm1urC+0hejIiIhaz+EW8Y/9Bly8ohS/lNhb9TUMABIRBVGl1YX7fqrErB8qkG90BXzMN7lWiKIY8D4ionBQaHLhlvWVuHtTFcqs7oCPWZnH0jkiCm851Q5MW12Ox7fqUeMIvPfixQwiCnd7yu24bGUZnt9dA1vgU8yAIiYA+NJLL0Gn03n9yc7Orr9fFEW89NJL6N+/P7p27Ypp06bhyJEjXs+h1+tx7733IiMjAxkZGbj33nuh1+s7+q0QUScgiiK+OmXGqOWl+OJk8xvJEzVOHNU7O+jIiIhazy2K+PcRI8YsL8H3Bc0H+LactaHC2oZdKBFRB3G4RczfZ8D4FaXY2kKmzJoCK+wuXpglovBjdrrx7I5qXLGqDAcrHW3++ogJAAJAVlYWjh07Vv/nl19+qb/vzTffxMKFC/HKK69gw4YNSE5OxvXXXw+DwVD/mDlz5mD//v348ssvsXTpUuzfvx/33XdfKN4KEUWxM0YnbllfiXs2VaHcJ1NGIgAPDtJgQleF1+3f8GozEYWZ43oHpn5Xjt9vq4bBJ1NGIQH+OCwWA3QN7aRdIvBtPrMAiSi8/Fpmx8RvSvH3X/0zZbQyAS+PjkeyquG0uMYuYlMxy4CJKLz8WGTFuK9L8fYhI9w+1yi6KCV495KEFp8jooaAyGQypKam+t0uiiIWL16MRx99FNdeey0AYPHixcjKysLSpUtx11134dixY1i3bh3WrFmD0aNHAwBef/11TJkyBTk5OcjKyurQ90JE0cctivjPURP+uqsGRqf/leOBOhn+OT4BI5IV+Pi4CZvPNlyBXplnxZND4zrycImIArK7RLx5wIDX9hlgD1DtOzpFgTcv1qG/Tg63CBzZ23CxdVWeBXe00ICaiKgjmBxuvLjHgMWH/U+WAWBSDyX+MU6HdK0MR6sc+PB4Q2/TlXkWTEpTdeDREhEFVmVz49md1fg0J3Df+Jv6qPHiqHgkqVoexBZRGYC5ubkYMGAAhgwZgrvvvhu5ubkAgLy8PJSUlODyyy+vf6xarca4ceOwfft2AMCOHTug1Wrrg38AMGbMGGg0mvrHEBGdq2N6B6Z8V44/bKv2C/4pJMAzw2Lx44wUjEj2ZP5NzVBBIjQ85mClA6drWAZMRKG1u8yOS1eW4oU9/sE/rUzAa2PisXpqEvrrPJPLp2eqvR6zsciG6kBRQyKiDrSx0JMpszBApkyiUoL3LknA/yYlIl3ryYeZ3tN7Lfs2zwpnoKghEVEHEUURX5+2YPTykoDBvzSNFF9OSsS7l3RpVfAPiKAMwJEjR2LRokXIyspCeXk5XnvtNVx11VXYtm0bSkpKAADJycleX5OcnIzi4mIAQGlpKRITEyEIDWfcgiAgKSkJpaWlzb52Tk5OO78bIooWDjfw0RkZ3i+QwyEKfvcPjXPhmb529IwxI+9Uidd9w+KU2F3dsFi/v7sAd6QFJwjIdYyImmNxAe/kyfF5kQxu+K9l4xNceLKvHV1lJpw80XC7XAQyVCrkWz3XlB1u4KOduZiSEpxegFzLiKg51Q7g9dMKfFsa+DR3SrITj/e2Q+c24kSjtaybG4iVqmFweda/CpsbX+4+hZG64FzQ4FpGRM0ptQl49aQcmyr91zIBIm7q5sQDmWZoLAY0Xk5aqmyNmADgpEmTvD4fOXIkhg4diiVLluCiiy4CAK/gHuCJmPoG/Hz5PiYQlgcTUSC7yux45OcqHA4wwCNWLuC5kXG4q58GkibWmJsdRuzeXl3/+VaTBn/LSmn342SbAyJqzoZCKx79RR9wUnmSSoJXRsdjZi91k/ulWTXVeP2Asf7zHdZ4PJKV2O7HybWMiJoiiiKWn7bgyV3VASeVp2mkeGOcDlc2U9Y7raQSnzca3ParKxG3Zuna/Vi5lhFRU9yiiA+PmfHc3uqAk8r762R462IdRqUoz+n5I6oEuDGtVov+/fvj1KlT9X0BfTP5ysvL67MCU1JSUF5eDlFs+CaKooiKigq/zEEiouYYHW48tV2PSavKAgb/JqersPW6FNzTX9tk8A8ArvEpndtV5kChiRM0iahjVFpduP+nSsz8oSJg8O+WPmrsuD4Fs3rHNHux1LcMeH2hDSYHy4CJqGMUmly4dX0l7t5U5Rf8EwDcP1CDbdenNBv8A/zXslV5FrhFlgETUcfIqXZg2upyPL5V7xf8k0uAp4bG4qcZKecc/AMiOABotVqRk5OD1NRUZGZmIjU1FRs3bvS6f+vWrfU9/0aNGgWj0YgdO3bUP2bHjh0wmUxefQGJiJqzvtCKsV+X4p3DJvhuCZNUErw/MQGfX9EFadqWE6y7a6S4KFnuddtKTgMmoiATRRFfnTJj1PJSr2yXOulaKb66KhHvXNIFXVrRU2ZYkhxpmobHWVwi1hVygiYRBZdn+JoRY5aXYE2B/wTyAToZfpiWjJdH66CVt3zae3kPFTSyhosdxWY3dpXZm/kKIqLz53CLWLDPgPErSrG1xH/NGZWswOZrU/DUsDgopM1Xr7YkYkqAn332WVx99dVIS0ur7wFoNptx6623QhAEPPDAA1iwYAGysrLQt29fzJ8/HxqNBjfccAMAoF+/frjyyivx2GOP4c0334QoinjssccwefJkpmATUYsqrC78cUc1vghwsgwAt/aNwQsXxbXqZLmxGZlq7Cxz1H++Ms+C+wdqz+tYiYiacsboxO+2VeP7ACfLdZkyzwyPa9XJcv3XCQKmZ6qw+LCp/raVeRZc69NUn4iovRzXOzDvF33Ak2W5BPj9hbF47ILYNp0sq2UCrkpTYXluw15vZZ71vLJtiIias6fcjod+rsKhKv+qMo1MwJ9HxGFOfw2kkvML/NWJmABgUVER5syZg4qKCiQlJWHkyJFYu3YtMjIyAADz5s2DxWLBH/7wB+j1eowYMQLLli1DbGxs/XO89957ePLJJzFz5kwAwJQpU/Dqq6+G5P0QUWQQRRFfnbbgqe3VKA/QUyZDK8Wb43S4rEfzZSVNmd5TjT/tqqn/fGuJHWUWF5LVbQskEhE1xy2KeP+oCX/dXQNDgJ4yA3UyvDU+ASNrJ5W31fRMtVcA8PsCK2wuEcrzvFJNRNSY3SXizQMGvLbPf1I5AIxOUeDNi3X1k8rbanqmdwDwm1wLnh8Z12LPeCKitjA53HhpjwGLDvtPKgeAST2U+Mc4Xf2k8vYi6PV6NjYgIgop+IGtAAAgAElEQVSgwOjE77bq8cMZ/1I2iQA8MFCLPw6LhaYNmTKBTFhRigOVDVmAb4zT4c5+mvN6zsbYbJqoczumd+CRLXpsL/XPlFFIgD9cGIt5bcyU8eVyixjwv7MotTSckX9xZSImp5/bxZFAuJYRdW67y+x4eEsVDgfIlNHKBPxlZBzu6d/08LXWMDjc6PtZMWyN2qJumpGMCxPP7eJIIFzLiDq3H4usmLdFj7wA/ZcTlRK8PDoeN/Ruevja+YjYHoBERMHiFkW8e9iIsctLAwb/BibIsHZaMl4YFX/ewT8AmJHpfYLMPoBE1B7sLhGv7q3BhBWlAYN/Y1I8PWX+MPT8e8pIJQKuyfAu+f2GaxkRtQOTw40/7tBj0rdlAYN/V6UpsfX6FPzfgOaHr7VGrFyCy7v77sv8WyYQEbVVlc2NBzdX4brvKwIG/27qo8aOmSm4sU/zw9fOR8SUABMRdYQT1Q48uFmPHQGaPiskwBND4zDvAi3k7dSHAfCUAb+wx1D/+aYiG/Q2N3RKXqMhonOzt9yOBzdXBZxUrpUJeG5kHO4+z0wZX9MzVXj/WEMZ8Hf5FjjdOsjacb0kos5lU5END2+pCjipPFEpwStj4jGrV/tmykzPVGF1oz6pK3MteHZ4XLs9PxF1Pt/kWvC7rXq/SeUAkKaR4vVxOkxqYVJ5e2jXAOCWLVvO6esuvvji9jwMIgoBtyi264lkKJRbXZixphxFZv+FeWyqAm+O0yH7HHvKNKe/To7seBmOV3tO1J0isLrAilv7xrT7axFR86JhLTtV48SM78tRY/fv8jI5XYUFY+JbNam8rcZ3U0KnEKCvfd0qm4gtZ22Y2D34G1oi8hYNa9nuMjtuXFsesNffzX3UeHFUPBLbOHytNaZmqCET9HDWLqHHqp04pnegXxD2gETUvGhYy9YUWDB7YyV8d2UCgHsHaPCnEW0bvnY+2nX3d80117Tp6osoihAEAZWVle15GETUgZxuEQ9srsI3eRZM7KbEh5d1QYwsMjPX3jls8gv+xcoF/HVkPO7sFxPUXz4zMtWYv78hC3BlnoUBQKIOZHa6MXtDJTaftWFGphqLJiREbObagv0Gv+BfkkqCV0fH4/p2zpRpTC4RMDVDjSUnzPW3fZNnZQCQqANVWF34zfpK7K9wYHa/GLw0Kj5iB1i8uKfGL/iXrpXijXE6XHGOw9daQ6eU4JJuSmwoamgDszLPygAgUQfKNTjxm/UVKDC68NiQWDw+JLblLwpDoiji+V01fsG/AToZ3ro4AReltF9/0dZo1wDgypUr2/PpiCgCfHDMhC9Pefo8/XDGhpf3GPD8RfEhPqq2Mznc+M9Ro9dtk3oo8cbFCeihCf5E3msyVV4BwA2FVhgd7g67GkTU2S3YZ8DaQs/J3v9OWTA0SYEHB2lDfFRtd9bswv9Omr1uu6m3Gi+PjkeXIGTK+JqeqfIKAK7Ks+C1MfERf/WeKFI8u7OmvufnO4dNGJOixHW91C18Vfg5WOnA+kLvPsz3dWCmzPRMtVcA8JtcC35/YWQGIIgi0aO/6Ot7fj6/uwZjUxUYm6oM8VG13YYim1c7FokAPHGhJ6B5vv2Xz0W7BgDHjx/fnk9HRGFOFEV8cNTkddsHx0x4fEhsxPWvW3LCjCpbw7UZnULAB5d16bAA3IWJcmRopfU9bqwuYO0ZK67vxSxAomBzuEV8kuMdNFt40Ig5/TUh2Zydj3ePGOFolDHTM1aKxRMSIO2gbMbLuquglQkw1tbOlVjc2FFqx5gI3LQTRRq9zY3lp73XstcPGHBtT1XEZQEuPOR9UXZMigKvjNF12OtPy1Th8a2oz9rZX+lArsGJnrFsoU8UbKdqnPixyPsCwBsHjBEZAPznQe+1bEamGk8NC11P0cg6QyeisLKrzOHXYN7gEL2awEcCl1v022je01/Todl3giBgRqbPBM1cTp0j6gir860otXjXmRWaXVh6ytzEV4Qno8ON//hclJk7SNthwT8AUMkETE73Ls3jNGCijvHFSTOsPrMy9lU4sKnYFvgLwlSRyX/9fWhwx2Zkp6ilGJvqXZq3MpdrGVFH+Pi4/7nk9wVWHK5yhOBozt3+CrtfILOj1zJfQb+EYbPZsHLlSuzduxfV1dVwu7032IIg4O233w72YRBREHwUYHEGgHcOG/HgQC1Ussi42rwq34pcQ8OOWSEB/m9Axy/O0zNVeLtRIPKHM1ZYnWLEfB+JIlWgjSYAvHXQiFv6Brf/Z3v6b44Z1Y16/yUoBfwmBL1EZ/RU46vTDSfKK/OseOEiMeIykIgiiSiKTe7L3jhgxKUR1IvTN5O5T5wUU9I7/vinZ6rxS4m9/vOVeVY8fAHLgImCye4S8WlO4Auwbx0w4J1LunTwEZ27t30STMamKjAyuWN7/vkKagCwsLAQM2bMwKlTpxAfH4+amhokJCRAr9fD7XYjMTERGo0mmIdAREFSY3dj2enAV0JLLW58dsKMu/qH/8+3KIr450GD12039YlB15jg98rydVGKAt1iJCiuHURicorYUGTF1IzI691DFCnyDE6/PlN1juqd+L7AiikR8DPodItY5JfJrIUmBH1Er+ihhEqK+kykAqML+yocGJoU2k0vUTTbVeao75fl68ciG/aW2yPiZ9DgcPtVkswdFNuhmcx1pmeq8PSO6vrPd5TZUWRyoXsH9IYm6qxWF1hRZg0w+hvA0lMWPDPciXRt+JfinzE6seyU97nywyHO/gOCXAL8l7/8BWVlZVizZg12794NURTx/vvvo6ioCH/605+gVquxYsWKYB4CEQXJ0lMWmJ2+84wa/POgAS530/eHi+2lduwq804nnxuixv8SQcA1Gb5lwCw3IQqm/+aY/SazNfbmAWMz94aPlXmW+h6igCeT+d4BobkIo5VL/CZ0sgyYKLiayv6rEylr2SfHzV5TzBOVEtzSNzQXYdK0MoxI8p78u4prGVFQNVWVAQBOEX4XO8PVv46Y0PhUuW+cDFeHIJPZV1ADgD/++CPuuecejB49GhJJw0splUo8/vjjGDduHJ5++ulgHgIRBYnvRvP2rBg0TjQ5ZXBhZV7497Dzbcx6VZoSAxLkTTw6+K7x6QO4usAKRwQEUokikdMt4tMc77XsHp/M5W2ldmwrCe/+WZ5MZu+17Ja+MUhRhy5LZUZP/56mosi1jCgYAlVl+K5lK/IsOF0TOEMwXATKZJ4zQIMYWeja1k/32ZetZACQKGjyDE5s8KnK8F3LPj5uRpUtcIZguKi2u/GhTybzQ4O1YdFSJqirqdFoRK9evQAACoUn5dxgaCi1Gzt2LLZs2RLMQyCiINhbbse+ioasOQHAE0NjcVMf715TbxwwhPUJ34lqB77L9w5SPjQ4tL1dLu6qQJdGE5Sr7SI2R1jzbqJIsfaMFUXmhk2kRibguZFxuLy795S5N8I8c+aXEjt+LQ+PTOY6k9NUXheFTtQ4cVQf3sEHokjlW5XRI0aKV0bHY2BCQ5mcW/S/6BluVuRacMbUkMmskgJzQtxOxvdixpYSO8p9J60QUbv4xKcqY1iSHC9cFI9UdcOGwuQU8d6R8F7LPj5ugsHR8E6SVBLc3KfjezIHEtQAYLdu3VBUVAQA0Gg0SEhIwIEDB+rvLygogFweukwbIjo3vtl/V/ZQIl0rwyM+fQ32VjjwUxgHrxYdMnn9krkwUY4JXUPcmFUiYFqGT+kcy4CJguKj495Npmf1ViNWLsE8nybvawqsOBLGk+d8T+onp6vQTxfa/ZVOKcHEbt6BVJYBEwWH777st9kxkEkEv7Xs0xMmlFrCM3gliiLe8lnLbu0bg+QQZjIDQO84GQb5BFJ9Lx4T0fkLVJUxO1sDlUzAAwO9zzH/ddgEszM8swAdbhHvHPJ+H/83QAN1mAx1DGoAcOzYsdiwYUP95zNmzMA///lPvPbaa3jllVfwzjvvYOLEicE8BCJqZ0aHG0t9Gpre0c9zdbafTo6pPsGrcM2cKbe6sOSE9+L88GBtWEyp9C03+TbfGhH9FIkiSZHJhR/OeJ/Ezc72rGWXdFNgmE/fJ98T03BxXO/AmgLv9xEOTaaBQGXADAAStbdAVRm3ZXkyTWb2UiOt0cAKmwv41+HwXMt+Puv/Ph4McSZzHb8yYK5lRO1u7Rlr/SBEwFOVMau352fvrv4axMkbztEqbO4mJwWH2vLTFhSawyuTubGgBgDnzp2LGTNmwGr1bEyfe+45jBkzBi+++CJefvllDB8+HC+//HIwD4GI2tmy0xavlOZUtcSroemjF3hv1jbWTp4LN/8+YkLjCo40jRTX9gyPSZ8Tuyu9fsmVWd3YVhp+30OiSPbfHBMax9UHd5FjeG3QTxAEPOqTOfPlSTPOGMOvhHWhT7+sYUlyXJwaHpM+p2ao0Hhw56EqJ06FeQ8yokgTqCojo3ZCplwi4CGfCwL/PmqCwRF+mTNvHzR4fT4lQ4Ws+PCoFPO9mPFjsQ36MO9BRhRpPmyiKgMA4hUS3NXPO4j2z4NGOMMsQSJQT+bfZmmQqAqfyeFBDQAOGjQIDz30EFQqT3BAp9Nh2bJlyM3NRX5+PlauXImUlJRgHgIRtTPfyUy/zYqBvNEZ3qgUJcb6nHyGW+aMxSnivSPe7+OBQVqv9xFKSqngNyWKmTNE7cctivjE58rx7OwYrwzgazJU6BPXsGFzisCiMMucKbW48PlJ7/fx8KDwyGQGgCSVFON8fh+wgT5R+2muKqPO7Vkxfr2FfZvTh9pRvQPfn/FuGRMumcwAMEAnQ9+4hjJghxv4/gzLgInaS6HJhbVNVGXUeWCQFopG0at8owtfh9n50U/FNhyo9MlkHhg+axkQ5ABgU+Lj4xEbG9pG+0TUdgcrHdhV5t0H6/Ys/5Rm38yZr3PDa/Lc5yfMqGh05TZOIeCO7PBozFrHdxrwqjxO0CRqLxuLbCgwNqQAq6UCbuztvQZIJQIe9hkK9NGx8Jo8994RE2yNMpnTtVK/TJVQm5HJMmCiYFnuU5WR4lOVAQAauQT/N8B7r7bokBE2V/jsKRb6XCgemSzHmJTwyGQGPFnh0zO9v68sAyZqP5/6VGUMSpDVV2XU6RojxS19fQdOGsPq/Mg3+29ahgp94mVNPDo0gn40LpcLGzZsQG5uLqqqqvz+gQRBwBNPPBHswyCiduBbZnJpdyV6xfkvI1elKTFQJ8Ph2omPdZPn/jFO1yHH2Ry3KOLtQ95lJndma+pTzMPFlWlKxMiE+ql+hWYXfi13YERy+GyIiSKVb/bLdb3U0Cn914Bb+sTgxT01KLV4gn51k+eeGBrXIcfZHLPTjX8f9d5oPjhQC1mYZDLXuSZTjSe2V9d/vrvcgTNGJ9K04bUhJopEvvuy23yqMurcO0CDtw4YYakN+hWb3fjfSTNuzw59X6oSswtf+GYyD44Nm0zmOjN6qvF6o77W6wttMDnc0ITZ/pEo0rjcIj72Kf+9s58m4BrwyGAtPjneMCn4YKUDG4psuKKHyu+xHe1wlQPrCsM3k7lOUHdf+/fvx2233YYzZ840GZllAJAoMpidns1iY7ObyJoTBAGPXBCL+zdX1d/26QkTnhoWi5QQT3NbnW/FyZqGlBmZANwXZqnZABAjk+DKHkp8k9eQDv9NroUBQKLzVGJ2YXW+b5lJ4LWsbvLcX3fX1N/2r8MmPDRYixhZaE/6luSYUWVr2FvFKwTcFmaZzADQXSPFRcly7GyUPb4q34r7w3DdJYokra3KAIBElRS3Z8fg3UbtT946aMRvs2IgCXGg7b0jJtgbJVZnaqW4JiP0J/O+hibKkaaR4ozJs4e0uESsK7SFTf9ooki1schW/3MFBK7KqNM3Xo5rMlVY2ej86PX9hrAIAL7tk/03KlmB0anKEB1N04K6e/39738Po9GITz75BKdPn0ZVVZXfn8rKymAeAhG1kxW5VlTbG042E5USTM1oetMzq3d4Tp5726dh/qzeavTQhE9j1sb8ps7lWcIqzZ0oEi05YYaz0Y9Rv3gZRjdTanZ3GE6ec7lFLPJZy+7uF36ZzHVYBkzU/nyz/yZ2C1yVUeehwVpIG8X6cqqd+C4/tH3sTA7/TOa5g7SQhlkmM9BEGTB7mhKdN9+17NqeqoBVGXV8W039fNaO3WWhHZZYbHbhy1Pee0PfAUzhIqg7xf3792PevHmYNm0adLrQl/4R0bnzHf7xm6wYKKVNb9DCcfLczlI7tpZ4/4J4aHD49iOdnK7yanZ7yuDCoarw6aVIFGncoui3ls1uosykTjhOnvuuwIpThoar5XIJcG8YZ9RN98mQ2VpiR6nF1cSjiaglFqfoV5VxZ7/mM4AztDLM6u39s/jmAUNILyx+mmOGvtHFZZ1CwG+zwi+TuY5vj9XvC6xh1UuRKNIEqsq4s1/zrQlGJCswoav3hds3DhiaeHTHePewEY1PcXvFSjEtDDOZgSAHAFNSUiCTsccLUaQ7pnf4Bc5aMzQj3CbP+fb+u6y7Ehd0kTfx6NCLU0hwWXfv1PFveLWZ6JxtLrbjdKPAmUIC3NKn5fKtcJs851tmcmPvGHSLCc9MZgDoGSvzWmtFIOSZR0SRbEWupU1VGXXm+Vz03FnmwC8locmccblFLPTJZJ7TXxvWPfVGpyiQqm44PoNDxMYirmVE56qtVRl1Hh3ivZatyrMip9rRxKODy+Bw432f89twzWQGghwAvPfee/H555/D4QjNPwYRtQ/f1OxxqQpkxbccOAs0eW7xISPsIbhaerrG6dUvAgjPxqy+/KYBs3SO6Jz5rmUzeqrRRdVy4CycJs9tL7Fh+/+zd9/hUZXp38C/Z0qmppIChBRCD0XsghRFFBUpVlQUrCuIdV1Xd111V313XV33Zxe7ILqiiAUUK13AgqBCIAZCIIQS0jMzmZnMzHn/mExmzplJSJme7+e6uGRKkgOSO895nrtUyjOZoz+WTZeVzrEMmKjr5LHsqoHtV2V4DE9T47x+0oPFZyKUObPygBX7TdIDGfmaMdooBAFTc+XtWbgBSNQVgaoy5hynKsNjkiyJQ4T/BN5wWfK7RXIgk6ZR4OoozmQO6QZg3759oVKpMGbMGDz99NNYtmwZPvroI79fRBS9bE4R7+2R3qgdLzXb1x+GGaDzWZQesrjwfmn4+2e9WGSSjJcvTFX5ZddFo6m5WknPnqI6B/ZE6ISLKJZVW51YKcugnduJCZh3jDDCd0nqmTwXbvI+ppOzNShMjd5MZg956dz6wzbU2SLXEoIoVgWqyph7nPJfX3fK+md9ddCGnTXhXVeIoohnZRuPswbokRXFmcwe0/OlhxmfH2hCcwRbQhDFqg2HbX5VGVd1oCoDcPfkvHOk9PDzvT0WHLGEt72IwyXiRVmP+xuHGiI+KK49Ia3PvfHGG1t//49//CPgewRBwMUXXxzKyyCibli5vwk1PjdpKQmCX0P39gScPPebCVcPDN/kuRqr069p/+0jEjt0whRpaVolxvXWYN1h70bDp/ut+OOo6L/hJ4om/9tjkUyaHJCkxLjeHZ+qHWjy3NNhnjxX2uDAyhjMZAaAISlqDE5W4fd6dx9ThwisKrfiqoHRe0pOFI0W/y5dz3S0KsP3/fLJ3M/saMQrE9KCdo3Hs6XSjq1V0k3HBTESy87srUGqRmidwl5rE/HdERvO6hud/b6IotUiWSzraFWGx8x8HR7d2tCaSWx3uSvN/nFqclCvsz2fljWh3CeTWaOM/kzmkG4ArlixIpSfnojCQN6zb9YAPbSqzm2cLRhuxOu7zfBU/v5e78CqA1ZM7cRGYne8UWyBxafBRB+9Apf2D8/XDoZpeVrJBuCK/U3446joHV5CFG1EUfRbaM4Z3LEyE193jUyUbABuaJk8d3JGxzcSu+PFnSb45pmMTFNjQp/oz2T2mJ6nw39+9Wb9fFrWxA1Aok6wOUX8b480ls3tRFUG4MmcScQ1q2tan/uwtAl/O8mBXGN4erfLS/Wm9NNgaEpsHGyqFQIuyNHhXZ//Dyv2W7kBSNQJVQGqMuZ0oioDAFQtAyfv3VLf+tybxWb88YREJCeEPgNPFEU8K4tlVw7QI1MX3ZnMIf2bGTduXId+EVF0Km1wYMMReZlJ50818hJVfhtuT4dp8pzVIeKVXdLgPK/QiIQO9MqJFhfl6SSlh9uqmnHAxGnARB21+agdJfXe7xm1Ari6CxtPJ2ck+GUNhmvyXHWATObbRhhjIpPZY5qsdG71IWtEJ8MTxZruVmV4XJirxeBk72afU/QfLhQqJfXNflM/F4yIrUNNeRnwyv1NcEVwmjJRrJFXZRQkKv0m+3bE7EF69PIZONnQLOLN3eEZOPndUTu2V8symYdHfyZz2IqTd+7ciVWrVmHVqlXYuXNnuL4sEXWDvDHraRkJXe41dcfIyEyee7/Ugsom708Yo0roVN+vaNBbr/SbiMWm00QdJ2+Yf2GuFhldPKG9a2RkJs+9vtuMJp8BSn31ClwSQ5nMADAqTY1co/fv3eYEvjnIWEbUUfJM5lkD9NB1sioDcA+zkLcPePt3C6qtoe+fJc9kPqGXuks3/pF0Vh8tEtXev/ejTS6/4UxEFJgoin6tDOZ2cPiHnF6lwC2FsoGTRSZYHaHfkPfLZM7RYnAMZDKHfAPws88+w6hRozB+/HjMnj0bV199NcaPH48TTjgBn332Wai/PBF1kd0p+mWbdKbJtNyINDXOzQ7v5DmXKOIFWXCeM0SPFE30NmZty0V5/qfNRHR8dTYXPinr+vAPuXOyNRgR5slz7kxm6Sbm/EIj1IrYyf4D3KWH8mylT8u4AUjUEaUNDqw/LB081JWqDI8rBujRR+9dDzU5/eNMsFVZnX4lzLfHWCYzAGhVAs7rJ12XreC6jKhDglWV4XHzMCMMKumG/NK9oR04+XtdM74sj82ezCG9C/7mm28wZ84ciKKIBx98EEuWLMGSJUvw4IMPQhRFzJ07F99++20oL4GIumhVuRXHrN7MuSS1gJn53cs2uWtUeCfPfXPQhmKfHzBKwV3+G4umyW6atxy142iYJ10RxaKley3wTWrJNSpxVjcmgAuCgLvCPHlu6V4LqnzicaJawJxu3PhHkrx07quDVjSF4aSeKNYFsyoDADRKAbfKytVe2WWCOYRl+a/tMkvicT+DEjO6ubaMFPlk8xX7rWFpbUMU694KYlUGAKRqFH5JKs/uaIQzhNO5X9gpPfg9MV2NM7NiI5M5pBuATzzxBIYMGYJNmzbh7rvvxoUXXoipU6fi7rvvxnfffYfBgwfjySefDOUlEFEXyRealw/Qw6DuXsjwTJ7z9cyO0GUBPif73Bf314WtwXWw5SWqMLqXNOto5QGeNhO1xz38QxrL5gw2dHsC+cx8HfJ8Slk9k+dCwSWKeF72uecONoSlwXUonJKRIMk6MjtErDnELECi9gSqypjTjaoMj+uGGJCc4I2HtTYRb5eEJnOmySHiVXkm8/DYy2T2mJytge/A0nKT068fGBFJ1dlc+DSIVRketxYa4dsNYW+DEysPhGZtUdnkxHuyDMPbh8dOJnNIV487duzA7NmzkZjo39g1MTERs2fPxq+//hrKSyCiLtjf6MDqClmZyeDuLzQ9k+d8fVjaFJKBFtur7H4DTG6Lgcas7ZFnAbIPIFH7fjrWjKJaaRbw7EHdj2WeyXO+3iw2o94e/MyZL8utklIZlQDMK4zN7D/A3Xvsolx5GTAPM4jaE6gq4+IgZM4lqhW4aag0njy/w4TmEGTOvLfHgmqfASZJCQLmBGFtGSkGtQLnZLMMmKgzgl2V4dHPqMLlA6Tx5JkQDZx8dZcZNp8/Q45R6ZcRHM1CugGoVqthsbR9imQ2m6FWR3+jRKKe5u0Si6RB84npaozqFZy05kCT5+R9+oJBnjEzvncCRqfHRmp2W+SlcxsO21AThobdRLFKnv03JUeLPvqul5n4CtfkOXl/wUv669AvRjOZPabJFsqryq2wO1k6R9SWUFRleNxSaITGJyweNDuxfF9wN7LcmczSqozrBxuQGKQ/Q6TIb/o/LWMZMFFbRFHEouLgV2V43Clrz/JzVTPWHw7ucB6Lw4XXdkvXZbcWGqGKoUzmkEbdMWPG4NVXX8XevXv9XistLcVrr72GsWPHhvISiKiTHC4R75RIg3Mwp+YGnDxXYgnqRtYBkwMfyRavt4/wz0SONYOS1RiWIt08/bycWYBEgTTYXX43scGMZeGYPLf1mN1vWvqCGGky3Z6xWQlI89k8rbeL2HjE1s5HEPVcgaoygpk5l6lTYvZAaSwLdubMqgNW7G3wrvNUgnvjMdZN6aeF7x7mngYHdtUFv6qFKB78dKwZRXXBr8rwGJqixvk50mSJYA+cfLfEglqbNzYmJwi4JsYymUO6Afjwww/DarVizJgxmDt3Lh577DE89thjmDNnDsaMGQObzYaHH344lJdARJ301UErDlu8JRoGlYBLC4Kb1iyfPGcJMOGyOxYWmeCbTDI0RYXJ/bqfXh4NLmIZMFGHLCttgsVnMy5br8Tk7ODGgVBPnntelv03sY8GJwQpGzuSVAoBU3Oli3SWARMFFqgqI9hx4PYRRvgmsBTVOvD1weBtysurMi4r0KGvITjZ2JGUolFgYh/pzxWWARMFFsqqDA/5kLbVh2z4pTo4WYBOl+g3/OOGIbGXyRzSqx02bBjWrFmD888/H99++y2eeuopPPXUU1i9enXrc0OHDg3lJRBRJy36XXrzemmBLuiBTaMUcGuhfPKcOSiT5+psLiwulv4ZFgw3Bi29PNLk5SZrKqxoCEHfMaJYJ19oXjNYD2WQSzRSNQq/TJxgTZ4ra3Tgk/3yTObYz5jxkMeyzw5YQzqxjygWhboqw6N/kgozZAeMTwcpc+bHSjs2yzKZb4uDqgwP/zJgbgASyYW6KsPjjCwNzsiUHpA8+1twWk19dsCKfY3eTGa1AvhDDGHVu6kAACAASURBVGYyh3y7csCAAVi8eDEOHDiA4uJiFBcX48CBA1i0aBEGDhwY6i9PRJ1QYXbi64PSjLJQBGcAmDvEgCSfyXM1NheWBGHy3KLfzTD5ZP1k6hS4YkBspWa3Z0SqCv0TpdNHvzrILEAiX9ur7PjFZxqjAOCaIJaZ+FowPDST517aaYLvflhhigrnBDmDMZIm9NEgSe39iztmdWFLZXB79RDFuq/DUJXhIe+ftemoHT9Udj8LUN77b1JfDUakxU8P+AtztZLsyZ21DpQ2sAyYyFc4qjI85LHso7ImlDV2/3tSXpVxeYE+6BmM4RC2fEWFQoHMzExkZmaisrISu3fvDteXJqIOWlJiltxwjkhT46T00CzSkhL8J889183Jc3aniIVF0uB8yzAjNMr4yP4D3JOUp+fxtJmoPfLsv8nZGuSEaHBGP6MKlxX4Z850p39WbYADkQUjjBDiJJMZcGeCy3v1MJYRSb0VhqoMj9HpCX7TOJ/uZubMvgaHX6uSeMpkBoB0rRJnZkkzjhjLiKTCUZXhMSVHi6E+PdNdov/mXWd9f9SGH47JM5ljM5aFdAPwzTffxC233CJ57p577kFhYSHGjh2L8ePHo7q6OpSXQEQd5HSJeFu20Jw7WB/SG855QZ489+G+JslJuV4l4IahoclgjCT5BM1vKmywOFgGTAQApmYXlpXKykyGhDYO3DlSWs62rZuT594sNsPsc1LeW6fAZQXxk8nsIY9lK/db4eIETSIA4a3K8JD3z/r8gBXFdc1tvPv4XiySZjIPT1X5bTLGg2l+/Zm5AUjkEc6qDMA9cPIO2ebckhIzjjV1feDkc7INxMnZGhSmxmYmc0g3ABctWoTERO+ieP369XjjjTdw2WWX4aGHHsK+ffvwn//8J5SXQEQdtOaQDQfN3sCoUwq4PMQ3nJk6Ja4eKP0aXZ08J4ointshLTO5ZpAeqZrYaszaESelq5Htk3JucYj4toITNIkA4KN9TWhs9saQLJ0CU2SZZsE2LFXt9zW6OnnO5hTxijyTuTC+Mpk9zsnWQO9TP11hceLnqq5vNhDFk3dkVRnDU1Uhq8rwcA8akn6NZ7uYOVNjdeIdWSbz7SMS4yqT2UM+oG1rVTMOmlgGTASEtyrD47ICveReyeoEXu7iwMm99Q58diB+MplDeme8f/9+yZCPjz/+GNnZ2Vi4cCHuuusu3HzzzVi1alUoL4GIOuitYmlQnNlfh5QwbJ7dPiIxKJPn1hyyoajWu9hSCMCtw2M3OLdHIQi4KE+62bCC5SZEAPwXmrMH6aEOUZmJr7uDNHluWakFR5qkPb+uD3EGY6ToVQq/HkCMZUTuqozFsqqM64YYQr55JggC7pZlNL+/14IKc+czZ94otkh6fvXVK3BJ/9D0L4y0vgYlTsuQlgHLS5+JeqJIVGUAQIJSwALZJt1ru0wwdWHg5ItFJskk9pFpakzoE7uZzCG9u7fb7VCrvadIa9asweTJk6FQuL9sQUEBjhw5EspLIKIOOGJx4otyeZlJeMrNCoI0eU6emj0tT4v8xNCeLkWSvHTui3Ir7E6WzlHPtqOmGT8dk2aQzQlxyZxHMCbPiaLo16fm2sH6sBzGRIrfBM39Td3qn0gUDyJRleExLU+LAp9hY80u91CizrA6RLyyS/ox8wqNSIjDTGaPafKDWZYBE2F5BKoyPOYM1iPFZ+BknV3Eot87N3Cyyur0m8R+e4z3ZA7pijIvLw9r164FAPz8888oKyvDpEmTWl+vrKyUlAgTUWS8u8cCn0NaDElW4XTZjWwoBZo892MnpkH+VtOMNYekWYO3j4jv2DImMwEZWm8Ib2gWse4wy4CpZ5Nn/53VVxPWg4DuTp77tsKGXXXSTOb5hfGZyexxXj8tEnxWo/sandhRy9I56tnkVRkz8rVhOwhQKgS/NdRbxWbU2TqeOfN+qQWVPpnMiWohLFk/kSQ/mN181I7KbvQcI4oHiyNUlQEARrUCNw+TrqFe3GHqVMLE67vNsPp8G2frlbg4xjOZQ/qT5IYbbsDHH3+MsWPH4pJLLkF2djbOPffc1te3bNkiKREmovBziaJfcJ4bhjITX4Enz3U8C/B5We+/MVkJOCUjfBuYkaBUCJiaywmaRB5NDhHv7/UfZBRO3Z08J89knpmvQ14cZzID7onwZ8viPzNnqCc7GqAq47owb55dNVCPTJ33NtHkEPH67o71z3KJIl6QxbI5gw1ITojfTGYAyE9UYVSat/JNBPAZy4CpB4tkVYbHLYUG6JTSXsPLSjuWBdjkEPGqrG/gvOGGsG1ghkpII/FNN92EZ555BgUFBbjgggvw4YcfQqdz75jW1tbi2LFjuPzyy0N5CUR0HBsO21DW6D3aSFAAVw4I/8lGoMlzv3dg8lyF2YkPZb0lbovT3n9y8tPmzw9Y4XCxdI56pk/KmlBv9/77T9cqMDU3vLGsO5Pnfqm2+2XxxnKT6c6QxzL2AaSeLNJVGQCgVQmYJ8s+XlhkQpPj+GuMrw/aUFzvzeJVCsC8wvjO/vNgGTCRV6SrMgAgXav0mzj87A4TXB1oNbJ0rwVVVm8mc5JaCPkk9nAI+VHMnDlzsGTJErz00ksYMmRI6/OpqalYu3Yt5syZE+pLCOi1117DqFGjkJWVhYkTJ2LTpk0RuQ6iSHurWHoKMj1fhzStso13h4588pyIjk2ee7nIJFkoD0hS4oLc8PSWiLTxvTVI9ultUW1zYdPRzg8dIIoH8oXmVQP1Eek31dXJc/KMmTN7J+DE9PjOZPa4MEcL3/9Vu+ocKKnnNGDqeVyi6BfL5oS5KsPjhiEGJKq9X/eY1YX/7Tl+5sxzsqqMS/rrQj7xM1rIe5quP2zrVOk0UbyIhqoMjwUjjJI1xu46B74sbz871xWgJ/PcIQYkxUEmc+z/Cbpg+fLluP/++3HPPfdg/fr1OO2003D55ZejvLw80pdGFFZVVidWHpBNZorQyYYgCH5ZgEv3WnConclzDXaXX5+c24YnQhHDjVk7I0Ep4IIcTgMmKq5rxmbZ5vecCC00E5QCbu3k5LmDJgc+3Cf93u0p2X8AkKZVYlxveRkwS+eo5wlUlXFVBKoyACBFo/ArPX5uRyOc7VQabKuyY+MRaSxe0EOqMgBgSIoaQ5K9m50OEfj8ANdl1PNEQ1WGR36iyq9v39PHGdL2RbkVexq8mcwqAbhlWOxn/wFh2AA8duwY/vvf/2LOnDmYMWMGpk2bJvk1ffr0UF+CnxdeeAFXX3015s6diyFDhuDJJ59EVlYW3njjjbBfC1Ek/W+PBb73pAOSlBjXO3IZJ9PzdOgvnzxX1HaAXvy7GQ0+k6V6aRS4cmBkbvojZZpsgvLKA00dSmsniieLZVPdzuydgEHJ6jbeHXpzOzl5bmGRGb49qQcnq3Bev56RyewxPZ89TYnkcSJSVRke8wuNUMuG9HzaTlmrPGNmQh8NRveQTGYP+bqMhxnUE0VLVYaHvD3L95V2bD7a9vBEeU/mSwp06Bcnmcwh3QDcvXs3zjjjDDzxxBPYu3cvNmzYgOrqauzduxcbN25ERUUFxDDfqNrtdmzfvl0yjRgAJk2ahO+//z6s10IUSaIo+t00zxkcmTITj0CT597cHXjyXLNLxMIi6Q+Xm4cZoFP1jOw/j0nZWhh8/syHLS78dIxlwNRz2JyiX1lapHu0GNUK3CSbPPfCjsaAk+fq7S6/hfJtI4w9JpPZY2quDr5/4u3VzdjfiQnKRLGuyur06xkX7ob5cn0NSswaID1Y/b9fTQHv3/Y3OvBxWc/NZPaYJjvMWH3IisZ2MsCJ4k00VWV4jOqVgHOy5QMnAyeZ/HTM7nf98dRfPqTbmH//+9+hVquxZcsWJCYmYuDAgfjXv/6FiRMnYtmyZfjzn/8c9qy76upqOJ1OZGRkSJ7PyMhAZWVlwI8pKSkJx6URhdXP9QqU1HsXKSpBxBmKIygpORLBqwJOBZCm1qGm2X0raHKIeOK7/bg+R3oj+EWlEgfN3kCuUYiYpDmKkpKj4bzcqDAmJQHfVHnD+aLth5HaX9o/i3GM4tVXx5SosXljQZJKRKGjApH+J3+uBnhOoYPN5Y5lhywuPL95H6ZlSdsavH1QhcZmb4ZMmlrESeKhiF9/JIxK0uCXBm+201tby3F1tjT2M5ZRvFpyUIVmlzcW5Ghd6N14ACUdHyQeEjMSBbwDLcSWLfpfa5rxzo+lOD1Vuqn131I1nKI387q/3oU8S3mPi2U6Eeir0eKQzZ1nY3MCi38sw3kZ0tjPWEbx6plSNQBvLDgpyQlUlqEk8FZL2FyWqsC3Fd573y/LrVi1fQ8GGqQHGo/vToDvNtlpKU7oavajpCZcV9o9gwYNavf1kG4Abt68Gbfeeivy8/NRW1sLAK0nRpdddhm2bNmCBx98ECtWrAjlZQQkz3ISRbHNzKfj/SUSxaIn19cA8J7UTs3T4fTh/SJ3QT5uszfika0NrY8/OKrFgxN6t2b3iaKID4qOAfBucs0eZMRphdFx/eF2tdKCb9bVtj7eWK/F8wPzWmNaSUkJ4xjFrXv2VgHwlnFcPdiIEUOiIxbMaajDq7u92X1LKw2468zM1uw+u1PEsp+PAPDeSM8fkRQ11x9uV9hN+OWH+tbHm81GPDzIe2DLWEbxShRFfP5bJQDvhvdNI1IweHBi2x8UJoMATK2qxsoD3lLWD2qScc1p6a2P62wufLrlCNwj3NzuOSkNgwfFR8+szrqkrh7P7/Tu3P5kS8GCQWmtjxnLKF7ZnCK++FG6rpk3Oh2DBkS+RdNAUcRrR45ha5X3/vGThjQsHO393ixrdGD1d9JkkvtOy8Sg7PhpyxLSEuDm5mb06dMHAKDVuv/S6uu9C7uRI0di27ZtobwEP7169YJSqfTL9quqqvLLCiSKV7U2Fz6RlWlcF0VjzY83eW79YTt+rfEGbwHArcOj5/rD7dwcLTQ+LYL2m5ySvx+ieFXa4MD6w9IeLpEu//UlnzxXXO/AFz6T5z4qa8Ihi3eRrFMKuHFo9Fx/uE3Lky6wv6+044il7UFQRPFi01E7Suq9m39qBXB1FPU0vmuUdCNy3WEbtld5S+TeKjbD7PBu/mXpFLi8IHquP9zkPU2/OmhFk4P9mSn+rdzfhBqf1k0pCQKm50Vm+IecIAi4c6Q0li0rbUK5yRt7X9xpgu+co8IUFSb1lZYOx7qQbgD269cPBw4cAADodDr07t0bP/zwQ+vrRUVFMBjCu9BNSEjA6NGjsWbNGsnza9aswemnnx7WayGKlKV7LbD53FPlGZWYGEXB7XiT557f0Sh57cJcLQZGsOF/pCWqFZjUVz4NmE2nKf4tlvXOOy0jAcNSoycWBJo890xLzxlRFP2aTF8zSB/Rhv+RlmtUYXQv7/8/Ee6bCaJ4J+8DemGuFhm66IkFp2Qk4EzZkDhP/yy7U8RC2cC2WwqN0ESw4X+knZKRgD5672222SFidQXXZRT/5IOMrhyohzaK+rNPzdViYJJ0UveLLdm6tTYXlpRIr/+2EcaI9scPhZBuAI4fPx6ff/556+PLL78cL7/8Mm6//XYsWLAAr7/+Oi688MJQXkJACxYswLvvvovFixejuLgY9913H44cOYLrr78+7NdCFG6iKGJxsXShee1gQ9Q1nG9r8lxRbTO+rpBm/PTEJtNy8swZeSNxonhjd4p4R7ZQmzsk+jJO2po8t+6wDTv8MpkZy6bnc4Im9SyBqjKiKZPZ4y5Z5syn+5tQ2uDAslILjjR5M34MKgHXD4m+6w8nhSDgolx5LOO6jOJbtFdlAO6Bk3eMlK61Fv9uQa3NhTd2m2HxydTto1fgsjjMZA5pD8C77roLEyZMgNVqhVarxQMPPICGhgZ89NFHUCqVmDVrFh599NFQXkJAl1xyCWpqavDkk0/i6NGjGDZsGN5//33k5uaG/VqIwu3HY3YU1XlTnZUCMHtQ9AU3z+Q535OYp38zYbgsu+fUDDVOz0yQf3iPc2GuDiqhDp6fW8X1DhTXNWNISvRkQxEF06pyK45ZvTedSWoBM/Ojo8zEl2fy3Lc+BxdP/2aCwyUtB5uWp0X/pJAuy2LC9DytpAfsxiM21FidPTozkuKbvCoj16jEWVFUleExOVuD4akq7Kx1ryFdIvDsb434oVI6LfOaQXqkakKaYxITpuXrJD1gV5VbYXeKSOjBmZEU3+RVGadnRldVhsesAXr88+eG1oMLs0PECztMWFwivf5bhhnj8vs1pNE5JycHM2bMaO3/p9Fo8PTTT2P//v0oLS3FCy+8AKMxMqfdN910E3777TdUVlZi3bp1OPPMMyNyHUThJk/NnpKjRR99dN5Y3THCCN+w+0t1s6QXIADcNiIx7lKzuyJFo8CEPtIbhk/LeNpM8Uu+0Lx8gB4GdXTedMp7znxZbpVsCALA7SMi3+w/GgxMVmNYincj1CkCnx1gFiDFp0BVGXOisCoDCNw/a9HvFsmhskIA5jOTGQAwNisBvXw2QuvtIjYcsbXzEUSxK1BVxpzB0ZdgAgAapeAXp576tRGVPpnMRpXg144qXoTtqNnpdKK+vh5JSUlQqXjCTT2P0yXioNmJskYHShuc2NfogNUpYkxWAi7K00GtCP1ir97uwkf7or/MxGNwihoX5molN3++OTP5iUpclBs/U5m6a1qeDqsPeReXK/Zbce/opAheEcWjZpeIcpM7hu1rcGBfoxMiREzso8W5/TRhuXHd3+jA6gp5mUl0LjQBYHzvBJyUrsbPVYGH85yRmYBTmcncalq+Dru2e3u9rtzfhGuj+GcVxSabU8QBk3dNtq/BgQSlgPP6aTGud0JYDhd/OtYcE1UZHpf01+HRnxtQbnKnLMrHWszI0yE/kfd5AKBSCLgwV4u3fTZFVpQ14Zw4miZK0aHJIaKs0YF9jQ6UNjiwv9GJxAQB0/J0ODE9PGuLWKnK8LhuiAFP/dKIhmZ3FJPHsmsH65ESp5nMIY/QP//8Mx555BFs3rwZDocDy5cvx8SJE1FdXY358+djwYIFmDhxYqgvgygsrA4R+03u4Luv0b2gLGtwoLTRgQMmJ5pd/h/zyi4zsvUNuHmYAXOHGEJaNrGs1CLpbZCtV2JydvSVmfi6a2Rim9kfC4YboQzDxmmsmJqnxR83e3+I/VrTjLJGR7sfQxSIudmFspYY5r4x9v6+3OSEM8Awwxd3mjEgSYl5hUZcNVAPYwiz8d4usUgWayemqzGqV/RuoHkyZ+auqQn4+m3sYyoxPU+HJ3w2ANccsqHBHuAHKNFxNNhd7rVYo7PlwMK7RqswO/1u+gDguR0mjExTY36hAZcW6EM6zOItWSZzNFdlAO5NrduGG3Hf9/UBX2dPZqnp+TrJBuBnB6x4agynAVPn1dlckvjlPYR14LAl8M/H//5qwhmZCZg/3IipuVqoQnjPJK/KuCKKqzIAIDlBgRuGGlqHGflSCsC8wviNZSHdAPzhhx8wffp0ZGVl4corr8TixYtbX+vVqxdMJhPefvttbgBSTKmzuVpPWfa1LChLGx0oa3DikCXwYvJ4KixO/H1rA/69vRFXDdRjXqEBg0PQu21RsTQ1+5rB+qjfQDs1MwFjsxKw6ai0x0yqRsDVA6P3lDwSMnVKjJH9Xa0oa8L5PGwmGVEUUWtztS4iPQvKspYFpW9D987Y2+DEvVvq8ejPDZg72ICbhxmQawzuUsPhEvGOrE9LNGcye1yUq8WAJCX2Njglzw9IUuKCHH6T+hqeqkJBohKlje6/K7vLXTY9OsLXRdFHFEUcs7pas5F9b4r3NTpRZe1aLPutphm3bqzDwz814MahBtww1IDMIE/lbYixqgyPawbp8e/tjaixSf9ux2Yl4KSM6D2IiYSJfTRIUgutWUbHrC5srrQjK8LXRdFHFEUcaXK1rMfc95X7Gt33mPsaHKizd23jeEulHVsqa9DPoMQtwwy4drAh6JltgaoyorX819e8QiNe3GmC/HxxZr4OeXGcyRzSP9mjjz6KAQMG4Ntvv4XZbJZsAALuKcFLly4N5SUQdZpLFFHZ5JKUt5X53CDLFzzB1OQU8UaxGW8Um3Futgbzhxtxdl9NUMpQtlfZ8ats4uQ1UVxm4uuukYnYdLRa8tyNQ41RfbIUKdPydNINwP1WnD8kghdEEeN0uReTng2+Mp9MvtJGBxq6uJjsiAa7iOd2mPDCThOm5Wkxv9CI0zODU1L39UGr5LTboBJwaUH0lpl4KBUC7hiRiDs31UmeXzA8MeoPYsJNENylS8/s8J7Mr9jfhNE5EbwoihiHS0RFSwuVfY3O1hvkfY1OlDU4YHKELpYds7rw+PZG/PfXRlxW4D6gDVa28bLSppirygAAg1qBPwwz4HGfLF2A2X+BJCgFnJ+jxful3o3eFWVNuKlXBC+KIsbudLeD8r3H9KzPyhqdaApUXhEkB81OPPhTAx7f3oirB+pxS6EBA5ODk2wSa1UZHr31Slw1UO/XHz/eqzJCugH4888/429/+xu0Wi0sFovf69nZ2Th69GgoL4HIj8XhQoXZiYMmJ8rNTpSbnDhoduKgyYGDZndJSKgqjXppFOifpET/RBX6J6lQaXFi6d6mgAH/6wobvq6wYWiKCvMKjbhigA56Vdc3vN6SNZk+t58GOUHOzAmVc/tpMDJNjd9aNjB1SgE3D43+U/JImJanxV9+8Jbm/HDMjsp8AYMieE0UGqZmV0vs8sQxB8pbHh80O3HI7ESo7ouzdAr0T1QhP1GJ/kkq7K134KOyJr82By4R+KTMik/KrDgxXY35hUbMzNd1a6raW7KF2qUFOiTGyGHAlQP1+Pf2Bhxq2cDM0Cpw5cDo37yMhOn50g3AbypsuLdvBC+IQqbe7mqNW+Uta7GDvrHM4oQrRLGsr16B/EQVCpJUyE9UYXuVHZ8dsPpVc9hdwLt7LHh3jwXjeidgfqER5+dou7V5L1+XxUJVhscfhhnwwk4TGlsy24amqDCFmcwBTcvXSTYAV+634oa0CF4QhYQoiqiziyg3Obz3lq1xzP3c0SZXlyrFjkchANmGlvvLRCVyjSpsPGLDmkP+Q2fMDhGv7jbj1d1mTMnR4tZCAyb06XqySaCqjOtiIJPZ444RiXinxNK6Xp7QRxO2vomREtK7f4VCAYWi7UX50aNHodNx4UvB4ykF8W7uOSSLyHKTE9UhzOAT4A7A+YlKFCSpWgKx9yY5OcH/++HhU5KxqNiMV3aZWm8Kfe2uc+CuTXX4x9Z6XD/EgJuGGtHX0LkyFFOzC8tKpWUmc2IoOAuCgEVnp+H272pRZ3PhwZOTkBXFPXIiqZ9RhZPT1djqM2xgbbUSnHMeW1yiiKNNLncM88Qvn4OLg6aul4N0hEIAcgzuuNU/UYmCRBXyk7zxLFB/v3+c6sTru814c7c5YJzdVtWMP6yvxUM/1uOmYUZcP0SPXtrOfR9XmJ34+qC0J2gslMx5aJQClkzqhfu+r4NTBP51WnK3Dnbi2UnpamTrlaiwuMuALQ4Rm2qVGBnh66LOcbhEHLE4JYcTnkNXz02ypzwyFFQCkJeo9K7HPDEtSYU8owo6lf9Nb1mjAy8XmbCkxNK6weVr4xE7Nh6pQX6iErcMM2L2ID2SAqzv2hPLVRkAkKZVYtHZaXj4pwYY1QL+b2xKVE4ujgbnZGugVwmt2Z4VFieKTAqwOCO2NLdkIvveVx40SQ9ezSHMRtYogTyjqnVd5olp/ZPcG37yXqX3nJCIotpmvFxkwtK9Flid/p/zy3Irviy3ojBFhXnDjbi8QB8wJrYnUFXGJTFQleExIFmFlyek4slfGtFXr8Tz41IjfUkhJ9TV1YXsX+q0adOgUqnw0UcfoaamBgMGDMDHH3+MiRMnwm63Y9y4cSgoKMB7770XqkugOCCKIuwu97Q2m1N0nxT7Zu55fm9yoMLihC1AgAsmtQLIbzlhyW8JvgVJ3hMXbScDp0ezS8SKsia8WGTCT8cCT4oE3IvZmf11mF9oxMkd7LWy+Hcz7vjOW3aWpVNgxxW9wzJ5mMLv6V8b8fetDa2PT0l24ptLciN4RQS4Y5nNCdhcIuxOETU2nww+2YHFIUvgoUHBpFWiNYa1Zia3xLMco7LL8aHJIeKDUgsW7jRJplsG+vpXDNBjXqERhakdK0N5YnsD/rnNW3Y2PFWFjTMywzKtk8Lvvi11eHmXN7Pg/AwH3rsoL4JXRID7gMLmdK/L7C4RVVaXz+aed2Ov3OTEYUvgoUHBZFAJ7oPWluqKgpaYlp+oQj+DssuN7xvsLrxTYsHLu0woa2x7cZmoFnDNID1uKTR2eALu3Ztq8aZPX+ZzszX44Lz0Ll0nRb85q6vx6X7v4dWc7GY8e15+5C6IAEhjmc0potLqaq0I81aIuePaYUtosvd8JamFlg2+lk0+n9/3NSi7vMlebXXirWILXt1larfHcy+NAtcPNeCmoQb07mCixaxvqvFluc+/7cF6PHtm/G+ixbKQbgCuWbMGl112Ga666ipcfvnlmDlzJhYuXIhevXrhP//5D7Zu3YrPP/8cp556aqgugeC+GSttcMAFd08oEe6yLPcvES7JY0CEKHnsFFset7xPDPhxIpwi0OyzUee5yfXc8Hqet3fwsd0pwuoUQ1aO257kBAG5Ru8Ji6c0pH+SEtl6ZchLNH6stOOlIhM+KWtqd+F8WkYC5g83YFqert0F7jkrKiUZYfeMMuLBk5ODeckURUobHDjpQ297BQVE/H5VH6R3Mtsq2jQ2u7C/0emOPyI6FMucouw9HYxldpc7dnnjkPexzdXynM8NsPtxy3t84pnv40jEslSN4N3kazm08GQn99YrQpqxIYoi1h+24cUis2RxGMjZfTWYX2jE5H6aNq/J6RJxwrKjOGj23og/eUYybh4W371aerLvjtgwdVVV62ODUkTp7OyQTmUNh7qWzf+OxTJp3OpIuy2LvAAAIABJREFULHP6xjKnCJur5b+S9Rlaf98aq9p47I6D3sehPpwIJF2rcFdX+GQje9ZomTpFSA8BnC4RX5Rb8VKRCRuP2Nt8nwDgwlwt5g834systnuemppdGPreEUnvwiWT0nBRXuxkzVDnLCu14KZ1ta2P+2ld+O3KfjF/eHWsyV3W2lYsc0riVMdimfy+0zeWee4LbZ41l8vnMKJ1feaNd/YAj303/EKYsNem3jp32wFPdVhBojerL00T2lhmd4r4uKwJLxWZsK2q7WQTtQK4uL8OtxYaMbqdctgKsxMjPzgiadGw+qIMDgOKciHdAASAZcuW4d5770V9fT1EUYQgCBBFEcnJyXjmmWcwY8aMUH75Hs3pEvH0byb836+NIW2QHGuUAtBHr0SOUYkcgxL9jEr0M7hPiXOMSmQblJ0u5QiVgyYHXtttxlvF5nbL/foZlLh5mAFzA0x22lHTjHGfVEqe235ZVodPqSk2nfnxUeys9WZfPXtmSkyVffuyOUU8srUBr+82BSxh6KnUCnfLgX6eX0YVclriWD+DO5ZFy6CcPfXNeHmXGe+WWNotkRmYpMK8QgOuHKj3KzP+5qAVl33tHQakUwrYNat30KfZUfRwukQMXXoEx3wmub4/uRfOi9FeY6ZmF+7/vh7v7bFE5MYzWmmUaIljqpY1mftXbsv6rK9B2emytFD5tdqOhUVmLCu1tHuoMypNjfnDjbikv85vw5pVGT1Pg92Fgf87LPk3s2FGJkamBWcIQ7hVWZ24e1MdVu7375fZk+mUQusazBPLcozee8w+emVUHGCJoojvW5JNVuy3tttjdUxWAuYVGjE1V+uXbCKvyhiRpsaG6Rkxv7Ed70K+AQgAFosFq1evRmlpKVwuF/r3749zzjkHRmNsnNq/sduM64foY+of8xGLE7esr8W6w/7NP+NdklpAv9bNPW/Q9Swoe+u7Xg4SKeZmF5bubcLCIhN+r2+7pE6vElonOw1qmex075Y6vOpTQnVWXw0+nsIyk3j3+LYGyYS+5AQBz56Zihn5sZVhUNrgwA1ra7C9uu2TyniVqhFaDyf6GZXI9T2wMCqRqVXETMN4jzqbC2+XmPFykVmSySeXnCBg7mADbh5maB1WdO3qaqzwKaG6coAOCyewk3q8u+u7Wsngl946BRZOSMVZfWNrE/CXajtuWFuDvQ097xQjXavwOajwuSFueZyuDW02cihUNjnxxm4zXt9tlmxQy2XqFLhxqAE3DDEgQ+fOwp+8slLS6uWPo4x4iFUZcW/W11X48qD3vqwgUYnXz0qLuYEDGw7b8If1NZK+bz1Flk7hjWOyA4scY+gz+ELhgMmBV3eZseh3MxraSTbJMSrxh2EGXDvInWzCqozYFZYNQI8NGzbg/fffx5EjRzB48GDMmzcPOTk54fryXZbyZgWm5mrx3JkpSIuBErpvDloxb0MtqtpZkMQatQLQKAQkKAXoVYLsZEUpuUkONGgjXrhEEasrbHipyIRvK9rf3D2vnwY3DjXi5vU1koD+1llpmNk/tjaBqPN21TZjzMeVfs9fO0iPx09PjprMsPYsK7Xg7k11AZuwx6oEhXsQRIJCgEEt+Gzu+SwkWzKRY2WybVc4XCI+O2DFSztN2FLZdkmdUgCm5elwxQAd5qyukWRNfXFhOs7I0oThaimS1lRYcfFX1ZLnBAB3jDDigZOSujVROhxEUcQru8x48Mf6iLQBCJUEBaBVutdliS2xLMfojWM5PrEsngfd2JwiPiy14KUiM36rafugKkEBXD5Aj7P7aiSloACrMnqKd0rMWLCxTvKcSgAePDkJt48wRv0muMMl4olfGvHk9sa4yvrTKL33mCkJCr8Mvn4GFXKN7h580ZC9FyqmZhf+t8eChUWmdg+qDCoBVw/SY2iKCvdsrm99nlUZsSPoG4CPP/44nnrqKezYsQNZWVmtz7/zzju4/fbbIYreL5eeno5vv/0WubnR3Zw+5c0KAEBfvQILJ6RhQp/ovOFodol4bGsDntlh8nstKUFATkvzUIXgnvCogPu/SkGAIHnO/z2C5zkASgWggPc9gs/HJSiABKUAjeeX52ZXKUCjENxBVvLY5zmf172P3c9F+w/FSNhd557s9N6eJjR1sMN2ulaBoit6R/0NEwWHPPvTY2CSCq9NTG23r0ckmZtduO/7eiwpsfi9lqZRoE9L7zpPDFIK3pjUkVim9DwntB3LNEq0xqCElljmudl1xyf5YwFaWXxLUPq8p+UxY5m/n4/ZsbDIhOX7mjpcFjkkWYUtF3P4R08giiLmrqmRNND3ODFdjdcmpGFAcnRuntTaXFiwsRafH/C/9iydAulaBZS+caoDsUzpWZMBAT8uUCzTtMYg6drMN7619dgT7+SP+b0nJYoivjtqx0s7Tfj8QMfLIlmV0XM0u0RMW1UV8NDrrL4aLByf2uHBC+FWYXbi5nU12HTU/9r7GZRI0SjajEnyWOa7BjteLHP/cj9ua12lUQjQqrz3kQltPPbGwJbnlALUjGV+XKKIrw+6k03WHup4JeFVA/V4aTyHf8SCoG8ATp06FUajEUuXLm19zmazYdCgQVAoFFi8eDFOPvlkfPXVV7j11lsxa9YsPP3008G8hKDzbAAC7lPnu0cZ8ZcTk6KqV0dZowM3rasJOD12fO8EvDIxDX2i9IcKdU+N1YlFv7snOx06Tjr+7SOMePRUlpn0FC5RxEtFZjz8Yx0cojReqRXAQycnYcHw6Dp13lnTjBvW1qA4QKn7tDwtnjszlaeLceqwxYnXd5nxRrEZNbb2Y9n/Oy0ZC4azzKSnaHaJ+Pe2Rjz1awNESOOVQSXgyTOScdXA6GrVsuWoDTetqw1Y6n7dYD3+eXpyXGfG9WRljQ68XGTCkhLLcTPY3zwrFRf314fpyijSLA4X/vZDA94o9j+c7aVR4PlxKbggN7qqdL4ob8KtG+r8fi5H6z0xBU9RbTMWFpmwdK8FtuN0r2BVRuwI+gbgsGHDcMMNN+Dee+9tfe6rr77CrFmz8MADD+BPf/pT6/N33nkn1q1bh+3btwfzEoLOdwPQ4+R0NV6bmIb+SZE/df6krAm3f1frV7evEID7RyfinlGJMdcnijqv2SXi07ImvLjTJJn46+unSzIxMDk2Gw5T163ctgf/2JeIkgCbapP6avDS+FRkRfiAQBRFvFlswV9/qPMb9KFRAv/v1GTcONQQVTf4FBpNDhEflFrw0k4TdtX5/5tNUAC7Z/WOiZYcFFzv/bQXj+41oMLifydyaX8dnhqTEvEDAqdLxP/9ZsK/tjVAnpyfpBbw9NgUXFLADZ+eoMHuwpISC14uMmG/yf/fLKsyeq5XNpfiX/u0qLX534bfPNSAR05NjvjgG5tTxN9/qsdLRf6blRlaBV6ZkIqzs2OrFyt1TZXVibeKLXhtlwlHmvwPaIemqLB5JqsyYkXQV0m1tbXo3bu35LkNGzZAEARMmTJF8vzo0aNx5MiRYF9C0N090gj5P+etVc2Y8Gkllu71L1ELlyaHiD9uqsPcNTV+m3/ZeiVWnp+OP49O4uZfD6FWCLi0QI9vp2Xi66kZuKS/Dr5rypn5Om7+9VBDjCLWTsvAnMH+N52rD9lw5ieV+Krcv0QtXOpsLly3tgZ/3Oy/+TcoWYVvLsrETcOMXFj0EDqVgDmDDdg0MxMfT+mFKf2kJ8o3DDVw86+HOjnZhY0zM3FRrv9N54f7mjD+00p8fzRyw8+OWJy45KtqPPaz/+bfSelqrJ+Ryc2/HiQpQYFbhxvx86VZWDIpDWf2lrbduGOEkZt/PdTZ6U5snJGFcb39W7G8utuMc1ZUoqg2csPPShscmPLZsYCbf2f31WDjjExu/vUg6Vol/nRCIn69vDdemZCK0b2k95P3jErkGj2GBD0DcNSoUZg9ezbuu+++1ucmT56M33//Hfv375f841i0aBEefPBBHDhwIJiXEBLrDllxy/ragLveVxTo8J8xKUgK4/CJ4rpmXL+2BkW1/tkR5+do8eK42BhYQqF10OTAiv1WqBXu3gyxMPiBgq+kpASDBg0C4M4YvuO7WtQHmPQ1r9CAv5+cDG0YT51/OuaejHkgQHbE1QP1ePKM2BhYQqFVUt+MLw5YkaJRYNYAPW+aeyhPLBNFEYt+t+Av39f79cBVCsCfRyfiT2Gufvi2wr1ODDSA7fYRRjwYAwNLKPR+qbZjdYUNuUYlLu6vi6oWHBQ+nljmdIl4+jcT/hkgY1irBB6LQPVDWwPYlALwt5OScOfI6GodQ+EniiK+r7Rjw2EbRvVKwJQcbgbHkqBvAF533XXYtm0b1q1bh5SUFOzYsQMTJ07EBRdcgCVLlkje+9e//hVr1qzB5s2bg3kJIVNtdeK2jXVYFSBTJs+oxGsT03BqZmib6ouiiCUlFtz3fT0ssm7pagXwyCnJmFfIMjki8vLdAASAcpMDf1hfi80BmjmPSFPjtYmpGJoS2mxRlyjiuR0mPLq1wW/wg1El4KmxKZg1gJkyROQlj2W765px49oa7AxwGDomKwGvTEhFjjG0rVraG8DWS6PAS+NTcR5vjojIhzyW/XTMjhvX1gQsFb8gR4vnx6WgV4gTO9obwNbPoMQbZ6XitEz2eCOKdUHfANy5cycmTZoEg8GAoUOHYseOHbBYLFi1ahVOPfXU1veJoogTTjgBkyZNivohIL5EUcTru83424/1fqVqSgH464lJuGukMSSnzg12F+7ZXIcPSpv8XitIVOKNs9KidqonEUWOfKEJuPtUPfVrI/69vdHv1FmnFPDP05Jx3ZDQNNU/1uTEvA21+LbCv1RvVJoab5yVynJ1IvITKJZZHSL+sTVwn6rkBAHPnpmKGfmhaarPAWxE1BWBYlmD3YU/banD+3v97/P66BVYOD4NE/uGZgOuvQFsF+Vq8fw4DmAjihdB/04ePnw4PvnkE5xyyimoqqrCaaedhuXLl0s2/wB3X0Cj0Yjp06cH+xJCShAE3DTMiNXTMlGYIj1VdorAoz83YMaXVagIMPWtO7ZV2THx08qAm3+XF+iwbkYmN/+IqMOUCgF/Hp2Ezy9IR65ReoPa5BRx9+Y6XLu6BjXyk45uWnfIinGfVAbc/LtlmAFfX5TBzT8i6jCtSsC/Tk/B+5N7IV0rXdbW20XMXVODO76rhbm5/cnSnfVJWRMmfFrpt/mnEIC/npiIj6ekc/OPiDosKUGBVyak4eUJqUhUSw9fD1tcmPllFf7+Uz2aXcHL3RFFEW/sNuOclZV+m38aJfCfM5Lx9qQ0bv4RxZGgZwD2JE0OEQ/9VI9Xd/mfOqdqBDx3ZiouyuveqbMoinipyIyHf6qHfO2qVwl44oxkzB4YmiwdIooPgU6afdXbXfjjpjp8uM//gKGvXoGXJ6RhfJ/unTo7XCIe39aIp35thPyHTkqCgBfHp+LC3NBk6RBRfDheLDtqcWL+hlqsPuR/wDAoWYXXJqbihF7dOyxtcoh44Id6vFHsv/brq1fg1YlpOLM3y+SIqG3Hi2X7GtzZxVur/LOLT0pX47WJaShI6l57gzqbC3duqsUnZf6trQYlq/DGWWkYmcYDWaJ4o7z//vv/HumLiFVqhYDz+mlxQi811hyySRpRW53A8n1NONrkxIQ+Gqi7UBJcbXXi+nW1eGWXGfLDnsJUFT6ako5J2Vpu/hFRu2pqatCrV682X9cqBUzP0yLPqMTaQzbJYUNjs4j39ljQ7BIxtrcGyi7Em4MmB678pgbvB8hgHpOVgI+npOPkDN4wE1H7jhfLjGoFLh+gQ6JawIYjNsnaqcbmwjslFuhVAk7JSOjS2qm4rhmXfFWFrw76bzCen6PFh+f1wpAQ908loth3vFiWqlHg6kF6uEQRW2T9mg9b3LGst16BEWnqLsWyn47ZMfPLKvxQ6b/BePVAPd45Jy3k/VOJKDKYARgkh1tOndcGOHUekqzCa508RfnuiA03r6vBIYt/ycqNQw147NRk6MI4qZOIYtfxTpp97a134Kb1NdgW4NT5lAz3qXN+YscXhZ/tb8KCjbWok00dFgDcc0Ii7h+dCFUYJ3USUezqTCz7pdqOm9bVoiRAT6tzsjV4cVwqsjpYossBbEQUTJ2JZesP2zBvfeB7wssKdHhqTAqSEzpWotveADaDSsB/OYCNKO4xAzBIEtUKXDFAB4NKwIbDNviG6GqbC++UmJGYoMDJ6e2f1DhdIp78pRELNtahQTZ+PSlBwCsT0nDHyMQuZRQSUc90vJNmX2laBa4eqIfdKeL7Sump86GWU+dsgxIjjnOgYXOK+OsP9Xjgxwa/gUlZOgXeOacX5gw2QMEbZiLqoM7Est56JWYP1ONYkwu/1kgPNPY1OrF0rwXDUtUYcJwyuga7C7d/V4f//Grya8XSP1GJD89Lx7R8HTf/iKjDOhPL8hJVuGqgHnsaHH4HGkW1Dizf14STM9TINrQfy441OTF3TQ3eKLZAvpU4Kk2Nj6f0woQ+nFhOFO+4ARhEgiDg9CwNzu2nxYbDNtT6ZLw4ReCbChu2VdlxVl8NDGr/k5rDFieu/rYa7+5p8uuRdWqGGh9PScfpWSyTI6LO6cxCE3APCDk7W4szshKw9pANJp9jYrsLWLnfitJGByb20UCj9L/p3VPfjMu+qsbn5f59Zc7J1mD5eekoZF8ZIuqkzsayBKWAC3N1GJqixppDVth8DiMsDhEflDahzu7C+D6agJnI26vsuPjLKnwnK8ED3APY/je5F/I6kRFNRAR0PpbpVApc0l+H3jol1h+2SbL36u0i3t1jgQLAGZkJAQ9W1x2y4uKvqvFbjX9G9C3DDHjz7DRk6ji0iKgnYAlwiJiaXbjv+3q8U2Lxey1Tp8DC8amYlO09Zfmq3Ir5G2pRbfNP775rpBEPnJTErD8i6pLOlJrIVVudWLCxDl8E2MzLT1TitYlpOCXD21R/6V4L7tlUJ9k0BACVADx0chJuG2Fk1h8RdUl3Ylm5yYE/rK/F5gCbeSPS1Hh9Ympr/z4OYCOiUOpOLNtd14wb19ZgZ63/Zt7YrAS8MiEV/Vr69x1vANsL41IxtZsDK4kotjADMEQSlAKm5uowKFmFtYds8N3XMztELN3bBFOziNMyE/DI1gbc+329ZIgIAKRrFXh7UhpuGGrsUuN9IiKg8yfNvvQqBS7tr0O6VoH1h23wDVN1dhHvlligUggYnqrGXZvq8K9tjbDLbphzjUp8cF46Lu7PG2Yi6rruxLLkBAWuGqCHSgFsOmqX3AxXNrnbG6RrFcgxKjmAjYhCqjuxLF2rxOyBBjQ2u/ymBJebnXh3jwUFSSroVQKuOs4AtlMyWVlG1NMwAzAM9je6T53l/bQA90myvKE0AEzso8HLE1LRu4MNqomI2tKdk2ZfRbXuU+dddf6nzm3Fspn5Ojw9NgUpmo41qCYiakuwYtn3R224aX0tyk1Ov9faimUcwEZEwRKsWPZluRULNtaiyupfQRYolnEAGxHxjiwM8hJV+OyCdPx5dCLksVYemJUC8OBJSVh+Xi9u/hFRVClMVWP1tEzcPNTg95o8lmmVwNNjU/DmWanc/COiqHJ6lgYbpmfi0v7+pW/yWJaUIGDR2Wl4akwKN/+IKKpMydFi44xMnN3XP5NPHsuydAp8PCUdfzspiZt/RD0Y78rCRKUQ8NcTk7Dy/HT0MwTe2OtnUGLlBem454REKBmYiSgK6VQCnhyTgnfPSUNaGxt7Q5JV+PaiTFw3xMAyOSKKSikaBV6bmIoXxqXA0MbG3ikZaqyfnokZ+eyRRUTRqbdeiQ/P64VHT01CgBmTANwD2DbOyMTEABuFRNSzcAMwzMb2dgfgGfnSMetTc7XYMCMTYzjll4hiwIW5Onw3MxMT+0hj1rWD9Fg9LQPDOeWXiKKcIAiYPciA9dMzcWK6NGbdNdKIVRdmIJ9TfokoyikEAbePSMTXUzMwMMkbs1QC8MgpSfjg3F7I4JRfIgJ7AEaMKIpYVW7FmgobxvXRYHoeG0oTUWgEq9dMIC5RxPJ9Tfj+qB0X5Gol082JiIIplLHM7hTx3l4LdtQ049L+OpzOA1kiCpFQxjJTswtLSiwoNzlx5UA9RvJAloh8cAOQiCjOhXKhSUQULoxlRBQPGMuIKFJYAkxERERERERERBTHmAFIREREREREREQUx5gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhERERERERERBTHuAFIREREREREREQUx7gBSEREREREREREFMe4AUhEFKccLhFfllvx8c97I30pRETdVlJSEulLICLqNsYyIooUVaQvgIiIgu+oxYnLvq7GbzXNALT4t9aEWwqNkb4sIiIiIiIiigBmABIRxZlykwMXrjrWsvnn9vBP9agwOyN4VURERERERBQp3AAkIooje+qbccHnVdjbIN3sszqBf25riNBVERERERERUSRxA5CIKE7sqHFv/h1sI9Pv3RILdvpkBRIREREREVHPwA1AIqI48GOlHVNXHcMxq0vyvErw/l4E8I+t9eG9MCIiIiIiIoo4bgASEcW4dYdsmPllFertouT5awbp8ebZaZLnvjpow7pDtnBeHhEREREREUUYNwCJiGLYqgNNuOKbKpgd0s2/+YUGPHtmCi7K1eLEJGlJ8MM/1cMlSt9PRERERERE8YsbgEREMWpZqQXXrq6BTdby777RifjnaclQCAIEQcAd/aV9/7ZXN2P5vqYwXikRERERERFFEjcAiYhi0FvFZty8rhayxD88emoS/nJiEgTB2/xvRKILM/N1kvc9srUBNiezAImIiIiIiHoCbgASEcWY53Y04q5NdfDdvhMAPD02BbePSAz4MQ+dnCQZCHLA5MRru80hvU4iIiIiIiKKDjGzAfjf//4XZ599NnJycjBgwADMmjULRUVFkvfMnz8fKSkpkl+TJ0+WvMdms+Hee+9FQUEB+vbtiyuvvBIVFRXh/KMQEXWJKIr457YGPPhjg+R5lQC8OjEV1w0xtPmxBUkqXD9U+vqT2xtQZ3O18RFEREREREQUL2JmA3Djxo248cYb8eWXX+LTTz+FSqXCzJkzUVtbK3nfWWedheLi4tZfH3zwgeT1v/zlL1ixYgVef/11fP7552hsbMSsWbPgdMqaaBERRRGXKOIvP9Tjie2Nkuc1SmDJOWm4rEB/3M/x5xMSkaj2pgHW2UX836+N7XwEERERERERxQNVpC+go5YvXy55/PLLLyM3NxdbtmzBBRdc0Pq8RqNBVlZWwM9RX1+Pt99+Gy+88ALOPvvs1s8zcuRIrF27Fuecc07o/gBERF3kdIm4c1MdlpRYJM8bVAL+N7kXJvTRdOjzZOiUuHNkIh772ZtBuHCXCTcNMyDHGDM/DoiIiIiIiKiTYiYDUM5kMsHlciElJUXy/ObNmzFw4ECcfPLJuOOOO3Ds2LHW17Zv347m5mZMmjSp9bl+/fphyJAh+P7778N27UREHWV3irhxXa3f5l9KgoBPzk/v8Oafx63DDeij94Z+mxP45zZmARIREREREcWzmN0AvP/++zFy5Eicdtpprc9NnjwZCxcuxCeffILHHnsMW7duxfTp02Gz2QAAlZWVUCqV6NWrl+RzZWRkoLKyMqzXT0R0PBaHC7O/rcbHZU2S5zN1Cqy8IAOnZCR0+nPqVQr85cQkyXPv7bHgt5rmbl0rERERERERRa+YrPn661//ii1btuCLL76AUqlsff7SSy9t/f3w4cMxevRojBw5El9++SWmT5/e5ucTRRGCILT5eklJSXAunIiog0wO4I9FGmxrUEqez9K48EJhEzTVJpRUd/zz+caxUwEU6LUotbjPgEQA9647jOdG2IJw5USxq9ImoMQsYHiiCynqSF8NBcI1GRHFA8YyIgqFQYMGtft6zG0A/uUvf8Hy5cuxYsUK5Ofnt/vePn36oG/fvigtLQUAZGZmwul0orq6Gunp6a3vq6qqwtixY9v8PMf7SyQiCqYaqxN/+Loa2xqkWXkDkpT4eEpWp/v1lZSU+MWxf+msmPWNdwdxS50SB/U5ODtb2/ULJ4phW47acPU31ai3i8jWK7HignQUJMXcMimuBYplRESxhrGMiCIlpkqA77vvPixbtgyffvopBg8efNz3V1dX4/Dhw61DQUaPHg21Wo01a9a0vqeiogLFxcU4/fTTQ3bdREQddcTixNRVVdhWJd38G56qwqoLM4I2rOO8fhqM6y0tIX7opwa4RDEon58olhxrcuL6tTWot7v//VdYnFiwsZbfD0REREQUN457J1leXt6lT5yTk9Olj2vLn/70JyxduhRLlixBSkoKjh49CgAwGAwwGo0wmUx4/PHHMX36dGRlZeHAgQN45JFHkJGRgYsuuggAkJycjGuvvRYPPfQQMjIykJqaigceeADDhw/HWWedFdTrJSLqrP2NDsz8sgr7Gp2S50/JUGPZuelI0QTvzEYQBDxySjImrfQOSvqtphkflDZh1gB90L4OUbRziSJuWV+Lw/+fvfsOb6ps/wD+PdlJkzRNJ5QNZa9CC7KhLAGRPRQFF6Ko+Kq/V0Vlq7iVoYAi+qIiWwTZe28oe5Qt0JWmzd7n/P4oNDlJS1d2n891cZWeJvQAzclz7uceRpp1/HC2FT9eMuCVptIAnRlBEATqRMPmAAAgAElEQVRBEARBeE+pAcCWLVs+sj9eSdRqdYVOqCSLFy8GAAwaNIh1/L333sPkyZPB5XJx8eJFLF++HBqNBvHx8ejSpQt++eUXyGSyosd/+umn4HK5eP7552E2m9G1a1csXLiQ1UuQIAjC364W2DB4qwr33YIQXRIEWNYrGjK+9xO228QKMLSuGGtvOoeMzDqpxaDaYoh45b/uE0Qo+uasHrvuF9//csYJLfrUEJFSYIIgCIIgCCLkUQUFBY+sb/njjz8qFAB8+umnK3xSBEEQVcmZPCuGbcuDyswO/j1eU4RfuysrHYx7VK+Zm1o72v2VDZvLt56VIscbLWTFPp4gwsn+TAsGbVWBfsRKqGO8AP/0iwGnAmshwrtI3yyCIMIBuZYRBBEopW5pjxkzxh/nQRAEUSUdzbZgxI48aK3sCMTwemIs6BIFPse3QYe6ch5ebByBhRcNRce+OqvDMw0jEOXFkmOCCDY5Jgde2qtmBf+ihRy82kyKj09pi44dyrbip0sGTCClwARBEARBEEQII3d3BEEQAbL7nhlDtnkG/8Y1lGCRH4J/D/23lQxyvvN7aawMvjmr88v3JohAcNAMXt6Xj2wTO+t2UdcovNNSil6JQtbxGSe1uKm1+/MUCYIgCIIgCMKrKtzU5tixY0hPT4dGowFNsxfQFEXh3XffrfTJEQRBhKt/bpvwwh41rOzLJ15vJsWsVHmFWi9UVLSIi7dayjDjpDPradFFPV5qHIHaMtL7jAg/X53VYY9b3793WkrRq4YIAPBdRwU6rsuB1lYYnDfaGbx+MB8bHielwARBEARBEERoKvednUajwejRo3H06FEwDAOKosAwhQvkh78nAUCCIIiS7b1vwbjdajjc+o59kCzDf1vJ/Br8e+iVplIsvmTAPWPhBGIrDXxyWosfuyr9fi4E4Ut771vw2Wl2hmvHeAEmJ8uLPq8h5eHjdpGYdLCg6NjBLCt+vmzA+CakFJggCIIgCIIIPeUuAZ4+fTpOnz6NhQsX4vTp02AYBmvXrsXJkycxduxYtGzZElevXvXFuRIEQYSFaSc0HsG/2e0i8W5r/2b+uRLzKHzQhj34Y+V1E87kWQNyPgThC9lGB8bvU8P15Rcj4uDn7krw3Erun02SIK06uxR4+gktbulIKTBBEARBEAQResodANyyZQvGjh2LkSNHQi4v3C3ncDioV68evvvuO1SrVg0ffPCB10+UIAgiHJxWWZGeZyv6nAIwr5MCrzYLfFbR6PoSNI1iJ4ZPPa4tyvImiFDmoBm8tFeNHJe+fxSAH7tGoZqE6/F4iqIwp5MCMpf+mAY7g9cP5IMmrwmCIAiCIAgixJQ7AKhWq9G8eXMAAJ/PBwAYDM7pkb1798aOHTu8dHoEQRDh5ZcrBtbnvRKFeLZhRIDOho3LoTAzJZJ1bG+mBbvceqURRCj64owO+7PYGa3vtJIhLVFU4nNqSnn4OJX9mjiQZfV4HRMEQRAEQRBEsCt3ADAuLg45OTkAAJlMBplMhoyMjKKv5+fnw+FweO8MCYIgwoTGSmPNDRPr2HONgiP491DPRCG6VmOXPU49roGDJhlPROjac9+ML9LZff86JwgwubWshGc4jW0oQY/q7q8JLW6TUmCCIAiCIAgihJQ7AJiSkoKDBw8Wfd6rVy/MmzcPK1aswJ9//okffvgB7dq18+pJEgRBhINV140w2J2BtOoSDvrWLDn7KBAoisLMFDnr2IV8O1ZcNwbojAiicrKMDozfm8/q+xcr4mBxNyW4nNJ7blIUhbnFlAK/cbCAlMcThI/ZaQbLMgx4aa8ac87poLPRpT+JIAgiyFgdDDI0ttIfSBA+Vu4A4Msvv4ykpCSYzWYAwKxZs6BUKvHKK69g4sSJUCqV+Oyzz7x+ogRBEKGMYRgscSsbHNswwmPwQDBoHSPAiHpi1rFPT+tgspNgBxFa7DSDF/eqkWtm9/1b3C0KCcX0/StJTSkPs9xKgfdlWvDrleANjB/LseCDYwXYcNtU+oMJIsgwDIP1t0zouC4HEw8UYPUNE6ad0CJ5dTZ+vKiH1X2SFkEQRJC6q7ej/+ZcPLFZhWwjqZQkAosqKCio9DsowzA4f/48uFwuGjZsCB6PV/qTCIIgqpBjORb02agq+pxDAedGJCAxouxBiIrKyMhAUlJSuZ5zS2dHu7XZsLokW8xIkePNFqWXTBJEsPj4lBZfnWGX/r7XWobJyfISnlEyhmEwZFse9rj0xJTyKBwaEoda0uBa9yy8qMf7RzVFn/+vhxKD6ogf8YzQUJFrGRF69mVaMOOEBidVJWfL1JVxMbWtHIPriEFRwbeRRhCPQq5lVceue2a8tDcfakvhgrpTggB/940JygQAomoodwZgcSiKQosWLdC0aVMS/CMIgijGksvs7L/Ha4r8EvyrqDoyHsY3YU8m/vqsDmoz2bkkQsOue2Z87Rb861pNiHdbVSyITVEU5nRUQMpzLtr1dgaTgqgUmGEYzD6tZQX/AOCrM7qgOUeCKMmZPCuGbVPhyS2qRwb/AOCmzoHn9+Sj5z+52J9JBlURBBFcaIbB5+laDNuWVxT8A4CDWVbMPa8P4JkRVV25o3Wu/f8epVOnTuU+GYIgiHCUb6Gx7ha7DO+FIBv+UZz/ayXD7xkGaKyFgQOtlcFXZ3X4tJ0iwGfmGw6aQYGVhtkBVJNwwCFZJSHrvsGz71+cmIOfukaVqe9fSWrLeJiZGom3DxcUHdtz34KlV40YF+DXNM0weP+oBj9e8pxQfE5tw/FcK9rFCYt5JkEE1g2tHZ+c0mLNzeLL1TkU0LuGCAcyLaw+ugBwSmXDwC0q9KkhxLS2kWim5PvjlCssQ2PD4Wwrakt56FadvB4JIhzlmR14eV8+dt7z3JzoW1MUEvcARPgqdwDwiSeeKFOqvVqtrtAJEQRBhJs/rxnhmjhXS8pFWmLwL/yjhBy801KGqSe0Rcd+umTAy02kqCML3mxvhmGgtzNQm2nkWwp/qR/8Yv3ezD6msTJFAaOGkTys7B0d1H9PongP+/7luey4cyhgcTcl4svR968kzzWSYN0tE/a5ZB19dFyDtEQhagaoFNhGM3jtQD5WXi+539/Plw0kAEgElWyjA1+e0eHXKwaU1GJ2QC0RprSVo7GCj2yjA188eLx7C8Btdy3YfjcHTzWQ4INkGWoEUVm+xkpj3U0T/sgw4liutej4682kmJUqJyXMBBFGTuZaMW63GncN7IoZDgV81EaO/7SQkg1mIqDK3QPwwIEDHsccDgdu376NX375BRRFYdq0aejWrZvXTpIgCCJUMQyDdn/lIENjLzo2ta0cb7f0Xy+9yvSaMdsZpKzNZi1khtcTY3E3pbdOr0wYhsGFfDtu6uyFATszO5j3MJD38Jg3BkU2jORh24BYKIRe6ZZB+MnMkxp8c5ZdXjM5WYb3Wpe/719Jbuns6LQuh5WNlFZdiDV9ov1+M2+yM3h+jxpb/jWzjgu5gMXl/kPAAS6NSkC0KHhbD5SG9M0KDxorjXnn9Pjhoh7GEiJ/nRIEmN42EqlxAo+vXdPYMPOkFutvm4t5JiDiAhOaSPFWS1nArt80w2B/pgV/ZBix4bYZphKGlnyQLMO7Xrw2EaGBXMvCD8Mw+PmyAZOPaTzWoDEiDn7upiRZv0RQ8MoQkIccDgf69OmDXr16YfLkyd76YwmCIELWgSwLntjsHP7Bo4CLoxIQJ/bfTXhlF5rLrxnxyv581rHdA2ORHON5Y+ZtehuNVddNWHxZjwv59tKf4GXdqgmxuk80+KRZc0jYcdeM4dvzWMe6VxdiTe/oSpX+FmfxJT3+7wi7197cTgqMbei/0h6tlcZTO/NwMMvKOh4v5mB1nxg8szMPt/XOKODMFDkmhfAgH3LTHNrMdgaLL+vxzVk9qyeWq+ZKPqa1laNXorDUYPqxHAumndDicLa12K8rBBTeaSXD+MZSiHj+uYbf0tnxR4YRf14zemQAleTz9pGY0FRa+gOJsEGuZeHFYKPxn0MFWHXDMwv/sTgBlnRXonoQ9/0mqhavbotxuVwMHz4cv/32mzf/WIIgiJD1i9vwjydqi/0a/POGkfXFaO7WV2nKcY1PhwpkaGx470gBmq7IwluHC/wW/BNz2TeJezMteOdw8Ax5IEp2z1DYc8dVghf6/pXkhcYR6JzADoJ/dEyDu3r//KyqzA4M3KLyCP7VlnKxpX8sWij5eKExOxi55IoBNPlZJvzMQTP4PcOAlLXZ+Oi4ttjgX20pFz91jcK+J2PRu4aoTJm07eKE2NQvBst6KtEo0rPkt8DKYMpxLVLWZmP5NaPPfvb1NhrLMgwYsDkXrVdn48szukcG/4RuS4D3jmrw5zWjT86NIAjfulpgQ89/cosN/k1sFoEN/WJI8I8IKl5vkGE2m0n/P4IgCAC5JgfW32YvCJ4Pwca/HIrCzBQ5hm5zZlYdyLJi+10L+tQUee372GkGm/814+fLBuy5X7mpjiIuoBRyECXkQCnkQCniIErw4OODY0Vfe/B1hYADOw08uUXF6tO09KoRSXIe3gjhzKlwZ6cZvLhHzQoscChgcXclYn0UcOdQFOZ3jkLHdTlFZYxaG4M3DxVgdW/flgL/q7dj6LY8VmsBAGiq4GFN3xhUe9DrcEySBJ+c0sL64J/lls6BXfcs6FXDe69bgigJwzDYeMeMj09pcbmg+MB4rIiD/7aS4blGERBwy/+aoSgK/WuJ0aeGCMuuGTH7tBaZRnaA8a7BgVf252P+BT1mpMiRVr307MLSMAyDw9lW/HHNiL9vmqAvqYnhAzUiuHg6SYKnG0iQbXRgyLY8Vvnz6wfyIedTGFBbXKnzCkc775mx/a4ZHAqQcDmQ8CmIuRQiHnyU8Jy/xDwKETwOxC7HKvJzRRBl8ddNI944UODx+pfxC9cHg+qQ1zMRfLwWANRqtdi/fz/mzZuH5ORkb/2xBEEQAAonak0/oUWBlcY7LWVo7Yfy08pads3I6gNSX85F12rBf97FSUsUoUd1IXa7BOamn9CgZ6Kw0tlVOSYHll414tcrhkdmTXAooEuCEIkR3GKDd0qR85i4guVePA6wrJcSPTfkskonp57Qoo6ch4Hk5iwofXxKiyM57Ey4D5Ll6Jzg2347dWQ8TG8rx7tHnaXAO+9Z8HuGEc/6qBQ4Q2PDkK15Hq+V1Fg+VvaOQZRLz7MYEReD64pZw0F+vmwgAUDC5w5mWTDjhJa1meJKxqfwRnMpJjaTQsqvfEESj0NhbMMIDK8nxoILBsw5p4PWxr4pP6+2Ydi2PHSrJsSMFHmF1hF39XYsv27CsgwDbugeXeIr5lIYWEeEMQ0k6FJNWNT4v46Mh9/TlBi1I69ojeBggOf3qLGqdwzpE/YAwzD49pweM09qS3/wI/AosAKEzoAh50HA0Hm8royHpxpIwqL3r41mSPsSH7E6GEw5rsGiSwaPrzVR8LA0TYmkyOCeSE5UXeXuARgVFVXirhnDMKhVqxaWLVuGZs2aeeUECYIgHDSDvptycSLXBqAws+vksHjWjW6woRkGbdZk45bLDcKsVDneaO7/LDJv9Zo5k2dF9/W5cH3TmN9ZgWeSyh/oYBgGx3KsWHzZgHW3TI8c2hEj4mBcQwmeaxThtymrlwts6LMxF1qr828r5lLY3D8mJILPVcnWf80YtYPd9y+temHvRn9M2qMZBk9sVuGQSx8yOZ/C4SHxSPRy2U+6yoph2/JYE44BoEd1IX5LUxYbSDmabUHfTc4+pBwKODM8PmATiyuD9M0qO4ZhkGOiwecACiHHb1Mnz6ltmHlCg+33is/iFnCAFxtH4J1WMsT4cCBNnrlwwvDPlw0lvr8MryfGR23kpU57N9kZbLxTOMV3z30LSrtxahcrwJgkCQbXFSNSUPI65e9bJjy/Rw3a5Q+M4FH4+/EYpMRW7fcZhmEw/YQWc87rS3+wlz0WJ8DGfjE+aR3xkC+vZRfzbRi9Iw9ZRgdebiLFjBS5T/8uVc09gwPP71YXu7kxsr4Y33ZQIMILmxoE4SvlDgDOnj3bIwBIURQUCgXq1auHtLQ0cLmkzp0gCO9ZcEGPycfYzfYnNZdiZmpkgM6odLvvmTHEpWRWyAUujgzMBE5vLjQn7FNjhUs2UXUJByeGxUPCK9tix2CjsfqGCYsvG3BObXvkY9vHCfBS4wg8WUcMYQBKePbcN2PYtjy4Dm9MEHOw44lY1AjB4Ek4uqu3o8v6HORbnP9J1SQc7B8U59PggrubWjs6rsthTfrsnSjESi+WAh/IsuCpHXnQuWU1Daojwo9dlSW+RhiGQZf1uTjv8nr7v5YyfNQ29CaPkgBg6RiGwfrbZsw8qcF1beEGFJcq3DiLEXEQLeIgRsR1+f3D4w+OCQuP88oZMLils+PTU1qsumEqNkBGARjdQILJyTLU8uP185bOjo9PabG6mP5cAMB/EJD8bysZ6/2ZYRicVNnwR4YBa26aWJtBxakm4WB0fQmeTpKUK/Pnt6sGvHGwgHVMIaCwqX8smkZVzQwiB83gncMF+PVq4Poi/tBZgacrsLlZVr66ltlpBp3W5eCKS3uIoXXFWNQ1imQDesGe+2a8uCffYxNOwAE+a6/A840kPm3/QRDe4NUpwARBEN52R29Hh79yYHDrryHiAieHJXg9w8Zbnt2Vhw23zUWfj6wnxo/dlAE5F28uNO/o7Uhdmw2LS+XT1LZyvN3y0ZmN1zV2LL6sxx/XjI+8kRJzKYyoL8ZLjSPQMjrwGRD/u2LAm4fYN2fNlXxs7h8DGdnhDSgbzWDAJna/Ri4FbHg8Bh19XPpbnIUX9Xj/KHuj4vvOCozxwk3k5jsmPLdHzXrdAcDYhhJ820FRanbHL5cNeOuw8+c4TszB+REJIdcbiwQAHy1dZcXkY5oSp+KWh0JAPTJQ+PC4mEvhp8sG/Hql5Ey7fjVFmNJWHtCAVrrKiqkntNiXWXxmopxP4c0WMgyrJ8b6W4XZflc0jx7oI+AA/WuJMSZJgh7VheUOmj40/7wOHx1nl7kmiDnYMiC21OzEcGN1MHhlfz7W3mQHbGUP/n8cDAOTnYHBXvjR6PLLZKeLjj/8msHOsDbxyipRwsWJYfEVbidSGl9dy5ZcNuDtwwUex/vXEuGX7iVvFBGPRjMMvj6jw6endR4bHDWlXPyvuxJtqnjWLhE6SACQIIigxTAMRm7PK7GU6NkkCeZ1jvLzWZUu0+hA85VZrEXn5v4x6BAfmL4+3l5oTj2uwVyXshwZn8Lp4fEeGVcOmsHWu2YsvmTArlKGetSXc/FiYymeDsLeO1OOazDPrQypbw0hlvWMJmU1AVTc/8u0tnK8VUow2ldohsGAzSpW8EUuoHBkcHylJgCuuG7ExP35HjexbzaXYnqKvEzZBnobjSYrsljZg0u6RWFoPUmFzysQSACweFlGB2ad0mJZhrHU8lR/6hAvwLS2cjwWoPc+dwzDYOc9C6ad0FRqsnzraD7GJEkwvJ7Ea61IPj6lxVdndKxjtaVcbBkQWzTUJ9wZ7TTG7VJ7rPmihRys6RNd4fYbVodrkJCBwU57BA+1NhqTj2qKBiYBZdvcrChfXMu0Vhpt12Qj11x8JL5nYmGriLJWbBCF8i00JuxTY9tdz3Vs70QhFnWNgjIA1T0EUVGlBgBfe+218v+hFIX58+dX+KQIgiAAYNV1I8bvyy/x6xwKODQ4Do0VwVUm82W6Fp+cdi7kmyh4ODQ4LmBlAd5eaBZYaLRenYUCl0y+CU0i8PljCgCAylw41GPJ5dKHevStIcL4JhHoXl3otx5V5eWgGYzdrcbGO2bW8VeaRuCz9ooAnVXVtvmOCU/tVLOO9U4UYkVv//T9K8l1jR2d/2aXAvetIcTyXhUrBV50UY/33LIKAWB6Wzn+U84b0/8eLsBPl50NyzslCLCxX2y5zymQSACQzWxn8MNFPb45oyt2Ci2XKuwp5z4Mw9eaRvEwrW0k+tSo/LRdX3DQDFbeMOGTU9pHvke5ihFxMLK+GGMaRKCZ0vtrDoZh8O5RDX5yGyrQRMHDxn4xYR9g0FhpjN6R55G9Wl3Cwbq+MWjoh3XeR8c0mH+h9M1Nb/DFtezjk1p8dVb3yMd0ThBgea9orwzeqQpOq6wYu1uNf/Xs6wQF4INkGd5pJQvatStBlKTUAGCLFi083rxNJhNUqsKG0gqFAgzDQKMpXKDGxMRAIpHgzJkzPjplgiCqgjyzA+3W5rD6bHSIF0BlppHhUpYzoJYIf/SMDsQpFstBM2i1Opt1U/F5+0hMaCoN2Dn5YqHpXrLEo4Cfuyux8Y4J626aWLvo7qKFHIxtKMHzjSP82guqMgw2Gv03q3Amj9238MvHIjG+SeD+b6uiO3o7uv6dwwpAJ0q42DcoNiA9Nt39cEGPD9x6li7oEoWnGpQ9245hGHyersNn6eybOQrAdx0VGNeo/GXFl/Jt6LAuh3XsyJDg20B5FBIALMQwDP6+ZcaUExqPG9OH+tYQYlZqJBoq+LA4GOSZaajMjgcfC389PKYy08izPDzuYPXULI9aUi4+SJZjRD1xSGRHm+0Mfrqkx9dndazryUM8CuhTs3CKb5+aIp/3UKMZBq/uz2f12QWANjF8/P14+LadUJkdGLYtz+P9tZ6Mi7/6xqC2n8qgi9vcfLlJBL54zPsbfd6+lt3V25GyNhtml8vBC40icCDLgqtupeztYgVY2Ts66KotggnDMPjlihHvHy3wWM9GCzlY3C0KPRJFgTk5gqikcpcAZ2RkYMiQIRg1ahQmTpyI6OjCG++8vDx8//33WLlyJdatW4cGDRr45IQJgqga3IdNCLnAgUFxuJhvx7jd7MyfbQNi0C4uOEqMtvxrwugdzvMTcylcGpUQ0IWWL26aLQ4GKWuzS7z5LE5qLB8vNZFicICGelRWptGBnhtycN/oXA1yKGBFr2j0rkEWgv5gdTDov9k5ERwozHLa2C8maMoMHXRhKfCRHGcmS6SAwpEh8WUq5aMZBpOParDILROIzwF+7BqFIXUrXrbbb1MuK8NmfJMIfOmDm1tfIQHA0vv8NYrk4dP2kehZiZtTO80g31JCoNDsDBTmmWmoLDTixVyMSZLg+UYRIXltL7DQ+OasDj9e0sPsAJoqeHg6SYJR9SWIFft3U8FGMxi7S43N/7IzzrskCLCqdwxEPupJFyh39XYM3ZbnEaRqFsXD2j4xiPdz+XNxm5tHh8SjfqR3g5Devpa9sk+N5S5r5jgxB6eGxcNkZzB4q8qj5L1VNB9/9YkO+8zSijDYaLx1uAArr3sODkqN5eOX7koyCI4IaeUOAA4ZMgSJiYkllvi+9tpryMzMxNq1a71yggRBVD077xVOX3U1pY0c77SSgWEY9PonFydVzgBAh3gBNvWLCYpSo1E78rDVZeE+JkmC7wPcp9BXN80rrxvx8iNKtIHCYS3D60nwUuOICvfvCSZn86zot0nFGkoj5VHYMiAWzX1QFkawfXhMg+8vsPv+zUiR480Wgen7V5JrGhs6/53DysboW1OE5T2Vj7xO2WgGrx/wzACS8Cj8lqasVFAHANbcMOLFvc7XrJxP4eKohJApB6vKAcDS+vxFCSl8kCzH840iKjyMoqoz2GgUWBlUl3ACup4w2xmM2K7C/ix2kLd/LRGW9lCGzf/vdY0dg7aqPMqwA5mhZnEwaLc2G7ddNjefrC3C0jTvVpp481qWrrKix4Zc1nVhjkumeL6FxtBtKpxWsTMsmyp4WPd4DOL8HOQOZhkaG8btUuNigWeP0AlNIjArNTLkhmcRhLtyX1mPHTuGNm3alPj1Nm3a4NixY5U6KYIgqi6DjcZbblNXm0bxMKlFYZklRVGYnhLJ+vrhbGuxzXn97V+9HdvvsnftX6hAqV6oGF5PjJYlBL3qyrj4OFWOS6OqYX7nqLAI/gFAy2gBlnRXwvX+S29nMHpHHrKNZc+GJMpv422TR/Cvbw0h3mgefCXYDSL5+KiNnHVs679mrLzhmVHwkMnO4Nldao/gX6SAwrq+0ZUO/gHAwNpixIqcSz+tjcGaR5wTEXhme+H0ybZrsvFHMcE/HlXYj/T0sASMbyINm+BQIETwOUiM4AZ8M1HEo7CsVzTaxLDfXzfdMeO1A/mgmWAa9VIx59Q29Nuc6xH861FdiL/6Bq48VcilMLUt+9q9/rYZR7MDv8YsDsMwmHJcw7ouNFXw8EySM1M8SljYR/GxOPY67GKBHf03qXCvjH0ww93ft0xI25DrEfyL4FFY0i0Knz+mIME/IiyU++oqlUpx4MCBEr++f/9+SCTBP1Vu8eLFaNmyJeLj49GtWzccOnQo0KdEEASAT0/rcMdl55VDAfM6RbF673SpJkSvRHa534yTGjjowC6Kl141wvUUWir5Hgv4cMKhKHzdQYGHFSQUCrOcVveOxslh8Xi9ucxrExKDSd+aInzajh2Evmtw4KmdeTDaH9H8kCiV7UHp4R29HRfUNhzNtmDHXTNWXTdi4gF2tmmNCC4WdIkK2gbcrzaVol0s+4brvSMFyComUKy10hi+XYUtbmV/8WIONvWL9VqLAwGXwtiG7DXa4ssGMGEQUAg3DMNg3U0TUv/KxqxTWlbW8UN9awhxaHAcPmuvIP28woyMz8Hq3tForGCXGq64bsJ7RzUh/Zo9mm3BE5tzkWNiv18OrC3C8l7RiAhwRvKQumIku63dphzXBuW/+da7Zo9M0ZmpkR49OCMFHKzuE42u1djvJde0dvTflItbuopPxQ4HX6ZrMW63Gjq3gUmNInnYNTAWQ+sFf2yDIMqq3AXso0ePxty5cyGTyfDKK68U9fq7du0aFixYgPXr1+ONN97w+ol609q1a/H+++/j66+/xmOPPYbFixdjxIgROHLkCGrWrBno0yOIKutUrhULLrIzfCY0iUDbWM/ssWkpkdh5L6do1/Nivh0rb5jK1cYij2IAACAASURBVGjfm2w0g9+usnt2Pd8oIuCZBL6WGifAkSHxOK2yok2MwG/NugNtQpMIXNfYWVNVT6lseGVfPn7toQzaoJSvFFho6Gw0dDYGOisNvZ2BzsoUHdO7fSx6nK3wMQ8/msuYiMCjgCXdo4K6fxGXQ+H7Lgp0/jsHlgd/rwIrg7cOFWCZSylwSQ3wa0u5WNc3BnXl3n1NjWsUgW/O6ouunefUNpzItSE1LjyydMNBaX3+Git4+KRd5fr8EcFPKSocgvH4xlxWSepPlwxQCDj40C3LOBTsvmfGmF1qGN0C2k83kGBuJ0VQZLByKAqzUiPxxGZV0bFjuVasv23GoDriAJ4Zm51mMNWlXyFQmEHZM7H4DSMpn4MVvaIxbnceq2rmtt6BAZtU+PvxaDSIDN9N65L8ddOIT057Tk8eXk+M7zoqQqZFBkGUVbl7ANpsNrz55pv4888/QVFU0QKWYRgwDINRo0Zh/vz54PGC9yawZ8+eaNasGebOnVt0rE2bNhg0aBCmTZsWwDMjiKrLRjPovj6H1ai4ppSLw4PjSnzzfXmvmlVSV1PKxYmh8QFpQr7+lgljXYaTSHkULo1OCIqpfVW5b5Yv2enC0t8d99ilQW+1kGKaW5l6uLqjt+PpnWqcV9tKf7AXzUqV443mwdX3ryTzzukw5QT7Ju2nrlEYUV+Cu3o7hmzLY002BwpLuNb0jSnT0JCKcO9VOqq+GIu6Kn3yvbwp3K9lmUYHZp3U4s9rpM8f4XRTa8fjm3KR7ZYx90m7SLzWLPhaIJRk/S0TXtqr9piq+krTCHzaLjLoNs5G78hjZWXXk3FxZEi8V8pAvXEtW3LZgLcPO1vmUAD2DYpDi1L6EVsdDF7cq8aG2+yM8zhxYalw06iqEwS8oLah98ZcVkCazwE+bReJlxqH/yY+UTWV+86Uz+fjhx9+wMGDBzFlyhSMGzcOY8eOxZQpU3DgwAEsXLgwqIN/VqsV6enpSEtLYx1PS0vD0aNHA3RWBEHMO6/3mFL2bYdH77x90EYO1y//q3fg58uGEh/vS79eYX/fkfUlQRH8I3yHx6GwpLsSTd1KtL49p/fIBg1HDMNg4v58vwf/+tcS4fUQuumd2EyK1Fj2DdW7RwtwIMuCxzepPIJ/qbF8bOwf67PgHwC81Jjdm3TdLRPUZU2/JLzO9KDPX8qabCwrJvjHo4BXSZ+/KquunIe/+sZAIWD/v394TBMy7zV/ZBjw3B7P4N/7rWWYHYTBP6BwwJRrrO+GzoFfrgTHv7fWSmP2afbG0pgkSanBP6CwFcQv3ZUYUY+dzZhjovHEZhXSVcVnHoebAguNZ3bleQT//uobg/FNpCT4R4StcmcAhrrMzEw0adIEGzduRKdOnYqOf/7551i1ahVOnDjh8ZyMjAx/niJBVDm3TRSePiWClXG+2faLtWNmo9IXIV9d52NFpnPBE8ljsC7FBKkf9yHumigMOcleSP3e2oRG0ip1ea2yMs0Unjsjgtrm/PnlUgzmN7MgRRG+PQH35XHxziXv9KZ7iAKDCC4g4TKI4AERXOfnEi6QFEFjRDU7BCEWW79lpDDmNPsaV5z2Cge+aGKBD2N/AACaAYacEOG+xfkPOamOFc/WqNp9oPyNYYAdKi7m3eIj01L8D3XnKAferGtFHQl5P6nqzus4mHhOCBPtvI5wwGB2YyvSYoI3gP/nPR6+uenZYuDtulY8lRjc15zZ1/hYmxXYNWZxfrjFxy93necl4jBY09aMOGHZrxMOBph9TYC/s9l/GSmXwZxmFrSUh+/6xcEAb18U4lA++812cgMLhiYE72uJIMqitOzi4E3V8zH3qD7DMCVG+sO53IQgAo1mGPxniwpWxhnsixZyML9XDUSXob/XxzUc2Lg6G/oHO3gaO4WNpniPCZy+9McJDQBn78KUWD6eSE702/cvTbiXzQVaEoBVCVYM2Jxb1MPOwVB4/6oYO56IRVIY9tSx0wzGnMsB4Lx5kwsoVJdwIeVTkPE5rI/yh58LKEj5HMj4hR/lfApSvvOYhEeF5a57EoCPODpMdSsFdjWojgg/dlX6rYXBy2Ydpp90ns+GPDGmd48Pykych8LpWkb6/BHllQRAmWDGiO15RZl0NCh8dFWIFbWikRZkPysMw+CzdB2+ucnur1Y43E2BMUkRJTwzeMxOdGDrmuyiITwaO4UNxjhMbVu5Nh+VuZbd1dvx5+Fs1rFJLeXo1LxGuf+sX5IYvHdUg58uOTMb9Q4Kky6KsbxXNLpU8+4mX7D4+KQWh/LZP5fjGkrwXqfgWbsThK+UGgBs2bIlOBwOjh8/Dj6fj5YtW5a6OKcoCunp6V47SW+Kjo4Gl8tFTk4O67hKpUJsbGyAzoogqq7fM4w46DbBbHb7yDIF/wAgVszF682l+Czd+Ub+wwU9xjeOQLyv02gAWBwMfs8wso491yj4F7WEd7WNFWBRVyXGufSB1FgZjNyehx1PxJb55zlULL1qxFWX0lUKwKZ+sWhehvKjquq1ZlKsv23CiVzPkumxDSX4toPCY3KjLz3TUIJPT2uLAgk3dQ7svm8hAScfI33+iMroVl2EJd0L32scD36AbDTwzC41/uoTjfbxwRGwoRkGHxzTYOFFdsmsgAMs7qbEk0E0TONR4iVcTGohxezT7DXmC40iUCNAaYAfn9KyBmbFizmY1LxibTE4FIUv2kdCzKUw97xzI9tgZzBiuwp/9IwOu/eE9bdM+OosO/iXEsvHF48pAnRGBOFfpRbRdOrUCR07dgSHwyn6vLRfHTt29PmJV5RAIEDr1q2xe/du1vHdu3ejffv2ATorgqiasowOfHRcwzrWM1Ho0ZekNK81lyJG5LycGe0MvjzjOdHLF/65bYLK7CyTkAsoDK0bGgtbwrsG1RFjWlt25ulNnQPP7FLD4gif8j2drfjeQyT492hcDoXvO0dB6BYLfrO5FHM6+jf4BwAxIi4Gu92EB6qHalWgsdKYdVKDNqtJnz+icp6oLcb8zlGsY0Y7g5E78vzek7U4dprB6wcKPIJ/Eh6FFb2iQyb499DrzaSIFzvXmGYHip0a6w/pKitWXDexjn3YRl6pSbUURWFGihzvt2YP1jI7gKd25GHjbVMJzww9lwtsmLg/n3UsTszB0h7RARkgSBCBUOrWxYIFCx75eSh67bXXMGHCBLRt2xbt27fHkiVLkJWVheeffz7Qp0YQVcq7RwqgtTpvgyQ8Ct90UJS7BFDG5+DdVjK8e9QZTPz1igETm0lRT+7bHVr3htBP1ZdAwguxBmWE1/ynhRTXtXZWVujhbCveOJiPRV2iwqK8dc45PXJdgt5ibmHGElG6Rgo+FnaJwmsHCsClgMnJckwM4ECTFxtHsCapb/nXjH/1dtQMdIOrMGJ1MFhyxYAv03XIsxTfU6tvTRE+TpWHZbsAwjeeaiCBxkrjfZd1j8bKYOg2FTb3i0X9yMC8hi0OBi/uUeOfO+wJs5ECCqt6R6NdXHBkKJZHBJ+DD5LlePOQc+Lu8mtGTGwmLdPQDW9hGAZTjmtYmwdNFTyMaSCp9J9NURTeT5ZDzKMwzaVVhZUGxu1W48euURhar/LfJ5A0VhpjduYVtQwCCjde/tdDieoR4VWlQRCPUiXvUocOHYrZs2fjyy+/RJcuXXDkyBGsXLkStWrVCvSpEUSVseG2CetvsxeIH7WRo7asYovW5xpFoI7M+QZuZwrLJHzpaoENB9zKl59vTMp/qzKKKgxid0lgNzxfed3kt6xUX7pvcOB7lzIhAHi9uZQsnsthSF0J7j5TDRmjqwU0+AcA7eIEaBblvObSDPC/q8ZHPIMoK5phsOaGEe3+ysb7RzXFBv+aKHhY2ycaK3pFk+AfUW6vNJVicjI7ayvHRGPQVhXuGfw/yEBvozF6R55H8C9OzMHGfrEhGfx7aEySBI0VzmslA2CqWwWLr229a8Z+tzXnzNRIr2aPv9lChi/as/sb2hngpX35WJYRuhniNMPg5X35uK5lvy4+ax+JDkFSNk8Q/lLuAODBgwexcOFC1rFVq1YhJSUFDRo0wHvvvQeaDv6pQS+99BLOnTuHnJwc7N27lzURmCAI39JYafz3cAHrWJsYPiY0qXjwTMCl8KFbFtLamyakq0qfJFxR7tl/HeIFaKwgN3FVnYBL4be0aCS5ZWB8elqH1TdCO7jyyWktTC7lzLEiDia1CGwQKxRxKAoiXuCzQSmKwouN2f9/S68aYA2jkvVA2JdpQc9/cvHi3nzc0nkGYuLEHHzTQYH9g+KCbnADEVrebSXDq03Za6e7BgeGbFVBZfZfELDAQmPIVhV237ewjteUcrE5DPrD8jgUZqSwA2O771uw8565hGd4l51mMPU4e1M7rboQvWp4//rxclMp5nZSwPUdimaAiQcKsCRE20R8nq7D1n/Z/1djkiR4kWzaE1VQuQOAn3/+OY4ePVr0+dWrVzFx4kRwOBwkJyfjp59+8ggQEgRBuJpxQossk3OjgEcBcztFVXoXc1g9sUc5huuUS28y2Rn8eY0dzHmBDP8gHlAIOVjRKxpKIftt9rUD+TiabSnhWcHtvNqGZW4Dbz5IlkNWid5DROCNqC+GjO+89uaYaGy8Ez49n/zpgtqGEdtUeHKLCqdVnr3YIngUJifLcGpYPF5oTIZ8EJVHURQ+aReJp93KQK9q7Bi2LQ/ZRgdoxrcB/WyjAwM25+K424CjhpE8bOkfuHJkb+tTQ+iR3T/luAYO2vcbJv+7avAYvDUztXKTiB9lbMMI/Ng1Cu5t8d4+XIDvL+iLf1KQ2nTHhM/T2RUYyTF8fP1Y+VsOEUQ4KPcV+fLly5g0aVLR5ytXroRYLMaOHTsgl8vx6quv4vfff8fEiRO9eqIEEa7uGRxIrELlc4eyLFjiljn3nxYyr+wOcygK01PkGLYtr+jYnvsW7LlvRvfq3t0lXXfLhAKX/oVKISfkGlsTvlVPzsPvaUoM3qoqmrRqcQBP71Rj58BY1KlguXugTHXrPdQokodnG4Z2TyCisIfqqPoSLHbJ7Pj5sgFD6pL/27K6q7fjk9M6LC9hsi+PKmxT8W5rGeLEVef9nvAPDkVhbicFdDYaG1xaq5zJs6HRiiwAgIxPQc7nQCYo/CgXUJALOIXHBRzI+RRkDz4WHucg0u0xxQ1JuKO3Y/AWFW64Zbq2iuZjTZ9oxIjC5+edoijMSo1E9w25Rccu5tvx53Ujnkny3Qaw1kqzphAD/hm8NaK+BAIuhZf2qmFzKe778JgGJjuD/2slK/nJQSJDY8Mr+9hDP2JEHPzWQxkUWfgEEQjlvvvQarVQKJxjsnfu3IkePXpALi8svevQoQM2bNjgvTMkiDB2pcCGx/7KQVqiEK80laJnohCcMN6NMtsZVhNlAGgg53l1EZFWvXCH1rVPyvQTWuwa6N1/21/dgphjkiRkghjhoWOCEPM6R2GCywI0z0Jj5PY8bBsQC4UwNLLndt4zY5dbadeMVDnJYAoTLzSOYAUAD2RZcbnARloalKLAQuPbszosvKSHpYRqy0F1RJjaJjJssqCI4MTjUFjcTYlRO/Kw575nlrnOxkBncwCV6EIh5BZuGDiDhBSuauzINrFbP3WIF2B5r2hECkLj/a08WscIMLKemDU86ZNTWgytK/bZALg553RQuQzekvAofNjGP4O3BtURQ8yNxrO781jXuI9PaWGy0/iojTxos+i0VhpjdqqhtTm3ZbgU8GsPJWqQQVdEFVbuK1V8fDyuXLkCAMjMzMTZs2eRlpZW9HWtVgsuN3x2ewjCl366ZAADYOc9C0Zsz0Pq2mwsuqiH1hr8fTQr4quzOmS4lDAAwJxOCq/uwlGUZ5+W9Dwb1t30XknbebUNR3PYvQWfa0jKf4nijaovwbut2UHuqxo7xu1Ww+aH0qHKctCFkwdddU4QoK8Peg8RgdE0io8O8ezStlDt9eQPZjuDeed1aL06C3POFx/86xAvwPYBsfhfj2gS/CP8Qsil8HuaEqmxvgncWxyAykzjhs6B9Dwb9mdZPYJ/fWoIsaZPeAb/HvqorRxCl1vdTCONBRd8c728q7d7lNy+0VyKahL/3Wv3qSnCyl7RkLit1b8+q8cHxzRgfFxiXhE0w+DV/fmssmkA+KRdJDonkKEfRNVW7qvzwIED8dNPP+Hdd9/Fs88+C6FQiH79+hV9/fz586hTp443z5EgwlKBhfboIXdd68B7RzVotjIL7x0pwA2tvYRnh54Lahu+O8suYXiuoQSdfPBG3CZWgEF12MGJj09pvRZscc/+61ZNSG7wiEea3FqG4fXYJeJ7My0ew3CC0Z/XjbiYz74WfZwaGbS7/kTFuDdDX37NCIMtPDejKopmGKy4bkTqX9mYclzLagPxUGMFD3/2VGJTvxikxgmK+VMIwnekfA5W9Y7ByPpiVJdwIPVjmePQumL8nhbts0y4YFFLysOEJuzhSd+d0yHX5P2hK7NOaeE6yyVezMEbzf0/eKtbdRHW9Ilm9YsFgAUXDXj7cIFf+iCWxzdn9djoNo16ZH1xpYYNEkS4KPcd6+TJk5GTk4OVK1dCJpNh/vz5iIuLA1CY/bdhwwaMHz/e6ydKEOEmx+RAsyg+juV6TqnV2RgsumTAj5cM6FNDiAlNpehRXRiyN9wOmsGbh/Jhd1kfJIg5mJ7iuwbGU9rI8c9tMx4Os7yhc2DpVYPHxMvy0ttorLjuNvyDTBEjSkFRFOZ3isIdnYP1mv/1qhEpcQKf9g+qDIONxien2IN0RtYTo3UMCWyEm4G1xYgVaZD7oNRMa2Ow+oYJ48hwIwDA7ntmTD2hxTm153APAKgm4WByshxPN5CQ0ngioBRCDn7sqiz63EEz0NkYaG00tFYGWitd+LnLR62Nhs7KQPPgMTq3j1orzVrDuXuxcQS+aB9Z6WFuoeLtljIsvWoo2gTQ2Rh8ka7Dlx0UpTyz7NJVVqy4zq5e+bCNHNIADd7qEC/E331jMHSbirX58csVI86rbZjXOSoo2kZs+9fssW5pqeTju45k6AdBAABVUFDgtZA9TdPQ6XSQSCTg8wN/ASCIUHAq14qFl/T466YJj0q2aBTJw8tNIzCqviRgb/4VtfCiHu8fZZcQ/pamxMDavh2a8Z+D+fj1qjNYFyfm4NSw+Er9+y29asCkg86srTgxBxdGJoAfxIvejIwMJCUlBfo0CAAqswM9N+Titt65pS/iAtufiPOYYB0MvkzX4hOX5uNCLnB8aDxqkf45YWnmSQ2+OessN2uh5GPfk7FBc9MUiGvZmTwrpp/QYncxfdWAwuEK/2khw6vNIsI+84mouhiGgdkBVrDwYUCxppSL5Cq4KfT9BT0+POZc2/Io4MiQODSILP29vLRrGcMwGLhFhQMu/aybKnjYPygu4EHWc2obhmxVsfoSAgCfA7zTUoa3W8ogCFBP7BtaO7pvyIHWbUjf7oGxqB1ig9cIwlcqtVJxOBxQq9Ww2wtLgzgcDiIjI0nwjyDKoU2sAD92VeL8iAS831qGOHHxL8srGjveOaxB05VZ+PCYBrd0oVEefEdvx6yT7J24gbVFPg/+AcB7yXKIXRYhOSYaC9x6qZSXe1+sZ5MkQR38I4JLjIiLP9166ZgdwLhdedAEWe/PHJMDc86xXy+vNJGS4F8YG9cwAq5Xs3NqG07kFp/xFu5u6+x4ea8a3dbnFhv843OACU0icHp4PN5pJSPBPyKsURQFMY9CvISLpEg+2sQK0L26CE/WEVfJ4B8AvNQ4ArWlzl58dqZw6Jw3bL1rZgX/AGBWu+DIsGyh5GNjvxgkuN2v2Gjgs3Qduq3PwfEcz+omX9PbaIzZmccK/nEo4JfuUST4RxAuKrRaOXXqFAYPHozq1aujQYMGOHjwIAAgLy8PI0eOxN69e716kgRRFcRLuHg/WY5zIxKwqGsUkmOKD6RrrQy+v6BH8upsPL0zD3vvW4KyAS9QuIP5zqECGFzqRuQCCl885r0SiUepJuHi1Wbs8rW55/XIM1esT8tplRXpec6bYQrAWDL8gyinplF8fONWJnRD58DrB/KD6rX82Wkd9Hb2LvpbLb03sZsIPrVlPPSpye6f+vPlym2ahBq12YEPj2mQujabNenT1bC6YhwfGo/PH1MgRkQG3xFEVSTkUpjWlj2N9587ZhzOLj5buKxsNIOpx9mBxLTqQvRMDJ7BW40UfOx+Mg79anqe06UCO/pszMX7Rwug91MfWYZh8PqBAlwqYCdHzEiRo1v14Pl3I4hgUO5w+LFjx/Dkk08iPj4eo0ePxtKlS4u+Fh0dDb1ej99++w3dunXz6okSRFUh5FIYVV+CkfXEOJ5rxaKLBvx9y+TRe4UBsOmOGZvumNFEwcOEplKMrC8OqiyE1TdM2H6PvRCamRLp1+llk5rLsOQyu0/L12d1+LRd+YOQv7gN/+iVKCS7ikSFjG4gwdEcC3654ixR33DbjO8v6PF688AH2a4U2PC/q+yf93dby6AQBs/1hfCNFxtFYOu/zubpf90y4dN2DiiDMNDFMAysNGB2MLC4/DI78OCj63Hn48wOBtairzuPG+wM/rljYmWQuOqSIMDM1Mgqm/FEEATbkLpifH9Bj5Mq5+bw1OMabBtQ8dYJS68aWNNrKQAzU33XM7uiqkm4WNZTiXW3THj3iLN/LFB4j7LwogEb75gxp6MCaT4OXs49r8e6W+wNm2F1xXi9mf8HphBEsCt3D8CBAwdCrVZj586dMBgMaNCgAdatW1cU8Js9ezZWrFiB9PR0n5wwQVRF9w0OLLliwK9XDB49N1wpBBTGNYzAi00iAl6ml2d2oN3aHORZnOfbMV6Af/rFgOPnflLzzuswxWU3VcABTgwrXx8zjZVG0xVZrGzGZT2V6F/L96XMlUV6AAYns51B3025OOOSVcqlgH/6xaBDvPenY5fH6B152OISBKon4+LIkPiA9fUh/MdBM0hek407Ln0qZ6XI8UaLwAWm194w4qfLBtwqMMPB4bkE8Pzz/ZtG8TAjJRK9EkN3GBdBEL5xKMuC/ptVrGO/dldicN2S14clrcu0Vhpt1mSz1vrPJEkwv3OU907YB9RmBz48rsWf14zFfn10fTE+bRfpk42kXffMGL49D66DiJtF8bBtQCwiQqxnOkH4Q7lfFadOncIzzzwDkUhU7CIoMTER2dnZXjk5giAKVY/g4qM2cpwfkYDvOytKHBZQYGUw57werVdn49ldeTiYFbjy4A+PaVjBPyEXmNNJ4ffgHwCMbyxFjQjnosNKA5+eKl+fllXXjazgX3UJB31qkLICouJEPAr/66FEpMD5mnAwwAt71Mg1+SmyUYz9mRZW8A8ApqVEkuBfFcHlUHjBbfLvkisG0AF4L6EZBh8d0+CFvfk4nG1FpoWDHFPh4AF/BP8SJVz80FmB/U/GoXeN4te9BEFUbR0ThOhfi70enHFSA6uj/NfMOed0rOCfhEfhwzbyRzwjOChFXCzoEoW1faJRS+oZ5Ft+3YT2f+Vg7Q2jV+9LbunseGGPmhX8Uwgo/NEzmgT/CKIE5X5lcDgccDglPy07OxticfBnxBBEKBLxKIxJisC+J2OxuX8MBtcRo7h7cpopLCccsFmFLutz8b8rBtw3+C+gsOueGcuvs1Px320lR1IZJqP5gohH4f1kdvbKiusmXFCXrbk9wzBY4lb+O7ZhBHhB0IyZCG11ZDws7MLe2c800nhxbz4cdGACLlOOsyd2t48T4MnaJNhdlTzTUAKBy1Lvps6BPSVMwfUVk53B83vUmF/JwU0VIRdQmJEix4lh8Xg6KSIoGu8TBBG8preVs9bjN3UOj3Vjae7q7fje7Xr3RnOpX9vmVFZaogiHBsfh1absgVIAkGum8cLefDy1U417XrgnMTwY+lHgNvRjSXcl6pD2PARRonK/Olq3bo0tW7ZgwoQJHl+zWq1YtWoV2rVr55WTIwiieBRFoUO8EB3ihfhXb8eSywb8etWAfItnwOC82oY3DxUAAJIieehaTYiu1YTokiDwSSq+wUbjPw++30NNo3iY1CKwfTieqi/B9+f1RQ2CGQAzT2qwondMqc89nmvFxXxnPxYuRYZ/EN7Tr5YYb7WQ4luXibv7Mi2Yna7DR37e+V99w8QadAMAs1LlJPOpiokRcTGojhirXIZgLL5s8Hkfp4fyzA48vVONo2WYJMnnACIuBSGXgohLQfDwcx5VdFzIpSB0e1zhcbA+F3EpRAk56FpNSPpdEgRRZg0VfIxrGMEK+n2RrsPo+pIyX0tmndKyMpvjxRy80Tz0ethJ+RzMbq/AsHoSTDqQj4tugzm2/GvGwaxszEiJxHONJBWqDGIYBm8eKsCFfPafPbWN3G/vUwQRqsrdA3D37t0YPnw4nnrqKYwYMQKDBw/GwoULER0dja+++gonT57Epk2bkJqa6qtzJgiiGCY7g1U3jFh4Uc8KVj1KCyW/KCDYMUEAmRfS5T88pmHtYHIoYPuAWLSNDXzT9E13THh6p5p9rF8MOiY8ut/aK/vUrIzG/rVEWNYz2ifn6AukB2Dws9MMBm9V4UAWO+Cxsle0x1RWXzHbGaSszcZdl535wXXE+LWH0i/fnwguR7IteHyTs68VhwLODo9HDR/3l72ptWP4dhWua9kZIvFiDmY2MKJb0zqsAF4g2koQBEG4yzE50GZ1NvQu7WL+00KK6SmeAzzc12XpKiu6b8hlPWZuJ0XIbzZbHQy+PafDV2d0KG4gcMd4AeZ2UqBBOSuE5p/X4SO3ScmD6ojwa3cl2bAkiFKUOwAIAKtXr8Z///tfaDQaMAwDiqLAMAwiIyMxZ84cDBo0yBfnShBEGTAMgwNZViy6qMemf80oaxUhlwLaxggKswOrCdE+TgARr3xvoqdyrei1MZf1PSc2i6jQxF1fYBgG/TapcMQlq6RdrABbB8SUuGDIt9BosiKTtSu7unc0eoVQf179rQAAIABJREFU/z8SAAwN2UYHuq7PQbbJuUpWCCjsGxTnl6E+c87pMO2Ec0HN5wDHhsSjrpyU0lRFDMOg0985rA2l/7aS+bQf1fEcK0bvyGP1jwWAxgoeVvaOhiXzJrmWEQQRtL5I1+LT07qiz4Vc4MTQeNR0ew93XZcxDIOBW9gbgE0VPOwfFBc27QcuF9gw6UABjuV6ZnULucB7reV4o7kU/DL8fffet2DINhXrXqOJgoftT8RCSvr+EUSpKhQABACj0Yjdu3fj+vXroGkadevWRc+ePSGVSuFwOMDlhk6/AoIIV7d1diy7ZsSe+xaczLXCXo5Xu5ALtI8TPsgQFCA5RvDIN2YbzaD7+hxWOn5NKReHB8cF1Rvy4WwL+m1iT2v7PU2JJ2oX37v0hwt6fHDM2ROtlpSL9OHxIZV1QgKAoeNglgVPblHBtXd4mxg+NvePhdCHQzjyzA4kr8mG1qWXzitNI/BZ++AI3hOBseSyAW8fdrZ0iBdzcH5kQplu0sprw20Txu9Vewz36JIgwG9p0VAIOeRaRhBEUDPYaLRdk40sl428UfXFWNSVnUnvei3bfMeEp9yqU9b0iUbPMCtlddAMFl82YOZJLWuo3kMtlHzM66RA65iSK4bu6O3osT6XtUkUKaCwe2Ac6pHNSoIokwoHAItjsViwdOlSzJs3D2fPnvXWH0sQhBfobDSOZFuxL9OCvfctOKe2oTwvfhmfQsd4Abo8KBluruSzgmDfntVhxkl2On6wZsqN3pHHmnLaKJKHg4PjPIZ6MAyDdn/lIEPjDGpObSvH2y3ZA0WCHblpDi3umXgA8FLjCHzVwXfBuPeOFGDRJWfvIrmAQvqweJ/0CSVCh85Go8nyLFZJ26/dlRhc17vD3hY82Ghxf08aWV+M+Z2iiiZQk2sZQRDBbulVAyYddG6cUAD2PBmLVtHOwNbDa5mNZtBxHXudmVZdiLV9S+9PHaru6O14+1ABdtzzHCzFpYDXmknxfrIMEh47ecBkZ/D4plyccelTTAFY4cdWKQQRDsocKrdYLNiyZQtu3ryJqKgoPP7444iPjwdQmA24aNEiLFiwALm5uahXr57PTpggiIqR8TnoXUOE3g8CcmqzAweyrNifacHeTAuuah7dN1BnY7D1rgVb7xa+YSuFHHROEKBbdSHqyXj4LJ0dsBhZXxyUwT+gMIi39V9z0c3mFY0df14z4lm3XisHs62sRRmPAp5JkvjxTImqaFJzKY7mWLHpjjNIvfiyAe3jBBhR3/s/f9c1dvx8mT2t8P9aykjwj4CMz8GoBhLWz8fiy3qvBQAdNIOPjmuw4KLntMz/ayXDh8ky0s+JIIiQMqaBBAsv6IuGXzAAph7XYl3faI/r2dKrBtY6k0MBs1I9ewaGk1pSHlb1jsbKGyZMPqqB2iWbz8EAc8/rseG2CXM6RaFrtcIe3QzD4K1D+azgHwB8kCwjwT+CKKcyZQBmZmZiwIABuHXrFhim8OERERFYvnw5OBwOxo8fj/v376Ndu3Z4/fXX8cQTT5AFG0GEmEyjA/szLYUZgpkW/Kt3lP6kEkQLOTg2NA7RQRxAeHV/Pv68Ziz6vLqEg5PDEiB26Xv44h411tx0Dv8I1YEIJGsm9BRYaHRbn4PbLq/DCB6FnQNj0VhRvmbZpRm7Kw/rbzuDjTWlXBwfEl/uHqBEeLqgtqHT3zmsY0eHxKFRJX8OTXYGL+9TY4PLzx5QmAHybcfim9+TaxlBEKFg+10zRmzPYx1b1Tu6aBM+IyMD8bXro82abKjMzgDYs0kSzOsc5ddzDaRckwOTj2mw2mXivKuxDSWYmRKJFdeNeO+ohvW1AbVE+C1NGVIteQgiGJSpMdesWbNw584dTJo0CStWrMAXX3wBsViMN998E6NHj0bNmjWxefNmbN26FQMHDiTBP4IIQdUkXIysL8H8zlE4Ozwe6cPjMbeTAsPriREnLl8Pv9ntI4M6+AcU7hoKXU7xvpHGT5ec04tzTQ6sv81ekDzfKLSnsRGhQyHkYGmakvUzarAzGLdLDX1xo/Qq6Gi2hRX8A4CpbeQk+EcUaabko0M8uyfTksueGXvloTI78OSWXI/gn5RHYWXv6JCffEkQRNXWK1GIbg+y1x6adlwDh8vkiu/O6VjBPwmPwgc+HLIUjGLFXCzupsSKXtFIlHjeNyy9akT7v7JZvbgBoGEkDwu6RJHgH0FUQJnu6vfs2YMxY8Zg+vTp6NOnD8aPH4+vvvoKN27cQIcOHbBp0yY89thjvj5XgiD8hKIo1JHxMLZhBBZ3U+LKqAQcHhyHz9tHYkAtESIFJb/h9koUYkQ97/aH8oWaUh5eaixlHfvmrA4FD0oRll0zwjXO0kDOQ9dqJTcmJghvaxUtwJePsfv+XdHY8ebBgqJs/MpgGAZTjrNL95Nj+BgWAq9fwr9ecNv8+POaEYYKBqKva+zo/U8ujueyS7mqSTjY1D8m7BrfEwRR9VAUhRkp7GDexYLCwXwAkGWm8MMFPevrbzSXoloxQbCqoG9NEQ4PicNLjT03f7JNNGswmoxP4Y+eSsgFwTNgkCBCSZleOTk5OUhJSWEdS01NBQA888wz4HDIC5AgwhlFUWgSxceEplL80TMaN56qht0DYzEjRY6eiUJIHmQLNYviYW6nqJDJAn6npRRyvvNcC6wM5pzTgWYY/HKFneEyrpEkZP5eRPh4NkmCpxqw+/6tuWny6NlXEetvm3Es18o6Nis1kuyoEx6erCNGjMi51tPaGFZ7hLI6mm1B7425uKljt5hoquBh+4BYtIwmmywEQYSH1jECjKzP3lD79LQWBhuNBbf5rInnCWIOJjWXoiqTCzj4qoMCm/vHICmy5DEFi7pGISnSu61QCKIqKVPkzuFwQCRi78g+/Fwur1qpygRBAFwOheQYAd5sIcOaPjG49XQ1XBmV8P/t3XtUlNUe//HPwCh3HEXAe4ooommmpVZ61LRQymsalre0zOh0jnXynsegMLSDt8xf2TKzjnbCLPOS5KnURFPxaBcr7Wde0VQEBUEUgZnfH/4YHfGC6MzIzPu1Fmsxz+x5nr1Ze3155vvsi9b3DFEtv4rz9LKat6dGNbfd0fed3/L0nz/ydeCSL6hentKT4Wz+AcczGAyafl8VNa1qezM8IS1H2y9L3t2I88UWxf3PdkpN97real/D6yqfgDvz8jRo8GUbIM3fdeaGRqIuP3BWPddk2iz4Lkkda3op5ZFg1fEv8750AFAhTGoVaLOUx9F8s/62KVurT9jGu4mtAuVXiQE1knRfqJdSe4ZodIsAXb4aybiWAYquxywF4GaU+W7rwIED2r59u/X16dMXpg3t2bNH/v6ln1i0bt36FlQPQEVQ2dOg0Ao6beG5pn56b1eejp+98KX0XLE0alO2TZle9X1u+zUN4bp8jR76qHM1dV55QrmFFxIuhWZp6LqT2tAzuFy79b6/+4zNKCxPg0pNVwIu9VSEn2btzLPunv7zyUJtzyzUPcHXHrVnsVj0f347o0lpObo8XfhEuK9m329SZU9GnQJwPfX8jXou0l+zf7k43ffzy0ZPNzUZNZCHzDa8jQZNah2oXg18NHlbjnaeLNQT4b4a1zLg+h8GcE1l2gW4atUrT+mzWCyljpccO3ny5K2rJQDY0YLdZ/SPzdlXfT8lurruC624I6PYOdM1LD9wVkPX2f5vfai2l5IfCrqhabvZBWbd/dkxnSq4+O//6SZ+mn6f6RqfAqSYrzO15nCB9fUT4b56p8PVd6wsNls0IS1H7+0qPWV9XMsAjW8ZcENLKxDLAFQ02QVmtfrseKnRzyU+eziItU8BOEyZRgDOnTvX3vUAAKcZ3NhXc3/N1d7TxaXeizQZ1S6EdangfL3q+yi2qZ/e+e1iMuXrIwWa8XOeRt9V9qfiM37OtUn++RsNPFVHmQxv4m+TAPx8f76m3Bt4xVGo+UVmPfPdKa0+ZLvTr9EgzXrApEGN2OkXgOszeXlozF0BmnDZTraS1KW2F8k/AA5VpgTgk08+ae96XNOpU6f0xhtvaP369UpPT1dQUJCioqI0adIkVatWzVquefPmSk9Pt/nsiy++qLi4OOvr9PR0jR49WqmpqfL29la/fv2UkJCgypX5gg+4q0oeBv2zVRU9tb70yOWnIvzY/AO3jdfuraIdmYXamnFx/b83fjite4MrqWOt63+JOJhbpHd/s9158MUWAQrxYYo7rq9rbS/V8/fUobwLD0sKiqXFf+Trb3faJpBPnC3WgG+ytD3TdqffgEqGC9PZ+cILwI083cRP83bl2awv7WGQXrunihNrBcAdVYjVRo8ePaqjR48qPj5e33//vebNm6fvv/9eTz/9dKmyY8eO1e+//279GT16tPW94uJixcTEKC8vT6tXr9b777+vFStW6JVXXnFkcwDchnrV99bd1W13FfPxNCimIeuy4PZRycOgBZ2qKcjr4r9vs0V6+rtT+vNM6RGsl0vYcVrnL5m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"text/plain": [
"<Figure size 1296x576 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rcParams['figure.figsize'] = 18, 8\n",
"# note that the freq defaults to freq of dataframe's\n",
"decomposition = sm.tsa.seasonal_decompose(monthly_sales_df, model='additive')\n",
"fig = decomposition.plot()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could see the yearly seasonality more obviously in the seasonal component and the trend is heading downwards just like what we have observed."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4.2 Describing Patterns - Stationary\n",
"We could describe the time series as a stationary or non-stationary process as well. This is an important concept in time series and is rooted in several time series models' assumptions so let's take a quick look at it.\n",
"\n",
"The definition can get a bit hairy and there are 2 forms of stationary: weak-form and strict stationary. \n",
"\n",
"#### 4.2.1 \"Weak-form\" or \"Covariance\" stationary:\n",
"<img src='ts_pics/cov_stat.png' width=500>\n",
"1) Constant mean\n",
"2) Constant variance \n",
"3) Same covariance between periods of the same length.\n",
"\n",
"#### 4.2.2 \"Strict\" stationary:\n",
"<img src='ts_pics/cov_stat2.png' width=500>\n",
"Strict stationary is more restrictive as it requires the same distribution between 2 periods of the same length. In practice, we often refer to the weak-form stationary as the strict variant is rarely observed.\n",
"\n",
"#### 4.2.3 Other observable traits of stationary:\n",
"1) The observations in a stationary time series are not dependent on time.\n",
"\n",
"2) They don't have trend or seasonal effect\n",
"\n",
"#### 4.2.4 Visual Example of stationary\n",
"The concept of stationary can be a little slippery, sometimes it's helpful to look at the plot visually. To nail it down, a stationary time series could look like this plot:\n",
"<img src='ts_pics/stat_eg.png' width=500>\n",
"Notice that the magnitude and mean values don't change over time. The values don't increase over time(trend), the values are not corelated with time, and there's no seasonality patterns like our store sales.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 4.2.5 Why do we care about stationary?\n",
"1) Stability; A stationary time series has stable statistical properties over time.\n",
"\n",
"2) Statistical modeling methods such as ARIMA(we will come to that later) assume or require the time series to be stationary to be effective.\n",
"\n",
"3) We are interested in modelling the relative difference between timesteps rather than the absolute values. For example: We want the model to learn the % of increase or loss following a pattern rather than learning the value at $1,200 at a certain time."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 4.2.6 How do we make our time series stationary?\n",
"1. A log transformation or square root transformation are two popular options, particularly in the case of changing variance over time.\n",
"\n",
"2. The most popular option when we have time series data exhihiting trend is differencing. We could difference(intergration) by subtracting $Y_{t-1}$ from $Y_t$ of our time series to make it stationary. Recall our time series plot from above:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x216 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"monthly_sales_df.plot(figsize=(10, 3))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could use Panda's diff() to quickly perform differencing."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"diff_monthly_sales_df = monthly_sales_df.diff()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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2BMaIFyeIa1VFxsAC7uLh8kXVByzalpGCJKWY/cUvfoEvv/wS9fX12L59O26++Wb09vZi+fLl4DgOd9xxBx5//HGsXbsWBw4cwJ133om0tDRcc801AIAxY8Zg0aJF+PGPf4xt27Zh69at+PGPf4yLL744KdsZXzbRBdm+Di+zOVHBthAWXLuS5GjQ6vRjVV2v7Gt3TkhHZYa80GGOBqlJDeUxO3BjzzfzMp12p1uE2x/75/g0sfswzKrr97YNwOy5GPGC9JgNdGYBYHGZvJj9vMGFXh9LA2OkFknRzDY0NGDFihVob29Hfn4+pk+fjo8++gjl5eUAgHvuuQdOpxM/+9nPYLPZcO6552LNmjXIyMjof4znnnsO9913H5YuXQoAuPTSS/GHP/wh4c/F4xexVaEgc/hEHLX7MDo7eZrPVCBUZ3ZPuxeCKIIPo4PWmn/WOOCWXPuHp+uwpNxMORjU21nxkWp4BRG19uCdWR3PodDMo0mS/NXU68eIjNgulWT6V4mVR3WmHjyH/ojbkz1+dHsFZBgGxYYZ4yyC9Jgtl5zPE3L0KEvT9cu9XH5gQ6OH6tgyGIOZpBSz//znP0N+n+M43H///bj//vuD/kxOTg7+/ve/a31oEaOklw2wp8PLitkQePwi1X016dBfSNq9Iuq7/RiZmbjT1O0X8Y9D8pCE28elQc9zsq05gNlzpSJ1dh+8kqZTsYVHtklePBZZdbJittmpfTE7LE0Hs55DVaYetRKbsBqbD9MLmDXSUEMURRzv8aPHK2Jirvb3jPoQnVmO43DxcLPsurfupIsVs4y40OsT8FmDGxNzDShP1+7ezloAMaIkMQjAdLOh2dvhlXVAS606Spe6qy2xUoPX63rRIilk0vUcbhrdN2HOZAapDzlkRW71A/EJTlCSGQDy4TOAxdoOVZ476MDU1c2Y+1YLfrWtS9PHFkQRJ3qCa2YB4GJCarDupIuFAjA0x+kTcd6bLbjxkw5Mf70Z20PszEYKK2Zj5MsmZesmILnT+KkAKc+YUWjElDx5cbErga+hKIp46oC8K/vt0VZkGfs+JuQN4HiPj+miUwyyWCSLSYAOTtAi0paWGQSKWfn5zhwNhh4Or4Bffz1gwP/k/h50kZGIMdDsFGRNgywjR+1GnF9igkU3IOc63evH/k52LjK05c16Z7+zhkcA/m+HdsETrJiNAY9fxJbmEJ3ZDg9b3YaAXJVNLzBgahKL2Q1NHuyTWKpxAL4/Pr3/35lGHnmSm4BX6LvoM1IHqjOrIAMqIjqzzRp0ZhvIzuwZH89xRDHNHA2GHh+cdKFXEoPuE+khxVgg9bIjFLZ2LXoO84bJd8XWMYsuhsbsIO75XzS6NUtZZMVsDJB62WILj3T9wOq20y0G9VBlAFuJE3tmoRFT8+R6wd3tiVsQPEXYcS0pN1Pd2MpMQmpgZ+9vKhHKYzZAPOy5SI/ZfpkBIXMgbcMYZz+vH3NSX9OyQ095zGYoByJcMpyWGjAYWrKTmJERRGCNwvkfDayYjQFSL3t+iYkS7zOpgTJNvX6clAwlGHlgSp4RlZk6ZBoGFgRdHpGylYkHR7t81MX7jgnp1M9VKkgNGKmBVxBxpEtFZ5aUGWjQOVAaAAOAUZl6SNa/ON3r13SLmTG4sbkFfKzg61qjYTFLXqOUOrMAbdG1rdWDNhdbrJ/tNDj8eHxPNy55txWXv996Ji1Oezx+EXsVwqReI2wwo4UVszFA6mXnFpswmdgmZ0lgypB62cl5Bph0HHiOwyRSapCA8IRnDvRA2v+dkmfAeUX0VDk51X6M2XOlDEftPkh2c1FipZ0MAHoArNEZW3Hp9InodA/8YR0HFJj7/q5Rx2FUFiE1YENgQ4Z3TzihtHbRVmYgL0grgnRmh6XpMFnSjBEBfHQq+EwII3Vx+USsqevFNR+2YeJrTfj113ZsbvFgQ5MH3/+iMy67oQdt8oHvADvbvDjSFfv5zorZKFHSyyoVs6wzqwypl50hsSMipQbxDk+wuQW8dIQOSeAU/G2Zo0HqQm7hK3VlAe07s2RXttiig06SzMCGwIYuwbZYtTwHqM5sCJu5xUxqcNYiiiK2tXjw442dGL2yEd/9vBMfn3aDnGE+aPPhZBzkkaGaUq/VxS41YMVslJB62RIrj5GZ8pUtAOxNUorVYIcMS5BGeyZ6COyFww7ZAEaxhcfVFRbFnyVlBizSNnU4qEIvC9ADYG0uAb4YXCsoW640+WWXsudiQ2BDgjaXH581KHc+Tzn6AjS0gOzMSj1mSUjd7KenXfAyx5aUpsHhx5/3dGPmGy246N1W/KumF3ZP6Pd0e4hkzmjZGcJm87WjvTF3g1kxGyWkXnZusQkcx2FstgFGyava0CugVaN897MFj1+kTmypUfzUfLK7Hb8hMJ8g4u8H5XZct45Lh1GnnDpWmUkXs8yxIjUgh7/GKXjMAoCB55BvHvgQi4DMezhSgtlyBTsO1pkdGrxV70SopOTDGpwHHr9ILaZCGdVPyzfIzn27V8SmEI49jMGJ0yfi9bpeLDsjI3jwa7ssnIVEOqcChE7mjJYdITqzdd3+kN9XAytmo0RJLwv0aeDImxPTzcrZ3+mFdK6gxMqjLG3gBl+VqadcIU7EaQhsbb1T5jhh0XG4ZYw16M8XWXiYJbWI3SPCFmaVy4iePe0ePLm/Bwc00JGSMoMxWcFv6pTUIIYFaTBbrgBkZ5ZpZocGrxNbq+TyWQubtlMOv2wWoMTKw6wPHg/Ocxw1CMakBqnFU/t7MGZlI773eSc+UZARBMg387hzQho2XFmIJ8/PkX1PyzADoE+jS17Dv0HMpKw6GtsgGCtmoyCYXjYAafzPksDkUGEJBUaZPlVxCCxOr+FTB+R2XDeMsiDXHHwbjufoWFs2BBYfdrd7sODtVvzv1i4seqc1ppu7xy/iKPE+jQkRNU2ngMVQzAax5QowMlMv281pcgrodDNHg7OZ0w4/1fFcWimXNmnhaKDGY5aEjLFlxWzqsKvNg//Z2hVURmDggW+Wm/HywlwcvL4Yv5uZjUm5BipCe3e7F+5Q2wYRsr/TKxu+HZ6uk3m4A8Ab9c6Y5FysmI2CYHrZAKRudjAVs4NhS5zcwphRSLsGkLrZeNiFbG1xY3ur/L0hP2BKUMUs083Ghaf39/RfAHt9Ip7Y1xP6F0JAOhkMC+JkEKCI8Jpt1lBmQHZmDTztaMBibc9u3qx3yjqm0/INlF5VC0cD0tawPIiTgZT5w0wwSD4aR+w+TabNGfHnnePKC48peQY8MisLh64vxn8W5uGycgsMkiHUEqtOtjvqEbStW0hZ4bR8Ay4uM8vkDS1OAV80Ru+ewYrZKAimlw1AOxokX3NU3+3DBW+1oOqVJjy9P/qiQAu2KXRmSabm0ytFrXlqv1wru6jUFLJbF2AwOhr0+gT8dW83HtjWReWwpyI+QcQ6wn/zrXonen3RFZV0WELo97nYKr80kgVpJJAyA1IzCwDjzgJHA1EUNe3mnM28TnhrLq20YAyVBhf7OVAfRWc208hjTjGRBsYsulKC9Q3ya+Z1Iy348spCfH5FIW4fn468ELuO5H1YS93sTuL+fU6eEWY9h8uJQetYpAasmI2CYHrZABNyDJAselDX7Yc9yUboP9pow54OLzrcAu7f2qVoXpwIWpx+WbfAwNNWXAAt1djV5tW0q3yix4e1x+WatTsVQhKUIB0NyBtGMnjoazt+ud2Ov+3rweJ3WtGe4mbnm1s8Mm9WAOj2injvRHRbngfJGNuc0Dd1qjMbQzFLdWYVitlUdzTY1OxG9atNqHq5EU/s60724Qxqjtl9smEXDsDSSiuqswwy3eyJHj8cMToaqPWYJbmY6WZTDptboIrGh2ZkUUFOwZhO7JBqqZvdSTzWOWeGvK8bKS9m3znuirphwYrZCAmnlwWANAOPamLqfV8Sh8Dqu32UBczzB5PTnaXCEnINigMJ1Zl6pEm+3u4WNI0Gfu6gQyaMH5etx3wimzwYg01mIIoiVh0dKMybnAL+Z2tXEo8odt47oew7+OqR6Fbu5FBV+M4sGWkb3QXWJ4jU7yp1ZulY29QpZv2CiFs/70SbS0CPT8QvttmpaGjGAKS37DeKjBiWpoNFz8mKTREIOYGuhkg8ZqWQkoeNTW6WTDfI+aJRPuw1PkdP2QyGYkaB/BqkVWfW4RVwiDiPp5xpYM0tNqFYMmzb4xOjXjixYjZCwullAwym8IRXFAqAVUedsCVhyISUGJDC8wA6nsOk3PgMgfV4Bfz7sFxicEeQkAQlKon3u96e3C7o8R4/2on3cuVRp2JMZiogisE7sJ82uKMaxiK3bMltfZJijdwMWpyC7AaTa1KeJh+fwjKDLxrd1ELzf7Z2UVvpjD5ePyZ/XZZJulOkzCnW8yASj1kplZl6jJbouH0isP40kxoAfR3Ln26y4en9PZp5AWsB2bC6UGVzJsCUPKNsEPVkjz+mwdcAezu8smtgVaauf15Bx3NYOpKUGkQXoMCK2QgJp5cNMFhibQVRxMsKxazTL1KpV4kgVFgCCSk10GpB8FKt3DQ6z8Tj2pHB7bhIytP1su3Ahl4/XL7kaQV3BFlB/3iTDT2D6GKrloM2H+qD6JAFMfIsb7eCk8HoIIEJAciORrQyg3DDXwEqMnQyy7dWl4C2FJGKKF1fAOD7GzrxeUNqLqjixcFOLw5ILOJ0HHDFiIGbOSk3iWUIrNsryBa5Bl5Z4hIMyqIrRRfHWnLM7sOVH7Th+UMO3L+1C1Nea8Zf9nbHLAfRAlIvO3+YOchPKmPScVTdooXUYCfhH3sOMQ9zHXHv/fi0Kyo3F1bMRkg4vWyAybnkAFNyhsC+bPLgZBCP1ucP9kBIoLuBVxCpE1vJySAAVcyGSBBRiyCKeIaw4/ru2DRYQngvkph0HErT5NuB5HZeIvk6iNn0yR4/frvDnuCjiZ33ia6sgbhKvXIksrSYI10+mTl9qVWHLGPoS18xoZnt67BG/lmh0r+syn9Xx3OozpKf7wc7B3931u4Rgk5QewXg2592DIoB2MHC64TEYF6JCQWSc03LzizZlS1Lk8coh4O06ProlAv+IZ4G9tiebjgkjYsOt4Bfbbdj6upmPLW/B84kNTXqu32yQWQjD5xXFPzeGgxyp1SbYlb+GKRT0ZQ8A6oluwBeAXgzSMxzKFgxGwFKetk5xconDFmI1dh8SenevVTrCPq9Y91+fJLAraP9HV6ZRKPIwmN4kE4VQDsa7GqPfQhsY7OH+tCvGJsW8eOQgxTBOomJYEeIIv+ZAw7NDbDjDamXvXdyhmyg8kCnL6IBRrK7FW74CwDMeg5ZxoE/6hOBdlfk3YJw6V9SxlHT7INfN/tmvVP2mSaThLq9Iq79qH1QDEkmG1EUsaYuuMQAoM+BWDqzpMcsqfUPx+wiIzIln4E2lxBzSlMqc9rhx6tBpu1bXX1zCtNeb8JzB3sS7urxOSExmFloRBrZBVBBPBwNKCcD4r7OcRyuJT4Hke6+AayYjQhSL1ts4VGVqXyByDbxKJfok/xi4ieU7R4Ba+vlXZNqws/yuQQOglH+skRYAsnoLD0skljZVpeAht7YtnPWEKk7l4+wRCSSD0A6GiRrCMwniJT8ooCIYr37y054UsQyqbHXT3Wabx6ThoWE/ivYTUUJyslAhf0aQHdno7HnCpf+JTuuFIy1JfX4t41Px0MzMmVfa3EKWLqubcjHeu9u96KOWEgvKZffxMnrc32PP+puH+kxq1YvG8DAc1hUylwNAjyxrxvh1ASNvQJ+trkL577ejH/XOOBNUCd7PaWXjUxiEIDszO5s88YUZGD3CLIhRg60BBMAriGkBhubPTgZ4W4nK2YjgNLLlijrZQOQ4QmJHgIjuyZlaTo8OTdb9jMfnXKjLkEJVuTwVyi9LADoFYbAYtmy9Aoi3qyXF7PXECtCtVRmDo4UsEM2H3olN7sCM49nL5BHEx6w+fCXvalhl/QBITE4N9+AEqsOy0fJL3avHVWfFkN7zKrrUFG62SgcDSLpzFL2XIPc0eCY3UelWC2vsuKuiRn4IWFzV9ftx3Uft6ekhlsrSInBojIzFdyRZpA3QQSxL7QgGqj0rwg7swAtNfhgiOpm211+/PuwfF6V6rEAACAASURBVOH24PRM3Ds5Xea6E+CUw497NtowY00zXq51xFQQhsMviPi8kdTLRjb8FaA8XYdCyfBrr0/E/hiuQ2TNMyZbjwyFjvHITD2mE24KZNxzOFgxGwFfqdTLBkh2rO3LtfIP3w2jrJhZaMK0/IHjEgH841BwKYKWbG1V52QghfKbjeE1/LzBjQ6JsDzLyGFhaXQrWDI4IVnbqKTEYFqBEQtKzbihSl6kP7q7G4dTYNualBhcdqZzdWm5RbaF3eoS8KlKiQzlZJCjtjMrvzxGM9lLRtmWhujMjieO66BNW29lrXmF6I7PLjSi6kxn8TczMikPyZ1tXty8viNldgm0RBBFaldoWaXyQlqrIbD6GDuzQF+QjFTis6/Di1NnQShLpDxzwCFrGpRYeXx/fDoeODcLu68twl0T02W7iAHqu/2480sbZr/RgtV1vXHRHO/p8Mo8ubONHKVLVQvHcZrqZneF0ctKIYewV0UoNWDFrEo8fhFbWkgng9DF2GQiDGBPR+K0i0e7fNhMHO+NZ7pbt46Td03+U+uI2qhYLa1Ov0xXqudo7YwSU/K1GwJbTXw4rhhhgVHhAqQGWmaQnC3Ur4kLzblnXq/fzcxCvkRu4BGAezbaEjrwFyndXgGfE3GGl5X3LTYseg5XETd/Jcs5ErdfpHYeyKSlYJBes9F0ZtWkfwUoT9fBKunydLpFtMQQoxtPBFGkPH+l3XOe4/DE3ByqQ/TJaTd++FXnoD4P48GWFg9OSxY2Vj1HebkGoIbAohwEPBGjZhYA8sw6zCSKmw+HWBqY3SPg74Qc7wcT0mE6c+/IN+vw0Iws7LymCLePS4PSbOkRuw8rPu/E3LdaNB+IJCUGF5SYIhr0I6F0sy3RHy+psQ51z7+60gIdMRuxP4LZCFbMqmRnm0e2Mgullw1AakP2dcSmP4mEl4/Iu63fKDJi5JnjvbrCgjzJ9laXR8TqCFv6kULqZSflGVQ5CJDpYNF2Zl0+Ee8SW9jRSgwA+sZwvMeXlBs0ebE498yFKNeswyOzsmTf29Tswb9qEtOFj4ZPT7sh9WWvzNDJulQ3VMlX7u+dDO+VXEs4GZSl6RS3uZSI1Z5LFEU0EhrvUNZIPMfJvD2BwTsEtrHZgxOSzp9ZB2qxYdRxeGFBLtWNWXXUiQe3J95lo8PlR0uSdLtkV/bS4eagAzp0rG3k54AoirRmVmX6FwkpNYi3RZdXELGj1TNoUgz/X40DXRIrxxwTh/8aQw8NF1t1eGR2NnZeU4zvjkmjXFiAPv3+zes7NO3Qkv6ykVpykdCd2eivQTuJwv2c/OCd2UKLjvLGJRtQoWDFrEoi1csCfQWvVH/i8see6KIGvyDi1SPyi+eNkq6JWc/hO6PlhcHfDzriuqVJru7I1V8wxmbrZf6bzU4hqu3eD0+50O0deH6FFj6sTCQU2SYe2ZJJX7cfVOESb3p9Ag4QeqZpkpXv0koLLi6TP8dfb7dTdlGDhXcVJAbSz9jsIqNsq9TtB96qD70Ii1YvCyjIDCIshGweUaZZtxIOCUrQsbaDc0uXlDAtKbco2p1lGHisuiiPkuX8ZV9PwlLCRFHE3/Z2Y9yqJox+tQm/+borofINn4JWf2kQiQFAB3rURHHPaHMJsuZLup5Drim62z1ZzH7e4IrbYJNfEHH5+21Y8E4rxq9qwrMHepIqtXH5RDxBnKe3j0tHeogFcWmaDo+dl43tS4vw7WoryM2/+m4/VU9ES69PwObm2MISSKblG2TSkiN2HzqiWFh0ugXZbqyOAyblhr7vk1KD1+qcqptErJhViVp/WSkcxyVlCOzzRje1pUV2TW4Zm0ZpoUhZgpaQelm1xaye5zAhh9TNRn6cZITkVRWWmLZiAIUhsATrZve0e2Vdx8oMHXIkNyyO4/DHb2QjXdIB7/aKuHeTbdBpMb2CiA+JSemAxCAAz3G4nhgEC+dqQOpl1ToZAHRnNtJFFC0x4MMugEk972CMtXV4BawlirMbq4OHjhRadFizOF/msgEkJiVMEPvidR/Ybof7zNvx2J4ePHUgcTsUGxrdaJXYumUaOSwqC949IwM96uy+iK2eSKvA8gyd6oRDknHZetl75/LT/slasaHJ3X8fcvuB+7Z04ZbPOmFPUpTuS0ccMqlPmp7D7ePTQ/zGACMy9Hhibg62LS3CNwjP10jcWEKxqdkj280aka6j7kuRkmbgqXtuMC/zUJB62XE54Xdjl4wwy7THpxx+bG5Wd79nxawKotHLBqCTwOKvm32J6JpcWWGhtlbL0/W4lFhxP3cwPhd4X4RhCSSU32yEH6xur4APTmrjYiCF0s0m2NGAvMCcq7BAGJ6ux6+my62SPjjpojpFyWZTswc2YitvlsI5spyQGmxq9oR83cliUI3HbAC6MxvZDZVK/1JhAUd25QajPdfbx13oIYZhLiwJvbivzNTjtYvyZAsroC8l7LM4pYR5BRF3bOjEkwod4F9s7cL7JxLzGSBdDL5ZbunXWyqRYeBRlia3dSQT7MJBhrhEo5cNwHEcda2L18BrjcL5/ma9ExeubYnIW1oLfIKIv+yVnzu3jEmTNQzUMDJTj/+ekiH72tv1Tk3mVMiI4WhdDEi08Jul9LIqhtIyDDwuJZoYaiWQrJhVQTR62QBTyCGwOHdmbW4B75wILjGQcts4ue5nbb1Tkyxmkv2dXtnrV2jhI5qsjdXR4P0TLkh3SYan61R3hkNBBieQiTvxhoyxnRZEXP+9sWnUEMd/b+6KKjIwXpCFxcVlZugVOueVmXrMLlTf5aCcDGLozDb3+iPqaJNOBiUhnAwCkMX2gUHoaEAO3l030qpql2NqvhEvLsiVaQm9AvDtT7RPCev1Cfj2J+1YGSTnXQSw4vPOuBdIbr+It48TLgYqFtKkbjZSRwPyWhSNk4GURF3rgiUp1nX7cdE7LXjhcHzlcFJeP+aU6cKNPPCDieq6siQXlJhQIkn/6/GJeDdIcl4kUBG2UbrzkJA2Wduj2LUlk7/UDHwDoAIU3qjvVeWAwopZFUSjlw1Aygz2dMT35rTmmLN/Ow3ou4gFSym7oMQkGzjxiX1id60h9bLTw4QlkJADJJHe+MitzGWVlqi33KSQ3Y5Eywy+blN2MiDhOQ5/nZstKyJaXQJ+sa0rnoenGlEU8d4JUmIQ/IZ/Ayk1CBJv6/KJqOuOzskA6OsSSD0kPQJk3eNwkDKDUhWd2eFpOln30u6hh8iSyckeH74gHCeWh5AYkMwvNeOpuXIf5B6fiKvWtUUcUxwMm1vA0nXtWEdM3eeaeJm0yuETsfzj9rgs4AN8etolGx7KM/GYF6aLDSgNgcXWmY3GY1ZKucLAazwIlaTo8gN3f2XDHRs64YizX7Eginh8j9yb+8ZR1pBuJKHQ8RylB41VatDi9GN/pzyQ4HyVO8bhIHdOt7d5Ih5wJptOoYa/pCwsNSPHJHd1+eR0+MKfFbMqiEYvG6AiQyeLBLR76ClTLSFdDJaPsoIPUrhxHEdFuf6rxqG5DyS5RUF2CcMxNtsgsztp7BVUT5Z3ugUqsjfU8EUkJDMFrMPlp8T1pBWclLHZBtw7Wb7V9VJtb9y2eCPhQKdP9pkw6YAFpcE/Y1dVWGCS3FOO9/gV9d61dh+kcyrD03UhBzeUKLZG7zVLdWZV3Ag5jtNkmj1erDzqhPTqcE6+ISIdMgBcW2XF/xEpYZ3uPknAFR+04UhX9M+3sdePy95vpc6HEek6fPLNAsrh45TDjxs/aY86ZSsclFa/0qK440BCvqaRngNkUah1ZzZe8d2kfEGp8H/1qBML32mNKeo3HO+fcMmGL3kOuGdSRojfCM/1hERqfYM7poUUGWE7Nd+AXHNs73OAqky9bMDZ7hFxOIJBxBanH6cc8q426aMdDKOOw9UV9CBYOFgxG4ZY9LJA382JTrGKz4ewxualbDTI5CSSG0ZZZZ2gZqeAd45rqyWjnAwi0MsCfSf3hChfw7X1TkjvU6Oz9NT7ES3khHYii1lSjzRehbj+J5MzqOz3H220xd1jOBxkUMKFJaaQRWe2icelw+ULEtLzFKD1suRzV0ORhfSaVX/zaSQHwFTIDAA61nawOBqIoohXiMVyMAlTOH44MQN3KWzZbmjy4Lw3W/D7nfaIh56Odvlw8butOED4sk7I0WPdkgJUZupx67h03ErIq3a0eXHHBu29b3t9ArXjoHYhPSaLlBlE2JnVIP1L9vvpRGc2Dtc6URRxgiiSn5+Xg2cvyJH5LwN9neoFb7fiNY0GqcjjeIzoyi6rtMQ8WDUh14CJknuPIAKvxTAASfrLaqWXBfp280iLrkj8ZskZmQm5hpA6cRJypuX9E6wzGzOx6GUDUFIDjfVhAUi7nPOLjWEvYplGnip4n9MwEazN5Zflkeu40CkgwSB/R62jATl8sVQjiQEADEvTyTrGnW4xrO+pVqiVGEgx6jj8ZU42pM++vtuPh3cmN+r2PcrFIPwN/4ZRpK7KSXXXyAKANKNXAxmc0BTBlj+V/qVyi5K05xosjgbbWj04ah94TgY+eIqVGh6cnonfTM8E2UzyCMDvd3Vj7lst2NCozqB/d7sHl7zXKtM4An3+2u9eWiB7Hx+emYVFROf/zXonfqfx52DdSRccxKAcOdUeDPJcPdLlU22H5RNEWVcMiL0zS3rUxmN3sd0tyAYLrXoO+WYe11dZ8enlBdTnwuETcesXnfjxxk64NOysf9HooYZrfxRjVzYAmcwYTNMdDlEUqV21C2P0lyWJJQmM0suG2DVUYnaRUTYE6WSa2diJRS8bIBFDYD5BpDQ436qmjZ2VWEF0KjY1ezQbjCA/ABNzDUHNwkMRTXhCU6+fuhmqGb5QC89x1GIhUbG21PCXSunGzEIT1Zl6cn8PZaOSKBocftkqngOCJiNJWVhqltkF2T0i5VhxMAaP2QBFMUTaRjMABijH2g4GyMGvS4abY9rW5DkOd0/KwKarirBAoatU2+XD5R+04c4NnSEN9Dc0uvHN99tk9leB41uzOB/ZxPS5nufwjwtzqU79H3d3Y6WGnT4yW/7qSktQyRdJtomXDQz5RFBJdsE47fDLLPsKzHxU11wppVYdpM3RNpeAHo11q+RQWUX6gJ3Y2GwDPvlmAa6roq/f/6rpxUXvtmrmJkN2ZS8ZbqZ2BqPlmpFWyhJzXxT32sNdPjRIFtYWnbL7SyyQO6iROBrsJO7PU1XqZQPwHEcNgoX9nYh+ehDy/PPPY/LkySgqKsK8efOwceNGTR8/Fr1sANKea3ccJmg/Oe2WxW1mGDhcPkLdSm1MtoHSJj1/UBtDc3JrIlK9bADS0UDNguDNerm+b3KuAdVZ2lyUApBSg3hpyaSIokjbcqmcFAWAB87NlK16BRH44Ve2uBmhh+J9ogCdXmCgXASUMPActRVFFlukzjASJ4MAVGdWpczA6RNleek6Dig0q7vcknrJGpsv6Y4GTp9I7XKEkzCppTJTj9cX5+H5eTmUFy0AvHykFzPWtODlWnqS/e3jTiz7sE0WiBI4tv8syA0qvcky8nhlUZ4s8hkA7vqyE5uaY49r7fII+IgYWrmmMrLXi4q1VSk1oPSyUSZ/SdHxHIanx9fRgGwEkENnaQYez56fg7/OyZZp5gFgb4cX89a2UP7HkfJ1q4eK1P7J5OgcDJQotuooOUA0Cygy9eu8YmNE2/hqIO8pBzt96FaxgBFFkWqOBHPaCcW1VZF9XlK6mF2zZg1+/vOf495778UXX3yBmTNn4tprr8XJkyc1efxY9bIBRmfJU6xaokyxCgU5+HVVhSWi1TjZnV11NHxUqBq2xqiXDTAuxyCbxj/l8KMtTCoJ6WKghbcsSTIcDU46/GhzyY28I+k6Zhh4/Pm8bNnX9nV48UgS5AaRuBiQkK4Gn5x29w8GunwijhE3W9KMXg2UZlalzID0mC226FSHdAyz8sg0yIMuyG3jRPP+CSfskqn8fDOPi0IY/0cKx3G4ZqQV25YW4b9G0zexDreAO7+04fIP2lB7ZkDshcMO3Ly+A6Sf/l0T0/HU3Oywg1YVGXq8tCBXVhh5zliFxbrD8t4Jl8xVpiJDp3qaOwCtm1XXBKGcDNJj03r2P06cd6HIIpwcOgP6zpPvjE7DR0sKMJL4vt0r4jvrO/Dfm21Ryw7IruzcYiNmFmqnRQXoWO7Vdb0Rx9uSetlYU7+UyDbxsnNQBLBDRbRtY68ga6yZddHtio3PMWB8BL7gKV3MPvnkk7jxxhtx8803Y8yYMXj00UdRVFSEf/7zn5o8vhZ6WUA5xUpLqUGHy08JpL8VgV0O0JcVTmpU/lMbm3bWJ4jUoFK0/q4mHUdtv4YKT6jv9mEb8cG7WiMXAynJcDQgLyhT8gwRp5ldVGamtnH+tKebmpCNJ3aPQNk8kalfoZica8B4yUXSLwKrz3QPD3d5ZU4G5VE4GQAKbgYqO7O0xED93+Y4TmGaPblDYGTX+9qRFhhiTNBTItvE4/E5OfjgsnzFgb0vmzyY82YLbvq0HXd/ZQNZA/xmeiYempGlWgo2q8iEJ+bIrcLa3QKu/6g9psW8FnaASh16NZBDVEpFYTRUkJ1ZjXWzkQQ9TM4zYv0VhbhCYffx7wcdWPBOCxX1HY6DnV68S9xHSQcYLVgywiwbum7spa+DofAKIr5qIoe/tNXLBphOWnSpkBrsILqyk3ONqhw8lLhupPo6JmWLWY/Hg127dmHBggWyry9YsABbtmzR5G9ooZcNQEkNNBwCW13nlHUnqjJ1Eetn9DyH7xI2Xc8fcsQ04XvQ5pMNQOSb+ZgurPQQWPCL1RvElujsQiOGa9ShkEI+n0SkgJHDX9Fs4QDA72dlyVKuRAC3f9ERtuOtFZ+cdsFLnLejs9S/RxzHKXrOAkphCdG996TMQK0lHOlkoCb9SwoZnpDMIbCmXj8+IRY5WkkMgjG7yITPryjEr85VHhB7mzCc5zngibnZuDuKQZ1rq6y4b6r892q6fLjlsw74opDetLv8VOdsaYQSA4D2mlWrndbaYzbY42jtaBCpnViWkce/5+fi97OyQK5TD3T6sODtFjx/sEe1ROfxvfKu7NQ8Q1w6nlY9j8srCIlUBFKD7a0emaymwMxjQgQdzEiIJgmMbDJFqpeVEsmMS3xegQTQ3t4Ov9+PgoIC2dcLCgrQ0tIS9Pdqa2tV/40P60wABj5Q1VwXamvbIz5WACj26wAMfDA2nuhEbVpzVI9F8s99ZkjXJRfnOHHkyJGIH2euHjBwFnjFvoK9vtuPF7bWYU5udB2Kdxv1AAY+DOOtnqiOK0CJX/54Xx3vwJXWJsWfffmQ/DU5P70HtbW2qP92MPheDsDAB+5IpyvoORbJuReKL0/Iz8thvnbU1gY/50PxyyoeP9hngnjG46DJKeDmD07jsfFuxKHxJmNljRHSS9A3MlwRnx/TOQ48zBDOHP/eDi/e23UEG1v1AAYuokViD2prOyM+RocPAAYKkUaHT9X7uOeU/Fy1eLpRW9uh+u/me+W/v+VEBy4xK5/raojl3HvxlB6COHAs1VYBlo7jiODpRM03LcDUqRweOWrEZptycWPkRPxurAez0IBon+ayNGBnvhEftg2cj+sb3Lh93XHcV+VFJD2MNY16+CWvV6VVgKGtHpHeOgxeQHru1dq8OHi4FmEc+HCoVX590HU1obY2dsmYqUd+D9vfZEdtbauq31Vz/h3pkF+zuY7TqHWHL0QXGoCiSTz+95ARDe6B33f5gZ9u7sJbh9vxQLUHoWxOT7s4rD5qBiReL8sLenDkSHyCZc4383gFA93Utcd68YPCdqhZ875+3ADptW1aRmz31VAUOuX3ty1NThw+XBvy80DfnzpUnydKnJNpwk57+BcmZYvZAGSnVBTFkN3T6upqVY/r8YvYu7kRkIwQLZ1SFvUA0UXZHjx8ZOANrXObUF09IqrHkrKvw4tDjoFChgNw58zhKIuyC7msrQOvSuxC3rNn4b9m5Uf1WPWNHQAGHuvCylxUV0e/bbM424PfHx14DY8EeQ1rbF7USl4TngNunVmOQos2221SynwisKOh/9/NHh4jRo6CkRDj19bWqj73QuETRNQQ5+WSSeVRd1+qAdTxdvxRohX7qlOHj70l+MEE7QYfSLyCiE1b5c/jxsklqI5wwLIawPyGNlkwxkZPAVp4H4CB7t03RhaiOopuoiiKMG1r6Nc/OgUOxRVVyAgjWfC02wAMyHQmlOZFdO5fkObCY8cGqp/TgiXq60Us554oivhoXwuAgS7czROyY/ocR0o1gAsniVhzzIn7t3ahRaLHyzRweGVRPuZEMZhL8u+RIq74oFUmT3q9yYAZI/Lx/fH0Z8EviGh3C2hxCmh1+tF85v9vtPdC+nrdOCYLo0cPj+qYCvc09j9fr8jBUFSBUWHuQc1fNwIYeI3mjB0RcsteLd3ZHqBm4PrbLppQXV0e9vfUnH9eQUTzVw2yr10wcSSsenWbx9UAFk4U8NPNNqwi7K42dOhx0x4jnjk/J2jc6zObbPBLPq+js/S4dfYw1e4TkVIlivhtXTNOBzT+AocD+lJVOx57D7cCGOiQXjEmH9UqnYsiZaQgIm1vY/8Oa6eXg7GkMuj5JIoiDm9rgvT8u3TicFRHMXwb4Dt+B3ZuCt+IStliNi8vDzqdjurCtrW1Ud3aaCD1skUWHqNiME0en2OAjkO/ZcrxHj9sboGyjYkUcvBr/jBT1IUsANw6Ll1WzH50yo06uw8jo3juZIBDtHrZAONzDNBz6A9BONnjR4fLT9kDkVPXF5SY4lLIAoBFz2GYle+3SRFE4ESPL+wNJ1pqbD7ZeZlv5lEeo4fkz8/JwIYmt2zY8dfbuzCnyIipUUoYwrGxyUPFfEZrLXNDlVVWzL5W1wszsZiIZgAB6FssF1l0Mv/Spl4/MrJCf26jSf+SoqSXFEQxbjfXYOxu98pCG3QccF2EU8ZawHEclo20YmGpGb/dYcdbx52oytTjkVlZIZPvIsGi5/DSwjwseLtVNnD3P1u7UNvlQ49XQKtTQLPTj1aXgDaXQGl2lYhGYhBgTJYeLc6Bz+UhW+hrS69PkBX7Og4oVWkJFw4lr9lwzSO1kHZihRZedSEbINPI4+8X5GJRaS/u3WSTbcU3OwVc/WE77pqYjgemZcqaDc29fmo+5EeT0uP6WeM5DtdVWfDnvQOuQSuP9oYtZrs8AqVbjZdeFuhzsZiWb8AGieRya4snaDF7vMePDonWPF3PxVQ3AX2pee+cOIsTwIxGI6ZOnYr169fLvr5+/XrMmjUr5sen9LLF0etlAcCsp2Mq98Ro0eUVRGoVemOEg18k5xYYMU2icREB/COKEIUOlx9HJPpRnoPscaPBrOcwjhwCI3SzoigqDl/EE9rRIH6aU1Jcf26+IeabiZ7n8Ny8HGRJ4gu9AvDdzzpUWbFEA5n6dfFwc8RDbAHIgYpmp0ANp0SixSUpJhZCaoITSDcDtR6zAYosvCxOstcnUoEAieBlYvBrUZk5bgtDNWSbeDz6jWzUXF+M9y8r0KyQDVBo0WHlojzZ+SSIfdfAlUed+LTBjf2dPrQ41RWyU/MMqIrh3It0CIw8R0rTdJoN6uWaeGQY5Ock6e0bLaQzQkUMDZnrqqzYcGUhZhTQ95u/7evBRe+29jtiAMBT+3tkzhNlabqIbaGi4XqicP28wY2GMK4lXza6ZUX/mCw9hmm0WAlGJH6zpF52chTDySQ5Jh6vLw6/O5yyxSwA/OAHP8DLL7+MF154ATU1NbjvvvvQ1NSEW265JebH1sJfloRMAot1COzDky6ZRVOmkcOSCKyNgnHrOPmW2n9qHXBEWNSQTgITcqILSyAh/WbJWNvd7V4qpejyEYktZuMZnEAWs+do1DktT9fjr8RUd123H/eq2N6JFFEUFVK/ou8uWPU8rgyxYBmRrovp3CsiHA3URNo2OuSfF7XpXwE4jl64kb658cbjF7GaMP6PNr5Wa7RK8VNiQq4B/7wwN2bNOIc+T+dYIBsg4ey5SO/XWJO/pHAcR+0CaeU1SwUmxOjAUJGhx3uXFeBnUzKo93F3uxfz1rbihcMO2NwC/lkjb9bcPTE9Lk4dJGOzDbL7mYjw8bakv+y8OAyokUSSBEYlf8VpZ0+JlC5mly5diocffhiPPvoozj//fGzevBmrVq1CeXl4HU8ovIKCv2xJ7G8K2UXYG6M910tE1+SaSmtQk/BIuLrCgjyJ/KHLQ9/UwkGu3mZqlE4SLtaWlBgsKjXHLOUIBxmcEE97rq+JRcK5MUo3pFxZYcF3x9B+w6QtU6zs6/ThpKSDZNbFnitOejdKGRtq8kMFdGc29A3cL4iUhRfpiqAGOtY2sfZc6065ZFuG2UZOVTrb2cDi4WY8PDMr7M9lGzmMydJjbrERSyst+P74NPzy3Ez8bU42dl9bhIVBNJpqiTQ4gVxIa+VkEOzxtFq4hwtMiAYDz+F/p2Xi7UvyZbaTQF9X+e6vbLjw7RbKGeCm0fHRnypBXrdWHukN6b5AumTEet1UAykP3NvupaLDA5DJX7HuxkZCympmA6xYsQIrVqzQ9DG11ssGoFKsYpAZtDr9+JDobsUqMQhg1nO4eYwVj+0Z0PM8d8iB74y2qu6IkMlfseplA5AaTum2hiCKlCVXPIISSCqJc+OYPT7bwU6fiP2d8b1Y/HZmFjY3u3FActP86SYbZhQYNNMBkxKDC4eZY+7azyk2Yni6TlYkB4jWlisAmUgmNQRXosUlyLYCc018VItMMrHsQII7s+QiZtlIq+YpQ4OZ28enY2SmHl81uZFh4FFg4VFo4VFk0aHAzKPAoov760EuaA53eeEXxKBbt3RggrZb0GTHVCuvWfJxtPLGBYA5xSZ8eWUhfrTRhjeJhDDSDuyOCemaNITUcs1IC36xrav/enHA5sPeDq+ifOZkj08m3dNzfXah8abAokNFwMV6GAAAIABJREFUhq7/tfKJfbvKs4vkf1sQRaq5xDqzSUZrvWyASYTM4HCXD72+6DRHq+qc8BHamXM1LGxuGZNGZUjPfqMFv9tpx4FOb8jVo18Q8XWcOrMTzgzSBTje40fnme7RlhaPbHDDqk9MJ4kMToiXzGBPu0dWJFVk6JBHmnDGiEXfl1tvkbzIDp+I737WCbdfhUhQBXTqV+zvEc9xuD5Id5bUHUYKGZwQzmuW1L2VWKO7zJId5UR2ZttcCovlQSIxSCQXlZnx6+lZuHdKBr4zOg2XDLfgnHwjytL1CSnsCyw62S6Zy0/rYqXQ2/Uad2YJLatWXrNUR1ljT/BsE49/XZiDJ+ZmIy1IsZpp4PC9sYnrygJ97+/CUnlR+GoQz1lSYjCj0BjWVUUr1PjN1tl9spTATCNH7VrGE1bMKvBlo/Z6WaBv2lIawSeIwP6OyC8GoijiJWL68sZq9V1TNQxP1+NSohCs6fLhD7u6cd6bLZj1Rgv+b4cd+zrowvagzYcen3xSXauT2qI0SHdmNbiGkEJcOjz2jp8ayC5CfbdftVF3JHxNiOvJ7GytGJdjwO9nybdY93R48avtsXsunurxyXTOHKDZguOGKuUufLROBgEomUGYzizpZBBpYEIAsqMc6MolgtXEYnl0lj6hW4aMAcjrXSjtNNnhJB0IYiVe8wFqomxjheM4fLs6DZ9fUUDJ1QDg1nFpyDImviSi422dimEdZDEbj0CHYKjRze4k7k/n5Bnjqm0nYcUsgSiKlOZRC71sAHL7YE9H5ENgu9u9ONApdwoI1pWKhXsmpSPYqXi4y4c/7u7G3LdaMGNNC/7vazv2nilsyRN9eqG2J/VU4jXc1e6FTxCpLaSlcXYxCJBr4pEpmfJ1+sWwW9HRQIvr41dcfGe0FVcRKTXPHHDgg5ORaadJ3ie6fTMLjZpNx4/KMlATzByA0RrLDMJpZqn0ryinjZW6clpHiAaDlBgsH6XtYpmhHrWOBqIoUp1SrTucSvZcsWL3CDJttoGPfgGohlFZBny4pAD3TBy4v1Vm6OLqqx2KS8stsvtHi1OgtLGCKNLFbAIkBgHIzuz2FnpBtZOSGCR28cuKWQKO47BjWRG2LS3En7+Rje+Mtmqilw1Ax9pGroMjB78WlZqiGjAJx8xCE1YvzsPCUlPI1Jkjdh/+uKcb57/VgulrmvHMgR7Z92dqOKQEKAyBtXmxodEts4nJNHJYVJaYYRWO4xTsubTfEialG1oOf5FwHIfHz8vGcEJzd+cGW1j7mFDEQ2IghYy3HZGhi9ivkkQa+QuAGu4iidVjVgoZa3swAbG2+zu8VPc8Gd6yjD7UdmY73YJsmMmi41Bo0fYWT7oZnHL44Y1xt4AsiIen6WK2cwqHUcfhwRlZ2LGsCC/Mz8WnlxdSfuWJwqLncAXROFhJSA32dnjR7paHhcTz+k8yMdcAk+TlOd3rx2niPkB1ZhOolwVYMasIx3GozjLglrFp+OucHE07EtQQWITF7O52T3/+fIBvxSn9AwAWlprx+uJ81C4vwRNzs3FRmML2qN1PTdySWxSxQmY972r3YDUx+HX5CEtCh1UqMwlHA7u2xWynW0CdZCtOx9FWb1qTbeLxj3k5Mo1yh1vArV90RLXd3eURKMs7rYvZZZVWWfGpRXc+z8zLznm7Rww6zQsoyAxi8IEcH+E0uxaQXdn5w0yaGe8zIoeUydR0KZ8DShIDrbvpVj2PIsnnSxBBFTWRQnnMaqzzDUVlph5XVFiQE2fHm3CQi/B3j7tg9wwUr58TXdm5JSboE2AfFsCo46gdUekOrF8QqVqGdWbPcsgC5ECnV/XKdn+HF1eva5etvnNMiRlyyjHx+HZ1Gl5bnI8jy0vw5NxsLC4zIZwkleeAcxXMq2NhYq5BNpx2rNuPtYTE4JoESQwCkCbfWgcnkP6y4zTy7Q3HzEITfjFN7pX5VZMHf5LE36rlk1MuSO2Kq7P0UcdDByPbxGP14nzcOjYND07PxL2TY49d5Tm6wxXKa5bsXMeyZUp1ZuPsaOATRKyqoyUGjORB2nMdPpMGRxJPj1n542o7BEb+fiKL2cHCeUVGmX2Y0y9i7fGBe1oyLLlIyKaU1LHocJevP/IW6JuTGZ7gBTArZhNMgUUnm272COq6LYdtXly1rk2mLQKAn03JTLhdTraJx7eq07DqonzU3lCCp8/PwcXDzVDSzs8oMCJd46LLqucxhkjVIb0Cz0+gngig7bm0djSgJAYJXPXeMymdGjb4/a5ubCS6rOGgghLitAibmGvAo9/Ixj2TMjQr+CPRzZLpX7F0Zkm9ZLxlBh+fdsniUDMMHJaMGBresoMVMg3O4RNlri0B4uHVqgSpmyWHtyKFKsITOAE/WOhzYyGkBmd2SFw+EZuakzf8FYDSzUruSUrzHInW2LNiNglQQ2BhksCOdvlwxQdtVHTgDyek447xibUSIck28Vg+yoqVi/JQu7wEz5yfg0uHm5Fp6LPlUGM8Hg2kXEPKVRWWhG7BAHRwgtbF7A7SySCBeime4/DM+TnIN8u3F1d83oHf7bTj/9X0DYbtbveg1elX7Bp5BREfnpIXs5dqLDGIJ6SjQbABP1EU0UjE3cbSmSUdDWq7fIqTzlrx4mF5V/aqCkvMmmNGbHAcRy1qlGza4u0x2/+4RJFM/t1ISabMYDBBDnF/2eTByR4fNre44SLidrWc41HL9AJa3uc5Y9dIhiUkWi8LnAWhCanI5FwD1km6VLvbvfhWtfLP1nf3FbKkHdBt49Lw0IzMQTVhnGXkccMoK6X/iQdT84149ajyZP3SBAQlkNADYNrJDERRjFuMrVqKrTo8c34Orvmovf9rDb0C/rCLlhsYeKDozA5EiVWHEqsOggiZB2G+mdcsSCMRkF6zZPc1QJdHlAWuWHQcsozRf0ZzzToUWvj+bqlH6Bsu1FqeAQAtTr/sugQAN41mEoPBwJhsPTZLtnVrbF4sJnY26A5nnDqzGkfaUlrfOBXhg53R2QZMyzf0Ny764m2d6CJ2Yy8cpo3vfaSUpesxzMqj4cxi3eUH9nd6cU6+MaFOO8FgS+4kQDoa7A2SBHayx4fLP2jDaeLG+V+jrXhkVtagKmQTTbDObFmaDrM0CmiIhLI0nWxIqM0loNurjT3XKYdftvVr0XExp1pFw6IyM+6aGN6+xiv0HfO2Vi/WHnfh2YMOPHdI7ot8yXBz3CeWtaSI7MwGKWbp4S8+5s8pLTWIzxDYyiO9VBBLKi04zmaoWFuFITCyQxqvDqeWXrOCKCbsuFMBpXjbwaCXDaCkm/UKIlXDJKMzy4rZJEAWYnvbvdTWbIPDjys+aKPiOW8cZcVj52UP6UIW6EtTU3oFrq60gE/Ca6PjOcq2RitHA1JiMDXfkHAZRYAHpmVibnHsFyqtXQziDWl9Fyw4gU7/ir3LRC5c4jEEJooiXqyVSwy+HUF8NSO+UI4GxDngF0TqXhE/mYF2XrPNTgFuya9nGTlkJ9lZIJksG2mRNUVqunxU7P28JBazSrrZg51e2XtYbOE1ue5FytBdAiWR4Wk6ZBs52M5su/b4RNTZfRh1ZuuwudePK9e1UVvV14204G9zspNSrA020g08RmfpKZuaZQl2MZBSmamX2WfVd/sxOS/2xyWHv6YlYdUbwKjjsGZxPr5scuOo3YemXj8aegU09frR2OtHQ69fJidQojJDh/nDUquYLSLdDFR3ZjUoZhMQa7ut1YPDks+SnqO7RIzkQXZma2w+iKLYv9ho7PVD4uSEHBOHzDilWZVa+3ahAl38NpeAHq8Q1aBvvGNsU408sw6Lysz4gJD7BJiUa0B+kvxwgb4AJCnbWj3Y1U42W5JzfxraZ06S4DgOU/KM+FwSm7un3YtRWQa0ufy4al0baoki7aoKC546PyeltmbjzZR8g6yYHZWpDzkYFm8qM/QABt5TrYbAvm5LnpOBEkYdhwWlZiwoVf6+wyugqVdAQ69fVuQ29vpRZNHhe2PTYAllVjwIoTuzQYpZDW25ApBduVBxptFCDn5dMtyMAo2S2RixM8zalzJoP+Pa0u0V0dAr9Pv/0rrT+N3adTyH4ek6WbPleLcfE3KjKWbjH2ObaiwfZQ1azCZTYgD07SpLFzLHuv34iBjsTVbsNStmk8TkPIOsmN3d7sX8UgFXrWvHQcKq67JyM56bl5O0reXBytxiE1ZJhsCurbIkdVuUvBBrkQLmF0TsJmQG0wa5jjHNwKMqi0dV1tlzeaE1s8oyA3IwTIvtNlIzW9vlg9MnarYg6PEKeIMIHblpdHJdUhhyOI7DmGw9trUOXAtqbN6BYjbBjgAjMvTyYrbHhwlRhLgwj1mai8vMyDRyijtcyS5mrXoeE3MNsm4smeqYDL0swDSzSYMMT9jY7MbSD9uwj9DHLC4z4V8X5sLAClmK5aOsWFxmAgfgghIT7p4Yu0F+LMTD0eBwlw89kqmcXBM/ZKd9k0mhhZdptNvdQr8tjRQtPWYDZJt4lEqKYp8I/KfWEeI3IuPNeqfsHCu28FhYmtybJoOGlBpImx6JdgQgHz9ar1lKZsA6szDrOVxdQcvlTDpgdlHyP5ekbpa8DJJx84mCFbNJgtwO39bqpbKN5w8z4YX5eQkPRUgVDDyHVRflo+GmYVh7SX7St64ryWJWgwEwJYkBG8pJPHqeQ4GKFDAy2lMLmQHQN9go5fE9PXArFNPR8B9CYnBjtZXtAg1CxoQYAqOLwvh2OMmFe7QpYGQRzjqzfSjZW84uNCX9HgfQulkpZWm6pMmTWDGbJKoy9bCGODHnFhvx0sJcmAfByTvYGQwfcICWGZxy+FVHFQdjR2tqSQzOZiipgYKjARWYoFGk410T0yGd+zjd68dLhPtANBy2eWX+pQDw7WomMRiMkHKTGkln9gTZmY1zh5Pymo3S0YCSGQzxAbAAswuN1GucbIlBgFB2fcnSywKsmE0aOp7DxBzlN352oRGvLspjyTspRpqBl029+0XgVAy2NYBSZ5YVs8mimOjMkpG2Tp8oi5vWcUChWbs43f8aIy8yH9vTrSh1iASyID6vyIiRSUgXYoSH7MwesnkhnrF0THRRqEVn1uUT+w34AYADUMYkVAD6NNJ3TBjw9LbqOWp3JllUZuiQF8Q+LVl6WYAVs0lFafJ+eoEBqy7Ki8rmhJF8KKlBDENgLp+I/R1kZza5TgZDmSIr2ZmVF7NkcVtk4TV1H7lnUgZMkkM45fDjlSPRd2e9gohXjsp/nw1+DV7K0nRIk+xCdXlENDsFuHzyCOVEFIVKXrOiQox1KE4QYQmlaTomqZNw+7g0/GFWFr5VbcWqi/LiLh1RC8dxQaUGyUj+CsAqpiQyt0S+bTAlz4DVF+XHzR+QEX/Ii3wsxezeDq8skak8XZdUj8GhTjEhM2giJAXx8JiVUmLV4TtEsfmnPd1RS1k+POmSJctlGDhcWZFa/r9DCf6Mo4GUGpsXJx0+SM+AYdb4F4W5Jh7pksK61yei1RVZ4iE1tMaGv2RwHIfbxqfjybk5mFs8OCQGAYJJDabmsc7skOSb5WbcVG1FjonDknIz3licN6TTT84G6CGw6GUGTGIwuCiyhh4Ai0f6F8mPJmVAutY90ePHq1F2Z/9DSAyWVVqYtGmQQ8Xa2nw4TjgJlCegKOQ4ju7ORuhowAITUpcZCjuElRm6pNYv7MqVRHQ8h7/NzcGxG4fhpYV5yGVdt5SnMlO73PIdZPIXkxgkFdprVn7zpmy54lDMlqbpKClANN3Zpl4/PiTMzpnEYPCjFKBxvIcsChNzHyG3vcnjCAdZ/LLAhNThnHwjFSefzGRKgBWzDIamVGooM2Cd2cEF2WklnQsoWy6NZQYBfjQpHVJJfX23H6uORtadffVIr8wfcny2PqmTyAx10ENgdGc2UfZWsXrNkgt9ZsuVOmQaeYwjzsWpSb5+sGKWwdAQ8oJc3x35YAQA2NwCjkokCjynPDDISBzhZAaJ6MwCwPB0Pb5dLfeh/NPubvhUdmdFUaQkBt8ancb8i1MA0p7rkM2bcI/ZALE6GtQnOOiBoS2XlA/o63kOWFiaXL09K2YZDA0pMPOyiWNHFIMRALCT6MqOzdYjjTlcJBVSZtDqEuCXFJBUlG2cOrNAn3ZWaq9c1+3H6jpn8F+QsLnFgyOSQA8DD9xQNThsfxihGZ6mg0Uy3NXpFvE14UWdOJkB2ZlVX8yKoogTrDOb0vxkcgauHWnBmCw9/jArC+ODWI0mCnZ3ZDA0hOM4SvsVjW72ayINjkkMko9JxyHHNFBICCJkC5UGBxGYEKfOLNDXfbuR6M7+cXe3rLgOxotE4tdl5WbkMb1+SqDjOVRnyYu+072kK0CSOrMReGp3ugXYvQPnqkXHodDCypFUIt3A47l5udiytAgrxqWH/4U4w84eBkNjaK/ZyB0NviaGv85lyV+DAtqeq++99QsimpzxdzOQ8pPJGZA6MB2x+7DmWOjubLdXwJv18p9hiV+pxdic4MWqkQdKrIm5rZcTHeDTESQekvraERk6JnNhxAQrZhkMjSEdDY7ZI+vMiqJIDX+x4ZzBAR2c0NeNbXEJsoGqHBMX95jligw9leH+aJju7BvHnOiVmBeXWnVYMEhiMhnqIHWzUsrT9eATVBRa9bysm+oX6SHIYFAODExiwIgRVswyGBpDygwidTQ47fDLzOwtOg7jkqxHYvRRFCTStpF0MohzVzbAvUR39nCXD2/VB+/OvnjYIfv38mqrpilljPgzJit44Zfo4AEyNlftEBjVmWXDX4wYYcUsg6ExpMwgUsuaHYRednKeAQZWcAwKSOlAQFpApX8lqJgdmanHtSPlw1uP7u6GoOCgccjmxTZiWIh0RWAMfkJ1ZhMdPKAUa6sGZsvF0BpWzDIYGkMXs5F1ZncwicGghQ5O6OugU+lfcXQyIPnplAxI1zoHbT68fdxF/dx/iMGv84uNrIhIQUZk6GAKcnolOniALJ7VXuvIopcFJjBihRWzDIbGlKXrZFu/zU4Bzgias2z4a/BSTAzXBDqzifKYVWJUlgHXVMq7s4/sssu6sx6/iFeJYAWW+JWa6HkOozKVFyGJ1p5GG2nLomwZWsOKWQZDYww8hzKiM3fapU4mcMjmxU5myzVoCRZpS9ojxSv9Kxg/nZIhi5c80OnDO5Lu7LpTLrRJbMQyjRwuH8G8ZVOVYBr6RGtPyeJZTWfWJ4g4RQYmsM4sI0YSXswuWbIE2dnZsv+++93vyn7GZrPhtttuQ3l5OcrLy3HbbbfBZrPJfmb//v247LLLUFxcjHHjxuGRRx6JKmmJwYgHpKPBKVfoj5pXEPHoLjsueKsFPZJp8xwT7VvLSB7FQdwMkjUAFmB0tgFLie7sH3Z3918T/0MMfl070hp3twVG/Ag2BJbozix5bVKjmT3t8ENyiUOBmUc6C4RhxEhSevvf+ta38Mtf/rL/32azPAZtxYoVOHXqFF577TVwHIe7774bt99+O1auXAkAsNvtuPrqq3Heeefh008/RW1tLX7wgx/AarXirrvuSuhzYTCUqMzQ4TPJv085gxcOu9o8+OFXNuzr8FLfW1xmZv6LgwjSzaDZ6YcgimjslQcmxNtjVomfTc3AmmNOBOqEfR1evHfChWw3h49Ou2U/+//bu/e4qMr8D+CfYQZhBGV0cEDlJoIoXjMDzLu4oaSmKNKumGapO+Tmunkhc0s3C3VJvJVdXKJdrby0JpRoa1KiqWNZat7CVMQbCAkCCgkzvz/8MTIXQIYzMxz4vF8vXy/PnIczz3NeXw7feeY53zOFN36JWpCZm8BaO0qgaGHba0XHllLIJNAnp/llWpTc09aanJqrMUvUUHZJZlu2bAkPDw+z+86dO4e9e/di9+7dCA0NBQAkJSVh1KhRyMrKQmBgILZt24a7d+9iw4YNkMvlCA4Oxi+//IJ33nkHs2fP5h9/sjvjm8CulpvGZFmFDit+uo21P5cY1CitEunjjJVhCmt1kSzg4uiAVo4SFP//04vuaYHfyrWm1QxsvMwAuH+X+zg/OXZUK8218ngxHneVonrp2R5tHdFbyZsKxayrwvRPt28rmc3/9kkdJPBylRokqNnFlejetuZk1rjGLG9CJCHYZW7/s88+g7+/P8LCwrB48WIUFxfr92k0Gri6uuoTWQAICwuDi4sLjhw5om/Tv39/yOUPvlYLDw/H9evXkZ2dbbuBENXA+AJ95a7hr9rh3HIMSs1D0knTRNbd2QHJQ9pg8/C2cGvBr98aG+OlBucKKwweRCCX2n6GrMq83q0Mto8X3MOHOYaJa2xgS37gF7lOrWUwnvy0V61W08fa1r5u1rgWLWvMkhBs/pEoOjoa3t7e8PT0xNmzZ7F06VL8/PPP+PzzzwEAeXl5UCqVBhdbiUQCd3d35OXl6dt06NDB4Ljt2rXT7/Pz87PNYIhqYLyWrOoGsJJ7Wvzjh9v44EwpzK3wjvaXY3moG5TOvMA3Vh5yB2QVPdj+0aiUWvuWDnZLFru3dcRYX2ekVrv5q0z7oC8tHIBJ/rzxS+wc/7+iwZnCB4mhvZ6iZZyM1lXRwHSZAWdmqeEEiaJly5YhMTGx1jZpaWkYNGgQpk2bpn+te/fu8PPzQ3h4OH766Sf06dMHAMz+IdDpdCYJrvH+mn62uqysrFr3EwlBWwEAD9YlXiuX4CPNr1hxvgWulZvOtqpaaBEf8DsGtb2D33IK8Jvtukr15FLZAtUvnZmXfjPYbuPwu12vMzFtJEjNNp+wDmlbgYKcCyiwcZ9IeB1lLXCmWty1vPsbsrLybN4Pl3IZgAcVV37KyUdWi+sGbar/PpzLdwLwIAF2LLqBrCzDNedExgIDA2vdL0gyq1arMWnSpFrbeHl5mX39kUcegVQqxYULF9CnTx+oVCrk5+cbJK86nQ4FBQX62VeVSqWfpa2Sn58P4MEMbU3qOiFEQnH/6bq+HFKlToI5p5zNtpvapSX+8ZgblxSIRMCtIuy5WaLfzipzAvBgtqmz0hWBgT526Nl9gQCe/K0AX142fXCCuq8HAjuaj0MSl2cc72Jvxv2PvTIJ8Myj3vC2Q73WftI7QPYt/XaRrBUCA5X67ap7Xarc+P46gAfJ6+NdfTk7Sw0mSAQplUoolcq6G5px6tQpVFZW6m8ICwkJQUlJCTQajX7drEajQWlpqX47JCQES5YsQVlZmb4SQkZGBtq3bw9fX18BRkTUcJ1aSQ1qexrzdZVi7YA2GNLByYa9oobyNKpocMHoa1N7VDIwtqBPK5Nk1stFiqGMtSZjjK8zPhrWFt/f/B3j/eR2SWQB02UCxmtiqyu5pzW4JsokQEc73CxJTY9Np4IuXryIFStW4Mcff0R2dja++uorPPfcc+jVqxfCwsIAAEFBQRgxYgTmzp2Lo0ePQqPRYO7cuYiIiNB/ups4cSLkcjni4uJw+vRppKamYvXq1YiLi+ONDdRo1HSXrgSAOtgF341TMZEVIY86klV7VDIw1lvZAiO9DWdgJwe2hAOvj02GRCLBU35yvP6YG/ra8SmB5mrN1lTz3Xg9rberFDIHxiQ1nE0/yjk6OuLbb7/Fu+++i9LSUnTs2BFPPPEE4uPjIZU++IX44IMPsHDhQkRFRQEARo0ahZUrV+r3u7m5YceOHZg3bx6GDRsGhUKBF154AbNnz7blcIhqFWimsHmQmwzrBioQomISK1bGTwEz1hhmZgHgzRA3fH/zd+SXadGplRTqYFd7d4maoLZODnCVSfQPe7lToUN+mRbtzPyemDzGlssLSCA2jSQvLy/s2rWrznZt2rTB+++/X2ub7t27Iz09XaiuEQkuNtAFa06WoLRCB6lEh7m9WmN+71ZwknImQszat6z9C63G8rWpf2sZjk3wwP9OXsToPv6MO7IKiUQCn1ZSnL71IFG9VFxpNpk1fkKYH8tykUD4sYjISjq4SHE82gP7r5WjXek1DOpp/iZIEpe6lhk0lplZAGjdwgG9WmuZyJJV+bWSGSSz2SUVeExluvTBeGaWD0wgofD2aSIrcneWIsq/JTydza8hI/Fp7SiBvIbkUCoxfeQtUVNnXGvWuJZsFZMHJvBRtiQQXnWJiOpBIpHAo4alBh5yB0h5Qws1Mw9b0cBkmQFnZkkgTGaJiOrJs4abwBrTEgMiWzFX0cCYTqczvQGMa2ZJIExmiYjqqaaZ2cZQlovI1nyNatwaJ60AkHtXi7JqOW5rRwnaODEFIWEwkoiI6qmm8lycmaXmyHjt69XSSlRoDe8TMF0vK2NdeBIMk1kionryrCFpbSxluYhsqaXMAapqNz5W6oArpYZLDS4ZLT3gEgMSEpNZIqJ6Mn6kbRXOzFJzZZycGs/EGm/z5i8SEpNZIqJ6qmlmlsksNVfGyanxTWDG5bqMbxojaggms0RE9VTTmlkuM6Dmqq6bwPgoW7ImJrNERPXkWUM1A87MUnPlY1yey2gm9rJJjVn+rpBwmMwSEdVTWycHOBpdPds4SSCX8e5sap5Mlxk8mIktr9TharUbwiQAvF04M0vCYTJLRFRPEonEZKkBZ2WpOavtkbY5JRWoXqirfUsHOPODHwmIySwRkQU8jCoadGAyS81YRxcpquen+WValNzTAjC9GYzrZUloTGaJiCxgXNGAT/+i5kzmIIGX0exs1TpZ45u/WJaLhMZklojIAsbJLJcZUHNXU0UD47JcfGACCY3JLBGRBQa3dzLYHmK0TdTcGFcoqKpowAcmkLUxooiILDDaxxn/6NcamdfLEekjR3+PFvbuEpFdGa+FvVRcASjNzMyyLBcJjMksEZEFpA4SvNizFV7s2creXSFqFEweaVtSCSgNy3QBnJkl4XGZARERETWYcZJ6ubgCtyuAot8fFOZylppWAiFqKEYUERERNZjx8oFLJZW4WmZYT9bHVQYHCWvMkrCYzBIREVGDKZ0c4Fqt2OydCh1+LjbXyUODAAAWX0lEQVRMcPkYW7IGJrNERETUYBKJBD5GyerRQsM0gw9MIGtgMktERESCMK41+0OR1Gg/Z2ZJeExmiYiISBDGywhuV0iM9nNmloTHZJaIiIgEUdcyAiazZA1MZomIiEgQdS0j4AMTyBqYzBIREZEgapt5VTo5oJUj0w4SHqOKiIiIBOFTy8wsZ2XJWpjMEhERkSBcHB2gquEJX1wvS9bCZJaIiIgEU9O6WT4wgayFySwREREJpqaKBsY1aImEwmSWiIiIBONXQ9LKmVmyFiazREREJBjjR9pW4aNsyVoET2ZTUlIwevRo+Pj4QKFQIDs726RNYWEhZs6cCR8fH/j4+GDmzJkoLCw0aHPq1ClERkbC09MT3bp1w4oVK6DT6Qza7Ny5E6GhoVCpVAgNDUVaWprQwyEiIqJ6MLecQCoBvFw4M0vWIXgye+fOHQwfPhzx8fE1tnn++edx4sQJbNu2Ddu3b8eJEycwa9Ys/f7bt29j/PjxUKlU2LdvH5YvX45169Zh/fr1+jYajQbTp09HdHQ0MjMzER0djWnTpuH7778XekhERET0kMwtJ/BykULmIDHTmqjhBJ/zj4uLAwD8+OOPZvefO3cOe/fuxe7duxEaGgoASEpKwqhRo5CVlYXAwEBs27YNd+/exYYNGyCXyxEcHIxffvkF77zzDmbPng2JRIINGzZg0KBBmDdvHgAgKCgImZmZ2LBhA/71r38JPSwiIiJ6CB1dpJBKgMpqX6ayLBdZk83XzGo0Gri6uuoTWQAICwuDi4sLjhw5om/Tv39/yOVyfZvw8HBcv35dv2zh6NGjGD58uMGxw8PD9ccgIiIi25M5SOBtVJ6LD0wga7L5R6W8vDwolUpIJA++bpBIJHB3d0deXp6+TYcOHQx+rl27dvp9fn5+yM3N1b9WvU3VMWqSlZUlxDCI6o2xR/bC2CNba+fghEt4kMC6lhciKyvfjj0iMQsMDKx1/0Mls8uWLUNiYmKtbdLS0jBo0KCH6lT1RLaKTqczSXCN9xu/bq6NuWNXV9cJIbKGqiU0RLbG2CN7CL1VhKNFJfrtoYHtEejtbMceUVP2UMmsWq3GpEmTam3j5eX1UG+oUqmQn59vkHjqdDoUFBToZ1pVKpXJDGt+/v1PdFVtPDw8zLYxnq0lIiIi25oZ7II9V8qQVVSBUd7OCO/oZO8uURP2UMmsUqmEUqkU5A1DQkJQUlICjUajXzer0WhQWlqq3w4JCcGSJUtQVlYGZ+f7n+QyMjLQvn17+Pr6AgAee+wxZGRk4MUXX9QfOyMjw2AtLhEREdmej6sM341T4cS58+jbtUOd35oSNYTgN4Dl5ubixIkTOH/+PID71QtOnDiBW7duAbhfdWDEiBGYO3cujh49Co1Gg7lz5yIiIkL/VdjEiRMhl8sRFxeH06dPIzU1FatXr0ZcXJz+F+LPf/4z9u/fj1WrVuGXX37BqlWrkJmZCbVaLfSQiIiIqJ4cHSRoLTO/tJBISIIns8nJyRg8eDBmzJgBAJg0aRIGDx6MXbt26dt88MEH6NGjB6KiojBhwgT06NED7733nn6/m5sbduzYgevXr2PYsGGYP38+XnjhBcyePVvfJjQ0FMnJyfjkk08wYMAAfPrpp0hOTka/fv2EHhIRERERNVKSwsJCXd3NiKgheBMO2Qtjj+yJ8Ue2YPM6s0REREREQuHMLBERERGJFmdmiYiIiEi0mMwSERERkWgxmSUiIiIi0WIyS0RERESixWSWLJKQkID+/fvbuxvUTDH+yJ4Yf2RPjD9Tok9m1Wo1YmJi7N0N0eN5tAzPmzB4Hi3D8yYMnkfL8LwJg+ex4USfzBIRERFR89Wkktljx45h/Pjx8Pf3h7e3N0aOHAmNRmPQRqFQICUlBVOnTkWHDh3Qu3dvbNmyxU49bpzMfUrk1xp1Y/wJg/FnGcafMBh/lmH8CYPxZ5kmlcwWFxcjJiYG6enp+Prrr9GzZ09ER0ejoKDAoN3KlSsRGRmJAwcOICoqCrNnz8bly5ft1GtqKhh/ZE+MP7Inxh/ZU5NKZocMGYKnn34aQUFB6NKlC1auXAlnZ2fs3bvXoF1MTAxiYmLg7++PV155BTKZDIcOHbJTr6mpYPyRPTH+yJ4Yf2RPMnt3QEg3b97EG2+8gczMTNy8eROVlZW4e/curly5YtCue/fu+v/LZDIolUrcvHnT1t2lJobxR/bE+CN7YvyRPTWpZFatViMvLw9vvvkmfHx84OTkhLFjx+L33383aOfo6GiwLZFIoNPpbNnVRs3BwcHkfFRUVNipN+LB+BMG488yjD9hMP4sw/gTBuPPMk1qmcHhw4cxc+ZMREREoFu3bnB1dUVubq69uyU67u7uuHHjhsFrJ0+etFNvxIPxJwzGn2UYf8Jg/FmG8ScMxp9lmlQy27lzZ2zduhVnz57FsWPHMH36dLRo0cLe3RKdwYMH48SJE/jPf/6DCxcuYM2aNTh8+LC9u9XoMf6EwfizDONPGIw/yzD+hMH4s4zok1mtVgupVAoAWL9+PUpLSzF06FBMnz4dsbGx8PHxsXMPxaH6eQwPD8fChQuxbNkyDB06FJcvX8bzzz9v5x42Tow/YTD+LMP4EwbjzzKMP2Ew/hpOUlhYKOrFKuPHj0enTp2watUqe3dF1HgeLcPzJgyeR8vwvAmD59EyPG/C4HlsONHOzBYUFODLL7/EwYMHMXToUHt3R7R4Hi3D8yYMnkfL8LwJg+fRMjxvwuB5FI5oqxlMmzYNFy5cwIsvvogxY8bYuzuixfNoGZ43YfA8WobnTRg8j5bheRMGz6NwRL/MgIiIiIiaL9EuMyAiIiIiYjJLRERERKIlimR21apVGDZsGLy9vdG5c2fExMTg9OnTBm10Oh0SEhLQtWtXeHp64sknn8SZM2cM2iQmJiIiIgIdOnSAQqGo9T0LCgrQrVs3KBQKFBQUCD4mEg9bxp9CoTD5l5ycbLWxUeNn6+vfli1bMHDgQHh4eMDf3x+zZs2yyrhIHGwVf5s3bzZ7/VMoFDh27JhVx0jiJ4pk9sCBA3juueewZ88epKamQiaTYdy4cbh165a+zZo1a/D2229jxYoV2LdvH9q1a4fx48ejuLhY36a8vByjR4+GWq2u8z3j4uLQs2dPq4yHxMXW8bd27VqcO3dO/++Pf/yj1cZGjZ8t4+/dd9/Fq6++ir/85S84dOgQ0tLSEBkZadXxUeNmq/iLiooyuO6dO3cOkyZNgq+vLx555BGrj5PETZQ3gJWUlMDHxwebN2/GqFGjoNPp0LVrV8yYMQPz5s0DANy9exeBgYF4/fXX8eyzzxr8/M6dOzF16lQUFhaaPf6GDRuQnp6Ol156CU899RR+/fVXKJVKq4+LxMGa8adQKPDRRx/hqaeesslYSHysFX+FhYUIDg7G5s2bMWzYMJuNh8TF2n9/q9y5cwddu3bFnDlz8NJLL1ltPNQ0iGJm1lhJSQm0Wq3+q4rs7Gzk5uZi+PDh+jZyuRyPP/44jhw5Uq9jHz9+HGvWrMG7774LBwdRnh6yMmvGHwDEx8fD398fw4YNQ3JyMrRarWB9J/GzVvxlZGSgsrISeXl5CA0NRbdu3TB58mRcunRJ6CGQiFn7+ldlx44duHPnDiZPntzgPlPTJ8psLT4+Hj179kRISAgAIDc3FwDQrl07g3bt2rVDXl7eQx+3tLQUzz//PFasWIEOHToI12FqUqwVfwCwaNEiJCcn4/PPP0dUVBQWL16Mt956S5iOU5Ngrfi7dOkStFotEhMT8cYbb2DTpk2oqKjA6NGjcefOHeEGQKJmzetfdR999BEiIiLg6elpeWep2RDdQxMWLVqEw4cPY/fu3fpnGVeRSCQG2zqdzuS12ixcuBChoaH8ipdqZM34A4AFCxbo/9+rVy9otVq89dZbmD9/vuWdpibDmvGn1Wpx7949rFixQj/L9v777yMoKAi7d+9GVFRUwwdAombt61+VM2fOQKPRYOvWrRb3lZoXUc3Mvvzyy/jss8+QmpoKPz8//eseHh4AYPIpMD8/3+TTYm2+/fZbfPzxx1AqlVAqlfqktkuXLnj99dcbPgASNWvHnzmPPvoobt++3aAZDmoarB1/VccJCgrSv+bm5gZPT09cuXKlAT2npsCW17+UlBR4eXlhxIgRFveXmhfRJLMLFy7E9u3bkZqaii5duhjs8/X1hYeHBzIyMvSvlZWV4dChQwgNDX3o99ixYwcOHDiAzMxMZGZmYu3atQCAL774guVpmjlbxJ85J0+ehLOzM9zc3Bp0HBI3W8RfWFgYAOD8+fP610pKSpCbmwtvb+8GjoDEzJbXv7KyMmzZsgWTJ0/mfSv00ESxzGDevHnYsmULNm3aBIVCoV+j4+LiAldXV0gkEqjVarz11lsIDAxEQEAAEhMT4eLigokTJ+qPk5OTg1u3buHy5csAgBMnTgAA/P394erqioCAAIP3raov26VLF1YzaMZsFX/p6enIy8vDY489BrlcjszMTCQkJGDq1KlwcnKy/cCpUbDl9S8yMhLx8fFISkqCQqFAQkIC3N3dERERYfuBU6Ngq/irsnPnTty+fRuxsbE2HCWJnShKc9VU4HvhwoV4+eWXAdxfn7N8+XKkpKSgsLAQjz76KBITExEcHKxvr1ar8cknn5gcJy0tDYMGDTJ5PTMzE2PGjGFprmbOVvG3d+9eLF26FBcvXoRWq4Wfnx+mTJmCGTNmQCYTxedOsgJbXv+Ki4uxaNEipKWlQafTISwsDMuXL0enTp2sMDISA1v//Y2MjISLiwu2bdsm8EioKRNFMktEREREZA4XpBARERGRaDGZJSIiIiLRYjJLRERERKLFZJaIiIiIRIvJLBERERGJFpNZIiIiIhItJrNERHZS9WACIiKyHJNZIiIzrl27hvnz56NPnz7w8PCAv78/oqOjsXfvXnt3zSJqtRoKhUL/r2PHjujduzeeeeYZ7Ny5E1qt1uJj7969m0k5EdkNHytERGTk6NGjiI6Oxr179xAbG4vu3bvjt99+w9atWzFx4kT87W9/w6uvvmrvbtabo6Mj1q9fDwAoKytDTk4O0tPTMXXqVAwcOBCbN2+Gm5tbvY+7Z88efPjhh/onQhER2RKTWSKiagoLC/HMM89AJpPhf//7HwIDA/X7Zs+ejenTp2PVqlXo1asXxo0bV+NxKisrUVlZiRYtWtii2w/1fg4ODoiJiTF4bfHixUhKSsLSpUsxZ84cpKSkWLmnRETC4jIDIqJqUlJScP36dSxdutQgkQUAmUyGtWvXonXr1gZfq2dnZ0OhUCApKQkbN25E3759oVKpcOTIEQDA7du3MWfOHPj5+cHb2xtTpkzBjRs3zL7/jRs3MGfOHHTt2hUqlQp9+/bFmjVroNPpHvr96mvu3LkYPnw4du7ciaysLP3ru3btQkxMDLp16waVSoUePXrgtddeQ3l5ub6NWq3Ghx9+CAAGyxiys7P1bT777DOEh4ejffv28PHxQUxMDM6ePWtRX4mIjHFmloiomvT0dDg5OWHChAlm9ysUCkRGRuLTTz/FxYsX0alTJ/2+rVu3oqSkBNOmTYOrqys8PT2h0+kQGxuLzMxMTJkyBT179sQ333yD6Ohok2PfvHkTI0aMQEVFBaZOnQpPT08cOnQIr732Gq5fv47ly5cbtDf3fpaKiYnBvn378M033+iT+E2bNkEqlWLmzJlQKBQ4cuQI1q1bh6tXr2Ljxo0AgGeffRZXr17F/v378d577+mP5+7uDgBYvXo1lixZgjFjxuDpp59GaWkpNm7ciIiICHz77bfw8/OzuM9ERACTWSIiA2fPnkVAQACcnZ1rbNOzZ098+umnOHv2rEEye/nyZfzwww8GSWV6ejr279+PRYsWYcGCBQCAGTNmYMaMGTh58qTBcZctW4by8nIcPHgQKpUKwP1k0dPTE+vXr4darYavr2+t72epbt26AQAuXryof23jxo1o2bKlfvvZZ59F586d8eabb2Lp0qXo2LEjQkJC0LlzZ+zfv99kCUNOTg6WLVuGhQsXGqynffrppxESEoLExET9Gl4iIktxmQERUTUlJSVo3bp1rW1atWoFACguLjZ4/cknnzRJLPfs2QMHBwfMmjXL4HW1Wm2wrdPpsHPnTkREREAqlaKgoED/Lzw8HFqtFgcPHqzz/Szl6uoK4P74q1QlslqtFkVFRSgoKMDjjz8OnU6H48eP13nMtLQ0VFRUYMKECQbjcXR0RL9+/bB//35B+k5EzRtnZomIqnF1dcXt27drbVOVxFYlgFXMfWWek5MDlUplUiUgICDAYDs/Px+FhYXYtGkTNm3aZPZ98/Pz63w/S1UlsdXHdObMGbz66qs4cOAA7t69a9C+qKiozmP++uuvAICQkBCz+6vP+hIRWYrJLBFRNUFBQTh+/DjKyspqXGrw888/A3jw1XwVuVxu0lan00EikdT5vlV1XidOnIjY2Fizbfz9/et8P0udOXPG4D2KioowZswYyOVy/P3vf0enTp0gl8tx7do1xMXFPVRd2qo227dvh0xm+ufGwYFfDhJRwzGZJSKqZuTIkdBoNPjvf/+LP/3pTyb7i4qKsGvXLgQFBRmsl62Jj48PvvnmGxQVFRnMzp4/f96gnbu7O1q3bo2KigoMHTq0weOory1btkAikWDYsGEAgMzMTOTn5+OLL77AwIED9e0yMjJMframZL3q/Hh5eaFr165W6DUREdfMEhEZmD59Ojw8PLBkyRL91+RVKisr8de//hVFRUWIj49/qOM98cQT0Gq1Bnf6A8CGDRsMtqVSKcaOHYsvvvgCP/30k8lxioqKcO/evXqO5uEkJSVh3759iIqKQufOnfX9AWBQEkyr1eLtt982+fmq5QKFhYUGr48dOxYymQwJCQlmZ3KNl00QEVmCM7NERNUoFAr8+9//RnR0NIYMGYLY2FgEBwfj1q1b2Lp1K06dOoW5c+di/PjxD3W8UaNGYcCAAUhISMCVK1fQq1cvZGRkGNRhrbJkyRIcPHgQI0eOxJQpUxAcHIzi4mKcPn0aaWlpOHbsGDw8PCwem1arxZYtWwAA5eXluHz5MtLT03Hq1CkMGjQIq1ev1rcNCwtD27ZtoVarMWvWLMhkMqSmphrcIFblkUceAQDMnz8fI0aMgEwmw8iRI+Hn54elS5filVdewYgRIzBmzBi0adMGOTk5+Oqrr9CvXz8kJSVZPB4iIoDJLBGRidDQUHz33XdYvXo1du3aheTkZLi4uKBv375YsmQJ/vCHPzz0sSQSCT7++GMsXrwYn3/+OXbs2IEhQ4Zg27ZtJmtu3d3d8fXXX+Of//wnvvzyS6SkpMDNzQ0BAQGIj49HmzZtGjSue/fu6asqtGzZEu7u7ujTpw8WLFiAMWPGGKxhbdOmDbZu3YrFixcjISEBLi4uGDt2LKZPn44BAwYYHHfcuHHQaDTYsWMHtm/frq924OLighdeeAEBAQFYt24dVq1ahYqKCrRv3x5hYWGYMmVKg8ZDRAQAksLCQl3dzYiIiIiIGh+umSUiIiIi0WIyS0RERESixWSWiIiIiESLySwRERERiRaTWSIiIiISLSazRERERCRaTGaJiIiISLSYzBIRERGRaDGZJSIiIiLRYjJLRERERKL1f/ID6LQs80CPAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x216 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"diff_monthly_sales_df.plot(figsize=(10, 3))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 4.2.7 Testing for stationality\n",
"To test for stationality, we could use a statistical test, the Augmented Dickey-Fuller(ADF) test where the null hypothesis of the test is that the time series is not stationary (has some time-dependent structure). The alternate hypothesis is that the time series is stationary. In other words, if your time series is truly stationary, you should get a p-value of <=0.05 (95% confidence interval, significance level(α) of 0.05) which suggets us to reject the null hypothesis.\n",
"\n",
"Here's an example using the statsmodels library."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first line is the test statistic which we could use to compare against certain critical value in the Dicker-Fuller table to determine statitical significant.\n",
"\n",
"Conveniently, it also provide us the critical values of several common levels of significance(1, 5 and 10%), from the DF table.\n",
"\n",
"In this case, we could see that the test statistic is smaller than not just 5% but also all levels of signifcant. Therefore, we can confidently reject the null hypothesis and <b>say that this time series is stationary.</b>\n",
"\n",
"Alternatively, we could simply use the p-value associated with the test statistic, on the second line. This can be pretty handy as you could just quickly compare against the 1%(0.01), 5%(0.05) or 10%(0.10) confidence level to determine statitical significant.\n",
"\n",
"The third line(10) refers to the number of lags and we could say that there are some auto-correlation going back for 10 periods.\n",
"\n",
"Finallt, the fourth line(37) simply expresses the number of observations.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-5.19107018733927,\n",
" 9.168756655665654e-06,\n",
" 10,\n",
" 37,\n",
" {'1%': -3.6209175221605827,\n",
" '5%': -2.9435394610388332,\n",
" '10%': -2.6104002410518627},\n",
" 521.9616303121272)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"adfuller(monthly_sales_df.Sales.values)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4.3 Describing patterns - White noise"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A related topic of stationary is \"White noise\", which is a type of time series that the data doesn't follow a pattern. And if we cannot take advantage of the pattern in the past to infer the same for the future, then it cannot be predicted! Therefore, it's good to check for white noise pattern before we even consider modelling.\n",
"\n",
"How do we spot white noise? <b>These are the definition:</b>\n",
"\n",
"1) Constant mean($\\mu$) of 0\n",
"\n",
"2) Constant variance($\\sigma^2$)\n",
"\n",
"3) No(zero) autocorrelation (No relationship between past and present values)\n",
"\n",
"Have mean zero, and a finite variance: \n",
"$$E(X(t)) = 0, E(X(t)^2) = S^2\\text{, and } E(X(t)X(h)) = 0 \\text{ for } t\\neq h\\text{.}$$\n",
"\n",
"We will get to autocorrelation soon but it's basically the amount of correlation between a time series and a past version of itself. \n",
"\n",
"#### 4.3.1 Visual example of white noise\n",
"Again, to nail it down, a white noise looks like this in a plot."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rcParams['figure.figsize'] = 15, 5\n",
"random_white_noise = np.random.normal(loc=3, scale=2, size=1000)\n",
"plt.plot(random_white_noise)\n",
"plt.title('White noise time series')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could see the values are normally distribiuted around the mean of 3 (most values forming around 3) and the magnitude mostly staying within 2 units.\n",
"\n",
"Most importantly, it appears to behaves sporadically; there's zero correlation between past and future values, so there's no way that we could use the past patterns to project the future values."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 4.3.2 Why do we care about white noise?\n",
"\n",
"1) If your time series is white noise, <b>it cannot be modelled.</b>\n",
"\n",
"2) The residuals of a time series model should be white noise. That means that all of the signals in the time series has been harnessed by the model in order to make predictions. All that is left is the random fluctuations that cannot be modeled.\n",
"\n",
"#### 4.3.3 White noise VS Stationary\n",
"\n",
"If you were thinking that white noise sounds like the stationary that just went through, you are right! Note that while a white noise time series is stationary, not every stationary time series is white noise.\n",
"\n",
"#### 4.3.4 Modelling white noise\n",
"One of the things that confused me when I started learning these concepts is that stationary is a prequistite for modelling a particular time series but if white noise is also stationary, why can't we model the white noise?\n",
"\n",
"To be precise, what I was thinking: White noise = Stationary = Okay to Model?\n",
"\n",
"Here's a way to think of it: Remember that we difference the orginal time series to make it stationary. This act of differncing is effectively a way to eliminating/reducing the trend and seasonality, in an attempt to stablize the mean of the time series. We might difference it multiple times(orders) until all temporal dependence has been removed. \n",
"\n",
"If there's no signal left, the number of orders could actually be used to model the time series with a linear trend and seasonality.\n",
"\n",
"If there's some signal left, it's probably still largely stationary and the remaining signals might have some autocorrelation. We could then move on to model this autocorrelation signals. \n",
"\n",
"We will see a clearer picture as we go through a end-to-end example later."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4.4 Describing Pattern - Random Walk\n",
"The last important time series pattern we want to talk about is the \"Random Walk\", which is a special type of time series where values tend to presist over time and the differences between periods are simply white noise(random).\n",
"In other words, the prices of today is equals to prices of yesterday and some residuals of white noise\n",
"$$P_t = P_{t-1} + \\epsilon $$\n",
"\n",
"where $\\epsilon \\sim WN(\\mu,\\sigma^2)$\n",
" \n",
"#### 4.4.1 Visual example of random walk"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"rand_walk = pd.read_csv('RandWalk.csv')\n",
"rand_walk['date'] = pd.to_datetime(rand_walk['date'],dayfirst=True)\n",
"rand_walk.set_index('date',inplace=True)\n",
"rand_walk = rand_walk.asfreq('b') # convert/sample freq to business days(b)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x216 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rand_walk.plot(figsize=(10,3))\n",
"plt.title('Random walk')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could see that it's very different from the white noise we just talked about. In fact it looks like a series of stock or index prices where it exhibits some patterns. This is because the series itself is not random, although the differences are random.\n",
"\n",
"The random walk has it's root in finance, and is base on a financial theory that stock market prices are a random walk and cannot be predicted. However it's worth mentioning that this <a href='https://en.wikipedia.org/wiki/Random_walk_hypothesis'>claim is arguable.</a>\n",
"\n",
"Going back to the definition: we could definietly see small variations between consecutive time periods or in other words, values at $P_t$ depends on $P_{t-1}$\n",
"\n",
"To avoid some confusion that I had when I started learning the concepts we went through, here are some differences.\n",
"\n",
"#### 4.4.2 Random walk vs stationary\n",
"Random walk is a non-stationary process as we could see that it greatly violates the assumption of stationary. A stationary time series is one where the values are not a function of time. On the other hand, the observations in a random walk are dependent on time.\n",
"\n",
"#### 4.4.3 Random walk vs White noise\n",
"Not the same; white noise is like a sequence of random numbers. While the random walk values can appear random, the next value($P_{t+1}$) is always a modification of the previous value($P_t$) in the sequence. There is a underlying process that generates some consistency from step-to-step rather than spitting out random numbers. This is why random walk is also called a \"drunkard’s walk\".\n",
"\n",
"#### 4.4.4 Why do we care about Random walk?\n",
"If you have a random walk time series, <b>then it cannot be skillfully predicted.</b> This is simply because the next time step is a function of the prior time step and such model provide naive forecast. We call such models as \"persistence model\".\n",
"\n",
"Let's do a small experiment where we generate a time series of random walk and split the dataset into train and test sets."
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(660, 340)"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# generate the random walk\n",
"seed(1)\n",
"random_walk = list()\n",
"random_walk.append(-1 if random() < 0.5 else 1)\n",
"for i in range(1, 1000):\n",
" #add -1 or 1 to prev value\n",
" movement = -1 if random() < 0.5 else 1\n",
" value = random_walk[i-1] + movement\n",
" random_walk.append(value)\n",
"# prepare dataset\n",
"train_size = int(len(random_walk) * 0.66)\n",
"train, test = random_walk[0:train_size], random_walk[train_size:]\n",
"len(train), len(test)"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [],
"source": [
"random_walk_series = pd.Series(train+test, index = range(1000))#index=list(range(len(train)))+list(range(len(test))))"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(random_walk_series[:660],label='train')\n",
"plt.plot(random_walk_series[660:],label='test')\n",
"plt.title('Generated Random Walk')\n",
"ax.set_xlabel('Date')\n",
"ax.set_ylabel('Sales')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use the persistence model to predict the outcome using a rolling forecast method and we calculate the MSE for all predictions are collected from the test set."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Persistence MSE: 1.000\n"
]
}
],
"source": [
"# persistence\n",
"predictions = list()\n",
"history = train[-1]\n",
"#loop thru each step and take last observation as prediction for current step..\n",
"for i in range(len(test)):\n",
" yhat = history\n",
" predictions.append(yhat)\n",
" history = test[i]\n",
"error = mean_squared_error(test, predictions)\n",
"print('Persistence MSE: %.3f' % error)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Obviously, since the observations are constructed by generating either -1 or +1 of the previous values, calculating the MSE of \"predictions\" would also be 1. \n",
"\n",
"But what happens if we say that we know the variance of the process, then we can sprinkle a little variance when generating the values?"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Random MSE: 1.976\n"
]
}
],
"source": [
"seed(1)\n",
"predictions = list()\n",
"history = train[-1]\n",
"\n",
"for i in range(len(test)):\n",
" yhat = history + (-1 if random() < 0.5 else 1)\n",
" predictions.append(yhat)\n",
" history = test[i]\n",
"error = mean_squared_error(test, predictions)\n",
"print('Random MSE: %.3f' % error)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It ended up with even worse performance. We can conduct more experiments later, with more complex model if that doesn't convince you. So where does it go from here? There are 2 takeaways:\n",
"\n",
"1) The best model/predictor for a random walk is at most a persistence model. \n",
"\n",
"2) A persistence model could be a baseline model before you employ fancy time series modelling techniques. If the performance(skill) of your final model cannot beat a persistence model, it also means we are better off with just taking the previous value as a prediction. Ouch!\n",
"\n",
"#### 4.4.5 How to tackle a suspected random walk time series?\n",
"Granted that most time series out there are random walks, we could <b>try</b> to model the first order differences instead of the raw values. Remember in the stationary section where we talk about differencing the time series to make it stationary before we begin modelling. However, if making it stationary still shows no obviously learnable structure in the data, then it cannot be forecasted."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5. Modelling - ARIMA model\n",
"Finally, with some of the important concepts out of the way, we can start to look at modelling time series!\n",
"\n",
"ARIMA and it's variants(ARMA, ARMAX, SARIMA) is the classic model for almost all time series literature. ARIMA is a traditional time series model that models the Autoregressive(AR) and Moving Average (MA) nature of the time series. For time series with seasonality, like the one we talked about above, we could use the Seasonal ARIMA (SARIMA) to model such process. Let's look at the building blocks and assumptions of the simpliest ARMA model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.1 Autoregressive(AR)\n",
"\n",
"In time series, there's often a relationship between past and present values. For example, we could do a reasonable guess of the sales today given yesterday's sales, or maybe the sales 7 days ago. Therefore, we use <b>Autocorrelation</b> which is the correlation between a sequence of itself.\n",
"<img src='ts_pics/autocorr1.jpg' width=500>\n",
"<img src='ts_pics/autocorr2.jpg' width=500>\n",
"For example, the above picture illustrates the corelation between the current series and a lagged version of itself (t-1, lag of 1). The frequency of lagged values could be in days, weeks or months."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"ARIMA takes advantage and model this AR nature of a time series. We could picture this as a linear model that relies on a sum of past period values multiplied by a constant(coefficient) to predict the current period values.\n",
"<img src='ts_pics/ar_model.png' width=500>\n",
"\n",
"It's likely that the more lagged values(lags) we use in a ARIMA model, it could model more complex relationships and interactions. Hence, we often not only use lagged values of 1: AR(1), but also further lagged values: AR(2), AR(3), etc.\n",
"<img src='ts_pics/ar_model2.png' width=500>\n",
"\n",
"However, when we include more coefficients, it's more likely that some of them are not significant(different from zero) and just like any machine learning or Neural network models, more parameters might lead to overfitting. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Auto-correlation Functions (ACF)\n",
"We could imagine that it's extremely helpful to calculate the auto correlation of different lags simultaneously:\n",
"\n",
"$$\\rho(k) = \\frac{\\frac{1}{n-k}\\sum_{t=k+1}^n (y_t - \\bar{y})(y_{t-k} - \\bar{y})}{\n",
"\\sqrt{\\frac{1}{n}\\sum_{t=1}^n (y_t - \\bar{y})^2}\\sqrt{\\frac{1}{n-k}\\sum_{t=k+1}^n (y_{t-k} - \\bar{y})^2}} \\,,$$\n",
"\n",
"The top portion is essentially the covariance between the original data and the k-unit lagged data. The bottom is sum of the squared deviations of the original data set. \n",
"\n",
"And this is the main idea behind the ACF. We could calculate it manually or we could simply just use the plot_acf() function from statsmodels library."
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 106,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ngIoyQKUEKsrQzddNPZ