{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# DS 2500 Day 15\n", "\n", "Mar 3, 2023\n", "\n", "\n", "## Content:\n", "Regression \n", "- like a classifier, but predicts a continuous feature instead of a nominal one\n", "\n", "## Admin:\n", "- project teams:\n", " - if your team was matched, one person should send a note to all others to set a first meeting\n", " - if your team hasn't yet been created:\n", " - see note on piazza\n", " - email Alex when you've got team members\n", "- project mentors:\n", " - each team will be assigned one TA mentor, we hope to have this done for you the monday we're all back from break\n", " - our TAs pick which projects they'd like to support, so you all get a mentor who's interested in your project!\n", "\n", "#### Data Credit:\n", "The blue bike data was collected and cleaned by Piotr Sapiezynski (https://www.sapiezynski.com/) https://www.bluebikes.com/system-data" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Regression: Motivation\n", "### How many people use Boston's bike sharing on a hot (or cold) day?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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trip_counttempwindrain
date
2019-10-011218369130
2019-10-02907166111
2019-10-03114965490
2019-10-041176760160
2019-10-0593155690
\n", "
" ], "text/plain": [ " trip_count temp wind rain\n", "date \n", "2019-10-01 12183 69 13 0\n", "2019-10-02 9071 66 11 1\n", "2019-10-03 11496 54 9 0\n", "2019-10-04 11767 60 16 0\n", "2019-10-05 9315 56 9 0" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('bluebike_201910.csv', index_col='date')\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "sns.set(font_scale=1.5)\n", "plt.scatter(df['temp'], df['trip_count'])\n", "plt.xlabel('Temperature [F]')\n", "plt.ylabel('Number of trips')\n", "plt.gcf().set_size_inches(10, 5)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Regression:\n", " - predicting a continuous number from input data\n", "* We will predict the number of blue bike trips in October 2019 based on the temperature:\n", " * intuition from graph:\n", " - higher temp -> more bike trips" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linear regression\n", "Regression seeks to find coefficients $a_0, a_1$ so that the function:\n", "\n", "$$ \\hat{y} = a_1 x + a_0 $$\n", "\n", "is able to predict $y$ from $x$.\n", "\n", "* $x$ is our input data \n", " - (temperature on a given day)\n", "* $y$ is the outcome we're predicting \n", " - (number of bike trips on same day)\n", "\n", "To learn the function we \n", "1. observe paired observations of $(x, y)$ \n", " - (this is akin to observing the scatter plot above)\n", "1. find the $a_i$ coefficients which best map $x$ to $y$.\n", " - (this is akin to drawing a line through the scatter which \"best\" fits the points)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# What do $a_1$ and $a_0$ mean?\n", "\n", "## Algebraic meaning:\n", "- $a_1$ is the slope of the line\n", " - when x increases by 1, how much does y change?\n", "- $a_0$ is the y-intercept of the line\n", " - when x=0, what value is y?\n", " \n", "## Application meaning (from algebraic meaning):\n", "Returning to our blue bike example where:\n", "- x is the temperature\n", "- y is the number of riders on a given day\n", "\n", "\n", "- because $a_1$ is the increase in y when x increases by 1\n", " - it represents the increase in riders because the temperature goes up by 1\n", "- because $a_0$ is the value of y when x=0\n", " - it represents the number of riders our model predicts when temperature=0" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Often there is no $a_1$ and $a_0$ which \"fits\" every observation...\n", "\n", "Specifying $a_1$ and $a_0$ is equivilent to specifying a straight line. \n", "\n", "Can we fit a straight line through all these observations? (very often: no)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [0, 1, 2, 3, 4, 5]\n", "y_true = [0, 3, 2, 4, 3, 5]\n", "\n", "plt.scatter(x, y_true)\n", "plt.gcf().set_size_inches(7, 5)\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## ... lets find the line which \"best\" fits these points" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Regression Recipe\n", "1. Choose some \"form\" of the relationship between x and y:\n", " - `y_pred = a_1 * x + a_0`\n", " - this is a simple model, we could have chosen others too (more next lesson)\n", " - a polynomial: `y_pred = a_2 * x ** 2 + a_1 * x + a_0`\n", " - exponential: `y_pred = a_1 * np.exp(x)\n", " - remember the $a_i$ coefficients define the position of the line above\n", "1. Quantify what a \"good\" model is\n", " - We want to minimize average distance from predicted y to observed y\n", " - see MSE on next slide\n", "1. `.fit()` the model parameters to maximize how \"good\" the model is\n", " - Choose $a_0, a_1$ to draw a line which is as close as possible to all the points\n", " - \"as close as possible\" = minimize average distance from predicted y to observed y" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Mean of Squared Errors (MSE): Intuition\n", "Before formally defining **Mean of Squared Error (MSE)**, lets build our intuition of it:\n", "- MSE measures how closely a line (i.e. $a_1, a_0$) comes to all observations $(x, y)$\n", "- MSE is 0 when the line goes through all points exactly\n", " - in other words, some $a_1, a_0$ has, for every pair $(x, y)$:\n", " $$\\hat{y} = a_1 x + a_0 = y $$\n", "- MSE is large when the line is far from many pairs $(x, y)$\n", "\n", "# The best line $(a_1, a_0)$ is the one which minimizes MSE" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def get_mse(y_true, y_pred):\n", " # calculate the mean squared distance between the predicted and actual y\n", " return np.mean((y_pred - y_true) ** 2)\n", "\n", "def show_fit(x, y, slope, intercept):\n", " plt.figure()\n", " \n", " # transform the input data into numpy arrays and flatten them for easier processing\n", " x = np.array(x).ravel()\n", " y = np.array(y).ravel()\n", " \n", " # plot the actual data\n", " plt.scatter(x, y, label='y_true')\n", " \n", " # compute linear predictions \n", " # x is a numpy array so each element gets mulitplied by slope and intercept is added\n", " y_pred = slope * x + intercept\n", " \n", " # plot the linear fit\n", " plt.plot(x, y_pred, color='black',\n", " ls=':',\n", " label='y_pred (regression)')\n", " \n", " # for each data point plot the error\n", " for idx, (x_i, y_i) in enumerate(zip(x, y)):\n", " # compute predicted position\n", " y_pred_i = slope * x_i + intercept\n", " \n", " # plot error\n", " plt.plot([x_i, x_i], [y_i, y_pred_i], \n", " ls='--', lw=3, color='tab:red',\n", " label='error' if idx == 0 else \"\")\n", " \n", " plt.legend()\n", " plt.xlabel('x')\n", " plt.ylabel('y')\n", " \n", " # compute mean squared error\n", " y_pred = slope * x + intercept\n", " mse = get_mse(y_true=y, y_pred=y_pred)\n", " \n", " # add title which shows model and MSE\n", " plt.suptitle(f'y_hat = {slope:.2f} * x + {intercept:.2f}, MSE = {mse:.9f}')\n", " plt.gcf().set_size_inches(10, 5)\n", " " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "sns.set(font_scale=1.5)\n", "\n", "x = [0, 1, 2, 3, 4, 5]\n", "y = [0, 3, 2, 4, 3, 5]\n", "show_fit(x, y, slope=-1, intercept=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The error of the j-th data point is the distance between our estimate $\\hat{y}$ and the observed $y$ (length of dotted red line above)\n", "\n", "$$\\texttt{Error}_j = \\hat{y} - y = a_1 x + a_0 - y$$\n", "\n", "This definition \"Mean of Squared Errors\" is more than a name, its a recipe:\n", "\n", "How to compute MSE:\n", "1. Compute the error of every observation (length of red line)\n", "1. Square each error\n", "1. Compute average of all squared errors\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [0, 1, 2, 3, 4, 5]\n", "y = [0, 3, 2, 4, 3, 5]\n", "show_fit(x, y, 0, 1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1, 4, 1, 9, 4, 16])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "error = np.array([1, -2, -1, -3, -2, -4])\n", "error_sq = error ** 2\n", "error_sq" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.833333333333333" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mse = np.mean(error_sq)\n", "mse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", " MSE = \\frac{1}{n}\\sum_{j} {(\\hat{y}_j - y_j)^2}\n", "$$\n", "\n", "where \n", "- $(x_j, y_j)$ are the paired observations\n", "- n is the total number of paired observations\n", "- j is the observation index \n", " - (first observation is 0, next is 1, ...)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Manually \"fitting\" a regression line" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [0, 1, 2, 3, 4, 5]\n", "y = [0, 3, 2, 4, 3, 5]\n", "show_fit(x, y, slope=1.3, intercept=.5)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# In Class Assignment 1\n", "\n", "Given the paired observations:\n", "```python\n", "x = np.array([0, 1, 2, 3, 4, 5])\n", "y = np.array([1, 3.5, 4, 5, 4.5, 6])\n", "```\n", "1. Find an $a_1, a_0$ (slope, intercept) which get close to the minimum MSE (guess and check via `show_fit()`)\n", "1. Compute the MSE of the line $a_1 = 0, a_0 =$ `np.mean(y)` by hand\n", " - stuck? skip to the next part and come back to this computation\n", "1. Verify your answer using `show_fit()`\n", "1. This computation feels oddly familiar ... can you identify where we've seen it before?\n", "\n", "Use the `show_fit()` function to try and find $a_1, a_0$ which MSE is the smallest in the following dataset:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "x = np.array([0, 1, 2, 3, 4, 5])\n", "y = np.array([1, 3.5, 4, 5, 4.5, 6])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_fit(x, y, slope=0, intercept=np.mean(y))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# finding the \"best\" (by eye) slope and intercept\n", "show_fit(x, y, 1, 1.5)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# computing / verifying MSE\n", "show_fit(x, y, slope=0, intercept=np.mean(y))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 3. , 0.5, 0. , -1. , -0.5, -2. ])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_pred = x * 0 + np.mean(y)\n", "error = y_pred - y\n", "error" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.4166666666666665" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "error_sq = error ** 2\n", "mse = np.mean(error_sq)\n", "mse" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.4166666666666665" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# what a coincidence ...\n", "np.var(y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## ICA 1 motivates two questions:\n", "1. How can we avoid guessing and checking and find the best $a_0, a_1$?\n", "1. What is the relationship between MSE and the sample variance of y?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## How can we avoid guessing and checking and find the best $a_0, a_1$?\n", "\n", "```python\n", "from sklearn.linear_model import LinearRegression\n", "\n", "x = np.array([0, 1, 2, 3, 4, 5])\n", "y = np.array([1, 3.5, 4, 5, 4.5, 6])\n", "\n", "reg = LinearRegression()\n", "reg.fit(x, y)\n", "slope = reg.coef_[0]\n", "intercept = reg.intercept_\n", "```\n", "\n", "which yields\n", "\n", " ValueError: Expected 2D array, got 1D array instead:\n", " array=[0 1 2 3 4 5].\n", " Reshape your data either using array.reshape(-1, 1) if your data has a single feature or array.reshape(1, -1) if it contains a single sample.\n", " \n", "### don't forget\n", "\n", "the input $x$ of all our sklearn models must have shape (n_samples, n_features)\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6,)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.array([0, 1, 2, 3, 4, 5])\n", "x.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "this is a 1d array, sklearn can't identify whether its:\n", "- a single sample with 6 distinct features? (no)\n", "- 6 distinct samples each with one feature? (yes)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6, 1)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = x.reshape((-1, 1))\n", "x.shape" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression\n", "\n", "x = np.array([0, 1, 2, 3, 4, 5])\n", "y = np.array([1, 3.5, 4, 5, 4.5, 6])\n", "\n", "# reshape x to specify it is 1 feature and many samples\n", "x = x.reshape((-1, 1))\n", "\n", "# initialize sklearn model\n", "reg = LinearRegression()\n", "\n", "# fit the model\n", "reg.fit(x, y)\n", "\n", "# same as a_1\n", "slope = reg.coef_[0]\n", "\n", "# same as a_0\n", "intercept = reg.intercept_" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_fit(x, y, slope, intercept)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "ICA 1 motivates two questions:\n", "1. ~How can we avoid guessing and checking and find the best $a_0, a_1$?~\n", " - `from sklearn.linear_model import LinearRegression`\n", "1. What is the relationship between MSE and variance of y?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## What is the relationship between MSE and the sample variance of y?\n", "\n", "Remember,\n", "$$\n", " MSE = \\frac{1}{n}\\sum_j{( \\hat{y_j} - y_j)^2}\n", "$$\n", "\n", "Look familiar?\n", "$$\\sigma^2 = \\frac{1}{n}\\sum_j{(\\bar{y} - y_j)^2} $$\n", "where $\\bar{y}$ is the mean of our observed samples of $y$.\n", "\n", "\n", "# Sample variance is the MSE of a line which predicts each $\\hat{y}_j = \\bar{y}$\n", "\n", "What kind of line would give the same prediction (the sample mean) for each sample?\n", "- a horizontal line at the sample mean" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.array([0, 1, 2, 3, 4, 5])\n", "y = np.array([1, 3.5, 4, 5, 4.5, 6])\n", "y_sample_mean = y.mean()\n", "show_fit(x, y, slope=0, intercept=y_sample_mean)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.4166666666666665" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# feel familiar? (see MSE in graph above)\n", "np.var(y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## An Intuition Honing Example: MSE and Variance of Y\n", "\n", "Whats the minimum MSE of predicting $\\hat{y} = a_1 x + a_0$ where:\n", "- y = stock price increase on a given day\n", "- x = number of coffees consumed by CEOs parents on the same day" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "1. As x increases, we don't observe changes in y\n", " - assume: x and y uncorrelated\n", "1. Therefore, slope = $a_1 = 0$\n", "1. To minimize MSE our best y prediction is to assign intercept = $a_0 = \\bar{y}$\n", "1. From above, an estimate of MSE of this model is sample variance: `np.var(y)`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "# Variance of Y is the \"worst\" MSE you will get\n", "\n", "- At worst, if you try to predict some y using uncorrelated x\n", " - MSE = Var(y)\n", "- As x shows some stronger correlation with y (making it useful for prediction)\n", " - MSE decreases\n", " \n", "#### Don't forget: \n", "MSE is always positive\n", " - error is a \"distance\" from `y_true` to `y_pred`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## $R^2$ is the percentage of variance of y which can be explained by the model\n", "\n", "$$R^2 = 1-\\frac{MSE}{\\sigma_y^2}$$\n", "\n", "$R^2$ is the percent of variance of y explained by x (under model)\n", "\n", "Intuition:\n", "- $R^2 = 0$\n", " - x, using this model, doesn't explain any of the variance of y\n", "- $R^2 = .5$\n", " - x, using this model, explains half the variance of y\n", "- $R^2 = 1$\n", " - x, using this model, explains all the differences in y" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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8du7cOWbPns2aNWs4ePAg8+bNS/J9ySjLZTxZ7w8ePEjyruz49+953qNhw4axfv16vL29mTt3rknu/o5XsmRJJk6cyKBBg1i6dClLly417suTJw8fffQRU6dOtbi14zI7JWaZkJOTEy1atGDp0qWsW7eOdu3asXz5cuLi4mjXrt1ThxBSIzWfoG7evEn//v2Jioqie/fuNGvWjHz58uHo6IiVlRUTJkzgxx9/NPYSmMrYsWPTNJTZrl07k8aRVtu2bWPgwIFYW1szceJEateunaZy4ns4/v333zSdb4rFfUNCQti/f7/x+5MnT1KpUqVUl/O0pw/EL5WR0mEuS2FtbU2hQoUIDQ1N8P7ET/i/efPmU8+NvxszX7586RJbnTp18PT0ZO3ateTOnRt7e3uaNm2a5vJKlCjBuHHjuHfvHr/99hvbt29P14Q5NDSUcePGpfq8tm3bJlg64mmcnJxwdXUlPDycmzdvJpkwxd89mdb3aOzYsSxZsgRPT0/mzp2b7JzDtGrYsCFVqlRh06ZNXLhwAYPBQMmSJXn99deNP29ZZR6opVBilkm98847xk9ALVu2ZOXKldjY2NC+ffsXHsvOnTuJioqiUaNGfPrpp4n2x99taGqbN29O06RbS0jMdu3aRd++fYmLi2P8+PHP1csZv4ZSevWsPIvBYGDQoEHcvn2bJk2asHPnTr777juqVq2aZe+wfVL8BPInb5YpUqQIDg4OhIWFcePGjUR/2KOjo41TANKrDm1sbGjevDlz5szh9u3bNG7c2CQ9JzVr1uS3335L9Yem1IqMjEyyB/VZqlWrlqLEDB73OB08eJDTp08nmbzEL0eR0htvnvTDDz8wZ84c3N3dmT9/frJPQ3heOXPmTHLuavySLU+7C1fShxKzTKpYsWJUq1aNQ4cOMXHiRIKDg2nQoEG6fOJ6lvjEIKnhz9DQUPbt25fkefHDZck9/iU5Ga33JN7+/fvp3bs3MTExjBo16rl6KQDjKuv/XcX/RZk7dy579uyhTJkyjBs3joCAAL7++mv69u1rXEU+qzp37hx//fUXkHDJBXt7e+rUqcNvv/3G+vXr+fDDDxOct23bNqKjoylTpky6/ky3atWKVatWAaRoeNFgMDxzXlz8B7E8efI8f4DJyJ8/P+fOnUvXa/j5+XHw4EHWr1+faJ7nrVu3OHr0KHZ2dokm1j/Ljz/+yPTp03F1dWXOnDkpWjfQ1I4ePcoff/xhsukvknKa0ZeJvfPOOwDMnj0bMM2k/7SIf3TIli1bEqzbFBkZyeDBg5867yz+F3dSk70zshMnTtC4ceMkH6Vz/PhxevbsSVRUFEOGDEnRH8Pr16/z888/J7pzKjY2lvnz5xsX/X333XdN8wJS4dSpU0yYMAFHR0fGjx+Pvb097du3p3Hjxly5ciXdnvX4ot26dcv4nv538c9FixYl2YZPnDjBJ598Ajy+o/m/icoHH3wAPP4jff78eeP2oKAgvvvuuwTHPMnf358SJUrQqVOn53tRPB7COnjwIAcPHkxRcnHu3Dk6d+7Mjh07kvxAtWXLFuNNSM/7gcMStG3blpw5c7J7924CAgKM26Ojoxk8eDAxMTHGY560aNEiGjduzMCBAxOVuXDhQiZMmICTkxOzZs1K917lEydOJLktvm0OGTIkyZs0JP2oxywTa9CgAV5eXgQFBVGgQAHq1q1rljjq169PyZIlOXv2LI0aNaJatWrY2tpy+PBhrK2tad26tfFT+ZPq1KlD9uzZ2bJlC2+//TYFCxbE2toaPz8/k63j87ymTp1qnFQff8PDvXv3EgwZt2vXLsHw6IMHD4y9JP/14YcfEhkZiaenJ3/++Sd//vlnksc9ebdZREQEQ4YMYezYsZQtW5bcuXMTERHB+fPnCQoKwsrKij59+qT6U/vzun//Pv369ePRo0cMHz48wd18I0aM4OTJk6xatYpatWrRvHnzFxpbclasWMGKFSsSbe/cubNxbqWvr2+Cx1I9evTI+J7+947VFStWMHz4cHx8fChcuDBWVlZcu3aNM2fOYDAYKF++fKK7NuHx3Ym9evVi6tSptG7dmlq1amFnZ8e+ffuIjIykTZs2SSY38Q+hN8Vc0tQyGAwcOHCAAwcO4OTkROnSpcmdOzf379/n0qVLxgVSmzZt+tQpAytWrEj2Bo+UzgF7EZycnPjuu+/o0aMHgwYN4ueff8bLy4tjx44RFBREyZIljY/PetKdO3f466+/Eq3rdubMGUaOHAk8XgJnyZIlLFmyJNH5Sd1pnJZ2C49/P3l7e1OsWDGcnZ25cuUKgYGBWFtbM3jwYBo2bJi6SpHnpsQsE7O1taVq1aqsXbuWDh06mO3Wezs7OxYtWsSUKVPYsWMHv//+Ozlz5sTPz48+ffqwfPnyJM/z9PRkxowZTJ06lTNnznDkyBEMBgNeXl4Wk5j9/fffiZKnmJiYBNtSkxDH9x7evn072fkxTyZmXl5edO3alZMnT3L16lX+/PNPDAYDefLkoUWLFrz11ltUrFgxxTGYyrfffsvVq1dp1qxZovWknJ2dGT9+PO+88w5DhgyhQoUKKV4/Kr0FBQUlmRCfPHnS+PV/HyCdnHfeeYc9e/Zw7tw59u3bZ7yDr0aNGjRt2pRWrVo99S7XTz75hJIlSzJ//nz++OMPDAYDRYoUoWPHjk9NbOJXmX/ag+7TU/HixVm4cCF79+7lyJEjXL9+3ViXuXLlolGjRrzxxhvJDo0dPXqUo0ePPnV/auaAvQh169Zl5cqVTJs2jUOHDhEYGEjevHnp3r073bt3T3Ytuv+KiIgw3gR15syZpz4xIKk7jdPabt977z0OHTrE8ePHiYyMJFeuXLRo0YL33nsvTXPj5PlZGUx9K5xYjPv371O3bl3js9rc3d3NHZKIpKOYmBiqVavGSy+9xC+//GK2D2MiknaaY5aJzZ07l/v379OsWTMlZSJZwIkTJ7h//z4DBgxQUiaSQanHLJO5fPkys2fPJigoiL1795ItWzbWrl1LgQIFzB2aiIiIPIPmmGUyt2/fZuXKlTg4OFC2bFkGDBjw1KRs27ZtbNu2LUXlmvuxNiIiIlmBesyyMH9/f6ZMmZKiY6tVq/bUVddFRETENJSYiYiIiFgITf4XERERsRBKzEREREQshBIzEREREQuhxExERETEQigxExEREbEQSsxERERELIQSMxERERELocRMRERExEIoMRMRERGxEErMRERERCyEEjMRERERC6HETERERMRCKDETERERsRBKzEREREQshBIzEREREQtha+4ATOXOnfvExRnS9RoeHk6EhNxL12tkJapP01Odmpbq0/RUp6al+jS99K5Ta2srcubM8dT9mSYxi4szpHtiFn8dMR3Vp+mpTk1L9Wl6qlPTUn2anjnrVEOZIiIiIhZCiZmIiIiIhVBiJiIiImIhlJiJiIiIWAglZiIiIiIWItPclfksjx5Fc/duGDEx0cTFxaapjH//tSYuLs7EkWVdqk/TM1edWlvbYGtrj7OzG3Z29i/8+iIimUWWSMwePLjP3bt3cHJyxcHBHWtrG6ysrFJdjq2tNTExSiRMRfVpeuaoU4PBQFxcLFFRD7hz51+cnXOSPfvT1+gREZGnyxKJ2b174bi55cLePpu5QxHJdKysrLCxscXR0RlbWzsiIkKVmImIpFGWmGMWG/sIOzsHc4chkunZ2TkQE/PI3GGIiKSKwWA5i/RmicQMSNPQpYikjn7ORCSjmTdvNi1aNLGY5CzLJGYiIiIiBoOB/fv38vDhQwCcnJzIlcuTu3cjzBzZY0rMREREJMs4dOggLVo0Yc2aVQC0bduBOXMW4uLiaubIHssSk/8leVevXmHbts00bdqcvHnzmTscERERk4mLi2PMmBHkyeNF167dqFatOjNmzKZx49cTHXt33Chistnx4OEjnAd+aYZo1WMmPE7M5s79iZs3b5g7FBERkedmMBi4du0qANbW1vz55zHOnz8LPJ4L27p1OxwdHROdF7U2gLAVK4haG/Aiw01APWaSatHR0djbaxFRERGxTGPHjmDGjGmcOHEWFxdXFi9ega1txkh51GOWgW3Zsok6dapw6tTJRPv8/SfQsGE97t+/l2wZGzas5csvBwDwySfdqVOnCnXqVOHo0T8AaNu2OV980Z+tWzfRqVN7XnmlBtu2bebmzRvUqVOFDRvWJiqzTp0qzJ79Y4JtV678xeDBg3j99QbUr1+Tzp07snnzxrS+dBEREaOQkBDGjBlu7CVr3rwVQ4eOND6JJKMkZaAes+eyPzCIVbsuERIRhYeLA619i1KzjNcLu76f36tMnfoDq1evoGzZcsbtUVEP2bBhHY0aNSFHDqdky6hZsw49evRm+nR/+vUbhI9PSQAKFy5sPOb06UCuXPmLLl0+wMMjF7lyeaYqzosXL9CjR1cKFXqJvn0/w9XVjR07tjFkyFc8ePCAZs1apqo8ERERg8HAgwcPcHR05OHDB0yZMomCBV/irbc6UaZMWcqUKWvuENNEiVka7Q8MYv7Gs0T/7/E3IRFRzN/4ePz6RSVntra2tGzZhoUL59K7dz/c3NwA2Lp1E3fvRtC6dbtnlpEzZ04KFCgEwEsvFU6Q4MULDw9jxow5CW4MSM18tKlTf8DNzQ1//x/Jnj07ANWq1SAiIpyZM6fTtOkbWFur81ZERFLGYDDQtu0b5M6dh+nTZ+HtnZ/jx8+SK1cuc4f23Mz21/DgwYOUKFEiyX+XLl0yV1gptmrXJWNSFi86Jo5Vu15s7C1atMZgMLB+/RrjttWrf6FixcoUKVLMJNcoXtwnzXdrRkVFcfToH9SrVx87OztiYmKM/2rWrE1oaAhXr14xSZwiIpJ53boVxOLFC4DHE/gbNHiNWrXqGPdnhqQMLKDHbMCAAVStWjXBtvz585spmpQLiYhK1fb04u7ugZ/fqwQErOLNNztx+nQg586dYejQ0Sa7hodH2ht7REQ4sbGxLFu2mGXLFid5THh4WJrLFxGRzM1gMGBlZcWKFcsYPvwb6tb1pWDBQvTs2dvcoaULsydmhQsXpmLFiuYOI9U8XBySTMI8XF78MznbtOnA5s0bOXhwH9u2bcHDIxe+vvVNVn5Sj9mJvyszOjo6wfb/JlnOzi5YW1vTtGlzWrZsk2CfjY01sbFxFCxYyGSxiohI5nDt2lW6devCwIFf4ef3Kp06daZp02bp9jdjf2AQxf/z/YucNx7P7IlZRtXat2iCOWYA9rbWtPYt+sJjKV26LKVLl2XBgrmcO3eGt9/unKo7UOzs7IDHw44p5e7ugb29A5cuXUywfc+eXQm+z5YtGxUrVubChfMUK+aTIC5bW2ti/jMcLCIiWdetW7f4998gypWrgJdXXrJly05sbAwArq5uuLq6pct14+eNj3hi24ueNx7P7InZN998wyeffEL27NmpUqUKvXv3pmxZy7+TIv6NMuddmU9q27YDw4Z9jY2NDS1atE7VuYULF8HKyop16wLIkSMH9vb2FCxYCEfHHE89x8rKitdea8z69b/i7e1NsWI+nDkTyNatmxId+8kn/enV6wN69/6IFi1akyePF/fu3eXvv68RGHiSkSO/S/XrFRGRzKdTp/bExsbx2297sLe3JyBgwwu5bnLzxrNMYubs7Eznzp2pVq0abm5uXLp0iZkzZ/Lmm2+yaNEiKlSokKryPDyevizEv/9aY2trmvscniynboV81K1gGY8watDgVUaNGoqvb328vPKk6tz8+b3p06cfP/+8hN69PyI2NpapU2fy8stVgMdJWFL19+mn/bG2tmbJkoU8eBDJyy9XZfz4SbRq1Qxr6/8/p2TJEsybt5g5c35ixgx/wsLCcHFx5aWXCtOgQUOTvTfymLnr09raGk9PZ7PGYEqZ6bVYCtWpaWXk+ty5cycTJ05k5cqV2NnZMXXqFDw9PV/4awr939SkrcUbJNr+omOxMhgMhhd6xWTcvn2bZs2aUapUKebNm5eqc0NC7hEXl/RLCQq6ipfX849JW/LQ265d2/nqq4H4+/9IpUovmzucFLHk+syoLKFOTfXzZgk8PZ25ffuuucPIVFSnppUR6/P27dtkz54NJydntm3bzODBn7NkyQqTrSSQFp9N2/vUeePf9axt0mtZW1sl25lkUV0Vnp6e1KlThz///NPcoWQY165d4dChA0ydOokyZcplmKRMRESynhs3rlOpUikWLJgHgJ9fQ/btO2LWpAwezxu3/89og7nmjZt9jtl/xcWpByU1xo0bxalTJyhRohSDBw9NsM9gMBAbG5vs+TY2NknedSkiImIKa9euITj4Nu+99wH58nkzePC3NGzYCMBiFhd/ct54aEQU7macN25Ridnt27fZt29fhlw+w1ymTJn51H0bN65j1KihT90PMHnyDCpXrmLqsEREJAu7f/8+OXI8voFs3boALl++TJcuXbGysqJ794/NHF3SapbxomYZL7MPD5stMevfvz8FChSgTJkyuLi4cPnyZX766ScePnxIv379zBVWplK7dl1mzVqQ7DFaQ0xERExp9eqV9Ov3Cfv2/UHevPkYO3YCLi6uGp1JIbMlZiVKlGD9+vUsWrSIBw8e4ObmRrVq1ejRowc+Pj7mCitTSc81X0RERABiYmLYsGEtJUqUokSJklSuXIV27ToYEzE3t5xmjjBjsai7Mp9HVr8rMyNSfZqeJdSp7sqU5KhOTcuc9Rn/qKTw8DAqVChJ585dGTp0pFliMaX0rtNn3ZVpUXPMRERExPKNHDmUc+fOsmDBUlxd3diw4TdKlChp7rAyBcu4HUJEREQsVkxMDL/9toX4QbacOd3Jk8fLeOd/6dJlsLGxMWeImYZ6zERERCRZq1evpFevbgQEbKBWrTr07Nnb3CFlWkrMREREJIF79+4xZMiX+PrW5403WtG8eUucnJypXr2muUPL9DSUKSIiIsTGxvLXX5cBcHR05PjxY1y7dg2AbNmy0aTJ6xqufAHUYyYiIiL06vUhhw4d5NChP7G1tWXr1l0WszJ/VqIaF4tw9Ogf1KlThaNH/0jR8bNmzaBr107pHJVlu3nzBnXqVGHDhrXpdo179+7RuHF99uzZmW7XEBHzuHr1Cp9/3p979x4vDdGlywcMGzbauP6YkjLzUK1LhnPrVhBLly7kgw+6mzsUs/LwyMWMGXOpWbNOul3DycmJjh3fZurUScTExKTbdUTkxYiNjeX+/fsAhIQEs2TJQo4ePQJAjRq1aNbsDQ1XmpkSM3lu0dHRL/R6K1b8jIdHLmrWrJ3scTExMc98iLupxMXFvfDExd7enrJly5EzZ/quqt2iRWtu3rzBzp2/pet1RCR9PXz4kNq1q/DDD98DULlyFU6cOEe9eq+YNzBJQHPMMqgtWzYxbNhgZsyYS9my5RLs8/efwK+/BhAQsIEcOZ6+unC8DRvWMmrUUCZOnMr69b+yf//vGAxQs2Zt+vYdQM6c7sZj27ZtTvHiPvj5NWTBgjn8/fc1Bg78iqZNm/Pvv7eYNWsGBw/uIzw8HC+vfLRu3Zb27d9KcL0rV/5i8uTx/PnncbJlc6Bu3VeoU6deil73o0eP2LBhLa1bt0uw/ebNG7Rr9wY9e/YhMvI+Gzas5fbtf1m+fA158+bj1KkTzJ07i8DAE0RHP6JYseJ88EF3qlWrkaCcPXt2MmvWDK5du0quXJ60atWOBw8imTv3J37//f+HWevUqUK7dm+SN28+fvllGUFBN5k4cSqVK1fhypW/mDVrBseO/UFkZCQFCxbi7be78NprjY3nP3z4kJ9+ms7u3TsICQkmW7bs5M9fgM6du1K7dl0Azp07y6xZ0zlz5jT379/DzS0nJUuW4osvhuDi4mJ8zV9+OYSmTZsby96xYxuLFs3nr78uY2dnS4UKlejWrRfFihU3HjNy5Lfs2bOTmTPn8cMP4zl58jjOzi7Ur/8qH33UC3t7e+OxOXO6U7VqddasWcWrrzZK0fskIpbh/PlzHD36Bx07vk22bNlo1aotlSpVNu7X45IsT5bvMWvZsik//7wYePxHv2XLpqxY8TMAkZGRtGzZlICAXwCIiAinZcumrFv3KwAhISG0bNmUzZs3AnDr1i1atmzK9u1bAbh+/R9atmzKrl07gMcJScuWTdm373cALl68QMuWTdMUt5/fq3h45GL16hUJtkdFPWTDhnU0atQkRUnZk0aPHoaTkzPDho2hW7ce7N+/l08//ThRT9Dp04HMmTOTd97pwvffT6Z06bIEB9/mww87c+LEn3Tr1ovvvptEvXqvMHXqJH76abrx3JCQYD7+uBtXrvzFZ599zuDBw3j48CETJoxLUYynT58iIiKcihUrJ7l/+fIlnDlzmn79BjJ69Pc4O7tw6NABPv64G3FxsXzxxTeMHDkWD49cfPZZHw4dOmA898CBfXz11UDc3HIydOhoevb8hJ07f2PjxnVJXmvHjm1s3bqR7t0/ZuzYiXh75+fixQt8+GFngoJu0rfvZ4wdO5HSpcsybNhg1q0LMJ47efJ4Nm/ewNtvd2b8eH++/PIbatWqQ0REOPC47X36aS8ePXrEwIFfMWHCFHr2/ARnZ5dkeyjXrfuVr7/+HE9PT4YNG03//l/wzz9/06NHV65c+SvBsdHRj/j88/5Uq1ad0aPH07Rpc5YvX8LixfMTlVup0sucOHGcyMj7T722iFiGJ5+0OHfuT3z11SDj8OWgQV/x2mtNzBWapIB6zDIoW1tbWrZsw8KFc+ndux9ubm4AbN26ibt3IxL1KKVEuXIVGDDgcwCqV69JzpzuDBnyJTt2bKNhw//v7QkPD2PGjDnkzZvPuG3s2JFERT1k9uxF5MqVC4CqVasTE/OIpUsX0qHDW7i4uLJs2RLCw8OYP38pPj4+xMTEUbNmbfr06cm//956ZoynTp0AwMenRJL7HR0dGTduYoI5EhMmjMPHpyTjx/sbJ7PWqFGbrl07MXPmNGOv2axZM8iTx4vx4/2xtbX9Xz3Uol275okvxOMh3B9+mJYgAR4zZjhubm74+/9I9uzZAahWrQZhYWHMnDmdpk3fwNrampMn/+S11xrTsmUb47l16vgav7527QoREeH06tWX4sV9jNuffB/+Ky4ujunTp1CyZGlGjx5vnMBbuXIVOnRowdy5PzF06Kgn4o/io48+xte3PgBVqlTj3LkzbNmykffe+zBB2T4+JYmNjSUw8BRVq1Z/agwiYl7Hjh2he/euzJ+/lJIlS9G372f07/85OXLkMHdokkJZvscsIGADHTu+DYCdnR0BARto164j8PiPfEDABuMfTxcXVwICNtCs2RsAeHh4EBCwgUaNHn/6yJMnDwEBG/DzawiAt3d+AgI2GP/wvfRSYeOqyQDFihUnIGBDmmNv0aI1BoOB9evXGLetXv0LFStWpkiRYqku79VXX0vwva+vHzY2Nhw/fjTB9uLFfRIkZQAHDuzl5Zer4ubmRkxMjPFfzZq1iY6OJjDwJPD4l0axYsUTxffkMF9ygoODsbGxwdnZJcn9derUS5CU/fPP3/zzzzUaNmxsnAcWP/esRo1anDt3hsjISB48eMC5c2eoV+8VY1IGj9tA7dpJD7O+/HLVBElZVFQUR4/+Qb169bGzs0tUD6GhIVy9egWA0qXLsmHDWubO/YnAwFM8evQoQdn58xfE2dmFsWNHsHHjOm7cuP7Murl69QohIcG89lpjY1IGkCtXLqpWrc6xY0cSHG9jY2Nsi/GKFi3OrVtBicqOH84ODr79zDhE5MW6ePECZ8+eAaBgwZfw9s7PgweRwOO/S/EfliVjUI9ZBubu7oGf36sEBKzizTc7cfp0IOfOnWHo0NFpLC/hD6+trS2urm6Eh4cn2O7hkfiHPDQ0hF27dvDKKzUS7QMICwsDHg8H589fMNH+pMpMSlTUQ+zs7BIkHsmVExoaAsCkSd8zadL3SZ4TERGBtbUVBoMhwXy6eEltS+paERHhxMbGsmzZYpYtW5zkOeHhYQD07fsZuXJ5smXLRmbP/pHs2R2pW9eXHj164+mZGycnJ6ZMmcm8ebOYNGk89+7dJW9eb1q3bkfHjm8n+fojIiKAx+0iqVjjrx0ve/bs2NnZJdhmZ2eX5FBp/JyzqKiHSb4uETGPmJgYWrRoQpUq1Zg/fwkeHh6sWpX09AvJGJSYZXBt2nRg8+aNHDy4j23btuDhkcvYQ5daoaHBCb6PiYkhPDwMV1fXBNuTSgrc3Nzw8SlJ164fJVl2fA+bi4trouvA47lnKeHq6sbDhw+Jjo5OMEH9abHFD/F26fLBU28w8PDwICYmBisrK+7cCU20P6ltSV3L2dkFa2trmjZtnmCI8kkFCxYCHidFH37Ygw8/7MGdO6Hs3bubadP8uXUriKlTfwKgaNFiDB8+BoPBwMWLF1iz5hemTv0BZ2dnmjVrkajs+PcpPhl9UkhIMK6ubknGlBLxSd/zlCEiprF69UrWr1/LTz/Nw9bWlpkz5+LjU9LcYYmJKDHL4EqXLkvp0mVZsGAu586d4e23OycYikuNbdu2ULfuK8bvd+3aTmxs7FMn2j+pevVa/PHHIQoUKJjsTQeVK1dhyZIFXL58CR+f/79LcMuWTSmK8aWXCgOPb6woXLjIM48vUKAQ+fJ5c+nShWTXPbOzs6NkyVLs3r2THj0+MdZhZGQke/fuTlFs2bJlo2LFyly4cJ5ixXxS/D7kzOlOs2YtOXHiT3bt2p5ov5WVFcWL+/DppwNZuzaAixcvJFlOwYKF8PT0ZMuWTbRr96YxcQwNDeGPPw4lmMOWWvFDqYULF01zGSKSdpcvX6RAgULY2dkRHh7O9ev/EB4eRu7cLsY7uSVzUGKWCbRt24Fhw77GxsaGFi1ap7mckyf/ZPz4sdSt68u1a1eYOXM6xYr5UL/+q88898MPe3D48EF69OhK27YdyZ+/AA8ePOD69b/Zu3cPEyZMwcbGhvbt32T9+l8ZMOATPvqoJy4ubmzevIG//76aohgrVXoZgMDAkylKzKysrBgw4AsGDuzLwIF9adSoqXFY7+LFC4SEBDNw4FcAdO3anYED+9K/f2/atu1AbGwsS5YsJHt2R2OP0bN88kl/evX6gN69P6JFi9bkyePFvXt3uXr1CmfOBDJy5HcAdOvWhVq16lC0aDGcnJy5ePECO3dup2bNWgDs3buHgICV1K37Cnnz5iMuLo4tWzYSFxf31IcIW1tb07Nnb4YO/YYvvuhP8+atePAgknnzZmFtbcP773+Y5Hkpcfr0SdzdPYyJsYi8OIcPH+T11xsya9Z83nijFe+++x5dunQ1d1iSTpSYZQK+vn7Y2g6lbt1XyJXLM83lfPnlENatW8PXXw8iLs5ArVq16dNnQIp6fjw9czNr1gLmzp3F/PmzCQkJxsnJifz5C1KjRi3j3ZAeHrmYMmUmkyZ9z7hxo3BwyEa9eq/Qr99APv+8/zOvkzt3HipWrMzvv+9KcjgvKdWq1WDGjLksWDCHiRPHce/e4zXBihUrTpMmzYzH1ahRixEjxjF79gy++eYL3N09aNWqLcHBwWzatD5F1ypWrDizZy9i7tyfmD7dn/DwMFxcXClU6CXjTSHwOMHcs2cXP/+8mOjoaHLnzk2rVm3p0uUDAAoUKICjYw4WLZpHcHAw9vb2FC5cmOHDxyS7sG6TJs2wt8/GwoXz+PrrQdja2lGxYiWGDh1NwYIvpeg1/JfBYOD333cne0eoiJhOXFwcc+fOws3NjTZt2lO5chW+/XYkNWo8/tnXo5IyNyvDkwueZGAhIfeIi0v6pQQFXcXLq9BzX8PW1pqYmLjnLsfUdu3azldfDcTf/0djj1JqxC8wO3fuYooXT3oZivSQ1vrcsWMbQ4cOZvXqDU+dmG8qMTExdOnyFrly5eKHH6al67VMIT3a6NGjf/Dpp71YtGgFBQokvnHjv0z182YJPD2duX37rrnDyFRUp093926E8Y7z119viLe3NzNnzkv2HNWn6aV3nVpbW+Hh8fQpP0q7M7Br165w6NABpk6dRJky5dKUlGVEr7zSgOLFS7B48QKTlhsbG8vYsSPYsWMbx44d4bfftvDpp724evUv3n77XZNeKyOZP382r7/+RoqSMhFJm8mTJ1K1annjQrBLl658ZlImmZOGMjOwceNGcerUCUqUKMXgwUMT7TcYDM98VmRGfFitlZUVgwYN5uDBfSYv9+7dCCZPnkBY2B1sbW3x8SnJd99NomrVpJcByezu3btHhQqVaNWqrblDEclU7t+/z/LlS2natBl58nhRq1ZtHjyIJC7u8e9sFxfXZ5QgmZWGMlPBUocynyZ+iDI5kyfPoHLlKi8oooQyWn1mBJZQpxrKlORk9TqNi4vD2tqay5cvUbNmZUaP/v65bszJ6vWZHsw9lKkes0ysdu26zJqV/HBf/LpaIiKSfgwGA927v4+zsyvff/8DRYoUZc+eQwkeuSYCSswyNVdXNy0IKiJiJvfv32fv3t289loTrKysKFCgUIJnVj7tmb+StSkxExERSQczZ05j9OjhHD58gkKFXmLw4G/NHZJkALorU0RExARu3rxB585vceDA4xuT3nmnC2vXbtGUEUkV9ZiJiIikUWRkJLduBVG4cBFcXd04f/4sN2/eAMDT0xNPz7Qv+i1ZkxIzERGRNGrTphnW1jasX78VR0dH9u07YnxOrUhaKDETERFJoRMnjrNgwTzGjh2PjY0NAwZ8jqPj/0/oV1Imz0tzzERERJLx4MEDHj58CMDVq1dYu3Y1ly5dBKBBg9eSfX6tSGopMRMREXmKmzdvUKlSKZYuXQRAkybNOH78rJa6kHSjxExEROQJBw7sJyDgFwC8vPLy5pudKF++AgC2trZkz57dnOFJJqc5ZllUdHQ09vb2qd73vGWLiFii+EclAUybNomLFy/QokVrrKysGDJkuJmjk6xEPWaZwJUrfzF48CBef70B9evXpHPnjmzZssm4f8OGtdSpU4XDhw8wbNjXNGnix9tvP34o9ccfd6NLl7c4fPggH3zwLn5+tVi4cC4A16//wzfffEHTpo/L7dSpPWvWrEpw7aNH/6BOnSps2bKRCRPG0rz5a/j51XpxL15E5Dlt2rSBypXLEBwcDMCYMePZunW3JvKLWWT5HrP7c2byYO6sFB2bvUUrcgz4IsG2u+NGEbU2IGXnv/cBOd7vlmBb+KB+2JYomWh7Sl28eIEePbpSqNBL9O37Ga6ubuzYsY1hwwYTHf2QZs1aGo8dNWoYvr5+DBs2iqioKOP227dvMWbMcN59930KFCiIo6MjISHB9OzZFSsra3r2/AQPj1xs376V774bxZ07oXTp8kGCOKZNm8zLL1fhyy+HEBkZmabXIiLyIhgMBg4fPoSXlxcFCxaicOEilC9fgXv37pIrVy7y5fM2d4iShWX5xCyjmzr1B9zc3PD3/9E476FatRqEhYUxc+Z0mjZ9w3hsjRq16Nt3QKIywsPDGT16POXLVzRumzZtMqGhocydu4RixYoDULNmbe7du8fChXNp06YDzs7OxuNfeqkwX3+t7n4RsXx37oTSuvXrvPfeBwwfPoYSJUqyYMHP5g5LBNBQZoYWFRXF0aN/UK9efezs7IiJiTH+q1mzNqGhIVy9esV4fL16ryRZjptbzgRJGcCxY39QtGhxY1IWr3Hj14mKiiIw8GSC7fXq1TfFSxIRSRfTpvnTv38fANzdPVi69BcGDRps5qhEEsvyPWY53u+W4mFEW1trYmLiEmxzHvglzgO/TPP1XcdOSPO5ERHhxMbGsmzZYpYtW5zkMeHhYcavPTxyJXlMUtsjIiLw9i7w1GMjIsKfWYaIiLkYDAYCA09Rtmw5AMLD7xAcfJvY2FhsbGyoW9fXzBGKJC3LJ2YZmbOzC9bW1jRt2pyWLdskeUzBgoW4ceM68PQVqZPa7uLiSmhoSKLtISHBxv3PKkNExFxWr15J9+5d2bjxN15+uSqff/61fk9JhqDELAPLli0bFStW5sKF8xQr5oOtrenezpdfrsrixfO5ePFCguHMLVs24ODgQJky5Ux2LRGR5xUZGcmUKT9QpUpV/Pwa8tprjRkzZjwlSpQC9OFRMg7NMcvgPvmkP//8c43evT9i06b1HDt2hD17drJo0Ty++uqzNJfbocNbuLt78NlnfVi3bg0HDuxj1Kih7Nq1gy5dPkgw8V9ExFzie/bt7e1ZvvxnDh7cD4CTkzPvv/8hTk5O5gxPJNXUY5bBFStWnNmzFzF37k9Mn+5PeHgYLi6uFCr0En5+DdNcbs6c7syYMYcZM/yZNm0yDx5EUqBAQQYNGkzz5i1N9wJERNKof/8+7Nu3h717/8DW1pZdu/aTI0eOZ58oYsGsDAaDwdxBmEJIyD3i4pJ+KUFBV/HyKvTc10hq8r+knerT9CyhTk3182YJPD2duX37rrnDyFSep06Dg4NZvHg+3br1JHv27Gzduolr167y7rvvY2dnZ+JIMwa1UdNL7zq1trbCw+PpPbnqMRMREYsWfyfluXNnGDlyKGXLlqNBg9do2LCxuUMTMTnNMRMREYv08OFDXn+9IZMmjQegVq06HDx4nAYNXjNzZCLpx6ISM39/f0qUKEGLFi3MHYqIiJjB7du32bZtM/D4zvPSpcsaH5FkZWVF4cJFzBmeSLqzmKHMCxcu8NNPP5ErlxYqFRHJqkaPHsaqVSsJDLxIjhw5+O67ieYOSeSFsoges7i4OL766ivatWtHkSL6NCQiklWcPh3IG2805q+/LgPQp09/tm7dpbsrJcuyiB6zefPmERQUxJw5c+jRo0e6XMNgMGiBQZF0lklu8pZ0sD8wiFW7LhEaEYWjzQNerexFiwYv4+7uTkhIMDdv3qBw4SIUKvSSuUMVMSuzJ2Z///03kydP5vvvv0+3hQBtbOx49CgKe/ts6VK+iDz26FEUtrZZc9kCebr9gUHM33iW6Jg44uJiCfixJ3sLlCW312xqlsnL778f1gdnkf8x61CmwWBg8ODB1KlTh1dffTXdruPk5EpYWDD3798lNjZGn+pFTMhgMBAbG8P9+3cJCwsmRw7XZ58kWYr/7OUc3ToTAGtrG8rW/5Ci1duzatclQI9LEnmSWXvMli9fzqlTp9iwYcNzl5XcYm3gzMOHbty69S/h4beJiYl57uuJyP+ztbUlW7ZsFC1amGzZMlfPtKenHj+WFiEhIeTMmRNra2tu/H2JW5cO4VOzI/bZnMjrUwuA0Igo1a8JqA5Nz5x1arbELDQ0lO+++46PPvqI7NmzExERAUBMTAxxcXFERETg4OCAg4NDispLbuX/eI6OOXF0THvMWmHZtFSfpmfuOr179xF37z4y2/VNzdz1mVEdO3aEFi2aMHv2Aho2bEzlui0pXKkZVtY2CY5zd3FQ/T4ntVHTM/fK/2Ybyrx16xZ3795l/PjxVK1a1fjv6NGjnD9/nqpVq+Lv72+u8EREJIUMBgPr169l69ZNAJQtW54uXT6gSJGiALRrUAoH+4RzD+1trWntW/SFxypi6czWY1awYEEWLFiQaPuoUaOIjIxkxIgR5MuXzwyRiYhISsTExGBr+/jPyPjxY8mTJw8NGzbGzs6OYcNGGY+rWcYLwHhXpruLA619ixq3i8j/M1tiliNHDqpXr55ou4uLC0CS+0RExDLMmfMT06f78/vvh3FwcGDhwp/Jk+fpiVbNMl7ULOOloTeRZ7CIBWZFRMSyxcbGsnHjekJDQwAoVqw4dev6cv/+PQC8vfMbe89EJO0s7qdo4cKF5g5BRET+4/z5c3Tu/CYjRoyhW7ee1Kv3CvXqvWLusEQyHYtLzERExPwMBgNff/052bM78tVXQyhVqjSrVq2jRo1a5g5NJFPTUKaIiACPhyuPHTsCPF70NTIykgcPIo3769Spp+FKkXSmnzAREQFg8uQJjBs3isOHT5A/fwHGj5+sVflFXjD1mImIZFHBwcF8/nl//vzzGADt27/JjBmzjXdXKikTefGUmImIZCFxcXEEBwcDYG9vx5o1qzh58gTw+M7KFi1aY2enB9GLmIuGMkVEspB27VoAVvzyy6+4uLhy7NiZTPd8U5GMTImZiEgm9tdfl/nll+X07z8IKysr3nqrEzY2NhgMBqysrJSUiVgYJWYiIplMXFwccXFx2NracujQAX744XuaNWtByZKlaNOmvbnDE5FkaI6ZiEgmEhR0k9q1q7By5TIAWrZsw9GjpylZspSZIxORlFBiJiKSwV2+fImdO7cDkCePFxUrViZ37jwAODg4kDt3bnOGJyKpoKFMEZEMbtCgfly58heHDv2JlZUV06fPMndIIpJG6jETEclgdu/eyWuv+RIREQ7AyJHjWLdui9YdE8kElJiJiGQAf/11mVu3bgHg6uqKlZUVQUFBAPj4lDAuCisiGZsSMxERCxcaGkKdOlWZPt0fgAoVKrF58058fEqYOTIRMTXNMRMRsUDLli3hr78u8fnnX+Pu7sGUKT9Ss2Ztc4clIulMPWYiIhbi1q0g49cnT/7Jrl07iYmJAaBVq7Z4eeU1V2gi8oIoMRMRsQBr166hQoWSBAaeAuDrr4exYcM2bG01sCGSlSgxExExg+joaBYsmMuBA/sBqFOnLn369MPT8/GaYw4ODrrLUiQLUmImIvICRUdHG78eN24Ua9b8AkDOnO588cU3WgxWJItTH7lIJrA/MIhVuy4RGhGFu4sDrX2LUrOMlk+wNMOGfcPu3TvZunUX9vb2bN26S/PGRCQB9ZiJZHD7A4OYv/EsIRFRGICQiCjmbzzL/sCgZ54r6SsyMpKff15s7CUrW7Yc9es3MH6fN28+DVeKSALqMRPJ4FbtukR0TFyCbdExcazadUm9Zma2f//vfPJJD9zcctK4cVNat25n7pBExMIpMRPJ4EIiogBoeH6rcdtWn4bG7fLiREVF0bPnh1SrVp2PPupF/fqvsnbtFqpVq27u0EQkg1BiJpLBebg4EBIRRcMLvxm3bfVpiIeLgxmjyjoePHjAmTOBVK5cBQcHB2JiYjAYDABYW1tTvXoNM0coIhmJEjORDK61b1HmbzybYJu9rTWtfYuaKaKs5csvP2Pt2jX8+edZcuTIwfz5S8wdkohkYJr8L5LB1SzjRecmJRNs69ykpOaXpZPLly/SrVsXbt68AcBHH/Vi3rzFODo6mjkyEckM1GMmkgnULONF8H++F9N5+PAh9+/fx8PDA2trG3bv3smZM4HkzZuPkiVLAaXMHaKIZBJKzEREkhETE0OdOtWoXbsOkyZN46WXCnPixHns7e3NHZqIZEIayhQR+Y/jx48yefIEAGxtbfnkk09p166jcb+SMhFJL0rMRER4vNRF/N2U27dvw9//B0JDQwF49933qFOnnjnDE5EsQomZiGR5J0/+SaVKpdm7dw8A3br14Nix07i7u5s5MhHJajTHTESypCNHDvPoUQw1atSkePES1Kvni7OzMwBOTs5mjk5EsiolZiKS5RgMBnr37k7evPn45Ze1ZMuWjRkz5pg7LBERJWYimYVD85Zkz2bHg4ePzB2KRVqx4mfmzJnJ2rVbsLW1ZdasBRQsWNDcYYmIJKDETCSTcB74JZ6ezty+fdfcoViMY8eOULy4D05OzuTI4UTOnO6EhoaSO3duSpcuY+7wREQS0eR/EcmUzpw5TaNG9Vm27PEjkpo2bcaSJSvJnTu3mSMTEXk69ZiJSKZgMBiYPHkCdnb29OzZm1KlSjN9+ixee62xuUMTEUkxJWYikqH988/f5M9fACsrK44fP0a2bNmM+9q0aW/GyEREUk+JmUgmcXfcKGL+N/nfeeCX5g7nhZg2zZ9Ro4Zy9OhpcufOzcyZc7GzszN3WCIiaabETCSTiFobQNT/vs6siVlERDhz5vxE06bN8fEpQePGTbCxscbRMTuAkjIRyfBSNfm/UaNGzJw5k9u3b6dXPCIiiTx48ACAR49imDjxO3bu/A2AIkWK8dFHvbQgrIhkGqnqMbO1tWXChAlMnjyZevXq0a5dO3x9fbG21s2dIpI+3n+/E48eRbNw4TI8PDz4449TeHp6mjssEZF0karEbP369Rw/fpyVK1eyceNGduzYQa5cuWjdujVt2rTRYo0i8txCQkLYsGEt77zTGSsrK2rXrktMzCMMBgNWVlZKykQkU7MyGAyGtJz44MEDNmzYwMqVKzl27BhWVlZUrVqVdu3a0ahRI+zt7U0da7JCQu4RF5eml5JiWrzTtFSfphVct5rx61x7DpkxkrSJT7zmzZvNwIGfsnPnfrMvAqs2anqqU9NSfZpeeteptbUVHh5OT9+f1oKzZ89OmzZtWLp0KRs3bqRp06YcOnSIgQMHUrduXUaNGsWNGzfSWryIZBH//vsvLVs2Ze3aAADatevI7t0HzZ6UiYiYw3NNDouNjWXr1q2MGTOGjRs3YmVlRfXq1alQoQKLFi2iadOmbNu2Lclzjx49SteuXalbty7lypWjRo0avPvuu+zatet5QhKRDODOnVCOHz8KgIeHBzY2NsTFxQGQI0cOSpYsZc7wRETMJk3LZVy6dImVK1fy66+/EhISgoeHB++//z7t27c3zjO7evUqffv25bvvvuPVV19NVEZERASFCxemdevW5MqVi4iICJYtW0a3bt2YMGECr7/++vO9MhGxWB980Jm//77GgQPHsLGx4Zdf1po7JBERi5CqxGzlypWsXLmSP//8E4BatWrRvn17GjRogK1twqIKFSpEp06dGDx4cJJlvfLKK7zyyisJttWvX58GDRqwbNkyJWYimciRI4eZNGk806fPJkeOHHz11RCyZcuuO7pFRP4jVYnZ4MGDyZUrF926daNdu3bkz58/2eOLFStGixYtUh6MrS3Ozs5aJFIkEwgLu4OVlRWurm48ehTDqVMn+euvy5QtW47KlauYOzwREYuUqsTM398fPz8/bGxsUnR8+fLlKV++fLLHxMXFERcXR0hICMuWLePKlSsMHDgwNWGJCJD9vQ/I4ejA/cioZx+czu7cCaVy5bL06PExAwd+SfXqNTh06M9EPesiIpJQqn5LNmzY0OQB9O3bl82bNwPg5OTEDz/8QL169Ux+HZHMLsf73fD0dAYz3Tr/229buHTpIt269SRnTne++GIwder4AmBlZaWkTEQkBdK8jpmp/P3339y5c4fg4GDWrVvHli1bGDNmDM2aNTNnWCKSApGRkTg6OgLQrVs3du3aRWBgoJIwEZE0Mnti9l/du3fn6NGjHDhwIFUTg7XAbMaj+jS9F1mnW7duolu39/ntt90UKVKM8PAwcuRwylRJmdqo6alOTUv1aXoZdoHZ9FKuXDnCw8MJDQ01dygi8oS4uDi2bt3EyZMnAChfvhJvvNESG5vHiZirq1umSspERMzBon6LGgwGDh06hIuLC25ubuYORyRDCR/Uj4f2tkRFx+A6doLJyo1/VNLDhw/p1asbzZq1YMIEf/LkycOkSdNMdh0RETFjYta/f3+8vb0pU6YMOXPm5Pbt26xevZoDBw7w9ddf65O3SCo92vc7j0xc5uTJE/j9990sXx6Ao6Mjq1dvwMenhImvIiIi8cyW/VSqVIm1a9eybNky7t69i7OzM2XLlmX69On4+fmZKyyRLC0uLo7du3dSt64vNjY2uLi4kjt3HqKionBwcKBMmbLmDlFEJFOzuMn/aaXJ/xmP6tO0gutWM36da8+hNJWxefNGOnXqwMKFy2jUqImpQsuw1EZNT3VqWqpP09PkfxExm6ioKL76aiA//7wYgAYNGjJr1nzq129g5shERLImJWYiWUxcXBx//XUZAHt7e44fP8aVK4+/t7W15Y03WmFvb2/OEEVEsizNsBfJYj7/vD/r1q3h6NHTZMuWjV9/3ZTix6yJiEj6Uo+ZSCZ38+YNvv76C4KDgwHo0OEthg0bbUzGlJSJiFgOJWYimZDBYOD+/fsAREREMGfOTA4e3A/Ayy9XpW3bDtjZ2ZkzRBERSYKGMkUyoVdfrUfVqtUYM2Y8JUqU5NSpC+TM6W7usERE5BmUmIlkAleu/MWTN183b96CwoWLGL9XUiYikjEoMRPJoOIflQSwePEC/g0OZty4sRgMtvR9o5WZoxMRkbTQHDORDOjs2TP4+tbgyJHDAHTv/jGfb/+d/O+/TzYlZSIiGZZ6zEQyiGvXrnL37l3KlClL/vz5cXf3ICoqCgAPDw8zRyciIqagxEwkAzAYDLRp05yCBQvxyy9rcXJyJiBgg7nDEhERE9NQpoiF2rJlI507v0VcXBxWVlZMnjwdf/8Z5g5LRETSkRIzEQvyzz9/8+DBA+Dx+mPXrl3l339vAVCzZm3y5fM2Z3giIpLOlJiJWIizZ89QpUo5Vq9eCUDr1u3Yvv13vLzymjkyERF5UTTHTMSMli5dBMCbb75DiRIl+frrYdSr9woA1tb63CQiktUoMRN5we7du4uTkzMAAQG/AI8TMysrK3r1+sScoYmIiJnpI7nICzRv3mwqVChFWNgdAGbOnMvPP68yc1QiImIplJiJpKOHDx/y88+LuXr1CgBVq1bn3XffIy4uDgBXVzfj6v0iIiJKzETSgcFgACAs7A79+vU2TugvU6YsQ4YMx91dC8KKiEhimmMmYmIDBvTl/v17TJ8+Cy+vvGzfvpcSJUqaOywREckA1GMm8pyioqLYunWT8XsvLy/y5fM29pqVLFlKw5UiIpIi6jETeU4LF87lyy8HsmPHPsqUKcuAAZ+bOyQREcmg1GMmkkohISF07/4+v/22BYB27TqyYsUaSpcuY+bIREQko1NiJpICUVFRXL58CQAXFxcCA09x48YN4PGdlb6+9TVcKSIiz01DmSIp0KlTB4KCbrJr1wHs7OzYteuAVuYXERGTU2ImkoSzZ88wa9aPjBw5FgcHB3r16mNcewz0uCQREUkf+usi8j/R0dFERkYCcOPGdVatWsGZM4EA+PrWp379BhquFBGRdKXETITHC8G+/HJZZs+eCUD9+g04ceIsFStWNnNkIiKSlSgxkyzrzz+P8csvywFwc8tJhw5vUbnyywBYWVkZHzQuIiLyomiOmWQpcXFxxvlhM2ZMZe/ePbRo0RpbW1sGD/7WvMGJiEiWpx4zyTL27NlFlSrluH79HwC++WYYv/9+CFtbfT4RERHLoL9IkqmdOHEcJycnihQpxksvFaZ4cR/u3bsHQN68+cwcnYiISELqMZNM6/79+7Ro0ZTJkycCUKBAQZYtW60HiouIiMVSj5lkKgsWzOXQoQNMmfIjOXLkYMGCpZQvX8HcYYmIiKSIeswkwztz5jQGgwF4vOzFrVtBPHz4EIC6dX1xdXUzY3QiIiIpp8RMMrRt2zbj61uD3bt3AtC796esWLGGbNmymTcwERGRNFBiJhlKdHQ0kydPZP36tQDUrfsKI0aMoUKFigBamV9ERDI0JWaSIYSF3QHAzs6OlSt/5vffdwHg4OBAt249cXPLac7wRERETEKT/8XiDR36NatXr+Tw4RPY2dmxYcM2rcovIiKZknrMxOKEhd1h6tTJRESEA+Dn9yoffNCdmJgYACVlIiKSaanHTCxG/OOSrl69wtChg8mXLx+tWrWlbl1f6tb1NXd4IiIi6U49ZmJ2sbGxtG/fkuHDhwBQoUIl9u8/QqtWbc0cmYiIyIulxEzMIizsDuvXrwfAxsYGH58S5M9fwLi/aNHi5gpNRETEbDSUKWYxfvw45syZyYkT5/Hw8GDEiLHmDklERMTs1GMmL8Tlyxdp27YFgYGnAOjevRcHDx7Ew8PDzJGJiIhYDiVmkm4iIsK5evUKADlzunP9+t/cvHkdAG/v/FSqVMmM0YmIiFgesw1l7t+/nzVr1nDs2DGCgoJwdXWlfPny9O7dmxIlSpgrLDERg8HAa6+9QpEiRVmyZCU5c7qzb98RrcwvIiKSDLMlZkuXLiUsLIwuXbpQtGhRgoODmTVrFm3btmXhwoVUrFjRXKFJGh04sI/Vq1cyZsx4rKysGDJkBPny5TPuV1ImIiKSPLMlZkOGDEk0v6hOnTo0aNCA2bNn4+/vb6bIJDXu3o0gW7bs2NnZcfHiBTZuXE/fvgPImzcfTZq8bu7wREREMhSzzTFLatK3i4sLhQoVIigoyAwRSWqdP3+O8uVLsm7dGgDat3+TI0dOkTdvvmecKSIiIkmxqMn/oaGhXLhwgeLFtYaVpdq+fSvr168FoFix4nTq1IUSJUoBYG9vj52dnTnDExERydCsDAaDwdxBwOPJ4h9//DG7d+8mICCAokWLmjsk+Z/Y2FhsbGwAqFevHrGxsezdu9fMUYmIiGQ+FpOYjR07ljlz5jB69Ghat26d6vNDQu4RF5e+L8XT05nbt++m6zUszfLlSxkzZgS7dx/EycmJ69f/wdMzN/b29s9ddlasz/SmOjUt1afpqU5NS/Vpeuldp9bWVnh4OD19f7pdORUmTpzInDlz+Oqrr9KUlInpGAwGduz4jVu3Hs/zK1KkKNWr1+T+/XvA4/XHTJGUiYiISGJmT8wmTZrEjBkz+Oyzz3j33XfNHU6W988/f9OxY2sWLZoPQJUq1Zg+fRZ58niZOTIREZHMz6zPypwyZQrTpk2jT58+fPDBB+YMJUsbM2Y49+7dY8SIsRQoUJCVK3+lWrUa5g5LREQkyzFbYjZnzhz8/f2pX78+tWrV4vjx48Z99vb2lC5d2lyhZXoGg4ETJ45TocLjRyLdvXuXu3fvYjAYsLKyom5dXzNHKCIikjWZLTHbsWOH8f/4r+N5e3uzfft2c4SVJcyZM5MvvviMvXv/oHhxH0aMGKtV+UVERCyA2RKzhQsXmuvSWU54eBgTJnxHkyavU6NGLd54ozU5cjhRoEBBQI9KEhERsRRmn/wv6cNgMBAcHAyAg0M2fvllOceOHQXA09OTjh3fJlu2bOYMUURERP7DrJP/Jf289947BAXdYNOmHWTLlo1Dh/7E0dHR3GGJiIhIMtRjlklcv/4P338/hpiYGADatGlH585diYuLA1BSJiIikgGoxywDMxgMxMbGYmtry/Hjxxg/fiyvvOJHlSrVaN68pbnDExERkVRSj1kGFR4eRv36tZk/fzYAjRs35Y8/TlKlSjUzRyYiIiJppcQsA7l+/R+2b98GgKurG+XLV8DLKx8ANjY2eHvnN2d4IiIi8pw0lJmBDB78OQcP7ufEiXPY2toyefJ0c4ckIiIiJqQeMwt2+PBBmjTx499//wVg8OAhbN68A1tb5dMiIiKZkf7CW5gbN65jZWVF3rz5yJnTnQcPHhIUdIPcuXNTtGhxc4cnIiIi6Ug9Zhbk/v371K5dlfHjxwFQrFhxduzYS/nyFc0bmIiIiLwQ6jEzs7Vr13D06B8MGTKcHDly8MMPU6hU6WXjfj0uSUREJOtQj5kZ/PvvvxgMBgACA0+yfftWHj58CECLFq0pWLCQOcMTERERM1Fi9oLt3LmdihVLcvjwIQA+/fQzdu7cr+dWioiIiBKz9BYTE8Py5UvZvXsnAFWrVqd794/x9vYGwMHBQcOVIiIiAigxSzePHj0CHs8RGzduND//vBiAHDly8M03w7QYrIiIiCSiyf/pYOLE7/jll+Xs3n0QGxsbfv11I3nz5jN3WCIiImLh1GNmAtHR0fzyy3Lu378PQMmSpXnlFT8iIyMByJfPW8OVIiIi8kxKzEzg6NEj9OjxAevX/wpAkyavM2LEWJycnMwcmYiIiGQkSszSIDY2lo8//ogffvgegOrVaxAQsIG2bTuYOTIRERHJyJSYpVB0dDSHDj1e4sLGxoZHj6ITTPCvVasO1taqThEREUk7Tf5PoeHDhzB//myOHz+Du7sHP/4419whiYiISCajxCyFunR5nzfeaIqbW05zhyIiIiKZlBKzFCpatDg1alTm9u275g5FREREMiklZil0f85McHTgfmQUOd7vZu5wREREJBNSYpZCD+bO4sH/vlZiJiIiIulBtxGKiIiIWAglZiIiIiIWQomZiIiIiIVQYiYiIiJiIZSYiYiIiFgIJWYiIiIiFkKJmYiIiIiFUGImIiIiYiGUmImIiIhYCK38n0IOzVuSPZsdDx4+MncoIiIikkkpMUsh54Ff4unprIeYi4iISLrRUKaIiIiIhVBiJiIiImIhlJiJiIiIWAjNMUuhu+NGEfO/yf/OA780dzgiIiKSCSkxS6GotQFE/e9rJWYiIiKSHjSUKSIiImIhlJiJiIiIWAglZiIiIiIWQomZiIiIiIUw6+T/oKAgZs2aRWBgIGfPniUyMpIFCxZQvXp1c4YlIiIiYhZm7TG7evUq69evx9HRkRo1apgzFBERERGzM2tiVrVqVfbv38/s2bNp06aNOUNJ1v7AoGS/FxERETEFsyZm1taWP8Vtf2AQ8zeeTbBt/sazSs5ERETE5Cw/MzKzVbsuER0Tl2BbdEwcq3ZdMlNEIiIiklllmpX/PTyc0qXc0IjH6/1vLd4g0XZPT+d0uWZWojo0PdWpaak+TU91alqqT9MzZ51mmsQsJOQecXEGk5fr7uJASEQUW30aJtp++/Zdk18vK/H0dFYdmpjq1LRUn6anOjUt1afppXedWltbJduZpKHMZ2jtWxR724TVZG9rTWvfomaKSERERDKrTNNjll5qlvECHs81C42Iwt3Fgda+RY3bRURERExFiVkK1CzjRc0yXuoyFhERkXRl9sRs06ZNAJw8eRKAw4cPc+fOHbJnz46vr685QxMRERF5ocyemPXp0yfB9/7+/gB4e3uzfft2c4QkIiIiYhZmT8zOnTtn7hBERERELILuyhQRERGxEErMRERERCyEEjMRERERC2H2OWamYm1tlamuk1WoPk1PdWpaqk/TU52alurT9NKzTp9VtpXBYDD9c4xEREREJNU0lCkiIiJiIZSYiYiIiFgIJWYiIiIiFkKJmYiIiIiFUGImIiIiYiGUmImIiIhYCCVmIiIiIhZCiZmIiIiIhVBiJiIiImIhMs0jmdLq/v37TJw4kU2bNhEREUGxYsXo1asXDRo0eOa5165dY8yYMRw8eJC4uDiqVKnCoEGDKFas2AuI3DKltT79/f2ZMmVKou25cuVi79696RWuxQsKCmLWrFkEBgZy9uxZIiMjWbBgAdWrV0/R+WqjiT1PnaqdJrZ//37WrFnDsWPHCAoKwtXVlfLly9O7d29KlCjxzPPVRhN6nvpU+0za0aNHmTp1KufPnycsLIwcOXLg4+ND165d8fX1feb5L7qNZvnE7OOPP+b06dMMGDCA/Pnzs3r1aj7++GNmzJiR7BsWEhLCW2+9hYeHB2PHjsXGxobp06fzzjvvEBAQgJeX1wt8FZYjrfUZb+7cuTg6Ohq/t7OzS89wLd7Vq1dZv349pUuXpkaNGmzfvj3F56qNJu156jSe2un/W7p0KWFhYXTp0oWiRYsSHBzMrFmzaNu2LQsXLqRixYpPPVdtNLHnqc94ap8JRUREULhwYVq3bk2uXLmIiIhg2bJldOvWjQkTJvD6668/9VyztFFDFrZz506Dj4+PYcuWLcZtcXFxho4dOxoaN26c7Lljx441lCtXzhAUFGTcFhoaaqhUqZLhm2++SbeYLdnz1OfkyZMNPj4+hvDw8PQOM0OJjY01fr1161aDj4+P4cCBAyk6V200ac9Tp2qniQUHByfaFh4ebqhSpYrh448/TvZctdHEnqc+1T5T7tGjR4Z69eoZOnXqlOxx5mijWXqO2datW3F2dk4wzGZlZUWrVq24fPkyFy9efOq527Zto1atWuTJk8e4LWfOnNSvX5+tW7ema9yW6nnqU5JmbZ32H1G10aQ9T51KYh4eHom2ubi4UKhQIYKCgpI9V200seepT0k5W1tbnJ2dn9mbaI42mqV/Q124cIFixYol+kUdP45//vz5JM97+PAh165dw8fHJ9G+EiVKEBISQkhIiOkDtnBprc8nNW3alFKlSlGnTh0GDx6cJevRFNRG05faafJCQ0O5cOECxYsXf+oxaqMpl5L6fJLaZ9Li4uKIiYnh1q1bTJ48mStXrtC5c+enHm+uNpql55iFhYXx0ksvJdru6upq3J+U8PBwDAaD8bgnubm5Gc9N6pNPZpbW+gQoUKAA/fr1o1SpUtjZ2XH06FFmzZrF/v37WbVqVZJ1LU+nNpo+1E6fzWAw8PXXXxMXF0fXrl2fepzaaMqktD5B7fNZ+vbty+bNmwFwcnLihx9+oF69ek893lxtNEsnZvB4qC0t+1KyPytKa322bNkywfc1a9akYsWKvP/++yxevJiePXuaKsQsRW3UtNROn23cuHFs27aN0aNHU7Ro0WcerzaavNTUp9pn8j777DM++OADgoODWbduHX379mXMmDE0a9Ys2fNedBvN0omZm5tbkr044eHhAE/9dOHq6oqVlVWS58Zvi8+ms5K01ufT1K5dG09PT44fP26C6LIWtdEXR+30/02cOJE5c+bw1Vdf0bp162SPVRt9ttTU59Ooff6/AgUKUKBAAQD8/Pzo3r07w4YNo2nTpknOPTVXG83Sc8yKFSvGpUuXiIuLS7A9fi5UUuPKANmyZaNAgQJJzpk6f/487u7uWbL7Pa31mRyDwaDJ2mmgNvpiqZ3CpEmTmDFjBp999hnvvvvuM49XG01eauszOWqfSStXrhzh4eGEhoYmud9cbTRLv1MNGzYkIiIi0TpGAQEBFC5cONnF41599VX27dvH7du3jdvCwsLYsWMHDRs2TLeYLdnz1GdSfv/9d4KDg6lQoYIpw8wy1EZfDLVTmDJlCtOmTaNPnz588MEHKT5PbTRpaa3PpKh9Js1gMHDo0CFcXFyS7fUyRxvN0kOZvr6+VK9ena+++oqwsDDy589PQEAAR44cYdq0acbjOnXqxKFDhzh37pxxW9euXfn111/p1q0bvXr1wtbWlunTp2Nra0v37t3N8XLM7nnqs2XLlrRs2ZLChQtja2vLsWPHmD17NoUKFeLtt982x8uxGJs2bQLg5MmTABw+fJg7d+6QPXt246K9aqOpk9Y6VTtNbM6cOfj7+1O/fn1q1aqVYMjM3t6e0qVLA2qjKfU89an2mbT+/fvj7e1NmTJlyJkzJ7dv32b16tUcOHCAr7/+Glvbx6mQpbTRLJ2YWVlZMW3aNCZMmMDEiRONjxCaMmUKfn5+yZ6bK1cuFi9ezNixYxk4cCAGg4GXX36ZRYsWkS9fvhf0CizL89RnkSJFWLJkCf/++y8xMTF4eXnRrl07evbsiYuLywt6BZapT58+Cb739/cHwNvbO9lV69VGny6tdap2mtiOHTuM/8d/HU9tNPWepz7VPpNWqVIl1q5dy7Jly7h79y7Ozs6ULVuW6dOnW+TfeiuDwWBIl5JFREREJFWy9BwzEREREUuixExERETEQigxExEREbEQSsxERERELIQSMxERERELocRMRERExEIoMRMRERGxEErMRERERCyEEjMRERERC6HETERERMRCKDETEQFiYmLo2LEjlSpV4tKlSwn2LVu2jBIlSjBp0iQzRSciWYWelSki8j/Xr1+nZcuW5MuXj+XLl+Pg4MCFCxdo27YtZcqUYeHChdjY2Jg7TBHJxNRjJiLyP97e3owcOZKzZ88yduxYHj58SL9+/XBwcOD7779XUiYi6c7W3AGIiFiS1157jTfffJPFixdz+vRpzp8/j7+/P/ny5TN3aCKSBWgoU0TkP6KiomjWrBnXrl2jffv2DB8+3NwhiUgWoaFMEZH/OHfuHDdv3gTgwoULxMTEmDkiEckqlJiJiDzh3r17fPrpp7i5ufHpp59y7Ngx/P39zR2WiGQRmmMmIvKEb775hhs3bjBnzhxq1qzJmTNnmDlzJjVr1qRGjRrmDk9EMjn1mImI/M+KFStYv3493bp1o2bNmgAMHz6cvHnz8tlnn3Hnzh0zRygimZ0m/4uIAJcuXaJNmzaULFmSRYsWYWv7/wMKx44d45133qFu3brMmDHDjFGKSGanxExERETEQmgoU0RERMRCKDETERERsRBKzEREREQshBIzEREREQuhxExERETEQigxExEREbEQSsxERERELIQSMxERERELocRMRERExEIoMRMRERGxEP8Hkbazcy5MSXgAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import r2_score\n", "\n", "x = np.array([0, 1, 2, 3]).reshape(-1, 1)\n", "y = np.array([1, 3.5, 4, 5])\n", "\n", "reg = LinearRegression()\n", "reg.fit(x, y) \n", "\n", "# get the slope\n", "slope = reg.coef_[0]\n", "\n", "# get the intercept\n", "intercept = reg.intercept_\n", "\n", "# same as y_pred = slope * x + intercept\n", "y_pred = reg.predict(x)\n", "\n", "show_fit(x, y, slope, intercept)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.8992805755395683\n" ] } ], "source": [ "# computing R2 from our formula (just to check that Prof Higger isnt pulling our leg)\n", "R2 = 1 - (get_mse(y_pred, y) / np.var(y))\n", "\n", "# computing R2 from sklearn (easy to work with, doesn't inspire our intuition with its use)\n", "R2_easy = r2_score(y_true=y, y_pred=y_pred)\n", "\n", "assert R2 == R2_easy, 'r2_score() doesnt agree with our formula'\n", "\n", "print(R2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our linear fit explains 89% of variance." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Guess that $R^2$: part 0" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try with data than can be fit perfectly.\n", "x = np.array([0, 1, 2]).reshape(-1, 1)\n", "y = np.array([1, 3, 5])\n", "\n", "reg = LinearRegression()\n", "reg.fit(x, y) \n", "slope = reg.coef_[0]\n", "intercept = reg.intercept_\n", "\n", "show_fit(x, y, slope, intercept)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# two lines below compute the same thing:\n", "y_pred = slope * x + intercept\n", "y_pred = reg.predict(x) \n", "\n", "# computing R2 from sklearn\n", "r2 = r2_score(y_true=y, y_pred=y_pred)\n", "r2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Guess that $R^2$: part 1" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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7hhs3biAxMRHp6ekA/jtrkd3hiOzK7HYJ+UEQBADaw5XGaFPffdm8eXOmc3aaNWuGffv25eh2J3379sWZM2fw+++/o3PnzkhKSsKAAQO0Jod/SHx8vPr+ae9SfRbDwsJ0npXs0aOH0S72UCqVAN7OKfT29sacOXPUy3x8fODs7IyePXti7969GDlypNbE93cdPHgQr1+/1hpSMwRfX1/MnTsXISEh6N+/P/bt24c3b95kK1Fq3LgxDh06hNOnT+PUqVMa9wM8evQojh8/jhkzZmT6PZXVNnIyTaNNmza5vo9cdhjiOwB4O61l4cKFaN68OdasWYOKFSsiJiYGO3bswIYNG3Ds2DFs27ZN47OSlpaGyZMnIzQ0FJ9//jl69+4NJycn3Lt3D8uWLcOKFStw5swZbNy4UX37peLFi6N///4IDAzElClTkJycjBYtWiA5ORm7du3C1q1bIZVKkZ6ervcYSRsTOxPXtWtXLFmyBCEhIRg/fjysra3x+PFjnDx5Es7Oznr5MstsWE/1F+j7QzFHjhzBlClTkJiYmGmb784LK+ju3LmjvuLtXaokQXU2Ljk5OdM2VMsyG6p9X3baVM2LebfND50Z1FUnKx9K2nJzD7t58+ahdevWSEpKgkwmw9dff53jNpKTk9VXZepy48YN3LhxQ6u8UaNGRkvs3v2df/LJJ1rLa9asierVq+Pq1asIDw/PMrH70BWp+mRjYwMfHx8cOHAAt27dwp49e2BpaZntG9ZKpVJ4e3urb4qbmpqKkydPYtGiRbh37x7mzJkDb29vncOY+pgqkR9yu79m5fz585g/fz6qVq2KVatWqZOw8uXLY9KkSXj9+jW2b9+O5cuXY9GiRep6gYGB2LdvH/r27YuJEyeqy6tXr47Vq1eje/fu+PPPP7Fnzx707NlTvXz06NGIjY3F7t27te7f2K5dOyQnJ6vvqUmGxcTOxBUvXhxdunTB9u3bsW/fPvTs2RM///wzlEolevbsmaunHbwvJ/Oenj59ivHjxyM1NRVDhw7Fxx9/jDJlyqBo0aKQSCRYsmQJ1q1bp/4LV1/8/f1zNRT77hdbZmJjY3UmEaokQXWbicTERLx69UrnF7fqSrLsPvVBtV50dLTO5a9evcLLly+12ixTpgyuX7+eaT1VeW5vjaHryQI5dfz4cXViHx0djZiYmBz3p2zZsjrnP4WHh6N///4F8kbX78aYWdJWtmxZXL16FbGxsZm2888//+Cvv/6CmZkZ5HK5vrupU9euXXHgwAEsWrQI165dQ8eOHWFra5urtooUKYI2bdqgZs2aaN++PV6/fo2TJ0/qTHb1JSwsDGFhYTmul93EUrUPPn36NNN1VPtedr8DVE/VaN++vc7v8Y8++gjbt2/HuXPndNbTlXhbWFigXbt2iIqKwrlz5zS+/6RSKebPn4++ffvi2LFjePbsGWxsbODl5QVPT0+0a9cOALJ9c3PKPSZ2hL59+2L79u3Yvn075HI5du7cCXNzc4N+UWbm+PHjSE1NRfv27TF27Fit5Q8ePDDIdg8dOpTjiycAZCuxa9y4cZaTqG1sbFC2bFk8evQI169f13n7B9XtBLI7fOTh4QEAuHbtms7lqvZcXV1RvHhxdXm1atUQFhb2wXqqq5Dz2/379zFz5kxYWFio51uOHz8eW7Zs0csfIQVZxYoVYW1tjdevX0OhUOhcR1We1cUTu3fvhiAIaNasWaZn0/XNy8sLzs7O6qsz9XGmsGTJkqhUqRKuXbumvjWKoURGRmZ5hjcz2U3sVPvr7du3kZaWpjV15dGjR+rHgWV3zrMqEbSxsdG5XFX+/siIKrnMrJ4qIVfN+Xxf9erVta6q/+eff/DgwQPY2tpmesU96Y+4vwkpW9zc3NCoUSOcP38eS5cuRWxsLFq3bm2UR+6ovix0HXDi4+Nx5swZnfVUQ3qquXg5pY8zSXnh4+ODTZs2Yf/+/VqJ3aVLl/D48WOUKFEiy4ni76pbty7s7e3x6NEjnY90Uk1Cf3+ovXXr1ggICMDRo0eRkpKicbWqIAg4ePCgznr5IS0tDePGjUNycjImTpyIgQMH4tmzZ7hw4QICAgJ0/iEgJpaWlvD29sbBgwdx9uxZjQuOgLfzUlW3zcjs4CkIgvqMTH4Mw6qYm5uje/fu2LFjB+zt7eHl5fXBOoIgZDkfKyMjQ/3HmKET1FGjRhn0DG6ZMmVQtWpV3LhxA2FhYer7Raqo9tcWLVpk+0bXzs7OAN5+f/Tr109r+eXLlwFon33/3//+h8ePH+Py5cs6Lz5R3dA4J2fJAwMDAbydfqKPG3VT1sR7bwDKkb59+wJ4+3QDQD8XTeRGpUqVAACHDx/WGE5KTk7GtGnTMp13p7oi8u7du4bvpAEMGDAAFhYW2Llzp8ZVaImJiZg5cyYAYNCgQRrPdASAxYsXo0OHDli8eLFGuVQqxeeffw4A+O677zR+b2fPnsXOnTthaWmJ/v37a9SrVq0amjVrBoVCgTlz5qgn7APAqlWrcPv2bchkMr1ekZxdixcvxrVr1+Dl5aX+XXz//fewt7dHYGCg1pBSYbVlyxZ06NBBY36Tip+fHyQSCTZu3Khx37q0tDT1++zh4YF69erpbDs8PByPHz+GjY2Nzhvhvs/Hxwfu7u7qW6PkxdixYxEeHo5Dhw5pfY51WbZsGebNm4c7d+5oLUtKSsK0adOgUChQrFixbF1VXdCpbjq9aNEijakQUVFR6sRI142pBwwYgA4dOmjdj1T1/u7fvx8HDhzQWBYVFYXly5cDgFYSqaq3fPly9cVqKqGhoer7iL5f78mTJ1pTADIyMrBu3Tr8/PPPKF26NEaMGJFZ+KRHPGNHAN6eqSlVqhSio6Ph6uqqvkllfmvVqpX6L9f27dujUaNGkEqluHDhAszMzNCtWzedBxkvLy9YW1vj8OHD6NOnD8qVKwczMzP4+PigdevWRogkZ8qWLYvvvvsO06ZNw6BBg9C4cWPY2toiPDwcCoUCXl5e6kTtXTExMbh3757OK4sHDx6M8PBwnDlzBu3atUOjRo2QmJiI8PBwCIKAOXPm6JyvM3fuXPTq1Qu//PILLly4AA8PD9y7dw+RkZGwsbExyv3iTpw4gY0bN8LJyQn+/v7qMzmlS5fG3LlzMWLECEyYMAF79+5V3yutIBgxYoT6vVENF4aHh2tMc5gxY4bGGbYXL17g3r176jMu76pevTq++eYbzJ8/H/3790ft2rVRokQJXL16FdHR0XB2dsbixYszPdOlGk709fXN1n3gVIm9MYa5k5OTsWnTJmzcuBEuLi6QyWQoVqwYYmNjcfXqVSQlJcHS0hILFizI9D3/5ptvstxGQbq4olOnTjh9+jT27NmDjh07wtPTE2/evMGZM2fw5s0bfPXVV6hdu7ZWvX/++QePHz9Wz5lVad26NeRyOUJCQjBmzBisXbsWFSpUQGxsLC5evIj09HTUrVtXK1kcMWIEzp49i6ioKMjlctSpU0d9VaxqSsmAAQO0zhifO3cO06ZNg4eHB8qUKQNBEHDx4kU8f/4cpUuXxvr16zWmfZDhMLEjAG+/uBs2bIjffvsNvXr1Mtol6RYWFtiyZQtWrlyJY8eO4dSpU3BwcICPjw9Gjx6t9dQBFWdnZ6xduxarVq1CZGQk/vrrLwiCgFKlShWKxA54O0zh6uqKwMBAXL58GampqShXrpz6Jr45PbhaWFggMDAQGzduREhICI4fP44iRYqgWbNm+PLLLzN9lFPp0qUREhKCVatW4ejRozhy5Ajs7e3RtWtXjBo1Su/PFP2QmJgY9QHa399f6x5abdq0wWeffYZt27Zh8uTJWLt2bYG5pUJkZKTW3E2FQqExRy6nV3gPHDgQMpkM69evV9+brFSpUujfvz++/PLLTB/B9erVKxw+fBhA9u5dFx8fj+joaJQoUQI+Pj456qM+DB8+HLVr18bp06cRGRmJK1euQKFQoEiRInB1dUXjxo3Rt29flCtXLtM2PjQvriAldgAwf/581K9fHzt27MCZM2cgkUhQu3ZtfP7557ma/uDv748WLVpg165duH79Om7dugVra2vUqFEDHTt2RJ8+fbSuTLe1tcXPP/+MTZs24fDhw4iMjERqaipsbW3RokUL9OrVS2dfqlevjo4dO+LSpUu4ffs2JBIJypUrh169emHgwIFM6vKRRND35YVUKL169QrNmzfHmzdvcOLEiQJ11oOI8l9oaCjGjh2LqVOnag3ZE1HBxTl2BADYsGEDXr16hY8//phJHRHh7NmzKFu2rNHm2xJR7vCMnQm7e/cugoODER0djdOnT8PKygq//fZbljc2JSIiooKLc+xMWExMDHbu3IkiRYqgRo0a+PrrrzNN6nJyg85KlSrBz89Pn10lIiKibOAZO8qWgIAArFy5MlvrNmrUCJs3bzZwj4iIiOh9TOyIiIiIRIIXTxARERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKRYGJHREREJBJM7IiIiIhEgokdERERkUgwsSMiIiISCSZ2RERERCIhNXYHCooXL15BqRQM1r6jY3HExSUZrP2CzpTjN+XYAdOOn7GbZuyAacdvyrEDho/fzEwCB4dimS5nYvcvpVIwaGKn2oYpM+X4TTl2wLTjZ+ymy5TjN+XYAePGz6FYIiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSBjt4om///4bq1atws2bN6FQKFCsWDHIZDIMHjwY3t7eH6z/8OFDLFiwAOHh4VAqlWjQoAEmTZoENze3fOg9ERERUcFjtMQuMTERFStWRLdu3eDk5ITExET89NNP8PPzw5IlS/DRRx9lWjcuLg6fffYZHB0d4e/vD3Nzc6xZswZ9+/ZFSEgISpUqlY+REBGZhjdv0vDypQLp6WlQKjOyXPf5czMolcp86lnBY8rxm3LsQO7jNzMzh1RqCRsbe1hYWOZ6+xJBEArMNcnp6elo3bo1ypcvj02bNmW63sKFC7FlyxYcOXIEJUuWBAC8ePECrVu3RqdOnTBz5swcbzsuLsmglyc7O9sgJualwdov6Ew5flOOHTDN+M9ei8buE3cQn5iKErZF0M27MppWL9x/cL5+/QovX75A8eJ2KFLEGmZm5pBIJJmuL5WaIT3ddA/uphy/KccO5C5+QRCgVGYgNfU1kpISYGPjAGtr3feqMzOTwNGxeKZtFag5dlKpFDY2NrCwsMhyvbCwMHh6eqqTOgBwcHBAq1atcOTIEUN3k4goU2evRWPjgRuIS0yFACAuMRUbD9zA2WvRxu5aniQlJcDe3glFi9rA3FyaZVJHRDkjkUhgbi5F0aI2sLd3wqtXCbluy+iJnVKpRHp6Op49e4YVK1bg/v37GDBgQKbrp6Sk4OHDh5DJZFrL3N3dERcXh7i4OEN2mYgoU7tP3EHae3+tp6UrsfvEHSP1SD8yMt7AwqKIsbtBJHoWFkWQnv4m1/WN/uSJMWPG4NChQwCA4sWLY9myZWjRokWm6yckJEAQBNjZ2Wkts7e3BwAoFAo4OjrmqB9ZndbUF2dnG4NvoyAz5fhNOXbAtOKPT0wFALS9+d/owRFZW8Qnphbq38Pz52awsDDPUR2p1OjnDozKlOM35diBvMdvZmaW6+8Loyd2EyZMwJAhQxAbG4t9+/ZhzJgxWLBgAT7++OMs6+l7GIBz7AzLlOM35dgB04u/hG0RxCWmou2t39VlR2RtUcK2SKH+PbwdXcn+vCHOszLd+E05dkA/8SuVyky/Lwr8HDtXV1fUqlULPj4+WLJkCby8vDBr1qxMryixs7ODRCKBQqHQWqYqU525IyLKb928K8Pyvb/WLaVm6OZd2Ug9IiJTYvTE7n01a9ZEQkIC4uPjdS63srKCq6srbt68qbXs5s2bKFGiRI6HYYmI9KVp9VIY0LGqRtmAjlUL/VWxlLUHD+4jOHgdnj59YuyukIkrUImdIAg4f/48bG1tszzr1qZNG5w5cwYxMTHqMoVCgWPHjqFt27b50FMiosy9n8QxqRO/Bw/uY8OGH5jYkdEZbY7d+PHj4eLigurVq8PBwQExMTHYs2cPzp07h+nTp0Mqfdu1fv364fz584iKilLXHTx4MH799Vf4+flhxIgRkEqlWLNmDaRSKYYOHWqskIiIiLIlLS0Nlpa5vwktUWaMdsaubt26CA8Px7fffouBAwdi1qxZEARB/QSJrDg5OWHr1q0oVaoUJk6ciLFjx8LGxgZbtmxBmTJl8ikCIiIq7A4fPggvrwa4evWK1rKAgCVo27YFXr1KyrKN0NDfMGXK1wCAr74aCi+vBmjSpB7+/vtPAECPHp0wefJ4HDlyEP36fYKWLZsgLOwQnj59Ai+vBggN/U2rTS+vBggOXqdRdv/+PUybNgkffdQarVo1xYABvXH48MHchk4iZbQzdn379v1gAgcAmzdv1lleoUIFrFmzRt/dIiKifKR6SkdcYiocjfCUDh+fNli1ahn27PkFNWrUVJenpqYgNHQf2rfviGLFsr4dVtOmXhg2bBTWrAnAuHGTIJNVhVQqgatrBfU6169fw/379zBw4BA4OjrByck5R/28ffsWhg0bjPLlK2DMmAmws7PHsWNhmDVrGtLSUvDxx/IctUfiZfTbnRARkWlSPaVDdUNn1VM6gPyblyiVSiGXd8fmzRswatQ49fzuI0cO4uXLRHTr1vODbTg4OMDVtTwAoEKFiqhRo6bWLS8SEhRYu3Y9Spf+b1QpJ/PxVq1aBnt7ewQErIO1tTUAoFGjJlAoFAgMXANf384wMytQ0+bJSPgpICIioygoT+no0qUbBEHA/v171WV79uxCnTr1UKmSm162UaWKTCOpy4nU1FT8/fefaNGiFSwsLJCenq7+17RpM8THx+HBg/t66ScVfjxjR0RERhH371M6sltuKCVKOMLHpw1CQnbj00/74fr1a4iKisTMmfP1tg1HR6dc101MTEBGRgZ++mkrfvppq851EhIUuW6fxIWJHRGRARTpJIe1lQVep+T+mY9i5/jvUzp0lee37t174dChAwgPP4OwsMNwdHSCt3crvbWv62lJqqti09LSNMrfT9JsbGxhZmYGX99OkMu762y/XLny+ukoFXpM7IiIDMBm4hSTe5xaTnXzrqwxxw4w3lM6PDxqwMOjBjZt2oCoqEj06TNAfdut7LCwsADwdtg0u0qUcISlZRHcuXNbo/zkyRMar62srFCnTj3cunUTbm6yHPWLTA8/HUREZBSqCySMeVXsu3r06IVZs6bD3NwcXbp0y1HdihUrQSKRYN++EBQrVgzW1lZwcXFF0aLFMq0jkUjQrl0H7N//K1xcXODmJkNk5DUcOaJ9C5OvvhqPESOGYNSoL9GlSzeULFkKSUkv8eDBfURGXsPcud/nOF4SJyZ2RERkNE2rlyowT+bw9vaBVDoTzZu3zPHtSEqVKo1Ro8bi55+3Y9SoL5GRkYEVK9aiXr0GWdYbNWosJBIJtm3bjNevk1GvXgMsXLgMPXp00ljPza0KgoO3YMOGH7BmTQASEhSwtbVD+fIV4OPDJy7RfySCIAjG7kRBEBeXBKXScL8KUx+SMeX4TTl2wLTjF1Ps0dEPUKpU9udxvX+7j8LgxImjmDp1IgIC1qFu3fp5aqswxq8vphw7oJ/4s9rfzMwkcHTM/N6KPGNHRGQALxfOQ/q/F0/YTJxi7O5QFh4+vI/o6GisWrUc1avXzHNSR2RMTOyIiAwg9bcQqKbRM7Er2BYunIerVy/D3b0apk2bqbFMEARkZGRkWd/c3FznVa9ExsDEjoiITNrKlYGZLjtwYB/mzZuZ6XIA2ZpLR5RfmNgRERFlolmz5ggK2pTlOryHHBUkTOyIiIgyYWdnDzs7e2N3gyjb+KxYIiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHbnRARGYD150NQrGgRvEpO/fDKRER6wjN2REQGUGyQH5xHjUSxQX7G7gqZiL///hNeXg3w999/Zmv9oKC1GDy4n4F7VbA9ffoEXl4NEBr6m8G2kZSUhA4dWuHkyeMG28a7mNgRERGZmGfPorF9+2YMGTLU2F0xKkdHJ6xduwFNm3oZbBvFixdH7959sGrVcqSnpxtsOypM7IiIiIwsLS0tX7f3yy874OjohKZNm2W5Xnp6OjIyMvKlT0qlMl8Sn3dZWlqiRo2acHBwMOh2unTphqdPn+D48d8Nuh2Ac+yIiMhEHT58ELNmTcPatRtQo0ZNjWUBAUvw668hCAkJRbFixT/YVmjob5g3byaWLl2F/ft/xdmzpyEIApo2bYYxY76Gg0MJ9bo9enRClSoy+Pi0xaZN6/HPPw8xceJU+Pp2wvPnzxAUtBbh4WeQkJCAUqXKoFu3Hvjkk880tnf//j2sWLEYly5FwMrKCs2bt4SXV4tsxf3mzRuEhv6Gbt16apQ/ffoEPXt2xvDho5Gc/Aqhob8hJuY5fv55L0qXLoOrVy9jw4YgXLt2GWlpb+DmVgVDhgxFo0ZNNNr544/jWLduNR4+fAAnJ2d07doTr18nY8OGH3Dq1H/DxF5eDdCz56coXboMdu36CdHRT7F06SrUq9cA9+/fQ1DQWkRE/Ink5GSUK1ceffoMRLt2HdT1U1JS8MMPa/DHH8cQFxcLKytrlC3rigEDBqNZs+YAgKioGwgKWoPIyOt49SoJ9vYOqFq1GiZPngFbW1t1zFOmzICvbyd128eOhWHLlo24d+8uLCykqF27Lvz8RsDNrYp6nblzv8PJk8cRGPgjli1bjCtXLsLGxhatW7fFF18Mh6WlpXpdB4cSaNiwMfbu3Y02bdpn633KLZ6xIyIygIRJ4/DP0GFImDTO2F0xOLncFzt2bAXwNmmQy33x8887AADJycmQy30RErILAJCYmAC53Bf79v0KAIiLi4Nc7otDhw4AAJ49ewa53BdHjx4BADx+/AhyuS9OnDgG4G1CI5f74syZUwCA27dvQS73zVW/fXzawNHRCXv2/KJRnpqagtDQfWjfvmO2krp3zZ8/C8WL22Du3AXw8xuGs2dPY+zYkVpnoq5fv4b16wPRt+9ALFq0Ah4eNRAbG4MvvhiAy5cvwc9vBL7/fjlatGiJVauW44cf1qjrxsXFYuRIP9y/fw/jx3+DadNmISUlBUuWLMxWH69fv4rExATUqVNP5/Kff96GyMjrGDduIubPXwQbG1ucP38OI0f6QanMwOTJ32LuXH84OjphwoTROH/+nLruuXNn8M03X8Pe3gEzZ87H8OFf4fjx33HgwD6d2zp2LAxHjhzA0KEj4e+/FC4uZXH79i188cUAREc/xZgxE+DvvxQeHjUwa9Y07NsXoq67YsViHDoUij59BmDx4gBMmfItPD29kJiYAODtZ2/s2BF48+YNJk6ciiVLVmL48K9gY2Ob5RnS0NDfMH36N3B2dsasWfMxfvxkPHr0D4YNG4z79+9prJuW9gbffDMejRo1xvz5i+Hr2wk7dmzF1q0btdqtW7c+Ll++iOTkV5luWx94xo6IyADenDmFN8buBGVJKpVCLu+OzZs3YNSocbC3twcAHDlyEC9fJmqd0cqOmjVr4+uvv4FUaoYGDZrAwaEEZsyYgmPHwtC27X9nmxISFFi7dj1Kly6jLvP3n4vU1BQEB2+Bk5MTAKBhw8ZIT3+D7ds3o1evz2Bra4efftqGhAQFNm7cjkqV3AAATZs2w+jRw/H8+bMP9vHq1csAAJnMXefyokWLYuHCpTA3N1eXLVmyEDJZVSxeHAAzs7fnhJo0aYbBg/shMHC1+qxdUNBalCxZCosXB0AqfZtiNG7siZ49O2lvCG+HoJctW62RQC9YMBv29vYICFgHa2trAECjRk2gUCgQGLgGvr6dYWZmhitXLqFduw6Qy7ur63p5eat/fvjwPhITEzBixBhUqSJTl7/7PrxPqVRi3bqVqFrVA/PnL4ZEIgEA1KvXAL16dcGGDT9g5sx57/Q/FV9+ORLe3q0AAA0aNMLNmzdw+PABfP75Fxpty2RVkZGRgWvXrqJhw8aZ9iGveMaOiIjyJCQkFL179wEAWFhYICQkFJ980hvA2yQhJCRUffC1tbVDSEgoPv64MwDA0dERISGhaN++IwCgZMmSCAkJhY9PWwCAi0tZhISEqg+cFSpUREhIKDw93052d3OrgpCQ0Fz3vUuXbhAEAfv371WX7dmzC3Xq1FMnTTnRpk07jdfe3j4wNzfHxYt/a5RXqSLTSOoA4Ny506hfvyHs7e2Rnp6u/te0aTOkpaXh2rUrAICIiL/g5lZFq3/vDlNmJTY2Fubm5rCxsdW53MurhUZS9+jRP3j06CHatu2gngenmnvXpIknoqIikZycjNevXyMqKhLe3q3USR3w9jPQrJnuYeL69RtqJHWpqan4++8/0aJFK1hYWGj9HuLj4/DgwX0AgIdHDYSG/oYNG37AtWtX8eaN5p9SZcuWg42NLfz95+DAgX148uTxB383Dx7cR1xcHNq166BO6gDAyckJDRs2RkTEXxrrm5ubqz+LKm5uVfDsWbRW26rh+NjYmA/2Iy94xo6IiExWiRKO8PFpg5CQ3fj00364fv0aoqIiMXPm/Fy256TxWiqVws7OHgkJCRrljo6a6wFAfHwcTpw4hpYtm2gtAwCFQgHg7XB22bLltJbralOX1NQUWFhYaCQuWbUTHx8HAFi+fBGWL1+ks05iYiLMzCQQBAElSjhqLX93jmFW20pMTEBGRgZ++mkrfvppq846CQkKAMCYMRPg5OSMw4cPIDh4Hayti6J5c28MGzYKzs7/Q/HixbFyZSB+/DEIy5cvRlLSS5Qu7YJu3Xqid+8+OuNPTEwEAJ0xODo6qbetYm1tDQsLC40yCwsLnUO9qjl3qakpOuPSFyZ2RERk0rp374VDhw4gPPwMwsIOw9HRSX2GMKfi42M1XqenpyMhQQE7OzuNcl1Jhb29PWSyqhg8+EudbavO8Nna2mltB3g79y477OzskZKSgrS0NI0J/pn1TTVEPXDgkEwv0HB0dER6ejokEok6EXzXixfxOuu9vy0bG1uYmZnB17eTxhDru8qVKw/gbVL1xRfD8MUXw/DiRTxOn/4Dq1cH4NmzaKxa9QMAoHJlN8yevQCCIOD27VvYu3cXVq1aBhsbG3z8cRettlXvk64Y4uJiYWdnr7NP2aFKGvPSRnYwsSMiIpPm4VEDHh41sGnTBkRFRaJPnwEaQ4k5ERZ2GM2bt1S/PnHiKDIyMjK9UOFdjRt74s8/z8PVtVyWF23Uq9cA27Ztwt27d1CpUmV1+eHDB7PVxwoVKgJ4e2FKxYqVPri+q2t5lCnjgjt3bmV53zsLCwtUrVoNJ04cw9Cho9S/w+TkZJw+/Ue2+mZlZYU6derh1q2bcHOTZft9cHAogY8/luPy5Us4ceKo1nKJRIIqVWQYO3YifvstBLdv39LZTrly5f89C3gQPXt+qk484+Pj8Oef5zXm8OWUaii4YsXKH1gzb5jYERGRyevRoxdmzZoOc3NzdOnSLdftXLlyCYsX+6Nly5a4d+8eAgPXwM1Nhlat2nyw7hdfDMOFC+EYNmwwevTojbJlXfH69Ws8fvwPTp8+iSVLVsLc3ByffPIp9u//FV9//RW++GIY7O0dcOhQKP7550G2+li3bn0AwLVrV7KV2EkkEnz99WRMnDgGEyeOQfv2vuphydu3byEuLhYTJ04FAAwePBQTJ47B+PGj0KNHL2RkZGDbts2wti6qPmP1IV99NR4jRgzBqFFfokuXbihZshSSkl7iwYP7iIy8hrlzvwcA+PkNhKenFypXdkPx4ja4ffsWjh8/iqZNPQEAp0+fREjITjRv3hKlS5eBUqnE4cMHoFQq0bhxU53bNjMzw9ChIzFnzgxMnjwenTp1xevXyfjxxyCYmZlj0KAvdNbLjuvXr6BECUd1Ym0oTOyIiMjkeXv7QCqdiebNW8LJyTnX7UyZMgP79u3FlCmToFQq4enZDKNHf52tM0/Ozv9DUNAmbNgQhI0bgxEXF4vixYujbNlyaNLEU301qqOjE1auDMTy5Yvw/ffzYWVlhRYtWmLcuIn45pvxH9zO//5XEnXq1MOpUyd0Dkfq0qhRE6xduwGbNq3H0qULkZT09p5wbm5V0LHjx+r1mjTxxPz53yMwcA2+/XYySpRwRNeuPRAbG4uDB/dna1tublUQHLwFGzb8gDVrApCQoICtrR3Kl6+gvqgGeJugnjx5Ajt2bEVaWhr+97//oWvXHhg4cAgAwNXVFUWLFsOWLT8iNjYWlpaWqFixImbPXpDljZk7dPgI1tbW2Lz5R0yfPglSqQXq1KmLmTPno1y5CtmK4X2CIODUqT+yvCJXXySCIAgG30ohEBeXBKXScL8KZ2cbxMS8NFj7BZ0px2/KsQOmG39s80bqn51OnjdiT/QjOvoBSpUqn+31pVIzpKcrDdgj/Tpx4iimTp2IgIB16jNaOaG6QfGGDVtRpYp7gY//2LEwzJw5DXv2hGZ6YUNuvR97eno6Bg78DE5OTli2bLVet1UQ6Xrv//77T4wdOwJbtvwCV1ftC1/el9X+ZmYmgaNj5kP1vN0JERGZrIcP7+P8+XNYtWo5qlevmaukrjBq2bI1qlRxx9atm/TabkZGBubNm41jx8IQEfEXfv/9MMaOHYEHD+6hT5/+et1WYbJxYzA++qhztpK6vOJQLBERmayFC+fh6tXLcHevhmnTZmotFwThg89Kffeeb4WFRCLBpEnTEB5+Ru/tvnyZiBUrlkCheAGpVAqZrCq+/345GjbUfRsXsUtKSkLt2nXRtWuPfNkeh2L/xaFYwzLl+E05dsB040/5dQ+KF7dCUlIKrDp3NXZ38kzsQ7GZUQ2xZmXFirWoV6+BRplY4s8NU44d0E/8eRmK5Rk7IiIDsOrcFQ7ONkg3waRWTJo1a46goKyHK1X3VSMqCJjYERERZcLOzt7gN5Ql0idePEFEREQkEkzsiIiIiESCQ7FERAbwYnB/JEnN8CZdCYdg/d5SgogoM0zsiIgMIOPmDWR9kwwiIv3jUCwRERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERHlQlpaWq6W5bVtoqwwsSMiIpN3//49TJs2CR991BqtWjXFgAG9cfjwQfXy0NDf4OXVABcunMOsWdPRsaMP+vR5+1D3kSP9MHDgZ7hwIRxDhvSHj48nNm5cDwB4/PgRvv12Mnx937bbr98n2Lt3t8a2//77T3h5NcDhwwewZIk/OnVqBx8fz/wLnkTFaLc7OXv2LPbu3YuIiAhER0fDzs4OtWrVwqhRo+Du7p5l3YCAAKxcuVKr3MnJCadPnzZUl4mISIdX6wPxekNQttYt0kkOm4lTNMpeLpyH1N9CslXf+vMhKDbIT6MsYdI4SN2rapVn1+3btzBs2GCUL18BY8ZMgJ2dPY4dC8OsWdOQlpaCjz+Wq9edN28WvL19MGvWPKSmpqrLY2KeYcGC2ejffxBcXcvBxqY44uJiMXz4YEgkZhg+/Cs4Ojrh6NEj+P77eXjxIh4DBw7R6Mfq1StQv34DTJkyA8nJybmKhchoid327duhUCgwcOBAVK5cGbGxsQgKCkKPHj2wefNm1KlT54NtbNiwAUWLFlW/trCwMGCPiYhIjFatWgZ7e3sEBKyDtbU1AKBRoyZQKBQIDFwDX9/O6nWbNPHEmDFfa7WRkJCA+fMXo1atOgAAqdQMK1YsQ3x8PDZs2AY3tyoAgKZNmyEpKQmbN29A9+69YGNjo26jQoWKmD59tgEjJVNgtMRuxowZcHR01Cjz8vJC69atERwcjICAgA+2UaNGDdja2hqqi0REJHKpqan4++8/0aNHb1hYWCA9PV29rGnTZjh58jgePLivLmvRoqXOduztHdRJnUpExJ+oXLmKOqlT6dDhI5w8eRzXrl1Bkyb/Dbm2aNEqT7EQAUZM7N5P6gDA1tYW5cuXR3R0tBF6RESkPzYLFsPO1hoJia+N3RWDKzbIT2sYVCo1Q3q6Mlv1bSZO0RqezQk7/yW5rpuYmICMjAz89NNW/PTTVp3rJCQo1D87OjrpXEdXeWJiIlxcXDNdNzEx4YNtEOVUgXqkWHx8PG7duoWPPvooW+v7+voiLi4Ojo6OaNmyJcaOHaszYSQiym9FmjWHjbMNUmJeGrsrlAUbG1uYmZnB17cT5PLuOtcpV648njx5DACQSCQ619FVbmtrh/j4OK3yuLhY9fIPtUGUUwUmsRMEAdOnT4dSqcTgwYOzXNfV1RXjxo1DtWrVYGFhgb///htBQUE4e/Ysdu/eDTs7uyzrExERAYCVlRXq1KmHW7duws1NBqlUf4fF+vUbYuvWjbh9+5bGcOzhw6EoUqQIqlevqbdtEakUmMRu4cKFCAsLw/z581G5cuUs15XL5RqvmzZtijp16mDQoEHYunUrhg8fnuPtOzoWz3GdnHJ2tvnwSiJmyvGbcuyAaccvltifPzeDVJqzO2TldH1jGTv2awwdOgRffTUUXbt2Q8mSpZGU9BL379/H9etXsWDBIpiZvT2bZm6u/XuQSCSQSLTj/eyzvjh4cB8mTBgNP7+hcHJyxu+/H8GJE8cwbNhIODjYqdt8+7+k0PzOPkQsceRWXuM3MzPL9XdHgUjsli5divXr12Pq1Kno1q1brtpo1qwZnJ2dcfHixVzVj4tLglIp5Kpudjg72yDGhIdkTDl+U44dMO34xRS7UqnM9pw5IGdz7IytYkU3BAdvxoYNP2DlyhVISFDA1tYO5ctXgI9PW6SnK9XHh4wM7d+DIAgQBGiUS6VmsLW1x5o167F2bQACApbj9etkuLqWw6RJ09Cpk1y9fkaG6n+h0PzOslKY3ntD0Ef8SqUy0+8OMzNJliejJIIgGC6byYbly5dj9erVmDBhAoYMGfLhCllo1qwZatasibVr1+a4LhM7wzLl+E05dsB044+X+8LMTAKlUkCJkFBjdyfPoqMfoFSp8tlenwd3043flGMH9BN/VvvbhxI7o56xW7lyJVavXo3Ro0fnOak7deoUYmNjUbt2bT31jogo95RxsTDdQxsRGYvRErv169cjICAArVq1gqenp8YQqqWlJTw8PAAA/fr1w/nz5xEVFaVeLpfLIZfLUbFiRUilUkRERCA4OBjly5dHnz598jsUIiIiogLBaIndsWPH1P+rflZxcXHB0aNHM61bqVIlbNu2Dc+fP0d6ejpKlSqFnj17Yvjw4bxhMREREZksoyV2mzdvzvV6S5bk/maURERERGJl2tcjExEREYkIEzsiIsoWI99Egcgk5HU/Y2JHREQfZG5ugTdvUo3dDSLRe/MmFVKpRa7rM7EjIqIPKl7cDgpFLF69eomMjHSevSPSI0EQkJGRjlevXkKhiEWxYrl/NGqBePIEEREVbNbWxSCVWiApSYFXrxKgVGZkub6ZmRmUStO9k58px2/KsQO5j9/MzBwWFpZwcPgfLCwsc719JnZERJQtqoNOdpjqE0dUTDl+U44dMH78TOyIiAzAPmgj7O2LQaF4ZeyuEJEJYWJHRGQAUvdqsHa2QZIJn7kgovzHiyeIiIiIRIKJHREREZFIMLEjIiIiEgnOsSMiMoDY5o0Q++/PTifPG7UvRGQ6eMaOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQfKUZEZAAOe/bDsURxxMUnGbsrRGRCmNgRERmAuZMzLJxtYG5mbeyuEJEJ4VAsERERkUgwsSMiIiISCQ7FEhEZQEZsDN4oXyMjPgnmTs7G7g4RmQgmdkREBvCi60d48e/PTifPG7UvRGQ6OBRLREREJBJM7IiIiIhEgokdERERkUgwsSMiIiISCSZ2RERERCLBxI6IiIhIJJjYEREREYkEEzsiIiIikWBiR0RERCQSTOyIiIiIRIKPFCMiMgCnk+fh7GyDmJiXxu4KEZkQnrEjIiIiEgkmdkREREQiwcSOiIiISCQ4x46IyADSoyLx+lkxpCteQepezdjdISITwcSOiMgAFEMGQPHvz04nzxuzK0RkQjgUS0RERCQSTOyIiIiIRIKJHREREZFIMLEjIiIiEgkmdkREREQiYbSrYs+ePYu9e/ciIiIC0dHRsLOzQ61atTBq1Ci4u7t/sP7Dhw+xYMEChIeHQ6lUokGDBpg0aRLc3NzyofdEREREBY/Rztht374dT548wcCBA/HDDz/gm2++wZMnT9CjRw9cvHgxy7pxcXH47LPP8PjxY/j7+2PJkiVISEhA3759ER0dnT8BEBERERUwOTpj1759e3Tv3h1du3aFs7NznjY8Y8YMODo6apR5eXmhdevWCA4ORkBAQKZ1g4ODkZiYiF27dqFkyZIAgDp16qB169ZYs2YNZs6cmae+ERERERVGOTpjJ5VKsWTJErRq1QrDhw/HsWPHoFQqc7Xh95M6ALC1tUX58uU/eNYtLCwMnp6e6qQOABwcHNCqVSscOXIkV/0hIiIiKuxylNjt378fO3bsgFwuR3h4OIYPHw5vb28sXboUDx8+zHNn4uPjcevWLVSpUiXTdVJSUvDw4UPIZDKtZe7u7oiLi0NcXFye+0JElBdmjk6QOjvDzNHJ2F0hIhOS44sn6tSpgzp16mDq1KkIDQ3Fzp07sW7dOgQGBqJhw4bo2bMn2rdvD0tLyxy1KwgCpk+fDqVSicGDB2e6XkJCAgRBgJ2dndYye3t7AIBCodB5RjArjo7Fc7R+bjg72xh8GwWZKcdvyrEDphm/8+mTxu6C0Zni+/4uU47flGMHjBt/rq+Ktba2Rvfu3dG9e3fcu3cPK1euxP79+3HhwgXMmTMHXbp0wcCBA1GmTJlstbdw4UKEhYVh/vz5qFy58gfXl0gkue26TnFxSVAqBb22+S5nZxvExLw0WPsFnSnHb8qxA6YdP2M3zdgB047flGMHDB+/mZkky5NReboqNiMjA0eOHMGCBQtw4MABSCQSNG7cGLVr18aWLVvg6+uLsLCwD7azdOlSrF+/HlOnTkW3bt2yXNfOzg4SiQQKhUJrmapMdeaOiIiIyJTk6ozdnTt3sHPnTvz666+Ii4uDo6MjBg0ahE8++QTlypUDADx48ABjxozB999/jzZt2mTa1vLly7F27VpMmDAB/fv3/+C2rays4Orqips3b2otu3nzJkqUKJHjYVgiIiIiMchRYrdz507s3LkTly5dAgB4enrik08+QevWrSGVajZVvnx59OvXD9OmTcu0vZUrV2L16tUYPXo0hgwZku1+tGnTBlu3bkVMTIz6tisKhQLHjh3DRx99lJOQiIgMIvX0Sby0tUZq4msUadbc2N0hIhORo8Ru2rRpcHJygp+fH3r27ImyZctmub6bmxu6dOmic9n69esREBCAVq1awdPTU+OmxJaWlvDw8AAA9OvXD+fPn0dUVJR6+eDBg/Hrr7/Cz88PI0aMgFQqxZo1ayCVSjF06NCchEREZBAvvxkP1SybIifPG7UvRGQ6cpTYBQQEwMfHB+bm5tlav1atWqhVq5bOZceOHVP/r/pZxcXFBUePHs20XScnJ2zduhX+/v6YOHEiBEFA/fr1sWXLlmxfrEFEREQkNjlK7Nq2bau3DW/evDlP61WoUAFr1qzRW3+IiIiICjujPSuWiIiIiPSLiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKRyNWzYomIKGvmsqqwkJrhTbrS2F0hIhPCxI6IyAAcgjfB2dkGMTEvP7wyEZGecCiWiIiISCSY2BERERGJBBM7IiIiIpHgHDsiIgNI+XUPXhS3QkpSCqw6dzV2d4jIRDCxIyIygKTv5yPp35+Z2BFRfuFQLBEREZFIMLEjIiIiEgkmdkREREQiwcSOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSPDJE0REBmDh6YUillKkpqUbuytEZEKY2BERGYCd/xI4O9sgJualsbtCRCaEQ7FEREREIsHEjoiIiEgkmNgRERERiQTn2BERGcCr9YFA0SJ4lZyKYoP8jN0dIjIRTOyIiAzg9YYgvP73ZyZ2RJRfOBRLREREJBJM7IiIiIhEgokdERERkUgwscsnLVu2xI4dWwEAb968gVzui19+2QEASE5Ohlzui5CQXQCAxMQEyOW+2LfvVwBAXFwc5HJfHDp0AADw7NkzyOW+OHr0CADg8eNHkMt9ceLEMQDA/fv3IJf74syZUwCA27dvQS73xfnz4QCAyMjrkMt9ERHxFwDgypXLkMt9ceXKZQBARMRfkMt9ERl5HQBw/nw45HJf3L59CwBw5swpyOW+uH//HgDgxIljkMt98fjxIwDA0aNHIJf74tmzZwCAQ4cOoGXLloiLiwMA7Nv3K+RyXyQmJgAAQkJ2QS73RXJyMgDgl192QC73xZs3bwAAO3ZshVzuq/5dbt78I7p376x+vX79D+jdu5v6dWDgavTr10v9etWqFfj8877q1ytWLIGf30D168WL/TFs2BD16wUL5uCrr4apX8+Z8x3Gj/9K/XrGjKmYNGmc+vW0aZMwbdok9etJk8Zhxoyp6td+fn6YM+c79euvvhqGBQvmqF8PGzYEixf7v7P+QKxYsUT9+vPP+2LVqhXq1/369UJg4Gr16969u2H9+h/Ur7t374zNm39Uv5bLfY362WvZsqVRP3tyua/RPnvvy+/P3vjxX5n0Z8+Y33u//fabUT97xv7eM+XPnrExscsHr9YH4qOXSah0/pyxu0JE+cT68yG4WbcuDjuUMHZXiCifvFofiJiAlW+vijcSiSAIgtG2XoDExSVBqTTMryK2eSP1z04nzxtkGwWdKT9ayZRjB0w7fsZumrEDph2/KceeH8d7MzMJHB2LZ77cIFslIiIionzH+9jlA6eT5036LxgiIiJTUBCO9zxjR0RERCQSTOyIiIiIRIKJHREREZFIcI5dPkiPisTrZ8WQrngFqXs1Y3eHiIiIDKAgHO+Z2OUDxZABUPz7s6ne7oSIiEjsCsLxnkOxRERERCLBxI6IiIhIJJjYEREREYkEEzsiIiIikWBiR0RERCQSTOyIiIiIRMKotzuJjo5GUFAQrl27hhs3biA5ORmbNm1C48aNP1g3ICAAK1eu1Cp3cnLC6dOnDdFdIiIiogLNqIndgwcPsH//fnh4eKBJkyY4evRojtvYsGEDihYtqn5tYWGhzy4SERERFRpGTewaNmyIs2fPAgDCwsJyldjVqFEDtra2+u4aERERUaFj1MTOzMw0pviZOTrBzEwCpVIwdleIiIjIQArC8b7QP1LM19cXcXFxcHR0RMuWLTF27Fg4Ojoau1saSoSEwtnZBjExL43dFSIiIjKQgnC8L7SJnaurK8aNG4dq1arBwsICf//9N4KCgnD27Fns3r0bdnZ2OWrP0bG4gXr6H2dnG4NvoyAz5fhNOXbAtONn7KbLlOM35dgB48ZfaBM7uVyu8bpp06aoU6cOBg0ahK1bt2L48OE5ai8uLsmgp06NncEbmynHb8qxA6YdP2M3zdgB047flGMHDB+/mZkky5NRoprk1qxZMzg7O+PixYvG7goRERFRviu0Z+wyIwhCgbsoI/X0Sby0tUZq4msUadbc2N0hIiIiAygIx3tRJXanTp1CbGwsateubeyuaHj5zXioTsoWOXneqH0hIiIiwygIx3ujJ3YHDx4EAFy5cgUAcOHCBbx48QLW1tbw9vYGAPTr1w/nz59HVFSUup5cLodcLkfFihUhlUoRERGB4OBglC9fHn369Mn/QIiIiIiMzOiJ3ejRozVeBwQEAABcXFyyvGFxpUqVsG3bNjx//hzp6ekoVaoUevbsieHDh/OGxURERGSSjJ7YvXsWLjObN2/WKluyZIkhukNERERUaBWsqwyIiIiIKNeY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSBj9diemwFxWFRZSM7xJVxq7K0RERGQgBeF4z8QuHzgEb4Kzsw1iYl5+eGUiIiIqlArC8Z5DsUREREQiwcSOiIiISCSY2BERERGJBOfY5YOUX/fgRXErpCSlwKpzV2N3h4iIiAygIBzvmdjlg6Tv5yPp35+Z2BEREYlTQTjecyiWiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgk+OSJfGDh6YUillKkpqUbuytERERkIAXheM/ELh/Y+S+Bs7MNYmJeGrsrREREZCAF4XjPoVgiIiIikWBiR0RERCQSTOyIiIiIRIJz7PLBq/WBQNEieJWcimKD/IzdHSIiIjKAgnC8Z2KXD15vCMLrf39mYkdERCROBeF4z6FYIiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKR4JMn8kGRTnJYW1ngdcobY3eFiIiIDKQgHO+Z2OUDm4lT4Oxsg5iYl8buChERERlIQTjecyiWiIiISCSY2BERERGJBBM7IiIiIpHgHLt88HLhPKT/O5nSZuIUY3eHiIiIDKAgHO+Z2OWD1N9CkPrvz0zsiIiIxKkgHO85FEtEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJoyZ20dHRmDNnDj799FPUrVsX7u7uCA8Pz3b9hw8fYvjw4ahfvz7q1q2LL774Ardv3zZgj4mIiIgKLqMmdg8ePMD+/ftRtGhRNGnSJEd14+Li8Nlnn+Hx48fw9/fHkiVLkJCQgL59+yI6OtpAPSYiIiIquIya2DVs2BBnz55FcHAwunfvnqO6wcHBSExMRGBgINq0aYNWrVph3bp1SEtLw5o1awzU45w7ey06y9dERERU+BWU471REzszs9xvPiwsDJ6enihZsqS6zMHBAa1atcKRI0f00b08O3stGhsP3NAo23jgBpM7IiIiESlIx/tCefFESkoKHj58CJlMprXM3d0dcXFxiIuLM0LPNO0+cQdp6UqNsrR0JXafuGOkHhEREZG+FaTjfaF88kRCQgIEQYCdnZ3WMnt7ewCAQqGAo6Njttt0dCyur+6pxSe+vf/0kSqttcqdnW30vr2CzhRjVjHl2AHTjp+xmy5Tjt/UYi9Ix/tCmdipSCQSvbUVF5cEpVLQW3sAUMK2COISU3FE1larPCbmpV63VdA5O9uYXMwqphw7YNrxM3bTjB0w7fhNMfb8PN6bmUmyPBlVKIdi7ezsIJFIoFAotJapylRn7oypm3dlWEo1f8WWUjN0865spB4RERGRvhWk432hPGNnZWUFV1dX3Lx5U2vZzZs3UaJEiRwNwxpK0+qlALwde49PTEUJ2yLo5l1ZXU5ERESFX0E63hfKxA4A2rRpg61btyImJgbOzs4A3p6tO3bsGD766CMj9+4/TauXQtPqpUzy1DQREZGpKCjHe6MndgcPHgQAXLlyBQBw4cIFvHjxAtbW1vD29gYA9OvXD+fPn0dUVJS63uDBg/Hrr7/Cz88PI0aMgFQqxZo1ayCVSjF06ND8D4SIiIjIyIye2I0ePVrjdUBAAADAxcUFR48ezbSek5MTtm7dCn9/f0ycOBGCIKB+/frYsmULypQpY9A+ExERERVERk/s3j0Ll5nNmzfrLK9QoUKBesoEERERkTEVyqtiiYiIiEgbEzsiIiIikWBiR0RERCQSRp9jV1CYmenvKRbG3EZBZsrxm3LsgGnHz9hNlynHb8qxA4aN/0NtSwRB0O9ztIiIiIjIKDgUS0RERCQSTOyIiIiIRIKJHREREZFIMLEjIiIiEgkmdkREREQiwcSOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEnykWDa9evUKS5cuxcGDB5GYmAg3NzeMGDECrVu3/mDdhw8fYsGCBQgPD4dSqUSDBg0wadIkuLm5aa27adMmbN26FY8fP0apUqXQq1cvDB48GGZmxsvBcxv7L7/8gt9//x1RUVGIi4tDqVKl0KJFCwwfPhwlSpTQWNfd3V1nG9999x0+/fRTvcWSG7mNPyAgACtXrtQqd3JywunTp7XKxfTe+/j44PHjxzqXVaxYEQcPHlS/LqjvfXR0NIKCgnDt2jXcuHEDycnJ2LRpExo3bpyt+oV9v89L/IV9389L7GLY7/MSf2He98+ePYu9e/ciIiIC0dHRsLOzQ61atTBq1KhM+/qugrLPM7HLppEjR+L69ev4+uuvUbZsWezZswcjR47E2rVr4e3tnWm9uLg4fPbZZ3B0dIS/vz/Mzc2xZs0a9O3bFyEhIShVqpR63dWrVyMgIABDhw5FkyZNEBERgWXLliEhIQFff/11foSpU25jX7FiBRo3boxx48ahZMmSuH37NlatWoWjR48iJCQEtra2Guv7+vpiwIABGmWurq4GiSknchu/yoYNG1C0aFH1awsLC611xPber1y5EmlpaRplN2/exPTp09GmTRut9Qvie//gwQPs378fHh4eaNKkCY4ePZrtumLY7/MSf2Hf9/MSu0ph3u/zEn9h3ve3b98OhUKBgQMHonLlyoiNjUVQUBB69OiBzZs3o06dOpnWLVD7vEAfdPz4cUEmkwmHDx9WlymVSqF3795Chw4dsqzr7+8v1KxZU4iOjlaXxcfHC3Xr1hW+/fZbjbKaNWsKs2fP1qi/ZMkSwcPDQ3j69KmeosmZvMQeGxurVRYeHi7IZDJh06ZNGuUymUyYM2eOfjqtR3mJf8WKFYJMJhMSEhKyXE+M770us2fPFmQymXD37l2N8oL63mdkZKh/PnLkiCCTyYRz585lq25h3+8FIW/xF/Z9Py+xF/b9XhDyFr8uhWXf1/W5TUhIEBo0aCCMHDkyy7oFaZ/nHLtsOHLkCGxsbDSGnyQSCbp27Yq7d+/i9u3bmdYNCwuDp6cnSpYsqS5zcHBAq1atcOTIEXXZyZMnkZqaiq5du2rU79q1K9LT0/H777/rMaLsy0vsjo6OWmU1a9YE8PZUf2GQl/izS4zv/fvS0tLw22+/oX79+qhYsaIhuqt3eRkSKez7PZC3+Av7vp8fw6Bife/fV5j2fV2fW1tbW5QvX/6Dn9uCtM8zscuGW7duwc3NTevDrhpzv3nzps56KSkpePjwIWQymdYyd3d3xMXFIS4uTr0NiUSCKlWqaKxXoUIFWFlZ4datW/oIJcdyG3tmzp07BwBacQLA3r17UatWLdSsWRM9e/ZEaGhoLnutP/qI39fXF9WqVYOXlxemTZumfs/f3YbY3/uwsDAoFAp0795d5/KC+N7nlhj2e0MobPt+XhXW/V7fCvu+Hx8fj1u3bun83KoUtH2ec+yyQaFQoEKFClrldnZ26uW6JCQkQBAE9Xrvsre3V9d1dHSEQqGAtbU1LC0ttda1tbXNdBuGltvYM2trzpw5qFChAnx9fTWWderUCd7e3ihdujSeP3+O7du3Y+zYsYiJidGaf5Gf8hK/q6srxo0bh2rVqsHCwgJ///03goKCcPbsWezevVujDbG/97t27ULRokXRsWNHrWUF9b3PLTHs9/pWGPf93Crs+72+FeZ9XxAETJ8+HUqlEoMHD850vYK2zzOxyyaJRJKrZdlZntftG1peYld5/fo1RowYgYSEBGzZskXrQ71o0SKN1x06dEC/fv2wbNky9OrVC1ZWVjnvuJ7kNn65XK7xumnTpqhTpw4GDRqErVu3Yvjw4XnevqHp472Pjo7GmTNn0K1bN43J5CoF+b3Pi8K+3+tLYd73c0MM+72+FPZ9f+HChQgLC8P8+fNRuXLlD65fUPZ5DsVmg729vc4sOiEhAQB0ZumqcolEorOuqkyVzdvb2+P169daVxMBQGJiYqbbMLTcxv6ulJQUDBs2DNevX0dgYCCqVq36wTpmZmbo3LkzkpOTczzcq0/6iP9dzZo1g7OzMy5evKixDbG+9wCwe/duKJXKTIdi3ldQ3vvcEsN+ry+Fed/Xp8K03+tTYd73ly5divXr12Pq1Kno1q1blusWtH2eiV02uLm54c6dO1AqlRrlqg+ernF1ALCysoKrq6vOD+jNmzdRokQJ9WRNNzc3CIKgNb7+4MEDpKSkZDm+b0i5jV0lNTUVw4cPx8WLF7Fu3TrUq1cv29tWbdOY93PKa/y6CIKgEZNY33vgbax79uxBpUqVCt17n1ti2O/1obDv+/pWWPZ7fSnM+/7y5cuxdu1aTJgwAf379//g+gVtnxfPXmNAbdu2RWJiota9fEJCQlCxYkWdNx9UadOmDc6cOYOYmBh1mUKhwLFjx9C2bVt1WYsWLWBpaYm9e/dq1N+zZw+kUil8fHz0FE3O5CX2tLQ0DB8+HH/++SdWr16NRo0aZXu7SqUSv/32G4oVK2bUL7i8xK/LqVOnEBsbi9q1a6vLxPjeq5w/fx4PHz7M9l/sQMF57/OisO/3eSWGfV+fCtN+ry+Fdd9fuXIlVq9ejdGjR2PIkCHZrleQ9nnOscsGb29vNG7cGFOnToVCoUDZsmUREhKCv/76C6tXr1av169fP5w/fx5RUVHqssGDB+PXX3+Fn58fRowYAalUijVr1kAqlWLo0KHq9RwcHPDll19i9erVsLGxQePGjXHx4kUEBQWhf//+KF26dL7GrJKX2L/66iucOnUKI0aMQNGiRTWGIUqUKIFy5coBAIKDg3Hv3j00adIEzs7OiI2Nxfbt2/HXX3/h22+/RZEiRfIt3vflJX65XA65XI6KFStCKpUiIiICwcHBKF++PPr06aNeT4zvvcquXbsglUq15h2pFOT3HoD6LvlXrlwBAFy4cAEvXryAtbW1+gbNYtzvVXIbvxj2/dzGXtj3e5Xcxq9SGPf99evXIyAgAK1atYKnp6fG59bS0hIeHh4ACv4+LxEEQchzKyYgKSkJS5YswaFDhzQerfTunbQz+5Dfv38f/v7+CA8PhyAIqF+/PiZNmqT1F4kgCNi4cSO2bduGJ0+e4H//+x969eqFL774wqinpXMbe1aPYOnatSsWLFgAADh69CiCgoJw9+5dvHz5EtbW1qhevToGDBhQIP5qzW3848aNw9WrV/H8+XOkp6ejVKlS8PHxwfDhw9XzLVTE9t6r6np5eaFp06ZYs2aNzvYL+nuf2WfYxcVFfSZTrPs9kPv4xbDv5zZ2Mez3QN4++4V131fFo0th2ueZ2BERERGJBOfYEREREYkEEzsiIiIikWBiR0RERCQSTOyIiIiIRIKJHREREZFIMLEjIiIiEgkmdkREREQiwcSOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEpAfp6eno3bs36tatizt37mgs++mnn+Du7o7ly5cbqXdEZCr4rFgiIj15/Pgx5HI5ypQpg59//hlFihTBrVu30KNHD1SvXh2bN2+Gubm5sbtJRCLGM3ZERHri4uKCuXPn4saNG/D390dKSgrGjRuHIkWKYNGiRUzqiMjgpMbuABGRmLRr1w6ffvoptm7diuvXr+PmzZsICAhAmTJljN01IjIBHIolItKz1NRUfPzxx3j48CE++eQTzJ4929hdIiITwaFYIiI9i4qKwtOnTwEAt27dQnp6upF7RESmgokdEZEeJSUlYezYsbC3t8fYsWMRERGBgIAAY3eLiEwE59gREenRt99+iydPnmD9+vVo2rQpIiMjERgYiKZNm6JJkybG7h4RiRzP2BER6ckvv/yC/fv3w8/PD02bNgUAzJ49G6VLl8aECRPw4sULI/eQiMSOF08QEenBnTt30L17d1StWhVbtmyBVPrfgEhERAT69u2L5s2bY+3atUbsJRGJHRM7IiIiIpHgUCwRERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKRYGJHREREJBJM7IiIiIhEgokdERERkUgwsSMiIiISif8Dj1dh0DHr6R8AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try with data that is not correlated\n", "x = np.array([0, 1, 2]).reshape(-1, 1)\n", "y = np.array([1, 3, 1])\n", "\n", "reg = LinearRegression()\n", "reg.fit(x, y) \n", "slope = reg.coef_[0]\n", "intercept = reg.intercept_\n", "\n", "show_fit(x, y, slope, intercept)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# computing R2 from sklearn\n", "y_pred = reg.predict(x)\n", "r2 = r2_score(y_true=y, y_pred=y_pred)\n", "r2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Guess that $R^2$: part 2" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try with data that is a little bit correlated\n", "x = np.array([0, 1, 1.5, 2, 2.1]).reshape(-1, 1)\n", "y = np.array([1, 1, 2, 1, 3])\n", "\n", "reg = LinearRegression()\n", "reg.fit(x, y) \n", "slope = reg.coef_[0]\n", "intercept = reg.intercept_\n", "\n", "show_fit(x, y, slope, intercept)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.3209379240162824" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.metrics import r2_score\n", "\n", "# computing R2 from sklearn\n", "y_pred = reg.predict(x)\n", "r2 = r2_score(y_true=y, y_pred=y_pred)\n", "r2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Whats a 'good' $R^2$ value?\n", "\n", "... it depends:\n", "\n", "- if you're predicinting price changes in stock market: cross validated $R^2 = .01$ is fantastic!\n", " - if you keep using your model to make bets, you'll come out ahead\n", " - if this is the case, give me a call: I'd like to invest in your startup :)\n", "- if you're predicting how many people will rent a blue bike (y) given weather (x): cross validated $R^2 = .01$ is not so great\n", " - adding weather information into your model barely changes predictions\n", " \n", " \n", "More generally, $R^2$ should be interpretted in the context of the application. Like Accuracy, its context dependent:\n", "\n", "- baseball player who \"accurately\" gets base hit 50% of at-bats is better than any hitter to every play the game\n", "- pilot who \"accurately\" lands the plan without crashing 50% of the time might not be as celebrated ..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Shouldn't you be cross-validating $R^2$?\n", "\n", "... we're `.fit()` ing and `.predict()`ing on the same samples!\n", "\n", "- one cross-validates $R^2$ values to \n", " - estimate performance in predicting new samples\n", "- it is also common to **not** cross-validate an $R^2$ when we want to examine a model's parameters\n", " - how many more riders get on a blue bike when the temperature goes up 1 degree fahrenheit?\n", " - `y_pred = a_1 * temp + a_0`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# In Class Assignment 2\n", "\n", "Predict y=`trip_count` from x=`temp` by ...\n", "1. `.fit()`ing a LinearRegression to predict y from x\n", "1. visually inspect your results using `show_fit()`\n", "1. store the following values in a new dataframe `df_regress` (see table immediately below)\n", " - slope \n", " - intercept\n", " - mse\n", " - r2\n", "1. Repeat the three steps above for each new x value below. (Use a loop)\n", " - x=`wind`\n", " - x=`rain`\n", " - x=`temp_c` (temperature in celsius)\n", " - `temp_c` = (`temp` - 32) / 1.8\n", " \n", "Your final `df_regress` should look similar to below:\n", "\n", "| | r2 | mse | slope | intercept |\n", "|-------:|---------:|-------------:|-------------:|-------------:|\n", "| temp | 0.150487 | 3.548955e+06 | 144.646765 | 1157.497714 |\n", "| temp_c | 0.150487 | 3.548955e+06 | 260.364178 | 5786.194210 |\n", "| wind | 0.137007 | 3.605272e+06 | -119.156711 | 11469.348993 |\n", "| rain | 0.271195 | 3.044684e+06 | -2224.622727 | 10644.350000 |\n", " \n", "Using the results above, answer the following questions\n", "1. Which of the four features, `temp`, `wind`, `rain` or `temp_c` best predicts changes in `trip_count`? \n", "1. Explain, to a non-technical expert, the meaning of each value in the slope column above\n", " - i.e. if \"slope\" of \"temp\" is 144.64, what does this mean?" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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datetrip_counttempwindrain
02019-10-011218369130
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" ], "text/plain": [ " date trip_count temp wind rain\n", "0 2019-10-01 12183 69 13 0\n", "1 2019-10-02 9071 66 11 1\n", "2 2019-10-03 11496 54 9 0\n", "3 2019-10-04 11767 60 16 0\n", "4 2019-10-05 9315 56 9 0" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df_bike = pd.read_csv('bluebike_201910.csv')\n", "\n", "df_bike.head()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "import pandas as pd\n", "\n", "df_bike = pd.read_csv('bluebike_201910.csv')\n", "\n", "# converting tmep to celsius (from fahrenheit)\n", "df_bike['temp_c'] = (df_bike['temp'] - 32) / 1.8\n", "\n", "# initialize empty table of regression stats\n", "df_regress = pd.DataFrame()\n", "\n", "# initialize regression object\n", "reg = LinearRegression()\n", "\n", "# get target variable\n", "y = df_bike['trip_count'].values\n", " \n", "for feature in ['temp', 'temp_c', 'wind', 'rain']: \n", " # get x feature\n", " x = df_bike.loc[:,feature].values.reshape(-1, 1)\n", " \n", " # fit regression\n", " reg.fit(x, y)\n", " \n", " # observing regression\n", " m = reg.coef_[0]\n", " b = reg.intercept_\n", " show_fit(x, y, slope=m, intercept=b)\n", " plt.xlabel(feature)\n", " plt.ylabel('trip_count')\n", " \n", " # make predictions given model\n", " y_pred = reg.predict(x) \n", " \n", " # store regression stats (dataframe prints nicely)\n", " df_regress.loc[feature, 'r2'] = r2_score(y_true=y, y_pred=y_pred)\n", " df_regress.loc[feature, 'mse'] = get_mse(y_pred, y)\n", " df_regress.loc[feature, 'slope'] = reg.coef_[0]\n", " df_regress.loc[feature, 'intercept'] = reg.intercept_" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "260.352" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "144.64 * 1.8" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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r2mseslopeintercept
temp0.1504873.548955e+06144.6467651157.497714
temp_c0.1504873.548955e+06260.3641785786.194210
wind0.1370073.605272e+06-119.15671111469.348993
rain0.2711953.044684e+06-2224.62272710644.350000
\n", "
" ], "text/plain": [ " r2 mse slope intercept\n", "temp 0.150487 3.548955e+06 144.646765 1157.497714\n", "temp_c 0.150487 3.548955e+06 260.364178 5786.194210\n", "wind 0.137007 3.605272e+06 -119.156711 11469.348993\n", "rain 0.271195 3.044684e+06 -2224.622727 10644.350000" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_regress" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 4 }