{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MNIST neural network demo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A project by Sam Greydanus. MIT license" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a vanilla two-layer neural network for solving the MNIST written digit classification task. When I was first learning how to use neural networks, backpropagation was by far the most confusing part.\n", "\n", "I've broken the gradient computations into several smaller functions and included mathematical explanations of each step to make backprop more transparent" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load dependencies and data" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Extracting MNIST_data/train-images-idx3-ubyte.gz\n", "Extracting MNIST_data/train-labels-idx1-ubyte.gz\n", "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n", "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.cm as cm\n", "%matplotlib inline\n", "\n", "from tensorflow.examples.tutorials.mnist import input_data\n", "mnist = input_data.read_data_sets('MNIST_data', one_hot=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hyperparameters" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "resume = False\n", "batch_size = 16\n", "lr = 2e-2\n", "reg = 1e-4\n", "h1_size = 100 # first hidden layer\n", "h2_size = 10 # second hidden layer\n", "D = 28*28 # dimensionality" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Initialization" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = {}\n", "# first layer\n", "model['W1'] = np.random.randn(D,h1_size) / np.sqrt(h1_size) # Xavier initialization\n", "model['b1'] = np.random.randn(1,h1_size) / np.sqrt(h1_size) # see http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf\n", "#second layer\n", "model['W2'] = np.random.randn(h1_size,h2_size) / np.sqrt(h2_size)\n", "model['b2'] = np.random.randn(1,h2_size) / np.sqrt(h2_size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward propagation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### x $\\cdot$ W+b function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **x $\\cdot$ W+b** operation is just a linear transformation plus a constant. For a given input $x_j$ and output $h_k$ we have:\n", "$$h_k = x_jW_{jk} + b_k $$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def xW_plus_b(x, W, b):\n", " return np.dot(x,W) + b # in some cases you can even drop the bias b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Softmax function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The softmax function is $p_k=\\frac{e^{z_k}}{\\sum_i e^{z_i}}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def softmax(x):\n", " maxes = np.amax(x, axis=1, keepdims=True)\n", " e = np.exp(x - maxes) # improves numerics\n", " dist = e / np.sum(e, axis=1, keepdims=True)\n", " return dist" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ReLU function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ReLU function is $z_i=relu(h_i)$ where\n", "\n", "$$relu(h_i) =\n", "\\left\\{\n", " \\begin{array}{ll}\n", " h_i & \\quad h \\ge 0\\\\\n", " 0 & \\quad \\mathrm{otherwise}\n", " \\end{array}\n", " \\right.$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def relu(x):\n", " x[x<0] = 0\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Putting it together" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def forward(X, model):\n", " # evaluate class scores, [N x K]\n", " hs = [] # we'll need the h's for computing gradients\n", " \n", " z1 = xW_plus_b(X, model['W1'], model['b1'])\n", " h1 = relu(z1); hs.append(h1)\n", " \n", " z2 = xW_plus_b(h1, model['W2'], model['b2'])\n", " h2 = relu(z2); hs.append(h2)\n", " \n", " probs = softmax(h2)\n", " return probs, hs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Backpropagation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient of the softmax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The original softmax function is:\n", "$$p_k=\\frac{e^{z_k}}{\\sum_i e^{z_i}}$$\n", "We're using a cross entropy loss function which looks like\n", "$$L_i= \\left\\{\n", " \\begin{array}{ll}\n", " y - log(p_k) & \\quad y = k \\\\\n", " -log(p_k) & \\quad \\mathrm{otherwise}\n", " \\end{array}\n", " \\right.$$\n", "Taking the gradient of $L$ with respect to $f_k$, we get\n", "$$\\frac{\\partial L_i}{\\partial z_k}=\\frac{\\partial}{\\partial z_k}\\left(-log(e^{z_k}) + log(\\sum_i e^{z_i}) \\right) = \\frac{\\partial}{\\partial z_k}\\left(-z_k + log(e^{z_1} + \\ldots + e^{z_k} + \\ldots + e^{z_n}) \\right)$$\n", "$$\\frac{\\partial L_i}{\\partial z_k}=-\\mathbb{1}(y_i=k) + \\frac{e^{z_k}}{(e^{z_1} + \\ldots + e^{z_k} + \\ldots + e^{z_n})}$$\n", "$$\\frac{\\partial L_i}{\\partial z_k}= -\\mathbb{1}(y_i=k) + p_k$$\n", "Now we know how to calculate the whole gradient $\\frac{\\partial L}{\\partial z_k}$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def dsoftmax(h, y, batch_size):\n", " h[range(batch_size),y] -= 1\n", " return h/y.shape[0] # divide by batch size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient of the ReLU" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Propagating the gradient through the ReLU looks like:\n", "$$\\frac{\\partial L}{\\partial z_k} \\frac{\\partial z_k}{\\partial h_k} =\\frac{\\partial}{\\partial z_k}\\left( relu(h_k) \\right) =\n", "\\left\\{\n", " \\begin{array}{ll}\n", " \\frac{\\partial L}{\\partial z_k} * 1 & \\quad h \\ge 0\\\\\n", " 0 & \\quad \\mathrm{otherwise}\n", " \\end{array}\n", " \\right.$$\n", "Since we know $\\frac{\\partial L}{\\partial z_k}$ from calculations above, we can also calculate $\\frac{\\partial L}{\\partial h_k}$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def drelu(dz, h):\n", " dz[h <= 0] = 0 # backprop relu\n", " return dz" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient of x $\\cdot$ W+b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **x $\\cdot$ W+b** operation is just a matrix dot product plus a constant vector $b$. We can break it into indices as follows:\n", "$$ h_k = x_j*W_{jk} + b_k $$\n", "\n", "Now we just need to propagate the gradient through this function.\n", "\n", "$$\\frac{\\partial L}{\\partial h_k} \\frac{\\partial h_k}{\\partial x_j} = \\frac{\\partial L}{\\partial h_k} \\frac{\\partial}{\\partial x_j} \\left( x_j*W_{jk} + b_k \\right) = \\frac{\\partial L}{\\partial h_k} W_{jk}$$\n", "\n", "In practice, we'd like to vectorize this calculation. The best way to do this is with a matrix dot product\n", "$$\\frac{\\partial L}{\\partial x_j} = \\frac{\\partial L}{\\partial h} \\cdot W^\\intercal$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def dxW_plus_b(dh, model):\n", " return np.dot(dh, model['W2'].T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Putting it together" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def backward(y, probs, hs, model):\n", " grads = { k : np.zeros_like(v) for k,v in model.items() }\n", " dh2 = dsoftmax(probs, y, batch_size)\n", " \n", " # second hidden layer\n", " print(hs[0].T.shape, dh2.shape, model['W2'].shape)\n", " grads['W2'] = np.dot(hs[0].T, dh2)\n", " grads['b2'] = np.sum(dh2, axis=0, keepdims=True)\n", "\n", " # first hidden layer\n", " dh1 = dxW_plus_b(dh2, model)\n", " dh1 = drelu(dh1, hs[0]) # backprop through relu\n", " grads['W1'] = np.dot(X.T, dh1)\n", " grads['b1'] = np.sum(dh1, axis=0, keepdims=True)\n", " return grads" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evaluation metric" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# evaluate training set accuracy\n", "def eval_model(model):\n", " X = mnist.test.images\n", " y = mnist.test.labels\n", " hidden_layer = np.maximum(0, np.dot(X, model['W1']) + model['b1'])\n", " scores = np.dot(hidden_layer, model['W2']) + model['b2']\n", " predicted_class = np.argmax(scores, axis=1)\n", " return (np.mean(predicted_class == y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradient descent loop" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A note on regularization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I've added L2 regularization to the cost and gradients here even though I didn't touch on it in the _Gradients_ section above. Here's how it works.\n", "\n", "Overfitting is a problem which occurs when a model fits itself to individual examples in training data. This prevents it from generalizing well on new data. One way that neural networks overfit is by making certain weights very large; we use L2 Regularization to prevent this.\n", "\n", "The idea of L2 regularization is to add a penalty - the _regularization loss_ - to the loss function which scales with the sum square of all parameters in the model.\n", "$$L_{\\mathrm{regularization}} = \\frac{1}{2} \\gamma \\theta \\cdot \\theta$$\n", "\n", "Where $L_\\mathrm{regularization}$ is regularization loss, $\\gamma$ is a scaling hyperparameter, and $\\theta$ is an 1D vector of all the training parameters. The gradient, then, has the simple form of\n", "\n", "$$\\frac{\\partial L_\\mathrm{regularization}}{\\partial \\theta} = \\gamma \\theta$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(100, 16) (16, 10) (100, 10)\n", "iteration 0: test accuracy 0.925300\n", "\titeration 0: loss 0.012139\n", "(100, 16) (16, 10) (100, 10)\n" ] } ], "source": [ "loss_history = []\n", "smoothing_factor = 0.95\n", "running_loss = 0\n", "for i in range(2):\n", " X, y = mnist.train.next_batch(batch_size)\n", " \n", " probs, hs = forward(X, model)\n", " \n", " # compute the loss: average cross-entropy loss and L2 regularization\n", " y_logprobs = -np.log(probs[range(batch_size),y]) # we want probs on the y labels to be large\n", " reg_loss = 0.5*reg*np.sum([np.sum(w*w) for w in model.values()])\n", " loss = np.sum(y_logprobs)/batch_size + reg_loss\n", "\n", " grads = backward(y, probs, hs, model) # data gradients\n", " grads = {k : v+reg*model[k] for (k,v) in grads.items()} # L2 gradients\n", " \n", " # update parameters\n", " model = {k : model[k] - lr*grads[k] for (k,v) in grads.items()}\n", " \n", " # boring book-keeping\n", " running_loss = smoothing_factor*running_loss + (1-smoothing_factor)*loss\n", " if i % 1000 == 0: print(\"iteration {}: test accuracy {:3f}\".format(i, eval_model(model)))\n", " if i % 250 == 0: print(\"\\titeration %d: loss %f\" % (i, running_loss))\n", " if i % 10 == 0: loss_history.append((i,running_loss))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualize training loss" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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nycrLWVkhIiIqFm0K3QAAcM5NAjAJAERsvk5OPwfwtXPuN6nbn4vI7gDGAXg+353LylhZ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\nB+3a2qD74qOPghlK4ddy553pJ6K04ODPWnnqKQ1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WKZSfKukbwIXAMcBbwBFOVMzMzFpP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\nNScrZmZm1tScrJiZmVlT+x9qd09BswMpPwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Smoothed loss\")\n", "plt.xlabel(\"training steps\")\n", "plt.ylabel(\"loss\")\n", "\n", "train_steps, smoothed_losses = zip(*loss_history)\n", "plt.plot(train_steps, smoothed_losses)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sample model" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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YWPgEGxsbrr6WSCSC7e1t12ESGaWULiXjEYvFsLm5iVQqhXQ6jXQ6jVQq5anIjMdj3bxP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\nrISbPob1yrJNQQvVtZxU/4bPDsvR8TEPst+P6rgqi0LExWGhZYVCAXi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0j1L8hkE7t79ELukfXKIhy1FlL8os2WPAP4uLS2a75aHP7X9xfyYbsmUpmVSZ\nZLb5Juj3+zg8PLTlxRrweRi45WEky9J2pRgKWwZkMz8DP/IsIFsL5GJgyCXtAGzAMJPJ+MrKJFmW\nRIaiALJHazAYoNfr+dYiBZSUyCwQ3OgT5y/IAZjsH0gkEnZmjAtGepiRaTQaSmQWGJLIsHZbOi+S\nGR4K2T9AWW0SmePjYxwcHKDRaNgI3CJtXG49MPu+stmsLe8oFov2kMxyMpZGyqXZmPnAnZBO/8RA\ny6uvvmqb+TOZjLVZKWQxC3y+bDaLUqmEbreLjY0NVKtV2/Q/GAwAYOlVdhSXw218ZoBH9ludnZ1N\nEQBZ+0/iC2CKwLjRZkaZZcYEmCZULAFzo9jucgkK73Nvg8iXfMxtmvSHwyEajQYajQZ6vZ76ygdA\n0FgBKs7KcjAZpOTXLpHZ2NjwleSSBLmjGYKa/emnmeXm2c+1S9eWSWZIplm6Xq/X0Wg04HmezRKy\nP2zePliJzIJBRn9kRoZExo10zgJLcpiRYXpZicxigo6LkRqXxKTTaUSjUZ9CHTCZE0AnQyLDtHG/\n31+ojUvOcXDL52RGxo1GUnFNZmRIYqjAp7h/yBJILjcj88orr9jSVy6WQV40hwOAT61va2sL4/HY\n2vvZ2RkGg4HNygCLEQlU3A+CSnKkwiH7Bc/OznwNzCxDJYk5OTkBgKkMXlBGhn2jLkF2+2YYJJQl\nOq7P4oHwsug3szlB2Rt5301tfTwe+/426isfBkEzi6RqI1U6WSrGsjFXXnmW3DL9IslKkE/lWUKS\nYteuaMvuojAQ1VBrtZotXxsMBlhbW1soP6xEZsEgHbjMyBQKBSu9yxQjG7xcMCMjm/1rtRqazaYl\nMot0wH3sYASHTi8WiwWWlrkN0oxGuqVl0nEt0ucsMzJSwIKlkxxI12w2MR6P0e12pzIyJDOu3LLi\n/uH2FrCnxc3IsLFUKvFcBczIZDIZnJ6e2oMjSUyr1UIoFPKVlmlAZnXh2ps8EHIuEf1Ep9OxjczA\nS8EbZvAIl8S4pWAuuXEVJZkFJ2GiWqRLpngAdHsSeD8Xg4ru67q3N0VQD5HifiEzMuFwGNFo1NdH\nyL7BfD6PbDbrIzhBxMUdmOnONLpITc8tlXR7tehbJdHmuZH/U51OB/F43JKYVqtlM+Tu680LSmQW\nBEGNjJTWk1F5StLKdKJrQKwbHg6HthGcpTgcjLUILPoxw828saSMB/ugz5rEhURlOBxONb6zZ0SW\nSszz/cmtvkwWAAAgAElEQVRoJm2Yq1Ao4MmTJyiVSkin04jFYr73SflIlspJ+6UCj5YWPRxY3iNl\nPwuFgi0lo71yBoeUhb/q81M8gJFjqbLHMgvauSyLcCONGnleTtBWmO1jdjoej9uSQ/ZglUoljEYj\nNBoNS3iHw+FU1hrwSxwzm9JoNFAul211AwMorrqjuy9zXpdcQeU5JC3y1s3SBDVWu6VvSj4WB26f\nIFsAXKUx2fdCRUc5E65QKFgFMq5kMjklCEC7DsoWyuVmykmAXJIsr5v/a7xPvgcZdIxEIjg9PfUF\nDGjz7ryjeUGJzIJAsngaEA8LcvFgS4NzIdVQ6LBl1IgHXXWO84NbqiCjNiy1Yn8BJRlZmy0dSbvd\nxt7eHiqViv18F4HEAMHDvliCxEMIG7pLpRJSqZTVwmc2sdPpWBLOoW7MJroOXXH/kOU9LIWg+Ail\nsuVGeB0SA7yUm4/FYnbT5f2RSASpVAr5fH4qWkjbkAdISXDVPhYfbsQ5FAohlUohl8shn8/PXL1e\nD8YYnJ6eotfrTdmc26AvbapSqSAcDtssSyqVmirtkn6Mi72nMtMyawaMVNyTvTyy1OcitTO13cWC\n2yPIqhk5sJI9KbL3Re7rXKysoYiPLBGT/ssVrpB7PEkOr4NnRM7fcu1ZkpVZAzhJXtj/srGxYftk\nOp2OJeX0u/1+377WvKBEZoFAFkwpSBn5JLOnQoVUriJo+Iw+MSNDIiOnuaqDnB/c2m8e3jhpOpfL\nWUdHBwfADoWsVquoVCqoVqvY399HuVy2w67c8oh5fc5uYz/18Dc3N7G7u4snT57YbAyJTCgU8pWE\nUKhiFpHRjf5hwUGtJBQskyCRYUkZlcku6ocJAuWcSWJoOyRPLK9llo7Np8zYtdttK9k9Go0AvBxW\nqHay+JAZ3FAohGQyiVKpZGcSFYtF30Ewm82i2WzaftBms+mLNkvbY5aX8zLOzs5sGRoHCsdisamG\ne16LDDBSHln2EbgT0mWU2j2EugdSILiHR7F44ME+HA7bfY1EhQOBZVUF+18o1iOXbN6PRCK2B4V7\nG+3UzT7LsnHaUiQSQTqdtr4zGo36zoEkz+xPjUQiPj8t+234+nyvkUjEqqNSrnkwGFhfz+DjPKFE\nZkHgKleR2bvpdbJtVwHIrYUMIjIuk1fMB67jkBmZdDrty8jISA1VvEhgDg4ObEam2WzabNsibIau\nPUciERvB393dxRtvvGEbw7lCoZDd9K+SkdGI+8OCg1pJZCjOkM1mfaT7pkSG5IWERpbW5vN5m22p\nVqsol8t28RCwtrZmm5vl66p9LD7cmRvMyBSLRTx9+hSvv/46tra2fKpPqVQKkUjEkphIJDJTUEIq\nktHHAP7gUCgU8mVLRqORJTI8uLJHy23cd/tbLvraXUSQP1PbXSy4fZ4cXC0zh25DP8dlcB/kIhGQ\nWRLaqSyRldLHLKt11e9isRjG47HNmtO2+BhmrGW5JHusZTZGigdsbGz4rkOWR1IVkGfNfr8/z4/l\n+kTGGPNFAP4ygM8GsAPgvZ7n/bjzmO8G8OcAZAH8cwBf43neJ25/uauLICLjlpUxI+MiqKGLg7Yk\nkVkFrIL9uepPPLRdJSPT6XRQqVSwv7+Pt99+207ulaVliwA6Qjp8yupubm7i6dOneMc73oE33njD\nl7VhCpsZGTb6u0RmnqWRq2B/N4VLZLa2tmaWll2EWYczlllKNUY544NBmHK5jIODA99rSlGAdrs9\ndZBdpQPhqtqgPFAx0l0sFrG7u4s333wT29vbvioFBvWazSaSySQikchMAs2DHf0jD4PtdtseLI0x\nU+pjJNWRSMTa5ng89pWQyQqHVbKzWVhV+7sKpBoZBWtYMs0BwKVSaaoEMpFI+PqsZpXdkhjQ5/EM\nJ8vJe72er2xxOBwikUjAGGOz1/SbPAf2+310u13bT8PqB1cdkGcNOZeGS5J3ZjdJYq4q6HJfuMmr\nJwD8DoAfAPCj7g+NMd8C4OsAvA/A2wD+KoCPGWP+gOd5o5tf6mpD1ocnk0mbkpSH2VnRTVe2kXW7\nbMZasezLUtufnIfAlcvl8OTJE+zs7PgOhxwMSYlROrNms2lLa6Sk9iKpd9HhSzlpEnHq4DMtTWcM\nAM1m05KzarWKarWKer2OdrttSzjmjKW2v+vAlUx2+7iKxeJUWRmAqYhzUO0/MN1EPcu/8ToI/v9k\nMhlfuRDruNlXJq9hxcrLVsYG+dnK4X7xeBz5fB67u7tW3SmZTNqyQwY0Wq0WDg8PUS6XrZ9otVo2\n6HHZ3idJMm2PJTtSWpYESPYvyOnmj4nEnGNl7O8iSPlkWe7vDqgsFArI5/P2Np/P2zIz+kVjzFTv\nalB2TirasZRLfj0rI5NKpXz9tslkEqPRyFY0cLEkM5vNWht2/ST3ZVn1wGHFuVwOnufZwCMFNjqd\nju1xnUdFyLWJjOd5HwXwUQAwwTvPNwL4Hs/zfvL8Me8DcATgvQA+fPNLXW0whU0jpLHJae6zwAgR\nD4Ttdtun8LRKRGbZ7Y8HQmZecrmcncHBtbW15Ys2s1ym2+2i1Wr5pt3LCM0ifc7ugE/WCEsis7Gx\n4XPIo9EI9XrdEhmuRqNh7Xne/V3Lbn/XgSw3YN21zBpy46biHDdsHvRkZNGVlwXgG+jmkhWJWUSG\nJGZ9fR3D4RDdbhfNZtP3fwOs3gFzFWxQNveTyMhynFKphKdPn2Jra8uOHAiHwzZbS79xeHiI4+Nj\nVCoV36BcWYYaBB7UGLWmjcjSa/YJSClm+Xsu4XksWAX7uwo2Njasv3N7YGQTv5wDw74YEh6e3Uhk\ngvqkpJ9sNptotVq2EoGDreWSKo1c2WzWnh8Z5BkMBr5+2kqlgmKxaEvQgWB1UZboAi8zMlQRPDs7\nQygUshkg+t1arebrr3noHt07zQcZY94AsA3g53if53ktY8yvA/h8LJERPzRkRkYqXFw1I8M6yF6v\nZ6VqVzQjMxPLYH9M/8rZQJubmzYtzdR0LBazToZEJigjw2bTRczIuPNi2OfFMg2WktEZdrtdXyZG\nZmSWYfjlMtjfVeGWG8jsGvu4mJFhmQ/LC0hkJEENkrWNxWK+UodZ1yGvh6U+iUTCkphIJGJJTLVa\ntY2swPT8hFXHMtmgbDSmvPLW1ha2trawvb1tM9QkMrLRnr7w6OhoKiPDwM5lc7SYyQNg90jZzyIj\n57J3QR7UHotdXRXLZH+XgUSGwcZSqeQjK1xuE7/c49gLA7wUnCAZkU34JObc8xjEq9VqU31bPNNJ\n1bJer2eD4JlMxir6VSoVHB4e2kUS4/Z+yQGcJOxSKIVEhiIc9OkcuM6fyazTQ2bB77qwbRuAhwn7\nljg6/5liBmSDKzMyQQ3fQZBEptPpPFoigyWwP6n8VCwWbUmZnI1QLBanGk+p4iWJTK1Ws42ri0hk\nqHjChm2ZkWH5D0vLqFDmZmM4I0ceghf44LDw9ncdSDlOGe2TGZlsNutrhJYRbLlpu5FIALaUgXYy\nCzIj43melQaVctCtVgvVatX2SkhS9Yj8H7AENij7WGRGJpvNYnt7G6+++qpVKWPWL5VKWdLQ7/dR\nr9dRrVZtRoZEptlsTs0VmgUZPebe6pbFSBIse28WQVBlQbHw9ndVMPOQz+exs7OD3d1dX9aQZzS3\niZ9l03LRFnlOY9bQzbYcHR3h8PAQBwcH1rZljyCz226AZjAY2ExMLpezfdHsJ3zx4gVevHhhS7Pl\neA/uxyzvZWkZnx+Aj+RwDYdD1Go1HB0d+QJZAHy/+xBQ1bIFgewpIKsm25cbc5DjZFMYo5LsKVjE\n3onHDkZC6HQoYSs37VwuBwDo9XoYj8e++RgcSkVH5arizOs9uUsSGEbwZXmZVJnitOBqtYrj42Nf\nhJVlZYqHhRSkYIkgMzLuZypVFFmqQ1tlXbdbTgHAKuxx8+Truov385YbKv3l6ekpKpWKHTBHOxsO\nh5YAPUJCs7Dg502bcZXwdnd3sbu76yvXicViNprc6/XQaDRweHiIo6MjW1bGAJ4clnvRZ35VIqKE\n5XHAle6OxWK2cmJrawtPnz61wRu53DlDnOHiii9xrh9Lxkhm5Nrf38f+/j729vawv7+Pw8NDH+Ge\nZYvGGBSLRSuMQ7/bbDZRq9VwfHyM/f1936gH+kmWTdKvcih10Lw7uRqNhk+xUvbWBAlu3Cfumsgc\nAjAAtuBn5FsAfvuOX2ulICOTzMrw0EeG7xoGDZpqVvV6HUdHRzg6OsLx8bFvtsgjwdLan+ugZC22\nO4vAnaMyj01WHixlUyRveSiR5XIsE2Eamo27jUYDx8fHeP78Ofb393F0dIRGo2EHGy4Rltb+XHBD\nc1UUZX8TfRJtlDbLskeuRqMxpTy2trY2NROEQRtpS+7QNldlh9fKptudnR30ej0AsGSft24j6ooe\nThfOBqWvYJBDzs9IJpO2xLZQKFjVxkQigXA4bAnyaDTylRCyrKxer6PT6WA4HPoa8Ff08110LJz9\nXQTaJrO7cs4KZxixb3Vzc9M3E0YqJrKMiv7NLQfrdrvWF9IvciYLJbzZ01KtVtFut23f61UFJYLK\ngaVCmjHGzoOp1+tW9S+Xy+Hs7MyWeErfCrwkeNLnLxrulMh4nveWMeYQwHsA/N8AYIxJA/g8AN93\nl6+1apAHQhKZZDJpiYwsLXONmqU5TPPt7e3ZIYm9Xu/REJllsD/3s3Mdk9yEJYmRk6CDiMxDbtpu\npJz1s7RZDi+URIbqQ9ls1qqxMSXebDZxfHxs09+1Ws32/yxTNnEZ7O86YO+KnGtFIsMZCABsxJG2\nSj/EiPnx8fFUT8Ha2pqdscDIZjqdtvZDVSCWPDAjzY2Umy2/TiaTyOVy2N7ethOsy+UyKpUK1tbW\n7P/QPBpRHxKLaINB2Vo2TLOMent725bV5nI5pNNpe7CktDalaCWR4QytTqfjm+eyip/tMmAR7W8W\npE1ubGzYTAV9D3u1pKwyz2SxWMxXKQO8LFVkz4pUG2PFgVysmJGr1WpZex4Oh1fe490AD0nHLCLT\naDTsHnx2dmbfPzMxPG8yoMVbPt+i4SZzZBIA3sSEdQPAO4wxfxhAzfO85wA+AODbjTGfwER673sA\nvADwkTu54hXFrIyMlKqVkIbNjIwkMtVqFY1GY+WIzGOxv1kZGamWc1Gq+SEgp3CzWZdKbKVSaYrI\n8PCSSCR8GRkSmWfPnuH58+e+DWDRMjKPxf64cUmfFERkmJGhauJgMECtVsPBwQGePXuGZ8+e4cWL\nF1PZxo2NDWsrcrG0ksPdANhmWbmpcjNlGQczMvw9Xu/6+jpOTk7Q6XTQ7XZ9ajwP2Yx6l1gmG3R7\nYVhKxiGnUrWRGZl8Po9MJuPLxLFR2s3I1Go16y+YkZFEZhk/30XHMtnfLLjkmgd59v9ls1ns7OxY\nwQkpwsMmeQaYZekXS2upMErZ41qt5hviWy6X7dlMBoFkmZnMyACX27I71FKWb9Jf8tqo6nhycmIz\nMZlMxldSJsvM5P/vrBk488RNMjKfA+AXMGno8gD83fP7fxjAf+p53t8yxsQBfD8mw5B+GcCXe0uk\nHz4PyEFLVyktkyydGRmWlu3t7dnhSStYWrZy9hfkoIKIjGxgdWcYzHqe+4B7OCGRcQeDcfF7WTa0\nsbFhpxbL0rJnz575ZCoXMCOzcvYXhKDSMkYhuYEzGuk2sZLIfOpTn8InPvEJ/P7v//7UwSEUCvkG\nxjWbTVtOwdIz1l3Lfh1em1uDnUgkcHp6aklMOp22mRgGeWQwaNEI8jWxVDboHoKYkcnlctjc3LSy\n8+wVZEZGBmtkRobRbZagyhKeBRcDWRUslf3NgtzD2G/HnpjNzc2psrJSqWQzhG5fIEtrSQ5k5rBS\nqaBcLtuyf2aqWXHAJfd22dh/3fdyWWlZr9ez1RDD4dAGIUmcZJAIeHmuCPK7i4KbzJH5RQAX5pY8\nz3s/gPff7JIeB9yNnQc8pjeZdqcOuSsnKheNk1J41Wp1itWvClbZ/tzIi+uYJMmlOonbBBg0ZOs2\nGzuvwXWUcmUyGUtYKJtKBbZCoWDr3uVzydk4nU7HilQ0Go07+VveF1bZ/lxI23OlOkkw6H/6/b6d\nccTN+/j42Mp+ys+e5JeHTwpZjEYjS3JIRnhwYGQQ8PdcEOFwGPF43GZa1tbWUK1WfWIpjOwv6mZ8\nVSyTDboHq42NDTtegE3UVG2Uw1U3NjZ8/QPD4dAnSUuFsna7PTX7RXG/WCb7mwV3H6PgBGXlSa5L\npZLNECaTSV8whLZ2cnLis9NutzuVfSGROT4+tkuWQl5XjMT1gVLUhOJPDAixDy2Xy1l1Sdmu4K6g\n0jFZNsdrpcR50HBY+fd5CKhq2Zwg038bGxu+/gIu2VwrMzLuoZURe2rsU0d/NBpdi9UrFgfr6+uW\nuPDwVSwW0ev1rIRiOByeIi+yzIe3t8lqyAMIl5TbDYfDSKfTtpSsVCrZQwlVrRhZZ7SKBw9mDVkr\nrHa6OJAbpUtmJQlgVq3dbqNWq9n671arNZUN5sZGO+Wmz/KwtbU1O3Mok8mg3+9b25ElHCQrLoKI\nvPSV2gT+8KAfY2M/hUCo1sgDI5v7+Tmz5FQuliseHx+j3W7bDMy8S2wVywVmm1keFgqFfJLyFKYp\nlUo+ERIGbqQ/OTs7syMvuDgawZ2FVqvVfH7xpuXhQWVeDPRIX3xycoK1tTWk02k8efLEBgi4d7OS\n4smTJygUCkgmk76eHwmWdsrsZ6PR8O3fsn/3ofdyJTJzgFu2EQ6H7aRYSWSo2uL2yFxEZAaDgT3s\nSqasWC7IgZKs4WUEhFHrZDLpcxxsumaWg0MmR6ObZfTZmCtLwqg2xMXhnvl83ta30ymycZKH0dPT\nU18vBSOqjMYrkVksBEXr3Ejg6empzcbUajUcHh7aBmxJul0fxI2RZQ60a2YbO50O+v2+FYYIh8M+\n+3DJjJulDiI0SmYeHlSDisfjdtp5oVCYIjIsXZS1+/V6HcfHx76SnIODAxwfH6PVavlklvUzVVwH\nssIhGo1a5USWlW1vb6NYLFoBknA4bP0NAzEyIMfyMWYNqU7G21arhU6nY/2aOw/mKpC+180oMQAw\nHA4tkSHRSafTiEajKJVKlsjwNhqNolgsolgs2qGzQZD+mssdQOtmRjUjs+KQEQEeCGdlZKT6hDFm\nalMmkeEBkSVl8h9ND4jLBxIZkpZIJGI/R5beZLNZ33RfZmMajQYajYYdnDkYDG50DcYYK7vL26DF\nlDwHhGWzWZtJlD0xHNDK5lw3oqN2unhwSw7cjAxLBLl5cjjhRRkZ3rLslaVpAJDJZHwzFkajEcLh\nsG/jl88XRGZmZWX0sPvw4PwJlgoy6EEis7W1ha2tLVvLz8gyZdkPDw/x7NkzfOpTn8LR0ZGVrm21\nWr6eGP1sFVeFPH+xlD8oI5PP5+2+RyIjKx8YQG6326hWqzg4OMDe3h4ODw9toz+zNBSj4LqNKIUU\nYiEhcTMysqw2lUr5ehtJZEjmGERnRjQIUv5cDuV25xXOSzVQicycIImM7ImRWZlEIjGznjuoGVyW\nlknHrg5++cADQCgUsp81s3gcplkqlXyElYfKSqVis3nGGDtX47pghNzNFKZSKXufvJVfS319qbMv\nGyE5uLXf79voqmJx4EYAg3yRW1p2eHjoIzLMyBD0RTyAksSwfyWXy9mNnzXnkUhkpvCDVB+b1SPm\nbq566H04cJ9jwIOHRTcjQ3EPrn6/j3q9joODA7z99tv4+Mc/jqOjI9tPxaDIAoqBKJYAzBSy51QS\nGdplNpv1lVTTz0h1stFoZInD3t4e3nrrLbx48cJmX7gYtLlNORlvZUZG9rvIjEwkEgEAn4BBPp/3\nvZ+g/seLMjJS/px9aty/XXKmGZlHAFlaxmnZVChj+Q5Zs4ugHgiWEalzXw6wGY8CDa1WC9FoFLFY\nDMPh0M7BcJ1WNBq1U3jl93INh0PrmOioGe2+LowxlmRfdJtIJHwZGg7ackt96GQbjQYqlYqVT223\n2xgMBmq3C4SgqOUsOXiZtZEqOfzZLLjEVUbYZdRRyohe9Fw8XDCgEzR7SRvCHxZyn+M0cRmoY2kP\n//9dBTz6i1qthkajYWXoNfChuClkj4kU0mHlgxzW6soXA/5ePKkwJtVF2fNH25/VWB8E1z/JgCCv\n2R1AzaxSJpNBOp22Z0oGFikOJCt85FwY2W8TFABnWRnFXJh5bzabtnx9nqW7SmTmBNkjwwNgUGO/\ni/F4jMFg4OuD4GFwBaWWVw6e59kUbaPRsOWDnNdBh+RmNLhoM57n2XSyXKPRyEpJMgI6HA5vdK0s\nLeNhY9bXXNJ2pcIJb6lOVi6XffXuqzjvaNnBkkYZSZeqUqFQyBcVlGp6jJp3Op2p+VeXvaYb4GFw\nh683CyxRI4nhHKLBYOATPdE+mYeFO1SVJdNSSQ6Y/vx6vZ7NvDBo55JSheIu4AZdruMfJGHhWY6D\nfBOJhLVb7tdyXfSc8rXd2TCScEni5ZZ8k7yQ2HB/pt92CYwkV24LgxzxUS6Xsb+/b/duEpl5+lUl\nMnNA0IZNIiMHzQVBlnKwD0JGtfUwuNhwy6uYFmbEMpPJYDgcWqcjbYE2I52nq8w0Ho9tz1Uul/M1\nXF8XlAV3lxwIJr93ZcLZv8VF8lapVHB4eGgHt7IMSTMyiwPZ20AiQxU6EhmSbFcWnJH0oEG+F0Fm\ngWSAh0Rmll+krfEgzB4sljxIpTwlMQ+LoEOeS04Z9GCv50VEZtYMLYXiJrgsc+xmJ4L67TiHhmQ9\nlUpNiYwwMCQb7Wf5Mvf5pcqYrLZg1kj2o8q9mBnQVCpliYwkLu5YhSBVXAYNBoMBOp2O3b8PDg6s\nqIFLZOTf66GgRGYOmLVhXzUjw+baer2OSqXiq1VUIrPYkBkZ1qOura3ZTEw+n8dwOEQ0GrUlNnJA\nFTf/UCjkU6STzieZTNryi9s20ctI0GWLkR7OiWGpD5frCPf29mwzpBKZxYKc5yIzMjyISiLDgAxF\nH9gMelMiMysjc9FzybKyXq+HTqcTmJEBtEfmISEPeSQyN83IyMOSZmQUt8VFJOYqPoKPkT6QNu4O\nzeT/gCwJu2hei7RxqRgapBzqlq7xPfF/jtdFCWn+3H28K5wiy+ZIZJiROTg48KmxMes0L7+qRGZO\nkBs2lTEuizwCmDKq4+NjzcgsESSRMcbg9PQUxhhkMhnk83mfJrssKwPgc4qXvQZvZ0VIZC3sRV8H\n3bpfB93nRlllOR0zMvv7+/awora7WJBEJplMWlU6zgUikZF9NMzINBoNxGKxGxEZ1qvLTDVLL2XU\n0P09Zv9Y1saMTBCRUTwcLiot415HXzGLyJDM3DSzrFDMQtDeFpR9cSEf45L10Wjky4zIDIpcQb7R\nLRUHYM+I/D1Z3s3btbU1W/nAfZe+WWZyrgo52oM9vQxEksgweM5+xHkGh5TIzAHuHBk3I8ODatCB\nVDZdUe5UMzLLA7lpswk/EomgUqkgHo/bcrFsNuuTL5alZjID4qareTCQToUOSTYlXtXp8Pf4u8YY\nX0qb0SAXUhaczo5zbbhI2lgyolHyxYHneXYDY79Lp9Ox/oo2RPLBg6or/iCbZt1+L9eeOVSVmZ9I\nJOITD+D/jtswy/pz2WPG2TaUFWVmR5Z7KLG5f0jVMipDuaUu7jgCORQ1l8uhWCyi1WrZGTPuaAG3\njEehuAj0I6PRCIPBAKFQaEplrNPpTA2PlEE+KRLAfhSevTiPRe7LblZlVkZG9qXQlt1sTNDi/xAH\nT8u+GlZUXPS3kEvu2QwoHBwc4Pnz51YCXcrjL0KQSInMnOBGqmb1yLjNqS6RKZfLqvy0ZCCR4Wfc\narVQLpetE+r1elb7XU7EDupXkfNd6MxcGVpGqmV08yp2wiY//s5gMIAxxpYZUQVlFpGREVYKU7gl\nI2zgVTWpxQJ7uWQZKyPpiUTCp8wjsyiSxEhBCFfyk+RHllsUCgXflGlXPEISGbfOW5a30Z44cZvX\nHo1GfcRcS8zuH5JgplIp5PN523xMoiozcfF43NpePp/3zRSKRCI+tU4ZBGGAZt4HKsVygAf2Xq9n\ng3NUEOWt9FEALPGg3+G+l0wmcXZ2hrW1NUQiEfT7fV9Jtpz3IjM1l2WBeJ/MqrjPwf8fqW7qfj8r\nk83XY8CK/1fs3+UsnGaziePjYzsjp9Fo+FQhF0F8Q4nMHDCr2V9G3mfNRnC1vKkcoaVlywHZmMyD\nGTCZNMyG+Fqt5pMmlSlluWQkiI358jWkJDNV7riuQmTOzs586nidTgfGGDx58sSqo6VSqZm/K2Wm\n+boukZGRID1ULg5mERlG1mm/ksjEYjGcnJxYMiNt1W1Edae9x+Nx5PN57OzsoFAoIJVKWV9Iu+Bm\nKUstZVYoFov5iA5JDLMy0WjU9mvx99Tm7hcyI8MMC6WXSWQA2EMjf+fs7AztdtuOFRiNRohEIr7J\n4pwoPhqNAEzLeSsUQeDhfTQaWR8QDodtvyZXOBy2+yQJiSszv76+jmQyaQl7KpXCaDSaUgZzlcdk\nsDqo/NtVLZOkyH0e6Q8BTAV6LiMyJycnGAwGViSl1WqhUqlMrWq1anuySWQWZei6Epk5YVZpmZuR\nkURGRhFkaZmMdCuRWXzw0M7MjFT1kgdGl7jIoZTUh+fnHQ6HkUgkphRH6LBpM/V6Hc1m80r15mdn\nZ2g0GlYdr9FoYG1tDScnJ9jY2EA6nZ5pb3SQl2VkZCpdD5WLA0p5k8hIVT3Oq5IkghmZ8Xg8NVOI\nRFyWI1JEIJ1O29t8Po+trS1fRoZkJWiQnNycqfzH7MzGxgbq9brt66F/lSVq6ivvHzzgsVwsn89b\nW5BBOz6OxAfAVPlKKBRCu91Gu922h0oe0hg4USguA///OaSSc9uYjeGKRqMA/Gc1SRCAl6QhEokg\nmUzajG/QzJggtbCrqHy5SmNBX/O5eD+/dpv65d+At7LvmufKg4MDHBwcYH9/3zb2y0Aoz5py/54n\nrkqteLkAACAASURBVE1kjDFfBOAvA/hsADsA3ut53o+Ln/8QgP/Y+bWPep73Fbe50FWCW44xS7VM\nphhl/SIHKVK1jAcLOvxVxirYn1ufz8N+s9m00RZJcGUknAOvMpkMMpmM7Q+g5DLLZ0iQKPVMEsPI\nCqOYF2E8HqNWq6FardpFud10Om0ncgc5MdkHxCgPyYxswl42rIL9XQVuRoZynvl8Hv1+3w4klGVi\nJOjsk+Gi0pkk54lEAtls1so6y3JFRu15WHUHz/F/hHYnB8aS0LDvLJPJ2CGMLL/k4WVWlHLRsUw2\nKDMyVLUj0ZTzNCjmIOXlZdT37OzMik/IPVL2T/Fzlb5V+qbLJHavev9NnmuVsEz2Nwv0VawaWF9f\nt2qLDNqFw2FLCEhm5IBe3tJPAdN2cZltBRGZIEUxiVm2dxV/5paukdDJMyWb+Z89e2ZXq9XyKaEu\nmvDGTTIyCQC/A+AHAPzojMf8NICvBsC/7M0m8q0IpOGvr6/bhlRu4Pl83jdsTjaCuRkZOUFWkpdH\n1GewkvbHz9mcSxfTwcoIMkvSmAamwEOz2bSSxszS8DnYcyMd9FUzMp7n2SgVteLp3Plzee3STqVT\nPDo6wuHhoa9RcNEc4TWwkvbnwm32Z5RSlvqMx2NfszZLg7LZLLa3tzEej23mzm1OZUZGLhJxZv26\n3S48z/M1nbJXwiVLvGbgpfqZnKdULBatAMDa2pot011SLI0Nysix7JMKKnmRX5OYslTH8zxEo1Fk\nMhkUCgVf5LzT6fhuuRfKgbxBMzOChALcFbSfutK6a2trvteSIgQyQ75CWBr7mwWZ2WXQptPpoFqt\n2kxMo9Gw1Q8MyMjsMpdbNiazyC5xmCVKIUUEXCEUSZouUrS9CuQ4BAaqGKRkkPP4+BiHh4e291r2\nsi5qCfi1iYzneR8F8FEAMLP/okPP88q3ubBVAqPYrBFnKQVrhvP5PPL5vI1YykawWUSGZMZtuFpE\nI7tLrKL9uZsdo0D8mpk4qqwwwxGNRq0cIkt04vG4bzPl7zIbwnXVZn8pEsC+GNfOZKkOHZ4kMvv7\n+9jb20O5XF56IrOK9hcESWTYENtuty2hGA6HtiSDxIGEJpfLWRKTSCRQKpUCm1Xp7+S8GEbmSWQG\ng4El4VzMDBUKBeTzeV9Dqzw0y9k2xWLRRl5ZNtftduf9Z74Rls0G5cGMpdMukXHfBnue0uk0gMlQ\nwGQyOaWmJKPoXDx4cZ2envquga8thR/cvfUidUfZwM3lRquZsZT78qrszctmf7Mge++4Z1WrVQCT\nKgkGlqWfomiFLPGWA6KZtQkixS7Zlfs88DIA46qlye9lWdtNcHp6OvX/Uy6XcXx8bBcJjSQy/F9Z\n1DPmffXIfIkx5ghAHcDPA/h2z/Nq9/RaCw/Z2M8oITMy2WzWZmRcab6g0jJ3yKCUv1tUI5sDls7+\n3IgNAB8R2djYsJkYeRiUIgAsTXR7ClgDOxwO7bpqhFA6YDfKKG1NzoEYjUZTaernz5/bg8YyE5kr\nYunsz4UkMvRFbkbGVS6jn8tkMjbznM/n0e12p6SWWVorFzMlMiNJRT+5stksdnZ2rMyonDUjFYXk\nDJxisWiHw1L84jYHgiXAQtigbI525wEF1e7ze2ZkPM9DKBRCPB63dicXa/rr9Trq9TpqtZol2lJx\n0SUeJDJuhJrPe9EwYWm79MNB6o4sX3xE1RISC2F/s+AG4piRAWD9DoMrMgPD4LNc7nwYDquWe+cs\nkuz+H8hxCzLrI/sRbwNZLtxqtdBoNHB4eOhblUrFl/Fk68IinzHvg8j8NID/DcBbAN4J4K8D+Clj\nzOd7i/gXeABIjXwyejcjk8vlfBt9kGqZW1pGpzvrcPlIsZT2JzMyso6fMs1B5QxuSpsbtEyZBxHh\nq6aHeQCRrxHkzGTWSJYiufW27I1hj8WKYintz4UkMvyaREY2YMsNVkohJ5NJX0Q8qPHVLZlgGaS0\nk3q9jqOjI+zt7dlVLBZtr0wsFrNBIKkmZM4lVUlkGFWUg91WmMgsjA26nzXtZNZj5S2rEyj37c6P\nGY/HtqyWK51OW3VEWY7oytaura3Z/VNKz0oyQpt0wb1cCliwF5A9PzLazpLhR4SFsb+LwL3RGGOJ\nDEmMm0HmKhQK2NzctDOvBoOBVV3kLfsFpc0GZexcIkPRADnokiSYvu22JYoMarbbbdRqNTucem9v\nz1ZO1Go13/8C1UUX+Yx550TG87wPi2//pTHmXwD4JIAvAfALd/16y4Cg5n7WXFJ9KplMApieMCsP\ntDJaJNWuFtGw5oVltr+gxr95godBKaEr9etlrTl7dyjTzOgoa2/L5bLPZld13tEy258EySkjcVTV\nc2W8ZdkDMzJUnZIHU9em3QwkyxjPzs7sRsv5Bdxonz9/jufPn2MwGNgem1wuZ3tpuNkDL+V8qbRG\n/9lut9FoNKwwgOtvVwGLZINBgbgg9SYXDKDIaeRu8AQA0um0T9kxGo36FBJ5KzN/tFWZoebBjYtk\nehaRcSetd7tdxONxdDodRKNR21MoyZKMai9ydPu2WCT7uwpkoG8wGNj7GaCRAeZWq2Vtg/sZz3K8\nlURGLjebyGy2JDLxeNw+lxsokv2pQe/BRVD/F/1ftVr19a9ysY/1JoHPeeLe5Zc9z3vLGFMB8CYW\n0IjvG9JI3Umrl2l8u83dnMch1VwUF+Ox299tQVlJZhA3NzftnA82ZrPulrONKN9YqVTQbDbR6/Vs\nH9ci19neB5bV/iTRYHkMo5WVSgV7e3uIx+NWKlmuoN4Hl8x4njd10OMMJbm42ZbLZTSbTRthZ59Y\ns9lEvV63kUvZj8iDMEvM2Ecm59z0+/2pw+WqYZ42KH1DtVrF4eFh4HDfm0L2QlH2NpVK2cMml+w1\nkH1YMjDoZmdm7bGU4pVlQLLvgHu1HEBMcuQ+btVVRoHl9YHAdDaNQZZQKAQAGI1GU2MSQqGQrxcm\nSKTJLS2jz8xkMrblwPM8a7NXabR3KzHYUyv/F1iee3x8bL+uVCqo1Wo2IxUkVrHouHciY4x5CqAA\n4OC+X2tRIeuEXXWLi6JSJDLc5KnMokTm6lD7uzmMmQzZlMpP29vbKBQKVomKij29Xs8KDzC6U61W\nbQTLbRZcBud4F1hm+3MFKAaDge1ZicfjWF9fR6fTQaFQQKFQsBk8d8YHIckM69Jl5LzZbE71w1Sr\nVdv/0Gq17MZMf0giw+gmiQujmJQxZ0kFo52MqEciEZ/K3yra5jxtkESm1WpZIsPPIJFI2M/sunB7\naUhi2K8iSfLJyclUjxYDMEFLHjZn9chIUhQKhQKzOa7aHjPV9XodjUbjUYxLAFbHBwKT/pl2uw0A\ndrQByThJbVCzv5vh4OcuAz3GGNvLRxJDH8VA4GVERi76awZ86LsrlYpt6mewsdls2sb+ZdynbzJH\nJoEJs+YO9Q5jzB8GUDtf34lJfeTh+eP+JoCPA/jYXVzwMiKoTlj2wszKyHCzl0pVrP99LE7Qhdrf\nw4EHAzZtb21t+SavB2Vkjo+P8eLFCxwdHU1lZFwxg2XEY7I/t/RLZmTW19ft584+rmg0imw2a32d\nrEEnZO8fZ2JREpz12rLcodFo+NT2ZEZGEhk5r4RRVElk+HpypgzFMWQvwzIEh5bJBiWR4eebzWat\nJDIlu28KHvZIiFiSI0tY+VpuSVuQmpR76AzyVUESuTKTwyXtlkQ9FovZbFCr1brVe58Xlsn+bgMp\nukNfyNIzqh42Gg1fj6rsU3XLZ2dlfiWZYXktxUqonHaZYIQMEPH5pb8mgZG35XLZimNwMUC+yP0w\nQbhJRuZzMEkPeufr757f/8MAvhbAHwLwPgBZAPuYGO93eJ63st29l+Gy0rJZv8PadDk3RDMyan8P\nBTcjs7W1he3tbeTzeUtkuIlzVk25XPZJLcuMzKL1AN0Qj8b+JBGRGyOboEli1tbWEIvFkM1mbQ8E\ncPHgNhILHvAqlQqOjo5swylXu932RcjlkFVJZJiJYUQReCmywmzNycmJr7SM0U6+V0b1l8A+l8YG\n+XkxI5NMJq3aHMtWr4qgz4YHR0lig/qv3Mg3MD1LJGjNug5XbYo9ELJMzZ1xU61WYYyxP7utAtUc\nsTT2d1u49sPeGAo7uFU1rn25zyPvd4M8AKxsPQdgkyDLioaLrlWSc5bBVSoV7O/vY39/3xIZLpbl\nykyRzMIvC24yR+YXAVwk9/Inb345qwk2+1ORgvXZnFDskhkaPUkMszG1Ws3K1w4Gg0eZkVH7uz+4\n6miceZTJZJDP561SCyevM5pNxTL2cDFNzTpxNrmuAh6j/XFD46F0fX3dEhFGDqWACSVIZemNu4mP\nRiPbU+U2nbJ+u1qtotvt+iKazAxJn8j5M8y+cJ4S/SMPzbw+2jTVzNjTwFLeRccy2eDp6anNulEm\nWx6cGKyT0sjMcgRBHhTdkm35mIdGUHlaIpFAp9NBKpVCp9NBJBLx7edBTdXLEJxcJvu7K9Bv3eVn\nJG2XgW6SG54Z6UOluE4QOBtL9hxyuOXR0REODg6sIhlXvV5Hs9m072+ZiIuLpQ0JLBOY/qaCTi6X\nsylDzk8ApqNCo9FoSsq2VqsFRrkVituCjpPN0vF43A4e5KLtshdCKr64jY2PrbF/1cFSVw6W9DzP\nEhhOuD47O7PZDrmCytTc+QWs22ZTvyynkDYkSxlJkuTGz5Ix4OVhlz5YzpVhaU+z2bS9Xv1+fy5/\n21UFo9cswWGkmAGPer2OfD5ve2ZktkxCNkW7JWLu4+YBWXVB0O55YPU8D61WyydjHgqFpoQJViXo\no7gY9ElSxntra8vKO3PgLwMzDHwHgQEDOf+FGe6DgwPrW9mewED4quzNSmQeAK4UaDab9RmnJDIy\n+iiHF0ki0263V30Wh2IOYOSaGcNUKuUjMsViEYVCwTpelkZcRGKUyKwOZKkrM8ZsdCWJ4URsKUkq\nS35oE4PBAAcHB75FEuMGatxSH27aJNIkVlST4kFYknI240oiQ9LCUrnBYLDKs2XmAlmGQ6JIEsM5\nFpylJhcwPVfG7UtZpM9KEi1+L+d/UBiF0tBUM6Okb7vdtsFLJTKPA7IPhmt7e9sSmWKxiHw+b/dj\n2lAQxuMxut0u6vU6KpUKqtXqlLRyuVz2zemSFT3LvkcrkblnyGhgIpFAOp32ZWQ4nEtu1jwEslyH\nRIYyeXKjVyjuCm4JTjabtQcLkpl8Pu87TPBw6urmy2bZZXeSigmYkaGPGo1G9nBJEtPtdpHJZJDJ\nZKxkdyqVmmqmHgwGODw8xMHBga3frtVqPpWnWfXaVAviwa/T6dhMjJzDwCZ/2ip9cDabtSWPfC9U\n+Fmkw/EqgESGf2MqJNXrdaTTaaTTaWSzWezs7FiCHIlEEAqFpogMySrvo024s4DmlZWRmSIpOBEO\nh23vAzMx7H3gY2TJpOJxgD4pnU7bfZYZGQYN8/m8LxhzWUaGA4T39/etbL2UWpaS45qRUVwL1ykt\nk81aslGSGZl6vW4b/jUjo7hL0E7j8bjti3FLy/L5/FTPwqzSMs3IrBb4WZ6entoIND9zHsIajYYv\nss5DmzuZvd/v+0jM3t6ebTyVK8h2uGmTxMhMopwX451LmMZiMUtmSND53GdnZzbrTfUrxd2BsrGS\nKLplZNlsFv1+H57nIRwO2yGXgL+xnoc4kgWSlnmSF8JVH6XtySGGnDcjG7hlGXm32537+1A8HOib\n0uk0CoWCFdNxMzJuOWUQJJE5PDzEpz71KRwfH6Nardqh1NVq9UpiFssIJTL3ANf5cpNl9IlExi0t\ncyPbcpCWVD955KplinuClLBNpVLIZrNIp9N27gbLyajMwyUnabPBX27WWiqxOghq2pcCAHKKtVRb\ndKVtB4MBjo6OUK1WrcQy+wP4uIukRvlzqqRRaKLVaqHRaCCdTvvUrJiZkQMymdmRQSWWLK2Iwt7c\nISsMZIaFZYokuW5Qj/1LkiCwdFAuSW54K4UDuIL6a+4SQQTEvS8cDvuyhul0Gu12G61Wy/pWJTKr\niaA5grlcDoVCAaVSyY42KJVKyOfzlswzMyntO0iVjyISzHayeqfZbNqemFUOfCuRuWPQYOk0Q6EQ\nYrGYr6wsqIFLlpXxICAns1JylBGdVVKCUiwG5EGPyk6JRML2G/CAx4Zv1tqyr4FEm3aqRGb1wV6+\nwWDgm83BsthWq4VEIjE1Q2E0GtnhgN1u1ze/4DJ7kZF4eQ1u/wV9LyV/5WyZWCyGk5MTO1OGRD0U\nCvlKJvl6ittDKj9RtpufZbVaxfr6ug2MpNPpqQMcP89oNGqnqHMWGx/DeUbxeNx+rlRLc0cfPDR4\nNiAh47XR7i5SpVIsNzgziU390WjUEpjt7W3s7Oxgd3cX+Xwe2WzWng3d/wHgZXBAVkAwkCMl6R+T\nwq0SmTuGVC9xI4CSyNAZz8rI8LDIrAynX7N2nKUaCsVdQWZkkskkMpkMksnkVC+XlAXnwdElMowA\nKZFZbZBEkMSwBpuZGApDuBHE09NTdDoday9scr5q2YM7o4FkivYoBSv43DxIypkjFCag0hkPurRZ\nLY28G8jyLznZnNkazvnpdDqo1WqIxWJTg1T5ubEkLZFITA2VNsbY3iwulqxRyW6e5YMkMiRbJGYk\n0EpkVhNyYGsymUQymbTjDCSZYd9YIpEI7BMjmNFkv4tLZBqNhu2lZtZzlaFE5o7BTAyjP0wnuxkZ\nqRHOA6JLZGRGhmU7/X7f1zirUNwVXOJNIsNDHptYeWjkPAQ6TTcjI5XLFKsJ2oO0CyqKySVLtejr\n5NwDSWT4uIswq8St0+mg0WhYhbJcLmezPTIjQ5sMyshQJvgq16G4OmRGhrey+ZhDI/k5AP4DHD9T\nuViOJRfLdYbDoe1V4Wtyb54HJJEOysjMauRWLD+YkaHYSDabnSIxT5488UnXMyPjghkZ/u9wFhb3\nY2ZkWq2WLf9e9aC3Epk7hszIUGlCZmSoBMXHyihVkIGyhEeWlikU9wG3tEz2x8zKyNBxyvkI7JNR\nrD5IVN3666tGlm9DFFwlM2ZkIpEIwuEwcrkcer0ehsOhj8gwMr+xsYFOpxOYkSHZ0gj53SMouCHV\numb9zaPRqPVLXC6RWVtbQ6vVwmg0gud5thwNgO1PeMjAiquu5sqEu0RG7W01wb2Vgk+yN0YSGe6z\nQUNepb+TGRkGj9zSsm636xOQWmUokbljsC+GtZBMgwc5K+m03Eg3mwC73a7tidHooOI+Mau0zJ0Z\nw8h3vV630o5s2B4OhyvvNBWX46F9FQUEut2uJSOMfGazWdTrdasgxSUlmZktL5VKWFtb8w0ovEh4\nQHE3cEsFg8CDW7/ft0EV2SBPMiNnYXFJOeRYLBb4GjwcBi2WyZ6enloyIqsq3B4cmfW5TAjAVTxT\nLD9IRlihw+xwsVjE9va2JS/FYhHpdNr2ccnfcc+HwMsyWjb2M5C4t7eH4+NjNJtN9Hq9mcOEVxVK\nZO4YJDJSncRtJAWmnVtQnTeJzKpNYVUsJljHG9TszwMDszHtdhu1Ws0SGcqCMxKqUDwkqIAlI/uS\nyGSzWZtx4WLAiVHSfD6PUqkEYwza7TbW1tYsQVLMH0HCEnI/5Z7Kki3Z8E+xgGg0OlVmI0ve2JPK\nRUETeUsfKcUEGLjk7bzK1xTzh8y80c+kUikbKNne3sbTp0+xubmJQqGATCaDaDRqSUyQlLdcbO5v\nNBp2Psz+/r4NKLKse1WlloOg/213DJmRIZG5ijJJkPKOlM5TIqO4bwT1yJCE88AgiUxQRkaJjGIe\nIJHh1+PxeIrIuGpXbkYmn89jc3MTnudZEjMcDqfKOhTzgZRsliITboWDVC0j2SCJoYIeIXut5FBX\n9vu1223f6nQ6iEajduArF5XxANj+HsXjhSwhjEQiPiKzs7ODV155BYVCAalUysq/u0QmiMzQ7rvd\nrh1+ube3h/39fRwfH1si85iyMYASmTsH08qSyMgZHLMUU4IyMpTPewyqE4r5I6hHhmo/jDCenp7a\nAYLMyBwfH9vsoRIZxTzAzAkPuqPRaIrIxGIxjMdj23jLGV+SyHS7XUuE6IsViwHukTzMkbi6gUGp\nCEZVsGg0imQyGTh/zc3IsGyn0WhYifBarWa/TiQSviHBUkGUQ4UVjxdS1IHBExIZlpY9ffoU2WzW\nl8mb1XYgSUwQkXn+/DkODg6s5LKbkXkMuJYOoTHmW40xv2GMaRljjowxP2aMeXfA477bGLNvjOkZ\nY/6ZMebNu7vkxYbMyHB+zFWIzHg8tvW/jHa7w4wei1HOgtrf3UIOiZOOl9KmrN3lrCPgZUaG6lCc\nGMza3FUnMmqDiwnXfzYaDXsQrdVqqFarqNVqaLfbtu9FDsxkaRmnamezWSQSCUQikYWa7/GY7Y9i\nOGxw7na7VgJeLvaXMhjYaDTQbretfwpScOJBkf6N8uH0cYx8P3v2DC9evMDh4SEqlYrvua8z381V\n8VsWn/mY7e+qkKIiMuObzWZRKBSwubmJ7e1tbG5uIpfLWWXQoLIywN/YT/GnVquFWq1m7fLg4ACV\nSsVKLj+2vr7rCqp/EYAPAvg8AH8CQAjAzxhjYnyAMeZbAHwdgL8A4N8E0AXwMWNM+E6ueAkglctm\nNXAFyS1zgFy9Xke5XEalUrFZGSUyANT+7gyMRrMJkROF3b4Yme5mRMhVS5FDWh+BA1UbXGDIAyKj\n66wlPzo6smSG87iYnUmlUigUCtjZ2cH29jaKxSKy2azNqIfD4UVRllL7uwSS1HY6HV+v6SyiwSi6\n7Jlyp67v7u7i6dOn2N3dxc7ODra2tqb8pizDDYLc8yk7zYzOkoikqP1dAhIZme2VM9lY4RDU1A/4\nMzDsh6nVajg8PMTbb7+NT37yk3j27BkODg5QrVZ99j2LqK86rlVa5nneV8jvjTFfDeAYwGcD+JXz\nu78RwPd4nveT5495H4AjAO8F8OFbXu/Cw41yu4dBQqYK3UnYsolaew9eQu3v7sD+AFlLzsZDRohC\noZAvWujKg7P5td/v2015STbjG0NtcPFBmx2NRlZdj1nFUCiEeDyOdDqN09NTXw075XrH47GVFq/V\naohGo1boQg5ynNN7U/u7BDJrQzluWdng+ijuyzK4Q3EALlkmJEvL8vk8CoWCT510VqM/7VIGLyWR\nWYbMjNrf5SCRYTaG/VRBbQYXZWFoK91uF7Vaza5yuezLwsgWBBKZRbeju8Zte2SyADwANQAwxrwB\nYBvAz/EBnue1jDG/DuDz8UiMmNEduWZlZBihkWURJDKVSgWdTudRlOzcEGp/NwQdLZv62SPgZmQk\n2ZabMNV9mJHhIe8ROlG1wQUEiQwzMvS/LCOjzbI+HZg0aScSCZyenqLZbKJWq9lGXDmZfsHIutqf\nAwZbmJEJhUJ2BpsbsZb7MUsNgZf+kTOJ5ADLeDyOXC6HbDaLXC6HXC5nHyPLcIPgVmGQyCzxrA+1\nPwcXZWRkqTazu5LIuEpj4/EYvV4P9XodBwcHODg4wOHhoe1NlUTmEe/BNycyZvKX/wCAX/E87/fO\n797GxKiPnIcfnf9s5TErIyONFpguLZMZGapBVSoVDAYDy7Qfm3FeBLW/24EZGTYhMsLoZmQYgZak\nW2Zker0eer2etefHZKNqg4sLSWSoQAYAmUwGxWLRV1rGYZhUtDo9PbXBJP4v8PfPzs5m9jk+NNT+\ngsEKh36/b/fe65SWUeHs7OzMZlmYiUmlUj7VMt4yws6g5Sy4GZnRaLS0h0+1v2AwmyczMrNKy/h4\nCVlaJjMyBwcHeOutt7C3t4d6vW57ANkX81iGXwbhNhmZfwjg0wH80Tu6lpUAHaIciiknRptzKU9Z\nAyl7DuQwzFar5RvKtWyO7p6h9ncLyDKKbDZra73dBn/WbstmQ67RaGRLylxI5yzJu7xdAagNLiio\ncNXv9wHANvfzAEAp3VgsZufKsL/BVTvLZrM2QMXnGo1G83x7hNpfABhsGQ6HNqjY7XZ9/Xyj0chX\n1sPHuSSEB07ZvE2/mUqlkEwmbSmahIyqM8DDRm1OYW+1Wj6hgCXc49X+AkDBJ5awMmuXSqUsMQ6y\nNQCW5ErlRIo/lctlHBwcYG9vzyds0ev1Avfgx4QbERljzPcC+AoAX+R53oH40SEAA2ALfka+BeC3\nb3qRy4SgWRxk4pwjA0w3/XFJ4sJD5DLUzj4k1P5uD2ZkZLM/nS3Lyjh8ixtwv9+3aWw3uimzjTJd\nLhdtWZaqLSvUBhcfkoAbY6ysLrMt6XQa4/F4arjhxsYG4vG4Jfi7u7uIxWJWAUsOyZyXb1b7mw2p\nbkYSIgOE9Xod6XR6qgcmqCSMvx+JRKyv4/5+URkZiTT3ckrmVioVHB8f4/DwEPv7/3975xYjW1qW\n4fevc3V1Vffu47A3M8yM4wRJPAUPQRhnFBOVxCHeYLhBuDEEvdAbCAlxiF4YMSYYcAw3khCjCYnH\nC2AGFaIEkaBBBtCgOLj37N7VXefqqlVV3dW9vKh6//lrdfWxVnXVqn6fZKV3n1av2v32v9b3f9/3\nfjsoFou2Ybvb7UZmN136G8W9zyUSCWu5vLa2hu3tbWxvb1uHMgYy43DLtrmxTetvd7ZghIPfqXDp\nQGYo4LcDeNr3/bvu53zff9kYUwTwVgDfGH59AQOHiz+e/HLnn3GBDHsO3IVvXIo52PzHQCYqi9t1\nIP2FA2vAWVq2tbWFtbU12xMQDGRoRxp0AOIi6i7k3Ol0dzmNMVbTwOweAMNAGpx/XGMKYBDUJJPJ\nkUAml8vB932srKzYjA2DePbSbG5uwvM8uwnFICYWi43o9zq1LP2dDQNYdx2iTTOD0UKhYOfMALAV\nE0HcMiFWWzCwGedi52adaeXMB9Nms4lKpYK9vT27s763t4darWZtwaNwr5f+Rgne99xAhvfWra0t\nm8FLpVKnOh+686u48cIscr1et1k8VkcokBlwqUDGGPM8gHcCeBZA2xizPfxUw/f97vDfHwXwE+VB\nPQAAGTZJREFUIWPM/wD4HoDfBfAKgL8N5YrnnGAgQ7cK9hzwBjguIxMMZNyda4lV+guTcaVlwYwM\ngBOBTHC20fHx8Ugmxu0PC77lJG7qP4pIg9GBD7QMauLxuHUi4+YSgJFeGd/3RzIy7KVhIM4H0lgs\ndkLD17FGS3/n4/byEXcjplarIZ/PW23wnp1MJk+cixkZ4NV7Oz8WDH6CgS3XTs67qdVqNpApFou4\nf/8+SqUSPM+zrlPzvi5KfycJbuK5m4ScTbW1tWUHs14kI0OTEjqVMSPTbDbRarVGKnfmXTPXwWUz\nMu/FoJHri4GPvwfApwDA9/2PGGOWAHwCA0eLfwbwi77vz0VR8bSh80kwI8NUdLC0jMHLaaVlN7GJ\n+gykv5AYV1pWKBRGHMv4AMiFlUPmmJFxd4OCQYx7BG/41H5EkQYjgtvfxWC70WjYOnVqkkFMPp/H\n8fHxSCDDIOf4+NjWq7sPInyIuMb1Wfo7BwYRbhlrMCNDu21u6Jz2MMh+BwYxdK8Luk0Ffz5Ly1ge\nxACKpWUPHjzAK6+8gmq1esK9bM6R/sYQNHjKZrPWCZSBTNDFdhxuRqbRaNhBvvV6fSSQcTe49Wx4\n+TkyF7Jr8X3/wwA+fIXriTwUsjsl3S0ro4CDzhTuEbS8FQOkv/AImlLQ3z6ZTCKRSIxYzQYHuNG5\nKZlMIpvN4vj42O5o8nAtx3mw0ZW723REixLSYLRwb/SuxX2tVrO9EUtLS8jn89ael+VEDGaMMXYe\nDTelOG/muvsYpb/zca1r+TvhNHQ6giaTSVsay7UsWCI0rlw2+DMYeATv4YeHh6jVaiPuUqVSCcVi\nEaVSCdVqdeShNCr3e+nvVagHmjrxYPBCF1A2+fN7glbL7vrBzCF1ylkxbvnhTW/sH8ekc2TEEIqT\nqUU+INJb3nUtI66QXTEHb4yKusUscfXHhzx3x4nD4Nw5C+OcytisaIyxrkJCXBf+0JKZD7XsdaCz\nEDONfKilJXMsFrN9FTRuyWQydhf9JgyCjRpcd7gRw5LAcrls3Rh7vZ7NDLP/yS0ZCw4t5Ft3A5L3\nbjqh0dGx0+mgUqnYo1wuo1wuY3d3F+Vy2fY5qHQ8egSDXFY1cLbQ1tYWHn/8cTz00ENYWVkZ6Ylx\nA5ngJna/37elr7u7u7h///5IH5XneZHc/LsOFMiEgCtOphe523daIOOmBd1gZlwQI8Q8QC0ykGEz\n49HREQqFwsjhNvezTJLD5jjfQ4jrhOU+nufZvod0Oo1bt26h2WzC8zx0u127nrMUOJ1O251VDrVL\np9MnHkjEfBC8Z7IskMEr58zwd8b7NTBwJOPBMkNml6kLZntcq1z2ufDt/v4+SqUSSqUS9vb2UCqV\nUC6XbYnQuEBG9/r5J5ili8ViWF5exsbGBm7fvo3XvOY1uH37Nm7fvm0DGWprnEU33fVYXugORN/Z\n2cG9e/esZjj0UpxEgcyEBG1n3YwMy8tYrnNWejoY2GhxE/NAMKB2MzL5fB6Hh4eIxWJYW1vD+vq6\nfcvdb7f/yxhjb/r1en2WL0vcQI6Pj0dmyxweHiKVSmF9fR37+/t2+jvXam5ExWIxrK6u2h4yZmSA\nVx9G5mVIphgQXLc4HJNBDYf4sqwsk8nYvkEOw3TPxXJb16yH2ThaK7OHkH04u7u7KBaL9qhWq+h0\nOuh2u7aM0S0n070+GgT7QZeXl7G5uYlHHnkEjz/+OB555BGsrq7i1q1bIxmZYCDjaoiZPGZkGMjc\nvXvXjj6g8Yg4iQKZkKBQ3QZnNyNzmlXjaeVlCmLEvODeaIOBjO/7SKVS1it/a2sL29vb8H1/5KbN\n2l7P82x/ghDXCYNrANYaN5VK2QGZLC1jv5i7fgczMnzYpRvaaXaqYnZw3WJpmZuZofOca8zDvhkG\nMe7GozvAkMGr6zjqeZ59CGU52c7OzshRrVZHZmnpHh89ghkZN5B5+OGH8eSTT+Kxxx6z7mTcyD7N\nFIL9VLxPjsvIBPuvxEkUyIRMsDm61+shkUjY3b9gk/84x7IoNP2JmwGtJHO5nH0ITKfTtkF6dXUV\niUTC7lhz3gL1zynWLLfwPG+krEOI64S7oPy353loNBoolUp2tki73R4pkWRgk8vlbF/Y5uamLVVy\nAyQxnwR/78YY1Ot1lEolu2PueR6Wl5dHDrqNssIilUpZO3r3YEO/e+zt7dmmftori2jjVtywD5pa\nyefzyOfzKBQK9mvGVeKQfr9vh0zTkYyaYSlZr9dT4HsBFMiEDBdMNvy12+2R6cDBJkSmFVmGwwZC\nIWaNm33hQ0AqlUI+nx/JtACwxhbGGFu6wdpellrs7e2hXq+j3W7LeUVcO8FNJN/30e120Wg0sLu7\ni2QyiePjY+zv72NrawtHR0dIJpP2wYQGFxsbG2g2m/YBmJlGMb+4v3dg0Ke3v7+PSqUCYwwODg6s\noYN7sB+KO+zpdNpmX9yDM2rcg7M/PM/Txs2C4Jac0pV2eXnZlpy6g1Ld3qpx9Pt9O1+I/VQPHjxA\npVJBq9Wyc4VUoXM+CmRCwk1jM8vCQIaRu+sT79ZHMnPDrIxrGynELKENrevi5GYR3fkHDMI5b6NW\nq6FaraJcLtvBXvV6Xe4rYma4u5uxWAzdbhf1et0GMbQI7/f7SCQStnySfwcrKyvY2NhAp9MZCWJo\nHiDmE9cqmffW/f19ALC9CYVCAaurq/ZYWVkZcanLZrPIZrO2/Mc9OPTSbfjnod6GxcEdO8AghuWm\n1AlNQtxyxHGwt6pWq1mXMvZS7e/v22yMgpjz0eobAuwdAE5mZDzPs3M63JkDwYxMr9cbeSiUcMWs\nYUbGzcwE63VpY9pqtWwJGWt9Wbqxt7eH3d1d+3nP85SRETPBfaBl0N1oNGwQU6/X0ev1kEwmkc/n\nsbm5OTIkc2VlxQ6DZWlIs9lUz9ec4waw7EflwyKHnOZyOaytreHWrVv2LWeA0GJ+aWnJZpfdo9Pp\noNfrodvtotvt2vu5u9kjog8d7lhuTUt29s0xI3Pe0FQA1viGgcy9e/dQKpVQqVSsNmcwcDeSKJAJ\nES6SDE46nQ5arRYymYxd2NzFNOhYEaHpvuKGwFrfIO7C2mq1UC6X7QRtNtRyknWxWMTOzo7NOvLm\nLsR1E9zdZBM4g5hUKoWjoyMbxHQ6Hetalc1msbKygn6/b3sqGo0GstmsMjJzzrhd7WBfUyaTwfr6\nOtbX1+2wSj6o5nI5u/sebOS/f//+yEwhloiLxYOlZZlMBsvLyyP6cEvLgowLRIIZmbt379peGZaW\nKYC5GFp9J4TZGL7ljIxarYalpSXb6O+WjC0vL9syG4qWMwy4CErAYpq49bnFYtHWhLNZMZ/PI5fL\n2Swi3/Jm7d60W60W6vU6qtWqbXQtl8solUqo1+totVojZZPKOIp5wc2OM0Bx+xtbrRaazabdYEok\nEsjlcjg+PrZOZtytp5PZuHlgYv7hfBnP82x5UK/XQ7vdtmVl2WwWzWbTrm2c7eGubWJxYYkpB19u\nbW1hc3MTKysr9nlvHNzgdrN0HI7KZ0HXOVFDdi+HApkQcIOZg4MDtFot1Go1O3wrmGlhXTaboVly\n0+127QOfboBimnA3qFqtolgsIp1OY21tDaurq+j1evbGHFx83ZJJetu3Wi3b7Mq3bPCn+4pc+cQ8\nEmwCpwEAAxnqmQNeWWIWj8fHWjK7QxK1IRUtGMh0Oh3EYjEcHR3Z0nAeqVRqxMiEZbIss9Xattgk\nk0nkcjncunULW1tbuHPnDra2trC6unpmZpYW4O7g1N3dXZRKpZFNbW5oy9nzciiQCQkGM3xAdG05\n3RtaLBbDwcHBCccTZWTEdeJmZFz70V6vh6OjI1vby5pvHuMce5hRZHATnHLN8wZ3q4WYB5hpZFDj\nBuvMyPBvJB6P28ZeZi7dZl8OfnV7cUQ08H3fmjew9y+VSiGRSIzY6dJ+mRrh7rmycIsPAxlmZO7c\nuYONjY0LZWTYj0Unz729PdsTw0CGLQbKyFwOBTIh4mZkKFz+G4C9EbIcxz2CkbgWQzFN3IwMddvt\ndu0uUCKRQDweP+HEw6FvHPxWrVZt6ZjbA8MMjpvN0bBXMW8Em8AZvAdLy3K53MjOfDKZxMrKCgqF\nwkhpGRt7mZkR0YEZGQYxtNB1J7kzU8OsG6st3KHBWtsWl2Bp2Z07d0asus8KZOjmWa1WUSqVTpSW\nuSWsbpZYnM+lAhljzAcB/DKA1wPoAPgygA/4vv8d52s+CeBXA9/6Od/33zbhtUYCNjFzcnSr1bIL\nIg/u+vAB0fM8m5VhWY8Ww5NIf+HhDuNyJ1/zpp1IJGCMsWVjDLjpRMYemFKpZOvEeYN3SywWLXCR\nBhePoD7ZJ0HnPU5kB2DLi3K53IiTFa1XOa2bD8BhI/1ND9/3bYAixnPT9RePx5HNZpHP5215GXun\nMpkM4vH42Hud+zxYrVat2125XB4pK1MW5mpcNiPzFICPAfja8Ht/D8CLxpgf8H2/43zdZwG8GwBX\n8hsz0jZorQzAlvDE43EcHR2h0WicKNlpt9u2edC13RMjSH8h4brrxWIx+L6PdDptdxw7nQ4qlcpI\nPwxLbTjFms4q7iDXcQHMogQxQ6TBBYdZ9XK5jGw2i1gshs3NTWxsbKDf7yMWiyGdTtvA37Vk5bo/\nrUAG0p+YLTdafyy5jsViiMfjtnKBf+/8mw/e/2gC1Wg0UK1WbTaGPaSsWBBX41KBTDCiNsa8G8Ae\ngDcC+JLzqZ7v+6WJry6CBJtHAdisDHe+l5aWRspvWNbDpv+DgwMFMmOQ/sLDnXfEXeRYLGZ3jhqN\nBpaXl601OEvH2NzPkjNmEN3+l0XugZEGF5/Dw0Ps7++jXC6P/E0w07K0tIRCoWA1Ho/H7bTvg4MD\nJBKJMyd6T4L0J2bJTdefG8S4R3D4pTuvyHXDazabqFQqNhvjGkaIqzNpj8wqAB9ANfDxZ4wxuwBq\nAP4RwId83w9+zUISHLh2fHyMVqtld7nZOMoSHJbjuPNkFMhcGOnvijAjA8DuIrsD/jKZDDKZjP24\nWxPOgW88WAo5LguzqAGNgzS4YLCHMRaL2aDm8PAQsVgM2WwWq6urNnhnRoaBTK/Xs7u0U8rIBJH+\nxCy5cfobl5HhxoWbkeGGNnuuGMiwtKxcLtuWgoODg5twr5waVw5kzOA39lEAX/J9/9vOpz4L4C8B\nvAzg+zBIPX7GGPMm/wb8ptxInJadzMQ0m027WxcswXFndajZ/3ykv8lgPTgzMXQtc1Pl8Xh8pBE6\nuDgHtXqDghcA0uCiwuDFLTEzxtgm3+3t7ZFAho5W7J+ZZkbGRfoTs+Qm6u+00jJmZMYFMv1+/0Rp\n2d7eHqrVqm0tUEZmMibJyDwP4A0A3ux+0Pf9TzvvfssY8xKA7wJ4BsAXJvh5kSH4QCf3iakg/U2A\nmzWRPq+MNLiAcAeVGcp4PG6be3kUCgVUKpWROUkM8K+xN0z6E7PkxumPZdhsCeh0Onb0BkduAK+u\nITzccQW0X2amlz2m4upcKZAxxnwcwNsAPOX7/oOzvtb3/ZeNMWUATyDiIhbzgfQnZo00uNi4JcIA\n4HkeKpUK7t27B2MMOp2Ode3jweHGnU5n6nMgpD8xS26q/g4PD235daVSwe7uLvL5PPL5PADYbCxH\nb9D1s1gsWocy9pYGTXLE1bl0IDMU8NsBPO37/t0LfP1rAawDOFPsQlwE6U/MGmlwsXHLffl+u922\nJWbdbhfVahWNRuPEDitLRabZ5yj9iVlyk/Xn9pGWy2UUCgXb35JIJJDNZu3QVFotV6tVFIvFExnc\n4KgCcXUuO0fmeQDvBPAsgLYxZnv4qYbv+11jTA7AcxjURxYxiMB/H8B3ALwQ2lWLG4n0J2aNNHgz\ncEtEjDFot9s2iKnX69jZ2UGn07GBC//tDkmcRiAj/YlZctP15wYylUoFuVwOwKuDMlla2uv17PDL\nYrFoMzIMZJiRWdARBdfOZTMy78XAoeKLgY+/B8CnABwB+CEA78LAzWIHA/H+tu/76mYSkyL9iVkj\nDd4Agg8X7XYb3W7XzgOjEcY423HXyGUKSH9iltxo/fX7fXieh0ajgUqlYs09stksCoWC3cBwMzK7\nu7tjAxkOXlUQMzmXnSMTO+fzXQC/MNEVCXEK0p+YNdLgzYSN/LNG+hOz5Kbrz83IpNNp62AGvDrS\nIJfLYWdnB/fv38fOzg4ePHiAvb091Ot17O/vo9fryZk2ZCadIyOEEEIIIcRC4zb7c1huv99Hu91G\nrVZDsVjE17/+dTzxxBMol8v2qNVqI9kYBTHhokBGCCGEEEKIM2BGhjMCu90uPM9DrVazDmYvvvii\nnRvYbDaxv7+PVqsFz/M0/HJKKJARQgghhBDiDBjI9Pt9G6xUq1Wk02l71Ot1fOMb37AzZOhiyJkx\n03Q0vKkokBFCCCGEEOIMaJnMrIwxBgDsv40xODw8xEsvvQQAJ1zJ5FA2HRTICCGEEEIIcQ5uUHIa\nh4eRN2iLFGc6UFwTmVlfgJhrrkMf0qA4DelPzJpp60P6E2ehNVDMknO1MQ+BzKOzvgAx1zy6ID9D\nRJNHF+RniOjyaMTPL6LNowvyM0Q0efS8LzCzrtczxqwD+HkA3wPQnenFiHkig4GAX/B9vzLNHyQN\nijFIf2LWXIsGpT9xCloDxSy5sP5mHsgIIYQQQgghxGWZh9IyIYQQQgghhLgUCmSEEEIIIYQQkUOB\njBBCCCGEECJyKJARQgghhBBCRI65CWSMMb9ujHnZGNMxxnzFGPPjIZ33OWPMceD49gTne8oY83fG\nmPvDcz075mt+xxizY4zxjDGfN8Y8Edb5jTGfHPN6PnPBc3/QGPNVY0zTGLNrjPlrY8yTYV3/Rc4/\nyfVPk2npb3ju0DQYZf0Nv39qGoyy/gCtgRc9v9bA6SD9Xez80t/0iIIGo6y/4fcvnAbnIpAxxvwK\ngD8E8ByAHwXwHwBeMMZshPQjvglgG8BDw+MtE5wrB+DrAN4H4ITlmzHmAwB+A8CvAfgJAG0MXksq\njPMP+SxGX887L3jupwB8DMBPAvg5AEkALxpjsiFd/7nnn/D6p8I16A8IT4NR1h8wXQ1GUn+A1sDL\nnH+I1sAQkf4ufv4h0l/IREiDUdYfsIga9H1/5geArwD4I+d9A+AVAO8P4dzPAfj3KV33MYBnAx/b\nAfBbzvsFAB0A7wjp/J8E8FchXf/G8Ge8ZUrXP+78oV1/iL/HqelveL6paDDq+jtDI6G8hqjob3hd\nWgMvfn6tgeH/HqW/i59f+pvO7zJyGoy6/s7QSKQ0OPOMjDEmCeCNAP6BH/MHr/TvAbwppB/z/cM0\n3XeNMX9mjHk4pPOOYIx5DIPI0n0tTQD/ivBeCwA8M0zZ/Zcx5nljzNoVz7OKQcRfBaZy/SPndwjr\n+ifmmvQHXIMGI6g/YLoanHv9AVoDr4jWwJCQ/q6E9Bcii6LBCOoPWAANzjyQwSBaiwPYDXx8F4P/\nzEn5CoB3YzA19r0AHgPwT8aYXAjnDvIQBr+wab0WYJCOexeAnwXwfgBPA/iMMcZc5iTDr/8ogC/5\nvs9a0dCu/5Tzh3b9ITJt/QHXp8HI6A+YrgYjpD9Aa+Bl0RoYLtLf5ZD+wmdRNBgZ/QGLo8HEVb4p\nSvi+/4Lz7jeNMV8F8H8A3oFBeitS+L7/aefdbxljXgLwXQDPAPjCJU71PIA3AHhzeFd3/vlDvP7I\nsEgaDPn3N00NSn9DFkl/gNbAqCH9nYr0d00skgYjdA8+9fxha3AeMjJlAEcYNP24bAMohv3DfN9v\nAPgOgAu7SFyCIgZ1ndfyWgDA9/2XMfg/vIwrxscBvA3AM77vP3A+Fcr1n3H+E1zl+kPmWvUHTFWD\nkdAfMF0NRkx/gNbAidAaODHS3wRIf6GwKBqMhP6AxdLgzAMZ3/cPAfwbgLfyY8P00lsBfDnsn2eM\nWcbgP+vM/9irMPxlFDH6WgoYuDeE/lqG538tgHVc8PUMxfV2AD/j+/5d93NhXP9Z5w/j+sPmuvU3\nPP9UNBgF/Q2/Z2oajJr+AK2Bk6I1cDKkv8mQ/iZnUTQYBf0Nv2exNBiWa8AkBwbpPQ+DmrnXA/gE\ngAqAzRDO/QcAfhrA6wD8FIDPY1Drt37F8+UA/DCAH8HAieE3h+8/PPz8+4fX/ksAfhDA3wD4bwCp\nSc8//NxHMBDU6zAQ2tcA/CeA5AXO/TyAGgb2eNvOkXG+5srXf975J73+KOovbA1GWX/T1mBU9Tdt\nDYapv6hrcJr6i7IGpT/pb5b6i5IGo6y/RdXgzEQ75sW/D8D3MLB4+xcAPxbSef8CAwu/DoC7AP4c\nwGMTnO/pobiOAsefOl/zYQzs6zwALwB4IozzA8gA+BwG0XIXwP8C+JOL/qGfct4jAO8KfN2Vrv+8\n8096/VHUX9gajLL+pq3BKOtvmhoMU39R1+A09Rd1DUp/0t+sjyhoMMr6W1QNmuGJhRBCCCGEECIy\nzLxHRgghhBBCCCEuiwIZIYQQQgghRORQICOEEEIIIYSIHApkhBBCCCGEEJFDgYwQQgghhBAiciiQ\nEUIIIYQQQkQOBTJCCCGEEEKIyKFARgghhBBCCBE5FMgIIYQQQgghIocCGSGEEEIIIUTkUCAjhBBC\nCCGEiBwKZIQQQgghhBCR4/8BZQK13NKezw4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = mnist.test.images\n", "y = mnist.test.labels\n", "hidden_layer = np.maximum(0, np.dot(X, model['W1']) + model['b1'])\n", "scores = np.dot(hidden_layer, model['W2']) + model['b2']\n", "predicted_class = np.argmax(scores, axis=1)\n", "\n", "for i in range(0,10,5):\n", " img1 = np.reshape(X[i+0,:], (28,28))\n", " img2 = np.reshape(X[i+1,:], (28,28))\n", " img3 = np.reshape(X[i+2,:], (28,28))\n", " img4 = np.reshape(X[i+3,:], (28,28))\n", " img5 = np.reshape(X[i+4,:], (28,28))\n", " plt.figure(i, figsize=(10,4))\n", " plt.subplot(151) ; plt.title(\"predicted: \" + str(predicted_class[i]))\n", " plt.imshow(img1, cmap=cm.gray)\n", " plt.subplot(152) ; plt.title(\"predicted: \" + str(predicted_class[i+1]))\n", " plt.imshow(img2, cmap=cm.gray)\n", " plt.subplot(153) ; plt.title(\"predicted: \" + str(predicted_class[i+2]))\n", " plt.imshow(img3, cmap=cm.gray)\n", " plt.subplot(154) ; plt.title(\"predicted: \" + str(predicted_class[i+3]))\n", " plt.imshow(img4, cmap=cm.gray)\n", " plt.subplot(155) ; plt.title(\"predicted: \" + str(predicted_class[i+4]))\n", " plt.imshow(img5, cmap=cm.gray)" ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }