dtw.ipynb

{
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  "name": "",
  "signature": "sha256:1da68ef5916d0f0c56026752e830fd2b9c319204968662d234c9ab34617bb206"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So you just recorded yourself saying a word and try to match it against another instance. The signals look similar, but have varying lengths and different activations for different features. So, how do you decide the similarity. Dynamic time warping (DTW) is probably something which can come to your rescue. Quoting wikipedia:\n",
      "\n",
      "\n",
      "\"In time series analysis, dynamic time warping (DTW) is an algorithm for measuring similarity between two temporal sequences which may vary in time or speed. For instance, similarities in walking patterns could be detected using DTW, even if one person was walking faster than the other, or if there were accelerations and decelerations during the course of an observation.\""
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this post I will try and put forward a naive implementation of DTW and also explain the different pieces of the problem."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Customary imports\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Creating two signals"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([1, 1, 2, 3, 2, 0])\n",
      "y = np.array([0, 1, 1, 2, 3, 2, 1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Plotting the two signals"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,'r', label='x')\n",
      "plt.plot(y, 'g', label='y')\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f7973fa8790>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, it appears that both the signals show similar behaviour: they both have a peak and around the peak they slop downwards. They vary in their speed and total duration. So, all set for DTW."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Aim"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our aim is to find a mapping between all points of x and y. For instance, x(3) may be mapped to y(4) and so on."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Making a 2d matrix to compute distances between all pairs of x and y"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this initial step, we will find out the distance between all pair of points in the two signals. Lesser distances implies that these points may be candidates to be matched together."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distances = np.zeros((len(y), len(x)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distances"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([[ 0.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  0.]])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will use euclidean distance between the pairs of points."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(y)):\n",
      "    for j in range(len(x)):\n",
      "        distances[i,j] = (x[j]-y[i])**2  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distances"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([[ 1.,  1.,  4.,  9.,  4.,  0.],\n",
        "       [ 0.,  0.,  1.,  4.,  1.,  1.],\n",
        "       [ 0.,  0.,  1.,  4.,  1.,  1.],\n",
        "       [ 1.,  1.,  0.,  1.,  0.,  4.],\n",
        "       [ 4.,  4.,  1.,  0.,  1.,  9.],\n",
        "       [ 1.,  1.,  0.,  1.,  0.,  4.],\n",
        "       [ 0.,  0.,  1.,  4.,  1.,  1.]])"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Visualizing the distance matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will write a small function to visualize the distance matrix we just created."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def distance_cost_plot(distances):\n",
      "    im = plt.imshow(distances, interpolation='nearest', cmap='Reds') \n",
      "    plt.gca().invert_yaxis()\n",
      "    plt.xlabel(\"X\")\n",
      "    plt.ylabel(\"Y\")\n",
      "    plt.grid()\n",
      "    plt.colorbar();\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(distances)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jTPEX9z2xd2fm2xFxAoNkctuU4++LiM3AV4EHpxk7IpYxqL62D7817QS+G9iQmdcCq4Ct\nXTv7uQ3/s51fux8Ri4GngG9m5kPTjp+ZyxiMg2yMiGOnGHo5g1WTO4ALgS0RcdoU4yewFSAzXwJ2\nAadPMX7j2jAG8ixwPfBwF8/fHf7CbAduzswdU469FPhAZq4H9gD7h9dUZOYVBz3LDmBlZr46rfgM\nEtj5wOcj4gwG1XATXanGtCGBLKS1+7MNxFwLnATcEREHxkI+lpnvTCH2I8DmiHgaWASszsx3pxB3\nofgGcH9EPDP8vLxr1a8kSZIkSZIkSZIkSWpeRFwZEf8ZEacc9L0vRsQjTT6XjixtWMquApn5z8AD\nDF7HZ7iKdwXwmQYfS0eYI34/EJUbvgr/PHA/cAuwdPhGsyTNLSLOi4i9EfHXTT+Ljjx2YXQZ8BqD\n94lmmn4YHVlMIB0WEecBXwEuYbAd5O2NPpCOOCaQjhpux/ct4IuZ+Qvg08AXurirlsqZQLrr74Ef\nZeaDAJn578CfAw9ExHGNPpkkSZIkSZIkSZIkSZIkSToy/C/eg2TEMjRjAwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f79a4934810>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From the plot above, it seems like the diagonal entries have low distances, which means that the distance between similar index points in x and y is low."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Warping path"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to create a mapping between the two signals, we need to create a path in the above plot. The path should start at (0,0) and want to reach (M,N) where (M, N) are the lengths of the two signals. Our aim is to find the path of minimum distance. To do this, we thus build a matrix similar to the distances matrix. This matrix would contain the minimum distances to reach a specific point when starting from (0,0). We impose some restrictions on the paths which we would explore:\n",
      "1. The path must start at (0,0) and end at (M,N)\n",
      "2. We cannot go back in time, so the path only flows forwards, which means that from a point (i, j), we can only right (i+1, j)  or upwards (i, j+1) or diagonal (i+1, j+1).\n",
      "\n",
      "These restrictions would prevent the combinatorial explosion and convert the problem to a Dynamic Programming problem  which can be solved in O(MN) time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "accumulated_cost = np.zeros((len(y), len(x)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Let us now build up the accumulated cost"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Since we start from (0,0), the accumulated cost at this point is distance(0,0)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "accumulated_cost[0,0] = distances[0,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lets see how accumulated cost looks at this point."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(accumulated_cost)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BgIg4jOGBU49ngjO2DTBSFzQXYOqqCgDszTAI1WYuOxlgpE4YzOOqtcuqAjtfZOaXM/O/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\nSZIkSZIkSVIf/D/6GPD6aqkZyQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7973e93250>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* If we were to move along the first row, i.e. from (0,0) in the right direction only, one step at a time"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(1, len(x)):\n",
      "    accumulated_cost[0,i] = distances[0,i] + accumulated_cost[0, i-1]    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(accumulated_cost)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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m3rqg2BuAq4EA9gLnZubXFhF7n3YcAXwReF5m5oJjfwn4YfP2W5n5ykXGb6MuzP78/7Li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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f79a40c2850>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* If we were to move along the first column, i.e. from (0,0) in the upwards direction only, one step at a time"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(1, len(y)):\n",
      "    accumulated_cost[i,0] = distances[i, 0] + accumulated_cost[i-1, 0]    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(accumulated_cost)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f79a40c2990>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* For all other elements, we have $ \\mathrm{Accumulated\\ Cost\\ (D (i, j)) = \\min\\{{D(i-1, j-1), D(i-1, j), D(i, j-1)}\\} + distance(i, j)}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(1, len(y)):\n",
      "    for j in range(1, len(x)):\n",
      "        accumulated_cost[i, j] = min(accumulated_cost[i-1, j-1], accumulated_cost[i-1, j], accumulated_cost[i, j-1]) + distances[i, j]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(accumulated_cost)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CPpqZp8447rLrtCwj9grgSiCABeDczPzeLGIvacfRwLeB0zIzZxz7HuCn1dcfZubbZhm/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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f79a40c2950>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, now we have obtained the matrix containing cost of all paths starting from (0,0). We now need to find the path minimizing the distance which we do by backtracking."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Backtracking and finding the optimal warp path"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Backtracking procedure is fairly simple and involves trying to move back from the last point (M, N) and finding which place we would reached there from (by minimizing the cost) and do this in a repetitive fashion."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "path = [[len(x)-1, len(y)-1]]\n",
      "i = len(y)-1\n",
      "j = len(x)-1\n",
      "while i>0 and j>0:\n",
      "    if i==0:\n",
      "        j = j - 1\n",
      "    elif j==0:\n",
      "        i = i - 1\n",
      "    else:\n",
      "        if accumulated_cost[i-1, j] == min(accumulated_cost[i-1, j-1], accumulated_cost[i-1, j], accumulated_cost[i, j-1]):\n",
      "            i = i - 1\n",
      "        elif accumulated_cost[i, j-1] == min(accumulated_cost[i-1, j-1], accumulated_cost[i-1, j], accumulated_cost[i, j-1]):\n",
      "            j = j-1\n",
      "        else:\n",
      "            i = i - 1\n",
      "            j= j- 1\n",
      "    path.append([j, i])\n",
      "path.append([0,0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "path"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "[[5, 6], [4, 5], [3, 4], [2, 3], [1, 2], [1, 1], [0, 1], [0, 0]]"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "path_x = [point[0] for point in path]\n",
      "path_y = [point[1] for point in path]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(accumulated_cost)\n",
      "plt.plot(path_x, path_y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pv/RqlDoir6vRTEfX6QA/f3g9Tz+/icGBaUyJ8NyRnd40jb322DF4HZHX6YbPelp26r4M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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7973ebd950>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above plot shows the optimum warping path which minimizes the sum of distance (DTW distance) along the path. Let us wrap up the function by also incorporating the DTW distance between the two signals as well."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def path_cost(x, y, accumulated_cost, distances):\n",
      "    path = [[len(x)-1, len(y)-1]]\n",
      "    cost = 0\n",
      "    i = len(y)-1\n",
      "    j = len(x)-1\n",
      "    while i>0 and j>0:\n",
      "        if i==0:\n",
      "            j = j - 1\n",
      "        elif j==0:\n",
      "            i = i - 1\n",
      "        else:\n",
      "            if accumulated_cost[i-1, j] == min(accumulated_cost[i-1, j-1], accumulated_cost[i-1, j], accumulated_cost[i, j-1]):\n",
      "                i = i - 1\n",
      "            elif accumulated_cost[i, j-1] == min(accumulated_cost[i-1, j-1], accumulated_cost[i-1, j], accumulated_cost[i, j-1]):\n",
      "                j = j-1\n",
      "            else:\n",
      "                i = i - 1\n",
      "                j= j- 1\n",
      "        path.append([j, i])\n",
      "    path.append([0,0])\n",
      "    for [y, x] in path:\n",
      "        cost = cost +distances[x, y]\n",
      "    return path, cost    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "path, cost = path_cost(x, y, accumulated_cost, distances)\n",
      "print path\n",
      "print cost"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[5, 6], [4, 5], [3, 4], [2, 3], [1, 2], [1, 1], [0, 1], [0, 0]]\n",
        "2.0\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let us compare our naive implementation with that of [mlpy](http://mlpy.sourceforge.net/) which also provides a DTW implementation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import mlpy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dist, cost, path = mlpy.dtw_std(x, y, dist_only=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.cm as cm\n",
      "fig = plt.figure(1)\n",
      "ax = fig.add_subplot(111)\n",
      "plot1 = plt.imshow(cost.T, origin='lower', cmap=cm.gray, interpolation='nearest')\n",
      "plot2 = plt.plot(path[0], path[1], 'w')\n",
      "xlim = ax.set_xlim((-0.5, cost.shape[0]-0.5))\n",
      "ylim = ax.set_ylim((-0.5, cost.shape[1]-0.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANkAAAD9CAYAAAAxg9JWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAADPVJREFUeJzt3V2IXOd9gPFnnapxU+wgRBUSZCIV+qoFOzGmxo0bKolU\nrQoObUNRLpJFu1LAH7nQVdPWqbxanGCDcS5KWhFsa1eFtAUHt0koVQSppNBcuCJpZBFw/nEigSlB\nuCY4tnCNZW0vduTK0mjn45z3fD4/WPBIM/O+WuvRmZ3dc/4gSZIkSZIkSZIaaKbMJzt48OBKkcff\nf//9HDp0qKztVL7+iRMnCq1/+PBh9u7dO/XjN2/eXGj9hx9+mAMHDhR6jiKfg6NHj7Jr165C6xdR\nxvrnzp27pqkbCj1jyTZu3Njr9bds2VLr+ps2bap1/a1bt3Zy/UZFJnWRkUmZGZmUmZFJmRmZlJmR\nSZkZmZSZkUmZGZmUmZFJmf3SqDuklP4K+DiwDvhyRBzJviupQ9Y8kqWUtgMfiYi7ge3Ar1ewJ6lT\nRh3J/gA4k1L6F+Bm4M/zb0mq1szMDHfccUe25x8V2a8BtwD3sHoU+wbwm9l2I1VsZmaGRx99lN27\nd+dbY63fTCk9ArwUEV8a3P4B8PsR8T/D7n/+/PmVuk8XkeqyZcuWoeeTjTqS/QewH/hSSukDwK8C\nL1/vzkVPuFxYWGBxcbHQc9S5ftGTNo8fP86OHTumfnzRkzaXlpaYn58v9BxFPgdnz56t7Jy6K49g\np0+fZnZ2lueeey7L+mu+8RER/wr8V0rpP1l9qfhARBQ6+1mq27DAXn311WzrjXwLPyL+ItvqUsWq\nDgz8ZrR6pI7AwMjUE3UFBkamHqgzMDAydVzdgYGRqcOaEBgYmTqqKYGBkamDmhQYGJk6pmmBgZGp\nQ5oYGBiZOqKpgYGRqQOaHBiM8bOLGt+5c+dqfY4y1i96JkHRPUz6+JmZGZ588kl2797NqVOnWFxc\nZMOGDWzYsGGq9YueyTBs/x7J1FqXA9u7dy+nTp1i586dXLhwoe5tXcPI1ErDAnvllVfq3tZQRqbW\naVNgYGRqmbYFBkamFmljYGBkaom2BgZGphZoc2BgZGq4tgcGRqYG60JgYGRqqK4EBkamBupSYGBk\napiuBQbjzSf7PnD5T/nTiNiXd0vqs64FBiMiSyndCBAR01+gXRrDzMzqnIauBQajj2QfBt6TUvrW\n4L4PRsSz+belPrn8EhHoXGAwenTSrcBdEfFUSuk3gH8DUkRcGnZ/Ryepz3bs2MGJEycmHp0UwAsA\nEfHjlNLLwPuB/x52576PTlpeXi60fpWjg3KtP8lJl1e/yXHnnXe+/bJxWtu3b5/6sUVHV13PqHcX\n54HHAQbzyW4Gflb6LtQ7w95F7KpRR7KngKWU0ncGt+ev91JRGlcX36Zfy5qRRcRFYLaivagH+hYY\n+M1oVaiPgYGRqSJ9DQyMTBXoc2BgZMqs74GBkSkjA1tlZMrCwP6fkal0BvZORqZSGdi1jEylMbDh\nnOqiUlw5vsjA3skjmQozsLWVeiSrez5XGepev4g6Pv9Xzwfbt28f69evZ/369VOtX3Q+WJFTXcp4\n/LD5bh7JNLVhX4M1acJlUxiZpuKbHOMzMk3MwCZjZJqIgU3OyDQ2A5uOkWksBjY9I9NIBlaMkWlN\nBlackem6DKwcRqahDKw8RqZrGFi5xvrZxZTSRuB7wMciIvJuSXUysPKNPJKllNYBXwEu5N+O6mZg\n5Rvn5eJjwCG8Bn6ndXk+WN3WjCylNAe8FBHHBr9UbOSGGqnr88HqNmo+2UlgZfBxO/Aj4I8j4vyw\n+7/44osrmzZtKn2TUhssLi5y8ODByeaTRcS2y/+dUjoO3Hu9wAAOHDhQaJNLS0vMz88Xeo461x92\nwt4kis4Hm/aEyzLngxU56bKM+Whzc3NTPzbXfDzfwu+pPs0Hq9vYlx9wOHt3+DZ9tTyS9YyBVc/I\nesTA6mFkPWFg9TGyHjCwehlZxxlY/YyswwysGYysowysOYysgwysWYysYwyseYysQwysmYysIwys\nuRwC2AHOB2u2UiMreqpHWc9R1/p1zwc7ffp07fPB6lb0/0GO+XS+XGyxq18izs7OOh+sgYyspRzA\n1x5G1kK+ydEuRtYyBtY+RtYiBtZORtYSBtZeRtYCBtZuRtZwBtZ+RtZgBtYNRtZQBtYdRtZABtYt\nI392MaX0LuAJILF6Tfz7IuKHuTfWVwbWPeMcye4BLkXER4G/Br6Yd0v9ZmDdMzKyiPg6cO/g5mbg\n5zk31FfOB+uusU51iYi3UkrLwJ8Cf5Z1Rz3kfLBum2hOTkrpfcCzwG9FxOtX//7zzz+/snXr1rL2\nJrXK/Pw8y8vLk80nA0gpzQKbIuIR4HXg0uDjGrt27Sq0yTLmU9W5ft3zwYqecNn2zz/A9u3bp35s\nrvl447zx8TXg9sHUzaPA/oh4o/Sd9Izzwfpj5JFs8LLwkxXspTd8m75f/GZ0xQysf4ysQgbWT0ZW\nEQPrLyOrgIH1m5FlZmAysowMTGBk2RiYLjOyDAxMVzKykhmYrmZkJTIwDWNkJTEwXY/zyUrgfDCt\npdTI6pjPVbY2zwcrcppHWc9R9HSbubm5Wtcv+udfXl6+5td8uViA88E0DiObkvPBNC4jm4JvcmgS\nRjYhA9OkjGwCBqZpGNmYDEzTMrIxGJiKMLIRDExFGdkaDExlMLLrMDCVxciGMDCVac2fXUwprQMO\nAx8E3g18ISK+WcXG6mJgKtuoI9mngJci4veAXcCX82+pXgamso36KfynWb0WPqwGeTHvdurjfDDl\nsmZkEXEBIKV0E6vBfb6KTVXN+WDKaeScnpTSLcAzwN9GxPJa9z1z5szKrbfeWtLWpHY5cuQIc3Nz\nk80nGwz9OwY8EBHHRy1y2223Tb9DYGVlpdB8rkl1bT5Y0RMOy5jPVeRzsLCwwOLiYm3r79mzhyNH\njhRaf5hRb3w8CLwXeCildHzwcWPpu6iB88FUlVFfk+0H9le0l8r4Nr2q1LtvRhuYqtaryAxMdehN\nZAamuvQiMgNTnTofmYGpbp2OzMDUBJ2NzMDUFJ2MzMDUJJ2LzMDUNJ2KzMDURJ2JzMDUVJ2IzMDU\nZK2PzMDUdK2OzMDUBq2NzMDUFq2MzMDUJq2LzMDUNq2KzMDURq2JzMDUVq2IzMDUZo2PzMDUdo2O\nzMDUBY2NzMDUFY2MzMDUJRNFllK6K6U08nLdRRiYumbU6KS3pZQ+B3waeC3fdpwPpu6Z5Ej2AvAJ\nxpgEMw3ng6mrxo4sIp4h4xDAhYUFwPlg6p6Jjkoppc3AP0bER4b9vvPJ1GdTzSebVJH5ZMeOHWPn\nzp2sW7eOixfrmZpbdD6a88mcTzbMNG/hr5S+C6nDJjqSRcQ54O48W5G6qZHfjJa6xMikzIxMyszI\npMyMTMrMyKTMjEzKzMikzIxMyszIpMyMTMrMyKTMSj3VpW5FTzUp+hxFTzUp+hxzc3OF1y/6HNu2\nbSv0+Msn79Zlz549hR4/7PPnkUzKzMikzIxMyszIpMyMTMrMyKTMjEzKzMikzIxMyszIpMyMTMps\n5M8uppRuAP4O+BDwBvCZiPhJ7o1JXTHOkexPgF+OiLuBvwQez7slqVvGiex3gaMAEfEs8NtZdyR1\nzDiR3Qz84orbbw1eQpZqZcU5Fuqmcc4n+wVw0xW3b4iIS8PueObMGYrOJ3vzzTcLPb6os2fP1rr+\n0tJSresXPR9M1xonsu8CHweeTin9DvDc9e5YZD4ZOB+s6HywMk64PHnyZOHn0DuNE9k/AztTSt8d\n3C42JU7qmZGRRcQKcH8Fe5E6yW9GS5kZmZSZkUmZGZmUmZFJmRmZlJmRSZkZmZSZkUmZGZmUmZFJ\nmRmZJEmSJEmSJEmS+mj6S0OVqCmXAk8p3QU8GhE7Kl53HXAY+CDwbuALEfHNitZ+F/AEkIAV4L6I\n+GEVa1+1j43A94CPRURUvPb3gVcGN38aEfvKfP5xrlZVhbcvBT74i/744Ncqk1L6HPBp4LUq1x34\nFPBSRMymlNYDPwAqiQy4B7gUER9NKW0Dvkj1n/t1wFeAC1WuO1j7RoCc/7A25Sc+mnAp8BeAT1DP\n0f1p4KHBf98AXKxq4Yj4OnDv4OZm4OdVrX2Fx4BDwM9qWPvDwHtSSt9KKX178I98qZoSWSWXAl9L\nRDxDhX+5r1r7QkS8llK6idXgPl/x+m+llJaBvwH+ocq1U0pzrB7Fjw1+qep/5C4Aj0XEHwL3AV8t\n++9eUyIb+1LgXZVSugX4d+DvI+Kfql4/IuZY/brsiZTSr1S49DyrF889DtwOHEkpva/C9QP4KkBE\n/Bh4GXh/mQs05WuysS8F3kWDv1THgAci4njFa88CmyLiEeB14NLgoxIR8fZ1vQeh3RsR56tan9XI\nPwR8NqX0AVZfVZX6srUpkTXpUuB1jJd5EHgv8FBK6fLXZn8UEf9bwdpfA5ZTSieBdcD+iHijgnWb\n4ilgKaX0ncHt+b69ipIkSZIkSZIkSZIktdD/AeW9FXJYUuKpAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7973ed9790>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The path looks almost identical to the one we got. The slight difference is due to the fact that the path chosen by our implementation and the one chosen by DTW have the same distance and thus we woulc choose either."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dist"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "2.0"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not bad! Our implementation gets the same distance between x and y. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let us look at another interesting way to visualize the warp. We will place the two signals on the same axis and "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x, 'bo-' ,label='x')\n",
      "plt.plot(y, 'g^-', label = 'y')\n",
      "plt.legend();\n",
      "paths = path_cost(x, y, accumulated_cost, distances)[0]\n",
      "for [map_x, map_y] in paths:\n",
      "    print map_x, x[map_x], \":\", map_y, y[map_y]\n",
      "    \n",
      "    plt.plot([map_x, map_y], [x[map_x], y[map_y]], 'r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5 0 : 6 1\n",
        "4 2 : 5 2\n",
        "3 3 : 4 3\n",
        "2 2 : 3 2\n",
        "1 1 : 2 1\n",
        "1 1 : 1 1\n",
        "0 1 : 1 1\n",
        "0 1 : 0 0\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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O8Xh9naaeXCQ8wjRznk89uVu6MP8UqHDf31rr3knhbmvtJ9baRuBJ4FivF9gZ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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7973ebdfd0>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above plot shows the mapping between the two signal. The red lines connect the matched points which are given by the DTW algorithm Looks neat isn't it? Now, let us try this for some known signal. This example is inspired from the example used in R's dtw implementation. We will see the DTW path between a sine and cosine on the same angles. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "idx = np.linspace(0, 6.28, 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.sin(idx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = np.cos(idx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distances = np.zeros((len(y), len(x)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(y)):\n",
      "    for j in range(len(x)):\n",
      "        distances[i,j] = (x[j]-y[i])**2  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance_cost_plot(distances)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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luCz32CpXlWjIkA7MLNreSo0bm1tNP5vbJOLeDvdiEVcaN9Zk1FgsWMQNYsZq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\nP8p6V6qTkCtBAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7973d8ca50>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "accumulated_cost = np.zeros((len(y), len(x)))\n",
      "accumulated_cost[0,0] = distances[0,0]\n",
      "for i in range(1, len(y)):\n",
      "    accumulated_cost[i,0] = distances[i, 0] + accumulated_cost[i-1, 0]\n",
      "for i in range(1, len(x)):\n",
      "    accumulated_cost[0,i] = distances[0,i] + accumulated_cost[0, i-1] \n",
      "for i in range(1, len(y)):\n",
      "    for j in range(1, len(x)):\n",
      "        accumulated_cost[i, j] = min(accumulated_cost[i-1, j-1], accumulated_cost[i-1, j], accumulated_cost[i, j-1]) + distances[i, j]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x, 'bo-' ,label='x')\n",
      "plt.plot(y, 'g^-', label = 'y')\n",
      "plt.legend();\n",
      "paths = path_cost(x, y, accumulated_cost, distances)[0]\n",
      "for [map_x, map_y] in paths:\n",
      "    #print map_x, x[map_x], \":\", map_y, y[map_y]\n",
      "    \n",
      "    plt.plot([map_x, map_y], [x[map_x], y[map_y]], 'r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pZA8cgp6QYEwUR36Fbeok3G3a4W55L7osY1kwD8fLr+Fu0pywCeOxrFyO4+XX\n0CKjUNavRY+KRr3hRuSd29BKl0G32ZAO7Mf58KMsiYzk85lTebtkKYQ9uwMLt0SfuCu43VCI/7f/\nvcDvX70bHoEuSShbNpEz5AM8DW7DkrgC8chhtPIVaJxWhxmx0HstTKkOW0sBlVYQKfZE0aOZ9n5r\nXFdgpmpLiCLzSi/gChGB8w4KIeKtXyD2i7eBczVvu3zXBwTeQJ1x/RuvSgEX1AqaXtnPZ8LERSAt\n9ywzD0xDKw0LK8J9B1SGjn+B/z0zEUSR3J5PE9XvdcImjMPRuw/eatXxVK+J5ZclCGfOoBctiqfR\nXVhWLEM8dhRPo8booohl5XIcr76BWrcelpXLEc6cQa1RC9vcWYjJJ/HeVAn5QBLe0mVomZ1N4xsr\nokca1nDBY1A7QmZmYMP1wqR7/oOB36B6hIx01CrVjIx5Hg+5Dz+Ksn4ttsk/4ujbn61FxvJkW/hl\nAoyZC3WeBgSdnKa9qFSyOFWrr+Vf+/X58vCjGOsZ/gnBePecgkKvuarXxNXG5pSNvLryJTTdmMS9\n0wTuOwB1x81nf5ckKsXZcXXpRsR7g7GNG43jhVdAUXB16YoyoB+2mVPJfaoXrtbtsKxYhnXhPHKf\nfg619q3ImzYgZGYYk8qVy1E2rjdW8M6dhbxjO2qlSsi7d4IgoAsC4vFjQdon1/i/8Pv4oXBz8v+3\nVu6CIapiLItW69Q1Vtbt3Y2rbXu0qGhsk380Zqpj1rFsgs6XPE/5U3GEfbYb0Wmj27507l68j20f\n9sT24/dYp0zEOm0K1lnTscybjWXBPCyLf8aybAnKyuUoqxNR1q5B3rAeecsm5B3bkHbvQvp9L9KB\n/YiHDiIeO4qYfBIhJQXOnEHISIfsbHA6weMp1Ee8q4Xp03MpWTL0CUknLc0Qes0VvSauFob9+jaH\nk3cFzjeUgUU3QdNDOlPHPQOAHhmFs9sjSCmnsM6fA4Dzwc7osox1yiQAXPe2NpK0LZgHgLtJMwSv\nF2X1qjw8v1o9ZAWv39lz+JCROyxk9a6QnY0uCHn23S3MDdf/pVPWy4AUDPzu+9rCD2ORN29CrXkL\nrgc6EvbDWCwrfqFRo/YkJsq8yBf0ZjhqhkLt3+vy4+zVRj8LZwIzr8gtnk/c1cX8jiApKOqGuoP8\nbQICa6jAGyLA+s5Dhd9geehqYF9/+UVfSc4r+gbKQ0VfOY/Daf4rCu9+GEFapkKuquBF4qReisTE\nUqbQa+LZV/n9AAAgAElEQVQfx+GMQ/QdtppSWTDy6170b/IhAHK99dC6BR+viSSjt9E29/GnCPtu\nJGHfjcT1QEf0hATcd7fEumgh0u5dBv3T4DaU9WsRUlNxN2lOxLCPsKxcRvbb7xq08oZ1OHoZiR/l\nndtxdXrION6/D61sOeSN69HiiwAgnjmDHhmFmJER2Ju3MGf8/73AL4qGL/Z0Kp46dQFQtm7G2aMn\nzkceJeyHsfzSbTKrhA6+CwRUFEqUdnLitiSaxECCA2QN7i7VlE6VOgeEWbxqcGGUqoYIr6qx29b5\n2vmPfZy4TRZ84q6/PGTBle9aVG9wNbCq+hZRqQhut69ff5sQQfcaWAVch4JDpQeZEpwiObmIKfSa\n+Efx/LKn6VwCmh+C+DHjONewD3G2eNR6DXA3aYZl5XLkdWtRG96GduNNRqBfuhh562bU2rfi7NwN\n66KF2H6aRM7g93G3botl3W9YFy3A2fURtKhoLCuXw8cRqDVqIm/fih4VhbdkKeQd28npNxAwtmH0\nlimLsn4tiIZdWzydih4Tg5CVGUL1mBz/ZUFLKIaYmoq3kh0tMsrY9QZoP+R2vqAm7ZhLgp5KKsUD\nWTf/N3QiHyalknpDsJ/pwiqq3DOUSnH2Qru3Kybu+rNt5nEfnW+A8A02ecTcvIJtnkEpVMxV8wu7\nIX2FvMfnw8RAqotkSpJ22bsMmzBxcdieuo0Np9axrzE8uh16r8jlnSX9eaPd1wDkvNYPy8rlRHzy\nIRnTDXont+czWJcuJmz0KLJGfIu7xT1ocXHYZkwlZ+BgXPe1JXJAP6wL5uJ8tAeeRndhXTgP8dBB\nPPUbomzbirxtK2rNWlgX/4wWFR3YhtFTv4FxY04juPtTM4snjgcCvynuXia0hAQjZ4Yoot5SG2XN\nKoTMDFatjmQ0PfmSF+nOBIbxGpomoCg6S9K/KdCPqqv0+uVJlnb69Sp8iouEP9umbPzKr+YK4MUb\nCwq90dFXeAW0CRM+bDq1gR6LHgEgIwwGNIWRC6Da1xPZ3+hlKsXZUes3wN24KZbEFcbiq/oN8DRp\nhlrJjnX2DMPaWby4QQ+P/Q7Lil9wt7gXT63aKKt+RchIx92kGdaF87D8usLYmOXbb1A2rEWtYQR+\n5cA+tLLlkZP24epgbOkk5GQDIZux/J4JFlPcLRRoCcUMWiQzwxB4dR1521YAJvIwDsJonC/V2KKO\nK0jtlUlqr0yOPJVC+egKSBroaWfwpqcZm7i7XMas9joQY68k8gu9gqCTnY2ZvtnEP4K3Vr9BiuNU\n4Hx0HdhRDB7bovPDpOBqzJzX+gIQ8ckHRoEgkPvE0wgeD2ETxgHg7GJsQWTzibzu1m0RVBXLkkW4\n/ekbVixDDRV4QzZfVytVMvLvx8YBIJ1KRouKRkxNRYuJQdB1dN9ifZPquUwE8l6fPo2n9q0AKFs2\n0ahRKxIT42nIOjKIAYwEbPlnomFyGP3qD6BqtydodPQYDKhQ4D30UJHVL3AGjuWCQqxPhCXMSowu\nBMXT/AJrHiH1L9r87fc+Xxu5oICsyH/dxp9a4i8wYUIu3bsbAd5i0TlyJLg7mj998/z5ULbsJf2K\nTZg4L34/vJ5Bn23mywZQt2t/etftA4BSayVix3Z8uUgkvZcOgmBsrtLoLiwrlyNv2oBatz7Ozl2J\neO8dbOPH4HixN+otdVAr34xl8UKEc2m4Wrcj4v3BWBfMw9XpIbwVbkBZnYgWXwRvuQooG9aR/YGR\nC0je4XP2LFsKmpECQjp2FK1YMcN1WLUaAIJ/Huk0xd3LQjDwp6Leagi88pbNPPaYh8REmZ0Ylit/\n1s3z4UD6frbWgNQIsOoSTUo1xqIJQa48VGQNHKuBVbjnFWJ9PLnlIrY9vBahh9BK5x0cJJm7ZImj\nUcbxjr0WVGQchPM6Q9lEPZKTRdq1g61br/anMXE9od+yF1l6EBoehzvKfUmP6j2Js8XjadwE172t\nsS5agHXuLFz3PwiA47W+WFb9anD9U2ZCZCTObt0JHzXCaNexC87O3YgcMhDr7Jk4e/REtVfGsuIX\nyMkx0jeMH4O8ZTOeBg2xTZuCkJODFh+PvHM77qbNARDSjby+4vFjaAnFkA4dRI+KMm7axyAIbtPO\neVnQfZsaC6dT0W67g1RLabyLNvPEIiugk5CgI8tckHN2e938sGccqfVgVD0AL92rlmdYky8u+94S\nEqI4nZKRT2wtODgUEE7zi6v52uR3DxVwIqneS2+Tb1D7WwOfwxUov8kn9GqIlOYEm6h32d+jCRP5\n8dvJ1axx7eWtZjB8CQyZncHQOsY2igDZg97FsmwJEe8MwNWyFYSF4bntDtx3NMKy/BfkLZtQ69Ql\n94mnCPv2a8JGj8TVsQuuTl2IeG8QtqmTcPboiatNOyKGD8WyYpmRvmH8GCwrl+GpbwR+ZeN61Bq1\nsPy6Aq1kKQDkw4fwFi+BdPQoaq1bEDQNXfFl5fX6EsKZds7LQ+iMv2PHMF50N6ADMynLcY5RDlnW\n/9RTPufATFIdKXnKJuwZT62E2jxarcfl32DIytp/UxrmS0XHjgXF3pIlNebO/U9KUCauALyalxeW\nGQuyPm8IHffAQ7th5tTv2F/9SSrF2dFuvIncp3oRPuJzwr/5EkdvgwZyvNYXy5pVhH/yIZmTpqNV\nuAH3Pa2wLlqIvHkj6q318NzVFMuKZcY+uq2NwG9dMJfsj4ejSxKWlcvJ+vQrAJT1awOBH98s3p+e\nWd62Ba353cZN+zPxeo04JBQi1fOf/M8KDfyrVkmsx7BS1WcDQCB52IUwZueo85b3X90XVVPPW2fi\nwjif2LtwoYM6da7iTZm4brA5ZSP9V/flWNZRwNg4pUd7yJXhy/kanyx6NdDW0ft1tKIJhH8xHDH5\nJACeOxrhvv1OrL8sCVi/c3sag0jYd0bGzoDI+9Mk1Oo18ZYrj2XJInSrDbVufeStm9GKFUeLiTUE\nXt/m69KRw2jx8UhJ+/CWK4egquhhvtjjSyMhqMaOgSbVc5kIFXcBZtOeHozjKOX+1vWLOq7Icz4z\naRpvz3qCLrtz2XXyMRqWu6ugkKooBYVURSkgtlIsFinTdZ7rQnhy33V/R0T9t8Av9jocAhkZArVr\nRyAI0KhRmJm338RlYcSWz/lt7zwiIiNZ9/AWikeUAMBb9EuKD3qLSSuLktXVaKtHRZPz5kCier9A\nxLuDyBrxLeCb9T/YhvBhH5E5cRqeRnehVr4Z69xZ5Ax6F1erNmhR0VinTSGn3wBc97UlfORXKKt/\nxd2kGcr6tShrEvHUb4B16WK8pXwUjy91g7x5I+57Wxs34fu/FlTfokvfVrEm1XOZ0Hwcv3g6lWrV\nNHbtslOVvYH68zl5/gwH0vfz+FZ4fznAPN/PpePvLmfKI6LKSt70DIHyfOkZQsv9riBFCan39eEr\nC7iGZOU8ziKloCNIUQq6hhSloGson6uodpjMztkyz74QyZoNNlRkTusJ5gbtJi4LKTmnqDRpHjOW\n6gx6rVog6APkPt0L67zZ2GbNwNX2Ady+fPnOro9gG/sdtmlTyH38SYPKuaMR7oa3Gyt3t21BvaUO\nuT2fIer1l7F9PxbHG2/hav8gYRPGo6z6FVfrdoSP/Arrgnk4u3Un4qP3sKxcjqd+Q6xLFyOeOoUW\nEYm8czueuvVRNqxDDw83bszjYw18e/r6Z/qC07RzXhb02Dh0RUFISfUthtPB2Bb5T50854Nf6M28\nDbaWBJsKd5duRnf7w0ExM7/Y6vHkTefgK8OrEq6I5GblGuUeT0ER1eMpKKKqnjzir+DxGPUuF2JO\nju+6fCLwNeocmhpyPI82tGOembffxCVj+KaP2VHOUMd6j9hAZofdRN1g2CSRJLK++Ia4ZncQ1ecV\n0m6/Az2+CEgSOe99ROz9rYjs35f0hb+AIBiz/o7tjFn/hJ9wduxCxLuDCPt+LI6XX8PZuRthE8Zj\n+2kSWSO+xVusONaf55P9wSdoMbFYVi4n60uDGlI2bsBbvQbyxvU4O3Qx7seXVkXIdRivDuM1OACY\ngf+y0LFTOBM9xfBsPcN+JNq08bB5s+Ejv9jVowGhV4FFlYyyucJKajf9+JJSOYQnRJF9pfPxQ3AT\n9/zOIdVT0CEUOlD5B5hAWYhryDdQFbwuxH3kG+CEAtcZjqGpkwRkVBQ8zKfNlf8eTFy3cHvdTNz7\nA+7S8Mq9MGKhTkb3+2H5nsA+1t5KdnLe6E/k4AFEvtmHrJFjAPDcdgeutu2xzpuNdeY0XB0642l0\nlzFjX/wz8o5tqDVvwfnwo4R//QXWOTNxdXoI9YYbsS6cR3ZONu5WbQj7fgzK5o14GjfBOm82Wkws\nuqKgbFhrzPTXrwWLkR7dv2pXyMz0nRsTncDCLZPquXSkpgokHpNJoThV2AvobNwoMXHipVEJ5xN6\nNV2j1y896Vu/P83LtyyEu74C8G/ibrFcU86hscfNDdpNFA4+WD8Yt2bQJF/Xg9uPwcM7U0nu2wt5\n+OhAu9xnn8e6YC62mdNwtXsA933GhCP77SFYlvxMxJC3cd3bGiIiyHmtL7Gd2xP+yUdk/jCZ3Mef\nJGzkV0bWzk4P4erclYiP3sM6dzau1m0J+34MlgVzcTdtjnXebJR1a1Br3oK8fSu53R41bsA3s/dr\njuLpVMDYMwRCcvMXItVz/aiDfxP+wTOF4oSTSzgOUlL+3MXzZwhN5ZDaKzPg5U93pfP2b2+ZLp+L\nRMG8/fDQQx6T3zdxUdiQvI5vd4Tk1xLgqbawKwFK/jgV64wQUlGSyPr8a3SrlajXX0ZIOwuAVq48\njmdfQDp5gvARnwPguaspnrr1sS5agLRzB1q58rjvuQ9l+1bkTRtwdjZUYutPk/Dc0QgtJhbrgnm4\nfRusWFYsw9PgNoOi9aWIl44bidikg38YCSRPnkCLiUVMP2fcny/wc7WpHrvdLgJfAzUBF9AzKSnp\nj5D6V4AngNO+oqeTkpKSLvNeCxUjeYZjlMVBeKH22+3m7ny35SsemJ9EkVw4/NuD1CxV1xBEQ509\nIekPDCFVMkTQ+CgsOZ5gfcD5Y1wTKpjq/mvy1wdEVznoBf4Xwe/wEQSR06d1PvvMwuefW2jUyGs6\nfEz8LQxf0JuobA/33fo/hjcNLqyU2uxHa9mEqFdfRK1WA+/NVQDw2iuT0+ctIocMJPKtN8j6xngi\nyH3xFWyTJhA+4nOcDz+KVrqMMet/6EEihn1E5viJ5D75DNaf5xM2eiRZo8bhvrMxltWJiCeO476n\nFbapkxHTzqJWrIRl9SoyOxvWTyn5JLrVirx7J94bKyLvT0KtXBl510685cobOfkVBdGRj/IpBFwq\n1dMesCQlJd1ut9sbAMN8ZX7UAbonJSVdcwvurVbABfNoxzwMFf9iXTx/BkmUaCJX5t3lScbj1NqV\nwMqL6iOmUO7EQMBh43fqyFJwYJBkdMXvtFGCrh7/8fnqfYNN0OmTz/XzV/V5nEUhrqBAvUIdWWL3\nDzJv9I9l9UkZDwpn9SIkJsabDh8Tf4kD55IY+sUuSmXBj19G5anzVqxE1udfE/NEd6J7PEz6kpXo\nUdGAn/KZg23GVIPyadUaPTKKnP6DiH7xWSKGDCRr5Fg8TZvjubUe1oXzkHbtxHNHI9QqVbHOm0PO\noJM4O3fFsjoR29TJuFq3wzZ1sjHrb9KM8NGjjP8BQNm0AbVKVeQ9u3G1bIW8dzfehGIoHg9aTCzS\nwT/Q4+ONBJAU7gKuSw38dwCLAJKSktbb7fa6+epvBd602+0lgAVJSUkfXsY9FipiYnRIDZ5frIvn\nr+D2upnp3MD8V6B4NsgaPHBDO56u+lSIwOlPXxAipPpeo2wS2enZBYXWgDvIE0yfEDj2BFMj/I36\nUDeQ4Mz1vU+++mvA9fNtyLEbhQocJjm5lOnwMfGneGXFC9S+Fb5ZAA++NoLMWo8SXbZyoN7d9n4c\nz75A+DdfEvXSc2SO+SGQtjzr82+Ia34nka+/zLmGt6HHxePq3BXP2G+xzZxO7uNPo9ZvQM7rfYl9\nqIMx6x/3o2HtfPVFbONH43ihN3rf17BNnULacy+hh4djmT+HnEHvwuhRKNu2oN5UEXnTRlzt2qNs\n24oeZ2TnJMxgIPSICARdxxsegZid7bvxq7+AKxrIDDn32u12MSkpyR8tJgMjgCxglt1ub52UlLTg\nMu7zstGxYxjfHwvSHkWKaFgsF+/i+SsEXD4xcNw3dd+sLaRRtYF/y+UTlRBF7j/h6vkrhLp+/ANQ\niCXUP1hcqD4w6HhCcv14PAUdP/nq8XoD7qAxo0RkPMionKUIqRS72t+KiWscRzIOsf7UWtbXg1JZ\nMCBR40inVghLtwVm9gA5A95B3rYF6/w5hI0cQe6zzwPgrXyzQfm8+7ZB+Xz9HYgi2UM+Iq5tSyL7\n9yF90Qo8Te/GU+dWrAvmIu3ehbNDZyLefZuwH8bheKUPrjbGTF/ZvhV385ZY583GW6wEuqLgz9sT\nNvlHtGLFjRvyU7L+CZeP/9dtYQh+sbcQXT2XBLvdPsxut3cKOT+Wrz465PhZu93e/8/60yVJ13Vd\n18uXN378CD2/0PHfqEu2lddB1w9RXj+EcVy6tK5v3qwXOup/V19nEAV+6o6qW/hvdp3j7rt13UhN\nGPwpUuTK/N5MXB9oPLZx8P/ubfRRdYw/nOxGDXXd6czb+ORJXS9RQtclSdcTE4PlHo+u16tn/MHN\nmRMsf+gho2z8eON8wQLjvGNH4/yNN4zzceN0ffly47hHD12fNMk4HjJE15s00XVB0PXPPjPKXn/d\neO3SxXht3dp4bdHCeL3lluAff8uWBeLbpcbwS53xrwHaAtPsdntDYIe/wm63xwA77HZ7VcABNAPG\n/FWHp09nEa8ZnyPNN+MNPb/Q8Z+189c5nQUFzhMnoE2bwqV5AObf/0vg+GT2CRpOrA0IpOdmkJxy\nDln88688ISGK09fCjP8awNKlUZQqpZGc7Def6RQrplGqlIPTp//00usO5t9FEBf6LmYkTSXxaMgG\nSgL0am3skf3AqnU4O3cla9TYwGwaORJl1DhiHmyD1rET6ctWoRU3VvZKw74i7u5GaE8+xbmba6HH\nxSP2GUD8nDlob/QlrXFLqHsnsbfURpk+nbTE9ehdHiV+6FDU4Z+RvmQl8WXLIUydRlrvfhSxWFCn\nTsfVrj2RK1eSneEgEnAm/YFVklD/OIQCeJJTUAB3tgML4NFB8X0cd7YDKV98u1RcauCfBbSw2+1r\nfOc97HZ7VyAyKSnpO7vd3hdYgeH4+SUpKWnRZd1lIWEanf66USGiVGRpHqn6GFsXjeL2Y/vZfvAJ\n7qjQ7PwCp9/FkxCDnO0xRFa/CyifKKvLynXj4PkrhG7YUqOGlyVLFEqVigQwXT4m8uDjlQaxMKHV\nFO654b5gxZNO3F0ewDZ3FnrRosZGKL7/Fc9td5AzYDCRg94i6sn/kTFjHigK3purkPN6PyLfe4fI\n/n3JGvEtWpmyOHq9SMSwjwj/cjiOfgNxvNaXmEe6ED78Y7K+G4/7vrZY589B3rgBZ6cuRnrmxJW4\nGzfB+ssSHK/3A0DauwetSBGUzRvx2isj79mNt0xZxOMGeSJk+wK77z51RSlUqueSAn9SUpIOPJu/\nOKR+MgbPf03A7+Tpw9BAWWE6ef4MYXI4Xy2EhieARbMwxsw/R9wlvlfAUZPf2umzi+pKyMAR6t7x\nDSR6HndPqNXUNzD5B54Q+2le905I/YUGNiXE3fNnA5ssg0WjZkUn2zc6QVFo284nfPn2ojPz+Jjw\n49eV3/L7wFN8fwscu+1Q3kqbjcwfJhN7/32Ejf0OLaEYjlffCFTnPvs8yqYNWOfPIeK9dwwRFsh9\n7iVjYde0KYbL555WOJ5/2bB3fv0lzocfC+yza507C8drfQ1r5/w5hI0eiePNAUQMH4rtp8m4HuiA\n9ZclSAcPoMXHY/l1OZ66DbAuXoizdTvkvXvw1qiBZf06tLg4xHM+D78vJbOuWMxcPRcLm1U3nj18\nKGwnz4Xg9rr5ad8k5nSCuidB8cLdpZvS+aZOIWKn3+VjiKERFpGcTEcw/UFARPUEc/eEunJCBVSP\nJ8TB48mbt8fpNNwBofV+sfUaRkLI8RpEPCjkEsZTfMt0Opl5fEyg6zqvHxhG+RLw5BaY13sg6bMf\nJDamZLBNTCwZP80ktnULIj56D61oAs7HHjcqBYGsz0cg7d1N+Ndf4Klb30jY5nf5tGhM5Gsvca5B\nQ/TYOHIGvEN0ryeJGDyQrNHf43j1DWIefYjw4R+RNXIsarUaWBfMJeed9/DUa4CyaiXZbw9BF0Ws\nC+fjvqsptlkzcLbvgBUgIsK4x0jDeqoVTUA6esS4NV9KZmT56i/g+rcg1MkjyzpFi+oIQuE7eS6E\ngMMnFo7GGmUzhFVUvXfoBR0+EQlROP5JLlfXL+ze8XiCA09gkMo3sKieC9tT/Xl5QuvzlQUtpyHX\n+I6too7L4TTaelU2rNGQMVZCn6HoP/cdmbimsfDQfA67k2n2GMyZDG13e9jzYDOEORsCwRRAK16C\njKmziG3Tksg3eqMVKRrIyKlHRZM5biJx9zYl6sVnSb+5Ct6KlfBWqYrjtb5EvD+YyAH9yPpypJG3\nZ8y32ObOwrn2Kdz3tMJToxbW2TNx9H6D3CefIerl5wgbPwbnQw8TtXE91mVL8Nx2B8pvq3G2/QDb\nrBnG3zsg+Oya/jTMenhESH4e41WXpWtiAdc1j/y7OqmqgCD8+c5ahY3z5fFRdZWBa/oxuc2Mf+Qe\n/hKCYFAtioJOMG3F1c7ZA4aIlxkyCL51gZ26zDw+/11ousZbq4ydsrKtcN/DMGU6tN95gqz2LXFN\nnW9k3PTBe2NFMiZNJ+aBNkQ/+wQZ8bPw3H6nUXdzFbKGfUH0sz2JfvwRzv28HCIicDz/MpYF87D9\nNAlXu/a4W9xL9rsfEteqORH9+5K+ZKXB9T/WlfBPPybr0xFEDB6AbcI40hLXEfmWDetPk8h9/Eks\na1YhOI2/V+lAkpGq4bBBTQnn0oyb9OXj1yIjA5k6ESVjs3WrtVC+t+s2V8+qVVKBsr/aWauwEZrH\n5+QzaVSMrYSISOsb2/1j93A94Xw7dS1b5jD5/f8oNqdsZMjagZzMOREocynQsTOMrwVRO3YTe3+r\nwE5afqi31CFz/ETQNKK7P4S0c0fw+g6dyX3iKeTf9xL16ovGE7Esk/XFN+iKQuSrLyGkn0O9tR7O\njl1Qdm7HNmUi7nvvw1O9JtZZM5COH8PZvQdiWhrWX5biatUa+Y8DaGWMjZ4sqxJRb66CZd1veGrV\nRvp9D95y5ZGOHPbdhCHi6pFRCFm+iY8oFmpa5us28PsxjU7/uJvnfJBFmb71+6Oh8dnSfnjPpCJk\nZhiZ+Twe4w/MxF9iwgQj+EdH6+i6QNWqERQvHknHjv/cgG7i2sCo7V/z7Y5vkAWZTY/sDEyykl/I\npPXidBxP90Le9zuxbVoiHTyQ51rPXU3JGvEtQnYWMV07IB4OCsLZ77yP59a62GZOwzbOyNnjp3yk\nU8lEDnwTMBaB6eHhRLz3DkJ2Fo5X30DQdcKHf0zu/55AlyTCvhsZSNxmWf4Lnjq3oqxJxN3gdoTc\nXLTSZRA0DW+pMogZ6WjR0QFhV7dag6t2BcGkev4O6tb1snGjfFWcPBdCvRIN6LEVxs7JhvcqFqj3\nu3KKBFw5StD94nsN5NxRQvPvBF0yyIqRXydQpwR32ZLzOWryOHou4MgJddwoStARFDgOfe/zWE39\nDqBCQs2ahjDfoUMYq1bJgICumw6f/xpSck7hWDKL77doTOt6K+Wiy+dtIIrkDP4APS6eiA/fJbbN\nPaT/NAtvjZqBJq72HRDOnCbqzT7EdHmA9PlL0RMSwGIhc/QPxN3diMgBfVFr1kKtWz9I+UyZaFA+\nd9+D44VXiPjoPcI//YSc/oNQq1bHOms6jtfeMPL0zJ0FVhve4iWwzp6B49nnUbZsRg83JiqCx5eG\nQTb+R7SE4kiHDxpl+e3ZTqcxQSwE2/Z1G/jLl9fZuDF4/k85ef4ME/aMZ20Z+LEGRHgFWpRqjkUj\nj2tHQcPrdAddN37h0+EIOICC7p1rI6fOXyGwRWTIwBEcFHyJ4EIHFVkxBqAwKzG6ENwaMmRQemxV\nGF2x4EFhGc2Zy/2mw+c/hDE7v+XGsxpdd8G9727BUXoGlvs65G0kCDh690GLjSOy32vEPtCajB+n\noja8LdDE2fMZxNOpRHz6CTFdO5Axaz56VDRa6TJkjhpHTOf2RPd8jHO/rEIvWpSsz78mruVdRL76\nEucS1+Ho9SK2iT8Q9u3X5Hb/HzmvvkHME90JHz6U3J7PYJs7i7Ax3+Lq9BDhX30WcPDI+/cb/P4f\nxpOIkG7k3tfDbAGnXX7HnVCIrMB1Gfg9HpgxQ+aGG7yBVbtXWwD0b9GYmgDdOwDo3H9TFN/d832e\ndgkJUaRfjKtH00KcMJ48jpyAXdPvzvHktXIG3DV5HDtqXitpAUeONzDwBKykfqtpSH95to7M06cv\nEZwnmEBOzHUUtJn6HA+WC3zsJ0KOb2Mtc7n/Yn4dJv7FcHvdjN45iuy64BHhq4U6cf/rQU7vvcYC\nqXxPmM7Hn0SPjSXq+aeJ7dKezDE/4L77nkC9o+8AxNOnCfvxe6L/9wgZk6aB1YqncRMcffsT8f5g\nop95goyfZuKtVh1H7z5EfPQeEQPfJPvzr8kZOJjop3oQ+c4AMsdOMDJ1zpiKo3cfPDVqYfl5Phk/\nzSL8q89Qfl2BWqUqllUr/8/eeYc5UbV9+J7JpO5mG7t0KQIBqVJsKMWCWLAg8FlQeRXsvihNEftr\nF+xdFEFQAZEmFkSlifQindAR6W5vaTPfH5NkJ20bW7JLfte1F7szk8lkyDznnOfc5/fg6nY+hhXL\nVcM2XwPgUEcAssVSNLELRR4+sR5/qLT4poLA8887uOqq6ODU/WinRvP3zuWxDHu5SjT6JYrqTL/R\n6LUCVeEAACAASURBVCdxasVsgaKQlmLh5JH0QMzU+/t/H9Cxaa2ChJv9NAeqP5UXU9Vo6l9TyXXl\ngACfd4UNDeC7mdD8zdfRr19L9kefo6QG4r6OmwahJCSQcPcdJNx5Kznvf4LjJu/cnyCQ+/pbiP/+\ni/GnBVgfvk8twajTkT98JNL6tRgX/oRl/Mvkj32a/OEjMfy4APM303BefyOOG27C9fmnGH/8Hv2f\nf6i9/mFDsLw9gYJ77idh+AMYli7GdW5nDIt/o+Ce+7Hs2I6nQUMA5PoNkfbuwZOainhKNWRTrAmI\nPsoHikb2FdTrrzWTuydOCCGo3+OPm9i8OTo+Yji0U0Fh6MI7+O3gL9VwRVEuX3rIbEaxJqAkp6DU\nrYvcsBFyk6a880NjMhu0YQsdycUKKMyeHSN8zgQ9v/T5gL83NoQu98HKTqkYli4m+YoeSOvWhLzO\neUVfMmfOQ7HEYX1gGKZJE4t2ShLZH3+O88LumObNJv7Jx9QgK4rkvPcxnqbNVPuFX34CvV6lfCSJ\n+JHDEXKyyX3xVRRBIP6psTiv7oe7zTkYZ83AdW5n5NRUTNMmU9h/oDd9o3ZOxX//9V6Yl9Wvk1q0\nYleSELw2zLLeAB5vJb9Y4A9UuAnvqsY3i1NwicYF/RcB8G/BqViJxnLKR/gkJyuAwPjxFcM4xxS9\nWn54CRmFGSQak9g99JD/ebKPyqblwj3kjXsG8dhRkm64GtNnH4cESveFF5E55weUOqlYx47C8ubr\nRceYzWRPnY77nHaYJ03E8pYKhihJyWRNmoZiMmF96D7EA/v9KR/d0SPEPfsk7k6dKbxlMNL2rZi+\nnqoSPh4PcR++R8GddyFmZoIgeG2Zf8fTpCn6NauQU9P8aR7fdSiSFOi9r9erI17NMaerqHD1UnQ6\n5eTRDFK6tgcgff1WgIC/I/3uO+7vvwWac4DXGQMU+fJEw6RuJN005xq6f/sH9XLhoqa96diwG3EJ\nceQ5ZT8dU+SVoyF8tLSOlrYJomnC0Tb+SVW93r9QJFpVWkdKWYYWLeLJy1MHCrXRvC3mzqlqwMTz\n2Jy9i/t7Psmo8x4Pe4x+2RIS7r8b8dQpCvsPIOeN9yA+PuAY3b49JA66Ed3fh8i/7yHynn/J/zyI\nx46qCOihg+RMeIfCO+8CwPjNNBIeeRBXh05kLvgFJImkvpei37qZzOmzcbfrQMqFncFkJP3P9SRd\nfxW6PbvJnPcTSTdeg6eVDU/zFhh//J6CQbdg/nY6zot7YFixHE9KCoKsIGZm4ElLQ8zO9uObsjUB\nwelAcDjw1KsPBoM/9tWtm1CuGF5rcvzVacRWXnUQG/HSbyApwKol+Eo0xlXR+yu+Vbs+iibYSE27\nT0vbBGCfXnzUt89n6Bbw2qAGSR9UilHbmGmvIS0RKdcZaOaml0LQ0iF3JeDOcyCiR1Z0MbSzlmp3\nxi4+e2MXafnwR+EW6CqH7by4evYm47c/SBg2BNOc75C2bSV70jQ8tqIqXJ6zW5K54BcS/+9GLJ98\ngJiVSc6b74EkIddvoPr69LuS+MdGIKfUwdnvehy33k7B2tWYp00hftwYct96n5x3PyL5yl5YR/5X\npXxGjCb+xeewvDWB/JGPkXDf3Zi+norjuhtUf54bBmD88fsip01v7l6p1wDdjm3qNkkfyuxXYPUt\nqEU9fqcDLCcO+s8ZzT19UMmELlPboTt2nAa5qoHbTc2u57GLHyXzZJaGqHH5PWyKvGyKiJoiWicc\njROGttGYvRURNkGIqP/9QqmeaMdHT5JKFzZwmLOi/jtQFsV6/HDj3Gto/tMffPAjJDqgoFs3Ct78\nwF8wPUQuF3H/ewbLJx+gWOLIees9HP0HBhwipP9L4m0D0W9Yj+PqfmR/MglMJgCkTRtIuvFa8LjJ\nmuG1digsJKnfleg3byLnrfcpHHwnlvGvEDf+FQpuH0Luy+NJueR8xCOHyViykoS7BqPbv4/sTyaR\nOPROHFddg37dGpAVFG8eX8zM8JM9clwcSBJiVhagLuJSdJK/4Lqnbj0wGk+7x1/jA//AgWamLFMX\nQzXnQEBJxWju7X27azoP/XZvwDZJlNjywBbqKI2q6apKIR8+qnEW9Tc+4fBRDYkT0iAFGLP5thUh\nnXEGkfysvCBjN1egC6nLxaKfFPS40OMikyT+w2RySIgF/lqkk/knaD+5FQoKDbLh3Z9g4A41H57/\n8KPkjxgD5vDzeYb5c7A+8hBiXi75w+4j77mXwFAECgu5OSQMGYxh+RKcl/Qk+8tv/OZu+iW/kzh4\nEIrJTOa8n/C074B48ADJfXoiFBSQ+cMi3G3aktz3UqRtW8icMQchN5fEoXfguPIqHP0HkvDAMAoG\n34m0bQvS5r8o/L9bMU//CsdlfTD+vghPs+aI/xxGcLnwNGiITmMxIcfFIbhc/oleT1pdMJnO7FRP\nsBEbUCOCPkQwcJPdjFw4kilXzqiGKyqlqhAfjUuzkleKYDc+zPcgNTW603wxlU1jlo5A8X7TjibA\noJvhBrvIjMV1iHt7AsZ5s8l9/S1cvS4Nea3z+v5ktm1Pwt23Y/nsE/QbN5D92RTkRo0B1RMn6+tv\nSbh/KMYf5pN4Uz+yvpmNUqcOrt6XkfP+J1jvH0riLTeRueAX5GbNyflwIom3DSLh7jvIWLSU7Hc/\nIrlvbzXls3Qlzu6XYPzlZwruugd3y1aYZnxN7tPPY920EUH2LtDyFluRrQnoXC4UozEgxaPoDaAo\n/qCvboxRPVFhxFZeaSmfRQOXAtA2pR0Pn/dwNV9ZzVOweRvARRd5or7xj6l0Wvr3Yn7a/0PI9nk2\nmQFPtyX/vofQHTxA0qAbsD54D8KpUyHHelq2IuOn3ykc8H/o168l+Yoe6Jf8XnSA0Uj2xMkU3HYH\n+k0bSbq+L+I/hwFw9B9I7kuvoTtxnMSb+yOcPInzir7kjXwM3aGDWB++T6V8HhmF7p/DxD3/NLkv\nePHO554kf/hIBLcbaddO5NQ0DAt/wt2mLfqN65ETE9F530euk1rk0AkoBn1g0IdY4NcqWozYyqtO\ndTvTt9nVbE/fxgM/PhBDO8shH9rZoIGMzebh++/17NhRK77eZ7yeWfEECjJPXvgsJx7MRnlW8Xea\nvhg4j7wXXiHzlyW4OnXGNGsGKRd3xfjNtNAgGRdHzocTyXntTYTsbBJv7o/ljdeKVsVKErlvvU/+\ng8ORdttJuq4vur27AdXaIe/R0Uj795F420DVlG3MEzh7X4Zx0UIsb08gf8QY3G3bY546GfHUSQpv\nH4K0aydCTg7us1tgmvkNhf0HIGZl4W7ZSk3ttGiFmP6vv7fvs2WQzRYEt8e/gt2nirJtqNE5/sua\n743oz17Tenu/H/yV3SNvYvAWSIyrQ0JcaihFo/1d612jD6Zt9CXjn9rXhkE9Q0ojBtM0VYCGljev\nvWiRjsGDLYBSa/DOMzXHv/foX8wc04Pfm8ONN73AQ50fiXwv3G7Mn39C3CsvIuTn4ex+CbkT3sHT\nslXIodKGdSQMG4Lu8N84Lu9DzgefFvn2Kwrm994i/sXnkFNTyZo+G3fHc0FRiB81HPO0KTh79Cbr\n628RcnNJvqIH4pF/yJoxB6VOHZKu7I3coCGZ331P8hU9QdKR+/hTJIwdReGgWzDOmYWnaTN0+/fh\nadoMaf8+1ZbZW3VL0etR9Ab/hK5WcnIKSnz8mZ3jf/JJR0Dgr8mTeeuOr8EqgKiAIzsdChRErXeN\ny1Xdl1isFFEMcOwMbCi0zqFlaMisFuLcSpkbsu1vxXEtJgox8YdyCcuWmWJ4Zw3Vx9/+l8nehe0/\nLP8f+RM6w9XXhj9Ykii47yEc/W4g/onRGH/+keTeF5E/fCT5j4wKKGLi7tKNjEXLSHhwGMbfFiH1\n6UX251/iPrcLCAIFw0eiJCYR/9gIEvv3I3vaDFwXXaxaO5w6hfHnH1Rrh08mkf35lyRdfxUJ999N\nxq/LyX9kFHFvvo7lg3fJH/kY8c8/hbR7F+7mZ2Oc+x2OK/pi+vkHnF26YdiwDsVk9lfhUsD7d6RG\nPtbj59q2e1m4UCIlRcZorBmTuuHkQzu1Xj7DOtzHyz2K1iSgKGrtXH85xECixk/MaH4Pa8YWjH8G\nH+8rhxiAfwbSNOGM2PykjQYN9Zu0aQkg/3GuCnUbjKTneYbnUJf41+SOwZnY4/+34BRtv2jB5XsV\nnl8M3Q97d1x3HRnDR+Pu1DnyixUFw48LiH9iNLpjR3G3bEXuhHf81bb88niwvPk6lgmvgl5P7kuv\nqwu2vEZoxrnfYX3oXtDpyP5sCs4rr4aCAhJv7o9h1Z8UDL2X3JfHY5oyCetjI3B16Urmt/NJ7ncl\n0o5tZH7zHfHjxqA7dJC8x58k/uX/UdjvekwL5uPqdC76vzbhbtkKaY+aUpITExFycyPWwpaTklCs\nCWceznlZ870B+Ob557v5/vuCijCsqzaFQzt1go5lt6w+PQO3aFck9NPbUKRYjaQfzwx07AxqfALq\n/HobsqfHiki4EVCYwc38jVr5KBb4a5aGLRzC/L1z1D8UuGIfPLcULj6kbnL06Uv+6LG4O3eNeA4h\nJ5u4l/+HadJEBEWh4NbbyXv2hYByjAD6338l4YGhiBkZFA66hZzxb4PF4t+XePft4HCoNXcH3oyQ\nlUnS9Vcj7dhG3tinyB8xBuvD92H6djoFdw2jcPCdJPW9FLlhI3Kfep7E++7Ceenl6PbvQzzyD+7W\nbZC2bkGJjwdBRMzOUkstutxFi7vCSE5MRElIPLMC/4kTAg0dB9hPM0AN/CkpMjNn1syevk9XzbqU\nDSfWh2y/vEmf6KnNWw0qb7ALh/nW1Lkfn860wJ/ryqXVZ2fhUYJ6vgqMdZzH80v0GFb9CYDj8j5q\nA9D1vIjnkzaswzrqEaRtW5Dr1CH3f6/gGHhzgMWxePhvEobdiX7DetzntCV70lQ8LdT5AWnNahIH\nD1JX+L78uurjf+woSdf2Qff3IXLeeJfCAf9H8tWXI+3YRvYHn6Lbu5u4N8dTMORudPv3Y1i2mPx7\nH8Ty6Yc4e12KYeli3G3bIW3fhiJJKPHxqqdPMZITElASk0478Nco7CGcEVt6es3AN4uTFu1UnlXo\n2VhlkXs27l29F1ZDFYp3KsyZE3PurClaf3wtTy0fi0fxMOa8JwLMDU88lM0rr6wha95PZM5eoPLy\nvy0i+erLSby5P9La1WHP6e7SjYxflpD7zAsI+fkkPHQviYNuRNy313+M3PgsMuf9TMHd9yDt2E5S\nn94Yvp+nvv78C8ic+yOeuvWwjnsMy/hXkOvVJ2vmHOQ6dYgf8yiGxb+R/cVUZGsC1tGP4LiqH+5z\n2mKeMonCG/qjiCKG337Bc1ZT9CtX4KmTiu7AAfW9U1MDgr4iCCiiTrVV0aqCsqM1KvD7VNPxzZI0\nuptqPvXuHy/hzs2O1eQth3x4Z1KS6tx54YWx2rw1RR9v+oAZu74iXm/lng73hz9IEHBd0pOsuT+S\nOfdHnJf0xLD4N5Kv7UPioBuQVq8KfY1eT8HDj5C+fA2Oy/tgWLaYlF4Xqi6cPl7eaCT31TfI/ugz\nBNlD4tA7iHtmHLhceNq1J/P7hXiaNCNu/CvEPfU4nuYtyPp6FpjMqjHcsWPkvPcxQkEBCfffTc7L\nr6PodMS9PYHCWwcj7d2Dq2s3BKcTuWlThPw81ZTNu/ZAARSDQS0mI3tAUQJj/ZmIc/pSPVrV9CF8\nsNLSrGw9sJvnHrcxc2Zgy6xEwi81lEyRS2cExDNgn8YwLcy+ADKntPhnMMkTCf8sxaRMRaQ3akva\n50xJ9RzPO8aYZ9owcKvMnh4dGTl2ifq90yjSvdCv+hPL+FcxLF8CgLNHb/LHjMV1YffQN1IUjPPn\nED/uMcSTJ3C3OYec8e/gvuBC/yG6nTtIuPt2pD27cV1wEdkTJyPXb4B47Kg6utixncKBN5Pzzofo\nVywPsHYwzf4Wy/tv47jmOtytbMS98wYFt9yO8acFgIISb0U8eQJkGSUxCfHfU2ov32xGKCgIAR/U\n7gvIcfEoKSlnFs5Zt66C+ZRCQYH6WWvyZF1xmrJtElvqwndtweoU6FGvO3qZQKpGO+HpdCLm5RVR\nNTXAUM1XWD60odL7a/BiMpIkiOH3BbuChjRU6r5LlsVxvrc27xrOZyXdY7V5o1iTtk6k41GZoRuB\njZtxf9Ma56BbKbxlcGQzNq9cF3Yn67v5SKtXETfhFQxLF/v9d/JHjw0kegQBxw034ex9GXEvPIf5\ny0kkX3clBXfcRd7Tz6EkJeNpcw6ZvywhfsR/Mc2bTfJll5A9cTKui3uQOfdHEm8bhGnWDIScbLI/\nnUzOex+T4LN2mP8z0oZ1GH/8HteTz+Fucw7m6dMouGsY5i8+w9muA7p/DuNuaUPaY1d7+vFWxJzs\nsJ/NH93PxB6/2w2W4wcQRUhLU2pcr600SkwxctabTQLQzptaDeLjPp+X/WRaQ7XgRiEE/yyGmikO\n/wx7fBj8078eIchoTXtNQftEtxtFa/52mtpNS2yo2FxN6zScCT1+p8fJOV+cTY4jmy5H4T+b4K7t\nRuJz1ck9V+cuFN48GOs9/+GkR1/i+aS1q4mb8CqGxb+p5+9+CfljnsB1cY/QY9esxjp6ONLOHchp\ndcl96TUcN9ykjkwVBfPEj4h77imQZfLGPUPBw4+qWOddgzEs+R3nRReTPXU6phlfE//k47ibn03W\nF1+TdPONiKdOkvvaG8Q/Pgq5YSMUvR7dgf3IaXURM9LVtE9KHcT0f0v8TLLFglIn9cygeoIRzk8+\nKaB//9ppa7Dw6DzumHNHwDYBgT9uXVu70c4wCgh2sly0JiC44dE0WsGN2IvPiuzcKqPHxXbaYqd1\nLNUTpZq+4yuGL34gYJtF1rGhzks0W7AYw++/qh0Ag4HCq67FccttOHtfHpIKCpa0bg2WN17D+Jta\n9c550cXqCOCSnoEpR6cTy4fvYnnzdYTCQpyXXUHOa28iN22mnmfNahKG3Ynu2FEcV11Dznsfo5jM\nWB+6F9P8Obg6dCJr+my1kXh7Aq5Onckd9yxJgweiJKfguL4/5s8/wdGnL8ZFC3G3siHttuOpWw/d\niaKOniKKas9eUUICtGI2I6em1f7AHw7hrIkPbmnVb94VrPkntF7oRQ0uZl7/n6rhiqpPFRXsOnWK\n4+hR32yJwvbteaSm1qzJ8jMh8J83rSMHsw+EbPdhzeLxYxhnzST+269h+3ZA9ad3DLpFTQW1blPs\n+aUN69QGYNFCAFwXXETe6LG4evYOxDr37cX62EgMyxajmM3kjX6CgvsfAr0e4eRJEu6/G8PypXia\nNiNr0jQ8bdsR/9gIzFMn427RkqyZc7G8+Trmr77E2fNSnJdeRvzzT+M67wKErEwk+y5cnbug37gB\nT51UxOwsBJdLTVkKAjid/sDsy+37pBiNyHXr1X6cM9pr6Va0Vg9bHYCvfd73SwDiDdZYUfZyykf4\nJCSoj9Enn5ScJoiparX26GqcHieSKLHhjm0Bz4BvLYtcrz4FDw2HrVvJ+GUJBXffg+B0YPngHVJ6\nnE9S397qQi2Nw6VW7i7dyP7qWzIWLsZx5VXoV68kadANamGVxb/58+fy2S3I+nYu2R9ORImLI/6F\nZ0ju0wtp/VqUtDSyZs4lb8RodAcPkHztFarl8oR3yP/vCKS9e0i6ri8F9z6I46prMCxbjLRpI4XX\n90e/djXu9h1RRBHx2DEUUURAnbuTLXGggKAJ+hCmZ36muXPWdoQzkq49+3psya1Zs+tn3p8/AvnI\n3winTiFkZUJenoqhxVDPYtWxo5rP37IlF71e4Z13DDG0M8r0v5XPcDTvCINst9DYelbxBwsC7nO7\nkPvqG/y7ZTdZn03BccWVSH9twjp2FHU62LDe8x8Mv/1SVKRcI3fnrmRPm0nGoqVqRay1q0m6uT9J\n11yB/vdF6vMkCDgG3kz6H2spuO0OpO1bSbrmCuLHjkLIzyP/iWfImjYDxWjC+uhDxI94mLzRY8l9\n+n/ojvxD0k3Xkv/wo7guuAjTvNkoSUmqL//sb3H2vQbd0SO427RF/PcUcoK3pq67FH5cZ8rk7pmA\ncGoVbkj/5aq3uW/AM8QX873wUzJ6Q9lRT72hzE6fiqEYF9BwTp56Q0SXTy0Giq6oxkJFpzdqMtpZ\nm1M9x3KP8vutrUnLA91lV3HFkAnIZzWJeHykeyEeP4bx2xmYpk9Dsu8CwFOvvpoKuvm2iKkgactf\nWCa85kUtwdWlK/mjx+K8/Ep/Ckj/5x/Ej34Eac9uPPUbkPvyeJzXXod46CAJQ+9Ev3kTrvYdyf78\nSwwrlhM/+hG13ONHE4l7+X9IO7aTf8/9mL+aiiKAnJaGdOBAgE2DotOp76dprEJy/JKE3KBh7c/x\nyzIYjxxAUWo3wulTuC/1q6teIP7N8bRIBwt6+ja6AoMihCVhBKcrEPV0RSBoohT11BaAF4wGZJ22\n4SoB5fQ3YuExz/c/seD0op0nqMvnDMWFoUZ8p2pz4L/vl7sZMW4WPQ4VbXM3PxtXj944e/XGdXGP\nAG+dEu+FoiBt2oBp+lcYZ89CzFJXxLq6dKXw5sE4+g9ASUoOeZlu6xbi3ngN4w/z1eM7dyF/1OM4\n+1ylBmSHA8u7b2J55w0EpxNH36vJfWUCcmoa8U8+jnnqF8gJieS89zG4XSTcPxREkZzX3yJuwqvo\n/j5Ewe1DME+bgqdJU8S/D6EkpyCm/6v67zsdJdJriqhDbtSo9gf+7CxIyT6I1aoQH187EU6tgr/U\npXLuLI/CoZ4uZ4lOnxExUKczLAYaWlO3CAst+t0Z1uVTr3hwFzoCXT5DENDy21V3ZR0b6BoL/NUo\nh9tB888a4va4aHNKNWIbeqopHXdm+Jl2RRBwd+iEq2dvnD17k9TvSk7mlpLqKyzEuPBHjNO/wrD4\nNwRZRjEacfiooF6XhVBBum1biXvzdYzfzwXA1amz2gD0vRoEAd2e3apFw4rlKJY48p54ioKh92Gc\nNQPrYyMQCgvJ/+8InN0vIXHoneAoJG/cM1g+fBchIwPn5X1UqsfWGsm+CzkpGSErs1RutYooIjdq\nXHsDv7aIeitpP3Z7LvHx1XmVVaPgBzxsUXZBYuktq2o93lmqYKcopcY8nxgtsnWTWpg9l3jW0Y36\n9RWmTYv+zkRtDfwvrXqedza8EbBNEiWWDviDcw7mYli2BP3ypejXrCpq5I1GnOddoDYEPXqp9swl\nIJ0A4rGjaipoxldFqaD6DYpSQbbWAcfrdmzH8ubrGOfPQVAUXB06qQ2Atx6AccbXxD87DjEjA1fH\nc8l94x0USa+u9t2/D+fFPch/cDgJD92DmJlJ/v0PYf5yMnjceJqfjbRzB560NHQnTwLeGrvuIrvy\nYKIH1EZQbnxW7Qz8vspaZwrCqVXwA34mO3dWRrALRDthwoRC7rwzuovcQO0N/C0mNiLHFfq5Qr7f\neXnoV6/EsHwplj+XwcaN/l1yQiKui3vg7NkLV89L1YpbxVmCKArSxvVqKmjOd0WpoK7d1FTQjTcF\npIJ0u3ZiefM1jHNnIygK7nYdyBv1OM5r+iGkpxP/7DhM305HEUUK7rmf/AeHYx07GuNPC/DUq0/e\nU88R9+Jz6I4fo3DAIIxzZ6NYLKDTqQVYPB4wmREK8ku8X7U68OsPqzl9beCH2p/fh+If8FxXLl2/\nbIdLdvHuZR/Rr8UNVXx1VavKCHabN6sosMcDGRkCDRsqrFyZV5oOY7WqNgb+b3ZM5ZHFD9GjcW++\nu35+qV+Xlmbl1M4D6Fcsw7B0CYZli9EdPODf72nQEFePXjh79sbVszdy/QaRTxYpFXT1tRTeMhhX\nr8v8wIHOvksdAcz9DkGWcbdtT96ox3Beez36P5YRP+ZRtYxio8bkvjIB3d49xL34LAD5/x2Bac4s\ndAcP+C2ZfSkexRKHmJerLtwSBLUhIHxwVgD5rCa1O/C/zhgAHkPNZ5/pgR9gwtpXmbD6ZTo4U1h4\ny3J0BnMgNSNJpTJAqwmq7GD32GNGJk82IAjq0Dqaa/PWxsDfaUobjuYdYWa/ufRuclmpXxfuXogH\nD2BYvhT98iUYli/1u10CuG2tvY3Apbi6X4ySkBj2vOKxoxhnTldTQbvtgCYVdMtgPK3U1Kpuz261\nAZj9rdoAnNOW/JGP4biiL5Z338Dy/jsILheOa6+ncMAg4seORnfiOI4+fdEdOoS0aweujuei37zJ\nb9Ug+8zZSvjstTrwX9psL8uX10zs7nRV0gNuT9/JoYHnc+vWyOeI6OKpxTH1YdBOgyHg73Bop3pM\n0PmDsU+DIcQsLcTB02Ao0cEzrW5CpQa7fv3MrFlTM75ntS3wr9swB89/h/CvBZp0u5ouvYbgsdnw\nNG0egPSGU4n3QpbRbd+mNgTLFmNYuQIhX02jKDod7nO7qLRQj964up0fUItXPUhB2rAO0/SvMc6Z\nhZidBYCr63kU3uJNBSUmodu7G8tbEzB+NxPB48Hdug35Ix/DbWuD9fGR6NesQo63kj98BIbff8Ww\n6k88zZojx8Wj37YFT7Oz0R3Yh5yQiJidpdovi6IKXhA5OHsan0X6hm1ALQv8E8ft5IEHihbXnAk9\nfZ9K+lK/vuZltn39KrdsBbOi46rGV2LwOXcWa44WTPBUbe3bcsnb4BRrQ+1dtxDOhtpf0D3C2oQJ\n76h4ZyEmvmUQh2gKROf3rbYF/qFvdubLt/aSFLQyXzEa8ZzdEretNR7vj9vWBs/ZLfwBusz3wulE\nv34t+mVLMCxbgrRhnR+bVMxmXBdchLPnpbh69cbdroMafH0qLMT48w+Ypn+FfsnvRamga/pRePNg\nXL0uRTx4gLi3J2D8drraANhak//oaIS8POJefA4xKxNXl664W7XGPONrFJMJT/MWSDu24Umri+7k\nCRSTCaEwcslFrTyNGpO+UbWsqD2BX4EO1n3s2iWSmqqg09XcIurlUXFf6nBo593t7+XVnhNOv9MT\nNwAAIABJREFU7019tW+9OGcgvhnk0ul0haKdbm3DoqKdEV06/e9TgoOny4kBGVdBYagNtbYhq6AG\nbAKjGIN6H2OBv3K1J2M33b/pis4DzTOh7Um4U3c+17paoLPvRLLbEfID77+i0+Fp2gyPrQ3GczuQ\n3bi52ii0tFFW3E/IyUa/coXaECxfirRju3+fnJKC85JefnRUbtbcv088eqRogZi3OLqnfgMc/3cr\nhTffhiJJWN55A9PMbxDcbtwtW1Fw933oV6/ANG8Oik6H88qr0C9fhpibg7tZc6QD+5GtCYg52Sii\nDhTZvzo3Yo+/YSPSN+0AakHg73VxYYAD54ABLj76qHQtYG1ScQ94OLRTFHQsr6VF2csc7MIVb/ev\nTXCH7HvuSZHtm2V0eFjBxeRijaV6qkAD5l3H8n+WBmyTRImlN3sRZUVB/OcwOvsupN271H/tu9DZ\ndyJmZIScz9P4LDytbOrIwNYad6vWeFq3RklOKdX1iMePqcjo8qUYli1B98/honM3aarOD/TohfOS\nXihpaUWpoG++wjj3u5BUkKtrN8yTJmKa/pXaAJzdAsdV12D6fj66vw/iadAQ9Hp0hw4i10lVi7AY\nTf4i6+EwzoDP27Ah6Zt2AjU88LvRKRLuAIonLU3mm2+i7wGsbBX3gEdCOy9r0ofptRDtrIpgp8U7\nDQaFw4dzK/X9yqvaEviP5x+n42QbSpjisSUiyoqCcOoUqSf/Jmf1BnS7dyHt2oVu9y50x46GHC6n\npuFu3cbbKLTG420Y5Hr1IwMQioJu/170S9W0kP6PZX7cE8DdrgPOHr1w9eqN84LuoNMFpoIUBcVk\nwnFNP5yX9UG/8k9MM79GcLlwN2uOp0VLPz3kadIU3aGD/qCvSJLaQSlBngYNSf+rFgR+FzpFHxT4\nITqH3JWtsjzgD/56D7PsMxjdbSyPnT+ukq+s6lUVwc6Hd/77r4DTKbBwYR6dO0dfZ6M2BP71x9fy\n4cZ3+X7fPMb3epsh7e4u13nC3QshOwudfRe63XakXTvVRsG+C/HQwZAUoJyQGNQYqKMF+awmgfl9\nAI8Hactfalpo6RL0a1YieC2DFb0eV9fzvGmhS5Hr1cM4bzamb6Yh7d2jvrxBQxxXXYuYkY7xh/kI\nLheehg1R9AakgwdQzOaiESkqp1/cAi5Q00vpm9UFaLUi8J+J+GawyvKA70zfQc/pF1DHbWTLnTuR\nTHEhRmc1WVUZ7JYv1zFggAVQEIToQztrQ+Af+vMdLNg3n1RzGuvv2IpJMpXrPGW6F/n56PbuQbL7\nGgM7OvtOdPv2hvSuFbMZd4tWgZPKttZ4mp+tPlcABQXo1672E0PSpo3+QC3HxeO6+BJcPXrjSUnB\nsPJPjPNm+60nXB3PRYmPR792tWrFnJICefmIjkIUoxHB4QgZB4UN/HXrkb5VnWOo0YHfl+rRKlpz\nrZWtsnypj+cd4/Enbcz/BnSab4zW6MyHbfo4/7BGZ36Ms4R94YqyB7mBBjh1huzTuHGWuE9PWr3E\nKgt20e7cWdMD//G8YzzxVGuGrlOIr9OI7u2uQ0lMQklKQk5KVv9NTA74OwSz9KpC7oXLhW7/vqJ5\nhF071dHCHjtCQWCDr0gSnrNb4GnVGnfr1nhaeRuGFq0QnA70K/7AsGwx+mVL/D19UAO0q/slKAkJ\n6Oy70K9eqaaCjEY8jRqj+/uQWoDFy/D7evja4B828KfVJX2b+j41uti6TgcmvUJh4ZnhwFlRmrJt\nEtvTYEY7SHQK9K5/CXpZCHTj9Lt2OlUTtMLCMMZrUVrGUhRJDWcn7XPgDLtPH7iuoLh9mkbqvGVx\ndMSICz2bOJfVXBgryl6B+mzLJ3Q7rHDjLoB/4M+PS3yNYjYjBzUOSmISNKiLxWBBTkpC8Tca6u++\n4zEYij+5Xu/v2Tu122UZ8e9D3sZgl3cewdso2Hdh/EFzfYKAfFZTf2NQ8N8RyMkpCMeOYlizCv3y\npZjmFs1ZeJo0RU5NQ/znMNK+verbxcUVYZw6nX/VbrGqgPrT5WotbDabCHwIdAQcwDC73b5Xs/86\n4GnADUyy2+2fFXc+WadTRI8LvR5SU2u/A2dxKm1vJhzaeWPLm/j0ysllf1NFiVyU3YdehnHcLG6f\n3yI64j5neKdOzT4fzhlwPU4XEYu1V8ADAXCEBjTiCBA9nZCa3ON3epy0mdScXFcO1kJIKYC7Gw9g\n+Nn/QcjMRMzKRMjIUP/NzETIykTMzFD3ZWaozpVZWWXCdRVLnNowJCb5Gwjf3/6GIjl4m3ekEc6/\nQ1EQTxz3jgwCGwPx5ImQwz31G+BpZUNOqwsuF+KxI0jbtiF6MVVFEFBS6iDkZKvfd4ry+yVSPYlJ\npO9WPayrusd/I2Cw2+3dbTbbBcAb3m3YbDY98CbQDcgHVthstvl2uz307nilPq8Cn3xSQL9+Udr7\njDLN2zM7IOir2+Yw5rxxZUc7BUHtIRkM/mFmNCzpSkuzklmWYBfOalq75sAZed9rLwjYt6tF2Xei\nFuzwpXpiOj19Z59JrteILcek/rxQMI8r2j9Bq+RepTuJLKtBMiODOqKLzP3/qA1ERoa3ocgs+tfX\naGRlqr3rHdvKdL1yvNU/uojUaLi6X4Lj6n7qcYKAePIUuiOH0e3Z7UdQDcuXhp7balUtI1wuxFMn\n/XUxFITSV9cqTaWuElTewH8x8DOA3W5fbbPZumn2nQPssdvtWQA2m+0PoCcwq6STPvmkkSZN5DO2\nt18Wfb7lk5BtCgqjlgxnfv+fq+GKokCiqOaFjcYyN2AjLg8tyv7rr/mkpUVDE1iz9ea610O2uWU3\nz6x4ovQOs6KoBt7EJEiz4mpShs6Nx6OOGnyjC+2/3kYioPHwNSYHDyBtK9soS05IVBuH5BQ8ZzUF\nSU3fCA6H2nClpyMe+Sd09CKA1zKqxDRMYZ6DgQPNpwUflDfwJwDZmr89NptNtNvtsndflmZfDhDe\nFSlIsZxq6fXzwMUBf3+/dx5DF96B1ZDAbwd/4fKmV1bTldVcTZ1awB13mMnLE8jOFpg4Uc+4cc6S\nXxhTRK09uhqn7EQv6lkz+C8aWRtX/UXodCgpdVBS6lDmLqXbjZCVhZiZHthAlNBoSHv3hKw+Llal\nSPH4ZMDNsmUSnTrFAUoXEDaU9WOVN/BnA1bN376gD2rQ1+6zAqHL7TTaQOeiE4kiaWnWYo6u/SrP\n5/9P6m2MX/8Svx5cyP6cPQzscgOSGBVz96elqvwuXH45HDkCBQXQrBlMmmTkueeMJJaq21L5qonP\nxSsLnudo3hH+0+k/nHv2OeU/kaL4V2aTnU2a4PSn9QJ+nBG2l3dfWV+jeMBsAl0KJFjVY3zHud0R\nJ2bLkqj3jUm9o9P5QJlb0/JGhhXAdcC3NpvtQmCzZt9OoJXNZksG8lDTPMXWCbyAtYCaU50ypYCT\nJ8/cVM/pTOLdcfbt3PTsU7TI2IMyxoLss2yuCHfOcPuCCqmH7gsySgve53XyDOvOKUmV7s5ZnOLi\n4jhxQiQpSaFnz+pn+mvi5O6x3KN0//oPHjwG7RauwPHxNaFmgsF+S1prDa0v1GmU2KxMhaLTmn8t\ncZCYpEGlDZrnrwR0WhDVFJFHvR8Lvs7jQv6kEcdYTfii8WVReQP/HKCPzWZb4f37LpvNdisQb7fb\nJ9pstpHAQtTG6XO73R66njpI0UJP1GSdcmfyRxP41wImRaZdYmMkj1JkfOZwIObmBtIwTmf0unPq\n9QE4Z4A7Z1BD5G9gAvaVXJA9pNExGHj/EwsX7TfRDT3/UofFyy6lU6e4M5o2K49e+PNp3lwNjXMA\ndnt/ihTssOrvEJjNKPoEbzDUh/wfGuLMOGQhJJgGnKPYfcFob9B6EoM+tIOiRYc1tuNVtVjy6fUW\ndu0KfK8GDWSOHhWvL8/5omIBV6NGijJlSl7soaL8PbvTKsoeztwsrJ1zBNSzLO6cxTp3OgN6hH53\nTmeEHqHWhK0Se4S9WMIyelVr56Sm9fidHifNJzZE53CSVAhOHdzW4S6e6flqUcAsZ8GgmnYvTley\nDD17WrDbRXwh2/ddrNELuA4f5oxO71SEwuGdk7d+zl3t7ykZ79Tp1AkwipbQR8MYoEw4pyYHHNxo\nhaYQnEVrCoLxTqeTRx/SIeFGj4t8LKziwsr9oLVQb6+fgEt24tLDMa/bwcf7p3Lr+Q/Rylz7nGQr\nUz//LGG36+jTx8XWrWqv/3Qx46gI/DGdvsLhnW6ljMhcTZYgqPMLkoSCWsSnvI3X3hmh9g1JSUqM\n6S+DJm7+KGRbmRHOM1wDB5pZvlznxfsVnn3Wic1WMR3kWOCvJdLinZmFGXSe2g6DaODOtuVzQDyT\nNWtWQQjTX6+eTPv2sVFpSVp/fC2bT/5FljOLbvXO54ebFiHUkhrQFaLgkalTm0YtGpk+NkKkcKPC\nxTg5SFP+pgmDBpkrbJ4pFvhroZJMydzVfhjvb3ybMcsepU+zvrUC7axK+Zh+gHbtPPz6q56FCyWu\nvjq2srw4Tdz8MYsOLgTgka6jKi7oB+CcCkJ6eomFdorSeoFzU1qrEN88VdE+TaU432rvMJXi/HNR\nvnkptzs8nRR0/tLORWk9bjJJJIX0Cl3nFIsGtVQ3tRqE9Z23eXTVccyvNsViSQpbND2AhtFiaRo6\nRltQPRD1NITSEmXFOfV6DSURSO5Upzp2LJrI3bVL5Ndf9QwZYopKy+Zo0fG8YyzfMptxyz00cJsZ\nsOt7BNfs8AGzNDhnMZP3qdX0GcPJTwkFf4dNJuSEhMj0WRBhpqWMPpmk1oN2oecvOqEglnwhZVAs\n8NdS/bjve7ItcDIODHIuzYRERB/OGfywRSvOKUlFOKdBH4hzhluPoG3Mwq1HCF7HELIewfcgBu77\n4Y04+mLCgZHVygUsW2aJ4Z1hNGXbJM497GHsCoACWD2t2OOVCB0ITCZkvTUsG4+kxTkrqIOi/W6F\n66AEdF7CdFAqIZU1Z09km/CKUFQk3xRFUc4kPKs4VQSqFg7tHNrhXl7pEaEoezDOGVBQPcwQ2j+8\nDtN7q4hi697hddhi68EkThU3YB9xPw+iTlxWJd4Z7Qij0+Pk3C/P4VTBSZqng9ED/c+5hVEXPRV5\nRBfDOSNq1y6RHj3i/H9H+q7VaJwzpopVJLTz7vb3hkc7awPOCWoD5m90gh04tY1OGOdOX0MUZBct\nuF08/5SIhBsJN98xoPI+cA3WvD2zOVVwEoD93hrn49Nn0S9+NK2Sm1TjldVMvfuuWk8gOVnBZKp4\noiwW+GuhwqGdHsVT+1E6nQ7MZj/OCRXTgK35pXKH3bVBn/z1Qci2GL5ZdmkRTotFYceO3JAywBWh\nWOCvhQp27hzy0238tH8BFzboXk1XVLMVinfCjBkFtGkTy++DinDaktuw+dRfPNf9JR4897/VfUnR\nKUVRjdrCkUYuFyMe1pGxTqETHrbRjvx8A507V85cUizHH2WqjPzlhuPruOq7y7BIFvYMO1xj0M5o\nyuVu3qyidIWFkJEhMnCgiw8/LKyy94+mexGsYQuHsGDfPKx6KxuH7CBeH1+xb6CtEOdykppo4t9j\nGYFpOlfQvJR2nil4n29eqbgKcVpEU5v+C96nnWvSoJ3hC/6UHgUu7VxSLMcfU0Q1im9Mp2Pwzax8\n9O82JSm+bqAzYEmugcFmVobwCFpkrFNb7F1fVFQ9GOsMpibcZvWhj4IFQD68U5ahRYt4Zs2S+O67\n+DMe7Tyed4zjy+fx6laZFuYE6tufDuLkXeGDaXBQLGNJzTrV8FmDFerMqfmeG42Bz1TwsxLGSPDL\nr804MeDEwDRur9RrjwX+M0BTtk3CLahGWXmFOSRhRvR4QumdKFQaxXDSYbBO34NXLNap2ReAegYh\ngeHQvpdej+PCPBNODOxRWrJsWcMzGu2ctHUiD6yWGfIXwN/A5yW+RhHFwE6A///PgGw2h9+n6ZQY\n4y0UyoTuK40zZ8D3IBDlLK5T4kNCtfsq2pnzywNm/vyzauaSqr8rRSzVo1VFD+nDoZ03tRrEx32C\nHlBf/jHMEDWcS2dEk7Owx5dvZaRBUHDmF2qKsBe30Kfq1yWkk0wqp1AQKx3tjMZUj9Pj5JwvzsaZ\nl037E+AW4YY2g3jkwrEhNsdaTv50Zyuj8V5UhMaPNzB+vNH/d2m+U7FUT0xhFQ7tnLN7FqO6PR6I\ndvqGrXp91BRcT0uzklWeB9y3LiEsulny0v6QdQmaBual5wT0uNDjYgfnVPiKypqkObtnkePMBj2s\nb6Ru25Yzh74pj9MquVm1XltNU24uTJxoICFBxmJRH8fKpMZigb+WK1JR9tFLH2HejT9VwxVVgXzr\nEkwVvy7hz99D0c569c5MtHPCuldDtsUQzrIp0IFT4PHHnYwaVfl1nmOBv5YrGO2ct2c29/zyHxJi\nRdnLpXBo5223uc64/P66Y2twyy4kUWL14E2cZY0t0gqRlkYqBt/s7K37sJM2TJ6sp08fd6V/n2I5\n/ihTZecvPbKHHtPPZ2/mHpolNmfFreuiFu+M1lyuD+1UFCgsBFkW2LAhl4SEynvPaLsX183py+qj\nK/m/1rfy/uWho8pyq7i5Jm8BnRSrgYwTmSXPNQWtwI5kIRJiIheyT3uuYLdNd5lopOJUnkpvsRx/\nTKWSTtQx5Jy7uOj+cbQ/sQ/zS82JsySF0gthaIpiEU99EFlRIuIZfHwYY6z8ZMRsRyjNo9dXK+Kp\nde58910DL75opGXL+DPGufNY7lHOm7uSISeh84qtWOfcV3ywDA6IFcC6J1fyZwyn06WRIuGbLvSk\nk8J6ulbZZ4kF/jNQGY4MTlog0wQFnhzMLgu6goLT7rFUhiLx2opOV+KDVpaHsMzFur0NlWdWHNdi\nIoNkVioXsWyZVOvxzheXj+Oz38DqBNji/QmvyMGyFKx7hH3mBAv5biWgGHtFdDZCiq4HdzYq2Dvh\n68PVZwUSS/VEmSp7SF+mouwl5CiDCZlyDbudzlDE07vPrIPC3Pwgd85ihtYVOOwuj67hB37iGqDi\nnTujJdXjcDto/llDEnNc1M0Dlw4GtL2NMd2fqZJgCdFzL05XbjecdVY8Hk9gAfWyKJbqialUKlNR\ndkEAg0FdqevdVJWIpznNSk5FPeCyXL51CiGNUmAj9swTqnNnISaW0bNirjWKNX7ty7hlF//Gwb9e\n1+A3Ts7ketPI8M6vMUXUnDkSHo+AxaKQmFi1NZ1jgf8M0xlblF0UK6UR2/DTmeXcOWnrxJBtMYSz\nbAouor5sWR5NmlTtqplY4D/DpMU78135dJvWgXxXHre2qVxvkNqqYLxTFBXWrMnDaCzhhTVM64+v\nZdWRP8l15XJ5kz6xIK+ljzy+FGfJCwVfeEYkbovMdbjYTSt20JbrrrNU+ZxQLMcfZarq/OV7G9/m\nhZXP0ECqw/q7diLpoydi1ZRcrg/vzM4WyMsTEAS191aRhE9134v7Fw3l5/0/kO/OZ0H/RZzf4IKy\nnyS40psvULrdRXM7pUi3JZglstNzSm8L4vaUDtWsBPqoOB2jHg04CgjlnhMqb44/FvijTFX9gO/L\n3MOioV14arn6tyIIoc6aJdW6jWSKJoWSGVqyoiRiJqFOAln5LnWf/5qql8QoTtdfb2bVqvBpn9Pt\nzVVn4D+ed4z+75zDS794qC9buDDtvIDAWHyx9Kr3UCqPiqWPpDAkmH9bGcwAJYlX34jzI5ybOJfF\nXAaUHwaITe7GVC7Nss9kR2P4uQWYZJHzU7uilxVwe0If6MJCxNycKn2gE0/z9aEPdKhTY0jjVdoH\nWhfYGPVeFUd3r63uj1zDPlpw9Kg6Gqiq2ryVoSnbJnH2KQ837QBJyYedS4FiXFNDiqWH6SD47l04\n3LaEDoI1xUp2oSdyB0WvD8J9o6eDsGxtdMwJxQL/GSynx8mX27/gRGv4oTWAzJB2HRjf6+2ynSjS\nEF471C4HMWM16cjNyA0cwnvPVabVluGG8B4PQn5+6BDe5Sr3/XxF8/v5rOFOppb7XNEip8fJpK2f\nkt4S4sepKYI7O93Di70mVNsiOmuaFUcNzRDce68zIPBXtqtrJMUC/xmscGjn1O2Tubfjg2VD8yqp\nWLs1zUpBVT/gilJCQxZm0s47uffy8yI7t8pIuPmDS4CaT/jM2zOb9MJ0ABx6dduknV8wpNN9MXyz\nDAokeSAtTUaSKteBszjFAv8ZrHBop6zIPPnHY8y8bm41XFEUyDfHIUllLto+5ncCCB+dTmH9+jyk\nGvyUvbfxrZBtMXyzbBo4MDS94wv61bW6uwZ/JWM6XQU7d7625iXeWPcaLRJbxZw7y6mpUwu44w4z\nWVkC+fkCc+ZIDBoUndXNStL642uJ89bPnXndXHqfdVk1X1EFq6TRnccdRBppyCGPO3KaUkspuV30\nXiZwBW5EZL5iMDtoW+1zPzGqJ8pUnfRGZmEG3b5sz7kHC2mqr8tbfT5B1BuDJsI0k2Q6KXw5ugrK\n/VY3wng6OnRI4Lzz4vwlg08X7ayOe3HrggH8dmgRXep246cBvyEUs/q5KNCFpsXCYpXBabPi5oHc\n7gBnTZMOHLkFmrmcQFwzJDVXiUhmWTWBUYxhAlAx+f0Y1RPTaSvJlMwznksZNXE+8A982K9c5/HT\nG+Fw0CASI4DakHSBdEe8hXgPIftCsE5JCqI2NKhdOOJDCqR7QogPSRfamJVRI0eaUBT1mVQUapx5\n2/G8Y1z2xSLmrgKjsgHpoaSowjHDrTYJa9zn+56EM4QrDsn0b4tUg1kiIoqsJcf0Es+/FM/6LSYc\nGNlAF6D6535igT+mAP3TpjEPXw0pBWAVTAw95y5MihTGl9xLxgRRNEXUjDvQXM3tBqcTMS8PvEPo\n0hiomSPuqTopvrKUkRqzoH1Iep5bY/IWaNSzjXY8zmvVPrwvi8avfYV4K+xKBUUSaFu/K5LRrE7i\nawOhtvHWBTXAwTbdZWq89UWjySBstk79ZE5lOYqO9wbbqlyzURZdiI63b7H4/64ukkerWOCPyS+n\nx8lXB7/jhH9RZiH2DjIv93ipct/Yl0LQ5EYFt4s6CUb+PZbhH66XHRd1h+Zm/Riom4hIqNsd2tB5\n3yfi2gZ3YGN2KUW9+o5s5klewo2+cu9jBcnpcTJj19c4zocPzwfwMKxDl/AOrtWhNCuKVDNSgIoC\nr7+ujk9SU2X0+uojebSKBf6Y/CqTc2dFKpKBWpoV2VwdJTdOX4MGGFm5XEGPi0JMeJCqfXhfWr23\n4S0cHkfAtsnbquB7UIvkwzcBFEWgXz8XkyYVVvNVFSk6x0YxVYsiOXc++Os91XA1NVvffuegTgM9\necTj8favnnjCUSPy+x/99X7INh/CGVPJ8uGbiiL453lWrdKxeXP0hNtYjz8mv7R4Z7Yji67TOlDg\nyifPlYtbdkdtbd5olQ/t9HggPV1gwgQjAwa40UdxxuerHV+S7cziooYXM/eGHxGqscQlEN4F05OH\neCwj1NzN4y4+1ecO2h+MZPpSihFoIu3x/v1hUoEfbfegx4WEm1zi6ccCDp1qGlXzO7EnOaawSjAm\ncuc5/8H4wdt0ObqbUwuuoGXddkUTeGG8agJIB78XSyjpgKSLTNFoyB/cyQiZhSGTqdE6iRcsbW3e\nceOMfPaZgcaNVS4+Wmvz/jLzaW49CiOF8zF/PTUEqYzIsQcjle6giX8fL+8PyEET/8H2GtogHkaR\nSnJWh4om/9VnIM07qe9CjxMDchQmVmKBP6aIEhAYtgFa/wts3QBsqPJrSA2zzWe8hk7ym4Bp6Y5w\nlI2vUVK8Rm0BhmDB6J62QQvA+YIatGAjMG2DFrTGIWdtHC0wk6NYOUG9qMQ7F237ju8/zECnALND\nV+xWhAKM3TT3C70+tGC5Lujee//fjPFmCj1E/n/T/r9KQd+P4pBM7XcmXEdE8/8a0BEJwn3DrdSN\ntvmd2AKuKFO0LFry1ebNyD5Oaj7oZRjc6hZGnzs6cGgcyVPdox1uB9XT9Wjq73q0pmuBPUeTDhx5\nhZF7hlrKJvh9gq8tCgrH+3QtC/iRa4HSo32V/b1QFIWuU9vTccPfNM4Go8HCE5e8QJwlKSyqGbIm\nIxyOGbweQhQrZHFftDwjkeTxqLV03e7y19ItrWILuGKqUPkJHwmOJqjbxp+aRb/U0bRKblcl12BK\ns5JdGTV3g9YRaBuNsHlhDeYZ7jXhkNKANQ5uN19+DhJunBj4i04V85kqUL8d+oXDuX9z2A/t5FPQ\n1B49CGcNUDDJYzYrJCVVbS3d0ioW+GMKq1pXm7eSau6WVl/vjt7hv6IojF02OmR7DOEsvcKld6xW\nJapSeVrFAn9MYaUlfJweJxd93YVjeUfp32pgNV5VzVVwbV5BUFi+PI+EhOq9rvXH17LowEIO5RwM\n2VerXTiDfYfcnlDyJ4gmCt3m9o/omi3T0RI3Em7+ohOruZATJ6J3pXYs8MdUogw6A6O7jWX0ogeZ\n9c1I/u+GVugMpqK8rk4KzevqinxQqqtgR7TJh3fm5grk5Ai0bBlfIQZup6NP//qIH/bNR0Dgj1vX\nFvXutc6VuTkhtQcCUl3+bZ5QZ0ttesyX/ippv3a+yDcfpJ3f0UFiXkHgNk/QnI6WJNLOB/mCuFyx\nvfApmt/3cjYt2Vuh569oRcUTGZvcLVK0Tlz9k3OY325vy6iVZX+t3zzLR7po0U6/94sUQnMYzEac\niuCfXAwkaTRkThCFE9jwaNFRH9EjhU5I+reFQUulYhq2criR9u9vZsWKstXmrYzvxfG8Ywz/Xxu+\nmC2T6NaRIFhKxCijUUrA/7mGBtKUYCwyZdPSQhpiRyeFUl5aXyJJCqWFNN5DH35qZttuE24kNnEu\nO2hbYfWWi1NscjemStVXO77kh87gEtXavENa34lJ0WkYb02PzU/taHpskXpkwV43vsDjpXAM1fy5\nS6NSBR5/sNHx6gbVwM2NxCTuZjq3VouB26StE8kXZTJMkKcomNLOQqc3hnep1Fx/qCmoT1hcAAAg\nAElEQVSb1qgtsGGOiMD6Gk7tfi0CG67h9u5PbZDCyYyCcje8laEBN8ITtnj/St1oMGIrTrHAH1OJ\n8tfmrQtP9AGQWdoym0+vnFx5b6oopCWbOXkkvfSpBE2eNoS08Ru9hVl0FJzX1a7a9ITBR8OlHyI0\nbILDUUQReY+7CBc6r4mbHRvTubXy7mMEOT1OPtv8MTlnQecHAGSGdehRMygeqxWix/YGgPffN6Ao\nAlarQnx8dJI8WpU58NtsNjMwDUgDcoAhdrv9VNAx7wAXe/crwI12uz379C83pupQOPO2eXvmMOa8\ncZVHfPhWQ1osAfRN9DjCl18DB5pZvkxEwo3LO6apasJn5s6vyXEFpo5iFE/Zpa2lazAobNmSi8VS\n8uuqW+VZS/wA8Jfdbu8JfAk8FeaYLsCVdrv9Urvdflks6NdshUM7FRTu+nkwvx38pRquqGZr1qwC\n6jfAH/RB4auvqg77W398LS+sei5ke8yIrRgpCjidkJ+PkJ2FkP4v916fxd5lx2ikHAbA6RS46KK4\nqDJji6QyJ8dsNtt3wGt2u32NzWZLBFbY7fb2mv0icARYAdQDPrfb7V8Ud87Y5G6RonVyV6stJ//i\n8m97kGRMJs1Sl6U3r6wUA7eacC/Kq82b1Zy+wwHp6SKgFEv4VOS9uOvn2/lx3/fUMaWy5o6/iPfW\n1S23PJ7QxXHB9I+2poJ2W7i0XXBazuMuStt53MQZRPKy8wJrJwS9xu8l5HEHpt5cQef3p+bcRcSP\nP22n2V8CBfQEL/MqaqNZlfn9SpnctdlsQ4FHgzYfB3w9+BwgMWi/BXgXeNN7/sU2m22d3W7fUp4L\njCn61CGtE8PMvXjp+aVYnRmITzRAbzAHlrPT6SJPenr9TQJ9cXQaTx3vj9VCnEspIiq0k4DB27TE\nTvDEoJbYCSZ6NNip34dFi6KWo+xiaeQzcFMX/oiAUCUlGo/nHSNh/vfM2qrQyKyj0S93Bs51hEMf\nvYE9YC5DG9iroSRjXDlfp4hiENlV9B1B0pRo1E5m67QT3EVeT3N/UCfpHRj5iasr9PNVtooN/Ha7\n/XPgc+02b4/f6v3TCmQGvSwfeNdutxd6j/8d6AQUG/jT0qzF7T6jVBPuRb3GrVjXcCmp+WDETbvk\nBkgexR8McDogP8/fqwv4twyq9nSpIBQ1RL7GINK/5dj3f8sk+iPhQs8eWvIp93H0qMiQIXEcPhx4\nKRXxvfjf2nHcuF3hpp0Ax7w/Xmkb3eBrNZvAGl+2z3w6x1bS+QWNs+vpskATzoN16wK3NWoE8+eL\nUf8Ml2d8vgK4BlgLXA0sC9rfGvjGZrN1AXTAJcDkkk5aW4f0ZVVNSG84PU4m/vM9L93u2+JhWIee\npSNCfAuDAob+QasmvftTrAYyTmYFmblpiJ1SpgYChv5uLWKqHfq7ENweglMHAT1dLTXkM5QrKAxM\nVQThqCXpIe19Rc80biefOGRZ5uTJonRBRXwvnB4nEzdM5IOBcH8huHRwR4ehPN97fNRgkaVRqe+F\nAjgBpww4vD8VI0UBRbGghjhVDRrIbNyo/p+dPFlhb1UpKk/g/wiYYrPZlqPeydsAbDbbCGCP3W7/\n3mazfQmsBFzAZLvdvqOiLjim6tdplWjU9qCheN+cNCvuKG8EI8pXQCSgcQpt4EYNF9m0XjVwO049\n8omjfv3KIXwmrH1VLakoQoZ3KDVxzxRu7/pAjOQppYKN2Hr0cLFnj/p3tCOcWkVFEx+b3C1STejx\nXzXrUjacWB+yvVNaZxYNWlph71MT7kVFSOvhA/DUUw6GD3cGHHO692LdsTX0n3stDjm013t5kz41\nyo+nWr4XisLNA/Ss+kPxu6w6MJGWJvPNN9VnxFbeyd1Y4I8y1bRg5/Q4ueSb8ziYfYCmCc3487b1\nFUb41LR7UV75CB9ZhsJCyM0V8EEkPsrndO/FtbOvYO2xNdzQoj8T+04p+QUlSZOyCxjRaCd9g1Ng\n2tXZQSk77aK4gLSeL22nSb/FGUTys/ND0nbatJzgTfWpvwedQ0vteDRpwpD0ozuit08+Ztqzlf2c\nXa2rdGOBv5aoJga7qdsn0/qe4fQ6AJLBhMFoCayIpbUtkKSiZf8B3jleQkdD65jizRS4lTD7vUv1\ntZWXJF2RTYDvPbVUkeQ7Rh/4nj6ax3+sLoT6CCSFpErNhXfvbvGnDnxq0EBmwQKRs84q3/fiQMZe\nVtzZmSZZ0DqhJa3im6mB0BM8f6HBF7WBMEwAr0lePlqF/p9rftd6M4WhepauMHr9NyWOU49HeZs8\n4mtk4I9ZNsR02jqaewQ5FerlgkFx0tp6FjpZKWKrfbYFIT2+koOHuQquv6wqQgL1/oasTA2dFmXV\nYqmSxON7TDgxkEs8b/MoR2nI0aMi118PGzeW73qf/vF+Zm6EBCfAHu9PKT+L0ehvdANMzvyNrK6o\nUfZhucHYrrZBDtfY60tqfAOvKyk1gYwcR2CjHnIO333XnOM0J7BfrAElFUurWOCP6bTk9/Hp69si\nc3f7S3m154SSXxxM+HgCG4Y6CUbST2SGIXg8gbRO8FC+FD3WAIrHn2bwaM7nCugF+9+jpF6y1p+n\nHA3dMM3vm+nIV9we8djS6EDmPhZmrabeGDC7wC3CHR3v5rleXpKnhhSuD1A1Tfo//7yDSy/V4UuU\nRLsRW3GKBf6YTkthCZ9tnzG0w72nT/ikWfFYa1baq1iV0NDhdjP8AR0b14Ebid20AtQAM39++QL0\nA7/dA0ChXv0B+HTPlwzu+mCM5CmltH48IJCSImM01iyKJ1ixwB/TaSmcj4+syNz3y138fvOKarii\nKFYpUNa3fwykfHQ6hVWr8mjSxFomNnz98bWsOvIn64+vDdlXqytrFSctYutvbD2a0ZlmDYj3mLGj\ndbg2wSW42UVrTlDPH/SjsaRiaRWb3I0y1cTJXa0+3PQe//vjSS7IsjLvxp/QGc2BOVtt7lUzqYYo\nhuRfa/q9KK98lE92tkBenoDq4yPQo4e71JW67vvlbn7c/z0Oj4Mfb/qVbvXPL9rpKzsYHAC1i+GC\nRybBx2hTbB5Nak27KK4sx/gJIXdRGi04lef9XS8ouAodgQvqIp2jDH47JWkTnejMJiB60jwxqqeW\nqKYHu7+zDzF/aHueKwfOH0xciHoJj69x0ElePx8pcNJUJwVOmmqpjLDUkC6QEPJN+kU65v/bO/c4\nOcoy33+rqntmemZ6cpmZXCCBgFKACOZwDzfh6KLAriwaBURBdrnq8aNHznIkePusyOLuUY8oclBU\ndLmJUXEBwXCJBCILAQRCFihu4RJznYQkM5mZnq73PX/U7a1L91wySc90v99P+jPdb71VXV3pfp/n\n/T3P+1RQB6hanyoGLVVDaIRGD8Z2py7w6vH8768ewA2/F7QLiw6zLT6o16C2znghTRPDv67h9cwM\nJlf6nuQzvgNW/Pug/D9fd0MhvGnOIxzPA/wNMPkHfi31aMaV2168mbvfCx2D0OIanL3fWbSQi3t7\nyfzppKfm51ibCORgyQvCumWMwYHMKboxNFTrj73TpNIMcxa/7smHg87POZ+r+OqI7tR1/bM/pM8S\n9LTCViQtXXO8O2uNdIBMpshmGcmR9FEzclRjmJVxM5I+fjC6u7vIpt3kHP366QIrVtRHJo+KHvg1\n40aY4dMNl30YQHL7nn/lN6ffNabjdXcX2TLSH7gqXySzf4aTL2J9ytGdt5LGqqp8UR4mS2iERk+R\nJ7b3CD9rvEzzCOvMlNwSP1v5Ywb2gfmT7c5aE4h4QDdionj6O4se+DXjRlaGzyNrHubm//oFs9tm\n84G9T951b26a0NQETU11c8euCzPyxqvV8Xlq/Qp+/Oz1DLjx+xLqO2uNjoUZ1900JdOnT/xbKo4U\nrfFPMCazxl+phk8hV2BucS/+NMobtkzmazFeJOv4VLthy8VL/oE7X/kNMsPc1bQej5SVA8oiOQtz\nK8/IXO/5lLYmtvZsrzwrE+7IZmXlMrgi1eeu3xnkKCMxuJpFPMXhwMT09nVwt06op8FuyB3ilF8e\nyRdue5WpA3DgjEPYp8sGc7hAqQlWjrYpbfQOuuk+gT6dCrj6/cwqWUTBPpUyjZR9J0Kp4iDDp6fH\npBSv2xYL9K7vW8dnvn0Ax64W7NO+FxcceEFFmSuWSROTsYaRooRLrIZNJbnKFbHBe7KWdwC4kB9z\nI95aiHoa+LXUo9ll5K08JzYfxJmrXqVtCHjxOeC5UR1jJ28KuNOEBiIIgPpGqWImkWVVzjayrMqZ\nJJZ37GS2ydFWjpfPy3HVNW2UsSiT40324rd8LBbovfbp73Ht3YJj3gZ4E/jarr0Oyc/Y3IxobR15\n1pVpVe8TC/Saseyp9qlt9A6UE8Fga1SZV1hWLJCuHusTnyzy9MpmSjSxw7/XVz0EdFW0xz/BqCeP\nv+SWOPTfD2Lr1vW0DkFOwLn7f4orDrvCz6t2M6b2kXc6tdjMOz3bKueCp4K1yrECL3TMnq4iAahB\nV3cE7y+USpG7iC420kMXs2cLnnhqM++6cU9m95Q4bC0MmfCBfU/hvPddNPaZzwjSTWvFrviNqHX2\n29q8CqkBE9HTD9Aev2bCEQZ78zDolwv43ppbmf3uIzj3oPOHP0B3kaHJbgSztG1XpDOJMoyWqm9/\n+1tNrHzGy/BZxyx66GLGDM8LvfLRyymJEm9MgzemeW97r3k/R8z/pg7ojoBkMLe3F5qbJcWiJJ+f\n3KUZKqEHfs0uI7OcA4KvLV/EJw/89LjV7Z/QjFO20b8sLLLHHiIW6D30UJcNHX/k5kfT9fUnfVmG\npMF03cgQDm7FXP9OtBo36CcSBtNNGlN/1qjO1ITggGUWB+GSo8xGurmdsxgcNJg+XU5YT39nmRDz\nNy31RNST1JPkU/ecydDSe1nwNnxw31M4Ys5xka6tBnz9UsEd04ts7S0pOmyki3sabUKvVeULKylr\nZARvJ1Flyu7uIg8+2MenP13wXwueey7HfuftwWxjLXu9eRE/uPiUaPbgutnSljoY+v3UrJlYv0qZ\nL2qQV6iBXZF4z4xBuOzG96l0rBqyN6t5k70ntMQToLN66oR6Hvi/vvxKLrn4BxyyodZnEqEGXVPB\n27C9giEx1WClGQtchgHcmEGzsg1YEOhVA5tqoNeyKE5rZ9uOofA8rv52gU2Df+DGt39Z60uYIqrx\nHxjatNFVjXMqKK4Y9GSwV1omLW0FBspSuY5Vrmn4XpWdh+9f18rzLzZRJsdaZvMYx4yoNMZEQA/8\ndUK9DvxBoNdat573bgBLwqlzP8S5+5+r5F3Hg6bF1jy97/RmT9PdMoafNohbTniqSa812wMOg7+h\nZ+qGx4q2peWCVPC4xtz7LnhsVoHy41+itVDki5e5UaaKmuniD8jqDCvVzzc6ySBwZppsVr/dkAI7\nXr+R+I3TYTLW2dfBXc2EJgz0dsDaDq/tjyyhNO/UioHeYneR/oluBJOLkwKdWQ3gjsKQxBcfRTJM\nR1sT27f0hoZu0a9+Tq77eVwDbj0Yetr6oWMbs5/5Zy7+7OQYtGpJ1upcw5B0dtbP6txq6IFfs1vI\nCvRKJF9Z/uXJHeg1jFCSoLl515WL6C4ysHE7T61fwe9f+S3/7yPPp/scfj1rV1zKwoX7jbh8824n\nMJSBARSuMqNLzKZE1B7bVmwm37M9HpdQFo6FxjPc5qYM65HLcizAxcLlYd7Pco5DSoN8Xk54eWc8\n0FLPBKNepZ4kv3rxVn74q0v43Ao4eubRHDRrvic/hJKDSVtHG30D5UTwVtFpAw04FsyNdHUsM9ov\nPIYZ6bumFdN6UY8TaNOxfa2aBYWD78UlixfS/OD9FMpgCElOeLJZToAlILdhf6xnzmNqe5mPn9HP\nzG5F6ooNiiIxQPqzFFUic6NBN5TPhDpIR9KYt00ocl1wHDHhpLEkf2YBx/JnYHLJPKClHs0k441t\nqzn1Zfj8EwD/6T/StO3OkxoF6YwiMzIYioGQuaThUQLDYT/VoKkBTisyhu0FjL5t/K9HlrBgTbUz\newlYBL3Av+/Cz6wYxphRbGpCKiuVM4PhoXGOG3E1uB4ZYyXQ7Rvq1mKBvpIbXptYzCJp7JXYhno+\n3/p2KytfaMLF4hnmA/W3OrcaeuDX7HbC8s0L4K79obkMx88+lqsXXB3p3sL1Vu5u2hafyqveaOBd\nKp5m5KmKhObu+h6uq3i4QSDZzfZ+kx6t7yXHgsL+OaW8WiGgVMLo7x8377fLf1RjFe/hMr5DmRxT\npxvceFM5Pkgrs5xYwFYdpFUjFg7UE2f1bmt3kR1jnBUn758bMNk8/Z1FD/ya3U4Y6DXglU6vbZVY\nzr7WU8yduldUvrkeVu4OR6Y8Ehk/ymWeX/8XVvas4IePfT8m63xs3zP47MGf5auLcjz/LOQo8xyH\nsJEZzJwpuOWWfoYaQK8eKY1QbnmkTAgTrjX+iEbQ+CuWb5Z59i3O4/4zHyWXb6Z75pS6vxYj4fz7\nPsUfXrsrVW45Z+Z4+Mz/ZL9pduXyzceVWXz79kinD4Kp6oxI1fHV52Hg1Z8BxfoqM6tgNqXMwhAi\nnsWkvm/SyAlXSc1VjpWaYXnbWnImg30D3rbEOcdeCzeKWwiXl1+UWLiUyfF5fsBDfACY3N6+zuOv\nExph4E8ipeTSm0/jp4seZWriRlMpXTmQIlSN3Jci1ABtTLYItODYdivSmsNVwFa6r2nFNeZwf1PR\nlRPnlhU4Ns2E7hz1l8p5RHECr//GgR6Wf30hx78BpvQfAkw8r7/FyDMl3447JOjvFViUsfxsFQuX\nybM2efyQ6rVWvgebtuRwseinwMXcMOHunzsWdHBXM2kxDIO957yP3x/wKLN6oQmLo2YcQWsuT3mg\nlM4kEap355UJoFTCjG0Tca/SdSflTcanAdXLrA0BWzCBfGpLjsc4gn5ayTWZLDgeJbAarGg100HS\nwHilsqey+irGK5lpZZoZhjHon1NeW+k4RJhhldzXonPmVDZt2RHfV824UmIR6iKtfBOUSvFxspEC\nuip64NfUnJJb4pY3FvO9M4IWl5PmtvNPx3+Jw6ceN35vJKUiXbhp+UENBAdB42QOeWBUVNkjlDKU\n/rGgsojLEWpKZUzaCCQUwbptb/P65pd5bv3TWErK5numHsAR3YcljhU9f+CPRujtb6KLf+BnDFBg\ndqfg2dsmp1eboruINIafFSc1fe9GNpLJuEJ3vNEDv6bmZN2rd+lbD7D6D6+y/Kynxm9xl2FEBdpI\nL7CaSPOBi+9eyANvPp1qz5mv8PCZN1cst/yvFVakrltnMHNme+YtGzMJjGRoYES2oYzFBETitRs3\nljJru6jQP308pG9AC3kKW3ckDGbawH5smcnHEVi4/JU9+BZXIjExTcnMmY0X0FXRGv8EoxE1/qxg\n7zcfhI++AF3ts5je1p2WJVQN3jSyNXulfxgDSEoZqm5vmnEtPrbd398wExJF8rWq55sZ7xG9f9Av\nKYO8vsnhma+cxfT+SNc3pKfrmwK6WqZzSOd7QchosBMiDGa+tEoiym5C6xfh87zpMr2jTM6sMohP\nQlmsGiXy7MFfw5vX1IunrzV+zaTlvoVLY6+vefwqpt3zr3TvAKtvHUauDyvI8FC9wTplOnBY1R6b\ngWWxFnWYPihsM8K/EoPNTKOXIgOihd7tFvPebURB8oqG1YwbuAqGNRUMTxo8yzPQaSOYCIhXNare\n+02Z3s7W3sGKRvXLV7by1DNNfpjbC+huYEY46Deypx+gB37NhKLklrj5hV+w4TT4H6d5bQd1zuMr\nR389yu+HqOaLyJIKEl6sECOQFkRCzkikFQavU3JGhnwhRAX93o176Mr2jb3rGCzt4PXNL7Nm6xsU\nhiDvet7+PsW9mT/rYAYHShhCIIXw3tf3+EMJRE1h9J87L3gpjAKTy/gO93IqALNnCJ59ZJJ6vd1F\nShVmxQsXFlj2TPawVk+e/s6ipZ4JRiNKPSq/ful2PvfgRan27sIMnj3vxclbzG0YLrn/H1n65oNs\nGdyc2pYzc6y8dCWdcs/hDyRlTJ8/5+xmHltuJOSeMhaCBUeWuOFHfYrBSxhSVZMXMmVII0MoovbA\n0ImoLWYcY31ktkH1DXrSQAZthSaL/h2DSpZX1Oc/7rTCz7qYhdzKOYC3UGvJkh11V4BN5/HXCY0+\n8Gfp/QtXwS2/gZwEw8rFtXHTjDRzw4znzKv6v9ImFQ0+0OxlYp90mxnJG0ak0YcSh+GfhxpLMM20\nzKG2+cfZXu7l7nuv4cOOxPL1fINI2zckNFk52s1WIJjpeAO8IUU08xGi7rT5neE2zuKT3AbUr7ev\nNX5NXaDq/d3dRf7pnitYuuYaHp4HLWU4cOq7yGHiDpXoyBejvH7Vwwy9wDKUPG8y8lZlQpJR9qkR\n7cCFw/YqA9vG7T030cl9fBgXi+aCyekfFVHgO8N4eYZQ0ehTfcyYDh/vkwiax/oYCSPu9zEUg54w\n9NO7O9i8td/v4/W/+NJW/vx4kz+X8eY17zAVaNxc/WrogV8zYQmLue0JJ5/rteXN1zluzxNY0/sW\nfzrzofGVfhIxg1ACUeSMUP5ISSIiY5+ETKK2ScF1T36PlzauZNvAViw/e8cS8ME5/51P7HdmTCYp\ntubZrqYwhjKJSEswUvgL29RsH5ef32hhIjAR/IkTuZ2zvc/dLznhrRGmee4KkvGaYPaiXnu1rb0V\nuSP6vF+41GTVk/0UcHmNfWnk4msjRQ/8mgnLHavuSOX3D7kl/tuvHuDU7bD6zx/lfTMPjdIwFc9S\nmr4kE8o1hueBmgkP1DSr7x96rEYkz5hqe3BMI35MKwdNzVEfy/Q8VFMpxXD3cg7YIJkhoqHKAF7b\nupQt1nvobJ4OSE++KeQxewfiA7s6WEo1rVNGsyBlBrR/t8GmjRITwUIW8wnuCPVwc5lg1ZwyB7+3\nTLE1Q2eX0QBs+O+XmjGpN1lJ9RORIUvOtsYgT3Uqz29Wnp/DzTFdX3v62WiNf4LR6Bq/yt/+/oM8\nseaJWFtXH6z7P95KVs2uRRpGBSMXxTPScRWvZEK6TZV9onhHTApKxmTCNlOJk5i0tLZw3xJYuyGH\nwMTFxCVHPwW+y5dYwxygMbx9rfFr6o7HL3g8ZgSDG7bP++J6ZvV60kh383Q6rDZ+cNL1WBjZUoEi\ni8Q948Bblr4nKir0k5FXnZAjvIwUmdo3TPUMvF3f8+3pXc/LPS+wZttbdPbDNN8hnVnoZk77XMDP\nypH4fwVISd4yKQ+Vo21CRH2F8P8GwV4Zedr+MQzXe14eEuzY7rUFss87TOUklvIWc3ExkZgce7xk\n8W8GavC/XgX/s/79OW0s3eCd+xB53IxhTOv61dEDv2bSEJZ2mAJvT/HaFry5mcNf3cyqrd/nsNlH\npeWcUOJRpB/lIQMPNZ/PaE/294+VcZyo3Yh7yEpfV5T50XWnUy70QEtc3rGMTVx08MfpLHRiSK9i\nqTf4+wN/axODfYNRuqaUeBk+vhSUNDyhrJIwBELQIgTLlsLGDYSD/9UsCp+bCMxHBM/OdZl/SJmO\n1nLqGOGxpfIeSXlHJPqrWn5mX6n0Fem+Pvcp34m1zOLdvMIO5V5tjeDp7yx64NdMGrJu2P6NP8HJ\nrwEP3w/cv7tPadRcXXGLhAd+VHXf8bwN5cnDd4FBYEW6OZSA1IehxkqMKL02w0AGMZRYiQxDMbiK\nkVXbV72QY/PWnGqeeJ196KcAoGvwjAKt8U8wtMYfUe1aBLJPqWc989d5ue4FI093SxffPeH/erKP\niHuYoVSTfKhST8X+svpxkgFX//HQG0vY2LsWKQSDgzt41xZodiFvWMyfcSg5w/e9pFdgQfrevOG3\nBXJOPmcxpEo9qucvfa9fiqhNBNvibUbwWgiGSpItPWDge9X+rV6+yVf5HUGpVMnRR7n8+CeDYBj+\n+ygSk+qV+zMQ9bpG6wvSbcnzSe5nKLOJa67J88IqAxPBYyxgHbNj34dA2qm3BVrDoRdw1Ql64I+o\ndi2yVvge8ybccBd0WUW62mYyIEq4CNqai5HnGHqrgUdpxL1N1ZvFSEhFRszDDV7L4Hj+sXpKWyiJ\nElNapvPks3dy0Hp/QRZRTR1DQiFXoD3fHp6/EQz0EA3u/sBvGgZCRK9TBiDcTzEGqf7KtvH5L6oJ\nd3I6Z3Bn+LqRpR0d3NU0FFmyjyWgUAbRv51t/SVPK3fLmE19kRccePgy7WGONbUwiVpYobqk0u8/\nRoY5ttPZKXpp4498KJRWuroNjj3ejcU/YkYxaDeISzdGwnAGsRXTiMdSDMNvN7nl1jyvrc4hMSiT\nR2AiMViiXFWdsjk2JoTh1x5/hPb4I0Z6LQLZJ5bzL+GbD8G8d+CQmYfS2drJoCgzu7inMkgZyoBk\nRINOeAcnI7qbU/DX9IZfGfvlGKzvX89geYApLdN4ctkvmNXrnYOB5937R/PaDP+vhI7mdvYq7h3J\nNeB78N5f6Xv1+Zyf1QOeAQs+ZOjxk54JGPHXhpoxhLKfPzMoD8H2bZ7cZPgziBJ5BmnBP2Vcclh4\nGUUGkkKzoKszIZmpEpMQURZSsD0oO6FKRqG8kza8gzRxGvfwIB+MtTeqvKOy2z1+27bPABY6jnNO\nxrYLgYvw1plf5TjOPWN9H41mOLJu5NJWgs8/AVMGgZXpG5qMN/sqzz8yqj17gVUj6rmrp+cW0DxM\nnw10UaIJiYHApH/QYM26HF0zoKnFN5rBwzeSgXGVpkFoTA3Cfq+vttjW60lrwtvAAM0M0YTApI82\nVjMvdh6NLO+MB2P6Ltm2/X28WexfMrbNAj6PV1K8ADxq2/b9juOUduZENZpKZMk+fc2w55dg2oDn\n+F7yJJy9ElrzbUgkJTHEHsU9wDAYdAdxpaQ13+oPUp4/6/0zwnlxvzuAkC5tTUXW9P2VwfIAc6fM\nY1vfJgrrN4eLyoICa0B4o7/gr2kY5Mx82I9q0pKUYUzANAyE3zd08WTiiYw1KhDtZlsAAAUmSURB\nVMfJaE+870jdxhlsSjcKYN0ID5BB1r3EttJBNxsZoinWbpqSri5Dyzs7yVidiOXA74CLM7YdCSx3\nHGcIGLJt+xXgEODJMb6XRlOV5I1cgsBvX7NnAAD68142jXD7MCVMK4Hbt4a8mSfnljClwLKaEb5E\nYWEgpUBKb9BFSgrSW+xlGSZzhPAqZ65zaGE0mqkERu4DqcethcZfjX5a6KUVMCiTQ2Cl+kSGK1Ko\nvOeG0sN7/iIH8Br7IjF4if1Tg37g5XsSYOPKO+NB1YHftu1/BL6YaP6M4zh32LZ9YoXdisBW5fV2\nYMqYz1CjGSVZM4Cr3u89AD7+PNyxGDwlshzJG0MDsaErOZhHP5asIa7xKDBAgRGu7pUVnivcxtlc\nzr/F2rq6vAE+n0d7+eNI1YHfcZyfAj8d5TG34Q3+AUVgyyiPodGMGXUGkJX2ufg9cOQF0DoErTLH\nHbeVaR/a3Wep2UGB07iHx1iAxKCUiDBoHX/XsSviRU8A37JtuxloAQ4Enq+2g2EYY4pMazTD8g0e\nx5MfQ6QJK+YEr8oUr8zcsx/8JaHeTW6HgJmjeOd7+YZ/n8O6Qx4K/AfQxfDx4NGyAe9as3at+ZEZ\nMzp2fWS+AdmZgV9ZNQK2bf9P4BXHce6ybfta4BE8WXKRDuxqasY3OKrWp1B/GE8Dc4btptFoNBqN\nRqPRaDQajUaj0Wg0Go1Go9FoNBqNZuzUNI3Stm0T+BHeyt5B4ALHcV6t5TntTmzbzgM/A/bGS4u7\nCngBuAlvIfzzwOccx9n5kpGTBNu2ZwBPAR/AuwY30YDXwrbtK4C/A/LAD/FWy99Eg10Lf4y4Ea+y\ngwAuBFwa6FrYtn0UcI3jOCfZtv1uMj77aOuj1XoV+N8DTY7jHAN8GfhOjc9nd3MOsNFxnBOADwPX\n4V2DRX6bAZxew/PbrfiG8AagD++zf5cGvBb+qvgF/u/iRLwacI36vTgZaHMc5zjgn/FuYtYw18K2\n7cuBnxCtl0j9JpT6aMcAHwL+xbbtpqzjBdR64D8W/xaajuM8Dhxe29PZ7fwa+Jr/3MRbuHKo4zjL\n/LZ7IVGLtr75N+B6YK3/ulGvxcnAStu27wTuwlssdViDXot+YIpt2wZe6ZcSjXUtXgE+SqTOZP0m\njsCvj+Y4zjZ/n0OqHbTWA38HXomHANef2jUEjuP0OY7Ta9t2Ec8IfIX4/0kvDVLnyLbtz+DNfpb4\nTX4N35CGuRZAN15124XAJcCtNO61WI5XAeBFvNngtTTQtXAc57d48k2A+tmDOmgdjLI+Wq0H2WRd\nH9NxnIYqu2fb9lzgIeCXjuPchqfdBRSBd2pyYruf84G/sW17KTAf+AXeABjQSNdiE7DEcZyy4zgO\nMED8h9xI1+JyPG92f7zvxS/x4h4BjXQtID4+dOB99lHXR6v1wL8cvHomtm0fDTxX29PZvdi2PRNY\nAlzuOM5NfvNfbNv260hyCrAsa996w3Gc9zuOc6LjOCcBzwDnAvc14rUAHsWL+WDb9h5AK/Bgg16L\nNiJVYAtemZmG/I34ZH32J4Djbdtutm17CiOoj1bre+7+Ds/LW+6/Pr+WJ1MDFuF5cl+zbTvQ+r8A\nXOsHZ/4LWFyrk6sxErgM+EmjXQvHce6xbfsE27afwHPOPguspgGvBV7c5+e2bT+C5+lfgZf11WjX\nIshaSv0m/KweXR9No9FoNBqNRqPRaDQajUaj0Wg0Go1Go9FoNBqNRqPRaDQajUaj0Wg0Go1Go9Fo\nJgL/HzhpWenej1CDAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f79712d8cd0>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Ok, this does look nice. I am impressed!"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Conclusions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We worked out a naive DTW implementation pretty much from scratch. It seems to do reasonably well on artificial data."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "References\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. [Wikipedia page on dtw](http://en.wikipedia.org/wiki/Dynamic_time_warping)\n",
      "2. [R's dtw package](http://dtw.r-forge.r-project.org/)\n",
      "3. [mlpy page on dtw](http://mlpy.sourceforge.net/docs/3.4/dtw.html)\n",
      "4. [DTW review paper](http://www2.hawaii.edu/~senin/assets/papers/DTW-review2008draft.pdf)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Feel free to comment!"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}