sudoku.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sudoku\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "Sudoku is a logic-based, combinatorial number-placement puzzle. Despite its Japanese name, the game was actually invented by an American and later gained popularity in Japan. \n",
    "\n",
    "There are many ways (e.g. graph coloring) for computer algorithms to solve Sudoku. Here we use Binary Integer Linear Programming to solve the puzzle via convex optimization. In this particular optimization problem, we have no objective function to maximize or minimize. We merely need to satisfy the constraints below.\n",
    "\n",
    "1. Only one element in each column\n",
    "2. Only one element in each row\n",
    "3. Only one element in each sub matrix\n",
    "4. Each cell in the matrix should be filled\n",
    "5. Given elements in the cells are set on\n",
    "\n",
    "The trick is to convert an N by N Sudoku matrix into a flattened array `x` of length N^3. Each element inside the array represents the existence of number N in the cell (N,N). To use `cvxopt` to solve the problem, we just need to create constraint matrix `A` to put everything mentioned above in the form of `Ax=b`.\n",
    "\n",
    "More details can be found in the original paper\n",
    "\n",
    "https://pdfs.semanticscholar.org/1ca8/21d0145e3f7b02e37e283042b4e601bf388d.pdf\n",
    "\n",
    "Reference to graph coloring for Sudoku\n",
    "\n",
    "https://github.com/je-suis-tm/graph-theory/blob/master/sudoku.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cvxopt.glpk\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#the constraint of given elements\n",
    "#set given elements in the matrix as one\n",
    "def get_given_constraint(puzzle,num):\n",
    "\n",
    "    #initialize\n",
    "    given_constraint=np.zeros((len(puzzle[puzzle!=0]),num**3))\n",
    "\n",
    "    #flatten the puzzle and find out its index inside the array\n",
    "    indices=[ind+(val-1)*(num**2) for ind,val in enumerate(puzzle.ravel()) if val!=0]\n",
    "\n",
    "    #the constraint of given elements\n",
    "    for ind,val in enumerate(indices):\n",
    "        given_constraint[ind,val]=1\n",
    "        \n",
    "    return given_constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#only one element in each column\n",
    "#the summation of each column for each element should be one\n",
    "def get_col_constraint(num):\n",
    "\n",
    "    #initialize\n",
    "    col_constraint=np.zeros((num**2,num**3))\n",
    "\n",
    "    #only one element in each column\n",
    "    for element_ind in range(num):\n",
    "        start=element_ind*(num**2)\n",
    "        end=(element_ind+1)*(num**2)\n",
    "        for col_ind in range(num):\n",
    "            for cell_ind in range(start+col_ind,end,num):\n",
    "                col_constraint[element_ind*num+col_ind][cell_ind]=1\n",
    "                \n",
    "    return col_constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#only one element in each row\n",
    "#the summation of each row for each element should be one\n",
    "def get_row_constraint(num):\n",
    "\n",
    "    #initialize\n",
    "    row_constraint=np.zeros((num**2,num**3))\n",
    "\n",
    "    #only one element in each row\n",
    "    for itr in range(num**2):\n",
    "        for cell_ind in range(num*itr,num*(itr+1)):\n",
    "                row_constraint[itr][cell_ind]=1\n",
    "                \n",
    "    return row_constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#only one element in each submatrix\n",
    "#the summation of each submatrix for each element should be one\n",
    "#this function gets overly complicated by five layers of loops\n",
    "#the actual execution should be really fast\n",
    "#as some of the loops merely create the submatrix coordinates\n",
    "def get_sub_constraint(num):\n",
    "    \n",
    "    subnum=int(num**0.5)\n",
    "\n",
    "    #initialize\n",
    "    sub_constraint=np.zeros((num**2,num**3))\n",
    "\n",
    "    #only one element in each submatrix\n",
    "    for element_ind in range(num):\n",
    "        start=element_ind*(num**2)\n",
    "        end=(element_ind+1)*(num**2)       \n",
    "        for col_ind in range(0,num,subnum):\n",
    "            for row_ind in range(0,num,subnum):\n",
    "                h_samples=[i for i in range(col_ind,col_ind+subnum)]\n",
    "                v_samples=[i for i in range(row_ind,row_ind+subnum)]\n",
    "                for v_index,v_pointer in enumerate(v_samples):\n",
    "                    for h_index,h_pointer in enumerate(h_samples):\n",
    "                        cell_ind=start+v_pointer*num+h_pointer\n",
    "                        sub_constraint[element_ind*num+int(col_ind/subnum)+row_ind][cell_ind]=1\n",
    "                        \n",
    "    return sub_constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#each cell must be filled\n",
    "#the summation of each cell for different elements should be one\n",
    "def get_must_constraint(num):\n",
    "\n",
    "    #initialize\n",
    "    must_constraint=np.zeros((num**2,num**3))\n",
    "\n",
    "    #each cell must be filled\n",
    "    for must_ind in range(num**2):\n",
    "        must_constraint[must_ind][must_ind::num**2]=1\n",
    "        \n",
    "    return must_constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#use cvxopt integer linear programming\n",
    "#the answer may not be unique\n",
    "#depends on sudoku itself\n",
    "def solve(constraints):    \n",
    "    \n",
    "    #equality constraints\n",
    "    #the only thing that matters\n",
    "    equality_coeff=cvxopt.matrix(constraints)\n",
    "    equality_value=cvxopt.matrix(np.ones(constraints.shape[0]))\n",
    "    \n",
    "    #linear coefficient\n",
    "    #no objective function to maximize\n",
    "    linear_coeff=cvxopt.matrix(np.zeros(constraints.shape[1]))\n",
    "    \n",
    "    #inequality constraints\n",
    "    inequality_coeff=cvxopt.matrix(np.zeros(constraints.shape))\n",
    "    inequality_value=cvxopt.matrix(np.zeros(constraints.shape[0]))    \n",
    "    \n",
    "    #binary constraints\n",
    "    #the constraint should cover the whole length of vector x\n",
    "    #the default is (0,1) and u cannot alter it\n",
    "    binary_set=set(range(constraints.shape[1]))\n",
    "    \n",
    "    #result\n",
    "    status,solution=cvxopt.glpk.ilp(\n",
    "        c=linear_coeff,G=inequality_coeff,h=inequality_value,\n",
    "        A=equality_coeff,b=equality_value,\n",
    "        B=binary_set)\n",
    "    \n",
    "    return status,solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create output\n",
    "#convert flatten matrix to a regular n by n matrix\n",
    "def extract_solution(solution,num):\n",
    "\n",
    "    #initialize\n",
    "    sudoku=np.zeros((num,num))\n",
    "\n",
    "    #revert flatten matrix to real sudoku\n",
    "    for i in range(num):\n",
    "        submatrix=np.array(solution[i*(num**2):(i+1)*(num**2)]).reshape(num,num)\n",
    "        for j in np.column_stack(np.where(submatrix==1)):\n",
    "            sudoku[j[0],j[1]]=i+1\n",
    "            \n",
    "    return sudoku"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#main function\n",
    "#all combined into one\n",
    "def sudoku_ans(puzzle):\n",
    "\n",
    "    #get the level of sudoku\n",
    "    num=puzzle.shape[0]\n",
    "    \n",
    "    #create constraints\n",
    "    col_constraint=get_col_constraint(num)\n",
    "    row_constraint=get_row_constraint(num)\n",
    "    sub_constraint=get_sub_constraint(num)\n",
    "    must_constraint=get_must_constraint(num)\n",
    "    given_constraint=get_given_constraint(puzzle,num)\n",
    "\n",
    "    #aggregate\n",
    "    constraints=np.vstack((col_constraint,row_constraint,\n",
    "               sub_constraint,must_constraint,\n",
    "               given_constraint))\n",
    "\n",
    "    #solve via ilp and create output\n",
    "    status,solution=solve(constraints)\n",
    "    sudoku=extract_solution(solution,num)\n",
    "    \n",
    "    return sudoku"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#viz sudoku\n",
    "def viz(sudoku,colors):\n",
    "\n",
    "    ax=plt.figure(figsize=(5,5)).add_subplot(111)\n",
    "    \n",
    "    #plot blocks with graph coloring\n",
    "    for latitude in range(sudoku.shape[0]):\n",
    "        for longitude in range(sudoku.shape[1]):\n",
    "            ax.add_patch(patches.Rectangle((latitude,longitude),\n",
    "                    1,1,facecolor=colors[sudoku[latitude][longitude]],\n",
    "                                           edgecolor='k',fill=True))\n",
    "\n",
    "    #show answers\n",
    "    for latitude in range(sudoku.shape[0]):\n",
    "        for longitude in range(sudoku.shape[1]):\n",
    "            plt.text(latitude+0.5,longitude+0.5,\n",
    "                     str(sudoku[latitude][longitude]),\n",
    "                     ha='center',va='center',fontsize=20)\n",
    "\n",
    "    plt.xlim((0,sudoku.shape[0]))\n",
    "    plt.ylim((0,sudoku.shape[1]))\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "easy=np.array([\n",
    "[0,0,2, 0],\n",
    "[0,0,0, 0],\n",
    "[0,1,0, 0],\n",
    "[4,0,0, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "easy_ans=sudoku_ans(easy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAAElCAYAAABect+9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAGKNJREFUeJzt3XtQ1HXfxvFrQXA57cISoCCsOgoKoZjHUWlIczQV8dCIhxr/MCVtykbLHE3FVMZDZk6jpYjhmCkmaqMxmYcmT4mCgkq6iCIII/KsIgdBaWWfP5y7Jx+5A/S++f4+cr3+Y/c7zjVN82a/sDvo7HY7iIgkcFA9gIiosRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKjVVMO63Q6u6FN0H9ri0gVJYUICg5TPUNzCnNz0KVrF9UzNOfK5SvwNQernqE5pQW5Vrvd7tPQOV1TPkuo0+nsw+dtfK5hL5q0FXH4+qhF9QzNmTEoBOln01XP0Jy+vftiVtIR1TM0Z93UwZl2u71XQ+d4JSQiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMRgsIhKDwSIiMZr0h1RVuXUlE3cLc1FRWoTK0iLYah/AP6wPIqKnqp6m3N5Nq1FguYTSohuoKi+DU2s9TH7+6D7gdUSNngx3o5fqiZqQlpaGJYuXAADmL5iPmNExihc1r5qqclw7dwI3LqTDWpyPqjIrHFs5wTugA0IHDkXYgGHQOWj/9YuIYOWdSkNlaREcnVtD7+EF250S1ZM048jurQjsHIouPfvDw9MbtQ9qkH85Cz9t/QonDqRg7vpdMPm2VT1Tqdslt7Fm9Rq4urqiurpa9RwlrmYcw6/bvoSb0RvtukTAo5cvqsvLkHfuOI4kr0HBxTMYPmMxdDqd6qn/SESwQgePh97DE65evrhbmIv0HV+onqQZaw9kwsm59VOP/5i0Fj9v/wYHv9+IiR/GN/8wjbDb7Vj62VIYjUZEvRaF7d9tVz1JCS+/doh+fyk6dOv3xCup/uOmYuey95CXeRx5mcfRuderClc2TPuvAQF4m0PgZvLTfP1VqC9WANAz6g0AQGlxQXPO0ZyUnSnIyMjAwkUL4eLionqOMoFde6BjRP+nrn1uRhPCo0YCAIot2SqmNYmIYFHTXTh1FAAQ0DFE8RJ18vPzsWH9BsROiEWPV3qonqNZjo6PL1o6R0fFSxom4kpIDTuUkoSHNdWouV+JgtxLuHYxEwEdQzB04nTV05Sw2WyIXxwPPz8/zJg5Q/Uczap79AiXTx0CALR/ubfiNQ1jsF4Qh3dtQUWZ9a+vQ/tEYsrcFfDwNClcpU7S5iTkWnKxKXET9Hq96jmadXJ3Iu4U56N9eF+YGSxqLitTTwIAKu5acT3nPPYmfo6EuNGYuXwjgoLDFK9rXjk5OdiavBWTJk9CeLdw1XM0K+vwHpz75Qd4tQ3C0HfmqZ7TKPwZ1gvGYHoJEZFD8MGqLbhfcQ/JKz5RPalZ2Ww2xC+KR2BQIOLejVM9R7Oyj+7DbzvWw+RvxriP10DvblA9qVH4CusF5d0mAG3MnVCUdxlV5XfhbmwZV8OamhoUFhYCACIHRNZ7JmF5AhKWJyB2Qixmz5ndnPM04fyhVBzbuQHeAR0w9qPVcDXIeXMxg/UCK79TCgDQOWj/tz//KU5OThgVM6re5yxXLLBYLOge0R1msxnh4S3vupiRtgMnUzfDJ7ATxsxZBRcPo+pJTcJgCVZSeA0u7gYYTT5PPF5XV4f9365DZdkddAzrATdh/1M+D71ejwWfLqj3ucRNibBYLBgxYkSL+2gOAKTv34bT+5Lhaw7GmNkrxVwD/05EsEpys3A7NwsA8PB+OQDgXvF1ZB9IBgA4u7qj66A3Vc1TJufMcezZuBqdu/WCj38Q3AyeqCiz4mr2WVhv3YTB5IO35ixTPZM04I+TB3F6XzJ0Dg7wDw5H1pG9T50xePshdOAwBesaT0SwKm7fRPGl3594rPqeFdX3Hv8a38Xg3SKD1aVnfwwcOR7XL51D0bUrqKmqhLOLC/zatUffITF4bezbcDN4qp5JGlBhffz5W3tdHbIOpdZ7JiCkO4P1nxAcGY3gyGjVMzQnoEMwJs5arHqGGNOmT8O06dNUz1CiX8wU9IuZonrGc+PbGohIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDJ3dbm/8YQcHO5pwviVwcm6NP2sfqp6hOc7OzqitrVU9Q3McnZzx6E/+d6lHpt1u79XQoVZN+iftdsxKOvLMi15E66YORvrZdNUzNKdv7774+qhF9QzNmTEoBMPnbVQ9Q3PSVsQ16hyvhEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGIwWEQkBoNFRGI07Q+pKlJTVY5r507gxoV0WIvzUVVmhWMrJ3gHdEDowKEIGzAMOge2FwDS0tKwZPESAMD8BfMRMzpG8aLmt3fTahRYLqG06Aaqysvg1FoPk58/ug94HVGjJ8Pd6KV6ohK3rmTibmEuKkqLUFlaBFvtA/iH9UFE9FTV0xpNRLCuZhzDr9u+hJvRG+26RMCjly+qy8uQd+44jiSvQcHFMxg+YzF0Op3qqUrdLrmNNavXwNXVFdXV1arnKHNk91YEdg5Fl5794eHpjdoHNci/nIWftn6FEwdSMHf9Lph826qe2ezyTqWhsrQIjs6toffwgu1OiepJTSYiWF5+7RD9/lJ06NbviVdS/cdNxc5l7yEv8zjyMo+jc69XFa5Uy263Y+lnS2E0GhH1WhS2f7dd9SRl1h7IhJNz66ce/zFpLX7e/g0Ofr8REz+Mb/5hioUOHg+9hydcvXxxtzAX6Tu+UD2pyUTcowK79kDHiP5PXfvcjCaER40EABRbslVM04yUnSnIyMjAwkUL4eLionqOUvXFCgB6Rr0BACgtLmjOOZrhbQ6Bm8lP9E1ERLD+iaPj4xeJOkdHxUvUyc/Px4b1GxA7IRY9Xumheo5mXTh1FAAQ0DFE8RJ6ViKuhP9O3aNHuHzqEACg/cu9Fa9Rw2azIX5xPPz8/DBj5gzVczTlUEoSHtZUo+Z+JQpyL+HaxUwEdAzB0InTVU+jZyQ6WCd3J+JOcT7ah/eFuYUGK2lzEnItudiUuAl6vV71HE05vGsLKsqsf30d2icSU+augIenSeEqeh5ig5V1eA/O/fIDvNoGYeg781TPUSInJwdbk7di0uRJCO8WrnqO5qxMPQkAqLhrxfWc89ib+DkS4kZj5vKNCAoOU7yOnoXIn2FlH92H33ash8nfjHEfr4He3aB6UrOz2WyIXxSPwKBAxL0bp3qOphlMLyEicgg+WLUF9yvuIXnFJ6on0TMS9wrr/KFUHNu5Ad4BHTD2o9VwNbTMNwHW1NSgsLAQABA5ILLeMwnLE5CwPAGxE2Ixe87s5pynSd5tAtDG3AlFeZdRVX4X7kZeDaURFayMtB04mboZPoGdMGbOKrh4GFVPUsbJyQmjYkbV+5zligUWiwXdI7rDbDYjPJzXxX8pv1MKANA5tNzfKksmJljp+7fh9L5k+JqDMWb2yhZ5Dfw7vV6PBZ8uqPe5xE2JsFgsGDFiRIv7aE5J4TW4uBtgNPk88XhdXR32f7sOlWV30DGsB9xa8Dc7yUQE64+TB3F6XzJ0Dg7wDw5H1pG9T50xePshdOAwBetIS3LOHMeejavRuVsv+PgHwc3giYoyK65mn4X11k0YTD54a84y1TOVKMnNwu3cLADAw/vlAIB7xdeRfSAZAODs6o6ug95UNa9RRASrwvr4M0/2ujpkHUqt90xASHcGi9ClZ38MHDke1y+dQ9G1K6ipqoSziwv82rVH3yExeG3s23AzeKqeqUTF7ZsovvT7E49V37Oi+t7jt364GLwZrP+EfjFT0C9miuoZYkybPg3Tpk9TPUOJgA7BmDhrseoZmhQcGY3gyGjVM56LyLc1EFHLxGARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJobPb7Y0+7ODgYG/K+ZbA2dkZtbW1qmdoTivn1rDVPlQ9Q3McWjmhzvan6hlalGm323s1dKhVU/5Fu92O9LPpzz7pBdS3d1/MSjqieobmrJs6GMPnbVQ9Q3PSVsTh66MW1TM0Z8agkEad45WQiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIjCb9IVUtSUtLw5LFSwAA8xfMR8zoGMWLmldNVTmunTuBGxfSYS3OR1WZFY6tnOAd0AGhA4cibMAw6Bxa5vejW1cycbcwFxWlRagsLYKt9gH8w/ogInqq6mlK7d20GgWWSygtuoGq8jI4tdbD5OeP7gNeR9ToyXA3eqme2CCRwbpdchtrVq+Bq6srqqurVc9R4mrGMfy67Uu4Gb3RrksEPHr5orq8DHnnjuNI8hoUXDyD4TMWQ6fTqZ7a7PJOpaGytAiOzq2h9/CC7U6J6kmacGT3VgR2DkWXnv3h4emN2gc1yL+chZ+2foUTB1Iwd/0umHzbqp75j8QFy263Y+lnS2E0GhH1WhS2f7dd9SQlvPzaIfr9pejQrd8Tr6T6j5uKncveQ17mceRlHkfnXq8qXKlG6ODx0Ht4wtXLF3cLc5G+4wvVkzRh7YFMODm3furxH5PW4uft3+Dg9xsx8cP45h/WBOLuDCk7U5CRkYGFixbCxcVF9RxlArv2QMeI/k9d+9yMJoRHjQQAFFuyVUxTztscAjeTX4t8dflP6osVAPSMegMAUFpc0JxznomoYOXn52PD+g2InRCLHq/0UD1HsxwdH79w1jk6Kl5CElw4dRQAENAxRPGShom5EtpsNsQvjoefnx9mzJyheo5m1T16hMunDgEA2r/cW/Ea0qJDKUl4WFONmvuVKMi9hGsXMxHQMQRDJ05XPa1BYoKVtDkJuZZcbErcBL1er3qOZp3cnYg7xfloH94XZgaL6nF41xZUlFn/+jq0TySmzF0BD0+TwlWNIyJYOTk52Jq8FZMmT0J4t3DVczQr6/AenPvlB3i1DcLQd+apnkMatTL1JACg4q4V13POY2/i50iIG42ZyzciKDhM8bp/pvmfYdlsNsQvikdgUCDi3o1TPUezso/uw2871sPkb8a4j9dA725QPYk0zmB6CRGRQ/DBqi24X3EPySs+UT2pQZp/hVVTU4PCwkIAQOSAyHrPJCxPQMLyBMROiMXsObObc54mnD+UimM7N8A7oAPGfrQargbtvwGQtMO7TQDamDuhKO8yqsrvwt2o3auh5oPl5OSEUTGj6n3OcsUCi8WC7hHdYTabER7e8q6LGWk7cDJ1M3wCO2HMnFVw8TCqnkQCld8pBQDoHLT9m2XNB0uv12PBpwvqfS5xUyIsFgtGjBjR4j6aAwDp+7fh9L5k+JqDMWb2Sl4D6d8qKbwGF3cDjCafJx6vq6vD/m/XobLsDjqG9YCbxr/haT5YVL8/Th7E6X3J0Dk4wD84HFlH9j51xuDth9CBwxSsU6skNwu3c7MAAA/vlwMA7hVfR/aBZACAs6s7ug56U9U8JXLOHMeejavRuVsv+PgHwc3giYoyK65mn4X11k0YTD54a84y1TMbxGAJVWF9/Pk4e10dsg6l1nsmIKR7iwxWxe2bKL70+xOPVd+zovre41/luxi8W1ywuvTsj4Ejx+P6pXMounYFNVWVcHZxgV+79ug7JAavjX0bbgZP1TMbJDpY06ZPw7Tp01TPUKJfzBT0i5mieoYmBUdGIzgyWvUMTQnoEIyJsxarnvHcNP+2BiKif2GwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxGCwiEgMBouIxNDZ7fZGH3ZwcLA35XxL4OjkjEd/1qqeoTkOrZxQZ/tT9QzNcXJujT9rH6qeoUWZdru9V0OHWjXlX7Tb7fj6qOXZJ72AZgwKwfB5G1XP0Jy0FXGYlXRE9QzNWTd1MNLPpqueoTl9e/dt1DleCYlIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRgsIhIDAaLiMRo0h9SVWnvptUosFxCadENVJWXwam1HiY/f3Qf8DqiRk+Gu9FL9cRmd+tKJu4W5qKitAiVpUWw1T6Af1gfRERPVT1NmZqqclw7dwI3LqTDWpyPqjIrHFs5wTugA0IHDkXYgGHQOfD7NACkpaVhyeIlAID5C+YjZnSM4kUNExOsI7u3IrBzKLr07A8PT2/UPqhB/uUs/LT1K5w4kIK563fB5NtW9cxmlXcqDZWlRXB0bg29hxdsd0pUT1LuasYx/LrtS7gZvdGuSwQ8evmiurwMeeeO40jyGhRcPIPhMxZDp9OpnqrU7ZLbWLN6DVxdXVFdXa16TqOJCdbaA5lwcm791OM/Jq3Fz9u/wcHvN2Lih/HNP0yh0MHjoffwhKuXL+4W5iJ9xxeqJynn5dcO0e8vRYdu/Z54JdV/3FTsXPYe8jKPIy/zODr3elXhSrXsdjuWfrYURqMRUa9FYft321VPajQxr43rixUA9Ix6AwBQWlzQnHM0wdscAjeTX4t/tfB3gV17oGNE/6eufW5GE8KjRgIAii3ZKqZpRsrOFGRkZGDhooVwcXFRPadJxATr37lw6igAIKBjiOIlpHWOjo8vFDpHR8VL1MnPz8eG9RsQOyEWPV7poXpOk4m5Ev7LoZQkPKypRs39ShTkXsK1i5kI6BiCoROnq55GGlb36BEunzoEAGj/cm/Fa9Sw2WyIXxwPPz8/zJg5Q/WcZyIuWId3bUFFmfWvr0P7RGLK3BXw8DQpXEVad3J3Iu4U56N9eF+YW2iwkjYnIdeSi02Jm6DX61XPeSbigrUy9SQAoOKuFddzzmNv4udIiBuNmcs3Iig4TPE60qKsw3tw7pcf4NU2CEPfmad6jhI5OTnYmrwVkyZPQni3cNVznpnYn2EZTC8hInIIPli1Bfcr7iF5xSeqJ5EGZR/dh992rIfJ34xxH6+B3t2gelKzs9lsiF8Uj8CgQMS9G6d6znMR9wrr//NuE4A25k4oyruMqvK7cDfyakiPnT+UimM7N8A7oAPGfrQaroaW9+ZiAKipqUFhYSEAIHJAZL1nEpYnIGF5AmInxGL2nNnNOa9JxAcLAMrvlAIAdA4t97c/9KSMtB04mboZPoGdMGbOKrh4GFVPUsbJyQmjYkbV+5zligUWiwXdI7rDbDYjPFzb10URwSopvAYXdwOMJp8nHq+rq8P+b9ehsuwOOob1gFsL/p+S/k/6/m04vS8ZvuZgjJm9skVeA/9Or9djwacL6n0ucVMiLBYLRowYwY/m/KfknDmOPRtXo3O3XvDxD4KbwRMVZVZczT4L662bMJh88NacZapnNruS3Czczs0CADy8Xw4AuFd8HdkHkgEAzq7u6DroTVXzlPjj5EGc3pcMnYMD/IPDkXVk71NnDN5+CB04TME6el4igtWlZ38MHDke1y+dQ9G1K6ipqoSziwv82rVH3yExeG3s23AzeKqe2ewqbt9E8aXfn3is+p4V1fcev+3DxeDd4oJVYX38eUp7XR2yDqXWeyYgpDuDJZSIYAV0CMbEWYtVz9Cc4MhoBEdGq56hKf1ipqBfzBTVM8SYNn0apk2fpnpGo4l9WwMRtTwMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRgMFhGJwWARkRg6u93e+MM63f8AKPjvzSGiFspst9t9GjrUpGAREanEKyERicFgEZEYDBYRicFgEZEYDBYRicFgEZEYDBYRicFgEZEYDBYRifG/j8CLNfGqriQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz(easy_ans.astype(int),\n",
    "    {1: '#4a7899',\n",
    " 2: '#6f9dbd',\n",
    " 3: '#97bed9',\n",
    " 4: '#c9cbc9'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "medium=np.array([\n",
    "[0,0,7, 8,0,5, 2,0,0],\n",
    "[8,0,0, 6,0,4, 0,0,5],\n",
    "[0,1,0, 0,9,0, 0,8,0],\n",
    "[4,0,0, 2,8,9, 0,0,7],\n",
    "[0,0,0, 0,0,0, 0,0,0],\n",
    "[5,0,0, 7,6,1, 0,0,2],\n",
    "[0,7,0, 0,3,0, 0,6,0],\n",
    "[3,0,0, 1,0,6, 0,0,4],\n",
    "[0,0,2, 5,0,8, 1,0,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "medium_ans=sudoku_ans(medium)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAAElCAYAAABect+9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzsnXlYlOe9/j8MszMwMOyLwCAqhsYVJYqKUaMmhhiJTaJJPMYsPdW0JzU9aWwvuyQ5J41pTtvUND3NdbK5NOqVGiIe3EUUXFBUFBHZkVVAVoHZmN8fI/xEJok5mWco6fv5xyvv85B71nveZ/veHna7HQkJCYnhgGyoH4CEhITEnSIZloSExLBBMiwJCYlhg2RYEhISwwbJsCQkJIYNkmFJSEgMGyTDkpCQGDZIhiUhITFskAxLQkJi2CAZloSExLBB/k06e3h42CfcFSvqsXwl5y6VEB1uGBLtiprrjBwRPCTapVcbiBsZMSTal0urUciH5jfNYu3FX68ZEu3mtm7GxcUMiXb+5TJGhPoMifbVunbCg7yHRLvmWkeT3W4P/Lp+Ht/kLKGHh4f9+rld3+qB/V8xTEjhkzefHBLtFT/bzOcbXxoS7YdfeJtTn709JNpTH3mJiOCh+QBXN3SwcvG4IdH+KC2fupOfDol2aOLjbFx//5Bov/BaBm+8eO+QaK/7w+Ezdrs94ev6SUNCCQmJYYNkWBISEsMGybAkJCSGDZJhSUhIDBu+0SrhN8Fut7Ml7QAff7aXotIqbL02YqMiWL54Ls8+tghPT09R0qz97U6aWm44bdPr1Pxp/VJh2n0UlFSz63AeReW1dHT14K1VExkWQMq9k0iId/0KVPqhU7z67rav7COTeXBix+9crg3Q1WPBZLZhsfZisdqw20GrlmMQvNLXY7ZSVddGdX0HLR09dHVbkMk88PNRExtpYFSkHx4eHkIfw4Fjeby/LYPi8hpa2jsI8vdjXJyRHyxfRMLdo4Vq386p/Bo+ScsHYPmD32P6xBFCdDKOllJzrZ2mlm5udFtQyGX4+qi5a2QA08ZH4KVRCNEVZlir1/+ebemHCTT48vCCGWjVao6cPMe6De+Tk1fAR2+9IvSDpFUrmD8jbtB1tVLMC3kr2/ecYGt6Nj46DQnxMfjpvWjv7Ka8+hoXi68KMazRxnCefXS+07ZzhWWcvlDCtImDXw9X0XHDjMXai4cHeMpkWG29wrRupaKmjRP5NWhUckIDdXiFKeg2WamsbSPnXDU1DR3MnhIp7LP2+sYtvLtpF356b+5PTsDg60351Xr2Zp1m9+FTvPOr1Sy9f6YQ7dtpaetmx55LqJSemMw2oVrZZ68SFuRNbKQfOq0Ss8VGVX07B09UkHuhlh8+Phlfb7XLdYUY1u5Dx9mWfpio8GAObH4bfz89ABaLlVUvv8muAzn87YuDLF88T4Q8AFqNktT7xgv7/38Z2XlFbE3PZvyYSF55bjEatXJAu9Um5oM02hjOaGO407ZV694BYMl99wjRBtB7q/CUyZB7emCy2Ghq6RamNUBXp2JuYjQRwd4DTGnS2BB2Z5VQWddGZV070WF6l2tfa27lvS3pBBr0HNqygQDD/9fIPl3A0jWv8dZfd7jFsOx2O5t3XcBLq2B8XAgHj5cL1fvV6pko5INHSXuzy8jMrSQzt5KH54xxua6QOaz0Q8cBWPPUkn6zAlAo5Kxb49hL9f6n6SKkh5TeXjufpB1FpZSzduWiQWYFIBc4FHZGaVUdF69UEmTQkzTpLmE6aqUchVwmfPh1O6GBOkaE+AzS1aoVjIn2B6C+qVOIdnVdI729dibFxw4wK4CkhHh0Wg3Nre1CtG8n81QlV8qbeTJlHEqF+M+YM7MCGDc6CIDmVjE/WELusBqaWgCIihi8Ozw63HHtfGEpbe2d6H10Ih4CFquN7Lwymlu7UCnljAj1Jc4YhEwmbp3hcnkNDc1tTJ84Gp1WzemLZVTVNaGQyxkVFUJcTJgw7S/j7/scPx4PzZ2Kp+c/1xqLzKPvXzEmahwRilIh5+ylUppb2/H3/f871I+fLaSzq5uFyVOEaN9KfWMnXxwqYnZiNLFRBooqmoVrfhmFZU0AhASI+V4LMay+N66qpmFQW8Ut165UVDNlnJh5lbaOHv57W86Aa4EGHc99fxpxMWKO2ZRUOp6br7eWtW9uorK2aUB7fGwELz+Tgt5bK0T/dnpMFvZk5SGTebB4XqJbNP9R6O21U3K1FYBwQbv1/fQ6frFmOb/+4yaSH/8pC2cl4Kf3prKmgX1HzzBr6t289cqzQrT7sPX28nHaefx8NKTc694JfoCsM1WYzTZ6zFZqGjqoqG0jJMCL5IRIIXpCDGvBrCl8tieLP29OI3XhLPz0jg+M1Wrjt+9t6e/X2i7mVn3m5JGMMQYRHqxHrVLQeL2T/TlFZJ4q5ncfHOKXqxcSGebnct22ji4A9hw7T7C/nt/8aCmjo0NpvN7Oh38/wtnCCjb8zy7+48XHXK7tjAM55+i40U3S5LEEB7j++f4jc+ZSHa0dPUQEews9H/f8sgcYERbI2tf/wpa0Q/3XjREhPPZg8qChoqvJyCqhur6dn6y8xy1Dwds5euYqnV3m/v8eHWVg6fyx6LSDp0NcgRDDSl04i+27MzmQfYZpqatZmJyIRq3iyMlzVFTXMzIyjNKqWjwFDc+W3DfwDFpEiC9PpyaiVsrJOFrIzgP5/NuKZJfr2uw3V8bs8PIzKRgjHOP5yNAAXnnuIVa/+gEFJdVcLqt1y/Dw8/0nAEi9b5pwrX8kLpU2UVDahF6nYuYkMcv6fby76QveeO9Tnnl0Iau+v4BAf19KKmr5zz//jTW/3EjBlUrW/+gJIdoVNa3sO1bG3HuMxEQMzQ/SL55PAhyrxFV1bezJLuVPW3P5l8XjhPxQCHEMmUzG1j+u59W1qwjy92P77sNsSdtPWHAA//vhm/j5Op5IoMFXhPyXMucexy3z5fLBQ1VXoNM4lnGDA/T9ZtWHSqlg4thoAIor64Xo30rZ1XryiyoI8tczfdJY4Xr/KBSWNXHqYi2+3ioWJMWgUgrbuUPOmQJe37iV+TMn85sXVxAVHoxWrWJcnJEPNrxEaKCBv2xNp9LJ1Mi3xdbbyyef5xPkr2XR7FEu//9/U7y9lMTHBrJqyQS6eizs2FsoREfYuymXe/LCiiW8sGLJgOvdPSYuFpWjUSuJGylmnPtl+OhUAJjNViH///BgR/kbL43KabtO6zA0s8UiRP9Wdu5z3F09NDfxn2ayvaC0kdyLdfh6q1mQFINGJc6sAPYfywMgaXL8oDatWsWE+JFkZOZyoaiCqHDXzpuazDauXXdsjv7JG/uc9tmafpGt6ReZPTWKpQvErRDfip+PmiCDF3WNndzoNuOlce3QUOw76oRt6YfpMZlZljIHhcK98sWVjknwQIOYOY342HA8ZTJqG1uxWG2Dln6r6hz6QYLnNUxmCxlZpx2T7XOnCtX6R+FC8TXOXKrHoFczf1oMasFmBWC2OH74mlucb13ou64U8DmXe8qYNsF5nbSr9e1U17czcoQfQf5eGN08XOy4YQLErM4Ke1fbO7vw0Q1cDcu7eIVX3/kYnVbDv/9gmRDd6vpWfH006LQD73KaWjrZlJYLwPSJRiHaPjotMyaP4UhuIdszjvNEyoz+tnOFFZwtrECrUTHxrmgh+n0czDlPe2c3Mybf9U8x2X6+qIGzlxvw12uYP90odBh4K4kT4vhgx142f36Qp5bMIzTo/xeYPJhzltz8K6hVChLGuX71Tqnw5ImUu5227T5STHV9O4njw4Uczbl2/QYalRxvr4HfsV67nf055XR2WYgK9UGjdv2pEmHvbOq/rkejUjI2Ngqdl4bLpVXsP3YalULBx//1c6IjQoTonrpQye7MAsbGhBBg0KFRybnW3Mm5yzVYrDbGx4XxwCxxczpPp87mSkUdO/aepKCkmlFRITS2dHDifDEyDxlrlt3XPzQUxc4DjuGgyJ3tt9PdY6Hb5LjjsPU6ikKaLDautzk2EMpkHkKOapRUXefs5QY8PCDY34tLZU2D+ui0SkZFur5a7YNzEpk19W6yTl1g1mMvcf/sKQT56ymuqGX/sTzsdjs/X70Mg35oiiCK4krFdTKOlWIM12PQa9CqFXR2mSmvaeV6Ww/eWiVL5onZriTMsB6al8TOvVls351Jj8lESKCBp5bM58WnlxLp4vH8rdw1MoT6xnYqa1soqWrEZLai1SgZHR1I0qQYkiYZhe7G9vXWsuGny9mx5yQn8ou5UlGHRqUkIT6GR+ZPZYxR7OpgeXUD5wvL3T7Zbrb20tUzcG7QZrPTZXNc85R54Cvge9txc0ndbsepWYHDyEQYlkwmY/Pvf8aHO/aRtj+HjMxcuk0mfH10zJ0+gWceXcjse9x/PEw0sZF+TP1eGJW1bdQ1NtFjsqJQyAjw0zI3LoTpEyPQCri7AoGG9eOVqfx4Zaqo//2XEhcTLGxj6J3i7aVh1SOzWfXIbLdrGyOCh6Sksl6nQq9zvtggkolxIUyME3O3fico5HKeX/YAzy97YMgew+0sSh7FomRxK4chAToWz3H/JlWQ6mFJSEgMIyTDkpCQGDZIhiUhITFskAxLQkJi2CAZloSExLBBMiwJCYlhg2RYEhISwwbJsCQkJIYNkmFJSEgMGzzsdvsdd5bJZPZv0t+VKOQyLFb3REfdjlLhidkiNjbpy7Xl/VUB3I2Hh+PIy1DgKfPoP5PoblRKBSaz+BJAzpDLZViH6HMu93RfPJsTztjt9oSv6/SNjubY7XbeePHe//tD+has+8NhIgTV5v46qhs6qDv56ZBohyY+zidvPjkk2it+tpnr53YNibZhQgob198/JNovvJbB5xtfGhLth194m5WLx319RwF8lJY/JMe6AKY+cmevtzQklJCQGDZIhiUhITFskAxLQkJi2CAZloSExLBBMiwJCYlhg7ACfhlHS6m51k5TSzc3ui0o5DJ8fdTcNTKAaeMj8NKIqUgI0NVjwWS2YbH2YrHasNtBq5Zj0GuEad7KgWN5vL8tg+LyGlraOwjy92NcnJEfLF9Ewt3iCp+t/e1OmlpuOG3T69T8af1SYdp2u50taQf4+LO9FJVWYeu1ERsVwfLFc3n2sUV4ero35PNUfg2fpOUDsPzB7wmpbX4rBSXV7DqcR1F5LR1dPXhr1USGBZBy7yQS4mNcrtdjtlJV10Z1fQctHT10dVuQyTzw81ETG2lgVKSfsMq66YdO8eq7276yj0zmwYkdv3O5tjDDyj57lbAgb2Ij/dBplZgtNqrq2zl4ooLcC7X88PHJQmp8gyPU0WLtxcMDPGXu3Vvy+sYtvLtpF356b+5PTsDg60351Xr2Zp1m9+FTvPOr1Sy9f6Ywfa1awfwZg+tpq5XifiAAVq//PdvSDxNo8OXhBTPQqtUcOXmOdRveJyevgI/eekVoaepbaWnrZseeS6iUnpjM4vfPbd9zgq3p2fjoNCTEx+Cn96K9s5vy6mtcLL4qxLAqato4kV+DRiUnNFCHV5iCbpOVyto2cs5VU9PQwewpkUJe89HGcJ59dL7TtnOFZZy+UMK0icOspvuvVs8cFHMFsDe7jMzcSjJzK3l4zhgh2npvFZ4yGXJPD0wWG00t3UJ0budacyvvbUkn0KDn0JYNA2LKs08XsHTNa7z11x1iDUujJPU+99YR333oONvSDxMVHsyBzW/j7+d43haLlVUvv8muAzn87YuDLF88T/hjsdvtbN51AS+tgvFxIRw8Xi5ULzuviK3p2YwfE8krzy1Gox6Yw2e1iTFMvU7F3MRoIoK9B5jSpLEh7M4qobKujcq6dqLDXB8pN9oYzmhjuNO2VeveAcQFoAibw3JmVgDjRjsSkZtbxZmIWilHIZe57Re9j+q6Rnp77UyKjx1gVgBJCfHotBqaW51n2A1n0g8dB2DNU0v6zQpAoZCzbo1j0+v7n6a75bFknqrkSnkzT6aMQ6kQOwzt7bXzSdpRVEo5a1cuGmRWAHJBQ+HQQB0jQnwGfca1agVjov0BqG/qFKL9ZZRW1XHxSiVBBj1Jk8QEt7o9SLXwZrJJSIDO3dLCMY4IRamQc/ZSKc2t7fj7+vS3HT9bSGdXNwuTpwh9DBarjey8Mppbu1Ap5YwI9SXOGIRMJm59paGpBYCoiMHhH9E3E5LOF5bS1t6J3kfc+17f2MkXh4qYnRhNbJSBoopmYVoAl8traGhuY/rE0ei0ak5fLKOqrgmFXM6oqBDiYsQmJH0ZMo++f937g/33fY4frofmThWWNi7csLLOVGE22+gxW6lp6KCito2QAC+SE9wbU+8O/PQ6frFmOb/+4yaSH/8pC2cl4Kf3prKmgX1HzzBr6t289cqzQh9DW0cP/70tZ8C1QIOO574/TViaUJ8xV9U0DGqruOXalYpqpowTM7dh6+3l47Tz+PloSLnXPYkuJZWO5+brrWXtm5uorB0YMxYfG8HLz6Sg99Y6+3Mh9PbaKbnaCkC4G4+y9Zgs7MnKc6SNz0sUpiPcsI6euUrnzew4gNFRBpbOH4tOO/j2+bvA88seYERYIGtf/wtb0g71XzdGhPDYg8mDhoquZObkkYwxBhEerEetUtB4vZP9OUVknirmdx8c4perFxIZ5vok6AWzpvDZniz+vDmN1IWz8LsZHGq12vjte1v6+7W2ixuiZGSVUF3fzk9W3iN8KNhHW0cXAHuOnSfYX89vfrSU0dGhNF5v58O/H+FsYQUb/mcX//HiY255PABnLtXR2tFDRLA34UHuM6wDOefouNFN0uSxQtPGhRvWL55PAhwrd1V1bezJLuVPW3P5l8Xj3PqCuot3N33BG+99yjOPLmTV9xcQ6O9LSUUt//nnv7HmlxspuFLJ+h89IUR7yX0DD81GhPjydGoiaqWcjKOF7DyQz7+tSHa5burCWWzfncmB7DNMS13NwuRENGoVR06eo6K6npGRYZRW1eIpaFhaUdPKvmNlzL3HSEyEuC/L7djsN1ef7fDyMykYIxzzs5GhAbzy3EOsfvUDCkqquVxW65bh4aXSJgpKm9DrVMycJHYbx+18vt+RNp563zShOm7bOOrtpSQ+NpBVSybQ1WNhx95Cd0m7jZwzBby+cSvzZ07mNy+uICo8GK1axbg4Ix9seInQQAN/2ZpOpZOhk0jm3OMYIl0uF6Mrk8nY+sf1vLp2FUH+fmzffZgtafsJCw7gfz98E7+bkc+BBl+Xa9t6e/nk83yC/LUsmi0uPNQZOo1jW05wgL7frPpQKRVMHBsNQHFlvfDHUljWxKmLtfh6q1iQFINK6b7p6bKr9eQXVbglbdztk+5+PmqCDF7UNXZyo9uMl+a7MzTcfywPgKTJ8YPatGoVE+JHkpGZy4WiCqLC3ZdO7XMzkdlsFldXSy735IUVS3hhxZIB17t7TFwsKkejVhI30vXzliazjWvXHZtlf/LGPqd9tqZfZGv6RWZPjWLpAtetXoUHGwDw0jhPvNZpHYZmtoitrVVQ2kjuxTp8vdUsSIpBo3Lv13rnPsfd1UNzE4VNtvfhdsMC6LhhAty/iiGavkJ7zS3Oty70XVcq3PuyF1c6JoMDDe4fgm9LP0yPycyylDkoBDxvuaeMaRMinLZdrW+nur6dkSP8CPL3wuji4WJ8bDieMhm1ja1YrLZBW3mq6hyve5DAecsLxdc4c6keg17N/GkxqN1sViazhYys047J9rlThesJeXbXrt9Ao5Lj7TXwl6fXbmd/TjmdXRaiQn3QqMXuvnY3iRPi+GDHXjZ/fpCnlswjNMjQ33Yw5yy5+VdQqxQkjHP9KlZ1fSu+Php02oGveVNLJ5vScgGYPtHoct0+2ju78NENXA3Lu3iFV9/5GJ1Ww7//YJkQXaXCkydS7nbatvtIMdX17SSODxdyNMdHp2XG5DEcyS1ke8ZxnkiZ0d92rrCCs4UVaDUqJt4V7XJtgPNFDZy93IC/XsP86Ua3DgP7OJhznvbObmZMvkvoZHsfQp7hlYrrZBwrxRiux6DXoFUr6OwyU17TyvW2Hry1SpbME7O8DdDdY6Hb5Ljb6Suza7LYuN7m2Kwqk3kIORb04JxEZk29m6xTF5j12EvcP3sKQf56iitq2X8sD7vdzs9XL8Ogd/2dzqkLlezOLGBsTAgBBh0alZxrzZ2cu1yDxWpjfFwYD8wSN7+Q+q/r0aiUjI2NQuel4XJpFfuPnUalUPDxf/2c6IgQYdpDydOps7lSUceOvScpKKlmVFQIjS0dnDhfjMxDxppl9/UPDV1JSdV1zl5uwMMDgv29uFTWNKiPTqtkVKTByV+7jp0HHMNBUTvbb0eIYcVG+jH1e2FU1rZR19hEj8mKQiEjwE/L3LgQpk+MQCvw7sps7aWrZ+B8jc1mp8vmuOYp88BXwOhIJpOx+fc/48Md+0jbn0NGZi7dJhO+PjrmTp/AM48uZPY9Yo7N3DUyhPrGdiprWyipasRktqLVKBkdHUjSpBiSJhmF7vx/aF4SO/dmsX13Jj0mEyGBBp5aMp8Xn15KpBvn69yNr7eWDT9dzo49JzmRX8yVijo0KiUJ8TE8Mn8qY4xiVgc7bm4VsttxalbgMDKRhlVe3cD5wnK3TLb3IcSwQgJ0LJ7jns17ztDrVOh1zidCRaOQy3l+2QM8v+wBt+rGxQQL2xh6J/x4ZSo/Xpk6ZPrOWJQ8ikXJ4lcOvb00rHpkNqsemS1cq4+JcSFMjBvau1ZjRLDba8BL9bAkJCSGDZJhSUhIDBskw5KQkBg2SIYlISExbJAMS0JCYtggGZaEhMSwQTIsCQmJYYNkWBISEsMGD7vdfsedZbJv1N2leHg4dvUOBSqlApNZ7In7L0Mh98RiFZ/84oyhfN5yuQyr1X1pR7cylK+5p6cHNtvQfNCVCnn/Af4h4Izdbk/4uk7faKe73Q4rF4/7+o4C+Cgt3+27avuY+shLbFx//5Bov/BaBp9vfGlItB9+4W3qTn46JNqhiY/zxov3Don2uj8c5pM3nxwS7RU/28z1c7uGRNswIYUIN5ZVvpXqho476icNCSUkJIYNkmFJSEgMGyTDkpCQGDZIhiUhITFskAxLQkJi2CCkHlaP2UpVXRvV9R20dPTQ1W1BJvPAz0dNbKSBUZF+worJpR86xavvbvvKPjKZByd2/E6IvjNO5dfwSVo+AMsf/J6Qcr23UlBSza7DeRSV19LR1YO3Vk1kWAAp904iIT5GmO6BY3m8vy2D4vIaWto7CPL3Y1yckR8sX0TC3eLqo2UcLaXmWjtNLd3c6LagkMvw9VFz18gApo2PwEsjrljk2t/upKnlhtM2vU7Nn9YvFaZtt9vZknaAjz/bS1FpFbZeG7FRESxfPJdnH1uEp6e4fMauHgsmsw2LtReL1YbdDlq1HINeI0wTBBlWRU0bJ/Jr0KjkhAbq8ApT0G2yUlnbRs65amoaOpg9JVKIaY02hvPso/Odtp0rLOP0hRKmTRRXnvl2Wtq62bHnEiqlJyaz+L092/ecYGt6Nj46DQnxMfjpvWjv7Ka8+hoXi68KM6zXN27h3U278NN7c39yAgZfb8qv1rM36zS7D5/inV+tZun9M4VoZ5+9SliQN7GRfui0SswWG1X17Rw8UUHuhVp++PhkISWx+9CqFcyfMfgzpVaKzSxYvf73bEs/TKDBl4cXzECrVnPk5DnWbXifnLwCPnrrFWE3Bh03zFisvXh4gKdMhtXmnj1zQgxLr1MxNzGaiGDvAS/YpLEh7M4qobKujcq6dqLDXJ8mMtoYzmhjuNO2VeveAdxXf9put7N51wW8tArGx4Vw8Hi5UL3svCK2pmczfkwkrzy3GI16YISa1SbGMK81t/LelnQCDXoObdkwIN06+3QBS9e8xlt/3SHMsH61euagxBqAvdllZOZWkplbycNzxgjRBtBqlKTeJ6b09Zex+9BxtqUfJio8mAOb38bfz/GaWyxWVr38JrsO5PC3Lw6yfPE8Ifp6bxWeMhlyTw9MFhtNLd1CdG5HyBxWaKCOESE+g9xdq1YwJtofgPomcbHlziitquPilUqCDHqSJrkum+6ryDxVyZXyZp5MGSc8Pr23184naUdRKeWsXblokFkByAUNEarrGunttTMpPnaAWQEkJcSj02pobnUefeYKnJkVwLjRjnDT5lb3fJncSfqh4wCseWpJv1kBKBRy1q1xbHp9/9N0YfpqpRyFXCY0J8AZbs8Fknn0/eveJ/r3fY43+KG5U4WHPQLUN3byxaEiZidGExtloKiiWaje5fIaGprbmD5xNDqtmtMXy6iqa0IhlzMqKkRoVLpxRChKhZyzl0ppbm3H39env+342UI6u7pZmDxFmP6XUXgznCEkQCdUx2K1kZ1XRnNrFyqlnBGhvsQZg5DJxH3OGppaAIiKGFzHP/pm6Mf5wlLa2jvR+4h9/u7ErYbV22un5GorAOFuPALQY7KwJyvPEfY4L1G4nq23l4/TzuPnoyHlXveEcZRUOmLofb21rH1zE5W1A5NU4mMjePmZFPTeWmd//q3w0+v4xZrl/PqPm0h+/KcsnJWAn96bypoG9h09w6ypd/PWK8+6XPd2ss5UYTbb6DFbqWnooKK2jZAAL5ITXJ84fSttHT3897acAdcCDTqe+/40YcEgfT8KVTUNg9oqbrl2paKaKePcN2crGrca1plLdbR29BAR7E14kPsM60DOOTpudJM0eaxbwh4zskqorm/nJyvvET4U7KOtowuAPcfOE+yv5zc/Wsro6FAar7fz4d+PcLawgg3/s4v/ePExIfrPL3uAEWGBrH39L2xJO9R/3RgRwmMPJg8aKorg6JmrdN6MvwIYHWVg6fyx6LSDh8euYubkkYwxBhEerEetUtB4vZP9OUVknirmdx8c4perFxIZ5vrP3IJZU/hsTxZ/3pxG6sJZ+N3MurRabfz2vS39/Vrb3Tv1Ihq3Gdal0iYKSpvQ61TMnCR2Wf92Pt/vCHtMvW+acK2Kmlb2HStj7j1GYlwcjf5V2Ow3V2ns8PIzKRgjHPM3kaEBvPLcQ6x+9QMKSqq5XFYrZHj47qYveOO9T3nm0YWs+v4CAv19Kamo5T///DfW/HIjBVdGVearAAAgAElEQVQqWf+jJ1yueyu/eD4JcKxgVdW1sSe7lD9tzeVfFo8T9gO55L6BxQAiQnx5OjURtVJOxtFCdh7I599WJLtcN3XhLLbvzuRA9hmmpa5mYXIiGrWKIyfPUVFdz8jIMEqravEUOCwdCtzybArLmjh1sRZfbxULkmLcGqlddrWe/KIKt4Q92np7+eTzfIL8tSyaLT4P71Z0GseyfXCAvt+s+lApFUwcGw1AcWW9y7VzzhTw+satzJ85md+8uIKo8GC0ahXj4ox8sOElQgMN/GVrOpVOhi8i8PZSEh8byKolE+jqsbBjb6FbdG9lzj2OqYDL5WKes0wmY+sf1/Pq2lUE+fuxffdhtqTtJyw4gP/98E38biYFBxp8hegPFcKdo6C0kdyLdfh6q1mQFING5d55/p37HHdXD81NFD7ZbjLbuHbdsYnwJ2/sc9pna/pFtqZfZPbUKJYucN1qZXiwI+HXS+M8QLYvLt1scX19q/3H8gBImhw/qE2rVjEhfiQZmblcKKogyo0p0H4+aoIMXtQ1dnKj24yXRtzQ8HZ8bgb5ms3i6kvJ5Z68sGIJL6xYMuB6d4+Ji0XlaNRK4kaKnb9zN0Ld40LxNc5cqsegVzN/WgxqN5uVyWwhI+u0Y7J97lThenJPGdMmRDhtu1rfTnV9OyNH+BHk74XRxcPF+NhwPGUyahtbsVhtg5b6q+ock/BBAuaS+oq+Nbc437rQd12pcPuiNB03TID7V6WLKx2vd6DB/fWltqUfpsdkZlnKHBRD8JqLRNizOV/UwNnLDfjrNcyfbnTrMLCPgznnae/sZsbku9wy2a5UePJEyt1O23YfKaa6vp3E8eFCjub46LTMmDyGI7mFbM84zhMpM/rbzhVWcLawAq1GxcS7ol2unTghjg927GXz5wd5ask8QoMM/W0Hc86Sm38FtUpBwjjXr5heu34DjUqOt9fAO8teu539OeV0dlmICvVBo3b9rvPq+lZ8fTTotAO1m1o62ZSWC8D0iUaX6/bR3tmFj27gqm/exSu8+s7H6LQa/v0Hy4RpDxVCXKSk6jpnLzfg4QHB/l5cKmsa1EenVTIq0uDkr13HzgOO4aC7drYPNU+nzuZKRR079p6koKSaUVEhNLZ0cOJ8MTIPGWuW3dc/NHQlD85JZNbUu8k6dYFZj73E/bOnEOSvp7iilv3H8rDb7fx89TIMetffbVypuE7GsVKM4XoMeg1atYLOLjPlNa1cb+vBW6tkyTwxy/qnLlSyO7OAsTEhBBh0aFRyrjV3cu5yDRarjfFxYTwwS9y8aeq/rkejUjI2Ngqdl4bLpVXsP3YalULBx//1c6IjQoRpd/dY6DY57qxtvY6SziaLjettjk26MpmHkONQQgyr4+bSst2OU7MCh5GJNKzy6gbOF5a7ZbL9HwVfby0bfrqcHXtOciK/mCsVdWhUShLiY3hk/lTGGMVsHpXJZGz+/c/4cMc+0vbnkJGZS7fJhK+PjrnTJ/DMowuZfY+YoyuxkX5M/V4YlbVt1DU20WOyolDICPDTMjcuhOkTI9AKuLsCuGtkCPWN7VTWtlBS1YjJbEWrUTI6OpCkSTEkTTIK3Qn+0Lwkdu7NYvvuTHpMJkICDTy1ZD4vPr2USMFzhWZrL109A+fnbDY7XTbHNU+ZB74CRsNCDGtiXAgT48S5+51gjAgeshrwzliUPIpFyeJXDr29NKx6ZDarHpktXOtWFHI5zy97gOeXPeBW3ZAAHYvnuGdz7u3ExQQL2xh6J/x4ZSo/Xpk6JNp6nQq9zvkCj0i+W5s0JCQkvtNIhiUhITFskAxLQkJi2CAZloSExLBBMiwJCYlhg2RYEhISwwbJsCQkJIYNkmFJSEgMGzzsdvsdd5Z5eHyD3q5FqZD3H7J1Nwq5DIvVPakgt6NUeGK2iE/bcYZKqcBkdn11hztB7umB1TY0n7ahfL+H8jX38HCcThkiztjt9oSv6/SNdrrbgU/efPL//Ii+DSt+tpmN6+8fEu0XXssYsl3zUx95ievndg2JtmFCCm+8eO+QaK/7w2Ei3FhG+1aqGzpYuXjc13cUwEdp+Xy+8aUh0X74hbepO/npkGiHJj5+R/2kIaGEhMSwQTIsCQmJYYNkWBISEsMGybAkJCSGDZJhSUhIDBuE1S1e+9udNLXccNqm16n50/qloqSdciq/hk/S8gFY/uD3hJQpTj90ilff3faVfWQyD07s+J3LtQHsdjtb0g7w8Wd7KSqtwtZrIzYqguWL5/LsY4vwFBRVD5BxtJSaa+00tXRzo9uCQi7D10fNXSMDmDY+Ai+NmCJ6AF09FkxmGxZrLxarDbsdtGo5Br1GmCZAj9lKVV0b1fUdtHT00NVtQSbzwM9HTWykgVGRfm6Jci8oqWbX4TyKymvp6OrBW6smMiyAlHsnkRAfI0z3wLE83t+WQXF5DS3tHQT5+zEuzsgPli8i4W4xNcqEFlrXqhXMnzG4PK1aKe7D64yWtm527LmESumJySxuT9NoYzjPPjrfadu5wjJOXyhh2kRxKbyr1/+ebemHCTT48vCCGWjVao6cPMe6De+Tk1fAR2+9IuwLlH32KmFB3sRG+qHTKjFbbFTVt3PwRAW5F2r54eOThZTMBUcOocXai4cHeMpkWG3u2UNVUdPGifwaNCo5oYE6vMIUdJusVNa2kXOumpqGDmZPiRRqWtv3nGBrejY+Og0J8TH46b1o7+ymvPoaF4uvCjOs1zdu4d1Nu/DTe3N/cgIGX2/Kr9azN+s0uw+f4p1frWbp/TNdrivWsDRKUu8TUxr3TrHb7WzedQEvrYLxcSEcPF4uTGu0MZzRxnCnbavWvQOIqy+/+9BxtqUfJio8mAOb38bfz5GOY7FYWfXym+w6kMPfvjjI8sXzhOj/avXMQUk9AHuzy8jMrSQzt5KH54wRoq33VuEpkyH39MBksdHU0i1EZ5CuTsXcxGgigr0HmNKksSHsziqhsq6Nyrp2osPEpF5n5xWxNT2b8WMieeW5xWjUA2PMrDYxP87Xmlt5b0s6gQY9h7ZsGJDqnX26gKVrXuOtv+4QYljf+TmszFOVXClv5smUcW6Ljb+d0qo6Ll6pJMigJ2mS67IIbyX90HEA1jy1pN+sABQKOevWODb7vv9puhBtwKlZAYwb7Qh1bW4VZyJqpRyFXOaW4dethAbqGBHiM0hXq1YwJtofgPomMVHxvb12Pkk7ikopZ+3KRYPMCkAuaAqguq6R3l47k+JjB5gVQFJCPDqthuZW55Fv3xahd1gWq43svDKaW7tQKeWMCPUlzhiEzE3x2fWNnXxxqIjZidHERhkoqmh2i+7t/H2fw0wemjtVWJhrQ1MLAFERg2uMR98MJDhfWEpbeyd6H52Qx+CMwpshJCEB7tP8R0Dm0fevGBO9XF5DQ3Mb0yeORqdVc/piGVV1TSjkckZFhRAXIyZwBMA4IhSlQs7ZS6U0t7bj7+vT33b8bCGdXd0sTJ4iRFuoYbV19PDf23IGXAs06Hju+9OEF++39fbycdp5/Hw0pNw7NCEFAD0mC3uy8hxhrvMShen0fWiqnMTBV9xy7UpFNVPGiZtHyzpThdlso8dspaahg4raNkICvEhO+G4lEH8Vvb12Sq62AhAu6HhRSaXjPfX11rL2zU1U1g5Mp4qPjeDlZ1LQe2ud/fm3wk+v4xdrlvPrP24i+fGfsnBWAn56byprGth39Ayzpt7NW68863JdEGhYMyePZIwxiPBgPWqVgsbrnezPKSLzVDG/++AQv1y9kMgwceGmGVklVNe385OV9wzZUBDgQM45Om50kzR5rNAw1wWzpvDZniz+vDmN1IWz8LuZAWi12vjte1v6+7W2ixmi9HH0zFU6b8a8AYyOMrB0/lh0WvfFxA81Zy7V0drRQ0SwN+FBYgyrraMLgD3HzhPsr+c3P1rK6OhQGq+38+Hfj3C2sIIN/7OL/3jxMSH6zy97gBFhgax9/S9sSTvUf90YEcJjDyYPGiq6CmGGteS+gYdHI0J8eTo1EbVSTsbRQnYeyOffViQL0a6oaWXfsTLm3mMkxsWR8N+Uz/c7wlxT75smVCd14Sy2787kQPYZpqWuZmFyIhq1iiMnz1FRXc/IyDBKq2rxFDwc/8XzSYBj5a6qro092aX8aWsu/7J4nLAv7z8Sl0qbKChtQq9TMXOS67fO9GGz31wJtcPLz6RgjHDMFUaGBvDKcw+x+tUPKCip5nJZrZDh4bubvuCN9z7lmUcXsur7Cwj096Wkopb//PPfWPPLjRRcqWT9j55wua7bJ93n3OMYnl0uHzx0cQW23l4++TyfIH8ti2aLzwH8Ksqu1pNfVOGWMFeZTMbWP67n1bWrCPL3Y/vuw2xJ209YcAD/++Gb+N1MtQw0+Ap9HH14eymJjw1k1ZIJdPVY2LG30C26Q0lhWROnLtbi661iQVIMKqW4GRedxrFFJDhA329WfaiUCiaOjQaguLLe5do5Zwp4feNW5s+czG9eXEFUeDBatYpxcUY+2PASoYEG/rI1nUon0xPfFqFzWM7wuRm+aDaLqW1lMtu4dt2xYfUnb+xz2mdr+kW2pl9k9tQoli4Qs2oHsHOf4+7qobmJwibbb0Uu9+SFFUt4YcWSAde7e0xcLCpHo1YSN9K9c0l+PmqCDF7UNXZyo9uMl+a7OTQsKG0k92Idvt5qFiTFoFGJ/WqFBztS0700zsNMdVqHoZktrq+ttf9YHgBJk+MHtWnVKibEjyQjM5cLRRVEuTiB2u2GVVzpmBwMNIgZHsg9ZUybEOG07Wp9O9X17Ywc4UeQvxdGgcNFk9lCRtZpx2T73KnCdO6EbemH6TGZWZYyB4XC7W85HTdMgLgVs6HmQvE1zlyqx6BXM39aDGrBZgUQHxuOp0xGbWMrFqtt0LaSqjrH9yxIwFxSXyHN5hbnWxf6risFfNaEvLLV9a34+mjQaQe6f1NLJ5vScgGYPtEoQhqlwpMnUu522rb7SDHV9e0kjg8XcjTnVg7mnKe9s5sZk+8SOtl+K+2dXfjoBq4K5V28wqvvfIxOq+Hff7BMiO616zfQqOR4ew18v3vtdvbnlNPZZSEq1AeN2r0nHNzB+aIGzl5uwF+vYf50o9Bh4K346LTMmDyGI7mFbM84zhMpM/rbzhVWcLawAq1GxcS7ol2unTghjg927GXz5wd5ask8QoMM/W0Hc86Sm38FtUpBwjjXr84LeXVPXahkd2YBY2NCCDDo0KjkXGvu5NzlGixWG+Pjwnhgltg5naFm5wHHcFDUznZnpP7rejQqJWNjo9B5abhcWsX+Y6dRKRR8/F8/JzoiRIjulYrrZBwrxRiux6DXoFUr6OwyU17TyvW2Hry1SpbME7eVorvHQrfJ8atv63XU+DVZbFxvc2xWlck8hBwLKqm6ztnLDXh4QLC/F5fKmgb10WmVjIo0OPnrb8/TqbO5UlHHjr0nKSipZlRUCI0tHZw4X4zMQ8aaZff1Dw1dyYNzEpk19W6yTl1g1mMvcf/sKQT56ymuqGX/sTzsdjs/X70Mg971oyghhnXXyBDqG9uprG2hpKoRk9mKVqNkdHQgSZNiSJpkdPuuZHdSXt3A+cJyt0y238pD85LYuTeL7bsz6TGZCAk08NSS+bz49FIiXTyXcCuxkX5M/V4YlbVt1DU20WOyolDICPDTMjcuhOkTI9AKvLsyW3vp6hk4J2qz2emyOa55yjzwFTAD0XFz+4bdjlOzAoeRiTIsX28tG366nB17TnIiv5grFXVoVEoS4mN4ZP5UxhjFbB6VyWRs/v3P+HDHPtL255CRmUu3yYSvj4650yfwzKMLmX2PmCN5QgwrLiZY+MbQ/wuLkkexKFn8yqExInhIasD/eGUqP16Z6nbdkAAdi+cM3eZcvU6FXud88lkkE+NCmBgn5q71TvH20rDqkdmsemS2W3UVcjnPL3uA55c94Fbd7/xZQgkJie8OkmFJSEgMGyTDkpCQGDZIhiUhITFskAxLQkJi2CAZloSExLBBMiwJCYlhg2RYEhISwwYPu91+x51lMpn9m/R3JXJP96Wh3I5SIe8/8OluVEoFJrPrT9zfCUP5mnt4OHaQDwWeMo/+Iz7uRiH3xGIVl+z0VQzlZw04Y7fbE76u0zfa6W6324kQVPL166hu6GDl4nFf31EAH6Xlc/3criHRNkxIoe7kp0OiHZr4OJ+8+eSQaK/42WY+3/jSkGg//MLbvPHivUOive4Ph4fklATA1EdeYuP6+4dE+4XXMu6onzQklJCQGDZIhiUhITFskAxLQkJi2CAZloSExLBBMiwJCYlhg7B6rl09FkxmGxZrLxarDbsdtGo5Br1GlCQAPWYrVXVtVNd30NLRQ1e3BZnMAz8fNbGRBkZF+gktHmi329mSdoCPP9tLUWkVtl4bsVERLF88l2cfW4SnoPjwPg4cy+P9bRkUl9fQ0t5BkL8f4+KM/GD5IhLuFlezau1vd9LUcsNpm16n5k/rlwrT7qOgpJpdh/MoKq+lo6sHb62ayLAAUu6dREJ8jBDNjKOl1Fxrp6mlmxvdFhRyGb4+au4aGcC08RF4acQULkw/dIpX3932lX1kMg9O7PidEH1nnMqv4ZO0fACWP/g9IWXIhRlWxw0zFmsvHh7gKXPffp6KmjZO5NegUckJDdThFaag22SlsraNnHPV1DR0MHtKpDDTWr3+92xLP0ygwZeHF8xAq1Zz5OQ51m14n5y8Aj566xVh2q9v3MK7m3bhp/fm/uQEDL7elF+tZ2/WaXYfPsU7v1rN0vtnCtEG0KoVzJ8xuBSyWim+lvv2PSfYmp6Nj05DQnwMfnov2ju7Ka++xsXiq8IMK/vsVcKCvImN9EOnVWK22Kiqb+fgiQpyL9Tyw8cnCynPPNoYzrOPznfadq6wjNMXSpg2UVxZ6ttpaetmx55LqJSemMzi9pEJMyy9twpPmQy5pwcmi42mlm5RUgN1dSrmJkYTEew9wBgmjQ1hd1YJlXVtVNa1Ex3m+jSR3YeOsy39MFHhwRzY/Db+fg4Ni8XKqpffZNeBHP72xUGWL57ncu1rza28tyWdQIOeQ1s2DEjezT5dwNI1r/HWX3eINSyNktT7xJTG/Sqy84rYmp7N+DGRvPLcYjTqgVFiVpu4L9CvVs8clFgDsDe7jMzcSjJzK3l4zhiX6442hjPaGO60bdW6dwD35QnY7XY277qAl1bB+LgQDh4vF6YlbA5LrZSjkMvcXrs9NFDHiBCfQbpatYIx0f4A1DeJiWtPP3QcgDVPLek3KwCFQs66NY4NmO9/mi5Eu7qukd5eO5PiYwfFhCclxKPTamhudR7LNJzp7bXzSdpRVEo5a1cuGmRWAHKBw3BnZgUwbrQj3LS51T0/1H2UVtVx8UolQQY9SZPEZW7eSuapSq6UN/NkyjiUCrFTHu4PqRtCZB59/4ox0YamFgCiIgbXs4++GQJxvrCUtvZO9D46l2obR4SiVMg5e6mU5tZ2/H19+tuOny2ks6ubhclTXKp5Oxarjey8Mppbu1Ap5YwI9SXOGIRMJm5t53J5DQ3NbUyfOBqdVs3pi2VU1TWhkMsZFRUiJKb9Tii8GUoREuDa9/nr+Ps+x4/mQ3OnuiW8t76xky8OFTE7MZrYKANFFc1C9f5pDKu3107J1VYAwgUdL+oziSonEd0Vt1y7UlHNlHGunV/w0+v4xZrl/PqPm0h+/KcsnJWAn96bypoG9h09w6ypd/PWK8+6VPN22jp6+O9tOQOuBRp0PPf9acJCSUoqHa+rr7eWtW9uorJ2YHpNfGwELz+Tgt5b6+zPXUbWmSrMZhs9Zis1DR1U1LYREuBFcoL7krZ7TBb2ZOU5wnvnJQrXs/X28nHaefx8NKTc654Qkn8awzpzqY7Wjh4igr0JDxJjWAtmTeGzPVn8eXMaqQtn4Xczl81qtfHb97b092ttFzMkfX7ZA4wIC2Tt639hS9qh/uvGiBAeezB50FDRlcycPJIxxiDCg/WoVQoar3eyP6eIzFPF/O6DQ/xy9UIiw1wfKNvW0QXAnmPnCfbX85sfLWV0dCiN19v58O9HOFtYwYb/2cV/vPiYy7Vv5eiZq3TejP0CGB1lYOn8sei0g4eoojiQc46OG90kTR7rlvDejKwSquvb+cnKe4QPBfv4pzCsS6VNFJQ2odepmDlJXOJz6sJZbN+dyYHsM0xLXc3C5EQ0ahVHTp6jorqekZFhlFbV4iloiPTupi94471PeebRhaz6/gIC/X0pqajlP//8N9b8ciMFVypZ/6MnhGgvuW/gwfSIEF+eTk1ErZSTcbSQnQfy+bcVyS7Xtdlvrj7b4eVnUjBGOOaOIkMDeOW5h1j96gcUlFRzuaxW6PDwF88nAY7V8aq6NvZkl/Knrbn8y+Jxwn4gb+fz/Y7w3tT7pgnXqqhpZd+xMubeYyQmwj3J5vBPsHG0sKyJUxdr8fVWsSApRmiUuEwmY+sf1/Pq2lUE+fuxffdhtqTtJyw4gP/98E38bqZ5Bhp8Xa6dc6aA1zduZf7MyfzmxRVEhQejVasYF2fkgw0vERpo4C9b06l0MlwVyZx7HEOFy+VidHUax5aB4AB9v1n1oVIqmDg2GoDiynoh+rfj7aUkPjaQVUsm0NVjYcfeQrfoll2tJ7+owi3hvbbeXj75PJ8gfy2LZovP+byV7/QdVkFpI7kX6/D1VrMgKQaNSvzTlcs9eWHFEl5YsWTA9e4eExeLytGolcSNdP28xv5jeQAkTY4f1KZVq5gQP5KMzFwuFFUQJTAF+nZ8bgacms1i6omFBztSlb00zoNU+6LazRb31nny81ETZPCirrGTG91mvDRih4Y79znurh6amyh8st1ktnHtumOT8E/e2Oe0z9b0i2xNv8jsqVEsXeC61crvrGFdKL7GmUv1GPRq5k+LQe0Gs/oqtqUfpsdkZlnKHBQK1z+WvgKDzS3Oty70XVcK0P4qiisdk+CBBjHDovjYcDxlMmobW7FYbYO2GVTVOfSDBM7ffRkdN0yAuFXpPkxmCxlZpx2T7XOnCtUCR2HHaRMinLZdrW+nur6dkSP8CPL3wuji4eJ30rDOFzVw9nID/noN86cbhQ4Db6e9swsf3cAVqbyLV3j1nY/RaTX8+w+WCdFNnBDHBzv2svnzgzy1ZB6hQYb+toM5Z8nNv4JapSBhnOtXc6rrW/H10aDTDrzLaWrpZFNaLgDTJxpdrgvgo9MyY/IYjuQWsj3jOE+kzOhvO1dYwdnCCrQaFRPvina59rXrN9Co5Hh7DXzevXY7+3PK6eyyEBXqg0Ytdqf/wZzztHd2M2PyXW6ZbFcqPHki5W6nbbuPFFNd307i+PDhdTSnu8dCt8nxq99XbtZksXG9zbGRTibzEHJkoaTqOmcvN+DhAcH+XlwqaxrUR6dVMirS4OSvvz2p/7oejUrJ2NgodF4aLpdWsf/YaVQKBR//18+JjggRovvgnERmTb2brFMXmPXYS9w/ewpB/nqKK2rZfywPu93Oz1cvw6B3/Z3OqQuV7M4sYGxMCAEGHRqVnGvNnZy7XIPFamN8XBgPzBI3r/J06myuVNSxY+9JCkqqGRUVQmNLByfOFyPzkLFm2X39Q0NXcqXiOhnHSjGG6zHoNWjVCjq7zJTXtHK9rQdvrZIl88Qfj9l5wDEcdNfO9qFEmGGZrb109Qyct7DZ7HTZHNc8ZR74ChgldNxcWrbbcWpW4DAyUYb10Lwkdu7NYvvuTHpMJkICDTy1ZD4vPr2USIFzRzKZjM2//xkf7thH2v4cMjJz6TaZ8PXRMXf6BJ55dCGz7xFzbOaukSHUN7ZTWdtCSVUjJrMVrUbJ6OhAkibFkDTJKPTEg6+3lg0/Xc6OPSc5kV/MlYo6NColCfExPDJ/KmOMYlYHYyP9mPq9MCpr26hrbKLHZEWhkBHgp2VuXAjTJ0agFXx3VV7dwPnCcrdMtv8jIO4soU6FXud8IlQkE+NCmBgn5i7mTvjxylR+vDJ1SLQVcjnPL3uA55c94FbduJhgYRtD7xRvLw2rHpnNqkdmu00zJEDH4jnu2TD5ZRgjgoesBrwzFiWPYlGyuJXD7/y2BgkJie8OkmFJSEgMGyTDkpCQGDZIhiUhITFskAxLQkJi2CAZloSExLBBMiwJCYlhg2RYEhISwwbJsCQkJIYNHna7/c47e3jceWcX4ynz6D+T6G5USgUms3vLk/wjaCvkMixW98SzDdb2xGIVl3bzVcjlMqxD9LyVCnl/5Q13M5TPGzhjt9sTvq7TNz6aU3fy0//bw/mWhCY+zucbXxoS7YdfeJs3Xrx3SLTX/eEwKxeP+/qOAvgoLZ+N6+8fEu0XXssYsiMnUx95ievndg2JtmFCChGCMge+juqGDj5588kh0V7xs8131E8aEkpISAwbJMOSkJAYNkiGJSEhMWyQDEtCQmLYILR28IFjeby/LYPi8hpa2jsI8vdjXJyRHyxfRMLd4usIFZRUs+twHkXltXR09eCtVRMZFkDKvZNIiI8RoplxtJSaa+00tXRzo9uCQi7D10fNXSMDmDY+Ai+NmIJuPWYrVXVtVNd30NLRQ1e3BZnMAz8fNbGRBkZF+gktoueMU/k1fJKWD8DyB78npGRu+qFTvPrutq/sI5N5cGLH71yuDWC329mSdoCPP9tLUWkVtl4bsVERLF88l2cfW4Snp7i8vq4eCyazDYu1F4vVht0OWrUcg14jTLOPtb/dSVPLDadtep2aP61fKkRXmGG9vnEL727ahZ/em/uTEzD4elN+tZ69WafZffgU7/xqNUvvnylKnu17TrA1PRsfnYaE+Bj89F60d3ZTXn2Ni8VXhRlW9tmrhAV5Exvph06rxGyxUVXfzsETFeReqOWHj08WUhq6oqaNE/k1aFRyQgN1eIUp6DZZqaxtI+dcNTUNHcyeEuk202pp62bHnkuolJ6YzOK2J4w2hvPsoy6ZD70AACAASURBVPOdtp0rLOP0hRKmTRRXpnj1+t+zLf0wgQZfHl4wA61azZGT51i34X1y8gr46K1XhL3mHTfMWKy9eHiAp0yG1ebeLQlatYL5Mwa/tmqluCqrQgzrWnMr721JJ9Cg59CWDQMSh7NPF7B0zWu89dcdwgwrO6+IrenZjB8TySvPLUajHhixZLWJ+wL9avXMQcktAHuzy8jMrSQzt5KH54xxua5ep2JuYjQRwd4DviCTxoawO6uEyro2KuvaiQ4Tnx5jt9vZvOsCXloF4+NCOHi8XJjWaGM4o43hTttWrXsHEFfrfPeh42xLP0xUeDAHNr+Nv5/jtbVYrKx6+U12Hcjhb18cZPnieUL09d4qPGUy5J4emCw2mlq6heh8GVqNktT7xJTd/jKEzGFV1zXS22tnUnzsoHj0pIR4dFoNza3O46i+Lb29dj5JO4pKKWftykWDzApALvA23ZlZAYwb7Qj5bG4V86EKDdQxIsRn0K+5Vq1gTLQ/APVNnUK0byfzVCVXypt5MmWc2yLMb6e0qo6LVyoJMuhJmuS6XLxbST90HIA1Ty3pNysAhULOujWO/Uzvf5ouRBtArZSjkMvcPtQfSoTcYRlHhKJUyDl7qZTm1nb8fX36246fLaSzq5uFyVNESHO5vIaG5jamTxyNTqvm9MUyquqaUMjljIoKERpX/lUU3gzECAnQuV1b5tH3r/gPdn1jJ18cKmJ2YjSxUQaKKpqFazrj7/scZvLQ3KnCgkUbmloAiIoYXM8++mbgyPnCUtraO9H7uP99F43FaiM7r4zm1i5USjkjQn2JMwYhk4lbyxNiWH56Hb9Ys5xf/3ETyY//lIWzEvDTe1NZ08C+o2eYNfVu3nrlWRHSlFQ6ItF9vbWsfXMTlbUDk3PiYyN4+ZkU9N5aZ3/uMrLOVGE22+gx/7/2zjwsyuve4x+G2RkYGPZFNlExNK4oUVSIGjUaYyRm0TTWmKW9mqSJ6U2T9LG9SdOmMV1uU7P05qlp4tKoT2uIWNxFVFxwF0Q2GZBVkF1gNub+McAjYRqTmzlDyX0///g87zn4e2d5v3PO7/zO+VqpqmvDWN1CSIAXKYmud33+Krq77ZRcawYgXHAFta27m0/SL+Dno2Hh3YNnztBlsrA7+6zDWHR2krA4vT/EFVV1A9qMt1wrMlYyaYx4uy9309LWxZ+35vS7FmjQ8fRDU4SZkghLuj+zdD7DwgJZ8+aHbE4/2Hc9JiKER+5LGTBVdBUtbR0A7D56gWB/Pa8/t4SR0aHUN7by8T8Oc67AyLq/7ORXLzwiJH4vR85co73HcgxgZJSBJXNGo9OKtSz/Mmcu19Dc1kVEsDfhQWIFKzO7hMraVl5ccdegTQUB9uecp+1mJ8kTRws1Fp07YxJ/353N+5vSSZs3A78ez0er1cZvPtjc16+51T1TcXcyfeJwRsUEER6sR61SUN/Yzr6cQrJOFfPbDQf5+ap5RIa5/r0XJljvbfyCtz74jCcfnsfKh+YS6O9LibGaX7//N1b/fD35ReWsfe4xl8e12XtWSuzw8pMLiYlw5I4iQwN45en7WfXGBvJLKrlytVro9PBnzyQDjpWcipoWdh8r5U9bcvnBojHChaOXy6UN5Jc2oNepmD7B9SUFt2Ksambv0avMuiuGWBfbk39TPt/nMBZNu2eK0Dhp82awbVcW+4+dYUraKualJKFRqzh88jzGylqGR4ZRWlGNp8Ap0mCx+J7++1sjQnx5Ii0JtVJO5pECduy/yI+Xp7g8rpB3MudMPm+u38Kc6RN5/YXlRIUHo1WrGBMfw4Z1LxEaaODDLRmUOxlKf1t0GkfJQHCAvk+selEpFYwfHQ1AcXmty2M7w9tLSUJcICsXj6Ojy8L2PQVuiVtwtYFTedX4equYmxyLSimu5M7W3c2nn18kyF/LglRxnnRfh6vXarlYaHSLsahMJmPLH9fyxpqVBPn7sW3XITan7yMsOIB/fvw2fj1OwYEGX6H38e/EzLscqYArZa5/tkHQCGvf0bMAJE9MGNCmVasYlzCczKxcLhUaiXKxG3J4sMPR2Uvj3MS117LcbHHvkS1+PmqCDF7U1Ldzs9OMl0bc1DC/tJ7cvBp8vdXMTY5FoxJaH4zJbON6o6OI8MW39jrtsyUjjy0ZeaROjmLJXDGrdgA79jpGV/fPShKWbL8VudyTZ5cv5tnli/td7+wykVdYhkatJH64e/OWg4lPj3my2SzmiBwh3+Te83xuNDkvXei9rlS4PnxCXDieMhnV9c1YrLYBZQYVNY4kfJCgHNpX0XbTBIhdrbtUfJ0zl2sx6NXMmRKLWrBYAcg9ZUwZF+G07VptK5W1rQwf5keQvxcxAqeLJrOFzOzTjmT7rMnC4nwdtmYcostkZunCmSgEfM//XSkudzxfgQYxaQ8h72TSuHg2bN/Dps8P8Pji2YQGGfraDuScI/diEWqVgsQxrl9J8tFpmTZxFIdzC9iWeZzHFk7raztfYORcgRGtRsX4O6JdHvt64000KjneXv1Hd912O/tyymjvsBAV6oNGLaYS+EJhHeeu1OGv1zBnaozQaeCtKBWePLbwTqdtuw4XU1nbStLYcCFbc27lQM4FWts7mTbxDqHJ9ltpbe/AR9d/xflsXhFvvPsJOq2G//zhUrfchzuprG3G10eDTtv/e97Q1M7G9FwApo6PERJbyDf6vplJzJh8J9mnLjHjkZe4N3USQf56io3V7Dt6FrvdzmurlmLQi1HhJ9JSKTLWsH3PSfJLKhkRFUJ9UxsnLhQj85Cxeuk9fVNDV1JkbCTzaCkx4XoMeg1atYL2DjNlVc00tnThrVWyeLaY5e2SikbOXanDwwOC/b24fLVhQB+dVsmISIOTv/5usGO/YzooqrLdGWk/WotGpWR0XBQ6Lw1XSivYd/Q0KoWCT37/GtERIcJid3ZZ6DQ5ZjO9p/GaLDYaWxzFyTKZh5BtYKculbMrK5/RsSEEGHRoVHKu32jn/JUqLFYbY+PDmD9DTP5QiGDJZDI2/eGnfLx9L+n7csjMyqXTZMLXR8esqeN48uF5pN4lrqTf11vLup8sY/vuk5y4WEyRsQaNSkliQiwPzpnMqBgxq4NxkX5M/l4Y5dUt1NQ30GWyolDICPDTMis+hKnjI9AKGl219ZRQ2O04FStwCNl3VbDKKuu4UFDmlmT7rdw/O5kde7LZtiuLLpOJkEADjy+ewwtPLCHSxfnZL2O2dtPR1T9XZLPZ6bA5rnnKPPAVMCa4Y3gItfWtlFc3UVJRj8lsRatRMjI6kOQJsSRPiBFWfS9szqCQy3lm6XyeWTpfVIivxNtLw8oHU1n5YKrbYoYE6Fg0c3AKJsfHhzA+Xtyv+f+VBSkjWJAifuUwJiJ4UI5Ufn5FGs+vSHN7XHDsH9XrnC8uiSQ+NlhYYejt+O4ViEhISHxnkQRLQkJiyCAJloSExJBBEiwJCYkhgyRYEhISQwZJsCQkJIYMkmBJSEgMGSTBkpCQGDJIgiUhITFk8LDb7V+7s0wms3+T/q5EIffEYhXndvNVyD3db6HUi0zmQXf34LzncrkMq3VwXrdSIe879cPdqJQKTGb3Hj/Ui4eHY3vVYKCQy7AM0ucNnLHb7Ym36/SNtubY7fZB2f4AMPnBl3jrhbsHJfar/32IT9/+/qDEXv7TTUQIPov9X1FZ18bn618alNgPPPs7Gs/vHJTYhnELWb/23kGJ/ewvM6k5+dmgxA5NepQVi8bcvqMA/tpjuHs7pCmhhITEkEESLAkJiSGDJFgSEhJDBkmwJCQkhgxCzsPKOHiKN97b+pV9ZDIPTmz/rYjwZB4ppep6Kw1NndzstKCQy/D1UXPH8ACmjI3ASyPmED2ANb/ZQUPTTadtep2aP61dIix2R5cFk9mGxdqNxWrDbgetWo5BrxEW88vkl1Sy89BZCsuqaevowlurJjIsgIV3TyAxIVZITLvdzub0/Xzy9z0UllZg67YRFxXBskWzeOqRBXh6utcj8dTFKj7tSSIvu+97Qo+G3n/0LB9tzaS4rIqm1jaC/P0YEx/DD5ctIPFOMWezdZmtVNS0UFnbRlNbFx2dFmQyD/x81MRFGhgR6Te0DvAbGRPOUw/Pcdp2vuAqpy+VMGW8OCfcY+euERbkTVykHzqtErPFRkVtKwdOGMm9VM1/PDpRyNGxvWjVCuZMG/j61EpxQgkOD0SLtRsPD/CUub8UY9vuE2zJOIaPTkNiQix+ei9a2zspq7xOXvE1YYK1au0f2JpxiECDLw/MnYZWrebwyfO8uu4jcs7m89d3XhH2AH2ZppZOtu++jErpickstgznzfWbeW/jTvz03tybkojB15uya7XsyT7NrkOnePcXq1hy73SXxzVWtXDiYhUalZzQQB1eYQo6TVbKq1vIOV9JVV0bqZMihbznwgRrZEy407aVr74LiD13+xerpg9wywHYc+wqWbnlZOWW88DMUcLiazVK0u4RdwT0v0LvrcJTJkPu6YHJYqOhqdNtsY+dLWRLxjHGjorklacXoVH3tzGz2sQ8vLsOHmdrxiGiwoPZv+l3+Ps53JAsFisrX36bnftz+NsXB1i2aLaQ+Ldit9vZtPMSXloFY+NDOHC8TFis6zea+WBzBoEGPQc3r+vnpH7sdD5LVv+Sd/5nuxDB0utUzEqKJiLYu58oTRgdwq7sEsprWiivaSU6zPXOVG7NYZVW1JBXVE6QQU/yBHHedM7ECmDMSIex6o1m9z3I7kStlKOQy9w2muilu9vOp+lHUCnlrFmxYIBYAcgFTcsyDh4HYPXji/vECkChkPPqakft3EefZQiJ/WWyTpVTVHaD7y8cg1IhdhpaWVNPd7edCQlx/cQKIDkxAZ1Ww41m5zZ735bQQB3DQnwGfM+0agWjov0BqG1oFxLbrYZp/9jr+HLdP2uyW0wuv0xBjzlDSIBOaByL1caxs1e50dyBSilnWKgv8TFByL6DluUAV8qqqLvRwtTxI9Fp1ZzOu0pFTQMKuZwRUSHEx4ox/QCoa2gCICpi4Bnj0T0mEBcKSmlpbUfvI+5zr61v54uDhaQmRRMXZaDQeENYLICYYaEoFXLOXS7lRnMr/r4+fW3HzxXQ3tHJvJRJQu/BGTKP3n+HUA7LGV0mC7uzzzpMLmcnuSVm9pkKzGYbXWYrVXVtGKtbCAnwIiVRrBNvS1sXf96a0+9aoEHH0w9NGbTD+0VSUu6wJff11rLm7Y2UV/d37UmIi+DlJxei99Y6+/NvRe+DWlE10BrdeMu1ImMlk8aIyZvaurv5JP0Cfj4aFt7tHhMSP72On61exn/9cSMpj/6EeTMS8dN7U15Vx94jZ5gx+U7eeeUpt9xLL93ddkquNQMQLmh3htsEa3/OedpudpI8cbTbTC6PnLlGe4/9FcDIKANL5oxGpxVnEz994nBGxQQRHqxHrVJQ39jOvpxCsk4V89sNB/n5qnlEhrnn9buLlrYOAHYfvUCwv57Xn1vCyOhQ6htb+fgfhzlXYGTdX3byqxcecXnsuTMm8ffd2by/KZ20eTPw6/G6tFpt/OaDzX39mlvFTFEAMrNLqKxt5cUVdwmfCt7KM0vnMywskDVvfsjm9IN912MiQnjkvpQBU0XRnLlcQ3NbFxHB3oQHDXHB+nyfw+Qy7Z4p7grJz55JBhyrZxU1Lew+VsqftuTyg0VjhL2hi+/pvxcrIsSXJ9KSUCvlZB4pYMf+i/x4eYqQ2IOFzd6zGmmHl59cSEyEI1cYGRrAK0/fz6o3NpBfUsmVq9Uunx6mzZvBtl1Z7D92hilpq5iXkoRGreLwyfMYK2sZHhlGaUU1noKm48aqZvYevcqsu2KIjXDvD9F7G7/grQ8+48mH57HyobkE+vtSYqzm1+//jdU/X09+UTlrn3vMLfdyubSB/NIG9DoV0yeIK+NwS1Ll6rVaLhYa3W5y2Yu3l5KEuEBWLh5HR5eF7XsK3H4PM+9yTBWulA2cugx1dBpHiUhwgL5PrHpRKRWMHx0NQHF5rctjy2QytvxxLW+sWUmQvx/bdh1ic/o+woID+OfHb+PX4yQaaPB1eWxbdzeffn6RIH8tC1LFey/eSs6ZfN5cv4U50yfy+gvLiQoPRqtWMSY+hg3rXiI00MCHWzIodzJVdjUFVxs4lVeNr7eKucmxqJTixkFuGWHt2OsYXd0/K2lQku29+PmoCTJ4UVPfzs1OM14acVPDL+PTY3hpNg/OkSkiCQ92uEl7aZybeuq0DkEzW8Qc2SKXe/Ls8sU8u3xxv+udXSbyCsvQqJXED3d93tJktnG90VEk/OJbe5322ZKRx5aMPFInR7FkrutWxvcdPQtA8sSEAW1atYpxCcPJzMrlUqGRKIEO1Pml9eTm1eDrrWZuciwalVhJES5YJrOFzOzTjmT7rMmiw92WtpsmQNwqxr+iuNyRiA40DM5RMSJJiAvHUyajur4Zi9U2oKykosbx2oPcnFPZmnGILpOZpQtnolC4/qsu95QxZVyE07Zrta1U1rYyfJgfQf5exLh4uth7VtiNJuelC73XlQJedy+Xiq9z5nItBr2aOVNiUQsWK3CDYB3IuUBreyfTJt7hlmT79cabaFRyvL36/9p32+3syymjvcNCVKgPGrXrq84ra5vx9dGg0/aP3dDUzsb0XACmjo9xedzBxkenZdrEURzOLWBb5nEeWzitr+18gZFzBUa0GhXj74gWEr+1vQMfXf8VyLN5Rbzx7ifotBr+84dLhcRVKjx5bOGdTtt2HS6msraVpLHhQrbmJI2LZ8P2PWz6/ACPL55NaJChr+1AzjlyLxahVilIHCNm1fJCYR3nrtThr9cwZ2qM0GngrQiPsmO/YzoosrL9VoqMjWQeLSUmXI9Br0GrVtDeYaasqpnGli68tUoWzxazvH3qUjm7svIZHRtCgEGHRiXn+o12zl+pwmK1MTY+jPkzxOXwOrssdJocv7y2nlNKTRYbjS2OQlmZzEPYlqQn0lIpMtawfc9J8ksqGREVQn1TGycuFCPzkLF66T19U0NXk/ajtWhUSkbHRaHz0nCltIJ9R0+jUij45PevER0RIiTuYHLfzCRmTL6T7FOXmPHIS9ybOokgfz3Fxmr2HT2L3W7ntVVLMehdP6IvqWjk3JU6PDwg2N+Ly1cbBvTRaZWMiDQ4+etvh1DBKqus40JBmVuT7XGRfkz+Xhjl1S3U1DfQZbKiUMgI8NMyKz6EqeMj0AoYXQHcMTyE2vpWyqubKKmox2S2otUoGRkdSPKEWJInxAitQjdbu+no6p8js9nsdNgc1zxlHvgKmpH6emtZ95NlbN99khMXiyky1qBRKUlMiOXBOZMZFSOuePT+2cns2JPNtl1ZdJlMhAQaeHzxHF54YgmRAvM3g4lMJmPTH37Kx9v3kr4vh8ysXDpNJnx9dMyaOo4nH55H6l1itoe19ZQK2e04FStwCNmQE6yYiGC3H6kcEqBj0Uz3FO99mfjY4EEtDNXrVOh1zhPf7sDbS8PKB1NZ+WCqW+M+vyKN51ekuTXm7ViQMoIFKWJXDhVyOc8snc8zS+cLjfNlxseHMD5+cEat3829IhISEt9JJMGSkJAYMkiCJSEhMWSQBEtCQmLIIAmWhITEkEESLAkJiSGDJFgSEhJDBkmwJCQkhgySYElISAwZPOx2+9fuLJPJ7N+kvyuRy2VYre61repFIZdhGaTYHsDgvOMOMw+LVaxV1b9CpVRgMos5juZ2DObnPZiv21Pm0bcHdRA4Y7fbE2/X6RttzbHb7axfe+///Za+Bc/+MpPG8zsHJbZh3EIiBJ1RfTsq69p464W7ByX2q/99iBWLxty+owD+mn6RmpOfDUrs0KRH3b6lrJfJD77Ep29/f1BiL//pJj5f/9KgxH7g2a/3fktTQgkJiSGDJFgSEhJDBkmwJCQkhgySYElISAwZJMGSkJAYMrjVqv7UxSo+Tb8IwLL7vifkrGtwrGZuTt/PJ3/fQ2FpBbZuG3FRESxbNIunHlmAp6c4s8uOLgsmsw2LtRuL1YbdDlq1HINeIyxmL5lHSqm63kpDUyc3Oy0o5DJ8fdTcMTyAKWMj8NKIOWm1y2yloqaFyto2mtq66Oi0IJN54OejJi7SwIhIP6EnrQLsP3qWj7ZmUlxWRVNrG0H+foyJj+GHyxaQeKeYAx0zDp7ijfe2fmUfmcyDE9t/KyT+mt/soKHpptM2vU7Nn9YuERL3VvJLKtl56CyFZdW0dXThrVUTGRbAwrsnkJgQ6/J4bhOsppZOtu++jErpickstrZn1do/sDXjEIEGXx6YOw2tWs3hk+d5dd1H5JzN56/vvCLsAWq7acZi7cbDAzxlMqw299XzHDt3jbAgb+Ii/dBplZgtNipqWzlwwkjupWr+49GJQs50N1a1cOJiFRqVnNBAHV5hCjpNVsqrW8g5X0lVXRupkyKFvedvrt/Mext34qf35t6URAy+3pRdq2VP9ml2HTrFu79YxZJ7p7s87siYcJ56eI7TtvMFVzl9qYQp48X4B/SiVSuYM21gDLVSzI/TrWzbfYItGcfw0WlITIjFT+9Fa3snZZXXySu+NnQFy263s2nnJby0CsbGh3DgeJmwWLsOHmdrxiGiwoPZv+l3+Ps5rKUsFisrX36bnftz+NsXB1i2aLaQ+HpvFZ4yGXJPD0wWGw1NnULiOOMXq6YPsNgC2HPsKlm55WTllvPAzFEuj6vXqZiVFE1EsHc/UZowOoRd2SWU17RQXtNKdJjrbb6u32jmg80ZBBr0HNy8rp89+7HT+SxZ/Uve+Z/twgRrZEy407aVr74LiDdf0WqUpN0j5uz2r+LY2UK2ZBxj7KhIXnl6ERp1f49Pq03MoMQtOaysU+UUld3g+wvHoFSIm44BZBw8DsDqxxf3iRWAQiHn1dWOgryPPssQFl+tlKOQy4RPgZzhTKwAxox0uDHfaBYjnqGBOoaF+Ax4zVq1glHR/gDUNrQLiV1ZU093t50JCXH9xAogOTEBnVbDjWbn3n2iKK2oIa+onCCDnuQJrjNP/Xehu9vOp+lHUCnlrFmxYIBYAcgFpV2Ej7Bq69v54mAhqUnRxEUZKDTeEBqvrqEJgKiIgWYQ0T0OKhcKSmlpbUfvoxN6L/8uFPQ4m4QEuP/1yjx6/xUj4DHDQlEq5Jy7XMqN5lb8fX362o6fK6C9o5N5KZOExP5X/GOv40fz/lmThTudW6w2jp29yo3mDlRKOcNCfYmPCUImExf3SlkVdTdamDp+JDqtmtN5V6moaUAhlzMiKoT4WHEOSUIFy9bdzSfpF/Dz0bDwbvc42fR+YSuq6ga0GW+5VmSsZNIYsfmFwSL7TAVms40us5WqujaM1S2EBHiRkuh6u/avorvbTsm1ZgDCBW1t8tPr+NnqZfzXHzeS8uhPmDcjET+9N+VVdew9coYZk+/knVeeEhLbGV0mC7uzzzqczmcnCY/X0tbFn7fm9LsWaNDx9ENThDk4lZQ7niNfby1r3t5IeXV/q6+EuAhefnIhem+tsz//VggVrMzsEiprW3lxxV3Cp4K9zJ0xib/vzub9TemkzZuBX4+RpNVq4zcfbO7r19wqZory78CRM9do7/GOAxgZZWDJnNHotAOH7iI5c7mG5rYuIoK9CQ8StxfzmaXzGRYWyJo3P2Rz+sG+6zERITxyX8qAqaJI9uecp+1mJ8kTRwt3Op8+cTijYoIID9ajVimob2xnX04hWaeK+e2Gg/x81Twiw1x/Dy1tHQDsPnqBYH89rz+3hJHRodQ3tvLxPw5zrsDIur/s5FcvPOLy2MIEy1jVzN6jV5l1VwyxEeIt6ntJmzeDbbuy2H/sDFPSVjEvJQmNWsXhk+cxVtYyPDKM0opqPAUOmQebnz2TDDhWLCtqWth9rJQ/bcnlB4vGCBWOW7lc2kB+aQN6nYrpE8SUr/Ty3sYveOuDz3jy4XmsfGgugf6+lBir+fX7f2P1z9eTX1TO2uceE3oPvXy+z+F0nnbPFOGxFt/Tf2N6RIgvT6QloVbKyTxSwI79F/nx8hSXx7XZe1a+7fDykwuJiXDkSCNDA3jl6ftZ9cYG8ksquXK12uXTQyFPra27m08/v0iQv5YFqWLNJL+MTCZjyx/X8saalQT5+7Ft1yE2p+8jLDiAf378Nn491seBBl+33tdg4O2lJCEukJWLx9HRZWH7ngK3xC242sCpvGp8vVXMTY5FpRQ3kM85k8+b67cwZ/pEXn9hOVHhwWjVKsbEx7Bh3UuEBhr4cEsG5U5SBK7m6rVaLhYa3ep07oyZdznSL1fKxLxmncZRGhMcoO8Tq15USgXjR0cDUFxe6/LYQr5JJrON642OgrYX39rrtM+WjDy2ZOSROjmKJXNdu5Iil3vy7PLFPLt8cb/rnV0m8grL0KiVxA93bz5nMPHzURNk8KKmvp2bnWa8NOKmhvml9eTm1eDrrWZuciwaldh1nX1HzwKQPDFhQJtWrWJcwnAys3K5VGgkSrBt/Y69jtHV/bOShCfbvwqfHvdvs9kq5P8PD3ZY0HtpnLuM67QOQTNbXH+ul5Bvk9xTxpRxEU7brtW2UlnbyvBhfgT5exHjxuni1oxDdJnMLF04E4XCrUX+g07bTRMgbrUO4FLxdc5crsWgVzNnSixqwWIFYLY4HsobTc5LF3qvKwV/3iazhczs045k+6zJQmPdjuJyRxI80CBm+p8QF46nTEZ1fTMWq21AOU1FjSN+kIDcoZBPUanw5LGFdzpt23W4mMraVpLGhgvbmtPa3oGPrv8Kxdm8It549xN0Wg3/+cOlQuIOJtcbb6JRyfH26v+r1223sy+njPYOC1GhPmjUYiqgLxTWce5KHf56DXOmxgidBt5K0rh4Nmzfw6bPD/D44tmEBhn62g7knCP3YhFqlYLEMWJXqQ/kXKC1vZNpE+8QnmwHqKxtxtdHg07b//NuaGpnY3ouAFPHoBChFAAADwZJREFUxwiJ7aPTMm3iKA7nFrAt8ziPLZzW13a+wMi5AiNajYrxd0S7PPZ3cpiR9qO1aFRKRsdFofPScKW0gn1HT6NSKPjk968RHREiLHZnl4VOk+NXv/e4WZPFRmOLo2hTJvMQsj2myNhI5tFSYsL1GPQatGoF7R1myqqaaWzpwlurZPFsMWUcJRWNnLtSh4cHBPt7cflqw4A+Oq2SEZEGJ3/97bhvZhIzJt9J9qlLzHjkJe5NnUSQv55iYzX7jp7Fbrfz2qqlGPRiFxt27HdMB0VXtvdy6lI5u7LyGR0bQoBBh0Yl5/qNds5fqcJitTE2Poz5M8Tl0Z5IS6XIWMP2PSfJL6lkRFQI9U1tnLhQjMxDxuql9/RNDV3Jd1Kw7p+dzI492WzblUWXyURIoIHHF8/hhSeWECk4j2G2dtPR1T93YLPZ6bA5rnnKPPAV8OzERfox+XthlFe3UFPfQJfJikIhI8BPy6z4EKaOj0AraHTV1lNCYbfjVKzAIWQiBEsmk7HpDz/l4+17Sd+XQ2ZWLp0mE74+OmZNHceTD88j9S6xW1fKKuu4UFDm1mT7HcNDqK1vpby6iZKKekxmK1qNkpHRgSRPiCV5QozQ3Ra+3lrW/WQZ23ef5MTFYoqMNWhUShITYnlwzmRGxYgpHnW7YC1IGcGCFLErh8+vSOP5FWlCY/wr9DoVep3zZKRIQgJ0LJrpnuLcLzM+PoTx8eJGrbdDIZfzzNL5PLN0/qDEj4kIdvsZ8PGxwcIKQ78u3l4aVj6YysoHU90W87tbjCQhIfGdQxIsCQmJIYMkWBISEkMGSbAkJCSGDJJgSUhIDBkkwZKQkBgySIIlISExZJAES0JCYsjgYbfbv3ZnmewbdXcpKqUCk9n1u7+/Dh7AIL1s5J7udd65FU+ZR9/2InczmJ+3UiHv21TtbhRyGRbr4HzeSoUnZotYR6uv4Izdbk+8XadvVOlut8Pn61/6v9/St+CBZ39HzcnPBiV2aNKjrFg05vYdBfDX9IusX3vvoMR+9peZbq/g7mXygy/x6dvfH5TYy3+6iQhBRzrfjsq6Nt564e5Bif3qfx+i8fzOQYltGLfwa/WTpoQSEhJDBkmwJCQkhgySYElISAwZJMGSkJAYMkiCJSEhMWQQfh5WfkklOw+dpbCsmraOLry1aiLDAlh49wQSE2KFxd1/9Cwfbc2kuKyKptY2gvz9GBMfww+XLSDxTjHnRnWZrVTUtFBZ20ZTWxcdnRZkMg/8fNTERRoYEenndgv7Uxer+DT9IgDL7vuekGOpMw6e4o33tn5lH5nMgxPbf+vy2ABrfrODhqabTtv0OjV/WrtESFyAji4LJrMNi7Ubi9WG3Q5atRyDXiMsZi+ZR0qput5KQ1MnNzstKOQyfH3U3DE8gCljI/DSiDmwEcBut7M5fT+f/H0PhaUV2LptxEVFsGzRLJ56ZAGeQ9GqftvuE2zJOIaPTkNiQix+ei9a2zspq7xOXvE1YYL15vrNvLdxJ356b+5NScTg603ZtVr2ZJ9m16FTvPuLVSy5d7rL4xqrWjhxsQqNSk5ooA6vMAWdJivl1S3knK+kqq6N1EmRbhOtppZOtu++jErpicksrr5mZEw4Tz08x2nb+YKrnL5UwpTxYl22tWoFc6YNjKFWintoweH9aLF24+EBnjL31swdO3eNsCBv4iL90GmVmC02KmpbOXDCSO6lav7j0YlCjuMGWLX2D2zNOESgwZcH5k5Dq1Zz+OR5Xl33ETln8/nrO68I+Z4LE6xjZwvZknGMsaMieeXpRWjU/a2lrDYxD9D1G818sDmDQIOeg5vX9XP9PXY6nyWrf8k7/7NdiGDpdSpmJUUTEezd78OaMDqEXdkllNe0UF7TSnSYeCdiu93Opp2X8NIqGBsfwoHjZcJijYwJZ2RMuNO2la++C4g/61yrUZJ2j9ijkJ2h91bhKZMh9/TAZLHR0NTptti/WDV9gGMNwJ5jV8nKLScrt5wHZo5yedxdB4+zNeMQUeHB7N/0O/z9HN9ni8XKypffZuf+HP72xQGWLZrt8thCcljd3XY+TT+CSilnzYoFA8QKQC5oyFhZU093t50JCXEDLMqTExPQaTXcaHZuCfVtCQ3UMSzEZ8Avi1atYFS0PwC1De1CYn+ZrFPlFJXd4PsLx6BUiHmvb0dpRQ15ReUEGfQkT3Ct9+S/C2qlHIVc5vapPuBUrADGjHSYm95oFiOeGQePA7D68cV9YgWgUMh5dbWj2PejzzKExBYywrpSVkXdjRamjh+JTqvmdN5VKmoaUMjljIgKcbl99a3EDAtFqZBz7nIpN5pb8ff16Ws7fq6A9o5O5qVMEhb/XyHz6P1X/Be7tr6dLw4WkpoUTVyUgULjDeExnfGPvY4v9v2zJgs3FrVYbRw7e5UbzR2olHKGhfoSHxOETPb/b12poMcIJCRAJ+T/r2toAiAqYuCZ8tE9Ji8XCkppaW1H7+PaexAiWCXlDotsX28ta97eSHl1fyeVhLgIXn5yIXpvrbM//1b46XX8bPUy/uuPG0l59CfMm5GIn96b8qo69h45w4zJd/LOK0+5PO5X0d1tp+RaMwDhgrd82Lq7+ST9An4+GhbePTimFABdJgu7s886jEVnJwmP19LWxZ+35vS7FmjQ8fRDUwbdrEE02WcqMJttdJmtVNW1YaxuISTAi5REMe7mvYOAiqq6AW3GW64VGSuZNMa1uUshgtXS1gHA7qMXCPbX8/pzSxgZHUp9Yysf/+Mw5wqMrPvLTn71wiMiwvPM0vkMCwtkzZsfsjn9YN/1mIgQHrkvZcBUUTRnLtfQ3NZFRLA34UFiBSszu4TK2lZeXHHXoE0FAfbnnKftZifJE0cLNxadPnE4o2KCCA/Wo1YpqG9sZ19OIVmnivnthoP8fNU8IsPc5zDubo6cuUZ7j9UawMgoA0vmjEanHZiKcQVzZ0zi77uzeX9TOmnzZuDX4/lotdr4zQeb+/o1t7o+/SFEsGz2npUSO7z85EJiIhxz6sjQAF55+n5WvbGB/JJKrlytFjI9fG/jF7z1wWc8+fA8Vj40l0B/X0qM1fz6/b+x+ufryS8qZ+1zj7k8rjMulzaQX9qAXqdi+gQxTte9GKua2Xv0KrPuiiE2YnAf0M/3OYxF0+6ZIjzW4nv6b0yPCPHlibQk1Eo5mUcK2LH/Ij9eniL8PgaLnz2TDDhWLCtqWth9rJQ/bcnlB4vGCPmBTJs3g227sth/7AxT0lYxLyUJjVrF4ZPnMVbWMjwyjNKKajwFTMeFTPB1GsdSanCAvk+selEpFYwfHQ1AcXmty2PnnMnnzfVbmDN9Iq+/sJyo8GC0ahVj4mPYsO4lQgMNfLglg3Inw1lXU3C1gVN51fh6q5ibHCvUvt3W3c2nn18kyF/LglSxvo+34+q1Wi4WGt1qLOqMmXc5psRXysR/1v8OeHspSYgLZOXicXR0Wdi+p0BIHJlMxpY/ruWNNSsJ8vdj265DbE7fR1hwAP/8+G38epyCAw2+Lo8t5AkKD3Y4/HppnBuK9lpYmy2uP+9o39GzACRPTBjQplWrGJcwnMysXC4VGokS6AKdX1pPbl4Nvt5q5ibHolGJrdE1mW1cb3QUT7741l6nfbZk5LElI4/UyVEsmStu1W7HXsfo6v5ZScKT7V+FT4+hrdk8OGdbDRZ+PmqCDF7U1Ldzs9OMl8b1U0O53JNnly/m2eWL+13v7DKRV1iGRq0kfrjrc2hCnqKEuHA8ZTKq65uxWG0Dll8rahxJ+CABuaTeg9duNDkvXei9rlSIE5BLxdc5c7kWg17NnCmxqAWLFTgO+psyLsJp27XaViprWxk+zI8gfy9iBE4XTWYLmdmnHcn2WZOFxfk6FJc7vmeBhsE522owabtpAtyzKn0rWzMO0WUys3ThTBQCnjEhT5KPTsu0iaM4nFvAtszjPLZwWl/b+QIj5wqMaDUqxt8R7fLYSePi2bB9D5s+P8Dji2cTGmToazuQc47ci0WoVQoSx4hZQbtQWMe5K3X46zXMmRojdBp4K0qFJ48tvNNp267DxVTWtpI0NlzI1pxbOZBzgdb2TqZNvEN4sh2gsrYZXx8NOm3/0XxDUzsb03MBmDo+Rvh9uJvrjTfRqOR4e/V/3d12O/tyymjvsBAV6oNGLabSv7W9Ax9d/1X+s3lFvPHuJ+i0Gv7zh0uFxBX2ND2RlkqRsYbte06SX1LJiKgQ6pvaOHGhGJmHjNVL7+mbGrqS+2YmMWPynWSfusSMR17i3tRJBPnrKTZWs+/oWex2O6+tWopB7/pf3ZKKRs5dqcPDA4L9vbh8tWFAH51WyYhIg5O//m6wY79jOii6sr2XU5fK2ZWVz+jYEAIMOjQqOddvtHP+ShUWq42x8WHMnyEuj9bZZaHT5BjV9x4nbbLYaGxxFG3KZB5CtscUGRvJPFpKTLgeg16DVq2gvcNMWVUzjS1deGuVLJ4tbjtU2o/WolEpGR0Xhc5Lw5XSCvYdPY1KoeCT379GdESIkLjCBMvXW8u6nyxj++6TnLhYTJGxBo1KSWJCLA/OmcyoGDHFozKZjE1/+Ckfb99L+r4cMrNy6TSZ8PXRMWvqOJ58eB6pd4nZwtHWs7Rst+NUrMAhZN9VwSqrrONCQZlbk+13DA+htr6V8uomSirqMZmtaDVKRkYHkjwhluQJMUKr0M3Wbjq6+ufIbDY7HTbHNU+ZB74CZqRxkX5M/l4Y5dUt1NQ30GWyolDICPDTMis+hKnjI9AKGl0B3D87mR17stm2K4suk4mQQAOPL57DC08sIVJgbljofMXbS8PKB1NZ+WCqyDADUMjlPLN0Ps8sne/WuOPjQxgfL+aX5duwIGUEC1LErxzGRAS7/Qz4+NjgQS0M1etU6HXOF5dEEhKgY9HMwSsMfn5FGs+vSHN73P9/+xYkJCSGLJJgSUhIDBkkwZKQkBgySIIlISExZJAES0JCYsggCZaEhMSQQRIsCQmJIYMkWBISEkMGD7vd/vU7e3jUA+XibkdCQuL/KVF2uz3wdp2+kWBJSEhIDCbSlFBCQmLIIAmWhITEkEESLAkJiSGDJFgSEhJDBkmwJCQkhgySYElISAwZJMGSkJAYMkiCJSEhMWSQBEtCQmLI8L+DOsQYAjXzPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz(medium_ans.astype(int),\n",
    "    {1: '#1c170d',\n",
    " 2: '#604f2e',\n",
    " 3: '#877041',\n",
    " 4: '#947d49',\n",
    " 5: '#a2895c',\n",
    " 6: '#b09473',\n",
    " 7: '#caad8d',\n",
    " 8: '#e7c9a8',\n",
    " 9: '#eed0b3'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "hard=np.array([\n",
    "[7,0,0, 0,0,0, 4,0,0],\n",
    "[0,2,0, 0,7,0, 0,8,0],\n",
    "[0,0,3, 0,0,8, 0,0,9],\n",
    "[0,0,0, 5,0,0, 3,0,0],\n",
    "[0,6,0, 0,2,0, 0,9,0],\n",
    "[0,0,1, 0,0,7, 0,0,6],\n",
    "[0,0,0, 3,0,0, 9,0,0],\n",
    "[0,3,0, 0,4,0, 0,6,0],\n",
    "[0,0,9, 0,0,1, 0,0,5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "hard_ans=sudoku_ans(hard)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz(hard_ans.astype(int),\n",
    "    {1: '#ff1d00',\n",
    " 2: '#ff7000',\n",
    " 3: '#ffc400',\n",
    " 4: '#ceff00',\n",
    " 5: '#27ff00',\n",
    " 6: '#00ff80',\n",
    " 7: '#00d8ff',\n",
    " 8: '#0031ff',\n",
    " 9: '#4000ff'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}