Single-Layer-NN-MNIST-CLASSIFIER.ipynb

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   "source": [
    "# Single Layer NN using TensorFlow\n",
    "The following code classifies MNIST dataset using a single layer NN with softmax activation function, Cross entropy loss function and Mini-batch Technique\n",
    "\n",
    "## Softmax Function\n",
    "$$\n",
    "\\sigma(z){_j} = \\frac{e^{z_j}}{\\sum_{k=1}^{K}e^{z_j}}\n",
    "$$\n",
    "\n",
    "## Cross Entropy\n",
    "$$\n",
    "Cross Entropy = -{\\sum_{i=1}^{i=n}Y_{i}^{'}.\\log(Y^i)}\n",
    "$$\n",
    "\n",
    "## Mini-batch Technique\n",
    "Taking a btach of 100 images in a single iteration. 2 Reasons to use it:\n",
    "1. Analyzing Single image results in a curvy descent. Knowledge of 100 images at a single time gives a more precise consensus of the gradient\n",
    "2. We do distributed processing using GPUs on which matrix multiplications works faster. (Optimised for GPUs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [],
   "source": [
    "import os\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL']='2'\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Load Data\n",
    "MNIST dataset is a handwritten numbers dataset. We download it from tensorflow examples.<br/>\n",
    "Make sure to change the path according to your need"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting tutorials/data/MNIST/train-images-idx3-ubyte.gz\n",
      "Extracting tutorials/data/MNIST/train-labels-idx1-ubyte.gz\n",
      "Extracting tutorials/data/MNIST/t10k-images-idx3-ubyte.gz\n",
      "Extracting tutorials/data/MNIST/t10k-labels-idx1-ubyte.gz\n",
      "Extraction of images is complete.\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"tutorials/data/MNIST/\", one_hot=True)\n",
    "print(\"Extraction of images is complete.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## TensorFlow Placeholders\n",
    "Tensorflow placeholders are like variables waiting for input. They are access points to the computational graphs on which we can just feed into the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, [None, 784])\n",
    "W = tf.Variable(tf.zeros([784, 10]))\n",
    "b = tf.Variable(tf.zeros([10]))\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Model\n",
    "Our model is a Softmax Function applied over the weighted sum of the image pixels along with a bias added to it.\n",
    "$$\n",
    "Y = softmax(X.W + b)\n",
    "$$\n",
    "Where,<br/>\n",
    "X = flattened image vector (1, 784)<br/>\n",
    "W = Weights matrix of shape (784, 10) -> 784 weights for each pixel and 1 column for each class [0-9]<br/>\n",
    "b = bias vector with 10 columns, each column representing a class<br/>\n",
    "## Role of Mini-batch\n",
    "Since, we are using mini-batch technique. We will use X as a flattened image matrix with 100 rows, each row representing a flattened image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Y = tf.nn.softmax(tf.matmul(X, W) + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Placeholder for correct Label\n",
    "We need a Placeholder, to hold the correct labels, which will help us to compute the accuracy and cross-entropy of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Y_ = tf.placeholder(tf.float32, [None, 10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Loss Function\n",
    "As discussed above we are using cross-entropy loss function\n",
    "$$\n",
    "Cross Entropy = -{\\sum_{i=1}^{i=n}Y_{i}^{'}.\\log(Y^i)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "cross_entropy = -tf.reduce_sum(Y_ * tf.log(Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## % of correct answers found in batch\n",
    "Graph nodes to compute the accuracy of our model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "is_correct = tf.equal(tf.arg_max(Y_, 1), tf.arg_max(Y, 1))\n",
    "accuracy = tf.reduce_mean(tf.cast(is_correct, tf.float32))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Optimizer\n",
    "We are using the simplest Gradient Descent technique as an optimizer, with a learning rate of 0.003. This means we will be adding the 0.3% value of our gradient to the weights everytime. \n",
    "## Why Gradient?\n",
    "Gradients have a unique property to point towards the minima of the curve. Thus resulting in, change of weights to reach a minima in the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(0.003)\n",
    "train_step = optimizer.minimize(cross_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Session\n",
    "According to definition on tensorflow documentation:\n",
    "> A Session object encapsulates the environment in which Operation objects are executed, and Tensor objects are evaluated.\n",
    "\n",
    "Well, we can say this is a kind of main function to our computational graph. That is, it starts the execution of the graph in the order, we added the computational nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "sess = tf.Session()\n",
    "sess.run(init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Training\n",
    "Time to train the system. We run 2000 iterations on the train step and compute the accuracy and cross-entropy on each step. Along side we compute the accuracy and cross-entropy on the test set on each iteration, to see the improvement on alien data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
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   "outputs": [],
   "source": [
    "# no. of iterations\n",
    "n_iter = 2000\n",
    "\n",
    "# test set\n",
    "test_data = {X: mnist.test.images, Y_: mnist.test.labels}\n",
    "\n",
    "# lists to hold train accuracy and cross-entropy\n",
    "acc_train_li = []\n",
    "cross_train_li = []\n",
    "\n",
    "# lists to hold test accuracy and cross-entropy\n",
    "acc_test_li = []\n",
    "cross_test_li = []\n",
    "\n",
    "for i in range(n_iter):\n",
    "    # load batch of images and correct answer\n",
    "    bacth_X, batch_Y = mnist.train.next_batch(100)\n",
    "    train_data = {X: bacth_X, Y_: batch_Y}\n",
    "    \n",
    "    # train\n",
    "    sess.run(train_step, feed_dict=train_data)\n",
    "    \n",
    "    # find accuracy and cross entropy on current data\n",
    "    a, c = sess.run([accuracy, cross_entropy], feed_dict=train_data)\n",
    "    acc_train_li.append(a)\n",
    "    cross_train_li.append(c)\n",
    "    \n",
    "    # find accuracy and cross entropy on test data\n",
    "    a, c = sess.run([accuracy, cross_entropy], feed_dict=test_data)\n",
    "    acc_test_li.append(a)\n",
    "    cross_test_li.append(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Plot the graph\n",
    "We plot 2 graphs:\n",
    "1. Accuracy graph - To display the accuracy on the train data and test data\n",
    "2. Cross-entropy graph - To display the cross-entropy loss on train and test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
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   "outputs": [
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GbL7gmJT9SAptqrsn/FR0E5GXJ6KGIvU7+2z73f/+p56tWCEyYYK6\n339/de3QQWTrVue35u+EE+z7gQNFKlRQ97fdZj+/5Rb/70Gkbl0VD7/3ffo4/2/aVF0PPDDY32S/\nW2+175s1E/n8c3XfpYu3+6OOUteKFdV106bwYe2/v51XLVuKtG6d6Oa440RmzhQ599ySpWvatMRn\nixaJNG4s0rCh/ax8+eR+HXtsamEfcIDI0Uer+xeGrpY81nu6c6d/6quLZPZsf38zKJQ6/BkqDuXY\n4vm8A1Ol99nFUp7N0pUPpX+TqQLF8fI33bZpI9KMefJO/3GSm2s/v55H5C36yumMjj+bzpHyIDfJ\ntKvekR4tf4k9L5YD+ElAZN99RfJZJw1ZLNVYLXVZpuoRqgJtoqJcx6NiUSSd+VR6t18sdfhTmjFP\nKrNBDmKujORMKf5+rlzD4zKIIXZbYL78TgNZQ1WZxHFyX9ad8kGtC6QDU+Ut+kqzegUJ+dCHt2VB\nneOkYNCDIiArqCVQLNlsky6NF8j9J0yUL24bJxZFci2PyRi6y6QG50lDFsu5vCHbyZK/suvJaqol\nZPJoThcBGc+JciXD4s8fILET+JZW8ibnBBbmcUySz+koAnIyHzncd2eMPMsl8iPNQ1XO/+NsuYIn\n4/4JyEzayZQjb4mXg36+jLryAy1EQL4/8XoRkJXU8PR3PXnyKZ2lAb/L8sx6Dr9Tajyx3wROSHi2\nkP193a9r79NhuX6bs3Md/4+he/z+/ZOeEgG5iOelywmFsuTKh2RLvX1jDaqco8xyKYjnzXay5G7u\nkHXkS5NKy2VTD7vzmofdqH6nQfz+ew6WNVk1ZWurI3zj2mvfr+P3f1JHBOQxrpW7+iyQs3hHns24\nNP7eb8yLsPsBkGOZLBX4W0Akh61SnVW6DCmtX6l5tDN+fhW4cmVnu+jd23731Vfq2bJlIh9/rO4P\nOEBdO3QQ2bjRvy847DD73o+03XhjcH9Sv74uUO/fqac6/9eE0v081d/AgfZ969Yin32m7k85xdv9\neeepa6VK6rpuXfiwGjcWOf54dX/xxSKXX57o5t//VvkwdGjJ0jVzZuKzefMU2VWkrViRh9pFchKf\nSBbbff06IXH88P1ZFMmp+82TPu1+kTzWS2FmtkzmWIFiOZAFDreHHCLxRvsCF4qArDm5r5zABDmc\nGWJRpPKajfIVdufemm/kCL6SDAoFRCqzQUDkTgbLAg6UG3hYBOQ9zpB+vCYg8iFd4wPhqipNHIP2\n53SU+7hVXq84QMbQXU7mI8mgUP5b9+64m/3yV8duix0J/pHmjrjp3/0MlAWoGcVnHC/71NjsmWGb\ncbLmu7kjdGYvpZ5sIzupu1k5R8lwesuPNJdDmS0X8KLj/cU8p/KF6r5+FJKR8OzHRidLG2bJVDqI\ngLzOedKdMfIMl0oHpjrcnsxHAiLVWRV/Nrrh1fH7J8+cJIeiGPvhzJBDmS3n8Gb8/QpqxfNzPCfK\nGbwnT2B/X4OV0oWPZVGnC+Wxrp9KNtvkQl6QMzuulmce3CDl2CJDGCT7s1BAJJMd0pvhUo+lAsXy\n7rsiUqzI+1m8IwJSixUCxfL2wff55su93CZPkdiQb+LB+P03tJYTGS8nHbJcBEWU/nzhQzWL6tVL\n5e+Id+VIpsttdV+Wv//zgmRQKAfwk3TmU2nFt3IqYwVELq0+Qn6ghbTmG6nBSjmS6dKEn2XtqkKp\nwUp5rOmzMue1OXLE4cXSqNIqeYTrZTENpQprZSD3y7aMcjLmwg/i8RKQNVSNx3X9fq0EVLRERGTH\nDpHffhPZuFHm9bhVhjDIkc4nuFo68rkcwhw5lzekZk312W23FEptlstvNBIBeYZLBYqlJn/FP9fj\nz0zayXJqy6+VD07Ix58POl2+4Chpx0y5nKckh61yxRXqdVaWmsidUm2GRKRtzwHg05wQkYi0OVDR\nnkQKKOmVxhdfqGe//y4ydqy616Tt6KNF1q717bekdm37fuBAW3ozyGjf117r/z2I1KunC9T7d9xx\nzv8bNVLX004L9jfZz5QAtm0rMn68uu/Wzdv9xRerqyZtf/0VPqwGDUQ6dlT3AwYEk7aHHy5ZumbN\nSnw2e7bIIS2LpXetz+MPHyx/pwjIbzSSs3hH2jBL1Q3elhe4UNoxU3qdsE6qsFau5TERkEe4Xq7j\nUanBSqnMBmnHTLEokue42BFgD0bJn43ai4B8wkkiKCKl339W+XRZjxL/fsbx8lu/2x3f38DD8jA3\nyF/UjD+bT1OHm6e5LGlmLGJfz+fvc5rc0+C5pN8vbtIp4ZlFkUO60w01EP7d7LBAv87nJXmF/nIZ\nT8udDBYBGVfnAmnA7/IhXUVA7uBuebnvBG8/br5ZjmWyvMgF8WdX8KSUY4tcy2NyFF9Ij5a/yJAW\nb8kxTJGHucHx/V/UlF9pLF34WCbfM0WkVSvJoFCqskY686lUZJOclPulXHfOCtk45HG5nXvkTgbL\nfvwiA3qsiPvTjHmOidjzXCSHMMcR1SEMkg/oliBpbcyvchBz5dRTRY7nM+nExHg71ERd/xrV/Fs6\n86nUZrm04Afpy1uO90O5WZZTO/7/yJEil1xivz/hBJEnn0zeXj76yO5/yrFFzuHN+LtevUR+Gviy\ntGGWPM1lAiIH873koiSY1VgtgpL63cxQuaDVNwIiNVgppzNaarNciPUvSqpbLEuWeA1mamJXUOAf\nz/r1FVlxP9ffdO2qJmxt29qTdDNP+/QRefBBiZdJPuskh61Sg5Xy1rMb4qss5oRe46OP1Lt/8aqM\noJc0ZX5CPPLzlVvd9+s6ns+6BLc6jG58IIcwR044QUSKi2XqhC3SuZKSIrx664KE7666Sl0zM9W1\nTh2RiLTtOYhIm1dkfSqweymsb1/73dTYxHjxYpExY9S9Xno8+ujw5GTgQJGcHHVvkjbd0Px+dero\nAvX+tWnj/L9ebAWiR49w8fL73WCMae3b2x3T6ad7u9dES+flH3+ED6tOHZFjjlH3l13mTdr691f5\n8OijzueX8bR05HMBNdDdw+3xd+XYImcyUs7infhs9Nf73pabUeK65ShWXdD6OPmw+r8SAh1BL8f/\nYzlVvqNlqERtR40gL3KBbCVHxuIUfS48uIe050vHsxkcHr//H23lSa6QLLbL1Kki33ytJFmPc03c\nzZucI+dXHSVHM0368lb8uZYMrSNfJtJJrmSYgMSXsDTJ3Ex5uYfbJYNCacl3Mn9/FcdarJBDD5V4\n/mSxXSrwd1xSty6zmjThZ3lk6A7pUkMt1YznRBnHKfHkaCkfiGSzTebMEfm+QrvYgFYszflRTuIT\nOSNjdHyp1PydxTvSr8OvAmpwFZSURredxvwqA7lffqS5gN1G6rJMmjFPqrImYTLWqpVI5852/DrX\n/VFy2BpfihUQKJbRo73bXE6OmlS423y/fiL7sEQuqvaegFOSns6vu70yJ3f4CBjNCWGY33vvOUlb\np04izzyT/LuPP/bvf3r2tCe1fj8B6cLHAiKHH+7tpp2xUrp0qddgJlKzZjBpq1PHsVIZ/+mVkDPO\nEPn6a7VqoCeWjvp2lsh9PoLDN98UmTJF3Ztjg3uMCPpVqKDc3nmn3Sa8yB3YpE3/f/zx6v8vvlAC\nhlYtCz0J9zWxrsGy7DyJSNueg51F2tLY4GH3g4jz/xEjoGFDtSu2Vqpu3Ng2VFi4UF2nT4dTTkk9\nvPvus++ffDLY7YoVcOut/u/de/3FNmcu8ZYAplL4jBmg9Tl9j1QqKsYCqm/9k2U08Nx1P4dtbKcc\n3Xmfb2jDMhrEw2o77TFaUo4uczayqPZR1OEAVlCXfNazgjosHdcKnjqPGqs6A83JZjsjOJseqOMH\nevIeozgTgA58wc08xNNcweHYOx4/zZUwCB6M/V8HdUZe3uwpnAr8mnUAswtb8hjXk08B0zmajzmF\nvgynMpvoxjgAmjGfBTSP+3s/tzKI+xEsJnMcHZlCdszC7EJephZ/sYpatGkDF/z9JJcvuJqfDjuH\nGT8cSXVWM45TmUMrLuNZQPiQbvTiXbZSIZ7n2TkWWeygiEyu5T8cyxSmcSwtG8DcdfA7vwPQlXHM\noD0H8wPTONaR/59xAifzCU9wHY9zPcfzOTM4EoC5HMI7Z4/ih/vfZyW1qAs0ZjG5bKSQbArJ5lFu\n5DX606p9ZRZNrwBZsHKfNvRb/TojOJvt2CaXm7B3A91BDpmZ0HKLfTTGfFownxZUzVcnHLgxkrOp\n/1usbpHBmbzL5xzPwJi3i9mXodzKUJyNYzn1WI46VibfZdWXm2sbm2wil19yWrAd2E45FnIATVgE\nWA4rb7Nv2L7du/5nZcEfNGRifkNYW7LjnsDZdv322kr1+Eh3vHNzw21mHXTqhUiwFWulSnDC358y\nheMAe8NmN8x9zvzC+/vv4LCKilQ5uC2qdRq19aiX8RTAyJH+FscZGbal6IoVie+9NmJ2Qxuw6Pjs\nIIefaJb8Q2yDo6wsZQxTsCnTs3/XG/DqOuse1yJEACg19rczfvjMOrzE6vqndblA5MQTk8+o3L9+\n/dR14ECR7ORqNmn/8vKcS629enm7u/jixGcN+D2m8Kj+b8Msub/3HLmRh+Ropsl+/CIH873M4RD5\nrtYJ0p9X5BDmyEjOlOe5KL4cphVqf6VxXK+qP6/ISM6Ui3heBORylFLv9xws68vXktc5z6HkbP52\noOT8U4iJ4bp0kcKsHPmTOvI9Ss9jfMUesnq/tiIgz3KJpz+DGCINWSwvcb4sv0pNp1dRXU7jfanP\nH3I8qpCbNtjkm79DhyqJTwemxp/17+Fc3spkh2SyQ85kpFzOU3IOb8aXVUHkiCPUMk0mO2TNGtu4\nQy8NmX49/rh9/+WXIsXFIu+/rwxictgaf6cNQEDkZD6STHb4psGiKC4B8zKAGTzYvm/VSl332SfR\n3e+/q+tjj4msWuUdlv6ppS+lN+h+16yZWs6fMME7HP3r00ctj0Gi4U+TJuqqZqrOX42YbvzDD6vw\nV692tmHtp/5pCe8HHyj/9DKT+bv6avXONF7S32kjoHvv9U7Haaclqhf88kuiuzPslXJ55BH7fv/9\nRZp72BVM8FkxNn+jR9uStkWLlM7pSy/Z773UDsaPV/XOK29BSd21zq/79/LLIv/9r/PZ6tXebhcv\nVteDDvKTQNhlrCX+H37o7O/y8tQSpJmexYtFtm1T/190kch339nvlRTK+Ts4pjrWt6/I998ryRyI\nvPOOyJw5zniYKC4W+eYb9fPL/7lzldsHHnA+v+QSu+7r77V6jnZz3HHq/69t+wN5+unEMDa71EOV\nNNYjwhF2S4AtaZs0SWTlSpEffoiXIaX12ylbfliWdbJlWQssy1poWdYtHu+rWJY1yrKs7yzLmmFZ\nVsB+84kI2johaEuCMDCPJBJJ/fuwaNECWra0//eblbqPcTqDUfxBQ+bSkit4iuqs5mvaces7rXiY\nm/mCY1jE/szlEA7leyQjk1c5n+9oRS/e42JeZAmN+N/hV7IPaj+dfVlMEVnczhBe5Xx68R4vcAmg\npF2LaURLfuCr/s/SjzepxGYWsV88Tv878DwAsijiGS7jdN7nX/0EPvmEucddSV1W0JIfGEs3hnUa\nTfVr1JlQ79KLffmVTAqZwIkM4ypy2cB93M7vNOJCXmbNgNs4nJnUYiVj6c4yGvA5nTnv+D/ZkuG/\nudeBB4KQ4TDB3lbeuf9DEVkUkcV79OIZruBtzuUb2sbf633aisiiWjXo1CleWrGfjbZtHf9iWdC9\nu7KmNyVapiTmE06hKED4LWTEJWBeO6p7zd4NK/c4tGTEstRO9F7bqGjENjH39HvTJiV9OfFE733R\nNHJz4UwlRE1wV7++/3daatOkCTRvruJttgt3G9HnTep2GnTigz56DWwJjY6bn7To2GPtdADUq6fi\nFgQzvbVrO9PbtKm67rtvsB/g7OP2209Jh0yJoLtfAGjTJli6JeL//vzz1WqFCa+TA1q2hEaN1L2u\nK26YGyXr85332cd5gsmWLU7JYc2ayl/9LC/P+d7dvsDeh++AA1S82rRR/2dmBtdPy1Jx94s/2HF1\n+3PssfZqjt/3uuyCJKN16tgnlWiU5XgToWzRtKmqw+lsa5UMZU7aLMvKAJ4CugAHAX0ty3LLlW8D\nZovIoUB/IMRR4TaCKrfXBrOpwDwNoSwbUWZmsuUO4UB+Yv8573IwcwE4hO8YxZksoSF1WcFTXMVq\narKWqtzQZxlDSeDHvHLEs/H7aqzhEW7gMv7LR6c8mbBxZHfUYY3LqUNP3mMMp7OApjRjAbVZwR9t\nzmA5dQDYn0Us5ADW5Tbk9c6v8QIX0Z6vuIKnWU/VeN7NPOtR6vInl/M03RmrBo0j1RLflxzFYval\nmEy6MIFrGOZYptP5NIvDcc83Nud7nGFlwIuwp7rBqblPWzKEXWJL96gaL2LhFbegZzr9+hq0JO/l\nz7p19pJZ0IkCluV/wkFQm9J56D6Y3eve9EsPkkH7KpokSJM2HZ5f2VmWM4/CqDCYg7w7rfqc1zB1\nxSufzO+8SEmy+IkEuwmTvjB9orlsqePsrk87dniXrY5DXp4zPl4noPhtnmwuj+bmertJBh1fd7vL\nyvIPV8NdH8uVS8w3r43bARo1aoRlWdFvD/hVrNgoob6UBXaGpO1w4GcRWSIiO4D/A053uWkBfA4g\nIj8BjS3LCn0yXlmSNjPzy5q0xTcJ5nJeG53LYO7ibN6hK+MQMpjJERz31FnM5RC68AlTOI5pdOAY\nprEvv3Is6nDb/rzGmnL1eJGLOI0POIap3M2dHMNU1uQ2ZgdZzMg4knVU4yYeYQmNlVCXDFZjT6fP\n5xXqsJzGLGY0PenFu7ThG7ZRnpXUJjMTuvEh51jDAaWL9p/+3yJWBpfwAjNpj1sCJQIrqMt/uRyI\ndVLt2mFRzGaSb4PvN5AEzaShdEib33FUXgh7HFiyePvBa6D3ipvXM78TPlIlbX//HZ60uaUIYZAq\nadPtJ6id6s2HTdKmyVOy0y7cpC1MxxyGtIWpK159l/mdVz1KVr+Li0tO2sIgDGkDZ/64JxSVKztP\nmfCq//ocZne6TdKW7pmvfkcZZmb6n/+soeuarntecKdXY/HixZ5LZG+/HVuNS/KrVEm5z8tT/8dX\n8bD/d/+uvDLRHxHhvffUfatWtj+vvJLo7qij7P+rV1fPvvsu0c+lS9U1K0vYbz91f/75wt13O/3r\n0SPx29at1fXMM73TbaazbVv/pcb27b3zBVR69fObbrKfX321092UKcpdtWqL4+VWlqRtZxgi1AfH\nttpLUUTOxHdAT2C6ZVmHAw2BBsAqP09XroSxY5OfW2l2zumQNt1xPfJI+mf1mSjPFtoxy6FkblFM\n5dUo7FIAACAASURBVKULaTJtBn9yK3VZAYVwF/fwNxWphGrtVShg1vXDafdYXz5BWVB05aO4NGox\n+1KFdRSQzwWZsIj9WYRaR9PLgo0EGvI72RXLg9HZ6A6zIb+zg2zqs4wlNHbEvYgsNhtVJicHvqUN\n34pah1hFLbZWgnIeA7j23z1w2Z1UOAYVNJCkSgxSHZSKisKdiQnhJW1lRdq0v0FETud9jRrqaCkv\nYqvLy68T0oNg0DFQGRn+SuyLF/t/p6UaZp0xy9g9wPnVMRNepE0rmScjbebZs5CepM2UrMbOtQ5V\nV4qLE6U8ySRtZv7ocztNiNhpzsjwPjPXjdxc59F5YSay9erZ5WyG54bpl5vIVqrkNFLwIrp+pCg7\n2/Y7XSLqVye8/HOXk85XPbHxknDqfkWT0x07gvM2bL+h3VWrFv7IPr9ww05yze+1OoBXeWVnq7wq\nV87OM/fECLzzWNf9IEOboO+94uqGGecgEqb9N9t2WZ0tDLvPMVZDgaqWZX0LXAHMBu9D3gYPHszg\nwYPp02cwF100mSuvDPY4rKTNL5N1R5Hq2YQtWsBnn6n745jM17ThJMazhYpM5TgOZQ4N+IM6LOf/\n6MO4X5tz7CvnK8IWw0wOpxKbWUY9TuBTrmIYqzudxfNcDMD7dE9YPiygCmAxbJiyjn3mGWe8iouV\npKsgw6nIpCvvFipSSHYCYfPCKafA5MmJ0ofBg+Hoo9X/Eyc6v3Fbh+mOwDz6y8SPP9r3333nT8yK\ni1VYRx3l/b5Xr8Rjzsx4T5qkvn/4Yaebxx+Hjz9W94ccAv/5D3z7rf1+lm3c6khrVlZi2jXmzVM6\nWuDU6wGYMiXR/ejRqizN+OvO2DxySqdn+nT1zcSJtt7UcCUM5ZtvEuv6O++o64EH2s/++1/1va4X\nDRp4659p3TAvSZu2rLYsuOgimDYt0c0ffyQ+08jOhqlTncdePf98oru5SlvAV9I2cKCqp2AvZenJ\n3pQp0Levutcds+58Y+dXx3HJJc7/0yFtL7+s6vHXX8MTT6jnbtL2v//B6a61CBG4915nfXOTtunT\n1fF0un6a8Vu4EGLHPsZRXKzq9Oef22kfNQp+/tk/fbpP69ZNtRWzPPwG0BdftPPfJG2m+59+sstt\nyhTVXk1UruzU23OTALPdm+Ri8mTo0kURR0ht4m3qGHuRjhNPhI4dVd+hdyT49tvE4+d0XevQwY5D\nr17qW4AFC1QZgKobCxYkj1v37s7/a9VSxHj+fPvZ6NH27gRTp6o8TgWjR6vjHP0wdSqcc479vy5j\njWnT4K231H3z5qr+ffml/T47W8X3u+/g2ZjWjmXZ7U+7NevhGWc4n+l6++mnqt6ee25iPIPI5qhR\nqj8Guwx0mkyiZpa/rqevveb0f9IkdWwiTOahhwbHuUppY2dI2pahJGcaDWLP4hCRjcAF+n/Lsn4D\nPE+M1ZkwZIjKpGQIS9r8CtY9e5vMcXRhPNtwKiMN4XY2kstD3AIIT227hA7PbOAoruYtzqU+fzKe\nk+Pu59DaOx4ImRRy4WmreH5sXQZzF+M4lVkczkRO4IyKMIDn+ZN6fEEH3/RUqqQ6sho1nM/d+hWW\nZdsrpYqsLDjuONX4NBnTUpUrrlCDyPHHq+faf7f+h46HH9lq0UIpyq9bpwYYc5bvRv36iqSYHYNG\ndjZcfjnceGPioeqgFIozMhLrQefOttJ/+/YqLqbiftu2Ko9Xr7bTqv02/zfRvLmtW+MeGI917vJB\nnTrqvFxQeXTFFepek4GqVVWeFBTY3+i8rFsXvoidV3zCCXbYGrpMDj1UXVu3tgefLl1g333h7bft\neF5wgWp3JrRiudekRvtrWSq+HXyqq58hRHY2HOM6uq9GDVW3zS0k3AYIbkOEU06x81XXP92ujz3W\nljDqjllL3jp3tsNt3FgNJqY0Mh3SVrOm+oG9rOYmbe3a2UunGsXFKl6mAr6btOly10TerMv77ZfY\n9rQhQqdOtls9KPqlT5f3eedB797Od35Lj82b2/VOhyPidH/ggXa5uduA9tuMj057ixZq0D3mGLvd\nm+k+7jinP6mstvTrR3zrIy9JS+/eSoKlJaag2pAbupzNc6hr1lTEfPJke2IFqp6Fga6rlSsr/489\n1jYI0WjSxPZvn33C+WuiRw81CfCDu22a6QBne7csdQa4iexsVS+BuDFORoY9MddGgGa5t22ryKR7\nvNL9W8+eNlHUCGqn9erZhF4blh1xhOr3kpG2fv2gf397TG3QAJo1A+jI7bd3jNfvu+++2z8CaWBn\nSNpmAftbltXIsqwcoA/ENNxjsCwr37Ks7Nj9xcAUEQnUFAg7YyqppM3s6CqxieOYyklMQLAYTQ/O\nYBTD6cPt3MeDDCSHbTzEzXRa9CLZo0YwnQ7U50+2GCSvDsu5lP86wjmVD5l9kuohisiioKISwQzm\nbmYZq8l6dno3g5nICUnT754h+lnWpUPa3LMd85kbyUibWwLnFzf3YOb2J1k6kulHeSkI65mf35KE\n12CVbCkhmR6MGb4XzLjoNIUR9Ztl5W5DXsttpp9ecdEEx0vS5qcH5IafhMZv2VC347A6baY/uv6Z\n9dBdj/VSrplXOj9McpqqTpsbOtwwOm1e/Z3Xcjj460e5l7+TlW2qejmp6IsVFye6D6q/brfuZVav\n9PuFmw688ifscqG7res4JItLmD45XcOKkobrBZ1HYb/3qveWlVh/g/ppf3WbxHiFhddY4NUWtDuz\nfL3GxNJGmUvaRKTIsqwrgQkokviSiMy3LGuAei3PA82B1yzLKgZ+BC5M7m+48EsqadOde0OWUD8m\nIPwgZkfRg/fjm8Nq7M8v3MQjAGz78hvKHdWGgTxAJf6mGQv4F6+zlQo8xwDe5Dxy2E4mRaymJl27\nn6pyKQBh1vBNuCuPzgP3BqTpNFQvBfZkldWPtAUp6XopKPu5SZYOc9A14+1H2sxOxA9eg1WyjkLn\nQ6rGEBp6kLIsO01hLDHNjjKItHnpk3nFVRMcrwHIbfCQLG5u+NV1P+tQvzpgplnXM7O+aX9SJW0l\ntR7V33ulP8ykKhlpc3/jJm1mmaU62HnFJxXSJhJeP9TLb/eEIKyOV2noJacKN2lzWzmXBH6T2LJA\nsr4qVXIUVu83TD/tfp/sWZjw/EibO+x/HGkDEJFPgKauZ88Z9zPc75NhZ0jamjOPHRv3owpbeIfe\ntGJO/N3xTORzOjvc7yCLH1FrNS8f/BjntTmMCmxmG+UStqgAi7+pjMlhwqQpVdLmns0EbYeQKoJm\nGm7Edea2OJ/r9Life31bWtBE1SsP/AbWIHgNPqbfXvEPSm9QfDT0IFW+vPc2Fm54Eagg0mYu5Wh4\n5YWfgQGEl7T5dd5+z/3qcBhJm85304DJPfnQ5ellAOEnacvKskmRGS+zvfqVZZgO3qvvMsPxIi3J\nSFuysk11EE6FtBUVlUzSpsvUi7QF1bd0jNFMpNNv+k1IS0PSpkmbu65u2VL6/WYypFpf/KRXXta/\nGskIb2mQNi9iaPrhDttr/NsbDBFSRljSZroL2ly3HNuY1+1mTuZj2jKLLHYwj4N49JkKrKMa7ZlJ\nebbx2k0/UJG/mcTxVGAzD3FT3I8t2Fryk+qdi2XBVip4ELbkcfUzfEjV2tDdMDp0UMqXuhLOnQs/\n/KB0N555Bt5801lBhw+3dXDq1HH6lcqSim4A994Lz8Xo+m23we23q/vTToMHHlD3Xbqo6z33OL/V\nGD1axTkoHI077nD+/8MP6vf++7auWBiMGaPi6AWvvdZ03owa5b3x6dSpSgHXzGttuPDjj3DSScHx\nKVdOKfY+/TR8/71KUzJrs5Ejnc/cA1hOjrLIfv11+2gfv4F93Dh47DG1YawfMjNVmu68MzgtXhOR\n3NzUSNvHH8Nll3m/1wrl33wDH31k37vrUGYmvPee2hBz5EgnIR0xQl31MvCsWfCBoeTht8TppQuj\n4VUmo0ap66OPKuMNUArPffok+q3TN3JkYvgjRyZKYQ4/HF56yTYmSCZpM9vy++8nvjfx4YeJhhp+\neO89pePWqZNTD8uv/r77rtJnBds4xL08qsv48svh6qv9w042bnzzDXzyCcyZ4/2+f3+V1rFjbQOW\nIOTnq/bphcsvt42c0sHMmaovdGP2bGUMpnU93Zg2TRkATPBZ1bnnHn8jKi988om66rIYMUIdnZgO\nMjJUHo8d63wGavNirTOoy/+xx5zGW2Yf9d576poKaRs3zja+8Kor117r/P/DD526nUFW+6WFPZa0\npbM8GrSX1IDiZ2j+4cN8TFdmcTg78BZp9X/oILagpuJbqcAtPMQRqBr6Obbm+XqrqqPgvHamd8NM\nk5/OkznAmRZmbmszDXdnnpWllI11RW7RQg1SVaqoQe/cc52ddZ8+tnJyt25Ov7waQzKRd61adud+\n1ln2jtHly9skSpMjTd7cjadHj/A7TTdzbeN80EEqzd27e1uiuuuV/v/00/0Js9eArcv+jDO8iWzT\npmogMvNQGy7oMvGKj0a5ckqxt21b231Qm7CsRIs898QgO1uVcb9+3rNNsz537QrXXedMW/XqTmKb\nlaXSZCpqe8GrzpxwQmqk7eSTvaUOYMfxsMPsEwyaN0+sQzk5SpE5I0Pllem/Ph1A51nbtk6lcT9y\nZqbBa+ndXSa6rdWqZStG9+jhXVd1/Nxx9XuWmamMSbSBRbKlb7O83daK7rScemr45U6dx1lZzn7L\nr/6eeaYdF92PuqW42tDh1FODpb/JSNthh6l+RxvRuFGxogqjW7dwWww1b+4kT2aeVq6s6m26OPzw\nROMDUH3LXXf5E4cOHVS/eOKJ3u+rV/c3ovKCNo7R4e2zj/dE1YQm4W5Ylspjc6wx+1LdnnRdq1XL\nabhi1uOePZ3fh0HXrsErJ507O+upu97rPqg0VrL8sMceGJ/O8uiOHcqYoA3fUEgWX6L2pfiRFqwo\nCjhPB5hERxZmtmCAx7u1qFGpL8OpxN+cwsdsl2xHZQmzrGmmKQxpMwcKv44qlf2Fkr1zSyqD9s9x\nw6tD9hpUIFFpviRi/qDGE2ZZKkzYfgq1ZQmvfE41n9yTmGR+hlnmdO8NFgZebSM7O329kHTrSxgd\nGz8JuF+bCSJtyZBMP6aks3mzvymN5dF0YOZJmPzReeG3PJqsDHe2TlsYRfmw3+4KhGn/6SwJpqKT\nZuqY6Xu/pfjSrMdeaU9WJulu3pwK9ipJ244d0JmJTKEj0+lANts5m3dowXyOL/rM8d0IYptDzZ4N\nwAd0545qro2+YviFA6jPUrZSgTXU4E36UVTkrIBhN9DU8DsaxSQIpp9hSZufZZkJv0ruHrDSkbQF\nwW1Nl86gnUonmWyDz7AIkrQlQ7JO3C8+XmGGIcYmUiVtydKUk+N0H/ZUCK9wc3KC65LX9iwafhbS\n6cTDDT/S5ldOpdke3CjpxCDZgLwzSEOqpE3nhZ8hQrL8LqlOW0mxM4jwzkZp6nEF6aSJ2GOCn5Sz\nNHTaNLwIfnFxarqXZYE9tgqFnTEtXWrf79gB5bE1kH+iKe/Qh62xA7wL7n6CbbFl0Q+IrQe0agW/\n/MLTXBFoqfMnTkmdWyqVKmnzk7SZFTCMpM0PqUigtFv3gJWOTltQHNyDVKom5F5ugzqSMAPVrpa0\npUIGvNwGxd9dnl4Sr1RJm4mSStqC2kxmZnLSlipKi7T5SRtLW9JWmqTNq2yD+thdJQVyS+PdW378\nkyRtJQlnZ8JrF4FkKKmkzW8pvjRJm19/GpTXO8Oad48lbeEqqfDwfds4iumA6nBzsXdn3ZfF/E1F\nNlGZA/JXsvXCKyiOZcnxL53HG6/GpmVNmrCDnHjH8F/nFmuA0rsAW9HZPaNz60N56flccIG6ZmQo\nZc4rr1SbQ+r1/6FD1Rr+jTeq/80OqmdPuOaaRD/dlUhX4A8+sBWS3Zg4EV54IVHJ9f77lRGB1j0L\naiCnnmrviA/hSFvDhmqXdff2FBMnJu62DbZydIsWKm5eCOpIdBn1728/c28YmcqSDcCDDyYP14Rf\nh6LJgamQCyofevZUeidulGR59OWX4dJLE914KasPG5bobvx4VWcffdRWAA6TBx98YO+GbiInx1+l\nYOpUlQ9eeff004n6V2HhNeA/9RQMGmT/f/XV9k7oGpMm2Urdug2DOomhQQPVbj/8MPE7E3oDZxPu\nrUjcaNMmcff9VJDMEEG/f+ON9MNIhptvtv1PZYKkJS0vvKDqkK4rQROFadO8TxxJhpLksRthCcTE\nifZYsivhFd9XX3X+X1qStjfegJtuSnyujclElI7goEHKoM29iS4o/bb//Mf5LB3S9uSTts7fCy/Y\n7ToZaWvUSB15WabwO0h1d/yp6Cpcf73OPuevdWv7/jbujf+zmIbSP/MNh+NCMqQ8m6U6q6RaNZFV\nq0T684oUPvmMuAEizZs7/9e/pk1FBg1S9/rdkUc63Z19trpefrm6XnZZYty1+y5dnGEff7z9XkTF\nE0Quvtj+duFC9TP90mjb1n7+1FMJSUuKSy91+vnJJ+r/4uLEvHj++cTvQaRXr8Rnc+d6h/fOO3aa\nkgFE7rnH/v/cc53xeffdxPzQ+Owz73cgcthhwXE0ceaZtj8FBep++fLk34mI3Hqrd5mdf75/vP0w\neHDiN3ff7Z/GSy9N7mffvvb3jzwSPk4gsmSJ/zuvNJvPr7pKtZEgHHJIcHzKl08tvldeGc5tkB8T\nJoj07Jl62T30UOI3I0em7k9YmH2UiEiNGolhzZjhX3feeqv041SuXPL0rl2r3Lz8sroWFjrj9dVX\npRcfrzJJBSD/z96dh9lV1fn+f3+TECaTQMAEEiBhEERBAwhXfk6FXgW9CjSXIUAr3aJNiwOiKKBN\nE9oJHBra9up1iA3YQi6ozaC0omI5YoM2iEjAiIIkzAQygECG7++Psys5qdScM9Sq8349T56cWmcP\n65zadepT37XX3nnQQRu2bbll47+nUDvmmuHCC9f39+qr++77k0/W2letGto2IXOffYbXD8g855zh\nrdOzXu/fpyMFmd/8Zubb3ja872GVWxqWg4qdiJD9pN2eSxUAnMz8dY9n8WfOWHM+AE+xJVvxF37H\nC3maLXmaLdl+XO0vhUv4G756at/b7i+x9z5/DTYeHu0p5/ZU3Aa6dMdgF9bseb73dbX6e08GunDt\nSNRfmLe3/vrQl/7ez97nrQxmoOUG+itroPvJ9ryOobye+v0P9N4Mx0i+Z8Md+hloNnWP+tc/3O1v\nynvQe1LDSLbfjHPaBjPYOS/9acc5ZYNNRGj18OhwftZ6bn3Wu9/tPmett/4+u8eSRk5EaIZGnkfY\n82dlOxU7PNrfB0rPbXVmcQ+78acNntuH2t3H7+AFADxbd1mP+h+m/r7J/f3A9dWX/kLbUA7w3s/1\n94NfHxYGOsenflLDSD40GvFBM5wDved1DfWX6EhD20DX7RtpaBvqXQB6DOV7NlR99XU4ExEG2+Zw\nP6w25bgZbCJCMzQqtDVKs8+/qv9+DjQ82ipDOb56fr56/jjv7wLLo1WzJiK0M0gMZXJbI4z0NTay\nX6Ph+Cqy0pa54YUt6/VUsH7Y624F9SbyLGsYx22sv1jMuHEjPyj6qrT1/ouv5wKsQznABzvI+rr9\nzUD939TQ1ttI+j6cQNHzuob6S3SgyyoM9CHZjEpbzy+VdlTahnv8DvT6e9R/SA13+5vyC2rixMZX\n0gbTiNDW12fBSDX7F3H99hs1k3pTDCe09fxx3ttor7SNxdmjPZp9OZNG3jd2pEZDpa3I0Pboo/Cn\nP23c/o53wEMP1R5P4+F17TvzZ2ZzD8+wOTfxP9iMVbxk9yf43d21hLdgQa3cvs028Pa397/fgYZH\n//ZvN/zQ730D9BtuGNq2+nru/PNrV8/v/XzvsNDfwfTv/w4rVtSu8j2cuwD015/eXz/3ufDII/2v\n/6//Ci972YZtp54Ku+3W9/LDGR4955zaRXp7nHlm7QKcp5/ed1/rvepV6yd19OWd74Q99xy8Dx/4\nwPrJIo2qtH3iE/1fSb0/w/kw+exnN550Mdg2h7P9U05ZfyeN4br88toFOgeqhMLgIWu44Wm4dxvp\n7X3vqx3nM2dCV9fw1p07F5Yv37CtmX/Vz5+/4bHd13s1Z07/dxdo1y+uiRNrn9F9fa/e+97a5IxG\nmTu3/1n8Q9H7PYbBj+nR7JWvrB3jvU2cCCcPerfwTfPRj/Z9V5ChaHSl7X3vq01+a5tGniDX7H9U\nZ/8tWdKTdzf8l7femku23iN/zX4bPHH0UWvWfflJzsiT+XI+8MDwThiGzH333fDrnn8zZmy8bE9b\nzzL77lv7//TTa/+fccb65yZPXt8PyHzTmwbuS8/J7vXbePDBzPvuq3svGqhn8kSPH/5ww6//9V/X\n77eviQjDdcMNtW0tWzbybfT055prhv9+QO0k95FYu7a2/mOPDW35f/iHxn3PPvShjbfT30SEoTr6\n6PXrf/zjjennBj+zvdp3223o2znkkIH7s9VWw/v5vvDCoe+7Fb72tcb/LPdn5szhvVdf+1rj+zB+\n/ND7cMcdrXtvGqkZn8+Q+Vd/1dht9qifiNAosOGkvmaCzMMPb9y2LrtsJOuR2cAcVGSlrd8S+M9+\nxown/8CMuqZPcQbjJqwve3yQTwHw8RGUTAeqtPXW+y+0ngpMX+cRDVbJ6m/5+iG08eNbNzTQ3/XV\nGmW457QNpBFXwx6Odp5o3IzqR/02m7H9TdHoayK14hpLw9HK93s0DNsN5/WWfEL/UG/3pcZo9PBo\nu42CH9Xh67fE3EfN/IN8qs9r90QM/wd/OBMRVqzoe5meYdP6bY00tP3lL+vbBpqIsKkG61+jP/B7\nX6dtUzTyworNWL+R37O+9tnIC7COhg+semM9tLXypOfhHifN/gNhMKMhZI5UM66aP9p+NkeTZn/G\ntlqRh36/FaVeoW17aida9RXaBroNzqb2Z8stN/7m9kwG6Km0DRTaBvtA6qvSNm5c6z7IBgpxjTio\ne1/1fFO068O9HT/czdjnpkxEaLbBQtZwf75HW2iz0ta/kittrbjVUaM06xgs9dgeDZ+BRQ6P9ltp\ne8tbNvjyMbYHYNddN150Uy99cfrpsPvutbsW9A5t8+fDsmW1x+98Z+0q7RdcAJdeuv4E+R6f+lTt\nxOXHHx9633qef9Ob4K67ahMM6oPpl788vNc1mLe+dcPt9+7fYYfBiSfW2g89dNP31/OD0YgP5pe8\nBP7qr0beh5F49auHflux+u/lpjrhhI0rvMccA/fdN/Jtnn76+pNuW1H5Gc77/vd/37hfgEcdBS99\naWO21SijtdI2dy4cckjj+/DVr46OSyo004UXwuzZjd3mhz+8/ur92lgj/viH2nE/3AlGTdHIE+Sa\n/Y/qjMjbb8+cPn3DE5o35y8bNsD6yQefzJwwYcOnly7d8CTrwU8mrN1toa/2SZOGto16Z57Z976h\ndoX9gTz1VG25m27K/PWva4+feqo2GaEVJ+f+5CfN3c9//demb7/3XSSGAzJf8IJN2/9QnXtuOSdU\nb+qkhh4DTUTYdddN336Prbcu573ty1e+0rr+77ZbWe/VH/5QVn9L9c//3Pj3GWp3EWoFqN3BoJ1o\n8ESEUVAUH77Vqze+L2H9PUV7Gz9+4+rcSIZHhzMRYVMMtdJWf17eQJf8kBrB46u1Wll1Gg3Do8NR\n8vCoWmu0nfawqQr7Ua1Zs2bDmYV7cwePMG19w0c+wn9fevu6L3uG9noP8TVzIsJItzXYc/XPtyu0\nNfsDfjSEg1b1oaRfPqPh+zIcJb23fWnl+136e6WytPLYnjSpdftqhSLPaXv00Q2/3pPf1x5EwJ//\nDDvtxMqfrH++/sT2nqpYI4PHSCptjQ5trfxLuRM+4EsLKK0w1s83Gm2stPWvtP6qfcZapa3I0Nb7\nZPev8tbag623hp12Ajb8wBs/Hj7+8drTp51Wa4sY/g9+K4ZHTzoJjj9+4GX6uil5RO2uDrNmNa4v\n7bLHHu294vQHP9i6/ZcUgBsVZI8/vvY9XrSoMdsbq7q6anftaIWzz4Y77mjNvhph2rS+J5ipsV77\n2trEqkY66yzYa6/GbrM///N/whvf2Jp9tUqRoa3eu9+xmqlfeHyj9vogNX587UMJ1oe2ceOGP6uk\nkcOj/bn44qH3I2LDfW+xBdxzT+P6Mtj+m2W77eB3v2vuPgZywQWt21cnhrbLLmvMdgZT0nvbl+c/\nH7q7W7Ovk05qzX4aZaut4I9/bHcvxr599oEf/rCx2/zEJxq7vYF8//ut21erFF9k3mrNCp6guntw\n3W+V+tDWV0UtYuPJDINp5C+BTdlWfWhrxzBe6b8MNTKtONYclpak/hVfaTv/S1PXf1H3id97eLS3\niOHfJqmvsDLS20c1KrS14zwjQ1vjlPReGqgkqb2Kr7RtoJ9KW393RGjnvS03hZU2tYOhTZLaq/hK\n2wbq0sQLXlCbePDkk82ttJ199vpbVA3H614H3/nO8NfrrR2/SGfPrp0/p033mtfAggXt7sXQlBba\nzjgDli5tdy8kqXHGVmjbZpt1D3fdFZYvrwW2/iptwz2nrS/nnTey9V75Srjllk3ffzuGR6dN2/Bm\n9Rq5gw+G228ffLnRoLRz2v7xHxu3LUkaDYofHl0T4zmOqlSx3XYbPNczBNrfRIRGVNrarbTqh8rl\nddokqb2Kr7Q9s/lkvv/0a3n0S99i+5fM3uj5zTdv7vBou/mLVJKkzlB0aNuNu9nq6cdZzQSefv1f\nwU4bL9NfaIPGTERoNyttahWPNUlqr+KGR089tfb/VlvBVRwJwGom9DuLc6DQ9rKX1SYrDMWrXgX/\n+38Ps7NNlgm77NLuXoxORxxRO19MjfPKV8KMGe3uhSR1ruJC289/XrsFxq9+Bfvu8TRQC239DV32\nFdquvrr2/ytfCStXDm2/3d3wvveNrM/NtMsuVkD68p73wC9+0e5ejC2HHw5LlrS7F5LUuYoL3/TX\ngwAAIABJREFUbQCrVlVDm888A4y80iZJklSKskPbU08BkIwbsNLWjgvgSho+q8aS1L8i48zq1dXN\n3uuuajuc4VFJkqTSFDd7NAKefba6MO7TT69r76+aNmsWbL99a/omaeRe8QrYZ59290KSRq/iQhvA\nihUwadKGbf1V2q64ovn9kbTpfvKTdvdAkka34oZHn3mmdt7L5ptv2O55a5IkaSwrLuosXw6TJ29c\nWRvO3QpG450NJEmSBlJsaOvNICZJksay4kLbypWwzeS1cMMNG7QPZ3jUq7pLkqTSFDkR4ZX5Y3jN\nawD4+iWr4aShV9pWrx47lwDxmlaSJHWOllTaIuKwiLgzIn4fEWf28fzkiLgmIm6NiN9GxN8MtL1Z\n8ef1X1QJbKiVtrES2CRJUmdpemiLiHHA54BDgRcCx0fE83st9k7gd5k5BzgE+ExE9FsFfM7mq+q2\nv+H/kiRJY1ErKm0HAYsy897MXAUsAI7otUwCPVdemwQ8lpmr+9vg1puvf6qnwmZokyRJY1krQttM\n4L66rxdXbfU+B7wgIu4HfgOcNtAGt5q4caWtE6/T1tcsWkmSNDaNlokIhwK3ZOarI2J34PsR8aLM\nXLnxovO48o83civQRecOjy5fvvFdISRJUvt0d3fT3d3dtO1HNnkKYkS8FJiXmYdVX58FZGZeULfM\nt4FPZObPq69/CJyZmb/qta2E5PrXXMBrf3gWAFdekRx7LKxZ05nVNkmSNDpFBJnZsLJSK2LOzcAe\nETErIiYCc4Frei1zL/A/ASJiOrAn8Mf+Njgh1w+Pek6bJEnqBE0fHs3MNRHxLuB6aiFxfmYujIhT\nak/nl4CPAhdHxG3Vah/MzKX9bXMzVm3UZmiTJEljWUvOacvM7wJ79Wr7Yt3jB6id1zao/8W3GZ+r\nYMIEWL3aC8xKkqSOUNxZYN/mTWyWq2DzzQH4y1/a3CFJkqQWKC60AYxfuz60rVjR5s5IkiS1wGi5\n5MewTMhV8Ld/C1tsYWiTJEkdocxKW66C5z0PPvpRQ5skSeoIhYa21bDZZgBssUWbOyNJktQCZYa2\ntavWhbYPfAD+9Kc2d0iSJKnJigxtE+pC2+abw+zZ7e2PJElSsxUZ2satra7TJkmS1CGKDG31w6OS\nJEmdoMzQtsbQJkmSOkuRoW3cmmcNbZIkqaMUGdp4xtAmSZI6S5mh7VlDmyRJ6ixlhrZVhjZJktRZ\nigxt4wxtkiSpwxQZ2qZO9jptkiSpsxQZ2qy0SZKkTlNkaOPeew1tkiSpo5QZ2sDQJkmSOkq5oS2z\n3T2QJElqmciCwk9ErO/tM8/AxInt7I4kSVK/IoLMjEZtr8xK24teZGCTJEkdpczQFg0LrZIkSUUo\nM7SNK7PbkiRJI1Vm+rHSJkmSOkyZoc1KmyRJ6jBlph9DmyRJ6jBlph+HRyVJUocpM7RZaZMkSR2m\nzPRjpU2SJHWYMkOblTZJktRhykw/VtokSVKHKTO0WWmTJEkdpsz0Y6VNkiR1mDJDm5U2SZLUYcpM\nP1baJElShykztFlpkyRJHabM9GNokyRJHabM9OPwqCRJ6jBlhjYrbZIkqcOUmX6stEmSpA7TktAW\nEYdFxJ0R8fuIOLOP58+IiFsi4r8j4rcRsToitul3g1baJElSh2l6+omIccDngEOBFwLHR8Tz65fJ\nzE9n5n6ZuT9wNtCdmU8MsNEm9liSJGn0aUXJ6iBgUWbem5mrgAXAEQMsfzxw+YBbtNImSZI6TCvS\nz0zgvrqvF1dtG4mILYHDgG8OuEVDmyRJ6jAT2t2BXt4E/GygodF5AAsXwrx5dHV10dXV1aKuSZIk\n9a+7u5vu7u6mbT8ys2kbB4iIlwLzMvOw6uuzgMzMC/pY9lvAFZm5oJ9t1Xp77LHw//5fE3stSZK0\naSKCzGzYifitGGe8GdgjImZFxERgLnBN74UiYgrwKuDqQbfoRARJktRhmj48mplrIuJdwPXUQuL8\nzFwYEafUns4vVYseCXwvM/8y6EY9p02SJHWYpg+PNtK64dETToCvf73d3ZEkSepXicOjjWelTZIk\ndZgy04/ntEmSpA5TZmiz0iZJkjpMmenHSpskSeowZYY2K22SJKnDlJl+rLRJkqQOU2Zos9ImSZI6\nTJnpx9AmSZI6TJnpx+FRSZLUYcoMbVbaJElShykz/VhpkyRJHabM0GalTZIkdZgy04+VNkmS1GHK\nDG1W2iRJUocpM/1YaZMkSR2mzNBmpU2SJHWYMtOPoU2SJHWYMtOPw6OSJKnDlBnarLRJkqQOU2b6\nsdImSZI6TJmhzUqbJEnqMGWmHyttkiSpw5QZ2qy0SZKkDlNm+tltt3b3QJIkqaXKC21f/Sq85S3t\n7oUkSVJLlRfaXvxiz2mTJEkdp7zQZmCTJEkdyNAmSZJUAEObJElSAQxtkiRJBTC0SZIkFcDQJkmS\nVABDmyRJUgEMbZIkSQUwtEmSJBXA0CZJklQAQ5skSVIBDG2SJEkFMLRJkiQVwNAmSZJUAEObJElS\nAQxtkiRJBWhJaIuIwyLizoj4fUSc2c8yXRFxS0TcHhE/GmBjTeunJEnSaDWh2TuIiHHA54DXAPcD\nN0fE1Zl5Z90yU4D/A7wuM5dExPYDbLDJPZYkSRp9WlFpOwhYlJn3ZuYqYAFwRK9lTgC+mZlLADLz\n0X63ZmiTJEkdqBWhbSZwX93Xi6u2ensCUyPiRxFxc0S8ud+tGdokSVIHavrw6BBNAPYHXg1sDdwY\nETdm5h96LzjvwgthyhQAurq66OrqamU/JUmS+tTd3U13d3fTth+Z2bSNA0TES4F5mXlY9fVZQGbm\nBXXLnAlskZnnVV9/BfjPzPxmr21l3ncf7LRTU/ssSZK0qSKCzGzYEGErhkdvBvaIiFkRMRGYC1zT\na5mrgZdHxPiI2Ar4H8DCPrfm8KgkSepATR8ezcw1EfEu4HpqIXF+Zi6MiFNqT+eXMvPOiPgecBuw\nBvhSZt7R5wYNbZIkqQM1fXi0kSIi8/77Yccd290VSZKkAZU4PNpYVtokSVIHMrRJkiQVwNAmSZJU\nAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgEMbZIkSQUwtEmSJBXA0CZJklQAQ5skSVIB\nDG2SJEkFMLRJkiQVwNAmSZJUAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgEMbZIkSQUw\ntEmSJBXA0CZJklQAQ5skSVIBDG2SJEkFKC+0SZIkdSBDmyRJUgEMbZIkSQUwtEmSJBXA0CZJklQA\nQ5skSVIBDG2SJEkFMLRJkiQVwNAmSZJUAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgEM\nbZIkSQUwtEmSJBXA0CZJklSAloS2iDgsIu6MiN9HxJl9PP+qiHgiIv67+vcPreiXJElSKSY0ewcR\nMQ74HPAa4H7g5oi4OjPv7LXoTzLz8Gb3R5IkqUStqLQdBCzKzHszcxWwADiij+WiBX2RJEkqUitC\n20zgvrqvF1dtvR0cEbdGxHci4gUt6JckSVIxmj48OkS/BnbJzKci4vXAVcCefS04b968dY+7urro\n6upqRf8kSZIG1N3dTXd3d9O2H5nZtI0DRMRLgXmZeVj19VlAZuYFA6zzJ+CAzFzaqz2b3V9JkqRG\niAgys2Gnf7ViePRmYI+ImBURE4G5wDX1C0TE9LrHB1ELk0uRJEkS0ILh0cxcExHvAq6nFhLnZ+bC\niDil9nR+CTg6It4BrAL+AhzX7H5JkiSVpOnDo43k8KgkSSpFicOjkiRJ2kSGNkmSpAIY2iRJkgpg\naJMkSSqAoU2SJKkAhjZJkqQCGNokSZIKYGiTJEkqgKFNkiSpAIY2SZKkAhjaJEmSCmBokyRJKoCh\nTZIkqQCGNkmSpAIY2iRJkgpgaJMkSSqAoU2SJKkAhjZJkqQCGNokSZIKYGiTJEkqgKFNkiSpAIY2\nSZKkAhjaJEmSCmBokyRJKoChTZIkqQCGNkmSpAIY2iRJkgpgaJMkSSqAoU2SJKkAhjZJkqQCGNok\nSZIKYGiTJEkqgKFNkiSpAIY2SZKkAhjaJEmSCmBokyRJKoChTZIkqQCGNkmSpAIY2iRJkgpgaJMk\nSSqAoU2SJKkAhjZJkqQCtCS0RcRhEXFnRPw+Is4cYLkDI2JVRBzVin5pbOvu7m53F1QIjxUNh8eL\n2qXpoS0ixgGfAw4FXggcHxHP72e584HvNbtP6gx+sGqoPFY0HB4vapdWVNoOAhZl5r2ZuQpYABzR\nx3LvBr4BPNyCPkmSJBWlFaFtJnBf3deLq7Z1ImIGcGRmfgGIFvRJkiSpKJGZzd1BxP8GDs3Mv6u+\n/mvgoMx8T90yVwCfzsybIuLfgG9n5jf72FZzOytJktRAmdmwYtSERm1oAEuAXeq+3qlqq/cSYEFE\nBLA98PqIWJWZ19Qv1MgXLkmSVJJWVNrGA3cBrwEeAG4Cjs/Mhf0s/2/AtZn5raZ2TJIkqSBNr7Rl\n5pqIeBdwPbVz6OZn5sKIOKX2dH6p9yrN7pMkSVJpml5pkyRJ0qYr5o4IQ71ArzpHRNwTEb+JiFsi\n4qaqbduIuD4i7oqI70XElLrlz46IRRGxMCJe176eq9kiYn5EPBQRt9W1DfvYiIj9I+K26nPnola/\nDrVGP8fLuRGxOCL+u/p3WN1zHi8dKiJ2iogbIuJ3EfHbiHhP1d6Sz5ciQttQL9CrjrMW6MrM/TLz\noKrtLOAHmbkXcANwNkBEvAA4FtgbeD3w+Wrii8amf6P2eVFvJMfGF4CTM3NPYM+I6L1NjQ19HS8A\n/5yZ+1f/vgsQEXvj8dLJVgPvy8wXAgcD76zySEs+X4oIbQz9Ar3qLMHGx/ARwCXV40uAI6vHhwML\nMnN1Zt4DLKJ2XGkMysyfAY/3ah7WsREROwCTMvPmarlL69bRGNLP8QJ9Xzf0CDxeOlZmPpiZt1aP\nVwILqV0VoyWfL6WEtkEv0KuOlMD3I+LmiHhb1TY9Mx+C2g8XMK1q730MLcFjqNNMG+axMZPaZ00P\nP3c6z7si4taI+ErdcJfHiwCIiNnAHOCXDP93z4iOl1JCm9SXl2Xm/sAbqJWoX8HGs4+daaP+eGxo\nIJ8HdsvMOcCDwGfa3B+NIhHxHGq33jytqri15HdPKaFtKBfoVYfJzAeq/x8BrqI23PlQREwHqMrP\nPfeyXQLsXLe6x1DnGe6x4THTwTLzkVx/eYUvs/50Co+XDhcRE6gFtq9l5tVVc0s+X0oJbTcDe0TE\nrIiYCMwFrhlkHY1hEbFV9ZcOEbE18Drgt9SOi7+pFjsJ6PmBugaYGxETI2JXYA9qF3rW2BVseE7S\nsI6NaohjWUQcVJ04/Ja6dTT2bHC8VL94exwF3F499njRV4E7MvNf6tpa8vnSittYbbL+LtDb5m6p\nvaYD/xG1+9FOAL6emddHxK+AKyLircC91GbtkJl3RO0et3cAq4BT6/6K1hgTEZcBXcB2EfFn4Fzg\nfODKYR4b7wQuBrYAruuZQaixpZ/j5ZCImENtlvo9wCng8dLpIuJlwInAbyPiFmrDoB8CLmD4v3uG\nfbx4cV1JkqQClDI8KkmS1NEMbZIkSQUwtEmSJBXA0CZJklQAQ5skSVIBDG2SJEkFMLRJkiQVwNAm\nSZJUAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgEMbZIkSQUwtEmSJBXA0CZJklQAQ5sk\nSVIBDG2SJEkFMLRJkiQVwNAmSZJUAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgEMbZIk\nSQUwtEmSJBXA0CZJklQAQ5skSVIBDG2SJEkFMLRJkiQVwNAmSZJUAEObJElSAQxtkoYkIk6IiJsj\nYkVELImI70TEy9rYn1kRsTYillf/VlT/HzPE9ddGxG7N7udQRMRJEfHTdvdD0ug2od0dkDT6RcT7\ngA8CpwDXA88ChwJvAn7ex/LjM3NNC7qWwJTMzBGu268WvoYeI3kNkjqIlTZJA4qIycB5wKmZeXVm\n/iUz12TmdZl5VrXMuRFxZUR8LSKeAE6KiIkRcVFVlVscERdGxGbV8ttFxLUR8XhEPBYRP67b35nV\n8ssjYmFEHDJYF/vp979FxOci4tvVtm6MiF2r535crXdbT3UuIl4VEfdFxAcj4gHgq9Wyb4+IRRHx\naERcFRE71u1jbUS8OyLujoiHI+KTVftm1et6Yd2yz42IJyNiu2G+/ztGxNXV9n4fEW+re+7Aqvq5\nLCIeiIhPV+2bV9+LR6v3+L8i4rnD2a+k0cfQJmkwBwObA1cNstzhwBWZuQ1wGfAPwEHAi4AXV4//\noVr2/cB9wHbANOBDABGxJ/BO4IDMnEytmnfPIPvtM7RVjgPOBbYB7gY+BpCZr6qe3zczJ2fmldXX\nO1TL7gL8XUS8Gvg4cDSwI/BnYEGvfRwJ7F/9OyIi3pqZq4DLgb+uW+544AeZ+dggr6e3/1ftdwfg\nGODjEdFVPfcvwEWZOQXYHbiiaj8JmAzMBKYCfw/8ZZj7lTTKGNokDWY74NHMXDvIcjdm5rUAmfk0\ncAJwXmY+VgWV84A3V8uuohaCdq2qdj1DrGuAicA+ETEhM/+cmX8aYJ8BPBIRS6uK0tKI2Kvu+f/I\nzF9Xff86MKeP9eutAc7NzFWZ+Uz1GuZn5m+qIHY2cHBE7FK3zvmZuSwzFwMXUQtnAJdW6/d4M/C1\nAV7Lxi8uYidqofnMqk+/Ab4CvKVaZBWwR0Rsl5lPZeZNde3bAXtmzS2ZuXI4+5Y0+hjaJA3mMWD7\niBjs8+K+Xl/PoFYh6nFv1QbwKWqVr+sj4g8RcSZAZt4NvBeYBzwUEZdFxA4AdRMNlldhBmrngW2X\nmVMzc9vq/7vq9vlg3eOngOcM8hoeqcJZ/Wu4t+eLzHyS2vsxs26ZxX29xipAPVkNu+5FrRJ2zSD7\n720GsDQzn+q1j579vxXYC7izGgL9X1X714DvAQuqoebzI2L8MPctaZQxtEkazI3AM9SGAQfS+0T6\nJcCsuq9nAfcDZObKzDwjM3enNqz6vp5z1zJzQWa+om7dC6r2SdVQ5uSqqtVjoOHR4er9Gu6vfw0R\nsTW1Clb9/neue7xLtU6PS6hV2N4MfCMznx1mf+4Hplb7rd/HEqiF3Mw8ITOfC3wS+EZEbJmZqzPz\nI5n5QuD/ozZh5C29Ny6pLIY2SQPKzOXUzgv7PxFxRERsGRETIuL1EXH+AKsuAP4hIraPiO2Bc6iG\nByPif0XE7tVyK4DVwNqI2DMiDomIidRmqP4FGGhYNhh5aHsQGOySH5cDfxsRL4qIzamd3/bLzKyv\nKn4gIraJiJ2B09jwnLevA38FnEhtuHQg46oJBOv+VeH0F8AnqrYXASez/n08sXpvAZZRC51rI6Ir\nIvapqqMrqQ2XDja8LWmUM7RJGlRm/jPwPmoTCR6mNux5KgNPTvgo8CvgNuA31eOPVc89D/hBRKyg\ndsmQ/5OZP6Y24eF84BFqVabnUjuPrN+uAY/Hhtdpe+8QX9Y84NLqPLij+9x45g+phc1vUatu7QrM\n7bXY1cCvgf8GrqWadVqtv7hqz8z82SD9OZjaEO5T1MLqU1XoOqHa7/3AN4FzMvNH1TqHAb+LiOXA\nhcBx1bl4OwDfoBbkfgf8iGGeTydp9InBLm9UnTtyKTCd2l9qX8rMf42Ic4G3U/sAB/hQZn63Wuds\naudarAZOy8zrq/b9gYuBLYDrMvO9VfvEah8HAI9S++CpPxdGkkadiFgL7JGZfxxgmfnAksz8x9b1\nTNJYNJSL664G3peZt0bEc4BfR8T3q+f+ufoLfJ2I2Bs4Ftgb2InaX9PPqy5++QXg5My8OSKui4hD\nM/N71Mr9SzPzeRFxHLVzM3r/NStJRYmI2dSGR/drb08kjQWDDo9m5oOZeWv1eCWwkPUzl/o6l+QI\nYEF1Iuw9wCLgoGoG2KTMvLla7lLWn9h8BLUTdqFW0n/NCF6LJLVav0MVEfFP1IaGP5mZ9/a3nCQN\n1bDOaav+apwD/FfV9K6IuDUivhIRU6q2mWw49X9J1TaTDWdcLWZ9+Fu3TnXbmCciYupw+iZJrZaZ\n4/sbGs3Mf6xmug40WUOShmzI9x6thka/Qe0ctZUR8XngnzIzI+KjwGeAtw24kaHr77Y03ptPkiQV\nIzMbdlmiIYW2iJhALbB9LTOvrjrxSN0iX6Y2awpqlbX66xbtVLX1116/zv3VBSAnZ+bSvvoysvtC\nqxPNmzePefPmtbsbKoDHiobD40VDFdHIy0gOfXj0q8AdmfkvdR3Zoe75o4Dbq8fXAHOjdrPoXYE9\ngJsy80FgWUQcFLVX8RZqU+V71jmpenwMcMOIXo0kSdIYNWilLSJeRu3CkL+NiFuonXj7IeCEiJhD\n7TIg9wCnAGTmHRFxBXAHtQs6nprry2PvZMNLfny3ap8PfC0iFlG7RYwzRyVJkuoMGtqqGzn3dc+6\n7/bR1rPOJ4BP9NH+a2DfPtqfoXaZEKlhurq62t0FFcJjRcPh8aJ2GfTiuqNJRGRJ/ZUkSZ0rIlo/\nEUGSJLXW7NmzufdeL/FXglmzZnHPPfc0fT9W2iRJGoWqKk27u6Eh6O971ehKmzeMlyRJKoChTZIk\nqQCGNkmSpAIY2iRJkgpgaJMkSW21du1aJk2axOLFi9vdlVHN0CZJUiF22AEimvdvhx0G7wPApEmT\nmDx5MpMnT2b8+PFstdVW69ouv/zyYb+ucePGsWLFCnbaaadhr3v33Xczbty4df2ZMWMGRxxxBDfc\nMPQ7Ys6fP59DDjlk2PtuNUObJEmFeOih0bH9FStWsHz5cpYvX86sWbP4zne+s67t+OOP32j5NWvW\nNLinG4qIdf255ZZbOOSQQzj88MO57LLLhrR+Zjb85u7NYGiTJEkjlpkbXaPsnHPOYe7cuZxwwglM\nmTKFr3/96/zyl7/k4IMPZtttt2XmzJmcdtpp68LcmjVrGDduHH/+858BePOb38xpp53GG97wBiZP\nnszLXvayIV9oePr06bz3ve/lnHPO4YMf/OC69o997GPsvvvuTJ48mX333Zdrr70WgNtvv513v/vd\n/PSnP2XSpElMmzYNgGuvvZb99tuPKVOmMHv2bD760Y9u8nu1qQxtkiSp4a666ir++q//mmXLlnHc\nccex2Wab8dnPfpalS5fy85//nO9973t88YtfXLd870rX5Zdfzsc+9jEef/xxdt55Z84555xh7f+o\no47igQce4O677wZgr7324sYbb2T58uV8+MMf5oQTTuCRRx5hn3324XOf+xyveMUrWLFiBQ8//DBQ\nGwK+7LLLWLZsGddeey2f/exnue666zbxXdk0hjZJktRwL3/5y3nDG94AwOabb84BBxzAgQceSEQw\ne/Zs3v72t/PjH/943fK9q3VHH300++23H+PHj+fEE0/k1ltvHdb+Z8yYQWaydOnSddvrqaLNnTuX\n2bNn86tf/arf9bu6uth7770B2HfffTnuuOM26G87GNokSVLD7bzzzht8fdddd/HGN76RHXfckSlT\npnDuuefy6KOP9rv+DnWzIrbaaitWrlw5rP0vWbIEgKlTpwJw8cUXM2fOHKZOncq2227LXXfdNeD+\nb7zxRg455BCmTZvGNttsw/z58wdcvhUMbZIkqeF6D3eecsop7Lvvvvzxj39k2bJlnHfeeU29t+q3\nvvUtdtxxR3bffXf+9Kc/ceqpp/LFL36RpUuX8vjjj7PXXnut239fkxCOP/54jjnmGJYsWcITTzzB\nySef3PZ7wRraJElS061YsYIpU6aw5ZZbsnDhwg3OZ9tU9WHq4Ycf5rOf/Swf//jH+eQnPwnAypUr\nGTduHNtvvz1r1qzhy1/+Mnfeeee6daZPn87ixYtZvXr1uraVK1ey7bbbstlmm/HLX/6SBQsWNKy/\nI2VokySpENOnj77tD/VSGZ/5zGe4+OKLmTx5Mu94xzuYO3duv9sZ7uU3ImLdddpe/OIX8/3vf5//\n+I//4MQTTwRq56S9+93v5sADD2TGjBksWrSIl770pevWf+1rX8vznvc8pk+fzowZMwD4/Oc/z1ln\nncWUKVM4//zzOe6444bVp2aIdpf6hiMisqT+SpI0UhHR9uE4DU1/36uqvWEXgLPSJkmSVABDmyRJ\nUgEMbZIkSQUwtEmSJBXA0CZJklQAQ5skSVIBDG2SJEkFMLRJkiQVwNAmSZJUAEObJEml2GEHiGje\nvx12GFI3Jk2atO62UePHj2errbZa13b55ZeP+OUdfPDBXHbZZf0+f9dddzFu3Lh1+54xYwZHHnkk\n3d3dQ97HF7/4RV772teOuI/tZGiTJKkUDz00Kra/YsUKli9fzvLly5k1axbf+c531rUdf/zxTe3i\nhAkT1u37lltu4RWveAVvfOMbueKKK4a8jeHe23S0MLRJkqQRy8yN7ru5du1aPvKRj7D77rszbdo0\n3vzmN7N8+XIAnnrqKY4//ni22247tt12Ww4++GCWLVvGGWecwc0338zb3vY2Jk+ezAc+8IFB9z19\n+nTe//73c/bZZ2+w/Ec+8hF22203Jk+ezIte9CKuu+46AG699Vbe+9730t3dzaRJk9bdHP6qq65i\nzpw5TJkyhdmzZ/OJT3yiUW9PQxnaJElSQ33qU5/iBz/4Ab/4xS9YvHgxm222GaeffjoAX/nKV1iz\nZg0PPPAAjz32GJ/73OeYOHEin/70pznwwAOZP38+y5cv51Of+tSQ93fUUUexePFi7r33XgCe//zn\n88tf/pLly5dz5plnMnfuXJYuXcqcOXO46KKL6OrqYsWKFdx///0ATJkyhcsvv5xly5Zx1VVX8ZnP\nfIbrr7++8W/MJjK0SZKkhvriF7/I+eefz/Tp05k4cSLnnHMOCxYsAGCzzTbjkUceYdGiRYwbN44D\nDjiALbfcct26vat2QzFjxgwyk6VLlwJwzDHHMG3aNABOPPFEZs6cya9//et+1z/kkEOw5xq8AAAg\nAElEQVTYe++9AZgzZw7HHHMMP/7xj4fdj2YztEmSpIa67777eMMb3sDUqVOZOnUq+++/PwBLly7l\n5JNP5pWvfCVHH300u+yyCx/+8IdHFNTqLVmyhIhg6tSpAMyfP58Xv/jFTJ06lW233Za7776bRx99\ntN/1f/7zn9PV1cW0adPYZpttuOSSSwZcvl0MbZIkqaF22mknbrjhBpYuXcrSpUt5/PHHefLJJ5k6\ndSoTJ07kvPPOY+HChfzkJz/hyiuvXFeFG+kEgW9961vstNNOzJo1i0WLFvGe97yHr3zlK+v2vfvu\nu68Lhn3t47jjjuP4449nyZIlPPHEE5x00kmbHCSbwdAmSZIa6pRTTuHMM89k8eLFADz88MN8+9vf\nBuCHP/whCxcuJDN5znOew4QJExg/fjxQm1jwxz/+ccBt14ephx56iAsvvJALLriACy64AICVK1cy\nfvx4tt9+e1avXs3//b//lz/84Q/r1pk+fTr33Xcfq1evXtfWEyg322wzfvGLX3DllVc25o1oMEOb\nJEmlmD591G2/r8rVmWeeyWtf+1pe/epXM2XKFF7+8pdzyy23ALWhzCOOOGLdzM43vvGNHHvssQCc\nfvrpXHLJJWy33XacddZZfe5v7dq1TJ48mUmTJjFnzhx+9KMfcc011zB37lwA9ttvP/7+7/+eAw44\ngJkzZ3Lvvfdy4IEHrlv/sMMOY/bs2UybNo1ddtkFgC984Qu8//3vZ8qUKXz6059e15/RJkZj+a8/\nEZEl9VeSpJGKiFE5RKeN9fe9qtobdlE4K22SJEkFMLRJkiQVwNAmSZJUAEObJElSAQxtkiRJBTC0\nSZIkFWBCuzsgSZI2NmvWrBHfIUCtNWvWrJbsx+u0SZIkNYHXaZMkSepAhjZJkqQCGNokSZIKYGiT\nJEkqgKFNkiSpAIY2SZKkAhjaJEmSCjBoaIuInSLihoj4XUT8NiLeU7VvGxHXR8RdEfG9iJhSt87Z\nEbEoIhZGxOvq2vePiNsi4vcRcVFd+8SIWFCtc2NE7NLoFypJklSyoVTaVgPvy8wXAgcD74yI5wNn\nAT/IzL2AG4CzASLiBcCxwN7A64HPx/pLOn8BODkz9wT2jIhDq/aTgaWZ+TzgIuCTDXl1kiRJY8Sg\noS0zH8zMW6vHK4GFwE7AEcAl1WKXAEdWjw8HFmTm6sy8B1gEHBQROwCTMvPmarlL69ap39Y3gNds\nyouSJEkaa4Z1TltEzAbmAL8EpmfmQ1ALdsC0arGZwH11qy2p2mYCi+vaF1dtG6yTmWuAJyJi6nD6\nJkmSNJYN+YbxEfEcalWw0zJzZUT0vgloI28K2u99uubNm7fucVdXF11dXQ3crSRJ0sh0d3fT3d3d\ntO0P6YbxETEB+Dbwn5n5L1XbQqArMx+qhj5/lJl7R8RZQGbmBdVy3wXOBe7tWaZqnwu8KjPf0bNM\nZv5XRIwHHsjMaX30wxvGS5KkIrTrhvFfBe7oCWyVa4C/qR6fBFxd1z63mhG6K7AHcFM1hLosIg6q\nJia8pdc6J1WPj6E2sUGSJEmVQSttEfEy4CfAb6kNgSbwIeAm4ApgZ2pVtGMz84lqnbOpzQhdRW04\n9fqq/QDgYmAL4LrMPK1q3xz4GrAf8Bgwt5rE0LsvVtokSVIRGl1pG9Lw6GhhaJMkSaVo1/CoJEmS\n2sjQJkmSVABDmyRJUgEMbZIkSQUwtEmSJBXA0CZJklQAQ5skSVIBDG2SJEkFMLRJkiQVwNAmSZJU\nAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgEMbZIkSQUwtEmSJBXA0CZJklQAQ5skSVIB\nDG2SJEkFMLRJkiQVwNAmSZJUAEObJElSAQxtkiRJBTC0SZIkFcDQJkmSVABDmyRJUgHKC22Z7e6B\nJElSy5UX2taubXcPJEmSWq680LZmTbt7IEmS1HKGNkmSpAIY2iRJkgpQXmjznDZJktSBygttVtok\nSVIHMrRJkiQVwNAmSZJUAEObJElSAcoLbU5EkCRJHai80GalTZIkdSBDmyRJUgEMbZIkSQUwtEmS\nJBWgvNDmRARJktSBygttVtokSVIHMrRJkiQVwNAmSZJUAEObJElSAcoLbU5EkCRJHai80GalTZIk\ndSBDmyRJUgEMbZIkSQUwtEmSJBVg0NAWEfMj4qGIuK2u7dyIWBwR/139O6zuubMjYlFELIyI19W1\n7x8Rt0XE7yPiorr2iRGxoFrnxojYZcAOORFBkiR1oKFU2v4NOLSP9n/OzP2rf98FiIi9gWOBvYHX\nA5+PiKiW/wJwcmbuCewZET3bPBlYmpnPAy4CPjlgb6y0SZKkDjRoaMvMnwGP9/FU9NF2BLAgM1dn\n5j3AIuCgiNgBmJSZN1fLXQocWbfOJdXjbwCvGbBDhjZJktSBNuWctndFxK0R8ZWImFK1zQTuq1tm\nSdU2E1hc1764attgncxcAzwREVP73auhTZIkdaAJI1zv88A/ZWZGxEeBzwBva1Cf+qrgrTPvssvg\nllsA6Orqoqurq0G7lSRJGrnu7m66u7ubtv0RhbbMfKTuyy8D11aPlwA71z23U9XWX3v9OvdHxHhg\ncmYu7W/f8445Bo4+eiTdliRJaprexaTzzjuvodsf6vBoUFcBq85R63EUcHv1+BpgbjUjdFdgD+Cm\nzHwQWBYRB1UTE94CXF23zknV42OAGwbsicOjkiSpAw1aaYuIy4AuYLuI+DNwLnBIRMwB1gL3AKcA\nZOYdEXEFcAewCjg1M7Pa1DuBi4EtgOt6ZpwC84GvRcQi4DFg7oAdMrRJkqQOFOsz1egXEZmXXgpv\nfnO7uyJJkjSgiCAzBzxXfzi8I4IkSVIBygtt3hFBkiR1oPJCm5U2SZLUgQxtkiRJBSgvtK1a1e4e\nSJIktVx5oe2ZZ9rdA0mSpJYztEmSJBXA0CZJklSA8kLbs8+2uweSJEktV15os9ImSZI6kKFNkiSp\nAIY2SZKkApQX2jynTZIkdaDyQpuVNkmS1IEMbZIkSQUoL7StXt3uHkiSJLVceaHNe49KkqQOVF5o\ns9ImSZI6UHmhzUqbJEnqQOWFNittkiSpA5UX2qy0SZKkDlReaLPSJkmSOlB5oc1KmyRJ6kDlhTYr\nbZIkqQOVF9qstEmSpA5UXmiz0iZJkjpQeaHNSpskSepAhjZJkqQCGNokSZIKUF5oW74cfvjDdvdC\nkiSppcoLbQDPPtvuHkiSJLVUeaHtjW90BqkkSeo45YW2iRPhmWfa3QtJkqSWKi+0bb65oU2SJHWc\nMkOb57RJkqQOU15oc3hUkiR1oPJCm8OjkiSpA5UZ2hwelSRJHaa80ObwqCRJ6kDlhTaHRyVJUgcq\nM7Q5PCpJkjpMeaHN4VFJktSBygttVtokSVIHKjO0WWmTJEkdprzQ5vCoJEnqQOWFNodHJUlSByoz\ntFlpkyRJHcbQJkmSVIDyQtvEiQ6PSpKkjlNeaLPSJkmSOpChTZIkqQDlhbbnPAdWrmx3LyRJklpq\n0NAWEfMj4qGIuK2ubduIuD4i7oqI70XElLrnzo6IRRGxMCJeV9e+f0TcFhG/j4iL6tonRsSCap0b\nI2KXATu0zTbw+OPDfqGSJEklG0ql7d+AQ3u1nQX8IDP3Am4AzgaIiBcAxwJ7A68HPh8RUa3zBeDk\nzNwT2DMierZ5MrA0M58HXAR8csDebLMNPPEEZA6h65IkSWPDoKEtM38G9C5tHQFcUj2+BDiyenw4\nsCAzV2fmPcAi4KCI2AGYlJk3V8tdWrdO/ba+AbxmwA5tsQWMGwdPPz1Y1yVJksaMkZ7TNi0zHwLI\nzAeBaVX7TOC+uuWWVG0zgcV17Yurtg3Wycw1wBMRMXXAvU+eXKu2SZIkdYgJDdpOI8cqY6An582b\nV7tO2yc+QddRR9HV1dXAXUuSJI1Md3c33d3dTdt+5BDODYuIWcC1mfmi6uuFQFdmPlQNff4oM/eO\niLOAzMwLquW+C5wL3NuzTNU+F3hVZr6jZ5nM/K+IGA88kJnTNu4FRERmJuy7L/z7v8OLX7zJb4Ak\nSVIzRASZOWAxajiGOjwabFgBuwb4m+rxScDVde1zqxmhuwJ7ADdVQ6jLIuKgamLCW3qtc1L1+Bhq\nExsGtvXW8OSTQ+y6JElS+QYdHo2Iy4AuYLuI+DO1ytn5wJUR8VZqVbRjATLzjoi4ArgDWAWcmutL\nee8ELga2AK7LzO9W7fOBr0XEIuAxYO6gvTa0SZKkDjOk4dHRYt3w6OGHw1vfCkceOfhKkiRJbdCu\n4dHRxUqbJEnqMIY2SZKkAhjaJEmSCmBokyRJKoChTZIkqQCGNkmSpAIY2iRJkgpQZmibMsUbxkuS\npI5SZmibMQMeeKDdvZAkSWqZMkPbzJmwZEm7eyFJktQyZd7G6umnYfLk2v/jysydkiRpbPM2VgBb\nbFELbY8+2u6eSJIktUSZoQ0cIpUkSR3F0CZJklSAckPbjBlwyy3t7oUkSVJLlBva9tgDrryy3b2Q\nJElqiXJD2xveAAXNfJUkSdoU5Ya2yZNhxYp290KSJKklyg1tkybB8uXt7oUkSVJLlB/aHCKVJEkd\noNzQNnFi7d/Kle3uiSRJUtOVG9oAZs+GP/2p3b2QJElqurJD2+67wx//2O5eSJIkNV3ZoW36dHjk\nkXb3QpIkqenKDm3bb+9N4yVJUkcoP7T953+2uxeSJElNV3Zoe+lL4ac/bXcvJEmSmi6yoOucRURu\n0N9nn4Wtt679H9G+jkmSJPUSEWRmwwJK2ZW2iRNhyy1h2bJ290SSJKmpyg5tANtt52QESZI05pUf\n2nbaCRYvbncvJEmSmqrsc9oAdtwRHnzQe5BKkqRRxXPaevvMZ2DChHb3QpIkqanKr7Q99VTtem0r\nV8K48jOoJEkaG6y09bbVVjB5cm2IVJIkaYwqP7QB7LYb/OEP7e6FJElS04yN0PbCF8Ltt7e7F5Ik\nSU0zNkLbnDnwm9+0uxeSJElNMzZC2377wZe+BDfe2O6eSJIkNcXYCG0HHwxvfSt885vt7okkSVJT\njI3QFgGHHw533tnunkiSJDXF2AhtADNnwne+Az/9abt7IkmS1HDlX1y3x/3314Lb9tvDI4+0tmOS\nJEm9NPriumPn/k877ggHHAAzZrS7J5IkSQ03doZHI+Dcc2Ht2nb3RJIkqeHGTmiD2vDobbfBM8+0\nuyeSJEkNNbZC23771c5pe/e7290TSZKkhhpboS0CPvlJuPlmuOWWdvdGkiSpYcbO7NEeDz5Ym5QA\nUNBrkyRJY0ujZ4+OrUobwA47wO9+V3u8bFl7+yJJktQgYy+0AbzgBbVbW22zjdU2SZI0Joy94dEe\nTz0FW29de/zww/Dc5zavY5IkSb2MquHRiLgnIn4TEbdExE1V27YRcX1E3BUR34uIKXXLnx0RiyJi\nYUS8rq59/4i4LSJ+HxEXbUqf1tlqK9hzz9rjnXduyCYlSZLaZVOHR9cCXZm5X2YeVLWdBfwgM/cC\nbgDOBoiIFwDHAnsDrwc+HxE96fMLwMmZuSewZ0Qcuon9qnn722v/P/MMrFzZkE1KkiS1w6aGtuhj\nG0cAl1SPLwGOrB4fDizIzNWZeQ+wCDgoInYAJmXmzdVyl9ats2nOOAPuvbf2+O/+rnZ/UkmSpAJt\namhL4PsRcXNEvK1qm56ZDwFk5oPAtKp9JnBf3bpLqraZwOK69sVVW2PssgssXgyXX167Y8LTTzds\n05IkSa2yqTeMf1lmPhARzwWuj4i7qAW5eg2d6TBv3rx1j7u6uujq6hp8pZkz4Ve/gpe8BLbcsnbx\n3Ze8pJHdkiRJHa67u5vu7u6mbb9hs0cj4lxgJfA2aue5PVQNff4oM/eOiLOAzMwLquW/C5wL3Nuz\nTNU+F3hVZr6jj30MffZoXx54AGbMqD3+7W9hn31Gvi1JkqQBjJrZoxGxVUQ8p3q8NfA64LfANcDf\nVIudBFxdPb4GmBsREyNiV2AP4KZqCHVZRBxUTUx4S906jbXjjvDRj9Ye77svnHNOU3YjSZLUaCOu\ntFXB6z+oDX9OAL6emedHxFTgCmBnalW0YzPziWqds4GTgVXAaZl5fdV+AHAxsAVwXWae1s8+N63S\nBnD77bUL7/bMJi3oOnWSJKkcja60jd2L6w7kySfhyCPhBz+AF78YPvQhOPbYTd+uJElSxdDWyP7+\n/+2de3RcVb3Hv3smmbwmmaRpmqR50Ae09EFbnlLaCiKFFsQKglZQ7l1iERS54kLxUQUKuNSF1/qC\nBV7w9oosHiKCVi0gz1KgtFCghJY+0yRN07ybSWaSeZz7xzd7nUmaPiIlzWm+n7Vmzcx57PPbv/07\n+3zP75yzz9VXAw88wN+xGJD2YZ/LEEIIIYQgEm1H2t5EgmItOxu4+WYgEuETpjfeCKxfDxzO06lC\nCCGEEP040qJNqSW/H6iqAu66C7jlFk7LzQVaW4Hly3XPmxBCCCGGBcq0WTo7gc2bgddfB772tb7z\n4nGKOyGEEEKIw2TYDPlxzJGTA5xyCnDttRzD7Yor3HmnngqsWAF8hAPmCSGEEEIcDGXaDsby5cCq\nVcA//+lOe+EFoKYGWLSIl1GFEEIIIQZADyIcLXsffRT4zW+Al192py1cyEupZ54JnH02sGYN74VL\nJoEJE46OnUIIIYQYFki0HW17q6v5Oqxbb2UWLpXjjuN8AOjq4lOoQgghhBiRSLQNJ3sTCWbWior2\nn3fbbcBZZwGvvQbMmAE0N/Ny6sUXA+npFHf5+UBBwdDbLYQQQoiPHIm24Wrv5s28LHriicB99/GB\nhgMxeTKXB/hKrXvv5Xp+P+DTsyFCCCHEsYBEm1fsjcfd3//6F/DNbwLnncf74gDe//bLXwKPPML/\nEyZQzC1YADQ28vvUU4FnngHmzmVGLpmUqBNCCCE8gkSbh+wdkJ4eYOtWYOpU/u/uBh57jJm3O+4A\nMjI4LZVgECgs5CXVf/wD+MtfgOef5yXYxYuHvg5CCCGEOCQSbR6yd9B0dfF1Wps3Aw8/DIwaBUyZ\nAtx/P/8PxLPPAueey7c6jB/P4UnOPZf3yyUSwOOPAyedBNTWMkv3yU/yPauHuhTb3g6EQh9NPYUQ\nQogRgESbh+w9oti3MjQ2Ag0NzNT94he8xBqJuA86dHQAl1wCrFtHcbZnT99y2too6D73OWDJEoq+\nxYuBWbM4/6KLgMxM4M9/5iDDFRUs1+fjK71Mv9hLJlnmqFHuK7/6LyOEEEKMQCTaPGTvkBCPA9u2\nARMn8v63oiLgD3/g67hKS4Flyzi/uJhPrjY3910/GATCYQ5XUlREsWeZN4/j0hUVAdOmcWDh228H\nrrrKzfDdeivfFvH73wNPPUXBduONQEsL78sLBPa3edcuZg5vuoli8N13afPPfvZRekoIIYQYUiTa\nPGTvsKOri+9YLSoColEKrPR03if33nscmuSuuyjivv1tCriuLmDfPt5r9+abwJYtzKwdLmeeCXz2\ns7xUO2YM8M47fNOE5a67KPZeegnYvp0ibv164IILgKefZhbx3HOBkhI301dXx3sD09OB8nJmFF94\nAZg/f2AbqquBysr9M4A263ggX2VnH349hRBCiH5ItHnI3mOSeBzYu5dZvESCQigW42XZnTspBsvL\neVl17VrgySeZ3du3j9m3aJQC8dlnmWlra+N4dt3dwN/+xku/A3HRRcDKlbzH7/333em5uRw25emn\n+X/ZMorLmhrg5pspBG+5hZeTd+5kRvH222nb7bcDV1/N4VZCIV4yfuIJCsAVKzj9pJOAj32MWcdT\nTuG9gQ88wGWnTKGQTEvra6vj0EfFxftPN4ZPDp9+OkWnJZnkNq+6ipfBD4VEpRBCDHsk2jxkrxgE\n8ThfFTZxIgXWhg0c5iQ3l0LpzTeBE05gRi4/n8OgBIO8pFpQAHz1qxw+5Z573EvA6enAOecA06fz\nwYrKSmbu7rkHGDeOZVRXM/tXU+Pacv31FFirVvFJ30MxaRJFnc8HvP020NREsTh3LrcTCgEvvghs\n3Mhs4DPP8D7C2bNZ1+JiDsJ8zTUUdUuXUmAuWMDsZ0cHH05Zs4aXm1etogBetAi44QZeuu7uBj74\ngMLvpz91bWtvZ/l2uJjOTt6zmCoMn3wSOP98ZjCPP/7Dt+VAfPrTFNT23slkknXV/Y9CiGMYiTYP\n2Ss8RCzGrF//t1vY7FhnJ5/MraykSLr7boqgsWMpyqqrKTTr6ynM/H7+zsujiHzrLeDSSylMFyzg\ntO3b+R8AcnKYvXvjDV6eLiykyCsocB8mmTGDAhNguY5DQQdw+f73K1rsvYmW8eNp+0038eniZ591\n52VmAt/9LrBjB4VcJEKf5ObyMvf06bTTGN6LuHs38IlPcAzCkhLgr39lOcEgM5VLllAIPvQQcOWV\nwI9/zLeIzJoFfOlLrNPChdzumjW8JH/22XyYJhzmdtesYdv89rcs44or3P+TJwOf+Qzvo1y3jg/Q\nWBGcn0+hn5rRBCgY162jYM7MZKa0uprbGjWq77KtrSwnmeQyEyYwVgD3v30K23GA1avpb7tuMMiM\n9KpVFNmpHOwJbRsfp5/Ocm1mdahF7he+wNsZbAY9FqPPjiUGesDqcEgkDi8rLkY0Em0esleIw+JQ\nB42eHh4gMjMppkIhijmfj2P2hcMUS9OnM6O1dy8F5NSpFH4VFVx/+XJm83p6mKEbPx74wQ8ogOrq\n+DQywAP1449TzHR1uXakpXHeypXAGWcAmzZRNK1f777SDeDl5JYW3v/45S+z/IwMipw1aw5cz8JC\niqPWVleE2u+Kir7Z0P7Mncs67Nix/7ypU2nnq68CZWW0u7OT80pLmb2srqZgu/ZaZnNzcuin55/v\nW9aiRRS5kQhtPftsCrOWFmY733yTQu7kk+nDwkL64+9/5/rTpwMf/zjbZ80aDrrd1ASMHk37ly6l\nwLXZ0ttu4+V9gOVaAfWTn1AM5+ay/a+8knWZNg34+c/p75YWCq2JE/l7xQra/p3v0I7Vq+nrOXMo\ncmfOBF55hdt0HD5c9OtfM9ZaW3mCsnu364uTT6agX7KEArO4mDYGg7zFYOdOirxRo1h2MknBH4sx\nK/zBBzwRqqjgw1LBION3/nyeCCxezHhduZLffj9jwN6isWED7TzhBLbpvHn0x8aNPEmaP5/l1tdz\noPJJk+i7rVsZD4kE2zgUYjtnZDBm58+nLx2HJ0xPPrn/G26WLWO7PPII6zQQsRj3GWPcfTwSYb1n\nzmTGffZs1vtgbN3K2Jo2jT5ta2M9zjyT+4btCyz/jgjt7mb9D0Ystv8J0IEYaCD4t97iSemSJYO3\nLxod+GShsZH+POusYZu1l2jzkL1CeJ6uLnaYoRAPcFlZh7ee41AY9T8gJZM86AYCfIq4pMQVafbe\nwHCYQiYQoIg47TQKzHic815+mcJqzhweYBsaXGFaU8OD7Be/yOX/9CeKjV27mJ3cuBG48EIKjj/+\nkdmuWbN4Gf2hh3i/ZXo6bd+0iQeCSy7hwXvePB7cL7mEQmzPHj49HY3ysnhVFfCtb/Fy/nHHsS6z\nZzMjOXYsBdSGDazThRdSAO3YQTsuvphC8bHHeO/kPfewXpdfTh9ecAEP8nv2UOCFw/RJbq475I/1\naTLJrFxXF3DZZTzQp6UxYzhtGvC739E35eWcl5vrCuNwmO1hhw+aOZMiYdkyHnRXrHDFeX9KS3mg\nrqvj/2nTKJjDYfqyvp6Z1S1bDlxGRgZvKbCv+bP1sGRm0t+Hw6hRvJfWvp1m5ky2kyUvj6Jz27a+\n06JRxnpeHsVMdzdPcmw2vbWVdtkM+OLFvM+2p4ffn/oUReXatW7c1tRQXJaUMH4vvZRZ4cxMbucr\nX2Esx+Nsz3XruL2SEgp4v5/i+4MPXFuzsrjs/Pmsx+TJzMQ//jjnf/7z3P6JJ/JE4eGHuc6cORTs\ns2ezLYqKmO0G+L+9nfcXNzay/caN4++lS3mSMmEC29Pv50nQ5ZezHi++yBi7804KzeeeA77xDbbp\nokXAD3/IbVxzjXtbh73/94kngOuu4/yKCsZSTg73taVL2Y7Ll/Ok6NvfZkxVVlLkr1/PetXW0q6y\nMu5jc+bQB3Pnso4TJnDar37FsU/XrGGbRCLc57dv576Vn882f+klXm1oaOA606Zxvy8ro48XL2Z/\nkUgw03/vvWwjK9R7kWjzkL1CCDEo+mcoBps16ez8cJdRHYciZt8+itmDDcAdj7vZ2MxMd9mODgrN\n/jZEozywh0I8+MViFJqRiHsyEIlwmdNOo5DfsYM+Of54iqKGBi7b3MxpySTrnEy6WaipU3mQNobr\nGEObXnmFQm7WLNq8Zw+3N2MGxVZHB8X7rl3MANbU8EA+ZQqF2ujR/FRUcJDypiYKsD17KDJ6eiiI\nm5uZ1Zs5k360A5+//jrvvZ0xw73U/9JLFIKxGMXLpk20ffRoXva/9VYK/Acf5OsQ33iD6192Gf2U\nSFDUVVVRWAUC7i0I993H+tTVUYwVF9PWpqa+7eL3U8CtXt13+ujRFDotLYyL665j1nP8eH7Pnk2R\n2NpKH0+axDqcdx6FlH0Ya906Cr/vf5/ZwR/9iPWw4tgK1TvvZFs2NbEttm3jvPb2vsK6P3PmUBg+\n95w7rbycJwmJhDstL49xEg670xYupF/Ly93RC5JJd/5ZZ7GOqetYTjut7xBZqRQW8tPeDtPQINEm\nhBBCiMMkVfwnk/xvM96p4tqOCPBRv+M6HqfIDoUoDoGDn2g4jjvM0969HD6qp4diza63axdPFtrb\nKcJ8Pn7q6ymq7XJWQ6xdy8z7xIkUvKeeykxeWRlPFk4/nfeijhnDTGFjI8Xlvn0U5ps3U4zOm8cT\niVWrKHyzs5n19PuB9HSYSy+VaBNCCCGEGO4c6cujH7GcFkIIIYQQRwKJNiGEEEIIDyDRJoQQQgjh\nASTahBBCCCE8gESbEEIIIYQHkGgTQgghhPAAEm1CCCGEEB5Aok0IIYQQwgNItBBWst8AAAvRSURB\nVAkhhBBCeACJNiGEEEIIDyDRJoQQQgjhASTahBBCCCE8gESbEEIIIYQHkGgTQgghhPAAEm1CCCGE\nEB5Aok0IIYQQwgNItAkhhBBCeACJNiGEEEIIDyDRJoQQQgjhASTahBBCCCE8gESbEEIIIYQHkGgT\nQgghhPAAEm1CCCGEEB5Aok0IIYQQwgNItAkhhBBCeACJNiGEEEIIDyDRJoQQQgjhASTahBBCCCE8\nwLARbcaYBcaYTcaYD4wxNx9te4T3eeGFF462CcIjKFbEYFC8iKPFsBBtxhgfgN8AuADANABfMMac\nONCyb789lJYJL6OOVRwuihUxGBQv4miRdrQN6OUMAFscx6kGAGPMwwAWAdjUf8GLLwaSSWDWLGD8\neCAvD9i0CVi4EPD5gK4uICsL6OwE/H4gkQAmTuT0ZBLo7gYKC4GxY4GaGqCnh7/z84HMTGD3bqC+\nHjjxRGDfPqC8HAiHOT0rCxg9mmVt2gTMnMlluruBkhKgtRXIzgbS02lrKAS0twNbtwLjxnG5jAza\n4fcDLS38PWYMkJvL7VdX83vcOCAaBTo6gIICYM8eTs/PB9LSgNdeA0aNAiIRbqu4mHXp6QEmT2b5\n8Thtb2+nHwIB1j0tjfWJxYDKSs7v7gaMYR0KC/nb52P53d1ATg7LTk+nHzo6WNdRo4DaWtrQ2sp6\nlJXRR5mZgOPwk5EBNDVxHceh34JBlheNclpaGv+HQsB779He0lJuNyuL5VdWAtu3s92DQZazahVw\nzjlsx85OoLGR9a6tZTsZQ3+2tLBMSyBAv5aVcRu5ubTl+ecZW6NH89PSwrLGjqVtxnA5Y9h+NTW0\nJRikL2MxrldQQD/k5XF7sRjraQzbo6mJ3+++y3qdcALLi0bp8927WebYsW77tLTQr8Eg28TakkzS\ntqYm+jEzk75sbKRNRUVcPpHgvPp6ltvRwXVt/QMBYPVqxn1WFqfZtozHGcsFBYz3cNitczzOulVU\ncHoyyY+tqzGsf04O7Y1EuE4oxOmlpWyL9HQ3ZvLzue3ubtpi69TTw2ltbfyeMIHtnkgw7nNy6O+u\nLk6Lx7l+Wxtj2+ejzYEAyxo9mn6qq2N9s7JoSyhEO9raaGMoxHU6OhjPGRncnq1rTY0br7EY5xcW\nsr7Z2ayzz8f28fm4TiTCbUYiXGfdOmDuXLeMcJj1KShgXeNx1i0ri7b5fGzLkhLalZbm7qvJJG2w\nbQAw1rKy2L52ubY2LtvaCkyaxBgyhnHb2cn1Ghq4D/n9tCke53r5+Yytqir2s34/bYjF6MPKStq1\nbx/7qKoq7m9jxtD+cBjYsYPzMjLYDra+Ph/nOw6nRSL0/1NPAfPmuWXaOIxG3X7X7+d66en8tLW5\nPs/Opj/S01k/2093dbHewaDrt717+V1ayu00NdFniQTLt/v13r2Mz/Z2tkVGBvvyUIjTs7PpBxs7\noRD3Zb+f6+fmso7t7fzu6qKPMzLon0mTWE5nJ+0OBFjfRIKf2lrguOPcfj8WYzuHw4xv22Z5efRj\nWhrLikRY37w81ssYlt/e7u6DbW1cNi+P5Xd1sX22bmU/6fMBmzez/X0+oLmZ38XF7r4PsO7WR7af\nD4dpSzzOdfx+7ofRKI/B6elcprOTfonFeOybN4/xNXEiY7Onh/Obm/ldWkr7a2tZbnm5a0ckwnJt\nf5pMsm5NTfRFdja3H41y/+3upr83bgSmTOHyNn6qqxnjNTWM67Q0+isvj3Xt6Rm8GDoUw0W0lQGo\nSflfCwq5/di+HXj1VWDbNu4ozc1suNWr6cxwmM4OBNwgWLmSjRGLAVu20Jnd3e6OGIlwnViMvxsa\neCAIBDg/M5ONkEhwua4uNlJBAXcIu77dIZJJrtvVxe+SEtqanc15WVnscNraGExVVaxbYaF7MGxo\nYJk5OQzYykquW1tLe6JRdpb2d2cnO8JIhJ2vPWCGQiwjmaQNaWluh5ObS/8VFHAdu5PGYrQlmeS0\neJz2lJayTu3t7Ezy81nm2LGskzH0L0C/xOOcZneOkhJOs8KmuJg7it/P4C4p4Y7o9/Pgv3Nn37bP\nz3c7E4vtcAFux86z9X7xRR7UbAcXDHIZezAaM4a2OQ7r6/O5BziL3++2ofUHwJ3W1iMSYZsORGYm\nbdm3zxUkANuvpcXdse1JhqW4uK9o8Ptd8RMMunWw5fl83E5Hh1tGTg7bvL3d7RwttvO3YsDv53Qr\nflK/09O5TH4+7e3sZIw0N/etZzTKZXw+2trczDizQtIKqWDQPSDaOtv2KypyRUQy2deXWVl9T1Q6\nOtyDbWpc+P1uXOXmugdAGweBgLsv2IPcgw+6fYj1Z1YW5/X0cP/t6mJsW2HjONxOIMATmLq6vu2Y\n6vO0NLe9bLwBrnhMxYqvRMLdvq1fal3t77Q0d3+18zIy2Lb9KSqiOBqI/n60FBS4fo9G6Zdg0G2j\n/u2UkUF/1Nf3bRPrl/6xnrp9Y1wxEwiwLCvU+5NaTlERbbTtZ+cb4550WGE30Po2flNtsQIwHHYF\niz1+3HHH/vYAbr+QSiDA7VvxGY+7wjR1HzqQ//1++jscdoXQQMvZbaXGk+3f8/K4v6SuZ4Xsgdrj\nw+LrvZaXGh/2xCV1n+pvD8D6WpGX6s9U/9rl7T45ELm59Js94euPPcam2mD7qgMRDLIdrc/GjGF/\nBrh9VP9yjxTGOVDLDyHGmM8CuMBxnGt6/38RwBmO49zQb7mjb6wQQgghxGHiOI45UmUNl0xbHYDK\nlP/lvdP6cCQrLoQQQgjhJYbFgwgA3gBwvDHmOGNMAMBiAE8dZZuEEEIIIYYNwyLT5jhOwhhzPYCn\nQSF5v+M47x9ls4QQQgghhg3D4p42IYQQQghxcIbL5dFDosF3RX+MMTuNMW8bY94yxqztnVZgjHna\nGLPZGLPKGBNKWf57xpgtxpj3jTHnHz3LxUeNMeZ+Y0yDMeadlGmDjg1jzCnGmHd6+53lQ10PMTQc\nIF5uMcbUGmPe7P0sSJmneBmhGGPKjTHPGWPeM8a8a4y5oXf6kPQvnhBtgxl8V4wokgDOcRznZMdx\n7BAx3wXwrOM4kwE8B+B7AGCMmQrgcwCmAFgI4G5jjB5sOXb5PdhfpPLvxMY9AK52HGcSgEnGmP5l\nimODgeIFAP7bcZxTej//BABjzBQoXkYycQDfchxnGoDZAL7eq0eGpH/xhGhDyuC7juPEANjBd8XI\nxmD/GF4EYEXv7xUAPtP7+9MAHnYcJ+44zk4AW3CAsQCF93EcZzWA1n6TBxUbxpgSALmO47zRu9z/\npawjjiEOEC8A+5j+LILiZcTiOM4ex3E29P4OA3gfHPFiSPoXr4i2gQbfLTtKtojhgwPgGWPMG8aY\nr/ROK3YcpwHgzgVgTO/0/jFUB8XQSGPMIGOjDOxrLOp3Rh7XG2M2GGP+J+Vyl+JFAACMMeMAzALw\nGgZ/7Pm34sUrok2IgZjjOM4pAC4EU9TzQCGXip60EQdCsSEOxt0AJjiOMwvAHgA/P8r2iGGEMSYI\n4E8A/qs34zYkxx6viLbDGnxXjCwcx6nv/W4E8BfwcmeDMaYYAHrTz70vF0EdgIqU1RVDI4/BxoZi\nZgTjOE6j4w6v8Du4t1MoXkY4xpg0ULD9wXGcJ3snD0n/4hXRpsF3RR+MMdm9ZzowxuQAOB/Au2Bc\n/GfvYv8BwO5QTwFYbIwJGGPGAzgewNohNVoMNQZ970kaVGz0XuJoN8ac0Xvj8FUp64hjjz7x0nvg\ntVwKYGPvb8WLeABAleM4v0yZNiT9y7AYXPdQaPBdMQDFAJ4wfB9tGoA/Oo7ztDFmHYBHjTFfBlAN\nPrUDx3GqjDGPAqgCEAPwtZSzaHGMYYx5CMA5AAqNMbsA3ALgJwAeG2RsfB3A/wLIBPB3+wShOLY4\nQLx8whgzC3xKfSeArwKKl5GOMWYOgCsBvGuMeQu8DPp9AD/F4I89g44XDa4rhBBCCOEBvHJ5VAgh\nhBBiRCPRJoQQQgjhASTahBBCCCE8gESbEEIIIYQHkGgTQgghhPAAEm1CCCGEEB5Aok0IIYQQwgP8\nPwF4MlGm9r6mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27d94bf2f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = list(range(n_iter))\n",
    "\n",
    "blue_patch = mpatches.Patch(color='blue', label='Train Data')\n",
    "red_patch = mpatches.Patch(color='red', label='Test Data')\n",
    "\n",
    "plt.figure(0, figsize=(10, 12))\n",
    "\n",
    "plt.subplot(211)\n",
    "plt.title(\"Accuracy\")\n",
    "plt.legend(handles=[blue_patch, red_patch])\n",
    "plt.plot(x, acc_train_li, color='blue')\n",
    "plt.plot(x, acc_test_li, color='red')\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.legend(handles=[blue_patch, red_patch])\n",
    "plt.title(\"Cross-Entropy Loss\")\n",
    "plt.plot(x, cross_train_li, color='blue')\n",
    "plt.plot(x, cross_test_li, color='red')\n",
    "\n",
    "plt.savefig(\"acc_loss.png\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Final Loss and Accuracy\n",
    "Let's have a peek at the final loss and accuracy of the training and test sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Set Accuracy: 0.9200000166893005 \t Train Set cross-entropy Loss: 25.540407180786133\n",
      "Test Set Accuracy: 0.921000063419342 \t Test Set cross-entropy Loss: 2800.803466796875\n"
     ]
    }
   ],
   "source": [
    "print('Train Set Accuracy: {} \\t Train Set cross-entropy Loss: {}'.format(acc_train_li[-1], cross_train_li[-1]))\n",
    "print('Test Set Accuracy: {} \\t Test Set cross-entropy Loss: {}'.format(acc_test_li[-1], cross_test_li[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Conclusion\n",
    "Using a Single layered neural network resulted in an accuracy of approximately 92%. Considering the situation of using this system in a post office to detect hand written numbers can be a devastating.<br/>Why? Because, according to our finding it will misinterpret 8 out every 100 images (92%)."
   ]
  }
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