{
"metadata": {
"name": ""
},
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Chapter 3: Linear Regression ##\n",
"\n",
"### Simple Linear Regression ###"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pandas as pd\n",
"import numpy as np\n",
"import scipy as sp\n",
"import statsmodels.api as sm\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.linear_model import LinearRegression\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Data from R ISLR package - write.csv(Boston, \"Boston.csv\", col.names = FALSE)\n",
"boston_df = pd.read_csv(\"../data/Boston.csv\")\n",
"boston_df.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"
\n",
"
\n",
" \n",
" \n",
" | \n",
" crim | \n",
" zn | \n",
" indus | \n",
" chas | \n",
" nox | \n",
" rm | \n",
" age | \n",
" dis | \n",
" rad | \n",
" tax | \n",
" ptratio | \n",
" black | \n",
" lstat | \n",
" medv | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 0.00632 | \n",
" 18 | \n",
" 2.31 | \n",
" 0 | \n",
" 0.538 | \n",
" 6.575 | \n",
" 65.2 | \n",
" 4.0900 | \n",
" 1 | \n",
" 296 | \n",
" 15.3 | \n",
" 396.90 | \n",
" 4.98 | \n",
" 24.0 | \n",
"
\n",
" \n",
" 1 | \n",
" 0.02731 | \n",
" 0 | \n",
" 7.07 | \n",
" 0 | \n",
" 0.469 | \n",
" 6.421 | \n",
" 78.9 | \n",
" 4.9671 | \n",
" 2 | \n",
" 242 | \n",
" 17.8 | \n",
" 396.90 | \n",
" 9.14 | \n",
" 21.6 | \n",
"
\n",
" \n",
" 2 | \n",
" 0.02729 | \n",
" 0 | \n",
" 7.07 | \n",
" 0 | \n",
" 0.469 | \n",
" 7.185 | \n",
" 61.1 | \n",
" 4.9671 | \n",
" 2 | \n",
" 242 | \n",
" 17.8 | \n",
" 392.83 | \n",
" 4.03 | \n",
" 34.7 | \n",
"
\n",
" \n",
" 3 | \n",
" 0.03237 | \n",
" 0 | \n",
" 2.18 | \n",
" 0 | \n",
" 0.458 | \n",
" 6.998 | \n",
" 45.8 | \n",
" 6.0622 | \n",
" 3 | \n",
" 222 | \n",
" 18.7 | \n",
" 394.63 | \n",
" 2.94 | \n",
" 33.4 | \n",
"
\n",
" \n",
" 4 | \n",
" 0.06905 | \n",
" 0 | \n",
" 2.18 | \n",
" 0 | \n",
" 0.458 | \n",
" 7.147 | \n",
" 54.2 | \n",
" 6.0622 | \n",
" 3 | \n",
" 222 | \n",
" 18.7 | \n",
" 396.90 | \n",
" 5.33 | \n",
" 36.2 | \n",
"
\n",
" \n",
"
\n",
"
5 rows \u00d7 14 columns
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
" crim zn indus chas nox rm age dis rad tax ptratio \\\n",
"0 0.00632 18 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 \n",
"1 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 \n",
"2 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 \n",
"3 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 \n",
"4 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 \n",
"\n",
" black lstat medv \n",
"0 396.90 4.98 24.0 \n",
"1 396.90 9.14 21.6 \n",
"2 392.83 4.03 34.7 \n",
"3 394.63 2.94 33.4 \n",
"4 396.90 5.33 36.2 \n",
"\n",
"[5 rows x 14 columns]"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# LSTAT - % of population with low status; MEDV - median value of home\n",
"ax = boston_df.plot(x=\"lstat\", y=\"medv\", style=\"o\")\n",
"ax.set_ylabel(\"medv\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
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I8vJqYbM97D5/r/vnQwKqdesLGV0jP79I5OSUiPz8Ip9z1M9SUgoN5dW7nlGto3ipeSLl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\ndJMsF96vVmQbHZSYmIiMjAwIgoCsrCy5YoRNCeuJKCEjQDm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"text": [
""
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# The statsmodels library provides a small subset of models, but has more emphasis on\n",
"# parameter estimation and statistical testing. The summary output is similar to R's\n",
"# summary function.\n",
"# X is an \"array\" of column values, y is a single column value\n",
"X = boston_df[[\"lstat\"]].values\n",
"X = sm.add_constant(X) # add the intercept term\n",
"y = boston_df[\"medv\"].values\n",
"ols = sm.OLS(y, X).fit()\n",
"ols.summary()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"OLS Regression Results\n",
"\n",
" Dep. Variable: | y | R-squared: | 0.544 | \n",
"
\n",
"\n",
" Model: | OLS | Adj. R-squared: | 0.543 | \n",
"
\n",
"\n",
" Method: | Least Squares | F-statistic: | 601.6 | \n",
"
\n",
"\n",
" Date: | Fri, 23 May 2014 | Prob (F-statistic): | 5.08e-88 | \n",
"
\n",
"\n",
" Time: | 20:55:56 | Log-Likelihood: | -1641.5 | \n",
"
\n",
"\n",
" No. Observations: | 506 | AIC: | 3287. | \n",
"
\n",
"\n",
" Df Residuals: | 504 | BIC: | 3295. | \n",
"
\n",
"\n",
" Df Model: | 1 | | | \n",
"
\n",
"
\n",
"\n",
"\n",
" | coef | std err | t | P>|t| | [95.0% Conf. Int.] | \n",
"
\n",
"\n",
" const | 34.5538 | 0.563 | 61.415 | 0.000 | 33.448 35.659 | \n",
"
\n",
"\n",
" x1 | -0.9500 | 0.039 | -24.528 | 0.000 | -1.026 -0.874 | \n",
"
\n",
"
\n",
"\n",
"\n",
" Omnibus: | 137.043 | Durbin-Watson: | 0.892 | \n",
"
\n",
"\n",
" Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 291.373 | \n",
"
\n",
"\n",
" Skew: | 1.453 | Prob(JB): | 5.36e-64 | \n",
"
\n",
"\n",
" Kurtosis: | 5.319 | Cond. No. | 29.7 | \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.544\n",
"Model: OLS Adj. R-squared: 0.543\n",
"Method: Least Squares F-statistic: 601.6\n",
"Date: Fri, 23 May 2014 Prob (F-statistic): 5.08e-88\n",
"Time: 20:55:56 Log-Likelihood: -1641.5\n",
"No. Observations: 506 AIC: 3287.\n",
"Df Residuals: 504 BIC: 3295.\n",
"Df Model: 1 \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"const 34.5538 0.563 61.415 0.000 33.448 35.659\n",
"x1 -0.9500 0.039 -24.528 0.000 -1.026 -0.874\n",
"==============================================================================\n",
"Omnibus: 137.043 Durbin-Watson: 0.892\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 291.373\n",
"Skew: 1.453 Prob(JB): 5.36e-64\n",
"Kurtosis: 5.319 Cond. No. 29.7\n",
"==============================================================================\n",
"\"\"\""
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Scikit Learn provides a larger number of models, but has more of a Machine Learning POV\n",
"# and doesn't come with the statistical testing data shown above. However, it produces an\n",
"# identical linear model as shown below:\n",
"reg = LinearRegression()\n",
"X = boston_df[[\"lstat\"]].values\n",
"y = boston_df[\"medv\"].values\n",
"reg.fit(X, y)\n",
"(reg.intercept_, reg.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"(34.553840879383131, array([-0.95004935]))"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Drawing the regression line on top of the scatterplot\n",
"ax = boston_df.plot(x=\"lstat\", y=\"medv\", style=\"o\")\n",
"ax.set_ylabel(\"medv\")\n",
"\n",
"lstats = boston_df[\"lstat\"].values\n",
"xs = range(int(np.min(X[:,0])), int(np.max(X[:,0])))\n",
"ys = [reg.predict([x]) for x in xs]\n",
"ax.plot(xs, ys, 'r', linewidth=2.5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"[]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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WLFnCoUOH2L9/v+9nKD9CXfU9+OB8DhyowWA4S58+3Rg//nKefDKfigrbVXcx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\nCCE8mHQCQgjhwf4fzUY3xN/t/wQAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Prediction\n",
"test_data = [[5], [10], [15]]\n",
"reg.predict(test_data)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"array([ 29.80359411, 25.05334734, 20.30310057])"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Multiple Linear Regression ###"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# regression with 2 input columns\n",
"X = boston_df[[\"lstat\", \"age\"]]\n",
"reg2 = LinearRegression()\n",
"reg2.fit(X, y)\n",
"(reg2.intercept_, reg2.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"(33.222760531792929, array([-1.03206856, 0.03454434]))"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# regression using all input columns\n",
"xcols = boston_df.columns[0:-1]\n",
"X = boston_df[xcols]\n",
"reg3 = LinearRegression()\n",
"reg3.fit(X, y)\n",
"(reg3.intercept_, reg3.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
"(36.459488385089394,\n",
" array([ -1.08011358e-01, 4.64204584e-02, 2.05586264e-02,\n",
" 2.68673382e+00, -1.77666112e+01, 3.80986521e+00,\n",
" 6.92224640e-04, -1.47556685e+00, 3.06049479e-01,\n",
" -1.23345939e-02, -9.52747232e-01, 9.31168327e-03,\n",
" -5.24758378e-01]))"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Plotting a fitted regression with R returns 4 graphs - Residuals vs Fitted, Normal Q-Q,\n",
"# Scale-Location (Standardized Residuals vs Fitted), and Residuals vs Leverage. Only the \n",
"# Q-Q plot is available from statsmodels. The residuals vs Fitted function is implemented\n",
"# below and is used for plot #1 and #3. The Residuals vs Leverage is TBD.\n",
"def residuals_vs_fitted(fitted, residuals, xlabel, ylabel):\n",
" plt.subplot(111)\n",
" plt.xlabel(xlabel)\n",
" plt.ylabel(ylabel)\n",
" plt.scatter(fitted, residuals)\n",
" polyline = np.poly1d(np.polyfit(fitted, residuals, 2)) # model non-linearity with quadratic\n",
" xs = range(int(np.min(fitted)), int(np.max(fitted)))\n",
" plt.plot(xs, polyline(xs), color='r', linewidth=2.5) \n",
"\n",
"def qq_plot(residuals):\n",
" sm.qqplot(residuals)\n",
"\n",
"def standardize(xs):\n",
" xmean = np.mean(xs)\n",
" xstd = np.std(xs)\n",
" return (xs - xmean) / xstd\n",
" \n",
"fitted = reg3.predict(X)\n",
"residuals = y - fitted\n",
"std_residuals = standardize(residuals)\n",
"\n",
"residuals_vs_fitted(fitted, residuals, \"Fitted\", \"Residuals\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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0Nn/kp+984Lbp8ePHZ/6ffcPLmDFjCtY4Iig4zGZg7lw5p3afPkBkpLwBLzhY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"text": [
""
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = sm.qqplot(residuals, dist=\"norm\", line=\"r\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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ly3nkkUewsjLttF1Vi9dsbGxYunQpwcHB6PV6Jk+eLIPMotqpnUVPAXpsyWYo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\nYSShIIQQwkhCQQghhNH/A7FW0BrkRa4+AAAAAElFTkSuQmCC\n",
"text": [
""
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"residuals_vs_fitted(fitted, std_residuals, \"Fitted\", \"Std.Residuals\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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G/NRqqxOYSEl6nm3bdslW4yQ2NtZh+Gf//v0MCipJlUrDwn6F+c+rrzrM2d2B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\n",
"text": [
""
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Nonlinear Terms and Interactions ###\n",
"\n",
"Python offers formula parsing support via the [Patsy](http://patsy.readthedocs.org/en/latest/) toolkit. StatsModels uses Patsy to provide formula parsing support for its models. But this can be easily implemented as temporary columns in Pandas dataframes as shown below."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# fitting medv ~ lstat * age\n",
"boston_df[\"lstat*age\"] = boston_df[\"lstat\"] * boston_df[\"age\"]\n",
"reg5 = LinearRegression()\n",
"X = boston_df[[\"lstat\", \"age\", \"lstat*age\"]]\n",
"y = boston_df[\"medv\"]\n",
"reg5.fit(X, y)\n",
"(reg5.intercept_, reg5.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 13,
"text": [
"(36.088535934612942,\n",
" array([ -1.39211684e+00, -7.20859509e-04, 4.15595185e-03]))"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fitted = reg5.predict(X)\n",
"residuals = y - fitted\n",
"std_residuals = standardize(residuals)\n",
"residuals_vs_fitted(fitted, residuals, \"Fitted\", \"Residuals\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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cr9tqtWL//v2Ii4tDzZo14eLiku5+x44dR3R0OwButi09AcyCk5MrzOaSOa7z\nSfTtOxQxMZsB1EBiInH+fDBWr16Nt956y6G6cooMjURUVFS6rl8k87VLmCCLqFTAxImAJAGffgrc\nvg00agT89htQtSrq1auHHTvqZXj4zp070apVZ8TGjgVAbN7cDlu3rkP9+vVz7RTGjPkcU6ZMgVbr\nCg8PM0JDf0GJEiVyrf68QkhICH777RgePToEwADgBHr1aoDOnTvmaCjsuLg4NG7cGqdOhUGtdoPR\neBP79u1A8XTyrZcuXQom0zeIjh5t0/gzVCodvLxOo1u373H//n2YzWZotY83YTndRkVF3Qfgb/uk\ngsXi/3yn/7Xz00yukE9lPz9Mnpwy9OTqSu7b99RDgoPbE1iUat7iG7Zu3SUXxCps3bqVJlMZArcJ\nkGr1ZFar1iDL5VksFu7fv5+7du3io0eP7Kg051m6dCmdnd9I9VvI1Gj0OX4eEydOpsHQhkmBDTWa\niQwKSt9LzGq1sk2bLjSZitNkeokGgzuHDRvGgwcPsmjRctTpzDQYXLhsWYrzw+HDh1msWADVag1L\nlqzEEydO5Mh5BAW1oU7Xh0A4gd00Gj15PAeiE+QEWWk7n3pETEwMZ8+ezQ8++IA9evRgz5492bNn\nzywJtBfCSDyZ+Ph4DhnyEUuXrs46dZry4MGD9q9k1qwUQ+HsTO7a9cTdGzVqQ+DHVA3TUjZt+rrd\n5Jw6dYqbN2/mhQsX0v1+4sSJ1GqHp6r/PvV65yzVFRcXZwv17U+z+SX6+pbi5Qzcg/MiZ86csa18\nP0xAplo9hWXKVMnxet9++z0Cc1L9BkdZtGjG7vSyLPPIkSPcuXMnHzx4QFmWWaxYAFWqeanCjHjx\n9OnTjIyMZIECvgRWEogjsIgFCxbJtFvxwYMH+dNPP/Hif5wy0uP+/fts2vQ16vUu9PIqwQ0bNmT6\nGjiaHDESHTp04JgxY1iiRAkuXryYTZo04YABA7Ik0F686EYiLi6O7703mD4+ZejvX5Pbtm1L8333\n7u/TaGxGYB+BhTSZPHj+KYvhssT8+aRKpdzxRiP5hNg869b9REkqQmA9gXWUJD9u3rzZLjI++2wi\njUYfuro2p9HowaVLlz+2z6pVq2gy1SQQa2tgVrJUqcpZqm/y5Ck0GFqn6hF/ySZN2mX3NHIVZZGd\nG9VqJ/r7V8vQuNqTefO+sa2TiSJgpZNTf7Zv/1amj4+MjKRWa0wTwsXZuQuXLVvGP//8k2Zzjf+E\nIKnAY8c4JPo8AAAgAElEQVSO0Wq18vTp0zx9+jQtFstj5fbtO5SSVIxm86uUJI8MF4M+D+SIkahc\nWbmRktZGJCQksFatWs9ckT150Y1Ez559aTS2pBJFdNNjboEGgzl5WAUg9fo+nDlzZs6IWbYsJXqs\nRkN+/32Gu65atZo1azZhrVrBzxwN9Ny5cxwzZiw//vgT/v3338nbz549S6PRi0CY7XxP02Bw5cOH\nD9Mcb7Va2b79mzSZStLVtTHNZu8nPmHJssyoqKh0PZmetUecuswpU6Yn5y9w9EJCWZYz1dOWZZnn\nzp3j+fPns+XZZbVa2a3bu9TpXGk0+rBSpTq8d+9epo599OgRr127Rq3WhUABAh4EPqYkleXOnTt5\n7tw52/8gwvab3KVe78Z//vmHNWo0tA1bFWeNGg0ZFRVFUmnLvv76axoMPgRu2o47TEkqkK4xeR7I\nESNRs2ZNkmS9evV44sQJ3rlzhyVKlHh2dXbkRTcSZrM3gSvJjZRGM5xffPFF8vcuLp4EziZ/bzR2\n4jfffJNzgjZtIg2GlC7c+PGK26ydOH36NJ2dPalWD6NKNZImk0dyA79t2za6ur6SpgdpMhVPN9Kp\nLMs8ePAgt23bxrt372ZY3+HDh+ntXYJarYEFCvhw0aJFXLlyJf/880+S5Jw58yhJ9Qk8IiDTyWkQ\nX3ut21PPY+LEKZSkygR2EPiRRqMn92ViPseRPHr0iHXqNKHRWIhGYyHWq9eM0dHR2Srz9u3bvHLl\nSqbDwY8fP4lOThI1GjOBKgSuErhIwJ+1ajVINlx9+w6lyVSOen1fmkyl+eGHYzhw4IfU67vZnvos\nNBjeYv/+wxgVFcXKlV+mwRBAoBIBfwI3+DxGfk1NjhiJ+fPnMzw8nKGhoSxevDg9PDz49ddfZ0mg\nvXjRjYS3d0nbUFLSk0JXTp8+Pfn7yZOnUZLKEphHJ6f+9PEpmfN/+r17lfDiSaL69iUz6I2dO3eO\na9euzfRcSefOPalSTUplCOaxWbMOJMlr165RkgraxtdJ4Be6uvowNjaWp0+fZv36LVmyZFX26tU/\nU41bbGws3d39bPMnMoEQAhJNpldpMpXgBx8MocViYefOPajXu1OSCrNixZeeaHSSKFGiMpUIo0nn\nMYF9+w7O1DVwFAMHfkiD4Q1bI5tIg6EThw0blaWy7t27x/79h7F16zc4c+acTBkJJXJwSVsDHkzg\nl1TXbyWDgzsk7yvLMrdu3cqZM2dy2bJlfP/9QfTwKENgY6pjNvHll1vwo48+oV7flSkxm0YT6EZg\nKX18Sj4Xa2HSI0eMRF7kRTcSixcvpST5EZhAJ6de9PUt9ZgRWL16Nbt1683hwz/i7du3c0fY33+T\nRYqkGIr27cn/rEZdsWIlJcmTZnNbSlJRDhw44qnFNm/ekcCKNDd67drNkr9fu3YdjcYClKRCLFDA\nh3v27OGtW7fo6upDlWoOgQM0GDqxefMOT6hF4cyZM3R2LpXmyQR42db7j6QkFUvOdXHjxg1euHAh\n0z3ismVrEtieXK5KNZJDhz79/B1JnTrNmTbX83rWr986w/23bdtGb++SdHIysnbtJrx58yZJMioq\nisWKlaeTU18qK6frsE+fgcnH7dy5k6+80pZ167bkDz+sTN4+YcIEajQf2uruTGBqsha1+lO+9Vaf\nxzRcuXKFrq4+VKtHE2hKoIvNGFip1/dg375D2LZtNwKLU53XbqpU7vT2LpFvPJWyQo4YiXHjxiW/\nPvvss+SXI3nRjQRJhoSEcNCg4fz88/GZHtfNFa5fJytWTGlhGzQgbUEa4+LibPMlJ2xfR1CSivLQ\noUNPLHLZshWUpDJUIsgeoSQFcs6ctE+zMTExvHz5cnIuhuXLl9PZuX2qRiCOGo3uqStjw8PDqdeb\nUw3nhRPwIXCGymToq1nOrjZs2HAC7lTyPo8lYMyRWET2pHfvATZ3z6QIuO+wb98h6e57/vx528r7\nEAIPqdGMYuXKdUkqK6hdXJqk+j0iqNHoGB8fz71799q8rRYRWEtJKpEcIHLFihU0meoQiKeS78Gd\nwJs0GLrTza1Qut5In376GTWagbZ6HhKoTJWqEJ2dy7BKlbqMjIzkpElTKUlNqGShs1Cv78FOnbo/\n1xkRyRwyElOmTOHUqVM5depUjh8/ni+99JJwgRU8mfv3yfr1UwxFQAB54QJv3rxJg8EzTS89s43u\nzJlz6OdXjr6+ZTlhwv+eOhywdu1aOjs3ZoonzB1qtfpMhZSZNm0mJakQnZ27Uokb1MZWxiFKkkem\n3CTTo3LlBgQ+JdCLQH8Cg9m7d/8slZVbREREMCCgJl1cKtLZOYAVK77EBw8epLvvkiVL/rP+wkqN\nRs+YmBiuWrWKLi6vpvouhhqNnrGxsXzzzd4Evkr13RZWrqysYbFYLGzRogOdncvRbG5Bk6kgBw8e\nzNmzZzMsLCxdHR999DFVqjEE7lKZkD7MggWL8ujRo8m/f2JiItu160q93s328qBarWXJkpV47Nix\njC/IpUtkhw7JHZ/8Rq4MN8XFxbFBg6wvQrIHwkjkA2JjleGmpDu/YEFaduz4TzrNozQaPezmfhkT\nE8ODBw/y77//5qNHj1i6dCXqdN0JzKPJVOWZxtIPHz7MxYsXc8mSJfT1LUWdzoWSVCBb7pEBAXVs\nveykyzIj3eGSvEZCQgL37dvH/fv3MyEhIcP9fv75Zzo7V6MSLZcE/qFe70yr1cp79+6xYMHCVKsn\nEthJo7Et27Z9g2SSt9iUNMOJVao0TC7XarXyjz/+4MaNGzM0DKTSNk2YMJnBwe2oUhkJmAi4Ua32\n4ogRo9M95vz587b1FYupuEcvobu7X/oLC3fvJj08FJHNmpEOjmGXFXLFSISHh7NUqVLPXJE9EUYi\nn2CxkB9+mGIonJx4Zdw4enkVo8FQkEajK1etWmOXqi5evMhChUrTbK5ESfJju3ZdGR4eztGjx7Jb\nt95ctGhxlicjZVnm/fv3s+0WOWfO15SkcgS2EVhNSfJmaGhotso8e/Ys//zzz8dcfh2BxWJho0at\naDLVpU43kJJUiN98813y9xcuXGDLlp0YGFiPgwaNSI6eeujQIdsw1Wwq+UgKc/XqZ/tfWK1WNmjQ\ngkZjawLfEmhA4DUCN6jRtOM77/RL97iDBw/SbK78n6fbyo8PgX7/PenklLLT0KEZOmbkZXLESFSs\nWDH5FRAQQA8PD86aNStLAu2FMBL5jIUL09xg8rBhvHXjxhN7pf8lNjaWR48e5YULF9Jt7OvWbU61\nOskDKpaSVI/fP2HNhiOQZZnz5n3LSpXqs2bNJpw9ezZXrlzJo0eP8vjx46xatQE9PIqzZcuOvHPn\nzlPL6tnzAxqNPnRxqU6z2ZMzZ87k9evXc+ls0icxMZE//PADp02bluwyHB0dzUuXLj0xd/e+ffv4\n2mtvskWLTtz0hEWZGXHs2DGaTCVSPcU8IuBGJWd1Aer1buzR4z0OHToizer4S5cu0WDwoBJtVlmJ\nbzB48NKlS0knlDYCspOT8n/Op+SIkbh06VLy69q1a890Y+cUwkjkQ3bvJgsWTLnZWrcmM9n7vXjx\nIv38ytDFJYAGgxe7dXv3sQlGD4/iBM6l6hFO5MCBw3LiTOzCF1/8j5LkRxeX12kweNNgcCfwHYFz\ndHIaxCpV6j7xyWf9+vU0mSoRiLTNcRSlWl2fJpMHQ0JCcvFMnsyKFStpMLhSkgqzQAFf/vXXXzlS\nz/79++niEphqDmoygbq2ielVtgnvqVSrP6Srqw+vXLmSfOyAAR/SZPKnXt+fJpN/isddRATZtGny\nf/aBwcBPm7Tmnj17cuQccgO7Gonw8PAnvhyJMBL5lAsXlEls2033t8aJZZ2MfOWVV5/ooVW7dhOq\n1f9L7iGaTDW5fHna0BsNGrSkRpOU+CiaJtPLXJhHe3xXr161GYWkVb4LqbjZpkz46vUFnvg0MWnS\nJGq1w6isG6hIINp27G/08CiSaS0HDhxgrVpBLFGiCgcM+NCueREuXLhAo9GDKd5sG+jmVihHOprR\n0dEsXrwCtdpRVLzgyhNYZqu3um2IL2nx6RB+9NHHaY7funUrp0+fzq1btyob/vmH9PdP/q8eV2lY\nFGMIzKTR6JmcpTO/YVcjUaxYMRYvXpzFihWjSqWiu7s73d3dqVKpWLx48WwJzS7CSORjIiP5sEGD\n5JvvPlzZRtOa9eu3yPCQAgUKMfUKc+BzjhyZdhL6ypUrLFKkHF1cytNo9M5Vd8ZFi5awWrXGrFUr\nOFPxqPbt20ezuXqq8/mdQBkmxYIC7lKrNT4xKuvPP/9Mk6k8lXUD76YqK5EqlTpT8ycXLlygs7On\nbdL2AI3GFnzzzd7PdO5PYtOmTTSbW6QZ75ck3zS9+Owybtw4GgzuVKk09PevziZN2rBkyaosVKgU\ngTdsTxYVmLLYkgS+5IABQzMudMsWskCBZNF/+hSmCdNTHb+QTZq8ZrdzyE1yZLjp3XffTePLvWXL\nFvbubb8/UlYQRiLniYqK4t27d7Mdq2fDhg2cPXt2mvAT82bP5nRtYOrVavwSKloz6GHWqvUK1eok\nF8lomkwvcenSpY/tFxcXx2PHjmU7xtCzoCxsLEngZwJraDT6PDUmU0REBF1cvFL1bn+mWl2ABkNz\nAhNoMlV8qieWLMscMOBD6nRm21DKJSoL9GaxbNnMpY6dNWsW9fo+qX6Gu9TrXTJ97k/jxIkTNBp9\nCdxhijeba6Yjsybx6NEjzps3j1988UWa4aqRI0dT8WDaSSCBwHj6+ZWlLMvcvXs3VSpXAtUIlKQS\nemMfgY00Gr2S50vSkJhIjh6d5n+Z8NFHbNSgNYGlqTavYoMGr2b38jiEHDESFSpUyNS23EQYiZxD\nlmW+//5garVG6nRm1q4dlKFfPKmEJT958iQvXryYpmGWZZnt2nWls3NVGgzvU5L8OHeuEj/qxx9/\npLNzA76OH/kQzik3ZVAQmc7q8HPnztHHpyTN5so0Gn3ZuXOPPLPoqUaNIKZdkfwN27d/+6nHhYaG\n0tXVmzqdmQUK+DAkJISzZ8/m4MHDuXr16kwbuWvXrnHkyNHU6Uw0Gr1YuHDZdONWpce3335Lo/H1\nVNr/obOzR6aOTU1kZCR//fVX7tix47HJ6TFjPqck+dJsDqYkeTyzN1t0dDT9/avRaGxDtXoEjUYf\n/vDDSsqykgND8WBK0i8T0HPXrl2UZZlduvSkwVCSGk0barUedHMrzsDAuvz5558frygsjGzUKOW/\n6OzMLT16Uacz0cnJhSqVB4ENVAJqFn1m76u8Qo4YieDgYI4fP56XLl3ixYsX+cUXX7Bp06ZZEmgv\nhJHIORYsWEhJqkHF28NCna4XO3dOf/Hk9evXWbx4BTo7l6XR6JVmiCc0NJQmUzkqsf1J4AJ1OhPj\n4+MZHx9vi8wZxArat3lapU25Of38lDhQ/yFpDcQ///zzWAN67949XrhwwSG512vXbsa0eTKmsUuX\ndzJ1rNVqZXh4uF0MXnR0NK9fv/5MbroRERH09S1FJ6cPCMyhJJXh//731TPVu379emq1HlSpPOnk\n5MfAwJceGyY7deoUf/nllyzl3Pj+++8pSS2ZMiG9nwULFmFiYiLVag2BACqrsUnFcUHP4cNHklQ6\nKhs3buRXX33FHTt2ZFxJaCjp45PyH6xQgcdWrbKFvrlo29yDBoMvq1VrnCZsSH4jR4zEvXv3OGDA\nAFapUoVVqlThwIEDxcT1c0z37u9T8VdPumeOskiR9J8cg4LaUqMZa7uBoylJdfndd4pf/OrVq+ni\n0i5NL0+nc02eoI6Pj+fixYs5ZcoUHtixg+zaNeUm1WrJGTMyFUl22LDR1OlcaDIVYbFiAbme/GfL\nli00Gr2phNqYSknysFuSp5iYGM6YMYODBw/PciiQp3Hnzh2OGDGab7/9HteuXftMx164cIEajbNt\nKOYogXZUq8tyzJhxdtM3ZcoUOjkNTPU/Ck8eEmvSpC2B0lQiw75LxeW1HgcPHspJkybxs88+5+nT\npzMu3GolJ05MCXUPkG+/TT56xLlz59JoTD0Ul/m5nryMCPAnyDZffDGBBsPrTIqOqVLNyHBS2du7\nFFOHJAemJEc1vXLlim2B1O8E4qlWT2bJkoEZD6PIMjl3btoFS61akbduZah18+bNtqeVuwRItXoC\na9V6JdvX4FnZsWMHO3bswa5d331qHKrMEh8fz6pV69nSfU6kyVSen3zyOaOiopIXoTmauXPnUqXq\nlur3f0BAz9df7263Oo4ePUqj0ZNKgMUw6vVvsXXrziTJhw8fskaNhgSMBLwItKbJVJAmkxs1mmZU\nqT6gJHmkP/9w+7by/7KJj1drOKfKS9xm825SHAMCqbjQkkAICxbMvNdYXsWuRmLgQCVCY+vWrR97\nvfqqYydthJHIOaKjo1m58st0dq5Os7kpCxYszLNnz6a7b8OGrajRTLTdRHGUpEZpwshv376dHh5F\nqVZrWLFi7czFPNq3jyxaNMVQeHqS6Y0hk/z888+pUo1K1UjdoSS5Zem8c4MjR45wyZIl3JvOcNp/\nUUJcvMSUUNZhVKmcqNEYqNUa2LfvkKfOWyQkJPD48eM8c+ZMjkzkL1y4kFpts1TX/xwBI2fOnG3X\nejZt2sRChcrSZCrItm27MjIy8rHvO3XqyXff7Usvr5IEyhJoQSXu1mesU6dZ2gI3bya9vJL/Y+dV\nalbGcALzKUm+3LhxI2VZZqdO3WkylabZ3Iomkwd/++03u56XI7CrkUjqEe3cufOxV3ZDCWQXYSRy\nlvj4eG7fvp0bN2584tDipUuX6OdXhmZzZUpSEbZq1THdeYFnHnO/f5/s0iWNlwn79iX/kw9CiRD6\nElNSki5huXI1nq2uHGb9+vXs02cAmzVrTaPRl87OXSlJxTlsWPqxhJJQAuKlHq6zENBRiUp7n5JU\nk998Mz/D4+/evcty5arTZCpNg8GHdesGP3HFc1aIjIxk4cJlqVK9RWA6AT9WrVrniUMyFouFGzZs\n4Pz58588FJQF5s+fT42mHlNWXS8lEEhv77IcO/ZT7t2+nezTJ83/6q9iJWnG56k2rWONGkEklTmN\nvXv3cv369bx27ZpdtTqKHB9uCg8PzxOx1oWRyDvExMRw//79PHXqlH17q7KspEZ1cUm5qcuVI48c\nSd7FarWybds3aDKVoKtrQxYo4JsmjaujmTJlOiWpNIHxBCQCl5PH1Y1GH545cybDY48fP24LWf4p\ngX8IvEOgdqrG7Ft27pzxBHmnTj2o1fai4vpZlICJNWrUt/sTxf379/nJJ5+yW7d30nVLTkKWZX78\n8Thqta4EzNRqa9Bo9OCGDRvspmXUqI9t1yvpGl0l4EKtNpAvoTvPqTQp/yWzmVy2jJ079WTaObhf\nWLVqI7tpymvkiJFo2LAhIyMjGR4ezuLFi7NmzZocPNix2bSEkchdoqOjuXDhQn711Vc8ceJE7lZ+\n8SJZt27Kze3kRE6YQNrWVMiyzEOHDjEkJOSZHCoSExMZHh6eY+spZFmm0VjANgRzlkDaREaurvX5\n+++/k1TiUv3vf1PYq1c/Lly4kDt37qTR6E6glm2s3ZUqlRtVqqQer0y9/m2OHj02w/r9/WsRqE/g\nEyqOBQ+o0VTgDz/8kCPn+zRmzJhDvT7Qdi3O2IzXCLq5FbJL+bIsc8SIEXRyKkklv7tMYAi18OSn\n+ISJSDEQ/xYqzBYBNVm5cm22b9/Jtir8BwIbKUklk3NZPI/kiJGoXLkySfK7777j2LHKn7Jixacn\nfc9JhJHIPaKjo23DFs2p0/WjJHmm72eeA6xbt459+w7m5C8nMO6TT0hNqp5g1ark4cNZKnfZshU0\nGFyo05lZtGi5DOdcsoMsy9Rq9VRiK8USSJ0S9XeaTB68ffs2ExMTWatWY9sE9QxKUi0aDAUJ/Go7\n1UcEKlCjqUWjsSBdXFrRxaUuy5at+tjYfGpef/1tAgWZ4sJJAl+wVKkK7NLlnVwdEdiyZQuLFKlI\nZZ1BkpY1BF6lWq1NNtRxcXGcP38+x4377DGX1SNHjnD48I/48cefpDu39cEHQ2yxrBoR0FGtdmGQ\nux8PqTxSJqfhxOFwolb1LoHlBOpQparGAgV8WatWEGvVCuaSJcty5Zo4ihyLAnvz5k0GBwdz//79\nJMnAwMBnV2dHhJHIPebNm0ejsQ1T/NRD6Ofnn+P1jhv3pc1zaQr1+k4sX74G43btUoackloajYYc\nOZJ8hhW8p0+fpiR5EThFxXtrLosVC7CbblmWuXjxUgYFvcZChcpRp3uFwHHbkJOJGo2Rrq7eyUH4\ndu3aRWfnQKaE5LhPQJVqXJ0E+hBow/fe68e1a9dy06ZNT121fPbsWTo5eRCYYSsjnkBNAt0JTKHJ\n5MGTJ0/a7bwzYuzY8TSZylBxU02dM2ICgWqsWbMxSWWSvXLll6nRNCIwkmq1F0eNGpN8jRRPubFU\nq4fSbPZOs2Dw5s2b1OvdCEQQII24ymlaZ1pTubaeRFlWQhXb01nS5kgCehoMr3PevHk5fi3yAjli\nJFavXs3AwEC+//77JJUkHe3bt392dXZEGIncY/z48VSrP0p1Y93M0qrcZ8FisdDJyUjgevLwitFY\njR9++CEvnTlDfvyxspYiSVTp0mQmA64tXbrUlj0twTYUdI9arYFRUVF20T5z5hxKUlkCP1Klmkqt\n1oXe3qVYrVpD/vXXX3z48GGaIa5ff/2VZnOjVNfXSsCFwBymjKsXplrtyRo1GmQq6dHOnTvp7OxJ\ng6EClbmQQCopWGsmGx+Valyyu7K9uHHjBuvXb0FnZw/6+1fn7t276eQkEQizGWVPAr2pzK8YGBBQ\nIzkH9rp166hWV2GKN9d5AjrevXuXdeo0Y0qwPlKl+jRNRr+zZ89Sry9CgGyC7byAEsn/DatGwwnQ\nUw9PAg0JNE91rWMJGKjTvcMZM2bY9VrkVcQ6CYHdUfIP+xI4RCCCev3bbNu2a4b7nz17loGBdWg0\nurJChZfS9WCJjY194urouDglH3XKStphBHxoNDanJHkoDeXx42TNmmk9oHr3VjyjnsCOHTtoNBYn\nUIJAMQLO1Gpd7DY3UbhwAJUopIoktXoER48ek+H+ERERNjfhrwicoErVh4CvTZ8HFY8mPYF2BBZR\nkoo9ccxclmW6ufkS2E4gisqK5MpUUrC62baTwCT26TMg0+f166+/snHjtmzUqE26QQxlWWa5ctWp\n0Yy2GYUf6OzsZevhJz2FXqJe78969eqxXr1m7NSpB//++2+S5MyZM23nmLJ4DdBw7dq1rFixHpX1\nNimT9q1bd+aOHTt46dIl3rx5kx4wcQmqpvk/xAQGkseP09XVl8C/VDzDihEYZyuvDYHadHb2fObs\niA8ePOCQISPZsmVnfvnl5DyRQiEz5IiROHv2LF955RUGBCiP5MePH+f48eOfXZ0dEUYid1m6dDnd\n3Pyo05nYsmXHDMfCY2Ji6OVVnCrVHAL3qFJ9Sw+PIslhGh4+fMgmTdpSo9FRq9Vz5MhPMmycg4La\nUK9/m8BKAoWpLNQigcM0Gl0VI2OxkNOmkUZjSuNQsCD59dcZZg2TZZkuLn5UVkiTwA3q9UW4a9cu\n3rt3j0OGjORrr73Fb76ZnyXD4edXjsDBVL3ejx4LS/1f/v33X9av35J+fuWpBKy7ZmskL1GleiNV\n7/cogS50cyvEAwcO8PDhw7x37x4jIyOTje7Dhw+p1Rpt+88k0D5VI72FygT6UkqSZ/Lw8dNQevlG\nWwPbkEajz2OGIiwszDaXIiefu9ncgn5+pajRjLEZjpU0GNxoNJYksIIq1SS6uHjy/PnzPHHihO2p\nZ7Nt375Uq70YEhLC//3vK0pSNQJHCOymTudHnc6Frq71aTK4c22zlryHlKGlh1BzmM6Xe3btIkmO\nHj2WWm1h27U1UKVypbt7KRYoUJQvv9yUh59xbisuLo7ly9egXt+DwHIajU3Yvn23ZyrDUeSIkahf\nvz737dvHKlWqkFRusiSD4SiEkcibHD16lC4uFdJ07s3mqsmN0dtvv0e9vpvtCeEWJSmQK1asIKm4\ns969ezd5TUVkZCQ7d+5JV1cfqtXN0pSZOrwHSSVPRZMmaZ8qKldWYvL8B1mWbTF/kp5SVhEwU6XS\nUKfzoFbbnYASv2rgwA+f+Roobq8BBNYTmEOTySO5t/xf4uLiuHz5cs6aNSvZa8zZOXX+BZla7csE\nOhL4w/ZkMZbAqwSMNBrLETBSrdZTpzPx22+/pyzLtjzi6wiMouLdlHRZrlCtdmH9+q0ynQ8hOjqa\nGk0BAq8QGECgAAF3GgxelCQ31q/fgjdv3mRUVJRtaOmWra4EOjsHcN26daxXrzmdnT1Ytmw1FixY\nNI0R1WiGcNy4z0iS7dt3pkrlTsWbqzirVq3LxMREyrLMzz6bQD+/cixatCK1WonASTbCDh5DuTS/\n+0a8ysLYSEkqyDt37jA2NpYNGzajSlWISnKm0zQaa3HKlOmZ/k0fPnzIsLCw5E7D77//TheX6qkM\nYjR1OvNTswnmBXLESFSvXp0kk40EmeLx5CiEkcibXL582ZYKMqnX/5BGY8okY9GiFW294aR7eibf\neacvd+3aRVdXb+r1BWg2e6VpwP755x9bWIZTtmOW0tu7xOO9fFkm16whixVLayw6diT/E8/J17c0\ngY02Ld62RiuOwEACTW03/x1qtfqnBg28efMme/Xqx+DgDpw2bSYtFgu/+eY71q3bki1bdsqwlxoX\nF8eqVevRZGpEg+F9Go2e3LhxIxcsWESjsRDV6pGUpBYsXLgMVSo3Kq6w7Wy9bDebzqShKBcCO6jX\nF2Tt2sGsWrUh1WoTAQ2VMOLHCERSpepIk6kQP/hgyGOhPeLi4njo0CF+++23XLx4cXLk36lTp9oM\nRFKDuNbW419D4Da12lGsUKEWZVnmJ598TpOpLFWqj2kyNWBQ0KuPLaT08Slj05M0HPchP/nkU9tP\nKLbWHyMAACAASURBVHPFihX84INBnDbtq3TDj5w8eZKVTCW5Dq+l+Z0jzGZ2UklUwUy12pULFy6i\nLMts0qQNVaoWVDyr3qcygb6adeu2TFN+WFgYhw4dyW7deqeJYfXRR2Pp5CTRYCjIgICaDAsL4/bt\n22k2101VfQL1eneGhYU98b+SF8gRI9G8eXOeO3cu2UisWbOGzZs3f3Z1dkQYibzLe+8NoskUSI1m\nBE2myuzR44Pk72rXDqZK9W1yL1mv78rRo8fYcitstW3/jc7OnoyIiEg+TnFZNdNg8KCXV/Enu2/G\nxJCff552CMpgoDxmDCd/PI5ly9Zk2bI1aDQWoMFQmkDPVDd7jK1h1VPJjWx4Yqa2iIgI+viUpFY7\nnMCPlKQ6/OCDzE0GL1q0iCZTk1SN7y56eZUgSe7Zs4dffPEFP/vsM5tXz1ICfxFoQKALFXfajjbD\ndoeAPwFXm+b5VIbofKgkE5pFZZhFS2XYriV1unps1y5lXmnFipXU611sx7vRYGjIQoVK886dOxw9\nejSBwamu0fdU3EyTPsvU6cwMDw/n7du3OXDgQL755ptcuHBhugb2iy8mUav1sz2ROFOrdeWpU6ee\neK1u3brFU6dOMfLqVV7r2pXxqYzDIxg4Tmtgca/iVKsnEDhDjeZjliwZaOu0FGTKU6NMJb9EoC3E\niY5t277B69ev08urOLXagQTmUpJKc+rUGdywYYMtsdMdKk91H7Fx41f56NEjFi5c1pYFbwcNhjfY\noEGLXMthkh1yxEicP3+er7zyCo1GI319ffnyyy+nJAnPIX799Vf6+/uzdOnSnDRp0mPfCyORd5Fl\nmevXr+eXX37JdevWpblxTpw4QbPZm87OHejs3ID+/tUYGhpKs7lyms6/2VztsfHyuLg4hoWFZT7E\nx9Wr5BtvpOlt3oWWw9GXRiyn0ejBrl27UqerxRSPmn22XvltAteo0VRIzoGRHsuXL6ez86upqrhH\nrVafqUihI0eOpErlT6AcgU4E/qFe75xmn0mTJlGjSR0B9bLtyaAAgQOpts8jUIjAtFTbfrYZlaSG\n3ZVK6Iw5BLyoVmuZmJjIc+fO/SfF6A8EilGr7cfBgz/knDlzbMbjLyoTv69QmVRPctG9TicnI9et\nW8f/t3fmcTZX/x9/3XXu/dx7586+mBnLLJYxjEFj32PsRNbSQl8iRUmkhMquRFQoRZIiFUIpS0jp\nJxQjW0PW7PuYuTP39fvjnJm5E2NrGGPO8/GYB/eznM/5nDvzfp9z3ptOZ5MKy4eRkRWv+l1Nn/4+\nzeZyBPYSOESLpRaHDx+Z5zgNHjyMPmYnXzQH8Bh0ub7POUYHoyzefO211+ntXTmX4rLbo/nDDz/Q\nbPaj8GTLUhJlKYoQnZKTgiTqdFbqdJ51KbbT6QzlkCEv898R3E5nKEnhyfXgg4+wYsU6fPLJ/tes\nIng3cVu9m86fP5/tvjdv3rybftCNkpGRwaioKKakpEjf6fgr9nSVkii8HDlyhJ988gkXLlzIS5cu\n8dChQ7RYfCmMtZSCwy//cuWsXUtWqZJLuBxBMPuiGZ0WH+r1YXJ22U0KQ889/Lls2rRDnk3Pnj2b\nNlt7j+vP0mAwX3eL6u+//5YrhJEE/iDwHIFwNmzYOtd1Y8eOpV7fxaP9LQTsUuBP9hB83SjqXE/w\nuHYxRd3srPMOivQT+yhcYs2MjKzIMWPG0GZrQGAaxVaSiyII7w0++OCjHD9+PIWx25die6uYbKsm\ngRcIhPLJJ/vSyyuQYhVDCq+q0nzuuStLhLZo0Zme7qzAClaqVO+q47Rq6VIONPvzCAJzfX/rUIM1\njIn83/968ezZs9y6dSs1rQRzVgwXabEEcsWKFdTrnQTayPHoyZzVVlZzqym2HHt4HDtETfPjjBkz\nqGkNPBTiLJYvX/36v3N3MfmqJM6fP88JEyawd+/enDp1KjMzM7lw4UKWK1futmaB/emnn5iUlJO1\ncfTo0Rw9enTuTislcU8xduyb1LRQOhztqGnFOHr0hPx9QGYmeweV5DaUyCVs9sOLT+BdGvEJgcYE\nSuYStAbDi3z88d55Nnvs2DH6+YVRrx9J4FtqWmM+/PAT1+zK5s2baTY7KVxTc2a+en1gdlLNkydP\nsnr1+2XlNY3AUxTeWCXlv+vl8WYUWz8VCCRJAfgegU8obBhhFPmeyhFYRzGDLiWV0ykCn0kXVRtF\nkF08gQQCdprNpRgSUloarR8g8CGBRrLNGRRbWa8R6MM2bR6i2KI7Kd/nDIHebNjwyrTtPXo8RYMh\nJ3OvTjeJSUntc1+UmspLY8fyrN2e6/tKRhl2gJ5i5TeNBoMPP/jgI7rdbiYlPUC9viZFwF4Vms3+\nHDhwII3GPhQG/KbyHR0UtomsZsfKcfST77iBVuv97NHjKaanp7NBgxa022Pp7Z1EpzOEv3nkDiuM\n5KuSeOCBB/joo4/yvffeY7t27XjfffexTp06tz2B2vz58/nEEzl/aB9//DH79u2b6xqlJO49NmzY\nwLFjx2bnM8pv5s79lHZrMXZFN+6GTy7hkwI9+6Ek7YiQM+YO1OurU6/3Y3BwDAcNGprnFtLevXvZ\npk1XVqnSkEOGDL+mv/yxY8dotfrLWWukxwz1PL28fHno0CGSZIsWHWky9aGIwt5EsXJwEFjoocBq\n0mCwEdDo5RVKscL4mEAnKdQTaTLZCIymSO1BKdQ94xa+o7BT1JMKopQ8r9Fg8JbKpDxztuMuSeX0\nvsfwzWbTph1osQRTRFFXJWAhoDE0NPqK0rd///03/f3DabU+RIulBx2OoBybxPnz5OTJvODrm+v7\n2YkodsUc6vEpcyrRNSMwkBaLL48ePcrx4yfQZCpP4XzwPnW6N1iqVFlaLN1kM5kEXpXjGEoReZ0k\nld4eOXY+LF68AgcMGJL9PR4/fpxTp07lBx98UCi8l65HvioJz9QbGRkZDAwMvOkC5rfCggULlJIo\nYqxfv55OZwgdjvK0WHw4fvztiX799ttv+cgjvfhM7378qHZd7v/XHvdp6PhlmfJ8vEkTms2BUohu\noabV5HPPDb6pZ2VmZvLNNyexefNO7NPnWR4/flzWX2gjBVZzKaQmEkhg27ad+fzzg9mz59PSDTbF\no2vD5Ux9rvy8mWLVsJjAGFqtvtTrvaXgWyiv1yhsF7M92ukh2zkij4fLmXdPii2mfwhcpk5Xl3p9\nHYpCP56ZZzNoMvnTYilO4WiwhJoWwa+++opff/21bDuBIt1FBnW6buzaNffK6tixY9yyZQunTJnC\nyZMnc//+/cJ+9MILpE9u5b0bUeyGqjTASYcjUdo8gglEUATCpWXbr3r1eoa5bTKr6ecXwYCACIqV\nWA0Kz6ZXCcQyIKAEdTorxRbcCgLlWKZMpVw2tKzIdadT5NMaMWL0v7/mQke+KglPl9erfb5dbNiw\nIdd206hRo64wXgPgsGHDsn9u1OdbcfchIoSLSYEnjIOaFsotW7b8p3YzMzN54sSJPFcAs2fPpmZo\nzl54lzsRk0s4ufR6fogqjMs25v4fASdr1mycy+vqWjzxRF9qWi0Cc2gy9WXx4mU5depUWiztZJtp\nBF4nYGViYk36+ITSYBhAYIJ0ee2XPQO2Wltw0KBBDAwsTqMxy7V1dHaXLZb2MsPqBArX2EcJBNDL\nK4omk5N6fX05gzaxZMny1OvDpbDd4PHajzInt9J0irKgFygK+LxEYC2Nxm5MTGzADz74kBUq1Gax\nYuUYEVGGiYn3c9SoURQeVe8S2E+xvbWCxYuLyWZGRgY7d36cZrM3LZZAJiY24PmVK4VzgWfiRoB/\n6a18HB/QKA3OVmsxzps3jzt27KDF4s2cRIm/UtP8eeLECX744YfUtPso8jf1JmCnwRDEgIAS1Ov9\n5ftm1R05R4vFn/Pnz2dMTGX6+0ezfftOuWxJmZmZdDqDpQIhgSPUtLB8qzx4p1i1alUuWZmvSkKv\n19Nut2f/GAyG7P87HI7/1PFr4XK5GBkZyZSUFKalpSnDdSEnK0guL2F96tQpms0OTxlBh6PDf0pp\n/fPPP9PfP5xms5MORwC//fbbK64Rld+qEsikDplsjRlcq9PnElYEuAZ12A3P0oqqNJt7sGPHx677\n/LS0NGlPOJPdlN1+Pz/44AP6+4dTr3+Fwm8/gTExlTh48JB/eTGtoE7nQ4fjQdrt1VilSl2eOXOG\nlSvXoabVy1YCItbDTU2rT4PBSrEtFSJXBSYCvjQYQilyJm2X/WktFYaNwsMo65kDKVYgLoqtHC8C\nXQkMptivj6Fe789ly5aRJCdMeIsmUxjFdlRZeX0ohROAP8Wqxsny5UWc1cSJk6lp9WjFMXbFbK7T\nBV8x1qxTh4emTKHNEsAcR4ZNtFic2Wngv/rqa2qaHx2OMtQ0P375pahH4Xa7+cQTfanXe1FsSZ2V\niuQFCo+rKv/6HSt9TdfbkydP0mz2/tc9DxZYqvX84p7J3bR06VKWLl2aUVFRHDVq1BXnlZIoHPz6\n668MCIigl5cPbTY/fvPNN1dckzNj+17+MR6lpoXf8ozt0qVL9PEJZU5a6jXZabk9cblcrF69ETWt\nMXW6l6hppThu3Jvkhg282Lw5M/4lwM5A47vowGaBJUXg3jVITU2VSuISc5RES86bN48pKSns1Olx\n1qrVnKNHT2BGRgaffXYghb0g63FbGBISw08++YSLFy9menr6VeMqgGAaDLVpsYRSp3NSGKwvS8F9\nvxT6wQRaerS9UyoYbwpD9GaKLSo7cwzbDtmGSSodoVB0uqc4fvx4kmRgYEl5/Sr53YVRbHE5PQT8\nOup0Vi5ZvJhDGjbne6jLM/DONa7pAI80akT++mv2+I0bN5Fmsx/1+gRm2Uc8gyzPnj3LzZs385ln\nnmdcXG0mJbXPLtFqsTgJjPF4xC4KO4sfxdbePgKvMSKi7DUr9WVmZsoV7hLm5wq3oLlnlMT1UEri\n7ictLY1+fmEUkbkk8BM1LSDbOOvJypUrPfZ+Azh8+JUTg+vhdru5YMECduv2OL28ApiztUA6nbWv\nuiWZlpbG6dOnc9iw4VesNpKXLOEbBjOP/stuQYCsWJF86y3y4ME8+9O2bVdara0IfE+DYSQDAiLy\nLIq0YcMGmb78KwIbqWk1+OKLw3JdM27cOJpMnkFtp6nTedFkKkWRWmQic4yylT2UyV9ylp/1eSGF\n3cBMYeQtT2F38CfwGIE3pVKYSrHdNE8qkAUEwhkTU5ZfffUVLZZiFKk/svrziRTG3hSG8B0MwWEO\nhMYdV1mhHYeVo1CWYZhLuz2QR48ezX7XFStW0MvLn8AQCtfcCAKv0OEI4kVZwrZLl+60WpsSWEWd\n7k06nSHcuHEjdToTRSxHljvsG7JPXSlWE05qWugNxXqtX7+e3t7B2bayceNuPJXH3YpSEoq7hj17\n9tBmK5FLNjidDa+69UOK5f369etvOVBzyJDh1LRychbZmGK7I53AMVqtQbnqD/wbl8vFF14YysjI\nBCYk1OOcOXMYHl6OQB8akca2+IKLEXbF6oIAWaMGOWECmZLCc+fO8aOPPuKoUaM4aNAg1qnTgGXL\n3sfWrbtctVCOJ0uXLmVcXE2WKhXPl19+9YrtuY0bN1LTQii8nS7SaOwlbRf3UbhufkexQhhAwDO2\nIo3ChtGcIrrcJpXRYCl8B1IYdJ0sUSJOzp6D//Wa5SmM4AkEXqTBEEVNC2bueIPJBHxZCj/yWTzA\nH2Fm5r8UrAvgItj5AErQhEgK28WVvxetW3f9V9sLCDSlwxHD5ORkZmRkyCzBZ7Ov0bRODAuLlAqt\nHkVsR3X5vmU8lGQGrdYQpqSk0O12c+LEt5mY2JhNmz54Vc/N8+fPc8uWLbmUWGFGKQnFXcO5c+dk\njeZd8o/zBDUt9Kqpw/8raWlpNBotzEkul0kgllZrLWpaOF966dVr3t+37/Nyr/8XOXO2SSHzjYdw\nmc+29zUkX3+djIy8UlkA/N1s4Uv6YJZHIEWSuiq02wOvu0Xx8cefsHbtFmzcuB3XrVuX53Vz5syV\nCQ9N1Ot9CcykyOxaimIF4UWxQnBSrOBSpGJIojBq+0hlYaDYGvKVP1UJ+LJSpSocOXKkNI4fI3BR\njqm3bP9y9ncpnmUn8Drj0ZvDYeWWqylRgNvhw/FBxfhI47YUnkZWAsny9FlqWniuVCvt2nVjTpZe\nUnh1NaDF4uSZM2e4bNkyuWI4yhwl0YJmsz+BbylWRZXk99iYItAwy403jRZLIPfv389XXnlNZpdd\nwqxkjNeaTNwLKCWhuKuYNu19Wq1BMkgugi+8MPS2PEekx9aYU92NtNlasn///jdk2/D1zfKVzxJK\nz1EEoxmlgBxNq7UVX35ZZCul203+8otw24yKuqpgPAI/fgKNPVCD3WrneOudPn2aS5cuZcuWDzIy\nMoHly1ejxRIhZ8szaLX68/333+eCBQvyXH20b/8IRSqOrMfVpdhieYDAg7LvJSgq4flKpaFRbEm5\nqdcHE3hEKsVXKWwLdSg8mVrIa72lwjFTBPHdJ5/lZiR2szu8+TGMPADtqu+/BwaORzwT0Z6Ag0aj\njV999ZXcVutKsVrpSIslkk8+mTvf1Zo1a2gy2SkCBR8k4EOz2ZuzZn3ssTXXRgr/WQT60N8/ghZL\nEMXK6R8KrySnVKA+FAGHs2k2N2eTJm3pdrsZEFCSwqAvum0w9Odrr71+67+IhQClJBR3HcnJyZw3\nbx5/9TBM5icnTpxgr1796O0dTr3+CQrD7Ex6ewffcFbO4OAo5s6FlJXm4jzFnn4Y4+OrXT3Zn9tN\nbtnCRZWqchssVxWYBHjK15cb4uLY1+rNKvoYmhBAUevhVYpZ+j6K2X5xGgxB9PZuQ00L4KJFi7If\nlZaWxh07dvCBB7oydylQB4XL6qcUNgWRnNBstrNGjfvltpS/VARD5PlMj/tjKOIIsoL7lkvBep5G\nnGMc6vFxWDgLNfg3QvN8x99g5lA0ZEVdeYpZfHsCz8v31Dht2jR26fIwS5Ysx9jYKuzbty9Xrlx5\nRWK8Tp0eo5dXTQJTqNc3YfHi5bhnzx6SZJ8+/SmC9jpSbH8lEahLH58QNmjQnFZrcwIf0WxuRJ3O\nQbHS2kmgEb28gvjyyyOyv8egoEh6ZqQ1Gvty5Mibt4cVJpSSUBQpLl26xMjICjI6+UPq9SVpNgew\nUqUbywywZcsWNm36IEuWLC/dOSfRYOgnZ9KrPOTfG+zZs+812xKFeYIZg5fZG1O5AO14Mo9ZNgFe\nhpm/wsppaMxeKMVqCKE/HqBIIRFCsVIYTC8vO8+fP8/du3ezWLFo2u1RNJudNBqdFCklpsoZ808e\nzb9AwMi6de+nxdJRCn8Xgdb09Q2nwWBnThR2pnze03TiNGvjR/bFWL4PA/8PlXkZ5rwVH/Rc7mXj\nIKuNJWGh2KILo4i4rkixQvmCwlZSU56LIzCUmhbAtWvX8sSJE1y1ahWTk5N5/vx5bty4kV5efh79\nc9FuL5Od8PG5516QisdMT+cEu70158yZw5Ejx7BNm4dYv35D6vUDPbq7n97eIbm+M1HMqByBudTp\nRtLbO5j7/pVW/l7jVmSnEQpFIWXt2rU4ftwOl2sKAB3c7k4AgvHDD1/Bz8/vmvfu3bsXtWs3xoUL\nrwB4HF5e/VCx4qdo0qQ+Fi8uh507D2RfazZvRVhYzDXba9euHfr0WYspU97EbjyHd1EeeixDLVsA\nql1sgUY4itr4FnZ5vRfSURVAVazwaOVLnIMDf8GJv/A0/kIZ/JUWjOeiYpFus8PvcDsAz+AUiHTU\nhl4/AgEBxXDpkg0XLhg82jEAaIYNG36ByzUdGtLgxFk40QQ+p39EKGwojnIoiRiUQDJK4h+UxBT4\n4u1/vdVvuT6d1emxhnqsxgisQjP8jgi400qiVatmOLisOJDxhrzyBQBnAYQB6AlgBoA2AFwAagCo\ngEuXJqBPn4HYt+8v6HQxuHBhB9zuVAA6AGYANeW143H5shc+/3w+QkJC4HBY4eU1CWlpBJAKwCKf\neQFpaWk4dOgfZGRkwtfXF2bzIVy+nNX7g9C0rNEXPP98fwQG+uPTTxfC398bw4f/iBIlSlzzey6K\n6KR2KVTodDoUwm4r8plvv/0WHTq8jvPn18ojaTCbg3D48F/w9/e/5r1jxozB0KGHkZExWR7ZBV/f\nhjh16iB+/fVXNGzYAm53C+h0/yAo6G9s3rweTqfzun36448/MHPmbJBAjx6PoGnTDjh8eAGAOOiR\niNJogsoohypYh8r4CJXhgjcyb/rdL8OA0zDDhcsg9CAANwJAZII4BT1C4MRhOKGDETf/t3IKwDaD\nE3/ondhuOgfGl8PPFy5gyx9pAHZ6XFkcJtMluFwfQCgCAFgEYBqAXgDaA7ADuAigOYBAAGUAxMNg\n6IDMzDkAWkIolTgA5wCMAFAXwJsAtgA4DbNZg8t1DDpdGPR6C9zuvdDpIpGZ2Q9m888ICfkRmZkZ\nOHasKVyuRFitk6HX74fL1Qzp6VHQtPcwY8YEdO3a5abH4l7iVmSnUhKKQsvFixdRrlwVHD3aGi5X\nA1gsM1CvHrB8+cI87/n88/kYNOg1nDhxCJcutYfbPV2e2QZ//xY4cWI/AGDfvn347rvvYLVa8cAD\nD+D06dN45pkX8ddff6Nu3WoYN+5VWK3W6/bxqacG4MMPtyM19T0AvwB4AlZrIFyu44iKKoNOHVqi\nRdkYjH+sJyIyHIjEBUQiDZEIRykchhfS//tA5cEl6LAPUdiHffgb3tgHfySjNbagAQ7rv0X1GtuR\nmBiPiRPfAXA/xCz/BwBTATwI4BMAwwEUB+AF4FvZcjsA1QF8DuAEgLUASgDoA+ArAK/Dap2G1NRt\nEKsLvbzvUQCbAfwuP7sAOAB8BqAHgEEA/CFWKjZUq1YSoaHFUbJkMVSoUAb9+n2OCxeWy3tPQ68P\nxquvDsPZsxfQokVT1KtX77pj8vPPP+PPP/9EbGwsEhMTb3pM73ZuSXbm43bXHaOQdltxGzhy5Ai7\ndn2CiYmN+dxzL1615GUWq1evpqaFEnhWGms1iqjkT6hpsRw9evxV7ztz5gyDg0vRYBhGUYnsQSYl\nPXBD/UtLS+MTT/Sl0xnKkJBovv/+TCYnJ+fyu9+zZ49M2b2AIlVGOQKtqMM5huEnVtWFsGtQCDvA\nxJ4I5WBYORYWTgc4E4/yQzzKj/AI5+giOUen5ycwczbKcQp6cyQG8AWEsxcc7AwvNkM8q6IpA+Ck\nMGbPZEBAcVqtwcydDHA1y5atTqPRj8JNtrj81yRtIEZpON5OEY9SksIt1kTARrPZj97e/gRe9mjz\nbwIaw8LKccSIUQwOjqSI8SCBQx42iyy345PSvtGXuYv/LCXgpN3uwylTppAk586dS7u9jcc1F2kw\nmLON1GlpaXz11VFs3borX3ppeHZQnidDhoygppWgzfYwNS2cr7029oa+48LErcjOQiltlZJQ3Ap9\n+z5HkUo7miIB3WcE/BkXV5MzZ36UZ/nJRYsW0eFo5CGA0mgy2a5Ig32juFwu/vHHH9yxYwczMzM5\nbdo0atpjHu2foPAOyqphHSgVR6g0BP8ojcLFKTyaSOA4bbZILl26lOHhsRRBd1ntvUMRm/CQhwB+\nn4A3Q0Ii+cMPP0hjdjOKWIhMAt1Yrlw8RfR2VnqRVyi8nrbLvl3weMYDss0LtNtjuXz5clkfu4nH\nMxcRcLJ+/SYsXboSTSYnc3I+WShiG8pQuL1Okf9PpAiOy0pomEmgNkX09EACobzvvro8ceKEzIs1\nisAPtFpbsl27h0mKaPwmTdrSam1BYBYtlg5MTGyQK2AxJSVF1mc/Jp9zmF5ePjx8+PAtfcd3K0pJ\nKBTX4KWXXpHCdp6HcPuCdeq0vOZ933zzDR2OWh7C7jyNRivPnz9/zfvcbjfPnDmTq4znqVOnGBdX\njXZ7NDWtOOvUacqJEyfSaq3v0f5uOVsfTFHTOstd9QWK+AbKc60oPIeiaTI5s+NQWrXqTKNxkGzv\nMkUepzJSqP4pj29hUFA03W43T5w4IeMS2kiFFEa9PoAtWrQlMM5jrP6kWE08S+Em3IginfgoKeiP\nEfiLFosPjx49KutnBElB35nCVXcogbYU8QsRFLEZVSliO0LkNXqKwke+8rNOKqX3KWpc5C6fCpj4\nySefcO/evWzZshPj4+tywIAh2auIvXv30moNYU6qjgzabDHctGlT9veyYcMGOp1VPd6V9PaOu+31\nc+40SkkoiiQul4sHDx68ZsI2kjx8+DDN5gCKoLIsYTCVzZt3vOZ9ly5dYlRURZrNPQnMoabVZ9eu\nPa55T3JyMiMiytBo1KhpPpwz5xO2aNGRer2Doq6Dm4CLRmNLGgx2mc66BUWiv2CKbK33MXepz9UE\nalG4fpaXArQ0ATMfffRRRkSUodkcxOLFy7B48XK028vSbA6hTmen2FoLpyg/2oZAG+r1Tr7wwguc\nPn06W7XqQKu1HoHxNJtbMy6uGqdOnSoFeJar6QipZP0o4i0c1Ol8abWG0Gz2ocPRmHq9L728fOnv\nX5IOR1ZywQFS6WVFWWfINtp5KMbh8po35fOelgrQjyK4sb78fwDFyiJrTNwENOp0XuzcuQvfeOMN\nnjhxItd38eeff1LTinsoWzcdjgq56qifPn2aDkcQc6LsF9LHJ/S6E4HChlISiiLH2rVr6eMTQqs1\nmJrmy8WLF1/z+hUrVshtjhcJvEybLeCGAv1OnTrFZ555ns2adeTYsW/kmfqcFLUTAgJKUJQSFXUP\n9Hofms0PUQStecZgzKFYEVwg0I8GgyZrJgRIZdFQCs0Miq2ycIrZvp0iId8wOQs3U6TsnkGgD41G\nJ+fNm8f69ZvRbg+XgtotZ9O1KbafXqJOF0pNe5gORxAHDBjIBx7oxhdffIXnz59nRkYGw8JipHCO\npliN7KMItvOWSqwUgWgWKxbNatUa0GzuLGf3K2Uf11HU8Y7MJaRFnz0r3P1EsUrJ+jxY9jErhpUS\nXAAAIABJREFUIjpTjl1Wje/5FJHVg2VfphJw0GzuyODgUrmqyGVkZDA+vqZU8mtoMj3HqKiKVwRH\nrlu3jv7+4TQYvBgUVCKXErlXUEpCUaS4ePEivb2D5eyPBDbQZgu4bqT19u3b+fzzg/jccy/wjz/+\n+M/9WLhwIUuUiGNAQAk+8URfNmjQnGLm7hl75qAwzj5BYYgVKwkx0x6efZ3NFsHPP/+cOp1RCttO\nFHYAG4Vx2MT4+HgK+0JW2z/I9v/yOFafVqsf9frXKFYb/+dx7h2K5HcaxcpCHEtMbHTFu+3bt4/C\nGP0/5qwodkrB/IgU4mMIWOjlZZeCO+s5T8l+XqIIpnuEwHc0Gp+QCqAqRVS7i2I7yioV30jZRz0h\nCw+Jn4elwhpGUW7VV75HGYo8U3oC8dTrW3LYsBG53uPUqVPs1q0ny5evyY4dH7sidXwWbrebFy5c\nyNM+VdhRSkJRpEhOTqbDEZNLGDuddbhy5co71of169dLz6AfCOyiyVSRBkNlKbS3McuGIeo9rKAw\nSlehMDoXk8L2D3ndGmqaH222ACmYL1Js0YRSzNqLE7CzS5eHKKrFZb33bjnDPiU/p1OsNmrLz50o\n7BlZK4n6FPaAHhQz+ikEfqbRGHDVEsXDhw+XimqNVEQNpYI5JN8lUJ73JVBNCvNpHopIL885Cfiy\nbdvONBj8KYzaNnncTrEqeYsinYdTjk0vCi+nFbItnbxuB0UCw2oURu1+8vpgAmbGxVW5Y78DhYlb\nkZ36q7nFKhSFgdDQULhcxwDslkeOIj39T0RERNyxPixa9A1SU58E0BBADFyuRsjMbADgXXmsE4Ay\naNiwFjStK8zmEbBaA2E0noGIG5gAoA6AaHh5tUHdurWQmtoXwAMQ8QaPAngJwEYAewEk4Pjxf6DT\nTQHwvXz3/0Gv1wFoBGCdvMcPIv6AACYC+BoiVqEUgO0AkgG8DxG78QKAEdDpLPjtt9/gcrnQv/8g\nFC8ehwoVask3TYMIjKsOEfugA9AbQGl5fgqAeRBheJny8x+y7/EALgPQAKRi27YtyMw8BRFzUR4i\nwC4VwM8A+gGYDyBKPvNTAKEQcRmdIaKwTwCoAr0+DsBWAK8CmCX7Mx/A70hOPow1a9bc3JepuCpK\nSSgKLT4+Ppg8+U1YrbXg7d0SmlYZL744ANHR0XesD06nA2bzAY8jwdDpPoVQECuh02WiXLkQrFix\nBBs2fI/Ro0vi7bcfxPffL4LDMRkOx1JoWjji4wNx8OBueHsHwO0OhhCy6yCUQJJs2wigBb7/fj3I\nJIiUF5UBnIfb3R96/V+w2zsgIGAthFA9DeBJACsg0lechRDicUB2gpASEIrEAbNZg9FoxNNPD8T0\n6b/hwIE52LbteQwfPh6AFcBhAP9AREGHA1gl+9QPQIg8/wqAHfJcGoQS3A9gLoDnAHhhz55ICIVW\nGkI51IcQRb6yTzoAAdDp9BBBdF4A/gbwAYDVAByw272xd+82PPbY47IP6fIZAwHcD7IWNm/efHNf\npuLq3IYVzW2nkHZbcZvYuXMnv/zyS/7++++3dP+5c+f44IOP0MenGEuVqsgVK1bc8L3Hjx9nSEgk\nzebHCbxCqzWYnTt3o8mk0WIJYExMJf79999XvffQoUP8/PPPuXDhQvbu3Z+1ajVnq1btabWGye2r\nRhR2iOfkVtEpiliC7hRZUIfIbZasbadFjI2tzq+++oo2WzkK28FA6nTxjI6uyClT3mXFirWo19sp\njM+XCLxOoCS9vDqySpW6dLlc9PEpxtz2jf/J7aIst1M3hSFak9tVQRR2j4cpDO6Rsm0DhQ0mliJQ\nrilFAF9WmvMeFF5cD1Cvd9Jg6EKRlfVdCnfYIdTp/OR2VpYXFClcajsyPLw0W7RoQ53OiyIILyue\nYxoBP1os3oyLq5Evdqd7hVuRnYVS2iolochPmjfvQC+vhyk8d5ZQ0wKYnJx8w/cfP36co0eP4eDB\nL3HDhg0kyQsXLvDw4cO5YiSuhsvlYqVKtejl9SiBr+nl9TBLlYpjZGQlhofHsnLlmtKe4SP37Z+l\nKMLTVioIzziG/2OJEhVIkoMHv0Kj0UovL1/GxVXLFeG9cuVKWq2BUoiHUqcLY1RUHC9cuECSDAmJ\nJvBzdrsGw0PU6bylYlpKoKdUDOUpvIoiKewnpDBkWymK/QQReJLCPpNVIChF2ht+l8Je1NseMeJ1\nxsQkUNhdGsvzyXQ4wmgwOCkyv+6kcJEtQeCcVEz+UjkN8RiHIxS2jkPU6WbQzy+MZ8+evdlfi3sS\npSQUiltAVLU7ly1kLJZenDx58h159ubNm2m3xzDHPTSDNlvJXBX85s37jBZLGEWE+FIpfDtLwelD\nYdTdSk2rlas29oULF/jPP/9c4alz5MgRenn5EDgtn3mZNlup7OCyDz+cRU2LIDCeRmNvBgWV5Lhx\nE+jtHS6FcpYRfb3sUzsPAU2pJJozxw220r/Ox0hB/xKBX2gyPcn4+JqcPn06Na0GhTuwm0bjYNat\n24z33VdfKhYHxepqlxyvEh7tl/F4n5EUxvWsoLgaXLNmzR35Pu92bkV2qlThiiKPpnnj3Ll9ACoA\nIAyG/fD2rlFg/RF/yzl06tQRLlcGxo0TqbwfemgAkpP/wu+/r8euXUZcvtwRmmZFnz7d8dprQ7Pv\n27x5M2bP/gxWqxeefvrJbFvN+fPnYTQ6kZaWldXWCwZDCC5cuAAAeOyxR1CsWAi++mop/PwC8cwz\nvyAoKAhly5ZG69ZdIGwHlyBsInMB/AhhWL8POt1UWK0OpKZWB7kEwp6wS15TF8ASCBtFKQCvAwBc\nrqrYuTMcxYoVQ5s25bBwYXEYjQ6Ehjrx559nceyYH8R3sw/C9vATRLK/swCaAugCkWgwHCIh4HkI\new4AXEZGxuEbyuCryIP811W3n0LabcVdyvTp71PTwgm8QoulHUuXTrhqArjbwdW2m+67r/51t6m+\n/PJLalopihKkO6hp1TlixOjs89988w01LZjAOOp0Q+hwBGXXb3a5XIyMrCATFqZQp5vCgIDi192S\nadCgFXW6rIp4brnl1Zw6XTsCFur1ZkZGVuCKFStosdgpXHzPEPiOwqah0de3GKdOnUqLJZo55WYv\nErDTai3BypVrc8eOHdy1axeXLVsmt40mUsTC3Ee93o96vQ9zyrRmtZFBIIC9ez/FJ5/sT5utAoGX\naDJVZrlyVThw4GA2adKGPXv24rZt27LHYdq0aezf/3nOnj37no2N8ORWZGehlLZKSSjym5UrV/Kl\nl4Zy0qRJ2Xvzd4qzZ8/yqaeeY61azfn008/fUCqITp26Uxh4s7Zw1jA2tgbdbjfT0tJYqVJdAl9m\nn9fpXuZTTz2bff+BAwdYr14L+vqGs0qV+tyxY8d1n1mqVDz/HZQXGRnPp58ewD179mQr1lmzPqbJ\n5EsR75BJ4GtmBcd16PAw9XqzFP4tKIzMNSjsG7UJGGkwWPjuu9M5dOhQAo96PC+FgCZrU7enMOpn\nbdNl0maL5pYtW+h2u/n008/IpIVtKYzgHSjiQcrRaHRy1qyP2bRpO2pafQKjabPdx8cee/LWv8RC\nglISCkURoU+f/tTrX/QQoLNZtmwifXxCqNMZaDIFUWSLzTr/Flu27HBLuYgOHz7MFStWsFWrDnLF\n4yJwmpqWyGnTZlxxfYkScRTGZCdFDeoqFNHWDup0pSi8tE5Q5IGqSpEixZ8i4C+TwE5qWhj79etH\nvb6bxzvsptHoLZVMQ6loOhP4hjrdw/TxCedvv/1GkjItykapKD2TMx4jYKbJZJUrsaykf+fo5eXL\nQ4cO/efv5m5GKQmF4i5kyZIl/N//+vKll17h8ePH86XNffv20ccnlEZjb+r1L9Bs9qFIu22kiHRu\nSZ2uDIVxeQkBH2paJH18Qm8oV5Vn3222ADqd9Wm1BjMioizNZgeNRit79nzmqls0ISExFF5LnSk8\nkLJSa2ymMD5nCewfCNSlMLyb5daUUAgmU38OHTqUdnsARb3sBOr1xfjyy8NpNgvPJaFoWlFsZdUh\nMIgGg4M9evSkweBD4FWKGhn3eyiatOzVisOR6HHcTZutJHfu3Jkv38/dyq3IThVMp1DcRqZOfQ8d\nO/bFjBmRGDfuH1SsWB2nTp36z+2WKFEC27b9ihEjIvDkkxfhcrkAOAG0hTDw7oJefwQhId2h0z0K\nYCIuXdqLM2cmoU2bGyvh6XK50KnTI7h4cTHOnl2F1NTfcfLkeaxYsQRnzhzHtGmToNPprrive/eH\nIIzHNSAitE0AMiACA90AgiFKlq4AcAE6XUcIA/evsoVMmM2b4HQ64XYTwkA+EkZjIEigX7/+0LSW\nAL6BMJi/CWEYH4PMzMH44IOvkZk5FsByiEjsnyCq6W0C8BiAEHh7O2G1HoNe/xaAvTAYhiE42IHI\nyMgb/QqKDrdBWd12Cmm3FUUQX98wAluzZ6xWaydOnTo1X5/x5ptvUgS2ZQXAnSDgTZPJyilTplDT\nunvMmDOp0+mZnp5+3XaPHDkiC/HkuK96e7fm3LlzOWnSJPbv/zwXLFhwxWoiMzOT5csnShtDgFzJ\nxMr/O6WdYQB1Om8+9lgPrlq1itOmTaPF4k+7vSvt9qqsW7cZR4x4lQZDf4/nJ9PfvzjdbjenTZvB\n1q27UqcLoChmRIoMuDa5sihJYdTXKPJg1aNICtidgB+/+OIL7tq1i9Wq3c+AgBJs0KAVDx48mK/f\ny93IrcjOQiltlZJQFBY0zZfAYY9tlL6cMGFCvj7jrbfeokgC6BmLEM9+/Z7jmjVraLNFEjgujy9g\naGjUDbW7c+dOWq1+FIZnEthFqzWQ5cvfR6u1JYXBNzZXbEYWly5dYrlyVaXA9iaQVQTpLIUdYhbN\nZmeu7bc9e/bwo48+4uLFi5mRkcHRo0fTZOrj8U5bGBhYKtdzYmOrUCT8+4AiMnu3vPYjAjG0WIL4\n1luTqWmB9PZuTas1gv37D/pP412YUUpCobjLeOSRXrRam8n9+HnUtACOGzeOnTs/ykGDXrqiQI4n\n+/fvZ2JiQ1os3oyMrJhnfYNz587RYHBQ1MgmgR9pMjmzo6wHDXqFFksAvb0r0+kMuaE6CZs2baLd\nHkiDoZ2c/QfTbHbwmWeepd1elTleRUdpNFquqM1AkrNnz6amVaEIetvtIexHE3iSJpP1qllnPd/f\n2ztYpjufQ00ry/HjJ+a65sCBA/TzC6MIqmudy8YAeDEhoRbdbjd37drFL774gv/3f/933Xe/l1FK\nQqG4y7h8+TKfemoAIyLKMz6+DuPiKksjrYNACYaGRvL06dNX3JeZmckSJcpRr+8rVyKf0+EI4rvv\nvst33nnnCpfVDRs20OEIpsFgo6b58dtvv811ft++ffzll19uOD1FvXotKdxTSSCVev0TfOyxXlyw\nYAHt9hYewjgjz3rfbreb//vf0zKtyBsehuNaNJuDOHz4qOv2Y9euXXz44f+xWbOOnDXr41xbW+vW\nrWPTph1Yr14r9unzFK3WSLlSIYF1NBrtVx3booxSEgrFXczs2bMp0kecpAj+6k29Pprvv/9+ruvc\nbje7d+8j99NjKKrC7aZeX4teXnG0Wp+gpgVcoQjcbjdPnTp13UC8GyEurhZzV9D7gG3bPszBg4fK\nfr1PYBeNxieZmNjgmm39/PPP9PePoLd3dZrNxRkVVZGLFi36T/375ZdfqGkBBKYT+JSaVoING7ag\npkXQ6UyipgVw6dKl121n165dnDFjBhcsWHDd8rf3AkpJKBS3gXXr1jE6OoHe3iFs1uxBnjx58pba\n6dnzaYoEdVmCdxuBYL799tu5rlu8eDFttlipTESMg6jsVpzAWnlsOSMiyuXH612VV155jZpWh8B+\nAsnUtLJ89dXXqWlhBL6lcDkNo8nkd80tsyzOnTvHNWvWcNOmTfkS2fzII70IjPcYy29YsWId/vbb\nb1yyZAkPHDiQ6/qjR4+yWbMHGRwczZo1m3DXrl38/vvvqWkB1LRHabfXYpUqda+6bXYvoZSEQpHP\n7Nu3T1aK+4LAAZpMfVizZuNbamvMmHHU65t57Oe/Tb3el3v27Ml13ciRI2kwDPQQgCcJWAhUYE6M\nwRHabP758YpXJSMjg337DqDdHkinM5SPPfYE7XY/isR9OQbyvLaabjePPvrkFUoiPr7uVa/NzMxk\nuXJVaTQ+T2AH9fqJDAgozrCw0hQJE4XXl6Y14YwZVwYH3ksoJaFQ5DOzZs2i3d7ZQxi5aDCYmZqa\nelPt7Ny5k8WKRVGn85HbRzVoMHhz3rx5V1w7f/582myVmZN+eyb9/UvQai0mVx+pNJt7slmzB2+q\nD8ePH+eOHTtuera8c+dOubUzjUA4RSpuElhGX9/QAsl5lLPdNI3AXGpacX7yydyrXpuSkkJNK0bP\nmhTe3rXo5eWgZ01uvX4QX3vttTv8JncWpSQUinzmyy+/pN1ew2P2v49ms3bT+/5ly1alTjeZIvp4\nHs3mQC5ZsuSq17rdbnbt2oOaFk6nszr9/MK4detWzpjxAW02PxoMJjZo0JKnTp264eePGjWeXl7e\ntNujGBAQwa1bt97wvTNnzqTN9rB8/zEE/AhE0eEI4o8//njD7eQ369atY7NmHdmwYVvOn78gz+v+\n+ecfms1OD6O2izZbaSYm1pUutukE/qSmhd/zKcWVklAo8pn09HRWqVKXmtaMwCvUtFJXuGFeD7fb\nTb3eQOBy9qzVy6sPJ02adM17tm3bxh9//PGK7ZybVVDr16+X9SEOyufPYkRE2Ru+f/HixbTbKzOn\nMt0PNJtt/8lzKD09nQcOHLhjxuLHH+9DTbuPwHharUmsV68Zjx07xtq1k6jXm2ixePOdd6bdkb4U\nJIVGSXz++eeMjY2lXq/PLnSSxahRoxgdHc0yZcpc4b2RhVISijtJamoq33nnHb788tA8fyevR2ho\nNHMigy/SZqvIxYsX53NPr2T48JE0GEwUVeU8o64NNxR1TQr7RIMGLWmzVafF0odWawg//HDWLfdp\n5cqV9PYOotUaQpvN74a8kP4rbrebH330EXv37se33347l3JKT08vEmnCyUKkJHbs2MGdO3eyfv36\nuZTE9u3bGR8fz/T0dKakpDAqKuqqsyalJBSFjXXr1tHhCKLT2Yg2W0l27drjtgumBQsWUNPKUlSP\ni2ZOAr1vGBhY/KbaysjI4Oeff85JkyZx48aNt9ync+fO0eEIJPC97Mt62mwBPHbs2C23qbhxbkV2\nFkhlurJly171+Ndff40uXbrAZDKhZMmSiI6OxsaNG1G9evU73EOFIn+pVasW9uz5A5s3b0ZAQAAq\nV6581eR4+cnKletw6VIPAB0hEuGVhU4XDLv9CL74YsFNtWUwGNChQ4f/3Ke//voLOl0QgEbySE0Y\njVHYtWsXAgMD/3P7ivznripfevjw4VwKITw8HIcOHSrAHikU+UdQUBCSkpLu2PMiIkLg5fUr0tII\nYAIAf0RHz8NPP21HQEDAHeuHJ8WKFUN6+iEAewFEATiItLQ9iIiIKJD+KK7PbVMSjRs3xtGjR684\nPmrUKLRq1eqG28lrtjV8+PDs/9evXx/169e/2S4qFPc0ffs+hdmzG+DAgQYAQqDTrcK8ecsKTEEA\nQGBgIN58cxyef74mjMaqcLk2YcSIl1G8ePEC69O9zOrVq7F69er/1IZO7lMVCA0aNMAbb7yBypUr\nAwDGjBkDABg8eDAAoGnTphgxYgSqVauW6z6dTocC7LZCUWi4fPkyvvnmG1y8eBENGzZEeHh4QXcJ\nALBr1y78+eefiI6ORmxsbEF3p8hwK7KzwIsOeXa4devWmDdvHtLT05GSkoLdu3cjMTGxAHunUBRu\nLBYL2rdvj0ceeeSuURAksWfPHuzduxcHDx4s6O4orkOB2CS+/PJLPPPMMzhx4gRatGiBhIQELFu2\nDLGxsejYsSNiY2NhNBrxzjvv3HbjnkKhuLM89dQAzJ69HC7X/TCZ3kOvXu3xxhujCrpbijwo0O2m\nW0VtNykUhZM9e/agYsVaSE3dBVFu9RQslhjs3r31rlnp3MsUyu0mhUJRdDhx4gRMpggIBQEAfjCb\nQ3Hy5MmC7JbiGigloVAo7hjly5eHwXAUwBwAlwDMhNl8HqVLly7gninyQikJhUJxx3A4HFi5cgki\nI8fDYPBFTMwUrFr1DaxWa0F3TZEHyiahUCgURQRlk1AoFApFvqKUhEKhUCjyRCkJhUKhUOSJUhIK\nhUKhyBOlJBQKhUKRJ0pJKBQKhSJPlJJQKBQKRZ4oJaFQKBSKPFFKQqFQKBR5opSEQqFQKPJEKQmF\nQqFQ5IlSEgqFQqHIE6UkFAqFQpEnSkkoFAqFIk+UklAoFHcta9euxcMP90T37n2wdevWgu5OkUTV\nk1AoFHcl3333Hdq27YbU1CEAUmGzvYG1a79DQkJCQXet0HIrslMpCYVCcVdSu3ZzrF/fDUAXeeQN\ndOmyA3Pnvl+Q3SrUqKJDCoXiniEtLR2At8cRBy5fTi+o7hRZlJJQKBR3Jb17PwxNexbAdwC+hqaN\nQK9eDxV0t4ocxoLugEKhUFyN7t0fg9vtxuTJr8FoNGLo0ClISkoq6G4VOZRNQqFQKIoIyiahUCgU\ninxFKQmFQqFQ5IlSEgqFQqHIE6UkFAqFQpEnSkkoFAqFIk+UklAoFApFnigloVAoFIo8UUpCoVAo\nFHmilIRCoVAo8kQpCYVCoVDkSYEoiYEDB6JcuXKIj49Hu3btcPbs2exzo0ePRkxMDMqWLYvvvvuu\nILqnUCgUCkmBKIkmTZpg+/bt2Lp1K0qXLo3Ro0cDAJKTk/HZZ58hOTkZy5cvR58+feB2uwuii4WG\n1atXF3QX7hrUWOSgxiIHNRb/jQJREo0bN4ZeLx5drVo1HDx4EADw9ddfo0uXLjCZTChZsiSio6Ox\ncePGguhioUH9AeSgxiIHNRY5qLH4bxS4TWLmzJlo3rw5AODw4cMIDw/PPhceHo5Dhw4VVNcUCoWi\nyHPb6kk0btwYR48eveL4qFGj0KpVKwDAyJEjYTab0bVr1zzb0el0t6uLCoVCobgeLCA+/PBD1qxZ\nk6mpqdnHRo8ezdGjR2d/TkpK4s8//3zFvVFRUQSgftSP+lE/6ucmfqKiom5aVhdI0aHly5djwIAB\nWLNmDQICArKPJycno2vXrti4cSMOHTqE+++/H3v27FGrCYVCoSggCqR86dNPP4309HQ0btwYAFCj\nRg288847iI2NRceOHREbGwuj0Yh33nlHKQiFQqEoQApl+VKFQqFQ3BkK3LvpZpg/fz7Kly8Pg8GA\n3377Lde5ohiEt3z5cpQtWxYxMTEYO3ZsQXfnjtK9e3cEBwejQoUK2cdOnTqFxo0bo3Tp0mjSpAnO\nnDlTgD28cxw4cAANGjRA+fLlERcXh8mTJwMomuNx+fJlVKtWDZUqVUJsbCxefPFFAEVzLAAgMzMT\nCQkJ2c5CtzIOhUpJVKhQAV9++SXq1q2b63hRDMLLzMxE3759sXz5ciQnJ+PTTz/Fjh07Crpbd4zH\nH38cy5cvz3VszJgxaNy4MXbt2oVGjRphzJgxBdS7O4vJZMLEiROxfft2/Pzzz5g6dSp27NhRJMfD\nYrFg1apV2LJlC37//XesWrUK69atK5JjAQCTJk1CbGxs9rb9LY3DzfslFTz169fnpk2bsj+PGjWK\nY8aMyf6clJTEDRs2FETX7hg//fQTk5KSsj//2zOsKJCSksK4uLjsz2XKlOHRo0dJkkeOHGGZMmUK\nqmsFSps2bbhixYoiPx4XL15k1apVuW3btiI5FgcOHGCjRo24cuVKtmzZkuSt/Y0UqpVEXhTFILxD\nhw4hIiIi+3NReOfr8c8//yA4OBgAEBwcjH/++aeAe3Tn2bdvHzZv3oxq1aoV2fFwu92oVKkSgoOD\ns7fhiuJYPPvssxg/fnx2dgvg1v5GCsS76VrcSBDejXCve0Xd6+/3X9HpdEVujC5cuID27dtj0qRJ\ncDgcuc4VpfHQ6/XYsmULzp49i6SkJKxatSrX+aIwFkuWLEFQUBASEhLyTEtyo+Nw1ymJFStW3PQ9\nYWFhOHDgQPbngwcPIiwsLD+7ddfx73c+cOBArtVUUSQ4OBhHjx5FSEgIjhw5gqCgoILu0h3D5XKh\nffv26NatG9q2bQugaI8HADidTrRo0QKbNm0qcmPx008/YdGiRVi6dCkuX76Mc+fOoVu3brc0DoV2\nu4kenrutW7fGvHnzkJ6ejpSUFOzevRuJiYkF2LvbT9WqVbF7927s27cP6enp+Oyzz9C6deuC7laB\n0rp1a8yaNQsAMGvWrGxhea9DEj169EBsbCz69++ffbwojseJEyeyPXZSU1OxYsUKJCQkFLmxGDVq\nFA4cOICUlBTMmzcPDRs2xMcff3xr43Ab7Sb5zsKFCxkeHk6LxcLg4GA2bdo0+9zIkSMZFRXFMmXK\ncPny5QXYyzvH0qVLWbp0aUZFRXHUqFEF3Z07SufOnRkaGkqTycTw8HDOnDmTJ0+eZKNGjRgTE8PG\njRvz9OnTBd3NO8LatWup0+kYHx/PSpUqsVKlSly2bFmRHI/ff/+dCQkJjI+PZ4UKFThu3DiSLJJj\nkcXq1avZqlUrkrc2DiqYTqFQKBR5Umi3mxQKhUJx+1FKQqFQKBR5opSEQqFQKPJEKQmFQqFQ5IlS\nEgqFQqHIE6UkFAqFQpEnSkkoFNfAYDAgISEBCQkJqFy5Mvbv349atWoBAPbv349PP/00+9qtW7di\n2bJlN/2M+vXrY9OmTfnWZ4UiP1FKQqG4BpqmYfPmzdi8eTN+++03lChRAuvXrwcApKSkYO7cudnX\nbt68GUuXLr3pZxSFXEKKwotSEgrFTWK32wEAgwcPxtq1a5GQkIBx48Zh2LBh+Oyzz5CQkID58+fj\n4sWL6N69O6pVq4bKlStj0aJFAES6iM6dOyM2Nhbt2rVDamoqVEyr4m7lrkvwp1DcTaTRaNVTAAAB\ndklEQVSmpiIhIQEAEBkZiS+++CJ71j927FhMmDABixcvBiAS6m3atCm7MtyQIUPQqFEjzJw5E2fO\nnEG1atVw//3347333oPdbkdycjL++OMPVK5cWa0kFHctSkkoFNfAarVi8+bNVz3379k/yVzHvvvu\nOyxevBgTJkwAAKSlpeHvv//G2rVr0a9fPwCi2mLFihVvU+8Viv+OUhIKRT5xtdXAwoULERMTc8Vx\ntb2kKCwom4RCcYs4HA6cP38+z89JSUnZW08AslckdevWzTZ4b9u2Db///vsd6rFCcfMoJaFQXIOr\nrQ6yjsXHx8NgMKBSpUqYNGkSGjRogOTk5GzD9dChQ+FyuVCxYkXExcVh2LBhAIDevXvjwoULiI2N\nxbBhw1C1atU7+k4Kxc2gUoUrFAqFIk/USkKhUCgUeaKUhEKhUCjyRCkJhUKhUOSJUhIKhUKhyBOl\nJBQKhUKRJ0pJKBQKhSJPlJJQKBQKRZ4oJaFQKBSKPPl/o5C2nVlbD18AAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# fitting medv ~ lstat + I(lstat^2)\n",
"boston_df[\"lstat^2\"] = boston_df[\"lstat\"] ** 2\n",
"reg6 = LinearRegression()\n",
"X = boston_df[[\"lstat\", \"lstat^2\"]]\n",
"y = boston_df[\"medv\"]\n",
"reg6.fit(X, y)\n",
"# save the predicted ys for given xs for future plot\n",
"lstats = boston_df[\"lstat\"].values\n",
"xs = range(int(np.min(lstats)), int(np.max(lstats)))\n",
"ys6 = [reg6.predict([x, x*x]) for x in xs]\n",
"(reg6.intercept_, reg6.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
"(42.862007328169383, array([-2.3328211 , 0.04354689]))"
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fitted = reg6.predict(X)\n",
"residuals = y - fitted\n",
"std_residuals = standardize(residuals)\n",
"residuals_vs_fitted(fitted, residuals, \"Fitted\", \"Residuals\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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owty7dw9Vq9ZFdHQQzGZXqFS/Y+vWP1GnTp0Cv/bp06dRu3YzmEwbAQRBofgMfn4bcPLk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\nISIirv4GPN/ITUnY14MAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# fitting medv ~ poly(lstat,4). We already have lstat^2 and lstat from previous\n",
"boston_df[\"lstat^4\"] = np.power(boston_df[\"lstat\"], 4)\n",
"boston_df[\"lstat^3\"] = np.power(boston_df[\"lstat\"], 4)\n",
"X = boston_df[[\"lstat^4\", \"lstat^3\", \"lstat^2\", \"lstat\"]]\n",
"y = boston_df[\"medv\"]\n",
"reg7 = LinearRegression()\n",
"reg7.fit(X, y)\n",
"ys7 = [reg7.predict([x**4, x**3, x**2, x]) for x in xs]\n",
"(reg7.intercept_, reg7.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 17,
"text": [
"(46.800943987797865,\n",
" array([ -1.17511270e-05, -1.17511460e-05, 9.23027375e-02,\n",
" -3.27115207e+00]))"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fitted = reg7.predict(X)\n",
"residuals = y - fitted\n",
"std_residuals = standardize(residuals)\n",
"residuals_vs_fitted(fitted, residuals, \"Fitted\", \"Residuals\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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lI3ldSXz55ZeUpAYEUuxf3GUsXrxCjvX3559/0mSq6KAkEqnVuqWVZM9OZPt+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"text": [
""
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Plot the different lines. Not that the green line (reg7) follows the distribution\n",
"# better than the red line (reg6).\n",
"ax = boston_df.plot(x=\"lstat\", y=\"medv\", style=\"o\")\n",
"ax.set_ylabel(\"medv\")\n",
"plt.plot(xs, ys6, color='r', linewidth=2.5)\n",
"plt.plot(xs, ys7, color='g', linewidth=2.5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": [
"[]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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YWBjt27cnPDxcX3mstomMDCYuLoKIiBgCAp6jadMRNGx4BEV372nmrsZAJxSv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\njGwEJBKJ5CJGNgISiURyEfP/AaHRBDtJ50F1AAAAAElFTkSuQmCC\n",
"text": [
""
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Qualitative Predictors ###"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Data from ISLR package: write.csv(Carseats, 'Carseats.csv', col.names=FALSE)\n",
"carseats_df = pd.read_csv(\"../data/Carseats.csv\")\n",
"carseats_df.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Sales | \n",
" CompPrice | \n",
" Income | \n",
" Advertising | \n",
" Population | \n",
" Price | \n",
" ShelveLoc | \n",
" Age | \n",
" Education | \n",
" Urban | \n",
" US | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 9.50 | \n",
" 138 | \n",
" 73 | \n",
" 11 | \n",
" 276 | \n",
" 120 | \n",
" Bad | \n",
" 42 | \n",
" 17 | \n",
" Yes | \n",
" Yes | \n",
"
\n",
" \n",
" 1 | \n",
" 11.22 | \n",
" 111 | \n",
" 48 | \n",
" 16 | \n",
" 260 | \n",
" 83 | \n",
" Good | \n",
" 65 | \n",
" 10 | \n",
" Yes | \n",
" Yes | \n",
"
\n",
" \n",
" 2 | \n",
" 10.06 | \n",
" 113 | \n",
" 35 | \n",
" 10 | \n",
" 269 | \n",
" 80 | \n",
" Medium | \n",
" 59 | \n",
" 12 | \n",
" Yes | \n",
" Yes | \n",
"
\n",
" \n",
" 3 | \n",
" 7.40 | \n",
" 117 | \n",
" 100 | \n",
" 4 | \n",
" 466 | \n",
" 97 | \n",
" Medium | \n",
" 55 | \n",
" 14 | \n",
" Yes | \n",
" Yes | \n",
"
\n",
" \n",
" 4 | \n",
" 4.15 | \n",
" 141 | \n",
" 64 | \n",
" 3 | \n",
" 340 | \n",
" 128 | \n",
" Bad | \n",
" 38 | \n",
" 13 | \n",
" Yes | \n",
" No | \n",
"
\n",
" \n",
"
\n",
"
5 rows \u00d7 11 columns
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 20,
"text": [
" Sales CompPrice Income Advertising Population Price ShelveLoc Age \\\n",
"0 9.50 138 73 11 276 120 Bad 42 \n",
"1 11.22 111 48 16 260 83 Good 65 \n",
"2 10.06 113 35 10 269 80 Medium 59 \n",
"3 7.40 117 100 4 466 97 Medium 55 \n",
"4 4.15 141 64 3 340 128 Bad 38 \n",
"\n",
" Education Urban US \n",
"0 17 Yes Yes \n",
"1 10 Yes Yes \n",
"2 12 Yes Yes \n",
"3 14 Yes Yes \n",
"4 13 Yes No \n",
"\n",
"[5 rows x 11 columns]"
]
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# convert non-numeric to factors\n",
"carseats_df[\"ShelveLoc\"] = pd.factorize(carseats_df[\"ShelveLoc\"])[0]\n",
"carseats_df[\"Urban\"] = pd.factorize(carseats_df[\"Urban\"])[0]\n",
"carseats_df[\"US\"] = pd.factorize(carseats_df[\"US\"])[0]\n",
"# Sales ~ . + Income:Advertising + Age:Price\n",
"carseats_df[\"Income:Advertising\"] = carseats_df[\"Income\"] * carseats_df[\"Advertising\"]\n",
"carseats_df[\"Age:Price\"] = carseats_df[\"Age\"] * carseats_df[\"Price\"]\n",
"X = carseats_df[carseats_df[1:].columns]\n",
"y = carseats_df[\"Sales\"]\n",
"reg = LinearRegression()\n",
"reg.fit(X, y)\n",
"(reg.intercept_, reg.coef_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 21,
"text": [
"(5.773159728050814e-14,\n",
" array([ 1.00000000e+00, -7.59808882e-16, 1.38777878e-17,\n",
" 5.55111512e-17, 3.25260652e-18, 4.02455846e-16,\n",
" 2.22044605e-16, -3.05311332e-16, -4.16333634e-17,\n",
" -4.33680869e-18, -3.64291930e-17, -8.67361738e-18,\n",
" -1.22277147e-19]))"
]
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# R has a contrasts() function that shows how factors are encoded by default. We can do \n",
"# this manually using scikit-learn's OneHotEncoder\n",
"from sklearn.preprocessing import OneHotEncoder\n",
"\n",
"colnames = [\"ShelveLoc\", \"Urban\", \"US\"]\n",
"enc = OneHotEncoder()\n",
"X = carseats_df[colnames]\n",
"enc.fit(X)\n",
"X_tr = enc.transform(X).toarray()\n",
"colnos = enc.n_values_\n",
"colnames_tr = []\n",
"for (idx, colname) in enumerate(colnames):\n",
" for i in range(0, colnos[idx]):\n",
" colnames_tr.append(colname + \"_\" + str(i))\n",
"col = 0\n",
"for colname_tr in colnames_tr:\n",
" carseats_df[colname_tr] = X_tr[:, col]\n",
" col = col + 1\n",
"del carseats_df[\"ShelveLoc\"]\n",
"del carseats_df[\"Urban\"]\n",
"del carseats_df[\"US\"]\n",
"carseats_df[colnames_tr].head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" ShelveLoc_0 | \n",
" ShelveLoc_1 | \n",
" ShelveLoc_2 | \n",
" Urban_0 | \n",
" Urban_1 | \n",
" US_0 | \n",
" US_1 | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
"
\n",
" \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
"
\n",
" \n",
" 2 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
"
\n",
" \n",
" 3 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
"
\n",
" \n",
" 4 | \n",
" 1 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
"
\n",
" \n",
"
\n",
"
5 rows \u00d7 7 columns
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 22,
"text": [
" ShelveLoc_0 ShelveLoc_1 ShelveLoc_2 Urban_0 Urban_1 US_0 US_1\n",
"0 1 0 0 1 0 1 0\n",
"1 0 1 0 1 0 1 0\n",
"2 0 0 1 1 0 1 0\n",
"3 0 0 1 1 0 1 0\n",
"4 1 0 0 1 0 0 1\n",
"\n",
"[5 rows x 7 columns]"
]
}
],
"prompt_number": 22
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Writing Functions ###\n",
"\n",
"We write a convenience function to plot a scatter plot and a regression line of two variables."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def regplot(x, y, xlabel, ylabel, dot_style, line_color):\n",
" x = x.values\n",
" y = y.values\n",
" reg = LinearRegression()\n",
" X = np.matrix(x).T\n",
" reg.fit(X, y)\n",
" ax = plt.scatter(x, y, marker=dot_style)\n",
" plt.xlabel(xlabel)\n",
" plt.ylabel(ylabel)\n",
" xs = range(int(np.min(x)), int(np.max(x)))\n",
" ys = [reg.predict(x) for x in xs]\n",
" plt.plot(xs, ys, color=line_color, linewidth=2.5)\n",
"\n",
"regplot(carseats_df[\"Price\"], carseats_df[\"Sales\"], \"Price\", \"Sales\", 'o', 'r')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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VGk1jl2Ws2SxWrLIqFJVotbal1erDXbt2OdvfvXtXTcWdmNJjBy0W7xQ3pK9d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\nc81FF6nX26jVtqSSR7Eq12cz2LNnP+fxkpOT+cUXXxRaB7M1a9bQbm+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"text": [
""
]
}
],
"prompt_number": 23
}
],
"metadata": {}
}
]
}