1. Neural Networks and Deep Learning/Week 3/Planar data classification with one hidden layer/Planar data classification with one hidden layer v5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Planar data classification with one hidden layer\n",
    "\n",
    "Welcome to your week 3 programming assignment. It's time to build your first neural network, which will have a hidden layer. You will see a big difference between this model and the one you implemented using logistic regression. \n",
    "\n",
    "**You will learn how to:**\n",
    "- Implement a 2-class classification neural network with a single hidden layer\n",
    "- Use units with a non-linear activation function, such as tanh \n",
    "- Compute the cross entropy loss \n",
    "- Implement forward and backward propagation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Packages ##\n",
    "\n",
    "Let's first import all the packages that you will need during this assignment.\n",
    "- [numpy](https://www.numpy.org/) is the fundamental package for scientific computing with Python.\n",
    "- [sklearn](http://scikit-learn.org/stable/) provides simple and efficient tools for data mining and data analysis. \n",
    "- [matplotlib](http://matplotlib.org) is a library for plotting graphs in Python.\n",
    "- testCases provides some test examples to assess the correctness of your functions\n",
    "- planar_utils provide various useful functions used in this assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Package imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from testCases_v2 import *\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "import sklearn.linear_model\n",
    "from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(1) # set a seed so that the results are consistent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Dataset ##\n",
    "\n",
    "First, let's get the dataset you will work on. The following code will load a \"flower\" 2-class dataset into variables `X` and `Y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, Y = load_planar_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the dataset using matplotlib. The data looks like a \"flower\" with some red (label y=0) and some blue (y=1) points. Your goal is to build a model to fit this data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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toITNj86k/0cP1YFlNU9JkZVXnllCQb4Fa7kDo1FmztfxTJzaiYnXdMZsNnBg\nTxb//eCvivaEAPt2Z/LG88uY8cmUirTUn+fsYsXvB7DbTn/Gm/86jsOhUZBv4fChExU+YtumFPbs\nzODVDyYR2bh2+9VWB29kxUjAl8B+IcT7F2+SK+ERfh7To4UGEY38L2r8I4m5JB047dRPYbM6WDB7\nJw88MYRNa4+x7s8kNA0GDW/JoOFxGIwKJcXlTH/id/JOlFVohOzb7czzlk/mCw8d1Yob7+yN0djw\nHLzQNLfdgU4fUPttF8+FJSuPJSOfoDQlB6FqSIqMf3QE4/98H78mYW7P2fXWD5QccX6upQHBJLfp\nSlFoJGZLCTFJCYSdyGTbM58xasErtXkrFQS3j6kyDfXQF7/R/v7JhHRoUYtW1Q6f/2sDWRnFFf+2\nn5wALvwpgd9/2cPwsW1ZsyzJxamDs9FJQV4Ze3dl0KVHUxwOjd9+3ovqcP3O2m0qWzccRzHILj5C\naAJruYNF8xK488G6e1vzhDdm7IOAW4AESZJ2ntz2vBDCfXnieWIwKky+rgsLf9qNzXr6D2syK0y4\nuiMm88XdQtKBHFQ3wk1CwIG9Wbw9fQVHEk9UXPto0gmWLT7AsDGtWPD9LiwW17Q/VRUn/9d5/Mol\nh9i+OYXbHuhHh85N8PE1kpNVzC8/7mbfrkz8AkyMmdSeoaNa16uCluoQ0bsdkrsmGyczLwy+Fxci\nqwnW3DyDoqQ0xBnrNUVJ6ay9+Q3Gr3jX7TmHPnd+lYtCwtk5cDyarIAsYwkIoig0krh98RiWx9eK\n/e4IatWUJsO6OQuk3DxLNYdK8q8bLknHnptTys5tqciyRI8+0YSE+VXsy8ooYufWVI/n2m2C5YsP\netzvcGikpRTQpUdT9u5Kr+TUz+RM33MKTRPs251ZzTupXbyRFbOeGq45nDi1Ez6+Bhb+mEBxkTP0\nMvnaLoydfPEysUHBPhg8hHpKS2wc2JPlss1mVUk9XsAPX8ZXe0Kan2fhozdWYzDIjL+yEyt+P4C1\n3I6mQV5uGd9/sZWk/Tnc/fDAi76f2kQ2KAz95llWTXsFzeZAOFQUHxOKj4lBnz2ONb+YxK//IG9n\nEqGdW9LmjvH4RFQd2qpJyk8UkrU+wcWpAwiHStZfe7Bk5+PbqPK6iuOkqmVil/5oZ7W50wxGjnTs\nTYtt2TVneDUYMXc6P0ZPw15YWQNHkmXkS1AyYOFPu1k0d4/zpVCC77/YxrTbejJmkvN3v2jenosa\n32CUaXKjtyOPAAAgAElEQVQyRr5upWd10lOTNXcoioyqaihK/ar1vCS0YiRJYvSE9oy6oh2qQ0Mx\nyF5bDOrZvzn/++9mt/u0Kj7Q840yCOF8TfxtwR40IVxmVjaryqb1x5h4TSeimtWd47sQmk/sz5Xx\n/2XfJz9TlJhKowGdaH//ZKy5RcyNvQm13IZmd6D4mtj1+neM//M9Inq2rRNbbYWlyAalQtb3TGSj\ngq2gxK1jD2jRmPyDKRSHRLgdVxIaAdeO9bq954PR35du/7iZ7S/OQjureEqSJFpcM7SOLDtNUYGF\n1cuTyEgtJLZ1OINHtPKYnXJoXzaL5+9xyYQD+GHWNhbN30O5xY6mVZ6MVRdJAj9/E116Ogu0cnMu\nTBQuN6eUR+6Yx+MvjiSujfvvR11wSTj2U0iShMHLsWqz2cCTL43i/df+RFMFAoHNqnrU1b5YPI0r\nAfsTsohqFozV6mD54v2s//MIQsDAYS2JbhHCgtm7SE8pJCDQzLjJ7ZlwdaeKWH5dEtyuOQP+9XDF\nvx0WK/Pa3Iqj5LTQlmqxoVpsrJ72Ktcc+qZOsjQCWjRGNhuhtLKuvGw0Ehjnvgqz52t3smraK0hC\nQ0iVv3+SItP53vFet/d86fDgVRxfsI78hKM4SixIioxsMtLjn7cRGFt3DT4ADh/K4e2XVqCqArtd\nZevGZH6evYt/vDme6JiQSsevXHKwUlwcnJOtwvwLF3A7RWTjAJ59dWzFTLtdx0YcP5qP6ji/h4Xd\nrmK3q7wzfQUfzbr2okPD3qJ+WFHHtG4fycezrmXPrgzKSm0sW7Sfo0l5tWqDLEv4+hlx2FVef+4P\n0lMLKxZrFs5NQFW1ill+UWE5C+cmkJVZwl0P1b+Fm82PzHRx6mdSfCSdoqS0OskgkQ0Kfd97gI0P\nfuSSoqn4menz7n0ewxUtrh5Mp0emsm9tMjmNYxBnrSsERATSunPdl+YbfExMWPMhKYs3krxoA6bg\nANrcPq7OW9wJIfj0nXWUl59ej7LbVOw2lRcfXcx9jw2i/xBXrf/iYqvb9QJvoCgS9zw8iPDI04kX\nY6d0ZPXyJCxn/M4k2a2GnFs0TbB9S0ql+6gr6n66V08wGBW6945m4LA4WsSF1+hCprvJqgB69Ilm\n64ZkMtOLXFbgVYdW6Utus6psXHOE/LyyGrPzQjkye6XnnQIyVu30vL+GaXPbOEb8NJ2I3u0whQQQ\n0bsdI36aTts7rvB4jiRJ9H33AR7/6jZCA42cUg0wmw34+hl59PkR9WbhWzYotLhqMEO+fJp+7/9f\njTv1osJysjKK0VTPHjAjtYjiosqpmOB0iF98vIFD+13XKLr3jsZkrv7budmn+seGhvvRpoOrumdY\nuB8vvXUFHbs0QZKczr/PgBa079y4ysSvU1htDv73ny3cd+Mc3nt1JcnH8qttT03Q4Gfs2ZnFZGcW\n06RpEBGNqpdvOm5KBzasOeJ2JfxcmMwK/YfEsmH1UVRVqxSLN5kVYuPCOXYkF9UhMBhlEPDws8Pw\n8TUSvzkZa3n1mh4YjArHD+cRekamQF0jhKikfHg21hOFtWSNe5pP6EfzCf3O6xwhBDa/QO57fjRF\nhRbSkgsJi/Cj7+DYy1LWIj+vjE/fWUfSwRwkyfnw69Q9iolXd6Jtx0YuoTZV1apMr7DbNRbP28Pj\nL57uQzt0VCuWLdpPfm4ZjnOERwICzdx6X18cdo1N64+xZ0d6Rcjz1KxbUSQURSYkzJcnp492Gwps\n2jyYZ14Zg6aJinvKTC/in0/9js2muk2wOIXQoKzUubaxOz6dfbsyeXL6SDp0iaKowMKeXRkYDApd\nejatle9Lg3XsFoudT95aw8F92RgMzqyXzj2i+L8nhpwzDtY0OpiHnx3O5x/9hcVi9+jgzT4GBo+M\nY++uTIoKyolrE861N/egZetwpt3Wi13xaaxbeZhD+7LQNIhpGcot9/ahTftGHEk8wYG9WQQEmOk9\nIKaidNk/wIQkVW9xVtMEwaG+Hvfn55Wxb3cmZh8DXXo0xVwL8T9Jkgjv1ZbcbYfc7pd9jATUcbz3\nfDl+JI+PZqympNiKLEtomuDGO3oxbEybujatTtBUjVeeWkJe7plvi4Jd29LYuzODLj2b8vAzwyrW\nf5rFhGA2G6qcsGSkuT7sfXyNvPzuBBbNS2Dz+uNICEpL7ZXGMJkUxkxqT7/BsQAMGhGH3a6iqRpF\nheWUWxz4+BlJOZpPcKgPcW0izrm+c+bbV5OmQcz45Eo+mrGKo4m51U6acDg03pq+gkHDW7F53VEU\ng/NvoamCex4ZSN9BsdUb6ALxqlZMdendu7fYtm1bjV7jozdWs3t7msvT3mhU6De4Bfc8MqhaY2ia\nID2lgNXLElmzIqnCwRsMMmYfA/98bwKRjc8tdqWpGpomqrXwe/jQCd58cdk53xYkWaJJVCAzPqnc\nJEEIwbzvdvDHrwdQFAlOPij+/swwuvSoHAvOTCti3g872b87Ez9/I6MntGPMxPYXvDCb9dcelo5+\n0m32iTkiiOuTf6wXFan5e49xbN4ahKbR4qrBhPeo7KjLLXYeu3tBxWzsFCazwuP/GEmHLpfWQ6o6\nFBZY2LE1FaEJuvVqRliEaxHgrm1pfPD6nx6dnNls4OZ7+zB0VOuKbQk70vnw9VVuZ9+SBD37Nefh\nZ4dXaVfq8XzeemkFNpsDIZy/z649m/F/Tw7BYKjZqPKDt/5EiYdwkiRLiPNItjCZFN7415QLqlit\nrlZMg3TsxUXlPHrXfLevTkajzPtfXoMiy/j5G5EkCZtNJflIHj6+BprFhLh9oifsSGfpr/sozLfQ\nuVsU467sWGMhkIU/7mbRvD1UfDaScxX/RFYpikFGCEFIqC9PvTza7ZcjflMy//1gPdazHg4ms8J7\nn00lKPi0UFVmWhHTn/wNa7mj4odqNMlEx4QQHhlAoyaBjJ7QzmWhqTrkbD3AutveovBAMsgSstGA\nf3Qkoxe+SkjH2PMaqyaI/8dX7P1gLppdRWgCxcdI61vHMmDmIy6f/+rf9/Pt51txiMrfic7do3jq\n5bptUu1tVi45yOyv4pGdEUKEJph8XReuvL5rxTHzvt/BorlV55DHtY1g+tuu6xYpx/J45ZmllSYt\nJpPCCzPGEdsq/Jz2qarGnp0ZFBWU06ptxDklP7zFvTfMdvvGYTTKgFQpLbMqFIPMpKmdmHpT9/O2\no9ZFwOoTBXmWivDL2aiq4JE75iEhER7pR7fezVi74jCyJKGqKn7+Zm66qzd9B7Vw+YF36dHU7Wy3\nJrhyWlf6D23J9s0pCCHo2bc5TZoFkZNVzLGTMfVW7Ty/Uv7x6/5KTh2cs/bN648xZuLpwq75P+x0\nceoAdpvG0aS8isygJQv3ce+jgxg4tPor/pF92jN13ywcFiu5O5IwBvoS2rllvRCjytm8n70fzkO1\nnJ6Fq2VWDn+7nJgpA4ke37di+5aPF+EwN3EbI87JKqkNc2uN1OQC5syKr+SkFs/fQ/tOjWnXqTGA\ni3CWJ2zWyk6weWwYb828ks8/ci6WShIEh/px+wP9quXUwVkQ1K1X7auGdu4WxfYtKZXeUjQhMJmU\n83Ls6kntmZqkQTr2Rk0CPOaLn94uyM4sqVRybLNZ+PTddcz/fqfHGXFt0DgqkCuu6uiyLbJxYLVC\nP4WF7hcv7TaVogLXffsTMs8ZNxSa4PMP/6JHn+jzXvgx+JppPLDTeZ1T0yR+vdSlA1JhaCSpLTtg\n9/El77MN3D24G/4BZk5sO4hyMAmlYziq0TV0JAmNlq2r54wuFdYsT3QbKrHZVFYuOVTh2IeNbs33\nX2z1+L0xGCT6DnIvXxAW4c8zr46htMSG3eYgONS3Xjzsz8X1t/VkX0ImNqujohLVbDYwZlI7evaL\n4fXn/6h2DrzZx0DHrjUbwmuQ6Y5mHyPjp3Q4r3Sps8nOLObtl1dQF6Gqi6VT1ybO2PpZ+PgYaNux\nkcu26upNa5pgy1/V19Cvz9hLLBVNMlLiOrJrwFhymsVSEBHFLjWU5/6+iIK8Mk7EHyL8RBpGWzlo\nrjMySdOYfF2XujC/xiguLHc/IRLO8OYpTGYDN9zey20aoGKQCQnzY/SEquU+/ANMhIT5XRJOHZyL\nqK9/NJlhY9rQpGkgbTs24r7HBnHtzT1o1TaC1z6YiMlscLkfk0nGZFJcFmMNBpnwCH9694+pUXsb\n5IwdYOpN3fHzN7F4/l5KS6yYzAZsVke1V7WFgMJ8C4cPnqB1+wvvaF8XTJzamY1rj2Ips5+OmxsV\noqKD6dTNteH06Intmfvt9mqldhYV1OzrY23R4uohJC/cQJlNcLRDTzTl9M9AlWSKi8qZ//1OxsZF\nYpBleq77jUNdB5DbpDkCCf/iAnoWHiE65o46vIvzo7TERsKONEqLbaQl57NnVyY+vs6F8sEj4pAV\nma69mrF9S6rbzJNuvV0LysZf2ZHmsaHM/2En6SmFSBIEBvkweGQrRk9oV+8aVHiD8Eh/brvffZps\n0+YhvDVzCr//so89O9MJCvZh3OQOxLYKY/73O9m+JRVFkRkwrCVTb+zm9Qr6s2mQi6dnIoTA4XA2\n5fji4w2UW6qXIw7g62fkrocG0GdgC5KP5fPnkoPk55bRqXtThoxqVa/zl7Myivjpmx3s2ZGO0aQw\nZFRrrprWBbPPWSJWqsZ/PviLHVtSEFBJvvhM3v73lR4bCxw7nMvaFUmUltjo0Tea3v1javzLe6Fo\nDpWlo54gIc3Ggfa9Kwl7gfNNZub/ruWnmBuwZOWDEGiSjJAlzD5G+n/yMG1uq389Xt3x16rDfP3v\nzW4/X7PZQLfezXjwqaHY7SrTn/iNrIziivUpg0EmONSX1z+eXK+/75cLl3VWjDscDo3H7ppHUaH7\nlCV3GI0KMz6ZzP7dmc7MCIczbdFkVvAPMPPP9yZUayHpUiA1uYCDe7PYsTmZhJ2VpUhbt4/gxTfd\nV2cuXrCHhXN2Y3doCE1g9jHQpGkQL8wYVyu58xeCarPzy6sL+X1XMQ65so0BgWZmfns9BQeSWT7p\necqzC5AUGc1qp+Oj19Dr9bsuiTBCRlohLz32m1vdlVOYzArPvz6Olq3DsVjsLJ63hw1rjqCpgr6D\nWnDl9V0rdSS6XFFVDZvVgY+vsU4+f92xu2HR/ATmfbezWhoUBqNMr37Nue3+/jxy57xKMx1FkRgw\nLI57LjGp3XOhaYK532znj0X7UTWBLEn0GdiC+x8b5DavPSerhOce+tVtVkCPvtEuhSrnZYeqYiso\nwRQcUGOSs6UlNrefrcEgM3xcG265x5kdI4TgxLaDWHOLiOjTDp/wS0eBc/asbSxbdKBKUTtZlph6\nUzcmX9uw1gy8ic2mMvurbaz/8zCqqhEU7MO023sx4DwyxbxBraY7SpL0FTAJyBZCdPbGmDWBj9mI\n0Si7tL7yREioL02aBfPJ22tw9yRQVUH8xuQG59hlWWLa7b245uYezn6yAaYqQyrbN6fg6Um5Y0sq\nM99dx9+fGYamCYoKLJh9jVW+0gshSHh7DrvfnI1abkM2Gej06LV0f+kWZHdNPS4C/wATdzzQn1n/\n3oSmaqiqQJHAZJBp37kxmiaQZQlJkojsc/Ha/3VBQZ7lnEqlikHG5zIPs5SWWNm09hj5eWXEtY2g\ne69mLhOST99Zy55dGRWTgPw8C199shGjSanxhdALwVvvyV8DnwDfeGm8GqFT9yj4pnqvTyeyS/lt\n/p5z6lQ0VAwGmZAq5ApOIYSockF69/Y0Fs/fw/LfDlBabEMIQZceTbn77wPdvt7vev17Et6cXaE3\no1nt7H3vJxxl5fR95/4Lvh9PDBoRR5haypcv/0ZOWBQqgjKL4D9vriK2fWOeeXXsJd23tnP3pmzd\neLzK7kAI6DPw0uuu5C0O7s3inX+urHi4m0wKkY0DeGHGePwDTGSmF7k49VPYbCpzv9leLx27V9Id\nhRBrgdrVub0AmkYHM3Boy2rHfaty6ooi0XtA/ftAa5vufaKRqlA2tNtUFvywk4I8C3a7isOhsXt7\nOjNeXEZhgYWtG46za1sadruKarOT8PacSiJijjIr+z/5hYKDyV63X3OobL3tdXJDGoMsg6yAJOGQ\nFI4czGHWzI2Ulrhp2O0lhBBkb9rHsflrKT6a4fXx+w2JrXIdSJYl7nyof7Ue4g0Ru13l7ZdXYLep\nFfnpNptKemohc752tjtMPV6AwUM4MSuzfhap1c+VrRrkjgf7075LY5b/dpCSIiv5eaXVCs2cicms\nEBBo5rpbe9SQlZcOTZoGMW5yB35bsMfjzP3s1mKqqpGRWshjdy3AWDEbFlwxtiVlZn9MbrTcNaud\nhd3uofHgLgz/8UWvxbkzV+8k0z/CreqahsTGtUfZujGZq6Z1ZdI13o0ylhzP4o+xT1OWkYskS2g2\nB82nDGTYt88hG73z0zSZFF79YBIzXviD1OTTQluyDEHBvjw/YxyNm5y76K2hsmzRfrcV6kLAhjVH\nuOuhAYRH+ju7nrnhTHmO+kStOXZJku4F7gWIiam7ma4kSQwcFsfAYXEApKcW8tEbq8nLLUWRZewO\n5+uWuw9blqFrr2i69Ihi8IhWl31c8hTX3dIDh0N1u0hXtbMXqJbTf+efFyYi9x9PYMEJOm9ZhdHu\nmsGk2RxkrUtgxaQXmLTxE6/Ybs0rRlMUj7KyQjjfOhb+tJtmzYPp0be5V64rhGDZFc9SfDgdcUaL\nt5RFG9nxz2/o9dqdXrkOODN8XvtoMgk70lmzLAmLxUbfQS0YOCyu3nT8qSt2bEnxuO+UD4htFUaj\nJoGkJRe4fL9NZoUJV3f0dHqdUmufqhDiM+AzcGbF1NZ1z0XT6GDenDmF9NRCLGV2wsL9ePqBXyod\nJ8kSvfo356Gnh9WBlfWfabf2JDe7lF3b03DYVZSTzjI4xIcT2dXvJ6kpBgpDI9ndfxQ91i9BPuvJ\noNkd5CUcIS/hCGFd4i7a7sgBHQnN+he0rlqQyWZVWbxgr9cce+72REpTsl2cOoBqsbJ/5i9edezg\nnNB07dmMrj1rX2elvmC3q2SlFxEQaCbkpICfUkXGVXCIczYuSRJPTh/FxzNWk3IsH8Ug47CrjBzf\nlnGTO9SK7efL5f24PokkSTRrfrrv4nW39GDe9zudub/Cmfro42Ng2m296tDK+o2syDz0zDCOJJ5g\nz84MfHwN9B3YgiNJufz7vXXn17REVigOiWT9FTfR4uAuYg7vcZlQywaFosQ0AmIbYwy4uLL0gOaN\naDmgLcnHDpLeoq3bYqVT5Od6r1uVJSMXyUOWj72wFCHEJZEnXx8pyCtj+5ZUtJOyw5GNA1jx2wHm\nfrcTEKgOjbi2Efzfk0PpN7gFiQdy3Oq8nDkbDwn15aW3ryAro4iCPAvRLULwD6i/uf3eSnecDQwH\nIiRJSgWmCyG+9MbYdcG4KR2JbRXOskUHyMstpVO3KMZMat9gipFqkrg2ES7d2nv29eOG23vx0zc7\nAIGqCnx8DJSW2KpOw5MkNIOR4+26IWsazY/uq9hlLypj1bUvO/8hS7ScNoKh/3v2gvPdS45m0OpA\nCsG5WRxt142yoLBK/QslWaJVW+91oQ/v2QbN5tSrF0BxSDjFIRGYyi3EhUq6U79AVvx+kDmz4p3N\naoA5s+Lp1rspu7enu0wuEg/k8NaLy5n+7hUsX3yQ7MziimQJWZaIbhHCmEmVZ+ONo4I8Vl/XJy6r\nAqXaJiOtkEXz9nD4YA7hkQFMnNrJRaslO7OY5GP5hEf4E9sqrEH/mO12lfSUQvwDnBoi/3hkMRZL\n5UYc7jDYyhm0dE5V3dWI7N+RSRv+dd52CSH42jCmYjFAAPHDJlMaEIw4Q0PGbDbw0jtXEB0T4mGk\n82f9Pe+S+OMadnYZQlFoBEgSkhCYA3x4/s0raB4b6rVrXQ6kJhfw8pO/V5bFkHBbamH2MfDEiyOJ\niQtj2aL9bFx7FFmWGDKyFaMmtK+Xaa565WkdczQplxn/WIbdplbMTE1mhetv7cnwsW3493vr2B2f\njsEoo6mCyCYBPDl9VL3qX1qTpKcWMmdWPAln9Kf0hKRpDF09H8VmRbN51vppc/cEBn/2xHnb8kPk\n1Vhziyr+7TAYSerUh+zoOIRiIK5tBH+7u88Fz9iTvl3Orle/pTQ1h6A2zej56p3ETBmIpqr866HZ\n7ExzoMmuTiQ0zJf3v7im3jTJvhT4/OO/WP/nkWofbzYb+NvdvS+pFofVdewNUra3PvDNZ1uwljtc\nnJbNqvLj19uZPSuehO3p2O0qljI7VquD9JRCPnx9VR1aXLs0jQ7m8RdHMmvBzdz99wEEBXuOV/oE\nmLn+wCx6vFq1mmLil0tYf8+7WLLPr0N8x0emovidvr7BYafDnk1MOrKOL+f/jZfevuKCnfrut+ew\n4b73KUpKQy23kZ9wlNU3vcbh71cgKwr7CgyVnDo4e/YmHci5oGtejmzfksKG1UfP7yQJl7W1hoTu\n2GsAVdU4mnjC7T67XWX1H4mVRJk0TZCWXEB6SqHb805hszrYviWFzeuPUeShocalxpBRrfn46+vo\n2rMpBqPrV9JkVhg/pQMBTcMJan2OjA4hSJy1lJ873XlexT5dn7uJltcPRzEbMQb5Y/D3Iahtc8Yt\nfRPlAvu+ApSmnyD++S9cmnqAs1vTlif/g9A0rOWewlESJSXVF6y7nHHYVT778C+Pb34Gg1ypP4Fi\nkGkSFUirdt5bN6lP6FkxNYAkSc4Gt6r7L5qqui+Ists1MtMLPfZx3BWfxsx31las6zkcGldN69og\nxJskSeLBp4by2Ud/sSs+DYNBQVU1Ro5vy5ST/TZjJg3A4O+Do7SKB5omsOWXsOXJ/zBq/j+rdW1Z\nURjy1dP0fOUO8nYm4ds0nPAebS56zWPllS9WNPQ4G3thKZasfFq2ieDIocqTANWh0tqLi7UNmcQD\nOVXKWgSH+jD52s7M/34XVqsDTT0pa/HwwAa7rqU79hpAliWax4Zy/PD5qyykJhfQs1/lAq6CfAuf\nvLWm0kx/0dw9tGwdTufutdOPtSbx8TXy8LPDKSospyCvjMgmgS6CYbLRwMSNn/Brn/sRbnpqnkJo\nGqm/bz7v6/tHR+If7Z2mKsVH0inY6zk0oGkaxiA//nZnb96avtwlY8NkNjDqirYENdAsrKyMIhbM\n3sW+XZn4+RsZNaE9o69oe0EqoHByIuXBP0sSvPzuBIKCfRk2ug35eRZ8/YwNshHImeiOvYYYNb4t\nsz7d5HYmYTDIHnVoMtOK3W7fsPqI2zZ9VquDpb/up3P3pmzfksLvC/aSl1tG63aRXDmtyyUZQwwK\n9vFYqh3WuSU35//Krz3voygpHeFwnx9/oamPmt3B4e9WcGjWEoSq0ermMbS5YzwGn3M7gqy/9rD/\nk18ozysipF1zZJMR1UOoJWZSf4z+vrRu78vzr49j/vc7OZp0gqAQXyZe3YlBIy6++Ko+kpVRxPTH\nf6fc6kBogqLCcuZ+u53E/dk8+NTQCxqztYdwiiRLdOkeRVCw8wEpKzLhkf4XbPulhO7Ya4gBQ1sy\ne1Y8ljLXH7bZbCC2dTiH9mVVcvpGk0J0C/eOuCDfgt2NzAE4pVkXz9/Dwp92V8z88nLL2Lktlede\nG9vgmi4bfMxcufNzkr5ZzsYHPkCcFdqSjAqx1zidxIltB0n83x84ii3EXDWI5pMHeJT/1VSVZROf\nI2fjvopwT/6uwyT97w8mrP0QxeS+eEm12fl9+KOc2HSgYlvGqh3g4eEtGRUGfflUxb9btg7nyemj\nqv8HuMSwltspyC8nNMyXBbN3VTj1U9isKju3ppJ6PJ/oFuef4mkwKtz36CA+fXcd6hkKjSazgVvv\n6+vNW7lk0B17DWEyG3jmlTG8+8rKk5oTzhZ9w8a0Zvi4Nrz85O+VqjEVRWbIqFZux2vXsRGrlyVW\n6kepGGTatI/klx93u+TvCk1gLXfw3RdbefHN8V6/v7pGMRlpd/cEfBuHsPqG1xCqimZzYAjwxSci\nmD7v3MeOl78m4d2f0MrtaJrG0QXriOjRmnHL33HrpFMWbyJn036XGL6jzErB3mMcnbOK1reOrXSO\n0DR+7nQHxYfPWqw96dQlg4w4w8ErPib6ffwQ5uAAL/0l6i8Oh8YPX25l7crDyLKEEAJNFS5O/RQC\nwf49WRfk2AF69G3Oqx9OYuWSg2RnltC2YyOGjW5NQGD9rQ6tSXTHXoO0bB3Ox7OuZX9CJqUlNtp2\nbFSRp/7o8yP47KO/sJTaEUIQGu7HA08MITDIfQiie59oIhsHkJlWVBHGkSTnG0DrdpFsXHvUbb/S\nwwdzGnR5eszkgUzdN4tDXy2hNCWbJsO60fL64ZQczyLhnR+x2VQOd+xDZkxrNMVAQHE+ytu/Mu4f\n11Qa6/iCdTjcKEs6Sss5MudPt45915uzKzv1M5AMCoqPGbXchjk8iJ6v3kG7uyde3E3XEiVFVjat\nP0ZBXhmt20fStUfT84qDf/vZFjasPlJlH91TyLJ80XHvJk2D+NtdfS5qjIaC7thrGEWR3S5sduoW\nxQdfXENmehGKItOoSUCVzldRZP4xYxzzvt/JhtVHcThUuvRoyrTbelGQV+Y2/g7O19SG6tRPEdCi\nMT3/ebvLtmPz16LaVXb3G0NxaATaySrSkqAwftxSTOtDJyrlppccy/J4DYOf+5nf/o8WVGmbMcCP\nGzLmopZZMQT4XjKfxf6ETD54bRVCCGw2FbOPgUZNAnnhjbH4+p3bAZeV2vhr1RG3LRPdIYSgVz/v\nCKzp6I69TpFliabR1dcV9/Uzccs9fSt6cZ4ispE/ZrOBcotrmMZgkBk4rOqejA67ysZ1R1m38jC+\nvkbGTelAx65RVZ5zKSDsKkVBYRSHhFc49VOoksz873fw9D/HuGwvPHDc43jNJvR3u91WVLVyZctp\nw5EVBTnw0qkotttVPp6xGusZmUfWcgcZqYXM/XYHt97X75xjnMgpRTHI1XbsN9zeS5fB9iK6Y28A\nyMZP5hEAACAASURBVIrMoy+M4O3pK9A0gc3qwGw2ENkkkBvv8KxIabOpPP/3heRknXZOO7elMWBY\nS+5/bHBtmF5jxFw5kNI58bgVWpckjp2Viio0jfIc98VhktGAT2Qwfy49xOL5eygssBDVLJjrbulB\nWNc4Tmw96PY8Y5AfPV+pulq2PrJvd6bbbC6HQ2PDmqPVcuzhEf6oHjKWzsZoUujS49JP161P6I69\ngRDXJoIPv7yGbRuTyc8tI7Z1OJ26RVWpNTL3m+0uTv0UG9ccZdQV7WjT/tw53Qk70vnj1/0U5lvo\n1D2K8VM6VGhd1yXhPdoQO7AdSdnuQ1TBZ7WCk2QZn0YhlGcXVDpWNiisO2xn7cb4illsyrF8Pnlr\nDdfffT3KnrdQLa7VpebwIK49+j2mgLr/W5wvNqvDQ3tyqhUvB2ej8P5DW7Jp3bEqz5EkZ2y80WXc\nxakm0CUFGhA+vkYGj2zF5Ou60KVH03MKSK3787DHfYvnJZzzegt/2s3Hb64mYUc6ycfyWb74AM8/\nvIicrNO5+DlZJWzblMyRxBMe1wHAGWMtt9jRPFTlXgjX/fd+fAJ9OFvaz2RWmDTV2ebOXmph86Mz\n+S54snPGftbfTDYZCOrTkdUb0lxCE+B841myJY+RC14hpJOzGbTia6b9g1cyLfVHrzl1IQSJB7L5\na9URjh3O9cqYVdG+c2O3+uRI0LFrk2qPc/v9/Rg4rCVGo4KPrwGj0blAajYrKAYZH18DwaG+PPys\n3rzG2+gz9suYquKfJedo4FxYYGHR3ASX3HqHQ0Mts/PjNzu4/7HB/PeD9ezYkupUsNQE4ZH+PPnS\nqEpFIpvXH2PO1/EU5FswKDJDRrfmhtt7XbRsqtGo8MLbE3jvlT8pKbYiyxJ2u8rYSR0YOLylsz3d\nuGfIjT+Eaj1Zb3DyGSAZDSAEQW2bE/3ULRi+3+925lmQV0b40O5cnfAVQtOQ5OrNlQ7uzSIjrYgu\nPaIIjwwg5VgeG9YeI+VoPoFBZvoNjqVLz6Zs35zC1//ehKXMjqzISBLExIbyxEujaqx6MjDIhynX\n/T97Zx0exfm14Xtm1iKEuEAgQUKCO0GKW3GqtP3q7vKjSl0odVfq7rTFpThFgzsEkpAQd9mszcz3\nx0Jg2d0kkI1A974urovszM68k+yeeee85zxPF+b9saeqJFeUBPQ6DVffVKOwYBUarcTN9wzg6pt6\nU1RQSXCoLzq9hr07s8hIKyYs0p8efaLRaLzzS0/jEdleQRAuBt4FJOBzVVVfqW7//4Js7/nAs9MX\nOOWaT3Ll9T2ZcKl78+YNq1P4+pONTgu2AAaDhlET4lky74BDMDy5WPzSuxOrqkO2bjzGJ2+vc6jp\n1+okunSP4sEnhzsdu6LcwpK5+9i0Lg2NVmTo6DhGjI3jeHoJC+bsJT21kFaxwUy4tDMxbYMBkG02\n1n6/gR37CvCNCKJ9tB8hx45QmZ7LoS8XIRvNlDcLJC8qFqtOhyJKWHUGmpUW0Co7BatGR9LgidhU\n109Avr5aDBqV0CA9Nq2B5kE+jBwf7zJvfCylkJkzljj83nz9tPanldMmyScbbMrLnIXANBqRnomt\nuPccOzVry86k4yz6ey/FhZUkdIlgwqVdCIu48OvvmzINpscuCIIEHAJGAxnAFuBqVVX3uXuPN7A3\nDVKPFvLc9AVOC2UGHw0ffHslWq37GXPShmN89t6/LgO7r58WRQGTCyMNvV7DU6+MpXUbe9B97J6/\nyT5e6rSfVicx892JDm41lUYLTz+0gKJCY5XRsE4vERHVjKxjxfb6flEERUGjEbn/yRG0kMv4+dp3\n2BZvX/BTJA2SzYrObKLXvwvRmio5mtCTjLad7abWLgg9nkKlfwDGgGDU6mbkqlrlvKTXaxg9MZ4r\nrutVtVlRVG6f9qPbDuKzQaMR+fC7K72VJP8xGlKPvR+QrKrqUVVVLcDPwBQPHNdLPRPbNpjHXhhN\nULAPgmCPSW3jQpj1wZRqgzpA155RrnVwtCKDhrV1GdQBBFTWzviaP7vczNLxj5OT4boSRRIgPdVx\nIXPF4kMUF1VWBXWwt6OnpxbZGz1PBl1RxKbA7FeWs3DsY2yP64MiaarKHmWNFpPBl+SOvSkJCiOj\nbScUjYaqX8IZ//JbtsGqM6CvKEOyWRFtVlxe/Gk16mazjSVzD5CXU1712rqVRzwS1MGug2I8IVdh\nKSln73tz2PTgh6Qv3FTtWoaX/waeyLG3BNJP+zkDqLkeykuToGPXSN758nIqyi1otCJ6fe0+EnqD\nljvu689Hb61DlVVkBPR6ifCoZlx2bU92bcskJ8tZ0MxitFC+YiWWSiPF+9LQjmmDxeC8yGg1mmnu\n7ziWpI3HXFdYqLisajSaZLJDWrrcqEoSeS1iUcGpzt0JQcBi8CXm8E6C87JIa9+FwohaNNMIsGvr\ncUaOjwcgPeXsDECqw+CjITDIh+PLklg2YUaVGNq+9+bg0yKESw98fV5W5HjxDA22aiEIwu2CICQJ\ngpCUl+d1hmlq+PnrXAZ1VVEo3pdK2dFMh9eNWQUcueYJBqz+m5i9SbRK20/8llXcfVksPj5arr7J\nefFTUmxEpCejqzRWvdYqebd9Bnw6ioKPsQx5wzaHl318zm6xUEVAsbqX91UEkdyWbZyMq10iiuRE\nt6N5YS4BxQWuZ+xnvkUA6TTjkIQuEbUadxXuuok1Ilfd0BvVZmPZxBlOCpeVmQUsG/eEy/daSso5\n9PkCdrz0PceXJaEqnqtC8tJ08MSM/Thw+vQl+sRrDqiqOhuYDfYcuwfO66WeSV+wkXW3vI611Ihs\ntSFqNcRcOpg+M29h4wMfYMwqRLLJtC48NRNdfeXzTMv4hZ79WnHPo0P45ZttZGWU4OenI3zbdlod\n2OVwjuij+zH7+HM8Nh5RkVEFCb+yIrpsXkFJt3EO+44Y14Hkg3lOQmgAKMqpVMyJn/3Li4kszeGQ\nq7z4yaApnMXc5sRbwo8fJS2uK2oN8yJFgV59o6t+7pXYCl8/LcaKM25kp+XmT3+zoCqIGg2n+7X4\n+Gm5/YFB9OrXiuTvlqK6qWzKXb/HqUonZ91ulk54AhQVm9GMxs9A8/hWjFv5Flr/s9d+r8wtwpxf\nQrN2LZD0F7a++fmGJwL7FiBOEIQ22AP6VcA1Hjiul3qkYPthSo9kEjm0Gz5hzop6hTuPsHLaC8jG\nU1UZimwh5cflpM9dj63SDC5qzmWjifwtBwnv34kefaLp0cce2MxFZfwc9SXKGTXlAtB+7xZiDu2k\nIiAInakS34pSNH4GAjvFOuzbO7EV/QfHsmF1CjabgigKCIJAgi2PA2ZfZFFC0WgRbVYkRWZMSytq\nSQTtD2wlOb6XfXFUEE8F9VqWJgIIskxkhr3u389spMORXRyK73VKqVAQqgK0oCpo9Fquu62vg1mG\nIAjM+mAyM59YQm52edXbWolGivPKKA8MBVXFYCyn9eHdhJXkEPLuk+zYm4/BoGX42Dj6DYqt6k8o\nO1qN/Z9qFy/TnpAyUKw2/pnyNLayUyJntvJKivaksHXG5/R/775a/R5M+SXsfv0XDs6ej7XMiKTX\nIWoker54I53vdxZW89I41Dmwq6pqEwThXmAJ9nLHL1VV3VvnkXmpF0qTjzN/wL2YC05VokQM6crF\ny9900Cnf/fovTt2UJ3GlgFiFIKCYXVTDBDUjLLEjuf/udfn4r7VaCCzIqTqGZNDR9uoRZxxa4OZ7\nBjBqQgI7kzLQaCT6DmxNc1+JZdNeZNeBEowBQfiWFtG9SwijZ89AscmEPvIpzeat5FBcT8oCQ6vO\n4ZbTUyCCgEYjEBrqRyI+mHVtiBjUheEX92X1jG84qA2juHkogiLjX1GKf/sWtB/dg2ETOhHZIsDp\n0IFBvrz+ySVUlJspKzERFtmMyow8/u59B7byShSL/WlE42eg0wOX0vumRC5xM8zWUway4/lvXW4T\nNBIav1NKoVkrd6DKzrN7xWwl+dultQrsFSfGac4vqXp6kSvNyEDS459hCAuk3dUXrq78+YRHGpRU\nVV0ILPTEsbzUH6qi8HevO5wCc86a3ay47DlG/fVi1WvF+9JqlUd2PodKaGJHl9uGfPsE8wfci6XM\niOzGt1TQSAR1a8uwH550mx5oHRtE61jHp4zxC15mcGo2ZcnHCegQjX9rez5bsdrIzSnncFwPe1Cv\nTT79jH0EUeTZ96bg63sFAJU5hfzR4QbkMiPtOdW9q/E1MOW3OwloV7PuiZ+/Hj9/u2Kkf0wEl+z+\ngj1v/krm0q0YIoLo/MCltJo4oNpjhPSIIyA+mtKDGU7bOt13iUMaxlrNzfhMs213JM343D4hcPGx\nUExW1t74GmF9E2o2HfdS73g7T89DFFnGeDwfXXM/dGdh2HBs3ga3s+30eRtQTuTRAYJ7tKNw1xG3\nZsyCJCL56JDNNlSrzT7L9tEx4MP73drI+cdEcPnRH0j7fTU5G/aR+++eqhuILiSA3i/dTKvxifi2\nODcT52axkTSLPdXyrqoqXzz4E+uUGAgUag7qrnLdADYbh/bm0uNEvvzQF4tcLsrKViv73ptD/3fv\nPeux+0aF0O+Nu876fZO3fsqyCU+Qs8YuASFIAgl3TaHvG3c67Bc5uGvV08CZRA7tXqtzpc/b4Pbz\nAKBabSwa/j8uT/mB7BU7SP52KbLZQttpw2k99aJztiv0cvZ4A3sTx+6j+SfGrEKiL+6HLqQZ25/6\nCmt5Jaqi0GJkL+LvmIQhrDmhfePd2r4BFG5Pdn8iVaUytwi/lnbhr66PTCPl11UOOfaTCJJI9PhE\nEt+9lz1v/krehn00axtFl+lXEuZmtn4SjUFHu2tH0+5au2SuzWhCNlnQBTXzqFZ5ZaWVpx+cT162\nWrtcuqK4DfyKxUZF2aknjKLdR13Ocit0vqw9WEHaN1vp0SeaDp3C611/XetrYPzKt7GUVmDKLcY3\nOszljdUQFkjXx65izxu/VjlECZKIxldPvzdrd0Op7rN1EmupkX8mPUnuuj1V5zm+eAuBb/xKcPd2\nlB3NJGJQFxLumoxPRPBZXKmXs8EjkgJni7fz1DVlKVkc/GwBZUeziBzSDUtxOTtf/sGe61ZVRJ3G\n9axLFND46tH4Ghj+27NEDu7m8viZK7azZNTDrk8uClxfsdChuiF79U5W/d9MKjNPCU9pfPXogpox\nceMHVTeBpoaiqMy4fy5ZGc4drU6c+PxHNJcwp2ZSHBTuVCkjyjIzXxtDi472FMuu135mx/PfIlee\nuulltOnI0U69QZJQENDrNXTuEcU9/xsEqlorM+yGIO3vf9nzxq9UZhUQMbgb3Z/8v1qnTjbe/z4H\nPp3nthIHQNRrQVXdfk5RVESDDo1Bx4T17xOY0PpcL+U/SYNJCpwL3sDuTPqCjaya9gKKze7dKfnq\nXc6Wa0LjZ+DyI9/jE+7aO/LHiMsw5zlL08ZcNoQRvz3r9LqqqhTtSSHtr3VUZhUSltiRNlcOQ+PT\nNL0ky8vMzHx8CZnHXXe0no4g2BUx73tsKG0i9XwZfxvbBo1HljSnZvmyTIvsFF7696kqn1RTfgm/\nx12HtcQueVzp24wtw6c4NTppUIjbvZGI1MPogvxpOaYP3Wf8H0Fdqjc/aapYSsqZP+A+ytNzq10j\nObOu3vWOAhGDuzJ+1dseHuWFTUNKCnipI7LZwur/exmb0Vw10zmXoA6gygrJ3y51u/2SvV/g3/Y0\nhyQBosf1Y9hPT7ncXxAEgru2pefT1zPwoweJu2Fskw3qO7Zk8MBNv9cqqIPKhMu68NZnl9K5exQ5\nq3fhbyyjy6Z/EFXltDp3yGnZln17TzXVGUKbM37NOwT3aIeo15IX086lhowNkYyW7UFVsRSWkfLz\nSv7qfiv/TH262sXMpoquuT9TdszmotnTiR6fiHBGzlzUazGEBdZugVpVyf13D7K55oXbspQsUues\nJW/Tfq9cQi3x5tgbEUWWSftjLXve+g1bhWe+6LLJQmlyptvtPqGBXJH8PcacIsqPZhLYKeasFmCb\nKmWlJj58Y02V0bdbVBWNJHD/jOF073Oqr+7w14tRbTLp7buiCOKp4CRKyMDHb67lva+vqJKYDe7a\nlinbZlOZU8jffx7g6GLX2vZOcgUqpM9dzx8drmPkny8Q2q/jeeODCiDptLS9egRtrx7B8WVJbHrw\nQ0oPZiDqNLS7bjSxVwxlxSXPVOXXq0Wg2puAYrWx+rpZpM9dj6jToCoKfi3DGLPk1aqqJy+u8Qb2\nBsRWaUZVFLR+PqiKwopLniFr5Y7afQlqicbfQHj/6hcwAXwjgvCNcJ2uOR/ZvC7NZRnemYRF+PPy\ne5PQGRxVERWrjIpAUXhLl4utsqxy5GAe8Z0dA4pPRDB9hsWxYmWakxGHKNsIy0xxOY7K7CIWDHmQ\ngHYtGfnXCzTvcP4ZObcc3YdL936FzWRB0mkQRBFVVWkzbTgpv6ys9nMtiCJRw3tVpbdcse3Zr0mf\ntwHZZKlarC5NPs6y8U8wdfcX59UNsaHxBvZ6xlxYyurrX+H4ok1Vgce3VRhd/neFx4O6IInomvvT\nZpqzjvn5jKqq5G3aT+mhDJrHtyK0X4LTl7q83FyjcXL3Pi156MnhLgNCu/8bSc6m/biRXEcQ7Iuy\nrmgXH0q33i3ZtfWUy5Io29CZjESnHHB/XVaZkoPpLBr2P65M+6mq1PR84/SFYUEQGPTZdNpcOYzD\n3yxBMVsI7BTL3rd+P7F+ZEXjq0fyNTDwkwerPe6Bj/52WKAGe6qxPC2Hwh3JhPSMq5fruRA4Pz9J\n5wk2k4W/ut+G8Xi+w+vG9Dw2/++jWs0wXSEadMTfPoFWEwew47lvyNu4H0SB6PGJ9jryJpoDPxdM\nBSUsGf0opYczsD+7qwR0iGbs0tcwhDSv2q9jl0gW6Pe61JERRejZtxX3PT7U7Syv7TUjOfDJPAIL\ncigOjnCatasqtHfjASsIAnc/PJgNa1JYufgQpkorhtXriNi3E82ZAmdnoqrYKkykz99IzCXnt4H4\nSQRBoOWYPrQcc2qNr8Ot4zk4ewGlhzMIH9iZuBvHVpsCVBUFa6nR5TZBI2HMKiSkp8eHfsHgDez1\nSMovK52CehXVBHVDWHM0zXypSM91Ki0TJJG2Vw2n35t3IUoSLUf1RrZYEUTxgmwAWXPtLIr3pjo0\nBBXvSWXNdbMYs/CUUVdcxzDax4dyaH+eg7SvJAnceFd/LhrRrtpHd8VqozK7kPjibJIGjkPWaO3B\nXVURRIFLruparUa9KAoMGtaWQcPaAlC0pwvLJs6gIj2vxg5e2WyhPDW7xt/F+Yx/6wh6v3RzrfcX\nRJGADtGUHnLuqpVNFkJ6tj+r81fmFGIuLLMLllWT/rlQ8FbFeBhTQQnFB44hmy1kLt9W/c4uAo3G\nz8Cgzx5mctInRA3rgWTQoQnwRdRpiBrZk8sOfcvgLx91aBaRdNoLMqib8kvIWrXDqctTsdrIWrkD\nU8Gp6hdBEPjfUyOYOq0boeF+NAvQM2h4W177eCpDRrWv0dj7yPf/YC4oxVBagt502kxREFBV+PPn\nXQ4m3TUR1KUNV6T8yLjVbxM+qItLvfiTiDotQd3autymyDLG7EJstWz7v5Do9+ZdSGc8fUq+etpf\nNxrfqBC377OZLChWG5aScspSs5g/6D5+iZ7GX91v44fAyex5+7f6Hnqj452xnwU563az/+O5mHKL\naDGyF4Iokr/1EAHtW9LmquFse/orji/ZUpUrDe3Todrj+UQGYy2twGY026s1/AxET0ik1cT+CKLI\n2CWvUZ6WQ0V6Ls3jW9lLyf5DmAtLEbWSS1ExUSNhLixzSMdotBITL+vCxMvce7W6I33eBmwVJgrD\nozH7+DulYixmmfl/7OWmu/vX+piCIBB5UVcmrH2Xwl1H2DnrR1J/X+OgiinqNDRrE0nUCOe8wr73\n5rD1qS+RzRYEUSTuxrH0e/ueJtPsVN+0mtCfEb8/y5bHZlOy/xj6kAA6P3Q5XR6+0uX++UkHWX/3\nOxRsO2yXPjipuHkask1my/RPKN6XRsnBdGSThTZXDiPhzsnnJF3cVPE2KNWSna/8yK6XfrDL1Z5W\n44xq/3IqNtleFXBac4Zk0CGb3dioARO3fIRcbuLIj8tRFYW204YTNbKXd7X/BIrVxk/hl2I50Qh0\nOrpAP67OmeORBcfS5OPM6XIzqsXG0fgeHOvQ3eXTVGSLAF79qG6uj8eXJbHhnveoSMumOCicgoGD\nkNq0okvvaEaPj6+S+d3+/DfOyo2iQOspgxj5x/N1GsOFSMnhDOb2uuOcihEkHz3+MRFM2vxRkw/u\ntW1Q8s7Ya0HF8Tx2vvCdsz7IiXh9sqlIVRzz4Sc1UCzFZU459d6zbiWst90yrbYiTP81RK2G3rNu\nZfPDnzg0bEm+enrPus1jVSRbn/zCLmQG6M2ViLINReOchw0MrPuidMvRfbjs4Dcs/n0X637bi8Uq\nw5Eijh4pYt5vu+nRN5pp1/dkx4vfOb9ZUTn2978kf7+M9PkbyV1nb/CJGtGTXi/dTPO4aOf3/EfY\n/drPtVapPBO50kx5WjYHP1tAl4cu9/DIGgdvYK8FGQs323UuzgFraQX/VzSXfe//Rd76vQR1a0O3\nx6++IJqCGoKEOydjCAtk+7NfU56ajX9sJD2fv5HYy4Z47ByZy7ae5o6UwpFOzhMi0Walk+oZz1Jj\nhYU/ftvr5N+qqrB9cwb7tmfSza85fmXO0g8oKmtvfM0uWnaC1N9Xc3zJFiYnffKflczN27AP1YXx\nS22RKy2k/LLSG9j/SwiSeM7pEd/oMHQBfvR48v88PKoLn/27s/lnwUFKSirp9uxDXDquQ5WGuSeR\nfPRQbHc00lotdNv0D3v6jkA98TdXRZGYQ7tQjxth1tV1Pt++XdlIkogV13X3ZqvCkU696bZpuesD\nnGlUooK13MT2579h6Hcz6jy+85Fm7VrYJaDrwIVUJlynqhhBEK4QBGGvIAiKIAg15n3OV1pN7H9O\nswGNr56ez91QDyO68Jn76y7eemkFSRuPcXh/HnN/282M++ZRXOR5jZX428YjnWaUHViQw8Alv9A5\naRUJO9YxYOlvxCTv9ljlkSSJ1RXJAFAcElnDHmegKGSt2H7OYzrf6frINCTfcw/MGj8D8bdP9OCI\nGpe6ljvuAS4F1nhgLE0Wn/Ag+r1zD5KPHkE67Vd24ttpN53QE9a/I6Jei8bPgLa5H71m3kLcDWMb\nZ9DnMUWFRub+tgeL+dSM1mqRKSs18edPOzx+vs6PXoVpYH/29xvGgR4DKQ6OQFAVgvMyCcs6htZq\nRvLVE3fzuJoPVpvz9YhCqaFoQa+TnES2akIX1KwuwzqvibioK/3fvw+Nv8+pm/QJ8xdDeCCRI3sS\nflEX+r5+Bz2euQ7JR2f//Qr2oB49rh9tpg1r1GvwJHVKxaiquh8476s4FJuMbLJUuyKecPtEIgZ1\n4dDnCzDlFhM+sDPGrALyNu4nIC6aTvdNJbBTLObicsz5Jfi1Dv9PNELUB7u3ZSJKApxR5SjLKkkb\n0rnp7uot484Gm03hrZfXkBwYh9XPfiPJb9WeyPRDtN+1GRQFjb8PoX3iib91vEfOqddruPOhi/j4\nzbVYLM7pGK1WYuTkznSf+BC7XvmJyuxCAjvHULg92a0LkuSrp9N97txR/xt0uGkcba8eSf6WA4ha\njX3CpdcS1LWtU4xqM204R39eiVxppvWUQYQP7OwyjpkLS7GWVeLXKszBarCp85/OsVvLK9l4//sc\n/WkFqk1G42dA1GrQhzYn4Y6JdLxnqkPlRVDnWBLfvqfaY+oD/dEHehdG60J1qQpJ8uwkYsncfezf\nk+Pwmk0QyW6TQP/+0QRZyomZehEtx/WrlYNQbemV2IpZH0zmz592sn5NCqIooMgKWq2GNu1DmDKt\nOzqdRIfTnhI2PvABh79YhM3oWNInajW0uXwo8bdNcHjdWl5J8rdLyVy+Db/oMBLunERgxxiPXUNT\nRGPQuTWaOZ3AjjH0ev5Gt9uNWQWsuW4WOev2nNBg8qX/+/d7dNG+Pqmxjl0QhH8AVwm/J1VV/fvE\nPquAh1VVdVucLgjC7cDtAK1bt+6dlla3hQ5PsGDIA+RvOeiyAUby1RM5pBujF8w6759I6ouSg+kY\nswoI6trGoVGorlSUm3ng5j+cqkY0WpHRExO46obeHjmPqqrcPu0nl7NmVJWh/aO4+YnRHjlXdVRW\nWtm64RilJSbaJ4QRlxDm8jOnqir7P/yLPW/+himvGL+WobSaNID42ybSPN5RHbIyp5C5fe/CUlSO\nrcKEoJEQtRoGffY/2l0zyunYiiyTuWwrFel5hPSKI7R39c11Fwon49/pv29FlpkTfwPlx3Id+1J8\n9IxZ9AqRQ07dOGSLFcVqQ+tXc/17yeEMrKVGgrrEOjiVnQ0eq2NXVdX5U3AOqKo6G5gN9gYlTxyz\nLuQnHbQ/2roI6mA3ushZu5vcf/cQcVHXBh5d08aYmc/yqU9TtDfN3pxlttLh9okkvnXXWT2u5mSV\nsm7FEUpLzHTt2YKe/aKRJBE/fz033pXINx9vQpYVZFlFb9AQFu7PlCtrno3VluPpJdUqQmat2QlP\njCbtaCF5OeW0bN2cqJaeu4GdxMdHy0Uj2tW4nyAIdLr3EjrdW3PKZcujs6nMLqoKTKpNRrbJ/Hv7\nW7SePMgh7VhyOIPFI6ZjLTWiyAqgEtYvgdHzX0bjazjn62rKlKVms+mBD8hYtBlBFGg1sT+J79yL\nX3QYxxdvoTKv2MkJSq40s/35bxi3/E0qc4tYf+fbZCzYhKqqBHZszYCPHyJiYGenc5UczmDFZc9R\ndjTT/tQnQN837yL+Fs+k9lzxn03FFGxPrkmbCZvRTOby7d7AfhqqqrJ03OMU70tDlZUqWdVDny/A\nv1UYXaa7bvc+k7X/HObrTzejyAqKAhvWpBDZIoAnXx6D3qDlouHtaB8fxtrlRygtrqRLzxb0hNXl\nkAAAIABJREFUTmyFphohrrOlvNSMCG6KDsGw/yDPPbyAjLRiRFQUBOI7R3D/40PRG5r2+knanLUu\nLepEjUTmP1uJmWpXklRVlX8mzsCYWeDQIZ23cT+bH/mUgR8+0GBjbijMhaXM63c3lsIyVEVBBY79\nvZ7c9fu49MDXlBw45nbCV7L/GIrVxoKB9znM6It2p7B0zKNM3PQhQZ1jq/aXzRYWDXmQytxiUNWq\nz9qmBz7Av3U4LUfXTzFhXcsdLxEEIQMYACwQBGGJZ4ZV//jHRiBK1V++pNeiC/RroBGdHxRsO0zZ\n0Syn8k/ZaGbPG7/W6hh//LCDzz/YiM2qVJVkm002MtNLmPfH3qr9IlsEcMV1PbnlvoEkXhTr0aAO\n0LpNkFuRTdFqJb1tR1IP5WO1KpitKlarwv4dmXzz6SaPjqOhUU/TlS/YfhhjVoGzporJQvLXiy9I\nK7qDn87HVmFCPa0fQJUVLKVGkr9dSkBctNtUSUBcS9Lnb3Q9ozdZ2Dnze4fXjs3dgNVocv79Gs3s\nnPmDh67ImToFdlVV/1RVNVpVVb2qqhGqqjbZ2r68TftZPOYRfgydyp9db6EyuxBtoF/1HaUCF5xp\nhTtUReHg5wv5q/ut/BpzFetufZ3ytByn/SqO5TqWfJ6GKb9mr9Hliw8y97fdLrdZrTLrVri2mKsP\nDAYNoeH+zlo+qkqHQ1sp8Qt28jKVEdi4KgWL2XV1SlOh1eQBLv9OitVGi1G9qn42F5QiuFkUlk3W\n2hlTn2dkrd7hZOABIBtNZK/eRfT4RHRB/k6/P8lXT49nrqdwRzK2Mud+ClVRKNh6yOG1sqOZyJWu\npQ7KjmbV4Sqq54JOxdhMFo4v3kzuhn3sf//PKi0Jc2EZa298FY2fD/qgZtiMZlSbbJeHlUR7maKq\nctGXj+IbGdzIV9EwrLv5dVJ/X1NVcZH8zVLS5qxj8tZPaNbmlPl1ULe2bkvumtWinf3376pvopHr\n0BZ+tuzYepySEpOT4JeoyGg7xCIoMrgIeqosYzRa0emb7ten3+t3kr1yJ5bSCmSjGUESEXVa+n9w\nH7qAU0+hob07uE07NO/Y2qEqrDK3iMNfLKJoTwrBPdsTd9PFHl00byj8Y6MQJNHpqVPQauxP8hqJ\n8WveYeWVz1O44wiCJCEZtCS+ey8tRvai4lguGj+DS8ExB6N47PLNGh8d1jNvBIJAcLc2Hr+2kzTd\nT2Ydyd2wl2UTnkCVVbsjvNOsDGzllSgWK4bwIAbNno6uuS+5G/ah9fch5tLBGELPvw/tuVC8P42U\n31Y7zGJOPppuf/Zrhnz7RNXrAe1a0PLivhxfssVhJiL56unzym3VnkdVVYwV1TsK9enf+hyv4uzZ\nvC7NpeOSImkwRrVGzXLd5SrZrAQ0b9qLir4tQrl0/1cc/HwhWcu34dcqnI53TyG4u+MirT7YLoW7\n7905DmWUko+e/u+cKu3N33qIxSOmo1htyCYLqXPWsvOl75mw7j2CutRfgKoPOt07lSPfL3MQlgP7\n+kPCHZMASJ+/kaI9qSdMtFUkg47ABPtnM/aKoWye/rHTcSVfPd0evcrhtZYX98UnMhibKdvBNEfy\n0dHjmfrrSj9/Ku7PAlulmaXjHsdSXIG1zFitg41isWEuLKX0cDrhAzrT5X9XEH/7xPM+qKuqyqEv\nFvJrzFV8JY3i15irOPTFQhRFoTK3CGvFqaCVtWK769+RonB86Vanl4f99BTxt09E8rV34vq1Dmfw\nV48RM2WQ2/EossL2LRkI1aS+dDqJqVd5ruqlJqxunjwApAA/YlL3IZ5hbSfabHQuPIpwrr6GDYiu\nuT9dp1/JmIWvMOjT/zkF9ZP0eulmEt+/j4D4VmgDfIkY3JWxS16lxSh7Wamqqqy++iWsZcaqp17F\nbMVaamT+oPswF9XegKQpENSlDYM+m27vEA/wtf9r5sPQH2YQ0L4lmcu3kfTop8hGM7ZyE7LRTGVW\nIYtHPYK1zIjW34dxK9/CLyYCjb8P2gBfNP4+JL5zD1HDe1KaksWOF79j0cjpLB4+nXbXjabFyF6I\nOg2iTot/myhG/vE8Yf0S6u0aLxg9dsUmc3xpEpVZBZiLytj61Jeo1XxxzyRqZC8uXvY6ssVK0e4U\ntM18GsU5XlVV8jbuoyIjn5BecQS0a+GwPT/pIDtnfk/e5oPoQ5rR4Zbx9kaqM9rP97z5K9uf/cZh\nFibqtXaNeJMFVGg1IZFBn00nfcEmNtzzLrZy5xlqs3YtuPywCwlZ7PW+ssmCxtdQba2/zaYw68kl\npCQXIMvuP28vvTORVrFBbrd7mvdfXU3ShmMut3Xv05JuSavYvK+YlDadsBh8MFSU0+bANloUZeIT\nHsTFK950SFNdqJQdzeTPrre6zEsDhPZLYNLGD6s9hrWiEmtJBYaIII82etUFm9FE9ppdCKJIxJBu\nVQYmS8Y+alf8PAONn4HEt++mw632RjBVVSnceQRbeSUhvTugygorp71A5tIkhzSPaNDh3zqccSvf\nsjdAhgScc2/Mf0qPvXhfKotHPmzPlcsKNosVzmbRRxAwhAZw+OvFbHrQ/gFVbDL+MRGM+OP5qkew\n+qY8LYclYx7BmFWIIAooFhvRExIZ+sOTSDotaX//y+qrX0Q22WeRlVkFbH7oI/a8/gtTts+ucliS\nzRZ2vPCdU4eiYrY65FPT529k0YjpjFv9NhvufsdpPJKvnoS7JrsdryhJiLVozPj+8y0kH3Tj/QqI\nksDd0wc3aFAH+w3HLSoM//Vpgp77hj1v/YbNqpAa353D3QawX6vDv7SQoitf57bNb17wDWyKTa72\nGgt3HSV7zU4OfDyPtL/WgaLScmwf+r15F4aIINbf9Q5pc9YCoPX3oc9rt9PhJs/o7tQFja+B6Iv7\nOb3uzn/WVmGiPD2v6mdBEAjpccp7deWVz5O1fJtT7l4xWag4lsuhLxbS46nrPDT66jnvUzGqorDk\n4sepzC3GWma0B7OzXMnX+OoJS+zIhnvfw1pqxFpqRDaaKTmQzsKhDzaI36Sqqiwd/wRlR7KwlVfa\nx2CykLFwM9uf/RpFlll/+1tVQf10jJkF/HvHW1U/l6fl1KpMTbHaKDuaRdGOIwz/7Vk0vno0fgYE\nrYTGz0DUiJ50uv/SOl2XxWxj1ZJDbrf36hfNF79eQ9+BDd/q3rFLBDqd8+xRp5Po2CUCSael54s3\nIUgi+3oPJaNtZ2w6PQgC5c1D2BDZlaT5nhclqwuVRgu52WXYqmm8OlsC4qLRBbsXGBO1GlZc9hyp\nf6yxTx6sNtLnb+SP+Bv4IWgyKT+tqJpUmAtKWX/7Wxz50Y0kcSOjyLJbAxeNv49bE21zYSnH5m1w\nW1ggmywc/WmFx8ZZE+f9jD13/V6sJeU1OsE7IAoIooAgigiiSJeHryR9wSanxRRUFbnSQtqctbS7\nZqRnB34GhTuSqTiW41BbC/ZutwMfzaX9DWPti8BuSJ+/EdliRdJpMYQ2dzKAdodqkynak0LHe6Zy\nZfovpM1Zi7mwjMhh3Qnre+45wIxjxeRll5GdWVrtnyaiRbMa+wnqi8Ej27Ngzl6sVrlqjKIooDdo\nGDLa/gVWrDLlGl8KI1qiSI5fF0XSMHfBEfpOcvYrbWjMJitffbSJpA1piJKIIMDkK7ox/pJOdX6i\nEASBId8+zuKR052cwMD+GVVl2XVppIv9VVlh/V1v1/t36lzY9uQXrssQBQHfqGBaTXQtQFeZU4R0\nogvbHZ5y/KoN531gN+WXuPSndIUgiVWfM9WmIOgkgnu2p9sT1zAnwfUKtc1oojzF9aNZ1T4nyior\nMvIo2nWU40uTEDQScTeMpcv0K2rVlm3MKnQr02otM7Lv/T+r/dCoqopitSHptOiDA4gen0jGwk3V\nvgfsH7ZmJ0q09EH2nH1dKC8189bMFaQdLcRmrbl0sVe/hl/HOImfv47n3hjP959tYefWDAC69W7J\ntbf2rTL00Bh0WDq0Q1BUcPHnySpwnXduaD58fS37dmVhtSpw4vf+1y87MfhoGDkuvs7HjxrWg96z\nbmPrU1/AaSksyaBDF+RPZVbhWR3PVlaJKb/Eo0UKqqKQNmcth75YiGyx0e6akbS7dlStdVlsJgv7\nP/zbtcWeACPnzyR7zS7MBaWED+iEX3RY1Wb/2EiHxq8zEX10dLil4dJP531gD0vsaDeMdoHG34Aq\nq4g6DbLJYn9MOm36qFisFO48wsHZ8wnu0Z7ytFynmb/G14ClrILFox/BWlpBzCWDSbhrUpW1Xc66\n3Syb9CSqomArd+ww2zXrR47NXc/EDR/UaNIQ0ivOvWejAIc+W+A0mz+doE4xDkJEg796lOVTniZv\n8wFErWS/fptsd28/eVhRRBfkT4sxnmtr/uC11aQkF6BUs0h6OsGhjdfZa8ovwU+EB2YMcykGdZKe\nt49j198pLo/RLKDxyx7zcsrYtyvbHtRPw2KW+euXXR4J7ADdHr0KrZ+Bbc98Zf/OKSqxlw/BJzKY\nfe/NcZuGcIkgUJGe67HArqoqq656kYxFm6vqy/M27efAp/MZv+adqoXR6jDlFrl8wgC7u9LCgfdX\nXaNisdL+5nEMeP8+BFFE46On8/Qr2PvGb05rW4JOQ1jfBOJPlFI2BOd9YPeNCiH+9olOcqaSr54x\nC19BH9yM0iOZ5Py7l33v/IFicbwJyEYzhz5fyEVfPsLxpUkO6ZiTQvz7P/ir6vWi3SkcnD2fyVs/\nQdRpWDZhhr2k0gWyyULJwXSO/f1vjXKfvpHBxN14McnfLXWREqLaDkDJoGPAGZoeugA/xq18i+J9\nqZQcPk7zDtFkLt/G1hlf2BdmrTKBnVoz4vfnPValUJBXQfLB/FoHdVEEH99zU7mrCwU7kll746uU\nHLBXxAR1acPgrx9zW489+Oah/LE6m5Iyq8PToU4vMXZKxwYZc3VkZ5ah0YouBc1Ki03YbAoajWfS\nXR3vmUr8HZMwZhWgD26G1s+HstRs9n/4N1D7wC6IAv4erCjKXrXDIaiD/btdsi+NI98urZU7kiE8\nCNVNZLdVmJwako58s5Tgrm1IuNNeYNDz2RvQBfixa9aPWIrKEPVagnu0p9vjVxM9PrFBq4HO+8AO\nkPjOPQR2imHPG79iyismpHcHes+8hfD+nVBVlfK0HDLmb3AK6ieRzVZCe3VgwIcPsP7Ot6vSF4Io\nIJutDmWTssmCMauAPW/+RmBCqxoXKW3llWQs3ETsZUMoT89FtdrwbxPlcmY44MP7adY2ir1v/Yap\noBRDaHNM+cWoLqo3BK2ELtCfiMHd6Pns9QR3bevy/IGdYgnsFGv/f8cYOtw6geK9qeiD/GnWtoXL\n95wtqqqyY0sG837fg62WnaOiKNC1Zwv8/Bs2sBsz81k09CGHm3HB9mQWDH6Ayw99W1VZdDqiJDLj\n1Qm8/vw/lJeaEUQBq1Vm0LC2jJnY+IE9PLKZ27RXswC9x4L6SUSNhH+r8FPniI1k2M9PsebaWfYS\n2DMnJmcgaCTibr7Yo74FqXPWYnNxXpvRxJEfl9cqsGsMOhLumsyBj+c6XMPJJqUzJ1c2o4k9b/1e\nFdgFQaDL/66g80OXI5ssSAZdo1VMXRCBXRAEEu6YVNU1djob7nmXI98tc9n+C/ba7rbThmEzmkh6\ndLZD8Hf3aKmYraT+toqEu6bU+PgpaCRUReHPrrdQdiQTRAFDaHMGf/UoUcMdF90EUaTrI9Po+sg0\nAHbO/IHtz33t8rgB7Vpy6b6vqj23KzQGnce1tn/4PIk1/yRjroV+iiiBVqshPMKf2x4Y6NFx1Ib9\nH89DPvMGr6ooZisHP19A9ydcm45HtgzgjU8vIflgHqXFJtrEhRIc4tsAI66ZiKhmdOgUzsF9OQ4B\nXqeXmHRFwyiTtp40kKtz/yB79S6OLdjA4S8WIWokVFVFlRV7/llVQRRIuHMSfV+9w6PnF7Uau1Wl\ni3mWqKt9mOsz6zZM+SWk/LgCQSuBohLSpwP5Ww+5fGo25xc7vSYIQqMbY18Qgd0dBdsPk/yti9TG\nCSQfPb5RwXR68HJSflmFrdLsNsfm9F69joiLuiBqJLdPAgCiViJtzjqHGWLFsVz+mfwUk7d+Um0T\nVPSERHbO+sFp/JJB12T8GTMzSli17LCTKYY7Lr+2J+07hNGhU3ijzGbyN+9zuaAsmyzkb3Fflgn2\nL2xcQni1+zQW9z0+lM/fW8+OpAw0GhFVgfGXdGLMxPrrbjwTSa+j5Zg+tBzThz4v30rehn2Iei3h\nAzqDqmLKK0YfEnDOJhPV0fbqERycPd/pu6LxM9S6Zl6x2lh97cukz9uAqNeiKgo+kUF0e/xqVl7x\ngsv3hNahcqw+uaADe9pf/7qs+wZ7Dr7nczcQf/tEdAF+FO1Ncdl56e69HW4bT2ifeCIGdyV7zS6n\nrjzRoEOAE9Upm52OIZut7H37dwZ+/JDb84T0aE/bq0aQ8svKqieOqpvRA5fVaqz1za5tx6utBjid\nNu1DmHBJl3oekXuOL0sie41rZUlRryXwNB3t8w0fHy33PTaU8lIzpSUmQsP9GlWkTOvnUyVJcBLf\nFqH1dr6wvgl0vGsy+z+eay9CUFQ0/j5EjehJ7JVDa3WM7c9/ay8bPq2IofxYLpsf+oio4T3IWrnd\nSR+p98u3evxaPMEFHdhFSUQQBVQX6cfAjjF0fXiaw8/uFNsESQRRRLXa0Pj7ENY3vmqFe+TfL7L7\n1Z858Ok8bGWVhPbpQFhiR/xahdN66iC2PfWly1Zs1SZTuPNojdcw6LPpRI9P5OCn8+xVOZcNqboZ\nNQU0Gqla/RewpwQMBi13Pzy4gUbljDEznxWXPOO2/FPUaki4o+Y8bFPHP0CPf0DjpgEai76v30ns\nFcM48sM/yGYLbS4fStTIXrV+Mjzw0V/O31VFxZhVyEVfPUpwz/Yc/GQe1lIjof0S6PfGnU3WQrBO\ngV0QhNeBSYAFOALcpKqqc9KpkYi9fAi7Xv0Z+YzcmOSrJ+6mix1eazNtOEmPf2ZfgDltQVTy1TP0\nhycp2HYYa0k50eP702JUryoLOEmnpcfT19HjadetwkHd2iL56p0eEQWN5FaUyWE/QSD20sHEXtp4\nQbE6+vRvxc9fOetqaHUSXXpEERTiS2zbYPoPjm1U16HD3y5FcfNkcdLL8vS6ZC/nJ2H9Es5JXEtV\nVSwlrqvbBFHAXFBK7xdvpveLN9d1iA1CXZfLlwFdVFXtBhwCnqhh/wYlsFMsXR6+wq5CeCIQa/x9\nCO3dgQ63OjbiaP19GL/2XYK6tkEy6ND4GfCJDGb4r88SM2UQvZ6/kcR37qXlmD5n5evZ/voxdn33\nM2YNkk5L54eaRjqlLgQG+zJqfAeHy9NqJWLbBnP3w0O44Y5Eho6Oa3QruYpjuShu+gQCO8cQMahu\nKSJrRSVFe1IwF5bW6TheGgdBEAjs5FrWQrHYmuzM3B11mrGrqrr0tB83ApfXbTiep9fzN9Fq4gCS\nv16CtbySmEsuotXEAS4bhgITWjN1x2eUp+ciV5oJaN/yrIK4K/RBzRi/5h1WX/sypYcyQBDwiQhi\n8FePNop6pKfZsSWD5YsOOfR1qapK/yFtXOqwNBYRg7pw5Pt/nNZRRJ2WqGE9zvm4qqKwdcbn7Hv/\nL0SNhGyx0nrKQC764pFaOdc3FHk5ZSxbcJCM1CJi2oUwanw8IWFNI53XVOj35l0sv+QZh3SM5Kun\n3TUj63V9oD7wmGyvIAjzgF9UVf2+pn3rQ7b3fKDieB6K1a4aeSEoAqqqyvTb/qQgv8Jpm8FHwwff\nXonWwz6l54pstjCn081UZOSeMjwQBHTN/Zi6+3P8Wp5bGmbxE9+xeF02pQHBaM0mWh3ZQ6ucVKLH\n9mHkny968ArOnQN7c3jrhRXYbDKyrKLRiEgakcdfHE3buPMrYNU3mf9sZctjn1G8JwV9iN2EpPP/\nLm8yUsMek+0VBOEfINLFpidVVf37xD5PYm87c+vOKgjC7cDtAK1bN5xLTlPiXINHU6WsxERJibtK\nIoHjx4qJbRfSoGNyh6TXMWnTh2ye/jGpv61Gscm0GNWLxHfuOee/y6F92fyyx4YSHAGCgKzVcaRz\nXyoCghCWJFFxPK/R/+aqqvLp2+scegxsNgWbTeGzd9cz6wP3ssz/RVqM6s2Urb1r3rGJU2NgV1V1\nVHXbBUG4EZgIjFSrmf6rqjobmA32GfvZDdNLU0Rv0Lit+1dkBV+/hpcLqA5DaHOGfPM4Q7553CPH\n++mLJGfFR42WrNYdaJedTNnRrEYP7DmZZZSXue7jyM0po7jQSGBw02i08uI56pRAFgThYuBRYLKq\nqq6XlL1csOgNWrr2bIF0huyuIApERQcQHulew/tCIC3VdQGYqMgU+wQSUAtz7/pGqO4brlJjqaqX\n85O6VsV8ADQDlgmCsEMQhE88MCYv5xG33DeAiBbNMBg0aLQiBh8NgUE+3PdY7ZpCzmcMPm4qfQSB\nlv3i8I1q/DRUeGQzt8bb/gF6jqUUUVlZvbSzl/OPulbFuLYT8fKfoVmAgZnvTmL/7myOHysmLMKf\nbr1bOs3iGxpFUUlPLUJRVGLaBNWLmcfwsR1YMm+/o5yCqqLXiVz29X0eP9+5IAgC7TqEkZ/rvMBd\nXFjJe7NWoaoqV17fizGTGl/QzItnuKA7T700DKIo0Ll7FJ27Nw1j5/27s/nozbVYTPYFQ61O4o6H\nLqJrT8+oWZ5k6lXdSE8tYv/ubBDsGlQ6vYbHXhiNrhbmKg3F7u2ZbrdZTtyUfvoqiciWAXTr1fjp\nIy91x2PljmfDf7Xc0Uv9U5BXwRP3znVSmtTpJV58eyKRLQI8fs701CKOHM4nMNCHLj1beFwmt67c\nesWPLrXazyQiyp/XPr6kAUbk5Vypbblj0/oEevFSR1YsOYTsQhNetin8s/Cgx89ntcrs2p7Jgjl7\n+eaTTfz0VRIlxbUTk2soErpE2B8naiA3u7z+B+OlQfCmYrxcEBQVGvnzp538u/IoNhfGJLKskpVR\n4tFzKorKG88v5+ih/KqUxsrFh9myPo2Z705CoxFRFLXKP7WxuOqm3hx+LBeL2UY17opn5QfvpWnj\nDexezntKS0w889ACysvNbm35tFqRdvGe7bLctyuLlOSCqqAOIMsK5WVmnvnfAkqKTCBAi+gAbr5n\nQKN1eUa3DuSFtyYw97fdJG04hqnStSGK6C19vGDwpmK8nPcsmbsfo9Hi3mtVAI1WYsTFnjF1Psne\nHVmYTc5BUrapFOYbkWUF2aaQnlrMK08vIy+nzKPnPxsiogK47f5BPDhjuNva9nYdvPICFwrewO7l\nrLCYbaxdfoSvPtrIgjl7KG0C+eSdW4+79fwUBGgXF8pTs8YSGORZUS5ff12tF0ptVpnFc/d79Pzn\nQkKXCGLaBDsFd41W5Po7ExtnUF48jjcV46XWFBYYeeGRhRiNVswmG1qdxN+/7mb60yOI7xzRaONq\n5sZYQpIEJl7elUuv7l4v5x04tC1//+rakelMZFkl5XBBvYzjbBAEgcdfGsPPX21l/aqjWCwybeJC\nuO62vrSODWrs4XnxEN7A7qXWfPPJJkqKTVWGFScbcz54bQ3vfnlZvTQB1YbEi2I5sCfHyUhDlESG\njqq/HrqQMD9uuqs/X328EUGwL6aeTAc5jUUUaBHdvN7Gcjb4+Gi56e7+3HhXot1f2ptbv+DwBnYv\ntcJmU9i17bhLFyKLxcbR5ALaxze84FV5qZnfv9/uclw33JlY75rjg4a3pWuvFmzdeAzridnvG8+v\nwHRGm75GKzJ2ctPq7BQE4Uz/Fy8XCN7A7sUJi0UGVXU0Q1ZVt+VwAoLLEsOGYMWSQ5hcLGDq9BK2\nWjTleIKA5gaGjz3lsPPYC6P48LU1lJWaARVBFBg6qn2TU7v0cuHiDexeqsjJKuOrjzZycF8OqNAu\nPpSb7u5Py1aBaLQS7eJCST6Y5/Q+VVUbrZRv/+5sR62WE1jMMvt35zgE3IaibVwob8y+hH9XHeW7\nTzcDsGpZMisWH2LI6Diuu63vBWG04qXp4q2K8QJARbmFFx5dxIE92SiyiqKoHD6Qx4uPLaa4yF75\ncsNdiRh8NEgnKkEEwT4zvv7OxEazwQsJ9XMpPStJQqNav5lMNr6bvRmTyYap0obZZMNqVVi7PJl/\nVx5ttHF5+W/gDexeAFi7PBmLxeaYblHtZXorFtlb8VvHBvHye5MZcXEH2rQPod+gWGbMHMugYW0b\nZ9DAqAnxaLXOH2NJEhk2pvHER7duPObShMRibhpljzarzMa1KXz54Qbm/LiDvByvnMCFhDcV4wWA\n5IN5WMzOKQ2rVSH5wKn0S0iYH9fe2rchh1Ytse1CuO7Wvnz32Ra7VPCJ6pTb7h9IRJTnBb9qS1mJ\nGaubdYeyUlMDj8aRinILLz62iMICI2aTDUkjsuivfdz6wEAiIptRmG+kVWwQYRH+jTpOL+eON7B7\nASCyRQAajei0CCqKApEtGy9A1oYho+Poe1Es+3dlI4oCHbtFotc37kc7rmMYGklEPuP3KYgCCY1Y\n8w8w5yf7DP3k31q2KcjAR2+sRasVEQQBq0XG10/HmIkJjJ6Y0Oh6N17Ojrpa470oCMKuE+5JSwVB\n8KzgtZcGY/jYDi7NMTRakVETEhphRGeHj4+WXomt6NE3utGDOtjb89vFh6I9fe1BAL1e4pKruqMo\nKru3Z/Ld7M38/t12MtM9K1BWHRtWp7iuYlLBalGwmGVU1T6z//vX3Tz14PxGf8rwcnbUSY9dEIQA\nVVVLT/z/fqCTqqp31vQ+rx5702Tvziw+fnNtlXa3KIrc8eAgevSNbuSRucdaXom5qAzfqBBETeMs\n4LrDapWZ99tuVi49jNlkI6FzBNNu7EVEVABvvbic5IP5mE02RElAkkSuuLYHYyd3qvdx3Xn1z2dl\nh6fRiIwaH8/VN9coA+6lnqmtHrvHjDYEQXgCaK2q6l017esN7E0XRVZIOVKIqqrEtguwy1kaAAAS\ny0lEQVRpcqYRJ7GWV7L+zrdJ/WMNgiQi6bT0eulmOt49pbGHViPLFx3k56+3Oq1paHUSs96fRFhE\n/ZqAf/j6Gjb/m3ZW79EbNHzw7ZWNVv3kxU6DGW0IgjBTEIR04P+AZ6rZ73ZBEJIEQUjKy3OuhfbS\nuKiqypp/kplx/zzefGE5f/60k/TUokYfU96m/WQs2oQp3zFVseKy50j9Yw2K2YpsNGMpLmfLo5+S\n/N3SRhpt7Vm19LDLhWpVUdn877F6P39cx7PvEDabbHz69rp6GI2X+qDGZKQgCP8AkS42Pamq6t+q\nqj4JPHlixn4v8Kyr46iqOhuYDfYZ+7kP2YunUWSFl59cyuHTql/27Mji0P5cHn1+FHEJ4Q0+puJ9\nqSydMANzQSmCKCKbLXR+6HJ6z7yF0kMZ5KzbjWJ2TCfIRjPbnvma9teNafDxng3ulCgVRcFmq/9u\nWa1WQqsTsVrOrlt4Z9Jx8nPLCQ33Vss0dWoM7KqqjqrlsX4AFuImsHtpunz89jqHoH4Si1nm+8+2\n0D4hjH9XHsVqkYnvHM41N/chOqb+lAAVq41FI6ZjyitxsPXZ/96fBHaMQRvgi6iVkF0oBlccy623\ncXmKxItimP/HHqxnBHiNVqJHn/pfz+jULQpU152vggiqm3iv0YpkZpR4A/t5QF2rYuJO+3EKcKBu\nw/HS0BTmV5C0wf3jf+qRQlYtPUyl0YrNprB3ZzYvPr6YnKz6M43IWLQZudLi5NVmM5rY9epPBLRv\nieJmZuvbIqTexuUpxkzqSFCIr0PFjN6gof9FscS0Da7380dENWPIqHYO1UOSJODnr+ONTy7Bx1fr\n8n2yTfEG9fOEutaFvSIIQjygAGlAjRUxXpoWqUcK0WhELLL7FMCZqQOLWWb+77u55b6BHhuHzSqz\nfnUK61cfxZSZj61NV0qaBWMx+BJQmEvM4V34lZdgyi4kqHMsIT3ak590EMVySgBM42eg+5P/57Ex\n1Re+fjpeeHsiq5YcYvP6Y/j4aBg+tgN9BrRusDFcd3s/OnQKZ+m8A5SXmenaM4oJl3YhKMSX8Eh/\n0o6esb4iQEy74CYjPeyleuoU2FVVvcxTA/HSODQPMpz1exRF5cDeHI+NwWaVefmppaSnFp1aVIxJ\n4KSmrMnHj/yo1vRct4ioXrEAjJo3k9XXzCR71Q5EvRbVJtP10WnE3zHJY+OqT3x8tIyb2plxUzs3\nyvkFQaD/4Db0H9zG4fXtm9PJznR+GhOAyVd0baDReakrjd/J4aVRaRsXSlCw71mnVgKDfWu1X1mp\nibwc+4JbQHPXN5ENa1LJSC12rBQ5Xf1QFFFEkSPdE7n6pYkA6IOaMWbRK1TmFFKZU0RA+5ZofM/+\nJuXFkdX/JLv0cQXYtjmdbr1aNvCIvJwL3sD+H0cQBB55biSvPfsPJUWVWKyy28Wzk+j0EuOmVt9I\nY7PKfPXRRjatS0WjlbBaZXontubW+wY46rwD61cfxWx2HUxOpyQ4grB+jl2wPhHB+ETUf166IbCU\nlJP8zVLyNu+neUJrOtw8Dt8WDSuH7EoCGezLHe62eWl6eAO7F8IimvHax1M5cjCft2euoLzM4nZf\njVZk3NROVFZYefKBeZQWm2gXH8ql1/Rw8Mz8/vMtbPo3DatVqar+2LY5na8+ErjjoYucjlkbtBdw\nc0zpkUzmD7gH2WjGZjQjGnTsfvVnRi+cReTgbk77FxdVkp9bTniEPwGBtTPpLi8zs3LJIfbvyiYk\n3J/RE+JpFRtESbEJg0GDwUdL4uBYDu/Pc7rR6g0a+g6I8ci1eql/vIHdC2CfubdPCEOrdR88I6L8\neeqVcSyYs4dvPtlU9eXfsSWDvTuzmTFzDG3ah2A2WVl3ojzydKwWmS3rj3HtbWYHUakhI9tzcE9u\ntbN2jUZk4NDGkweub9bd+gbmwjI4YfGnmCwowKqrXmJa+s8Iov3mZzHbmP3uenZsSa96Euo7MIZb\n7h3g9m+nqiqb1qXy2XvrkW1Klc/p+lVH0ersTlOqCt16t+T6O/rRolVzjqefSo3p9RLt48Po1tub\nhjlfaJr94l4ajeq+vJde0wNFUVm+8KBDEFZVe8D56Uu7TERpiQnRjUOQpBEpKnQsQO/dvzVde0ZV\nO66o6ACuurFXbS/jvMJaUUnuv3uqgrrDtjIjhTuPVP385Ycb2ZGUgdWq2EtQrQpJG47x/WdbqvYp\nyKtg2fwDLJ2/n7ycMn78MolP3/4Xm1WpqiBVFBWbzX4Mq1XBZlPYufU4b76wgidmjuGqG3vTPj6M\nDp3Cuf6ORKY/M8Jren0e4Z2xe3Fg0uVd2bQuFVPlqcAtCBAdE0i/QbFs3XgMSSM5NdcAVbZ5zYPc\nL6wqskLoGc5Goij8f3t3Hh1VfQVw/HvfmyWBQBKyYAiJCWFHRAoq1ogCLiAKKrUVq5XqqVq6iOJW\ncau2dpGKp9TW0kU8ra31HJe6oBb3agUREHoApajIYkhCWLMw669/vICEmSFBkpnJy/38BXnDvN/8\nwtz5zW+5l+lXjuaD97fGzTro9VrMvHEsmd1cWjM0TkA/QDiwZ7+hPsCydz+L2X4aCkZ4541PuPTK\nUSxe9BHP/H21s43FwD8WLscY4hb7PlQkHKVm214+3VDHhEmDmDBp0NG8KpVCOmJXLRT0zuLuuedy\nwol98fltuvfwcc6UIdzx84lYlnOIJW5pIMCf4Rxs8flsJk4dgs/fcmrA57cZd85A/BkeAoEw0cgX\nAcrrs51gFJekRSrejuLt0Y1eJ1TEvWZ7PeSNdM4B7tzRlDApm4kaFj2zlmceX0UoFCEUjBAKRQiH\nDZFI2zN4mKhJagph1THc+25RX1pRcTbXzxkX99qgYb3x+uwWI3pwRtWnn/lFcLrgkhFYtlOZJxKO\nYtnCWZMHU1Key/VXPcWunY1YljBidF+uvaGS7JxMSo7NZePHdS0PnAr07tMjpfVLk6HyDzeyaOws\nIoEQ0WAIsS0sv5fTFt5yIB1xfkH3hEE6HI7y7BOriR5Z+pcYliUHKifV1TZQXbWH3kU9Xd//btNu\naXuPhKbt7dw+3VDHL+9aTDgcJRox2LZFef88Zt85PmYrYzgcpaHeWSxdvWIrD/3yrZjplm7dfTz4\n52nsrGvk3ltfIhSMENgXxu/34PFazPnZORSX5CTzJaZEw5Za1s5/mu3vfUjPQSUM++GF5Awta/GY\nxxcu59UXP4qbHfJoiUB+YRb3zjuPhx/4N2tWbcPjtQiHIgwfWcy1sytd/c2pM0h6PvYjoYE9/UWj\nhuVLNvHmYqfI9ZjTyqgcV4HP72Hp2xtZ+LslBIMRolFDfkF3brh9PEWtHDe/ZeYzcU81Apx+dn+u\nnHkK+5pCLHl7I1s27qS4NIcxY8vJzIyfu6Qr2bmjkZefW8e6/1YTaApRV9tAsI37yvcveh5unl0E\nyvvn8f2bT+cfjy5nxdLNLdZRvF6bE08t5ZpZlQmfQ3U8DezqSzPG8PADb7Ny2ZYDpxB9fptjinoy\n/apRzLv39RZBRQSyevp5YMFF+PwejDEs+fdGXn52HfV7AwwbUcSUi4dzw9VPJZqeJyPTy+//fkky\nXl6ns+3zPfz4pkUEAxHn246Az2u3KbB7vBYFhVlYtrB1U/y5cxEnq6PHY5OTm0ltTQMmzoeA12sx\n/9GL3buI3QkkrdCGcp//ratl5XtbWhwtDwYibKvaw19+vywmoDjbHSMsa84S+dc/LOORh5bw6YY6\naqvreevVDdw+6zn8GYm/xh+8kKpa+tuf3j+QXRMAA8FghAQ7Sh3N17JzMrnhjnExRbUPZgxEI87v\nsGZbfdygDmDZFnt2B77kq1DJpIFdxVi+dDPBYOxhoWAgQk11/KmUwL4wNVV7qa3ey5uLN7TY5x6N\nGJqawuTlJV6AO26k1kFPZM2qqkMzGAPOTqKEpQubH79rRyNz73mNgt7OqP1oCNArv205glRqaWBX\nMWxbEo4GMzI8ca9lZHjoU5LN2tXb4h5kMVHDzh2NlFXE5nXJyPTwjW+58/BRe0gUkG3L4uLLT2Dg\n0EJ8fjtuv0cihurP9/LRmmqiR7Dt8VA+v4fJFw077MlklT40sKsYY04rw+OJfQP7/R7Omjw4JmeL\niBCORHnysZW888anCfejZ2R6uXvuuXznB1+luDSHvILunHH2AH7y4PkcU9yzI16KK5x06rHYdvy3\n6oRzBzPnvnP41YKLONx6WbC5DJ6IM++enZvZppTNIpDVw8+0S0dwvqbt7TTaZe+SiMwG5gIFxpjt\n7fGcKnVKy3sxceoQXnp2HaGgk0fEn+Fh8LDenH/xcCoGFfDIb5ewZ9c+IpEoxhjCIUN1Vb0zR5tg\n2uCMs/ojIlROqKByQvwDOSrW9BmjWb+2ht279hHYF8brtRBLmHnTaXi9NuvX1jD3nlfj9vuhjHE+\noH/9yNd4753P+OOv/5MwR4/HY3H/7y4gN78bctgJfZVujjqwi0gJcDbQ8eXVVdJM++ZIRo0p5Z03\nnGReo8aUMmxEEZYlDB/Zh18tuJCqrbu58/oXCIW+iCj7g4uIE8xDwQg+v4fy/nlMnnZcil5N55bV\n089986fw/rubWL+2ml753akcX0Fur25EI1Hm/+LNhDnU42locLJ3DuuXRUVjFevohWlOMobIgd/d\n17/1FXrpwaROqT1G7POAm4F/tsNzqTRSVpFHWUX8GqIiQl1tY3OGwdgdF8bAJTNG0VAfZNDQQgYO\nLdRR31Hwem1OGVvOKWNbVjz65H91cRe6D6e4JIdoOMKiyuvovbmGbNvHjsI+7M4tJNAjm4rxxzH5\nshPpNyC5ueBV+zmqwC4iU4GtxphV+qbtevzNe9bj8Xgsxk8cqMG8g4XD0cP2sddnEQp+8cHr89lM\n//YoNj//Lvu278KEI/jDTRRt/piizR+DCKWF9fQbMCkZzVcdpNXALiKvAMfEuTQHuA1nGqZVInI1\ncDVAaWnyivaqjtN/UD4+nycmb4zHY3FyZZkG9SToNzA/4YnS/oPyOX5UMYuf/5D6+iDFJdlcMmMU\nw0f24YMXXiPcsC/2HxnDjpUbOrjVqqO1GtiNMWfG+7mIDAfKgf2j9b7AChE5yRizLc7zLAAWgHPy\n9GgardKDZVtcd9sZ3H/3K0SjhmAggj/DQ6+8blx6VauH41Q78PlsrrjmZBY+vOTAQrftsfB6La74\n7hhKy3KZ+vXYCkw9+hXh6ZZBuL4p5lrPAVpQo7Nrt5QCIrIRGN2WXTGaUsBdGhuCLH17Izu2N1Le\nP48Ro4sTbs9THePj9dt56dm11FTtZcCQQiZOGUJ+YVbCx4ebAjxx7HQCdXs4eDuN3c3PWc/9lKJx\nI5PRbHWEkp4rRgO7Up3Lrg838dq0u6j/rBrLtsESTp43kwEzJqa6aSqBtgb2dsvBaYwpa6/nUkp1\nvJzBpVy05hF2r99MaG8TucPLsX2aSdMNNLmyUl1c9sCSVDdBtTOdCFVKKZfRwK6UUi6jgV0ppVxG\nA7tSSrmMBnallHKZlNQ8FZFa4LMOevp8QFMHt077qXXaR63TPmpde/bRscaYgtYelJLA3pFE5P22\nbODv6rSfWqd91Drto9aloo90KkYppVxGA7tSSrmMGwP7glQ3oJPQfmqd9lHrtI9al/Q+ct0cu1JK\ndXVuHLErpVSX5urALiKzRcSIiBZvPISI3C8iH4rIahF5WkRyUt2mdCEiE0XkIxHZICK3pro96UhE\nSkTkdRFZKyJrROS6VLcpXYmILSIrReT5ZN3TtYFdREpwyvZtSnVb0tRi4DhjzPHAeuBHKW5PWhAR\nG3gImAQMBaaLyNDUtiothYHZxpihwBjge9pPCV0HrEvmDV0b2IF5wM2ALiLEYYz5lzFmf7HSJTil\nDRWcBGwwxnxijAkCjwNTU9ymtGOMqTLGrGj+816cwKU19Q4hIn2BycAfk3lfVwZ2EZkKbDXGrEp1\nWzqJK4EXU92INFEMbD7o71vQgHVYIlIGjASWprYlaelBnAFmNJk37bSFNkTkFeCYOJfmALfhTMN0\naYfrI2PMP5sfMwfna/VjyWybcgcRyQKeBGYZY/akuj3pRETOA2qMMctF5Ixk3rvTBnZjzJnxfi4i\nw4FyYJWIgDPFsEJETjLGbEtiE1MuUR/tJyIzgPOACUb3ve63FTi4pFDf5p+pQ4iIFyeoP2aMeSrV\n7UlDpwJTRORcIAPoKSJ/NcZc1tE3dv0+9iMpst2ViMhE4AHgdGNMbarbky5ExIOzmDwBJ6AvAy41\nxqxJacPSjDijpkeBHcaYWaluT7prHrHfaIw5Lxn3c+Ucu2qT3wA9gMUi8oGIPJzqBqWD5gXl7wMv\n4ywIPqFBPa5TgcuB8c3/fz5oHpmqNOD6EbtSSnU1OmJXSimX0cCulFIuo4FdKaVcRgO7Ukq5jAZ2\npZRyGQ3sSinlMhrYlVLKZTSwK6WUy/wfuoiIWc8YlM0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f90101c24a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the data:\n",
    "plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You have:\n",
    "    - a numpy-array (matrix) X that contains your features (x1, x2)\n",
    "    - a numpy-array (vector) Y that contains your labels (red:0, blue:1).\n",
    "\n",
    "Lets first get a better sense of what our data is like. \n",
    "\n",
    "**Exercise**: How many training examples do you have? In addition, what is the `shape` of the variables `X` and `Y`? \n",
    "\n",
    "**Hint**: How do you get the shape of a numpy array? [(help)](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The shape of X is: (2, 400)\n",
      "The shape of Y is: (1, 400)\n",
      "I have m = 400 training examples!\n"
     ]
    }
   ],
   "source": [
    "### START CODE HERE ### (≈ 3 lines of code)\n",
    "shape_X = X.shape\n",
    "shape_Y = Y.shape\n",
    "m = shape_X[1]  # training set size\n",
    "### END CODE HERE ###\n",
    "\n",
    "print ('The shape of X is: ' + str(shape_X))\n",
    "print ('The shape of Y is: ' + str(shape_Y))\n",
    "print ('I have m = %d training examples!' % (m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "       \n",
    "<table style=\"width:20%\">\n",
    "  \n",
    "  <tr>\n",
    "    <td>**shape of X**</td>\n",
    "    <td> (2, 400) </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**shape of Y**</td>\n",
    "    <td>(1, 400) </td> \n",
    "  </tr>\n",
    "  \n",
    "    <tr>\n",
    "    <td>**m**</td>\n",
    "    <td> 400 </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Simple Logistic Regression\n",
    "\n",
    "Before building a full neural network, lets first see how logistic regression performs on this problem. You can use sklearn's built-in functions to do that. Run the code below to train a logistic regression classifier on the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Train the logistic regression classifier\n",
    "clf = sklearn.linear_model.LogisticRegressionCV();\n",
    "clf.fit(X.T, Y.T);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now plot the decision boundary of these models. Run the code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of logistic regression: 47 % (percentage of correctly labelled datapoints)\n"
     ]
    },
    {
     "data": {
      "image/png": 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Jzqy/mf2Moa/1FtjFNNLL6Mew8yP0NRRPzL3KwwunSfkixMwMwVtUyxxbvsSp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\nBIVCoVDk+P8B2BAvSDnlqLAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fdf578048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the decision boundary for logistic regression\n",
    "plot_decision_boundary(lambda x: clf.predict(x), X, Y)\n",
    "plt.title(\"Logistic Regression\")\n",
    "\n",
    "# Print accuracy\n",
    "LR_predictions = clf.predict(X.T)\n",
    "print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +\n",
    "       '% ' + \"(percentage of correctly labelled datapoints)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:20%\">\n",
    "  <tr>\n",
    "    <td>**Accuracy**</td>\n",
    "    <td> 47% </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**: The dataset is not linearly separable, so logistic regression doesn't perform well. Hopefully a neural network will do better. Let's try this now! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Neural Network model\n",
    "\n",
    "Logistic regression did not work well on the \"flower dataset\". You are going to train a Neural Network with a single hidden layer.\n",
    "\n",
    "**Here is our model**:\n",
    "<img src=\"images/classification_kiank.png\" style=\"width:600px;height:300px;\">\n",
    "\n",
    "**Mathematically**:\n",
    "\n",
    "For one example $x^{(i)}$:\n",
    "$$z^{[1] (i)} =  W^{[1]} x^{(i)} + b^{[1]}\\tag{1}$$ \n",
    "$$a^{[1] (i)} = \\tanh(z^{[1] (i)})\\tag{2}$$\n",
    "$$z^{[2] (i)} = W^{[2]} a^{[1] (i)} + b^{[2]}\\tag{3}$$\n",
    "$$\\hat{y}^{(i)} = a^{[2] (i)} = \\sigma(z^{ [2] (i)})\\tag{4}$$\n",
    "$$y^{(i)}_{prediction} = \\begin{cases} 1 & \\mbox{if } a^{[2](i)} > 0.5 \\\\ 0 & \\mbox{otherwise } \\end{cases}\\tag{5}$$\n",
    "\n",
    "Given the predictions on all the examples, you can also compute the cost $J$ as follows: \n",
    "$$J = - \\frac{1}{m} \\sum\\limits_{i = 0}^{m} \\large\\left(\\small y^{(i)}\\log\\left(a^{[2] (i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[2] (i)}\\right)  \\large  \\right) \\small \\tag{6}$$\n",
    "\n",
    "**Reminder**: The general methodology to build a Neural Network is to:\n",
    "    1. Define the neural network structure ( # of input units,  # of hidden units, etc). \n",
    "    2. Initialize the model's parameters\n",
    "    3. Loop:\n",
    "        - Implement forward propagation\n",
    "        - Compute loss\n",
    "        - Implement backward propagation to get the gradients\n",
    "        - Update parameters (gradient descent)\n",
    "\n",
    "You often build helper functions to compute steps 1-3 and then merge them into one function we call `nn_model()`. Once you've built `nn_model()` and learnt the right parameters, you can make predictions on new data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 - Defining the neural network structure ####\n",
    "\n",
    "**Exercise**: Define three variables:\n",
    "    - n_x: the size of the input layer\n",
    "    - n_h: the size of the hidden layer (set this to 4) \n",
    "    - n_y: the size of the output layer\n",
    "\n",
    "**Hint**: Use shapes of X and Y to find n_x and n_y. Also, hard code the hidden layer size to be 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: layer_sizes\n",
    "\n",
    "def layer_sizes(X, Y):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    X -- input dataset of shape (input size, number of examples)\n",
    "    Y -- labels of shape (output size, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    n_x -- the size of the input layer\n",
    "    n_h -- the size of the hidden layer\n",
    "    n_y -- the size of the output layer\n",
    "    \"\"\"\n",
    "    ### START CODE HERE ### (≈ 3 lines of code)\n",
    "    n_x = X.shape[0] # size of input layer\n",
    "    n_h = 4\n",
    "    n_y = Y.shape[0] # size of output layer\n",
    "    ### END CODE HERE ###\n",
    "    return (n_x, n_h, n_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The size of the input layer is: n_x = 5\n",
      "The size of the hidden layer is: n_h = 4\n",
      "The size of the output layer is: n_y = 2\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess = layer_sizes_test_case()\n",
    "(n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)\n",
    "print(\"The size of the input layer is: n_x = \" + str(n_x))\n",
    "print(\"The size of the hidden layer is: n_h = \" + str(n_h))\n",
    "print(\"The size of the output layer is: n_y = \" + str(n_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output** (these are not the sizes you will use for your network, they are just used to assess the function you've just coded).\n",
    "\n",
    "<table style=\"width:20%\">\n",
    "  <tr>\n",
    "    <td>**n_x**</td>\n",
    "    <td> 5 </td> \n",
    "  </tr>\n",
    "  \n",
    "    <tr>\n",
    "    <td>**n_h**</td>\n",
    "    <td> 4 </td> \n",
    "  </tr>\n",
    "  \n",
    "    <tr>\n",
    "    <td>**n_y**</td>\n",
    "    <td> 2 </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 - Initialize the model's parameters ####\n",
    "\n",
    "**Exercise**: Implement the function `initialize_parameters()`.\n",
    "\n",
    "**Instructions**:\n",
    "- Make sure your parameters' sizes are right. Refer to the neural network figure above if needed.\n",
    "- You will initialize the weights matrices with random values. \n",
    "    - Use: `np.random.randn(a,b) * 0.01` to randomly initialize a matrix of shape (a,b).\n",
    "- You will initialize the bias vectors as zeros. \n",
    "    - Use: `np.zeros((a,b))` to initialize a matrix of shape (a,b) with zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_parameters\n",
    "\n",
    "def initialize_parameters(n_x, n_h, n_y):\n",
    "    \"\"\"\n",
    "    Argument:\n",
    "    n_x -- size of the input layer\n",
    "    n_h -- size of the hidden layer\n",
    "    n_y -- size of the output layer\n",
    "    \n",
    "    Returns:\n",
    "    params -- python dictionary containing your parameters:\n",
    "                    W1 -- weight matrix of shape (n_h, n_x)\n",
    "                    b1 -- bias vector of shape (n_h, 1)\n",
    "                    W2 -- weight matrix of shape (n_y, n_h)\n",
    "                    b2 -- bias vector of shape (n_y, 1)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(2) # we set up a seed so that your output matches ours although the initialization is random.\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 =  np.random.randn(n_h,n_x) * 0.01 \n",
    "    b1 = np.zeros((n_h,1))\n",
    "    W2 =  np.random.randn(n_y,n_h) * 0.01 \n",
    "    b2 = np.zeros((n_y,1))\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    assert (W1.shape == (n_h, n_x))\n",
    "    assert (b1.shape == (n_h, 1))\n",
    "    assert (W2.shape == (n_y, n_h))\n",
    "    assert (b2.shape == (n_y, 1))\n",
    "    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[-0.00416758 -0.00056267]\n",
      " [-0.02136196  0.01640271]\n",
      " [-0.01793436 -0.00841747]\n",
      " [ 0.00502881 -0.01245288]]\n",
      "b1 = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "W2 = [[-0.01057952 -0.00909008  0.00551454  0.02292208]]\n",
      "b2 = [[ 0.]]\n"
     ]
    }
   ],
   "source": [
    "n_x, n_h, n_y = initialize_parameters_test_case()\n",
    "\n",
    "parameters = initialize_parameters(n_x, n_h, n_y)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\">\n",
    "  <tr>\n",
    "    <td>**W1**</td>\n",
    "    <td> [[-0.00416758 -0.00056267]\n",
    " [-0.02136196  0.01640271]\n",
    " [-0.01793436 -0.00841747]\n",
    " [ 0.00502881 -0.01245288]] </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**b1**</td>\n",
    "    <td> [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**W2**</td>\n",
    "    <td> [[-0.01057952 -0.00909008  0.00551454  0.02292208]]</td> \n",
    "  </tr>\n",
    "  \n",
    "\n",
    "  <tr>\n",
    "    <td>**b2**</td>\n",
    "    <td> [[ 0.]] </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 - The Loop ####\n",
    "\n",
    "**Question**: Implement `forward_propagation()`.\n",
    "\n",
    "**Instructions**:\n",
    "- Look above at the mathematical representation of your classifier.\n",
    "- You can use the function `sigmoid()`. It is built-in (imported) in the notebook.\n",
    "- You can use the function `np.tanh()`. It is part of the numpy library.\n",
    "- The steps you have to implement are:\n",
    "    1. Retrieve each parameter from the dictionary \"parameters\" (which is the output of `initialize_parameters()`) by using `parameters[\"..\"]`.\n",
    "    2. Implement Forward Propagation. Compute $Z^{[1]}, A^{[1]}, Z^{[2]}$ and $A^{[2]}$ (the vector of all your predictions on all the examples in the training set).\n",
    "- Values needed in the backpropagation are stored in \"`cache`\". The `cache` will be given as an input to the backpropagation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: forward_propagation\n",
    "\n",
    "def forward_propagation(X, parameters):\n",
    "    \"\"\"\n",
    "    Argument:\n",
    "    X -- input data of size (n_x, m)\n",
    "    parameters -- python dictionary containing your parameters (output of initialization function)\n",
    "    \n",
    "    Returns:\n",
    "    A2 -- The sigmoid output of the second activation\n",
    "    cache -- a dictionary containing \"Z1\", \"A1\", \"Z2\" and \"A2\"\n",
    "    \"\"\"\n",
    "    # Retrieve each parameter from the dictionary \"parameters\"\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Implement Forward Propagation to calculate A2 (probabilities)\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    Z1 = np.dot(W1,X)+b1\n",
    "    A1 = np.tanh(Z1)\n",
    "    Z2 = np.dot(W2,A1)+b2\n",
    "    A2 = sigmoid(Z2)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    assert(A2.shape == (1, X.shape[1]))\n",
    "    \n",
    "    cache = {\"Z1\": Z1,\n",
    "             \"A1\": A1,\n",
    "             \"Z2\": Z2,\n",
    "             \"A2\": A2}\n",
    "    \n",
    "    return A2, cache"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.262818640198 0.091999045227 -1.30766601287 0.212877681719\n"
     ]
    }
   ],
   "source": [
    "X_assess, parameters = forward_propagation_test_case()\n",
    "A2, cache = forward_propagation(X_assess, parameters)\n",
    "\n",
    "# Note: we use the mean here just to make sure that your output matches ours. \n",
    "print(np.mean(cache['Z1']) ,np.mean(cache['A1']),np.mean(cache['Z2']),np.mean(cache['A2']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "<table style=\"width:50%\">\n",
    "  <tr>\n",
    "    <td> 0.262818640198 0.091999045227 -1.30766601287 0.212877681719 </td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have computed $A^{[2]}$ (in the Python variable \"`A2`\"), which contains $a^{[2](i)}$ for every example, you can compute the cost function as follows:\n",
    "\n",
    "$$J = - \\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(} \\small y^{(i)}\\log\\left(a^{[2] (i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[2] (i)}\\right) \\large{)} \\small\\tag{13}$$\n",
    "\n",
    "**Exercise**: Implement `compute_cost()` to compute the value of the cost $J$.\n",
    "\n",
    "**Instructions**:\n",
    "- There are many ways to implement the cross-entropy loss. To help you, we give you how we would have implemented\n",
    "$- \\sum\\limits_{i=0}^{m}  y^{(i)}\\log(a^{[2](i)})$:\n",
    "```python\n",
    "logprobs = np.multiply(np.log(A2),Y)\n",
    "cost = - np.sum(logprobs)                # no need to use a for loop!\n",
    "```\n",
    "\n",
    "(you can use either `np.multiply()` and then `np.sum()` or directly `np.dot()`).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: compute_cost\n",
    "\n",
    "def compute_cost(A2, Y, parameters):\n",
    "    \"\"\"\n",
    "    Computes the cross-entropy cost given in equation (13)\n",
    "    \n",
    "    Arguments:\n",
    "    A2 -- The sigmoid output of the second activation, of shape (1, number of examples)\n",
    "    Y -- \"true\" labels vector of shape (1, number of examples)\n",
    "    parameters -- python dictionary containing your parameters W1, b1, W2 and b2\n",
    "    \n",
    "    Returns:\n",
    "    cost -- cross-entropy cost given equation (13)\n",
    "    \"\"\"\n",
    "    \n",
    "    m = Y.shape[1] # number of example\n",
    "\n",
    "    # Compute the cross-entropy cost\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    logprobs = np.multiply(np.log(A2),Y)+np.multiply(np.log(1-A2),1-Y)\n",
    "    cost = -1/m* np.sum(logprobs)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    cost = np.squeeze(cost)     # makes sure cost is the dimension we expect. \n",
    "                                # E.g., turns [[17]] into 17 \n",
    "    assert(isinstance(cost, float))\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost = 0.693058761039\n"
     ]
    }
   ],
   "source": [
    "A2, Y_assess, parameters = compute_cost_test_case()\n",
    "\n",
    "print(\"cost = \" + str(compute_cost(A2, Y_assess, parameters)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "<table style=\"width:20%\">\n",
    "  <tr>\n",
    "    <td>**cost**</td>\n",
    "    <td> 0.693058761... </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the cache computed during forward propagation, you can now implement backward propagation.\n",
    "\n",
    "**Question**: Implement the function `backward_propagation()`.\n",
    "\n",
    "**Instructions**:\n",
    "Backpropagation is usually the hardest (most mathematical) part in deep learning. To help you, here again is the slide from the lecture on backpropagation. You'll want to use the six equations on the right of this slide, since you are building a vectorized implementation.  \n",
    "\n",
    "<img src=\"images/grad_summary.png\" style=\"width:600px;height:300px;\">\n",
    "\n",
    "<!--\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)} } = \\frac{1}{m} (a^{[2](i)} - y^{(i)})$\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial W_2 } = \\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)} } a^{[1] (i) T} $\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial b_2 } = \\sum_i{\\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)}}}$\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial z_{1}^{(i)} } =  W_2^T \\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)} } * ( 1 - a^{[1] (i) 2}) $\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial W_1 } = \\frac{\\partial \\mathcal{J} }{ \\partial z_{1}^{(i)} }  X^T $\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} _i }{ \\partial b_1 } = \\sum_i{\\frac{\\partial \\mathcal{J} }{ \\partial z_{1}^{(i)}}}$\n",
    "\n",
    "- Note that $*$ denotes elementwise multiplication.\n",
    "- The notation you will use is common in deep learning coding:\n",
    "    - dW1 = $\\frac{\\partial \\mathcal{J} }{ \\partial W_1 }$\n",
    "    - db1 = $\\frac{\\partial \\mathcal{J} }{ \\partial b_1 }$\n",
    "    - dW2 = $\\frac{\\partial \\mathcal{J} }{ \\partial W_2 }$\n",
    "    - db2 = $\\frac{\\partial \\mathcal{J} }{ \\partial b_2 }$\n",
    "    \n",
    "!-->\n",
    "\n",
    "- Tips:\n",
    "    - To compute dZ1 you'll need to compute $g^{[1]'}(Z^{[1]})$. Since $g^{[1]}(.)$ is the tanh activation function, if $a = g^{[1]}(z)$ then $g^{[1]'}(z) = 1-a^2$. So you can compute \n",
    "    $g^{[1]'}(Z^{[1]})$ using `(1 - np.power(A1, 2))`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: backward_propagation\n",
    "\n",
    "def backward_propagation(parameters, cache, X, Y):\n",
    "    \"\"\"\n",
    "    Implement the backward propagation using the instructions above.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing our parameters \n",
    "    cache -- a dictionary containing \"Z1\", \"A1\", \"Z2\" and \"A2\".\n",
    "    X -- input data of shape (2, number of examples)\n",
    "    Y -- \"true\" labels vector of shape (1, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    grads -- python dictionary containing your gradients with respect to different parameters\n",
    "    \"\"\"\n",
    "    m = X.shape[1]\n",
    "    \n",
    "    # First, retrieve W1 and W2 from the dictionary \"parameters\".\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    W1 = parameters[\"W1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    ### END CODE HERE ###\n",
    "        \n",
    "    # Retrieve also A1 and A2 from dictionary \"cache\".\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A1 = cache[\"A1\"]\n",
    "    A2 = cache[\"A2\"]\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Backward propagation: calculate dW1, db1, dW2, db2. \n",
    "    ### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above)\n",
    "    dZ2 = A2-Y\n",
    "    dW2 = 1/m*np.dot(dZ2,A1.T)\n",
    "    db2 = 1/m*np.sum(dZ2,axis=1,keepdims=True)\n",
    "    dZ1 = np.dot(W2.T,dZ2)*(1 - np.power(A1, 2))\n",
    "    dW1 = 1/m*np.dot(dZ1,X.T)\n",
    "    db1 = 1/m*np.sum(dZ1,axis=1,keepdims=True)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    grads = {\"dW1\": dW1,\n",
    "             \"db1\": db1,\n",
    "             \"dW2\": dW2,\n",
    "             \"db2\": db2}\n",
    "    \n",
    "    return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dW1 = [[ 0.00301023 -0.00747267]\n",
      " [ 0.00257968 -0.00641288]\n",
      " [-0.00156892  0.003893  ]\n",
      " [-0.00652037  0.01618243]]\n",
      "db1 = [[ 0.00176201]\n",
      " [ 0.00150995]\n",
      " [-0.00091736]\n",
      " [-0.00381422]]\n",
      "dW2 = [[ 0.00078841  0.01765429 -0.00084166 -0.01022527]]\n",
      "db2 = [[-0.16655712]]\n"
     ]
    }
   ],
   "source": [
    "parameters, cache, X_assess, Y_assess = backward_propagation_test_case()\n",
    "\n",
    "grads = backward_propagation(parameters, cache, X_assess, Y_assess)\n",
    "print (\"dW1 = \"+ str(grads[\"dW1\"]))\n",
    "print (\"db1 = \"+ str(grads[\"db1\"]))\n",
    "print (\"dW2 = \"+ str(grads[\"dW2\"]))\n",
    "print (\"db2 = \"+ str(grads[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected output**:\n",
    "\n",
    "\n",
    "\n",
    "<table style=\"width:80%\">\n",
    "  <tr>\n",
    "    <td>**dW1**</td>\n",
    "    <td> [[ 0.00301023 -0.00747267]\n",
    " [ 0.00257968 -0.00641288]\n",
    " [-0.00156892  0.003893  ]\n",
    " [-0.00652037  0.01618243]] </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**db1**</td>\n",
    "    <td>  [[ 0.00176201]\n",
    " [ 0.00150995]\n",
    " [-0.00091736]\n",
    " [-0.00381422]] </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**dW2**</td>\n",
    "    <td> [[ 0.00078841  0.01765429 -0.00084166 -0.01022527]] </td> \n",
    "  </tr>\n",
    "  \n",
    "\n",
    "  <tr>\n",
    "    <td>**db2**</td>\n",
    "    <td> [[-0.16655712]] </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question**: Implement the update rule. Use gradient descent. You have to use (dW1, db1, dW2, db2) in order to update (W1, b1, W2, b2).\n",
    "\n",
    "**General gradient descent rule**: $ \\theta = \\theta - \\alpha \\frac{\\partial J }{ \\partial \\theta }$ where $\\alpha$ is the learning rate and $\\theta$ represents a parameter.\n",
    "\n",
    "**Illustration**: The gradient descent algorithm with a good learning rate (converging) and a bad learning rate (diverging). Images courtesy of Adam Harley.\n",
    "\n",
    "<img src=\"images/sgd.gif\" style=\"width:400;height:400;\"> <img src=\"images/sgd_bad.gif\" style=\"width:400;height:400;\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters\n",
    "\n",
    "def update_parameters(parameters, grads, learning_rate = 1.2):\n",
    "    \"\"\"\n",
    "    Updates parameters using the gradient descent update rule given above\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters \n",
    "    grads -- python dictionary containing your gradients \n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "    # Retrieve each parameter from the dictionary \"parameters\"\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Retrieve each gradient from the dictionary \"grads\"\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    dW1 = grads[\"dW1\"]\n",
    "    db1 = grads[\"db1\"]\n",
    "    dW2 = grads[\"dW2\"]\n",
    "    db2 = grads[\"db2\"]\n",
    "    ## END CODE HERE ###\n",
    "    \n",
    "    # Update rule for each parameter\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = W1-learning_rate*dW1\n",
    "    b1 = b1-learning_rate*db1\n",
    "    W2 = W2-learning_rate*dW2\n",
    "    b2 = b2-learning_rate*db2\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[-0.00643025  0.01936718]\n",
      " [-0.02410458  0.03978052]\n",
      " [-0.01653973 -0.02096177]\n",
      " [ 0.01046864 -0.05990141]]\n",
      "b1 = [[ -1.02420756e-06]\n",
      " [  1.27373948e-05]\n",
      " [  8.32996807e-07]\n",
      " [ -3.20136836e-06]]\n",
      "W2 = [[-0.01041081 -0.04463285  0.01758031  0.04747113]]\n",
      "b2 = [[ 0.00010457]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads = update_parameters_test_case()\n",
    "parameters = update_parameters(parameters, grads)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "\n",
    "<table style=\"width:80%\">\n",
    "  <tr>\n",
    "    <td>**W1**</td>\n",
    "    <td> [[-0.00643025  0.01936718]\n",
    " [-0.02410458  0.03978052]\n",
    " [-0.01653973 -0.02096177]\n",
    " [ 0.01046864 -0.05990141]]</td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**b1**</td>\n",
    "    <td> [[ -1.02420756e-06]\n",
    " [  1.27373948e-05]\n",
    " [  8.32996807e-07]\n",
    " [ -3.20136836e-06]]</td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**W2**</td>\n",
    "    <td> [[-0.01041081 -0.04463285  0.01758031  0.04747113]] </td> \n",
    "  </tr>\n",
    "  \n",
    "\n",
    "  <tr>\n",
    "    <td>**b2**</td>\n",
    "    <td> [[ 0.00010457]] </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 - Integrate parts 4.1, 4.2 and 4.3 in nn_model() ####\n",
    "\n",
    "**Question**: Build your neural network model in `nn_model()`.\n",
    "\n",
    "**Instructions**: The neural network model has to use the previous functions in the right order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: nn_model\n",
    "\n",
    "def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    X -- dataset of shape (2, number of examples)\n",
    "    Y -- labels of shape (1, number of examples)\n",
    "    n_h -- size of the hidden layer\n",
    "    num_iterations -- Number of iterations in gradient descent loop\n",
    "    print_cost -- if True, print the cost every 1000 iterations\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- parameters learnt by the model. They can then be used to predict.\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(3)\n",
    "    n_x = layer_sizes(X, Y)[0]\n",
    "    n_y = layer_sizes(X, Y)[2]\n",
    "    \n",
    "    # Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: \"n_x, n_h, n_y\". Outputs = \"W1, b1, W2, b2, parameters\".\n",
    "    ### START CODE HERE ### (≈ 5 lines of code)\n",
    "    parameters =initialize_parameters(n_x, n_h, n_y)\n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Loop (gradient descent)\n",
    "\n",
    "    for i in range(0, num_iterations):\n",
    "         \n",
    "        ### START CODE HERE ### (≈ 4 lines of code)\n",
    "        # Forward propagation. Inputs: \"X, parameters\". Outputs: \"A2, cache\".\n",
    "        A2, cache = forward_propagation(X, parameters)\n",
    "        \n",
    "        # Cost function. Inputs: \"A2, Y, parameters\". Outputs: \"cost\".\n",
    "        cost = compute_cost(A2, Y, parameters)\n",
    " \n",
    "        # Backpropagation. Inputs: \"parameters, cache, X, Y\". Outputs: \"grads\".\n",
    "        grads = backward_propagation(parameters, cache, X, Y)\n",
    " \n",
    "        # Gradient descent parameter update. Inputs: \"parameters, grads\". Outputs: \"parameters\".\n",
    "        parameters = update_parameters(parameters, grads, learning_rate = 1.2)\n",
    "        \n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Print the cost every 1000 iterations\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.692739\n",
      "Cost after iteration 1000: 0.000218\n",
      "Cost after iteration 2000: 0.000107\n",
      "Cost after iteration 3000: 0.000071\n",
      "Cost after iteration 4000: 0.000053\n",
      "Cost after iteration 5000: 0.000042\n",
      "Cost after iteration 6000: 0.000035\n",
      "Cost after iteration 7000: 0.000030\n",
      "Cost after iteration 8000: 0.000026\n",
      "Cost after iteration 9000: 0.000023\n",
      "W1 = [[-0.65848169  1.21866811]\n",
      " [-0.76204273  1.39377573]\n",
      " [ 0.5792005  -1.10397703]\n",
      " [ 0.76773391 -1.41477129]]\n",
      "b1 = [[ 0.287592  ]\n",
      " [ 0.3511264 ]\n",
      " [-0.2431246 ]\n",
      " [-0.35772805]]\n",
      "W2 = [[-2.45566237 -3.27042274  2.00784958  3.36773273]]\n",
      "b2 = [[ 0.20459656]]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess = nn_model_test_case()\n",
    "parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10000, print_cost=True)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\">\n",
    "\n",
    "<tr> \n",
    "    <td> \n",
    "        **cost after iteration 0**\n",
    "    </td>\n",
    "    <td> \n",
    "        0.692739\n",
    "    </td>\n",
    "</tr>\n",
    "\n",
    "<tr> \n",
    "    <td> \n",
    "        <center> $\\vdots$ </center>\n",
    "    </td>\n",
    "    <td> \n",
    "        <center> $\\vdots$ </center>\n",
    "    </td>\n",
    "</tr>\n",
    "\n",
    "  <tr>\n",
    "    <td>**W1**</td>\n",
    "    <td> [[-0.65848169  1.21866811]\n",
    " [-0.76204273  1.39377573]\n",
    " [ 0.5792005  -1.10397703]\n",
    " [ 0.76773391 -1.41477129]]</td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**b1**</td>\n",
    "    <td> [[ 0.287592  ]\n",
    " [ 0.3511264 ]\n",
    " [-0.2431246 ]\n",
    " [-0.35772805]] </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**W2**</td>\n",
    "    <td> [[-2.45566237 -3.27042274  2.00784958  3.36773273]] </td> \n",
    "  </tr>\n",
    "  \n",
    "\n",
    "  <tr>\n",
    "    <td>**b2**</td>\n",
    "    <td> [[ 0.20459656]] </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Predictions\n",
    "\n",
    "**Question**: Use your model to predict by building predict().\n",
    "Use forward propagation to predict results.\n",
    "\n",
    "**Reminder**: predictions = $y_{prediction} = \\mathbb 1 \\text{{activation > 0.5}} = \\begin{cases}\n",
    "      1 & \\text{if}\\ activation > 0.5 \\\\\n",
    "      0 & \\text{otherwise}\n",
    "    \\end{cases}$  \n",
    "    \n",
    "As an example, if you would like to set the entries of a matrix X to 0 and 1 based on a threshold you would do: ```X_new = (X > threshold)```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: predict\n",
    "\n",
    "def predict(parameters, X):\n",
    "    \"\"\"\n",
    "    Using the learned parameters, predicts a class for each example in X\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters \n",
    "    X -- input data of size (n_x, m)\n",
    "    \n",
    "    Returns\n",
    "    predictions -- vector of predictions of our model (red: 0 / blue: 1)\n",
    "    \"\"\"\n",
    "    \n",
    "    # Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold.\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A2, cache = forward_propagation(X, parameters)\n",
    "    predictions = (A2>0.5)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictions mean = 0.666666666667\n"
     ]
    }
   ],
   "source": [
    "parameters, X_assess = predict_test_case()\n",
    "\n",
    "predictions = predict(parameters, X_assess)\n",
    "print(\"predictions mean = \" + str(np.mean(predictions)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "\n",
    "<table style=\"width:40%\">\n",
    "  <tr>\n",
    "    <td>**predictions mean**</td>\n",
    "    <td> 0.666666666667 </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is time to run the model and see how it performs on a planar dataset. Run the following code to test your model with a single hidden layer of $n_h$ hidden units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693048\n",
      "Cost after iteration 1000: 0.288083\n",
      "Cost after iteration 2000: 0.254385\n",
      "Cost after iteration 3000: 0.233864\n",
      "Cost after iteration 4000: 0.226792\n",
      "Cost after iteration 5000: 0.222644\n",
      "Cost after iteration 6000: 0.219731\n",
      "Cost after iteration 7000: 0.217504\n",
      "Cost after iteration 8000: 0.219471\n",
      "Cost after iteration 9000: 0.218612\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f8fdbc2c128>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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X4tNtwqCBqXyWw8McqSzt/EXuc0pFr00oV6uK+WtOc3vj+9UlF5TCccBzFfGkgWX11+JW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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9010293908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build a model with a n_h-dimensional hidden layer\n",
    "parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)\n",
    "\n",
    "# Plot the decision boundary\n",
    "plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)\n",
    "plt.title(\"Decision Boundary for hidden layer size \" + str(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\">\n",
    "  <tr>\n",
    "    <td>**Cost after iteration 9000**</td>\n",
    "    <td> 0.218607 </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 90%\n"
     ]
    }
   ],
   "source": [
    "# Print accuracy\n",
    "predictions = predict(parameters, X)\n",
    "print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:15%\">\n",
    "  <tr>\n",
    "    <td>**Accuracy**</td>\n",
    "    <td> 90% </td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accuracy is really high compared to Logistic Regression. The model has learnt the leaf patterns of the flower! Neural networks are able to learn even highly non-linear decision boundaries, unlike logistic regression. \n",
    "\n",
    "Now, let's try out several hidden layer sizes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6 - Tuning hidden layer size (optional/ungraded exercise) ###\n",
    "\n",
    "Run the following code. It may take 1-2 minutes. You will observe different behaviors of the model for various hidden layer sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy for 1 hidden units: 67.5 %\n",
      "Accuracy for 2 hidden units: 67.25 %\n",
      "Accuracy for 3 hidden units: 90.75 %\n",
      "Accuracy for 4 hidden units: 90.5 %\n",
      "Accuracy for 5 hidden units: 91.25 %\n",
      "Accuracy for 20 hidden units: 90.0 %\n",
      "Accuracy for 50 hidden units: 90.25 %\n"
     ]
    }
   ],
   "source": [
    "# This may take about 2 minutes to run\n",
    "\n",
    "plt.figure(figsize=(16, 32))\n",
    "hidden_layer_sizes = [ 1,2, 3, 4, 5, 20, 50]\n",
    "for i, n_h in enumerate(hidden_layer_sizes):\n",
    "    plt.subplot(5, 2, i+1)\n",
    "    plt.title('Hidden Layer of size %d' % n_h)\n",
    "    parameters = nn_model(X, Y, n_h, num_iterations = 5000)\n",
    "    plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)\n",
    "    predictions = predict(parameters, X)\n",
    "    accuracy = float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100)\n",
    "    print (\"Accuracy for {} hidden units: {} %\".format(n_h, accuracy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**:\n",
    "- The larger models (with more hidden units) are able to fit the training set better, until eventually the largest models overfit the data. \n",
    "- The best hidden layer size seems to be around n_h = 5. Indeed, a value around here seems to  fits the data well without also incurring noticeable overfitting.\n",
    "- You will also learn later about regularization, which lets you use very large models (such as n_h = 50) without much overfitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optional questions**:\n",
    "\n",
    "**Note**: Remember to submit the assignment by clicking the blue \"Submit Assignment\" button at the upper-right. \n",
    "\n",
    "Some optional/ungraded questions that you can explore if you wish: \n",
    "- What happens when you change the tanh activation for a sigmoid activation or a ReLU activation?\n",
    "- Play with the learning_rate. What happens?\n",
    "- What if we change the dataset? (See part 5 below!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**You've learnt to:**\n",
    "- Build a complete neural network with a hidden layer\n",
    "- Make a good use of a non-linear unit\n",
    "- Implemented forward propagation and backpropagation, and trained a neural network\n",
    "- See the impact of varying the hidden layer size, including overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice work! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5) Performance on other datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "If you want, you can rerun the whole notebook (minus the dataset part) for each of the following datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Datasets\n",
    "noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()\n",
    "\n",
    "datasets = {\"noisy_circles\": noisy_circles,\n",
    "            \"noisy_moons\": noisy_moons,\n",
    "            \"blobs\": blobs,\n",
    "            \"gaussian_quantiles\": gaussian_quantiles}\n",
    "\n",
    "### START CODE HERE ### (choose your dataset)\n",
    "dataset = \"noisy_moons\"\n",
    "### END CODE HERE ###\n",
    "\n",
    "X, Y = datasets[dataset]\n",
    "X, Y = X.T, Y.reshape(1, Y.shape[0])\n",
    "\n",
    "# make blobs binary\n",
    "if dataset == \"blobs\":\n",
    "    Y = Y%2\n",
    "\n",
    "# Visualize the data\n",
    "plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congrats on finishing this Programming Assignment!\n",
    "\n",
    "Reference:\n",
    "- http://scs.ryerson.ca/~aharley/neural-networks/\n",
    "- http://cs231n.github.io/neural-networks-case-study/"
   ]
  }
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