1D nugget effect comparison.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing required packages\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial.distance import cdist\n",
    "import pandas as pd\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def exponential_variogram_model(d, range_, sill, nugget):\n",
    "    '''\n",
    "    Exponential variogram function.\n",
    "    \n",
    "    Parameters:\n",
    "        d (numpy.array): lag distances\n",
    "        range_ (float): range parameter of model\n",
    "        sill (float): sill parameter of model\n",
    "        nugget (float): nugget parameter of model\n",
    "        \n",
    "    Return:\n",
    "        gamma (numpy.array): calculated semivariances\n",
    "    '''\n",
    "    # calculate partial sill\n",
    "    psill = sill - nugget \n",
    "    \n",
    "    # semivariance for exponential model\n",
    "    gamma = psill * (1. - np.exp(-d / (range_))) + nugget\n",
    "    \n",
    "    return gamma\n",
    "\n",
    "def exponential_covariance_model(d, range_, sill, nugget):\n",
    "    '''\n",
    "    Exponential variogram function.\n",
    "    \n",
    "    Parameters:\n",
    "        d (numpy.array): lag distances\n",
    "        range_ (float): range parameter of model\n",
    "        sill (float): sill parameter of model\n",
    "        nugget (float): nugget parameter of model\n",
    "        \n",
    "    Return:\n",
    "        cov (numpy.array): calculated covariances\n",
    "    '''\n",
    "    # calculate partial sill\n",
    "    psill = sill - nugget\n",
    "    \n",
    "    # covariance for exponential model\n",
    "    cov = psill * (np.exp(-(np.absolute(d) / (range_))))\n",
    "    \n",
    "    return cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a248429340>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot models of spatial correlation\n",
    "d = np.arange(0,8,0.1)\n",
    "vario_plot = exponential_variogram_model(d, range_=1, sill=1, nugget=0.2)\n",
    "cov_plot = exponential_covariance_model(d, range_=1, sill=1,nugget=0.2)\n",
    "\n",
    "plt.plot(d, vario_plot, label='variogram')\n",
    "plt.plot(d, cov_plot, label='covariance')\n",
    "plt.axvline(x=1,color='red', linestyle='--', label='range')\n",
    "plt.axvline(x=3,color='red', linestyle=':', label='practical range' )\n",
    "plt.title('Nested Variogram/Covariance with normalized range and sill. Nugget effect = 0.2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kriging_1D(krig_locs, data, range_, sill, nugget, nugget_type='pure'): \n",
    "    '''\n",
    "    Function to perform kriging over 1D discretized domain.\n",
    "\n",
    "    Parameters:\n",
    "        krig_locs (numpy.array): discretized set of 1D loactions to interpolate.\n",
    "        data (numpy.array): input data locations and values.\n",
    "        range_ (float): range parameter of model\n",
    "        sill (float): sill parameter of model\n",
    "        nugget (float): nugget parameter of model\n",
    "        nugget_type (str): either \"pure\", \"exact\" or \"filtered\".\n",
    "\n",
    "    Return:\n",
    "        results_df (pandas.DataFrame): results of kriging interpolation.\n",
    "    '''\n",
    "    \n",
    "    # empty arrays for results (estimated values and variances)\n",
    "    kriging_result_vals = np.zeros(len(krig_locs))\n",
    "    kriging_result_vars = np.zeros(len(krig_locs))\n",
    "    \n",
    "    # calculate distances between all input data points\n",
    "    dist_all_to_all = np.zeros((len(data), len(data)))\n",
    "    for i in range(len(data)):\n",
    "        dist_all_to_all[:,i] = np.absolute(data[:, 0]-data[i, 0])\n",
    "    \n",
    "    dist_grid_to_all = np.zeros((len(krig_locs), len(data)))\n",
    "    for i in range(len(krig_locs)):\n",
    "        dist_grid_to_all[i,:] = np.absolute(data[:, 0]-krig_locs[i])\n",
    "    # calculate distances between all grid points and all input data point)\n",
    "                                            \n",
    "    # Main loop that goes through whole domain (grid)\n",
    "    for i in range(len(krig_locs)):\n",
    "\n",
    "        # STEP 1: Multiple if elif conditions to define moving neighbourhood:\n",
    "        a = dist_grid_to_all[i]\n",
    "        b = dist_all_to_all\n",
    "        prop = data[:, 1]\n",
    "        # STEP 2: Multiple if elif conditions to calculate kriging at point\n",
    "        val, var = ordinary_kriging(a, b, prop,range_, sill,nugget, nugget_effect=nugget_type)\n",
    "        # STEP 3: Save results\n",
    "        kriging_result_vals[i] = val\n",
    "        kriging_result_vars[i] = var\n",
    "        # create dataframe of results data for calling\n",
    "        d = {'X_loc': krig_locs, 'est_value': kriging_result_vals, 'est_variance': kriging_result_vars}\n",
    "        results_df = pd.DataFrame(data=d)\n",
    "        \n",
    "    return results_df\n",
    "    \n",
    "def ordinary_kriging(b, a, prop, range_, sill, nugget, nugget_effect):\n",
    "        '''\n",
    "        Ordinary kriging interpolation for single point.\n",
    "\n",
    "        Parameters:\n",
    "            a (numpy.array): distance vector between target point and input data locations\n",
    "            b (numpy.array): distance matrix between input data locations\n",
    "            prop (numpy.array): property values at input data locations\n",
    "            range_ (float): range parameter of model\n",
    "            sill (float): sill parameter of model\n",
    "            nugget (float): nugget parameter of model\n",
    "            nugget_effect (str): either \"pure\", \"exact\" or \"filtered\".\n",
    "\n",
    "        Return:\n",
    "            result (float): calculated semivariances\n",
    "            pred_var (float):\n",
    "            w (numpy.array): set of calculated kriging weights\n",
    "        '''\n",
    "        # empty matrix building for OK\n",
    "        shape = len(a)\n",
    "        C = np.zeros((shape + 1, shape + 1))\n",
    "        c = np.zeros((shape + 1))\n",
    "        w = np.zeros((shape + 1))\n",
    "\n",
    "        # filling matirces based on model for spatial correlation\n",
    "        C[:shape, :shape] = exponential_variogram_model(a,range_,sill,nugget)\n",
    "        c[:shape] = exponential_variogram_model(b,range_,sill,nugget)\n",
    "\n",
    "        np.fill_diagonal(C, 0)\n",
    "\n",
    "        # for exact kriging\n",
    "        if nugget_effect == 'exact':\n",
    "            c[c==nugget]=0\n",
    "\n",
    "        # matrix setup for OK\n",
    "        C[shape, :] = 1.0\n",
    "        C[:, shape] = 1.0\n",
    "        C[shape, shape] = 0.0\n",
    "        c[shape] = 1.0\n",
    "\n",
    "        # Solve Kriging equations\n",
    "        w = np.linalg.solve(C, c)\n",
    "\n",
    "        # calculating estimate and variance for kriging\n",
    "        pred_var = w[shape] + np.sum(w[:shape] * c[:shape])\n",
    "\n",
    "        # for filtered kriging\n",
    "        if nugget_effect == 'filtered':\n",
    "            pred_var = pred_var-nugget\n",
    "\n",
    "        result = np.dot(prop, w[:shape])\n",
    "\n",
    "        return result, pred_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simple 1D example with two locations and data values at these locations\n",
    "locs = np.arange(0,3,0.1)\n",
    "inp = np.array([[1,-1],[2,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare(range_, sill, nugget):\n",
    "    '''\n",
    "    Function for interactive plot of comparison between nugget effect types.\n",
    "\n",
    "    Parameters:\n",
    "        range_ (float): range parameter of model\n",
    "        sill (float): sill parameter of model\n",
    "        nugget (float): nugget parameter of model\n",
    "    '''\n",
    "    \n",
    "    results_df1 = kriging_1D(locs, inp, range_=range_, sill=sill, nugget=nugget, nugget_type='exact')\n",
    "    loc1 = results_df1['X_loc'].values\n",
    "    val1 = results_df1['est_value'].values\n",
    "    var1 = results_df1['est_variance']\n",
    "    \n",
    "    results_df2 = kriging_1D(locs, inp, range_=range_, sill=sill, nugget=nugget, nugget_type='new_value')\n",
    "    loc2 = results_df2['X_loc'].values\n",
    "    val2 = results_df2['est_value'].values\n",
    "    var2 = results_df2['est_variance']\n",
    "    \n",
    "    results_df3 = kriging_1D(locs, inp, range_=range_, sill=sill, nugget=nugget, nugget_type='filtered')\n",
    "    loc3 = results_df3['X_loc'].values\n",
    "    val3 = results_df3['est_value'].values\n",
    "    var3 = results_df3['est_variance']\n",
    "\n",
    "    fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(14, 4))\n",
    "    \n",
    "    axes[0].plot(inp[:,0], inp[:,1], 's', markersize=10, fillstyle='none', color='black', label='data value')\n",
    "    axes[0].plot(loc1, val1, '-o', label='exact')\n",
    "    axes[0].plot(loc2, val2, '-o', markersize=3, label='new value/filtered')\n",
    "    axes[0].set_ylim(-1.5,1.5)\n",
    "    axes[0].legend()\n",
    "    \n",
    "    axes[1].set_ylim(0,1.5)\n",
    "    axes[1].plot(loc1, np.sqrt(np.round(var1,2)))\n",
    "    axes[1].plot(loc2, np.sqrt(var2))\n",
    "    axes[1].plot(loc3, np.sqrt(var3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7fd39ea77bf040d9a18b46340cceba63",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=6, description='range_', max=11, min=1), FloatSlider(value=1.0, descript…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(compare, range_=(1,11,1), sill=(0.5,1.5,0.1), nugget=(0,1,0.1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iQyMxqs2oIkfIyrmXM3tuj4JC9Zjq6BzU+faWexEDLl5ARPbAIoeIiDQzd/dcrDu6DuXdy+OLp7+Aq45/LdlKcVdoy2HO4hACgYerBy7duoSv/v4KX/39FQDA39sfnYM6o1HlRpiwZQLSMu+e28PFC4jImvi3CRERaeLg5YOI/ilrwYGFjy9EYIVAjRNRYaLbRmPJ/iWFFjmeek/sH7IfmSoTmxI2YfOpzdiUsAkXky/eLniKkrN4AUfziKgkOCeHiIjsLtWQij6r+yAtMw3Pt3gevRr30joSFcHcuT33VLoHDSo3wNDwofiy55c4P/o8jgw/gnmPzjNrpM5gMmDp/qVmZeLcHiIqCIscIiKyu9d+fg0HLx9ESKUQzOg2Q+s4ZKacuT1RYVHwdfeFQIpcHEJEUL9yfQwJHwKjyWjWdZIyktByfku89P1LWH5gORKuJ9y1mMGG4xsQOi8Ui/YuQlJGEhTU7bk9ofNCseH4Bqv8zERUOvFxNSIisqt1R9dh9q7Z0Ov0+LLnl/B289Y6Elkg99yeTZs2oXPnzmafa8mLSfdd3Id9F/dh9q7ZAIDqPtXRrnY7tKvdDgHlA9B/bX++mJSICsSRHCIisptzN89h0DeDAAATH5iIltVbapyI7MncF5NGtYzCpv6bML7reDwW8hj8PP1wIfkCVh9ejeifotFrZa98C5zczH0xKR95I3JOHMkhIiK7MJqM+M/a/+Ba6jU8HPwwXmnzitaRyM7MWbxA76LH6+1fR7BfMDoFdQKQtdT4sWvHsPXMVmw7uw2f7vsUJlX0i0mX7l9a6AIGXM6ayHlxJIeIiOxiytYp+O3kb6jqXRWLn1oMnfCvoLKmOC8mBf43r2dgi4FY8PiCIl82miMpIwlB04PQa2UvTPpzEn7951dcT7sOIGsEJ2JlBFIMKXcVXQaTASmGFESsjOCIDlEpxZEcIiKyuZ3nduLtjW8DABY/uRjVfKppnIi0UtIXkwKWze05deMUTt04hVWHVt3eV8+vHhRUvu/ryY3LWROVXixyiIjIppLSk9B3dV9kmjLxSutX+PgP2eXFpHqdHoNbDsbwe4dj9/nd2HV+F3af342/Lv6F44nHzbqOwWTAsrhlZuWMT4xHzLYYxMbF3i7c+oX2Q3TbaC5+QKQBFjlERGRTw78fjvh/49HMvxkmPjBR6zjkBMyd25NTYDSu2hj9m/cHkDU6c/DyQbRcYN6iFzfTb+Lt395GM/9maFatGe7xu+euRy05t4fI8bDIISIim/ki7gssi1sGT1dPfNnzS7i7umsdiZxAztyevIUFkDWCo3fR5zu3B8gqflpUb4FybuXMfuTtoz8+uv21t94bTf2bopl/MzSv1hyVPCthwDcDuJw1kYNhkUNERDbxz7//4MX1LwIAZnSbgYZVGmqciJxJSef2mPPIm6u4omvdrgivHo6/Lv2F/Rf341zSOWw/ux3bz243Oyvn9hDZH4scIiIqsfzmI3jqPZGUkYSeDXticMvBWkckJ1SSuT3mPPLm5uqGOY/MuaNguppyFfsv7sf+S1lbbFysWctZmzu3h4isg0UOERGVSEHzEZIykiAQPNP4GYiIximJ7lTcR94qe1XG/XXvx/117wcALNu/zKzrJWckWy88ERWJLykgIqJiK+xdIwCgoDDwm4F81wg5pJxH3qLCouDr7gud6ODr7ouosCjEDY0za7EAHzcfs65lbjsisg4WOUREVGwx22JgMBb8uA/wv/kIRI4o55G3G2NuwPiuETfG3MCsR2aZvUhAv9B+d73YNC+9To/I0EhrxCUiM7HIISKiYouNiy10TgPwv/kIRM4oum009C5FFDkueoxqM8pOiYgIYJFDREQlYO48A85HIGeVM7fHS+9114iOXqeHl96rwOWsich2WOQQEVGxcT4CkXXm9hCRdXF1NSIiKjZz3jXC+QhUFpRkOWsisj6O5BARUbFFt42Ggiq0DecjEBGRvXEkh4iIim33+d3INGUCyHo7fKbKvH2ssHeNEBER2RKLHCIiKpaT/55E1HdRAIBxncbhSsoVLItbhuSMZPi4+SAyNBKj2oxigUNERHbHIoeIiCxmMBrQZ3Uf3Ey/iR4NeuDdTu9CRDgfgYiIHALn5BARkcXGbhqLHed2oLZvbSx6YhFEROtIREREt3Ekh0qdoKAgnDp1yuz2gYGBSEhIsF0gojLm139+xcQ/J0InOnzx9Bfw8/TTOhIREdEdWORQqXPq1CkolbWaU3xiPGK2xSA2Lvb2PIB+of0Q3Tb69jwA/gszkfVcvnUZ/db0g4LC2I5jcV/gfVpHIiIiuovDP64mIsNE5KSIpInIHhEp8G9UEQkSEZXP1s2emck88YnxGLZ+GHwn+EL3ng6+E3wxbP0wxCfGm3X+huMbEDovFIv2LkJSRhIUFJIykrBo7yKEzgvFhuMbbPwTEJUtJmXCgLUDcDH5IjoGdsTbHd/WOhIREVG+HLrIEZFnAcwAMB5ACwBbAWwQkYAiTu0GoHqu7Tdb5ixrSlqcACUvUOIT4xGxMgIphpS7XkJoMBmQYkhBxMoIizIRUeGmb5+ODSc2wM/TD188/QVcdC5aRyIiIsqXQxc5AEYDWKyUWqiUOqyUehnABQAvFnHeNaXUxVxbhu2jlg6OMHpijQIlZlsMDMaC37AOZK3+NG37NLN+LiIq3J7zezDmlzEAgM+e+Ay1fGtpnIiIiKhgDjsnR0TcAIQBmJLn0E8A2hVx+tci4gHgOIBpSqlVNohoV+bMPSnKhuMbELEyAgaj4XZxkVOgLNm/BKt6rUL3et0LzZBTnORlMGV9ZsTKCMQNjSs0k7kFynub38PotqPxb+q/+Dft39t/oiuwaO+iuwqk/DIti1tWaBsiKlpSehJ6r+4Ng8mAl+59CU82eFLrSERERIWSnAncjkZEagA4B6CTUur3XPvfBfCcUqp+PudUBtAfwBYAmQCeAPB/APorpWLzaR8FIAoA/P39w1asWGGLHwXnUs/hv2f+i18u/4JUYyo8XTzxQNUH8EztZ1DTs2aR5++4tgPjDo2DwWSAEcbb+13gAr1Oj3GNxqF1pdZFZhi8ezDSTGkFtvHQeWBR+KICM007Ng3rL6y/I0NeLnDBY9Ufwwt1X0ByZjJuZd7K+tOY9WdyZjLmxs+FQRVeoFiLQKDGKWzcuNEu13NWycnJ8PHx0TqG03L0/h1/ZDx+vvQz6nrXxdyWc+Gmc9M6ktkcvW9LO/av7RTVt126dNmjlAq3YySiUqU0FDkdlVJ/5No/FkAfpVQDMz9nDoAOSqnQwtqFh4er3bt3lyRyvvIbPQEAvU4PvYverNGT0Hmh+Y6e5PDSexU5ejJs/bAiRz/0Oj0GtRiE9zq/h5vpN+/aor6NQpqx4CLJFppUbYKKHhVR0bNi1p8eFTF94nS4P+COdGN6kef7uvvi5ps34aj3eWmxadMmdO7cWesYTsuR+3fZ/mX4z9r/wEvvhd0v7EbDKg21jmQRR+5bZ8D+tZ2i+lZEWOQQFcJhH1cDcBWAEUC1PPurArhkwefsADDQWqEsYY3Hu8x9tOv9ze/j9favIykjCckZyUhKz/4zIwlJ6Un4dN+nZj3eNX/PfMzfM9/8H7IAPm4+KO9eHhU8KqC8R/af2d9/uu9TZBiLnibl6+6LAy8euGv/9O7TMei1QWYVbZGhkZiN2SX6WYjKquPXjuPF9VlTIGd2m1nqChwiIiq7HLbIUUpliMgeAA8CWJnr0IMAVlvwUc2RtViB3ZlToKRnpmP498PxbONncctwC8kZybiVkf2n4RY+/+tzZJoyC/0Mg8mApXFLsTRuqVVyV/GqAl9337u2//793yILJSCrOLkx5kahbcwtUAoS3TYaS/YvKfwzXPQY1WYUixyiYkjPTEfv1b1xy3ALzzZ+FoNaDNI6EhERkdkctsjJNhXAMhHZiax5NkMB1AAwDwBEZAKAVkqp+7O/7w/AAGAfABOAxwEMB/CG/aMDsXGxRRYFRmXEj/E/4sf4H0t8vQaVG6CcWzn4uPmgnHu5/33tVg4zd840e/Tk8muXCzxW0uIEsKxAKUiwXzBW9VqV76OAAODh6oFVvVaZvSgDEd3pzV/fxN4LexFUIQjzH5vPl+oSEVGp4tBFjlLqKxGpBOBtZL3v5iCAR5RSp7KbVAeQ97fYtwEEIutRt2MABuW36IA9JGckm932P83+Ax+9D7zdvOGt94aPW9bXo34chbTMoufB+Lr74vDwwwUev2W4ZdfRk8IUVqDknqtUVIHSvV53xA2Nw7Tt07AsbhmS0pOgd9Ejw5iB+wLuK3SuExH9T97VGz1cPZCamQoddPiy55co71Fe64hEREQWcegiBwCUUnMAzCng2IA83y8BsMQOsczi4+aDpIykItv5uvtiyVP5x467FFcqRk8sKU6AuwuUnGWxI0MjMarNqEI/IzAwsMB/Vc7wzgBeAX7+52dIVQGuZLUnovzltzhKamYqAMBF54J/U//VMh4REVGxOPrLQEu1fqH9oNfpC21jzuiJ3qWIz7Bg9MRL73VXJr1ODy+9l0WjJ1FhUfB194VOdPB190VUWBTihsZZNHoS7BeMWY/Mwo0xN2B814gbY25g1iOzisyQkJAApdRd28aNG6GSFYa3Gw4A6De/H5RSSEhIMDsTUVlS2It5AdxeHMXclwUTERE5ChY5NmSNAsVaxQlgvQKluMWJvbzW7jW46lzx5YEvcfLfk1rHIXJY5q7eOG37NDslIiIisg4WOTbkTKMnpUlghUD0bdoXRmXE5K2TtY5D5LDMWRzFYDJgWdwyOyUiIiKyDhY5Npa3QBGIU46eOJox7cdAIPhs32e4mHxR6zhEDsncxVEsWUSFiIjIEbDIsYPcBcpvnX5jgWIHDas0RI+GPZBuTMe0bXzUhig/Pm4+Vm1HRETkKFjkkNN6s8ObAIA5u+dwhSiifPQL7QcXcSm0jTmrNxIRETkaFjnktMJrhOPBug8iOSMZs3bO0joOkcN5ov4TMCpjoW3MWb2RiIjI0bDIIaf21n1vAQBm7JiBWxm3NE5D5DhSDal47efXAACu4lri1RuJiIgcCYsccmqdAjuhTa02uJZ6DQv3LtQ6DpHDiP4pGgcvH0RIpRDsGbLHKqs3EhEROQpXrQMQ2ZKI4K0Ob+GJFU9gytYpeDH8Rbi7umsdi0hTXx/+GnN3z4WbixtW9FyBUP9QzHpkFmY9wsc6iYjIOXAkh5zeoyGPomnVpjiXdA6xcbFaxyHS1Okbp/H8uucBAB8/8DFaVG+hcSIiIiLrY5FDTk8nOozpMAYAMHHLRBhNhU+0JnJWmaZM9F3dF9fTruOxkMcwovUIrSMRERHZBIscKhOeafwM6lasixOJJ7Dq0Cqt4xBp4v3N72PLmS2oUa4GPn/yc4iI1pGIiIhsgkUOlQmuOle83u51AMCEPydAKaVxIiL72pSwCR/+/iEEgtgesajsVVnrSERERDbDIofKjP7N+6O6T3Xsv7QfG05s0DoOkd1cTbmK575+DgoK/3ff/6FLnS5aRyIiIrIpFjlUZni4eiC6bTQAYPwf4zVOQ2QfSikM+mYQziedR/va7TG281itIxEREdkcixwqU6LColDRoyK2nNmCP079oXUcIpv7ZOcn+PbYt6jgUQFfPP0FXHV8cwARETk/FjlUppRzL3d7Ranxf3I0h5zbvgv78NrPrwEAPn3iUwRWCNQ4ERERkX2wyKEy5+VWL8Nb740fTvyAvRf2ah2HyCaSM5LRe3VvZBgzMDRsKJ5u+LTWkYiIiOyGRQ6VOZW8KmFI2BAAwMQ/J2qchsg2Xt7wMo5dO4YmVZtg6sNTtY5DRERkVyxyqEwa3XY03FzcsOrQKhy9elTrOERW9UXcF1j812J4unpiRc8V8NR7ah2JiIjIrljkUJlU07cmBjQbAAWFSVsmaR2HyGpOJJ7A0PVDAQAzus1A46qNNU5ERERkfyxyqMx6vf3r0IkOy+KW4fSN01rHIbJYfGI8hq0fBt8JvtC9p4PvBF+0+7QdkjOS0atRLwxuOVjriERERJpgkUNlVrBfMJ5t/CwyTZmI2RqjdRwii2w4vgGh80KxaO8iJGUkQUEhKSMJV1KuQCDo1agXRETrmERERJpgkUNl2pgOYwAAC/cuxOVblzVOQ2Se+MR4RKyMQIohBQaT4a7jCgoDvhmA+MR4DdIRERFpj0UOlWmh/qF4LOQxpGamonts9zse+xm2fhh/SSSHFLMtBgbj3cVNbgajAdO2T7NTIiIiIsdicZEjIq1F5C0RmS4iM3NvtghIZGtdArsAAPZe3HvHYz+L9i5C6LxQbDi+QeOERHeKjYvNdwQnN4PJgGVxy+yUiIiIyLG4WtJYRF4F8DGAEwDOA1C5Dqt8TyJyYPGJ8Xhn0zv5HjOYDDCYDIhYGYG4oXEI9gu2czqi/CVnJFu1HRERkbOxdCRnJIARSqkQpVRnpVSXXFtXWwQksiU+9kOlkY+bj1XbERERORtLixxfAN/bIgiRFvjYD5VG/UL7Qa/TF9pGr9MjMjTSTomIiIgci6VFzpcAutkiCJEW+NgPlUbRbaNhUqZC2+hd9BjVZpSdEhERETkWi+bkADgD4D0RaQ8gDsAd/wSulJpqrWBE9uDj5oOkjCSz2hE5iu1nt8OojAAAV3FFpsq8fUyv00PvoseqXqs4j4yIiMosS4ucwQCSAbTL3nJTAFjkUKnSL7QfFu1dVOgja3zshxzJP//+gxfXvwgA+LDLh7iQfAHL4pYhOSMZPm4+iAyNxKg2o1jgEBFRmWZRkaOUqmOrIERaiG4bjSX7lxRe5PCxH3IQBqMBfVb3QVJGEiIaReCt+96CiGDWI7O0jkZERORQiv0yUBHxERFva4Yhsrdgv2Cs6rUKXnqvfCdye+m9+NgPOYx3N76Lned2IqB8ABY8tgAionUkIiIih1Scl4EOF5HTAG4AuCkip0RkmPWjEdlH93rdETc0DlFhUfB194Vk/wcAFjy2AN3rddc4IRHw6z+/YtKWSdCJDl88/QUqelbUOhIREZHDsqjIEZG3AEwE8CmAh7K3zwFMFJEx1o9HZB/BfsGY9cgs3BhzA6axJozrPA4AsDRuqbbBiABcuXUFkWsioaDwbsd30SGgg9aRiIiIHJqlIzlDAUQppd5TSv2avY0D8GL2RuQUXmr1EnzcfPBT/E/Yc36P1nGoDFNK4fl1z+NC8gV0COiA/+v4f1pHIiIicniWFjlVAezKZ/9OAP4lj0PkGPw8/TAkbAgAYOKWiRqnobJs9q7Z+PbYt6jgUQFfPP0FXHWWLopJRERU9lha5BwD0Def/X0BHC15HCLHMarNKOh1eqw+tBpHr/L2JvuLuxSHV396FQCw6PFFCCgfoHEiIiKi0sHSImccgHdF5BcReU9ExonILwDeBjDW6umINFTTtyb6N+sPBYXJWydrHYfKmBRDCnqv6o10YzpeaPkCejbqqXUkIiKiUsOiIkcp9TWA1gAuAngMwBPZX7dSSq21ejoijb3e/nXoRIel+5fi7M2zWsehMmTUD6Nw+OphNKzcENO7Tdc6DhERUali8RLSSqk9Sql+SqkwpVTL7K/32SIckdbqVaqHiEYRMJgMmLptqtZxqIz4+vDXWLB3Adxc3PBlzy/hpffSOhIREVGpUmSRIyJ+ub8ubLNtVCJtjGmftTr6gj0LcC3lmsZpyNmdvnEaz697HgAw+cHJaFatmcaJiIiISh9zRnKuiEjV7K+vAriSz5azn8jptKjeAt3u6YZbhlv4ZOcnWschJ2Y0GdHv6364nnYdj9Z7FC+3elnrSERERKWSOUVOVwCJub7Ob+uS/SeRU8oZzZm5YyaSM5I1TkPO6qM/PsIfp/9AdZ/q+PzJzyEiWkciIiIqlYp84YJSanOurzfZNA2Rg+oY2BFta7XFtrPbsHDPQoxqO0rrSFTKxSfGI2ZbDGLjYpGckQzPrZ5IMaQAAJb2WIoq3lU0TkhERFR6WbTwgIgYcz26lnt/JRExWi8WkWMREbzZ4U0AQMy2GKRnpmuciEqzDcc3IHReKBbtXYSkjCQoqNsFjqvOFQajQeOEREREpZulq6sV9OyEO4CMEmYhcmiPhjyKJlWb4FzSOcTGxWodh0qp+MR4RKyMQIohBQbT3cVMpikTESsjEJ8Yr0E6IiIi52BWkSMio0VkNAAFYGjO99nbawDmAThiy6BEWtOJ7vbcnElbJsFo4uAlWS5mW0yRIzUGowHTtk+zUyIiIiLnY+5IzsvZmwAYnOv7l7O/dwcw1BYBiRzJs02eRVCFIBxPPI6vD3+tdRwqhWLjYvMdwcnNYDJgWdwyOyUiIiJyPmYVOUqpOkqpOgA2A2iW8332Vl8p9bBSaodtoxJpz1XnitfavQYAmPDnBCilNE5EpY25q/NxFT8iIqLis3ROTjcAqXl3ioiHiLhZJ9Jdnz1MRE6KSJqI7BGR+4po31RENotIqoicE5F3heuwkhUNbD4QVb2rYt/Fffj5n5+1jkOljI+bj1XbERER0d0sLXL+C2BYPvuHZh+zKhF5FsAMAOMBtACwFcAGEQkooL0vgJ8BXAJwL4ARAF4DMNra2ajs8tR7YlSbrCWkJ/w5QeM0VNr0C+0HF3EptI1ep0dkaKSdEhERETkfS4uc9gB+ymf/zwDalTzOXUYDWKyUWqiUOqyUehnABQAvFtD+OQBeAPorpQ4qpVYDmARgNEdzyJpeDH8Rvu6+2JSwCdvPbtc6DpUig1sMhkmZCm2jd9HfLqSJiIjIcpYWOV4AMvPZbwJQruRx/if78bcw3F1U/YSCC6q2AP5QSuV+pO5HADUABFkzH5Vt5T3KY/i9wwFwNIfMp5TCxC0ToaCgEx30Ov0dx/U6Pbz0XljVaxWC/YI1SklERFT6WVrkxAHok8/+vgAOljzOHSoDcEHWo2e5XQJQrYBzqhXQPucYkdWMbD0SHq4eWHd0HQ5etvbtT85o6f6lWHloJXzcfPBz5M+ICouCr7svBAJfd19EhUUhbmgcutfrrnVUIiKiUk0sWR1KRB4FsBZZ829+y959P4BeAHoopb6zWjCRGgDOAeiolPoj1/6xAPoopRrkc85PAM4opZ7PtS8QQAKAtkqp7XnaRwGIAgB/f/+wFStWWCt+gZKTk+HjwwnFtqBF304/Ph3fnP8GD/o/iLcavGXXa9sT79uSO5d6Di/seQGpxlS8Uf8NdKvW7fYx9q/tsG9ti/1rO0X1bZcuXfYopcLtGImoVHG1pLFSar2IPA7gbQAzs3fvA/CEUmqDlbNdBWDE3SMwVXH3aE2OiwW0R37nKKUWAFgAAOHh4apz587FzWq2TZs2wR7XKYu06Nug5kH4buZ3+O3yb1jQewGCKgTZ9fr2wvu2ZAxGA+77/D6kGlPxTONnMKHnBOSeJsj+tR32rW2xf22HfUtUMpY+rgal1A9KqQ5KKe/srYMNChwopTIA7AHwYJ5DDyJrlbX8bANwn4h45Gl/HlmjOURWFVQhCH2a9oFRGTFl6xSt45CD+vD3D7Hj3A7U8q2FeY/OA9dBISIisi2Lixw7mwpggIgMFpGGIjIDWYsIzAMAEZkgIr/mar8cQAqAxSLSRESeBjAGwFTFtzaSjYxpPwYA8Om+T3EpuaBBRiqrtpzegg//+BACwbIey1DRs6LWkYiIiJxekUWOiNwUkcrZXydlf5/vZu1wSqmvALyCrMfj/gLQAcAjSqlT2U2qAwjO1f4GskZuagDYDWA2gBhkFUtENtG4amM8Uf8JpGWmYcaOGVrHIQdyI+0G+q3pB5My4Y32b6BzUGetIxEREZUJ5szJeRlAUvbXL9kwS76UUnMAzCng2IB89h0A0NHGsYjuMKb9GKw7ug5Ttk7BrJ2zkJyRDB83H/QL7YfottFcDriMemnDS0i4noCw6mF4r8t7WschIiIqM4oscpRSS/L7moj+53radehEB4PJAEOGAQCQlJGERXsXYcn+JVjVaxWXBS5jlh9Yjti4WHjpvfDF01/AzcVN60hERERlhqPPySFyePGJ8YhYGZHvW+wNJgNSDCmIWBmB+MR4DdKRFhKuJ+DF9S8CAKY/PB31K9fXOBEREVHZYs6cHJOIGM3Z7BGYyNHEbIuBwWgotI3BaMC07dPslIi0ZDQZEbkmEjfTb+KpBk9hcMvBWkciIiIqc8wZyXkm1/YygH8BfAbgheztMwCJ2ceIypzYuFgYTEUUOSYDlsUts1Mi0tLEPyfiz9N/orpPdSx8fCGXiyYiItKAOXNyVuV8LSLrALyplFqYq8lnIrITwFMoYIEAImeWnJFs1XZUeu08txNjN40FACx5agkqe1XWOBEREVHZZOmcnK4ANuazfyOAziVOQ1QK+bj5WLUdlU7JGcnou7ovjMqI0W1G48HgvO8xJiIiInuxtMi5CiAin/0RAK6UPA5R6dMvtB/0On2hbfQ6PSJDI+2UiLQwcsNIxP8bj1D/UIy/f7zWcYiIiMo0c96Tk9u7AD4XkS4AtmXvawPgAQDPWzMYUWkR3TYaS/YvKXRejt5Fj1FtRtkxFdlKfGI8YrbFIDYu9vb7kNrWbouf4n+Ch6sHlj+9HO6u7lrHJCIiKtMsGslRSi0F0A5ZIzpPAHgSwDUA7fkOHSqrgv2CsarXKnjpvfId0fFw9cCqXqv4QlAnsOH4BoTOC8WivYuQlJEEBYWkjCT8FP8TAGBA8wFoXLWxximJiIjI4vfkKKV2KKWeU0q1VEq1yP56hy3CEZUW3et1R9zQOESFRcHX3Rc60d1++WPnoM58EagTyHkfUoohpcBRu6X7l/J9SERERA7A4iJHRPxF5FURmSMilbP3tReROtaPR1R6BPsFY9Yjs3BjzA0Y3zXi5MiTcHNxw48nfsTxa8e1jkclxPchERERlR4WFTkiEgbgKIDnAAwG4Jt96EEAH1k3GlHpVqNcDUSGRkJBYcrWKVrHoRLi+5CIiIhKD0tHcqYAmKGUagEgPdf+HwG0t1oqIifxartXIRAs2b8EF5Mvah2HSoDvQyIiIio9LC1ywgDkt8DABQD+JY9D5FwaVG6AJxs8iXRjOmZsn6F1HCoBvg+JiIio9LC0yEkFUDGf/Q0AXC55HCLn80b7NwAAc3fPxc30mxqnoeLi+5CIiIhKD0uLnG8AjBWRnJdAKBEJAjAJwGprBiNyFm1qtUHHwI64kX4DC/Ys0DoOFVN02+iiixy+D4mIiMghWFrkvArAD8AVAF4A/gRwAsB1AG9bNRmRE8kZzZm2fRrSM9OLaE2OKNgvGG1rt833mF6nh5fei+9DIiIichCWFjmZADoDeArAGwBmAOimlOqklLpl3WhEzqP7Pd3RtGpTnE86jy8OfKF1HCqGrw9/jV9P/gp3F3f0bdL39vuQfN19ERUWhbihcXwfEhERkYNwNbehiLgAuAGgmVLqNwC/2SwVkZMREbze/nVEronEx1s+xoDmA6ATi19TRRq5mHwRUd9GAQCmPDQFL7V6SeNEREREVBizf8tSShkBnALgZrs4RM7r2cbPIqB8AI5eO4p1R9dpHYfMpJTC4HWDcS31Gh6s+yCG3TtM60hERERUBEv/KfkDABNFpLItwhA5M72LHtFtowEAk7ZMglJK40RkjkV7F2H98fWo4FEBnz35GUfgiIiISoHiLDzQAcA5EYkXkbjcmw3yETmV51s8Dz9PP2w/ux1/nP5D6zhUhPjEeIz6MWu1tNmPzEYt31oaJyIiIiJzmD0nJ9sqAAqA2CALkdPzdvPGS/e+hPd/fx+TtkxCx8COWkeiAhhNRvRf2x+3DLfwTONn0KdJH60jERERkZnMKnJExAvAZGStqqYH8CuAl5VSV20Xjcg5vdz6ZUzeOhnfH/8eBy4dQFP/plpHonxM3joZW85sQXWf6pj76FyI8N92iIiISgtzH1d7D8AAAOsBfAngAQBzbZSJyKlV9qqM51s8DyDrF2lyPPsv7se7G98FAHz25Gfw8/TTOBERERFZwtwi52kAzyulopRSIwE8CuCp7GWlichC0e2i4SIu+PLglzh947TWcSiX9Mx0RK6JhMFkwIvhL6LbPd20jkREREQWMrfIqQ3g9ixppdROZL0YtIYtQhE5u6AKQXi2ybPINGVi6rapWsehXN7Z+A4OXD6Aen71MPlBjrQRERGVRuYWOS4AMvLsy4TlCxcQUbbX270OAFi4dyGupVzTOA0BwO+nfseUrVOgEx2W9lgKbzdvrSMRERFRMZhb5AiAWBFZl7MB8ACwMM8+IjJTs2rN0O2ebkgxpGD2rtlaxynzbqbfRP+1/aGg8FaHt9CmVhutIxEREVExmVvkLAFwHsC1XFssgDN59hGRBd5o/wYA4JOdnyDFkKJxmrJt1A+jkHA9AS2rt8S7nd7VOg4RERGVgFmPmymlBto6CFFZ1CmwE+6tcS92nd+Fz/Z9hpdavaR1pDLpmyPf4LO/PoO7izuW9VgGvYte60hERERUAuaO5BCRDYjI7dGcmG0xyDRlapyo7Ll86zJe+PYFAMDEByaiUZVGGiciIiKikmKRQ6Sxpxo8hXp+9ZBwPQEr/16pdZwyRSmFqG+jcCXlCrrW6YoRrUdoHYmIiIisgEUOkcZcdC54rd1rAIBJWyZBKaVxIucVnxiPYeuHwXeCL3Tv6eA13gvfHP0GPm4++PzJz6ET/l8iERGRM+Df6EQOILJZJKr5VMP+S/vxU/xPWsdxShuOb0DovFAs2rsISRlJUFBIy0wDAGQYM/D35b81TkhERETWwiKHyAF4uHrgldavAMgazSHrik+MR8TKCKQYUmAwGe46nmHMQMTKCMQnxmuQjoiIiKyNRQ6RgxgaPhS+7r7YmLARu87t0jqOU4nZFgOD8e7iJjeD0YBp26fZKRERERHZEoscIgdR3qM8hoYNBQD0XtX79rwR3wm+GLZ+GEcZSiA2LjbfEZzcDCYDlsUts1MiIiIisiUWOUQOJNQ/FADwz/V/bs8bScpIwqK9ixA6LxQbjm/QOGHplJyRbNV2RERE5NhY5BA5iPjEeER9F5XvMYPJgBRDCueNFJOPm49V2xEREZFjY5FD5CA4b8R2+oX2g6u4FtpGr9MjMjTSTomIiIjIlljkEDkIzhuxnZGtR8IEU6Ft9C56jGozyk6JiIiIyJYK/6dNIrIbzhuxnW+OfgOTMkEgcNW53lFM6nV66F30WNVrFYL9gjVMSURERNbCkRwiB8F5I7Zx+MphvLvxXQDAp098iqiwKPi6+0InOvi6+yIqLApxQ+PQvV53jZMSERGRtXAkh8hB9Avth0V7FxX6yBrnjVgm05SJAd8MQLoxHc+3eB4DWwzEwBYDMeuRWVpHIyIiIhviSA6Rg4huGw29i77QNpw3Ypmp26Zi57mdqOVbCzEPxWgdh4iIiOyERQ6Rgwj2C8aqXqvgpfeCXnd3seOl9+K8EQvkfkxt4eMLUd6jvMaJiIiIyF5Y5BA5kO71uiNuaNzteSOS/R8A+PTxTzlvxExGkxEDvxmIdGM6BjUfhG73dNM6EhEREdkRixwiBxPsF4xZj8zCjTE3YBprwjsd3wEAfPn3lxonKz2mbpuKHed2oJZvLUx9eKrWcYiIiMjOWOQQObjhrYbD3cUd3x79FkevHtU6jsM7fOUw3tmYVRgueGwBH1MjIiIqg1jkEDm4qt5V8Z9m/4GCwrTt07SO49DyPqbGx/uIiIjKJhY5RKXA6LajAQBL9i/B5VuXNU7juHIeU6tZriZiHuZqakRERGUVixyiUqBB5QZ4PORxpGWmYc6uOVrHcUhHrh65/ZjawscXooJHBW0DERERkWYctsgREXcR+URErorILRFZJyK1ijhngIiofDYPe+UmspVX270KAJi9azZSDakap3EsuR9TG9h8IB9TIyIiKuMctsgBMB1ATwB9ANwHwBfAdyLiUsR5KQCq596UUmk2zElkF/cF3Id7a9yLqylXsXT/Uq3jOJRp26dh+9ntqFmuJldTIyIiIscsckSkPIDnAbymlPpZKbUXQCSAUAAPFHG6UkpdzL3ZOi+RPYgIottGAwBitsXApEwaJ3IMR64ewdu/vQ2Aj6kRERFRFocscgCEAdAD+Clnh1LqDIDDANoVca6niJwSkbMi8p2ItLBhTiK76tmoJwLLB+J44nF8e/RbreNojo+pERERUX5EKaV1hruISF8ASwHoVa6AIvIbgONKqSEFnNcWQAiA/QDKARgJ4BEAzZRSx/NpHwUgCgD8/f3DVqxYYe0f5S7Jycnw8fGx+XXKorLSt6vOrsLs+Nlo6tsUM1vMtMs1HbVvvzrzFeb9Mw+V3Srj83s/h4+r42U0h6P2rzNg39oW+9d2iurbLl267FFKhdsxElGpYtciR0Q+BPB/RTTrAqAG8i9yNgI4qpQaaub1XAD8BWCjUmpEYW3Dw8PV7t27zfnYEtm0aRM6d+5s8+uURWWlb5PSkxAwPQDX065j+/Pb0bpWa5tf0xH79sjVI2g+rznSjelY33c9Hqn3iNaRis0R+9dZsG9ti/1rO0X1rYiwyCEqhL0fV5sOoGER204AFwG4AKic5/yqAC6ZezGllBHAbgD1SpibyGGUcy+HIWFZg5kx28rGu2DiE+MxbP0w+E7whe49HXwn+KLz4s5IN6ZjQPMBpbrAISIiIutztefFlFJXAVwtqp2I7AFgAPAggOXZ+2ohqwjaau71RESQtVjB/uLkJXJUL7d6GVO3TcXqw6vxz7//oG7FulpHspkNxzcgYmUEDEYDDCYDACApIwlJGUkQCB65hwUOERER3ckhFx5QSt0A8CmAySLyQPbiAcsAxAH4JaediPwqIhNyfT9WRB4Wkboi0jz7M0IBzLPrD0BkYzV9a6Jv074wKROmb5+udRybiU+MR8TKCKQYUm4XOLkpKAz4ZgDiE+M1SEdERESOyiGLnGyjAHwN4CsAWwAkA3g8+xG0HMHIehdOjgoAFiBrFbafANQE0FEptdMegYnsKWc56U/3fYrE1ESN09hGzLYYGIx3Fze5GYwGTNs+zU6JiIiIqDRw2CJHKZWmlHpZKVVJKeWllHo8exnp3G2ClFIDcn0/SikVqJRyV0pVVUo9rJTaZvfwRHbQ1L8pHg5+GCmGFMzb7ZyDlbFxsfmO4ORmMBmwLG6ZnRIRERFRaeCwRQ4RFS1nNOeTnZ8gPTNd4zTWl5yRbNV2REREVDawyCEqxR6o+wBC/UNxMfkilh9YrnUcq/NxM+/9G+a2IyIiorKBRQ5RKSYieLXtqwCAKdumwBFf7lsS/UL7Qa/TF9pGr9MjMjTSTomIiIioNGCRQ1TKPdvkWdQsVxOHrhzCDyd+0DqOVUW3jYarrvCV7vUueoxqM8pOiYiIiKg0YJFDVMq5ubhhROsRALJGc5xJsF8w2tVuBwAQyB3H9Do9vPReWNVrFYL9grWIR0RERA6KRQ6RE4gKi4KPmw9+O/kb9l3Yp3Ucq/k5/mf8evJXuOnc0LdpX/i6+0InOvi6+yIqLApxQ+PQvV53rWMSERGRgyn8ORAiKhUqeFTACy1fwLTt0xCzLQaxT8dqHanEUgwpGLp+KABgXOdxePO+NzVORERERKUFR3KInMTI1iPhIi5YcXAFztw4U/QJDm7cpnH4599/EOofilfbvap1HCIiIipFWOQQOYnACoF4pvEzMCojZuyYoXWcEtl3YR+mbpsKgWDh4wuhdyl8hTUiIiKi3FjkEDmRnJeDLtizADfSbmicpngyTZkY/O1gGJURI1qPQKuarbSORERERKUMixwiJxJWIwydgzojKSMJi/Yu0jpOsczcMRN7L+xFQPkAfNj1Q63jEBERUSnEIofIyeS8HHTsprHwneAL3Xs6+E7wxbD1wxCfGK9xusKd/Pck3tn4DgBg7qNz4ePmo3EiIiIiKo1Y5BA5IYHgluEWkjKSoKBuj+yEzgvFhuMbtI6XL6UUXlz/IlIMKejdpDceqfeI1pGIiIiolGKRQ+RE4hPj8cyqZ6Cg7jpmMBmQYkhBxMoIhxzRWX5gOX6M/xEVPSpi+sPTtY5DREREpRiLHCInErMtBgajodA2BqMB07ZPs1Mi81xNuYpXfnwFABDzUAz8ffy1DURERESlGoscIicSGxcLg6mIIsdkwLK4ZXZKZJ7on6JxNeUqutbpigHNB2gdh4iIiEo5FjlETiQ5I9mq7ezh5/ifsXT/Uni4emD+Y/MhIlpHIiIiolKORQ6REzF3NTJHWbUsxZCCoeuHAgDGdhqLe/zu0TgREREROQMWOUROpF9oP+h1+kLb6HV6RIZG2ilR4cZtGod//v0Hzfyb3X6RKREREVFJscghciLRbaOhdymiyHHRY1SbUXZKVLB9F/Zh6rap0IkOCx9fWGRuIiIiInOxyCFyIsF+wVjVaxW89F75juh46b2wqtcqBPsFa5DufzJNmRj87WAYlREjWo3AvTXv1TQPERERORcWOUROpnu97ogbGoeosCj4uvtCJzroJOt/6uO7jkf3et01TgjM2D4Dey/sRWD5QHzQ9QOt4xAREZGTYZFD5ISC/YIx65FZuDHmBozvGjH7kdkAgBV/r7B7lvjEeAxbPwy+E3yhe0+HcuPL4Y1f3gAAzH10rsMsgkBERETOg0UOURkQGRqJih4Vsf3sduw4u8Nu191wfANC54Vi0d5FSMpIgoJCsiEZRmWEi7jYLQcRERGVLSxyiMoAbzdvvNDyBQDAjB0z7HLN+MR4RKyMQIohJd8XlBqVERErIxCfGG+XPERERFR2sMghKiOGtxoOF3HBykMrcfbmWZtfL2ZbDAzGu4ub3AxGA6Ztn2bzLERERFS2sMghKiMCygegZ6OeyDRlYs6uOTa/XmxcbL4jOLkZTAYsi1tm8yxERERUtrDIISpDXmn9CgBg/p75SDGk2PRayRnJVm1HREREZC4WOURlSJtabdCqZiskpiYiNi7Wptcyd9U0rq5GRERE1sYih6gMEZHbozkzdsyAUspm1+oX2i/fF5LmptfpERkaabMMREREVDaxyCEqYyIaRaBGuRo4dOUQfvnnF5tdJ7ptNFx1roW20bvoMarNKJtlICIiorKJRQ5RGaN30WP4vcMBANN3TLfZdYL9ghFWPQwAIJA7M+j08NJ7YVWvVQj2C7ZZBiIiIiqbWOQQlUFRYVHwcPXA98e/x9GrR21yjZ/jf8afZ/6Eh6sHIkMj4evuC53o4Ovui6iwKMQNjUP3et1tcm0iIiIq2wp/loSInFJlr8qIDI3Ewr0LMXPHTMx+dLZVPz89Mx0vbXgJADCu0zi80eENq34+ERERUWE4kkNURo1sPRIAsHj/Yvyb+q9VP3vqtqk4du0YGlRugFFtOeeGiIiI7ItFDlEZ1bhqYzxY90GkGFKwaO8iq33uqeun8MHvHwAAZnWfBTcXN6t9NhEREZE5WOQQlWE5ozmzds1CpinTKp856sdRSM1MxbONn8X9de+3ymcSERERWYJFDlEZ1r1ed9Tzq4fTN05j7ZG1Jf68Dcc3YM2RNfBx80HMQzElD0hERERUDCxyiMownehuj+ZM3z69RJ+VlpmGlze8DCBrsYGavjVLGo+IiIioWFjkEJVx/Zv3R3n38thyZgt2ndtV7M/5eMvHiP83Ho2rNMaI1iOsmJCIiIjIMixyiMo4HzcfvNDyBQDAjB0zivUZ//z7Dyb8OQEAMOfROdC76K2Wj4iIiMhSLHKICC+1egk60eGrv7/C+aTzFp8/8oeRSMtMQ7/QfugY2NEGCYmIiIjMxyKHiBBYIRA9GvRApikTc3fNtejcdUfX4btj38HX3ReTH5xso4RERERE5mORQ0QAgFfavAIAmLdnHlINqWadk2JIwYgNWfNvPujyAar5VLNVPCIiIiKzscghIgBA+9rtEVY9DFdTrmL5geVmnTPhjwk4deMUmvk3w7B7h9k4IREREZF5WOQQEQBARG6P5kzfMR1KqULbH792HB9v/RhA1mIDrjpXW0ckIiIiMguLHCK67ZnGz6CaTzUcvHwQv538rcB2Sim8tOElZBgzMLD5QLSr3c6OKYmIiIgKxyKHiG5zc3HDsPCsx86m75heYLuvD3+Nn+J/QgWPCpj0wCQ7pSMiIiIyD4scIrrDkPAhcHdxx/pj63H82vG7jidnJOOVH18BAIzvOh5VvKvYOSERERFR4VjkENEdqnpXxXNNn4OCwic7P7nr+Ie/f4izN88irHoYosKiNEhIREREVDgWOUR0W1BQEEQEnw35DADwyZ+fQDwFXbp0gYhAqggm/T4JUMCe9/cguG6wxomJiIiI7sYih4huO3XqFJRSUBcV2tRqA7gB7v/nDhknKDe+HGq+WRNwAaLCoqDOKpw6dUrryERERER3cdgiR0SiRGSjiFwXESUiQWae11NEDolIevafPWwclcjpbDi+Afsu7AMApBvToaCQlJGEc0nnAABd63TVMh4RERFRoRy2yAHgBeAnAOPMPUFE2gL4CsAXAJpn/7lSRFrbIB+RU4pPjEfEygikG9MLbDNo3SDEJ8bbMRURERGR+Rz27X1KqekAICLhFpz2CoCNSqmPsr//SES6ZO/vY818RM4qZlsMDEZDoW0MRgOmbZ9mp0RERERElnHkkZziaIus0Z/cfgTANxUSmSk2LhYGUxFFjsmAZXHL7JSIiIiIyDIOO5JTTNUAXMqz71L2/ruISBSAKADw9/fHpk2bbBoOAJKTk+1ynbKIfWsdyRnJZrVLSk8CAPa5FfDetR32rW2xf22HfUtUMnYtckTkQwD/V0SzLkqpTSW4jMp72Xz2ZTVUagGABQAQHh6uOnfuXILLmmfTpk2wx3XKIvatdfi4+SApI6nIduXcy+EmbrLPrYD3ru2wb22L/Ws77FuikrH342rTATQsYttZgs+/iLtHbari7tEdIipAv9B+0Ov0hbbR6/SIDI20UyIiIiIiy9i1yFFKXVVKHSliSynBJbYBeDDPvgcBbC3BZxKVKdFto6F3KaLIcdFjVJtRdkpEREREZBmHXXhARKqJSHMAIdm7GolIcxHxy9XmVxGZkOu0GQC6isibItJARN4E0AVZI0hEZIZgv2Cs6rUKXnqvu0Z09Do9vPReWNVrFYL9gjVKSERERFQ4hy1yAAwFsA9Z77oBgPXZ3z+Rq00wgOo53yiltgLoDaA/gDgA/wHwrFJqhz0CEzmL7vW6I25oHKLCouDr7guBwNfdF1FhUYgbGofu9bprHZGIiIioQA67uppSahyKeBGoUioon32rAKyySSgiJxcYGAgRyffYTdzE7Oz/5G5PRERE5GgceSSHiOwsISEBSqm7to0bN+a7PyEhQevIRERERHdhkUNERERERE6FRQ4RERERETkVFjlERERERORUWOQQEREREZFTYZFDREREREROhUUOERERERE5FRY5RERERETkVFjkEBERERGRU2GRQ0REREREToVFDhERERERORVXrQMQERERkePYs2dPVVdX10UAmoD/IE6OSYnIDaPR+LnJZJobFhaWkbcBixwiIiIius3V1XVRtWrVGlapUuVfnU6ntM5DlJdSChkZGfrz58+/fPPmzZYA+udtw+qciIiIiHJrUqVKlZsscMhRiQjc3d0NgYGBNwB0yK8NixwiIiIiyk3HAodKg+z71CXfY3bOQkREREREZFOck0NEREREJVKzZs2m58+fdzO3fY0aNTLOnTt3wJaZqGzjSA4RERERlcj58+fdlFJ7zN0sKYicQc+ePYO6dOlyT0k+48KFC64iEvbdd9+Vs+V1rGHmzJmVvLy8WmiZgUUOEREREZVq58+fd+3Xr19AzZo1m7q5ubWsVKlSs7Zt24asWbPGV+tszk5Ewj7//POKufcNGjQo8fjx45qO1PFxNSIiIiIq1Z544ongtLQ03Zw5cxIaNmyYfuHCBddff/213JUrV/KdlE625ePjo3x8fDK1zMCRHCIiIiIqta5eveqyZ88enw8//PDsk08+mRQSEpLRqVOnlPfff/9SVFTUvznt5syZ49ekSZOG3t7eLfz8/Jp179697smTJ/U5x7/77rtyIhL23//+17dx48YNPTw8WoaFhdWPj4/Xr1+/3qd+/fqNvLy8WnTp0uWeixcv3i6ech4Re/3116tXqlSpmZeXV4uIiIig5ORkKSizyWTC22+/7V+7du0mHh4eLUNCQhrNmTPHL3ebzZs3ezVu3Lihu7t7y4YNGzbavHmzt6V9k5qaKoMGDapdqVKlZu7u7i2bNWvW4Mcff/TJ3Wbfvn0eXbt2vadcuXLNvby8WjRv3rzBzp07PXMytG/fvl7FihWb+fj4tAgLC6v/yy+/3M5Rs2bNpgAwaNCguiISlvN9fo+rTZ48uXJAQEATvV7fMiAgoElMTEzl3MdFJGzKlCmVu3fvXtfT07NFrVq1mubtE0uwyCEiIiKiUqt8+fJGLy8v09q1ayukpKQUWFhkZGTIO++8c37Xrl1/r169+nhiYqJrr1696uZt98EHH9SMiYk5s3nz5sM3b9507dWrV/CHH35YY+7cuad++OGHo8eOHfN84403auQ+Z+fOneUOHDjg+cMPPxxdtmxZ/O+//+770ksv1Sooy8iRI2vGxsZWmTZt2um//vrr4OjRoy9GR0cHrlixojwA3Lx5U9ejR496AQEB6X/++eehDz/88Oxbb71V4OcVZNiwYbW+/fbbirNnz07Ytm3boYYNG6b26NGj3qlTp/QAkJCQoO/atWt9EVHr1q07tn379kNRUVGXMzOzBmFu3Ljh0rdv32u//vrr0T/++ONw48aNU59++ul6Fy5ccAWAXbt2HQaAmJiYU6dOndqf831eS5curfDmm28GDB069NKePXv+HjJkyOU33ngjYPny5eVzt5s8eXKNxx9//PquXbsOPfnkk4kjR44MOnbsWLHmb/FxNSIiIiIqtfR6PWbPnn1y5MiRQV9++WWVhg0bprRq1Sq5d+/e/3bt2vVWTrtXXnnlWs7XjRo1ypg3b97pli1bNo6Pj9cHBwcbco6NGzfuXLdu3ZIBYODAgZf/7//+L+CPP/443KFDhxQAePbZZ699++23d8xB0el0asWKFQnly5c33XvvvWmXLl06+8orrwTNnDnznK+vryl325s3b+oWLlzov3bt2mM512nQoEHizp07vefOnVuld+/eNxYsWOBnMBgkz2deGD58eB1z++XmzZu67ELqVO/evW8AQGxs7Kk6deqUi4mJqTJz5szzMTExVT09PU3r16//x8PDQwFAaGhoes5nPPHEE0m5P3Px4sWn/f39K6xZs8Z32LBhiTVq1MgEgIoVKxoDAgIKfDxt+vTp1Xr06JH41ltvXcm+xuW9e/d6xcTEVOvbt++NnHYRERHXhg0blph9zrnPPvus6i+//OITEhKSaO7PnYMjOURERERUqg0YMOD6hQsX9q9YseLEAw88cGPXrl0+999/f4MxY8ZUy2nz559/et1///3BNWrUaOrt7d2iffv2DQHgn3/+uWOkIDw8PDXn62rVqmUCwL333nt7n7+/v+HatWt3DBTUr18/tXz58reLmU6dOt0yGAxy+PBh97xZ9+3b55Geni49evSo5+Xl1SJni42NrXLq1CkPADh8+LBnfp9pSZ8cPnzYPTMzU7p06ZKcs8/V1RUtW7a8deTIEU8AiIuL8wwPD0/OKXDyOnfunGvfvn0Dg4KCmpQrV665j49Pi8TERP3p06ctGl2Jj4/3aNeuXXLufe3bt08+ceKEZ+59oaGht/tZr9ejYsWKmZcvX9ajGDiSQ0RERESlnpeXl+rRo8fNHj163ARw4dlnnw2MiYmpMW7cuEsZGRny+OOP1+vQocPNTz/99GS1atUyL1++7NqtW7f66enpd/yjv5ub2+1f+EWynn5zd3e/Y59S+dYEZjEajQIAX3311Ym6detm5Hftknx+DpMpqz4Skbs+LOfnUkoV+HgfAPTp06fO1atXXSdOnHjmnnvuSffw8FAPPfRQSEZGhsUDJYXlyJG773OO5/wcluJIDhERERE5nYYNG6YZjUZJSUmR/fv3e1y/ft118uTJ57p3757cokWLtIsXL1rtH/uPHTvmefPmzdu/V//+++/eer1eNWzYMD1v2xYtWqS6ubmpkydPujVp0iQ99xYSEpIBAI0aNUrN7zMtydS4ceN0vV6vfvvtt9vv1cnMzMTevXu9GzRokAoAzZo1S9m9e7dPWlpavsXOnj17fIYMGXK5d+/eN8LDw9PKly9vvHLlyh0jK66uripnDk9BgoOD07Zs2XLH+322bNniExwcnFrQOSXFIoeIiIiISq2LFy+6tGnTJmTOnDl+O3bs8Dxy5IjbZ599VnHWrFnV2rRpc9PPz88UHByc4ebmpmJiYqoeOnTIbcWKFeU/+OCDmtbKYDQapU+fPkG7d+/2WLNmje97771Xq3fv3lfzzscBgIoVK5qGDBlycezYsbWnT59e6eDBg+5bt271/Pjjj6tMmTKlMgC88MILiS4uLir3Z06ZMqW6JZl8fX1N/fr1u/L+++/X/Oqrr8rv3bvXIzIyMvDatWv60aNHXwGA0aNHX05JSXF57LHH6m7evNnr4MGD7vPnz/fbunWrJwAEBQWlrVixotKePXs8Nm/e7BUREVFXr9ffMdpSs2bNjN9++8339OnTrgUt2T1q1KiLa9as8ZswYUKVAwcOuH/00UdVv/nmG7/o6OiLlvxMluDjakRERERUapUvX94UHh5+a86cOf6nT592NxgMUrVqVcNTTz117aOPProAADVq1MicNWvWyffff7/m0qVLq4aEhKROmjTpTERERD1rZGjVqlVSw4YNUx966KH6aWlpum7duv07e/bsswW1nz59+nl/f//MTz75pNrrr7/u7u3tbWzYsGHKa6+9dinnZ1q9evWJl156KaBdu3aN6tSpk/bBBx+cfe655+6xJFdOhmHDhgUlJSW5NGzYMGXNmjXHAwMDDQBQp04dwy+//HIkOjq6Vvfu3euLCEJCQlIXLFiQAACLFi1KGDJkSGD79u0bValSJWPMmDHnp0+ffsdIzvjx48+8+eabtevWrRvq7+9vOHfu3F0vAY2MjLx+4cKFM7NmzfJ/5513ateoUSNj0qRJp3MvOmBtYo1n/pxBeHi42r17t82vs2nTJnTu3Nnm1ymL2Le2w761Lfav7bBvbYv9aztF9a2I7FFKhdvi2vv3709o1qzZVUvOqVmzZtPz58+bPRm9Ro0aGfn9Mlwa9ezZMygxMdF148aNJ7TOUhbt37+/crNmzYLy7udIDhERERGViLMULOQ8OCeHiIiIiIicCkdyiIiIiIiKafXq1QlaZ6C7cSSHiIiIiIicCoscIiIiIiJyKixyiIiIiIjIqbDIISIiIiIip8Iih4iIiIiInAqLHCIiIiIicioscoiIiIjIav6+/Ld75NeRAT7jfVro3tOF+Yz3aRH5dWTA35f/dtc6W0mISNjnn39eUescJVWzZs2m7777rn9JP6dVq1b1//Of/wRYI5MtsMghIiIiIqv479//9Q1fGN5oxcEVlW8ZbukUFG4ZbulWHFxROXxheKP//v1fX1td++TJk/o+ffoE+vv7h+r1+pZVq1YN7d27d2B8fLw+d7uePXsGdenS5Z7c+7788svynp6eLV5++eWaBX3+qVOn9vfu3fu6uXm+++67ciISduHChVL9XsqZM2dW8vLyapF3/7fffntixowZZ7XIZA4WOURERERUYn9f/tu9/9r+wWmZabpMlSm5j2WqTEnLTNP1X9s/2BYjOkeOHHFr1apVwyNHjnguWLDg5KFDhw5++umnJ48ePerZpk2bhkePHnUr6NzZs2f79e/fP/itt94698knn5wrqF1AQECmp6ensnZ2c6Snp0vRrezL39/fWLFiRZPWOQrCIoeIiIiISmzinxP9M42Zhf4ynmnMlElbJlW19rWHDBkSICL4/fffjz355JNJ9erVy3j88ceTfv/992MigiFDhuT7WNUHH3xQddSoUUHTpk1LeOeddy4Xdo3cj6sdPXrUTUTCFi9eXKFdu3b1PD09WwQHBzdes2aNb87xxx9/PAQAatSo0UxEwnr27BkEACaTCW+//bZ/7dq1m3h4eLQMCQlpNGfOHL+c6+R89vz58/3atGkT4uHh0TImJqZyzojK8uXLywcFBTVxd3dv2bp165BDhw7dUcBNnjy5ckBAQBO9Xt8yICCgSUxMTOXCfq5x48b5h4SENPL09GxRtWrV0GeffTbw6tWrLkDWaNTIkSODUlNTdSISJiJho0ePrgHc/bjalStXXJ5++ukgX1/f5h4eHi3btWsXsnv3bo+c4zn5v/nmm3L16tVr7Onp2aJ169YhR44cKbAALYlSPXxGRERERLYl70mYtT4rU2XKsrhlVZfFLSuy0FFj1R5zPvPSpUsuf/zxR/nXX3/9XLly5e4YWShXrpxp4MCBlydPnlzzypUrLlWqVDHmHBs5cmSNBQsW+C9dujS+d+/eNyz/aYD33nuv5kcffXS2adOmp8eOHVt94MCBdbt27RoXHBycsXjx4vgBAwYE7969++8qVapkent7q+zr1vz2228rTps27XSTJk3SNm3a5DNq1KhAPz8/Y+4c77//fs0PP/zwbNu2bRP0er1av369b0ZGhowfP77GggULTnp7e5tGjhwZ0KNHj3sOHz58SKfTYenSpRXefPPNgPfff//MY489dvPbb78t/8YbbwRUr17d0Ldv33x/Rp1Op6ZMmXKmfv366SdOnHAbNWpUwODBgwPWrl178oEHHkh+//33z4wfP77m0aNHDwBA+fLl8x296d27d9A///zj8dVXX52oVKmSccyYMTUfe+yxkBMnThzw8fFRAJCRkSGTJk2qvmDBgpNeXl5qwIABdQYPHhz4559/Hi9O/xeGRQ4RERERlVp///23h1IKjRo1SsvveOPGjdOUUjh48KB7ly5dUgBgy5Ytvps2bSr/5ZdfnihugQMAw4YNu5RTPMTExJyrW7dupe3bt3s9/PDDyZUqVTICQI0aNTKrV6+eCQA3b97ULVy40H/t2rXHunXrlgwADRo0SNy5c6f33Llzq+TOMnjw4MsDBw78N/f1jEajTJ069fRDDz10CwCWL19+smHDhk3XrVtX7qmnnkqaPn16tR49eiS+9dZbVwAgNDT08t69e71iYmKqFVTkvPvuu7dHsOrXr5+Rmpp6tm/fvvcYjcaTHh4eqnz58kYRQUBAQGZB/XDgwAH33377rcL3339/tHv37skAsHLlypNBQUFNFyxYUGn06NFXc/LPnTv3VLNmzdIBYMSIERdHjBgRZDQa4eLiYvl/AYVgkUNEREREBTJ3RMVnvE+LW4ZbRU6F8NZ7G5PfSv6rxMHyEMn/STmlsqbR6HT/i1avXr3UpKQkl48++qjGAw88kFy5cmVjvicXoUWLFqk5XwcGBhoA4OLFiwX+fr1v3z6P9PR06dGjR73ceTMzM6VGjRoZudu2atXqVt7zdTodOnXqlJLzfUhISEaVKlUMBw8e9HzqqaeS4uPjPSIjI6/mPqd9+/bJv/zyS4WCMq1bt67cxIkTq8XHx3smJye7mEwmGAwGOXPmjD4oKMhQeA9kiYuL89DpdOjatevtzJUqVTKGhISkHjp06PYja25ubiqnwAGAWrVqGTIzM+Xq1asu/v7+xfrvoCCck0NEREREJdajQY9rruJa6MR8V3FVTzd8+po1r9u4ceM0EcHBgwc98jt+6NAhDxFBgwYNbv9yXbVqVcPmzZuPJiUluXTu3DnkypUrxRpGcHNzu/3z5hRRJpOpwHlJRqNRAOCrr746sXPnzkM52969e//+6aefjuVum/fRO3OJyF3/HRRUAB47dsztmWeeqRcSEpL2xRdfxG/btu3QjBkzEgDLFjtQShXYNve1XVxcVH7HCuuz4mKRQ0REREQlNqbDmEuuLkUUOS6u6o32bxQ6wd9S/v7+xg4dOtz8/PPPqyYlJd3xu21SUpLu888/r9qxY8cbeUcK6tSpY9i8efPRlJQUXadOnUIuXrxo1eel3N3dTQCQmfm/p7xatGiR6ubmpk6ePOnWpEmT9NxbSEhIRoEfls1kMuH333/3yvn++PHjbleuXNE3btw4DQCCg4PTtmzZUi73OVu2bPEJDg5OzftZALB161Yvg8EgixYtOvPAAw/cCg0NTT9//vwdCwG4ubmpooqQZs2apZpMJvz222/eOfsSExN1x44d8yzoMUJbY5FDRERERCXWuGrj9CVPLYn3cPUw5R3RcRVX5eHqYVry1JL4xlUbpxf0GcU1d+7c00ajUTp27Biybt26cidOnNB/99135Tp16hSilMK8efNO53deYGCgYfPmzUcNBoOuU6dO9a35Tpt77rknQ0SwevXq8ufPn3e9ceOGrmLFiqYhQ4ZcHDt2bO3p06dXOnjwoPvWrVs9P/744ypTpkwpdBU0IGskZPTo0QG//PKL99atWz379esXFBwcnPrkk0/eBIBRo0ZdXLNmjd+ECROqHDhwwP2jjz6q+s033/hFR0dfzO/zGjZsmG4ymfDBBx/4HzlyxG3+/Pl+8+fPv2NRiODg4PT09HRZs2aN74ULF1zzFpIA0LRp0/T777//+vDhwwN/+OEHn507d3pGRETU9fb2Nr3wwgtWHbkzF4scIiIiIrKKZxo/c3P3C7sP9Wna54q33tsoEHjrvY19mva5svuF3YeeafzMTVtct3Hjxuk7duw4VL9+/dTBgwfXadCgQdNBgwbVqVevXur27dsPN2jQoMBRktq1a2du3rz5KAB06tQp5Ny5c1YpdOrUqWOIjo4+/9FHH9WsVatWs0GDBgUAwPTp08+/9tpr5z/55JNqLVu2bPzoo4+GrF27tkJwcHCRIzlubm7qjTfeuPD888/X6dy5c0OTySRff/11fM6jcpGRkdfHjx9/Zu7cuf4tWrRoPH/+/KqTJk06XdCiA61bt0794IMPzsydO9e/efPmTRYvXlz5gw8+uOMFnw8++OCtvn37Xhk0aFCdGjVqNBs7dmy1/D7ryy+/TGjevPmtZ5555p6OHTs2TEtL03333XfHclZWszfJmYxV1oWHh6vdu3fb/DqbNm1C586dbX6dsoh9azvsW9ti/9oO+9a22L+2U1TfisgepVS4La69f//+hGbNml0tuiXZ08yZMyuNGTMmICUlZZ/WWRzJ/v37Kzdr1iwo736O5BARERERkVNhkUNERERERE6FRQ4RERERkYMbMWLENT6qZj6HLXJEJEpENorIdRFRIhJkxjkDstvm3fJdN52IiIiIiJyPwxY5ALwA/ARgnIXnpQConntTSmmyPjcRERFRKaS4MBWVBtnv78n3palWWwvc2pRS0wFARCxdOUQppfJdC5yIiIiICiciNzIyMvTu7u4GrbMQFSY1NdVDRPL9vd+RR3KKy1NETonIWRH5TkRaaB2IiIiIqLQwGo2fnz9/3ruot9wTacVkMsmtW7c8ExIS3DIzM9/Lr43DjuQU01EAgwDsB1AOwEgAW0SkmVLqeN7GIhIFICr722QROWqHjJUBcO1522Df2g771rbYv7bDvrUt9q/tFNW3gba6sMlkmnvz5s2WBw4c6ADAxVbXISoBk4hczMzMfK9ly5Y/5tfAri8DFZEPAfxfEc26KKU25TonHMAuAHWUUgkWXs8FwF8ANiqlRlgU1kZEZLetXt5V1rFvbYd9a1vsX9th39oW+9d22LdEJWPvkZzpAGKLaHPaWhdTShlFZDeAetb6TCIiIiIicmx2LXKUUldhx2FtEREAoch6fI2IiIiIiMoAh52TIyLVAFQDEJK9q5GIVABwWimVmN3mVwA7lVJvZn8/FsB2AMcB+AIYgawi50X7pi/UAq0DODH2re2wb22L/Ws77FvbYv/aDvuWqATsOifHEiIyDsDYfA4NVEotzm6TAGCTUmpA9vfTADyNrOLoBoB9AMYppbbZPjERERERETkChy1yiIiIiIiIisMZ35NDRERERERlGIscKxKRYSJyUkTSRGSPiNxXRPumIrJZRFJF5JyIvJu9WALlw5L+FZEgEVH5bN3smbk0EJGOIrIu+x5UIjLAjHN475rB0r7lfWs+EXlTRHaJyE0RuSIi34pIEzPO471rhuL0L+9f84jIcBGJy+7bmyKyTUQeLeIc3rdEFmKRYyUi8iyAGQDGA2gBYCuADSISUEB7XwA/A7gE4F5kLZLwGoDRdglcyljav7l0A1A91/abLXOWUj4ADiLr5bmpRTXmvWsRi/o2F963ResMYA6AdgC6AsgE8IuI+BV0Au9di3SGhf2bC+/fwp0F8AaAlgDCkdU/a0UkNL/GvG+JiodzcqxERHYAiFNKvZBr33EAq3JWf8vT/kUAkwD4K6VSs/e9jayV4Gop/hdzh2L0bxCAkwDuVUrttlvQUk5EkgG8lLO4RwFteO8Wg5l9GwTet8UiIj7IWnDmKaXUtwW04b1bTGb2bxB4/xaLiCQCeFMpNT+fY7xviYqBIzlWICJuAMIA/JTn0E/I+lew/LQF8EfO/2Fl+xFADQBB1s5YmhWzf3N8LSKXRWSLiETYJGDZw3vX9njfWq4csv5O+7eQNrx3i8+c/s3B+9dMIuIiIr2RNeq7tYBmvG+JioFFjnVUBuCCrKHk3C4haznr/FQroH3OMfqf4vRvMoBXATwD4BEAvwL4SkT62SpkGcJ713Z43xbfDAB/ASjslQG8d4vPnP7l/Wum7Dk2yQDSAcwD0EMpdaCA5rxviYrBYV8GWkrlHTKWfPYV1T6//ZTF7P5VSl0FEJNr124RqQzgdQCxtolXpvDetQHet8UjIlMBdADQQSllLKI5710Lmdu/vH8tchRAcwAVAPQEsEREOiulDhbQnvctkYU4kmMdVwEYcfe/qFTF3f/6kuNiAe1RyDllVXH6Nz87ANSzVqgyjPeuffG+LYRkvQS6D4CuSql/imjOe9dCFvZvfnj/5kMplaGUOqGU2p09r/QvAKMKaM77lqgYWORYgVIqA8AeAA/mOfQgCn7GdhuA+0TEI0/78wASrJ2xNCtm/+anOYALVopVlvHeta/m4H2bLxGZAaAvsn4BP2LGKbx3LVCM/s1Pc/D+NYcOgHsBx3jfEhUDixzrmQpggIgMFpGG2X851EDWs7YQkQki8muu9ssBpABYLCJNRORpAGMATOVKKfmyqH9FpL+I9M1uW19EXgUwHMAnmqR3YCLiIyLNRaQ5sv4/ISD7+4Ds47x3i8nSvuV9az4RmQ1gILJGGf4VkWrZm0+uNrx3i6k4/cv71zwiMlFE7pOs9wo1FZEJyFqy+4vs47xviaxBKcXNShuAYcj6V5V0ZI08dMx1bDGAhDztmwL4HUAasv6layyyl/XmVrL+BdAfwCEAtwDcBLAbQD+tfwZH3JD1l6vKZ1ucX99m7+O9a4O+5X1rUd/m168KwLhcbXjv2rF/ef+a3beLAZzK/rvsMoBfADxcUL9m7+N9y42bhRvfk0NERERERE6Fj6sREREREZFTYZFDREREREROhUUOERERERE5FRY5RERERETkVFjkEBERERGRU2GRQ0REREREToVFDhGRxkQkIfvFiURERGQFfE8OEZUpIrIYQGWl1GMaXHscgAilVJM8+6sAuKWUSrF3JiIiImfkqnUAIqKyTil1ResMREREzoSPqxERZRORjiKyQ0TSROSSiEwTEbdcx0VEokXkuIiki8hZEZmQ6/hEETkqIqnZj6B9LCIe2ccGABgLoLGIqOxtQPaxOx5XE5EAEVkjIknZ29ciUivX8XEiclBEeotIfHabtSJS2fa9RERE5Pg4kkNEBEBEagLYAGAZgAEAggEsAmACEJ3dbDyAFwGMBvA7gCoAWuT6mFsABgE4B6ARgHkA0gG8A+ArAE0APAagc3b7G/nkEABrAaQB6ApAAZgFYK2I3Kv+94xxEIBnAfQA4A1gBYCPAAwpXg8QERE5DxY5RERZhgG4AGCYUsoE4LCIjAEwX0TeQdbI9ygAryilPss+5wSAbTkfoJT6INfnJYjIeACvAnhHKZUqIskAMpVSFwvJ8QCAZgCClVIJACAifbOvdT+AX7LbuQIYoJS6kd1mAYCBxf7piYiInAiLHCKiLA0BbMsucHL8CcANwD0APAC4A/i1oA8QkQgAr2S39wHgkr1ZmuN8ToEDAEqpf0TkPLJGh3KKnFM5BU628wCqWngtIiIip8Q5OUREWQRZj4blR2UfL/hkkTbIemTsRwCPI+sxtrcB6K2cI4chn2P8/3QiIiJwJIeIKMchAM+IiC7XaE4HABkA4pE1IpOOrEfGjudzfnsA53I/siYigXnaZKDokZ1DAGqKSFCux9XqAqiRfYyIiIiKwCKHiMoiXxFpnmff98h61GyOiMwAUBfARACzct5fk71/goikI2vhgUoAwpRScwEcQ1Zx8hyy5uk8DKBPnmskAAgUkZYATgNIUkql52nzC4D9AL4QkRHIGtn5BMBeAL+V8OcmIiIqE1jkEFFZdB+AfXn2rQbQHcBkAH8BuA5gOYC3crV5E8C/yFotrRaASwCWAoBS6lsRmQxgOgBPAD8BeBfAnDzXeBpZ83oqIGuhgMW5QyillIg8BWAmgE3Zu38B8LLi25uJiIjMIvw7k4iIiIiInAknqRIRERERkVNhkUNERERERE6FRQ4RERERETkVFjlERERERORUWOQQEREREZFTYZFDREREREROhUUOERERERE5FRY5RERERETkVFjkEBERERGRU/l/em1VCdLOtvAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create figure 3 (a)\n",
    "locs = np.arange(0,3,0.1)\n",
    "inp = np.array([[0.5,0.5],[1,-1],[2,1]])\n",
    "\n",
    "range_=1\n",
    "nugget=0.0\n",
    "sill=1\n",
    "    \n",
    "results_df1 = kriging_1D(locs, inp, range_=range_, sill=sill, nugget=nugget, nugget_type='exact')\n",
    "loc1 = results_df1['X_loc'].values\n",
    "val1 = results_df1['est_value'].values\n",
    "var1 = results_df1['est_variance']\n",
    "    \n",
    "fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(10, 7))\n",
    "    \n",
    "axes.plot(inp[:,0], inp[:,1], 's', markersize=12, fillstyle='none', color='black', label='Sampled location')\n",
    "axes.plot(loc1, val1, '-o', label='OK interpolation', markersize=10, linewidth=2, color=\"green\")\n",
    "\n",
    "axes.set_ylim(-1.5,1.5)\n",
    "#axes.set_ylim(-1.5,5)\n",
    "axes.set_ylabel(\"Prediction\", fontsize=14)\n",
    "axes.set_xlabel(\"Location\",fontsize=14)\n",
    "\n",
    "axes.legend(loc=(1.04,0), fontsize=14)\n",
    "axes.grid()\n",
    "axes.tick_params(axis='x', labelsize=14)\n",
    "axes.tick_params(axis='y', labelsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create figure 3 (b)\n",
    "locs = np.arange(0,3,0.1)\n",
    "inp = np.array([[0.5,0.5],[1,-1],[2,1]])\n",
    "\n",
    "range_=1\n",
    "nugget=0.5\n",
    "sill=1\n",
    "    \n",
    "results_df1 = kriging_1D(locs, inp, range_=range_, sill=sill, nugget=nugget, nugget_type='exact')\n",
    "loc1 = results_df1['X_loc'].values\n",
    "val1 = results_df1['est_value'].values\n",
    "var1 = results_df1['est_variance']\n",
    "    \n",
    "results_df2 = kriging_1D(locs, inp, range_=range_, sill=sill, nugget=nugget, nugget_type='new_value')\n",
    "loc2 = results_df2['X_loc'].values\n",
    "val2 = results_df2['est_value'].values\n",
    "var2 = results_df2['est_variance']\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(10, 7))\n",
    "    \n",
    "axes.plot(inp[:,0], inp[:,1], 's', markersize=12, fillstyle='none', color='black', label='Sampled location')\n",
    "axes.plot(loc1, val1, '-o', label='Exact', markersize=10, linewidth=2, color=\"blue\")\n",
    "axes.plot(loc2, val2, '-o', markersize=5, label='Filtered', color='red', linewidth=2)\n",
    "axes.set_ylim(-1.5,1.5)\n",
    "#axes.set_ylim(-1.5,5)\n",
    "axes.set_ylabel(\"Prediction\", fontsize=14)\n",
    "axes.set_xlabel(\"Location\",fontsize=14)\n",
    "\n",
    "axes.legend(loc=(1.04,0), fontsize=14)\n",
    "axes.grid()\n",
    "axes.tick_params(axis='x', labelsize=14)\n",
    "axes.tick_params(axis='y', labelsize=14)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}