{"cells":[{"cell_type":"markdown","metadata":{"id":"_FO1xbko7UGW"},"source":["# K-Means clustering\n","\n","## Introduction\n","The goal of this week is to gain your first hands-on experience with unsupervised learning, focusing on clustering.\n","\n","In particular, you will implement the k-means clustering algorithm using both pure Python and the scikit-learn library."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"H8BY9AuK7UGY"},"outputs":[],"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","import sklearn"]},{"cell_type":"markdown","metadata":{"id":"E7jAxsg27UGZ"},"source":["## Dataset\n","Same as last week, we use scikit-learn to construct a synthetic dataset with\n","- 5 classes\n","- 2 numerical features\n","- 500 items\n","\n","We will use `X`-s for the input values\n","\n","Notice: `t`-s contains the true labels of the data points.\n","Although k-means does not use these labels (unsupervised learning), we keep them to evaluate how well our clustering matches the true groups."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"9Y1c3-K07UGZ"},"outputs":[],"source":["from sklearn.datasets import make_blobs\n","X_np, t_np = make_blobs(n_samples=500, centers=5,\n","                  n_features=2, random_state=2026)\n","X1 = [(X_np[i,0], X_np[i,1]) for i in range(X_np.shape[0])]\n","t1 = [t_np[i] for i in range(X_np.shape[0])]"]},{"cell_type":"markdown","metadata":{"id":"WQ4Ue63Z7UGZ"},"source":["This is a general form for representing data we will use a lot in this course. We store the features in one list and the labels in another list of the same length. For example, y[14] is the label the dataset ascribes to the input X[14], where X[14] is a pair (two-tuple) of numbers.\n","\n","(Later on we will use numpy arrays and not lists, e.g., the X_np, t_np, above.)\n","\n","We can then take a look at the training set using scatterplot."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Jc4iVZR27UGZ","colab":{"base_uri":"https://localhost:8080/","height":447},"executionInfo":{"status":"ok","timestamp":1776168621425,"user_tz":-120,"elapsed":285,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"6bd9e673-1ce9-4615-a9c4-e489acd73a87"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["<matplotlib.collections.PathCollection at 0x7b494a3366c0>"]},"metadata":{},"execution_count":3},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["plt.scatter(X_np[:, 0], X_np[:, 1], c=t_np)"]},{"cell_type":"markdown","metadata":{"id":"d6KmOpaS7UGa"},"source":["To better visualize data, the function allows both cases:\n","* without y: to visualize data in a true unsupervised setting (no labels)\n","* with y: to compare clustering results with the true labels for evaluation"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Jc5ohgnw7UGa"},"outputs":[],"source":["def show(X, y=None, marker='.'):\n","    if y is None:\n","        # Unsupervised: no labels available → plot all points the same\n","        plt.plot([a[0] for a in X], [a[1] for a in X],\n","                 marker, label=\"data\")\n","    else:\n","        # Labels available (e.g., for evaluation/teaching)\n","        labels = set(y)\n","        cl = {lab: [] for lab in labels}\n","        for (a, b) in zip(X, y):\n","            cl[b].append(a)\n","        for lab in labels:\n","            plt.plot([a[0] for a in cl[lab]],\n","                     [a[1] for a in cl[lab]],\n","                     marker, label=f\"class {lab}\")\n","    plt.legend()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"f9pnLfhb7UGa","colab":{"base_uri":"https://localhost:8080/","height":430},"executionInfo":{"status":"ok","timestamp":1776168697550,"user_tz":-120,"elapsed":181,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"9c758a69-3545-4e62-c95a-149616173446"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["show(X1, t1)"]},{"cell_type":"code","source":["show(X1)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":430},"id":"r7W1ZYoP56W9","executionInfo":{"status":"ok","timestamp":1776168712572,"user_tz":-120,"elapsed":264,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"619a28d1-f518-4d0a-845b-cf7e184f1b48"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 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\n"},"metadata":{}}]},{"cell_type":"markdown","metadata":{"id":"WtQdU3QJ7UGb"},"source":["## K-Means clustering\n","We will now implement the K-Means clustering algorithm.\n","We first need to calculate the distance between two points using the same function in last exercise."]},{"cell_type":"markdown","source":["### (L2-) distance function:\n","It should work for points in *n*-dimensional space for any integer *n*>0. Check that dist((3,4,0),(0,0,12)) is 13."],"metadata":{"id":"5LotBuLc8_AR"}},{"cell_type":"code","execution_count":null,"metadata":{"id":"jUJOEajZ7UGb"},"outputs":[],"source":["def distance_L2(a, b):\n","    # Euclidean distance in a procedural way\n","    s = 0\n","    for (x,y) in zip(a,b):\n","        s += (x - y) ** 2\n","    return s ** 0.5"]},{"cell_type":"markdown","metadata":{"id":"iNQ3DDdT7UGb"},"source":["### Centroid (mean point):\n","\n","The next thing we need is a way to compute the center of a cluster. Implement a procedure which takes a list of points as argument and returns their mean (i.e., the centroid)."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"PMZ1Zpvg7UGc"},"outputs":[],"source":["def mean_point(points):\n","    # Compute the center (mean) of a list of points\n","    n = len(points)\n","    d = len(points[0])\n","    center = []\n","    for i in range(d):\n","        s = 0\n","        for p in points:\n","            s += p[i]\n","        center.append(s / n)\n","    return center"]},{"cell_type":"markdown","metadata":{"id":"M8Dpz_Xm7UGc"},"source":["### Exercise: the K-Means algorithm\n","\n","We will use a class for implementing the clustering algorithm. We have chosen a format that we can later reuse for various other learning algorithms. The format is inspired by scikit-learn. We will have a superclass where we can put methods common to different algorithms.\n","\n","The class will have three methods: one `__init__` where we set the hyperparameters, one `fit` where the training (clustering) takes place, and one `predict` which assigns a cluster to new data points after the model has been trained.\n","\n","The training will have the form:\n","\n","```python\n","cls = PyKMeansClusterer(k=5)  # OR some other number, default 3\n","cls.fit(X_train)\n","```"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"GipKdk3X7UGc"},"outputs":[],"source":["# This is usually done as a design placeholder or base class.\n","\n","# Plan to add shared methods later (e.g., fit(), predict())\n","# Serve as a parent class for other classifiers:\n","\n","class PyClusterer():\n","    \"\"\"Common methods to all python classifiers --- if any\n","\n","    Nothing here yet\"\"\""]},{"cell_type":"code","execution_count":null,"metadata":{"id":"mBT7mxVu7UGc"},"outputs":[],"source":["class PyKMeansClusterer(PyClusterer):\n","    \"\"\"k-means clustering using pure python representations\"\"\"\n","\n","    def __init__(self, k=3, dist=distance_L2, max_iter=10):\n","        self.k = k\n","        self.dist = dist\n","        self.max_iter = max_iter\n","\n","    def fit(self, X_train):\n","        X_train = [[x for x in xx] for xx in X_train]\n","        self.X_train = X_train\n","\n","        # Use the first k points as initial centroids\n","        self.centroids = X_train[:self.k]\n","\n","        for i in range(self.max_iter):\n","            ########## explain below\n","            clusters = [[] for _ in range(self.k)]\n","            for x in X_train:\n","                c = self.predict_one(x)\n","                clusters[c].append(x)\n","\n","            new_centroids = []\n","            for j in range(self.k):\n","                if len(clusters[j]) > 0:\n","                    new_centroids.append(mean_point(clusters[j]))\n","                else:\n","                    new_centroids.append(self.centroids[j])\n","            ############\n","\n","            if new_centroids == self.centroids:\n","                break\n","\n","            self.centroids = new_centroids\n","\n","    def predict_one(self, a):\n","        ########## explain below\n","        distances = [self.dist(a, c) for c in self.centroids]\n","        cluster = distances.index(min(distances))\n","        ############\n","        return cluster\n","\n","    def predict(self, X):\n","        return [self.predict_one(z) for z in X]"]},{"cell_type":"markdown","source":["## Answer below questions:\n","\n"],"metadata":{"id":"dqXZPCFQBwtd"}},{"cell_type":"markdown","source":["###1. What is `fit()` actually do? Especially the part inside `explain below`?"],"metadata":{"id":"0b9W5n7gD-Hs"}},{"cell_type":"markdown","source":["###2. What does `predict_one()` and `predict()` actually do?\n"],"metadata":{"id":"76tFRWBVECta"}},{"cell_type":"markdown","source":["###3. How does the function initialize the centroids? is it a good way?\n"],"metadata":{"id":"rGoOiCH2Dz_H"}},{"cell_type":"markdown","source":["## 4. what's the `max_iter`? is the default value appropriate?"],"metadata":{"id":"uqULiUx7F7OA"}},{"cell_type":"markdown","metadata":{"id":"qXWw0eX27UGc"},"source":["## Experiments and evaluation\n","Why we do not have a standard evaluation for k-means?\n","\n","* In kNN, we have true labels and can directly measure accuracy by comparing predictions with the correct classes.\n","* In k-means, the setting is unsupervised, meaning there are no labels used during training. The algorithm only finds structure in the data, not “correct answers”"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"dyvI4cbI7UGc","colab":{"base_uri":"https://localhost:8080/","height":430},"executionInfo":{"status":"ok","timestamp":1776172017352,"user_tz":-120,"elapsed":388,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"e4bfdf55-5951-4dac-89bc-cf8bc38f3f9d"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"iVBORw0KGgoAAAANSUhEUgAAAioAAAGdCAYAAAA8F1jjAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAabFJREFUeJzt3Xl4U2XaP/DvSelOFwqFttBKLJsIQmEAWyojiyKDIgKCyLwsLyiKowMoQucnm6PD4gI4og6OIuggoKLjjMOiIC8DrYBIEZEiYKFgGzYhhdIFmvP7Iz0hyznJydacpN/PdXlhk7M8CcK5vZ/7uR9BFEURRERERBqkC/QAiIiIiJQwUCEiIiLNYqBCREREmsVAhYiIiDSLgQoRERFpFgMVIiIi0iwGKkRERKRZDFSIiIhIsxoFegDeMplMKC0tRVxcHARBCPRwiIiISAVRFHH58mWkpaVBp1POmwR9oFJaWor09PRAD4OIiIg8cOrUKbRq1Urx/aAPVOLi4gCYP2h8fHyAR0NERERqlJeXIz093fIcVxL0gYo03RMfH89AhYiIKMi4KttgMS0RERFpFgMVIiIi0iwGKkRERKRZQV+jQkREpEQURVy/fh21tbWBHkqDExYWhkaNGnndOoSBChERhaSamhqUlZXh6tWrgR5KgxUTE4PU1FRERER4fA0GKkREFHJMJhOKi4sRFhaGtLQ0REREsCloPRJFETU1NTh37hyKi4vRtm1bp03dnGGgQkREIaempgYmkwnp6emIiYkJ9HAapOjoaISHh+PkyZOoqalBVFSUR9dhMS0REYUsT/8vnnzDF98/fweJiIhIsxioEBERkWYxUCGieldmrET+8fMoM1YGeihEQeXEiRMQBAGFhYWBHkq9YaBCRPVq3d4S9F64DQ+/vRu9F27Dur0lgR4SEalUVVWFJ554Ak2bNkXjxo0xfPhwnDlzxq/3ZKBCRPWmzFiJvA0HYRLNP5tE4E8bfmBmhTSPWUCzadOm4V//+hc++ugj/N///R9KS0sxbNgwv96TgQpRiNLiX6zF5yssQYqkVhRx4jwbcpF21XcW0GQyYfHixWjTpg0iIyORkZGBF198UfbY2tpaTJw4EXq9HtHR0Wjfvj2WLVtmc8z27dvRs2dPxMbGIjExEb1798bJkycBAAcOHEDfvn0RFxeH+Ph4dO/eHd9++63svYxGI9555x28+uqr6NevH7p3746VK1ciPz8f33zzjW+/BCvso0IUgtbtLbFkLnQCsGBYZ4zqkRHoYUHfLBY6ATbBSpggoHUz9rkgbVLKAvZpl4zUhGi/3DMvLw9vv/02lixZgtzcXJSVlaGoqEj2WJPJhFatWuGjjz5C06ZNkZ+fj0cffRSpqakYOXIkrl+/jqFDh+KRRx7Bhx9+iJqaGuzZs8fS/G7MmDHIysrCm2++ibCwMBQWFiI8PFz2Xvv27cO1a9cwYMAAy2sdOnRARkYGCgoKcPvtt/v+ywADFaKQE4i/WNVKTYjGgmGd8acNP6BWFBEmCPjLsE4BHxeREmdZQH/8d3v58mUsW7YMr7/+OsaNGwcAyMzMRG5uruzx4eHhmD9/vuVnvV6PgoICrF+/HiNHjkR5eTmMRiPuvfdeZGZmAgBuueUWy/ElJSWYMWMGOnToAABo27at4tgMBgMiIiKQmJho83qLFi1gMBg8+rxqMFAhCjFq/2ItM1ai+HwF9M1i6zVQGNUjA33aJePE+ato3SyGQQppWn1nAQ8fPozq6mr0799f9TnLly/Hu+++i5KSElRWVqKmpgZdu3YFACQlJWH8+PEYOHAg7rrrLgwYMAAjR45EamoqAGD69OmYNGkS3n//fQwYMAAPPvigJaDRCtaoEIUY6S9Wa/Z/sQZ65U1qQjSyM5sySCHNk7KAYXVTJf7OAkZHu3fdtWvX4plnnsHEiROxZcsWFBYWYsKECaipqbEcs3LlShQUFCAnJwfr1q1Du3btLDUl8+bNw6FDhzB48GBs27YNHTt2xKeffip7r5SUFNTU1ODSpUs2r585cwYpKSnufVA3MFAhCjGu/mLlyhsi94zqkYGds/riw0dux85Zff1a79W2bVtER0dj69atqo7ftWsXcnJyMGXKFGRlZaFNmzY4fvy4w3FZWVnIy8tDfn4+OnXqhDVr1ljea9euHaZNm4YtW7Zg2LBhWLlypey9unfvjvDwcJuxHTlyBCUlJcjOznbzk6rHqR+iEORseqW+59yJQkFqQnS9/PmIiorCzJkz8eyzzyIiIgK9e/fGuXPncOjQIUycONHh+LZt22L16tXYvHkz9Ho93n//fezduxd6vR4AUFxcjBUrVmDIkCFIS0vDkSNHcPToUYwdOxaVlZWYMWMGRowYAb1ej9OnT2Pv3r0YPny47NgSEhIwceJETJ8+HUlJSYiPj8eTTz6J7OxsvxXSAgxUiEKW0l+sXHlDpG2zZ89Go0aNMGfOHJSWliI1NRWPPfaY7LGTJ0/G/v37MWrUKAiCgNGjR2PKlCnYuHEjACAmJgZFRUVYtWoVLly4gNTUVDzxxBOYPHkyrl+/jgsXLmDs2LE4c+YMmjVrhmHDhtkU59pbsmQJdDodhg8fjurqagwcOBBvvPGGX74HiSCKouj6MO0qLy9HQkICjEYj4uPjAz0coqCwbm+Jw8obLSxfJvKVqqoqFBcXQ6/XIyoqKtDDabCc/T6ofX4zo0LUAHHlDREFCwYqRA1Ufc25ExF5g6t+iBo4LbbaJyKSMKNCFIR81azNX632A9VMjohCDwMVoiBjH1zMHNQBnVsmuB0U+KvVvlb3GSKi4MRAhSiIyAUXC/5j3qzMVVBgn+XwRz8VV8EPMy1E5C4GKuS1awYDak6cRETrmxDuxzbKJN+sTeIsIyKX5ejTLtnn/VScBT87fjrHTAsRuY3FtOSVSx9/jGP9+qNk/Hgc69cflz7+ONBDCmly+/hYk4ICa0pZDgA+38NEaZ+hmAgd2/YTkUcYqJDHrhkMKJszFzCZzC+YTCibMxfX/Ljdd0Nnv4+PPbmMyLcnflXMcvh6DxOlfYYqamoVxxAIXOlEwerEiRMQBAGFhYWBHkq94dQPeazmxMkbQYrEZELNyRJOAdXxR03GqB4ZuHT1GhZuLIL1s18uIyJN+dizDmis+6n4YrxyzeTKjJWaadvPYl8iz61YsQJr1qzBd999h8uXL+PixYtITEz06z0ZqJDHIlrfBOh0tsGKToeIm/iXPuDfpb+LNtkGKToAG6Zko0t6E5vjrKdbrI+Vm+JRGq8nwYt9Mzkp02Lftr++C2r9tdKJqKG4evUq7rnnHtxzzz3Iy8url3ty6oc8Fp6SgtTn55uDFQDQ6ZD6/HxmU6D8QPTFVINcwaoJwNUak8vjAOCvD2c5BExK4/3bjuPovXAbHn57N3ov3IZ1e0s8Hrevp5k84azYl8gp4y9A8Q7zr35mMpmwePFitGnTBpGRkcjIyMCLL74oe2xtbS0mTpwIvV6P6OhotG/fHsuWLbM5Zvv27ejZsydiY2ORmJiI3r174+TJkwCAAwcOoG/fvoiLi0N8fDy6d++Ob7/9VnFsU6dOxaxZs/y6W7I9ZlTIK4kjRiA2Nxc1J0sQcVMGg5Q6/lj6K1G7+7HScd1uagJ7SuNduLEIog+zD76eZnIXd44mj3y3GvjXHwHRBAg64L5lQLexfrtdXl4e3n77bSxZsgS5ubkoKytDUVGR7LEmkwmtWrXCRx99hKZNmyI/Px+PPvooUlNTMXLkSFy/fh1Dhw7FI488gg8//BA1NTXYs2cPhLo6sjFjxiArKwtvvvkmwsLCUFhYiPDwcL99Nk8wUCGvhaekMECx488HopppFCkImHlPByzedMTldIu+WSwEAPYJGPu91X0VbAWqTkQrU1AURIy/3AhSAPOv/5oKZPYHElr6/HaXL1/GsmXL8Prrr2PcuHEAgMzMTOTm5soeHx4ejvnz51t+1uv1KCgowPr16zFy5EiUl5fDaDTi3nvvRWZmJgDglltusRxfUlKCGTNmoEOHDgCAtm3b+vwzeYuBCrEPih/4+4FoXbAaE6FDRU0tyoyVSE2Ixt92HLdkQqTOtbe1TPRol2RPgi1XmZJA14lw52hyy6/HbwQpErEW+PVnvwQqhw8fRnV1Nfr376/6nOXLl+Pdd99FSUkJKisrUVNTg65duwIAkpKSMH78eAwcOBB33XUXBgwYgJEjRyI1NRUAMH36dEyaNAnvv/8+BgwYgAcffNAS0GgFa1QaOPZB8R9/12SkJkSj5NcKPPBGvqWG5PEP9mHBf2ynaxZvPKL4QJaW6X574leHbAoATMq92a0+K+v2lrisadFCnUhqQjSyM5sySCHXkjLN0z3WhDAg6Wa/3C462r3/JteuXYtnnnkGEydOxJYtW1BYWIgJEyagpqbGcszKlStRUFCAnJwcrFu3Du3atcM333wDAJg3bx4OHTqEwYMHY9u2bejYsSM+/fRTn34mbzGjEqLUZEmU+qDE5uYGJLMSipkd+9UvviSXmdj4g2MPG6XpGvvpF/upHx2ACbmtMSG3tarsg5r2+d+e+BWXrl5zuBfrREizElqaa1L+NdWcSRHCgPuW+iWbApinXqKjo7F161ZMmjTJ5fG7du1CTk4OpkyZYnnt+PHjDsdlZWUhKysLeXl5yM7Oxpo1aywFse3atUO7du0wbdo0jB49GitXrsQDDzzguw/lJQYqIejSxx/fCEDqVuIkjhjhcJyW+qCoHTPd4KydvjWdAIcgQC6oEOyiBxHAjp/OYVSPDJcBSvH5CvxaUeO0ff6sTw7aBCfS7VgnQprXbay5JuXXn82ZFD8FKQAQFRWFmTNn4tlnn0VERAR69+6Nc+fO4dChQ5g4caLD8W3btsXq1auxefNm6PV6vP/++9i7dy/0ej0AoLi4GCtWrMCQIUOQlpaGI0eO4OjRoxg7diwqKysxY8YMjBgxAnq9HqdPn8bevXsxfPhwxfEZDAYYDAYcO3YMAHDw4EHExcUhIyMDSUlJfvlOGKiEGNksyew5EGJjEZOVZROAaKUPitYyO9KYtJjdsa7/kCvYlTNzUAeHIEAuyBFF26yKCNe1I9ZZGQGOWRmpfb59kAKYD37h/lvRuWWCTY0NkSYltPRrgGJt9uzZaNSoEebMmYPS0lKkpqbisccekz128uTJ2L9/P0aNGgVBEDB69GhMmTIFGzduBADExMSgqKgIq1atwoULF5CamoonnngCkydPxvXr13HhwgWMHTsWZ86cQbNmzTBs2DCb4lx7b731ls37ffr0AWCeXho/frzvvgQrgija1/UHl/LyciQkJMBoNCI+Pj7Qwwm4im92o0TpPxaZTEV9ZzLkAgClMWesWoXYXj39NhYlWs3uyK2UAWBTsDs0Kw2f7S9FrShCB3OQMvm3joVxB05dxP3L81Xd98NHbkd2ZlOH18uMlei9cJtNwCPAnJkxiTcyJelJMXj47d2K15eCG3aJJV+qqqpCcXEx9Ho9oqKiAj2cBsvZ74Pa57dfMyo7duzASy+9hH379qGsrAyffvophg4danlfFEXMnTsXb7/9Ni5duoTevXvjzTff1OTyqGAhmyWRyGQq6rMPilIAoJXMDqDN7A6gXP+xc1Zf7JzV16aG5JmB7V3WlFTU1Mq+7k7tiGxWBsBfH8pC08aRNu3z5ZY+W59j/ZmsMzi+6LUSiH4tROQ7fl31U1FRgS5dumD58uWy7y9evBivvfYa3nrrLezevRuxsbEYOHAgqqqq/DmskGbpFquwaZ1Ug2J/Tmyvnn59EDvbwFBLHW6d1e0EkqsGctYrWNSsaFHa5XjWoA6qV/kc/MXo8JoOQPfWTRzGs3B4ZzjZ9NnhMwHqVhC54otrEFFg+TWjMmjQIAwaNEj2PVEUsXTpUjz33HO4//77AQCrV69GixYt8Nlnn+Ghhx7y59BCnyA4dusCApapcFW4q5UOt1rK7pQZK7Hv5EWIooiMpBjZepTVBScs0zLuZA6U+ryM6pGBIV3TZPuz2I9t0UbHTpkm3CjAtSb1Ltl6+Aye++yQ4rikDI4veq0Eul8LEflGwIppi4uLYTAYMGDAAMtrCQkJ6NWrFwoKChQDlerqalRXV1t+Li8v9/tYtUip2NMhc2HNi0yFt8WlagIALXS4lbI79lNU9T2udXtLbApQBQB3tk/G10fO2Ry38QcDDpy6iCLD5RtFrQIwa1AHTO7jvGmTs6ZxO34657RzrLMVR3mfHERsZCN0v6mJw8aEv7+9NcLDdJYASaj7cKJozsZMzG2teH13u+L6cxsDIqo/AQtUDAZzv4cWLVrYvN6iRQvLe3IWLFjgtCLZl7S68sNZsads5gJA81mzEH/PQI8+h6fFpfbfnxYCADUCnd2RMgHWz1gRcAhSJFsPn8XrXx+zPJRFEVjwnyJAhGwhrTW5oGTmPR2waFORbCYCMAcAsRFhiiuOTAD+sGa/JcDp0y7ZJtNj3xkWAFbuPIG/7/wZK/5bjL/vLMbMQR283oKA+/oQhYagW56cl5eH6dOnW34uLy9Henq6z++j1ZUfroo9FYtpa687ZF7UBGGeFpcqfX9amN5RI5DZHbX9USTJ8ZGyxy/aWIQhXdPcbtK2aGMR7EPdWlG0BBNSQPNAVkt8uv8XxbGaRGDWhoOA6Liqx35zQum60nmLNx5RvU+REu7rQxQaAhaopNQ9BM6cOWPZc0D6WdqjQE5kZCQiIyP9OjatrvwAXNd6hKekoPnT03H2pZdtDjn7yquIHzwY4SkpbgVhnjSFc/X9Bfo71Dp9s1jFEiN7w7u1xIBbWmDOPw85HG8CXE5zyAVFJjiWOOkAh2Biw/5fXI7R+n2lGhGlKZrbWiU6rGhyF/f1IQp+AdvrR6/XIyUlBVu3brW8Vl5ejt27dyM7OztQwwJQfys/rhkMqPhmN67VTXXZ/yzHkjGxZlfrEXVrJ8cT68bvbPWNp/ezH7tWV84Ei9SEaEzK1Su+/8LQWzF78C345xM5eGVkV6QmRGPWoA4Ox6mZ5pBb/QMAgzql2Kz+mXSHXrZBnDWph4ozcnv6KK1AkgILb/fk4b4+RMHNr4HKlStXUFhYiMLCQgDmAtrCwkKUlJRAEARMnToVL7zwAj7//HMcPHgQY8eORVpamk2vlUBQ+3D2hv1mgKWz8lRtDqhmKa+z8bsbRKi5n81n6dsP5Rv/4/jECtDKmWD1v7l62eW8OgCdWybglrR4NI+/0Txpcp9M5A3qYPkDbT3NIW08WGasBACbn1MTojHzHscgZ/MPZ7BhSrZlQ8UJuXrZgMaaCOARq00Mpf2DrMkFT9IUjTubHxJRw+HXzrTbt29H3759HV4fN24c3nvvPUvDtxUrVuDSpUvIzc3FG2+8gXbt2qm+h7860/qzRuWawYBj/frLr8yR6HRos22r0+kVZ7UeSuOXvbeLezm7n+JnkQIVUbTcPzY3V5PFyVojLTM++IsRCzfe2AlZADCocwo2/WBQXI1TZqy0K1Itxtv/LbbUiFjXlUjnK3WOte5IK7cKyf4vDp0A7JrVDwAsY9jx0znZJdBKn5tTNOQrodqZ9sSJE9Dr9di/f7/TMgmt8EVnWrbQd8JVMOApp23urXjbQl5p/BfeeQdnX3nVJ0GY088iCGj6+OOIu/NOVP90RJPFyWpYFx4DkP13pf8+3O2Kat8mf+Y9HXDyQgXW7Dkle3yYIGDnrL5Od0Z2JkwQsGFKNoYuz7fdMFAA8mf1s2Rk7FvlA47BigBg4XDHFvgMQCgQGKj43q+//oq5c+diy5YtKCkpQXJyMoYOHYo///nPSEhIkD1H8y30g52/Cj+dtrmX+GCqRG78lz7++EaQIgho/vR0rwIGp59FFHHhjTdw4a23zJkVKSbWUHGyKzaZKesskUzGyP57lNubx9k+NrIrcDYVOS1YlesLYn8dZ2pFEacvVjpkR6zvqbQKyeEcmHuoWC9j1jeLrXsvqP9/iIgAlJaWorS0FC+//DI6duyIkydP4rHHHkNpaSk+VihX8IWAFdM2ZHJ1HwlDh/q9hbxDIa0o4uwrrzot3nVFWmXklMnkWHkZBMW1ct+X5XPIBF7W36NSV1SpTkSO7AocUXmPHMAcANnXfLizvFknAP/3k3x/lq9+PANAueBWjgnAzI+/t7Stz1mwDdkL1LWwt6+lIdISQ4UBe8r2wFDh+d+XaplMJixevBht2rRBZGQkMjIy8OKLL8oeW1tbi4kTJ0Kv1yM6Ohrt27fHsmXLbI7Zvn07evbsidjYWCQmJqJ37944efIkAODAgQPo27cv4uLiEB8fj+7du+Pbb7+VvVenTp3wySef4L777kNmZib69euHF198Ef/6179w/fp1334JVphRCRC5niLJU//ol6kmaeqi+uefnRbSelo/IrvKyBU/F9f6olmfUvM8WXZLtj3piirXoExXt0xYKe6YlHuzw/XkrgOY/6/kgW4tLbsrS7scr//2tOy15/zzECIa6TCqRwYWDOtsU6PizI6j5y3/bn28sxb27mafiOrThqMbML9gPkyiCTpBh7nZczGs7TC/3S8vLw9vv/02lixZgtzcXJSVlaGoyHHLCsAc1LRq1QofffQRmjZtivz8fDz66KNITU3FyJEjcf36dQwdOhSPPPIIPvzwQ9TU1GDPnj0Q6rLCY8aMQVZWFt58802EhYWhsLAQ4eHhqscqTds0auS/cIKBSgDZT834eqrpmsGAX1etxq+rVik/cAUBVT8cRMmECR7Xj+hiVHT6lJkq8de0j68KoVVN0UnsAi9PuqJKK3CkhmtS8SlgnlKxH4UOwIS6lvP217FudKYTzAHNhNzWlt2Vvzt5EX9Ys9/pRxJxI7Do0y5ZdW8XZ9RMVZlE8+ftkBKHLulNvLshkZcMFQZLkAIAJtGE+QXzkZOWg5RY3/8ddvnyZSxbtgyvv/46xo0bBwDIzMxEbm6u7PHh4eE23dr1ej0KCgqwfv16jBw5EuXl5TAajbj33nuRmWnuVH3LLbdYji8pKcGMGTPQoYN59V/btm1Vj/X8+fP485//jEcffdTtz+kOTv2EqEsff4xjffvh15UrnT9o66Z/7PuqVH5/0GVPF4np6lWXxyTcfz/afL0NGatWoc22rX4rpHW3T4wzDlN0gnAj4LL+d5nAy5Mlt+v2lphb19dd/tlB7TGqRwZG9cjArrx+ePSOmy1TMGGCgAXDOyteb1SPDOyc1RcfPnI7ds3qhz8NvsVmN+MmsRGqsiNSYKE0nfTH/m1U7YosUTtVZQIw9I187nZMAVdSXmIJUiQm0YRTl+UL3L11+PBhVFdXo3///qrPWb58Obp3747k5GQ0btwYK1asQEmJ+c9OUlISxo8fj4EDB+K+++7DsmXLUFZWZjl3+vTpmDRpEgYMGICFCxfi+PHjqu5ZXl6OwYMHo2PHjpg3b55bn9FdzKiEIMvDWu3//spMB50YNcqS/UgaNw5J48YqZkDUZB6M//wnkqf+0atVTGp40knXGfspOgCy/y53bXe6otpnFcS6NvJDuqRZ2s3/afAtmJDb2uF6SiuLrNvU2zv4i1HV59cBiInQoXl8lGyG6KGeGUhLjLZZgjw0K02xtf7MQR1UT1WJTqaKiOpLRnwGdILOJljRCTqkx/l+6xYAiI5277/1tWvX4plnnsErr7yC7OxsxMXF4aWXXsLu3TdaDqxcuRJPPfUUNm3ahHXr1uG5557Dl19+idtvvx3z5s3Dww8/jC+++AIbN27E3LlzsXbtWjzwwAOK97x8+TLuuecexMXF4dNPP3VrqsgTzKiEILdqKwTBsTkcYFMo+uvKlTjWt5/6JnRy7UlFEVf3F6obkxf80awvPCUFsb16Wqbm5P5didquqM5qWpxdb93eEkvhqrNiVetC1TJjJRZtlJ/vtmcC8MAb+djx0znFDJF19mbnrL54ZWRX7JrVD4/20Vv+gtEByFPY0VnKPsn9ZST3HRDVp5TYFMzNngudYP4vVKpR8ce0D2CeeomOjrbp2u7Mrl27kJOTgylTpiArKwtt2rSRzYpkZWUhLy8P+fn56NSpE9asWWN5r127dpg2bRq2bNmCYcOGYeXKlYr3Ky8vx913342IiAh8/vnn9bL0mxmVEKS6tqJuygKATU2H0lLjsjlzEdmuPaJv62zz1jWDAeGt0tF67VqYKitR/fNxnJn/vMMlrn5TgIRB93j8udQIpl2arXlS06K0ssg+A2FfqDop17EdvjPSdXfO6qu494599iY1IRp/+l1HTOitV5VRGtUjAx1S4jD0jXybRCB3OyYtGNZ2GHLScnDq8imkx6X7LUgBgKioKMycORPPPvssIiIi0Lt3b5w7dw6HDh3CxIkTHY5v27YtVq9ejc2bN0Ov1+P999/H3r17odebt+EoLi7GihUrMGTIEKSlpeHIkSM4evQoxo4di8rKSsyYMQMjRoyAXq/H6dOnsXfvXgwfPlx2bFKQcvXqVXzwwQcoLy9HeXk5ACA5ORlhYWF++U4YqIQgy8aEL79i6fmRNGEChIhwXPjbCstr1j1UpOkNXXQ0Tjz0kHywUjcllPrn5y3nyRWuxvXtizPP/9lh6unS+o/Q7PHHPQ4a1K7kCaZdmiWe7PSrZmWRXDDz9/8Wy061OCNd1909c5xNP9nrkt4EC7nbMWlUSmyKXwMUa7Nnz0ajRo0wZ84clJaWIjU1FY899pjssZMnT8b+/fsxatQoCIKA0aNHY8qUKdi4cSMAICYmBkVFRVi1ahUuXLiA1NRUPPHEE5g8eTKuX7+OCxcuYOzYsThz5gyaNWuGYcOG2RTnWvvuu+8sU0pt2rSxea+4uBitW7f23ZdghZ1pQ5B9k7LmzzyN+MGDcaxvP4fgofX69Q4ZkgvvvOOw+7KNupb7ABTb8f+6arW5kNeOp912/bmlgZa408VVrmOsfafa/OPnZdvjP3rHzXhnZ7F5VRDMK3yc/UUgdbCtqKlV3WXXU+xkS74Qqp1pg40vOtOyRiXEKDV1u/z117LFtSdGjXKoPXHZF6WuONVZ4Wr8oEGyp+rcLBQDfLuSR+vc3el3otVmgXIZCKWdiSfktr6xKiivHxYOt60/Gd6tpc3PQ7PS8MAb+aoat3mLux0TkTVO/YQYpeDh+rnz8ifU1Z5Yt7OvOvSD85tYF6fa17RY79Isw1TpftdRX6/kCQXWdScCgEf76DGht97h4e5qSkn6VW6F0jMD2+PE+auIidDhgTfyXdbCEBH5AzMqIUZp1UvcnXfKr8YBbLrTXjMYzH1VnDGZULFzp+xWAFLhqi9X3/hjJY9WeNI23mEpM4B3/ntC8Xj7VTlKHV/tMxnSzxU1tapWJBER+QMDlRCjFDxE39YZqX92XIkjHWPpC6JyaXPZ7Dm4ZjAgccQItNm21aGRm7MgxlefSUvZFE8CDrVLi+0pFdF+8X2Z4v29mU5Rmj7iahwiqg8spg1R1wwGh1Uv1wwGXN2/HxfXfIjKvXstxyYMHYq0hQssxzgUyCr0Tk9bssTlcmO5cfjyM2mBJ/vUqCmEdedcib/2yVm3t8Rh+oh78ZCWsZhWG1hM2wBdMxhUtba3b0Z26eOPcaxff5ROm24TpACA8fPPba6XNG6c7c7OIx+UvUftpUs2Y5Ebm5qmaGr58lq+4skuyYD6Bm9y7NvzW1N7f3epnT4iIvI1FtMGEU+X6DqsmrFnMuHq/kJUff+9zQaGiaNGotnjjwMAjOs/ss2qCALOPP+8pc1+3F134fKWLTabDkpj88VOxlrlyS7JgMJOyXDcB0eJVPz6xfdleOGLw27f3xPu9EQhIvIVZlSChLtLdK2zGy7rTgQBpdOnO2xgeGndepR/8YW5RuTPz9tkWQDYtNm/vHmzzc/S2KRMTsn48TjWr79iG/5g5Wn9hpQVsT5VBLDjp3Oq752aEI3Bt6WyfoSIQhoDlQBSO40DOF+ia88+OKg69IP8fj4SUVTcwPDsy684FM0mPjjC9YaHdVkaX/U/cee7qk+e7JIs6dMu2WYhlgjbaRtnBbrSewBU3d+TYl8iIi3g1E+AuDuNo4uR/z9k+wZqcpmXs6+8am6p/8qrlvvZTNU4U7eZYMKge27Uu6z/yPUH1OnM1/ZB/xOtd6V1Z5dka86mjXb8dE6xQFeueFdpDx6l4wNVYyLt9BwbEVYvXW6JQs2JEyeg1+uxf/9+dO3aNdDDqRcMVAJAaRrHuumaPdNV+SJL+wZqSpmXqE6d0WbbVtv9fDxY8FVz4qSq85o/PR0x3bIcG8IJgmJ3WutaFuleupgYt7+rQPCkfkNpI8KYCJ3iZoMAHN7L23AQn07JQXZmU4d7qN24sD5YB0ySQAdOROSeyZMn46uvvkJpaSkaN26MnJwcLFq0CB06dPDbPTn1EwDuTONI1DY9UzpOFx1tbsR2Uwau7tunqlcKAEAQEJPV1fn17TSf8QziBw9GzYmTaP70dNvjRREnHnrIoVbFZrqqbz8c69sPJePH48SoUW5/V8FErgW+swZrclkYkwgMXZ4v24fFk54rrviiSZ3EX6uUiMg/unfvjpUrV+Lw4cPYvHkzRFHE3XffjdraWr/dk4FKAHjSaVVt0zOH4wDzrscPPYTSWXk41q8/zi5apG6ggoDUPz9vcw/L9RW63KYtWYKwhARL0HH2lVfR9NFHbI+3q1WR25/IkrWRy96EQFdaqdnb2/8thiiaW+BLy36dFejKvQc41rdIlI5/4YvDHu3Z48smdRJ2uaVgUJ91ciaTCYsXL0abNm0QGRmJjIwMvPjii7LH1tbWYuLEidDr9YiOjkb79u2xbNkym2O2b9+Onj17IjY2FomJiejduzdOnjRvc3LgwAH07dsXcXFxiI+PR/fu3fHtt98qju3RRx9Fnz590Lp1a3Tr1g0vvPACTp06hRMnTvjs89tjoBIAnnZaVeoCK3dc67VrHYID42efqc6ktJg7F22+3iZ7j8QRI9B63TrHYEWnQ0TLlg5TNRf+tsIx4LDKiqjqhivdy4ddaQNVoOuqBb6zAl3pPbngQ+6B78ueK572jAGUAyaAq5RI++p79WJeXh4WLlyI2bNn48cff8SaNWvQokUL2WNNJhNatWqFjz76CD/++CPmzJmDP/3pT1i/fj0A4Pr16xg6dCh++9vf4vvvv0dBQQEeffRRCHV/J4wZMwatWrXC3r17sW/fPsyaNQvh4eGqxllRUYGVK1dCr9cjPT3dNx9eBmtUAiRxxAjE5ua63Wk1PCVF1bGmq1dV1ZLED70f5Z/90+H1yJtvdnofqSW/fZGr6epVx6BDFB2721plRSwZJqVgRadD67VrYaqs9FlX2kAW6KrpveKsQHdUjww0axyBiav22VxD6YE/qkcGLl29hgUbixzec6fniqc9YwDHzRGtx6x2lRRRIHhSU+iNy5cvY9myZXj99dcxbtw4AEBmZiZyc3Nljw8PD8f8+fMtP+v1ehQUFGD9+vUYOXIkysvLYTQace+99yIzMxMAcMstt1iOLykpwYwZMyw1Jm3btnU5xjfeeAPPPvssKioq0L59e3z55ZeIiIjw+DO7wkAlgNQGHZ5w+fCvU/7ZP50GEc7IBVvXDAbZHZXtVx1ZZ0WkDJPNXwbSmKz2KvIVf/zFI61mUbOKRamI1j7IUCrQlYpSrTl74JcZK7Fok2OQonRfb8etxDr4ionQ4WqNya1VUkSBUN+7tx8+fBjV1dXo37+/6nOWL1+Od999FyUlJaisrERNTY1lRVBSUhLGjx+PgQMH4q677sKAAQMwcuRIpKamAgCmT5+OSZMm4f3338eAAQPw4IMPWgIaJWPGjMFdd92FsrIyvPzyyxg5ciR27drlt60KOPUTouSmlxKGDlUuhJWmBgTBYWrF2RSJfVt7pWmtphMnOp22kqa1kv73f28sbRYENH96us8zHZ4UMzvjbt2GN71X5IpSdQA2TMlWXDmjVB+iA2zu66pI1ptxW18jO7MpuqQ38XiTRKL6VN+7t0crrIpUsnbtWjzzzDOYOHEitmzZgsLCQkyYMAE1NTWWY1auXImCggLk5ORg3bp1aNeuHb755hsAwLx583Do0CEMHjwY27ZtQ8eOHfHpp586vWdCQgLatm2LPn364OOPP0ZRUZHLc7zBjEoIk8t4xPbpg9Lp020PlKZmAMuv0lLhqkM/OGRCXAUOStNaajJIv773nk1R7dlXXkX84ME+/T8X2WyTh3/xeLr815e9V0wArtYoZ85k2/ULwKdTctAlvQkA9b1WPB03UbByyPj6eff2tm3bIjo6Glu3bsWkSZNcHr9r1y7k5ORgypQplteOHz/ucFxWVhaysrKQl5eH7OxsrFmzBrfffjsAoF27dmjXrh2mTZuG0aNHY+XKlXjggQdUjVcURYiiiOrqapWf0H0MVEKcfXAg29sEsG1/P3uO7WsSN6ZIPJnWqq8Uqy//4vG2bsNXvVecTb/Y14dImRApSHE32Arknj/uTLER+YqnNYWeiIqKwsyZM/Hss88iIiICvXv3xrlz53Do0CFMnDjR4fi2bdti9erV2Lx5M/R6Pd5//33s3bsXer0eAFBcXIwVK1ZgyJAhSEtLw5EjR3D06FGMHTsWlZWVmDFjBkaMGAG9Xo/Tp09j7969GD58uOzYfv75Z6xbtw533303kpOTcfr0aSxcuBDR0dH43e9+57fvhIGKxkmZDV1MDExXr1p+9XSDP4eHtH19CuC8CNePc7NKdTVVPxxEbK+ePr2Xr/7i8bZuw11KQYerh7azTIg3wVZ90lKHXWp4/FlTaG/27Nlo1KgR5syZg9LSUqSmpuKxxx6TPXby5MnYv38/Ro0aBUEQMHr0aEyZMgUbN24EAMTExKCoqAirVq3ChQsXkJqaiieeeAKTJ0/G9evXceHCBYwdOxZnzpxBs2bNMGzYMJviXGtRUVH473//i6VLl+LixYto0aIF+vTpg/z8fDRv3txv34cgih60J9WQ8vJyJCQkwGg0Ij4+PtDD8SmblSn2vFypcs1gsO1Sq7YBnE6HNtu2+u0P7IV33sHZl16u13t6a93eEofAwd8P0DJjpc+mX8qMlei9cJtDsLVzVl/NBCrBMEbSlqqqKhQXF0Ov1/utyJNcc/b7oPb5zYyKRjmsTLHn5UoV6/87SBgyxNxjxRU/z80CQNStnRxf9GMWxxcCUbfhy+kXT7M09cmTrA+niYhCAwMVjVLVBM0HD/DK7w/C+E+7PipSYW3d8uCmjz6CsMQmiOnWzafLhOX4stC1PgWybsMXtF4k6+4UG6eJiEIHAxWNUtUHxcUD3HqTP6nHifXPlz7+2Fw4K1OjkrZkCRolJaHqh4Nur/pRy348QP1X2NMNWgi2lHZXdifrI1ccnPfJQcRGNkL3m5p49BmZnSEKHAYqGhWekuJ6SkYUUbFzJxJHjJAPQqwe9glDhsD4+eeWny0N2BT20pE2IiyZMMEvHRmddYatzwp70g5XuyurzfooLeH+w5r9HmVXmJ0hCiwGKhp1zWAwBxbOiCLK5sxFrdFok/Ww6QIL3NjnR2Iy2b5vJ2m8uW2zt8uF5TIm0uuuOsPWZ4U9+YY3WQdXuytLS6XVZH3kpomUrufuuNw9n4i8x860GqWqRgUwBx0vv2Lz0HcWhFifJ7sDsiDg13dX4li//qg69IPHHRmdbeLlbWfYQG0mSMrW7S1BzgJzd96cBfLdeZ11vvXl7srONmJ093rOiniJqH4wUNEo2bbNgiD/mkxjNtkgxJpOh+bPPO14PavGb2dfeRXNn57u9i7PShkTKbDwpiV1fe9iSvKsg44yYyVmfXIQ0n+FIoBZnxy0CUhcbTPg692VR/XIwM5ZffH66CyH63qyv5G34yEizzFQ0SjZPXP+/LzDa7LBhv3r9vv8WO2/03rtWuWgxmRCVKfOTvfokeMqY6K0H5C3ARCp42pPH1esg46cBduwcONh2CdDRAD7Tly03E9u+sT6/kpZEG+WSqcmROPeLmle7U/ki/2NiMg7rFHRMKWiUvvXwhISZAtT4wcPtjkueeofHa5lunpVuRNtXZbD3XoRNUuMPSmYre9dTEORt4Wh9kGHCOCfhWWyx0oxh9oeKH3aJWPpQ11grLwGUQSaxESge2vPVulY83bptdaXbhOFOgYqGicXJNi/pnYTQLlr6WIUUtheLAtWu8TYHwEQKfNFYaizWhJrggB0u8m8l5CaHiiuVvx4S64I153iXy0s3SYCgBMnTkCv12P//v3o2rVroIdTLzj1EyLCU1IQ26un24GF6ap8UWDaK6+4nOZxVtSaOGKE21NGrng6ZURm7hSGKk0P6ZvFQqn6SXpdJwALh3W2PNhdTZ84W/GTt+EgDpy66HJc7rKZvlq4DX/b4bjbLBEpE0URgwYNgiAI+ExNZ3MvMKPSwCllKaQ+Kkqc9UGR+GOJMXuseE5td1dn00OpCdGYNagDFmwssjknTBCwYUo2rtaYZKdH3N0UUWISgaHL87FwuLkjstppK2fZkgOnLmLWhoOWGU9RBBb8pwgQgcm/zZQfCBHZWLp0KQRXizZ8hBmVBs6TLEWgi1o9zR41dGoKQ9UUvk7+bSbyftfBshpGuk6X9CbIzmyqOEWSmhCN1s1iUHy+wuZ6zlb8AOY6mLxPDrocl0RuhZGUifnbjuMYujxftixr0cYirzM1FLquXKzC6SMXceVild/vZTKZsHjxYrRp0waRkZHIyMjAiy++KHtsbW0tJk6cCL1ej+joaLRv3x7Lli2zOWb79u3o2bMnYmNjkZiYiN69e+PkyZMAgAMHDqBv376Ii4tDfHw8unfvjm+//dbp+AoLC/HKK6/g3Xff9c0HdoEZFXI7S6FU1Fq+cRPiB93DAELDXBWGqi18ndwnE0O6pLlVYKqUqbFvjy/HBMB+aZHcuOQCrVkbDgKiw+my93C2ySE1XD/uKsX2D4ogiub6qzt/3wEde6f57X55eXl4++23sWTJEuTm5qKsrAxFRUWyx5pMJrRq1QofffQRmjZtivz8fDz66KNITU3FyJEjcf36dQwdOhSPPPIIPvzwQ9TU1GDPnj2WbMiYMWOQlZWFN998E2FhYSgsLER4eLji2K5evYqHH34Yy5cvR0o9/V3PQCXEKXWHtefONI3SPkRnFy3C2Zde8ul+QOR7zgpD3dn8z50CU1eFvNYB1NWaa5i0ap9NYKEDABXjkgu0lBa12WN/FJJz5WKVJUgBzP89bf9HETI6JqFxkyif3+/y5ctYtmwZXn/9dYwbZ+4SnpmZidzcXNnjw8PDMX/+fMvPer0eBQUFWL9+PUaOHIny8nIYjUbce++9yMw0T23ecsstluNLSkowY8YMdOjQAQDQtm1bp+ObNm0acnJycP/993v1Od3BqZ8Q5q/maA7TRdbY2yQoSVMjAPzSN0RNIW9qQjSyM5uiY1oCJt2ht5laWjC8s6pxuZpGUsL+KKTk0tlKx31bTYDxrH+mCQ8fPozq6mr0799f9TnLly9H9+7dkZycjMaNG2PFihUoKTH3rUpKSsL48eMxcOBA3HfffVi2bBnKym60FJg+fTomTZqEAQMGYOHChTh+XLmw/PPPP8e2bduwdOlSjz+fJ5hRCVFq9tPxhjRdVL5xE84uWmT7JnubBBW5KZmds/r6tG+IJ4W8AoBH++gxobfeMgYp6xIToUNFTS3KjJU247OfRtLVNW6WS6qECQKevac9bmuVyP4opCixebRDA3BBByQ0989/L9HR7l137dq1eOaZZ/DKK68gOzsbcXFxeOmll7B7927LMStXrsRTTz2FTZs2Yd26dXjuuefw5Zdf4vbbb8e8efPw8MMP44svvsDGjRsxd+5crF27Fg888IDDvbZt24bjx48jMTHR5vXhw4fjjjvuwPbt2z35yC4Joqg2MapN5eXlSEhIgNFoRHx8fKCHoxkV3+xGyfjxDq9nrFqF2F49fXafawYDjvXr77BqqM22rZZARe30E9W/MmMlei/c5hBA7JzV1+cP7nV7SywBhJTBsF61o3YsaprWlRkrLYHWjp/O3QhcADzUMx05mc08bibnzeaLVH+qqqpQXFwMvV6PqCjvpmh+3FWK7f8ogmgyByl3jvFfjUpVVRWSkpLw2muvYdKkSQ7v2/dRefLJJ/Hjjz9i69atlmMGDBiA8+fPo7CwUPYe2dnZ6NGjB1577TWH90aPHo2Kigp8LrMprsFgwPnz521e69y5M5YtW4b77rsPer1e9vMo/T6ofX4zoxKi6qs5mqvmbmqWMVPgqC2e9QWlQl7pwX/hSrXLsahtWmddPyPdd+XOE/j7zp+xZs8prN17yqNmct529qXg1LF3GjI6JsF4thIJzaP9UpsiiYqKwsyZM/Hss88iIiICvXv3xrlz53Do0CFMnDjR4fi2bdti9erV2Lx5M/R6Pd5//33s3bvXEjQUFxdjxYoVGDJkCNLS0nDkyBEcPXoUY8eORWVlJWbMmIERI0ZAr9fj9OnT2Lt3L4YPHy47tpSUFNkC2oyMDNkgxVcYqIQotd1hfUFp1ZC/p5/Ie+4UzyrxpsOr/VSPnO9/uYTszKYAXNe6OBvH33f+7HZXXuvPBsDrzr4UvBo3ifJrgGJt9uzZaNSoEebMmYPS0lKkpqbisccekz128uTJ2L9/P0aNGgVBEDB69GhMmTIFGzduBADExMSgqKgIq1atwoULF5CamoonnngCkydPxvXr13HhwgWMHTsWZ86cQbNmzTBs2DCb4lwt4NRPiLtmMASsOVp9TT+Rd1xNybg619MMg9xUjxzr6R+l6aFnB7XHoo1FiuPIP34eD7+92+HaHz5yuyUIcvXZJubq8fZ/i926BgWOL6d+yHOc+iGX/NEdVi3uzRMcPN10z9u9g9TuG2Q9/WNfLCsVxC78T5GlYFbqnWI9DnczR3Kf7Z2dxRBgW5jLJc1E/sflyeQ33JsneEhLg92ZwlCahtl34qL8CXWkpdCxEWGK0z3W7IOBUT0ysHNWX3z4yO3YOasvWjaJdljVI4rAdydvjENNV15Xn80kAo/00ft86TYROceMCvkV9+YJXXJZCgB4au1+VNRcl50Csq9JcZVQUQoGpOxKmbESRwzlsufaT2q7kzmKjQhzWJIaJgiY0Nu8XNqXS7eJyDkGKuR3gZx+asj8vYxWylLkfXIQ1j2KlaaAyoyVmPXJQUtw4ixIEQC8/nAWut3kuIRY+ly7jp7HG9uPy15HANC9dRPZMStdTyqYXbmzGG//t9hhisc6YGKAQlR/GKgQhaD6WkY7qkcGYiMb4Q9r9tu8LrfEed/Jiy4zKIB5PnrSHXrZIMX6czk7f8Hwzm7vPyRNQ9lfWgdgw5RsdEl3DHyIyP9Yo0IUYtTsgOxL3W9q4tC2XifAochUzQLD/h2aAwKw4r/Flp2PJfafS87swbdgV14/jOqRYamFUfrc9tcTIZ/lMQG4WmOSeYeCQZAvbA16vvj+GagQhRg1++q4y9lDX5oCEqyCFVEEdvx0zua437ROclk8u63orGKA5WqVkA7Ab1o3QfH5Cvzt/46j98JtePjt3Q4Bj0TtqiMBjkEX4Pw7ocCTdgC+etXz/+7Je9L372xHZlc49UMUYnzRxM2ammmkPu2SbdIRImzrVMqMlVi5s9jl1I/9+9ZTSErFu5J7OqXggTfyZVfryNXMuLqehUx0xQ612hcWFobExEScPXsWgLnxmSCoWWdGviCKIq5evYqzZ88iMTERYWFhHl+LgQpRiJHrNeLpMlq1vVKKz1coBhk7fjrncsoGqEvvKgRYUsHrzEEdsHjjEdRapZN1AvD4nZl4c/txxXvI1cykJkTjgayW+OS7X5yOSxShqo1/h5Q4VNTUcg8gDZHavUvBCtW/xMRE2bb77mCgQhSCPG3iZk/tXkBKWZyYCJ3TIEU6R+r82iwu0hKI6AA8e097m0BHJwAz7+mA21olIiZCh6s1JrRuFoPi8xVY/rXy9vRyGaUyYyU+3W8bpMhlWOzPVfpOhr6RD5EZFk0RBAGpqalo3rw5rl27FujhNDjh4eFeZVIkDFSIQpTcUlx3qZ1GUsriVNTUKgYpYYKADVOy8cXBMry9w7wkWCcA99yago2HDDCJwKJNRRBF2HSdXbzpiOzuzkrTOEoZJaWmbo/20eOd/55QzEYpTRmJLrJOFDhhYWE+eWBSYAQ8UJk3b57DBkjt27dHUVFRgEZERBKllvXF5yss70vksjhlxkrZh7oOwF+GdULz+Cj83apniUkE/vODwXKcXOChNI1jPU6dADzUMwM5NzdF99aOy5wB5SDMVVM3h3sBsF8T5K8dqIkaooAHKgBw66234quvvrL83KiRJoZFRLANQL7/5ZLTzf/sszhyAcSk3JsxIbc1UhOikX/8vKqVN9aUCoOlca7cVYy3dxRjze4SrN1TojgNo5QFApzvwmz/ncRE6ByKeLkHEJHvaCIiaNSokdfFNkTkG3IdbaVfx/z9G7c3IbTPtACwZGQO/mJ0OR5BAATRnLXQCcCzg9o7vZ99hsbZGO3HtuOnc5bdmV3VmlgHZb4qXiYiR5oIVI4ePYq0tDRERUUhOzsbCxYsQEaG/F8O1dXVqK6utvxcXi6/zwcRuc/Zslu1hbVypIe6/fXV9IKaNagDIAIL6zI5izYWITE6XDaA8GSM1vsGebobtK+Kl4nIUcAbvvXq1QvvvfceNm3ahDfffBPFxcW44447cPnyZdnjFyxYgISEBMs/6enp9TxiotDkqqOtVNNhzZ0pDrnrq5n1qai6Zi6qhfy4rHkzRm8b5XmyAzURuRbwQGXQoEF48MEHcdttt2HgwIH4z3/+g0uXLmH9+vWyx+fl5cFoNFr+OXXqVD2PmCg0uXpQSzUdYXVNs9yd4lDbCdbea9sc+6MoBRDSGKVgRSdA9Ri9DcSIyD80MfVjLTExEe3atcOxY8dk34+MjERkZGQ9j4ootMjVoahZiuzNFIfc9QWV0z/2dAJw/koVDpy6KNtkTbqmO9f2ZaM8IvIdQdTYjk1XrlxBRkYG5s2bh6eeesrl8eXl5UhISIDRaER8fHw9jJAouDmrQ1m3t8ThQe3LxmX213/stzdj+XblRm1qSZ+jT7tkSzGsJEwQZPuuKCkzVrLWhKgeqH1+Bzyj8swzz+C+++7DTTfdhNLSUsydOxdhYWEYPXp0oIdGFHJcFYz6uyjU/vr//r5U9bk6AEO6puGzQsdzpM+xbHRXjwt+Jb5olEdEvhPwQOX06dMYPXo0Lly4gOTkZOTm5uKbb75BcnJyoIdGFHLUrIrx94Pa+vo9WyepOkcAMHNQByzcpNwIsrauha0vN2QkosALeKCydu3aQA+BqMHw9c7K3uqS3gTDu7neGFAQgJZNop3WnEibGs68pwMWbzrCOhOiEBHwQIWI/EOpcZuaglG5c/3llZFdMTb7Jrz935/xxfcG2SXLJhGy2RKJYH4bf1iz37xx4aAOuK1lIutMiEKA5opp3cViWiJHzgpmAecFo0rn1kfwUmasxL4TF/HU2v2yBbE7fjpn045/yp2Z6JASr3h8fQUp9RnYEYWKoCmmJSLfUtNhVakORencS5XXnO7xY32+Nw/s1IRo3NslGr9cqjTfD7b9WuSKfeX2C6rPTQFdBYVE5B0GKkQhRqlg9ruTF9Ek1nkQoXTuwo1FlvoQ+8BHCk4O/mKUDWbcDV7W7S3Bok3mIEWo29vH2caH/qy7cTV2b9ruE5E6DFSIQoxSY7U/rNkPEc7/r1/uXB0c60KkjMWOn87ZPKgllkzMVXP7e7XZBvsHvygCizcewZAuaU736vFHozY1mRJv9j8iInUC3kKfiHzLvtW9rq7SVM1eOXJt8mcO6iDbWj4mQicbpEikTIzS3kFylB78X3xf5vS8UT0ysHNWX3z4yO3YOauv11MvrvY9krDtPpH/MaNCFIKsaznOX6nCkx8W2rzv7P/65epAEmPCHTIWFTW1TvfukVuh4yrbIJfRAYAXvjiMv/znsNOMjC/7v6jNlLDtPpH/MVAhClHSg7vMWOl2DYf9Q18ueDlw6qLi+WGCgGcHtbfUrLhzX+sHv7X6rP9wp+7F3918iRo6Tv0QhThvdz22vk52ZlPLeRU1tbLHzR58C3bO6ovJfTI9uq80jfPc4Fsc3lPaNdnX3P3O7L8bIvIdZlSIGgB//F+/Utbhd7elWq7v6X1TE6Ix+LZU/OU/h32ymseTZdPMlBBpAwMVogbC13v4qK3P8PS+vqr/8KbPCTcoJAo8dqYlIq8463Ib6OuXGSvRe+G2gHatJSJ57ExLRPWiPndbdhf7nBAFPxbTElG9KjNWIv/4ead9UXyFfU6Igh8DFSKqN+v2lqD3wm14+O3d6L1wG9btLfHr/Xy14omIAoc1KkRULwJZL+LvOhoich9rVIhIUwJZL8LVO0TBi4EKEfmNdf8Sf+5yTEShi4EKEfmFXP8S7otDRO5ijQoR+ZyzehQArBchItaoEFHgOKtH4Z44ROQOLk8mIp/3NmH/EiLyFQYqRA2cP3qbsH8JEfkKa1SIGjB/9zZh/xIiUsIaFSJyyd+9Tdi/hIi8xakfogaMtSREpHUMVIgaMNaSEJHWceqHqIEb1SMDfdols5aEiDSJgQoRsZaEiDSLUz9ERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItIsBipERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItIsBipERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWoU6AGQ9hgqDCgpL0F0o2hUXq9ERnwGUmJTAj0sIiJqgBiokI0NRzdgfsF8mEST5TWdoMPc7LkY1nZYAEdGREQNEad+yMJQYXAIUgDAJJowv2A+DBWGAI2MiIgaKgYqZFFSXuIQpEhMogmnLp+q5xEREVFDx0CFLDLiM6AT5P+T0Ak6pMel1/OIiIiooWOg0gAZKgzYU7bHYSonJTYFc7PnOgQrUo0KC2qJiKi+sZi2gbEulpUrkh3Wdhhy0nJw6vIpRIVFoaq2Culx6QxSiIgoIARRFMVAD8Ib5eXlSEhIgNFoRHx8fKCHo2mGCgMGfjLQYUXP5uGbGYgQEVG9Uvv85tRPAyJXLMsiWSIi0jIGKg2IXLEsi2SJiEjLGKg0IPbFsqFWJKtUJExERMGLxbQNjHWxbCgVyboqEiYiouDEYloKeiwSJiIKPiympQaDRcJERKFLE4HK8uXL0bp1a0RFRaFXr17Ys2dPoIdEQYRFwkREoSvggcq6deswffp0zJ07F9999x26dOmCgQMH4uzZs4EeGvmJr4teQ71ImIioIQt4jUqvXr3Qo0cPvP766wAAk8mE9PR0PPnkk5g1a5bL87VSo2KoMKCkvAQZ8RkN7gHpzmdXKnr15PuzP8dQYQi5ImEiolCl9vkd0FU/NTU12LdvH/Ly8iyv6XQ6DBgwAAUFBbLnVFdXo7q62vJzeXm538fpSkNeceLOZzdUGCzHAuY6kvkF82GsNmLpd0vd+v6U7ssAhYgotAR06uf8+fOora1FixYtbF5v0aIFDAb5aYEFCxYgISHB8k96emDrEJQevg2hl4e7n12p6HXJviVufX8N+TsnImpoAl6j4q68vDwYjUbLP6dOBXZlR0NeceLuZ5crehUgQITt7KOr768hf+dERA1NQAOVZs2aISwsDGfOnLF5/cyZM0hJkU/hR0ZGIj4+3uafQGrIK07c/exyRa/Tuk9zeQ374tuG/J0TETU0AQ1UIiIi0L17d2zdutXymslkwtatW5GdnR3AkanXkFecKH12AIqreoa1HYbNwzfj3YHvYvPwzZjQaYLT72/D0Q0Y+MlATNwyEQM/GYgNRzc06O+ciKihCfiqn3Xr1mHcuHH429/+hp49e2Lp0qVYv349ioqKHGpX5Ghp1U9DXXFi/dnzS/M9KiyW+/5cdZxtyN85EVGwC4pVPwAwatQonDt3DnPmzIHBYEDXrl2xadMmVUGKlqTEpmj6YenP5dPSZ1cqcs1Jy5G9p/2Y7I9RqkXZcmIL7m59t+a/cyIi8p4mimn/8Ic/4OTJk6iursbu3bvRq1evQA8ppMhNn/iDO0WuasYkV4sCAC99+5JfPwcREWmHJgIVUuZuF9eD5w5i9aHVOHjuoOV8fy7ltR6f2iJXtWOyr0WxxiXJREQNQ8CnfkiZu43k/t/O/4fPj39u+XlI5hDcn3m/YpbD22kTufHNzZ7r8JraKR25MQ1rOww5aTnYcmILXvr2Jb98DiIi0i5mVDTCPnPibibk4LmDNkEKAHx+/HNcvXZV9VJed7I3zupRrFf1yAVWnixrvrv13VySTETUADFQ0QC5eg13m5rtP7tf9vVTV06pWsrrbh2Lq6xIj5QeipkOV8uLpYDp4LmDlsCJS5KJiBomTv0EmFJm4oNBH0An6ByW5iplELKaZ8m+3jW5Kzond0ZOWo7iUl53V+sAN7IicuMzVBhQeLbQfP/mXWWvIU3pSGMCzL1XDl04ZNn3x/q60rSXs89BREShh4FKgCllJqpqq1TVe0g6J3fGkMwhDjUqnZM7A3C+fFptzYj9cmLr8QkQMLXbVOSX5mNe/jxLW3wBAqZ1n4Zbm97qsDRaGpN1rYsc+8CJAQoRUcPBQCXAnGUmeqT0cCuD8GLui3io/UMoPFdoyaR4OwaJTeEsdBjbcSzGdByDqd2mYsm+JRAhYum+pTDBNtgQIeLVfa9arjm121SboMU+m6OEhbNERA1TwDvTeksrnWndYZ+ZcHd1j9J1vOFsDHIdYiVymwqqId2jVeNWmLhloqrjpY60REQU/IKmM62W+aObq1JA4G7thafBjRJnY5CbGpJ4EqQAzmtx7LFwloio4WJGRYGvAwHA9d419X0dJdtLtmPnLzuR2zIXd2bciYPnDmLMf8Z4HJQ48+7Ad3Hq8imb73pqt6no1KwTosKiUFVbxcJZIqIQxIyKFzxZBaOGO43O6uM6cn7/n9/jwLkDAIB1P61Dq8atUFpR6laQohN0+FOvPyExIhGlFaUOq3isj3NWiyNltIiIqOFioCLDX4GAmqLV+ryOve0l2y1BiuT0ldOKx+sEHW5PvR35pfk2r5tEE6qvV6NLqy4YGDsQg/SDcOryKfxw/gdL0GI/nWO/mscfGS0iIgo+bPgmw93OqWr5qmmZv5qfbT65WdVxAgS8/NuX8cGgD1BQWiB7zEvfvoS7P74bK39YiZLyEqTHpWNCpwkuu9YC/t+fiIiIggczKjLse4T4spjTF03LDBUGtGrcCh8M+sCtGg5XxcH6eL2q+4sQcabiDERRdDolZL80WcqKuBqrP6e2iIgouLCY1glDhUFzXVA9nRJRc56hwoC7Pr5L9VgECADUr/xRW/Dr62Jhf6zeIiIi76h9fnPqxwlXe9bUN0+nRNSelxKbgvk581WPRwpQpCkoKXBR4myvIvtx+Gpqy909jIiISFs49RNEPJ0Scee8YW2HIaZRDGbsmKFqTCJEvNTnJSRFJaGipgJPfv2k4rHu1Pn4aorMH6u3iIio/jCjEkQ8LfJ197yuzbuqHpMAAV2Su6BHSg/sO7vP6bFjO451K0DwNqPl7g7URESkPQxUgoinUyLunpdfmu9yGkciQkTh2UIcPHcQ7x16z+mxY24Zo+qavuKv1VtERFR/WEwbhDwt8lVznrN9fZxxteePAAFbRmyp9ykX9mMhItImdqYNYfbN0ewprXJxdR7gfF8fZ1yt/BEhYsuJLbi79d1uByverNrJScvBojsWmaeomndhbQoRUZBhRiXEeJtB8DSjopYAAeNuHYcxt4xRtUz5H4f/gVWHVkGE6PbnYTaFiEi71D6/GaiEEF/1H7F+wLua0vGUAAHTuk/DhE4TlMeQPx8m2AZMgerFQkREvsU+Kg2QmlUuhgoD9pTtgaHCAEOFAZuKN2FT8SabnirD2g7D5uGb8XKfl70ajwABj932mOx7UtfalT+sdHjPsqwYjlkdtat2uOKHiCg0sEYlhLjarNBZpkSAgHk58yxTIymxKSiJKnErm2LdqVaaaslJy8GKgysUp5Je3fcqBukH2WQ5nNXJqF2146+NG4mIqH4xoxJCnC1DPnjuIOblz7M8uO0DEBEi5uXPs8msyC3vdUZq/ma96WBKbAqmdpvq9Lx/HP6Hzc/RjaJll0cLEBSXVVtnigD/bdxIRET1ixmVECPX0XXD0Q2Ylz9P1cqcA2cPIEVvfpjbb87oik7Qya6subXprU7PW/3jaktxrZT1sR6rTtBhbMexigW4SkWzvuhuS0REgcVAJQRZL0OW6j1UT+HYJTKkh/2WE1vw0rcvORyugw4mON9hWm4axpp17Yh9UCRAwAeDPkByTDJKykssn0/iqk2+miXZRESkXQxUQpxSvYfSap4uyV0cXkuJTcHdre/GK9++YlPgqhN0+GDQB6iqrXKasXCVmZFqR+TGKkLElpNbsPrH1bLLjD3d/4iIiIIDa1RCnFydiQAB//jdPzC9+3SH4/+6/6+y18kvzXcovp2bPRedkzur2o9HWkn07sB3Mb37dNnaEaWW96sOrVLc+Zlt8omIQhsDlRAnV1Q6L2ceOid3xm9a/Mbh+M+Pf47tJdttXlOaPspJy3F7LD1SemBCpwmWoEUqulUa69hbxjrc13qqiEWzREShjVM/DYBSUen+s/tlj3/y6ycxP2e+0+kVEaJX0yv2dTRSi3z7sQLA6sOrnS4zZtEsEVHoYqDSQMgVlWY1z1I83rog1Z89SZRW7FiPdWq3qViyb4lNfxb7z8KiWSKi0MSpnwZI6jmSHJOMIZlDZI/xxfSKfW8TufflVuxYH7/h6AYs/W4pRIgQIGBqt6nISctxel0iIgodzKg0MHIZjLsy7sKTXz9pc5y30ytKmRLraR5XK3bsAxkRIpbsW+KQXeFGg0REoYuBSgOilMHYPHwz5ufMdwgsPJ1eUbqPsdqIpd8ttdxjarepTqeUlGpjJPY9U4iIKPQwUGlAnGUwlDIm1hkQKcth/bM795EyIdLPS79biqndptoEL3Oz5wIA9pTtQXSjaKeN4qzHz0CFiCg0MVBpQFwVxdpnTOynb+69+V78++d/yzZec3mfug621kyiCZ2adcLm4ZstAVJ+aT4GfjJQ8Z6iKDq012fPFCKi0MVi2gbEnaJYuembz49/7rTw1dl9pnafqtiYTeqvAsDhnv/++d/4YNAHlp4r83LmsWcKEVEDwoxKA2KoMKBV41aq2t4rtd635mzaRW4qKSEywWkdjNKUUVVtlSWQYc8UIqKGhYFKAyG3Ckd6+MtxtZEg4HraxX4qyVWQobZfC3umEBE1HJz6aQDU9CuxJzd9MyRziOVnAQLGdhzr9likaR65QIPt8ImIyJ4giqLjFrpBpLy8HAkJCTAajYiPjw/0cDRpT9keTNwy0eH1dwe+6zSrApiDHOsMiKHCgH8c/gdWH1oNE5wX1XrK/p5ERBR61D6/OfXTAHjTAl9ummX1j6stK3j80cuEUztERCTh1E8D4MspFWe9WIiIiHyNGZUGwlerZfy5QSEREZE9ZlSCkKvN/pQ4K2R15xrBWPDq6XdGRESBxYxKkFHa7K8+BVsvEy18Z0RE5Bmu+gkihgqDpb28RCfosHn4Zs0HC4HC74yISJvUPr859RNEWMjqPn5nRETBjYFKEJEKWa2xkNU5fmdERMGNgUoQCdZC1kDid0ZEFNxYoxKE2LnVffzOiIi0hZ1pQxg7t7qP3xkRUXDi1A8RERFpFgMVIiIi0iwGKkRERKRZDFSIiIhIsxioEBERkWYxUCEiIiLNYqBCREREmsVAhYiIiDQroIFK69atIQiCzT8LFy4M5JCIiIhIQwLemfb555/HI488Yvk5Li4ugKMhIiIiLQl4oBIXF4eUFLY2JyIiIkcBr1FZuHAhmjZtiqysLLz00ku4fv16oIdEREREGhHQjMpTTz2Fbt26ISkpCfn5+cjLy0NZWRleffVVxXOqq6tRXV1t+bm8vLw+hkpEREQBIIiiKPrygrNmzcKiRYucHnP48GF06NDB4fV3330XkydPxpUrVxAZGSl77rx58zB//nyH111tE01ERETaUV5ejoSEBJfPb58HKufOncOFCxecHnPzzTcjIiLC4fVDhw6hU6dOKCoqQvv27WXPlcuopKenM1AhIiIKImoDFZ9P/SQnJyM5OdmjcwsLC6HT6dC8eXPFYyIjIxWzLURERBRaAlajUlBQgN27d6Nv376Ii4tDQUEBpk2bht///vdo0qRJoIZFREREGhKwQCUyMhJr167FvHnzUF1dDb1ej2nTpmH69OmBGhIREZF3jL8Avx4HkjKBhJaBHk1ICFig0q1bN3zzzTeBuj0REZFvfbca+NcfAdEECDrgvmVAt7GBHlXQC3gfFSIioqBn/OVGkAKYf/3XVPPr5BUGKkRERN769fiNIEUi1gK//hyY8YQQBipERETeSso0T/dYE8KApJsDM54QwkCFiIjIWwktzTUpQpj5ZyEMuG8pC2p9IOCbEhIREWmemtU83cYCmf3N0z1JNzNI8REGKkRERM64s5onoSUDFB/j1A8REZESruYJOAYqRERESriaJ+AYqBARUWgy/gIU7/Au+8HVPAHHQIWIiELPd6uBpZ2AVfeZf/1utWfX4WqegBNEURQDPQhvqN0mmoiIGgjjL+bgxHrKRggDph70PMAw/uL9ah7uA2RD7fObq36IiCi0OKsrURMgyAUU3q7m4T5AHuPUDxERhRZv6kqcTRmd3gfkv27+1R1cOeQVBipERBRaPK0rcRZQfPo48Pd+wJb/Z/7108fVj4crh7zCqR8iIgo9nnSJVQoojmwCDqyxff3AGqDHJKBVd9fXlTI89jUzXDmkCjMqREQUmhJaAvo71NeWKE0ZXTHIH3/qG/Xj4MohjzGjQkREBNwIKP411ZxJkQKK5rcCOxY7Hp9+u/prB2ofoBBYacRAhYiISKIUUHR52Hb6p8vD6qZ9rDlbOeSPgCJEVhqxjwoREZEap/eZp3vSb3c/SAGUgxF/BBS+6iXjx4wM+6gQERH5UqvungUogHIworTSKLO/d4GBt71knI25nrGYloiIyJ+cLXve/aZ/li57u0eRhnq/MFAhIqLg4ovNBuvL6X3Af1+RD0ZO7TE3kHMgeL902duVRhrq/cKpHyIiCh6+mI7wpu7CnXM/fdyx/4q1I18A8GOZaGZ/YPjfAQhAek/3PquGer8wo0JERMHBF9MR3uyq7M65p/c5D1IA4ODHAASZN0TvMxfSWD+eAHzyv8Dxre6dr6HeL8yoEBFRcPDFZoOeFq66e25JgevxKGVT5DIX7mRyfFWgG6jeL3YYqBARUXDwdjrCm0DH3XMzstWNyYHOMXPh7nSXL1b8SLzdNdoHOPVDRETBwdvpCG9WwsidC53yua26m5vCKVJ4/I541zYIOb0P+NdTytNdcoXF3q740RgGKkREFDy6jTU3LRv3b/Ov7hTSehPoSOfa1JSIjrUf1oHDA28Co9fBoQ5F0AGjP5QPJtJ73vj5u9XA3/sD9n1ZpeyIUs2MhupLfIFTP0REFFy8mY7wpu4isz8gCFaBg2hb+yE3RdOkNRxqUUQTEBFru68QdMCAuTfGc3of8PlTjucC5sAjPMZ5HYpG6kt8gYEKERE1LJ4GOq56izgEDn8EHvpQua5GfwdQeQn4ao75/a/mAdFN6q6lFKTU1bBcq3Bdh2L/OYN0g0IGKkRERHLsH+zOinllgxgT8OEoc63K9+tsd2ROaGm+/ldzb2RopOBGFCG/IkgHTPzKXP9i/MW9wmKNtMP3BAMVIiIie0oPduvpGvvaD/vAQXLgQ2D0WnMwY72hoVJwI0sHDFl241ypDkVpLNb8tZ9QPWGgQkREDcaVi1W4dLYSic2j0bhJlPxBzh7scrUfUuZlwDzz9I1DsCGaMyvAjaAnsz9QcR7mQlur7IlcsCNYZVKsqa1D8eVy5QBgoEJERA3Cj7tKsf2DIoiiuSb2zt93QMfeaY4HunqwW9d+2GdeOo0ADq5XHoRoMhfJCkLdPQRYghWbQt06UqZEaddmNfU2GmqH7wkuTyYiopB35WKVJUgBzPHA9g+KcOVilePBavuQyGVefvhYxWhEq6ChLkD53at1iRW7QCV3mve1JEG+XJmBChERhbxLZysd25GIwIFtpxwPVvtgV6oxyXlKpjmcE6IJqK2CbAHtzld9s0u0N/1nAoxTP0REFPISm0fLzqwUfnUKXfqlO9aryNR/ONS3yE6p6IC0LPOy5LUPOd7QfBAc6lLSb3d8HTBf21e1JBpoh+8JBipERKRprgpg1RTINm4ShS4DMlD4ZYntGyJgPFspf57Vg12+vqUlrvR9HZc2vYXEsF/QuNGv5sDk4wmQDToA8+tdRgPffwibeaizh4C75gNfzrE7vG7KKUh7oPgCAxUiItIsVwWwqgtkAXTp18ohUBF0QELzaKdjkK1v+UcRqiuuoeDTVIjifAiCiDvj3kDHmK/qzlLYGRki8P1au0xLXYfbqQcBCHW9VUw3ppyOb62/HigaDIgYqBARkSYpBQgZHZPQuEmUy/ftNW4Shb7/0wHb/1FkeebfOaaDw7H2GRrZ+hYTkP/pcUs8IooCtpc/hozI/WgcdsHqSIXpHHvSqqLeTwGdht+YcgLM+/jILZUGbgQV1v/uaYCh0aZwDFSIiEiTlAIEaarG1ftyOvZOQ0bHJBjPViJBZqpILkOT0THJsb5FLv5AGIzXU24EKkIY8NAamVoVmZOtVxVZ15IU75BfKr37LSD/r1bXkZY4exhgaLgpHFf9EBGRJkkFsNasp2oSZaZs1EzlAPITM0oZGsAcsEgLeQQdcHNWsuO9BRFXxSa4Utv0xrRN+3uA+167sYJI6bE7YK75V2nnZYncUmno7IIUq08kBRj2K4Wsd3WW42ofowBiRoWIiDSpcZMo3Pl75amakh9/tT1BkJ/KseaspsVZhsY6E9MoUodPFu1zuLYoCthy6WnzdYe1QMdut5rfsF5BVHGurtjWTsV5qykewVxY2/uP8q3yu40F9q1U/uLsu86qmdLRcFM4BipERKRZSlM1UvbDmgAgo2OS4iogVzUtckuYrTM0jZtEoXGTKJw+clF+1TFuXPfrDWeQ8ZvMG/eXpnNkNxO0z5CIdat/BHPNiv1S6VO7nQcq1gGG2ikdd/YOqmcMVIiISNOkAMGaswZuB7465VbG5Ni+s2jTvbnLDI5EqSeL7YUBw89GtOlul92RCwiyp9QFKna+mmsurLVv249eUFz+bB9guLPPj9q9g+oZAxUiIgo6stkPASj88kanWTUZEwDY9fEx5H9yzBLUOCu2BcyBU/YDmSj49Lj5WkotU5QCGfuAAADyX3c8QanZW0JLYMhrttM5A+YBad0cAwx3p3Q02BSOxbRERBR0pOyHdYFrlwEZDsdJNSZy59gcVxfUXLlYhcZNotCyfRPFWpcfd5XeCFIAdBt4k+NBApCSmaD8ARJaAvo7bgQGd83HldqmOF3dyVyMC9g2e7MvhO02Fpj6Q11L/B/M9SzS9ezvE8T7/ADMqBARUZDq2DsNTVvGouyYEaltEhCbEIkDX5U4ZEzOnixHy/ZNLOdkdEzCsX1nsevjYzbHuVraDDjWuQDA/i0nkTMs80ZfFQHo+3vnRb32fsSD2H6uE0QIEGDCnQlvoeOoIZZmb1euN8Gl2pZIvOcxNO4zxnyS2uyHRqd01GKgQkREQUluBc/tD2SiYMNxm+MKPjuOtj1aWAKHxk2i0KZ7c+R/ckyxcFaJUp1LXFIUxv0lx+mUkRJL8APzWmwROmwvn4KMpjej8XtZ+LGiL7aXT4EIHYQ1JtxZfQgd77pV+YJy3WU1OKWjFqd+iIgo6Cit4IlLcgwQrKd/JHJTR3eO6QAAOH3kIq5crMKVi1WWf5fI9W4BgC3vHELJj786nTJSolQYbDxxAleuN7EEKUBdELPhjM2YbHy32rzMedV95l+/W+3WWLSIGRUiIgo6SpkNQYDsEuNGkTqcPnLRZsmyfeFsyY+/YvWf8h2ua716yKF3i3RvF+37nVEq8j1rTIJY29ISpFjfS3aKSsPdZb3BjAoREQUdpa61KTcnoF2vFJvXm7eOxyeL9uGfS/Zj9Z/y8eOuUst7UuEsAIfaE4kUhJw5YXTo3WJznEzmRo3GTaJw+wOZDq8XbDqP8D5TIMB2ebHiFJWGu8t6g4EKERFphtx0ixxnUzc/7TbYHHvm53KHKSL768tlaKyJJqDsmNHpMWrb98tpflO87D2v6+/BncNTLUGZUm8XAPLt9jXSXdYbnPohIiJNcNbeXo791A0AHN131nkjNsiv7nHVxE3QAaltEhSPcRZAWHfKBSDbNddZV9yW7W9Fxm8yXRfqari7rDcYqBARUcC5am+vROpaax3kuCKX+bDvSgtpWkm8EYS0aJ3g0Lk2e2gmmt8UrxhAKI3LPhBz1RVXrjuvrCBfiiyHgQoREQWcsw0BXT2g5XqbSAQd0K5nCn7aY3DaFh+Qz9DYZzGkYwzHjRABpGYmOFxLyqCER+pc1r1YB2JquuKqEsRLkeUwUCEiooBztSGgM0r1Jb1HtLHs4XP7/TerCgDsMxdyx5b8+KviFNX+LSdvNH5zQS4QU505aUBYTEtERAGnVByr5qGttAJIClKk63vS48Se0hTVlYtV+G7LSeRvUBekSGP0tPi2IWFGhYiINEFu6sW+94kctbse+4LSFJXhZ6NDR1wH1psXCv4bY6hhoEJERJohVxzryQogfwUASlNULot4BaD7wJvw3eaT5s+k8n7WK4YaalDDQIWIiDTF2xVAvhyHfZCglL1JzVReumz+EMC+zSctGRU1n8k+WLv9AfMKI2k8DSWIYaBCRESa4s0KIF9xltFRyt7YLG+2Zz3tU8fZZ5IL1qSpJUEA2vVKwU+7DaozTsGMgQoREWmKNyuAfEFNRkcue2MdwJw5WY5vPjtuybrcPjQT33x6XPVnctYpVxSBI98YbH72dJ+hYOC3VT8vvvgicnJyEBMTg8TERNljSkpKMHjwYMTExKB58+aYMWMGrl+/7q8hERFREPBmBZAvOMvouCKtLup2900Y+2IOhk7LwtgXc9Dt7pvc+kxyK5mc8XSfoWDgt4xKTU0NHnzwQWRnZ+Odd95xeL+2thaDBw9GSkoK8vPzUVZWhrFjxyI8PBx/+ctf/DUsIiIKAvVVHCtHKaMjtwOzM/ZZF3c+k0OnXBdCeamzIIpqGg577r333sPUqVNx6dIlm9c3btyIe++9F6WlpWjRogUA4K233sLMmTNx7tw5REREqLp+eXk5EhISYDQaER/vuKkTERE1DL4sLv1xV6lNwWy7nso1If4sar1ysQrGs5U4e7IcBVZTSXLddoOtRkXt8ztgNSoFBQXo3LmzJUgBgIEDB+Lxxx/HoUOHkJWVJXtedXU1qqurLT+Xl5f7faxERKRt7i5ndsU6+9EoUodPFu2TrVlx1qXWF6SsTMv2TdC2RwubbIzabrvBLmCdaQ0Gg02QAsDys8FgkDsFALBgwQIkJCRY/klPT/frOImISNucdYv1hhQgXKs2KTZ588d9XY1HqdvulYtVOH3kot/uHyhuBSqzZs2CIAhO/ykqKvLXWAEAeXl5MBqNln9OnTrl1/sREZG2eVP8qoZSi35RdOybonRffwcRP+4qxeo/5eOfS/Zj9Z/y8eOuUr/cJxDcmvp5+umnMX78eKfH3HzzzaqulZKSgj179ti8dubMGct7SiIjIxEZGanqHkREFPr8vZzZnSZvcvf19bSUPU8b5AULtwKV5ORkJCcn++TG2dnZePHFF3H27Fk0b94cAPDll18iPj4eHTt29Mk9iIgo9NXHXj9qmrzJ3bc+gggtNMjzJ78V05aUlODXX39FSUkJamtrUVhYCABo06YNGjdujLvvvhsdO3bE//zP/2Dx4sUwGAx47rnn8MQTTzBjQkREbqmP5cyumrzJ3bc+gohAN8jzN78FKnPmzMGqVassP0ureL7++mvceeedCAsLw7///W88/vjjyM7ORmxsLMaNG4fnn3/eX0MiIqIQpnavH18vJ3Z23/oIIupz9+hA8HsfFX9jHxUiIlLL3/Uiive0CyL8cU+p50qwLFfWfB8VIiKi+hSootP66rLr692jtYKBChERNQiBLDoN1SCiPgSs4RsREVF9UuqHEipFp6GKgQoRETUIgd6VmTzDqR8iImowArkrM3mGgQoRETUorBcJLpz6ISIiIs1ioEJERESaxUCFiIiINIuBChEREWkWAxUiIiLSLAYqREREpFkMVIiIiEizGKgQERGRZjFQISIiIs1ioEJERESaxUCFiIiINCvo9/oRRREAUF5eHuCREBERkVrSc1t6jisJ+kDl8uXLAID09PQAj4SIiIjcdfnyZSQkJCi+L4iuQhmNM5lMKC0tRVxcHARBCPRwSEF5eTnS09Nx6tQpxMfHB3o4pAJ/z4ILf7+CC3+/zJmUy5cvIy0tDTqdciVK0GdUdDodWrVqFehhkErx8fEN9g9lsOLvWXDh71dwaei/X84yKRIW0xIREZFmMVAhIiIizWKgQvUiMjISc+fORWRkZKCHQirx9yy48PcruPD3S72gL6YlIiKi0MWMChEREWkWAxUiIiLSLAYqREREpFkMVIiIiEizGKhQQLRu3RqCINj8s3DhwkAPi+osX74crVu3RlRUFHr16oU9e/YEekgkY968eQ5/jjp06BDoYVGdHTt24L777kNaWhoEQcBnn31m874oipgzZw5SU1MRHR2NAQMG4OjRo4EZrIYxUKGAef7551FWVmb558knnwz0kAjAunXrMH36dMydOxffffcdunTpgoEDB+Ls2bOBHhrJuPXWW23+HO3cuTPQQ6I6FRUV6NKlC5YvXy77/uLFi/Haa6/hrbfewu7duxEbG4uBAweiqqqqnkeqbUHfQp+CV1xcHFJSUgI9DLLz6quv4pFHHsGECRMAAG+99Ra++OILvPvuu5g1a1aAR0f2GjVqxD9HGjVo0CAMGjRI9j1RFLF06VI899xzuP/++wEAq1evRosWLfDZZ5/hoYceqs+hahozKhQwCxcuRNOmTZGVlYWXXnoJ169fD/SQGryamhrs27cPAwYMsLym0+kwYMAAFBQUBHBkpOTo0aNIS0vDzTffjDFjxqCkpCTQQyIViouLYTAYbP6sJSQkoFevXvyzZocZFQqIp556Ct26dUNSUhLy8/ORl5eHsrIyvPrqq4EeWoN2/vx51NbWokWLFjavt2jRAkVFRQEaFSnp1asX3nvvPbRv3x5lZWWYP38+7rjjDvzwww+Ii4sL9PDICYPBAACyf9ak98iMgQr5zKxZs7Bo0SKnxxw+fBgdOnTA9OnTLa/ddtttiIiIwOTJk7FgwQK2lCZSyXpa4bbbbkOvXr1w0003Yf369Zg4cWIAR0bkOwxUyGeefvppjB8/3ukxN998s+zrvXr1wvXr13HixAm0b9/eD6MjNZo1a4awsDCcOXPG5vUzZ86wDiIIJCYmol27djh27Figh0IuSH+ezpw5g9TUVMvrZ86cQdeuXQM0Km1ioEI+k5ycjOTkZI/OLSwshE6nQ/PmzX08KnJHREQEunfvjq1bt2Lo0KEAAJPJhK1bt+IPf/hDYAdHLl25cgXHjx/H//zP/wR6KOSCXq9HSkoKtm7daglMysvLsXv3bjz++OOBHZzGMFCheldQUIDdu3ejb9++iIuLQ0FBAaZNm4bf//73aNKkSaCH1+BNnz4d48aNw29+8xv07NkTS5cuRUVFhWUVEGnHM888g/vuuw833XQTSktLMXfuXISFhWH06NGBHhrBHDhaZ7eKi4tRWFiIpKQkZGRkYOrUqXjhhRfQtm1b6PV6zJ49G2lpaZb/SaA6IlE927dvn9irVy8xISFBjIqKEm+55RbxL3/5i1hVVRXooVGdv/71r2JGRoYYEREh9uzZU/zmm28CPSSSMWrUKDE1NVWMiIgQW7ZsKY4aNUo8duxYoIdFdb7++msRgMM/48aNE0VRFE0mkzh79myxRYsWYmRkpNi/f3/xyJEjgR20BgmiKIoBjZSIiIiIFLCPChEREWkWAxUiIiLSLAYqREREpFkMVIiIiEizGKgQERGRZjFQISIiIs1ioEJERESaxUCFiIiINIuBChEREWkWAxUiIiLSLAYqREREpFkMVIiIiEiz/j86uAW63+AjtQAAAABJRU5ErkJggg==\n"},"metadata":{}}],"source":["# Train the model\n","cls = PyKMeansClusterer(k=5)\n","cls.fit(X1)\n","\n","# Predict cluster assignments for the data\n","y_pred = cls.predict(X1)\n","\n","# Show the predicted clusters\n","show(X1, y_pred)"]},{"cell_type":"code","execution_count":null,"metadata":{"scrolled":true,"id":"thNhIZt87UGc","colab":{"base_uri":"https://localhost:8080/","height":430},"executionInfo":{"status":"ok","timestamp":1776172027484,"user_tz":-120,"elapsed":417,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"5719f789-21b7-4d7b-8ac7-2ee4229ff0a4"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["# Optional: compare with the true labels\n","show(X1, t1)"]},{"cell_type":"markdown","source":["## How do the clustering results look?\n","## If the results do not look good:\n","* Does increasing the number of iterations improve the result?\n","* Does changing the initialization method make a difference?"],"metadata":{"id":"BYa2VA6HFMNa"}},{"cell_type":"code","source":["# Increase max_iter\n","cls = PyKMeansClusterer(k=5, max_iter=100)\n","cls.fit(X1)\n","\n","# Predict cluster assignments for the data\n","y_pred = cls.predict(X1)\n","\n","# Show the predicted clusters\n","show(X1, y_pred)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":430},"id":"53SaW8-TEsrC","executionInfo":{"status":"ok","timestamp":1776172037315,"user_tz":-120,"elapsed":347,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"fd2c8140-15a8-4097-85f8-e7b451ba9281"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["Now we try Random initialization, which choose k random data points as the initial centroids. Simple and much better than always taking the first k points"],"metadata":{"id":"vLBBsLbZG_38"}},{"cell_type":"code","source":["import random\n","\n","class PyKMeansClusterer(PyClusterer):\n","    \"\"\"k-means clustering using pure python representations\"\"\"\n","\n","    def __init__(self, k=3, dist=distance_L2, max_iter=10, random_state=None):\n","        self.k = k\n","        self.dist = dist\n","        self.max_iter = max_iter\n","        self.random_state = random_state\n","\n","    def fit(self, X_train):\n","        X_train = [[x for x in xx] for xx in X_train]\n","        self.X_train = X_train\n","\n","        rng = random.Random(self.random_state)\n","\n","        # Choose k random data points as initial centroids\n","        self.centroids = [list(p) for p in rng.sample(X_train, self.k)]\n","\n","        for i in range(self.max_iter):\n","            clusters = [[] for _ in range(self.k)]\n","\n","            for x in X_train:\n","                c = self.predict_one(x)\n","                clusters[c].append(x)\n","\n","            new_centroids = []\n","            for j in range(self.k):\n","                if len(clusters[j]) > 0:\n","                    new_centroids.append(mean_point(clusters[j]))\n","                else:\n","                    # Keep old centroid if a cluster becomes empty\n","                    new_centroids.append(self.centroids[j])\n","\n","            if new_centroids == self.centroids:\n","                break\n","\n","            self.centroids = new_centroids\n","\n","    def predict_one(self, a):\n","        distances = [self.dist(a, c) for c in self.centroids]\n","        cluster = distances.index(min(distances))\n","        return cluster\n","\n","    def predict(self, X):\n","        return [self.predict_one(z) for z in X]"],"metadata":{"id":"OUI4V5SVEy5m"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["# Train the model\n","cls = PyKMeansClusterer(k=5)\n","cls.fit(X1)\n","\n","# Predict cluster assignments for the data\n","y_pred = cls.predict(X1)\n","\n","# Show the predicted clusters\n","show(X1, y_pred)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":430},"id":"GCiHB986HVcv","executionInfo":{"status":"ok","timestamp":1776172296348,"user_tz":-120,"elapsed":205,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"b5d51358-5c82-46ab-c882-a105919f0e2a"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"iVBORw0KGgoAAAANSUhEUgAAAioAAAGdCAYAAAA8F1jjAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAaXtJREFUeJzt3Xl4VOXZP/DvmZDdLAQCSSCBMSwBQQgUMCFSEWykCmUTRFrAXxAsVl+hsqSvbFZksSpYUatWBFoEVPTVYkALUoREQCBIkSBgIEASNmGCISSQOb8/hjPMcs7MmS1zZvL9XBeXZubMnGcWOHfu537uRxBFUQQRERGRBun8PQAiIiIiJQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItKsJv4egKeMRiPKy8sRExMDQRD8PRwiIiJSQRRFXLlyBSkpKdDplPMmAR+olJeXIzU11d/DICIiIjecOnUKrVu3Vrw/4AOVmJgYAKYXGhsb6+fREBERkRpVVVVITU01X8eVBHygIk33xMbGMlAhIiIKMM7KNlhMS0RERJrFQIWIiIg0i4EKERERaVbA16gQEREpEUURN27cQH19vb+H0uiEhISgSZMmHrcOYaBCRERBqa6uDhUVFbh69aq/h9JoRUVFITk5GWFhYW4/BwMVIiIKOkajEaWlpQgJCUFKSgrCwsLYFLQBiaKIuro6nD9/HqWlpWjfvr3Dpm6OMFAhIqKgU1dXB6PRiNTUVERFRfl7OI1SZGQkQkNDcfLkSdTV1SEiIsKt52ExLRERBS13f4sn7/DG+89PkIiIiDSLgQoRERFpFgMVImpwFYYaFB6/gApDjb+HQhRQTpw4AUEQUFxc7O+hNBgGKkTUoNbtKUPfRVvxyNu70HfRVqzbU+bvIRGRSteuXcMTTzyBZs2a4bbbbsOIESNw9uxZn56TgQoRNZgKQw3yNxyEUTT9bBSBP234LzMrpHnMAppMnToVn332GT744AP85z//QXl5OYYPH+7TczJQIQpSWvyHtfRCtTlIkdSLIk5cYEMu0q6GzgIajUYsWbIE7dq1Q3h4ONLS0rBgwQLZY+vr65GXlwe9Xo/IyEh07NgRy5Ytszpm27Zt6N27N6KjoxEfH4++ffvi5MmTAIADBw6gf//+iImJQWxsLHr27Ilvv/1W9lwGgwF///vf8fLLL+Pee+9Fz549sWLFChQWFuKbb77x7ptggX1UiILQuj1l5syFTgAWDu+K0b3S/D0s6JtHQyfAKlgJEQS0bc4+F6RNSlnAfh0SkRwX6ZNz5ufn4+2338Yrr7yCnJwcVFRUoKSkRPZYo9GI1q1b44MPPkCzZs1QWFiISZMmITk5GaNGjcKNGzcwdOhQPPbYY3j//fdRV1eH3bt3m5vfjR07FpmZmXjjjTcQEhKC4uJihIaGyp5r7969uH79OgYOHGi+LSMjA2lpaSgqKsJdd93l/TcDDFSIgo4//mFVKzkuEguHd8WfNvwX9aKIEEHAC8O7+H1cREocZQF98b29cuUKli1bhtdeew3jx48HAKSnpyMnJ0f2+NDQUMyfP9/8s16vR1FREdavX49Ro0ahqqoKBoMBDz74INLT0wEAnTp1Mh9fVlaG6dOnIyMjAwDQvn17xbFVVlYiLCwM8fHxVre3bNkSlZWVbr1eNRioEAUZtf+wVhhqUHqhGvrm0Q0aKIzulYZ+HRJx4sJVtG0exSCFNK2hs4CHDx9GbW0tBgwYoPoxy5cvx7vvvouysjLU1NSgrq4O3bt3BwAkJCRgwoQJyM3NxX333YeBAwdi1KhRSE5OBgBMmzYNEydOxOrVqzFw4EA89NBD5oBGK1ijQhRkpH9YLdn+w+rvlTfJcZHISm/GIIU0T8oChtycKvF1FjAy0rXnXbt2LZ555hnk5eXhiy++QHFxMR599FHU1dWZj1mxYgWKioqQnZ2NdevWoUOHDuaaknnz5uHQoUN44IEHsHXrVnTu3Bkff/yx7LmSkpJQV1eHy5cvW91+9uxZJCUlufZCXcBAhSjIOPuHlStviFwzulcadszqj/cfuws7ZvX3ab1X+/btERkZiS1btqg6fufOncjOzsaUKVOQmZmJdu3a4fjx43bHZWZmIj8/H4WFhejSpQvWrFljvq9Dhw6YOnUqvvjiCwwfPhwrVqyQPVfPnj0RGhpqNbYjR46grKwMWVlZLr5S9Tj1QxSEHE2vNPScO1EwSI6LbJC/HxEREZg5cyZmzJiBsLAw9O3bF+fPn8ehQ4eQl5dnd3z79u2xatUqbN68GXq9HqtXr8aePXug1+sBAKWlpXjrrbcwZMgQpKSk4MiRIzh69CjGjRuHmpoaTJ8+HSNHjoRer8fp06exZ88ejBgxQnZscXFxyMvLw7Rp05CQkIDY2Fg8+eSTyMrK8lkhLcBAhShoKf3DypU3RNo2e/ZsNGnSBHPmzEF5eTmSk5Px+OOPyx47efJk7N+/H6NHj4YgCBgzZgymTJmCgoICAEBUVBRKSkqwcuVKXLx4EcnJyXjiiScwefJk3LhxAxcvXsS4ceNw9uxZNG/eHMOHD7cqzrX1yiuvQKfTYcSIEaitrUVubi5ef/11n7wPEkEURdH5YdpVVVWFuLg4GAwGxMbG+ns4RAFh3Z4yu5U3Wli+TOQt165dQ2lpKfR6PSIiIvw9nEbL0eeg9vrNjApRI8SVN0QUKBioEDVSDTXnTkTkCa76IWrktNhqn4hIwowKUQDyVrM2X7Xa91czOSIKPgxUiAKMbXAxc1AGuraKczko8FWrfa3uM0REgYmBClEAkQsuFn5u2qzMWVBgm+XwRT8VZ8EPMy1E5CoGKuQxXnwajlxwIXGUEZHLcvTrkOj1fiqOgp/tP5xnpoWIXMZiWvKIv/eMaWzk9vGxJAUFlpSyHAC8voeJ0j5DUWE6tu0nIrcwUCG3cc+Yhme7j48tuYzItyd+UsxyeHsPE6V9hqrr6hXH4A9c6USB6sSJExAEAcXFxf4eSoPh1A+5jXvGOOeLabHRvdJw+ep1LCoogeXbL5cRkaZ8bFkGNJb9VLwxXrlmchWGGs207WexL5H73nrrLaxZswb79u3DlStXcOnSJcTHx/v0nAxUyG3cM8YxXy79XbzJOkjRAdgwJQvdUptaHWeZ8bI8Vm6KR2m87gQvts3kpEyLbdv+hg5ofbXSiaixuHr1Ku6//37cf//9yM/Pb5BzcuqH3KaU5uc/+L6dFpPLZBkBXK0zOj0OAP76SKZdwKQ03r9tP+61GiRvTzO5w1EWkMghwxmgdLvpvz5mNBqxZMkStGvXDuHh4UhLS8OCBQtkj62vr0deXh70ej0iIyPRsWNHLFu2zOqYbdu2oXfv3oiOjkZ8fDz69u2LkydPAgAOHDiA/v37IyYmBrGxsejZsye+/fZbxbE9/fTTmDVrlk93S7bFjAp5hHvGyPPltJjaTJbScT3aNIUtpfEuKiiB6MXsg7enmVzFLCC5Zd8q4LP/AUQjIOiAwcuAHuN8drr8/Hy8/fbbeOWVV5CTk4OKigqUlJTIHms0GtG6dWt88MEHaNasGQoLCzFp0iQkJydj1KhRuHHjBoYOHYrHHnsM77//Purq6rB7924IN3/BHDt2LDIzM/HGG28gJCQExcXFCA0N9dlrcwcDFfIY94yx58sLopppFCkImHl/BpZsOuJ0ukXfPBoCANsEjO3e6t4KtvxVJ6KVKSgKIIYzt4IUwPTfz54G0gcAca28frorV65g2bJleO211zB+/HgAQHp6OnJycmSPDw0Nxfz5880/6/V6FBUVYf369Rg1ahSqqqpgMBjw4IMPIj09HQDQqVMn8/FlZWWYPn06MjIyAADt27f3+mvyFAMVYh8UH/D1BdEykxUVpkN1XT0qDDVIjovE37YfN2dCpM61d7aKdyvj5U6w5ez75O86EWYBySU/Hb8VpEjEeuCnH30SqBw+fBi1tbUYMGCA6scsX74c7777LsrKylBTU4O6ujp0794dAJCQkIAJEyYgNzcX9913HwYOHIhRo0YhOTkZADBt2jRMnDgRq1evxsCBA/HQQw+ZAxqtYKDSyHEFhO/4+oKYHBdp10Qt944kFPy30nyMUQSWFBzBjln9FYOG0gvVuPhzrV02BQAm5tyOv+8oVR1sqfk+aWG1GLOApFpCumm6xzJYEUKAhNt9crrISNe+l2vXrsUzzzyDl156CVlZWYiJicGLL76IXbt2mY9ZsWIFnnrqKWzatAnr1q3Ds88+iy+//BJ33XUX5s2bh0ceeQQbN25EQUEB5s6di7Vr12LYsGHefmluY6ASpNRkSfz9m63ceIIts+PLC6Lc52cZpEiUggDboMJ26kcH4NGctng0p62qYEtN+/xvT/yEy1ev252LdSKkWXGtTDUpnz1tyqQIIcDgpT7JpgCmqZfIyEhs2bIFEydOdHr8zp07kZ2djSlTpphvO378uN1xmZmZyMzMRH5+PrKysrBmzRpzQWyHDh3QoUMHTJ06FWPGjMGKFSsYqJBvqc2SaOE3WwkzO65z1E7fkk6AXRAgF1QINtGDCGD7D+cxulea0wCl9EI1fqquc9g+f9ZHB62CE+l0rBMhzesxzlST8tOPpkyKj4IUAIiIiMDMmTMxY8YMhIWFoW/fvjh//jwOHTqEvLw8u+Pbt2+PVatWYfPmzdDr9Vi9ejX27NkDvV4PACgtLcVbb72FIUOGICUlBUeOHMHRo0cxbtw41NTUYPr06Rg5ciT0ej1Onz6NPXv2YMSIEYrjq6ysRGVlJY4dOwYAOHjwIGJiYpCWloaEhASfvCcMVIKM3AUo/6ODiA5vgp5tmlpdDLSyAkJrmR1pTFrM7liOS+7zkzNzUIbda5ALckTROqsiwvnnYBlgCrDPykjt822DFMB08PO/uQNdW8VZ1dgQaVJcK58GKJZmz56NJk2aYM6cOSgvL0dycjIef/xx2WMnT56M/fv3Y/To0RAEAWPGjMGUKVNQUFAAAIiKikJJSQlWrlyJixcvIjk5GU888QQmT56MGzdu4OLFixg3bhzOnj2L5s2bY/jw4VbFubbefPNNq/v79esHwDS9NGHCBO+9CRYEUbSt6w8sVVVViIuLg8FgQGxsrL+H43eFxy/gkbd3yd4nl6lYt6fMruDTl5kMuQBAaczvP3YXstKb+WwsSrSa3ZEbFwCrz29oZgo+2V+OelGEDqYgZfIv7QvjDpy6hN8sL1R1XqXPocJQg76LtloFPAJMmRmjeCtTkpoQpfidlB4jQlvvNQW+a9euobS0FHq9HhEREf4eTqPl6HNQe/32aUZl+/btePHFF7F3715UVFTg448/xtChQ833i6KIuXPn4u2338bly5fRt29fvPHGG5pcHhUoHP2WLZepaMgVEEoBgFYyO4A2szuOxrVjVn/smNXf6vN7Jrej08+zuq5e9nZXakdkszIA/vpwJprdFm7VPl9u6bPlYyxfk+V77Y3MllazY0Skjk8701ZXV6Nbt25Yvny57P1LlizBq6++ijfffBO7du1CdHQ0cnNzce3aNV8OK6hJy2KVPli5LpzJcZHISm/m03/EHXVq1VKHW612LnVWT2T5+an5PJV2OZ41KEP153DwjMHuNh2Anm2b2o1n0YiucLDps91rAryzMzd39yYKfD7NqAwaNAiDBg2SvU8URSxduhTPPvssfvOb3wAAVq1ahZYtW+KTTz7Bww8/7MuhBT+FX2H9lalwdqHVSm8LrWV39p68BFEUkZYQJZspW1V0wjwt40rmQKnPy+heaRjSPUW2P4vt2BYX2HfKNOJWAa4l6fPdcvgsnv3kkOK4pPfaG5ktrWbHiMg1fiumLS0tRWVlJQYOHGi+LS4uDn369EFRUZFioFJbW4va2lrzz1VVVT4fqxYpXZSUNqIDPMtUeJo+VxMAaKG3hVY6l67bU2ZVgCoAuKdjIr46ct7quIL/VuLAqUsoqbxyq6hVAGYNysDkfo6bNjlqGmfbn8W2dsTRiiOl4u3kuEj89q62CA3Rmd9f4eaLE0VTNiYvp63i87u6Ik1Lq9qIyH1+C1QqK039Hlq2bGl1e8uWLc33yVm4cKHDimRv0urctqNiT6ULyOwHOuHXdya79TrcLS61ff+0EACo4e/sjhRsWn6MImAXpEi2HD6H1746Zv7cRRFY+HkJIEK2kNaSXFAy8/4MLN5UIpuJAEzfseiwEOVaKAB/WLPf/F3p1yHR6ntg+/4CwIodJ/DOjh/x1teleGdHKWYOyvA4s6Wl7BgRuS/glifn5+dj2rRp5p+rqqqQmprq9fNodeWHs3S2UjHtDaMouxeMsyDM3fS50vunhekdNfyZ3VHbH0WSGBsue/zighIM6Z7i8ue7uKAENg3DUS+K5mBC+kyHZbbCx/vPKI7VKAKzNhwERPtVPbabE0rPKz1uScER1fsUKQmk4JiIlPktUElKSgIAnD171rzngPSztEeBnPDwcISHh/t0bFqe23aWzk6Oi8TMQRmm36gtLNl0xHzRciUIcyd97uz98/d7qHX65tEQBPsNAeWM6NEKAzu1xJz/O2R3vBFwOs0h9/kaAbvz6wC7YGLD/jNOx2h5v9LfI6Xv2J2t4+1WNLkqkIJjIpLn01U/juj1eiQlJWHLli3m26qqqrBr1y5kZWX5a1gAGm7lR4WhBoXHL6DCUCP7sxyl1RqW6eyureLsHieN39HqG3fPZzt2ra6cCRTJcZGYmKNXvP/5oXdg9gOd8H9PZOOlUd2RHBeJWYMy7I5TM80h9/kCwKAuSVarfyberZdtEGdJ6qHiiNz3wNF3zBsr0hpiVRsR+Y5PMyo///yzuc0uYCqgLS4uRkJCAtLS0vD000/j+eefR/v27aHX6zF79mykpKRY9Vrxh4aY27bNalim0R1lOdSksx2N39UMiZrz2XYnHdM7lXu5eOj/5ejxzteldgu3dIC5k2uL2FvNkyb3Swcspm0sPyfbaT7bn2fen4GFNit4Nv/3LDZMycLVOqP5c3tnR6nDKSkRwCSLTQx1N7Myzr4HnKIhIkd8Gqh8++236N+/v/lnqbZk/PjxeO+99zBjxgxUV1dj0qRJuHz5MnJycrBp0ya/dxH09T+cclmNj/adMd/vbKrJWTrb2fhdDcIcnc/2tYgA1uw+ZdVOXTo/YOpCq7XiZK2RAolZv87AooISc+ZCAHB/1yQMe71QNqCd/Mt089Ji6fN8YeP3ePtmwKMUEHdtLZ+Bu1pnNC99XrenzCqDIrf6XSfYb2K4/Yfzqv4ecYqGSJ0TJ05Ar9dj//79Dsskgglb6DtQYajxyT+cjtrcW/K0hbzS+P+2/bjpN2+LNufuFgo7ei0CgCfvbYcBnVpYLZ/VUnGyGpYZCACy/++oXseVlWO2mbaZ92fg5MVqrNl9Svb4EEHAjln9He6M7EiIIGDDlCwMXV5ovWGgABTOutecgbFtlQ/YBysCgEUj7D9XX/09InIkWFvo+zNQ+emnnzB37lx88cUXKCsrQ2JiIoYOHYo///nPiIuz/4UHCIAW+oHOV4WfajaT88ZUidz41+0pMwcpAoAZ93f0KGBw9FpEAK9uPYbXvjpmNQWgpeJkZ2yntQDT67D8f6XAy9WVY7IrcDaVOCxYlZu2c9RLR+7xpy/V2GVHLM+ptArJ7jEw9VCxXMYsBXSiYgN9IgoU5eXlKC8vx1/+8hd07twZJ0+exOOPP47y8nJ8+OGHPjuv34ppGzO5lvEjerTyeQt5uWmaJZuOOCzedUaqcXDEKNpf1AKhuFbu/ZJeh+X/yxUku1q0DCiswJF57yzpBNgFtK4sb9YJwH9+kO/P8u/vzwJQLriVYwQw88PvzG3rsxduRdZCdS3s1RSTE/lLZXUldlfsRmW1cp8vbzEajViyZAnatWuH8PBwpKWlYcGCBbLH1tfXIy8vD3q9HpGRkejYsSOWLVtmdcy2bdvQu3dvREdHIz4+Hn379sXJkycBAAcOHED//v0RExOD2NhY9OzZE99++63subp06YKPPvoIgwcPRnp6Ou69914sWLAAn332GW7cuOHdN8ECMyp+Ijcnr2YzOXdI0w/Hzl1xuBrH3eZ2cjUOzvi6uNYbzfpcueDbZjbcWdYtl52SK0i1NDHndrvnU8py6QAM69HKvLuytMvx+m9Pyz73nP87hLAmOozulYaFw7tadcp1ZPvRC+b/tzzeUSZNq32LiABgw9ENmF80H0bRCJ2gw9ysuRjefrjPzpefn4+3334br7zyCnJyclBRUYGSEvstKwBTUNO6dWt88MEHaNasGQoLCzFp0iQkJydj1KhRuHHjBoYOHYrHHnsM77//Purq6rB7924IN38xHjt2LDIzM/HGG28gJCQExcXFCA0NVT1WadqmSRPfhRMMVPzIdmrG21NNFYYavLujFH93sFpDAPDdmcsY+843bl8kosNCnB4jCIAgwm5Fii9466KnZopOYht4ubNyTMpO2a7cAUxTKrZN2HQwFa/KPY9lMbVOMAU0j+a0NQfE+05ewh/W7Hf4mkTcCiz6dUhU3dvFETVTVUbR9HozkmLQLbWpZyck8lBldaU5SAEAo2jE/KL5yE7JRlJ0ktfPd+XKFSxbtgyvvfYaxo8fDwBIT09HTk6O7PGhoaFW3dr1ej2Kioqwfv16jBo1ClVVVTAYDHjwwQeRnm7qVN2pUyfz8WVlZZg+fToyMkyZ8fbt26se64ULF/DnP/8ZkyZNcvl1uoKBSpCy3StGiQiYa1aAW7/1ZiTFoLquXlVGorqu3ul4hme28lnGyJI3m/XZXvCFm9WjImD1/3KBlzsrx9btKTO1rr/5/DMG3aof6tch0aozrLPnc7SKJjkuEk2jq1VlR6TAQoQoG7D9z4B2eHXLMdUVKGqnqowAhr5eiEXMrJCflVWVmYMUiVE04tSVUz4JVA4fPoza2loMGDBA9WOWL1+Od999F2VlZaipqUFdXZ250DYhIQETJkxAbm4u7rvvPgwcOBCjRo0yN1qdNm0aJk6ciNWrV2PgwIF46KGHzAGNI1VVVXjggQfQuXNnzJs3z52XqhoDlSAkt1eMI3JTFNIqEJ0A5OXo8f9y9C5NWdjasO8Mnsnt6NEqJjW8vRGd3L40cv/v6ZJbu3oY0dRGfki3FHOm7U8PdLJa+mvZgl5umstRhu7gGYOq168DEBWmQ4vYCNkM0cO905ASH2kVkA3NTFFsrT9zUIbqqSoxgIquKXilxaZBJ+isghWdoENqjPe3bgGAyEjXvutr167FM888g5deeglZWVmIiYnBiy++iF27bq3GXLFiBZ566ils2rQJ69atw7PPPosvv/wSd911F+bNm4dHHnkEGzduREFBAebOnYu1a9di2LBhiue8cuUK7r//fsTExODjjz92aarIHSymDUIuFVMCsoWSloWib39diuyFyoWQtsXBct1JRQB7T1xSNygPqO2k6wrLzqZK/6/msY6o7eZr+3zr9pSZC1cdFataFqpWGGqwuEB+vtuWEcCw1wux/YfzdgXgUkZndK807JjVH+8/dhd2zOqPl0Z1x85Z92JSP735HxgdgHyFHZ2l74/cP0aBUHRNwS0pOglzs+ZCJ5i+oVKNii+yKYBp6iUyMtKqa7sjO3fuRHZ2NqZMmYLMzEy0a9cOx48ftzsuMzMT+fn5KCwsRJcuXbBmzRrzfR06dMDUqVPxxRdfYPjw4VixYoXi+aqqqvCrX/0KYWFh+PTTTxtk6TczKkFIbW2FZQ2EZT2D0lLU/A3ydQMVhhqkJkSZO5keO38Fsz85ZPcchT9ewIPdUtx9WaoEapdTd2pa1E5z2dbsTMyxb4fviPS8O2b1V9x7R67e6k+/7oxH++pVZZRG90pDRlIMhr5eaFUHw47GpAXD2w9Hdko2Tl05hdSYVJ8FKQAQERGBmTNnYsaMGQgLC0Pfvn1x/vx5HDp0CHl5eXbHt2/fHqtWrcLmzZuh1+uxevVq7NmzB3q9aRuO0tJSvPXWWxgyZAhSUlJw5MgRHD16FOPGjUNNTQ2mT5+OkSNHQq/X4/Tp09izZw9GjBghOzYpSLl69Sr+8Y9/oKqqClVVVQCAxMREhIQ4r1d0BwOVIGRblKkDMLGfHqE6HV7fdtzcB8S2BuLEhauICtOZO5/aMorA0OWFVk295ApXB3ZqiTmfHLKbelq76xSevLe920GD2pU8gdjl1J0AS800l1ww887XpaqLhG2f19U9c1wpEO+W2hSLAjDIpMYhKTrJpwGKpdmzZ6NJkyaYM2cOysvLkZycjMcff1z22MmTJ2P//v0YPXo0BEHAmDFjMGXKFBQUFAAAoqKiUFJSgpUrV+LixYtITk7GE088gcmTJ+PGjRu4ePEixo0bh7Nnz6J58+YYPny4VXGupX379pmnlNq1a2d1X2lpKdq2beu9N8ECO9MGIasmZQIwa1AGhnRLQfbCrXbBw/89kW2XIfnb9uN2uy9bkrqhArDrWCrd9+6OUrz9dandY93ttttYlq+60sVVrmOsbadapc7Bk+622JMH1n1h5EgdbNUWWHuCnWzJG4K1M22gYWdasqNUlBkVFiJ7IbLNkADyuy9bcrQSRLrvwTuTZQOVqDDXy6K8uZJH61xdop6XozcvP3dlg0pne/IMzUwx91uRflbaY8jbfNURmogCEwOVIKM0HXC+6prs8Za9MqSLg7MVIZZLTB3t0iznap1tNxDnvL2SJxjYtvaf1E+PR/var8xyNqUk/ddRA0Lb6cBgDhSJSHu46ifIKK16GdCpJWQW4wCwXlmhZkWIUQS2/3BedisA6SLozdU3vljJoxXutI2Xa+3/969PKB5vuypHKRNiu6JI+rm6rl7ViiQiIl9goBJklIKHbqlNsWhEV9lgxfKir3Zp86yPDqLCUKN4EXQUxHjrNWnpt3l3Ag61S4ttKWWYNn5XoXh+tcuk5QRzoEhE2sepnyCktOqlX4dE/PWRTKwuOoFdpbd6mgzNTDEfI1fTINc6XeqL8mC3SMWaAm+uvtHySh53Cn09qbtRWn7+/MbDeOHzw16vHwnUJd9EFBwYqAQYtUt0bYMHy4uprU/2l+OZ3I7m420LNEf3TsWaXfa/7V+uqUPh8QvmsciNzZuFkVossnQ34PCk7sY2cLDkq/oRLQeKRBTcGKgEEHeX6NpeTG3ViyL2nriEA6etNzB8pHcqnhxg2qDq/V1lVquGBACzb/ZK0QnA/XckoeBQJUSZsXljJ2OtcjfgkN0pGfb74CiRAoeN31Xg+Y2HXT6/O7QYKBJR8GONSoBQ+s1dqSbBsmbCWd2JAODJ9/fj7a+td1les/sUPj1QjuS4SCwa0dVcpyD917LN/uf/rTRPD1mOzd06jEDhbv2GlBWxfKgIU5GyWslxkXjgzmTWjxBRUGOg4keuFGCq3QsGsC/SPHjaILufD2AKUhw1+1r0eYm5aHbnrHvx/mN34eFeqU43PKwXRew7ecml4MoRd4pVG4Inhb79OiRa7YskLRWXXqOj1yzdB0DV+bX6/hEROcOpHz9xdRonOkx+DwXbBmpymZclm45g5qAMLCk4Yi6GzO3SEgUWWRAlIoB9Jy/hgTtvpf3f333K6eszTWsoN4RzZQpB611p3a3fcBR8bv/hvOJrlns/lPbgUTreX++flOGLDgtpkC63RMHmxIkT0Ov12L9/P7p37+7v4TQIBip+4E4BZnVdvezttg3UlC5+d7aKN1/MpAZeajdPsDyu9EK102wKAMwclIFftE2QrcNQ6k5rWcsinSs6LCQgutK6U7+h1DU2Kkyn+JoB2N2Xv+EgPp6SLbs1gZa6+soVdPs7cCIi10yePBn//ve/UV5ejttuuw3Z2dlYvHgxMjIyfHZOTv34gSvTOBK1tRByx+kEU3CQHBeJts2jsPvET6o3pBMA9Gx7ay8guee3lX9zb6HSC9WYOSjDPC0BAEYAw14vtKtVsZyuyl64FdkLTf8/VGaDxGBqNpaXoze/n9K0jaMGa3LfHWmzSLn6H3d6rjjjjSZ1Ek+mA4mo4fXs2RMrVqzA4cOHsXnzZoiiiF/96leor5f/ZdobGKj4gTsFmGprIWyPA0wXg2GvF+KP64vRd9FWLNjouPOsRAdg0YiuVueQnl/pi/PamEzER4Wag47FBSV4/Je3W9Vi2F6c5DqtStczuaxPMBSLSoHZ21+XQhRNLfClhnmOvh9KgaJtfYtE6fjnNx52q7jZm03qJMEUeFLwul5ZiepvduF6ZaXPz2U0GrFkyRK0a9cO4eHhSEtLw4IFC2SPra+vR15eHvR6PSIjI9GxY0csW7bM6pht27ahd+/eiI6ORnx8PPr27YuTJ08CAA4cOID+/fsjJiYGsbGx6NmzJ7799lvFsU2aNAn9+vVD27Zt0aNHDzz//PM4deoUTpw44bXXb4uBih+4W4CpthX66F5p2DAly2pFiVEEPtp3RnUm5fmhd2Bn/r2y5xjdKw0fP5FtFXxIryM1IdJuquGNbcftAg7Li5OabrjSF9Wbzcb8VWDqrAW+o++HOVCUCT7kLvhygavE1WyGqyvPLDnKxAVD4EnB7fKHH+LYvQNQNmECjt07AJc//NCn58vPz8eiRYswe/ZsfP/991izZg1atmwpe6zRaETr1q3xwQcf4Pvvv8ecOXPwpz/9CevXrwcA3LhxA0OHDsUvf/lLfPfddygqKsKkSZMg3Pw3YezYsWjdujX27NmDvXv3YtasWQgNDVU1zurqaqxYsQJ6vR6pqaneefEyWKPiJ+4WYKqthaiuq1dVSzK8Rwo27Cu3uz09McbhebqlNsUimW6lctMWRth3t7W8OCl1WrU8dsOULFytM3qt2Zg/C0zV9F5x9P0Y3SsNzW8LQ97KvVbPoXTBH90rDZevXsdCmT2cXClu9kWTOna5Ja27XlmJijlzAePNekCjERVz5iI6JwehSUleP9+VK1ewbNkyvPbaaxg/fjwAID09HTk5ObLHh4aGYv78+eaf9Xo9ioqKsH79eowaNQpVVVUwGAx48MEHkZ6eDgDo1KmT+fiysjJMnz7dXGPSvn17p2N8/fXXMWPGDFRXV6Njx4748ssvERYW5vZrdoaBih/5soGWs4u/ZMO+cvMSZYna33DlLqYVhhrZAtEZgzparTqy3cHX8iIm/eItwnqvIm/xRYGpK03tlIpobd9zpe+HFGRZcnTBrzDUYPEm+ek+V7IZasetxPL7EhWm82rgSeQrdSdO3gpSJEYj6k6W+SRQOXz4MGprazFgwADVj1m+fDneffddlJWVoaamBnV1deYVQQkJCZgwYQJyc3Nx3333YeDAgRg1ahSSk5MBANOmTcPEiROxevVqDBw4EA899JA5oFEyduxY3HfffaioqMBf/vIXjBo1Cjt37kRERITbr9sRTv0EKbnpgxE9WjnspwKYvhC2FzxHUyRyO+7KTVtM7pfucNpKmtaadLepnkW8OaYZ93f0eqbDnWJmR1yt2/Ck94pcUaoOwIYpWYrvk9LUmu1n7WwqzBubQ0rfl26pTd3eJJGoIYW1bQPobC6VOh3C2vgmAxsZ6drfibVr1+KZZ55BXl4evvjiCxQXF+PRRx9FXV2d+ZgVK1agqKgI2dnZWLduHTp06IBvvvkGADBv3jwcOnQIDzzwALZu3YrOnTvj448/dnjOuLg4tG/fHv369cOHH36IkpISp4/xBDMqQUwu43FPx0Q8+X6x1XFSUADc+h8pQ3DwjAGLC0pcmiJRmrZQk0F6Z8ePVrUbSzYdwZDuKV69oHmaGbDkbnbGm71XjLBfpm5Jtl2/AHw8JducqVI7FcY9f6ixCU1KQvJz829N/+h0SH5uvk+yKYBp6iUyMhJbtmzBxIkTnR6/c+dOZGdnY8qUKebbjh8/bndcZmYmMjMzkZ+fj6ysLKxZswZ33XUXAKBDhw7o0KEDpk6dijFjxmDFihUYNmyYqvGKoghRFFFbW6vyFbqOgUqQsw0O5HqbANbt8GdtOAiI9t1qXZkicWday5MaCFd4czdgT+s2vNV7Rc2KMdvXKwUprgZb/tzzJ5j3jSLtih85EtE5Oag7WYawNmk+C1IAICIiAjNnzsSMGTMQFhaGvn374vz58zh06BDy8vLsjm/fvj1WrVqFzZs3Q6/XY/Xq1dizZw/0ej0AoLS0FG+99RaGDBmClJQUHDlyBEePHsW4ceNQU1OD6dOnY+TIkdDr9Th9+jT27NmDESNGyI7txx9/xLp16/CrX/0KiYmJOH36NBYtWoTIyEj8+te/9tl7wkBF42w7eXra0dP2oqWD6TdyS44awflqwztAua7mu9OXZZuZecJbmQFvZmfUcDfIcvR6GypA9JSWOuxS4xOalOTTAMXS7Nmz0aRJE8yZMwfl5eVITk7G448/Lnvs5MmTsX//fowePRqCIGDMmDGYMmUKCgoKAABRUVEoKSnBypUrcfHiRSQnJ+OJJ57A5MmTcePGDVy8eBHjxo3D2bNn0bx5cwwfPtyqONdSREQEvv76ayxduhSXLl1Cy5Yt0a9fPxQWFqJFixY+ez8EUVTbn1SbqqqqEBcXB4PBgNjYWH8Px6vkOnlKPP2HusJQY9WlVu2y5RBBwI5Z/X12Afvb9uNY+Ll14aevz+mpdXvK7AIHX19Apc/PG9MvFYYa9F201S7Y0tJ7HghjJG25du0aSktLodfrfVbkSc45+hzUXr+ZUdEopU6eEk9Xqlim74dltsJH+844fUxDLCXt2irO7jYt/nZvyR91G96cfvHmVJivuJP14TQRUXBgoKJRapqgeeMCfuDUJWywCVIEARBE05RQiCDg8V/ejqbRYejVtqlXlwnLaeipFG/xZ92GN2i9SNbV7wWniYiCBwMVjVLTB0UnwOEF3PY3Stuf1+0pw6wNB+2KZkUReO2RTCREh+O7M5ddXvWjltxvvIHw232w0kKwpbS7sivfC7ni4PyPDiI6vAl6tmnq1mtkdobIfxioaFRyXKTTKRlRBLb/cB6je6XJBiGWv1EOy2yFj/efMf88c1AGFheUKO6l06ONKXMy9p1vfLLzrqPfeLX+2z35hrPdldV+L5SWcP9hzX63gm1mZ4j8i4GKRlUYavDxfpspGVgvGZY2ortcc90q6yEFIZYBhmXAYxRhdb/tOfJy2gLwfDWI0m+hapbDauG3e3KNJ1kHZ7srS98NNd8LR9lIV4NtX3QxJiLXsDOtRskFCXKzQPWiiEU2QYlSEGLJKMJq00IzAXjr61L0XbQVB88YXN7lWeKoW6unnWH9tZkgKVu3pwzZC02fd/ZC+e68jj43b+6u7GgjRlefz9tdjInIdQxUNEput1kdIHub7fSNYhBiIUQQMGtQht0/5qJFwLOk4Ahm3p/hcst0Z7vsyr02bwRA1HAsg44KQw1mfXSr1kkEMOujg1YBibPPzdu7K0tbMrw2JtPt75rSuAKhuJsomDBQ0Si5fVUWjuhqd9vMQRmy/5BaBiHSPj92++/8Mh0bpmQpBjX1oog7W8c73KNHjrPfQt3dM8ZZAETqeJqRsgw6shduxaKCw/YF2QD2nrhkPp+zz00pC+JJMXVyXCQe7Jbi0f5E3tjfiIg8wxoVDVMqHrS9LT4qVLbh2JDuKVbHPZPb0e65quvqZaeUgFu/ObpaL6JmKak7BbOB0kFVyzwtDLUNOkQA/1dcIXusFHOo/dz6dUjE0oe7wVBzHaIINI0KQ8+27q3SseRpcTaLu4n8i4GKxskFCba3qd0EUO65osNCZM+rE+x3UXZlzGqWkvoiACJl3igMVdPfBzAFKdLKMTWfm7MVP56S+665UvzL4m7SihMnTkCv12P//v3o3r27v4fTIDj1EySS4yKRld7M5X9Mq+vqZW9/9eFMpxcIR1MIUo2AK1NGzjAN7xlXCkOVPlt982jFqULpdp0ALBre1a43jtLn5mjFT/6Ggzhw6pLTcbnKavpq0Vb8bbv9brNEpEwURQwaNAiCIOCTTz7x6bmYUWnklH7b7dnWcQdaNVMIvvgtlGl496nNSDn6bJPjIjFrUAYWFtjvx7RhShau1hllPxdXN0WUGEVg6PJCLBrRFQBUT1s5ypYcOHXJ1OhQmr4SYdpfSgQm/zJdfiBEZGXp0qUQFFbWeRszKo2cO1kKfxe1ups9auzUfNZqPtvJv0xH/q9vFXFLz9MttanDzyU5LhJtm0eh9EK11fM5WvEDmOpg8j86qPo7J7fCSMrE/G37cQxdXijb6HBxQQkLs0nRz5eu4fSRS/j50jWfn8toNGLJkiVo164dwsPDkZaWhgULFsgeW19fj7y8POj1ekRGRqJjx45YtmyZ1THbtm1D7969ER0djfj4ePTt2xcnT54EABw4cAD9+/dHTEwMYmNj0bNnT3z77bcOx1dcXIyXXnoJ7777rndesBPMqJDLWQqlKYSN31XggTuTGUBomLPPWm3h6+R+6RjSLcWlzJZSpsa2pkmOEbBrJCQ3LrlAa9aGg4Ao34fI9hwszCY53+8sx7Z/mDp5CwJwz28z0Llvis/Ol5+fj7fffhuvvPIKcnJyUFFRgZKSEtljjUYjWrdujQ8++ADNmjVDYWEhJk2ahOTkZIwaNQo3btzA0KFD8dhjj+H9999HXV0ddu/ebc6GjB07FpmZmXjjjTcQEhKC4uJihIaGKo7t6tWreOSRR7B8+XIkJSX55PXbYqAS5NQWDLoyTaPU+fP5jYfxwueH2WJc4xx91q4ULLvynXFWyGsZQF2tu46JK/daBRY6AFAxLtlGiSqKf5Wej+jnS9fMQQpg+j5t+2cJ0jon4LamEV4/35UrV7Bs2TK89tprGD9+PAAgPT0dOTk5sseHhoZi/vz55p/1ej2Kioqwfv16jBo1ClVVVTAYDHjwwQeRnm6a2uzUqZP5+LKyMkyfPh0ZGRkAgPbt2zsc39SpU5GdnY3f/OY3Hr1OV3DqJ4j5qjmao86f7G0SmKSpEQA+KVhWU8grTel1TonDxLv1VlNLcj2E5MblbBpJCQuzScnlczV2wa5oBAznfPNv3OHDh1FbW4sBAwaofszy5cvRs2dPJCYm4rbbbsNbb72FsjLTv/cJCQmYMGECcnNzMXjwYCxbtgwVFbdaCkybNg0TJ07EwIEDsWjRIhw/rlxY/umnn2Lr1q1YunSp26/PHcyoBClf71Ei/Qa88bsKPL/xsNV97G0SWOSmZHbM6u/VgmV3CnkFAJP66fFoX71dD6GoMB2q6+pRYaixW4JvOY2kE0y/AcslVUIEATPu74g7W8ezMJsUxbeIhCBYZ+YEHRDXwjffl8hI15537dq1eOaZZ/DSSy8hKysLMTExePHFF7Fr1y7zMStWrMBTTz2FTZs2Yd26dXj22Wfx5Zdf4q677sK8efPwyCOPYOPGjSgoKMDcuXOxdu1aDBs2zO5cW7duxfHjxxEfH291+4gRI3D33Xdj27Zt7rxkpwRRVJsY1aaqqirExcXBYDAgNjbW38PRjMLjF/DI27vsbn//sbuQld7Ma+epMNSg76KtdhegHbP6Wy0/dXezOvItNZ+ft6zbUybbmNDVsahZcVZhqDEHWtt/OH8rcAHwcO9UZKc3d7uZHL/PgeHatWsoLS2FXq9HRIRnUzTf7yzHtn+WQDSagpR7xvquRuXatWtISEjAq6++iokTJ9rdb9tH5cknn8T333+PLVu2mI8ZOHAgLly4gOLiYtlzZGVloVevXnj11Vft7hszZgyqq6vx6aef2t1XWVmJCxcuWN3WtWtXLFu2DIMHD4Zer5d9PUqfg9rrNzMqQaqhmqM5a+7maSdU8q2G7ParVMgrXfgv/lzrdCxqM4WW9TPSeVfsOIF3dvyINbtPYe2eU259F/l9bpw6901BWucEGM7VIK5FpE9qUyQRERGYOXMmZsyYgbCwMPTt2xfnz5/HoUOHkJeXZ3d8+/btsWrVKmzevBl6vR6rV6/Gnj17zEFDaWkp3nrrLQwZMgQpKSk4cuQIjh49inHjxqGmpgbTp0/HyJEjodfrcfr0aezZswcjRoyQHVtSUpJsAW1aWppskOItDFSClNrusN7g6ALky+kn8pw3AlpPOrzaTvXI+e7MZXMW0Fmti6NxvLPjR5e/i5avDQC/z43YbU0jfBqgWJo9ezaaNGmCOXPmoLy8HMnJyXj88cdlj508eTL279+P0aNHQxAEjBkzBlOmTEFBQQEAICoqCiUlJVi5ciUuXryI5ORkPPHEE5g8eTJu3LiBixcvYty4cTh79iyaN2+O4cOHWxXnagGnfoKcZQq8of8xbajpJ/KMsykZZ491N8MgN9Ujx3L6R2l6aMagjlhcUKI4Dne+i7avLS9Hj7e/LnXpOch/vDn1Q+7j1A855c89Srg3T2Bwt9uvpxkztfsGWU7/yGUKZ9zfEYs+LzEXzEq9UyzH4ep3Ue61/X1HKQRYF+by+0zke1yeTD7DvXkChzvdfpWmYfaeuCT/gJukpdDRYSGK0z2W5HbettxHqlXTSLtVPaII7Dt5axyufhflXptRBB7rp+f3maiBMaNCPsW9eYKXUuO/p9buR3XdDdkpINuaFGcJFWc7b1cYanCkskr2sbaT2q58F6PDQuyWpIYIAh7ta1ouze8zUcNhoEI+58/pp8bM18topSxF/kcHTS3ub1KaAqow1GDWRwfNwYmjIEUA8NojmejRxn4JsfS6dh69gNe3HZd9HgGQ3VhT7rtoWzC7Ykcp3v661G6KxzJg4veZqOEwUCEKQg21jHZ0rzREhzfBH9bst7pdbonz3pOXnGZQANN89MS79bJBiuXrcvT4hSO6urz/kDQNZfvUOgAbpmShW6rjHcWJyDdYo0IUZBp6d+uebZrata3XCbArMlWzwHBARgtAAN76utRu2wfb1yVn9gOdsDP/XozulWauhVF63bbPJ0I+y2MEcLXOKHMPBYIAX9ga8Lzx/jNQIQoyavbVcZWji740BWS59ZMoAtt/OG913C/aJjgtnt1ack4xwHK2SkgH4Bdtm6L0QjX+9p/jTve5UrvqSIB90AU4fk/I/6QdgK9edf97T56T3n9HOzI7w6kfoiDj7WXhaqaR+nVItEpHiLCuU6kw1GDFjlKnUz+291tOISkV70ru75KEYa8Xyq7WkauZcfZ8ZjLRFTvUal9ISAji4+Nx7tw5AKbGZ4LMRqrkG6Io4urVqzh37hzi4+MREhLi9nMxUCEKMt7sSqy2V0rphWrFIGP7D+edTtkAN9O7CgGWVPA6c1AGlhQcQb1FOlknAL+/Jx1vbDuueA65mpnkuEgMy2yFj/adcTguUYSqNv4ZSTGorqvnHkAaIrV7l4IVanjx8fGybfddwUCFKAh5a1m42r2AlLI4UWE6h0GK9Bip82vzmHBzIKIDMOP+jlaBjk4AZt6fgTtbxyMqTIerdUa0bR6F0gvVWP6V8vb0chmlCkMNPt5vHaTIZVhsH6v0ngx9vRAiMyyaIggCkpOT0aJFC1y/ft3fw2l0QkNDPcqkSBioEAUpbywLVzuNpJTFqa6rVwxSQgQBG6ZkYePBCry93bQkWCcA99+RhIJDlTCKwOJNJRBFWHWdXbLpiOzuzkrTOEoZJaWmbpP66fH3r08oZqOUpoxEJ1kn8p+QkBCvXDDJP/weqMybN89uA6SOHTuipKTETyMiIolSy/rSC9Xm+yVyWZwKQ43sRV0H4IXhXdAiNgLvWPQsMYrA5/+tNB8nF3goTeNYjlMnAA/3TkP27c3Qs639MmdAOQhz1tTN7lwAbNcE+WoHaqLGyO+BCgDccccd+Pe//23+uUkTTQyLiGAdgHx35rLDzf9sszhyAcTEnNvxaE5bJMdFovD4BVUrbywpFQZL41yxsxRvby/Fml1lWLu7THEaRikLBDjehdn2PYkK09kV8XIPICLv0URE0KRJE4+LbYjIO+Q62kr/HfvONy5vQmibaQFgzsgcPGNwOh5BAATRlLXQCcCMQR0dns82Q+NojLZj2/7DefPuzM5qTSyDMm8VLxORPU0EKkePHkVKSgoiIiKQlZWFhQsXIi1N/h+H2tpa1NbWmn+uqpLf54OIXOdo2a3awlo50kXd9vnV9IKaNSgDEIFFNzM5iwtKEB8ZKhtAuDNGy32D3N0NmntaEfmO3xu+9enTB++99x42bdqEN954A6Wlpbj77rtx5coV2eMXLlyIuLg485/U1NQGHjFRcHLW0Vaq6bDkyhSH3POrmfWpvnbdVFQL+XFZ8mSMnjbKc2cHaiJyzu+ByqBBg/DQQw/hzjvvRG5uLj7//HNcvnwZ69evlz0+Pz8fBoPB/OfUqVMNPGKi4OTsQi3VdITcbJrl6hSH2k6wtl7dat8fRSmAkMYoBSs6AarH6GkgRkS+oYmpH0vx8fHo0KEDjh07Jnt/eHg4wsPDG3hURMFFrg5FzVJkT6Y45J5fUDn9Y0snABd+voYDpy7JNlmTntOV5/Zmozwi8h5B1NiOTT///DPS0tIwb948PPXUU06Pr6qqQlxcHAwGA2JjYxtghESBzVEdyro9ZXYXam82LrN9/sd/eTuWb1Nu1KaW9Dr6dUg0F8NKQgRBtu+KkgpDDWtNiBqA2uu33zMqzzzzDAYPHow2bdqgvLwcc+fORUhICMaMGePvoREFHWcFo74uCrV9/n99V676sToAQ7qn4JNi+8dIr2PZmO5uF/xKvNEoj4i8x++ByunTpzFmzBhcvHgRiYmJyMnJwTfffIPExER/D40o6KhZFePrC7Xl8/dum6DqMQKAmYMysGiTciPI+pstbL25ISMR+Z/fA5W1a9f6ewhEjYa3d1b2VLfUphjRw/nGgIIAtGoa6bDmRNrUcOb9GViy6QjrTIiChN8DFSLyDaXGbWoKRuUe6ysvjeqOcVlt8PbXP2Ljd5WyS5aNImSzJRLBdDf+sGa/aePCQRm4s1U860yIgoDmimldxWJaInuOCmYBxwWjSo9tiOClwlCDvScu4am1+2ULYrf/cN6qHf+Ue9KRkRSreHxDBSkNGdgRBYuAKaYlIu9S02FVqQ5F6bGXa6473OPH8vGeXLCT4yLxYLdInLlcYzofrPu1yBX7yu0X1JCbAjoLConIMwxUiIKMUsHsvpOX0DTacRCh9NhFBSXm+hDbwEcKTg6eMcgGM64GL+v2lGHxJlOQItzc28fRxoe+rLtxNnZP2u4TkToMVIiCjFJjtT+s2Q8Rjn/rl3usDvZ1IVLGYvsP560u1BJzJuaqqf292myD7YVfFIElBUcwpFuKw716fNGoTU2mxJP9j4hIHb+30Cci77Jtda+7WWmqZq8cuTb5MwdlyLaWjwrTyQYpEikTo7R3kBylC//G7yocPm50rzTsmNUf7z92F3bM6u/x1IuzfY8kbLtP5HvMqBAFIctajgs/X8OT7xdb3e/ot365OpD4qFC7jEV1Xb3DvXvkVug4yzbIZXQA4PmNh/HC54cdZmS82f9FbaaEbfeJfI+BClGQki7cFYYal2s4bC/6csHLgVOXFB8fIgiYMaijuWbFlfNaXvgtNWT9hyt1L77u5kvU2HHqhyjIebrrseXzZKU3Mz+uuq5e9rjZD3TCjln9MblfulvnlaZxnn2gk919Srsme5ur75nte0NE3sOMClEj4Ivf+pWyDr++M9n8/O6eNzkuEg/cmYwXPj/sldU87iybZqaESBsYqBA1Et7ew0dtfYa75/VW/YcnfU64QSGR/7EzLRF5xFGXW38/f4WhBn0XbfVr11oiksfOtETUIBpyt2VXsc8JUeBjMS0RNagKQw0Kj19w2BfFW9jnhCjwMVAhogazbk8Z+i7aikfe3oW+i7Zi3Z4yn57PWyueiMh/WKNCRA3Cn/Uivq6jISLXsUaFiDTFn/UiXL1DFLgYqBCRz1j2L/HlLsdEFLwYqBCRT8j1L+G+OETkKtaoEJHXOapHAcB6ESJijQoR+Y+jehTuiUNEruDyZCLyem8T9i8hIm9hoELUyPmitwn7lxCRt7BGhagR83VvE/YvISIlrFEhIqd83duE/UuIyFOc+iFqxFhLQkRax0CFqBFjLQkRaR2nfogaudG90tCvQyJrSYhIkxioEBFrSYhIszj1Q0RERJrFQIWIiIg0i4EKERERaRYDFSIiItIsBipERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItIsBipERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItKsJv4eAGnP9cpK1J04CV1UFIxXryKsbRuEJiX5e1hERNQIMVAhK5c//BAVc+YCRuOtG3U6JD83H/EjR/pvYERE1Chx6ofMrldW2gcpAGA0omLOXFyvrPTPwIiIqNFioEJmdSdO2gcpEqMRdSfLGnZARETU6DFQIbOwtm0AncJXQqdDWJu0hh0QERE1egxUGqHrlZWo/maX3VROaFISkp+bbx+s3KxRYUEtERE1NBbTNjJWxbIyRbLxI0ciOicHdSfLoIuMhLGmBmFt0hikEBGRXwiiKIr+HoQnqqqqEBcXB4PBgNjYWH8PR9OuV1bi2L0D7Fb0tNu6hYEIERE1KLXXb079NCKyxbIskiUiIg1joNKIyBbLskiWiIg0jIFKI2JXLBtkRbJKRcJERBS4WEzbyFgWywZTkayzImEiIgpMLKalgMciYSKiwMNiWmo0WCRMRBS8NBGoLF++HG3btkVERAT69OmD3bt3+3tIFEBYJExEFLz8HqisW7cO06ZNw9y5c7Fv3z5069YNubm5OHfunL+HRj7i7aLXYC8SJiJqzPxeo9KnTx/06tULr732GgDAaDQiNTUVTz75JGbNmuX08VqpUbleWYm6EycR1rZNo7tAuvLalYpe3Xn/bB9zvbIy6IqEiYiCldrrt19X/dTV1WHv3r3Iz88336bT6TBw4EAUFRXJPqa2tha1tbXmn6uqqnw+Tmca84oTV1779crKW8cCgNGIijlzUW8w4NxLL7v0/imdlwEKEVFw8evUz4ULF1BfX4+WLVta3d6yZUtUKkwLLFy4EHFxceY/qampDTFURUoX38bQy8PV165U9HruLy+59P415veciKix8XuNiqvy8/NhMBjMf06dOuXX8TTmFSeuvnbZoldBAGxnH528f435PSciamz8Gqg0b94cISEhOHv2rNXtZ8+eRZJCCj88PByxsbFWf/ypMa84cfW1yxW9tnjmj06fw7b4tjG/50REjY1fA5WwsDD07NkTW7ZsMd9mNBqxZcsWZGVl+XFk6jXmFSdKrx2A4qqe+JEj0W7rFqStXIl2W7egWV6ew/fv8ocf4ti9A1A2YQKO3TsAlz/8sFG/50REjY3fV/2sW7cO48ePx9/+9jf07t0bS5cuxfr161FSUmJXuyJHU6t+GumKE8vXXr1jh1uFxXLvn7OOs435PSciCnQBseoHAEaPHo3z589jzpw5qKysRPfu3bFp0yZVQYqWhCYlafpi6cvl09JrVypyjc7JkT2n7Zhsj1GqRanatBmx9+dq/j0nIiLPaaKY9g9/+ANOnjyJ2tpa7Nq1C3369PH3kIKK3PSJL7hS5KpmTLK1KADOLVrk09dBRETaoYlAhZS52sW15ruDuLjiPdR8d9D8eF8u5bUcn9oiV7VjsqtFscQlyUREjYLfp35ImauN5Mpn5cPwySfmn+OGDkXc0KGKWQ5Pp03kxpf83Hy729RO6ciNKX7kSETn5KBq02acW7TIJ6+DiIi0ixkVjbDNnLiaCan57qBVkAIAhk8+gbGmRvVSXleyN47qUSxX9cgFVu4sa469P5dLkomIGiEGKhogV6/halOzq3v3yt5ed/KkqqW8rtaxOMuKRPfprZjpcLa8WAqYar47aA6cuCSZiKhx8vvyZE9pZXmyu5SW4LZduxYnHn5YcWmurZrvDuLEqFF2t7ddvx6Rd3Z1uJTX2TJgV8bdbqupJ87VffsBAYjKzHT4HNKYAFPwc+3Qf2/t+2PxvFabF3JJMhFRwAuY5cmNnVJmwlhTo6reQxJ5Z1fEDR1qV6MSeWdXAI6XT6utGbFdTmw1PkFAiz9OM/VRmT3nVlt8QUCLZ/6IiDu62C2NlsZkVesix2aZMwMUIqLGgxkVP/N2U7Oa7w7i6r59iOrRwxykeDoGwL5wNmH8eCSMH4eqjRtNmwqKomlaRinYuPmcLf44zSpokT23grSVKxHdp7eq10RERNqm9vrNQMUPbDMTrq7uUXoeTzgag8NgQm5TQTWkDFHrVJRNmKDqeEdTUUREFFg49eMFvujmqhQQROfkuJQ5cTe4UeJoDLJTQxJ349yb0zlt165VlYlh4SwRUePEjIoCbwcCgHtFq758HiVXvtqGn//zH9z2y18ipv89pkLd0aPdD0ocSFu5EtdPlVm91y3+OA0RXbpCFxkJY00NC2eJiIIQMyoecHXPGrVcaXTWEM8j58TDY1BTXAwAuLx2LUJTU3H9zBnXghSdDi1nz0ZIfDxulJ+xX8VjcVxYmzRE9+ktn80xnAF+Og5E1nv0moiIKHAxUJHhq0DA3OjMJhPiatMybz2PrStfbTMHKZLrp04pP0CnQ3RWFqp37rS+3WiEeO0aojK7I3TQ/Yh94AHUnSzDtf8evBW02Ezn2K3m2bcK+Ox/ANEICDpg8DKgxziPXh8REQUeNnyT4WrnVLW81bTMV83PqgoK1B0oCEh55RW0XbsW1YWFsoecW7zY1Dhu9TsIrfkB0Rmt0Cwvz2nXWgCmTIoUpACm/372tOl2IiJqVJhRkWHXI8SLxZzuFM7aul5ZidDWqWi7dq1LNRzOioPD0m9XNwBRxI3KSgCi4ykhoxEVL/wF0YPPIjQawOBlCO0xzvlYfzp+K0gxn7Me+OlHIK6VujESEVFQYDGtA1rsgupuka+ax12vrMSxe/qrH4wgmP7r5CuU1v8ColvWAUII8PRB58GG4QywtIt1sKL2sUrP99NxICGdgQ4RkUaovX5z6scBZ3vWNDRXNyp09XGhSUlIfv7P6gckBSjmKSgBgE3QIogIi7lx8/ibWRFn4lqZalKEkJvPEQIMXupekLFvlSnoWTnY9N99q1x/DiIi8htO/QQQd4t8XXlc/MiREKKiUT5tmrpBiSJSXn4ZTRISEBZ2GdUvj0fFt3GAKACCiORfGBAadfPcgg5IUDm91GMckD7AFNgk3O5+JkWu1iV9ADMrREQBgoFKAHF3tY+rj4vqkam+46xOMK3uSUoCvngW8elXEZ18DXVXmiAs5satIAUAsv7gWoAQ18qzgIK1LkREAY9TPwHE3dU+rj4utPwLtOhmgN00DkQ061QFCNKGgyKSe15G6IVC4PReoPCvpsdHGRHdss46SIEA9HnctRfsqYR0UxbHkhCiPqtDRER+x2LaAORuka+qx1kUsl48HI1zB2IB3JrGiU+/iutXdTIZE5n6FEuCADx9qOEzGftWmaZ7xPpbtS7sx0JE5HfsTBvE7Jqj2VJY5eL0cYDVdEmzTtWIbVNjF5SERhkRGlVn80An8a4oAt9/AnQe6nqw4smqnfQBwIh3AAhAam9O+RARBRgGKsHG046u0nSJ6CgocdPmPwGb/xfI/gPQ5/fqlinvegMofA2A6PrrYXdbIqKAxxqVYOKNjq52S4MFLw9SNNWyvHIHsPNV5cOkZcWFf4U5W+PK62F3WyKioMBAJZg4WuUiMZwBSreb/ms4A/x3g+mP5QW8xzhTc7WR7zmd0XFMB/SbqXCfCHw5G9i5zP4u2yDD0etRoua9ICIizePUTzCxmbYBYL3KxXIqxK74VQCGvHpraiSuFfBTM7gWqUjZF/FW4Wr6AODrF+WDDgD4ci7QZaT1NJBckCH3ehxx9l4QEVFAYEYlmDjq6Hp6L/DZUxYXbvulx/j0KevMitzyXodEYOQKYPy/TBmZHuNM5x44z/Fjdr1pfVNotMKUk065Q61lpgjwbndbIiLyG2ZUgo1cR9d9q0xBiNPsiAic2g3EDTP9KF3speW9zggh8itrUjIdP67oNVOPFWmsn/2PdbM5QWdqFicdY0upaNYb3W2JiMivGKgEI8uOrlK9h7vFJtLF/vtPTKt2bEnTK44yFnLTMJZE463aEbvaFB2Q928gJsk0JSS9PomzNvmedrclIiK/YqAS7BTrPRQatKX2tr8trpWp/8kXz9rXfOR9CVy/6jhj4SwzI9WOyI7VaAqSil6TX2bMNvlEREGNNSrBTrbORAdM3ALc95z98Vufl3+e41tspmMEUwaldU9Af7fzoEBaSTT+X6bzytWOyLa815mWKCstM2abfCKioMZAJdjJFZUOWWYKMNrk2B9/YA1wZJP1bXLTR6Jgml5xdSz6u4G+/3MraJGKbpXGmvUE7DI/lsuMWTRLRBTUOPXTGCgVlZYVyR///mhgyF8dT6/A6Nn0im0djdQi33asAFC03PEyYxbNEhEFLQYqjYVcUWlalvLxlgWpvuxJorRix3KsA+cBX84D4KBol0WzRERBiVM/jZHUcyQmCej2iPwx3phese1tIne/szb3+1YB/54HU5AimIKW9AGOn5eIiIIGMyqNjVwGo/NvTNM9ljydXlHKlFhO8zhbsWMXyIjAv+cAX86BW5sUEhFRwGGg0pgoZTCePmiqSZGWD3s6vaJ0nppLpuyIFLwMnOd4Skk2kLEs6LXpmUJEREGHgUpj4iiDoZQxscyASFkOy59dOc+Xc2G1E/K/5wMD598MXiwCJMA0tRMa7bhRnOX4GagQEQUlBiqNibOiWNuMie30zZ0PA9+tlW+85vQ8MgGHWG9qr//0wVsB0vEtwNIuNudcdzOQ0d3MqFj2c2HPFCKiYMZi2sbElaJYuembA2scF746Os/A+cqN2aT+KoD9Ob9bZ+p+O/5fwNP/Ne3wzJ4pRESNBjMqjYnhDNC0rbq294qt9y04mnaRm0qKjHdcB6M0ZXT96q1Ahj1TiIgaFQYqjYXcKhzp4i/H2UaCgPNpF9upJGdBhtp+LeyZQkTUaHDqpzFQ06/Eltz0TbdHbv0MHZA1xfWxSNM8coEG2+ETEZENQRRFmS10A0dVVRXi4uJgMBgQGxvr7+FoU+l2YOVg+9vH/8txVgW4ucrHIgNiOAPselN5N2NvsD0nEREFHbXXb079NAaetMCXm2aRghTAN71MOLVDREQ3ceqnMfDmlIqjXixERERexoxKY+Gt1TK+3KCQiIjIBjMqgcjZZn9KHBWyuvIcgVjw6u57RkREfsWMSqBR2uyvIQVaLxMtvGdEROQWZlQCiTvLjH3FG9mZhqCl94yIiFzGQCWQsJDVdXzPiIgCGgOVQCIVslpiIatjfM+IiAIaA5VAEqiFrP7E94yIKKCxM20gYudW1/E9IyLSFHamDWbs3Oo6vmdERAGJUz9ERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItIsvwYqbdu2hSAIVn8WLVrkzyERERGRhvi9M+1zzz2Hxx57zPxzTEyMH0dDREREWuL3QCUmJgZJSUn+HgYRERFpkN9rVBYtWoRmzZohMzMTL774Im7cuOHvIREREZFG+DWj8tRTT6FHjx5ISEhAYWEh8vPzUVFRgZdfflnxMbW1taitrTX/XFVV1RBDJSIiIj8QRFEUvfmEs2bNwuLFix0ec/jwYWRkZNjd/u6772Ly5Mn4+eefER4eLvvYefPmYf78+Xa3O9smmoiIiLSjqqoKcXFxTq/fXg9Uzp8/j4sXLzo85vbbb0dYWJjd7YcOHUKXLl1QUlKCjh07yj5WLqOSmprKQIWIiCiAqA1UvD71k5iYiMTERLceW1xcDJ1OhxYtWigeEx4erphtISIiouDitxqVoqIi7Nq1C/3790dMTAyKioowdepU/Pa3v0XTpk39NSwiIiLSEL8FKuHh4Vi7di3mzZuH2tpa6PV6TJ06FdOmTfPXkIiIiDxSWV2JsqoypMWmISmarTe8wW+BSo8ePfDNN9/46/REREReteHoBswvmg+jaIRO0GFu1lwMbz/c38MKeH7vo0JERBToKqsrzUEKABhFI+YXzUdldaWfRxb4GKgQERF5qKyqzBykSIyiEaeunPLTiIIHAxUiIiIPpcWmQSdYX1J1gg6pMal+GlHwYKBCRETkoaToJMzNmmsOVqQaFRbUes7vmxISERFpnZrVPMPbD0d2SjZOXTmF1JhUBilewkCFiIjIAVdW8yRFJzFA8TJO/RARESngah7/Y6BCRESkgKt5/I+BChERBaXK6krsrtjtUfaDq3n8j4EKEREFnQ1HNyD3o1zkfZGH3I9yseHoBreeh6t5/E8QRVH09yA8oXabaCIiahwqqyuR+1Gu1ZSNTtBh84jNbgcYldWVHq/m4T5A1tRev7nqh4iIgoqjuhI1AYJcQOHpah7uA+Q+Tv0QEVFQ8aSuxNGU0cHzB7Hq0CocPH/QpfFw5ZBnGKgQEVFQcbeuxFFA8b87/hePfP4IXvz2RTzy+SP43x3/q3o8XDnkGU79EBFR0HGnS6xSQPGfU//Bp8c/tbr90+Of4uGOD6NrYlenzytleGxrZrhySB1mVIiIKCglRSehV1Iv1bUlSlNG52vOyx5ffL5Y9Ti4csh9zKgQERHhVkBhW/TaPr49/vbd3+yO757YXfVz+2sfoGBYacRAhYiI6CalgGJI+hCr6Z8h6UNUTftYcrRyyBcBRbCsNGIfFSIiIhUOnj+I4vPF6J7Y3eUgBVAORnwRUHirl4wvMzLso0JERORFXRO7uhWgAMrBSGV1JeYXzocR1iuNslOyPQoMPO0l42jMDY3FtERERD7kaNnzPw//0xykSLyxdNnTPYq01PuFgQoREQUUb2w22FAOnj+Id757Rza7ceD8Aaw8tNLuMQIEj5cue7rSSEu9Xzj1Q0REAcMb0xGe1F248tj/3fG/dv1XLG0t2woR9mWicre5IzslG4vvXgwBArq16ObSa9VS7xdmVIiIKCB4YzrCk12VXXnswfMHHQYpAPB56ecQIMje52nmQhrr9O3TMePrGSgsL3Tp8Vrq/cKMChERBQRvbDYoF+ioKVx19bH7z+1X9ZrksidymQtXMjmevE5L/ur9YouBChERBQRPpyM8CXRcfWxmi0xVY7IlQLDLXLg63eWNFT8ST3eN9gZO/RARUUDwdDrCk5Uwco91VPTaNbErhqQPUXw+pSmfF/u9aBWEHDx/EPMK5ylOd8kVFnu64kdrGKgQEVHAGN5+ODaP2Ix3c9/F5hGbXSqk9STQkR5rG2DY1n5YBg4Lchbgr/3/avcYHXR4tf+rssFEtxbdzD9vOLoBYz8fazc9JGVHlGpmtFRf4g3sTEtERI1KZXWlW3UXldWVyP0w16rviWW3V7kpmta3tUbeF3l2z/Vu7rs4deWU+XgBAqb2nIpHuzwKwJRJkQtSpHP+Y9A/8NuC3zrsPOvu62wo7ExLREQkw926i7KqMofN2ewKWAvnY1n/ZYp1Nb2SesFQa8Are1+BCBFL9y1FXHgcAGBe4Tz5IAWmAKjmRo3TOhTb1xmoGxQyUCEiIpJhe2F3VMwrW8AKI5786kkMSR+Cf/34L6tMS1J0EiqrK7F031JzQCLVn4iiKBukCBDwj1//A10Tu6KyutKlwmKttMN3B2tUiIiIbMjVfziq/ZArYJV8dvwzLLtnGab/Yjr+Megf5gBBaXWOUpAyL3ueea8hV+pQtNQO3x3MqBARUaPx86VruHyuBvEtInFb0wjZYxz1IZHrLSJlXp7u8bR5GseSCBFPfvUkgFsBRXZKNn669hMECFbH66Czm17SQWfOpFhS2+fEm8uV/YGBChERNQrf7yzHtn+UQBQBQQDu+W0GOvdNsTvO2YXdsvbDdkrl1/pfY2PpRsUxGEUj5hXOgwABRpiKaKVgxTZoAW4FNkq7Nqupt9FSO3x3cOqHiIiC3s+XrpmDFAAQRWDbP0rw86Vrdseq7UMil3kpOFHgdCwiRHPWRIQIQRDwbJ9nzT9byuuS53EtSaAvV2agQkREQe/yuRrYNuMQReDAVvs9ddRe2JUyLxPumKBYryLHKBpRW18rW5vy94N/90otiSf9Z/yNUz9ERBT04ltEQhBgF6wU//sUut2balevIlf/YVvfojSlckezO7DsnmV46qunFAtjrepSBB0yW2TKTv0Y4b1aEi20w3cHMypERKRpP1+6htNHLslO06i5HwBuaxqBbgPT7O8QAcO5GtnHJEUnoVdSLyRFJ+H7neVY9adC/N8r+7HqT4X4fmc5kqKT8GyXeWhV1QHRtXGmQEMUMX37dIdByuD0wVbdakVRxNHLRzG151S746UpJ7lW+Y0FMypERKRZzgpg1RbIAkC3e1uj+Msyq9sEHRDXItLhGGTrW/5Zgtrq6zj/cRwGi08Agoht+rUoafmN6RiZIEW6/V8//svqfhEi5hfNx+YRmwEAS/cuhRG3+p0Ulhc2WA8ULTaFY6BCRESapBQgpHVOwG1NI5zeb+u2phHo/7sMbPtnCUSjKUi5Z2yG3bG2Uzyy9S1GoPDj4zDHG6KAfj+Oxqn4w6gON5iPk53OsalrkW47deUUHu3yKAbpB5mnnAAg96Nc2aXSAMxBheX/uxtgaLUpHAMVIiLSJKUAwXCuxmEAId0vp3PfFKR1ToDhXA3iZHqpyGVo0jon2Ne3CIBt0kQHHeKuJZoDFZ2gk61VUVqGLAUmlrUkuyt2yxbs/vPwP7Hy0Erz80jP6W6A4ah3jL8zK6xRISIiTZIKYC1ZTtXEy0zZqJnKAexiDADKGRzAFLBIC3kEHXB7ZqL9EwgiIm/EILo2zhww3JN2D+ZlzzOvArLdSVnydI+nAcCuDkVuqbQAwSpIMb0e6zb8trUszmpcHPWO8TdmVIiISJNuaxqBe36rPFVT9v1P1g8Q5KdyLDmqaXGUobHMxDQJ1+GjxXvtn1wUcN8PEwAB6PFQMrLadwJgvYLoYs1FTN8+3e6hP137yTzFY7mTsrRU2nJKZkT7Efjghw8UX6Nt11k1UzpabgrHQIWIiDRLaapGyn5YEgCkdU5QbJPvrKZFbgmzZYbmtqYRuK1pBE4fuWQX0FgRgX0fVKBrpt58fmk6R2kzQcsMiQgRL+99GQDwaJdH7ZZKF58rdhioWAYYaqd05AIirTSFY6BCRESaJgUIlhw1cDvw71MuZUyO7T2Hdj1bOM3gSJR6slg/MVD5owHtelo/Vi4gGNdpHN77/j27p1i6dykG6QfZte3v3qK7bJ0LYN+czpV9ftTuHdTQGKgQEVHAkc1+CEDxl7dqKtRkTABg54fHUPjRMXNQ46jYFjAFTlnD0lH08XHTc8kU1poGID9224AAAFZ+v9J+dZBCs7ek6CTMy55nFew83eNpdGnexS7AcHVKR4tN4VhMS0REAUfKflgWuMo1dJNqTOQeY3XczaDm50vXcFvTCLTq2FSx1uX7neW3ghQAPXLb2B8kAEnpcYrjt2wmlxSdhKk9pyK6Ng4phnaIrjU9zlGzN9uW+I92edT8fLbnCeR9fgBmVIiIKEB17puCZq2iUXHMgOR2cYiOC8eBf5fZZUzOnaxCq45NzY9J65yAY3vPYeeHx6yOc7a0GbCvcwGA/V+cRPbw9Ft9VQSg/28dF/Xa6mPIxdX9aYBo2lX56/T1eHjo/eZmb5HXYhBf2xJ5fX+Lh3oMA6A++6HVKR21GKgQEVFAklvBc9ewdBRtOG51XNEnx9G+V0tz4HBb0wi069kChR8dUyycVaJU5xKTEIHxL2Q7nDJSYi4MFk1Ll3XQ4Z4fH0b3qPYYtuVBdKjsjX4/joYOOlQeMqJo1GFk3dtJ8fnkustqcUpHLU79EBFRwFFawROTYB8gWE7/SOSmju4ZmwEA5n2D5PYQkuvdAgBf/P0Qyr7/yeGUkRKlwuAfy04h8lqMOUgBTEHMvg8qFPc12nB0A3I/ykXeF3nI/SgXG45ucGksWsSMChERBRylzIYgQHaJcZNwHU4fuWS1ZNm2cLbs+5+w6k+Fds9ruXrIrneLdG4n7fsdUSryDb0Yi/jaluYg5dbJ5KeotNxd1hPMqBARUcBR6lqbdHscOvSxvii3aBuLjxbvtdr5WCIVzgKwqz2RSEHI2RMGu94tVsfJZG7UuK1pBO4alm53+6HPz2FCt9/BCOvlxUpTVFruLusJBipERKQZctMtchxN3fywy7pN/Nkfq+ymiGyfXy5DY0k0AhXHDA6PUdu+X06LNrGy57y75S/xi1GtIHXeV+rtAsi329dKd1lPcOqHiIg0wVF7ezm2UzcAcHTvOceN2CC/usdZEzdBByS3i1M8xlEAYdkpF4Bs11xHXXGzOnZC10y900JdLXeX9QQDFSIi8jtn7e2VSF1rLYMcZ+QyH7Zdac17B4q3gpCWbePsOtdmDU1HizaxigGE0rhsAzFnXXHluvPKCfSlyHIYqBARkd852hDQ2QVarreJRNABHXon4YfdlQ7b4gPyGRrbLIZ0TOVxA0QAyelxds8lZVBCw3VO614sAzE1XXHVCOSlyHIYqBARkd852xDQEaX6kr4j25n38LnrN7erCgBsMxdyx5Z9/5PiFNX+L07eavzmhFwgpjZz0piwmJaIiPxOqThWzUVbaQWQFKRIz+9OjxNbSlNUP1+6hn1fnEThBnVBijRGd4tvGxNmVIiISBPkpl5se5/IUbvrsTcoTVFV/miw64hrx3LzQsF3Yww2DFSIiEgz5Ipj3VkB5KsAQGmKymkRrwD0zG2DfZtPml6TyvNZrhhqrEENAxUiItIUT1cAeXMctkGCUvYmOV156bLpRQB7N580Z1TUvCbbYO2uYaYVRtJ4GksQw0CFiIg0xZMVQN7iKKOjlL2xWt5sy3La5yZHr0kuWJOmlgQB6NAnCT/sqlSdcQpkDFSIiEhTPFkB5A1qMjpy2RvLAObsySp888lxc9blrqHp+Obj46pfk6NOuaIIHPmm0upnd/cZCgQ+W/WzYMECZGdnIyoqCvHx8bLHlJWV4YEHHkBUVBRatGiB6dOn48aNG74aEhERBQBPVgB5g6OMjjPS6qIev2qDcQuyMXRqJsYtyEaPX7Vx6TXJrWRyxN19hgKBzzIqdXV1eOihh5CVlYW///3vdvfX19fjgQceQFJSEgoLC1FRUYFx48YhNDQUL7zwgq+GRUREAaChimPlKGV05HZgdsQ26+LKa7LrlOtEMC91FkRRTcNh97333nt4+umncfnyZavbCwoK8OCDD6K8vBwtW7YEALz55puYOXMmzp8/j7CwMFXPX1VVhbi4OBgMBsTG2m/qREREjYM3i0u/31luVTDbobdyTYgvi1p/vnQNhnM1OHeyCkUWU0ly3XYDrUZF7fXbbzUqRUVF6Nq1qzlIAYDc3Fz8/ve/x6FDh5CZmSn7uNraWtTW1pp/rqqq8vlYiYhI21xdzuyMZfajSbgOHy3eK1uz4qhLrTdIWZlWHZuifa+WVtkYtd12A53fOtNWVlZaBSkAzD9XVlbKPQQAsHDhQsTFxZn/pKYG9vbVRETkGUfdYj0hBQjXa42KTd58cV5n41HqtvvzpWs4feSSz87vLy4FKrNmzYIgCA7/lJSU+GqsAID8/HwYDAbzn1OnTvn0fEREpG2eFL+qodSiXxTt+6YondfXQcT3O8ux6k+F+L9X9mPVnwrx/c5yn5zHH1ya+vnjH/+ICRMmODzm9ttvV/VcSUlJ2L17t9VtZ8+eNd+nJDw8HOHh4arOQUREwc/Xy5ldafImd15vT0vZcrdBXqBwKVBJTExEYmKiV06clZWFBQsW4Ny5c2jRogUA4Msvv0RsbCw6d+7slXMQEVHwa4i9ftQ0eZM7b0MEEVpokOdLPiumLSsrw08//YSysjLU19ejuLgYANCuXTvcdttt+NWvfoXOnTvjd7/7HZYsWYLKyko8++yzeOKJJ5gxISIilzTEcmZnTd7kztsQQYS/G+T5ms8ClTlz5mDlypXmn6VVPF999RXuuecehISE4F//+hd+//vfIysrC9HR0Rg/fjyee+45Xw2JiIiCmNq9fry9nNjReRsiiGjI3aP9wed9VHyNfVSIiEgtX9eLKJ7TJojwxTmlniuBslxZ831UiIiIGpK/ik4bqsuut3eP1goGKkRE1Cj4s+g0WIOIhuC3hm9EREQNSakfSrAUnQYrBipERNQo+HtXZnIPp36IiKjR8OeuzOQeBipERNSosF4ksHDqh4iIiDSLgQoRERFpFgMVIiIi0iwGKkRERKRZDFSIiIhIsxioEBERkWYxUCEiIiLNYqBCREREmsVAhYiIiDSLgQoRERFpFgMVIiIi0qyA3+tHFEUAQFVVlZ9HQkRERGpJ123pOq4k4AOVK1euAABSU1P9PBIiIiJy1ZUrVxAXF6d4vyA6C2U0zmg0ory8HDExMRAEwd/DIQVVVVVITU3FqVOnEBsb6+/hkAr8zAILP6/Aws/LlEm5cuUKUlJSoNMpV6IEfEZFp9OhdevW/h4GqRQbG9to/1IGKn5mgYWfV2Bp7J+Xo0yKhMW0REREpFkMVIiIiEizGKhQgwgPD8fcuXMRHh7u76GQSvzMAgs/r8DCz0u9gC+mJSIiouDFjAoRERFpFgMVIiIi0iwGKkRERKRZDFSIiIhIsxiokF+0bdsWgiBY/Vm0aJG/h0U3LV++HG3btkVERAT69OmD3bt3+3tIJGPevHl2f48yMjL8PSy6afv27Rg8eDBSUlIgCAI++eQTq/tFUcScOXOQnJyMyMhIDBw4EEePHvXPYDWMgQr5zXPPPYeKigrznyeffNLfQyIA69atw7Rp0zB37lzs27cP3bp1Q25uLs6dO+fvoZGMO+64w+rv0Y4dO/w9JLqpuroa3bp1w/Lly2XvX7JkCV599VW8+eab2LVrF6Kjo5Gbm4tr16418Ei1LeBb6FPgiomJQVJSkr+HQTZefvllPPbYY3j00UcBAG+++SY2btyId999F7NmzfLz6MhWkyZN+PdIowYNGoRBgwbJ3ieKIpYuXYpnn30Wv/nNbwAAq1atQsuWLfHJJ5/g4YcfbsihahozKuQ3ixYtQrNmzZCZmYkXX3wRN27c8PeQGr26ujrs3bsXAwcONN+m0+kwcOBAFBUV+XFkpOTo0aNISUnB7bffjrFjx6KsrMzfQyIVSktLUVlZafV3LS4uDn369OHfNRvMqJBfPPXUU+jRowcSEhJQWFiI/Px8VFRU4OWXX/b30Bq1CxcuoL6+Hi1btrS6vWXLligpKfHTqEhJnz598N5776Fjx46oqKjA/Pnzcffdd+O///0vYmJi/D08cqCyshIAZP+uSfeRCQMV8ppZs2Zh8eLFDo85fPgwMjIyMG3aNPNtd955J8LCwjB58mQsXLiQLaWJVLKcVrjzzjvRp08ftGnTBuvXr0deXp4fR0bkPQxUyGv++Mc/YsKECQ6Puf3222Vv79OnD27cuIETJ06gY8eOPhgdqdG8eXOEhITg7NmzVrefPXuWdRABID4+Hh06dMCxY8f8PRRyQvr7dPbsWSQnJ5tvP3v2LLp37+6nUWkTAxXymsTERCQmJrr12OLiYuh0OrRo0cLLoyJXhIWFoWfPntiyZQuGDh0KADAajdiyZQv+8Ic/+Hdw5NTPP/+M48eP43e/+52/h0JO6PV6JCUlYcuWLebApKqqCrt27cLvf/97/w5OYxioUIMrKirCrl270L9/f8TExKCoqAhTp07Fb3/7WzRt2tTfw2v0pk2bhvHjx+MXv/gFevfujaVLl6K6utq8Coi045lnnsHgwYPRpk0blJeXY+7cuQgJCcGYMWP8PTSCKXC0zG6VlpaiuLgYCQkJSEtLw9NPP43nn38e7du3h16vx+zZs5GSkmL+JYFuEoka2N69e8U+ffqIcXFxYkREhNipUyfxhRdeEK9du+bvodFNf/3rX8W0tDQxLCxM7N27t/jNN9/4e0gkY/To0WJycrIYFhYmtmrVShw9erR47Ngxfw+Lbvrqq69EAHZ/xo8fL4qiKBqNRnH27Nliy5YtxfDwcHHAgAHikSNH/DtoDRJEURT9GikRERERKWAfFSIiItIsBipERESkWQxUiIiISLMYqBAREZFmMVAhIiIizWKgQkRERJrFQIWIiIg0i4EKERERaRYDFSIiItIsBipERESkWQxUiIiISLMYqBAREZFm/X+oMSrnA1tHPQAAAABJRU5ErkJggg==\n"},"metadata":{}}]},{"cell_type":"markdown","source":["If it still not better, increase `max_iter`\n","\n"],"metadata":{"id":"ndvsBuZ6HonL"}},{"cell_type":"code","source":["# Train the model\n","cls = PyKMeansClusterer(k=5, max_iter=100)\n","cls.fit(X1)\n","\n","# Predict cluster assignments for the data\n","y_pred = cls.predict(X1)\n","\n","# Show the predicted clusters\n","show(X1, y_pred)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":430},"id":"LBnsi0C3Hj7L","executionInfo":{"status":"ok","timestamp":1776172407197,"user_tz":-120,"elapsed":436,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"358ffef0-ca85-403a-d185-911d68f916b2"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["## Try different number of clusters"],"metadata":{"id":"1bl4PMGuLZgX"}},{"cell_type":"code","source":["# Train the model\n","cls = PyKMeansClusterer(k=3, max_iter=100)\n","cls.fit(X1)\n","\n","# Predict cluster assignments for the data\n","y_pred = cls.predict(X1)\n","\n","# Show the predicted clusters\n","show(X1, y_pred)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":430},"id":"KgtozPCuIBcR","executionInfo":{"status":"ok","timestamp":1776173376060,"user_tz":-120,"elapsed":291,"user":{"displayName":"ziyu Zhang","userId":"05382179476966223598"}},"outputId":"446e450f-1e4d-49b4-b19f-141787815993"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"code","source":[],"metadata":{"id":"6_ohcGRwLrtE"},"execution_count":null,"outputs":[]}],"metadata":{"kernelspec":{"display_name":"Python 3 (ipykernel)","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":"3.10.12"},"colab":{"provenance":[]}},"nbformat":4,"nbformat_minor":0}