{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# `numpy` Neural Networks: Mini-batches, Momentum & learning Rate Decay\n", "\n", "We've got a multi-layer neural network that can learn to classify the \"hard\" data. However, training is a bit unstable. Let's implement some tricks of the trade to help improve the training process. Thanks to Eric Postma for suggesting this direction!\n", "\n", "These training improvements require adjusting some functions that we've already defined. In this notebook we will copy/paste a new version of each function that is being adjusted so that we can compare to the old version. We'll comment important changes in the code.\n", "\n", "First, all the boilerplate from the previous notebooks. Maybe it's getting time to use a `common.py`..." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The toy dataset" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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gS0lPvSmjx2drHJmq8AsPjHZjDbYFE3N1Kq2A/qxLO4x4cqLMnuF8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\nFWKNv8VisVyF/H+8zSyfuafZRgAAAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x11029e5c0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def rescale(X):\n", " return (X - X.mean(axis=0)) / (X.var(axis=0))\n", "\n", "np.random.seed(1337)\n", "n_samples = 1000\n", "X0 = np.random.normal(loc=[0,0], scale=[2,0.5], size=(int(n_samples/2), 2))\n", "X11 = np.random.normal(loc=[0,4], scale=[0.5,1], size=(int(n_samples/4), 2))\n", "X12 = np.random.normal(loc=[0,-4], scale=[0.5,1], size=(int(n_samples/4), 2))\n", "X1 = np.vstack([X11, X12])\n", "X = np.vstack([X0, X1])\n", "\n", "X = rescale(X)\n", "\n", "y0 = np.zeros(shape=(int(n_samples/2), 1))\n", "y1 = np.ones(shape=(int(n_samples/2), 1))\n", "yhat = np.vstack([y0, y1])\n", "\n", "# shuffle the data\n", "inds = np.random.permutation(np.arange(n_samples))\n", "X = X[inds]\n", "yhat = yhat[inds]\n", "\n", "X0 = X[(yhat==0).reshape(-1)]\n", "X1 = X[(yhat==1).reshape(-1)]\n", "\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Activations & cost function" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def relu(z):\n", " return np.where(z>0, z, 0)\n", " \n", "def drelu_dz(z):\n", " return np.where(z>0, 1, 0)\n", "\n", "def sig(z):\n", " return 1 / (1 + np.exp(-z))\n", "\n", "def dsig_dz(z):\n", " return sig(z) * (1 - sig(z))\n", "\n", "def J(y, yhat):\n", " eps = 1e-8\n", " return -(yhat*np.log(y+eps) + (1-yhat)*np.log(1-y+eps))\n", "\n", "def dJ_dy(y, yhat):\n", " eps = 1e-8\n", " return (1-yhat)/(1-y+eps) - yhat/(y+eps)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Model initialization, forward & backward passes. Set the random seed so that we always initialize to the same values, so that we can compare different training strategies fairly." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def init_model(shape):\n", " np.random.seed(1234)\n", " w = {}\n", " b = {}\n", " for layer in range(1, len(shape)): # no weights for the input layer\n", " w[layer] = np.random.normal(0, 0.5, size=(shape[layer-1], shape[layer])) # dim: from_units, to_units\n", " b[layer] = np.random.normal(0, 0.5, size=(shape[layer], 1)) # dim: to_units, 1\n", " return w,b\n", "\n", "def forwardn(x0, w, b):\n", " n_layers = len(w)\n", " x_prev = x0\n", " for l in range(1, n_layers):\n", " x_l = relu(np.dot(x_prev, w[l]) + b[l].T) # output of a hidden layer\n", " x_prev = x_l\n", " return sig(np.dot(x_prev, w[n_layers]) + b[n_layers].T) # output of output layer\n", "\n", "def backwardn(x0, w, b, y, yhat, alpha):\n", " n_layers = len(w)\n", " z = {}\n", " x = {0:x0}\n", " \n", " # x and z values for calculating derivatives\n", " for l in range(1, n_layers+1):\n", " z[l] = np.dot(x[l-1], w[l]) + b[l].T\n", " x[l] = relu(z[l])\n", " \n", " delta = {}\n", " \n", " # deltas and updates\n", " for l in range(n_layers, 0, -1): # start with last layer and move backward\n", " if l == n_layers: # base case\n", " delta[l] = dJ_dy(y, yhat)*dsig_dz(z[n_layers])\n", " else: # recursive case\n", " delta[l] = np.dot(w[l+1], delta[l+1]) * drelu_dz(z[l]).T\n", "\n", " # update weights and biases\n", " w[l] -= alpha * np.multiply(delta[l], x[l-1]).T\n", " b[l] -= alpha * delta[l]\n", " \n", " return w, b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Training function" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def trainn(X, yhat, shape, alpha, n_epoch):\n", " n_samples = X.shape[0]\n", " n_input = X.shape[1]\n", " \n", " # keep track of performance during training\n", " costs = np.zeros(shape=(n_epoch,1))\n", "\n", " # random nonzero initialization\n", " w,b = init_model(shape)\n", "\n", " for epoch in range(n_epoch):\n", " for i in range(n_samples):\n", " x0 = X[i,:]; yh = yhat[i]\n", " y = forwardn(x0, w, b) # prediction for one sample\n", " w, b = backwardn(x0, w, b, y, yh, alpha) # take step\n", " \n", " # ### Some niceness to see our progress\n", " # Calculate total cost after epoch\n", " predictions = forwardn(X, w, b) # predictions for entire set\n", " costs[epoch] = np.mean(J(predictions, yhat)) # mean cost per sample\n", " # report progress\n", " accuracy = np.mean(predictions.round() == yhat) # current accuracy on entire set\n", " print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n", " \n", " print() \n", " return w, b, costs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Train the MLP from the previous notebook" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training accuracy after epoch 149: 99.4000%\n", "CPU times: user 12.9 s, sys: 739 ms, total: 13.6 s\n", "Wall time: 13 s\n" ] }, { "data": { "image/png": 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"text/plain": [ "<matplotlib.figure.Figure at 0x1118f0b38>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "shape = (2,3,4,1)\n", "alpha = 0.01\n", "n_epoch = 150\n", "%time w, b, costs = trainn(X, yhat, shape, alpha, n_epoch)\n", "plt.plot(costs); plt.title('Mean cost per sample after each epoch');" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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jsRGmr4XAIBUDvcTsu63Ex2klDLZc/GpEtOmg7ykKlSFB12YrGp7eBzsA8bAI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\nVA0MDDx9u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"text/plain": [ "<matplotlib.figure.Figure at 0x111ba2c18>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1 = np.linspace(-4,4,250)\n", "x2 = np.linspace(-1.5,1.5,250)\n", "fun_map = np.empty((x1.size, x2.size))\n", "for n,i in enumerate(x1):\n", " for m,j in enumerate(x2):\n", " fun_map[m,n] = forwardn([i,-j], w, b)\n", "\n", "X0 = X[(yhat==0).reshape(-1)]\n", "X1 = X[(yhat==1).reshape(-1)]\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Mini-Batches\n", "\n", "So far we have been doing stochastic gradient descent (SGD), which takes one step per sample. However, this can be a bit chaotic: we make a lot of updates using not a lot of data. We can start to smooth our process out by using so-called mini-batches (small groups of data points), and taking a step in the average direction dictated by doing backprop on each of those points.\n", "\n", "We first adjust our backward pass to accept multiple samples, and update `w` and `b` with the mean steps.\n", "\n", "Our new backprop functions, `backward_mini` will now accept a matrix `X0` as input, calculate the updates for each row, and average over those before making one update to `w` and `b`.\n", "\n", "Let's update our notation and call the update rule\n", "\n", "$$ w^\\ell\\ \\rightarrow\\ w^\\ell - \\alpha\\,dw^\\ell $$\n", "\n", "(and similar for $b$). This will allow us to talk more generally about changes to the update rule. \n", "\n", "Consider mini-batches of $m_{batch}$ samples, and let's consider weights between layers with $n^{\\ell-1}$ and $n^\\ell$ units. In the SQG case, $\\delta^\\ell$ had a shape of $(n^\\ell,\\, 1)$ (the same shape as $b^\\ell$). Now we stack our calculated $\\delta$s so that we get a matrix of shape $(n^\\ell,\\, m_{batch})$, one column per sample. The block of samples itself has shape $(m_{batch},\\, n^{\\ell-1})$. Recalling that $dw^\\ell = \\delta^\\ell x^{\\ell-1}$, we see the the dimension of size $m_{batch}$ is summed over (effectively summing over all the samples). For that reason we adjust the update rule to\n", "\n", "$$ dw^\\ell = \\delta^\\ell x^{\\ell-1} / m_{batch} $$\n", "\n", "so that we get an average instead of a sum. The approach for $db$ is simpler: we simply take a mean over the axis corresponding to the features. It's important here to take the mean using `delta[l].mean(axis=1, keepdims=True)`, where `keepdims=True` prevents numpy from making annoying 0-dimensional vectors after the mean.\n", "\n", "Because the steps we take are averaged over several samples, they are more stable than in stochastic gradient descent, so we can afford a larger learning rate and still expect to converge onto a solution." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def backward_mini(X0, w, b, y, yhat, alpha):\n", " n_layers = len(w)\n", " batch_size = len(yhat)\n", " z = {}\n", " x = {0:X0}\n", " delta = {}\n", "\n", " # x and z values for calculating derivatives\n", " for l in range(1, n_layers+1):\n", " z[l] = np.matmul(x[l-1], w[l]) + b[l].T # matmul instead of dot\n", " x[l] = relu(z[l])\n", " \n", " # deltas and updates\n", " for l in range(n_layers, 0, -1): # start with last layer and move backward\n", " if l == n_layers: # base case\n", " # delta is a column, so make the deltas from the samples go along axis 1 by transposing\n", " delta[l] = (dJ_dy(y, yhat) * dsig_dz(z[n_layers])).T\n", " else: # recursive case\n", " delta[l] = np.matmul(w[l+1], delta[l+1]) * drelu_dz(z[l]).T\n", " \n", " dw = np.matmul(delta[l], x[l-1]).T / batch_size # mean over samples\n", " db = delta[l].mean(axis=1, keepdims=True) # mean over samples\n", " \n", " # update weights and biases\n", " w[l] -= alpha * dw\n", " b[l] -= alpha * db\n", " \n", " return w, b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The training script requires minimal adjustment. We add an extra parameter `batch_size` and use it to loop through the training set taking steps of that size, passing these blocks to the backward function." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def train_mini(X, yhat, shape, alpha, n_epoch, batch_size):\n", " n_samples = X.shape[0]\n", " n_input = X.shape[1]\n", " \n", " # keep track of performance during training\n", " costs = np.zeros(shape=(n_epoch,1))\n", "\n", " # random nonzero initialization\n", " w,b = init_model(shape)\n", "\n", " for epoch in range(n_epoch):\n", " for i in range(0, n_samples, batch_size):\n", " X_batch = X[i:i+batch_size,:]\n", " yh = yhat[i:i+batch_size]\n", " \n", " y = forwardn(X_batch, w, b) # prediction for mini-batch\n", " w, b = backward_mini(X_batch, w, b, y, yh, alpha) # take step\n", " \n", " # ### Some niceness to see our progress\n", " # Calculate total cost after epoch\n", " predictions = forwardn(X, w, b) # predictions for entire set\n", " costs[epoch] = np.mean(J(predictions, yhat)) # mean cost per sample\n", " # report progress\n", " accuracy = np.mean(predictions.round() == yhat) # current accuracy on entire set\n", " print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n", " \n", " print() \n", " return w, b, costs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use a batch-size of 32, and increase the learning rate $\\alpha$ from 0.01 to 0.1. Note that at $\\alpha=0.1$, the previous SGD training run doesn't even converge!" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training accuracy after epoch 1999: 99.7000%\n", "CPU times: user 11.8 s, sys: 1.95 s, total: 13.7 s\n", "Wall time: 12.1 s\n" ] }, { "data": { "image/png": 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SO7paRkQkm/gld9OXmEREsolhct/W565uGRGR9OKX3PWYPRGRrOKX3Lf7hqqS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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x111ae9ef0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "batch_size = 32\n", "shape = (2,3,4,1)\n", "alpha = 0.1\n", "n_epoch = 2000\n", "%time w_mini, b_mini, costs_mini = train_mini(X, yhat, shape, alpha, n_epoch, batch_size)\n", "plt.plot(costs_mini, label='Mini-batch gradient descent')\n", "plt.plot(costs, label='SGD')\n", "plt.legend()\n", "plt.title('Mean cost per sample after each epoch');" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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URVEOGyHY5eOw2BOfi4j8GvB6YExErgM/CsQAjDE/B3wMeDPwAtAEvnMv9qsoiqIoyt3T\nt7AcB/YqS+ht2yw3wPftxb4URVEURdk7DtNqshs0qlVRFEVRTijGyLGxsByPWSqKoiiKsi/sR+E4\nEXmjiDwbVbj/3zdYPisinxCRv4wq4L95u22qYFEURVEUZc8QERd4P7bK/aPA20Tk0XXDfgT4iDHm\nrwBvBbZtXa2CRVEURVFOKAb2o5fQa4AXjDEvGmO6wIexFe/X7zofPR8Bbm63UY1hUZTjStWH611o\nhpB2YDoOBf1JK4qyG+Ru+gONicinh15/wBjzgaHXG1W3f+26bbwb+F0R+cdABvjG7XaqZzdFOY5U\nffhSCxIOZBzoGvv64ZSKFkVRdoxNa951llDJGPOqe9z124BfNMb8BxH5KuBXRORxY0y42Qp6ZlOU\n48j1rhUriejOKCGD91WwKIqyC/ahNP9Oqtt/F/BGAGPM/xCRJDAGLG62UY1hUZTjSDOE+Lq7orjY\n9xVFUXZIv/nhbh474EngkojMi0gcG1T70XVjrgLfACAijwBJoLjVRvVWTFGOI+nIDZQYOnl0jX1f\nURRlF4R7bLswxvgi8k7g44ALfMgY87SI/BjwaWPMR4F/Dvy8iHw/1jP1HVGR2U1RwaIox5HpuI1Z\nAWtZ6RrohDCfOtx5KYpyrDAGgt3HsOxgu+Zj2LY8w++9a+j5M8BX72abKlgU5ThS8GyA7fUuNKIs\noXkNuFUUZffcRdDtoaBnN0U5rhQ8FSiKotwTNobleLiS9WynKIqiKCcYbX6oKIqiKMqR5i7rsBwK\nKlgURVEU5cSiLiFFURRFUY4BO+wPdOioYFEU5d7RvkaKcizZr7Tm/UDPKIqi3Bva10hRjjXqElIU\n5fizE8uJ9jVSlGNLvzT/ceB4yCpFUQ6evuWkZ6zlpBdZTqr+2nHa10hRlANAb38URdmYnVpOtK+R\nohxrNOhWUZSDYb8CXis96BjoYsVIwYWUY1sBDLObvkYanKsoRwqtw6IoysGwXwGvVR9WQhCsWAkM\n3O7BqAuewBeaVnQINs2ga2ClB0mB0djGfY00OFdRjiQadKsoyv6z1wGvfQvIlQ6ExgoVzwVXwDew\n0LWCJOaAGLjZs+tNxiAXs5aVzawmw3NtBlANrOhZqcNrsipaFOUwMBp0qyjKQbCXAa/DQbYAcQck\nsq50jd2uOJD3rOhYDiHp2MdyOBAj17tbz7UZWGtNYCAl0A43DuZVFGXfMdgYlt08Dgu9pVGU48xe\nBrw+37ZWjzCAVmi3mXKsdWUybq0n3e5AIPVFDJGgAft6fYzL+rlWA4iJdS35BtLuQOiolUVRDpzj\nYmHRs4OiHGd2E/C6nqoPz7Wg6EMvtDErBQfSHgQCKwHkDLiO3WYnhPHYQCDFI+tLf9+wtVjqz7UZ\nWsuKb6w157S3tdBRFGXf0KBbRVEOhoJng1avd+0FX7CO3ufa0A6gFkAPKyIeTsJs0q5X9eGz9YEr\npxHFq6yEEDPgOeCEUAkgaay4eDgSQX2BNOKsjWHpi5rNxFJ/rit1a8FJu1aspF273nqhoxlFinIg\nHBfBojEsinLcKXjweBoeTFrREXOg7cOLHVj0oRFAxYdP1eBq265zvQttbPxJTMAIJAAfWPatWAhD\ne/sVwwbbrvgD0dFfZ9QDE8JzHXi2Bd1trCQFzwbYjsesWEkNWW+m44NxOy1apyjKPdGvdLubx2Gh\ntyuKchzZyPownIXzrG/FhgOEDNxFn2/aoNkrHRtLkhDIRKnK4lrx0TV2PR+bpjzi2Xosn48sKyuh\n3W/bt4KobcARK3Cudq1V5pXpgTVnPeutQmnnzjRoLfevKAeGFo5TFGV/2KyeSTe0FouyD7XQio5+\nOnIncussRK4gV6yVJDCwHIBnrAjpixwHmyWUjjKAfGPjXD7ThLlEZMHpWneTCxCJFtdYS8yf1OFB\nHya8gcAZduv0H5vRDO2xDaNxLoqy95jj4xJSwaIoR5HN4jeqPjxRt1aNtGOrz6Zdu065B0uBdfMI\n1rLSjqwlXhQca4ByYEVGOxIiBgii/fY1QhMYMdAyrGYBdQx0fcgKlEK7/XBoXYw9o/Qft7pwrQNn\nY9ZKs5tCcVruX1EOBA26VRTl7tnMgjIZs0GutcBWl20EUOpZMXPKs9aO/nknLVA3VlAYbAxIiLWq\ndIz9N+9YgdMvm+IRWVbECp26gWQIHez+bMEGuNyzgqe/7WH8aB8JsWIn60DTQDyMCsUFNvuoXyhu\nM2F2L9lPiqLsChUse4DBEJgQV/SuSjlBbBa/8aW2FQA9Y4VJXKxAuN6zQiMmMO5ZF05MwIlEhsGK\nGbDCwzc24Ha92Oifs3zsmaGNdRn1t9EXKCYasxndyCJjojk2AmvNiUV1XVrrBNhmpfq3i3NRFOWe\n6QfdHgeO9K/fAB3j40ZnUgcHZ11wkIoZ5b5js/iNfu+euNgYFRNG8SPAgthsnls96yLKuNY1VPQH\nFpR+AO6w+2dYtPjRe4GxGUMOdvv+0Lj1ImcjTLQNwYoVX2zwboi1roRYa0vFh3PxzQNrt4tzURRl\nTzAqWO6dtjG84IfkxN7OZRwhEQmUWHSmHhYz9t/BB69iRjmWrI/faAZQ8q2Voh5YIeBGXZT7lhPx\n4ULSBtx2QutqSWLFg8sgNiUY2s/6+NXhWJZmtI4TVbLtC5edYBgIq0ZoxYqPDb4FGHHtoJIPZ7yB\nYAENrFWUQ0CzhPYA77mQ1nfHqF5KU5rPEr/YI3uxRZBzOe00ARhx7O1jxrEfeEIcFTPK8WY4fsMP\nh4qzeTYzJ8CKCYkehoH75lwcFnvWbdRiYIHpB+H2x++E/vhhkdPf51aawmAFV4gN9jWOFScSleNv\nRSX9k44NAM4MnYY0sFZRDhRz0rKEROSNwH/Cnh4/aIx5z7rl3wH8e+BG9Nb7jDEf3G678U7AV/3e\nS/B7a9+vFNIsns9x83yB4oMupfksyQe61CcTTKaqKmaUo89WVVyH4zdu+tYCMRZVhF3wbYxKF/tr\n8xgE297wYQorFPKOzeTpx5x4DOJaNulNuCG+sa6m3rYj19KJ9jkWt/NcCiBtbKq0H9qg3nEX6lHR\nOA2sVRRlG+5ZsIiIC7wf+OvAdeBJEfmoMeaZdUN/3Rjzzt1s+1pijH9/9quZNkvMNItMditMNsqM\nVpuMfrbJw59dWDO+5zrcOjtCaS7LjfkCVx6yYiZ7qUWn4DEV31zMxOiLGm9LMQMqaJR7ZLMsoOF0\n3378Rj+eRaLv4KkYdDpWELjYEvoSRssNLETF4DoMNSbECg7PbG0Z2YjVOitD7NRS0zE2e6kaQBrb\nnyiI5pwGAgemXCukypHLKymDbs8av6IoB8JJimF5DfCCMeZFABH5MPDNwHrBsmvaPcPvL40iibMg\njyD5BEwkOO3XmHFqzLRLAzHTqTDRWmb2xhKzN5Z45Z9dW7Ot5XSSG1MFluYz3DhfIHxIKF3IkX+g\nQRh3OOstAzDu1slFYiYd/Q2T/biZofgZFTPKXbObKq7r41kKLtwiihMRCM2gf5CDtVD0Rckp17pf\nksbGhXTYvWDpZwRFYSer7+3ErRRirUKLUUn/amjn34+HaYXwYNaOrQeQi1nry/Wu7Rw9FYMHNTNI\nUfaXk5UlNAUMq4PrwGs3GPe/isjrgOeA7zfGXNtgzBpMGBI2mkgr8ueLg8Q8ikDRjfMZJpH4HHgg\n2SSJsMdZr8WUU2e2U2I6qDDbLDHZLjPSbDPy/G14fu0+QhFunh7hxswI16ZGuf1AAR6B4nyO07M1\nEGHSWwKsmAHIOR0VM8rOWe/+qfi2j84wfmjdP9vWIwltlVonalboYQNjE0DChTCwAqdfb0X6sSRR\nZVsT2tiW3bTkEex+hIFrqJ9xtBUGGzAcF+iIFVCuDEr/T8XsMX6hacVbEFXi7ac/V4KNC81pU0RF\n2VNOkoVlJ/wm8GvGmI6I/APgl4Cv32igiLwDeAdAkjSEASZcXYjxozNmdPGXVvRBr9RpAi+5Di/F\nckAOiT8ISZCRBIWwxTm3YcVMu8SMX2G2WWSivcR0qcp0qcpr//LKmrk0EnGuTIxya3aEa5OnePHB\ncW7OFUg+1mPydBVg12IGND37RLGR+2fFt7+8QsyOaQbb1yN5vg03u7ZoXNaFCQeKQZQFZOy64x7k\n4/CXTVtG38igYBxYUbNR/ZXtMFjrjGCtI9sF3Q5zq2vn2wnXVrzthNZ6AgO3161IrHhiIwG72OMa\ntjztxJ2mKMqOOWmVbm8AM0OvpxkE1wJgjCkPvfwg8N7NNmaM+QDwAYC8jJp1C4ee29SFYTEDYHyg\na0XNqpgRhzJQcV2ejo0BY0g8BlmInY4x4a8w6TaY6i4xY6pWzDSKjHSaPHr1No9evX3HPBcKOS5P\nnOb2XJ5r507x1MPT3JwrkH+ozVzWHm5fzJx2GwAUnA5gXU1biRn7rwYB3xds5P4Z9az1IOVa60Mp\nMneMefZ7POwiAitWrnWtNSHp2HVaBs64Npi1Y2zjwcmYTR0ede3FPzA2ZqT/VarvVqmso+8eWl+/\nZTOSWMHUM/CqjJ3b+iJw1agz9O3QHlPOsYIlwB7n+jRnbYqoKHuLWXtpPcrsxS/8SeCSiMxjhcpb\ngW8dHiAi54wxt6KXbwG+uAf73RN8cbkRO8X11FnIgMkk8Qu2y2w802O6XmLMWWJuuchMq8jF8m3m\nK0UmqjUmqjV4du32Ak+ozSZZmUsSXBCac3HcB0LaFz04awbBk8rJYKMicCNelH0TXYwDY8VGeii6\nNR4FotaDKGhVrPBoh+BGASXF0LpZstF6N3tQ860wWBXyDCwi/fc2s470Y2E2Krk/zHbWFRcYdSDr\n2e2NeBt3br7ath2gu2EkuoyNc8m59ndy2rszzVmbIirKnnNi6rAYY3wReSfwceyp6kPGmKdF5MeA\nTxtjPgr8ExF5C/b+rAJ8x73ud4OJDD3fhfVlxbpyxI1OgrEYsXhkqo/HuQ5cy0zyl0xiMkmYhPCR\nOCOJBtONEuNmidnlIjPtIhdLC0yuLFF4sUXhxRZ8Yu0U21mPxfkczXmPxoWA5lyc2MUe7Qsx8vmB\n9QWsBUatL/cBmzXxG43B42n7+gtNa4UYpmusOMnFbFxKPGpomHGsSykwNp6kG1W/Pe1FBeYC626J\nMUhfHhYqm52X+sXl1tdduRsyYq1Htagkv8FaUYYtIM804MmGPYb+V7gvlPwAzsfssVV8yEdxLtNx\nbYqoKHuM4YTFsBhjPgZ8bN177xp6/kPAD+3Fvu6KnYoZgG5vjSsJQJYGYgbAjcdoxOM8S5JnU/PA\nPGEuBTlwMw7j8WWm6yUmTIWZlRIzTStmCvUms08twVN3TrE6kaI4n6N6wWX5fJLYhYDEhR6dWY9C\n/E4xA9adpGLmiLOTJn6bjUnKwC3SipoUtgNbw2Q1Uyey2gVRSrOLjV0xw2OG2MxyspcGiroBJ7Rz\ncLH9j4bjTK62bZxNv+R//99+80UHeyxeABPrOj33+w+t/6y0doui3CUnK0voeLPeeWeCLcUMRNaZ\nvphx14qZMB5jIR5ngQKkztr3xlJw2pBNBcw2i4w7Vc4FZaZrZWYaRc5XihQWWhQWWvCptdPpeQ6V\n2QwLF/OsXHRYmU2RvNijcT7OyHiTgnt3YgZU0BwIO2nit9mY6117QU5KdAGPMmlcbBBsDECs2KhF\nsSxC1HeI7eNMhjsu90v47yZ7aDNCoBvYjKBslNbcNXC7Bw8k4Urbjhuu1NsXLjFsnE7fzdUPTO5b\nVFZCbYqoKHvMSYphuX/ZQMxAZJ25CzHTiMf4Ig5fip+F1HlwIZxM4pwLGYu3mGsucpYq040S57oV\nZholJleWmHixxsSLtTsq/jaycUoXsixeyFG65LA8lyJ9oUNzNs7pbGO1nkxO7HFoCvYhsZMmfpuN\n+VLLVoPNOTbDp99JGaw7pf8djQw0xIg6Igd3Fncbft3/8w6LFFdscbkeA7fQ3Vhe+j2I4mKfN6L0\n6npo3VnlAOIMehcN13fpBwkHG5xB+7Eq2hRRUfaUE+USOpHcrZgBW09mSMyEQNHzKJJGkqeAeUgn\nCceTJIIuU16N2eYi5/piplNhdqVIrt4m8/kKc5+v3DG94kSWysUMC/M5Fh4UludSpB7o0J7wOBOz\ncTsFp7tEbSW6AAAgAElEQVSlmAFNwT5U+paXP62B69hA1jg2CNdjICb6pflj2O9eOyqn32atSBn+\nyvbX7cf5esB4zH6vl3ybseNE297t3VccG1TsyqCFAFH2UzVSQk0zECvDNV1crLDxjRVew2isinIf\nEJg77wLC6EcWEq4+PyiMUcFystlKzEBUTyZ63hczUYsA6jYFWlwHYjE6wEuex0tEFX8B8knIGUZS\nIVPuCnPNRc6FS0w3bJG8qVqFMwt1zizUeejP1rYvaMc9bk/nuTFb4NqDBcxDUJ1Lkb3UIsi6nHFr\ngBUzYK0zKmYOkYIHcwkblJtw4HJog3CHU4v72T0iNqW5a6zLqD9mq/OfYSB2+oXYHKxwCLg7N1GI\nFTp+OIhNCcWmOS8FkBWomDsbKfZrvLjGur/aAVR7a2u3aKyKcsTYSoDY52E0zqx53YvWCzC0o2Ud\nM3j/INEYFmVzdpvRtCpm1rqalmIxqp7H05xDEnP2hD+WxD0dMB7rMB2JmcmgYsVMq8zpdp3zL1Y4\n/2IF/vvaaVVG0tyetWJm4aECi/M5Ug92KZxvYDy5Q8ykxZDRejL7z3BQrsHGtPRjWzpmkN2TcQZF\n2mr9AFw2dus42F9/0rEBsqFYgdGv6+IKxIxdvhJu3jBRsAXpetF++g0Z+7ExnRA8F0ZcmykUGFv1\nNi12nZ4ZBNo6kQsp6cJc3GYJ1UPwNFZFOVi2s4LYMYPXQbSsLzZ60bIe0I7EQDO0392VMIG3EtJe\njJEo+fgLHuamkC126DZcFv3O/h3YJmgMi3J37DajaQMxEwI3XJeb8TRPcB5J2Iq/nEqSDjucc5vM\ndkrMUGXKLzNTL3GuVWZ0ucnoU00efeo2/H+DafQ8h5vjBRZnc9yYLXD1IY+FC3nSD3UYn1gB2FDM\nAGQ0PfveGQ7KBStKQqzLpBZYS0QPSIkVCEt+JEgiYbM+lgUG1owEMJeGxR7UwoGFI+9YkVILNhY8\nHgPrTb8NAFirTHNoH2DFRiewFpwk9nucdSOXUGjdXa4MrDlno5o0KceKlddk7/kjVE4uG4kP2LkV\npBeN6w5ZQQAaxl4+m2GMlTCJ0wppLSRIFbv4Cy6ZhS7OLYOzYBgptxiptCgstchXW8T8jefki8Py\n2cl7POLdoy4hZe/ZTUaTOEgnUupDYqYOPO+6PM8pJD6BJOKQAzmT4HRQY9JtMtMpMxNWmG0VmepU\nGG8vM3ezwtzNCq/+1JU1U1jOJrl29hTl81luThfwH3a5fTFP+sEOYdxhJlZebSy5XswkozknxdWM\npu3oB5r2rS2hsQGoDoDAOc9e9Eu+/S5Mx2x2jm/uDLwFK0ICbCwJwPmkreOy5Nu04eUojXqjInJx\n7L58AymsFaYZ3DnWYLchxgqRRJRu3TVWZDlYAZNxojo0Ame9QQE9jVlRNmA7F4x9PRAgq883sIK0\no9Xaxn7PmpEIqYW2RtJyO0lrMUF6sYt/yyW32IZbkK+0iZV88kttxss1CtUm6XaPnVKPJajGs1QS\nOapuhrKboxzPUSFNovjEjrezFxhEBYtywOxSzABW0AyJmUVg0fX4LBNIfAZckFNxEnGHc36VSafJ\ndLfMdLjEXLPIVKfMSL3NyAu34IW1uw9EuHm6wPWpApXzOa7PFDAPCbcv5Bmdb4AIMzHbwmDcrTHq\n2lTXjcQMgGMcYv3nJ1nMDFtbvBDOxa01ZCW0FoyusT2FRGBpgxNo/2sSEqVFY9ONRwIrdjpmUNJ/\nuKx/H8FaczxgxIHxOKwEkA6hZtaO68evGGA2ActduOpbC04/RmYZeDwGkwkrxNwhUaMxKyeG3YqQ\n/utV8bGFFaQWxgGohfa7VOlmSFR69G559K675EptnAXIV1rEij6FaouxSplTy00KtRY7peu4LMWz\nlBN5lrwspXieipNhyaRY8jJUwzjLTprlIEbX8TC96Pfp+9DyoQUmCKCzmf91/zgmHiEVLCeC3WQ0\nDYsZgLpDy3V4EXjRzQJZJH4JEiC5GKdiAZN+lXNOg+lOhZmwYtOz20vMlOyDz63dfTMe46WJMa7P\nFLh27hSXL40hD8HtC3kmx601ZljMAIw4ndU07a3ETJ++qLkvxcxWab39qrllH/IxaHVtttD664Fg\nC7r1q9/e6FmhImJjY+pDrqT1LqX+Rx13oq7KvbXCph8EDDZWZSWE8w5cNtZtFYq1ELlY0XS9B49m\ntL7KfcTdBqIOW0H6cSBbWUHKgXUXlv0MyaUevRse2cUOwYKQL7eRoiFR9CksNxmrlBirNji10sQL\ndxbYGiAsRZaQspelHM9TIc1SLMNymGTJS7MSxKgGcZoSw/jRidT3oQ0mCCGIzrdBADTsdx9Wff0m\nHPpxmRCzw7mdRPRsoNw9Iix5GZa8DF/I2LsXf8T2jAnzDueaS5xxlzgXlphbKnK+tsClhQVON+o8\ndu0Wj127dccm62fiLM+l6M07NOYSuBdC2hdiyIXI/aBsTNW3F/tKLwqSjXry9ANy41hx4jMoGNcw\nthdRL7DxKzGsUPCBhLFCZz39WintSBR1Qpu9NOpBo2eXedE+vagCb2Bsif1aYP+GKceKlgDIibUM\nwUCcXO/a9/oxOypaTibGIMuG+O0AdzEksWjwSiGjJYNXCZEyOCVDstgjUfJx17e32IJyLsNiLs9C\ndoRiNk8lkaeUybEsGSqpHPUwTSWZo91L4kZNQ72mtYg4Tfu9lMgFJJ0umJ27g44c+5TWLCJvBP4T\n9ozzQWPMezYY8y3Au+0s+Jwx5lvXjxlGzwQnnd2kYG9gfVmtJ+Pa224vbs2vxGO2Q3ZqhC9lbDq2\nfzYJZyGe9ZlplBkX27pgqlvi/MoCF4qLZItdssUufHrttAJXWJ5NUT2fZnleqM8liF/wac3HSE31\nyHmbW1+ANRaY+86lVPWtOyXhwOkYeD5cDaxASHoQ+NbV0jOD2BUHe6fXCq3ocLFiRbDjPLGxJxtZ\nWMAKoLgMmiq2QitG+hV2Pez6bWyq9WkPbkQ1Yggh4UYWHjMo0zx8HBlnUI7/YbW0HAV2kjkzGGvo\nRdUHw9WMGQPG0KmFBAsGtxgQLAqxckBYhng5gKKQKPmkigGjiz28zs6tDcvpFAu5ERbyecrJPKVs\njmU3y7JkWUpmqZk0S4ksdT+N73h49R5uKxIhKz1YAWlHIrnbw2WJdK+3mq251lIy+Dc0ZluryYYc\npdScPZ6KiLjA+4G/DlwHnhSRjxpjnhkacwnbsuerjTFLIjK+3Xb1LKBszTZZS+vFDC17Wy6RgBHX\nGYiZmP26hYkEV4CrqbN8mrOYdBL/fAqZCykkW8zWi1bM1MpMtkvMLy0ys1xm9KUmoy8172wqmfao\nXkyzdD5N/aKhPpsgeaFHaz5GtmBPNjmne6eYYW32kn3vGIqZ6117wrzVtdYVwWbuCDDpwdVw0Heo\nLzDACpeV6IVL1L/ItWKkZe7s7tzPLDLARBS7AtZiEhgrNPyetdD0x+UcG78iAjMJeKlt05fzziBO\n5WWZwXEkHPuAQTn+610VLHvMvWTOBJjV2JF+/RC/EeIWQ/wiuOWQoAxh0SFeDpAiJEs9EosB2YUO\nsebORUgtkWAxN8JiLs9SIkc5k2XZyVJJZamRYSXMsBTPUgtSdNw4bqNvBelB3Vo/pC84Ol2gSswv\n2fAt37cuG4bER/TvsABZIz6i9+7gKImPu2AfLCyvAV4wxrwIICIfBr4ZeGZozPcA7zfGLNk5mMXt\nNqpnAeXu2UDMDBZFJwKfITFj/xE3ehKlZIvnrYqZWiLB0yR4JmoqadJJSIP7oMt4fIWZfofsWomp\ndonzlUVON+ucfWqFs0+t3DHF5bEUty7mWboYg4smssz06Ex7nEpYS9FwbMyxFDOVHtzuDjJ+nCid\n2RP7OO3CQg+CodiR9R2ZV4vDBYPKsw7WTeRgC9FFi1fjU4bL+wcC5xNQcG3tlIIHxZ4NAO5n/YxG\nlXRv9AZxKi/LwKx1I9IMrWVlmH45fmVH7NQKEqxaPe60gvRFSLsDXjmkVxRipYBeyQoQUxQoQrrY\nI3PbJ7vYIVHfeXXBZixOMZujlMmzlMhSTudYdjIsJbPUyVBO5KiFaap+mpaXsOIDcNpdaK21gphu\nD1gBv0IcNrSC9I+tv6yPCc3xsH4cAPtwuFPAtaHX14HXrhvzIICI/Cn2LPJuY8zvbLVRFSzK/rAD\nMbP6uudvKWYAgpjHrUSCW4wgyXHgIUwhBQXIpAIm3ahtQWibSk61SsxWS4yUWoyUWvDna6cXOEJx\nJsvtiyPceiDO0vk0yYtdkvNdemMuo+6dYmZ9PZlhMQMHVFemH6vSr0o7HVk6GiaqUCuDRoIuViy8\nJgdP1m3Mya2e/dv0LSD9oNu+GyeMXEH5yNLSNFFashkUhnOjecTErtMxVlh0Qvt3e03WCpZ+APAw\nWc9mBT2evvPY0pHVJTEkDE9wavO+ZM4Ehl5F6JRcYuUAv+iSKPmEJSG12MNdMKRu98iWOmSqO89W\n6bqujQVJRQLEy7DiZqgkc6yYNJVEjmWToRjP0+m4SNsKHGl3oA3SiawgUeaM6dUgqNoks54da/rH\nOGwF2cgFY9+4c5InTITsFMNdWVjGRGTYcf8BY8wHdrkND7gEvB6YBv5YRF5mjKlutYKiHCybxM3Y\nRRuIGbB3VpuImUbM4/lEgueZQJKz4IKZSCHjhrFEi7lWkXNUOeeXmaqXrbCpVTl7pcbZKzX4w7XT\naWTiFOdy3LowQuVBh8r5NMkHemTnW4RJh1HHur0yq3Vl7HyGO2S7kXjZ0yJ5m8V4tKNYE2fopCPR\n//rmdwPMxO1JfqE3CJ7tL+uX9vfsbJmP29fXOjZdue8O6neIdrAZP6c8qARWZMRkbWbPcIXeuGyf\nqrzb8ceQ9SLkbjNn+iGejdCxcSErLl4lwC859KIKqmbBIb3Yxb1tyBbbFIo9sksdnPUX903wxaGS\nyVJJZFlKZ1n2IgHiZKhGImTJZCjH8zS6NpVeWlFAaqcLTR9qRFYQwG8CTcT3B5aQKCMmDPrf08Hn\nY9bFhdyBCpC9wQC7FywlY8yrtlh+A5gZej0dvTfMdeDPjTE94CUReQ4rYJ7cbKMqWJSjxVZiJoye\n91OxtxEzBijGPIokITGHJG3FXzOaJB72mPTqzLaKTFJlplHkXLfCdL1EvtEm80yZ88+U75je4niO\nyvkMt+ZH8B9yqMylyVzq0JqIcTa+TMHpW2bsXIfFDFirzFZiBrYQNJvFePjGpiIHRK4cGbJSGGvp\nKPagItZyUuoNrngMhtGJLC8xYzsqB9h91QO73BUb1JuLgmcbIeQ9eDS9cYzJcM2YnaQq73b8EeBu\ni5htZAVZX0G11XKJlUI6xTjxsk+wECNccGwcyO2AXKnNuWKX3FKbWG/nbrNq0gafVlJWhCwlc1Qd\n64pZNhnKJk0llqPWi2NEVuuCSKcHDTDdrk3bBei1gNYdrpj7IhD1BLEPH/uTwCURmccKlbcC6zOA\nfgN4G/CfRWQM6yJ6cauNHt0zgaJsRv/XtZWY6Ubm7H5mk9taI2Y6wOWYx2UKEBsHHkTyScxEgpGg\nxaRb43xrkUmzxEyjxGSnzLlGhfHFGuOLNR5+4vaaKbXjHremRlg6n+b2/Ajhw0JlPkPugRZ+1uWs\nZ62cBaezpZgBa53ZSMxII8DJrnVDERdbaTYwg7gVsGnNcbHZOzHHxpLc7FmLRdqBXhSIaxjUVenr\npAbgd23/H2RQKG7Ms2OXQ5v5cy6+sWtnmK1qxuzF+D1krwJRt6ofUuuliFUCOsUYyZKPf8shs9CF\n2xBfCMiXW0yUm4wstUg3d54q2/TiVNJZqrEMy7Es5URfhORZIkMpnqfqJ6jGMoTtYG0gapM1RcxM\n0AXKg5iPDawg6oK5z9jjP5UxxheRdwIfx541PmSMeVpEfgz4tDHmo9Gy/1lEnsHeHv1LY8ydd4lD\niDnCX6q8jJrXyjcc9jSU+wVZZ/bsi5m+K8V1V91MEgUBE7Np2pJM4GTijPeWmXTqzLcWmAqWmGkW\nmWyVGe00Nt1tsZC1HbKnCjQfTMAjUDmfITffxHiy2rrgtGOtRDkn2FDMeM90cLoGSUQZWERxI36I\nNA2yEtoS+QZrcTntQc4bWGSaUTXbsg+nonL61ej336/N4koUaCv28wojYSPR9lysJcYAX5M70taP\nPrstYrZRIOpmfWRqYRyMoVVN0FqI2z4yt1xyCx2cW4ZspUO8aEu4Zypt8ittnB2ecnuOSyWZZTme\noZLMUnWzVBxbQXWJNOVYjuUgQdXL0O1GG+321lZQBejHgPQFSBCsxoOoFeTo8efmD1gxlQOrlZ+4\nMG0m//X37Wqdy3/vh/9iG5fQvnD0zzaKsldsV3MmCO60zAyJmdB1uQnciif5C+YgdgniIPmEbSrp\ntZhyasy1i0z5ZWabJSabZc5U65yp1nnZF27ae4qIrutyfbzA4mye69MFrl86zc0LIyQf6TE+sQyy\nVsxk0iFnX+ziGghTAhlbGC58KAFA7GaINB0baDsVR57rWPFhDI6IfX8mssaci1sh81zLupQaUS0W\nT2ywbSA246eKtaY0QytmulGAbUIORazcbSDqZt1022ZgAakZ26ugFtrqqbVakmTRlnD3b7rkim2c\n25Art4iXfUaWWkxVqhSWm5s2s7tzrsJSIs1yLEM5mWfJzVBKjFBx0iyZNBUvy3IYZ8nN0OxFojGy\nhphub1WE2HTcEII6UB+IEQ1EVe6GY/I1UMGiKH22qjkTBIPfdNvGqQyLmRpQd11eiBeAAsQegzQ4\np+KMBTXOuU2mukvMUmWmV2amWWS8vcyFW2Uu3CrfkcVUzaS4cnaU0lyW61OnuD3nM51sUJzsMUGT\nZCMg1upx7bE0btbOLPcwgEtShIQExDMhbpR140RBddIxcMbF6YQYY5C0g/SMNR2ccm39FT+0wsXt\nu5eMFUeTUVHATmgDbPeIrVwxGxUkg7VWkH4cyGo6bnSszTAKyjZxqlEzu6VmmvRil+6tONnFNuFt\nwVkw5CttEiWfQrXJ1NIyp6uNXTWza3iJqI9Mjoqbo5SwJdwrsRzLYYKql2bFj7EcxgjFGVhBulE8\nURAMWUDaQHtDK8i2IkQFiLJbzL7UYdkXVLAoyk7YRsxAdJOyTsyErsttYMGN26aS3hQkEpCH5JjD\nOX+Zc26Dqe4SM6bKXGuR6XaZQqNF4cs34MtrpxEKLJ9KUx7P0jmXono2y+dePcXN+REKF5vgCHPx\nEpOxJVJnYsy/UMMPhXjC4HQh3jG0HvKIi5C4aZCEsaImF6UzxwxO22BSQC9EUo4VKKdcdtqU8F4D\nUYMhAdLPim4a6wYbuGKiHjJBlmorTbrUpXMjRrbUwSwI+XILp2gYqbbIljtMVlYYq9YZaWzUb2Bj\nOo5HOZFjKRb1kYnloj4ykRXEy7ASxqg6aXq9cG0fmSarRcns96OHCdrqglGOJsfkK6aCRVEOiY4T\n43J8jJfS0wCEeSsCuvkY6UybmXqZCVNmtlrk65tfIF9scmqpzqlKk1OVJnzJbuf1v2af9JIOlbkM\nnXkPM29onY/TnjDEQvB8g58WWuc9goJLKA5+wQUSmOUA5/ku7nUfkxLCmRjSMEjL2FToCc9WxD3I\nzJ3A4C4GOLdD3GJAomiLmI2VDV45xCkZ4qWAWDEgUfGRHZ5wfcdhcSTHYi7P7cII5eQIlViOcjpH\njQzlVJZGmKGczNFrx0CEWMNfW0GVKG0XBsGrHHyHXUXZO9TCoigngy2sL51cmtbcOfxsGq/eJHV1\ngeTSkl242r4gqq4bBfwmEwlMMsFVYlxJn+cJztN4NEfa61Fzk2SDNqdWaox1qmQrLXor8EDxNuP1\nGhPP1uDZO6fYGI2zMp+hOy/Uzsfx5gNiF3t05mOM5AJ4pUvmohC/GRJvgox6BJMuzikb1+HQ/zc6\nsZlw0z4yvegzuCNzJjQEFVvCPVg0eKWAsCQEZYiXAqQEiaJPshiQKnVx1lfj3YRQhGI+y0JuhMV8\nnnIiTzmTY9nJspTKskx2tZldqxvHiINXt0LDbfaQlS6Uh8RHt0WCFvHuUOZM33pyr/VD1FqiHEWO\nyddSBYuyr3QKOVpzk/i5FF6tRerKTRLV2mFP60DoFHKsPP4AbqeDV2sQJmKsPHYBnnrefgbDriRY\nDfTtxh1aE+P4mRRes0P6+gKf/XSMNz5+A+mlWI7n6Yydpp4d4bdufgWlapbEWId4OmSmWWLcrXI2\nsJV+ZxtFLhQXyFS6ZCpd+Iu1cwwdoTqdojyfoXTRoTaXITbvkxgL6KaFnG9dXJnIxRVDcKoBzs0A\n0wgJUtDICmFHCIvgVkKCom1oZ0ogRUgVe+QWfDKl7q466pYyORYzp6IKqmkq6Qwrji1eVjdWgKyE\nGerdBKHj4jatqHCaXVhmbf2Qno0LSfRjR/qffc9fWzvEPrH/qttGOSkck6+vChZl3+gUcqy87FJ0\nwW7aC/bLLpHvX7Dvc1pzk7idDm5Udrz/b2tukkT12Q2zljqFHCuPXLDrVVcIEjGql2b48he6fOyJ\ncb7i8Qa5qYByM84nvnSBq36aMBXDeekmTrvLS8Dl5BlMesZmEE2lkMmQkWSH2UaRCVliplbiXLfM\nbL3ITKXM6NUmo1eb8Edrp9NJuFQuZCjPZ2nOAAL5aptTl1tI1eBWQhJLPU7vQoQspdIU83kqSVvC\nvRrLUhPriqkZK0ZK7giXz81B1+C1OoSedWGNXF0gWYr6RfV8IMR0K7i+jwurVhCzUf2Q9RWU1Qqi\nKJa7q3R7KKhgUfaNbS/YW3A/WGbs3Jtr3nM6Pfzs5sXWNv3MZia4+bkqz1RfQfhFb/V9hwbG96mf\nGSH21At2I279DjfTSjzGF4jxdHIWmMWkk4RnksTmfMZjdWYbRc72xUynzOxKkTONGue+uMK5L97Z\nVHKYTsKjnklxOTlGJZ1l2cuylLRddZf7fWSCNKVEnjBqoui07Py7ODRH8/RSCbx6g/TNMs2JNO7N\nJdxWBxOGtq6d59FwDLFbC3YDJ6ybrqIoKliUfeRuLthw/1hmvFqLMBFbFRcAYSKGV2+tEWQEUQdC\nV+hMnCZxs4g7VDt/+DPb8DNtd/Cz6TVxFuvdTIMU7Lp97bo4nkcA3IrHuEUOSZ4BHsTkk4RTSbJ+\ni0l3hZlmkVNODRBekb/CQrxAM5ak6capp1IEBs6k6vzKX9o6UvWRLCvzZ+klE3i1JvnnrpK7vgAs\nI1HMhwkCOiNZlh+ew2m1cFZW8OMe1akxgrhHoli1kTGR+JBul14uM6iTc8AC5H4Q0IqyGcdFz6tg\n2UdO+kluqwv2eoY/q95IDq/WvCvLzFEideUmKy+7BFjRESZiBIkEsdvlVUGGH9KaPQsCqau3wQ9o\nzZ5Frt7Ga9oU3OHPbEef6U5TsNeJmc4otGbP4ufSxFpdegstmm3DC4whSZvJ1JkIiGVgKXWKIGYt\nPYV6kXIxxFy9QW16nPKD0zjtLk6lih+PU3r5JdqEODFvEHx8+SatiVM4jSbGdWmdGyNMxK3YcoTY\ncu3OY6w1D+XMWps9y/KrHwfXwW20CF2HXv74CWhF2RQVLCeb+8VKcC9sdsHOPHd1zbj1n1V7chw/\nmcDp9vBabfxUks7pEfx8ZnW7h/UZ9oVVZ6xAmIwjnQ7J4vKGc0pUa+Sfet4KsWwar94i89zVNW6f\nzvQobhQc2hsdIblQoTl7lvb4KJnLN+kWsnTHRolVa1Rf/hDu0jK9uUlg6890U4zZUEgDrDx8Hrfd\nxq0s4ycTLF2cZOTpL5Oo1kHssf2P+Gm+8XVVUq0mzYZHKukTP5vgj58dIex0WHl4Dun1CJMxgmwK\n8X2MCVl59WPkn34Bb6VufwuPP0CQ8PAabdpT4zg9H6fTxU8m6I6N4GczxFbqJBYqOGGwKvSqL3/o\nQG8AOoUcy695HEKD22hhPJfumVHixcqBCeiTfuOjHAAaw3KyuZf4jfuFzS7Y60+2d3xWjRZBIk73\n9AiUoTU1DsYQW2kQJrxDE359YYUI3UIOMQZSCbo9f/s77qHzwbBbJ0zGcdpdepkk/rkztM+NIT2f\nMO7RHivgn8qTWFwitlwjTMTozU2SvHKT4NSIdROFBvF9ao9fpLXJxWyt+8ngZ1PEl2urQnrp1Y/R\nPZUnzKYghNjyCslbZdxWm+bUBPFSdXVbz+ceonG5xleNvMR4skapneETCw9zcyRHwTxLtzBC4Lm4\nYWDFiuPQS6cQY+74Lfj5DJ1M2ooVP6CXTtEdK2BEME6XMO7RnJ8iffkGySs3aUffk7u9Adjswr+V\nIGjNTWIcscG/cY8gkyaIxwiSCUKvuKP93gt646McBDutY3TYqGDZJ+42fuOw2K+7uES1tirQ+vuo\nPb52H/3Pyk8n6Y7aC7GfThK0O9ZSaQw4QryyfFfCb6fHtt24vrDqnBnF9e1FNvRcgmyGxAZ33Jtd\nbMT3V906TrtLL5+me7qA+CFuu0MYj2HiHoSGeLGCn8vQHSvgdLq49QbBqREKn3t2zfadZnvDi9n6\nOTTOTxIm4sRqTYQexnHpjJ+iV8jj1RoI0D01QpCIk758izAbW/PZrDw6T2ulwbXFMbxme/Vv1jtr\nrV+hK4gDEvXWkTAE14EgoDk9sSrQYuVlnHaH3sRpK1DjHt0zBYyAW2/aRpQGEjcX8JodOlMTdEfz\n4Lo4nW70Xehs+T3oFHLUHrlAZ3KMwPMwAqlbReLV+upnlbxyk8ZD5wnSSYznIqcD2uOnOPXk0wDU\nL87gp9P4mZTdd7eH0+0SJhP4p/J0CrnV78Z+WED0xkfZd/pd248BKlj2id3Ebxw2O7mLW3+XDgZc\nZ8cn6K324dVa1vVxZhSn5+PVm4AhSKfoei6JygrxyvJqTMduhN9O71B3Mq4vrPoXXQDxA8JEfM2c\n+p9V44Fp8AOSCxWE3up3IXQ9gkSCIJkkiMfojJ+2x9VsY2IeJhHHBCG1Ry/gtrs4JrRFzeIe4fgo\nrfL9Mp8AACAASURBVKj7rp9OggidM6Orc/JqzTUXs/UXvP4Fv3t6BO96m+7pEYzrImGIEAkME+KP\nZKk9eoHkQpna7NmBdWOlgZ9N0RkftX1w4jHcZiuqM+OBIwQxD4ksP8bzMI5gnBididM43S5GBH/2\nLKlrt0m/dIPO+Cj+iLVYeY02GIN0ezg9n97oCK2zZwhO5XCabbyVBsZzaU2Nk7yxuCqohv+OfZdd\n+0zBfkfrLfz/n713DbLrOs/0nrXWvpxrn76iATTuINEkRYmkSJGSCFEXS449tiXbskeKlZFdM5Wp\nzJRTqXKSSX4kU6lJfmSqUqlKJjNJHHtcyUx5rJQmqihl2ZbtEW3xKt6v4AUAARC3Bvp+7nvvtVZ+\nrLX3Od3oBgEKlADzvFXA6XN6997r7LPPXu96v/f7vrEqplJCj9WILy9TuriE6vdZv/8uTBig+gmy\nl2ADRToxxsp9d2ADRVYrYQOJrpRBgIxCp2qlKfGlFZp3HsQGwQemgHwQC59RiGmEjRCjkNCHHdfq\n37gZ8F6ruOHJHO1NotaZRK8WotlspFWt9pbHKJ8+T+u2h3x4Q7uVbmaonjhLVq8QX15+T+K33U24\needBtzIPlE+FtZgwIBurMvn4i8WYm3cees8VfE5CZc9lrGRjVUwUIJMM2exQvrS84VxZ6yJB3bkd\nlM9dIuj23LVQC1FLq6w99FEI/VcwTTGVMtpahNFuvHGElgK53saEAbpRR/YTSC0mDmjecQAjJdJa\nt/IXgqwUY0JVnJfNE57sJ66uSewaGZpS5M53PyGrlj25UGAMSluCZoeVT9+DyAzSGrRSZONjiDTF\nVp1HJRurEV1yn1G0vE5WiUEFmDjG2DwDSqJDhbEhIo6QvT4gqB87iQ0CTBxiPcFBSoLmOlkcksxM\nufNhLDYMSKbGkVmGCUP6Uw3C1RaLn7oHsGTVEsn0hCNE43VMGCC0a/JoK2WE1lgB6XiddHwM0emR\nTTcIF5aRmTMji0xjSWgfmiNqdVCdHiYMQQoQYEKFTDWqnyKSlN7uGSpnL163AnKt4aksDOkf2L3h\nuhRav++FzyjENMKWGCksH25cq3/jZsB7reKuMIl6dSGdalA5u1Bsc7VwSHf3DLoco5LsCqUkXm0S\nrjbRpcirFQnlhWVUt4cJFTqOi+23In6bCVX7wC7WP3KI+MIi3T2zhOstMIZksgEWwuU1dLVc3KiT\nsSrrdx9GaF1M/HrTCr65byetQ7tJZqewxmLKJZ96I9ABtG/bS3xuwXseoD8zSTpRxwYKtMWUI6rH\nz6LjgN7sFMm9806kaneQSmKlxBoNYQhGuL/DglJklRhhLVa6lb6wlrTiwmZI6UrHhwodR6hej96u\nGc79wsNkE+PoSgnZ61N+d4HS8hqy3aN3eA5hLe09s2RRSFYpO4IkwP1nwQiCyyvIJCUbqyF7fYKl\nNbKphiMAUYgpxchOj7DZwlTKZN0EKwW6USe+sIg6d4nuoTmMALTBVEpQEchWl7DTcyQARxJ0tYyO\nQlASkWiSiTGyehWEwBoBxjqTszHYLMAgIBCYUNE+tBuZaiyWdKyGjUJ3/1USqxTp7DQYgxA+ySgI\nnIE2DjFWkO6YQPedAqbaHUdsSxFycRWVadKxqvtDIUFIwsuLBElKf3YSIdx1ud13Zyv0x+ssf+Ij\nmErJqVtTmu6OCWpvntrg00nGa/T27kTojKDVxQSKzr6dBMvrTPqQ1fViFGIaYUuMCMsIw/6NnySu\nV/J9r/DVBpOoJxT5z7D1DXrzjTFo95yRdrKxZbpuvLiKiYMNY9BxiPLbdvbsQmCJLyxesRrMj2WV\nKjJOVLtLb+8sNgzIyjF6vI6JwuK4pYuLWAmLn3/AGT2VRGQapETXq6hmm97cLKrb4+wvf57e3A5I\nU2S3jxmve1+GQSQZ0mishe78AVSzRTY+5lScOHIExFq0FNhDc+iqCwMRKIQ26FrFrfylgCACBFZK\nt38LKLCl2LV/1ylCWzCG5l0HIQoBi8ksCjDlGF2JIc0cWbI4ZaNWJp0ep7WyTtBPHfno9MgaNZJG\nDQJ/PDEsCxt0rUx31xQizdDVComUZJUSVgiEtYg0g0CRjo8VRlSsJV5Ycp/LbXvJ4tCTIUc6MBZT\niclqVRhK7y6dukDnyD5sZrBGo8eqrteSMYW6gZQuxBS6cyBSja5XsUDQT8lqZVcB1xh3biyDv0Vg\nUW4fvR4Ygy7FqCxDRwEECplm9KYnEFiskKSNmvNRlUuIJMV6NczUKmTNNoQhlVPnN3x3ehMNuvtm\nsVFIOl6n9srb1M9c3PDdXPjZT5LsmEJog+p0Ua0uZnKMlU9+zGWMeTXFRAFBq4OwxvmlYu//aXXe\n98LnVvPWjfATwoiwjPDTwPuRfN8rfDVMaGQ/8at/hojLlcXQejumKZ2/VBRAi5bW6MztQFfLWCBt\n1OnvmCBYXd82XTdp1LFAvNakduJMMa7NyG/C3T2TRcaJBUwUIttd0ulxrAqcIiIktlKis2OSsFpx\n5lZtEVmKrpSg00NqVyKfSkyw2iIdrwMWUYrQQVCYSIW2RM0WVimyUkRnzyyq7+qTEPsJ0/i4UDlG\nG42OIoQQzufmQzei71Jm9fiYm2CLm4d1E30+cVvlVBip3Gdg/cQdBpjUuDB04Cdl2EgUsJjJBlmr\nS+2t05SW1+jsmUWXY7JyvImsAFKQ1croigsTCcD0wEgJSmGFQDZbiCjECEHWqBP0EoQ2lM4tEXR6\nrIzVIFcnfGE8pAVrSacbrNXnEakmXlwhCwNEkjnVoVJy5xgxGJev2Iux/hwJrAQbRmAtttPDCuGI\nijFeEfFqkRVuX5682DAElSCzDGGtMznHEZlxypHNMmSnR9qoIcbr2Ewj/DgEoEsxFqi/cYr6sZPF\ndyepVOgc2QfGEC2touOIlaP3wWMvUD9zkf543WVkzUwi/LF1tYwNFLLTJZ2eoHzmYvEdS6YnCBdX\nQMhCybSwLbm4loXKzeKtG/lobiLcQqX55Y3YiRDi54QQbwohjgsh/sstfh8LIb7lf/+0EOLAjTju\nCFdiWNkQOMk392Jshzx8JfsZWa2C7GcbCE759HlnEo1DF04pReg4IlxaQ3sSoVbWWP/o7Zg4IGh2\nEDpzRcjKJQCCbo/S5RVUu0t/epz+zATR5WVKl52y0vPpusNjCFpd4rUmViq6e2bp7t1JMjlG886D\nG8af34RNHLnwQhiQTDUwgfOqWOFX2YEzhaI1VMukOybI6lV0KYQoRPb62DBAhwG2VkZ2ewjrs1yC\nAItACj/5+XCDVQpdKWFUAEqgSxGUYxeqUdJN0j67xHovhC1iEw4mjtDV8iD1uXgcuokIRxQQOE+H\n8BOwklihHPnJCYpXI4odCbxRWmClcKEZf1wThZ7UGEcG8nEJAWHolB8hEO0uphT7YzoiYMoldBxh\nSxGEAf2JOuHiwByd1cp+nHLje/Kkx5RidLVMZ9cM6c5pjBRYa7265I3dftuCxAlP6Kz/nX9NN2oD\nchgohNYD0iKEJ0BAt4/QhqxcIqtXXQhJCFclOAqdQhOGoITzvwgBUYANQ4SxBGstRJKga2X6kzX3\nfVtapT8zSfsjB33RuzZBkhF4I2/LE5ru/t3oSskbm61TqbTzbGVjNUSm8VcXMtOuLk2jDtbS2TNL\n67a9tA/sLnokDSNfqOTfv9xblmcx5Rj+Llsovr95LZ6fBK51rCP85CDs9f37aeHHVliEEAr458CX\ngLPAM0KI71prXx/a7O8BK9ba24QQXwf+KfC1H/fYH1ZcbXXyfiXfq4Wvhv04phZSPrNAniUku32q\nb53ZYG6VvYRgrU0yG9GbdQXQTOxCI5OPv0h3/27C5pUG3DxdN8fFLz6Irk+STE0gkwTl0247B+bo\nH3tnA6Fa/+jtoDVZKSZr1EBAsN4i2THpDbdm4NFQgZ/c3IrfSoURFqEkou9UAoxBGEs61fATo1vZ\nWwTkk5vW/sYvIFKQ6YESkMNPsCaO3PGFHIwj0+5nJQbm221hCxKRjgeDiRv/9yJw+9SZez0YWosI\n4Z5bi42ioVBeUvhI8EPaQJIsgwnfh9Oc1OJVjig/pnbnJnKfN0CyY9wpJVeDlO7uVylhM42tlBB4\n0pITkoJ0DI0R3PGlJzLWYK1E9rqYctmRuNwom+/LWLc8CwK3//x8a3ddCKUwaQalyPmsun1MZkgD\nBUIik4Sg08MEChtFqE4PiSQZr9Kbm6V89hKk7vNMdkygWzHhegvZdwbt/nid9m17SCbGCgOxTTP3\nmSiFCRTh0hrJZAMrQCYpJCnZRAORpgTGQKYxpYi0VqE/Xt8yLPpe3pSbwVs38tHchPgQhYQeBI5b\na08CCCH+CPgKMExYvgL8N/7nbwP/ixBCWHurdDC4efBeIZ8PSvK9GqHpj9fpHJxDtbvIXoIux/Rn\nJiFNySZKBK0O8eJacWN0dVg2kiqjFN3DOwsSplbWyMbHyGoVhO8fk42PoZptSFOWH76XcK1ZbCsy\njS7FJNPjqF4ftd4ha1TdpGWMn4iFmyDzlbjxXX3DAJv33wkrjkhkGl2OnTIhbRGisJkjMygDWYaJ\nIqzO3L5zz4QrHkMR0iiIip9t88s+VNdWaj4nDnmTv3w/+XvK95mrSJubARbbWggUSaNGWimhWm1s\npv2kLTaSlfzAPvRklPIhldyUS1Efx51jZxBOZidJds0MbfseyLdR0oWytHETfzBEVrZCrq6Qkxvn\n9UFrT+AYnBvpQ1Hah4o8wXKqlSdy4JQxISBJB6nemcaWAkwpIlEKISwiyQiX1wbEr5fQnxobhLGy\nzKlulRJWG1Q/YfkTH4FMI5IUEbowlI5C9z6MQaaZ467NNqYUuesqwl3j7W7haymduYjQ+orJ/XoW\nKj8tb12OkY9mhPeLGxESmgPeHXp+1r+25TbW2gxYA6ZuwLE/dHivkM9PQ/Lt7t+NancdB4gCl93h\nFZhoZR2ZZBtUoJxU5cgqJZcqrXUhEa994m7UegsbBkP1QSxpowaBIquUCJod0kaNlaP3YSLF2Bvv\nEK6sg7HosYqbQJKsCIcMFAQ7IAEWR1y890N2e4SdLkIprBVIrd32fiWOUkhrCM4tEK21nNoSOvPr\n4Nu0SRWAQdileM5gDL6uyrarnGF1ITfHZn5cuanUp+UCG1WTzTvSLpumc2AOmWgmf/gCYr01ZE6F\n/VzkG+ov+J3o3/KN4C/ZLxecJycMPCmTg1BN/t5y4hKGjmxsO4bthia8x4gB2cnVkff6O+NIpFXS\nHT/TiH42MOwWnzdOFSrH5NWyVD/xxe2UU2y0QUvl6gKNjzmPU/73Sjo1LgzR3nyem9CzRp1wtenS\nwpXCeG+PDQOXMj45RrDWdsqJzA3VLoQnjMH0U4QQyDQjXGkSLa0StDugDdVT56mdeJfK2QWCTs9P\n7uXiFPTH66SNOq35A3T2zLrsMW7euk+bv/9w8471w4JbJSR0QzwsNxJCiL8vhHhWCPFsSv+nPZyb\nDlm9vE0apbuBbedHAVi9Z57Fo/eyes/8DY0XZ/Uy8aVllxlTrzpDqjHYOKJ0aRkrYfnhe4tjq5W1\nDaSqt2MSLL7AmiNhOg5Jdky5bI5yjI4jZ1QEpE+NFkBWr7i6KJMNuntmsXHoSub78yLyFffwxJeH\nGrRxk5WQTnZvtgk7PUSS+clPYZQchG7SjHCtSeXEu6ggILq0hMyzUqwd8lqIK1WOnJww/Oh/5zOO\n3hMWd6wsG5AGk7+PTZP7VjcVa6GfIKREl2Oadx1k7d4jTpnwZGo/F/ha8ChVuly0k1Tp8bXgr9gv\nLvqQVDAgE1g3yUs5UJCuk6dsGOtwCCoP4xSq1DZ/a4xTe/zk79Qfi1VioHYN+2Hy8yQcqTJhgFU+\nhVxr6Ped8iWVuztK/760r73ir5lsYgzpK/32d01jyjGy2ye+vDLwD0nvgymVIDOYaonqqQtD1ySI\nXt9dp9Uy2pqiEKHINOUzFwnS7KqTe664Bs0OVht0HNGd20F/vPYT96ZcK24GH80Im2DF9f37KeFG\nhITOAXuHnu/xr221zVkhRAA0gKWtdmat/V3gdwHGxOQoZLQJm0M+WaVEb8ckVgWs3jNfKBnXUiL+\nRhWLcmMKKJ+7RHP+gHvRGJfhACQzk1ghKJ9dcCvB2/e6m/1YFdHrY1Xgbs7dXvGebBxhlCBaXCOd\nbDiBpJdAFGGFIFpac4cpRaAN/R2Trqy9lJg4wiqJanWLVFTSbBAyySe2TLtJQ1pk2xEga63LPEkz\nhE89FhbU6joISdjqQhgSXl4lmZ3ClErINMMY74uwhg3hEGMcGfEhjy2hlFu2XE2VyH0jOidGdkCK\nlKSIrubhLtioIuUKTBSifQjHxhE06hvUjKPBq6zaGk2cPN+kAhaOqtc4rXf5HYtiwnWymtn+vV0L\nin0IX1dGUyhiuSq11f5zBSYYUnoE3p9ih4gVAyLkM7yKEF+Qh9UcmSP25C1Xj3AKmBASQ1Yc1+Lq\nEJFm2HKMSFKSyQbResupKLqH1ManyotCGaycXXBp4akzYUtrkWmGDRR6okH0zvnCtKzjkPjC4lXr\nEA0rrjJJSaYarq1FbWNhxJsJN4OPZoQheD5/K+BGEJZngNuFEAdxxOTrwG9s2ua7wG8CTwK/Bvy7\nkX/l/WE4BdkodU1VZ38ck9u1pB/mY1J9t8LUcQRCUL6w5BoYGkvQ76PLJfozE66irRDEl5fRcUxw\n4TLSDEIayWQD1elCpYy0lmh5jf5Ug3R2CpNkMFalE+wiaHWwxvjy8m5CC/oJGT71NI7cJNhLEEqA\nUNh+Av0UqiVU4m7yNlBIrV1V01KEarUxgcTi0o1dZdw61ugii6iojJqmIAXKWnSvj5ISLXAkxRs2\nXSjGbq1n5pP+FfaRzX4VhlJ6vUKQT7y5amBxxEfbId8MjkQZ430h3jgcqsHvi5CTYFasctFObhhK\nizI7xfLgheGx5GPMj38tpGuzN2WY8Gjt35ca7CtJIXY1ajacp5zMFD6h3LOSD5KN2UT5OZVqiFh6\nglSQSnedFHdw//cWEFGI6vWhl6DrVZKJMWSSupT0coyplEitcWnJPnQXtDuYICTdUSWJQ9YPzTlv\nixCu3QK4rK0kgyAounTnxCRXR7eb3If9IEG3R3C2V6Q+38wE4Kftoxnh1sSPTVistZkQ4reBPwMU\n8C+tta8JIf4J8Ky19rvA7wP/SghxHFjGkZqbEjd7fYDh1Un38E5kL6G0sFyoE3AlEXm/JrdrVWaG\nxyR6fSjHxJdWUN0euroTqw3R0hrJVMPVvvCy96C3zsZqtrpahsxQPnXOlauvlRHaIpttwsSNO62W\nIdPYkksJVu2u8zFIiTSWYGHJpR2XIvf3qUF2O4RrLayUiKUVokVXfj8nflZKbJoh8n5GxqDrVUw5\nxkqJSlxIwFZDR1q0QfQTUC5TSAQBottDZq6qqpbSmT2HJ9Acw4Rkq4lcCDeJ5t6SnJTk4RfjDZw4\n5cmGChuG2EA602ocuUlZMwjl+EwpYa0neJ745MezsGAnqNEtFBaAGl0W7MTGsYuhnzO9vYLka8UU\napAVxbEKQlIQCv9zKL2fxW8bRwPlKCdHSebOa642MaymDN5PcR5hozdGSm8c9unPOYHTQ16gPAQX\nOiOztaClwk6Nu9BakmKiEKEU0dIaJmihx+tY6zK1VLPtTk+94oixMWQTDW9QFkhjXB0YayFyIUar\nFL3pcWwpRvaSonXFcPbcMG6Wuioj3OK4ReSDG1I4zlr7PeB7m177x0M/94BfvxHH+iBxq/TZyFcn\nOREZngq3IiLv96b2vpQZgcti2DVNMj2OSDPipTWCbo9eaaZoMJcXnct76wxLxKrdJWh2iNaasLxO\nZ8+sq2paKRF0+6h+4uqn1CuEK+vIigvLEASITBM014uqqmNPvsTK0fvcca0hGa9jSxHVN09TOn0e\nPdHYkKrd2zUDQPX0BYJOj86eWfozE/78OYOm0NqRIYAwdFVQo9DVFhGCoOtUGQIJpXiwiodB1tLw\nqr8gJMOhCDYYYVESOj2XXqycb0QIQfnkWackKUWwsk53bgYbhWRaQ7nkPS/aVUotu7HYUrRR4Rj6\n7B4zd/M19ShYp6zsFZe4U57mtNnBN9Rf8Ji5m9PsHPzNZqE0J13565kmaHVQzQ66VnbXZpGxJTcq\nIML/V5TBHxpjXvlXG08qLC41KCdxQyGqwv+CJz12yBvDptc9cbM4EpiTOe3IhA3UwMMkgChAtrsI\nX4cGKRBZH1Nz30V1eQWZaddVu1Z1iqJ1jSAl7lBqrYWeGnPhTANkGVIbSgtLyMTVZVHNdhECuto9\n6FbqWTbCzYufppH2ejCqdDuEW60+wLUSkfd7U7tWZSYnela61OO8iWG0uEoWh95UFyJ6iQsXSUH5\n0vKG8Q5LxPn+dBy641VLrvtv6tQZCcgll1ZaPXUeXYoRWFQvKZon6lJE+cyCK4v+2Aus3X8n6Y4p\nVLdH/OYpwnaX3v7d23ZtNmFIe0+D3twMJgyRaVqEIFSakSHcmIwh6CfYbg+kQvb6zp87VnN+Ge+T\ncdBgxIC0MFjxy17fVT71XYGL1Oh8gsUrDXhiY92KP51qEF9aYeKZ1wbN8w7spn14DzoKC++ElWKI\nWA2pKjn8cU7bnXwreYSj4evMizMcEAu8rvfxLrPU6PI19Sjf0p/jtN05MLxmZug9MfCWWEu4uk7Y\n7NCfbPhuzF0wlmy8NthO642m3fz9DxtvrX/fXi1RXdfqwSlJdiPxAdcpWojC3yL7iSORSrkD5Od3\n6L2jDeFai6Re9fVa3GenVlvu7UnXkkAmqfNJhSFo48KEAmQQUDp3CV0tIQzEl5dJaxWyahkhBKLZ\nJpsad+nQWjt/lCdPqtlCGDeY67kHjfwgI9wQjAjLrYdbrT7AtRKR93tTu1ZClBO9/sygNL4JFP2p\nMYSxZKXYTZR+9R1dXkZ1ekV2wHuOt90rVqyuk7MuVBoTh1TOXCCtVTCVksuw0Brpx7h49F6CZpfS\nxSUq5y5teC9ZOS7qubiJ0JlJTaDo7ZhEWYvq9KFkXLglDFz/nDRDBgGq1ye6vELJe3FKp8+z9Nn7\nXXl3KcAaV9Jda0e2pMAEgbs3SF8FV7uKp1iLEdIVflMBZJnLYJLSrfLzydzgiYFFZhlWqeLzWL1n\n3l3DrS6i13dpskmGbHXR1bKbcI3FYor6KgNC5PeN5TQ7OZ3s5BvhX3JOzHjjraUpvAFXvsrpbKeb\ncHuJq5abKxpDZAUhMWFEWjbO77zedhN9/hkKUXyWBGJAoPJwUZ595X+W/RRhPLnLXH+josaOGA5H\niYGHyKedm+FCezCowZO3PTDWZd9Zi0oSlwlvHTmy5Rjb7/sMtRQbuJ5XrvZPhI0Cgk6X8rlLCKMJ\nFtconz7vCi2WY4RxPYNMtYLN68bgSJQ0BhMGqF7C2Ctv07z7cJF9lEw2irRp0ds+Y3LkBxnhx8aI\nsNx6uNXiwddDRN7PTe1aCVFO9DY0RpSCdHqC6NIyKs0Kg23p1ePoicaW493OP1SE6lptkplJjO9l\nU1ppbmFMLIMxpLUKUmfIjht35+AclZPnit5GWaVUZC+FS2vOvCyceTmbqiKxlN91Teva+3eRjCmy\nconA9pxPptVx2SDW0p+ZRPT76IkGsp+glXIVW31dDTd3C9RqCxUoV+VUCKc+rDbpz0ySzEw4teby\nKunUeFGMzVo/8RrtU5lxq/7FNcrL6+g4QlfiK0KZ/R1TBJ0uKvUp2l4dsALX+bdScl2UlRoiG/4D\n9U9nxSoXGTbgWmfAZQmwCG28auFlEWtdSXl/TCst8XoLLMSnzpNONkiVxEYhqt1Bh6Gvd2OhnznS\nkofEjHXKTZ6Sro1TiXx4xfrGj/RTRBC4bB/PObGgOn13LUjhTLs58fGqjfCeGosjRcHKOqqfuC7U\nvveSNIZgYQ1TK7uGlO5lRzBaHQKtMdEEotOncvwswuji+5F/33ozDbLxMVeSX2sEETbNkFgXkUo1\nY2+cAimJV5t0m11XAyYn/32vSpbjK6rbjjDCjcBPu7bK9WBEWIZwK8aDP8jV1bUSopzo5U3bROa6\n6Mp+4lal/WTb8vs53ss/VLQGCAJvSOwTrrU2mKLz87B6z7zL+hmS1VW7S392kvCUq/WQTA6yl9Kp\nhuuSCy6F2rcXSCYbVM4uUD19AbVzit60m7yDVpfKmQvItRadOw+BkiggGa9iYjc2aQzGT842CJC9\nlMqFxWLM+XuV/ZSw3SVZWSdodckqsQspTTZACDfJrXQxYzWnvvgwFLUKWbfvUqrLsWt1kLjQiko1\nMknR1Qqq1yet1TFRMJQl49Kzk7GKM0BLgbBgc0+HV3IWbIOaGDLgWkuNDgtMIBI3FmKnrshMY5Rw\n4TghfHbXeqHgKATRxSUwlrQc0909DeMBanHFNZ0MQmzPFCFAW4oH1W7TzKduC0Sn54yuFmSzgy2X\nkKmGfoLVFjNWde0V0gSRRdhAotpdlLEkFQth4KrKZplriCnAWku02iS+tEx/xySiUob1tisCV/Zm\n8NS9XxOFlE9dwEYBulJCNduUFpY3tKkY/n6ULq+RpBmdg3vcfrRG+uq34UrTkXytkR2noJRPn6d1\n20NFWDVX1+JLKzdtaHqEvwG4RZofjgjLEEbx4CtxLYSomICHFBAdRYSr65ggoLzg/CpXC6+9l3/o\neojZVqG9+NIynQNzhS9GV8tF9lJvzpmBwfX8kb0EE6ii9HrQ6VE+d4nqyUG2Rn+8zuUvuolFtbuu\nu+7MpGuYiED025jpCVS3T9hZcxOetQXB2nydTTzzGgDrH72d+vEzGKXo75ikv2saaSzhwrKbyH3I\ny6iArFFzKpAFmehBaEdKolaXXqAw5ZJLGU+dMiCsUw5MHCGscWRFSUq9FkhDN64XasTj2Uf4WvBX\nCKtp2TI12aMh2vxZej9BmhXp3WGni+qn9Bs1pz5pQ2m1WRiN46U1TKXkejX1UiSC8tIqEy++41/Q\nSQAAIABJREFURTZWZf3IfoLlpq+tY2kdmiPzdW1ElmHDENPrEyQJKs3QUZn49HlEqmnP78cohUxT\nlDbY9TZRs002UUd1ugitiZodVw9lqkFSLSETn8XTafsaKxBfcgXfqqcuUD59npUH7iQbH0OurBfE\nwYQBstOlfGmZrFYmOHvpPbMIy6fPk47d7iow4z6DdGIM0XXXmOtHNVgUxatNwtUmuhSR1cqujlCa\nkdYrmFBte5wRRvixMFJYbk2M4sHXj60UkLDZQqbZhpTrq4XXbqR/aKvQntSayqlBN+g8Eyno9orM\nJXfMhGhpjc6+nU4x8uPWcUx4canwiaSNOjoKiNZcQ0aR12WRAl0qUT1zHnNxif6OSXSlTHzuEvWh\nho1bXWer98wXpE2RDtSgqXHC5qpTSxo1F16wBtXuMfHsG/QO7kaXIoJ04MsIewn9MCDo9FGJC6Gk\npQCJwEpJFgimO4v85kvf52dPPM2h5fNYBM/PzfPDAx/jsf338PKOQ/zf2VEeDo6xy1xmwUzx/exe\nzmVThCYDLZD9lCjJCDt9TByRea+SlRJTiQjXmzTOLmK1prNriqxRJej0qL99gXi9jb2wBFIWPg6A\n2jvn6eyZRfUTKqfOk45X6U9PEq42iRdXUStN9ESdrFah+uZp9Hgd7a+5qVeOUz9zkdV7jmAiV8W2\n8IJ0e0RJSvnCZXSt6tLntaHxzKvOnD0EG8eFcoT/fI1SLiMLrqybsw3y70bzzkN0DuxGdbpU3n4X\n3aiiK2Uqp85tuC4A4sVV0kYNU4pRPUe2dBxhSqOw0AgfDEYhoRE+VNiuuq4wesOkv1147Ub6h7YL\n7Q1nBA1nIm32sAijCfMQjVdAwotL9LwKFDQ7dHfPYOKYrJwRdp2cLzKNqZYLYmRqYbFiv5ZJZktl\naGGZZGYCHUeofkK01sK2e0RLy0TrXUrNDvLsJdbvOoQJXSjIVEqIIKC01saGAaZaQghLtdXFxLCn\nvcQ3j/0JX3nzCWLtqrdm3qPx4NljPHj2GP/pY99itVTl8f0f5YcHPsa399zPucZODCWU6GMCgQkk\nJogJsxQRC8qtDt2xCjoIsVFIeXmdxpkFIgtCW0pnFwd9kzINpRJkGdWFFdbm9yGkRCYp0kK03iJo\nddFjNaJml8YrzxGvtQYn5uwCAHa4BYIdtDcon77gVL9ej/LZheIayFPZs8xQvopCInsJWSnGDJm8\ndRQ4tScOrqvsQbzaJH7yJfrHThY+q9JVrovy6fO0vrgpLCSdWX0UFhrhA8GIsIzwYcb1htdupH/o\nWo69QRWqhd5gK1wDxE6/SBPOMax+AATtHghBVq+ifLq1jl2bgPqxk+9rFbylMmQ05RNnyabHyapl\ngm6PcK2FQFI5v4gIA0r9FHHiLN0Du0knxghTTXV5jQ4N0jqoTkJaU9zVPsk3n/0+XzzxAhKLEYI/\nvevj/J+f/jle3HeIsK341JkXOXriNR45/hL7ly/zC28+xS+8+RQAJ6Z28sMDd/HDA/fz9NzdpCIF\nqeiPldF9Q5haApsycXaBKEkIehoZSvS462kFIHruvQlPXESaufG/c4H27CRZo07Q7DD12inilXVs\nXsjN2kHxO8D6mLsQdpDNYwaZQvFam7FXT9Ddv5OsXiVodai+/a77XN5duLJ+zCbEi6vINCOrVwoz\nucwMstt632UPrlW9jVebBKvr2Dgujl2+5DLrbtaMxRFuYdxCpltxM1fIHxOT9iHxMz/tYYzwE0KR\nJVRzqbk3U5Vhlx49KNKXlUt05nZg45BgreXDNJbGj64ML1wrho3HBWkrlxh75QRCSj/5Vgg6fSpn\nFyjlJKDkuvPavEtvo0J/qkQSRaztnuAL7zzPb736pzxwzmVT9ZXiO5+5j29/9UHeqtxOPYU0jUiM\nwCQxttIjCzP2XFzmoZeO89l3XuCTr5+gPpRamyjFC3O38cODd/PY3vt4Zech4n4HpTuUWm4iDzuG\noOPIRNB1xEP13JilfxRJ5rJ4GJCY/LnN9CD92BMXm1etzYmMMRv7KMEGpcU93VqFuQJD98KtPovW\nbfuovHOOsDOoKm1xZfCnH39x+/2+D6zeM4+Jgw3k1fmvsm2r3o7wNwNP279k3S7/xFywpbm9dt8/\n/J3r+pu3/6vfec5a+8AHNKRtMSIsI4xwDdhqAkkadbJ6hXC1eWMIlhBF4TddqxC0u5TPLBCvtRC+\n2JuIIlftFhBl16Hb1t2qOxt3z/tTMemk5edPPMd/8PpfcXjJhU/WS2X+8IsP8a++/ADV21M+0rgA\nwIGS60O6nFUJL0gmThoqHc1KqcyzM9MszsSsNWPufvMC9/zFCp9581U+dvo0aujesVyu8eSh23j8\n8DxPzc2zUB8naEPYdtuEnrjkj6rrH3sZsutJTLKRsOQ1bwBsloeS/OMwgRkiL8BVCcwG8rLpd5vR\nb9Q2EOisUkLq7CdCIrYkr5vCmiP8zcRPhbD8g+skLP/1iLBcgRFhGeFmwQcygWwuj++Lnwk5qEci\n8kdPUohjl3YLmDFHVNIJ97w3HVJNu/ythR/xG6/+NbNNl5lybrLBH/7Kg/w/X7qXub3utTvrFzlS\nckrQuGoDYFckh0+ssxKUWFNl4lRDX/D03jmOxa4c//G35jFZQNTuct/L73D02DEefu1N9qxsbL6+\nPFPjzcO7+d7e+/je3nvJUpceHBQEZkBklFdfchVmED7KigaB+WOeeWRT/1zrgsQU6ovZqMLY4c7W\nOYow0rWrLz9pEnEzK44jfHD4aRCW/f/R9RGWt/7xiLBcgRFhGeFmwg2bQLYjKnnRNOkaKQKIUuwf\nB2Ef03BEJZl0r3VmAna0V/nqu4/x6y8/SS1xoZtje3fyF796B/2PlTgSLrFSKtPbB6v1MrfHC+xU\nawCEwk3sY8cyVGrphhE96whS1lOkoeLxg/sBOL28k3dO3k6moIvEZAHtTpl5+xqff/5VfvGZ19n5\n1gpxf6j7tlI8t/8gj91+hKfm7uDY7G6Cju+u3bEbyAsM1Jego4sQkvCqhsjJzDCBSfMQUq6+bCIs\nWg/CPVupMFuRF/cCm+GugV3OTzQiESN8ABgRlu0xMt2OMMI14oakvA+VkRd5t+KCsFw97LOrusK9\nB84yPt7lclLnh9FtxJcT/v2X/opffO05Qj8ZP/mRg3z379zD+Y+M8421F+mEIWPlNtNpkx1nmpy9\nrcpYtUtDpsMjo95NySqCUBhK1v2uX1KUOprbYkeOpnc0uTc9Tel4RNwxNMsRx/Y3aM1KgqmARz9/\nF0tZhV0nVtnz4jKHX1lg55k1PnXyOJ86eRz4Hku1Ko8fPlIQmJV6A4Cg7c5H6MlM2FEEHXeLUr3Q\nP/rwUTdXXjJE35O7dGPYyBYpydlGtQXXoNP9YDYaeGGIqCj/dEBk3DWwiaAMN3scYYRbEbfI5Tsi\nLCOM8EFiCzWlICrXEvapu8cdu7p8addxVqIaZyoN5lfP8T8//gP2v30ZAC0Ef/rwXfzBr3yK9JMh\nHxm7wFdPvMpEtUUtUkyqNkRQSfvcfilBzyhKfmzF9FyFILUEkSbyqkslFZiaYC5YAWBXa5W55S6t\n2YhmEBOmhnuaktemZzho11mvxQTGYO4LeP2je3g2Ocjc8hrPX9jJJ59/hwefO8XupTW+/NILfPml\nFwB4a3YnPzxyhCf3zfPM/sO0x1ytk7Blh8hLrsi4cxV03a1L9nRh4JW5t2SziTfThfoiChXG7c9q\ns4G8wCADKQ8jCTnsgRnuWcSA3GzV/XpEYka4FXALZQmNCMsII9wCuH/iNK1+zNyZS/zya28wd9F5\nRpJA8W+OPsj/8aXPsHa3Cx/djiMx9W6fdGzjBGtC5x/RXIn+nKT6psZY0BHIBGQflvYPbhNTFxLS\nWJIGCqwgjRSZUcyfXqTW1uxdXmMprHCxVqMVRFR1yoXJBn9+2138+WfuotmOOHR+kYeePc0jr7zF\nJ994hyMLFzmycJG/x1/TVwHPzx3kiQPz/Gj2CO+Ud2GF3GK0I4wwwocNI8IywggfBK7FUJv7VCKn\nKOR+FVuroMecspJMlYl0yoMX3uDO508xse6Kp7UrMU999jAnPr2TP3jQhZIfGH8XgDtqFzgUXWas\n0WZKt9GRpOLDP+XEYqsQCEnox6S9HmzGQ8y8JDqvidoGXRG0DwoqDYu0LpV3vJeSVgSB0CTWjV9b\n2H2+S6IUY+t9dol1jqwpTkxNsBzXeGrvHuajSwAsVyuwQ/Knd9zFn3IX3bWQu166yNFXj/PIi29z\n97vn+dSZt/nUGZeCvVit88SBIzy9a54n9x5hvVYHXLgIIOiYQm3Jw0bS13rJlReSdKC2bMo6EluY\ndsUVpl2xpdoCmxSXzZ6XzdfASHEZ4WbFLXJpjgjLCCPcSIhNvpStfCqh96f4Mu+FT6XmHrPxCv2p\nmLGkza9e+gFfO/YYEz2XybM0WeOJLx3m+U8fYFejSVeFfGLGFde7o+zTlKNFdqp14j2axvEULQRh\nDCKBMIHkYEgoApQfq1pJUec1om2wVUk6F5I03O+q7yaUnusjWgZdE6QliDJFGlkir9PULmfEiSZS\nGl0GmUIlSbl9cYkfPFBjekeTj/rJf7FUA2C5XAXgcqXGmfFJ/vCzD/K/dh9hYq3Nx585y2deeZuj\nLx1n1+o6X37tOb782nMAvDmzi8cPzfPUrnle2H2Qfj3c4HmBQbhIdRwRUf1oYNrdVLiONBukSm9j\n2mXItFsUsssJTN7ex5rtw0U5hgnMiLyMcDPhFrkcR4RlhBF+XAxPRJuJylY+ldhn/mzyqWQ+PblR\nbvFrp/6MXzn2I8qZ669zbN9OTj8yy+sP76I8nnIgW2G/XOHZ/bv4ePUUAPtC12RyRrVpSA2TYOYD\novOGqAO2KhGHQmJAvZ4g2hYrLKJjsGPK/T6xlN7KkEdC5IWE8IUUhMVGIDsQrlj0OATTiiCyiAQq\nLY0JQAQWIQUmElgtCLTl9t4SpajPqnGZTdOBM6wuR46wzMZVlnLy0qvBFLy4ey8vfmUv/13n59n1\n9jpHXz7Owy+c5KE3TzJ/+QLzly/wd3mUXhDw7L7DPLlnnif3H+HUzE4QoshAGhCYgQoju16FKbKN\nsgGZuQbTbvFZX5F1JK4w7V5BYIZ+N1JfRrhZIBh5WEYY4W8+rsVQu0XYx/ry6kXYZ8Jl4OxXC3zj\n2KN84czLBH5ie/RjR/jf/9ZnOPnZKfb01vil9Bi3m8u0xiI6eyz7xxYLQ+yk8mGb9YzaeYtsW2Qt\nQM9FIATqnEa+3Ec0DXYygDGFPJsgehZTVY5sxQCG8HiKOpmBtBAr1wiwbbGAvGyQQhLGoCcltiZQ\nHeuTaiwCS+7km+z36CsYk25sbeXOw5Rxoa3VoMJq5M7HztgTl7IL+yxXKyzVq/zg43fwb//2fYRp\nxh3PL3D0pRN8+qWT3H36PEdPvsnRky5z61KtzhOH5nlyzzxP7TvCes2pOUFHDky7nrgUlXe7GdKH\nksRWhev884K8bFN5V2h9hWn3yqyjkWl3hJsUH8ClJoT4OeB/wt0Zfs9a+99vs91XgW8Dn7DWPnu1\nfY4IywgjXC82hX2Kl5UqUpOvFvbJxvM6KhFYy0ezk3zz5R/w0AXn20il5DtH7+H3fulheg84NeYT\nDedPaVYUa5EEMmZUkxlgUjoVpioF4bsp9VcyhBHYskBoTbCoEYAdCxBt4/6tJTChILXYkkCsaqj4\n+EYkERdSRGaxJa8YWRCpdRm8gcBOB4i+gTEJgUD1LCKx2DIYAVJDWoGwaphUKT3rJv+KT5euewIz\nLjusK0fYVlWuwjgysxxVWfIkJg8hXfzCON/+wv38Xu8oE6ttPvr0OT71zDscfe04s6tNfvnlZ/nl\nl9097/Wdczx++AhP7pnnlamDJEFI2N6YdRR2FKq7KWW6n3thrsEDM5R1dFUPDLhmhiMPzAg3Gz6A\nLCEhhAL+OfAl4CzwjBDiu9ba1zdtVwf+E+Dpa9nviLCMMMK14BrDPsOpyQCi7Pv7+Kq02USZ7nSE\nMprPrL3Eb774KPNL5wFoxRH/5jMP8a2v30dtPiXEcs/YKQCOlJw/ZV+4zIyvTFuXPvXYj628BqVX\nNUIIqEiEBrliscZAKKFmESsGQiAS0DaQWkTbAsL93bjCSHcDsyWB0EAgIDEgvfk0lqhYYbuG0isZ\neiLAdBJEG0QbKIENQYwpxJyiIgShX8KVhJvgU09gqiKjIl2hu3HlOlU3vfoyE5RZDd15W46cWlIQ\nmEoVJuH13XM8/vO38T/YL7LjjSYPv3iCTz73Dg++cYq7Lp7jrovn+A/5Ad0w5JkDh3li3zxPHJzn\n9I7ZInxUFK5ru89RFSbevP9RiCh6H23hgQEXRrqaB8Y/XpEyPfLAjHAz4MZfTg8Cx621JwGEEH8E\nfAV4fdN2/y3wT4H//Fp2OiIsI4xwNVwLURkK+xSZPlWnqOi8Kq0P+zBu+Mqlx/g7z/81u5sulHOp\nUecPfvbTfP9rd9Cqlbhj4hJ3VF3Z/Nti1wdoOOwzvp4RnzPEHTBVgZiLsOMB0fnERSUqCoFw3+7U\nIFY0BBbRNiD9e5JA4kvWpxaqEjID5zRyXMGOEFoaLqSAcalAPtJjZ93+RdsiDMhYQS1wVWcTi9Bg\nxyRSSSoXIBMQjrtzlfpJOPV3yFhoStZN6L2CxDjFqC57BYmZ9KrLdOgIy0rmHnfE1YGB9+M1Hvv4\nEb77G/cSJRmHn7vEp184yUMvvMNdpy/yyNtv8MjbbwBwcazB47cd4Ym98zwze4SVSo1wi8J14AhM\n0BmQF9ii8m6aDZGYjZV3hfasROsBeRl5YEa4mXDjL5854N2h52eBh4Y3EEJ8HNhrrf1jIcSIsIww\nwvvGVv6UQknZJuxTKhWNCHVj0IgQoFzt8LVjj/HVHz5Bo9cF4MTuaX7/Fx/m+V/dRxoF3NlwJGW+\ncpEDkaulslO53j952Gds3VB7y2BjgaxJZALBWxl6XiHbFlGWkIEIcYSkpV1luFA4YqINWOmiyolx\nNyqNIy59p55QlnCkDG90YRew7PchwOwNYNK/366FwKIuZm6+jCRojUzBVgKYUqjEEryVkRwJseOD\nzKTQT86pNUT+VMeeuFSKx4y+cOpLXbpzNi4dgZlSjsA0wxLLoVNfZofVF2DxizX++Isf4//qfQp5\nTvPQi+/w4DOnOfrycXaurfHV55/hq88/gxGC13fP8cT+Izx+eJ6Xpw+SqWBD5d1h8gIQbA4j9Qbm\nXdKNpGbYxFt4YPLQ0nDl3RvlgRmRlxGuE+8jJDQthBj2m/yutfZ3r/l4QkjgfwR+63oOOiIsI4yQ\n4z3UlK0q0sJQ2KdWKTJ9ejPeXBot8c2XHuWX3nyWWLtJ6oU79vD7v/ow5/69CawUfHzsLAC3lZya\nciBc3DbsU7sAKlYQS6eixAAWdS6DqsRqhVzWzvrvVQFi6cJA+LYAxkIC9HFKi8QRl7XMbbuawarf\nR9+4kFBdQd8g1yz0e47crPn9hwZhLVjh9guo84kzFZcVYAjPG/SEQPly99JPqkqIog5MHjZK/d0z\ntIaSn5ArZP58eOJmvInXRoUKMx24z2HNqzCLPoy0UqqwWK5x8rZZnvnFQ/wL8zmm3mjyyeff4YFn\nT/PAsTPcfe4sd587y99/4t/RjiJ+dOgwT+yf57HD85yZ3UHY8eSlnZt3N6swYeGFKSrvRjmBGQon\n5c0bg6t4YK5SefeqHhj3wtYGXrejrV8fYYTrvzQW36OX0Dlg79DzPf61HHXgbuBR4a7XncB3hRBf\nvprxdkRYRhjhGsM+VxR42yLs051xk9bt2Rl+67kf8IWTryKtxQjB9z9+F9/6xsfpP+z282DtNAAH\nY1dULQ/7zKgudZF7Ptx4YuFX9u0MqgoQiOUMuZA5UqEEfKzsfCaTyvlTWn7iqzqCQ6aha5yiInEq\nS4ojJokPF+WPJe0UmZ5xLtrAutfXNSz5vykBPRx5AYh82CgAEpCXUuz+kjPxdgyWweSan16DKMiL\n8RO0HCIwulBiNnpgSnnrAJsOGXjd57K+KYy0GlbY4dOoizowD1R45oGD/Mk3P0pnNeDe185y31Nn\nePilkxw5c4nPv3GMz79xDIDz4+M8fsipLz/adYS1cpWgnReuy4mLHSpmt3UhO9GPruw+PWTiLYjK\nVQrZXa1tAFyHiXdEXkbI4UO9NxjPALcLIQ7iiMrXgd8oDmntGjCdPxdCPAr8Z6MsoRFGuFa8R9in\n6JicE5UJR1T6k26i7M5IHmy+zt99+gfcf/YdwJXO/84j9/LH3/wo7+6d5M7GAvdW3e+2C/tUpSD2\nbszQKxKhfy6qgQv1tDPkmQQC6cI9BnijB/tCWDZOLSkUGGA5cwQkxN2cUgY3KeF/Nv6fBFoGMk9S\nhPXb+yZ/ym/Tw/2c1/nPcPtXboei6dKgSSxUJJKtVv5yA3mBgfqCAOM7HSn/GG5SY0oi22DghUEG\nUtsOwkd5BtKO0J3rlZzAxDWWy1Wauyp85zP38x3uh7OGTzx/mvueOcOnXjzJ7tVVfv35H/Hrz/8I\nIwSv7N3D44fmeey2I7w6c4BUBYRtcWXzxu4mAtPV23tgknSjgXf4cdjEu8kDs2Uhu+08MMMEZuSB\nGWEINzpLyFqbCSF+G/gz3F3iX1prXxNC/BPgWWvtd9/PfkeEZYQRfkyEOuNL51/ga4/9NQfXnFqy\nVi7zrx/+FP/6qw9weaLO3pmVG3IsOxci3+wjzqeOGEhAC5denBh4O4E7yo6EkMG6gbKfqCzQYUBi\nctJirjwObevuDkK4fWnnVyFv8KyH/uUQ+PFYiHCTYN8gEos5GN2Q9/+TwOJUnT/50t186zP3I4xl\n/7EVHn72JI+8/hYPvH2Ke868yz1n3uUfPvoXtKOYp/ffxlNzR/jRzDxnxqbf+wAjjHCz4QPgq9ba\n7wHf2/TaP95m289dyz5HhGWEETyEFINYRa6s+Gq0olzC1AapyQBiwvIrJ57kb7/0Q2Y6buV+bmKc\n3//iUf6/X/0InXLM4cklZmhz15hLSz5Svsje0DUuzH0q49LXKPGr3pJQhaIifRilUCfGA8RuA8e6\nfpwS6tKFfNa1C+Gc7DkPSh768b4SV/UN9/qwwrIZOYFJcaoMQ8+vBo1TWSaUG0dJIiMJhyLUuO87\ndLqDfDNxIauqhPkI9vkMqvy9FoqLGXhe/O9yxWXYtGuuYtoF6It+YdptG8fWctPudNAsqu6ueNNu\nXnl3qe8f61X+6O77+SPuxywLPnHsFA8/d5JHXnub2y9c4gtvv8YX3n4NgHONCZ7cO88T++d5fuo2\n1kuVQdioqwq1ZVB5d1D7JS9cd7XKuwPPy/aVd7cz7V5z1tFIbfnQYVTpdoQRbnZsYU70BrDBo3Q3\neVstk8y6Caw7E/K5d1/hv/izbxc9ft7YuYv/7ZeO8uQvHUQHijsmnYH2jqp7vK3kMoDmghVmlJs8\nt/OpKCGuICoqL1K3msH51PlSrHWze9en+nT85LOuB3FpiyMdNem2cyVXBmGgGw2NIyuhhLkI9kQw\nHrhxv9xGvZNASbjxpBb1XNeJNPtKW4SMhiZYkYeGrs+0C1CypiAzVeHIQF55d1y1N1TdBYrKuwWB\nKdVY9JlHS7Uqp/dN89Ije/kXfJbKuz2OvnSCTz7/Dp959Thzayv82tpT/NqrT6GF4JXdex2BOTDP\nsal9JFX3GYfetDsgMBqZ133p5j6XLSrvJnnK9PaVd7cz7V5z1tHItPvhwy3y0Y4IywgjiC1Wnt7L\ngq+xYgOJjt12acPyj77jyMqL+/byz77+OR699wj7Zle4v+GM8PMVR1AO+ToquU9lXCbUvYSwnU9l\neOJWm8d2NnFqyq4AziTuG2wMLDIIzwz/icZt0zUDhUSwdRjox4Fk4IFpWqhraGYuNXp3CO/03b9c\ntekYmAxAgnqmCwsGKhL2ROjGJlXpijfFBgJzNdMuOAJTKuq/uMfhyrvDVXeBovJuM3BK2nJQYyZX\nYUqOzCyWnXl3sVLlufkD/OWX76TZivjIyQs8+OxpPvPq29z/1hnuPef+/YOn/pxWHPP03tt54uA8\nT83Oc7YxvaHmS+AJZ9G8cUh9AZ99tE3hug2Vd7Un2R9k9+kRefmbgw/GdPuBYERYRhghh5DgFZUi\nLuHNtzZUBWF54NLbTPbavDMzzS//o/+Y6UMrTNDh3omzfLTqUpSvFvYpic0E5coJ+gqiAk6lOO3q\nkhBLmA1gUUMXRxQawAru5qM2/W2G+7ZnvHdo5/1geG6zQBPoJFAXfsw+ldolODkitZQ5rwvShYcS\nC290UXeUnSoDaJuTkI2rfunfoMFua9odJjBmE4m5HtPuuGoz48nLqvaVd8MrK+8uVav0ZmO+c++9\nfId7yZYln3j1FJ949jSPvPw2hy8s8jPHX+Vnjr8KwLsTkzxxYJ7HD87z7MztdGqOKA36HnnTbntQ\nebcw7V6t8u6P2316ZNr9UCEXXG8FjAjLCCMMI78RSzdZ2MBPjJFC+wpnP/v6iwD8v5+8B1uyVCNn\nEqkFfSa9NyInKjMyT8MdhH3y4mlbERW4Cll5o1tk4KC9AXZMuRBLy7isHTmoSFtkBIE30PrXcsLy\nQc4xFkeOen6suSEXfKVdP34NxNZV1B336ddnk4KwbD4XetOqfysVZksCM+SLgat7YEqbPDBVkRTq\ny3aVd9d0mcXYN20s+fBRpcL5PRP8wef28Ac8THw64YGnz3D0leN8+pWT7F1Z5msrT/K1F54kk5JX\ndu3j8UNHeGrXPK/u3If0hCWsDho3FiEkX2OnUF/ybKPeoO/RVSvvfpAemOH9jXBr4Bb5uEaEZYQP\nPYqaK1IUCkue1mx9aMiGEh0JlNF84W23Qv7ewx9BljLqkVM9KjKh5D0SYZ6OW1R29dK/UNdGUDYj\nDwVNC7iYOuIRCFj07tmKcoXcfA0Ut2Pc8zZQ9q/n6kte4faDRpcBScpDUcOkygAVAStpGYNWAAAg\nAElEQVQZLKQwLqG+/W3pagRmOw+M3JAe/d4emMhP1EnhgUmG2gbkzRs3Vt5tqjIzQRMYqC/Lmxo3\nLlaqPHXwEE99/RDrrYg7Tlzk/qfOcPTlE9z39rvcd+4U9507xW/zfdZLJZ7afzuPH57nqd3znGtM\nEbZt0T4g2JQyXXSf7oVF4borKu9erfv0UOXdH9sD4zbmCoxIzAg/JkaEZYQPH7YxFQohCrPtwMPi\nHnUo0TE8+P+39+bBcaTpeefvzazKKlQB4H3fJ7rZJMHuZvNosqeP6UszihlZx0gjy0dI8uyu17F2\nWLG25ImQvfbanpV2vXZYCntmrVl7w1rJ8nhG6nOO1sxI07yabN5kk80DvG/wxlnH5z++/LIShaoC\nQIAACnh/EYhCFQqZWUUw6833e57nvXiKaV2dnJ49h7blM0lQoDFhC5ZGv5u0Zz8kAum7lOGVazAY\nZKHi6AxdNeLB1CJc6rEi2hy2GGnwbUejp2g/GFyeiogNdAtXZSjS/2oqGwp3480Lp0kZiMGId93b\n7Y4pvmbuYy3UgbHR/g+LYPK2ozR14NNT/D0cTPeldEyPpoHprpG822Gsddt12ZyI1yXv3g6ytIfd\nl1sNjRRmJXl/w3reZz09tz2e2nuVbYfOsO3AGZZdb+f1k0d4/eQRAM7PmMGOZS3sWtjCnsWr6Gyy\nbqdScF2l6dNh98VpYWIi3ii4rlLybrkGplIBoxqYCYW6hBRlvFNLbOvcQclwSSjlUUgJr50/BMA7\nT7eSSoVX20mrech6PQRh2yLp6p4RWx02cLHXOnAe5G2h4j78u4GrvbaTUcBOYm7yYEkaTnVCTmwI\nXDXypSWTiGr3XYfGj90fSBOTCAPnCvQtcDx330CvgCmA8awYN7YsNFiqFYAFU6zpQBqSBqZG8m6T\nscVLR6iBcU6kjnD5aHoiy8xw+vTsMhHvzUwj52fN5PznZvJvu15m3rV7tO65xPMHz7D1UBtL2ttZ\n0r6TX963k7zncXDREj5c0cLuhS0cnbuIXKR3iU2f7jf/qLSM1E8DEytgTLiEVDN5Ny7ghYoFjGpg\n6og6efu1YFEU90HneaVPr4RbCgo7LIGH5+d55exhAN7e3EomnBXT6LsloZ7oA8ydqj1xtmTXaXmE\nAuZu3rp8eoq20+K6JYIVrca7JwlCfYuB891w1wxsY87TPwCufLko/rsZbFy/b+xyU61tp7Fi2vgS\nUHw/hnDNxtixzjN9mJKwOS0jRKUuTLXUXRicBqZS8m5O+mpgIhGvsYVLk9cd5b/cD+ce3Q27L7OD\nLLdS4VJSOgvT4MDyJRz48hL+RUeaJz69xrrdl9jycRsbTl9i4/k2Np5vA77L3UwDu5av4sOVLexe\n0MLNpukANZN3/dgSEvRN3pXe8GOhVvJuXMALFUW8EhW1FTQwtbovse0po0SdvN3DKlhEZDrwX4Cl\nwDngS8aYfpGeIlIAjoR3LxhjvjCc/SrKY0GkJLYNNSzFpL0tBMKWKydo7unm+MK5nF4yg+WBTbV1\nS0JpyZGMlhoIb/t/MA5pKQhst6E5YbNXjoWBcR5WgOsEra6AceFtbiZQPI+lGuXFSbUCJEqyxbaQ\npiTAC/NfyoPonMAXSoWUFx5buSC4aKylOQfMTkZR/o+DEdPAVAiyy4XbqhVkV2v69MxQA3MvzIFx\nBUx7Q5biTI8fPvsk/7V7I9mHPbR8dI2tB86yef85lly/zU8dPcxPHbXF9NmZs/hw1Wp2LXqCj5as\noLPZFkdRAdPh9RsbEA+yc0LeWkF2kQamVpBdsboGpqKAN/xZn+24bSmPDzN5loR+E/hzY8zXROQ3\nw/v/sMLzuowxG4a5L0UZUfqIbQE8r5/YthiEHZaU8PpBuxz03ta1eKkCTcmSdgXKCpayK8ZKGpZB\nE9evpL1QSxCeYVyx4ZZm3P/o+Fygas0KL/bceJFSq7nhYeP9/aLt4sxPwAOBB4VSp8Zg4//nJm3I\nXQq7g57YWTGH7Q4VsWLgBmCaZ4uwniIsaxjgTRkZRkIDA7YL4/7NH3X69NTQWfagaF97NLwxFmTX\nnm6EqXB59nS+9dPT+Xr3i8y7fJc1u6+ydf9ZNh48z/JbN1l+6yZ/fdcOcp7H/iVL+XB1C7sWtXBs\n3kJyXR6JDrds1FcDk+hMlJaOut2ty4MJl416c30EvFA5yK6WBqaSgNferdCF0SC7x0+dvJXDLVi+\nCLwUfv+fgB9TuWBRlLomWcjz2ZOhO2jTupHd+N287aJ0lsLT+ug3MmFGSSrUpuQKoevGlAoE6C9o\nhdrFhytUHHGdSiXiepUC0GngXOhY8oAZiZJ4J2/sB01a7GO9xmpt4niUOjaBQKNvn7usYcj6lcnM\n1QVT+eRz8/hvn3uGzgcJ1hy5zvajp3nx8Claz11kc9tZNredBd7nTkOGPYtXs3veanYtWs1tb9pY\nH74yDpgsHZY5xpir4ffXgDlVnpcWkX3Ya7CvGWP+dJj7VZShU8MdBKGVObIx2/8axcBe8W26cYLm\n7m6Oz5vPpaVTSZKnMVmyMwOkvRx++Glf0R10N49cztsPeleYgM1XSfUNTyMWnsbCwD4GMCsBXQV7\n9Vkudi0vQKq+D5SKEieireQeqvT8cvLhV5PAdB9mhK/JmJIOJWesE6mn13ZTJPa7YN+LBQFsahrE\nwT8+HlW0C27ZqLpoF2zHpVBDtJsxzjJdPXn3brLv2IBb6TBxN0zevZ3NcHHKNP5o+3N8vfMFmjq6\neHbfRT5z5BQvHD7NovY7vHnyIG+etFlCZ6bPtsm781r4eMEKOhuDSKzbP3k3XDbqKVmnayXvlpaL\nKiTvDle0C7psNJLUyds3YMEiIh8Acyv86KvxO8YYI1K1TltijLksIsuBH4rIEWPMmSr7+wrwFYA0\nmYEOT1GGTvkHk0u3jSfdJpyGJQyLC0/w7zzTSioIMzlC7UrWi2tY7K877Uq0NHQ3j3+yx1p344WJ\nhy1WwhRdUuHz4y6ZqQlbwFzqtY6fxWlbtJzrhbSxj3W5FnuF1xtfFmqgf9rtQCerwZzMcgbO91p7\ndcYv6VDmpmFfh/15Suyt07B42PdjVQrMYCqtsWFERLsAUlu064qXWsm7btkoPrwRStkvd9KZqHhp\nz2ZhFhyes5DDn1/IP+98k8VXb/Pc3gts33+GrSfPsOL2DVbcvsFf4yf0+j77Fy5j94IWdi1u4cys\neRjx+ifvdiXxO+2x1UzefZyi3djjdocq2h0OE6bDYox5tdrPROS6iMwzxlwVkXnAjSrbuBzenhWR\nHwNPAxULFmPMN4BvADTL9Dp5G5W6pLxw8b3+7qCUR1DI8dI5O433rc3ryaRC3UHCfpBkwoIloNjP\nHRRt+nLefjinPOv4uRuKVTsLsCJVKljALo+Uu2SmJvoukxzttJ2anIF7eWriUbIiO0eRT1/9i0d/\n8e1Q6MUuA13vhfmpkg7FHfPOh7YoSRm778C3+0yKLQ6T47dgifOool0YePp0NdFuPHk3K/Zvr1ry\n7oNCQzR9ulLyLjPhx6ta+M7PbCCRL7D68A22HznN9gNnWH/uElvOn2bL+dP8vZ3vcjuTZdfS1exa\n2MKuJau50zTFHmuH1z+4zuldukrJu9Ldt/sST96Nui2PKNq1N4NM3tXipTYDifLHEcNdEnoL+BvA\n18LbPyt/gohMAzqNMT0iMhPYBvzOMPerKMPHfZK4k5t4faL4wbqDNl08SSbXy6GlC7m4cBorAzvQ\n0NmZXYclKUUCZ2Mu//DqsMJZr6sYJtUKNIi1BV/JwQKxnQkYnEums2jtxW152053XRRnYXbf+9jI\n+65w5pArTuJWZ/f9cHCW5fYCLCnToSxOw/W8nR3UU7QFW4PYic4wqiLbkWbwol37SMQQRLvx5N10\nmPVSnrwbLR956aiIqZW866ZP35jazLc/8wzf7Hqe5gddrP/oMs9/3MYLx06xsP0unz9+gM8fPwDA\nqVlz2LH8CXYtWM3hacvpTgax4Lr+ybtRcF3UfYkF1w1TtAthAVNLtGsfUNHuYKiTt2K4BcvXgD8R\nkV8DzgNfAhCRjcD/aIz5deBJ4Osi4jwLXzPGHB/mfhXlkYncQe5+qFsRP1awhB+m+ZTw8mVrF31/\ny1N4qQLZhP3QaIq5g8AWLFGHJZoTFD7iloHuFsKugtiOxBTfdklu5WFR+JxBfYAbuFO0BYknpfC3\nBHbbhfAMlMCGzYW/UjGTxdmO412XoRB/O42BK71wutsWXU+krSW7IyxWUp7tPz8oQtLAkgBWTwyR\n7aPMPYqQYr+xAZU0MM5xVC15N+PlaC66JaTqybuuCxNP3mU6nJw7j12vreD/Mp9l5ukOth06zfMf\nn2XLiTZW3bzOqpvX+Zv8Bb2+z8eLl7NzcQs7l7ZwdtZcjHh9kndLwXUueTd0G3Ul+6TuwhA1MLEC\nppYGBjR5dzAIE2hJqBbGmHbgsxUe3wf8evj9TmCEbRWKMkQqXGVFMfzRZGY/sjO7ycyB18tnLtrl\noB+88CRBKi62dZ2VMN0Wg1/FvmwWJPFO9tjOSENYYOSMtf4aAzfytguT8Wq7ZJyj6ErOLif5YfGT\nDEWuBlusJMRuq7tg91Og1FmBUvHiOi5JgSagfRhnriJ2ySlnSgXavo4wDC4JjWHBVvRhOlakO8ZC\n28dJJRFvdQ3M4JJ3XfFSK3m3FFhXPXnXTZ9uD7svc0PrdHs6y00n4G3MsmvDSt77xXUkcgWWHbjF\n9oNn2HygjXVtV9jadoqtbaf4jb94h1vZRnasWM2uRS3sXNbCvaZmEh2ueHEW6lLybjx1FypoYHpz\npbEBNZJ3JVw2qiri1enTg6NOXm79X9YoymBxHyDxZNv4/YRfiuIPOyxbrx4jk+/l0OJF3FrUSJoc\nzcm+2hXXYfFj57zyHBamJii2gH+/YJdEMr61AWd823lYkoK1A4jM3cTmVKj5aPTggQmXWDyYInDH\nlAS2uYIV5KaxU5NzlNxArtPiA40C08KUtzu9g5shVI4rfhLYrBj7xtjbK3lYF9j32S17xV1Ek4hq\nXZjBinjjAl77WH8Rby4qZqon70ZOpHD5yCXvzkxmo7EBTvvinEjtLzbyzout/H/dW+F6kS2H2ti8\n9xzbjpxm/u37fPHwfr54eD8AJ+bOY+eSFnYsa+HwjGX0JAISnf2D66KxAZ39k3fFTaCulbxb6Fuw\nlIt4Bz19epJ3X6ROXqMWLMrkJRp0WCpgjEu2Dd06b5y06/dvbWqNxLZNCTc7yN4PcB86/cW2fT6I\npiZgU2Op6AjCkLTBajjcxGb3VRAbylYAMNBetO4bH7vtbmyvt5vScpGb5BwX2nUY6Oq1RdBANUQl\ni3O5aK/X2P33Gqud6SzaOUgzE0PT6UwChqqB8foVKv1FvKWuS/Xk3UyogamUvDujbAlpTrJ/8m57\nJsvZZbPZ++Yyfs+8xIxPH7LlYBub9p5j0yfneOLaVZ64dpVf3fNjuhMJ9i2zy0cfLm+hbc48EmG3\nJVlFA+N3J2NLSK7rUiF513VbqiTvDjh9OnrPQ7F9seyPu5IGpk4+3AfNJBLdKkr9EUu2BUrZK7EO\nSyEQ0vkeXjj7CQDvblkbDTmMtCthweLSbQORqsMOow+mqV7JojyYJaA4LvEWrJD2Wq40WNAXaPbt\n913GOnJyxb5CXJ/+ybdCaWhi7yDOWs5NVClB1xUz7Tn78x5swZQOC7PLvTA/aV1BdSy0fVwMVwMD\nfadP10reTYbbrpS86zQw5cm7MxP3AbgdNEY5MO0uB+bpLPueXsYPvvwUyd48i/bf5tk9F9h2+AxP\ntV1l+6lP2X7qU/7Bn7/NjaYmdi5rYceK1eyZ10J7tonkQ7dsVNLAuKImGhtQKXm3XAPjlpHyg5s+\n/UgamEoi3jovYiaFhkVR6ol+YlsXGBfemoQfBcUVAmHr5RM05HPsX7SEG/ObmJu8B8SC4mJiW3DB\nrWVi20qUW5QHSzzxNuPbdKRb7orS2GLgZgGkAHfDk6uHLRg6Q1Gu07E4V4/BPiCm9tRl16Fxzyli\nCyB3dSZAI9aJ1GVKVuoitiCakYCHRavVWZLSNNtB8Dg0MPaZJipeKgXZpcV1YsqD7FL21u/kQaiB\nqRpk93Ij337+Gb7NM3CtyHMHzvPMRxfYdvAMs+884GcO7+NnDu8D4Pj8+exY1sKOlS0cmrmM3kSS\nRIdPsqO8+1IWZNedxAut07WC7KLi5VE0MJNl+nSdHK6eMZSJTcyyXHqoTGybsP8NTNKn4AqWFLx6\nIZwd1NpKkMr1E9tGBUv4v72a4HbEiCfeBmK7KlP9WKicgaBordIZD/JFuwSUFEiEwlvXkYlHt7gw\nt1onLUM4DiB23zmKEuE+PA+SBbtPF7c/zbealm4DiwLbVaql1RloTMEkZ7gaGBh4+rT7e64VZNdh\nXA5M5SC7e0GmTwrvhWUzOfD5JfyB2c7UE52s332J5w+eZePR86y5coU1V67wt3b8iK5kkj0rlrNj\nWQu7Fz7B6ZlzosIl0sDElpGi4sUF2fVYZ1S0bNSd6+dAGooGxhQKfQW8oBqYMUTPBMrkoZrYNjbw\n0HVYUtLD9gvWff/uc+tJBzmaE5XdQX5U/0h/se1IEk+8rbScdKILMgLXiraAEA+aTKloyRt78izQ\ndznHLfFUotxV5DJe4ktCeWyHxivabTX79lOyyQsLJGxnaCDdSlxUXG1MgdKHxzF9eiANTDqmgWkO\nNTAdZUF294vpUgpvKOJ1XZibTzexc81KdrKSh/dTrD16mdbdl9h68CxPtF3npRMneenESeAtrk1p\n5sOVLXy4cjUfzWvhTraRXCTelf45MF19uzBeVxIvEu8OXQODSB8BL1QOsqs5fboOui+6JKQodcxL\nZ4+RLuTZu3wZ16ZOZQp3xvqQLNWWk+LFTGO+tHTUmLDC3As9YeFQYZvxbkk5PtAsdpkn65XSdcuX\nj3KAFz5uijAngHsu/8XYT8mBdCtxUTFUHlOgTCh6gwT7n1nCj55s4V/zWRqu9LL98Bm2HjjLZ46e\nZu69+/z8x3v5+Y/3AnBs7kJ2LVrNziUtHJuyFIM/wB6UQaEFi6KMU8rdQU50m/Ijd9Drx+3soLc3\nraeYLpIJcrHZQX3dQckKu6jcon/MuGLGLR05J9LJLqstSVK5YHG4DgoQzftp9mFFGs50l9xITsDr\nlpFc4FwBO6soCAuldNEm33YaWJSEVenahUdcVOyoNKZAqcrgXUePLtoNxNBbJtpNRdbpUvJuh2+X\nZ2YU+7qOZgf3S2MDGkLtS5i8e6cxw4HVi/nzz7XwsCNFy4XrPL+3je3HTrH55DmeunaJp65d4tf3\n/pDOZMC+hSvYubSFj2avpm3q7KizUpp/VMp88btCsa6zTvfm+2teKiXvOn1LjeTdcsu0oy5Eu0Y7\nLIoy/qjmDgoLl2LCoxAI2Vw329pOUkR4f8saSBVoDHr6uYNS0ZKQ3W4lh1C1CcCPHV9s4izYsLYG\nwHjWOQSlJZ602I5JntK8ISfITYfLSIHYgLvztmCjQKlYSWKXm0y4z9Up241Jis2AWRgMXocSFxU7\n1P78yDzy9OkKYwOgsmi3PHk3h0vgzdecPu3Sd+8lw8yXsuTd2w1ZbmWz9M5O8qdrW/lTWum54/Pc\n8fNs3neO7cdO8+TFa3ym7RM+02adfFebp7JzyWp2Lm1h7+zV3EtnbeZL2bJRPHnXBdcNSrT7OKdP\n99G8MPpowaIoY0jZVUzcIRS5g8LCxSTtf4Ni4FMIhG0Xj5Mq5Plo6XLa52TxKdCY7KGxLIrfD0/W\n8Tj+mu6g0SCuA1mash/413O2OCmE7h1D6TaNtR+7+zlKhUgeuxzUa2B60i7pXMqVNC/pcJ95rLB2\nim8ty9Nl4BC8SpSLigc9pkAZCgNPn+77N1xJtFs+NqBY1oWpNX064/X0Sd0FouRd5zq6HTTS7mYf\nhd2Xm5lGriyYxjdfmM83eZ7kpTzPfXSeF46eZtvhM8y7f5efO/IRP3fkI4oiHJu/kJ1LWtg9t4XD\nc5fQ2+O6L+ExdvhRcJ3fXRZcF0verSnadbfhxU+5eNcYeTTR7igiaIdFUcYHtdxBUf5K2GEJPOsO\nOm+Xg97d0EoqFV4lJnv625lHyx00FCrpQNICPabUQXGJtwmsotI39vs8Jesz4e30MInXBcDNTNhk\n3a5C6XeneKFjaZj5KgOJipURp5Jot/pyZly029cyXe46ik+fdsm7qVjybjx1F+iXvDs98ZCZYffl\nTt7ezo4NbwS42dDInkXL2fNzy/ntjhSrz13nuY/Os/3IaTaeOM+6yxdZd/ki/wMf8DBIsXfxCnYs\na2HPvBbOTZtFstOv0H3pn7wbiXSdeLfS9OnIOl2hcBmOaHe0GIdC4EromUCZHIjXbykocgdFcfxC\nxnTx/MWTFER4d6N1B4FNt81GdubQQhlzB9n7Y6BbKaeSDmRRAGd67P/2AqV8lAT2g6Y1DRfzdjZR\nMhSy5A0EQEPCak8+emg7LykP5oSqnVt5O1gx49kOS3Ni+DbkR82oUUaEoWpgqibvxqZPl7uOAumb\numtv+yfvuiWk8uTde2EXZk4qG3VfbmWzMNvju+vX8l3W0nU7wbNHz7Nxr81+WX3lBi+fPs7Lp63z\n7/LUaexYtpo9C1rYvWgVHY12m5UKmET58EbXfYkKmUQsuK6C6yiWuguD0MCMQbNFOyyKMt6IMlnK\nOiwu3TYlvHzhKMligQ+fWMnNWVkWBTcBaPR7+gXFjRuxbZxKOpDGBKwQ2xm5l7evf4oP82L6ks57\n1k30IDxzTfVhVsIWKa6IyHp9l9oWebYTsqlxNF+hMko8imU6osL06biIt1wDUyl5tynsaFZP3k1H\nGphbQTg2IBwfcLshQ/uCZv7/Fzfz+90vMfvWfVp3X7bTpw+dZcHdO3zpwB6+dGAPBRGOzl/EjuUt\n7FrYwuF5S+jtDguXDo9EVxUNTFdJ/+KFxUul5N0BNTCFQt+xAflRPocMlME0jtCCRZkceFIxih+g\nGBYs+ZTw+oFwOWjLOiRtxbZgCxbXYUm6q8kysW1cvzJmYttqOpB1mb6dCxfQ9mm3LXIafGhKwNLY\ncfeEeS6gglhlRJN3yzUwlZJ3XSezVvLu/dgSElRO3r3dm4HpcGDxYg58aTH/e+fnaDlzndbdF9m6\nv41nP71A62X79bf5AQ9SKfYsW8mOFS3sXtDClcaZIPHMl/CYY/OPnPbFJe9KT9hh6c1FE6idBqZS\n8m5cwCu9o3/RI3VixNOCRZlYDEVsGxUs9n7GdLG17RQFET7Y+gR+UCil28Y6LIH0PUmPudA2zmB0\nIJUC2jrCzktzorLgVQWxSgUeNXl3IA2MT7GPgBcqJ++64sUl70bLR74tXGYmHnAv6Du88XZDFmYI\nP2xdw7e6NtLQ1UvLx9d4/sBZtn58lhVXb/HqiWO8euIYABenTefDlS3sWtTC7qWr6Gyyf/OJjlLy\nrps+HQ1vjJJ3K2hgygoY8qUAOwpF6BqDLq12WBRlDCk7kYpIf7FttBRkn/vy5SMEhQIfrlpFx+yA\nFDmaEm5NvZtkeMJ0W6426HDMGUgHUkmYOyVpLc9JqVzoqCBWGQQjpoHB6yPghcrJu7U0MADT/Yex\nJaS+ybtzUlnaQwHvtZlT+fYbz/D/dL/ArBv3WbvzClsPtrHpYBuL7tzmy3t38eW9uyiIcGjRYj5c\nFS4fLVhMrssnGRYvURcmKmCKsdRdN7QxlgOD1cL00cA8GIMOixYsijIOiMfxO7FtotwdFIbFHbWz\ng955tpWGUGzrwuLSXi66wnOrJONKbDsUqgW05QawI6sgVhkCj1MDA7bzUk0DEw+ya/b6amDiQXZ3\ng75LSO3pRpgKx5cu4PgvL+D/7HiNeUfusflAG8/tO8fTn17kmQvneebCef4Xvs/9dJpdK1axc0kL\nO1a0cK15BgCJDmed9kh2uVlIoQOpy02ddoF2uah4oTcH7aPcsTWoS0hRxhUipeUizxUq9s+/EAhT\nux+y+eIpcp7He5ufYmpgT27NCXuyy3o9kdjWxSmUd1jGXHA7WFSPoowBj6qBqRVkV66BqRRk1x12\nXyoF2d33bZiQmz59O2GXjWa5+UfpDLe2NrJj6yr+rHsDDZ29rPzoBpv3t7Fp3zmWXr3NG8eO8Max\nIwCcmzGDD1e3sHNJC3uWraSzqYFEhz3ucgdSfPq0H+u+uCDL0UQ7LIpSR7x4+SgJU+RHT7VwL5th\nKh1jfUiPD9WjKMoj0ZUJ+MmWVfxkyyrud6ZZcOMOz+29wGcOnGbbydMsbW9n6a6d/MquneQ9j8Pz\nlrB7wWp2LnqCTxsXUvTG6UWBFiyKMg6Ix/GXuYPcklAhEF6+fBiA97asRdIFMklrqYyHxZW7g6Jd\njAd30FBQPYoyThiMaNcLOysuTTfuOqo0NiD+3GTMQj0Y0a5bNoqSdwsZbiedZbpv8m57Nguz4C+W\nr+LtL6zDKxRZeeQmLxw9zQsHzvB02wWeudzGM5fb+NsffY976QZ2L1nF7gUt7Fzcwq3GafYYOz0S\nTvPSkRj1Dosm3SrKaFPFHRQ5g0QqRPHb+03FDjZeP03O8/jhltUkggLNQZjAGYvjH9fuoKGiehRl\nHDJ40a59pJJlGujjOqol2k2XiXazYi9QXGjdVL8zsky75N17BVvMRAMc01naM1YL076tiT/d9jT/\nb+fzNHZ007rvMts+PssLx0+x9GY7b5w8zBsn7cXRuemz2LFsNbsWPMHBacvpDNIksx7F5CgvLRuj\nGhZFGROqdTh8v18UfyEsWF69dBjfGP7yiRa6ZyZJkSPruw6LS7fNjX93kKJMIGqJdmHwrqNaot0g\nLGZK06ft//vuqIDJRY4jV8Q88G3BMsu5jpKN3C4bG3Ark4WZcHLOXPa8spR/xStMPdvJ9sNn2Lb/\nLM9/cpqlt2+y9PZN/urHO8h5HgcXLmXXohb+YaVESgXQgkWZqMTdQWDPZIm+dtWf2JgAABXLSURB\nVOZiKDp9/bANi3t7Y8kd1JQsiW0BklKof3eQotQxj+w6GoZot9sUyRDOPSpL3u0wAWC7MDMTVrxb\nafr0rYZwSSmTZffaFbz/s2vxC0WWHbrFtkNn2Lb/DK1nL/HchbNsuHSO/3X+/KG9MSOALgkpyngg\ncgb5/ZJtC4HHjK77PHvpLL2+z/eeW8PM4D5gk23B2pnBxvHXvTtIUSYQg3cdVZ8+PaAGRgw501cD\n45J3m8JuTJPXzVQvBZSmT09P2IJlZjLD7JjjCOBmbxhg90KW919Yx3/u2gy3YPPhNuZevA+7Dw/t\njRgJtGBRlNEnSraNi23dfbckFLglIfhM2xE8DD9Z+QQd05IsCcW2TruSkVIcfy2xLdSJ4FZRJjBD\nnT49GA2M7wLs+nVjBp4+PcN/yP2w+3I37L64AiZK3k1nac9kObd4Fvu7l5Dcd2DoL3yYaIdFUUaL\nCkszcbEtgCQSUYelEEbx51PCZy/YsLh3W1tJBPlSFH/Y/g3Ck1IgxYkhtlWUScRIJO+6/++1kndr\nTZ8u18C48QEuefdekImKl/aGLCcTuUd+vY+EAYr1UbFowaJMDGqJbQE8r6RdCTss0/P3efpaGz2J\nBB9sWEM63VOK4vftSaY0oVnFtopSz4y0Bmaw06eraWDi06ej4Y1Bhu96o1ywgC4JKcqYUElsC+B7\nJXdQOEPn1XOH8DD8+KkW7k9JMTt4SHOivFAJY7RRsa2iTCRGQgMDA0+frqaBiSfvuu7LfT9NKnze\naKJLQooylsTEtmDD4oqBE9van71xyrqD3trcikkVaUjmaEy4JSFnZw7nfVBdbKvaFUWZGAxVAwMD\nT5+upoGJB9lFGhivO7pIGlUeQw6LiLwJ/Bvs6fM/GGO+Vvbzvw/8OpAHbgK/aow5X2ubWrAoE4Jq\nYlsJUyON72OSpWTb2R13efryOboSSX60aRVeOk9T0ENjLCgOSldM8a6KalgUZXIw2hqYtCmQoO9+\nRoOR7rCIiA/8PvAacAnYKyJvGWOOx552ANhojOkUkf8J+B3gF2ttV8+8yqTks+etdfAvVj1JVzoY\n46NRFEUZI8wjfA3MJuC0MeasMaYX+GPgi312a8yPjAlnIsBuYOFAG9UOi1K/1HIHuXkcTnSb8CN3\nUCEFr16wy0HvbVhPIrBXN42JntLsoFD4Fo/j186KokxeRkO0G4iJtHKjhZ0lNOQWy0wR2Re7/w1j\nzDdi9xcAF2P3LwGba2zv14D3B9qpFixK/RM/kTixbZn41iR9iqHYdk7PHdbfOE9nkOSD1idJp8Ls\nhGR3lGwbYIsYl26rDiFFUeIMdbkookIBExftjsll0dBXoW4ZYzaOxK5F5FeAjcCLAz1XCxZlYlAu\nfHWLybE4/mh20DnbXfnzdWvobA6Ykyql25bEtlYE50Wbk+iKSJNtFUWJU014X1m02991FBftyhic\nXx6hwzIQl4FFsfsLw8f67lfkVeCrwIvGmJ6BNqoFizKxKHcHhUtDxaRHwc0OOmXD4t7esg6TKpBJ\n2uWfxkRPzM7sroIIb/ufRNQdpChKLSp1YSpf8JREu6NergxelzIU9gKrRGQZtlD5JeCX408QkaeB\nrwNvGmNuDGajWrAodY94UtMdBFAMfAqBMP9BO+uuXqQjSPGXG1fiBQWawnTbRr+7X8GSVHeQoigj\nwNA0MKOJGXFbszEmLyJ/B/ge9rrvm8aYYyLyT4F9xpi3gN8FGoH/GmoPLxhjvlBru1qwKPXHEMS2\nJmn/xIuBRyEFr3xiuys/fPJJio1CklIcf5PXHYltfWdndlc+WqwoijKC1NLAjDaPIzjOGPMe8F7Z\nY78d+/7VoW5zWGdhEfkFETkmIkURqSrAEZE3ReSkiJwWkd8czj4VJUK8vuJazys9Ft43Sd8KbpNC\nISW83mb1K28/u4FUkCcV5GlOdtOc7Cbj2SWhtORISklwC5puqyjK48MXL/oaCw0Lxgzta4wY7mXj\nUeBngb+s9oRYgMxPAWuAL4vImmHuV1FKiGe7LiLge/Yr4UPChsWZpEch5bGg8yZP3rzMg3SKH29Y\nRSbVSybVS9bvIev3kPZyBBQJKNoofqzY1ouJbVVwqyiKMjYMa0nIGPMJlNrxVYgCZMLnugCZ47V+\nSVEGjRf7+ws7LibmDgKbbvv6adtd+f7Ta+hp9GkMbOZKo2+XhLJeT6RdCdzcIBXbKooykTGR03rc\nMxoaliEFyIjIV4CvAKTJPN4jU+oaiRUqEmpWIrFtou9k5nxKeOOk1a+8v20tfrpAUzLMX4nF8Sej\nPATCW9WwKIoywRnDZZ6hMGDBIiIfAHMr/Oirxpg/G+kDCtPyvgHQLNPr411URocqnTyRmEvIiW19\n11mxhcbCrhs8ee0K99Npdj+7lGSyJLZ12StJKUSJk74WKIqiTBbq5JN2wILlUZS8ZQwqQEZRBo1b\nkokLbt33ZUtBxTCO/9Xztrvy/fVr8bMGnxyNCbskVAqLy+FHMxTdJGbVrCiKMrF5DMFxj4XRuIyM\nAmREJMAGyLw1CvtVlIg3Pz0AwDtPt47xkSiKoowzJoNLSET+iohcArYC74rI98LH54vIe2ADZAAX\nIPMJ8CfGmGPDO2xFiRF3B0V2ZucOEhZ3X2fl7evcyWb4yfqVkTuoKdFNU6KbrNdL1usloEgSSFbY\nhbqDFEWZkBjsLKGhfI0Rw3UJfQf4ToXHrwCfi93vFyCjKMMmnm7rtCuJUrItWHfQS1cPA/C9Z9aQ\nzwiNSbsUFIltwwnNSSlGS0DqDlIUZTIgmLpZEtKkW6XuiLuDwIpuxSu3M9v7hQA+e9EWLO9tfwo/\nnScbiW1toRKP41d3kKIokw4tWBRlBBHpN5E5yv/xJBbF39cdtKzjGsvvXedOJsP+DYsJEiV3UGPM\nzgyQxKg7SFGUyYcWLIrymIi7g9x9l7+S7Ju/8to5Gxb3/oZ1JDJFEhRpTpSC4sDamQF8UXeQoiiT\nDKdhqQO0YFHqF1dU+F7/DktKwBjeOGULlnc2rScT2E5KNlGyMdtbW7Co2FZRlMmIalgU5XERF9sC\n+H5JbJtw2hVh1e0rLLl7i/ZMI7vXLWFlcBOoILYNLy98kYpiW/szXSpSFGWCogWLoowAsaWZSmJb\n+7jXzx2UTwkvXw7dQWvXIRmqalf8cLa6HXioYltFUSYTY5utMhS0YFHqg1iHo4/YFsIOi/25064U\nk4bXztl023ef3kCQytFUzR2kcfyKokxWDFqwKMqIUy62DXUr+F5f7Qqw+v5lFt+/xc2mRnatWcqU\n4B5NCdtZyUZR/HkAkrE4fhXbKooy6VDRraI8JlxRIbEOS7IUFAfwxhkbxf/es+sppIVskKPRL3cH\nhdqVCrtQsa2iKJOFehHdag9cmXgYwxsn7HLQ2xt1dpCiKMpEQDssSv1QwR0ENt22GOuwrLl1kQX3\n73CjsZmPn1qIeAUag56ow1LSrpTcQWDj+MvFtuoOUhRlwlMnHRYtWJTxSZmWJO4QiruDICxYgpKd\n+ZVL1h303XXr8RvstK7GZA+ZsoIlCJeE3PKPOoMURZl0GKCoBYuiDJ8B3EFgw+JcFH8xKPJq6A56\n55lWgpQV1jYlemjyrOg2GYpt3ZarZa8oiqJMfNTWrCgji3j93UGJUsFSDMW2T92+wPyHd7gydQp7\nWxYzPbgHQFOyu6Y7C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"text/plain": [ "<matplotlib.figure.Figure at 0x111b65668>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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qyp5yXCIsB+Vuez9w3hjzTOAvgd/ebEER+XYR+ZiIfGxuoyFPUY4b3Qbxq0Z2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\nq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"text/plain": [ "<matplotlib.figure.Figure at 0x111b65390>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1 = np.linspace(-4,4,250)\n", "x2 = np.linspace(-1.5,1.5,250)\n", "fun_map_mini = np.empty((x1.size, x2.size))\n", "for n,i in enumerate(x1):\n", " for m,j in enumerate(x2):\n", " fun_map_mini[m,n] = forwardn([i,-j], w_mini, b_mini)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend()\n", "plt.title('Decision function SGD')\n", "plt.show;\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map_mini, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map_mini, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.title('Decision function mini-batch gradient descent')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that we can go through *many* more epochs in the same amount of wall-clock time, as we take far fewer update steps per epoch. However, the convergence happens in around the same number of epochs, so in the same amount of time we can make much more progress. Comparing the plots, we see that the gradients are a bit sharper, i.e. the model is much more sure of itself, and we also have improved our accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Momentum\n", "\n", "The idea behind momentum is to take update steps that are an average over the current step calculated from backprop, and the previous step. The motivation is that small oscillations should cancel out, while actual progress should not be affected by the averaging.\n", "\n", "In practice this is done by taking an exponentially weighted moving average of the $dw$ and $db$ obtained by backprop, and updating using the average step. The weighting is parameterized by the momentum parameter $\\beta$. At step $t$, the updates are:\n", "\n", "$$\\begin{align*}\n", "dw_{mom}[t] = \\beta\\, dw_{mom}[t-1] + (1-\\beta)\\, dw_{backprop}[t]\n", "\\end{align*}$$\n", "\n", "So the $dw$ calculated from backprop $\\tau$ steps ago appears as a term in the weighted sum with a weight $\\beta^\\tau$. A typical value for $\\beta$ is around 0.9, which corresponds to having the last approximately 10 steps significantly contributing to $dw$.\n", "\n", "In our implementation we now need to keep track of what the previous $dw$ and $db$ were for each layer, and update these values using the newly calculated ones from backprop. We do this by keeping them in a dictionary." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def backward_mom(X0, w, b, y, yhat, dw, db, alpha, beta):\n", " n_layers = len(w)\n", " batch_size = len(yhat)\n", " z = {}\n", " x = {0:X0}\n", " delta = {}\n", "\n", " # x and z values for calculating derivatives\n", " for l in range(1, n_layers+1):\n", " z[l] = np.matmul(x[l-1], w[l]) + b[l].T\n", " x[l] = relu(z[l])\n", " \n", " # deltas and updates\n", " for l in range(n_layers, 0, -1): # start with last layer and move backward\n", " if l == n_layers: # base case\n", " \n", " delta[l] = (dJ_dy(y, yhat) * dsig_dz(z[n_layers])).T\n", " else: # recursive case\n", " delta[l] = np.matmul(w[l+1], delta[l+1]) * drelu_dz(z[l]).T\n", " \n", " # Updates from backprop\n", " dw_new = np.matmul(delta[l], x[l-1]).T / batch_size\n", " db_new = delta[l].mean(axis=1, keepdims=True)\n", " \n", " # Exp. weighted average\n", " dw[l] = beta*dw[l] + (1-beta)*dw_new\n", " db[l] = beta*db[l] + (1-beta)*db_new\n", " \n", " # update weights and biases\n", " w[l] -= alpha * dw[l]\n", " b[l] -= alpha * db[l]\n", " \n", " return w, b, dw, db\n", "\n", "def train_mom(X, yhat, shape, alpha, n_epoch, batch_size, beta):\n", " n_samples = X.shape[0]\n", " n_input = X.shape[1]\n", " \n", " # keep track of performance during training\n", " costs = np.zeros(shape=(n_epoch,1))\n", "\n", " # random nonzero initialization\n", " w,b = init_model(shape)\n", "\n", " # initialize dw and db to zero\n", " dw = {l:np.zeros_like(wl) for l,wl in w.items()}\n", " db = {l:np.zeros_like(bl) for l,bl in b.items()}\n", " \n", " for epoch in range(n_epoch):\n", " for i in range(0, n_samples, batch_size):\n", " X_batch = X[i:i+batch_size,:]\n", " yh = yhat[i:i+batch_size]\n", " \n", " y = forwardn(X_batch, w, b) # prediction for mini-batch\n", " w, b, dw, db = backward_mom(X_batch, w, b, y, yh, dw, db, alpha, beta) # take step\n", " \n", " # ### Some niceness to see our progress\n", " # Calculate total cost after epoch\n", " predictions = forwardn(X, w, b) # predictions for entire set\n", " costs[epoch] = np.mean(J(predictions, yhat)) # mean cost per sample\n", " # report progress\n", " accuracy = np.mean(predictions.round() == yhat) # current accuracy on entire set\n", " print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n", " \n", " print() \n", " return w, b, costs" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training accuracy after epoch 149: 99.4000%\n", "CPU times: user 21.2 s, sys: 1.16 s, total: 22.4 s\n", "Wall time: 21.5 s\n" ] }, { "data": { "image/png": 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csWPHMm7cOLZs2bJPZZRP/P0pgDV376udau4SRL3VsA+mcDjM/PnzmT9/PjNnzuRXv/oV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\ngViFtqL5KDIAAAAASUVORK5CYII=\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1119fa8d0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "batch_size = 1\n", "shape = (2,3,4,1)\n", "alpha = 0.03\n", "beta = 0.9\n", "n_epoch = 150\n", "%time w_mom, b_mom, costs_mom = train_mom(X, yhat, shape, alpha, n_epoch, batch_size, beta)\n", "plt.plot(costs_mom, label='SGD with momentum')\n", "plt.plot(costs, label='SGD')\n", "plt.legend()\n", "plt.title('Mean cost per sample after each epoch');" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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URVEOGyHY5eOw2BOfi4j8GvB6YExErgM/CsQAjDE/B3wMeDPwAtAEvnMv9qsoiqIoyt3T\nt7AcB/YqS+ht2yw3wPftxb4URVEURdk7DtNqshs0qlVRFEVRTijGyLGxsByPWSqKoiiKsi/sR+E4\nEXmjiDwbVbj/3zdYPisinxCRv4wq4L95u22qYFEURVEUZc8QERd4P7bK/aPA20Tk0XXDfgT4iDHm\nrwBvBbZtXa2CRVEURVFOKAb2o5fQa4AXjDEvGmO6wIexFe/X7zofPR8Bbm63UY1hUZTjStWH611o\nhpB2YDoOBf1JK4qyG+Ru+gONicinh15/wBjzgaHXG1W3f+26bbwb+F0R+cdABvjG7XaqZzdFOY5U\nffhSCxIOZBzoGvv64ZSKFkVRdoxNa951llDJGPOqe9z124BfNMb8BxH5KuBXRORxY0y42Qp6ZlOU\n48j1rhUriejOKCGD91WwKIqyC/ahNP9Oqtt/F/BGAGPM/xCRJDAGLG62UY1hUZTjSDOE+Lq7orjY\n9xVFUXZIv/nhbh474EngkojMi0gcG1T70XVjrgLfACAijwBJoLjVRvVWTFGOI+nIDZQYOnl0jX1f\nURRlF4R7bLswxvgi8k7g44ALfMgY87SI/BjwaWPMR4F/Dvy8iHw/1jP1HVGR2U1RwaIox5HpuI1Z\nAWtZ6RrohDCfOtx5KYpyrDAGgt3HsOxgu+Zj2LY8w++9a+j5M8BX72abKlgU5ThS8GyA7fUuNKIs\noXkNuFUUZffcRdDtoaBnN0U5rhQ8FSiKotwTNobleLiS9WynKIqiKCcYbX6oKIqiKMqR5i7rsBwK\nKlgURVEU5cSiLiFFURRFUY4BO+wPdOioYFEU5d7RvkaKcizZr7Tm/UDPKIqi3Bva10hRjjXqElIU\n5fizE8uJ9jVSlGNLvzT/ceB4yCpFUQ6evuWkZ6zlpBdZTqr+2nHa10hRlANAb38URdmYnVpOtK+R\nohxrNOhWUZSDYb8CXis96BjoYsVIwYWUY1sBDLObvkYanKsoRwqtw6IoysGwXwGvVR9WQhCsWAkM\n3O7BqAuewBeaVnQINs2ga2ClB0mB0djGfY00OFdRjiQadKsoyv6z1wGvfQvIlQ6ExgoVzwVXwDew\n0LWCJOaAGLjZs+tNxiAXs5aVzawmw3NtBlANrOhZqcNrsipaFOUwMBp0qyjKQbCXAa/DQbYAcQck\nsq50jd2uOJD3rOhYDiHp2MdyOBAj17tbz7UZWGtNYCAl0A43DuZVFGXfMdgYlt08Dgu9pVGU48xe\nBrw+37ZWjzCAVmi3mXKsdWUybq0n3e5AIPVFDJGgAft6fYzL+rlWA4iJdS35BtLuQOiolUVRDpzj\nYmHRs4OiHGd2E/C6nqoPz7Wg6EMvtDErBQfSHgQCKwHkDLiO3WYnhPHYQCDFI+tLf9+wtVjqz7UZ\nWsuKb6w157S3tdBRFGXf0KBbRVEOhoJng1avd+0FX7CO3ufa0A6gFkAPKyIeTsJs0q5X9eGz9YEr\npxHFq6yEEDPgOeCEUAkgaay4eDgSQX2BNOKsjWHpi5rNxFJ/rit1a8FJu1aspF273nqhoxlFinIg\nHBfBojEsinLcKXjweBoeTFrREXOg7cOLHVj0oRFAxYdP1eBq265zvQttbPxJTMAIJAAfWPatWAhD\ne/sVwwbbrvgD0dFfZ9QDE8JzHXi2Bd1trCQFzwbYjsesWEkNWW+m44NxOy1apyjKPdGvdLubx2Gh\ntyuKchzZyPownIXzrG/FhgOEDNxFn2/aoNkrHRtLkhDIRKnK4lrx0TV2PR+bpjzi2Xosn48sKyuh\n3W/bt4KobcARK3Cudq1V5pXpgTVnPeutQmnnzjRoLfevKAeGFo5TFGV/2KyeSTe0FouyD7XQio5+\nOnIncussRK4gV6yVJDCwHIBnrAjpixwHmyWUjjKAfGPjXD7ThLlEZMHpWneTCxCJFtdYS8yf1OFB\nHya8gcAZduv0H5vRDO2xDaNxLoqy95jj4xJSwaIoR5HN4jeqPjxRt1aNtGOrz6Zdu065B0uBdfMI\n1rLSjqwlXhQca4ByYEVGOxIiBgii/fY1QhMYMdAyrGYBdQx0fcgKlEK7/XBoXYw9o/Qft7pwrQNn\nY9ZKs5tCcVruX1EOBA26VRTl7tnMgjIZs0GutcBWl20EUOpZMXPKs9aO/nknLVA3VlAYbAxIiLWq\ndIz9N+9YgdMvm+IRWVbECp26gWQIHez+bMEGuNyzgqe/7WH8aB8JsWIn60DTQDyMCsUFNvuoXyhu\nM2F2L9lPiqLsChUse4DBEJgQV/SuSjlBbBa/8aW2FQA9Y4VJXKxAuN6zQiMmMO5ZF05MwIlEhsGK\nGbDCwzc24Ha92Oifs3zsmaGNdRn1t9EXKCYasxndyCJjojk2AmvNiUV1XVrrBNhmpfq3i3NRFOWe\n6QfdHgeO9K/fAB3j40ZnUgcHZ11wkIoZ5b5js/iNfu+euNgYFRNG8SPAgthsnls96yLKuNY1VPQH\nFpR+AO6w+2dYtPjRe4GxGUMOdvv+0Lj1ImcjTLQNwYoVX2zwboi1roRYa0vFh3PxzQNrt4tzURRl\nTzAqWO6dtjG84IfkxN7OZRwhEQmUWHSmHhYz9t/BB69iRjmWrI/faAZQ8q2Voh5YIeBGXZT7lhPx\n4ULSBtx2QutqSWLFg8sgNiUY2s/6+NXhWJZmtI4TVbLtC5edYBgIq0ZoxYqPDb4FGHHtoJIPZ7yB\nYAENrFWUQ0CzhPYA77mQ1nfHqF5KU5rPEr/YI3uxRZBzOe00ARhx7O1jxrEfeEIcFTPK8WY4fsMP\nh4qzeTYzJ8CKCYkehoH75lwcFnvWbdRiYIHpB+H2x++E/vhhkdPf51aawmAFV4gN9jWOFScSleNv\nRSX9k44NAM4MnYY0sFZRDhRz0rKEROSNwH/Cnh4/aIx5z7rl3wH8e+BG9Nb7jDEf3G678U7AV/3e\nS/B7a9+vFNIsns9x83yB4oMupfksyQe61CcTTKaqKmaUo89WVVyH4zdu+tYCMRZVhF3wbYxKF/tr\n8xgE297wYQorFPKOzeTpx5x4DOJaNulNuCG+sa6m3rYj19KJ9jkWt/NcCiBtbKq0H9qg3nEX6lHR\nOA2sVRRlG+5ZsIiIC7wf+OvAdeBJEfmoMeaZdUN/3Rjzzt1s+1pijH9/9quZNkvMNItMditMNsqM\nVpuMfrbJw59dWDO+5zrcOjtCaS7LjfkCVx6yYiZ7qUWn4DEV31zMxOiLGm9LMQMqaJR7ZLMsoOF0\n3378Rj+eRaLv4KkYdDpWELjYEvoSRssNLETF4DoMNSbECg7PbG0Z2YjVOitD7NRS0zE2e6kaQBrb\nnyiI5pwGAgemXCukypHLKymDbs8av6IoB8JJimF5DfCCMeZFABH5MPDNwHrBsmvaPcPvL40iibMg\njyD5BEwkOO3XmHFqzLRLAzHTqTDRWmb2xhKzN5Z45Z9dW7Ot5XSSG1MFluYz3DhfIHxIKF3IkX+g\nQRh3OOstAzDu1slFYiYd/Q2T/biZofgZFTPKXbObKq7r41kKLtwiihMRCM2gf5CDtVD0Rckp17pf\nksbGhXTYvWDpZwRFYSer7+3ErRRirUKLUUn/amjn34+HaYXwYNaOrQeQi1nry/Wu7Rw9FYMHNTNI\nUfaXk5UlNAUMq4PrwGs3GPe/isjrgOeA7zfGXNtgzBpMGBI2mkgr8ueLg8Q8ikDRjfMZJpH4HHgg\n2SSJsMdZr8WUU2e2U2I6qDDbLDHZLjPSbDPy/G14fu0+QhFunh7hxswI16ZGuf1AAR6B4nyO07M1\nEGHSWwKsmAHIOR0VM8rOWe/+qfi2j84wfmjdP9vWIwltlVonalboYQNjE0DChTCwAqdfb0X6sSRR\nZVsT2tiW3bTkEex+hIFrqJ9xtBUGGzAcF+iIFVCuDEr/T8XsMX6hacVbEFXi7ac/V4KNC81pU0RF\n2VNOkoVlJ/wm8GvGmI6I/APgl4Cv32igiLwDeAdAkjSEASZcXYjxozNmdPGXVvRBr9RpAi+5Di/F\nckAOiT8ISZCRBIWwxTm3YcVMu8SMX2G2WWSivcR0qcp0qcpr//LKmrk0EnGuTIxya3aEa5OnePHB\ncW7OFUg+1mPydBVg12IGND37RLGR+2fFt7+8QsyOaQbb1yN5vg03u7ZoXNaFCQeKQZQFZOy64x7k\n4/CXTVtG38igYBxYUbNR/ZXtMFjrjGCtI9sF3Q5zq2vn2wnXVrzthNZ6AgO3161IrHhiIwG72OMa\ntjztxJ2mKMqOOWmVbm8AM0OvpxkE1wJgjCkPvfwg8N7NNmaM+QDwAYC8jJp1C4ee29SFYTEDYHyg\na0XNqpgRhzJQcV2ejo0BY0g8BlmInY4x4a8w6TaY6i4xY6pWzDSKjHSaPHr1No9evX3HPBcKOS5P\nnOb2XJ5r507x1MPT3JwrkH+ozVzWHm5fzJx2GwAUnA5gXU1biRn7rwYB3xds5P4Z9az1IOVa60Mp\nMneMefZ7POwiAitWrnWtNSHp2HVaBs64Npi1Y2zjwcmYTR0ede3FPzA2ZqT/VarvVqmso+8eWl+/\nZTOSWMHUM/CqjJ3b+iJw1agz9O3QHlPOsYIlwB7n+jRnbYqoKHuLWXtpPcrsxS/8SeCSiMxjhcpb\ngW8dHiAi54wxt6KXbwG+uAf73RN8cbkRO8X11FnIgMkk8Qu2y2w802O6XmLMWWJuuchMq8jF8m3m\nK0UmqjUmqjV4du32Ak+ozSZZmUsSXBCac3HcB0LaFz04awbBk8rJYKMicCNelH0TXYwDY8VGeii6\nNR4FotaDKGhVrPBoh+BGASXF0LpZstF6N3tQ860wWBXyDCwi/fc2s470Y2E2Krk/zHbWFRcYdSDr\n2e2NeBt3br7ath2gu2EkuoyNc8m59ndy2rszzVmbIirKnnNi6rAYY3wReSfwceyp6kPGmKdF5MeA\nTxtjPgr8ExF5C/b+rAJ8x73ud4OJDD3fhfVlxbpyxI1OgrEYsXhkqo/HuQ5cy0zyl0xiMkmYhPCR\nOCOJBtONEuNmidnlIjPtIhdLC0yuLFF4sUXhxRZ8Yu0U21mPxfkczXmPxoWA5lyc2MUe7Qsx8vmB\n9QWsBUatL/cBmzXxG43B42n7+gtNa4UYpmusOMnFbFxKPGpomHGsSykwNp6kG1W/Pe1FBeYC626J\nMUhfHhYqm52X+sXl1tdduRsyYq1Htagkv8FaUYYtIM804MmGPYb+V7gvlPwAzsfssVV8yEdxLtNx\nbYqoKHuM4YTFsBhjPgZ8bN177xp6/kPAD+3Fvu6KnYoZgG5vjSsJQJYGYgbAjcdoxOM8S5JnU/PA\nPGEuBTlwMw7j8WWm6yUmTIWZlRIzTStmCvUms08twVN3TrE6kaI4n6N6wWX5fJLYhYDEhR6dWY9C\n/E4xA9adpGLmiLOTJn6bjUnKwC3SipoUtgNbw2Q1Uyey2gVRSrOLjV0xw2OG2MxyspcGiroBJ7Rz\ncLH9j4bjTK62bZxNv+R//99+80UHeyxeABPrOj33+w+t/6y0doui3CUnK0voeLPeeWeCLcUMRNaZ\nvphx14qZMB5jIR5ngQKkztr3xlJw2pBNBcw2i4w7Vc4FZaZrZWYaRc5XihQWWhQWWvCptdPpeQ6V\n2QwLF/OsXHRYmU2RvNijcT7OyHiTgnt3YgZU0BwIO2nit9mY6117QU5KdAGPMmlcbBBsDECs2KhF\nsSxC1HeI7eNMhjsu90v47yZ7aDNCoBvYjKBslNbcNXC7Bw8k4Urbjhuu1NsXLjFsnE7fzdUPTO5b\nVFZCbYqoKHvMSYphuX/ZQMxAZJ25CzHTiMf4Ig5fip+F1HlwIZxM4pwLGYu3mGsucpYq040S57oV\nZholJleWmHixxsSLtTsq/jaycUoXsixeyFG65LA8lyJ9oUNzNs7pbGO1nkxO7HFoCvYhsZMmfpuN\n+VLLVoPNOTbDp99JGaw7pf8djQw0xIg6Igd3Fncbft3/8w6LFFdscbkeA7fQ3Vhe+j2I4mKfN6L0\n6npo3VnlAOIMehcN13fpBwkHG5xB+7Eq2hRRUfaUE+USOpHcrZgBW09mSMyEQNHzKJJGkqeAeUgn\nCceTJIIuU16N2eYi5/piplNhdqVIrt4m8/kKc5+v3DG94kSWysUMC/M5Fh4UludSpB7o0J7wOBOz\ncTsFp7tEbSW6AAAgAElEQVSlmAFNwT5U+paXP62B69hA1jg2CNdjICb6pflj2O9eOyqn32atSBn+\nyvbX7cf5esB4zH6vl3ybseNE297t3VccG1TsyqCFAFH2UzVSQk0zECvDNV1crLDxjRVew2isinIf\nEJg77wLC6EcWEq4+PyiMUcFystlKzEBUTyZ63hczUYsA6jYFWlwHYjE6wEuex0tEFX8B8knIGUZS\nIVPuCnPNRc6FS0w3bJG8qVqFMwt1zizUeejP1rYvaMc9bk/nuTFb4NqDBcxDUJ1Lkb3UIsi6nHFr\ngBUzYK0zKmYOkYIHcwkblJtw4HJog3CHU4v72T0iNqW5a6zLqD9mq/OfYSB2+oXYHKxwCLg7N1GI\nFTp+OIhNCcWmOS8FkBWomDsbKfZrvLjGur/aAVR7a2u3aKyKcsTYSoDY52E0zqx53YvWCzC0o2Ud\nM3j/INEYFmVzdpvRtCpm1rqalmIxqp7H05xDEnP2hD+WxD0dMB7rMB2JmcmgYsVMq8zpdp3zL1Y4\n/2IF/vvaaVVG0tyetWJm4aECi/M5Ug92KZxvYDy5Q8ykxZDRejL7z3BQrsHGtPRjWzpmkN2TcQZF\n2mr9AFw2dus42F9/0rEBsqFYgdGv6+IKxIxdvhJu3jBRsAXpetF++g0Z+7ExnRA8F0ZcmykUGFv1\nNi12nZ4ZBNo6kQsp6cJc3GYJ1UPwNFZFOVi2s4LYMYPXQbSsLzZ60bIe0I7EQDO0392VMIG3EtJe\njJEo+fgLHuamkC126DZcFv3O/h3YJmgMi3J37DajaQMxEwI3XJeb8TRPcB5J2Iq/nEqSDjucc5vM\ndkrMUGXKLzNTL3GuVWZ0ucnoU00efeo2/H+DafQ8h5vjBRZnc9yYLXD1IY+FC3nSD3UYn1gB2FDM\nAGQ0PfveGQ7KBStKQqzLpBZYS0QPSIkVCEt+JEgiYbM+lgUG1owEMJeGxR7UwoGFI+9YkVILNhY8\nHgPrTb8NAFirTHNoH2DFRiewFpwk9nucdSOXUGjdXa4MrDlno5o0KceKlddk7/kjVE4uG4kP2LkV\npBeN6w5ZQQAaxl4+m2GMlTCJ0wppLSRIFbv4Cy6ZhS7OLYOzYBgptxiptCgstchXW8T8jefki8Py\n2cl7POLdoy4hZe/ZTUaTOEgnUupDYqYOPO+6PM8pJD6BJOKQAzmT4HRQY9JtMtMpMxNWmG0VmepU\nGG8vM3ezwtzNCq/+1JU1U1jOJrl29hTl81luThfwH3a5fTFP+sEOYdxhJlZebSy5XswkozknxdWM\npu3oB5r2rS2hsQGoDoDAOc9e9Eu+/S5Mx2x2jm/uDLwFK0ICbCwJwPmkreOy5Nu04eUojXqjInJx\n7L58AymsFaYZ3DnWYLchxgqRRJRu3TVWZDlYAZNxojo0Ame9QQE9jVlRNmA7F4x9PRAgq883sIK0\no9Xaxn7PmpEIqYW2RtJyO0lrMUF6sYt/yyW32IZbkK+0iZV88kttxss1CtUm6XaPnVKPJajGs1QS\nOapuhrKboxzPUSFNovjEjrezFxhEBYtywOxSzABW0AyJmUVg0fX4LBNIfAZckFNxEnGHc36VSafJ\ndLfMdLjEXLPIVKfMSL3NyAu34IW1uw9EuHm6wPWpApXzOa7PFDAPCbcv5Bmdb4AIMzHbwmDcrTHq\n2lTXjcQMgGMcYv3nJ1nMDFtbvBDOxa01ZCW0FoyusT2FRGBpgxNo/2sSEqVFY9ONRwIrdjpmUNJ/\nuKx/H8FaczxgxIHxOKwEkA6hZtaO68evGGA2ActduOpbC04/RmYZeDwGkwkrxNwhUaMxKyeG3YqQ\n/utV8bGFFaQWxgGohfa7VOlmSFR69G559K675EptnAXIV1rEij6FaouxSplTy00KtRY7peu4LMWz\nlBN5lrwspXieipNhyaRY8jJUwzjLTprlIEbX8TC96Pfp+9DyoQUmCKCzmf91/zgmHiEVLCeC3WQ0\nDYsZgLpDy3V4EXjRzQJZJH4JEiC5GKdiAZN+lXNOg+lOhZmwYtOz20vMlOyDz63dfTMe46WJMa7P\nFLh27hSXL40hD8HtC3kmx601ZljMAIw4ndU07a3ETJ++qLkvxcxWab39qrllH/IxaHVtttD664Fg\nC7r1q9/e6FmhImJjY+pDrqT1LqX+Rx13oq7KvbXCph8EDDZWZSWE8w5cNtZtFYq1ELlY0XS9B49m\ntL7KfcTdBqIOW0H6cSBbWUHKgXUXlv0MyaUevRse2cUOwYKQL7eRoiFR9CksNxmrlBirNji10sQL\ndxbYGiAsRZaQspelHM9TIc1SLMNymGTJS7MSxKgGcZoSw/jRidT3oQ0mCCGIzrdBADTsdx9Wff0m\nHPpxmRCzw7mdRPRsoNw9Iix5GZa8DF/I2LsXf8T2jAnzDueaS5xxlzgXlphbKnK+tsClhQVON+o8\ndu0Wj127dccm62fiLM+l6M07NOYSuBdC2hdiyIXI/aBsTNW3F/tKLwqSjXry9ANy41hx4jMoGNcw\nthdRL7DxKzGsUPCBhLFCZz39WintSBR1Qpu9NOpBo2eXedE+vagCb2Bsif1aYP+GKceKlgDIibUM\nwUCcXO/a9/oxOypaTibGIMuG+O0AdzEksWjwSiGjJYNXCZEyOCVDstgjUfJx17e32IJyLsNiLs9C\ndoRiNk8lkaeUybEsGSqpHPUwTSWZo91L4kZNQ72mtYg4Tfu9lMgFJJ0umJ27g44c+5TWLCJvBP4T\n9ozzQWPMezYY8y3Au+0s+Jwx5lvXjxlGzwQnnd2kYG9gfVmtJ+Pa224vbs2vxGO2Q3ZqhC9lbDq2\nfzYJZyGe9ZlplBkX27pgqlvi/MoCF4qLZItdssUufHrttAJXWJ5NUT2fZnleqM8liF/wac3HSE31\nyHmbW1+ANRaY+86lVPWtOyXhwOkYeD5cDaxASHoQ+NbV0jOD2BUHe6fXCq3ocLFiRbDjPLGxJxtZ\nWMAKoLgMmiq2QitG+hV2Pez6bWyq9WkPbkQ1Yggh4UYWHjMo0zx8HBlnUI7/YbW0HAV2kjkzGGvo\nRdUHw9WMGQPG0KmFBAsGtxgQLAqxckBYhng5gKKQKPmkigGjiz28zs6tDcvpFAu5ERbyecrJPKVs\njmU3y7JkWUpmqZk0S4ksdT+N73h49R5uKxIhKz1YAWlHIrnbw2WJdK+3mq251lIy+Dc0ZluryYYc\npdScPZ6KiLjA+4G/DlwHnhSRjxpjnhkacwnbsuerjTFLIjK+3Xb1LKBszTZZS+vFDC17Wy6RgBHX\nGYiZmP26hYkEV4CrqbN8mrOYdBL/fAqZCykkW8zWi1bM1MpMtkvMLy0ys1xm9KUmoy8172wqmfao\nXkyzdD5N/aKhPpsgeaFHaz5GtmBPNjmne6eYYW32kn3vGIqZ6117wrzVtdYVwWbuCDDpwdVw0Heo\nLzDACpeV6IVL1L/ItWKkZe7s7tzPLDLARBS7AtZiEhgrNPyetdD0x+UcG78iAjMJeKlt05fzziBO\n5WWZwXEkHPuAQTn+610VLHvMvWTOBJjV2JF+/RC/EeIWQ/wiuOWQoAxh0SFeDpAiJEs9EosB2YUO\nsebORUgtkWAxN8JiLs9SIkc5k2XZyVJJZamRYSXMsBTPUgtSdNw4bqNvBelB3Vo/pC84Ol2gSswv\n2fAt37cuG4bER/TvsABZIz6i9+7gKImPu2AfLCyvAV4wxrwIICIfBr4ZeGZozPcA7zfGLNk5mMXt\nNqpnAeXu2UDMDBZFJwKfITFj/xE3ehKlZIvnrYqZWiLB0yR4JmoqadJJSIP7oMt4fIWZfofsWomp\ndonzlUVON+ucfWqFs0+t3DHF5bEUty7mWboYg4smssz06Ex7nEpYS9FwbMyxFDOVHtzuDjJ+nCid\n2RP7OO3CQg+CodiR9R2ZV4vDBYPKsw7WTeRgC9FFi1fjU4bL+wcC5xNQcG3tlIIHxZ4NAO5n/YxG\nlXRv9AZxKi/LwKx1I9IMrWVlmH45fmVH7NQKEqxaPe60gvRFSLsDXjmkVxRipYBeyQoQUxQoQrrY\nI3PbJ7vYIVHfeXXBZixOMZujlMmzlMhSTudYdjIsJbPUyVBO5KiFaap+mpaXsOIDcNpdaK21gphu\nD1gBv0IcNrSC9I+tv6yPCc3xsH4cAPtwuFPAtaHX14HXrhvzIICI/Cn2LPJuY8zvbLVRFSzK/rAD\nMbP6uudvKWYAgpjHrUSCW4wgyXHgIUwhBQXIpAIm3ahtQWibSk61SsxWS4yUWoyUWvDna6cXOEJx\nJsvtiyPceiDO0vk0yYtdkvNdemMuo+6dYmZ9PZlhMQMHVFemH6vSr0o7HVk6GiaqUCuDRoIuViy8\nJgdP1m3Mya2e/dv0LSD9oNu+GyeMXEH5yNLSNFFashkUhnOjecTErtMxVlh0Qvt3e03WCpZ+APAw\nWc9mBT2evvPY0pHVJTEkDE9wavO+ZM4Ehl5F6JRcYuUAv+iSKPmEJSG12MNdMKRu98iWOmSqO89W\n6bqujQVJRQLEy7DiZqgkc6yYNJVEjmWToRjP0+m4SNsKHGl3oA3SiawgUeaM6dUgqNoks54da/rH\nOGwF2cgFY9+4c5InTITsFMNdWVjGRGTYcf8BY8wHdrkND7gEvB6YBv5YRF5mjKlutYKiHCybxM3Y\nRRuIGbB3VpuImUbM4/lEgueZQJKz4IKZSCHjhrFEi7lWkXNUOeeXmaqXrbCpVTl7pcbZKzX4w7XT\naWTiFOdy3LowQuVBh8r5NMkHemTnW4RJh1HHur0yq3Vl7HyGO2S7kXjZ0yJ5m8V4tKNYE2fopCPR\n//rmdwPMxO1JfqE3CJ7tL+uX9vfsbJmP29fXOjZdue8O6neIdrAZP6c8qARWZMRkbWbPcIXeuGyf\nqrzb8ceQ9SLkbjNn+iGejdCxcSErLl4lwC859KIKqmbBIb3Yxb1tyBbbFIo9sksdnPUX903wxaGS\nyVJJZFlKZ1n2IgHiZKhGImTJZCjH8zS6NpVeWlFAaqcLTR9qRFYQwG8CTcT3B5aQKCMmDPrf08Hn\nY9bFhdyBCpC9wQC7FywlY8yrtlh+A5gZej0dvTfMdeDPjTE94CUReQ4rYJ7cbKMqWJSjxVZiJoye\n91OxtxEzBijGPIokITGHJG3FXzOaJB72mPTqzLaKTFJlplHkXLfCdL1EvtEm80yZ88+U75je4niO\nyvkMt+ZH8B9yqMylyVzq0JqIcTa+TMHpW2bsXIfFDFirzFZiBrYQNJvFePjGpiIHRK4cGbJSGGvp\nKPagItZyUuoNrngMhtGJLC8xYzsqB9h91QO73BUb1JuLgmcbIeQ9eDS9cYzJcM2YnaQq73b8EeBu\ni5htZAVZX0G11XKJlUI6xTjxsk+wECNccGwcyO2AXKnNuWKX3FKbWG/nbrNq0gafVlJWhCwlc1Qd\n64pZNhnKJk0llqPWi2NEVuuCSKcHDTDdrk3bBei1gNYdrpj7IhD1BLEPH/uTwCURmccKlbcC6zOA\nfgN4G/CfRWQM6yJ6cauNHt0zgaJsRv/XtZWY6Ubm7H5mk9taI2Y6wOWYx2UKEBsHHkTyScxEgpGg\nxaRb43xrkUmzxEyjxGSnzLlGhfHFGuOLNR5+4vaaKbXjHremRlg6n+b2/Ajhw0JlPkPugRZ+1uWs\nZ62cBaezpZgBa53ZSMxII8DJrnVDERdbaTYwg7gVsGnNcbHZOzHHxpLc7FmLRdqBXhSIaxjUVenr\npAbgd23/H2RQKG7Ms2OXQ5v5cy6+sWtnmK1qxuzF+D1krwJRt6ofUuuliFUCOsUYyZKPf8shs9CF\n2xBfCMiXW0yUm4wstUg3d54q2/TiVNJZqrEMy7Es5URfhORZIkMpnqfqJ6jGMoTtYG0gapM1RcxM\n0AXKg5iPDawg6oK5z9jjP5UxxheRdwIfx541PmSMeVpEfgz4tDHmo9Gy/1lEnsHeHv1LY8ydd4lD\niDnCX6q8jJrXyjcc9jSU+wVZZ/bsi5m+K8V1V91MEgUBE7Np2pJM4GTijPeWmXTqzLcWmAqWmGkW\nmWyVGe00Nt1tsZC1HbKnCjQfTMAjUDmfITffxHiy2rrgtGOtRDkn2FDMeM90cLoGSUQZWERxI36I\nNA2yEtoS+QZrcTntQc4bWGSaUTXbsg+nonL61ej336/N4koUaCv28wojYSPR9lysJcYAX5M70taP\nPrstYrZRIOpmfWRqYRyMoVVN0FqI2z4yt1xyCx2cW4ZspUO8aEu4Zypt8ittnB2ecnuOSyWZZTme\noZLMUnWzVBxbQXWJNOVYjuUgQdXL0O1GG+321lZQBejHgPQFSBCsxoOoFeTo8efmD1gxlQOrlZ+4\nMG0m//X37Wqdy3/vh/9iG5fQvnD0zzaKsldsV3MmCO60zAyJmdB1uQnciif5C+YgdgniIPmEbSrp\ntZhyasy1i0z5ZWabJSabZc5U65yp1nnZF27ae4qIrutyfbzA4mye69MFrl86zc0LIyQf6TE+sQyy\nVsxk0iFnX+ziGghTAhlbGC58KAFA7GaINB0baDsVR57rWPFhDI6IfX8mssaci1sh81zLupQaUS0W\nT2ywbSA246eKtaY0QytmulGAbUIORazcbSDqZt1022ZgAakZ26ugFtrqqbVakmTRlnD3b7rkim2c\n25Art4iXfUaWWkxVqhSWm5s2s7tzrsJSIs1yLEM5mWfJzVBKjFBx0iyZNBUvy3IYZ8nN0OxFojGy\nhphub1WE2HTcEII6UB+IEQ1EVe6GY/I1UMGiKH22qjkTBIPfdNvGqQyLmRpQd11eiBeAAsQegzQ4\np+KMBTXOuU2mukvMUmWmV2amWWS8vcyFW2Uu3CrfkcVUzaS4cnaU0lyW61OnuD3nM51sUJzsMUGT\nZCMg1upx7bE0btbOLPcwgEtShIQExDMhbpR140RBddIxcMbF6YQYY5C0g/SMNR2ccm39FT+0wsXt\nu5eMFUeTUVHATmgDbPeIrVwxGxUkg7VWkH4cyGo6bnSszTAKyjZxqlEzu6VmmvRil+6tONnFNuFt\nwVkw5CttEiWfQrXJ1NIyp6uNXTWza3iJqI9Mjoqbo5SwJdwrsRzLYYKql2bFj7EcxgjFGVhBulE8\nURAMWUDaQHtDK8i2IkQFiLJbzL7UYdkXVLAoyk7YRsxAdJOyTsyErsttYMGN26aS3hQkEpCH5JjD\nOX+Zc26Dqe4SM6bKXGuR6XaZQqNF4cs34MtrpxEKLJ9KUx7P0jmXono2y+dePcXN+REKF5vgCHPx\nEpOxJVJnYsy/UMMPhXjC4HQh3jG0HvKIi5C4aZCEsaImF6UzxwxO22BSQC9EUo4VKKdcdtqU8F4D\nUYMhAdLPim4a6wYbuGKiHjJBlmorTbrUpXMjRrbUwSwI+XILp2gYqbbIljtMVlYYq9YZaWzUb2Bj\nOo5HOZFjKRb1kYnloj4ykRXEy7ASxqg6aXq9cG0fmSarRcns96OHCdrqglGOJsfkK6aCRVEOiY4T\n43J8jJfS0wCEeSsCuvkY6UybmXqZCVNmtlrk65tfIF9scmqpzqlKk1OVJnzJbuf1v2af9JIOlbkM\nnXkPM29onY/TnjDEQvB8g58WWuc9goJLKA5+wQUSmOUA5/ku7nUfkxLCmRjSMEjL2FToCc9WxD3I\nzJ3A4C4GOLdD3GJAomiLmI2VDV45xCkZ4qWAWDEgUfGRHZ5wfcdhcSTHYi7P7cII5eQIlViOcjpH\njQzlVJZGmKGczNFrx0CEWMNfW0GVKG0XBsGrHHyHXUXZO9TCoigngy2sL51cmtbcOfxsGq/eJHV1\ngeTSkl242r4gqq4bBfwmEwlMMsFVYlxJn+cJztN4NEfa61Fzk2SDNqdWaox1qmQrLXor8EDxNuP1\nGhPP1uDZO6fYGI2zMp+hOy/Uzsfx5gNiF3t05mOM5AJ4pUvmohC/GRJvgox6BJMuzikb1+HQ/zc6\nsZlw0z4yvegzuCNzJjQEFVvCPVg0eKWAsCQEZYiXAqQEiaJPshiQKnVx1lfj3YRQhGI+y0JuhMV8\nnnIiTzmTY9nJspTKskx2tZldqxvHiINXt0LDbfaQlS6Uh8RHt0WCFvHuUOZM33pyr/VD1FqiHEWO\nyddSBYuyr3QKOVpzk/i5FF6tRerKTRLV2mFP60DoFHKsPP4AbqeDV2sQJmKsPHYBnnrefgbDriRY\nDfTtxh1aE+P4mRRes0P6+gKf/XSMNz5+A+mlWI7n6Yydpp4d4bdufgWlapbEWId4OmSmWWLcrXI2\nsJV+ZxtFLhQXyFS6ZCpd+Iu1cwwdoTqdojyfoXTRoTaXITbvkxgL6KaFnG9dXJnIxRVDcKoBzs0A\n0wgJUtDICmFHCIvgVkKCom1oZ0ogRUgVe+QWfDKl7q466pYyORYzp6IKqmkq6Qwrji1eVjdWgKyE\nGerdBKHj4jatqHCaXVhmbf2Qno0LSfRjR/qffc9fWzvEPrH/qttGOSkck6+vChZl3+gUcqy87FJ0\nwW7aC/bLLpHvX7Dvc1pzk7idDm5Udrz/b2tukkT12Q2zljqFHCuPXLDrVVcIEjGql2b48he6fOyJ\ncb7i8Qa5qYByM84nvnSBq36aMBXDeekmTrvLS8Dl5BlMesZmEE2lkMmQkWSH2UaRCVliplbiXLfM\nbL3ITKXM6NUmo1eb8Edrp9NJuFQuZCjPZ2nOAAL5aptTl1tI1eBWQhJLPU7vQoQspdIU83kqSVvC\nvRrLUhPriqkZK0ZK7giXz81B1+C1OoSedWGNXF0gWYr6RfV8IMR0K7i+jwurVhCzUf2Q9RWU1Qqi\nKJa7q3R7KKhgUfaNbS/YW3A/WGbs3Jtr3nM6Pfzs5sXWNv3MZia4+bkqz1RfQfhFb/V9hwbG96mf\nGSH21At2I279DjfTSjzGF4jxdHIWmMWkk4RnksTmfMZjdWYbRc72xUynzOxKkTONGue+uMK5L97Z\nVHKYTsKjnklxOTlGJZ1l2cuylLRddZf7fWSCNKVEnjBqoui07Py7ODRH8/RSCbx6g/TNMs2JNO7N\nJdxWBxOGtq6d59FwDLFbC3YDJ6ybrqIoKliUfeRuLthw/1hmvFqLMBFbFRcAYSKGV2+tEWQEUQdC\nV+hMnCZxs4g7VDt/+DPb8DNtd/Cz6TVxFuvdTIMU7Lp97bo4nkcA3IrHuEUOSZ4BHsTkk4RTSbJ+\ni0l3hZlmkVNODRBekb/CQrxAM5ak6capp1IEBs6k6vzKX9o6UvWRLCvzZ+klE3i1JvnnrpK7vgAs\nI1HMhwkCOiNZlh+ew2m1cFZW8OMe1akxgrhHoli1kTGR+JBul14uM6iTc8AC5H4Q0IqyGcdFz6tg\n2UdO+kluqwv2eoY/q95IDq/WvCvLzFEideUmKy+7BFjRESZiBIkEsdvlVUGGH9KaPQsCqau3wQ9o\nzZ5Frt7Ga9oU3OHPbEef6U5TsNeJmc4otGbP4ufSxFpdegstmm3DC4whSZvJ1JkIiGVgKXWKIGYt\nPYV6kXIxxFy9QW16nPKD0zjtLk6lih+PU3r5JdqEODFvEHx8+SatiVM4jSbGdWmdGyNMxK3YcoTY\ncu3OY6w1D+XMWps9y/KrHwfXwW20CF2HXv74CWhF2RQVLCeb+8VKcC9sdsHOPHd1zbj1n1V7chw/\nmcDp9vBabfxUks7pEfx8ZnW7h/UZ9oVVZ6xAmIwjnQ7J4vKGc0pUa+Sfet4KsWwar94i89zVNW6f\nzvQobhQc2hsdIblQoTl7lvb4KJnLN+kWsnTHRolVa1Rf/hDu0jK9uUlg6890U4zZUEgDrDx8Hrfd\nxq0s4ycTLF2cZOTpL5Oo1kHssf2P+Gm+8XVVUq0mzYZHKukTP5vgj58dIex0WHl4Dun1CJMxgmwK\n8X2MCVl59WPkn34Bb6VufwuPP0CQ8PAabdpT4zg9H6fTxU8m6I6N4GczxFbqJBYqOGGwKvSqL3/o\nQG8AOoUcy695HEKD22hhPJfumVHixcqBCeiTfuOjHAAaw3KyuZf4jfuFzS7Y60+2d3xWjRZBIk73\n9AiUoTU1DsYQW2kQJrxDE359YYUI3UIOMQZSCbo9f/s77qHzwbBbJ0zGcdpdepkk/rkztM+NIT2f\nMO7RHivgn8qTWFwitlwjTMTozU2SvHKT4NSIdROFBvF9ao9fpLXJxWyt+8ngZ1PEl2urQnrp1Y/R\nPZUnzKYghNjyCslbZdxWm+bUBPFSdXVbz+ceonG5xleNvMR4skapneETCw9zcyRHwTxLtzBC4Lm4\nYWDFiuPQS6cQY+74Lfj5DJ1M2ooVP6CXTtEdK2BEME6XMO7RnJ8iffkGySs3aUffk7u9Adjswr+V\nIGjNTWIcscG/cY8gkyaIxwiSCUKvuKP93gt646McBDutY3TYqGDZJ+42fuOw2K+7uES1tirQ+vuo\nPb52H/3Pyk8n6Y7aC7GfThK0O9ZSaQw4QryyfFfCb6fHtt24vrDqnBnF9e1FNvRcgmyGxAZ33Jtd\nbMT3V906TrtLL5+me7qA+CFuu0MYj2HiHoSGeLGCn8vQHSvgdLq49QbBqREKn3t2zfadZnvDi9n6\nOTTOTxIm4sRqTYQexnHpjJ+iV8jj1RoI0D01QpCIk758izAbW/PZrDw6T2ulwbXFMbxme/Vv1jtr\nrV+hK4gDEvXWkTAE14EgoDk9sSrQYuVlnHaH3sRpK1DjHt0zBYyAW2/aRpQGEjcX8JodOlMTdEfz\n4Lo4nW70Xehs+T3oFHLUHrlAZ3KMwPMwAqlbReLV+upnlbxyk8ZD5wnSSYznIqcD2uOnOPXk0wDU\nL87gp9P4mZTdd7eH0+0SJhP4p/J0CrnV78Z+WED0xkfZd/pd248BKlj2id3Ebxw2O7mLW3+XDgZc\nZ8cn6K324dVa1vVxZhSn5+PVm4AhSKfoei6JygrxyvJqTMduhN9O71B3Mq4vrPoXXQDxA8JEfM2c\n+p9V44Fp8AOSCxWE3up3IXQ9gkSCIJkkiMfojJ+2x9VsY2IeJhHHBCG1Ry/gtrs4JrRFzeIe4fgo\nrfL9Mp8AACAASURBVKj7rp9OggidM6Orc/JqzTUXs/UXvP4Fv3t6BO96m+7pEYzrImGIEAkME+KP\nZKk9eoHkQpna7NmBdWOlgZ9N0RkftX1w4jHcZiuqM+OBIwQxD4ksP8bzMI5gnBididM43S5GBH/2\nLKlrt0m/dIPO+Cj+iLVYeY02GIN0ezg9n97oCK2zZwhO5XCabbyVBsZzaU2Nk7yxuCqohv+OfZdd\n+0zBfkfrLfz/n713DbLrOs/0nrXWvpxrn76iATTuINEkRYmkSJGSCFEXS449tiXbskeKlZFdM5Wp\nzJRTqXKSSX4kU6lJfmSqUqlKJjNJHHtcyUx5rJQmqihl2ZbtEW3xKt6v4AUAARC3Bvp+7nvvtVZ+\nrLX3Od3oBgEKlADzvFXA6XN6997r7LPPXu96v/f7vrEqplJCj9WILy9TuriE6vdZv/8uTBig+gmy\nl2ADRToxxsp9d2ADRVYrYQOJrpRBgIxCp2qlKfGlFZp3HsQGwQemgHwQC59RiGmEjRCjkNCHHdfq\n37gZ8F6ruOHJHO1NotaZRK8WotlspFWt9pbHKJ8+T+u2h3x4Q7uVbmaonjhLVq8QX15+T+K33U24\needBtzIPlE+FtZgwIBurMvn4i8WYm3cees8VfE5CZc9lrGRjVUwUIJMM2exQvrS84VxZ6yJB3bkd\nlM9dIuj23LVQC1FLq6w99FEI/VcwTTGVMtpahNFuvHGElgK53saEAbpRR/YTSC0mDmjecQAjJdJa\nt/IXgqwUY0JVnJfNE57sJ66uSewaGZpS5M53PyGrlj25UGAMSluCZoeVT9+DyAzSGrRSZONjiDTF\nVp1HJRurEV1yn1G0vE5WiUEFmDjG2DwDSqJDhbEhIo6QvT4gqB87iQ0CTBxiPcFBSoLmOlkcksxM\nufNhLDYMSKbGkVmGCUP6Uw3C1RaLn7oHsGTVEsn0hCNE43VMGCC0a/JoK2WE1lgB6XiddHwM0emR\nTTcIF5aRmTMji0xjSWgfmiNqdVCdHiYMQQoQYEKFTDWqnyKSlN7uGSpnL163AnKt4aksDOkf2L3h\nuhRav++FzyjENMKWGCksH25cq3/jZsB7reKuMIl6dSGdalA5u1Bsc7VwSHf3DLoco5LsCqUkXm0S\nrjbRpcirFQnlhWVUt4cJFTqOi+23In6bCVX7wC7WP3KI+MIi3T2zhOstMIZksgEWwuU1dLVc3KiT\nsSrrdx9GaF1M/HrTCr65byetQ7tJZqewxmLKJZ96I9ABtG/bS3xuwXseoD8zSTpRxwYKtMWUI6rH\nz6LjgN7sFMm9806kaneQSmKlxBoNYQhGuL/DglJklRhhLVa6lb6wlrTiwmZI6UrHhwodR6hej96u\nGc79wsNkE+PoSgnZ61N+d4HS8hqy3aN3eA5hLe09s2RRSFYpO4IkwP1nwQiCyyvIJCUbqyF7fYKl\nNbKphiMAUYgpxchOj7DZwlTKZN0EKwW6USe+sIg6d4nuoTmMALTBVEpQEchWl7DTcyQARxJ0tYyO\nQlASkWiSiTGyehWEwBoBxjqTszHYLMAgIBCYUNE+tBuZaiyWdKyGjUJ3/1USqxTp7DQYgxA+ySgI\nnIE2DjFWkO6YQPedAqbaHUdsSxFycRWVadKxqvtDIUFIwsuLBElKf3YSIdx1ud13Zyv0x+ssf+Ij\nmErJqVtTmu6OCWpvntrg00nGa/T27kTojKDVxQSKzr6dBMvrTPqQ1fViFGIaYUuMCMsIw/6NnySu\nV/J9r/DVBpOoJxT5z7D1DXrzjTFo95yRdrKxZbpuvLiKiYMNY9BxiPLbdvbsQmCJLyxesRrMj2WV\nKjJOVLtLb+8sNgzIyjF6vI6JwuK4pYuLWAmLn3/AGT2VRGQapETXq6hmm97cLKrb4+wvf57e3A5I\nU2S3jxmve1+GQSQZ0mishe78AVSzRTY+5lScOHIExFq0FNhDc+iqCwMRKIQ26FrFrfylgCACBFZK\nt38LKLCl2LV/1ylCWzCG5l0HIQoBi8ksCjDlGF2JIc0cWbI4ZaNWJp0ep7WyTtBPHfno9MgaNZJG\nDQJ/PDEsCxt0rUx31xQizdDVComUZJUSVgiEtYg0g0CRjo8VRlSsJV5Ycp/LbXvJ4tCTIUc6MBZT\niclqVRhK7y6dukDnyD5sZrBGo8eqrteSMYW6gZQuxBS6cyBSja5XsUDQT8lqZVcB1xh3biyDv0Vg\nUW4fvR4Ygy7FqCxDRwEECplm9KYnEFiskKSNmvNRlUuIJMV6NczUKmTNNoQhlVPnN3x3ehMNuvtm\nsVFIOl6n9srb1M9c3PDdXPjZT5LsmEJog+p0Ua0uZnKMlU9+zGWMeTXFRAFBq4OwxvmlYu//aXXe\n98LnVvPWjfATwoiwjPDTwPuRfN8rfDVMaGQ/8at/hojLlcXQejumKZ2/VBRAi5bW6MztQFfLWCBt\n1OnvmCBYXd82XTdp1LFAvNakduJMMa7NyG/C3T2TRcaJBUwUIttd0ulxrAqcIiIktlKis2OSsFpx\n5lZtEVmKrpSg00NqVyKfSkyw2iIdrwMWUYrQQVCYSIW2RM0WVimyUkRnzyyq7+qTEPsJ0/i4UDlG\nG42OIoQQzufmQzei71Jm9fiYm2CLm4d1E30+cVvlVBip3Gdg/cQdBpjUuDB04Cdl2EgUsJjJBlmr\nS+2t05SW1+jsmUWXY7JyvImsAFKQ1croigsTCcD0wEgJSmGFQDZbiCjECEHWqBP0EoQ2lM4tEXR6\nrIzVIFcnfGE8pAVrSacbrNXnEakmXlwhCwNEkjnVoVJy5xgxGJev2Iux/hwJrAQbRmAtttPDCuGI\nijFeEfFqkRVuX5682DAElSCzDGGtMznHEZlxypHNMmSnR9qoIcbr2Ewj/DgEoEsxFqi/cYr6sZPF\ndyepVOgc2QfGEC2touOIlaP3wWMvUD9zkf543WVkzUwi/LF1tYwNFLLTJZ2eoHzmYvEdS6YnCBdX\nQMhCybSwLbm4loXKzeKtG/lobiLcQqX55Y3YiRDi54QQbwohjgsh/sstfh8LIb7lf/+0EOLAjTju\nCFdiWNkQOMk392Jshzx8JfsZWa2C7GcbCE759HlnEo1DF04pReg4IlxaQ3sSoVbWWP/o7Zg4IGh2\nEDpzRcjKJQCCbo/S5RVUu0t/epz+zATR5WVKl52y0vPpusNjCFpd4rUmViq6e2bp7t1JMjlG886D\nG8af34RNHLnwQhiQTDUwgfOqWOFX2YEzhaI1VMukOybI6lV0KYQoRPb62DBAhwG2VkZ2ewjrs1yC\nAItACj/5+XCDVQpdKWFUAEqgSxGUYxeqUdJN0j67xHovhC1iEw4mjtDV8iD1uXgcuokIRxQQOE+H\n8BOwklihHPnJCYpXI4odCbxRWmClcKEZf1wThZ7UGEcG8nEJAWHolB8hEO0uphT7YzoiYMoldBxh\nSxGEAf2JOuHiwByd1cp+nHLje/Kkx5RidLVMZ9cM6c5pjBRYa7265I3dftuCxAlP6Kz/nX9NN2oD\nchgohNYD0iKEJ0BAt4/QhqxcIqtXXQhJCFclOAqdQhOGoITzvwgBUYANQ4SxBGstRJKga2X6kzX3\nfVtapT8zSfsjB33RuzZBkhF4I2/LE5ru/t3oSskbm61TqbTzbGVjNUSm8VcXMtOuLk2jDtbS2TNL\n67a9tA/sLnokDSNfqOTfv9xblmcx5Rj+Llsovr95LZ6fBK51rCP85CDs9f37aeHHVliEEAr458CX\ngLPAM0KI71prXx/a7O8BK9ba24QQXwf+KfC1H/fYH1ZcbXXyfiXfq4Wvhv04phZSPrNAniUku32q\nb53ZYG6VvYRgrU0yG9GbdQXQTOxCI5OPv0h3/27C5pUG3DxdN8fFLz6Irk+STE0gkwTl0247B+bo\nH3tnA6Fa/+jtoDVZKSZr1EBAsN4i2THpDbdm4NFQgZ/c3IrfSoURFqEkou9UAoxBGEs61fATo1vZ\nWwTkk5vW/sYvIFKQ6YESkMNPsCaO3PGFHIwj0+5nJQbm221hCxKRjgeDiRv/9yJw+9SZez0YWosI\n4Z5bi42ioVBeUvhI8EPaQJIsgwnfh9Oc1OJVjig/pnbnJnKfN0CyY9wpJVeDlO7uVylhM42tlBB4\n0pITkoJ0DI0R3PGlJzLWYK1E9rqYctmRuNwom+/LWLc8CwK3//x8a3ddCKUwaQalyPmsun1MZkgD\nBUIik4Sg08MEChtFqE4PiSQZr9Kbm6V89hKk7vNMdkygWzHhegvZdwbt/nid9m17SCbGCgOxTTP3\nmSiFCRTh0hrJZAMrQCYpJCnZRAORpgTGQKYxpYi0VqE/Xt8yLPpe3pSbwVs38tHchPgQhYQeBI5b\na08CCCH+CPgKMExYvgL8N/7nbwP/ixBCWHurdDC4efBeIZ8PSvK9GqHpj9fpHJxDtbvIXoIux/Rn\nJiFNySZKBK0O8eJacWN0dVg2kiqjFN3DOwsSplbWyMbHyGoVhO8fk42PoZptSFOWH76XcK1ZbCsy\njS7FJNPjqF4ftd4ha1TdpGWMn4iFmyDzlbjxXX3DAJv33wkrjkhkGl2OnTIhbRGisJkjMygDWYaJ\nIqzO3L5zz4QrHkMR0iiIip9t88s+VNdWaj4nDnmTv3w/+XvK95mrSJubARbbWggUSaNGWimhWm1s\npv2kLTaSlfzAPvRklPIhldyUS1Efx51jZxBOZidJds0MbfseyLdR0oWytHETfzBEVrZCrq6Qkxvn\n9UFrT+AYnBvpQ1Hah4o8wXKqlSdy4JQxISBJB6nemcaWAkwpIlEKISwiyQiX1wbEr5fQnxobhLGy\nzKlulRJWG1Q/YfkTH4FMI5IUEbowlI5C9z6MQaaZ467NNqYUuesqwl3j7W7haymduYjQ+orJ/XoW\nKj8tb12OkY9mhPeLGxESmgPeHXp+1r+25TbW2gxYA6ZuwLE/dHivkM9PQ/Lt7t+NancdB4gCl93h\nFZhoZR2ZZBtUoJxU5cgqJZcqrXUhEa994m7UegsbBkP1QSxpowaBIquUCJod0kaNlaP3YSLF2Bvv\nEK6sg7HosYqbQJKsCIcMFAQ7IAEWR1y890N2e4SdLkIprBVIrd32fiWOUkhrCM4tEK21nNoSOvPr\n4Nu0SRWAQdileM5gDL6uyrarnGF1ITfHZn5cuanUp+UCG1WTzTvSLpumc2AOmWgmf/gCYr01ZE6F\n/VzkG+ov+J3o3/KN4C/ZLxecJycMPCmTg1BN/t5y4hKGjmxsO4bthia8x4gB2cnVkff6O+NIpFXS\nHT/TiH42MOwWnzdOFSrH5NWyVD/xxe2UU2y0QUvl6gKNjzmPU/73Sjo1LgzR3nyem9CzRp1wtenS\nwpXCeG+PDQOXMj45RrDWdsqJzA3VLoQnjMH0U4QQyDQjXGkSLa0StDugDdVT56mdeJfK2QWCTs9P\n7uXiFPTH66SNOq35A3T2zLrsMW7euk+bv/9w8471w4JbJSR0QzwsNxJCiL8vhHhWCPFsSv+nPZyb\nDlm9vE0apbuBbedHAVi9Z57Fo/eyes/8DY0XZ/Uy8aVllxlTrzpDqjHYOKJ0aRkrYfnhe4tjq5W1\nDaSqt2MSLL7AmiNhOg5Jdky5bI5yjI4jZ1QEpE+NFkBWr7i6KJMNuntmsXHoSub78yLyFffwxJeH\nGrRxk5WQTnZvtgk7PUSS+clPYZQchG7SjHCtSeXEu6ggILq0hMyzUqwd8lqIK1WOnJww/Oh/5zOO\n3hMWd6wsG5AGk7+PTZP7VjcVa6GfIKREl2Oadx1k7d4jTpnwZGo/F/ha8ChVuly0k1Tp8bXgr9gv\nLvqQVDAgE1g3yUs5UJCuk6dsGOtwCCoP4xSq1DZ/a4xTe/zk79Qfi1VioHYN+2Hy8yQcqTJhgFU+\nhVxr6Ped8iWVuztK/760r73ir5lsYgzpK/32d01jyjGy2ye+vDLwD0nvgymVIDOYaonqqQtD1ySI\nXt9dp9Uy2pqiEKHINOUzFwnS7KqTe664Bs0OVht0HNGd20F/vPYT96ZcK24GH80Im2DF9f37KeFG\nhITOAXuHnu/xr221zVkhRAA0gKWtdmat/V3gdwHGxOQoZLQJm0M+WaVEb8ckVgWs3jNfKBnXUiL+\nRhWLcmMKKJ+7RHP+gHvRGJfhACQzk1ghKJ9dcCvB2/e6m/1YFdHrY1Xgbs7dXvGebBxhlCBaXCOd\nbDiBpJdAFGGFIFpac4cpRaAN/R2Trqy9lJg4wiqJanWLVFTSbBAyySe2TLtJQ1pk2xEga63LPEkz\nhE89FhbU6joISdjqQhgSXl4lmZ3ClErINMMY74uwhg3hEGMcGfEhjy2hlFu2XE2VyH0jOidGdkCK\nlKSIrubhLtioIuUKTBSifQjHxhE06hvUjKPBq6zaGk2cPN+kAhaOqtc4rXf5HYtiwnWymtn+vV0L\nin0IX1dGUyhiuSq11f5zBSYYUnoE3p9ih4gVAyLkM7yKEF+Qh9UcmSP25C1Xj3AKmBASQ1Yc1+Lq\nEJFm2HKMSFKSyQbResupKLqH1ManyotCGaycXXBp4akzYUtrkWmGDRR6okH0zvnCtKzjkPjC4lXr\nEA0rrjJJSaYarq1FbWNhxJsJN4OPZoQheD5/K+BGEJZngNuFEAdxxOTrwG9s2ua7wG8CTwK/Bvy7\nkX/l/WE4BdkodU1VZ38ck9u1pB/mY1J9t8LUcQRCUL6w5BoYGkvQ76PLJfozE66irRDEl5fRcUxw\n4TLSDEIayWQD1elCpYy0lmh5jf5Ug3R2CpNkMFalE+wiaHWwxvjy8m5CC/oJGT71NI7cJNhLEEqA\nUNh+Av0UqiVU4m7yNlBIrV1V01KEarUxgcTi0o1dZdw61ugii6iojJqmIAXKWnSvj5ISLXAkxRs2\nXSjGbq1n5pP+FfaRzX4VhlJ6vUKQT7y5amBxxEfbId8MjkQZ430h3jgcqsHvi5CTYFasctFObhhK\nizI7xfLgheGx5GPMj38tpGuzN2WY8Gjt35ca7CtJIXY1ajacp5zMFD6h3LOSD5KN2UT5OZVqiFh6\nglSQSnedFHdw//cWEFGI6vWhl6DrVZKJMWSSupT0coyplEitcWnJPnQXtDuYICTdUSWJQ9YPzTlv\nixCu3QK4rK0kgyAounTnxCRXR7eb3If9IEG3R3C2V6Q+38wE4Kftoxnh1sSPTVistZkQ4reBPwMU\n8C+tta8JIf4J8Ky19rvA7wP/SghxHFjGkZqbEjd7fYDh1Un38E5kL6G0sFyoE3AlEXm/JrdrVWaG\nxyR6fSjHxJdWUN0euroTqw3R0hrJVMPVvvCy96C3zsZqtrpahsxQPnXOlauvlRHaIpttwsSNO62W\nIdPYkksJVu2u8zFIiTSWYGHJpR2XIvf3qUF2O4RrLayUiKUVokVXfj8nflZKbJoh8n5GxqDrVUw5\nxkqJSlxIwFZDR1q0QfQTUC5TSAQBottDZq6qqpbSmT2HJ9Acw4Rkq4lcCDeJ5t6SnJTk4RfjDZw4\n5cmGChuG2EA602ocuUlZMwjl+EwpYa0neJ745MezsGAnqNEtFBaAGl0W7MTGsYuhnzO9vYLka8UU\napAVxbEKQlIQCv9zKL2fxW8bRwPlKCdHSebOa642MaymDN5PcR5hozdGSm8c9unPOYHTQ16gPAQX\nOiOztaClwk6Nu9BakmKiEKEU0dIaJmihx+tY6zK1VLPtTk+94oixMWQTDW9QFkhjXB0YayFyIUar\nFL3pcWwpRvaSonXFcPbcMG6Wuioj3OK4ReSDG1I4zlr7PeB7m177x0M/94BfvxHH+iBxq/TZyFcn\nOREZngq3IiLv96b2vpQZgcti2DVNMj2OSDPipTWCbo9eaaZoMJcXnct76wxLxKrdJWh2iNaasLxO\nZ8+sq2paKRF0+6h+4uqn1CuEK+vIigvLEASITBM014uqqmNPvsTK0fvcca0hGa9jSxHVN09TOn0e\nPdHYkKrd2zUDQPX0BYJOj86eWfozE/78OYOm0NqRIYAwdFVQo9DVFhGCoOtUGQIJpXiwiodB1tLw\nqr8gJMOhCDYYYVESOj2XXqycb0QIQfnkWackKUWwsk53bgYbhWRaQ7nkPS/aVUotu7HYUrRR4Rj6\n7B4zd/M19ShYp6zsFZe4U57mtNnBN9Rf8Ji5m9PsHPzNZqE0J13565kmaHVQzQ66VnbXZpGxJTcq\nIML/V5TBHxpjXvlXG08qLC41KCdxQyGqwv+CJz12yBvDptc9cbM4EpiTOe3IhA3UwMMkgChAtrsI\nX4cGKRBZH1Nz30V1eQWZaddVu1Z1iqJ1jSAl7lBqrYWeGnPhTANkGVIbSgtLyMTVZVHNdhECuto9\n6FbqWTbCzYufppH2ejCqdDuEW60+wLUSkfd7U7tWZSYnela61OO8iWG0uEoWh95UFyJ6iQsXSUH5\n0vKG8Q5LxPn+dBy641VLrvtv6tQZCcgll1ZaPXUeXYoRWFQvKZon6lJE+cyCK4v+2Aus3X8n6Y4p\nVLdH/OYpwnaX3v7d23ZtNmFIe0+D3twMJgyRaVqEIFSakSHcmIwh6CfYbg+kQvb6zp87VnN+Ge+T\ncdBgxIC0MFjxy17fVT71XYGL1Oh8gsUrDXhiY92KP51qEF9aYeKZ1wbN8w7spn14DzoKC++ElWKI\nWA2pKjn8cU7bnXwreYSj4evMizMcEAu8rvfxLrPU6PI19Sjf0p/jtN05MLxmZug9MfCWWEu4uk7Y\n7NCfbPhuzF0wlmy8NthO642m3fz9DxtvrX/fXi1RXdfqwSlJdiPxAdcpWojC3yL7iSORSrkD5Od3\n6L2jDeFai6Re9fVa3GenVlvu7UnXkkAmqfNJhSFo48KEAmQQUDp3CV0tIQzEl5dJaxWyahkhBKLZ\nJpsad+nQWjt/lCdPqtlCGDeY67kHjfwgI9wQjAjLrYdbrT7AtRKR93tTu1ZClBO9/sygNL4JFP2p\nMYSxZKXYTZR+9R1dXkZ1ekV2wHuOt90rVqyuk7MuVBoTh1TOXCCtVTCVksuw0Brpx7h49F6CZpfS\nxSUq5y5teC9ZOS7qubiJ0JlJTaDo7ZhEWYvq9KFkXLglDFz/nDRDBgGq1ye6vELJe3FKp8+z9Nn7\nXXl3KcAaV9Jda0e2pMAEgbs3SF8FV7uKp1iLEdIVflMBZJnLYJLSrfLzydzgiYFFZhlWqeLzWL1n\n3l3DrS6i13dpskmGbHXR1bKbcI3FYor6KgNC5PeN5TQ7OZ3s5BvhX3JOzHjjraUpvAFXvsrpbKeb\ncHuJq5abKxpDZAUhMWFEWjbO77zedhN9/hkKUXyWBGJAoPJwUZ595X+W/RRhPLnLXH+josaOGA5H\niYGHyKedm+FCezCowZO3PTDWZd9Zi0oSlwlvHTmy5Rjb7/sMtRQbuJ5XrvZPhI0Cgk6X8rlLCKMJ\nFtconz7vCi2WY4RxPYNMtYLN68bgSJQ0BhMGqF7C2Ctv07z7cJF9lEw2irRp0ds+Y3LkBxnhx8aI\nsNx6uNXiwddDRN7PTe1aCVFO9DY0RpSCdHqC6NIyKs0Kg23p1ePoicaW493OP1SE6lptkplJjO9l\nU1ppbmFMLIMxpLUKUmfIjht35+AclZPnit5GWaVUZC+FS2vOvCyceTmbqiKxlN91Teva+3eRjCmy\nconA9pxPptVx2SDW0p+ZRPT76IkGsp+glXIVW31dDTd3C9RqCxUoV+VUCKc+rDbpz0ySzEw4teby\nKunUeFGMzVo/8RrtU5lxq/7FNcrL6+g4QlfiK0KZ/R1TBJ0uKvUp2l4dsALX+bdScl2UlRoiG/4D\n9U9nxSoXGTbgWmfAZQmwCG28auFlEWtdSXl/TCst8XoLLMSnzpNONkiVxEYhqt1Bh6Gvd2OhnznS\nkofEjHXKTZ6Sro1TiXx4xfrGj/RTRBC4bB/PObGgOn13LUjhTLs58fGqjfCeGosjRcHKOqqfuC7U\nvveSNIZgYQ1TK7uGlO5lRzBaHQKtMdEEotOncvwswuji+5F/33ozDbLxMVeSX2sEETbNkFgXkUo1\nY2+cAimJV5t0m11XAyYn/32vSpbjK6rbjjDCjcBPu7bK9WBEWIZwK8aDP8jV1bUSopzo5U3bROa6\n6Mp+4lal/WTb8vs53ss/VLQGCAJvSOwTrrU2mKLz87B6z7zL+hmS1VW7S392kvCUq/WQTA6yl9Kp\nhuuSCy6F2rcXSCYbVM4uUD19AbVzit60m7yDVpfKmQvItRadOw+BkiggGa9iYjc2aQzGT842CJC9\nlMqFxWLM+XuV/ZSw3SVZWSdodckqsQspTTZACDfJrXQxYzWnvvgwFLUKWbfvUqrLsWt1kLjQiko1\nMknR1Qqq1yet1TFRMJQl49Kzk7GKM0BLgbBgc0+HV3IWbIOaGDLgWkuNDgtMIBI3FmKnrshMY5Rw\n4TghfHbXeqHgKATRxSUwlrQc0909DeMBanHFNZ0MQmzPFCFAW4oH1W7TzKduC0Sn54yuFmSzgy2X\nkKmGfoLVFjNWde0V0gSRRdhAotpdlLEkFQth4KrKZplriCnAWku02iS+tEx/xySiUob1tisCV/Zm\n8NS9XxOFlE9dwEYBulJCNduUFpY3tKkY/n6ULq+RpBmdg3vcfrRG+uq34UrTkXytkR2noJRPn6d1\n20NFWDVX1+JLKzdtaHqEvwG4RZofjgjLEEbx4CtxLYSomICHFBAdRYSr65ggoLzg/CpXC6+9l3/o\neojZVqG9+NIynQNzhS9GV8tF9lJvzpmBwfX8kb0EE6ii9HrQ6VE+d4nqyUG2Rn+8zuUvuolFtbuu\nu+7MpGuYiED025jpCVS3T9hZcxOetQXB2nydTTzzGgDrH72d+vEzGKXo75ikv2saaSzhwrKbyH3I\ny6iArFFzKpAFmehBaEdKolaXXqAw5ZJLGU+dMiCsUw5MHCGscWRFSUq9FkhDN64XasTj2Uf4WvBX\nCKtp2TI12aMh2vxZej9BmhXp3WGni+qn9Bs1pz5pQ2m1WRiN46U1TKXkejX1UiSC8tIqEy++41/Q\nSQAAIABJREFURTZWZf3IfoLlpq+tY2kdmiPzdW1ElmHDENPrEyQJKs3QUZn49HlEqmnP78cohUxT\nlDbY9TZRs002UUd1ugitiZodVw9lqkFSLSETn8XTafsaKxBfcgXfqqcuUD59npUH7iQbH0OurBfE\nwYQBstOlfGmZrFYmOHvpPbMIy6fPk47d7iow4z6DdGIM0XXXmOtHNVgUxatNwtUmuhSR1cqujlCa\nkdYrmFBte5wRRvixMFJYbk2M4sHXj60UkLDZQqbZhpTrq4XXbqR/aKvQntSayqlBN+g8Eyno9orM\nJXfMhGhpjc6+nU4x8uPWcUx4canwiaSNOjoKiNZcQ0aR12WRAl0qUT1zHnNxif6OSXSlTHzuEvWh\nho1bXWer98wXpE2RDtSgqXHC5qpTSxo1F16wBtXuMfHsG/QO7kaXIoJ04MsIewn9MCDo9FGJC6Gk\npQCJwEpJFgimO4v85kvf52dPPM2h5fNYBM/PzfPDAx/jsf338PKOQ/zf2VEeDo6xy1xmwUzx/exe\nzmVThCYDLZD9lCjJCDt9TByRea+SlRJTiQjXmzTOLmK1prNriqxRJej0qL99gXi9jb2wBFIWPg6A\n2jvn6eyZRfUTKqfOk45X6U9PEq42iRdXUStN9ESdrFah+uZp9Hgd7a+5qVeOUz9zkdV7jmAiV8W2\n8IJ0e0RJSvnCZXSt6tLntaHxzKvOnD0EG8eFcoT/fI1SLiMLrqybsw3y70bzzkN0DuxGdbpU3n4X\n3aiiK2Uqp85tuC4A4sVV0kYNU4pRPUe2dBxhSqOw0AgfDEYhoRE+VNiuuq4wesOkv1147Ub6h7YL\n7Q1nBA1nIm32sAijCfMQjVdAwotL9LwKFDQ7dHfPYOKYrJwRdp2cLzKNqZYLYmRqYbFiv5ZJZktl\naGGZZGYCHUeofkK01sK2e0RLy0TrXUrNDvLsJdbvOoQJXSjIVEqIIKC01saGAaZaQghLtdXFxLCn\nvcQ3j/0JX3nzCWLtqrdm3qPx4NljPHj2GP/pY99itVTl8f0f5YcHPsa399zPucZODCWU6GMCgQkk\nJogJsxQRC8qtDt2xCjoIsVFIeXmdxpkFIgtCW0pnFwd9kzINpRJkGdWFFdbm9yGkRCYp0kK03iJo\nddFjNaJml8YrzxGvtQYn5uwCAHa4BYIdtDcon77gVL9ej/LZheIayFPZs8xQvopCInsJWSnGDJm8\ndRQ4tScOrqvsQbzaJH7yJfrHThY+q9JVrovy6fO0vrgpLCSdWX0UFhrhA8GIsIzwYcb1htdupH/o\nWo69QRWqhd5gK1wDxE6/SBPOMax+AATtHghBVq+ifLq1jl2bgPqxk+9rFbylMmQ05RNnyabHyapl\ngm6PcK2FQFI5v4gIA0r9FHHiLN0Du0knxghTTXV5jQ4N0jqoTkJaU9zVPsk3n/0+XzzxAhKLEYI/\nvevj/J+f/jle3HeIsK341JkXOXriNR45/hL7ly/zC28+xS+8+RQAJ6Z28sMDd/HDA/fz9NzdpCIF\nqeiPldF9Q5haApsycXaBKEkIehoZSvS462kFIHruvQlPXESaufG/c4H27CRZo07Q7DD12inilXVs\nXsjN2kHxO8D6mLsQdpDNYwaZQvFam7FXT9Ddv5OsXiVodai+/a77XN5duLJ+zCbEi6vINCOrVwoz\nucwMstt632UPrlW9jVebBKvr2Dgujl2+5DLrbtaMxRFuYdxCpltxM1fIHxOT9iHxMz/tYYzwE0KR\nJVRzqbk3U5Vhlx49KNKXlUt05nZg45BgreXDNJbGj64ML1wrho3HBWkrlxh75QRCSj/5Vgg6fSpn\nFyjlJKDkuvPavEtvo0J/qkQSRaztnuAL7zzPb736pzxwzmVT9ZXiO5+5j29/9UHeqtxOPYU0jUiM\nwCQxttIjCzP2XFzmoZeO89l3XuCTr5+gPpRamyjFC3O38cODd/PY3vt4Zech4n4HpTuUWm4iDzuG\noOPIRNB1xEP13JilfxRJ5rJ4GJCY/LnN9CD92BMXm1etzYmMMRv7KMEGpcU93VqFuQJD98KtPovW\nbfuovHOOsDOoKm1xZfCnH39x+/2+D6zeM4+Jgw3k1fmvsm2r3o7wNwNP279k3S7/xFywpbm9dt8/\n/J3r+pu3/6vfec5a+8AHNKRtMSIsI4xwDdhqAkkadbJ6hXC1eWMIlhBF4TddqxC0u5TPLBCvtRC+\n2JuIIlftFhBl16Hb1t2qOxt3z/tTMemk5edPPMd/8PpfcXjJhU/WS2X+8IsP8a++/ADV21M+0rgA\nwIGS60O6nFUJL0gmThoqHc1KqcyzM9MszsSsNWPufvMC9/zFCp9581U+dvo0aujesVyu8eSh23j8\n8DxPzc2zUB8naEPYdtuEnrjkj6rrH3sZsutJTLKRsOQ1bwBsloeS/OMwgRkiL8BVCcwG8rLpd5vR\nb9Q2EOisUkLq7CdCIrYkr5vCmiP8zcRPhbD8g+skLP/1iLBcgRFhGeFmwQcygWwuj++Lnwk5qEci\n8kdPUohjl3YLmDFHVNIJ97w3HVJNu/ythR/xG6/+NbNNl5lybrLBH/7Kg/w/X7qXub3utTvrFzlS\nckrQuGoDYFckh0+ssxKUWFNl4lRDX/D03jmOxa4c//G35jFZQNTuct/L73D02DEefu1N9qxsbL6+\nPFPjzcO7+d7e+/je3nvJUpceHBQEZkBklFdfchVmED7KigaB+WOeeWRT/1zrgsQU6ovZqMLY4c7W\nOYow0rWrLz9pEnEzK44jfHD4aRCW/f/R9RGWt/7xiLBcgRFhGeFmwg2bQLYjKnnRNOkaKQKIUuwf\nB2Ef03BEJZl0r3VmAna0V/nqu4/x6y8/SS1xoZtje3fyF796B/2PlTgSLrFSKtPbB6v1MrfHC+xU\nawCEwk3sY8cyVGrphhE96whS1lOkoeLxg/sBOL28k3dO3k6moIvEZAHtTpl5+xqff/5VfvGZ19n5\n1gpxf6j7tlI8t/8gj91+hKfm7uDY7G6Cju+u3bEbyAsM1Jego4sQkvCqhsjJzDCBSfMQUq6+bCIs\nWg/CPVupMFuRF/cCm+GugV3OTzQiESN8ABgRlu0xMt2OMMI14oakvA+VkRd5t+KCsFw97LOrusK9\nB84yPt7lclLnh9FtxJcT/v2X/opffO05Qj8ZP/mRg3z379zD+Y+M8421F+mEIWPlNtNpkx1nmpy9\nrcpYtUtDpsMjo95NySqCUBhK1v2uX1KUOprbYkeOpnc0uTc9Tel4RNwxNMsRx/Y3aM1KgqmARz9/\nF0tZhV0nVtnz4jKHX1lg55k1PnXyOJ86eRz4Hku1Ko8fPlIQmJV6A4Cg7c5H6MlM2FEEHXeLUr3Q\nP/rwUTdXXjJE35O7dGPYyBYpydlGtQXXoNP9YDYaeGGIqCj/dEBk3DWwiaAMN3scYYRbEbfI5Tsi\nLCOM8EFiCzWlICrXEvapu8cdu7p8addxVqIaZyoN5lfP8T8//gP2v30ZAC0Ef/rwXfzBr3yK9JMh\nHxm7wFdPvMpEtUUtUkyqNkRQSfvcfilBzyhKfmzF9FyFILUEkSbyqkslFZiaYC5YAWBXa5W55S6t\n2YhmEBOmhnuaktemZzho11mvxQTGYO4LeP2je3g2Ocjc8hrPX9jJJ59/hwefO8XupTW+/NILfPml\nFwB4a3YnPzxyhCf3zfPM/sO0x1ytk7Blh8hLrsi4cxV03a1L9nRh4JW5t2SziTfThfoiChXG7c9q\ns4G8wCADKQ8jCTnsgRnuWcSA3GzV/XpEYka4FXALZQmNCMsII9wCuH/iNK1+zNyZS/zya28wd9F5\nRpJA8W+OPsj/8aXPsHa3Cx/djiMx9W6fdGzjBGtC5x/RXIn+nKT6psZY0BHIBGQflvYPbhNTFxLS\nWJIGCqwgjRSZUcyfXqTW1uxdXmMprHCxVqMVRFR1yoXJBn9+2138+WfuotmOOHR+kYeePc0jr7zF\nJ994hyMLFzmycJG/x1/TVwHPzx3kiQPz/Gj2CO+Ud2GF3GK0I4wwwocNI8IywggfBK7FUJv7VCKn\nKOR+FVuroMecspJMlYl0yoMX3uDO508xse6Kp7UrMU999jAnPr2TP3jQhZIfGH8XgDtqFzgUXWas\n0WZKt9GRpOLDP+XEYqsQCEnox6S9HmzGQ8y8JDqvidoGXRG0DwoqDYu0LpV3vJeSVgSB0CTWjV9b\n2H2+S6IUY+t9dol1jqwpTkxNsBzXeGrvHuajSwAsVyuwQ/Knd9zFn3IX3bWQu166yNFXj/PIi29z\n97vn+dSZt/nUGZeCvVit88SBIzy9a54n9x5hvVYHXLgIIOiYQm3Jw0bS13rJlReSdKC2bMo6EluY\ndsUVpl2xpdoCmxSXzZ6XzdfASHEZ4WbFLXJpjgjLCCPcSIhNvpStfCqh96f4Mu+FT6XmHrPxCv2p\nmLGkza9e+gFfO/YYEz2XybM0WeOJLx3m+U8fYFejSVeFfGLGFde7o+zTlKNFdqp14j2axvEULQRh\nDCKBMIHkYEgoApQfq1pJUec1om2wVUk6F5I03O+q7yaUnusjWgZdE6QliDJFGlkir9PULmfEiSZS\nGl0GmUIlSbl9cYkfPFBjekeTj/rJf7FUA2C5XAXgcqXGmfFJ/vCzD/K/dh9hYq3Nx585y2deeZuj\nLx1n1+o6X37tOb782nMAvDmzi8cPzfPUrnle2H2Qfj3c4HmBQbhIdRwRUf1oYNrdVLiONBukSm9j\n2mXItFsUsssJTN7ex5rtw0U5hgnMiLyMcDPhFrkcR4RlhBF+XAxPRJuJylY+ldhn/mzyqWQ+PblR\nbvFrp/6MXzn2I8qZ669zbN9OTj8yy+sP76I8nnIgW2G/XOHZ/bv4ePUUAPtC12RyRrVpSA2TYOYD\novOGqAO2KhGHQmJAvZ4g2hYrLKJjsGPK/T6xlN7KkEdC5IWE8IUUhMVGIDsQrlj0OATTiiCyiAQq\nLY0JQAQWIQUmElgtCLTl9t4SpajPqnGZTdOBM6wuR46wzMZVlnLy0qvBFLy4ey8vfmUv/13n59n1\n9jpHXz7Owy+c5KE3TzJ/+QLzly/wd3mUXhDw7L7DPLlnnif3H+HUzE4QoshAGhCYgQoju16FKbKN\nsgGZuQbTbvFZX5F1JK4w7V5BYIZ+N1JfRrhZIBh5WEYY4W8+rsVQu0XYx/ry6kXYZ8Jl4OxXC3zj\n2KN84czLBH5ie/RjR/jf/9ZnOPnZKfb01vil9Bi3m8u0xiI6eyz7xxYLQ+yk8mGb9YzaeYtsW2Qt\nQM9FIATqnEa+3Ec0DXYygDGFPJsgehZTVY5sxQCG8HiKOpmBtBAr1wiwbbGAvGyQQhLGoCcltiZQ\nHeuTaiwCS+7km+z36CsYk25sbeXOw5Rxoa3VoMJq5M7HztgTl7IL+yxXKyzVq/zg43fwb//2fYRp\nxh3PL3D0pRN8+qWT3H36PEdPvsnRky5z61KtzhOH5nlyzzxP7TvCes2pOUFHDky7nrgUlXe7GdKH\nksRWhev884K8bFN5V2h9hWn3yqyjkWl3hJsUH8ClJoT4OeB/wt0Zfs9a+99vs91XgW8Dn7DWPnu1\nfY4IywgjXC82hX2Kl5UqUpOvFvbJxvM6KhFYy0ezk3zz5R/w0AXn20il5DtH7+H3fulheg84NeYT\nDedPaVYUa5EEMmZUkxlgUjoVpioF4bsp9VcyhBHYskBoTbCoEYAdCxBt4/6tJTChILXYkkCsaqj4\n+EYkERdSRGaxJa8YWRCpdRm8gcBOB4i+gTEJgUD1LCKx2DIYAVJDWoGwaphUKT3rJv+KT5euewIz\nLjusK0fYVlWuwjgysxxVWfIkJg8hXfzCON/+wv38Xu8oE6ttPvr0OT71zDscfe04s6tNfvnlZ/nl\nl9097/Wdczx++AhP7pnnlamDJEFI2N6YdRR2FKq7KWW6n3thrsEDM5R1dFUPDLhmhiMPzAg3Gz6A\nLCEhhAL+OfAl4CzwjBDiu9ba1zdtVwf+E+Dpa9nviLCMMMK14BrDPsOpyQCi7Pv7+Kq02USZ7nSE\nMprPrL3Eb774KPNL5wFoxRH/5jMP8a2v30dtPiXEcs/YKQCOlJw/ZV+4zIyvTFuXPvXYj628BqVX\nNUIIqEiEBrliscZAKKFmESsGQiAS0DaQWkTbAsL93bjCSHcDsyWB0EAgIDEgvfk0lqhYYbuG0isZ\neiLAdBJEG0QbKIENQYwpxJyiIgShX8KVhJvgU09gqiKjIl2hu3HlOlU3vfoyE5RZDd15W46cWlIQ\nmEoVJuH13XM8/vO38T/YL7LjjSYPv3iCTz73Dg++cYq7Lp7jrovn+A/5Ad0w5JkDh3li3zxPHJzn\n9I7ZInxUFK5ru89RFSbevP9RiCh6H23hgQEXRrqaB8Y/XpEyPfLAjHAz4MZfTg8Cx621JwGEEH8E\nfAV4fdN2/y3wT4H//Fp2OiIsI4xwNVwLURkK+xSZPlWnqOi8Kq0P+zBu+Mqlx/g7z/81u5sulHOp\nUecPfvbTfP9rd9Cqlbhj4hJ3VF3Z/Nti1wdoOOwzvp4RnzPEHTBVgZiLsOMB0fnERSUqCoFw3+7U\nIFY0BBbRNiD9e5JA4kvWpxaqEjID5zRyXMGOEFoaLqSAcalAPtJjZ93+RdsiDMhYQS1wVWcTi9Bg\nxyRSSSoXIBMQjrtzlfpJOPV3yFhoStZN6L2CxDjFqC57BYmZ9KrLdOgIy0rmHnfE1YGB9+M1Hvv4\nEb77G/cSJRmHn7vEp184yUMvvMNdpy/yyNtv8MjbbwBwcazB47cd4Ym98zwze4SVSo1wi8J14AhM\n0BmQF9ii8m6aDZGYjZV3hfasROsBeRl5YEa4mXDjL5854N2h52eBh4Y3EEJ8HNhrrf1jIcSIsIww\nwvvGVv6UQknZJuxTKhWNCHVj0IgQoFzt8LVjj/HVHz5Bo9cF4MTuaX7/Fx/m+V/dRxoF3NlwJGW+\ncpEDkaulslO53j952Gds3VB7y2BjgaxJZALBWxl6XiHbFlGWkIEIcYSkpV1luFA4YqINWOmiyolx\nNyqNIy59p55QlnCkDG90YRew7PchwOwNYNK/366FwKIuZm6+jCRojUzBVgKYUqjEEryVkRwJseOD\nzKTQT86pNUT+VMeeuFSKx4y+cOpLXbpzNi4dgZlSjsA0wxLLoVNfZofVF2DxizX++Isf4//qfQp5\nTvPQi+/w4DOnOfrycXaurfHV55/hq88/gxGC13fP8cT+Izx+eJ6Xpw+SqWBD5d1h8gIQbA4j9Qbm\nXdKNpGbYxFt4YPLQ0nDl3RvlgRmRlxGuE+8jJDQthBj2m/yutfZ3r/l4QkjgfwR+63oOOiIsI4yQ\n4z3UlK0q0sJQ2KdWKTJ9ejPeXBot8c2XHuWX3nyWWLtJ6oU79vD7v/ow5/69CawUfHzsLAC3lZya\nciBc3DbsU7sAKlYQS6eixAAWdS6DqsRqhVzWzvrvVQFi6cJA+LYAxkIC9HFKi8QRl7XMbbuawarf\nR9+4kFBdQd8g1yz0e47crPn9hwZhLVjh9guo84kzFZcVYAjPG/SEQPly99JPqkqIog5MHjZK/d0z\ntIaSn5ArZP58eOJmvInXRoUKMx24z2HNqzCLPoy0UqqwWK5x8rZZnvnFQ/wL8zmm3mjyyeff4YFn\nT/PAsTPcfe4sd587y99/4t/RjiJ+dOgwT+yf57HD85yZ3UHY8eSlnZt3N6swYeGFKSrvRjmBGQon\n5c0bg6t4YK5SefeqHhj3wtYGXrejrV8fYYTrvzQW36OX0Dlg79DzPf61HHXgbuBR4a7XncB3hRBf\nvprxdkRYRhjhGsM+VxR42yLs051xk9bt2Rl+67kf8IWTryKtxQjB9z9+F9/6xsfpP+z282DtNAAH\nY1dULQ/7zKgudZF7Ptx4YuFX9u0MqgoQiOUMuZA5UqEEfKzsfCaTyvlTWn7iqzqCQ6aha5yiInEq\nS4ojJokPF+WPJe0UmZ5xLtrAutfXNSz5vykBPRx5AYh82CgAEpCXUuz+kjPxdgyWweSan16DKMiL\n8RO0HCIwulBiNnpgSnnrAJsOGXjd57K+KYy0GlbY4dOoizowD1R45oGD/Mk3P0pnNeDe185y31Nn\nePilkxw5c4nPv3GMz79xDIDz4+M8fsipLz/adYS1cpWgnReuy4mLHSpmt3UhO9GPruw+PWTiLYjK\nVQrZXa1tAFyHiXdEXkbI4UO9NxjPALcLIQ7iiMrXgd8oDmntGjCdPxdCPAr8Z6MsoRFGuFa8R9in\n6JicE5UJR1T6k26i7M5IHmy+zt99+gfcf/YdwJXO/84j9/LH3/wo7+6d5M7GAvdW3e+2C/tUpSD2\nbszQKxKhfy6qgQv1tDPkmQQC6cI9BnijB/tCWDZOLSkUGGA5cwQkxN2cUgY3KeF/Nv6fBFoGMk9S\nhPXb+yZ/ym/Tw/2c1/nPcPtXboei6dKgSSxUJJKtVv5yA3mBgfqCAOM7HSn/GG5SY0oi22DghUEG\nUtsOwkd5BtKO0J3rlZzAxDWWy1Wauyp85zP38x3uh7OGTzx/mvueOcOnXjzJ7tVVfv35H/Hrz/8I\nIwSv7N3D44fmeey2I7w6c4BUBYRtcWXzxu4mAtPV23tgknSjgXf4cdjEu8kDs2Uhu+08MMMEZuSB\nGWEINzpLyFqbCSF+G/gz3F3iX1prXxNC/BPgWWvtd9/PfkeEZYQRfkyEOuNL51/ga4/9NQfXnFqy\nVi7zrx/+FP/6qw9weaLO3pmVG3IsOxci3+wjzqeOGEhAC5denBh4O4E7yo6EkMG6gbKfqCzQYUBi\nctJirjwObevuDkK4fWnnVyFv8KyH/uUQ+PFYiHCTYN8gEos5GN2Q9/+TwOJUnT/50t186zP3I4xl\n/7EVHn72JI+8/hYPvH2Ke868yz1n3uUfPvoXtKOYp/ffxlNzR/jRzDxnxqbf+wAjjHCz4QPgq9ba\n7wHf2/TaP95m289dyz5HhGWEETyEFINYRa6s+Gq0olzC1AapyQBiwvIrJ57kb7/0Q2Y6buV+bmKc\n3//iUf6/X/0InXLM4cklZmhz15hLSz5Svsje0DUuzH0q49LXKPGr3pJQhaIifRilUCfGA8RuA8e6\nfpwS6tKFfNa1C+Gc7DkPSh768b4SV/UN9/qwwrIZOYFJcaoMQ8+vBo1TWSaUG0dJIiMJhyLUuO87\ndLqDfDNxIauqhPkI9vkMqvy9FoqLGXhe/O9yxWXYtGuuYtoF6It+YdptG8fWctPudNAsqu6ueNNu\nXnl3qe8f61X+6O77+SPuxywLPnHsFA8/d5JHXnub2y9c4gtvv8YX3n4NgHONCZ7cO88T++d5fuo2\n1kuVQdioqwq1ZVB5d1D7JS9cd7XKuwPPy/aVd7cz7V5z1tFIbfnQYVTpdoQRbnZsYU70BrDBo3Q3\neVstk8y6Caw7E/K5d1/hv/izbxc9ft7YuYv/7ZeO8uQvHUQHijsmnYH2jqp7vK3kMoDmghVmlJs8\nt/OpKCGuICoqL1K3msH51PlSrHWze9en+nT85LOuB3FpiyMdNem2cyVXBmGgGw2NIyuhhLkI9kQw\nHrhxv9xGvZNASbjxpBb1XNeJNPtKW4SMhiZYkYeGrs+0C1CypiAzVeHIQF55d1y1N1TdBYrKuwWB\nKdVY9JlHS7Uqp/dN89Ije/kXfJbKuz2OvnSCTz7/Dp959Thzayv82tpT/NqrT6GF4JXdex2BOTDP\nsal9JFX3GYfetDsgMBqZ133p5j6XLSrvJnnK9PaVd7cz7V5z1tHItPvhwy3y0Y4IywgjiC1Wnt7L\ngq+xYgOJjt12acPyj77jyMqL+/byz77+OR699wj7Zle4v+GM8PMVR1AO+ToquU9lXCbUvYSwnU9l\neOJWm8d2NnFqyq4AziTuG2wMLDIIzwz/icZt0zUDhUSwdRjox4Fk4IFpWqhraGYuNXp3CO/03b9c\ntekYmAxAgnqmCwsGKhL2ROjGJlXpijfFBgJzNdMuOAJTKuq/uMfhyrvDVXeBovJuM3BK2nJQYyZX\nYUqOzCyWnXl3sVLlufkD/OWX76TZivjIyQs8+OxpPvPq29z/1hnuPef+/YOn/pxWHPP03tt54uA8\nT83Oc7YxvaHmS+AJZ9G8cUh9AZ99tE3hug2Vd7Un2R9k9+kRefmbgw/GdPuBYERYRhghh5DgFZUi\nLuHNtzZUBWF54NLbTPbavDMzzS//o/+Y6UMrTNDh3omzfLTqUpSvFvYpic0E5coJ+gqiAk6lOO3q\nkhBLmA1gUUMXRxQawAru5qM2/W2G+7ZnvHdo5/1geG6zQBPoJFAXfsw+ldolODkitZQ5rwvShYcS\nC290UXeUnSoDaJuTkI2rfunfoMFua9odJjBmE4m5HtPuuGoz48nLqvaVd8MrK+8uVav0ZmO+c++9\nfId7yZYln3j1FJ949jSPvPw2hy8s8jPHX+Vnjr8KwLsTkzxxYJ7HD87z7MztdGqOKA36HnnTbntQ\nebcw7V6t8u6P2316ZNr9UCEXXG8FjAjLCCMMI78RSzdZ2MBPjJFC+wpnP/v6iwD8v5+8B1uyVCNn\nEqkFfSa9NyInKjMyT8MdhH3y4mlbERW4Cll5o1tk4KC9AXZMuRBLy7isHTmoSFtkBIE30PrXcsLy\nQc4xFkeOen6suSEXfKVdP34NxNZV1B336ddnk4KwbD4XetOqfysVZksCM+SLgat7YEqbPDBVkRTq\ny3aVd9d0mcXYN20s+fBRpcL5PRP8wef28Ac8THw64YGnz3D0leN8+pWT7F1Z5msrT/K1F54kk5JX\ndu3j8UNHeGrXPK/u3If0hCWsDho3FiEkX2OnUF/ybKPeoO/RVSvvfpAemOH9jXBr4Bb5uEaEZYQP\nPYqaK1IUCkue1mx9aMiGEh0JlNF84W23Qv7ewx9BljLqkVM9KjKh5D0SYZ6OW1R29dK/UNdGUDYj\nDwVNC7iYOuIRCFj07tmKcoXcfA0Ut2Pc8zZQ9q/n6kte4faDRpcBScpDUcOkygAVAStpGYNWAAAg\nAElEQVQZLKQwLqG+/W3pagRmOw+M3JAe/d4emMhP1EnhgUmG2gbkzRs3Vt5tqjIzQRMYqC/Lmxo3\nLlaqPHXwEE99/RDrrYg7Tlzk/qfOcPTlE9z39rvcd+4U9507xW/zfdZLJZ7afzuPH57nqd3znGtM\nEbZt0T4g2JQyXXSf7oVF4borKu9erfv0UOXdH9sD4zbmCoxIzAg/JkaEZYQPH7YxFQohCrPtwMPi\nHnUo0TE8+P+39+bBcaTpeefvzazKKlQB4H3fJ7rZJMHuZvNosqeP6UszihlZx0gjy0dI8uyu17F2\nWLG25ImQvfbanpV2vXZYCntmrVl7w1rJ8nhG6nOO1sxI07yabN5kk80DvG/wxlnH5z++/LIShaoC\nQIAACnh/EYhCFQqZWUUw6833e57nvXiKaV2dnJ49h7blM0lQoDFhC5ZGv5u0Zz8kAum7lOGVazAY\nZKHi6AxdNeLB1CJc6rEi2hy2GGnwbUejp2g/GFyeiogNdAtXZSjS/2oqGwp3480Lp0kZiMGId93b\n7Y4pvmbuYy3UgbHR/g+LYPK2ozR14NNT/D0cTPeldEyPpoHprpG822Gsddt12ZyI1yXv3g6ytIfd\nl1sNjRRmJXl/w3reZz09tz2e2nuVbYfOsO3AGZZdb+f1k0d4/eQRAM7PmMGOZS3sWtjCnsWr6Gyy\nbqdScF2l6dNh98VpYWIi3ii4rlLybrkGplIBoxqYCYW6hBRlvFNLbOvcQclwSSjlUUgJr50/BMA7\nT7eSSoVX20mrech6PQRh2yLp6p4RWx02cLHXOnAe5G2h4j78u4GrvbaTUcBOYm7yYEkaTnVCTmwI\nXDXypSWTiGr3XYfGj90fSBOTCAPnCvQtcDx330CvgCmA8awYN7YsNFiqFYAFU6zpQBqSBqZG8m6T\nscVLR6iBcU6kjnD5aHoiy8xw+vTsMhHvzUwj52fN5PznZvJvu15m3rV7tO65xPMHz7D1UBtL2ttZ\n0r6TX963k7zncXDREj5c0cLuhS0cnbuIXKR3iU2f7jf/qLSM1E8DEytgTLiEVDN5Ny7ghYoFjGpg\n6og6efu1YFEU90HneaVPr4RbCgo7LIGH5+d55exhAN7e3EomnBXT6LsloZ7oA8ydqj1xtmTXaXmE\nAuZu3rp8eoq20+K6JYIVrca7JwlCfYuB891w1wxsY87TPwCufLko/rsZbFy/b+xyU61tp7Fi2vgS\nUHw/hnDNxtixzjN9mJKwOS0jRKUuTLXUXRicBqZS8m5O+mpgIhGvsYVLk9cd5b/cD+ce3Q27L7OD\nLLdS4VJSOgvT4MDyJRz48hL+RUeaJz69xrrdl9jycRsbTl9i4/k2Np5vA77L3UwDu5av4sOVLexe\n0MLNpukANZN3/dgSEvRN3pXe8GOhVvJuXMALFUW8EhW1FTQwtbovse0po0SdvN3DKlhEZDrwX4Cl\nwDngS8aYfpGeIlIAjoR3LxhjvjCc/SrKY0GkJLYNNSzFpL0tBMKWKydo7unm+MK5nF4yg+WBTbV1\nS0JpyZGMlhoIb/t/MA5pKQhst6E5YbNXjoWBcR5WgOsEra6AceFtbiZQPI+lGuXFSbUCJEqyxbaQ\npiTAC/NfyoPonMAXSoWUFx5buSC4aKylOQfMTkZR/o+DEdPAVAiyy4XbqhVkV2v69MxQA3MvzIFx\nBUx7Q5biTI8fPvsk/7V7I9mHPbR8dI2tB86yef85lly/zU8dPcxPHbXF9NmZs/hw1Wp2LXqCj5as\noLPZFkdRAdPh9RsbEA+yc0LeWkF2kQamVpBdsboGpqKAN/xZn+24bSmPDzN5loR+E/hzY8zXROQ3\nw/v/sMLzuowxG4a5L0UZUfqIbQE8r5/YthiEHZaU8PpBuxz03ta1eKkCTcmSdgXKCpayK8ZKGpZB\nE9evpL1QSxCeYVyx4ZZm3P/o+Fygas0KL/bceJFSq7nhYeP9/aLt4sxPwAOBB4VSp8Zg4//nJm3I\nXQq7g57YWTGH7Q4VsWLgBmCaZ4uwniIsaxjgTRkZRkIDA7YL4/7NH3X69NTQWfagaF97NLwxFmTX\nnm6EqXB59nS+9dPT+Xr3i8y7fJc1u6+ydf9ZNh48z/JbN1l+6yZ/fdcOcp7H/iVL+XB1C7sWtXBs\n3kJyXR6JDrds1FcDk+hMlJaOut2ty4MJl416c30EvFA5yK6WBqaSgNferdCF0SC7x0+dvJXDLVi+\nCLwUfv+fgB9TuWBRlLomWcjz2ZOhO2jTupHd+N287aJ0lsLT+ug3MmFGSSrUpuQKoevGlAoE6C9o\nhdrFhytUHHGdSiXiepUC0GngXOhY8oAZiZJ4J2/sB01a7GO9xmpt4niUOjaBQKNvn7usYcj6lcnM\n1QVT+eRz8/hvn3uGzgcJ1hy5zvajp3nx8Claz11kc9tZNredBd7nTkOGPYtXs3veanYtWs1tb9pY\nH74yDpgsHZY5xpir4ffXgDlVnpcWkX3Ya7CvGWP+dJj7VZShU8MdBKGVObIx2/8axcBe8W26cYLm\n7m6Oz5vPpaVTSZKnMVmyMwOkvRx++Glf0R10N49cztsPeleYgM1XSfUNTyMWnsbCwD4GMCsBXQV7\n9Vkudi0vQKq+D5SKEieireQeqvT8cvLhV5PAdB9mhK/JmJIOJWesE6mn13ZTJPa7YN+LBQFsahrE\nwT8+HlW0C27ZqLpoF2zHpVBDtJsxzjJdPXn3brLv2IBb6TBxN0zevZ3NcHHKNP5o+3N8vfMFmjq6\neHbfRT5z5BQvHD7NovY7vHnyIG+etFlCZ6bPtsm781r4eMEKOhuDSKzbP3k3XDbqKVmnayXvlpaL\nKiTvDle0C7psNJLUyds3YMEiIh8Acyv86KvxO8YYI1K1TltijLksIsuBH4rIEWPMmSr7+wrwFYA0\nmYEOT1GGTvkHk0u3jSfdJpyGJQyLC0/w7zzTSioIMzlC7UrWi2tY7K877Uq0NHQ3j3+yx1p344WJ\nhy1WwhRdUuHz4y6ZqQlbwFzqtY6fxWlbtJzrhbSxj3W5FnuF1xtfFmqgf9rtQCerwZzMcgbO91p7\ndcYv6VDmpmFfh/15Suyt07B42PdjVQrMYCqtsWFERLsAUlu064qXWsm7btkoPrwRStkvd9KZqHhp\nz2ZhFhyes5DDn1/IP+98k8VXb/Pc3gts33+GrSfPsOL2DVbcvsFf4yf0+j77Fy5j94IWdi1u4cys\neRjx+ifvdiXxO+2x1UzefZyi3djjdocq2h0OE6bDYox5tdrPROS6iMwzxlwVkXnAjSrbuBzenhWR\nHwNPAxULFmPMN4BvADTL9Dp5G5W6pLxw8b3+7qCUR1DI8dI5O433rc3ryaRC3UHCfpBkwoIloNjP\nHRRt+nLefjinPOv4uRuKVTsLsCJVKljALo+Uu2SmJvoukxzttJ2anIF7eWriUbIiO0eRT1/9i0d/\n8e1Q6MUuA13vhfmpkg7FHfPOh7YoSRm778C3+0yKLQ6T47dgifOool0YePp0NdFuPHk3K/Zvr1ry\n7oNCQzR9ulLyLjPhx6ta+M7PbCCRL7D68A22HznN9gNnWH/uElvOn2bL+dP8vZ3vcjuTZdfS1exa\n2MKuJau50zTFHmuH1z+4zuldukrJu9Ldt/sST96Nui2PKNq1N4NM3tXipTYDifLHEcNdEnoL+BvA\n18LbPyt/gohMAzqNMT0iMhPYBvzOMPerKMPHfZK4k5t4faL4wbqDNl08SSbXy6GlC7m4cBorAzvQ\n0NmZXYclKUUCZ2Mu//DqsMJZr6sYJtUKNIi1BV/JwQKxnQkYnEums2jtxW152053XRRnYXbf+9jI\n+65w5pArTuJWZ/f9cHCW5fYCLCnToSxOw/W8nR3UU7QFW4PYic4wqiLbkWbwol37SMQQRLvx5N10\nmPVSnrwbLR956aiIqZW866ZP35jazLc/8wzf7Hqe5gddrP/oMs9/3MYLx06xsP0unz9+gM8fPwDA\nqVlz2LH8CXYtWM3hacvpTgax4Lr+ybtRcF3UfYkF1w1TtAthAVNLtGsfUNHuYKiTt2K4BcvXgD8R\nkV8DzgNfAhCRjcD/aIz5deBJ4Osi4jwLXzPGHB/mfhXlkYncQe5+qFsRP1awhB+m+ZTw8mVrF31/\ny1N4qQLZhP3QaIq5g8AWLFGHJZoTFD7iloHuFsKugtiOxBTfdklu5WFR+JxBfYAbuFO0BYknpfC3\nBHbbhfAMlMCGzYW/UjGTxdmO412XoRB/O42BK71wutsWXU+krSW7IyxWUp7tPz8oQtLAkgBWTwyR\n7aPMPYqQYr+xAZU0MM5xVC15N+PlaC66JaTqybuuCxNP3mU6nJw7j12vreD/Mp9l5ukOth06zfMf\nn2XLiTZW3bzOqpvX+Zv8Bb2+z8eLl7NzcQs7l7ZwdtZcjHh9kndLwXUueTd0G3Ul+6TuwhA1MLEC\nppYGBjR5dzAIE2hJqBbGmHbgsxUe3wf8evj9TmCEbRWKMkQqXGVFMfzRZGY/sjO7ycyB18tnLtrl\noB+88CRBKi62dZ2VMN0Wg1/FvmwWJPFO9tjOSENYYOSMtf4aAzfytguT8Wq7ZJyj6ErOLif5YfGT\nDEWuBlusJMRuq7tg91Og1FmBUvHiOi5JgSagfRhnriJ2ySlnSgXavo4wDC4JjWHBVvRhOlakO8ZC\n28dJJRFvdQ3M4JJ3XfFSK3m3FFhXPXnXTZ9uD7svc0PrdHs6y00n4G3MsmvDSt77xXUkcgWWHbjF\n9oNn2HygjXVtV9jadoqtbaf4jb94h1vZRnasWM2uRS3sXNbCvaZmEh2ueHEW6lLybjx1FypoYHpz\npbEBNZJ3JVw2qiri1enTg6NOXm79X9YoymBxHyDxZNv4/YRfiuIPOyxbrx4jk+/l0OJF3FrUSJoc\nzcm+2hXXYfFj57zyHBamJii2gH+/YJdEMr61AWd823lYkoK1A4jM3cTmVKj5aPTggQmXWDyYInDH\nlAS2uYIV5KaxU5NzlNxArtPiA40C08KUtzu9g5shVI4rfhLYrBj7xtjbK3lYF9j32S17xV1Ek4hq\nXZjBinjjAl77WH8Rby4qZqon70ZOpHD5yCXvzkxmo7EBTvvinEjtLzbyzout/H/dW+F6kS2H2ti8\n9xzbjpxm/u37fPHwfr54eD8AJ+bOY+eSFnYsa+HwjGX0JAISnf2D66KxAZ39k3fFTaCulbxb6Fuw\nlIt4Bz19epJ3X6ROXqMWLMrkJRp0WCpgjEu2Dd06b5y06/dvbWqNxLZNCTc7yN4PcB86/cW2fT6I\npiZgU2Op6AjCkLTBajjcxGb3VRAbylYAMNBetO4bH7vtbmyvt5vScpGb5BwX2nUY6Oq1RdBANUQl\ni3O5aK/X2P33Gqud6SzaOUgzE0PT6UwChqqB8foVKv1FvKWuS/Xk3UyogamUvDujbAlpTrJ/8m57\nJsvZZbPZ++Yyfs+8xIxPH7LlYBub9p5j0yfneOLaVZ64dpVf3fNjuhMJ9i2zy0cfLm+hbc48EmG3\nJVlFA+N3J2NLSK7rUiF513VbqiTvDjh9OnrPQ7F9seyPu5IGpk4+3AfNJBLdKkr9EUu2BUrZK7EO\nSyEQ0vkeXjj7CQDvblkbDTmMtCthweLSbQORqsMOow+mqV7JojyYJaA4LvEWrJD2Wq40WNAXaPbt\n913GOnJyxb5CXJ/+ybdCaWhi7yDOWs5NVClB1xUz7Tn78x5swZQOC7PLvTA/aV1BdSy0fVwMVwMD\nfadP10reTYbbrpS86zQw5cm7MxP3AbgdNEY5MO0uB+bpLPueXsYPvvwUyd48i/bf5tk9F9h2+AxP\ntV1l+6lP2X7qU/7Bn7/NjaYmdi5rYceK1eyZ10J7tonkQ7dsVNLAuKImGhtQKXm3XAPjlpHyg5s+\n/UgamEoi3jovYiaFhkVR6ol+YlsXGBfemoQfBcUVAmHr5RM05HPsX7SEG/ObmJu8B8SC4mJiW3DB\nrWVi20qUW5QHSzzxNuPbdKRb7orS2GLgZgGkAHfDk6uHLRg6Q1Gu07E4V4/BPiCm9tRl16Fxzyli\nCyB3dSZAI9aJ1GVKVuoitiCakYCHRavVWZLSNNtB8Dg0MPaZJipeKgXZpcV1YsqD7FL21u/kQaiB\nqRpk93Ij337+Gb7NM3CtyHMHzvPMRxfYdvAMs+884GcO7+NnDu8D4Pj8+exY1sKOlS0cmrmM3kSS\nRIdPsqO8+1IWZNedxAut07WC7KLi5VE0MJNl+nSdHK6eMZSJTcyyXHqoTGybsP8NTNKn4AqWFLx6\nIZwd1NpKkMr1E9tGBUv4v72a4HbEiCfeBmK7KlP9WKicgaBordIZD/JFuwSUFEiEwlvXkYlHt7gw\nt1onLUM4DiB23zmKEuE+PA+SBbtPF7c/zbealm4DiwLbVaql1RloTMEkZ7gaGBh4+rT7e64VZNdh\nXA5M5SC7e0GmTwrvhWUzOfD5JfyB2c7UE52s332J5w+eZePR86y5coU1V67wt3b8iK5kkj0rlrNj\nWQu7Fz7B6ZlzosIl0sDElpGi4sUF2fVYZ1S0bNSd6+dAGooGxhQKfQW8oBqYMUTPBMrkoZrYNjbw\n0HVYUtLD9gvWff/uc+tJBzmaE5XdQX5U/0h/se1IEk+8rbScdKILMgLXiraAEA+aTKloyRt78izQ\ndznHLfFUotxV5DJe4ktCeWyHxivabTX79lOyyQsLJGxnaCDdSlxUXG1MgdKHxzF9eiANTDqmgWkO\nNTAdZUF294vpUgpvKOJ1XZibTzexc81KdrKSh/dTrD16mdbdl9h68CxPtF3npRMneenESeAtrk1p\n5sOVLXy4cjUfzWvhTraRXCTelf45MF19uzBeVxIvEu8OXQODSB8BL1QOsqs5fboOui+6JKQodcxL\nZ4+RLuTZu3wZ16ZOZQp3xvqQLNWWk+LFTGO+tHTUmLDC3As9YeFQYZvxbkk5PtAsdpkn65XSdcuX\nj3KAFz5uijAngHsu/8XYT8mBdCtxUTFUHlOgTCh6gwT7n1nCj55s4V/zWRqu9LL98Bm2HjjLZ46e\nZu69+/z8x3v5+Y/3AnBs7kJ2LVrNziUtHJuyFIM/wB6UQaEFi6KMU8rdQU50m/Ijd9Drx+3soLc3\nraeYLpIJcrHZQX3dQckKu6jcon/MuGLGLR05J9LJLqstSVK5YHG4DgoQzftp9mFFGs50l9xITsDr\nlpFc4FwBO6soCAuldNEm33YaWJSEVenahUdcVOyoNKZAqcrgXUePLtoNxNBbJtpNRdbpUvJuh2+X\nZ2YU+7qOZgf3S2MDGkLtS5i8e6cxw4HVi/nzz7XwsCNFy4XrPL+3je3HTrH55DmeunaJp65d4tf3\n/pDOZMC+hSvYubSFj2avpm3q7KizUpp/VMp88btCsa6zTvfm+2teKiXvOn1LjeTdcsu0oy5Eu0Y7\nLIoy/qjmDgoLl2LCoxAI2Vw329pOUkR4f8saSBVoDHr6uYNS0ZKQ3W4lh1C1CcCPHV9s4izYsLYG\nwHjWOQSlJZ602I5JntK8ISfITYfLSIHYgLvztmCjQKlYSWKXm0y4z9Up241Jis2AWRgMXocSFxU7\n1P78yDzy9OkKYwOgsmi3PHk3h0vgzdecPu3Sd+8lw8yXsuTd2w1ZbmWz9M5O8qdrW/lTWum54/Pc\n8fNs3neO7cdO8+TFa3ym7RM+02adfFebp7JzyWp2Lm1h7+zV3EtnbeZL2bJRPHnXBdcNSrT7OKdP\n99G8MPpowaIoY0jZVUzcIRS5g8LCxSTtf4Ni4FMIhG0Xj5Mq5Plo6XLa52TxKdCY7KGxLIrfD0/W\n8Tj+mu6g0SCuA1mash/413O2OCmE7h1D6TaNtR+7+zlKhUgeuxzUa2B60i7pXMqVNC/pcJ95rLB2\nim8ty9Nl4BC8SpSLigc9pkAZCgNPn+77N1xJtFs+NqBY1oWpNX064/X0Sd0FouRd5zq6HTTS7mYf\nhd2Xm5lGriyYxjdfmM83eZ7kpTzPfXSeF46eZtvhM8y7f5efO/IRP3fkI4oiHJu/kJ1LWtg9t4XD\nc5fQ2+O6L+ExdvhRcJ3fXRZcF0verSnadbfhxU+5eNcYeTTR7igiaIdFUcYHtdxBUf5K2GEJPOsO\nOm+Xg97d0EoqFV4lJnv625lHyx00FCrpQNICPabUQXGJtwmsotI39vs8Jesz4e30MInXBcDNTNhk\n3a5C6XeneKFjaZj5KgOJipURp5Jot/pyZly029cyXe46ik+fdsm7qVjybjx1F+iXvDs98ZCZYffl\nTt7ezo4NbwS42dDInkXL2fNzy/ntjhSrz13nuY/Os/3IaTaeOM+6yxdZd/ki/wMf8DBIsXfxCnYs\na2HPvBbOTZtFstOv0H3pn7wbiXSdeLfS9OnIOl2hcBmOaHe0GIdC4EromUCZHIjXbykocgdFcfxC\nxnTx/MWTFER4d6N1B4FNt81GdubQQhlzB9n7Y6BbKaeSDmRRAGd67P/2AqV8lAT2g6Y1DRfzdjZR\nMhSy5A0EQEPCak8+emg7LykP5oSqnVt5O1gx49kOS3Ni+DbkR82oUUaEoWpgqibvxqZPl7uOAumb\numtv+yfvuiWk8uTde2EXZk4qG3VfbmWzMNvju+vX8l3W0nU7wbNHz7Nxr81+WX3lBi+fPs7Lp63z\n7/LUaexYtpo9C1rYvWgVHY12m5UKmET58EbXfYkKmUQsuK6C6yiWuguD0MCMQbNFOyyKMt6IMlnK\nOiwu3TYlvHzhKMligQ+fWMnNWVkWBTcBaPR7+gXFjRuxbZxKOpDGBKwQ2xm5l7evf4oP82L6ks57\n1k30IDxzTfVhVsIWKa6IyHp9l9oWebYTsqlxNF+hMko8imU6osL06biIt1wDUyl5tynsaFZP3k1H\nGphbQTg2IBwfcLshQ/uCZv7/Fzfz+90vMfvWfVp3X7bTpw+dZcHdO3zpwB6+dGAPBRGOzl/EjuUt\n7FrYwuF5S+jtDguXDo9EVxUNTFdJ/+KFxUul5N0BNTCFQt+xAflRPocMlME0jtCCRZkceFIxih+g\nGBYs+ZTw+oFwOWjLOiRtxbZgCxbXYUm6q8kysW1cvzJmYttqOpB1mb6dCxfQ9mm3LXIafGhKwNLY\ncfeEeS6gglhlRJN3yzUwlZJ3XSezVvLu/dgSElRO3r3dm4HpcGDxYg58aTH/e+fnaDlzndbdF9m6\nv41nP71A62X79bf5AQ9SKfYsW8mOFS3sXtDClcaZIPHMl/CYY/OPnPbFJe9KT9hh6c1FE6idBqZS\n8m5cwCu9o3/RI3VixNOCRZlYDEVsGxUs9n7GdLG17RQFET7Y+gR+UCil28Y6LIH0PUmPudA2zmB0\nIJUC2jrCzktzorLgVQWxSgUeNXl3IA2MT7GPgBcqJ++64sUl70bLR74tXGYmHnAv6Du88XZDFmYI\nP2xdw7e6NtLQ1UvLx9d4/sBZtn58lhVXb/HqiWO8euIYABenTefDlS3sWtTC7qWr6Gyyf/OJjlLy\nrps+HQ1vjJJ3K2hgygoY8qUAOwpF6BqDLq12WBRlDCk7kYpIf7FttBRkn/vy5SMEhQIfrlpFx+yA\nFDmaEm5NvZtkeMJ0W6426HDMGUgHUkmYOyVpLc9JqVzoqCBWGQQjpoHB6yPghcrJu7U0MADT/Yex\nJaS+ybtzUlnaQwHvtZlT+fYbz/D/dL/ArBv3WbvzClsPtrHpYBuL7tzmy3t38eW9uyiIcGjRYj5c\nFS4fLVhMrssnGRYvURcmKmCKsdRdN7QxlgOD1cL00cA8GIMOixYsijIOiMfxO7FtotwdFIbFHbWz\ng955tpWGUGzrwuLSXi66wnOrJONKbDsUqgW05QawI6sgVhkCj1MDA7bzUk0DEw+ya/b6amDiQXZ3\ng75LSO3pRpgKx5cu4PgvL+D/7HiNeUfusflAG8/tO8fTn17kmQvneebCef4Xvs/9dJpdK1axc0kL\nO1a0cK15BgCJDmed9kh2uVlIoQOpy02ddoF2uah4oTcH7aPcsTWoS0hRxhUipeUizxUq9s+/EAhT\nux+y+eIpcp7He5ufYmpgT27NCXuyy3o9kdjWxSmUd1jGXHA7WFSPoowBj6qBqRVkV66BqRRk1x12\nXyoF2d33bZiQmz59O2GXjWa5+UfpDLe2NrJj6yr+rHsDDZ29rPzoBpv3t7Fp3zmWXr3NG8eO8Max\nIwCcmzGDD1e3sHNJC3uWraSzqYFEhz3ucgdSfPq0H+u+uCDL0UQ7LIpSR7x4+SgJU+RHT7VwL5th\nKh1jfUiPD9WjKMoj0ZUJ+MmWVfxkyyrud6ZZcOMOz+29wGcOnGbbydMsbW9n6a6d/MquneQ9j8Pz\nlrB7wWp2LnqCTxsXUvTG6UWBFiyKMg6Ix/GXuYPcklAhEF6+fBiA97asRdIFMklrqYyHxZW7g6Jd\njAd30FBQPYoyThiMaNcLOysuTTfuOqo0NiD+3GTMQj0Y0a5bNoqSdwsZbiedZbpv8m57Nguz4C+W\nr+LtL6zDKxRZeeQmLxw9zQsHzvB02wWeudzGM5fb+NsffY976QZ2L1nF7gUt7Fzcwq3GafYYOz0S\nTvPSkRj1Dosm3SrKaFPFHRQ5g0QqRPHb+03FDjZeP03O8/jhltUkggLNQZjAGYvjH9fuoKGiehRl\nHDJ40a59pJJlGujjOqol2k2XiXazYi9QXGjdVL8zsky75N17BVvMRAMc01naM1YL076tiT/d9jT/\nb+fzNHZ007rvMts+PssLx0+x9GY7b5w8zBsn7cXRuemz2LFsNbsWPMHBacvpDNIksx7F5CgvLRuj\nGhZFGROqdTh8v18UfyEsWF69dBjfGP7yiRa6ZyZJkSPruw6LS7fNjX93kKJMIGqJdmHwrqNaot0g\nLGZK06ft//vuqIDJRY4jV8Q88G3BMsu5jpKN3C4bG3Ark4WZcHLOXPa8spR/xStMPdvJ9sNn2Lb/\nLM9/cpqlt2+y9PZN/urHO8h5HgcXLmXXohb+YaVESgXQgkWZqMTdQWDPZIm+dtWf2JgAABXLSURB\nVOZiKDp9/bANi3t7Y8kd1JQsiW0BklKof3eQotQxj+w6GoZot9sUyRDOPSpL3u0wAWC7MDMTVrxb\nafr0rYZwSSmTZffaFbz/s2vxC0WWHbrFtkNn2Lb/DK1nL/HchbNsuHSO/3X+/KG9MSOALgkpyngg\ncgb5/ZJtC4HHjK77PHvpLL2+z/eeW8PM4D5gk23B2pnBxvHXvTtIUSYQg3cdVZ8+PaAGRgw501cD\n45J3m8JuTJPXzVQvBZSmT09P2IJlZjLD7JjjCOBmbxhg90KW919Yx3/u2gy3YPPhNuZevA+7Dw/t\njRgJtGBRlNEnSraNi23dfbckFLglIfhM2xE8DD9Z+QQd05IsCcW2TruSkVIcfy2xLdSJ4FZRJjBD\nnT49GA2M7wLs+nVjBp4+PcN/yP2w+3I37L64AiZK3k1nac9kObd4Fvu7l5Dcd2DoL3yYaIdFUUaL\nCkszcbEtgCQSUYelEEbx51PCZy/YsLh3W1tJBPlSFH/Y/g3Ck1IgxYkhtlWUScRIJO+6/++1kndr\nTZ8u18C48QEuefdekImKl/aGLCcTuUd+vY+EAYr1UbFowaJMDGqJbQE8r6RdCTss0/P3efpaGz2J\nBB9sWEM63VOK4vftSaY0oVnFtopSz4y0Bmaw06eraWDi06ej4Y1Bhu96o1ywgC4JKcqYUElsC+B7\nJXdQOEPn1XOH8DD8+KkW7k9JMTt4SHOivFAJY7RRsa2iTCRGQgMDA0+frqaBiSfvuu7LfT9NKnze\naKJLQooylsTEtmDD4oqBE9van71xyrqD3trcikkVaUjmaEy4JSFnZw7nfVBdbKvaFUWZGAxVAwMD\nT5+upoGJB9lFGhivO7pIGlUeQw6LiLwJ/Bvs6fM/GGO+Vvbzvw/8OpAHbgK/aow5X2ubWrAoE4Jq\nYlsJUyON72OSpWTb2R13efryOboSSX60aRVeOk9T0ENjLCgOSldM8a6KalgUZXIw2hqYtCmQoO9+\nRoOR7rCIiA/8PvAacAnYKyJvGWOOx552ANhojOkUkf8J+B3gF2ttV8+8yqTks+etdfAvVj1JVzoY\n46NRFEUZI8wjfA3MJuC0MeasMaYX+GPgi312a8yPjAlnIsBuYOFAG9UOi1K/1HIHuXkcTnSb8CN3\nUCEFr16wy0HvbVhPIrBXN42JntLsoFD4Fo/j186KokxeRkO0G4iJtHKjhZ0lNOQWy0wR2Re7/w1j\nzDdi9xcAF2P3LwGba2zv14D3B9qpFixK/RM/kTixbZn41iR9iqHYdk7PHdbfOE9nkOSD1idJp8Ls\nhGR3lGwbYIsYl26rDiFFUeIMdbkookIBExftjsll0dBXoW4ZYzaOxK5F5FeAjcCLAz1XCxZlYlAu\nfHWLybE4/mh20DnbXfnzdWvobA6Ykyql25bEtlYE50Wbk+iKSJNtFUWJU014X1m02991FBftyhic\nXx6hwzIQl4FFsfsLw8f67lfkVeCrwIvGmJ6BNqoFizKxKHcHhUtDxaRHwc0OOmXD4t7esg6TKpBJ\n2uWfxkRPzM7sroIIb/ufRNQdpChKLSp1YSpf8JREu6NergxelzIU9gKrRGQZtlD5JeCX408QkaeB\nrwNvGmNuDGajWrAodY94UtMdBFAMfAqBMP9BO+uuXqQjSPGXG1fiBQWawnTbRr+7X8GSVHeQoigj\nwNA0MKOJGXFbszEmLyJ/B/ge9rrvm8aYYyLyT4F9xpi3gN8FGoH/GmoPLxhjvlBru1qwKPXHEMS2\nJmn/xIuBRyEFr3xiuys/fPJJio1CklIcf5PXHYltfWdndlc+WqwoijKC1NLAjDaPIzjOGPMe8F7Z\nY78d+/7VoW5zWGdhEfkFETkmIkURqSrAEZE3ReSkiJwWkd8czj4VJUK8vuJazys9Ft43Sd8KbpNC\nISW83mb1K28/u4FUkCcV5GlOdtOc7Cbj2SWhtORISklwC5puqyjK48MXL/oaCw0Lxgzta4wY7mXj\nUeBngb+s9oRYgMxPAWuAL4vImmHuV1FKiGe7LiLge/Yr4UPChsWZpEch5bGg8yZP3rzMg3SKH29Y\nRSbVSybVS9bvIev3kPZyBBQJKNoofqzY1ouJbVVwqyiKMjYMa0nIGPMJlNrxVYgCZMLnugCZ47V+\nSVEGjRf7+ws7LibmDgKbbvv6adtd+f7Ta+hp9GkMbOZKo2+XhLJeT6RdCdzcIBXbKooykTGR03rc\nMxoaliEFyIjIV4CvAKTJPN4jU+oaiRUqEmpWIrFtou9k5nxKeOOk1a+8v20tfrpAUzLMX4nF8Sej\nPATCW9WwKIoywRnDZZ6hMGDBIiIfAHMr/Oirxpg/G+kDCtPyvgHQLNPr411URocqnTyRmEvIiW19\n11mxhcbCrhs8ee0K99Npdj+7lGSyJLZ12StJKUSJk74WKIqiTBbq5JN2wILlUZS8ZQwqQEZRBo1b\nkokLbt33ZUtBxTCO/9Xztrvy/fVr8bMGnxyNCbskVAqLy+FHMxTdJGbVrCiKMrF5DMFxj4XRuIyM\nAmREJMAGyLw1CvtVlIg3Pz0AwDtPt47xkSiKoowzJoNLSET+iohcArYC74rI98LH54vIe2ADZAAX\nIPMJ8CfGmGPDO2xFiRF3B0V2ZucOEhZ3X2fl7evcyWb4yfqVkTuoKdFNU6KbrNdL1usloEgSSFbY\nhbqDFEWZkBjsLKGhfI0Rw3UJfQf4ToXHrwCfi93vFyCjKMMmnm7rtCuJUrItWHfQS1cPA/C9Z9aQ\nzwiNSbsUFIltwwnNSSlGS0DqDlIUZTIgmLpZEtKkW6XuiLuDwIpuxSu3M9v7hQA+e9EWLO9tfwo/\nnScbiW1toRKP41d3kKIokw4tWBRlBBHpN5E5yv/xJBbF39cdtKzjGsvvXedOJsP+DYsJEiV3UGPM\nzgyQxKg7SFGUyYcWLIrymIi7g9x9l7+S7Ju/8to5Gxb3/oZ1JDJFEhRpTpSC4sDamQF8UXeQoiiT\nDKdhqQO0YFHqF1dU+F7/DktKwBjeOGULlnc2rScT2E5KNlGyMdtbW7Co2FZRlMmIalgU5XERF9sC\n+H5JbJtw2hVh1e0rLLl7i/ZMI7vXLWFlcBOoILYNLy98kYpiW/szXSpSFGWCogWLoowAsaWZSmJb\n+7jXzx2UTwkvXw7dQWvXIRmqalf8cLa6HXioYltFUSYTY5utMhS0YFHqg1iHo4/YFsIOi/25064U\nk4bXztl023ef3kCQytFUzR2kcfyKokxWDFqwKMqIUy62DXUr+F5f7Qqw+v5lFt+/xc2mRnatWcqU\n4B5NCdtZyUZR/HkAkrE4fhXbKooy6VDRraI8JlxRIbEOS7IUFAfwxhkbxf/es+sppIVskKPRL3cH\nhdqVCrtQsa2iKJOFehHdag9cmXgYwxsn7HLQ2xt1dpCiKMpEQDssSv1QwR0ENt22GOuwrLl1kQX3\n73CjsZmPn1qIeAUag56ow1LSrpTcQWDj+MvFtuoOUhRlwlMnHRYtWJTxSZmWJO4QiruDICxYgpKd\n+ZVL1h303XXr8RvstK7GZA+ZsoIlCJeE3PKPOoMURZl0GKCoBYuiDJ8B3EFgw+JcFH8xKPJq6A56\n55lWgpQV1jYlemjyrOg2GYpt3ZarZa8oiqJMfNTWrCgji3j93UGJUsFSDMW2T92+wPyHd7gydQp7\nWxYzPbgHQFOyu6Y7CDSOX1GUSYoWLIoywpS7gzyXueJH7qDXz9oo/nefW08xDdnAZq40+j2kvdJU\nZii5g+IdFnUHKYoy6dCCRVFGEE8qim3trUchJYgp8vpJq195b+tTSNqKbcHG8VcT20a7iGlYVGyr\nKMqkQDUsivKIVBHbikh/sW3S/vkWA49CILRev8DcB/e4PHUaR9bMIyH5KI4/4/Wq2FZRFKUfBkx9\nJMdpwaKMTyp1OCLtiv2zdXH8hZRHIQWvnrdi2/da15NK2wnMTQlXsPREBYuKbRVFUWLokpCijADx\nOP7IHeQ6LG7goWCShtfOWP3K25tbaQhscZJNlNJtk2KLGBXbKoqihOiSkKKMMCLg9dWulMLiPDbc\nPMuszgecnzWdQyvnszS4CVAKi/NyNcW2oIJbRVEmKdphUZRHJwqKi6XbiuusONFtmL2STwmvHw+X\ngzavRRqKZJPWHdTk2+yVjPSo2FZRFKUSWrAoyujgFYu8/ol1B72zed0YH42iKEo9ocFxijI0quhI\nImeQSL/AuELSdkNab59lVscDzk+fwaerZ5OUPM1J21lpDDssaS+n7iBFUZRyDFBUl5CiDJ1qSzK+\nH+WwlMS29v5r58KwuKdbSaVtim02YZeEXLptQCES26o7SFEUJYZ2WBRlGMTdQWC1LGXuoELKwy8W\nePWMXQ56a3MrmdAd1JzoAmKTmaUQ9VPUHaQoihJDCxZFGQGiGH4/5g4qTWZ+9tpZpnV3cHruLD5Z\nNoflwQ0AGmP5KwBpKQzoDlLBraIokw+jtmZFeRQquYMAxPcid1AxcHZm4ZVLoTtoy1q8hkLkDoq0\nK1KaH1TLHaQoijIpMWA06VZRBkmFpZlIbOuX5gfFo/gBJFngxYtHAPj+9idJpvKxzootXNzAQx+j\nYltFUZQ6RgsWZXxQvhzjtCtxLUvCTWe2hcezN04xraeTU3Nmc37ldFKSpyl0B8XFtmDTbVVsqyiK\nUgFdElKUR6Bf4RIWGQm/j9gW4PUTYRT/xlYyaSe2DYPiIu2KdQ159BfbarKtoigKKrpVlGERE9sC\nGN/ro11JFPK8cuYoAO9sXUdj4LQrrlApaVfAxvFX67Co2FZRlEmLMZrDoihDoVxsK6HANorjTyb6\nuIO2XDrFlO4uTs6ZR9uyGaxLXAEgU6VgScZ0MqphURRFiaEdFkUZgBpi29JkZtdh8SOxbSEFr1wM\n3UHrW0kGeRqTtlBp8krJtmDFtvbW00JFURSlAkY7LIoySOJLMpXEttiwuEJYsHiJAi+dC5eDNq6n\nIZWLovhL2hXXYSltWoPiFEVRytFZQory2Hj+/Amae7s5Pn8+Z+fMppm7Y31IiqIo9YlBXUKKMiRc\nR8V1QVz+Sphua5IexcD+7PXj1h301qZWiukimVQvWaddCZeCAtygQ4vXR8OinRZFUZSIOgmOG9ai\nvoj8gogcE5GiiGys8bxzInJERA6KyL7h7FOZoHgSfnn2S+yXSdhIfpP0yacE38/z8pljALy7ZS0E\nRTLJHI1+D41+D1nPfiWlSFKKBCIEIhUdQr546hBSFGVSYwBTNEP6Ggwi8qaInBSR0yLymxV+nhKR\n/xL+fI+ILB1om8PtsBwFfhb4+iCe+7Ix5tYw96dMQCKHEP0TbqP5QYFHIRCeu3qSbG8PR+ct5PLi\nqfgUaEp201Qhih9iHRYV3SqKovTHmBHvsIiID/w+8BpwCdgrIm8ZY47HnvZrwB1jzEoR+SXg/wB+\nsdZ2h1WwGGM+CQ9uOJtRJhvu7yXW3ajlDgIoBB6FFLwauoPe3WDdQQCNyZ7+YtuYO0hRFEWpzmC7\nJkNgE3DaGHMWQET+GPgiEC9Yvgj8k/D7bwG/JyJiTHUF8GhpWAzwfRExwNeNMd8Ypf0q9YB4/d1B\nkXalNKG5kBIepNM8SKV4d+N6GlI2LK45USpYkmKj+P2o/umbbqsoiqKUMfIalgXAxdj9S8Dmas8x\nxuRF5B4wA6i6EjNgwSIiHwBzK/zoq8aYPxvo90O2G2Mui8hs4AcicsIY85dV9vcV4Cvh3Z4PzLeO\nDnIf9cZMavzDTACqv77y+rkA9Ibfd4S3t8Pbc+HtfnsT9Qv/2b+Mfv0Q8O8e+TAfmcn77zcxmMiv\nbyK/Npj4r69lNHf2gDvf+8B8a+YQfy1dpkf9xmg0IgYsWIwxrw53J8aYy+HtDRH5DrZdVLFgCV/0\nNwBEZJ8xpqqYt56ZyK8N9PXVO/r66peJ/Npgcry+0dyfMebNx7DZy8Ci2P2F4WOVnnNJRBLAFKC9\n1kYf+wK/iGRFpMl9D7yOFesqiqIoijLx2AusEpFlIhIAvwS8Vfact4C/EX7/88APa+lXYPi25r8i\nIpeArcC7IvK98PH5IvJe+LQ5wIcicgj4CHjXGPPd4exXURRFUZTxiTEmD/wd4HvAJ8CfGGOOicg/\nFZEvhE/7A2CGiJwG/j7Qz/pcznBdQt8BvlPh8SvA58LvzwKtj7iLiSzOncivDfT11Tv6+uqXifza\nQF9fXWCMeQ94r+yx34593w38wlC2KQN0YBRFURRFUcYcDalQFEVRFGXcUxcFi4j8hogYERmq9Wpc\nIyL/TEQOhyMLvi8i88f6mEYSEfldETkRvsbviMjUsT6mkWSwoynqiYHitOsdEfmmiNwQkQkn/BeR\nRSLyIxE5Hv5d/t2xPqaRRETSIvKRiBwKX9//NtbHNNKIiC8iB0TknbE+lvHIuC9YRGQR1ll0YayP\n5THwu8aY9caYDcA7wG8P9At1xg+AtcaY9cCnwG+N8fGMNG40RUWLfr0Ri9P+KWAN8GURWTO2RzXi\n/Efgcdg4xwN54DeMMWuALcD/PMH+/XqAV4wxrcAG4E0R2TLGxzTS/F2sSFWpwLgvWID/G/gH9I8b\nq3uMMfdjd7NMsNdojPl+qBYH2I314k8YjDGfGGNOjvVxjCBRnLYxphdwcdoThjCw8vaAT6xDjDFX\njTH7w+8fYD/4FoztUY0cxvIwvJsMvybMOVNEFgKfB/7DWB/LeGVcFywi8kXgsjHm0Fgfy+NCRP65\niFwE/ioTr8MS51eB98f6IJSaVIrTnjAfeJOJcPLt08CesT2SkSVcMjkI3AB+YIyZSK/vX2Mvzkc8\nJ3+iMFqzhKpSK/of+EfY5aC6ZaDRBsaYrwJfFZHfwvrW//GoHuAwGczoBhH5KrZd/YejeWwjwQiN\nplCUUUNEGoH/Bvy9si5u3WOMKQAbQj3cd0RkrTGm7vVIIvLTwA1jzMci8tJYH894ZcwLlmrR/yKy\nDlgGHAon+S4E9ovIJmPMtVE8xGExhNEGf4j1rNdVwTLQ6xORvwn8NPDZgVIMxyMjMZqijhhMnLYy\njhGRJLZY+UNjzLfH+ngeF8aYuyLyI6weqe4LFmAb8AUR+RyQBppF5D8bY35ljI9rXDFul4SMMUeM\nMbONMUuNMUux7eln6qlYGQgRWRW7+0XgxFgdy+NARN7Etji/YIzpHOvjUQZkMHHayjhF7JXdHwCf\nGGP+1Vgfz0gjIrOc01BEGoDXmCDnTGPMbxljFoafdb+EjanXYqWMcVuwTBK+JiJHReQwdulrQtkQ\ngd8DmrATug+KyL8f6wMaSaqNpqhXqsVpj+1RjSwi8kfALqBFRC6JyK+N9TGNINuAvwa8Ev5/Oxhe\nsU8U5gE/Cs+Xe7EaFrX/TiI06VZRFEVRlHGPdlgURVEURRn3aMGiKIqiKMq4RwsWRVEURVHGPVqw\nKIqiKIoy7tGCRVEURVGUcY8WLIqiKIqijHu0YFEURVEUZdyjBYuiKIqiKOOe/w5ZJpJsCs3o4AAA\nAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x111b65630>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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YWg0ojNl/P//H9v1zwllxCamFRVEURTm/PPcoZIqQydvXnX+fe/S2rSxnAWPkRN08h0EF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\nzJgU5Kk3B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"text/plain": [ "<matplotlib.figure.Figure at 0x111d9de48>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1 = np.linspace(-4,4,250)\n", "x2 = np.linspace(-1.5,1.5,250)\n", "fun_map_mom = np.empty((x1.size, x2.size))\n", "for n,i in enumerate(x1):\n", " for m,j in enumerate(x2):\n", " fun_map_mom[m,n] = forwardn([i,-j], w_mom, b_mom)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend()\n", "plt.title('Decision function SGD')\n", "plt.show();\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map_mom, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map_mom, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.title('Decision function SGD with momentum')\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again the more stable steps afforded us a higher learning rate, but we see that the effect was less pronounced than with mini-batching for this problem. Furthermore, although we made a lot of initial progress, we see that the training was a little unstable towards the end. This is an indication that the learning rate was actually slightly too large at that point. To help deal with this problem, we turn to learning rate decay." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Learning Rate Decay\n", "\n", "Learning rate decay involves gradually decreasing the learning rate $\\alpha$ as the epochs go by. This allows for starting with a higher learning rate, to make big gains at the start of training, and then as we approach the minimum to slow down learning and start making more fine-grained adjustments to get as close as possible to the true minimum.\n", "\n", "One approach is to define a number of steps and make the steps after a set number of epochs. We will take a smoother approach, and have the learning rate decay exponentially. This process is governed by another parameter, the decay rate $\\gamma$. After each epoch we multiply the decay rate by $1-\\gamma$:\n", "\n", "$$ \\alpha \\rightarrow (1-\\gamma)\\, \\alpha $$\n", "\n", "Then after $n$ epochs, $\\alpha$'s value is $(1-\\gamma)^n$ of its original value. We have been training with $\\alpha=0.01$ and 150 epochs.\n", "\n", "To demonstrate, let's choose our $\\gamma$ and initial $\\alpha$ so that our decaying $\\alpha$ will cross our constant alpha about halfway through training. It's a bit hard to see on a linear scale, but a log scale makes it clear what's going on:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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8ZDdPTFtNarr2ChdxNRXgHqJKqSI8dls15q05yLJdJ5yOIyIi+YSXl+GF9mE8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\nUsvJOUWuyggdh+NAnHNun5l1Ai4HbgO+BYyt5PuLiJRFNbt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"text/plain": [ "<matplotlib.figure.Figure at 0x111bf2b70>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "epochs = np.arange(0,150)\n", "gamma = 0.015\n", "alpha = 0.03\n", "plt.figure(figsize=(12,5))\n", "plt.subplot(1,2,1, )\n", "plt.plot(alpha*(1-gamma)**epochs, label='Decaying alpha')\n", "plt.plot(0.01*np.ones_like(epochs), label='Constant alpha')\n", "plt.ylabel('alpha'); plt.xlabel('Number of epochs');\n", "plt.legend();\n", "\n", "plt.subplot(1,2,2)\n", "plt.plot(alpha*(1-gamma)**epochs, label='Decaying alpha')\n", "plt.plot(0.01*np.ones_like(epochs), label='Constant alpha')\n", "plt.ylabel('alpha'); plt.xlabel('Number of epochs')\n", "plt.yscale('log');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To implement decay, we only need to tweak our training script a little, as the backpropagation is unaffected. Before we being looping through the epochs, we initialize the variable learning rate, and after each epoch we multiply this value by `(1-gamma)`. Let's test it out with our values from above!" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def train_dec(X, yhat, shape, alpha, n_epoch, batch_size, beta, gamma):\n", " n_samples = X.shape[0]\n", " n_input = X.shape[1]\n", " \n", " # keep track of performance during training\n", " costs = np.zeros(shape=(n_epoch,1))\n", "\n", " # random nonzero initialization\n", " w,b = init_model(shape)\n", "\n", " # initialize dw and db to zero\n", " dw = {l:np.zeros_like(wl) for l,wl in w.items()}\n", " db = {l:np.zeros_like(bl) for l,bl in b.items()}\n", " \n", " alph = alpha\n", " \n", " for epoch in range(n_epoch):\n", " for i in range(0, n_samples, batch_size):\n", " X_batch = X[i:i+batch_size,:]\n", " yh = yhat[i:i+batch_size]\n", " \n", " y = forwardn(X_batch, w, b) # prediction for mini-batch\n", " w, b, dw, db = backward_mom(X_batch, w, b, y, yh, dw, db, alph, beta) # take step\n", " \n", " # Decay the learning rate\n", " alph *= (1 - gamma)\n", " \n", " # ### Some niceness to see our progress\n", " # Calculate total cost after epoch\n", " predictions = forwardn(X, w, b) # predictions for entire set\n", " costs[epoch] = np.mean(J(predictions, yhat)) # mean cost per sample\n", " # report progress\n", " accuracy = np.mean(predictions.round() == yhat) # current accuracy on entire set\n", " print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n", " \n", " print() \n", " return w, b, costs" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training accuracy after epoch 149: 99.8000%\n", "CPU times: user 22 s, sys: 1.54 s, total: 23.6 s\n", "Wall time: 22.3 s\n" ] }, { "data": { "image/png": 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a2alhsW8DQ4FfmtliM1tQZHVlU51OdT2JKTfsr7plRGSAK6VbBne/F7i3YN4V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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x111bc6908>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "batch_size = 1\n", "shape = (2,3,4,1)\n", "gamma = 0.015\n", "alpha = 0.03\n", "beta = 0\n", "n_epoch = 150\n", "%time w_dec, b_dec, costs_dec = train_dec(X, yhat, shape, alpha, n_epoch, batch_size, beta, gamma)\n", "plt.plot(costs_dec, label='SGD with decay')\n", "plt.plot(costs, label='SGD')\n", "plt.legend()\n", "plt.title('Mean cost per sample after each epoch');" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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URVEOGyHY5eOw2BOfi4j8GvB6YExErgM/CsQAjDE/B3wMeDPwAtAEvnMv9qsoiqIoyt3T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\nAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x110307908>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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KcrapXoInHoJGBcrTcPcLYOr8bW3yxS96kCeeuHJIAzw6bC+h02G7OB2jVBRFUZSjoHoJ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\ny3R6WYw4uK2+Lefe2d7UDkx/gwwbdn6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GXS3R3jyJyHJ0pUwqJXk5cVV7rUVkOQSKbGyk\nZ0TFWuKZefe97NtOHoeeDDnSgbGYckxercBAendy9gqtAzuwucEajR6pgHJKT6FuIKULMYXuGIhM\no2sVLBB0M/JqCbLcfSYK3fErPovAotw6Oh0wxqWD5zk6CiBQyCyns2EcgcUKSTZadT6qUoJIM6xX\nw0y1TF5vQhhSPnt51W+nMz5Ke8c0NgrJxmpU3/6I2vmrq36bM7/yBOnUJEIbVKuNarQxEyMsPvGw\nyxjzaoqJAoJGC2GN80vF3v/TaH3sG5/7zVs3xM8JQ8IyxKeBjyP53ip8NUhoZDf1d/8MEBdHPAaJ\nUmdqA8nlWZTvShvNL9PaOoWulLBANlqjOzVOsLRyw3TddLSGBeLlOtVT53vjWoviItzeNtHLOLGA\niUJks022YQyrAqeICIktJ7SmJggrZWdu1RaRZ+hyAq0OUmtnpizHBEsNsrEaYBFJhA6CnolUaEtU\nb2CVIk8iWtumUd1xdBhA7CdM4+NCpRhtNDqKEL6Ev/WhG9F1KbN6bMRNsL2Lh3UTfTFxW+VUGKnc\nd2D9xB0GmMy4MHTgJ2VYTRSwmIlR8kab6ofnSBaWaW2bRpdi8lK8hqwAUpBXS+iyCxMJwHTASAlK\nYYVA1huIKMQIQT5aI+ikCG1ILs0TtDosjlShUCd8YTykBWvJNoyyXDuIyDTx3CJ5GCDS3KkO5cQd\nY0R/XL7hJMb6YySwEmwYgbXYVgcrhCMqxnhFxKtFVrh1efJiwxBUisxzhLXO5BxH5MYpRzbPka0O\n2WgVMVbD5hrhxyFwdW8sUPvgLLX3T/d+O2m5TOvADjCGaH4JHUcsPv0ovPgGtfNX6Y7VWHz8AdKN\nEwi/bV0pYQPlKiBvGKd0/mrvN5ZuGCecWwQhe0qmhRuSi9u5UblXvHVDH809hPuoNL+89SK3hhDi\n14QQJ4QQJ4UQ/9U678dCiL/w778ihNh1N7Y7xPUYVDYETvItvBg3QhG+kt2cvFpGdvNVBKd07rIz\nicahC6ckETqOCOeXXWXSOEYtLrPy0H5MHBDUWwid096xibyUABC0OyTXFlHNNt0NY3Q3jhNdWyC5\n5pSVjk/XHRxD0GgTL9exUtHeNk17+ybSiRHqh3evGn9xETZx5MILYUA6OYoJnFfFCn+XHThTKFpD\npUQ2NU5eq6CTEKIQ2eliwwAdBthqCdnuIKzPcgkCLAIp/OTnww1WKXQ5wagAlEAnEZRiF6pR0k3S\nPrvEei+E7cUmHEwcoSulfupz73HgIiIcUUDgPB3CT8BKYoVy5KcgKF6N6K1I4I3SAiuFC8347Zoo\n9KTGODJQjEsICEOn/AiBaLYxSey36YiAKSXoOHLVdMOA7niNcK5vjs6rJT9OuXqfPOkxSYyulGht\n3ki2aQNGCqy1Xl3yxm6/bI/ECU/orH/Pv6ZHq31yGCiE1n3SIoQnQEC7i9CGvJSQ1youhCSEa2oY\nhU6hCUNQwvlfhIAowIYhwliC5QYiTdHVEt0JV61YzS/R3ThB84HdWCkIl5sEaU7gjbwNT2jaO7eg\ny4k3NlunUmnn2cpHqohc488uZK6R3ZR8tAbW0to2TWPfdpq7trjvag2KG5Xi91d4y4ospgKDv2UL\nvd9v6dzl69b5SeF2xzrEzw/C3tm/Tws/s8IihFDAvwSeBy4CPxFCfNNa+97AYn8ALFpr9wkhfhf4\nF8A3ftZt/7LiZncnH1fyvVn4atCPY6ohpfMzFFlCst2l8uH5VeZW2UkJlpuk0xGdaVcAzcQuNDLx\n0pu0d24hrF9vwC3SdQtc/ern0LUJ0slxZJqifNpta9dWuu+fWUWoVh7aD1qTJzH5aBUEBCsN0qkJ\nb7g1fY+GCvzk5u74rVQYYRFKIrpOJcAYhLFkk6N+YnR39hbhetdEriqru/ALiBTkuq8EFPATrIkj\nt30h++PItftbib759oawPRKRjQX9iRv/eRG4dercvR4M3IsI4Z5bi42igVBe2vOR4Ie0iiRZ+hO+\nD6c5qcWrHFGxTe2OTeS+b4B0aswpJTeDlO7qV06wucaWEwSetBSEpEc6BsYIbvvSExlrsFYiO21M\nqeRIXGGULdZlrLs9CwK3/uJ4a3deCKUwWQ5J5HxW7S4mN2SBAiGRaUrQ6mAChY0iVKuDRJKOVehs\nnaZ0cRYy932mU+PoRky40kB2nUG7O1ajuW8b6fhIz0Bss9x9J0phAkU4v0w6MYoVINMM0ox8fBSR\nZQTGQK4xSURWLdMdq60bFr2VN+Ve8NYNfTT3IH6JQkKfA05aa08DCCH+NfBbwCBh+S3gv/V//xXw\nvwohhLX3SweDewe3Cvl8UpLvzQhNd6xGa/dWVLON7KToUkx34wRkGfl4QtBoEc8t9y6Mrg7LalJl\nlKK9d1OPhKnFZfKxEfJqGeHLsedjI6h6E7KMhaceIVyu95YVuUYnMemGMVSni1ppkY9W3KRljJ+I\nhZsgiztxXxmWMMBqF0YiLDsikWt0KXbKhLS9EIXNHZlBGchzTBRhde7WXXgmXPEYeiGNHlHxs21x\n2ofq9krMF8Sh6JlTrKfYp2KdhYq0trdOb1kLgSIdrZKVE1Sjic21n7TFarJSbNiHnoxSPqRSmHLp\n1cdxx9gZhNPpCdLNGweWvQWKZZR0oSxt3MQfDJCV9VCoKxTkxnl90NoTOPrHRvpQlPahIk+wnGrl\niRw4ZUwISLN+qneusUmASSJSpRDCItKccGG5T/w6Kd3JkX4YK8+d6lZOsNqguikLjz8AuUakGSJ0\nYSgdhW4/jEFmueOu9SYmidx5FeHO8Wa752tJzl9FaH3d5H4nNyqflreuwNBHM8THxd0ICW0FLgw8\nv+hfW3cZa20OLAOTd2Hbv3S4Vcjn05B82zu3oJptxwGiwGV3eAUmWlxBpvkqFaggVQXycuJSpbXu\nScTLjz+IWmlgw2CgPoglG61CoMjLrhNyNlpl8elHMZFi5IMzhIsrYCx6pOwmkDTvhUP6CoLtkwCL\nIy7e+yHbHcJWG6EU1gqk1m55fyeOUkhrCC7NEC03nNoSOvNr/9e0RhWAftil95z+GHxdlRve5Qyq\nC4U5NvfjKkylPi0XWK2arF2Rdtk0rV1bkalm4oU3ECuNAXMq7OQqv6e+yx9Ff83vBd9jp5xxnpww\n8KRM9kM1xb4VxCUMHdm44RhuNDThPUb0yU6hjtzqc8aRSKuk236uEd28b9jtfd84VagUU1TLUt3U\nF7dTTrHRBi2Vqws0NuI8TsXnlXRqXBiivfm8MKHnozXCpbpLC1cK4709NgxcyvjECMFy0yknsjBU\nuxCeMAbTzRBCILOccLFONL9E0GyBNlTOXqZ66gLlizMErY6f3Eu9Q9Adq5GN1mgc3EVr27TLHuPe\nrfu09vcP9+5Yf1lwv4SE7oqH5W5CCPFPhBCvCSFey+h+2sO555DXSjdIo3QXsBv5UQCWjh5k7ulH\nWDp68K7Gi/NaiXh2wWXG1CrOkGoMNo5IZhewEhaeeqS3bbW4vIpUdaYmwOILrDkSpuOQdGrSZXOU\nYnQcOaMiIH1qtADyWtnVRZkYpb1tGhuHrmS+Py6iuOMenPiKUIM2brIS0snu9SZhq4NIcz/5KYyS\n/dBNlhMu1ymfuoAKAqLZeWSRlWLtgNdCXK9yFOSEwUf/ns84uiUsblt53icNptiPNZP7ehcVa6Gb\nIqREl2LqR3az/MgBp0x4MrWTK3wjOEaFNlftBBU6fCP4ATvFVR+SCvrkAusmeSn7CtId8pRVYx0M\nQRVhnJ4qdYPPGuPUHj/5O/XHYpXoq12DfpjiOAlHqkwYYJVPIdcaul2nfEnlro7S75f2tVf8OZOP\njyB9pd/u5g2YUoxsd4mvLfb9Q9L7YJIEcoOpJFTOXhk4J0F0uu48rZTQ1vQKEYpcUzp/lSDLbzq5\nF4prUG9htUHHEe2tU3THqj93b8rt4l7w0QyxBlbc2b9PCXcjJHQJ2D7wfJt/bb1lLgohAmAUmF9v\nZdbaPwX+FGBETAxDRmuwNuSTlxM6UxNYFbB09GBPybidEvF3q1iUG1NA6dIs9YO73IvGuAwHIN04\ngRWC0sUZdye4f7u72I9UEJ0uVgXu4tzu9PbJxhFGCaK5ZbKJUSeQdFKIIqwQRPPLbjNJBNrQnZpw\nZe2lxMQRVklUo91LRSXL+yGTYmLLtZs0pEU2HQGy1rrMkyxH+NRjYUEtrYCQhI02hCHhtSXS6UlM\nkiCzHGO8L8IaVoVDjHFkxIc81oVS7rblZqpE4RvRBTGyfVKkJL3oahHugtUqUqHARCHah3BsFMFo\nzas9biJ/OniHJVuljpPn65TBwtPqXc7pzavHXKgWxtx4324HvXUIX1dG01PEClVqvfUXCkwwoPQI\nvD/F9olP7z3Ry/DqhfiCIqzmyByxJ2+FeoRTwISQGPLedi2uDhFZji3FiDQjnRglWmk4FUV3kNr4\nVHnRUwbLF2dcWnjmTNjSWmSWYwOFHh8lOnO5Z1rWcUh8Ze6mdYgGFVeZZqSTo66tRXV1YcR7CfeC\nj2aIAXg+fz/gbhCWnwD7hRC7ccTkd4F/tGaZbwK/D7wM/PvA3w/9Kx8PgynIRqnbqjr7s5jcbif9\nsBiT6ro7TB1HIASlK/OugaGxBN0uupTQ3TjuKtoKQXxtAR3HBFeuIU0/pJFOjKJabSiXkNYSLSzT\nnRwlm57EpDmMVGgFmwkaLawxvry8m9CCbkqOTz2NIzcJdlKEEiAUtptCN4NKgkrdRd4GCqm1q2qa\nRKhGExNILC7d2FXGrWGN7mUR9SqjZhlIgbIW3emipEQLHEnxhk0XirHr65nFpH+dfWStX4WBlF6v\nEBQTb6EaWBzx0XbAN4MjUcZ4X4g3DoeFMjK4DcG0WOKqnVg1lAYlNomF/guFn0b2P9fb/u2QrrXe\nlEHCo7XfL9VfV5pB7GrUrDpOBZnp+YQKz0pxwFidTVQcU6kGiKUnSD1S6c6T3hXcf94CIgpd48ZO\niq5VSMdHkGnmUtJLMaackFnj0pJ96C5otjBBSDZVIY1DVvZsdd4WIVy7BXBZW2kOQdDr0l0Qk0Id\nvdHkPugHCdodgoudXurzvUwAPm0fzRD3J35mwmKtzYUQfwh8B1DAn1lr3xVC/AnwmrX2m8D/Dvy5\nEOIksIAjNfck7vX6AIN3J+29m5CdlGRmoadOwPVE5OOa3G5XmRkck+h0oRQTzy6i2h10ZRNWG6L5\nZdLJUVf7wsve/d46q6vZ6koJckPp7CVXrr5aQmiLrDcJUzfurFKCXGMTlxKsmm3nY5ASaSzBzLxL\nO04i9/nMINstwuUGVkrE/CLRnCu/XxA/KyU2yxFFPyNj0LWKawAoJSp1IQFbCR1p0QbRTUG5TCER\nBIh2B5m7qqpaSmf2HJxACwwSkvUmciHcJFp4SwpSUoRfjDdw4pQnGypsGGID6UyrceQmZU0/lOMz\npYS1nuB54lNsz8KMHadKu6ewAFRpM2PHV49dDPyd6xsrSL5WTE8NsgMhn2L5HqHwf4fS+1n8snHU\nV46Kz6a5O66F2sSgmtLfn95xhNXeGCm9cdinP4eqTwJ7Y8eNPXRGZmtBS4WdHHOhtTTDRCFCKaL5\nZUzQQI/VsNZlaql60x2eWtkRY2PIx0e9QVkgjXF1YKyFyIUYrVJ0NoxhkxjZSXutKwaz5wZxr9RV\nGeI+x30iH9yVwnHW2m8D317z2h8P/N0BfudubOuTxP3SZ6O4OymIyOBUuB4R+bgXtY+lzAhcFsPm\nDaQbxhBZTjy/TNDu0Ek29hrMFUXnit46gxKxarYJ6i2i5TosrNDaNu2qmpYTgnYX1U1d/ZRamXBx\nBVl2YRmCAJFrgvpKr6rqyMvHWXz6Ubdda0jHatgkonLiHMm5y+jx0VWp2p3NGwGonLtC0OrQ2jZN\nd+O4P37OoCm0dmQIIAxdFdQodLVFhCBoO1WGQEIS9+/ioZ+1NHjX3yMkg6EIVhlhURJaHZderJw6\nIoSgdPqiU5KUIlhcob11IzYKybWGUuI9L9pVSi25sdgkWq1wDHx3L5oH+YY6BtYpK9vFLIflOc6Z\nKX5PfZcXzYOcY1P/M4WyMvh8UHHxZeXVSgtdLZHXyqzK2FpVT8X/1yuDPzDGovKvNp5UWFxqUEHi\nCoLCgP8FT3rsgDeGNa974mZxJLAgc9qRCRuovodJAFGAbLYRvg4NUiDyLqbqfovq2iIy166rdrXi\nFEXrGkFK3KbUcgM9OeLCmQbIc6Q2JDPzyNTVZVH1Zi8EdLNr0P3Us2yIexefppH2TjCsdDuA+60+\nwO0SkY97UbtdZaYgela61OOiiWE0t0Qeh95UFyI6qQsXSUFpdmHVeAcl4mJ9Og7d9iqJ6/6bOXVG\nAnLepZVWzl5GJ7ErvN5Je80TdRJROj/jyqK/+AbLnzlMNjWJaneIT5wlbLbp7Nxyw67NJgxpbhul\ns3UjJgyRWdYLQagsJ0e4MRlD0E2x7Q5Ihex0nT93pOr8Mt4n46DBiD5poX/HLztdV/nUdwXupUYX\nEyxeacATG+vu+LPJUeLZRcZ/8i7xcsMrhJtp7t2GjsKed8JKMUCs5PXhG69SnGMTf5E+y9PhuxwU\n59klZnhP7+AC01Rp8w11jL/QX+Kc3dTLzumlEhchmsJbYi3hQp2w0aQ7Oea7MbfBWPKxan85rVeb\ndov9HzTeWr/fXi1RbdfqwSlJa4gPuE7RQvT8LbKbOhKplNtAcXyLBx/GC5cbpLWKr9fivju11HBf\nmXQtCWSaOZ9UGII2LkwoQAYByaVZdCVBGIivLZBVy+SVEkIIRL1JPjnm0qG1dv4oT55UvYEwbjB3\ncg0a+kGGuCsYEpb7D/dbfYDbJSIf96J2u4SoIHrdjf3S+CZQdCdHEMaSJ7GbKP3dd3RtAdXq9LID\nbjneZqd3x+o6OeueSmPikPL5K2TVMqacuAwLrZF+jHNPP0JQb5Ncnad8aXbVvuSluFfPxU2EApTA\nBIrO1ATKWlSrC4lx4ZYwcP1zshwZBKhOl+jaIon34iTnLjP/xc+48u5SgDWupLvWjmxJgQkCd22Q\nvgqudhVPsRYjpCv8pgLIc5fBJKW7yy8mc4MnBhaZ51ilet/H0tED/vttITpdlyab5shGG10puQnX\nmH7ZfjtAiHoEyXKOTZxLN/F74fe4JDZ6462lLrwBV77DuXyTm3DbXTcBG9tXTAqyISQmCsl8w8Zg\nuYFJ4v53KETvuyQYMCoXZKrIvvJ/y26GMJ7c5a6/Ua/GjhgMR4m+h8innZvBQnvQr8FTtD0w1mXf\nWYtKU5cJbx05sqUY2+36DLUMG7ieV672T4SNAoJWm9KlWYTRBHPLlM5ddoUWSzHCuJ5BplLGFnVj\ncCRKGoMJA1QnZeTtj6g/uLeXfZROjPbSpkXnxhmTQz/IED8zhoTl/sP9Fg++EyLycS5qt0uICqK3\nqjGiFGQbxolmF1BZ3jPYJu+cRI+PrjveG/mHeqG6RpN04wTG97JJFuvrGBNLYAxZtYzUObLlxt3a\nvZXy6Uu93kZ5OellL4Xzy868LJx5OZ+sILGULrimdc2dm0lHFHkpIbAd55NptFw2iLV0N04gul30\n+Ciym6KVchVbfV0NN3cL1FIDFShX5VQIwqUVwqU63Y0TpBvHnVpzbYlscqxXjM1aP/Ea7VOZcXf9\nc8uUFlbQcYSuJKw8fADV6RDUm5gkJp2aRHXaqMynaHt1wApB0Gg5cieEn7BtP5QCYAUC6wy4FAZc\n916DEpuY73lXTBgMeENcQ0KVa+cHkobIKwfx6Utkk6Nkyu2/bLR6/g9rLXRzR1qKkJgZ8Mb4FHTr\n90HkuSPAWOhmiCBw2T6ec2JBtbruXJDCmXYL4uNVG+E9NRZHioLFFVQ3dV2ofe8laQzBzDKmWnIN\nKd3LjmA0WgRaY6JxRKtL+eRFhNG930fxe+tsHCUfG3El+bVGEGGzHIl1EalMM/LBWZCSeKlOu952\nNWAK8t/1qmQpvq667RBD3A182rVV7gRDwjKA+zEe/EneXd0uISqIXtG0TeSui67spu6utJvesPx+\ngVv5h3qtAYLAGxK7hMuNVabo4jgsHT3osn4GZHXVbNOdniA862o9pBP97KVsctR1yQWXQu3bC6QT\no5QvzlA5dwW1aZLOBjd5B4025fNXkMsNWof3gJIoIB2rYGI3NmkMRkmntgQBspNRvjLXG3Oxr7Kb\nETbbpIsrBI02eTl2IaWJURDCTXKLbcxI1akvPgxFtUze7rqU6lJMWG+hMkdqVJYj0gxdLqM6KVmt\n6ojFQJZMWG+TjpSdwoGf5wW4XkeAtcyYUaqyRZ0KRaZTVbSYEeOINEcY6/wwxrgwiZQQKLSQSOuM\n1s5sK5DWUL40Czhlq711imwsQC0suqaTQYDFuiJslZKrDVPUR0lzCCTWCkSr44iOBVlvYUsJMtPQ\nTbHaYkYqrr1CliLyCBtIVLONMpa0bCEMXFXZPHcNMQVYa4mW6sSzC3SnJhDlEqw0XRG4kjeDZ+7Y\nmyikdPYKNgrQ5QRVb5LMLKxqUzH4+0iuLZNmOa3d29x6tEb66rfhYt2RfK2RLaeglM5dprHvWA/c\ngQAAIABJREFU872waqGuxbOL92xoeohfANwnzQ+HhGUAw3jw9bgdQtSbgAcUEB1FhEsrmCCgNOP8\nKjcLr93KP3QnxGy90F48u0Br19aeL0ZXSr3spc5WZwYG1/NHdlJMoHql14NWh9KlWSqn+9ka3bEa\n177qJhbVbLvuuhsnXMNEBKLbxGwYR7W7hK1lN+FZ2yNYa8+z8Z+8C8DKQ/upnTyPUYru1ATdzRuQ\nxhLOLvTq0whtMIEiH61SujDrfBVZ3vNwCCmJm23aYeAKmmkD5JgwcMsa4wimsWgpEEohsxQw5ML5\nZISQ/Cg/wtfDHyKspmnKVGSHUdHkO9lnCNIUHYXIPCestwk6KZ3xGhaJ1Jp4YaVXjTeeW8SWShih\nEN0uwliS2UXGXnsPPT7C8qFdBPPLxL62TmPvNnJtIHImahuGmGaHIM1QWY6OEuJzVxCppnloJ0Yp\nZJahtMGuNInqTfLxGqrVRmhNVG+5eiiTo6SVBJn6LJ5W09dYgXjWFXyrnL1C6dxlFj97mHxsBLm4\n0iMOJgyQrTal2QXyaong4uwtswhL5y6Tjex3FZhx6kw2PoJou3PM9aPq3xTFS3XCpTo6icirJVdH\nKMvJamVMqG64nSGG+JkwVFjuTwzjwXeO9RSQsN5AZvmqlOubhdfupn9ovdCe1Jry2X436CITKWh3\neplLbpsp0fwyrR2bnGLkx63jmPDqPEtHD5LXSmSjNXQUEC27hoyiqMsiBTpJqJy/jLk6T3dqAl0u\nEV+apTbQsHG982zp6MEeaVNkfTVocoxwZdmpJSMVdLnkwketLhNvnvBeCa80AEJJgm6ODEOCVheV\ntbBRSBYFLioiJXkgEeRsayzxqx+9xK9/9Apj3QYfbNzJa1sP8f1dj3FubJq/zJ7m6eB9NnGNGTPJ\n3+VHuZRPEOUZQkpkJyXspkT1tmvMFxdeJTDlmHCpwei5GWye09o2RT5SJWh2qH1wlni5gb08B0Kg\nw6CnclVPXaS106XsV85cIhur0d04TrBUJ5lbQi2uoMdGyKslKifOocdqrnt4vcnk2x9RO3+VpaMH\nMbGrYtvzgrQ7RGlG6co1dLXi0ue1YfQn7zhz9gBsHDtfS/G95tqFIj2Jvd2KvsVvo354D61dW1Ct\nNuWPLqBH3fdYPntp1XkBEM8tkY1WMUmM6jiypeMIkwzDQkN8MhiGhIb4pcKNqusKo1dN+jcKr91N\n/9CNQnuDGUGDmUhrPSzCaMIiROMVkPDqPB2vAgX1Fu0tGzFxTF7KCdtOzhe5xlRKPWJkqmHvjv12\nJpm8ViaoN1e9Fs8uuu6/SYTqpkTLDWy7S3xtibDVIWmnyNlFlg/uQGQambnGeyKOiOotCBW6UkIK\nS6ndxkaWjZ0Vnj//Ks+ffZ3HLp9atb29C5f5jRMv88/4Pzg1sYW/3/MZ/n7Po/zbyYfohiW0KCFN\nBxNITCDRtYSom6JCQWmpjhivkUchNooozy8xevIScZpjc01y+oozwQLWm2GF1pQvzrJyZA9aCGSa\nIawlXGwQNprkI1XClSYjb59yx9AbYRkkGOvUoBwMu5UuzvTOgSKVPc8NpZsoJLKTkicxZsDkraPA\nqT1xcEdlD+KlOvHLx+m+f7rns0pucl6Uzl2m8dU1YSHpzOrDsNAQnwiGhGWIX2bcaXjtbvqHbmfb\nq1ShaugNtsI1QGx1XZrwwPKD6gdA0OyAEOS1ivOM+LtgtKH2/unbuwteUwslaLhJUKW6dwcvraV8\n+jLZ5KgLQ7RToqU6IlBUri0jkoTEgLhwjea2KfJaGWUMlWYDqapkcUiYp0zmizx/5nV+5ezrPHql\nT1I6Qcj3DzzCtx/8HOdGt3Jo7gxPn3yHL548zt6Fy+xduMx/9NrfUI8SXtz7AN/f+RDH9jzBfGXc\nVfkVAZ3xCjaGoKsJ8owNZy4Td7rIdoYQEjtSdQX2oN/o0Vd5Jc9J2iniows0t2xwCky9yeSbJ4iW\n6gMF51wRPWvWFKcrCsytes3e/BxYo6ash3huCZnl5LVyz0wuc4NsNz522YPbVW/jpTrB0go2jnvb\nLs26zLp7NWNxiPsY95HpVtzLFfJHxIT9vPjKpz2MIX5O6GUJVUsEjXuryrBLj+4X6ctLCa2tU9g4\nJFhuOFXDWkZfvT68cB3WTrA+JTedqLHywD5nUs606/hbjhl5/wwiCGht3UheqxKmOeWr80Q+XGEr\nrjuvrjqDaDoa0h1TbGjXeXruQ7724Ss8cvV0b3PtMOTYIwf4/lNH+Pu9j2NlCZ1FBDInzyJkuY2W\nKUc/PM+TPz3Blz98kwOXZlYN+fiW3Rzb/TB/v+dR3pvchxWKUrNB2GlRXnGKU9jQqJYjKKrlCIvo\nuEm+KEtPmmEHyIvbEb9fRZl+WN0rCfopx4NNJgv1ZS0+xjVu0AReEOjGvh2Uz1wibPWrSltcGfwN\nL715x9u4GYqQ1qDi6PxX+Q2r3g7xi4FX7PdYsQs/NxdssnW73fGf/tEdfeaj/+aPXrfWfvYTGtIN\nMVRYhrhncC/7h9aGrIJ2h+TaInmtTLhUv7UBc5CkiMIcK1Y9j+ttRt4/Q3vnFvRolaDVoXb6MnGq\nESIgOX8N4mXXeyYIyMcrAGSjzlfRHVNsai7wzNzbfOXN4zxyqa9OtcOI7x15iO9/aS8vPbmLDZtb\n7KrM8wRvsCtxfUhDoRGXApJTIUlTs7Q34UdP7uTfbdxPcDrnqVdP8fj3r/CFjz7g6OUzHL18hn/6\n0r9lpjrKsX1HeWnXHl7eeYBGxRGnqC6Jms4bFNbdpUa1CwLjiUs7XUVewIeL8KSmKJW/5tH6rAYh\n7AB5WUd9WXvsb5O8rKfQlM9cRg6W7ueTK3twP2YsDnEf497VLVZhqLAMMcRtYL077rW+mFW4gYoC\nIIpaI56wFM9F4O8fwgAReXNn4iZ/W/YqSiUiG3OvdUfd58aDJb56+jhfPfcWD1/pT2itKOSFz+7j\nb596gFPPTdEpheysuoytPaU5Noeum/amwGXnJMuabSebrIQxi6pMlGlsR/L6rs28F7lOze9+8ABR\nU/Pge6d58qcneO6dd9i8tNTbZqoUF3Zu4NKBSY7v3M3/Fx7lgp4karjrTNRwJCJouIk/aOV98uLJ\noOj0w0c2W6O++JCSHSAwPy/15Y7PgZ8R97LiOMQnh09DYdn5H9+ZwvLhH386CsuQsAwxxG3ilhPI\nOipK/6l/T6k+YVlDVETcJylF/Q9TdUQlq7n30rGA9rhkS32eL868za+eOH4dSfnBZ/bz4+f38Orn\ndvNw6TJH5q+xK19gpRTT2WapjyRsCpaZUA0AasKRgpH3c2Rm6YQBLeu2l3UUeSh5Ze92AE7Ob+Pk\nqYNkCppWYjLF5o+W+cq5l/nSTz7gyMkrq+LhixsqfPfAA3x7x2d4ffseZNMdl9BtmqhhCJuevDQd\nGZGewMhO2iMxPfVlHQJjr1Nfricwq8iLf+063Ma1cEgihvikMSQsN8YwJDTEELeJ60JWRUO9Qdwg\n3COUJzBh2FdSotC9V6goSUFSYvKa96OMuWU7Y4rHWqf4+sxLPPTyWaYvL/c22Ywjvv+ZA7z8lT38\n+PE9TG9ssKs8z1fqJ/jyxdN0I0VS6TKR1Rk/22Z2f0w4bqhJN8Enfh+Sdo6uCAIyIuveSxNJ1LLs\nj5wvZ+P0Cp/JzyA+KhM2LPVyxAdPj/L2b29FfiR5a34n1bc67Ds+y663rzE+1+R35l7ld370KitJ\nwov7DvKDg4d4aesRFio10hVF1HDHJmr48FHD7XPQDPvkZa36UhCYIEOsUV964SNPQKzWLnQE64eP\n1gsdDXx+EPdy2HKIIT427l3dYhWGhGWIIW4X63U4htUkZS1BKVSUsAj3RAMExakYxptmeyRlNKQz\n7j63QS3w/EfH+Y1XXufg5Su9TaaR4uLRCf7quUd469e2kyYBO8sLPMZFdsTzbA0X2X1xhdFyCx1J\nSiKDABJl2D7TQm+ICF3/YKTfr6AiCVPIYwhcJz6SVGOqsClwKsLUYoOpa10aUxH1LTFhZnisrnh/\nwyQ7aLCyLWZ5c5Wf/mqVH7YPMfJukwd/epnSex32XbjGr79znF9/5zhGCI7v3M6xfUd4cfth3tu0\njaju9jmqexWmqVaRFwDVdo+yPUBgCg9MWBAX/7wgLplYRV7cVzmovtw978sQQ9x3uI+yhIaEZYgh\n7jFsbs7zzKV3+OrZ4xxeuNh7PY0C3ntgK+8+voUPH9jEhmoTq0LSZP2fcamVo6urSZaJIGha9DrL\nZ1sU8YncZUJFIFJQqaW5q19hdfRKRh4L8lCCFWSRItMB+88uUG5ots2vcC2scLVaZSVIWNxf4zuH\nHuLPRh5n68wiX3jpDF8+foIvvHeaR8+e59Gz5/nP+VtmqyO8sOMwL+w6whtj+2iFyV04kkMMMcQv\nEoaEZYghbge3keUjlFxXUYG+P8UmUU9RGUxD3tqc4+ml1/jK+eMcWrjU21Qjjvneg0cIjlpefXA3\n4bhmImkxTZ0NUYPRTpdwzKURb/Em2ilVZ0K1qNRSkkxjYkHkhxp1BbYqCIRCeoVF+X3T4wp7SBFe\nzgkaGlMRtHcpkjHFhHXqRaWdklcEAYYyLjyjhWDqcoeuChhZSdkk6hxcVpycHGchqvGjHds4ElyF\nKTi29yDHOEhrPuCJt87whR+f4cs/PcHmpWV++71X+O33XiFVild37OOl7Yf50YbDXBrZ0A8XeaWl\n8LuoVthTWwqlped7KZQWNZht5MnXQOr0TcNFxeu3ES4aYoj7FvfJ6TwkLEMMsR7W8aasJSjrZvkU\nvpTYkRE8UTFFlk8t7qUhb1SLPHfhLb78wXEOz60hKY8e4lufe4g3n9lKNw75J40fszNfpFTJGA9d\nNdwpvUI+KnkocS0NJqV7rMmMsgC1zVI+YTECglhCCiqFbHdIOEBYWMqRlzKCpsZWFGZriB514y1d\n6BC93oWGwVQFeQJhJghiS+hJTDKTE2eG0Bh0GURmKaUZB+bmOfZ4hU3TywSZIwNXkxEAZis1ZneM\n8qdffob/vvErHDwzwxd+dIbn3vyQR09e4OkzJ3j6zAng33B6cooXdhzhh7sO887UbrTs+16CZkDY\n8OTFE5cegfHF6kQ365OXwu/Sq/miVtd9gesIDKi+afcO/C5DDHHf4D45fYeEZYghCtwsy0epm6Yh\nAy4VeZ00ZIBsxJOUYJFn59/h+VNvcmj+cm/99Tjmu48e5luPP8Trz2xn40ZHSo5W/TKZ5uDZWSKZ\nUgq6BJllRHeZ2xMyErirTdlPtIkQhELCuIJDlvCyRrUMtqywu0MCQL2bQtOAANHS2JEAKgEitcgT\nGeKghMsp4ZtdLBYbCUQLgkWDGQO1QZFHFpFC0jCggACsAhMKtLYE2rC/M08p6jDpM5KmQ2cWnolG\nAZhNasyWazAF33r4Yb7Fw+hL8NRPT/Hkj0/z7Fsn2TM/y575WX7/jWPU44QX9xzkpW1HeHHXIeq1\nao+8FH6XsOX9Ls0Bv8sgeYHVBGaQvMB1BAZjEbJPXoCbE5gheRniPoJg6GEZYoh7HzerlTKQhgye\npNwkDRnAluJ105C31a/xzMKPef70cQ4u9EnKSinmu0eP8N0vHuTFR/YyOeUKkD1SvcyOkquXsjOe\nA1ytlCzJ2TzToNrOyMsCs1cwMmoo+/0IhTetLjmSIpoaKgqzNQIE8lIGb7WRdYOZCJCjAVxIoWsQ\nVTBCQOzWpT5Kkae7rut8rBAGZNNgAHVNgxAEMZjJAKoa0TJIVRxW1/xQCMtEp0OuLGPS7VtdueMz\nGRQEpspcVAMceQG4UhrlzL4pXv2He/hny/+AR96/wOd/dJbn3jjBgUuzfO3943ztfWfcfXvzdl7Y\neYQf7j7CqU1bQIjrso3CZohq+dBcYdYtCEya9U27a1WYQQJjfLhIG39+rENgbqS+FBgSmSHuVXwC\np6YQ4teA/xn3I/nfrLX//AbL/TbwV8Dj1trXbrbOIWEZ4pcHHyfLJ/QhnsFwzzppyOCyfIo05Cmx\nwFfPHucrb73JwWv97J6VJOH7nz3At598kA+fnSaLAnbUFnmQGXaVXcXZHfE8mwJXjG1Kueycmkxh\nEuRGMCJCAiU/VkWfsMjzXYK3U6wGSgJyCOY0YLEjAbJpoGmQyymMa8gsxBKWNLLsJ+hYYq90ILeI\nRAA+yybzIlMgEBtCRGqgJiEA1QGTWiiBEAKRC/KyJapYJqSm49OkyyL3++PK24/J1gB5cerLptg9\nXk1GmSmN0NkU85dPfJa/5LPEp1Ke/clHPPHKGb7w3hmOXj7P0cvn+cOXnXH32P7DvLTtCC/vOEDX\nk8aooYjWZht5FUa2stXkBdYlMH2iUqgu6xGYNepLgaEKM8S9jE8gS0gIoYB/CTwPXAR+IoT4prX2\nvTXL1YB/CrxyO+sdEpYhfrGxHkn5OKbZJL5pGjLAtJzni1ff4vmPjnNobkBJSRK+99mDfPuJh3j/\n2Wm2bHAk5LPlC4AjKABbvWl2o1phTDojbVm4CbLixxoiXbiHvqIy6EUJ3k4BgSgL0CAWjSugFklE\nFVg0EAKRcCGhzEJT0+u2OKZACQQCEgnauuVTAxIwYGOJiBW2rQneTjETEbbVQTRBNMEkFkKBGA2Q\n20LKUhH6STvpPaZ+//JV5AXoFbTbGNTZFBfqi/O+zDxU452HtvG93z1C0s7Y++MZnnjpLF964wSb\nFlf4+huv8PU3XqGrFK/u2scP9h/mpS0PMFObAOinTnsVJmiF/dBR0eeos1qFIc3A921a1W2a1QSm\nKFh3t2q+DDHEzw13//T7HHDSWnsaQAjxr4HfAt5bs9x/B/wL4L+8nZUOCcsQv5i4DdPsurVSinBP\n4kjJIEkZzOoB17tn5/IsX5x9i+dPHufA/ICSUor57mcO88Ov7OfHj+5m06QjKY9XLrA9ceGewawe\ngAnlJuyKyCn7oSY9cuJrpiAJljXykkY2M2xFwNYIxgLEpRwMiLJ0/EPiCMliDoGEhnavCeEeU+vI\nTGahIiE3cEk70rIxcMtfyQDjiIvF3Y1NB1hANt1bIhJQDRC5htQiNNgRiZSC+LJFY1FjPkzjJ/NB\nAjNIXmBAfVGtHnmZ9u0DNkeeuBTm3d+s8Wdffoo/s08y/k6TZ1/9iCdfOcPRkxd55tQJnjnljLun\nNkxxbP8RXtx+hDe27CZtue85qqtVoSPo9zuSXoURnayvvhQkJveXzgECIwrPi69hs6rfEQxrvgxx\n7+Lun3JbgQsDzy8Cnx9cQAjxGLDdWvstIcSQsAzxS4TbqTh7I9PsYGbPOlk94BoMdv2ku4lZfuXk\ncb766nEOXOt3Zl4pJ3z/iQP83VOHOf/sJHmk2FOd47P0Scr2cIGNwQqwOqsH6JGUsDDNAqEPMxSp\nx3LJEJzIsZGAivQm2S4cktCyUPKqSCAcIWloMEAoHDHRBqx00YvUuAuVxhGXrg8PlSQcKMEHbdgM\nLPh1CGB7CJMuJEXHmW3F1dzNsZEErREZ2LKCyQCVWoIPc/KDIXYsQPrJWPV8N/Y69aXi06XLJmdE\nOKVpzJO5Iny0wR/D6XCEzT6EdOXzo7z6+b38zX/4CKNLLQ68MMMzr57kidfPsHdulr1zs/zBy8eo\nJwkv7j3IsQNHeHnTIRq1qhtLr+Lu6vBR0Mr6hep84boegSmq66bZdd2m12vYOFRfhrgX8TFCQhuE\nEIN+kz+11v7pbW9PCAn8T8B/cCcbHRKWIX6xsJaoDJhm183qgVWm2UJFKbJ6uuNu2S3M8tyFt/iV\nE6tJynI54fufP8h3njrMuWc3sHXcTZ6fS84BsC1y4Z6iweCkag4QlH5WD7CKpPQISlGN1odsxKUU\nEUtE7Ce6BHdHfzGFsoRcOoIB0PKPsXRhHbxHx1hIgS5OaZE44rKcez9LDkvaEZSuceSnptzfywa6\nbUdulv36Q9G/4Dl+gbycYkYUlBRgUJc0ZiwqOCPG74+0dhV5Acj8xB1KQ4b7u+xTqAsCU6gwk0GD\n6dB1rZ6KHImZjUdgDC5unuT//vok/0vjOTa/tszTr57kyR+fZt+la3zt3eN87V1n3H1r63aOHTjC\ni9uO8P7U1oGw0WDF3cL7EvlH73sZDB8VjRmLejDrEZj1uk3DUH0Z4tPFnZ9Wc7foJXQJ2D7wfJt/\nrUANeBA4Jtz5vQn4phDiH97MeDskLEP8QsP/GBBBgCiX3IsDBAVWNxgsTLPtccnuxas8d+ktfvXE\ncfbPDZCUSsL3PneIV5/fxeuP7WSbJymPl86vyuoBrmswWJGmR1Bi70G5TkVB9gjKWsiWD98ALGRw\nNXNEQgl4uORUpAnl/Cm+IzIV5YhIrqFtnKIicSpLhiMmhUeleEy8IbdjcIVcrHt9RcO8/0wCdHDk\nBSDCXfgCIBXI2RyzU0EkXBbRqn0q2gKsJi+DxyEUtk9e/BU1UZ7sDRCYwvsyplwq+EbfRmBz5FOo\nkxFmnhvhB88d4i87jzN9eZlDP7jK06+e5LG3LvDIxfM8cvE8/xl/y9XREX647zDHDhzmJ9MHaUUx\n0YoYUF9WZyCpVlEDJkK01zfvriIwH1d9KV4fqi9D3G34UO9dxk+A/UKI3Tii8rvAP+pt0tplYEPx\nXAhxDPgvhllCQ/xyolfcbaDIm1dbbMURl3SjuzPvNRgclWy1s/zqh2/y/AvH2T8701vdUqXES0/v\n5fvPHGTm2RF0qNhVnudxzvdMs5uCpdVZPXBdg8GbmmY9Bid2taYeDGXpQj3NHM51nTclFC5k80EH\ndoSwYJxaggBfv46F3BGQEHdxyuhfpIT/2/h/EmgYyD1JEdYv77OFlF+mg/u7qPOf49av/ArrxvUp\nSi2UFQiJ9pPxjcgL3J76kvQ8PlmPvBTHvCAwkz3z7grTofe+xCMwCh/u3cSH/3gT/+NCmd0/usZT\nr57iyVdOs2lhha+//gpff90Zd1/Zv5cf7D3CS1uPcGF8A+mK2/Daho1BIyAo6r+0VlfcHWzY2DPr\nrtew8Sbqi3sYho+G+GRwt7OErLW5EOIPge/grhJ/Zq19VwjxJ8Br1tpvfpz1DgnLEEMAY90G//zf\n/Z88OHe+99piqcx3HnuAbz32MK9/YSsTG1wtkR3eLPupYFvkvCWXUkcMJKAFjEinjnyUwqGST/rJ\nYcVAyU9uFmjRJzEFaTHXb4amdVcHIdy6tHUqixcP0AP/ChRGX2292mKd+tM1sLt0N4/CXUO3FPLC\nF/bzwhf2s1QvcejsVZ750Sm+/NYJHjl9gWc/+JBnP/gQ+Decmpjixe1HeGHnYd6t7UIXhWeGGOJ+\nxyfAc6213wa+vea1P77Bsl+6nXUOCcsQvxxQqqe22MA9msg9dsYFf/Kt/4sH586zkiR867GH+dtn\nD/PyA3sY3+ju1h8cucrOsjPOrpeGDDAmu+umIQOrVJWbKSqwjqoyiLEAtoTwviNPhNLVQomlC9d0\nDJzuOA9KEfrxN/gutQf3+qDCshYFgclwqgwDz28GjVNZxpUbR+LVn90lN25AXUidEtQyUJbogxFy\nx9pGh7cOF2k/+BBL4m8PO0WrAP8d9FWuds+0Wxie5yNntN0Ur3C15NWX8gh2WvHXDz/KX/MoXLI8\n+8ZHPP3KKb749kfsXZhl78Isv3/8GCtxwku7D/HSlsO8tPMQzWqFsLk62yhoFK0CnO9FdtK+2lL4\nXYKBcFG2vml3leJys3CRW2jgtaHaMsTtYVjpdoghfl4YuEj3zLa97KCBR7WGsITuvUNLF3hs5jTz\nlSr/4H/4T5idGOHBrZc5wlV2Vxw52Z4s3DQNGVyWz3ppyHBzf8pNCcpaLOVwOXO+FGvdfrZ9qk/L\nT1oruh+XtjjSUZVuOYtTQoow0N2GxpGVULp0620u5ZqlHN5qwpnUxXOqEjKLer3twnc7kjsKF4W9\nzVmkl3l6Ppc1BKYi8uvCRYW3aFI1mAodiZnzNV9myo7AXC3XOLF/My/85gH+6+Xf4tETF3jqR6f5\n8vET7L88y9c+eJOvffBmv+Lu9gd4YedhTk/5irvVwu/ixhc0Q2SrT16gHzYizVaTF1iXwAzDRUN8\nIrhPTo0hYRniFxuFh0VIbOA9LJ64aK+wPHfuHQD+5rFHWNxUJiSn7CePXYkjLEeSi9elIcc9H0U/\ny2c9A617vIkv5U5wMXVqyuYAzqfuF2wMzNEPzwyuXuOWaZu+QiJYPwz0s8AXlcMAdQs1DfXcha+2\nhHCm6/4Vqk3LwETgPvdqE67mqLLsExxA27VG3bU7BwiD8pexQnVZS2AyYYkHyAtA2X+HI7IzUKiu\nSJV2Zt1p3+/oWqnG1UqNxpYSf/75J/hznqB8qssXX/+Qp185xRPvn+5X3H3l/2WmOsIP9h3hpS1H\neGX7ftJqv+Ju0FxTcXegYeOg1wVYn8AU5MWTj/UaNg7VlyHuCJ+M6fYTwZCwDPGLgbXNCovsoOJR\nSWwREgodqSgUlufOOMLyncceIIl8Nk/g0mdjP7GFQveIyqjsExRYneWzHkFx7/0MJKXAkjfauoHB\ndABzGto4ojAKLOIuPmvtFTnu155z69DOx8EgAbJAHWilUBN+zD6VWuE9McB87rwuSJf5lFpHcA65\nENLgMVtffQGJwhRXW1+wbT0CU5CXyE/s8Trqy4hZU3F3oN9RUXH3auKbNlaqvPHwTr7zjQdJ2ikH\nXp7hqZdP8dzxD13F3Td/zNff/DGpUry6Yx/H9h3hR5uPMFtU3C2yjQbCR6o90KwResRlVcPGol1A\nQVwyfzwGCMww22iIO0EhuN4PGBKWIX6xsJYYDNZjCQqi4hWWEHYuz7JnYZalUplXDu9kOnQ9fEqq\nSEN2BCFCr7237xGVfrbP9T/7u0JUwJGVD9r9DBztDbAjyoVYGsZl7ch+RdpeRhB4A61/rSAsn+Qc\nZXHkqOPHWhhywVfa9ePXQGxdRd0xn359Me2pLAVudBwHVRjpv4/1CEzf82JWPUbCEtvMXrjDAAAg\nAElEQVQik8v5gnrhI9vPNipSpdeGj676irtXf3OMf/XlL/Gv7BfZ+M4KX3ztI5555RRHT1/k6TMn\nePrMCeD/4dTkFMf2uayjNzcPVNxtyF6tl6BZpEr31RcAuun13aYDr74MNmxc0216LYEBNew2PcRq\n3Cdf+ZCwDPGLiYFQUPG8510JvHEzEjxz5V0Ajh04gikJyqGbCKrKEZVE9BUWVXCfm9yP3DWCshZF\nKGiDcLVXQlxBtznvni0rV8gtoG+yVbjnTaDkXy/Ul6LC7SeNNn2SVISiBkmVwZl/FnOYyWBMQu32\nL0s3U2EGCcx1KdOFGRqzirwAfQLjHyuD/Y58rZciZXpD6IjMpmiF2ZInMU+M8OITB/jrf/wZRpda\nPPjCJZ597SOe/Olp9s7Psnd+lj/gGCtJwku7D/KDfUd4edNhGjWXZt8rWFe0DCiK1rXDVeQFuJ7A\n5Pn63abpExiMXb/btPtjqL4Mcc9iSFiGuH9xo+7Lg+/1+gVJrK/DUmQHmRC+eMGFg/7uwQdQ/397\n7x4k13med/7ec/qc6bkCxH1A4kZcZwCCAAlChHjBRbSXUiTKTsW05MSVLcmlzW5SpTip2rVXFe9u\ndr2ljb2JU5vURtzE2U3isuU4lq2SSPEiEQRAECRBArzifiXuBEhcBzPd0/3tH9/3nXP6MhdgBjPT\ng/fHmurpnkb36QFx+un3fd7njUs0O99Ai/uUHTnPQyTlpEAQuMcOB3v+0aanbNsmEsDUMpzqsyba\nIlaMNIe2otFXtm8wPk9FBGJjE2i9QKh+/2l1xt1sW8d7UoZiOOZd/2vyx5TtmYfYEerY2Gj/62Uw\n/baiNPXWTk/VYnG4Jt6seMle5jMCpiUjXiCTtOuEy6zcVWZHdvKoM/YLG9thGhydO5ujvz6bP7z2\ny8x7+zM27j7E428dYcmZT/nyvvf48j6XuDt3PluXdLPj3m4OzJxbk/USXc+l+46ceVf8yoDsxulk\n31Gd6gtYAVN32zQMWX3xqIiZVOiUkKKMITXTQXUqLCTjzPY+9xSv8cD5k/TmcmxduYwoLtLmvCst\n1RUWyoktZLAKy53DwCcFO4Fzrd8KFf/m3wucLdhKRgm7ibk9gAV5ONRjfQ79g5yR+k1tE3ug675C\nE2auD+WJybnAOb8U2h9K4K8bKAiYkt1zNC1Xty10qwzHAwPBgNWXMr6lVKbk1yg44eIFTK/7/6M9\n6E0D65J9R66NFNvLC/l2zn+pg5e+tIr/eHMDnWcus2rbGZ58+xAPf3CCNaft1z/kBc51dLBtcTdb\nl3aze9ZSbkY2cbc6adeH1XkTr9wsInHVvqNCbRUmFSrptmmwAmbA6otHqzCTjwb561PBojQ+mTem\nemZbAJMLM94V+7NNJz8kwLBjxVJudMRMiW7SmrOfTr1QiV2mRyhmwIrKQDH6o8blfjvl01e2lRZf\nLRGsaTVbPcnh/C0GTvTCZTP0GHM/tQFw1e2i7J9twcb1h8a2mwZ77DzWTJttAWWfx+ACVwz0C8wI\nYUrOrhYYRW63+mJvDRLxUm/btL0s1G6bDiqzX7Lm3Qv5DrgHPlxyLx9+616uXMqz5PULPLH7MI+9\ndYQ5l6/y7J5dPLtnF325HLsWL2b7om5e7+zm1NTpRNd84m5YcZm7ERE6ERP4PUf1VgYk5l0nVHwC\nbzBY9cWiI9STkAb56xqRYBGRacAPgYXAceBZY0xNDKiIlIAP3NWTxphnRvK8ijIk1TksYYCJKvNX\nNh3100GrMJEhHxdpDt2m4KC6wmIy3ojKjBXPHfWvdORs9spHLjAuwBpwvaHVCxgf3uZ3AmXzWAai\nWpwMJECSJFtsINyUHAQu/6U6iM4bfCEVUoE7tmpDcNnYlQNFYFbkovzv0O/SMdzqCwy97wisgMmK\nF6BWwIQ9mRFqv+/ItpHO5zs4+0wHf/nMQ/ybnidZfPhTHnjtNI/vPsyqg2fZeOAAGw9Y4+6h2bN4\nbfFKti7t4qPZi+gPQwoZAZN4X3z76EaVgOktpuIlaR+5t4L+/krxAqmAca9dA+wmGebuaQn9DvBz\nY8z3ReR33PX/oc79bhpj1ozwuRRlYKp3B/nrfn9QGFLOpRWW1kIvjx4/REmEV9Ytg6YSLVExNdtm\nxpnBaoPxaQVR6V/JB276xZ1hvNjwrRn/Lzq7F2igYkWQuW9WpAxW3Aiw8f5h2VZx5ubgmsC1Ulqp\nMdj4/zmRDblrwj5BX+asWMRWh8pYM3AzcE9gf9FjHOU/oupLRsAMVn0Bu7DRb5v2ybtewMzI7jvK\nd8B6ePPBxbzJYnrPhDzy5gke3PEJj75zjKXnL7D0/AV+a+erXM3n2bZiOdsWrWTbkhVc72gjduIl\nXdjos1+s7yXXU0zMu3Kzqn1U7E9bSE64JALGCRcNsJuENMhfyUgFy9eBTe77/w/YSn3BoigTig2n\n9xOXS+yev4jPOtrG92Au99sqiourz4anAenCwybnTSmW3NSNSQUC1BpaYXDx4YWKJ+tTqUfWr1IC\negwcdxNLATA9Zysv4HwxYkeuI7HH31v1eAFpxSYWaAtrovwVuHJPC6883cWfPvEINy5HPHzgJBt3\nHWbL+/tZcu5Tvrr3Pb669z3KCO93zuf1e7vZPr+LY02dgxvTFcVxt1RYZhtjzrrvzwGzB7hfXkR2\nYz+Dfd8Y81cjfF5FqY8/QSf5K+4TXy5Ikm3LMWw8ZdtBr6xcSRjbd/XmXJGWsNLDEon/tD0K00H1\nhAnYfJWm+uFpQLrwEGBmDm6W7KfXarNrtQAZiGw1xZto600P1bt/Nf3uq11gWgjT3WsyJvWhFI2d\nROor2GqKZP4s2N/FvTGsbx/Gwd956lVcBmsXgZs2GqRdBLbiUnQK0m+YzlZcUrOu9bz4dtGFJld5\nae7gbGsHl+5t57lHH+c5Hqfj0E027TnIxrcP8eiBo6w5e4I1Z0/w93e/wLm2KWy7v4udnV28ee9S\nCu0ucfdamEnatbeFPc7n0ltMJo6S1QBVFZfsZunBNkxru6iBaJC/hiEFi4i8Asyp86PvZa8YY4zI\ngDptgTHmtIjcD/xCRD4wxhwZ4Pm+A3wHIE/LUIen3I1UCQYJpHY6yG/SzaTbmpw34pZ4/JN9ALy0\n+gFykYtrzxWScebEbOv+JY94L68PfqsWJgH2tiZ33D7vPzslMzVnBcypgp34mZ+3ouV4AfLG3nbT\nv1HUee5sW6iZ2rTboU5WwzmZFQ2cKNjx6pYw9aHMycPuG/bnTWIvvYclwI4yL20CM3ErAbc9bVRH\nwBSNH512U0cuoLCiXeSnjcqVfpdZ8VU685X7js62drBrzWJ+8uurab5ZoHvnWZ5801Zf5ly5wrPv\n7+LZ961x9+37FvPa4m52zu7iokvcjW5UTh2FPf2JaVe856Vq2sgUium6gCrhkhUw2i5qHCZNhcUY\n89RAPxOR8yLSaYw5KyKdwIUBHuO0uzwqIluBtUBdwWKMeQ54DqBDpjXIr1EZF+qYXKWqwuL3B5Vz\nASU3zrzu/CHaC73s75zD0Xun0xbb3TGtuUISxV9dYQlFajwstzQd5IPfmgLoKdltyj1l+/3iplSw\ngG2PVE/JTM1Vtkk+7LEtmaKBK/0MSkA6iuwnikIq/S8BtebbW6GAbQOdL8DcptSH4o9553UrSpqM\nfe44tM8ZiR03jyauYMkyUr9LdfUlK2Cy4gWg1f0/mAiY8DqXnHiZ7RJ3Z2eqLwCfPDOdP3pqPn9k\nNtP5/hU2vXuQjW8d5sHjp3j8+AEeP+4Td2fz2uJudnR28d6chRTarEiJb4TkkpFpl7jbU2fayIsX\n72/xoiYrXLT60hgMZcqfQIy0JfRj4O8C33eXf119BxG5B+gxxvSJyAzgMeCfjfB5FaWCaqEivrLi\nL3NBujtov20HvbR2JSYuk3cVltawkETx+8A4X2HJviFVTwcNC2+c7Sm5pFqBZrFjwWeKcK/YygQM\nb0qmp2zHi4/12ykbX0XxI8z++xAbeX/T7Rzy4iQ76uy/Hwl+ZPlSCRZU+VDm5+F8v90d1Fe2I9rN\nYjc6w5ibbEeT0Zw2KrvbfGCdF81ewLQHBdoD2xqcXrOw0QqWi/k2zjnxcn5DB7/Y0M0Pv/UI91y+\nweptp9n0zkG++N4RFl86z+JL5/kWr3Il38zrC5ezbXE3u2Ytp6fNJu5GblFjdK0y8yXsKSYJu8nC\nxsj+zBQzCxvrbJuGYVRf/O1afRk7GuRXO1LB8n3gz0Xk28AJ4FkAEVkH/D1jzG8BXcAPRMTPLHzf\nGPPxCJ9XUVIkGHA6KLs/qBQLYspsPuzGmdd1QVxO4vibw0JFFL+9dA+XSUStZljjzN44e7nkqgpi\nKxJTQlsludgP89x9hvUGbuDzshUkgaThbznsY5fcGSiHDZtzf6RuJosfO85WXW6F7PuKMXCmAId7\n7Wtekbcj2TecWGkKbP35WhkiAwtiWDY5TLYjrb6UE7+U875QKWB6TX8madftO3LVFz91NDPXkuw7\n8t6XT1vaYTrsn9vJ/m908r9d/TKL377IpncO8sTbh1ly7lO+sn8vX9m/l7II781dwLbFXezo7Obg\n9LnEybbpdFza7zsKXOJu0Fu1KqBQrL9tGoasvtgLbR+NFcIkagkNhjHmEvClOrfvBn7Lfb8TeGAk\nz6MoQzKA2TbZHxQJpQi6Pz3F7GtXOdsxhY+XziGQEi2RPdm2hX3JOHNMara1DzvCEoQ3zva46kK/\na+fMieyJ90K/bQO1BINPyXjj7pmirdaETvxEzuRqsGIlJ/axekv2eUqklRVIxYuvuEQC7cClEZy5\nytiWU9GkPp3dN1wYXARtTrCVQ5iGNelOEKPtneBWzbtevPj4muy2aXu7oVhn2zRAS5C2j6ZVVV8+\ncysDZsd20/T55g7Ofamdv/7SGv6fnie498znrN1+ko3vHGLdRydYe/o4a08f57u8wNkpU9i+qIut\nS1byzoyl9EYx8fUgE1RXue8ocO2joK+YVl98+yg3SPUls20aNOtlzGmQX1/jf6xR7h7qmW0hFSnZ\n+2TMtmArLHY6yC47fGXlSnJNbmLDpdu2hH213pXM841od5A3zl69blsiLaEdA24JbeVhQROsGsJk\nnjXuRgJtAVwzrsUSwBSBz01qsC2WrCE3j92aXCSdBvKVlhBoE7jHvU1+XhjeDqFqvPjJYbNiwI40\nA5zphwdiW/3yba/sFNFdwlDto8G2TYMVMFnxAtmFjamA8dWXjnJl4u40N4U0O7rCXL9tunkKTIfd\nSxex+1uLuHapiRVvnGPj7oM8+fZhOq9c4dm9u3h2r0vcvX8J2xZ2sXPOSs50TMtkvVStDLgREbqM\nlyTzpTczfeSTdotV3pei+30YM+C2aa2+jD7SIL8vFSzK5CCobAWZ6gpLLJRiYfMxG7j80ppVxHE6\nHQSQl/7Eu+LL8l6khBVvLLcpXKbmYH1bKjpisWJluB6OrHG3KYCS2FC2EoCBS2X78TzEPnYvttbb\nS9ou8pucs0a7GwZuFqwIGkpD1BtxrjbtFYx9/oKx3pmest2DNCN3az6dSUy9NuJg26YBkHKFeIHa\nhY2xmHTbtFi/S9I+Mql5N5k8cu2jOa59dKG5nbNfm8qffW09/9f1LSw9coE120/y5O5DrD50ho0H\n97Px4H7gRxyaNZtt93ezdUk3H81eSCkIia45AXMjTKouvn3kR6iDm8WBt02HGQEzwLZpNe+OMneR\n6VZRxp6qk72I1OwQSjYzZ9Jt512/wJLPznOluZmdKxcxNbIn7TZfYQn6Eu9KLLWfgEeF7IjycFpA\nWbxxF6yR9lwxXSwYCnSE9vubxk7kFMuVRtyQ2uRbIV2aWBjGWctPE9VL0PVi5lLR/rwPK5jyTpid\nLsDcyE4FNbDR9k4xlAcmIKxTfQndz+yfjShXiBcgFTCZjdPpuoAbQGbrdNTGnNh5YJrbYSZsW7Oc\nbSyncDpg/dvHeXjHCTbsOcrSC+dZeuE83971Kleam9m+dDnbF3azbbFP3PXVF3uZbR9VV1/qCpjB\ntk1jBUx19aVmYaOad4fFXeFhUZRxJRvHn3hXKs226f4g2Ox2B/1i9Qr68wHN3mzrPoHmg2LSEvJv\nHWHyZhGM3u6g6hHl4ZJNvG0JbTrSRX8yN1YMfFoCKcFldwIPsIKhx6S7gLywSMLixJ6xBtu67Cs0\n/j5l7HuD/3QmQBt2EummSUepy1hBND0H18vWq7OgSdNsh8FgHpjq6ktFgF1GvGQvswKmJSNegAoB\nMyuzrBGgM7bto7P5KZxbPJV//yvz+MOrv8yqD0+zZvspnnz7IIvOfMZX39/LV9+3xt298+bz2v12\n2/SxzrkgklZfrgfpvqNk8shVX1yAHX2F2upLPQHjW0kDLmwMK8ULaPWlHg3ya9AzhjI58EIlM8YM\npBuaY2HLITfOvH4F0lSi2ZkA23LpokNvtp2QsSDZxNtYbFVlapgJlTMQl+2odEsA/WXbAooEcs54\n6ysy2egWH+Y22EnL4NYBZK77iaKce44ggKhkn9PH7d8TWk9Lr4F5sa0qDebVGWpNwV3MbQfY1REw\npSSF1/4legHTLkV63Oh0kv+SJPDaiuTFuJ0L+XbYEvDCFx/gBR4gOtLPF948xsM7TrDuwxM8dNJ+\n/fZWa9zduqKLbQu62bVoKdc7mjLVl0rvix+lDntixHtf+jL5L5Am72aqMKlQqRUwWfECQ1RfPCpk\nJiR6JlAag3onluxG5sxWZqicDgLo6L/G2lMnKIQhOx9aTC5KBUtLUmEpELgTeZg8hfOwTISdLEO1\nk/bfhBaBc2UrICSAdpOKln5jT8QlKts5vsVTj+qpIp/xkm0J9WMrNEHZPlZHaP9u2gMnkLCVoaF8\nKwOlAa/Qakw1IxqhJqCMbynZSy9g8qY88LbpjICZHdmwxTlN9vLCqg6OrZrJzr+9hPyNAvNf/4zV\nOz7hid2H6fz8Ct98cxfffHMXvbkcu5YsYduibl5b2s2FDpe4m9k2bS9z6fqAnsoJpAoBU6hfhakQ\nMMOpvnju0iqMtoQUZQKx6fhHBMawc8lSbjQ3jffh3D4DtZOyYqatP20dteWsMfdknxMOdR4zWy2p\nJgQ6xLZ5WoM0Xbe6fVQEAne7KcPsGK74/Bdj3zWH8q1kTcVQf02BMuHpbY15/Ykl/NVDDyJlw7wP\nP2fzngNs3n2INcc/YdP+/Wzavx9e+EsOTZ/D9kVd7JzdxXuzFzKwclbuKCpYFOXOIEFVtSMIEj+L\nj+L3U0J+4eGmE3ac+cXVq4jcdFBbZFtB2Th+XzavNx004fFixreO/CTSgZvWWxJRX7B4fAUF0n0/\nHSEszsOR3nQayRt4fRvJB86VsLuKYieU8mWbfNtjYF4ES/ODC4+sqdhTb02BUsNtJ+6628pJK9RU\nLGu0l7UVl2RUOqzddwRwId/B+Ra396i9g+c3rOY/9DzKtM+v8/Drp9j01kGe+PgQSy+dY+mlc2ni\n7oIVbF/UxZszl9PT7hJ3M4F1AKG7DHqL6b4jv7AxWdToFHh/f7o+oLpdZIwm7oL9J90gL0kFi9I4\n1JkO8pfiW0E1+StCS7GXDZ8coCzCyw910+Sj+J13xbeEIikNOh006hNDd5JQbOIs2LC2ZsAEdnII\n0hZPXmzFpJ9035A35OZdGykWG3B3wv6+KJGKlQjbbjLuOZc12WpMJDZT4754+D6UrKnYc5ePP98O\no73vqJ6AqWkXhZUCZnbuCp2xWxGQdyPTrXbqaO998/j511aQK5ZYuvsCm/ccYNPugyw+f5GvHNjD\nVw7soSTCB3MWJMsaD03rJL5ujblZARPe9Im7Ayxs7CtAv/t/z7eLvIAplZJpq7s+cbdBXoIKFqXx\nqJ7OCaRuFD9AKYL1Zw4Ql0rsXryAT6e3Mje+BEBz6CsrbkMzpZqCtP8Emp0Quu3poLEg6wNZ2GTf\n8M8XrTgpuekdn25rsKFyfZnrRVIh0o9tBxUMTItsS+dUMfW85N1z9mONtVNCO7I8TYYOwatHtal4\n2GsKlMG43cTdevuOwAoYL15aXcmu3dh/S8nG6bAnY9a1VZfO2E0dNXVwtsWl7j7Vzn9+ah3/d89G\n5p3+jId2nGTzuwdY//EJ1pw9zpqzx/kuz3O2YyrbF3Xx2v3dvDtziU3cvRYk6wK83yXnk3a9Yfdm\nlIoXn65byPhdBtk2DXdH4q6gFRZFufNk9wdVTwfl7EmkHAlPnLbtoJcf7kKa0t1BbaGbDgrS/UGh\n9+42UjUlSz0fSF6gz6QVFJ94mwPKAqGx3/eTjj7jLqe5JF4fADcjZ5N1b5bSPzslcBNLI8xXGUlG\njTJshm4fDVx9sX9e6m6bBio2TifixZt1y2n7KGkdZbdNT4c3li3hjW8t4fqnEat2nWHTuwfZ9M4h\nOq9c5tn33uDZ996gN5fjzUVL2D7fVl/Otk9Lsl6iG37qKB2XDt2odE37qNiPKVTtO6ojYO6K6kuD\nHKeeCZTGJTsZ5FtCPjDOeVckLPHY6X0AvPLoCoK4znRQJo4/ea+eSNNBt0I9H8i8GI702X/tJdJ8\nlBxWoDyYh0/67W6iyBlZ+g3EQHPOek/eum4rL00BzHYx/hf77WLFlsBWWDpyIx9Dvt2MGuW2uNXq\nC7islwGqL1kBkxUvAK2S7juaXuV96YzttJFvH51v7uDkrBn8h2dm8H9e+yWWHznPuh3H2fTOIVYf\nOc3GQ/vZeGg/AAdnzWH7wi62Ll7JvlnzbeJuZmWAbyGFPZWJu3KzUDMqXVfADFZ9gUmRuKsVFkUZ\nDTL/4Gt2B9WpsFA1zrzm4lGm9N3k8KxZnJp/DxGlNIo/Y7YFm0+R3R3UkNTzgbTlYLHYysiVfvs7\nnRJCZ8Zf0nPFThNdc2euqSHMzFmR4kVEa1B5Ap4X2ErI+raxfIXKHeS2s17qCJiyu81vm/b/zlpM\nuu+o3WW+TK9a2Dg76uBi3v5/da65A2bBK2tW8gorKZ4Wvvj2ER7ZeYLH9h5h2YVzLLtwjm+/9SqX\nm5vZvnQFO+Z3sf3+Lq63tyTVl2Rho28j9USEyah0nX1HgCkW62+bzlwaI41dfdFofkUZZTIn0uoY\nfgmDZCqoHFUKls2H7O6gFx9cRT62J6XWMI3iB4hdHH8oZsDpoIYx3A7kA3mgpbJy4QPaDvZakdMc\nQnsOFmZOtH3lNEFPDbF3HSM175YTA7vzvpAKmF5Xdcm7f3vJviPXPpoa9jAzZ31Qft+Rbx+da+7g\n5JIZvP0r9/P7V7/Mmg9P8fCOE2x89xCLzlzia+/v4WvvW+PunvkL2L6wm9cWd3N8zhybuJvJevGT\nR37fUeATd3t9G6mQipdcVfWlWFuFadTqizTIIJ4KFqVxyQbHVUXxlyIBY9h8xI0zP1w7HVRbYTGZ\n6PMGM9t6huMDqRfQdsNVXjpy9Q2vaoi967nd0enI/xm/RoBShXgBKGS2TQO0BMU6o9NWuMyKrHC5\n2NTO+ZYOinMi/uqxtfwVa4kPFfnim0dZ/8Zx1n18nHUn7Ndvv/Y8Z6ZMZevyLnbM72bXwqVcb4/T\nxN0blYm73sQb9MQE1dUX3z7KCpjq6osTIPX2HQ05Oj0e2kUrLIoyymR3B2Wvh2HtssNYWHHxFJ3X\nLnO+vYP3l85lQVQ5HeQrLFFSYWlgs22WoXwg9Yy5UyI78hxJfaGjhlglw3CqL/W2TQOE5CrEC6TV\nl3TfUX+FeAHoKFcm7s7MXU0Sd2fHduro09XtHFzdybbfXEbzjQILXr/Ew6+fYOM7h5h7+TK/8dYb\n/MZbb9Ab5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"text/plain": [ "<matplotlib.figure.Figure at 0x1131c1d30>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1 = np.linspace(-4,4,250)\n", "x2 = np.linspace(-1.5,1.5,250)\n", "fun_map_dec = np.empty((x1.size, x2.size))\n", "for n,i in enumerate(x1):\n", " for m,j in enumerate(x2):\n", " fun_map_dec[m,n] = forwardn([i,-j], w_dec, b_dec)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend()\n", "plt.title('Decision function SGD')\n", "plt.show();\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.imshow(fun_map_dec, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n", " vmin=0, vmax=1, aspect='auto')\n", "plt.colorbar()\n", "plt.contour(x1, -x2, fun_map_dec, levels=[0.5], colors=['r'], linewidths=2)\n", "plt.title('Decision function SGD with decay')\n", "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see again that we converged more quickly, but this time without the wobbles brought about by jumping over the minimum with a large step size towards the end of training. We also got a record high accuracy so far!\n", "\n", "Of course, training set accuracy isn't everything, we have to be sure that we aren't overfitting. For this, we examine some regularization techniques in the next notebook." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }