{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "LezvU_JFKPIb"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sklearn.linear_model as linear_model\n",
    "from sklearn.model_selection import train_test_split\n",
    "import sklearn.preprocessing as preprocessing\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AIOhMmjKKTPs"
   },
   "source": [
    "# 1 Polynomial Regression with SGD\n",
    "\n",
    "In this exercise we will have a look again at overfitting and underfitting using the example of a polynomial regression.\n",
    "However, we will find the optimal coefficient not by solving the linear problem as in Exercise 2, but by minimizing a loss function through Stochastic Gradient Descent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function generates data from a polynomial of degree $d$ with given coefficients $\\{c_k\\}_{k=0}^{d}$ and noise level from a Gaussian of standard deviation $\\xi$, namely $y_i = \\sum_{k=0}^{d} c_k x_i^k + \\xi \\mathcal{N}(0, 1)$ where $x_i$ are uniformly distributed points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "_xLwEsVtKTEL"
   },
   "outputs": [],
   "source": [
    "# This function generates data from a polynome, possibly with noise\n",
    "def generate_polynome_data(polynome, noise_std, n, bound, seed):\n",
    "    \"\"\"\n",
    "    arguments:\n",
    "        - polynome  : list of coefficients representing the polynom (polynome[i] multiplies X^i)\n",
    "        - noise_std : standard deviation of the gaussian noise\n",
    "        - n         : number of data points\n",
    "        - bound     : for points x the sampling inverval is +-bound\n",
    "    returns:\n",
    "        - (X, y)    : list of n points with y = poly(x) + gaussian noise\n",
    "    \"\"\"\n",
    "    rs = np.random.RandomState(seed)\n",
    "    degree = len(polynome) - 1\n",
    "    samples = rs.uniform(-bound, bound, size=n)\n",
    "    xs = np.copy(samples)\n",
    "    samples = np.ones((n, degree + 1)).T * samples\n",
    "    powers = np.power(samples.T, np.arange(0, degree + 1, 1))\n",
    "    return xs.reshape(-1, 1), np.sum(powers * polynome, axis=1) + rs.normal(\n",
    "        0, noise_std, size=n\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fYggcS-iUg1q"
   },
   "source": [
    "## 1.1 Generate data\n",
    "\n",
    "Generate $n$ noisy data points (say $5 \\leqslant n \\leqslant 10$) from the polynomial $y_i = x_i^2  + 0.5 x_i^3$ with a given noise level.\n",
    "These represent the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "MrL0B_lUKTBq"
   },
   "outputs": [],
   "source": [
    "# Create 100 noisy datapoints within the training interval [-3, 3]\n",
    "n = 100\n",
    "train_bound = 3\n",
    "noise_std = 1.0\n",
    "polynom = np.array([0, 0, 1, 0.5])  # function y = x^2 + 0.5 * x^3\n",
    "X_train, y_train = generate_polynome_data(polynom, noise_std, n, train_bound, seed=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 279
    },
    "id": "INC5GWlNQvAT",
    "outputId": "208d076c-e89c-4331-b333-e745599519dd"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the training data in a plot\n",
    "x_plot = np.linspace(-train_bound, train_bound, 100).reshape((-1, 1))\n",
    "y_plot = (\n",
    "    polynom[0]\n",
    "    + polynom[1] * x_plot\n",
    "    + polynom[2] * x_plot**2\n",
    "    + polynom[3] * x_plot**3\n",
    ")\n",
    "plt.scatter(X_train, y_train, label=\"Training data\")\n",
    "plt.plot(x_plot, y_plot, linestyle=\"--\", color=\"black\", label=\"Ground truth\")\n",
    "plt.legend(edgecolor=\"None\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"poly(x)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Yaaz_XX1bZi-"
   },
   "source": [
    "We want to create some data for the test set too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "NFTRqawrO30F"
   },
   "outputs": [],
   "source": [
    "n_test = 40\n",
    "X_test, y_test = generate_polynome_data(\n",
    "    polynom, noise_std, n_test, train_bound, seed=43\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zBQF-qFHU3QB"
   },
   "source": [
    "## 1.2 Polynomials of different degrees\n",
    "The loss function that we use for the training is the L2 metrics\n",
    "$L(c) = \\frac{1}{2n}\\sum_{x_i \\in X}(y_i-\\hat{y_i})^2$, where $\\hat{y_i}$ is the output of a polynomial on the input $x_i$ and $y_i$ is the ground-truth output. \n",
    "\n",
    "\n",
    "What are the gradients with respect to the coefficients $c$?\n",
    "\n",
    "$\\frac{\\partial L(c)}{\\partial c_k} = - \\frac{1}{n}\\sum_{x_i \\in X} (y_i-\\hat{y_i}) x_i^k$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to write the functions to compute the loss function and its gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function that generates the feature matrix\n",
    "def create_features(X, d):\n",
    "    X_features = X**0\n",
    "\n",
    "    for i in range(1, d + 1):\n",
    "        X_features = np.concatenate(\n",
    "            (X_features, X**i / scipy.special.factorial(i)), axis=-1\n",
    "        )\n",
    "\n",
    "    return X_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to predict the labels\n",
    "def predict_label(X, c):\n",
    "    y_pred = X @ c\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to compute the loss\n",
    "def loss(X, y, c, lambd):\n",
    "    y_pred = predict_label(X, c)\n",
    "    n = X.shape[0]\n",
    "    return np.sum((y - y_pred) ** 2) / (2 * n) + lambd * np.mean(c**2, axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "CYACZ6d_Y2Nr"
   },
   "outputs": [],
   "source": [
    "# Fucntion to compute the gradient of the loss\n",
    "def grad(X, y, c, lambd):\n",
    "    y_pred = predict_label(X, c)\n",
    "    n = X.shape[0]\n",
    "    return -(X.T @ (y - y_pred)) / n + lambd * 2 * c / c.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now write a function that performs the training using the Stochastic Gradient Descent scheme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 370
    },
    "id": "dmt7_oasOLMN",
    "outputId": "50e73e96-303e-4d7b-cbb4-e163695e995d"
   },
   "outputs": [],
   "source": [
    "# Perform the SGD training\n",
    "def sgd_training(\n",
    "    X_train,\n",
    "    y_train,\n",
    "    X_test,\n",
    "    y_test,\n",
    "    d,\n",
    "    BATCHSIZE=16,\n",
    "    EPOCHS=1000,\n",
    "    lr=0.001,\n",
    "    lambd=1e-12,\n",
    "):\n",
    "    # create the features\n",
    "    X_train_features = create_features(X_train, d)\n",
    "    X_test_features = create_features(X_test, d)\n",
    "\n",
    "    # set initial values for the parameters\n",
    "    c = np.random.RandomState(seed=42).randn(X_train_features.shape[1])\n",
    "\n",
    "    # lists to store the training and test errors\n",
    "    MSE_test = []\n",
    "    MSE_train = []\n",
    "\n",
    "    # for several epochs (= runs over complete training data)\n",
    "    for e in range(EPOCHS):\n",
    "        # compute current errors on test and train\n",
    "        MSE_train.append(np.mean((y_train - X_train_features @ c) ** 2))\n",
    "        MSE_test.append(np.mean((y_test - X_test_features @ c) ** 2))\n",
    "\n",
    "        # split the training set into batches and do a gradient step for each batch\n",
    "        for b in range(\n",
    "            0, ((X_train_features.shape[0] // BATCHSIZE) - 1) * BATCHSIZE, BATCHSIZE\n",
    "        ):\n",
    "            idxs = np.random.randint(0, X_train_features.shape[0], BATCHSIZE)\n",
    "\n",
    "            X_batch = X_train_features[idxs]\n",
    "            y_batch = y_train[idxs]\n",
    "\n",
    "            # run a gradient step on every batch\n",
    "            c = c - lr * grad(X_batch, y_batch, c, lambd)\n",
    "\n",
    "    return c, MSE_train, MSE_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# degrees of polynomials\n",
    "ds = [1, 2, 3, 5, 10, 50, 100, 150, 200]\n",
    "\n",
    "cs = []\n",
    "MSE_trains = []\n",
    "MSE_tests = []\n",
    "\n",
    "for d in ds:\n",
    "    c, MSE_train, MSE_test = sgd_training(X_train, y_train, X_test, y_test, d)\n",
    "    cs.append(c)\n",
    "    MSE_trains.append(MSE_train)\n",
    "    MSE_tests.append(MSE_test)\n",
    "\n",
    "MSE_trains = np.array(MSE_trains)\n",
    "MSE_tests = np.array(MSE_tests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1400x1000 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the learning curves\n",
    "fig, axes = plt.subplots(3, 3, figsize=(14, 10), sharex=True)\n",
    "axes = axes.flatten()\n",
    "\n",
    "for i in range(9):\n",
    "    d = ds[i]\n",
    "    ax = axes[i]\n",
    "\n",
    "    ax.plot(MSE_trains[i], label=\"Train\", color=\"tab:blue\")\n",
    "    ax.plot(MSE_tests[i], label=\"Test\", color=\"tab:orange\")\n",
    "\n",
    "    ax.set_title(f\"$d = {d}$\")\n",
    "    ax.set_yscale(\"log\")\n",
    "    ax.set_ylim(6e-1, 7e1)\n",
    "    ax.set_ylabel(\"Loss\")\n",
    "    ax.set_xlabel(\"Epochs\")\n",
    "    ax.legend(edgecolor=\"None\")\n",
    "\n",
    "fig.subplots_adjust(hspace=0.4, wspace=0.35)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compute the final test error as a function of the model complexity (degree of the polynomial). \n",
    "Show that you recover the well-known U-shaped curve of the bias-variance tradeoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Test loss')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Best MSE on the test set\n",
    "MSE_test_last = np.mean(MSE_tests[:, -10:], axis=-1)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(ds, MSE_test_last, marker=\"o\")\n",
    "\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(\"$d$\")\n",
    "ax.set_ylabel(\"Test loss\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the curves of the different polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x31149d510>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the learned polynomials\n",
    "plot_bound = 3.5\n",
    "X_plot = np.linspace(-plot_bound, plot_bound, 50).reshape((-1, 1))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(\n",
    "    X_plot, X_plot**2 + 0.5 * X_plot**3, c=\"k\", linestyle=\":\", label=\"true cruve\"\n",
    ")\n",
    "ax.scatter(X_train, y_train, c=\"k\", label=\"training point\")\n",
    "\n",
    "for i in range(len(ds)):\n",
    "    X_plot_features = create_features(X_plot, ds[i])\n",
    "    y_plot = predict_label(X_plot_features, cs[i])\n",
    "\n",
    "    ax.plot(X_plot, y_plot, label=f\"$d = {ds[i]}$\")\n",
    "\n",
    "ax.set_ylabel(\"$y$\")\n",
    "ax.set_xlabel(\"$x$\")\n",
    "ax.legend(edgecolor=\"None\", ncols=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yRWrZhjSbXZm"
   },
   "source": [
    "# 2:  SGD for Linear Regression on a health dataset\n",
    "\n",
    "In this exercise we want to repeat how to load a real-world dataset.\n",
    "\n",
    "Then, we want to implement SGD to infer the parameters and compare this with the LinearRegression classes results from sklearn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import diabetes dataset from scikit-learn toy-dataset examples\n",
    "from sklearn.datasets import load_diabetes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _diabetes_dataset:\n",
      "\n",
      "Diabetes dataset\n",
      "----------------\n",
      "\n",
      "Ten baseline variables, age, sex, body mass index, average blood\n",
      "pressure, and six blood serum measurements were obtained for each of n =\n",
      "442 diabetes patients, as well as the response of interest, a\n",
      "quantitative measure of disease progression one year after baseline.\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      ":Number of Instances: 442\n",
      "\n",
      ":Number of Attributes: First 10 columns are numeric predictive values\n",
      "\n",
      ":Target: Column 11 is a quantitative measure of disease progression one year after baseline\n",
      "\n",
      ":Attribute Information:\n",
      "    - age     age in years\n",
      "    - sex\n",
      "    - bmi     body mass index\n",
      "    - bp      average blood pressure\n",
      "    - s1      tc, total serum cholesterol\n",
      "    - s2      ldl, low-density lipoproteins\n",
      "    - s3      hdl, high-density lipoproteins\n",
      "    - s4      tch, total cholesterol / HDL\n",
      "    - s5      ltg, possibly log of serum triglycerides level\n",
      "    - s6      glu, blood sugar level\n",
      "\n",
      "Note: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times the square root of `n_samples` (i.e. the sum of squares of each column totals 1).\n",
      "\n",
      "Source URL:\n",
      "https://www4.stat.ncsu.edu/~boos/var.select/diabetes.html\n",
      "\n",
      "For more information see:\n",
      "Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004) \"Least Angle Regression,\" Annals of Statistics (with discussion), 407-499.\n",
      "(https://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Load boston dataset\n",
    "diabetes = load_diabetes()\n",
    "\n",
    "# Check what it contains\n",
    "print(diabetes.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the dimension of X is (n, d)= (442, 10) the dimension of y is (n,)= (442,)\n"
     ]
    }
   ],
   "source": [
    "# Extract the dataset\n",
    "X = diabetes.data\n",
    "y = diabetes.target\n",
    "# print the dimension of the X matrix and the y vector\n",
    "print(\"the dimension of X is (n, d)=\", X.shape, \"the dimension of y is (n,)=\", y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LMC5b5f+fx1vzvawuwbjvncv/vxufOvYfq0sArhlML5cUGxurmJgYh21ubm5Ftp08ebKeeuqpi/aXmpp6xbWMHDnS/nPTpk3l5+enbt26KS0tTTfffPMV9wsAAAAAuPpYSE1/BOziQvZfPfroo4qKirpomwYNGqhWrVrKyMhw2J6bm6tffvnlsp7Xbt++vSTp6NGjhG4AAAAAuM6ULnSXk5Huy+Hr6ytfX99LtgsLC9Pp06e1d+9etW7dWpL04YcfKj8/3x6kS2Lfvn2SJD8/vyuqFwAAAABgnVItpJavgnLxMiEkJETdu3fXiBEjtGvXLqWkpGjMmDG6//777SuX//e//1WjRo20a9cuSVJaWppmzpypvXv36tixY3rnnXc0aNAgderUSc2aNTNSJwAAAADAnFKNdJdiDbYbwooVKzRmzBh169ZNTk5O6tu3r55++mn7/pycHB06dMi+Ormrq6s2bdqkpKQknT17Vv7+/urbt68ef/xxqy4BAAAAAFAKpVtI7QZYQbM0qlatqldffbXY/QEBAQ4fXPj7+2vbtvK/gi4AAAAA3ChK+Uw3I90AAAAAABSHrwwDAAAAAMCQ0j3TXU6+MgwAAAAAABMY6QYAAAAAwBCe6QYAAAAAwBCmlwMAAAAAYEgpp5fnlVUdAAAAAACUO6Ub6WZ6OQAAAAAAxWIhNQAAAAAADGEhNQAAAAAADCll6GakGwAAAACA4pQudLN6OQAAAAAAxWIhNQAAAAAADCndQmr5TC8HAAAAAKA4TC8HAAAAAMAQRroBAAAAADDEqTQHF5ST/wMAAABgjS5dumj8+PHF7rfZbFq9enWJ+9u6datsNptOnz5d6touiI+PV4sWLcqsv0sxcQ1/FRUVpd69e9vfX+r3UF789bqvBka6AQAAAFyzTpw4oSpVqlhdxlXVoUMHnThxQpUrV5YkLVu2TOPHjzcawletWqUKFSoY67+sRUVF6fTp05f1gYwkLVy48KovCF661csZJQYAAABgUK1atawu4apzdXW96tddtWrVq3q+4mRnZ8vV1dVY/xc+yLiaSje9vKCgXLwAAAAAWCc/P18TJ05U1apVVatWLcXHx9v3/XV6+fbt29WiRQu5u7urTZs2Wr16tWw2m/bt2+fQ5969e9WmTRt5enqqQ4cOOnToUInrefLJJ1WzZk1VqlRJw4YNU2ZmZqE2L774okJCQuTu7q5GjRrpueees+87duyYbDabVq1apa5du8rT01PNmzfXjh077G2+++479ezZU1WqVFHFihXVuHFjrV27VpLj9PKtW7dqyJAh+u2332Sz2WSz2RQfH68ZM2aoSZMmhepq0aKFpk6dWuJrveCv08sDAgI0c+ZMDRgwQBUrVlSdOnX07LPPOhyTnp6uXr16ycvLS97e3oqMjNSPP/5o339hWv7ixYvl7+8vT09PRUZG6rfffrO3uTDde9asWapdu7aCg4MlSQcOHNDtt98uDw8PVatWTSNHjtSZM2fs/S5fvlxr1qyx35OtW7dKko4fP67IyEj5+PioatWq6tWrl44dO1bofH++7rFjxxb791dQUKD4+HjVrVtXbm5uql27tsaOHXtZ97ZUoTu/oKBcvAAAAACUnaysLP3+++8Or6ysrGLbL1++XBUrVtTOnTs1Z84czZgxQxs3bizU7vfff1fPnj3VtGlTffbZZ5o5c6YmTZpUZJ9TpkzR/PnztWfPHrm4uGjo0KElqv31119XfHy8Zs+erT179sjPz88hUEvSihUrFBcXp1mzZik1NVWzZ8/W1KlTtXz58kI1TJgwQfv27VNQUJAGDBig3NxcSdLo0aOVlZWljz76SAcOHNBTTz0lLy+vQvV06NBBSUlJ8vb21okTJ3TixAlNmDBBQ4cOVWpqqnbv3m1v+/nnn+uLL77QkCFDSnStlzJ37lw1b95cn3/+uSZPnqxx48bZfy/5+fnq1auXfvnlF23btk0bN27UN998o/79+zv0cfToUb3++ut69913tX79en3++ed6+OGHHdps3rxZhw4d0saNG/Xee+/p7NmzioiIUJUqVbR792698cYb2rRpk8aMGSNJmjBhgiIjI9W9e3f7PenQoYNycnIUERGhSpUq6eOPP1ZKSoq8vLzUvXt3ZWdnF3udF/v7e+utt5SYmKjFixfryJEjWr16tZo2bXpZ97FU08tzs/8rSYqNjS3y05/rRXR0tNUl4C8iIiLUrU2Q1WUAAADgCiQkJGj69OkO26ZNm+YwgvhnzZo107Rp0yRJgYGBWrRokTZv3qw77rjDod2rr74qm82mJUuWyN3dXaGhofrvf/+rESNGFOpz1qxZ6ty5syRp8uTJuvvuu5WZmSl3d/eL1p6UlKRhw4Zp2LBhkqQnnnhCmzZtcsg706ZN0/z589WnTx9JUv369XXw4EEtXrxYgwcPtrebMGGC7r77bknS9OnT1bhxYx09elSNGjVSenq6+vbtaw9wDRo0KLIeV1dXVa5cWTabzWHKuZeXlyIiIpScnKy2bdtKkpKTk9W5c+di+7pcHTt21OTJkyVJQUFBSklJUWJiou644w5t3rxZBw4c0Lfffit/f39J0ssvv6zGjRtr9+7d9poyMzP18ssvq06dOpKkZ555Rnfffbfmz59vv56KFSvqxRdftE8rX7Jkif24ihUrSpIWLVqknj176qmnnlLNmjXl4eGhrKwsh3vyyiuvKD8/Xy+++KJsNpv9nvj4+Gjr1q268847i7zOi/39paenq1atWgoPD1eFChVUt25dtWvX7rLuY6lC9wWZmZlKTEwsi64Au5xT31hdAgAAAK5AbGysYmJiHLa5ubkV275Zs2YO7/38/JSRkVGo3aFDh9SsWTOH4FxcAPpzn35+fpKkjIwM1a1b96K1p6amatSoUQ7bwsLCtGXLFknS2bNnlZaWpmHDhjmE/dzc3ELPCxdXQ6NGjTR27Fj94x//0AcffKDw8HD17du30H24lBEjRmjo0KFasGCBnJyc9Oqrr5ZpLgsLCyv0PikpSdIf98nf398euCUpNDRUPj4+Sk1NtYfuunXr2gP3hT7y8/N16NAhe2Bu2rSpw3Pcqampat68uT1wS398AHDhuJo1axZZ7/79+3X06FFVqlTJYXtmZqbS0tKKvc6L/f3169dPSUlJatCggbp376677rpLPXv2lItLyaN0mYRuAAAAALjAzc3toiH7r/66arbNZlN+Kb8p6c99Xhj1LG2fkuzPFS9ZskTt27d32Ofs7FziGoYPH66IiAi9//77+uCDD5SQkKD58+frkUceKXEtPXv2lJubm95++225uroqJydH99133xVdl5X+HK5L48yZM2rdurVWrFhRaJ+vr2+xx13s78/f31+HDh3Spk2btHHjRj388MOaO3eutm3bVuLV3kv1TDcAAAAAXC3BwcE6cOCAw/Phf36muSyEhIRo586dDts+/fRT+881a9ZU7dq19c0336hhw4YOr/r161/Wufz9/TVq1CitWrVKjz76qJYsWVJkO1dXV+Xl5RXa7uLiosGDBys5OVnJycm6//775eHhcVk1XMyfr/vC+5CQEEl/3Kfjx4/r+PHj9v0HDx7U6dOnFRoaat+Wnp6uH374waEPJycn+4JpRQkJCdH+/ft19uxZ+7aUlBSH44q6J61atdKRI0dUo0aNQr+b0qxa7uHhoZ49e+rpp5/W1q1btWPHDh04cKDExxO6AQAAAFwXHnjgAeXn52vkyJFKTU3Vhg0bNG/ePEn/fyS5tMaNG6elS5cqOTlZhw8f1rRp0/TVV185tJk+fboSEhL09NNP6/Dhwzpw4ICSk5O1YMGCEp9n/Pjx2rBhg7799lt99tln2rJliz3Q/lVAQIDOnDmjzZs369SpUzp37px93/Dhw/Xhhx9q/fr1JV4srqRSUlI0Z84cHT58WM8++6zeeOMNjRs3TpIUHh6upk2bauDAgfrss8+0a9cuDRo0SJ07d1abNm3sfbi7u2vw4MHav3+/Pv74Y40dO1aRkZEX/Uq0gQMH2o/78ssvtWXLFj3yyCN68MEH7VPLAwIC9MUXX+jQoUM6deqUcnJyNHDgQFWvXl29evXSxx9/rG+//VZbt27V2LFj9f3331/RPVi2bJleeuklffnll/rmm2/0yiuvyMPDQ/Xq1StxH4RuAAAAANcFb29vvfvuu9q3b59atGihKVOmKC4uTpIuuUBaSfXv319Tp07VxIkT1bp1a3333Xf6xz/+4dBm+PDhevHFF5WcnKymTZuqc+fOWrZs2WWNdOfl5Wn06NEKCQlR9+7dFRQUVGiV9As6dOigUaNGqX///vL19dWcOXPs+wIDA9WhQwc1atSo0HT30nr00Ue1Z88etWzZUk888YQWLFigiIgISX98yLFmzRpVqVJFnTp1Unh4uBo0aKDXXnvNoY+GDRuqT58+uuuuu3TnnXeqWbNmxV7nBZ6entqwYYN++eUXtW3bVvfdd5+6deumRYsW2duMGDFCwcHBatOmjXx9fZWSkiJPT0999NFHqlu3rvr06aOQkBD7V755e3tf0T3w8fHRkiVL1LFjRzVr1kybNm3Su+++q2rVqpW4D1tBGXxRdXR0NAupoczdCAupDW79qNUlGDdRhadClTebC67sf8SvFzdnl/75t2vdfb9ss7oE4+71a3PpRtc5dzlfutF1Llvl/5/HW/MLf2VSefO9c/n/d+NTx/5z1c61YsUK+/dYl+XU6utFQUGBAgMD9fDDDxdavK40AgICNH78eIfv7r5c8fHxWr16daHvUL/RsJAaAAAAgOvGyy+/rAYNGqhOnTrav3+/Jk2apMjIyBsycP/0009auXKlTp48WWbfzY2yR+gGAAAAcN04efKk4uLidPLkSfn5+alfv36aNWtWiY9v3LixvvvuuyL3LV68WAMHDiyrUo2rUaOGqlevrn/961+qUqWKwz4vr+Jnjaxbt0633Xab6fLwfwjdAAAAAK4bEydO1MSJE6/4+LVr1yonJ6fIfcV9//O16mJPCl9sSvefvze7OMeOHbuCihzFx8crPj6+1P1c7wjdAAAAAG4Yl7Pq9PWsYcOGVpeA/8Pq5QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQF6sLAIozuPWjVpdg3PK9860uwbj9LWKsLsG4frVOWF2CURXc860uwbhf27SyugTjTqecsboE487+5mZ1Ccadz6xgdQnG1Wtz3OoSjMs/Z3UFAK4mRroBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAADAMm+++aaaNm0qDw8PVatWTeHh4Tp79qwk6cUXX1RISIjc3d3VqFEjPffcc/bjhg4dqmbNmikrK0uSlJ2drZYtW2rQoEGWXAdQHEI3AAAAgDKVlZWl33//3eF1IRz/2YkTJzRgwAANHTpUqamp2rp1q/r06aOCggKtWLFCcXFxmjVrllJTUzV79mxNnTpVy5cvlyQ9/fTTOnv2rCZPnixJmjJlik6fPq1FixZd1WsFLsXF6gLKu9jYWGVmZlpdxnUnIiLC6hIAAABwhRISEjR9+nSHbdOmTVN8fLzDthMnTig3N1d9+vRRvXr1JElNmza1t58/f7769OkjSapfv74OHjyoxYsXa/DgwfLy8tIrr7yizp07q1KlSkpKStKWLVvk7e1t/gKBy0DoNiwzM1OJiYlWl3FdelmLrS4BAAAAVyA2NlYxMTEO29zc3Aq1a968ubp166amTZsqIiJCd955p+677z65uroqLS1Nw4YN04gRI+ztc3NzVblyZfv7sLAwTZgwQTNnztSkSZN06623mrso4AoRugEAAACUKTc3tyJD9l85Oztr48aN2r59uz744AM988wzmjJlit59911J0pIlS9S+fftCx1yQn5+vlJQUOTs76+jRo2V7EUAZ4ZluAAAAAJax2Wzq2LGjpk+frs8//1yurq5KSUlR7dq19c0336hhw4YOr/r169uPnTt3rr7++mtt27ZN69evV3JysoVXAhSNkW4AAAAAlti5c6c2b96sO++8UzVq1NDOnTv1008/KSQkRNOnT9fYsWNVuXJlde/eXVlZWdqzZ49+/fVXxcTE6PPPP1dcXJzefPNNdezYUQsWLNC4cePUuXNnNWjQwOpLA+wI3QAAAAAs4e3trY8++khJSUn6/fffVa9ePc2fP189evSQJHl6emru3Ll67LHHVLFiRTVt2lTjx49XZmam/v73vysqKko9e/aUJI0cOVLvv/++HnzwQX300UcO09ABKxG6AQAAAFgiJCRE69evL3b/Aw88oAceeKDIfV999VWhbWvWrCmz2oCywjPdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAxxsboAoDgTlWd1CcbtbxFjdQnGNd+3wOoSUEpnHxlmdQnGudza3uoSjKve5rzVJRjntSbF6hKMyztTYHUJxtmcbFaXYJxbsJfVJQC4ihjpBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAADADSEqKkq9e/e2uoxrSnx8vFq0aFGqPrZu3SqbzabTp0+XSU1XW5cuXTR+/Hhj/RO6AQAAAFjmSgKP6ZAEa5W33y+hGwAAAAAMy8nJsbqEG052drbVJUgidAMAAACwSFRUlLZt26aFCxfKZrPJZrPp2LFj2rZtm9q1ayc3Nzf5+flp8uTJys3NvegxeXl5GjZsmOrXry8PDw8FBwdr4cKFV1zbm2++qaZNm8rDw0PVqlVTeHi4zp49a9//4osvKiQkRO7u7mrUqJGee+45+75jx47JZrPptddeU+fOneXu7q4VK1YUOZU7KSlJAQEBDvekd+/emj17tmrWrCkfHx/NmDFDubm5euyxx1S1alXddNNNSk5OLvG1fP/99xowYICqVq2qihUrqk2bNtq5c6dDm3//+98KCAhQ5cqVdf/99+t///uffV9WVpbGjh2rGjVqyN3dXbfeeqt279590XN+8sknuu222+Th4SF/f3+NHTvW4f4999xzCgwMlLu7u2rWrKn77rvPfv1F/X4l6csvv1SPHj3k5eWlmjVr6sEHH9SpU6fsfXbp0kVjxozR+PHjVb16dUVEREjSRf+ergZCNwAAAIAylZWVpd9//93hlZWVVajdwoULFRYWphEjRujEiRM6ceKEKlSooLvuuktt27bV/v379fzzz+ull17SE088Uewx/v7+ys/P10033aQ33nhDBw8eVFxcnP75z3/q9ddfv+z6T5w4oQEDBmjo0KFKTU3V1q1b1adPHxUUFEiSVqxYobi4OM2aNUupqamaPXu2pk6dquXLlzv0M3nyZI0bN06pqan2AFgSH374oX744Qd99NFHWrBggaZNm6Z77rlHVapU0c6dOzVq1Cg99NBD+v777y/Z15kzZ9S5c2f997//1TvvvKP9+/dr4sSJys/Pt7dJS0vT6tWr9d577+m9997Ttm3b9OSTT9r3T5w4UW+99ZaWL1+uzz77TA0bNlRERIR++eWXIs+Zlpam7t27q2/fvvriiy/02muv6ZNPPtGYMWMkSXv27NHYsWM1Y8YMHTp0SOvXr1enTp0kFf/7PX36tG6//Xa1bNlSe/bs0fr16/Xjjz8qMjLS4dzLly+Xq6urUlJS9MILL+i///3vRf+ergaXq3YmlFuxsbHKzMws0z4jIiJUq0x7BAAAwNWSkJCg6dOnO2ybNm2a4uPjHbZVrlxZrq6u8vT0VK1af/zX35QpU+Tv769FixbJZrOpUaNG+uGHHzRp0iTFxcUVeYwkOTs7O5yzfv362rFjh15//fVCwexSTpw4odzcXPXp00f16tWTJDVt2tThWubPn68+ffrYz3Xw4EEtXrxYgwcPtrcbP368vc3lqFq1qp5++mk5OTkpODhYc+bM0blz5/TPf/5T0h///f3kk0/qk08+0f3333/Rvl599VX99NNP2r17t6pWrSpJatiwoUOb/Px8LVu2TJUqVZIkPfjgg9q8ebNmzZqls2fP6vnnn9eyZcvUo0cPSdKSJUu0ceNGvfTSS3rssccKnTMhIUEDBw60P5cdGBiop59+Wp07d9bzzz+v9PR0VaxYUffcc48qVaqkevXqqWXLlpKK/puQpEWLFqlly5aaPXu2fdvSpUvl7++vw4cPKygoyH6uOXPm2Ntc6u/Jycn8ODShG6WWmZmpxMTEMu93n567dCMAAABcc2JjYxUTE+Owzc3NrUTHpqamKiwsTDabzb6tY8eOOnPmjL7//nvVrVu32GOfffZZLV26VOnp6Tp//ryys7OvaGXu5s2bq1u3bmratKkiIiJ055136r777lOVKlV09uxZpaWladiwYRoxYoT9mNzcXFWuXNmhnzZt2lz2uSWpcePGDmGwZs2aatKkif29s7OzqlWrpoyMjEv2tW/fPrVs2dIeuIsSEBBgD9yS5OfnZ+87LS1NOTk56tixo31/hQoV1K5dO6WmphbZ3/79+/XFF19oxYoV9m0FBQXKz8/Xt99+qzvuuEP16tVTgwYN1L17d3Xv3l333nuvPD09i61x//792rJli7y8vArtS0tLs4fu1q1bO+wrzd9TWSF0AwAAAChTbm5uJQ7ZZWXlypWaMGGC5s+fr7CwMFWqVElz584t9OxySTg7O2vjxo3avn27PvjgAz3zzDOaMmWKdu7caQ+GS5YsUfv27Qsd92cVK1Z0eO/k5GSfon5BUQusVahQweG9zWYrctufp4gXx8PD45JtrrTv4pw5c0YPPfSQxo4dW2hf3bp15erqqs8++0xbt27VBx98oLi4OMXHx2v37t3y8fEpts+ePXvqqaeeKrTPz8/P/vNf7/m1gGe6AQAAAFjG1dVVeXl59vchISHasWOHQzhNSUlRpUqVdNNNNxV5zIU2HTp00MMPP6yWLVuqYcOGSktLu+K6bDabOnbsqOnTp+vzzz+Xq6ur3n77bdWsWVO1a9fWN998o4YNGzq86tevf9E+fX19dfLkSYdr27dv3xXXWBLNmjXTvn37in3++lJuvvlm+zPSF+Tk5Gj37t0KDQ0t8phWrVrp4MGDhe5Pw4YN5erqKklycXFReHi45syZoy+++ELHjh3Thx9+KKno32+rVq301VdfKSAgoFCfFwvaJfl7Mo3QDQAAAMAyAQEB2rlzp44dO6ZTp07p4Ycf1vHjx/XII4/o66+/1po1azRt2jTFxMTYp1z/9Zj8/HwFBgZqz5492rBhgw4fPqypU6decoXt4uzcuVOzZ8/Wnj17lJ6erlWrVumnn35SSEiIJGn69OlKSEjQ008/rcOHD+vAgQNKTk7WggULLtpvly5d9NNPP2nOnDlKS0vTs88+q3Xr1l1RjSU1YMAA1apVS71791ZKSoq++eYbvfXWW9qxY0eJjq9YsaL+8Y9/6LHHHtP69et18OBBjRgxQufOndOwYcOKPGbSpEnavn27xowZo3379unIkSNas2aNfSG19957T08//bT27dun7777Ti+//LLy8/MVHBwsqejf7+jRo/XLL79owIAB2r17t9LS0rRhwwYNGTKkUED/s5L8PZlG6AYAAABgmQkTJsjZ2VmhoaHy9fVVTk6O1q5dq127dql58+YaNWqUhg0bpscff7zYY9LT0/XQQw+pT58+6t+/v9q3b6+ff/5ZDz/88BXV5O3trY8++kh33XWXgoKC9Pjjj2v+/Pn2hcSGDx+uF198UcnJyWratKk6d+6sZcuWXXKkOyQkRM8995yeffZZNW/eXLt27dKECROuqMaScnV11QcffKAaNWrorrvuUtOmTfXkk08Wmgp/MU8++aT69u2rBx98UK1atdLRo0e1YcMGValSpcj2zZo107Zt23T48GHddtttatmypeLi4lS7dm1Jko+Pj1atWqXbb79dISEheuGFF/Sf//xHjRs3llT077d27dpKSUlRXl6e7rzzTjVt2lTjx4+Xj4/PRcNznTp1Lvn3ZJqt4K8PFVyB6OhoIwtplQc3wr0xdY376v2tzPu81uTmlf/PvZrvu/gnvrj2nX2k6E+xyxO3vt2sLsG8zPNWV2Bc5pqUSze6zuWdKfV/tl3znD1tl250nXOpU3ghqPKm0tPvWV0CcM0o///FDwAAAACARQjdAAAAAG4o6enp8vLyKvaVnp5udYklNnv27GKv48J0eFiLrwwDAAAAcEOpXbv2RVcNv/Ds8fVg1KhRioyMLHJfSb4uDOYRugEAAADcUFxcXNSwYUOryygTVatWVdWqVa0uAxfB9HIAAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgiEtZdOLu7q7o6Oiy6KrcycjIuGSb2NhYZWZmXoVqzCjJNV6JzQXeRvq9lvSrdcLqEoBLyvs93+oSjLPVDba6BONyli21ugTjbC42q0swLud/5f8a884XWF2Ccc4+WVaXAOAqKpPQnZCQUBbdlEsl+TAiMzNTiYmJV6EaM/jABQAAAACKxvRyAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAy3Tp0kXjx4+3ugxJks1m0+rVq6/a+ay+9j9f77Fjx2Sz2bRv3z7L6rlarvbv2eWqnQkAAAAAYLdq1SpVqFChRG27dOmiFi1aKCkpyUgt/v7+OnHihKpXr26kfxNsNpvefvtt9e7d+7KOO3HihKpUqWKmqCIQugEAAADAAlWrVrW6BDtnZ2fVqlXL6jIkSTk5OSX+MOJKXO3rZHo5AAAAgGvCr7/+qkGDBqlKlSry9PRUjx49dOTIEUlSQUGBfH199eabb9rbt2jRQn5+fvb3n3zyidzc3HTu3LlLnuvIkSPq1KmT3N3dFRoaqo0bNxZqc/z4cUVGRsrHx0dVq1ZVr169dOzYMfv+qKgo9e7dW/PmzZOfn5+qVaum0aNHKycnx97mueeeU2BgoNzd3VWzZk3dd9999n1/nV5eXNuoqCht27ZNCxculM1mk81m07fffquGDRtq3rx5DjXv27dPNptNR48eveQ9+LO/Ti/funWrbDab3n//fTVr1kzu7u665ZZb9OWXXzoc99Zbb6lx48Zyc3NTQECA5s+f77A/ICBAM2fO1IABA1SxYkXVqVNHzz77rEMbm82m559/Xn/7299UsWJFzZo1S5L0/PPP6+abb5arq6uCg4P173//26FfSbr33ntls9ns7yVpzZo1atWqldzd3dWgQQNNnz5dubm5Duf767T6VatWqWvXrvL09FTz5s21Y8cOe/vvvvtOPXv2VJUqVVSxYkU1btxYa9euLfG9JXQDAAAAKFNZWVn6/fffHV5ZWVmXPC4qKkp79uzRO++8ox07dqigoEB33XWXcnJyZLPZ1KlTJ23dulXSHwE9NTVV58+f19dffy1J2rZtm9q2bStPT8+Lnic/P199+vSRq6urdu7cqRdeeEGTJk1yaJOTk6OIiAhVqlRJH3/8sVJSUuTl5aXu3bsrOzvb3m7Lli1KS0vTli1btHz5ci1btkzLli2TJO3Zs0djx47VjBkzdOjQIa1fv16dOnUqsqaLtV24cKHCwsI0YsQInThxQidOnFDdunU1dOhQJScnO/STnJysTp06qWHDhpe83yXx2GOPaf78+dq9e7d8fX3Vs2dP+4cKe/fuVWRkpO6//34dOHBA8fHxmjp1qv36L5g7d66aN2+uzz//XJMnT9a4ceMKfcgRHx+ve++9VwcOHNDQoUP19ttva9y4cXr00Uf15Zdf6qGHHtKQIUO0ZcsWSdLu3bvt13vixAn7+48//liDBg3SuHHjdPDgQS1evFjLli2zB/niTJkyRRMmTNC+ffsUFBSkAQMG2IP66NGjlZWVpY8++kgHDhzQU089JS8vrxLfQ6aXo9Tc3d0VHR1dpn1GRESUaX8AAAC4ehISEjR9+nSHbdOmTVN8fHyxxxw5ckTvvPOOUlJS1KFDB0nSihUr5O/vr9WrV6tfv37q0qWLFi9eLEn66KOP1LJlS9WqVUtbt25Vo0aNtHXrVnXu3PmS9W3atElff/21NmzYoNq1a0uSZs+erR49etjbvPbaa8rPz9eLL74om80m6Y+A5+Pjo61bt+rOO++UJFWpUkWLFi2Ss7OzGjVqpLvvvlubN2/WiBEjlJ6erooVK+qee+5RpUqVVK9ePbVs2bLImi7WtnLlynJ1dZWnp6fD1OioqCjFxcVp165dateunXJycvTqq68WGv0ujWnTpumOO+6QJC1fvlw33XST3n77bUVGRmrBggXq1q2bpk6dKkkKCgrSwYMHNXfuXEVFRdn76NixoyZPnmxvk5KSosTERHu/kvTAAw9oyJAh9vcDBgxQVFSUHn74YUlSTEyMPv30U82bN09du3aVr6+vJMnHx8fhnkyfPl2TJ0/W4MGDJUkNGjTQzJkzNXHiRE2bNq3Y65wwYYLuvvtuex+NGzfW0aNH1ahRI6Wnp6tv375q2rSpvc/LQehGqSUkJBjp9yu9YqRfAAAAmBUbG6uYmBiHbW5ubhc9JjU1VS4uLmrfvr19W7Vq1RQcHKzU1FRJUufOnTVu3Dj99NNP2rZtm7p06WIP3cOGDdP27ds1ceLES9aXmpoqf39/e+CWpLCwMIc2+/fv19GjR1WpUiWH7ZmZmUpLS7O/b9y4sZydne3v/fz8dODAAUnSHXfcoXr16qlBgwbq3r27unfvrnvvvbfIkfjLaXtB7dq1dffdd2vp0qVq166d3n33XWVlZalfv36XvAcl9ef7UrVqVYffR2pqqnr16uXQvmPHjkpKSlJeXp79vvz13oaFhRVaEK5NmzYO71NTUzVy5MhCfS9cuPCi9e7fv18pKSkOI9t5eXnKzMzUuXPnir2fzZo1s/984ZGFjIwMNWrUSGPHjtU//vEPffDBBwoPD1ffvn0d2l8K08sBAAAAlCk3Nzd5e3s7vC4VukuiadOmqlq1qrZt22YP3V26dNG2bdu0e/du5eTk2EfJS+vMmTNq3bq19u3b5/A6fPiwHnjgAXu7vy74ZbPZlJ+fL0mqVKmSPvvsM/3nP/+Rn5+f4uLi1Lx5c50+fbrQ+S6n7Z8NHz5cK1eu1Pnz55WcnKz+/ftfcnr9tahixYpl0s+ZM2c0ffp0h9/ZgQMHdOTIEbm7uxd73J9/jxdmNlz4PQ4fPlzffPONHnzwQR04cEBt2rTRM888U+KaCN0AAAAALBcSEqLc3Fzt3LnTvu3nn3/WoUOHFBoaKumPMHTbbbdpzZo1+uqrr3TrrbeqWbNmysrK0uLFi9WmTZsShbeQkBAdP35cJ06csG/79NNPHdq0atVKR44cUY0aNdSwYUOHV+XKlUt8XS4uLgoPD9ecOXP0xRdf6NixY/rwww8vu62rq6vy8vIKHXPXXXepYsWKev7557V+/XoNHTq0xLWVxJ/vy6+//qrDhw8rJCRE0h/3MSUlxaF9SkqKgoKCHEb//3pvP/30U3sfxSmu7wt/C9IfQfmv96RVq1Y6dOhQod9Zw4YN5eR05fHX399fo0aN0qpVq/Too49qyZIlJT6W6eUAAAAALBcYGKhevXppxIgRWrx4sSpVqqTJkyerTp06DlOYu3TpokcffVRt2rSxL2bVqVMnrVixQo899liJzhUeHq6goCANHjxYc+fO1e+//64pU6Y4tBk4cKDmzp2rXr16acaMGbrpppv03XffadWqVZo4caJuuummS57nvffe0zfffKNOnTqpSpUqWrt2rfLz8xUcHHzZbQMCArRz504dO3ZMXl5eqlq1qpycnOTs7KyoqCjFxsYqMDCw0FTu0poxY4aqVaummjVrasqUKapevbr9e7EfffRRtW3bVjNnzlT//v21Y8cOLVq0SM8995xDHykpKZozZ4569+6tjRs36o033tD7779/0fM+9thjioyMVMuWLRUeHq53331Xq1at0qZNm+xtAgICtHnzZnXs2FFubm6qUqWK4uLidM8996hu3bq677775OTkpP379+vLL7/UE088cUX3YPz48erRo4eCgoL066+/asuWLZf80ODPGOkGAAAAcE1ITk5W69atdc899ygsLEwFBQVau3atw9Tfzp07Ky8vT126dLFv69KlS6FtF+Pk5KS3335b58+fV7t27TR8+PBCq1t7enrqo48+Ut26ddWnTx+FhIRo2LBhyszMlLe3d4nO4+Pjo1WrVun2229XSEiIXnjhBf3nP/9R48aNL7vthAkT5OzsrNDQUPn6+io9Pd1+7LBhw5Sdne2wEFlZefLJJzVu3Di1bt1aJ0+e1LvvvitXV1dJf4wqv/7661q5cqWaNGmiuLg4zZgxw2ERNemPcL5nzx61bNlSTzzxhBYsWHDJhZN79+6thQsXat68eWrcuLEWL16s5ORkh9/x/PnztXHjRvn7+9sXnYuIiNB7772nDz74QG3bttUtt9yixMRE1atX74rvQV5enkaPHq2QkBB1795dQUFBhT5YuBhbQUFBwRWfHZcUHR2txMTEUre5Ec2v+3erSzCuX40Tl250nfNbX/KpN7g2/T647P8Ffq2pOG2M1SUYl7NsqdUlGJf3a6bVJRh3/rjVFZjn5FL+/9PU4+YKl250nfN+qfB3XsOcjz/+WN26ddPx48dVs2bNMulz69at6tq1q3799Vf5+PhccT8BAQEaP368w/eR32iYXg4AAAAA16GsrCz99NNPio+PV79+/coscKNsMb0cAAAAQLmyYsUKeXl5Ffkqamr39eo///mP6tWrp9OnT2vOnDkO+26Ue3A9YKQbAAAAQLnyt7/9zeH7vv/sr1/xdT2Liooq9Pz0BaW9B126dFFZPIl87NixUvdxvSN0AwAAAChXKlWqpEqVKlldhqW4B9cOppcDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYIiL1QUAxbk5O9/qEoyr4F7+r/HsI8OsLsG4vN/L9+/Re3my1SUYd3rAEKtLMK5CDWerSzAu60SB1SUY51Sh/F+jZ3Nvq0swruB8ttUlALiKGOkGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAy6xfv1633nqrfHx8VK1aNd1zzz1KS0uz79++fbtatGghd3d3tWnTRqtXr5bNZtO+ffvsbb788kv16NFDXl5eqlmzph588EGdOnXKgqsBCiN0AwAAALDM2bNnFRMToz179mjz5s1ycnLSvffeq/z8fP3+++/q2bOnmjZtqs8++0wzZ87UpEmTHI4/ffq0br/9drVs2VJ79uzR+vXr9eOPPyoyMtKiKwIcuVhdAAAAAIDyJSsrS1lZWQ7b3Nzc5ObmVqht3759Hd4vXbpUvr6+OnjwoD755BPZbDYtWbJE7u7uCg0N1X//+1+NGDHC3n7RokVq2bKlZs+e7dCHv7+/Dh8+rKCgoDK+OuDyELoNc3d3V3R09EXbZGRkSJJiY2OVmZl5Ncq65kVERFhdAgAAAK5QQkKCpk+f7rBt2rRpio+PL9T2yJEjiouL086dO3Xq1Cnl5+dLktLT03Xo0CE1a9ZM7u7u9vbt2rVzOH7//v3asmWLvLy8CvWdlpZG6IblCN2GJSQkXLLNhVCemZmpxMRE0yVdN1brZatLAAAAwBWIjY1VTEyMw7aiRrklqWfPnqpXr56WLFmi2rVrKz8/X02aNFF2dnaJznXmzBn17NlTTz31VKF9fn5+l188UMYI3QAAAADKVHFTyf/q559/1qFDh7RkyRLddtttkqRPPvnEvj84OFivvPKKsrKy7P3t3r3boY9WrVrprbfeUkBAgFxciDe49rCQGgAAAABLVKlSRdWqVdO//vUvHT16VB9++KHDCPkDDzyg/Px8jRw5UqmpqdqwYYPmzZsnSbLZbJKk0aNH65dfftGAAQO0e/dupaWlacOGDRoyZIjy8vIsuS7gzwjdAAAAACzh5OSklStXau/evWrSpImio6M1d+5c+35vb2+9++672rdvn1q0aKEpU6YoLi5OkuzPedeuXVspKSnKy8vTnXfeqaZNm2r8+PHy8fGRkxNxB9Zj/gUAAAAAy4SHh+vgwYMO2woKCuw/d+jQQfv377e/X7FihSpUqKC6devatwUGBmrVqlXmiwWuAKEbAAAAwDXr5ZdfVoMGDVSnTh3t379fkyZNUmRkpDw8PKwuDSgRQjcAAACAa9bJkycVFxenkydPys/PT/369dOsWbOsLgsoMUI3AAAAgGvWxIkTNXHiRKvLAK4YKwsAAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAY4mJ1AUBx7vtlm9UlGPdrm1ZWl2Ccy63trS7BOFvdYKtLMOr0gCFWl2Ccz3+SrS7BuNwDH1pdgnEVPv3Y6hKMs1WoYHUJxmXvTrO6BONcWwVYXQKAq4iRbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAA3BCioqLUu3fvUvdz7Ngx2Ww27du3r1T9BAQEKCkpqdT1WGHZsmXy8fGxuozrAqEbAAAAgGW6dOmi8ePHGz+mvCMEX7sI3QAAAAAASVJeXp7y8/OtLqNcIXQDAAAAsERUVJS2bdumhQsXymazyWaz6dixY9q2bZvatWsnNzc3+fn5afLkycrNzb3oMXl5eRo2bJjq168vDw8PBQcHa+HChVdcW35+vubMmaOGDRvKzc1NdevW1axZsxzafPPNN+ratas8PT3VvHlz7dixw2H/W2+9pcaNG8vNzU0BAQGaP3/+Rc95+vRpDR8+XL6+vvL29tbtt9+u/fv32/fv379fXbt2VaVKleTt7a3WrVtrz5492rp1q4YMGaLffvvNfk/i4+MlSVlZWZowYYLq1KmjihUrqn379tq6dau9zwsj5O+8845CQ0Pl5uam9PR0/frrrxo0aJCqVKkiT09P9ejRQ0eOHLni+3kjI3QDAAAAsMTChQsVFhamESNG6MSJEzpx4oQqVKigu+66S23bttX+/fv1/PPP66WXXtITTzxR7DH+/v7Kz8/XTTfdpDfeeEMHDx5UXFyc/vnPf+r111+/otpiY2P15JNPaurUqTp48KBeffVV1axZ06HNlClTNGHCBO3bt09BQUEaMGCA/cOBvXv3KjIyUvfff78OHDig+Ph4TZ06VcuWLSv2nP369VNGRobWrVunvXv3qlWrVurWrZt++eUXSdLAgQN10003affu3dq7d68mT56sChUqqEOHDkpKSpK3t7f9nkyYMEGSNGbMGO3YsUMrV67UF198oX79+ql79+4OAfrcuXN66qmn9OKLL+qrr75SjRo1FBUVpT179uidd97Rjh07VFBQoLvuuks5OTlXdD9vZC5WFwAAAACgfMnKylJWVpbDNjc3N7m5uTlsq1y5slxdXeXp6alatWpJ+iPI+vv7a9GiRbLZbGrUqJF++OEHTZo0SXFxcUUeI0nOzs6aPn26/X39+vW1Y8cOvf7664qMjLys+v/3v/9p4cKFWrRokQYPHixJuvnmm3Xrrbc6tJswYYLuvvtuSdL06dPVuHFjHT16VI0aNdKCBQvUrVs3TZ06VZIUFBSkgwcPau7cuYqKiip0zk8++US7du1SRkaG/T7NmzdPq1ev1ptvvqmRI0cqPT1djz32mBo1aiRJCgwMdLiXNpvN4Z6kp6crOTlZ6enpql27tr3m9evXKzk5WbNnz5Yk5eTk6LnnnlPz5s0lSUeOHNE777yjlJQUdejQQZK0YsUK+fv7a/Xq1erXr99l3c8bHaH7BhQbG6vMzEyry7ioiIgIq0sAAADAFUpISHAIwJI0bdo0+5Tni0lNTVVYWJhsNpt9W8eOHXXmzBl9//33qlu3brHHPvvss1q6dKnS09N1/vx5ZWdnq0WLFpddf2pqqrKystStW7eLtmvWrJn9Zz8/P0lSRkaGGjVqpNTUVPXq1cuhfceOHZWUlKS8vDw5Ozs77Nu/f7/OnDmjatWqOWw/f/680tLSJEkxMTEaPny4/v3vfys8PFz9+vXTzTffXGx9Bw4cUF5enoKCghy2Z2VlOZzH1dXV4VpSU1Pl4uKi9u3b27dVq1ZNwcHBSk1Nveg9QWGE7htQZmamEhMTrS4DAAAA5VRsbKxiYmIctv11lLusrVy5UhMmTND8+fMVFhamSpUqae7cudq5c+dl9+Xh4VGidhUqVLD/fOFDgitdhOzMmTPy8/NzeN76ggurksfHx+uBBx7Q+++/r3Xr1mnatGlauXKl7r333mL7dHZ21t69ewuFfC8vL/vPHh4eDh9yoGwRugEAAACUqaKmkhfH1dVVeXl59vchISF66623VFBQYA+CKSkpqlSpkm666aYij7nQpkOHDnr44Yft2y6MEF+uwMBAeXh4aPPmzRo+fPgV9RESEqKUlJRCNQYFBRUKwJLUqlUrnTx5Ui4uLgoICCi236CgIAUFBSk6OloDBgxQcnKy7r333iLvScuWLZWXl6eMjAzddtttl1V7bm6udu7caZ9e/vPPP+vQoUMKDQ0tcT/4AwupAQAAALBMQECAdu7cqWPHjunUqVN6+OGHdfz4cT3yyCP6+uuvtWbNGk2bNk0xMTFycnIq8pj8/HwFBgZqz5492rBhgw4fPqypU6dq9+7dV1STu7u7Jk2apIkTJ+rll19WWlqaPv30U7300ksl7uPRRx/V5s2bNXPmTB0+fFjLly/XokWL7Auc/VV4eLjCwsLUu3dvffDBBzp27Ji2b9+uKVOmaM+ePTp//rzGjBmjrVu36rvvvlNKSop2796tkJAQ+z05c+aMNm/erFOnTuncuXMKCgrSwIEDNWjQIK1atUrffvutdu3apYSEBL3//vvF1h4YGKhevXppxIgR+uSTT7R//379/e9/V506dQpNmcelEboBAAAAWGbChAlydnZWaGiofH19lZOTo7Vr12rXrl1q3ry5Ro0apWHDhunxxx8v9pj09HQ99NBD6tOnj/r376/27dvr559/dhj1vlxTp07Vo48+qri4OIWEhKh///7KyMgo8fGtWrXS66+/rpUrV6pJkyaKi4vTjBkzilxETfpjevratWvVqVMnDRkyREFBQbr//vv13XffqWbNmnJ2dtbPP/+sQYMGKSgoSJGRkerRo4f92fkOHTpo1KhR6t+/v3x9fTVnzhxJUnJysgYNGqRHH31UwcHB6t27t3bv3n3RZ+MvHNe6dWvdc889CgsLU0FBgdauXeswpR4lYysoKCiwuogbXXR0tBITE+3//2qd71rn4lrH6hKM+/XhVlaXYJzLre0v3eg6Z6sbbHUJRv1vyiKrSzDO5z/JVpdgXO6BD60uwbj8Tz+2ugTjbDfAf+xm776y6cDXE9dWAVaXYJznpPL/v6tASTHSDQAAAACAIYRuAAAAADeU9PR0eXl5FftKT0+3ukSUI6xeDgAAAOCGUrt2be3bt++i+4GyQugGAAAAcENxcXFRw4YNrS4DNwimlwMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDXKwuAJK7u7uio6OVkZFx2cfGxsYqMzPzso65kvNY4V6/NlaXYNzplDNWl2Bc9TbnrS7BuJxlS60uwagKNZytLsG43AMfWl2CcS5Nb7e6BONyvthjdQnG2eo3tLoE4yqcK///3pC3l9UVALiKCN3XgISEBElSdHT0ZR+bmZmpxMTEyzrmSs4DAAAAALh8TC8HAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAC4ISxbtkw+Pj729/Hx8WrRooXx83bp0kXjx4+/aJuAgAAlJSUZr+Wv9+Bq2Lp1q2w2m06fPn1Vz3utcLG6AAAAAAA3ri5duqhFixZXJXD+1YQJE/TII48YP8+qVatUoUIF4+fBtYnQDQAAAOCaVVBQoLy8PLm4lH108fLykpeXV5n3e0F2drZcXV1VtWpVY+fAtY/p5QAAAAAsERUVpW3btmnhwoWy2Wyy2WxatmyZbDab1q1bp9atW8vNzU2vvPKKnJyctGfPHofjk5KSVK9ePeXn50uS3nnnHQUGBsrd3V1du3bV8uXLLzqtuajp5UuXLlXjxo3l5uYmPz8/jRkzxr7v9OnTGj58uHx9feXt7a3bb79d+/fvL9Tfiy++qPr168vd3V1S4enlGRkZ6tmzpzw8PFS/fn2tWLGiUG2XOtf+/fvVtWtXVapUSd7e3mrdunWh+1NSa9asUatWreTu7q4GDRpo+vTpys3NlSQ98MAD6t+/v0P7nJwcVa9eXS+//LIkKT8/XwkJCapfv748PDzUvHlzvfnmm1dUS3nESDcAAAAASyxcuFCHDx9WkyZNNGPGDEnSV199JUmaPHmy5s2bpwYNGqhKlSoKDw9XcnKy2rRpYz8+OTlZUVFRcnJy0rfffqv77rtP48aN0/Dhw/X5559rwoQJl1XP888/r5iYGD355JPq0aOHfvvtN6WkpNj39+vXTx4eHlq3bp0qV66sxYsXq1u3bjp8+LB9NPvo0aN66623tGrVKjk7Oxd5nqioKP3www/asmWLKlSooLFjxyojI8OhzaXONXDgQLVs2VLPP/+8nJ2dtW/fviuawv7xxx9r0KBBevrpp3XbbbcpLS1NI0eOlCRNmzZNAwcOVL9+/XTmzBn7rIANGzbo3LlzuvfeeyVJCQkJeuWVV/TCCy8oMDBQH330kf7+97/L19dXnTt3vuyayhtCNwAAAIAylZWVpaysLIdtbm5ucnNzc9hWuXJlubq6ytPTU7Vq1ZIkff3115KkGTNm6I477rC3HT58uEaNGqUFCxbIzc1Nn332mQ4cOKA1a9ZIkhYvXqzg4GDNnTtXkhQcHKwvv/xSs2bNKnHdTzzxhB599FGNGzfOvq1t27aSpE8++US7du1SRkaG/TrmzZun1atX680337QH1ezsbL388svy9fUt8hyHDx/WunXrtGvXLnvfL730kkJCQuxtSnKu9PR0PfbYY2rUqJEkKTAwsMTX+WfTp0/X5MmTNXjwYElSgwYNNHPmTE2cOFHTpk1TRESEKlasqLffflsPPvigJOnVV1/V3/72N1WqVElZWVmaPXu2Nm3apLCwMHsfn3zyiRYvXkzoFqH7huTu7q7o6Giry7ioiIgIq0sAAADAFUpISND06dMdtk2bNk3x8fEl7uPPI9qS1Lt3b40ePVpvv/227r//fi1btkxdu3ZVQECAJOnQoUP2EHtBu3btSny+jIwM/fDDD+rWrVuR+/fv368zZ86oWrVqDtvPnz+vtLQ0+/t69eoVG7glKTU1VS4uLmrdurV9W6NGjRxWFC/JuWJiYjR8+HD9+9//Vnh4uPr166ebb765xNf753OlpKQ4fDiRl5enzMxMnTt3Tp6enoqMjNSKFSv04IMP6uzZs1qzZo1Wrlwp6Y+R/XPnzjl8QCL98eFDy5YtL7ue8ojQfQNKSEiwuoQSeUnPW10CAAAArkBsbKxiYmIctv11lPtSKlas6PDe1dVVgwYNUnJysvr06aNXX31VCxcuLHWtF3h4eFx0/5kzZ+Tn56etW7cW2vfnwPzXuq9ESc4VHx+vBx54QO+//77WrVunadOmaeXKlfYp35dzrunTp6tPnz6F9l14Jn3gwIHq3LmzMjIytHHjRnl4eKh79+724yXp/fffV506dRyOv9zfeXlF6AYAAABQpoqaSl4cV1dX5eXllajt8OHD1aRJEz333HPKzc11CIrBwcFau3atQ/vdu3eXuOZKlSopICBAmzdvVteuXQvtb9WqlU6ePCkXFxf76PqVaNSokXJzc7V37177yPyhQ4ccFnsr6bmCgoIUFBSk6OhoDRgwQMnJyZcdulu1aqVDhw6pYcOGxbbp0KGD/P399dprr2ndunXq16+f/fnx0NBQubm5KT09nankxSB0AwAAALBMQECAdu7cqWPHjsnLy8u+EnlRQkJCdMstt2jSpEkaOnSow+j0Qw89pAULFmjSpEkaNmyY9u3bp2XLlkmSbDZbiWqJj4/XqFGjVKNGDfXo0UP/+9//lJKSokceeUTh4eEKCwtT7969NWfOHAUFBemHH37Q+++/r3vvvbfQdPjiBAcHq3v37nrooYf0/PPPy8XFRePHj3e4lkudq3Hjxnrsscd03333qX79+vr++++1e/du9e3bt0Q1/FlcXJzuuece1a1bV/fdd5+cnJy0f/9+ffnll3riiSfs7R544AG98MILOnz4sLZs2WLfXqlSJU2YMEHR0dHKz8/Xrbfeal+Aztvb2/6s+I2MrwwDAAAAYJkJEybI2dlZoaGh8vX1VXp6+kXbDxs2TNnZ2Ro6dKjD9vr16+vNN9/UqlWr1KxZMz3//POaMmWKpJJPcx48eLCSkpL03HPPqXHjxrrnnnt05MgRSX8E97Vr16pTp04aMmSIgoKCdP/99+u7775TzZo1L+uak5OTVbt2bXXu3Fl9+vTRyJEjVaNGDfv+S53L2dlZP//8swYNGqSgoCBFRkaqR48ehZ6jL4mIiAi99957+uCDD9S2bVvdcsstSkxMVL169RzaDRw4UAcPHlSdOnXUsWNHh30zZ87U1KlTlZCQoJCQEHXv3l3vv/++6tevf9n1lEe2goKCAquLwB+io6OVmJho/JjrRb96vawuwbgFNc5YXYJx1cfdYnUJxuVu/8zqEozK+y3r0o2uc27DH7C6BONcmt5udQnG5ayYY3UJxtnqFz/9s7zI3/e51SUYZ/OtanUJxnn+4xljfc+cOVNvvPGGvvjii0u2nTVrll544QUdP37cWD3ApTC9HAAAAMA178yZMzp27JgWLVrkMO35z5577jm1bdtW1apVU0pKiubOnasxY8Zc5UoBR0wvBwAAAHDNGzNmjFq3bq0uXboUmlp+wZEjR9SrVy+FhoZq5syZevTRRy/ra8rKgx49esjLy6vI1+zZs60u74bESDcAAACAa96yZcvsC6MVJzExsdw+ellSL774os6fP1/kvqpVy/+jDdciQjcAAAAAlBN//a5sWI/p5QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQF6sLAIrjLmerSzDu7G9uVpdgnNeaFKtLMM7mYrO6BKOyThRYXYJxFT792OoSjMv5Yo/VJRhXYeBEq0swLnf3e1aXgDJQ8OMpq0sAcBUx0g0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAMt06dJF48ePL9M+ly1bJh8fnzLtE7hShG4AAAAAAAwhdAMAAAAAYAihGwAAAIClcnNzNWbMGFWuXFnVq1fX1KlTVVBQIEn69ddfNWjQIFWpUkWenp7q0aOHjhw54nD8smXLVLduXXl6euree+/Vzz//bN937NgxOTk5ac+ePQ7HJCUlqV69esrPz79obVu3bpXNZtOGDRvUsmVLeXh46Pbbb1dGRobWrVunkJAQeXt764EHHtC5c+fsx61fv1633nqrfHx8VK1aNd1zzz1KS0uz78/OztaYMWPk5+cnd3d31atXTwkJCZKkgoICxcfHq27dunJzc1Pt2rU1duzYK7u5sByhGwAAAIClli9fLhcXF+3atUsLFy7UggUL9OKLL0qSoqKitGfPHr3zzjvasWOHCgoKdNdddyknJ0eStHPnTg0bNkxjxozRvn371LVrVz3xxBP2vgMCAhQeHq7k5GSHcyYnJysqKkpOTiWLRPHx8Vq0aJG2b9+u48ePKzIyUklJSXr11Vf1/vvv64MPPtAzzzxjb3/27FnFxMRoz5492rx5s5ycnHTvvffaQ/7TTz+td955R6+//roOHTqkFStWKCAgQJL01ltvKTExUYsXL9aRI0e0evVqNW3a9IrvL6zlYnUBAAAAAMqXrKwsZWVlOWxzc3OTm5tbke39/f2VmJgom82m4OBgHThwQImJierSpYveeecdpaSkqEOHDpKkFStWyN/fX6tXr1a/fv20cOFCde/eXRMnTpQkBQUFafv27Vq/fr29/+HDh2vUqFFasGCB3Nzc9Nlnn+nAgQNas2ZNia/piSeeUMeOHSVJw4YNU2xsrNLS0tSgQQNJ0n333actW7Zo0qRJkqS+ffs6HL906VL5+vrq4MGDatKkidLT0xUYGKhbb71VNptN9erVs7dNT09XrVq1FB4ergoVKqhu3bpq165diWvFtYXQfQ1xd3dXdHT0ZR2TkZFhpJbY2FhlZmYa6bskIiIiLDs3AAAASichIUHTp0932DZt2jTFx8cX2f6WW26RzWazvw8LC9P8+fN18OBBubi4qH379vZ91apVU3BwsFJTUyVJqampuvfeex36CwsLcwjdvXv31ujRo/X222/r/vvv17Jly9S1a1f7yHJJNGvWzP5zzZo15enpaQ/cF7bt2rXL/v7IkSOKi4vTzp07derUKfsId3p6upo0aaKoqCjdcccdCg4OVvfu3XXPPffozjvvlCT169dPSUlJatCggbp376677rpLPXv2lIsL8e16xG/tGnLhGY7LcbkhvaQyMzOVmJhopO+SWqF/WXp+AAAAXJnY2FjFxMQ4bCtulPtqcHV11aBBg5ScnKw+ffro1Vdf1cKFCy+rjwoVKth/ttlsDu8vbPvz8+E9e/ZUvXr1tGTJEtWuXVv5+flq0qSJsrOzJUmtWrXSt99+q3Xr1mnTpk2KjIxUeHi43nzzTfn7++vQoUPatGmTNm7cqIcfflhz587Vtm3bCp0X1z5CNwAAAIAydbGp5EXZuXOnw/tPP/1UgYGBCg0NVW5urnbu3GmfXv7zzz/r0KFDCg0NlSSFhIQUefxfDR8+XE2aNNFzzz2n3Nxc9enT53Ivq8Qu1LhkyRLddtttkqRPPvmkUDtvb2/1799f/fv313333afu3bvrl19+UdWqVeXh4aGePXuqZ8+eGj16tBo1aqQDBw6oVatWxuqGGYRuAAAAAJZKT09XTEyMHnroIX322Wd65plnNH/+fAUGBqpXr14aMWKEFi9erEqVKmny5MmqU6eOevXqJUkaO3asOnbsqHnz5qlXr17asGGDw9TyC0JCQnTLLbdo0qRJGjp0qDw8PIxdT5UqVVStWjX961//kp+fn9LT0zV58mSHNgsWLJCfn59atmwpJycnvfHGG6pVq5Z8fHy0bNky5eXlqX379vL09NQrr7wiDw8Ph+e+cf1g9XIAAAAAlho0aJDOnz+vdu3aafTo0Ro3bpxGjhwp6Y9Vxlu3bq177rlHYWFhKigo0Nq1a+3TrG+55RYtWbJECxcuVPPmzfXBBx/o8ccfL/I8w4YNU3Z2toYOHWr0epycnLRy5Urt3btXTZo0UXR0tObOnevQplKlSpozZ47atGmjtm3b6tixY1q7dq2cnJzk4+OjJUuWqGPHjmrWrJk2bdqkd999V9WqVTNaN8ywFVz4Ajxcl6Kjo408e22q38vxYD1zU36uFVPcrFus7mqp2fzcpRtd52wutks3uo5lnSj//5rwiij/Iwc2T3MjOteKCgMnWl2Ccbm737O6BOPyd++8dKPr3SW+F7o8qBj/H6tLKNLMmTP1xhtv6IsvvrC6FNxAGOkGAAAAUK6dOXNGX375pRYtWqRHHnnE6nJwgyF0AwAAACjXxowZo9atW6tLly6FppaPGjVKXl5eRb5GjRplUcUoT1hIDQAAAEC5tmzZMi1btqzIfTNmzNCECROK3Oft7W2wKtwoCN0AAAAAblg1atRQjRo1rC4D5RjTywEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhLlYXgLIXGxurzMzMUvWRkZFRRtVcuWzlW12CceczK1hdgnF5ZwqsLsG4nP/ZrC7BKKcK5f93aKtQ/v9ZtNVvaHUJxuXufs/qEoxzaXuP1SUYl3PoK6tLMK7gl9+sLgHAVUToLocyMzOVmJhYqj6io6PLqBoAAAAAuHExvRwAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAJbp0qWLxo8fb3UZdtdaPbj+EboBAAAAXNeys7OtLgEoFqEbAAAAgCWioqK0bds2LVy4UDabTTabTWlpaRo2bJjq168vDw8PBQcHa+HChYWO6927t2bNmqXatWsrODhYkrR9+3a1aNFC7u7uatOmjVavXi2bzaZ9+/bZj/3yyy/Vo0cPeXl5qWbNmnrwwQd16tSpYus5duzY1bodKKdcrC4AAAAAwI1p4cKFOnz4sJo0aaIZM2ZIkqpUqaKbbrpJb7zxhqpVq6bt27dr5MiR8vPzU2RkpP3YzZs3y9vbWxs3bpQk/f777+rZs6fuuusuvfrqq/ruu+8KTRM/ffq0br/9dg0fPlyJiYk6f/68Jk2apMjISH344YdF1uPr63t1bgbKLUI3AAAAgDKVlZWlrKwsh21ubm5yc3Nz2Fa5cmW5urrK09NTtWrVsm+fPn26/ef69etrx44dev311x1Cd8WKFfXiiy/K1dVVkvTCCy/IZrNpyZIlcnd3V2hoqP773/9qxIgR9mMWLVqkli1bavbs2fZtS5culb+/vw4fPqygoKAi6wFKg9CNIrm7uys6Otqy80dERFh2bgAAAJROQkKCQ3CWpGnTpik+Pr5Exz/77LNaunSp0tPTdf78eWVnZ6tFixYObZo2bWoP3JJ06NAhNWvWTO7u7vZt7dq1czhm//792rJli7y8vAqdMy0tTUFBQSWqD7gchG4UKSEhweoSlKwXrC4BAAAAVyA2NlYxMTEO2/46yl2clStXasKECZo/f77CwsJUqVIlzZ07Vzt37nRoV7Fixcuu68yZM+rZs6eeeuqpQvv8/Pwuuz+gJAjdAAAAAMpUUVPJi+Pq6qq8vDz7+5SUFHXo0EEPP/ywfVtaWtol+wkODtYrr7yirKws+7l3797t0KZVq1Z66623FBAQIBeXoqPQX+sBSovVywEAAABYJiAgQDt37tSxY8d06tQpBQYGas+ePdqwYYMOHz6sqVOnFgrPRXnggQeUn5+vkSNHKjU1VRs2bNC8efMkSTabTZI0evRo/fLLLxowYIB2796ttLQ0bdiwQUOGDLEH7b/Wk5+fb+7icUMgdAMAAACwzIQJE+Ts7KzQ0FD5+voqIiJCffr0Uf/+/dW+fXv9/PPPDqPexfH29ta7776rffv2qUWLFpoyZYri4uIkyf6cd+3atZWSkqK8vDzdeeedatq0qcaPHy8fHx85OTkVWU96erq5i8cNgenlAAAAACwTFBSkHTt2OGxLTk5WcnKyw7Y/rzm0bNmyIvvq0KGD9u/fb3+/YsUKVahQQXXr1rVvCwwM1KpVqy6rHqA0CN0AAAAAyoWXX35ZDRo0UJ06dbR//377d3B7eHhYXRpuYIRuAAAAAOXCyZMnFRcXp5MnT8rPz0/9+vXTrFmzrC4LNzhCNwAAAIByYeLEiZo4caLVZQAOWEgNAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEBerC0DpuLu7Kzo62mFbRkaGRdWUrVvzvawuwbh6bY5bXYJxNieb1SUYl3e+wOoSjPJs7m11CcZl706zugTjKpw7b3UJKAM5h76yugTjKvx9ktUlGJe9aIrVJQC4igjd17mEhIRC2/4awgEAAAAA1mB6OQAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAgGW6dOmi8ePHF7s/ICBASUlJxuuw2WxavXq18fPgxkPoBgAAAADAEEI3AAAAABhUUFCg3Nxcq8twcC3WVF4RugEAAABYKjc3V2PGjFHlypVVvXp1TZ06VQUFBUW2TU9PV69eveTl5SVvb29FRkbqxx9/dGjz/PPP6+abb5arq6uCg4P173//22H/kSNH1KlTJ7m7uys0NFQbN24sca3Hjh2TzWbTypUr1aFDB7m7u6tJkybatm2bvc3WrVtls9m0bt06tW7dWm5ubvrkk0+Un5+vhIQE1a9fXx4eHmrevLnefPNN+3G//vqrBg4cKF9fX3l4eCgwMFDJycmSpOzsbI0ZM0Z+fn5yd3dXvXr1lJCQ4FDTvn377H2dPn1aNptNW7duLVVNKD0XqwsAAAAAUL5kZWUpKyvLYZubm5vc3NyKbL98+XINGzZMu3bt0p49ezRy5EjVrVtXI0aMcGiXn59vD9zbtm1Tbm6uRo8erf79+9vD5dtvv61x48YpKSlJ4eHheu+99zRkyBDddNNN6tq1q/Lz89WnTx/VrFlTO3fu1G+//XbRZ8qL89hjjykpKUmhoaFasGCBevbsqW+//VbVqlWzt5k8ebLmzZunBg0aqEqVKkpISNArr7yiF154QYGBgfroo4/097//Xb6+vurcubOmTp2qgwcPat26dapevbqOHj2q8+fPS5KefvppvfPOO3r99ddVt25dHT9+XMePH7/sui+3JpQeobucio2NVWZmptVlXLGIiAirSwAAAMAVSkhI0PTp0x22TZs2TfHx8UW29/f3V2Jiomw2m4KDg3XgwAElJiYWCt2bN2/WgQMH9O2338rf31+S9PLLL6tx48bavXu32rZtq3nz5ikqKkoPP/ywJCkmJkaffvqp5s2bp65du2rTpk36+uuvtWHDBtWuXVuSNHv2bPXo0eOyrnHMmDHq27evpD9G1tevX6+XXnpJEydOtLeZMWOG7rjjDkl/fBAxe/Zsbdq0SWFhYZKkBg0a6JNPPtHixYvVuXNnpaenq2XLlmrTpo2kPxaRuyA9PV2BgYG69dZbZbPZVK9evcuq90prQukRusupzMxMJSYmWl1GqRzRK1aXAAAAgCsQGxurmJgYh23FjXJL0i233CKbzWZ/HxYWpvnz5ysvL8+hXWpqqvz9/e2BW5JCQ0Pl4+Oj1NRUtW3bVqmpqRo5cqTDcR07dtTChQsd+rgQuC+c73L9+RgXFxe1adNGqampDm0uhGdJOnr0qM6dO2cPvBdkZ2erZcuWkqR//OMf6tu3rz777DPdeeed6t27tzp06CBJioqK0h133KHg4GB1795d99xzj+68887Lrvtya0LpEboBAAAAlKmLTSW/kVSsWNH+85kzZyRJ77//vurUqePQ7sK96tGjh7777jutXbtWGzduVLdu3TR69GjNmzdPrVq10rfffqt169Zp06ZNioyMVHh4uN588005Of2xVNefn4PPyckpk5pQeiykBgAAAMBSO3fudHj/6aefKjAwUM7Ozg7bQ0JCCj3LfPDgQZ0+fVqhoaH2NikpKQ7HpaSkOOw/fvy4Tpw44XC+y/XnY3Jzc7V3716FhIQU2z40NFRubm5KT09Xw4YNHV5/Hrn39fXV4MGD9corrygpKUn/+te/7Pu8vb3Vv39/LVmyRK+99preeust/fLLL/L19ZUkh2v686Jqpa0JpcNINwAAAABLpaenKyYmRg899JA+++wzPfPMM5o/f36hduHh4WratKkGDhyopKQk5ebm6uGHH1bnzp3t06Yfe+wxRUZGqmXLlgoPD9e7776rVatWadOmTfY+goKCNHjwYM2dO1e///67pkyZctk1P/vsswoMDFRISIgSExP166+/aujQocW2r1SpkiZMmKDo6Gjl5+fr1ltv1W+//aaUlBR5e3tr8ODBiouLU+vWrdW4cWNlZWXpvffeswf5BQsWyM/PTy1btpSTk5PeeOMN1apVSz4+PnJyctItt9yiJ598UvXr11dGRoYef/zxS15DSWpC6RG6AQAAAFhq0KBBOn/+vNq1aydnZ2eNGzeu0HPZkmSz2bRmzRo98sgj6tSpk5ycnNS9e3c988wz9ja9e/fWwoULNW/ePI0bN07169dXcnKyunTpIklycnLS22+/rWHDhqldu3YKCAjQ008/re7du19WzU8++aSefPJJ7du3Tw0bNtQ777yj6tWrX/SYmTNnytfXVwkJCfrmm2/k4+OjVq1a6Z///KckydXVVbGxsTp27Jg8PDx02223aeXKlZL+CMhz5szRkSNH5OzsrLZt22rt2rX2qeVLly7VsGHD1Lp1awUHB2vOnDkleub7UjWh9GwFxX0BHq5b0dHRknTdL6T2jP/frS7BuIFtLv9rHq43NifbpRtd57J/troCszxbVLK6BOPyTpyxugTjKjSufelGuObZvL2sLsG4Cn+fZHUJxmUvuvxR1etNxfj/WF2CMceOHVP9+vX1+eefq0WLFlaXg+sAz3QDAAAAAGAIoRsAAAAA/s/s2bPl5eVV5Otyv8sbkHimGwAAAADsRo0apcjIyCL3eXh4qE6dOuIJXVwOQjcAAAAA/J+qVauqatWqVpeBcoTp5QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAAAwhNANAAAAAIAhhG4AAAAAAAwhdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQF6sLQNlzd3dXenq61WWU2vfOeVaXYFz+OasrMM8t2MvqEoxz9smyugSjCs5nW12Cca6tAqwuwTzv8v/PYsGPp6wuwbiCX36zugTjshdNsboE41zHzLK6BABXESPd5VBCQoJq1KhhdRkAAAAAcMMjdAMAAAAAYAihGwAAAAAAQwjdAAAAAAAYQugGAAAAAMAQQjcAAAAAAIYQugEAAAAAMITQDQAAAACAIYRuAAAAAAAMIXQDAAAAAGAIoRsAAAAAAEMI3QAAAAAAGELoBgAAAADAEEI3AAAAAACGELoBAAAAADCE0A0AAAAAgCGEbgAAAAAADCF0AwAAAABgCKEbAAAAAABDCN0AAAAAABhC6AYAAAAAwBBCNwAAAAAAhhC6AQAAAFimS5cuGj9+fLH7AwIClJSUZLwOm82m1atXGz+Play4xqv1+7uWEboBAAAAADCE0A0AAAAA17ns7GyrS0AxCN0AAAAALJWbm6sxY8aocuXKql69uqZOnaqCgoIi26anp6tXr17y8vKSt7e3IiMj9eOPPzq0ef7553XzzTfL1dVVwcHB+ve//+2w/8iRI+rUqZPc3d0VGhqqjRs3lrjW7OxsjRkzRn5+fnJ3d1e9evX0/9q787ias/8P4K9b2kVZsqZCVLQRg+z7NiFGQ2RnZhCKse9ZhyzDiGGEoZgIY8kuZJ9S2UpEMbLUNCTRcn9/9O3+3CmEW6d77+v5eHhMnfvB605X3ffnnPM+ixYtAgDcv38fEokE165dk12fmpoKiUSC06dPy8b2798PS0tL6Orqok2bNtiyZQskEglSU1MBAMnJyejXrx+qVasGfX192NraIiAgQC5H69atMWbMGIwfPx4VKlRAp06dCv0c8iQmJqJv374wMjJCuXLl0KNHD9y/fx8AcPToUejq6soy5Rk3bhzatm0r+/zcuXNo0aIF9PT0YGpqCk9PT7x69eqTs6gyFt1ERERERKRQb968wYsXL+R+vXnz5r3Xb9myBaVKlcLly5exatUq+Pr6YuPGjfmuy8nJQY8ePZCSkoLQ0FAcO3YM9+7dg5ubm+ya4OBgjBs3Dt7e3rh+/TpGjRqFIUOG4NSpU7I/w9XVFdra2rh06RL8/PwwefLkQj+31atXY//+/di1axdiYmKwfft2mJubF/r3x8fHo0+fPujZsyciIyMxatQoTJ8+Xe6ajIwMNGzYEAcPHsT169cxcuRIDBw4EJcvX873/01bWxthYWHw8/MrdAYAyMzMRKdOnWBoaIizZ88iLCwMpUuXRufOnfH27Vu0a9cORkZG2L17t+z3ZGdnY+fOnXB3dwcA3L17F507d0bv3r0RFRWFnTt34ty5cxgzZswnZVF1pUQHoKKhq6uLCRMmiI7x2T7nTh0RERERlQyLFi3C3Llz5cZmz56NOXPmFHi9qakpVqxYAYlEgrp16yI6OhorVqzAiBEj5K47ceIEoqOjER8fD1NTUwDA1q1bUa9ePVy5cgWNGjXCsmXLMHjwYPzwww8AAC8vL1y8eBHLli1DmzZtcPz4cdy+fRtHjhxB1apVAQALFy5Ely5dCvXcEhISYGlpiebNm0MikcDMzOxT/tdg/fr1qFu3Ln766ScAQN26dXH9+nUsWLBAdk21atUwceJE2edjx47FkSNHsGvXLjRu3Fg2bmlpiaVLl37S359n586dyMnJwcaNGyGRSAAAmzdvhpGREU6fPo2OHTvi22+/xY4dOzBs2DAAuf//U1NT0bt3bwC5X2d3d3dZIzxLS0usXr0arVq1wrp166Crq/tZ2VQNi24VlbfERZmdwhbREYiIiIjoM0ydOhVeXl5yYzo6Ou+9vkmTJrLCDwCaNm2K5cuXIzs7W+66W7duwdTUVFZwA4CNjQ2MjIxw69YtNGrUCLdu3cLIkSPlfp+zszNWrVol92fkFdx5f19hDR48GB06dEDdunXRuXNndO/eHR07diz074+JiUGjRo3kxt4tpIHcGeWFCxdi165dePToEd6+fYs3b95AX19f7rqGDRsW+u/9r8jISMTFxcHQ0FBuPCMjA3fv3gUAuLu7o0mTJvj7779RtWpVbN++Hd26dYORkZHsz4iKisL27dtlv18qlSInJwfx8fGwtrb+7HyqhEU3EREREREplI6OzgeLbGXWoEEDxMfH4/Dhwzh+/Dj69u2L9u3bIygoCBoaubt3392PnpmZ+cl/x08//YRVq1Zh5cqVsLW1hYGBAcaPH5+vWZqBgcFnP4+0tDQ0bNhQrmDOU7FiRQBAo0aNUKtWLQQGBuL7779HcHAw/P395f6MUaNGwdPTM9+fUaNGjc/OpmpYdBMRERERkVCXLl2S+/zixYuwtLSEpqam3Li1tTUSExORmJgom+2+efMmUlNTYWNjI7smLCwMgwYNkv2+sLAwuccTExPx+PFjVKlSRfb3fYoyZcrAzc0Nbm5u6NOnDzp37oyUlBRZsfr48WM4OjoCgFxTNSB3OfmhQ4fkxq5cuSL3eVhYGHr06IEBAwYAyN2HHhsbK3sOitCgQQPs3LkTJiYmKFOmzHuvc3d3x/bt21G9enVoaGigW7ducn/GzZs3Ubt2bYXlUkVspEZEREREREIlJCTAy8sLMTExCAgIwM8//4xx48blu659+/awtbWFu7s7wsPDcfnyZXh4eKBVq1ZwcnICAEyaNAn+/v5Yt24d7ty5A19fX+zZs0e2R7p9+/aoU6cOBg0ahMjISJw9ezZfI7MP8fX1RUBAAG7fvo3Y2Fj88ccfqFy5MoyMjKCnp4cmTZpg8eLFuHXrFkJDQzFjxgy53z9q1Cjcvn0bkydPRmxsLHbt2iWbPc5bYm9paYljx47h/PnzuHXrFkaNGpWvQ/uXcnd3R4UKFdCjRw+cPXsW8fHxOH36NDw9PfHw4UO568LDw7FgwQL06dNHbgXD5MmTcf78eYwZMwbXrl3DnTt3sG/fPjZS+w8W3UREREREJJSHhwdev36Nxo0bY/To0Rg3bly+fdlAblG6b98+GBsbo2XLlmjfvj1q1qyJnTt3yq7p2bMnVq1ahWXLlqFevXpYv349Nm/ejNatWwMANDQ0EBwcLPv7hg8fLtfE7GMMDQ2xdOlSODk5oVGjRrh//z4OHTokW1r+22+/ISsrCw0bNsT48ePh4+Mj9/stLCwQFBSEPXv2wM7ODuvWrZMV/XkF7YwZM9CgQQN06tQJrVu3RuXKldGzZ89P+V/6Ufr6+jhz5gxq1KgBV1dXWFtbY9iwYcjIyJCb+a5duzYaN26MqKgoWdfyPHZ2dggNDUVsbCxatGgBR0dHzJo1S26/PAES6fsOwCMSbLJ5P9ERitykun+LjlDkdOoafvwiJSd99f4jUFRCKdW/P1uqphq8OShTWnSCIid98lx0hKKXowZv2zQkH79GyWmPKXyBp6y0KtQUHUGpLFiwAH5+fkhMTBQdhYoA93QTEREREREVo19++QWNGjVC+fLlERYWhp9++olLslWY6k9fEBERERERFdLChQtRunTpAn8V9izvj7lz5w569OgBGxsbzJ8/H97e3u89w7ywtm/f/t7c9erVU0hu+jxcXk4lFpeXqwYuL1cBXF6uGri8XDVweblK4PLyki0lJQUpKSkFPqanp4dq1aoVc6LCefny5XubrWlpacHMzKyYE1EeLi8nIiIiIiL6n3LlyqFcuXKiY3wyQ0NDGBqq/mSHMlL96QsiIiIiIiIiQVh0ExERERERERURFt1ERERERERERYRFNxEREREREVERYdFNREREREREVERYdBMREREREREVERbdREREREREREWERTcRERERERFREWHRTURERERERFREWHQTERERERERFREW3URERERERERFhEU3ERERERERURFh0U1ERERERERURFh0ExERERERERURFt1ERERERERERYRFNxEREREREVERYdFNREREREREVERYdBMREREREREVEYlUKpWKDkEk2ps3b7Bo0SJMnToVOjo6ouMUCT5H1cDnqBr4HFUDn6PyU/XnB6jHcyQq6Vh0EwF48eIFypYti3///RdlypQRHadI8DmqBj5H1cDnqBr4HJWfqj8/QD2eI1FJx+XlREREREREREWERTcRERERERFREWHRTURERERERFREWHQTAdDR0cHs2bNVusEIn6Nq4HNUDXyOqoHPUfmp+vMD1OM5EpV0bKRGREREREREVEQ4001ERERERERURFh0ExERERERERURFt1ERERERERERYRFNxEREREREVERYdFNpKbYQ5FKori4OBw5cgSvX78GwNcpUXFLSEgo8N+dVCpFQkKCgERERMqP3cuJ3pGdnY3o6GiYmZnB2NhYdJwvNnjwYKxduxYGBgZy4/fv38fAgQNx9uxZQck+n5eXV6Gv9fX1LcIkpEjJyclwc3PDyZMnIZFIcOfOHdSsWRNDhw6FsbExli9fLjoiFeDFixeFvrZMmTJFmEQcVfu5oampicePH8PExERuPDk5GSYmJsjOzhaUjIhIeZUSHYBIpPHjx8PW1hbDhg1DdnY2WrVqhfPnz0NfXx8HDhxA69atRUf8IpGRkbCzs8Pvv/+Opk2bAgC2bNkCT09PtG3bVnC6zxMREVGo6yQSSREnKT4hISEoXbo0mjdvDgBYu3Ytfv31V9jY2GDt2rUq8UZ/woQJKFWqFBISEmBtbS0bd3Nzg5eXl1IW3cbGxoV+HaakpBRxmqJhZGT00ecolUohkUhUplhT9Z8beV+v/0pLS4Ourq6AREXn7NmzWL9+Pe7evYugoCBUq1YN27Ztg4WFhez7rbJZvXp1oa/19PQswiRE9C4W3aTWgoKCMGDAAADAn3/+ifj4eNy+fRvbtm3D9OnTERYWJjjhl7l8+TKmTZuG1q1bw9vbG3FxcTh8+DB8fX0xYsQI0fE+y6lTp0RHKHaTJk3CkiVLAADR0dHw9vaGl5cXTp06BS8vL2zevFlwwi939OhRHDlyBNWrV5cbt7S0xIMHDwSl+jIrV64UHaHIqeO/R1X9uZG3ikgikWDmzJnQ19eXPZadnY1Lly7BwcFBUDrF2717NwYOHAh3d3dERETgzZs3AIB///0XCxcuxKFDhwQn/DwrVqwo1HUSiYRFN1ExYtFNau358+eoXLkyAODQoUP45ptvUKdOHQwdOhSrVq0SnO7LaWlp4aeffoK+vj7mz5+PUqVKITQ0VDbrrUoePnwIAPmKNlUQHx8PGxsbALlvFLt3746FCxciPDwcXbt2FZxOMV69eiX3Jj9PSkoKdHR0BCT6coMGDRIdoci1atVKdIRip6o/N/JWEUmlUkRHR0NbW1v2mLa2Nuzt7TFx4kRR8RTOx8cHfn5+8PDwQGBgoGzc2dkZPj4+ApN9mfj4eNERiKgAbKRGaq1SpUq4efMmsrOzERISgg4dOgAA0tPToampKTjdl8vMzIS3tzeWLFmCqVOnomnTpnB1dVXaO/j/lZOTg3nz5qFs2bIwMzODmZkZjIyMMH/+fOTk5IiOpzDa2tpIT08HABw/fhwdO3YEAJQrV+6T9tSWZC1atMDWrVtln0skEuTk5GDp0qVo06aNwGSKk52djd27d8PHxwc+Pj4IDg5WmSXXec6ePYsBAwagWbNmePToEQBg27ZtOHfunOBkiqOqPzdOnTqFU6dOYdCgQTh8+LDs81OnTuHIkSNYv349LC0tRcdUmJiYGLRs2TLfeNmyZZGamlr8gYrQ27dvERMTg6ysLNFRiNQWZ7pJrQ0ZMgR9+/ZFlSpVIJFI0L59ewDApUuXYGVlJTjdl3NyckJ6ejpOnz6NJk2aQCqVYunSpXB1dcXQoUPxyy+/iI74RaZPn45NmzZh8eLFcHZ2BgCcO3cOc+bMQUZGBhYsWCA4oWI0b94cXl5ecHZ2xuXLl7Fz504AQGxsrMrM7C9duhTt2rXD1atX8fbtW/z444+4ceMGUlJSlHa57rvi4uLQtWtXPHr0CHXr1gUALFq0CKampjh48CBq1aolOOGXe3e5bnh4uMos1/0vVf+5kbddJS4uDnfv3kXLli2hp6f33r3eyqpy5cqIi4uDubm53Pi5c+dQs2ZNMaEULD09HWPHjsWWLVsA5P7MqFmzJsaOHYtq1aphypQpghMSqREpkZr7448/pL6+vtLExETZmL+/v3Tv3r0CUynG0KFDpWlpafnGw8PDpfXq1ROQSLGqVKki3bdvX77xvXv3SqtWrSogUdF48OCBtFu3blI7Ozvpxo0bZePjx4+Xjh07VmAyxUpNTZX6+PhIv/nmG2mXLl2k06dPl/7999+iYylEly5dpJ07d5YmJyfLxp4/fy7t3LmztGvXrgKTKY6Dg4N0y5YtUqlUKi1durT07t27Uqk09/tNpUqVREZTOFX+uZGcnCxt27atVCKRSDU0NGRfxyFDhki9vLwEp1OchQsXSm1sbKQXL16UGhoaSs+ePSv9/fffpRUrVpSuXr1adDyF8PT0lDZs2FB69uxZqYGBgexruXfvXqmDg4PgdETqhUeGEampN2/eKO1e2Ty6urqIiopCnTp15MZjYmLg4OAgO+uZSDQDAwNcvHgRtra2cuORkZFwdnZGWlqaoGSKo6+vj5s3b8Lc3ByGhoaIjIxEzZo1ce/ePdjY2CAjI0N0xCKTmpoKIyMj0TEUwsPDA0+fPsXGjRthbW0t+zoeOXIEXl5euHHjhuiICiGVSrFw4UIsWrRItn1HR0cHEydOxPz58wWnUwwzMzPs3LkTTZo0kfs3GRcXhwYNGqjM9iQiZcDl5aT2Tpw4gRMnTuDp06f59gH/9ttvglIpzrZt2+Dn54f4+HhcuHABZmZmWLlyJSwsLNCjRw/R8b6Ivb091qxZk++IlDVr1sDe3l5QqqKRk5ODuLi4Al+nBe1LVDZRUVEFjkskEujq6qJGjRpKfZNIR0cHL1++zDeelpYm17BKmanDcl0AWLJkCczNzeHm5gYA6Nu3L3bv3o0qVarg0KFDsLOzE5zwy6jiSQL/lZ2djbCwMIwePRqTJk1CXFwc0tLSYGNjg9KlS4uOpzDPnj3Ld946kNu4UpW2ChApAxbdpNbmzp2LefPmwcnJSbY/T5WsW7cOs2bNwvjx47FgwQJZ0yYjIyOsXLlS6YvupUuXolu3bjh+/LisI/uFCxeQmJioMvtHAeDixYvo378/Hjx4gP8uTlKV848dHBxk//7ynuO7/x61tLTg5uaG9evXK+VZwd27d8fIkSOxadMmNG7cGEDuHuDvvvsOLi4ugtMpxogRIzBu3Dj89ttvkEgk+Pvvv3HhwgVMnDgRM2fOFB1PYfz8/LB9+3YAwLFjx3Ds2DEcPnwYu3btwsSJE3H06FHBCb+MKp4k8F+ampro2LEjbt26BSMjI9npEKrGyckJBw8exNixYwH8//fUjRs3quQpJkQlmtDF7USCVa5cWbp161bRMYqMtbW1NDg4WCqVyu+xjI6OlpYvX15gMsV59OiRdNq0aVJXV1epq6urdPr06dJHjx6JjqVQ9vb20m+++UZ68+ZN6T///CNNTU2V+6UK9u7dK61bt65048aN0qioKGlUVJR048aNUmtra2lgYKD0999/l1avXl3q7e0tOupn+eeff6QuLi5SiUQi1dbWlmpra0s1NDSkPXv2VJmvYU5OjtTHx0dqYGAglUgkUolEItXV1ZXOmDFDdDSF0tXVlSYkJEil0tw9syNHjpRKpVJpTEyM1MjISGQ0hejSpYvsa1a6dGnpvXv3pNnZ2dJvvvlG2rt3b8HpFKdhw4bS48ePi45RpM6ePSstXbq09LvvvpPq6upKx40bJ+3QoYPUwMBAevXqVdHxiNQK93STWitfvjwuX76sEp2DC6Knp4fbt2/DzMxMbj/XnTt3YGdnp9R7njMzM9G5c2f4+fmp1DE2BTEwMEBkZCRq164tOkqRady4MebPn49OnTrJjR85cgQzZ87E5cuXsXfvXnh7e+Pu3buCUn4eqVSKxMREVKxYEY8ePcKtW7cAANbW1ir5NX379q3KLtcFgKpVqyIoKAjNmjVD3bp14ePjg2+++QYxMTFo1KiR0u+TvX79Otq1a4cGDRrg5MmTcHFxkTtJQFV+XoaEhGDq1KmYP38+GjZsCAMDA7nHy5QpIyiZYt29exeLFy9GZGQk0tLS0KBBA0yePDlffwkiKlpcXk5qbfjw4dixY4dKLX18l4WFBa5duwYzMzO58ZCQEFhbWwtKpRhaWlrv3Qesar766ivExcWpZIGWJzo6Ot/rFMhtBBQdHQ0gdwn648ePizvaF5NKpahduzZu3LgBS0tLlf06/v7773B1dYW+vr7KLtcFAFdXV/Tv3x+WlpZITk5Gly5dAAAREREq8bWtX78+YmNjsWbNGhgaGiItLQ2urq4YPXo0qlSpIjqewnTt2hUA4OLiIreVRfq/o9FUYdsOANSqVQu//vqr6BhEao9FN6m1jIwMbNiwAcePH4ednR20tLTkHvf19RWUTDG8vLwwevRoZGRkQCqV4vLlywgICMCiRYuwceNG0fG+2IABA2TndKuysWPHwtvbG0lJSbC1tc33OlX2xk0AYGVlhcWLF2PDhg2yxmKZmZlYvHix7OzjR48eoVKlSiJjfhYNDQ1ZgabKqzImTJgg26M+YMAAdOrUCZqamqJjKdyKFStgbm6OxMRELF26VDaT//jxY/zwww+C0ylG2bJlMX36dNExitSpU6dERyhy7du3x4ABA+Dq6qoyM/dEyorLy0mttWnT5r2PSSQSnDx5shjTFI3t27djzpw5siW51apVw5w5czBs2DDByb7c2LFjsXXrVlhaWha4PFDZb5rk0dDQyDcmkUhUakbm/PnzcHFxgYaGhuwmQnR0NLKzs3HgwAE0adIE27ZtQ1JSEiZNmiQ47af7888/sXTpUqxbtw7169cXHadIZGVlISQkBAEBAdi3bx/09fXxzTffwN3dHc2aNRMdjwpJ1U8SUCfjxo3Drl278O+//6Jbt24YMGAAunbtmu/GLREVPRbdRCrs9evXkEql0NfXR3p6Oq5fv46wsDDY2Njk2zurjNThpgmAjx7TU9CybGX08uVLbN++HbGxsQCAunXron///jA0NBSc7MsZGxsjPT0dWVlZ0NbWhp6entzjKSkpgpIVjfT0dAQHB2PHjh04fvw4qlevrnR78T/m5s2bSEhIwNu3b+XGlb0bvYaGhkqfJJDnzJkzH3xcFY5iBHKPmzx+/Dh27NiB4OBgaGpqok+fPnB3d0erVq1ExyNSGyy6iVRYx44d4erqiu+++w6pqamwsrKClpYWnj9/Dl9fX3z//feiIxLJUdVCZsuWLR98fNCgQcWUpPg8f/4cgYGB8PPzw61bt1RiRQYA3Lt3D7169UJ0dLRsxQnw/4Wpsj/Pffv2YfLkyZg0aZLseLvLly9j+fLlmD17NrKysjBlyhS4ublh2bJlgtN+vvetIMqj7F/HgmRkZODPP//EggULZCuJiKh4cE83qR1XV1f4+/ujTJkycHV1/eC1e/bsKaZURSM8PBwrVqwAAAQFBaFSpUqIiIjA7t27MWvWLJUpuuPi4nD37l20bNkSenp6smXXymz//v3o0qULtLS0sH///g9eq+wFKVBwIaNKb4BVsaguSN4M9/bt23HixAmYmpqiX79+CAoKEh1NYcaNGwcLCwucOHECFhYWuHz5MpKTk+Ht7a3URWieBQsWYNWqVXKroWxtbVG9enXZSQIGBgZK/3z/+ecfuc8zMzMRERGBmTNnYsGCBYJSFZ2kpCQEBgbi999/R1RUlOyGChEVDxbdpHbKli0rezNftmxZwWmKVnp6umxp7tGjR+Hq6goNDQ00adLko0uWlUFycjL69u2LU6dOQSKR4M6dO6hZsyaGDRsGY2NjLF++XHTEz9azZ08kJSXBxMQEPXv2fO91qrKn+7+FzKVLl5CSkqL0b+zfdffuXWzevBl3797FqlWrYGJigsOHD6NGjRqoV6+e6Hhf7Ntvv8WBAwegr6+Pvn37YubMmWjatKnoWAp34cIFnDx5EhUqVICGhgY0NDTQvHlzLFq0CJ6enoiIiBAd8Yuo8kkC7yro53+HDh2gra0NLy8v/PXXXwJSKdaLFy+we/du7NixA6dPn0bNmjXh7u6OnTt3qszRb0TKgkU3qZ3NmzcX+LEqql27Nvbu3YtevXrhyJEjmDBhAgDg6dOnKtHJdMKECdDS0kJCQoLcEWhubm7w8vJS6qI7JyenwI9V1X8LGU1NTZUqZEJDQ9GlSxc4OzvjzJkzWLBgAUxMTBAZGYlNmzapxEywpqYmdu3apbJdy/NkZ2fLbmZWqFABf//9N+rWrQszMzPExMQITvflVPkkgcKoVKmSSnwdgdznYmxsDDc3NyxatAhOTk6iIxGpLRbdpPaysrJw+vRp3L17V9a06e+//0aZMmVkR8Eoq1mzZqF///6YMGEC2rVrJ5t1Onr0KBwdHQWn+3JHjx7FkSNHUL16dblxS0tLlZjJL0hGRoZSNy96H1UvZKZMmQIfHx94eXnJNYZr27Yt1qxZIzCZ4mzfvl32saq+ToHcc6wjIyNhYWGBr776CkuXLoW2tjY2bNiAmjVrio73xdauXQsXFxdUr169wJMEgNztIMp+PNp/u7RLpVI8fvwYixcvhoODg5hQCrZ//360a9euwP3rRFS8WHSTWnvw4AE6d+6MhIQEvHnzBh06dIChoSGWLFmCN2/ewM/PT3TEL9KnTx80b94cjx8/hr29vWy8Xbt26NWrl8BkivHq1Svo6+vnG09JSVGpI22ys7OxcOFC+Pn54cmTJ4iNjUXNmjUxc+ZMmJubq8Txb6peyERHR2PHjh35xk1MTPD8+XMBiRQvJycHCxYsUOnXKQDMmDEDr169AgDMmzcP3bt3R4sWLVC+fHns3LlTcLov16xZM8THx8udJPDNN9/InSQwcOBAkREVwsHBQa4RXp4mTZrgt99+E5RKsTp06ICsrCycPHlSJScWiJQJi25Sa+PGjYOTkxMiIyNRvnx52XivXr0wYsQIgckUp3LlyqhcubLcmKo0UGnRogW2bt2K+fPnA8jd35yTk4OlS5d+8DgxZbNgwQJs2bIFS5culXtd1q9fHytXrlSJYkbVCxkjIyM8fvwYFhYWcuMRERGoVq2aoFSK5ePjo/KvUwByDcZq166N27dvIyUlBcbGxkrfwDEzMxNWVlY4cOAAvvvuO9FxilR8fLzc5xoaGqhYsaJKrdBQ9YkFImXCopvU2tmzZ3H+/HnZvrU85ubmePTokaBUVFhLly5Fu3btcPXqVbx9+xY//vgjbty4gZSUFISFhYmOpzBbt27Fhg0b0K5dO7k3wvb29rh9+7bAZIqjyoUMkNtkbPLkyfjjjz9kN4fCwsIwceJEeHh4iI6nEOrwOn2fcuXKiY6gEFpaWsjIyBAdo1gU1CwuNTVVpYpudZhYIFIW3ORBai0nJ6fAzs8PHz6U23dJJVP9+vURGxuL5s2bo0ePHnj16hVcXV0RERGhUp1ZHz16hNq1a+cbz8nJQWZmpoBExaNcuXIqUXADwMKFC2FlZQVTU1OkpaXBxsYGLVu2RLNmzTBjxgzR8RRCXV6nGRkZ+Omnn9C1a1c4OTmhQYMGcr+U3ejRo7FkyRJkZWWJjlKklixZIreKpm/fvihXrhyqVauGyMhIgckU5+zZs5gxYwYnFohKAM50k1rr2LEjVq5ciQ0bNgDIXZ6clpaG2bNno2vXroLT0cckJCTA1NQU06dPL/CxGjVqCEileDY2Njh79my+mZmgoCCVaIinDrS1tfHrr79i1qxZiI6ORlpaGhwdHWFpaSk6msKoy+t02LBhOHr0KPr06YPGjRurzI2hPFeuXMGJEydw9OhR2NrawsDAQO7xPXv2CEqmWH5+frLmf8eOHcOxY8cQEhKCXbt2YdKkSTh69KjghF+OEwtEJQeLblJry5cvR6dOnWBjY4OMjAz0798fd+7cQYUKFRAQECA6Hn2EhYUFHj9+DBMTE7nx5ORkWFhYqMT51UBuF/pBgwbh0aNHyMnJwZ49exATE4OtW7fKuglTyTZv3jxMnDgRpqamMDU1lY2/fv0aP/30E2bNmiUwnWKoy+v0wIEDOHToEJydnUVHKRJGRkbo3bu36BhFLikpSfZv8cCBA+jbty86duwIc3NzfPXVV4LTKQYnFohKDon0v20bidRMVlYWdu7cicjISKSlpaFBgwZwd3eHnp6e6Gj0ERoaGnjy5AkqVqwoN/7gwQPY2NjIGnOpgrNnz2LevHlyr9NZs2ahY8eOoqNRIWhqar73BpGJiYnK3CBSh9epjY0NAgMDZcdpkXKqWrUqgoKC0KxZM9StWxc+Pj745ptvEBMTg0aNGuHFixeiI36xhw8folOnTpBKpbhz5w6cnJxkEwtnzpzJ9/2IiIoOi25Sa2fOnEGzZs1QqpT8oo+srCycP38eLVu2FJSMPsTLywsAsGrVKowYMULu2LDs7GxcunQJmpqaKtVMjZTb+24QnTx5Em5ubnj27JmgZPSpDh8+jNWrV8PPz6/AZlykHMaMGYMDBw7A0tISERERuH//PkqXLo3AwEAsXboU4eHhoiMqRFZWFgIDAxEVFcWJBSKBuLyc1FqbNm0KnH36999/0aZNG5WZfVI1ERERAACpVIro6Gi5JjHa2tqwt7fHxIkTRcVTuJo1a+LKlSty3WeB3E67DRo0wL179wQlo4/J674ukUhQp04duf2/2dnZSEtLU/mjmVSNk5MTMjIyULNmTejr60NLS0vu8ZSUFEHJFCcoKAi7du1CQkIC3r59K/eYqhSjK1asgLm5ORITE7F06VLZmdWPHz/GDz/8IDid4pQqVQoDBgwQHYNI7bHoJrUmlUoLbIKTnJycr3kMlRynTp0CAAwZMgSrVq1CmTJlBCcqWvfv3y/wBtCbN2/YgbaEW7lyJaRSKYYOHYq5c+eibNmysse0tbVhbm6Opk2bCkz4ZT7lSDdVKEYBoF+/fnj06BEWLlyISpUqqVwjtdWrV2P69OkYPHgw9u3bhyFDhuDu3bu4cuUKRo8eLTqewmhpaRV4c3bChAkC0ijO/v37C32ti4tLESYhondxeTmpJVdXVwDAvn370LlzZ+jo6Mgey87ORlRUFOrWrYuQkBBREekzvHjxAidPnoSVlRWsrKxEx/lieW+eevbsiS1btsgVbNnZ2Thx4gSOHTuGmJgYURGpkEJDQ+Hs7JxvK4uy27JlS6GvHTRoUBEmKT76+vq4cOEC7O3tRUcpElZWVpg9ezb69esHQ0NDREZGombNmpg1axZSUlKwZs0a0REVYsuWLahQoQK6desGAPjxxx+xYcMG2NjYICAgQGm3DmhoFO40YIlEwtV8RMVItX76ExVSXvEilUphaGgot7dJW1sbTZo0wYgRI0TFo0Lq27cvWrZsiTFjxuD169dwcnLC/fv3IZVKERgYqPQdeHv27Akg983RfwsWLS0tmJubY/ny5QKS0acyNDTErVu3YGtrCyD3ht/mzZthY2ODOXPm5DtHV1l8TiG9ePFifPfddzAyMlJ8oGJgZWWF169fi45RZBISEtCsWTMAgJ6eHl6+fAkAGDhwIJo0aaIyRffChQuxbt06AMCFCxewdu1arFixAgcOHMCECROU9mi0nJwc0RGIqAAsukktbd68GQBgbm6OiRMncim5kjpz5ozsjO7g4GBIpVKkpqZiy5Yt8PHxUfqiO+/Nk4WFBa5cuYIKFSoITkSfa9SoUZgyZQpsbW1x7949uLm5wdXVFX/88QfS09OxcuVK0RGLzcKFC9G3b1+lLboXL14Mb29vLFiwALa2tvn2dCv7dpfKlSsjJSUFZmZmqFGjBi5evAh7e3vEx8dDlRZHJiYmonbt2gCAvXv3onfv3hg5ciScnZ3RunVrseGKma2tLQ4dOiR3nCERKVbh1qAQqajZs2fDwMAAz549w7lz53Du3Dl2EVYi//77L8qVKwcACAkJQe/evaGvr49u3brhzp07gtMpTnx8PAtuJRcbGwsHBwcAwB9//IFWrVphx44d8Pf3x+7du8WGK2bKXrh17twZFy5cQLt27WBiYgJjY2MYGxvDyMgIxsbGouN9sbZt28q2tgwZMgQTJkxAhw4d4Obmhl69eglOpzilS5dGcnIyAODo0aPo0KEDAEBXV1elVzIU5P79+8jMzBQdg0ilcaab1Fp6ejrGjBmDrVu3ymYVNTU14eHhgZ9//lnuKCoqeUxNTXHhwgWUK1cOISEhCAwMBAD8888/0NXVFZxOsUJDQ7Fs2TLcunULQO5ZwZMmTUKLFi0EJ6PCkEqlsu8xx48fR/fu3QHkvoafP38uMhp9orxGjqpq+vTpqFatGgBg9OjRKF++PM6fPw8XFxd07txZcDrF6dChA4YPHw5HR0fExsaia9euAIAbN27A3NxcbDgiUjksukmtTZgwAaGhofjzzz/h7OwMADh37hw8PT3h7e0t2+9FJdP48ePh7u6O0qVLo0aNGrIlgWfOnJHtnVUFv//+O4YMGQJXV1d4enoCAMLCwtCuXTv4+/ujf//+ghPSxzg5OcHHxwft27dHaGio7HtLfHw8KlWqJDgdfYpWrVoV6roffvgB8+bNU7pVKrVr15Y7SvPbb7/Ft99+i+TkZJiYmKhM8621a9dixowZSExMxO7du2VHMv7111/o16+f4HREpGrYvZzUWoUKFRAUFJRv/9apU6fQt29fLjVXAlevXkViYiI6dOggO2f14MGDMDIykt1IUXbW1tYYOXJkvqNsfH198euvv8pmv6nkioqKgru7OxISEuDl5YXZs2cDAMaOHYvk5GTs2LFDcMLi825HbFVWpkwZXLt2Temep4aGBpKSkmRFd54HDx7AxsYGr169EpSMioq6/JskEokz3aTW0tPTC5xlMjExQXp6uoBE9KmcnJxgZ2eH+Ph41KpVC6VKlZIdAaMq7t27h6+//jrfuIuLC6ZNmyYgEX0qOzs7REdH5xv/6aefoKmpKSARFTVlm9Pw8vICkHtawqxZs+S2V2VnZ+PSpUuyvgSq4uzZs1i/fj3u3buHP/74A9WqVcO2bdtgYWGB5s2bi45HRCqEjdRIrTVt2hSzZ89GRkaGbOz169eYO3cumjZtKjAZFUZ6ejqGDRsGfX191KtXDwkJCQByZw8XL14sOJ3imJqa4sSJE/nGjx8/zm6zSiQ1NRUbN27E1KlTkZKSAgC4efMmnj59KjhZ8WrRooXcMY1UMkRERCAiIgJSqRTR0dGyzyMiInD79m3Y29vD399fdEyF2b17Nzp16gQ9PT2Eh4fjzZs3AHIbdC5cuFBwOiJSNZzpJrW2cuVKdO7cGdWrV4e9vT0AIDIyErq6ujhy5IjgdPQxU6dORWRkJE6fPi3X4Kd9+/aYM2cOpkyZIjCd4nh7e8PT0xPXrl2TnZ8bFhYGf39/rFq1SnA6KoyoqCi0a9cORkZGuH//PkaMGIFy5cphz549SEhIwNatW0VH/GLh4eHQ0tL66Fnkhw4dEhmT3iOvQdyQIUOwatUqpT/67GN8fHzg5+cHDw8PWRNOAHB2doaPj4/AZIqRmZmJzp07w8/PD5aWlh+8dv369ewtQVTEuKeb1F56ejq2b9+O27dvA8jdP+vu7s6ZGCVgZmaGnTt3okmTJnJ70uLi4tCgQQO8ePFCdESFCQ4OxvLly2X7t62trTFp0iT06NFDcDIqjPbt26NBgwZYunSp3Gv1/Pnz6N+/P+7fvy864hdr1KgRpkyZgt69e+PevXuoV68eevXqhStXrqBbt25qdRY5wH2yJZ2+vj5u3rwJc3Nzua/VvXv3YGNjI7cCTllVrFgR58+f/2jRTURFjzPdpLYyMzNhZWWFAwcOYMSIEaLj0Gd49uxZvmY/APDq1StIJBIBiRQvKysLCxcuxNChQ3Hu3DnRcegzXblyBevXr883Xq1aNSQlJQlIpHj/PYu8ZcuW2LFjB8LCwvDtt9+qXdFNJVvlypURFxeX73iwc+fOqcyNkgEDBmDTpk0qtd2KSFmx6Ca1paWlpRJ3stWZk5MTDh48iLFjxwKArNDeuHGjyuzJL1WqFJYuXQoPDw/RUegL6OjoFLjyIjY2FhUrVhSQSPF4Frm8AQMGqPwSbWU2YsQIjBs3Dr/99hskEgn+/vtvXLhwARMnTsTMmTNFx1OIrKws/Pbbbzh+/DgaNmwIAwMDucd9fX0FJSNSPyy6Sa2NHj0aS5YswcaNG1GqFP85KJuFCxeiS5cuuHnzJrKysrBq1SrcvHkT58+fR2hoqOh4CtOuXTuEhobmm5Eh5eHi4oJ58+Zh165dAHJvECUkJGDy5Mno3bu34HSKoS5nkZubm2Po0KEYPHgwatSo8d7r8p4/lUxTpkxBTk4O2rVrh/T0dLRs2RI6OjqYOHGi7Eausrt+/ToaNGgAIPcG37tUZTUYkbLgnm5Sa7169cKJEydQunRp2Nra5rsLvGfPHkHJqLDu3r2LxYsXIzIyEmlpaWjQoAEmT54sa+akCvz8/DB37ly4u7sXOFvh4uIiKBkV1r///os+ffrg6tWrePnyJapWrYqkpCQ0bdoUhw4dyvc1VUbqchb5ypUr4e/vj+vXr6NNmzYYNmwYevXqBR0dHdHRqJCys7MRFhYGOzs76OvrIy4uDmlpabCxsUHp0qVFxyMiFcSim9TakCFDPvj45s2biykJ0ftpaLz/dEeJRILs7OxiTENf4ty5c4iKipLdIGrfvr3oSEUuIyMDmpqa0NLSEh1FocLDw+Hv74+AgABkZ2ejf//+GDp0qGxmkUo2XV1d3Lp1CxYWFqKjEJEaYNFNRErlUzqScz8lUfFKTU1FUFAQ7t69i0mTJqFcuXIIDw9HpUqVUK1aNdHxikRmZiZ++eUXTJ48GZmZmbC1tYWnpyeGDBnCJbwlmJOTE5YsWYJ27dqJjlKkrl69il27diEhIQFv376Ve4yr+YiKDzexEgF4+vQpYmJiAAB169YtsCM2lQxGRkYffSMrlUo5A0zCrV69utDXenp6FmGS4qEOZ5G/KzMzE8HBwdi8eTOOHTuGJk2aYNiwYXj48CGmTZuG48ePq8ySelXk4+ODiRMnYv78+QVu21GFm7aBgYHw8PBAp06dcPToUXTs2BGxsbF48uQJevXqJToekVrhTDeptRcvXmD06NEIDAyUFWiamppwc3PD2rVrUbZsWcEJ6b8+pUFaq1atijBJ8Tpx4gRWrFghd073+PHj1WJ5srIq7LJViUSCe/fuFXGaoqcOZ5EDucvKN2/ejICAAGhoaMDDwwPDhw+HlZWV7Jrr16+jUaNGeP36tcCk9CHvbtt590auKt20tbOzw6hRozB69GjZv0kLCwuMGjUKVapUwdy5c0VHJFIbLLpJrbm5uSEiIgI///yz7IipCxcuYNy4cXBwcEBgYKDghETAL7/8gnHjxqFPnz6y1+nFixcRFBSEFStWYPTo0YITEgFly5ZFeHg4atWqJVd0P3jwAHXr1lWZIxo1NTXRoUMHDBs2DD179ixwr/qrV68wZswY9gUpwT52A1cVbtoaGBjgxo0bMDc3R/ny5XH69GnY2tri1q1baNu2LR4/fiw6IpHa4PJyUmsHDhzAkSNH0Lx5c9lYp06d8Ouvv6Jz584Ck1FhpaamYtOmTbIZ4Hr16mHo0KEqtUph4cKFWLFiBcaMGSMb8/T0hLOzMxYuXMiiW8nk3etWtf2+6nAWOQDcu3cPZmZmH7zGwMCABXcJpwpF9ccYGxvj5cuXAIBq1arh+vXrsLW1RWpqKtLT0wWnI1Iv72+JS6QGypcvX2BxVrZsWRgbGwtIRJ/i6tWrqFWrFlasWIGUlBSkpKTA19cXtWrVQnh4uOh4CpOamlrgTaCOHTvi33//FZCIPsfWrVtha2sLPT096Onpwc7ODtu2bRMdS2HyziLPzMwEoJpnkQP4aMFNyuOff/7BsmXLMGzYMAwbNgzLly9HSkqK6FgK07JlSxw7dgwA8M0332DcuHEYMWIE+vXrp/IN5IhKGi4vJ7W2YcMG/PHHH9i2bRsqV64MAEhKSsKgQYPg6uqKUaNGCU5IH9KiRQvUrl0bv/76K0qVyl24k5WVheHDh+PevXs4c+aM4ISK0b9/fzg6OmLSpEly48uWLcPVq1e5DUIJ+Pr6YubMmRgzZgycnZ0B5B4ftnbtWvj4+GDChAmCE345VT6L3NjYuNArE1SpaFNlZ86cwddff42yZcvCyckJAPDXX38hNTUVf/75J1q2bCk44ZdLSUlBRkYGqlatipycHCxduhTnz5+HpaUlZsyYwckFomLEopvUmqOjI+Li4vDmzRvUqFEDAJCQkAAdHR1YWlrKXatKM6eqQk9PDxEREXINjADg5s2bcHJyUpnlcz4+Pli2bBmcnZ3l9nSHhYXB29tbrsuuKnTBVkUWFhaYO3cuPDw85Ma3bNmCOXPmID4+XlAyxVPFs8i3bNki+zg5ORk+Pj7o1KmTXC+QI0eOYObMmSpxA0Ud2NraomnTpli3bh00NTUBANnZ2fjhhx9w/vx5REdHC05IRKqERTeptU/p3Dl79uwiTEKfo1KlSti2bRs6duwoN37kyBF4eHjgyZMngpIplrp1wVZFurq6uH79OmrXri03fufOHdja2qpMkzF10Lt3b7Rp00auxwIArFmzBsePH8fevXvFBKNPoqenh2vXrqFu3bpy4zExMXBwcFCJzvMF9VgAcn9W6OjoQFtbu5gTEakvNlIjtcZCWrm5ublh2LBhWLZsGZo1awYACAsLw6RJk9CvXz/B6RRHlWZB1VXt2rWxa9cuTJs2TW58586d+VbVKBN1O4scyL2pt2TJknzjnTt3xpQpUwQkos/RoEED3Lp1K1/RfevWLdjb2wtKpVhGRkYf3BZRvXp1DB48GLNnz5Y7Qo2IFI9FNxFy93G92/3a0dFRcCIqjGXLlkEikcDDwwNZWVkAAC0tLXz//fdYvHix4HRFQ1U7X6u6uXPnws3NDWfOnJHt6Q4LC8OJEyewa9cuwek+34oVK+Q+f/bsGdLT02FkZAQgtwmgvr4+TExMVKboLl++PPbt2wdvb2+58X379qF8+fKCUtGn8vT0xLhx4xAXF4cmTZoAyN22s3btWixevBhRUVGya+3s7ETF/CL+/v6YPn06Bg8ejMaNGwMALl++jC1btmDGjBl49uwZli1bBh0dnXw3BIlIsbi8nNTa06dP8e233+L06dNybxLbtGmDwMBAlTrmRpWlp6fj7t27AIBatWpBX19fcCLF27p1K3766SfcuXMHAFCnTh1MmjQJAwcOFJyMCuuvv/7CihUrZDf4rK2t4e3trTI3+Xbs2IFffvkFmzZtks0exsTEYMSIERg1ahTc3d0FJ1QMf39/DB8+HF26dMFXX30FALh06RJCQkLw66+/YvDgwWIDUqF8bGZXIpFAKpVCIpEgOzu7mFIpVrt27TBq1Cj07dtXbnzXrl1Yv349Tpw4gW3btmHBggW4ffu2oJRE6oFFN6k1Nzc33Lt3D1u3boW1tTWA3CZcgwYNQu3atREQECA4IZF6dL4m5VerVi0EBQXlu4nw119/oU+fPiq1TeLSpUtYvXq13A0UT09PWRFOJd+DBw8Kfa2yHhOnp6eHqKiofFtY7ty5A3t7e6SnpyM+Ph716tVTmcajRCUVi25Sa2XLlsXx48fRqFEjufHLly+jY8eOSE1NFROMCuXVq1dYvHgxTpw4gadPnyInJ0fucVVpKqZOna9VWU5ODuLi4gp8rarC8UT6+voIDQ0t8Ptp69at+aaelFK3bt2wceNGVKlSRXSUT1anTh24urrm2241ZcoUBAcHIyYmBlevXkWPHj3w6NEjQSmJ1AP3dJNay8nJgZaWVr5xLS2tfG+KqeQZPnw4QkNDMXDgQFSpUkVl9zk/fvxY1ijuXc2aNcPjx48FJKJPdfHiRfTv3x8PHjzAf+91K/Py1XflLWXduHEjGjRoACB3lvv7779XiWPD3pWdnY29e/fK9QJxcXGRHT1FquPMmTNK28l82bJl+Oabb3D48GHZzbCrV6/i9u3bCAoKAgBcuXIFbm5uImMSqQXOdJNa69GjB1JTUxEQEICqVasCAB49egR3d3cYGxsjODhYcEL6ECMjIxw8eFC25FpV1a9fH/3798/X6MbHxwc7d+7kebJKwMHBAXXq1MHcuXMLvEFUtmxZQckU59mzZxg0aBBCQkJkNzOzsrLQqVMn+Pv7w8TERHBCxYiLi0O3bt3w8OFDub3rpqamOHjwIGrVqiU4ISmSoaEhIiMjUbNmTdFRPkt8fDzWr1+P2NhYAEDdunUxatQomJubiw1GpGZYdJNaS0xMhIuLC27cuAFTU1PZWP369bF//35Ur15dcEL6EAsLCxw6dEi2H19V7d69G25ubmjfvn2Bna979eolOCF9jIGBASIjI/Od062KYmNjZU2ZrKysUKdOHcGJFKtr166QSqXYvn07ypUrBwBITk7GgAEDoKGhgYMHDwpOSIqk7EU3EZUMLLpJ7UmlUhw/flz2JtHa2lrllkKqqt9//x379u3Dli1bVLJj+btUvfO1qmvbti1+/PFHdO7cWXQU+kIGBga4ePEibG1t5cYjIyPh7OyMtLQ0QcmoKChz0X3mzJkPPq4KvSSIlAX3dJPak0gk6NChAzp06CA6ChWCo6Oj3NLcuLg4VKpUCebm5vn254eHhxd3vCLTsGFD/P7776Jj0Cd495zfsWPHwtvbG0lJSbC1tc33WlXWc4C9vLwwf/58GBgYwMvL64PX+vr6FlOqoqWjo4OXL1/mG09LS4O2traAREQFa926db6xd39+qkIvCSJlwaKb1N6JEyfyzSCOHz+es90lVM+ePUVHECI7OxvBwcGy16mNjQ169OiBUqX4bbykcnBwkJ31m2fo0KGyj1XhHOCIiAhkZmYCyL3J9b5mhqrU5LB79+4YOXIkNm3ahMaNGwPIPULsu+++g4uLi+B0RP/vn3/+kfs8MzMTERERmDlzJhYsWCAoFZF64vJyUmu//PILxo0bhz59+qBp06YAcrsMBwUFYcWKFRg9erTghETAjRs34OLigqSkJFnjptjYWFSsWBF//vkn6tevLzghFUQdzgFWR6mpqRg0aBD+/PNP2YqFzMxM9OjRA/7+/irRFI/+36JFi/D999/DyMhIdBSFCQ0NhZeXF/766y/RUYjUBotuUmvVq1fHlClTMGbMGLnxtWvXYuHChTy3soS7cuUKcnJy8NVXX8mNX7p0CZqamnBychKUTLGaNm2KihUrYsuWLTA2NgaQO4MxePBgPHv2DOfPnxeckNRdZmYm9PT0cO3aNbW5CRQXF4ebN28CyF15og5N8pTd/v37C32tKq9auH37NpycnNh/gKgYsegmtVa6dGlcu3Yt35ulO3fuwNHRkT+QSrjGjRvjxx9/RJ8+feTG9+zZgyVLluDSpUuCkimWnp4erl69inr16smNX79+HY0aNVLaM2TVyaJFi1CpUiW55eUA8Ntvv+HZs2eYPHmyoGSKU7NmTQQHB8Pe3l50lCK3adMmrFixAnfu3AEAWFpaYvz48Rg+fLjgZPQhGhoacp//d/uHqu13frevBJDbOPbx48dYvHgxsrKycO7cOUHJiNSPxscvIVJdLi4uBZ7FvW/fPnTv3l1AIvoUN2/eRIMGDfKNOzo6ymagVEGdOnXw5MmTfONPnz7l7JqSWL9+PaysrPKN16tXD35+fgISKd706dMxbdo0pKSkiI5SpGbNmoVx48bh66+/xh9//IE//vgDX3/9NSZMmIBZs2aJjkcfkJOTI/t19OhRODg44PDhw0hNTUVqaioOHTqEBg0aICQkRHRUhXBwcICjoyMcHBxkH3ft2hVv377Fxo0bRccjUiuc6Sa15uPjg2XLlsHZ2VluT3dYWBi8vb1RpkwZ2bWenp6iYtJ7lC9fHgcOHJB97fKcP38e3bp1y9dERlkdOnQIP/74I+bMmYMmTZoAyH2dzps3D4sXL0bz5s1l1777mqWSQ1dXF7du3YKFhYXc+L1792BjY4OMjAxByRTH0dERcXFxyMzMhJmZGQwMDOQeV5XTBCpWrIjVq1ejX79+cuMBAQEYO3Ysnj9/LigZfYr69evDz89P7vsnAJw9exYjR46UNa1UZv/tK6GhoYGKFStCV1dXUCIi9cW2t6TWNm3aBGNjY9y8eVNuZtTIyAibNm2SfS6RSFh0l0AdO3bE1KlTsW/fPlnzotTUVEybNk2ljoDLW3XRt29f2fLHvPulX3/9texzZe6CrepMTU0RFhaWr+gOCwtD1apVBaVSLHU5WSAzM7PAfhENGzZEVlaWgET0Oe7evVtgc7SyZcvi/v37xZ6nKBTUoDE1NZVFN5EAnOkmIqX16NEjtGzZEsnJyXB0dAQAXLt2DZUqVcKxY8dgamoqOKFihIaGFvraVq1aFWES+lxLly7F0qVL8dNPP6Ft27YAco8r/PHHH+Ht7Y2pU6cKTkiFNXbsWGhpaeU7d3zixIl4/fo11q5dKygZfYqWLVtCV1cX27ZtQ6VKlQAAT548gYeHBzIyMj7p+25JtWTJEpibm8PNzQ1A7o3boKAgVKlSBYcOHVKL/gtEJQWLbiJSaq9evcL27dsRGRkJPT092NnZoV+/frKjfIhKAqlUiilTpmD16tV4+/YtgNwl55MnT1apfcCpqakICgrC3bt3MWnSJJQrVw7h4eGoVKkSqlWrJjreZ/Py8pJ9nJWVBX9/f9SoUUO23ePSpUtISEiAh4cHfv75Z1Ex6RPExcWhV69eiI2Nld2gTUxMhKWlJfbu3asS/TIsLCywfft2NGvWDMeOHUPfvn2xc+dO7Nq1CwkJCTh69KjoiERqg0U3qR0vLy/Mnz8fBgYGcm+kCvLfmQxSTt26dcPGjRtRpUoV0VEKLSoqCvXr14eGhka+DrT/ZWdnV0yp6EulpaXh1q1b0NPTg6WlJXR0dOQef/jwIapWrZqvy7IyiIqKQvv27WXLc2NiYlCzZk3MmDEDCQkJ2Lp1q+iIn61NmzaFuk4ikeDkyZNFnIYURSqV4tixY7h9+zYAwNraGu3bt5frYq7M9PT0ZDcVxo0bh4yMDKxfvx6xsbH46quvVKbvCZEy4J5uUjsRERHIzMyUffw+qvJDl4AzZ84o3bFaDg4OSEpKgomJCRwcHPIdbZOH+7iVS+nSpdGoUaP3Pm5jY4Nr166hZs2axZhKMby8vDB48GAsXboUhoaGsvGuXbuif//+ApN9uVOnTomOQEVAIpGgY8eO6Nixo+goRcLY2BiJiYkwNTVFSEgIfHx8AOTebODPDaLixaKb1M67b574RopKqvj4eFSsWFH2MakHZV58duXKFaxfvz7feLVq1ZCUlCQgEdGHhYaGYtmyZbJO5TY2Npg0aRJatGghOJliuLq6on///rC0tERycjK6dOkCIHfCQRWWzxMpExbdREQl0LtdZwvqQEtU0ujo6ODFixf5xmNjY2U3kIhKit9//x1DhgyBq6ur7HSSc+fOoV27dvD391f61RkAsGLFCpibmyMxMRFLly5F6dKlAQCPHz/GDz/8IDgdkXrhnm5SO66uroW+ds+ePUWYhIqLoaEhIiMjlWrJ7v79+wt9rYuLSxEmoeKkjK/VPMOHD0dycjJ27dqFcuXKISoqCpqamujZsydatmyJlStXio5IJGNtbY2RI0diwoQJcuO+vr749ddfVeKc7sJSxr4nRMqGM92kdvLOcyYqyQp75jH3dFNJsXz5cvTp0wcmJiZ4/fo1WrVqhaSkJDRt2hQLFiwQHY9Izr179/D111/nG3dxccG0adMEJBJHGfueECkbFt2kdjZv3vzJvycsLAxOTk75Og0TFZWcnBzREUgAZW7gWLZsWRw7dgxhYWGIjIxEWloaGjRogPbt24uORpSPqakpTpw4kW9v8/Hjx2VHiBERKQqLbqJC6NKli9J2FCZg2rRpKFeunOgYRc7W1haHDh3iG0Ylpgo7vpydneHs7Cw6BtEHeXt7w9PTE9euXUOzZs0A5N5g9/f3x6pVqwSnIyJVw6KbqBBU4Y2wqvr7779x7tw5PH36NN/scF5znKlTp4qIVuzu378vOw6PlNPNmzdRtWpV0TE+i6enJ2rXri37d5dnzZo1iIuL455uKlG+//57VK5cGcuXL8euXbsA5O7z3rlzJ3r06CE4HRGpGjZSIyoEZW5upMr8/f0xatQoaGtro3z58nJLcyUSCe7duycwXfHj67RkUbemjdWqVcP+/fvRsGFDufHw8HC4uLjg4cOHgpIR0YfwZwdR0eNMNxEprZkzZ2LWrFmYOnUqNDQ0RMchkqNuTRuTk5MLfM5lypTB8+fPBSQi+ri//vpL1qm8Xr16cHR0FJyIiFQRi24iUlrp6en49ttvWXBTifQ5TRuVWe3atRESEoIxY8bIjR8+fJgzaFTiPH36FN9++y1Onz4NIyMjAEBqairatGmDwMBAtTpbXl36nhCJxKKbqBCUuaOwKhs2bBj++OMPTJkyRXQUIrXn5eWFMWPG4NmzZ2jbti0A4MSJE1i+fDn3c1OJM3bsWLx8+RI3btyAtbU1gNyeCoMGDYKnpycCAgIEJ/w8+/fvL/S1Li4uANSn7wmRSNzTTVQI3O9UMmVnZ6N79+54/fo1bG1toaWlJfe4r6+voGRi8HVasgUFBWHXrl1ISEjA27dv5R4LDw8XlEqx1q1bhwULFuDvv/8GAJibm2POnDnw8PAQnIxIXtmyZXH8+HE0atRIbvzy5cvo2LEjUlNTxQT7Qv9d+SWRSOSawb47iZCdnV1suYjUHddkklqbPXs2Hjx48NHrXr58yUKmBFq0aBGOHDmCJ0+eIDo6GhEREbJf165dEx1PYQrbEG79+vWoVKlSEaehz7F69WoMGTIElSpVQkREBBo3bozy5cvj3r176NKli+h4CvP999/j4cOHePLkCV68eIF79+6x4KYSKScnJ9+NWgDQ0tLKdxKGMsnJyZH9Onr0KBwcHHD48GGkpqYiNTUVhw4dQoMGDRASEiI6KpFa4Uw3qTUHBwdcv34drVq1wrBhw9C7d2/o6OiIjkWFZGxsjBUrVmDw4MGioxQpDQ0N2Wu0T58+0NXVFR2JPpGVlRVmz56Nfv36ya1ImDVrFlJSUrBmzRrREYnUSo8ePZCamoqAgADZMX2PHj2Cu7s7jI2NERwcLDjhl6tfvz78/PzQvHlzufGzZ89i5MiRsgZyRFT0ONNNau3atWu4cuUK6tWrh3HjxqFy5cr4/vvvceXKFdHRqBB0dHTg7OwsOkaRCw8Ph52dHby8vFC5cmWMGjUKly9fFh2LPkFCQgKaNWsGANDT08PLly8BAAMHDlTavaMA0KBBA/zzzz8AAEdHRzRo0OC9v4hKkjVr1uDFixcwNzdHrVq1UKtWLVhYWODFixf4+eefRcdTiLt378qaxL2rbNmyuH//frHnIVJnnOkm+p/MzEz8+eef2Lx5M44cOQIrKysMGzYMgwcPVrujf5TFokWL8PjxY6xevVp0lGKRlZWF/fv3w9/fHyEhIahTpw6GDh2KgQMHqlWnXWVUs2ZN7N69G46OjnBycsKIESMwatQoHD16FN9++y1SUlJER/wsc+fOxaRJk6Cvr4+5c+d+8NrZs2cXUyqiwpFKpTh+/Dhu374NALC2tkb79u0Fp1Kcli1bQldXF9u2bZNtPXry5Ak8PDyQkZGB0NBQwQmJ1AeLbqL/efv2LYKDg/Hbb7/h5MmTaNasGf7++288efIEv/76K9zc3ERHpP/o1asXTp48ifLly6NevXr59uft2bNHULKi9ebNG/zyyy+YOnUq3r59C21tbfTt2xdLlixBlSpVRMejAgwfPhympqaYPXs21q5di0mTJsHZ2RlXr16Fq6srNm3aJDoiEamYuLg49OrVC7GxsTA1NQUAJCYmwtLSEnv37kXt2rUFJyRSHyy6Se399ddf2Lx5MwICAqCjowMPDw8MHz5c9sPo559/ho+PD548eSI4Kf3XkCFDPvi4qp2TfPXqVfz2228IDAyEgYEBBg0ahGHDhuHhw4eYO3cuXrx4wWXnJVReY6NSpXJP6gwMDMT58+dhaWmJUaNGQVtbW3BCItX3KauiPD09izBJ8ZFKpTh27Fi+2XwehUpUvFh0k1qztbXF7du30bFjR4wYMQJff/01NDU15a55/vw5TExMlLqbKSk3X19fbN68GTExMejatSuGDx+Orl27yh0N8/DhQ5ibmyMrK0tgUnqfhIQEmJqa5nujK5VKkZiYiBo1aghK9mWMjY0L/eZdWZfQk+qwsLAo1HUSiaTQp0YQERVGKdEBiETq27cvhg4dimrVqr33mgoVKrDgJqHWrVuHoUOHYvDgwe9dPm5iYsIlyiWYhYUFHj9+DBMTE7nxlJQUWFhYKO15uStXrhQdgajQ4uPjCxzPm39Sxdnf0NBQLFu2TNap3MbGBpMmTUKLFi0EJyNSLyy6Sa1JpVIYGxvnG3/9+jV++uknzJo1S0AqKiwLC4sPvklSlZmKY8eOoUaNGnIz24D8LKm2tjYGDRokKCF9jFQqLfC1mpaWptRHwPE1R8ps06ZNWLFiBe7cuQMAsLS0xPjx4zF8+HDByRTj999/x5AhQ+Dq6ipbLn/u3Dm0a9cO/v7+6N+/v+CEROqDy8tJrWlqahY4+5ScnAwTExOlnX1SF6tWrZL7PDMzExEREQgJCcGkSZMwZcoUQckUi69T5eXl5QUg97U6YsQI6Ovryx7Lzs7GpUuXoKmpibCwMFERFebFixcFjkskEujo6HDfOpUos2bNgq+vL8aOHYumTZsCAC5cuIA1a9ZgwoQJmDdvnuCEX87a2hojR47EhAkT5MZ9fX3x66+/8pxuomLEopvUmoaGBp48eZLvuKWTJ0/Czc0Nz549E5SMvsTatWtx9epVlWmkpqGhgaSkpHxF94MHD2BjY4NXr14JSkYf06ZNGwC5SzybNm0qV3hqa2vD3NwcEydOhKWlpaiICqOhofHBlSfVq1fH4MGDMXv27HyrNoiKW8WKFbF69Wr069dPbjwgIABjx47F8+fPBSVTHB0dHdy4cSNfl/K4uDjUr18fGRkZgpIRqR8uLye1lNf8RyKRoE6dOnJvFLOzs5GWlobvvvtOYEL6El26dMHUqVOVvujOmyWVSCSYNWtWgbOkDg4OgtJRYZw6dQpAbqf9VatWoUyZMoITFR1/f39Mnz4dgwcPRuPGjQEAly9fxpYtWzBjxgw8e/YMy5Ytg46ODqZNmyY4Lam7zMxMODk55Rtv2LChyjSkNDU1xYkTJ/IV3cePH5cdIUZExYNFN6mllStXQiqVYujQoZg7dy7Kli0reyxv9ilvuRkpn6CgIJQrV050jC8WEREBIHc/cHR0dL5ZUnt7e0ycOFFUPPoE794AevjwIYDcmV9VsmXLFixfvhx9+/aVjX399dewtbXF+vXrceLECdSoUQMLFixg0U3CDRw4EOvWrYOvr6/c+IYNG+Du7i4olWJ5e3vD09MT165dQ7NmzQAAYWFh8Pf3z7c9i4iKFpeXk1oLDQ1Fs2bNoKWlJToKfQZHR0e5VQpSqRRJSUl49uwZfvnlF4wcOVJgOsVRh1lSVZeTkwMfHx8sX74caWlpAABDQ0N4e3tj+vTpKrHcWk9PD1FRUfmWyt+5cwf29vZIT09HfHw86tWrh/T0dEEpSZ3lrR4CgKysLPj7+6NGjRpo0qQJAODSpUtISEiAh4cHfv75Z1ExFSo4OBjLly+X7d+2trbGpEmT0KNHD8HJiNQLi25SOy9evJAVL+9r/JOHRU7JNnfuXLnPNTQ0ULFiRbRu3RpWVlaCUhW9Fy9e4OTJk7CyslLp56lKpk6dik2bNmHu3LlwdnYGkNtFeM6cORgxYgQWLFggOOGXq1OnDlxdXbF48WK58SlTpiA4OBgxMTG4evUqevTogUePHglKSeosr8fCx0gkEpw8ebKI0xCROmHRTWrn3U7Q72v8k3e8D7tCl1xZWVnYsWMHOnXqhEqVKomOU6T69u2Lli1bYsyYMXj9+jXs7e1x//59SKVSBAYGonfv3qIj0kdUrVoVfn5+cHFxkRvft28ffvjhB5UoQvfv349vvvkGVlZWaNSoEQDg6tWruH37NoKCgtC9e3esW7cOd+7cybekl4iKzl9//SWb6a5Xrx4cHR0FJyJSPyy6Se2EhobC2dkZpUqVQmho6AevbdWqVTGlos+hr6+PW7duwczMTHSUIlW5cmUcOXIE9vb22LFjB2bPno3IyEhs2bIFGzZskO39ppJLV1cXUVFRqFOnjtx4TEwMHBwc8Pr1a0HJFCs+Ph4bNmxATEwMAKBu3boYNWoUzM3NxQYjUkNPnz7Ft99+i9OnT8PIyAgAkJqaijZt2iAwMDDfyS1EVHRYdBOR0mrdujXGjx+Pnj17io5SpPT09BAbGwtTU1N4eHigatWqWLx4MRISEmBjYyPbI0wl11dffYWvvvoKq1evlhsfO3Ysrly5gosXLwpKRkSqys3NDffu3cPWrVthbW0NALh58yYGDRqE2rVrIyAgQHBCIvXB7uWk1kJCQlC6dGk0b94cQO75zr/++itsbGywdu1aGBsbC05IH/LDDz/A29sbDx8+RMOGDWFgYCD3uJ2dnaBkimVqaooLFy6gXLlyCAkJQWBgIADgn3/+ga6uruB0VBhLly5Ft27dcPz4cdnJCBcuXEBiYiIOHTokOJ1imJubY+jQoRgyZAiPIyIqAUJCQnD8+HFZwQ1A9v6mY8eOApMRqR/lb5dK9AUmTZoka6YWHR0NLy8vdO3aFfHx8XJdTqlk+vbbbxEfHw9PT084OzvDwcEBjo6Osv+qivHjx8Pd3R3Vq1dH1apV0bp1awDAmTNnYGtrKzYcFYqFhQViY2PRq1cvpKamIjU1Fa6uroiJiVGZ7RHjx4/Hnj17YGFhgQ4dOiAwMBBv3rwRHYtIbeXk5BR4OouWlhZycnIEJCJSX1xeTmqtdOnSuH79OszNzTFnzhxcv34dQUFBCA8PR9euXZGUlCQ6In3AgwcPPvi4qhQzQG5DqsTERHTo0AGlS5cGABw8eBBGRkaybthUcr3bwPFdycnJMDExUammjeHh4fD390dAQACys7PRv39/DB06FA0aNBAdjUit9OjRA6mpqQgICEDVqlUBAI8ePYK7uzuMjY0RHBwsOCGR+mDRTWqtXLlyOHfuHGxsbNC8eXN4eHhg5MiRuH//PmxsbHiWLBEphIaGBpKSkvIV3Q8ePICNjQ1evXolKFnRyczMxC+//ILJkycjMzMTtra28PT0xJAhQwo8NYKIFCsxMREuLi64ceOGbMtHYmIi6tevj/3796N69eqCExKpD+7pJrXWvHlzeHl5wdnZGZcvX8bOnTsBALGxsfxhpCS2bdsGPz8/xMfH48KFCzAzM8PKlSthYWGBHj16iI732by8vDB//nwYGBh8dKsDj18qufK+dhKJBLNmzYK+vr7ssezsbFy6dAkODg6C0hWNzMxMBAcHY/PmzTh27BiaNGmCYcOG4eHDh5g2bRqOHz+OHTt2iI5JpPJMTU0RHh6O48eP4/bt2wAAa2trtG/fXnAyIvXDopvU2po1a/DDDz8gKCgI69atQ7Vq1QAAhw8fRufOnQWno49Zt24dZs2ahfHjx2PBggWyJbpGRkZYuXKlUhfdERERyMzMlH38PpwxLNnyvnZSqRTR0dHQ1taWPaatrQ17e3tMnDhRVDyFCg8Px+bNmxEQEAANDQ14eHhgxYoVsLKykl3Tq1cv2RneRFT0JBIJOnTogA4dOoiOQqTWuLyciJSWjY0NFi5ciJ49e8LQ0BCRkZGoWbMmrl+/jtatW+P58+eiIxIBAIYMGYJVq1ahTJkyoqMUGU1NTXTo0AHDhg1Dz549C2zg9OrVK4wZMwabN28WkJBI9f33WMIP8fT0LMIkRPQuFt2k9nJychAXF4enT5/m6+bZsmVLQamoMPT09HD79m2YmZnJFd137tyBnZ0dXr9+LTpikXjx4gVOnjwJKysruVlEIlGys7Px+++/w8XFhUctEglkYWFRqOskEgnu3btXxGmIKA+Xl5Nau3jxIvr3748HDx7gv/efJBKJSnUUVkUWFha4du1avi7lISEhcueSKru+ffuiZcuWGDNmDF6/fg0nJyfcv38fUqkUgYGB6N27t+iIpOY0NTUxatQotGzZkkU3kUDx8fEFjue9x+GWJCIxeE43qbXvvvsOTk5OuH79OlJSUvDPP//IfqWkpIiORx/h5eWF0aNHY+fOnZBKpbh8+TIWLFiAqVOn4scffxQdT2HOnDmDFi1aAACCg4MhlUqRmpqK1atXw8fHR3A6olz169fnzBlRCbNp0ybUr18furq60NXVRf369bFx40bRsYjUDpeXk1ozMDBAZGQkateuLToKfabt27djzpw5uHv3LgCgatWqmDt3LoYNGyY4meLo6ekhNjYWpqam8PDwQNWqVbF48WIkJCTAxsYGaWlpoiMSISQkBFOnTsX8+fPRsGFDGBgYyD2uyvvZiUqiWbNmwdfXF2PHjkXTpk0BABcuXMCaNWswYcIEzJs3T3BCIvXBopvUWtu2bfHjjz+yU7kKSE9PR1paWr5zkFVBnTp14OPjg27dusHCwgKBgYFo27YtIiMj0a5dOzaMoxJBQ+P/F8+9u4RVKpVyuw6RABUrVsTq1avRr18/ufGAgACMHTuWPzuIihH3dJNaGzt2LLy9vZGUlARbW9t83Xbt7OwEJaPCeP36NaRSKfT19aGvr49nz55h5cqVsLGxQceOHUXHU5jx48fD3d0dpUuXhpmZGVq3bg0gd9m5ra2t2HBE/7N582aYmppCU1NTbjwnJwcJCQmCUhGpr8zMTDg5OeUbb9iwIbKysgQkIlJfnOkmtfbuzEweiUTCmRkl0bFjR7i6uuK7775Damoq6tatC21tbTx//hy+vr74/vvvRUdUmKtXryIxMREdOnRA6dKlAQAHDx6EkZERnJ2dBacjym2m9vjx43yrTZKTk2FiYsLvp0TFbOzYsdDS0oKvr6/c+MSJE/H69WusXbtWUDIi9cOZblJr7+vyScohPDwcK1asAAAEBQWhcuXKiIiIwO7duzFr1iyVKrqdnJzyzVh069ZNUBqi/PJuVv5XWloadHV1BSQiUj9eXl6yjyUSCTZu3IijR4+iSZMmAIBLly4hISEBHh4eoiISqSUW3aTW/nvUFCmX9PR0GBoaAgCOHj0KV1dXaGhooEmTJnjw4IHgdIqTnZ0Nf39/nDhxosDz5E+ePCkoGdH/v8mXSCSYOXMm9PX1ZY9lZ2fj0qVLcHBwEJSOSL1ERETIfd6wYUMAkDUbrVChAipUqIAbN24UezYidcaim9Tetm3b4Ofnh/j4eFy4cAFmZmZYuXIlLCws0KNHD9Hx6ANq166NvXv3olevXjhy5AgmTJgAAHj69KlKdUoeN24c/P390a1bN9SvX5/nrFKJkvcmXyqVIjo6Gtra2rLHtLW1YW9vj4kTJ4qKR6RWTp06JToCERWAe7pJra1btw6zZs3C+PHjsWDBAly/fh01a9aEv78/tmzZwh9eJVxQUBD69++P7OxstGvXDkePHgUALFq0CGfOnMHhw4cFJ1SMChUqYOvWrejatavoKETvNWTIEKxatUqlbngREREpAotuUms2NjZYuHAhevbsCUNDQ0RGRqJmzZq4fv06WrduzeM0lEBSUhIeP34Me3t7WWO8y5cvo0yZMrCysgIAPHz4EFWrVi2wcZ4yqFq1Kk6fPo06deqIjkJEREREn0g534ESKUh8fDwcHR3zjevo6ODVq1cCEtGnqly5MhwdHeUK6saNG8sKbiD35sr9+/cFpFMMb29vrFq1CrxHSkRERKR8uKeb1JqFhQWuXbuWr6FaSEgIrK2tBaUiRVP2YvXcuXM4deoUDh8+jHr16uU7T37Pnj2CkhERERHRx7DoJrXm5eWF0aNHIyMjA1KpFJcvX0ZAQAAWLVqEjRs3io5HBAAwMjJCr169RMcgIiIios/APd2k9rZv3445c+bIjtOoWrUq5s6di2HDhglORory7n59IiIiIqLixKKb6H/S09ORlpYGExMT0VFIwVSh6M7KysLp06dx9+5d9O/fH4aGhvj7779RpkwZlC5dWnQ8IiIiInoPLi8n+h99fX3o6+uLjkFFQNnPtX7w4AE6d+6MhIQEvHnzBh06dIChoSGWLFmCN2/ewM/PT3REIiIiInoPFt2kdhwdHQtdhIWHhxdxGioOyr6gZ9y4cXByckJkZCTKly8vG+/VqxdGjBghMBkRERERfQyLblI7PXv2lH2ckZGBX375BTY2NmjatCkA4OLFi7hx4wZ++OEHQQlJ0W7evImqVauKjvHZzp49i/Pnz0NbW1tu3NzcHI8ePRKUioiIiIgKg0U3qZ3Zs2fLPh4+fDg8PT0xf/78fNckJiYWdzQqBFdX10Jfm3eUlqmpaVHFKRY5OTnIzs7ON/7w4UMYGhoKSEREREREhcWim9TaH3/8gatXr+YbHzBgAJycnPDbb78JSEUfUrZsWdERil3Hjh2xcuVKbNiwAUDuHvW0tDTMnj0bXbt2FZyOiIiIiD6ERTepNT09PYSFhcHS0lJuPCwsDLq6uoJS0Yds3rxZdIRit3z5cnTq1Ak2NjbIyMhA//79cefOHVSoUAEBAQGi4xERERHRB7DoJrU2fvx4fP/99wgPD0fjxo0BAJcuXcJvv/2GmTNnCk5HlKt69eqIjIxEYGAgoqKikJaWhmHDhsHd3R16enqi4xERERHRB/CcblJ7u3btwqpVq3Dr1i0AgLW1NcaNG4e+ffsKTkaFERQUhF27diEhIQFv376Ve4zd54mIiIhINBbdRIUQEBAAFxcXGBgYiI5C71i9ejWmT5+OwYMHY8OGDRgyZAju3r2LK1euYPTo0ViwYIHoiJ9t//79hb7WxcWlCJMQERER0Zdg0U1UCGXKlMG1a9dQs2ZN0VHoHVZWVpg9ezb69esHQ0NDREZGombNmpg1axZSUlKwZs0a0RE/m4aGhtznEokk33njeefNF9TZnIiIiIhKBo2PX0JEvDdVMiUkJKBZs2YAcpvivXz5EgAwcOBApW8wlpOTI/t19OhRODg44PDhw0hNTUVqaioOHz6MBg0aICQkRHRUIiIiIvoANlIjIqVVuXJlpKSkwMzMDDVq1MDFixdhb2+P+Ph4lbpRMn78ePj5+aF58+aysU6dOkFfXx8jR46U9SMgIiIiopKHM91EpLTatm0r2/s8ZMgQTJgwAR06dICbmxt69eolOJ3i3L17F0ZGRvnGy5Yti/v37xd7HiIiIiIqPO7pJiqEd/cLU8mRt/y6VKncRTuBgYE4f/48LC0tMWrUKGhrawtOqBgtW7aErq4utm3bhkqVKgEAnjx5Ag8PD2RkZCA0NFRwQiIiIiJ6HxbdRIXAortkSkhIgKmpqayhWB6pVIrExETUqFFDUDLFiouLQ69evRAbGwtTU1MAQGJiIiwtLbF3717Url1bcEIiIiIieh8W3USFUL9+fRw+fFhW8FDJoKmpicePH8PExERuPDk5GSYmJirV1VsqleLYsWO4ffs2gNzz5Nu3b5/vhgMRERERlSwsuokAvH37Fk+fPkVOTo7cuKrMlKoqDQ0NPHnyBBUrVpQbf/DgAWxsbPDq1StBycSwtbXFoUOHeHOIiIiIqARh93JSa3fu3MHQoUNx/vx5uXGpVAqJRKJSM6WqxMvLC0DuOdUzZ86Evr6+7LHs7GxcunQJDg4OgtKJc//+fWRmZoqOQURERETvYNFNam3w4MEoVaoUDhw4gCpVqnCprpKIiIgAkHtzJDo6Wq5hmra2Nuzt7TFx4kRR8YiIiIiIZLi8nNSagYEB/vrrL1hZWYmOQp9hyJAhWLVqFcqUKSM6SonAhn9EREREJQ9nukmt2djY4Pnz56Jj0GfavHmz7OOHDx8CAKpXry4qDhERERFRPhqiAxAVtxcvXsh+LVmyBD/++CNOnz6N5ORkucdevHghOip9RE5ODubNm4eyZcvCzMwMZmZmMDIywvz58/M1xSMiIiIiEoEz3aR2jIyM5PZuS6VStGvXTu4aNlJTDtOnT8emTZuwePFiODs7AwDOnTuHOXPmICMjAwsWLBCckIiIiIjUHfd0k9oJDQ0t9LWtWrUqwiT0papWrQo/Pz+4uLjIje/btw8//PADHj16JCiZYmVkZEBXV/ej1+3YsQM9evSAgYFBMaQiIiIiosJg0U1ESktXVxdRUVGoU6eO3HhMTAwcHBzw+vVrQckUS1dXF40bN0arVq3QunVrNGvWDHp6eqJjEREREVEhsOgmtRYVFVXguEQiga6uLmrUqAEdHZ1iTkWF9dVXX+Grr77C6tWr5cbHjh2LK1eu4OLFi4KSKda5c+dw5swZnD59GufPn0dWVhacnJxkRXiHDh1ERyQiIiKi92DRTWpNQ0Pjg2dza2lpwc3NDevXry/U8l4qXqGhoejWrRtq1KiBpk2bAgAuXLiAxMREHDp0CC1atBCcUPGysrJw5coVrF+/Htu3b0dOTg57DxARERGVYOxeTmotODgYlpaW2LBhA65du4Zr165hw4YNqFu3Lnbs2IFNmzbh5MmTmDFjhuioVAALCwvExsaiV69eSE1NRWpqKlxdXRETEwMzMzPR8RQqNjYWGzZsgIeHB3r37o0///wT3bt3h6+vr+hoRERERPQBnOkmtda4cWPMnz8fnTp1khs/cuQIZs6cicuXL2Pv3r3w9vbG3bt3BaWk99HU1MTjx49hYmIiN56cnAwTExOVmQGuVq0aXr9+jdatW6N169Zo1aoV7OzsPrhKg4iIiIhKBs50k1qLjo4ucEbUzMwM0dHRAAAHBwc8fvy4uKNRIbzvnmFaWppKbQeoWLEi0tPTkZSUhKSkJDx58kRlmsQRERERqTqe001qzcrKCosXL8aGDRugra0NAMjMzMTixYthZWUFAHj06BEqVaokMib9h5eXF4DchnezZs2Cvr6+7LHs7GxcunQJDg4OgtIp3rVr15CamoozZ84gNDQU06ZNw82bN+Hg4IA2bdrwPHIiIiKiEozLy0mtnT9/Hi4uLtDQ0ICdnR2A3Nnv7OxsHDhwAE2aNMG2bduQlJSESZMmCU5Ledq0aQMgt5Fa06ZNZTdMAEBbWxvm5uaYOHEiLC0tRUUsMsnJyTh9+jT27duHgIAANlIjIiIiKuFYdJPae/nyJbZv347Y2FgAQN26ddG/f38YGhoKTkYfM2TIEKxatQplypQRHaVI7dmzB6dPn8bp06dx8+ZNlCtXDs2bN5ft77a3txcdkYiIiIjeg0U3EVEJZ2JigpYtW8qKbFtbW9GRiIiIiKiQWHST2tm/fz+6dOkCLS0t7N+//4PXuri4FFMqIiIiIiJSRSy6Se1oaGggKSkJJiYm0NB4fwN/iUTCvbJUYmRnZ2Pv3r24desWAMDGxgY9evSApqam4GRERERE9CEsuomISri4uDh07doVjx49Qt26dQEAMTExMDU1xcGDB1GrVi3BCYmIiIjofVh0k9o7ceIETpw4gadPnyInJ0c2LpFIsGnTJoHJiHJ17doVUqkU27dvR7ly5QDkdjEfMGAANDQ0cPDgQcEJiYiIiOh9WHSTWps7dy7mzZsHJycnVKlSBRKJRO7x4OBgQcmI/p+BgQEuXryYr4FaZGQknJ2dkZaWJigZEREREX1MKdEBiETy8/ODv78/Bg4cKDoK0Xvp6Ojg5cuX+cbT0tLkzignIiIiopLn/V2kiNTA27dv0axZM9ExiD6oe/fuGDlyJC5dugSpVAqpVIqLFy/iu+++Y4d9IiIiohKORTepteHDh2PHjh2iYxB90OrVq1GrVi00bdoUurq60NXVRbNmzVC7dm2sXLlSdDwiIiIi+gDu6Sa14+XlJfs4JycHW7ZsgZ2dHezs7KClpSV3ra+vb3HHI3qvuLg42ZFh1tbWqF27tuBERERERPQxLLpJ7bRp06ZQ10kkEpw8ebKI0xAV7N2bQx/Dm0NEREREJRcbqZHaOXXqlOgIRB8VERFRqOv+23GfiIiIiEoWznQTERERERERFRE2UiMiIiIiIiIqIiy6iYiIiIiIiIoIi24iIiIiIiKiIsKim4iIiIiIiKiIsOgmIiIiIiIiKiIsuomIiIiIiIiKCItuIiIiIiIioiLCopuIiIiIiIioiPwfUkouwOyK5nsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualization of the dataset\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "df = pd.DataFrame(\n",
    "    X,\n",
    "    columns=[\n",
    "        \"age\",\n",
    "        \"sex\",\n",
    "        \"body_mass\",\n",
    "        \"blood_pressure\",\n",
    "        \"total_serum_cholesterol\",\n",
    "        \"low_densisty_lipoproteins\",\n",
    "        \"high_density_lipoproteins\",\n",
    "        \"total_cholesterol\",\n",
    "        \"tryglicerides_level\",\n",
    "        \"blood_sugar_level\",\n",
    "    ],\n",
    ")\n",
    "df[\"target\"] = y\n",
    "corr_mat = df.corr()  # compute the correlation matrix of the features vectors\n",
    "sns.clustermap(corr_mat, vmax=0.8);  # plot a clustered heatmap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Normalization\n",
    "[Normalize](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.normalize.html) the input data using the L2 norm, as well as the target data by the maximum value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = preprocessing.normalize(X, norm=\"l2\")\n",
    "y = y / y.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split the data\n",
    "X_train, X_validation, y_train, y_validation = train_test_split(\n",
    "    X, y, test_size=0.2, random_state=14\n",
    ")\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X_train, y_train, test_size=0.3, random_state=14\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "--JJrC4wDkvE"
   },
   "source": [
    "## 2.2 Implementing gradients for Linear Regression\n",
    "\n",
    "The model we consider is $\\hat{y} = w x + c$.\n",
    "\n",
    "We need to calculate the gradients for the training dataset $X$ of the loss\n",
    "$L(w,c) = \\frac{1}{2n}\\sum_{x_i \\in X}(y_i-\\hat{y_i})^2 $\n",
    "\n",
    "What are the gradients?\n",
    "\n",
    "- $\\frac{\\partial L(w,c)}{\\partial w} = -\\frac{1}{n}\\sum_{x_i \\in X} (y_i-\\hat{y_i})x_i $\n",
    "- $\\frac{\\partial L(w,c)}{\\partial c} = -\\frac{1}{n}\\sum_{x_i \\in X} (y_i-\\hat{y_i})$\n",
    "\n",
    "Implement them below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "LegAO75e9XY_"
   },
   "outputs": [],
   "source": [
    "def grad_w(X, y, w, c):\n",
    "    # outputs parital L(w,c)/ partial w\n",
    "    y_pred = w @ X.T + c\n",
    "    return -1 / X.shape[0] * ((y - y_pred) @ X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "D3DpUg3SIL-W"
   },
   "outputs": [],
   "source": [
    "def grad_c(X, y, w, c):\n",
    "    # outputs parital L(w,c)/ partial c\n",
    "    y_pred = w @ X.T + c\n",
    "    return -1 / X.shape[0] * (y - y_pred).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "id": "FsnscJ9rGunO",
    "outputId": "276f66bb-9982-458c-8f56-be480956d8f8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SGD = MSE test 0.02750899902868835\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up stochasic batch gradient descent\n",
    "BATCHSIZE = 16\n",
    "EPOCHS = 400\n",
    "lr = 0.15  # set the learning rate\n",
    "\n",
    "# set initial values for the parameters\n",
    "w = np.random.RandomState(seed=43).randn(X_train.shape[1])\n",
    "c = 0\n",
    "\n",
    "\n",
    "MSE_test = []\n",
    "MSE_train = []\n",
    "\n",
    "# for several epochs (= runs over complete training data)\n",
    "for e in range(EPOCHS):\n",
    "    # compute current errors on test and train\n",
    "    MSE_train.append(((y_train - (w @ X_train.T + c)) ** 2).mean())\n",
    "    MSE_test.append(((y_test - (w @ X_test.T + c)) ** 2).mean())\n",
    "\n",
    "    # split the training set into batches\n",
    "    for b in range(0, ((X_train.shape[0] // BATCHSIZE) - 1) * BATCHSIZE, BATCHSIZE):\n",
    "    \n",
    "        idxs = np.random.randint(0, X_train.shape[0], BATCHSIZE)\n",
    "\n",
    "        X_batch = X_train[idxs]\n",
    "        y_batch = y_train[idxs]\n",
    "\n",
    "        # run a gradient step on every batch\n",
    "        w_ = w - lr * grad_w(X_batch, y_batch, w, c)\n",
    "        c_ = c - lr * grad_c(X_batch, y_batch, w, c)\n",
    "\n",
    "        w = w_\n",
    "        c = c_\n",
    "\n",
    "# plot the resulting learning curve\n",
    "plt.plot(np.nan_to_num(MSE_train, nan=1000.0), label=\"train\")\n",
    "plt.plot(np.nan_to_num(MSE_test, nan=1000.0), label=\"test\")\n",
    "plt.xlabel(\"epochs\")\n",
    "plt.ylabel(\"MSE\")\n",
    "plt.legend()\n",
    "plt.yscale(\"log\")\n",
    "print(f\"SGD = MSE test {MSE_test[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "id": "TQxbUWAXUDPD",
    "outputId": "3fb847f4-f7c3-46ec-ad62-09177f7ec2d8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'true test labels')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the predictions\n",
    "plt.plot((w @ X_test.T + c), y_test, \".\")\n",
    "plt.xlabel(\"labels predicted by the model\")\n",
    "plt.ylabel(\"true test labels\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WjDQNM3ngs1g"
   },
   "source": [
    "1. Explain in your own words what information the learning curve gives to you."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TJc7647MjcYx"
   },
   "source": [
    "## 2.3 Loss Curve Quiz\n",
    "\n",
    "What is wrong?\n",
    "![L1](https://developers.google.com/static/machine-learning/testing-debugging/images/metric-curve-ex03.svg)   ![L2](https://developers.google.com/static/machine-learning/testing-debugging/images/metric-curve-ex02.svg)     ![L3](https://developers.google.com/static/machine-learning/testing-debugging/images/metric-curve-ex01.svg\n",
    ")\n",
    "\n",
    "*(From https://developers.google.com/machine-learning/testing-debugging/metrics/interpretic)*\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JtwgA-hMTV_k"
   },
   "source": [
    "## 2.4 Comparison with Library solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "id": "TpWuNtORKl4X",
    "outputId": "e1dd0753-2bc4-4e9d-f4ab-daf93cc858be"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sklearn = MSE test 0.026190964610037434\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSE_train = []\n",
    "MSE_test = []\n",
    "for i in range(10, X_train.shape[0]):\n",
    "    lm = linear_model.Ridge(alpha=0.01, fit_intercept=True).fit(\n",
    "        X_train[:i], y_train[:i]\n",
    "    )\n",
    "    MSE_test.append(((y_test - lm.predict(X_test)) ** 2).mean())\n",
    "    MSE_train.append(((y_train - lm.predict(X_train)) ** 2).mean())\n",
    "\n",
    "plt.plot(MSE_train, label=\"train\")\n",
    "plt.plot(MSE_test, label=\"test\")\n",
    "plt.xlabel(\"datapoints\")\n",
    "plt.ylabel(\"MSE\")\n",
    "plt.legend()\n",
    "\n",
    "print(f\"sklearn = MSE test {MSE_test[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "id": "lwrULmf4ThgI",
    "outputId": "80b58f39-4d38-40d4-8f0e-e05d450fe310"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'true test labels')"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lm.predict(X_test), y_test, \".\")\n",
    "plt.xlabel(\"labels predicted by the model\")\n",
    "plt.ylabel(\"true test labels\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0eTReXEjlGwL"
   },
   "source": [
    "1. Should you rather use the Library or your own implementation?\n",
    "\n",
    "Answer:\n",
    "- Own code:\n",
    "  - Might be quick rather than downloading and installing.\n",
    "  - Makes it explicit to you what is happening\n",
    "  - Easy to make mistakes\n",
    "  - Important learnings from doing things yourself\n",
    "  - Easy to customize\n",
    "- Libary:\n",
    "  - Probably tested by many people, should work\n",
    "  - Optimized for efficiency, nice software architecture…\n",
    "  - Problems on the big libaries may occur, especially for experimental features [https://github.com/scikit-learn/scikit-learn/labels/Bug](https://github.com/scikit-learn/scikit-learn/labels/Bug)\n",
    "  - Be careful of small taylormade libraries (e.g. few stars on github)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7NmeoFdhfQDU"
   },
   "source": [
    "## 2.5 Validation data set\n",
    "1. We did not use the validation data set so far, do we need it at all?\n",
    "2. Are there hyperparamters for SGD?\n",
    "3. How would can you estimate true the generalization error?\n",
    "\n",
    "Answer:\n",
    "- So far we did not play with hyperparameters\n",
    "- SGD Hyperparameters\n",
    "  - Learning Rate\n",
    "  - Epochs\n",
    "  - Stopping time\n",
    "  - Initialization\n",
    "  - ...\n",
    "- After doing hyperparameter search, only by using the validation set"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
