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model-development.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center>\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%204/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\" />\n",
"</center>\n",
"\n",
"# Model Development\n",
"\n",
"Estimated time needed: **30** minutes\n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"- Develop prediction models\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some questions we want to ask in this module\n",
"\n",
"<ul>\n",
" <li>do I know if the dealer is offering fair value for my trade-in?</li>\n",
" <li>do I know if I put a fair value on my car?</li>\n",
"</ul>\n",
"<p>Data Analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
"\n",
"<p>A Model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Setup</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Import libraries\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"load data and store in dataframe df:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>symboling</th>\n",
" <th>normalized-losses</th>\n",
" <th>make</th>\n",
" <th>aspiration</th>\n",
" <th>num-of-doors</th>\n",
" <th>body-style</th>\n",
" <th>drive-wheels</th>\n",
" <th>engine-location</th>\n",
" <th>wheel-base</th>\n",
" <th>length</th>\n",
" <th>...</th>\n",
" <th>compression-ratio</th>\n",
" <th>horsepower</th>\n",
" <th>peak-rpm</th>\n",
" <th>city-mpg</th>\n",
" <th>highway-mpg</th>\n",
" <th>price</th>\n",
" <th>city-L/100km</th>\n",
" <th>horsepower-binned</th>\n",
" <th>diesel</th>\n",
" <th>gas</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>3</td>\n",
" <td>122</td>\n",
" <td>alfa-romero</td>\n",
" <td>std</td>\n",
" <td>two</td>\n",
" <td>convertible</td>\n",
" <td>rwd</td>\n",
" <td>front</td>\n",
" <td>88.6</td>\n",
" <td>0.811148</td>\n",
" <td>...</td>\n",
" <td>9.0</td>\n",
" <td>111.0</td>\n",
" <td>5000.0</td>\n",
" <td>21</td>\n",
" <td>27</td>\n",
" <td>13495.0</td>\n",
" <td>11.190476</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>3</td>\n",
" <td>122</td>\n",
" <td>alfa-romero</td>\n",
" <td>std</td>\n",
" <td>two</td>\n",
" <td>convertible</td>\n",
" <td>rwd</td>\n",
" <td>front</td>\n",
" <td>88.6</td>\n",
" <td>0.811148</td>\n",
" <td>...</td>\n",
" <td>9.0</td>\n",
" <td>111.0</td>\n",
" <td>5000.0</td>\n",
" <td>21</td>\n",
" <td>27</td>\n",
" <td>16500.0</td>\n",
" <td>11.190476</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1</td>\n",
" <td>122</td>\n",
" <td>alfa-romero</td>\n",
" <td>std</td>\n",
" <td>two</td>\n",
" <td>hatchback</td>\n",
" <td>rwd</td>\n",
" <td>front</td>\n",
" <td>94.5</td>\n",
" <td>0.822681</td>\n",
" <td>...</td>\n",
" <td>9.0</td>\n",
" <td>154.0</td>\n",
" <td>5000.0</td>\n",
" <td>19</td>\n",
" <td>26</td>\n",
" <td>16500.0</td>\n",
" <td>12.368421</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>2</td>\n",
" <td>164</td>\n",
" <td>audi</td>\n",
" <td>std</td>\n",
" <td>four</td>\n",
" <td>sedan</td>\n",
" <td>fwd</td>\n",
" <td>front</td>\n",
" <td>99.8</td>\n",
" <td>0.848630</td>\n",
" <td>...</td>\n",
" <td>10.0</td>\n",
" <td>102.0</td>\n",
" <td>5500.0</td>\n",
" <td>24</td>\n",
" <td>30</td>\n",
" <td>13950.0</td>\n",
" <td>9.791667</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2</td>\n",
" <td>164</td>\n",
" <td>audi</td>\n",
" <td>std</td>\n",
" <td>four</td>\n",
" <td>sedan</td>\n",
" <td>4wd</td>\n",
" <td>front</td>\n",
" <td>99.4</td>\n",
" <td>0.848630</td>\n",
" <td>...</td>\n",
" <td>8.0</td>\n",
" <td>115.0</td>\n",
" <td>5500.0</td>\n",
" <td>18</td>\n",
" <td>22</td>\n",
" <td>17450.0</td>\n",
" <td>13.055556</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 29 columns</p>\n",
"</div>"
],
"text/plain": [
" symboling normalized-losses make aspiration num-of-doors \\\n",
"0 3 122 alfa-romero std two \n",
"1 3 122 alfa-romero std two \n",
"2 1 122 alfa-romero std two \n",
"3 2 164 audi std four \n",
"4 2 164 audi std four \n",
"\n",
" body-style drive-wheels engine-location wheel-base length ... \\\n",
"0 convertible rwd front 88.6 0.811148 ... \n",
"1 convertible rwd front 88.6 0.811148 ... \n",
"2 hatchback rwd front 94.5 0.822681 ... \n",
"3 sedan fwd front 99.8 0.848630 ... \n",
"4 sedan 4wd front 99.4 0.848630 ... \n",
"\n",
" compression-ratio horsepower peak-rpm city-mpg highway-mpg price \\\n",
"0 9.0 111.0 5000.0 21 27 13495.0 \n",
"1 9.0 111.0 5000.0 21 27 16500.0 \n",
"2 9.0 154.0 5000.0 19 26 16500.0 \n",
"3 10.0 102.0 5500.0 24 30 13950.0 \n",
"4 8.0 115.0 5500.0 18 22 17450.0 \n",
"\n",
" city-L/100km horsepower-binned diesel gas \n",
"0 11.190476 Medium 0 1 \n",
"1 11.190476 Medium 0 1 \n",
"2 12.368421 Medium 0 1 \n",
"3 9.791667 Medium 0 1 \n",
"4 13.055556 Medium 0 1 \n",
"\n",
"[5 rows x 29 columns]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# path of data \n",
"path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv'\n",
"df = pd.read_csv(path)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>1. Linear Regression and Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>One example of a Data Model that we will be using is</p>\n",
"<b>Simple Linear Regression</b>.\n",
"\n",
"<br>\n",
"<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
"<ul>\n",
" <li>The predictor/independent variable (X)</li>\n",
" <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
"</ul>\n",
"\n",
"<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
" Y: Response \\ Variable\\\\\n",
" X: Predictor \\ Variables\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" <b>Linear function:</b>\n",
"$$\n",
"Yhat = a + b X\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li>a refers to the <b>intercept</b> of the regression line0, in other words: the value of Y when X is 0</li>\n",
" <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
"</ul>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Lets load the modules for linear regression</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Create the linear regression object</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm = LinearRegression()\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>How could Highway-mpg help us predict car price?</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this example, we want to look at how highway-mpg can help us predict car price.\n",
"Using simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable.\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"X = df[['highway-mpg']]\n",
"Y = df['price']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using highway-mpg.\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can output a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
" 20345.17153508])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Yhat=lm.predict(X)\n",
"Yhat[0:5] "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the intercept (a)?</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38423.3058581574"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the Slope (b)?</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([-821.73337832])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>What is the final estimated linear model we get?</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we saw above, we should get a final linear model with the structure:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b X\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plugging in the actual values we get:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 a): </h1>\n",
"\n",
"<b>Create a linear regression object?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1 = LinearRegression()\n",
"lm1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm1 = LinearRegression()\n",
"lm1\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #1 b): </h1>\n",
"\n",
"<b>Train the model using 'engine-size' as the independent variable and 'price' as the dependent variable?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"X = df[['engine-size']]\n",
"Y = df['price']\n",
"lm1.fit(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 c):</h1>\n",
"\n",
"<b>Find the slope and intercept of the model?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Slope</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([166.86001569])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-7963.338906281042"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# Slope \n",
"lm1.coef_\n",
"\n",
"# Intercept\n",
"lm1.intercept_\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 d): </h1>\n",
"\n",
"<b>What is the equation of the predicted line. You can use x and yhat or 'engine-size' or 'price'?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"#price = -7963.34 - 166.86 x engine-size"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# using X and Y \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Multiple Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>What if we want to predict car price using more than one variable?</p>\n",
"\n",
"<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
"Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
"Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Y: Response \\ Variable\\\\\n",
"X_1 :Predictor\\ Variable \\ 1\\\\\n",
"X_2: Predictor\\ Variable \\ 2\\\\\n",
"X_3: Predictor\\ Variable \\ 3\\\\\n",
"X_4: Predictor\\ Variable \\ 4\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"a: intercept\\\\\n",
"b_1 :coefficients \\ of\\ Variable \\ 1\\\\\n",
"b_2: coefficients \\ of\\ Variable \\ 2\\\\\n",
"b_3: coefficients \\ of\\ Variable \\ 3\\\\\n",
"b_4: coefficients \\ of\\ Variable \\ 4\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The equation is given by\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>From the previous section we know that other good predictors of price could be:</p>\n",
"<ul>\n",
" <li>Horsepower</li>\n",
" <li>Curb-weight</li>\n",
" <li>Engine-size</li>\n",
" <li>Highway-mpg</li>\n",
"</ul>\n",
"Let's develop a model using these variables as the predictor variables.\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using the four above-mentioned variables.\n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(Z, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the value of the intercept(a)?\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-15806.624626329209"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What are the values of the coefficients (b1, b2, b3, b4)?\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" What is the final estimated linear model that we get?\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we saw above, we should get a final linear function with the structure:\n",
"\n",
"$$\n",
"Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
"$$\n",
"\n",
"What is the linear function we get in this example?\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #2 a): </h1>\n",
"Create and train a Multiple Linear Regression model \"lm2\" where the response variable is price, and the predictor variable is 'normalized-losses' and 'highway-mpg'.\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2 = LinearRegression()\n",
"Z = df[['normalized-losses', 'highway-mpg']]\n",
"lm2.fit(Z, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm2 = LinearRegression()\n",
"lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
"\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #2 b): </h1>\n",
"<b>Find the coefficient of the model?</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm2.coef_\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>2) Model Evaluation using Visualization</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've developed some models, how do we evaluate our models and how do we choose the best one? One way to do this is by using visualization.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"import the visualization package: seaborn\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"# import the visualization package: seaborn\n",
"import seaborn as sns\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Regression Plot</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
"\n",
"<p>This plot will show a combination of a scattered data points (a <b>scatter plot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's visualize **highway-mpg** as potential predictor variable of price:\n"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 48268.07842273542)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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Ymvl1Veb6LUC3tfY04CvAlybx+YiIiIiI5G3SArhNG8j81pv5ZYFrgAcy1x8A3pf5/BrgYWttzFq7F9gNrDTGzAGqrbVPW2st8OBxt8ne12PA27K746dcV75PTEREREQkD5N6CNMY4zbGPAe0A7+21v4emGWtPQSQ+Zgtzp0HtA65eVvm2rzM58dfH3Yba20S6AVmjLSmRNKhL5rI41mJiIiIiIzfpAZwa23KWnsBMJ/0bvY5I3z5yXau7QjXR7rN8Ds25lZjzDZjzLauzqMc7Y9xuDdKMuWM8gxERERERCZWQdoQWmt7gI2ka7ePZMpKyHxsz3xZG9A05GbzgYOZ6/NPcn3YbYwxHqAG6DrJ499trV1urV1eP2MmAOF4kgM9EQZiyQl4hiIiIiIiuZnMLigNxpjazOdB4O3ATmAdcFPmy24Cfpz5fB1wXaazyWLShy23ZMpU+o0xl2Tqu2887jbZ+7oWWJ+pE89JyrG090Vp74/iOKoOFxEREZHJN5l9wOcAD2Q6mbiAR621PzXGPA08aoy5BXgd+ACAtXaHMeZR4GUgCXzGWpudIX4bcD8QBH6R+QVwD/CQMWY36Z3v68az0IFokmjcoaHKT9DnHv0GIiIiIiLjZMawYVwWzrvgIvujX2865Z/XhnzUhbyM0kxFRERERGRExpjt1trlx1/XKPrj9ITjHOyNEk/qgKaIiIiITDwF8JOIJVIc6ImoXaGIiIiITDgF8FOw1nK0P8aRvigpHdAUERERkQmiAD6KwViSA90RIvHU6F8sIiIiIjIKBfAcJB2HQ70ROgdiTLdDqyIiIiIysRTAx6A3kuBAT4RYUrvhIiIiIjI+CuBjFE86HOyJ0hvRAU0RERERGTsF8HGw1tI5EONwb5RkSu0KRURERCR3CuB5CMeTHOiJMBhLFnspIiIiIjJFKIDnKeVYjvRF6eiP4ahdoYiIiIiMQgF8gvRH0wc0owkd0BQRERGRU1MAn0CJlMOh3ijdg3G1KxQRERGRk/IUewHlxlpLdzhOOJGiscqP163XOJKfrz7+Gt9+ci+D8RQVPjefuGwxf/z204u9LBERERknpcNJEkukONAdoS+qdoUyfl99/DXuXL+bSCKFxwWRRIo71+/mq4+/VuyliYiIyDgpgE8ix1qO9sc40hclpQOaMg7ffnIvLgMelwuXcWU+pq+LiIjI1KQAXgCDsSRt3WHCcbUrlLEZjKdwmeHXXCZ9XURERKYmBfACSTmWw71Rjg7EdEBTclbhc3P8myeOTV8XERGRqUkBvMD6IgnautWuUHLzicsW41hIOg6OdTIf09dFRERkalIXlCLItiusC3mpDfmKvRwpYdluJ+qCIiIiUj7MdCuHOO+Ci+yPfr2p2Ms4JuB106B2hSIiIiJlxxiz3Vq7/PjrSn1FFs20K+xXu0IRERGRaUEBvAQ41tKhdoUiIiIi04ICeAkZjCU50B0hohZzIiIiImVLAbzEJB2HQ70RtSsUERERKVMK4CUq264wltRuuIiIiEg5UQAvYYmUw8GeKD3heLGXIiIiIiITRAG8xFlr6RqMc7AnQiLlFHs5IiIiIpInBfApQu0KRURERMqDAvgUkm1X2K52hSIiIiJT1rQL4EcHYkQTU/tg44DaFYqIiIhMWdMugHcOxvnYfVvZsLN9Srf5y7Yr7FS7QhEREZEpZdoFcAO098f4x5+9wp888hyvHekv9pLy0htJcKBH7QpFREREpoppF8AXzazgLafNAODFA33c9p1n+PL/vEr3FG71F0+m2xX2hnVAU0RERKTUTbsA7nO7+MdrzuHfrj2PRTNCWODnLx7mxnu28Oi21inb6s9aS+dgjEO9EZJT9DmIiIiITAfTLoBnXbywjm/duJzPv+00qgMeBuMpvvlEC7c8sI3NLZ1Ttq46Ek9xoCfCQCxZ7KWIiIiIyEmYqRo0x+u8Cy6yP/r1pmHX+iIJHnh6Pz9+7gDZ7n4rF9Vx2+olLJxRUYRVTozKgIeZFX5cLlPspYiIiIhMO8aY7dba5cdfn7Y74ENVB7187srT+NaNy7l4YR0AW/Z184kHt/P1Dbun7PCbgWiStu7IlG+7KCIiIlJOtAN+HGstT+3p5BtP7OFgTxSAmqCXj79lEe8+dw7uKbqbXBvyURfyYszUXL+IiIjIVKMd8BwZY3jLaTO596YV3LqqmZDPTW8kwX88vos139nOs693F3uJ49ITjnOgJ0I8qQOaIiIiIsWkHfBRdA3GuefJvfzypcNk/0utWjqTNW9tZk5NcHIWOYmMMdRX+KgJeou9FBEREZGyph3wcaqv8PHn7zyDuz5yEWfPrQZg066jfOy+rdzz5N4pNw7eWkvngNoVioiIiBSLAniOzphdxVevu4C/+cMzaaj0k0hZvvv717nx3i38z8tHcKbYOwnZdoWDalcoIiIiUlAqQRmHSCLFI1taeXhb67Ga6jPnVPHZK07jzDnVE7HMglK7wtK2cWc7aze10NodpqkuxJpVzaxe1ljsZYmIiMgoTlWCogCeh8N9Ue5+ooWNr3Ucu/YHZ83iE5cvZmalf0Ieo1C8bhcNVX4CXnexlyJDbNzZzu3rduB1G4JeN5FEikTKcsfVZyuEi4iIlDjVgE+C2dUBbn/vWXzlQ+dzWkMlAP/z8hFuvHcL//X716dUx5FEyuFgT4SuwfiUnQJajtZuasHrNoR8HoxJf/S6DWs3tRR7aSIiIjJOCuAT4Pz5tXzjoxfxhXecTm3QSzTh8O0n9/Lx+7eyaVfHlAq0PeE4B3ujU+rFQzlr7Q4TPO5diaDXTVt3uEgrEhERkXwpgE8Qt8vwnvPm8ODNK/nAxfNxuwyHeqP8/bqX+bPHXqClY6DYS8xZLJE+oNkbmZoTQMtJU12IyHGTTCOJFPPrQkVakYiIiORLAXyCVQY83LZ6CffctJxLmusBePb1Hm59aDv/8fguesNTI9Rm2xUe7o2ScqbODn65WbOqmUTKEo4nsTb9MZGyrFnVXOyliYiIyDjpEOYk+/3eTu7asIfW7ggAlX4PH3vzQq4+fy4e99R4/eN2GWZW+qnwe4q9lGkp2wWlrTvMfHVBERERmTLUBSWj0AEcIJly+NFzB3ng6X0MxtLlBAvrQ3z6iiWsWFRf0LXkoyrgZUaFT+0KRURERHKQdxcUY8xCY8zbM58HjTFVE7nAcuZxu7j24vk8dPNK3nv+HFwG9neF+eL3X+RvfvjSlDlQ1x9NcKAnQjQxtaZ/ioiIiJSSnAK4MeaTwGPA2syl+cCPJmlNZas25ONP3346az96MRc01QDwdEsnN9+/jbVP7JkSUymz7Qq71a5QREREZFxy3QH/DPAWoA/AWrsLUBHqOC1prOT/feB8/v69ZzG7OkDSsTyyrY0b793Cz188NCUOPXarXaGIiIjIuOR6qi5mrY0bk679NcZ4gNJPiSXMGMOq0xt40+J6/nt7G//1+9fpDif48v+8xo+fO8hnrziNc+fXFHuZI4olUhzsiVBf6aM64C32csqWRtGLiIiUl1x3wJ8wxvw1EDTGvAP4b+Ank7es6cPvdfPRSxbywM0refuZ6VC1q32Azz/yHP/405c50hct8gpH5ljL0X61K5ws2VH07f1RaoNe2vuj3L5uBxt3thd7aSIiIjJOuQbwvwQ6gBeBNcDPgb+drEVNRw1Vfv76D8/kP6+/gDNmp8+3bni1g4/dt5X7n9pX8gcfw/Ekbd1hwvHSr2OfSjSKXkREpPzkGsCDwL3W2g9Ya68F7s1ckwl29twavv7hC/nLq86gvsJHLOnw4NP7+dh9W1m/s72kDz6mHMvh3igd/bGSXudUolH0IiIi5SfXAP4bhgfuIPD4xC9HAFzG8Adnz+bBm1fw4ZVNeN2G9v4Y//SzV/j8w8/x2pH+Yi9xRP3RBG3dalc4ETSKXkREpPzkGsAD1tqB7G8ynysBTLKQz8MnLm/mvo+t4LLTZgLw0sE+bvvOM3z5V6/SNRgv8gpPLZFyONQbpbuE1zgVaBS9iIhI+ck1gA8aYy7K/sYYczEQmZwlyfHm1ga545qz+fIHzmPxzAos8POXDnPjvVt4ZGsriVRptgK01tIdjnOgJ1Kyayx1q5c1csfVZ9NYFaA3kqCxKsAdV5+tLigiIiJTWE6j6I0xK4CHgYOZS3OAD1lrt0/i2iZFMUbRT6SUY/npC4e473d76YumDzzOrwty21uXcElzPdlWkaXGZYzaFYqIiMi0cqpR9DkF8MwdeIEzAAPstNYmJnaJhTHVA3hWXyTBg0/v50fPHSDb/W/Fojo+vXoJC2dUFHdxx9nS0sXDW1s51BdhXm2Qz6w+jbedNavYyxIRERGZVOMK4MaYK621640x7z/Zn1trfzCBayyIcgngWfs6B/n6hj1s398NgMvA+y6cx02XLqSqBHabt7R0cef6XXhchoDXRTThkHQst7/nLN517pxiL09ERERk0pwqgI9WA/7WzMf3nuTXeyZ0hQXi87ioC/lwu0qzVGOsFs2o4F//17n80/vOZl5tEMfCD545wA33bOHHzx0s+nCch7e24nEZgl43hvRHj8uw9okW2vuiOBreIyIiItPMiKPorbV/Z4xxAb+w1j5aoDVNuroKH7UhL33RJH2RxJQ/IGiM4c1LZrJ8YT0/ePYA39m8n75okjt/s4ufPH+QT1+xhIsW1BVlbYf6IlQHhv81C3hdHO6LMBBLEk04NFT5Cfrcp7gHERERkfIyahcUa60DfLYAaykoYww1QS/z64I0VgfweXJtCFO6fB4X161o4sGbV/Kuc2ZjgJajg/zZf7/A363bwcGewjeumVMdJJoY/gInmnCYXZ1uK590HA71Rjg6oOE9IiIiMj3kmjp/bYz5M2NMkzGmPvtrUldWIMYYKv0e5teFmF0TIOCd+jux9RU+/vydZ/CNj17EOXOrAfjtrqN8/P6t3PPkXiLxwg3IuW5FE0nHEkmksKQ/Jh3LdSuahn1dXyQ9vCeW1PAeERERKW+5tiHcC5zwhdbaKTcNZPny5Xbbtm0jfk00kaI7HC9oUJ0s1lrW7+zg7k0tdAzEAJhR4eOTly/m7WfNwlWAtoXZLiiH+yLMrg5y3YomVjaf/PWbMYa6kJfakG/S1yUiIiIymfJqQ2iMCQKfBi4jHcR/C3zTWjvlhvHkEsCzookUvZEEg7HkJK9q8kUSKR7Z2srDW1uJJ9MlIctmV/G5K0/jzDnVRV7diQJeNw1VfrzuqV8aJCIiItNTvgH8UaAP+G7m0vVArbX2gxO6ygIYSwDPiiVT9IYTDJRBED/cF+Vbm1rY8GrHsWvvOGsWn7hsMQ1V/iKu7EQuY5hR6SuJdooiIiIiY5VvAH/eWnv+aNemgvEE8Kx40qEnHC+LIP5CWw9f27CH3e0DQLozyUfetIAPXNxUcgdSK/0eZlb6cZVJ60gRERGZHsbbBzzrWWPMJUPu7E3A7yZqcVOFz+OisTrA/LoQlYEROziWvPPm1/KNj1zE/37H6dSFvEQTDvc8uY+P3beVTa91lFRHkoFYkrbuSFnU5IuIiIjkugP+Cukx9K9nLi0AXgEcwFprz5u0FU6wfHbAj5dIOfRkSlNKKbCO1UAsyXc27+cHzxwgmRmMc0FTDZ+54jSWNFQWeXXD1QS91Ff4MAU4PCoiIiKSj3xLUBaO9OfW2v15rK2gJjKAZyVTDj2RBP3RqR3EW7vCfOOJPWxu6QLSY+3ffd4cbn7zYmpCpVOH7fO4aKjy4/dM/ZaRIiIiUr7yCuDlZDICeFbKsfRGEvRFEjhT+L/r1n1d3LVhD/u7wkC6BvumNy/kmvPn4imRriTGGOpDvpJ6YSAiIiIylAJ4xmQG8CzHsfRFE/RGEqScqfnfN5lyWPf8Qe5/av+xQ6cL6kN85oolrFhUOjOYgj43DZX+knlhMBk27mxn7aYWWrvDNNWFWLOqmdXLGou9LBERERmFAnhGIQJ4lrWWvkiS3kiCpOOMfoMS1BtOcN9T+/jpCwfJvpa4pLme2966hKb6UHEXl+F2GWZU+qn0T+2DsSezcWc7t6/bgddtCHrdRBIpEinLHVefrRAuIiJS4hTAMwoZwLOstfTHkvSGEyRSUzOI7+kY4Osb9vBcaw8AHpfh/RfN46OXLCyZ4FsZ8DCzorzaFV5/92ba+6OEfG/8Nw7HkzRWBfjerZeMcMuJox14ERGR8cm3DaHkwRhDdcBLU32IxupAyfXZzsWShkr+3wfO4++vPos5NQGSjuXRbW3cdO8Wfv7ioZIotRmIJjnQEyGaKJ92ha3dYYLe4YdNg143bd3hgjx+dge+vT9KbdBLe3+U29ftYOPO9oI8voiISDmaeklwiqv0e5hfF2JWdQC/d2p18TDGsGppA/d9bAWfuGwxAa+L7nCCL//Pa9z23Wd4oa2n2EskkXI42BOhazA+pTvSZDXVhYgc94Iikkgxv64w5T9rN7XgdRtCPg/GpD963Ya1m1oK8vgiIiLlSAG8SCr8HubVBpldEyAwxYK4z+Piw29awIM3r+QPzpoFwO72Af7kkef5x5++zJG+aJFXCD3hOAd6IsSTU7PkJ2vNqmYSKUs4nm5xGY4nSaQsa1Y1F+Txi70DLyIiUo4UwIss5PMwtzbInJogQd/UCuIzK/385buW8fUPX8iy2VUAbHi1g5vu28r9T+0reilIPOlwoCdCbzhR1HXkY/WyRu64+mwaqwL0RhI0VgUKegCz2DvwIiIi5UiHMEtMNJGiOxyfcmPXHWt5/JV2vrWphc7BOAANlX7WvLWZK85oKPrkyunQrnAybNzZzp8/9jz90SRJx8HjclEV8PBv156vg5giIiKj0CHMKSLgdTOnJsjc2qm1I+4yhj84axYP3rySj7xpAV63oWMgxj/97BU+//BzvHakv6jri8RTtHVH6I9O3d3wYrEAJn0GAJP5vYiIiIybdsBLXCSe3hEvdjnHWB3sifDNJ1p4cvdRAAxw1TmzueWyxdRX+Iq6tkq/hxmVftxl1K5wspRCG0QREZGpSjvgU1TQ52Zu5rDmVOqaMrc2yB3XnM2XP3AezTMrsMAvXjrMjfdu4eGtrUU9HDkQS3KgOzLlynyKQYcwRUREJp4C+BQR8qW7pky1w5oXLahj7Q0X8/m3LaU64CEcT3H3phZueWAbT+05WrRWgUnH4VBvhM6BWFm0K5wsOoQpIiIy8RTAp5ig740a8YoSmUA5GrfLcM0Fc3nw5pW8/8J5uAwc6Inwtz/awRe//yL7OgeLtrbeSIIDPRFiSe2Gn0yx2yCKiIiUI9WAT3HxpENPJM5gLDVldnL3dQ5y14Y9bNvfDYDLwPsumMdNb15IVcBblDUZY6gP+agJnfj4030Ue/b5t3WHmT8Nn7+IiMh4naoGXAG8TCRSDr2RBP3R5JQI4tZaNrd0cdfGPRzoiQBQHfDw8bcs5j3nzSnaAcnj2xVmR7F73Yag100kkSKRsgXtxS0iIiJTkw5hljmv28XMSj8L6kPUhny4itx3ezTGGC5dMoN7blrOmlXNhHxu+qJJ7vzNLtY8tJ1nXu8uyrqy7QoHYklAo9hFRERk4imAlxm3y1Bf4WNBfYgZFX48rtL+X+zzuPjQiiYevHklf3jObAzQcnSQP/vvF7j9xzs4mNkdLyTHWtr7orT3RXm9a1BdQERERGRCTY1TfDJmLpehJuSlOuihP5akN5wgkSpe67/R1Ff4+LN3nsHVF8zla+t389LBPp7cfZTf7+3kAxfP58NvWjCsF3UhDMTS/a57InEq/W/UhqsLyNhM9xp6ERGR45X29qjkzRhDdcBLU32IxuoAPk9p/y8/fVYVd153AX/77jNpqPSTSFn+a0srN927lV/tOIxT4Pr2Dy1vIppw6I8mcBxHXUDGKFtD394fpTbopb0/yu3rdrBxZ3uxlyYiIlI0OoQ5DYXjSXojiZIfRBNNpHh4a+uwwT1nzK7ic1ecxllzqwu2ji0tXTy8tZUjfREWzKjgtrcu0Q5ujq6/ezP7OgfoiySJpxx8bhfVQQ+LZlRqkqaIiJQ9dUHJUAB/QzSRojeSYDBz4LBUHemLcvemFja82nHs2tvPbOSTlzfTUOUv6FqMMdSFvNSGfAV93Klq+T/9mt5wApfLYAxYC45jqQl52fa37yj28kRERCaVuqDICQJeN7OqA8yvC1EZSHf5KEWzqgP8n/ecxX986HxOa6wE4PFX2rnp3i18Z/N+YonC7eRba+kajHOwJ1LSNfWlIp50wIDLGAwm3Z3HcOwdDRERkelIAVzweVw0VgVoqgtSHfSWbBA/b34t3/jIRfzZH5xOXchLNOlw7+/28fH7t7HptY6C9j+PJlIc6I7QH00U7DGnIq87/XfJcSzWWhwn/f/I5y7Nv2MiIiKFoAAux3iG9BKvC/mKNgxnJG6X4Q/PncMDN6/kg8vn43EZDvdF+fufvMz//u/n2dMxULC1ONbS0R/jSF+UlDO9SrlydfqsamZU+PC4DSlr8bgNMyp8LJ1VuBp+ERGRUqMALidwuwx1FT6a6kq3l3il38On3rqEez+2nEubZwDwXGsvax7azlcef43ecOF2pgdjSQ50R0r+UGsxrFnVjM/jZnZNgDNmVTG7JoDP41YXGRERmdZ0CFNGZa0t+V7iW/d1cdeGPezvSg/IqfR7uOnNC7nm/LnHxsoXQk3QS32Fr2TLeIoh2we8rTvMfPUBFxGRaURdUDIUwPMzGEvSE0kU9OBjrpIph3XPH+T+p/YfGyW/oD7Ep1cvYeXi+oKtw+dx0VDlx+9xj/7FIiIiUrYUwDMUwCdGJJ6iJxIvybKL3nCC+57ax09fOEi2NPuS5npue+sSmuoLM8HSGEN9yEdNyDv6F4uIiEhZUgDPUACfWKXcS3xPxwBf37CH51p7APC4DH904TxuuHQhlf7CjLUP+tzMrPTjLWAZjIiIiJSGgvcBN8Y0GWM2GGNeMcbsMMZ8PnO93hjza2PMrszHuiG3+StjzG5jzKvGmHcOuX6xMebFzJ991WQKbI0xfmPMI5nrvzfGLJqs5yMnN7SXeFWgtFoYLmmo5P994Dz+/uqzmF0dIOlY/nt7Gzfes4WfvnCoIJ1LIvF0u8I+tSsUERGRjMnclksC/9taeyZwCfAZY8xZwF8Cv7HWLgV+k/k9mT+7DjgbuAq4yxiTLaL9BnArsDTz66rM9VuAbmvtacBXgC9N4vOREWTrnpvqgtQEvemBKyXAGMOqpQ3c//EV3HLZIgJeFz2RBP/+69e47TvP8Hxbz6SvwbGWo/0xDveqXaGIiIhMYgC31h6y1j6T+bwfeAWYB1wDPJD5sgeA92U+vwZ42Fobs9buBXYDK40xc4Bqa+3TNl0v8+Bxt8ne12PA20wpbcFOQx63ixmVfppKrJe4z+PiI29ayAMfX8k7zpoFwO6OAf70kee54ycvc7gvOulrCMeTtHWHjx0QFRERkempIIWpmdKQC4HfA7OstYcgHdKBbD+yeUDrkJu1Za7Ny3x+/PVht7HWJoFeYMakPAkZk2wv8QX1IWZUlk4v8YYqP3/1rmV8/cMXsmx2FQAbX+vgY/dt5f7f7SMyyd1dUo6lvS9Ku4b3iIiITFuTfhLNGFMJfB/4E2tt3wgb1Cf7AzvC9ZFuc/wabiVdwsKCBQtGW7JMIGMMNUEv1QEPA7EkPSXSS/zMOdV87cMX8vgr7XxrUwudg3Ee3LyfX7x0mFtXNXPlsoZj9exbWrp4eGsrh/oizKkOct2KJlY259fWcCCWJJpwmFnlI+QrzIFQERERKQ2Tui1pjPGSDt/ftdb+IHP5SKashMzH9sz1NqBpyM3nAwcz1+ef5Pqw2xhjPEAN0HX8Oqy1d1trl1trlzc0NEzEU5MxMsZQFfDSVB9iVnUAv7f4PbJdxvAHZ83iwZtX8pE3LcDrNnQMxPj/fv4Kf/zwc7x6uJ8tLV3cuX4XnYMxqgMeOgdj3Ll+F1taTvhrNmZJx+Fwb5SO/hiOdsNFRESmjcnsgmKAe4BXrLX/PuSP1gE3ZT6/CfjxkOvXZTqbLCZ92HJLpkyl3xhzSeY+bzzuNtn7uhZYb6dbX8UpqMLvYV5tkLm1wZLY/Q363Nxy2WLu//gKVi2dCcCOg318+rvP8K+/ehUDBL1uDIag143HZXh4a+vIdzoG/dEEB3oiREtwuJGIiIhMvMlMP28BbgBeNMY8l7n218C/AI8aY24BXgc+AGCt3WGMeRR4mXQHlc9Ya7OJ5DbgfiAI/CLzC9IB/yFjzG7SO9/XTeLzkQkW8LqZXeMmlkzREy5+L/E5NUH+/uqzefb1br6+YQ8tRwfpCsdxGagP+agNpbu7BLwuDvdFJvSxEymHgz0RjbIXERGZBjSIR0pGPOnQE46XRJeQlGP52YuH+M/1u48dlvS6DQ2VflwGZlYG+PcPnT8pj+11p1s6BkqgTEdERETGr+CDeETGyudx0ZgZ6lMZ8BR1F9jtMlx9/lz+5l1nEvKlg3AiZTnYG6V9IM4VZ0zeWYLsbnjnQIzp9gJZRERkOih+Aa7IcXweF41VARIhh55wgoFYsmhBdPWyBkI+N/c/tY+WowPEU5Z40uHO9bvY1xXmpksXUh30Tspj90YShOMp7YaLiIiUGZWgSMlLOZbeSIK+SAKniH9frbVsbuniro17ONCTrgGvDnj4+FsW8Z7z5k7a0KEtLV089kwbh3ojLKivYM2qZlYvaxz9hiIiIlJUpypBUQCXKcNxLP3RJL2RBEkn917iE93HO5Fy+MEzB3ho837C8fQ54cUzK/jM6iVctLBu3Pd7Mtk2iB5XugNLwnFIOXDH1WcrhIuIiJQ4BfAMBfCpz1qb81CfoQE24HURTTgkHcvnr1ya9zCdrsE49z65l1+8dPjY9KfLTpvJp97azNzaYF73nfWFR57nQM8gA7EUiZSD1+2iOuBh8cxKHl5z6YQ8hoiIiEwOHcKUsnH8UB+f59R/jR/e2nps93ii+3jXV/j4s3eewTc+ehHnzqsG4MndR/n4/Vv51m9bCMfz7+ayv2uQ7sEEScfichmSjqVzIM6rR/qJJ4s/UVRERETGTgFcprQKv4f5dSFm1wROelDxUF+EgHf4X/OJ7uN9+qwq/uNDF/B/3n0mjVV+EinL97a0cuO9W/nlS4fzqluPJx0w6amdBoPLGDDp6wd6IvSGExP2PERERKQw1AVFykLI5yHk8xBNpIf6ZHef51QH6RyMERwSzqMJh9nVE1MikmWM4YpljVy6ZAaPbG3l4a2tdA3G+ddfvcqPnz/IZ69Ywtlza8Z8v163IZZM178bA9ks73MbrLV0DsYIJ5I0VPrxuE/+enrjznbWbmqhtTtMU11IhzhFRESKTDvgUlbS0zUDzK0NUuH3cN2KJpKOJZJIYUl/TDqW61Y0Tdrj3/TmRdz/8RXHeoW/erifz33vOf7556/Q0R8b0/0tmlFJbdCLx21wrMXjNtQGvSycUXnsayLxFAd6IvRHT9wN37izndvX7aC9P0pt0Et7f5Tb1+1g4872/J6oiIiIjJsCuJSlgNfNrOoAf3TxPN573hy6BuPs6RikazDOVWfNyvsA5mhmVQf4P+85izs/dAFLG9Nh+fFX2rnp3i08tHk/sUQqp/u5bkUTXo+bmZV+Fs+sYGalH6/HfcILiJRj6eiPcaQvemxyJ8DaTS143YaQLz3YKOTz4HUb1m5qmbgnKyIiImOiAC5l7endnfxyxxFmVftZ2lhJfYWPX758hC0tXQV5/HPn13DXRy7iz//gdOpCXqJJh/t+t4+P3b+VJ17rGHXA0Mrmeq46a1bOLyAGY0nausMMxtIlOK3d4WHlNwBBr5u27vDEPEGRMrdxZzvX372Zy760nuvv3qx3j0RkQiiAS1nL7gBX+L34PG6qg158HsPD2/LvgpIrt8vwrnPn8ODNK/nQ8vl4XIYjfTH+4Scv84VHn2dP+8Apb7ulpYtfvnyE+gofSxoqcnoBkXIsR/qitPdFmV8bJHLcbnskkWJ+XSjn9SuAyHSlEi4RmSwK4FLWjt8BdhlDld/L0f4o1UEvxkzO9MqhtrR08YVHnucTD27j1cMD/MnblnJp8wwAnm/rZc13tvOVX79GTzh+wm3zaaM4EEvy/ovm0RuOs+tIP68c6mXXkX76IgnWrGrOae0KIDKdqYRLRCaLAriUtaa60El3gJvq0/XUC+pD1IV8kzpG/s71u+gcjFEd8NA5GOO7W17nmvPn8qX/dS4LZ4RwLPzkhUPccO8WHtveRnLIcKF82yg6DqQs2OyoIANjaYqoACLTmUq4RGSyKIBLWVuzqplEyhKOJ7E2/TGRssd2gN0uQ12Fj6a6EDMq/HhcE/tPYqQd7BWL6vnWDRfz2StOo9LvYTCW4q6Ne/jEg9v5/d5OIN1GMZoYPnBnLG0UH97aSqXfw8L6CpobKmmeWUlN0JtzgFYAkensVC/gx1LCJSJyMgrgUtZWL2vkjqvPprEqQG8kQWNVgDuuPvuEPtgul6Em5KWpPsjMKj/eU/TUHqvRdrA9bhfvv2geD928kmvOn4vLwOtdYf7qBy/x1z98kbcta8yrjeKwx7eQTDl4XIbWrsGcbq8AUnyqwS+e0V7Ai4iMlwbxSNlbvawx58EzxhiqA16qA14GY0l6IomcWwaeTK6DgGpCXj7/9qW89/w5fH3jHp59vYfNLV1s3dfNpc0z6AnHOToQY3Z1kOtWNOXcRvFkjx+Op5hZFaAvmqA64B3x9mtWNXP7uh2E40mCXjeRREoBpICyNfjeTP/3bA3+HaBhSgWwelkjd5AuxWrrDjNfg6xEZIIogIucQoXfQ4XfQySeoicSJxIfexC/bkUTd67fRSSRIuB1EU04I+5gNzdU8uVrz+N3uzv5xhN7ONQb5cndR9NlLD73qG0Lc3785U0c7Y8xGBt5iqYCSHENrcGH9MTXcDzJ2k0t+n9QIGN5AS8ikisz1h/oU93y5cvttm3bir0MmYJiyRS94QQDmR7budrS0sXDW1s53BcZ0w52POnwlV+/xv+8fOTYwUmv21AV8PIXf3BGzrvgoz2+yxhmVPqoGmU3fKrauLOdtZtaaO0O0zTFXkBc9qX11B7XrcdaS28kwW+/eGURVyYiIrkwxmy31i4//rp2wEVy5Pe4aax2U5dy6MkE8VxewK5srh/X5E2fx8WRvhhzagIMxJL0RdP1p12Dcf7llzu566MXMbs6kPfjOzY9RTMcTzGz0j9pHWGKYaqXcDTVhWjvjx7bAQfV4IuIlAMdwpSyN9GH2LxuFw1VfprqgtQEvbgmsZf4ob4IFX43s6sDNNUFCXjS/2R7Igk+dt9W7vvd3hMOSY7X8VM0y8FUb6OoQ4AiIuVJAVzK2mQOkvG4Xcyo9NOU6SU+GUF8aBvCoNdNU12Q+pAXr8sQTzo8tPl1brp3C7955ciY68NP5tgUzf4ojjP1y9OmehvFXLv4iIjI1KISFClrhTjElu0lXhP00hdN0BtJkJqg8HrCIcqkg9/r5vNvW8pr7QM8uq2VowNx/r+f7+SHzx7kc1eexhmzq/J+3IFokmjcYWaVb1j5w1RTDiUcOgQoIlJ+tAMuZa2QO6Aul6E25GNB/cQN9VnZXM9VZ82iazDOno5BugbjXHXWLC4/vYFbLlvM/R9fwaqlMwF4+VAft333Gf71l6/SNXjiWPuxSjoOh3un9m64SjhERKQUKYBLWSvGIBlj3hjqM6Miv0ONW1q6+NHzB0k4Di4DCcfhR88fZEtLFwBzaoL8/dVn8+8fPJ/mhgoAfrnjMDfcs4WHt7xOPOmMdPc5GYgmaeuOEI5PvdpwlXCIiEgpUhtCKWtDu2AMHSRTyBDmOJa+aIKecAJnjP/ePnH/VvZ3hXEZgzFgbbprycL6EN/+2IphX5tyLD9/8RD3PLmXvmg6LM+tDXDbW5fw5iUzhrWyG6+qgJcZFT5cZdQpRUREZLKoDaFMS6UwSCZbmlId8NITSdAXyT2It/ZEcBmOBV5jAMfS2hM54WvdLsN7z5/L6jMaePDp/fzouYMc7Inyf368g4sX1vHp1UtYPLMir+fSH00QiacKWhs+lft4T4Tp/vxFRMqRdsBFCizlWHrCcfqjyVGD+Dv/YxNYi2tIPbnjOGAMv/qTVSPe9vXOMHdt3M2Wfd0AuAxcff5cPvbmRVQH8x+6Uxnw5FRik0+ALIV3MIppuj9/EZGp7lQ74KoBFykwt8sca19YX+EbMcA21YVwMmUnFotjLY5NXx/Nghkh/u/7z+Wf/+gc5tcFcSz86LmD3HjvFn707IG8O7Wka8NH7huebxvIqd7HO1/T/fmLiJQrBXCRSXaqQUDuoV1TKv143Sf+c7z18maqg14MkEpZDFAd9HLr5bl18TDGcEnzDO65aTmfemszFT43fdEkX12/m08+uI3t+7vzem7H+ob3RU8a6PMNkFO9j3e+pvvzFxEpVwrgIpNo4852Pve9Z/j93k7auiP8fm8nn/veM8N2gI0x1AS9NNWHaKwO4PO88c9yZXM9X3znMs6aU0NDlZ+z5tTwxXcuG/Noe6/bxQeXN/HgLSt597lzMMC+zjB//tgL/J8fvcSBk9SUj8VAZopmfzQx7Hq+AbIYXWxKyXR//iIi5UqHMEUm0d/+8AX6Y28EKMdCfyzF3/7wBZ78q7ef8PWVfg+V/vSwoJ5wgmgixcrm+jEH7qG2tHTx8NZWDvVFmFMd5LoVTVx9/hy+tmE3Lx7o43d7Otmyr4v/ddF8PnrJghMOV57s9idbT8qxdPTHGIylmFnpw+N20VQXYl/nAH2RJPGUg8/tojroYdGMypzWvmZVM7ev20E4nhxWAz1d+nhP9+cvIlKutAMuMokO9MbGdD0r5PMwtzbI3NpgXt1GtrR0cef6XXQOxqgOeOgcjHHn+l10Dyb4jw9dwP9595k0VvlJpCwPb23lxnu38suXDh87HHqq22f7kJ9MOJ7uG94bSXBpcz3t/XHiqXQf83jKob0/zqU5vqBYvayRay+aR0d/jFcO99PRH+Pai+ZNmwOI6mMuIlKetAMuMolOdcwx1+OPAa+b2TVuYskUveEEAyMceDyZh7e24nGZY2Ug2V3Uh7e2srK5niuWNXLpkhk8uq2V721ppWswzr/+6lV+/NxBPnvlklFvfyqOtXQOxNj4WgczK7wMxFLHdsCrAh6ebunij3NY/8ad7Tz2zAEaqvwsyDz2Y88c4Lz5tdMmhGoUvYhI+dEOuMgkOlV/k7GOsfF73DRWB2iqD1EV8OY8VOdQX4SAd/g/84DXxeG+yJDfu7nx0kU88PEVXJkJeq8e6edz33uOnUf6OP5s6PG3H8mBngjVQS8L6kOcMauK5oZKZlb6c64BVxcQEREpRwrgIpNoXo1/TNdH43W70rvB9SFqQyO3MASYUx0kmhg+jj6acJhdHTzhaxurA/ztu8/kq9ddwOmzKo997f7OCJ2D8WNlKae6/UiPn3IsiVS6jeJYDhGqC4iIiJQjBXCRSfRPf3QeVX432ZzsMlDld/NPf3ReXvfrdhnqK3w01YWYUeHH4zr5P+XrVjSRdNKh15L+mHQs161oOuV9nzOvhrs+chF//s4zqPR7sEDnYJx9nWE6B+MkUs6Itz/V4zvWoS+SIJZwcj5EqC4gIiJSjhTARSbR6mWNfPLyZir9HtwuQ6Xfwycvn7hR4i6XoSbkpak+SEPVib3EVzbX8/krlzKjwk9/NMmMCj+fv3LpqF1VXMbwrnNm871Pvom3Lp2JAZKOpXMwTtDrob7Sl9P6VjbXc9VZs+gajLOnY5CuwTjvOLOR02dXkUg5o95+zapmEilLOJ7E2vRHdQEREZGpTqPoRSZRMUaJD8SS9ITjxJOjB9xctXWH+eYTLTy1pxNI17C/+7w53PyWRdSGTh3Gs11UPC5DwOsimnBIOpbPX7mUS5bMoL7SR3XAO+JjZ0fZt3WHmT/GUfYiIiLFdKpR9ArgIpPo+rs3s/foAP3R5LAuIItnVvK9Wy+Z1McejCXpiSSIHVfCkY9t+7r4+sY97O9M12BX+NMHON93wdyTTvL8wiPP0zkYG1bHHUmkmFHh598/dH7mPjzMqEj3DRcRESknpwrg+oknMoleO9JHx0CMcDyVKaVI0TEQY9eRvkl/7Aq/h3m1QebUBAkcd5BxvJYvqudbN1zMZ684jUq/h8FYim9s3MMnHtjG7/d2nvD1uXRhGYwlOdATOWGKpoiISLlSH3CRUWRLIFq7wzSNsQQiEncYWupsgZQD4fjElYeMJuhzE/QFicRTdIfjRPPcEfe4Xbz/onm8bVkj9z+1j5+8cJDW7gh/9YOXeNPiem5bvYQF9elDknOqgyfsgJ+si0p2iuZALMnMyhNr2UVERMqJfsqJjCBbw93eH6U26KW9P8rt63awcWd7TrePneKg4amuT6agz31sumbQl/+OeE3Iy+ffvpS7b7iYCxfUAvD7vV3c8sA27tq4m4FokutWNDEQS7Kvc5A9HQPs6xxkIJY8ZReVSDyVnqIZ1m64iIiULwVwkRHkOwjGOcUZi1NdL4SA182cmokL4s0NlXz52vP4h6vPZk5NgJRjeWz7AW64dwu/39uFtRYMGENOE4istXQOxjjQEyGWnLj6dRERkVKhAC4ygnwHwbhPEThPdb2QJjKIG2O4fOlM7vvYCj5x2WICXhe9kQQ/fO4Ag/EUjZUBmmdWsqi+gkq/h4e3to56n7FEioM9UboH40y3w+IiIlLeVAMuMoKmuhDt/VFCvjf+qYxlEMxpDZW8dmQAS7r+O7sJfFpDZc5ryKcGPRfZIB5NpGvEI/Hx7zr7PC4+/KYF/MHZs7jnyb38ascREilLW0+ESr+HhkrfmEbZW2vpDscZjCdpqPLj90zMYVIREZFi0g64yAjyHQTzl+86k/pKH36vC6/b4Pe6qK/08ZfvOjOn2+dbgz4W2SA+EV1TZlb6+eJVy1jaWIkvs92frgUPc6QvRkNlYEz3F0862g0XEZGyoQAuMoLVyxq54+qzaawK0BtJ0FgVGNMQndXLGvnytedzYVMds6sDXNhUx5evPT/n2+dbgz4e2cOac2ryL0255S2LCfncx0puLNAXTbK/a5DHXzkypjCd3Q1XbbiIiEx1KkERGcXqZY15lXzkc/vW7jC1weGTIsdSg56PbPvCfEtTjDG43QZSFgs4Nh3C//nnO/nRswf57JVLWDa7Ouf7y+6G1wa91Ia8GFMCBfUiIiJjoAAuMsnyqeHOtwZ9IuRTI/7w1tZM7bf/2LX+aIJwwqE3kuDlQ318+rvP8s6zZ/GJyxYzY8jXjWRobfjMSv+EDRoSEREpBJWgiEyifGu4861Bn0jj6ZpyskmYlQEPQa+Lr3zwfJY0VADwqx1HuPHerXxvy+vEk7n3SE/vhkc4OhDDcVQbLiIiU4MCuMgkyreGO98a9MkwliA+pzpINDE8UGcnYZ7fVMs3P3oxf/r2pdQEvUQSKb71273c/MBWfrf76Jjqw/siCdq6I4TjyXE9JxERkUIy062jwPLly+22bduKvQyZJi770npqg8PrlK219EYS/PaLVxZxZRNnpNKULS1d3Ll+Fx6XIeB1EU04JB3L569cysrm+mNfNxBN8uDmffzw2YOkMjvZFy+o5dNXnMbimRVjWk+l38OMSj9ul2rDRUSkuIwx2621y4+/rh1wkUnUVBcikhgeTAtdwz3ZRtoRX9lcz+evXMqMCj/90SQzKvwnhG9Il6V8evVp3HPjclYuTv/Z9td7+OSD2/jqb3bRF8l9NP1ALElrV5jecEItC0VEpCRpB1xkEm3c2c6fPfY8A7EkKcfidhkq/Z4xtSKcaqKJFF2DcaKJ8bcK3NzSyV0b99DWnR7YUx3w8LE3L+K9588d08621+1iRqVv2CFWERGRQjnVDrh+KknZm+xJkqMxADZdeoI1lHthRMCb7iMeiafoCseJjSOIX9I8g4sX1vGjZw/w4NP76Ysm+er63ax7/iCfueI0Ll5Yl9P9JFIOh3ujBH1uZlT48Xn0pp+IiBSfdsClrGW7kHjdhqDXTSSRIpGyBTvIeP3dm09oIxiOJ2msCvC9Wy+Z9McvBeF4ku5wYlxBHKA7HOe+3+3jZy8cIvvd6i1LZvCpty5hXl0w5/sxxlAV8FAX8qk+XERECkI14DItFWOS5FCt3WGCx/WoLtQgnVIR8nmYVxtkVnVgXDvQdSEfX3jH6Xzzoxdx3vwaAH63p5ObH9jK3Ztacu58Yq3NdEsJMxBTtxQRESkeBXApa8UOwNPhEGauKvwe5teFxh3El86q4isfPJ/b33MWjVV+EinLw1tbufHerfzypcM4Ob6bl3Is7X1RDvdGSaZy7zkuIiIyURTApawVOwCX0iCdUpEN4o3jCOLGGFaf0cADH1/Bx968EL/HRddgnH/91at85rvP8tKB3pzvKxxP0tYdoXcMHVZEREQmgmrApawVuwY8u4a1m1po6w4zvwiHQEvdQCxJ92CcxDh2o9v7onzrt3v5zZDJom9b1sitq5ppqEqPtd/S0sXDW1s51BdhTnWQ61Y0ndAG0e91M7PSh9+jkfYiIjJxTlUDrgAuZW+qB+Bid3EplP5ogp5wYlxB/KUDvXxtw25eOzIAQMDj4vqVC2ieWcFdT+wZdRAQpHfXa4Je6kLDByfJ1DZd/v2ISGlSAM9QAJeppBR28AvJWstALDmuIO5Yy692HOHbv22hO5wuK/G6DdUBL/VDQnUkkWJGhZ9//9D5J70fr9tFQ5WfgFe74VPddPv3IyKlR11QRMZp4852rr97M5d9aT3X372ZjUPKHSZbsbu4FFq6VaCX+XVBZlb58bhy/xblMoZ3nTObB29eyXUrmvC6DYmUpXMwTltP5NhgoIDXxeG+yCnvJ5FyONgT4ehADMeZXhsU5Wa6/fsRkalDAVxkBNkdtPb+KLVBL+39UW5ft6NgIbzYXVyKxZj0znVTfZAZlWML4hV+D7euaubem1ZQHUj3X48kHF7vjnCkL8pgLMXs6tH7h/dFEhzoiRCJj3+ipxTXdP33IyKlT5MwpezlUwM6dAcN0j2tw/Ekaze1FOQt7Ka6EPs6B+iLJImnHHxuF9VBD4tmVE76Y2cVs4Y2W5ddHfDQF03SG06QdHIrTZlXF+Sv33Um//qrnfRFkyQdS280SV80yYVNtSRSDl73yME+kXI41BuhMuBhRoVfA3ymmKa60AmDsKZrG1ARKS3aAZeylu8OdrF30C5trqe9P0485eAyEE85tPfHufS4A4STZSLeAZiIEp5sEG+qDzKjIvcd8ZXN9fzFO5dx9pxqqgIe3MZggZ+9dJhbHtjG5pbOnO5nIJqkrTtMf1QtC6cStQEVkVKlHXApa/nuYE/EDlo+O8hPt3TRUOmjP/rGDnhVwMPTLV38cc4rGL98//sNPQQ3NMDfAePaRTfGUBPyUh300BdJ0hOJkxqlTntlc/2xjie9kQQPPLWPdc8fpK07wl//8CVWLq7n029dwoIZI/8/TTmWjv4YA7EkMyr84xomJIW1elkjd8CU7oIkIuVJAVzKWmt3mNqgd9i1sexgr1nVzO3rdhCOJ4d1Uch1By3fANraHWZmpZ+GqsCxa9bagu3A5/vfb7JKeMYTxAFqgl7++G1Lee/5c/n6ht0883oPW/Z2sX1/N3904VxuvGQRlYGRvy1G4ikOJCLUBr3UFqBlodro5Wf1skb99xKRkqMtHClr+U7CXL2skTuuPpvGqgC9kQSNVYExtTDLtwtDsSd55vv4k13Ckw3iC+pDY6rRXjyzgn+79jz+8ZqzmVMTIOVYHtt+gBvu3cJPXzg4api31tIdjtPWPbmHNIt9CFhERCaHAriUtYmoAV29rJHv3XoJv/3ilXzv1kvGtJuWbwAtdg1rvo9fqBcQ2SDeVBeivsKXUxA3xvCW02Zy38dW8MnLFxP0uumNJPj3X+/iU9/ZznOtPaPeR/aQZntflOQ4BgiNRm30RETKkwK4lLV8d7Dz1VQXonMwRkvHADsP99HSMUDnYKxgO/D5yvfx16xq5uhAjJcO9PLigV5eOtDL0YHYpL2AcLkMtSEfTXUh6kI+XDmUh/gyUzMfvHkF7zx7FgB7Ogb5wqPP8/c/2cHh3uio9zEQS9LaHaEnHGcih5sV+xCwiIhMDtWAS9krZg3opc31bNnXhcswrIvJ9Sty72JS7BrWfB7/hbYe+iLJYdf6IkleaOuZ1OfkchnqKnxUB730RhL0RRI4owTjGZV+vnjVMq65YC5fW7+blw/1s+m1ozy9p5MPLm/iwysXEPSdejqmtZauwTj90SQzKn3DDu6Ol9roiYiUJ+2Ai0yip1u6qPK7STmWWNKScixVfjdPt3QVe2kF8e0n9+JxGwJeN0Gvm4DXjcdt+PaTewvy+G6Xob7CR1N9iJpgbgcml82u5j+vv5C//sNlzKz0kUhZvvv717npvi08/sqRUXe4EymHw71RDvdGSeRZllLsEiQREZkcCuAik+i1I30MxlN4XS4CHhdel4vBeIpdR/qKvbSCGIynOL4c22XS1wvJ7TLMqPTTVBekKuAd9euNMbz9zFk8cPNKbrhkAV634ehAnH/++U4+973n2Hl49P9/4XiStu4I3YPjL0spdgmSiIhMDpWgiEyiRMriOJYUFmvBGDBAPDVxdcKlrMKXbt04NIQ7Nn29GDxuFw1VfmqCXroG44TjyRG/Puh18/G3LOZd58xh7aYWnnitg5cP9fHp7z7LO8+exScuW8yMSv8pb5/tljIQG39ZSrFLkEREZOJpB1xkkqUsZDdArU3/frr4xGWLcSwkHQfHOpmP6evF5PO4mF0TYE5NEL939BcDs2sC/N17z+IrHzyfJQ0VAPxqxxFuvHcr39vyOvHkyKUm2bKUI5PULUVERKYWBXCRSeYyYHnjV46tqsvCH7/9dD5/5WkEvW6STnpH+fNXnsYfv/30Yi8NgKDPzbzaII3VAbzu0b8dnt9Uyzc/ejFfeMdSaoJeIokU3/rtXm5+YCtP7jo6aqnJ4CR1SxERkanFTLcfAsuXL7fbtm0r9jJkmjjn737BQOzEHc8qv4sX/+FdRViRnIq1lt5Igp7w8I4pW1q6eHhrK4f6IsypDnLdiiZWNtczEE3y4OZ9/PDZNwb3XLSgls9ccRqLZ1aM+nhet4u6Ch+VflUCioiUK2PMdmvt8uOvawdcZBK5jOtYC0IDb3xu9E+v1BiT6SFeHzp2UHNLSxd3rt9F52CM6oCHzsEYd67fxZaWLioDHj69+jTuuXE5Kxen20o+83oPn3xwG3f+Zhe9kcSIj5dIObT3RTnQEyGaKOyhVBERKS5tvYhMIp/HhTtucLkMxqRrwB3H4vNMnwC+cWc7aze10NodpqkuxJpVzSV9qNDtMjRU+akOenh0eyselzk2DCfoTR8qfXhrKyub06F7wYwQ//L+c9nc0sldG/fQ1h3hx88dZP3Odm66dBFXnz8HzwjlLbFEioM9EUI+D/UVvmn1d0NEZLrSd3qRSbS0sYqZVT48LkPKsXhchplVPpY2VhV7aQWxcWc7t6/bQXt/lNqgl/b+KLev28HGne3FXtqo/B437f0xqvyeYf3DA14Xh/siJ3z9Jc0zuOem5dy2egkVPjf90SRf27CbTz60nW37Ru/7nm5bGKajP6aDmiIiZU4BXGQSrVnVjNftZnZNgDNmVTG7JoDX7Z42g1TWbmrB6zaEfOkQG/J58LoNaze1FHtpOWmqCxFLOXjdBrc7XUcUTTjMrg6e9Ou9bhcfuHg+D96yknefOwcD7O8M8xfff5G//dFLHOg+Mbgfrz+aoLU7QtdgHMeZXmd0RESmCwVwkVFs3NnO9Xdv5rIvref6uzePafd29bJGrr1oHh39MV453E9Hf4xrL5pX0iUYE6m1O0wy5dDSMcDOw320dAyQTDm0dYeLvbScZCdRRhIp3MaQTDmkrOW6FU0j3q4u5ON//8HpfPOjF3He/BoAntrTycfv38rdm1oYjI3cf9xaS084Tmt3WB1TRETKkAK4yAjyLaHYuLOdx545QEOVnzNnV9FQ5eexZw5MiRKMiVDl93CgJ0rSsbhdhqRjOdATnTKdP46fRDmrOsg/v+9c3nvBXDyu0b99Lp1VxVc+eD63v+csGqv8JB3Lw1tbufHeLfzipcPDuq2cTMqxdA3Gae2K0BdNKIiLiJSJqfFTUKRI1m5qIZ5M0TmQJJ5y8LldVAU8rN3UktMu9tASDICQz0M4nsz59lPdscCYzY32uOtTwKkmUQa9brrD8VG7nRhjWH1GA5c21/Po9ja+9/vX6Q4n+LdfvcqPnzvAZ684jXPm1Yx4H0nH4Wh/jN5wYtwTNUVEpHTou7jICF470kdfNIkLkylBsHQOxkmm+nK6fWt3mNqgd9i1oNc9ZUow8jUQTzGvNsDRgfixFzCzK/0MxnNvu1eqXVRcLsOMSj+VAQ9dg3Eiozwnv9fNDZcs5KqzZ3P3phZ+s7Od144M8McPP8eVyxq59fLFNFYHRryP7ERNdUwREZnaFMBFRpDIzI13ZcZXGpNuIxjPcZ58U12I9v7osB3LSCLF/LrQxC+2BGWff3ND5bFr4XiSxqqRg2ZWtgTI6zbDSoDugJxD+GQHeL/HzZyaIOF4ks6BOIlROpg0VPn5m3efyTUXzOXrG/bw6pF+1u9s53e7j3L9yiY+uLyJQKbt4amE40kiiRTVAQ91Id+xv58iIjI1aPtEZAQ+jwssONZisemaXUvOO4/ZQ3zheBJr0x8TKTttuqDk+/zz7aJSyDaIIZ+HpvoQM6v8uHMIxOfMq+HrH7mQv3jnGdRX+IglHe5/aj8fu28rG3a2j1qmk53c2dodpi86chmMiIiUFgVwkRHk28f7+EN8jVUB7rj67JIooSiEfJ9/a3f42BCcrLGU8BSjDWJ1wEtTXYjakG9Y//CTcRnDVefM5sGbV3D9yia8bkN7f4x//Nkr/Mkjz7PrSP+oj5dyLEf7Y7R1hwnHR+6uIiIipUElKCIjWLOqmdvX7WB2jefYFMSx7mCf6hDfdJHP82+qC7Gvc4C+yBuHYKuDHhbNqBz9xhSvBt/lMtRX+KgKePjXX+zkv7a8TiSRIuh188GL53PDmxcN+/qQz8MnL2/mD8+dwzc37uF3ezp58UAvn/rOM/zhuXO4+bJF1IV8Iz5mPJmuDw/63NSFfKOWsYiISPFoB1xkBNN9B7vYLm2up70/fYDTZSCecmjvj3NpZgz8aJrqQnQOxob1Ie8cjBWsBv8bG3Zz71P7iCVTeFwQS6Z4YPN+Hnpq30m/fl5tkH983zn827XnsWhGCAv87MVD3HjPFv57W+uo9eUAkXh6tH17XzSnrxcRkcLTDrjIKKb7DnYxPd3SRXXATW8kScKCy0BN0MPTLV38cQ63v7S5ni37unAZhgX461fkFuDz9e0n9+Iy4HG5sdbiMumWgo9ubzthF3yoixfW8a0bl/PTFw5y3+/20RdN8o0nWvjJC4f49OolXNI8Y9THHoglGYynqMoc1MylLl1ERApDO+AiUrJ2tfczEE3hdbsIeF143S4Goil2tY9eGw3pAN9Q6cPnduFY8LldNFT6eLqla5JXnjYYT5HNvcYYjDG4TLoTzmjcLsM1F8zjwZtX8kcXzsNloK07wl//8CX+8vsv8Hrn6GU01lr6Iglau8J0a7S9iEjJ0A64yChKtQ/1dBBPOmDShxUh0wbS2PT1HLR2h5lZ6adhSNtDa23B+rBX+NwMxpJYUlibXr8BKv0eGqsDdA3ESTojP5fqoJfPXXka7zlvDndt2M3213vYsq+b7Q9u430XzOXGSxdSFfCOeB+OtXSH4/RHk9SEvFQHPKMeEBURkcmjHXCRERSyjZ2cyOtOh0THsVhrj+3g+ty5hcemutAJu82F7MP+tmUNpCw46e6VOBZSNn290u9hfl0wp24pAItnVvCv157HP15zNnNrA6Qcy/efOcCN927lJ88fJJXD7nbScegciNHWHWEgpo4p08HGne1cf/dmLvvSeq6/e7O+d4mUCAVwkREUo42dvOH0WdXMqPDhcRtS1uJxG2ZU+Fg6qzqn2xe7D/vhvjh1Ic+xMhSXgbqQh8N98fTvM91S5tUGCfpO3rVkS0sXX3jkea7/1mb+96Mv4HW5uPemFdx6+WKCXje9kQRfeXwXa76znedae3JaVyLl0N4X5UBPRK0Ly5g2EERKlwK4yAjy7UMt+Vmzqhmfx83smgBnzKpidk0An8edc4Audheb1u4w1QEvQa8br9sQ9LqpDnhP+Pvj87iYUxNkVnUAj+uNb8tbWrq4c/0uOgdjVAc8dA7GuHP9Lp57vYfrVi7goVtWctXZswFo6RjkC48+z9+v28Gh3khO64slUhzujXKwJ0I0h7p0mVq0gSBSulQDLjKC6T5KvthWL2vkDtJBoq07zPxx1OAXs4tNld/DrvYB3C6D22VIOpYDPVGWNp68j3mF30PI56YnnKAnkuDhra14XObYi8BsL/qHt7aysrme+goff3HVGVx9wRy+tn4PLx/qY9Ouozzd0skHlzfx4ZULTrmzPlQ0kW5dqB7i5aVYffBFZHQK4CIjyA7iCceT4x7EI/mZym0gj42Tz5Zn2+Oun4QxhroKH5UBD0f6o1T6h4fhgNfF4b7hO9zLZlfzn9dfwPrMgeGjA3G++/vX+eWOw9x6eTNvO7Px2EHWkUTiKSLxCCGfh7oKL36PgvhUpg0EkdKlEhSRERS7hEGKL59DbAPxFPNqA8Nq2OfVBhiMj17u4XW7WDSjgqRjhx3SjCYcZlcHT/h6YwxvO3MWD9y8khsuWYDP46JzIM7//cVOPve9Z3nlUF/O6w7HkxzojtDRH8vpcKeUpmKfgRCRUzMj7cSUo+XLl9tt27YVexkiMgVkD7Fl67ez74Dk+iLs+rs3s/foAP3RJPGUg8/toirgYfHMSr536yU5Pf6fP/Y8fZEEScfidhkq/B6++M5lrBxlGujhvih3P9HCxtc6jl37g7Nm8YnLFzOz0j/6k89wGUNdyEd1UK0Lp6JsG9XxlnCJSH6MMduttcuPv64SFBGRU1i7qYV4MkXnwPAAvXZTS04h5mSTODsG4nx4Ze6TOC1gXAYXb/QRz8Xs6gC3v/csrmnr4evr97C7Y4D/efkIm3Z18NE3LeTai+fj84z+JqhjLZ2DMfqiCWZU+oaVM0jpm8olXCLlbNJKUIwx9xpj2o0xLw25Vm+M+bUxZlfmY92QP/srY8xuY8yrxph3Drl+sTHmxcyffdVktmCMMX5jzCOZ6783xiyarOciItPTa0f66ByMk0xZ3MaQTFk6B+PsOpJbOcfTLV00Vg2fxNlYlfskzrWbWqgJelnaWMWy2dWcPquaugofP3zuQM4HJc+fX8s3PnoRX3jH6dQGvUQTDt9+ci8fv38rv911dMR69KESKYfDvVEO90aJJdUxRUQkH5NZA34/cNVx1/4S+I21dinwm8zvMcacBVwHnJ25zV3GmOxPl28AtwJLM7+y93kL0G2tPQ34CvClSXsmIlI0+Q4Syef2iVQ6nLpcmTHymYbe8VRuobW1O0wy5RwrXYkkUiRTTs5dKE7VBvNgT4S5tUEaqvzD2haeittleM95c3jw5pV84OL5uF2GQ71R/m7dDv7ssRdo6RjIaT3wRn14e18054mkIiIy3KQFcGvtJuD4bZ5rgAcynz8AvG/I9YettTFr7V5gN7DSGDMHqLbWPm3T2zQPHneb7H09BrzNqEBRpKzkO0gkW0P97OvdHO6N8Ozr3fz5Y8/nfHufx4XjWKLJFNFEimgyhePYnEo3AHAcOgYSZM8xOhY6BhLYUcbPZ402ybMq4B3TNM3KgIfbVi/hnpuWc0mmhvzZ13u49aHt3Pn4LnojidyeFzAQS9LWHVYQFxEZh0J3QZllrT0EkPmYLUybB7QO+bq2zLV5mc+Pvz7sNtbaJNALzJi0lYtIweU7SORLv9xJdziBBTxuFxboDif40i935nT7huxhxcwo+WwbwYYcDzF2DJ480J7q+vFy6WKRyzTN4y2oD/HPf3Qu//f959BUF8Sx8OPnD3LjvVv4wTMHSKZyD9QK4iIiY1cqbQhPtnVjR7g+0m1OvHNjbjXGbDPGbOvo6DjZl4hICcp3EmnL0cHMAUiDweAyBpdJX8+FtekWgD63i4DHhc/twhiTc9107BSB9FTXjzeWNpjZaZqNx03THMmbFs/gnpuW8+nVS6jwu+mPJvnaht188qHtbNuXW5161rEg3h8dU4AXEZmOCn2c/YgxZo619lCmvCT7PnAb0DTk6+YDBzPX55/k+tDbtBljPEANJ5a8AGCtvRu4G9JtCCfouYjIJJuIQSKOtSSTKaxNdxFxGXDnWK2W7eN9dCB+rAvK7Ep/Tn28If142cfNOv73oxlrF4tKv4eQ101XOE5fDiUlHreLay+ez9vPbOS+3+3jpy8cYn9nmL/4/otc2jyDT69ewry6E/uOn8pANMlgLEV1wENtyIfbpcpAEZHjFXoHfB1wU+bzm4AfD7l+XaazyWLShy23ZMpU+o0xl2Tqu2887jbZ+7oWWG+nW1NzkTK3ZlUzfZEEu47088qhXnYd6acvksh5kEhDhZekk669tqQ/Jp309Vw01YXwuF00N1SybHY1zQ2VeNyunF8AzKtOl6pY+8avodcni8tlmFnpZ15dkGf3d/OFR57n+m9t5guPPM+WU3RgqQ35+NN3nM7aGy7m/Pk1ADzd0snH79/K2if2MBhL5vz41lp6Iwlau8L0hOM5v2MgIjJdTGYbwu8BTwNnGGPajDG3AP8CvMMYswt4R+b3WGt3AI8CLwO/BD5jrc1uMd0GfJv0wcw9wC8y1+8BZhhjdgNfINNRRUTKiwUw6UmPmFPUmZ1CVdB3rH82mY+uzPVc5DtJ8J/+6Dyq/G6ym8AuA1V+N//0R+eN4VmM39O7O7lz/W56InGqA146B2PcuX7XKUM4wGmNlfz7B8/n7957FrOq/SQdyyPb2rjx3i384sVDOGMI0461dA3Gae2K0BfN/YCnTJx8uwiJyOTQJEwRKVnX3735hBKUcDxJY1Ugp0mSl31pPW7DsBKSmZU+HAu//eKVOa0h30mCxZxEOPS/n7WWpGMZjCWZUeHn3z90/qi3jyVSPLq9je/9/nWimbr1pY2VfPaK0zg3s0s+Fl63i/oKHxV+DfMphHwnuYpI/jQJU0SmnNbuMG4DLR0DwwJ0rocwm+pCvHq4j0gihWMh5aTojyY5Y3b1mNcy3q2KYk4ibO0OUxtMl9sYY/C6DZV+D0f6Ijnd3u91c8MlC7nq7Nl867ctPP5KO7vaB/j8I89xxRkNrFnVTGN1IOf1JFIOR/qiBLxu6it8OQ8TkvEZ2kUIIOTzEI4nc57kKiKTp1S6oIjIKUznt5Cr/B4O9ERJOha3y5B0LAd6olTmuIM6u9pHV3h4H+6ucILZ1bmVoOTbh7zYmupCHB2I0dIxwM7DfbR0DNAdjrNwRgXVwdzq4AEaqvz89R+eyX9efwFnzK4CYMOrHdx031YeeGof0cTYJmNGEykO9qSH+STUMWXS5NtFSEQmjwK4SAmb6gEwX8dK5OyQX0Ovj+I3OzsybQjTfUuzn/9mZ27tSPPtQz4R8nkBdmlzPR2Z8huXgXjKoWMgzpuXzGBmpZ+5tUG87tx/DJw9t4avf/hCvnjVGdRX+IglHR54ej8fu28rG3a2j/mwZbp1YYSjAzG1LpwEow1yEpHiUQAXKWGlEACLKdsG0OM2pKzF4zbMqw3k3AZwMJ7C6zb4PW4CXjd+jxuv2+R8+2LvIOb7Auzpli4aq3z43C4cCz63i8YqH09nDmEGvO5jkzRz5TKGd549mwdvXsH1K5vwug3t/TH+8Wev8CePPMeuI/1jeo7WWvoiCVq7I3QOxEg50+tc0mTK9xCxiEweBXCRElbsAFhs+bYBrPC5iSctkUTq2K940lKR48TIYu8g5vsCrLU7TDLlHDt8F0mkSKacYX9/jElP0hzrbnjI5+GTlzdz78dW8JbT0kOIXzzQx6e+8wxf/p9X6Q7Hx/Rch7Yu7BqMK4hPgLEMchKRwtIhTJESNhGDaKayNauauX3dDsLx5LAuDrnu4J09p4qn93YPu2Yz1wvx+PBGF5TW7jBNY+yCku8hVKylY+CN9n+OhY6BBPNrT3wBkt0N7xqM05vDAJ+sebVB/vGac3hmfzdf37iHvUcH+fmLh3ni1Q5uuHQhf3ThvDEFe8daejJDhGqCXmqCXlwa5jNuxTwELCKnph1wkRI23d9CzncHb8eh/hO+ybky1wvx+Bt3tvNnjz3Ps63dHOmL8mxrN3/22PM5l5BU+tzpQ6gpi9sYkqn0IdRcd/C7BtNB2gz5NfT68YwxzBhHbTjARQvruPuGi/n8206jOuBhMJ7im0+0cMsD23h6T+eY68Mda+kOx2ntTg/zcbQjLiJlRDvgIiVs9bJG7oCi9ZEuBfns4A3GU3g9Bpd5I0w61sm5Bjzfx/+XX7xCTziB2xjcxmAd6Akn+JdfvJLTfZpjE4R4Iz3bIddHEUs5eF2QykzhNAY8Jn19JAGvm3m1wZzH2We5XYZrLpjHFWc08sDT+/nxcwdo647wNz96iRWL6vj06iUsnFGR8/0BpBx7bFe+NuijOujJ+fmLiJQqBXCREqe3kMevwudmMJ7E2tSxAGoMVPgK861vb2c43XklU0JhDFjHsrcztxKS/liSebWBYYOEZlf7GchxLHyFL1024x+ym510HCpy6L+dHWdf4fPQ0R8j6eTepaQ66OVzV57Ge86bw10bdrP99R627uvmlge28b4L53HTpQupCuTeBhHSQbxzMEZvJEFNyEt1QEFcRKYulaCISNl627IGUk669tlCZhhP+nqhJFPDD4EmU7mXUuR7CPUTly0mmbJEM48dzTz+Jy5bnPMagr50bXhlYOwvWhbPrOBfrz2Pf7zmbObWBnAs/OCZA9xwzxbWPX9wXActk45D50CMtu70ePvpNs1ZRMqDAriIlK3DfXFC3uHf5kJeF4f7xtahY7yqAh6O3zd2Mtdzke8ZgPPm11IdHP5Y1UEP582vzen2WS6XobEqwKzqAO4xHog0xvCW02Zy700ruPXyxQS9bvqiSf7j8V2s+c52nn29e/Q7OYlEyuFofzqI90dzL5MRESkFCuAiUrZeO9JHwrH43S4CHhd+t4uEY9l1pK8gjz94ilKRU10/Xr6HQNduaiHkcxPyuTPtDNOfj7ePfIXfw/y6EBU5TiIdyudxcd3KBTx0y0redc5sDNDSMcj//u8X+Lt1OzjUGxnXmhIph47+GK1d4ZxLc0REik014CJSthKZco+hNdiOY4mPoQwkH/GUxePKlMBkatDTEylzf/x8zgDsau+nezCe3oW3kHTSZSiJPJ6/22WYVR2gP5qgcyCOM8YSkPoKH3/+zjO4+vy5fG3DbnYc7OO3u46yuaWTDy5v4sMrFxAc0uVlS0sXD29t5VBfhDnVQa5b0cTK5voT7jeRcmjvi9LtdlFX4aNyHC8SREQKRTvgIlK2fB4X2HRLO4tNh0WbuV4AFT43x5c5O5ac2wjmKxxLHeuAYkl/TNn09XxVBbzMrwsOC8tjccbsKr563QX8zR8uo6HSTyJl+e7vX+fGe7fwPy8fwbGWLS1d3Ll+F52DMaoDHjoHY9y5fhdbMpM8TyYbxNu6wzm/0yAiUmgK4CJStpY2VjGzyofHZUg5Fo/LMLPKx9LG3Abx5Ottyxpw7PBDoI4t3CHQaOLkQftU18fK43YxpybIjAr/uDqSGGN425mzuP/mFdx4yUJ8Hhedg3H+5Rc7+dz3nuWeJ/ficRmCXjeG9EePy/Dw1tZR7zuedDjSF+VAT4RwXEFcREqL3qMTkZKWzyTJNaua+fwjzxKOp7BAMpXC4zYFG2R0uC9OfchLTySBY9PlJ7VBb8EOgZ6qOGSiC3BqQl6CPjcdAzFi4wj3Qa+bj71lEVedO5u7n2hh42sdvJIZlhT0urDWknQsXreLupCXw32514vHEikO96bwe93Uh3zj3rGXqSmf7x8ik0kBXERK1sad7dy+bgdet6E26KW9P8rt63ZwB+T0Q/SFth76IsN3P/siSV5o6ynID+HW7jBVAQ+xpHOsj3dVwJP7KHnyCxCFCuCQLuuZVxukJxynO/xGe8Bca7gBZlcHuP29Z/G+th6+tmEPu9sHiCTSfWTcrnR5yZG+2JiH+UA6iB/qjRDwuqmv8BHIoRe6TG35fv8QmUwqQRGRkrV2U0ume0d66ErI58HrNjl38fj2k3vxuA0Br5ug103A68bjNnz7yb2TvPK0fEfJ5zvK/lRFIZM5vqY25GNebRC/1z2uGm5It0/8xkcuYmaF79i1lAPJbE/3MQwFOl40keJgT4RDvZEJK8WR0rR2UwuJVIrDvVFePdLP4d4oiVRqTF2ANu5s5/q7N3PZl9Zz/d2bc/63JzIaBXARKVmt3WGCx+1UBr3unHeQB+MpsJZYMt39I5ZM/34so+jzccIoeXPc9VFkR9lbhxNG2efCfYrv8Ke6PlGyu+Hff6Zt3DXcbpchdZIOKxZo7YnS0jGQ1xoj8XQQP9wbTf+9kLKzq72fo/1xko7F7TIkHcvR/ji72vtzun2+L4BFRqISFBEpWU11Idr7o4SGjI6PJFI5T4L0u12EE6ljO77WQsJywnCekeRTApLvKPl8R9kvbazi1cP9WPNGG0RjKdgh1EN9UWoCHlI23f4RIOB15VzDHU86eFzgdrlwrCXlWBwLScdy60Pbec95c/n4mxdREzr1WPuHntrHo9vbiCRSBL1uPnjxfG5486Jjfx6OJwnHk1T6PdSGfAXrkCOTL550wIDLDGlDamz6eg6yL4DdxpzwAlglLJIvfacRkZKV7yTI+op0MLNDfg29PppsDWl7f3RYDWmuO2D5jpLP1xevWsaMSh9+twuPK/2CZEaljy9etawgj99UFyKadPC6XXjcLjAQTTjMrg7mdHuv2+BYiCUdEql0+DakD7M6FtY9f5Ab7t3CD55pI5k6MVQ99NQ+Hti8n1gyhdsFsWSKBzbv56Gn9p3wtQOxJG3dYTr6Yye9L5l6vO508HYci7X22ItAnzu3d6CGvgA2xuByGVyGnF8Ai4xEAVxESla+kyAxhoZKL9np6S4DDZXenEtA8q1BX7Oqmb5Igl1H+nnlUC+7jvTTF0nk/AKieWZFpnXhG33MHZu+novVyxr5t2vP58IFdcypCXLhgjr+7drzC7Z7N/QFlMtAMuWQcizXrWjK6fb1IR8nm/OzsC7IbauXUOF3MxBL8rUNe/jkg9vZum94bfmj29twmfQOusu4Mh/T10+lP5qgtTtC50CM1PFN3GVKOX1WNTMqfHjc6XImj9swo8LH0lnVxV6aiEpQRKS05TMJMlvCMrvmjR3ncDxJY1Ugp9u3doepDQ7fLR9LDTpkdt1Npu7bjK0DyRevWsafP/Y8/dEkyZSDx5VuwzeWHex8/vvla/WyRu4g/UKmrTvM/EwJz4UL6ugKx491SjklYzAM/29mAONy8YGL5/OOMxu573f7+NmLh9jfFeaL33+RS5rr+fTqJcyvCxFJpHCRLkWwmdu6TbqMaSTWWnojCfqjSWqCXmqC3mNlQDJ1rFnVzO3rdjC7xkPQ6yaSmQI7lhfAu9oHMNamy78yffyXNoy9C4/I8RTARaRsZX8Ah+PJcf0AzrcGfe2mFmqCXubUvFFyEY4nWbupJadQnN3BPj7AjiVQf/Xx1/j2k3sZjKeo8Ln5xGWL+eO3n57z7fN1qhcAAZ+Ljv7YiPW43eE4x/+pk7kO6Y4rf/qO04+NtX++rZfNLV1s29fN+y+ah9dliKXeiO8WSFoI5Fjn7VhLdzhOXzRBbdBHddAzroFDUhynegGY67+fiXgBLHIqCuAiUrby/QGcb4CfiB30fHawv/r4a9y5fjcuAx5X+sXDnet3AxQ0hJ+M3+NmXm2Q7nCCnvDJBxNFTtGt5vjrSxor+fcPns9vdx3lm0+0cLgvyqPb2jjVpnVNcGw/+lKOpXMwRk8kTk3QS3VAO+JTRT7/fibiBbDIqSiAi0hZy/cH8LVtPSfsIOd6f/nuoOcr3e/cpntoZ7ugmPT1YgdwSJfl1Ff4CPncdPTHSBx3+DF2it3xk103xrDq9AbetLie/97exn/9/nWix32dAWpD49/FTjmWrsE4vZGEgvg0UcwSromgSaClS4cwRUROYePOdh575gANVX7OnF1FQ5Wfx545kHMXlHwPYeZrIJYk5aRrV8nUsKYccm6DWCgBr5v5dUGqj3u3YDyTPP1eNx+9ZCEP3LySuuPaE1b6PQS87py7sJxKNoi/3hWmezCuw5pSkvLt4iSTSwFcROQU8u2CAvkdwszXsEFAQz6WYh2zMYaZlX5m1wTwuPL/0dRQ5eeL71zGjArfsbZz/bEkh3pjzKj0TcgUzGyNeGsmiDsK4lJCJuL7l0welaCISEkr5luo+dZw53sIM19Br2EgZk9o5Rfyll4Azwr5PMyrc9M5EDuhA0pWrqtf2VzPhU01/GZnx7Drv9nZzosHerl1VTNXnNGQ9wuSbBDPlqaoa4qUgok4gyKTRzvgIlKyiv0WalOmld1QY6nhbu0OE/S6h10r5A/Ac+fVURv0DOuDXhv0cM68uoI8/ni5XYbG6sC4SlCGeuipfTy+s+OEr3cZaO+P8U8/e4XPP/wcrx3JbTT5aI7tiHeH6QlrR1yKK9/vXzK5FMBFpGQV+y3UfCdxFvsH4JpVzVQHfSyeWcE5c6tZPLOC6qCvYDXoxfbA0/tPet1auHzpTABeOtjHbd95hi//6lW6Bk/ejWWssjXird0qTZHiyff7l0wuBXARKVnF3kHOdxJnsX8Arl7WyLUXzaOjP8Yrh/vp6I9x7UXzpkwXhHyLOE7VYdwC/3D12Xz5A+exeGYFFvj5S4e58d4tPLK19YRuLOOVctI74q93hemaooc1N+5s5/q7N3PZl9Zz/d2bdYBvCsl7krBMKtWAi0jJKnYbP8i/jWE+fcjzNbSLy4JMH/PHnjnAefNrp8QPYY8LEifJwp4JKq++aEEdd99wMT994RD3/W4vfdF0ff7PXjzEbW9dwiXN9RNyYNWxlp5MjXh1wENN0IvHXfr7X9kSMK/bDCsBuwOmxN8fmfptFPNVym0YS/87gIhMW8XeQZ4Iq5c18r1bL+G3X7yS7916SUG/+Re7hCdfx7clfOP6xE2kdLsM11wwl4duWcn7L5qHy0Bbd4S/+dFL/OUPXmR/5+CEPA68MeK+tTty0r7npWaq//2R6a3YZ4hGowAuIiVLb6Hmp9glPPk6fVY1s6v9VPjceN2GCp+b2dV+zphdw/y6IP7jntvxThXRT3a9KuDls1ecxrdvWs7FC9OHVLfu6+aWB7bxtQ276Y8m8nsyQ1hr6Y8maCvxIN7aHSaZcmjpGGDn4T5aOgZIppwp8/dHprdSfwGpEhQRKWnT/S3UfJRCCU8+1qxq5vZ1O5hd4yGYKaHJvgPidbuYVxukJxynO5zAHt9rkfEN8lk0o4J//V/n8nRLJ9/Y2MKBngg/eOYAj798hI+/ZTHvOW8O7glqMZgN4gOxJJV+D7UhL94SKk2p8nvY1T6A22VwuwxJx3KgJ8rSxspiL01kVKXehrF0/qWLiMiEmuolPLm8A1Ib8jGnJjChwdUYw5uXzOSem5Zz66pmQj43fdEkd/5mF2se2s4zr3dP2GNB6e6IH3tRY4f8GnpdpIQVuwvVaLQDLiJSpop9CHQi5PIOSHaU/dGB+ISWivg8Lq5b0cQfnDWLe57cyy9fOkzL0UH+7L9f4PKlM1mzqpm5tfmNtR9q6I54hc9NTciL3zNymc1kGoinmFcb4OhAnHjKwed2MbvSz2A8/ymiIpMt+w5aOJ484R20UqAALiJSxqZLCY8xhoYqPxV+Nx39sQlt+Vdf4ePP33kGV58/l69t2M2Og338dtdRNrd08oGL5/PhNy0YVuaTL2stA7EkA7EkIV+6NCUwSr37ZMiWMDU3vFFyEo4naawKFHwtImNV6hsQCuAiIlI2Qj4P8+vcHB2ITfh9nzG7iq9edwEbXu1g7RMtdAzE+K8trfxqxxE+efli3n7WLFwT1J0lKxxPEo4nCXjd1Ia8Exr0R1PqO4gioynlDQjVgIuISFlxuwyzqgPUBU8eVmsD4w+xxhiuXNbIAzev4MZLF+L3uOgcjPMvv3yVz/7Xs7xyqG/c9z2SaCLF4d4obd1hBmPJSXmM46kLkcjkMdPtMMXy5cvttm3bir0MERGZZBt3tvOph7YSHVKy7HfDP1x9Liub6yfkMY70Rbl7UwsbXu04du0dZ83ik5cvZmalf0Ie42T8Xjd1Bd4RF5GxM8Zst9YuP+G6AriIiJSrjTvb+eYTe3i9K0xjVYDrVjRNWPge6oW2Hr62YQ+72wcACHhdfORNC/jAxU34PON/s/mhp/bx6PY2IokUQa+bD148nxvevOjYnwe8bupCPoK+4h3WFJFTUwDPUAAXEZk6JnKUdDSRmtQ2fynH8qsdh7nnyb10h9PdWObUBFjz1mYuP23mmKd3PvTUPh7YvB+XAWPAWnAs3HTJwmEhHNJBvL7CV5TDmiJyagrgGQrgIiJTQ3aUtNdthh0CzKcO2XEsnYMT267weAOxJN/ZvJ8fPHOAZKYbywVNtXzmiiUsach9iM17//NJIvHUsRbcJvMr6HPzk89ddtLbBH3pHfFsEJ/IFzAiMnanCuA6hCkiIiVpMkZJu1zpdoWzqgM5TbTc0tLFFx55nuu/tZkvPPI8W1q6Rr1Npd/Dp966hHtuWs4lmXKX51p7WPPQdr7y+Gv0hnML/+F4Coc3JndawMlcP5VIPMXBngiHeiP8z0uHuX3dDtr7o9QGvbT3R7l93Q427mzP6fFFZPIogIuIjGDjznauv3szl31pPdffvVnhpYBau8MEjyupmKhR0hV+D/PrQiMeYtzS0sWd63fRORijOuChczDGnet35RTCAZrqQ/zzH53Lv7z/XBbUh3As/OT5Q9xw7xa+/0wbyVFKYU5VsZJLJUsknuKujXswWAJe94S9gBGRiaHj0yIipzC0BGLoDuIdoLfxc5RPCUR2EMzQkDyRo6TdLsPsmgB90QRdA3Gc40oyH97aisdljr0IyJbBPLy1dUwHOVcurueiBbWse/4g9z+1n4FYkq9v2MNPnj/EZ65YwopFJ7+voMfFYOLEkB7M8VDnob4I1QEPiaSDy2VwZ57LRLyAESmEci6h0g64iMgpTEYJxHSSfQEz3hKINauaSaQs4XgSa9MfJ2MQTHXAy9zaIP7jdtsP9UUIeIf/mAx4XRzui4z5MTxuF++/aD4P3byS954/B5eB17vCfPH7L/LXP3yR1q4TQ/HSWdVUB9xkN7wNUB1ws3RWdU6POac6SDQT4B3Hkkg69EcTzKkJjnn9IoWW7/ePUqcALiJyCpNZAjEd5PsCppCDYHweF3NrAtSFfMeuDQ2wWdGEw+zq8QfYmpCXP3376ay94WIuaKoBYHNLF7c8sI1vPrGHgSFDdq5b0USF38v8uiBLGyuYXxekwu/luhVNOT3WdSuaSDqWSCKFJf0xnrK8/8J5tHWHhz2WSKkp9w0QlaCIiJzCZJdAlLvW7jC1Qe+wa2N9AVPIUdLGGOoq0j21O/pjXLeiiTvX7yKSSBHwuogmHJKOzTkAj2RJQyX/7wPn89vdR/nmxhYO90V5dFsbv375CDe/ZTFXnTOblc31fJ6lPLy1lcN9EWZXB8fUx3yk28eTDu19UbrdLmpDXir9njG3SRSZTBPx/aOUKYCLiJzCmlXN3L5uB+F4clgbvIkugShXU/UFTMDrZl5tkCvPSgf/8Qbg0RhjWLW0gUsWz+C/t7fy3d+/Tnc4wf/79Wv8+PmDfPaKJaxsrs/r8Ua7fSLl0NEfo3swQU3IS3VAQVxKw1T9/pEr9QEXERlB9hBQW3eY+WV2CGiyTUYf70IbiCU52h874YDmZOjoj/Gt37bw+Ctv1LhecUYDt65qZlZ1YNIfH9IHU2uCXqoDXlw5tGkUmSzl8P0DNIjnGAVwEZHCKYcXMMmUQ8dAjMgI/bcn0ssH+/jaht3sPNwPpOvTr1vexIdWNp1wJmGyuIyhOpjeEfe4dVxMiqMcvn8ogGcogIuIyHj0hON0hxMU4uemYy2Pv9LOtza10DkYB6Ch0s+tq5q5cllDwcpEjDFU+j3UBL34cmx/KCJvUADPUAAXEZHxiiVTtPfFSIwyRGeiROIp/mvL6zy6rZVEKv3z+py51Xz2ytM4fVZVQdaQVZEJ4oEC7cKLlAMF8AwFcBERyYe1ls7BOH2R3EbKT4SDPRHWbmrht7uOAume4FedM5tbLltMfYVv5BtPsIDXTW3IO+IUURFJUwDPUAAXEZGJEI4n6eiPkXIK93P0mde7uWvDHlqODgIQ8rn56CULef+F8wpeIuL3uqlTEBcZkQJ4hgK4iIhMlJRjOToQY7CAQ21SjuWnLxzivt/tpS+aftx5tUFuW93Mpc0zCt5GUEFc5NQUwDMUwEVEZKL1RxN0DcYLuhveF0nw4NP7+dFzB8g+7PKFdXz6iiUsmlFRsHVk+Twu6kI+KvwK4iJZCuAZCuAiIjIZkimHowNxwvHCjnjf1znIXRv2sG1/NwAuA++7YB43XrqQ6uMmCRaCz+OiNuSjUkFcRAE8SwFcREQmU380QedAvCDDe7KstWxu6eKujXs40BMBoDrg4eNvWcR7zpuLuwhDdbwacy+iAJ6lAC4iIpOtWLvh8aTDD589wEOb9xPODA5aPLOCz1yxhIsW1BV0LVlet4uakJcqBXGZhhTAMxTARUSkUPqiCboKvBsO0DUY594n9/KLlw6TfeTLTpvJp97azNzaYEHXkuVxudJj7oMK4jJ9KIBnKICLiEghJVIOHf0xoonCjLIf6rUj/Xx9w25ePNAHgNdtuPbi+XzkTQuK1rXE7TLpIB7w4ipCaYxIISmAZyiAi4hIMRRylP1Q1lo2vtrB2k0ttPfHAKiv8PHJyxfzjrNm4SrSbrTLGKqDXmqC3qLUqIsUggJ4hgK4iIgUSyyZoqM/RjxZmFH2Q0UTKR7Z2srDW1uJZR7/jNlVfO6K0zhrbnXB15NljKE6kB5z73EXdpiQyGRTAM9QABcRkWKy1tI1GKe3gKPshzrSF+XuTS1seLXj2LW3n9nIJy9vpqHKX5Q1QTqIV/o91Ia8eBXEpUwogGcogIuISCmIxNO74Umn8LvhAC+29fK1DbvZ1T4AQMDj4sNvWsAHLp6P3+suypqyKgMeaoM+fB4FcZnaFMAzFMBFRKRUpBxLR3+s4O0Khz7+/+w4zLef3Et3OL0jP7s6wKfe2szlS2cWvVtJhT9dmhIo8gsCkfFSAM9QABcRkVLTG0mPsi/Wz+TBWJLvbN7P9585QDIz1/6Cpho+s/o0ljRWFmVNQwV9bmqDPoI+BXGZWhTAMxTARUSkFBXzgGZWW3eYb2xs4emWTiA91v7d583h429eRG3IV7R1ZWnMvUw1CuAZCuAiIlKqrLV0DsbpK9IBzayt+7q4a8Me9neFAaj0e7jpzQu55vy5JdGpRNM1ZapQAM9QABcRkVIXjifp6I+Rcor3MzqZclj3/EHuf2o/A7F0jfqC+hCfXr2ElYvri7auobLTNasCHg31kZKkAJ6hAC4iIlNBMuXQMRAjEi/8BM2hesMJ7ntqHz994SDZ1wOXNNdz21uX0FQfKurastwuQ1VAQ32k9CiAZyiAi4jIVNIbTtAVLt4Bzaw9HQN8fcMenmvtAdKh9/0XzuOGSxeWTE22MYaqgIdaDfWREqEAnqEALiIiU00smaK9L0YiVbwDmpCuUf/t7qOsfaKFQ71RAGqDXm6+bDHvOmd2yew+Z4f61IUUxKW4FMAzFMBFRGQqcpz0Ac3+aHEPaALEkw6PbW/jO7/fTzSRflFwWkMln7lyCefPry3u4obQdE0pNgXwDAVwERGZygZiSY72x3BK4Of30YEY3/7tXv7n5SPHrq0+vYFb39rM7OpAEVc2nIK4FIsCeIYCuIiITHXJlEN7f4xoorgHNLNeOdTHf67fzc7D/UC6X/d1y5v40MomgiU0xdIYQ4XfrTH3UjAK4BkK4CIiUi66B+P0RBJFP6AJ4FjL46+0861NLXQOxgFoqPRz66pmrlzWUHL9uiv9HmpCXvye0nmBIOVHATxDAVxERMpJNJGeoFnsA5pZkXiK/9ryOo9uayWRSmeMc+ZW89krT+P0WVVFXt2JQr50aUqghHbqpXwogGcogIuISLlxHMvRgdixgTml4FBvhLVPtLBp11EADHDVObO55bLF1FcUf6z98YK+dGlK0KcgLhNHATxDAVxERMpVfzRB50C8JA5oZj37ejdf37iHlo5BAEI+Nx+9ZCHvv3BeSdZh+71uaoNeKkqkt7lMbQrgGQrgIiJSzhKZA5qxEjmgCZByLD978RD3PrmXvmh6l35ubYDb3rqENy+ZUXL14ZA+SFob8pXMkCGZmhTAMxTARUSk3Flr6Q4n6AnHi72UYfqjCR54ej8/evbAsbH2Fy+s49Orl7B4ZkVxF3cKXreLmpCXKr+nJF8oSGlTAM9QABcRkekimkhP0Ew6pXFAM2tf5yB3bdjDtv3dALgMXHPBPG66dCHVQW+RV3dyHlc6iFcHFMQldwrgGQrgIiIynZTSBM2hrLVsbuniro17ONATAaA64OHjb1nEe86bWzJj7Y/ndhlqgl6qA15cJbpGKR0K4BkK4CIiMh2F40mO9sdLbjc8kXL4wTMHeGjzfsLxdN364pkVfGb1Ei5aWFfk1Z2ayxiqg15qgt6SfbEgxacAnqEALiIi01Wp7oYDdA3GuffJvfzipcNkk8lbTpvBp966hHm1waKubSQuY6gKeKgJevFozL0cRwE8QwFcRESmu1LdDQd47Ug/X9+wmxcP9AHgdRuuvXg+H3nTAkK+0u1IYoyh0p8e6uNVEJcMBfAMBXAREZHM8J7BGAPR0hnek2WtZeOrHazd1EJ7fwyA+gofn7x8Me84axauEj8EWRnwUBv0lWSfcyksBfAMBXAREZE3DMSSHO2PldTwnqxoIsUjW1t5eGsrsWR6t/6M2VV87orTOGtudZFXN7oKf7o0RWPupy8F8AwFcBERkeGSmeE90RIa3jPUkb4od29qYcOrHceuvf3MRj55eTMNVf4iriw3IV+6NEVBfPpRAM9QABcRETm57sE4PZEEpZoNXmzr5WsbdrOrfQCAgMfF9W9awAcvno9/CoTbgNdNbchb0rXsMrEUwDMUwEVERE4tmkjR0R8jkSq9A5oAjrX86qXDfPvJvXSH091cZlX7+dRbl7Bq6cwpMSTH53FRF/JRoTH3ZU8BPEMBXEREZGSlfEAzazCW5Dub9/P9Zw6QzMy1P39+DZ+94jSWNFYWeXW58bpd1Ia8VGrMfdlSAM9QABcREclNKbcrzGrrDvONjS083dIJpMfav/vcOXz8LYuoDfmKvLrceN0uqoMac1+OFMAzFMBFRERyV8rDe4bauq+LuzbsYX9XGIAKv5sbL13E+y6YO2X6cntcLmqCXqoCHo25LxMK4BkK4CIiImM3FXbDkymHdc8f5P6n9jMQS5fPNNUF+fQVS3jT4hlFXl3u3C5DdcBLtcbcT3kK4BkK4CIiIuMzVXbDe8MJ7n9qHz954SCZ8nDetLie21YvYUF9qLiLGwOXMVQHvdQoiE9ZCuAZCuAiIiL5icRTHB0o3U4pWS0dA3xtwx6ea+2B/7+9+w+Wqi7jOP7+eLnAFVQ0icHQMHRG0QwTrzlqaamJOpFWCqNF6mhNOmrpmGaT2Ewz5lRq4ZiaP/D36KiTP0knNbRQEEERwUQkRRAiBbx4L7/u0x/7vbFd717Ouvfu7oHPa2Znz/nunj0Pzzxzefa7391DYWb5hP134XtfGs7A/vn5BRJJbNe/D4OaGumTk+U0VuAGPHEDbmZmVrn29uD9j9axurW+Z8MjgucW/Ic//u1Nlq5qA2CHpkbOOHQ4Y/YdmquZZUkM6Nfgy9zniBvwxA24mZlZz6n33w3vsG5DO/fNfIc7X3ibtvWFWEcMHsA5R+zBF3YdVNvgPoGB/fqww7aN9OtT/xcg2pqVasBz//ZJ0jGSXpe0QNLFtY7HzMxsa9K/sYFhOzaxQ1NjrUPpVt8+23DKQZ/lttObOXrkEADe/Pcafnzvy1z+8Gu8t7qtxhGWp2XtBt79oJX3VrXRtn5jrcOxMuV6BlxSA/BP4ChgMTADGB8Rr5U6xjPgZmZmvSMvs+EA85auZtLTC5i39EOg0KCfPHoY45p3oykHl7XvrKlvYWlKU9/8xb4l21JnwJuBBRGxMCLWAfcAY2sck5mZ2VapYzZ80LZ96/6CMnsP3Z4/jN+fS8bsxacG9mXdhnZuf/5tJtw8nb/OW0beJihb121k6apW3l3Zypq19XsFUyvIewP+GeCdov3FaczMzMxqQBI7DejLLoP61/0XBbeROGrkEG47rZlTDtqNxgaxomUdv3psPufeM5vX3/uw1iGWbe36jSxb3cbiDz7632+hW/3Jz2/wdK2rt9cfe8sq6SzgrLTbIun1T3CunYEVn+A428Q5rIzzVxnnrzLOX2Wcv8pUPX//Ah6r5gl7l+uvMpXk77NdDea9AV8M7Fq0PwxY0vlJEXEDcEMlJ5L0YldreCw757Ayzl9lnL/KOH+Vcf4q4/xVxvmrTG/kr74/G9q8GcCeknaX1BcYBzxU45jMzMzMzErK9Qx4RGyQdA7wF6ABuDki5tY4LDMzMzOzknLdgANExGNUZ5lWRUtYDHAOK+X8Vcb5q4zzVxnnrzLOX2Wcv8r0eP5y/TvgZmZmZmZ5k/c14GZmZmZmueIGvAuSbpa0XNKrRWMTJb0raXa6HVvLGOuZpF0lPS1pnqS5ks5L4ztJelLSG+l+x1rHWo+6yZ9rMANJ/SVNl/Ryyt/ladz1l0E3+XP9lUFSg6RZkh5J+66/MnSRP9dfGSQtkjQn5erFNOYazKhE/nq0Br0EpQuSvgy0ALdFxL5pbCLQEhG/qWVseSBpKDA0Il6StB0wE/gm8H3g/Yi4QtLFwI4R8dPaRVqfusnfSbgGN0uFy+8NiIgWSY3Ac8B5wIm4/jarm/wdg+svM0k/AUYD20fE8ZKuxPWXWRf5m4jrLzNJi4DREbGiaMw1mFGJ/E2kB2vQM+BdiIipwPu1jiOvImJpRLyUtj8E5lG4QulYYHJ62mQKTaV10k3+LIMoaEm7jekWuP4y6SZ/lpGkYcBxwJ+Khl1/GZXIn1XONVhH3ICX5xxJr6QlKv7oJgNJw4H9gReAIRGxFApNJvDpGoaWC53yB67BTNLH17OB5cCTEeH6K0OJ/IHrL6urgYuA9qIx1192V/Px/IHrrxwBPCFppgpXAwfXYDm6yh/0YA26Ac/uOmAEMApYCvy2ptHkgKSBwP3A+RGxutbx5E0X+XMNZhQRGyNiFIWr4zZL2rfGIeVKify5/jKQdDywPCJm1jqWPOomf66/8hwSEV8ExgBnp6W1ll1X+evRGnQDnlFELEv/KbUDNwLNtY6pnqW1o/cDd0bEA2l4WVrf3LHOeXmt4qt3XeXPNVi+iFgJPENh/bLrr0zF+XP9ZXYI8I20hvQe4KuS7sD1l1WX+XP9lScilqT75cCDFPLlGsyoq/z1dA26Ac+oo2iTE4BXSz13a5e+xHUTMC8iflf00EPAhLQ9AfhztWPLg1L5cw1mI2mwpEFpuwk4EpiP6y+TUvlz/WUTEZdExLCIGA6MA56KiFNx/WVSKn+uv+wkDUhf4EfSAOBoCvlyDWZQKn89XYO5vxJmb5B0N3A4sLOkxcBlwOGSRlFYF7QI+EGt4suBQ4DvAnPSOlKAnwFXAPdKOgN4G/hObcKre6XyN941mMlQYLKkBgqTDPdGxCOSpuH6y6JU/m53/VXEf/8qc6XrL7MhwIOFuRz6AHdFxBRJM3ANZlEqfz36N9A/Q2hmZmZmVkVegmJmZmZmVkVuwM3MzMzMqsgNuJmZmZlZFbkBNzMzMzOrIjfgZmZmZmZV5AbczKzOSRou6WO/OSvpl5KO3MyxEyVd2HvRmZlZufw74GZmORURv6h1DGZmVj7PgJuZ5UODpBslzZX0hKQmSbdK+jaApGMlzZf0nKTfS3qk6NiRkp6RtFDSuen5FxVtXyXpqbT9tXTpdCRdJ+nFdM7Lix5/sOOFJR0l6YHOwaaZ98kp1kWSTpR0paQ5kqZIakzPWyTp15Kmp9seaXyEpOclzUgz/S29klUzsxpwA25mlg97AtdGxD7ASuBbHQ9I6g9cD4yJiEOBwZ2O3Qv4OtAMXJaa36nAYenx0cDANH4o8GwavzQiRgP7AV+RtB/wFLC3pI5znAbcUiLmEcBxwFjgDuDpiPg80JrGO6yOiGZgEnB1GrsGuCYiDgSWdJ8aM7N8cQNuZpYPb0XE7LQ9Exhe9NhewMKIeCvt393p2EcjYm1ErACWU7jU8kzgAEnbAWuBaRQa8cPY1ICfJOklYBawDzAyCpdPvh04VdIg4GDg8RIxPx4R64E5QAMwJY3P6RT/3UX3B6ftg4H70vZdJV7fzCyXvAbczCwf1hZtbwSaivZV5rF9ImK9pEUUZrD/AbwCHEFh1nqepN2BC4EDI+IDSbcC/dNr3AI8DLQB90XEBklnA2emx48tPm9EtEtan5p3gHb+//+fKLFtZrZF8gy4mVn+zQc+J2l42j8543FTKTTZUynMev8QmJ0a5e2BNcAqSUOAMR0HRcQSCstCfg7cmsaujYhR6VbukpGTi+6npe3n2bTMZlyZr2dmVtc8A25mlnMR0SrpR8AUSSuA6RkPfRa4FJgWEWsktaUxIuJlSbOAucBC4O+djr0TGBwRr/XAP6GfpBcoTAqNT2PnA3dIugB4FFjVA+cxM6sL2vSJoJmZ5ZWkgRHRIknAtcAbEXFVL55vEjArIm6q8HUWAaPT+vTi8W2B1ogISeOA8RExtpJzmZnVC8+Am5ltGc6UNAHoS+FLk9f31okkzaSwPOWC3joHcAAwKb2hWAmc3ovnMjOrKs+Am5mZmZlVkb+EaWZmZmZWRW7AzczMzMyqyA24mZmZmVkVuQE3MzMzM6siN+BmZmZmZlXkBtzMzMzMrIr+C+JccYptuDyuAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\n",
"One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data, and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data. Let's compare this plot to the regression plot of \"peak-rpm\".</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 47414.1)"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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kynjZdcwsLWmPpOtV/v6DzrljzrljBw8erM+NAgAAAHagkV1QDprZ3ujzXknvljQu6Zyk90U/9j5Jvx99fk7SfVFnk1sULrZ8PCpTmTezt0f13T9ZcZ3i77pX0iNRnTgAAADQkhrZB/xGSZ+LOpmkJH3BOfcHZvaopC+Y2fslfU/Sj0mSc+6imX1B0rckFSR9yDlX3Ov4pyR9VlKvpC9GH5L0a5J+08xeUDjzfV8Dbw8AAACwa9ZpE8bHjh1zTz75ZLMPAwAAAG3OzJ5yzh2rHGcregAAACBGBHAAAAAgRgRwAAAAIEYEcAAAACBGBHAAAAAgRgRwAAAAIEYEcAAAACBGBHAAAAAgRgRwAAAAIEYEcAAAACBGBHAAAAAgRgRwAAAAIEbpZh8AkuH8+JTOXJjQ5HRWo8N9OnV8TCeOjjT7sAAAABKHGXBs6fz4lD569hl9fXJar84t6+uT0/ro2Wd0fnyq2YcGAACQOARwbOnjX3xOM9m8XCB5ZnKBNJPN6+NffK7ZhwYAAJA4lKBgS5euZZUyKZUySZKZ5AKnS9eyTT4yAACA5GEGHAAAAIgRARxbGjvQr8BJgXNycgqcU+DCcQAAAGwPARxb+rl7jmq4LyOTVPADmaThvox+7p6jzT40AACAxCGAY0snjo7ol+69Q2+5aVg37unVW24a1i/dewdtCAEAAHaARZioyYmjIwRuAACAOmAGHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIgRARwAAACIEQEcAAAAiBEBHAAAAIhRutkHgGQ4Pz6lMxcmNDmd1ehwn04dH9OJoyPNPiwAAIDEYQYcWzo/PqUHzl3U1Pyy9vZmNDW/rAfOXdT58almHxoAAEDiEMCxpTMXJpTxTH1daZmFlxnPdObCRLMPDQAAIHEI4NjS5HRWvRmvbKw34+nydLZJRwQAAJBcBHBsaXS4T0t5v2xsKe/ryHBfk44IAAAguQjg2NKp42PK+07ZXEHOhZd53+nU8bFmHxoAAEDiEMCxpRNHR3T65G0aGezR7FJeI4M9On3yNrqgAAAA7ABtCFGTE0dHCNwAAAB1wAw4AAAAECMCOAAAABAjAjgAAAAQI2rA2wDbxAMAACQHM+AJxzbxAAAAyVJzADez7zOzd0ef95rZYOMOC7Vim3gAAIBkqSmAm9nfl3RW0plo6Iik32vQMWEb2CYeAAAgWWqdAf+QpB+SNCdJzrnnJVFk3ALYJh4AACBZag3gK865XPELM0tLco05JGwH28QDAAAkS60B/L+a2T+V1Gtmf1nSf5T0nxt3WKgV28QDAAAkizm39US2maUkvV/SX5Fkkv5I0kOuliu3mGPHjrknn3yy2YcBAACANmdmTznnjlWO19oHvFfSrzvnfjX6ZV40xko/AEBDsMcBgHZVawnKVxQG7qJeSX9c/8MBAIA9DgC0t1oDeI9zbqH4RfQ5bTYAAA3BHgcA2lmtAXzRzO4sfmFmb5W01JhDAgB0OvY4ANDOaq0B/0eS/qOZvRR9faOkn2jIEQEAOt7ocJ+m5pfV17X2MsUeBwDaRU0z4M65JyQdlfRTkv6hpDc6555q5IEBADoXexwAaGebzoCb2Tudc4+Y2d+s+NatZibn3O808NgAAB3qxNERnVZYC355OqsjdEEB0Ea2KkH5i5IekfTXq3zPSSKAAwAa4sTREQI3gLa0aQB3zv3v0SY8X3TOfSGmYwIAAADa1pY14M65QNJPx3AsAAAAQNurtQ3hl83so2Y2amb7ih8NPTIAAACgDdXahvDvKaz5/ocV4yxHBwAAALah1gD+JoXh+26FQfxPJf27Rh0UAAAA0K5qDeCfkzQn6dPR1/dHYz/eiIMCAAAA2lWtAfwHnHN3lHz9J2b2TCMOCADQ+s6PT+nMhQlNTmc1So9uANiWWhdhft3M3l78wsz+vKQ/a8whAQBa2fnxKT1w7qKm5pe1tzejqfllPXDuos6PTzX70AAgEWqdAf/zkn7SzL4XfX2TpOfM7JuSnHPu9oYcHYC6YLYS9XTmwoQynqmvK3wJ6etKK5sr6MyFCf5fAUANag3g9zT0KAA0THG2MuNZ2WzlaYmwhB2ZnM5qb2+mbKw34+nydLZJRwQAyVJTAHfOfbfRBwKgMZitRL2NDvdpan559f+UJC3lfR0Z7mviUQFActRaAw4goSans+rNeGVjzFZiN04dH1Ped8rmCnIuvMz7TqeOszUEANSCAA60udHhPi3l/bIxZiuxGyeOjuj0yds0Mtij2aW8RgZ7dPrkbZxRAYAa1VoDDiChTh0f0wPnLiqbK6g342kp7zNbiV07cXSk4YGbxcMA2hUz4ECbY7YSSUSrQwDtjBlwoAPEMVsJ1BOLhwG0M2bAAQAth8XDANoZARwA0HJYPAygnRHAAQAth1aHANoZARwA0HJOHB3RvXce1tX5FT33yryuzq/o3jsPU/8NoC0QwAEALef8+JTOPn1FBwe79cZDgzo42K2zT1+hCwqAtkAABwC0nNIuKGbhZcYznbkw0exDA4BdI4ADAFoOXVAAtDMCOACg5dAFBUA7I4C3gfPjU7r/wcd09yce0f0PPkaNJIDEowsKgHZGAE+48+NT+tmzz+jr35vWK7NL+vr3pvWzZ58hhANItBNHR3T65G0aGezR7FJeI4M9On3yNrqgAGgLbEWfcJ/40rims3l5KVPaS8k5aTqb1ye+NM4LFYBEO3F0hOcxAG2JAJ5wE68tKmVSykySZCY5c5p4bbHJRwYAAIBqKEEBAAAAYkQAT7hb9vcpcFIQODnnFAROgQvHAQAA0HoI4An3sR95o/b2ZWQpyXdOlpL29mX0sR95Y7MPDQAAAFUQwBPuxNER/fK9d+gto8M6NNSjt4wO65fvvYOFSwAAAC2KRZhtgE4BAAAAycEMOAAAABAjAjgAAAAQIwI4AAAAEKOGBXAzGzWzPzGz58zsopl9JBrfZ2ZfNrPno8vhkuv8vJm9YGbfNrMfLhl/q5l9M/rep83CXWfMrNvMPh+Nf83Mbm7U7QEAAADqoZEz4AVJ/4tz7o2S3i7pQ2b2Jkkfk/QV59ytkr4Sfa3oe/dJuk3SPZJ+xcy86Hd9RtIHJd0afdwTjb9f0rRz7vWSPinpEw28PQAAAMCuNSyAO+deds49HX0+L+k5SYclvUfS56If+5yk90afv0fSw865FefcJUkvSLrLzG6UNOSce9Q55yT9RsV1ir/rrKR3FWfHAQAAgFYUSw14VBryFklfk3SDc+5lKQzpkor98w5Lmiy52uVo7HD0eeV42XWccwVJs5L2N+RGAAAAAHXQ8D7gZjYg6T9J+kfOublNJqirfcNtMr7ZdSqP4YMKS1h00003bXXIANAw58endObChCansxod7tOp42P08QeADtPQGXAzyygM3//eOfc70fCrUVmJosupaPyypNGSqx+R9FI0fqTKeNl1zCwtaY+k65XH4Zx70Dl3zDl37ODBg/W4aQCwbefHp/TAuYuaml/W3t6MpuaX9cC5izo/PrX1lQEAbaORXVBM0q9Jes45969KvnVO0vuiz98n6fdLxu+LOpvconCx5eNRmcq8mb09+p0/WXGd4u+6V9IjUZ04ALScMxcmlPFMfV1pmYWXGc905sJEsw8NABCjRpag/JCkvyPpm2b2jWjsn0r6uKQvmNn7JX1P0o9JknPuopl9QdK3FHZQ+ZBzzo+u91OSPiupV9IXow8pDPi/aWYvKJz5vq+BtwcAdmVyOqu9vZmysd6Mp8vT2SYdEQCgGRoWwJ1zX1X1Gm1JetcG1/kXkv5FlfEnJf1glfFlRQEeAFrd6HCfpuaX1de19tS7lPd1ZLiviUcFAIgbO2ECQExOHR9T3nfK5gpyLrzM+06njo81+9AAADEigANATE4cHdHpk7dpZLBHs0t5jQz26PTJ2+iCAgAdpuFtCAEAa04cHWl44KbVIQC0NmbAAaCN0OoQAFofM+AAUCLps8elrQ4lqa8rrWyuoDMXJhJ1O6Tk3xcAsBFmwAEg0g6zx5PTWfVmvLKxJLY6bIf7AgA2QgAHgEg7bJQzOtynpbxfNpbEVoftcF8AwEYI4AAQaYfZ43ZpdTg5nVXBDzRxdUHjr8xp4uqCCn6QqPsCADZCAAeASDvMHrdLq8OBLk9XZpZV8J08MxV8pyszy+rv8ra+MgC0OBZhAkDk1PExPXDuorK5gnoznpbyfiJnj+NoddhoZtFGyqa1PZVdyTgAJBgBvAWx8h9ojhNHR3Tv5Rk99NVLWsz56u/y9IG7b6nr44/Hd23mVwo6vLdHry3klPMDdXkpHRrq1sJKodmHBgC7RgBvMcWV/xnPylb+n5Z4kUbHa3R4PT8+pbNPX9HBwW7dFM2An336im4/srcuf4fHd+1Gh/s0Nb+ssYMDq2PZXEEjgz1NPCoAqA9qwFsMK/+B6uJoS9foxx+P79q1y2JSAKiGAN5i2qELA9AIcYTXRj/+eHzX7sTREd1752FdnV/Rc6/M6+r8iu6983DdzxScH5/S/Q8+prs/8Yjuf/Ax+owDiAUBvMW0QxcGoBHiCK+Nfvzx+K5daTnQGw8N6uBgt84+faWuAZnNfgA0CwE8BtuZYeG0K1BdHOG10Y8/Ht+1i+OMByVBAJqFAN5g251haZcevkC9xRFeG/344/FduzjOeFASBKBZOq4LSiFwml7MKZNOqctLqSvd2PcgpTMsktTXlVY2V9CZCxMbvui2Qw9foN5OHB3RaYWPqcvTWR1pUAu/Rj/+eHzXptgFpfjcKdX/jEccfwMAqum4AB4ETtPZ3OrXKbOyMN4dfZ5K1Wezh8nprPb2ZsrGmGFB3Nql9zThtXOcOj6mnz37jK5ML6kQBEqnUhrsSesXfvRNdf0b7bDxEoDk6bgAXilwTit5XysVtaWZKJAXg3lmh7PlzLCg2eg9jaRykmTR7pcWfV1HcZ1VAYBKHR/AN5L3A+X9QIslY2amjGdlwbzLSyntbRzMmWFBs+2kDApotjMXJrSnN6Mb9/SujjXi/y1nVQA0AwF8G5xzyhWccoWgbDxlVjZLXgznXsqYYUHTUQaFJJqczsozaeLqwupW9AcGuvh/C6AtEMDrIHBOy3lfyxVlLOlUGMRvH92rX33fMXVHIR2IE2VQSKLB7rSen1qQlzJ5KVMhcLoys6xbRwa2vjIAtDgCeAMVgkCFXKCSNZ+rs+WrH14Yyr06LfoEKlEGhSRyLqr4LhZ+u4pxAEgwAnjMNpstz6QtDOTFMpY6dmNB56IMqrW0S0eaRlvI+Tq8t0evLeRWS1AODXRrMedvfWUAaHEE8Bg8PnFdDz8xqZfnlnTjUK/ue9uo7hrbV/Yz4Wy5tKTqZSwZb61dYjplmy78BCqx0Kw10JGmdsXSqbGDayUn2VxBI4M9TTwqAKgPUlyDPT5xXZ965HldW1zRUE9a1xZX9KlHntfjE9drun4hCJTNFTS7lNdr8yt6aWZJ37ue1aXXFnV5OqtX55Z1bWFFc8t5rRSYGQJaGVuf1y6OnU8BoFmYAW+wh5+YVMH3NZP1lfcDZbyUBro9PfzE5LpZ8O3YqCOLRTXm3asfXsN3+wRQGzrS1I7SqdpR1gQkDwG8wb57fVHzS3lZypSKVvJPL+ZVCBa3vvIOuCobC1XrX57x6MgCxK2dOtLEEfoondoaZU1AMhHAGyxXCCQLu59Ikpnk2/qZ60barH956YLPYq059eVoVUmf6WuXjjSEvtbBRltAMhHAGyzjmVYKUhA4mUnFDlpdXvO7mwRVZsslyUvZ6qZCGS+12r+cVolopvPjU/ro2We0sFKQHzi9trCij559Rr987x2JCRrtUlZB6GsdlDUByUQAb7Cb9w/o8vSiFnNrNeD9XWkdGe5v9qFtyA+c/GB9q0QvVWXHT1olIiYf/+Jzmsnm5ZnJM5MLpJlsXh//4nOJDH1J7mbNLpWto53KmoBOQq1Bg933tlFl0p4ODHTrlgP9OjDQrUza031vG232oW2bHzgt5XzNlXRkefHaor53LatXZsNuLPPLeS3nfQVBkuMFWtGla1kFgdOKH2i5EGjFDxQETpeuJSf0FUs3puaXy0o3zo9PNfvQtmWwO60rM8sqBK5sl8qBbuZ04nbq+JjmlvJ6/tV5PffyrJ5/dV5zS/nElTUBnYZnywa7a2yfPqJb9fATk3plbkmHNugDnmTFHT8rFRd6FmvLi7PmZsyYY/vyfqDK/2VBNJ4U7VK6wS6VrcVJkoUL7mXJPrsCdAoCeAzuGtvXVoG7Vnk/UN4PlM2tjZmZ0ilbrSvvSq/VmgOb2eikSpJOtrRLvS67VLaOMxcmtKc3oxv39K6OJfFNHdBpCOCIlXNOed+tm7WkVSI6QbvU67JLZetolzd1QKch3aAlhK0SAy0sF3R9MadXZpc1eT2rF19b1JWZJV2dX9HsEvXlnWyjLjxJ6s7TLrs7tsvtaAejw31aqlgwn8Q3dUCnIYCjpRVbJc4v53VtYW3h5+T1rF6dCxd+zkULP32CeVs7efuhbY23ohNHR3TvnYd1dX5Fz70yr6vzK7r3zsOJKxU4cXREp0/eppHBHs0u5TUy2KPTJ29L3O1oB7wZApKJEhQkUrG+vFJpD/NiOUt3moWf7eCT990p6Wmde/YV+VH3jZO3H4rGk+H8+JTOPn1FBwe7dVO0Ec/Zp6/o9iN7ExteedvbXO3SWx7oNNZpq9Zvf/Od7ve+fKHZh4GYFTcUKq0t70pzAgjxuv/Bx9bVgBdrp3/7g29v4pFtT+lOmKU7ejILDgDlzOwp59yxynFmwNERVmfMV9bGih1Z1kI5rRLRWO2ygU27tFMEgGYhgKNjbdSRRVrfwzzDrp+og4EuT89PLShwYelGwfd1eXpJt44MbHndVkLnDTTC+fEpnbkwocnprEYppUGbI4ADVVTrYS5J6VRKmbStBfRo5jxNu8RYJP0FejHny3eSKfyQJN8pcf2z26WdIlpHaVlT6S6xp6VEPcaBWhHAgW0Id/2UllQemIrlLGnPwpAezZqnPaOkpU7a4QV6an5F6VS4eZBzkpnkWTi+mVZ743Hq+JgeOHdR2VyhrAaczhvYKcqa0GkI4EAdrJWzSNL62cxiGGfmfOfa5QU6ZVa2wZQfrC+BKtWKbzzovIF6o6wJnYYADsQgLGmpPnOeiWbJ0x715ptphxfoW/b36YWri7LAySycBQ+c9PoDG5dutOobjxNHRwjcqBvKmtBpCOBAE4U7gIa7gFYqrTcvdmcJy1w6c9a8HV6gP/Yjb9RHzz6jhZXCai/zvd0ZfexH3rjhddrhjcdOtVrpDRqHsiZ0ms58JQcSoBAEWsr5mlvK67X5cBfQ713P6sXXFnV5OqupuWVdX8xpvkN2Am2HHf9OHB3RL997h94yOqxDQz16y+iwfvneOzYNlZ261Xix9GZqfrms9Ob8+FSzDw0NwO6q6DRsxAO0kWqz5hkvJa9NylmKM6KdVHd8fnxKP3v2Gc0vF1QIAqVTKQ32pPVLWwT3pGuXTYsAdDY24gE6wEZdWryodCUTXaY9Uya1tjA0KTq17thJkoVrBmSdsf17J5feAGh/HRfAL11b1D/+/De0pzejPb0ZDUWX1T56MrSPQ3vwAyc/8FWt2V2xhWKmJJhn0mvtFFvpMdCJNcFnLkxoT29GN+7pXR1rhUWYjdYONf8AsJGOC+C5QqBnLs/W9LMZz9aF8qGeyuCeLvt+d8Zr8C0A6muzHUGl6rPnXU3o1NKK7fji0KkzwSzKA9DOOi6Ajwx26++8/SbNLhU0u5TX7FJec0t5zUSXhZKFbHnf6bWFnF5byG3yG8v1pFMbzqpXC+1DvZlElQCg82w2e57xUupOh/Xm3WlPXenG1Zu3aju+RuvUmWB6jQNIIudc1GLWbXoGueMC+HBfl/7uD91S9XthZwV/NZjPLuU1t1zQbDYXXpaMF4P77FJepc0nlguBludXttzZrlR/l1c1tA9FQb3ye0M9mbZZVIdkC/ubBypN56W7gnqpsJQl3CF0d2UtzAR33kxwp9b8A2gs55yCKCQXw7IUXoY7Fa9dFr8fOMkp/HptbO1rp7XrFPV3bxyzOy6Ab8bM1N+dVn93Wq/b27v1FRTeAYsrleE8+rpKcJ9bymt+uVC2iGox52sx5+vl2eWaj3WwJ11WElM6sz5UZdZ9sCetVAvV8qJ9le8KWl2xrCUM5eHnXd7mi0KZCWYmGEBnKQ3KpWG3+HXVkOycnFT1+6Vhu9kI4LuUMtNgT0aDPRkdGa7tOn7gtFBlRn1t1n392OJKeZqZXy5ofrkgaanG45QGe9aC+maLT4vf6+/yWmoBHtrHVotCizuCFheGplOmv/dDN+tjv/OsrswsrW5iM9Cd1i/86JtiP/64MRMMoJUUQ20x6LqK2eHS2eDASaoyVu3ng6AkLKt8NrndEMCbwEuZ9vRltKcvs/UPR/J+oLliSUy14J4Ng/tcSW176eYdgdPq+LaOc7XsJb0uoNM5Bo2w0e6g1xZyq0/QQeCUkuQCp/noDWs6VSx5ae3dQjuxkwuAnSsth9gouLrVwKrVsFsMyGXfU/g9rX4v+nr187VwrU2+j90jgCdExktp/0C39g9013ydXCEoq1WvOtteUjIzs5RT3l97YPmB0/XFnK4v1r4ItWrnmI1m2qNQT+cY1OLhJyY10J3WwZLHwFLe16999UXddnjPup9fmz0P6869YqvFKKg3441ip3ZyATpNEIQlEn4UZv1grWQiCMrLJwJXPgMstV65BOqPAN7GutIpHRzs1sHB2kK7c07LUWgvzqhvFNpLZ9rpHIM4vDy3pKGe8qesnkxKr8xVL8MKF4hKUvVi9JSFQbz4kYoWj3pRyUtxAWk9Fzx3aicXoBk2W0C3buY4WJvp3UhlfbGcVn+vX1I64QeEZmyNAI5VZqbejKfejKdDQz01Xadq55jKLjJLec2slsg0pnPMUJWQTueY9nLjUK+uLa6ot+SMyXI+0KGh2hZMVwqcU7DFYlFpratLKmXyzJRKSZ6tzaJ70XhpmN9Ip3ZyATZTrSNFWZcJhQG5cuFdUBmkSxboUSqBVkcAx67spnPMTLYitC8XysJ7aWhvdOeYaqF9gM4xLeW+t43qU488r6W8r55MSsv5QIXA6b63jTb07xa7umwwkV5VaRgvBvR0KqUb9/TotYUV9XWlZQofP53QyQXJEwSlnSQ2Xly3UZeKdTXIFTXF1BOj0xHAEbvSzjG1RqfKzjEz62bay0N7vTrHrO18SueYZrtrbJ8+olv18BOTemVuSYeGenXf20Z119i+Zh/aOmGXl/XB4n94yxF96pHnVfDzZW8i/uZbDuulmaXVUpiUhY8TszCkW/R16bhn0c+28ZkdFqyuKdYNV1s4J1UPxyqZDV4Lx2u/Y/V7JXXHlX2MATSGddoD7fY33+l+78sXYv2bj09c18NPTOrluSXd2MKhIWm2+nfN+4HmK7rGlAb0arPty/nq27HXqrRzTGW7x/KZdzrHdKri/9t6vokoBve1oB6GdSu5DGfcJZPJUlqdgZe0+r3wc1Ppf8dq45XXLf5ccaz4urLWdSGUKvmZrZQuWC3dgOj0ydtiC+GuIpCWht/Sl86qM74q70hR2amiWieKyhljAjGQbP3daR3a0/uUc+5Y5fcI4A32+MR1feqR55VOWdmM10feeSshfBca9e+6UeeY0hn3zTrH7MR2OscUP7rSLEJFMpmV1NJH5Tmrwb2YSCX91G89rdcWltVbuvFSrqD9A936N3/rzo1/f3RZGmQrA261nw+PTQReAHWzWQCnBKXBHn5iUumUrS4cK87kPPzEJAF8Fxr177qbzjHrQvu62fa12Xh/t51jMql1i0zpHIMkcM6p4Jy0xcmmyzNZDfWkV8sjpPDx+dLMkla2Wjm7nePZ8AvEjbPF6CQE8Abbbus01KZV/l0b0TlmpqTN4+qs+3JF55h8oOX8il6d23nnmK3aPQ7SOQZNVO+uN2htpWc1h3rSura4ok898rw+Is4Woz0RwBuMF5HGSPK/6047x8xXdIkpdo6ZzebW7ZBa3DW11HY7x5jCzjHVQvtQb0Z7qnyv0Z1j2mGG7Df/24v6wlOXtZT31Zvx9ONvPaK/8xdubvZhtZxmdb1Bc3C2GJ2GAN5gvIg0Rqf9u6ZsrU58O51j5pdL69cLG8y2r4X2xdzaqX0naW65oLnlgi5P1945ZrBnbTa9np1j2mGG7Df/24v63GPfVcokLyWtFHx97rHvSlLiQnij3wwlqesNdq9VzmoCcSGANxgvIo3Bv+vWvJRpb1+X9vZ11XydvB9oriSYV5tZn6nYJbW0c0zgtDq+nePcqHNM6cev/9klyTl1pz3JJXOG7AtPXY7Cd1SPb5KCQF946nKiAnjcb4YozW5/ST6rCewEATxGvIjU111j+xITvJIi46W0f6Bb+wdqW4QqSSt5v2TH0+rlMJWz7aWdY/zA6fpiTtcXa12EuiJT1HovZXp1bln//A++lYjOMUt5X5VrYc3C8SSJo1ygHc54oHaddlYTIIA3GC8iaHfdGU8HM972Osfkg/KQvlzeQaZ8tr2wrnOMk1QIt9+TJP3Jt69u+XcrO8ds1e5xqCetdJ07x/RmPK0U/LLedy6azU+SOMoFqAnuLJzVRKchgDcYLyJAOTNTb5en3i5Ph/bU3jnmT7/zmv7t+RdkZkqnwtPT+cDprTcNq787XR7cl/Kab8HOMT/+1iNhzXcQyKy4G2E4niRxlAtQE9x5OKuJTkIAbzBeRIDdMzMd/4GD+u61xZo7iATOaaGkHCacZa/eNab4Md/gzjEHhnr0l95wUH/2369ppRCoN5NKZBeU+942qk/80bhenVuWHzh5qbCzz4dOvL5uf4Oa4Nq1Q3cgoNMQwBuMFxGgPh6fuK4vfetV7evvWq0R/dK3XtUPHBqqGjZSZhqKgu92O8eshfJiUM+t9mavLJPZTeeYbD7Qb3zte/q9Z16uUhKT3rBUpq/GzjENZ9FW9Q04FGqCa0OZI5BMBPAG40UEqI+Hn5hUvuBrJucr7wfKeCn1d3l1LefaTeeY2SpdY2az1evbKzvHzERlM7VKl3SO2Sq0Fy970qm6hfaHn5jUQHdaB0sW69a7tI6a4NpQ5ggkEwG8wXgRAerjxWsLWlgpyGRKmangO80s5eUHC009rt12jln3sUFoL+0cUwicri3mdK3mzjHhNu57ttmjfaPOMXGV1lETvDXKHIFkIoDHgBcRYPfyvlMQSE5OTmHVg0nK+clr8LmbzjHVwnl5cF8L9qWdY3KFQFcXVnR1ofZFqL0Zr2qPdpPptYWcetKevFR45iDvO90wWNuiWtQPZY5AMhHAASRGUPK5U+f01t9p55jFnL/hjHq10F7ZOWYp72sp7+uVuY0WoZaXzbw0u6y//n9/taKd4+46x2BzlDkCyUQAB5AYpvLQTWzbmJlpoDutge60Dqu22VA/cFpYKazWtJdupFS5KHVqbkXT2bx8V/42aHHF1+KKr5dm6tM5ptiTvXR8oCetVCssQm0BlDkCyUQAB5AIzgXrZrydJLmgyk9jJ7ySxZ3b6RyzOsOezWt2eYPQXjITn91F5xhJSplWZ9YT1zmmAShzBJKHAA4gEcxSMoXBrVgDHn6j+VvMdzIvZRru69JwX5e0v7br5ApBRbvHMKjPVZTIvDy7pKn5lbIFqFL9O8dUhvVGdI4BgFIEcKBBzGw1JBZfw4sjpa/pZut/1rm1UgsXneIvnulPpcKfNQt/nxV7MUffdypef+16ZT8bHsjqsQTOyQ/Cj8A5BW7tb5bellTJ71DJ36h2rI3QlU5pJe/LUrb2bxS4DTt1tJN222ilK71155hif+tDQz3qyaSUzfnK+04/cWxUo/t6q4f25fLSmVbqHAMApQjg6BilITL8WhWXa99PRS02ip+vfs/C8JeKAnPK1gJw6Vgq4YvKgiCM78XbvB2lbxhKg3nZrHWk+LtdMfhHgb70jUDx8vsPDuh71xe1sFxQLuoDPtiX0ZHhPnVnvPCYo99R7U1EUnXqRiuV/a37u9Jayvv60+df07/6iTu2vH5p55jS3VBnKhalzpXVtjeuc8xG4X2oJ620R2gHOg0BHC0jVRJupXCmN7VBCK52uRqGS35+daaY08jbsps3EMV/6/J/8q1+39Z/76f/0uv1wLmLGuzJrG42kvedPvzOW3V4b/VFhkE0q+8UhnrnVBLww3EXqMrPrL0hKIb5yjcGcenUjVZ22996V51j1i0+LQ/upaF9+51j1uvv9qoE841n2wd60nSOARKOAI6aWZVZ32qzxutnh9eCdWlQDr+2Hc2yovOcODqiey/P6KGvXtJizld/l6cP3H2LThwd2fA6qZQp1YBeKcWAvla241QInIKg/HKzsp5adepGK83ob13WOWaDN3WVAue0ULGpUjG8zyzlNVcyu14M8PPLhbLfsdPOMdXKYKq1etzTm1F/N51jgFZCAG9zpbPDqZTJM1MqtT78pkoCcbWSCmaR0Wznx6d09ukrOjjYrZuiWeCzT1/R7Uf2bhrCG8HM5Jm2NQvpirX20Wx6IXAq+IHyfjie98P+zZVB/cahXl2ZWdTCiq98VHoz0O3p8N7+et+slpKU/tYps9Xgu53OMZWbKs2tm20vrI7PLeW1uEHnmMltdI7ZqBRmo9Dem4m3c0y7rXUANkMAbyGVC92KJRjFILwuKKe0VnO8wSwzoRnt4syFCWU8U19X+LTV15VWNlfQmQsTsQfwnTAzpT3b8km34AfyXbjrp++c/sL379O/uzATPa6lvB/o2mKgv377nliOu1naub+1lzLt6+/Svv6umq+T94OKoF6oMtteHuiXC2stOgMnTWfzms7W3jkm41l5YF9t/bhxu8eekjMW29Gpax3QuQjgO7Su7ri03rikHMNbnWkun3kuDcultcxAI5wfn9KZCxOanM5qdLhPp46PJSK0lpqczmpvb6ZsrDfj6fJ0tklH1BhpL1X2xPz1yVmNDHZrPlp82p1OabAnredeWdDYwQH5gVMhCBQEUiEIVjva+CVlMMVSmKShv/WajJfSgYFuHdikc0yl5byvubJwXlhf317Rt720c0zed7q2kNO1hdo7x3SnUxvMtJeE9ooe7l3pVMeudUDn6rgAnjJTf3e6rC1bysoX61WOUbOMJDs/PqWPnn1GCysF+YHTawsr+ujZZ/TL996RqBA+Otynqfnl1RlwKVzwdmS4r4lH1XiT01kdGOjWwcG1hYTOudU3Hl7K5KWKs44bzz6WlsAE0cJT3zkV/KgUJnDKF4KWCuqUJOxOT8ZTT8bTyFDti1CLnWNmlnJl9eubzbaXLkJdKQSaml/R1Pz2OsesFHxlvFT4/9ks+n8tzS7l9V+/c5XOMWg7HRfA057phhqfjIB28PEvPqeZbD58UTOTC6SZbF4f/+JziQrgp46P6YFzF5XNFcq6oJw6PtbsQ2uoer3xqLUEprQePV8IlPcD5aJa9Ti7v1CSEL8dd45Z8dfq1yuC+1zJLHuxtn1uKV+2q+1SPqxvXylU39X2n/3nb60bo3MMkq7jAjjQaS5dy4blUqm19oAucLp0LVmlGyeOjui0wlrwy9NZHUloKc12xf3Go2xGvaLaIe8H0YdbLX3xg3AWvd5lLpQkJIOZaaAnrYGetA4P19Y5xg+cFlbWymFmsnk9Mzmj//Lcq6vb3Ob98P/WUE9GK4VACyv16xyz0c6ndI5BnAjgABLjxNGRtg/clVrpjUfGSymzyan/IHDKB2FA3+3seae2X+wEXspWQ27R3bce0Ntu3ley6HagrOSo4AdlnWEqS2Hmlstn3Wey+dWZdam8c4zaqHMMkosA3oLaYcEcWsfYgX6NvzKvnL/2YmSSjh4aaN5BYVuS8sYjlTJ1pzx1p7Xh7HmuEH1sEcyb0QcczbXZotu0l9p255hcIaja6rGyzWNpnftKHTvHlJfE1L9zDJKNAN5izo9P6YFzF5XxTHt7M5qaX9YD5y7qtJSIF2C0nr29aVVGHBeNA3Epzp73leQn55xyUSjP+y66DD+S0gccrasrvfPOMWuhvLCuln224iOWzjEVte5daRahJh2vwC0m6b2O0Xoe/+7MtsZbGWeH2ouZqTvtqTtdPgMYBE6v29urod60fv3PXtSVmSUdGurRTxyjCwoaayedY5by/rqOMdW6x5R+7LZzTF+XVzLLnq5aJlMZ3FmE2loI4C2mU3odIz5+9ExfWpbo3Np4UnB2qHOkUqaelKe/evvr9Fdvf93qeHHGvB415mg9SWw7aRZOmPV1pbfVOWZhpbC+zWOxXCZbOtu+NgNf+j88m/OVzfl6eba2RaiSNNCdXp1Z3yiwl4b2gW46xzQSAbzFjA736cVrC5pbCjfd6PJSGupN6+b91OtiZ7yUVQ3bSXti5ewQ1mbMtXGHlkIY0gtBEPY4DwjnSdBJbSfNTIM9GQ32ZLbfOSabL6trrz7bHob2ys4xCysFLawUdGWmtuNMWWlorz6rXvnR380i1FoRwFvMO8b26fEXr69uO53zA03N53T/29rrCaidtVqZxMnbD+l3v/GyKjPIydsPNeeAdoizQ9jMaoeWKmv0CsW+5n4YyvN+oJVoBh2tgbaTm6vWOWYr6zrHrKthL2g2m9Ns1Jt9dimvbG5tsX7g1jrHTNbYOcaL3kBtJ7T3ZFIdGdoJ4C3m0YnrOjjQtbrtdJcXbjv96MR1fbjZB9diWi3oFo+p1cokPnnfnZKe1rlnX5EfOHkp08nbD0XjydGpO2Fi99JeSmlP67pNlC4CLS4ELc6kI160nay/XXeOWTfbXlIyE31vZimvXEnnGD9wu+ocs6c3oz09xdDe3p1jCOAtZqttpxFqxaArtW6ZxHvefESvzOVW36y8581HmnYsO9WpO2GicTZbBJor2XSo2D6RcpbGoe1ka9hp55jyMpgqLR6X12rbZ7N5FQI6xxDAWwyzfLVp1aDbimUSrfpmZbtaaUMatLfiItBqM+als+SlC0LruQtoJ6LtZHIVO8fcsM3OMWX169l8WSlM5ffmlnffOaY345UF9a06xwz1pJXeZOOx3SKAtxhm+WrTikFXas03UK36ZmUnkrIhDdqTmakrbVVn0vyoxjznB1GHFspZtuOusX36iG4t2QkzGV1QsH2lnWNu3FPbGY7AOS2uFNbNshd3Q60W3OeXC2WdY5byvpbyvl6Za43OMQTwFsMsX21aMehKrfkGqlXfrABbacV1HhvxUiZvg1nzlcJaOUvpZkMot9lOmOhsqZLOMUeGa7uOHzgtLG/Sn71KN5nFFb/sd+ykc8xgz9os+77+jUt5COAtiFm+rbVi0JVa8w3U6HCfLr22sG5h7y0HaG2J1tUupVNmtnqKvlSxznwlH2jF97WS33koT2L/bKDRvJRpT19Ge/p20TlmXWgvnYWv3jmm+P2tEMCRSK0YdEuPrRWOo6haa8urCzn9rbt4gW6GJM3qNlM7lU5VU15nHgaE1VBeCFZbJ261+LOT+mcDjbbrzjEVwX1xxdcvb/S36nPI65nZr0v6a5KmnHM/GI3tk/R5STdLelHSjzvnpqPv/byk90vyJX3YOfdH0fhbJX1WUq+kP5T0EeecM7NuSb8h6a2Srkn6Cefci426PWg9rRZ0W9WjE9c1Mti1bnMnWlvGr11mdePQiaVTGy3+lKr0Mg/CkpbPP0n/bKCZNusc09+d3jCAN7Iny2cl3VMx9jFJX3HO3SrpK9HXMrM3SbpP0m3RdX7FzIrPQJ+R9EFJt0Yfxd/5fknTzrnXS/qkpE807JbE7Pz4lO5/8DHd/YlHdP+Dj+n8+FSzDwkJNjmdVVfFSu4uL9XWQaZVlc7qFhciZTzTmQsTzT60ljM63KfL01ldfGlW37wyq4svza6e7epEaS+lnoynwZ6Mhvu7NDLYo8N7e3V1YUVDPWll0imlvZRSURinfzbQ2hoWwJ1zFyRdrxh+j6TPRZ9/TtJ7S8Yfds6tOOcuSXpB0l1mdqOkIefcoy48//YbFdcp/q6zkt5lbbCVUnGGbGp+uWyGjBCOnRro8nRlZlkF38kzU8F3ujKzrP6u5G9kEKd6vDGenM6q4AeauLqg8VfmNHF1QQU/4M1QFYeGujSzVFhtPRY4aWapoENDtZ8a7gSjw31aLgRKmclLmTJeSr5zunl/v24Y6lndtCSV/JdHoK3E3ZX8Bufcy5IUXRbPuR6WNFnyc5ejscPR55XjZddxzhUkzUra37AjjwkzZKi31felVvJROo4t1euN8WB3OnwzFO1IWgjCN0MD3SzHqfRH36r+b7vReKc6dXxMed8pmyvIufAy7zv9g7/4/ervTmv/QLdet7dXNx/o1+i+Ph3a06N9/V0a6EmrK92ZW4ADraBVnvWrPQO4TcY3u876X272QYVlLLrpppt2cnyx6cS6RzTW/EpBh/f26LWF3GoN+KGhbi2sFJp9aIlRrwWBqwvpis9UrmIcq4qdBUrzoXMq6ziA7S1Iz3gpZbyU+kpOIjgXLvzMFcLFn7nog42FgMaKO4C/amY3OudejspLilMZlyWVbnd1RNJL0fiRKuOl17lsZmlJe7S+5EWS5Jx7UNKDknTs2LGWflZp1f7WSK7R4T69eG2hbCznB7p5P20Ia1WvN8YLOX/9m6GBbi0SKtcxCwN3tXGU282CdDNTd9pTd9rTYMl4PurGspL3tRyFct4oAvUTdwnKOUnviz5/n6TfLxm/z8y6zewWhYstH4/KVObN7O1RffdPVlyn+LvulfSIa4Nnh41OJza7vzWS6x1j+zQ1Hwa+YhvCqfmc3kGHhJqNDvdpKV8eknfyxnh0uE+5il7POT/gDXYVh4fCjgLOrX2UjqOxMl5KA1EJy+G9vbp5f59et7dX+we6KV9BYjw+cV0/8/lndP+vPqaf+fwzenyi6jxtUzQsgJvZb0t6VNIPmNllM3u/pI9L+stm9rykvxx9LefcRUlfkPQtSV+S9CHnXPHV7qckPaRwYeZ/l/TFaPzXJO03sxck/YyijipJd+LoiE6fvE0jgz2aXcprZLBHp0/eRouyKugWU5tHJ67r4ECXuryUAhd2QDk40KVHW+iJqNXV640xb4Zq94t/43YNdnsq7uqcMmmw29Mv/o3bm3tgHaq4odCe3oxGBnt0ZLhPN+/v05HhPo0M9Wi4r0sD3WllPII5WkOxR/61xZWyHvmtEsKtDSaNt+XYsWPuySefbPZhYJdK+ymX7oTJm5X17v7EI9rbmyl7UXTOaXYprz/9uXc28ciSpbiBzm42frr/wcc23JX0tz/49gYdeXLV498c8SvWled9p3whWK0x3+lOn8BO/Mznn9G1xZXVHvlSeOZyf3+3/tVP3BHLMfR3p3VoT+9Tzrljld9rlUWYwLa0+y559cS6gvrazZTF5HRWBwa6dXCwZ+33Occi6w08e3lGF1+a1WLO1+xSXs9enuHxnQBrdeWSSiqGShd85n23GsoJ5miEl+eW5Jk0Ob2ivB8o46U03JdpmR75BHAkEt1ianfq+Jg+8vmva25pcbW10FBvWr/wo29q9qElRr12sOTNUO0+/cff0aceeUEpk9Kp8N/pU4+8IEn68Lvf0OSjw06ULvgsFQTFGfPycF4ICObYuf6utL57bVGplCkVtX19dW5F37e/v9mHJin+RZhAXdRrUVwnePbyjOaWylsOzi0V9OzlmeYcUALVqz8/i6xr99BXL0XhO6WUpaLLcBztJZWy1V0+9w9069CeHt20v0837+/X6/b26sBgt/b0ZtTb5SmdIragRqVtX4sfpeNNxgw4EunU8TE9cO6isrlCWQ04QWa9h756SWnPyl64CkGgh756iZnEGtXrjMt2ejZ3usWcr3RF1kqZaNlYRbFWfnI6q9E2+j+VSpl6Up56MtVnzHN+oJX8Wo15p61pw+YW875uGOrWdDZfUoLSpWy+NZ5DCOAtqF2fTOuJIFM7gszuNaJ0hKiwuf6u8I11qqShRuDCcaypV3lUkpQF87XlFFop+KsbCa2woVDHu3GoV9cWVzRa8jy9lPc10t8arUwJ4C2mE59Md2o3m090kv4uT4u5gpzz5Vy4kYlZWB+XNJ/+4+/ooa9e0mLOV3+Xpw/cfUsss/j1OuPC47t2H7j7Fn3qkRdUCMKWjYELPz5w9y3NPrSWcubChHIFX9cWyjvrdOKC9Gr15blCcabcX50p9wNCeSe4722j+tQjz2sp76snk9JyPlAhcLrvbaNbXzkGFFO1mHrVmgJF7zp6UH4Qhhen8NIPwvEkKS7KW8r7ZYvyPv3H32n4365Xf34e37X78LvfoI+88/XqzXgqBGHJz0fe+XrKpip859U5XVvMqeA7eWYq+E7XFnN6/tW5Zh9aS+hKr20odOOeXn3f/n6N7uvTDUM92tvXpb6uNHXlbequsX36yDtv1f7+bs0vF7S/v1sfeeetuqtF9l1I3hRYm6O7B+rtuZfnZSovebBoPElKF+VJYRlNnLXs9TjjwuN7ez787jcQuLeQ98NHdiqq1TEr1kgzy7uRjJdSxkuptBKh4K/VkhdnzfO+o6484e4a29cygbsSAbzF0KYM9XbpWlYZz+SVzPL4QaBL15IV+tqhlp3HN+qtK53SUs5X4JzMogYPLhxH7dJeSmkvpb6utTHnXNgSMQrmxZBOMEc9EMBbDN090Ah+4FQISmrAJaW9ZG0X3d/laXGlIKfy29HfnZynsZ0+vjt1YXan3u7tuHVkUC9eW9Dc0loN+FB/RjfvH2j2oSWemakrbeGbmYp1e3k/UMFf61+e9wPlC47e5agZb5FbTL1qTYGikcFu+a6iBtyF40nyrqMHq96OJNWy7+TxXVy4OTW/XLZw8/z4VIxHHr9Ovd3bder4mDKep0N7evQDNwzq0J4eZTyPSZsGy3gp9XZ52tOb0YGovry0d/nBwW7t7etSf3daGS8ls2RNeKDxkjN11EHo7oF6chvMyGw03qpemctpuC+t2aWCAheWn+zpTeuVuVyzD21btvv4Ll24KUl9XWllc4W273LRqbd7u2jJ2lo26l3unFstX8kX1urN836ynodRPwRwoM29Ml89oL66wXirmpzO6vDePh0ZXptJcs4lbgHjdssqOnXhZqfe7p1g0qb1mVnUJlFl5SzFTYVWCsFqH3NqzDsDARxocxv1vC0krBfu6HCfLr22oPnl8n7HtxxITq3rTvqAjw73ra/x7U23fY0vC1bRCcpnzMM3nKWz5cWuLMU6c7QPasABJMI7xvbp6kJOOT/cmCXnB7q6kNM7WrTFVDU76QP+jrF9mpovv91T88m63Ttx6viY8r5TNleQc+ElC9LRCYqz5QPdae3r79KhPT0a3bdWX75/oFsDPWFtOZKLGXCgzVX2AC8dT5JHJ65rZLBr3UzwoxPX9eFmH1yNJqez8kyauLqwehsODHRtWlbx6MR1DfV4ml0qKF9S+56k270T1DYD5arNlvuB00rB10qeuvKkIYAjsWhRVptUSqq23jJpm79NTme1v79bBwZ6VseSVgM+2J3W81ML8lImL2UqBE5XZpZ168jG5STPT81rYdmPOimEfZ4Xln09P5WsjZR24tnLM7r40qwWc75ml/J69vIMj/EqeC7sXF4qPJNW2b98JQrixZryXCGgRWKLIYAjkXZSS9upChs852403qraoSbYuXBxVa7g5BSehUiZNl1wlSsEkkkpK9np0MIX1Hb26T/+jj71yAvR7qfhff2pR16QJHbHLMFzISqZmXoy6zuxFBd85vxgtRMLvcubJ2FzYEiS8+NTuv/Bx3T3Jx7R/Q8+Vtf+vWcuTChX8PXK7LK+/eq8XpldVq7gb1pLi2Rrh5rg1xZz4U6FxfqfaEb7tcWNO9Jkog2TgiAM70G0eLYrYRspbddDX70Uhe+UUpaKLsNxrNnJugJ0plQqDOZDPRntL+ld/n0lteVDvRn1ZDx5qfZ+fmkFzICjIRo9K/OdV+c0t1xQSibPTAXf6dpiTgV/bvcHj5bUDjXBuUIgzzOlS+p/CkGw6Wz2G24YqtL9JZOo7i87sZjzlVJY31rc+dSzcBxraNeI3QpL4tbPmBdKO7GUzJwHtEisCwI4GuLMhQnlfV/XFsoXzNVrE428Hz4BpFIlp+UDp5zPE0M7S3q/44xnWsqH/1eL9dzS5rPZxe3rD+1Jb2v7+qTr9lLK5tfCtot2Qe3LcOK2VDuUZqE1pb2U0p7U27U+mBfLV1Z8f3VzIYL59hDA0RDPT81rNptXqmSx2WvzOeX9+iwc60qntJTzFbiSIOPCcZRLWRhcqo0jXm+4YUjPvTyrueW13TyHetK69YahDa/TDjP/O+Glqr+YbzTeqYpv0LK5Qke9QUPzhME8JXVJxW4sklZ7lefKdvpkU6GNEMDREI1eOHbryOD6zUn6M22/OclO9GQ8Zauctq883ZgESe/28I6xfXr8xevyUqZM9MZofsXfsqd30mf+d2IhV/25YqPxTtWpb9DQejJeShkvVdaRRdJqa8Ti5UohUCEgmBPA0RA7OdW+HZ16Wn4n9vWmqwbwfb3Jevi3Q7eHRyeuqzeT0sLK2v0x0O21fU/vnSg+Z5iVj3X4a3ZV7fIG7dN//B099NVLWsz56u/y9IG7b6HjTRvoSqfUlU6pv3ttrHK3z3wH9jBP1iswEqPRC8eY9dmGVEpD3SnNraw9sQ11p2QJawRe2u1Bkvq60srmCnVbVxCHiy/NamHFL9sEaWHF18WXZpt2TK2qL+OFNeBu/TjaD20nO0txt8/utKSSYO4H0aLPQqAVP9xgqF1DOQEcDRHHDHW7zPo02kCXp5dmyp/AFnKBXrc3WUGmHbo9rHbwKE3gjs4e1fyDvzimf/2V58vWL6QsHEf7CdtLOvmBVIi63ljUdpIA3jm8lKm3y4sWfobP98WNhcIPfzWgJx0BHA1x4uiI7r08s+50IoE5fq8t5tYtwgy26D3ditqh20Oxh3dlGUVQbZVshyuGLkoSOsPCSrgw2aTV/viBC8fR2co3Fto4lCdtwScBHA1xfnxKZ5++ooOD3bopmgE/+/QV3X5kLyE8ZtcWqgftjcZb1anjY/ro2Wd0ZWZJfuDkpUwD3Wn9wo++qdmHVrPBnvRqoCj2tpakgW6eiqv58LvfQODuEFZcLFSySZVcNA5UqCWUt3p7xGQVgSIx2J2tdWz01NOaT0mbM0ly0dbtrrySIwk+cPctksKZPae19pDFcaBT9WbCR3NxoW0xM/VlkvYoR7MUQ/me3oxGBnt0eG+vbj7Qr9F9fTq0p0f7+7s12JNRd8Zb7dDWTEy7oCHaoV4XreXMhQmlvbCvvO/Cy3T0pi4pZ1VuP7JX/V2eFnP+ah/w/i5Ptx/Z2+xDA5pqdLhfz72yfp+II8P9TTgatJNie0RVtEcs61se9S6Ps4yFAI6GaId63XYRncmtOp4kz0/Na3oxp0CSnFQIfC1Hi3uT4syFCY0M9ZQ9LpLWySVO//jhp3Xu2VdWS45O3n5In7zvzmYfFhrAOad0yuSZrbau9V2yanqRLNX6lhfbIxZryovhvBDUf9EnARwNwe5srSOVMvlVFvmlErYVZnbFl19aduIkPxpPisnprDyTJq4urLbnPDDQlcgzQ43eFOkfP/y0fvcbL69+7Qcu+vppQngbWsj5Ory3R68t5FYfG4cGuukQhFittUcs7xIWBGEwXymUz5rvpr6cGnA0xImjIzp98jaNDPZodimvkcEenT55G7N8TdC7QQ1l0morc374QuxKPkrHk2CwO60rM8sqRDO6hcDpysxy4hZhFjdFmppfLtsU6fz4VN3+xrlnX5G01o6uWLJZHEd7GR3u00pFa7mVQsBZU7SEVGqtvvzAQLdeF9WX3xTVl+/r79JAdzosdalRsp71kSj06W4NR/b2afzVhXXjh/cm64XNS6XkXBCG72Kf4Gg8KVZPpxffPbiK8YSIY1OkamdtNhtHsr1jbJ8ef/G6Uhaujcj5ga4u5PS37trX7EMDNpT2UkpXKWNZiWrKN5vmSs4rF4Ad2egUbtJO7Y4d6JeZKeOl1J0Ja/fMTGMHkrNIq3iaPe2ZfOeU9kyH9/Yk7r6YnM6qt2JHynovsvZS1btieAkrnUJtHp24rpHBLnV5KQVO6vJSGhns0qMT15t9aMC2FLuxDPVkNNiT2fDnmAEH2twrs8vbGm9VP3fPUf3s2Wc0v1xQwQ+UTqU03JfRz91ztNmHVrPi4uSxgwOrY9lcQSODPU08qu0bHe7Ti9cWNLdUWK3XHepN6+b9A1tfuUZ3fd9ePXppuuo42s/kdFb7+7t1YGDtseCcS+T6CKAWzIADba4QTR1W1tIWElb2cOLoiH7p3jv0lpuGdeOeXr3lpmH90r13JKrM6dTxMeV9p2yuIOfCyyQuTn7H2D5NzYeL5YrlAlPzOb1jrH7lApPXqwevjcaRbKPDfVrKl58JonMW2hkBHGhzXhS4153KT/CZ/GS9dVjTLouTH524roMD5eUCBwfqWy5wZXZlW+NItnZ5cwrUihIUoM3dOjKob78yL2clixddOJ4kxc4bGc/KOm+clhIVYNthcfLkdFYHBrp1cLBx5QLttIMrtnbi6IhOK1zge3k6qyMNaG0JtBICONDmymqng7B2erAnnajaaSmezhuoTRwbbbXLBlKoXTu8OQVqRQkK0ObaoXZaiqfzBmoTR7nA4b3VF6ZuNA4AScIMONAB2mFmKY5ZV9QmjnKBX3zvn9OHf/tpLeR8BS7sDT3Q5ekX3/vn6vY3AKBZCOAAEuHU8TE9cO6isrmCejOelvI+i7SaqNFv6k4cHdGn77+TmmAAbYkSFACJ0C4dRFC7Zy/P6OJLs3ppdlkXX5rVs5dnmn1IAFAXzIADSIx2KKU5Pz6lMxcmNDmd1Sizuhv69B9/R5965AWlTEqnwnKjTz3ygiTpw+9+Q5OPDgB2hxlwoAOcH5/S/Q8+prs/8Yjuf/AxnR+favYhdaRiK8Wp+eWyVorcH+s99NVLcoFT3ndaKYSXLnB66KuXmn1oALBrBHCgzRH6WkdpK0Wz8DLjmc5cmGj2obWc+eWCgoqxIBoHgKSjBAVoc+3UPzvp5RuT01nt7c2UjdFKsTo24gHQzgjgQJuLK/Q1OhzHtRNmI28HrRQBABIlKEDbGx3u01LeLxurd+iLo8wljvKNRt+OODawaRdDPel1u15aNA4ASUcAB9pcHKEvjnAcx06Yjb4dtFKs3QfuvkWplCnjmbrT4WUqZfrA3bc0+9AAYNeYSgDaXBy7FsZR5hJH+UYct6MdWinGodhq8KGvXtJizld/l6cP3H0LLQgBtAUCONABGh364gjHceyESY12a/nwu99A4AbQlihBAbBrcZS5xFG+QY02ACAO5lxnNXU6duyYe/LJJ5t9GEDbKXYPaVSZS1za5XYAAJrPzJ5yzh1bN04ABwAAAOpvowBOCQoAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAEKPEB3Azu8fMvm1mL5jZx5p9PAAAAMBmEh3AzcyT9G8l/YikN0m638ze1NyjAgAAADaW6AAu6S5JLzjnJpxzOUkPS3pPk48JAAAA2FDSA/hhSZMlX1+OxgAAAICWlG72AeySVRlz637I7IOSPhh9uWBm327oUSFuByS91uyDQKy4zzsL93dn4f7uLO1+f39ftcGkB/DLkkZLvj4i6aXKH3LOPSjpwbgOCvEysyedc8eafRyID/d5Z+H+7izc352lU+/vpJegPCHpVjO7xcy6JN0n6VyTjwkAAADYUKJnwJ1zBTP7aUl/JMmT9OvOuYtNPiwAAABgQ4kO4JLknPtDSX/Y7ONAU1Fe1Hm4zzsL93dn4f7uLB15f5tz69YsAgAAAGiQpNeAAwAAAIlCAEfLMjPPzL5uZn8Qff1/mNkVM/tG9PFXS372583sBTP7tpn9cMn4W83sm9H3Pm1m1VpXogWY2YvRffUNM3syGttnZl82s+ejy+GSn+c+T7AN7m8e423KzPaa2VkzGzez58zsHTy+29cG9zeP7xIEcLSyj0h6rmLsk865N0cffyhJZvYmhR1wbpN0j6RfMTMv+vnPKOwBf2v0cU8sR46d+kvRfVtsSfUxSV9xzt0q6SvR19zn7aPy/pZ4jLerT0n6knPuqKQ7FD638/huX9Xub4nH9yoCOFqSmR2R9KOSHqrhx98j6WHn3Ipz7pKkFyTdZWY3Shpyzj3qwsUOvyHpvY06ZjTEeyR9Lvr8c1q7/7jPOwv3d4KZ2ZCk45J+TZKccznn3Ix4fLelTe7vjXTk/U0AR6v615L+iaSgYvynzexZM/v1ktOVhyVNlvzM5WjscPR55Thak5P0X8zsKQt3r5WkG5xzL0tSdDkSjXOfJ1+1+1viMd6OxiRdlfT/RGWFD5lZv3h8t6uN7m+Jx/cqAjhajpn9NUlTzrmnKr71GUnfL+nNkl6W9H8Vr1Ll17hNxtGafsg5d6ekH5H0ITM7vsnPcp8nX7X7m8d4e0pLulPSZ5xzb5G0qKjcZAPc38m20f3N47sEARyt6IcknTSzFyU9LOmdZvZbzrlXnXO+cy6Q9KuS7op+/rKk0ZLrH5H0UjR+pMo4WpBz7qXockrS7yq8f1+NTkMqupyKfpz7POGq3d88xtvWZUmXnXNfi74+qzCg8fhuT1Xvbx7f5QjgaDnOuZ93zh1xzt2scGHGI865v118oo78DUn/X/T5OUn3mVm3md2icKHG49EpzXkze3u0cvonJf1+fLcEtTKzfjMbLH4u6a8ovH/PSXpf9GPv09r9x32eYBvd3zzG25Nz7hVJk2b2A9HQuyR9Szy+29JG9zeP73KJ3wkTHeVfmtmbFZ6CelHSKUlyzl00sy8ofEIvSPqQc86PrvNTkj4rqVfSF6MPtJ4bJP1u1GEqLek/OOe+ZGZPSPqCmb1f0vck/ZjEfd4GNrq/f5PHeNv6nyX9ezPrkjQh6e8qnATk8d2eqt3fn+bxvYadMAEAAIAYUYICAAAAxIgADgAAAMSIAA4AAADEiAAOAAAAxIgADgAAAMSIAA4AKGNmnzWze5t9HADQrgjgAIBdMTOv2ccAAElCAAeANmFmN5vZuJl9zsyeNbOzZtZnZm81s/9qZk+Z2R+VbP/9983sCTN7xsz+k5n1Vfmd/zyaEU9VjJ8wsz8xs/8g6Zsb/e3oZ180s//TzB41syfN7M7oOP67mf2DWP5xAKCFEMABoL38gKQHnXO3S5qT9CFJ/0bSvc65t0r6dUn/IvrZ33HOvc05d4ek5yS9v/QXmdm/lDQi6e8654Iqf+suSf+rc+5NG/ztf1jys5POuXdI+lOFO9vdK+ntkk7v8vYCQOIQwAGgvUw65/4s+vy3JP2wpB+U9GUz+4ak/03Skej7P2hmf2pm35T0P0q6reT3/IKkvc65U27jLZMfd85d2uRv313yvXPR5Tclfc05N++cuypp2cz2bvtWAkCCpZt9AACAuqoMy/OSLkazz5U+K+m9zrlnzOx/knSi5HtPSHqrme1zzl03sz8v6Uz0vQcUznAvbvG3S79eiS6Dks+LX/NaBKCjMAMOAO3lJjMrhu37JT0m6WBxzMwyZlac6R6U9LKZZRTOgJf6kqSPS/p/zWzQOfc159ybo49zqq7yb3+1XjcKANoJARwA2stzkt5nZs9K2qeo/lvSJ8zsGUnfkPQXop/9BUlfk/RlSeOVv8g59x8l/aqkc2bWu4O//Znd3RQAaE+2cWkfACBJzOxmSX/gnPvBTvrbAJA0zIADAAAAMWIGHAAAAIgRM+AAAABAjAjgAAAAQIwI4AAAAECMCOAAAABAjAjgAAAAQIwI4AAAAECM/n+8xyrxYgLj4gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\" we see that the points for \"highway-mpg\" are much closer to the generated line and on the average decrease. The points for \"peak-rpm\" have more spread around the predicted line, and it is much harder to determine if the points are decreasing or increasing as the \"highway-mpg\" increases.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #3:</h1>\n",
"<b>Given the regression plots above is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\". Use the method \".corr()\" to verify your answer.</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>peak-rpm</th>\n",
" <th>highway-mpg</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>peak-rpm</th>\n",
" <td>1.000000</td>\n",
" <td>-0.058598</td>\n",
" <td>-0.101616</td>\n",
" </tr>\n",
" <tr>\n",
" <th>highway-mpg</th>\n",
" <td>-0.058598</td>\n",
" <td>1.000000</td>\n",
" <td>-0.704692</td>\n",
" </tr>\n",
" <tr>\n",
" <th>price</th>\n",
" <td>-0.101616</td>\n",
" <td>-0.704692</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" peak-rpm highway-mpg price\n",
"peak-rpm 1.000000 -0.058598 -0.101616\n",
"highway-mpg -0.058598 1.000000 -0.704692\n",
"price -0.101616 -0.704692 1.000000"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[['peak-rpm', 'highway-mpg', 'price']].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692 compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n",
"\n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Residual Plot</h3>\n",
"\n",
"<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
"\n",
"<p>What is a <b>residual</b>?</p>\n",
"\n",
"<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
"\n",
"<p>So what is a <b>residual plot</b>?</p>\n",
"\n",
"<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
"\n",
"<p>What do we pay attention to when looking at a residual plot?</p>\n",
"\n",
"<p>We look at the spread of the residuals:</p>\n",
"\n",
"<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data. Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.residplot(df['highway-mpg'], df['price'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<i>What is this plot telling us?</i>\n",
"\n",
"<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
"\n",
"<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First lets make a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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f/pBHH32UAQMGsGDBAurUqfOd1w0aNIg2bdpwxBFHcO2119K7d28AGjduzCOPPMKYMWPo0aMHAwYMSGhcXaLMORfYwSqrT58+LtFmbBEREZFUNG/ePLp06RJ1GRJT0u+HmU13zvUp6flaORYRERERiVE4FhERERGJUTgWEREREYlROBYRERERiVE4FhERERGJUTgWEREREYkJNRyb2TVmNtfM5pjZWDP77vYnIhKNxYvhJz+B/PyoKxERkYBVrVqV3Nzcb25Lly7lqKOOAmDp0qXfzDcGmDVrFuPGjSv3OY499lj2H8F700038etf//pbj82aNavU0XY33XQTf//738t9/rCEFo7NrDnwE6CPc647UBUYHdb5RKQctmyBU0+Fe+6BPn3gww+jrkhERAJUq1YtZs2a9c2tdevWfPDBB0Bw4bgkY8aM4ZlnnvnWY08//TTnn39+IMdPhrDbKnKAWmaWA9QGVoZ8PhEpi3Nw6aUwfz78+99Qpw4ceywkuA2oiIikp4MOOgiA66+/nqlTp5Kbm8utt97KjTfeyDPPPENubi7PPPMM27Zt49JLL6Vv37706tWLl19+GYAdO3YwevRoevTowXnnnceOHTu+c45OnTpRv359Pv74428e+9///sfo0aP573//S9++fenZsydnnXUW27dv/87ri69Gr1u3jtatWwNQWFjIddddR9++fenRowf/+c9/AFi1ahVHH300ubm5dO/enalTp1b6fcqp9BEOwDm3wsz+DnwF7AAmOOcm7P88M7sSuBKgZcuWYZUjInG33QbPPQd/+xv84Adw7rn+dsklkJfnH6+iyxFERILws5/BrFnBHjM3F+66q/Tn7Nixg9zcXADatGnDiy+++M3XbrnlFv7+97/z2muvAdC0aVOmTZvGP//5TwB+85vfcNxxx/HQQw+xadMm+vXrx7Bhw/jPf/5D7dq1ycvLIy8v75vtnPc3ZswYnn76afr3789HH31Ew4YN6dChAw0aNOCKK64A4IYbbuDBBx/kxz/+cULf84MPPsjBBx/Mp59+yq5duxg0aBAnnHACL7zwAieeeCK//e1vKSwsLDFwl1do4djMDgFOA9oAm4Bnzex7zrknij/POXc/cD/47aPDqkdEgAkT4De/gfPOg1/8wj/WsCG8+ab/G/yOO2DIEDj99CirFBGRSoq3VVTEhAkTeOWVV77pA965cydfffUV7777Lj/5yU8A6NGjBz169Cjx9aNHj+aoo47i9ttv5+mnn2bMmDEAzJkzhxtuuIFNmzaxdetWTjzxxHLVlJeXx3PPPQfA119/zcKFC+nbty+XXnope/bs4fTTT//mB4LKCC0cA8OAJc65tQBm9gJwFPBEqa8SkXB89RWMHg3dusGDD4LZvq9VqwZ33w0vvACPPKJwLCISkLJWeFORc47nn3+eTp06fedrVvzfjgM4/PDDad26Ne+88w7PP/88H8aua7nkkkt46aWX6NmzJ4888ghTpkz5zmtzcnIoKioCfCgvXtM999xTYqB+9913ef3117nwwgu57rrruOiiixL9VksU5menXwEDzKy2+XfyeGBeiOcTkdI88AB8/bUPwHXqfPfrOTlw4YXw+uuwZk3y6xMRkaSoW7cuW7ZsOeB/n3jiidxzzz045z/QnzlzJgBHH300Tz75JOBXgfPy8g54jjFjxnDNNdfQrl07WrRoAcCWLVto1qwZe/bs+eY4+2vdujXTp08H+GaVOF7Tvffey549ewBYsGAB27ZtY9myZTRp0oQrrriCyy67jBkzZpT7/dhfaOHYOfcx8BwwA5gdO9f9YZ1PRMowbhwMHAjt2x/4OZdcAnv3wgH+0hIRkfTXo0cPcnJy6NmzJ3feeSdDhw7l888//+aCvN/97nfs2bOHHj160L17d373u98B8IMf/ICtW7fSo0cPbrvtNvr163fAc5xzzjnMnTuX0aP3DSr705/+RP/+/Rk+fDidO3cu8XXXXnst9957L0cddRTr1q375vHLL7+crl270rt3b7p37873v/999u7dy5QpU8jNzaVXr148//zz/PSnP630+2PxnwpSQZ8+fdz+8/JEJACrV0OzZvDnP/ue49L07w87dsBnn3279UJERBIyb968Uuf6SnKV9PthZtOdc31Ker4uSRfJBm++6e9POqns515yCcyeHfzl1SIiImlA4VgkG7z+Ohx2GPTsWfZzR4+GGjXg4YfDr0tERCTFKByLZLo9e/wIt5NOSqxN4pBD/LSKJ5+EXbtCL09EJBOlUttqNqvI74PCsUim++AD2Lw5sZaKuEsugQ0b/IqziIiUS82aNVm/fr0CcsScc6xfv56aNWuW63VhzjkWkVQwbpyfY3z88Ym/Zvhw34bx8MNw5pnh1SYikoFatGhBfn4+a9eujbqUrFezZs1vRsklSuFYJNO9/rrf9a5evcRfU7UqXHSR30p69Wo49NDw6hMRyTDVqlWjTZs2UZchFaS2CpFMtmwZzJ0LJ59c/teOGQOFhfsmXYiIiGQBhWORTPbGG/6+PP3Gcd27Q8OG8O67wdYkIiKSwhSORTLZuHHQpg106lT+11apAoMHw9SpwdclIiKSohSORTLVzp0weXLiI9xKcvTRsGgRrFoVbG0iIiIpSuFYJFO98w5s316xfuO4IUP8vVaPRUQkSygci2Sq99/3rRHHHFPxY/TqBXXqqO9YRESyhsKxSKaaPRs6doTatSt+jJwcGDRI4VhERLKGwrFIpsrLgx49Kn+cIUNgzhy/Y56IiEiGUzgWyURbtsDixXDEEZU/1tFHg3O+TUNERCTDKRyLZKK5c/19ECvH/fpB9epqrRARkaygcCySifLy/H0Q4bhmTR+QNbFCRESygMKxSCaaPRvq1oVWrYI53pAhMH06bN0azPFERERSlMKxSCbKy/P9xhXd/GN/Rx8Ne/fCRx8FczwREZEUpXAskmmcC25SRdxRR/mZyWqtEBGRDKdwLJJpVqyATZuCmVQRV68e5ObqojwREcl4CscimSbIi/GKO/po31axe3ewxxUREUkhCscimSYejoNcOQZ/Ud7OnTBtWrDHFRERSSEKxyKZZvZsaNkSDj442OMOHOjvP/002OOKiIikEIVjkUwT9MV4cc2aQdOmMHNm8McWERFJEQrHIplk926YPz+ccAzQqxfMmhXOsUVERFKAwrFIJpk/388jDrrfOC43129NvWtXOMcXERGJmMKxSCYJa1JFXK9ePnzPnRvO8UVERCKmcCySSfLyoHp16NgxnOPn5vp7tVaIiEiGUjgWySSzZ0PXrpCTE87x27eHgw7SRXkiIpKxFI5FMklYkyriqlSBnj21ciwiIhlL4VgkU6xfDytXhhuOwbdWzJoFRUXhnkdERCQCCscimWL2bH8f1qSKuF69YOtW+PLLcM8jIiISAYVjkUwR1rbR+9NFeSIiksEUjkUyxcKFfsvoQw8N9zzdu/sL/nRRnoiIZCCFY5FMsWQJtGkDZuGep0YNPxFDK8ciIpKBFI5FMsXixdC2bXLOlZurlWMREclICscimaCoyK8cJysc9+oFq1f7m4iISAZROBbJBKtXw86dyV05BrVWiIhIxlE4FskES5b4+zZtknO+eDhWa4WIiGQYhWORTLB4sb9P1spx/fo+iGvlWEREMozCsUgmWLzYT6lo1Sp559RFeSIikoEUjkUyweLF0KKFH7OWLL16waJFsGVL8s4pIiISMoVjkUwQn3GcTLm54Ny+nflEREQygMKxSCZI5ozjuPhFeZ99ltzzioiIhEjhWCTd7dwJK1YkPxy3aAH16sHcuck9r4iISIgUjkXS3dKl/j7Z4djMbyOtcCwiIhlE4Vgk3SV7xnFx3bopHIuISEZROBZJd8mecVxct26wbh2sXZv8c4uIiIRA4Vgk3S1eDLVqQdOmyT93t27+XqvHIiKSIRSORdJdfFKFWfLPrXAsIiIZRuFYJN0tXhxNvzHAYYfBwQcrHIuISMZQOBZJZ875C/Ki6DcGv1qti/JERCSDKByLpLP16/32zVGFY9gXjp2LrgYREZGAKByLpLMoJ1XEde3qQ/qaNdHVICIiEpDQwrGZdTKzWcVum83sZ2GdTyQrxcNxVD3HoIvyREQko4QWjp1zXzjncp1zucCRwHbgxbDOJ5KVotwAJC4ejj//PLoaREREApKstorjgS+dc8uSdD6R7LB4sZ9vXKdOdDU0awb162vlWEREMkKywvFoYGxJXzCzK81smplNW6tdtkTKJz7jOEqaWCEiIhkk9HBsZtWBUcCzJX3dOXe/c66Pc65P48aNwy5HJLNEOeO4OE2sEBGRDJGMleORwAznXEESziWSPfbsgeXLo185Bh+ON2yAAv1vLiIi6S0Z4XgMB2ipEJFKWL4cCgtTJxyDWitERCTthRqOzaw2MBx4IczziGSlVJhxHNe1q79XOBYRkTSXE+bBnXPbgYZhnkMka6XCjOO4Qw+FQw5ROBYRkbSnHfJE0tWSJVCtGjRvHnUl+yZWaNaxiIikOYVjkXSVn++DcdWqUVfiaWKFiIhkAIVjkXSVnw8tWkRdxT7dusHGjbB6ddSViIiIVJjCsUi6SsVwDOo7FhGRtKZwLJKOnNvXVpEqFI5FRCQDKByLpKONG2HnztRaOW7SxE+smD8/6kpEREQqTOFYJB3l5/v7VArHZtClC8ybF3UlIiIiFaZwLJKO4uE4ldoqADp3VjgWEZG0pnAsko5SceUY/MrxmjWwYUPUlYiIiFSIwrFIOlqxAqpU8TvTpZIuXfy9+o5FRCRNKRyLpKP8fB+Mq1WLupJv69zZ36u1QkRE0pTCsUg6SrUxbnGtW0ONGgrHIiKSthSORdJRqm0AEle1KnTqpLYKERFJWwrHIuloxYrUDMegcW4iIpLWFI5F0s2WLfD116kbjjt3hiVLYMeOqCsREREpN4VjkXSzYoW/T8WeY/Arx87BwoVRVyIiIlJuCsci6SZVZxzHxce5qbVCRETSUE7UBYhIOcVXjlM1HHfo4LeSDikcFxXBU0/BlCnQpAk0awbt2sGIEX70s4iISGUoHIukm1TdOjquVi1o0yaUcPzxx/DTn/r7Qw7x7dd79/qvHXMMPPQQtG0b+GlFRCSLaJ1FJN3k50PDhlCzZtSVHFiXLoGPc/vlL2HAAFi2DB55BNatg127oKAA7r8fZsyAHj3g3nt9y7OIiEhFKByLpJtUnXFcXOfO8MUXUFgYyOEefhj+9je4/HJYsAAuvti3UFSp4lsrrrgC5syBgQPhhz+Ea65RQBYRkYpROBZJN6k84ziuSxe/rLt0aaUP9dlnPvAedxzcdx/UrVvy81q2hAkTfNvF3XfDbbdV+tQiIpKFFI5F0k06rBzHJ1ZUsrXi66/h7LOhQQMYO9ZvwFcaM7jjDhgzBq6/3rdfiIiIlIfCsUg62bkT1q5N3Yvx4jp39veVvCjviiv8fiLPPOPbJxJRpYoPxcOG+TaMN9+sVAkiIpJlFI5F0snKlf4+1VeOGzTwabYS4fidd+DZZ+GPf4TBg8v32urV4YUXoHt3uOCCfQM+REREyqJwLJJOUn3GcXFdulQqHP/pT9C0qb+4riLq1oX//c+3Pn/ve4FdGygiIhlO4VgknaT67njFxce5VWBsxPvvw+TJfnxbrVoVL6FjR/jXv/wq9F//WvHjiIhI9lA4Fkknqb4BSHGdO8PGjbBmTblf+qc/QePG8P3vV76Miy6C88+Hm27yoVtERKQ0Csci6WTFCt8vUK9e1JWULT6xopytFR9/DOPHw7XXQp06lS/DzG8M0qqV7z/evLnyxxQRkcylcCySTtJhjFtcBce5/fGPfgPAH/4wuFLq1YMnnoDly+HnPw/uuCIiknkUjkXSSTqF4xYt/NJvOVaOP/sMxo3zAfagg4ItZ+BA38P84IPw+uvBHltERDKHwrFIOsnPT49+Y/D9DJ07lyscP/ywH8MWRK9xSW66CY44ws8/Xr8+nHOIiEh6UzgWSRd798Lq1emzcgzlGue2Zw889RSceqpvqwhDjRrw2GM+GP/oR+GcQ0RE0pvCsUi6KCjww3rTLRzn58OWLWU+9Y03/OZ/F18cbkm5ufD73/td9554ItxziYhI+lE4FkkX6TTjOC6+jfQXX5T51Ecf9ZvqjRgRck3A9dfDkCH+or/Fi8M/n4iIpA+FY5F0kU4zjuMSHOe2fj28+qoftVatWvhlVa3qV42rVPHn3LMn/HOKiEh6UDgWSRfptHV0XPv2kJNT5ji3p5/2ATXsloriWraE//wHPvrIbzoiIiICCsci6SM/319RFtbVamGoVg3atStz5fjRR6FnT39LpvPOg0sugT//2W9XLSIionAski5WroRmzfyItHRSxsSKzz+HTz9N7qpxcffcA127wjnnwMKF0dQgIiKpQ+FYJF2sWuXDcbrp0gUWLTpgY+/TT/ve3/PPT3JdMQcdBK+84ms49VTYtCmaOkREJDUoHIuki9Wr0zcc790LX35Z4pdfeslPjmjaNLllFdemDbzwgi9x9GhfroiIZCeFY5F0ka4rx/FxbiW0VixZArNnw2mnJbmmEhx9NNx7L4wfD5ddpoAsIpKtFI5F0sGuXbBxIxx6aNSVlF8p4fjll/19KoRj8NtK/+lPfhe9MWNg9+6oKxIRkWTLiboAEUnA6tX+Ph1XjuvW9ePnShjn9vLL0L07tG0bQV0HcMMNUKcO/PznsH07PPcc1KoVdVUiIpIsWjkWSQfxcJyOK8fgV4/3Wzlevx7efTd1Vo2Lu+YaPwP5jTdg6NADtkuLiEgGUjgWSQerVvn7dFw5Bn9R3vz54Nw3D73+OhQVpWY4BrjySr9qPH8+5Ob6WczFyhcRkQylcCySDtJ95bhLF9i6dd8uf/iWisMOgyOPjLCuMpx5JuTlQe/efrOQs8+GZcuirkpERMKkcCySDlat8pt/NGkSdSUV06WLv4+1Vuzc6adCjBrl5wunspYt4a234K9/hXHjfIfIDTf4rC8iIpknxf9ZEhHArxw3bgw5aXoN7X4TKyZPhm3bUrelYn9Vq8L118MXX/jV5D//GTp2hEce8a0hIiKSORSORdJBus44jmvaFOrX/yYcv/yyH2IxdGi0ZZVXy5bw5JPwwQf+1//3f9C3L0ydGnVlIiISFIVjkXSwenX69huDbwmJXZTnHLz5JgwbBjVqRF1YxQwc6APyk0/CmjV+A5Gf/1wbh4iIZAKFY5F0kO4rx/DNOLcvvoDly+HEE6MuqHKqVIHzz/etFj/6Edx5J5x8st+rRURE0pfCsUiqKyqCgoL0XjkGv3JcUMD4F7cDcMIJEdcTkNq14Z//hP/+F95+G/r1gwULoq5KREQqSuFYJNVt2AB79qT/ynFsYsX4V3fRoQO0aRNxPQG7/HI/1WLTJr+C/PXXUVckIiIVoXAskurSfcZxXJcu7KI6U6bXTfuWigMZPBheeAGWLIHLLtOmISIi6UjhWCTVpfvueHGtW/NetePYsTsnY8MxwJAhfiby88/D3XdHXY2IiJRXqOHYzOqb2XNmNt/M5pnZwDDPJ5KRMmXluGpVxtc/j2q2h2OPjbqYcF17rZ/hfN118OGHUVcjIiLlEfbK8d3Am865zkBPYF7I5xPJPJmycgxM2HMsg6pP46CDoq4kXGZ+g5CWLeHii6GwMOqKREQkUaGFYzOrBxwNPAjgnNvtnNsU1vlEMtbq1VCnDumeKFevhs82tebEXS9nxd7L9evDbbfBwoXwzDNRVyMiIokKc+W4LbAWeNjMZprZA2ZWZ/8nmdmVZjbNzKatXbs2xHJE0lQmzDgGJkzw9ycwAT7/PNpikuSMM6BbN7/dtLaZFhFJD2GG4xygN3Cvc64XsA24fv8nOefud871cc71ady4cYjliKSpdN8dL2bCBGjcYC+5zIK5c6MuJymqVIEbbvA/C7zwQtTViIhIIsIMx/lAvnPu49h/P4cPyyJSHhmwcuwcTJwIw0+sQpUa1bNm5RjgnHOgUye4+WaNdhMRSQehhWPn3GpguZl1ij10PJA9/yKKBCUDVo7nzIE1a2DY8Cp+G+ksWTkGqFoVfvMb+OwzePXVqKsREZGyhD2t4sfAk2aWB+QCfwn5fCKZZccOv9Vamq8cT57s748/Ht+Em0XhGOD886FtW/jTn7R6LCKS6kINx865WbF+4h7OudOdcxvDPJ9IxsmQGcdvvQXt2/vRZnTtCl99BVu2RF1W0uTkwM9/DtOm+VV0ERFJXdohTySVZcCM47174Z13YqvG4FeOAeZl19jzc87xF+j9739RVyIiIqVROBZJZRmwcjxtGmzeDMcdF3sgHo6zrLWiSRMYOtSHY7VWiIikLoVjkVSWASvH8X7joUNjD7RtCzVqZF04Bjj3XFiwAPLyoq5EREQOROFYJJWtXu0/i2/UKOpKKmzyZOjZE74ZY161qp9YkUXj3OLOOMN/+2qtEBFJXQrHIqls1Spo2tQnqjS0Ywd88EGxfuO4LJxYAf4HhKFD4dln1VohIpKqFI5FUtnq1WndUvHBB7Br1wHCcZZNrIg791xYuNDPPRYRkdSjcCySylatSuuL8SZP9mPMhgzZ7wtZOrEC1FohIpLqFI5FUlmarxxPngz9+kHduvt9oWtXf5+FrRWNGvmVdE2tEBFJTQrHIqmqsBAKCtJ25fjrr/0Yt++0VICfWFGzZlaGY/Azj7/8UlMrRERSkcKxSKpat84H5DRdOZ4yBYqKYNiwEr6YxRMrAEaO9PdvvRVtHSIi8l0KxyKpKs03AJk8GWrXhgEDDvCErl2zduW4eXNo187vHCgiIqlF4VgkVaX5BiCTJsHRR0P16gd4QhZPrAA45hiYOtWvrouISOpQOBZJVWm8crxypR9EUWK/cVx8YkWWtlYccwxs2ABz5kRdiYiIFKdwLJKq4ivHaRiO41tGKxwf2DHH+PspUyItQ0RE9qNwLJKqVq+GevV8426amTwZGjb020YfUJs2WT2xolUrf1PfsYhIalE4FklVq1en5aqxc77f+LjjoEppf8NUreovysvieWbHHAPvvqt5xyIiqUThWCRVFRRA06ZRV1FuCxbAihUHGOG2v549sz4cr1uXtZ0lIiIpSeFYJFWlaTieNMnfl9pvHNejh/8+CwpCrSlVxfuO1VohIpI6FI5FUlWahuPJk6F1a78JXpniTclZunrctq2feaxwLCKSOhSORVLR7t2wcWPahePCQnj7bb9qbJbAC3r08PeffRZqXanKzK8ev/OO+o5FRFKFwrFIKlqzxt+nWTieMQM2bUqw3xj8SIvmzbN25Rh8OC4o8L3aIiISPYVjkVQU78FNs3Ac7zc+7rhyvKhHj6xdOQb1HYuIpBqFY5FUlKbhePJkn3WbNCnHi3r29Nvp7d4dWl2prGNHqF8fpk+PuhIREQGFY5HUlIbheMcOeO+9BKdUFNejB+zZA/Pnh1JXqjODXr18S4qIiERP4VgkFaVhOP7gA9i1qwLhOMsnVgD07g2zZ/ufEUREJFoKxyKpqKAADjoorbaOnjQJcnLg6KPL+cKOHaFGjazuO+7d2/9gMW9e1JWIiIjCsUgqSsMZx5MnQ//+ULduOV+YkwPdumX1ynGvXv5erRUiItFTOBZJRWkWjjduhGnTyjHCbX9ZPrGiY0f/IcHMmVFXIiIiCsciqaigoJwjH6I1ZYrfxKLc/cZxPXtm9TbSVatCbq5WjkVEUoHCsUgqSrOV40mToE4d31ZRIfGd8rK8tWLWLCgqiroSEZHspnAskmr27oX169MqHE+e7C/Eq169ggdQOKZ3b9i6FRYtiroSEZHspnAskmrWrvU9CmkSjpcvhy++qES/MUCjRnDYYVndd9y7t79X37GISLQUjkVSTZrNOJ482d9XuN84rkePrF457toVqlVT37GISNQUjkVSTZqF4wkToHFjOOKISh6oZ0/4/POs3Ua6enX/Hioci4hES+FYJNWkUTguLITx42HkSKhS2b9N4ttIf/FFILWlo969fVuFc1FXIiKSvRSORVJNGoXjTz6BDRt8OK60+DbSWdx33KuXvxZz+fKoKxERyV4KxyKpZs0aqFmzAlvNJd8bb/gV4xNOCOBgHTv63oIsDse6KE9EJHoKxyKpJj7j2CzqSso0bhwMHAgNGgRwsGrVfNNtFifDHj38DxvqOxYRiY7CsUiqSZMNQAoKYPr0gFoq4vr08ftQZ2nTbe3a0KmT3wxERESioXAskmrSJBy/+aa/P+mkAA/apw98/TV8+WWAB00vXbvCvHlRVyEikr0UjkVSTZqE4zfegEMPhdzcAA/ap4+///TTAA+aXrp29T8b7NoVdSUiItlJ4VgklRQV+R3yUjwc793r5xuPHBlwa3S3bv5ixGnTAjxoeunSxf8xWLgw6kpERLKTwrFIKlm/3g8PTvFw/PHHsHFjwC0V4C/Ky83N+nAMfj8UERFJPoVjkVSSJjOO33gDqlaFYcNCOHifPv5Kv8LCEA6e+jp18qvx6jsWEYmGwrFIKomH4yZNoq2jDK+9BoMGQf36IRy8b1/Yti1rd8qrVQvatFE4FhGJisKxSCpJg5XjJUv8Ph2nnRbSCeIX5WV5a4XaKkREoqFwLJJK0iAcv/yyvz/99JBO0KkT1KmT9eF4wYKs7SwREYmUwrFIKiko8BelHXJI1JUc0Isv+p3c2rYN6QRVq8KRR2b9OLddu/wqvYiIJJfCsUgqKSjw/cYpunX02rXw3nshrhrH9enjt4nbsyfkE6UmTawQEYmOwrFIKknxDUBee83P4E1KON65M2vTYTwc66I8EZHkUzgWSSUpHo5ffBFatgx4V7ySZPlOeQcfDIcdpnAsIhIFhWORVJLC4XjrVr8r3umnJ6Hro317nxCz/KK8LF04FxGJlMKxSKpwDtasSdlwPGGCv0jsjDOScDIzv3qc5eF4/nz/x0JERJJH4VgkVWzc6C9AS9Fw/OKL0KABDB6cpBP26QN5eT6RZ6GuXWHLFlixIupKRESyi8KxSKpI4RnHu3f7i/FOOQVycpJ00r59/Q8LeXlJOmFq0cQKEZFohBqOzWypmc02s1lmlr2fj4okIoXD8cSJsGkTnHtuEk+a5TvlaWKFiEg0krFyPNQ5l+uc65OEc4mkrxQOx08/7fclGT48iSdt2RIaNcraiRVNmvj3XOFYRCS51FYhkipSNBzv2OG3jD7zTKhePYknNoMBA+CDD5J40tRh5vuO1VYhIpJcYYdjB0wws+lmdmVJTzCzK81smplNW7t2bcjliKSwggK/dXLDhlFX8i1vvOEvDBs9OoKTDxkCX3zhp3hkoc6d/cQKERFJnrDD8SDnXG9gJPAjMzt6/yc45+53zvVxzvVp3LhxyOWIpLCCAmjcGKqk1gc6Tz/tyzr22AhOHh+N8d57EZw8eh06+C27N2+OuhIRkewR6r/CzrmVsfs1wItAvzDPJ5LW1qzxjaYpZOtWP6XinHOSOKWiuD59oGbNrA3H7dv7+0WLoq1DRCSbhBaOzayOmdWN/xo4AZgT1vlE0l4K7o736qu+5ziSlgrwTc79+8PUqREVEK0OHfy9wrGISPKEuXLcFHjPzD4DPgFed869GeL5RNJbCobjp5+G5s1h0KAIixgyBGbO9MvYWaZdO3+vcCwikjyhfVDqnFsM9Azr+CIZxbmUC8ebNsGbb8KPfhRxG/TgwVBYCB99BMOGRVhI8tWpA82aKRyLiCRTal35I5KttmyBnTtTKhw/95zfGS+yloq4gQN9Os/S1or27RWORUSSSeFYJBXER5WlUDh+7DE/Sqxv34gLqVcPcnOzNhx36AALF0ZdhYhI9lA4FkkF8Q1AUmRaxeLFPoteeKHfjCJyQ4b4tordu6OuJOnat4fVq7Oy5VpEJBJlhmMzu83M6plZNTObbGbrzOx7yShOJGuk2O54Tzzh77+XKv+nDx7sx2bMnBl1JUkXH+f25ZfR1iEiki0SWTk+wTm3GTgFyAc6AteFWpVItkmhcOwcPP44DB0KLVtGXU3MkCH+PgtbKzTrWEQkuRIJx9Vi9ycBY51zG0KsRyQ7xcNxCuwS+dFHPohddFHUlRTTtKlvvlU4FhGRkCUSjl8xs/lAH2CymTUGdoZblkiWWbMGGjaEatXKfm7IHnsMatWCs86KupL9DBkC778PRUVRV5JUdev6nw10UZ6ISHKUGo7NrArwKjAQ6OOc2wNsB05LQm0i2SNFZhzv2uU3/jjzTB/KUsrgwbB+PcyfH3UlSadxbiIiyVNqOHbOFQG3O+c2OucKY49tc86tTkp1ItmioCAlJlW89prf/COlWirisrzvWOFYRCQ5EmmrmGBmZ5mlxEAnkcyUIivHjz/ud2Q7/vioKylBu3Zw6KFZG45XrIDt26OuREQk8yUSjn8OPAvsMrPNZrbFzDaHXJdIdkmBcLxuHbz+OlxwAVStGmkpJTPzIzQmTcq6vuMOHfz94sXR1iEikg3KDMfOubrOuSrOuerOuXqx/66XjOJEssKOHX776IjD8dNPw969KdpSETdihP9BIi8v6kqSKj6xQhfliYiELyeRJ5nZIUAHoGb8Mefcu2EVJZJVUmTr6Mce87s0H3FEpGWU7oQT/P0bb/his0S7dv5efcciIuFLZIe8y4F3gfHAH2L3N4VblkgWSYGto+fNg08/TfFVY/A9x716wZtvRl1JUtWvD40aKRyLiCRDIj3HPwX6Asucc0OBXsDaUKsSySYpsDve44/7PuMxYyIrIXEjR/p5x19/HXUlSaWJFSIiyZFION7pnNsJYGY1nHPzgU7hliWSRSIOx0VF8MQTcOKJfmE25Y0YAYWFMHly1JUkVYcOCsciIsmQSDjON7P6wEvARDN7GVgZZlEiWSXicPzOO7B8eRq0VMQNHAgHH+z7jrNI+/b+92mn9icVEQlVmRfkOefOiP3yJjN7GzgYyK6GP5EwrVkD9epBzZplPzcEjz/uTz9qVCSnL7+cHBg2zPcdO+dHvGWBdu38t7t0KXTuHHU1IiKZ64Arx2bW18xGFn/MOfdO7JepfD27SHqJcMbxzp3w/PN+u+hatSIpoWJGjID8fJg7N+pKkqZNG3+vWcciIuEqra3ib8C8Eh7/PPY1EQlChFtHjxsHmzfD+edHcvqKGzHC32fR1Ip4OF6yJNo6REQyXWnhuKFzbun+DzrnFgENQ6tIJNtEuHI8dqzP5UOHRnL6imvRArp3z6q+40MP9Z03CsciIuEqLRyX9iFrnaALEclaEYXjzZvh1VfhvPN8G2/aGTkSpk6FrVujriQpzPzqscKxiEi4SgvHk8zsz2bfvtrFzP4AvBVuWSJZYs8e2LAhknD80kuwa1eazDYuyYgR/v17K3v+OmrTRj3HIiJhKy0c/wJoCywys+djt0X4Gcc/T0p1IplubWw/nQjC8VNPQevWMGBA0k8djEGDoE6drOs71sqxiEi4DhiOnXPbnHNjgOHAI7HbCc650c657PgcUyRsEW0dvWYNTJrkV43TdhJajRp+pNsrr/idTLJA27Z+Y8CNG6OuREQkc5W5CYhzbrFz7tXYTR/oiQQpog1Ann3WbzKXti0VceeeCytW+O2ks4AmVoiIhC+RHfJEJCwRheOxY/2whyPSfWL5qFF+QPPTT0ddSVIoHIuIhK+0TUDaJLMQkay0Zo2/T2I4XrUKPvgAzjknaacMz0EHwamn+qXwvXujriZ02ghERCR8pa0cPwdgZpOTVItI9iko8CufBx2UtFO++qrfhviMM8p+bloYPdpf2JgFUysOPhgOOUQrxyIiYSptumkVM/s90NHMvjOdwjl3R3hliWSJ+IzjJF4V9+KL0K6db6vICCNHQr16vrXihBOiriZ0bdsqHIuIhKm0lePRwE58gK5bwk1EKivJW0dv3gyTJ8Ppp6fxlIr91azpl8FfeMEPbs5wGucmIhKuA64cO+e+AG41szznXPbs0SqSTAUF0KpV0k43bpzfNyNjWiriRo+GRx+F8eP9RXoZrE0b3xpTVARVdEm1iEjgEvmr9QMzu8PMpsVut5vZwaFXJpIN1qxJ6sV4L73kF6rTduOPAzn+eGjYMCumVrRp4xfIV62KuhIRkcyUSDh+CNgCnBu7bQYeDrMokaxQVOQvJEtSON61y68cn3YaVK2alFMmT7VqfvzGyy/Dtm1RVxOqtm39vVorRETCkUg4buec+31sM5DFzrk/4LeVFpHKWL/e78SRpHD81luwZYvvN85Io0fD9u3w2mtRVxIqzToWEQlXIuF4h5kNjv+HmQ0CdoRXkkiWSPLW0S+95CfGHX98Uk6XfIMHw2GH+R1OMlirVv5iSoVjEZFwlDbKLe4q4LFifcYbgYvDK0kkSyRxd7yiIt9xcNJJUKNG6KeLRtWqcMEFcOedfkvp5s2jrigUNWr4nwG0EYiISDjKXDl2zn3mnOsJ9AB6OOd6Oefywi9NJMMlcXe8GTN8Fs/wQQ5w1VW+VeU//4m6klBp1rGISHgSHgTknNvsnNscZjEiWSWJK8cTJvj74cNDP1W02raFk0/24TiDZx5r1rGISHg0JVMkKgUFfsrCIYeEfqoJE6BXr6TuNxKdH//Yr8o/91zUlYSmTRvIz4fdu6OuREQk8ygci0QlvjteyFvVbdkC778PJ54Y6mlSx7Bh0LEj/POfUVcSmjZtwDn46quoKxERyTwJhWMzO8rMzjezi+K3sAsTyXhJ2jp6yhTYuxdOOCH0U6WGKlXgRz+Cjz6CadOiriYU8VnHuihPRCR4ZYZjM3sc+DswGOgbu/UJuS6RzFdQkJR+4/HjoXZtOOqo0E+VOi65xM+ty9DV49at/f3SpVFWISKSmRIZ5dYH6Oqcc2EXI5JV1qyB7t1DP82ECTB0aAaPcCtJvXpw0UXw4IPwt79B48ZRVxSoww6DnByFYxGRMCTSVjEHODTsQkSyinNJWTlesgQWLsyilorirr7aT6x44IGoKwlc1arQsqXCsYhIGBIJx42Az81svJm9Er+FXZhIRvv6az9qIORwHB/hlpXhuEsXvx3gv/4FO3dGXU3gWrdWOBYRCUMibRU3hV2ESNZJ0tbREyb4FcZOnUI9Ter69a/99Ir//tePeMsgrVvDm29GXYWISOZJZIe8d4D5QN3YbV7sMRGpqCRsALJ3L0ye7FeNQ54Wl7qOOw6OOQb+/GfYvj3qagLVujWsXJnRe52IiEQikWkV5wKfAOcA5wIfm9nZYRcmktGSsHX0p5/67o2sbKmIM4M//cn/MPLvf0ddTaDiEys061hEJFiJ9Bz/FujrnLvYOXcR0A/4XbhliWS4JKwcvxP7fOfYY0M7RXoYMsTvgHLLLX5HlAyhcW4iIuFIJBxXcc6tKfbf6xN8nYgcSEGB36yiUaPQTvHuu/6atAybYlYxf/wjrF8Pd98ddSWBUTgWEQlHIiH3zdikikvM7BLgdWBcuGWJZLiCAh+Mq1YN5fCFhX7L6KOPDuXw6adfPxg1Cv7+d9i4MepqAqFZxyIi4UjkgrzrgPuBHkBP4H7n3K/CLkwko4W8dXReHmze7DsKJOaPf/RN2HfcEXUlgdCsYxGRcCQyyg3n3PPA8yHXIpI91qwJtd946lR/r3BcTM+ecM45cOedcNVV0Lx51BVVmmYdi4gE74Arx2b2Xux+i5ltLnbbYmabk1eiSAYKeXe8qVOhVSu/sijF3HKLn3F33XVRVxIIhWMRkeAdMBw75wbH7us65+oVu9V1ztVLXokiGSjEcOycvxhPq8YlaNsWfvUrGDsWpkyJuppK06xjEZHgJTLn+PFEHivl9VXNbKaZvVbe4kQy0rZt/hZSOF640Hdt6GK8A/jVr/yy+o9/DHv2RF1NpWjWsYhI8BKZVtGt+H+YWQ5wZDnO8VNgXnmKEsloIW8d/e67/l4rxwdQuzbcdRfMmQP/+lfU1VSKxrmJiASvtJ7jX5vZFqBH8X5joAB4OZGDm1kL4GTggUCqFckEIe+ON3Wqn23cqVMoh88Mp53mNwb5/e9h9eqoq6kwhWMRkeCV1nP8V+Bg4LH9+o0bOud+neDx7wJ+CRQd6AlmdqWZTTOzaWvXri1P7SLpKeTd8aZO9avGZqEcPjOYwT/+ATt2+DaLNKVZxyIiwSu1rcI5V4SfbVxuZnYKsMY5N72Mc9zvnOvjnOvTWFt5STYIMRzn58OSJWqpSEjHjnDttfDYY2l7cZ5mHYuIBC+RnuOPzKxvBY49CBhlZkuBp4HjzOyJChxHJLOE2HOs+cbldMMNfoLFlVfCzp1RV1MhGucmIhKsRMLxUOBDM/vSzPLMbLaZ5ZX1Iufcr51zLZxzrYHRwFvOue9Vsl6R9FdQAPXrQ/XqgR/6gw+gTh2/34UkoHZtuO8+P+Lj5pujrqZCFI5FRIKVyA55I0OvQiSbhLg73iefQJ8+vg9VEjR8OFx0Edx6K5x3HhxxRNQVlUvxWcc1akRdjYhI+itz5dg5twyoD5wau9WPPZYw59wU59wpFapQJNOEtAHIrl0waxb07x/4oTPf7bf71fwrroDCwqirKRfNOhYRCVYim4D8FHgSaBK7PWFmPw67MJGMFVI4/uwz2L0b+vUL/NCZr1EjuPNO+PhjuPfeqKspF41zExEJViI9x5cB/Z1zNzrnbgQGAFeEW5ZIBgspHH/yib9XOK6gCy6AE06AX/8aVqyIupqEtWrl7xWORUSCkUg4NqD454yFscdEpLx27YJNm0ILx82aQYsWgR86O5j5VeO9e+Gaa6KuJmGadSwiEqxEwvHDwMdmdpOZ/QH4CHgw3LJEMlR8d7wQxrh9/LFfNdbmH5XQti389rfw7LMwfnzU1SQkJwcOP1zhWEQkKIlckHcH8H/ABmA98H/OubtCrkskM4W0dfTGjbBggVoqAnHddX7v7R/9yO+glwY0zk1EJDiJrBzHGeBQS4VIxYW0O960af5ekyoCUKMG/Pvf8OWXcMstUVeTEIVjEZHgJDKt4kbgUeAQoBHwsJndEHZhIhkppHD88cf+vk+fQA+bvY47Ds4/34fjBQuirqZMrVvDqlW+pV1ERConkZXjMUBf59xNzrnf46dVXBBuWSIZKqStoz/5BDp3hoMPDvSw2e3226FWLd9e4VzU1ZSqdWtf4vLlUVciIpL+EgnHS4Gaxf67BvBlKNWIZLqCAr+/c506gR3SOR+O1W8csEMP9VtKT5oEr74adTWl0qxjEZHgJBKOdwFzzewRM3sYmANsNbN/mNk/wi1PJMOEsHX08uU+c6vfOARXXeUvzvvVr/yItxSlcCwiEpycBJ7zYuwWNyWcUkSyQAgbgMT7jbVyHIKcHLj1Vjj9dHjwQfj+96OuqESadSwiEpwyw7Fz7lEzqw50jD30hXNuT7hliWSoggJo3z7QQ37yiR+w0KNHoIeVuFGjYPBg+P3v/S56Bx0UdUXfoVnHIiLBSWRaxbHAQuBfwL+BBWZ2dLhliWSoEFaOP/0UcnOhevVADytxZvC3v/nfu9tvj7qaA9I4NxGRYCTSc3w7cIJz7hjn3NHAicCd4ZYlkoH27oV16wINx0VFMHMm9O4d2CGlJAMGwNln+5C8enXU1ZRI4VhEJBiJhONqzrkv4v/hnFsAVAuvJJEMtX69Hy0R4Bi3JUtg82bo1SuwQ8qB/OUvfpDwH/4QdSUlat0aVq7UrGMRkcpKJBxPN7MHzezY2O2/wPSwCxPJOCFsADJzpr/XynESdOjgp1f897+waFHU1XyHZh2LiAQjkXB8FTAX+AnwU+Dz2GMiUh4hheOcHOjePbBDSml++1v/hv/971FX8h0a5yYiEoxSw7GZVQGmO+fucM6d6Zw7wzl3p3NOH9yJlFcI4XjGDOja1U+rkCQ49FC45BJ4+GG/X3MKUTgWEQlGqeHYOVcEfGZmLZNUj0jmCjgcO+fDsVoqkuzaa/3FlXffHXUl36JZxyIiwUikraIZfoe8yWb2SvwWdmEiGWfNGj9vrV69QA63apU/pC7GS7L27eGcc+Dee+Hrr6Ou5huadSwiEoxEdshLzUuzRdJNfMaxWSCHi1+Mp3AcgV/9Cp55xgfk66+PuppvaJybiEjlHXDl2MxqmtnPgHOAzsD7zrl34rdkFSiSMQLeACQejnNzAzukJKpXLzjhBLjrLti5M+pqvqFwLCJSeaW1VTwK9AFmAyPxm4GISEUFHI5nzPDTxerWDeyQUh7XX+9/Tx99NOpKvqFZxyIilVdaOO7qnPuec+4/wNnAkCTVJJKZVq2CZs0CO9zMmWqpiNSxx0K/fnDbbf4CvRSgWcciIpVXWjjeE/+Fcy41/uYXSVeFhf7quUMPDeRwGzf6j881qSJCZr73ePFieO21qKsBNM5NRCQIpYXjnma2OXbbAvSI/9rMNierQJGMsHYtFBUFtnKsi/FSxKhRfobaf/8bdSWAwrGISBAOGI6dc1Wdc/Vit7rOuZxivw5mFpVItli92t8HtHKscJwicnLgssvgjTfgq6+irobDDoOqVRWORUQqI5E5xyJSWfHd1AJaOZ4xA1q0gMaNAzmcVMZll/n7Bx+Mtg4061hEJAgKxyLJEHA41sV4KaRVKxgxwofjFLgwT+PcREQqR+FYJBkCbKvYsQO++ELzjVPKlVfCihW+vSJiCsciIpWjcCySDKtWQf36ULNmpQ/1+ef+2r4ePSpflgTk5JP9pwL33x91JZp1LCJSSQrHIsmwalVgF+PNnu3vjzgikMNJEKpVg0svhXHjIh8yrFnHIiKVo3AskgyrVwfWb5yX5xeg27cP5HASlMsu86n0oYciLSM+zm3ZskjLEBFJWwrHIskQ4O54s2dD9+5+ZJekkDZt4IQT4IEH/KYvEdGsYxGRylE4Fgmbc37lOKC2irw8tVSkrCuugPx8mDgxshKaN9esYxGRylA4Fgnbli2wfXsgK8cFBX4Xal2Ml6JOOQUOPhiefjqyEjTrWESkchSORcIW4IxjXYyX4mrUgDPPhBdfhJ07IytD49xERCpO4VgkbAHOOM7L8/daOU5ho0fD5s3w5puRlaBwLCJScQrHImELeOW4aVNtG53SjjsOGjWCsWMjK6F1a78nye7dkZUgIpK2FI5FwhbwyrFWjVNcTg6ccw68+ips3RpJCZp1LCJScQrHImFbtcr3oh5ySKUOs3ev3x1P4TgNjBnj9/l+9dVITq9xbiIiFadwLBK2+O54ZpU6zKJF/hovXYyXBgYN8jPVIppaoXAsIlJxCsciYQtoxnF8UoVWjtNAlSpw3nnwxhuwcWPST69ZxyIiFadwLBK2gHbHy8vzgadLlwBqkvCNHg179sBLLyX91Jp1LCJScQrHImGLt1VUUl4edOwINWsGUJOEr08faNs20tYKhWMRkfJTOBYJ0+7dsH59YGPc1G+cRsz86vHkyX5bwyRTOBYRqRiFY5EwFRT4+0qG4y1bYMkS9RunnfPOg8LCSForNOtYRKRiFI5FwhTQjOM5c/y9wnGaOeIIaNMGXnkl6afWrGMRkYpROBYJU0C748W3jVZbRZoxg9NOg0mTkr4hiMa5iYhUjMKxSJji4biSK8ezZ0PdutCqVQA1SXKNGgW7dsHEiUk9rcKxiEjFKByLhGn1ar962LRppQ6Tl+dXjSu5j4hEYfBgvztiklsrNOtYRKRiFI5FwrRqFTRqBNWqVfgQzvmVY/Ubp6lq1eCkk+C11/zFeUmSkwMtWigci4iUl8KxSJgC2B0vPx82bVI4TmunnQbr1sGHHyb1tBrnJiJSfgrHImEKYHc8XYyXAU480a8gv/xyUk+rcCwiUn4KxyJhCiAcz57t7xWO01i9enDccUnvO27Txs863rUrqacVEUlroYVjM6tpZp+Y2WdmNtfM/hDWuURSknOBtFXk5UHLlnDwwQHVJdEYNQoWLID585N2yrZt/R/DZcuSdkoRkbQX5srxLuA451xPIBcYYWYDQjyfSGrZsAH27Alk5Vj9xhlg1Ch/n8TV43bt/P2XXybtlCIiaS+0cOy8+NT7arGbC+t8IikngBnHu3f7hUa1VGSAFi2gd++k9h23bevvFY5FRBIXas+xmVU1s1nAGmCic+7jEp5zpZlNM7Npa9euDbMckeSKbx1diZXj+fNh716tHGeM007zEyvWrEnK6Zo2hdq1YfHipJxORCQjhBqOnXOFzrlcoAXQz8y6l/Cc+51zfZxzfRo3bhxmOSLJFcDW0fFJFQrHGWLUKN8E/PrrSTmdmV891sqxiEjikjKtwjm3CZgCjEjG+URSQnzluBJtFXl5UL06dOgQUE0SrZ49/Q9Lb76ZtFO2a6eVYxGR8ghzWkVjM6sf+3UtYBiQvMu0RaK2ahXUqQN161b4ELNnQ9euldpgT1KJGYwYARMn+n6ZJGjb1odjpys+REQSEubKcTPgbTPLAz7F9xy/FuL5RFLLqlWBjHHTxXgZZuRI2LgRPv00Kadr1w62b4eCgqScTkQk7eWEdWDnXB7QK6zji6S81asr1W+8fj2sXKl+44wzbBhUqeJbKwYODP10xSdWVPJnNRGRrKAd8kTCUsmVY+2Ml6EOOQQGDIA33kjK6TTrWESkfBSORcKyYgU0b17hlyscZ7ARI2DaNEjC+MrWrX2rsy7KExFJjMKxSBg2b4atW/3GDxWUlweNGlV6gz1JRSNG+CvkJk4M/VTVq8Phh2vlWEQkUQrHImHIz/f3lVg5jl+MZxZQTZI6jjzS/+STpJFuGucmIpI4hWORMKxY4e8rGI6LimDOHF2Ml7GqVIETT4Tx4/1vdsi0EYiISOIUjkXCUMlwvHixH7+lcJzBRozw20jPnBn6qdq186Pctm0L/VQiImlP4VgkDPFwfNhhFXp5fNtoXYyXwU44wd8nobUiPs5NrRUiImVTOBYJQ34+NGwItWpV6OWzZ/te427dAq5LUkeTJr73OAnhOD7OTeFYRKRsCsciYajkGLe8POjQAWrXDrAmST0jR8KHH8KmTaGepvhGICIiUjqFY5EwBBCO1VKRBUaMgMJCmDQp1NM0aAD16ysci4gkQuFYJAyVCMfbtvkQo4vxskD//lCvXlLmHbdtq7YKEZFEKByLBG33bj+FoILheO5cvz+EwnEWyMmBoUOTEo7btdPKsYhIIhSORYK2apVPtxXcHS8+qULhOEsMHw5LloS+rNu2LSxd6rs4RETkwBSORYJWyRnHeXlQpw60bh1cSZLChg3z9yGvHrdrB3v27Nu8UURESqZwLBK0Sobj2bP9xXhV9H9ndujYEQ4/PPRw3L69v1+0KNTTiIikPf3zKxK0SoRj5/zKsVoqsoiZb614661Qex46dvT3CxaEdgoRkYygcCwStPx8qFnTz88qp5UrYcMGjXHLOsOGwcaNMGNGaKc47DA/N1vhWESkdArHIkGLj3EzK/dLZ8/291o5zjLHH+/vQ2ytMPMbyyxcGNopREQygsKxSNAqMeM4PqlCK8dZpkkTyM0Nve+4Y0etHIuIlEXhWCRolQzHLVrAIYcEXJOkvmHD4IMP/C4wIenY0U+M27MntFOIiKQ9hWORIDlX6XCsloosNXy430Bm6tTQTtGhg7/mb8mS0E4hIpL2FI5FgrR+PezaVaENQHbvhvnzFY6z1pAhUKNGqK0VmlghIlI2hWORIFVijNsXX/iPu9VvnKVq1YJBg2DSpNBOoXAsIlI2hWORIFUiHGvbaGH4cP8HoaAglMM3bOgnDGpihYjIgSkciwSpEuF49myoVg06dQq4Jkkfw4f7+5BXj7VyLCJyYArHIkHKz/cDZZs1K/dL8/KgSxcfkCVL5eb6pd0Qw3GHDgrHIiKlUTgWCdKKFdC0aYUSriZVCFWr+g1BJk70k09C0LGj/xkuxIlxIiJpTeFYJEgVHOO2YYN/qcKxMHy4/8Mwf34oh49flLdoUSiHFxFJewrHIkGqYDiObxutSRXCsGH+PqTWing41kV5IiIlUzgWCVJ+viZVSOW0aQPt2oU277h9e3+vvmMRkZIpHIsEZccO2LixwivHDRtW6Do+yUTDh8OUKaHs83zQQXDYYQrHIiIHonAsEpT4GLcK7I6Xl+dbKswCrknS07BhsGULfPJJKIfXODcRkQNTOBYJSgVnHBcV+ZVjtVTIN447DqpUCa21QuFYROTAFI5FglLBcLx4MWzfrnAsxRxyCPTpE2o4Xr/eT0kREZFvUzgWCUp+vr8vZzjWpAop0bBh8PHH8PXXgR+6Qwd/r4kVIiLfpXAsEpQVK/zVTvXqletleXm+17hbt5DqkvQ0fDgUFsI77wR+6Pg4ty++CPzQIiJpT+FYJCgrVlT4Yrz27aFOnRBqkvQ1cCDUrh1Ka0XbtpCTA/PmBX5oEZG0p3AsEpQKbgDy2WfqN5YS1KgBRx8dSjiuXt2vHn/+eeCHFhFJewrHIkGpwAYgX38NX34JvXqFVJOkt+HDfe/D8uWBH7prV4VjEZGSKByLBGHPHli5Elq2LNfLPvvM3yscS4mGD/f3IWwl3a2b/8Fsx47ADy0iktYUjkWCkJ/vBxa3alWul82Y4e979w6hJkl/3btD06ahtFZ07QrO6aI8EZH9KRyLBGHZMn/funW5XjZzJhx6qL+JfIeZH+k2aZL/4StA8ekoc+cGelgRkbSncCwShHg4rsDKsVaNpVTDh8PatfsGYgekQweoWlV9xyIi+1M4FglCPBwffnjCL9mxw4/SUr+xlGrYMH8fcGtF9eo+ICsci4h8m8KxSBCWLfO9ETVrJvySOXP8Hg9aOZZSNW8OXbqEdlGe2ipERL5N4VgkCMuWVfhiPK0cS5mGD4d334WdOwM9bNeufmJFwIcVEUlrCsciQVi6tEIX49WvX+6XSTYaPtz34XzwQaCH7dbNX+eniRUiIvsoHItUVlGR36ShnCvHM2f6VWOzkOqSzHHMMX6/54BbK7p29ffqOxYR2UfhWKSyVq+G3bvLFY737oW8PLVUSILq1oUBAwK/KK9jR02sEBHZn8KxSGVVYIzb/Pm+z1MX40nChg+H6dNh/frADlmjBrRvr4vyRESKUzgWqawKhGNdjCflNmyY39Lu7bcDPWzXrlo5FhEpTuFYpLIqEI5nzoRataBTp5BqkszTrx/Uqxd4a0W3brBoEezaFehhRUTSlsKxSGUtXQoNGvi+0ATNnAk9e/p+T5GE5OTA0KGBh+OuXf287QULAj2siEjaUjgWqaxyzjguKto3qUKkXIYNgyVL/HDigHTr5u/VWiEi4ikci1RWOcPxokWweTMceWSINUlmGj7c3wc40q1jR6hSRRfliYjEKRyLVIZz5Q7Hn3zi7/v3D6kmyVwdO0LLljB+fGCHrFkTOnSA2bMDO6SISFoLLRyb2eFm9raZzTOzuWb207DOJRKZDRtg27Zyh+M6daBLlxDrksxkBiNG+JXj3bsDO2xuLsyaFdjhRETSWpgrx3uBXzjnugADgB+ZWdcQzyeSfEuX+vtyhONPP4U+fXQxnlTQyJGwZUugW0nn5vo/yhs3BnZIEZG0FVo4ds6tcs7NiP16CzAPaB7W+UQiER/j1rp1Qk/fvdtfjNevX3glSYY77jg/ueLNNwM7ZPzi0M8+C+yQIiJpKyk9x2bWGugFfFzC1640s2lmNm3t2rXJKEckOOWccTx7tp8n27dviDVJZqtXDwYPhjfeCOyQubn+fubMwA4pIpK2Qg/HZnYQ8DzwM+fc5v2/7py73znXxznXp3HjxmGXIxKsZct8A3GDBgk9PX4xnlaOpVJGjoS8PFixIpDDNW0KzZopHIuIQMjh2Myq4YPxk865F8I8l0gk4pMqzBJ6+iefQJMmfuCASIWNHOnvA26t0EV5IiLhTqsw4EFgnnPujrDOIxKpCoxx69cv4SwtUrLu3aF588BbKz7/HHbuDOyQIiJpKcyV40HAhcBxZjYrdjspxPOJJN/SpQlfjLd5M8ybp5YKCUB8pNvEibBnTyCH7NXLbyOtzUBEJNuFOa3iPeecOed6OOdyY7dxYZ1PJOm2bPGzrxJcOZ4+3e8ZonAsgRg50v/E9dFHgRwuPrFCfcciku20Q55IRZVzUkX8YjxNqpBADBvmR7oF1FrRpg3UratwLCKicCxSURUIx+3bJzzYQqR0Bx8MRx0VWDiuUkU75YmIgMKxSMVVIByrpUICNXKkT7OrVgVyuF69/EYghYWBHE5EJC0pHItU1LJlUL06HHpomU9duRLy8xWOJWDxkW7jxwdyuNxc2LYNFi0K5HAiImlJ4VikopYu9QOLq5T9v9HHsb0hFY4lUD16wGGHweuvB3K4+EV5aq0QkWymcCxSUeWYcfzee1CzJhx5ZMg1SXYxg1NO8ZuB7NpV6cN17QrVqumiPBHJbgrHIhVVjnA8dSr07++7MEQCddppsHUrvP12pQ9VvTp066ZwLCLZTeFYpCK2bYPVq6Ft24SeOmMGDB6chLok+xx3HNSpAy+/HMjheveGadP8TG4RkWykcCxSEfErljp0KPOpH3/sr/5XOJZQ1KwJJ54Ir7wCRUWVPtyAAbBhgy7KE5HspXAsUhELF/r7BMLx1Km+NXTgwJBrkux12ml+JMqMGZU+VPzP6YcfVvpQIiJpSeFYpCLi4bh9+zKf+t570LOn37NBJBQnnwxVqwbSWtG1K9Srp3AsItlL4VikIhYtgqZN/X67pdi714cMtVRIqBo29H/IAgjHVar4kYMffRRAXSIiaUjhWKQiFi5MqKXis8/8BXkKxxK6UaNg9mxYsqTShxo4EPLy/BAMEZFso3AsUhEJhuOpU/29wrGE7rTT/P0rr1T6UAMH+mv7Pv200ocSEUk7Csci5bVlix/jlkA4fu89aNMGmjdPQl2S3dq180OKA2it6N/f36u1QkSykcKxSHklOMbNOR+OtWosSXPaafDuu34WWyU0aACdOumiPBHJTgrHIuWV4Bi3L7+EggKFY0miUaP8UO033qj0oQYO9OFYm4GISLZROBYprwTHuKnfWJKub19o1gxefLHShxowANat8z/kiYhkE4VjkfJauBAOO8xv2VuKt96Cxo2hc+ck1SVSpQqceSaMG1fpURPxzUDUdywi2UbhWKS8EphU4RxMmgTDhvm8IpI0550HO3bAq69W6jDdusFBB6nvWESyj/7ZFimvRYvKDMdz5viBFsOHJ6kmkbhBg/x4lGeeqdRhqlb1m4EoHItItlE4FimPzZthzZoy+40nTfL3w4YloSaR4qpUgXPO8RflbdpUqUNpMxARyUYKxyLlkeCkiokT/Sisww9PQk0i+zvvPNi9u9Izj48+2g+/eO+9gOoSEUkDCsci5ZFAON61C955Ry0VEqH+/aFVq0q3VgweDNWqweTJAdUlIpIGFI5FyiMejtu1O+BTPvoItm9XS4VEyMyvHk+cCOvXV/gwtWv71oq33gqwNhGRFKdwLFIeCxdCixY+NRzAxIn+YqZjj01eWSLfcd55sHdvpWceH388zJxZ6U33RETShsKxSHkkMMZt4kT/qfbBByepJpGS9OrlLxytZGvFccf50YRTpgRTlohIqlM4FimPMsLxxo0wbZpaKiQFxFsr3nrLT1ipoH79/H436jsWkWyhcCySqI0bff9mKeH47behqEgX40mKOO88/wfy+ecrfIjq1f3UCoVjEckWCsciiVq0yN+XEo4nTvS7ivXvn6SaRErTvTt07QpPPVWpwxx3HHzxBaxYEVBdIiIpTOFYJFFljHFzDl57zbdUVKuWxLpEDsQMLrrIDypesKDChzn+eH+vqRUikg0UjkUStXChDxtt25b45RkzID8fTjstyXWJlOaii/z4lIcfrvAhevaEBg0UjkUkOygciyRq4UK/5V3NmiV++eWX/c69p5yS5LpEStOsGZx0Ejz6qB/tVgFVqsDQob7v2LmA6xMRSTEKxyKJKmNSxUsv+R3FGjVKXkkiCbn0Uli1CsaPr/Ahjj8eli/f13ovIpKpFI5FElVKOF6yBGbPVkuFpKiTT4YmTeDBByt8iPgEljfeCKgmEZEUpXAskoiCAj/KrXPnEr/88sv+XuFYUlK1anDhhfDqqxWeedy+PXTpAq+8EnBtIiIpRuFYJBGzZ/v7I44o8csvveSnZrVrl7ySRMrl0kt9z/ETT1T4EKNGwTvvwKZNwZUlIpJqFI5FEpGX5+9LCMfr18PUqXD66cktSaRcunaFAQN8a0UFr6o77TSfr9VaISKZTOFYJBGzZ0PTptC48Xe+9NprfhMytVRIyrv0Uvj8c/j00wq9vF8/37qs1goRyWQKxyKJmD37gC0VL78MzZvDkUcmuSaR8jrvPKhdu8IX5lWt6kcVjhsHu3cHXJuISIpQOBYpS2EhzJ0LPXp850tbtsCbb/qWCrPklyZSLvXq+YD8xBP+AtMKOO002LwZ3n034NpERFKEwrFIWb78EnbuLHHl+PnnYccOuOCCCOoSqYif/hS2b4cHHqjQy4cNg1q19k1oERHJNArHImUpZVLF44/7EVcDBiS5JpGK6tnTb3d3zz0V2jGvdm0/8/iVV7RbnohkJoVjkbLk5fn9c7t2/dbDy5fD22/78bFqqZC08rOf+T/AL7xQoZePGgVffbVviIuISCZROBYpy+zZfnm4Vq1vPfzkk37l7Hvfi6gukYo65RQ/lPvOOyv8crMKZ2sRkZSmcCxSlhImVTjnWyoGDYK2bSOqS6SiqlTxvccffeRv5dS0KRx7LDz1lForRCTzKByLlGbbNn9B3n7heOZMPy72wgsjqkuksi65xE+vuOuuCr38ggtg0aIKj0wWEUlZCscipfn8c780tl84fvxxqF4dzj03orpEKqtuXbjiCnjuOd9/XE5nnQU1alRqN2oRkZSkcCxSmvikimIzjvfu9R8nn3oqHHJIRHWJBOHqq/0Pf//8Z7lfWr++/3/g6adhz57gSxMRiYrCsUhp8vL87KpijcUvvQRr1vhPpUXSWuvWfgn4vvsqtCnIBRfA2rUwaVLwpYmIREXhWKQ0s2dDt27+AqaYu+/2WXnkyAjrEgnKDTf4Le/uuKPcLx050n968uSTIdQlIhIRhWOR0uw3qWLGDHjvPf9pdNWqEdYlEpQePeDss/2FeevXl+ulNWrAOefAiy/C1q3hlCcikmwKxyIHUlDgPzMuFo7/8Q+oUwcuvTTCukSC9vvf+8kst99e7pd+73t+N+qXXgq+LBGRKCgcixzIfttGFxTA2LG+1/jgg6MrSyRw3bvDeef5n/7Wri3XSwcNglat4LHHQqpNRCTJFI5FDmS/cPyf/8Du3fDjH0dYk0hYbrzRLwH//e/lelmVKv6TlIkT/dxjEZF0F1o4NrOHzGyNmc0J6xwioZo9G5o0gSZN2L0b7r0XRoyATp2iLkwkBF26wPnn+7Fua9aU66WXX+578O+7L6TaRESSKMyV40eAESEeXyRceXnfzDd+6ilYvRp+8pOIaxIJ0403ws6dcOut5XrZYYfBGWfAww/Djh0h1SYikiShhWPn3LvAhrCOLxKqwkK/O94RR7B7N/zxj9Crl185FslYHTv6PdH/9S9YsqRcL/3BD2DDBnj22ZBqExFJksh7js3sSjObZmbT1pbzQhCR0Hz+uV8C69WLhx/2OeHmm8Es6sJEQvbnP0NODvziF+V62dChvuXo3/8OqS4RkSSJPBw75+53zvVxzvVp3Lhx1OWIeB9+CMDO3kdx880wcKA2/ZAs0bw5/Pa3fnhxOba+M/Orxx9/DDNnhlifiEjIIg/HIinpww+hUSPun9SW/HytGkuWueYaaNcOfvpT2LMn4ZddfDHUquUvXhURSVcKxyIl+fBDtvU9lr/81Rg6FI47LuqCRJKoZk2/nfTnn5erT6J+fT/w4oknYN268MoTEQlTmKPcxgIfAp3MLN/MLgvrXCKBWr8evviCuwt/REGBXzUWyTqnngonnuh3zyvH9SDXXOPb9dV7LCLpKsxpFWOcc82cc9Wccy2ccw+GdS6RQH30EUtpxc3vDOGMM+Coo6IuSCQCZnDXXX5b6d/8JuGXdesGp5wC99zj9xQREUk3aqsQ2Y/74EOu5l9UyanC3XdHXY1IhDp3hp/9DB54AN5+O+GX/epXvq3i4YfDK01EJCwKxyL7eenVKrzOyfzxj8bhh0ddjUjE/vAH6NDB7xG9ZUtCLxk0yE94uf122Ls35PpERAKmcCxSzJZNhfx4zvfp2TBfu+GJANSuDY88Al99Bddem9BLzPzq8ZIl8Nxz4ZYnIhI0hWORYn73ow2sdM247+o55OREXY1IijjqKL8pyP33w/jxCb3k1FN9V8Ztt4FzIdcnIhIghWORmDfegLufaswP+TcDLuwQdTkiqeWPf4SuXeGyy2DTpjKfXqUKXHed3xDkjTfCL09EJCgKxyLAihVw0UXQ45Cv+Fuj26Bt26hLEkktNWv69orVq/3mIAm48EJo08ZPg9PqsYikC4VjyXqFhfC97/mxU8/Uu5JaR/XSdngiJenb1491e+wxePTRMp9erRr87ncwbRq8+moS6hMRCYDCsWS9m2+GKVPg37duofOy8RpsLFKaG2+EoUPhqqtg1qwyn37hhdC+vX9ZUVH45YmIVJbCsWS155/3k6ouvBAubv2Of3DgwGiLEkllOTkwdiw0aABnnQUbN5b59N//Hj77DF58MUk1iohUgsKxZK3334cLLvBZ+D//AT780P9L3qdP1KWJpLamTeHZZ/14t4suKnNJeMwYP7ni97/3bUwiIqlM4Viy0hdfwKhR0KoVvPIK1KqFD8c9e/q5riJSuqOOgjvugNdeg7/+tdSnVq0KN90Ec+fCM88kpzwRkYpSOJass2IFjBjhF4nfeAMaNsRv4/XJJ2qpECmPq6+G88/3V92VsdvHOedAbi789rewa1dyyhMRqQiFY8kqy5bB0UfD+vV+weubiW3TpsG2bTB4cKT1iaQVM3jgAf9D5fe+B+++e8CnVqkCf/sbLF0K//xn8koUESkvhWPJGosX7wvGEyf6qVTfGDfO/+s9fHhk9YmkpVq1fG9Smza+V2nOnAM+ddgw/6nNzTfDhg1JrFFEpBzMpdBk9j59+rhp06ZFXYZkoPnz/T/MO3b4YNy7935POPJI32s8dWok9YmkvWXL/ApylSq+f//ww0t82uzZvr3ipz/1LctSSTt2+AsjV66EPXv8bivO+d+HQw+F1q2hXr2oqxRJOWY23TlX4hX4OckuRiTZ3nrLT5yqXh3efht69NjvCatWwYwZ8Je/RFKfSEZo1co38R99tF8enjIFGjf+ztOOOAIuucS3Vlx9tTajTJhzsGSJ/8Hjgw9g+nT/32vWlP3a+vV9SO7f38+oPuYYH5xFpERaOZaM9vDDcOWV0LGj7zFu0+YAT7r0Ur+hQc+eyS5RJLO8/TacdJJPvZMnlxjCVqyADh3g5JP9RDg5gO3bYcIEePll/4NHQYF//KCD/MjJ9u39DyWtWkGLFn4FwMzfCgv9avLSpX5Vf9EiH6y3bPHH6NIFzj4bLr4Y2rWL7FsUiUppK8cKx5KR9u71u9z+7W++jfh///OLJyU6+2z46CNYvlzbRosE4e234ZRTfGB76y1o3vw7T/njH/3c48mT4bjjIqgxVe3c6cPwU0/5HrAdO/xfXiNH+lX5gQOhe3c/H6+89u6FmTP978+ECf73xjl/3EsugfPO0yhLyRoKx5JVCgr8pgNvvw0/+AHcfTdUq3aAJ+/Z42e5jR4N99+f1DpFMtp77/kV5CZNfAhr2fJbX96xA7p2hTp1/Ic2Odnc5Oecn5jz8MN+98FNm/wPFmecAaefDkOGlPKXWCXk58Pjj8Mjj8CCBf736he/gB/+0K9Oi2Sw0sKxplVIRvnwQ3+x3YcfwqOPwr//Xca/Ke+/7z9mPOmkpNUokhUGD/Yrn+vW+ZXJzz//1pdr1YI77/Qbg/z73xHVGLWdO30gPvJI6NfP//qkk/z7tmwZ/OMfflk9jGAMPoD/+tf+iuUpU/yVkr/6lW/TuPlm2Lw5nPOKpDiFY8kIhYXw5z/7BZaaNX2XxEUXJfDC11/3//AMGxZ6jSJZp39/3zexc6dvBxg//ltfPu003/Z0442wdm1ENUZhxQrf99Wihb/eYdcu/xPCqlXw5JP+76MqSfzn2cxfpDd+vP/L86ij/MYuHTv6wF7G9uAimUbhWNLeV1/5xZUbbvC7cE2fXo7r6saN8/8o6CNEkXAceaTffbJ1a78qWmwHEDPf9rRtm1/AzHhz5vje3jZt4NZb/U/zkyf7x3/wg1IujEii/v3h1Vf971nbtj689+/vP44TyRIKx5LW/vc/H4RnzPBtFE89VY5/X5Yu9R/1qqVCJFwtW/oe5JNPhh//GH70I9i9G/BDE372M3jwQd/llHGc8y0LJ5/s59g9+yxcdZWfHvHii/4n+1S8ELhvX/8b8sQTfurFUUfB//0fbNwYdWUioVM4lrS0datf0DjvPP/J36xZvo2iXP/GjBvn708+OYwSRaS4unV9GLzuOt9CcNRR8MUXgJ9a0bKlH7sYy8zpr7DQB+H4bOFPP/UjOr76yvcSlzhXMsWYwQUX+N+n66/3F+917QovvRR1ZSKhUjiWtPPRR9Crl7/A+re/9QtSFRrTOW6cf2GHDkGXKCIlqVoVbrsNXnjBb2DRuzf8978cVMfxr3/5D3L+/veoi6ykrVvhX/+CTp3g3HP9Sut99/kL7H73Oz8dJ90cdBD89a++1aJpUz9F47zzEtuARCQNKRxL2ti1y/clDhrkf/322/6C6gpdyL1jhx8vdfLJqfmRpkgmO+MMv4/0UUf55eKzzuKUI1dx1lnwpz/5joO0s2yZXxVv0cJv/deoETz/vJ8E8f3v+/Ec6a53b78CfvPNfvW4a1ffy5ZCI2FFgqBwLGlh5ky/IdQtt/jrWWbP9tfRVdgrr/iAPGpUUCWKSHkcdpifjnD77X5qTMeO/KPzv6lWzfGDH6RJ3nLOb+V8zjn+4rU77/RbZ3/4of+I68wzK7ZZRyqrVs1/ZDdjhv/k7YIL/NiRFSuirkwkMArHktL27PFtev36+XGpr73mL9w5+OBKHviBB/wsz6FDA6lTRCqgShX4+c/9sONjj+WwP/+IW2r9kUmT4KGHoi6uFLt3+xXT/v39R1mTJ/tV4yVL4OmnYcCAqCsMX7du/geD22+HSZP8fz/4YJr8VCNSOoVjSVlz5/rRqL//vW/dmzs3oGvnlizxf5lfdllyZ4mKSMnat/fjw15/navqPcWxvM0139/GVw9NSq0Zu7Nn+zDfooVfMd28Ge691289f8stcPjhUVeYXFWr+vcjL89vIHL55X7l/Kuvoq5MpFKUDCTl7NjhZxb36uXb+J57zs/Fb9AgoBM89JAPxZdcEtABRSQQJ51ElTl5PPj75RQVweWXFeF69PRTEnbujKamr77yw5j79IEePfyc5qOPhjfe8FcQXnWV3wM7m7Vv76/h+Ne//Pi37t3hP//RKrKkLYVjSSkTJ/pRoH/+M4wZ4//tOeusAE+wd6/f8WnEiOxb5RFJBzVq0Pami/jbP2oykRP474az/JzGQw/18xsnTfJj0sJSVORXQv/yFx+IW7Xyg5gLC31IXrnS/8Q+YoQ+eSquShX44Q/96nq/fv6HhuOPhwULoq5MpNzMpdBPdn369HHTpk2LugyJQEGB/3Tuqaf8ZLX77vOz8QP3+utwyil+lNQZZ4RwAhEJQlERnHACfPyxI+9f79Hm7Yf89IctW/w4sWHD/A5zgwf7nUQqGlS3boV583z/7DvvwLvvwvr1/msDBvi/J844QyMfy8M5f13Hddf5Ff/f/hZ++UuoUSPqykS+YWbTnXN9SvyawrFEqbDQX8Pxq1/B9u1+VNv110PNmiGd8PTT/ZXk+fkVnAEnIsmybJnfAbNLF59Zq+3d4eeTP/usD7KrV/snHnIIdO7st6hu3dqv9tarB9Wr+//Pq1XzIXj9en9l79q18OWX/kKGpUv3nbBNGz8G59hjffhu3jz533QmWb0arrnGX6TYubPvzz722KirEgEUjiVFTZjgFxM++8z/e3Tfff7vz9CsWuVbKX7xC7j11hBPJCJBeeYZGD3aLz7efHOxLzgHixf7XYA++MAPR16yxF8ct3dv6QetW9cH4a5d/ZSFbt3gyCP9Nn0SvDff9C0XS5b4Vfi//a2COzeJBEfhWFLKp5/6jaLGj/f/Pv3lL36zpdD34rjlFr80/cUXfs9pEUkLl1/ur6OdPDmB6Yt79/ofhLdt87Mgd+/29wcd5Hena9jQryhLcu3YAXfc4Xfa270bfvITf+V1/fpRVyZZSuFYUsJ77/mVn/Hj/aegN9wAP/pRktrQnPM9g82b+49jRSRtbNvmF3a3bPGfNDVqFHVFUmGrVvmPAR55xAfja67xQbnSw+tFyqe0cKxLbSVUO3fCY4/5ecVDhvhNlW65xbf5/fznSbw+4/XXfY/h5Zcn6YQiEpQ6dXzb6rp1frxwmMMqJGTNmvmPAaZP9xdT3nij7xG/6SbYuDHq6kQAhWMJQVGRbwH82c/8Qu3FF8OGDX4K0tKl/uK7evWSWFBhoW+naN/eNy+KSNrJzYV//9tfq/Cb30RdjVRar17wyit+xWToUPjDH/w1IT/4AcyZE3V1kuVyoi5AMsOWLb5bYeJEPyUtP9+39Y0a5f+uGzo0CT3FB/L44/4v2//9TxMqRNLYZZfBtGlw222+zeLcc6OuSCqtVy948UXfL3PXXX4O/X33+Y1WfvAD/49I7dpRVylZRj3HUm5FRf4i8WnT/MV1H30En3zir4OpWdPPJj33XDj11CSvEJdkxw5/8V2zZvDxxxEmdBEJwu7d/oftWbP8VMYePaKuSAK1fr1vu7j3Xj/d4qCD/AjO88/34/W0wCEB0QV5UiG7d/vpSPPm7bvNn+9v27f759Ss6X/wHzrUb4Z01FEhziiuiL/9zc+Le/ttzdcUyRCrVvnN66pW9QFZ44gzUGEhTJ3qd4Z67jnfj3zIIX5nwpNP9vcNG0ZdpaQxhWMpVVGR/wF9zhy/8+ecOf72xRffHhfasqUfxt+lix8L2qePv0/ZH+Q3bPCzNI86yl+QJyIZY+ZMPx+9VSufoTQRLIPt3u3HHD3/PLzxBqxZ43dE7NfPt18MGQKDBvnwLJIghWP5lk2b/Fi199/3F85Nm7ZvJRj87OHu3ffNxu/SBTp18p9upZXrroPbb/efv+qzV5GMM2kSnHSS//n3zTdT7FMrCUdRkf9H6/XX/UUu06b5OdZm/h+uIUP23fSRgpRC4TjLOeen5rz+uv/h++OP/d8v1apB797Qv7/forV7d79hVNqF4JIsXuy/mdGj/TxNEclIY8f6dtQzz/Tj3lL2kywJx/bt/qKXqVP97YMP/GBs8Cs9/fr5jzn79vX/4NWtG229kjIUjrOQc/5iuf/9z7drLVvmf7Du2xdOPNFf19C3L9SqFXWlIdi50y8lLV7s+0QOPzzqikQkRHff7UdHnn66D8hJm58uqWfvXv9p4dSp/uPRadP8P4Dg/xHs1Mn/4xcPzLm5GfoPoZRF4TiLrFzpJ5c98oi/cK5aNT894uyz/fSIrLh+4Yor4IEH4NVX4ZRToq5GRJLgnnv8RmsnneRbU9ViId9Ys8Z/fPrpp/vGLK1e7b9Wtar/2DQelvv0gSOO0BbjWUDhOMM5B1OmwD//CS+95FsmBg+GSy6Bs87KsgtVHnrID0P97W/9XtUikjXuvx+uuspPznn++RQYJSmpyTm/khQPyvH7DRv816tX972Gffr4VozcXB+g9RNXRlE4zlDbtsETT/hQPGeOXxW+/HJ/a98+6uoiMHOmb6cYNMg3V1etGnVFIpJkjz7qfz7u3NlvwNa2bdQVSVpwzm/hWjwsT5/ud7gC/+9Jly4+KBe/ZcXHsZlJ4TjDfPkl/OtffpH066/9nOEf/9hfe5a1rVPr1vkLL/bs8duRNm4cdUUiEpHJk+Gcc/y0r+ee04hzqaD4nNNZs/xt5kx/v2LFvuccfvi+oNyrl2/JaNvW/+GTlKZwnAGKimDCBL9KPG6c/yH27LPh6qv9YmlWb/z25ZcwciQsXw5vvQUDB0ZdkYhEbNEif53FokXwxz/6yY45OVFXJRlh7Vq/3XU8LM+a5S/yKSryX69d289BPeKIb9+aNImyatmPwnEaW7fOX1x3//2wcCE0bQrf/76/HXZY1NWlgI8/9hfdOec/Qz3qqKgrEpEU8fXXvs3suef8z8yPPgodOkRdlWSk7dv37aRV/LZ27b7nNGnie5eLB+Zu3aBOnejqzmIKx2nGOb9Jx333+b/Ud+/2bbQ/+IH/qFAX0ca89JIfcHrYYX7XJP2rJyL7cc7PQv7Rj2DXLrjpJj/VQtdWSVIUFOwLyvHwPHfuvp23zHwbRjwsx8Nzhw76qCNkCsdpYu1a/5f4f/4Dn38OBx8MF17oV4m7d4+6uhSycSP84Q/wj3/4PuNXX1WPsYiUasUKv8Dw6qt+y+k//xnGjFFrqESgqGjfHP7iwXnBgn2tGTVq+AsA92/NOOywLO+jDI7CcQr7+mvfDTB2rO8pLiz0ee/734fzztOnLd+yd6/vL7nxRh+Qr7zSbw9du3bUlYlImnjrLbj2Wt8uesQR8NOf+g+gsvZiZkkdO3fCvHnfbc1YuXLfcw455LutGd27+9U0KReF4xTinL9+bNw4v4IxZYrPfK1a+VWMMWOgR4+oq0wxW7bACy/A3//uf7oeOhTuuktvlIhUSFERPPUU3Habzx7xMZijR/vxtlqYk5SyYcN3+5nnzIHNm/c9p2XLb7dlHHGEn2eoPswDUjiO0N69/gfBTz6Bd96Bt9+G/Hz/tc6dYdQoOO00f7GI/kIuZvdu/2Y9/rgPxjt2QMeO8Ne/whln6M0SkUqLb6B0991+saKoyM+IP/tsGDbM/72sD6YkJTkHX3317V7m2bP91Iw9e/xzcnL8dtnFV5i7dfPj5xSaowvHZjYCuBuoCjzgnLultOenazh2zv8At3Kl38J93jx/mzvXT3iJ9903auTnbQ4dCsOH6/qxb+ze7d+4OXPgww/hgw/8EPZdu/z2fqNHw0UXwYABCsUiEoq1a+HFF/1F0G+95VvcqlX79o7CPXr4rKFPsCVl7d7te5f3b81Ytmzfc8zg0EP9anOrVv4+fmvRwoeVRo38T4YZ/G9uJOHYzKoCC4DhQD7wKTDGOff5gV4TRThevtx/al9Y6Fd5Cwv3/XrPHti61X99/9uaNf4Cj/ht27ZvH7dRI99L37u3/8v1yCP9wqcu/oi5/37faL14sV9Kj1+EUL26f7MGDoSjj4YRI/yFCSIiSbJ5M7z/vv+07913/Ujb+CIH+J/ZW7eG5s2hQQPfBnrIId/+da1afiJGjRr+GiqN3pRIbd7sV+zmz/crzvvfdu787mtq1PA9R40a+fv4rU4d/we8dm1/2//X8aATD9b73+/a5c+3Y4e/HXmkvyVZaeE4zDkh/YBFzrnFsSKeBk4DDhiOo3Dxxf7T+/KoXdsPR2je3PennXSS/4uveXP/aUXnzhqeUKbNm/1PH8ccA23a+FE2HTv6HYY0Y0lEIlSvnt9XaORI/9/xjdJmz/abiixd6m8rV/q8sXGjv7j6QH75S7j11mRULnIA9er5RaeSNslyzm+q8NVXfrFq3TpYv37fffw2Z47vf96+3d/ii1qV9Yc/RBKOSxPmyvHZwAjn3OWx/74Q6O+cu3q/510JXBn7z07AF6EUlDyNgHVRF5GF9L5HQ+97dPTeR0Pve3T03kcjU9/3Vs65Epcyw1w5LqlR5TtJ3Dl3P3B/iHUklZlNO9AyvYRH73s09L5HR+99NPS+R0fvfTSy8X0PswM2Hzi82H+3AFYe4LkiIiIiIpELMxx/CnQwszZmVh0YDbwS4vlERERERColtLYK59xeM7saGI8f5faQc25uWOdLIRnTIpJm9L5HQ+97dPTeR0Pve3T03kcj6973lNoEREREREQkSpq6KyIiIiISo3AsIiIiIhKjcFwGMzvHzOaaWZGZ9dnva782s0Vm9oWZnVjs8SPNbHbsa/8w89vCmFkNM3sm9vjHZta62GsuNrOFsdvFSfsG05yZjYi9/4vM7Pqo60lXZvaQma0xsznFHmtgZhNjfyYnmtkhxb4W2J/9bGZmh5vZ22Y2L/b3zE9jj+u9D5GZ1TSzT8zss9j7/ofY43rfk8DMqprZTDN7Lfbfet+TwMyWxt6zWWY2LfaY3vuSOOd0K+UGdMFvTjIF6FPs8a7AZ0ANoA3wJVA19rVPgIH4Wc9vACNjj/8QuC/269HAM7FfNwAWx+4Pif36kKi/91S/4S/0/BJoC1SP/X50jbqudLwBRwO9gTnFHrsNuD726+uBW2O/DuzPfrbfgGZA79iv6wILYu+v3vtw33cDDor9uhrwMTBA73vS3v+fA08Br8X+W+97ct73pUCj/R7Te1/CTSvHZXDOzXPOlbRr32nA0865Xc65JcAioJ+ZNQPqOec+dP5PyGPA6cVe82js188Bx8d+4joRmOic2+Cc2whMBEaE911ljG+2KHfO7QbiW5RLOTnn3gU27Pdw8T+vj/LtP8dB/dnPas65Vc65GbFfbwHmAc3Rex8q522N/We12M2h9z10ZtYCOBl4oNjDet+jo/e+BArHFdccWF7sv/NjjzWP/Xr/x7/1GufcXuBroGEpx5LS6X0LV1Pn3CrwIQ5oEns8yD/7EhP7CLIXfhVT733IYh/tzwLW4Bcn9L4nx13AL4GiYo/pfU8OB0wws+lmdmXsMb33JQhz++i0YWaTgENL+NJvnXMvH+hlJTzmSnm8oq+RA9P7Fo0g/+wLYGYHAc8DP3PObS5lsUXvfUCcc4VArpnVB140s+6lPF3vewDM7BRgjXNuupkdm8hLSnhM73vFDXLOrTSzJsBEM5tfynOz+r1XOAacc8Mq8LIDbY+dH/v1/o8Xf02+meUAB+M/ys4Hjt3vNVMqUFO20Rbl4Sows2bOuVWxj9LWxB4P8s9+1jOzavhg/KRz7oXYw3rvk8Q5t8nMpuBb2fS+h2sQMMrMTgJqAvXM7An0vieFc25l7H6Nmb2Ib03Ue18CtVVU3CvA6NjVmW2ADsAnsY8ltpjZgFivzUXAy8VeE59EcTbwVqxnZzxwgpkdErtS9ITYY1I6bVEeruJ/Xi/m23+Og/qzn9Vi79ODwDzn3B3FvqT3PkRm1ji2YoyZ1QKGAfPR+x4q59yvnXMtnHOt8X9fv+Wc+x5630NnZnXMrG781/icMQe99yVL9hWA6XYDzsD/NLQLKADGF/vab/FXcH5B7GrN2ON98H/ovgT+yb6dCGsCz+Ib2z8B2hZ7zaWxxxcB/xf1950uN+Ak/BX+X+LbYCKvKR1vwFhgFbAn9uf9Mnyv2GRgYey+QbHnB/ZnP5tvwGD8x455wKzY7SS996G/7z2AmbH3fQ5wY+xxve/J+z04ln3TKvS+h/9+t8VPn/gMmBv/91Lvfck3bR8tIiIiIhKjtgoRERERkRiFYxERERGRGIVjEREREZEYhWMRERERkRiFYxERERGRGIVjEZEymFmhmc0yszlm9qyZ1T7A8z4I6Hynm9mNsV9fZWYXVeJYj5jZ2WU8Z4qZ9Yn9eqmZNaro+Yod82oz+7/KHkdEJNkUjkVEyrbDOZfrnOsO7AauKv5FM6sK4Jw7KqDz/RL4d+yY9znnHgvouIGLf+8leAj4STJrEREJgsKxiEj5TAXam9mxZva2mT0FzAYws63xJ5nZL81stpl9Zma3xB5rZ2Zvmtl0M5tqZp33P7iZdQR2OefWxf77JjO7NvbrKWZ2q5l9YmYLzGxICa83M/unmX1uZq8DTYp97Xgzmxmr6yEzq1HaN2pmL8VqnWtmVxZ7fKuZ/dHMPgYGmtktsfPlmdnfAZxz24GlZtYv8bdWRCR6OVEXICKSLswsBxgJvBl7qB/Q3Tm3ZL/njQROB/o757abWYPYl+4HrnLOLTSz/vjV4eP2O80gYEYpZeQ45/qZ2UnA7/FbHxd3BtAJOAJoCnwOPGRmNYFHgOOdcwvM7DHgB8BdpZzrUufchtgWy5+a2fPOufVAHWCOc+7G2Pf2INDZOefi2zLHTAOG4HfLEhFJC1o5FhEpWy0zm4UPe1/hwyDAJ/sH45hhwMOx1VNiAfMg4Cjg2dix/gM0K+G1zYC1pdTyQux+OtC6hK8fDYx1zhU651YCb8Ue7wQscc4tiP33o7HnluYnZvYZ8BFwONAh9ngh8Hzs15uBncADZnYmsL3Y69cAh5VxDhGRlKKVYxGRsu1wzuUWf8DMALYd4PkGuP0eqwJs2v84JZ0LOLiUr++K3Rdy4L/D9z93vKaEmdmx+JA/MLb6PQWoGfvyTudcIYBzbm+sdeJ4YDRwNftWw2vivx8RkbShlWMRkeBNAC6NT7UwswbOuc3AEjM7J/aYmVnPEl47D2hfiXO/C4w2s6pm1gwYGnt8PtDazOLHvhB4p5TjHAxsjAXjzsCAkp4UWxE/2Dk3DvgZkFvsyx2BORX9RkREoqBwLCISMOfcm8ArwLRYC8W1sS9dAFwWa1WYC5xWwsvfBXpZbGm6Al4EFuIvEryXWAB2zu0E/g/f1jEbKALuK+U4bwI5ZpYH/AnfWlGSusBrsee9A1xT7GuDgEkV/D5ERCJhzpX06ZuIiETFzO4GXnXOpW2wNLNewM+dcxdGXYuISHlo5VhEJPX8BShxo5E00gj4XdRFiIiUl1aORURERERitHIsIiIiIhKjcCwiIiIiEqNwLCIiIiISo3AsIiIiIhKjcCwiIiIiEvP/IvrY1f17PZUAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(width, height))\n",
"\n",
"\n",
"ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
"sns.distplot(Y_hat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
"\n",
"\n",
"plt.title('Actual vs Fitted Values for Price')\n",
"plt.xlabel('Price (in dollars)')\n",
"plt.ylabel('Proportion of Cars')\n",
"\n",
"plt.show()\n",
"plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see that the fitted values are reasonably close to the actual values, since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 3: Polynomial Regression and Pipelines</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n",
"<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
"\n",
"<p>There are different orders of polynomial regression:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center><b>Quadratic - 2nd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X +b_2 X^2 \n",
"$$\n",
"\n",
"<center><b>Cubic - 3rd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\\\\\n",
"$$\n",
"\n",
"<center><b>Higher order</b>:</center>\n",
"$$\n",
"Y = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We saw earlier that a linear model did not provide the best fit while using highway-mpg as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We will use the following function to plot the data:</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
" x_new = np.linspace(15, 55, 100)\n",
" y_new = model(x_new)\n",
"\n",
" plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
" plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
" ax = plt.gca()\n",
" ax.set_facecolor((0.898, 0.898, 0.898))\n",
" fig = plt.gcf()\n",
" plt.xlabel(Name)\n",
" plt.ylabel('Price of Cars')\n",
"\n",
" plt.show()\n",
" plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets get the variables\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"x = df['highway-mpg']\n",
"y = df['price']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function.\n"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 3 2\n",
"-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
]
}
],
"source": [
"# Here we use a polynomial of the 3rd order (cubic) \n",
"f = np.polyfit(x, y, 3)\n",
"p = np.poly1d(f)\n",
"print(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's plot the function \n"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"PlotPolly(p, x, y, 'highway-mpg')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"np.polyfit(x, y, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function \"hits\" more of the data points.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #4:</h1>\n",
"<b>Create 11 order polynomial model with the variables x and y from above?</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 11 10 9 8 7\n",
"-1.243e-08 x + 4.722e-06 x - 0.0008028 x + 0.08056 x - 5.297 x\n",
" 6 5 4 3 2\n",
" + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"# Here we use a polynomial of the 11rd order (cubic) \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p1)\n",
"PlotPolly(p1,x,y, 'Highway MPG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# Here we use a polynomial of the 11rd order (cubic) \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p1)\n",
"PlotPolly(p1,x,y, 'Highway MPG')\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can perform a polynomial transform on multiple features. First, we import the module:\n"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.preprocessing import PolynomialFeatures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create a <b>PolynomialFeatures</b> object of degree 2: \n"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"Z_pr=pr.fit_transform(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The original data is of 201 samples and 4 features \n"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 2)"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"after the transformation, there 201 samples and 15 features\n"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 6)"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z_pr.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Pipeline</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.pipeline import Pipeline\n",
"from sklearn.preprocessing import StandardScaler"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create the pipeline, by creating a list of tuples including the name of the model or estimator and its corresponding constructor.\n"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we input the list as an argument to the pipeline constructor \n"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Pipeline(memory=None,\n",
" steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False))])"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe=Pipeline(Input)\n",
"pipe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can normalize the data, perform a transform and fit the model simultaneously. \n"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n"
]
},
{
"data": {
"text/plain": [
"Pipeline(memory=None,\n",
" steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False))])"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe.fit(Z,y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Similarly, we can normalize the data, perform a transform and produce a prediction simultaneously\n"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([15388.77780567, 15388.77780567, 16771.84474515, 11641.85647791])"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ypipe=pipe.predict(Z)\n",
"ypipe[0:4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #5:</h1>\n",
"<b>Create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([16231.78938339, 16231.78938339, 17052.24372355, 13833.33798916,\n",
" 20396.97271047, 17872.69806371, 17926.6223148 , 17872.69806371,\n",
" 22028.89401561, 14695.7334135 ])"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"pipe=Pipeline(Input)\n",
"pipe.fit(Z,y)\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"\n",
"pipe=Pipeline(Input)\n",
"\n",
"pipe.fit(Z,y)\n",
"\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 4: Measures for In-Sample Evaluation</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
"\n",
"<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
"<ul>\n",
" <li><b>R^2 / R-squared</b></li>\n",
" <li><b>Mean Squared Error (MSE)</b></li>\n",
"</ul>\n",
" \n",
"<b>R-squared</b>\n",
"\n",
"<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
" \n",
"<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
"\n",
"<b>Mean Squared Error (MSE)</b>\n",
"\n",
"<p>The Mean Squared Error measures the average of the squares of errors, that is, the difference between actual value (y) and the estimated value (ŷ).</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 1: Simple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.7609686443622008\n"
]
}
],
"source": [
"#highway_mpg_fit\n",
"lm.fit(X, Y)\n",
"# Find the R^2\n",
"print('The R-square is: ', lm.score(X, Y))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\".\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The output of the first four predicted value is: [13728.4631336 13728.4631336 17399.38347881 10224.40280408]\n"
]
}
],
"source": [
"Yhat=lm.predict(X)\n",
"print('The output of the first four predicted value is: ', Yhat[0:4])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>\n"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import mean_squared_error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we compare the predicted results with the actual results \n"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value is: 15021126.025174143\n"
]
}
],
"source": [
"mse = mean_squared_error(df['price'], Yhat)\n",
"print('The mean square error of price and predicted value is: ', mse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 2: Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.4966263556974878\n"
]
}
],
"source": [
"# fit the model \n",
"lm.fit(Z, df['price'])\n",
"# Find the R^2\n",
"print('The R-square is: ', lm.score(Z, df['price']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~ 80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\".\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we produce a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"Y_predict_multifit = lm.predict(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we compare the predicted results with the actual results \n"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value using multifit is: 31632832.975589428\n"
]
}
],
"source": [
"print('The mean square error of price and predicted value using multifit is: ', \\\n",
" mean_squared_error(df['price'], Y_predict_multifit))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 3: Polynomial Fit</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"let’s import the function <b>r2_score</b> from the module <b>metrics</b> as we are using a different function\n"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import r2_score"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We apply the function to get the value of r^2\n"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square value is: 0.6741946663906517\n"
]
}
],
"source": [
"r_squared = r2_score(y, p(x))\n",
"print('The R-square value is: ', r_squared)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~ 67.419 % of the variation of price is explained by this polynomial fit\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>MSE</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also calculate the MSE: \n"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361226"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_squared_error(df['price'], p(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 5: Prediction and Decision Making</h2>\n",
"<h3>Prediction</h3>\n",
"\n",
"<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create a new input \n"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [],
"source": [
"new_input=np.arange(1, 100, 1).reshape(-1, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Fit the model \n"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X, Y)\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Produce a prediction\n"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
" -7129.03882782])"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yhat=lm.predict(new_input)\n",
"yhat[0:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we can plot the data \n"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(new_input, yhat)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Decision Making: Determining a Good Model Fit</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
"<ul>\n",
" <li><i>What is a good R-squared value?</i></li>\n",
"</ul>\n",
"</p>\n",
"\n",
"<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
"<ul>\n",
" <li><i>What is a good MSE?</i></li>\n",
"</ul>\n",
"</p>\n",
"\n",
"<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
"\n",
"<h4>Let's take a look at the values for the different models.</h4>\n",
"<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
"<ul>\n",
" <li>R-squared: 0.49659118843391759</li>\n",
" <li>MSE: 3.16 x10^7</li>\n",
"</ul>\n",
"</p>\n",
" \n",
"<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
"<ul>\n",
" <li>R-squared: 0.80896354913783497</li>\n",
" <li>MSE: 1.2 x10^7</li>\n",
"</ul>\n",
"</p>\n",
" \n",
"<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
"<ul>\n",
" <li>R-squared: 0.6741946663906514</li>\n",
" <li>MSE: 2.05 x 10^7</li>\n",
"</ul>\n",
"</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and or even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
"\n",
"<p>So to be able to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
"<ul>\n",
" <li><b>MSE</b>The MSE of SLR is 3.16x10^7 while MLR has an MSE of 1.2 x10^7. The MSE of MLR is much smaller.</li>\n",
" <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
"</ul>\n",
"</p>\n",
"\n",
"This R-squared in combination with the MSE show that MLR seems like the better model fit in this case, compared to SLR.\n"
]
},
{
"cell_type": "markdown",
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"<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>\n"
]
},
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"source": [
"<ul>\n",
" <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
" <li><b>R-squared</b>: The R-squared for the Polyfit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
"</ul>\n",
"<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting Price with Highway-mpg as a predictor variable.</p>\n"
]
},
{
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"source": [
"<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>\n"
]
},
{
"cell_type": "markdown",
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"source": [
"<ul>\n",
" <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
" <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
"</ul>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Conclusion:</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense, since we have 27 variables in total, and we know that more than one of those variables are potential predictors of the final car price.</p>\n"
]
},
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"### Thank you for completing this lab!\n",
"\n",
"## Author\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
"\n",
"Bahare Talayian\n",
"\n",
"Eric Xiao\n",
"\n",
"Steven Dong\n",
"\n",
"Parizad\n",
"\n",
"Hima Vasudevan\n",
"\n",
"<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
"\n",
"<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
"\n",
"## Change Log\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"| ----------------- | ------- | ---------- | --------------------------------------------- |\n",
"| 2020-10-30 | 2.2 | Lakshmi | Changed url of csv |\n",
"| 2020-09-09 | 2.1 | Lakshmi | Fixes made in Polynomial Regression Equations |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"\n",
"<hr>\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
]
}
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