{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class 2: Optimization\n",
    "\n",
    "Optimization is a general topic, and not specific to LCA. Please read through the following to get a detailed introduction on optimization:\n",
    "\n",
    "[Gaël Varoquaux - Scipy Lectures - Mathematical optimization](http://www.scipy-lectures.org/advanced/mathematical_optimization/)\n",
    "\n",
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from brightway2 import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some more imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from stats_arrays import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We assume that you have [Seaborn](http://stanford.edu/~mwaskom/software/seaborn/) installed already. If you don't:\n",
    "\n",
    "    conda install -y -q seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "sns.set(style=\"white\", palette=\"muted\", color_codes=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copy our first project which included ecoinvent 2.2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "if \"Class 2\" not in projects:\n",
    "    projects.current = \"Class 1\"\n",
    "    projects.copy_project(\"Class 2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make sure we have the right project, and that things are set up the way we want them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "projects.current = \"Class 2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we are going to make a model of transport choices, and optimize for the subsidy that should be given to ebike purchases. Please note that this is a **toy model**, and the results will be completely wrong. Let's start by making some simple assumptions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "avg_distance = 36.7           # km\n",
    "population = 10000            # people\n",
    "days = 10 * 250               # years * days/year\n",
    "costs = {\n",
    "    \"electricity\": 0.05,      # CHF/km\n",
    "    \"ebike\": 7.5e3,           # CHF over 10 years, including maintenance\n",
    "    \"new car km\": 0.25,       # CHF/km\n",
    "    \"new car\": 1.5e4,         # CHF over 10 years, less resale\n",
    "    \"old car km\": 0.3,        # CHF/km\n",
    "    \"bike maintenance\": 500,  # CHF over 10 years\n",
    "    \"old car resale\": 2.5e3,  # CHF\n",
    "    \"car sharing\": 0.6,       # CHF/km\n",
    "    \"green penalty\": 5e3,     # CHF\n",
    "    \"postbus\": 0.4,           # CHF/km\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up our system. Our median distance values come from the [2010 microcensus](http://www.bfs.admin.ch/bfs/portal/en/index/themen/11/04/blank/03.html), but the distribution is made up.\n",
    "\n",
    "In our model, each person travels their distance each day."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SystemSetup(object):\n",
    "    def __init__(self):\n",
    "        self.distance_params, self.distances = self.get_distances()\n",
    "        self.trips = self.get_trips()\n",
    "        self.bikes = self.when_bike_possible()\n",
    "        self.ebikes = self.when_ebike_possible()\n",
    "        # Following the microcensus, there is a 0.7 chance that one has a bicycle, and a 0.8 chance that one has a car. We will assign these at random.\n",
    "        self.has_bicycle = np.random.random(size=population) < 0.7\n",
    "        self.has_car = np.random.random(size=population) < 0.8\n",
    "        # Each trip has an 0.8 chance of being possible using public transport.\n",
    "        self.can_use_ov = (np.random.random(size=(population * 5))\n",
    "                                    .reshape(self.ebikes.shape)) < 0.8\n",
    "        # There are also 20% of the population that are against cars, \n",
    "        # and will pay an additional penalty for private car use.\n",
    "        self.against_cars = np.random.random(size=population) < 0.2\n",
    "    \n",
    "    def get_distances(self):\n",
    "        params = LognormalUncertainty.from_dicts(\n",
    "            {\n",
    "                'loc': np.log(avg_distance),\n",
    "                'scale': 1,\n",
    "                'maximum': 200,\n",
    "            }\n",
    "        )\n",
    "        distances = LognormalUncertainty.bounded_random_variables(params, size=population).ravel()\n",
    "        return params, distances\n",
    "\n",
    "    def get_trips(self):\n",
    "        \"\"\"Figure out how many trips people take - they can take a different vehicle for each trip. Assume that everyone can take between 1 and 5 trips. We will split up the distances randomly.\"\"\"\n",
    "        trips = (np.random.random(size=(population* 5))\n",
    "                          .reshape((population, 5)))\n",
    "        trips_occured = ((np.random.random(size=(population * 4)) > 0.5)    \n",
    "                                  .reshape((population, 4))) * 1\n",
    "        # At least one trip, and the others are random\n",
    "        trips[:, 1:] = trips[:, 1:] * [trips_occured]        \n",
    "        # Normalize so that each person sums to one\n",
    "        trips = trips / trips.sum(axis=1).reshape((-1, 1))\n",
    "        # And multiply by each persons total distance\n",
    "        trips *= self.distances.reshape((-1, 1))\n",
    "        print(\"Total number of actual trips:\", (trips > 0).sum())\n",
    "        return trips\n",
    "\n",
    "    def when_bike_possible(self):\n",
    "        \"\"\"We assume that the fraction of trips taken by bicycle goes down linearly with distance to 25 km. \n",
    "        There is also only an 0.7 chance that any given trip possible with bike or electric bike will be \n",
    "        taken due to e.g. weather.\"\"\"\n",
    "        chance_bicycle = (1 - self.trips / 25) * 0.7\n",
    "        # Eliminate non-trips where distance = 0\n",
    "        chance_bicycle[chance_bicycle == 0.7] = 0 \n",
    "        # Turn probabilities into boolean array of possible true or falses\n",
    "        chance_bicycle = (chance_bicycle > np.random.random(size=(population * 5))\n",
    "                                                    .reshape(chance_bicycle.shape)) \n",
    "        print(\"Bikes can be used on this many trips:\", chance_bicycle.sum())\n",
    "        return chance_bicycle\n",
    "\n",
    "    def when_ebike_possible(self):\n",
    "        \"\"\"Similar to above - ebikes can be used up to 70 km.\"\"\"\n",
    "        chance_ebike = (1 - self.trips / 70) * 0.7\n",
    "        chance_ebike[chance_ebike == 0.7] = 0\n",
    "        chance_ebike = (chance_ebike > np.random.random(size=(population * 5))\n",
    "                                                .reshape(chance_ebike.shape)) \n",
    "        print(\"EBikes can be used on this many trips:\", chance_ebike.sum())\n",
    "        return chance_ebike\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of actual trips: 30002\n",
      "Bikes can be used on this many trips: 11063\n",
      "EBikes can be used on this many trips: 16451\n"
     ]
    }
   ],
   "source": [
    "system_setup = SystemSetup()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to understand some of the values we just created, so we graph them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Graphics(object):\n",
    "    def graph_distances(self, params, distances):\n",
    "        plt.plot(*LognormalUncertainty.pdf(params, np.linspace(0, 200, 1e4)), label=\"Predicted\")\n",
    "        plt.xlabel(\"Distance\")\n",
    "        plt.ylabel(\"Probability\")\n",
    "\n",
    "        sns.distplot(distances, label=\"Observed\")\n",
    "        plt.legend()\n",
    "        plt.xlim(0, 200)\n",
    "        plt.tight_layout()\n",
    "\n",
    "    def graph_trips(self, trips):\n",
    "        f, axes = plt.subplots(1, 2, figsize=(12, 6))\n",
    "\n",
    "        num_trips = axes[0]\n",
    "        trip_hist = axes[1]\n",
    "\n",
    "        mask = trips > 0\n",
    "\n",
    "        sns.distplot(mask.sum(axis=1), kde=False, ax=num_trips)\n",
    "        num_trips.set_title(\"Number of trips per person (count)\")\n",
    "\n",
    "        sns.distplot(trips[mask], color=\"g\", ax=trip_hist)\n",
    "        trip_hist.set_title(\"Trip distances (km)\")\n",
    "        trip_hist.set_xlim(0, 100)\n",
    "\n",
    "        plt.setp(axes, yticks=[])\n",
    "        plt.tight_layout()\n",
    "\n",
    "    def graph_options(self, te):\n",
    "        sns.violinplot(data=te.evalulate_all_options(10000.))\n",
    "        sns.despine(left=True)\n",
    "        plt.ylabel(\"Total cost\")\n",
    "        plt.xticks(range(6), te.labels)\n",
    "        plt.tight_layout()        \n",
    "\n",
    "    def graph_by_cost(self, te):\n",
    "        for label, options in zip(te.labels, te.option_kwargs):\n",
    "            plt.figure(figsize=(10, 6))\n",
    "            plt.title(label)\n",
    "            sns.violinplot(data=te.calculate_costs(te.allocate_transport(**options), 10000., split=True))\n",
    "            sns.despine(left=True)\n",
    "            plt.ylabel(\"Total cost\")\n",
    "            plt.xticks(\n",
    "                range(10), \n",
    "                [\"Bike\", \"Buy Ebike\", \"Run Ebike\", \"Buy car\", \"Run new car\", \"Run old car\", \"Sell car\", \"Green tax\", \"Postbus\", \"Mobility\"]\n",
    "            )\n",
    "            plt.tight_layout()        \n",
    "\n",
    "    def graph_choices(self, te):\n",
    "        choices = te.choose_best_option(te.evalulate_all_options(0.))\n",
    "\n",
    "        plt.hist(choices, bins=np.arange(-0.5, 5.5, 1))\n",
    "        plt.xticks(range(6), te.labels)\n",
    "        plt.xlim(-1, 6)\n",
    "        plt.ylabel(\"Count\")\n",
    "        plt.tight_layout()\n",
    "\n",
    "    def graph_costs_curve(self, te):\n",
    "        xs = np.linspace(0, 25000, 100)\n",
    "        results = [te.best_model_result(x) for x in xs]\n",
    "\n",
    "        ys1 = [obj[1].sum() for obj in results]\n",
    "        ys2 = [obj[0].ebike_bought.sum() * premium for premium, obj in zip(xs, results)]\n",
    "        ys3 = [te(x) for x in xs]\n",
    "\n",
    "        plt.plot(xs, ys1, label=\"Individual costs\")\n",
    "        plt.plot(xs, ys2, 'g-', label=\"Subsidy total\")\n",
    "        plt.plot(xs, ys3, 'r-', label=\"Total\")\n",
    "        plt.legend(loc=6)\n",
    "        plt.ylabel(\"Costs (CHF)\")\n",
    "        plt.xlabel(\"Subsidy per electric bike (CHF)\")        \n",
    "\n",
    "\n",
    "graphics = Graphics()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning: using a non-integer number instead of an integer will result in an error in the future\n",
      "Warning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "image/png": 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b1NbWUldXd8qXaZpnOr2IiMgFwZHpAi40oaYtHdIhJ5tuVTXq08ukb58ku/Y6\nqK4xSEWiLK99nx6xdJC7yNWXg/EDvHr0ZXo5e7d4biQcYcaAWeTm5maidBERkbOmTs5J0iHHwufN\n3pADMOGyOGDw8fp0N8fj8+AL+PAFfIwuuASAPYndTY81fnl93gxWLSIicvYUck4Sjhj4vBa2hk8m\nW2ZWnax0WJKcHJMNm10kEi2nk+e7Cujt6UN57BiVscoMVSgiIvLpKOScJBw2mro40NzJ6cqrHZ+O\n3Q7jxsSJxQ127jt1P67SwCgAttdv7ezSRERE2oVCzglMEyLRliGnLlGLz+7LiplVJxs3Jr2f1Zad\neadMJ+/t6U0PZz4HwvsJJuszU6CIiMinoJBzgmjMBhj4GgYdJ80k4VSYgCM7B9n6cyxGDk9SXefi\n0FFPi2OGYTAydxQWFtvrtmWoQhERkfOnkHOCcCT9cTR2coLJIAABZyBjNXW0CQ3TyTdtPzXIDfAN\nJMeew57QbqKpaGeXJiIi8qko5JwgEj055KRv0/gdp45ZyRYX9UnRsyBK2UEvNbUtByDbDBsjAiNJ\nWSl2BT/JUIUiIiLnRyHnBJFo+iLv86UXu6tvCjnZ28kxDBg9vA7LMliz/tRxRyX+ITgNJ5/U7yBl\npTJQoYiIyPlRyDnBqZ2c9O2qbA45AEMGBPF6Uqzf7CKRaHnMaXNS4h9K1IyyP1SWmQJFRETOg0LO\nCZrG5Pha3q4KZHnIsdth1LB6ojGDzducpxwfHhiBgcH2+m1YJ0/DEhERuUAp5JzgdGNyPDYPDlv2\n734xakQ9NpvFx+tdp0wn9zv89PP2pyZRTWWyIjMFioiInCOFnBOcGHJMyySUDGX1zKoT+X0pSocl\nKa+ws++A/ZTjI3JLAdgd29XZpYmIiJwXhZwTRE6YQh5KhrCwsn48zokmjktPJ1+55tQByEWunhS4\nCjmaOEJFXN0cERG58CnknCActeFxW9jt3WNm1cn69knR76Iku/c6qahs+adhGAYjAuluzoqaDzJR\nnoiIyDlRyDlBJGrD501PH+8Oa+SczhXjG7o5a0/t5gzwDcRjeFlTt4pwMtzZpYmIiJwThZwGpmWl\nQ043m1l1suFDkvTIM9m01UkofOrigCWeEuJWnBWV6uaIiMiFTSGnQShiYlnGaVY77l4hx2aDieNi\npFIGazecOp18oGswTsPJ0vIlWhxQREQuaAo5Deoi6Qt2Y8ipTwRxGi7cdncmy8qIsRcncLst1mxw\nkUy2POb6Ex45AAAgAElEQVSyuRiXeznV8So21WzITIEiIiJnQSGnQV24IeT4LCzLIpisJ+DsXuNx\nGrlcMO6SOKGw7bSLA07KmwzA0vIlnV2aiIjIWVPIaVAfTg849nktwqkwJma3u1V1ossvi2OzWaxc\ne+rigL3cvSkNjOST4E4OhA9kpkAREZE2KOQ0CEbTnRyvx+q2g45PlBuwGDU8QUWlnT37Tl0ccEav\nWQC8p26OiIhcoBRyGgQj6U6O54SQ0507OQATm6aTnzouaVTuaIrcPVldtbLp8xIREbmQKOQ0CEab\nb1fVd5Pdx9vSp5fJwH5J9pY5OHa85Z+KzbBxdc+ZJK0kHxx/P0MVioiItE4hp0GwYXaVx2MRTHTP\nhQBP54rL092cjz4+dXHAK4uuwm1z8/7xpaSs5CnHRUREMkkhp0FjJ6dxTI7dsOO1ezNcVeYNHZyk\nZ2GKLdud1NS2XBzQa/dyZeFkahI1rK9el6EKRURETk8hp0FjJ8ftMqlPBvE7AhiG0cazsp9hwKQJ\ncSzLYOWaU8fmXF08A9B0chERufAo5DQIRkxcTpOkESNpJbr1zKqTjRqRIC/XZP0mJ+FIyz+ZYk8v\nLs4dzZ7QbspC+zJToIiIyGko5DQIRlN43Fa33ZjzTOx2uGJ8jGTKYP0W3ynHG6eTv1u+uLNLExER\naZVCToNgxMTjManX9PHTunR0Ap/XZP0WH5GY2eJYaWAUvT19WFv9MbWJmgxVKCIi0pJCDhBPmsQS\nFh63ecLMKoWcEzmdMGFcnFjcxqL1dS2OGYbB1cUzSVkp3j++LEMVioiItKSQwwnTx90mwYY1cgJO\nhZyTjR8bx+k0eWNVLfFky27OxIIr8dl9vH/8PRJmIkMVioiINGsz5Hzta1/jzTffJJHI3gtXfbgx\n5FjUJ+sxMPDZTx170t15PTBmZITqYIp311W3OOa2u5lcNJVgsp6Pq1ZnqEIREZFmZxVyli1bxmc+\n8xkeeeQRNm7c2Bl1dar6cHohu3Qnpx6/w4/NUJPrdC4dVY/DBi8sPUpNTS11dXVNX+O8l2PDxuIj\nb1Nbmz5mmmbbJxUREekAjrZ+YOLEiUycOJFoNMpbb73Ffffdh9/v5/bbb+eLX/wiLtepK+F2NfUN\nt6tcnigxM0aBqzDDFV24HEaYkoE17Nzbg2dXr2PEkGiL472dfTgcP8QbR18lJ+FnxoBZ5ObmZqha\nERHpzs6qXfHRRx/xyCOP8J//+Z9MmzaN733ve1RUVPD1r3+9o+vrFI2dHHuOpo+fjcvHBjEMi483\nBvD6ffgCzV+jCi4GoCy1D69PK0aLiEjmtNnJmTFjBv369ePWW2/lBz/4AV5v+sI1ceJEbr311g4v\nsDM0dnJwp2cNaWbVmeXlJhldmmDTNhc7djkoHda8b1WRqycFrgIORg5Q6hyVwSpFRKS7a7OT89vf\n/pZnn32Wm2++uSngrF+/HrvdziuvvNLhBXaGxoHHpivdydFqx22bfEUcw7D44CM3ltX8uGEYDA+U\nArA3tjtD1YmIiJwh5Hz88cesWrWK++67j9WrVzd9ffjhh3znO9/pzBo7XH0k3YlIOnS76mwVFpiM\nGpHk2HE7n+xp2RAc4BuIx+ahLLaPaCrayhlEREQ6Vqu3q1asWMHq1aspLy/nv/7rv5qf4HAwe/bs\nTimuszR2chJGCCzIUcg5K1OuiLFlu4P3P3QzrCRJ436mdsPOsMAINtVu4OO6VdyQf2NmCxURkW6p\n1ZBz//33A/DKK69w8803d1pBmdA48DhqhHAbHhy2NocqCVBUmO7mbN3hZNdeB8NKmsfmDPMPZ2vt\nZpbXLOMzAz6L3bBnsFIREemOWr2a/9d//Rf3338/K1euZOXKlaccf+yxxzq0sM5UH0nhcUHEDFPg\nKsh0OV3KlCtibN3h5P0P3Qwd3NzNcdvdDHAPZG9sD+uq13B5wcTMFioiIt1OqyFn9OjRAEyYMAHD\nMLBOGF1qNF7JskR9OEkgL4KFpVtV56hnkUnpsATbP3GyZ5+dIYNTTceGuIeyL7aXRcfeZnz+hKz7\nuxERkQtbqyFnxIgRHD58mCuuuOKUY9l2saqPpOjVM71nlULOuZtyZYztnzh5/yM3JYPCTd2cHLuf\ni/2j2RzcxCfBnQwPjMhsoSIi0q20GnLmzJlzxicuWbKk3YvJhGTKIhIzcQfqSQB+e06mS+pyevU0\nGTE0wY5dp3Zzpva4ms3BTSw+9rZCjoiIdKpWQ062hJi2hKLpC7IzJx1y1Mk5P1Mnxdixy8HSFR5K\nBoWaujkDvAMpyRnC5tpNHIkcpo/3oswWKiIi3UarIeeJJ57gvvvu46GHHjrt8WwZeNwYcgxPerXj\nHIc6OeejV8/mmVYnr4J8Te/r+N3uX7Pk2CLuGnR3BqsUEZHupNWQc/HF6T2IJkyYADSPw7EsK6vG\n5DSGHMvdGHLUyTlf066KsW2ng/eWuxk+pDnkXJI3lmJ3MauqPuLGvjeR58zLYJUiItJdtLri8cyZ\nMwG45ZZbuPrqq8nLy6OgoICZM2fyr//6r51WYEcLNuxblXTU4jY8Ws/lUyjMNxlzcYKKKjtbtjub\nHrcZNmb2upaklWRpefe4DSoiIpnX5t5Vb7/9NjfffDMvv/wyCxcu5KabbuK9997rjNo6RSiaAsMk\nbq8lx+bLdDld3tQrY9jtFss+dJNqHn/MFYWTCDgCLCt/l3AynLkCRUSk22hzad8nnniChQsX0qtX\nLwAOHTrE17/+daZPn97hxXWGUCSFwxsCw8KnmVWfWl6uxWWXxPl4vZtN2z2M8dU3HZvSYxpvVrzB\nPw/8g1mF17V4nt/vx2ZrM3OLiIictTZDjtPppLi4uOn7vn37Yrdnzy2dYDSFw5cej+NTJ6ddTL4i\nzvrNLlau89Ov1wcUFaXH4NgsOy7DxXvV7+Iy3TiN9C2tSDjCjAGzyM3NzWTZIiKSZVoNOf/85z8B\nGDRoEPfddx+33HILdrud1157jZEjR7Z5YtM0+eEPf8jOnTtxOp389Kc/ZcCAAU3HlyxZwlNPPYXD\n4eDWW2/l9ttvbzq2YcMGfvGLX/Dss88CUFZWxty5c7HZbAwbNoyHH3643QY/h6IpHDnpboNCTvvw\n51hMvCzOitVudu3vyYDBzX9mpdZINtZu4KB1gItzR2ewShERyXat3h949913Wbp0KW63G7/fzzvv\nvMNbb72Fw+FoscVDaxYtWkQikWDBggV8+9vfZt68eU3HEokE8+bN409/+hPPPvssL7zwApWVlQD8\n/ve/53vf+x6JRKLp5x977DEeeOAB5s+fj2VZLF68+NO85xZCkRTOnMZOjm5XtZcrL4/hcpqs25xH\nNNb8+LDACJyGix3120iaydZPICIi8im12sk5MZScLBKJtHnitWvXMnXqVADGjh3L5s2bm47t3r2b\nAQMGEAgEABg/fjyrV6/m+uuvZ+DAgTz55JN85zvfafr5rVu3Nk1lnzZtGsuXL+eaa65ps4azEYqm\ncPjUyWlvXi+MHVnD6o0FfLjazYwp6aTjsrkYERjB5rr0Vg8jc0dluFIREclWbY7Jeeutt/jVr35F\nJBLBNE1M0yQej7NixYozPi8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LiEh26DYhp6JhjZxCVxGReLqT43V1m7ffbZUOSzJ1UpTa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\njhBCCCGykoQcIYQQQmSl/w8+rt3cC46cAQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c58470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphics.graph_distances(system_setup.distance_params, system_setup.distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning: using a non-integer number instead of an integer will result in an error in the future\n",
      "Warning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "image/png": 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YcMC+971e9Dj55JN177336s9//rOWLFlykFf14Orq6jRp0qQj3g4YDIxgFaD936G6++67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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1128d09e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphics.graph_trips(system_setup.trips)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a data structure to store our model results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import collections\n",
    "\n",
    "fields = (\n",
    "    \"bike_used\", \n",
    "    \"ebike_bought\", \n",
    "    \"ebike_used\", \n",
    "    \"new_car_bought\", \n",
    "    \"new_car_used\", \n",
    "    \"old_car_sold\", \n",
    "    \"old_car_used\", \n",
    "    \"ov_used\", \n",
    "    \"car_sharing_used\",\n",
    ")\n",
    "\n",
    "ModelResult = collections.namedtuple('ModelResult', fields)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now define our model (finally!). Actually, this is the easy part - most of the work in optimization is getting the input data in a reasonable state, and checking your assumptions. Well, and doing sensitivity analysis of your input parameters, uncertainty analysis of your results, and then choosing algorithms... there are a lot of \"most of the work\" elements, I guess.\n",
    "\n",
    "Our model will be semi-agent based. Each person will evaluate all possible options, and choose the lowest cost for their preferences and trip schedule. The options are:\n",
    "\n",
    "1. Buy new car + sell old car\n",
    "2. Buy electric bicycle\n",
    "\n",
    "We assume that if you don't have a bicycle already, you don't want one.\n",
    "\n",
    "However, for each trip we will still need to choose between old car, new car, bicycle, electric bicycle, car share, and public transport."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class TransportEvaluator(object):\n",
    "    def __init__(self, costs, setup):\n",
    "        \"\"\"Set up model with input parameters, and calculate preliminary cost arrays\"\"\"\n",
    "        self.distances = setup.trips            # 2-d array; population by trips\n",
    "        self.costs = costs                      # dictionary\n",
    "        self.has_bicycle = setup.has_bicycle    # Boolean array; 1-d (population)\n",
    "        self.has_car = setup.has_car            # Boolean array; 1-d (population)\n",
    "        self.ov_trips = setup.can_use_ov        # Boolean array; can use public transport; population by trips\n",
    "        self.bike_trips = setup.bikes           # Boolean array; can use bike; population by trips\n",
    "        self.ebike_trips = setup.ebikes         # Boolean array; can use bike; population by trips\n",
    "        self.against_cars = setup.against_cars  # Boolean array; 1-d (population)\n",
    "\n",
    "        self.labels = [\n",
    "            \"New car\", \n",
    "            \"Sell car\", \n",
    "            \"Sell car, buy ebike\", \n",
    "            \"Buy all\", \n",
    "            \"Buy ebike\", \n",
    "            \"Status Quo\"\n",
    "        ]\n",
    "\n",
    "        self.option_kwargs = [\n",
    "            {\"buy_new_car\": True},\n",
    "            {\"sell_car\": True},\n",
    "            {\"sell_car\": True, \"buy_ebike\": True},\n",
    "            {\"buy_new_car\": True, \"buy_ebike\": True},\n",
    "            {\"buy_ebike\": True},\n",
    "            {}\n",
    "        ]\n",
    "    \n",
    "        self.options = self.calculate_all_options()\n",
    "\n",
    "    def __call__(self, ebike_premium=0.):\n",
    "        \"\"\"Call the model. \n",
    "\n",
    "        ``ebike_premium`` is financial incentive offered to ebike purchase.\"\"\"\n",
    "        mr, costs = self.best_model_result(ebike_premium)\n",
    "        return costs.sum() + mr.ebike_bought.sum() * ebike_premium\n",
    "\n",
    "    def choose_best_option(self, options):\n",
    "        return np.argsort(np.hstack(options).reshape((6, -1)), axis=0)[0, :]\n",
    "\n",
    "    def construct_empty_model_result(self):\n",
    "        return ModelResult(\n",
    "            np.zeros(self.distances.shape, dtype=bool),\n",
    "            np.zeros(self.distances.shape[0], dtype=bool),\n",
    "            np.zeros(self.distances.shape, dtype=bool),\n",
    "            np.zeros(self.distances.shape[0], dtype=bool),\n",
    "            np.zeros(self.distances.shape, dtype=bool),\n",
    "            np.zeros(self.distances.shape[0], dtype=bool),\n",
    "            np.zeros(self.distances.shape, dtype=bool),\n",
    "            np.zeros(self.distances.shape, dtype=bool),\n",
    "            np.zeros(self.distances.shape, dtype=bool),\n",
    "        )\n",
    "\n",
    "    def add_rows(self, in_mr, out_mr, mask):\n",
    "        one_d_attrs = [\"ebike_bought\", \"new_car_bought\", \"old_car_sold\"]\n",
    "        two_d_attrs = [\"bike_used\", \"ebike_used\", \"new_car_used\", \"old_car_used\", \"ov_used\", \"car_sharing_used\"]\n",
    "        for attr in one_d_attrs:\n",
    "            getattr(out_mr, attr)[mask] = getattr(in_mr, attr)[mask]\n",
    "        for attr in two_d_attrs:\n",
    "            getattr(out_mr, attr)[mask, :] = getattr(in_mr, attr)[mask, :]\n",
    "\n",
    "    def best_model_result(self, premium):\n",
    "        all_costs = self.evalulate_all_options(premium)\n",
    "        choices = self.choose_best_option(all_costs)\n",
    "        costs = np.hstack(all_costs).reshape((6, -1))[choices, np.arange(choices.shape[0])]\n",
    "        result = self.construct_empty_model_result()\n",
    "\n",
    "        for index in range(6):\n",
    "            mask = choices == index\n",
    "            self.add_rows(self.options[index], result, mask)\n",
    "\n",
    "        return result, costs\n",
    "\n",
    "    def calculate_all_options(self):\n",
    "        return [self.allocate_transport(**kwargs) for kwargs in self.option_kwargs]\n",
    "\n",
    "    def evalulate_all_options(self, premium):\n",
    "        return [self.calculate_costs(obj, premium) for obj in self.options]\n",
    "\n",
    "    def calculate_costs(self, mr, premium, split=False):\n",
    "        \"\"\"Calculate costs for a model result. \n",
    "\n",
    "        Premium is subtracted from each ebike purchase price.\"\"\"\n",
    "        values = [\n",
    "            # Bicycle maintenance\n",
    "            (mr.bike_used.sum(axis=1) > 0) * self.costs['bike maintenance'],\n",
    "            # Ebike cost, including maintenance\n",
    "            mr.ebike_bought.astype(float) * (self.costs['ebike'] - premium), \n",
    "            # Ebike operating cost\n",
    "            (mr.ebike_used * self.distances).sum(axis=1) * self.costs['electricity'] * days,\n",
    "            # New car purchase\n",
    "            mr.new_car_bought * self.costs['new car'],\n",
    "            # New car operating cost\n",
    "            (mr.new_car_used * self.distances).sum(axis=1) * self.costs['new car km'] * days,\n",
    "            # Old car operating cost\n",
    "            (mr.old_car_used * self.distances).sum(axis=1) * self.costs['old car km'] * days,\n",
    "            # Old car resale\n",
    "            -1 * mr.old_car_sold * self.costs['old car resale'],\n",
    "            # Car penalty\n",
    "            ((mr.old_car_used + mr.new_car_used).sum(axis=1) > 0) * self.against_cars * self.costs['green penalty'],\n",
    "            # Public transport\n",
    "            (mr.ov_used * self.distances).sum(axis=1) * self.costs['postbus'] * days,\n",
    "            # Car sharing\n",
    "            (mr.car_sharing_used * self.distances).sum(axis=1) * self.costs['car sharing'] * days\n",
    "        ]\n",
    "        if split:\n",
    "            return values\n",
    "        else:\n",
    "            return sum(values)\n",
    "\n",
    "    def allocate_transport(self, buy_new_car=False, buy_ebike=False, sell_car=False):\n",
    "        \"\"\"Allocate transport using precedence order list.\n",
    "\n",
    "        Choose transport from the lowest to highest cost, namely:\n",
    "\n",
    "        * bike\n",
    "        * electric bike\n",
    "        * new car\n",
    "        * old car\n",
    "        * public transport\n",
    "        * car sharing\n",
    "\n",
    "        ebike is only available if ``buy_ebike``.\n",
    "        new car is only available if ``buy_new_car``.\n",
    "        new and old car are removed if ``sell_car``.\n",
    "\n",
    "        This is a silly algorithm, but the whole model is made up, so...\n",
    "\n",
    "        \"\"\"\n",
    "        # If bicycle available, use bicycle when possible\n",
    "        trips = self.distances.copy()\n",
    "\n",
    "        bike_used = np.ones(shape=trips.shape, dtype=bool)\n",
    "        bike_used[~self.has_bicycle, :] = False  # No bike, can't use it\n",
    "        bike_used[~self.bike_trips] = False      # Trip not suitable for bike\n",
    "        trips[bike_used] = 0\n",
    "\n",
    "        # Buy and use ebike, if possible\n",
    "        if buy_ebike:\n",
    "            ebike_used = self.ebike_trips * ~bike_used\n",
    "            trips[ebike_used] = 0\n",
    "        else:\n",
    "            ebike_used = self.ebike_trips * False\n",
    "\n",
    "        if not sell_car:\n",
    "            if buy_new_car:\n",
    "                new_car_used = trips.astype(bool)\n",
    "                old_car_used = trips.astype(bool) * False\n",
    "                trips = trips.astype(bool) * False\n",
    "            else:\n",
    "                new_car_used = trips.astype(bool) * False\n",
    "                old_car_used = trips.astype(bool) * self.has_car.reshape((-1, 1))\n",
    "                trips[old_car_used] = 0\n",
    "\n",
    "        else:\n",
    "            old_car_used = trips.astype(bool) * False\n",
    "            new_car_used = trips.astype(bool) * False\n",
    "\n",
    "        ov = trips.astype(bool) * self.ov_trips\n",
    "        trips[ov] = 0\n",
    "        mobility = trips.astype(bool)  # All remaining\n",
    "\n",
    "        return ModelResult(\n",
    "            bike_used,\n",
    "            ebike_used.sum(axis=1) > 0,\n",
    "            ebike_used,\n",
    "            new_car_used.sum(axis=1) > 0,\n",
    "            new_car_used,\n",
    "            self.has_car * (True if (sell_car or buy_new_car) else False),\n",
    "            old_car_used, \n",
    "            ov,\n",
    "            mobility\n",
    "        )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "te = TransportEvaluator(costs, system_setup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False], dtype=bool)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([True, False]) * ~np.array([False, True])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11063, 16451)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system_setup.bikes.sum(), system_setup.ebikes.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10000, 5), (10000, 5))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system_setup.ebikes.shape, system_setup.trips.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's investigate how much the different options cost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jyKG0wrWriAyMpzf5YcihtMKQoyFWxUinWGSkQQw5lFbYXKUhXklIp3ia0yCGHEorMn/9\niAyP+ZsGMeRQmmHI0QwDIxHpHEMOpRX2ydEQb5dJp5i/aRBDDqUV9skhMj7mbxrEkENphZUcDTEw\nkk7xq0mDGHKIKDq8TSa94leT/DDkUFphcxURUfpgyCEiImPgPYx2DFIVY8ihtMI+OUTGxxZVGsSQ\nQ0TRYZMf6Ry/ohowyGfIkENE6vB2mXSKX00axJBDacYgtydEFBQrObEzykfIkENphT9+GuKHSTrF\nSg4NYsihtMKOxxrilYTIsIxydjPkUFphyCEyPhYZaRBDDqUX/vhph1cS0hujlB9IMww5lFZYySEi\nSh8MOZRWZEVO9iEQEemfQapiDDmUZljJiRk7HBNRimDIobQisx8JkXHx9NaOQT5LhhxKK2yuIjI+\nFhtpUFa8diyKItasWYPW1lZ4PB4sW7YM06ZNw+rVq5GRkYFrrrkGZWVlMJlM2LFjB7Zv346srCws\nW7YMt956K1wuF5544gnYbDZYLBZs3LgR48ePx+HDh7FhwwZkZmaipKQEy5cvBwCUl5fj448/RmZm\nJtasWYPCwsJ4vTVKYQoYcoiMjgVbGhS3kPPWW29h/PjxePbZZ9HX14fvfOc7mDlzJlauXInZs2ej\nrKwMe/bswaxZs7Blyxbs3r0bbrcbpaWlmDt3LrZu3YoZM2Zg+fLlePfdd7F582asXbsWZWVlKC8v\nR35+PpYuXYra2lrIsoyDBw9i586daGtrw4oVK7Br1654vTVKMYrPLx4rORrgFYR0jpUcGhS3kLNw\n4ULcddddAABZlpGVlYVjx45h9uzZAIAFCxZg3759yMjIQFFREcxmM8xmMwoKClBXV4eqqio8+uij\nAID58+fjhRdegCAIEEUR+fn5AIB58+ahsrIS2dnZKCkpAQBMnjwZkiShp6cH48aNi9fboxTiG2wk\nWUrikRgEryBElCLi1ifnoosugsVigSAI+NGPfoQf//jHkOULFxuLxQK73Q5BEJCTkzNsuyAIEAQB\nFotl2GMdDgesVmvE+yAC/EIOKzlEhsdiIw2Ka8fjtrY2fP/738c999yDb33rW8jIuPBygiAgNzcX\nVqsVDodjaLvD4UBOTs6w7Q6HA7m5ubBYLMMeG24fRAAgKReqN7LCSk7MeAUhnWOxMXZGOcvjFnK6\nurrwyCOP4IknnsB9990HAJg5cyYOHDgAAKioqEBxcTEKCwtx6NAheDwe2O121NfXY/r06SgqKkJF\nRcWwx1qtVpjNZjQ3N0NRFOzbtw/FxcUoKirC3r17oSgKWltbIcsy8vLy4vXWKMX4hhyJISdmRvnx\nI+NiDqdBceuT8+KLL8Jut+P555/H888/DwBYu3Ytnn76aYiiiGnTpmHhwoUwmUx46KGHsGTJEsiy\njJUrVyI7OxulpaVYtWoVlixZguzsbGzatAkAsG7dOjz++OOQJAnz5s0bGkVVXFyMxYsXQ5ZllJWV\nxettUQry7YfDPjlExsdKjhaMkRRNisLMS8ZmG7Dh3z59GgBw59SF+PrUO5J8RKmtYccOdOzbhyyr\nFcVPP53swyEa8pcdqyDLXlw58zZMn/WtZB9OSjtnH8B/7a8DAKy986YkH416nAyQDI/NVRobvC/i\n/RHpFL+asTNK/YMhhwxPkr0B/5vUUSQGRdI3NlfFzhgRhyGH0oBX8fr8Ny/QsVJkDsMnfTNIESKp\njPIZMuSQ4Q3veMxKTqxYySG9YyUndmyuIkoRvv1wWMmJHSs5RMZnjIjDkENpwMs+OZpiyCG9M0gR\nIqlYySFKERxdpTGGHNIrNlORH4YcMjx5WJ8cXqBjxT45pFvGKD6QhhhyyPB8F+Xk2lWxG2quYu9O\n0il+NWkQQw4Znjws5LCSE6uhkGOQNnsyHn41aRBDDhmeAp+Qw3p27HgFIZ1jJYcGMeSQ4clsrtKU\nwmUdiChFMOSQ4cm+F2Nel2P3ZXMVh5KTXjF/0yCGHDI8xSfZKEw5MTPK/BlkXGyuip3JIB8iQw4Z\nnsKOx9r6MuQw7JBe8atJgxhyyPB8L8as5MRu6BPklYR0yiBFCNIAQw4Znm+wYSVHA4N9chhyiEjn\nGHLI8HyDDS/MGhj8DNnxmHSKpzkNChtyTp48OWLb4cOH43IwRPHgO7qKlZzYMSiSbrGZSjNGOc+z\ngv3h0KFDkGUZTz75JH7+859DURSYTCZ4vV6UlZXhz3/+cyKPk0g138kAff+bVOIQctIrY1yXdcEo\nH2XQkFNZWYmDBw+io6MDv/rVry48ISsL999/f0IOjkgLwycDNMqpmzycDJD0jh2PNWCQ0ztoyPnn\nf/5nAMAbb7yBe+65J2EHRKQ1rl2lrWGj1b6s8BKRsRgk44Tvk3PllVfit7/9LTweDx555BHMmTMH\nf/rTnxJxbESakHyWcuCyDhrwbaZikxXpEIuMsTPKdBthQ87Pf/5zXH/99XjvvfcwatQo7N69G7/5\nzW8ScWxEmvCt3kgMOTHzr+QQ6Q2LixowyKkdNuTIsoybb74ZH330Ee666y5cdtllkHn3RilEli8E\nG4nf3dixkkM6x+wdO6N8hGFDzpgxY/Dyyy/jk08+wa233opXXnkFFoslEcdGpAmJlRxNsZJDesdK\nTuyMcmaHDTm/+MUvMDAwgP/8z/9EXl4eurq6sGnTpkQcG5Em2CdHW75DxxlyiAzKIOd20NFVgyZN\nmoQbb7wRf/7zn/Huu+9izpw5mDRpUiKOjUgTw/vksHklZr4/fmyuIh0yyPU5qYzyEYat5Lz00kso\nLy/HZZddhilTpuDFF1/E5s2bE3FsRJrwreRIsjeJR2IQbK4inWNzFQ0KW8l58803sXPnTowePRoA\nsHjxYtx7771YtmxZ3A+OSAuS7NtcxcpDrBR2PCadY/aOnVE+w7CVHEVRMGrUqKF/jxo1CmazOa4H\nRaQlSblQvVGgMOjEiB2PSe9YyYmdUebJCVvJmTNnDlasWIH77rsPiqLgjTfewC233JKIYyPShFce\n3tlYkiVkZIbN9xSMb/WGIYd0iF/L2MkG+QzDhpw1a9Zg69ateOONN6AoCubMmYPFixcn4tiINOHf\nD8ereGEGq5FqDRtdJXG0GukPKzmxM0qVNmzIcTqdUBQFv/rVr9De3o5t27ZBFEVkZYV9KpEu+M+N\nw87HseEQciLjM8pixmFr9o8//jg6OzsBAFarFYqi4F/+5V/ifmBEWvH6V3JkVh9i4tsnh5Uc0iGD\nXJ+TymuQ9qqwIaelpQU/+clPAJwPOT/5yU9w+vTpuB8YkVb8Q45vR2SKjqIow4KNwtFVpCNG6Syr\nB1K6hJyMjAwcP3586N/19fVRja46cuQIHnzwQQDAsWPHsGDBAjz44IN48MEH8cc//hEAsGPHDnz3\nu9/F4sWL8dFHHwEAXC4XVqxYgQceeABLly6FzWYDABw+fBjf+973UFpaivLy8qHXKS8vx6JFi3D/\n/fejuro64uMj4/NvrvIPPRQ5/1DDSk7sOhpt6GzqSfZhGIIJ7IyjFa/kM4lqCgeesB1rVq1ahR/8\n4AeYOHEiAMBms+HZZ5+NaOcvvfQS3nzzzaG1rmpqavDwww/j4YcfHnpMZ2cntmzZgt27d8PtdqO0\ntBRz587F1q1bMWPGDCxfvhzvvvsuNm/ejLVr16KsrAzl5eXIz8/H0qVLUVtbC1mWcfDgQezcuRNt\nbW1YsWIFdu3apebz0A2PKGHN5kO47auT8c2SK5J9OClN8h9dxSHkqvmHGoac2FVuPQIAuGfNbUk+\nktR3oZKTuhdlvRB9bmhESUZmRmYSj0a9sCFn7ty5+PDDD1FXVwez2Ywrr7xy2Lw5oRQUFKC8vHyo\nD88XX3yBpqYm7NmzBwUFBVizZg2qq6tRVFQEs9kMs9mMgoIC1NXVoaqqCo8++igAYP78+XjhhRcg\nCAJEUUR+fj4AYN68eaisrER2djZKSkoAAJMnT4YkSejp6cG4ceNUfSh6cLbTidYuJ157r54hJ0b+\nzVPseKweQw7pmQkmKGAzqhY80vCQM9qcmiEnoslCsrOzceONN+Laa6+NOOAAwJ133onMzAsfzKxZ\ns7Bq1Sq8+uqryM/PR3l5ORwOB3JycoYeY7FYIAgCBEEYqgBZLBbY7XY4HA5YrdZhj7Xb7RAEIeA+\nUhp7zmmGzVXaYcihVCBJYrIPIeWJfiEnVSV0RrQ77rgD11133dB/19bWwmq1wuFwDD1mMPT4bnc4\nHMjNzYXFYhn2WEEQkJubG3QfKY0TPWjGv7mKMx6rx5BDqUDmjUzMPN4Lv5PuFD7PExpyfvjDHw51\nCq6srMQNN9yAwsJCHDp0CB6PB3a7HfX19Zg+fTqKiopQUVEBAKioqEBxcTGsVivMZjOam5uhKAr2\n7duH4uJiFBUVYe/evVAUBa2trZBlGXl5eYl8a6RjkiKje18Puvf1fPnv1D1hk21EyGGzAOnJl/eG\nMis5MRN9zvVUruQE7ZPz05/+NOQTn3nmmYhfxPRlVWLdunVYt24dsrKyMGHCBKxfvx4WiwUPPfQQ\nlixZAlmWsXLlSmRnZ6O0tBSrVq3CkiVLkJ2djU2bNg3t4/HHH4ckSZg3bx4KCwsBAMXFxVi8eDFk\nWUZZWVnEx0bGJysSHPVOAMDFJeNYyYkBR1eRrn3Zyi9LrOTEyrdPjm9VJ9UEDTmzZ8+GyWQKOKOp\nKYqmlClTpmDbtm0AgGuvvRZbt24d8ZhFixZh0aJFw7aNHj0azz333IjHzpo1C9u3bx+xffny5Vi+\nfHnEx0Xpw380FUOOemyuolTA5qrY+QYbQ1Zy7rvvvqH/7unpwcDAABRFgSzLOHv2bEIOLq2x47Fm\nZIV9crQyopLD5irSIZmzmsds2BDyFD7Pww4h37RpE15//XV4vV7k5eXh3LlzmDNnDr72ta8l4vjS\nVgrPvaQ7/tVIhhz1GHJIzwbnyVEYcmLmTZfRVe+88w4++ugj3H333diyZQt+97vfYcqUKYk4trTm\n9vAk1Yp/qPGv7FDk2CeH9Gzw+8mQEzvf6o03hW9mwoacSy+9FDk5OZg+fTpqa2sxZ84cnDp1KhHH\nltZcDDmakBV5xHo2rOSox9FV2uIq7to5/1kqPv9NsfBdysErpe7nGba5ymq14o033sB1112HV199\nFRMmTEB3d3ciji2tOVzsOKeFQIHGy0qOen4XD4ac2Ejihc9PlmVkZCR0Vg9DUXzOdYU3MjHzba4y\ndCVnw4YNsNlsmDNnDqZMmYKysjL8+Mc/TsSxpTXBeWGeB96VqOc/ESDATomx4OgqbUmi5PPfqXsh\n0QOGHG15fSo5qbxAZ9iQU1lZiUceeQQAsHr1arz55pvo7e2N+4GlO9+Qw6qOeoEm/uNkgOqxuUpb\nXp+Q42UTdUwYcrTlG3JSuZITtLnqd7/7HQRBwLZt29DS0jK03ev14q233sIDDzyQkANMV/aBCyFH\ncIqwjjEn8WhSV6DFOLl2lXrseKwtyeNbyeFnGQvf7yZDTmwURYGsGLySc8UVV0BRlBFNJaNGjcK/\n/du/xf3A0p1vJcf3vyk6gfrfsJKjHpurtMVKjnaGVXJSuPKgB7LfdV9K4S4TQSs5t99+O26//Xb8\nzd/8DfLz89HY2AhJknDNNdfAbGZVId6EAW/A/6bosJKjLTZXacu3ksOQExvfkMNpImLj9avcpHIl\nJ+zoKqfTiYULF2Ls2LFQFAVdXV0oLy/HTTfdlIjjS1tOn344TvbJUS1QoAkUfCgyMis5mvL6TJ0v\np/D6QHrgOzcO58mJjX+oMXTIefrpp/HLX/4Ss2bNAgAcPnwYP//5z7Fr1664H1w6G3D7hBw3L8pq\nBQo5IkOOamyu0pbsM6LKyz45MfEdNckRlLHxDzWp3PE47Ogqp9M5FHAA4KabboLb7Y7rQRHgcl84\nSTn7sXpeJUAlJ8A2igxDjrYkr8+FmZWcmLCSox3/RY1TuZITNuSMHTsW77///tC///KXvyAvLy+u\nB0WA2+euzs35M1QLVMlhnxz1GHK0JfkEGymF1wfSA3lYyOFnGQsjNVcFDTl/+MMfAADr16/Hiy++\niFtuuQU333wzXnzxRaxbty5hB5iuRJ8fPw/L2Kox5GiLIUdbvtUbmTczMVGGNVfxHI/FiI7HRhxd\n9corr+C9+wIaAAAgAElEQVTee+/FlVdeiV27dsHhcEBRFFit1kQeX1pSFGXYWiEiy9iqeeWRw+/Z\nJ0c9/1Dj3xGZouNbvWElJza+I6oURYaiKDCZTEk8otRlpD45YTseD7JYLPE8DvLhH2pSeXG0ZAsU\naDi6Sj2OrtLWsLWreDMTE/9+OIoiw2TKTNLRpDZJNk6fnKAh59SpU7j99tsD/s1kMmHPnj1xO6h0\n5x9yWMlRj81V2mJzlbZ8gw1HV8VmxGzcsgxkMOSoYaQ+OUFDTkFBAX7zm99wccgk8PiFGvbJUS9Q\n1UYM0IRFkRkRcrwMjLHwHV3FBTpj47+UA5d2UM+/D44hQ47ZbMbll1+eyGOhL3n8fuz8Qw9FLlCg\nYSVHPfbJ0ZbX51zn2lWxkUeEHH6eao2s5KTuNSjo6KqioqJEHgf5cPv92PnOmUPRYXOVtvwrN2yu\nig0X6NSO4ndec0JA9UaEnBRu0Qkacp566qlEHgf58A81Lk4GqFqgSg6bq9Rjx2NtDVugk81VMZED\n9ckhVfwnA/QfUp5Kwk4GSIk34LeMA0OOeoFDjicJR2IM7JOjLd/qDSs5sZElv0qOxJsZtfxH9KZy\nnxyGHB0a8Kvk+IceipwY4IfOwx8/1fxDjf/dM0Vn2IzHDDkxkaXhNy8Sz3PVRL/zWlYUyCnaZMWQ\no0P+lRv/0EORC9zxmD9+anEIubaGzZPDyQBjInn9Qw4rtmoFmpvNm6LfT4YcHfJfkJMLdKoXqGlK\nUiRI7JSoyog+OWyuiolvsJG8qXmnrBde0e33b1eSjiT1iQFuXkSGHNKK/+gqSVY45btKgZqrAHY+\nVouVHG35hhyF53hMvOKA378ZctQKFGg8Kfr9ZMjRIf95cgDOlaOWJ0jJWmQpWxWGHG0pPh065RTu\n3KkHol+o8XoYctRyM+RQPAWa4ThQ8KHwPEFGUnlYyVFlxGSAbK6KiW/HY/bJiY3XM7ySI4rOJB1J\n6nN7R16D/FsYUgVDjg65AwSaVP2CJVuwik2wCg+FFnB9IFLNd+0qidXamIj+zVV+oYci5w7wXXQF\nCD6pgCFHhwLNi8MRVuoEq9hwrhx12FylLQ4h187ISg6bq9QarOS0fLoHLZ/uGbYt1TDk6JDTNbIJ\nwDnA5hU1glVygnVIptBGVG5YyVFN8srD+uRIoswFkWPg39GYfXLUc30ZuHsbatHbUHt+G0MOacXu\nHHkBFgbY90ENN5urNDUYcj7u68PHfX28KMdADHAzI3LiT9W83uFDyCW/f1PkAvbJYcghrdgdIy/A\n/QG2UXjBJv4L1iGZwvgy5JxwuXDC5WKfnBiIrgBLjgQIPhQZ/2UcOOOxeoECTaqO8GXI0aE+x8iT\nM9A2Ck2SJUhK4LsPznqszojKDSs5qgWs5DDkqOYfarh2lTqKogQcLs7mKtKE1ysH7JMTqLpDoYUK\nMmyuUskv1LC5Sr1ATVMi+96ppvjNYu7/b4pMsJmNOeNxEEeOHMGDDz4IADh9+jRKS0vxwAMP4F//\n9V+HfiB37NiB7373u1i8eDE++ugjAIDL5cKKFSvwwAMPYOnSpbDZbACAw4cP43vf+x5KS0tRXl4+\n9Drl5eVYtGgR7r//flRXV8f7bcWNPciPXKB+OhRaqCDDkKPOiFDD5irVAlVtPOyTo4qijPweygG2\nUXjBJv1jyAngpZdews9+9jOI4vkL9DPPPIOVK1fitddeg6Io2LNnDzo7O7FlyxZs27YNL7/8MjZt\n2gSPx4OtW7dixowZeO2113DPPfdg8+bNAICysjJs2rQJW7duRXV1NWpra1FTU4ODBw9i586d+OUv\nf4n169fH823FlSNIB2N2PI5eqAn/uKyDSgFCDas56ngDTBUhcZ06dQJ9Bfm9VIWVnCgUFBSgvLx8\n6Efw2LFjmD17NgBgwYIFqKysxNGjR1FUVASz2Qyr1YqCggLU1dWhqqoKCxYsAADMnz8f+/fvhyAI\nEEUR+fn5AIB58+ahsrISVVVVKCkpAQBMnjwZkiShp6cnnm8tbhxBKjnBtlNwrORoL2CgYTVHFW+A\neXECBR+iRPIGWV7Em6LneVxDzp133onMzMyhf/v+QFosFtjtdgiCgJycnGHbBUGAIAiwWCzDHutw\nOGC1WiPeRyoK1B8HAJycDDBqDDnaCzSaipUcdQJN/sdZj9VRApZySI1gYUaUUvMzzkrki2VkXMhU\ngiAgNzcXVqsVDodjaLvD4UBOTs6w7Q6HA7m5ubBYLMMeO7gPs9kccB+pyHdmY+lcJQAgc+LcoOGH\ngvNIwefJCPU3Ci7QDMeKJAFZCf0pMQT5y4tGVcv587zo8rlcv4qSzhvkOyixkhPezJkzceDAAQBA\nRUUFiouLUVhYiEOHDsHj8cBut6O+vh7Tp09HUVERKioqhj3WarXCbDajubkZiqJg3759KC4uRlFR\nEfbu3QtFUdDa2gpZlpGXl5fIt6aZAZ+Oh7K9HrK9HgDgYofEqLml4DOeuhlyVAkacihqg4HmTG89\nzvSeP89lVnIoyaSgzVWs5ARlMpkAAKtXr8aTTz4JURQxbdo0LFy4ECaTCQ899BCWLFkCWZaxcuVK\nZGdno7S0FKtWrcKSJUuQnZ2NTZs2AQDWrVuHxx9/HJIkYd68eSgsLAQAFBcXY/HixZBlGWVlZYl4\nW3ERbI0qtyhDlhVkZJgSfESpy+UNHnJcIQIQBacEWHWcK5GrIwco/8speiFJugBNpmzCUsdofXLi\nHnKmTJmCbdu2AQCmTp2KLVu2jHjMokWLsGjRomHbRo8ejeeee27EY2fNmoXt27eP2L58+XIsX75c\no6NOnkCLc/r+7aLRbBaIVKhqTagARMEFCjSBgg+FF7B/E0OOKoH6hQUaVk7hBQszwSo8esfJAHUm\nVMhxc+RFVAa8A0H/5grxNwpOFkeO8gu0jcILWMlJ0c6dyRYw0LBDvCrBKjkcQk6aCFfJociFCjlO\nkSEnWrIkBbxwMOSoE6iTMTseqxMo5LCSo06wMJOqzVUMOToTqoPxAENOVAZEZ/C/eZ0c+hwl2R24\n+U/2cDi+GoE6GXMIuToBQ06KXpSTLVjIkZXUbLJiyNGZYB2PAY6wipbTGzzkKFA4wipKUpAwE2w7\nhRYo0HB0lTqB1qmSuXaVKqGapTwpOJKSIUdnBkJVcjghYFQcoiPk351h/k7DBa3kBNlOoQWc8TjA\nNgovUKCRZd4UquEOsdq4JwVDOEOOzjhCTPrHpR2i4wzRXBXJ32k4KUiYCbadQgs44zFDjioMOdoJ\ntkAnEDoA6RVDjs4IIVYb5yKd0QlXqXF4WcmJBkOOtrwBKrNcu0odWRr5u8lJKtUJFWQYcigmiqKg\n3xE85PQ72PchUrIih+yTAwAOD0NONCRX4LmFgm2n0ETPyJsWkf3uVAlUtZFkVr7VcIWoJroYcigW\nDpc3ZO/1PoEhJ1KhRlYNcoipuYhrsjDkaEt0BajkMOSoInkD/DYqCmSJn2e0QgUZVnIoJr320CEm\n3N/pAiGCTsXhOibTcGyu0o6iKPAGquQECD4U3mDI+bS6B59W91zYLvE3M1ouMcTglxTsM8aQoyM9\n9tAXi3B/pwsiqdIw5ERHGgg8gWKw7RSc1yMh0NJKsiRzrhwVBkNOY4sTjS0Xqrhekb+Z0QoVZEI1\nZekVQ46O9PSHPiFtYf5OF0QSYNhcFR02V2knVLMUm6yiJ3mDVBkDNWNRUIqihAwyAyGqPHrFkKMj\nPWGao4QBLzwpmKSTweGJoJITwWPogmAVGy8rOVETQ8x5xRFW0fMGCTnBtlNgoiRDCjETPCs5FJNI\nKjW97HwcESGCKk0kj6ELgoUZNldFL1B/nEEcYRU9KUizVLAKDwUWrs+Nk5UcikVvBH1uwjVp0XmC\nxx72MXZWcqISLOSwkhO9QHPkXPhb6l1Iks3rDdxk6hXZlBqNcCEmFddPZMjRkUgqOeGatOi8SAKM\nW3JBDDCJGAUmOQMPy/c62IE7WoHmyBnE5qroBetgHKzCQ4E5Q3wvAVZyKEaRhJzuPt6ZREIQw1dy\nonkcAd4gIUf2eCBzdtmohKrksLkqesGapdgnJzqOMCHHkYLfTYYcnZAkOaL+NhxhFRl7BM1VACCw\nySpiwUIOELzKQ4GFCjJiiPXrKLBgzVJsropOuBAjyjI8KTYhIEOOTtjsHoTo1D6kq48hJxJ2d39k\nj/NE9rh0pyhKyL43oQIQjeQJsUadhyEnaqInWMhhf7FoODzhm++FMNUevWHI0YmunshOxs4IH5fO\nPJIbHjmyvkuRVnzSnex2A3LwSerY+Tg6bmfw76eba9RFTQyyjIvo4fcyGnZ3BCHHlVr9GBlydKLd\nFtnJeM42ACWSkk8ai2bUFEdYRSZciOEw8ui4QoykDPU3Ckx0Bwk5QbZTYPYIAkwkQUhPGHJ0oqUz\nspNxwC1xDaswommCEthcFZFwIYaVnOg4Q/Stc/azH0k0FEWBxx34ZiXYdgqsP4KQ0+9KresPQ45O\nnGmP/GQ8c44nbijRdCZmJScy4RbhlLlIZ8QURYEzRLOzo4fV2mhIXjcUOXBnWI+L53ekZEWB3R0+\nwPSxuYqipSgKGloj7xvS0MJ+JKFEM5Mxh5BHJtz6VFy/KnIuwRNyEU6vWwrZMZmGcw8EP4fdLp7f\nkRLcIuQIsnXfACs5FKXWLiecUYyoONHcF8ejSX3BZjsOdHccyczIFL6SE+7vdIG9K/zkifZu9iWJ\nlNsVvMnZKw5AllJrNFCy9IToDD/scQOpda4z5OjA8abeqB5fd6YPkhT8TjDd+QcXT7cHXkGCJMho\nfq0Vnu4LJzNHV0VG9oT+AZTC/J0uECIIMJE8hs4L1yTFak5keiMML70DnpRqTmXI0YEvGnqierzL\nLaExiuatdOPfz+bcn7qAL89Jsdd7/t9fcktuLu0QAfbJ0U4kVZpIqj10XrgQw87HkbE5IzuHJVlJ\nqRFWDDlJJstK1CEHAI7WR/+cdOE7YsrrkCD2Di9Xi71eeB0XOiqymhMem6u0E0mAEWys5EQqXIjx\nsJITEZsj8nO4O4rHJhtDTpI1tNrhGIi+zfjIKVscjsYY+n1CjiIFLqv6buesx+Gx47F2ImmKsncx\n5ERKDBdy3KyKRaI7wkoOAHQ7Uud8Z8hJssMnulU972RzH4SB1CkZJoqiKOhzR9cxO9rHp6NwzVGs\n5ERGdHvhimCNOmefC5KYWmsEJUu4EMPmqvBkWYmqOtPFSg5F6vMTXeEfFICiANUnWc3x5xQdkJTo\nLg4MOeGFnfGYa1dFJJoOxQKXcIlIuFmNRTc/x3B6BtyQo+hM3CWwkkMRsPW70diq/i7jszp1AcnI\netzR91XqVfGcdON1hL5b5gKdkYlmaDg7H0fG4wn9OYlh/k5AZ5ShJdrHJxNDThJ9djy2kPL5iW54\nQ0wqlo5sA9FXt2wD6poM00m4ECMKbBKIRDTBxd7Ji3MkRFe45ip+juF02KOrdjlFL4QUGWHFkJNE\nh2o7Y3q+yy2hppFVCF82V/SBpVvFc9KN2B+6c7bs8XCunAj0RxFc+tn5OKxQ61YNEhlywupQUZlR\n85xkYMhJEsEpoqYxukkAAzlYyyYrX13O6INj90AXZIUVsWAURYEnTMgBwgchAvo7Iq94RfPYdOUV\nXVDCnLucDDC89v7o+y2d60+NEM6QkyRVJ7ohR7JQSJjOYIdqOyPbT5rocHZE/Ryv7EWvK/bAaVTS\nwAAUb/hpDjx97MAdisclYiDE6uP+HD0D8Hq4JEEo7oHw3zn3AMN3KAOiF30qVhZvj7KJK1kYcpLk\n4LHQFQfF1Q2IAuAVINa/fv7fAfQ7RJw4w4sLcL7i0OE8p+q5ap+XDtw9kTWJenoZFEPpa4++MtPX\nwaaWUFwRhBzJ64ZXTI2mlWRo61NXkWlV+bxEy0rGi957772wWq0AgPz8fDz22GNYvXo1MjIycM01\n16CsrAwmkwk7duzA9u3bkZWVhWXLluHWW2+Fy+XCE088AZvNBovFgo0bN2L8+PE4fPgwNmzYgMzM\nTJSUlGD58uXJeGsRGXB7ceRk6H4g3pb3MLQWgacX3pb3YJ62JOBjPz3WiWun5ml8lKnH7unHgFfd\n3cU5RzuuvXimxkdkDJ4IQ06kYShd9bZH32zS22bHxVPGxuFojMHliCxYu5y9sI6dFOejSU2tYZqd\ngq1T1TvggdPjxUXZSYkREUt4Jcf95aRhW7ZswZYtW7BhwwY888wzWLlyJV577TUoioI9e/ags7MT\nW7ZswbZt2/Dyyy9j06ZN8Hg82Lp1K2bMmIHXXnsN99xzDzZv3gwAKCsrw6ZNm7B161ZUV1ejtrY2\n0W8tYp/XdcMbZCZeAFC8TsDjd/J6es9vD+DTmg42WQFoc7Spfm57DM81uogrOQw5IfW0Rt9souY5\n6WTAEdmgAafAwQXBtPQGvq4M2DogOuzwOvpRu2MzBmwjuwK09Om/0pjwkHP8+HEMDAzgBz/4Ab7/\n/e/j8OHDOHbsGGbPng0AWLBgASorK3H06FEUFRXBbDbDarWioKAAdXV1qKqqwoIFCwAA8+fPx/79\n+yEIAkRRRH5+PgBg3rx5qKysTPRbi9i+6jBNI3KQdvgg23vtHhw/zaaCdkF9UIklIBldpCHHbePk\nlMEoigLb2eiblW0tbIoOxWmPbOCFU+AAjUAURcHZ3sBBpen93wNfdup299nQ9P7uEY8J9lw9SXid\nacyYMfjBD36ARYsWoampCT/84Q+H/d1iscBut0MQBOTk5AzbLggCBEGAxWIZ9liHwzHU/DW4vbm5\nOTFvKEp9gidsU5UaFYfbcd2V4zTfbyqJJah0OM7BK3uRlaHv0msyeCIML2yuCs7Z54poOYcRz+t1\nYcDuxpicUXE4qtQn9Ec20MDRF/2AhHTQ7XDD5R05Q7zoFODuG37eu/u6IToFmC+6cK1NhZCT8ErO\n1KlT8bd/+7dD/52Xl4fu7gsXfUEQkJubC6vVCofPLKsOhwM5OTnDtjscDuTm5sJisQx77OA+9Kji\ncDvi0bL06RcdcLrSeyRGq9Ci+rmSIqFTxcisdBBNJSdY+3266zqjvtLaHcNzjUyRZTjskZ2zQj8H\nFgRypidwZ3hZCnwt8d/e0ueEV9L39BsJDzm7d+/Gxo0bAQDnzp2Dw+FASUkJDhw4AACoqKhAcXEx\nCgsLcejQIXg8HtjtdtTX12P69OkoKipCRUXFsMdarVaYzWY0NzdDURTs27cPxcXFiX5rYcmygj0H\n1V+IQ3GLMv56pD0u+04FoiSiwxHbD1ksIcnI3N2RVR5ltxtSmDWu0lVnDJN2djSxQhaIU+iCIke2\nTp3Q18YAHsDpICEnUpKs6H6UVcJr83/3d3+Hn/70p3jggQcAAM888wzy8vLw5JNPQhRFTJs2DQsX\nLoTJZMJDDz2EJUuWQJZlrFy5EtnZ2SgtLcWqVauwZMkSZGdnY9OmTQCAdevW4fHHH4ckSZg3bx4K\nCwsT/dbCqqrrQkdP/IYy/mn/Wdwx+3JkZJji9hp61e5og4LYfsRa7C346qTZGh2RMciiCNEe+agg\nt82GrIsuiuMRpR5FUdDRqL6/UkfD+QqZyZR+53Uo9t7Im6e9ogsuZy/GWNK7Sd+Xoig4bYt9wsmm\nHgFXjLeGf2CSJDzkZGVl4dlnnx2xfcuWLSO2LVq0CIsWLRq2bfTo0XjuuedGPHbWrFnYvn27dgeq\nMUVR8Pa+M3F9jXO2AXx2vAuzr7s0rq+jRy0aVGFahLMaHImxhGqqCnRn7LbZYJkyJZ6HlHJ62+3w\nONWv8+Oyu9Hf6cDYCfq9kCSDvbc16scz5FzQ5XDDocFkk6dtdmCafofnczLABKlt6sWJM/EfDvqH\nj5vSsix71h57R/MW+1ku7+An0IipLlGEIEmwyzL++9w5dIliyMenu7YTsY/s0WIfRtPfE92Njb0n\nulBkdE02bZa7ONvrhKjjfjkMOQmgKAq2v9+QkNdqahPCzqZsRGf7Yw85ohx7vx6jCRRa3rTZMPiT\n1iNJeNOn2hNp/510oSgKWmvDd44Nd2MSyT7SjT3KkNPfyz53vhq7tQk5sqIE7cCsBww5CfBpTSdO\nNiduUq/X/1wPjxhZhzwj8EgezSbza9agImQkrq7hFQSHJKFHGv7d6vF64fhym4shZ5i+dgGCLXhn\n7N6Bbjg9ApyigDePvY7egSDLt3Q60McFO4d4XALcruh+U6MNRUYmydr0xxmkVWCKB4acOHMMiPif\nP55M6Gt29LjwvxWnE/qayXTW3hxzp+NBZ/rT53OLhNsv5HiDVBwGt/uHonTXdDh0E0lF43tD3127\nuxd/bXwv6GNPh9lXOom2Pw4ADDhsXMPqS619Dng0bGJqYMhJX6+8exK99ugnAYvV/1acRkNLekwJ\nf7qvScN9NWq2LyOINrS4u7uhyPptn08kj1NE89Hg0zoMiE7Y3cPnwOl392JADDwk93R1O8Q0nwtr\nkJqQE8vzjKZe41DSKbhgd6nvXB9PDDlxVPF5G/YeSU4fD1kBnttRA8eAPr94Wjrd36TZvs45z8EZ\n5CKTbhRZxsC56L6/itfLzsdfavjsLCRv8MAnBVmmJeh2j4TGKja5ANENHx/+vPSdS8xXQ5f2N8D1\n3fq8qWbIiZOmNjtefutEUo+hs8eFzbtrDb14p6zIaOjVtlN3U19iOonrndtmg+KNvnIw0M4Liccp\n4tSn2vfvOrn/DDw6vWNOpFAVmVCduO3sfIx+lwdt/dpP2nmyQ5/rrDHkxEGP3Y1nX62GGOIuLlGq\n6roTNrIrGVrsZ+GWtG1nP9VzStP9pSpnm7q7ZbXPM5LaikZ4Pdp3/hfdXtTtbdJ8v6lE8ooQ+kYG\naVufB44BCY4BGTvfa4Wtb2Q3gWiHnRvRiY74VFzqu+3wBFgHK9kYcjTm8kj4xavV6ElCP5xg3tp7\nBh9+Zsy26FM92nfqPtWb2I7ieuVQucit42x6T6rY09qPxs/jdzFtONiC3nP67egZb/a+VigB5rPa\n80kXBos4fYIXez4Z2Z/M3tMSdF2mdHH8XHzWQpNkBafi0AwWK4YcDUmSjPKdNWhsi31o3vXXX4/1\n69dj/fr1uP7662Pe38tv1sVl9fNkO9FTp/k+zzna0eviooiqQ86Z+M7srWeSKKHq7VpoNNgvIEVR\nUPVWbcj+PkbW29U0YpvTJaFPGB5e+gQvnK7hlQVFkdHfk74hvMfpjnm9qlCOtOivPx5DjkYURcEr\n755EVZ02QWLx4sWYOXMmZs6cicWLF8e8P1kB/mPbF2hqM84doMvrQlOcRkOdsB2Py35ThSLLEJqa\nVD3XbbPB06+/O7pEOPr+Kdi74t9xvb/DgZoP6uP+Onpk6xj5viUpcKoMtD3Q89NFdWt8Q0hDtx39\nLv20YgAMOZp5e+8ZvH9Q301CblHGv22pRlevMeaKONVzIqJlGNRUxY6necgZaG+H16n+Yt1/Kv36\nNZ0+0oamzxP3G9Bw6Cyav0ivTt6yLKEnxpDS3Z7cASHJ4pVkVDXHv5p/6Iy+5spiyNHApzUd2PoX\nbTv3bt++HbW1taitrdV04dE+wYP/92o1nAaYb+NY97GIHqemKnbCVgdRSt9RLLGGlHQLOV1nenH4\nj9o3nYbz+TvHYTurz1Et8dDTUR/zhH49nQ3wuNNvmojqNhucYvx/96uau+DWUQdkhpwY1bf044Vd\nkV1so1FTU4OnnnoKTz31FGpqajTd99kOB/5zZ01KDy2XFRnHIww5aoiyBw296VvW7j0eWyWrt7Y2\nbRaK7e904JOd1VCScD7JkoL9O6ohdKfHRfvc2aMx70NRZHS2avubqneyrOCTxsSsf+aWZFQ166ea\nw5ATgx67G5teOwoxSHuwnh05acO2v6TuRfxM/2k4REdEj1VbFTvW/YXaw0tpktuNvrrYqhIemw0D\naTCUfMDuxv7tR+B1J+/OVXR5UbntCFyCO2nHkAiy5EXbmc812Vdb02ea7CdVVLfZ0DOQuL4ylU0d\nuqnmMOSoJMsKnt91DL2CvjpZRePtfc347Lh+Enc0jnVFHkDUVsVqumoi6vNjNH0nTqiaBNBfzxfG\nDomi24v9245goD/54cLZ58L+7dVxmZtHLzpaauD1aDOJXfe5kxgQ9DcSKB4kWcZf6xPbd8slSjhw\nujOhrxkMQ45Kf9zfjGONqT/M+MU/1KLfkXpB7VhX/MvNdk8/Wu3pN3lYd1WVNvv5XJu7bj1SFAWf\nvVWL/s7IqomJ0HdOQNXbxm0mPHNqn6b7a67/RNP96VVVczf6VcySHes0Jp80dcDpSX7fT4YcFYQB\nEX/4qCnZh6EJx4A35VYs73R2oHMgMXcJNWnWZCW5XLAdjb3fAwA4W1vhbNX3iEO1Gg61oP2E/qqg\nrcc7EzrCK1H6us/EPKrKX/OpfYZfldztlfDXBnVVnFinMfFIMvY1JGftRl8MOSocPNYJZxLb4LX2\nUVVbSt391UTRVBWraJrFjMBWXQ1F1G5UWefBg5rtSy9cghvHPtLmgqv1pJ8AUPNBPdwpWJ0NpaH2\nA8336RVdaD5Vqfl+9eSTpg4MiMm7Vh1q7kSvM7nNuQw5KjSf00+JWgsDbgk2HfQriFQiQ067ox3d\nA8abKTqY9r17Nd1f56efQtYwNOlB8xfnIIna9NXSetJPAPB6JJw9lpiRNInQ09WIDg1GVQXScGwP\nPG5j/Z4PsrtFfNKk/nugxTQmsgJ8nOD+QP4YclS4JG90sg9BU6PMGbCMMSf7MCJi99hxpj+xzWuJ\n6P+jB8Lp03Cc1vaz9Tochuub09Go/w6rqXCMkVAUGcer/jdu+/eKLtR/8ee47T+Z/lrfDm8M0xpo\nNY3JF209aOtP3hQHDDkqzL1xAsxZpvi9QEZWdNtj9LUbJ2J0dmZc9q212iQEjnQZSt720Udx268i\nG2eUWkaGdud+vCb91PIYk6n5VCX6berWUIvUmVP70NudWv0Sw+kSXDh8Vj8V6A9OtCatSwRDjgp5\nOWtPRdMAACAASURBVKOwsvRGmLPi8/GZsi4CsvOGb8zOO79dY9dfmYcH775a8/3Gy7HuxIecxt6G\niOfkSVWOlhbNRlX5c7a0oPvw4bjsOxnGTrRqtq94TfqZO0G7Y0wWoe8c6j5/K/4vpCio3v8avGLq\nNNmH8+HJ1niuERu1JpuAhu7krJvIkKPSrGsuxtp/uAmTLh4Tl/1nXX4Xhv7vyc778t/aMQG47auT\n8cTfF2LMqPhUiLTmkTw4aUv8ujMKFNR1G3stq+a34nsxaX77bcgazL2jB1fffAWydFz5NI/OwrSb\npyT7MGLiFd2o3v8qZDkx35kBoRu1n/0+pQZgBNPcI+BEp/4WyE1WNYchJwbTrxiL/7f8ZvzDN6+B\ndYy2QcE0+mLAbAGyrDBPW3L+3xq5cdo4PPOPs/Hod65Ftlm/P9b+TvWchFdJzoWyNgkVpESxHTmC\n3trauL6Gu7sbrXv2xPU1EiX7IjOK77kOJh02CWVkmjD7nuuRPTo1+tgFIssSjlT+D+y9iR0K39r0\nGeq/eC+hr6k1RVHwwUl9TiHQIbhQ0574ueVS4xZex7IyM3DnLVOw4CuTUVl9Dn850ILT7YJ2L2DS\n5ofUnGXC126YiG/MvgxX54/VZJ+JVhvHtarCqbMdhyRLyMxInVAYCVd3N+pffz0hr3X2j39E7rRp\nyL06dZpHg5l09SX42vcK8envj2o20ipWWdmZuOXvbsSlU8cl+1BUUxQZxw7uQldbciqn9TV/wagx\nuci/em5SXj9Wp7r6cbZXv+uYfXyqDTMnjkVmRuLqKww5GhmdnYnbiy/DbV+djJPN/fjgs1Z8WtMB\ntye5P4D5EyxY8JVJWPCVyci5KHXv7oDzlZxkcUtunLWfRcHYgqQdg9Zkrxcnf/c7SK4ETYimKDj5\nyiso/Jd/gTknJzGvGUcTrhqP2x+9GVVv1aK7ObkrgV9SkIeib83ERWNTd+SnV3Tj6CevoaMluVXT\nY4d+D5ezD1ffeBdMptRq7KhsTP7ke6H0DnhQe64XN0wen7DXZMjRmMlkwvQrxmL6FWPx8Den49Dx\nLuw93I7qehsS1Rw51pqNksKJmH/TJBRMSv0OiADQ6+qBzZXc0QINvacME3JkjwcnfvtbOM6cSejr\niv39qH3hBcz8x380RNCx5I3BvAe+gobPWlD7cUPC147Kys7EdbdehSu/ejlMGlV9k2HAYUNVxX9D\n6NPHoq4Nx96H0H8ON84pRVbWqGQfTkTa+526ruIMOnimiyHHKEZlZ6KkcCJKCieix+7GviPnUPF5\nG852av9FzMo0oXjmpVhw0yTcOG0cMjNT6w4knMa+xmQfAhr7GnAbvp7sw4iZ5Haj7qWX0H9SXWXs\n+uuvH5q4bvv27VGPCnK2tqLmuecwc/lyjMrLC/8EnTNlmDBt9hRcPvNSfPFBPc5+kZi76SsKJ+H6\n26ZhlCU7Ia8XD4os42zjAZw88g5ET2y/i7F+L/11nD2KT947h5lfvRcXT5oe074SoUpHQ8ZDae1z\nor3fiUm52o8WDoQhJ0HG5YzCt+ZdgW+W5KOxTcCegy346+F2eKXYyjuTLx6Du+ZMwdzCibCmyIR+\nauhh1mGbDo4hVqIgoO43v4EQw6R/g7P0Dv73U089FfU+XJ2dqPmP/8DMf/xHjJkwQfWx6Mlo6ygU\n/+11KLhxEj7/Yx2cvfFpBrSMH4Ob7p6BSwtSt+8NAPR2nUbtZ7vR33NWk/1p8b3057B34NBHv8aE\nKTfi2q/8LcZYEleBiFZrn/6rOIPa+gcYcozKZDLhqstycNV3rsXib1yF9w+24k/7myEMRDdq6Lor\n8/DNkisw6+rxhpn4K5Q+t7pe+abMwJ9NsO2h9Lp7oShKyjYL9NfX4+Qrr0DsS27/kUGenh4cffZZ\nXFVaikuKipJ9OJq59Mrx+PqjN+Pzd45rvrxC/o2TcNPd05GZlbod4J32LtTX/AWtTYeSfSgR6zh7\nFF2ttZg68zYUTF+A7FGJuUBHSlEU2DRcIyojM3A0CLY9WjZH4hZGZchJolxLNu67dSruvOVybH+/\nAR8cDD+B07icbPzDt6aj+NpLUvZiq4bgUTeRVJYlE+a8LIi9F0KkOS8LWZboLxKiLMIjuTEqK7U6\ndyqyjNY9e9D8zjvQomPY9u3bhzULxEL2eHDqlVfQf/Ikpt57LzKyU7fpxVemORNf/c51UBSgpVab\noDPlhoko+ta1KXve9/e0orF2D9rPHAHiMFWdlt/LQGTZi4aav+B03cfIn/Y1FMz4Pxh9kT5Gqnpl\nBaKk3SAX80VWjBo7Hu6+C8uDjBp7McwXadPH05nARUMZcnTAOsaMH3x7BopmXIJNrx+FHGS9kWvy\nc7H6oVkpM3mflnJH5ap+7sSFl+DsjnZAPh9wJi68RNV+sjOykZ2ZGp0QB4kOB+q3bNF0HpzBWXq1\n1FFZCaGpCdc8/LBhmq9MJhNGWbULbWOso1Iy4PR0NKCh9gN0tcV3LqZ4fC8DkbweNNV9jNMn9+Ky\nqcW48trbYMm9NO6vG4o5MwNXjLPgTI92M7NP/cZ3Ubf7ZUCRMWrsxZj6jfs02/dVFydu0EH6XS11\n7CvTL8Z9t07Frg9GdrLNyjTh8QdSZ3ZirV0yRv2PSPbF2ciyZEJRFOQ/cJnq/Vx60YSUusgIp0/j\nxH//Nzy9iZ+ASw1nayuO/uIXuPrBBzH+xhuTfTgx8ThFnNh/Gg0HtelvAgAnPzkDmIBr5lyB7BTo\nf9dvO4sTR95B97nEz1KeCIosoaXhU7Q0HMDlV83G1TfchdEXJa8j/bUT8zQNOWPGT4DZkgNFUTDz\ne/+fZvvNNJlw9aXqb1qjlZ5XTB0LNuT7krzRKT/PTSwmWibFvI9YA8pEy8SYjyERFEVBR2Ulmn7/\neyhSYoc0x0p2u3Hiv/4Ll33968j/5jdhykytvicuwY3GqlacOtAMKQ7DyU/uP4PGz1pw9S35mPqV\nyzFaw0qRVpz2Lpw8+ke0nzHOemWhKWhpOIC2pipcMX0+rrrudpizE99n5/pJ47C/sQN2t6jpfrW+\nsSu+4hKMSmCfMoYcnak+ZQu4vb17AO3dTky6WF8d3hJlWt7VuGTMJega6EraMcy5LDVmQT39hz+g\n/eOPk30YMWndsweOlhZc+9hjMCVwdlQ1vKKE9hNdOHO0HR2Ntnh0Nxn+eh4Jx//ahLq9TZhw1Xjk\n3zgJk6+5BJk6WKLl1NH30HDsfSiKPmaBTiRZ9qLp+Ic4W78f18/+HiZdMSuhr39RdhYeKJ6G/zl4\nCk6PPteJu3HyOHx9uvpquhr6/vWIgizLeOqpp3D//ffjwQcfxJkET3KmhdYuJ/YcCr7uyOt/rk/g\n0ehLZkYmvjH1zqS9/vTx16Jg7NSkvX6kemtrUz7gDOo7fly370WRFXQ02lD1di3+9Nw+HPrfY+ho\niH/AGXYMCnCu3oZDbxzDH5/bh6q3a9HZaIMSpE9fvJ0fNfXntAw4vryiC7VVf4AsJ76KerFlNB74\n6jSM1kHg9XftxLH41vVXJLzJ3zCVnPfffx+iKGLbtm04cuQINm7ciBdeeCHZhxUxRVHw27frgnY6\nBoBDtV34/EQ3vjJdu8U6U8msCV/BB6f3oMOZ+KnL75yq7Srw8SC53WiIw6iSZGp+5x2MKyzE6Iv1\n8Z3v73Sg6XArWmrOwe3UtlkgFl6PhDPV7ThT3Y5RlmxMuX4Cpn7lcuQksPLberoqYa+ldx6XHbZz\np3DJ5BkJf+0JOWPw8M3T8XbNGTT3atdHR60MEzDvqkmYe+XEpEx3YphKTlVVFebPnw8AmDVrFr74\n4oskH1F0PjvehZqG8B1E/+fdkyGDkJFlmDLw99d/H6MzEzuE+5vTvo383CsS+ppqtH7wATw9Pck+\nDE3Joogzb76Z7MNAb7sdB37/BT546QAaDp7VVcDx53Z4UH/gLPb8+lMc/EMN+s5puGBwCN3tdQl5\nnVTR1Z6cRUYBYLxlFB6cfTUWzpwCcxJnv78s9yL8YM4MzJ82CZlJms/NMCFHEARYrRc67WZmZkKW\nU6ds+uFnka3Zcs42gOOnU2O0TDxMtEzEgzf8AzIStHDeLZO/hvlT/k9CXitWWaNTa/6eSGWNGZPU\n1z/2UQM++u9DaK3r1HS/mRmBC+nBtqvRUtuBD18+iON/jf+yKNOuvyNpMwJnBpncM9j2eMu7ZCqm\nTJuTlNceZDKZ8NX8S/DY3Gtx9SXqRjPlXTUTeVfNjPp55swMfH36Zfj+LddgQk5yz1/DhByr1QqH\n40JpTpZlZOi8w6KvhtbIJ7traFE3MZ5RXD3uGnx3+qK4v870cTPwnWvuTZlh4xNLSv7/9u49LKpq\nb+D4d4AB5M6ACCgq4gUFeRU171aaVq/ZxTvqoMVRO+fRQlMpzFt1tDQ7p7xmmafIg0FKnjxPdUoS\nb6ik4i28gcZFLiKIDEdhmJn3D18nCfHKMMP4+/yjz549a6+12Hv2b6299lrYu5t2cjK7Ouqiru0P\nSmFrS/Mh5huLVVak4XTq/S+BcTtNlE64OtR85djNwYMmyvp/xHRq93nKi0376MLbL5h+Q1+nU/eR\nODRpuFeEAZwcbXF3qRkcurvY4eTYsGNTXD2aEz7gTzwyaBoubpbxNqZ7E3vGhLcholsQPi731hBq\n3nMQzXve/Xp9CqBrCy/+0q8jvVr7YGMBv52NJwq4g/DwcHbu3AlAeno6HTo0/LPQB+GgrP2nsHEN\nwsY1qPa+9pY3qKyhdfd7hNHBY1FwdxeRc5ATzkF3f/MI8Q4lMvRFbG0aT13b2NvTYuhQkx7D2dYW\nzz+81u1pZ4eziV719n30URxU5lsvqPDsJZMOJh4Q+CSK//8ZdnPwoH+gacZ+GQxQkGn6tddsbGwJ\naNub/kNj6dD1WZQOziY/5g2Denlz457q7mLHoF73N+nn/XB28+F/+kbS+8lomvp3tMiGURsvV6J6\nd+CZkABcTDDfWltvNyb3CeZ/OwXg4mA5050oDIZ6mOfdAhgMBhYuXMipU9efCy9ZsoTAwEAz5+ru\nbdh2mh8P5N1xPwWw/NWeD+2r5H904uIxNv4ah85Qf28ydGvWnREdRjeqAOcGg17PuYQEilJTTXaM\nYq2WuIsX0XM9wHnW0xNvZf3/qLkHB9Nu0iSzPq7SXqsmLek4RedMN9bpmxNxGAwGXgiNNNkxmgWp\n6P58CMoGnkxUr9dxpSSH4vyTFOefoqzEtG+97j9aik5noE9X0wbGChtbVD5t8fbrgLdvMM5ujWui\n0KpqHXvPFZF6vpAHHeLp6WTPUx0DGnQW43thNUFOY1dYcpVZK/aju8Oq5L1CfXhldEgD5apxOFt6\nhs+PfUaVvuqB0+rbvD/PtH22wcb8mEr5+fOc37yZChNNpfBJYSEGg4Epvg8+SeMfOXh50eqFF/AM\nDbWIG4derycj5RyZabnoq+t/nN83J+IAeD5EXe9p29rZEPRIAB0HBKKwgIV8qyoruFR4muL8UxTn\nn6TqWuN59O7s5oO3bzBefh1QNW2DrZ3lTcR4r4o11/guI+e+Zkq2USjo26YZfVr7YGfGwc13IkGO\nBfn3nmw2/lD3XDiuTkqWTnsEdwuc5dTccq5ks/7oOq5WX73vNJ5oPYQnWg2xiBtrfTDo9RT/8gu/\nbd1KtaZ+37BJ+f+VzB+txzFANvb2NB8yBL/HHsPGBD1DD0pbWU1eRhHZRwsoya2/ldwP5e0FILx5\n/U026dXSnZZhfvh3aNrgvTd3y2AwoCnLpzj/FJcKTlFyMQuDGeaWqYud0hEv3/Z4NWuPt18Hsw2q\nNjWDwcCx/FJ+yMil6i4X+QzwcGZoSABezpb/soMEORZErzfwbtwRjmfeumt89vjOdO3QcM+ZG5sC\nTT6fHv2Y8vtYsXxY2+fo12KACXJlftXXrpH/888U7tpFdYX55834IxulkqY9e9J88GDsPcy39s+9\n0JT8l/zTxRScKaYkt6w+Fnd/IAoFeAV40KydF/7tm+Lsad43Wu6HrrqK0otZFBec5lLBKTRlBQ2b\nAYUCD6/WePt2wMuvPe6eARY/23Z9Kiq/SvyhTDSVt58tOdTPk2dCArBtJHUjQY6FuVxeyewVB6i4\nVvNEe7JXCyb+bzsz5arxuHT1EmsOr7inQGd4+1H09Dfv654NQa/VUnzwIAUpKfz3Qt0zazcUew8P\nfB99FJ9evbBzarxjzKquainKKqHgTDEFmSVU3+EmUV+UjnY0C/LCt50XPm1U2DtaXu/Xg7h2tYxL\nBWe4VHCKixcyqNbefy9tXRydPGnq3xFv3w54+gShtG98wWF9unKtiviDmRRXVN7y8z6BPjzW1q9R\n9XZLkGOBkn+5wKf/+n1iLXcXez54tedDuwL5vcorz2XN4ZVo9XeesG1Qq8EMCXyqAXJlOQwGA1fO\nnqVgxw5KzTBppktgIH6PPYaqc+dGtwDnneh1ei5lXyb/TDH5p4u5euXWN4v75eTuiG97b/zaeePV\n0r1RTZPxIHQ6LUW5x8jN3E9J0dkHSkthY0uzFp1p0aYnqmZtUTTy8Xf1rbxSy9rdGbUeXXX28+TZ\nzq3MlKv7J0GOBarW6XlleSqXNdcH0o4d3IZn+ze+k8ucMop/5fPjn2G4zfu/XZt1Y0xwRKNqldS3\nq0VF5Ccnc3H/fgwmnjzTMyyM5k88gUurh+NcNhgMlBVqyD5WQM6xArTX7q+HR+loR8swX1p29sPN\nx/mhPl8BKsovkpe1n7ysNKoq736smbObDy2CeuHfuhv2Di53/sJD7MBvRfx46vfeXgdbG17u19Gi\nXg2/WxLkWKgdh/L5955sXJoomRERipuzDDa+Vz9kfUdy9k+3/MyriTcze8zGrh5nl23MKi9fJj85\nmcK9ezFo63HJAoUCr/Bwmj/xBE7+Dbv6sCXRVevIP1VM1i+5lORduavveAW406Z7C3zbeWNrJ70N\nf6TX68g5u5dTh/9120VBlQ7OdO4Zgbdf8EMfIN4tvd7ApsOZFFy5igIFA9v78T/NLWP9uHslQY6w\nWlW6Spbtf5crVbVvKpM6R9HRq5MZcmXZtOXl5O/YQcGuXegr7/9Ri8LGhqY9e+I/aBCOTZvWYw4b\nN4PBQF5GEce3n+Va+a2nPGji5kDoE23x79BUbsp34XLxedJ3f07ltdrXuZsqgC59J9LE2dMMOROW\nQIIcYdUOFRzkq5P/rLGtvSqYqLDJZspR46DVaMjatInSY8fu+bvOrVrRdsIEmvj4mCBn1kFbWU3q\npiO1enW8AtzpPSYMO3vpYbwXldfKOXV4K//VlBi3eTYNpF3np7Gxlbp8mEmQI6yaTq/jrb0LuHbT\n/DkTQ1+kk3eoGXPVOBgMBi7u38/5zZvRV93FRIsKBc2ffJIWQ4ZY3YBiU9BWVnPsxzNUXL4GgIuq\nCZ2faCsBjhD1SIIcYfW+yojnUOEvACht7FnQ9y2Uto1vAJ25XCsu5sznn9929mR7T0/aTZyIayNa\nSkUIYf1kNJuwel2adTX+P9Q7VAKce+To7U3w1Kko65jd2EapJHjqVAlwhBAWR3pyxEOhsKKQKl0l\nvs5+EuTcp/Jz5zjx0Ufwh1fNg8aPp+kjj5gpV0IIUTcJcoQQd61o3z5yv/8eg+76GkNNe/ak5TPP\nmDlXQghxaxLkCCGEEMIqyZgcIYQQQlglCXKEEEIIYZUkyBFCCCGEVZIgRwghhBBWSYIcIYQQQlgl\nCXKEEEIIYZUkyBFCCCGEVZIgRwghhBBWSYIcIYQQQlglCXKEEEIIYZUkyBFCCCGEVZIgRwghhBBW\nSYIcIYQQQlglCXKEEEIIYZUkyBFCCCGEVZIgRwghhBBWSYIcIYQQQlglCXKEEEIIYZUkyBFCCCGE\nVZIgRwghhBBWSYIcIYQQQlglCXKEEEIIYZXsGvJgBoOBAQMG0Lp1awDCw8OZMWMG6enpLF68GFtb\nW/r27cu0adMAWLlyJSkpKdja2hIbG0tYWBglJSXMmjWLyspKfHx8WLJkCY6OjiQnJ7N69Wrs7OwY\nMWIEo0aNasiiCSGEEMLCNGiQk52dTUhICGvXrq2xfeHChaxYsYKAgACmTJlCRkYGer2etLQ0EhMT\nyc/PZ/r06Xz99desXr2aZ599lueff55169axadMmxo8fz7vvvsvmzZtxdHQkIiKCgQMH4uXl1ZDF\nE0IIIYQFadDHVSdOnKCoqIjIyEimTJnCuXPn0Gg0VFVVERAQAEC/fv3Yu3cvhw4dom/fvgD4+fmh\n0+koKSnh0KFD9O/fH4ABAwaQmppKVlYWLVu2xNXVFaVSSbdu3UhLS2vIogkhhBDCwpisJycxMZEv\nvviixrYFCxYwdepUnnzySQ4ePMjs2bNZtWoVLi4uxn2cnZ3JycnBwcEBDw+PGts1Gg0ajQZXV1fj\ntvLy8hrbbt5el+rqagoKCuqrqEIIIYQwI19fX+zsaoc0JgtyRo0aVWtczLVr17C1tQWgW7duFBUV\n4ezsTEVFhXEfjUaDm5sbSqWyxvaKigpcXV1xcXFBo9GgUqmoqKjAzc0NFxeXWvu6u7vXmbeCggIG\nDRpUX0UVQgghhBlt376dFi1a1NreoGNyVq1ahbu7O3/60584efIk/v7+uLi4oFQqycnJoUWLFuzZ\ns4dp06Zha2vLsmXLiIqKIj8/H4PBgKenJ+Hh4aSkpPDCCy+wc+dOunfvTlBQEL/99htlZWU0adKE\ntLQ0oqKi6syHr68v27dvb8CSCyGEEMJUfH19b7ldYTAYDA2VifLycmbPnk1FRQV2dnbMnz+fwMBA\njhw5wuLFi9HpdPTr14/o6Gjg+ttVO3fuRK/XExsbS3h4OJcuXSImJoaKigpUKhXLly/H0dGRn3/+\nmVWrVqHX6xk5ciTjxo1rqGIJIYQQwgI1aJAjhBBCCNFQZDJAIYQQQlglCXKEEEIIYZUkyBFCCCGE\nVZIgRwghhBBWSYIcE9i/fz/du3evMeHg+++/T1JSkhlz1fitW7eOF198EbVaTWRkJCdOnKhz3/37\n9zNz5kwA48zZjY2llnfYsGEmTf/111/n+PHjNbYVFxezaNEiAAYOHEhVVZVJ83A/9u/fT+/evVGr\n1ajVasaMGUNGRka9H0etVpOVlcWKFSvYtGlTvaffkBqqzm51zu7atYuEhATy8vIYM2ZMvR9TWIYG\nnSfnYWJvb88bb7zBhg0bAFAoFGbOUeN29uxZkpOTjT/qJ0+eJCYmhq1bt97xu42x7h+28t7sVvn3\n9vZmwYIFZsjN3VMoFPTp04fly5cDsGfPHj788MNaa/XV5/Eau4aus5vdWB4oNzfX5McypXXr1pGa\nmkp1dTUKhYKYmBhCQkI4ffo0V65coXv37nV+98svv2TChAn3fWytVsvq1avZvXs3jo6OKJVKoqOj\nCQsLu+8065v05JiAQqGgV69eeHh4sHHjxlqfx8XFMXbsWMaOHUtcXBylpaU8//zzAKSnp/PII48A\n12dm/uOkhufPn2fChAmMHTuWSZMmUVJSwunTp4mKimLSpEk899xzHD58GIDHH3+cqKgolixZYuIS\nm56rqyv5+fl8/fXXFBYWEhwcTGJiIgCnTp0iMjIStVrNK6+8gkajuWN6iYmJjBgxghdeeIEVK1YA\n1y/4iRMnMnr0aKZOnYpWq2XLli2MHz+ecePGkZqaatIy3sySy1teXs60adOIiIjg7bffBqjRq5CZ\nmYlareb8+fM1Zj2Pjo7m6NGjNdL647Vww7p165g4cSKRkZFkZ2eTm5tbq7UdHx/P9OnTqaqq4sCB\nA4wbNw61Wk1sbCzV1dV3rJP6ZjAYuHlGjrKyMuMiwWq1mnPnzhnzvXLlShISEli6dCkAOp2OYcOG\n1eih0mg0REdHExUVxbBhw4iPj2/A0jSM+q4zrVZLbGwsEyZMYNy4cRw4cMC475w5c1Cr1bz22mtU\nVlayZcsWli9fbgwW9Xo9s2fP5pNPPgHqPjctyY3G0IYNG4iLiyM2NpbY2FgAfvjhB86ePXvb7z9o\nMLl8+XK0Wi2JiYnExcXxzjvvMHfuXIsKHKUnxwRuXLQLFixg1KhRxhYDXD8pv/vuO+Lj49Hr9bz0\n0kv069cPDw8PCgoK2LlzJ/7+/hw9epRjx44xZMiQGmm/9957vPzyy/Tr14/k5GQyMjIoKysjJiaG\n9u3bs23bNrZs2ULXrl0pKCjgm2++ue0SF41Fs2bNWLNmDV9++SWrVq3C0dGRGTNmMGTIEObNm8eS\nJUsICgri66+/5pNPPrntI5tLly7x6aef8u2332Jvb88HH3yARqPh8uXL/OMf/0ChUBAVFcWxY8dQ\nKBS4u7uzevXqBiytZZe3oqKCt956C5VKRXR0NMnJybfsVWjdujWOjo5kZmbi5eVFXl5ejRZeXdcC\nXF+od/To0aSkpLBs2TJef/31GmnHxcWRkZHBRx99BMC8efOIj49HpVLx4YcfkpSUVGtZmYawb98+\n1Go1Wq2WkydP3rIeb9TV0KFDGT58OLNmzWLXrl306tULe3t7437Z2dkMHTqUwYMHU1hYSGRkJBER\nEQ1WloZSn3WWmJiISqVi8eLFlJaWolar2bZtG1qtlpdffpk2bdqwbNkyEhISaqyZqNVqmTVrFj16\n9CAiIqLOczMwMND0FXIPbm4M9e/fn+DgYGPDKCkpCXt7ezp16sSFCxf45z//aeztWblyJZs2beLy\n5cssWrSIsLAwsrKyjAHg008/TXJyMhs3bmTr1q3Y2NgQGhrKm2++aTy2Vqvl+++/Jzk52bjN39+f\n8ePHk5SURM+ePdm0aRMffPABcP0x+p49e8jNzSU2Nha9Xo9CoWDu3LkEBwebrI4kyDEhDw8PYmNj\niYmJITw8HIAzZ85w4cIFIiMjgeut4t9++43BgwezY8cO0tPTmTJlCnv27CE9Pb1WL8z58+fp0qUL\ncH1sAsAvv/zC6tWrcXR0pKKiwnjxenp6WkWAA9d/8F1dXVm8eDEAx48fZ/LkyfTs2ZPMzEwWhGle\nMQAABsBJREFULlwIXF98tXXr1rdNKycnh3bt2hl/HG+MZVEqlcycORMnJycKCwuNvQHm+GGz5PIG\nBQWhUqkA6NKli7G1fSujRo1iy5Yt+Pv789xzz9X47PTp07e8FgB69OhhTH/ZsmW10t27dy92dnYo\nFAouXbrExYsXefXVVwGorKw02zisXr16GX/Uz507x9ixY9m5c2eNffR6PXB9IeEePXqwa9cutmzZ\nwrRp02rs5+Xlxeeff85//vMfXFxczNI71RDqs85Onz7NwYMHOXLkCHC9B6e0tBQvLy/atGkDQNeu\nXdm7dy+dO3eu8T03NzfjGoi3Ojezs7MtLsi5XWNo+PDhNG3alLCwMFJTU1m3bh2Ojo7Mnz+f3bt3\n8+c//5mNGzeyYMGCOseLJiUlsXDhQkJDQ4mPj0en0xnXnywtLcXd3R0bm5oPhJo3b056enqttG4E\nqkuXLmXSpEkMHDiQkydPMnfuXDZv3lzPNfM7CXJM7PHHH+fHH38kKSmJOXPmEBgYSNu2bfn0008B\n2LBhA8HBwXTs2JHXXnsNlUpFv379WL9+Pe7u7sabyQ1BQUEcO3aM3r17s23bNsrKyti8eTPLli0j\nKCiIFStWkJeXB1Dr5GvMTp06xVdffcWaNWtQKpW0bt0aNzc3bG1tja0zX19f0tLSuHz58m3Tatmy\nJVlZWVRVVWFvb090dDTjx49n+/btJCQkcPXqVUaMGGHskTNHPVpyec+fP09ZWRlubm4cPHiQsWPH\ncuLECS5evAhQY4D0U089xfr16/H09DT2utzQpk2bWtdChw4d+OGHHzhy5AiBgYGkpaXRoUOHWnlY\ns2YNc+fOZdOmTYwePRpfX1/WrFmDi4sLP/30k0UE9zceuwA4ODhQVFREYGAgv/76q3GdndGjR7Nu\n3TrKyspo3759je9v2LCBLl26EBERwb59+0hJSWnQ/JvDg9ZZUFAQfn5+TJ06FY1Gw2effYaHhwel\npaXk5OQQEBDAgQMHavUchISE8PHHHzNy5Ej69+9f57lpaW7XGILfnyqoVCpiYmJwcnLi3Llzxkb3\nDTc/Mrz5/0uWLOGzzz4jNzeXLl261PjM09OTy5cv1wh84Hqg6uPjUyuvN76blZVlbMQEBwfXeEHH\nFCTIMQGFQlGj+z42NpZ9+/YB1/+ovXv3JiIigsrKSrp06UKzZs1QKBRUVVXRu3dv4yrsjz76aK20\n58yZw/z581m9ejVOTk4sW7YMrVZLdHQ0vr6+hIaGGm821mTw4MFkZmYycuRInJycMBgMzJkzBxcX\nFxYuXMjs2bPR6XTY2Njw17/+lcLCwjoHZqpUKiZPnoxarUahUDBw4EA6d+5MkyZNGD9+PJ6ennTq\n1ImioiLAPAM8LaG8GRkZJCUlGZ/x35zeG2+8QUlJCT169KBv3760atWK6OhoDhw4QGhoqDENe3t7\nevToQWlpKW5ubjXSqetaAEhNTWXLli0olUoWL16MVqutVb4333yTUaNG0adPH+bOncuUKVPQ6/W4\nurry3nvvPfgf4R4pFArjoxdbW1sqKip44403cHBwQK1Ws2jRIvz8/IxlBAgLCyM7O/uWgz8ff/xx\n3nnnHX766Sfatm2Ls7NzrbfKGvvg4/quszFjxjBv3jzUajUajYZx48ahUChwdXXl73//OwUFBbRs\n2ZLhw4fz7bffGutPoVDg4ODAwoULiYmJISEhoda5easbt7ndrjGkUCjQ6/WUl5ezYsUKUlJSjI/e\nbgQcN/51dHS8ZSMlISGBRYsWYW9vT1RUFOnp6caBzEqlkqeffpq//e1vzJw5ky+++ILc3Fx27NjB\nxx9/jEajMaaZl5dHWVkZcL1xk5aWxsCBA8nIyKBp06YmrSNZu0oIcUtXr15l7dq1zJgx44HSefvt\ntxkyZIixdSl+p9frGTduHOvXr8fZ2dnc2WkUpM5qWrt2Ld99952xMTR58mQGDRpESkoKS5cuZf78\n+cTHx3PhwgVUKhXNmjXD39+fqVOnEhkZia+vL/PmzeMvf/kLOp2OkJAQDhw4wNatW0lMTOSrr77C\n2dkZX19f3n777RpjoHQ6HatWrWL37t3GwMpgMPDSSy8xcOBApk+fTnFxMUFBQRw+fJjvv/+evLw8\n5s2bR1VVFdXV1cybN4+QkBCT1Y8EOUKIW7rx1tbNAzTvVVRUFJ6enrz//vv1lS2rkZOTw/Tp0xkx\nYgRqtdrc2WkUpM4sX1VVFWfPnqVTp07mzgogQY4QQgghrJT1jEwVQgghhLiJBDlCCCGEsEoS5Agh\nhBDCKkmQI4QQQgirJEGOEEIIIazS/wG7ZMfLkBp1iAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11297af98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphics.graph_options(te)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why do the ebike options cost so much?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAAtCMgAAAGBBSAYAAAAsCMkAAACABSEZAAAAsCAkAwAAABaEZAAAAMCCkAwAAABYEJIB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\nrCQDwHcRAbnpqfj3cf363dK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115f10588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mTJighIQE3X///ZKkSZMmaefOnZKkgoIC9e7dW5GRkdq2bZuqqqpUXl6u/fv3q0ePHrLZ\nbMrLy5Mk5eXlKSoqSlarVWazWSUlJXK73crPz1dUVJRsNps2bdokt9utw4cPy+VyqW3btt4aGgAA\nAJo5k9vtdntjx/PmzdN7772nrl27etpmzpyphQsXKigoSB06dNDcuXNlsViUlZWl1atXy+VyaerU\nqRoyZIgqKiqUmJioo0ePKjg4WOnp6Wrfvr127NihtLQ01dbWKiYmRo8//riks2e3yMvLk8vlUnJy\nsmw2mzeGBQAAgEvgyB+2S5LaDO+mlt2a3uSm10IyAAAA0JCmHpK5mAgAAABgQEgGAAAADAjJAAAA\ngAEhGQAAADAgJAMAAAAGhGQAAADAgJAMAAAAGBCSAQAAAANCMgAAAGBASAYAAAAMCMkAAACAASEZ\nAAAAMCAkAwAAAAaEZAAAAMCAkAwAAAAYEJIBAAAAA0IyAAAAYEBIBgAAAAwIyQAAAIABIRkAAAAw\nICQDAAAABoRkAAAAwICQDAAAABgQkgEAAAADQjIAAABgQEgGAAAADAjJAAAAgAEhGQAAADAgJAMA\nAAAGhGQAAADAgJAMAAAAGBCSAQAA/MDtdvu7BHwHQjIAAICPuV1u7XnrhEq3O/xdChpASAYAAPCx\n2iq3Kspq9M2/Tvu7FDSAkAwAAAAYEJIBAAAAA0IyAAAAYEBIBgAAAAwIyQAAAIABIRkAAAAwCPLW\njqurq5WcnKzDhw+rqqpKU6dOVbdu3ZSUlKSAgABde+21SklJkclk0po1a7R69WoFBQVp6tSpGjRo\nkCoqKpSQkKCysjJZLBYtXLhQYWFhKioqUlpamgIDAxUdHa34+HhJkt1u14YNGxQYGKjk5GRFRkZ6\na2gAAABo5rwWkt955x2FhYXp+eef16lTp3Tvvffquuuu04wZM9S3b1+lpKQoNzdXffr0UUZGhnJy\nclRZWanY2Fj1799fmZmZ6tmzp+Lj47Vu3TotWbJEs2bNUkpKiux2u8LDwzVlyhQVFxfL5XJp69at\nysrKUmlpqaZNm6bs7GxvDQ0AAADNnNdC8tChQ3XHHXdIklwul4KCgvTpp5+qb9++kqSBAwcqPz9f\nAQEBstlsMpvNMpvNioiI0N69e1VYWKjJkydLkgYMGKDFixfL4XCourpa4eHhkqSYmBgVFBQoODhY\n0dHRkqROnTqptrZWJ06cULt27bw1PAAAADRjXluT3Lp1a1ksFjkcDk2fPl2PP/64XC6XZ7vFYlF5\nebkcDodCQkLqtDscDjkcDlksljp9nU6nrFbrRe8DAAAA+CG8+sG90tJSjRs3TiNGjNDdd9+tgID/\nPJzD4VBoaKisVqucTqen3el0KiQkpE670+lUaGioLBZLnb6N7QMAAAD4IbwWko8dO6YJEyYoISFB\n999/vyTpuuuu05YtWyRJeXl5ioqKUmRkpLZt26aqqiqVl5dr//796tGjh2w2m/Ly8ur0tVqtMpvN\nKikpkdvtVn5+vqKiomSz2bRp0ya53W4dPnxYLpdLbdu29dbQAAAA0Mx5bU3y0qVLVV5erkWLFmnR\nokWSpFmzZmn+/Pmqrq5Wt27dNHToUJlMJo0dO1ajR4+Wy+XSjBkzFBwcrNjYWCUmJmr06NEKDg5W\nenq6JCk1NVUzZ85UbW2tYmJiPGexiIqK0siRI+VyuZSSkuKtYQEAAOBHwOR2u93+LgIAAODHpPqM\nS7veOCZJumlSBz9X4x9H/rBdktRmeDe17Nb0VgBwMREAAADAgJAMAAAAGBCSAQAAAANCMgAAAGBA\nSAYAAAAMCMkAAACAASEZAAAAMCAkAwAAAAaEZAAAAMCAkAwAAAAYEJIBAAAAA0IyAAAAYEBIBgAA\nAAwIyQAAAIABIRkAAAAwICQDAAAABoRkAAAAwICQDAAAABgQkgEAAAADQjIAAABgQEgGAAAADBoN\nyZ9//vkFbUVFRV4pBgAAAGgKghrasG3bNrlcLs2ePVvz5s2T2+2WyWRSTU2NUlJS9P777/uyTgAA\nAMBnGgzJBQUF2rp1q7799lv96U9/+s8dgoI0atQonxQHAAAA+EODIfnXv/61JGnt2rUaMWKEzwoC\nAAAA/K3RNcldu3bVq6++qqqqKk2YMEH9+vXTe++954vaAAAAAL9oNCTPmzdPP/vZz/T3v/9dLVq0\nUE5OjpYtW+aL2gAAAAC/aDQku1wu3XLLLfroo490xx136KqrrpLL5fJFbQAAAIBfNBqSW7VqpVde\neUUff/yxBg0apBUrVshisfiiNgAAAMAvGg3Jv/vd73TmzBm9+OKLatu2rY4dO6b09HRf1AYAAAD4\nRYNntzinY8eOuuGGG/T+++9r3bp16tevnzp27OiL2gAAAAC/aHQmefny5bLb7brqqqvUuXNnLV26\nVEuWLPFFbQAAAIBfNDqT/PbbbysrK0stW7aUJI0cOVL33Xefpk6d6vXiAAAAAH9odCbZ7XarRYsW\nntstWrSQ2Wz2alEAAACAPzU6k9yvXz9NmzZN999/v9xut9auXatbb73VF7UBAAAAftFoSE5OTlZm\nZqbWrl0rt9utfv36aeTIkb6oDQAAAPCLRkPy6dOn5Xa79ac//UnffPONVq1aperqagUFNXpXAAAA\n4LLU6JrkmTNn6ujRo5Ikq9Uqt9ut3/zmN14vDAAAAPCXRkPyoUOH9MQTT0g6G5KfeOIJffnll14v\nDAAAAPCXRkNyQECA9uzZ47m9f//+73V2ix07diguLk6S9Omnn2rgwIGKi4tTXFyc3n33XUnSmjVr\n9MADD2jkyJH66KOPJEkVFRWaNm2axowZoylTpqisrEySVFRUpIcfflixsbGy2+2ex7Hb7XrooYc0\natQo7dy586LrAwAA8DWTyd8VoDGNLixOTEzUxIkTdeWVV0qSysrK9Pzzz1/UzpcvX663335bFotF\nkrR7926NHz9e48eP9/Q5evSoMjIylJOTo8rKSsXGxqp///7KzMxUz549FR8fr3Xr1mnJkiWaNWuW\nUlJSZLfbFR4erilTpqi4uFgul0tbt25VVlaWSktLNW3aNGVnZ/+Q4wEAAAA0HpL79++v9evXa+/e\nvTKbzeratWud8yZ/l4iICNntds8a5l27dungwYPKzc1VRESEkpOTtXPnTtlsNpnNZpnNZkVERGjv\n3r0qLCzU5MmTJUkDBgzQ4sWL5XA4VF1drfDwcElSTEyMCgoKFBwcrOjoaElSp06dVFtbqxMnTqhd\nu3Y/6KAAAADgx63R5RaSFBwcrBtuuEG9evW66IAsSbfffrsCAwM9t/v06aPExEStXLlS4eHhstvt\ncjqdCgkJ8fSxWCxyOBxyOByeGWiLxaLy8nI5nU5ZrdY6fcvLy+VwOOrdBwAAAPBDXFRIvlSGDBmi\n66+/3vN1cXGxrFarnE6np8+50Hx+u9PpVGhoqCwWS52+DodDoaGhDe4DAAAA+CF8GpInTZrk+VBd\nQUGBevfurcjISG3btk1VVVUqLy/X/v371aNHD9lsNuXl5UmS8vLyFBUVJavVKrPZrJKSErndbuXn\n5ysqKko2m02bNm2S2+3W4cOH5XK51LZtW18ODQAAAM1Ig2uSn3rqqe+844IFCy76QUz/9xHO1NRU\npaamKigoSB06dNDcuXNlsVg0duxYjR49Wi6XSzNmzFBwcLBiY2OVmJio0aNHKzg4WOnp6Z59zJw5\nU7W1tYqJiVFkZKQkKSoqSiNHjpTL5VJKSspF1wYAAAAYmdxut7u+DTk5OTKZTKpvs8lk0n333ef1\n4gAAAJqjmgqXPll5TJJ006QOfq7GP478Ybskqc3wbmrZremtAGhwJvn+++/3fH3ixAmdOXNGbrdb\nLpdLX3/9tU+KAwAAAPyh0VPApaen680331RNTY3atm2rI0eOqF+/frrtttt8UR8AAADgc41+cO9v\nf/ubPvroI915553KyMjQa6+9ps6dO/uiNgAAAMAvGg3JP/nJTxQSEqIePXqouLhY/fr10759+3xR\nGwAAAOAXjS63sFqtWrt2ra6//nqtXLlSHTp00PHjx31RGwAAAOAXjc4kp6WlqaysTP369VPnzp2V\nkpKixx9/3Be1AQAAAH7R6ExyQUGBJkyYIElKSkqSJL3xxhverQoAAADwowZD8muvvSaHw6FVq1bp\n0KFDnvaamhq98847GjNmjE8KBAAAAHytweUWV199tdxu9wUXE2nRooWee+45rxcGAAAA+EuDM8mD\nBw/W4MGDdddddyk8PFwHDhxQbW2trr32WpnNZl/WCAAAAPhUo2uST58+raFDh6pNmzZyu906duyY\n7Ha7brzxRl/UBwAAAPhcoyF5/vz5euGFF9SnTx9JUlFRkebNm6fs7GyvFwcAAAD4Q6OngDt9+rQn\nIEvSjTfeqMrKSq8WBQAAAPhToyG5TZs2+sc//uG5/cEHH6ht27ZeLQoAAKA5M5wXAU1QgyH5rbfe\nkiTNnTtXS5cu1a233qpbbrlFS5cuVWpqqs8KBAAAAHytwTXJK1as0H333aeuXbsqOztbTqdTbrdb\nVqvVl/UBAAAAPtfoB/fOsVgs3qwDAAAAaDIaDMn79u3T4MGD691mMpmUm5vrtaIAAAAAf2owJEdE\nRGjZsmUXXHEPAAAAaO4aDMlms1k//elPfVkLAAAA0CQ0eHYLm83myzoAAACAJqPBkDxnzhxf1gEA\nAAA0GY1eTAQAAAD4sSEkAwAAAAaEZAAAAPiNyeTvCupHSAYAAAAMCMkAAACAASEZAAAAMCAkAwAA\nAAaEZAAAAPiN2+3vCupHSAYAAAAMCMkAAACAQZC/CwAAAPgxenfnKknSTfq1nytBfQjJAAAAPmYy\nSZ8c2urvMvAdWG4BAAAAGBCSAQAAAANCMgAAAGBASAYAAAAMCMkAAACAASEZAAAAMPB6SN6xY4fi\n4uIkSV9++aViY2M1ZswYPfPMM3L/33UI16xZowceeEAjR47URx99JEmqqKjQtGnTNGbMGE2ZMkVl\nZWWSpKKiIj388MOKjY2V3W73PI7dbtdDDz2kUaNGaefOnd4eFgAAAJoxr4bk5cuX6+mnn1Z1dbUk\nacGCBZoxY4beeOMNud1u5ebm6ujRo8rIyNCqVav0yiuvKD09XVVVVcrMzFTPnj31xhtvaMSIEVqy\nZIkkKSUlRenp6crMzNTOnTtVXFys3bt3a+vWrcrKytILL7yguXPnenNYAAAAaOa8GpIjIiJkt9s9\nM8affvqp+vbtK0kaOHCgCgoK9Mknn8hms8lsNstqtSoiIkJ79+5VYWGhBg4cKEkaMGCA/vnPf8rh\ncKi6ulrh4eGSpJiYGBUUFKiwsFDR0dGSpE6dOqm2tlYnTpzw5tAAAADQjHk1JN9+++0KDAz03D4X\nliXJYrGovLxcDodDISEhddodDoccDocsFkudvk6nU1ar9aL3AQAAAPwQPr0sdUDAfzK5w+FQaGio\nrFarnE6np93pdCokJKROu9PpVGhoqCwWS52+5/ZhNpvr3QcAAADwQ/j07BbXXXedtmzZIknKy8tT\nVFSUIiMjtW3bNlVVVam8vFz79+9Xjx49ZLPZlJeXV6ev1WqV2WxWSUmJ3G638vPzFRUVJZvNpk2b\nNsntduvw4cNyuVxq27atL4cGAACAZsQnM8kmk0mSlJSUpNmzZ6u6ulrdunXT0KFDZTKZNHbsWI0e\nPVoul0szZsxQcHCwYmNjlZiYqNGjRys4OFjp6emSpNTUVM2cOVO1tbWKiYlRZGSkJCkqKkojR46U\ny+VSSkqKL4YFAACAZsrkPn+hMAAAALyu+oxLY/+/cZKkzL9k+Lka/zjyh+2SpDbDu6llt6a3AoCL\niQAAAAAGhGQAAADAgJAMAAAAGBCSAQAAAANCMgAAAGBASAYAAAAMCMkAAACAASEZAAAAMCAkAwAA\nAAaEZAAAAMCAkAwAAAAYEJIBAAAAA0IyAAAAYEBIBgAA8DGTyd8VoDGEZAAAAMCAkAwAAAAYEJIB\nAAB8zO32dwVoDCEZAAAAMCAkAwAAAAaEZAAAAMCAkAwAAAAYEJIBAAAAA0IyAAAAYEBIBgAAAAwI\nyQAAAD7GZambPkIyAACAj3ExkaaPkAwAAAC/aaqz6oRkAAAAwICQDAAAAL9pqktPCMkAAACAASEZ\nAADAx5rUMaTKAAAfM0lEQVTqOlz8ByEZAADAx5rqEgP8ByEZAAAAMCAkAwAAAAaEZAAAAMCAkAwA\nAAAYEJIBAAAAA0IyAAAAYEBIBgAAgN801XNGE5IBAAAAgyB/POh9990nq9UqSQoPD9ejjz6qpKQk\nBQQE6Nprr1VKSopMJpPWrFmj1atXKygoSFOnTtWgQYNUUVGhhIQElZWVyWKxaOHChQoLC1NRUZHS\n0tIUGBio6OhoxcfH+2NoAAAA+B6a6oVVfB6SKysrJUkZGRmetscee0wzZsxQ3759lZKSotzcXPXp\n00cZGRnKyclRZWWlYmNj1b9/f2VmZqpnz56Kj4/XunXrtGTJEs2aNUspKSmy2+0KDw/XlClTVFxc\nrOuuu87XwwMAAEAz4PPlFnv27NGZM2c0ceJEjRs3TkVFRfr000/Vt29fSdLAgQNVUFCgTz75RDab\nTWazWVarVREREdq7d68KCws1cOBASdKAAQP0z3/+Uw6HQ9XV1QoPD5ckxcTEqKCgwNdDAwAA+F7c\nbpe/S0ADfB6SW7VqpYkTJ+qVV15RamqqZs6cWWe7xWJReXm5HA6HQkJC6rQ7HA45HA5ZLJY6fZ1O\np2f5xvntAAAATdGXXx7Uv8+c0KkzZZo0aZIOHjzo75Jg4POQ3KVLF91zzz2er9u2bavjx497tjsc\nDoWGhspqtcrpdHranU6nQkJC6rQ7nU6FhobKYrHU6XtuHwAAAE3RwufT5HLXSpIOHTqk+fPn+7ki\nGPk8JOfk5GjhwoWSpCNHjsjpdCo6OlpbtmyRJOXl5SkqKkqRkZHatm2bqqqqVF5erv3796tHjx6y\n2WzKy8ur09dqtcpsNqukpERut1v5+fmKiory9dAAAAAaVVZWpkOHD9Vp+/rrr1VWVuanilAfn39w\n78EHH9RTTz2lMWPGSJIWLFigtm3bavbs2aqurla3bt00dOhQmUwmjR07VqNHj5bL5dKMGTMUHBys\n2NhYJSYmavTo0QoODlZ6erokeZZu1NbWKiYmRpGRkb4eGgAAQKOqq6u/Vzv8w+R2N9UTbwAAADQ/\nR44c0SOPPHJB+2uvvaYrr7zS9wX5yZE/bJcktb2nm1pc09bP1VyIi4kAAAAABoRkAAAA+E1TXdNA\nSAYAAAAMCMkAAACAASEZAAAAMCAkAwAAAAaEZAAAAMCAkAwAAAAYEJIBAADgNyaTvyuoHyEZAAAA\nMCAkAwAAwG+4mAgAAABwmSAkAwAAwOdW7X1Pq/a+5+8yGhTk7wIAAADw47P1m12SpEf9XEdDmEkG\nAAAADAjJAAAAgAEhGQAAAH7DeZIBAACAywQhGQAAAH7DeZIBAAAAg6a63IJTwAEAAPhYZGSk4uLi\nJEkZGRnauXOnnyuCETPJAAAAPhYXF6fevXurd+/enrD8Y8VyCwAAAMCgqS63ICQDAAD4WEZGhnbt\n2qVdu3YpIyPD3+WgHqxJBgAA8LGdO3cqISHB32U0CSy3AAAAAAxYbgEAAABcJgjJAAAA8BuWWwAA\nAADncbndLLcAAAAAJOngwYM6Uflvnag8pV+lztDBgwf9XdIFCMkAAADwqXnz5snldkmSDn9bqvnz\n5/u5ogsRkgEAAOAzZWVlOnToUJ22r7/+WmVlZX6qqH6EZAAAAPhMdXX192r3F0IyAAAAYEBIBgAA\nAAwIyQAAAIABIRkAAMCHzGbz92qHfxCSAQAAfCgsLExXdfppnbbOnTsrLCzMTxWhPoRkAAAAH0uc\n8ZQCTIGSzgbkWbNm+bkiGAX5u4BLxeVy6ZlnntFnn30ms9ms+fPn6+qrr/Z3WQAAABeIuDpCoa3a\nye12afny5f4uB/VoNjPJ//jHP1RdXa1Vq1Zp5syZWrhwob9LAgAAaIDp7H9NzSaKNTvNZia5sLBQ\nAwYMkCT16dNHu3btuiT7ddfWqvLzg3JX11y40STJXaf3eRvqZ7K2krnDTyS5VX30uNyO043so87G\netr/81hBV7STuVOHBh8bANB01LhcMsmkwICGf2agGfuRf9sjIyMVFxcnScrIyNDOnTv9XNGFmk1I\ndjgcslqtntuBgYFyuVwKCLj439BqnadV9nqON8rzaDNiiAItrc4+3r/LderdDV59vNa23rLceuNF\n93/55Ze1ceNGL1bkewMGDNCkSZMuqu+PffxS8zsGP/bxSxyD7zt+b6qqdem3Hxdr+zcn6rQPDP+J\npvftoQBT00hOPAfgbXFxcerdu7fn64SEBD9XdKFmM8dvtVrldDo9t79vQJYk1+mKS12W31WVHPZ3\nCQCA/3O6uka7j566oP2ToydVXevyQ0XwF5NJuuGnfXXDT/v6uxSfu1xOgWdyu93Gv+dflt5//32t\nX79eCxYsUFFRkRYvXqxly5Z97/24a12S+7w3qnqWQpw9Yu4LV0Kc33b+YXV7/iOZTDIFn30SuKuq\n6/aT6T9/fjk3m2A6b9sFX5r+r5th5uH8m4GBMjWRmQkA+DFwu93KPXhEHx8+Xu/2ylqX2rUwa+g1\nnSRJ7x34RqcqqmQOrH9i55ddrlS/n17htXrhH1XOWu3OPPscuWnSj2+p5O9+9zsNHTpU0tnlFmVl\nZU3uA4zNZrnFkCFDlJ+fr1GjRkmSFixY8IP2YwoMUGMT7JcqcppaBV6iPQEAmoovTjq1qHDfd/aZ\nP/AGXf+TNp7bs/I+abDv9m9O6JW7blFYq+BLViP878c+ffXggw8qdeZsfeM8pqt+0kmz587xd0kX\naDYh2WQyKTU11d9lAAB+5K5pa9EjN3RRXsnRBvu0DAqo8/U1bS0N9h3W7SoCcnP0I0/JXbp00cKY\nx3W6ukIdh1+nVl2a3oVUmk1IBgCgKTCZTLq3R2fd26PzRfW/pl2I0v/nJi9XhSaHpZCSpNbmljIF\nNc2PyDXNqgAAAPCj0FRPFd1EywIAAAD8h5AMAAAAGBCSAQAAfK1ZnID3v9PyZ+0lSYHtWvq5kvrx\nwT0AAABf43N7Cv3F1bLc0klBbVr4u5R6MZMMAAAAnzMFBTTZgCwRkgEAAHwu4P+uJ9aiDRcWa6qa\nzWWpAQAALienSirVIjRQLduw+rUpIiQDAAAABiy3AAAAAAwIyQAAAIABIRkAAAAwICQDAAAABoRk\nAAAAwICQDAAAABgQkgEAAAADQjIAAABgQEgGAAAADAjJAAAAgAEhGQAAADAgJAMAAAAGhGQAAADA\ngJAMAAAAGBCSAQAAAANCMgAAAGBASAYAAAAMCMkAAACAASEZAAAAMCAkAwAAAAaEZAAAAMCAkAwA\nAAAYEJIBAAAAA0IyAAAAYEBIBgAAAAwIyQAAAIABIRkAAAAwICQDAAAABoRkAAAAwICQDAAAABgE\n+fLB3G63Bg4cqC5dukiSbDabnnjiCRUVFSktLU2BgYGKjo5WfHy8JMlut2vDhg0KDAxUcnKyIiMj\nVVZWppkzZ6qyslIdOnTQggUL1LJlS3344YdavHixgoKC9MADD+ihhx7y5dAAAADQjPg0JH/11Vf6\n2c9+pqVLl9Zpf+aZZ/Tiiy8qPDxcU6ZMUXFxsVwul7Zu3aqsrCyVlpZq2rRpys7O1uLFi3XPPfdo\nxIgRWrZsmVatWqUxY8Zo4cKF+stf/qKWLVsqNjZWgwcPVvv27X05PAAAADQTPl1usXv3bn377bca\nO3aspkyZogMHDsjhcKiqqkrh4eGSpJiYGBUUFKiwsFDR0dGSpE6dOqm2tlZlZWUqLCzUgAEDJEkD\nBw7UP//5T33xxRe6+uqrFRISIrPZrJtvvllbt2715dAAAADQjHhtJjkrK0uvv/56nbaUlBQ9+uij\nuuOOO7R9+3YlJCRo0aJFslqtnj4Wi0UlJSVq0aKF2rZtW6fd4XDI4XAoJCTE01ZeXl6n7fz2htTU\n1Oibb765VEMFAADAZapjx44KCrowEnstJD/00EMXrAuuqKhQYGCgJOnmm2/Wt99+K4vFIqfT6enj\ncDgUGhoqs9lcp93pdCokJERWq1UOh0NhYWFyOp0KDQ2V1Wq9oG+bNm0arO2bb77R//zP/1yqoQIA\nAOAylZubq86dO1/Q7tM1yYsWLVKbNm00adIk7dmzR1dddZWsVqvMZrNKSkrUuXNn5efnKz4+XoGB\ngXr++ec1ceJElZaWyu12q127drLZbNqwYYPuu+8+5eXlKSoqSt26ddOXX36pU6dOqVWrVtq6dasm\nTpzYYB0dO3ZUbm6uD0cOAACApqhjx471tpvcbrfbV0WUl5crISFBTqdTQUFBmjNnjrp27aodO3Yo\nLS1NtbW1iomJ0eOPPy7p7Nkt8vLy5HK5lJycLJvNpuPHjysxMVFOp1NhYWFKT09Xy5YttX79ei1a\ntEgul0sPPvigRo8e7athAQAAoJnxaUgGAAAALgdcTAQAAAAwICQDAAAABoRkAAAAwICQ7AWbN2/W\nbbfdpri4OMXFxWnkyJEqLi5WWlqaSktL9eKLL2rVqlX+LvOiNDSWS7W/uLg4zwc14+LidPLkyTr9\n9+zZo0WLFkmS5+IyvnR+vWPHjtX999+v6dOnq7q6+gfv8+uvv5bNZqtzDMaOHSuXy6WkpCTt2rWr\nTv9jx44pNTVVkjR48GBVVVX9V2O6VC71c6Mp8Mb3+3Lly2ORlJSkjRs3XtA+fPjwS/5Yl9qyZcs0\nfvx4z3HavXt3g303b96sGTNmSPLP+9l/q6SkRL/+9a81cuRIjRs3To8++qj27dvn9cfdtm2b9u7d\n6/XH+b6Mr5GRI0dq5cqV32sfH3zwgb799lt9/fXXeuyxx7xUqXdt3rxZvXr10rp16+q0Dx8+XE89\n9VS998nJydGf//znC9pnzJih6upqz3vCxo0btWbNGknS6tWrVVNTc+kH8B18egq4HwuTyaT+/fsr\nPT1dkpSfn68//vGPnstxm0wmf5b3vTQ2lv92f0bGz5H26tVLvXr18tzX1+qr98knn9SHH36oO+64\n4wfv99prr1VGRka9j2d0xRVXKCUl5Qc/lrdc6udGU+Ct7/flyJfHwmQyXVbvi+fs27dPH374oWfS\nY8+ePUpMTNT//u//Nnrfy228Z86c0a9+9SvNmzdPffr0kSTt3LlTqamp9b6XXUrZ2dkaNmyYevbs\n6dXH+b6Mr5GqqioNHTpUI0aMqHORtO/y+uuvKzU1VcHBwd4s1euuueYa/e1vf9Ndd90lSdq7d68q\nKioa7N/Q8//3v/+9Z7vJZFJMTIxn20svvaT77rvvElbdOEKyF7jd7jph79SpUwoLC1NcXJxnRlCS\nvvzyS82cOVPz589Xp06dNGvWLM9M6tNPP60ePXr4vHaj+sbSvn17SWdnfufOnauuXbsqMzNTx48f\nV4cOHXTw4EH95je/UW1trUaMGKG//OUvnjcA4/6M0tLSdOTIEbVq1UoLFizQ559/rtWrV3teONLZ\nF5HD4dCcOXP07rvvasWKFQoICNDNN9+sJ5980qvjr6qq0tGjR9WmTRtt3ry5Tm0xMTHatGmTkpKS\nFBwcrEOHDuno0aNauHChrr/++ot+zGXLlunUqVNyu92aN2+eAgIC9OSTT2r16tWePpmZmSooKFB6\nerqKior0hz/8QYGBgQoPD9fcuXPrvXLQpXapnxsVFRV66qmnVFpaqqqqKs2ZM0fdu3fXrFmz5HA4\n9O2332r06NGKjY1VXFyc2rdvr1OnTumVV15RQMCl+aOYN77fmzdv1vLlyxUcHKySkhINGzZMjz32\nmEpLSzVnzhxVVFSoZcuWevbZZ/Xqq6/KZrPpjjvu0MSJEzVgwAA98sgjevrpp/XAAw/opptu8ux3\n8eLFys3NVW1trWJjYzVy5Eilp6dr9+7dOnnypHr27KkFCxboxRdf1L/+9S+dPn1a8+fPV7du3fx2\nLCRp4cKFKiwslCTdfffdGjt2rGfbmTNnlJCQoBMnTujqq69WbW3tBXVlZWVp1apVcrlcGjx4sKZN\nm6aVK1fqgw8+0JkzZ9SuXTvZ7Xa98847+stf/iK3261p06bptttuu6hxfx8hISEqLS1Vdna2BgwY\noF69eikrK0vS2ZAwf/58zzn+09LSGt1fUxqb0fr169WvXz9PQJakyMhIT0BOSkrSyZMnderUKb30\n0ktavny5tm/fLpfLpUceeURDhw6t95js3r273tfHObt27dKmTZtUXFys7t27Kzc394LjsWbNGhUW\nFio9PV2JiYnq06ePT04Da3yNOBwOBQYGas+ePUpPT1dQUJCCg4M1b948hYWFafr06XI6nTpz5oye\neOIJ1dTUaM+ePUpKStJvf/tbHTp0SJMnT9apU6c0ePBgPfbYY0pKStKwYcM0YMAA5eXl6d1339WC\nBQv01FNP6auvvlJFRYXGjh2re++91+vjbYjJZFKvXr108OBBORwOWa1Wvf322xo+fLhKS0v19ttv\n6/XXX1dwcLAiIiL07LPPyu12a9OmTdqwYYNOnz6t+Ph4/fznP9fgwYP13nvvSTp7fHNycnTgwAFF\nRETo2LFjeuKJJ9S9e3d16NBBY8aM0alTpzR+/Hjl5OR4ZWwst/CSjz/+WHFxcRo1apRmzZqlYcOG\n1dn+xRdfaObMmUpPT1ePHj20dOlS3XbbbXr99dc1d+5cPfPMM/4pvB7njyU5OfmCsUj/+a1w2LBh\nys3Nlcvl0saNG9WvX78LfkM+t79z/87/k8uIESP0+uuv6+c//7mWLVt2wW+bzz33nGprazVnzhyd\nPHlSdrtdK1as0JtvvqkjR46ooKDAa+MfNmyYHnjgAd1+++3q169fg/1NJpM6d+6sV155RXFxcXXC\n7Tn79u2rcwyee+45z7aYmBitWLFCEydO1PPPP3/BMcjIyND27dv1pz/9SWazWbNnz5bdbldGRoau\nvPJKvfXWW5du8I24lM+NVatWKTw8XKtWrdILL7ygHTt26KuvvtLdd9+tV155RS+//LJee+01T/+7\n775br7766iULyMYxXcrvd2lpqeeH+csvvyzp7HM5Li5OGRkZmjBhgn73u99pyJAhysvLU2VlpcrL\ny/Xxxx9Lkj799NM6AfnTTz/Vxo0blZ2draysLM8PpzZt2ujPf/6zsrOztWPHDh05ckQmk0ndu3fX\nqlWrLjoge+tYrF+/XocOHdKaNWv05ptv6q9//as+++wzSWd/IK5atUrdu3fXG2+8ocmTJ1+wtOP4\n8eN6+eWXlZmZqbfeekvV1dVyOBw6efKkXnvtNa1Zs0Y1NTX65JNPZDKZ1KZNG7355pteC5FXXnml\nlixZosLCQo0aNUp33nmnPvroI0nS7NmzlZKSooyMDA0cOFDLly//ztnjpjY2o6+//lpXX3215/av\nfvUrxcXFaejQoZ7n2W233abMzEz961//0qFDh/Tmm29qxYoVWrp0qcrLyxs8JvW9Ps7p3bu3BgwY\noISEBHXs2PGC47Fr1y6NGTNGFRUVSkpKUk1NjU+vk3DuNTJu3DglJCTo6aef1oIFCzzjHD16tBYs\nWKCSkhKdPHlSS5Ys0e9//3vV1NTo5z//uXr16qXnnntOQUFBqqiokN1u16pVq/TRRx9pz549df7K\ncu7/TqdT27Ztk91u18svv+y5krG/3X777Xr//fclSZ988oluuukmnThxQna7Xa+//rrefPNNhYaG\navXq1TKZTAoLC/M8P+bOnVvvBNq5MT/44IO64oor9MILL+jBBx/0/LXmr3/9q+655x6vjYmZZC/p\n16+fZ5blwIEDGjlypLp27erZvnHjRgUFBXmeAJ999pk2b97sWdPz73//2/dFN8A4llGjRikvL69O\nH5fLJUmyWCzq27evNm7cqJycHMXHx3/n/oxuueUWSdKNN96oDRs21Nl27NgxffbZZ5436q+++kpl\nZWWaNGmSpLNvHCUlJf/FSOt3rt6TJ09qwoQJ+ulPf1pvv/Nf4Nddd52ksz9Ez82ana979+4N/omy\nb9++ks4eg+eff/6C7QUFBZ7nzvHjx3X06FFNnz5dklRZWenTtY6X8rlx4MABDRw4UJIUERGhcePG\n6ciRI1qxYoXef/99Wa3WOuvRzn89eWNMl/L73aNHDwUEBKhVq1Zq2bKlpLOv+XMzbpJkNpt18803\na/78+fr44491++236+9//7u2bdumG2+8sc7+Dh48qMjISJlMJpnNZiUmJqq6ulrHjx/Xk08+qdat\nW+v06dOe49WlS5cmcSy++OIL3XzzzZKkoKAg9enTp86a1vOfA9dcc43CwsLq3L+kpETXXnut55er\nc+t7zWazZsyYodatW+vIkSOecXvrOXLOV199pZCQEM8s8a5duzR58mTdeuut2r9/v2eyo6amptHv\nQVMbm1GnTp3qfF5i8eLFkqSRI0deUNNnn32m3bt3Ky4uTpJUW1urQ4cO6Ysvvqj3mNT3+qjPued7\nfcdj8uTJGjVqlE8nCaT6f549/fTTnmWCUVFRSk9PV/fu3TVq1Cg9+eSTqqmp8Rybc0wmkyIjI9Wi\nRQtJ0g033KCDBw/W6XP+e2lycrJmz54th8Ph1ZB4Mc69/ocNG6ZnnnlG4eHhioqK8mzr3r27Wrdu\nLensz7dNmzapT58+np917du3l9Vq1YkTJy7q8f7/9u4upKn/D+D4e66QXPOptCyX6elCohrRRWAF\nZSzBiiKaaD4kWKMugoo0pwsstwrmCsJYgmK0m54ISqIu6qagqEElkVi0LoxA20UPsBxT5/9CdnDT\nXz/6u/3s4vO6ER/Ow/dzjud8vp/zOWowGNDpdPh8Pnp6ehLa4ieV5P/AggULplQQamtrsVqtNDY2\nEg6HURSF2tpaPB4PbW1t7N69e5b29vcij9MBkpOT+fr1KzBR2YooKyvj1q1bfPv27Y9bRt68eQOA\n1+tVLzIRCxcupKuri48fP/L06VNyc3PJycnh6tWr6ow9NpmIp/T0dJxOJzabDb/fT3JyMn6/H4Av\nX77w48ePuGynt7cXmIjBdD14breb1NRUrl+/TkZGBosXL8btduPxeLBYLBQVFcVlP/7UTM8NRVF4\n+/YtMJEw1NfX093drU4WSkpKopKxeFeQY8XzeE9XQVQUhRMnTuDxeDh16hSlpaVoNBpWrVpFZ2cn\nGzduZN26dTidTrZt2xa1bEFBAX19fYyPjzMyMkJdXR1PnjxhcHAQl8vFsWPHCAaDarxmGqt4xUJR\nFDVxHhkZ4fXr11HJ4+TvDwwMTLlpLlu2jE+fPqkvrx49ehSv18vjx4+5ePEiNpuNcDgct3H/m/fv\n33P69Gm14r18+XJSU1PRarUUFBTgdDrxeDwcP36c4uLi367rbxtbrK1bt/Ls2TP1+gQTLYODg4NT\nKp2KorB+/Xo8Hg/d3d2UlJRgMBjIz8+fNib/1p+t0WgYGxujv79/2niEQiHOnTtHa2srLS0ts/6i\nbXZ2tvqiodfrJT8/nw8fPhAIBOjo6FD3FSaOY2Qc/f39hEIhRkdH6e3tVSdNsddSv9/Pu3fvaG9v\np6OjA6fTqSbQs8lgMDA8PIzH44lq//D5fAwPDwMT7WeRyVTkfj80NEQwGJwyKY4ViRWA2Wzm8uXL\n5OTkkJ6enojhAFJJTgiNRqM+gtFqtQQCARobG6fMcIuKinj48CGdnZ0cOnSI5uZmbty4QSAQ4MiR\nI7O099GmG4vVaiU5OVntsc7JyWHRokXqMmvWrGFgYICqqqrfrm/y1yLVtJ6eHi5dukRaWhrnz5+n\nr69vygXU4XBw4MABbt68SW1tLZWVlYTDYXJzc9mxY0fcxz95+4qiUF1djcPhwOVyodfrKSsrQ1EU\ncnNzo5ab/DFWpN1i8s9HqlHPnz/nzp07zJ07l7NnzzIyMjJlPTabDbPZTFFREc3NzVgsFsLhMHq9\nPqp1I5HifW6Ul5djtVqprq5mbGxM7UW22+08evSIFStWoNPpEvrXPRJxvP/ppbSGhgZaWloIhUIE\ng0FsNhsAJpOJpqYmCgsL2bBhA3fv3lWfsEQUFhayadMmKioqCIfD7Nu3D6PRiNvtpqamhqysLIxG\no3pz/X9eEktELDZv3syLFy8oLy8nFApRWlqq9ixrNBoqKiqwWq1UVFSwdOlS0tLSopbPzMzk4MGD\nVFdXo9FoKC4uZvXq1cybN4/KykoyMjJYuXLljMb9J0wmEz6fj71795KSksL4+DgNDQ3Mnz+flpYW\n6uvrGRsbIykpCYfDobYlTOdvG1uslJQUrly5gsvlwu/3Mzo6ilarpampiSVLlkTtU3FxMS9fvqSy\nspJfv35hMpnQ6XR/HJMIo9HIhQsXcLlcU+IxNDSEy+Viy5YtmM1m9fPGxsaEx+Sffrftdrvadztn\nzhwcDgfZ2dm0t7fz4MEDwuGw+vRv7dq1nDx5kjNnzqDX6zl8+DA/f/5k165dKIqC2WymqamJnp4e\ndUKZlZWF3++nvLwcrVZLXV3dfz5pmmxyHEpLS7l37x55eXkMDAyQmZnJzp07qampISkpiby8POrr\n67l//z7fv39n//79DA8PY7fb1XVNt36YqMpbLBauXbuGyWSitbWVtra2xI5N/i21iLfITburqwud\nTjfbuyP+InJuCCGEmKlgMEhVVRW3b99O6Hak3ULE1efPn9mzZw/bt2+XJEhEkXNDCCHETL169Qqz\n2YzFYkn4tqSSLIQQQgghRAypJAshhBBCCBFDkmQhhBBCCCFiSJIshBBCCCFEDEmShRBCCCGEiCFJ\nshBCCCGEEDEkSRZCCCGEECLG/wA9QLsXle+alwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115e774e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EZAAAAMCEkAwAAACYEJIBAAAAE0IyAAAAYEJIBgAAAEwIyQAAAIAJIRkAAAAwISQDAAAA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\ngBgkC4IgCIIgCEKA/wFEQsMfVmLylwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116406550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JIRkAAAAwISQDAAAAJoRkAAAAwISQDAAAAJgQkgEAAAATQjIAAABgQkgGAAAATAjJAAAA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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115ea3b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qldVqVWRkpPbu3avc3FwNGzZMkhQfH685c+bI4XDI5XIpIiJCkhQXF6ecnBwFBwerS5cu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\nIYQQQgghCvwERhDp7vdksXgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116adaf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xrvo6ydeCn9//MrnNZlNwcLCsVqvsdru73W63KygoqFy73W5XcHCwLBZLub6X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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116c736d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphics.graph_by_cost(te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r9PT089rYnXfeqZycHMXGxmrdunWKiYlRbGysnn32WXk8HtXX16umpka9evVSXFycKioq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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1164a5c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphics.graph_choices(te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JfSFEh+ajVTFxhJWJI6ycOl9JWraTDbuKeH/jBZZ+foHYAf6kxtuIHeCPWiXd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\nf/L3GOZqrlTZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1128d0a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphics.graph_costs_curve(te)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can change some assumptions and see how the model reacts.\n",
    "\n",
    "Let's change the cost of the old car to 0.5 CHF/km"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of actual trips: 29910\n",
      "Bikes can be used on this many trips: 11193\n",
      "EBikes can be used on this many trips: 16274\n"
     ]
    },
    {
     "data": {
      "image/png": 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dCgAA4Ic6aeQ0NzcrOzu7PWYBAAA4bU76EvJ///d/15o1a+Tz+dpjHgAAgNPipEdyXn/9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\n6CUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1129c48d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "costs[\"old car km\"] = 0.5\n",
    "\n",
    "te = TransportEvaluator(costs, SystemSetup())\n",
    "\n",
    "graphics.graph_choices(te)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's assume people travel more (and switch the old car cost back to its previous value):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of actual trips: 29935\n",
      "Bikes can be used on this many trips: 8048\n",
      "EBikes can be used on this many trips: 14017\n"
     ]
    },
    {
     "data": {
      "image/png": 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1ao0ePbrFBgIAAGgOl/yCzvj4eD311FM6ffp0o+Xz5s3z21AAAACX65KRM2vWLCUkJCgh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112825860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "avg_distance = 75\n",
    "costs[\"old car km\"] = 0.3\n",
    "\n",
    "te = TransportEvaluator(costs, SystemSetup())\n",
    "\n",
    "graphics.graph_choices(te)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We return to our initial assumptions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of actual trips: 29996\n",
      "Bikes can be used on this many trips: 10942\n",
      "EBikes can be used on this many trips: 16318\n"
     ]
    }
   ],
   "source": [
    "avg_distance = 36.7\n",
    "te = TransportEvaluator(costs, SystemSetup())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we can finally do some optimization!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     jac: array([ 0.])\n",
       "       x: array([ 5000.00000441])\n",
       " success: True\n",
       "     nit: 1\n",
       "    nfev: 26\n",
       "  status: 0\n",
       " message: b'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'\n",
       "     fun: array([  2.89663053e+08])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "minimize(te, 5000., bounds=[[0, 1e6]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can play around here with entering bounds and or constraints. \n",
    "\n",
    "One could also edit the `__call__` method to ignore values less than zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning: Method Powell cannot handle constraints nor bounds.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "       x: array(6002.587928961546)\n",
       " success: True\n",
       "     nit: 1\n",
       "   direc: array([[ 1.]])\n",
       "    nfev: 13\n",
       "  status: 0\n",
       " message: 'Optimization terminated successfully.'\n",
       "     fun: array(291329793.3406154)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(te, 6000., method=\"Powell\", bounds=[[0, 1e6]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Play around with this bit for a while. See the [SciPy optimize docs](http://docs.scipy.org/doc/scipy/reference/optimize.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the next step, we want to also consider environmental impacts. We will do this in a simplified fashion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class EnvironmentalImpacts(object):\n",
    "    def __init__(self):\n",
    "        self.db = Database(\"ecoinvent 2.2\")\n",
    "        self.get_datasets()\n",
    "        self.method = ('IPCC 2013', 'climate change', 'GWP 100a')\n",
    "        self.lca = LCA({self.bike: 1}, method=self.method)\n",
    "        self.lca.lci(factorize=True)\n",
    "        self.lca.lcia()\n",
    "\n",
    "    def get_datasets(self):\n",
    "        self.bike = self.db.search(\"transport, bicycle\")[0]\n",
    "        assert self.bike['name'] == 'transport, bicycle'\n",
    "\n",
    "        self.ebike = self.db.search(\"transport, electric bicycle\")[0]\n",
    "        assert self.ebike['name'] == 'transport, electric bicycle'\n",
    "\n",
    "        self.euro3 = self.db.search(\"transport passenger petrol euro3\")[0]\n",
    "        assert self.euro3['name'] == 'transport, passenger car, petrol, EURO3'\n",
    "\n",
    "        self.euro5 = self.db.search(\"transport passenger petrol euro5\")[0]\n",
    "        assert self.euro5['name'] == 'transport, passenger car, petrol, EURO5'\n",
    "\n",
    "        self.train = self.db.search(\"passenger train sbb\")[0]\n",
    "        assert self.train['name'] == 'operation, average train, SBB mix'\n",
    "\n",
    "    def evaluate_for_method(self, te, premium, method=None):\n",
    "        if method is not None:\n",
    "            self.lca.method = method\n",
    "            self.lca.load_lcia_data()\n",
    "\n",
    "        mr, costs = te.best_model_result(premium)\n",
    "\n",
    "        total = 0\n",
    "\n",
    "        # print(\"Bike distances:\", (mr.bike_used * te.distances).sum())\n",
    "        # print(\"Ebike distances:\", (mr.ebike_used * te.distances).sum())\n",
    "        # print(\"New car distances:\", (mr.new_car_used * te.distances).sum())\n",
    "        # print(\"Old car distances:\", (mr.old_car_used * te.distances).sum())\n",
    "        # print(\"Public transport distances:\", (mr.ov_used * te.distances).sum())\n",
    "        # print(\"Car sharing distances:\", (mr.car_sharing_used * te.distances).sum())\n",
    "        # print(\"Total distance:\", (mr.bike_used + mr.ebike_used + mr.new_car_used + mr.old_car_used + mr.ov_used + mr.car_sharing_used).sum())\n",
    "\n",
    "        self.lca.redo_lcia({self.bike: (mr.bike_used * te.distances).sum()})\n",
    "        total += self.lca.score\n",
    "\n",
    "        self.lca.redo_lcia({self.ebike: (mr.ebike_used * te.distances).sum()})\n",
    "        total += self.lca.score\n",
    "\n",
    "\n",
    "        self.lca.redo_lcia({self.euro5: (mr.new_car_used * te.distances).sum()})\n",
    "        total += self.lca.score\n",
    "\n",
    "\n",
    "        self.lca.redo_lcia({self.euro5: (mr.car_sharing_used * te.distances).sum()})\n",
    "        total += self.lca.score\n",
    "\n",
    "        self.lca.redo_lcia({self.euro3: (mr.old_car_used * te.distances).sum()})\n",
    "        total += self.lca.score\n",
    "\n",
    "        self.lca.redo_lcia({self.train: (mr.ov_used * te.distances).sum()})\n",
    "        total += self.lca.score\n",
    "\n",
    "        return total\n",
    "\n",
    "env_impacts = EnvironmentalImpacts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get some LCIA methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gwp = ('IPCC 2013', 'climate change', 'GWP 100a')\n",
    "resources = ('ReCiPe Endpoint (E,A)', 'resources', 'total')\n",
    "metals = ('ReCiPe Endpoint (E,A)', 'resources', 'metal depletion')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11609ac88>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6vTz55JOsXr2aFStWsHDhQgDy8/NJSkoiLy+PsWPHsmzZMgDmzJlDdnY2+fn5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\nFPgiIiIhQIEvIiISAv4PSBMF+pam+KsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11299fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0, 10000, 100)\n",
    "ys = [env_impacts.evaluate_for_method(te, x) for x in xs]\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11e0ee1d0>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TWbduXeNvkQSEjm1DmD+hB9cPaschVzVpT+3gb6/vo9Zn+Hs0EZEmrd6w2+12\nHA4HbrebyZMnM2XKFEwmE0VFRQwdOpTy8nLi4uLo2bMnGzZswOPxcPjwYTZu3MixY8dwu904HA4A\nHA4HLpeOuuTns1pMJF/ajgUTexITFczLH5aQkb0bb43P36OJiDRZP3nyXHFxMWPHjiUpKYkrrrgC\ngOjoaN5++21GjBhBRkYG3bp1Izk5mZtvvpn09HT69OlD69atcTqdeDweADweD+Hh4Y27NRKQesbY\nefTWnvTu4uCjzUeY9exOKqpq/T2WiEiTVG/YS0tLGTduHKmpqQwbNgyACRMmsGfPHuD4UbjZbKas\nrAy32012djazZ89mx44d9O3bl/j4eHJzcwHIzc0lISGhkTdHApUjxEL6H7vRv1c4n+9wM/1v+ZS7\na/w9lohIk1PvqcZLlizB5XKRmZlJZmYmAFOmTGH69OnYbDbsdjvp6elERkaya9curr32WsxmM6mp\nqTidTkaNGsW0adMYPXo0QUFBzJ8//5RslASmYJuZvyR34bF/7uWdz8q468nt3HdjV6JPC/b3aCIi\nTYbJMIwmczZSYWEhgwYNYvXq1cTExPh7HGmiDMPg6TeLeSn3IPZgMynDOnJxn9b+HktE5BdrjO5p\ngRppdkwmEzf9PpqpwzvhMyAjew+PvVxApVcn1YmIKOzSbF0aH8nCST3p2j6UNz8tY3LmNnbvP+bv\nsURE/Ephl2YtJiqEBRN7cNWFbSg4WMmdi7ezebfb32OJiPiNwi7NXpDNzMSrYpg+KhZvjY97ntmp\nuItIi6WwS8C4uE9rZozqrLiLSIumsEtAuah3hOIuIi2awi4B5wdx36W4i0jLobBLQLqodwQzRh+P\n+1+e2UHedt2nQERaBoVdAtZFZ0Vwz5gu+AyY9fedrNtyxN8jiYg0OoVdAtr5Z7Tivhu7YrWYSM/a\nxfufH/b3SCIijUphl4DXt1sYc8d1IzTIzIMv7uHlDw/iqdTd4UQkMCns0iL0inWQcUt3wuwW/vZ6\nESPTN5P21A7+9XEJB8u9/h5PRKTB1Ht3N5FA0j3azsJJcbzzWRnrvz7CxnwXG/NdLM7Zx2X9Iplw\nZQfswRZ/jykiclIUdmlR2kYEkTyoHcmD2lFyxMv6r4/yxielvPNZGV/ucvPn62LpFevw95giIr+a\n3oqXFiuqVRBD+7fh0Vt7ct3FbTlw2Mtdf93O8+8WU1vbZO5mLCLyiyjs0uLZrGb+ODiajJu70ybc\nRtbqA9xbbzwGAAAWz0lEQVT15HYOHNZn7yLS/CjsIt/q09VJZkocvz0ngm/2VjBp4Vb+rWvfRaSZ\nUdhFvscZauXPI2K5Y1hHvNU+7l22i7+u2kd1jc/fo4mI/CwKu8h/MZlMXH7eaTx6W086RgXzz7Ul\npD6ZT4kuixORZkBhF/kRXdqF8thtPRl0bmu2FlYwY+kOyt3V/h5LRKReCrtIPUKDLUwd3onrLm7L\nvkNV/OWZnVq1TkSaNIVd5CeYTCZuvLw9g887jR1Fx7j3uZ1UVeszdxFpmhR2kZ/BZDIxKSmGi3q3\n4stdHjKyd+tadxFpkhR2kZ/JYjbx5xGxnNvdyb+/Psr8lwp05C4iTY7CLvILBFnNzLy+C3Exdt77\n/DC3Pb6Vr3a7/T2WiEgdhV3kFwoNtpBxS3f+cFEURYeqSP1rPn9dtY9Kr47eRcT/FHaRXyEkyMz4\noR14aHx3oiOPX+t+2+Pf8MVOHb2LiH8p7CIn4azOThalxDFsQBTFZV6m/S2fR14q4Iinxt+jiUgL\npbCLnKSQIDO3XNGBBRN70LV9KO98Vsb4R77mnc/KMAydOS8ip5bCLtJA4jo6ePy2ntwyJBpvjcEj\nLxXw57/lk7+vwt+jiUgLYq3vwerqatLS0igqKsLr9TJx4kQ6derEzJkzAejcuTPp6elYLBb+8Y9/\nsHLlSkwmExMmTODSSy+lsrKS1NRUysrKcDgcZGRkEBkZeUo2TMQfLBYTwxLbMuDsCJbkFLJuy1Fu\nX7SNS/q2Zuzl7WkbEeTvEUUkwNV7xJ6Tk0NkZCRZWVksXbqU++67j0cffZSpU6eSnZ0NwHvvvYfH\n4+Gpp55i+fLlPP3008ydOxeA7Oxs4uLiyMrKIikpicWLFzf+Fok0AW0jgrhnTFfm3tSNru1DWfP5\nYW6e/zVPv1mkJWlFpFHVG/bBgweTkpICgM/nw2q1snDhQhISEvB6vZSUlBAWFobJZAKgoqICj8eD\n2Xz8ZfPy8hg4cCAAiYmJrFu3rjG3RaTJObd7GAsn9eSu4Z1o5bCy4oODpCzayo4ivT0vIo2j3rDb\n7XYcDgdut5vJkyczZcoUTCYTRUVFXHnllZSXlxMXF4fdbmfo0KEMGTKEa665hjFjxgDgdrtxOp0A\nOBwOXC5X42+RSBNjNpsYFB/J0qm9uHZgW4oOeZmyeDuvry/VyXUi0uB+8uS54uJixo4dS1JSEldc\ncQUA0dHRvPXWW4wYMYKMjAw2btzIxo0bWbNmDe+//z7vvvsuX3zxBU6nE7f7+HW9Ho+H8PDwxt0a\nkSYs2Gbmpt9Hc+/YroTYzCx8pZAHl++hokpvzYtIw6k37KWlpYwbN47U1FSGDRsGwIQJE9izZw9w\n/CjcbDZTUVFBSEgIQUFBBAUFERYWhsvlIj4+ntzcXAByc3NJSEho5M0RafrOPyOcRSlx9Opk5/1N\n5dwy/2seeGE3r64t4ZsCD94arWAnIr9evWfFL1myBJfLRWZmJpmZmQBMmTKF6dOnY7PZsNvtpKen\n06ZNG9auXcvw4cOxWCz069ePiy66iH79+jFt2jRGjx5NUFAQ8+fPPyUbJdLUtY0I4sHxPVj2TjGv\nf3KI9zeV8/6mcgCsFhNxHe306eqkT1cnvTo5CLbpylQR+XlMRhP6kK+wsJBBgwaxevVqYmJi/D2O\nyClhGAb7SqvYureCrXsr+LrAw87iY/i+/ZNptZjo283JuMHRdGkf6t9hRaRBNUb36j1iF5HGZzKZ\niIkKISYqhEHxx9d5cB+r4avdHr7Y6ebzHW42bHORl7+Vqy+M4vrL2mEPtvh5ahFpqhR2kSbIGWrl\ngl6tuKBXKwA2bD3KE/8q5J9rS8j9spzxV0STeHZE3aWmIiLf0Qd3Is1AQlw4S+44g+sHteNoRQ3z\nsvcw+7ldlLur/T2aiDQxCrtIMxFkM5N8aTuWTD6Dc7o5+eSbo0x8bCuffHPE36OJSBOisIs0M9Ft\ngpk7rhu3DInGfayWWX/fxaJX9lLp1WVyIqKwizRLZvPxm808dltPYk8P4bX1h7h90Va27tVStSIt\nncIu0ox1bR/K47f1JOmiKApLqrhzyTay3t1PTW2TuYpVRE4xhV2kmQuymfnT0A7MvakbkWE2nl+9\nn6lLtrP3YKW/RxMRP1DYRQLEud3DWDw5jkHntmZbYQWTFm7lmTeL2F9W5e/RROQU0nXsIgHEGWrl\nruti6X9mKxa9UsiLHxxkRe5B+vUIY8gFbTg/LhyLRde+iwQyhV0kAA3oHcF5ceF8+GU5b3xyiA3b\nXGzY5qJNKxtD+7dh8Hmn0cqhP/4igUh/skUCVLDNzKXxkVwaH8mu/cd4ff0hVm8s49m3islavZ//\n69uaqy5sQ7dou79HFZEGpM/YRVqALu1Cue3qGJZNP4sJQzsQ1crG2xvKmLRwG4+uLKBWZ9GLBAwd\nsYu0II4QC1dfFMWVF7ZhwzYXz71TzFsbyjhaUcP0kZ0J0u1hRZo9/SkWaYHMZhPnnxHOg+O707eb\nk3VbjvKXZ3bgqaz192gicpIUdpEWzB5s4d4bu3JR71Z8ucvD9L/l68YyIs2cwi7SwgVZzcwY1ZnB\n50WSX3SMO57YTvZ7+ynQAjcizZI+YxcRLGYTKX/oSGunjRc/OMBzb+/nubf30zEqmN+cFcGl8a2J\niQrx95gi8jMo7CICgMlk4obftecPiVF8+s1R1n51hM+2HWX5+wd48YMD9O8VzrUDT+fMWIe/RxWR\neijsInKCsFArl5wbySXnRlLp9bH+myP888MS1m05yrotRzkz1sG1A9vSv1c4JpNWsRNpahR2EflR\nIUFmLu7TmoFnR7B5t4eXcg/yyTdHuW/ZLnp0COWGy9rTr2eYAi/ShCjsIvKTTCYTZ3dxcnYXJ3sO\nVJK9Zj8ffFHOzGd3clZnB2N/156zuzj9PaaIoLPiReQXij09hOmjOpOZEscFvcL5areHP/81n7uf\n3kH+vgp/jyfS4umIXUR+la7tQ5l9Q1e+LvDw97eLydvuIm+7i4F9Ihh7WXui2wT7e0SRFklhF5GT\n0quTg4ybu7Mx38UzbxaR+0U5azeX8399W9Ork4OYqBA6tQ2mlcOqz+JFTgGFXUQaxLndw+h7W08+\n2nyEv79dzLt5h3k373Dd4+F2C53bhdK9Qyg9ou107xBK9GnBmM2KvUhDUthFpMGYTCYSz47gN2e2\nIr+ogoKDVewtqWTvwUoKDlby5S43X+x01z0/JMhM24gg2kbYjv+7dRCd2obQvUMobcJtOsIX+RUU\ndhFpcBaLibiODuI6nriYTUVVLTuKjpG/r4Lt+46xe/8xSsqr/+fytRFOK92jQ+kWHUrbiCDatAoi\nqpWNNq1sOEMtir7Ij1DYReSUsQdb6i6b+z5PZS0l5V4OHPayc/8x8vcdj/+GbS42bHP94HXCQi3E\ntguhy+mhxLYLIfb0EGLahNDKoeCLKOwi4neOEAuOdqF0bhfKBb1a1X293F3DngPHKD1STenRakqP\nVHOw3Mu+kiq+2u1h8y7PCa/jDLHQISqYmDbBtGllI8xuJdxuIcxupbXTSoc2wThD9deeBDb9Fy4i\nTVaE00qEM+x/Plbp9bG3pJLd+4+x50Al+0qrKCytIn9fBVv3/vj19K3DrHSMCqFjVDDn9gijf69W\nWHQCnwSQesNeXV1NWloaRUVFeL1eJk6cSKdOnZg5cyYAnTt3Jj09nW3btjF37ty679u0aRNPPPEE\nCQkJpKamUlZWhsPhICMjg8jIyMbdIhFpEUKCzPToYKdHB/sJX6+tNThw2EuZq5qjFTW4jtXiqqil\n7Gj18RP5Sqr4Yufxk/heW3+I6NOCGJbYlkvjIwm2ac0uaf7qDXtOTg6RkZE89NBDHDlyhKuvvpre\nvXszdepUEhISmDFjBu+99x6XXnopy5YtA+CNN96gXbt2DBgwgGeeeYa4uDgmTZrE66+/zuLFi7n7\n7rtPyYaJSMtksZiIbhNc7wI5lV4few4c441PDrF642EWvVLIc+8U8/vzTqNDm2DC7dbj/zisREXY\nCLIq+NJ81Bv2wYMHc/nllwPg8/mwWq0sXLgQk8mE1+ulpKSEsLD/vE1WUVHBokWLyMrKAiAvL49b\nbrkFgMTERJ544onG2g4RkZ8tJMhcd9b+Db9rz78+LuW19aUsf//gD55rs5qIi7FzVmcHZ3V2Ehdj\nJ8h24lv3FrMJq8WkE/ekSag37Hb78be43G43kydPZsqUKZhMJoqKivjjH/9IWFgYcXFxdc9/6aWX\n+P3vf09ERETd9zmdx89+dTgcuFw/PLtVRMSfIsNs3Hh5e0b8ti1f7HRT7qnBVVHLEU8NRzw17Cw+\nxpY9Hjbv9gA/DP93zCYIspkJspkIspoJtpkJ/t7//u6xkG//d7DNTGiwGXuwpe7fQTYTNosJi9mE\nzWqq+4HBYj7+j9lswmL+7vczgQm+/Zc0UyVHvA3+mj958lxxcTGTJk0iOTmZK664AoDo6Gjeeust\nVqxYQUZGBhkZGQCsWrWKhQsX1n2v0+nE7T6+GIXH4yE8PLzBN0BEpCGEBltOOCP/+zyVtXxTcDzu\nu/Yfw+f7z2OGYVDrM6iqNqiu8VFVbeCt9lFRVUu5+/iva2qNU7QV0txUe378h8Vfq96wl5aWMm7c\nOGbNmkX//v0BmDBhAjNmzCA2NhaHw4HZfPzHR5fLhdfr5fTTT6/7/vj4eHJzc+nTpw+5ubkkJCQ0\n+AaIiDQ2R4iFfj3D6dfz1x2c1NYaeL+NflW1D2+1j6pqH8e8PioqazlWdfwHAW/N8R8Cjv/jo6bW\noNZ3/PtrfQY1PuPbHyoMDAN8+nmh2XMd9vKPtxr2NesN+5IlS3C5XGRmZpKZmQnAlClTmD59Ojab\nDbvdTnp6OgC7du0iJibmhO8fNWoU06ZNY/To0QQFBTF//vyGnV5EpBmwWEyEWiyE6oZ38l8KC838\n4+GGfU2TYRhN5me+wsJCBg0axOrVq3/wQ4KIiEigaYzu6RoOERGRAKKwi4iIBBCFXUREJIAo7CIi\nIgFEYRcREQkgCruIiEgAUdhFREQCiMIuIiISQBR2ERGRAKKwi4iIBBCFXUREJIAo7CIiIgFEYRcR\nEQkgCruIiEgAUdhFREQCiMIuIiISQBR2ERGRAKKwi4iIBBCFXUREJIAo7CIiIgFEYRcREQkgCruI\niEgAUdhFREQCiMIuIiISQBR2ERGRAKKwi4iIBBCFXUREJIAo7CIiIgFEYRcREQkgCruIiEgAsdb3\nYHV1NWlpaRQVFeH1epk4cSKdOnVi5syZAHTu3Jn09HQsFgsffPABTzzxBABnn302f/nLX6isrCQ1\nNZWysjIcDgcZGRlERkY2/laJiIi0UPUesefk5BAZGUlWVhZLly7lvvvu49FHH2Xq1KlkZ2cD8N57\n7+F2u3n44Yd58sknWb58OW3btqWsrIzs7Gzi4uLIysoiKSmJxYsXn5KNEhERaanqPWIfPHgwl19+\nOQA+nw+r1crChQsxmUx4vV5KSkoICwtj48aN9OzZk4yMDPbu3cvw4cOJjIwkLy+PW265BYDExMS6\nI3oRERFpHPWG3W63A+B2u5k8eTJTpkzBZDJRVFTEjTfeSHh4OHFxceTm5rJ+/XpeffVVQkNDSU5O\npm/fvrjdbpxOJwAOhwOXy1XvMLW1tQDs37+/IbZNRESkSfuud9/1ryHUG3aA4uJiJk2aRHJyMldc\ncQUA0dHRvP3226xYsYKMjAyuuOIKevfuzWmnnQZAQkICX3/9NU6nE7fbDYDH4yE8PLze36ukpASA\n5OTkk9ooERGR5qSkpITY2NgGea16w15aWsq4ceOYNWsW/fv3B2DChAnMmDGD2NhYHA4HZrOZs846\ni+3bt3P48GHCwsLYtGkTI0aMID4+ntzcXPr06UNubi4JCQn1DtO7d2+ysrKIiorCYrE0yAaKiIg0\nVbW1tZSUlNC7d+8Ge02TYRjGjz2Ynp7Om2++SZcuXeq+NmXKFB566CFsNht2u5309HTatGnD66+/\nztKlSwEYMmQIN998M5WVlUybNo2SkhKCgoKYP39+3VG9iIiINLx6wy4iIiLNixaoERERCSAKu4iI\nSABR2EVERAKIwi4iIhJAfvI69lPB5/Mxe/Zstm3bhs1m4/7776dTp07+HqtZ+V/r+nfr1o3p06dj\nNpvp0aMHs2bNwmQy8eKLL7J8+XKsVisTJ07kt7/9rdb1/wUOHTrEsGHDePbZZzGbzdrHjeDJJ5/k\nvffeo7q6muuvv574+Hjt5wbk8/m4++672b17N2azmTlz5mCxWLSPG8imTZt4+OGHWbZsGXv27Dnp\n/fr5558zd+5cLBYLF110EZMmTap/AKMJeOutt4zp06cbhmEYn3/+uTFx4kQ/T9T8rFy50pg7d65h\nGIZRXl5uXHzxxcaECROMTz75xDAMw7jnnnuMd955xzh48KAxdOhQw+v1Gi6Xyxg6dKhRVVVlPP30\n08bChQsNwzCM1157zUhPT/fbtjRlXq/XuPXWW43LL7/c2LFjh/GnP/1J+7iB/fvf/zb+9Kc/GYZh\nGB6Px3jsscf033ID++CDD4zJkycbhmEYa9euNSZNmqR93ED++te/GkOHDjVGjBhhGIbRIH9HXHXV\nVUZBQYFhGIZxyy23GFu2bKl3hibxVnxeXh6JiYkAnHPOOWzevNnPEzU/gwcPJiUlBfjPuv5btmzh\nvPPOA2DgwIF8/PHHfPnll8THx2Oz2XA6ncTGxrJ161by8vIYOHAgcHxd/3Xr1vltW5qyBx98kFGj\nRhEVFQWgfdwI1q5dS1xcHLfeeisTJkzgkksu4auvvtJ+bkAhISG4XC4Mw8DlcmGz2bSPG0hsbCyL\nFi3C+PZK8pP9O8LtdlNdXU3Hjh0BGDBgAB9//HG9MzSJsH9/TXkAi8WCz+fz40TNj91ux+Fw1K3r\nf8cdd5ywD79bq9/tdhMWFnbC191uN263G4fDccJz5UQvv/wykZGRDBgwAADDMOr+8IL2cUMpKytj\n8+bNPP7449x7771MnTpV+7mBxcfH4/V6GTx4MPfccw9jxozRPm4gv/vd705YOfVk96vH4zmhjz9n\nfzeJz9idTicej6fu1z6fD7O5SfzM0ax8f13/oUOH8tBDD9U95na7CQ8P/8G+9ng8hIWFnfD1n7Ou\nf0v08ssvYzKZ+Pjjj/nmm2+YPn06hw8frntc+7hhtG7dmm7dumG1WunSpQvBwcEcPHiw7nHt55O3\ndOlS4uPjmTJlCvv37+eGG26gpqam7nHt44bz/Zb9mv3qcDhOeO53r1Hv79nA2/CrfLemPMDnn39O\nXFycnydqfr5b1z81NZVhw4YB0KtXLz755BOAurX6+/Tpw4YNG/B6vbhcLnbs2EHPnj1P+P/g56zr\n3xI9//zzLFu2jGXLlnHGGWfwwAMPMGDAAO3jBtavXz8+/PBDAA4cOEBlZSX9+/fXfm5Ax44dqzsy\nDA8Pp6amhjPPPFP7uBGc7N/DTqcTm83G3r17MQyDtWvX/uT+bhJLyhqGwezZs9m6dSsA8+bNO2F9\nevlp/2td/7vvvpv777+f6upqunXrRnp6OiaTiRUrVrB8+XJ8Ph8TJ07ksssu07r+v9CYMWO47777\nMJlMzJw5U/u4gT300EOsX78en8/H1KlT6dChg/ZzAzp69CgzZszg8OHD1NTUMHbsWM466yzt4wZS\nWFjIXXfdxQsvvMDu3btPer9u2rSJuXPnUltby4ABA7jjjjvq/f2bRNhFRESkYTSJt+JFRESkYSjs\nIiIiAURhFxERCSAKu4iISABR2EVERAKIwi4iIhJAFHYREZEA8v8Xeurj3U14DAAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1160b72b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0, 10000, 100)\n",
    "ys = [env_impacts.evaluate_for_method(te, x, resources) for x in xs]\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x116030550>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xwB8KcTX7ue3yvlxzofbARUTkRIp4ENp5wMmS5wowTVhw3QDSz9NtXUVE5KsU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e0c7160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0, 10000, 100)\n",
    "ys = [env_impacts.evaluate_for_method(te, x, metals) for x in xs]\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Finally, we can optimize for multiple critieria at once. Let's make a scoring function that mixes GWP, metals, and costs.\n",
    "\n",
    "Remember, the results are not real! This is a toy model. We will also use some magic constants to get a nice curve for the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MCDA(premium):\n",
    "    \"\"\"Yes, I know the individual values are pretty wonky...\"\"\"\n",
    "    c = te(premium) / 3e8\n",
    "    m = (env_impacts.evaluate_for_method(te, premium, metals) - 247) / 6\n",
    "    g = (env_impacts.evaluate_for_method(te, premium, gwp) - 47000) / 1500\n",
    "    return c + m + g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118814be0>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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O5/jatWtx7733YtOmTd5vbS8UGSZDlYHD7ETe8tnhCvz1o3yIjTYnDFVK8EBK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\nREGOYU5ERBTk/h94PPOlaSWgGwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e0c0a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0, 10000, 500)\n",
    "ys = [MCDA(x) for x in xs]\n",
    "plt.ylabel(\"Combined impact metric (unitless)\")\n",
    "plt.xlabel(\"Subsidy (CHF)\")\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nelder-Mead [ 5362.5]\n",
      "Powell 5500.98999999999\n",
      "CG [ 5500.]\n",
      "BFGS [ 5500.]\n",
      "L-BFGS-B [ 5500.]\n",
      "TNC [ 5500.]\n",
      "COBYLA 5499.9999\n",
      "SLSQP [ 5500.]\n"
     ]
    }
   ],
   "source": [
    "ALGORITHMS = ('Nelder-Mead', 'Powell', 'CG', 'BFGS', 'L-BFGS-B', 'TNC', 'COBYLA', 'SLSQP')\n",
    "\n",
    "for algo in ALGORITHMS:\n",
    "    r = minimize(MCDA, 5500., method=algo)\n",
    "    print(algo, r['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very interesting - our function is not smooth, and this confuses most of the algorithms. In the end, the [Nelder-Mead](https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method) is the only smart enough to get away from local minima..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
