{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo 1: Linear Regression\n",
    "\n",
    "In this demo we will show:\n",
    "* Linear regression using the closed form solution and gradient descent. \n",
    "* Adaptive Learning rates.\n",
    "* Gradient descent to minimize other (non-convex) functions. \n",
    "* Linear regression on polynomials.\n",
    "* A real life example on Diabetes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "# Code source: Sebastian Curi and Andreas Krause, based on Jaques Grobler (sklearn demos).\n",
    "# License: BSD 3 clause\n",
    "\n",
    "# We start importing some modules and running some magic commands\n",
    "% matplotlib inline\n",
    "% reload_ext autoreload\n",
    "% load_ext autoreload\n",
    "% autoreload 2\n",
    "\n",
    "# General math and plotting modules.\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Project files.\n",
    "from util import gradient_descent, generate_polynomial_data\n",
    "import plot_helpers\n",
    "from regressors import LinearRegressor\n",
    "from regularizers import Regularizer, L2Regularizer\n",
    "\n",
    "# Widget and formatting modules\n",
    "import ipywidgets\n",
    "from ipywidgets import interact, interactive, interact_manual\n",
    "import pylab\n",
    "# If in your browser the figures are not nicely vizualized, change the following line. \n",
    "pylab.rcParams['figure.figsize'] = (10, 5)\n",
    "\n",
    "# Machine Learning library. \n",
    "\n",
    "import sklearn\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.datasets import make_regression\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.preprocessing import scale, PolynomialFeatures\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "# from sklearn import datasets, linear_model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression \n",
    "\n",
    "We will start by fitting by linear regression a set of data points of the type $D = \\left\\{(x, y)_i\\right\\}$, $i = 1, 2, \\ldots, n$.\n",
    "\n",
    "The objective of linear regression, is to find coefficents $\\hat{w}$ such that the residual between $\\hat{y} = \\hat{w}^\\top \\tilde{x}$, and $y$ is small. (Remember that $\\tilde{x} = [x, 1]$). From now on, $x$ will be considered the extended version unless stated otherwise, hence dropping the tilde notation. \n",
    "\n",
    "The goodness of fit in Linear regression is usually calculated as the sum of squared residuals, but other loss functions are also available. \n",
    "\n",
    "The risk function is defined as: $$ R(\\hat{w}) = \\mathbb{E}[\\frac{1}{2}(y-\\hat{w}^\\top x)^2)]$$\n",
    "where the expectation is taken over the data generating the distribution of points. As the whole data generating distribution is not known, the expectation is approximated by samples from the **training** set. \n",
    "\n",
    "The risk is approximated by the empirical risk as:\n",
    "$$ R(\\hat{w}) \\approx \\hat{R}(\\hat{w}) \\frac{1}{n} \\sum_{i=1}^n (y_i - \\hat{w}^\\top x_i)^2.$$ \n",
    "\n",
    "\n",
    "By grouping the data into the feature matrix $X$ and target matrix $Y$, such that:\n",
    "\n",
    "$$ X = \\left[ \\begin{array}{cc} x_1^\\top & 1\\\\ x_2^\\top & 1 \\\\ \\vdots & \\vdots \\\\ x_n^\\top & 1  \\end{array}\\right]$$\n",
    "$$ Y = \\left[ \\begin{array}{c} y_1\\\\ y_2 \\\\ \\vdots \\\\ y_n  \\end{array}\\right].$$ \n",
    "\n",
    "The empirical risk function can be expressed as:\n",
    "$$\\hat{R}(\\hat{w})= \\frac{1}{n}(X\\hat{w} - Y)^\\top (X\\hat{w} - Y) $$\n",
    "\n",
    "\n",
    "### Closed form solution\n",
    "\n",
    "The closed form solution to the regression problem is given by:\n",
    "$$\\hat{w} = (X^\\top X)^{-1} X^T y.$$ \n",
    "\n",
    "The closed form can be computed with a total number of operations given by $\\approx O(d^3+nd^2)$ .\n",
    "\n",
    "### Gradient Descent\n",
    "\n",
    "When the number of dimensions or examples grows, the closed form solution becomes expensive to compute. However, the parameters $\\hat{w}$ can be updated via a gradient descent rule: \n",
    "\n",
    "$$ \\hat{w}_{t+1} \\gets \\hat{w}_t - \\eta_t \\left.\\frac{\\partial \\hat{R} }{\\partial \\hat{w}} \\right|_{w=w_t},$$\n",
    "\n",
    "where $\\eta_t$ is a parameter of the algorithm, $k$ is the iteration index, and $\\frac{\\partial \\hat{R}}{\\partial \\hat{w}}$\n",
    "\n",
    "The gradients of $\\hat{R}$ with respect to the parameters are:\n",
    "\n",
    "$$ \\frac{\\partial \\hat{R} }{\\partial \\hat{w}} = \\frac{1}{} X^\\top(Xw - y) $$ \n",
    "In the *vanilla* gradient descent method, $\\eta(k)=\\eta_0$ is a constant. However other algorithms exists that modify this. We will discuss these later. \n",
    "\n",
    "The computational complexity of Gradient descent is $O(n_{\\text{iter}} \\cdot  n d)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ShyUtazYhAwAA6EVZrym7TtIxku4ws++b2fUZxwMAAJCJrHdf/maWvx/5Mzkp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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10723c438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate the data.\n",
    "\n",
    "num_points = 100  # Number of training points.\n",
    "noise = 0.6  # Noise Level (needed for data generation).\n",
    "\n",
    "a_true = 3  # Slope.\n",
    "b_true = 1  # Intercept. \n",
    "w_true = np.array([a_true, b_true])\n",
    "\n",
    "X, Y = generate_polynomial_data(num_points, noise, w_true)\n",
    "\n",
    "# Plot Data\n",
    "fig = plt.subplot(111);\n",
    "plot_opts = {'x_label': '$x$', 'y_label': '$y$', 'title': 'Generated Data', 'y_lim': [np.min(Y)-0.5, np.max(Y)+0.5]}\n",
    "plot_helpers.plot_data(X[:, 0], Y, fig=fig, options=plot_opts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Closed Form Solution:\n",
    "\n",
    "The closed form solution to the regression problem is given by:\n",
    "$$\\hat{w} = (X^\\top X + \\lambda I_d)^{-1} X^T y.$$ \n",
    "\n",
    "Because there are only 2 parameters, the inverse of $(X^\\top X + \\lambda I_d)$ is fast to do $\\approx O(d^3)$. Hence, the closed form can be computed with a total number of operations given by $\\approx O(d^3+nd^2)$ ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f599d555c6c745109b4cbbc8edca4321",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=-3.0, continuous_update=False, description='Regularization 10^:', max=3.0, min=-3.0, readout_format='.1f', step=0.5, style=SliderStyle(description_width='initial')), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def change_reg_coefficient(reg):\n",
    "    dim = X.shape[1]\n",
    "    w_hat_closed_form = np.dot(np.linalg.pinv(np.dot(X.T, X) + np.power(10., reg) * np.eye(dim)), np.dot(X.T, Y))\n",
    "    print(\"w_hat = {}\".format(w_hat_closed_form))\n",
    "    # Plot closed form solution\n",
    "    fig = plt.subplot(111)\n",
    "    plot_opts = {'x_label': '$x$', 'y_label': '$y$', 'title': 'Closed Form Solution', 'legend': True,\n",
    "                 'y_lim': [np.min(Y)-0.5, np.max(Y)+0.5]}\n",
    "\n",
    "    plot_helpers.plot_data(X[:, 0], Y, fig=fig, options=plot_opts)\n",
    "    plot_helpers.plot_fit(X, w_hat_closed_form, fig=fig, options=plot_opts)\n",
    "\n",
    "interact(change_reg_coefficient,\n",
    "         reg=ipywidgets.FloatSlider(value=-3,\n",
    "                                    min=-3,\n",
    "                                    max=3,\n",
    "                                    step=0.5,\n",
    "                                    readout_format='.1f',\n",
    "                                    description='Regularization 10^:',\n",
    "                                    style={'description_width': 'initial'},\n",
    "                                    continuous_update=False));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "523bb39f86f34c51b8a13eab50d08ea3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.1, continuous_update=False, description='Learning rate:', max=2.0, min=0.1, readout_format='.1f', style=SliderStyle(description_width='initial')), IntSlider(value=10, continuous_update=False, description='Number of iterations:', max=20, min=5, style=SliderStyle(description_width='initial')), FloatSlider(value=-3.0, continuous_update=False, description='Regularization 10^:', max=1.0, min=-3.0, step=0.5, style=SliderStyle(description_width='initial')), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Gradient Descent solution. \n",
    "\n",
    "def change_learning_params(eta0, n_iter, reg=0):\n",
    "    regressor = LinearRegressor(X, Y)\n",
    "    regularizer = L2Regularizer(np.power(10., reg))\n",
    "    w0 = np.array([0., 0.])\n",
    "    opts = {'eta0': eta0, 'n_iter': n_iter, 'n_samples': X.shape[0]}\n",
    "    trajectory, indexes = gradient_descent(w0, regressor, regularizer, opts)\n",
    "\n",
    "    contourplot = plt.subplot(121)\n",
    "    dataplot = plt.subplot(122)\n",
    "    contour_opts = {'x_label': '$w_0$', 'y_label': '$w_1$', 'title': 'Weight trajectory', 'legend': False,\n",
    "                   }\n",
    "    data_opts = {'x_label': '$x$', 'y_label': '$y$', 'title': 'Regression trajectory', 'legend': False, \n",
    "                'y_lim': [np.min(Y)-0.5, np.max(Y)+0.5]}\n",
    "    plot_opts = {'contour_opts': contour_opts, 'data_opts': data_opts}\n",
    "\n",
    "    plot_helpers.linear_regression_progression(X, Y, trajectory, indexes, regressor.test_loss,\n",
    "                                               contourplot, dataplot, options=plot_opts)\n",
    "\n",
    "interact_manual(change_learning_params,\n",
    "                eta0=ipywidgets.FloatSlider(value=1e-1,\n",
    "                                            min=1e-1,\n",
    "                                            max=2,\n",
    "                                            step=1 * 1e-1,\n",
    "                                            readout_format='.1f',\n",
    "                                            description='Learning rate:',\n",
    "                                            style={'description_width': 'initial'},\n",
    "                                            continuous_update=False),\n",
    "                n_iter=ipywidgets.IntSlider(value=10,\n",
    "                                            min=5,\n",
    "                                            max=20,\n",
    "                                            step=1,\n",
    "                                            description='Number of iterations:',\n",
    "                                            style={'description_width': 'initial'},\n",
    "                                            continuous_update=False),\n",
    "                reg=ipywidgets.FloatSlider(value=-3,\n",
    "                                           min=-3,\n",
    "                                           max=1,\n",
    "                                           step=0.5,\n",
    "                                           readout_format='.2f',\n",
    "                                           description='Regularization 10^:',\n",
    "                                           style={'description_width': 'initial'},\n",
    "                                           continuous_update=False),\n",
    "                );\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adaptive Learning rates. \n",
    "\n",
    "* Annealing \n",
    "    $\\eta_{t} = \\frac{\\eta_0}{(1+t)^{0.6}}$\n",
    "\n",
    "* Bold driver heuristic:\n",
    "\n",
    "    If $\\hat{R}(\\hat{w}_t) > \\hat{R}(\\hat{w}_{t+1})$, \n",
    "    \n",
    "    $\\eta_{t+1} = \\eta_{t}/5$\n",
    "    \n",
    "    else\n",
    "    \n",
    "    $\\eta_{t+1} \\gets \\eta_{t}*1.1$\n",
    "\n",
    "    \n",
    "* AdaGrad:\n",
    "    $\\eta_t = \\frac{\\eta_0}{\\sqrt{\\sum_{j=0}^t g_j^2}}$, where $g_j$ is the 2-norm gradient of $L$ at time $j$. \n",
    "\n",
    "       \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e392dcf182954ba8abc7e13333061160",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(RadioButtons(description='Learning rate heuristics:', options=('Bold driver', 'AdaGrad', 'Annealing', 'None'), style=DescriptionStyle(description_width='initial'), value='Bold driver'), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def change_heuristics(learning_rate_scheduling=None):\n",
    "    regressor = LinearRegressor(X, Y)\n",
    "    regularizer = L2Regularizer(0)\n",
    "    w0 = np.array([0., 0.])\n",
    "    if learning_rate_scheduling == 'None':\n",
    "        learning_rate_scheduling = None\n",
    "\n",
    "    opts = {'eta0': 2,\n",
    "            'n_iter': 10,\n",
    "            'n_samples': X.shape[0],\n",
    "            'algorithm': 'GD',\n",
    "            'learning_rate_scheduling': learning_rate_scheduling\n",
    "            }\n",
    "    trajectory, indexes = gradient_descent(w0, regressor, regularizer, opts)\n",
    "\n",
    "    contourplot = plt.subplot(121)\n",
    "    dataplot = plt.subplot(122)\n",
    "    contour_opts = {'x_label': '$w_0$', 'y_label': '$w_1$', 'title': 'Weight trajectory', 'legend': False}\n",
    "    data_opts = {'x_label': '$x$', 'y_label': '$y$', 'title': 'Regression trajectory', 'legend': False,\n",
    "                'y_lim': [np.min(Y)-0.5, np.max(Y)+0.5]}\n",
    "    plot_opts = {'contour_opts': contour_opts, 'data_opts': data_opts}\n",
    "\n",
    "    plot_helpers.linear_regression_progression(X, Y, trajectory, indexes, regressor.test_loss,\n",
    "                                               contourplot, dataplot, options=plot_opts)\n",
    "\n",
    "interact_manual(change_heuristics,\n",
    "                learning_rate_scheduling=ipywidgets.RadioButtons(\n",
    "                    options=['Bold driver', 'AdaGrad', 'Annealing', 'None'],\n",
    "                    value='Bold driver',\n",
    "                    description='Learning rate heuristics:',\n",
    "                    style={'description_width': 'initial'})\n",
    "                );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient descent to minimize other (non-convex) functions.\n",
    "\n",
    "Gradient descent works can be used as a minimizing algorithm for other functions, even if they are non-convex. Gradient descent, if it converges, converges to a local minimum. Lets look at the function $$f(w) = \\sin(w_0)\\cos(w_1).$$ We would like to find parameters $(a,b)$ that minimize the function $f$. \n",
    "\n",
    "The gradients are:\n",
    "$$\\frac{\\partial f}{\\partial w_0} =  \\cos(w_0)\\cos(w_1),$$\n",
    "$$\\frac{\\partial f}{\\partial w_1} = -\\sin(w_0)\\sin(w_1).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b84868ab0c884689b79b9649a88a767f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=4.0, continuous_update=False, description='Learning rate:', max=10.0, min=0.1, readout_format='.1f', style=SliderStyle(description_width='initial')), IntSlider(value=10, continuous_update=False, description='Number of iterations:', max=50, min=5, style=SliderStyle(description_width='initial')), RadioButtons(description='Learning rate heuristics:', index=3, options=('Bold driver', 'AdaGrad', 'Annealing', 'None'), style=DescriptionStyle(description_width='initial'), value='None'), FloatSlider(value=-0.9, continuous_update=False, description='w_0:', max=3.0, min=-3.0, readout_format='.1f', style=SliderStyle(description_width='initial')), FloatSlider(value=1.1, continuous_update=False, description='w_1:', max=3.0, min=-3.0, readout_format='.1f', style=SliderStyle(description_width='initial')), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class sincos(object):\n",
    "    def __init__(self):\n",
    "        pass\n",
    "\n",
    "    def get_number_samples(self):\n",
    "        return 0\n",
    "\n",
    "    def loss(self, w, *args):\n",
    "        return np.sin(w[0]) * np.cos(w[1])\n",
    "\n",
    "    def gradient(self, w, *args):\n",
    "        return np.array([np.cos(w[0]) * np.cos(w[1]), -np.sin(w[0]) * np.sin(w[1])])\n",
    "\n",
    "def optimize_sincos(eta, n_iter, learning_rate_scheduling, a0, b0):\n",
    "    regressor = sincos()\n",
    "    regularizer = L2Regularizer(0)\n",
    "    w0 = np.array([a0, b0])\n",
    "    if learning_rate_scheduling == 'None':\n",
    "        learning_rate_scheduling = None\n",
    "\n",
    "    opts = {'eta0': eta,\n",
    "            'n_iter': n_iter,\n",
    "            'n_samples': 0,\n",
    "            'algorithm': 'GD',\n",
    "            'learning_rate_scheduling': learning_rate_scheduling\n",
    "            }\n",
    "    trajectory, indexes = gradient_descent(w0, regressor, regularizer, opts)\n",
    "\n",
    "    contourplot = plt.subplot(111)\n",
    "    dataplot = None\n",
    "    contour_opts = {'x_label': '$w_0$', 'y_label': '$w_1$', 'title': 'Weight trajectory', 'legend': False}\n",
    "    plot_opts = {'contour_opts': contour_opts}\n",
    "\n",
    "    plot_helpers.linear_regression_progression(np.array([]), np.array([]), trajectory, indexes, regressor.loss,\n",
    "                                               contourplot, dataplot, options=plot_opts)\n",
    "\n",
    "\n",
    "interact_manual(optimize_sincos,\n",
    "                eta=ipywidgets.FloatSlider(value=4,\n",
    "                                           min=1e-1,\n",
    "                                           max=10,\n",
    "                                           step=1e-1,\n",
    "                                           readout_format='.1f',\n",
    "                                           description='Learning rate:',\n",
    "                                           style={'description_width': 'initial'},\n",
    "                                           continuous_update=False),\n",
    "                n_iter=ipywidgets.IntSlider(value=10,\n",
    "                                            min=5,\n",
    "                                            max=50,\n",
    "                                            step=1,\n",
    "                                            description='Number of iterations:',\n",
    "                                            style={'description_width': 'initial'},\n",
    "                                            continuous_update=False),\n",
    "                learning_rate_scheduling=ipywidgets.RadioButtons(\n",
    "                    options=['Bold driver', 'AdaGrad', 'Annealing', 'None'],\n",
    "                    value='None',\n",
    "                    description='Learning rate heuristics:',\n",
    "                    style={'description_width': 'initial'}),\n",
    "                a0=ipywidgets.FloatSlider(value=-0.9,\n",
    "                                          min=-3,\n",
    "                                          max=3,\n",
    "                                          step=.1,\n",
    "                                          readout_format='.1f',\n",
    "                                          description='w_0:',\n",
    "                                          style={'description_width': 'initial'},\n",
    "                                          continuous_update=False),\n",
    "                b0=ipywidgets.FloatSlider(value=1.1,\n",
    "                                          min=-3,\n",
    "                                          max=3,\n",
    "                                          step=.1,\n",
    "                                          readout_format='.1f',\n",
    "                                          description='w_1:',\n",
    "                                          style={'description_width': 'initial'},\n",
    "                                          continuous_update=False));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression on polynomials.\n",
    "\n",
    "Higher order features can be constructed from data $D = \\left\\{(x, y)_i\\right\\}$, $i = 1, 2, \\ldots, n$. For example cubic polynomial features can be created by forming the data and target matrices as:\n",
    "\n",
    "$$ X = \\left[ \\begin{array}{cccc} x_1^3 & x_1^2 & x_1 & 1\\\\ x_2^3 & x_2^2 & x_2 & 1 \\\\ \\vdots & \\vdots \\\\ x_n^3 & x_n^2 & x_n & 1  \\end{array}\\right]$$\n",
    "$$ Y = \\left[ \\begin{array}{c} y_1\\\\ y_2 \\\\ \\vdots \\\\ y_n  \\end{array}\\right].$$ \n",
    "\n",
    "The predictor is again of the form $\\hat{Y} = X\\hat{w}$. Even if the features in the data matrix $X$ are non-linear on the data, the estimator is linear on the parameters $\\hat{w}$. Hence, the empirical risk function is again:\n",
    "$$\\hat{R}(\\hat{w})= \\frac{1}{n}(X\\hat{w} - Y)^\\top (X\\hat{w} - Y),$$\n",
    "\n",
    "and linear regression problem is identical as in the previous example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "134f8a0a1de14996ac5d2a57139fb816",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=-3.0, continuous_update=False, description='Regularization 10^:', max=3.0, min=-3.0, readout_format='.1f', step=0.5, style=SliderStyle(description_width='initial')), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate the data and calculate the close form solution\n",
    "\n",
    "num_points = 100  # Number of training points.\n",
    "noise = 0.3  # Noise Level (needed for data generation).\n",
    "\n",
    "w_true = np.array([-.5, .5, 1, -1])\n",
    "X, Y = generate_polynomial_data(num_points, noise, w_true)\n",
    "\n",
    "def change_reg_coefficient(reg):\n",
    "    dim = X.shape[1]\n",
    "    w_hat_closed_form = np.dot(np.linalg.pinv(np.dot(X.T, X) + np.power(10., reg) * np.eye(dim)), np.dot(X.T, Y))\n",
    "    # \n",
    "\n",
    "    # Plot closed form solution\n",
    "    fig = plt.subplot(111)\n",
    "    plot_opts = {'x_label': '$x$', 'y_label': '$y$', 'title': 'Closed Form Solution', 'legend': True, \n",
    "                'y_lim': [np.min(Y)-0.5, np.max(Y)+0.5]}\n",
    "    plot_helpers.plot_data(X[:, -2], Y, fig=fig, options=plot_opts)\n",
    "    plot_helpers.plot_fit(X, w_hat_closed_form, fig=fig, options=plot_opts)\n",
    "    \n",
    "    print(\"w_hat = {}\".format(w_hat_closed_form))\n",
    "\n",
    "interact(change_reg_coefficient,\n",
    "         reg=ipywidgets.FloatSlider(value=-3,\n",
    "                                    min=-3,\n",
    "                                    max=3,\n",
    "                                    step=0.5,\n",
    "                                    readout_format='.1f',\n",
    "                                    description='Regularization 10^:',\n",
    "                                    style={'description_width': 'initial'},\n",
    "                                    continuous_update=False));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "062b8817725e43e3a89481ee300f3d94",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.01, continuous_update=False, description='Learning rate:', max=1.0, min=0.001, readout_format='.3f', step=0.001, style=SliderStyle(description_width='initial')), IntSlider(value=10, continuous_update=False, description='Number of iterations:', max=50, min=5, style=SliderStyle(description_width='initial')), FloatSlider(value=-3.0, continuous_update=False, description='Regularization 10^:', max=3.0, min=-3.0, readout_format='.1f', step=0.5, style=SliderStyle(description_width='initial')), RadioButtons(description='Learning rate heuristics:', index=3, options=('Bold driver', 'AdaGrad', 'Annealing', 'None'), style=DescriptionStyle(description_width='initial'), value='None'), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def optimize_cubic(eta, n_iter, reg, learning_rate_scheduling):\n",
    "    regressor = LinearRegressor(X, Y)\n",
    "    regularizer = L2Regularizer(np.power(10., reg))\n",
    "    w0 = np.array([0., 0., 0., 0.])\n",
    "    if learning_rate_scheduling == 'None':\n",
    "        learning_rate_scheduling = None\n",
    "\n",
    "    opts = {'eta0': eta,\n",
    "            'n_iter': n_iter,\n",
    "            'n_samples': X.shape[0],\n",
    "            'algorithm': 'GD',\n",
    "            'learning_rate_scheduling': learning_rate_scheduling\n",
    "            }\n",
    "    trajectory, indexes = gradient_descent(w0, regressor, regularizer, opts)\n",
    "\n",
    "    contourplot = None\n",
    "    dataplot = plt.subplot(111)\n",
    "    data_opts = {'x_label': '$x$', 'y_label': '$y$', 'title': 'Regression trajectory', 'legend': False,\n",
    "                'y_lim': [np.min(Y)-0.5, np.max(Y)+0.5]}\n",
    "    plot_opts = {'data_opts': data_opts}\n",
    "\n",
    "    plot_helpers.linear_regression_progression(X, Y, trajectory, indexes, regressor.test_loss,\n",
    "                                               contourplot, dataplot, options=plot_opts)\n",
    "\n",
    "\n",
    "interact_manual(optimize_cubic,\n",
    "                eta=ipywidgets.FloatSlider(value=1e-2,\n",
    "                                           min=1e-3,\n",
    "                                           max=1,\n",
    "                                           step=1e-3,\n",
    "                                           readout_format='.3f',\n",
    "                                           description='Learning rate:',\n",
    "                                           style={'description_width': 'initial'},\n",
    "                                           continuous_update=False),\n",
    "                n_iter=ipywidgets.IntSlider(value=10,\n",
    "                                            min=5,\n",
    "                                            max=50,\n",
    "                                            step=1,\n",
    "                                            description='Number of iterations:',\n",
    "                                            style={'description_width': 'initial'},\n",
    "                                            continuous_update=False),\n",
    "                reg=ipywidgets.FloatSlider(value=-3,\n",
    "                                           min=-3,\n",
    "                                           max=3,\n",
    "                                           step=0.5,\n",
    "                                           readout_format='.1f',\n",
    "                                           description='Regularization 10^:',\n",
    "                                           style={'description_width': 'initial'},\n",
    "                                           continuous_update=False),\n",
    "                learning_rate_scheduling=ipywidgets.RadioButtons(\n",
    "                    options=['Bold driver', 'AdaGrad', 'Annealing', 'None'],\n",
    "                    value='None',\n",
    "                    description='Learning rate heuristics:',\n",
    "                    style={'description_width': 'initial'})\n",
    "                );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing the Polynomial Order.\n",
    "\n",
    "If the order of the polynomial is not known, then how should we select it? **Answer**: Cross-validation!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f28200f16a4148d88b9632b56ebed58c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, continuous_update=False, description='Noise level:', max=3.0, readout_format='.1f', step=0.5, style=SliderStyle(description_width='initial')), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return x * np.sin(x) \n",
    "\n",
    "x_plot = np.linspace(-1, 11, 100)\n",
    "f_plot = f(x_plot)\n",
    "X_plot = x_plot[:, np.newaxis]\n",
    "\n",
    "def resample(noise):\n",
    "    N = 20\n",
    "    folds = 5\n",
    "    n = int(N/folds)\n",
    "\n",
    "    xraw = np.linspace(0, 10, N)\n",
    "    # rng = np.random.RandomState(0)\n",
    "    np.random.shuffle(xraw)\n",
    "\n",
    "    #noise=1\n",
    "\n",
    "    x = dict()\n",
    "    y = dict()\n",
    "    for i in range(folds):\n",
    "        x[i] = xraw[n*i:n*(i+1)]\n",
    "        y[i] = f(x[i]) + np.random.normal(size=(n,)) * noise\n",
    "\n",
    "    \n",
    "    def change_degree(degree, reg, fold):\n",
    "        X = np.array(())\n",
    "        Y = np.array(())\n",
    "        for i in range(5):\n",
    "            if i == (fold-1):\n",
    "                Xval = x[i]\n",
    "                Yval = y[i]\n",
    "            else:\n",
    "                X = np.concatenate((X, x[i]))\n",
    "                Y = np.concatenate((Y, y[i]))\n",
    "\n",
    "\n",
    "        X = X[:, np.newaxis]\n",
    "        Xval = Xval[:, np.newaxis]\n",
    "\n",
    "        model = make_pipeline(PolynomialFeatures(degree), Ridge(alpha=np.power(10., reg)))\n",
    "\n",
    "        model.fit(X, Y)\n",
    "        \n",
    "        fig = plt.subplot(111)\n",
    "        lw = 2\n",
    "        plt.plot(x_plot, f_plot, color='cornflowerblue', linewidth=lw, label=\"Ground Truth\")\n",
    "        y_plot = model.predict(X_plot)\n",
    "        plt.plot(x_plot, y_plot, color='r', linewidth=lw, label=\"Degree %d\" % degree)\n",
    "        \n",
    "        opts = {'marker': 'b*', 'label': 'Training Points'}\n",
    "        plot_helpers.plot_data(X, Y, fig=fig, options=opts)\n",
    "        \n",
    "        plot_opts = {'x_label': '$x$', 'y_label': '$y$', 'y_lim': [np.min(f_plot)-3, np.max(f_plot)+3], \n",
    "                     'legend':True, 'legend_loc': 'lower left'}\n",
    "        opts = {'marker': 'mX', 'label': 'Validation Points'}\n",
    "        plot_opts.update(opts)\n",
    "        plot_helpers.plot_data(Xval, Yval, fig=fig, options=plot_opts)\n",
    "        \n",
    "        print(\"Train. Error: {:.2f}\".format(1/X.size * np.linalg.norm(model.predict(X) - Y, 2)))\n",
    "        print(\"Valid. Error: {:.2f}\".format(1/Xval.size * np.linalg.norm(model.predict(Xval) - Yval, 2)))\n",
    "        \n",
    "        \n",
    "    interact(change_degree,\n",
    "             degree=ipywidgets.IntSlider(value=1,\n",
    "                                         min=1,\n",
    "                                         max=15,\n",
    "                                         step=1,\n",
    "                                         description='Polynomial Degree:',\n",
    "                                         style={'description_width': 'initial'},\n",
    "                                         continuous_update=False),\n",
    "             reg=ipywidgets.FloatSlider(value=-3,\n",
    "                                               min=-3,\n",
    "                                               max=3,\n",
    "                                               step=0.5,\n",
    "                                               readout_format='.1f',\n",
    "                                               description='Regularization 10^:',\n",
    "                                               style={'description_width': 'initial'},\n",
    "                                               continuous_update=False),\n",
    "             fold=ipywidgets.ToggleButtons(value=1,\n",
    "                                        options=[1, 2, 3, 4, 5],\n",
    "                                         description='Validation fold:',\n",
    "                                         style={'description_width': 'initial'},\n",
    "                                         continuous_update=False),);\n",
    "\n",
    "interact(resample, noise=ipywidgets.FloatSlider(value=1,\n",
    "                                               min=0,\n",
    "                                               max=3,\n",
    "                                               step=0.5,\n",
    "                                               readout_format='.1f',\n",
    "                                               description='Noise level:',\n",
    "                                               style={'description_width': 'initial'},\n",
    "                                               continuous_update=False),);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real data sets: Diabetes prediction\n",
    "\n",
    "In this example we will use a diabetes dataset from sklearn. First we will split into train and test data to evaluate the prediction performance. Then a linear regressor using only one feature will be evaluated. In the second cell, a linear regressor using all the features but with no feature transformation is implemented. Finally, a 5th order polynomial transformation on the single feature used in the first cell is evaluated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the diabetes dataset\n",
    "diabetes = datasets.load_diabetes()\n",
    "\n",
    "Y_all = diabetes.target\n",
    "X_all = scale(diabetes.data) # zero mean unit variance\n",
    "n_all = Y_all.size\n",
    "n_test = 20\n",
    "\n",
    "# Split the data into training/testing sets\n",
    "X_train = X_all[:-n_test]\n",
    "X_test = X_all[-n_test:]\n",
    "\n",
    "# Split the targets into training/testing sets\n",
    "Y_train = Y_all[:-n_test]\n",
    "Y_test = Y_all[-n_test:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [ 33.73295272]\n",
      "Mean squared error: 4058.41\n",
      "Explained variance: 0.16\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c3d438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now let's train a 1D linear regression based on a single feature\n",
    "\n",
    "use_feature = 3\n",
    "# Use only one feature\n",
    "\n",
    "X_train_1D = X_train[:, np.newaxis, use_feature]\n",
    "X_test_1D = X_test[:, np.newaxis, use_feature]\n",
    "\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "# Train the model using the training set\n",
    "regr.fit(X_train_1D, Y_train)\n",
    "\n",
    "# Make predictions on the testing set\n",
    "Y_pred = regr.predict(X_test_1D)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', regr.coef_)\n",
    "# The mean squared error\n",
    "print(\"Mean squared error: %.2f\"\n",
    "      % mean_squared_error(Y_test, Y_pred))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Explained variance: %.2f' % r2_score(Y_test, Y_pred))\n",
    "\n",
    "# Plot outputs\n",
    "plt.scatter(X_test_1D, Y_test,  color='black')\n",
    "plt.plot(X_test_1D, Y_pred, color='blue', linewidth=3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [  1.44360014e-02  -1.13033495e+01   2.42834645e+01   1.55888584e+01\n",
      "  -3.87242964e+01   2.34407995e+01   4.89200200e+00   8.78083524e+00\n",
      "   3.53656217e+01   3.61947824e+00]\n",
      "Mean squared error: 2004.57\n",
      "Explained variance: 0.59\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZSSmlEymlr+Svvws8AdxwwWZrPm8MWf0hAX8REYcjol52MX3kBuDYkvXjXHzS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b32160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now let's use all features\n",
    "\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "# Train the model using the training sets\n",
    "regr.fit(X_train, Y_train)\n",
    "\n",
    "# Make predictions using the testing set\n",
    "Y_pred = regr.predict(X_test)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', regr.coef_)\n",
    "# The mean squared error\n",
    "print(\"Mean squared error: %.2f\"\n",
    "      % mean_squared_error(Y_test, Y_pred))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Explained variance: %.2f' % r2_score(Y_test, Y_pred))\n",
    "\n",
    "# Plot outputs\n",
    "plt.scatter(X_test_1D, Y_test,  color='black')\n",
    "plt.scatter(X_test_1D, Y_pred, color='blue', marker='*')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [  0.          32.39842197  13.12177699  -0.36124814  -2.5108258\n",
      "   0.25200116]\n",
      "Mean squared error: 3799.76\n",
      "Explained variance: 0.21\n"
     ]
    },
    {
     "data": {
      "image/png": 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SbL9a0q2Srk7ec7ftl/Sr2LWYn5/vqR3AeGLJGgD90jFkRcR3Jf20y8+7RdKXI+K5iPiJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b02198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now let's use all features\n",
    "\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "PF = PolynomialFeatures(degree=5, interaction_only=False, include_bias=True)\n",
    "\n",
    "X_train_poly = PF.fit_transform(X_train_1D)\n",
    "X_test_poly = PF.fit_transform(X_test_1D)\n",
    "\n",
    "\n",
    "# Train the model using the training sets\n",
    "regr.fit(X_train_poly, Y_train)\n",
    "\n",
    "# Make predictions using the testing set\n",
    "Y_pred = regr.predict(X_test_poly)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', regr.coef_)\n",
    "# The mean squared error\n",
    "print(\"Mean squared error: %.2f\"\n",
    "      % mean_squared_error(Y_test, Y_pred))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Explained variance: %.2f' % r2_score(Y_test, Y_pred))\n",
    "\n",
    "# Plot outputs\n",
    "plt.scatter(X_test_1D, Y_test,  color='black')\n",
    "plt.scatter(X_test_1D, Y_pred, color='blue', marker='*')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Regularization Paths\n",
    "\n",
    "As discussed in classed, the rgularizer can be of different types. Ridge regression has an $l$-2 cost on the weights, while Lasso regression an $l$-1 cost. To analyze the difference between them, we will show how the regression coefficients change as the regularization parameter $\\lambda$ increases. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dfPr4Q+zesJZzH36S/kkjuqVeIYToapKkCSE6xeWqpahoIemZ/6Gk6GdsFgfl\njmiSEi5k+JAL8PGJ7PIYqsvLmH/PrbjdLi5+/HkCQsO6vE4hhOhqbU3SelZX6UKIHsNq9SU6eibT\nJr3MMUeuoNjnHrIrwsnLep5ffzuM9etvp7R0VRN943mOf3AIp9x+LzVlZXz5/BO4nM4uq0sIIXoa\nSdKEEK3y8QnmrMOv4vjDFzBv86P8uGs6WbnfkZp2FitST2PPnv8anQB3gZghiRx/zY3s3rCORe++\n0SV1CCFETyRJmhCizYbFBPP6VWdD6G3c9NPDLM6/nLq6ctau+z+WLT+ZvLyv0Nrl8XpHH3EME0+a\nw8pvPmfjb794fPtCCNETSZImhGgXP7uVx04fy19Pn8r8tZO5e9E9hPV/DK0169bfzNJlJ5Gb+7nH\nk7WjLrqS+FHJfP+vf7AnI92j2xZCiJ5IkjQhRIecnTKQT687FJe2cOkHYdSFv01y8j9Qysr6Dbex\nfMVpFBcv9Vh9VpuN2bfcjV9QEF88+yjVFeUe27YQQvREkqQJIToseUAo//m/Q4kP9+eKt9JYuHMs\n06Z+zZjRz+F0lLBy1YWsWXMtVVUZHqkvMCycU267l4qiQr7++1O43Z6/tCqEED2FJGlCiE7pH+rP\nR9dO59DESO76ZA3Pfr+VmJg5HHLIDyQOvZ2i4iUsXXYiW7c+tu+1VJ2qb9gIZlxxLTvXrGLxh/M9\nsAdCCNEzSZImhOi0YD87r182hXNTBvLiz9u49cPVuLQPCQnXM/2QH+kfezq7Ml9n6bITyc//odP1\njTv2RMYdeyLLP/uIrcuWeGAPhBCi55EkTQjhEXarhSfOHMsdM4fz2epsrpufRq3Tha9vNKNGPU5K\nyifYbaGsWXsta9feQG3tnk7Vd8zl19B/2Ai+fek5Cnfv8tBeCCFEzyFJmhDCY5RS3DBjGI+clsyP\nm/bwp7fTqHEY942FhoxnypTPSRx6OwWFP7J02Uyysj7ocP9qNrudObfdg93Xl8+feZTaqkpP7ooQ\nQnidJGlCCI+76JDBPHXmOH7dms8Vb66gqs54U4DFYich4XqmTf2GoKDRbNp8H6v/uILa2rwO1RMc\nEcWcW+dSuieXb//5N7S7azrUFUIIb5AkTQjRJc6ZMpC/nTOepemFXPb6Cipq97/SKSBgCJMmzmfE\niL9SUrKCZctnsWfPdx2qJ35UMkddfBXbU5ex9D8feip8IYTwOknShBBd5vSJ8fz9vImk7SrmknnL\nKKtx7FumlIX4ARcwdcqX+PkNYO2669mwcS5OZ0W765l44mxGH3EMSz56j/RVKzy5C0II4TWSpAkh\nutSc8XH884KJrNldylVvplKGF9uMAAAgAElEQVRdd2DfZoGBQ0mZ/BEJg68nJ+cTli+fQ2np6nbV\noZTiuKtvoN/goXzzwjMU52Z7cheEEMIrJEkTQnS5E5P789y5E1ixs4hr56dR5zzw3jGLxYfExNuZ\nNOk9NC7SVp5HZuZbaK3bXIfdx5dTbr8XZbXyxTOPUldT7endEEKIbuXVJE0pFaaU+lgptUkptVEp\nNV0pFaGU+kEptdX8DPdmjEIIz5gzPo7HTx/Lwi35Rj9q7sYJWHjYFKZO+ZLIyCPZsvUvrFt/U7s6\nwA3tF8Psm+6icHcm373yQruSPCGE6Gm83ZL2d+C/WuuRwHhgIzAX+FFrPQz40ZwWQvQB500dxP2z\nRvH12hzu+XQN7iYSNbs9lHFjXyEp8S7y879jRerpVFRsbnMdg8dN4PDzL2HL77+S+tV/PBm+EEJ0\nK68laUqpEOBIYB6A1rpOa10CnAq8ZRZ7CzjNOxEKIbrCVUcM5aYZSSxI3c0jX29ssrVLKQuDB1/D\nxAnzcTorWZF6Bjk5bU+4ppxyJsOnHcav771J5oa1ngxfCCG6jTdb0oYC+cAbSqlVSqnXlFKBQIzW\nOgfA/OzX1MpKqauVUqlKqdT8/Pzui1oI0Wm3Hj+cyw5N4PXFO3jxp23NlgsPn8rUqV8SEjKeDRvv\nYOvWx3C7nc2W30spxQnX3Ux4bBxfPf8k5UUFngxfCCG6hTeTNBswCXhZaz0RqKQdlza11q9qrVO0\n1inR0dFdFaMQogsopfjz7NGcPnEAz/6whY9SM5st6+sTxcQJbxEffzG7Mufxx5qrcDhKW63Dxz+A\nU26/D0dNDV899yQup6PVdYQQoifxZpK2G9ittV5mTn+MkbTlKaX6A5ifnXvBnxCiR7JYFE+eOY7D\nk6K459O1LNrSfIu4xWJnxPCHGDnyMYqLl7Ii9QwqK5tvgdsrMn4gJ1x3M9lbNrJw/uueDF8IIbqc\n15I0rXUukKmUGmHOOhbYAHwBXGrOuxT43AvhCSG6gY/NwssXTSKpXxDXzU9jXVbLLWQD4s5l0sT5\nOJ3lrEg9k4KCn1utY8T0I5g861RWffslGxcv9FToQgjR5bz9dOeNwLtKqTXABOAx4AngeKXUVuB4\nc1oI0UcF+9l564qphPrbufzNFWQWVbVYPiwshalTPiMgYDB/rLmazN3vtFrHERdczoCRY/j+Xy9Q\nsCvDQ5ELIUTXUn2hH6GUlBSdmprq7TCEEJ2wJa+cs15eQnSwL59cdyhhAT4tlne5qli3/hYKCn5k\n4MArGJY0F6WszZavKC5i/tyb8fH358LHnsM3INDTuyCEEG2ilErTWqe0Vs7bLWlCCAHA8JhgXr0k\nhcyiaq5+p/FbCRqyWgMYN/Zl4uMvJTPzddau/T9crubfMhAUHsHsW+dSuieP/770nHR0K4To8SRJ\nE0L0GIcMjeTps8exfEcR9/1nbauJlFJWRgz/M8OHPUB+wf9YufICauua724jfuQYjrzwCratWMqK\nLz7xdPhCCOFRkqQJIXqUUycM4KZjh/FR2m7+tSi9TesMHHgZ48a+QkXlVlJTz6SqakezZSedfAoj\nph/Bb++/LR3dCiF6NEnShBA9zq3HDWP2uP48+d9N/HddbpvWiY4+jsmT3sPlqiI17RzKytc1WU4p\nxcxrbiQstj9fv/A0VaUlngxdCCE8RpI0IUSPo5TimbPHMz4+jFs/XN1q1xx7hYSMY/KkD7Fa/Vm5\n8kKKipY0Wc7HP4DZt9xNTUU537z4LNrd8v1vQgjhDZKkCSF6JD+7lVcvmUxEoA9XvrWC3NKaNq0X\nGDiUyZMX4OfXn9V/XEnenm+bLNcvYSgzLruGnWtWsfzzjz0ZuhBCeIQkaUKIHqtfsB+vXZpCRY2T\nq95eQVVd6+/tBPDzjWXypA8ICUlm3bob2Z31XpPlxh57AiMOPZLFH85n98amL48KIYS3SJImhOjR\nRvUP4R8XTGRDdhm3frgat7ttXWfY7WFMnPA2kZFHs3nzA+zc9VqjMkopjv/TDYTFxvL135+iqqxt\nl1WFEKI7SJImhOjxZoyM4b5Zo/lufR5Pf7+5zetZrf6MG/sy/fqdzLZtj7Mj45+NyvgGBDD7lrlU\nV5TzrdyfJoToQSRJE0L0ClcclsCF0wbx8i/b+XTl7ibLuLRmT62DHVW1rK+oJr2qliKnYsSovxEb\ncyrp6X9je/rfGvW/1i9hKMdc+icy/ljJcuk/TQjRQ9i8HYAQQrSFUoqHThlDen4lcz9dy+DIAHwj\n/FhSUsGy0kq2VtaSUV1LXRMd4NqVIingagb4H0lCxjfMcjzPIcNvQSm1r8y4405i1/q1LP7wHQaM\nHE38yDHduXtCCNGIvLtTCNFraK35Ma+U//tlE+XhPrh9jIsBg/18GBXkR2KAHwN87QTZrARYLNS4\n3ZQ6XeTUOthYUcO6iiryzIcPRtmL+dPQsZweE4G/1dhObVUV8+fejNNRx8VPvkBASKjX9lUI0Xe1\n9d2dkqQJIXq8MqeLBblFvJlVwLaqWnyUgrxq4utg/unjGRrk36btaK3ZWFHNB1u+4JvSAHarQYTZ\nrFwZH8V1A/sRZLOSt2M7799/O4PHTeS0u/58QGubEEJ4grxgXQjR6+XXOXh0ezaTlqzn/q1ZhNis\n/H3kIDYcnsxryQlkry/kH19vbvPL0pVSjA4O4OFJ5zJ/wGru1w8w1p7Dsxl5HLJ0I29kFRCVMJQj\nL7qS9JUrWP3dV128h0II0TxJ0oQQPU6508Vj27OZ+vsGXty1hxmRIfx38nC+mTycc/tHEGSzMnNM\nLLcfP5z/rMri1Ta+43MvpRQjhj/AcXHjubbqOl7rv4phgb7cs2U3p6zcSuARxzFkYgoL579Owa6M\nrtlJIYRohSRpQogew+nWvJ1VwPSlG3lh1x5Oig5j0dSRvDomgQkhAY3K3zAjiVlj+/PEfzfx86Y9\n7apLKcWIEX+hf+yZ+Gc/wt/Cf+Ll0YNJr6plZtoWss64HJ+AQL5+4WmcdXWe2kUhhGgzSdKEED3C\nz4VlHJu6mbu27CYxwJdvJw/npdGDGRbo1+w6SimePnsco2JDuOn9VWzbU9GuOpWyMGrU48T0m016\n+lNMrvuMRdNGckxEMI9mFfPrJbeRnZvDovfe6OzuCSFEu0mSJoTwqqyaOi5dm875a9KpdbuZl5zA\nZxOTmNhEy1lTAnxs/PvSFHxsFv70diqlVY521a+UldGjnyE6+gS2bn0EZ+EXvJE8hD8nxrHQYWHB\nJXfy0+LF7FglDycJIbqXJGlCCK9wac2/M/M5YvkmFhVV8EBiHIumjmRWdFi7n6gcEObPKxdPZndx\nFTd+sAqnq31vDbBY7CSPeZ6I8MPYuOkeCgt/4fpB/fhoQiI1/kG8f+Z1zPvwAypLitu1XSGE6AxJ\n0oQQ3W5teRUnp23hgW1ZHBIayMKpI/i/Qf3wsXT8T9KUhAj+emoyi7bk88S3m9q9vsXiw9ixLxEU\nNIq1626gtHQVh4UH8+XkYYQFBvLWjHP42wcftPlJUiGE6CxJ0oQQ3abS5eLhbVmcmLaFrBoHr4we\nzLvjhjLI39cj2z9v6iAuOzSB137bwcdpTb86qiU2WxATxs/D17cfq/+4isrKbSQF+PHt1FEMssLL\nSVP490+/eCRWIYRojSRpQohu8VNhGUcv38zLmfmcHxvJb9NGclpMuMc7i71v1igOTYzk3k/XsnJX\n+y9P+vhEMWH8m1gsNlatvoyamhz6+dr5+oiJxFeV8ZAO4dNtGR6NWQghmiJJmhCiS+XXObhufQYX\nrEnHz6L4bGISz4wcSJi9a14dbLda+OcFk4gN9ePad9LYU1bT7m0EBAxmwvjXcTrLWf3H5TgcZYT5\n2Pl02mhiivO4cWch/8sv6YLohRBiP0nShBBdQmvNe9mFHLFsE1/nl3J7Qgz/mzKCQ8KCurzu8EAf\nXr1kMuU1Tq57dyV1zvY9SAAQHDyGcWNfpqoqg3XrbsDtdhAfE8sr0X5EFuZx5dp0UksruyB6IYQw\nSJImhPC4bVU1nLF6G7dtzmRkoB8/ThnBnUP649uJBwPaa2RsCE+fPY60ncU8/OX6Dm0jIuJQRo54\nhKLixWzZ8jBaa6YedQx3Zq8joKyYC1ZvY1NltYcjF0IIgyRpQgiPqXW7eXZHLjOWb2ZDRQ3PjhjI\npxOTWuyQtivNHhfHtUcl8u6yXXywfFeHthEXdxaDB11DVvb7ZO5+E6UUZ15+NRf98gm6qpLzV28n\nr7Z9fbMJIURbSJImhPCIpSUVHLdiM09n5HJSdCi/Th3JhXGRWDz8YEB73XnCCI4cHs2fP1/foQcJ\nABIT7yA6eiZbtz5GQcHPBISGce6Fl3D6l69TXFPLJWvTqWpn32xCCNEaSdKEEJ2SVVPHdeszOG3V\nNqpcbuaPG8q/xiTQz9fu7dAAsFoUL5w3oVMPEihlYczoZwkOHsW69TdTXrGJpCmHMCN5DCd//wFr\nyqu5ceNO3NKHmhDCgyRJE0J0SLXLzd8ycjl82Sa+KSjl1sExLJo2kuMiQ7wdWiNhAcaDBBW1HX+Q\nwGoNYNy4V7FZg/jjj6uorSvgmMuuZkJ5ASetW8zX+aU8m5HbBdELIQ5WkqQJIdpFa80Xe0o4YvlG\nntqRy4zIYH6dOpK7h/Yn0Gr1dnjNGhkbwtNnjSdtZzEPdfBBAj/fWMaNfxWHo5h1a2/A7ufDidff\nwujfvuXIinz+lpHHj4VlHo5cCHGwalOSppRKVEr5muNHK6VuUkqFeSIApZRVKbVKKfWVOT1EKbVM\nKbVVKfWhUsrHE/UIITpHa83/CsuYmbqFq9dnEGy18vGEROYlD/HYGwO62qxx/bnu6ETeW7aL9zv4\nIEFIcDKjRj5OSekKtm57jEHJ45l00hwmffASiVa4YcNOdlXXejhyIcTBqK0taZ8ALqVUEjAPGAK8\n56EYbgY21pt+EnhOaz0MKAau9FA9QogO+q24nDkrt3LRmnRKnS5eGDWIH1JGcHh4sLdDa7c7Zo7g\nqOHR/PnzdaTt7NiDBLGxpzBw4BXs3v02OTmfcsT5l9Ivuh+zvnoTl9ZctT6DGnmQQAjRSW1N0txa\naydwOvC81vpWoH9nK1dKxQOzgNfMaQXMAD42i7wFnNbZeoQQ7efWmh8Lyzhj1TbOWr2drFoHTw2P\nZ/G0UZwTG4HN4t2nNjvKeJBgInFh/lw3P428DjxIAJCUeDdhYdPYtPl+quu2ceL1t+K7K53LM9ey\npryaB7ZleThyIcTBpq1JmkMpdT5wKfCVOc8Tj249D9wF7P2XMxIoMRNCgN3AgKZWVEpdrZRKVUql\n5ufneyAUIQQYDwTMzy7kqOWbuHBNOulVtfwlKY7fp43ikgFR2HtpclZfaICdVy9OMR4kmJ9GrdPV\n7m1YLDbGJr+A3R7B2jXXEZXQj5Q5p+Pzxftc4ufmnexCPsgp7ILohRAHi7YmaZcD04FHtdY7lFJD\ngPmdqVgpNRvYo7VOqz+7iaJNPtOutX5Va52itU6Jjo7uTChCCGBXdS1PpueQ8vsG7ticiZ/Fwj9H\nDWL59FFcPbAffta+9ZzRiNhgnjl7PCt3lfDwlxs6tA0fnyjGjX2JOkcB69bfzPSzziViwEAS3nmB\nQ0P8mbtlN+vKqzwcuRDiYNHWv7rHa61v0lq/D6C13gF09l0ohwGnKKUygA8wLnM+D4Qppfa+eTke\nyO5kPUKIZlQ6XXyYU8SZq7YxdelGnt+Zx+SQAD6ZkMj3KcM5MzYCn258lVN3O3lsf649yniQ4OO0\n3R3aRkjIOEYM/yvFxUvYufufnHT9rdQUF3Fe6v8Is9m4dsNOKl3tb6kTQoi2/vW9tIl5l3WmYq31\nPVrreK11AnAe8JPW+kLgZ+CsevV+3pl6hBAHqna5+b6glJs27mTskvXcvGkXWbV13D0kluXTR/P2\nuKEcFh6M8vKbArrLHTOHM31oJPf9Zy3rs0s7tI24uLOIizuXnTtfwRaWxdRTzybzp2+511bF9qpa\nHtwq/2sKIdpP6RZ6yDbvQ7sAOBz4td6iYMCltT7OI0EodTRwh9Z6tlJqKEbLWgSwCrhIa93i8+wp\nKSk6NTXVE6EI0Sfl1zn4X2EZ3xWUsrConGq3JthqYU6/MM6NjWBqaOBBk5Q1paCiltkv/IaPzcKX\nNxxOaED7b7l1uWpITTuLmpocJk/6D588/BTV5WXk3vwXXsktYV5yArOiPdJzkRCil1NKpWmtU1ot\n10qSNhiju43Hgbn1FpUDa+rd4O9VkqQJcaAih5NlJRUsKang95JK1ldUo4EBvnZmRoVyYlQo08MC\n+/SlzPZK21nMea/+zpHDovn3JSlYOvCARFXVDpavOI2gwGHEhz/C+w/cTeJhR/HPabPYWV3HT1NG\nEOcnXT8KcbDzSJLWW0iSJg5m1S43GyurWVNezdryKlaWVbGx0uhWws+iSAkJ5NDwII6PDCE5yP+g\nbjFrzVtLMnjwi/XcMXM4N8wY1qFt5OV9zbr1NzFo4JXkrx7M7x+/z8Tb7ueq2gAmBAfw0YRErPIz\nEOKg1tYkzdZaAXNjZ2B0MtsP4wlMBWitdc97SZ8QfVSVy82O6lq2VtawvaqWbVU1bKqsYUtVDS7z\nf61wm5XxwQGc2i+M6WFBTAgJwFday9rskumDWbmrmGd/2MK4+DCOHN7+J8djYmZRXLKcXZnzSD7y\nJbalDmXzvBd5cO4T3L2zgJd27eHGwTFdEL0Qoq9pU0uaUmobMEdrvbHVwl4gLWmit6tzuyl0OMmp\ncZBV6yC7to7sGgdZtXVk1RjTe+qc+/qjUUC8nw/DAnwZFxzAuGB/xgYHEO9rl5ayTqqqc3L6P5ew\np7yGL288nPjwgHZvw+2uJTXtbKqrM0mKe4kFf36SpKnT+fL4c/kmv4QvJg1jUkhgF0QvhOgNPHq5\nUym1WGt9mEci6wKSpAlvcmtNpcttDi4qXG4qnW4qXC6qXG5j2uWiwumm1OmiyOE0h/3jFU28Qsjf\nYmGAn504Xztxvj4M9PMhKdCXYQF+DPH3xb+P9VvWk6TnV3Dqi4sZGh3Igmun42tr/4vjq6t3sXzF\nKQQEJOHcdQZLPnyPo26eyzWE42ux8MOU4T36hfRCiK7jqQcHzjBHjwJigc+AfU9aaq0/7WScHtHV\nSVqpw8mi4op90/WPmG7Q125LOW/DRQdsp8GKupnxxus1XKabLNdoutF6LdTRwj62vF6DZbqNsTVa\nr4VYAJcGl9a4NbjR+6cxPvcuc9Vbpvcta1zWqTW1bk2dW+PQmlq3mzpzulYb4w63plZr6txunO24\nrTPIaiHCbiPcbiXCbiOy3niE3UZ/XzsD/HyI87UTZrNKq5gX/XddLtfOT+OCaYN47PSxHdpGXt5X\nrFt/M4MHXcvSeVmU5e9h1EN/44KtuVwcF8lTIwZ6OGohRG/gqXvS5tQbrwJm1pvWQI9I0rpaZk0d\nf1qf4e0wRDtZFVhRWBVYlNo3bVEKS7PLwK4UPhYLvhaFj1IE2W34Wiz4WJQxmMt9LApfczzAaiHI\naiHQaiHIZiXQaiHQaj1gXoDF0mvfd3kwOjE5lmuPSuSVhduZNCicsybHt3sbMTGzKSpazM5d/+Lw\ny57hs7+8SfmHr3PtqZfycmY+x0WGMDMqtAuiF0L0BfJ0ZxtUu9xkVB/YVVv9Bg7V4G1Wqpnxhus1\nLtvCdlpYr6ED12tHbA2nPbSPB66n6o23VF/zsTVcZlWqUaJlkRYo4QFOl5uL5y1n5a5iPr3+UMbE\ntT+hcrmqWL7iVFzOSmxF17D43Y847sY7udUnhj11Tn6ZOpIonzY9wyWE6CM8fU/aC03MLgVStdZe\nfyOA3JMmhOgqnujotrx8AytSzyQi4nA2fBRMcXY2hzzyPKdvyWNGZDBvJA+RS9tCHETamqS19c5j\nP2ACsNUcxmG8EeBKpdTzHY5SCCF6uKggX/554SRySqu5bcFq3O72X30IDh5NUtJdFBb+xOTzE3DW\n1bFr/qvcM7Q//y0o4/2coi6IXAjR27U1SUsCZmit/6G1/gdwHDAKOJ0D71MTQog+Z/LgcO6fNZof\nN+3h5YXbO7SNgfGXERl5DNn5L3PI+ceSnracI3as47CwIO7fltXolgohhGhrkjYAqN+pTyAQp7V2\nUe9pTyGE6KsumT6YOePjePb7zSzeVtDu9ZVSjB71JDZbKO7Izxkweji/vPUvHu8fhE3BDRt24uxA\nK50Qou9qa5L2FLBaKfWGUupNjBefP6OUCgT+11XBCSFET6GU4okzxjI0Ooib3l9FbmlNu7fh4xPJ\nmNHPUlWVzqg5GpfDybo3XubxYfGkllXx4q68LohcCNFbtSlJ01rPAw7F6CftM+BwrfVrWutKrfWd\nXRmgEEL0FIG+Nl65aDI1DhfXv5tGnbNxJ8StiYg4jMGDrqag5AumXTSBHavTGL4xldP6hfFMRi6r\ny6q6IHIhRG/UWme2I7XWm5RSk5parrVe2WWRtUNXP91Z46xhZ9nORvMbd2/R+OmsJue1Yb2Gs9qy\n7aaeDmvcdUbrdXly2215Yq2jx6gj227LfliUBaUUVmXFoiz7BquyolDyFJ7gqzXZ3PDeKi4/LIEH\n54xp9/put4O0ledSVbWDPUuOIHdTLqc9+QKnbC8k0Grh+5QRBMgbJYToszzVme1twNXAs00s08CM\nDsTW62SUZXD2l2d7OwzRQ+xL3LBgtRiJm1VZsViMefsSOjPRs1qs2C32/YPV3vy0Oe5r9cXf5o+f\nzQ9/m3+jIcAWYHzaAwjxCcHf5i/JYzeaPS6OtJ3FvLE4g8mDw5k9Lq5d61ssdsaMfo7lK05h0NGZ\n5Gy0sPTVf/D36+/inDU7eGR7No8Nb3/nuUKIvkU6s22DsroylucsP2Be41clNT6ODcs0Oa+Jw9+R\nbTdZVxt+tm1Zz1Pb7ugxalNdHjpGe8u43C7c2o0bN27tNqbrjWs0Lu3C7d5fZu/g0i60NpdrN063\nE6fbicPt2D+4mhk3h1pnLTWutt/zZLPYCPEJ2TcE+wYTYg8h3C+cKP8oovyjiPSPJNI/kii/KCL8\nI7Bb2t/fl9ivzunmvFd/Z3NuOZ/fcBhJ/YLbvY3c3C9Yv+FWAvTJLHl1B0dfchWfD5/Cq7vzeX/c\nUI6JDOmCyIUQ3ubpzmwDMFrVBmmtr1ZKDQNGaK2/6nyonSed2Yq+yK3d1DhrqHJWUe2sPnBwGJ+V\nzkrK68opqy2jrM4casuMeXVlFNcUU+4ob3L7Yb5h9A/sT3xwPAOCBhAXFMeAoAH7xv1t/t28x71P\nTmk1s1/4jfBAHz7/v8MI9G3/mwM2bLiTnNzPqNp8Att/281Zj/yNC/PrKHE4+XnqSCLs8jYCIfoa\nTydpHwJpwCVa62SllD/wu9Z6QudD7TxJ0oRoXo2zhsKaQgqrCymoLqCguoDC6kLyq/PJrswmqzyL\n7Ips6tx1B6wX7R/N0LChJIUlkRiWSGJoIolhiYT6yrsm61u8rYCL5y1j9rg4/n7ehHZfdnY6K8zX\nRlWzccEgfH0jmXjf48z6Ywczo0J4bUyCXMoWoo/xdJKWqrVOUUqt0lpPNOf9obUe74FYO02SNCE6\nx63dFFYXklWRtW/YWbaT9JJ0tpdup9pZva9stH80iWGJjAgfQXJUMmOixhAfFH9QJxL//HkbT3+3\nmYdPGcOlhya0e/2y8nWkpp6Fv208S16sYNJJp7L+mFN5JD2Hv48cxLn9IzwftBDCazz14MBedWbr\nmTY3noh0YitEn2FRFqIDookOiGZCvwMbyN3aTW5lLttKtrG9ZDvbS7azrWQb7296f1/rW5hvGGOi\nxpAcmUxylDFE+Ud5Y1e84rqjElm5s5hHvt7A2PhQJg0Kb9f6IcHJJCXdzdatjzDh7GNZ+dEXnDYh\nhf+FBnPf1t1MDwtkkL9vF0UvhOip2tqSdjxwPzAa+B44DLhMa/1Ll0bXRtKSJkT3c7gcbC3ZyrqC\ndcZQuI7tJdtxa6PvsIHBA5kcM9kY+k0mPrhvt7aVVjmY9Y9fcbk1X914OJFB7UuqtNasWXsNhYWL\nyFmUQnm2YsYjz3HyxmySg/z5ZGIS1j58/IQ4mHj6cuc7wFqgGkgHlmmt2/9elC4iSZoQPUOVo4pN\nRZtYW7CWtLw0Vu5ZSWltKQD9/PsxKWbSvsQtMSwRi+pbfYGtyyrljJeXMG1IBG9ePhWrpX1JlcNR\nzLLls9EuCyvnhTE4eRq1F13HzZsyuW9of24cHNNFkQshupOnk7QZwOHAEcBQYDWwSGv9984G6gmS\npAnRM7m1m/SSdNLy0kjbk0ZaXhp7qvYAEO4bTkpsCikxKUyJndJnkrYPlu9i7qdruWlGErfNHNHu\n9YtLVrBy5QXYneNZMa+aoy+7hpcHjuW7gjK+mTyMscEBXRC1EKI7eTRJMzdoBaYAxwDXAtVa65Gd\nitJDJEkTonfQWrO7YjdpeWmsyF3BitwV5FTmAPuTtskxk5kSO4WksKRembRprbnr4zV8lLabNy6b\nwjEj+7V7Gzt2vEj6jueo3nEoW38s56SHnuLc/DpCbTa+TxmOn7yNQIhezdMtaT8CgcDvwK/Ab1rr\nPZ2O0kMkSROi98qqyGJF7gpSc1NJzUslqyILMB5GSIlJISU2pdclbTUOF6e/tITskmq+uvFwBka0\nr/VLaxerVl9KaekqMr5NxlUdzKC5j3HJ5mz+FB/FX4fJ2wiE6M08naQ9B0zGeKJzMbAIo5+06hZX\n7CaSpAnRd2RVZJGam2okbvWStlDf0H2XRlNiUhgWPqxHJ20ZBZXMefE3EiID+eja6fjZre1av7Y2\nj2XLZ2PRIax41Z+kSYexdPbFzMsq4O2xQ5gZJf3VCdFbefxyp7nRIOBy4A4gVmvdI54JlyRNiL4r\nuyKb1LzUfZdH6ydtE6MnkhyVzNiosYyJGtPjOtr9fn0uV7+Txv+zd5/hcVR338e/Z2Z3tUW9F0uy\n5d7AFWyDCSWhB2McEo9i/tYAACAASURBVAIYAiSE3CHlvtNIbw+B9E6AhARjCKGHBAMJJWBawL3g\n3lWtrtX2Mud5MbIt23KRvbIk+/+5rrlmdsrZs0eW96cp51x7ZgU/mjux18e3tLzOylU344zNYMlf\nOph982f4Zu4IqiMxXpo+mnK3qw9qLYToa6k+k3Y79kMDU4Gd2GfS3tBav3q8FU0FCWlCnDq6h7bV\nTavZ1rFt77aKjArG541nVO4oRuXYU5G3qF+7/rj7hQ3c+/pWfn716cyb2vvLlJu33M2uXX8ktPls\nti7u4Ozv/pSPN4QZ4XXz7JQRuIyBezZRCNGzVIe0r2AHs2Va60QK6pdSEtKEOHV1xjpZ17KONc1r\nWNO0ho1tG/eebQPIcGUwInsEFRkVVGRWUJFRQXlmOeUZ5WS6+n4A80TS4voH3mVldTtP3jaLCWW9\nO9tnWXGWr7iWzs71bH9+LDqSTe6Xf8hntjbI/WlCDFJ9crkzlZRS5cBDQDFgAfdrrX+tlMoFHgOG\nAjuAj2qt2w5XloQ0IUR3nbFOtrRvYVPrJja1bWJrx1aqO6v3dv+xR3ZaNhUZFZRllFHqK907yHxp\neiklvhLcDndK6tPUGWXO794E4Nnbz6Ygo3d3ikSju3lvyRVguVn+QCZDxkxh+bxP8kBtCw9MGMpl\nBdkpqacQ4sQYDCGtBCjRWi9XSmVgD+B+JfAJoFVrfbdS6g4gR2v9tcOVJSFNiJOT1hricayoPQqd\ncrns6RgvX4YTYWo6a9jVuYtqfzW7Onexy7+L2kAtDcEGEgdcKMhz5+0LbekllPnK9ga5kvQSPA7P\nUb/32toOPnLv20wozeKvn5qBy9G7y5Rtbe+yYuV8nNZE3rs/wuQ5H+Uno2ayLRzhpWmjqZRho4QY\nNAZ8SDuQUupZ4Hdd07la6/quIPea1vqwPUJKSBNi8Ej6/cRra+2prp5EczOJ1haSrW0kW1pItLVh\nBYPoSAQrEoFk8uBCnE4MpxMjIwMzLxdHfj7OsjJcQ8pxDRtK2qjROMtKexXmklaSpnATdYE6agO1\n1AXqqA/W77cct+L7HZPrzqUio4IxuWMYlzeOsXljGZ41HKfp7PE9/rmqjs89uoJrppdz11UTex02\nd+16gM1bfoTVMpvVTzYz9fN38Gkri0q3i2enjMQj/acJMSgMqpCmlBqKfc/bBGCX1jq727Y2rfVB\noxUrpW4FbgWoqKiYunPnzhNTWSHEIWmtSba3E6+pJV5X1xXE9p9bgcD+BzkcOHJyMHNzceTlYubk\nYqSnY7jTUG6PPU+zLzvqWMye4vY82Rmwg11TE/HaWpIdHXuLNdLT8Zx2Gp6pU/BOn4538mSUs+fw\ndDQsbdEcbqYuUGdPQTvMbWvfxsa2jQTjQQCchpPROaOZWTqTmaUzmVQwab/Q9tN/beD3/9nK968Y\nz42zhvaqDlpr1r7/eRobX6Rt5VnUruyk5I4f8fndYeYV5fC7sRUn9fioQpwsBk1I6+rW43XgTq31\n00qp9qMJad3JmTQhTgydSJBobCReX0+8rp54Q70dvvYEsdo6dHj/7hON9HScZWU4S0t7mJdi5uSk\nLFgk/X5i27YR2biJyPp1hFesJLppE2iNkZ6O76yzyPjQh8g4/zwMb+qGV7K0RXVnNetb1rO+dT0r\nGlewumk1SZ3E4/AwvXg6s0pn8aHKD5HvLuDWhUv5z8YmFt58BrNG5PfqvRKJAEuWziMWa2HL30dg\nxXy0f+47/LyujW9VlXC7jO8pxIA3KEKaUsoJPAf8S2v9i651G5HLnUKccFY4TKKlhWRzM4nmZuKN\njST2hLF6e0rs3g2Wtd9xRlYWzrJSXN0DWLdlM7Pvn6A8nKTfT+i99wi8vpjA66+TaGxEeTxkXHAB\n2R+9Gu/06X1y9ikQC/Bew3u8U/cO79S/w07/ThSKacXT+GD5JTzwYhYtAXjmf85iWL6vV2UHg9tY\nsnQuTqOIZQ+4KR4+gZev/BT/bO7goYnD+JB0dCvEgDbgQ5qy/1dcgP2QwBe7rf8p0NLtwYFcrfVX\nD1eWhDQh9tGWhdXZSdLvJ9nhJ9nRjrVn2e/H8nd0re+w7wVrskOZFQweXJjTibO4GGdJCc6SEhyl\nJV3LpThLS3AWF2P4ehcw+pO2LMLLltGxaBH+51/A8vtxVVWRO/96subOxXCn5mnOnmzr2Ma/tv+L\n57c/zw7/Djyml2j7aaTHzuPZW+eRn967G/+bW15j1apPkcZE3r0/yogPXMRvp13EjnCU56eOYpSv\n7z6LEOL4DIaQdjb2OKBrsLvgAPgG8C7wOFAB7AKu1lq3Hq4sCWmiL2it7bNGloXeM09aYCUPvy6Z\nRFsarGS3fZLQfV0yiY7H902x2MHLB6yzojGscAgdCmOF90wHvg7blxsP83utnE6MrCzMzEwceXk4\nCvIx8/Nx5OXjyM/HkZ9nvy4owJGfjzpJO0u1wmH8L7xI26OPElmzBjMvj9wbbiDnuusw0/sueGqt\nWdm0kic3PckL218kbsXwJMbxsw99kXMqZvaqrOrqBWza/AMc4bNZ+lALI66ezzeLx5PhMHhh6iiy\nnY4++hRCiOMx4ENaKvV1SIts2kT1LZ/cb52mh3brqSl7at8D1x3NPodY1+NPT94zJe85kOzpesLw\neFBeD4bHi+Hx9Pja8HkxMjMxM7MwszIxMzPtUNYVzJTbLTeXd6O1JrRkCS1//BPBN97AzM0l/9O3\nkn3NNRhpfdutRXuknR+9+WcW7XgSw9nJtKLpfG7y7UwpmnLUZWzc+D1qaheSbLiANc/WUXrr//JV\nM59Z2ek8fFoVTkN+1kIMNBLSUiheX0/zPX84eENPX3Q9ruuh0AP26/lL82jLP7Z6DJj3THk9jrzP\nUX9207DPJBkmyjRAGV3rTDCMw65Tpn0chkKZXduMfesMlwvldNoBrPv8gGUcDglVJ0h49Woaf/lL\nQu/8F+eQIRTd8TXSL7igz9v/T29s5MdvLyCrZDFR3cFZpWdx++TbmZA/4YjHWlaC1as/RWvb23Su\n+wBb32zA8YXv8KOwg4+X5PKL0eXy70eIAUZCmhBCHKPg22+z+667iG7egm/WTIq/+11clZV9+p53\nLlrHH9/cyMWztvF+8O+0R9v5YMUH+dK0LzEk4/BDPyUSnSxddjXRyG7qFk+hcXM7LV/4Pvf7E3xp\naBFfGVbSp3UXQvTO0Ya0k/NmEyGEOA6+WbMY9swzFH3rW4TXrGXbnCtpXbDAvrewj3z9krFcNqGS\nF98aw2eqHuD2SbfzVt1bXPnslfx+5e8JJ8KHPNbhyOD00/6EMpwMOW8DmUUeiu69i7mZafx8x24e\nrmvps3oLIfqOhDQhhOiBcjjIvf46qp77J74zz2T3XXez8/r5RLdt75P3MwzFzz96OmeNyONbz2ym\nlA/zzyv/yfkV53Pvqnu58u9X8vLOlznU1Q+PZwiTJv2ZZDLAqDn1ONISjL//LmZ7nXx1YzXPNh52\nCGQhxAAkIU0IIQ7DWVTEkHv/QOmP7ya6bRvb586l5YE/98lZNbfT5I83TGNaZS5ffGwlK7ZrfnLO\nT/jzRX/G5/Lxv6/9L7e9fBvVndU9Hp+ZMYHTTruXaLyO064N4TDjzH7o50zyOPjsup283OJPeZ2F\nEH1HQpoQQhyBUoqsOXOo+uc/8J19No0//Sm7bvkkiaamlL+X1+XgzzdN57QhWXzu0eX8Z0Mj04un\n8/jlj3PHGXewqmkV8/4xjwXvLyBpHRwUc3NmMmHCrwhHNzJpfhRnMsRFj/yKUS4Hn1y7nTdaO1Ne\nZyFE35CQJoQQR8lZWMiQ3/2WkjvvJLxyJduunEvw7bdT/j7paQ4evOkMRhdn8OmHl/Hm5mYchoPr\nxl7H3+f8nTOLz+RnS3/G9c9fz8bWjQcdX1hwEePG/oxgeA1TbkziigW4/PHfUeE0mL9mG4slqAkx\nKEhIE0KIXlBKkT3vKoY98ThmTja7bvkkjb/+NTqRSOn7ZHmcLLz5TKryfXzyoSW8vaUZgGJfMb85\n/zf89JyfUhes45rnruE3y39DNBnd7/ji4isYN/ZuAuEVTPmEhTvcxpWP30Ol0+CGNdt4rVUufQox\n0ElIE0KIY5A2ciTDHn+crLlzafnDvez6xE3Edzem9D1yfC4e/uSZVOR6+cSDS3hp3W7ADooXD7uY\nZ+c8y6VVl/LHNX/kI//4CMt2L9vv+JKSeYwdczeB8HKm3BjDE23jw4/8igpTccPq7Sxqak9pfYUQ\nqSUhTQghjpHh9VL6ozsp/fHdhNetY/u8eYSWLEnpe+Snp/HYrTMZW5zBbQ8v4+8ravduy3Znc+fZ\nd3LfB+8jbsX5xIuf4Ifv/JDO2L7LmaWlH2H8uF8Qir7PpPlBclxxLlvwU0abFp9au4O/SvccQgxY\nEtKEEOI4Zc2Zw7DH/oaZns7OT9xEy4MPHrKrjGOR43PxyKdmMH1oDl98bCX3vb51v/Jnlc3i6Sue\n5vqx1/Pk5ie58tkreXXXq3u3FxdfwcQJvycc3cKYj9RSVuzig3+8kyk6yv9trOYXOxpSWl8hRGrI\niANCCJEiyc5O6r7+dQIvv0LmpZdQ8sMfYvhSN1h7JJ7kS0+sYtHqeubPqOS7Hx6Hw9z/b+01TWv4\n7jvfZXPbZj5U+SG+ceY3yPfkA9DW9i6r19yGodJoXjqNze9Vs+T6z/OGN4+ri3P42ehy0gz5212I\nvibDQgkhRD/QWtPypz/R9MtfkTa8iry7f0nAkUfb7hCdrRECbRGiwQSxSIJEzEIpUIbCmWaS5nXi\nyXCSkecmK99DdrGXnCIvRrcgZlmaH7+4gfsWb+OcUQX89prJZHmd+9UhbsV5cO2D3LvqXtIcaXx5\n2peZO2IuSikCgU2sXHUTibifRN0FrHx2Cxsuv47nhoxlRpaPP04YSoHLeeDHEkKkkIQ0IYQ4wbSl\naarupHZTO7VLtlG/tZ2YM3PvdmUofNkuPOkuXG4Th8tEa9CWRTyaJBJMEO6MEQ3te1LUdBrklfoo\nHZnNkDG5lIzIwuV28Nd3d/Hdf6ylLNvDH2+YxsiijIPqs6NjB99/5/ss3b2UM4rP4Dszv0NlZiXR\naCOr13wGv38lnuQlvPuXarZNmsU/z7iIHJeTB8YPZUpW6s4ACiH2JyFNCCFOgEQ8ya61rWxZ3kj1\nulYiwTgAmfluCktcOP77ImlbljHkygso/7/bMJ2OI5YZDSfwN4VprQ/SVN1J085OGrZ3YCU0hqEo\nqspkyJhcQvlOvvzSBsLxBD+6aiJzJpUdVJalLZ7e/DS/WPoLYlaMmybcxM0TbsalDDZs/AYNDX8n\n3T2d1X9TbCebRVfeQpvh5LsjSrm5LB+lVMrbTIhTnYS0FGrb6Wf1gnU9buveegf/X6YO+/JIlFIc\n6afTm/8/tTq6KuwpUx+4Ys/Lgw444oojbu6+Svfwngftf6QPcrgd1CGqoew2V4Y9RykM1bXesF93\nre7az369d33XcXsnAwzTwDDBMAwMh4FhgDINTFNhGArDoVCGgWEqe53TwOE0MB3Gob8cD/XRutXF\nrtC+uTrwtbH/656O2/91t3XGAftwYFmc9F/sVtKiZkMbm5fuZtuKJmKRJJ4MJxXj8ygfm8uQMTn4\nstLsfaNRdt/5I9offxzfrJmU/vznOHJyev2e8ViShi0d1GxspWZDG427OkGDLzeNdWaC18NBzj2z\njO/NmYDHZR50fFOoiZ8u+Skv7HiBEl8JX5n+FS4ov4DauofZvPkunI4cWlZOYu2SJl6f+0nWZBdx\nYV4mvxxTQZ7ryMFSCHH0JKSlUOv7zYQWru+z8oU46XQLdnQFWsyuuXHo13uWldOwJ5eJchoYLhPl\nMlBOE5VmYngcGD4nhteB6XVi+Jwot9mn4VBbmvptHWxesputyxsJd8ZxuU2qJhcwcnoRQ0bn7Hfv\n2IHan3qKhu//ADM/jyG//jWeiROPqz7hQIztq5rZuqyR6g2taAvaDYuGLIOPXT2Ws6eU9HjckoYl\n3PXeXWxu28yZJWdyx/Q7KDRDrFn7eSKRWtLi57NkYT0rJ32AV6eeT47LyU9GlXNxQdZx1VcIsY+E\ntBTSCYukP9aLA3rZpofY/bClpOg9+qv8QxY/SD+XtjSW1mhLg7ZvHreS9pRMWug9ywkLbWmSCY1l\nWViJrv0si2RCk4xbJOIWyViSxJ7leJJEzOp6nSQZs+9fikXt5e725CIAh6lw+5ykeR24vfbcXnbg\nSXfhSXfi9jowDLW3zuiuNurhNZa2m+9w++g9++x5bbcNXdOeZZ08wuu4hY4l986tmIWOJyF56B+I\nchqY2WmYWV1TdhrOAg+OAi+OAg9GD2eXjvhz1Zrm6gCbluxmy9LdBNqimE6DoRPzGTW9iIoJuTic\nR19ueO371H7+8ySamij6zrfJufrqXtepJ5FAnG2rmlj6Rg0dOwIYQDLbyazzKxg3owRvpmu//RNW\ngic2PcFvV/yWUDzE3JFz+dS462mvvY/6hqdwp41g139KWVln8srlN1DjyWRuYTY/HDmEfDmrJsRx\nk5AmxCkgmbCIhhJEQ3GioQSRYJxoME7IHyfkjxLyx/ZNHbG990vtpcCXlUZmnpuMrim70Lv3qcI0\n78B6yk8nLXQ0iRVOkAzGsUIJrFAcKxgn2REj2REl2R4l0RHF6oztF7LN7DQchV5cZem4hmTgKs/A\nPCC87NHWEOwKZo207w5hGIry8bmMnFbEsNPzcbmPPagk2tqo+9KXCb79NlkfmUfxt7+NkZZ2zOUd\nqLExyH0PryG2NUBx0gAFFeNyGX1mMcMmFeDsFlbbIm3cs/Ientz8JKYyuXbMtVxVWsWurT8iHm/H\nEZnJ8if9vDPhXN6adA4ZTgdfryrh+tI8zJP8krYQfUlCmhDiIMmERbA9SmdLBH9LhM6WMJ0tETpb\n7deBtqh9NquLN9NFdpGXnGIvOcU+sou95JX68GWnDfj7znTCItESJt4YJtEYIt4UIrE7RHx3yD6z\nB5hZLjuwDc0inudmx65ONi9rpLk6AArKRmUzcloRwycX4k5PXWDVySRNv/0tLffeh3v8eIb85tc4\nyw6+6f94vL2lmR8/vobM3TGm4MIV1TjT7Muzo88spmx0jn0WFajprOGelffw3Lbn8Dl93Dz2Y5zp\nqqNp91M4HYW0bxjJO8sNXj//arYVlHFauofvjCjl7JyDnygVQhyZhDQhRK8lkxb+pjDtu0O0NYRo\n2x2ivSFEW0Nwv24h0rwOckt95Jamk1fqI6/MXnb7BtaZt57oeJJYXZBYdSeBzW1Ed/pxRJIARC1N\nZ5oD94hsys4dQkZl5hFKOz6dr75K3Ve/hnI4KP35z0g/66yUlh9NJPnj4m3c85+tFEQ0H87KIrM5\nTjySxJflYuQZxYw+s5j8IekAbGnbwm9X/JZXq18l3ZnOjVVnM1GtIxLcgMuoYucb2bwWHsGbsy+n\n3e3j/NwMvlFVwoQMb0rrLcTJTkKaECJltNZEAnFa64O01gVpqQvSWhegpTZILLwvvPmyXOSWpZNb\n6usKb+nklPj2u8TWn2KRBHWb26nZ0Mau91toawgBUFGZwfBSH7lorJqAfakUcJb4cI/LwzMuD2ep\nr0/OHsZ27KDmc58numULBV/4Anm3fgqV4l7/Gzsj/PKlzTy2ZBce0+CGiiJGRRQNG9qxLE1emY9R\nZxYzanox6TlpvN/yPg+ufZB/7/w3plLcVDGOicZWkvFmHNYINi/28ZJ7Ou9Nu4Cw08VFeZl8cWgx\nkzMlrAlxNCSkCSH6nNaaYHvUDm21QVrqArTWBWmtD5KMdz3UoCAz37M3tNkBLp2sIg/mYZ6GTFXd\nmmsC7N7up2ZDK7t3dKItjekwKBmRRdWkAqomFeDLTtvvuERTmMj6VsLrWojt8oMGMysNz/g8PJMK\ncJVnpDSwWaEQ9d/+Dv5Fi0g//3xKf3QnZnZ2ysrfY3tzkN++upm/r6jFYRjMHVfMhzIyaV/fxu7t\nflAwZHQOo84oZviUAhrjDSxct5BntjxDPBHiY6VlTHM1opJ+TKuCzUtyeNGcxfLTzybscjM13c3N\n5YVcXpgtw0sJcRgS0oQQ/cayNP6m8N7Q1lJrn3lrbwzvvefNMBU5xV4y8z2k57hJz00jI8dNeq4b\nT7oTp9skzePAdB66z7hEPEmow34wItgeJdgRo6MpREtNgObaANGgfZZPKSgcmsmQ0TkMGZNDcVUW\njqM8u5cMxIhsaCX8fguRzW2Q0Ji5brynF+CdVICzKDU982utaVv4MLt/8hPMnGxKfvADMs47LyVl\nH2hHc5AH3tzOE8uqicQtplbmMHdEIZUB2LG8CX9TGIfTYNgku3uRjKEGf9/5NE9teordwWrOznBw\nYTZ4dCcG2ezeOYRFrVNZOuJs2jJzyTMV1w8pZH5pHkPcPT+cIcSpTEKaEGLAScSTtO8O7Q1trXXB\nvQ8sdL9s2p1hKlxuB8pU6KTe172JpfedrevG4TLIK0snryyd/CHp5A1JJ78sHZfn+LuOsCIJwmtb\nCK1qJLqlHTQ4i714Ti/Ee3oBjlz3cb9HZN066u74OtFNm8iaM4fCO752TJ3fHo22YIzHllbzxNJq\ntjYFcTsNLh5XxCWlebhqwmxd3kg0mMB0GgwZk0PF+Fz8xXU83/QsL+/8N8OdQc7PdjHMGUShSQRL\neH3bOBZnncvWijGAYprPxdyyQi4vyKYwbeDfsyjEiSAhTQgxqETDCQKtdmCLBOPEwvYg5LFwgmg4\nidb2kEiGoVBdIza43A68WS58WWl75550p905bh9LdsYIr2kmtKqJ2E4/AK7KTLyTC/FMzMc8joco\ndCxG0z330PKnBzB9Pgq/+hWy5s5N+b1qe99Pa1ZWt/Pkshr+saqOzkiCbK+Tc0fkMzMjnTy/Rf36\nVvzNEQByS30UjvBRl7WVt62XWNfxBpO9UWala/IcCbQ2qOsYxb/9s1iZNY3m7CKU1kxxm1xVXswH\n87Oo9KSu2xEhBhsJaUIIcYIkWiOEVjURWtFIojEEpsI9Ohfv5AI8Y/JQzmMLV5FNm2j43vcJL1+O\n+/TTKPraHXinTE5x7Q94z3iSVzc08vL63by2sYnWYAzTUEytyGZWYRYVUQPqwzTt8JPo6kw5u9RD\notjPFudqdjoWUZ5RzwSPRaHT3r4tOIo3AzNZ7ptOU4Y9EkKRTjA7O53zSwuZnZtBgUvOsolTh4Q0\nIYQ4wbTWxOuDhFY0ElrZhNUZQ7lNPBPy8U4uJG1YVq/P8mnLouPvz9L0q1+RaGwk46KLyP/s/+Ae\nNaqPPsU+SUuzqqadV9c38p+Njayr96O1PXzruOIMZmRnUB43cLbE6KwN7g1tphsSeQFac5ahs96i\nLKeecncEhwF1lLIyPJU1iYls8owl4rSfCC1OxpjgdjC9MJ/pBbmcluEh3TEwngoWItUkpAkhRD/S\nlia6tZ3QikbCa1vQsSRmVhreSQV4JxfiLO7dAwdWKETLn/9C61/+ghUMknHxxeR96pN4xo/vo09w\nMH8kzopd7Szd0crSHW2srG4nHLf7mHMqxaRMH2PS0ihKKFz+BPGW6L5RHxwxzNJ16IKV+HK2kp/Z\njNNhsYNhvK8nsDkxmu1qOK3OfACU1hQkIlSaMMrnYWxOFhML8qhK95DvdAz4zpSFOJxBH9KUUhcD\nvwZM4E9a67sPta+ENCHEQGbFkkTWtxBa0URkUytYdh9s3kmFeCbk4cjzHHVZyfZ2WhYsoO2hhVjB\nIJ6pU8mdfz3p55+P4TqxT1ImkhY7WoKsr+9kQ4OfDfWdrK/3U9dh37tmasi1FBWmkwqHk/ykgS9i\n4YhYKG3hTG/CnV2DM3sXjpxteDNriPoMtjOc7QynhnJq9RDqVSkJte+zOa04eYkAhTpBiWlSlual\nyOuhJCOdIdlZlGakU5DmxGfKmTgxMA3qkKaUMoFNwIeAGmAJ8HGt9bqe9peQJoQYLJKBGOHVzQRX\nNBKv7gTsJ0Td4/LwjM8/6k5zk52dtD/1FG0LHyZeW4uZlUXmZZeSeemleCZPRvVjQAnHkuxqDbGj\nJcjOliA7WkLUtYdp9Edp7IzQ2hkj01JkWYrsrindgmxlkWlEyUprx5PejNPXiCu9FtPXRLvPQaM7\nhxZXDk0U0kwBLRTQRAGdKqvHerisKOmJTjxWFK8Vxa3jeEniVRqfgkzTINPhxOd0k5nmJSPNS4bL\nR5bbR7rbS4bbjc/lwudy4HU4cSjkDJ5IicEe0mYC39NaX9T1+usAWuu7etpfQpoQYjBKtEYIr2sh\n/H4LsR0dezvNTRuZjXtENmlV2YccBH4PnUwSfPsdOv7+dzpffhkdjWJmZ5P+gQ/gnTED3xnTUz4u\n6PGKJSyaA1F2+yM0dkZp9EdoC8XpCMdpD8XpCMUIBmLEAnESwQREkpgJCw8JfEaY7LQOMtM6yEzr\nxOdqx3QFiLo14TSToNtBwOWm0+kh4PDhNzMIKS9hvITwEcJeDuNBq94/0GHqBCZJDCxMncQkiUMn\nMbted19v6n3LRtd3rUKjtMbomgMo3bUevd9+++3TbbtCAxqlwehapmsv275yu+sxXup92/R+++qD\n9um5DH3Ibepw++nDbOtn5W2d/OBT3+jT9zjakHb8HQf1jTKgutvrGuDM7jsopW4FbgWoqKg4cTUT\nQogUceS6yTi7jIyzy0gG4/YoB+tb7L7Ylu629yn0kjY8i7SKTJxl6TjyPfs9fKBMk/TZZ5M++2yS\ngQDBN9+k85VXCbz2Gh3PPttVRiHuceNIGzsGV3kFzrIyeyouQjn65mtAWxY6EsEKh+0pFMIKhEn6\nIyQDYdyBKOWhOGWhODqSxIol0TELnUiiExoSGm0pSGLPtQGYYDggUQiRIShlgmGCMlGGfeZQo4mT\nJKriREkQVTFiKkbMESJuthNzhEkYERJmlLDLIuS0iDssYk5N1ICYaRAzDeJKETNN4oZJ3HCQUCaW\nYWAphaUMksrApPk/ZgAAHfJJREFU2jNhkFSmvQ7TXsZ+nTRMophoZccsu45dEUwprP3W2estFCj2\nLuuDJmPvsnWYaKT3Wz5Qz/sdvG+qyzi6/frT2a4l/V2FvQbqmbSrgYu01p/sej0fOENr/bme9pcz\naUKIk4m2NPG6ANGt7US2tBPb4Ud3ddyrXAbO0nRcpek4Cj04ctyYuW4cOW6Uw+hWhkV08xZC771H\nZO0aIuvWEd26DaxuHQCbJo7CQszMTAyfz57SfRheL8rsCm97Lu8psGIJdExDTGMlQCcUJA20ZYDl\nQGsTcIByoYw0lNMLTi/K6UU5PSjzyN1s6GQMrBjsmVtR0DGUjpLQUYJGhE4zRsBIEDYsQqYmbCrC\npiJkKMKGInGES5JOwKXAoRROQ+FQBg5D4TQNnIaBY+/cxGGamIbCNE0M08Q0TUyHufe1w+HEMA1M\n09G13YFhKhQGyjRQykAZCqUUhjJQhr3OcJgo7JCt9q43USYYhj3KhjK6tikDTAVdZaAUGF3H0PUz\nNxVgvxdKQddZwv2eJu7hcq064Gziwdv3/Pztcg+5vcfXh/459HjZuIfyD2sQX3oe7GfSaoDybq+H\nAHX9VBchhDihlKFwDcnANSSDjA+Uo5OaRFOIWE2AeF2AWG2A4JKGvcHNPgjMDBdGhgvD48DwOjA8\nDsyCs0m/8BzSL1FgWVjBTpL+DpLt7STb/Vj+oB2+4kl0wiIZNEgGTDDTwExDmW577nCjTJf9reGA\nni8UWkACjCTKtFBmEqWiKFoxdCcq2YoZb8RI7Ma0mjGMIKYjgGkEMBxhjIwcdEYR/rQSmlQBTVYW\njXE3LRGDtrBFINJ9VAoDMPB6vaSnp+Pz+ShMTye9a/J6vbjd7oOmtLQ0DBlXVAwSAzWkLQFGKqWG\nAbXANcC1/VslIYToH8pUOIt9Xd12FAH22TYrECPRGiHRGiHZNbeCcaxwgnhHFCuUwAonwOrpikmm\nPSlQaaC8CuU0MNwOVJrZbW7ut87wOFAee264TXueZqLiu1HNa1ENq6FhNTSsgY7qbrdLmVA4DPJG\nQFY5ZM1AZ5TRbuZRGzSpbQ1RW99AQ0MDsVhsby19vjQKCgoYOTSH7OxssrOzycnJISsri/T0dEx5\nglOcxAZkSNNaJ5RStwP/wu6C489a6/f7uVpCCDFgKENhZqZhZqaRNrTnpxvB7mAXC7C0Pbj9njmg\nHAbKVGD28jKTlYTd78Oud7qm/0Jn/Z6aQf5IKD8Tpt8C+aPt1zlDwXTS2trKtm3b2Lp1K7t27SQY\ntB/aN02TkpISJk2aRGFhIQUFBRQUFOD1eo+tgYQ4CQzIkAagtX4eeL6/6yGEEIOZUsr+U9dUx3db\ndns1bHkJNr8MO96AqD1eKVnlMPRsO5SVTIKiceDa11FvIpFg27ZtbPrvv9i6dSttbW0AZGZmMmLE\nCIYMGUJZWRmFhYU4+ughBiEGK/mNEEIIcTCtofo92PAcbH4Jmtbb67MqYMI8qDwLKmZAdvlBhyaT\nSXbs2MHatWtZv349kUgEl8vF0KFDmTFjBlVVVeTn50ufY0IcgYQ0IYQQNq3te8nWPglrn4GOXWA4\noXImTL4ORl4I+aMO+VRdS0sLS5YsYc2aNQSDQVwuF2PGjGHChAlUVVXJmTIhekl+Y4QQ4lQXaIQV\nC2HV36B5k90XWdV5cN43YMyl4D70PW+WZbF161beffddtmzZgmEYe4PZyJEjcTqP3O2GEKJnEtKO\nRjwCbTv2X3e4vmCOehuH2XasZQ6WbYdbrw6xravvH8O053s7spRLJkL0mtaw8y1Y8gCs/ydYcfsS\n5ozPwNg54Ms77OHxeJwVK1bw7rvv0tLSQnp6Oueeey5Tp04lIyPjBH0IIU5uEtKORvMmuG92f9dC\nHFL38GYeEOQOsX7P3HSB6eyap9nLjq65mbZvu2PPsgtcXnCl2zdHu3z2stO7b3nP+rQM+32EGEji\nEVj5CLx3PzRtsM+SnfEpmHaz/RTmkQ6Px1m+fDlvvvkmnZ2dlJWVcdVVVzFu3Di5nClEislv1NHI\nLoeP/KXbiu5jmh1mxIaDth3uuJNhG4fYplO0zdo3Wcn95zrZbbmn9Xv2t7otJ+2zB4mu3s2TcYgF\nINzabV3XlIja2xMR+/ijosCTDZ4c8OSCN7fbch5klkBGCWSWQWYpuDOPslwhjkG0E5b+Gd75PQR2\nQ+lkmPN7GH+V/YfHEViWxdq1a3nllVfo6OigsrKSq666iqFDh8oDAEL0EQlpR8OTAxOu6u9aiIEi\nEbPDXDwEsaC9HAseMAUg3A7hNjv0hVrtL8amDRBqg1jnweW6MuzgllkK2RV2p597ppxh4Dj8QNtC\n9CjUCu/eB+/eC5F2qDoX5j1gd5txlOGqpqaG559/nrq6OoqLi7niiiuoqqqScCZEH5OQJkRvOVzg\nyAVyj72MeMTu/LOzHvx14K8Ff33XvA42vgDBpn37KwNyq6B4Ytd0OpScBumFx/1xxEkqHob//gHe\n/KXdp9mYy+Hs/4MhU4+6iFAoxCuvvMKyZctIT09n7ty5TJw4UYZVEuIEkZB2FPx+P2+99dZ+6w73\nF+SR/ro81mOl3J63KaX2DUjcbflY1xmGgcPhsAdSNs0el4/7S8rphtxh9nQo4XZo3QotW6FlCzSu\ng9rl8P4z+/bJKLW7R6icZd/0nT8a5Av01GYl7ac0/3OnHfpHXQIXfBuKxveqmPXr17No0SKCwSAz\nZszg3HPPxe1291GlhRA9kZB2FMLhMCtXrjzkdn2Ye7OOdVt/lSuOjlJqv/DmcrmOanK73Xi9Xrxe\nLx6PZ+8g0D2GPk82lE21p+7C7bB7LdSvhtplsPNtWPtU1zE5dlgbdRGMuljOtJ1qtr4K//62/e+j\ndApcdb99WbMXwuEwixYtYu3atRQVFXHddddRUlLSRxUWQhyOOhm+sKdNm6aXLl3a39U4KXX/9zEQ\nQ6XWeu9kWdZ+82NdZ1kWyWSSRCKx3/xQy4lEgng8TiwWO+SUTB7+YYM9gS0jI4OsrCwyMzP3Tnte\nezyens8wag3tO+2wtvMt2Pa6PbA1yg54oy+B0Zfaw/WIk5O/Hv71dfssa3YlfPC7MG5ur8+q7ty5\nk6eeeopAIMA555zD7NmzZQBzIfqAUmqZ1nraEfeTkCZE30skEsRiMSKRCOFwmFAoRCgU2m85FArh\n9/vx+/10dnYeFE6dTid5eXnk5+fvnefn51NQULB/1wda24Nfb3wBNj4Pdcvt9UUTYdK1cNpHwZd/\nAj+96DNW0u7n7NUf2k8gn/NlOOsLdpcxvSnGsli8eDGvv/46OTk5zJs3j7Kysj6qtBBCQpoQg5hl\nWQQCgb2hraOjg/b2dpqbm2lpaaG9vX3vvoZhUFhYSElJyX7T3uDmr7fHX1z5CNStsHuTH3mRHdhG\nXQym3PUwKNWvgn9+0Q7hVefCZb+AvOG9LiYUCvH000+zZcsWTjvtNC677DLS0noX8oQQvSMhTYiT\nWDwep7W1laamJurr62loaKC+vp5QKASAw+GgvLycyspKKisrGTJkiD08z+51sOqvsOoxCDbaXX3M\n+CxMvh7S0vv5U4mjkozD4p/C4p/Zfe9dfLc94PkxdIfR0NDAo48+SiAQ4JJLLmHq1KnSrYYQJ4CE\nNCFOMVpr/H4/tbW17Ny5k507d9LQ0ACAaZoMGzaM0aNHM2rUKLLSfbDpBXj7d1D9X3Bnw/Rb4IxP\nQ0ZRP38ScUhNG+HpW6F+JZx2DVxyt/2wyDHYtGkTTz75JGlpaVxzzTVyeVOIE0hCmhCCcDjMrl27\n2L59Oxs3bqStrQ2AkpISRo8ezcSJE8kLbYW3fwPrn7OHwJp2M5zzFblvbSCxLHjvPnj5e/YQZB/+\nFYybc8zFvffee7zwwgsUFRVx7bXXkpkpo10IcSJJSBNC7EdrTVNTE5s2bWLjxo1UV1cDUF5ezumn\nn874Uh+epffAikfsIHDWF2Dm/9jjkIr+46+HZ26F7Yvtewg//JtjPttpWRb/+te/ePfddxk1ahTz\n5s2T+8+E6AcS0oQQh+X3+1mzZg0rV66kqakJh8PBmDFjmD6ymIp1f0BtfA58hXDu12DKjfZZNnFi\nbXnFvrwZD9n3nk254ZjuPQOIxWI8+eSTbNq0iRkzZnDhhRfKyAFC9BMJaUKIo6K1pq6ujpUrV7Jm\nzRoikQilpaXMGl3I2C33YVa/DYXj7Uts5Wf0d3VPDckEvHYXvPFzKBwLVz8IBaOPubhwOMxf//pX\nampquOSSSzjjDPk5CtGfJKQJIXotFouxatUq3nnnHVpbW8nKymLGsAymbP0NaZ07Yeon4IPfO+ab\n1cVR8NfDU7fYHRNPng+X/ARc3mMuLhgMsnDhQhobG5k3bx7jx/dueCghROpJSBNCHDPLsti0aRNv\nv/02u3btwuf1Mruwk2k77sXhy4KL7oKJHznmS2/iELYvhidusi9vXv5LOP2a4yrO7/fz0EMP0d7e\nzsc+9jFGjhyZoooKIY6HhDQhREpUV1fzyiuvsGPHDrLSvZzrWMHp7S9gjPggzPkdZBT3dxUHP63h\n3XvhX9+EvBHwsYXHdXkToK2tjYceeohgMMi1117L0KFDU1NXIcRxk5AmhEgZrTXbtm3jlVdeoa6u\njnyfyYfC/2R0WpN9xmf8lf1dxcErHobn/hdWPQqjL4O594L7+LrEaG5uZsGCBcTjcebPny99oAkx\nwBxtSJPxYIQQR6SUYvjw4VRVVbF+/XpeffVVHg1eyiirmUue+Bw5G1+AS38C7qz+rurg0lELj11n\nD9d17tfhnK/2elD0A7W0tLBgwQIsy+Kmm26iqEg6JxZisJIzaUKIXksmk/z3v//ltddeQyfjzLbe\nYVZGHc6r7oFhs/u7eoPDznfg8fn2mbSr7ocxlx13kW1tbfzlL38hkUhw4403SkATYoCSM2lCiD5j\nmiZnnXUWEyZM4N///jf/eR9WBoNctuB2Rpx7LZzzZTDM/q7mwLXkAXjhq5BdCTc+B4VjjrvI9vZ2\nHnzwQeLxuAQ0IU4SciZNCHHctm7dyvOLnqOltY0prOHCygTuj9wv44AeKBG1w9myB2HEh2Den8CT\nfdzFdnR08OCDDxIOh7nhhhsoLS09/roKIfrM0Z5Jk+6mhRDHbfjw4dz2mf/hrFmzWMFE7tk5gq2/\n/whse62/qzZwdDbAgg/bAW32l+Dax1IS0Px+PwsWLCAUCjF//nwJaEKcRORMmhAipaqrq3n2qcdp\nbu9kKmu48KwppF1wx6l9+bNmKTx2PUQ64Mp7YPzclBQbCAR48MEH8fv9zJ8/n/Ly8pSUK4ToW3Im\nTQjRL8rLy/n0Zz/PrBnTWcYE/vBWM9X3X2ufSToVrXgY/nIJmC645aWUBbRgMMiCBQvo6Ojguuuu\nk4AmxEmoX0KaUuqnSqkNSqnVSqlnlFLZ3bZ9XSm1RSm1USl1UX/UTwhxfJxOJxdefBk333wLePP4\nc8NoFv/m01ibXu7vqp04iRg8/xV49rNQOQtufQ2KJ6Sk6FAoxEMPPURbWxvXXnstlZWVKSlXCDGw\n9NeZtJeACVrr04BNwNcBlFLjgGuA8cDFwD1KqVP4GokQg1tFRQW3ff7LjB85lFfjk3nor4/Sseh7\nkIz3d9X6lr8eFlwO790PM2+H654Cb25Kig6Hwzz00EM0Nzfz8Y9/nGHDhqWkXCHEwNMvIU1r/W+t\ndaLr5X+BIV3Lc4C/aa2jWuvtwBbgjP6ooxAiNdxuN/OuvYkrL7+UWmMI9y4Js/6e+dC+q7+r1jd2\nvAn3nQMNa+Ejf4GL7gQzNb0dRSIRFi5cSFNTE9dccw3Dhw9PSblCiIFpINyTdjPwQtdyGVDdbVtN\n17qDKKVuVUotVUotbWpq6uMqCiGOh1KKSdPO4LbPfp7s7BweaxnDc7/9CrE1z/Z31VJHa3j7t7Dg\nCnvkhU+9ChOuSlnxkUiEhx9+mIaGBj760Y/KYOlCnAL6LKQppV5WSq3tYZrTbZ9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a22518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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d4XBtC7csHR/T02aEQ0QoSE+gID2By+fkEwwa1uyt4vmNh3h+0yFue3wD33li\nI0sn53DlvAIWj8vC4RBGTpjEuAUns/Kpx5h+1jkk+iIzBUY4XqmopbSplW+NHjFgx5iWnMDGek3S\nlBrKNEkLQ3l9C799bXvY2/flT15fOj33rdxwy+xDqQOz6YDE2pe+5NH+vBwOwe0UXA4HLntuMpdD\ncDkduJ2CQwSnQ3CIdXyHgMPhwCGCw17ukGPXOx1iv+64vsNrB3hdTj65sLAPZ/8hYwzGBIAgxgTt\n54CdIAcwxlpuCIDpuk3I5RgwPe0bxBC0tzm2jM7Lc11BrpsR5Nrpfg7WNLFxfwVbDhzhybeaeWe1\nYdrIOIrSnYw8tYZA2nb++9qNTDnpWnypc4mPzz+u96Qv/rKvnDyvm/My+3evzp5MS4rn1YpaGgNB\nEiIwMlYpNfg0SQvDlLxUdv34/GiHoVTE+f11bNnyXSoq3wQ7wTGdE6MQydhQU+iGwkIwOGkLuGlu\ndPF+vYfEuESSc+MIygY2b74VgPS0U8jPv5bMzDMQifzIyC31TbxVVc//jB6BewBrMacnxxMEttY3\nMdu+8bpSamjRJE2pIciqsQoefQZjvzZHkylrO2vdh8vtxmgTpKHhA7Zs/RYtLYfIyjoHlzPRSkrE\ngYgDcCDiRJAPl+Ow13dcHsY22GXa663Xzg6vu1vetewuy+1lVsxORLouF3HhcMThcLgxxrCytIrf\nvvoBb31whIKEIJftuJfRc/KZfuE49h94iPUbbiY+vojios+Rk3MRDkfkRr/+bf8R4hzCJ/IGti/g\nNLuv23pN0pQasjRJC0NDw3bWbwg1O3l3HY/6trz7PlR9XN7t4r6U010h3cTe5/egu80jVX6k3uOB\nLLv75e2JVsdkyyo+SMdEK1Li40cxZ/YjpKbOiliZsU5EmF+czv03LuC9nRX85LmtvHVgFsF33mP8\nous5+aTPUn7kRUpL/8jmLd9g567fMmbMreRkX9DnOdk629bQzMMHK7l6RDrp7oH9+h3pdZPmcrKh\nrnFAj6OUGjjSl07WsWru3LmmpKRkwMpvatrH9h0/7eNeob/Mu+1X1e2Xfx/L6bb8bjYPsaLvZUcq\n9u6KiVD5fSqnr2V3U3Qf30urNkis44jj6POHy+RoTVWXZVj90OhUhnU0h33+Hy53OrxWDZpreNey\n+ANB/vjKFiru+yF+dyIfv+OXTB7pwxjDkYpX2bnzV9TXbyElZRbjx32H1NSZx3WcoDFcumY77zc0\n8+aCiRG7DVRPrli7neq2AC/OmzDgx1JKhU9EVhlj5va6nSZpSikFzz2xjM0P3c0bIz7CN7/wcU4Z\nmwmAMQEOHvwPO3b+ktbWcgrgHHvoAAAgAElEQVTyr2P06Fv6nNz+80AFt27by10TC/j4iMGZ9uSH\nOw7w573l7Fg8LeIT5iqljl+4SZr+1iqlFHDOReeRVlDM/Ir3uPGed3ly7X4ARJzk5V3OSQtfIn/k\nNezddy/LV5zLocNP283PvStvbeMHOw5wki+RqwfxpufTkuJpM4ZtDc2DdkylVORokqaUUoA4HCy5\n7kbiW2s5W7bz1UfWHk3UAFyuJCZM+B5zZj+Cy5nEpk1fYcWKCygvf6nHufmMMXx1616aAkF+Nr6g\n3/3a+mK6PXhgg86XptSQpEmaUkrZCqfNpHjWXMYefI+T8uP46iNreXrdgWO28fnmMn/+MqZM/hWB\nYAvrN3yWkpLLqKh4K2Sy9pd95bxcUcvtY/MYlzi4t58qiveQ5HTonQeUGqI0SVNKqQ4Wf+IG2pqa\nuT5+B3ML0/nKI2t5bWvZMduIOMjNvYiFC15g0sSf0tpWwdp117Nu/Y00Ne09ut26ukZ+uOMgZ2em\ncOPIzME+FRwiTE6KZ6vWpCk1JGmSppRSHWQWFDJ58Rlsfu0Ffv/RcUzMTeYLD65m84HaLts6HK6j\n/dXGjf0fqqtLeG/5OZTu/hMVLc3cvKmULI+LX00cNajNnB1NSIxja0Nzn26XppSKDZqkKaVUJ/Mv\n+Rj+tla2vvwM91w3j+Q4N5+6dyWHakJ3wHc4vIwa9SkWLniBjPRT2bbjLq5c/gIHmlu5e3LhgM+J\n1pMJiXFU+wOUtfqjFoNS6vhokqaUUp2k5+UzfsEprH3hGXwuP/dcP5fa5jZuur+EFn/3t8WKixvB\n1Kl/4FHfPWwMFHITf6Sg6cVBjLyriXY/uK06wlOpIUeTNKWUCmHBpVfQ2tTI2ueXMSUvlbuumMn6\nfTX8+NmtPe732z3lPF2TxJfzEzg3pY7NW77Otve/TzDYNkiRH2uCnaRta9B+aUoNNZqkKaVUCNlF\noymeNZdVzz1FW3Mz50zN5YZTirj33VKe33gw5D5PllXx410HuSwnjdvGjmPWzH8wquBG9u37B2vW\nXktbW9d+bQMty+Mm3e3UmjSlhiBN0pRSqhvzL/kYzXW1bH7rVQC+de4kZuSn8vVH17On4th7Yq6q\naeBLW/YwPzWRuyZY86E5HC7Gjfs2UybfRU3NGtasuYbW1spBP4+JifE6oa1SQ5AmaUop1Y2REyaT\nVTSatS88gzEGj8vB7z4+G4AvPrSaVr91x4GNdY1cu2EXuR43f5taTJzz2K/W3NyLmTH9TzQ0bmf1\nmo/T0lLW5VgDaUJiHNt0hKdSQ44maUop1Q0RYeZHzufI3t3s37oJgIL0BH5++QzW7avhx89t4e2q\nOi5Zsx2vQ3hwxmgyPaFHcmZknMaMGffQ3LyfzVu+MZinwcTEOOoDQfa3RKdfnFLq+GiSppRSPZi0\n6DS8iYmsfeGZo8va+6f9dfshrly7g/w4D8tmj2NMQs93FEhPO4ni4i9RWfkWVVUrBjr0oyboCE+l\nhiRN0pRSqgdubxxTTz+LD1a8S33Vh/3J5szPwz8jHUdNK38ZW0BenCes8vJHfhKvJ4cdO385aM2P\nH47w1CRNqaFEkzSllOrFjKXnEQwE2PDKCwC8XlnL57bsYVJCHAlrK7nzyU1hJ1xOZxxFxV+gpqaE\niso3BjLso9LcLnI8LrbqNBxKDSmapCmlVC/SRoykcPosNrz2Ijvqm7hhwy7GJnh5bM44vnnWBF7b\nVs6/V+0Lu7y8EZcTF1fAzh13YUxwACP/UPvgAaXU0KFJmlJKhWHKaUuoO1LODza8DwgPzhhDmtvF\n9ScXMb84nR8+vZn91eHVVDkcHkYXf4m6+k0cqXhtYAO3TUyM54OGZoI6wlOpIUOTNKWUCsPYeQup\nyh3Fi01BbszPJNfrBsDhEH5x+QzagkHufGZL2OXl5FxInDePPXv+OlAhH2NCYhxNQcPuptZBOZ5S\nqv80SVNKqTC4vXGsOfMSPG0t3JTrO2bdqIwEbl48hmc2HGRlaXiT1TocbgoKbqC6egU1tesGIuRj\njLcHD2xv1CZPpYYKTdKUUioM6+oaWZWSzZx171C5rqTL+ptPG01OipcfLttMMBhek2Je3hW4XMmD\nUps2Ot4LwM6mlgE/llIqMqKapImIT0QeFZGtIrJFRE4SkXQReUlEPrCf06IZo1JKGWO4c8dB0lxO\nTtu7lS1vde1HluBx8Y2zJ7J+Xw1PrtsfVrkuVxIj8z5OWdnzNDXtiXTYx0h3O0l1OdnRqEmaUkNF\ntGvSfgM8b4yZCMwAtgC3Aa8YY8YBr9g/K6VU1Dx/pIY3quq4pSiXWQtPZtfaVTTWVHfZ7tJZI5me\nn8rPnt9Gc1sgrLILCq5DxMmevX+PdNjHEBFGx3vZpTVpSg0ZUUvSRCQFWAzcA2CMaTXGVAMXA/fZ\nm90HXBKdCJVSCpoCQf53+34mJsZxw8hMJi8+ExMMsvH1l7ts63AIt507kYM1zTy4PLyaMa83h+ys\nszl06CmCwYHt1D8mwctOrUlTasiIZk3aaKAc+LuIrBGRv4pIIpBjjDkIYD9nh9pZRG4SkRIRKSkv\nLx+8qJVSw8rv9hxmX3Mbd4wbicshZBYUMmrqDNY89xQBf9d7YZ48JpOTRmfwh9d30NQaXm1abu7F\n+P3VVFa+E+nwjzE6wcv+ljYaA4MzN5tSqn+imaS5gNnAH40xs4AG+tC0aYz5szFmrjFmblZW1kDF\nqJQaxkqbWvjdnjIuyfZxSlry0eVzL7iU+qpKtv337ZD73fqR8Rypb+H+90rDOk56+iJcLh+HDz8d\nibC71T54oFSbPJUaEqKZpO0D9hljlts/P4qVtB0WkREA9nNZlOJTSg1jAWP4ypY9eES4fUzeMeuK\nZswmfWQBq5Y9EfJ2UHOL0lk8Pou739hJfYu/12M5HB6ys8+h/MhLBAKNETuHzsYk2CM8tclTqSEh\nakmaMeYQsFdEJtiLlgCbgaeA6+xl1wFPRiE8pdQw9+e95bxX08CPxuV3uXm6OBzMOf8Sykp3sHfT\nhpD737J0PJUNrdz/391hHS835yICgUbKj7zS79i7o9NwKDW0RHt05xeBf4rIemAmcCfwE2CpiHwA\nLLV/VkqpQbOtoZmf7DrIOZkpXJEbehagyaeeQXxKKque+U/I9TMLfJw6LpN7391Fq7/3PmA+3zy8\n3lwOH17Wr9h7kuhykuNx6TQcSg0RUU3SjDFr7X5l040xlxhjqowxFcaYJcaYcfZzeNN3K6VUBDQG\ngnx+824SnQ5+PqEAEQm5ncvjYeZHzmfn6pVU7N8bcpsbFxVzuLaFZzYc6PW4Ig5yss+nouIN2tq6\nTu8RKaN1hKdSQ0a0a9KUUipmGGP4+ra9bKpv4jcTR5Hlcfe4/cyPnIfT7Wb1s6F7ZZw2Potx2Un8\n9a1dIfuudZaTcwHGtHHkyMDddH1MfBw7mvTWUEoNBZqkKaWU7c/7ynnscBXfLM5laWZqr9snpPqY\nvPhMNr/xKo21NV3Wiwg3Lipm04Fa3tvZe6NAcvJU3O4MKirfPK74wzE6wUtlW4Dqtt4HNCilokuT\nNKWUAt6srOP72w9wflYqXy7MCXu/Oeddgr+tlXUvPRty/SWzRpKe6OGet3f2WpaIg4yMU6msfAtj\nwptjra+OjvDUwQNKxTxN0pRSw97uphZu3lTKuMQ4/m/iqG77oYWSkV9A8ay5rH3hGfytXe8YEOd2\ncs2CUbyytYw9Fb1Pr5GRfhptbVXU1m3s0zmE6+gIT+2XplTM0yRNKTWsNQQC3LBhF0Hg3qnFJLqc\nfS5jzvmX0FhTzdZ3QzdTXjV/FAD/XhV6gEFH6emLAKGiYmCaPAvjPThAR3gqNQRokqaUGraMMdyy\ndS9bG5q5e3IhxXZTYF+NmjqDtBF5bH4j9Bxneb54Fo/L4tFV+wgEex5A4PGkk5IyncqKN44rlt54\nHA4K4jza3KnUEKBJmlJq2Pr9njKeLKvmW6NHcEZGynGXIyJMPvVM9m7eQG156JukXDmvgIM1zbz5\nQe/3Gs5IP42a2nUDNhVHUbyXPU0DezN3pVT/aZKmlBqWXq2o5Y6dB7ko28cXRmX3u7xJp54BwOa3\nQk+fcdakHNITPfxrZe9NnhkZi4EglZWh7w3aX9leF2WtXW8Or5SKLZqkKaWGnV2NLfy/zbuZlBjH\nryZ2P2FtX6Rm55A/eSqb33w15JxoHpeDy2aN5OUth6mo77mpMSVlOi6Xb8D6pWV73JS3+sOau00p\nFT2apCmlhpVDLW1cuW4HToG/Tysm0dn3gQLdmbz4TKoO7ufQ9vdDrr9yXgFtAcN/1uzvsRwRJ+np\nJ1NZ9c6AJFI5HhetxlDtH5hpPpRSkRFWkiYiY0TEa78+XUS+JCK+gQ1NKaUiq6rNz1XrdnCkzc8D\n00dTGH98AwW6M37BIlxuD5vefDXk+nE5ycwo8PHE2p6TNIA03wJaWg7R3LwvojGCVZMGUNaqE9oq\nFcvCrUl7DAiIyFjgHqAYeHDAolJKqQir9Qe4Zv1Odja2cN/UYmanJEb8GN6EBMbOP4lt77xBwB+6\nz9eF00ewcX8tO8vreyzL55sHQHX1iojHmeVxAVCu/dKUimnhJmlBY4wfuBT4tTHmq8CIgQtLKaUi\n50irn8vXbGd9XRN3Tynk1PTkATvWhJMX09xQz56N60Ouv2B6HiKwbP3BHstJTByHy+WjqnplxGPM\n8Vo1aYdbNElTKpaFm6S1icjVwHXAMntZz3ceVkqpGHCguZVL13zA+43N3DutmPOyBranRtH0WXji\n43n/vdAjM3NT45hXlM6y9Qd6LEfEgc83d0Bq0rS5U6mhIdwk7QbgJOAOY8wuESkGHhi4sJRSqv9W\n1zZw7qr3OdjSxkMzxrCkH3Ohhcvl8TBmzgK2r3yPgD90EnTh9BG8f7iebYfqeiwrzTefpqbdtLSE\nnnvteCU7HcQ5RKfhUCrGhZukLTXGfMkY8xCAMWYX0DRwYSmlVP88eqiSS9dsx+tw8PTscZzkSxq0\nY49fuIjm+jr2blwXcv2500bgEHh6Xc+1aR/2S4tsk6eIkOVxa02aUjEu3CTtuhDLro9gHEopFREN\n/gC3bN3DF7bsYU5KIs/NGc+kpPhBjaFoxmw88fFse++dkOszk7ycPCaTp9cf6HGKjaSkyTidiRFP\n0sCahkNr0pSKbT0maSJytYg8DRSLyFMdHq8BFYMTolJKhWd1bQNLS97noYOVfGlUNo/MGEOGPZJx\nMLk8HkbPns/2lf/ttsnzgukj2F3RyKYDtd2W43C4SE2dPWD90rQmTanY1ltN2rvAL4Gt9nP741bg\nnIENTSmlwlPrD/Ct9/dx/qoPaA4GeXTmGL49Jg+3o/93Ejhe40+ymzw3bwi5/qzJOYjAq1t77m/m\n882jvmFbxO/jmeVxUaajO5WKaT0macaY3caY140xJxlj3ujwWG1PyaGUUlHjDxr+eaCCRcu3cO/+\nI3xqZCavz5/IKWkDN8VGuIpnzMEdF8/2Fe+GXJ+Z5GVmgY9XthzusRyfbz4A1dUlEY0vx+umyh+g\nJRiMaLlKqcgJ944Dl4nIByJSIyK1IlInIt3X0Sul1AAKGsOz5dWcuXIbt27bS36ch+fmjOeO8fmk\nuCJ3m6f+cHk8FE6bwa61q7rtd7ZkYjbr9tVQVtfcbTkpydNxODwRb/Jsn4bjiDZ5KhWzwh048DPg\nImNMqjEmxRiTbIwZ+LHsSinVQUswyMMHKzhtxVY+tbGUgDHcM7WIZ2aPY2ZKQrTD66J41lxqy8uo\n3L835PozJ+YA8PrW8m7LcDq9pKTMjPjggWy7r95hHTygVMwKN0k7bIzZMqCRKKVUN0qbWvjRjgPM\nencTX9m6F49DuHtyIW/Mn8j5WT5Eotf3rCfFM+cCsHNN6KbKSSOSyUuN45WtvTV5zqOufhN+f0PE\nYmuvSSvXmjSlYlaPw55E5DL7ZYmIPAI8AbS0rzfGPD6AsSmlhrHdTS08VVbN0+XVrK9rwilwdkYq\n143MZHFaUswmZh0lZ2SSNaqIXatXMu/Cy7qsFxHOnJTN46v30+IP4O2mqdbnm09p6e+pqV1DRvqi\niMTWXpOm03AoFbt6G5t+YYfXjcBHOvxsAE3SlFIR0RY0rK9r5O2qep45YiVmALOSE7h9TB6XZPvI\ni/NEOcq+K541l5Jl/6GlsQFvQtebui+ZmMMD7+3hvZ2VnDY+K2QZqSmzEHFSXb0iYklaZntzZ4vW\npCkVq3pM0owxNwxWIEqp4aUpEGRLfRPvVtfzTnU9K2oaaAhYIw1npyTw3TF5XJDto2AIJmYdFc+a\ny4onH2X3hrWMX3BKl/Unjckgzu3glS2Hu03SXK5EkpOnRrRfmsfhIN3t1Jo0pWJYWLM8isj/hVhc\nA5QYY56MbEhKqRNJ0BgOtbSxo7GFTfVNbKxvYkN9E9sbmwnYgx7HJXj5WG46p/iSOMmXdLSW50SQ\nN34S3oREdq0pCZmkxbmdLBydwbs7ep4f3Oebx759/yAQaMHp9EYktmyPW/ukKRXDwv0mjAMmAv+2\nf/4osAm4UUTOMMZ8ZSCCU0rFPmMMFW0BDra0crCljQMtbexvbmVnUwu7GlvY1dRCU/DDKShyPW6m\nJsdzXmYqU5PjmZeSSLbXHcUzGFgOp5PCGbPZtaYEEwwijq7jteYXp/P6tm1U1LeQkRQ6AfP55rNn\nz1+prVtPmn1Pz/7K9rh0dKdSMSzcJG0scGb7BLYi8kfgRWApEHo6baXUkNIWNFT7/dT4A9S0Bajy\nB6hp89vPAWr8Aar8fmraAlT7A1S3Bajx+6lqC9DaaR4wl0BhnJfiBC+npiVTnOBldLyXSUlxZHlO\n3ISsO8UzZvP+f9/iyL49ZI0q6rJ+flE6ACtLqzhnam7IMnypcwCorl4RwSTNzc6a+oiUpZSKvHCT\ntJFAIlYTJ/brPGNMQERaut+tdyLiBEqA/caYC0SkGHgYSAdWA580xrT25xhKqe7dvaeMX5Qeoj7Q\n88zzSU4HqS4nPrcTn8vFuEQvPlcCPreLEV43eV43I7we8rxuMj0unENg9OVgGTV1BgB7N60PmaRN\ny0/F63KwsrSy2yTN7faRlDghov3S2ps7jTFDYrSsUsNNuEnaz4C1IvI6IMBi4E4RSQRe7mcMXwa2\nAO2T4/4U+JUx5mERuRu4EfhjP4+hlOrGezX1xDkcfG5UNqkuJ2lul5WM2QlZqsv6OZr3wRzqUrKy\nSc3OYc/G9cw+96Iu670uJzMLfKwsreyxHJ9vPgcPPU4w6Mfh6H+/vWyPi5agodYfINV94vQDVOpE\nEdZktsaYe4CTseZJewJYZIz5qzGmwRjz9eM9uIjkA+cDf7V/FuBM4FF7k/uAS463fKVU7xoCQYrj\nvdxSlMuN+VlclpPGkowU5qQmMiYhjkyPSxO0CCiYMoN9WzYQDAZCrp9fnM7G/TXU9zAlRmrqbAKB\nBhoatkUkpva+gId18IBSManHJE1EJtrPs4ERwF5gD5BrL+uvXwPfANrbWTKA6g43b9+H1dQaKrab\nRKRERErKy7u/pYpSqmf1/iBJrnBvPqKO16gp02hpaKC8dFfI9fOK0gkaWL27qtsyfD7rDgbVNasi\nEpNOaKtUbOutfvsW4CbglyHWGaxar+MiIhcAZcaYVSJyevvibo7TdaExfwb+DDB37tzQdy9WSvWq\nIRAkL274deY/Hi2BFl7Z/Qov7n6Rww2HqWyupMHfgAMHIoJTnIgIDnEcXeYQBw5x4G2ymiN++K9b\nyD19Pp+Z9hlyEnOOlj27MA2nQ1hZWsnibuZL83pH4PXmUlO9ioL8a/t9Pnleaw66/c2apCkVi3qb\nzPYm+/mMATj2KcBFInIe1hQfKVg1az4Rcdm1afnAgQE4tlLK1hAIkOQMfTsiBYFggNVlq3mh9AWe\n2/Ucta215CbmMsY3htG+0SS4EjAYgiZI0ASPfW0MARPAGEOQIG2+HWQfcfLY+4/xxPYnuHLCldw8\n42ZSPCkkeV1MyUthxa7u+6WJCKmpsyNWk5Yf50aA3c39Gv+llBog4U5mm4BVqzbKGHOTiIwDJhhj\nlh3vgY0x3wK+ZZd/OvA1Y8wnROTfwOVYIzyvA3SyXKUGUEMgSKJTmzs7qmquYvnB5bxz4B3e3v82\nR5qOEOeM44yCM7hs/GXMz52PQ/r+nr38we/Z/NbrPHnhE/xp0595YMsDLNu5jK/M/goXj72YeUXp\n3P/e7p7v45k6h7KyZ2luPkBcXF6/ztPjcJDndbOnSQfQKxWLwh3O83dgFVZtPVh9xf4NHHeS1oNv\nAg+LyI+ANcA9A3AMpRTWRLT1gQBJwzxJM8awqWITr+55lXcPvMvmis0YDCmeFBaOWMjSwqUszl9M\ngjuhX8cpmDKDdS89h6u8iTsW3cE1k67hzuV3cvu7t/PE9ic4J+9WWv1BNu6vYU5hesgyUu350mpq\nVvc7SQMojPdS2qQ1aUrFonCTtDHGmCtF5GoAY0yTRHBSHWPM68Dr9uudwPxIla2U6l6rMfgNJHVT\na3OiK2ss46GtD/HcrufYX78fpziZkTWDz838HKfkncLkjMk4HZF7bwqmTAOs+dLyxk9kUsYk/nHu\nP3hi+xP8dOVP2VZ1M67ki1i3d3K3SVpS0iQcjniqa1aRk3NBv2MqivfwUkVtv8tRSkVeuElaq4jE\nY3fiF5ExgP7rpdQQV++3BlYnDLOatK2VW/nnln+ybOcygibIKXmn8NkZn+WMgjNI9aYO2HETUlLJ\nGlXE7g1rWXDpFYDVz+zScZcyN2cut711Gw35D/J4aTXXn/LjkE2qDoeL1JQZ1ESoX1phnJfyVj8N\ngQCJ2jdRqZgSbpL2XeB5oEBE/onV6f/6gQpKKTU4GgLWnF3DobmzqrmKl/e8zOPvP87Gio3EOeP4\n2PiPce3ka8lPzh+0OApnzGb1s0/R2tyEJy7+6PKClALuPfdezvnHrewOPMvX3mjjzkV3EueK61JG\nqm8Ou3ffjd/fgMuV2L944q0RnnuaWpmUFN/L1kqpwRRuknYt8AzWJLM7gS8bY44MWFRKqUHRYN8K\n6kStQTnSdIRX97zKi7tfpORQCQETYKxvLLfNv40LRl8woLVm3SmeOYeSpx9n76b1jJmz4Jh1boeb\nC0Z+nj+uSeBlnuVI0xH+sOQPJHmSjtnOlzqHUhOgtnYt6emn9Cuewnjrhu67NUlTKub0ZeDAIqwb\nqo/GukXUm8aY3wxYZEqpAdeepJ0oNWnN/mbWl6+n5HAJyw8uZ03ZGgyGopQiPjX1U5xVeBaT0idF\n9T6VeRMm4/J6KV23ukuSBjA930frK6fy1TPm8+ctP+Sml27i7qV3k+JJObpNaqo1l3hNzZoIJGlW\nTZpOw6FU7AkrSTPGvCoibwDzgDOAzwJTAE3SlBrC6u3mzqE4BYcxhv31+9lWuY1NFZtYdXgVG45s\noC3YhkMcTEyfyP+b8f9YWriUMb4xMXMDcZfbzagp0ylduzrk+mkjrdo9T8ss7jr9Lm554xY+/cKn\n+ctH/nK05s/lSiY+vpC6+s39jifN5STZ6WC3TsOhVMwJd560V4BE4L/AW8A8Y0zZQAamlBp47QMH\nYnl0pz/o52D9QfbU7WFP3R5Ka0rZVrWNbZXbqG+rB8ApTialT+KaSdcwN3cus7JnkexJjnLk3Sua\nMZudq1dSdegAabnHTqORnRJHToqXjftruHHRGfzmjN/w5Ve/zM9W/ow7Ft1xdLvk5CnU1m7odywi\nQlG8V5M0pWJQuM2d64E5wFSgBqgWkf8aY5oGLDKl1ID7sE/a4NekGWNoDjRzpOkI5Y3llDWVUd5Y\nbj2arOdDjYfYX7cfv/nwBuAJrgTGp43n/NHnMzF9IhPTJzLGN4Z419DpT1U005rrrHTd6i5JGli1\naRv21wCwOH8xN0y9gb9s+AsXjrmQhSMWApCcNJmysmdpa6vF7U7pUkZfjIr3sK2huV9lKKUiL9zm\nzq8CiEgScANWH7VcwDtwoSmlBtqHzZ2ha9KMMbQGW2kJtNDib6El0EJroJXmQDOtAXu5/Wj2d13W\nGmiloa2B2tZaalpqqG2ttR4t1nNbsOs9Iz0OD1kJWWTFZzEhbQJLC5cyKnkUo1JGMSp5FJnxmTHT\ndHm80nLzSM3JpXTdamad3XWus2kjfbyytYz6Fj9JXhc3z7iZF3e/yA/++wMev+hx4lxxJCdPBqC+\nfjNpaQv7FU9hnJeXjtQSNAbHEH9vlTqRhNvc+QXgVKzatN3A37CaPZVSQ1ijXZN28wvX4g80hEzC\n+sMlLuJd8aR4U0jxWI9sX7b12l6WGZ9Jdnw2WQlZZCdY64Z6EhaOohlz2PzGKwT8bThdx97gflp+\nCsbA5gO1zC9Ox+v0cvvC27nxxRu5e93dfGXOV0hKngJAXV3/k7SieA+txnCopY28OE+/ylJKRU64\nzZ3xwF3AKvvG50qpE0B9IIiYIIca9rAgdz5xzjg8Tg9epxevy2s9d3h4nJ5jt+m43BXXZZnLEe5X\nzPBTNH0W6158hoPvbyN/8tRj1k21Bw9s2F/D/GLrzgPzR8znojEX8Y/N/+CaydeQGZ+Jx5NNXf2m\nfsfSPg1HaVOrJmlKxZBwmzt/PtCBKKUGX0MggINW5mbP4a7T74p2OMNK/qSpIMK+LRu7JGnZyXHk\npsSxYV/1Mcs/M+0zPLXjKf617V98bubnSE6eTF1d/0d4dpyG42SSetlaKTVYht64e6VUxNT7gxBs\nIicxJ9qhDDtxSUlkFRSyb2vomrCpI1PZeODYe2oWpRaxOH8xj2x7hJZAC8lJk2ls3EEg0L9O/yO9\nHpxi3XVAKRU7NElTahir9bdCsJGcBE3SomHkpKkc2LaFgL9rL5KJucmUHmmgxR84ZvknJ3+SyuZK\nnt35LMnJUzAmQEPD+/2Kw+0QRno97G7WJE2pWKJJmlLDWGVrMxJs1pq0KMmfNJW2lmbKdu3osm58\nbjL+oGHXkYZjli/IXXgozoAAACAASURBVMD4tPHcv+V+kpImAVBXF4l+aR5Km/SuA0rFEk3SlBrG\natpaEdOiNWlRkj/JGqG5b8vGLusm5FiT8W47VHfMchHhmknX8EHVB6yt2o/LlRyROw8UxHnYrzVp\nSsUUTdKUGsbq/H4k2ERuQm60QxmWEn1ppOXlh0zSijMTcTmE9/9/e3ceH0d5H37888zM3qtbsm7J\n8oVtsJFBXAaCHY5SwhWOJJAUk9AmaZrmaH5poOmrJWmbtr80ebUpbVqSwI8riSGhXCHmSMqRQACD\nTQzGgE9ZsmXdx6605zy/P3YlS9bqXnlX3u/79ZrXzM48M/Odx5b2q2dmnufIwLhtly25jDxnHk/u\nexK/Pz0vD5Q7HXREYsRsPedjCSHSQ5I0IXLYYNxG6RCLfIsyHUrOqll1Mq27dmLbY589c1oGDaU+\n3m0LjNvHZbq4oOYCnmt5Dp9/JYHALrSOjys3E5UuBzbQGZVeloTIFpKkCZHDhmyFW2lcpgwekik1\nq04hPBiks/nAuG0rKvJStqQBXFh3IX3hPjrjHmw7RHBw75ziqHAlOtQ9HB4/CoQQIjMkSRMih0W0\nkdWDq+eCmlWJPtImei6tuXuQwcj41q31VetxmS5e6z0CQGCOtzzLk0naEUnShMgakqQJkaPiWhNX\nDgos6WE+k/JLy8gvK0+ZpK1Ivjywu338LU+vw8v6qvX8smUbhuGc8xueFc5EktYWkSRNiGwhSZoQ\nOSqYHLezyOnOcCSicvlJHN49vq+zkypSv+E57MK6Czk82I7hqpvzG56lTgtTSUuaENlEkjQhclRP\nZAiAEpc3w5GIymUrCHR1EuztGbO+rtiLyzImfC5tQ+0GTGXSHncxMLATrWf/ZqapFIucDnkmTYgs\nIkmaEDmqOdAJQJlLxmrMtPKlywFo2zO2Nc00FMvL/bx7ZPztToACVwFN5U1s7+smFusjFDo0tzic\nDo7I7U4hsoYkaULkqIPBRJJW7inIcCSifPFSlDJo2/P+uG0rFuXx3gS3OwE21m3kzf5uAAKBOT6X\n5rJok5Y0IbKGJGlC5KjWwcQXe7W3KMORCIfbTUltXeokrSKPtv4QfYOpk6ezKs7iUNRAo+bcqW2F\nyyktaUJkEUnShMhRR4b6AKj2lmQ4EgFQsXQ5bXveH/dc2fDwUO+1p25NW1q4lHxXKUH8c355oMJp\n0R2NE0q+VCKEyCxJ0oTIUe2hxHNOpW55cSAbVCxdTmign/6OI2PWD7/hufNQf8r9lFKcWXkm+0Px\nOXfDMdJXmrSmCZEVJEkTIkd1RQYB8JnyayAbVCxdATDulmdlgZuyPBfbD/ZOuO/ZlWezOxQlHG4j\nEumefQxO6dBWiGwiv52FyFE9kRAAflNGHMgGpXX1mJY1LklTStFYWzhpknZW5Vm0RhK/zudyy3N4\naKi2FCMcCCGOP0nShMhR/dEIAF5pScsKpuWgbPGScd1wADTWFrKvM0jvYCTlvtX+amxnNQAD/eNH\nLpiukSQtnPo8QojjK2O/nZVStUqp/1VKvaOUelsp9cXk+mKl1DNKqfeTc3n1TIg0i8ajBG2Ngzim\nUpkORyRVLF3Okb17sO34mPXragsBJm1Na6w4l9aoReuhn2Db4Vmdv9AycRmKtrC0pAmRDawMnjsG\nfEVr/YZSKg94XSn1DHAz8Cut9T8ppW4FbgW+lsE4iff1EXzppdQbJ/2Cm2DbRPtMdKgJyqsJjzPD\n9ZOdPCtjmlms6YtpkljTFZNpogwjMTfNsZ9Hzy0r9fpjtkfiEQLRAMFIkIHoAMFokN5wL839zWjl\nwm3Mvod6kX4VS1ew/alf0HOolZKaupH1a2oKUArePNjHhpMWpdz3zIoz+VHzg3zO0cLBlvuor/vj\nGZ9fKSUd2gqRRTKWpGmtDwOHk8sDSql3gGrgKmBDstg9wHNkOEkbPHiA1i//RSZDEGJW4gpsA+IG\nxEyImuC0YLEJp37s8xw8VVrRskl5w1IA2vftGZOk5bkdLF/kZ/vBnol25czKM/la2CToaGD//v+g\nqvI6HI7CGcdQ6ZKhoYTIFplsSRuhlFoMrANeAcqTCRxa68NKqZR/NiqlPg18GqCuri5VkbRpKYEv\n/8n4h6vVJI0QE371TbDPhG03M2zomKj8pF/FJ0JM6TrOLBqW1ATjJc4mJsMGQx+dmzaYWuHEwqHM\nxJyjc4c2cWDgwMQisWxpAzcOXIYDJw5cWDgxcdoGvhg4bQNXXGFqN/mBwZlfsJg3RVU1mJZF+4F9\nrDp/45htjbWFPLPzCFrrlC2xpZ5Szqo4i/uO7OSzxQH27/9Pli//qxnHUO5y8PbA0KyvQQiRPhlP\n0pRSfuDnwJe01v0T3gY6htb6TuBOgKampnm9Z1NVXM/nrv5Wym1q8lRjbNkU1zbR/qnWT1Q3KY8x\n4d23+TnfhPWQMrR5imEGz1ZNGMMc/40mul7LsDCUganMlMuWsjANE1OZmIaJpSycphOn6cQy5ufH\nNPyTx3F2dU74pS+OP9OyKKmpp+PAvnHbGmuLeHBrC83dg9SX+FLu/+en/TmfePIT9FWezMGW+6it\nvRm3u2pGMVQ4HfwqkrpPNiHE8ZXRJE0p5SCRoD2gtX44ufqIUqoy2YpWCbRnLsKEAlcBVy69MtNh\nCJFW4ZIyfO++Q/jdd3GvXJnpcERSWf1i9m1/fdz6xlEvD0yUpJ1adioX1l3Ifx/8LX9ZHudA852c\ntOL2GZ2/3OUgGLcJxOL4LemeRYhMyuTbnQr4EfCO1vq7ozY9BmxKLm8CHj3esQmRC0J+P+5ImP6n\nnsp0KGKUsvoGBvt6CfaOff5sRbkfj8NkW/PEb3gCfGHdF2iLROi0lnHo0IOEI50zOn9lshsOeS5N\niMzLZAdJ5wJ/BHxQKbU9OV0G/BNwsVLqfeDi5GchRJoFUeTn5TGw5alx40WKzCmrbwCgo3n/mPWW\nabCmumDSbjgAlhQu4aqlV/Gjg63YdpSDzT+a0fnLnYkbLPKGpxCZl7EkTWv9G6210lqv1Vo3Jqcn\ntdZdWusLtdbLk/PZj3EihJhQMB6nsLqSyL59hN9/f+odxHFRWrcYIOVzaacvLuKt1j4CU/Rj9plT\nP0N7TNFjLaGl9QGi0ckTu9EqpCVNiKwhXY0LkYO01gRiNkX19aAU/Y8/Try/n3ggiB0KoaNRtG1n\nOsyc5M0vwF9UnDJJO395KTFb8/KerkmPUe2v5pLFl3Dv4U7i8SAHW+6d9vkXJcfv7JShoYTIuIy/\n3SmEOP5CtsYG8vL8eM84g64f/JCuH/xwfEGlEh3jju4k1zTBMlFGssPd4Y51LRNlWkc74R0uZ1oo\n0wDTQrmcGC43yu3CcLlQI8tj1xk+H4bfh5mXh+H3Y/j8mH4fyuvNiTdRy+ob6EyRpDXVF+N1mjz/\nXjsXry6f9BifOuVTXL/vlwQdS2ltfYDF9Z/FMJxTnttvGjiUojsqSZoQmSZJmhA5KBBPDDvkMw0q\nv/kNAi/+Buw4OhZH23GIJ5fjMYjbiXksnmhdi8eO2RY/us6OJ8rFk8eIJ8rpcHI5HMYOh9DhCDoU\nwg6H0aEQTPeZOMPAyMvDKizELCnBLC7CKh49L8YqK8NRVYmjvBzlnDopyUZl9Q0c2PEm8VgU03KM\nrHdaBuuXlvD8ex1Tdp2ysngl51adyyMd2/h4YSft7VuoqJj6LXWlFMUOky5J0oTIOEnShMhBg/HE\nrUyfaeKsWUzx4sUZi0VrDdHoSMJmh8PYwUHswAB2IEA8EMAOBLEDA4nl/gHiPd3EunuIHmhmaPub\nxLu74djbs0olE7YqHNXVOJc04Fq6FGfDEpyL6zFcrsxc8DSU1jdgx2N0tRxk0eIlY7Z9YEUZz77T\nzv6uQRpKU3fFMexTp3yKP376U3yspISW1vunlaQBlDgsaUkTIgtIkiZEDojZmj1DYXYFh9gVCPFG\nf2KkAb+V+cdSlVLgdGI6nZCXN6tjaNsm3tdHvLubWHs70UOHiR46lJgOH2Zo2zb6f/GL0SfFUVeL\ne9Vq3KuT08mrsYqK0nRVc7No+A3PA/vGJWkXrCgD4IX3OqZM0s6oOINVJSfzUrCF8+OvMzDwDnl5\nq6Y8f7HDoisSn7KcEGJ+SZImxAKltSYYt+mOxuiNxemNxumJxeiKxDgUjnI4HKU1FBlZjiZvKZoK\nlnhcXFNexFkF/gxfRXoow8AqKsIqKsK1dGnKMvbQEJH9+wnv3Utkb+KN1tDbbzOwZctIGauyMpm0\nrcJzaiPedY0YvskToflQVFmN6XCM64YDoL7ER32Jlxfe62DT+sWTHkcpxUdP+ij/9PLfcH6tk5bW\n+1i1MvXoKaOVOC3ekqGhhMg4SdKmIRS3ORiKjFmX6gma1OvGr53O4zfTPn6Kg01n39THmm4c0ys4\nrXOmjGN215TynCnjmt7xAeIabK2Jk5jbGuLokfU2ENeaeHLZ1owsx7VO7KtJbtPEtCZiJ+daE7M1\nUZ2ckstjyhwzHy7XF4vTG4sRmyBwh1JUuhxUuRw0FfiodjlY4XOzyudmmdeN28x8C9rxZng8uFet\nwr1qbEtSvK+P0Du7CO3cOTIFfv3rxH8ey8Jzyil4zzgD75ln4j39NAyvd/5jNU1Ka1MPDwWJ1rSH\ntrYQjsVxTTEqwKWLL+Xbr32bVnwYbY+xbOmtOBz5k+5T7LDkmTQhsoAkadOwezDERVvfy3QY4gTi\nVArLUIm5UjiNY+bJ7Q6VmLyOxBt3juS6fMuk0DIpclgUOkyKrOTcYVHsMClxWBg58BZkOpgFBfjO\nPgvf2WeNrIsHggxt387gq68y+NprdN19N10/+AHK6cR7ztnkbdyIt6kJ55IliTdb50FpbT0Hfr8t\n5bYPLC/j3pcP8Pr+HtYvK530OF6Hl8uXXM7P9z/IFxYNcaT9CWqqb5x0nxKHRW8sTszWWIb8PxIi\nUyRJm4Yat5P/Wl0/rbKpvhdTD0g++eeJjzXddakGIJ96v1RSxzb1NaVaN/3rnN3xJzre9I41fq2p\nwFQKAzCUwlSJuUFyvQKT5PyY9QZq3P6O5DFyoRuJhcz0+/Cfdy7+884FwB4cZPCNbQRffIGBX/2a\ntudfAMDw+/GsXYP71FPxrF2L59RTsYqL0xJDUVUNbz//K8KDg7iOab07Z2kJpqH47Z7OKZM0gOtP\nup6fvvsTomYpbW2PTJmkFTsSrXM9sRhlTsekZYUQ80eStGkodFhcXZ4dDxQLIY4/w+sdSdoW3Xor\nkX37Gdq+naHfv8nQm7+n684fQLJbE0dtLd7T1uH7wAfwn3ceZkHBrM5ZXFUNQM+hFiqWrRizzeey\nWFmRN+UQUcNWFK2gsWwdrwR3c178dYaGmvF46iYsX5IcGqorKkmaEJkkSdo09HcO8fL/7Jm80BQN\nI1O2m8yhZWXKXaeMbfbBT31dU22fvMBcjj/nOp/Hf9O51tukm5XCMBSGqVBmYj782TCMxNxUWE6T\nFWeWY2bBG54LiVIK15IGXEsaKLzmw0CipS20cydDbyaStsALL9L36GNgmnjWNZK3YQP+jRsnfKkh\nleKqWgC6D7eOS9IA1tUV8si2Q8RtjTmNW5LXn3Q93375Ns6rUhxue5QlDX8+YdkSR+KroTsSh+P/\n3oQQIkmStGmIRW26WgMTbp/r2NRTDm49yeYpTz3H4CbdfcqwZ39d0zF5bJMffOp6m9PmOdX7lLtO\nFZvW2LZGxzV2PLE8kUgoxqkfrJ15kGIMw+vF29SEt6kJAB2PE9qxg4HnniPw/Au0/8t3aP+X7+Ba\nvYqCK6+k4Kqrpuzuo7CiAmUYdLe2pNzeWFvE/b9rZk9HgBXlU3ddclHdRfz97/6eXqOQtraHaVj8\n+Qlvuxc7jrakCSEyR5K0aSiu9HHj7WdnOgwhZkVrjbYTyZqdTNy0rfnFf/6eHc+1sOaCagjHSTxI\np1Cj52JWlGniaWzE09jIoi99iWhbGwNPP03fo4/R/k//TMe//huF11xD8ac+ibOmJuUxTMtBYXkF\nPYdSJ2nr6goB2N7cO60kzevwsqF2A//b/Swfzm+jv38bBQWnpSw70pImSZoQGSVJmhAnOKWGb3sC\nox4vWvvBGp750U5a7tmJ8V5Pih0Zm7Ql3poYn8gNz5O3V5VloBwGyjIgOR/+PLLsMDFcJio5GW4T\n5Uyuc1sYbitxvhOEo6KC4ptuovimmwi99x7d/+8eeh56iJ7Nmym89lpK/+xzOMrHj8VZVFVD9wRJ\nWkOJj3y3xbaDPXzkjOm1hn6o4UN8Zf+TfLjAyeG2RyZM0oqSLw5IS5oQmSVJmhA5aum6Rfw2/33i\nu3tx1+fjOaUE7EQrG8nWtlSfsTlmm422Sc41OmpjB6PoqA0xGx210bHkFLWnfZtbeSxMnwPD58Dw\nWom5z4Hpc2AWODELXIkp35kYwH2BcK9YQdW3/oGyL36Brh/8kJ7Nm+l79FGKN22i9LOfGdMPW3FV\nDQd+vw3bjmMYY/tDMwxFY10R25qn9/IAwPqq9bidhRxB4e56bsJyTsMg3zKkJU2IDJMkTYgcZVoG\njacvwrGtHXVSMXnnp77tlm46nkjW7HAcHYol5slpZN1QjHgwih2MYg/GiPeGibQGsIPRRA/Doykw\n/E6sEjdWqQer1IMjObfKPFmbwDnKy6n4669TfPMmOv7te3TdeSd9jz9O+W23knfxxYmBzqtqiEej\n9Hd0UFheMe4YjbWF3PHr9wmGY/hcU/86d5gOLqm/hFfaHqK8YJChoVY8nuqUZRNDQ0mSJkQmSZIm\nRA6rK3AxBLz+Vic1loHlMDAdBuboZUdy2RpeNhNzy8Cw1Iz7fFOmgTINDLcFBTMb5FxrjQ7FifeH\nifdFiPeGifWFE/OuIUK7urED0aM7mApHhQ9nlR9HtQ9HlR9npR/lyJ7EzVlTQ/W3/y9FH/0Ibd/8\nO1q/8EXyL7uMitv/lqJkNxzdhw6mTNLW1RVia/h9Sx/nLC2Z1vkua7iMv9q3mSsLoLf3FTyea1KW\nSwyyLuN3CpFJkqQJkcPs5n7CbpM9O3vYszPFc2nTMJLEjUvmEnOH08TldeD0Wri8Fi6PhcvrSCx7\nLbz5TrwFLpxuc8qETymF8lgYHgtHeeq+IexQjFjnELGOISKHg0QPBRh6u5Pga23JgBXOaj/O+nxc\n9fk46/Mx85yzuvZ08jY10fDwz+n64Q/p+Pc7GNy+jeLb/xaA7tYWlqw7Y9w+jTWJlwe2HeyZdpJ2\nWvlpaGclEVro6X2VysrUSVqxw+JwOJpymxDi+JAkTYgcZYdjhPf3U3JeFbdcUEs8ZhOP2sSiiXk8\ndnQ5Fo1PuC0etYnFRi0nt8ejcWJRm0BvmK5DQcKDMSJDE98+sxwG3gInvkIX3nwXvuRyfqmHgrLE\n5PRM/SvLcFs4a/Jw1uThXZdYp7Um3hsm2hog3DxA5EA/gZcPEXixFQCz2J1I2Gr8mCUezAIXVoET\n5bGO6+gQyrIo/exn8a1fT+tXv0r7n/4ZrnUrJnx5oMjnpKHUx/YZPJdmKIP1Veeyt+9nFPS+MmG5\nEofF2wEZZF2ITJIkTYgcFd7TB7bGvaIYt+/49Cpv25poKEZ4MDGFBqMM9UcI9kUI9oUZ7Isw2Bem\nqzVA884w0dDY222ePAcFZR6Kq/2UVvsprfFTUuPH6Z78V5lSCqvIjVXkxnNKYhglHbOJtAaIHOgn\ncqCf0Ps9DG5rH7uf08QsdI083+ZIzq0yL+Y81pln7Voafv5zDt92G959O2l78QXsm/4Ew+0eV3Zd\nbSEv7u5Eaz3thPKU0lN4/vBmVrqaCYXbcLvG30odHmR9JscVQqSXJGlC5KjQez0oh4Frcf5xO6dh\nqOStzuklOJGhGH0dQ8lpkP6OIXrbh9jzejs7Xzw0Ui6/zEPlkgKqlhdStbyQgkWeqW+dWgau5C1P\nSHYCPBAh1pt4xi3eGybeFybWEybWOUTo3e4xLy24VhSRd341rmWF85LEmH4/1d/7HiVf/jOam/fS\n9o1vUvWP3xpXrrGukIe3tXKoL0R1oWdax15Tuoa7wiYQpbfnVSoqrhxXpthhErY1g3Ebn2WOP4gQ\nYt5JkiZEjgq934NraWGiP7Ms5fRYlNXlUVY3trNWrTWBnjBdLQE6WwJ0HBygeWcX776SeO7Mk++k\nalkB9aeU0rC2FLd/6qRQKYWZ78LMd0GKYS21rYn3hIh2DhFpHiD4ymE6f/QWjho/hVcsHUn20kkp\nReXGD7L7x810PvYo3rPOpPDqq8eUWVebGLlgW3PPtJO0ZYXL6LI9xLB55/X7yT//Arz5Y8cYHR6/\nszMakyRNiAyRJG0aYj0h+p8+kHrjXIYfmu3IQbMdcmguwzBNds7ZDlt1vK8/A+ec06hcc/h31vFR\n/ZiN9GU2qr+zuCbeHyFvfdUcAswcpRR5xW7yit0sXpu8fak1vUcGOby7j0Pv99L6Xg973uhAGYqq\n5QUsaSyj4dQy8orH3zKc1jkNhVXiwSrx4DmpmPyNtQxua6f/mQN0fP9NvKctouCyBkx/el9CKK5O\ndFQbazyVtm98E8/atbiWLBnZvrIyD5dlsL25l8vXTu/f0zIsVpWcTEdgB0XRHWx94n/4wI03jylz\ndNSBOPXTy/2EEGkmSdo06Eic8IH+iQvMcTDsWZnt3ZXJg5mXc05+iXMZIX12hz3+dT5/A61PyFSJ\nnv1TjBgwPDqA4TTxrls0yxNkH6UURRU+iip8rD6vCq01Hc0D7N3ewd5tHby4+X1e3Pw+VcsLWX1e\nFUvXlWE5Z99CpCwD3xkVeNaWMfC/Bxl4sYXQu90UXr0c75rStF1XSU1yNIFrrsLYu5/Wr/wfGn72\nEMpMxO4wDdZUF7Dt4PRfHoDEc2ntr71F5coIO3/+BOdcdwMO59EuUUpk/E4hMk6StGlwlPuo/Mvx\nr78LIbKXUopF9fksqs/n7KuW0tMWZM8bHbzz8mGevXsnL262OPn8atZurMFXOLP+2kYzXCYFly7G\nu66M7gffo/uBdwg1llH44eUYrrnfJiwsryS/rJwDu3fxwb/+Ooe+8n/of/JJCq64YqRMY20h9/3u\nAJGYjXOat6/XlK1hx74nYGUvzqIj7PrN86z54CUj24tl/E4hMi57H0YRQog0Kqrw0XTZYj7xjbO5\n6svrqDmpiG1PH+Der7/E0z98i4O7uhO3gmfJUe5j0edOJe/COgbf7KD9P7YT7Ricc9xKKZY2ncmB\nHdvxbNyIa+VKOr737+jo0T7M1tUVEY7Z7GqbpMX/GEuMaoxmP7GYj0WnRNm25XH0qFvsw8+kdcuo\nA0JkjCRpQoicogxFzUlFXPqZNXz8m+ew5oIamnd289i/buf+v3mZrU/uI9ATmt2xTYOCi+sp/dQp\n2MEI7XdsZ2hX95xjXtZ0NvFolANvbafsi18gevAgvQ//z8j2xrpEp7bbZ3DLM7KnDVAcjlfiKeui\nu+19Wt95e2R7nmngUEpudwqRQZKkCSFyVkGZh/M+spyb//lcLr5lNfmlHl55bB/3/tVLPPEfb7J3\nWwfxuD3j47qXF7Hoz9dhlXrouvfto6MdzFL1ypNx+Xzs2foq/g0b8DQ20vmf/4kdDgNQVeBmUZ5r\nRoOtN7/9e+Jug99EbFA2pSujvP7koyPblVIUO0y53SlEBkmSJoTIeZbDZMUZFVz1pXV84u/O4bRL\n6+lsHuCX/72De257ide37J90tISUxyx0U/bptbiWFdHz8/fp/1XzmNuJM2FaFg2NTex941W0tin7\n8peJHTlC5/e/DyQSqnV1hdNuSdNa0/zWmzgbKni1tw23ZzHVpyt2v/Yye15/daTccIe2QojMyNok\nTSl1qVLqXaXUbqXUrZmORwiRGwrKPJx91VJu+tZ6PvS5tZTW+PndI3u59+sv8dov9hENT3/QccNl\nUnrTarzrFtH/zAH6tuyfdaK2tOkshgb6OfTeLnxnnUnBNdfQ9V//Tf9TTwPQWFvEvs4gPcHIlMfq\nbm0h2NNN/ZpGNHBY1WA79rNoeQXP3PnvDA0knm0rlkHWhciorEzSlFIm8B/AHwKrgRuUUqszG5UQ\nIpcYpsHitaVc+YVGrr+tiarlhbz6+D7u/5uX2fmbQ/R3Dk3rVqiyDIquX4Hv7EoCz7fQ9/jeWSVq\nDY2nY5gWe7YmxtusuP1v8TQ2cujWWwnt2sW64efSWqZuTTuwYzsA5597JRtqN/D9PVsBTeO1yxka\n6OdXd/0XkHh5oEteHBAiY9Rs/6qbT0qpc4DbtdZ/kPx8G4DW+h9TlW9qatJbt249jhEKcQJ56Q74\nzXczHUVGdNgFvB2v54hdRI+dR7/2MFnndDYmUduFzXDXGnpGXdmZgKlUyj6Vi2w/a6J1VNhFqAmO\nqnUEzcyfkUtNodTRrkcOrb+diP8QOuYkjo1Gc591M782LsJPIE3nFCL7ndX7Fvdf87l5PYdS6nWt\nddNU5bK1n7Rq4OCozy3AWaMLKKU+DXwaoK4uxRguQojp2f8ioODkq6csutDZGlqDBrv7LHb1WBwJ\nmYCmxG1T7NJUO22MSbMujdYhBsMuwlEH0ZiDuD2DGxIaHLYTU5vHrNYcMvp4xv0mxdrHWboBP+P7\nbovGwoRCA+Muyo4lEreZ/NFtKReWOjr6QnDHBfTUv0bMsHHaJg5bcY7jXWL+fLQMsC5ySE3v9Luy\nmW/ZmqSl+o0w5reP1vpO4E5ItKQdj6CEOCEN9UL5avjQdzIdSdpprent7WX//v3s3r2bPXv2EAqF\nUEpRU1PDpSefzMknn0xeXt7UB5tn0WiU7du38+tf/5rfWAfYtGkTpaXpG7lgMoODg/zqjv24e/+A\nSy+9lOXLl48MGv/54xKBECKVbE3SWoDaUZ9rgEMZikWIE1uoF0pXZDqKOdNaEwwGaWtro7W1lZaW\nFlpbWxkcTHQo6/f7WblyJcuWLWPJkiV4vd4MRzyWw+HgjDPOoK6ujnvvvZe7776bTZs2sWjR/A/d\n9eyzzzI0NMRNXb4+MgAADkhJREFUN91ERUXFvJ9PCDE92ZqkvQYsV0o1AK3Ax4AbMxuSECeooV7w\nFGY6imkLh8P09vbS19dHV1cXHR0ddHZ20tHRwdDQ0Ei5srIyVqxYQXV1NbW1tZSXl4+0DmWz8vJy\nbr75Zu655x7uuecebrnlFoqLi+ftfAcOHOCNN95g/fr1kqAJkWWyMknTWseUUp8HniLxrO1dWuu3\np9hNCDEboV5wZzZJi8fjhEIhgsEgwWCQQCAwsjw89fX10dfXNyYRA/B4PJSVlbF69WpKS0spLy+n\nqqoKt9s9wdmyX1lZGZs2beKuu+7i/vvv55ZbbsHn86X9PNFolCeeeIKCggI2bNiQ9uMLIeYmK5M0\nAK31k8CTmY5DiBNaNASxELgLgMQtQ9u2icVixOPxcdNE6yfbFo1GCYfDk06xWOpuHpRS+Hw+vF4v\n+fn51NTUUFhYSEFBAYWFhRQXF89L8pINysrKuOGGG7j33nv5yU9+wk033YTT6Uzb8aPRKA8++CAd\nHR3ceOONaT22ECI9sjZJE0IcB6FefsvpPP9CkPjzf0c8nv6OSw3DwOVyjZn8fj8lJSVj1rndbnw+\n35jJ4/FgGFnZneNxUVdXx7XXXsvmzZt55JFHuO6669JSH9FolM2bN7N7924uv/xyVqxY+M8kCnEi\nkiRNiFw21Ms+anFZJqc2nY1pmuMmy7JSrp9q2/D2XE6y0mHVqlVccsklPP300zz//PNs3LhxTsfT\nWvPwww+ze/durrjiCk4//fQ0RSqESDdJ0oTIZaFeAnipKMnjoosuynQ0YgLnnHMO7e3tPP/885SV\nlXHKKafM+livv/4677zzDhdffLEkaEJkOfkTV4hcNtRLEC8+nz/TkYhJKKW4/PLLqaur45FHHuHI\nkSOzOk5HRwdbtmxhyZIlnHPOOWmOUgiRbpKkCZHD9FBPIknz52c6FDEFy7K4/vrrcblcPPTQQ4TD\n4RntH4vFePjhh3E4HFx99dVyG1qIBUB+SoXIYaGBHmxM/AVFmQ5FTENeXh7XXXcdXV1dPPHEEzMa\nBmrLli0cPnyYK6+8kvx8ScqFWAgkSRMihwUHegHwFZRkOBIxXQ0NDWzYsIEdO3awbdu2ae2zdetW\ntm7dyvr161m1atU8RyiESBdJ0oTIYYGBxGDdvjxpWVlIzj//fBYvXsyWLVvo7e2dtOyBAwd48skn\nWbZsmbwcIsQCI0maEDksmBzX8kTtEPZEZRgGV155JVprHnvssQlve7a3t/PTn/6UoqIirr32WnkO\nTYgFRn5ihchhwaHEw+eSpC08xcXFXHzxxezdu5c33nhj3Paenh7uu+8+TNPk4x//OB6PJwNRCiHm\nQpI0IXJYMBQDNF6vN9OhiFloampi8eLFPPXUU2O65ejv7+fee+8lGo3yR3/0R/M6QLsQYv5IkiZE\nDgtGbbxmHNM0Mx2KmAXDMPjwhz+My+Xixz/+MQMDA3R3d3PXXXcRDAb5xCc+QXl5eabDFELMkow4\nIEQOC0YVPkemoxBzUVBQwA033MDdd9/NAw88QCAQIB6Pc9NNN1FTU5Pp8IQQcyAtaULksEDcwueU\nXwMLXVVVFddeey1tbW0opfjkJz8pCZoQJwBpSRMiV8UiBLWbSrc0pZ0IVq5cyS233EJhYSF5eXmZ\nDkcIkQaSpAmRq0K9BPHg87gzHYlIk9ra2kyHIIRII7nPIUSOig50EcaN3y/dbwghRDaSJE2IHDXY\n2w4gg6sLIUSWkiRNiBwV7OsCwJdfmOFIhBBCpCJJmhA5KtDfA8jg6kIIka0kSRMiRwWHB1cvWpTh\nSIQQQqQiSZoQOSoYDALgK67IcCRCCCFSkS44hMhRwaEQDmxcHnm7UwghspEkaULkqGAoik/FMx2G\nEEKICcjtTiFyVDAcx2fGMh2GEEKICUiSJkSOCkTB57AzHYYQQogJSJImRI4Kxk0ZXF0IIbKYPJMm\nRA6ybZtB24nfLc+kCSFEtpI/o4XIQaFQCBtDBlcXQogslpGWNKXUt4ErgAiwB/ik1ro3ue024BYg\nDnxBa/1UJmIUYiHTWhOJRBgaGmJwcJChoaGR5UAgQGdHBwA+rzfDkQohhJhIpm53PgPcprWOKaX+\nGbgN+JpSajXwMeBkoAp4Vim1Qmst92TEgmfb9pgpHo+PzKPRKLFYbMw81brR2yKRCJFIZGR5eB4O\nhxkaGsK2J34pIM/vo45WastPO441IIQQYiYykqRprZ8e9fF3wHXJ5auAn2qtw8A+pdRu4Ezg5eMc\n4hgdHR1s3rx52uW11guqrMQx+7KTlT82KUsXh8OBw+HA6XTidDpHlr1e75hlj8czMo18tjTecCfm\nodfg8b+HokvSFpcQQoj0yoYXBz4FDGdA1SSStmEtyXXjKKU+DXwaoK6ubj7jw7IsFi1KPb6hUmra\nx5lJ2fk8tsR8fI5tGMa4yTTNlOscDgeWZaWcj1420ahoECIBCAcS89HL4Z6jn/sD0NYFA21Hp8jA\nqIsxoWTpTKpKCCHEcTRvSZpS6lkg1aCAX9daP5os83UgBjwwvFuK8imbKbTWdwJ3AjQ1Nc2s6WOG\nivJ8fOQPzp1OWJCyVSXFuuNSbgJZFeNCqMeJYpxgpR0HbY+ahj/HQEcT2+0YRIKJpGkwMEnSFUiU\niQQTy7Gh1LEcSxng9IO3GPIqofxkWHYR5JVDfg2ULIHipeApnN7xhBBCHHfzlqRprS+abLtSahNw\nOXChPnq/qAWoHVWsBjg0PxHOQMcu+O/zMx2FOKGpRFLl8o+dF9Qcsy7v6GenD1x5x+yX/OzwwAxb\nFIUQQmSXTL3deSnwNeACrfXgqE2PAT9WSn2XxIsDy4FXMxDiWAU1cMX3xq+f8EswxfqUZTNVbqZl\n03nu+Ygxy+rRMBK3EpVxdDJGf1ZgWMlEK5lgObySVAkhhBgjU8+k3QG4gGeSz/j8Tmv9Wa3120qp\nB4GdJG6D/llWvNnpLYbTN2U6CiGEEELkkEy93blskm3/APzDcQxHCCGEECLryIgDQgghhBBZSJI0\nIYQQQogsJEmaEEIIIUQWkiRNCCGEECILSZImhBBCCJGFJEkTQgghhMhCkqQJIYQQQmQhSdKEEEII\nIbKQJGlCCCGEEFlIHR3bfOFSSnUABzIdRxYpBTozHcQJROoz/aRO00vqM/2kTtNP6vSoeq112VSF\nTogkTYyllNqqtW7KdBwnCqnP9JM6TS+pz/STOk0/qdOZk9udQgghhBBZSJI0IYQQQogsJEnaienO\nTAdwgpH6TD+p0/SS+kw/qdP0kzqdIXkmTQghhBAiC0lLmhBCCCFEFpIkTQghhBAiC0mSJoQQQgiR\nhSRJE0IIIYTIQpKk5Ril1Aal1ItKqf9SSm3IdDwLnVJqVbIuf6aU+tNMx3MiUEotUUr9SCn1s0zH\nslBJHaaf/Kynl3wXTY8kaQuIUuoupVS7UuqtY9ZfqpR6Vym1Wyl16xSH0UAAcAMt8xXrQpCO+tRa\nv6O1/izwESDne9JOU53u1VrfMr+RLjwzqVupw+mZYZ3Kz/oUZvjzL99F06G1lmmBTMAHgNOAt0at\nM4E9wBLACbwJrAbWAE8cMy0CjOR+5cADmb6mhV6fyX2uBF4Cbsz0NWV6SledJvf7WaavJ5ummdSt\n1OH81Kn8rKevPuW7aHqTNXH6JrKN1voFpdTiY1afCezWWu8FUEr9FLhKa/2PwOWTHK4HcM1HnAtF\nuupTa/0Y8JhS6hfAj+cv4uyX5v+jYpSZ1C2w8/hGtzDNtE7lZ31yM/z5H/4/mvPfRZORJG3hqwYO\njvrcApw1UWGl1DXAHwCFwB3zG9qCNNP63ABcQ+KXzJPzGtnCNdM6LQH+AVinlLotmcyJ1FLWrdTh\nnExUpxuQn/XZmKg+5btoGiRJW/hUinUTDiOhtX4YeHj+wlnwZlqfzwHPzVcwJ4iZ1mkX8Nn5C+eE\nkrJupQ7nZKI6fQ75WZ+NiepTvoumQV4cWPhagNpRn2uAQxmK5UQg9Zl+UqfzR+o2/aRO00vqcw4k\nSVv4XgOWK6UalFJO4GPAYxmOaSGT+kw/qdP5I3WbflKn6SX1OQeSpC0gSqmfAC8DJymlWpRSt2it\nY8DngaeAd4AHtdZvZzLOhULqM/2kTueP1G36SZ2ml9Rn+qnkK7BCCCGEECKLSEuaEEIIIUQWkiRN\nCCGEECILSZImhBBCCJGFJEkTQgghhMhCkqQJIYQQQmQhSdKEEEIIIbKQJGlCiBOKUiowD8fcr5Qq\nzcS5hRC5S5I0IYQQQogsJAOsCyFOeEqpK4C/BpxAF/BxrfURpdTtQANQCawA/gI4G/hDoBW4Qmsd\nTR7mq0qpjcnlG7XWu5VSDcCPSfwu3TLqfH7gUaAIcAB/rbV+dH6vUghxopGWNCFELvgNcLbWeh3w\nU+AvR21bCnwIuAq4H/hfrfUaYCi5fli/1vpM4A7gX5Pr/g34vtb6DKBtVNkQ8GGt9WnARuA7SimV\n/ssSQpzIJEkTQuSCGuAppdQO4KvAyaO2/TLZWrYDMDnaIrYDWDyq3E9Gzc9JLp87av19o8oq4FtK\nqd8DzwLVQHlarkQIkTMkSRNC5IJ/B+5ItpB9BnCP2hYG0FrbQFQfHdDYZuwjIXoay8M+DpQBp2ut\nG4Ejx5xTCCGmJEmaECIXFJB4xgxg0yyP8dFR85eTy78FPpZc/vgx52vXWkeTz7HVz/KcQogcJi8O\nCCFONF6lVMuoz98FbgceUkq1Ar8j8bLATLmUUq+Q+OP2huS6LwI/Vkp9Efj5qLIPAI8rpbYC24Fd\nszifECLHqaMt+0IIIYQQIlvI7U4hhBBCiCwkSZoQQgghRBaSJE0IIYQQIgtJkiaEEEIIkYUkSRNC\nCCGEyEKSpAkhhBBCZCFJ0oQQQgghstD/BycV6v6i966jAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec57908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y, w = make_regression(n_samples=10, n_features=10, coef=True, random_state=1, bias=3.5)\n",
    "from sklearn.linear_model import Lasso \n",
    "clfs = dict(ridge=Ridge(), lasso=Lasso())\n",
    "\n",
    "alphas = np.logspace(-6, 6, 200)\n",
    "coefs = dict(ridge=[], lasso=[])\n",
    "for a in alphas:\n",
    "    for name, clf in clfs.items():\n",
    "        clf.set_params(alpha=a, max_iter=10000)\n",
    "        clf.fit(X, y)\n",
    "        coefs[name].append(clf.coef_)\n",
    "\n",
    "fig = plt.figure(1)\n",
    "plt.plot(alphas, coefs['ridge'])\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Lambda')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization');\n",
    "\n",
    "fig = plt.figure(2)\n",
    "plt.plot(alphas, coefs['lasso'])\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Lambda')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Lasso coefficients as a function of the regularization');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}