{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Multiple Linear Regression\n", "\n", "In this example we will explore multiple linear regression, where we have multiple independent variables ($x$ values) to predict a single dependent variable ($y$ value). Remember, our model looks like this\n", "\n", "$$y_i = \\beta_0 + x_{i1} \\beta_1 + x_{i2} \\beta_2 + \\cdots + x_{id} \\beta_d + \\epsilon_i.$$\n", "\n", "In matrix/vector math, this is\n", "\n", "$$\\begin{pmatrix} y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n \\end{pmatrix} = \n", "\\begin{pmatrix} \n", "1 & x_{11} & x_{12} & \\cdots & x_{1d}\\\\\n", "1 & x_{21} & x_{22} & \\cdots & x_{2d}\\\\\n", "\\vdots & \\vdots & \\vdots & & \\vdots\\\\\n", "1 & x_{n1} & x_{n2} & \\cdots & x_{nd}\\\\\n", "\\end{pmatrix}\n", "\\begin{pmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\vdots \\\\ \\beta_d \\end{pmatrix}\n", "+\n", "\\begin{pmatrix} \\epsilon_1 \\\\ \\epsilon_2 \\\\ \\vdots \\\\ \\epsilon_n\\end{pmatrix}.$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import numpy as np\n", "\n", "# Just some color options for seaborn plots\n", "sns.set(style=\"darkgrid\")\n", "sns.set_palette(\"Dark2\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to the above libraries that we've seen before, we are going to import `statsmodels` for doing multiple linear regression." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll take another look at the hippocampus volume from the OASIS dementia data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Unnamed: 0IDM.FHandAgeEducSESMMSECDReTIVnWBVASFDelayRightHippoVolLeftHippoVolTrainDataDementia
01OAS1_0002_MR1FR5541.0290.011470.8101.531NaN4230380700
12OAS1_0003_MR1FR7343.0270.514540.7081.207NaN2896280111
27OAS1_0010_MR1MR7452.0300.016360.6891.073NaN2832257800
38OAS1_0011_MR1FR5232.0300.013210.8271.329NaN3978408000
410OAS1_0013_MR1FR8152.0300.016640.6791.055NaN3557349500
\n", "
" ], "text/plain": [ " Unnamed: 0 ID M.F Hand Age Educ SES MMSE CDR eTIV nWBV \\\n", "0 1 OAS1_0002_MR1 F R 55 4 1.0 29 0.0 1147 0.810 \n", "1 2 OAS1_0003_MR1 F R 73 4 3.0 27 0.5 1454 0.708 \n", "2 7 OAS1_0010_MR1 M R 74 5 2.0 30 0.0 1636 0.689 \n", "3 8 OAS1_0011_MR1 F R 52 3 2.0 30 0.0 1321 0.827 \n", "4 10 OAS1_0013_MR1 F R 81 5 2.0 30 0.0 1664 0.679 \n", "\n", " ASF Delay RightHippoVol LeftHippoVol TrainData Dementia \n", "0 1.531 NaN 4230 3807 0 0 \n", "1 1.207 NaN 2896 2801 1 1 \n", "2 1.073 NaN 2832 2578 0 0 \n", "3 1.329 NaN 3978 4080 0 0 \n", "4 1.055 NaN 3557 3495 0 0 " ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv(\"OASIS-hippocampus.csv\")\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single Linear Regression\n", "\n", "Let's start with just a single $x$ variable and see what information `statsmodels` will give us about a simple linear regression. We are going to look at the effect of age on the right hippocampus volume. The `statsmodels` function `ols` (which stands for **o**rdinary **l**east **s**quares) will create a linear regression model from a formula that looks like `\"y ~ x\"`. The `y` and `x` are column names from your data frame. This sets up a model with an intercept and slope." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.364\n", "Model: OLS Adj. R-squared: 0.361\n", "Method: Least Squares F-statistic: 127.7\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 1.04e-23\n", "Time: 13:58:05 Log-Likelihood: -1722.7\n", "No. Observations: 225 AIC: 3449.\n", "Df Residuals: 223 BIC: 3456.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 5891.2172 205.031 28.733 0.000 5487.171 6295.263\n", "Age -31.7067 2.806 -11.301 0.000 -37.236 -26.178\n", "==============================================================================\n", "Omnibus: 6.181 Durbin-Watson: 2.231\n", "Prob(Omnibus): 0.045 Jarque-Bera (JB): 5.859\n", "Skew: -0.361 Prob(JB): 0.0534\n", "Kurtosis: 3.320 Cond. No. 437.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "reg = smf.ols(\"RightHippoVol ~ Age\", data = df).fit()\n", "print(reg.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a lot of information here! Let's look at a few things going on:\n", "\n", "1. The estimated regression parameters, $(\\alpha, \\beta)$, are in the `coef` column. Note, the coefficient we are most interested in here is the slope $\\beta$, which is estimated to be -387 mm$^3$ / year. This says, for each year increase in age, hippocampus volume drops by -387 mm$^3$.\n", "2. The $R^2$ statistic is 0.364, meaning our fitted line explains 36.4% of the variance of right hippocampus volume.\n", "3. The column labeled `P>|t|` is a $p$ value for a hypothesis test of each parameter. This comes from a $t$ test, which we won't cover in detail in this class (but you would if you take a statistics course). The null hypothesis is that the corresponding parameter is zero. In other words, removing this parameter from the model would not make a difference. So, a small $p$ value means we have evidence to reject that null hypothesis, that is, the parameter is having some *statistically significant* effect in the model. Notice both intercept and slope have very small $p$ values (below the reported precision of $10^{-3}$).\n", "\n", "As always, let's plot the data and linear regression result:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "sns.scatterplot(x = \"Age\", y = \"RightHippoVol\", data = df)\n", "a = reg.params[0]\n", "b = reg.params[1]\n", "x = np.array([30,100])\n", "sns.lineplot(x, a + b * x, lw = 3, color = 'darkblue')\n", "plt.title(\"Right Hippocampus Volume vs. Age\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binary Independent Variables\n", "\n", "What if $x$ is a binary variable instead of continuous? It turns out that this makes perfect sense. In our hippocampus data, let's say we want $x$ to be the binary variable `Dementia` (for healthy = 0, dementia = 1). Remember we can look at the relationship of dementia and hippocampus volume by plotting the densities:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grouped = df.groupby(\"Dementia\")\n", "healthy = grouped.get_group(0)[\"RightHippoVol\"]\n", "dementia = grouped.get_group(1)[\"RightHippoVol\"]\n", "\n", "sns.distplot(healthy, hist = False, rug = True, kde_kws = {'shade': True}, label = \"Healthy\")\n", "sns.distplot(dementia, hist = False, rug = True, kde_kws = {'shade': True}, label = \"Dementia\")\n", "\n", "plt.title(\"Right Hippocampus Volume in Healthy vs. Dementia\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, consider the linear regression equation again:\n", "$$y_i = \\alpha + x_i \\beta + \\epsilon_i.$$\n", "This equation is just modeling the **means** of the two groups of data ($x_i = 0$ and $x_i = 1$). If $x_i = 0$, then $y_i = \\alpha$ (plus error). If $x_i = 1$, then $y_i = \\alpha + \\beta$ (plus error). Assuming that the errors have zero mean, then the $x_i = 0$ (healthy) group has mean $\\alpha$, and the $x_i = 1$ (dementia) group has mean $\\alpha + \\beta$. Let's check this with a linear regression call:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.259\n", "Model: OLS Adj. R-squared: 0.255\n", "Method: Least Squares F-statistic: 77.75\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 3.40e-16\n", "Time: 13:58:06 Log-Likelihood: -1740.0\n", "No. Observations: 225 AIC: 3484.\n", "Df Residuals: 223 BIC: 3491.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 3880.6061 48.303 80.338 0.000 3785.417 3975.795\n", "Dementia -662.4770 75.132 -8.817 0.000 -810.537 -514.417\n", "==============================================================================\n", "Omnibus: 0.255 Durbin-Watson: 1.979\n", "Prob(Omnibus): 0.880 Jarque-Bera (JB): 0.349\n", "Skew: -0.074 Prob(JB): 0.840\n", "Kurtosis: 2.877 Cond. No. 2.46\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "reg = smf.ols(\"RightHippoVol ~ Dementia\", data = df).fit()\n", "print(reg.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's double-check the `coef` column really does give us the means of the two groups:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Mean of healthy = 3880.6060606060605\n", " alpha = 3880.606060606061\n", "Mean of dementia = 3218.1290322580644\n", " alpha + beta = 3218.1290322580658\n" ] } ], "source": [ "print(\" Mean of healthy =\", healthy.mean())\n", "print(\" alpha =\", reg.params[0])\n", "print(\"Mean of dementia =\", dementia.mean())\n", "print(\" alpha + beta =\", reg.params[0] + reg.params[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Including Multiple Independent Variables\n", "\n", "Now let's see how to analyze multiple independent variables in the same model. We are going to take the age and dementia variables that we analyzed separately above and combine them into a single model. We'll use $x_{i1}$ = `Age` and $x_{i2}$ = `Dementia`, giving us the linear regression model:\n", "$$y_i = \\beta_0 + x_{i1} \\beta_1 + x_{i2} \\beta_2 + \\epsilon_i$$\n", "First, let's plot all three variables (age, dementia, right hippo volume):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "sns.scatterplot(x = \"Age\", y = \"RightHippoVol\", hue = \"Dementia\", data = df)\n", "plt.title(\"Right Hippocampus Volume vs. Age and Dementia\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing to notice here is that the difference in right hippocampus volume between healthy and dementia groups may partially be due to age. This is because the younger subjects (30-60 years) are all healthy, and younger people have larger hippocampi. To see this even more clearly, let's plot the means of the two groups as horizontal lines on the $y$ axis:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a = reg.params[0]\n", "b = reg.params[1]\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "sns.scatterplot(x = \"Age\", y = \"RightHippoVol\", hue = \"Dementia\", data = df)\n", "x = np.array([30,95])\n", "sns.lineplot(x, a, lw = 3, color = sns.color_palette()[0])\n", "sns.lineplot(x, a + b, lw = 3, color = sns.color_palette()[1])\n", "plt.title(\"Right Hippocampus Volume vs. Age and Dementia\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a case where regression using two independent variables together will give a better analysis." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.476\n", "Model: OLS Adj. R-squared: 0.471\n", "Method: Least Squares F-statistic: 100.8\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 7.28e-32\n", "Time: 13:58:07 Log-Likelihood: -1701.0\n", "No. Observations: 225 AIC: 3408.\n", "Df Residuals: 222 BIC: 3418.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 5657.5421 189.644 29.832 0.000 5283.809 6031.275\n", "Age -25.8293 2.692 -9.593 0.000 -31.135 -20.523\n", "Dementia -459.1694 66.765 -6.877 0.000 -590.744 -327.595\n", "==============================================================================\n", "Omnibus: 1.179 Durbin-Watson: 2.175\n", "Prob(Omnibus): 0.555 Jarque-Bera (JB): 0.858\n", "Skew: -0.100 Prob(JB): 0.651\n", "Kurtosis: 3.228 Cond. No. 446.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "reg = smf.ols(\"RightHippoVol ~ Age + Dementia\", data = df).fit()\n", "print(reg.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the following:\n", "\n", "1. The difference between the healthy group and the dementia group was -662 mm$^3$ in the previous analysis, but now when we include the age regressor, this difference reduces to -459 mm$^3$.\n", "2. The slope with respect to age has also changed (become less negative).\n", "3. Both the `Age` and `Dementia` variables have low $p$ values, indicating they are having a statistically significant effect in our model.\n", "\n", "The $\\beta_2$ parameter (the coefficient for the binary variable `Dementia`) is still a constant shift. But now instead of a shift in the mean, it is a shift in the regression intercept. So, a binary regressor is in essence fitting two parallel lines to the data, as we can see in the following plot:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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VoqKi+OOPPzzvvf/++5k8eTKrV6+mefPmdO3atULnwGq18t577/Hyyy/zySef4Ha7+cc//kGXLl3K3f7666/nH//4B++//74nn/fffz/jx4/Hy8sLTdM8Qwq/+eYbdu7cycsvv+x5/8qVKzFN09NEcsr48eP54osvWL16Na+//jpPP/00//vf/wgLC6NRo0Z4eXkRFBTE9OnTmTZtGg6HAyEE06ZNK1VzBdC7d29mz57N1VdfjaIodO/enaCgIJKSks56LN58802efPJJZs6cSZMmTWjevPkZt/38889ZuHAhiqJgGAbt27f3DHc9Wz5/++23s+bhlD59+jBhwgTuuusuFEXBz8+PGTNmnPOGfODAgbz55pulanrOdjzOVkapaimiKupNJekMXn/9de6++26Cg4NJSUlh1KhRLFu2jHr16lX5Z0+ePNnTg/ivYmJiWL9+fZmq2upw7NgxRowYUSrISlXr/fffJz4+nhYtWpCfn8/IkSP5+OOPz9nzX5JqEvmEL11SDRs2ZPz48ei6jhCCl1566ZIEe0k6m2bNmvHII4+gqiqGYTBhwgQZ7KVaRz7hS5IkSVIdIDvtSZIkSVIdIAO+JEmSJNUBMuBLkiRJUh0gA74kSZIk1QG1vpd+dnYhpll5/RIbNPAjM7Og0vZXE9TFMkPdLLcsc91RF8tdF8qsqgqBgb7lvlbrA75pikoN+Kf2WdfUxTJD3Sy3LHPdURfLXRfLfIqs0pckSZKkOkAGfEmSJEmqA2TAlyRJkqQ6oNa34UuSJEnVxzDcZGdn4HaXv3LjpZSerlZ45crLla5bCQwMQdPOP4zLgC9JkiRVmezsDLy8fPD1DT/nyntVTddV3O6aH/CFEBQW5pGdnUFwcMR5v09W6UuSJElVxu124utbr9qDfW2iKAq+vvUqXGsiA74kSZJUpWSwr3wXckxllb4kSZJUZ6SkJHPzzWNp1qw5AA6HnfbtO3LffRMJCmpwSfOybt1ajh5N4qabbmX+/NkAjB59XZV9ngz4kvQXuq6iaPKJRJJqq+DgED7//H9ASXv4hx++yzPPPMF7731ySfOxZ0+C599VGehPkQFfkk5jeAl+Td/H8mN7GNioNb1Cm6PaZfCXpNpKURTuvvteRoyIZ//+faxfv46VK5diGCY9evTk/vsfIjU1hSeffIymTZty6NBBoqNb065dB37++Qfy8/N45ZU3aNYsit27dzF9+ps4HHYCAuozadJTREY2ZOLEe4iNbcu2bVvJycnm4YcnER4ewYIFcwEID48gNTUFgLvvvpc5c75l0aKfsNuLsVgsTJ36Mk2aNLvosso2fEk6SVgFb21fxgNrZjL34FYmrpnJa38swrTW3ak4JakusFgsNG7cmH37EklM3M3HH3/BZ599TUZGBkuW/AzAgQP7uOWWO/j882/YsWMbqakpfPjhZwwaNISFC+ficrl47bWXeO65l/nPf77mpptu5fXXX/Z8hsvl5sMPP+PBBx/l44/fJyqqOaNGjWXUqLEMGzbSs11hYQFr1qxmxowP+fLLWVxxRV/mzJlVKeWUT/iSdJJLMZi57/dSaXMO/sFjcYOxyktFkmo5he++m0lOTjZ3330bUNK+HxYWTocOcQQFNSA6ujUAISGhdOnSDSh5Ov/jj2SOHk0iOfkYkyc/6tljYWGh5989evQCoHnzFuTn550xF76+fkyd+hLLli3h6NEjbNz4K61axVRKCeWvmCR5KGiKgnHaA72KArKHsSTVai6Xi6NHk+jUqSvx8Vdz0023ApCfn4+maeTm5mCxWEq9R9O0Un8bhklkZENP3wDDMMjOzvK8brVagZImBCHOXGuYlpbKgw/ey7XX3kDPnlcQFNSAffsSK6Wcskpfkk6ymhp3teldKu22mJ7oprxMJKm2Mk2TTz/9kNjY9gwbNpLFi3+iqKgIt9vNk0/+H6tWLT+v/TRt2oy8vDy2bfsDgB9/XMjUqU+f9T2apmEYRqm0PXsSaNSoMTfeeAtt2sSyZs1KTNM4wx4qRj7hS9IpLvhb6970i2zFmpS99IuMJto/FNUhn/AlqTY5cSKD8ePHAWCaBq1axTB16svUq1eP/fv3cs894zFNgx49rmDo0OGeDnVnY7VaefHF13j77TdwOp34+PjyzDPPn/U9cXGdefnlqQQFBXnSunXrybx5s7n11usRQhAX15mDBw9cXIFPUsTZ6hZqgczMgkpd/zgkxJ+MjPxK219NUNfKrGkqmqYSEOBdp8oNde9cQ90sM1y6cqemJhEe3rTKP+d81JapdU8p79iqqkKDBn7lbi+f8CXpLwzDxDBqz4+CJEkSyDZ8SZIkSaoTZMCXJEmSpDpABnxJkiRJqgOqtA3/tttuIysrC10v+ZgXXniBwsJCXn31VRwOB0OHDuWRRx4BYPfu3Tz99NMUFhbStWtXnn/+eXRdJzk5mUmTJpGZmUlUVBRvvPEGvr6+VZltSZIkSap1quwJXwjB4cOHWbBggee/mJgYnnrqKd577z1++ukndu7cyerVqwGYNGkSU6ZMYfHixQghmDWrZCrB559/nnHjxrFo0SLatWvHe++9V1VZliRJkqRaq8oC/sGDBwG46667GDlyJF999RXbt2+nadOmNG7cGF3XGTFiBIsWLeL48ePY7Xbi4uIAGDt2LIsWLcLlcrFp0yaGDBlSKl2SJEmSpIqpsoCfl5dHr169ePfdd/n888+ZOXMmycnJhISEeLYJDQ0lLS2N9PT0UukhISGkpaWRnZ2Nn5+fp0ngVLokVRddV1FVORGPJNVkS5Ys4tZbr+emm8ZU2sI0NUGVteF36tSJTp06ef6+7rrrmD59Ol26dPGkCSFQFAXTNFFOm6/8VPqp/5/ur3+fy5kmILgYISH+lb7Py11dLDP8We5Cl4NMeyG/pR2iZUAoTfyDCPKqnX1J6uK5rotlhktT7vR0FV2/fPqHZ2Wd4OOP3+Pzz7/GarUyYcJ4unfvTlRU8+rOWoWpqlqhc1hlAf/333/H5XLRq1fJCkFCCBo2bEhGRoZnm4yMDEJDQwkPDy+VfuLECUJDQwkKCiI/Px/DMNA0zbN9RciZ9i5eXSwz/FluXVfZWnCMO5Z/jnlyYsrrWnRmcschaM7L54esMtTFc10XywyXrtymaV7Q7HY/HdvJjMSVpBbnEe5dj4kxA7imUbuLyouuq2zcuIHOnbvi61sSKK+88iqWLVvKnXdOuKh9VwfTNMucw7PNtFdlv1b5+flMmzYNh8NBQUEB8+bN49FHH+XQoUMkJSVhGAY//PAD/fr1o2HDhthsNjZv3gzAggUL6NevHxaLha5du/LTTz8BMH/+fPr161dVWZakchWpLqZu+sET7AFmH9iCU6mcBS1OUSwKLpuBw+bGbTVl04FUZ/10bCcv7viRlOI8BJBSnMeLO37kp2M7L3rfJ05k0KBBsOfvBg2CSU9Pv+j91gRV9oQ/YMAAtm3bxujRozFNk3HjxtGpUydee+01HnzwQRwOB/379+fqq68G4I033uCZZ56hoKCAtm3bcvvttwPw3HPPMXnyZN5//30iIiJ48803qyrLklQ+RZBtLyqTbHe78MZSzhsqzrQI1mce4OkNC8h1FtMzLIrpfW/E6tCo3atdSFJZMxJXYjfcpdLshpsZiSsv+im/vCbkunJzXaXj8B9++GEefvjhUmm9evVi4cKFZbZt3bo1s2fPLpPesGFDvvzyyyrLoySdi5dp4ZaY7ryzfaUnLapeA/x1G1TSQ75TdfPQ2m89tQgb0g7x5tZlPNFhCDgr5zMkqaZILc6rUHpFhIaGeZawBcjKyiQ4OOQs76g9alcDpCRVAdMlGB/di1d6jqJnWBTjW/diZvzfsLkr5+leVRWS8rNKNRkArE87iEO4z/AuSaq9wr3rVSi9Irp27c7mzZvIzs7GbrezatUKevToddH7rQnkanmSdB5Uu8KIiI4MjojFqmgIh8AQlbOinmkKmvoHoaAg+DPodw9thk2Rl6hU90yMGcCLO34sVa3vpelMjBlw0fsOCQllwoS/89BD9+JyuRkxYhSxsRfXTFBTyF+T85TlKGRDxiHampE0VgJRKzg8UKr53C4DHRWTym9Ut5o6b/a5jmc3LqTA5aBzSBMmdYpHcVAFnyZdKooFnJqBAKymCk75u3E+TrXTV3Yv/VPi468mPv7qStlXTSID/nl6Yss8fs9Mgq0Q7lWP+MhY4iPbEBsQUeG5AaQLpyhgseiAwOms3F7y1Ul1KQwIiWbFyEcwMNGFhtWplanml2oOw2oyN2kr/962HKfh5qZWXXmkwyBUu/y9OB/XNGpXaQFeKiED/nlymn9WLaXa8/ji4Aa+OLiBxj6BxEe2IT4yllb+oTL4VyFFh3zFwbf71uFnsTGmeSe8XRYMo3Kq1qubcIEFDQsaQJXUJEiXhqoqHHfk8crmnz1pX+39jbjgxgwJjb2gcemSdLFkwD9P/+pyHe8lrmZl+l5yHH8O0TpalM2n+3/l0/2/EuUXzJCTwT/KL/gse5MqSlEUsiliyIK3cZolT/Yf7fqFRSMexGJo1Zw7SSpN01R+Oba/TPrSY7sZHN6mGnIkSTLgn7dgLz+mdBzGv4Ku44fdO1iSksCq1L0UuB2ebQ4VnOCDvWv5YO9aouuFEh8Zy5CIWBr5BlZjzmsH1aLw4Y41nmAPJf0qVhxPZHh4e1yu2lO9L9V8hmHSJaRpmfQrwlugChWzssZzSlIFyIBfQVZNp29YS/qGtcRhuPk14wCLkxNYnbYPu+HybLc3L529eenM2LOKtgERJ9v8YytlWEldVV57tmzjli5HpimI8mvAna2v4IvEDRjC5KpGMQxv2h53sQz2UvWQAf8i2DSdAeExDAiPodjtZG36fhYnJ/BL+v5ST6K7clPYlZvCW7uXExfYiPjIWAZHtCHYq/IX9qmthFtwb9t+zDu4FdfJY1vf6s2gRq1x2eUPqHT50RwqE9tcyb1t+yIQWISGZldkzwyp2siAX0m8davnKb7A5WB12l6WJCfwa8ZB3KeN196afYyt2cf4564ldG3QlPjIWK6KaE2g1acac3/5M01BkO7DslEP81XiRvwsNm5s1RWbW5ed26TLlupSsJ32Myu/qZePwsIC7rvvLqZN+zcREZHVnZ1LQgb8KuBnsTGsUXuGNWpPnrOYFamJLEnZzW8nDmGcrIIWwKbMJDZlJvHazkX0CI4iPjKWgeEx+Fu8qrcAlys3BChePNLmKoQAp90tg710eTs5Dh8h0IWG5lLk2giXgV27djJt2kscPXqkurNyScmAX8XqWb0Z3SSO0U3iyHIUsjx1D0uSd7M5M8kTqgwh+DXjIL9mHOTlHT/TK6Q5QyJi6R/eCl/dVq35v9wIAQ6HnG62rrBaSxYPqomdMg2bydf7f+O9natxmQajojryTJdrUIvl0N3z4djyHfafX8DMOYZavxFeQ6dg63x9pez7++/n8eijT/Dii1MqZX81hQz4l1CQzZfrm3bh+qZdSLfnsyxlD0uSE9iWfcyzjcs0WJO2jzVp+7CpOn1CWzIkMpY+YS3x1ipn7nZJutxZVQMvI5v8tbPQfOpTr+NwCpX6NWbOBVVVSCrK4a1tyz1p8w5upUdoFMMj2uFy1YxyVBfHlu8omv0QuIoBMHOOlvwNlRL0J09+9qL3URPJgF9NQr38GRfVjXFR3UgpzmVp8m4WJe9id26qZxuH6WZ56h6Wp+7BW7PQPyya+Mg29A5pgVWTp6466LqKYQiErJetMqqqYLOncmRqZ4SrZNirHvgyDZ/dQB7+1Zy786NpKuuPHiiTvjI5kaGRbashRzWL/ecXPMHew1WM/ecXKu0pvy6SUeMSM60Ct1JSPWkxNRSXQoR3ALe36MntLXpypDCLpcm7WZycwL78dM/7ig0Xi5J3sSh5F366jQHhMQyJjKV7cDMsqpx4pqoJXVCkuticnkTzgGAivALQHHKxyapgVd1k//iaJ9gDuLOPY9+zCr3NqBoxS51hmPQMb14mvV9kKzShyL4n52DmHKtQunR+ZMC/hEwvwT+3LmHWgc0oKNwS3Z2H2g9EO21u7Sa+Qdzdqjd3t+rNwfwTLElOYHFyAocLMz3bFLgdfH9sOxDpgOkAACAASURBVN8f2059izcDI2IYEtmWLg2aoCkyCFU2XVfZVnic25d95hn3f0OLLjzeMR7NKY93VRB/fboDTJe9GnJyYUxT0NgnkIntr+TDXWtxmybDmrXj6sZtcRVf/jcs1U2t3wgz52i56dKFkwH/EtF1lXUZB5i5//eTKYIvEjcwsFEMnf2alNs22dw/mPti+nFvdF/25qd7gv/xohzPNjmuYuYe2crcI1tpYPNlUHhrhjRsS8fARnJFv0pSrLqY+tv3pSb5mXVgMw/HXYU3MuBXNqepE3jNExT8PhdODmlVferj0y6evBrwdH+K5lC5q+UV3BbdU47DryCvoVNKteEDYPHGa2jd6mRX2WTAv0Q0TWXF8cQy6auT99E9ttlZOyMpikJMvTBi6oUxMeZKEnJTWJycwJLkBNLs+Z7tMh2FfJu0mW+TNhPm5c/gyFiGRLShbf1IuajPRRAKZNmLyqTb3S68kR0pK5tpClz1mtL4+S3kLnsb1SeIgKv+ThEB1Z21ClNcClb+bHKTwf78nGqnr6pe+qfMnv19pe7vcicD/iViGCZXNWrNrP2bS6UPaBhdoTZJRVFoWz+StvUjebjNVWzPPsai5ASWpewm01Ho2S7Nns9XBzfy1cGNNPSpz+CINlwdGUt0vbBLHvxVTcGhu3EKA4ui4eXWMY2a89PnZeqMi+7GjB2rPGnN/Bvgp9uQU6JXDYdpxeUbhc/YfyMUhXyXiag5D/dSJbB1vl520KtkMuBfIm63SZfgptwW04Nv9m5CURRuj+lJbEAEhuPCfslURSEuqDFxQY2Z1HYwWzKPsDg5geUpe8g5rSrseFEOnx9Yz+cH1tPUN4ghJ2cEbOEfUlnFO3MeNYXDriz+tuQLMooLiPAN4LOBdxCpBdSYIVamS3BnzBV0CmlMpr0Ai6rTO7w5Xi4LBjWjDDWRaQpKLo2ac3MoSZczRdTy8UWZmQWYZuUVMSTEn4yM/HNveAbCKnApJUHCIlQUZ+U/bbtMg00nDrM4OYEVqYmlVvQ7XUv/EE/wb+IbdMb9XUyZXTaDYT/NIKO4wJPWzL8Bs+InYHFc3qMLTi+36SVYenw3Cw5to01gOPe17YeXS8eoQTUV5+Niv981UV0sM1y6cqemJhEeXnblwOqg62qNGOVxvso7tqqq0KBB+eu0yCf8S0xxlm7TqwoWVeOK0BZcEdqCp42hrD9xkMXHS1b0KzKcnu3252ewP3E17yaupk1AOEMiYxkcEUukT+W1lTqFUSrYAxzOz8RAnLH1W9UUHBY3WY4i/C02bOjV2htetSh8vm89b29bAcD61IOsPL6XWYMnoBs1r9OeqpZM71rL7/Wly4gQQvYjqmQXcv3KgF/LWTWd/mHR9A+Lxm64+CX9AIuTd7E2bT8O888panfnprI7N5V/715Bh8CGDImIZVBkG0K9Lm6iE6uiEeEbQEphrietZUAImij/4ldVhTzNztgfP/DcKNwe05OH2g6otqBvV118lbixVNqhvBMUGHbqU3MWPVJ1BYdusCc7hXo2bxr51Ed3aGf94dB1lWLVhQC8hQVDzhAnVZCuWykszMPXt54M+pVECEFhYR66bq3Q+2TAr0O8NAuDIlozKKI1hW4Ha9L2sfjkin6u05bz3Z59nO3Zx3kjYSmdg5pwbUxnevg1I8jmW/HPdFv4bOAd3Lfqaw7nZ9IyIISPrrwVL6P89m9DN3ll88+lagW+SNzA+Na9CFJ8zrjwiKoqGJpAKAKLoVVu/wChEGD1JtNeWCrZqulQQ6b1VxSFfNXB8IUzyHGW9O/oGtqED/rdgmYv/0ZK6IKE4lSe3/QDOY4ibo/pxfXNO6Pa5Y+2dP4CA0PIzs6goCDn3BtXMVVVMc3acdOq61YCAyvWD0sG/DrKV7cxtGE7hjZsR77LzsrURBYnJ7DxLyv6bc46wub1R9AUhW4NmnlW9Auwep/X5xiGSaRWj1mDJ2AoAk0oJcH+DAHZJUwO5p4ok368MIcGPr7lP41aIMWdx79+X4rdcPFg+wG08AlGdVVOjYCPaWFq9+GMX/5fz1j8sc3jsIkadPlYYPr2FZ5gD/B7+hEO5GXQ2iu83H4uxaqLcUs+xTjZPf61LYsI9vZjSEibWtUOKlUtTdMJDo6o7mwAdbe/xik16BdLqir+Fi9GNu7IyMYdyXYWsSKlZEW/3zOTPFOAGkKw4cQhNpw4xCsnV/SLj4zlyrBo/CxnX9HPMEqeuk+12Z+tZ7s3FkY060Di1qWeNJumE10/DNNeNigpChQoDkb8+K6nlmJt8n4WXvN3mupBldJh0+02aesfyeox/8dvqYdpUT+ERt71a9TUugYmyac1q5ySUpRHrE9EmeOk6yob0g55gv0pcw9s4crQVmhywiFJqnFkwJdKCbT6cG3TzlzbtDMn7AUsS9nNyhN7+S3tsGcbtzBZm76ften7saoafUJbEh8ZS7/QlnhXsE3prwyXyc0tu1HodjLnwBbCferxUo9RWN3ld3S0WDR+OLyzVJMEwGd7fuWFTiMwHeUHfFVVMHQTpzDwViyYzrPfGKguBT9sxIe2wTTFGfd7ubKaOrfH9OSXlP2eNC9Np2dYFO5yhoWapiCqXnCZ9Fb1Q7EompwLXpJqIBnwpTMK9vLjpqhuPNh9IDuOHGdpym6WJCewMyfZs43TNFiRmsiK1ES8NAv9wloxJKINvUNbYrvAFf1Uu8J9rfoyPronKgpepuWMVcimKQjzLtuxMNwnAOUMHQM1TSVfs/PK5kXsyUllSONY7m7Tu2Ta03PEsZpUla3rasnNiSlwuw26NGjCjH438WnCOurbvJnc+Wq8DL3c0H1qLvihTdvyc9IuABr5BXJ/u/6IGnazI0lSCTkOv4LqYhvQX8t8rDCbJSeDf2JeWrnv8dWtXBkWw5DINvQMaV6lK/q5vU1uWPwxh/JK2v4bePny4/CJ2Ozl33C4bAZjF3/IsYJsT9q46O5MajcY/hy1WGPP9amV/danHiCqXjDNfBugO1WEKLkJsCsuVEXFYqhl5hE4vcyKAm6LSZFwUuR20cDmi82l15gJk85XTT3PF6sulrsulPls4/BlwK+guvCF+auzlflwQSaLTy7qc6igbGc7gHoWLwaeXM63a4Nm6Grltv+qqoLLarAnJ41iw0lcg8bYXJonmNlsOqqq4HC4ME3I1Yu5cv6bpfbho1tZNerRUpMB1cRzresqCcWppTrbDWrUmtd6jDmvPgc1scwXqy6WGepmuetCmeXEO1KVaebXgHuj+3JPqz7sz8/wrOh3tOjPp+c8l535R7cx/+g2Aq0+DIpoTXxkLJ2DmlTKin6mKdDsKh18IwEFw25iIEqeZq1u1qUmcrwwh6FN2+Kn2PBSLCgoiNMqsyN9A2rFDK7FqosXNv1YqrPdsmN7KOjqIEjzxaG7yXfbsWo6XtU8oZEkSZdWlQf8119/nezsbF577TWefPJJNm/ejLd3yZCuiRMnMnjwYHbv3s3TTz9NYWEhXbt25fnnn0fXdZKTk5k0aRKZmZlERUXxxhtv4Otb8bHgUtVTFIVW9UJpVS+Uv8f0Z3duaknwT0kgtTjPs122s4jvkrbwXdIWQmx+DI5sw5DItrSvhBX9Sp7o/4zaxRYXdy77gl1ZJX0O/rllCbOvuZcWPiE82OFKpm9fCYBV1Xi11xi8TSvuS7AajmpRsKtuUMBqaqWaES6WAPKcZdeSL3a7sHu5uGHxxxzOzwRgdFRHnu58DXoNGm0gSdKFq9Irff369cybN8/z986dO/nqq69YsGABCxYsYPDgwQBMmjSJKVOmsHjxYoQQzJo1C4Dnn3+ecePGsWjRItq1a8d7771XldmtkxRFwbCaFNtcOGxuTOvFP+YqikJs/Qgejr2KnwZO5PPedzAuqhvBttLVTBmOAv53aBN3rPucYSve5d8Jy9mdm1IpU75qmsqRgixPsIeS0QX/3LIEu3Bye4uerBr9KF8Pvos1Yx+jpVcIbnfVB3vDajLv2FauWvgWvedM47XtizC9K69qwQcL41v3KpXW0Lc+wd5+vL9ztSfYA8w/tI3jRTmoqpxIR5LqgioL+Dk5Obz11lvcd999ABQXF5OcnMxTTz3FiBEjmD59OqZpcvz4cex2O3FxcQCMHTuWRYsW4XK52LRpE0OGDCmVLlUuw8vkoV+/5Yo50+g99598nPgLhrXyOmUpikLHwEZMahvPokEP8nGvW7m+aWfqW0tPSZtSnMt/D25g3Nr/MGrl+7y7ZxX789Iv4nNLnmr/qtjtxBQCzaUS4PamnXdkSee+SzBjnqIonHAVMHXTDxS4HLiFybf7N7PoyC50S+Vcim6nyehmcfy77w30iWjJna17MXfovVhMlT05ZTtYHsjLkAG/GigK6BYVxVpycypJl0KVfdOmTJnCI488Qr169QA4ceIEPXv25JVXXmHWrFn8/vvvzJ49m/T0dEJC/pweMCQkhLS0NLKzs/Hz80PX9VLpUuXRLCrf7NvEr6kHATCEyQe71pBiz62SIKApKl0bNOWp9kNZOugfvN/jZkY37oi/xavUdkeLsvlk/zquX/Mx1676kI/2riWpIPMMey2f223SOjCc0L8M2ZvQti/1lD9nCazMDp3nousq61MPlUlffnwPLqVyahcUBUxFsC8njW5hTfGyWDlakI2KwuiojqW2VRWF7mHNatRQw9pA01TsNjfv7F3J5N/ns73weKXUrEnSuVRJG/53331HREQEvXr1Yu7cuQA0btyYd99917PNbbfdxvz582nRokWptttTqyqVt7rShbTxnqm34sUICbm4BWUuF/lOO7+lHy6TviPrOJ3aNCmVVhVlHhHWkRGxHXEabtYm72fBoW0sOZJAgevP5XwPFpzg/b1reH/vGtoGRTAyqiMjojrQxP/My/meYpomC4f/nU92/UJyYS63xnSnTWAE/j5e+Pt7nfP9UPnl7uJqUiatV3hzGvj7olXC0MVCl4OXNixg9v4tnrT/JKzj1+seZ2izdqQV5/PFng0E2nyY2mM4YT7++ASUnimxtny/K+JSljm9KJ/R379PalFJ35ZFR3bx/pXjGN6s/SVfXEae67qlSgL+Tz/9REZGBqNGjSI3N5eioiIeeOABRo4c6amiF0Kg6zrh4eFkZGR43nvixAlCQ0MJCgoiPz8fwzDQNI2MjAxCQ0MrnBc5LO/MdIvGVY1asyZ5X6n0bqHNOHGiwNOWfinK3MGrIR3aNGRS9GB+TT/A4uQE1qTtw37ain67slLYlZXCq5sX0a5+5MnlfNsQ5l3vjPu1ofNou0G4hYFmqDgLDTIKz68sVVHuSFsA97btyycJ6zCESf/IVoyN6kRWZlGl7N9pdbPmeOnz6TDcHMvPpqkWxB3Ne3Jj864ogLdpoTDHSeFpvQZr0/f7dJqmomkKLpdZpo/IpSyzqirsd6R7gv0p7+1YTZfAJlhcVbt09ulq67k+m7pQ5ks+LO+zzz7z/Hvu3Ln89ttvjB8/nnvvvZeePXvi4+PDt99+y5gxY2jYsCE2m43NmzfTpUsXFixYQL9+/bBYLHTt2pWffvqJESNGMH/+fPr161cV2a2z3C6D4U3bk5CVzJwDf+BjsfJE5yEEaj4IV/VUMXppFgZGtGZgRGuK3U7WpO9n8fFdrMs4gPO06XN35iSzMyeZfyUso1NQY4ZExjIoojUNbGW/6I6ikpsG4xL0wD8XzaFyT0xf7mx9BSYCq9DQ7GqpIYIXQ0ejXVAkK44netJURSHMux7CAcIpsFISVNxnWdPgdBaLhqKAy2WccybCy42igNtmsjX7GAlZKQxu3IYGui+qq3r6LQgB3rqlTLqvbkVF9qWQqlaVT7xzKuC/9tprfP3113z99de43W7i4+N57LHHANizZw/PPPMMBQUFtG3blldffRWr1crx48eZPHkymZmZRERE8OabbxIQEFChz5dP+OcmrAKXaqIIsJk6pqv6noDOpMDlYFXaXhYn72JDxiHcomywUlHo2qApQyJjGRgRU6ZjYEVdDuWuKFVVyNcd3Lr0PxzOz8Sm6UztPpz48NjzCnKnl1nTVBxWN8uP7eGEvYCRzTrijw3K9oW8bBk2kyc2zmX5sT9vgN7rfzN9glpiuEq+Q+WdZ1VVsFhKllmu7D4ObpvJhNVfsvXEMaCkb8ucoffS3BJ8SWcxrInf74tVF8osZ9qrhIAvhABHPiGRYZzIKjvOuTa73C6SXGcxK04u57vpxOFyF3LRFZUewVHER8YyIDy6TMfA83G5lft8aZqKXXdhN93YVA2roYH7/J4eTy+z4WUyZtEHHD05BbFF1fhh2AOEK/UuaWfHi1FgddB37hul0pr4BfFd/D1YnSU1HX89z4ZVcLQ4i5+SdhIX3Igeoc3RHedeZ+F8KYqC22awLfMYSQVZDG7UBr9quJGqqd/vi1EXyixn2qsExQsn4/jlQ/L9Q9DbjcQSNxa9WS+USp4mVjq3AKs3Y5rEMaZJHJmOApan7GFx8m7+yDriCf1uYbIu4wDrMg7w0g6N3iEtiI+MpX9YK3wuckW/y51hmCeXI77w9mBNU9mSecQT7AFcpsG/ty3nla6jKzxZkKIAFgWHcGFBQzPUS3LTYJhln5jtxpkjq2ZR+Tl5B09tmO9J6x/Zin/1uq7SlkMWomRmyG71mtGjfhRud81rKpFqJhnwz5MrcQUARn4GxvpPcaz/FKVeBNaOo7F2HIvWpOsl72ErQQObHzc068oNzbqSXpzH0pQ9LE5OYEfOcc82LtNgVdpeVqXtxUvV6RvWivjIWPqEtsBLK9ueKpVwmmX7PDhMNwIq1NqsKOD2Mnl7+wpWHt9Lu6AInu02HH+3rcqrsH01G7FBESRkpXjS7mnbF29hwSinD4NddfHWtmWl0lYn78Mh3PhQuTeKhmFiVH+3EqkOkQH/PPmMfIXC7x5E5KV60kReCo617+NY+z5qYGMsHcZgjRuL1rCjDP7VINS7Hrc0784tzbuTXJTDkuTdLElJYHfun+fMbrpZmrKbpSm78dGsXBkeTXxkG3oFN8d6gcv51kaGYdI1pCkNvHzJtBcCoKDwUPuB6IZabrA8474sgud++54fk3YCcKwgmz3ZacyKn4DV1PBSHViEE1OAXauH2115j7tWl8YXV43nuwNb2Jl5nDHNOxEX1BjDceb8m+U8bssHcKk2kG34FSBMA7/sbaSv+grXjgWIwvIng1GDm2PtOLYk+IfHVspnV6ea3u6VVJDFkpQEliQnsD8/o9xt/HQbV0XEEB8RS7fgZlhUrcaX+0KcXmZVUym2OPkqcSMZ9nzGx1xBqMW/wj3c3V4mPea8ViaQrh3zGJGmi8yZj1Lw+xz0oEaEjv8IM6IzDrPiNS+aRcWuukAB3VRRXX+2u+tWFROBaiplOuGV6qhoUZl9bAsvbPrR83qPsGbM6HNzrVtzoK5/v2sr2WmvCnrpC8ON+8BanFvn4Nr5PaI4t9zt1bDWfwb/kJaVlo9L6XK/SBSlZHncAsOOyzQJtPhgdWnlnvcD+RksTi4J/kmFWeXur77Vh6vCY7ghtisttGA0pXb90J9NeefaYtVAAcNlXtC15LIZjF38IcdO6w9gUTW2jP0/nAueJ3fZjD831iw0fX0feaJ+hT5DWAQbsg7x7MaF5DiKGRnVgWe6XINaXLGRCVDSsz8xL435h7bRJbgJgxq3QberlbLGw8XQNAVN0042BVx8U8jlfl1XhbpQZhnwq3hYnnA7ce1dgWvbXJy7fgZH+V8oLbI91rhrsXQcjRbUrNLyVNUu94vE8DJ5cO23rE8rmSK4VUAo/4u/G734zIFaCEFiXpon+Cef4YYt2ObLoIiSFf06BDaslOV8L2dVca41XSWhKIXbl33m6RfwbNdh3BYRRdq0gbjSD5TaPnLSUhzh3St03RZYHfSb+69S8xk8EjeIO6N6eYbfnUl5ZdY0FU1XEabA5ar+hnbDZrI/P4OVxxPpHdGC2ICIi+5EeLlf11WhLpRZBvxLOA5fuIpx7VmGc9tcXAmLwFX+ED6tSVesHcdg7TAatX7DSstfVbicLxJdV9mQe4gJK78qlf54p3huj+qJy3nuH2shBDtzklmcnMDSlN2k28sva7hXvZPL+cYSGxBxwf00FEVBtSiYCBT3pZ3P/8x5AqtVp149b06cyK/8XuM6OHWDo/lZRPgG4CUs+BpO8r75OwW/zym1aZPX95Kvnv+smpqmsi7nAPev/l+p9A4NGvJJv9vOOXvd5fz9BsACn+5fx4wdqzxJt8X04JG2V6E4L/wG9LIvdxWoC2WWw/IuIcXijbX9CKztRyAcBbh2L8a5dS6uxGXg/nOOeOPI7xQf+Z3i759Gj+qFpeNYrB1GofpXfPrgukxVFRKzyy6qlJCdghl1flFLURTaBzakfWBDHo0dxNasoyxJTmB5WiIn7AWe7VLteXx5cCNfHtxII5/6xEfGEh8ZS7R/6HkHf1VXyFPtfLBzDbnOYu5p25eG1vrVNvMbgKJDoerkw8RfUIBborvja1oRlbmCoBusbo2W1lCEs+S82BUvGtwwDcfRbbjS9oOm02DsS7h1fyrQJxDTNImuX/a66RzSBJuilztPQ03i0gw+TvilVNr/9m7igXZXYpM/4VIFyCf8CrrQO0RRnItz1084t83DvXcFmOX8mioqeou+WOPGYmk3AtX33AvEXAqX812xoiicUAoYtPDfpdK/GDSeON/GF9XWGdjAh0WJu0qCf0oiuWeorYnya0B8REnwb+4ffNZ9Or3cDJz/FoXuPweyL7zm7zSzBGEYl/5SVBQotDgZtPDfnuWEvXULy0Y+jK/LWuXjwzVNxdvMRXEXoeheOBVv7GbFh78ZVpP/HdjE9O0rcAuT9g0a8umA27A6tHOW4XL+fgM4bQa9504rNbukgsL6ax/H5rjwgH+5l7sq1IUyn+0JX5s6derUS5udS6u42FmpP1q+vjaKiio46wigWLzQI9tj63w9tiv+hhbcAuEqxsw+wp+DfgRmVhKuhEU41ryL+8gmMN1ogU1QLmCmuMpyoWW+VLx0Cz0jo9idnYKvbuOJzkPoFRx10Wvc+/t5EYgP/cOiuaV5dzoENkRXNJKLckqNUc9xFrM56wizkjazIiWRPJedEC9/Aqzepfan6xrLUvbw05GdpdJzncUMbBhDdUz1b7XqfL5vPetS/2xHd5smvrqNHiFRVT5OXgiBExtO1Q8HXrjFhU0WpBoKHYIbckdsL8a3uYJro+KwufTzuvYv9++3pikUCSfbTk7FCzA6qiMDwqNRjAuvGbrcy10V6kKZFUXBx6f8m2ZZH1QNVN8gbD1ux9bjdsz8dJw7FuLaNhf3ofV4fqFMN+49S3HvWUqRZsXSehDWjmOxxF6NUs4CMXWZ6lLoVq8pXw68CxD4CCtuZ+UGKouq0Se0JX1CW+IwhvJrxgGWJO9mddpeik+buW1ffjr7EtOZkbiK2IAIhpys9g/3rgcI/Cy2Mvv2t3qhoFTaAjoVpaplg0Z5aZc7xaVgQ+fUEa7pVfkeToWH2g2kZ1hzlh5NoF9kNH3DW6Laa945kqqXrNKvoKqsEjJzk3Fun49z6zyMI5vK38jijaXNEKwdx2BpE49i8S5/u0pUF6rBynM+5S42XPyStp9FybtYl34AR3lNNUDHwEbER8YysFkM967+miMFJUMCvXULi0Y8RIDbu9qGfRXbXAxe8G9PM4OvbmXpqIfxdtSOWQgVBRSLgkuYeKHhcp15HP7lTNdVFE0Bk0oZOVBTyl2Z6kKZZS/9GhLwT2dkJeHaNh/ntrkYx7eVv5HND2vsNVjixmCJHoiil316rAx14SIpT0XLXeh2sDp1H4uTd/FrxsFyV/RTKOlM1jG4ER0bNKJHWBRebh1RjSO/VF2hSHMy+8AWFEXh2uad8TEsmJU441110TQFu8XNRwlrSchOZXSzjlzVsDWqXUHo4NYN8t0O/HUbFrd20c1ANUldvK7rQpllwK+BAf90RsYBnNvm4tw2DzM1odxtFO8ALO2GY+04Fr1lP5RKnCO+Llwk5bmYcuc5i1mZtpfFyQn8duIQRjmXmYJCt9CmXNOwHQNCoqln9UbXVVRVweUyL/kTv9WqExDgXavOtdtmcuPSjzmYd8KT9nDHq7ir1RVsyT7Cfau+xm648dIsfDLwNtr7RtaKG53zURev67pQZhnwa3jAP52Rursk+G+di3niQLnbKL4NsLQfibXjGPTmvVHUC181Daq/zNWlssqd5Sj0LOe7OTOp3JZlXVG5IqIFAxpF0zeiJQFWb6ymhukoZ+MqVNvOdY5exID5b5VKa+Dly08jJjJk4TvkOIo86cFefvw0bCIWx8VdLzVFbTvX56MulFmOw69FtPA2eIc/jVf8UxjJ23Fum4dr6xzM7KOebURhJs4Nn+Hc8BmKfxjWDqOwxl2L1qSbXM63GgTZfLmuaWduatGV71O289TGBWW2cQuTNcn7WJO8D4BI3wAe7DCAQcGt0S+w57pEuQsiBVi9cZtmqWAPcMJegIGJVddx6m7yXXb8LF7ohnrB8yRYdYHNyAcFnIoPDkP+5ErVR377aihFUdAbdkRv2BEx9DmMo5txbp2Lc/t8RG6yZzuRn4Zj3Uc41n2EUr8R1g6jS4J/ozi5ot8lp2A5QwDKdZYe459cmMuT6+fzgm6hf2jJin69Q1rU6BX9VFVB11UMQ1T5cL9TbEJnTFQc8w5tLcmDojC123Csik7rwDD2nDZpU/sGDbGgkWbkcePPn5DjKEJXVF7oMZIhEbEVDvreajGuP+ZxbM4zCFcxAQMfwD/+UQoMn0otoySdL1mlX0GXe5WQME3chzfg2javJPgXlL86nBrUrGSCn45j0SLanjX4X+5lripVUW6nl5tBC/5Nvqukrl5B4fvhfycpL5MH1sw863v9dBsDwmOIj2xDj+AoLBfZVFOernh/CQAAIABJREFUqjrXPmoxSs5hCrf9iFeLnuiNO1Fg+Fb655THbTM5VpTN/tx0eoY1x0dYsQiNfM3O5PXz2JJxhG6hTXm11xisis4dKz9nZ+afN826orLu2sex2s//eKuqgnf+Po5N7VoqPfSeLyF29GUxP39dvK7rQplllX4doqgqluZXYGl+Bd4jX8V9cF3JvP47FiKK/lytzMw6jH3Fm9hXvIkaGv3nin6h0dWY+9rP5i4Zhvdxwi/kOouZENuXMIs/9YLLDq/01a2lZuQrcDv4/th2vj+2nQCLd8lyvpGxdG3Q9LJe0c+mCxy/z+LE1//wpPn1vJmA6/7F/7N33oFVV+f/f53PuvcmuVlkkwTCJmwBRUCmLFkCVlvrqra1Wm2LX0etraPDSa21Wu1Qf9ZVtSCiggFFFAVlz4S9yYKQndx7P+v3x4Ukl9yETAiQ9z+1D+fee56cz+c8ZzzP+11ht/5uV/FKdFFj6BYXi3GyJM/EIsx28Nzwa0G2EKaErEt4VYM9RfkBnzdsiwrDi0bD+yrLEhXbltayV6ybj7v3FPT2qbcd5wDtTHuNxPnE1CQkCblDZ7T0KThG/Ryl06UgyZiFhwJ4/e3yAox9X+Nd9S/0bR9hVRQhhScihUQB55fPLYlW8dsCzZIZkdCVMQk9cNtOMEFRJcI0J2vyDmBjkxIWxcKr7mBKfB/cipNjnlJKdE/V13gtg6ziXD4+spX/HdxITkURIYpGvCu8WVc1reFziF1K3kvXYdfov+/INqIn/Bwvrc8jAX4+q5onfUJAmFyOvWE+vqV/wWF5CUlIQxcaBysK2FUj6Ec7Qrm193Bko+GLKiHAoUDpqjcC7O5Rt0LKZU06dVRUCUu2UWSpRU4tL8b3+mLwuT6mvfYj/UbiQjgSsnUP+s7P/Tv/7UtArwjaTk4ehDZwNgljb6TIapw++YWAsz7WTvAKA69p4JJVXLqGYfiPfm3bJrM4x6/ol51Frqck6FfEOd1MSPQr+vWNTGp08G8Nn91SCYcf7IXtC3zOUp/eQ6moX3ugteCSPJS8+wvK1rxXZXMPvxH3NfMo1VR+v/YTPj+ygx6RcTwzfA5xwo3VSK2DMKmcogW/ofSb1/2/2eMK4n72DiVm45kyLZfNp4e2s/zoTkYkdGVm2gBkj2jWZuZCmMsai4vB5/ayvPaAXydsXwV61lJ8m+aj71gGhidoO7nTZWgDTyr6hSec5V6eG7TVsbZsmy2FR8jIzuSznCyOe8uDtksMiWBScjqTE/vQI6xhin6t4bNTNvB8Po/CT56ssrl6j6XDbW9Sbp+de/zTES6KOHhfGgERU0h0emYf5VI0HlXHxEJCEGI5MBogsxwMIVIlilWJbZlYSggVdlij+RVszeZPm5cwf+/GKtuElF48MXQWsq/pVzlt9fluTVwMPrcH/PaA3yDYnlJ8mUvQN81H37UcanDEV0EIlC4j0AbMQe0/Aym0w9nv6FnC+TDWpm2xoeAQGdmZfJ6zg6I6FP06hUYzMSmdSUnpdHXH1vl9reVzmFyBvudrytb9D2f3kYQOnkOp1fjgdwpCCISgQe+2LEs4rBIk28SQXXgtDTdFHHyge8AzLlQHqU/tJV9xcPuKt9hScJR4l5vnR32fHq64c8bC53OYXL7gKazT/lar5zyAs10tr1G4GHxuD/jtAb/RsCqK0Ld/jG/TAow9X4IVZIcjySjdxqANnIXadxqS68I69m+tsRZCIFSwsZFMqcVK1HTLZF3xQf6W+QVZhbl1tuvmjmViUjoTE9PpFBYowdyaz7eiSCjCxAzCZ99QSJLAp5kcLS/CtC1Sw6Jx6Eqdf0NFBmfZAY79v5/iy91J6MAZRF/zBD7hoHLpUxQtmVfVNmr6Q4iJ93D3N/9jZc6eKnuIorFi1j2oleeGD0F3mIz+8M9V8sXgF3P6eta9aO0Bv1G4GHxuD/jtAb9ZiHJ4yF3xNr7NCzD2fUPQi0NZRe05HnXAbLT0KQin++x3tIXRGmMtZCiWPLyw5QtKdA8/6zOKVGd0k4ldTodPM7g642Vyyosb1L53RAITE9OZmNSbpJDINv98my6LHy57lZ1F/vr5lLAoFkz5GUpl8KPtcKmEww8PwCqvrlBxD7+JsGvmIds69rHdeHatxNlrDKJDVwodDkYtmIfXDNzOL796LlHGOaqfV+G9g+t5YsOnVaY7+o7mJz1GIHxNf26aO9ZCgEMykMwKTCUMbyOSGs8V2vrz3RJoD/jtAb9ZqOmzVZyDb+uHfkW/g98F/4DiRO090S/n23siQjs/iUZaY6y9DoNxH/6Fihrldgun3EEXrQNmI5PCgsHQLG5f+SYbjh0OsP/h0hl8dXg3K/N246lD0a9fZEfm9BjE5e404lzhze5LS0NRZJYdy+Seb/4XYL9v0ERu7jwsaG17mOcgh383IMAmhUTQ8fdbKLMjqibHU/OE7jS5e+W7fJe3v6q9U1ZZMfseHJXnrpTO1CzyvKV8m7ePwbGdSHZFBtzfK4o/c/9Mc50QYKgWujCRJQnJFE3KA5AkQZh9ghMLH8W7fx0h/SYTMXHuyWuaRn/dWcPFMH/XF/Dby/IaiYuhrON01PRZON0oqUNwXHojjqE/RApPwq4swi6pcYRsGVj5O9G3LMTz9cuYuVkgyUjRnRDS+VN/3JCxliSBrllUSD5s1f//hRV816UoMp/lZrHk0PYAe7FeyfiOvaAFuFhUZC5JTGXBvo1Van0/6D6Um7oPY1J8OtenXUo3dxymbXG0sijgXjjfU8qKo7t4a/8a1hw/iNfUSXRF4FKCl/g0ql+ySZgoRSk9gsshISQJo5GUwYoiszx3Z0AwBj8N8ZjEHkGz6J0qFC97HmooGDhSBuAaej06GrbtH+fycu/J35AYnJDKt3n7KfRWEKm5eGL4LDqFRSMZ546ZUjIFEbKLfpEdiRAuxMm+2IpNpaKz8tgeUAVhTgeSWXc/LafNb9Ys5Dfffsi/Mr8mz1PKFandG+1bKKXkPjeVym3LMEuP4dmzGvPEYUL7TcKw2+A7roBPMynwliFUgYpMEDHLCwLtZXntO/xmoSE+m8f3+8v8Ni/AzNkevJEzHK3PVLSBs1G6j2lRRb/WwJn8FgK8DpObP3+NHYV5SELwsz6j+FGP4ShBdk2KIvFN4V5+9uXbAfbrewzl130nYfpa5jkVCngVk11FeSSGRhApu4Lu4kp1D1/k7mJpdibfHd8fVM5XQjA0pjMTk3ozPqEXEVrj6+YVRUI7tonseZP9pXmSTOyNLyL3n4PXavgzIISgQCrnyg+fw64RwD+86g46Kx2CvudOyYtv7RsUvHs/2BZSaBQdH1hOZVjXqnv/muMsSQLDabKjKA/HSRrjKC2EDoSeUwnjYFAUmW0VR/nhslerFm4z0/rzu0FTg463qsosza99QvKvsTcwLCIN2dbRrDIADOHAYzvr3Cy5rXwOPXAaSZck0+mZ/ZRYbet0SFIEW8uzuf2LNyk3fERqLl6/8hbStBhM48KL+u1H+u0Bv1lorM9m3s5qOd/8XUHbiJCok4p+s1G6jmy2ol9r4IwBXxX8OXMZb+wMvNr4bMaviLFDg06WptPie0v/yf6SAsDPpvfpjF/g1p0tLocrSQLbtht0wlXkq2B5zk6WH9/J6px9WEE0/RQhMSw2jYlJ6YyJ74FbdTaoH2GihNynx6LnV6s7CtVB6hO7KLEjGuwPgKXa7K04xjMbl2JYFnf1H8PAiBQkXSArEh5ZBwGqJSN0f7qJU/Ki2RVYlSVIIVFUCDdGjV3w6eMsSQJdMbEkGyxwmupZ4/5vDHTN5Mblr1XlM5zC17PvJdTnqNVecyj8ceti4lxuRiV1xwaWH9mBaZnc2/0yKte8Q8EHv8P2VeK+7Dqirn2GUiN42WS4qF3lIEcmkvTb7yiz21bA9zlMJn38fIBYUnJYFPMn3o7ma3vzTnPRHvDbA36z0FSfbdvGzNnm5/XftADrxIGg7URYHFr/magDZqF0HtZmFP3O5Leumvxk5ZtsPn4kwP7S6OsZEdk1aJCQZYFPNdlw/BAlPg9XJHXDaahtRoM9NtZN1uEcPs/dQUZ2JhtPHA7aTpNkRsR2ZWJSOqPju9d77B8ulXDw3k61kj1Tn9hBqdJ4TgdFkfBIBrZtE4KGrptYqs36wkP87rsPOeGtYFaXgTwwaBJSZd1H1UIIHJIXl6RTaWl4LbVN3z+fDp9mMH3J38mvDHxGl834JTFW7QlfUSQKpQr+vvVL/rdnA0IIru8xlB+njyShOJvDDw8KaN/hB39BvuxWdD3YyYkP3+p/U/C/3/gNQiLh7vlYaWPRz1H5Yl0o13yMXPBMLfu3cx7A0Ywqh7aK9jv89jv8ZqGpPgshkNzxqN1H4xh5O2rvSQiHG6s4G2oyxfnKMQ9vwLfuLbxr38AqOopwRSDCE8+pot+Z/HYoCqWml1W5+6psAsGDgyej1JGxbNsgGYJUVzTdwmIRPtGm7hJDQx3gg76RScxMGcCslIHEu8Ip1T3ke6oDi2nbHCgv4PPcHby1fy27S/KQhSApJBLltAWbJCys3Cz0vN1VNqVDKu7Rt+Oj9k70TLAs259sZlVTzFYoOrOX/IMyw4tl22w/kUO45mRQh+Sgf19JErgppOj9eylY+Ch23g4i00egC9d5E/Q1WcaWYXWN5y81LJqbegxDNms/f5Ik2FB4iCc3ZGBhY9k2m48fYXxyL2KPbKZ8/YKA9sI2CRk4I+idvGHLOFP6EjXmx4T0m0yH2X/AjOqGz2x7O2ahQMbhzABFyn4dOjKr0wCkIH+n8x313eG3B/xGoj3gNw1CCKSIRNSe43CM/Blqj7EILQSr8DD4ajDFeUsxD63Ft+Y/+Na9g1WahwiJQrjjz3rwP5PflmnTNz6JEr2SnUV5xLnc/GXk90hxRNeZuHcKtn3mjOpzgdN9DlMd9I9KZnbqIKYn9yfGEUaRr5KCGux+hm2xt+w4S3OyeOfAWvaVHkeVZJJCIpGFhIlG1MArMUtyMYpycHYbTsId/6VCjUEI4c8aV0xsxUaVGp9MJcsS6woP8vHBrQH2csPHVZ36Ilu1J/UQyjj24hwqtmVgVRTjO7wF34F1uAfPRKf5SYpnA7YJfeM60iUihjLdy7jkXjw9fDYuQwt6PaSoMq/uXkXmiZwAe7QzhLFpAyn+7G8BdvcVtyI6D6eu2wwDFZ/sxorsjAcXZiOTMM8WNGQmde3DhmOHyK8sZWhcJ14Y9X1CTO28Wdw1Buc0ae+pp56isLCQJ598klWrVvHEE0/g9XqZMmUKc+fOBSArK4uHHnqI8vJyhgwZwmOPPYaiKGRnZ3PfffdRUFBAWloa8+bNIzS0cVSc7Uf6zUdr+mxb5klFvw/Qt3yIXXEiaDspthvagFloA+cgx/dqlb6cjob4LQTYKhiShW3bOC0Vs4mkMmcDtgqGbIINTkvBPO24tqFjfbCsgIzsTDKyM9lXdjxom3DVybiEnkxKSmdoTGdCFQPFrMQSGh4Rgm3b6E6LX6x8l9W5+4jUXPxp2NUMi05rVNa4EHBclHPloucC7Df1HMY96VdiBzmSdtsFHLq/ay17p2f2U0JUg3+7LUBVJTwYqELG1uvO2VAUia9O7K4lw/yfK2/hcncMZZ89R+GSeWDqhPSdSOytrzaJ9x8FdMX0Vzk4QlBNCdFCPBNNhSz78zsUVcbULTRDbpML7pbAObvDX716NXPnzmXMmDE8+uijTJ48mTfeeIPExERuv/12brrpJkaPHs20adP44x//yMCBA/nNb35D3759uf7667n99tuZMWMGU6dO5cUXX6SiooL77ruvUX1oD/jNx9ny2TZ1jD1fnZTz/Qi7DoEYKSHdH/wHzEaOrT1ptxQutLG2XDZPb8xg/t6NuDUnvxs6ldGx3QNIf5ri856S/Krgf7iGBHNNRGkhjE/sxaSkdAZFp/jlfFV4amsG/92zrqqdJATfzL4Pp7dxFRymZvH6nm/5+9YvMW2L3lGJvD7+ZjSvHDQAukUxR37bF6vGNYUUGkXyY5spbWNJZ2eCUzGRjTLskwup+uY7y2nz9KalvL93PQLBDT0v5e4+Y5G9Ek7Jh2ZXgG1hSA4qm8D7LysSuzz53PjZq1QaOoqQ+POIaxgV0/2cURPXxIX2TgfDOQn4RUVF/PSnP+Wqq65ix44dzJ49mxdffJHXX/crRy1cuJDvvvuOu+66i5tvvpnPPvsMgHXr1vH888/zyiuvcNlll7FmzRoURSEnJ4cbbriBzz//vFH9aA/4zce58Nk2vOi7lqNv+gBf5mLwlgVtJ3cc4Cf4GTgLOSq1RfvQsB2+/0jaECaSEDhMGSuIBMG5hqxKvH94PX9YtzjA/sXV9xBlVt9bN2esbdtmR0kuGUczycjJJLcy+IItxhHGhMTejEvtyR82fMKhssBFwn8n/pjezoRGv7eWaqPLJrpl4hQqml73Lk6TTdjxCXn/ugVsC4RE/B3vQLcJ+M6je91wuZyiJU9Tvn4+anx3Ym/4G5WuZIx6SggtzcYQJrIsIRmiWWx9p0PXTGYv/QdHaoypU1b5ctb/oXnO/ZH/xTB/1xfwWy1F8eGHH2bu3Lnk5Pjvi/Lz84mNrRbtiIuLIy8vr5Y9NjaWvLw8CgsLCQsLQ1GUAHs7Lg4IxYGWPgUtfQoheqVf0W/zB+hZGVBDIMY8upnKo5upXPwIcupQtIGz0PpfjRSRdFb6aThNfr36Az47sgO36uC3Q6YyPqEX8jk+wjwdPgyWHc6qZV+Xf5DJcekYLVCPLISgd0Qi/WI68ssB48gsyGHx4W0sy87iWI0F23FvGe8cWMs7B9YSogTu5AWCVHc0lrfxi3RJFzh0BcfJaS1YaeEp+EwZR89JdHp6D+aJQ8jRnfBKoXjPo2DvkA2KPv4jxctfAsA4cYQjT4wm5bGNlFD3KYXkE2gorRL8bEFAsAfwmDo+00Dj3Af8ix2tEvDff/99EhMTufzyy1mwwJ/5aVlWQNKVbdsIIeq0n/rfmmhK0lZdK53mIDb2/OeJbyzOrc9uSLoBxt+A5SmjbNNHlH73LhVbM7BrUNSah9ZSeWgtlR89hKvHFbgvvZawoXNQwuOa/Mv1+e0zDf68cRmfHdkBQKnu5YHVC1g5517SYs+Nzntd8JkGQ+M78+1pLHX9YzoSFRWKbdsUeMo5XllGTExYkxMkj1eW8f7eDazK3cfElN48MGwyTzpmsSbvAIv2b+GTA1sp8FQn/FXUEIQRwOiO3TlSVsjliV3OQpKmG4iB2E4ATagXOLcwinI4tvb9AJtVVgAVBcSmdGzQd7T0e13krWBkYje+riE+1MkdTZjmIDaybcybF+P8fQqtEvAXL17MsWPHmDlzJsXFxVRUVHD06FFkuXqFd+zYMeLi4khISODYsWNV9uPHjxMXF0d0dDSlpaWYpoksy1XtG4v2I/3mo8353HUaWtdpKJVF6NsX+xX9dq+AUxzxtk3lzq+o3PkV+W/+AqXbKLSBs1H7TkcKaXhCVkPq8Fdm76ll33Y8mwjD1ebIWm7uOYxvcvay4dghZCHx0z4j6aCEkldczJqCg/xls/9abe6AK7m0QyekRnKsm5rF/307ny+z/WRLnx3OYtPxI9zX90q6yrHc0/1K7ul5Jd/l72PJke0sz91Jie6p+rwNrDi6ixVHd9ElLKZKzrdzWOtKMLe557uBCBGgxqRhltZImhQCHOEN8qc1/JYkwbMjruGxtZ/wdc4e+nZI4olhs5A9gmPl5/5vfL6OdWNw1o/0X3vttar/XrBgAWvWrOGxxx5j4sSJHDx4kOTkZD7++GPmzJlDx44dcTgcrF+/nsGDB/Phhx8yatQoVFVlyJAhLF68mOnTp7Nw4UJGjRrVGt1tx3kEIUDTFGwbfETiGHI9jiHXY5WfQN/2Eb5N8zH2fk1VbZdtYexe4V8QzL8Hpcc4tIGz0fpchXA2LznLgcKIhG70j0lmTMceFPsqeWfXWnpFJWC1sWAPoHpl/nHFD/FhIAsJ1ZJRDIlD5gnuqEH3e8eXb/PR1DtJlf3SuZZiY9oWDlup9+jfJ8yqYH8K7+9Zz6/6j0PWJI7rpaw8socBMR357aVXca8xkWuW/iPoXf++suO8vOsrXt71FT3D46uCf8eQxkswS5LAkC0M/Hf7VgMojBVFRrG9WELF10ZIkU6HVwon9uaXOPLkGGyP/8okatpv0KUQ6rnNaFVYlo3mVfjDJdP9Aj1IqIaMeYFmxJ9vOGs0Qw6HgyeffJK7774br9fL6NGjmTx5MgDz5s3jt7/9LWVlZfTp04ebbroJgEceeYRf//rXvPTSSyQmJvLss8+ere62oy1CgWLh4c2s73CrTq7tPhjXSZY6KTQax2U347jsZqySPHxbF6FvXoCxf3X15y0DY8dSjB1LqVAcqD2vRBs4BzV9EkJrXLkngKXb3NZnOP/YvpL7v1lAjCuU3w2dSrjsxG4DGcmnw7JsFJ+EUqPOXHXI/G/Xhlpt/7d3A/f3m0ieXsq89cso9FZwW+8RDIpKQaojyUtCIAkRIMjjkBVUIbE0J4sHVn9QZf9+tyHcP3AiN/UaxtMbl1bZFSGhSDKeGpStO0vy2FmSx992fEGfiEQmdezDxMTexDdA0U+WBcWShz+s+4Tdxce4qlNfbu01vF4GvjC5At+OLyhZ8y6OtCGEj/wRZXZ4myvjMk0Lb3gXUv+UiXHiMHJ4HIYSRqVVv96BrEp4JJ38ilIUVWrxMlLbthG6P08A6s+laMfZRTu1biNxMRwJnY624LMkCY6LciZ/9Dy65U9BjnSEsHT6L1Dryf61io7i27IQ36YFmIfXB2+khqCmT0YbMAu11wTESY74M/mtqBLvHd7AH9Z9Um0TEitn39vosrJzBVWV+ShnCw9+uzDA/uSwWYxN7smYhX+mssY9+2vjbmJIeKegO31Ltfn7jhW8krWqyvbw0KlM69SPiR8FcpkLBKvm3I8mZN7du475+zaSHBrJw0OnEmJqfJm9m6XZmXydvwefFTzlfFB0ChMTe3NlYm9inMGPMHWnyfRPXiSvBv3szb0uZ27vcdgn3ao5zg7FwvflXzmx8LGq9o5OlxD3i0WUnaSrVVV/9n9burIRohZzcVBYDptFh7bw4tYVyELwq4HjmZjYu9HXN+cr2sJc1to4J1n67WhHS0Iogn9s+aoq2IM/QeizIzuYkdg/qBY6gBTZEeeon+Mc9XPMggN+Xv/NCzCza7Cy6RXoJ5X+cLjR+lyFNnA2dtSMevtUic5HBzYH2AzbYvPxIwyvg0u/rUHXTSak9OY/O78jq9BfUZMencjkTul8eXR3QLAHeG3HavoPS0ai9g5Z0gV3pI9mauf+bMg/xPDELsRpbixsPEYgY6GN/5pA8ircmHYZczpf4t/dGxIWNpNOHuGX6V5W5PkV/VYf2xeg6LfxxGE2njjMM9uXMaRDJyYm9WZcYi+itJCqNqW6JyDYA3y4bxN39hkdNGtcM8vIX/Z8gM17cANCLwdHGOWSj+VHdtAxNJIBHZJRfW2DwKUhwV6WJTJLjvLY2o+rbA+uXkjvqxJJq0NtsB0XFtoDfjvOG0hBsraD2eqC3KEz8ri5OMfNxczf7Vf027QAK39ndSNvKb4N7+Lb8C57341C6TPtpKLfFQg58HXRkOkRGc+m08RzOofHnFeTp+qV+c+4WzjhK0eSBJFKCLJXIsZVe5cQ4wxDRgqQp60J2SvRVY2hR2ocpmlh+WwU1c9698/Mr6vaDY3rVFU+Z/isquB7+vFvmOpgWnI/piX3o9hXyfLcnSzNzmTN8QNVbS1s1hQcYE3BAZ7clsGlMZ2ZlJTO2ISehDpq594nhUUi6hgeG5AcoVjlgaVlQlI4qhdx9eKXqhYd/Tp05NWxN6F4zo/dsaxILNy/uZb9kwNbmdt7PF5vG7yHakeLop1Lv5Fo59I/R7CgT3wS7+xag3lyQKMcITw8ZCo0oWtSaAfUriNxDP8xWr8ZiJBorNJc7BpMcbbuwTy6Bd+Gd/GufhXrxEHQQpEiOyKEhLBhSMdOZBzOpMTnzzb/fvehXJnYC2G2rTr8+mDbIJmCMOGgU4cOeEp0LMsmOiyUb/P2V+2Q3aqDF0Z9H4ehgOonWfFKBsj+xc+p98y2/fkCVe+dBYMTO9ErKh4Tm2u7Deb+QRPR9OAseHXBKav0jkhgWnI/vtfpEjqGRFJp+MitLK5qY2FzuKKQFXm7eHP/GnYW5tItMo79JcdPfofCy2N+SJzkrlqU1Xy+bcVJSHxqgJBM2NDvoQ6czv3rFnOgtKDKnl9ZytTO/YiSqk8U2hJOJbhKkvALDkmCMstTVUZ6Crf1Hk6qM/q8WqQ2FW1iLmtlnFMu/XON9jv85qOt+CwUKBVe/rtnHWGqg9ldBuHSW06r3LZtzKOb8W3yH+9bRUeCthPhCWj9r0YbMButy2V4VYNSw4NL0dBsGfk8vg+tOdaSJNA1k32lxyn0VDAoNgWHoWBg8fXxPTz47UIqDB89I+P5f+NvJkTX6n3XVFVGFyaKLWG0YKJYvqeUz7KzyMjJZEvh0aBtHLLCwJgUZqYNYGxsD5x2dY7F6c+3S1QiV+ZTseVTHJ0GISf2oUh28tOVb7HxeKBc8NsTbqOPK7HNBUuHpKN5j1H6zX9QopMJGTSTciLwaSZ3fvkWa/IPAjAqqRvPDv8e8nlyStFctJW5rDVxzrj02wLaA37z0ZZ8FgJUVQFsfL56+EObCdu2cZdkkr/iDXxbFmKX5AZtJ0WloPafhTZwNnLHAedUzrclEGysJUkghKhaWHkdBiMWPINZ4z59Umo6jw+5us4M/qZAUSRUswyEjBdng97j7IpiluX4ef2zioOPWYisMTq+OxOT0hke24WOCVG1fBZCoCgSlmVhmjaqKvP1iT38rEb5YowzjCXT7m7Skb4QoMk2wjYxhNYiTIdqgH1TAAAgAElEQVSnIMsSzsJMjvxpBJzMeVFj00h68CtKrXB0zcRj68iSvzRT1aULUjUuGNrSXNZaaA/47QG/WbgYfYZqv23LxNi/2p/wt+VD7PLg6nBSTBf/rn/ALKSE9PMy+J9prIWAg+YJZi5+KcAe53KzaMqdOHwtkxbkkjzYh76j6NM/I7nCiZ71e3zuTmfUW1dVGSEEum5woPREVfDfU3osaPswxcFVnfsyOro7Q2M6o0r1VHxoNjtKc3l957ekhEby4/QrCDVUTLORAjOyINQ8QdGyv2Ic20f4mJ8iJQ+m4gzldA2FS/JS/PotlG9ZEmBPnPsJesrIqv5ejO/1xeBze8BvD/jNwsXoMwT32zYNjL0rTyr6LcKucX9cE1J8r2pFv7juZ6O7LYKGjLXPaTJywTMBFRMz0wbw6KCp0AI7fFmW0HK+I/uZCVU2oWikPp5FiQjOuifLglBKqNj8MUbBYdyX/xCfMw6v5T+631t6jKUnFf0OlgeXYI5UXVWKfpd0SPUr+gXpmyXbSAgs3WrSzjhcKuHIHy7DLKrWpY+//S2sXtNbZKfvkjwUvXojFduXBdgTfrkIo9OYqpOai/G9vhh8bg/47QG/WbgYfYYz+20bPozdX+DbtADf9sXgDd5WTupXregX3bmVetsyaMhY24rNttJs7l01n/zKUoYndOG5kdeieZVGy6kGg1M2KHnjVso3Lgqwx9zwAtKQm4OWYIbLZWQ/NQY97yTVsZBIfmglnuh+ATketm2zqySPjOwsMrK3k13Hgi3GEcr4xN5MTkqnf1Ryo6pB6oMkCRz568l+alyA3dHpEmLuXkSF3XztD1mWcBzbyNEnx1TV6ymRSXT83XeUWNU88hfje30x+Nxeh9+OCxpCgK5ZlJleDMskUgtBOwv10ULRUHtPQu09iRDdg75jmV/RL/NT0KtJZszsrVRmb6VyyWPIKYNP7vxnIUU2TOCkrUEYgoHuFD666ueAjWxL/nr0Fto72JKMEtUR4QwjpNdYbF8FFTtWoER1xAgyppIk0HMyq4M9gG1x4oNHibz1P1RSfVQuhKBnRAI9IxK4u9cYthdls7JoDwv3bibfUx0IjnvLeffAOt49sI54p5sJSelMTkonPSKxWVc1tg2SVjurX3KGYdMyiXOmaWHF9CLlkXUUf/ESSnQK7pG3UC4igJbNFfDKOrYEsiVQjLbBSdCOutG+w28kLoYV4ulo6z6bTotffP0uq3L3AdAjMo63JtyGUtm8CbSpftu+cvTMDP+x/45lYHiDtlPSLkcdMAut30yk8Phm9bUmJFnCq+hUmD6ciopqykgNlOttC2MtBDilMo5VFrPwyC7CFZXJSV2JcUVSote+55YkgXb0G3KevSrA7uo1hqgfv0OlXf/deGysm7z8EjYXHiHj6HaW5ezghK88aNvkkEgmJKYzqWM6PdxxTQr+YVIZx16cjWffGr9BVkh+8MtapxHNhSQJVEXCRuDzBdbYy7IgOjqsyWMtyYITopz/++Z/bCvIZkRiV564fBYun4ptg0N4UaxKTEnDS8hZXwicKkU8HW3h+W5ttB/ptwf8ZqEt+yzLEt+V7OcnX7wZYL9/0ERuShuG3oxM/pbw2/aU4Nu+GH3zB+g7P69W9KsJIaF0Hek/9u83Ayk0usm/J0mCQqmC6zL+RV5lKbKQeOCSScxJHdSgoN8WxlqSBAVSOZMXPV9FqxvvcvPxtLvqXMSFy6Uc/cMwjBpleUn3f4aeeCmGYSFJwi+iE+SO/HSfTdtifcEhMrK383nOTor1yqC/2Tm0A5OS0pmYlE4Xd8PlkIUQhIlSfIfWYxw/QEj/KfiUqKp8g9aELEt4VYPthdmoskyP8HgcutLohYbuMLn605fILq++Ehme0IUXRnyfCL2EgvceoDLzcxydLyHmhr9RoSacFeZJU7Mot33kVZTQ2d0BzVCwa4gftYXnu7XRHvDbA36z0JZ91jSZ1/atZt6mwASlaZ378fglV2P6mj7JtLTfVkXhSUW/BRh7vqpW9KsJSUHpPsbP6993KpKrcepwpmYxd/X7rKyhRy4QfDPnPlwN4PdvC2MtaYLfb/6E+Xs3BtifH3kdY2N6BA3asiwRahdR+vVrGAUHCR97B2Z4Kh7LgemwOFpZxJ7iY1wa35kQW0PSBUIBn2LisQycklIrOADolsma4wfIyM7ki9ydlNVxWtPdHVcV/FNCAyWYZVlCCGr1W5Yl/3VEHbTQrQHdZTLzk7+TU+FXKEwNi2b+lNsbfRpWqnoZ9cG8WvasWXMpfuVHVGzNqLKp8d1IuO8LyuzW1aE3NYuXd6zk3ycZHZ2yyvwpt5MiR11UiYrtd/jtuGCh6xaTU/vUCvjXdh0MZ28ebRCkkCgcl96E49KbsMqOoW9ZhG/zfL+i36l1t2Vg7PwMY+dnMH8uas/xaANno6ZPQTjOnNBlYLGrKC/AZmNzvLKMVDnqvKm31s3ag1eXiA74761LCMd15b3Y2Hh9FoZhYWoWj29cwoJ9mwA/FfPr42/hkogUtpZm8+Mv3qBM9xKuOXl13M10d8Zi1Qj6qiQzIq4rI+K64jOnsOrYPjKyM/kybxeVNRT9dpfms3tnPi/sXEHviAQmJ/VhcnI6HSLCWHv8AOWGjxEJXXHoCtbJsjjTtAjiZqtB0xTe3rO2KtgDHCo7wdJDmcxMGtCohYdTVnApaoDWQlp4B1RTDwj2AHreHoRRCXITAr4GPskEGzRbrpdV0yuMqmAP4DF1Hvp2If8efSOyeXEQC50J7QG/Hec1bNsmSnHxytgbeXJDBh5T546+o0iPTML0tl3xGiksFsfw23AMvw2rOBvflg/9in6H1lY3Mn3omUvQM5eA6kLtPdF/7N97IkINfi/tsBWuTOnNW7vWVNlcikpCSDi2p7W9aiEYcEe/0Xx8cGtVImCk5mJUUjcMT/AxlWVBpWrw76xvyC4v4pZel5PsiMIrjKpgD2DZNo+u/Zi3JtzKz796hzLdv2Mv8Xn4+Zdv89FVP0c1gtfia7LCmIQejEnoQaWp83XeHjJOKvp5a1zVZBXnklWcy1+yPkeTFHwn/y1cc/Lp9F8QYqnnZOElBOSUF9WyZ1cUNzoXQTVlnh1xDb/6+n28pkG45uSvV1wHSCgdUjEKDlX/ruZCKA4aq5JrOixe2bmKV7O+wbJtbuo5jDv7jEbyBO/rKXrrmjhaXoQhLOQWSog839F+pN9IXAxHQqfjfPBZUSQqJP9uI8RWW4S69Vz4bRYeQt+8EN+m+ZhHawudAOAIQ0ufgjpwNmqPcf7J9CSEAMNp8fj6JSw+uJ3O4dE8ffkcUrXoWsfVwdBQn4UQ2KqNbpu4aJm/d03Yis0Ju4LXslYR6Qjhxh6X4TLVgN13TRhOi6mfvEB+DWW8tybcSlJoJGMXPhvQNtoRyifT7+Ly/z1V63tWz7m/0dLG5YaXL3N3k5GTyar8vQGKfqdjWEIaTw2eRbhwoWkyCDB066wktUmSIMcuZspHL1SJH0lC8PnMuUSZrkYvQmzFxlAsyg0foYqGpsvICNTcdeT8ZSq27gFJJu6WfyL1mdGoHAVZlthSfpQbPns1wP7vsTdyWUTnoNc6HqfOtI9fpMBTnXB5S69h3N1vLNLJK4vzYS5rLpp8hz9o0KCgKz/bthFCsGHDhpbrZSuhPeA3Hxejz3Du/TaP7cW35QO/ol9uZtA2whmO2nca2sA5KN1GIWTVr42ugi6ZYIHLUhtM6NIQn2VZUCp7mbdpGftLjnN12kCmd+pf586rqZAkgaJKYFMvjbIsCzaWHeHmz/9fgP3yhC78deS1XLf0X+wvqRa9+dWAcdzUcxjfy/gXe4urGfh6RyXw+rhbUL31s/nVhxJfJV/k7eKz3Cy+ydsXVFVQFoKhcZ2JdobikBR+lD6cjo7IFqUlrguSZrC3vIDntn6JLAT3DBhHqjMSy9d0n0+HJps47TLM4jzk8Fi8IhSvFVzMpS44HArPZC7jtaxVAfbrug3mkQHTgiv7hcCBsgL+tuUL9pcc58qU3nyv22DiJTeWfvGwCzY54B89GlyI4hQ6dmz7dcTtAb/5uBB9tlUbXbYo0z24VWfQhK225LeZm+WX8938AdaxPUHbiJBo1H4z0AbORukyAlEPTWxdaIjPhtNi2icvBOjM3ztwAjelDcOsY6cvSQKfYmJLgGXXWoT4eevtJr2rkiTY4cnjuqX/CrCPTurOX4dfhxeDl7d9xY6iXGZ07s/E5HRUXaZEriTjUCZuzUmp7mFySh/cprNFsslVVWa3N4/vLflXvTv+U/hJ+khuTRuBU7TeLasQgjDPYXL/eQPKyB+BbWCsfI2Eu+ZTpsS3qfwOWZZYW3qA25a/EWB/cdT3GRXdPegCVpIlKhQv648dRJFkZEnikujUgIVoQ99pWRa47BKE7kEoKl4R0uhFy7lCi2TpL168mJUrV6LrOiNHjuTqq69u0U62FtoDfvNxoflsqTYZOZk8/N0iDNsiUnPx30k/IUmKCJjs26Lftm1jZm/11/hvWoBVeChoO+GOR+s/A23AHOROlyKkht1hNoRLP9su5qqPXwiwdwyNZP6k24Ny6UuSoFLVueeb91mVu4+ekfE8f8V1JEjhWMLGI+uszT9IclgUqSFRKL7Gi7mYTovvL/s3e07u2BUh8cFVP6OT0gHLshCKQMfEgYKh+8v0fA6DP2/8jDX5BxiW0IW5A8ajeVuOPMbnNDhaXsR/dn5LkbeCjqFRbD5+hG0nsoO21ySZkXHdmJSUzhXx3XHJLVum53Ao+D5/Blf3y7F9FSDJCCHjyc5EGX5nrVr9cw3TYfHnLZ/x7p512DbM7jqQ3wyaUu9JkiQJTMU6edWk1VqANuSdFkLgppCc56bjO7IVoWhEX/M4jqE/pLKF9A5aE80O+K+88gqLFi1i1qxZ2LbNwoULmTRpEnfeeWeLd7al0R7wm48LzWef02TE/KcDdl59OyTx6uibUGscbbZ1v23bxjy8Ad+m+X5Fv+LggUREdPSz+w2cjZwc/JruFBric6nqYdQHfw6wDYxJ5p+jbgj4+52CoVn8clU1MRL4leaWTv8F2RXFzF7yclUG/tiOPXh62BwUb+OSrCRJoDtMvsnZS3ZFMVM79cNtO6COGGZoFj/7+i3W51cvmIYndOH54dfVK2+sqDKV+FCQkE2p/rlFgeN2GevyD2Db0CsygbTQGNYVHOQnK96s+3OAS1YZFd+dSUnpDI/tikNu/s5f0xSc5QfJ/uvMKlZCrWMfEu96j0pXKoZhoqj+vALzLOUVnAmWZqOLk4p/ttzsa4+GPN9OWafs/bmUrg4co9Qnd1EqxzXr988Gml2Wt3DhQt555x3Cwvxfcs0113DttdeeFwG/He04HRWGt9Yx656ifDjPxO2EECipg1FSB+Oa9kfMg9/5ef23LMQuq76btouP4v3qBbxfvYAU3dlf5jdgFnJi3yYxxYUIjVlpA/lgvz/7XZNkHh063X9MH4S61ZYICPYAxz1leCyD36/7JKDc7oujuyjSK4gVYY3a5VuWjVwpMS6mZ1Vte32fN4QZEOzB38f6Mrotp83HR7bw9u61JLjCeXDIZDpIoXUmEmJAvOxmUkIfLGwctoLhtRgYk0KPyDh2FeVXNe3kjuZgabWoT6Wpk3FS7CdMcTAmoQcTE9MZFptWr6Jf/bAp3/RRAAWx7+h2Knd+jbjkejyawes7V3LCW86tvUYQq4YhGsjQ2FqQfALHWS4mk81KPAfW1rLr+XuQOsa3iYVQU9Hgv+SpYA/gdrtRlPaKvnacnwhVHEQ7Qjnhrc7mvTKlN4p9/pbuCElCSbscJe1yXDOfxNj3Nb5NJxX9Kgqr2lknDuBZ/iye5c8ixXZHGzjbr+gX37PBvyX7JB66ZAo/6TOSI2WF9O+QjMNU6k4MtGx6RsazswY/gEtREUJQ6Kmo1bzE5yFWddPoOi5qk9vU6YOQCFU0yo3qwu5wzYmoseqTJIFt29i2f2f/8ZEtPPjtQgC2cpTVeftYPnNunWV8AKZpI0yBjKhaDGk+mbcn3MaKo7vYX1rArC4DiZZCOFBYUKXot7+sOsmwzPDy8ZGtfHxkKxGqi3EJPZmYlM6QDp1QGnhVA/71rC93dy27nr8HQ9KZvOhvFHn94/He7g18NPVOUpWoeuV/VVWuYjA8G0x6ZwOmHEpI30kU5+ysNkoyWmIvPOdxsAeQH3300UfP1Oirr76ioKCAPn36YFkWb7zxBsXFxUyfPv0sdLF5qKz0tWgySmiog4qKetgfLkBcaD6rtsxVXfuyrSCbEp+Hyal9eGToNJTTjqPPV7+FkJCjO6OlT8Ex6uconS4FScEsPBTA629XnMDY9w3eVf9G3/YRVkURrrgUvCL0jL8hmYJw4SLFFe2n7K1nrncIhZEp3fj00HYqDB8uReX5K64jLSQGl6ay/Gj1xBrjDOPOvmOQjNbdWSpCpnNUB5YdzgL8bIRPD59NN1csGjqhdgkcWYvLIaOoCmWS4E8blwSU/fkskysSu5HoiGjUHGPbIBmCnuHxXNqhM05TBROitBCGdOjEtZ0GMy6xJxGqk+OeMkr06vpyr2WwoySXT45uZf7BjWRXFBGiaCS4ws94WmPbEBqfTOlXrwTY4257jeUFuSzcvynAXuitYHxyr6AEVkKAWy7H2P4xlV++iDM0FGdkLD679emBm4OGvNOGLRHRYyjGsX3oubuQI+JJ+Ol/MKK6Y9otV83QWhBCEBISPMGwQXf4eXl53HvvvVVleAMGDGDevHkkJSW1bE9bAe13+M3HhehzldKXAMWWkHSplrTrhea3rXvQd35+UtFvCdQhECMnD0IbMBttwNVIUSkt8tuSLPAqBpWWjktW0QwZ2wDLYbMybzf/3b2OVHc0v+w/rsUy5c8ES7XwCIODZSfo7O6Aw1LQbBk1ew3Zz04G058AEDnlXpTJD/B/az5i2ZGsgO9YPO0ukkRki8gCB4Nt22QW57A0O4ul2ZnkekqCtotzupmQ2JtJSen0jUyqM/i7JA/2wdWcWPRHhCQTNesxpJShLD9xmDu+fDug7cy0/vx+0AwsX23fQqQKit68g/KNH1bZoqY/hHPcPXjqOfGoEyrosp9Rz2mpmLrlV8FULbwnEzEcQkH1yc36WzecZwKcohLV1rEArxyO3rZyGutEk5P2Zs6cyQ033MCMGTNwOBxUVlZiWRahoWfeAbQVtAf85uNi9BkubL9tXwV61lJ/tn/WUjCC0/DJnS5DGzgLrf/VSOEJrdIXRZHwCANVyKDTasGzLtQc51BRSt688ei5u6obCEGnPx/kIArTP3mx6hpgXMeePD1sNqouEyJKEYYHIUlYsoNyM7TFy9ws22ZL4VGWZmeyLCeT497gC7YkVwQTk9KZlJROz/D4WsFfVWVUoxiHQ6XUcGEYFobLYubiv1eJ4WiSzOIZdxNnhwU90g/nBAfv6xJgE1oIKY/voNQOb5xfTpu/b1/BW7vW4NacPDx0GsM7pGHLgntWvcdX2f6cg2Hxabw46gdIlU0//bmQ3+lTaHLAz8jI4L333mP79u3MmjWL66+/npSUllnxny20B/zm42L0GS4ev21PKb7MJeibF/gV/WpwxFdBCJQuI6oV/cIarg7X1lFznN2ihMMP9cY+LZimPp5FuSsJr2KQVZhDjNNNvNON4pNwqx7wFFO5fx2S6kTrmA6uSEp9TS/hEoJ6FwymbbGx4DAZOZl8lrODIl/tXAiA1NBoJib1ZnJSH7q6Y4P6LcsSu715qLLCd3n7KfF5uDKlF5kF2VyV1C/oDj9owHeGkfKnTEqthgd8RZVZlL2Zh777MMC+es79rMs/yN0r3w2wP3X5bKYm9G2y4NDp77QkC7yqcfKqSUM1JEQrXye1NuoL+PXe4Xfr1o2ZM2cyefJkdu7cyeOPP86qVauIiIigc+fOrdTdlkX7HX7zcTH6DBeP30JxoCT2QRt0DR1n3IM3LBVb9/pr/Gu8PFbhIfSsDLwrX8Q48B2YPqSoTgjVeQ5733zUHGdJlhCVx/EeWF/170pMZ9yjb8drOZANiURHBG7hRBgCp0NB9hVy+PfDKFv1JmVr3qNi8xLCR9yApYQ2erNhqTYe1eCIt4jQEIe/YiCYqKIQJIVEMiq+OzekXcag6BQUSSK7sriKux+gWK9kw4nDvHdwfdXCIMYRRqQWUuW3LAu+KzjIT754A90yKfRW8NfNy/FZJhOSeiOs2gFQlmzsosP4jm6vskXP+B10HokZpH1dMGSLv21fwaGyEwH28cm9WJW7l43HDwfYY1yhjEno0eQrn5pjLcsSeXYps5a8zEvbvuLNnd+SHptEcmhkUJ/PFzT7Dv8UTNPkiy++4IMPPmDPnj1kZGSc+UPnGO07/ObjYvQZLk6/a/pslR1H3/oRvs0LMPZ9HXzLKauoPcahDpiN1ucqhLN1JVBbA6ePc7hSTskXL1G+YSFacj86zP4j5Ups0CATHiZR/OGjFH0ayNcf++NXcQ35AaWlweV0g8FWbRYc3sif1n2KjY1TVnh74o/p7ohtcPWBbpmsPqnotyJ3FxVm8AVrr/B4ZnUfxMiIriSFROJx6IxZ+Cxes3qx8J8rb2FQWEqdv+2Wy/HtW03lzq8IHTQTKb435VZIg/0FkFWJf+5ZyQtbVwTYl0y/G4+hM2vJywH2/078MemuxCYH/JpjrWsmt6x4ncwTOVX/7pQVvpx1L5qn7Sfn1YUWk8fNzs5m69at7Nq1iy5dupz5A+1oRytAkvyr74Ys5GRZwisZmMIixK7NvNWOuiGFxeC4/Ec4Lv8RVkmuX9Fv8weYB76tbmTq6FkZ6FkZVChO1F4T/HX+vSchtMZN/m0FJUYojrH/R8gVt2PJTkotDbuOAGMjMIpza9n1olwae6CvyyZPrM+o4t/3mAb3rZrPO+NvQ6VhAUiVZEbFd2dUfHc8ps43+XvJyM5kZd5uPDV2/jtK8nhi/acA9ItMYlJyH14dexOv7PiGEp+Hn6SPpE94Eoav7vel1AxF6ToRV4/J+Ayz3vK9umDqFjf3upwvs3ezteAoAsENPS8lVgsDFR4fNpPnNi/Hsm1+3m8M3dxxLaaCKSTBjsLAsfOYBpWGD63Ro3d+4IwB3+fz8emnn/L++++zd+9eZs2axauvvnre3eW34/yHLAu8qsmu4jxcikpKaDSar24qVKHAEaOQR1Z/RH5lKdd1G8J1XYe0uMjLxQApPAHnyNtxjrwdq/Awvi0L/XK+RzZWNzI86Ns+Qt/2EWihqOmT0QbMQu15Zb3H/ooqUYmOIiRk4wzsdWcJXkMA7pMlaXX3x2cJ1LE/I8xXSdjgq7ENnZI176FdcnW9gj/BUGnomKcRQh0qPYGQmva8OmWV8Ym9GJ/YiwrDx1d5u8nIzuSbY3vRa5AdbS3KZmtRNmIbdHJ3YEBMsl82uAE/axhWg08f6oLmlXl1zE14bR1FyH5GPa//x6cl9ufKjr39/ljqGYN9NbWuhQu13gW+sGBUYjdWZFdzE3RwhhKiaHUyNJ7vqPdI/5FHHmHx4sWkpaXxgx/8gKlTp6Jp54eAwCm0H+k3H23FZ5/TYPonf6+qhe4dlcgb429B9gQnH/E5TUZ/MA9PjWPKh4dO5XvJlzRIzrWt+H020VifzeP78W35AH3TAsycbcEbOcPR+lyFNmA2So+xiBoc8ZbTZtHBLby/dz0poVE8OHgyUXYIVhN2i01Fc8ZZUSSEWYC96WOKMv6CUJ1Ez/49ZpfLsOxwDMVCFyYWNqoto+p1l5XpDpOrP32pKlMe4Oq0ATw8aCqiBZX0SnUPK/J28cWxXazM3l2nuE+vyHi+33koY+J6EKG1/R2vLAtKZC9PrP+UfSXHmNF5ANd2HYzkEViqjVcyyK4oIjkkCs2UkS0Jj6Zz/6oFfJW9h15R8Tw38lq/xsNZfP5aGk3O0n/wwQf54Q9/SN++fVutc62N9oDffLQFnxVN4sVdK3h528oA+8ujr2dEVNdauwxZFmwoO8wtn78eYO8T7efM1/QzH5G2Bb/PNprjs5m/y0/tu3kBVv6uoG1ESBRq3+loA+fg6HkF7x7dxOPrl1T9e6TmYumMX6KexTvU5vgsyxLqka/JefaqAHvKHzZTEpnKs1s+4+1da7GxuSKxG8+NvLbOsjJZFhRJHh5Zs4gdRXmM79iTXw0Yj+JpvJhQQxAb62b30TxW5O/mzX3fsbfkWNB2ipC4LDaNKR37MCquO+42mqSpO02mf/JigIrjz/uN4Sc9R7IsO4v7Vy3AxkYWEi+PuZ7LItOwTRtdMbHqUHE8H9HkO/wnnnii6r+bopb317/+lYyMDIQQXHPNNfzoRz/iwQcfZP369bhc/hXjXXfdxYQJE8jKyuKhhx6ivLycIUOG8Nhjj6EoCtnZ2dx3330UFBSQlpbGvHnzzisegHa0DCxsDpcV1bIfKS9CRNeeQC3LJjEkopa9szu6wfeh7Wgc5LgeuCb+GueEBzBztqNv/gDfpvlYJw5UtbErCvGt+Q++Nf+hLCwWOaYb/SI6sy2iI7YQFPkqOVh6gh6OuDZxtH8mqJJJ6crXatnLNyykYORtvLVrTZVtZc4eFh3YzDXJgzGClJWZpk2E7WTeZdegY+K0FfDUX54H/sQ3DzqqkBG6aBSPQaQWwuzUgfSKi+cHS18J2sawLb7J38s3+XtRJZkRcV2ZlJjO6PjuuJS2c+J7wlsREOwB3t+znht7XsbDaxZV5UaYtsWvV3/Akql3o+oysk+qmhGCaUFcSGgQEfMrr7zCP/7xD3r27EmfPn147bXX+Pvf/17vZ9asWcO3337LokWLmD9/Pm+88Qb79u1j27ZtvPnmm3z44Yd8+OGHTJgwAYD77ruPhx9+mIyMDGzb5r333gPgscce4/rrr+fTTz+lb9++Z/zddlyYEKbg5p7DAmyKkJiUko5h1FYBjZQAACAASURBVJ48bRs6aKFcnTagyhbtCOWBSyYjm+13+K0JIQRKUl9cU35H+K834v7FFzhG342ITA5sWHaMsQdW89fN7/Dfb1/mzj3L6VWSTbTDdV4EewAkBTWlXy2zmtyXLQVHatm/zduPJeoOKpZl+wVjfAq2fuZgbzlt3j64hlu+fJ1HNnxEmepFlhv3fFuWTffwOEYldauyxbvc/Kr/OPpGB7Kp6pbJitxdPLhxIeOW/oUHN/yPr3M2YFNN3KRKFuFSCWHew4SLYhxSEF6HVoBbddSyxYeEY9oWlUZgHwo85fx/9s47vqry/uPv54y7crNJSELYe0hYIqCCi4AoynDXUWup1lpbW3e1LlBr+amloq1aR9VarSJUZchQFKsgKCB770AGIbnJHWf+/riQEHMTspBAzvv1cvDc59xzvvdezvc8z/N9Ph+rAV4NJzt12pY3duzYKm55gUCAK664gjlz5tR6nK7rqKrK3r17ueaaa3j77bcZO3Ys/fv358CBA4wcOZLbbruNvLw8brjhBhYsWADA8uXLmTZtGv/4xz8444wzWLZsGYqikJeXx7XXXsvChQvrHKAzpd94mkvMlsviu+I9vLB2MV7Zxd0DcslWk2oVyjBdFmVWhBItRJYvCbehYNZxyq65xP1jcjxjti0Lc9c3h+18Z2EHDsTsJ1La4ep72M43q2+DHP3qQ6Om9N0SHqOY/Kmj0fZFZXfd3YeTcvObbDNtLvrouSr9nznrckam9WywcMzRSC7B3zZ9wQtrFle0ZfgS+O+YW+u0JHJ03EKA7rIoMUKEDZ3W3gTcukKRKOfcmU8f453Ah01udk8uyM5hhCin6NmLscIBhOIifdLriC4jiVjH13DNdFk8s2ZhxayKS5L5z+hf0MaXxA2LXmftwUr76LMyu/Ds0MtrtUI+WWmSbXkNcctTVZVp06bxyiuvMHr0aAzDYMiQITz00EPEx8dz8803895779G1a1fS0ipVoNLS0jhw4ADFxcX4/f6Kcx1pd2iZSJrEGYkd6XtmG2QhoZryMZO3rEkk4iVJ9mGHbcxTfMquOSMkCaXDGSgdzsB7yRMY2/+HvmoGke//C0e5w9kHdxH57C9EPvsLUqvOuHLG4+o3ETmjZ0UfRYneqE/0eqsqycw9WEC7m14nw9JAUthsGORpETrFteKRwWP5v5XziZgGP+k2mOEZXdHDjU/2AGEM/rNlRZW2/cFSDmkh0oh9w68J2wYlIpFKHEICOwyWsCkxQtX6Jrm8pHh8bCut/M6CCGbu2cDMPRvwmxpntxvGOQUbGVC8k/xXfk67KeuIUH2JrSmRNYk7+pzPjT2Gsbe8mO7JGXgMBaEJXjnvOh5fMZdvC3ZxZkZnft9/JGpEbnGj/Dol/DZt2vD6669zzTXXAPDWW2/V2Tjn9ttvZ9KkSdxyyy189dVXTJ8+veK16667jpkzZ9K5c+cqT/G2bSOEqPjv0dT3ab+mJ53GkJZ28omLNJbmFHMyP97+7uYU94/FjxZz6zEwZAy2oRPc8CmBpe9QtmImVrCyVsMq3Ep44VTCC6fiatOb+DOuxNfzXPSi3dimRnKv85ETWyMa7BEfpaExR0ydebvWIoTgxm6DiFg2L2z6giEZ5Qzp34nrepzB2I59sbGJVz34VBc00cdbGCoj3RdPYbisSnu8y01afN1Ocqy4raBNsttHcaRSuveW04bz83Y9WXx/Dp+md+eztB7s8aVUvF4mu5iT2Zc5mX1J0so5u3AzVxfs4Mzuw5DrYefbUDJIpEdqdd+HP505gaCh4Vdc+FQ39XwmOiWoU8J/5JFHuPPOO3nqqaewbZt+/foxderUWo/ZunUrmqbRs2dPvF4vubm5zJ49m6SkJEaNGgVEE7uiKGRkZFBQUFkhWlhYSHp6OikpKQQCAUzTRJZlCgoKSE9Pr1eAzpR+42mJMUPLjPuExdx6KPIlQ0kY8xT6pkXoK2egrZsNkcpkpu1dS9GMP1J01GHCm0i7x1ZSaic3+NSN3ZZ3f99zSCovoHz2k6B6eWX0bznoTqi49wii9rvlRCin7sp7dTn3lDMu5cp5L6Ed3ld/bbfBqJZcazxCgMulkJDgpbAwUGudgKwIZo35JU9+O5edgWImdurPpR1yEJFSOkZK6LjjS27c8SWb/eksbjuIz9sPYe9RhXOHXHF8mNWPD7/+iFbffcbIzJ7kZvWib3IbpMODN1kWxNmlGIXbkTx+8KdTbvsbtjNBsdEUi4ip45FUPIZSRRAo/fB3Xc6pK5nd6Cn91q1b88Ybb9TLLW/Pnj1MmzaNt99+G4CFCxdy+umn8/jjjzNkyBB8Ph/vvPMO48ePp02bNrjdblasWMHAgQOZNWsWw4cPR1VVBg0axOzZsxk7diwzZ85k+PDh9QjdwcHhZEIoLly9RuPqNRqfHkLfMB9t5Qz09fNArz69bIdK2DP5TLzn3I7c5xKkxB/bsluQGjzIvkfOgMNJt/yrN8mesppyar5PKoqE2ziEJECXvITN+vvIG4ZFZ28KSyb8nnVFe2kbn0qK6oFIzaNoVTbxaEWULvg7EVkhYcQkQnIqeg3a8ZZhkyh5mTxgHDomPlSMsIUmeUmdOIWid+9GAN2CRYzIvQWzwwg2FK7nvYUvskC4KXRVJp7CSBlv7/iGt3d8Q4Y3gdzMXoxq05MzEtzsmXIm5mHFQm+Pc0j7xVsEzPrtxrJVm4UHNvDA0v8SMQ3a+pP518ibSLA9J08R6HGmTkV7BQUFTJ48mSVLliDLMueddx733XcfiYm1r8n89a9/Zc6cOciyTG5uLr/+9a956623eOuttzAMg9zcXO68804ANmzYwAMPPEBZWRm9e/fmiSeewOVysXfvXu69916KiorIzMzk6aefPuZ5j8YZ4TeelhgztMy4m2vMdqQMa9MnhOY/hZ63IXYnIVA6Do3q+ve9FMmfFrvfD2hMzF6voPTft1O2pKreQ8KVTxE//FcEg9Ur1N2SjnRgNQX//CVG8V7ih1xD8riHKTVqT3CyLKEoEoZhYZoWsizhDWxh759HIsenYZbkkZR7B56zbyFkRffKR5dAbWw7OrL3G/nsfrAvth6tqhceP+0eW00pKTWeV5IEbsIIS8NQ4tEO61h5RQjFKEXP34YrswcRKY6I5TrcP4hkRVh28AAf7tvO/H0bOKjFtvPNxmLEzqWcU7CRTuUFCCDrrvlEMgbX694dcRsMm/EU1lEpbXhWF54ecgXyYeGi5vr7bkoaLLxzhJtuuolevXpxxRVXYJom77zzDnv37mXatGlNfrFNjZPwG09LjBlaZtzNOeYjCWvXH3rHtvCt0llC6Xw2rn4TUU8bi+Srecq/MTH7vDKlH9xLYOH0Ku3J1z+P5/TrCYera7QmUMzOe7tViSH54vtwn3/3YUnf6vjlIMaelQRXz8bb83zUjoOxLCj5+FGss39GQPXhl2Wspf8m46yfUi6nEmeXYBTuQPIlYvtaYagJhD/+I4fmPVPlvVPGP4p6zh0xpYAVGbzhPIrevRu9cDvxw64jbsh1BMzKOhpJEse8xxqWxfKinSzYv575+9ZTqodj9mtfXsg5BRuZcNY1dBp0fb2KMvMoYcwPdkWkuOOYfdFtuLUjhd/N9/fdVDR6Sn///v384x+Vogz33HMPY8aMqeUIBwcHh6bFtiHiSqXtI99y6OMnsI0ICefcQtmO1QS/+y/G1i/giEysbWFsWYyxZTHM+B1Kt/Oi1f69xyC8Da8W98gGqhXEQhCREwmFTZJH/ZayL1/HPlw8JydmkNDvYkpjJHtJEmh71lV7YCn/dha+Eb8EqnvJe2SdwPynOTQnWjdVsuA5EobfRMqERykd9XsuX/QWxZEgkhDc1+8CrpQU4vR89kwehhmI1kb5ci4i7abXCYsYxY21FNL57FJ2TzkTqzxqX1v07j3YehjXiN+gHQ6hLgMqRZIY3LYDpVKIHcEivIpKvOrh832bKTcq19N3xrXi9bhWvL5nJ91K/05uVi9GZfYiO+7YNRqtPH48skr4qM92eFYX3I7QVgV1SvhZWVns2rWLdu3aAZCfn1/v4jkHBweHxqKZMoa3Hf7L/wrYRGwVOf104gffhBXIR1s9C33VDIztX1UeZBkYGz7B2PAJQcWN2v2CqKNfr9HInuhIqC6j1Hi5nJKPphD43xvISZmkXTcdOaMfmiuNdpO/J7DiA4Tbh7/vGIIiiVhG9pZlo7bqUK3d1fY0LNlz2KznB69ZQfbPrzqbWvrFqygTp3Dvik8qKugt2+bx7xZwSed+RN5/sCLZAwRXfYxRsJnEc2+hZNHz2Fr0GMmbQPzQn1AaY3QvhMAo2lmR7I8QWPI6rYfdiBbj4aQmFJfEv3csZ8rySu2WdG8888b+hlV7N/DR2k/5NHCIsFSZkjaV5rOpNJ/nNnxG78RMcrN6kZvViwxv7POqhsybI3/G75b8h91lxZyb3Y0/DBqDCIsWtvmuZuqU8CVJYty4cZx11lnIssxXX31FRkYGt9xyCwB/+9vfjvEODg4ODk2DZdmEK0ZtlbdyKT4dz5mT8Jw5CevQ3qij36oPMHctrzzYiKCv/Rh97ccIlxdPl2FoydkknH0jpHUjWIOfu0uBssUvUbIoqvRp7Q+w7+kLaf+nzZTqyURIxjXkF9i2TaluEivZV1yCL5mEMXdTOufPYNsorTqQctkUym03NTnzxVp5NYCtJVX1721sDkWCJBzaW71/wXbM1J7Rh5MvX0coKv6h1xKUkmM+aNi2jRxXfW1fScnGFkptJoLVKEfjzY1Lq7TlhwIUR8o5s3VfRmTloIeL+KxgJx/t28oXB7ZU7DwAWFuSx9qSPJ5Zv5B+ydnkZvViZGZPWnmOmro2oLsnnfdyfwESyJaEHJbqJTV8qlOnhD969GhGjx5d8WenUt7BwaE5IyW1wTP8V3iG/wrz4A70VTPRVs3A3Lu6oo+thQiti6p2Br58HVfbHHy5d0OXkYgfaMQrRoDiFTOqnsQ0iOxahdzhXEzTRtPq5ql6UFaZ0/Esxjx6LZIRYb9lMXvfDq5qnxbzOUGTvCSe90tKjhrlxw/9CT4gt0033tm2sqI9weUh1eXFM/QaQusWVLQLxYWn81BKdYiIVFzn3U1ioje6nl2LDpDpTsI/9FrKvnoz+j4uH62ufpqQ5Aez7uvrki1I9cSxM1B1tsDv8mAboBs2KCmck5nCOZn9KdMjLD6wiXn71vFVwbYqjn4ri/ewsngPU9fOZ2BqO3KzenF+Zg+SXT4Mw6rilWE7Y/sq1KloD6C4uJjly5cjSRKDBw8mvo7CDicap2iv8bTEmKFlxn2qx2wWbEFbOQNz1X/QD2yO2Ud4E6OOfjkTULoMR8gKHlmn7D93EDic+I7QdvL3lHva1nnPuCQJVpbv4YaFr1Vp75qYzpvn3YhLjz0G88tB9O1LCa6chbf3KNzdhqMJH0GjmD+t/ZJ5ezfRMaEVT+acS6eENCQLQivepXTRC8jxaaReNRU9qQuaWZkM6/pdx0nliPICjEN5uLJ6ERLx6Fb9BHQURWKbVshlc19EPzxyv7B9bx4bdAlyLdsIAUq1EIv2b+STvPUsK9yOGePDloXgjFYdGZXVi3Mzusd09FNVGV+8m2Ag0iTSxs2VRlfpz58/n/vvv5/u3btjmibbt2/n2WefZciQIcc69ITjJPzG0xJjhpYZd11jdksGbrsc24hgK15CUiJmPUZ8jUWWo0mioedMEIfYeWeHY/YTca1QT7sEd78JJHfsTt7UXPSC7SAESbl3EJd7Z43LADVR7opw1oyqwmVXdz2de/rkYtey+UBRJGRZwjStiup1vxIiWLSNkKQg6WFapXemzE7ANC1cikA1SrCFQkTyV/us6vP7FiK6pt+oe6kCYVlnRcEu2vqTaeNNQtHqZ/17MFLOwv0bmLd3Hd8e3BVz/K5KMkPTOjE6qxfDW3fFr7ox3TYL9q5nyf6tjMzuyZmtOyOFT00TrUYn/DFjxvDMM8/QvXt3ANauXcsDDzzABx980LRXehxwEn7jaYkxQ8uMuy4xe6QI5ppZFLx5O7YeRs3oRtbvZlMmpx13gRNZFkRUk7XF+9Atk36pbXHrchU1tbrgk0IceutWyr+tvIepmT2wwmWYxdVd7gCkhAx8fS8krs9I3J2GYMheQpa33jFYqs2cfWuYvHwOYVOnf6u2/P2cn+CKyA1Sl1NVCcUox5LdaGbdE+iJ+n3LcnRdvbG/lfxwgAV5G5i3by2ri6vXLAC4JYWzMrtQHCnn28LdFe3Xdx/CHb3PA+3US/qNTvgTJkxgxowZx2xrjjgJv/G0xJihZcZdl5gTKGbn3Z0rt8ABcTkXkXj9PyoEX44Xptdiwpy/s6ssuhac5vXz0UW34aqDO9zRCBGtui9b9g7hdQvw9hmFb9BlBAwfxs7laKtmoK2aiV2aF/N4KSkb9YipT5uc+jv6qaBJJqZtoiLjMpQfXQ3uVPp97wuWMD9vHfP2rWP9YcW+2lCExJcT7sYVOfW27NWW8OWHH3744WO9QV5eHqtXr6Znz55YlsX777+PpmkMHjyYcDiMx3N8/5I3hlBIa5gmcw3ExbkJBk9dHeZYtMSYoWXGfayYhQC5ZDuBz1+u0m6FAySefSMax+9eoKoyc/eu4/1t31W0BQ2NONXF4LQO9R7lRywXStuBpA6diJ7en5ChAgIpqQ1q9wtwn30rStfhCNWHVbwL9EoDGTtcirlzGdrS19C+fRc7UIDkb4Xwp9Ut+Vsgm1HHR6keo/Km5FT6fcerHvqltGVi+wGMadOHVHcch7RQjep+FjZ5wUO4hUqmNxFZnDo2uUIIfD5X7NfqMsLv3bs3phm7yEEIwfr16xt3hccRZ4TfeFpizNAy467TCF8qYde93bD1SiOY+KHX4r/8aXQ8eKwSZCwMZCJSfL0TcU24XAovb13CM6sWVmm/sssgHswZgx5pWCFWXWK2TQNj6xL01R+gfT8L+yhHv6OR0rsftvOdgJzerUHXc7yxXDa6MFFkCckQiFNwWvsIWwMFzDuwjne2LadUi63ul6R6OT+zB7lZvRiY2u6kT/6NntI/mXESfuNpiTFDy4y7LjG7JAN5/7fk/+MmjOI9+PqMIu3GlwiSgKdsOwf+/hO0vWvxdBpM65vfolxNb5KkLwSUKGHOn/lMxTYtgWD2xbeRJSU2+O95Xb9n02WzMbCfN9ctYVDxTi4o3IS1eg52JPaxcmYf1H4TcOVMQE7t0KBrO4IkCTwEkdExbYWwiGtQvJbH5s8rP+HdrSuQEFzXfQi/6n0OcuTUTfoAhstkwb4NvL/tO3YFDpIfiv2dpbrjuCCzJ6OyepGTnF3h6Hcy0eCEP2vWLC699FJeffXVmK/feOONTXOFxxEn4TeelhgztMy46xqzogg8ZgkSNoZwEbJ9+Clh3+PDMA5WFr25Owwk7bZZlNtNYz5uKzb7jQDPrFqAbpn8+rRz6eBNRdJrvzEriowsC3TdrHY/iBWzospE0FGFgq1bKIrMl8VbufmztyqP8/r5OHcS9qpFUUe/dXOrTPsfjdx2AK6cCbhyxiElZdcrZkkS+M1C8l/7BeFNX+DueDrpN71C0JVZr10KiiLx+cEtPL1qAROzu2HZNu/t3sijZ4ylX1zbH3WXxYlAliVSUuIoLAywpngfc/etY/6+dRwIx/69t/bEMzKrF6Mye9I7Kav+dRoniAZr6e/cuROATZs2Nf1VOTg4nLQYhk3ZEWlV+/C/zHCVZA8Q2bECiboJ0tQFYQiy5UT+NGgCNjaqJWPqNScqIQTxUhmhtfMJ7ViB/4wrIaUzwVqq6y2vzaxdK/l45xr6pGQyqdfZWMDf1nxepV9BqIwtwVJ69x2Lq8/FSEYIbf08wt++h75hPhiVSx7m7m8J7f6W0EcPIHcYgq//OBJOuwA5PhVTuAgLf40DE68dYP/zVxDZsQKA8OYvyXt2LBl3LqSMuuuhSLIEejn/6jEQ5j2NLclcfuGdfBssQUlsf3IlfBV02cSybRRbQtHlYyrqHYnPtqF3Uha9k7K4o+f5rCrew7x961iQt56iSOWa/4FwgDe3LeXNbUtp40uK2vlm9aRbQuuTJvn/EGdKv544o76WQ0uMuzExx4sS9jzUD6u8uKJNbd2FjLs+pcw+MUJdfqmcwr9fRWjTFxVt6Te+iOh7JZoRvS8cHbNQBX/bvJi/rans3zUxnbdG/ozfffkeS/K2VHn/mRf+ks7uVvisQ4S3fIVQPbg7DCAQhvDq2eirZqBvWlSru5/auiutf/UeQV/7mMV78RSz666O1drb/WkzAaluFsAQLXqUSjax/+FBVJxIVsh6bBW6t229nOlOJKZq8eGe73nqu3mEDJ3z2nTnz8MmIoWOnYRr+32btsWKol18sm8dC/M2cEgPxezXPi6FUYd1/TvH1/3z/7Fo8Aj/iFZ+TTga+g4ODkcIi3gyfvkO+5+/HCtYgpyQTutb3iYkJdZLhrUpEXpZlWQPcHDWY2T2Gh3T/EWTDN7auKxK2+aSfMKmzj0Dcvl6dqXMa5/ULLLjkvCFi9j9yCCssiIA1LROZN23GHvglbgHXokVPIS+5kO0lTMwtn4OVtXiQv3AZvb8sR+u7uei5ExE7XMRkjep4nVbyChJWRiH9lW0SXHJILvqpWcvSYLQZy9S5anCNAj+7w3cIx+gNv3/5oIQUGKFeeSbjyraFu3dyD83fs1Nnc+sdbbnWMhCYnCrDgxu1YF7+oxiWeEOPtm3jkX7N1J21GzNzvKDvLh5CS9uXkLX+HRys3qSm9WLdjF8B5obtSb8UaNGVfz/tGnTuP3224/7BTk4OJyc6JYEWQPJfnQ16CFQfYSkhBM7VRxzAtMGQcxkaduQ5PYROGoHAoAqKWSryXw2/vcs3LOB7LgkclKz8VkKJQv/ipqSjf+C27BNncDSdwitXYDS5zIMw0TyJeEefB3uwddBeSHm4qcp/fT5atekbVyEtnERvH8HavfzcPWbiNpzNGF/Iq1vfot9fxmLHS5DuLy0nvRPwlJ8rTr4sWKTEzOrtSuJmbVOh3ulMKoVwooEEN5kgiRg/siaAUeQZYnVhdWFkZbs38K1nc9AoWkq7FVJ5sz0zpyZ3pk/mBfyv4JtfLJvHZ8d2EToqNmazYF8Nm/MZ/rGxfRMzGBUVi9GZvYiy9dwC+bjSZ2n9MeNG8fMmTOP9/U0Oc6UfuNpiTFDy4z7VIvZL5VT8MJlhLdU2uWmXf88Uv9rOOJ1c3TMiirxTclOblr0RoXxylVdB3HnaSORNQlVlXCLCBYSYUPBJdtY6z5EUt2UfPYiQvWQdMGvsSLlmJ1HxtRsj7cK2HVP17oFoHhQe43C238cid2HImwD4YknTByaVSfvsyokSCXseXQwZsmB6NuntKXNA/+j1IwuuciyhBBUTO97pRChxdMp/nAK2DZyYgZt7v2UclfWjy4UBNERfpEU5PxZz1Rp/03f8+o0wm/s7ztk6iw5sIVP8tbxxYEtRKzY9Sl9k9swKrMXF2T1JN3z4y5nNcm2vPHjx58UUro/xEn4jaclxgwtM+5TLeZo0V6A4OqPiWz/hvghP4H0HlWK9n4Ys6ValKPxzYGddE1KJ8ubiByRiJODaGvmULr4RZTkNqRMmIzuz0Y+sIo9U86uPKms0mHK95QqGTEnGDxSBHPthxT+6w6scABv9+GkXP4nDn43P+rot2dl9YMAXHG4eo9BzRmP2v18hOKu9+chy4I4Sglv/RpZVlA7DKKcRGzbRnOZrC7aQ4keZlhGJ7yGSpx2gF33VNUT8PW9kKQbXqlVVliWBYoiV9H9byqO1xp+fSk3Inx+YDPz9q3jy/ytVRz9jiCAASlRR78LMnuQ4o5rknPXhpPwnYTfKFpizNAy4z5VY1ZVGUkSGIZZTROgppgVRcKyoprvqiLBqn+T/9ovKl6XvAm0e3IjRf/+HYGv3q5ybOrlT6CcdRuaFnvO3S2buKwysK1qVfpm4Ta0VTPQV87A3L8u5vHCk4Da5+Koo1/XEQhZrdfncWSL2pG4TY/FVfNfZktJAQBxios5Y2+ndcFW9k4ZVvVzadWBjHsWU07saWvTbbGtrJBPdq9jSOtO9Etti9zURjWHpYltbBRbRtHr5nt/vH7fAT3Mp/s3Mm/fOpbW4OjnkRSePv1yhqZ1avLzH02Di/YOHapUkzJNk5KSkiofalJSUqzDHBwcHJoVDbFDPXpkqholFH5atUjZCpViFO9FibGvXk6sfco7YspEjiRMmyq1BnKrTnjPvxPv+XdiHtiAtnIG2qoPsAoq7XztcCna8n+hLf8XwpeCetoluPqNR+l0FkI6tj780XUVsiyxomhXRbIHKDc0/rp6EY/1Ow/h8mJrlRXrcQPGYcj+mPUDkkvwr20r+PN3nwDw8rovGdcxhwf6j0HWmlDBTgdXM/K9j1c9XNI2h0va5lCsBVmUt4F5+9axvGhnxZWFLYOFeRuOe8KvjVoT/pAhQxBCVCT5M844o+K15i6p6+Dg4NAQZFkiLOtomKhCxm3K2JYLJSmTyC4JV0Y3zGBxdB3choTzb6V0yWuYgWjCVFt3xdvrPEqbYCpbbt0D76j78eTeh7nve/RVH6CtmoF1cGdFHzt4MKrpv/Q1RHxrXH0viar7tT8DIR07yQoBhyLVt6AVayEiqLS5ZxEFr9+CXrgD/+lXkjT6LkrN2A8VEclg+vefVWmbuX0V9w4YjdxEBXXNnWSXj4ntBzCx/QAKw2UsyFvPgrwNaJbB1R1PP6HX5uzDryen6pRnbbTEmKFlxt3SY5YkQYkc5oaFr7G9tJAEl4dnz7qCAUlt8YfyscsL0fZ8j5zQGuH2IWX0IWTHESdKiWz/BqF6cWWfRpkdf9yK2mzbxtz97WFHvw+wS/bF7CcS2+DKGRdN/m0HVBOLOTpuzWNw7sxnCBqVZjr/GfULfwFkJQAAIABJREFUuntaIwS4zVIEJoYUR8RSajT70d0mw2f+H+Ef6A58NfFuPJH6LTscD1rC77u2Kf06PXLdf//91dqcLXoODg6nGppicuf/3mN7aSEApVqYWxf/C00ywQiz56mRHHj1Zvb9ZRwHP34KbBvTsik14zE6XoCePYxSs2bVvKZACIHSbiC+sVNIvH8N8bfOwX3mJIQ/vUo/u2Qvkc+nE/jr+ZQ+2Y/Q7Ecw9q6OudbtMVTmjP01Ezv35/zsHrw7ahKdfK0qiu7KbT9ldiJhs+ZkD+CyFX7e68wqbaPa9kK1Tz0b2pORWqf0H3roIQ4cOMCKFSs4ePBgRbthGOzevfu4X5yDg0PLxaWAapRiI6EpiRhGw9zw6oVks+oH+7zDpkHQCGP/5z7so6RXQ2sXYJfsRSR0j466T4DegJAklI5DUToOxXvJkxjblqCt/AD9+/9iByvv2dbBnYQ/fYbwp88gpXXFlTOeyLnXgatt9HXDJlF4+WPORZhYKGbtksU1YWs2N3YbxsC0dny8aw1nZnRmeGZX5LA4wavsDnCMhH/ZZZexefNmNm7cWEWER5Zl+vXrd9wvzsHBoWUSJwcJL3+Pg/P/guSJJ/WKPyFn9idixfb5bipclsEZ6R34/CgJ3TjFhV9RiRzKq9bfDBQgErufED/7HyIkGbXLCNQuI7DH/xlj8+Jotf+aj7DDpRX9rILNhBc8xc4FTyFn9Kp09GvVCVuLOhCajVDdkyKCQQntGZzTEduy0UPmCU/2kiQwFIv8YABUG8moW1X/qUad1vD3799PRkbGj3E9TY6zht94WmLM0DLjbg4xK4qEvGUe+6dfXtkoJNo9vo4yNfbe9sZwdMzxcjn5kuC2Je/xbcFuMuMSmXbW5eT4k9G+nVltW17byWsotapL9NYFRZGQpKiDX2NjkqRocXWs97GNCPrGhdGCv7WzQSuv3gmQs/vhypmAmjMOObld4y6oGSHLEmVKhAe+nsV3hbsZltGJP55+MR5NOSHiQcebRu/DX7FiBc899xxFRUVVnoo+/PDDprvK44ST8BtPS4wZWmbczSFmj6xT+vpPKV/1cZX2Vtc8izT4Jmzbxm2UAKApieiNqIZ3KQK/xyIQkdF1C8UDb21dRrLXT+fEdA5FgszbuZZ7+19AvK6jrZ1L6WeVwjshTyb1XWmQJIFfBAhv+hw9fxv+QRPQ3K0aNHvhkk08VgBt71qU1HZY3lSClq/G/rYWRN8wH23l+xgbPsHWwzH7ye0H48oZj6vvOFypbQhJOkigWjJCr0GxuJmiu0yuXfQKmw7lV7Sd0bojz515FUo9twpKkkBTTQ7pQVRJxi+7UTSpWX0eDd6Hf4QHH3yQK664gp49e560toAODg4nB7akomb2gB8kfDWjO5IVxNrxFfkzHgRTJ+nie/H1GFWr3W0shIiO5sv+9wZ56xbi7ZNLwpBrKLI9TF/zeTUt/V/3PRfJ9KH0uYzUnqOwJBfltgvrKBEfVY1atB5LWS6OAPufvYjIrlUAHPzgj7S5dxFK+oB6qdIpioRauJZdT52Hffh6E867lfiLHqzx8xAuH66+l+Lqeympfsj74j9oK2egb1xQxdHP3LmM0M5lhD68H6PDYN7xZ/FhYjtGdB/Cvf1H10nVrrmgY1ZJ9gBLD2zHFFa9tfc1t8lVn7zM1sOaBcOzuvD0sMuRwyfHlsM6JXyXy8VPf/rT43wpDg4ODhDRIXHk7ZSvmIFesB0Ab+8LULNzsMv2sXfauIq++S/9lDb3LEJuPaheRXNeEaLwn7dQ/l10ljK4dj6RbUuRrnuhRvMciIrxGMQdFp2JJntFtvFZJQS/m4Nw+UjocR7lIjHm9QghMIt3VSR7AGyLg+8/QMov3sWS4nATRrLCGEo8EaPmROIySyl441cVyR6gdNHzJI/+HYhjPwBJ3nhc/S/H1f9yrNAh9DUfo636AGPzp5WOfraNsn0pPwGuQvDd2pnM3bqEC3PvQqgnh/CaImTiFBflR205TPfGI6jfQ4usSry28auKZA/w+b4trD+0n5y47BNrElVH6vRY0qlTJ77//vvjfS0ODg4OAJSLZDLv/Zzsh5fTbsoaWv3sdTQlgbJl/6nWt/SLV1DquetLsSMVyf4IZcvfJ9kyeGTw2CrJ4Kqup6PasW+VQoDPKGL3g30peP2X5L90A3snDyGOkhr720clniNYehghbPxmAaVv/5IDU88nNPcxEuQyappUlWyzimVuxXuFy2oKu0YkbxLu039C/M/fI/GPm/BNfBal89nYR51cxmZQ8U6GfjadQw92peyVK4mseKdKQSBEdfT9IkCCVUi8KEWVT+x8t9uUeWrYRBQR/Q7dssL/nXkZXrN+ugCWsNhwaH+19o3F+5Gkk2PGo9YR/tixYwEoLy/n6quvpm3btihK5SEnwxq+g4PDyYdpWgSIR/jjo+ujFiimhSurV7W+rjZ9sOzab7iqKiFjYtgyhmFhIxCKq0ryFaoH29DIScxm8fjf803+DrolpZPpiZrnxMKlCA599BesUGXSM4r3Evx+DmrO1dUkfS3LRknrjJLSFuNg5dbm5DH3oCgKe564AKNwBwAl857BChThv2wqYbP6+r6h+Ikfdi2H5j5d0SYnZSLFpTTK2l6KS8U95Ke4h/yUsvBu/u/133Ju/gZOK91b2cnU0dfPQ18/j6DiRu0xEle/iXh6j8YXKSDvL5eiF2xHTkgn89Z3ID0H3Twx0962AUNTOvLlxLs4qAVJdcWhGjJmPWs/ZEviss4DmLer0t9AIDi/bY8fZ8toE1Brwn/wwQd/rOtwcHBwqMbRxVCGYZHQ41w8nQYT3rYMAFdWT/xDf0JpDVr5Rwrkyv73JsEd3xI/9Frc7QahCx/JF93HwVmPVPRNueSPaFIcki6Ix01uWs+oeU6kthGqjfWDES6AFSylpkmHoEikzR+WUPrZixj5W0g452bs9F5YwYMVyf4IZcv+TfLEKYSJUdBnWySccRVCVilf+RGujG4kX/h7kJVGJfyj8cW3ocvF93DHygWkhkoYW7KL64J52LuOcvQzIuhrPkJf8xFBl5di2YUVis5wmKX57PvrBNo9upKSGsx2GoKl2hiyiWFZuISCS5drLc4WhsBlKJyW1qbBRamGYTEgpR0Pn34xL61bQpzq4r6BF5IgvM2qaK826lSl/80331Q9SAg8Hg8dOnTA749dDQjwl7/8hXnz5iGE4LLLLuPGG2/kf//7H0888QSRSIQLL7yQO+64A4D169fzhz/8gfLycgYNGsQjjzyCoijs27ePu+66i6KiIjp27MjUqVOJi6u7xaBTpd94WmLM0DLjbu4xCyGIEwEoL8S2TKT41pRTs4ytXyojf9pYIju/q2hLvWoqyhk/R7GCiJI9aNuX4uo8FDs+q9YK91hIksBXtpXdDw+Cw/aowuWl3eQ1lIrUWo91qRISJroVtZFNEIfYeVenivcBUFt3ofVdn1JuV/dU91PC3scGE9f7fLxdhmEc2kvJF6+R+duPKI/rfMxrr+t3bakWumQRNnV8sguPoaDlb6909Mtbc8z3aPfYKgKe9sfsVxdMl8Vrm7/ihTWfY9oW/Vpl89K516GEjj2D0BS/b1mVCAkNgcBrqU1u/9tYGr0tb8KECWzYsIGuXbsiSRKbNm0iLS2NUCjElClTuOCCC6ods2zZMp555hneeOMNDMNgzJgxPP/889xyyy288cYbZGZmcvPNN3P99dczYsQILr74YiZPnky/fv24//776dOnD9dccw0333wzl1xyCRdddBHTp08nGAxy11131Tl4J+E3npYYM7TMuE+mmIU49vaweH0fu+6vugwgJ2WS9YellJFQcXMsLCxrsBCLW9JQA7s4NGcqwu0j6cK7CLtao1v1m8L2SBEiX/yNgzMfOnyhKlm/n4ueeXrMpOIT5Rx88UpCm5ZUNgqJ9n/eSqmdfMzzNdV3beZvqnT0y98Ys4/kTUQ57dKonW/nsxBynerFqyGE4ACljPpwWpX2m3ufza3dR2BptX+HJ9Pvu6E0Wks/KyuLV199lVmzZvHBBx/w9ttvM2DAAGbNmsX06dNjHjN48GD++c9/oigKRUVFmKZJaWkp7du3r6gFGDt2LHPnzmXv3r2Ew+EK9b4JEyYwd+5cdF3nm2++qVD5O9Lu4ODgUKf8LFVPLEJxVyi/HRkMNEZ1LWK5CMZ3xX/VdOImTKVMzap3sgcIW248Z/2Cdk9uJOuu+bT/02bM1jk1jiAjkp+06/+GnHBYQ1+SSb3yz2iifrMUjUVO74Y3914S7vya9Lu/IOHsn4JcdQnCCpWgLfsnZS+No2RyT4Iz7kTf9iW2Vc91dFmwvrh64dyKgl1o9smxjn4iqdNj1u7du6tY4/bt25cdO3YcU31PVVWmTZvGK6+8wujRo8nPzyctLa3i9fT0dA4cOFCtPS0tjQMHDlBcXIzf768oFDzS7uDg4FAXLDUO32mjCX5fOVBInTgFTUkEo+lm/izLJmwdWbVv+PuGbC/IXqSMDEKWXetbmaZNyJdNm4eWQziAcMehCS9hy93g8zcGIQR62mkkX/YnEs79Jfq+dQTXLiC44TPM4sqCP7usgMhXLxP56mVEQmalo1+7QcfUeTFNi/5pbau1X9C2Bx6hYNRSvOBWLIxAEW5FJWKcHFX1TU2dEr6iKCxZsoSzzjoLgCVLlqCqKgcPHsQwjFqPvf3225k0aRK33HILO3bsqPKF2raNEALLsmK2H/nv0dRX+KemqY3GkJZWfT3tVKclxgwtM+5TK+Z4XJNeJbx1KeGd3xE/cBxKajtkX9X7wskdc+W1u6v86dgcn7jjseOTcWd0JWHoNSAkwtuWUvS/twgunwGllYM2uzSPyBcvEPniBZRWHYgffDnxg6/A3b5/jff6kkMhJg+5lKe/W0CpFmJsx76c26Y7Pr8Ltxx7q51Rkk9421LCQkLCJrnTYJSE9Jh9T2XqlPAfeughbr/99ork7Ha7mTZtGi+//DJXXXVVzGO2bt2Kpmn07NkTr9dLbm4uc+fORZYra1cLCgpIT08nIyODgoJKMYPCwkLS09NJSUkhEAhgmiayLFf0rw/OGn7jaYkxQ8uM+9SM2Yvc/jzUTucT0C3schvKK2M8NWM+Nk0Rt6pIyOiYwlVtCyJIUB6K9muVw8ZzkrjR8HFayR7Ozd/AeUVb8B+l628U7qB49p8pnv1npFadcOVMwNVvAnJGZQ2GokisLNrDV3lbeebsy/EpLpbkbWHyN7N5esjlKHr1pRS/HEKU7qHk81cIb/8Gb7ezUVLaETElgsaJmQ05njRaWrdv374sXLiQTZs2IcsynTt3RpZlevToUeMxe/bsYdq0abz99tsALFy4kKuuuoqnnnqKnTt3kp2dzUcffcTEiRNp06YNbrebFStWMHDgQGbNmsXw4cNRVZVBgwYxe/Zsxo4dy8yZMxk+fHgDPgIHB4dTBUWRcRmHAA7b5h57Hdg0LUxnibdWvFIY1QphWwaW4iVUy+4HIQTxchlly94huHkJvgHj8fc4nzIzdv1AUGj86btPsITEqqR2rEpqxzT7Aub1GID3uznoaz7EDlWKFVmF2wgvnEp44VSk1j2juv79JkBaFwamteOOJf/h452VuwMeGTwWD7Gn9GUrxL6Xf4a2JyoeV7bsXczSfFpPeo3onEjLodaE/9JLLzFp0iQee+yxmNMrDzzwQI3HjhgxgtWrVzNu3DhkWSY3N5eLLrqIlJQUfv3rXxOJRBgxYgSjR48GYOrUqTzwwAOUlZXRu3dvrr/+eiA6u3DvvffywgsvkJmZydNPP13jOR0cHE5tPFIEdq+g8P0HsC2D5Ivvw9vlHEL11NJ3qEqcVE5gzhOULJwOto2ny1Ba3/ofSok9UvRRRv5L1xNatxCAsuUzSBz1W3yjHiBsVk8rNjaaWXX51xISRtez8Xe7CGvC0+ibFqGvmoG2dg5EKmcerAPrCX+ynvAnjyO36YvafzxvDLiABzZ/R3G4nKu7DebidqdhhGt48DONimR/hNCGz6psf2wp1Lot79///jdXXXUVzz33XMzXb7vttuN2YU2FM6XfeFpizNAy427OMQshiAvtYPeDOVXa29y3mEhaP0yzYX/Pm3PMx5MjcUuSwFO8lr2Th1V5PeXSh1DPuQMtRplWgl3Ezrur7vUXqoe2T24iEMMuWFEl5uev53dfvlfR1imhFe/kTkL5gfGMrYeijn6rPkBfNxf0UMzrl9oPRBkwHl+/iQhfZo1xJohD7PpDb+xI5fKBnJBO9kPfUGo1nRhQc6HBU/pH1udjJfYvv/yyCS7NwcHBoW6oqkzZZ+9Uay9d/BJxVz7f4ITfWIQQeEUZihkGIaFLnpNqxkGWJSI7VlRrD2/5Es/wXwKe6gdJUjUhBKG6a9xVYOgWw1t35e3cn/Pvzd/QPak1l3cZiCsiY/3gIKF6cZ12Ca7TLsGOlKGvnxd19NswH8xKKWRr5wq0nSvQZj6I0mEIas4EXH0vRYqvWucVEX7Sr3+eAy/fGB3VyyrpP3uZkJTYZIqEJwu1Jvy1a9fy2GOPkZSUxOOPP05KSgr79u3j8ccf5/PPP2f16tU/1nU6ODi0cCzLitrm/gBXVu9jaukfT+LlMgpevoHg2gUgBPHDridpwuOUWXVXBK0LqiJQrDCm5EFrwi2FhmES131Etfa4AeMxJB/E2CuvCw/xZ/2UwBevVrSlXPowmuyHGjZuyZpEb28mkwdcgrAFesislux/iHD7cfWbiKvfROxQCdra2VFHv02LwDp8ItvG2P4VxvavCM26B6Xz2bj6TUDtMxYpLoWIpeDucSHtn9qKVZqHlJhFRMSh177B7JREfvjhhx+u6cVf/epXjB49GiEEy5cvR9M0brrpJlJTU3nhhRdITj62mtOJJhTSmlTnOC7OTTBY3e3qVKYlxgwtM+7mHLNl2fjT2xDe8ClmSVR8RW3dhdSrnyZk1M/57GgaE7OqymjfvEXJoucr2rTdq/Cfloud2K5Rgj5HEALilXIiy96kbN5TSKFCEtr3Qoulr18Pjo5bdrnwZvcktPlLsC0Sz/kF/hE3E4qxHg9g2CoJPc/Gn3MhauuupF7xJHKnYTFNfo7Gtm0sM/pPfRGqByXrNNwDLsc97OfIrTpja0Gs4t1UTi3YWAd3oq+bS+Tz6Ri7vgHLwE7qiKYmkZjdieJyCdOup73iSYQQAp8v9vdQ6xr+6NGjmTt3LqZpMmrUKMLhMPfddx8XXXTRcbvYpsZZw288LTFmaJlxN/eYJUngI4Ad2A+mgZSUTVDEN2o6vzExexSLwFuTKFv+fpX2lEsfQj3vTjSt8VsDvFKYwHu/I/DVvyrafH0vJPn6fxC0G66q98O4XYqN2wyAAF14CdfBPlaWBbIsYRhWk95n64MVyEf7/r/oq2ZgbP8qtgSj7ELtcQGpZ19DOPschLvp9VmaCw1ew/d6o+tQsiwTiUR48cUX6dWruj2lg4ODw4+BZdmU4Uf4uwBHCq1PnFWZgUrcwAnVEr6v74WEmshURbHDBL7+d5W24Oo5pNkRoOlkdDVDoJFQr4/TNG3ME7zfUYpPxzPs53iG/RyrZB/a6ploKz/A3HWU6Zupoa+dzf61s0H1ovYcFZ327zESoZ489RaNpdaEf/TgPzk52Un2Dg4OzYLmYkdqGCb+7ueSNPr3lCycjlDdpFz6EHZSOyzLRlYlwpIOgNtWjmnuEhuBcHmrVJkjq4eL5pomjlMFKTELz9m34jn7VsyDO9FXzURb9T7m3qPqzfQQ+uqZ6KtngtuPq9cY1H4TULudh1Aat0zS3Kk14VuWRUlJSUXiP/r/AZKSko7v1Tk4ODg0c8pMH97c+0i44DcAaLKfoCFhumwWHVjPk9/OJWTo/KznmdzQbQhSuH4FhpoUR8q4hyl6p9IlNPnCu9AkHzRgcC3LEoZkUqaFkWVxwnY3HG/klPbI5/4Gz7m/wSzYEnXzWzMTbe/ayk6RMrTv3kX77l2ENxG1z8W4ciaidBneYEe/5kyta/g9evSo0LSvdqAQrF+//rheXFPgrOE3npYYM7TMuJ2Ym4aabFynD7+K4SndMIz6ZWqfFEIqyyO08Qs8XYZAYlvKrfpP51uqza7wQaatXoQkJO7IOZ8sNRFxgs1kZFlCFTo2As2Um6TYMRZpafHs/35ppZ1v4daY/URcKuppl+DqNwGl4zCEdPIU+TV4DX/Dhg3H5YIcHBwcTmUUReLTndW94T/c8T1ntepS7/cLWl5EXGeUwV0JmQ0rkJMkQb4RYMKcv2MfXgv4bO8mFl76W5KEt97LJEKASzKQzRCm4m+wA51XCiMKNlHyyTNI/lSSx9xNUE3DMI/PQ4ic0Qvv6F54Rv0Bc9/q6B7/VTMOV/tHscuL0L5+Fe3rVxHxrXH1vRRXv4nI7U5HSPW3Po6FEAK3pCGZYQwlPqbAUVNz6s1ZODg4OJxgLMuib2p2tfb+aW2RbHHM/eexsG07hkFN3VFVmTfXLK1I9gCmbfHe1m/5ZdcRaJqByyUjhEDTjFofACRJ4OcQxTMfJbz9G+L6XkjC+bcTsOLq9eAgyxIifz17nzy3oq1s2bu0nfw9pTRMBU9VZSRJoOtmrQ9GQgiUNjkobXKwxzyMuXtFxcjfLs2r6GcHDhD58kUiX76ISMqO6vrnTEDO7ldv99YjyLJEnFnIwf/8kcie1fgHTiR+xM8JGE2r3fBDnITv4ODg0MSYpk23hHQu7ZjDrO2rAOjfqi0TO/XHCJ0YeTfbhtbe6rK36d54hIAEqYSyL/6FWVZEwvCfobnTiFixt+b5CJD37Fi03dFiOG33avTCHSRcOY2QWXdDGpUwh+b+X5U2K1RKaP2nKL0n1MkY6QiSJPCLAMFVswntWoV/6E+wkzvWSfVQCIHSbhBKu0F4L56MseNr9JUz0L6fhV1W6eRqH9pDZPFfiSz+K1JqR1w5E1BzxiNn9q5X8vfZJez903kYhTsAOLh7NWYgH+/FjxAxjl9arnUN/1TAWcNvPC0xZmiZcTsxNy2my0IXJoZt4REqLl0+YfvVAXSPydiPp3MgFI0325/MBxfeQopWzp5HBmGWHPaqlxXa/nEZQX/nmNcbbxWw656uVRslmfZ/3k5pDC39mvAoBmXv3l5FYwAg49cfYHQ8H9Ose8L3S2UUPD+R8NalFW3pk16DXuPRDysT1ve7tk0DY9uXaCvfjzr6BYtj9pPSu1c4+snp3Y75vvH6PnbdX3XXm+RNIPuxNQTsun9+Ma+lsfa4Dg4ODi0dIcAtaah2BNuGiJyIfowRqKxJyFSu+TZkKr8p8egKi0ffhK0FEQhsVxyWqRLe+HllsgcwDYo/eoL4q/9GmOoFa0JWQVbgKAc8OT6N+j7LaJZK8tgHKFvxAbYWNclRM7rh7ng6kXokewARPlQl2QMUz3qM1t3OQ6dhSVTICmrXEahdR2CPn4qx+TO0VTPQ1s6GcGlFPyt/I+H5TxKe/yRyZh/UfhOi0/6pHWK/r+qt5kUgJ2VicXyLJ52E7+Dg4FAH4uVyDr53H4Gv30ZJzCDthheQsgcTsU6evds+yjg08xEkRcW2LUAm8eL7iMTsbYOIncE14SPl0oc4OOPBaIOQSLvuOSJyItRD59+ybMLuDNpNWUfw+7lI/hQ8XYZRZsfTJCIDTTiBLRQXas9c1J65+PQw+sYFUUe/tXNAD1b0M/PWYOatITznUeTs/rj6TcCVMx4pqbKmQ5c8JI78DSWfPBttkBXSrp2OpiRBI+o0jhmDM6VfP5wpz5ZDS4zbiTk2bsUmsmgqxR9OqWwUEu2f2kIpKcf5CpsGVZVR8pYhYVOy+B8gySSOuAlbKKjpXdj9xxzM0vxoZ0mm7UPLCPq71Hj/9IoQSuQg2v5NuNv2JSL5idh1X7+PdX22bddr3f5o/FIZ+c+NI7J9eUVb+k2vwGkT0fWGTenXBVsrR1//yWFHv0/AiP34pHQ+m7ir/46UmAWATwoiBQvRC7bhbpsT/fxqqJmoD7VN6TsJv544N8SWQ0uM24k5Nj4CFPxlDNqe76u0Z9w+E6PDuSeFeI3HLaMWrmXX5DPBio4iheKi7R+/xkjpjhopJPDlG1iBAhLOmUTE0xrtGAlIiGiCaQ7xVxbtfYS261v8Q6+D1C4EjyraO96/bztcirZ2DvqqGeibFoGpV3ndPfTn+CZMrfjz8fj8nDV8BwcHh0ZgyV7cHQZUS/iu1l3RTmARXm0oioxqBrAlFc12ISSJkiX/rEj2ALahEfjmPTy591NqJeIa8RuEEJRpJnYd4rJtmkWyh+jyQCl+1P4/wTvwWsLH2JZ3PBCeBNwDr8Q98Eqs4CH0NR9G7Xy3LAbLROk4pEr/H/vzcxK+g4ODwzGIWAoplz5MZOtStLwNICSSL74P05Ny2MCneeGTQphbvqB44XTk+HRSxj+CoWYjxVWXQ5fjUiqSTlO4+51oGqNV0JRIviTcg6/DPfg6rOAhsHQkf9oJvSYn4Ts4ODgcA9uGcjmF1r+fjzCCCMWNLrwErYavWR8vVFXG3LyE/dOvqGgr/34O7aasRR0xiZJFL2CVR7eXyQnpxJ1+BaXNJEkeL2RZIiIb5AcDWC4L1fhxt0dKvubhO+MkfAcHB4c6YJo2ZcSDHB8tIG8eM9nVUIwyihf8tUqbHS6LblnrPpq2j66KVsQrCp5eF1BOIs02mCZAlgXFUpDffv4uq4r2cEbrjkw98zLiDVezWY74sWgaUWAHBwcHh2aBLSnICenV2uWENAzDjgrj5FxN4lk3UGomNCrpKaqE7bJR1eabSsKKwQ0LXuO7wt1Yts1X+7dx6+J/EZF/BPH6Zkbz/ZYcHBwcHOqNZrtIGf8owlNZqe3pPAQlrWvFNHZ93fp+iBAC02vxxo6l/H7pe3y8fw2Wp3mOljXbZEegqErbqsI9mDVoDJx06JFVAAAdU0lEQVTKOFP6Dg4ODqcQlmUT9mTSbspawlu+Rk5IR0nv2nRiNoCumvz683/z9YHt8P/t3Xt8VNW99/HP3nsm9wQITAhGRKUcUbSg4oVKk4OVcAkYm5cXwMKplorVSrXPAWNAEasUPXmwUoFTjxx8+uANKZLKgVgK6APGVkQLoqhUDbdQCBGSyW0ys/d+/kiJRORqQpLZ3/c/OGv2TNbPnVe+s9bsvRawbs+n/Fvfvdx70Q+goUV+RIuJMS06x8Rz6J8r+QGcldgJo5VXtWuPNMIXEfmaGF/jqnRxVoTT3BCtTYVtgyqnE3afEYTSLiPoJLXoHvNh7KawP+zFTzcSNtvfxX8xER+/zRxDgq9xRcSUmDiezhxLvP3tF7npaDTCFxE5QrJVS83bv6fy3WXE9OxPl9HTqLFST2kjl5ZmmgZxbg2WEcHGImQkndR3763VZ9MwMA0D54gPEQm+mHZ57Z8bcbkk6SzeuOGX1Dth4kw/MREL+zRX9OvINMIXEfmnWF+EylWzqViST/3n71D15n9R9h9DSXAr26xPlmWQZB/gy4W3snNqbyoW3ERCaC+WZWKaBolGNckcJNmown+GhnB+12LCBc0Xkbn/8mHEtsDSsK3BjYC/3uL8TgH89Rau967XAzTCFxFpEmPXsn/9omZt4X3boaEGfMkt9nP8FsQ6VZgGhIml3o095j4vcU6Qf8y/mVDpJgDq/17C3qeuJ33KOkw3zL4Ft1D/2V+xUtJI+8kijLOvPOGSuN+W2WDw837/yvXn9Wfzgd1c06M3qVYCTth7o+aORCN8EZF/cuAbb2kzfKe3wE6sZZNsVJFiVBJnNV7NFms0YJW+QdmjV7Hj38+l6qW7STarj/kephtuCvvDwv/4FMtt4MDie5q2hLWr9vOPp/OIc2u/6W1anBUy6e3vxk1nX0aam4wV9nacGAbExFjExFoY7fTCD2+fIRGRI4SsTnS7dS4YX/1p7PSDuwmbcaf8XglmLeG/PMuu6Rex4/7vUPPagyRbtcS61ez9bR72ob3gOlRvXMqh1+cQ6/vmC95cw8LXJaNZm5nYBXCp276h+bHhEHZ1+Sn39XQ5jks4bLfoBYEdkekzqPE38NQna3l86584aNXitsP583bYJRGRthGJuFgZV9Dr8U+p/3wjMT0uwElKb7bj2skwTQPj0E4qltzf1Fa17nckXHgtRmwSX1+Av+6DVSRddy+QctR71Vud6D5pMXt/cz1OfRAjJoHud/xfImY8cb2vpnbLqq8OtvxYyYHGqQo5Y+qsMNlFT1ETaZzFeeHTd1id+wu6GInt6sOQRvgiIkcIuTFUGd2w/yWHmsTe1DoJp/welmVSu23tUe3V7y4lpvv5R7XHnjsQx/rmDxWRiEs47bv0fOxDznnsQ8759Tacs6+mzk0g8KOniTn7EgDMhE6k3/kC9Zx6f+X0+f0W/7Pjg6awB4i4Dv/10QZ8Me0rYjXCFxH5Bt/mljbbdojrPeio9rjvXIMd04WuN82mYtmDYIeJOftiUvMeIXicC+3CtkWYFIhJOWL07lLj60b3e1dhOPVg+gmZyTTY7StkvCDGtL6hzXfMCzHbSqsG/tNPP82qVY3TTVlZWUydOpUHHniATZs2ER/f+Gn25z//OUOHDmXbtm1MmzaNmpoaBg4cyMyZM/H5fJSVlTFlyhQqKio477zzKCwsJDExsTW7LSLyrTiOi5V2AZ2u+zmVa+aD65Dw3REkXnETVZE44q6+nV5XjcW1Q7hWPDVmCu5prGnfuKFPEhhJjffAt791b6JeOGwz7Jx+PLl5LV+GagCI9/n5yUXXYLezXQhbLfBLSkrYsGEDr776KoZhMHHiRFavXs3WrVtZvHgxaWnNr4SdMmUKjz76KAMGDKCgoIAlS5Ywbtw4Zs6cybhx48jJyWHevHnMnz+fKVOmtFa3RURaRLWTQOKIB+k8/N/BsYlY8QTtxun2eieGemIav1R1AY/t2hZtYsN+Vo2+h5U7tlJvh8k9rz8Jtr/djfBbbe4nEAiQn59PTEwMfr+f3r17U1ZWRllZGQUFBYwePZq5c+fiOA579uyhvr6eAQMGAJCXl0dxcTHhcJiNGzcybNiwZu0iIh1BnRNLlduZKqMrtU5CuwsAaRmO7RBTb3HT2Zcx4dyriA/52+XiPq02wu/Tp0/Tf5eWlrJq1Sqef/553nnnHWbMmEFycjKTJk1i6dKl9OnTh0Ag0HR8IBBg3759HDx4kKSkJHw+X7N2ERGR9ibczqbwv67VL9rbvn07kyZNYurUqZx//vnMmzev6bnx48ezfPlyevfu3WyhAtd1MQyj6d8jneqCBl27Jp34oFMUCLTcilsdhRdrBm/WrZo7Frs+iFtfDZYPX3LgxC84Qkeu+3R5sebDWjXwN23axOTJkykoKCAnJ4dPPvmE0tLSpil613Xx+Xykp6dTXv7VYhEHDhwgLS2N1NRUgsEgtm1jWRbl5eVHffd/IhUV1U17QLeEQCCZ8vJgi71fR+DFmsGbdavmjsMwINms5sul+dS8V4S/ex/SbnuGUHJvws6JB0Ydte5vwws1m6ZxzIFuq32Hv3fvXu6++24KCwvJyckBGgN+1qxZVFZWEg6Hefnllxk6dCgZGRnExsayaVPj8pFFRUVkZmbi9/sZOHAgK1euBGD58uVkZma2VpdFRDqMWDPMl8umEyxZjFMfJLTjPfY8fi3xRHegAfh8JolGkCSqiPXpwoiT1Woj/IULFxIKhZg9e3ZT25gxY7jjjjsYO3YskUiE7OxsRo0aBUBhYSHTp0+nurqafv36MWHCBABmzJhBfn4+CxYsoEePHsyZM6e1uiwi0mH47Fpq/vZaszanrgo7WA6JR6/YFy1izDDW3s3sf+E+7OoDdMr6KUlZd1Jta8GhEzHc9rTuXyvQlP6358WawZt1q+aOI8GopeJ3N1G//a2vGg2TXk98RhVdTvj6jlp3inuAHfkXgPPVBXKB8fMwLhtP+AR73HfUmk9Fm0zpi4hI6wmZSQT+7T+xkrs1NhgmXW9+nAbz1Nb9b8/8PpNEqkikCr/fwOczqdte0izsAar/+iI++9g7DkojLa0rItIB2bZDfUJPMh5+D+oqMeKSaTDiqXdObyvf9ibeqMP+eA37lj8MjkOX0dOIvXgkdO9z1LH+sy7CtWKhHd773p5ohC8i0kFFbAg6KQRje1Lldo6asDdNA7OylH2/+xHhfX8nXP45+//7J7jln2J2PY+kq8Y0Hevr1osuox4gZB+9nr00pxG+iIi0K36/RfAvLx3VHnzr9yTc+BSdbp5Dat4juKFajMSu1BidcL/FZkdeocAXEZF2xbZdYs/pf1R77DkDcByXkJMAZgLE88/dAxX2J0NT+iIiJ8nvN0kwaoizGjDNU1v1U05eJGIT3y+buN5XN7XF9rqMhMt+eEaWr7UskyQjSLL9D1KMQ8SZoVb/mWeCRvgiIich0aqlYcsqKt58Bl+XDFLzHqUu7iwi7Xv59A7D77dwXZfIP2+tCzrJBO76A0b9IXBd3PjOVLvJNG4v2HoMwyDRPkDZ/x5O+B+fguUjNXcG8d+bSJ3bse+AUOCLiJyA32fSsHkF+5+7o6mt9sM/0/PRrVTRsRa5MQzw+9vPn36/6RDvVFL73irMxFRS+lxDtZuC47hUu4kQk9h4oAOtHfYAsWaIipcLGsMewI7w5bIHOeeKm8GnwBcRiWr+SCUH1v1nszanroqG3R9gnj24RRf3ak1+0yE+UkHluoUcsHykfP92aq0uROy2+XrCNA3iQnvZ+fBA3Ia6xj5278NZ96+jipbf+OxkWHY9oZ3vH9UeLv8cMyO9w5zrb6Lv8EVETsA1Y/B17nFUu5Uc6DB73BsGxEcq2Pngdzn0P7P58o+PsuvB/iTYh9qsTzFmmIOvPdYU9gDhfdsJfbERy2qbeIr4EknsP6p5o+UjpkffDh32oMAXETmhEHGk3vhrjNjEpraEi4didMqgo6xO7vdbVK5d0CxcnfogwbcXExPTRvewuw5OXdVRzU5dJae4E3qLCUUsOmX/kuRB4xq3HO7Wi7PufY16s21mHFqSpvRFRE7AcVxCiWdzzqyPCJW+h69TOkbqOdQ4iSd+sRxTmDg6D/9f1PxtRVObGZ9CfN9/peoE6+K3pqCTSPJNv6HLjbNxXYN6K4VIpGN8sDseBb6IyEkI2yZhOmGd9wMaHBfX7lgBEA7bdLr2Z1Su+2qUb8Ylk/y9H1HV0Da3Gti2gxu4kIyC9VS+PgczqRtdRk6h1uwMbXj3g+tCnR0DxDQ2REHYgwJfROSU2B10RTfXhTpfV8559AOq/t9CDMtP8uAft3m41jlxWN36k/yjZ3ExCdpmh/sw1VEo8EVEPCLsmETMbsQMnUanTvGNW8W2g3UEbNvB5vB1BAr71qKL9kREPMR1oaFB28p5kQJfRETEAxT4IiIiHqDAFxER8QAFvoiIiAco8EVERDxAgS8iIuIBCnwREREPUOCLiIh4gAJfRETEA7S0roiItDumaZBAEOq+bFweMKErtSR3+D3p25ICX0RE2p0kI8i+p/Oo//wdAGLPGUD6vSuoouPvS99WNKUvIiLtit9vUbf19aawBwjt/Bs1m5bh91vHeaUcjwJfRETaFdM0aNj9wVHtDbs2Y5pGG/QoOijwRUSkXQmHbZKuGntUe/I1EwiH28F+vh2UAl9ERNoVx3FxOp9D9ztfwN/jAvzd+5D20+eg27/oor1voVUv2nv66adZtWoVAFlZWUydOpWSkhJ+/etfEwqFGDFiBPfddx8A27ZtY9q0adTU1DBw4EBmzpyJz+ejrKyMKVOmUFFRwXnnnUdhYSGJiYmt2W0REWljdU48/gtG0f2X3wdcGnydqY04bd2tDq3VRvglJSVs2LCBV199leXLl/Phhx+yYsUKCgoKmD9/PitXrmTr1q28+eabAEyZMoWHHnqI119/Hdd1WbJkCQAzZ85k3LhxFBcXc/HFFzN//vzW6rKIiLQj4YhDDcnUkEJYYf+ttVrgBwIB8vPziYmJwe/307t3b0pLS+nVqxc9e/bE5/MxevRoiouL2bNnD/X19QwYMACAvLw8iouLCYfDbNy4kWHDhjVrFxE50wzDIMGoJYVDJBuVxPr0XbJ0LK0W+H369GkK8NLSUlatWoVhGAQCgaZj0tLS2LdvH/v372/WHggE2LdvHwcPHiQpKQmfz9esXUTkTDIMSDar+PK/x7Njyrnsnn4xzpZlxJn1bd01kZPW6gvvbN++nUmTJjF16lQsy6K0tLTpOdd1MQwDx3EwDOOo9sP/Hunrj0+ka9eWX6QhEEhu8fds77xYM3izbtV8NKehngOv/Ad1H61pfFwfZP+in3LuE9tJTgsc97Xtmc61t7Rq4G/atInJkydTUFBATk4O77zzDuXl5U3Pl5eXk5aWRnp6erP2AwcOkJaWRmpqKsFgENu2sSyr6fhTUVFR3aJXdQYCyZSXB1vs/ToCL9YM3qxbNX+zBILUblt3VHv97g+p9qVh2x3vynGd6+hkmsYxB7qtNqW/d+9e7r77bgoLC8nJyQGgf//+fPHFF+zYsQPbtlmxYgWZmZlkZGQQGxvLpk2bACgqKiIzMxO/38/AgQNZuXIlAMuXLyczM7O1uiwi8o0cK4H4C47+2xNz1oUdMuzFm1pthL9w4UJCoRCzZ89uahszZgyzZ8/mnnvuIRQKkZWVxfDhwwEoLCxk+vTpVFdX069fPyZMmADAjBkzyM/PZ8GCBfTo0YM5c+a0VpdFRL5RyLHonJNPw56t1H38JkZcEt1uKSTi6wTKe+kgDNd1o/rXVVP6354XawZv1q2aj800DeLcaiw3BIZFg5lIyO64+4/pXEen403pd9zfVhGRM8hxXGpJBBIbR/W6K086GC2tKyIi4gEKfBEREQ9Q4IuIiHiAAl9ERMQDFPgiIiIeoMAXERHxAAW+iIiIByjwRUREPECBLyIi4gEKfBEREQ9Q4IuIiHiAAl9ERMQDFPgiIiIeoMAXERHxAAW+iIiIByjwRUREPECBLyIi4gEKfBEREQ9Q4IuIiHiAAl9ERMQDFPgiIiIeoMAXERHxAAW+iIiIByjwRUREPECBLyIi4gEKfBEREQ9Q4IuIiHiAAl9ERMQDFPgiIiIeoMAXERHxAAW+iIiIB7Rq4FdXVzNq1Ch2794NwAMPPEB2dja5ubnk5uayevVqALZt20ZeXh7Dhg1j2rRpRCIRAMrKyrj11lsZPnw4P/vZz6ipqWnN7oqIiEStVgv8zZs3M3bsWEpLS5vatm7dyuLFiykqKqKoqIihQ4cCMGXKFB566CFef/11XNdlyZIlAMycOZNx48ZRXFzMxRdfzPz581uruyIinhZnNpBiHCKZL0kwazGMtu6RtLRWC/wlS5YwY8YM0tLSAKirq6OsrIyCggJGjx7N3LlzcRyHPXv2UF9fz4ABAwDIy8ujuLiYcDjMxo0bGTZsWLN2ERFpWYlmLfVv/pYd9/dh55TzOfjc7SSb1W3dLWlhrRb4jz32GAMHDmx6fODAAa6++mpmzZrFkiVLePfdd1m6dCn79+8nEAg0HRcIBNi3bx8HDx4kKSkJn8/XrF1ERFqOaRpQuZuDf/wV2GEAaj8oJvjW/yHGp2F+NPGdqR/Us2dP5s2b1/R4/PjxLF++nN69e2McMXfkui6GYTT9e6SvPz4ZXbsmnX6njyEQSG7x92zvvFgzeLNu1ewdh+s+9Ld3jnqu/uN1dLnuLqz4lDPdrVbl1XMNZzDwP/nkE0pLS5um6F3XxefzkZ6eTnl5edNxBw4cIC0tjdTUVILBILZtY1kW5eXlTV8PnIqKimocx22xOgKBZMrLgy32fh2BF2sGb9atmr3jcN2GYZD4ne8d9Xz8JSMIhkzC1dHz/8YL59o0jWMOdM/YbXmu6zJr1iwqKysJh8O8/PLLDB06lIyMDGJjY9m0aRMARUVFZGZm4vf7GThwICtXrgRg+fLlZGZmnqnuioh4guu6OEk96HpLIUZsIhgmSVeNIemqMYTDLTdYkrZ3xkb4ffv25Y477mDs2LFEIhGys7MZNWoUAIWFhUyfPp3q6mr69evHhAkTAJgxYwb5+fksWLCAHj16MGfOnDPVXRERz6h14om96sf0vOImwCVixBG049q6W9LCDNd1o/ojnKb0vz0v1gzerFs1e4cX6/ZCze1iSl9ERETajgJfRETEAxT4IiIiHqDAFxER8QAFvoiIiAco8EVERDxAgS8iIuIBCnwREREPUOCLiIh4wBlbWretmGbLb+/YGu/Z3nmxZvBm3arZO7xYd7TXfLz6on5pXREREdGUvoiIiCco8EVERDxAgS8iIuIBCnwREREPUOCLiIh4gAJfRETEAxT4IiIiHqDAFxER8QAFvoiIiAco8I/jqaeeYuTIkeTk5LBo0SIASkpKGD16NNnZ2Tz55JNt3MPW8/jjj5Ofnw94o+bx48eTk5NDbm4uubm5bN68OerrXrt2LXl5eYwYMYJHH30UiP5z/corrzSd49zcXC6//HIeeeSRqK+7qKiInJwccnJyePzxx4HoP9cAzzzzDMOGDWP06NEsWLAA8Ebdx+TKN/rrX//qjhkzxg2Hw25dXZ07ZMgQd9u2bW5WVpa7c+dONxwOu7fffrv7xhtvtHVXW1xJSYl71VVXuffff79bV1cX9TU7juMOHjzYDYfDTW3RXvfOnTvdwYMHu3v37nUbGhrcsWPHum+88UZU1/x1n376qTt06FC3rKwsquuura11r7jiCreiosINh8PujTfe6K5Zsyaqa3Zd133rrbfcUaNGucFg0I1EIu6kSZPcoqKiqK/7eDTCP4Yrr7yS3//+9/h8PioqKrBtm6qqKnr16kXPnj3x+XyMHj2a4uLitu5qizp06BBPPvkkd955JwBbtmyJ+po///xzAG6//Xauv/56Fi9eHPV1r169mpEjR5Keno7f7+fJJ58kPj4+qmv+uocffpj77ruPXbt2RXXdtm3jOA51dXVEIhEikQhJSUlRXTPARx99xODBg0lKSsKyLL7//e/zyiuvRH3dx6PAPw6/38/cuXPJyclh0KBB7N+/n0Ag0PR8Wloa+/bta8MetryHHnqI++67j5SUFABP1FxVVcWgQYOYN28ezz33HC+99BJlZWVRXfeOHTuwbZs777yT3NxcXnjhBU+c68NKSkqor69nxIgRUV93UlISv/jFLxgxYgRZWVlkZGREfc0A/fr1Y8OGDRw6dIhQKMTatWt57733or7u41Hgn8DkyZN5++232bt3L6WlpRjGV1sPuq7b7HFH98orr9CjRw8GDRrU1OY4TlTXDHDppZfyxBNPkJycTGpqKjfeeCNz586N6rpt2+btt99m1qxZvPzyy2zZsoVdu3ZFdc1Heumll7jtttuA6P8d//jjj/nDH/7AunXrWL9+PaZpRv3fMoBBgwaRl5fH+PHjmThxIpdffjmRSCTq6z4eX1t3oL367LPPaGho4MILLyQ+Pp7s7GyKi4uxLKvpmPLyctLS0tqwly1r5cqVlJeXk5ubS2VlJbW1tezZsyeqawZ49913CYfDTR90XNclIyOD8vLypmOire5u3boxaNAgUlNTAbjuuuui/vf7sIaGBjZu3Mjs2bMBSE9Pj+pzvWHDBgYNGkTXrl0ByMvLY+HChVF/rqurq8nOzm76YPfss89y5ZVXRvW5PhGN8I9h9+7dTJ8+nYaGBhoaGlizZg1jxozhiy++aJoOXbFiBZmZmW3d1RazaNEiVqxYQVFREZMnT+baa6/l2WefjeqaAYLBIE888QShUIjq6mpeffVVfvnLX0Z13UOGDGHDhg1UVVVh2zbr169n+PDhUV3zYZ988gnnnnsuCQkJAPTv3z+q6+7bty8lJSXU1tbiui5r166N+pqh8W/4XXfdRSQSIRgMsnTpUu69996or/t4NMI/hqysLLZs2cINN9yAZVlkZ2eTk5NDamoq99xzD6FQiKysLIYPH97WXW1VsbGxzJ49O6prHjJkCJs3b+aGG27AcRzGjRvHpZdeGtV19+/fn4kTJzJu3DjC4TDXXHMNY8eO5fzzz4/amg/btWsX6enpTY+j/Xd88ODBfPTRR+Tl5eH3+7nkkku45557uOaaa6K2Zmj8oJOdnc3111+Pbdv8+Mc/5vLLL4/qc30ihuu6blt3QkRERFqXpvRFREQ8QIEvIiLiAQp8ERERD1Dgi4iIeIACX0RExAMU+CJyWsLhMIMHD2bixIlt3RUROQkKfBE5LatXr6Zv375s3bqVzz77rK27IyInoPvwReS0jB8/npEjR7J9+3YikQiPPPII0LgH+dKlS0lMTGTgwIGsWbOGtWvX0tDQQGFhIRs3bsS2bS666CKmT59OUlJSG1ci4g0a4YvIKfv73//O+++/z/Dhw7nhhhsoKiri4MGDrF+/nmXLlrF06VKWLVtGTU1N02ueeeYZLMti2bJl/PGPfyQtLY3CwsI2rELEW7S0roicshdffJEhQ4bQpUsXunTpwtlnn82SJUsoLy9n+PDhTdsr33rrrfzlL38B4I033iAYDFJSUgI0XgNweEMXEWl9CnwROSW1tbUUFRURExPDtddeCzTuTLZ48WJycnI48lvCI3dkcxyHgoICsrKyAKipqSEUCp3Zzot4mKb0ReSUvPbaa3Tu3Jn169ezdu1a1q5dy5///Gdqa2vp168ff/rTnwgGgwAsXbq06XWDBw/m+eefp6GhAcdxePDBB5kzZ05blSHiOQp8ETklL774Irfddluz0XtKSgrjx4/nueee4+abb+aWW24hLy+PYDBIfHw8AHfddRcZGRn88Ic/ZOTIkbiuS35+fluVIeI5ukpfRFrMBx98wPvvv8+ECRMAWLRoEZs3b+Y3v/lNG/dMRBT4ItJiqqurKSgo4PPPP8cwDHr06MGvfvUrunfv3tZdE/E8Bb6IiIgH6Dt8ERERD1Dgi4iIeIACX0RExAMU+CIiIh6gwBcREfEABb6IiIgH/H+JTzhSKOpzcAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b0 = reg.params[0]\n", "b1 = reg.params[1]\n", "b2 = reg.params[2]\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "sns.scatterplot(x = \"Age\", y = \"RightHippoVol\", hue = \"Dementia\", data = df)\n", "x = np.array([30,95])\n", "sns.lineplot(x, b0 + b1 * x, lw = 3, color = sns.color_palette()[0])\n", "sns.lineplot(x, b0 + b2 + b1 * x, lw = 3, color = sns.color_palette()[1])\n", "plt.title(\"Right Hippocampus Volume vs. Age and Dementia\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variable Interactions\n", "\n", "In the above example we saw that combining a continuous predictor ($x_1$ = `Age`) and a binary predictor ($x_2$ = `Dementia`) gave us two parallel lines fit to our $y$ data, one line for each group represented by the binary variable. But what if we want to model two lines with differing slopes? The answer is to include a **variable interaction** in our regression model. This is a 3rd predictor variable, which is simply the multiplication of our binary variable with our continuous variable. So, it is $x_3 = x_1 x_2$. Our model with this new (derived) predictor variable looks like the following:\n", "\n", "$$y_i = \\beta_0 + x_{i1} \\beta_1 + x_{i2} \\beta_2 + x_{i1} x_{i2} \\beta_3 + \\epsilon_i.$$\n", "\n", "In our matrix/vector math, this is adding a column to the $X$ matrix:\n", "\n", "$$\\begin{pmatrix} y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n \\end{pmatrix} = \n", "\\begin{pmatrix} \n", "1 & x_{11} & x_{12} & x_{11} x_{12}\\\\\n", "1 & x_{21} & x_{22} & x_{21} x_{22}\\\\\n", "\\vdots & \\vdots & \\vdots & \\vdots\\\\\n", "1 & x_{n1} & x_{n2} & x_{n1} x_{n2}\\\\\n", "\\end{pmatrix}\n", "\\begin{pmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\beta_3 \\end{pmatrix}\n", "+\n", "\\begin{pmatrix} \\epsilon_1 \\\\ \\epsilon_2 \\\\ \\vdots \\\\ \\epsilon_n\\end{pmatrix}.$$\n", "\n", "Notice how this works. When the binary variable $x_2$ is zero, the $x_1$ slope is $\\beta_1$. When the binary variable $x_2$ is one, the $x_1$ slope is $\\beta_1 + \\beta_3$. Similar to the above case, where we saw that $\\beta_2$ was a shift in the *intercept* between the two groups, now $\\beta_3$ is a shift in the *slope* between the two groups.\n", "\n", "Let's see how this interaction term affects our model:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.476\n", "Model: OLS Adj. R-squared: 0.469\n", "Method: Least Squares F-statistic: 67.05\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 7.23e-31\n", "Time: 13:58:07 Log-Likelihood: -1700.9\n", "No. Observations: 225 AIC: 3410.\n", "Df Residuals: 221 BIC: 3423.\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept 5614.4439 206.834 27.145 0.000 5206.824 6022.064\n", "Age -25.2028 2.948 -8.550 0.000 -31.012 -19.394\n", "Dementia -169.2584 554.577 -0.305 0.760 -1262.194 923.677\n", "Age:Dementia -3.8458 7.303 -0.527 0.599 -18.238 10.547\n", "==============================================================================\n", "Omnibus: 1.115 Durbin-Watson: 2.175\n", "Prob(Omnibus): 0.573 Jarque-Bera (JB): 0.801\n", "Skew: -0.103 Prob(JB): 0.670\n", "Kurtosis: 3.208 Cond. No. 1.47e+03\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.47e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ], "source": [ "reg = smf.ols(\"RightHippoVol ~ Age + Dementia + Age*Dementia\", data = df).fit()\n", "print(reg.summary())" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b0 = reg.params[0]\n", "b1 = reg.params[1]\n", "b2 = reg.params[2]\n", "b3 = reg.params[3]\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "sns.scatterplot(x = \"Age\", y = \"RightHippoVol\", hue = \"Dementia\", data = df)\n", "x = np.array([30,95])\n", "sns.lineplot(x, b0 + b1 * x, lw = 3, color = sns.color_palette()[0])\n", "sns.lineplot(x, b0 + b2 + (b1 + b3) * x, lw = 3, color = sns.color_palette()[1])\n", "plt.title(\"Right Hippocampus Volume vs. Age and Dementia\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Selection\n", "\n", "We've seen that including multiple regressors will change the regression results from when we perform single variable regressions. So, how do we know which variables to include in a regression? Maybe include all of them? Maybe include just the ones who have $p$ values below 0.05? This is the question of **model selection**. Let's take a look at a sequence of models, each one adding a new variable to the $x$ data.\n", "\n", "Note: \n", "* **MMSE: Mini-Mental State Exam** is a test of one's memory function (higher test scores means better memory).\n", "* **eTIV: Estimated Total Intracranial Volume** is the total volume inside the skull." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "reg1 = smf.ols(\"RightHippoVol ~ MMSE\", data = df).fit()\n", "reg2 = smf.ols(\"RightHippoVol ~ MMSE + Age\", data = df).fit()\n", "reg3 = smf.ols(\"RightHippoVol ~ MMSE + Age + Dementia\", data = df).fit()\n", "reg4 = smf.ols(\"RightHippoVol ~ MMSE + Age + Dementia + eTIV\", data = df).fit()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.173\n", "Model: OLS Adj. R-squared: 0.170\n", "Method: Least Squares F-statistic: 46.72\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 7.73e-11\n", "Time: 13:58:08 Log-Likelihood: -1752.3\n", "No. Observations: 225 AIC: 3509.\n", "Df Residuals: 223 BIC: 3515.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 1572.6576 300.140 5.240 0.000 981.184 2164.131\n", "MMSE 74.7474 10.935 6.835 0.000 53.198 96.297\n", "==============================================================================\n", "Omnibus: 0.299 Durbin-Watson: 1.989\n", "Prob(Omnibus): 0.861 Jarque-Bera (JB): 0.290\n", "Skew: -0.086 Prob(JB): 0.865\n", "Kurtosis: 2.959 Cond. No. 211.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "print(reg1.summary())" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.439\n", "Model: OLS Adj. R-squared: 0.434\n", "Method: Least Squares F-statistic: 87.02\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 1.25e-28\n", "Time: 13:58:08 Log-Likelihood: -1708.5\n", "No. Observations: 225 AIC: 3423.\n", "Df Residuals: 222 BIC: 3433.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 4238.8694 358.853 11.812 0.000 3531.675 4946.063\n", "MMSE 50.8901 9.319 5.461 0.000 32.525 69.255\n", "Age -27.9945 2.726 -10.268 0.000 -33.367 -22.622\n", "==============================================================================\n", "Omnibus: 3.570 Durbin-Watson: 2.170\n", "Prob(Omnibus): 0.168 Jarque-Bera (JB): 3.243\n", "Skew: -0.227 Prob(JB): 0.198\n", "Kurtosis: 3.375 Cond. No. 867.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "print(reg2.summary())" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.484\n", "Model: OLS Adj. R-squared: 0.477\n", "Method: Least Squares F-statistic: 69.04\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 1.54e-31\n", "Time: 13:58:08 Log-Likelihood: -1699.3\n", "No. Observations: 225 AIC: 3407.\n", "Df Residuals: 221 BIC: 3420.\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 5027.6662 389.744 12.900 0.000 4259.576 5795.757\n", "MMSE 20.8767 11.304 1.847 0.066 -1.401 43.154\n", "Age -25.5129 2.683 -9.508 0.000 -30.801 -20.225\n", "Dementia -364.9137 83.752 -4.357 0.000 -529.969 -199.858\n", "==============================================================================\n", "Omnibus: 1.259 Durbin-Watson: 2.161\n", "Prob(Omnibus): 0.533 Jarque-Bera (JB): 0.935\n", "Skew: -0.083 Prob(JB): 0.627\n", "Kurtosis: 3.268 Cond. No. 984.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "print(reg3.summary())" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.546\n", "Model: OLS Adj. R-squared: 0.537\n", "Method: Least Squares F-statistic: 66.05\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 1.26e-36\n", "Time: 13:58:08 Log-Likelihood: -1684.9\n", "No. Observations: 225 AIC: 3380.\n", "Df Residuals: 220 BIC: 3397.\n", "Df Model: 4 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 3790.2662 430.634 8.802 0.000 2941.570 4638.962\n", "MMSE 13.2827 10.720 1.239 0.217 -7.844 34.409\n", "Age -25.6301 2.523 -10.157 0.000 -30.603 -20.657\n", "Dementia -443.8831 80.065 -5.544 0.000 -601.676 -286.090\n", "eTIV 1.0174 0.186 5.472 0.000 0.651 1.384\n", "==============================================================================\n", "Omnibus: 8.687 Durbin-Watson: 2.125\n", "Prob(Omnibus): 0.013 Jarque-Bera (JB): 12.242\n", "Skew: -0.250 Prob(JB): 0.00220\n", "Kurtosis: 4.028 Cond. No. 2.18e+04\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.18e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ], "source": [ "print(reg4.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The thing to note with all of these models is that MMSE starts out statistically significant, but by the time we add `Dementia`, it no longer is. The $p$ value goes up even further when we add `eTIV`. What if we picked the model with the highest $R^2$? This might seem attractive because that would be the model that explains the most variance in $y$. However, $R^2$ *always* increases when you add a new regressor. Notice in the summaries above that the $R^2$ goes up every time we include a new $x$ variable. So, $R^2$ is not a good model selector (it would say to add any $x$ variable you can come up with, no matter how insignificant the effect.)\n", " \n", "One way to select models is given by the AIC (Akaike Information Criteria), which you can see in the summary tables for each model above. The AIC works on the principle of Occam's Razor, that we should select the simplest model that explains our data. So, it balances how well the model explains the data with a desire to use as few variables as are necessary. The equation for AIC is\n", "\n", "$$AIC = 2d - 2 \\log(L),$$\n", "\n", "where $d$ is the number of $x$ variables we are including, and $\\log(L)$ is the log of the likelihood. We want to minimize AIC, which minimizes the number of parameters ($d$) and maximizes the model fit to the data ($\\log(L))$. Using the minimal AIC, we would select the 4th model above. Let's try adding one more variable, the education level:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.546\n", "Model: OLS Adj. R-squared: 0.535\n", "Method: Least Squares F-statistic: 52.60\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 1.09e-35\n", "Time: 13:58:08 Log-Likelihood: -1684.9\n", "No. Observations: 225 AIC: 3382.\n", "Df Residuals: 219 BIC: 3402.\n", "Df Model: 5 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 3790.7454 431.629 8.782 0.000 2940.067 4641.424\n", "MMSE 13.4917 10.926 1.235 0.218 -8.041 35.025\n", "Age -25.6672 2.553 -10.052 0.000 -30.700 -20.635\n", "Dementia -444.4658 80.436 -5.526 0.000 -602.994 -285.937\n", "eTIV 1.0207 0.189 5.402 0.000 0.648 1.393\n", "Educ -2.5372 24.091 -0.105 0.916 -50.017 44.942\n", "==============================================================================\n", "Omnibus: 8.560 Durbin-Watson: 2.124\n", "Prob(Omnibus): 0.014 Jarque-Bera (JB): 11.971\n", "Skew: -0.248 Prob(JB): 0.00251\n", "Kurtosis: 4.015 Cond. No. 2.18e+04\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.18e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ], "source": [ "reg5 = smf.ols(\"RightHippoVol ~ MMSE + Age + Dementia + eTIV + Educ\", data = df).fit()\n", "print(reg5.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the AIC went up when we added education. So, this would suggest we should probably not include it in our model.\n", "\n", "Finally, we should note that we've only looked at a fraction of the possible models here. If we have $K$ potential $x$ variables to choose from, then we have a possibility of $2^K$ combinations of any subset of these variables. That can be a lot of models to look at! So, the AIC only works if you have a small $K$, or have another way to limit the combinatorial explosion in the number of potential models. The best selection of $x$ variables according to AIC (at least that I was able to find) is the following (**nWBV: normalized Whole-Brain Volume** is the total volume of the brain as a fraction of eTIV): " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: RightHippoVol R-squared: 0.607\n", "Model: OLS Adj. R-squared: 0.600\n", "Method: Least Squares F-statistic: 85.09\n", "Date: Thu, 18 Mar 2021 Prob (F-statistic): 1.47e-43\n", "Time: 13:58:08 Log-Likelihood: -1668.5\n", "No. Observations: 225 AIC: 3347.\n", "Df Residuals: 220 BIC: 3364.\n", "Df Model: 4 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -1430.9202 971.471 -1.473 0.142 -3345.502 483.661\n", "Age -12.1608 3.258 -3.732 0.000 -18.582 -5.740\n", "Dementia -353.6171 63.695 -5.552 0.000 -479.148 -228.086\n", "eTIV 1.3037 0.177 7.383 0.000 0.956 1.652\n", "nWBV 5540.4570 918.578 6.032 0.000 3730.119 7350.795\n", "==============================================================================\n", "Omnibus: 6.671 Durbin-Watson: 2.051\n", "Prob(Omnibus): 0.036 Jarque-Bera (JB): 9.398\n", "Skew: -0.162 Prob(JB): 0.00910\n", "Kurtosis: 3.948 Cond. No. 7.17e+04\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 7.17e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ], "source": [ "reg = smf.ols(\"RightHippoVol ~ Age + Dementia + eTIV + nWBV\", data = df).fit()\n", "print(reg.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 2 }