Stat_654_Homework_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Srujan Jabbireddy - Homework 2\n",
    "\n",
    "**Due: 11:55pm Wednesday 19th February**\n",
    "\n",
    "We numerically explore the relationship between error distributions, objective functions (least squares, least absolute deviation, and weighted least squares), and computational speed.\n",
    "\n",
    "The following simulation creates a data set according to\n",
    "$$y_i = \\beta_1 + \\beta_2 x_i + \\beta_3 x_i^2 + \\epsilon_i.$$\n",
    "\n",
    "We generate $n$ observations from this model for $x$ on an equally spaced grid $[0,1]$. For $Y^{(t)}$, the errors ($\\epsilon_i$) have a t-distribution with 2 degrees of freedom. For $Y^{(n)}$, the errors have a standard normal distribution. For $Y^{(w)}$, the errors are heteroscedastic: $\\epsilon_i|\\sigma_i^2 \\sim N(0,\\sigma_i^2)$,  where $\\sigma_i \\sim 0.1 + \\text{Exp}(1)$ (that is, an exponential distribution shifted $0.1$ to the right). We plot each of these data sets and the true regression function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(1234)\n",
    "n <- 500\n",
    "x <- seq(from=0,to=1,length.out=n)\n",
    "X <- cbind(1,x,x^2)\n",
    "beta <- matrix(c(1,2,4),nrow=3)\n",
    "Yt <- X%*%beta + rt(n,df=2)\n",
    "Yn <- X%*%beta + rnorm(n)\n",
    "sig <- 0.1 + rexp(n) \n",
    "Yw <- X%*%beta + rnorm(n,sd=sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=7.5,repr.plot.height=3.5)\n",
    "par(mar=c(4,4,1,1),mfcol=c(1,2))\n",
    "ylim <- c(-5,10)\n",
    "plot(X[,2],Yt,xlab=\"x\",ylab=\"y\",main=\"t errors\",ylim=ylim)\n",
    "points(X[,2],X%*%beta,type='l',col='red',lwd=2)\n",
    "plot(X[,2],Yn,xlab=\"x\",ylab=\"y\",main=\"normal errors\",ylim=ylim)\n",
    "points(X[,2],X%*%beta,type='l',col='red',lwd=2)\n",
    "plot(X[,2],Yw,xlab=\"x\",ylab=\"y\",main=\"heteroscedastic errors\",ylim=ylim)\n",
    "points(X[,2],X%*%beta,type='l',col='red',lwd=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The t distribution produces a lot of outliers (some outliers are not shown because we restricted the y-axis to ylim in each plot) and there are also a lot of outliers in the case of the heteroscedastic errors. Given the data, out goal is to infer the parameters $\\beta$. We will mainly consider two methods. The least squares method we discussed in class is\n",
    "$$ \\beta_{LS} = \\text{argmin}_{\\beta} \\sum_{i=1}^n(y_i - \\beta_1 - \\beta_2 x_i - \\beta_3 x_i^2)^2 =  \\text{argmin}_{\\beta} (Y - X\\beta)^T(Y - X\\beta) = (X^TX)^{-1}X^TY$$\n",
    "A second possibility is to find the [least absolute deviations](https://en.wikipedia.org/wiki/Least_absolute_deviations) estimator. We call this $\\beta_{LAD}$ which has the form\n",
    "$$\\beta_{LAD} = \\text{argmin}_{\\beta}\\sum_{i=1}^n |y_i - \\beta_1 - \\beta_2 x_i - \\beta_3 x_i^2|.$$\n",
    "This may also be known as $L_1$ regression or quantile regression with the $0.5$ quantile.\n",
    "\n",
    "In this homework you will fit both $\\beta_{LS}$ and $\\beta_{LAD}$ and compare the methods based on parameter estimation accuracy and speed. In the case of the heteroscedastic errors dataset we will also compare to the weighted least squares estimator $\\beta_{WLS}= (X^TWX)^{-1}X^TWY$, where $W$ is a diagonal matrix, with the diagonal given by $1/\\sigma_i^2$ for $i=1,\\dots,n$ (assume that the $\\sigma_i$ are known). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1\n",
    "\n",
    "Fixing $X$, generate the $Y^{(t)}$, $Y^{(n)}$, and $Y^{(w)}$ datasets $N=100$ times (note that $n$ is the sample size and $N$ is the number of times we run the simulation). For the  $Y^{(t)}$ and $Y^{(n)}$ datasets, compute $\\beta_{LS}$ and $\\beta_{LAD}$ each time. Since $\\beta$ is a vector of length $3$, this will result in 4 matrices (LS for $Y^{(t)}$ and $Y^{(n)}$ and LAD for $Y^{(t)}$ and $Y^{(n)}$) with $N$ rows and 3 columns (you could store this output in other formats as well, but matrices are convenient). For the $Y^{(w)}$ datasets, compute all three estimators $\\beta_{LS}$, $\\beta_{LAD}$, and $\\beta_{WLS}$, and similarly store them in matrices. \n",
    "\n",
    "Make scatterplots of $\\beta_2$ versus $\\beta_3$ estimates for each data type and each estimator. This will produce seven scatterplots in total. Mark the true $\\beta_2$ and $\\beta_3$ on each plot and comment of the quality of the estimators in the different settings. Your scatterplots should look similar to the ones below.\n",
    "\n",
    "**Tips for Fitting** \n",
    "\n",
    "- For fitting $\\beta_{LS}$, you have many options in R (lm, lm.fit) and python (scipy.linalg.lstsq, sklearn.linear_model.LinearRegression). \n",
    "- For fitting $\\beta_{LAD}$ in R you can use l1fit from the package L1pack or  rq.fit from quantreg. For fitting $\\beta_{LAD}$ in Python the options are somewhat more limited:\n",
    "    * [statsmodels](http://www.statsmodels.org/dev/examples/notebooks/generated/quantile_regression.html) requires use of pandas, calls the quantreg R package\n",
    "    * generic optimizer such as [scipy.optimize](https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html)   \n",
    "  The latter is a more general method that will likely be slower. On the other hand, scipy.optimize will also be useful for many other problems. You may also use any other optimizer you find. \n",
    "- For fitting $\\beta_{WLS}$ in R you can use for example lm.wfit or lsfit (the latter may be more convenient here). In Python you can use for example the sample_weight option in sklearn.linear_model.LinearRegression or statsmodels.regression.linear_model.WLS. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The t distribution produces a lot of outliers (some outliers are not shown because we restricted the y-axis to ylim in each plot) and there are also a lot of outliers in the case of the heteroscedastic errors. Given the data, out goal is to infer the parameters $\\beta$. We will mainly consider two methods. The least squares method we discussed in class is\n",
    "$$ \\beta_{LS} = \\text{argmin}_{\\beta} \\sum_{i=1}^n(y_i - \\beta_1 - \\beta_2 x_i - \\beta_3 x_i^2)^2 =  \\text{argmin}_{\\beta} (Y - X\\beta)^T(Y - X\\beta) = (X^TX)^{-1}X^TY$$\n",
    "A second possibility is to find the [least absolute deviations](https://en.wikipedia.org/wiki/Least_absolute_deviations) estimator. We call this $\\beta_{LAD}$ which has the form\n",
    "$$\\beta_{LAD} = \\text{argmin}_{\\beta}\\sum_{i=1}^n |y_i - \\beta_1 - \\beta_2 x_i - \\beta_3 x_i^2|.$$\n",
    "This may also be known as $L_1$ regression or quantile regression with the $0.5$ quantile.\n",
    "\n",
    "In this homework you will fit both $\\beta_{LS}$ and $\\beta_{LAD}$ and compare the methods based on parameter estimation accuracy and speed. In the case of the heteroscedastic errors dataset we will also compare to the weighted least squares estimator $\\beta_{WLS}= (X^TWX)^{-1}X^TWY$, where $W$ is a diagonal matrix, with the diagonal given by $1/\\sigma_i^2$ for $i=1,\\dots,n$ (assume that the $\\sigma_i$ are known). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(requires internet connection to view)\n",
    "\n",
    "<img src=\"https://david-jones-statistics.github.io/statcomp/hw/betaT.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(requires internet connection to view)\n",
    "\n",
    "<img src=\"https://david-jones-statistics.github.io/statcomp/hw/betaNorm.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(requires internet connection to view)\n",
    "\n",
    "<img src=\"https://david-jones-statistics.github.io/statcomp/hw/betaHet.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy \n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "from statsmodels.regression.quantile_regression import QuantReg\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Number of Simulations:\n",
    "N = 100\n",
    "n = 500\n",
    "x = np.linspace(0,1,num=n) #Safer than np.arange for floating point\n",
    "#x = x[:,np.newaxis]\n",
    "X = np.column_stack((np.ones(n),x,x**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500,)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = np.array([1,2,4]).reshape((3,1))\n",
    "fx = np.matmul(X,beta)[:,0]\n",
    "fx.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For LS Linear regresssion using scikit-learn\n",
    "model = LinearRegression(fit_intercept=True,)\n",
    "\n",
    "#creating LAD function\n",
    "def LADN(b):\n",
    "    return(np.sum(np.abs(Yn - np.matmul(X,b.reshape((3,1)))[:,0])))\n",
    "\n",
    "def LADT(b):\n",
    "    return(np.sum(np.abs(Yt - np.matmul(X,b.reshape((3,1)))[:,0])))\n",
    "\n",
    "## initial guess for LAD estimator\n",
    "x0 = np.zeros(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ls_beta_t = np.mat(np.zeros((N,3)))\n",
    "ls_beta_n = np.mat(np.zeros((N,3)))\n",
    "ls_beta_t_1 = np.mat(np.zeros((N,3)))\n",
    "ls_beta_n_1 = np.mat(np.zeros((N,3)))\n",
    "lad_beta_t = np.mat(np.zeros((N,3)))\n",
    "lad_beta_n = np.mat(np.zeros((N,3)))\n",
    "lad_beta_t_1 = np.mat(np.zeros((N,3)))\n",
    "lad_beta_n_1 = np.mat(np.zeros((N,3)))\n",
    "ls_beta_h = np.mat(np.zeros((N,3)))\n",
    "lad_beta_h = np.mat(np.zeros((N,3)))\n",
    "wls_beta_h = np.mat(np.zeros((N,3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for k in np.arange(N):\n",
    "    Yt = fx + np.random.standard_t(df=2,size=n)\n",
    "    Yn = fx + np.random.normal(size=n)\n",
    "    sig = 0.1 + np.random.exponential(scale=1,size=n) \n",
    "    Yw = fx + np.random.normal(loc=0,scale=sig,size=n)\n",
    "    \n",
    "    #LS-error-sckit-learn\n",
    "    ls_beta_t[k,:]  = model.fit(X, Yt).coef_\n",
    "    ls_beta_n[k,:]  = model.fit(X, Yn).coef_\n",
    "    \n",
    "    #LS-error-scipy \n",
    "    ls_beta_t_1[k,:]  = np.linalg.lstsq(X,Yt,rcond=None)[0]\n",
    "    ls_beta_n_1[k,:]  = np.linalg.lstsq(X,Yn,rcond=None)[0]\n",
    "    \n",
    "    #LAD-error-Quantreg\n",
    "    df = pd.DataFrame(np.column_stack((X,Yt,Yn)))\n",
    "    #t,n  = X.shape[1], X.shape[1]+Yt.shape[1]\n",
    "    #dfSliced= df.iloc[:,np.array([0,1,2,t+k,n+k])]\n",
    "    df.columns= ['1', 'x','x2','Yt','Yn']\n",
    "    lad_beta_t[k]= smf.quantreg('Yt ~ 1+x+x2', df).fit(q=.5,max_iter=100000).params\n",
    "    lad_beta_n[k]= smf.quantreg('Yn ~ 1+x+x2', df).fit(q=.5,max_iter=100000).params\n",
    "    \n",
    "    #LAD-error-scipy\n",
    "    lad_beta_t_1[k] = scipy.optimize.minimize(LADT,x0,method='Nelder-Mead', tol=1e-6).x\n",
    "    lad_beta_n_1[k] = scipy.optimize.minimize(LADN,x0,method='Nelder-Mead', tol=1e-6).x\n",
    "    \n",
    "    #for WLS\n",
    "    ls_beta_h[k,:]  = model.fit(X, Yw).coef_\n",
    "    #lad_beta_h[k] = scipy.optimize.minimize(LADW,x0,method='Nelder-Mead', tol=1e-6).x\n",
    "    het = pd.DataFrame(np.column_stack((X,Yw)))\n",
    "    het.columns = ['1', 'x','x2','Yw']\n",
    "    lad_beta_h[k] = smf.quantreg('Yw ~ 1+x+x2', het).fit(q=.5,max_iter=100000).params\n",
    "    wls_beta_h[k] = sm.WLS(Yw,X,weights=1/np.power(sig,2)).fit().params\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x22df13e7be0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = plt.GridSpec(2, 2)\n",
    "fig=plt.figure(figsize=(10, 10), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.rcParams[\"figure.figsize\"] = (10,10)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "\n",
    "#LS - T-errors\n",
    "ax0 = plt.subplot(grid[0, 0])\n",
    "plt.ylim(-5,15)\n",
    "plt.xlim(-8,8)\n",
    "plt.scatter([ls_beta_t[:,1]], [ls_beta_t[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LS - t errors\")\n",
    "plt.tight_layout()\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='crimson', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()\n",
    "plt.legend()\n",
    "\n",
    "#LAD - T-errors\n",
    "plt.ylim(-5,15)\n",
    "plt.xlim(-5,5)\n",
    "plt.subplot(grid[0, 1], sharex=ax0, sharey=ax0);\n",
    "plt.scatter([lad_beta_t[:,1]], [lad_beta_t[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LAD - t errors\")\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='greenyellow', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()\n",
    "\n",
    "#LAD - Normal-errors\n",
    "ax1 = plt.subplot(grid[1, 1]);\n",
    "plt.scatter([lad_beta_n[:,1]], [lad_beta_n[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LAD - normal errors\")\n",
    "plt.tight_layout()\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='red', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()\n",
    "\n",
    "#LS - Normal-errors\n",
    "plt.subplot(grid[1, 0], sharex=ax1, sharey=ax1)\n",
    "plt.scatter([ls_beta_n[:,1]], [ls_beta_n[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LS - normal errors\")\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='darkorange', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x22df1b84cf8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = plt.GridSpec(2, 2)\n",
    "fig=plt.figure(figsize=(10, 10), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.rcParams[\"figure.figsize\"] = (10,10)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "\n",
    "\n",
    "ax0 = plt.subplot(grid[0, 0])\n",
    "plt.scatter([ls_beta_t_1[:,1]], [ls_beta_t_1[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LS - t errors\")\n",
    "plt.tight_layout()\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='crimson', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()\n",
    "\n",
    "\n",
    "plt.subplot(grid[0, 1], sharex=ax0, sharey=ax0);\n",
    "plt.scatter([lad_beta_t_1[:,1]], [lad_beta_t_1[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LAD - t errors\")\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='greenyellow', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()\n",
    "\n",
    "ax1 = plt.subplot(grid[1, 1]);\n",
    "plt.scatter([lad_beta_n_1[:,1]], [lad_beta_n_1[:,2]], alpha=0.25,color='black',label='truth')\n",
    "plt.title(\"LAD - normal errors\")\n",
    "plt.tight_layout()\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='red', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(grid[1, 0], sharex=ax1, sharey=ax1)\n",
    "plt.scatter([ls_beta_n_1[:,1]], [ls_beta_n_1[:,2]], alpha=0.25,color='black',label='estimate')\n",
    "plt.title(\"LS - normal errors\")\n",
    "plt.scatter([beta[1]], [beta[2]],marker=\"+\",facecolors='darkorange', edgecolors='k',linewidth = 2,s=100,label='truth')\n",
    "plt.xlabel(r\"$\\beta_2$\")\n",
    "plt.ylabel(r\"$\\beta_3$\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x22df1ef9b00>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABP0AAAKYCAYAAAAISo2+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAMTQAADE0B0s6tTgAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzs3XdYFFfbBvB7dukdFCuLoEas2BLFDhh7L2mWaNQQTfFVExI1MYDlMxo1Go1R9FLT9E2zRI0VxNi7gh0TkLVExBU7Crvn+4N3R9ZdYEHaLvfvuvZKnDk7c2Y5e545z86ckYQQAkRERERERERERGQ1FKVdASIiIiIiIiIiIipaTPoRERERERERERFZGSb9iIiIiIiIiIiIrAyTfkRERERERERERFaGST8iIiIiIiIiIiIrw6QfERERERERERGRlWHSj4iIiIiIiIiIyMow6WfBgoODIUlSgd6zatUqSJKEVatWFU+lqMzz8/ODn59faVdDVph2TETWJy4uDpIkITIyskDvK2t9GpWssnZeU9h2TETWi2M2Koyydn7DMZvlsqqk39GjR/HWW2+hZs2acHR0hJubGxo1aoTw8HBcvXrV5Hv0J2fBwcFm7SMjIwNz5sxBy5Yt4e7uDjs7O1StWhXNmzfH+++/j927dxfhERVcSZ5sJicnQ5KkfDsjSZKKpINgR2OZhg8fDkmSkJycXOL71reZvF4cmFFZU9g+86effpLfu3379lzL6eNEzpeTkxOqVq2K9u3bIzw8HCdOnHieQyhSJdn36/urvAZZkZGRRdJ3MDlkmfTnPsOHDy/xfZv67pp6EZW2Y8eOQZIkBAUFmVy/evVqub0mJSUZrX/06BEcHBzg5OSEx48fA+CY7XlwzEbm4JjNetmUdgWKghACEydOxOzZs2FjY4NOnTrhlVdewZMnT7B//37MmTMHixcvxnfffYeBAwcWej/3799Hhw4dcPz4cVSpUgUDBgxA5cqVcePGDSQmJiI6Ohrp6eno0KFDER5d7r7//ns8fPiwRPZFVFxKoh0PGzYs1xMdc08eicq66OhoSJIEIQSio6PRuXPnPMvXqFFDTlw8efIEN2/exPHjxzFnzhzMmTMHgwYNwtKlS+Hi4lICtQdatGiBc+fOoWLFiiWyP6LiUBLtOOd3l6gsatq0KTw9PXH06FHcvXsXbm5uButjY2PleBUbG4uRI0carN+3bx8eP36MTp06wd7evsD755iNqOhxzGa5rCLpN23aNMyePRt+fn7YtGkTGjRoYLD+999/x5AhQ/D6669jx44dCAkJKdR+5s+fj+PHj6Nz587YuHEj7OzsDNbfvn0b586dK/RxFJSvr2+J7YuouJREOx4+fDgDBVm1Cxcu4K+//sLLL78MjUaDP/74Azdu3EDlypVzfY+fn5/JX01PnjyJN998E6tXr4ZGo8GWLVuKseZPOTk5oW7duiWyL6LiUhLtOLfvLlFZoVAoEBwcjHXr1mH37t3o1auXwfrY2FgEBwcjPj7eZNIvNjYWANCxY8dC7Z9jNqKixzGb5bL423uTk5Mxbdo02Nra4o8//jBK+AHAgAED8NVXX0Gr1WLMmDHQ6XSF2tf+/fsBAGPGjDEKHgDg6emJ1q1b57ud+/fvw87ODm3atDFYrr+UXZIk/PDDDwbrFi9eDEmSsGLFCnnZs5dODx8+XE5oRkVFGVwOGxcXZ1SPXbt2ITg4GK6urnBzc0OPHj1KNAACwKFDhzBw4EBUqVIFdnZ2UKlUeOedd3Dt2jW5jP6SdP1l+DmP69lO4cqVK3j//fdRs2ZN2Nvbo0KFCujduzeOHDlitG/9LVpxcXFYvXo1WrZsCRcXF6NfF3755Re0b98e7u7ucHR0RKNGjTBz5kz5doOc4uPj8cYbb8DPzw/29vbw9vZGs2bNMG7cOGRmZhqU1Wq1WLJkCdq0aSNvu3bt2hg1ahQSExMNymZlZWHx4sUICgqCm5sbnJyc0LRpUyxatMhkexZCYNGiRWjQoAEcHBxQvXp1vP/++7hz547Jv8OdO3fw5ZdfIjQ0FD4+PrCzs4O3tzd69+6NgwcPmnzPnj170KtXL/j4+MDe3h5VqlRBUFAQoqKi5DKSJOG7774DAPj7+8t/t5yfcV63AGzfvh29evVCpUqVYG9vD5VKhT59+mDnzp0myz+vnLdaHD58GD169ICXl5fBpe76+TXu3r2LCRMmwM/PD7a2tgYDsDt37mDSpEkICAiAg4MDPD090aVLF5P1NmefBWlXVD4tW7YMAPDWW29h+PDhyMzMLPQ8QE2aNMHOnTvh7e2NrVu3Yv369fm+Z9KkSZAkCTt27DBY/vnnn0OSJNSqVcvoPVWqVDE4gXz2VqeC9P0A8PDhQ4SHh8PX1xf29vaoXbs2Zs2aBSFEAY7++Tx8+BAzZ85EkyZN4OzsDBcXF7Rq1Qpr1qwxKFeQeL1mzRqEhITA09MTDg4OqFevHqZPn24yBuk/m3///RejRo1C9erVoVQqDdrC9evX8d5778HPz0/u6/v3749jx44Zbe/Jkyf4+uuv0axZM3h6esLJyQl+fn659sPnz5/HiBEj5L6qUqVKaNeuHb799luTZYcPHw6VSgV7e3tUrlwZgwYNwoULF0x+tpcuXcIrr7wCT09PODs7o3Xr1ti8ebPJskD2OU5YWBjq168PNzc3ODo6omHDhoiKikJGRoZR+Xv37mHatGlo2LAh3Nzc4Orqilq1auG1116TP5vIyEj4+/sDAL777juDv5v+M87rlj2NRoNPP/0UDRs2hJOTE9zd3dG4cWNMnDgRDx48yPVYnoc+xj558gRTp05FQEAA7O3t5SsFc84btnXrVgQHB8Pd3d0oLsfExKBr167w8vKCg4MD6tSpg4kTJ5o8r8hvnwVtV2SZ9Ak7fQJPLzk5GUlJSejYsSM6dOiAXbt2Gb33eZN+HLMVPY7ZOGbjmM1yx2wWf6XfypUrkZWVhVdffRWNGjXKtdyoUaMwbdo0XLhwAbt37y7U1X4VKlQAAFy8eLHQ9QUAFxcXtGjRAocOHcK9e/fg6uoK4Oml7ED2ydXQoUPl95gT/Pr27Qsg+0S0Q4cOBp3rs53ipk2bsGHDBnTr1g2jR4/G2bNn8eeff+LIkSM4e/ZsidxetXLlSrz99tuwt7dH7969oVKpkJiYiOXLl2Pjxo04ePAgfH194eHhgYiICKxatQqXL19GRESEyePS/6Kn0WjQpUsX9O/fH2lpaVi/fj3atm2LdevWoXv37kb1mDt3Lnbs2IFevXohJCTEoJOdPHkyZs6ciYoVK2LQoEFwcXHBli1bMHnyZGzbtg07duyAra0tgOwvecuWLSFJEnr37g1/f3/cvXsXly5dwuLFizF9+nS57JMnT9CjRw/s3LkTKpUKgwYNgpubG5KTk7Fu3Tq0bdsWL7zwAgAgMzMTvXr1wrZt2xAQEIBBgwbBwcEBu3btwgcffIBDhw4ZnXCMGzcOX3/9NapWrYqwsDDY2tpiw4YNOHToEJ48eWJ0AnTu3Dl8+umnaN++PXr06AFPT0+kpKTgjz/+wJYtW7Bx40Z07dpVLr9161b06NEDbm5u6N27N6pXrw6NRoNz585h8eLF8t8oIiIC69evx6lTp/Cf//wHHh4eACD/Ny8RERGYOnUqXFxc0LdvX6hUKly7dg379+/Hjz/+iJdffjnfbRTWgQMHMHPmTLRt2xYjRoxAWlqawWf25MkThIaGQqPRoHPnznBzc5MHgunp6WjTpg3Onj2Ll156CePGjUNaWhp++eUXdO7cGd9++y3eeecds/dZkHZF5dOTJ0/w3Xffwc3NDf369cPDhw/x0UcfYfny5fj4448LNa9OpUqV8M4772D69On46aef5PiSm44dO+KLL75ATEwMOnXqJC/Xx65//vkHycnJcp99+vRp3LhxI89bFM3t+4HsfrJz5864du0aunXrBhsbG6xfvx4TJ05ERkaGwXuLS3p6OkJDQ3HixAk0a9YMI0aMgE6nw7Zt2zBo0CCcOXMG06dPB2B+vB45ciRWrFgBHx8f9O/fHx4eHjh48CCmTJmCmJgY7NixAzY2hqdyGo0GQUFBcHFxQf/+/aFQKOQrPpOSktC2bVtcu3YNoaGheOONN6BWq/Hrr79i8+bN+P3339GzZ095W8OHD8eaNWvQsGFDvPnmm3B0dMS1a9ewd+9ebN261aAf3rx5M1555RU8fvwYXbt2xRtvvIH09HScOnUKs2fPxpgxY+SyW7duRf/+/eX4Vrt2bVy5cgVr167F5s2bsWvXLjRr1kwun5iYiFatWuHWrVvo1q0bmjRpgkuXLqFv377o1q2byb/HrFmzcP78ebRu3Ro9evRARkYG9u3bh8jISMTFxWHnzp1QKpUAsgddXbt2xf79+9GqVSuMGjUKNjY2UKvViIuLQ7t27dC8eXMEBwcjPT0dCxYsQOPGjQ2+F02aNMmzfSQlJSEkJASXL19G8+bN5R+hL168iK+++gqjR4+Gs7Nzntt4HgMGDMCRI0fQrVs39O3bF5UqVTJY/9tvv2Hr1q3yeWHOOZ2WLl2KMWPGwNnZGa+88goqVaqEuLg4zJo1Cxs3bsS+fftMxvXc9lmQdkWWKzQ0FED2mCYn/b9DQ0Ph7u6OtWvX4uzZs6hfvz4A4O7duzh69Cg8PDwM+oGC4JitaHHMxjFbXjhms4Axm7BwoaGhAoCIjo7Ot+ygQYMEADFt2jR52a5duwQA0aFDh3zfv3HjRgFA2NnZiTFjxohNmzaJa9euFareU6ZMEQDEpk2b5GUTJ04USqVShISECB8fH3m5VqsVFSpUEDVr1jTYRocOHcSzf0L98URERJjc78qVKwUAoVQqxc6dOw3WTZw4UQAQs2bNMusYkpKSBADh7u4uIiIicn0BMKrnhQsXhK2trahVq5a4cuWKwbqYmBihUChE37598z1evczMTFGrVi1hb28v4uLiDNZdvXpVVKtWTVSpUkVkZGTIy/V1c3JyEsePHzfa5v79+wUAoVKpxPXr1w321bNnTwFAzJgxQ14+YcIEAUCsX7/eaFsajUZotVr535MmTRIARK9evQzqJIQQGRkZIjU11aie77//vsjKypKXZ2VliREjRhjtc9++fQKAqFWrlrh165a8/NGjRyIoKEgAEDVq1DDYZ3p6urh586ZRvdVqtahataqoW7euwfL+/fsLAOLkyZNG73l2O8OGDRMARFJSklFZIUz/Xbdt2yYACH9/f6P2oa+XOfTbHjZsWK7tM+ffVv/9ASCWLFlicps1atQQAETHjh3F/fv3jdaHhYUJACIsLEzodDp5+cWLF4Wbm5uws7Mz+Czy22dB2hVZB1N9Zl7WrFkjtzk9/Xf02X5eCPPj3s6dOwUA4evrm28dHj58KOzt7cWLL74oL7t3756wtbUVnTp1EgDE8uXL5XXz588XAMT3339vVK9n41defb8QT7+T3bp1Ew8fPpSX37hxQ7i7uwt3d3fx5MmTfI9BiKf9VZ8+fXLtM/T1ebae+vc+G0MfPXokunTpIiRJEidOnMj3ePX08bpfv34GxyXE07gwf/58g+X6tjN06FCRmZlptM3OnTsLAGL69OkGy/ft2yeUSqXw8vIS9+7dE0JkxwVJkkTz5s0NYo9eWlqa/P83b94Ubm5uwtbW1igGC2HYZ2s0GuHh4SEqVKggzpw5Y1Du9OnTwtnZWTRt2tRgub4NPXu869evl4955cqVBuv+/vtvgz5Y77PPPhMAxH//+195WXx8vABgdN4hRPY5mEajkf+tP/cZNmyYUVkhcv+7tm7dWgAQ//d//2f0nps3b4pHjx6Z3J6pbdeoUSPX9rlmzRqD9+jba6NGjUzGeX07kyRJbNmyxWh9cnKysLOzE66uruLcuXMG68aMGSMAiLffftvsfRakXZHlq1atmpAkyeC8dtCgQcLFxUVkZmaK06dPCwBi4cKF8vo//vhD7vty4pjtKY7ZDHHMxjGbKRyzPWXxSb969eoJACZPVJ71ySefCABizJgx8rKCBBAhhFiwYIFwd3eX/+AARJUqVcSgQYPE7t27za53XFycACDGjx8vL3vppZdEixYtxKJFiwQAceHCBSGEEMeOHcvzpConcwPI4MGDjdb9888/AoAYMGCAWcegDyDmvnIaN26cUQDNqW/fvkKpVIq7d+/mebx6+hP/jz76yOR6/QBz8+bN8jJ9xzxu3DiT7xk1apQAIJYuXWq07sKFC0KhUAh/f395mf6Lvm3bNpPb08vKyhLu7u7C0dFRXL16Nc+y+pOHKlWqmBzA3b59W0iSJF555RWjeq9YscKofM4Bg7k++OADAUBcvnxZXqYPIPo2mpfCBBB9gF67dq3Z9cxr23m9TA3CmzRpkus29QHEVPB88uSJcHJyEi4uLgbBW08/2IyKijJ7n+a2K7IeBU36hYSECABi//798jL9oOm1114zKm9u3Dt37pwAIBwdHc2qR3BwsFAoFHKCZPPmzXK/6+3tLd544w25bK9evQQAgxPE5036JSYmGq178803BQCRkJBg1jHo+ytzXjnrmZaWJpRKpUHSM6eTJ08KACI8PDzf49Vr0qSJsLGxEbdv3zZal5WVJSpUqCBeeuklg+X6Qe6NGzeM3qNWqwWQncQ1lQQdMmSIACC+++47IYQQd+7cEQBE69atTSbPcpozZ44AIMaOHZtnOSGexuNFixaZXK8/P9AnBPX19vf3N5kk0rePZ5N+uUlLSxMAxFtvvSUv0yf9crbR3BQm6Xf06FG5n3+ek/6cA47cXn369DF4j/7zMTUIEeLpeaGphKcQQkyfPl0AEJMmTTJap9FohKurq3BwcDAYDOe1z4K0K7J8gwcPFgDEzz//LC+rWrWq6Natm/zvSpUqGST49H3As30Ex2xPccxmiGO2bByzGeKY7SmLv71X/G+uHnNuXypI2dyMHTsWo0aNwo4dO7B//36cOHEC+/fvx+rVq7F69WpMmTIFU6dOzXc7rVq1gqOjo3yJ+507d3D8+HF8/PHHBpfD16lTR75MXL+8KLz44otGy1QqFYDsyW0LokaNGnk+2tvU533gwAEAwO7du03O3ZCamgqtVouLFy+iefPm+dZBv73Lly+bnEdHP9/CuXPnjC4Xb9GihcltHj9+HIDpz71OnTrw8fFBUlIS0tPT4eHhgddeew0LFixA3759MXDgQLz88sto06aN0VxW58+fx507d9CyZUtUq1Ytz+O6ePEibt26hRdeeEG+LexZjo6OBvN66Ott6olk7dq1M7oVTG/fvn1YsGABDhw4gNTUVDx58sRg/dWrV+X5twYPHoy1a9eiZcuWeO211xASEoI2bdrAx8cnz+Mx18GDByFJksHl6c9DPxeKuXJrE3oODg4IDAw0Wn7+/Hk8fPgQbdq0gZeXl9H60NBQTJ8+HSdOnDB7n+a2KyqfLl26hLi4OAQEBKBVq1by8m7duqFy5cpYt24d0tLSCnX7T0FjZmhoKOLi4hAXF4d+/fohNjYWtra2aN++PUJCQuRYptVq8ddffyEgIADVq1cvcL1McXd3R+3atY2WFzaurVy5MtdbjyMjIw3mwQGAI0eOQKvV5jqXm34eF3PnYHr48CFOnTqFihUrYv78+SbL2Nvbm9yen5+f0a2bAOR+p127diZvLwkNDcWPP/6IEydO4M0334Sbmxt69eqFjRs3okmTJhgwYADatWuHli1bwsnJyeC9+nmEcrvVNid9vD516pTJz0p/O965c+dQv359ud5t27aVb8fNKTg4WJ4/KqcHDx5gwYIFWLduHS5evIh79+4ZzO949epV+f/r16+PJk2aYM2aNbh8+TL69OmDtm3b4sUXXzQ5H1hB6T+fLl26QKF4/um0O3ToYHLer7zkF9cKcy7k6emJpk2b4q+//sL58+fRuHHjfLdZkHZFlq9jx4746aefEBsbi1dffRVnz57F9evXMX78eLlMcHAwduzYAZ1OB4VCIceK570lkGM2YxyzcczGMVu28jZms/ikX9WqVXH+/HmkpKTkW/bKlSvye56Hk5MT+vTpgz59+gDIvld82bJl+M9//oNp06ahX79+aNq0aZ7bsLOzQ9u2bbFz506kpqbiwIED0Gq16NixI+rVq4dq1aohJiYGY8aMQUxMDCRJKtIAYur+fH3HotVqi2w/ubl16xYA4Msvv8yz3P379wu0vV9//bXA26tSpYrJsvp5InJrL1WrVkVKSgru3LkDDw8PtGjRAnv27MGMGTPw22+/yXM2BAQEICIiAm+88QaA7PkDAJg12NUfV2JiotEgM7fj0tfb1FM7lUqlPM9JTuvWrcPAgQPh4OCATp06oVatWnB2doZCoUBcXBx2795tMAlu//79sWnTJsydOxcrVqzA0qVLAQDNmzfHzJkzDeb0Koz09HR4enrC0dHxubZTWLm1Cb1KlSqZPDEyp80AT9uAOfs0t11R+bRs2TIIIYwSVDY2NhgyZAjmzp2LVatW4aOPPirwtvWTc3t7e5tVvmPHjvj8888RExODfv36ISYmRp5su2PHjvjll19w+vRpPHjwAHfu3MHgwYMLXKfc5DbnTEnFNX1ffeTIEZODIj1zY9rt27chhMDNmzfz7PtNeZ6YBhj2Tz///DNmzZqF1atXy/P+ODg4YODAgZgzZ44cZwoT1/QPn8mN/rPKK6YBpo83MzMToaGhOHz4MBo2bIjXXnsN3t7ecrIzKirKIKYplUrExsZi6tSp+O233/DJJ58AAFxdXTFs2DDMnDkTLi4u+R5bbgry+RSX/OJaUbab/LZpbrsiy6ef106fMDOVFAsODsYvv/yCEydOoEaNGkhISED16tUREBDw3PvnmO35cczGMVteOGZ7qiyP2Sz+6b1t27YFgHyfDKPVauVfRZ99AtPzsrOzw3vvvSf/IU09hcqU0NBQCCEQGxuLmJgY2Nvby3ULCQnBrl278PjxY+zZswcNGjQw+cu9pXJ3dweQ/YUT2beZm3yZ+uUjr+1t2LAhz+1FmJjMPberWPTb/Pfff02uv379ukE5IPvXwE2bNuH27dvYt28fpkyZghs3bmDQoEFyG9UH75xXGeR3XP369cvzuJKSkozec+PGDaPtabVaOSjlNGXKFNjZ2eHo0aNYv3495s6di6lTpyIyMjLXk64ePXogNjYWt2/fRkxMDMaPH48zZ86gZ8+eOHv2bL7HlhcPDw/cvn0bjx49eq7tFFZ+VzYVZZsxZ5/mtCsqf3I+oVf/9Nycr7lz5wLIP7mSG30sa9mypVnlW7RoARcXF+zcuRO3bt3CqVOn5AGffgC0c+dOg0ncrYX+Oz1+/Pg8+2pzzw/022vatGme28t55ZpeUfZPjo6OiIyMxMWLF5GSkoIff/wRbdu2xY8//oiBAwfK5QoT106dOpXncQ0bNsygvKmYltvxbNiwAYcPH8awYcOQkJCA6OhozJgxA5GRkSYn5Qayr1r76quvoFar5Qnq69ati0WLFhk8hKQwCvL5FJeyFNfMbVdk+Xx9fVGrVi1cunQJarUasbGx8PDwMEi06R+uGBsbi9jYWAghCv3U3vxwzFZwHLNxzJYXjtkMldUxm8Un/YYPHw6lUol169bhzJkzuZZbsWIFrl27hoCAALM7pYLSP9HJ1Em4KTl//YqNjUWbNm3g4OAgr9NoNPj222/x4MEDs4Of/taXkvjl53kEBQUByH6EuLnyOrbCbC8/+hMSU7fQXLp0CVeuXIG/v7/JX+Ds7e3RunVrTJ06FV9//TWA7OAGAHXr1oWHhwfi4+MNHnNvir7swYMHzX7Mt/5JZ6Zud9qzZw+ysrJMHk/9+vVRr149g+U6nQ579+7Nc3/Ozs4IDQ3FvHnzMHnyZDx58gRbtmyR1xemTQYFBUEIga1bt5r9nrIgICAATk5OOHnypMlbLvQnl4V9Gl1e7YrKnw0bNiA1NRUBAQEYOXKkyVfNmjVx8eJFk/1BXlJTU+Vfg829Is/Gxgbt27fHhQsX8MMPPxgM3GrXrg1fX1853ikUCnmglx9LiGstWrSAQqEospjm4uKCBg0a4MyZM9BoNEVSR31M27t3r8k4kF//pFKpMHjwYGzbtg0vvPAC9u7dKw9I9DE4Z9+fm4LG65z1NvVZ5Rajgeynxz7LnO9C7dq1MXLkSOzevRsuLi4G/WxhYxoAbNu2DTqdzuz3lQV5nQulp6fj5MmTcHBwMDp/MFde7Yqsgz4O7Ny5E7t370aHDh0MbnOvW7cuqlatKif9cr6nuHDMZj6O2ThmywvHbKaVtTGbxSf9atasicmTJyMzMxO9e/c2ma1ev349/vOf/0CpVGLx4sWFnk9lyZIl8rwszzp//rx8mXK7du3M2l7z5s3h4eGBDRs24MyZMwZBQv//M2fOBGD+FRH6y4DNud25NL3//vuwtbXF+PHj5fl7cnry5IlRMMjr2Pr06YNatWrhm2++wZ9//mlynwcOHMDDhw/NruOIESMAANOnT8fNmzfl5VqtFh999BF0Oh1GjhwpL9+zZ4/Bo+P19L/e6OeqUSqVePfdd/Ho0SOMHj3a4BJsIPvY9fuzsbHBBx98gOvXr2Ps2LEmf0W5fv26QbvX3+Y3Y8YMg8FiRkYGJk2aZPJY/fz8kJiYaBDQhBCIiooy+Z2KiYkxWZdnjxUoXJv84IMPAAAffvihyV/XSvNqibzY2dlh8ODBuH//Pj7//HODdX///Te+/vpr2NraYujQoWZv09x2ReVPdHQ0AGDq1KlYvny5ydfkyZMNyprj1KlT6NSpE9LS0tC9e3f07t3b7PfqY9XMmTPh7OxscJVgaGgodu/ejX379qFx48Ym51AxxRLiWqVKlTB48GAcPXoU06ZNM3mi/vfffxv8wp/fcU2YMAFPnjzBiBEjTN5ecvv2bXk+IHP4+PigU6dOSE5ONpon8NChQ1i9ejU8PT3Rr18/AMDNmzdx6NAho+08ePAA9+7dg42NjTzf3bBhw+Dm5oZvv/0Wf/31l9F79NOrAMBbb70FDw8PREVF4fDhw0ZldTqdwcBNX++kpCQsWrTIoOyGDRtMDpb8/PwAGA8A//nnH/nW3ZySkpJM/nB8+/ZtPH782ODdBH6VAAAgAElEQVS2JU9PT0iSVKD22Lx5c7Ru3RonT57ErFmzjNbfunULGRkZZm+vJA0ZMgS2trZYuHChnEzVmzJlCu7evYshQ4bA3t7erO0VpF2RddDHha+++goajcbkDz7BwcHYs2cPtm/fDuD5k34csxUdjtk4ZssLx2xPleUxm8XP6QdkT6r94MEDzJs3D40bN0aXLl3QoEEDZGZmYv/+/Th06BAcHR2xZs2aXDvi8+fP5zppt6+vL6ZOnYqtW7dizJgx8PPzQ5s2baBSqfD48WMkJiZi27ZtyMzMxNixY/OdUFJPoVCgQ4cOctY3ZwDRXw7/999/Q6lUmn11on5i9P/+97+ws7ODr68vJEnC0KFDUaNGDbO2URLq1q2LFStWYMSIEWjQoAG6du2KOnXqIDMzEykpKdizZw+8vb1x/vx5+T0dO3bEr7/+iv79+6N79+5wdHREjRo1MHToUNja2mLt2rXo0qULevTogdatW6NJkyZwcnKCWq3GkSNH8M8//+D69etmf+Fat26Njz/+GLNnz0bDhg0xcOBAODs7Y8uWLTh9+jTatm2L8PBwufzcuXOxfft2BAcHo2bNmnBxccGZM2ewZcsWeHp6IiwsTC4bERGBQ4cOYePGjahTpw569uwJV1dXqNVqbN++HV9++aXcHqdMmYJTp05hyZIl2LhxI0JDQ1G9enWkpqYiMTER+/btw4wZM1C/fn0A2bevf/DBB1i4cKFcb1tbW2zYsAGenp4m5y4YP348Ro8ejaZNm2LAgAGwtbXFvn37cPbsWXnC7Zw+/PBDJCcnIzg4GH5+frCzs8OxY8cQGxuLGjVq4PXXXzf4u3355Zd4++23MXDgQLi4uMDDwwPvv/9+rp99586dMWXKFEybNg316tVD3759oVKpcOPGDezduxdBQUHybY3mWLVqVa6Tnjdp0gR9+/Y1e1v5+eKLL7Bnzx4sWrQIR44cQUhICNLS0vDLL7/g3r17WLRoEfz9/c3eXkHaFVmX3GISAISHh2Pnzp2oWLFinu339ddfx/jx4/H7779j4cKFBom25ORkeRLtzMxMpKWl4dixYzh27BiA7Cv89Ff7mUsfx1JTU9G1a1eDwXvHjh3l721BBnR59f1lyaJFi5CYmIjPP/8cP/zwA9q2bYvKlSvj2rVrOHfuHI4cOYI1a9bI3//84vWIESNw7NgxLF68GLVq1UKXLl3g6+sLjUaDpKQk/PXXX3jrrbewZMkSs+u4ZMkStGnTBuHh4di+fTtefPFFqNVq/Prrr1AoFFi5cqV8BczVq1cRFBSEevXqoVmzZlCpVLh79y42bdqEf//9F2PHjpXLVqxYEatXr8bAgQMREhKCbt26ITAwEHfv3kV8fDzUarWc8KxQoQJ+++039OvXD0FBQejYsSMaNGgAhUKBlJQUHDhwwCgJ9s0336BVq1YYN24ctm/fjsaNG+PSpUtYt26dyRjVq1cv1K5dG/PmzUNCQgKaNm2KlJQUbNq0CT169DAa0Jw6dQr9+vVD8+bN0bBhQ1SrVg03b97Ehg0bkJmZaZAodHFxQcuWLbFnzx4MHjwYderUgVKpRO/evU1OFq73448/Ijg4GJMnT8bvv/+O4OBgCCGQmJiI7du34/z583KyMj85v7umjBs3Ltd5LgvKz88P8+fPx3vvvYdmzZrh1Vdfhbe3N3bv3o0DBw6gbt26JhOZuSlIuyLrEBoaCkmSkJCQIP/7WSEhIVizZg2SkpLyfcgTx2wli2M2jtk4ZjNPmR6zFfh5v2XYoUOHxJtvvin8/PyEg4ODcHZ2Fg0aNBAffvihUKvVJt+jf/RyXq/GjRsLIbIf+T1nzhzRtWtXUatWLeHk5CTs7OyESqUS/fr1E3/88UeB6/z1118LAMLNzU1kZWUZrAsLCxMARIsWLUy+N7fHoR8+fFiEhoYKNzc3IUmSACB27dolhHj6+PeVK1ea3CYA0aFDB7Pqrn/8e36PEtd/jqbEx8eLYcOGCV9fX2FnZyc8PT1FgwYNRFhYmIiJiTEom5WVJSZNmiT8/f2FjY2NybreuHFDfPLJJ6JBgwbC0dFRODs7i9q1a4sBAwaIH374weAR6vrHv+s/m9ysWbNGtGnTRri4uAh7e3tRv359MX36dPHo0SODctu2bRPDhw8X9erVE25ubsLJyUnUqVNHfPDBByI5Odlou5mZmWLhwoXipZdeEs7OzsLJyUnUrl1bvP322yIxMdGgrE6nE99//70IDQ0Vnp6ewtbWVlSrVk20adNGzJgxQ6SkpBiVX7hwoahbt66ws7MTVatWFe+++65IT08XNWrUMPk3W7lypWjcuLFwcnISFSpUEH379hXx8fEmP6eff/5ZvP7666J27drC2dlZuLq6igYNGojJkyeL1NRUo23PnTtXrsuzbSa3diyEEJs3bxZdunQRnp6ews7OTvj4+Ii+ffsatY3cmPP492HDhsnl9f1BRERErtvM7fPL6fbt2+Ljjz8WtWvXFnZ2dsLd3V28/PLLJh/hnt8+C9quyPLl12YBiHfffVcAEOPHj893e2+//bYAIObNmyeEMB33HBwcRJUqVUS7du3ERx99JE6cOFGouut0OlGxYkUBQMyePdtg3dWrV+X9/fnnn0bvze27kF/fn9d30tx+Xm/YsGF5xsic2zT1nX38+LFYuHChaNWqlXBzc5PPEUJDQ8VXX30l0tLSDMrnFa/1Nm7cKHr06CG8vb2Fra2tqFy5snjppZfEp59+Ks6dO2dQ1pwYfuXKFTF69Gjh6+srbG1tRYUKFUSfPn3E4cOHDcrdvn1bREVFiZCQEFGtWjVhZ2cnqlSpIjp06CBWr14tdDqd0bZPnz4thg4dKqpVqyZsbW1FpUqVRPv27cXSpUuNyiYlJYn33ntP1K5dW9jb2wtXV1cREBAghgwZItatW2dUPjExUQwYMEC4u7sLJycnERQUJDZt2pTreU1KSooYNGiQqFatmnBwcBD169cXs2bNEpmZmUafk1qtFpMmTRKtW7cWlStXFnZ2dqJ69eqia9euJttqYmKi6Nmzp/Dy8pL/bvr959Wnp6WliY8//ljUqVNH2NvbC3d3d9G4cWMxefJk8eDBAxN/LUPmnLMCEElJSfJ78oqxQuR/Xqi3bds20alTJ+Hh4SHs7OxErVq1RHh4uLh9+7ZR2bz2WZh2RZYvMDBQABAVK1Y0+TdOTEw0iG+mcMxmiGM2YxyzccyWE8dsT0lCmDmZAREREREREREREVkEi5/Tj4iIiIiIiIiIiAwx6UdERERERERERGRlmPQjIiIiIiIiIiKyMkz6ERERERERERERWRkm/YiIiIiIiIiIiKyMTUntyN7eHt7e3oV6b2ZmJu7fvw+lUmm0TqvVwsXFBba2ts9bRSIi+p+bN2/i8ePHpV2NMu154hoREZUsxrX8Ma4REVmGgsS0Ekv6eXt748qVKwV6jxACarUaZ86cQXR0NBo2bGiQ+NNqtUhOTsaMGTPg6+tb1FUmIiq3fHx8SrsKZV5h4hoREZUOxrX8Ma4REVmGgsS0Ekv6FVR6ejqio6MRHx8PhUKB5ORkXL58GR07doSzs7Oc8AsMDIRKpSrt6hIREREREREREZUZZTLpJ4RAdHQ0EhISULNmTSgUClSuXBkxMTGIiYlBo0aNoNPpEBgYiLCwMEiSVNpVJiIiIiIiIiIiKjNKLOmXmZmJlJQUqFSqfJN0arUaCQkJ8Pf3h0KR/awRZ2dndO/eHWfPnsXrr7+OBg0amLUtIiIiIiIiIiKi8qbEnt57//59TJ48GV9++SXS09PzLKvRaKBQKOSEn56NjQ1cXV1RtWpV+Pr6MuFHRERERERERERkQokl/ZRKJfz9/ZGQkIBly5ZBCJFrWS8vL2i1Wuh0OoPl+mVeXl7FXV0iIiIiIiIiIiKLVWJJPyA78efn54f4+Hio1epcy6lUKgQGBiIpKQlarRYA+OAOIiIiIiIiIiIiM5X4gzyUSiUUCgU0Gg18fX1NlpEkCWFhYfLDPBQKBR/cQVQEdDpdnlfZkvWSJEl+ERFZC8a18kuSJKOpgIiILJkQQn5R+VNcca3Ek37m3qLr4eGB8PBwqNVqaDQaeHl58cEdRIV0+/Zt3Lx5U75ylsonhUIBe3t7VKpUCU5OTqVdHSKiQmNcIyD7YgJvb294enqWdlWIiArt4cOHSE1NxePHj42mOKPypTjiWokm/Qp6i64kSfD19c31ikAiyt/t27eRmpqK6tWrw8HBgYnzciwrKwv37t2DWq2Gt7c350clIovEuEZA9hUxGRkZuHr1KgAw8UdEFkmj0eDmzZuoUKECqlatChubEr8ui8qI4oprJdaicib8eIsuUcm5efMmqlevDhcXl9KuCpUypVIJe3t72Nvb499//4Wnpyf7YiKyOIxrpOfi4oLq1avj2rVrTPoRkcURQuDWrVuoVq0aXF1dS7s6VAYUR1wrsaSfi4sLZsyYwVt0iUqQTqeDVquFg4NDaVeFyhAnJydkZWVBCMH+mIgsCuMaPcvBwUGePohz/BGRJRFCICsri9PukIGijmsllvSztbXlbbpEJUw/CSwTO2QKJwkmIkvDuEbP0rcFxjQisjTst8iUoo5rvGE8H0IIPkyEiIiIiIiIiIgsCpN+eUhPT0d0dDTi4+OhVCqh1WrlOQk9PDxKu3pEREREREREREQmceKLXAghEB0djYSEBNSsWRP+/v7w9/dHQkICli1bxktxiazI/v37ERkZifT0dKN1wcHBCA4OLvlKAfjzzz8RGRlZKvsmIiLLxbhGRETWhHGt8Jj0y4VarUZCQgL8/f3lyROVSiX8/PwQHx8PtVpdyjUkKj1CCKSkpODkyZNISUmx+CT4/v37ERUVZTKILF68GIsXLy6FWmUHkaioqFLZNxFRecK4VjIY14iISgbjWsmwhLjG23tzodFooFAojJ6WolQqoVAooNFo+GASKpfK223v9evXL+0qEBFRMWJcIyIia8K4RjnxSr9ceHl5yY9Jzkm/zMvLq5RqRlR6yuJt74mJiRg0aBAqVaoEe3t71KtXD9988428XqfTYfr06QgICICjoyM8PDwQGBiIBQsWAAAiIyMRHh4OAPD394ckSZAkCXFxcQCMLxdPTk6GJEn48ssvMWvWLPj5+cHR0RHBwcG4ePEiMjMzMXHiRFSrVg3u7u7o168fUlNTDer8888/o3PnzqhatSocHR1Rr149TJw4EQ8ePJDLDB8+XD4OfZ0kSUJycjKA7L/F4sWL0aRJEzg6OsLT0xMDBw7EP//8U9QfMRGR1WJcY1wjIrImjGuMa8/ilX65UKlUCAwMREJCAvz8/OQMeXJyMgIDA6FSqUq7ikQlzpzb3kvyCtizZ8+idevW8PX1xdy5c1GlShVs27YNY8eORVpaGiIiIjB79mxERkbis88+Q/v27ZGZmYnz58/Ll4aPGjUKGo0GCxcuxNq1a1G1alUA+f9i9M033yAwMBDffPMN0tPT8eGHH6JXr15o2bIlbG1tsWLFCly+fBkfffQRRo0ahT/++EN+b2JiIrp3745x48bB2dkZ58+fx6xZs3D48GHExsYCAKZMmYIHDx7gt99+w4EDB+T36uv3zjvvYNWqVRg7dixmzZoFjUaDqVOnonXr1jh16hQqV65cpJ81EZE1Ylx7inGNiMjyMa49xbiWjUm/XEiShLCwMDlLrlAooNPp5MtiJUkq7SoSlbiydtv7hAkT4Orqir1798LNzQ0A0KlTJzx+/BhffPEFxo4di3379qFRo0YGE6x26dJF/n8fHx+5zk2bNoWfn59Z+/bw8MD69evlzyItLQ3jxo1D3bp1sWHDBrnc+fPnMX/+fNy9e1eu42effSavF0KgTZs2qFevHjp06ID4+HgEBgaiVq1aciAICgoy2PfBgwexbNkyzJ07FxMmTJCXt2vXDnXq1MG8efMwa9Yss46DiKg8Y1x7inGNiMjyMa49xbiWjbf35sHDwwPh4eGYMWMGxo8fjxkzZuCjjz6Cu7t7aVeNqFSUpdveMzIyEBMTg379+sHJyQlZWVnyq3v37sjIyMDBgwfRokULnDp1Cu+++y62bduGu3fvFsn+u3fvbhBM69WrBwDo0aOHQTn98pSUFHnZP//8g0GDBqFKlSpQKpWwtbVFhw4dAADnzp3Ld9+bNm2CJEkYMmSIwXFXqVIFjRs3li91JyKivDGuPcW4RkRk+RjXnmJcy8Yr/fIhSRJ8fX350A4ilK3b3m/duoWsrCwsXLgQCxcuNFkmLS0NkyZNgrOzM3788UcsWbIESqUS7du3x6xZs/Diiy8Wev/PBkw7O7s8l2dkZAAA7t+/j3bt2sHBwQHTp09HnTp14OTkBLVajf79++PRo0f57vvGjRsQQuR6SXjNmjULfDxEROUR49pTjGtERJaPce0pxrVsTPoRkdnK0m3vnp6eUCqVGDp0KN577z2TZfz9/WFjY4MJEyZgwoQJSE9Px86dOzF58mR06dIFarUaTk5OJVZnAIiNjcW1a9cQFxcn/1oEwOTj53NTsWJFSJKEPXv2wN7e3mi9qWVERGSMce35Ma4REZUdjGvPz9riGpN+RFQg+tve1Wo1NBoNvLy8oFKpSnyeSycnJ4SEhODEiRMIDAyUf6HJi4eHBwYOHIirV69i3LhxSE5ORv369eVO15xfbZ6X/nN6tqNfunSpUdmc9XJ0dJSX9+zZE1988QWuXr2KV199tRhrS0Rk/RjXng/jGhFR2cK49nysLa4x6UdEBVZWbntfsGAB2rZti3bt2mHMmDHw8/PDvXv3cOnSJWzcuBGxsbHo1asXGjZsiBdffBHe3t64fPky5s+fjxo1auCFF14AADRq1Eje3rBhw2Bra4uAgAC4uroWeZ1bt24NT09PjB49GhEREbC1tcVPP/2EU6dOGZXV12vWrFno1q0blEolAgMD0aZNG4SFheGtt97C0aNH0b59ezg7O+P69evYu3cvGjVqhDFjxhR53YmIrBXjWuExrhERlT2Ma4VnbXGNST8islj169fH8ePHMW3aNHz22WdITU2Fh4cHXnjhBXTv3h0AEBISgt9//x3Lly/H3bt3UaVKFXTq1AlTpkyBra0tACA4OBiTJk3Cd999h2XLlkGn02HXrl0IDg4u8jpXqFABmzdvxocffoghQ4bA2dkZffr0wc8//4xmzZoZlB00aBD27duHxYsXY+rUqRBCICkpCX5+fli6dCmCgoKwdOlSLF68GDqdDtWqVUObNm3QokWLIq83EREVP8Y1xjUiImvCuFb6cU0SQoiS2JGPjw+uXLlSErsiov/RarW4ePEi6tSpA6VSWdrVoTLCnHbBPjt//IyISh7jGj3L3DbBPjt//IyIShZjGplS1GM1Rf5FiIiIiIiIiIiIyJIw6UdERERERERERGRlmPQjIiIiIiIiIiKyMkz6ERERERERERERWRkm/YiIiIiIiIiIiKwMk35EVHBXrgCSlP3iU96IiMjSMa4REZE1YVyj/2HSj4iIiIiIiIiIyMow6UdERERERERERGRlmPQjIiIiIiIiIiKyMkz6ERERERERERERWRkm/YjIYu3fvx+RkZFIT08v0W37+fmhZ8+eRb5PIiIq3xjXiIjIWjCmlQ1M+hGRxdq/fz+ioqKKLZAU17aJiIhMYVwjIiJrwZhWNjDpR0TlwqNHj0q7CkREREWGcY2IiKwFY1rxYdKPiCxSZGQkwsPDAQD+/v6QJAmSJCEuLk6+pHvt2rVo2rQpHBwcEBUVheTkZEiShFWrVhltT5IkREZG5rvtnLZu3YpmzZrB0dERdevWxYoVK4rzkImIyIoxrhERkbVgTCs7bEq7AkRUxly5UrAy5pQHAB+fwtUnF6NGjYJGo8HChQuxdu1aVK1aFQBQv359AMDx48dx7tw5fPbZZ/D394ezs3ORbRsATp06hQ8//BATJ05E5cqVsXz5cowcORK1a9dG+/bti/BIiYjouTCuMa4REVkTC4hrjGllB5N+ROVV797A338bLz97tmDbadXKvHI5OmEDtWoBf/xRsH0C8PHxga+vLwCgadOm8PPzM1ifmpqKs2fPok6dOvKy5OTkItk2AKSlpWHfvn1yufbt2yMmJgarV68ud4GEiKjU5RbTAMY1M7YNMK4REZUpZSWuMaZZPN7eS0RWKTAw0CCIFLUmTZrIQQQAHBwcUKdOHVy+fLnY9klEROUX4xoREVkLxrSSwyv9iMqr3H6xMfdycf0vRgcOmHcpeBHfBpUf/WXexaVChQpGy+zt7TkJLRFRacjrKgTGNbMwrhERlSFWHtcY00oOk35EZKignb2PT4kPfMwhSZLRMgcHBwDA48ePDZbfunWrROpERESlgHGNiIisiRXENca0ksOkXxkmhIBarYZGo4GXlxdUKpXJLwdReWVvbw/A/Ee8V65cGQ4ODoiPjzdYvmHDhufeNhER0fNiXCMiImvBmFY2MOlXRqWnpyM6Ohrx8fFQKpXQarUIDAxEWFgYPDw8Srt6RGVCo0aNAAALFizAsGHDYGtri4CAgFzLS5KEIUOGYMWKFahVqxYaN26Mw4cPY/Xq1WZv29XVtXgOhoiIyj3GNSIishaMaWUDH+RRBgkhEB0djYSEBNSsWRP+/v7w9/dHQkICli1bBiFEaVeRqEwIDg7GpEmTsHHjRrRt2xYvvfQSjh07lud75s6diyFDhmD27Nno06cPDhw4gE2bNhXJtomIiJ4H4xoREVkLxrSyQRIllEHy8fHBFXMmnCSkpKTg008/hb+/PxSKp3lZrVaL5ORkzJgxw+BJNES50Wq1uHjxIurUqQOlUll0G75yBVCpsv9frS5zc0RQ3sxpF+yz88fPiKjkMa7Rs8xtE+yz88fPiKhkFVtMAxjXLFhRj9V4pV8ZpNFooFAoDBJ+AKBUKqFQKKDRaEqpZkREREREREREZAmY9CuDvLy8oNVqodPpDJbrl3l5eZVSzYiIiIiIiIiIyBIUKOm3d+9edO/eHZ6ennB0dMQLL7yAadOmFVfdyi2VSoXAwEAkJSVBq9UCeHprb2BgIFT6y3SJiOi5MK4REZE1YVwjIqKczH567+rVqzF06FC8+uqr+P777+Hi4oK///4b165dK876lUuSJCEsLEx+mIdCoYBOp5Of3itJUmlXkYjI4jGuERGRNWFcIyKiZ5mV9Lt69SrCwsLwzjvvYPHixfLykJCQYqtYeefh4YHw8HCo1WpoNBp4eXlBpVIx4Udlg48PwKdIkwVjXCMiA4xrZOEY14jIAOMa/Y9ZSb/ly5fjwYMH+OSTT4q7PpSDJEnw9fXlk3qp0PRJ4hJ6SDdZmPL8IwLjGpFlYlyjZ+nbQnmOaQDjGpElKu/9FplW1HHNrDn9/vrrL3h5eeH8+fNo0qQJbGxsUKlSJYwePRp3794tkooQUdFTKBRQKpXIyMgo7apQGfLw4UPY2NiU6xMNxjUiy8S4Rs/KyMiAUqmEQlG+n0/IuEZkeSRJgo2NDR4+fFjaVaEypKjjmtm39z58+BCvvPIKJk2ahPnz5+PIkSOIiIjA6dOnsWfPnnI9eCQqy7y9vXH16lVUr14dDg4O/K6WY1lZWbh37x5u3boFb2/vct0WGNeILBfjGgHZV0JkZGTg6tWrqFSpUmlXp9QxrhFZHkmSUKFCBVy7dg0VKlSAq6srbGzMfuwCWZniimtmtSidToeMjAxERERg4sSJAIDg4GDY2dlh3LhxiImJwcsvv2zwnnnz5mHevHnyv+/fv19klSYi83l6egIArl27Jj8NmsonhUIBe3t7qFQqODk5lXZ1ShXjGpHlYlwjPaVSiUqVKsltojxjXCOyTF5eXnBwcEBqaipu3boFnU5X2lWiUlQccU0SZkyK0qpVKxw8eBDHjx9H06ZN5eUXL15EQEAAZs2ahY8//jjPbfj4+ODKlSvPX2MiKjSdTsd5kMopSZLklzmsvc9mXCOyDoxr5ZckSQW69cna+2zGNSLLJ4SQX1T+FCSuFaS/NutKv8DAQBw8eNBoub4xlvc5NIgsBb+rRNkY14isA7+rRNkY14gsX0F+oCcyl1m9/4ABAwAAW7ZsMVj+559/AgCCgoKKuFpERETFh3GNiIisCeMaERGZYtaVfp07d0avXr0wdepU6HQ6BAUF4ejRo4iKikLPnj3Rtm3b4q4nERFRkWFcIyIia8K4RkREppg1px8APHr0CFFRUVi9ejWuX7+OatWqYfDgwYiIiIC9vX2+7+ccEURElqM89NmMa0RE5Ud56LMZ14iIyoeC9NdmJ/2eF4MIEZHlYJ+dP35GRESWg312/vgZERFZhoL015zRlYiIiIiIiIiIyMow6UdERERERERERGRlmPQjIiIiIiIiIiKyMkz6ERERERERERERWRkm/YiIiIiIiIiIiKwMk35ERERERERERERWhkk/IiIiIiIiIiIiK8OkHxERERERERERkZVh0o+IiIiIiIiIiMjKMOlHRERERERERERkZZj0IyIiIiIiIiIisjJM+hEREREREREREVkZJv2IiIiIiIiIiIisDJN+REREREREREREVoZJPyIiIiIiIiIiIivDpB8REREREREREZGVYdKPiIiIiIiIiIjIyjDpR0REREREREREZGWY9CMiIiIiIiIiIrIyTPoRERERERERERFZGSb9iIiIiIiIiIiIrAyTfkRERERERERERFaGST8iIiIiIiIiIiIrw6QfERERERERERGRlWHSj4iIiIiIiIiIyMow6UdERERERERERGRlmPQjIiIiIiIiIiKyMkz6ERERERERERERWRkm/YiIiIiIiIiIiKwMk35ERERERERERERWhkk/IiIiIiIiIiIiK8OkHxERERERERERkZVh0o+IiIiIiIiIiMjKMOlHRERERERERERkZZj0IyIiIiIiIiIisjJM+hEREREREYT7ItgAACAASURBVBEREVkZJv2IiIiIiIiIiIisDJN+REREREREREREVsamtCtgzYQQUKvV0Gg08PLygkqlgiRJpV0tIiIiIiIiIiKyckz6FZP09HRER0cjPj4eSqUSWq0WgYGBCAsLg4eHR2lXj4iIiIiIiIiIrBhv7y0GQghER0cjISEBNWvWhL+/P/z9/ZGQkIBly5ZBCFHaVSQiIiIiIiIiIivGpF8xUKvVSEhIgL+/PxSK7I9YqVTCz88P8fHxUKvVpVxDIiIiIiIiIiKyZkz6FQONRgOFQiEn/PSUSiUUCgU0Gk0p1YyIiIiIiIiIiMoDJv2KgZeXF7RaLXQ6ncFy/TIvL69SqhkREREREREREZUHTPoVA5VKhcDAQCQlJUGr1QLITvglJycjMDAQKpWqlGtIRERERERERETWjEm/YiBJEsLCwtCoUSMkJycjKSlJTviFhYVBkqTSriIREREREREREVkxm9KugLXy8PBAeHg41Go1NBoNvLy8oFKpLDrhJ4SwquMhIiIiIiIiIrJWTPoVI0mS4OvrC19f39KuynNLT09HdHQ04uPjoVQqodVq5SsXPTw8Srt6RERERERERESUA2/vpXwJIRAdHY2EhATUrFkT/v7+8Pf3R0JCApYtWwYhRGlXkYiIiIiIiIiIcmDSz8oIIZCSkoKTJ08iJSWlSBJyarUaCQkJ8Pf3h0KR3WSUSiX8/PwQHx8PtVr93PsgIiIiIiIiIqKiw9t7rUhx3YKr0WigUCjkhJ+eUqmEQqGARqOxiluYiYiIiIiIiIisBa/0s0CmruYrzltwvby8oNVqodPpDJbrl3l5eT3vIRERERERERERURHilX4WJrer+bp165bvLbiFvRpPpVIhMDAQCQkJ8PPzk/ebnJyMwMBAqFSqojxEIiIiIiIiIiJ6Tkz6WZBnr+ZTKBTQarVISEjA9evXIUlSsdyCK0kSwsLC5H0rFArodDr51mFJkori8IiIiIiIiIiIqIgw6WdB8nqgxpkzZyCEgE6nM0j8FdUtuB4eHggPD4darYZGo4GXlxdUKhUTfkREREREREREZRCTfhYkrwdquLq6wtPTE0lJScV2C64kSfD19eVDO4iIiIiIiIiIyjgm/SxIzgdqmLqab+TIkdiyZQtvwSUiIiIiIiIiKueY9LMg+T1Qo2HDhmjYsCFvwSUiIiIiIiIiKueY9LMg5j5Qg7fgEhERERER0f+zd+/Bbd33nfc/5xxewCtAkBJ1IUhCsRzrQoqJ7JXkeNts47S10p2mfzT25OlMZ9cx3bSbbtKR7D7Jzmz2mWS3sdNk+0d2G8neTafdWWsycRO3sb2t3cS1HVOJaVGEJMsr2QQJSryDIAkSIAmc8/wh44SkeQEpXsH3a0ZjGwTAA47Nr3/f870A2N5I+m0xLNQAAAAAAADAUkj6bUEs1AAAAAAAAMBizKWfAgAAAAAAAGArIekHAAAAAAAA5BiSfgAAAAAAAECOIekHAAAAAAAA5BiSfgAAAAAAAECOIekHAAAAAAAA5BiSfgAAAAAAAECOIekHAAAAAAAA5BiSfgAAAAAAAECOIekHAAAAAAAA5BiSfgAAAAAAAECOIekHAAAAAAAA5BiSfgAAAAAAAECOIekHAAAAAAAA5Ji8jb4A5AbHcRSJRBSNRuX3+xUIBGQYxkZfFgAAAAAAwLZE0g+3LRaL6cyZM2pvb5dlWUqn02psbFRzc7N8Pt9GXx4AAAAAAMC2Q3svbovjODpz5oxCoZD27dunYDCoYDCoUCiks2fPynGcjb5EAAAAAACAbYekX45yHEddXV1qa2tTV1fXspNv2b4+EokoFAopGAzKNG/962RZlurr69Xe3q5IJHLbnwUAAAAAAADLQ3tvjnEcR5cuXdLTTz+tzs5OlZWVybbtZbXbLqddNxqNyjRNN+GXYVmWTNNUNBpVbW3tqn5GAAAAAAAALI5KvxwSi8X0xBNP6Pd///f13HPP6fr16+rp6dHu3buzbrddbruu3+9XOp2WbduzHs885vf7V/1zAgAAAAAAYHEk/XJEJll3/vx5TU9PKxAIqKKiQv39/Wpra1NdXV1W7bbLbdcNBAJqbGxUR0eH0um0pFsJv3A4rMbGRgUCgbX5wAAAAAAAAFgQSb8ckUnWVVVVyTRNGYYh0zTl9XrV19en8fFxt912Mdm0685kGIaam5vV0NCgcDisjo4ON+HX3NwswzBW/bMCAAAAAABgccz0yxGZZF1JSYkcx5HjOG7izzRNxePxrNptM+266XRa8XhciURCRUVFKikpWfD1Pp9Pp0+fViQSUTQald/vVyAQIOEHANh0HMchXgEAAGBbIOmXIzLJutLSUlVXV6uvr89dupFOpzU0NKQTJ04s2W4bCAS0f/9+/ehHP9L09LRM05Rt28rPz9enP/3pBV9vGIZqa2tZ2gEA2LSWs6gKAAAA2Opo780Rmdl64XBYTU1Nqq6u1vDwsG7cuKH8/HwdP358Re22VD8AAHLBchdVAQAAAFsdlX45IjNbL3Og2bNnj8rKylRXV6eHH35Yhw4dyiqBF4lEdP36dX3qU5/6QHvvtWvXFIlEqOYDAGw52SyqIr4BAAAgl5D0yyGrMVsvMxvQsix5vV55vV73a5lFHhyKAABbTTaLqohvAAAAyCUk/XLM7c7Wy8wGtG171sEo89hSi0AAANiMiG8AAADYbpjph1kyswE7OjqUTqcl3ToQhcNhNTY2LrkIBACAzYj4BgAAgO2GpB9mycwGbGhoUDgc1nvvvafLly+rqqpKDzzwwEZfHgAAKzI3vnV0dLgJv5UsugIAAAA2O8NZp3V1NTU16u7uXo9vhVXgOI4uXbqkp59+Wp2dnSorK5Nt2+7hyOfzbfQlAlhD/M5eGj+jrclxnNuafQtga+J39tL4GQHA1rCc39dU+mFBL7zwgoaGhtTQ0KB9+/YpGAwqFArp7NmzWqdcMQAAqyoz+7apqUm1tbUk/AAAAJCzSPphXpFIRKFQSMFg0B14blmW6uvr1d7erkgkssFXCAAAAAAAgIWQ9MO8otGoTNOcteFQupX4M01T0Wh0g64MAAAAAAAASyHph3n5/X6l02nZtj3r8cxjfr9/g64MAAAAAAAASyHph3kFAgE1Njaqo6ND6XRa0q2EX2bTYSAQ2OArBAAAAAAAwEJI+mFehmGoublZDQ0NCofD6ujocBN+zc3NDD4HAAAAAADYxPI2+gKwefl8Pp0+fVqRSETRaFR+v1+BQICEHwAAAAAAwCZH0g+LMgxDtbW1qq2t3ehLAQAAAAAAQJayau/96U9/KsMw5v3T0tKy1tcIAMCqIq4BAHIJcQ0AMJ9lVfr95//8n/Wv/tW/mvXY4cOHV/WCAABYL8Q1AEAuIa4BAGZaVtJv//79On78+FpdCwAA64q4BgDIJcQ1AMBMbO8FAAAAAAAAcsyykn5/9Ed/pLy8PJWXl+s3fuM39Nprr63VdQEAsOaIawCAXEJcAwDMlFXSz+v16t//+3+v7373u/rJT36iv/iLv1AkEtHHP/5x/Z//83/W+hoBAFhVxDUAQC4hrgEA5mM4juOs5IWxWEwNDQ3y+/26ePHiB77+rW99S9/61rfcf47H44rFYiu/UuQEx3EUiUQUjUbl9/sVCARkGMZGXxaAOWpqatTd3b3Rl7GuiGsAkLuIa8Q1AMgVy4lpK076SdLnP/95/eVf/qUmJiZUVFS0aheF3BSLxXTmzBm1t7fLsiyl02k1NjaqublZPp9voy8PwAzb9Xc2cQ0ActN2/Z1NXAOA3LOc39e3tcgjky+kUgtLcRxHZ86cUSgU0r59+xQMBhUMBhUKhXT27FndRu4ZAFYNcQ0AkEuIawCwva046Tc8PKy///u/V1NTkzwez2peE3JQJBJRKBRSMBiUad76186yLNXX16u9vV2RSGSDrxDAdkdcAwDkEuIaACAvmyd99rOfVW1tre6++25VVVXp2rVr+vM//3P19fXpe9/73hpfInJBNBqVaZpuwi/DsiyZpqloNKra2toNujoA2w1xDQCQS4hrAID5ZJX0a2xs1Llz5/SXf/mXisfj8vv9uu+++/TXf/3Xuueee9b6GpED/H6/0um0bNuelfjLPOb3+zfw6gBsN8Q1AEAuIa4BAOZzW4s8loPBsNub4zh68sknFQqFVF9f7y7yCIfDamxs1KlTp5g1Amwi/M5eGj8jANg6+J29NH5GALA1LOf3dVaVfsBMjuMoEokoGo3K7/crEAgsmbAzDEPNzc3uMg/TNGXbtru9l4QfAAAAAADA6iHph2WJxWI6c+aM2tvb3Wq9TOLO5/Mt+lqfz6fTp08vO2EIAAAAAACA5Vnx9l5sP47juJV6+/btUzAYVDAYVCgU0tmzZ5VNp7hhGKqtrVVTU5Nqa2tJ+AEAAAAAAKwBkn7IWiQSUSgUUjAYdJdxWJal+vp6tbe3KxKJbPAVAgAAAAAAQCLph2WIRqMyTXPW9l3pVuLPNE1Fo9ENujIAAAAAAADMRNIPWfP7/Uqn07Jte9bjmcf8fv8GXRkAAAAAAABmIumHrAUCATU2Nqqjo0PpdFrSrYRfOBxWY2OjAoHABl8hAAAAAAAAJLb3YhkMw1Bzc7O7zMM0Tdm27W7vNQxDjuOs2nbe1XwvAAAAAACA7YSkH5bF5/Pp9OnT8ybjYrGYzpw5o/b2dlmWpXQ67SYEfT7fsr7Par4XAAAAAADAdkN7L5bNMAzV1taqqalJtbW1boVfpgJw3759CgaDCgaDCoVCOnv2rBzHkeM46urqUltbm7q6uuQ4zrzvn817AQAAAAAAYGFU+mFVRCIRhUIhBYNBd7uvZVmqr69Xe3u7Ll26pBdeeGFW5V5DQ4NOnjypdDo9q2JwqfeKRCKqra3dyI8LANimGD0BAACArYKkH1ZFNBqVaZpuki7DsiwZhqGnn35aQ0ND2rdvn0zT1Pj4uM6dO6dnnnlGDQ0Ns2YDLvZepmkqGo2S9AMArDtGTwAAAGArob0Xq8Lv9yudTsu27VmPp9NpxeNxdXV1uZV7juOora1N09PTSqVSqqysnNW+W1FRseB72bYtv9+/nh8NAABGTwAAAGDLIemHVREIBNTY2KiOjg6l02lJt5J04XBYdXV1Ki0tdSv3RkdH1dfXJ7/fL8uylEgkZrXvSnLfK5VKaWRkRDdu3NDly5fV0NCgQCCwYZ8TALA9ZTN6AgAAANhMSPphVRiGoebmZjU0NCgcDqujo0PhcFiNjY16+OGHZdu2W7mXSCTc5R+2bauoqEjSL9t3h4eH1dzcrDvuuEPPP/+8fvSjH+nll19WOBxWMpnUyMjIRn5UAMA2lM3oiZmyXV4FAAAArBVm+mHV+Hw+nT59+gMDzqVblXuhUEj19fUqKiqSbduKxWKqrq5WeXm5pNntu16vVx6PR/X19aqqqlJJSYlKSkp07do1nT17VqdOnWJwOgBg3cwcYzEz8Tff6Alm/wEAAGAzoNIPq8owDNXW1qqpqUm1tbUyDOMDVYDRaFT5+fnKy8tTU1OTDMNwW4EbGxsVCAQUiUR06dIlHT58WHv27JHX61VeXh5tVACADbHYGItM7JKY/QcAAIDNg0o/rAuv16sHH3xQDQ0NkqRTp07p+eef16VLl2Sa5qztvYZhsMEXALCpZG5gZRJ688UuSerq6lJLS4uqqqo0Njam8vLyD8z+I34BAABgPZD0w5pbrM1pbGxsVitw5tC0nDYqAADWw0JjLDKxKxaL6dvf/rba2tpUVlYmx3FUXV2to0ePyuPxcNMKAAAA64qkH1bEcZwFDz1znzezzck0TaXTaYVCIT311FM6derUvIefTBtVZg5gJlk4t40KAID1lBljMTd2ZeJdV1eXSkpK5PP55DiO+vr61NraqmPHjnHTCgAAAOuKpB+WbTkDyiORiEKhkILBoFuxl02bU7ZtVAAAbAaZeHfo0CGNjY2pv79fXq9XPp9Pvb29unLlik6cOMFNKwAAAKwbkn5YlsUq9+bbqns7s/mWaqMCAGCzyMQ7y7J09OhRtba2qq+vT6Zpanx8XHV1ddy0AgAAwLoi6YdlWW7l3u3O5luojQoAgM1kZrzzeDy69957NTo6qng8rqGhIX3xi1+U1+vd6MsEAADANmIu/RTgl7Kp3JspM5uvo6ND6XRakpjNBwDYkhzHUVdXl9ra2tTV1SXHcdyvzY13hmGotLRUyWRSJ06c4OYVAAAA1h2VfliW5VburfZsvmwXiAAAsJqWmmfLLFoAAABsNiT9sCwr2aq7WrP5lrNABACA1ZLtPFtm0QIAAGAzIemHZVlpJcPtzuabeeAKBoOKx+OKx+NqaWmRJJ0+fVqSOGgBAFbdcubZMosWAAAAmwVJPyzbRlQyZA5cu3fvVktLi/r6+mQYhmzbVjgc1sc+9jG9/vrrVAECAFbd7WyiBwAAADYKST+syHpXMkSjURmGoQsXLqivr08VFRVu0i8Siejxxx9XMBhctO0KAICVuN1N9AAAAMBGYHsvtgS/36+xsTH19va6Cb+MgoICdXV1ye/3L9h2BQDASrGJHgAAAFsRST9sCYFAQHV1dZqYmJDjOJIk27Y1MjKiiooK5eXlaXJyctZrZrZdAQCwUpl5tg0NDQqHw+ro6HATfmzmBQAAwGZFey+2BMMw9PDDD+uVV17R8PCwLMuSbduqrq7Wvn379I//+I8qLCyc9RrargAAq2U159k6jsPiKQAAAKw5kn7YMg4fPqyHHnpI58+fV2VlpUpLS1VSUqJwOKwDBw4oGo2qvLzcXeRB2xUAYDWtxjzbWCymM2fOsHgKAAAAa46kH7YMwzD06KOPyjAMhUIhTU1NaXBwUEeOHNFnPvMZnTt3TqFQSKZpyrZt2q4AABtioUo+x3F05swZhUIhFk8BAABgzZH0w5ayWHvVarVdAQCwUotV8o2OjioUCikYDC64eOp2qggBAACAmUj6YctZqL1qNdquAABYqaUq+e6//36Zpukm/DJmLp4ihgEAAGC1sL0XAABgFUQikUUr+ZLJpLtkaiYWTwEAAGAtkPTDtuc4jrq6utTW1qauri45jrPRlwQA2IKi0eiilXwej0eNjY3q6OhQOp2WJBZPAQAAYM3Q3ottjS2KAIDblVnc0dPTo9HRUaXTaVmW5X49U8lXWVmp5uZmtwWYxVMAAABYSyT9sG2xRREAcLtm3jwyTVPhcFidnZ36xCc+oZKSkg9U8rF4CgAAAOuFpB+2raVmL7FFEQCwmPluHlVXV+vll1/Wyy+/rIaGhnkr+eYunsqMmSAJCAAAgNVE0g/b1lKzl9iiCABYzHw3j0pKSnTy5ElduXJFDz30kA4dOrRoEo8xEwAAAFgrJP2wbfn9fnfO0szEH1sUAQDZWOjmUV5ensrKyrR79+5Fbx7NrBQMBoOKx+OKx+NqaWmRJJ06dUrd3d3LqgDMzBekahAAAAAk/bBtBQIBNTY2KhQKqb6+3q2wYIsiACAbt3vzKFMpuHv3brW0tKivr0+GYci2bV2/fl29vb3q7+/PugKQqkEAAADMZC79FGBrycxGamtrU1dXlxzHmfd5hmGoublZDQ0NCofD6ujocBN+bFEEACwlc/Ooo6ND6XRakpZ18ygajcowDF24cEF9fX2qqKhQRUWFfD6furu79cILLygYDLp/Moum5otrc+cLZvMaAAAA5DYq/ZBTllvl4PP52KIIAFiRzM2jTLLNNM15F3csxO/3a2xsTL29vfL7/e7zJycnZdu2HMdRPB6X1+tdctEUy6kAAAAwF0k/5Iz5tiim02m3yuHUqVPzHsDmblEEACBbt3PzKBAIqK6uTu3t7aqoqHBbe2OxmIqLi2UYhiKRiCSpvLx80UVTLKcCAADAXCT9kDNWs8qBQegAgGyt9OaRYRh6+OGH9corr2h4eFiWZcm2bVVWVioWi+nmzZuSpP/7f/+vqqur1dTUtOCsQJZTAQA2E85TwOZA0g85Y7WqHFY6CJ3ABgBYrsOHD+uhhx7S+fPnVVlZqZKSEl28eFGpVErFxcWqqqqSYRjq7e3VP/3TP+nBBx+cd1Ygy6kAAJsFi6WAzYOkH3LGalQ5rLRFmMAGAMjGfDeIHn30URmGoVAopOHhYXV2dqqhoUGmaWpoaMiNaY7j6OTJkwuOqrid+YIAAKyGlZ6nAKwNkn7IGXOrHEzT1PDwsN59910dOXJENTU1S77HSlqECWwAgGwsdoMoMxfwjTfekOM4Onz4sCRpdHRUiURCRUVFGhoaUiqVWvD9WU4FANhoLJYCNhdz6acAW0OmyqGhoUHvvPOOnn32Wf3gBz9QV1eX3n33XX3zm99ULBZb9D2yaRGeK5vABgDY3ubeIAoGgwoGg+4NIkmqra3ViRMnVFRUJMdxZBiGvF6vdu3apdLSUjmOs2TVema+YFNTk2pra0n4AQDW1UrOUwDWDkk/5BSfz6fPfe5zGhgYUDQaVVlZmSRpcHBQra2tOnv2rBzHWfD1M1uEZ1qsRZjABgBYSrY3iAKBgBoaGnTp0iXduHFDIyMjSqVSzOYDAGwJ2Z6nHMdRV1eX2tra1NXVtegZDcDK0d6LnOI4jp588kl1dnbqQx/6kDvTaGBgQJJ08eLFRUvKVzIInY2JAIClZLtsamRkRMlkUh0dHWpra5N064bWpz/9aWbzAQA2vcXOUw0NDXIcR6+++qqef/55RSIR5qEDa4ykH3JKJBJRe3u7SktL3YOVaZry+XwaGBiQz+fT5cuXF5x1tJJB6GxMBAAsJZsbRJkW4OvXr+u3fuu3FI/HFY/HNTQ0JI/Ho/Ly8g38BAAALG2h89T+/fuVSCT05S9/WVevXlU0GtW+fft09913K5FI6J//+Z8Vi8X0ta997QM3yACsHEk/5JRoNCqPxyNJ7jwkSe5yjStXrujMmTMqLy9f8I7S3EHoFRUVkqSOjo5VSxQCALaXbG4QzW0B9nq97ky/UCikrq4uGYbBkg4AwKY233nqmWee0aVLl1RVVaXp6WnV1NSot7dXzz77rDwejwzD0OXLl+U4jh5//HEq/oBVQtIPOcXv98vj8WjHjh0aHByU1+uVaZpKpVLq6enRnj17dPjwYfewtdCG3cwg9PLy8gU3LS6WKOQwBgCYKZsbRDNbgB3HmbW5N5VK6dvf/rYGBwdphQIAbHqZ81Rtba26urp06dIlBYNB9ff3yzAMmaapiYkJxWIx3XnnnSoqKpIktbe3z3s+A7AyJP2QUwKBgI4cOaJUKiVJ7iy/4eFhFRUV6YEHHpBlWZKWXh0/d9NiplpwqUQhK+gBAPNZ6gZRpgV4YmJCFy5cUF9fnwzDUDqd1vDwsD7ykY/oox/96JLxCACAzWTmTa3MhvpEIqGxsTEZhqFEIqGCggJJ0oc+9KEFz2cAlo9meeSUTCXF0aNHtXv3bu3fv1+BQEC//uu/rn/5L/+lSkpKZj1/sQ272W5aBAAgW5kbRE1NTaqtrZ2VrMts7n3ppZfU29uriooKeb1epVIpJRIJTUxMuM+3LEt1dXV644039OKLL7qbD9mGCADYbGbOtS0vL5ff79d7772neDyuiYkJ3bhxQ9evX1dFRYVM01QsFnNbfQHcHir9kHPmq6RwHEdf+cpXlrVhN9tNiwAArAbDMHTy5EmdO3dOkjQyMiLbtuXz+WRZlgYHBzU6Oiqv16tkMqnW1la9++67+s53viOfz6f9+/dLkq5du0YLMABg05g517aurk6GYbiV7IWFhbIsS7Ztq7u7W9FoVOPj427HFTEMuD1U+iEnza2kqK2tVWNjozo6OpROpyVpyQ27M+9IzbRYohAAgNuRTqd1+PBh3X///Tp+/Lg+8YlP6NixY0qn00okEurv75dt22ptbVVvb69KSkq0f/9+1dfX64c//KG+//3vq6ioSH6/X/X19W4LMNUSAICNkunGamho0JUrV9TZ2anq6mrt3btX1dXVqq+vV3FxsQYGBjQ2Nqa9e/fq0KFDxDBgFVDphy3FcZwVLctYyYbdbDYtAgCwmvx+v2zbVllZmVvR9+abbyoWiykej+vNN99UZ2enotGoLMvSrl27VF5erv7+fvX09CiZTOq1115Tfn6+qqur1dTUxGwkAMCGy3Rjvfjii/rOd76j/fv3q6CgQG+99ZY6OzvV29urVCqleDyuaDSq8+fPE8OAVUDSD1tGLBbLapPuQpa7YXcliUIAAG7H3Bao1tZW9fX1ye/3q6ysTAUFBQqHw5qYmNBHP/pRHT16VJJ04cIFTU5OqqCgQHl5ecrPz1d3d7ckaffu3YykAABsOMMwdOjQIfl8PpWVlck0Td17770aGBiQZVkqLCxUIBBQWVmZ+vr61NbWpj179hDDgNtA0g9bwnI36S5kuRt2l5soBADgdsy84dTS0qJ3331XJSUlqqys1B133CHTNDUxMaHXXntNBw8elMfj0cjIiEZGRmRZliYmJtTT0yPLsuQ4joaHh1VYWMhICgDApjC3m2pwcFA3btzQ1NSUHMfRjRs3VFpaql27dqm3t1dlZWXEMOA2kPTDlpDNJt3VuvszXwvxchKFAADcjpktUH/xF3+heDyukZERvfXWW3IcRzt37lRlZaUuXbqkD33oQ5qYmFBeXp4mJyeVTqdVXFzsVqdHo1GNjIyopqZmoz8WAACzbm61t7ertbVVExMTKi0tlWVZ8ng8Gh8fV09Pj0zTVF1dHWOVgNtA0g9bwnpt0r3dFmIAAFaDYRg6ePCg+vv7NT09Lb/fL8MwZNu2bt68qeHhYU1PTyscDiuVSml0dNSt6Esmk+5zi4uLJUnnz5/X8ePHqVQHAGy4zM2tlpYWfeUrX5Ft26qsrFRvb6/Gx8clScPDw6qpqdHDDz9M7AJuA0k/bAkzN+nOTPyt5ibd1WohBgBgNRmGIcdx3L9Go1FNTU3p137t15SXl6exsTH9v9J3tQAAIABJREFU9Kc/dW+ATU9PK5FIuFUSN27c0Ne+9jX96q/+KjexAACbgmEYKioqUk1NjSzLUn9/v/bu3avp6WlNTU1paGhI999/vw4dOrTRlwpsaebSTwE2Xmb2Q0dHh9LptCSt+ibdbFqIAQBYL8PDw/rwhz+snTt3amBgQD09Perp6ZF0aznH9PS0vF6vampq9Gu/9mtKp9Pq7u7WyMiI+vv7ZVmWgsGgSktL9aEPfci9ieU4zgZ/MgAAfrmx/iMf+Yh27typkZERJZNJTU9Pq7KyUp/73OfcG15dXV1qa2tTV1cXcQxYBir9sCWsxybd5bYQzzf7j0pAAMBqmVnl7jiOHMdRKpVyDztFRUWSpGQyqffee0+maSqRSMi2bU1OTmrPnj1ue1RFRYW8Xq97EysQCBDDAAAbauZSj2PHjml8fFzxeFxDQ0M6fvy4Dh06NO/4pUAgoJMnT7rz/ohfwMJI+mHLWOtNustpIWb2HwBgrdXU1CgejyscDmvv3r2yLEvxeFxXrlxRQUGBHMeRbdtqbW1VX1+fdu/erfLycl27dk2jo6NKJBLyer3avXu3ksmkpqamFIvFdP78ef3v//2/FQqFiGEAgA2zUGHHiRMn1NzcLEmzxi9NTk7q1Vdf1U9+8hP9/d//vRobG3XkyBHiF7AIkn7YUgzDWPYm3Wwr8uauj88chOa2EDP7DwCwHrq7u1VWVqZgMKiBgQHZtq3BwUFZlqVoNKoXXnhBO3bsUF9fnyRp165dKigoUGlpqaamppSXl6eamhoNDAzo2WefVWFhocbHx/XVr35VhYWFuv/++1VcXEwMAwBsmMUKO7q6utzxS5OTk3r22Wc1MDCggoICdXd3q7y8XKlUivgFLIKkH3Lacirysm0hzmb232psEgYAbG/RaFQej0f33XefRkZG1NLSonQ6rX379qmjo0PT09O6ePGiksmkfD6f0um0BgYG5PF45DiOxsfH1dPTI8uyNDo6qurqatXU1CgWi2l6eloXLlzQvffeSwwDAGw6juPo8uXLGh4eVmVlpd58800NDg7K6/XKMAwlEgn19/fL4/Ho4sWLxC9gAST9kLNWUpGXTQtxNBqVYRgaGxtTIpFQUVGRysvLF5z9t9Q1MlMJADCfzNiJzObeiYkJ7dy5U47jqKKiQqOjo+5yq1QqpcHBQSWTSVmWJZ/Pp+HhYY2OjiqVSqmwsFAVFRW644479NZbb8nr9aqvr0+jo6Pyer0rimEAANyu+Yo09u/fL0lqa2vTlStXdO3aNfX390u6NXopU3hRUVGhgYEBVVRUEL+ABZD0Q85aaUXeUi3ElmXp0qVLmp6elmmachxH1dXVampq+sDsv8UwFxAAsJiZYyc8Ho+7wTAWiymRSGh8fFxVVVWKRqNyHEeTk5OS5P61srJS5eXl6uzsVFVVlY4fP+6+h2EYbqWE1+udd34tAABrab4ijVQqpR/96EeSpJMnTyoWi6m9vV1jY2OSbsU40zRVVVWloqIiJZNJJRIJ4hewAHPppwBbT6YcPBaLaWxsbNZa95nVDCt53+eff17SreSg1+uVz+dTb2+v/umf/kkNDQ3u7L+l3mdmgAsGgwoGg24VImvoAQCZsRMNDQ0aGhrS2NiYhoeH5fV6ZZqmCgoKZBiGiouL5fF4JN2qgJicnNTU1JQSiYRGRkZk27YqKyvl9XpVXl6u6upqRaNR2batoqKieefXAgCw1uYr0hgfH9f09LSmp6cVj8dl27YkuTetUqmU+8+pVErxeFxHjhwhfgELoNIPOSdTQffGG2/o8uXLCofD2rVrl44ePSqPx3Nb1QyRSESXLl3S/fffrwsXLqivr88NUI7j6OTJk1m15zIXEACQjczYia6uLn37299WV1eXKisrNTg4KMdxlEwmVVZWJr/fr7GxMdm2LcuyVFxcLNM0NTo6KsuytGPHDvdrTU1NevnllyXdGlkxODj4gfm1AACstWg0KtM03fOQJCUSCZmmKcMwdOPGDb3zzjuyLEsFBQWanJxUQUGBCgsLFYvFlE6n1dDQoMcee4z4BSyApB9yyswKusOHDysej6u3t1e9vb1qbW3VsWPH1NnZueJqhkxgKi4u1r333qvR0VF3rt/Q0JB75ynb95kZ4CQxUwkA8AGGYaiurk5f/epXdebMGbW0tLjtTZJUXV3tzvYzDEM7duzQ3r17NT09rfHxcRUUFOjw4cMKh8PukqqHHnpIDzzwgLq7uyVJBw8eVHl5+YZ9RgDA9pOZXWvbthvTioqKZNu2HMfR9evXNTk5qbKyMlmWpeHhYfdrxcXFuv/++/WlL31J4XDYnY8uiZnpwAwk/ZBT5lbQHT16VK2trert7dW7776rsrIynThxYsXVDHMDk9frdWchDQ4OZl09mBnAfvPmTZWUlKi8vFyGYTBTCQCwoLlVf9evX9fExIQGBweVSCQkSWVlZSovL1cymZRt2woEAqqqqtKDDz6oyspK9xBUVlams2fPMlcWALBhZs6ura+vl2VZKikpUX5+vqampjQxMSHDMBSNRpVMJuU4jjv3LzNm6Rvf+MYHFoBcu3aN2Aa8j6QfNoXV2mI7t4LO4/G4FXnXr1/XI488ot/8zd9c8d2eQCCghoYGnT9/XpWVlSotLVVJScmyqgdjsZieeeYZdXZ26uLFiyopKdGuXbvU1NSk3t5eZioBABY0t+qvvb1dfr9f0WhUBQUF+tjHPqbx8XFJ0o4dO1RaWqrOzk5VVla6S6ocx9GTTz65rO32AACstszs2kynVqYa/dOf/rTC4bB++MMfamxsbNYcP8dxlE6n1d3drZdeekm//du/LcuyZi0A+dSnPuUm/Yht2O5I+mHDreYW2/lKxA3DUGlpqXw+nw4dOuT+sl9JonFkZETJZFIdHR1qa2uTdKvy4tOf/nRW1YOZ9uOZcwF7e3v13nvvaWhoSA899BAzlQAAS8pU/WXimGVZeuyxx/TSSy+ptLRU0q2kX1VVle6++27V1NSoq6tL0WhUiUSCubIAgE1hbjzz+/2qqanRV77yFXk8HndZR2bRYeac5ziOenp6NDY2Jp/P5y4AkaR4PC6v10tsA0TSDxtsvjXtt3NHZr4S8fm2Eq4k0Zi51uvXr+u3fuu3FI/HFY/HNTQ0JI/Hk9UspLntx5kqxMz7PPjgg/J6vVl/XgDA9mUYhmpraxUIBPTkk0+qvLxcwWBQAwMDkqSOjg55PB797u/+rr75zW+6MW9gYEB9fX3au3evu/VXmj1XNhAIMBMJALAuMvEsk5Tr6upSJBJRTU2Nrly5IsMwlJeXJ8dxZNu28vPzlUqlNDY2pra2NjU1Nc1aAJJIJNwzFTPTsd2R9MOGWu0ttguViM/cSrjSROPca83M89u1a5dCoVBW1zq3/dgwDPd9pqamNDw8rLq6umX8BAEA210mPn34wx/WXXfd5S6ZKigoUDQa1Xe/+111d3e7Mc/r9erq1av6xS9+ofvuu8+NeZkD1LVr13Tu3DlFIhH3xlggENDJkydVV1dHAhAAsKYyFexHjx7V9evX3bm10q1CjMnJSTmOo1QqpZ/97Gd6++23FQwGNT09LcuyVFRU5D6fmenY7kj6YUOtxRbb+UrEZx5QVppoXI1rna/9WCIYAQBWbm58ytxMkqSbN2+qvb1dR48edb9eUVGhYDCojo4OHTp0SH6/X+Pj43r55Zdl27b+y3/5LxoeHta+ffvU0NCgUCik119/Xf/wD/+gu+66S0eOHGEoOgBgzWTOTFVVVTpw4IBaW1sl3TozZdp8M0zT1Pj4uLuhvrq6WiUlJe7z53Z8AduNufRTgLUzMwk20+0mwTIl4k1NTaqtrZ1VkZBN8m41rtVxHHV1damtrU1dXV1yHMdtP+7o6FA6nXZfTzACAKzUYvEpkUjI4/HMinmGYeiee+5RRUWF3n33XXV0dOjll1+WJB0/flypVEo1NTUaGBjQj3/8Yw0MDKimpkbT09OqrKx0K+PnHrwAAFgNmTNTOBzWiRMntGfPHreyL8OyLBUWFsqyLE1NTSkej6u4uFi/+qu/qitXrqi1tVWXL19WQ0MDM9OxrVHphw2V7Qy+1bTSarvlXOtiMwOXaj8GAGA5FotPR44cUWdnp2zblmEYs1p/77rrLv27f/fvFIvFNDY2pkOHDmlgYECGYbjtUZFIRHfeead7Y2xqaoqh6ACANTV3ZNOxY8f085//XDdv3pR069xWUlKi4uJixeNxd4HH2NiYXn/9dXk8HhUUFKisrEyO43CTCtsaST9sqGxm8K22lSYas73WbGYGLtZ+DADAciwWnx555BGdOXNGb775pm7cuKH+/n5ZlqVkMqmDBw/qrrvuUmdnp8rKytxEX+aANLMi3bZt2batoqIihqIDANbc3JFNExMT+upXv6pr165pdHRUJSUlGhsbUyqVUl5engoKCjQ2NqYrV66orKxMO3fulCS99dZbK1oQCeQKkn7YcEvN4Fttt5NozOZas50ZOHNDFQAAt2Ox+PSZz3xG/+N//A91d3crPz9fklRZWanCwkI99dRT+sxnPuMm9srLy1VdXa3+/n4VFBRIuhU3R0ZGVF1drfLycubQAgDWxcytvo7j6BOf+IQGBgaUSCQ0NjbmLvjIy8vT5OSkbNvWjh07NDU1JY/Ho8HBQUnSxYsXqU7HtkXSD5vC3DXta+12Eo1LXetaLCcBAGApcw9HkUhEQ0NDeuqppzQ5OamDBw+6oy2SyaRGR0d18eJFfeYzn5lVAX/06FH94he/0HvvvaeSkhINDQ0pGAzq6NGjsm2bObQAgHVnGIYeffRRDQ8P66/+6q8Uj8eVSqVkmqYcx1F+fr6Ki4vdM5ht2/J6vRoYGJDP5+MMhm2LpB+2rbVKNLKhFwCwkWbOlU0kEmppaVE6nVZBQYHy8m79r5/H43EPQsPDw3rkkUf0xBNP6K233pLH49GuXbt07Ngx3XfffXr11VcViUTU09Mzq22YMRUAgPXk9XpVUVGh48ePK5lM6rXXXtP09LT7J5FIaHp6Wh6PR3l5ee5ZLJlMcgbDtkXSD5taplJhKx0qNmI5CQAA0gfnyvb396u8vFw9PT26efOmG0dnHoQsy9LZs2cViUTk8XiUTCZ155136vTp06qoqNADDzwwKxaXlZUtuKzK5/Nt8E8AAJCrIpGILl26pMOHD+tnP/uZO4PWMAzZti3HcdwKQMuylEqlFI/HdeTIEc5g2LZI+mHTWmwD7lodKlYjybgRy0kAAJA+OFe2qKhI+fn5bkXfjh07VFRU5B6EGhsb9fzzz+vSpUuzlk+Fw2E99dRT7uDzmW3DTz755KLLqohzAIC1kBmjFI/HdePGDRUVFWl6etpdPJUxOTmpd955R2VlZTp48KAee+wxSVJXV9eWKiYBVgNJP2xK2WzAXeiX9EoTd6uZZFzv5SQAAEgfnCubWcxh27aSyaSi0aiKiooUj8d14MABffazn9UTTzyx5PKpjGyXVQEAsNoyY5TGx8fdyj7btt2zm2VZbuVfMpnUgw8+qK9//euSpCeffFLt7e0yTVNjY2Oqq6vTww8/rMOHD3NGQ04j6YdNaaWHipUm7m4nybiQ9V5OAgDA3LmyhmG4iznGx8e1f/9+GYahI0eO6LHHHlM4HF7W8imWVQEANkpmjFJLS4sMw3Cr/BzHkSS34q+goEDFxcU6cOCARkZG9Mwzz+j8+fMqKyvTu+++q5GREV28eFH//M//rAcffFCPPvoo4ymQs0j6YVNayaHidhJ3VC4AAHLB3LmypmlqYmJCHo9HJ0+e1MMPP6yqqiq3+nxmktAwDI2OjiqRSCg/P19jY2Pq6emZVa3OsioAwEbJjFFyHEcdHR1KJBJuwi+zxddxHKVSKcViMT377LN68cUXdeHCBZWXlysWiymZTMrn82n37t0aGxvT+fPnZZom4ymQs0j6YVNayaEiEomovb1dlZWV6u/vV1FRkcrLy7NK3C03ybgVF4wAAHLfzLmyra2tun79uhurSkpK9NJLL7nzZTOHo6qqKl24cEHj4+MaHBxUOp1WT0+PPB6Pu/E3UzXPsioAwEby+Xx67LHH9JGPfET/9t/+W928eXPWQo9M4YdlWSorK1NHR4ei0ahSqZTS6bRKS0s1MTGh3t5elZWVqbKykiIP5DSSftiUVnKo6Ozs1Ntvv63p6Wn3MFNdXa2jR48u2XK0nCTjQi3Ej37qU/IePnzrSZGIVFOzuj8UAACy4PP5dOrUKX3lK19RPB7XfffdJ5/PJ9u23er3z33uczp79qza29uVSqXU2tqqZDKp3bt3KxqNqs6ydKGnRzp3Tk984QuzquZZVgUA2EiGYWjnzp06cuSIksmkO+PPMAxNTU25sej8+fOKRqNKp9MqGhpS+P3233t27VJnPK7CwkKVlpZqamqK8RTIWST9sCktdwOu4zh6/vnnFY1GFQgE3Of39/frF7/4hXbv3r1oy1G2Sca5LcSGYWh4eFivvPKK7K4u/ema/lQAAMhOd3e3uru73Rtf0i/HVly8eFFPPPGEuru7tW/fPo2Njcnv92t6eloFBQXyer3a5/VKg4OSpImJiQ9UzbOsCgCwkSoqKpRKpVReXq7i4mJNTExoenrarehzHEfDw8NKpVKSpLRtu68dGxvTdH6+vF6vSkpKNDg4yHgK5CySfti0lrMBNxKJuIeXgYEB+Xw+mabplnQfO3Zs0ZajbJOMM2f/TU1NqbW1VX19fZKk50Ihkn4AgE1hsbEVyWRS7e3tbkIwkUjIsiz5/X719PQoLy9v1uuSyaQ8c8ZdsKwKALBRYrGYnnnmGfX39ysWiymdTqusrEwlJSUaHR2VJNm27W74NQxDzozXj4+Pa+r9RR+dnZ2Mp0BOI+mHTS3bQ0XmcHPPPfe4ibhMi29FRYUeeOCBJSsQskkyZr6PYRhqbW1Vf3+/KioqZBiG8qen3ec5jiPqHQAAG2WxsRWJREIej8d9vKioyD0U5eXlKZVKuYPRJcnj8bCoAwCwKWQ6ry5duqRPfvKT+vnPf64rV66ov79f03POY5LcYo6ZMjfFLl68qIceeojxFMhpJP2QEzKHm4KCAt17773u9sGCgoJbs4nq6rJ6n6WSjJnvE4vF1NfX5yb85gaSmzdvai93iwAAG2SxsRVHjhxRZ2en0um04vG4JiYm5PV6NTQ0pLy8PFVWVir2fmuvJBUXFyvEog4AwCYws/PKNE39yq/8ilKplC5fvqzx8XGlUqlZ57OZN7EyLMuSz+dTPB5XfX29RkZGVF5eTuIPOclc+inA5pc53HR0dMi2bXm9Xu3YsUPDw8M6cuTIqh1SMt/n+vXrkuQGlFgspqqqKvd5sVhsVb4fAAArkRlb0dDQoHA4rI6ODndO7WOPPaY777xTP/7xj/XSSy+ppaVFQ0NDGh4elmEYCgQCysv75X3h7u5uFnUAADaFueMrxsbGNDQ0pPz8fBUXF7vdXovxeDwyDEM3b97Ul7/8ZX3+85/Xl7/8ZQ0PD6/HRwDW1Yor/Z566ik98sgjKikpUTweX81rApZtuYs/bvf7DA8P6+2333Yfr66uVsP+/dJrr0m61SoMYGshriHXLDS2wnEcjYyMaGJiQpJUWFgoy7JUXV2tj3/84/q93/s92V1d0u/8jiTpscce095jx0j4AVsIMQ25au74ikQioXQ6LcMwZL0/fzb9/pbehUxPT2toaEiS1N/fr7y8PF25ckUXL17U//pf/0sVFRXr8VGAdbGipN+NGzd06tQp7dmzRyMjI6t9TcCKLGfxx+1+n69//euS5JaWW5alWH+/+5w9e/as6vcEsLaIa8hVc8dWxGIxfeMb39Df/u3fqqysTFNTUyoqKtJHPvIRVVZW6tq1a/r+97+v8Xfe0d3vv8dzzz2nz951Fze0gC2CmIZcNnd8RVFRkQzDUDKZlNfrVTKZ1NTUlLu1dyHJZFIej0dFRUUqLS1VVVWVrl69qieffFJf//rXudGFnLGi9t4/+IM/0K/8yq/ok5/85GpfD3BbMoebpqYmd7vgWjBNU48//rjuuecevf7663ruuef02vtVfpLcrVEAtgbiGraDzPDz9vZ2lZWVye/3a+fOnZqYmND169dlWZauX7+u9vb2WbNtr169qrNnzy7ZLgVgcyCmIZfNHV8xNDSk4uJilZaWKi8vT8XFxUu+RyKZlHSr0j2dTisvL095eXkqLS3VxYsXFYlE1vpjAOtm2ZV+f/M3f6NXXnlFV65c0X/4D/9hLa4J2Hy6uz/wkNdxtGNyUkerq1Vx113aY9vSuXOSpL/77/9d/8/jjy+ddKypWYurBbAMxDVsF5nh50erqzX13nvyJpMyDEM7ioo02t2tsbffVuHAgI4eOSLfjHbAQ16vLr/xhm7+/Ofau3fvwt+AmAZsOGIatoO5HV6FAwN64YUX9OMf/1hd8biK0mnZkgxJmdtVMyNUjSTZtvJGR5Wfny+7q0vlu3Ypf3pae2xbY2+/LZkmcQ05YVlJv/7+fn3xi1/Un/3Zn6mG/wCwncyzCMSQ9IcLPP33vvMd6TvfWfp9qZoANhRxDdtJZvj5//c//+f8T7h69dZf53z90e9979bf/O3fLv4NiGnAhiKmYTuZNb7CMHRA0p9k+dqWzN+k07f+9PTc+iPdioUvvnjr74lryAHLau/9wz/8Q334wx/W5z//+SWf+61vfUs1NTXuHwbIAgA2G+IatpPM8HMAuWk5MU0irgHAdpB1pd8PfvAD/d3f/Z0uXLiQ1Zy0P/mTP9Gf/Mkvc+3cbcKWNs9chxs3bugb3/iGamtrZZqmykdH9bmnn5YkffU3fkOP/Kf/tHgbFIANRVzDdpMZfv7HExMKBAIyTVMjIyMKh8M6ePCgTp8+re9+97u6evWqDnm9boXfH99zj3osSyMjIxofH1dRUZF27NihQ4cOqb+/XwcOHNAf/MEfiJHnwMZZbkyTiGvIITPOao7j6D/+x/+o73//+5qamtLU1JQc3WrpzVT4HZc0c3hTnmXJtm35fD6dO3dOBw4cWL9rB9ZYVkm/eDyuP/qjP9IXvvAF7dmzR7FYTJI0NTUl6dYmuPz8fJWUlKzdlQIbaZ7/Cdqzd69qjh/Xxfc3R81UffSo9vyLfyGx9QnYlIhr2I4yw8/PSGoPhWSapmzbVuMDD6i5uVmW16vPPvaYzpw5o7ZXX3Vf92pHh24YhhzH0f79+zWVl6fLsZgG331Xx44d0886O/Upx1Htwt8awBoipmHbm3FWMyT97pe+pB+++aaifX2KxWLufwsZ3ZJuzHzg/Sr4nrExvRGJ6ABLcJBDDCeLVWzhcFjBYHDR5/z2b/+2fvjDHy749ZqaGnXPswwB2MpisZjOnDmjUCikykRC//UHP5AkjV6+rPKDBzf46oCVy/Xf2cQ1bGeO47jDz/1+vwKBwKzKINu29Y0vfEH/73/7b5Kkg2Vl6rEsjY+Pq7S0VAcOHJBlWYrFYvrEJz6haDSqL33pS2pqatqojwQsKZd/Z69GTJNy+2eE7cVxHD3xxBM6f/68DMPQSy+9pLLRUbe6r0Zzkn4zlJSU6MUXX9THPvaxrKtmgfW2nN/XWVX67dq1Sz/5yU8+8Pif/dmf6ZVXXtELL7ygqqqq5V0lkANmbo4ae/tt6f2kX3l5+QZfGYDFENewnc0afj6P7u5u9WQGmksqKChQicejyclJTUxMKBKJKBgMyjAMxeNx2bYtv9+/XpcPYA5iGjCbYRh69NFHZRiG2tvbtXPnTiVHR7N67fj4uH7nd35Hp06d0qOPPiqfz7fGVwusraySfh6PRx//+Mc/8Pj3vvc9WZY179eAzWqpCoflyhyeZC5rLw6ADURcAxYWjUaVSCRmPWZZlgoLC5VIJBSPx5VMJmXbtoaGhnTixAkF5tlyD2B9ENOAD8oUZ7S0tCgajerm8LA0NLToawzDkGmaGh8f109+8hOZpqlTp05R8YctLetFHkAuyLTjtre3y7IspdNpNTY2qrm5ed3v4qx28hEAgNXg9/s1OTnp/nNxcbF6kkmVlJRoenpa6XRaN27c0M6dO3X8+HE1NzcTvwAAm45hGEqlUurr61NxcfGSST/r/YUemZh28eJFRSIRBQIBzm3Ysm4r6fe9731P33t/sxuw2TmO487f27dvn0zTVDqdVigU0tmzZ9f1Ls5mSj4C+CXiGnBry++BAwek99sFq6ur1TM4qFgsptLSUuXn5+vXf/3X9aUvfUkHDx5Ud3e3Ojo6OAgBmwwxDdud4zh6/vnnNTw8rDuzGL+USqVkmqampqZ0+fJl+Xw+hUIhPfPMM5zbsGVR6YdtIxKJKBQKKRgMyny/FdeyLNXX16u9vV2RSGTB+UaraTMlHwEAmMswDH3+85+X3l/kEY/HVVZWpr1796q4uFh33323vva1r2l0dFTf/OY3OQgBADalSCTizqFNdna6jxd5PFIyOe9rbNuWZVlKJpN677339Md//Me6++679eEPf5hzG7YkhpBh24hGozJN0034ZViWJdM0FY1G1+U6skk+AgCwkWYm7Xbv3q39+/ervr5en/zkJ/X444/LMIxZN7CCwaCCwaB7EHIcZwOvHgCAW+c/y7J0zz33aNeuXbO+ZpqmSktL531dYWGh0um0fD6fenp69M4772h0dFSO43Buw5ZDpR+2Db/fr3Q6Ldu2ZyX+Mo+t1+bBbJKP61FxCABANv7Nv/k3SlZV6eDBg258amlp0SuvvKI77rhDhmHIcRzF43F5PB698cYb6urqUl1d3QZfOQBgO8uc/woKCnTPPfdIr78uSSovL1deLCbTNFVVVaXS0lLduHFD09PTkm5VuGc21DuOo/fee0/JZFKBQEBHjx6Vx+Ph3IYtg6Qfto1AIKDGxkaFQiHV19e7rUjhcFiNjY23v3mwpkbKorJhsyQfAQBYSKy0VGe+8Y3sqqf/AAAgAElEQVRbrbsvveS27j744IM6d+6cXnnlFV29elWRSESVlZVyHEfRaFSGYWh4eFhf/vKX9ad/+qc6fPgwrU8AgA0x9/z3p48/rp///OfquXpV+fn5SqVSKigocNt2MyzLcpeASFJ+fr6Ki4vV19en1tZWHTt2jHMbtgySftg2DMNQc3Oz245kmqZs23bnD63XoWS1ko9s/wUArIXFZs/+9Kc/ld/v1x133KFIJKLy8nJdvXpV6XRau3btUjQa1ejoqF599VVduXJFDz30kB599FFm/AEA1t3M8197e7vefvttDQ8Pu+MoxsbGNDExocHBwQ+8Np1Ou6MqEomELMtSaWmpent7deXKFZ04ceL2i0aAdUDSD9uKz+fT6dOnl0yW3U5CbanXrkbyke2/AIC1stDs2YqKCr3++uv61//6X8vn86m6ulqdnZ0aHR1VKpXS6Oio0um0SkpKtHfvXsXjcZ0/f16maTLsHACwITLnv5aWFn3ta1/Txz72MT3//PNyHMc9h801s+pPurXcIxKJaMeOHRofH1ddXd26Fo0At4OkH7YdwzBUW1u74PyFlSbUHMfRpUuX9PTTT6uzs1NlZWWzknkzX5tt8nGh78P2XwDAWllo9uzU1JQMw9Dk5KQMw9BHP/pRvfPOO5qampLjOO7Gw4mJCb399tuqqalRZWWlO+ycuUcAgI1gGIaKiopUVVWl8fFxDQ0NqaysTJOTk5I0b+JvJq/XK5/Pp6KiIt1xxx364he/KK/Xux6XDtw2tvcCM8xNqGW7jTAWi+mJJ57Q7//+7+u5557T9evX1dPTo927dy/42kzysampSbW1tVkn6tj+CwBYSzNnz85UUFAg27ZVWFgo6VYSsLi4WHl5eTIMw41jjuNodHRU4XBYeXl57rBzAAA2Sia2DQ8Pu49ZliXHcRY8hxmGocLCQjmOo8LCQt24cUN79uyhrRdbCkk/YIaVJNQyicLz589renpagUBAFRUV6u/vV1tbm+rq6lY1GZfN9l8AAFYqM3u2o6PDbXHKHJQOHDigoaH/n737D47jru8//tpd/bRk67SS/EPWnXVKCHEsnd3JhNgZaPl2gMFJO0nboZC2lBaoMiTphDBWOiSEOANpmRKgoQwZZKYdSiAkFErIjAMzkBCgQ9KMiX3n/CTkzjpZiWRpfbIk6+fefv/w3FlyJOv0c0+r52MmM+35bL29496799r3ft4Dcl1Xo6OjM35f7lEp0zRlGIYmJyd17Ngxua7LYecAAF/letvZs2eVzWbzm+cNw1BpaalKS0tnvN8wDJWVlamqqkpDQ0P5Db6/+93vdP/99yuTyfj0NwEWhtAPmGYxgVouKKyvr89/0TFNUzU1Nert7dXIyMiM3+t5nrq6unT06FF1dXXNOT04l7kmMNj+CwBYDrmzZ9va2pRKpZRMJvPLph588EHFYjGlUin19/frzJkzqqyslGVZsixLU1NT+cd8N2zYoBMnTigSiTAVAQDwVa63/b//9/9UXV2twcHB/He30tJSGYaR712lpaWqrq5WLBbLT7Rfcskl2r59uy6//PJ5nwIDigln+gHTTA/Upgd/FwvUckFhVVWVPM/L3zHKhYfDw8P537scCziWa/svAABzudjZs7nXU6mUTp48qaNHj8rzPJWUlOQnA0tKzv2/mLZt6/3vf7+eeeYZdXV1KRKJ6Oqrr37LzTUAAFZaKBTSHXfcoXe961264447lEwm5TiOxsbGVFFRke9jpmlqcnJSPT09GhoaUl1dnbLZrLZs2aLa2lrV1NRwXi3WDEI/YJrFBGq5oLC6ulpbtmxRb29vPsBzXVcDAwPat2+fmpqadP/99y95AcdybP8FAGA+cy2+MgxD4XBY3/ve9xQOh9XV1aXe3t78uX4VFRWqq6tTY2Oj6uvrdc899yiVSuX71c6dO/Xggw9qx44dPv3NAADrlWEYuuaaa/TLX/5Szz77rF588UU99dRTeu655zQyMqLJycn8+3JPalVVVWnLli1629vept7eXlVWVuZ/ndAPxY7QD5hmMYHa9KBwz549Onr0qN58802dPXtWNTU12rt3r9rb29Xd3T3veYGFNo2lbP8FAGCp0um0jhw5ooGBAdXU1GhwcFDj4+P5M5G2bdumxsZGxeNxjY+PKxwOyzRNTU1N6eWXX9bNN9+sxx9//C0Tf57n0dsAACvONE3t27dP+/bt03ve8x7dfvvtqq+v14YNGyRJo6OjchxH//u//6s9e/bozTff1JNPPpk/D3DDhg2yLMvnvwUwP0I/4AILDdQuDAobGxu1ceNG1dbWav/+/brqqqu0adMmJZPJec8LXMidorkmMAAAWGkDAwN67bXXNDk5qYaGBtXW1qqrq0uZTCZ/rm1DQ4PGxsYUiUTyva+kpESNjY166aWX9Oyzz2rfvn35P3M5jsAAAGChTp8+rY0bN6qxsTH/WigU0tatW/X73/9e//d//6ehoaH8meoTExOqqqrSD3/4Q7W2tnJzCkWN0A+YxUIDtelB4YkTJ3T48GF1dXXp8ccf149+9CPFYjHt379/1vMCp6amNDQ0pDfeeIOpBgBA0fM8T6lUSm+++aa2b98uSSotLVVLS4vOnj2rnp4e/cM//IPGx8f1k5/85C03u0pKSmQYhrq6uvKhn+d5+ZtnSzkCAwCAhZrrXPdsNqtt27app6dHY2NjKisrk2EYqq2tVWVlpb7//e/rqquuUmtrK9/hULQI/YBlMv2Mo+7ubl1yySUzvrRIUltbm44fP54/L3BkZEQ///nP5XmeHn744RmPEjPVAAAoNrlpvKeeekqjo6P63e9+p1AopO3bt8s0TU1MTGjr1q1qbm7W2NiYstnsrDe7PM+bcWMtnU4v2xEYAAAsxMXOdd+6das2bNigHTt2yHVdlZSUyLIs9fT06NSpU/rSl76kbdu28R0ORYvVacAyutiXlkQioWuvvVZtbW1KpVJKJpP6+c9/Lkl673vfq5aWFkWjUVbAAwCK0vRpvMsuu0zbtm1TKBRSJpPR66+/rkwmo7q6Om3dulXHjh3Tyy+/rPr6eiWTSU1NTUk6F/j19PRo586duvrqq/N/tuM48x6BAQDASsgd1zT9e1pukeP+/fslSeXl5SopKdHk5KTS6bRGRkZUWlqqrVu38h0ORY1JP2AZzfelxXXd/GPAL7zwgoaGhrRr1678IbBMNQAAitX0G1uGYaixsVG9vb2qr69XJpNRa2urEomETp06pd/85jeamJjIT0sMDw/npx+i0ahuvfVWdXd35x+HmuvRqtxrtm379dcGAKwDc53r3tXVperqar366qv56fXh4WFZlqXq6mo1NDTwHQ5FjdAPWEaFfGnJnRfoOI42btz4lq1Pi13sAQDASrrwxtaVV16pI0eOqLe3V67r6siRIxoeHpbneSopKVF1dbXGxsZkGIZqamq0e/duNTQ0aHBwUA8//LCGhoa0Y8cOfexjH9OuXbvmfLQqFospHA77/LcHAATdbOe6h8NhbdmyRd3d3bIsS57nyfM8ZbNZVVdXa9OmTZL4DofiRegHLKOLnQdx4ZcWphoAAGvJhX2roqJC11xzjU6fPq3jx4/LdV319vbKcRxVVlbKMAxVVlZqdHRUkvTSSy/JdV1deumlev755/Xmm28qHo/r6aef1oc+9CF96EMfkiQlEgmZpjnjnFsORwcA+KG7u1u2besP/uAP1NPTo/HxcU1NTcm2bZWXl+vkyZMqLS1VWVmZXNflOxyKDqEfsIxy50Hkzjy62JeWhQSEAAD4bba+lc1mdfr0ae3evVu/+93v9MYbb8gwjHy/y/3PU1NTOnv2rOrq6vT888+rt7dXtm2rtrZWp0+f1rPPPivTNHXgwAF1d3fPeLSKwA8A4BfHcVRRUaF3vvOdOnPmjEZGRvT8889rYGBAp06d0i9/+UtVVlZqeHhYO3fu1MaNG/0uGZiB0A9YZnOdB3Hhl5a5AsK2tjbt379fx44d4wsPAKBoXOzG1v79+3X33XfLNM38o0+GYeT/Z9d18+/v7e1VbW1tPhC0LEt1dXWKx+Pq7u5+y6NVAAD4JTfl7nmeysvLdfz4cY2MjKivr09jY2OSpLKyMkWjUW3cuFHf/OY3deDAAb6/oWgQ+gErYLbzIGZzYUBoWZYOHz6sL3zhC/nJP9a/AwCKxVw3tiRp7969SqVSMk1To6Ojqqio0NjYmEzT1MaNG1VWVibTNGdMAuYORa+urtbExARnIQEAikpuyj0ej+uNN95Qf3+/qqqqVFpaqlAopMrKStm2rXe+853KZrMs80DRMed/C4CVlAsId+/erSeeeELHjx9XS0uLotEo698BAEUn17f27NmjSCSSD/Fuuukm3XDDDdqyZYumpqbkOE7+3KN3vetdeve7362BgQFls9n8IeiDg4PasmWLqqqqOM8WAFB0clPu4XBYyWRSnucpk8mosrJSzc3N2rZtmwYHBzU4OKihoSG98cYb+vGPf6wTJ07w/Q1FgUk/oEik02klEglFo9H8Yg/WvwMA1opQKKTPfvaz+ru/+zu98MILOnHihJ588kn19/ert7dXJSUlGh0dlWEYSqfTqqqq0tatW7Vnzx6dOHGC82wBAEUpFArpL//yL/Xqq6+qoaFBk5OTeu6552RZlgzDUDab1a9//Wul02mNjIzo1Vdf1X/8x3/o+uuv12233cYTW/AVoR9QJBzHkWmaMzb5Sqx/BwCsLYZhqLq6Wo8++qhSqZQ2btyogYEBNTQ0qK6uTu95z3s0NTWlV199VSUlJfr973+vvXv3sqUXAFC06urqVFlZqc2bN8swDHV1damvry/f46ampjQ1NaXNmzdr+/btymQy+vGPf6zKykp1dHTQ3+AbQj/AR57n5c9FGh0d1dTUlLLZ7Izgz3XdFX3kaXoNLA4BACxWJpPRN77xDf3mN7/R8ePH1dPTo4aGBm3atEmmaerUqVP597a0tMjzPA0ODmrDhg35R34BAChGF26wv/LKK/Xcc8/p1Vdf1ejoqKRzSz8aGxtlWVZ+O/0zzzzDE1vwFaEf4JNMJqPOzk7F4/H80o7Tp0/rlVde0WWXXZZ/LZVKrdgjT7PVwOIQAMBCeZ6nBx54QI899pjOnj2rvr4+ZbNZDQwMSJKam5sVCoXU19enN954Q4lEQiUlJTJNU5lMRo8++qgmJiZ09913c+MJAFB0Zttgv23bNu3YsUPHjh2T4zhqaGiQZVmSlH+Ca3Jykie24CtCP8AHnuflG0ZLS4tM05TrupqcnNTQ0JCSyaQsy1I2m82HcMv9JWiuGnKLQ1g1DwAoVFdXlx577DFNTU2pqqpKZWVlmpqakud5GhgY0NatW1VZWamJiQmdPHlS9fX12rJliyoqKuR5nk6fPq0f/ehH+shHPqIdO3b4/dcBAOAtLtxgb1mWvvvd76qvr09DQ0MaGRlRdXW1GhsbZZqmstmsSktLWVIFXxH6AT6Ya2nHZZddpmQyqVtuuSW//n2lHrdlcQgAYLm8+OKLymQyCofDGh8fl2maKi8v1/j4uFzXzS/wOHnypCYmJnT27FmlUilVVVWpsbFRtbW16u7u1osvvkjoBwAoWrkN9uFwWF/84hfV3d2tt73tbTp+/LgmJyc1ODgoz/NUVVWl8vJy7d27lyVV8JU5/1sALLeBgYH840+5xiCdC90sy1JlZaX27NmjSCSyYtN2hSwOAQBgLp7nqaurS0ePHlVfX1/+9fLyclVXV6u0tFRlZWXKZrMaGhrSq6++qrKyMm3YsEGVlZWqqKjQyMiIenp6fPxbAACwcLkBim3btimbzcowDI2NjenMmTPq6emR67q64YYbdNNNN/H0FHzFpB+wgmZbkjE4OKhHH31Uv/3tb7Vx40ZJ0pYtW3TllVeqtLR0UUs7FrOMw7bt/JKQ1VwcAgBY+y48E/bMmTMaHx/XqVOnVF9fr8bGRp08eVLj4+PasGGDtm3bpqqqKl1zzTV6/PHHNTo6mg/+zpw5o66uLlVXV2vnzp1+/9UAAJiX4zgyDEPPP/+8HMfR29/+dk1MTGh4eFj9/f3at2+f7rrrrrcMWACrjdAPWCGzLcloa2vT2NiY0um0Wlpa1N/fr40bN6q3t1fPPfecGhsbF7y0Y7HLOC7cQLUai0MAAGvfbGfCTk1N6fXXX1d/f39+Yry6ulpVVVX6wz/8Q/3Jn/yJvve972nbtm26/PLL9fLLL2tkZETj4+MaGxvT5OSkNm3apEceeUQ33XQTy6QAAEXNtm0NDQ3pzTfflG3bMgxDFRUVKisrk2EYymQy6u7u5rgk+I7YGVgBF34hikajikajevbZZ/XYY48pGo3qqquu0ubNm3XmzBlJUjKZVDgcXtDSjrl+Tm4ZR+6x4dnkNlC1tbUplUopmUzmA7+VWBwCAAiG2c6ELSkp0fve9z5t3rxZ27dvVyQS0dve9jb97d/+rf7lX/5Fra2tymaz8jxPV199ta644or8762srFRbW5v27dunX/7yl/rXf/1XZbNZP/+KAABcVDgc1o4dO3T27Nn8d65sNqvBwUFt3bpV1dXVHJeEosCkH7AC5lqSUVdXp6NHj2p4eFg1NTW65pprdObMGY2OjurUqVP6wAc+oJqamiX/nEKXcVy4gWolF4cAAIJhrjNhq6qq1NbWphtvvFHbtm2b0VM2bdo0Y7q8ra1N3d3dqqmpUV1dncrLy/Wb3/xGkvTSSy8pm83qr/7qr3Ty5ElJ0hVXXLGi59wCALAQhmHoYx/7mJ5++mmdPn1almUpm81qy5Yt2rNnT34CEPAboR+wAub6QlRdXS1JGhkZUU1NjQzDUE1NjaqrqzUyMqK6urpl+TnTl3HMN1Ke20DF6DkAoBAXOxPW8zzt2rXrLT0lN12em07PZDKanJxUS0uLXNdVf3+/amtrZRiGXNfVD3/4Q337299WeXm5pHM3qa6//nrddtttPPoLACgKra2t+tCHPqRnn31WdXV1+WMtTpw4wXFJKBqEfsAKmOsLUVVVlUKhkPr7+7Vly5Yln6PHMg4AwGpb7JmwNTU1+uAHP6i2tjb19fXJsixFIhH94he/UG1trSTp7NmzeuONNySde0yqqalJ5eXlOn36tH784x+rsrJSHR0dTPwBAHxnGEZ+O28ikdDExIT6+/s5LglFhdAPWAFzfSE6ceKEbrjhBpWXl+v48eMyTVPZbHbRjYFlHACA1Xbh1F4hvWy2pVMTExN6+eWXJZ27WXXy5Ek5jqPx8XFJ56bWx8fHVVlZqdraWp0+fVrPPPPMvEdXAACwWjguCcWO0A9YJM/z5vxwn+8L0aZNm5alMSzmixcAAEu1kC85s237dV1Xk5OTOnXqlM6cOaO+vj6Nj4+rqqoqH/a5rivHcVRTU5M/ymJycrKgoysAAFgtHJeEYkboByzCbBMLuaAtd9bQfF+IlqsxcHcJAOCHQr/kzLV06rLLLlNpaamampr085//XJdeeqlM09Rrr70m13VVXl6u8fFxjY+Pq6ysTNlsVqWlpRxdAQAAUCBCP2CB5ppYSCQSOnTokA4cODBj4m817vpwdwkAUKwutnTKsiz90R/9kV544QWNj4/LMAyVlJSotLRUZWVl8jxPExMTGhkZUVlZmfbu3cvRFQAAAAUi9AMWaK6JhebmZsXjcc4aAgBgmvmWTu3cuVOXX3656uvr88Hfiy++qFdeeUXDw8MaGBhQXV2dbrjhhvyB6Rc7YgMAAADnEPoBC3SxiQXTNDlrCACAaeZbOnX11VfrV7/61Yxfr6urk23bsm1bf/EXf6Fdu3YpEonIMIyCjtgAAAAAoR+wYPNNLCzmrCEmFgAAQTXf0inTNGf99WuuuUbt7e2qqanJ/1kLOWIDAABgvSP0AxZovomFhZ41xMQCACDo5ls6VehSKo7YAAAAKJw5/1sATJebWGhra1MqlVIymcwHfu3t7QuaMLhwYiEajSoajeYnFjzPm/X3dHV16ejRo+rq6pr1PQAAFJvc0qk9e/bkH9Wd7dd3794tSTp27Nhb+lwhR2wAAADgHCb9gEUodCJhPgudWGAqEAAQZPP1uZU4YgMAACComPQDFmm+iYVCLGRiYTFTgQAArBWF9LncERvJZFKu60rSko7YAAAACDJCP2CFFPIY7vSJhelmm1goZCoQAIC1qpA+t5xHbAAAAAQdj/cCK6DQx3AXshSkkKlADi8HAKxVhfa55TpiAwAAIOiY9AOW2UIew13IxMJCpgLnq49FIACAYjNbn/M8T47jqL+/X6Ojo/metRxHbAAAAAQdk37AMlvoco5CJxYWMhU4FxaBAACK1YV9bmJiQr/+9a+VSqVk27a+9rWv6Ve/+hU9CwAAoEBM+gHLbL7HkwYGBt4yaVfIxMJSzzFiEQgAoJhN73OvvPKKHnroIR07diw//ffmm2/qyJEj9CwAAIACMekHLLPpjydND/5c19XY2JgeffRRpdPpRU3aLeUco4VOIAIAsNpCoZAOHDigW2+9VZJ0xRVXqLKyUp7n6dSpU5KkY8eO0bMAAAAKwKQfsMxyjyclk0m5ritJ+cdwh4aGlE6nlzRpt9hzjAo5IB0AAL91d3frxIkTqqur04YNG2QYhkzTVCgU0qlTpzQ2NkbPAgAAKAChH7DM5noMNxwOa+PGjWppaZlz0m4lLdciEAAAVpLjOKqoqJCkGTfEcr1zdHSUngUAAFAAHu8FVsBsj+EODAzo3/7t3y46aReJROR53qIe353PciwCAQBgpdm2rYqKCjU0NKi/v181NTUyTVNTU1MaHh7W7t276VkAAAAFIPQDVkjuMdzpZw7NddZfbtJupbfr7t+/Xz09PXrhhRe0ceNGZbPZgheBAACwGsLhsHbv3q2pqSlJyp/lNzw8rJ07d+qOO+6gZwEAABSA0A9YJfNN2jU1Nen+++/Pb9c1TVOu6+bP/Dtw4MBbvuQUOhU4PUw0TVOe56m2tlYf+9jH1NraypcnAEDRyB2TketboVBIY2Nj2r17t+64445luQkGAACwHhD6Aatk+peYRCIh0zRnTNp1d3cvaLtuoVOBnuflf2ZdXZ3Gx8cVCoU0MDCgn/zkJ2ptbV31awEAwMUsZVs9AAAAziH0A1bRxb7EJJPJebfr5kK/6UHefFOB6XRaR44cUX9/v44dOybDMOR5nhoaGjQxMfGWMBEAgGIw2zEZAAAAKByhH7DK5voSM3277lxn/uWk0+mCpwIHBgb02muvaXJyUrW1tTIMQ9lsVqdOnVImk9HAwMC8X6hWarkIAAAAAABYGYR+QJFYyHZdx3EKngocGxvT6dOn1dTUlA/qTNPUpk2b1NPTo7GxsYvWtdLLRQAAAAAAwPIz538LgNWQO/Ovra1NqVRKyWQyH/hduF13+lTgdLNNBVZUVKi2tlaDg4P592ezWQ0NDam2tlYVFRVz1nThY8TRaFTRaDT/GLHnect8FQAAAAAAwHJg0g8oIoUeXD7bVODU1JRefPFF7dixQ57nyfM8GYahuro6XXLJJRoYGNCpU6fyC0QaGhpUX1+vurq6OetZyGPEAAAAAACgeBD6AUWmkIPLL9wEPDU1pVdeeUWe56m8vFx33XWX2tradO2112pqakqXXHKJSktLtWvXLk1MTKisrEyO42j37t0zHhu+0EIeIwYAAAAALB5nqWO5EfoBa1RuKrCrq0tf+cpXND4+rl27dsmyLI2MjOiRRx7RI488otbWVo2Pj2toaEhTU1OqqKjQyMiIdu/e/ZbHhi+0kOUiAAAAAIDF4Sx1rARCP2ANMwxDhmFoYGBAra2tMk1Tnufp6NGjmpyclCTV1dWpurpaqVRK4XBYH/jAB1RXV1fQXaOFLBcBAMAPKzkVwcQFAGA1XHiWummacl03f5b6gQMH6D9YFEI/YI278BHcM2fOqLe3V7ZtK5PJaHR0VDU1NWpublYqlVJdXV3Bj+Re+Bhx7jzA2ZaLAACw2lZyKoKJCwDAauEsdawUQj+giCxmouDCR3BHR0dlGEZ+mUdlZaWkxZ/DV+hyEQAAVtNKTkUwcQEAWE2cpY6VQugHFInFThRc+AhuZWWlstmsTp8+ra1bt2rTpk2SlnYOXyHLRQAAWE0rORXBxAUAYDVxljpWijn/WwCstAsnCqLRqKLRaH6iwPO8OX9v7hHctrY2pVIpDQwMqLS0VGVlZdqzZ4/OnDmjkydP6oUXXlBbWxvn8AEAAqGQqYhi/LMBALhQbpAjmUzKdV1J4ix1LAsm/YAisNSJggsfwbUsSz/84Q/12GOPKZPJSJJqamq0e/duDQ4OvmVykIPKAQBrzUpORTBxAQBYTZyljpVC6AcUgeU4w2H6I7ie5+nw4cNqbm5WfX29qqqqVFVVpddee+0tZxFxUDkAYC1ayQ3zbK8HAKw2zlLHSiD0A4rAck8UpNNpHT9+XK2trTP+vAsnBxd7UDmTgQAAvxUyFbHYfsXEBQDAD5yljuVG6AcUgeWeKCh0cnAxjxUzGQgAKBYXm4pYar9i4gIAAKx1LPIAisCFyziSyWQ+8FvMRMH0ycHpLpwcXOhB5UtZOAIAwErITUXs2bNHkUgkP+G3HP1qtj8bAABgrWDSDygSyzlRUOjk4EIfK17qwhEAAFYD/QoAAIBJP6CoLNdEQaGTgwtdDb/QyUAAAPxAvwIAAGDSDwisQiYHF3pQ+XIvHAEAYCXQrwAAAAj9gEArZPvTQh4rXu6FIwAArAT6FQAAAKEfABW+Gn6uycC2tjbt379fx44dY7shAMB3C51kBwAACCLDW6V1m01NTeru7l6NHwVghXmel58MtCxLhw8fViKRyE9S5L5UhUIhv0vFIvGZPT+uEVD8pvcrbkqtb3xmz49rBABrw0I+r1nkAWDBcpOBu3fv1hNPPKHjx4+rpaVF0WhU0WhUiURChw4d0irdUwAAYFbLtSALAABgLZKko9EAAB82SURBVCL0A7Bo6XRaiURC0Wg0f1C6ZVlqbm5WPB5XOp32uUIAAAAAANYnQj8Ai+Y4jkzTnLEZUToX/JmmKcdxfKoMAAAAAID1jdAPwKLZti3XdZXNZme8nnvNtm2fKgMAAAAAYH0j9AOwaOFwWLFYTMlkUq7rSjoX+KVSKcViMYXDYZ8rBAAAAABgfSL0A7BohmGovb1dbW1tSqVSSiaT+cCvvb2dA9MBAAAAAPBJid8FAFjbQqGQOjo6lE6n5TiObNtWOBwm8AMAAAAAwEeEfgCWzDAMRSIRRSKRJf05nucRHgIAAAAAsAwI/QAUhUwmo87OTsXjcVmWJdd1848Jh0Ihv8sDAAAAAGBN4Uw/YJ3xPE9dXV06evSourq65Hme3yXJ8zx1dnYqkUiopaVF0WhU0WhUiURChw4dKooaAQAAAABYS5j0A9aRYp2mS6fTSiQSikajMs1z9yIsy1Jzc7Pi8bjS6fSSHx0GAAAAAGA9YdIPWCeKeZrOcRyZppkP/HIsy5JpmnIcx6fKAAAAAABYmwj9gHWikGk6v9i2Ldd1lc1mZ7yee822bZ8qAwAAAABgbSL0A9aJYp6mC4fDisViSiaTcl1X0rnAL5VKKRaLKRwO+1YbAAAAAABrEaEfsE4U8zSdYRhqb29XW1ubUqmUkslkPvBrb2+XYRi+1QYAAAAAwFrEIg9gnchN0yUSCTU3N+cXeRTLNF0oFFJHR4fS6bQcx5Ft2wqHwwR+AAAAAAAsAqEfsE7kpulyyzxM01Q2my2qaTrDMBSJRNjUCwAAAADAEhX0eO/Ro0d13XXXKRKJqLKyUrZta9++fXrooYdWuj4Ayyg3TXfffffp9ttv13333acDBw6opqam4D/D8zx1dXXp6NGj6urq8nXrL7BY9DUAQJDQ1wAAsylo0i+TySgcDuvGG2/U9u3bNTIyou985zv68Ic/rFQqpc985jMrXSeAZbKUabpMJqPOzk7F4/H848G5ScFQKLQC1QIrg74GrB+e56340RGr8TOAi6GvAQBmY3hLGNPZu3evenp61NXVNe97m5qa1N3dvdgfBcBnnufpi1/8ohKJhKLRqEzTnHEm4IEDB/iCEyDr9TObvgYEy2rcrOKG2NqwXj+z6WsAEDwL+bxe0vbe+vp6lZRwLCCwHqTT6RmBnyRZlqXm5mbF43Gl02mfKwSWjr4GBIfneflzbFtaWhSNRhWNRpVIJHTo0KFlOZ5iNX4GsBT0NQBY3xbUAbLZrLLZrE6fPq3vf//7+ulPf6qvfe1rK1UbgCLiOI5M08wHfjmWZck0TTmOwwIOrDn0NSC4CrlZtdS+tRo/A1gI+hoAYLoFTfrdfPPNKi0t1ebNm3X77bfrq1/9qm666aZZ3/vlL39ZTU1N+f+Gh4eXpWAA/rBtW67rKpvNzng995pt2z5VBiwefQ0IrkJuVs1nvuVVy/EzgOVEXwMATLegSb8777xTH//4x9XX16fHH39ct956q0ZGRnTgwIG3vPdTn/qUPvWpT+X/96ampqVXC8A34XBYsVhMiURCzc3N+XOLcmf6hcNhv0sEFoy+BgTX9JtV00O5Qm9WFXJW31J/BrDc6GsAgOkWFPpN3/h57bXXSpI+/elP6yMf+YgaGhqWvzoARcMwDLW3t+fPLjJNU9lsNv8FiCUeWIvoa0BwLeVm1YVn9eWWV+XO6sstr+KGGIoNfQ0AMN2SFnm84x3v0NTUlF5//fXlqgdAEQuFQuro6NB9992n22+/Xffdd58OHDigmpoav0sDlgV9DQiO3M2qtrY2pVIpJZPJfBg3382qQpdXLeVnAKuBvgYA69uSVjk99dRTMk1TLS0ty1UPgCJnGMaMu8hAkNDXgGDJ3axKp9NyHEe2bSscDs8bxi1kedVifwawGuhrALC+FRT6tbe3a9OmTXrHO96hLVu2qL+/X9///vf1yCOPqKOjg1FxAMCaQl8D1o/F3Kxa6Fl93BCD3+hrAIDZFBT67du3T//5n/+pb33rW8pkMqqurtbu3bv17W9/W3/zN3+z0jUCALCs6GsALoaz+rDW0NcAALMxPM/zVuMHNTU1qbu7ezV+FABgifjMnh/XCAi23Pbe2ZZXcZbt2sNn9vy4RgCwNizk83pJZ/oBAAAAQcRZfQAAYK0j9AMAAABmwVl9AABgLTPnfwsAAAAAAACAtYTQDwAAAAAAAAgYQj8AAAAAAAAgYAj9AAAAAAAAgIAh9AMAAAAAAAAChtAPAAAAAAAACBhCPwAAAAAAACBgCP0AAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAIGEI/AAAAAAAAIGAI/QAAAAAAAICAIfQDAAAAAAAAAqbE7wIAYDae5ymdTstxHNm2rXA4LMMw/C4LAAAAAIA1gdAPQNHJZDLq7OxUPB6XZVlyXVexWEzt7e0KhUJ+lwcAAAAAQNHj8V4ARcXzPHV2diqRSKilpUXRaFTRaFSJREKHDh2S53l+lwgAAAAAQNEj9ANQVNLptBKJhKLRqEzz3EeUZVlqbm5WPB5XOp32uUIAAAAAAIofoR+AouI4jkzTzAd+OZZlyTRNOY7jU2UAAAAAAKwdhH4Aiopt23JdV9lsdsbrudds2/apMgAAAAAA1g5CPwBFJRwOKxaLKZlMynVdSecCv1QqpVgspnA47HOFAAAAAAAUP0I/AEXFMAy1t7erra1NqVRKyWQyH/i1t7fLMAy/SwQAAAAAoOiV+F0AAFwoFAqpo6ND6XRajuPItm2Fw2ECPwAAAAAACkToB6AoGYahSCSiSCTidykAAAAAAKw5PN4LAAAAAAAABAyhHwAAAAAAABAwhH4AAAAAAABAwBD6AQAAAAAAAAHDIg8AgeJ5Hlt/AQAAAADrHqEfgMDIZDLq7OxUPB6XZVlyXVexWEzt7e0KhUJ+lwcAAAAAwKrh8V4AgeB5njo7O5VIJNTS0qJoNKpoNKpEIqFDhw7J8zy/SwQAAAAAYNUQ+gEIhHQ6rUQioWg0KtM899FmWZaam5sVj8eVTqd9rhAAAAAAgNVD6AcgEBzHkWma+cAvx7IsmaYpx3F8qgwAAAAAgNVH6AcgEGzbluu6ymazM17PvWbbtk+VAQAAAACw+gj9AARCOBxWLBZTMpmU67qSzgV+qVRKsVhM4XDY5woBAAAAAFg9hH4AAsEwDLW3t6utrU2pVErJZDIf+LW3t8swDL9LBAAAAABg1ZT4XQAALJdQKKSOjg6l02k5jiPbthUOhwn8AAAAAADrDqEfgEAxDEORSESRSMTvUgAAAAAA8A2P9wIAAAAAAAABQ+gHAAAAAAAABAyhHwAAAAAAABAwnOkHYM3zPI/lHQAAAAAATEPoB2BNy2Qy6uzsVDwel2VZcl1XsVhM7e3tCoVCfpcHAAAAAIAveLwXwJrleZ46OzuVSCTU0tKiaDSqaDSqRCKhQ4cOyfM8v0sEAAAAAMAXhH4A1qx0Oq1EIqFoNCrTPPdxZlmWmpubFY/HlU6nfa4QAAAAAAB/EPoBWLMcx5FpmvnAL8eyLJmmKcdxfKoMAAAAAAB/EfoBWLNs25bruspmszNez71m27ZPlQEAAAAA4C9CPwBrVjgcViwWUzKZlOu6ks4FfqlUSrFYTOFw2OcKAQAAAADwB9t7AaxZhmGovb09v8zDNE1ls9n89l5J6urqkuM4sm1b4XBYhmH4XDUAAAAAACuP0A/AmhYKhdTR0aF0Oj0j3BscHNQXv/hFxeNxWZYl13XzYWAoFPK7bAAAAAAAVhSP9wJY8wzDUCQS0Z49exSJRCQpP/3X0tKiaDSqaDSqRCKhQ4cOyfM8nysGAAAAAGBlEfoBCJx0Oq1EIqFoNJrf7GtZlpqbmxWPx5VOp32uEAAAAACAlUXoByBwHMeRaZr5wC/HsiyZpinHcXyqDAAAAACA1UHoByBwbNuW67rKZrMzXs+9Ztu2T5UBAAAAALA6CP0ABE44HFYsFlMymZTrupLOBX6pVEqxWEzhcHjVavE8T11dXTp69Ki6uro4TxAAAAAAsCrY3gsgcAzDUHt7e36Zh2maymaz+e29hmGsSh2ZTEadnZ1sEAYAAAAArDpCPwCBFAqF1NHRoXQ6LcdxZNu2wuHwqgV+nufN2CBsmqZc181vED5w4MCq1QIAAAAAWH8I/QAElmEYikQiikQiq/6zC9kg7EddAAAAAID1gTP9AGAFsEEYAAAAAOAnQj8AWAFsEAYAAAAA+InQDwBWQDFtEAYAAAAArD+EfgCwAnIbhNva2pRKpZRMJvOB32puEAYAAAAArE8s8gCAFeL3BmEAAAAAwPpF6AcAK8jPDcIAAAAAgPWLx3sBAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAIGEI/AAAAAAAAIGAI/QAAAAAAAICAIfQDAAAAAAAAAobQDwAAAAAAAAgYQj8AAAAAAAAgYAj9AAAAAAAAgIAh9AMAAAAAAAAChtAPAAAAAAAACBhCPwAAAAAAACBgCP0AAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAIGEI/AAAAAAAAIGAI/QAAAAAAAICAIfQDAAAAAAAAAqbE7wIAYLV4nqd0Oi3HcWTbtsLhsAzD8LssAAAAAACWHaEfgHUhk8mos7NT8XhclmXJdV3FYjG1t7crFAr5XR4AAAAAAMuKx3sBBJ7neers7FQikVBLS4ui0aii0agSiYQOHTokz/P8LhEAAAAAgGVF6Acg8NLptBKJhKLRqEzz3MeeZVlqbm5WPB5XOp32uUIAAAAAAJYXoR+AwHMcR6Zp5gO/HMuyZJqmHMfxqTIAAAAAAFYGoR+AwLNtW67rKpvNzng995pt2z5VBgAAAADAyiD0AxB44XBYsVhMyWRSrutKOhf4pVIpxWIxhcNhnysEAAAAAGB5EfoBCDzDMNTe3q62tjalUiklk8l84Nfe3i7DMPwuEQAAAACAZVXidwEAsBpCoZA6OjqUTqflOI5s21Y4HCbwAwAAAAAEEqEfgHXDMAxFIhFFIhG/SwEAAAAAYEXxeC8AAAAAAAAQMIR+AAAAAAAAQMDweC8ALDPP8zg7EAAAAADgK0I/AFhGmUxGnZ2disfjsixLruvmtwSHQiG/ywMAAAAArBM83gsAy8TzPHV2diqRSKilpUXRaFTRaFSJREKHDh2S53l+lwgAAAAAWCcI/QBgmaTTaSUSCUWjUZnmuY9Xy7LU3NyseDyudDrtc4UAAAAAgPWC0A8AlonjODJNMx/45ViWJdM05TiOT5UBAAAAANabgkK/J598Uh/96Ed1+eWXq6qqStu3b9f111+vI0eOrHR9ALBm2LYt13WVzWZnvJ57zbZtnyrDhehrAIAgoa8BAGZTUOj34IMPKpVK6bbbbtPhw4f1wAMPqK+vT3v37tWTTz650jUCwJoQDocVi8WUTCbluq6kc4FfKpVSLBZTOBz2uULk0NcAAEFCXwMAzMbwCjhZvq+vT5s3b57x2vDwsC699FK1trbqZz/72bw/qKmpSd3d3YuvFADWgNz23kQiIdM0lc1m89t7a2pq/C6vYEH/zKavAcD6EvTPbPoaAKwfC/m8LinkTRc2EEmqrq7WFVdcwcH0ADBNKBRSR0eH0um0HMeRbdsKh8MyDGPW93ueV/B7sXzoawCAIKGvAQBmU1DoN5vBwUH99re/1R//8R8vZz0AsOYZhqFIJKJIJHLR9+WmAuPxuCzLkuu6+anAUCi0StUih74GAAgS+hoAYNHbe2+55RaNjIzorrvuWs56AGBd8Dwv/xhwS0uLotGootGoEomEDh06pAJOXsAyo68BAIKEvgYAWFTod/fdd+s73/mOvvKVr+jKK6+c9T1f/vKX1dTUlP9veHh4SYUCQJCk02klEglFo1GZ5rmPYsuy1NzcrHg8zqM4q4y+BgAIEvoaAEBaROh377336vOf/7zuu+8+3XrrrXO+71Of+pS6u7vz/1VXVy+pUAAIEsdxZJpmPvDLsSxLpmnKcRyfKlt/6GsAgCChrwEAchYU+t177706ePCgDh48qDvvvHOlagKAwLNtW67rKpvNzng995pt2z5Vtr7Q1wAAQUJfAwBMV3Do97nPfU4HDx7UZz7zGd1zzz0rWRMABF44HFYsFlMymZTrupLOBX6pVEqxWEzhcNjnCoOPvgYACBL6GgDgQgVt7/3Sl76kz372s3r/+9+v6667Ts8888yMX9+7d++KFAcAQWUYhtrb2/PLPEzTVDabzW/vNQzD7xIDjb4GAAgS+hoAYDaGV8CKyHe/+916+umn5/z1QrZMNjU1qbu7e2HVAUDAeZ6ndDotx3Fk27bC4XBRBH5B/8ymrwHA+hL0z2z6GgCsHwv5vC5o0u8Xv/jFUuoBAMzBMAxFIhFFIhG/S1lX6GsAgCChrwEAZrPg7b0AAAAAAAAAihuhHwAAAAAAABAwhH4AAAAAAABAwBD6AQAAAAAAAAFD6AcAAAAAAAAEDKEfAAAAAAAAEDCEfgAAAAAAAEDAEPoBAAAAAAAAAUPoBwAAAAAAAAQMoR8AAAAAAAAQMIR+AAAAAAAAQMAQ+gEAAAAAAAABQ+gHAAAAAAAABAyhHwAAAAAAABAwhH4AAAAAAABAwBD6AQAAAAAAAAFD6AcAAAAAAAAEDKEfAAAAAAAAEDCEfgAAAAAAAEDAEPoBAAAAAAAAAUPoBwAAAAAAAAQMoR8AAAAAAAAQMIR+AAAAAAAAQMAQ+gEAAAAAAAABQ+gHAAAAAAAABAyhHwAAAAAAABAwhH4AAAAAAABAwBD6AQAAAAAAAAFT4ncBAAB/eZ6ndDotx3Fk27bC4bDfJQEAAAAAlojQDwDWsUwmo87OTsXjcVmWJdd1FYvF5Hme36UBAAAAAJaA0A8A1inP89TZ2alEIqGWlhaZpinXdZVIJDQyMuJ3eQAAAACAJeBMPwBYp9LptBKJhKLRqEzzXDuwLEvNzc2anJz0uToAAAAAwFIQ+gHAOuU4jkzTzAd+OZZl+VQRAAAAAGC5EPoBwDpl27Zc11U2m53xuuu6PlUEAAAAAFguhH4AsE6Fw2HFYjElk8l80Oe6rlKplEpLS32uDgAAAACwFIR+ALBOGYah9vZ2tbW1KZVKKZlMKpVKKRaLqaqqyu/yAAAAAABLwPZeAFjHQqGQOjo6lE6n5TiObNtWOBzWAw884HdpAAAAAIAlIPQDgHXOMAxFIhFFIhG/SwEAAAAALBMe7wUAAAAAAAAChtAPAAAAAAAACBhCPwAAAAAAACBgCP0AAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAIGEI/AAAAAAAAIGAI/QAAAAAAAICAIfQDAAAAAAAAAobQDwAAAAAAAAgYQj8AAAAAAAAgYAj9AAAAAAAAgIAh9AMAAAAAAAAChtAPAAAAAAAACBhCPwAAAAAAACBgCP0AAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAIGEI/AAAAAAAAIGAI/QAAAAAAAICAIfQDAAAAAAAAAobQDwAAAAAAAAgYQj8AAAAAAAAgYAj9AAAAAAAAgIAh9AMAAAAAAAAChtAPAAAAAAAACBhCPwAAAAAAACBgCP0AAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAIGEI/AAAAAAAAIGAI/QAAAAAAAICAIfQDAAAAAAAAAobQDwAAAAAAAAgYQj8AAAAAAAAgYAj9AAAAAAAAgIAh9AMAAAAAAAAChtAPAAAAAAAACBhCPwAAAAAAACBgCP0AAAAAAACAgCH0AwAAAAAAAAKG0A8AAAAAAAAImBK/CwAAFA/P85ROpzU5Oel3KQAAAACAJSD0AwBIkjKZjDo7OxWPxzU8POx3OQAAAACAJeDxXgCAPM9TZ2enEomEWlpaZFmW3yUBAAAAAJaA0A8AoHQ6rUQioWg0KtOkNQAAAADAWmd4nuetxg8qLy9XQ0PDavyoVTE8PKzq6mq/yygKXIuZuB7ncS3OK/ZrMTk5qeHh4fyE38jIiFzX9bmq4kZfCy6uxXlci5m4HuettWtx6tQpjY+P+11GUQtSX1tr/z5XGtfjPK7FeVyLmdbS9VhIT1u10C9ompqa1N3d7XcZRYFrMRPX4zyuxXlcCxQ7/o2ex7U4j2sxE9fjPK4Fihn/PmfiepzHtTiPazFTUK8Hz3ABAAAAAAAAAUPoBwAAAAAAAASMdfDgwYN+F7FW7du3z+8SigbXYiaux3lci/O4Fih2/Bs9j2txHtdiJq7HeVwLFDP+fc7E9TiPa3Ee12KmIF4PzvQDAAAAAAAAAobHewEAAAAAAICAIfQDAAAAAAAAAobQbwGGh4f1yU9+Uo2NjaqoqNCePXv0ve99z++yfDE0NKQ77rhD73vf+9TQ0CDDMLRej4d88skn9dGPflSXX365qqqqtH37dl1//fU6cuSI36WtuqNHj+q6665TJBJRZWWlbNvWvn379NBDD/ldWlH45je/KcMwVF1d7XcpgCT62nT0tXPoaTPR1y6OvoZiQk87j552Hn3tPHraxQW1pxH6LcCf//mf61vf+pbuuecePfHEE7rqqqt044036rvf/a7fpa26gYEBdXZ2anx8XDfccIPf5fjqwQcfVCqV0m233abDhw/rgQceUF9fn/bu3asnn3zS7/JWVSaTUTgc1j//8z/r8OHD+q//+i81Nzfrwx/+sD7/+c/7XZ6vTp48qQMHDqixsdHvUoA8+tp59LVz6Gkz0dfmRl9DsaGnnUdPO4++dh49bW5B7mks8ijQ4cOHdd111+m73/2ubrzxxvzr73vf+/TCCy+oq6tLlmX5WOHqyv2zMQxD/f39amho0D333LMu7yD19fVp8+bNM14bHh7WpZdeqtbWVv3sZz/zqbLisXfvXvX09Kirq8vvUnzzp3/6pzIMQ7Zt67//+781PDzsd0lY5+hrM9HXzqGnFYa+Rl9DcaGnzURPO4++Nj96WrB7GpN+Bfqf//kfVVdX6wMf+MCM1//+7/9ePT09evbZZ32qzB+GYcgwDL/LKAoXNhFJqq6u1hVXXKF0Ou1DRcWnvr5eJSUlfpfhm4ceekhPP/20vv71r/tdCpBHX5uJvnYOPa0w9DX6GooLPW0metp59LX50dOC3dMI/Qp0/Phx7dy58y3/xxCLxfK/DuQMDg7qt7/9rXbt2uV3Kb7IZrOamprSqVOn9PWvf10//elP9U//9E9+l+WLvr4+ffKTn9QXvvAFNTU1+V0OkEdfQ6HWe0+T6GvT0ddQjOhpWIj13tfoaeeth562fuPcBRoYGFBLS8tbXrdtO//rQM4tt9yikZER3XXXXX6X4oubb75Z3/jGNyRJZWVl+upXv6qbbrrJ56r8cfPNN+vtb3+7PvGJT/hdCjADfQ2FWu89TaKvTUdfQzGip2Eh1ntfo6edtx56GqHfAlxsRJrxaeTcfffd+s53vqN///d/15VXXul3Ob6488479fGPf1x9fX16/PHHdeutt2pkZEQHDhzwu7RV9YMf/ECPP/64nn/+eT4jUJToa5gPPe0c+to59DUUM3oaCkFfo6flrJeeRuhXoLq6ulnvEDmOI+n8XSSsb/fee68+//nP67777tOtt97qdzm+iUQiikQikqRrr71WkvTpT39aH/nIR9TQ0OBnaatmeHhYt9xyi/7xH/9RjY2NymQykqSJiQlJ57ZnlZaWqqqqys8ysY7R1zAfetp59DX6GoobPQ2FoK+dQ09bXz2NM/0K1NbWppdeeklTU1MzXk8kEpKk1tZWP8pCEbn33nt18OBBHTx4UHfeeaff5RSVd7zjHZqamtLrr7/udymrpr+/X729vfrSl76k2tra/H8PP/ywRkZGVFtbq7/+67/2u0ysY/Q1XAw97eLoa/Q1FBd6GuZDX5sbPS3YPY1JvwL92Z/9mQ4dOqQf/OAH+uAHP5h//Vvf+pYaGxt19dVX+1gd/Pa5z31OBw8e1Gc+8xndc889fpdTdJ566imZpjnrWStBtXXrVj311FNvef0LX/iCnn76aT3xxBOqr6/3oTLgHPoa5kJPmx997Tz6GooBPQ0XQ1+7OHraeUHsaYR+Bdq/f7/e+9736hOf+ITOnDmjSy+9VA8//LB+8pOf6KGHHpJlWX6X+P/bu2PUVMIwDKPfxSBiQCwE7bIDS0kjYym4CDtLu7TuwC1IIIWI9m7BFdi6gXSD9Z/CQqK55DbXkfEcsHGaD0EeeBG8ue12G8fjMfI8j4iI/X4fm80mIk4/E67X60WedzPz+Txms1kMh8MYjUax2+2+PX99fS3ostubTCbRaDSi1+tFu92Oz8/PWK/XsVqt4u3t7WF+Lh4RUavVYjAYXL3//v4elUrlx2dwS7p2Tdc07ZKuneka90zTrmnaia6dadrZQzUt8c/yPE/T6TR1Op1UrVZTt9tNy+Wy6LMK8/LykiLix9fhcCj6vJvJsuyvn8OjfcUWi0Xq9/up1Wqlp6en1Gw2U5Zl6ePjo+jT7sZ4PE7Pz89FnwEpJV27pGuadknXfqdr3AtN+07TTnTtTNN+V8am/Ukppf+4KQIAAAAAN+aPPAAAAACgZIx+AAAAAFAyRj8AAAAAKBmjHwAAAACUjNEPAAAAAErG6AcAAAAAJWP0AwAAAICSMfoBAAAAQMkY/QAAAACgZIx+AAAAAFAyXy12AEDzZ4HRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1600x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "## get axis limits\n",
    "xmax = max(np.max(ls_beta_h[:,1]),np.max(lad_beta_h[:,1]),np.max(wls_beta_h[:,1]))\n",
    "xmin = min(np.min(ls_beta_h[:,1]),np.min(lad_beta_h[:,1]),np.min(wls_beta_h[:,1]))\n",
    "ymax = max(np.max(ls_beta_h[:,2]),np.max(lad_beta_h[:,2]),np.max(wls_beta_h[:,2]))\n",
    "ymin = min(np.min(ls_beta_h[:,2]),np.min(lad_beta_h[:,2]),np.min(wls_beta_h[:,2]))\n",
    "\n",
    "## make plots\n",
    "fig=plt.figure(figsize=(20, 10), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.plot(ls_beta_h[:,1], ls_beta_h[:,2], 'o', alpha = 0.5, color='black',label='estimate')\n",
    "plt.plot(beta[1],beta[2],marker=\"+\",color='red',markeredgewidth=2,markersize=20,label='truth')\n",
    "plt.title('OLS with Heteroscedastic Errors')\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.plot(lad_beta_h[:,1], lad_beta_h[:,2], 'o',alpha = 0.5, color='black',label='estimate')\n",
    "plt.plot(beta[1],beta[2],marker=\"+\",color='red',markeredgewidth=2,markersize=20,label='truth')\n",
    "plt.title('LAD with Heteroscedastic Errors')\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.plot(wls_beta_h[:,1], wls_beta_h[:,2], 'o',alpha = 0.5, color='black',label='estimate')\n",
    "plt.plot(beta[1],beta[2],marker=\"+\",color='red',markeredgewidth=2,markersize=20,label='truth')\n",
    "plt.title('WLS with Heteroscedastic Errors')\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/latex"
   },
   "source": [
    "The LS estimator works better for normal errors. \n",
    "\n",
    "The LAD estimator works better (on average black points are closer to red point) with the t-distribution than LS estimator  because it is resistent to outliers. \n",
    "\n",
    "The WLS estimator works best for the heteroscedastic errors because it uses the correct inverse variances as the weights. \n",
    "\n",
    "The LAD estimator is better than the LS estimator for the heteroscedastic errors because it is robust to outliers. \n",
    "In general, models that are closer to the truth get better estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2\n",
    "\n",
    "Compare the speed of $\\beta_{LS}$ to $\\beta_{LAD}$ using a package such as microbenchmark in R or equivalent tools, such as %timeit, in Python, see [this section of the textbook](https://jakevdp.github.io/PythonDataScienceHandbook/01.07-timing-and-profiling.html). Empirically determine the computational complexity (in $n$) of $\\beta_{LAD}$ and $\\beta_{LS}$ (we know from theoretical analysis that $\\widehat{\\beta}_{LS}$ should be linear in $n$). Provide a plot to summarize your findings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "428 µs ± 9.11 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 428 µs ± 9.11 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit -o model.fit(X, Yn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jj reddy\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500 ms ± 127 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 500 ms ± 127 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame(np.column_stack((X,Yt,Yn)))\n",
    "df1.columns = ['1', 'x','x2','yt','yn']\n",
    "%timeit -o smf.quantreg('yt ~ 1+x+x2', df1).fit(q=.5,max_iter=3000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "45.8 µs ± 816 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "at = %timeit -o np.linalg.lstsq(X,Yt,rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "46.2 µs ± 2.4 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "an = %timeit -o np.linalg.lstsq(X,Yn,rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.8 ms ± 1.35 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "ct = %timeit -o scipy.optimize.minimize(LADT,x0,method='Nelder-Mead', tol=1e-6).x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27.8 ms ± 1.48 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "cn = %timeit -o scipy.optimize.minimize(LADN,x0,method='Nelder-Mead', tol=1e-6).x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "494 ms ± 77.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "dt = %timeit -o smf.quantreg('Yt ~ 1+x+x2', df).fit(q=.5,max_iter=100000).params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.3 ms ± 1.86 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "dn = %timeit -o smf.quantreg('Yn ~ 1+x+x2', df).fit(q=.5,max_iter=100000).params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 10000,  20000,  40000,  80000, 160000, 320000], dtype=int32)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ns = 10000*np.power(2,np.arange(6))\n",
    "ns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = {}\n",
    "Y = {}\n",
    "for ii in ns:\n",
    "    x = np.linspace(start=0.0,stop=1.0,num=ii)\n",
    "    X[ii] = np.column_stack((np.ones(ii),x,np.power(x,2)))\n",
    "    Y[ii] = np.matmul(X[ii],beta)[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000\n",
      "90.2 ms ± 4.93 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "20000\n",
      "122 ms ± 7.13 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "40000\n",
      "170 ms ± 10.6 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "80000\n",
      "289 ms ± 34.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "160000\n",
      "1.53 s ± 4.91 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "320000\n",
      "3.36 s ± 123 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "def LAD(betah,Xh,yh):\n",
    "    return(np.sum(np.abs(yh - np.matmul(Xh,betah.reshape((3,1)))[:,0])))\n",
    "\n",
    "def run_l1(ii):\n",
    "    scipy.optimize.minimize(LAD,x0,args=(X[ii],Y[ii]),method='Nelder-Mead', tol=1e-6).x\n",
    "\n",
    "tms = []\n",
    "for ii in ns:\n",
    "    print(ii)\n",
    "    a = %timeit -o run_l1(ii)\n",
    "    tms.append(a.best)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 10e 1\n",
      "480 µs ± 308 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "n = 10e 2\n",
      "397 µs ± 32.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "n = 10e 3\n",
      "458 µs ± 33.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "n = 10e 4\n",
      "1e+03 µs ± 62.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "n = 10e 5\n",
      "10.3 ms ± 731 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "n = 10e 6\n",
      "117 ms ± 2.55 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "n = 10e 7\n",
      "1.16 s ± 95 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "# Compute times for LS vs n\n",
    "for k in np.arange(1,8):\n",
    "    n = np.power(10,k)\n",
    "    x = np.linspace(0,1,num=n) #Safer than np.arange for floating point\n",
    "    x = x[:,np.newaxis]\n",
    "    X = np.column_stack((np.ones(n),x,x**2))\n",
    "    yn = np.dot(X,beta) + np.random.normal(size=(n,1))\n",
    "    print('n = 10e',k)\n",
    "    %timeit -n100 model.fit(X, yn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 10e 1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jj reddy\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.8 ms ± 727 µs per loop (mean ± std. dev. of 7 runs, 250 loops each)\n",
      "n = 10e 2\n",
      "17.5 ms ± 1.33 ms per loop (mean ± std. dev. of 7 runs, 250 loops each)\n",
      "n = 10e 3\n",
      "36.2 ms ± 3.89 ms per loop (mean ± std. dev. of 7 runs, 150 loops each)\n",
      "n = 10e 4\n",
      "146 ms ± 11.2 ms per loop (mean ± std. dev. of 7 runs, 150 loops each)\n",
      "n = 10e 5\n",
      "396 ms ± 44.1 ms per loop (mean ± std. dev. of 7 runs, 5 loops each)\n",
      "n = 10e 6\n",
      "11.5 s ± 386 ms per loop (mean ± std. dev. of 7 runs, 5 loops each)\n",
      "n = 10e 7\n",
      "1min 19s ± 5.62 s per loop (mean ± std. dev. of 7 runs, 5 loops each)\n"
     ]
    }
   ],
   "source": [
    "# Compute times for LAD vs n\n",
    "for k in np.arange(1,8):\n",
    "    n = np.power(10,k)\n",
    "    x = np.linspace(0,1,num=n) \n",
    "    x = x[:,np.newaxis]\n",
    "    X = np.column_stack((np.ones(n),x,x**2))\n",
    "    yad = np.dot(X,beta) + np.random.normal(size=(n,1))\n",
    "    df2 = pd.DataFrame(np.column_stack((X,yad)))\n",
    "    df2.columns = ['1', 'x','x2','yn']\n",
    "    print('n = 10e',k)\n",
    "    if 1 <= k < 3:\n",
    "        %timeit -n250 smf.quantreg('yn ~ x+x2', df2).fit(q=.5,max_iter=3000)\n",
    "    elif 3 <= k < 5:\n",
    "        %timeit -n150 smf.quantreg('yn ~ x+x2', df2).fit(q=.5,max_iter=3000)\n",
    "    else:\n",
    "        %timeit -n5 smf.quantreg('yn ~ x+x2', df2).fit(q=.5,max_iter=3000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot times\n",
    "def myLabel(plt,title):\n",
    "    plt.title(title)\n",
    "    plt.xlabel('n')\n",
    "    plt.ylabel('Time in ms')\n",
    "    \n",
    "grid = plt.GridSpec(1, 2, wspace=0.4, hspace=0.3)\n",
    "plt.rcParams[\"figure.figsize\"] = (10,5)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "\n",
    "k = np.arange(1,8)\n",
    "t = np.power(10,k)\n",
    "t = t[np.newaxis,:]\n",
    "yLAD = np.array([0.0088,0.0175,0.0362,0.146,0.396,11.5,76])\n",
    "yLAD = yLAD[np.newaxis,:]\n",
    "\n",
    "plt.subplot(grid[0, 1])\n",
    "plt.scatter(t,yLAD)\n",
    "plt.plot(t,yLAD)\n",
    "myLabel(plt,'LAD')\n",
    "\n",
    "k = np.arange(1,8)\n",
    "t = np.power(10,k)\n",
    "t = t[np.newaxis,:]\n",
    "yLS = np.array([0.480,0.397,0.458,1,10.3,117,1160])\n",
    "yLS = yLS[np.newaxis,:]\n",
    "\n",
    "plt.subplot(grid[0, 0])\n",
    "plt.scatter(t,yLS)\n",
    "plt.plot(t,yLS)\n",
    "myLabel(plt,'LS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot times\n",
    "def myLabel(plt,title):\n",
    "    plt.title(title)\n",
    "    plt.xlabel('n')\n",
    "    plt.ylabel('Time in ms')\n",
    "    \n",
    "grid = plt.GridSpec(1, 2, wspace=0.4, hspace=0.3)\n",
    "plt.rcParams[\"figure.figsize\"] = (10,5)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "\n",
    "k = np.arange(1,5)\n",
    "t = np.power(10,k)\n",
    "t = t[np.newaxis,:]\n",
    "yLAD = np.array([0.0088,0.0175,0.0362,0.146])\n",
    "yLAD = yLAD[np.newaxis,:]\n",
    "\n",
    "plt.subplot(grid[0, 1])\n",
    "plt.scatter(t,yLAD)\n",
    "plt.plot(t,yLAD)\n",
    "myLabel(plt,'LAD')\n",
    "\n",
    "k = np.arange(1,5)\n",
    "t = np.power(10,k)\n",
    "t = t[np.newaxis,:]\n",
    "yLS = np.array([0.480,0.397,0.458,1])\n",
    "yLS = yLS[np.newaxis,:]\n",
    "\n",
    "plt.subplot(grid[0, 0])\n",
    "plt.scatter(t,yLS)\n",
    "plt.plot(t,yLS)\n",
    "myLabel(plt,'LS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>LS</th>\n",
       "      <th>LAD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>0.480</td>\n",
       "      <td>0.0088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.397</td>\n",
       "      <td>0.0175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1000.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>0.0362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10000.0</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.1460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100000.0</td>\n",
       "      <td>10.300</td>\n",
       "      <td>0.3960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1000000.0</td>\n",
       "      <td>117.000</td>\n",
       "      <td>11.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>10000000.0</td>\n",
       "      <td>1160.000</td>\n",
       "      <td>76.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            t        LS      LAD\n",
       "1        10.0     0.480   0.0088\n",
       "2       100.0     0.397   0.0175\n",
       "3      1000.0     0.458   0.0362\n",
       "4     10000.0     1.000   0.1460\n",
       "5    100000.0    10.300   0.3960\n",
       "6   1000000.0   117.000  11.5000\n",
       "7  10000000.0  1160.000  76.0000\n",
       "8         NaN       NaN   0.0000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show times in a table\n",
    "timeData = pd.DataFrame(np.column_stack((t.T,yLS.T)),columns = ['t','LS'])\n",
    "timeData.index += 1\n",
    "\n",
    "yLAD = np.column_stack((yLAD,0))\n",
    "timeDataLAD = pd.DataFrame(yLAD.T,columns = ['LAD'])\n",
    "timeDataLAD.index += 1\n",
    "\n",
    "timeData = pd.concat([timeData, timeDataLAD],axis=1)\n",
    "from IPython.display import display\n",
    "display(timeData)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/latex"
   },
   "source": [
    "We see an almost linearity (atleast with 3 points) in LS plot but not much linearity(cannot join linearly in any three points) in LAD plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}