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{
"worksheets": [
{
"cells": [
{
"metadata": {
"id": "pFDCGN6VdOEx",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829430447,
"user_tz": 480,
"elapsed": 434,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "771c7740-fee9-4d24-c42b-5d2ed67226f0"
},
"cell_type": "code",
"input": "import matplotlib.pyplot as plt\nimport numpy as np\nimport pandas as pd\nimport seaborn as sns\nimport tensorflow as tf",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "I87OcwhptRef"
},
"cell_type": "markdown",
"source": "Start off by defining some hyperparameters."
},
{
"metadata": {
"id": "yH5J9H8HWeQI",
"cellView": "code",
"executionInfo": {
"status": "ok",
"timestamp": 1447829432048,
"user_tz": 480,
"elapsed": 337,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "4bf3ddb2-54c4-4c90-b79a-d39411895871"
},
"cell_type": "code",
"input": "num_vectors = 1000\nnum_clusters = 3\nnum_steps = 100",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "kzjvLTmxtfcP"
},
"cell_type": "markdown",
"source": "Generate some sample data as a list of random 2D vectors from two overlapping normal distributions."
},
{
"metadata": {
"id": "fMYs5yJ6VVYw",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829433747,
"user_tz": 480,
"elapsed": 331,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "aa838117-3a24-4d8a-b861-809e85d5fec7"
},
"cell_type": "code",
"input": "vector_values = []\nfor i in xrange(num_vectors):\n if np.random.random() > 0.5:\n vector_values.append([np.random.normal(0.5, 0.6),\n np.random.normal(0.3, 0.9)])\n else:\n vector_values.append([np.random.normal(2.5, 0.4),\n np.random.normal(0.8, 0.5)])",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "_M9CDBzGx-M9"
},
"cell_type": "markdown",
"source": "Create a scatter plot of the initial randomly distributed vectors."
},
{
"metadata": {
"id": "9yNy1wc8eSLD",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829436136,
"user_tz": 480,
"elapsed": 1121,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
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},
"outputId": "612b9408-0692-4114-fb9a-954f3e636299"
},
"cell_type": "code",
"input": "df = pd.DataFrame({\"x\": [v[0] for v in vector_values], \n \"y\": [v[1] for v in vector_values]})\nsns.lmplot(\"x\", \"y\", data=df, fit_reg=False, size=7)\nplt.show()",
"language": "python",
"outputs": [
{
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vbATHTn04rCuzY2NVNm60j0Gv5XBkf2XSv2+oyoHDqofLG0FJrhk5ttmX7Un6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\nxfPkijoT0SxyqaXZO5ZkbVOI7z7SxU/eueys2reUnLMmZrKcujyDxy2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ZoqmC45H83qnx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\nGIDQcvPIuS6sKM+AUiGb9WPd3gB+faQJ5lEPFHIWX95RgfL81LiN1ZSug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"text/plain": "<matplotlib.figure.Figure at 0xd1a9690>",
"output_type": "display_data",
"metadata": {}
}
]
},
{
"metadata": {
"id": "i7PQdXgnza89"
},
"cell_type": "markdown",
"source": "\nLet's start building our k-means TensorFlow graph with a few simple operators:\n- Store our vector input values in a 2D tensor constant. \n- Randomly shuffle the input vectors and then slice off the first `num_cluster` vectors as a 2D tensor and store the result in a Variable."
},
{
"metadata": {
"id": "M4ytBUbLzgQT",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829437949,
"user_tz": 480,
"elapsed": 349,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
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"displayName": "Shawn Simister",
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}
},
"outputId": "78656e26-76c6-4a50-e4ac-e21d6a1681a0"
},
"cell_type": "code",
"input": "vectors = tf.constant(vector_values)\ncentroids = tf.Variable(tf.slice(tf.random_shuffle(vectors), \n [0,0],[num_clusters,-1]))",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "FpiD9SXS0LCv"
},
"cell_type": "markdown",
"source": "Here's where things get a little more complicated. We extend both of our 2D tensors into 3 dimensions so that we can do an element-wise subtraction between them. This would be pretty straight-forward except that these two tensors have completely different sizes."
},
{
"metadata": {
"id": "xQ7wxywwbbTK",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447830676501,
"user_tz": 480,
"elapsed": 381,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "951bd47d-1ed2-4e24-a4ea-a74a3ba9d885"
},
"cell_type": "code",
"input": "expanded_vectors = tf.expand_dims(vectors, 0)\nexpanded_centroids = tf.expand_dims(centroids, 1)\n\nprint expanded_vectors.get_shape()\nprint expanded_centroids.get_shape()",
"language": "python",
"outputs": [
{
"output_type": "stream",
"text": "TensorShape([Dimension(1), Dimension(1000), Dimension(2)])\nTensorShape([Dimension(3), Dimension(1), Dimension(2)])\n",
"stream": "stdout"
}
]
},
{
"metadata": {
"id": "TJqHfY4pbb54"
},
"cell_type": "markdown",
"source": "However, because of the *shape broadcasting* feature in Tensorflow, the `tf.sub` operators is still able to figure out how to do the element-wise subtraction between the two tensors. That allows us to calculate the squared Euclidian distances (no need to take the square-root) and determine the cluster assignments for every vector and centroid all at once."
},
{
"metadata": {
"id": "CaVqPENC1GTK",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447830739233,
"user_tz": 480,
"elapsed": 393,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "1316a691-6439-4a62-f7dd-73ec8fbff086"
},
"cell_type": "code",
"input": "distances = tf.reduce_sum(\n tf.square(tf.sub(expanded_vectors, expanded_centroids)), 2)\nassignments = tf.argmin(distances, 0)",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "isp15ytJ1G4s"
},
"cell_type": "markdown",
"source": "Once we have the cluster assignments, we can go back through the input vectors and gather all of the members of each cluster and average them together to calculate the new centroids for that cluster."
},
{
"metadata": {
"id": "2_jmQ0gb1hWg",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447830741933,
"user_tz": 480,
"elapsed": 425,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
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"isMe": true,
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}
},
"outputId": "0f69df1e-ec76-4946-94a4-9bd9f8b64bae"
},
"cell_type": "code",
"input": "means = tf.concat(0, [\n tf.reduce_mean(\n tf.gather(vectors, \n tf.reshape(\n tf.where(\n tf.equal(assignments, c)\n ),[1,-1])\n ),reduction_indices=[1])\n for c in xrange(num_clusters)])",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "vWlzzqx01glW"
},
"cell_type": "markdown",
"source": "Finally, we create an operator which assigns the means, which we just calculated, to the `centroids` variable so that the next time we run the graph it is using the updated centroids.\n\nWe also create a operator to initialize all of our variable before we run the graph."
},
{
"metadata": {
"id": "5SYqvxOYc-F1",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829473596,
"user_tz": 480,
"elapsed": 334,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "eb9b1632-7370-4aa8-ccab-276eda0c7701"
},
"cell_type": "code",
"input": "update_centroids = tf.assign(centroids, means)\ninit_op = tf.initialize_all_variables()",
"language": "python",
"outputs": []
},
{
"metadata": {
"id": "u0WDaKaTyGQn"
},
"cell_type": "markdown",
"source": "Here's where we run our graph. For each step in `num_steps`, we update the centroids and fetch the values of those centroids as well as the cluster assignments for each of our input vectors. TensorFlow will figure out all of the dependencies so that all of the necessary operators in our graph will be evaluated in order to calculate the new centroids.\n\nAfter all the steps have completed, we display the coordinates of our final centroids."
},
{
"metadata": {
"id": "7Vd3FbnUP2sb",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829476050,
"user_tz": 480,
"elapsed": 729,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "8c69b6d5-8afd-4e49-88e6-23abc8918539"
},
"cell_type": "code",
"input": "with tf.Session('local') as sess:\n sess.run(init_op)\n for step in xrange(num_steps):\n _, centroid_values, assignment_values = sess.run([update_centroids,\n centroids,\n assignments])\n print \"centroids\"\n print centroid_values",
"language": "python",
"outputs": [
{
"output_type": "stream",
"text": "centroids\n[[ 2.45892787 0.76684326]\n [ 0.51400542 1.08303225]\n [ 0.49523357 -0.41180998]]\n",
"stream": "stdout"
}
]
},
{
"metadata": {
"id": "acr9S4-8zCLg"
},
"cell_type": "markdown",
"source": "We can now create a multi-colored scatter plot showing how our vectors have been clustered."
},
{
"metadata": {
"id": "V42q_YBWcNPr",
"cellView": "both",
"executionInfo": {
"status": "ok",
"timestamp": 1447829479003,
"user_tz": 480,
"elapsed": 1450,
"user": {
"sessionId": "894bf6d9230dc18",
"userId": "114584588709374914590",
"permissionId": "10586785709366787971",
"displayName": "Shawn Simister",
"color": "#1FA15D",
"isMe": true,
"isAnonymous": false,
"photoUrl": "//avatars3.githubusercontent.com/u/187935?v=3&s=50"
}
},
"outputId": "1f1aa33b-523a-4d0c-9c98-0e4f7575f034"
},
"cell_type": "code",
"input": "data = {\"x\": [], \"y\": [], \"cluster\": []}\nfor i in xrange(len(assignment_values)):\n data[\"x\"].append(vector_values[i][0])\n data[\"y\"].append(vector_values[i][1])\n data[\"cluster\"].append(assignment_values[i])\ndf = pd.DataFrame(data)\nsns.lmplot(\"x\", \"y\", data=df, \n fit_reg=False, size=7, \n hue=\"cluster\", legend=False)\nplt.show()",
"language": "python",
"outputs": [
{
"image/png": 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eRYtQB3sc7CUlVP3gh8ROnsRWWET1Lavp7g5d6dJ5IWkkM4kb0uO+Z0OtLB7B\n2PJY8No9TPfV0DLYNV3gKGCa7/xKkUpPRVbyrvIMXf+9JdxG3IijmwYWFicDp3nlxJv81YqXLls1\nbX7JHJaWLuJw7zGcmoNNdfdlvX6uR6In1ss0Xw2leT7XYaqT5C3EBFA0jYqnv4MRDqM4HZdMPBxP\nmq8g61h1OlFdLrxLl132/baiYgrW5P849zl21Y7X7r2gwpiSNdt8oiiKwhPzN7O/+xApM8WyssVZ\nRVI2zr6HrWfddMd6sCk2+hIDJIzkFQu4uG1uoqkoFumVASlDpzXcRsyI41O9l7xfVVQeqruP+2bd\nhU3RLjtuXeOrosZ3fS49zTcyYCrEBNJ8vglN3ADOmhpK7rkP1e3GVlRE2WNPoE5gt32uKYrC4/Me\nptpbhd9Vwn0z78xZgnJodtZVrWZ9zY0UOrIfqlw2F3fO2EBUj3I23MIXLdv4w/HXr7x0q3oNHnt6\nYqUCqIqCaYGNoWuV21XbVSecGabB/q5DbG/7hoHBAjZicpGWtxDXgcKbb6FwjJa/XU14/z5Cu3el\nty29fyP20qvPmh5vVd5Knl/8VK7DyGgNt/NR01YSRpJ1VatZXbEcgM5oV9akso5IJ4FEkBJX8SXX\nuKf2dlRF5ZOmLzAxsSk2fA4Pp4KNLCyZd9mu85ge5+Omz+iJ91FXNItbp9102SVf75z+kOP9DUB6\nYtuLS56Z8DkCYmiSvIUQYyZxtpned9/ObHqiv/J7an7y1zmOKjdieozPW7YTTIZY7J/P0sEJYKZl\n8lrDO8T0dF35LU2fUe2tpNpbSaGjAFXRMAf3E3dojkzr+mKqonJP7e2Uu0vZ2b6XtkgHhmXyasM7\nuG0ubpt2M+uqVqMqKtFUlPq+BvZ1H6In1otCulZ5gcOXeXA4Rzf1TOIGiOpRmoJnM/GLyUGStxBj\nKNHaQryxEUdlJe6580Z0bqqvD0vXcVQMPVFpMkv1dGftVpbq7cUyzWta0mhZ1oQWU7Esi2AyjFOz\n47KNfmOad05/xJlAIwBnAo34HF5mFdaSNJKZxD34yQQSQaq9lZS4inlo9r181boDTdW4u/a2q25a\nsqJ8KRWecl4++gcSRpKB+AADwMfNnxNKhrl12k38uv5PDCQG6In1oSkaJa4iYnqc3Z37qPJUUOOr\nwrRM2sId2FXbRXMEuKSLX+SeJG8hxkjs9Gm6//CbTPla/4MPUbD2hmGdO7D1UwJffQGkt+4s/fZj\nOa8Cdi3QAptBAAAgAElEQVSctTNR7PZMnXjX7NkjTtzJjna6X30FIxjAs3gppY9sHvd6BqZl8nrD\nu5wKnEFTNDbOvnfYs9Ev3mb0nPZIZ9ZxW7iTWYW1uGwuZhbW0jQ4A95j8zC94HzFvcWlC0Y8Ez69\nDEwhYZxfv6+icCbYzMzCGQwkBoD08rBIKkowGSacDBNIhGjoP81jczfRFGqlMdgEwIKSefTG+4jp\ncdZUrqS2cPqI4hHjT5K3EGMkeuRQJnEDRA4dHFbyNsLhTOIGiBw5jG/tDbhqr7zGd7Kyl5ZR+fyL\nRA7sR/V4KLxp5OPsvW+/lVnaFjl0EGftTApWrxnrULMc7zvJqcAZTMvCwuCjpq1XTaC9sX5+e+xP\ndMW78Tv8/HDZd/FdMC483VfNyYHTg0cK033Vmdcem/cw+wd36Vpatgif/dLZ4SMRSoXRTZ1wMoKF\nSbGzGE3VKHP78dm9mJaJgoLP7sWhOjCxBuv5W+imzlunPsCh2bGpNhyaneP9DfzNyh/isY9t0SIx\ndiR5iynDMk0SLWexTIPI3r3Em5txVldT+q3NmXXM0fqjDGz9hF6XA89tdw2razve2Ejgi62AQvGd\nd12xrKlWUDDk8cj+Mfm7MYizZhrOmmnXfL4Rya7qdnHVt/EQ0aP0xPrQTR1V0Sh3+6/abf/O6Q85\nM9h6jiRa+B+Hf8Pfrv5x5vVNdffzVesOQskwi/zzs1qvdtXGDVWrxiz+985swaZqVHsrCCcjlLpK\nmF00kztnrOe9M58Q1ePE9DjVngqeXLCZT5u/zGyDalkWUT1GzIilE7zDS4G9AHWcen7CyQiRVIRS\ntx+bKinoWsmdE1OCZZr0vPoK0ePHMEJBLMPAVlxCNBRE/XgLpZseQR8YoOeNV7EME8umEXn1Fab9\n9H9H81y5jrkRDtP9x99lyol2/f631PzN36K5L22RFK7fQKqnh/jpUziqqvDf/+CwYtd8PgrXbyC4\n7SsAPIsW48zDVvdY8a1eS+CLzwBQXS48i5YQPXGc6NHD2IqKKdxw65gvt+uPD2S+Ni0Dj91z1WGL\nvnh/+iFr8H3dsd6shO/UHNxde9sVz4+korx3Zgs9sT7qimZy78w7rnmzj7iertymKAoFTh/ra9ax\ntmoVuzv20RhswmNzo5s6A4kg7ZFONs99iKZQC9FUFEVRUBQVm6oR1+NEUzEernvgquP+JwfO0Bnp\nYkbBtGF3qx/vO8k7pz/AsAzK3WU8u/CxMZlfcD2S5C2mhGR7O9HjxwCwdAMzHsPyFaDYbOgD6T/M\n6aR+vlvbSqUwIuEhk7ceGMiqA24mEhiBwGWTt2p3UP74k9cUf8ld9+BbvgJL17FXVuXlePdYKb79\nDpzTpqEHBnDPmYs+EKD7lT+cn8He30/Zo4+P6Wcalkmpq4SkmUJVlGHVPl9ZsZSzg7t6KYrCNF/1\niP6/bWn6jNODE9r2dx+ixFXMuqrVnA40sq/rEC6bi9un3YLP4cUwDfZ2HWRv1yEsy2RN5Yqslvua\nyhV83ZbeHthr97LAn+5ROjcGHkgESRgJVEXjq9YdFDoK+Psb/jcOdh+hNdxOw8BpVEVBt3spdhWx\nrmr1kLHvH9yKNE3h0bmbmFdSd9V/89aWrzAGZ9J3x3o40H2EG6vHd0hkqpLkLaYERTu/plV1uzDj\nsXTlCtItWQB7RSU2vx+9rw8AR2UV9hL/kNe1l5VjKyxED6bX3tqKi7GVDn3O1RjRKANbP8EIhfAu\nX4F38ZLMZ4m0C4czwgcPZA0jxBvPjOln1feeoKH/FP2JAF67B6fm4obKq3dp3zXjVhQU6gPHKNKK\neOiicqNX0x3rIWUa2FQNhXSC7Yp281rDu5mlYt3RHl5c8gwfNH3Kly1fE06la84f728goSfYMD1d\ne/7WaTczo2Aa4WSEWUW1mTH0pWWL2Nd9iO5YLwDewTHss6E27Kqd+SVzWFe1mjdPvcfJgdN47R4W\nlsxjW9tO5hfPpdxz+TX6R/tOXHBkcay/YVjJG/J3OGiykeQtpgRHVRWFN95EcOcOVJeb4rvWYC8t\nw1FTg2fBQiBdFrTqhe8T3LkD2s9iFpeS6usbcmmW6nRS8fz3CO3cDopC4U23jLrLtuf1V4mfSU9k\nip1sQPP5xm1ymh4YoOfN19H7+vAsWEjJAxvzbic6R1X1kMejMZAI8O6ZjzAtgyJnIZZl8ezCx5jm\nG95n3DljA0+ufnDE9d8P99RzNtRGKBnCrtkpdfmZW1xHR6Qrk7ghXbTFMA0a+k8RvWCXL8My2dt9\nMJO8gUv25wYochby4pJneOvke5wONOHQ7CQNnf3dhzjUcwRN0fj23E08Nu9hEkaSrc1fsrtzHwA7\n2/fw/OKnKXNf+rB68dKxoguODdO4bIEYgDumb+Dd0x9mus2Xly8Z5h0TF5PkLaaMkvseoODmW1CU\nK++6pvl8JJoaMTrb0c80Ea0/SvUPf4Kt6Mq1ru0lJfgf2Djq+M6td062tlzwTYtka+u4Je/ed98m\n0ZyeVBXasxt7eQUFN6zLvJ7q7wfLxO7PfRW0K/HMX4B/4yaiRw6jFRVRcu/9Y3btYCKUSZaaooIC\n7jEeg02ZOl+17qAn1svswlrWVq3ik+Yv8Nrd6a5qU2dN5QpmF9XSFe3JKtJS6alkW9su2iIdmJaJ\nhYUy+F+Rs5DGYDOxVJxZRTMyddIty+Lj5s852HMEr93Dw3UP8MzCx/imYx/9iQBd0W7aIx0AGJbB\n7s59zCmehVNzcOyC4iwpM8WpgTPoZorWcAeVnvLMkra7a28lqsfojHRRWzidm6tvIJKK8lrDO7RH\nOqj0VPD4vEfwObJn0S/0z2Oar3pwwlopdpmwds3kzk0xZirFwOdbMQIBPEuW4p4zN9chTShbQeGQ\nrxuxGInWFmy2dMvAjMfTx0Mk79FKdrTT/cof0INBPAsWYq+pIdHYmH5RUXBOH781tMZAdl1qPXD+\nuH/LhwR3bAegYM1a/Bs3jVscAKHd3xA9eiSTgIeaa3CxgjVrx2WzlEpvBUXOoszM6yJHIW+efI+Y\nEWdV+TJuqVl3lStc3dbmL9nXfRCA04FGHJoDC4ukoWNaFi6bizKXn5SRImEkua/2Dk4FG3FrLhb5\nF/DHE69T7Ej3CsT0OHbVRrWvimpPJX88/kY6bmcRzy96Co/dzYn+U+ztOgCku+LfPvUBP1nxvczY\n8kdNWzPJG0A3Dd469T4DiQCGaWRNuovqMX5d/ydMy0BB5eG6+1lUOh+3zc2T87+V9e/85OwXmet2\nRrv4vGXbZYcSChy+EZVaNUyDfd2HiKaiLPIvuGJX/vVGkvcU0/z7PxLYne72ihw6SOXzL15xadP1\nSHU60QoKIZZefqSoaqb2thGNEPj8c8xYFN+q1bhmD2cM7+p63307kzSjx+opvvNuHGXlmTHv8fz/\n41myhMCX6TXkiqbiWZgeQkj19WUSN6Rb5b41a3FUjs+GHdETx+l7/8+ZYzMapeKZ74zLZ42EU3Pw\n3MIn2N99CE3R2Nt9iO5YDwBftm6n2lvJ7CH21B6OtgsS5bnjab5qPm/5GgCbqmFYJi/X/3GwdKnK\n/bPuYkX5ElpC6e1Dz63ZtiyLFxY/Q5W3gv9nz3/NXDOQCNAwcIoV5UsJp7KX1kX1aNbxLTXraAm1\n0R3rwWv30hhspmdwTNyu2fG7SvDavSwtXUQgGcz0AliYHOw5yqLS+Zf9d8Yu6NYHiBnxy75vpN49\n8xHHBsfY93Qd4IXFTw9rQuFUJ8l7igk3nMx8bZkm8abGqyYHyzAI7d6FEQrhWbxkVGt0JztFVal4\n5jvEvviEaCBE4U03g2WROHuWvi0fkGxtBdJJtuoHPxqTUqVmNPuPp2Xo+B98aNTXHY7iO+7CXl6B\n3tuLa+7c8/9vL7dT1TiuLU+2t2cfd7Rf4Z0Tz+fwsmHaTViWxZdtO7Jeu3CTkGs1zVdNZ7QLgISR\n4HSgidMDjaiKioKCZcH7jR9nupCTZpIPGj9hXnEdNb6qrGpsC/3zqfZV0hHppD8RQDf1dOEVzY5T\ncwIwr6SOr9t2ZZL28rLscWWf3cv3l36HmB7jeN8pXm14G8uy0r0BepICu4+/WvkSkC6xeiHvFeqs\nA6wsX8rJgTOYloGqaKwsv/yWs5ezq2Mv29t341BtPDDr7qwHphP9pzJfp/dmPyvJG0neU467ppp4\n4PzkmeG0pHrfeZPIoUMAhL7ZRdX3/wJHZeW4xZhrjspKpv3lj+juDtH/0Yf0vPE6lmVh9Pdh8/sB\nBcswSLa2jEnyLli7jv5PtgAMuY/2ePEuWXrJ9+ylZRSsWUtoz+70e5YtH9OJYBdzzZxJQFEyDwiu\nmbOu6TrR+qPpJWTz5mMvLRvDCNPLvRaWzKO+7zgATs3JrKLR94rcNeNWnJqTs6EWGgbOEEgEiRuJ\nzD7cAL2xvsyEuWAyhKqo/OeR3/HdxU/yxLxHOBNsRlNUZhbOIK4n+OOJt3BqDmJ6jP7EALfW3Mz8\nkjlAejLZC0ue5uTAGbw2Dwv8lx86My2LvngfSTOJPti6ViCrlvr6mhvpjvXSEmqjylvBHTPWX/Hf\nObtoJi8sfpqOSCeV3goqPcNbPdEW7mDr2S8BiFnw6/pXuKVmHYv9C6jxVVHsLKIv3pd5f0kO9mKf\njCR5TzG133mW5O9fRQ8G8C5dhnve5bu4LhQ7cX7Zh6Xr6SIjUyx5x5ubiJ86ia20DN/yFUC6AEtw\nZ7rrWFGUdPGWZBLF4URRVRxVY9OFXHjLehw1Nej9/bhm12ErvnR7x1hDA7FTDdjLyvGtWTsh67z9\nGzfhW70WsMY1cQO4Zs2m/MmnBwutlFC44dYRX2Ng6ycEvkr/kQ98/hmV3/8BjvKx3cRlU9191BZM\nI6rHWOifR/EYJApN1bht+s2c6D9FS7iNSCqKqqiZ9c4AJa4SEkZisNiKQqGjgHAqzMHuoxQ7C9FN\nnQX+uaiKSjAZJK7HcGoOKjzlYMG66tVZBV4KHQWX7BZ2oXAqwq+O/oFwMkzK0AerqSk4NQflnvMP\nRYZlsKHmJsrcJZkJcSkjhV27/H7wFZ4yKjwje6i6cAOUQDJIXI/zTcde9ncd5vnFT/LtuRt5v/ET\noqkYK8qXMLtoJjE9hqakS7leryR5TzH2woIRF7CwlfizujFtk2D/5XOC27cROXoEW1Ex/gc2XnEW\n+VDijWfo+u2vscx0V7He30/54w+DqqarYw22Bm1+P65Zs1Eddnyr1+Korsm6TqK1FUtP4ZxRO+Ll\nVq5Zs2HW7Mu+Fms4Qdcffpc5NoIBiu+6Z8jrRY8fI9HchKNm2mVb1sM1Vg8ow+GZvwDP/JFtuHGh\n8IH9ma/NZJJo/dExT96qorKyYnx6Rio9FTg0B+FUFE1RURUFwzRxaPZMi9dtc6GiZJZaHew+TCiV\nLhe7q3MfLyx+mmJnMQWOAkLJEArgdXgpHWE3ckP/acLJ9HUdmp2kCVWDLeUiZ3rSZ2u4nT+deIuE\nkcBtc7N5zka2tnxFR6STUpefJ+Z/K/PecwzToL7vBLqps9A/b1jV06YXTKPIWZgpJOPQHIMPNzpn\nAs3cWL2G7y5KFz+yLIv3z3zMwcFlbg/Muvu63apU+8UvfvGLXAcxXNFo8upvus55vc4R3yfX7DpS\n3V0oNhuFN91MwaqhqytNlGj9UXrffQcjFCLV002yqzPTah4OyzAIbvuS/i0fYgQDKPb0U7oVi1J5\n2wZiKQtF04gPzvz2rVxFxdPP4l224pKCKX3vv0ffn98hcmA/ybZWPEuWjlnrOLRrB8m2tvNxJxMU\nrLnyhibhgwfoef1VEi0tROuPonk8OKeNzzyFa/l5Go5Ufz8YBqpj+GvmI0cOY4TODwn5li275AFr\nvDT0n6Y51ILH5sFlc2a9Ntx75LI5mVVYi27qBFPhzIYhLpuLUCqM0+ZEIT3xy2lzUOOtoifWd676\nKnE9zjRfDeWeUuaV1JEydCo95Tww6y4KnSOrox9IBDN7dttVG4Zp4ra5mO6r4b6Zd2JTbXzUuJXO\naDeRVJRIKsqZYBPBZHoOQEyPEU5FWeg/X0ynI9LJKyfeYl/3IU4HGmkYOMPSskXYBh9ErnSf7KqN\nRf4F+Ow+gskQdtWW+d1aXbGCUvf5B5PGYDOfDnaxW1icDjRyY9Waay4rOxl5vc6rvwlpeQvA7vdT\n+d0Xch3GJZJd2Vsqprq7RnT+wCdbCO7cgREJYwSD2FBQ3W5sxef/GBStvxXf8pWYuo695PKtFyMU\nIrR7V+Y4duokieZmXLNmXfJeyzQxo1GSnR2Y0Siuujlo3qF3jLKXlYNpYqZSKDbtqpXWYieOZx1H\nTxzLWrudFXs0SmT/PlAVfKvWoDqH94dhvFiWRe+brxM5fAgUhZJ77h32zmOlj2ym9/VX0QMBPIuX\n4F0xdht7DOWzs9vY2ZGeG+C2uXl+8VPX3J1e7a3k0XmbeHD23bSGO/DZvdT3neCT5s+J63EcmoMi\nZyF/vfIH2DU7/7LvP9DNVOZ8z2DXdbGziAdn331NMYRTERr6T6MqGjE9RrGziOcWPUmNr/qSddd9\n8X50UwfSk+38rpLMhiXn6qkDfNOxjy1NW+mO9aIqGqXuEvrifbSG26grmnXVmLx2DzdUrWJeSR0f\nNH5KKBlmaenCS6q2JY1U1rFhGRiWicbli8JMZZK8xaTlml2XXuY02K3trpszovPjTem9iVWPF0vX\nQVVw1c25ZD2zVlAw9K++lt29DtnlWM/RAwG6fvdr4mfOYMai2Pyl2P1+qr7/F0PuMOasm4OZSg32\nDjhwzT0/wcgIh0FVs9ZE2/3ZFa+uVGDFTCXp/NUvSfWklz5FDh+i6ns/uGzsEyXR1JhO3ACWRf/H\nW4b9UOEor6D6R385zhFean/3oczXMT3Gif5TV639fTVum5u5xelhlC9bdxAZLHsa1+OUOIszW3E+\nUvcAHzR+QtJMcXP1DdT4Rj/M8XrDu5n12E7VyePzHrnsdVeUL2F7+zdAejjBa3NjDW7Eoipa1pj6\njvbdKIqKoiiYlkFcj+O1e/DYhr+WH9IPJU8v+PYVX68rmkmlp5LOaPrBfm3lqjEf97Ysi4gexWNz\nT+oWvSRvMWm5amdS8cx3iB6rT+8mddPNIzrfUVVFsqMdRVHSY+YPPXxN+0JrHi8ld91D/6cfg2Xh\nW7Ua54wZl7wv8OXnpHp60ltaWhZGKIhisxE9Vn/FljFAZO9uVKcTdXD8NrRzJ77lK+l77930bPCL\nWqiFt96OEYmQONuMo7rmiuPjqY6OTOKG9HItva8Pe3nuaqhbhnHRN6zMXITJymv3kjDOtzLPtX7H\nSjgVptBRQEyPoyoqswvP/2zNK6kbZs3w4bEsi47IBT1YikVHtOuS5L2/6xB7ug7iVB04bU6cmgNN\ntfH4vEeIpCKDE9PO/xzZNRuqrlDkKCSQDGFTbdw+fT1V3rGbk5AyUrzf+AnhVJgydxm3T78l8wA0\nVqKpKH888SZd0W58Dh9Pzts8aYvCSPIWk5p7ztxrrhJXcv+DKHY7qe4uXHVzrylxn1N4y3q8y1ek\ntxq9QjU2K5Xu0lNUNZ2kBlvqqmvoSTuK7aJfQ5tG7GRDZhmXZZr0vPkG+sAAvlVrcFRWUvrwty5z\npWxaQQGKpmZ2UlNsNtTBLnwzkSDR3Izq9Uzoun7X7DpcdXXET6druxfevP6yO7Tlkm7q7Ok8QFSP\nsdg/n4dm38tbp94nnIqwtHQhi0uvbdKdYRrEjcQla6WrPJV0Rbszre3RLk+L63EO9dQDsLx8SdbS\nr3O7n50JNqGbBi7NyTRvduJuDrZkdgxz290kjSQzCqaxvuZGZl8htvtn3s2bp9JFeBaVzufRuZvG\nfK/ubW27Msv4IqkIJwfOjHny3tG+m65oNwDhZJitLV/y5PzNY/oZY0WSt5iyVIdjTGqSn3Olme6W\naWJGIvhuWEfsxHFsxcXoAwOovgK8S5fhucps8IIbbyJ24jjJri5QINnaSuevfokeDmMr8WMMDGDG\nYwR3bCdyYD9VP/jhsNY424pLKH1kMwOffgKqSsl9D6B5PJjxOB3/63+S6k7/kSq+406Kbr2dVG8P\nqa4uHDU12IrSy9ksyyK8bw+p7m5cdXOydvu6FukiOc+RbG1BsdvHfYnatXjn9Iec6E8XO9rXdZAX\nFj/DT1Z8L6ts6Eg1B1t4/eS7JIwEMwqm88S8RzLLre6pvQ2bqtET76OucCYryrN/XsKpKL+r/xOB\nZJANNTdxc82VJzOmTJ3fHXstUyXuSO8xvrvoyayNQhaVLuBo73FMDJyaA+WiruFzO5ABmeIvS8sW\ncWLgFHEjwYrLbCYyu6iWv1n5F3zTsZf2aBc72ndzc/UNV9yg5FoEktkFc86VtB1LqcHx/czxRWPs\nk4kkbyFGQR8YoPO3L6P39WErKaHs6e9gxWPYBrcSVe1XH4/TPF6q/uLH6THz37yMPtCP4nCgkK7O\nZsbjqB4PiqZhJpPET58eMnmnenvpef1P6H19uBcspOavfpo1zh09Vp9J3ACBr77EXllFz6uvYBlG\neie1517AWVND54db6H3vQwCCu3ZS8dQzw6odMBRFVcelJOxQu1kNh2VZ7O06wDcd+9JDLYqGQzNo\nCp2l1F0yqtUFHzVtzXS9nw21sL/7cGY/brtm596Zd1zx3P/rm3+hN94PQHPoNVyai1WV55ez9ccH\nUBSFYmcR3dEeumM9mJZJIBGiO9bLW6ffZ/OcjZnx24PdRyh0nn8QPdB9OOvzZxZOx6baMhPVXJoz\nU0TlaO8xgMsm8MM99XzRmq6b0NB/ipSpc+eMDSO6T0NZUDI3Uyb13PFodES6+KptB1jpkrE1vipW\nVSyjvu9EZu/z0c5tGE+SvMV1Kd7VRfdr72DpKQpvWn/ZmePDMfD51sz+4Hp/P5E93wy5zj526iRm\nIoF7ztysSVqKqmIvKcHSzz3pK9j8frzLVxI/dRIjcr6Qhe0Ks+LP6fvz2yQ70hOSIocO4qipoXDd\nTVnvMcLpcXnV40F1uwnt3JEZjzYTCcK7d+F8ZDPBo/XnT7IsYg0nRp28x1pfvJ/XGt6hL97PjILp\n3FN7G33xAcrcpZfdzvJKdnXs5bOWr4gbcZJGClVRsalaJoldqyO9x+mIdmFZJo7BLuyUefUWnWmZ\nNAaaM4kb0g8Y29p3ZJL3h42fZibUrataw5rKFaiKxsDgmmlQONbXwDfefZmNSZy27OV558qqnlPm\nLuWZBY9xpPcYHrub0wNNxCKxzOvNoZbLJu+WcDuWBQPJAAk9yadnv2R52ZKspV6jsdA/D6e2mbOh\nNqq9FcwrGdkE1gvF9TivnHiTmB4bjL2NHy1/gQpPOS8tfY72wbXsYxX7eJDkLa47lmFw6j/+O5Gz\nrVhYxM6cZtpP/jprCdmwr5VKDXl8ocwENMBRUUHliy+h2O0YwQCq24PqdFK4fgP9H34AgK2wiOK7\n7sa6ZQO9f34bIxzGt2p1Vte1peuE9+4h3tyEGYtiLy1Lr6G+wIVroy3TJLTnG6xUEjMex4zHKH1k\nM9Ejh9Jj9IOtS2Vw/bWzvAwamzPnT6YCPud80vwFfYMJ7tRAI8f7TuKxu1AVjc1zNl51wlc0FeWN\nk+9xqLce0zLRFA1FSSdsn92XGQO9FtvadvJV6w5SRopgMkSJq5hSt/+SwiKWZbGl6TMO99bjc/jY\nNPs+vmrbwZlAU1YZVQWFUlf6/0FntDtrJvyujj2sqljGptn38etjr6AqGoUOH5qi0hcfyLzvnhm3\n82rDWwSTIWp81ZdtXdb4qjKT2GJ6nLbI+SJO58qeJo0kKVPPjOFXeyvZ1bGHxOASMtMy+KjpU55Z\n+Ng137+LzS6aOeqNYiC9zv1c4ob0Mrj+eAC3zz3iXc9yRZK3mFCRQweJN57BUVmF74Z1WV2RZiIx\nIeuQ9VCIcMNJjHh61yMzEiXZ0XHZ5G3EYukZ2qWll514VnjjTcRPncRMJlHsdgpuvPyMeDOVzCRu\ngGRXF9Hjxwjv/oZEawuq00nZ409RuO4mnNNrMYIBnLUz00vECqDqxZcue92eN18nfPAAek83KCr2\n8jJU1/kJYIrdnlWBzQgFSba1YSvxYxkGlmnS985b6KEQVjKBze/HWV1D0YbbAJj26GYi4fjgpL85\nFNxw4zDu8MS6cDerqB5FQQFcmIN7VV8teX/e8jUt4VZsikZEj2e6zL12L167O9NavhbH+9Jj5x67\nG7tmZ07RbDbPfTBTavSco30nMtuG9sf7ebXh7UxycalO4mY6ITo0e2Z9t3WZjWRMy2RR6Xw2zb6f\nL1u/HvyukjWxq9xTyo+Xf4+kmcqazHYlaypW8E3HPkLJMHOLZ7O6YjmHe+r5oPETDMtgkX8Bm+ru\nY3XFcg52H+FYfwN21YbP7qUv3k97pJMqz9hWwhutYlcxPruP8GD1Oq/di991adniyUySt5gw4YMH\n6H3rjcyxEYtRfPsd6KEg3b/7DcmuLuzlFVQ8851x3V/bSiazliyd76rOlmxvo/O3v8aMxdB8Piqe\ne/6ScpzOGbVU//gvSXZ24qioyHoAiBw5zMAnW0BRKL77XhS7PatlHm88TaK1BUg/uPR/+B7un/w1\nzpoaqLl65TDLNIkeq8dKJc99AyuRxNJslD3xFEZgAFfdnKyYVU+6hW8mEiiahj7QTyqRSNd2tyzs\n/jKqfviTzEOVzeul/PEnrxrLlUQOHyLRchbn9BnjtiHL6orl/PlMJ2BhU2041fPzDIaTeM+tsfbZ\nPYCFQ3NgU22oKFR6Klhfc+0PLEXOwszkMbtqY27x7EsSdzqG7G08zz2QWICJiV2x4XeX4FDttITa\nKHYWUeWtYHHpwsw49MryZZndtm6puYECh5fuWC+zCmdcUihFUZRhJe6UkeLfDvwys2Xo8f6T7Ok8\nwGct2xhIBLCwONB9mEX++cwrqWPj7HvoSwygmykCiRBRPcbLR//AIv8CXqp4YkT3bjw5NQfPLHyU\n7bxac/oAACAASURBVO27sSyLm6rXDquU62QiyVtMmPiZ0xcdn4Lb7yDw2db0TGvSVdQGPvuUsm9d\nuVDDaGkeD67KCuK9/WBZaD7fZdc+B774HDOWbv0Y4TDBbV9RtvnRS95nKyrOzM4+Rw8G6X3r9cwy\nrd43X6f4/gcZ2PIhVipFwZq1lxRusQwDS9fpefN1YieOYSvxU/74U1dcl62oKrbCQszk+TXIiqbh\nqK7G5vWh9/ZiBINwYfK2Oyh/8hn6P3ofK6VjJhNYyXTyVxSFVG/P2JV93bObvvfeTX/9zS7MRBzN\n4yX0/7P3nsF13Ve25+/EmxNyIkCCBHOWKIqURCrLysGWJVuynNV2B7+Zrqnu6fdlumq+TnXVm5pX\n3eNpp7blbMnKmcrMOZMgCBA53pxOng/n8hKXAElQpJWMVaUqHuBkXN3933uvvdbe3Ug+P9Hb7rgq\ni7TlNUuo8saYKMaJeaK82fsuo/kxIp7IJQlTiWKSwdwwI7kxPLJK1BPlkQX30RFrR7P0GQW4i+Gu\ntlvJGwWSeoqOaDuCIPDBwDYWxxZWzA8vjM1n2+AuiiUP7HX1q7Ecm72jBxAEkZDqL9/L5CBzf/td\nrKtfgyAIFS5emqUzkB0iXkwSUoIVwduwzSlKahfCUG6kwhZVt3TOpPsYK0xglZXX9DLzuz5Qx7eW\nPs6RieO82/9R+Z6PxU8wkB5G5eJqg58kqrwx7p13x6d9Gx8bs8F7Fp8Y1Lo6chXbrnOZXSxU7OcU\ni0wHM50mf+Swa6u5avVlm4OchRQMMufxr9Lz+2fBcYjeetvM7CUvI6hZ2Uw5cIMbmL3NLcz5p3/B\nsUxERcXKZMju24uZSiGIIpFNm8ns2UX+2FEAjPFxJl5+kYZvfeeC16n96teYePkFDK8P0evFO38B\nvnntDP/ip+U58+r77ie45tyMu3fuXBqf/iHglt0Tb75e7nd7L2Ce8nFQ6DxZsZ3dvw9jeLgsymKM\nj5Xv40oxuUf77WVfp2AW8UqeSy5E3jjzDgWzQMwbxbBNVtUuL5fZLxS480ae13q20JcdoC00h+9W\nT59R2o7NW73vMZgbQhBE+rNDHBg7jAPsGt7PN5c+XiZERT2Rso1nSAmWbTw3NK2jL9PP6z3voFsG\nK2uWoooKg9nh8vNOJ4Ty4unX2DW8F8M2OTB2GEWUWVazhF8e/R3d6V4iaognlzxKQ6AewzaZKMTJ\nGFne6f2AvFlgdd0Kbm65gYDiR5XUSQQ7gZZQIwfHj5ArBe+zLYazqPZVsXKSOttZfJbVyj6PmA3e\ns/jEEFq/AatQQOvpRqlvIHr7ne7Pr72OwqlTOKaJIEkEr506x2plswz/9P8rk68KpzqpffSxyn3y\nebK7d+E4NqFr1l3Ugax6/XVY8xaD41xwERDZfDNafx9WPo8UDBK5YeZjL0ptHWpdHcWeHuxCHikc\nQfR6EUQRQXSDghQK0fj0D9EGB5AjEZTqmrLv91nYuRxmKokxOoZSVzclU1UbGmj87tMVPxv/87MV\nUq65Q4cqgvdkVN17P1YuR/FUJ2pz8xWVyM+HUlNbEcAFSa5QU9NHRnBs+2Mvwi4G3wxLoNlSuVqV\nFPc/UcZ2bLb0fUBn4jRV3ij3zLujgsD0/OnX2DNyAMs26Un1knUyPNnx2JRzdyV7yuYfjmNzZPw4\niihj2AaKqHAsfpIbm9czmB1m+/BuRERuaFpfkZEHlQBLqhaxOLYQ0zb506mX+M2JPwGuaUdrqIWB\n7CCNgQaWVJ+bAjg2cRLdMnBwyVhbB3dxJt3PoXF3YZjVs/z+5PN8d/mT/Pr4n4gX44wV4oTVIB5J\nZcfQbuYEm5kfncuD8+/m1Z63MG2LDY3Xcn3jOg6NH2c0P4aDjV8O0Bisx7It3uv/iL7sII3+eq6t\nW8Pu0X0ArKlbSWOojrHiOfLkLK4Ms8F7Fp8YBFEkNo2Up3deO43f/xv0oSHUhsZpy8TFnu4K1nT+\n+DFsQ0dU3EDomCajv/x5ufyeO3SQxu//4KIEOEEQLppNqw2NNP3dP2AmEshV1ZdFphMVhcjmWyic\n/gmCxwuSxMQLz1H/1Lcr9/N6KzTbA8tXkt29C7tUyva0tjL47/8TxzDc+esnvoGnueWi15bC4fO2\nL6yrLioK9U98A62vF2NiAse6srGoyYhsvhl9ZIjcoUNIgQD+ZcvRBwfKfAPPnDl/kcB9OVhZs4wt\nfe8DIIsyi6sWsn/sMHtGXPvRtJ7mtZ63eXThOUW7/sxAuWQM0DlxmvzcPP7zlNNsx56yrdsGAu6o\nWE+6l7V1K/j9yT+XZ8D7s4M8veKbU/S6BUFgIDfEmfQ55v9HgzvYLe1DFESyRo6wGqI52MTdc2/D\nK3txoDzm1pfpJ2+6vf2zRLeJQpx9oweJF+PYto1uaYwXNAJKgLAaLFuRrmtYU55JP4vHFj3EhwPb\n0S2DdQ1riHoifDiwnV0jbrAezo2wrn4NP1j5bRycq+KLPotKzAbvWXwmoNTUXtRNa0pA8vsR5HNf\ncLnjRyn29yEoKoIgYCYSGKMjVywGInp9qI0uwcjK53BMC/m8e7kQzESiIvvXh4YusrcLtb6ehu89\nTbH7NHKsyq0klEhutqaR3rb1ktlx5MZNmBPjFM+cQa1vIHb7XRfdP7N7J/FXXwFA9Hio/9Z3Ueuu\nnB3smCb6wEDZVS215S1qHv4y+RPHEH1+IjdtvuJrXCnWNaxxHbAKCdrCrdT6qzlRUlc7i6RWqezV\nEmxmMDuM7dhYjk1Gy3Fs4iTXNKyu2K89OpemYCODWffvPifUwmh+FNtx7Td9speJYrJCNz1n5Ejr\naWp8bvbtOA4DWVef37Rt0loGy7HxyZ5yT75oamT1HLplYDs2z3e9xt1zb+PnR3+D5ViICHhlL5Zj\nuwHdcRdPum2we2Q/KS1dbi84juO6m4kq8y/iBhb1RLivvfJzNV6IV2yPFSam+H1/VmE7NpZtlVXv\nPg/4VIP3v/zLv/Dee+9RXV3Niy+++Gneyiw+4/C2thG95TYyO7YheL1U3/9g+Qsn/uorZHZux4zH\nEVQVOVaFKMtI4Stb7Tu2TeqD9zGGh7BNg2J3t2tMsnrNjLTFPa2trs55qVTsaZs7o+sq1TXlHnzu\nwP6K3wkzUGwTVZXaRx+f0bXAJZOdha1p5A4dQL3tyok8ViqFrZ0LTLauI4XD1Dx09eZ+rwbaI3Mr\nCF0Lou3sGtmHU8qcF54nBvLowgfIGXkOjh9BFiWqfFHe7vuA+bF5FRnme/0fMZ6fwCt7uW3OJnyy\nj2dPvYTtWAiCyMqaZYTUADkjT8EsokoKTYEGwqob8BzH4fmuVzmR6CStZygYRazSPWmWxsLYfNJ6\nBqsUjM/6Zie1JMtrlnBN3WqOxU+giG5LYE6wCc3SiBcTSIJM0Swykh/HsAxM20QSZPyqD0mQmBtp\nnfGsc6KYZDQ/To23islmtXPDV19F7y+B06keXuh6Dc3SWFa9mHvm3fG56M9/qsH7y1/+Mt/4xjf4\n53/+50/zNmbxOUHkxpuI3HhTxc/KXtui6OqAp1NIfj/V9z1wxUzm5LtbSH/0IY5tY4wMI4cjiIEA\n2f37CKxajbf1nFiErWlo/X1I4XB5NMvT3ELtY18jd/ggUjBM5KZNl//MN9+C1t+HmUohx2JEN998\nWcebqRRmIo5SV4854RLgHE0jvOEGQte5I1Cir7LcO3lO/EogV1chx2KYJdEYORy+pFf5p4nh3Cjb\nhnYhIHB32+0ktAQxb5Tl1ZWCKrIo88D8LzFecJn5sixhmhZ5o1AO3sfjneXSOzZsHdrF0yue4qkl\nX3XnngP1NATqeL1nC6qkYNgGtuMwN9zKeGGCKm+UpJbmRKKToqmRNwoYtklJQoewGmZl7XLSWpqu\nVDeWYxMskcYWRF3C3W2tmxgtjFM0C8iiwo3N15M2MmT1HIZtYNgmppF1ZWBllagnglQKWkurLq6i\np1sGiijTlxngD53PY9omsihzXf1aipZOY6CO1XV/mdHAq42XT79Zrn4cmTjOgmg7i6uuTMP/k8Cn\nGryvvfZa+vv7P81bmMXnHZO8ts/aakZu3ER2/z7yx44SveXWj6WcBqD397n/KPUIbV0vu3I55rk5\ncSubZfjnP3GDlCBQdfe9hK65FgDfgo6PZeZhaxpWPo8cjdH0dz/CymaRgsEZeXHbmkb2wD6M0TFy\nB/e7euV+vzvfbro90InXXiHfeRJzfAwxGEIKhbAyGXwLOspB/UohKir13/gW6e1bwXEIrd/wiYjw\nfBzkjQK/O/FceVSrPzvI91c8dUHGeY2viuZgE12pbmRHYk6gpWJUK6tnK/Y/u10fqKN+Ejt8ohhH\nERWingiGZbB9eA+HJ47hl/3c2XYr4JZ0HcApa605pLQ0lm1x9zyXQzKUG+F4vJOQEqAtPIctve+j\nSAqPLXyQnJGn1l9DWA2R1jLotlFmjzuOg+mAIircPudmdo/uwy97L+hsZtkWz3W9TFeyG7/sJ+IJ\no5l6+d4SWopHOu67zLf/6cFxHDRLr/hZcVIb47OM2Z73LD7XON9r27d4Mcl33i4HKX1wkMa//fuP\nNbusNrdQPHMGQZIQ/YGydad3XnuFFnru0IFydonjkHr/3XLw/jgodp9m7A+/w9Y01KYm6p946qJV\nBCubJXfUHaHzL17KyH/9DH14GGNiHBwHpboGO5vFzKTL8+h2Lkv+6GE3y06nCSxbTvUDD021J71M\nOLYNgnBO5CUSoequu6/onB8XtmPzSvebHIt3ElZDPDT/7orAORkJLVkO3OD2nlNamjr/9COEjnMu\nlNo4eGVvRal1QaydjwZ3ls95vhzqWcyPzKMvMwC47mFe2V3c5M08J5OnWFe/hu1DuyuOERAQRani\nM62IMmvqViCLMj89/AwFs0Baz/Ci9Rq1vlpub9vE3HArDg5+yUdqkra6g0PEG2Hv6H4yeoaMnuE3\nx//E95Z/g6BaOZd9YPwIXcnu8j0O5YbLgjIe2YPpmCSKSWKfE7UyQRC4tmE1O0rvOOKJsDD68TXT\nP0l8roJ3be2FWbOzOIe/tvdU++CXMG69AceyyJ/ppedUJ8huhuqkk1QFJOTAVHGIS72nmkcfZDji\np9A/QHD+fALz23EMg8C8uRUZsFAVIiOf2/YEfVf0Nzjx87cRLRNRlrBHR+DEIWpvv3Xafc1sjpP/\n8TP0hKtdbR49iD0+hixLWKKIrWlI2AiqitpQj224ixpBVUqja+59S4UsdY3TVyhm+ixDr77G6JZ3\nERWFOY89SnTVyst99KuKnf37OZHqRJQga2XYMvQeP9ow/cx8ICITORMkp7uaAyFPkAXNzVNMPM6i\nJ9HP6XQPRauI5Ej05noRAyY1AdcIpZYQ/1j1PY6OnSTkCbKyfsm0C8j7am+moTrGgeGjHB/romhq\nyKXPkt+nsKh2LjXRKJliludPvIFm6QgISKLI6taF1MSC/ObQ8xwcdg1kltZ2YKBjYZEvBdW8leNX\nx/9AY6gOSRJBqJRVdXBY27Sco2Mnyte2MNHULPNqK72+lYxQ3sdlz+sokoxhWxTNIieSnfTl+tk0\ndz33LJz6mb3UZ2koM8qvD/6ZZCHFiobFfGXpvYh/4YmER2u/xNq2JWT1HB1V8/Crny1/+QvhcxW8\nx8ZmZwQvhdra0F/xe5IwfFEsQSwztJWaGuI5CyFf+U5m+p7ka28gVEqi86WfFeL5in3s9sXIzXso\nnjmDqKoEbrnziv4GxXwRc1JZPp3MIV7gfLkjh8mPnfNfTh7vdLNnx0EIBsEwsGzX5KT68SfQuk5h\n6xpSMMTESy9A6TrSvI5p73mm70nr62P41dKMumbQ9YtnaPnfmsujfOfD1jSye/fgmAaB1WuQQ1ef\nlTw0MVHxHieyqYs+y8PzHmD70G4EBG5ouo50QgOmL6EeGjpJqlhioQsCtu2QSek4FZ8ziUX+JZxK\ndvPbgZeJeaKM5scYLYzTFp7DpuYNiIKIVRA5NnIawzZIFjPopklDoI6e8UHe6vqQoqmhiiqNgXri\nWhLLtrixeT0hq4q93cfZ23+4fMW9A4eRRBnDNN3PAALJYgZwMAwLAYGIJ0Jaz+KKrwr4ZC+3N97M\n6fHesta3JMhImnfK+2pV21DxkDfz2I6NIqpIiKiyQNbI4dhgmhZbTm2lw7+wgsA3k8/Sr478mZG8\nO+65s/cAMbGG1ef5m/8lEKaKsFRFLmWS49P9/pzpYvlzFbxnMYvpkHj7TXL79yGFQlQ/+DB1X3+S\nzM4diB4PkU03XxW5z4uJiYiKSt2T38TKZNxsVlGIv/YKhVOdKDW1VN/3wBTBGG1wgInnn8PKZAiu\nvYZYSbAGILJpMxMv/BnHspEjEYJrz7k+FXt6SL3/DiAQveXWKRKrUiBA7M4vkdzyFpIgUPvlR/G0\nzEGORBFkGbXkCpY7dBBBFLELeULrNxDeeMMVvR+rULmgcUzTXUBNCt62plE41YmgKKS3fojW53IK\nsvv20vD9HyD5rm7GsyjWwc7hvWUy0qWCQL2/lgfnX7zEP5AdYs/IAfozgwQUPzkjjwDEPJEyYWwy\nOhNdPHvKlYhNaRkkQSSoBhjOjeCXfVzXsJZTyW7AQREVarwxZFFmSayD9we2USw5dOm2TtHS+M6y\nr3MqeZqMnmPX8D7qfJVlfVmUubPtFvaOHsR2HGRBJK4l8cpe1zFNlKj1VZPQUmU99cZAPYqk8NWF\nD/Fe/0cYtsH1jddOO5sd8YT59rKv05vpZ6KY4I2eLW7QdhwkUb4iExc4pzN/bjt3gT1n8akG73/8\nx39k586dJJNJNm/ezI9+9CO+/OXP1hjJLD7byB87SnrrR4CrsDb+7B9p+uHfVzDBrwSO45B49WXS\nO3cADrG77iGyYeOU/QRRLPel0zu2lcevzESC+KsvU/3QI6Q//AAzlcS/dBmJN14r98nT27biaZmD\nf7HbFw0sX4no8ZHY8iaiqqIPDSGHwljZLGO/+3VZwGX0N8/Q9A//C9HNt5D66H1E1UPNI1/BO6+d\n4KrVU+7RmBhn4qUX3Bn44WHEQABB9ZA7uJ/ITZuviJ3vbZuLWldXFskJLFuO5D8XzGxdZ+QXP3VV\n1SwLK5MuEwnNVAp9oP9jEfsuhmpfjG8t+xqnU2eIesIV42A7hvawc3gvqqRy99zbaA1fXPgGIKml\n+N2J5zBsA83S0Syden8diiKxNDp9T/tUsqf8b9M2MXAIlvS9z5p9VHvPtSuyRg4bh+3De0jrGRzH\nqVh87hs9xK6RfQiCwInEKW5v3czC2AJOlmbT1zdey5q6laypW4lhGXSnz/DBwHYOjx+naBaJeCKs\nrV/N4YnjJWa5QMbIktRS1Pqr+crCBy75HoJqgKXVi/jzqVcIqgG8sodCiRE/lh8nqARYUbN0WgOW\nS2Fl7TK2Du4AXJ/xxbHPPuv708KnGrz/7d/+7dO8/Cy+ADDTqYptK52+wJ4fD4UTx0lt34ZZIn+N\nPfNfiKp6UUKaGa/00zYTceIvv0DukOu9nNm3BzuTRZAlpEAQRHGK53b81ZcwU+6zjf/xd9Q/9W30\nkWHsYhFKFQBb07BSKZc8ZVqYxRSjv/4VcnUNobXXTGGNj//x9+ijo9iGgZlOIcsSoseLY9nY+Rxc\nQfA+K+6SP3EMUVHxLVpc8ftiTzf6yIi7IQjuc9i2+yyCUCbSWdksyXe3YBcKBNdeg2/+go99T+CK\niaytq+y992cGebf/Q8AlXT136mX+Yc33Lznbu3fkIBPFODgODq5t6KLYAhY0zGFpYNm0x1R5oziO\nQ8EqAkJ5FAvOzUGvqVtJSktzKtlNQksRUcM4JRKcZmo4OHgkD3W+anYM70EvsaNN22QwN8xD8+9h\nND+GLMpU+6rK51ckhYWxBbzS/RbV3ih2KbvfPrgTyzZxgKDiwyt5GMmNXbYKWlgN4jgONpDVc67t\nqSgzUUzw4aCrtvb95U+xIDZzvfybmq+nMVBPSkvTHmn73BDfPg3Mls1n8bmGr2MhqffeLYuBBFZc\nmCTlOI7rnz04gLC0AzouXka1slnyx45iZdLlcTHHtsns2XXR4O1btIjMnl3lY3yLlpDdt8c93jQx\nx8fdknXRwtZ0vK2t+DrOzdXahUI5cANYRY3hn/6nO9YTn0CORBAUFTkaBVkm9f67gJvlO6aJrWnE\nx0ZR6uorWPFGKdMXZNm1JzUt8IDa2IhSe+WKaqLHQ3Dl1IwfqPBCF0QRpaYWubYWLIvITZvLkrij\nv30GrbcXM50m9dEH1Hz5UaKXUGIzLIOklibsCc3IBeys7OdZFK0ihm1e9Nhj8ZNsG9pFzshj2hai\nIKKIMqIosqS2g5ePvIkAbGy6riKAXlO/ii19H5DRcyiiTK2vhsVVHbRH2spa5KIgcmvrJm6ZcxP/\nY9//S9bIES8msBwbv+zHL/sAh97MAJqllWRXBRzLoMFf5zqKXYBFD2A5Nja2mx07eQpmAUVSMSyd\ntJ4lZxT4zYk/Ue2t4uEF99ISurQd7YcD2zkycZyxwkRplM3GL3uJF5PlfXRL59lTL/JP6350yfNN\nxmTv8VlcGLPBexafayhV1TR89/vkjx9DCoUILL9w8M5s30riLZdUpR09TPi2HMFr103byzbTaYZ/\n8mOsdAqnWHR73pKEFAhUlIOng699PvVPPkWh6xRKTS3BVavRhwYoZDJuH9hxEENhBBwcy6buyW+6\ngbgE0e9Hra8vZ6pOsYDjDyBIEnI0huT3E1i1mvCGjTh2aVHhOOXxOEojTMbEeEXw9i9aTO7wIQRB\nQKlvILx+A3I4TGDlqiseEbsQ7GIBQfXgbW0jfP0G0ju2I8gyNY98hcCyysWTY5pog4OYiXhZ/zzx\n6iv4F3SgNk4fUJJait8cf5a0nsYn+/jqwoemddmajLZQC0E1WJ69XhBtv2TQ70p2I4sSXslLzsnj\n4GA5Fu/3b+XgxBFUwVW+O5Pp5+kVT5V7v4fGjzJacKs2hm1QsAosrV6EV/ZQNIsV9p6CIPDg/Lv5\n+dHfYtluQMybebJ6ljp/DaIgYtimWyFwHFRJoWi6piNr61aWx8wA0nqGollEEiQcx2YsH0cUBCRR\nxsEhrAbLZXvLsZgoxBGAV3re4ukVT130XRyZOMFHgzuIF5Nl/XbLsRjOjyEgcJYIB2DaFrplsGN4\nD+K4zTxve9kNbaZIaWkmignq/DXT8gr+WjEbvGfxuYdSXUPkhpsuuV+xp2fSlkPizddJvPk6UihE\n7aOPVQSI/LGjWNksiBJKfYOrUx4K4Wlqouruey55Le/ceRX2mtUPPEzizdfRhwbd4F0iZ8mRCGp9\nfcWxgiBQ9/VvkProAxxdx0ylyl7ogizjbZ9P1ZfO3UNw9Rqy+/cherwggKCoiKpaEbjde3gItbkZ\nO5vFv3Q5asPlfYleDmxNK2fRUjBI3eNfJ3bHXURvuQ1EcdoFkyDLqHV1GMNDFT8zJiYuGLx3DO0h\nrbutkoJZ4IOBbRUmItPBr/h5asljHIufRJVUVlRP36+ejCqvm017ZQ9Fq4jt2O68tSASLySp8VYh\nixI5I0eyNB/elxlk6+Dusjyu4zhk9SzPnXoJwzbwy34eX/RI2UUsa+Q4OH6UgOwnLaQBqTxL7mbL\nCoooo0oeREFAtwy2De1EEAQ6k118Y8lXEQWRvaMHeevMezjY5Iw8jgOSKOIAETVMwSy4n0FBxHGs\nssBKUksTmUHpPF6Ml5/HxsGyLQREwHFjtlMSTRIlbm/bzJ+7XqY7dQZREtiib+XeeXeypm7FjIik\nZ9J9/LHzRUzbwCt5eXzxIxViOH/NmA3es/jCwLEs4q++TLH7NHbBndeVo1GqH3wEORpFHxrEGB1B\nUFXwerAMCykUwkylmHjxBRq+9zT5I4fdYydZagqShK+jg6a//YeP7yHu91Pz4MMA5A4fIrNzO4LH\nS9WdX5p+/2CwLG5iTIwz8stfYGUyrjXp5lsq9q2+/0GCa6/F0TW0gQHsQp7AipVTPMoFSSJ83fUf\n6/4vBce2ye7dg5VO4V+ylMKpTrRe1wHLymaJv/YqDd/+7iUz/PonnqJ/9P/CTCQQA36kYBBPy5wL\n7j+dc9elYDs2Q7lhwmqIBdF5SGKlal1SS/Fu30dolsbaulV0xNpZ37CWrJHlTLqfiCfCQGYQRZIJ\nKgHi2rlScUAJEPGEefPMu+wdPcBEIYHlWOVcVBU9ZPQMIOA4DtuGdvHAfPcz8GLXa/Rm+rEdGxsH\nHAdZlAmqARRJIagEEAUJr6SiWTqG5UqcKqLMcG6EjJ4jpAbY0vsBBTNP3ixSMAsElSBCKSe2sVlR\ns4TrGq7hV8f/wEQhztlPumGbJLU0/3nol9wz745pM+Stg7voTJxGM3UCih9d0xEFwWW2ixICAjFf\nlPmReWxu2UhTsIF3+j7EdhzGc3FMy+T5rlcYLYzzpbnTaxdMxvah3ZglQZmiVWT38D7ubb/zEkf9\ndWA2eM/iC4P0tq1k9+11e8bJBKLPh61pTPz5T3ha27CyWUSvD9vQkYNBHGOSxGk+x8Tzz5E77JLK\nxGAI38KFFDo7kXx+V33sKolFBJavILB85rrPSnUNTX/7D5jJJHIkMq3EqKe5GXDV32aKyZaqV4r4\nyy+S3e/aQaZ3bMe3uDKbnWxQcjFIoRBz/vm/k972EbamEVy9pqKlcD7OjlrlzTyKqLKx6eLSrrZj\n82znS3SlXJWwlmATjy96pCKA/+HkC+XssjczwDeXPkadv5Y7284tml46/QZHJlxhlLnRFoYz46ii\nygPtd+M4DntHDwBuP9sBJEFCFiWKVgGjJJSjSmrZnhNgtFTGFgWROl8NkuAGw9ZICw/Pvxev7OHI\nxHH2jh4kWUwRLyZdkxFRQhUV/vPQf9EcbKRgFEhoaSzHwnZsskaWqCeCbpssq1rMPe23E1QCBGU/\nCSHp5t0OpbaAykQxzvNdr/DDVZWCNn/sfIGPBnaUt1fXLuem0PUci5+kO9WL5Vj4ZB8eSeWGUX9f\n6wAAIABJREFU5uvKvfNqb4z+7BCmfdZARebA2GFub92ELF48BJ3/+0vtPxln0n10JbuJeqOsrl3+\nuTAbuRzMBu9ZfGFgJkrlvFK/9GwP2EylEONxEASkcBgJCHUsINXTV87Qg2vWkvrgfRzHxkomsUeG\nESWJ5h/9rzO2AJ0pbMMg/dEHmIkE/sVL8C9ZesljRFW9Kjad4Jq5jP72GfThYdS6Omq/9uQVP2P+\nxPHyvx3TRAr4kfx+rHweBIHw9RtmfC7R4yF686WzMoBqXxXfW/EkE4UEUe/0s9aTkSimyoEbXA3z\n4fwozcFGwCW/nQ3cALZjMZofp+68Uu197Xdybf0qulO9bB3ZQbjkwPXh4A4WxNoRBankHiYgizJR\nTxhRkMjoGQRBxHFsTNtkSdWi8jnnhudwPH7SfQeCyILoPMJqiOsa15b72cuqF7OsejH/fuCnRD0R\nskYO3dLRLYOCWaQ/O4hf9rskMsdBLOXcMW+Mxxc9TGPAbdGktDSjhXFEQcR2bFTJdR6LF91grlsm\ntmNXBLwDY0cq3kHGyHFr6yY2tWzk0Pgx9ozsRxIlFkTmUe09R9r7csf9/KnzRQqpPF7RiyopeCS1\n4tyGbbJv9CCapbG8ekmZZb6peSNDuRFyRo6YN8aGpnUX/fueRW+6n9+d+DMuFx6SxSS3tl6+MdBn\nGbPBexZ/MTim+RcjQk0H36LFZA/sR/R6sbKZsjtWYMUqlLpaiqe7yvtWXbcO/+33UDjdhRQI4Fu4\niOzuXefGsQB9dITkO2+Xy91XC/FXXiJ30M3McocPUfe1J8ozzrnDB8kdOYIciRC95ba/iJFH8t0t\n6MPDAOijox/rGY1Egonnn8NMxPEvXoIci6GXFkIA3jlthDfcgNbXh1JVhdrQeFWfYTJ8so+W0Mxm\nij2SioBY/lIH8Ern3rEiKTQE6hnOuWRBWZRpDJwrH1u2xZa+D+jLDNAYqJ8yypTRMygloZQ3zrxD\nQPYhizJe2Ythm6XusoMiKcQ8URqD5xZk98y7g2pvjISW4mT8VHmR0ZXq5rvLnyxn6gPZIQpmEa+k\n4pM9DOVGsCdl8A4OPtlbEqcR8Egqdb7qcuAGl0jnl32kdVc4RhZlCqZWNiwxbIOxwgT1/lp2DO3h\nROIUhmVMoqKBIsh0Jk4T8YSYH2kjb+TZM3qAd/o/ZOvQTm5q3sjGpnXEvFG+t+IbbB3fxvvdO/FI\nHu5rv6sieD/b+SI9abfNsm/0EN9Z9gRBNUCtv5q/WfktckaOkBKc0uK4ELpSPRV/41PJ7tngPYtZ\nXApWocDY737tfnHX1FD7+BMosY/n7HU58C9cRN3Xv0Gxu8slhDluGTawYiWCICD5A2iDAyg1tVia\nRvbQQbJ7dmNl0vgWdFD94CMM//THboYeCCJ6PFip1KUvXIKVzTL2h9+hDw3gmdNKzVcem1Y1TDvT\nU7Fd7D2Db0EHha5TjD/37LnzpdPUftX15XZMk/irL1M4eQIxEMS/fDl2Oo3a1Exw9Zpz5x7oJ/7y\ni9jFIqH11xNePzXjPbs4OQvnvO2ZIP7i82h97pdtZvcuIps2Y2UymKkUoWuuLVcT5KXTzz9fbWT0\nLGk9Q62v+qIqX0E1wO1tm3m7930cHDY1b6gY7QJ4tOOBkqmIxura5VT7zn12tw7tKpfExwrjLK1e\njE/xkjFdJbCz9qGrapexpKoD07bIGTl+e+I5+rODmLYJCBiWSWuopcIzWxJELMemPzPIeDFOWA0i\nCiJpPUO8mKAhUM8fTj7P1qFdmLaJgECdv5aQEiIzycUs5o1yTd0q3ux9FxGBoOqKpkyGKqn4FR+q\npGI7NmElxJmsq3gnIgACH/RvZ0n1wvJMfEDxYdhuAA8pASaKCX565Bl0S0cRFURBdMlwQJU3xgcD\n21hZu5SgEqAr2c2rne+Q1wvU+WtpmrQg0iydnnQvtuOUCX/bh3Zze5s7IqiI8mXPoFd5Yxfd/iJg\nNnjP4qoj/eH7ZelLY3yc5Juvl4PQXxq+9nZ87dP3ff1LluJpa2P4P39MKpelMDyMIMvI0RiFU514\n582j/lvfZez3vy0T1vylcSZ9eKiU1fsIXz+9tWXi7TfRSjaixZ4eUu+9U8EKPwu1sclVIrNtBI+n\nnJVqA5X2uGfPBZDe9hHpHdvLY1TZfXtQ6xsQFAVb1whfdz2O4zD2+9+6LHkg8cbreJpa8MypJHwF\nr1lHofMkjmUhSCLBa2dWipwMM5Ws2M4fPYKVySCIIvkjhwldd/1VK/NfCp2J0zzf9SqWYxL1RHli\n8VemuGFNxtq6layuXV6S9JyayfkVP3e03TztsROFeMV23sjz9+u/xbZTBwiqwQofbFVSUSXYPbKf\njJGlYBaxHAtJEGkI1BP1RtAtnRe6XuNMph9JEMmbBQQENEsjrUPUE8YjeYh4wkwU4mwf3l1aALjk\ns7SeZm64lTp/DfFigrAa4isd9zMn3MKy6kX0ZQao89dWKMgVTQ3btvFKXvJOnqASQpXUck/awUFC\nxCt7GMuPVzxPR6ydH6z8Nv9+4KeMF+IUS+YnBatY9hoXcOVcVUkpEwh/dfwPZPU8OA7DuRGe73qV\nry1+BHCDs1/2M5AbQivJwW4b2s3C2PwZKd9Nh5U1S0loSToTp6nyRrlrBuS4zxtmg/csrjrOz+zs\nYuECe37yKHZ1YaZcdTFsx+15R6Ku6lehiH/hIuqf/CZa7xnUxkZ8HQsxEglGfvGzsiyp1tdL/ZNT\nZ2HPBs3yds7Nxia3D4z4BIWuU5gTEwiSiFLfUB7p8jRXflFN3jYTCexs1l1UlEaPrFwOORql2NXl\nBm/DmHIPZioxJXj72ttp+P7foA8NoTY0fqwg61+2nPRHbkYmyHKFqIyt6xROHLvkeY14nPzRw0iB\nAIFVaz42IfCDgW1YjhvQklqSvaMH2dRy8R67KIjn6r8zQFrPUDAKzA3P4USiE90ySvKlcGL8NOsb\nr7ngsYalkyimsBw3OFqOTbyYZGnVQrYO7SqXxye0jJsFq0GiagQbmzp/HStrliILMpIoYU0KsAB5\ns0Bvph+PpOKRPOi2zmtntvDE4keneIeD21v+9fE/MlZwg3Kdv5b7593Fz47+mipvtCSy4lDjr2FD\n47VkjCw7hvdwVjvgrCqcIiqT3MVxuSLlxZCALMisqVtJWHW1989qtJ9FdpJQjiiIfLnjfv7v/T9G\nEiUCsh9VkunPDtIabiGr53ip+w0mCnHmR+dyZ9stlySfCYLAzS03cHPLlWn2f5Yh/eu//uu/fto3\nMVPk8/qld/orRyDg+dTfk+QPkDty2M0sRZHorbd/YlnYpWDlcuQOHUAURWzbwdENRJ8PK53CTKWx\nc1mCa6/BO3cuSsnEo3DiOPljR8vnMJMJIjfcWA42juOQO3QQc2LcHUUTRQRJJHLDTcRffMEtd584\nhm/BQkaf+SXFU6dK87AOgteLWluL2tiEUlWFUlWFPjiImckgKApqY7NLJhMEsrt34ViuWxSCgOTx\nuh7eCxfhm78AQZLQhwYw4252KPkDxG67Y9oqgRQIoNY3IJ1nleqYJvmjh9GHh5GrqgmGfNN+nnzz\n2lGqq1x9dFHEGBkB2ypbpQZWrr7oHLmZTDL8kx9T6OykcPKk2zufAXFvOuwfO1xhaNEabqHtY2Zs\n0+Hg2BF+e/I59o8domAWubHJZVgLgkjWyLF36BCyKDEvMlVPX7N03uvfSn92sPwzEYGQEuCRjvs5\nMn7cFXHBFTTJljJ0wzFYElvISGGM06luTia6WFO3glOpHhLFyqqHYZsUzEJZbz1n5BAFkfnRuVPu\n58DYIT4a3IllW8iSQsEssKRqIccTnUiCSEDx41f8fGvZ16gP1BL1RKj316KICotiHWUntBpfNV2p\nHgpmEadEjlMkGUWUaQk28u1lX2PVJCOY4dxomUcgCiIPzb+H2kle6SE1SLyYcEvwkit4s77xGmLe\nKC+efp3uVA+6rTOSH8UjecoEwy8iAoGZ8Vxmg/cXDJ+F4C1HIviXLEVtaCRy0yZ87Z8dc3slFsOx\nTKyxEcRQmKp77sMYc800sG20gX7kSLSCYOWYJtkD+8vbcixG+Ppz5iTJt98k+dabmPEJcBzCGzYS\nu/NuN+ifPAG4iwYrk0br63V1xC3LVW3DIbx+Q1ke1DEN0tu3gShijI2S3bsH/9LlCIKAMTriMucD\nQZRYFHXOHPxLlhK97Y5y0PQvXooY8ONpaSH2pXsuy2zEsW1Gf/1L0tu3UThxHO1MD3XXryNfMKbd\nX47GSLz6Msb4GDg2ViaDHI0RXLOW8MYbLyrCkTtyuHJBND5O+MabZiTcsWt4H2/3vk93qpeWUBN1\nvlpOJrqwHZtqbxV3td1aDgBXA7858SymbeI4DiP5UTRbJ6VnyBpZdxwLh+HcGIuqFlT0sAF2jezj\n2MTJsve1gIAiyiyItXNN/SpUSeFYvBMHh6yRwyt5UUQFj+QhpaeRS2X9glnAr/h5eP49TBQnGM/H\nsRzX4rOcATs2um1QtIqMFcaZF2mr6BX3ZQZ57tTLJLUUmqXj4OCXfdzUsoGmQD39mSEUUeaO1ptZ\nGDv3/2y1L0ZHrJ05oeZyxhvxhFlXv4aNTevIGwU0WyesuvK0QTXIuoa1FdyD5TVLqI9VERCDPDj/\nHhZWTf1OaI+0kTcLeGUvGxqvY0mpBbF9aDd589zirMobm3Zh8kXBTIP3bNl8Fn8RKNU1U0RCPiuI\n3Xo7tY89XPYWzu7cji2d632e38/1tMyh+r4HyOzaiejzUfWlStvI/NFzIzSuY1YGtaGBzPnEME3H\n0zIHM5nE1twys+M4GMlzRiZm0r22lUxgFQpgWfT+n/8HoseDFI2hVFcjhUI0/f1/Q1SmBihBlj+2\nEIsxPl6hQqf19VEYGADf9GQfK50ql+kFWUGuqqb2q1+bouw2Hc5fVEih0IzK5icTXWzpex+Aodww\nmqXx2KKH+eGqb5PV88S8EQQEhnOj+BVfuWx7NZAxsuSNAqdTZyiaRUzHQkRAEgRUUSZZTFUwuvsz\ng7x15l3ixQQe2UNQCWDaFnOCTTQFGjg8fozlNUt4csmj9GcG2T60mzOZPizbQpXUKa5cIgK6rXP3\n3DvI6nlOJU9jOhbumLardgZuGTtvFjgweqRc5gY4nepBFAQinjAZPYtpm9T5a/lT54u0hefww1Xf\nvqxZaFmUCakhNjZdR192kKJZJKElKVo6/3nolzy+6GEaSu9DFETuXLCJNRH3/7mklqJoamXZ10Pj\nR9k5vBeP5OGO1s0V5f7FVR2MDbjVCUEQWRS7MrOaLwpmg/cs/urhX7KM9I5tgBv8fB2LpuwTXL2m\ngtU9GVIkgplKYaZT2Lkc2d27sPM5whtvJH/8WAUxzDOnFeP/+R/oOAg+H5LHi9bdDRvc3py3tc0V\nlxkqQmleHcvCyucRZAUpFMLKZl2G+DTBO/nuO8RfewVwiN16O7ELKLhNB9HrRRDFspyny7oPwAVE\ny6RIBDkcxiw5uYk+X7mCcCn4FnQQ2Xwz2T27kfx+qu5/aEbHTSZQAYyVhE18sg+f7EO3dH5z4lmG\ncyOIgsTdc29jec2l5U8vhqZAA7tG9qNZGh5JxSd58EkeV+XMNgl5/XgFH82hylLuqz1vIwkioiCi\nmRpRT4Rr61dzeOJY+b+CWWRdwxoaA/XsGz2EVXr3hm2yPDqXkdwoSS2NKil0JrvZ0vchDjYLou0s\njM7n3YEPyep5TMesuLZuGUjnLYaqSmNtPtmLT/ZiWCYnEqeQRZmhSf7iF4Pt2Lxx5h26kj3U+Kq4\nd96dtIZbeHLJozzb+VLJAU1FszR2DO+d1h991/A+tvR9ADi0hlrY3LyRV7rf4mxf/Q+dL/C3q75T\nXkhsbLqOmCfKeDHOvHDrjIxT/howWzb/guGzUDb/rMPWNOyBXgrpPFIwiLd9PnIshlrfQOy22/E0\nXd6Xg6dtLlpfH3p/H5LflfQ0kykCK1YS3nADnqYmIjdtxts2F1FRcEwDY2QEsURi8y9ZUm4tiB4P\n/iXLyB057Jp6lL6ABUFAUBRErxe5qmrasnSxv4+hH/+7a6SiaRROdaLUNcz4eUSPBzEYpNjTjSBJ\nVN1xF7Wrll3w8+TKxi7E1jTUmlqq770fpapq2n2ng7dtLuENGwlduw45NLMMWRREDk8c5+wX/cLY\nfBZOysQOjh/lwNhhwM1G+7ODFyWTXQpHJ06wY3gPHtmDYRuIgohf8SEIAvfOu5N5kTYW1LWxufEm\nYl63mmA7NqdTZ8ojZe5IlsINTevRbL1sCAJgleRKwZ29Nm0Tr6wSVAMsruqgIVDPSH4MRZQ5mehC\nECiJqSTY2Lwe27EZyA6VpscnSfoKAk8teYy0kWXH0B4OjB0mp+WRRRlFUvArfgYyQxSsIkVLQ0Ag\n7AnTnTrDzuE9ZI08c0LNU97HR4M72Tq4A8M2SOlpElqSpdWLCKlBhnIjJCdJxdb5ajid6uG1nrc5\nlTzN4rp2TM3hNyeeLc9gp/Q0kiAxnB8pH2fYBuvq11aoqdX6q2kLtxD2XL1KymcVs2XzWcxiGlj5\nPCM//wlOKolpWsTuvIvw+g0XtLKcDrnDB0m99x6CLBG780t457VT/+RT9A0PnaeJ7hptnE/Wi9y4\nCUfX0fr6UJubiZ6nVa7EYjT98O8Z+flP0frOIAYCiF4f3tY25OpqoptvnrbErPf3l5nojmXhGAZj\nf/od2pluqh/+8oz6yaG11xBc42ZfM9lfqa6+6iI2F0NLqIlHOx7gePwUEU/okpnilWK8NBomCSIx\nT4SipVHtrWJhbAGr61yJ29raEGNjGSzb4q3e99g6uBPN1pEFCdO2iHrCxDwx1jWs5YWuVxkrTCAg\nEvGEqPa4LYm+zCDDuVEmigl8sodqb5AV1Ut4p/8jZFEqfawcdNvgLMXQsi02N29k18h+bNspj2UJ\nuHKsE8U4L3W/QVrPkigkSmXuIGE1RNHSMByzzF7P6FnihTijhTHAVZ4LKH5W1Z6b0x/MDvPmmXdJ\n62lEQaTKGyWlpcu/v7FpPf3ZQbJ6lrAaIqSG2DG8G4B8Ns+zR1/j3jlTK0G1vhq8so9iaUa8Jdhc\n4ZA2i+kxG7xncVlwTBMrm0UKBj9R9bQp91Fisl8u8kcOY0xMuKNiQOr996YVMrkQjIkJRp/5pcsG\nF0X0kRHm/PN/R/R6id1xF4k3XwfHIbh6zQV7v4IkEbvjrnPPYlnYuo6oniP4qHV1zPmn/53C6dOY\nE+N42uZekrHvaW1D9PldQpxtgygiqh5yRw4TWrd+ysjYhTCToP1pYl6kbVpmN7jyoYfGjzKUG0YU\nJG6dU+k2d2TiBPtHD+KTfdzaetMlxT/mRuawfWg3DjaSKLGx/jq+NPe2affdObyXHUN7ygHNp/jw\nK342tWxkZc0yElqSgewgqqii2zqmbbJ5jtsueb7rFXTbIOoJu+IxLRuoD9TRHGzgTLoXQXBNTwRB\nIGvk8Uoe8kaeRVUL+M7Sr/Ni9+sMZIdcSVNEgrKf9we2kdFzFA13vty0LIoFjaSWIqAEMG0DAbGU\nzctkjVzF84zmxyq2PxrcUZ6Ltx3XsWxxVUf599W+Kp5e8U0yeoaQGuKD/q0VxyeLbtC/dc6NvN37\nAQ42c8OtrKxdSmu4mYPjR/FIKtfWz3whPRl5I0/BLBLzRr9wOubTYTZ4z2LGMOITjP7qv9w56WiU\nuie/+Ykop02G1tfH2J9+j5XNEli+4rINQ85fcAjT9I0vhnznyfJMs2Pb6KMjWLksosdDeP31BFas\nwDHMGbO888eOMv7cn7CLRYLXrqPmgcrer6+9HS4gOnM+PE1NND79A+Kvv0LxVBdyNFpmoX/WkD2w\nH31wEE9r6xRf75lCs3SOx90RpyVVC12DDknhicVfYbwwgV/xV7C/B7PDvHz6jXN611qK7yx/4qLX\naA218NVFD3Iy3uUyrBsqeQ8D2SGOZA/js4KMF+NkjaxLIivdX9QTYXnNEoJqgO70GQRBIDKp9CsL\nEmP5CXrSvW4WLAjEPFEmCnG2Du6kOdDITc0bGcoNMyfUzEB2iEPjRxEReLnnDTRb5/rGa1lUtYCf\nHP4VJxKnsByblJHheLzTZclPIrOBW5b2Sh5EQUISxJIITIimYAOnkqcrnn0yHMAjKVR5Y2iWTke0\nnXX1a3il+00Gs8M0Bxu5ve3msprZoqoO9owexC69j5UNbnvgmvrVLIjOR7M0anxViIJIta+KW+bc\nOKO/+3Q4NnGSl7vfwHIsWoLNfHXRQyiXYWLyecQX++lmcVWRevedcuAyk0lS771DzUOPfKL3MPHC\nn7EyLmM1d+gg3nntBFfNfKUeWLGS3NEjmL09CIpC1T33Xdb1JY+KIEll8xNBkhB9/nO/91/cGGMy\nbNNk9LfPYIyPg+OQfPN1vK2tBFefKwUXe8+Q3bcXye8nctOmsl77dDDGxki8/irG8DByVQzHdhBw\nXczUlqs393ylSO/YRuKN1wHI7N6JYxgXJANeCGfFRs5mh0cmTvDowgcQBRFJlCrYyvvHDvNu34fk\njDyGbeIrlWTHChNTzDemw9xwawVr+yxOp87wx84XkCQB07So99Vi2GbZ7MOyLW5uuaHMeG8Lz0GR\nPKSKSQRBYHn1EkzHYkvf+6iiSsEu4Ng2yWKS9we34Zd9KKLMfe13sbFkyPHzI79FFRUSWqqszmY7\nNhubrmNBtJ1jiU4s28LGpmAW3UzZOat7dg66bVDljaGIMrIosap2OXe23cKO4b2uGEpkLouqKlnd\nNzatZzDreq3HvFHua7+LDwa2sW/0EAIwUYzjk33cXKomNAcbeXLJo3SneqnyRrlp/tryhIe7gHHf\ni+3YvHnmXU6neqj2VXHPvDsuaTBzPt7sfbcsgtOfHeDoxPGKOfMvImaD9yxmjLMuXRfa/iRgFfIV\n23Y+T7Gnh0JXJ0p1DYFVqy9a9nVKc9iRu26lGK6tKFWfv1/+8CGsTAbfokXlsTdfxyI8bW0YI6M4\njo13/gLGn/0jANHNN1/Ue7rivotFhn/5c/Qht08uyLIre7p/Xzl466OjjD7zy/J71oeGqH/qW9O/\nl3yewf/4n+hDrhiIIEl42+dT98RTly2Qk/rwfTI7tiN4PPie+jqGIbg69XV1eJqmkpguF4VTnVO2\nLzd4D2WHK8q6PekzpPXMlDJ4opjkjZ53Stm2Q1pPo0rVSIJYMbd8OejLDNKV7KYr2Y1tW0iS+zWa\nMXJEvVF0y+13B9VgRU/eI3nwiApWqbRt2CY/Pfwr+jKDFK0iASVA0SxiOCYFo0DRLFLtreLYxEmW\nVS8GoCFQS2+mF91ySYSKKPPBwHaWVC3EsAxwnPLiwcF1FXOAkBoq6Y47qKJCW7iFu+feTtQTxnSs\n8gJjQ+O1U543rWcYyAwR80bZ1LKBd3pdf+7R/Bh7Rg+UCXhBJcBEsVI+tjFQXzE+Nx12j+xn/9ih\n8rXe6HmHRzqmX1RbtsX+scNols7S6oXlv/dUX3dnusO/UJgN3rOYMcIbNlLsPu32Zz0ewhs2Xvqg\nq4zQNetIfejO+Ur+AGIwyMivflEmipmJBNFbptcxtnWdkV/8DH14iAlJxLdiNdFbb5uiMgaQeP1V\nMrt2Am4wa/ju0+6MdTBI9b0Putc0TfJHj6JUVSHIMqMD/TT9/X9D8vunnO98pHduxyhpqzuGgWNZ\niF4vSlV1eR+tv69igVTsPYNj2ziWSXLL2xjjY/gWdBBevwFjfAwrd05y0rEsrGz2sgN38UwPyXe2\nuBv5PF3/8WNMy3HvQxCoeehhAstXXtY5z4dSXUPxtFuedQwdM5Wk0HkSX8fCSxx5Dn7FR0mmDnAJ\nWp5pDEnyZqFcJpdFmZgnysLYAqq9MTY0Xr6me19mkF8f/yOWbZIzCjg4eB0V23boiMwnpIYYyY8A\nAptbNiIIAqZtMpIfYyQ3RtbIElIDOMDe0QPIgowqK+i2O07mAD7JdQRzHAfd0isY1rfN2URSS7N3\n9CAeScUre4kXE/zHwZ9h2hayKKHbJpOq5ARVP/e03cEfT71YFoqp9VXTFLywAt5ZjBfiPHPsDxSt\nIpZtkzfzeCQPqmPyq+N/IGfkMG0LSZDIGrmPpXw2mfQGbjvjQvhz1yvl0v6ekf18a9nXCKlBbm65\ngTfOvIuDTZ2/lqXVU8c9v2iYDd6zmDE8c1pp/MHfYYyNotTVX3Wf65lAbWzE09aG6PESu+tuMju2\nVTC88yeOlYO3lc2SeOsNrGzWLa0LrsGIY1lo42MU+l8id/ggtV99HN/8yhJh7tDB8r9tTaNw8gRK\nabGS2bsL0evFNnTIpLFyWeRIFFvTMJOJiwZvx3EQBKEclOXqaozxcQRRxDO3nfD/z957Bsl1plea\nz3XpbWV5j6pCwXsSJEAHgiRINg1o0GSTbEc11T2anpFWmtnZ+SspQhETMRGzuxEbMTvallrdUlt6\nNh1I0ICehPdAAeW9S2+v2x8366KyDFAFoEV0qw5/EJmV99bNi0Se73vf855z68XYQkdVFQiC/f4c\nlZUIosjk62+SOnIYgFxnJ6LLjbu1Ddnnt1oKpokginjXLZ5k9WQSDAM9m7ECMhIaoj9gX0fywIGr\nJu/QzrsxVZVsxzkKwwnyAwOM/uoXhO+9b8EGM+XuCDsbbmP/wGdIgsiupjtnmZqA5d1d5alkJGO5\n6FV5Kmjw1VLjrSJeSPDp0BncspsbqjYuqEd6cOQII5kxTNNAFi01ed7IIwkyeSPP0ysfZyQzilt2\nU+4uo6Cr/PLsCwynRyjoGqqh4lXcJAspa04cyxHNK3sJOP04JIWMlmUyp6EZGvX+Om6vuyioVCSF\nJ9p3o4gy52OdpNUsDslK9BIEE0yLmCezUQRBIOQMsKJsOaO5cQx0JFHCBA6OHmN5qJWvRg4Tzcep\n9lQUe9HLSt7vsfGT5PQcpmlaBixaDlmUcUiO4oiZtXACk4AjaFcIFoPl4RYOjx63F1kcpEeHAAAg\nAElEQVQzy/VTUA2tpCef0TL0JvtZE1nJxsp1NAUaSKsZqryVf/T9blgi7yUsEnIwuCjLzcVAz2TI\ndXdZs9eNF9XE6tgYsQ/2oY6Pkx8cQHRYPUslHC7ZqVrPXZwzHnv+N3ZsZa67i+CtlvLYyKTtnaSp\nqcT2vTuLvOVAgMI0hzSpZKFSzE+SZIRpqVSSPzCvq9zk3reJvfcOiCKRBx/Gv3kL6aNHIGUJzYK3\n7yBw83aMfJ7xl15Az2Twb95C+SOPkTp0ANHjJXzPLgAKgwMl5y4MDuLbsJHK736f6DtvocXi+Ddt\nIbjjzrku5ZJw1NahTk5iFPIIgoDs85YEeIhzRJwuFqLDQeSh3Uz87lU7vAUgc+L4otzhbqzeNEtA\nNhOKKPPUysc5NXGW0cyY1f/u/xjN0DEx7S/5geQge9ofvuzv7E70YRZLtAVDQ0Kk1l+Fpun0JvvJ\n6Tka/HX0Jvv57bmPmMxFGc9OFAlPRjc1ZFFGMzTCrqDVh9c1EmoSp+xANVSShRQ5LY8oiAynRxBm\nlPZFQeTRtgeYyEb5sP9TDo4eIVFI4VO81PiqqfVWcUzNktNzRPNx/IqPvtQgwrTOd0Ev8Eb3uyQL\nSeL5BN3xHs5FL7CirI1qTyUbKtYRdPrtaoZqqHY/H6ygEUkQMYr/SYLIzbVbZtnDLgTNgUa+tfJR\nuuN9RNzheRcAsiDhVbykp6niA46L/y7DrtCsfPU/ZiyR9xKuC+ipFMP/8Pe2IC60405MwyR9/Cj5\n3h57BErPZFAqKhEkiWxnJzU/3GUldXWcQykvp+yBh+xzTvV/AWs36nTiWbnSLodbixABzNkWYpFH\nHmPi5RfRkkl86zfgmZZLHdpxJ6NDgxjZLM7mJlzNLYhuN4Ftt8wZApI5d46JV160d9DjLzyPp30F\nNT/6MwqDg8jhMEqknMzZM4y//CJGNosgSeS7u6h69jmqvvtsyfkcDY3kurswdQPR5cLZaImpXI1N\nBG+9A3VsDFdL6xWN0k2++TvMQh4ME8HtQg4EkauqKQwPo5SXl4y4XS3kwEyL1N9PJccpOdhUuY5X\nLrzJVD25oBfI6XnbdexCvHtB4jW/w4ciKXZfe3qpXhJknJKTRCHJ8+deRTVUslqOZCFFhTtS3AkH\n+YtNP+Kl86/TEbuAW3IzmY/ikpw4JAXd0ElrGXtRMZmL8uXwQW6rKx1nFIvObRfiXRT0AoZpoOoq\nT618nK54j112B/iw/1NurN6ER3GTUa1Z6vZwG6OZUTvtywSi+TiHRo4SdoU4Pn6aP1n7NDdWbaIn\n0ceFWDeSIBJyhVENDd3Uyao5KC4JZEGm0l2xoHs4Fxr99bPU7TMhCAKPtT3IW937yOo5bqzaRMO/\nYbe1JfJewnWBzKmTJbGS0XffKYq4rLlyI1+wytGm1X8VJMkuI5fdez/cO9uG0dXURPbCBQAEUcTV\n2Exw2y0EbrmdxKsvkBmbsMxSRkbo+29/R3DHTgI3WTs/R1U1NT/693Neq7Ountof/zl6PIYcLpuT\nsKcjd+F8SWnfyOesRUh5Be42a0528u03SXzxOerwEIIoIpdbNqPqyNBshzTDsExYNA3TcKCUW7v9\nxKefEN33jvV+979P5be/V1LBuBwKw0Nkz50FQUCQBMxCHsmhUPXdZxEk6ZrP9fu3bUcdHyPbeQFH\nZSXh+2b/HV7T3zdNwSyLEqJxkWQWOhvsV7youlrcwwpsqdzAQHYQSZK5r/kunJKDwdQwqmGFubgk\nFxkxh24aOEQHdzfegYnJ9tqtGJgk8gnK3GEmp+WEC1ixoQCiICAx97jfYHoIMO3yvCSKrC1fRV9q\nsETAJQgCbaEWIq4y+lIDNPisUvz/c/QnDGjDGKaOKEhgmkhFJX5KTTGUHqUl2MTTK/eQ1wvs7/+U\nQ6NHcUgO2kOtnJ48S0pNk1YzaIbG3p73iOXjOCUHZyY7CDoD3Nd81xXtxudDSk3RHGjAp/hIFJK8\n3/cxN1ZvWrQ6/Y8Bl/3XmM/ncV7my2kJS7haCDM/Y8X6niBKxdEsDdHjQRZFnPUNOGpqLuvbXf74\nE8T3f2DNhK9bj7POUko7a2tZ+X/8Z/oPn2L0X34OWGK26Dtv42ppwVFxeZGX5HYjXaKEbOo6+b5e\nBMWBs7kZ0enEyFu7HDkQxFFTSsipQweLFqgOTLWAmc8h+gM46mar17Nnz5TsUrMdHTiqqkmfuNin\nN3WDzKmTiyJvU7eMbwRZxsjnESSZ+scfxfg9/fsXFYXyx/b8Xs49F26pu5mJXJTe5AAN/jqaA42c\nnjyHW3azq2lhLYZEIUm5uwzd1FFEhbArxI+2P834+EWxYIUnglNyMpoZJ6fncEpOHlv+IA3+Opyi\ng1+eeYH+1CCKqPBI2wPUeqt5rfMt+lODSLKEmJ2wyV8RXayf5nIGlm7ibPQ8fckBNMNAFkVcspOI\nqwxFlLmz/hYOjRwhnk8gizLl7jKaA40lbmm5YkWg2ABCN3UkUcE0TeL5JIooW+r1IpySg3uadrCt\n9kYkQSSvF+hK9JLRsoiCiCzKiILIoWlz3VMOb0+tuDbjpCfGT/N6114M02Q8O4FX8eBVPFyIdfHs\nmqdtA5l/K7gsee/cuZOHHnqIp59+msbG2bOOS/jjRmF0lPTxo0huD74bt86ZZHUt4F23nuy5s2TO\nnEZ0Ognu+Aaxd9/G1HXkSDmSz4e7rY3AzdtL4jovBdHpnLfMKzocyOEZPtymiZHOwMKyNeaFqetW\nbndPNwD+rTdRvucJEp99iuj2UPnU07Puo+T1WuY3ZWXoySSuZa2E7t41p1pcDofRM5mSx1Dsy49c\n9IhebBnaUVuLqRuYajEz3DCIHTuBv6nd3nUbagEjl0Py+a8bJ7Yzkx2802PN+d5ev53NlXML6pyS\ng2+27y55bnvt1kX9rpAryERuErn41RlyhWbdB5/iZUvlBn7XtRfdNMiqWX5x5gX+641/wdHxk3a2\nt2qovNPzAT9a/z2+2b6bvuQgPzv1KwB7xEsWJYbTo7Q5LgrJ3up+j/0Dn1rJZoaOS3biUTzcXbGO\nr4YPc3jsOMuCzVS5K3ApTtZFVpUYwximwcmJs8QKcQRBRCmOlgFktTyqoeJTfLzW+RZe5THq/bUc\nGj1Gd7yXCk+E7TVbcctunlr5GG917eN8vAufYok0FVEmPxWog1X2v1Y4H+sq3jcNwzTI6wW8ioeJ\n3CSJQvLfVL8bFkDer7zyCr/+9a/53ve+R2trK8888wx33rl4IcwS/vCgRqOM/PQn9o4x19tN5bcu\n7Uh1pRBEkYpvPmnt+BTFUl/X1ZI5cxo5EMS35YYr6uFeCnIwiKulhVxnp5X8JcvkurtwVFcjulxX\nfN5cd5dN3ADJL7+g/j/9F4K33DbvMZFHHmP8xRcwMikCO+9CcDiZeOVFJJ+fyO5HS0g88shjTLz6\nCnrCCj+Zcigru/9BxnMvFEfI2uwWwOVgahrjL79I5uxp1OgkgiJboixRIHrgIGZFNcFbbyd7voPx\nF36LUSjgWtZCxZNP/d4WcwtFVsvyu8696MVUrXd6PqDJ30BknhjTuaAbOscnTpPX8qyKtM8ZI3p0\n7CQ9iT4qXOUYAYPJfAyv4uHFc6/xy7PPU+et5dk1z9gkKYsygmU+CoJl3fnp4Jezzj09DSyWjyEK\nIqZ50Q8trxc4NXmWtrBF3oZpcHD0CDkth2FaYrGMlkU1NH5z7hU8itv2Bc9rOX64/nv2e4zlE3gV\nN+/1fcSxsZNohqVolwQJwzSLO2ZrTtzEQDd1zkQ7mMxFeafnfQA6Yhco6Cp3Nd5OZ7ybjJbBr/jw\nKh6qvZVsrFjHyxfesHffbcFS9frVYEqfIAsSIBT/byXKeZfK5rNRXl7Oj3/8Y370ox+xb98+/vqv\n/5q//du/5dvf/jbPPPPMUkn9jxj5nm6buAGy589fsaf4QjG9f+ysq8dZ9/tzBhNEkconnyZ15DCT\nb72OqevEP/qQ7IUOqp997orfpyDNsGAVxcvalLoam6j/3/7KMoc5fYrxF34LWEK+iZeeL+m/K2UR\nqr//J7POIQeDcz5/OSQPfkXm9KnitUuYuZz93kWHAy1q7Z4m33wdo2CZg+S6OkkfO4J/y+Jnpa8l\nclreJm4LJmktTYSFk/drnW9zNmoZx3w1cpjvr3mqpId6bOwkb3W/az/eVrOVB1t28d+++r9JaxkQ\nBHoSfbzW+RYbKtYwlp0g7CzdkbtlF2k1i1NyWP1s00QWFW6tvcl+TaO/Hrfswik7yahZxGJ4SU6/\nOPUgCiKOokhueooYWK5pki7Z5D2Zi9Id78WreHit823GsuMoooOUmsYpKZS7IkzkJjFMA226aNPU\nKRRL5n7Fx0DRVW0K/alBOuM9fDzwOYZpkiwkSRZSrK9YQ2uomW+teJSOqGUnu2meKsiVYFvtVtJq\nlv7UIA3+WktHICnsqL8Vh/T1LiK/DixIgZLNZnn55Zf55S9/SWNjI3v27OGLL77gueee4+c///nv\n+xqX8DVBnhHvKIdCv1fi/jogyDJKJGJZSBbfW2FwEC0WW1S85XS4mpvxbdxkzWILAuF77iV18IAV\n0VleTuiue+YVuQmCgB6PlTw3Xcg3HUY+T35gADk4/4jaQqCnLvZr5XBZcdZbR/R4kJwO3Cus0R1T\nVUuOm/n460DQGaDBX09fsh+wEqpqvHObj1jKahOXfLGqohqaTdwAaTVNT6KvZFypN3lxNG+q39wS\nbEI1Sh0GexJ9DKSmJhwEbq3dxpcjBxEQ8CteRjKjHBk7RqKQREDgvua7Siw8g84A3171BG91vcuB\nYpxoIp/Eq5T6BjyxfDc/OfHPJAophOJOWQBcssMmbtXQyWk5fn3uJcsmVbB831WjQEbN4JSCSKJo\ni93GsuMlSwHVUGkONHFD1UaOj5/i2PhJ+2e13moSRWOVZCFFVrMWF58NfolHdnNj9aY540SvFooo\nc/+yuUNh/i3isuT9N3/zN+zdu5edO3fy3//7f6e93XJBevjhh7nvvksLhpbwhw1XYxNl932D5IEv\nEd2eRfuA/6FACgYRJBFTLyp8nc45XdcWg8Ctt6NUV+OoqkabnGTy7TcBy8HMUNVLxmi621cQ/2i/\nXfXwrl036zV6KsXwT39i7YoFgciDDy/aYnQK3rXrSB34CqNQsNoXj+1BCgYpjAxTs2ktubBFhsHb\n7rDeh2kih8N41224ot93LSEKIt9s382pibPops7qshUk8gne6n6PjJZhQ8VatlZv5rOhA+zv/xQw\n2VazldvrrdErWZDwyB4y2kUNwUx1dJWngpMTp9FNg8lclKSa4ldnX6LCU05vwlo0yKKMW3bZQjMw\nkUSB/7jxOcYyE/gcXv759G9sNzETk8+GDrC5ckNJib/cXcayUBOdiR4KuooiygykhkuupznYyF9v\n/68MpoY5NXGWI+MnME2DLZUbWFexhtOT5zgXvWAr2DVDJ2vkKJNC6IY1yjWZi+GQHNxRt53jE6eI\n5mMli5GgM8C2mhuQRImNlesoGCrdiT4q3BFurbuZjJrBJbmYMKyqjEt2IghCSVb59YC8XuCNrncY\nSo9Q56vh/ua7/2h26Zcl79raWl5//XWCcxhz/NM//dPv5aKWcP3Af+NW/DcuTtTz+4A6Psbk229h\n5nP4t9501S5f06GURYjsfoz4B+/bGd2XG/+6FPKDg4z+/KcWGUoizvpSoac6PDTPkcXriZRT/exz\nZM6eRvL58a6fTZKpo4ftcjamSXz/B1dM3o6qaqqf+yG5zk7ksjLbsMa7Zi3+Cj+5YpiE/8atOBsb\n0ZNJnPUNV6ULmAv5gX5rzj2dxrf5BsJ337Og4xRRLlFS//Pp39ge2+/3fYRH9tjEDfDZ0JesjrRT\nXpy9frTtAd7sfpeclueGqo2z5o23VG2goBf4fPgATsmJX/GhmxphR5BHWu8nSYLl3uWci57n1ORZ\n+7iwM0S5O0K5O4Kqq8gzXL8kQSSjZWeV+AeSQ2S0LIog45Qcc46wiYJIvb+Wen8tu5pLNUhVngpy\nWp5oUSzmkV3kdOsc8UICj3yxL17pKeeh4H386uxLjKRHislhDpoDDSWe5FurN5f4tAedAb67+kle\nufAmXfEe3MVqxlwBLl8nPuz/hHPR8wCcmUzid/hmxcT+oeKy5P3cc8/N+7Oqqksbzi9hCdcKo7/6\nhU1W+ZdfQimvWLDqfCHwrll7xdGUM5E6+JXdGzZ1Ay1aGtbgbGq2/1wYGkSNRnE1NCL5L4qZlIoK\nghXzy95nRZte5Qy2EilfUOndUVUNVZf3xL4SjL/wW7tFkPjsE5yNjXjaF+9RHZ3hjW0R+Yz+8LQx\nqHp/LX+67rvznk8URG6puwndNPhs6Ev7eQGBOxpuoaLCz9hYksZAHaqpMZ6dpDnQUOL+Fs3HaQk0\nM56NohsaPoeXWl811d7SaYIT46e5EO9GL9quCoLAzobb6Ix3c3zstN3jdSuXXjhtq7mRnkQfsXyM\ngDPAd1vvx8Dk5fOv22VugFg+wUBqGLnYS9dMHY/sBpPLzr2HXSG+u/pJDo8eYyw7QVOggVVlC/en\n/9dAbBG+6X9oWDJpWcJ1D6NQuLjLBDBN1PGxa0re1wqmYczKCFeqqgneeRe58x0o5RUEbrFyi1OH\nDzLx+u8scwyPh6pnfzDL7nU++DZuJnPqFPn+PkSHg/AcJjV/SDBNEz2VLHluKvp1sVgearH72Iqo\nsDaykmguZj/XEmyeRZoLweaq9ZyePEcsH0MWZe6ov6Xk527ZzWNts1tL0VyMfz79W1SjQNgZIOwK\nc1PNFlaVtc/y4O5PDSEKAhGXNUte7a1EEkT+6eSviosSk69GjvBXW/7sksYkQaefH6x9hmTRNlUp\nlorXRlbx1Yjliy8JEm2hZfzizPP2+JWIYJXV81EmclEUUcYwDSLuufUfoiCypWr+SN7j46f4fOgA\nsijzxIYH8LI4a2XDNEgWUrhk15zBM5fDynAbXfFu+/GK8PJFn+N6xRJ5L+G6h+hw4GxotH3KRadz\nTvOShcLI5UidH0U1FJTwwlXJl0O245zlS561LCgFUUQOhQjfswslUo5vWvnbyOcZf+Ul9ETCzuhO\nHz1C6M6FCXJEp5Oq7z2Lnogjuj1XVea/WuT7eikMD+NsaMRRfWW7ckEQ8K7fSOrwIcBKjJtyn1ss\nHmzZRe1oNRk1y+pIOxF3GQ+33kdvci2mCU2B+iuy8PQpXp5d8zTj2QkCDj8+x8J0ET2JPlTDqsQI\ngkA8n2B9+eo5r6HGW8nRMSsHRhYk6ny19CT6SKoppqoH8XyCQyPH7L79FLJalrOT53FKTlaUtVkp\najNmn+9suI1yd4RYPkFbaBm1vmq8iteOGAUQBQlZlDk8esyO6lxbvpoHli2sjTGFscwEb3btswNH\nfnbkef509fdmtQ/mw/t9H7G35wPyep6wM8Se5Q+zKrK4nf36ijW4ZTdD6RHq/TW0BJsXdfz1jCXy\nXsIfBCq/9TSJTz/GyOXwbd4yi3Sn0rouBy2RYOSnP4F0Ct00KX90D55Vq6/6+kzTtPq1+bytWo88\n8hjetevmvK6J115Bi0Yx83lrhynL5Ht7F/U7rcVB6X3Q4nGie99ETybxbth4xaNchqqSPXMaOeTB\nrGmetyyfOnaUiVdftrzjJZHKp7+Dq/nKZnvLvvEgruZm9HQaz8pVVxyAI4tySX8WrB3itejHOiRl\nQVGa0xF0Bko+nyFXcN7Fw4aKtZZ7WbyHcneE2+u3cz7aiVkcDBOwjFtmfqayWo6fnfoNsbw1qbAy\n1s7DLfdxYOSILdbaXLkeQRBmObbtbr2f17v2ohs6cTVJRsvQ4K/h8NhxO8jkxPgptlSup3qebO7P\nhw5wfPw0PoeX+5p2EnaFiBcSNnEDZNQsOT2PbwHk3Zvs58P+z8gVS/zRfIw3u99dNHmDlVq2PNyy\n6OOudyyR9xKuW6SyKuPxLOVBNz63i9DOu2e9JpPT+O0H5+kdSVEb8fDkXcvxuedXk6YOHbCczGQJ\nUzeIffDeNSFvTLNkJn7qufkWFPneHiR/ADVjKYkFUSTb3UVhdHTRGdzTMf7Cb8kPWAro/MAAcjiC\nu2VxX1ymYTD6Lz8n39dLTJaQ6xqo/PZ35xwTTB85ZPu2m7pB6uiRKyZvQRRnCRE7ohc4Nn6ajJah\n0V/Ptpob/9XVwoZp8Gb3Ps5FzxNyBnm45f45TWCiuRjv939MXi+wsXwdKTXFiYkzjKRHKBgqPsVL\nlaeCe5vnzpufwnRxWEEvcHjsGIqoUNBVXLKLZYHGWS5yXfEehtLWZ8klOTkzeY4yV5hPB78A4PTk\nWUzT4IY5UthqfdX86brv8oszL9gjd0PpUQp6oZibbuHE+Bl+ceZFREHgnqYd9jjd+VgXH/Z/AsBk\nbpJXLrzJ99c8Ra23uiQFrClUj1e+fNY9XBzrm4JpmmhTpf0rqJpMoTfZz4VYN2FnkPUVa67qXF83\nlsh7Cdcdosk8v9rXwemeSRyKREXQzYPbmvjyzCjxdIE1y8q45warbP7h0QG6h63eaP94mncP9PHI\nbfOTlTDD/3jKUEXVDDI5Fa9L4cOjg/SMJKmJeLh7SwOKfPl/4IIo4r/hxouJZWVluJfPv0tw1NSi\nJeJWf9w0wR/CRMCYZnt6JSiMjpQ8VsdGSsjbNE2+OjPKSDSLJMDAeBpFFrl3ayM1EasMrI4M2y0K\nsMbb1LFRS6w2A6KntHSsO91kchoe16W/Wk50TfDV6VFcDpl7tzZQFpgtwDo0eozXO/faFpudsW6i\nuRiPtH3jMnfh2uLI2AlOjFsmNqOZMd7qfpdnVn1z1ut+e+4VosWd75HRE7gkJ4lCAlEQKXdHMDF5\nYsWji8qaPjBylL7kACFngIDDR5mrjD9Z+0zJOQzT4LOhr4jnE5imiSzK1HirGEgOklYzFAwVRVTo\nSfTPSd5TSBamzfuLEuXuGnsnvyzQxMHRo0wR6htd77Is0IhH8RDNlfoSTP19eRQ331n1BMfGTyKL\nCrtWbycZLZS8NllI8cnglxT0AluqNlDnq0E1NCKuMLXeajv0xCW7uLVu21WRbV9ygF+dfcmOdJ3M\nx/6gledL5L2E6w4v7e/kXF+MgmpQUA1kSeSX+zpQFIt43z3Qz8hEhp1b6klnS40yZj6ejmgyT7Z1\nDcqZ05gTY0Xv8130j6b45b4OMnkNWRQoaAaiKNA3mkIUBO7durBya9l938C9vB0jm8HVuvySwSWR\n3Y8i7vMR//JLErEUuZxBWnIhyAGa5znmyPlxhicyNFX7WdU0d6/e3dJK5uwZAARJnBVM8uHRQT48\nMoimG4zFsoR8TtxOmV+8c46/+OYGZEm0MrsF4WISmiDYffmZCN9zL3o8TmFkiHFPBW8MBDB+dZgd\nm+q4fcPccY2D42le2t+JUTz9RCLHf3hs9iz7mckOCsZFVXhOz9Nb3BleCrqh8/nwAWK5OMvDrbSH\nWy97zKWQmkZqAMlpedJTyOsFm7h1U6eg55GK9p2GaRSd4CzjFGURKVulvWgRSRBnkX80Fy9mhitk\ntSyariOJEgW9YBNynjxpzbru0xPneK//IzBhR8OtrIlYiv41kRV8Utypy6LM7tb7kEUZ3TQo6Cpd\niR77dxqmTlbL41E8NAca7YxygLbQxcVi0Bmw40xdspMkF9+PaZr8+tzLTBRnw8/HOtnVdCfv9n5I\nXs9T663hWyseJa1maQ+1UO27uummC7Fum7gBOqKdS+S9hCVcS0STuZLHum6i6yaSJJJIF8jmNY5c\nGKdnNMndW+o50xtFN0xEATa1zz3u9PnJYfZ+1YcJtDTcwY9+0ERKkxCdTt5+/RSZvPXFMx7PIUkC\nfo+lbB2eXNxOeGpGOpkp8NWhfgTgxlVVs0r5ksdD+UO7OVixnu7PDiEaOiOhevqOjfBs/Wxl76cn\nhnjngEVcX5we4bHbW1jXclGZHk8X6BlOEr71XoJVVVbPe+36WellnQOJ4j01wIR8QcftlEnlNHIF\nHZ/b6qOX3Xs/0Xf3IioSZbvunrf/LAeDVP/gTxmPZXnt5RP28+8fHmBdS4Swf7aQbiyWtYkbLPJW\nNWNWhSPkDJQQlSSIVHkunRqT1bK83f2+rSw/MXGGJ9p3syy48HS1mVhRtpyvRo6gFRcSa6e5r03B\nKTmo8lQykhnFNMDARDc1REFCM1TihThu2c0LHb/jqZWPLUg5ndcLmJioRf9xURDZWr2Z8ewk52Od\nBB0BVkXaccoOBEQ0Q7XvV1rN4FO8eBUPBUPDISo4JAepQprfde21vcff6HqHOl81IWeQW+tuptwd\nscbagk0EHD664324FRd1vlr7/YFl5Rp2WZ+JCk+EZ1bu4fRkBz7FO28wzExktZxN3GC5ur3V/R45\nPYcsSAymh1hVtnyWMO9KEXKVfob/0INMlsh7CdcdVjaFiacLFDQdwzAp8zsRRIHuoQSqbiCJAi6H\njKab5FWDHzywioGxNDURD3UVs3c1hmHy7sF+u4PWOZLifFKkNmQRi6ZfZBKHIpY8XlazuGQugIKq\n89M3zzCZtHrgp7qj/PDhNXOW301BYjh8+Z19R3/pfOq5vphN3uPxLP/w+mmyBesL+YGb13DDHXP3\nzSvCbvrGUiiyhCgKyMVrqol4Skrd/hu34ttyAxWVgZK4y/mg6saCngOIBF3IkmDf58ZK35z35s6G\nW8lqOc5FrUz21ZEV3NN4x7zXcHDkKPt69zOaHUMRFULOAGDSk+i/YvIeTo8wkhnnoZZdxPIJws4g\ny+fZyT/RvpuPBr7g86GvCDr8ZLQskiDidvhRRMtwZSQzwsmJM5clON3Q+eWZFxnJjCAi4JZd7Gnf\njVN08LNTv7Kd3IYzo9zZcCu7mnbws9O/tjowDm+x7B2xzWoAarzVpNW0TdyGaTKRG+f/OvT/Uu2t\n4qkVj9EUqEeLaUxkJ3np/OvEi3PRN1XfwNMrH+f0ZAeSILKybHlJCbvaWzWvmAKqKfQAACAASURB\nVG0+uGQnIWfILs2rhsZobhzDNJBFmTJXiIIxfyVtPhimwXt9H9EV76XCHeHe5p24ZRcbytcQzcXo\niF4g7Apxf/NsDc0fEpbIewnXHe6/uYnqMg+TiTy15R68LpmfvnWWoM9JPJ3HNCzrSYCw30lNxGv3\nay8H3TCJp/L885un2dJewc7NdaxuDnOicwLdMAn7nTy4vZGJeI6aiJetqxYvHhuLZW3iBhhP5BiP\nZ+e8xm1rqjjTGyWeLuCURe7cXOoJPTSR5pWPu+gaSqDpJgGvtWMrD17sER89P2ETN1g78xtWzn3d\nu25swDRNhiczbG4vx6FIOBWJm1dXI84Q1wmiuODYz6oyDysaQpzts76IVzeFqQiW9rE13eA3752n\nY8AihOZqP3XlXm5ZN/e8vlt28/jyhxb0+wt6gX19+zExkAWZnJYjX5wNvtxufT6ci57n5QtvYpoG\nkiDxzfbdNAXmH1H0KB62VG3gyJiVqz7lSS4iYkxTXQtc/p5O5KKMZCz9giRK5PU8IgIdsc5pFqxw\ncuIMdzbcysbKdeimwbu9HwImy4LNPNiyi4qhCP2pQaq9VXYIytQOOqWmUHWVqB4nlo/zP4/9I36H\nj0QhSUbNopmanYJ2YOQwd9RvL3Gy60n0kSykWBZsIq2mea/vY1Rd5aaaLQtqVYiCyJMrHuGDvk8o\nGCpD6WFUQyORT6AZGqZpsr588WLSAyNHODhyBLAEdJIo8VDLvQiCwJ0Nt3Jnw62LPuf1iCXyXsJ1\nB1EQ2LLiIvl0DycQBAGPS8apiMRSBQIehY3LK0pKx/OeTxS4e0s9e7/qI1YkVVXT+fj4EJGgiyMd\n44T8TjTdRJZEKkNubls/d792IQj6nCiySK6gE0vmMUyTz08Ns/uWFkRRmPXaP3tkLeOxLCG/E6+r\ntLz+4v5OxuM5XA6ZRLqAUxFZ1xIpITyXo1SEN/PxdDgViYdvuTI1eDavIYkCDmX2+UVB4ImdbXQP\nJREEaKqenfd9/MKETdxgaRC+d9/sEvSVQDcNu58ZdAZIFJJUuCNsrtxwReNFAIdHT9jn1E2do2Mn\nL0neYPmiu2U3Wc2a9VdEhdvrt/N+38cYpk6Nt7ok9GQu9CUHSeQTiEgYWIsyUZDwKl78M2bLfcrF\nStOWqg20h1vJ63nKXGHbGW46dEOnJdjEQGoI3TDQTQOpuIMeyYyT0/NFS1aBTCGH3+FHAJySs+Tv\n86OBz20lu1f2Wv38YvrZKxfe5E/WPD2vsct0hJxBW4D498d/Tk7O2cYwGyrWkSgkccsuEoUk+3r3\nk9VybKpcx9ryVfOecyJbmiF+LTPFrycskfcSrns0VvppqwtyfiCOJIncu7WBB7Y1L+ocN6+pZkVj\nmP/16kmyBa34RWQSTeRIZArIkohc5KR4unDJc82FVFbldE8UTJP1reU8saONn7xxCtM0CXgcHLsw\nSV25j62rZpcWnYpUUu5PZVV+8955BifSTMRzBLwORFEg5HeyY2MdN68pVX1vXVVJ51CCzsEEAY+D\nb9x85f3d+fDWF718cXoESRS4/6bGksXVFERBoKV2/jZDQSstoxdUfZ5XLh5u2cWNVZv4auQwoiCw\nrnw1T7Y/giReOor1cue81OO54JQcPNG+mw/7P8MwdW6pvYnGQD0rwm1ktCzlrjJEQbRiOUWH7Xw2\nhfd699sOaB7ZgygICILIHfXbCTr9rHWsYjg9yqnJcwQcPh5s2VVyvN/hw8/8grjXOt/m06EvUXUV\n0zQxTANBsHLHLb9zs/g+nPgchk3cD7RYBi1d8V7e6t7H+VgXLsmJIECykCwuLqxKg2HqTOZiCyLv\n6bi9bhuvdb4FIoDAsfGTnJg4Ra2vhqyatQWBg13DlLnC887bt4WWcWz8ov7iWmaKX09YIu8lXPcQ\nRYGn7lpO32gKSRKon6OvPROZnMbpniguh8Sq5jCiIBD2O9nQVs4Xp6fKkQLL60MkMipHzo8D4HZI\nLK9fnJAlkS7wf/72KIPjaUygKuzmL5/YSH2Fj/H4NB/p1MIWBe8e6KNvzOozC4JF5gGvA5ci0d4w\n+9oUWeI7u1agajqKPJusDMOkoz+GYZgsbwghS4sbt+kbTdn3TDdM3vi8lzXLynA5Fvf1sbaljC9O\njRBNWdWPq6luzIWdjbezsqwd1VCp99XOIu6UmiZdSFPmLlvQuNaOhluYyE0ymhmj1lfDrTN2sfOh\n2lvFkyseKXnO7/Dhd/jQDZ3fdrxKV7wbRVTY3foNWkPNGKbB213v8W7ffmRRIugMkNEyPNL6ACvK\n2uzzCMUZ63uadtjPTeai7OvdT07Ps7lyg60enw7DNHin5wM+GviMvH7R7c0pOZBFGb/Dx/JQK0GH\nn2Pjp3DJDp5Y8SgN/jokQUQURAp6gd+ce5nRzBh5vVCSM+6SnLhlN6Ig4JJcV2Q/u6KsjRrf90jk\nk/zy7ItMLSQGUkPktNy0xZPJeHZiXvJeHm5hz/LddCd6KXdHSkr9f0xYIu8lXNeIJvMkMwVqIh6a\nqv2XPwCrvPuT10/Zfee1vWU8fofVg9u1tYGKkAvVFIj4FGrLvdSWe2ms8pFIF1BVg0PnxljXGqEy\nNP+o13S8f3iA3tEUpmGCYPW8vzg1wurmMvYftfKdJVFgZePCFgXTx90CXgeVITcb2spZ1RSecx56\nCnMRt2ma/PM7ZznSMY5hQmttgH//6FqkReSyF7TSHbJhmiWivoXC61L404dW0zuSxOdxUFd+dbGr\nc2G+L/TzsS5eufAGmqFR5irjmZV7SgxI5kLA4efZNU9ftTHIdJyYOGN7bauGyls9+/hx6AccGjnK\n0fETGKZOQddJ5JOEXcEFGdI83/GanSA2lBqhzBUqSQQDy2P8yNhxDHPKqw0wLXr8/uqnCDoDVHsr\nEQWRe5p2zFmxyGo5Yvm4vVs3i6OE1r0RaPTXU+GJsLly/axY1YUi4PDjV3yIgmgL6wSsnPaUai1o\nZVGhznfphV9rqJnWUPMVXcMfCpbIewnXLY6eH+fVT7oxTJPKkJvv378St/PyH9nOoUSJYOxE1yQP\nbmvG6ZAQBYH1reW8+lkPb38+jscp8+TONjYtr+AX75zjTG8UURQ4cGaUHz68Zs5Rp5k42xu9aAZl\ngmGCKMCdm+qIBFxMJnK01QWpr1zYF9qm9nI6h+IYJsiSyK4bG2mrX5xVqKrpHLswSTSZ4/OTI+i6\niSDAqe5JTnZNsr718gliU2iq8tNY6aN31Pry3LS8/JIudpeC2ymzovHa+ckvFB/2f2LPIU/mJjk8\nemxWP3g+XEsXLm2a2AxA061rihUsXUfQ6SeeT6KbOmvLV1/W0lU1NJu4ATJahp+f+jV+h48dDbfa\nKV/xvGVk5FHcqHnrGlySk6AzwIqytpL3OJ24dUO3yuqCiN/hI+Dwk9NytuhOQEAWJCRRZEPFmkv2\nohcKQRC4q/F29va8j2kaNPrr2d36Db4aOUxWy7G+fPWcDnf/1rBE3ku4brHvYD9GcXU/Gsty9Pz4\nrH7vXPDNEH05ZbFkFOlwxxhne6wRmkxe43ef9fDw9mY+Pj6EYZjIskgk4KJrKEHYf3mlcpnfidsp\n2bPiIZ/Dvs71rQtLCZuO1c1lBDwOBifS1Ff4qF3kDtUwTH6+9xy9I0nGohlyBat3KYoCkigsuqcv\nSyLfuXcFnYMJFFlc9PjcmZ4onxwfQpZFdt3YcMnJgFRW5WxvDI9TYmVTeMFq98thZp3AnPXM/Cjo\nBSRBuqr++RRWla3g4MhRu3+7vXYrAO2hVg6NHsMtu3FKTm6q3sLOxtvt42L5OF8NH7Znvad2tooo\nU++roz81gG7oJAopFFEhUUjyeude6n21Vkk83MKXw4fwyG4yWhav7Mbv8NHonz+k5eOBz/l06Csk\nQeL2um2siazk2TVP8w8n/oWsliWvFyjoKpIosbps5TWNA91YsZbWYDM5LU/EbYnv7qjffs3O/8eA\nJfJewnWLmcrsmY/nQ1O1n9vX1/DZyREcisjuW5eVHJsvlJaBC6rO21/2YlL0UNYM0jmVssDCkrp2\nbmlgLJ4jm9fwexR+8MBqe6TrSlFf6VvwTn0mxuNZ+kZTpDIqqnaRpAzTJOR1smKOvvnlIEsi7Q0h\nzvfHeWl/J36Pwm3ra3FeQtkOMBHP8ev3z5PNa4iCwHg8x1/sWT9n3z2dU/n/fnfKXlxsbq/goe3N\ni7pO3dA5PXkO3dRZWdZum6HcUbedVzvftMvmCzUSeafnAw6NHkUSZO5fdtdlleKXg0dx893V36I/\nNYhX8SAiEMvHaQzU89SKx+mK91DmCpXsYHNanp+d+jUT2UlEQeR8rKvEIvXx5Q/x0cBnnIueJ61l\nbWc33dTJqBn8Dh813iq+vWoP52NdGKZBRs3iUdzcVHOD/Xs64z0cGTuOW3Kzsmy57bY2kYvzizMv\nUOUp586G2/jPN/yYaC5G0BlENzVUwxopu9Y+4VM6gSXMjSXyXsJ1i3u3NvLi/guomoGqGbzxeQ+H\nzo7x3ftW4CnurlVN58CZMfKazsa2ckI+i3Dv3FzPjk11c+7c1reVc7Rzkom4Nc6zZUUFr37chWGY\n6KaJIoq014dorl7YDrOlNsCf71lPIl2gLOAkndXI5FT7GhcCTTd450Af/aNp6iu93HNDw6KFZVPw\nuBSS6QLJjIpetDJzOyVkSeTZ+1dSGV5YOMRMDIxZNrJT1ZDxeI5v3XXp2M6BsRSj0Qx6sUeeV3Uy\nOW3OxU1Hf7ykKnCkY4wHbm5a8KLNMA2e73iV7oTly35w5CjfWfUEiqSwPNzCj9Z/n2QhRbmrbJbK\ney70JPo4NHoUAN3UeLNrH+3htkV5k88Fl+xkWaBx2rVa88dbqzfT4J/dy+1N9tOT6MMojq3l9QKx\nXJwKj1XVEQWB7uLMdUEvMGlEcUkuZFGmI95FhaccURCp9lZR6amYk2RHM2O80PGa3WeeskIt6Ko9\n9mZg8kH/J6wrX0WVLUj7+qJo/61jibyXcN1iVVOYv/zmBp7/4AKfnhwGE4YnMiReUvkvT1kBC798\nt4OuYjDJobNj/Gj3GntWer6Sa9Dr4H//9hYOnRwi4HXQ0R9HlkQrQ1kUcTpEW+C2UHhdCi6HxK/3\nWSYkkijw0PZmNrQtrLf84ZFBvjxtWU8OTqRxKhI7N9df8phT3ZN8cHgAURTYsamOofE0yazK2mVl\nKIqIJAnopoBpmBQ0gw1t5QS9Dv7+tVMUVJ1ta6vZ3L5wA5PekZRN3IAdCHMppHIa0w6hoBl43HN/\n7cxsd7gc8oKJGyBRSNrEDTCWHWcoPUJjwLqPPsWLT7FK9gOpITJqlsZA/bxWpdN9xQ3TIKulODPR\nwZryFVe9y7wQ7552rRYpbq5cP2fWdTQXKynz5/S8PZYFMJQeYTI3iSAIlLlCxPIJdFPHLTr5ZOBz\nME2qvVW83rmXgqFyQ9XGWUYlQ+lRm7gBEvkE1d4qO2XMKTuL8+AmmnntRvyWcOVYIu8lXNfwuBRG\nJrMlTcvhiTSGYZIr6DZxAySzKr0jqXlDO6bD53GwqtmaQz3XF8PllKmULWvU2nIPkeDlZ3pn4nRP\n1DYhsUaqeljfGllQ33Zkmod6Nqfx9pe9nOuL8Y2bm2ismq2yj6XyvLi/095Z//2rJ/F7HAiiwLEL\nE3icMg5ZYmQygylaY3KD42n+x2+OkM7ryKLASDRDTcSzYHe66kjpjr267PI7+LDPQSToIpPTLNVw\n2I08j9K9rT7IttVVfHVmFJdT5rHbFxdl6pQcSIKEbpOLMKeifLrBSMRVxrdXPVGccS5Fc6CRSk8F\nw+lRJnMxFFHhje69XIh3XfNkM9M0+Wjgc+L5BG2hZSVl84i7jJAzSKoYiFLprih5X17Fi2lCTs8h\nCiKyKONTPPYCoy85wFcjh+3FyJfDB1kWbKQ50Eh3opcjoyeKjmbWaCJAja+ap1c8zrnoBT4Z/ILJ\nYo9+Y8U623VtCV8vlsh7CdcEqqYXgy2UayYymkJLXYALQ3GbwCtCbkRRwOkQ8ThlWygmYInFFosb\nVlZyomuSyWQep0Ow40an0D+aYt+hfkzT5I6NdbMEW6msypuf99A5mCCVKeArhppYYzkswAwTWuuC\ndAzE0TSDWCpPwOtgJJrlV/s6+KsnN5aU0AfG0/QMJ9B0w77XmbyOx20iI6AbJhvbyjnVPQkCeJ0y\nbqdMOquSyKiIgoBqmERTeSaT+QWT97KaAA/f0syxCxP43MqC0tZWNoXZurKSwx3juBwSj9/RSjqn\n4lSkOdsCu7Y2cs+NDVf0GXLLbh5Ytou9Pe+jmzq31W2j3F0qGDRMgy+GDtiPJ3KTnIueZ/0cs8CK\npPDMym/yycAXfDT4GYqoYAJnox2k1UzJ7nexaA020xxoojvRAwiUucJ8OXwQiud3SArtYWu+uy20\njFtrb+LQ6DEkQSqZ8e5LDjCaGcMwjWKCmMCyYKOdoQ1Q6amYlcaWVXOMZyd4/tyr9mLHq3io9VXj\nkl3cVLWF17reZjQzTpO/nnua7sQhKdT55rayXcK/PpbIewlXjbO9UV7Y34mqGSyvC/LEzrYr7tfO\nhUdva0HTDE71RCkPuvj2LsuEQhJFntzZxhuf91BQDW5ZV71gIhocT3Hw1DARv4u2+iA/fHgNo9Es\nQa+jpB97omuCX793HlEQEEWBX+3r4D8+vr5kVOrVT7ro6I9jmFY1AFR0w6C9IUQqoy5IvHbT6ioc\nssjhjnGrtFwMCckWdDvtC+CdA318cHgAo1gK93usxZLfoyBPKzGvb42w+9Zl/O7TLg6eswxogj4n\nyUyhmMBmvbaxKIozzIvPXQqbllewafnsUnsqqzIRz1ERcpcEnAiCwEO3LOP+m5swDINf7jtP93AS\nt0PioVua+fTEMEMTGZqq/OzZ0YrbKV/V4m9VpP2SdqhTO1Ndv1j6dVwi4cshKVR6K4jnkximjizK\nVLgjKOKVjcpNQRIl9ix/iLHsBC7ZyW/PvVLy8/7koE3eYEV3xgoJOqIXeL1rL7F8HIfk4P2+j8io\nWZJqmoDiQxAEMmqW2+q20ZccoMpbyW21N5PT83YmedgZojnYyPlY57QqhTVm9nDr/SiizO8699JR\nDIQ5lo8TdAZsZfwSrg8skfcSrhqvf9aDWrS+7BiIc6Jzko3LFz5HfDmIosCT8wijGqv8/Lvda+c9\nVtMN3vish56RJNVlHh66pZnekRT/9NZZJhJZBGBTewXPPbCahhnq7ncO9PHhkUHGY1lEUaAi5Kag\nGUST+RLyHo9ZTlOiIFDmd5LN61a5P5rln946w7/bvXbO1KyZ2NRewYrGEP/z1ZOMxbLkCjpVYQ8u\nh3VsvqDz5uc9ZHJWpUGRRcr8PkaKi46gzxpZ29hWYVcHHty+jI1tFSQyBV7+qLPknu66oYFEusBP\nXj9NMqOyrqWMh29Ztqg+M1gObP/yzjnyqo7HKfO9+1bMEsXJksjnZ0btPnm2oPMve8/ZGe2dQwn2\nHx1ccHb61eAby+7mtc69aIbKivDyy4ZonJo4g0d2kVLT6KZOg79uQeYpl8KxsZO80/shpmlwe/12\nqr1VJR7cNd7SkcjeZL9NpgCfDH6BV7YWqoIgohkak/kYkiCS0bJsrFhXQrbfaL6b5aFl5PUCbaFl\nuGUXVZ5KREGye90V7nJbjBfLl6bYRXOxq3q/S7j2+FrJe//+/fzd3/0dhmGwZ88efvjDH36dl7OE\nK4Q6w7N6vijIuZAv6Lz2aTdDE2kaKn08sK25hOhUzWA0msHnVgj6Fq9s/fjYEIeL1qeTyTwuh0Qs\nVWAymbMdpk53Rzk/EJ9lPfrVmVFkSUCSRHTdIJfXqIp4qAiV9sOX1wf54vQI8VSBXEHDMMGjy/g8\nCpPJPLFUnooZbm2abvDpiWFiqTxrlpXRWmuZsHhcCjs31/Mve8+iSCK5gsbbX/bxwLZmcgXNbhGA\nNeLWP5bG61bQDJNYKs937l1PcMZOv77Sx7EL46i6SSToJq/qSKLAfTc18b9eO2krvI9emKC5JsDG\nBYrspvDR0UHyRZ/yTF7j0xPDPHJbC/F0gS9PjyBgecvP9DbPa4ZN3mBloB/pGCeZKbCyKTzrnl0r\ntIfb+PNNzai6elmXNbAU1z6H1y6Th5whxrOTvNPzPjk9z462m1jmXLjAMa1meLvnfZs03+/7iO+s\n+hYuyclkLkpbqGVBYSou2UlaS5f06wVBwKt4OBPtKBmHEwShZCcPUOkp57G2Bzk8egyX7CqZo14e\namEgNTh19LwxqNcaOS1HspAm5Apetar/jx1f293RdZ2//du/5R//8R+pqqpiz5493HXXXbS2/ut8\nSJZw7XD7hlr2HugDoDzgYk3zwgMJ3j3Yx8luyzBlMmn1eqdU1rmCxk/fPMNINIskCjx8S/OinMGs\nc+ZmPM5bLm3TBHCCYBmbzITHKaNqBpGAk1ROY0VTmEdva5nl6X3v1kZ6R1PEU3lM0yLmVFYlr+o0\nVfkJeGaXZV/9pJvjnROAFen5vftW2MK00WjW7psDdA4mAEt9HfY5LW9wE5wOuWShoxsmmZw6i7wB\nu3SvFA1rvC7r2Kld/BQyOXXWsTN//vrnPUSTedobQuzYWDfnPH6+oPOPb5y2FwZne2N86+7lHDgz\nSjKrIgDb11Zx/MIkJpZ9bCan8conXQB8cnyI5x5aTXnw90PgiigvmBy2Vm9m8MIwBjpOycnmynW8\n0PGanUP90qm3eKLtUernGPOaie5ELwPJQVRdLbGoNUyde5p2oBka+/s/5RdnnqfBX8cttTchCiKN\n/nqWh1rpiFm771tqb6IttIwXzv+OVCFF0BnAI7msGFfAscCy/nw2ojfVbMHv8DGaGacxUE/LFeah\nLwb9yUGe73iVvJ4n7Arz9IrH8TmuvYXuHwu+NvI+duwYjY2N1NdbX9QPPPAA+/btWyLvP0BsW1tN\nc42fdFajodJ3WeOO6ZhuYwowkbhItkfOjzMStWZMdcPk3QP9s8h7PJ7l0NkxHIrEzWuqZhHrisYw\nxzsnpz0OsaqpjPMDcXqHkyiyyOrmsjntRx+9rYXnP7xAJqexY2MlD21vnrMfK4oCfreC162QzeuW\nmloARRLZtbVhzvvROXixLGmYJt3DSZu8q8JuTNMkkS5QUA1kUSCv6jgdEnt2tPL6Zz1ousGNqyoZ\nnczSP26Jk2oj3nl3q83VAVY3hTlyfpygz8kTd1q7sBtWVLD/2BBgLVZWNV164fXqJ912ZvfQRIaQ\n18mOTXUMjKVI5TSCXge3ra9lJJopmdkeT+TQdYMf7V5D30iKoM9BTcTLlvZKhiczNFT6+NlbZ+3X\n5zWDjr747428F4Pl4RaeXfM0E9lJanxVeGWPTdxgubVN5qKXJe/Phw7wYf8nmKZJWs3gUdzIokSN\nt9oO8tjf/6mdKtaXHMAhOripZguiIPJo2wOMZcdRRIWwy6oS/XjDD9AMjZ5EP69ceBPVKLA81Mrq\nOcJJFovVkRUl55nIRq2AH1eIWD7O6YlzuBU368tXXxODlg/7PyGvW98H0VyUL0cOsbPhtqs+7x8r\nvjbyHhkZoabmonKxqqqKY8eOfV2Xs4SrxEKFYjOxoiFk7ywBVk3zvZ4poJpJnMlMgX9844xdSr4w\nEOcHD64uec2a5jIcd4v0DCepjnhYu8xSH/+Pv9zBsdPD6KZJbcQ7Z5+3qdrPf3pyI4Zh2j/XdIP9\nRwcZjWZpqwuyvD7Iqe4oDoeEJIgIogCGScjvpMzvZEXD3GNrVWEPnUOJaY8vktSGtnK+ODXCRDyH\nIosUNIP3DvVz/01NbG6vwDCtUbENrRFCPifHOycwTVjXGplXKPjl6RFO9URxKBL5gm63Ou7cXE9t\nuZdD58bwexyo2qVneMdi2dLH8Swbl5fzHx5fTzxdIOxzoMgSkiSgyKL9e5yKhN/jwO2UWTltlK+x\nym8vWoI+B7noxfMHrmBy4PeFcncZ5dMiLi8qxcEpO2jw1132HIdHre83QRDwO7y0hpaxqqydFeE2\ne757ODNWcsxwZtT+syAIVHpmiwVl8f9n772C5LjONO0ns7xr7x3aNxrohrcECBAgCNCKFClRGoqS\nhhqNtDPrQvvH7t3uf/HP9UZsxGxsbOzESKOZlTQylKMBPQGQBEDCuwbQ3rtqU95m5n+RjUJX22qH\n7gbOcyNlsyrrVKKq3jznfN/7GqnKKOc/bv8RUTWKzbj8NzwnOz7m6vB1ABqyN9HqaU+Yt3R6u3mx\n6pklv4Y6xbL2nimNYGZWTbwXU1Gamyv6C1NhPV2n53JdFOWn0T3ko6o4g82V91t7nkyzcafHQ/eg\nD4NB5tWnapPeW3/LMDFFTSwdD46HsDmt00IzcnNdzOSKvKV+fp/0qfz242bO3dLjMZt7PJz88r5t\na1VpBnsaCugdDpCdbuXp/eVsmMUH/Idf38KbnzQz5ouwoy6Pg1MMWYryXLgnrUKEoiq5uS7e/KSZ\nM1d6AbjSMsJP/mIHTx+cf7Wq5aOWpCX29qEA+7bpr/n2+a5Ev/ydHg//z2s7yZ10MzH5mm+ry0u8\nPpLE9voCPGEFk1Fmc839GMhc4EcvbeHds+16xfnBSsrmiVr94Utb+MV7t/H4I+zeVMATu1d+qXax\n/CjzW3zW9RXBWIgdRY0UuabntE8lw5lG0Hu/n39baT2Ple1MesxmbxX9rf2J48aSmlX/Pvf7hrg5\ndgvjRGrdxeHLWIxmjEZdPlp9bWRnO5BlGVVV6fMNYjGayXVM9/Wf6728IB/l51d+R0yJkW51cWLT\nQbJs6+e37EGzauKdn59Pf//9D+nAwAD5+XN/AYaH53d0etTJzXWtu+tUkmWjJEsXi6ljf+3Jatye\nMA6rCafNlPTfDaqKomiomkYspmAxGxkfDRBKYdl+sdfpdvtIwnAkFleJxpVEIV1nv5fXj9UkzeLn\neo3n9pbN+ri8dAuhSFxv/5IkSnMdDA/7OHe9PzGbjcVVzl7tSSkX22KUW+LIYgAAIABJREFUkgoL\njZLG8LAPTdO4dHso4ZwWi0e5eLOPnXW6EE+9Tgc25WOS9O2NmpIM3v2sLbGCsKc+j2f23hfcHKeJ\n7z51v/BqvuttBL53PPXHrzaNLr0gLNeV2mfpaMEh3vS/jS/qpzazikpL1bTnNbq2EClUGQgMUeYq\nptJSverXYSToJz55RUaTiMdVkPW/ucwuRkYCKKqSsHzV0P3k9xftTjxtvu9cBjm8sfE7eCJecmzZ\nKH4Dw/61/RlYCVK9WVs18W5oaKCzs5Oenh7y8vJ45513+O///b+v1nAEaxSDLJM/ixd3usPCCwc2\n8Mcz7XiDMdIk+Pl7d/jLZzam1JoFelHc+191M+oNU1uawWMNs5tQaJrGmDeMe2Lp2GI2JO2xO2zT\n7Tx7hvy8eboNfzjGjppcnt47fyvU3e5x3j7bSSSiYLAaeeGxDQkxzXCakyrOM1KswD+xp4xAOM7g\naJDKojQOTLxPSdLd1ybXGmS6ZneXk2UpkZjW1udNCHckqnDyfBej3gjP7C2bM3f8USXfkcffbH1j\n1nzwLl8PvmiATdl17CnYsQojnJl8ey4N2fXcGGkCYG/BTpxmB5eHrmMzWnmm/BigB5t0eLvwRv0E\nYyF+2/wnsm1Z87biTUaEkaTOqom30Wjkv/7X/8pf/dVfJVrFRLGaYDKqpuH2hLGYDNMqqN8518lX\nt4eQJYlQVEnYmfaNBGjpGU9Yn04+16gnjNViTFpWf/tsJzfa9YK2zkE/Tptp1or27iE/4Ziit2Yp\nKhaTgcPbirjZPordYuTFgxXTnvPm6Ta9Ohw43zTIhnzntLFNJhJV+N9/ukEgNCHQEgQmVYR//VAl\nfzzTjicQpaEym4aK1Cr7nTYT3zsxcxHTq0eqeOtsJ4FQjF11eVQWpRbIYjTcrwMY84XRgObucUY8\nYf7dy40L7hd/VJhJuL/o+4ozvV8Aut3p9zZ9a8VsSKNKjDO9Z+n29VKVUZ6oaJ+L5yqPs7tgOxJy\nIhDlQFFyHrokSUSUKMGYvjWgahpvt71P9Y4fL3vimGCV+7wPHz7M4cOHV3MIgjWKoqr86sMWWvo8\nyJI+c9xTr2+rtPd7+eq2XsijqioefxSr2ZCoozAZk5fN44rKLz9qpq3Pi0GWeG7/Bo5PLE31uwPE\n4qoeSmKQGRgNsWWWe0hZlpAkKckx7eCWQp7dN/verD+U3Hrln9KaNZlrrSP85pMWPP4okqRnb+uO\naPeXu3PSbdOK8pZKXqadHzxbP/8Dp1CW72JHTQ5f3BhAA9ImvNXH/BGCkThxRWVwNEhepp1M1+qk\nT7WMt3O6RxfFJ0oPUJlevirjmI8LExXmAIFYgKaRu+wt3DnHMxbPH1re5svBSyiqwtXhm/T6+/l2\n3cvzPm+mYrnJVKZvIN+elzB0cZmdRNUYyiwrDYKlIa6oYE1yt2uclol2KlWD97/qTvRiR2OT9t8k\niXSnOVGZvrUqm6ri5JnjzfZRLt4ZZmAkwMBokD9/3oGmaaiqhjcYxT0eYngshD8Uo7xg9tlOSa4z\nycDk0NaiGXu4JzPZac5hNU4zgrlHMBznT5+3E1dUZFnSfdE1DZNRZvfG+YuhUsEfihGKzH7zAHDx\nzhBvnm7l3M2BpASx2XjhQAV/+/VGSvOcOCZWNHIzbIx4w/yvP9zgVx+38L/+eIPOFBLI5qJzwMfP\n3m3ip+800THgnf8JgD8W4I+t7zAccjMccvP7lncSs8K1htWQfHNjNa7ctsOdsRYU9d53SOPWyF3C\n8QhRJUaXt4fR8BiKqnC2/wLvtn/I3UnObnMhSzKv13+DivQN5NqycZjsNObUC7OVFUJcVcGaZCbZ\nuBfzUVmURmG2nf4R/Yf48S2FHNtZSkxRp1Wag572FZ4QrXhcZdSnm6m09XmJxfXnKKqGUZaoKJx7\nqfLFgxUcaCzAIMspzSaf2VvGhgIXgVCMurLMGQ1UQN97V1QNq1kPEQlHFTKdZr51tGbG97RQ7m8z\nwFO7S9m3qSDRS242GbBZjFy4PcTb5/T2p+tto0TjKq8cm38JvTTPyV8+vZHzTUNYTDKPby3i5Pmu\nhKNaLK5y7tYAG+a4MZqLYDjOLz9qJhyN4wlEuXB7iPryTL51tGZOFzZf1E9cvX+zEldj+KJ+7EsI\nFFkpnqk4xu9b3iYUD1GXWUNjzsJXQlIlx5aVZMVqNVqIazF+2fR7PVoUmQJHHv2BAQCuuW/yzdoX\n51y1GAwO83bb+/hiAeoyqyhyFGA1WqjJEFuhK4UQb8GapLY0g/ICFx0DPiTg6I7ihCOVyWjgjWc2\n0trrxWwyJPZoLcxcZZ7mMCf1HOekW5FlCUXVhTwSVZAkCbvVSAqTzQUZh0iSlJLjXIbLQmVRGm19\nXrLSrOSkWfnuibqUQk3mo3vIn9hmCIbj/OtHLbjHQ4z7o7T2eTEaJF48WDEtnzuVvO57FOc6eTn3\nfqGReUrB4NStjIXgCUSIxBRCkTihiW2HgdEgf/qsfc4thBxrFpnWTMYmhCrLmkWWLXX3vwdJqauY\nf7/tr4lryorPVL9T/01+euMX9AUGcJmdfKPma9wauctoWK/90FC5NXKHTOt946IOT9ec4v3n1pOM\nTDz/6vANytPKptmxCpYXId6CNYnRIPPd43X0jwaxmQ3TqpdNRkOS2Qfo1eAz+Qdsq87hcvMwwXAc\nWZY4tkvvb+4Y9BGLqxOCrWGQJcymxYvMYuga9HGjfRSXzcQ3D1dxt2ccRdXYVJ6FZZnGEp/wmo/E\nFMYmHO1OX+0jFtfNZOKKxjtnOznQWJiwqoXU8rpn44ntxXQP+Rn1RchyWTiyfX4Tk9nITrOSOZGI\nBmAwSBgNMr7Q3FauJoOJ1za+wuWha0hI7MjbsqaXcCVJwiSt/PjSzC7+444fJ1W9Xxy8mvQYy5Sk\ntVz7zEWcESXK+f6LdPp6MMumRGCLHk8qWEnW7idZ8MgjyxLFOak5t529OcAnl3sJR+KkOy0UZNk5\nsbuUnAwbRTkO/vqFzXT0e8lJt1FZlMat9hE+vtiDMiFsLrt5WZanp3Lu5gAdE+5uj28pTPKz7h8J\n8M/v3SE+sZc/MBbkm08s/2ylLN9JRWEa11r1gBa71YgkyURi9+1L46rGvk35RGMKnYM+irIdHN2x\neMHNcFr4t19vJBCO4bCaCIRj9A77ycu0LXgWbjYZ+P4zG/nwq27ONw0mihO3Vk03AZmK0+Tg8eL9\ni30b6wJVU+ny9SAjU+oqTtkAa3IR2ZacTTSN3qXX34dRNvHN2hN0eLsSQSmNOTOvcPyh5W06vF0o\nqsJoNECOLROHyUF1xvTOC8HyIsRbsO4ZGgvy/lfdxOIqbk+I4fEQvkCUEU+Yf/9Ko24rmWEjb9L+\n6MXbQ1jMRozGGIqiEYmpHGicvcd7MXx1e4j3vtIDW+50jxONKVjNRsZ9ETZuyMTtCSWEG6C1N7VC\nrIVikGW+81QNpbkOPrzYg9lkQFU1DPL9PfvDW4swGGSOTHF6WwqyLOGym7nbPc5vP20lpqhkuSy8\n8Wz9gm+U0h1mXnmiisPbimjp9ZDutFC/YWbr2UcJVVP5bfOfafd0ALA5eyPPV56Y8/EzVX7fW6Xw\nRLz4YgE+6z1HVImyu2AHm2fxSVc1lQ6v/vlOs7gwG0zUZlTz5IZDCe/1xXBp6Bqne75AkmSeKju8\nLD7tDyNCvAXrnnumJXFFTcR8qprGmF/fK50aVgK6GBhkiZx0G9G4Qv2GzGUX7+6h5KXDszcG9Agz\n9NCVJ6YsJeemL1+FcZ87wP/8/XXG/VHyMqz85NVtHNlRQprDzK2OMTKcZg5vK55wrzOSv4Ql8vn4\n+FJPIiZ21Bfhq9tDi15Gz8mwkbNCUaGLIRgL8XnXbUL+OJuzNyY8yh8U/YHBhHAD3By5zcHifWRY\npgftfNh1istD17EYzDxfeWJaUpgsyaRb0vjF7d/hj+mf3bfb3yfXljVjm5imacTVOGORcUyykTRz\nGvuLdpNlXfxN1Wh4jA87T6Ghf17eaf+A8rTSNVlkuNoI8Rase4pznBRm2eke9iNJEmaTjMEgU5zj\nmFG4AY7v3UBnn4eOAR+VRWm8fGj5q2JLch2J2E/Qq67v5Vdr6DcbT+8p42qrG5fNzM46PZCkIMue\ncmW2qmq8fbaDps4xMl0WXj5URXa6lZ+928SIR3dN6x8J8rN3b/MfvrGFnXV5Cbc2YFkK4hbKImIN\n1iTheIR/afo1PsVHPK5we7SFV2tfXFRuw2KZfrMgYZxh37zN08HFwSsAhOIh/tx6kv+w/UfTxhpR\nIgyH3KiaisVgxigbGQ2Pzyje5wcu6WOQjCiqSqEjP6VY1LkIxkIJ4QZQNIVQPCLEewaEeAvWPSaj\nzPef3sitzlE8/gjeYAybxcje+jxudoxiMsjUlKQn/VBZLUa+/WTNio5r98Y8FEWjvV+vim/r8zDm\njyRuKPIz7WyuyGLvpnxa+zz88sNmFFVDAl56vGJWp7euQR9NnWOkO8zIssSlZjdo4Av6+d2pVn70\ntc34Q8n93OOByIznehAc21nKrz9tIRZXyUm3sntj3vxPWgf0+vsZi4wnAjs6vJ0EYsEHmkGdb89l\nT8FOvhy4CEg8UXJgxtcPxpLT4CJKFFVTMUjJ9Qfn+i8SjIWIqTH8kkShPZ8i58wBPqPhMYyyIVGV\nvhzFgPmOPPLsuQxNpKuVukqSqt4F9xHiLXgosJgNbK+5PzuIxVV+9m4TfRO94I2VWSsyu54LSZLY\n31BAboaNX350l7iiEY4opDvMHN5aTLrTzLvnO3FaTQyOhVAm9r814Eqze0bx7nMH+Pl7dxKPTbOb\n0DSNUW+E6EQ1+bVWNzvrcvngQjdo+jh21y2vYHYMeDl7YxCzSebI9uI5vcyrS9L5j9/Ygi8YIzvN\nmrLv/FrHOWU2aJJN06q0HwRHSg+yt2AnsiTNau5SlVFOuiUdT0Q3PtqSuxmDPL1w8Ia7iUxrBoFY\nEA2NbXkNs9q0VmdUcHPC71w/rlzyezHJRl7b+A2aRu4gSzL12XXCnW0WhHgLHko6B3wJ4QbddOT4\n7rIVqSifj1sdo6iaXsCV4bKQl2mnqjiN//PWLeKKLsLWKUlojlnG2drrSQg36L7nsbiacJ2zWgyc\nPN/Ff3ltBwWZdpp7PWwsy0iEiSyEWFyl3x0gHo0nbT+M+SL84sPmRN9873BgXi9zh9WEw/rgr/1K\nku/I42jpIS64L6HJEic2HMVkWJ33aDfZUDUVRVWmibI7NIqixvnuxldp83ZgNVhnrQZ3mh0E40Fc\nE7P3Qsfsn5uNWTUYpBfo8vWQZ8+ZtSJ9oVgMZrblNS7LuR5mhHgLHkqmiqFBljAZVucOPs2ZPBtL\nd5hp7/clhBt0y9eqojQ6J9rKntpdOuO5cqYUtRXlONiQ7+Lkl10YZAmb5b7RzIEthRzYsrgiPI8/\nwj+dvIM/HMMoS3znqVqKJ0xYhsaCSfGiY/4IgXAM1yxWscFwnFNXevGHYmyvyaW65OFZBt1dsJ1n\nGw+temzn1eEbfND5Kaqm8VjRbg4W7wPg057POd9/AYCajCpeqn52zpns8xUn+HPbSbxRH5uy6tic\nvXHO163JrKQmc+kzbsHCEeItWBNcbXHTPxKkotBFXdnSW4BK8pwcaCjgixsDGAwSz+8vx5JCzvdK\ncKChkFFvmPY+L3lZdk7sKWNoLHkPMj/TzuvH52+JqS/P4uiOMNfbRkl3mHl+/wZsFiNtfV76RgJo\nqgYS/N3PL7Ah38U3j1TNWrQ3F1/cGGDMH8FklAlFFT6+1Mt3J1LJ8rPsmI1ywv40O80656z615+0\n0Dmoi9ud7nH+6rl6CrMf3L7ww04oHuL9zk9RNX315fO+89RkVuEyORLCDdA83kqPr4+ytNnbAXPt\n2fyg4TsrPmbB0hHiLVh1Pr/ez4cXewA9NvOVw5U0VCQbcHQMeBkYCVKa70rZuOXYrlIObyvGIEur\nGk9pMsrT9tudNhPP7C3jSrMbh800ZzLZVB7fUsTjW5Kret94diODo0E+vdyXCHRp6/dy+mo/x2eZ\nxc/F1FCSyccZTguvH6/j3K0BLEY9FnW266tpWlLLnKJq9A4HhHgvI3rxmZL8t3gEl2mGXOwH9DWI\nKjEuDV0lqkRpzNm0pL5vwcwI8RasOne7x5OOm7s9SeJ9tcXNHz5rB/Tl728/WUN1cWpLr3MVR6ma\nRp87gMkgr2if82zsqc9PxJwuFaNBpjjXSXxSfChAYB4L0dnYv7mAO13jhGMKFqPM4W3JNwuleU5K\n8+Z3g3N7wngDEfyhGFazkUyXhcLstdX2o6iKnrSlKdRlVmNehaKzpZBuTqMms4rmifSvIkchRc4C\njLKRA0V7+bzvPAC1GdXcdN/m0+7PKU8rZW/hLoKxIE6zc9ltY3/b/Ce6ffoN+ZXhG/yg4TvksjL5\n5I8qQrwFq05OupWuSbOz7Cn7uldb3In/r6ga11pHUhbvqYx6w/zxs3ZCMRV/IEIoqs9YHmso4Kld\nC5+hLgexuEL/SJA0h5kM59Jyr3fU5tI54ENDv9GZHEk6mdl84O+RlWblb15qQJFliCspFfrFFRXj\nlLqCt77owGY1EVc0VE2joSIrsXe+0gyNBfn9mXY8/giNVdk8vads2nvWNI03W96ibcLo5OLgVb5T\n/8017YE+FUmSeKnqWVrHO1A0haqMikT/98HifTTk1BNXFS4MXubq8A0Aun29fN73JbIk4TQ7+Xbt\n18leptCWUDycEG79OESPr48KFl40KZid9fMJFaxpYnGFd8930ecOUJrn5MSesmk/5LNxfHcZ0bjK\nwGiQisI0DjQmf8md9mThcNkXX9H75uk2et0BFFVjaDRIhsuCzWLkixsDHGgowL7CFdGj3jAnz3cR\njMTZWZdLXWkmP323CbcnjEGWeOnximlbBguhsTKbdIeZgdEgpXnOacvTmqbxzrlOLje7cdpMvHyo\nkrL8mWdENouR3FwXw8M+QpE475zrZHg8RGVhGsd2lSaWyj3+CL/8qJnBsRAluQ7+4sla7Fb9p8Uf\nimGYqLIHEv/7IPjDmXYGRvWOgy+bhijOcbJlih+6J+pNCDfAYHCIfv/AnPvCaxFZkmctHLvntjYU\nvH8T7I8FkIB0Sxr+qJ8zved4qfrZZRmLxWDGbrQTjN/r9pBmdHwTLA0h3oJl4eNLvVxu1n8cBsdC\n2C3GlH2yLWYDrxyevQf7+O4yPP4o/aNByvNdHNqyeBene6la91AmKr4lWBFnrKGxIL891YbHH6Gh\nIovuIT/DE85nfe4A3TV+3BPHiqrx8cXeJYk3QFm+a1ZBvtUxxoU7ugGGJxDlD2fa+Q/f2DLvOU+e\n7+JGu544NjgWIs1hTrSffXChh8GJArye4QCnrvbyzF59D39HbW6insFslNlc8eAiOT2BaNKxd8ox\n6EIjS4akPWObce3Yry4n5WlliYxuIGl7QJmyZ74UZEnmlZoX+KDrU6JKlD0FOyhwPBzGPGsJId6C\nZWF4PLl6+p5ALQdOm4k3nq1flnPVb8jk4t1hrGYDDpsJi9mABDy5swSb5f7XoX8kwBc3BjAaZA5t\nLSJzkTPGP3zWnrg2F+8OE44qidfRAH8wWVBW2lkzEE7eA/eHU9sTd3tm//cNRZPd3EKR+0JwoLGQ\n/Ew7o74wlUVpC8pCXypbqrI5d2sQAIvJwMay6UVTNqONZyuO8X7nJ6iaysGifeTal3bztFY5WLwX\nu8nGcNBNmtnFV4OXiSgRzAYz+wp3LetrFTkL+P6mby/rOQXJCPEWLAvVJem09t1PxapZ5J70cuMP\nxbjTNYbNYqR+QybP7ttAYbYdVZYpybJhMRkwGuQkj29/KMbPT94hPGF80jng42+/3pDyNsBkfMH7\n4ihJElkuS2Kf3WSUObytGH84Tv9IEKMssbk8i4HR4JKytOeiriyTM9f68U8Usu2s1V3pBkaDdPR7\nyc20UVU0/d+upiQjyfSmdlKv9q66PDr6faiahtEgsaM2eZ9d7+t+8J+H47tLKc514PFHqSvLmPXG\nYXP2RjZnb5y3DmC9EowFMckmTAYTu/K3Jf6+Na8Bd2iEbGsWLvODqUMQLB9CvAXLwr5NBdjMRn3P\nO9+55KXf5SAYjvEPb91KLJ9ur87hawcr2FmXl9jLnYnBsWBCuEE3IfEFY4uafW+rzuGz6/2APvt7\n/ala7vR4CIZjbK3OoTjXyV89V0/vcIDfn27jzPV+zlzv58Tu0kW5os1FXFH54no/ZqNMfqaNg42F\nNFRm0zXoS8oVf3bfhmn+44e3FeGymxia2POe3ItfvyGTHz5fT/9oEJvZQLrjwe1rz4UkSQv6HD5s\nwq1qKn9ue4/bo3cxykaeqzjOxqz7fv5OkwOnafaWPU/ES/NYKw6Tg41ZNQ/d9VnvCPEWLBtbq3PY\nWj1zdfNq0NLrSdr3vNLi5tn9G+adQeem27AYZSITJiTpDvOs1daX7w5z6mofBlnimb0bprmHPbmz\nhKJsO55AlJqSDLLTrRRNVFt7/BH6RwLkZ9oZGA0yPmmsp6/2zSne/SMBfneqDW8gSkNlFs8/Vo48\nz4/rZ9f7+fL2UOK4e9hPQ2U219tGknLFrzS7p4m3JElJaWRTyc+088nlXpp7PEjAsV0lPNaQurtb\n95Af93iIsnzXtG4DweJoHmvj9uhdAOJqnHc7PqQuszolEfZEfPzTrV8RiuvbJV2+Hk6UH13R8QoW\nhhBvQUqoqobbE8JqMZI2iw3mWmOq65fNYsSQgllLmsPMa0/V8vn1AYwGiSPbi2fsF3ePh3jrbAf3\ndO+3n7bwk1e3TXNyqy+fXqR18c4w75zTn1uW56SxMvkx891g/PGzdka8+r7z5WY3pXnOpGCWmZha\nl+Ae158/1dZ0MdX8Lb0emnt0cxgN+OhiD7s35qcUQnK5eZg/f96Bhl7U9v2nN1KUohGPYHZianI9\nQ1xV0NCQUnBqaRlvSwg3wI2RJiHeawwh3oJ5iSsqv/yombY+L7Ik8ey+sjlnYWuFquJ0HttcwJe3\nB7GajXz98cqUl/7mqti+hzcYY9KElUhcJRSNp2TD+sFXXYnndg352VqdTXVROi19HkxGmef233dc\nO3O1j2ttI6Q5zDy/v5xMlyWxZ32PwJQI0JmoKcngVsdY4vjeKsH+zQUMjARp6fOQm27j6b1l855r\nKtoURzb9UJvxsVP56vZQ4pHRuMrVVrcQ72WgJrOKnIFs3CE9U35f4c6Er3koHuLDzlOMRTzUZlZN\nK1hzTYkVdcyxvC5YHYR4C+bldtcYbRPFaKqm8d6X3WyvzZ13mfZB4g1E+ehiD6FInF0b86gt1SuL\nn9pdyrFdJSuyX1ec4yDLZWF0ov2sLM+ZVPg2F1NlTZZlXnuqBl8whtVswGzSbwBud47x8eVeQHcr\ne/NUK3/1/Ca21+Qm9tJtZgP1G+b3g99WnYPRINE16Kco25EwcDEZZV49Or9b2lzUlGQkbj4Aju4o\nwWRMzUt+cpX/TMeCxWExmPlu/at0+XqxGa0UO+9vY7zT/iEt420A9AcGcJldbM6+761fm1nNrvzt\nXB2+icNk54XKEw98/IK5Ed8SwbxMmVRNm2U9KJo6x2jr85CXaWdXXW6SIP/yo+aEIUdbv5e/fn5T\nwvI0HFWwmg0pCXgsrqbshW4xG3jj2XqutrgxGCR21KR+Q3N8dynvnOtMLJtvLs9CkqRp4n9vaXzq\n8ZM7SyjJdST20ucrprvS4k4Y6OSkW2nt8xCOxtm7KX/e6zLqDfPhhR7C0Th76vPZOMONgixL/MWx\nGgbHglhMhjnzvafyzN4y/vWjFtxevZ1s/zIX6j3KmA3mGeM/hydm44njoBuyk4Nxniw7xJNlh1Z0\nfILFI8RbMC8byzIpzXPSPeTXe6J3lTzwWXdTxyi//rQ1cewPRhMmMHFFTQg36GYn/SNBHDYT//eD\nuwyMBsl0WvjOU7VzFkO9fbaDC3eGMRtlXnq8MqXZrNNm4kDjwmM3d9blUV2cTjASJy/ThkGeeW+4\nKMeOqqqAfkNxb0UBSDl97dzNAd77qhuATy/3IkkSdquRG+2jKKo27/h/8WFz4qaha8jPX7+wifzM\n6a1ssiwtKnAkJ93Gj762mbe+6KB7yM9bX3Ssagrco0B5WhlXh69PHElsSFsda2DB4hHiLZgXk1Hm\n+0/XMTASxGYxLmhWtVy09HqmHHs5skP//0aDTFG2g76RgH4sSxTl2DlzrS8h6mP+CO+e78RmMeIL\nRjm4vZTqAmfS+e85j0XjKn8400Zd6Y45Z+CfXunlq6Yh7BYjXztYQWnewnpl050W0id5mY/5Ioz7\nIxRk2bFZ9La733zSiqJqKKrGkW1FPLkrddvOwbEgXYP+hPMd6LnhTIg36D3sc4l3OBJPmv0rqsbw\nWGhG8V4Kp670cq1Nnw2O+SPYLUaeWUDSmmBhPFV2mHRLGuPhcWoyq6hIX3idg2B1EeItSAmDLD+w\nQImZyM2wTTlOvoH4i2M1nLrSq3uG1+aRl2knMmGGEldUPP4oAyNB7FYjLruJvg/v8K0j1VRNmMmE\np7iExeIqiqrNKt5tfV5OXekDIBiJ85tPWvhP39pGLK5gkOWk56lznOceTZ1j/O6ULtTpDjNvPFvP\n6at9hKIKJqMBExAIx2edoU+lc8DHv7yv9257A1FMRhmbxYjJKCftt8+X8GW1GJNujExGeUWKyaba\n1o56I7M8cv0Qiofo8HTjMNnXnFe6QTawf5ld1QQPFiHegnXBnk35+EMx2vq85GboFdG3O8e43jaC\n027iyPZinttfnvSc3RvzaOocY8QTJhpX0DQ9ItNklDGbDAyMBhPiXVOcQW66NWH7uWtj3pxtTlN9\nsv2hKG+ebuV62ygWk4FXDldSVZTO78+0catjFKfNzKtHqhI3QJGoQseAF7vVRGmek1NXelEmys89\ngSgXJvVj32MhOxVXW9yJ3m2X3YQE5Gfa2FWXi9lkoM8doDjHwaHcpd/mAAAgAElEQVRt8/vEf+ep\nGk5f7ScUiVFXlplSwthCqSvL5Fbn/Ur4jRtSy3++fHeYll4PuROmM4txwVsJgrEgP2/6VzwRvdDz\nsaI9PF68f5VHJXiYEOItWBfIksSxSZGdXYM+fvNpS6Ldaswb4bWnapOeU5zr5N+82MDfv3mNaFzF\nF4gSjirEFRVZlthQcL8VzGI28IPn6mnp9WA1G+eNHK0sTsNpNeIP6zP2/Cw719v04I5ITOEPZ9o5\nuqM4EebhDUb50+cd/M1LDYSjcf7x7SaGPWHCkTiyLBEIx7GaDNgmlrMNssThbUV0D/kJRuK4bCYO\nbtGXtz2BKC09HtId5mmmMPdwTBJYSZKo35DJq0cWV1Fut5o4uqOYf/ngLr/5tBWLycCrR6qpLEpb\n1PlmYktVNhaTTPeQn+Icx4y98VO51jrCn77o0A86xwhHlFnb3Dz+CKO+CPmZ9sSWwUpye6wlIdwA\nXw5cFuItWFaEeAvWJT3D/qQe68l54JOxmg1kuiy09/tw2k2YTQYaKrN47mAV2Q7TlMcaU7bTTLOb\n+eHzm7jZMYrNYkRT4c9nOxL/PRJTCISnBnbox7c7xxn2hFFVjXF/BA3IdFnw+KOYTfqy9J76fOxW\nI//u5UbG/RGyXFYsZgPj/gj/8NYt/KEYwXAcq9lAmsNMXFExGw0c3FLInvp8DjYW0j8SoL3fR36W\njRO7UytIuts9zufX+zEaZY7vKiU3V7/BuXh3mO6JaxyJKbx7vpN/+/XGlM6ZKnVlmSkX4QF0DyXb\n23YNzWx329Lj4deftBBTVFwTITeLDZpJFYvBMuV4fRgbCdYPQrwF65KiHAcS9/uli2fYh9U0jX95\n/y4j3ghGg4Sqwg+fr6e2NHNOb/NUSXdaeKyhkNZeD2+f7WDcF8FiNmCzGNm7KZ/GymzO3xokOCHa\nuzbmoWoaPW4/wXAMo0FG1fQisHGfLtyvHKqkoSo7sbdtsxiT+p6bOscY90cZ8YaJxhQkYGgshCRJ\n5GXZOHm+K5Hj/frxugWFbYx4wvzmk5bEcvv//eAu/1+17toWn7CKvcfU49VAr2wfThwXzVLpfupK\nLzFFH68vFOP8rcFFGdEshPqsGlrH22kavYPFYOG5iqdW9PUEjx5CvAXrkvKCNF4+VMnV1hFcdhPH\ndk6fWQbC8UShlX3CKnW2FnVV0+ga9CEhUZbvnFfwRjxhPIEo2WlWfvNJC5G4SprDTCyu8uKBcrZN\nWJX+6GubaevzkO6wUFmUxpun27jW6iYSU/EHY0iAjH6joaoaw57wnEVp9olqeUXRQANN0sXfIE8U\nxhkkvIFoomVrIeY0I95wkse5LxQjMOHktr02l0t3hxkPRJElUtorn41gOE73kI90p2VJ6Wk7anOJ\nRBVa+jzkZdg4uqN4xscZDBKaphGJKsiyhMGw8m2OsiTztaqnebr8KEbZmHA2EwiWCyHeggeGqmqc\nvtbH4GiQisI09tTnL+l8DZXZNFTOvsxtNRuS9qUNsjRjm5uqafz64xbudI8D0FiZzcuHKmc977VW\nN3/8rANV03BajQSjSsLYxWI2JLV/pTvMCc/xWFzletsIkiSR6bKgqhoOm5ERTxg0sFmN02xPp9JY\nlU12mpU+dwBVljBIEpKkV4EbZIl0h5nSvLltXbsGfbT2esh0WdlanZ0Q+KIcB3aLMbFSkJ9pw2k3\nMxqK4rSZ+PGLm+kdDpDuMJOTsbhcbm8wyj++3YQnEEVCTzDbtXHxVrv7GwrY3zC3qcvjW4q43HyN\nSFTBaJATXQgPArNYLhesEEK8BQ+Mjy/18PmNAQBud40jS9K0H+5YXNULtOymGY1gOgd8BMMxKorS\nsJrn/vgaDTJ/cayW97/qIhpXOdBQOK3lDKB/JJgQboDrbSMc2lo4a/7zqSt9qBNTeH8ojsUoJ2as\nmU7LrMu3BoOEzWxI5HnLsh5Z+dVEZbksSXPejNx7zOvH6/jVR81EYgrRmML+zQXkZNjQNI0tVdlz\nFmR1Dfr4+Xt3EpXtI94wT+7U25icNhPff7qOr24PYTLIHNhSmBTkYjUbE9X5i+VqizuR9KahJ50t\nRbxTIRCOkTFxs2SQJS43u3l234aUXPQEgrWKEG/BA6N7SlFZ95A/8cMdV1TeO9/FZ9f7MRhkNuS7\neP14bdJ+78eXejhzTffzzkmz8oPn6uf1wS7KcfCXz9TP+RjTDMuoc7UcaZpGMBxHlvWM7oNbijAa\nZBRVY0dt7qzOYLIk8Y0nqvnjZ+2EonH2b8rnyI4SakszGBwNsiHfRUkKRi+VRWn8zUsNuD0h8rPs\ndA36GB4LUVmUPi0hbCp3uscTwg36Hvo98QbIy7RPa7lbTsxT/M5TSR1bKhaTAVmSkCf+nU1GeUFt\ndwLBWkSIt2BZCEfjROPqnHGhxTmOpKrw4tz7M9Q3T7Vx5lofsbiKNLEUfL5pkCe26fuYqqbxxcSs\nHcDtDXO7a2zeGMxUyMu081hDQeL8R7YXk+GcuRrZG4jQ5w4y6g0jSXqR1L5NBSlbeVYWpfGTV7cm\n/a26OH3e1rQRT5hPJ3rBH9tcQEmek0yXhc+u9fPRpR5An8W+dqx2ztlx5pT3NfV4pdlRm8vtrjE6\nBnxYTQaefQAuarWlGWytyuZq6wgmo8yLBytWJKhGIHiQCPEWLJnLzcO8fbYTRdVoqMji5UMzR28e\n3VmCwSAzMBKkvNDF7olZt6Zp3OkeT1SOa5pGJKYkVTTLkoTZKCeWnEGfUS0XT+0qZf/mAiRpeg74\nPToGvPyP31zDG4giSXoxWDimrHgBVFxR+ef37ySWm9v6vPztSw2kOczc6hxNPE7V9AS4ucR7R10u\nbk+YO11jZKVbeeFA+YLH0zPsJxCKUV6QtmD/cZNR5nsn6giE41hMhgcy85YkiZcer+SZvRswGqWU\nXeqWg4uDV+n0dZNny2F/4W4MsvBrFywPQrwFSyKuqLwzIdwAN9pH2VKVTU3JdIcso0FOWqK9hyRJ\nZKVZCIZjjPkjoIHLbp6WGf7iwQrePN1GNK7SUJE1Y7rVUpjPOeytLzqJxBQ09Kp1VdGtR+9Jd1xR\nOXWlj/6RABvyXRzYUrgsAS6+YCwh3KD3WQ+Ph7BZDNjMRn0wE68z24rBPWRJ4um9ZYtulTp9tY9P\nJiJKc9Kt/ODZ+bcupiJJ0oq4tM3Hgw46uTJ8gw+7PgWgeayVmBrnSOnBBzoGwcOLEO9HjJvto1xt\nceO0m3hyZ8mss8xU0Sb6lCczWw+w2xPi/K1BZFnisYZC0ifFX756pJq3z3Yw5otQUZjG8d2lifau\ne9SVZfJfXttOLK7OW6y2EkRjChaTgfDk2b/ZQGufl9rSDD653JtYem/t82IyyuxbhnhLl91EusOc\nEHCryYCmafyP317DG4wRiSrkZlipK81g3+alVfDPhaZpfDZRcwB6vnhT5xg7alPfurhnTOOwmh76\n1LAeX1/ysb9vlkcKBAtHiPcjRNegj9+dak0sT4/5Inz/6Y1LOqfJKHOgsZDPrus/6iU5DqpnmHUH\nw3H+6eSdRCtUS4+Hv3mpIVEYlpthm7ewDPSAFIN5dXpmH2ss4N1znfhDMTRNI91pxmU3J/LN+9yB\npMf3TjleLEaDvtT86ZU+FEVlf0MBn1zqxRuIEorovcuby7MSKVyfX+/ny6YhbBYDLzxWvmyBMpIk\nYTLKCcMTAPMClr3D0Tj//N4d+kb0zO9vHa2monD5LFbXGkXOAm6ONCWOCx0rd2MlePQQ4v0I0ecO\nJCVKLZe4PLmzhI1lGURiKmX5zhkrtYfGg0k9zKMT8ZeztWOtRfZtKqA0z8Xn1/q42TGGLEtUFqUl\n/MXL8px0DNx3bVtoROhcZKVZeflQJcFwnLfPdXCt1Z3olZYkiWttIzyzbwMdA14+vKgXsHmD8K+f\ntPCfXt22bON44bFy3jzTRiyuUr8hk00peJDf46umIfpG9IjWSEzhvS+7+DcvNizb2NYa23MbiSkx\nOrzd5NtzOVi8d7WHJHiIEOL9iBCLK7jHw/iDUawWI0aDvKziMt/sLstl1WdtE0vqdotx3ramtUhx\njoNXj9bg9oSIxlQKsuyJfuHD24oxGmT6J9q+lmpCMxNvne2gqXMMdSLj2yDpjmGBUGxiSXpK2lkw\nRlxRly1ta+OGTP5z8XZicWXatsY9hsaCXG8bxWEzsqsuL/HayhR7O0WZxe7uIUGSJPYW7mRv4c7V\nHorgIUSI9yPCrz5qoa1f34cNR+IcaCzkxJ6V9XeeTJrDzLeP1nD6ah8GWeLojuJlrRZ/0My0YiDL\nEo9vXbxtaCoMj4cAPWfbOBFMkuG0kOG06CsBhWlJLmkbyzIXJNyqps1bZGcyyrNWiY94wvzj201E\nJm7SeoYCfOOJKkBvE7va7GY8ENVT07av7LUSCB5mhHg/AkSiCm39ejyhxWzEYobqkvQFVwkvlcqi\ntGWNkXwUqSlOx+0JYzbpaWJpdhPZ6TZenGj5SnPoaWc32kawWYxsr81J6bzeYJR//aiF/pEAZflO\nXj1Ss6jozLZ+b0K4QW9du8fASJDasgwsJgPbqnNmtKoVCASpIcT7EcBkknHaTIk9Z4kHb86x3hj1\nhvnT5x14A1Eaq7I5sn3m0IsHzbFdpaQ7LYx4w9SUpM/Ykpfpsix4BeDDCz2JEJfOQT+nrvbyzN6F\nG6hMjdq8d3y9bYQ3T7cl/p7uMAvxFgiWgBDvRwBZkvj2kzW8c1bvU963KX/ZKpDXI7G4wle3BvD5\nwtRvmHlZ+c3TbYmCvtNX+8jPtM1YnHWna4wrLW5cdjNPbCte1Gx16tiutY6garClMjvRTtUz7Ofk\ned2j/WBjwbI7kwXCyYEowSlZ5KlSXZzOsZ0lXLo7jMNm4vnHygG43TmW9LimzrFpffwCgSB1hHg/\nIhTnOPjrFzat9jCWHVXTaOocIxxRqN+QMWsR1T3iiso/nbzD0HiIWFylsjCN7xyvnbbPO+aLzHkM\nujf7rz9p4V6b+4g3zHeP1y3+vaga//z+3YQH/OW7w7zxbD2SBL/8sDmxj/3bT1vpGvRTmO1ge03O\nsgRs7KzNpaPfi6rp6WtLsZ090FjIgcbCpL/NNiMXCASLQ4i3YF3zxzPtXGsbAeDz6xZ++PymOWe/\nfe4Ave5AouCqrd/LqDc8rQBtY1kGl5rdAJgM8oze473Dfib700wNXlkobk8o6Rz9o0EGR4NkuCwJ\n4Y4rKu7xMF/c6MdiNtIz7OfFgxVLel2ATeVZpDvMDIwGKc51LilneyYObyvCH4rpNx059hnz1wUC\nQeoI8RasW2JxJSHcAGP+CG39HhoqZo/VtFuNTJ6nGmRpRre25/aXU5jtwBuMUr8hk/wZxKwox4EE\nid754pyZo0BTxW41YZClhGOdLEk4bCYcViMluQ56hgNEospEfre+nH6zY3RZxBv0dr9Ut1PGfBG+\nuj2EQZbYvzl/3hUPk9HAS4/PnpEuEAgWhhBvwbpjcDTIBxe6icUVVFVLWjaez+41J93G8T2lnLk2\ngAw8vXfDjD7bsjw9a3wqZfkuXnmiiqsTe95P7lh8UZvHH6Fz0MfBxkIu3BlC0+DYrpLE8vLrT9Xx\nZdMg3cN+bneOJd5zhuPB98oHw3F++m4TvqC+T97cM85fv7DpgQZ+CASPOkK8BeuKuKLyfz+4i2+i\ncl5VVaxmE6qmsW9TQUp2m/s2FfD8oWrc7qUtcwNsLs9i8wJcxmZiaDzEz95pIhRVkNBn/Tvrkvec\nLWZDooL8k8u9XGl247QZl23WnQo32kZ451wngXCccCSOfeKmZ3AshMcfFdXjAsEDRIi3YF0RCMcT\nwg1gNBp45XAVNSXpC8poXkt5zldb3ImoUw09x3yqeE/myPbiB966FgzH+ONn7cRVDVXT8AajmM0G\njAYZm9mAYxVSwgSCR5lVWed69913ee6556ivr+fmzZurMQTBOsVlM5Gfeb+4zGY26HvPa0iMF4p1\nitOcbRFpW33uAJ9e6eVaqzsRlLKchCIK8Ym9eKNBJsNlIctloTTXyV8cq32gbnlxRSU4pbVNIHjU\nWJWZd21tLX//93/Pf/tv/201Xl6wjpFlideP1/HF9X5iisrujXmrkg29nOzbnE/HoI+2Pi/pDvOC\ne7h7h/387N3bCXEdGgtxbNfyVHNrmkbngA9F0ygvcCWCVyoK0njj2fpZb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"text/plain": "<matplotlib.figure.Figure at 0xd182710>",
"output_type": "display_data",
"metadata": {}
}
]
}
]
}
],
"metadata": {
"name": "K-Means"
},
"nbformat": 3,
"nbformat_minor": 0
}
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@germanramos germanramos commented Jan 19, 2016

Excellent work!!!

I have put your code in a reusable function and added an stop parameter used when valid centroids values are reached:

import tensorflow as tf

def kMeansCluster(vector_values, num_clusters, max_num_steps, stop_coeficient = 0.0):
  vectors = tf.constant(vector_values)
  centroids = tf.Variable(tf.slice(tf.random_shuffle(vectors),
                                   [0,0],[num_clusters,-1]))
  old_centroids = tf.Variable(tf.zeros([num_clusters,2]))
  centroid_distance = tf.Variable(tf.zeros([num_clusters,2]))

  expanded_vectors = tf.expand_dims(vectors, 0)
  expanded_centroids = tf.expand_dims(centroids, 1)

  print expanded_vectors.get_shape()
  print expanded_centroids.get_shape()

  distances = tf.reduce_sum(
    tf.square(tf.sub(expanded_vectors, expanded_centroids)), 2)
  assignments = tf.argmin(distances, 0)

  means = tf.concat(0, [
    tf.reduce_mean(
        tf.gather(vectors,
                  tf.reshape(
                    tf.where(
                      tf.equal(assignments, c)
                    ),[1,-1])
                 ),reduction_indices=[1])
    for c in xrange(num_clusters)])

  save_old_centroids = tf.assign(old_centroids, centroids)

  update_centroids = tf.assign(centroids, means)
  init_op = tf.initialize_all_variables()

  performance = tf.assign(centroid_distance, tf.sub(centroids, old_centroids))
  check_stop = tf.reduce_sum(tf.abs(performance))

  with tf.Session() as sess:
    sess.run(init_op)
    for step in xrange(max_num_steps):
      print "Running step " + str(step)
      sess.run(save_old_centroids)
      _, centroid_values, assignment_values = sess.run([update_centroids,
                                                        centroids,
                                                        assignments])
      sess.run(check_stop)
      current_stop_coeficient = check_stop.eval()
      print "coeficient:", current_stop_coeficient
      if current_stop_coeficient <= stop_coeficient:
        break

    return centroid_values, assignment_values
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@narphorium narphorium commented Jan 29, 2016

Thanks @germanramos! That looks great.

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@vlad17 vlad17 commented Apr 27, 2016

This looks like it serializes the centroids and assignments, copies them from the backend to the python process, and then sends them back to the engine in the next step. Is there any way to avoid this copying without making max_num_steps ops?

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@narphorium narphorium commented Jun 6, 2016

That's a good point @vlad17. You can do iteration in TF with tf.tf.while_loop but it is a bit more advanced.

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@amineHorseman amineHorseman commented Jun 15, 2016

Good tutorial,

We can simplify the code of calculating the means by using tf.boolean_mask instead of tf.reshape(tf.where(..)):

means = tf.pack([
    tf.reduce_mean(
        tf.boolean_mask(
            vectors, tf.equal(assignments, c)
        ), 0) 
    for c in xrange(num_clusters)])

I think it's more intuitive

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@h4p h4p commented Sep 3, 2016

Hello,

when I input values of shape (1000,1), I'm getting a lot of NaNs in the centroid list.

array([[-0.0615779 ],
       [ 0.        ],
       [-0.01855482],
       [        nan],
       [        nan],
       [        nan],
       [        nan],
       [-0.03768255],
       [ 0.01288017],
       [ 0.01535422],
       [ 0.04958867],
       [        nan],
       [-0.01960552],
       [ 0.09472825],
       [-0.09461572],
       [        nan]]

Basically I want to do the same as this MATLAB code does:

  >> load fisheriris
  >> X = meas(:,3); 
  >> [idx,C] = kmeans(X,3);
  >> size(X) => [150,1]
  >> size(idx) => [150,1]
  >> size(C) => [3,1]

I think there's problem with the calculation of means, because this is where the assignment for centroids is coming from, but I'm not sure where the nan is coming from. Can somebody please give me a hint to fix? :)

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@nickleefly nickleefly commented Jun 13, 2017

tf.sub need changes to tf.subtract
and

means = tf.concat(0, [
    tf.reduce_mean(
        tf.gather(vectors,
                  tf.reshape(
                    tf.where(
                      tf.equal(assignments, c)
                    ),[1,-1])
                 ),reduction_indices=[1])
    for c in xrange(num_clusters)])

to

means = tf.concat([
    tf.reduce_mean(
        tf.gather(vectors,
                  tf.reshape(
                    tf.where(
                      tf.equal(assignments, c)
                    ),[1,-1])
                 ),reduction_indices=[1])
    for c in xrange(num_clusters)], 0)
@ghdcjs14

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@ghdcjs14 ghdcjs14 commented Nov 12, 2018

Thank you!!
In python 3 , I think it works!

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
import tensorflow as tf

num_points = 2000
vectors_set = []

for i in range(num_points):
  if np.random.random() > 0.5:
    vectors_set.append([np.random.normal(0.0, 0.9), np.random.normal(0.0, 0.9)])
  else :
    vectors_set.append([np.random.normal(3.0, 0.5), np.random.normal(1.0, 0.5)])
    
df = pd.DataFrame({"x": [v[0] for v in vectors_set], "y": [v[1] for v in vectors_set]})
sns.lmplot("x","y", data=df, fit_reg=False, size=6)
plt.show()

# k-means algorithm
vectors = tf.constant(vectors_set)
num_clusters = 4
centroides = tf.Variable(tf.slice(tf.random_shuffle(vectors),[0,0],[k,-1]))

expanded_vectors = tf.expand_dims(vectors, 0)
expanded_centroides = tf.expand_dims(centroides, 1)

assignments = tf.argmin(tf.reduce_sum(tf.square(tf.subtract(expanded_vectors,expanded_centroides)), 2), 0)

means = tf.concat(axis=0, values=[
    tf.reduce_mean(
        tf.gather(vectors, 
                  tf.reshape(
                      tf.where(
                          tf.equal(assignments, c)
                      ), [1,-1])
                 ), axis=[1]) 
    for c in range(num_clusters)])

update_centroides = tf.assign(centroides, means)

init_op = tf.initialize_all_variables()

sess = tf.Session()
sess.run(init_op)

for step in range(100):
  _, centroid_values, assignment_values = sess.run([update_centroides, centroides, assignments])
  
data = {"x": [], "y": [], "cluster": []}

for i in range(len(assignment_values)):
  data["x"].append(vectors_set[i][0])
  data["y"].append(vectors_set[i][1])
  data["cluster"].append(assignment_values[i])
  
df = pd.DataFrame(data)
sns.lmplot("x","y",data=df,fit_reg=False, size=6, hue="cluster", legend=False)
plt.show()
@yusinshin

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@yusinshin yusinshin commented Mar 20, 2019

In python 3.6, it still works well. Thank You :D

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
import tensorflow as tf

num_points = 2000
vectors_set = []

for i in range(num_points):
    if np.random.random() > 0.5:
        vectors_set.append([np.random.normal(0.0, 0.9), np.random.normal(0.0, 0.9)])
    else:
        vectors_set.append([np.random.normal(3.0, 0.5), np.random.normal(1.0, 0.5)])

df = pd.DataFrame({"x": [v[0] for v in vectors_set], "y": [v[1] for v in vectors_set]})
sns.lmplot("x", "y", data=df, fit_reg=False, height=6)
plt.show()

# k-means algorithm
vectors = tf.constant(vectors_set)
num_clusters = 4
centroides = tf.Variable(tf.slice(tf.random_shuffle(vectors), [0, 0], [num_clusters, -1]))

expanded_vectors = tf.expand_dims(vectors, 0)
expanded_centroides = tf.expand_dims(centroides, 1)

assignments = tf.argmin(tf.reduce_sum(tf.square(tf.subtract(expanded_vectors, expanded_centroides)), 2), 0)

means = tf.concat(axis=0, values=[
    tf.reduce_mean(
        tf.gather(vectors,
                  tf.reshape(
                      tf.where(
                          tf.equal(assignments, c)
                      ), [1, -1])
                  ), axis=[1])
    for c in range(num_clusters)])

update_centroides = tf.assign(centroides, means)

init_op = tf.global_variables_initializer()

sess = tf.Session()
sess.run(init_op)

for step in range(100):
    _, centroid_values, assignment_values = sess.run([update_centroides, centroides, assignments])

data = {"x": [], "y": [], "cluster": []}

for i in range(len(assignment_values)):
    data["x"].append(vectors_set[i][0])
    data["y"].append(vectors_set[i][1])
    data["cluster"].append(assignment_values[i])

df = pd.DataFrame(data)
sns.lmplot("x", "y", data=df, fit_reg=False, height=6, hue="cluster", legend=False)
plt.show()
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