Back-driving a truck with fuzzy controller.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <p style='text-align: center;'> Back-driving a truck with fuzzy controller</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing needed libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import skfuzzy as fuzz\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import control.matlab as mt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step1: Defining Fuzzy Sets \n",
    "According to problem situation: <br />\n",
    "$x(m) \\in [0,10]$ <br />\n",
    "$\\varphi(deg) \\in [0,90]$ <br />\n",
    "$\\theta(deg) \\in [-20,20]$ <br />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of triangular fuzzy set\n",
    "class triangularFuzzySet:\n",
    "    def __init__(self, a, b, c):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "        self.c = c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining Fuzzy Sets for $ x \\in Ai$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "indexA =[\"S1\", \"CE\", \"B1\"]\n",
    "num = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xRange = 10\n",
    "A = [triangularFuzzySet(a=-xRange/(num-1)+xRange/(num-1)*i,\n",
    "                        b=0+xRange/(num-1)*i, \n",
    "                        c=xRange/(num-1)+xRange/(num-1)*i) for i in range(num)]\n",
    "x = np.linspace(0,10,10000)\n",
    "for i in range(num):\n",
    "    plt.plot(x,fuzz.membership.trimf(x, [A[i].a, A[i].b, A[i].c]), label=indexA[i]) \n",
    "plt.xlabel(\"m\")\n",
    "plt.ylabel(\"$\\mu$\")\n",
    "plt.title(\"Fuzzy Sets for x(m)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining Fuzzy Sets for $\\varphi(deg) \\in Bi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "indexB =[\"S1\", \"CE\", \"B1\"]\n",
    "num = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "phiRange = 90\n",
    "B = [triangularFuzzySet(a=-phiRange/(num-1)+phiRange/(num-1)*i,\n",
    "                        b=phiRange/(num-1)*i,\n",
    "                        c=phiRange/(num-1)+phiRange/(num-1)*i) for i in range(num)]\n",
    "x = np.linspace(0,phiRange,9000)\n",
    "for i in range(num):\n",
    "    plt.plot(x,fuzz.membership.trimf(x, [B[i].a, B[i].b, B[i].c]), label=indexB[i]) \n",
    "plt.xlabel(\"deg\")\n",
    "plt.ylabel(\"$\\mu$\")\n",
    "plt.title(\"Fuzzy Sets for $\\phi(deg)$\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining Fuzzy Sets for $\\theta(deg) \\in Ci$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "indexC =[\"S1\", \"CE\", \"B1\",\"B2\"]\n",
    "num = 3\n",
    "S1 = 0\n",
    "CE = 1\n",
    "B1 = 2\n",
    "N = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "thetaRange = 40\n",
    "C = [triangularFuzzySet(a=-20-thetaRange/(num-1)+thetaRange/(num-1)*i,\n",
    "                        b=-20+thetaRange/(num-1)*i, \n",
    "                        c=-20+thetaRange/(num-1)+thetaRange/(num-1)*i) for i in range(num)]\n",
    "d = np.linspace(-20,20,4000)\n",
    "Ci = np.zeros([num+1,4000])\n",
    "for i in range(num):\n",
    "    Ci[i] = fuzz.membership.trimf(d, [C[i].a, C[i].b, C[i].c])\n",
    "    plt.plot(d,Ci[i], label=indexC[i]) \n",
    "plt.xlabel(\"deg\")\n",
    "plt.ylabel(\"$\\mu$\")\n",
    "plt.title(r'Fuzzy Sets for $\\theta(deg)$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2 & 3 : Generating rules from dataset and assinging a degree to each rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function compare the known facts with the antecedents of fuzzy rules to find the degrees of compatibility with respect to each antecedent MF.[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Degrees of compatibility\n",
    "def doc(fuzzy_set, singleton_input):\n",
    "    if (singleton_input<=fuzzy_set.a):\n",
    "        return 0\n",
    "    \n",
    "    if (singleton_input>fuzzy_set.a and singleton_input<=fuzzy_set.b):\n",
    "        return (1/(fuzzy_set.b-fuzzy_set.a)*(singleton_input-fuzzy_set.a))\n",
    "    \n",
    "    if (singleton_input>fuzzy_set.b and singleton_input<=fuzzy_set.c):\n",
    "        return (1-1/(fuzzy_set.c-fuzzy_set.b)*(singleton_input-fuzzy_set.b))\n",
    "    \n",
    "    if (singleton_input>fuzzy_set.c):\n",
    "        return 0\n",
    "    \n",
    "    print(\"Error:\" + str(singleton_input))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An observation of a truck driver operation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.array([[1,    90,   20 ],\n",
    "                 [1   , 80.1, 17 ],\n",
    "                 [1.16, 71.7, 15 ],\n",
    "                 [1.46, 64.3, 13 ],\n",
    "                 [1.89, 57.8, 11 ],\n",
    "                 [2.41, 52.4, 9  ],\n",
    "                 [3.01, 47.9, 6  ],\n",
    "                 [3.68, 44.9, 3  ],\n",
    "                 [4.38, 43.4, 1  ],\n",
    "                 [5.11, 42.9, -1 ],\n",
    "                 [5.84, 43.4, -3 ],\n",
    "                 [6.57, 44.9, -5 ],\n",
    "                 [7.28, 47.4, -8 ],\n",
    "                 [7.94, 51.4, -11],\n",
    "                 [8.56, 56.9, -13],\n",
    "                 [9.09, 63.3, -15],\n",
    "                 [9.52, 70.7, -17],\n",
    "                 [9.84, 79.1, -20]])\n",
    "\n",
    "dataset = pd.DataFrame(data, index=range(18), columns=[ \"x(m)\", \"phi(deg)\", \"theta(deg)\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Generating rules from dataset\n",
    "likely_x_set=  [indexA[np.argmax([doc(A[i],data[j,0]) \n",
    "                                 for i in range(len(A))])] for j in dataset.index]\n",
    "likely_phi_set=  [indexB[np.argmax([doc(B[i],data[j,1]) \n",
    "                                 for i in range(len(B))])] for j in dataset.index]\n",
    "likely_theta_set=  [indexC[np.argmax([doc(C[i],data[j,2]) \n",
    "                                 for i in range(len(C))])] for j in dataset.index]\n",
    "#Assinging a degree to each rule\n",
    "likely_x_set_degree=  np.array([np.max([doc(A[i],data[j,0]) \n",
    "                                 for i in range(len(A))]) for j in dataset.index])\n",
    "likely_phi_set_degree=  np.array([np.max([doc(B[i],data[j,0]) \n",
    "                                 for i in range(len(B))]) for j in dataset.index])\n",
    "likely_theta_set_degree=  np.array([np.max([doc(C[i],data[j,0]) \n",
    "                                 for i in range(len(C))]) for j in dataset.index])\n",
    "degree = likely_x_set_degree*likely_phi_set_degree*likely_theta_set_degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x(m)</th>\n",
       "      <th>phi(deg)</th>\n",
       "      <th>theta(deg)</th>\n",
       "      <th>likely_x_set</th>\n",
       "      <th>likely_phi_set</th>\n",
       "      <th>likely_theta_set</th>\n",
       "      <th>degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.00</td>\n",
       "      <td>90.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>S1</td>\n",
       "      <td>B1</td>\n",
       "      <td>B1</td>\n",
       "      <td>0.743111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.00</td>\n",
       "      <td>80.1</td>\n",
       "      <td>17.0</td>\n",
       "      <td>S1</td>\n",
       "      <td>B1</td>\n",
       "      <td>B1</td>\n",
       "      <td>0.743111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.16</td>\n",
       "      <td>71.7</td>\n",
       "      <td>15.0</td>\n",
       "      <td>S1</td>\n",
       "      <td>B1</td>\n",
       "      <td>B1</td>\n",
       "      <td>0.704807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.46</td>\n",
       "      <td>64.3</td>\n",
       "      <td>13.0</td>\n",
       "      <td>S1</td>\n",
       "      <td>CE</td>\n",
       "      <td>B1</td>\n",
       "      <td>0.635022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.89</td>\n",
       "      <td>57.8</td>\n",
       "      <td>11.0</td>\n",
       "      <td>S1</td>\n",
       "      <td>CE</td>\n",
       "      <td>B1</td>\n",
       "      <td>0.539566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2.41</td>\n",
       "      <td>52.4</td>\n",
       "      <td>9.0</td>\n",
       "      <td>S1</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.431182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.01</td>\n",
       "      <td>47.9</td>\n",
       "      <td>6.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.477192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.68</td>\n",
       "      <td>44.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.551462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.38</td>\n",
       "      <td>43.4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.617565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.11</td>\n",
       "      <td>42.9</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.645439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.84</td>\n",
       "      <td>43.4</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.512610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.57</td>\n",
       "      <td>44.9</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.393394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>7.28</td>\n",
       "      <td>47.4</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>CE</td>\n",
       "      <td>0.290011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7.94</td>\n",
       "      <td>51.4</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>B1</td>\n",
       "      <td>CE</td>\n",
       "      <td>S1</td>\n",
       "      <td>0.292003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.56</td>\n",
       "      <td>56.9</td>\n",
       "      <td>-13.0</td>\n",
       "      <td>B1</td>\n",
       "      <td>CE</td>\n",
       "      <td>S1</td>\n",
       "      <td>0.329793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>9.09</td>\n",
       "      <td>63.3</td>\n",
       "      <td>-15.0</td>\n",
       "      <td>B1</td>\n",
       "      <td>CE</td>\n",
       "      <td>S1</td>\n",
       "      <td>0.356083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.52</td>\n",
       "      <td>70.7</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>B1</td>\n",
       "      <td>B1</td>\n",
       "      <td>S1</td>\n",
       "      <td>0.373483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>9.84</td>\n",
       "      <td>79.1</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>B1</td>\n",
       "      <td>B1</td>\n",
       "      <td>S1</td>\n",
       "      <td>0.384216</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x(m)  phi(deg)  theta(deg) likely_x_set likely_phi_set likely_theta_set  \\\n",
       "0   1.00      90.0        20.0           S1             B1               B1   \n",
       "1   1.00      80.1        17.0           S1             B1               B1   \n",
       "2   1.16      71.7        15.0           S1             B1               B1   \n",
       "3   1.46      64.3        13.0           S1             CE               B1   \n",
       "4   1.89      57.8        11.0           S1             CE               B1   \n",
       "5   2.41      52.4         9.0           S1             CE               CE   \n",
       "6   3.01      47.9         6.0           CE             CE               CE   \n",
       "7   3.68      44.9         3.0           CE             CE               CE   \n",
       "8   4.38      43.4         1.0           CE             CE               CE   \n",
       "9   5.11      42.9        -1.0           CE             CE               CE   \n",
       "10  5.84      43.4        -3.0           CE             CE               CE   \n",
       "11  6.57      44.9        -5.0           CE             CE               CE   \n",
       "12  7.28      47.4        -8.0           CE             CE               CE   \n",
       "13  7.94      51.4       -11.0           B1             CE               S1   \n",
       "14  8.56      56.9       -13.0           B1             CE               S1   \n",
       "15  9.09      63.3       -15.0           B1             CE               S1   \n",
       "16  9.52      70.7       -17.0           B1             B1               S1   \n",
       "17  9.84      79.1       -20.0           B1             B1               S1   \n",
       "\n",
       "      degree  \n",
       "0   0.743111  \n",
       "1   0.743111  \n",
       "2   0.704807  \n",
       "3   0.635022  \n",
       "4   0.539566  \n",
       "5   0.431182  \n",
       "6   0.477192  \n",
       "7   0.551462  \n",
       "8   0.617565  \n",
       "9   0.645439  \n",
       "10  0.512610  \n",
       "11  0.393394  \n",
       "12  0.290011  \n",
       "13  0.292003  \n",
       "14  0.329793  \n",
       "15  0.356083  \n",
       "16  0.373483  \n",
       "17  0.384216  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.join(pd.DataFrame({\"likely_x_set\":likely_x_set, \n",
    "                          \"likely_phi_set\":likely_phi_set,\n",
    "                          \"likely_theta_set\":likely_theta_set,\n",
    "                          \"degree\":degree}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step4: Generating Rule base"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#N means there is no rule\n",
    "\n",
    "            #    phi(deg)    \n",
    "            #S1  CE   B\n",
    "rule_base = [[B1, B1, B1], # S1\n",
    "             [CE, CE,  CE], # CE x(m)\n",
    "             [S1, S1, S1]] # B1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 5: Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. **Degrees of compatibility**[1]\n",
    "2. **Firing Strength**: Combine degrees of compatibility with respect to antecedent MFs in a rule using fuzzy **AND (product)** operators to form a firing strength that indicates the degree to which the antecedent part of the rule is satisfied.[1]\n",
    "\n",
    "3. ***Qualified (induced) consequent MFs***: Apply the firing strength to the consequent MF **(here by product)*** of a rule to generate a qualified consequent MF.[1]\n",
    "4. ***Overall output MF***: Aggregate all the qualified consequent MFs to obtain an overall output MF.[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fuzzy_controller(x, phi):\n",
    "    # 1. Degrees of compatibility \n",
    "    # 2. Firing Strength: \n",
    "    u = np.array([[doc(A[i], x)*doc(B[j], phi) \n",
    "                   for j in range(len(B))] \n",
    "                  for i in range(len(A))])\n",
    "    # 3. Qualified (induced) consequent MFs\n",
    "    thetai = np.array([ [Ci[rule_base[i][j]]*u[i,j] for j in range(len(B))] \n",
    "                       for i in range(len(A))])\n",
    "    # 4. Overall output MF\n",
    "    theta = thetai [0,0]\n",
    "    for i in range(len(A)):\n",
    "        for j in range(len(B)):\n",
    "            theta = np.maximum(thetai[i,j],theta)\n",
    "            \n",
    "    #defuzzification : COA     \n",
    "    theta  = np.sum(theta*d)/np.sum(theta)\n",
    "    \n",
    "    return theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation1: $(x_0, \\phi_0) = (0,88)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_final:10.183024905363192    phi_final:88.24491217596699\n"
     ]
    },
    {
     "data": {
      "image/png": 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penvTnwJUqBCRMJRZcJiH31vPiO5tuP2M3l7HEREJeisy9nPf3JVkHSjhxxcMYBC7VKQ4sSigqZmVA82ATMABRyZ8tw5sO9oU4DXnXCmQbmbbgDHA4vqPLCICqWl5tGgSxWCP+lOAChUiEmYqKn388LVVVFT6+OvVwz2bdyci0hhU+hzPfLOdv36+hU6tY3nzzvGM7N6W5OTdXkcLas65PWb2ZyADOAx85pz7zMxuAz4ys8NAITCumsO7AClVft4d2CYi0iBS0vJI7NnW06nRKlSISFj5+1fbWLIjn79ePYxe8c29jiMiErT2FZZw/+urWLQ9j0tP78RvrxxKq9hor2M1CmbWFv/IiF5AAfCmmd0IXAlc7JxLNbMfA38Fbjv68Gru0lVzjhnADICEhASSk5NrnLOoqKhWxzUU5asb5aubcM13oNSxPaeYkW3L6nT/dc2nQoWIhI3UtDz+/tVWrhzRhStHdvU6johI0FqwNZf7XlvJ4bJK/vi907lqVFfMNAKtBiYD6c65HAAzexuYCAxzzqUG9nkd+KSaY3cD3ar83JVqpog452YCMwESExNdUlJSjUMmJydTm+MaivLVjfLVTbjmm7cmC1jB9ZNHM6J721rfT13zqc29iISFfYUl3DN3Jd3bNePRK4Z4HUdEJCg553g6eRs3z0qlfYsmfHDvJK5O7KYiRc1lAOPMrJn5H7xzgQ1AazPrH9jnPGBjNce+D1xrZk3MrBfQD1jSEKFFRFLT82gWE8mQLq09zaERFSIS8soqfHz/lRUUlVQwZ/pYWjTRU5+IyNEOlpTzwBur+WzDPi4f1pnff3cozWL0fFkbgakdbwErgApgJf7RD7uBf5uZD9gP3ApgZpcDic65h51z6wOrhGwIHHu3VvwQkYaSmpbPqB5tifawPwXUY6HCzGYBlwLZzrkhgW1/Ai4DyoDtwC3OuYLAbT8DpgOVwH3OuU/rK5uIhJdff7iB5Tv389T1IxjQUUuRiogcbeu+g9zx8nJ25hfz8KWDuWViT42iqCPn3CPAI0dtfifwdfS+7+MfSXHk598Av6nXgCIiR8k/VMbmfQe5fHhnr6PU69SPF4ELj9r2OTDEOXc6sAX4Gfyf9aIvBJ42s8h6zCYiYeLNZbt4OWUnd5zZm0tP9/5JV0Qk2Mxbk8WUfyyksKSCV28by62TeqlIISIShpak5wEwrnc7j5PUY6HCOfctkH/Uts+ccxWBH1PwNweCKutFO+fSgSPrRYuI1Nqa3QX84t11TOwbx48vGOB1HBGRoOLzOf786WbufnUFAzu2ZN59kxjbO87rWNJAsg+WUFLxfxYTEZEwlpKWT2x0BEO7tPE6iqc9Km7F3+0YarBedF2XYgr2ZWZqQ9cU/ELteiD4r6mgxMejKSW0jIJrux9mwfxvT3hMsF+TiMipcriskgfeXMVHa/dyTWI3fn3FEGKi1GM9XGzaW8iFf5vPHac3+T/Dn0UkfKWm+/tTBMP/B54UKszsF/ibA71yZFM1u1Vb4q3rUkzBvsxMbeiagl+oXQ8E9zUdKq3gmpmLKfGV8cYd40+6a3EwX5OIyKmyr7CE22YvY13mAX55ySCma6pH2OnXoSUtY6PYlK8enSLiV1Bcxqa9hdw/uf+Jd24ADV6oMLOp+JtsnuucO1KMOKn1okVETqTS57hv7ko2ZBby/NTRni+tJCISTNbtOcD02UspKqng2ZsSmTw4wetI4oHICGNsr3as3ZnjdRQRCRJL0vNxDsYFyRTABh3TYWYXAj8FLnfOFVe5SetFi0idOef41Qfr+XJTNr+6/DTOHtjB60giIkHjk3VZfO+ZRURFRPDWXRNUpAhz43rHsa/YkXXgsNdRRCQIpKbn0yQqgmHdguNDvnorVJjZXGAxMMDMdpvZdOApoCXwuZmtMrNnAJxz64Ej60V/gtaLFpFaeH5BOi8t3smMM3tz0/ieXscREQkaz81P4845KxjUqRXv3j2RQZ1aeR1JPDa+j/9T05S0PI+TiEgwSE3PY0T3NjSJCo7FN+tt6odz7rpqNj9/nP21XrSI1Non67L4zUcbuWhIRx68cKDXcUREgoLP53hs3kZmLUzn4qEd+evVw4mNDo4XoeKtQR1b0TwaFm/P4zsjup74ABEJWQcOl7M+s5D7zunndZT/8HLVDxGRU2LRtlzum7uK4d3a8Pg1w4mIUFM4EZGS8koeeHM189ZkMW1CTx66dDCRen6UgIgIY0DbSFLS8r2OIiIeW7YjuPpTQAP3qBAROdVW7SrgtpeW0TO+GS9MG61PCkVEgAPF5dw8awnz1mTxi4sH8chlKlLI/zWwXSQZ+cXsKVCfCpFwlpqeT0xkBCO6t/E6yn+oUCEijdbmvQeZ9sIS4ls04eXpY2nTLMbrSCIinsssOMxV/1rEyoz9PHHtcG4/s7eWH5VqDYrzF/dTtqtPhUg4S03LY3i3NkH1gZ8KFSLSKGXkFXPT86nEREYwZ/pYElrFeh1JRMRzW/Yd5MqnF5FVUMLsW8YwZXgXryNJEOvSwmjbLJrFaqgpErYOlpSzLrOQsb3beR3lv6hHhYg0OtmFJdz4fCqlFT7euGM83eOaeR1JRMRzq3cVMPWFJcRERvDGneO1soecUIQZY3vFsVgjKkTC1rKd+6n0uaDqTwEaUSEijUxuUSk3Pp9KblEpL94ymgEdW3odSUTEc4u253L9sym0jI3irTsnqEghJ218nzj2FBxmV36x11FExAOpaflERxoju7f1Osp/UaFCRBqNvKJSbng2lYz8Yp67OZERQfaEKiLihc/W72XaC0vp2rYZb905QaPMpEaOfIqq6R8i4Sk1PY/Tu7ahaUzw9KcAFSpEpJHIKyrlhudS2ZF3iOenjmZC33ivI4mIeO7fy3dz1ysrGNypFa/fMU79eqTG+ie0oF3zGFJUqBAJO4dKK1i7+wBjewVXfwpQoUJEGoH8Q2Xc8Fwq6bmHmDVtNBNVpBAR4cWF6Tzw5mrG9W7HK7dp5SOpHTNjXO92pGzPwznndRwRaUDLd+6nIgj7U4AKFSIS5PYfKuP6Z1NIz/WPpFCRQkQEnk7exv9+sIHzByfw/NTRNG+i/uhSe+N7x5F5oIQM9akQCSup6XlERhijegTfdGoVKkQkaO0/VMb1z6WSlnuIZ29OZFI/FSlERJ74Yit//GQzU4Z35ukbRgbVuvfSOB35NFXTP0TCS0paPkO7tA7KYrcKFSISlLILS7hm5mK25xTx3M2JnNm/vdeRREQ85ZzjL59t5vEvtvDdkV3569XDiYrUSzmpu74dWhDfoomWKRUJI4dKK1i9q4DxfYJv2gdA8JVORCTs7d5fzI3PpZJ90L8E6YQ+GkkhIuHNOcfvP9nEv75J49rR3fjtd4YSEWFex5IQ8Z8+FWn5OOcw098tkVC3LNCfYnwQ9qcAjagQkSCTnnuIq59ZTP6hMubcNlZFChEJe845fv3hRv71TRo3jeuhIoXUi3G949hbWMKOPPWpEAkHi7fnER1pJPYMvv4UoEKFiASRTXsLueqZxZRW+Jg7YxwjuwfnE6eISEPx+RwPv7eeWQvTuWViTx6dcpqKFFIvjgz/1vQPkfCwOC2PYV3b0CwmOCdZqFAhIkFhze4Crp2ZQmQEvH7HeE7r3NrrSCIinvL5HL94dy0vp+zkjjN78/ClgzUkX+pN7/jmtG/ZRA01RcLAwZJy1u05ELT9KUA9KkQkCCzensftLy2jbfNoXpk+ju5xzbyOJCLiKZ9z/OTfa3hr+W7uObsvD5zfX0UKqVdmxvjecSxOy1OfCpEQt2zHfiqDuD8FaESFiHjso7VZTJ21hE6tY3nzjgkqUohI2PP5HLPWlfHW8t3cP7k/P7pggN40SoMY3yeOnIOlpOUe8jqKiNSjxWl5xERGMLJH8E6zVqFCRDwzJ2Und7+6gqFdW/PmnePp2DrW60giIp7y+Rw/f2ctC/ZU8MPJ/fjB5H5eR5JaMrP7zWy9ma0zs7lmFmtm881sVeAr08zePcaxlVX2e7+hMo8LfLq6SH0qRELa4u15DO/ehtjoSK+jHJMKFSLS4JxzPP75Fn757jrOGdCBOdPH0qZZjNexJKC6F9deZxIJB845Hn5/Ha8t3cVlfaL5wbkqUjRWZtYFuA9IdM4NASKBa51zZzjnhjvnhgOLgbePcReHj+znnLu8gWLTM64ZnVvHsmhbbkOdUkQa2IHD5azPPBDU0z5AhQoRaWCVPscv313HE19u5apRXfnXTaNoGhO81dxwc6wX196mEgl9zjl+9cEG5qRkcOdZfbiyb7SmezR+UUBTM4sCmgGZR24ws5bAOUC1Iyq8YmZM6BvP4rQ8fD7ndRwRqQdL0/PxOYK6kSaoUCEiDaikvJJ7Xl3BK6kZ3JXUhz9+73SiIvU0FISO+eJaRE495xy/mbeRFxft4LZJvfjphepJ0dg55/YAfwYygCzggHPusyq7fAf40jlXeIy7iDWzZWaWYmZX1HPc/zKxbxwFxeVsyDpWNBFpzBan5dEkKoIR3dt4HeW4tOqHiDSI/ENlzHhpGct27uehSwczfVIvryNJNZxze8zsyIvrw8BnR724FpFTyDnHHz7ZzHML0pk2oSe/uGSQihQhwMzaAlOAXkAB8KaZ3eicmxPY5TrguePcRXfnXKaZ9Qa+MrO1zrntR51jBjADICEhgeTk5BrnLCoq+r/HlfgAeOmzVC7u5e20zGrzBRHlqxvlq5va5vt89WF6t4LFC+af+lBV1PXxU6FCROrdjtxD3PLiUvYUHOYf14/kktM7eR1JjuEkXlwf2a9OL5BD9T//hqJ8dRMs+ZxzvL21nA/SyjmnWxRntczmm29ygODJeCyNIZ/HJgPpzrkcADN7G5gAzDGzOGAM/lEV1XLOZQb+TDOzZGAEsP2ofWYCMwESExNdUlJSjUMmJydT3XH/2PANe11TkpLG1Pg+T6Vj5QsWylc3ylc3tclXUFzGrk8/5/7J/UlKqt8+SHV9/FSoEJF6tXxnPrfNXgbA3NvHMqpHO48TyQkc88V11Z3q+gI5FP/zb0jKVzfBku9vX2zhg7StXDemG7+5YigREf9/JEWwZDyWxpDPYxnAODNrhn902rnAssBtVwEfOudKqjswUDAuds6Vmlk8MBH4YwNk/o+JfeJ4Y9luyip8xERpiqZIqEhJy8c1gv4UoB4VIlKP5q3J4rpnU2ndNJp3vj9RRYrG4T8vrs0//vxcYKPHmURCzjPfbOdvX/ibCh9dpJDGzzmXCrwFrADW4n/NPTNw87XA3Kr7m1mimR2ZCjIIWGZmq4Gvgd875zY0SPCACX3jOVxeycqM/Q15WhGpZylpeTSNjmRY1+DuTwEaUSEi9cA5x8xv0/jdx5tI7NGWmTcn0q65lh9tDJxzqWZ25MV1BbCS///iWkROgZcX7+D3H2/i8mGd+f13T1eRIkQ55x4BHqlme1I125YBtwW+XwQMre98xzOudxwRBgu35TI2yJcwFJGTl5KWR2LPto1ipFTwJxSRRqWi0scv313H7z7exCWnd2LObWNVpGhknHOPOOcGOueGOOducs6Vep1JJFS8vWI3D723nsmDEvjL1cOIVJFCglDrptEM7dqGhdvzvI4iIqdIXlEpm/YeZFwjKT7WW6HCzGaZWbaZrauyrZ2ZfW5mWwN/tg1sNzN70sy2mdkaMxtZX7lEpP4cKq3g9peW8UpqBnee1Ye/XzuC2OhIr2OJiASFT9Zl8aM3VzOxbxxPXT+CaC3PLEFsYp84Vu8qoKi0wusoInIKpKbnA42jPwXU74iKF4ELj9r2IP41o/sBXwZ+BrgI6Bf4mgH8sx5ziUg9yCw4zFXPLObbrbn85jtDePCigRrOLCIS8M2WHO6du5IR3dsy86ZEFXEl6E3sG0+Fz7EkXaMqRELB4u15NIuJZGiX1l5HOSn1Vqhwzn0L5B+1eQowO/D9bOCKKttfcn4pQBsz0/qFIo3Eioz9XP7UQnblF/P81ERuGNvD60giIkFjSXo+d7y8jH4dWjJr2miaN1GLMAl+o3r457Ev3KZChUgoWJyWx+ie7RrNaL6GTpngnMsCCPzZIbC9C7Cryn67A9tEJMi9t2oP185MoVlMJG9/fwJJAzqXRGJpAAAgAElEQVSc+CARkTCxZncBt764lC5tmvLy9DG0bhrtdSSRkxIbHUlij7Ys3JbrdRQRqaPsgyVsyy5qNNM+IHhW/ahufLirdkezGfinh5CQkFDjdbKLioqCYW3tU0rXFPxC7XoACg8Wcc/Mz/gwrZwBbSO4Zzjs2bicPY14IctQ/D2JiHc27z3IzbOW0LZ5NK/cNo64Fk28jiRSIxP7xvOnTzeTW1RKvP7+ijRaqWmB/hSNpJEmNHyhYp+ZdXLOZQWmdmQHtu8GulXZryuQWd0dOOdmElgqLzEx0SUlJdUoQHJyMjU9JtjpmoJfqF1PcVkFN/3jC5bvK+fa0d14dMqQRrHM0YmE2u9JRLyzI/cQNz6fSpOoCF6ZPo6OrWO9jiRSYxMCn74u3p7HZcM6e5xGRGprcVoeLZtEcVrnVl5HOWkN/c7ifWBq4PupwHtVtt8cWP1jHHDgyBQREQkumQWH+d4/F7NiXyUPXTqY3105NCSKFCIip0pmwWFueC6VSp/jldvG0j2umdeRRGplaJfWtGwSxaLtmv4h0pgt3JbL2N5xRDWS/hRQjyMqzGwukATEm9lu4BHg98AbZjYdyACuCuz+EXAxsA0oBm6pr1wiUnsrM/Zz+0vLKSmv5P5RTZg+qZfXkUREgkpuUSk3PpdKYUk5c28fR98OLb2OJFJrUZERjO0dxwL1qRBptHblF7Mzr5hbJvT0OkqN1Fuhwjl33TFuOreafR1wd31lEZG6e3flHn7y7zUktGrCq7ePJXPjcq8jiYgElcKScqbOWkLmgcPMmT6WIY1kCTiR45nUN44vNu5jV34x3dppdJBIY3NkRNTEvvEeJ6mZxjP2Q0Q8UVHp4zfzNvDD11cxvFsb3rt7Ev0T9AmhiEhVJeWV3D57GZv3HuSZG0eR2LOd15FETokjb260+odI47RgWx4dWjahb4cWXkepERUqROSYCorLuOXFpTw7P52bx/fgldvG0q55jNexRESCSkWlj3vnrmTJjnz+cvUwLdMsIaVvhxZ0aNmEhdvzvI4iIjXk8zkWbctlUt94zKpbaDN4BcvypCISZDbtLWTGS8vZe6CEP3x3KNeM7u51JBGRoOOc48G31/L5hn38esppTBnexetIIqeUmTGhj79PhXOu0b3ZEQlnm/YeJO9QWaOb9gEaUSEi1fh4bRZXPr2IkvJK5s4YpyKFiEg1nHP89qONvLV8Nz+c3I+bxvf0OpJIvZjQN57cojI27zvodRQRqYEjU7ZUqBCRRs3nc/zls83c9coKBnRsyQf3TmJUj7ZexxIRCUrPfJPGs/PTmTq+Bz84t5/XcUTqzZE3OQu2qk+FSGOyYFsufTu0oGPrWK+j1JgKFSIC+LvV3/7SMv7+1TauTuzKazPGkdCq8T2piYg0hNeWZPCHTzZx+bDOPHLZaRoOLyGtS5um9G7fnPkqVIg0GmUVPpak5zOxT5zXUWpFPSpEhO05Rdz+0jIy8op5dMpp3DSuh150i4gcwyfrsvj5O2tJGtCeP181jIgIPV9K6DuzX3teW5pBSXklsdGRXscRkRNYmbGfw+WVjXLaB2hEhUjY+2rTPq54aiEHisuZc9tYbh7fU0UKEZFjWLQtl/vm+pdrfvqGkcRE6aWUhIcz+8dTUu5j2Y79XkcRkZOwcFsuEQbjGumICv3vKhKmnHP84+ttTJ+9jO5xzXj/3kmM6904n8hERBrCmt0F3P7SMnrFN2fWtNE0i9HAVAkfY3vFER1pzN+a43UUETkJC7blMqxbG1rFRnsdpVZUqBAJQwdLyrlzznL+9OlmLh/WmbfunECXNk29jiUiErS2ZRcx7YWltG0ew0vTx9CmWYzXkUQaVPMmUYzq0ZZv1adCJOgVlpSzevcBJjXSaR+gQoVI2Nm67yBTnlrIFxuzeejSwfztmuE0jdFcUxGRY8ksOMzNz6cSYTBn+lg1GpawdWb/9mzMKiT7YInXUUTkOFLT8qn0OSb0UaFCRBqBeWuymPKPhRSWVPDqbWOZPqmX+lGIiBzH/kNl3DxrCQdLKph96xh6xjf3OpKIZ87s1x7QMqUiwW7htlxioyMY2aON11FqTYUKkTBQUenjN/M2cPerKxjYsSXz7pvEWPWjEBE5ruKyCm6dvZSM/GKenZrIaZ1bex1JxFODO7UirnmMlikVCXILtuUyplccTaIa76hpdYESCXG5RaXc8+oKUtLyuXl8D355yWB1qRcROYHySh/3vLqS1bsK+OeNo9RsWASIiDAm9Ytn/tZcfD6npXlFgtC+whK2ZRdxdWJXr6PUid6tiISwFRn7ufTJBazMKOCvVw/j0SlDVKQQETkB5xw/f3stX23K5tdXDOGC0zp6HUkkaJzRrz25RaVs3FvodRQRqcbCbf4RTxMbcSNNUKFCJCQ555iTspNr/rWY6Cjj7e9P4MqRjbuqKiLSUP706WbeXL6bH5zbjxvG9vA6jkhQOaOf/82Ppn+IBKcF23Jp1zyGQR1beR2lTlSoEAkxJeWV/OjNNfzy3XVM6hvPh/ecoXnVIiIn6cWF6TydvJ3rxnTnh5P7eR1HGjEzu9/M1pvZOjOba2axZjbfzFYFvjLN7N1jHDvVzLYGvqY2dPbjSWgVy4CElszfmuN1FBE5inOOhdtyGd8nrtFPzVKPCpEQsiu/mDvnLGd9ZiE/OLcfPzi3X6N/khIRaSgfrsnkVx9u4PzBCTx2xRCtiiS1ZmZdgPuAwc65w2b2BnCtc+6MKvv8G3ivmmPbAY8AiYADlpvZ+865/Q2T/sTO7B/P7EU7OVxWqSXORYLI9pwi9hWWMqmRT/sAjagQCRnfbMnhsqcWsCu/mFnTErn/vP4qUoiInKRF23P5n9dXk9ijLU9eN4JIPX9K3UUBTc0sCmgGZB65wcxaAucA1Y2ouAD43DmXHyhOfA5c2AB5T9oZ/dpTVukjJT3P6ygiUsWRpYNVqBARz/l8jqe+2sq0F5bQsVUsH9w7iXMGJngdS0Sk0VifeYAZLy2nZ3wznrt5NLHR+oRY6sY5twf4M5ABZAEHnHOfVdnlO8CXzrnqOlJ2AXZV+Xl3YFvQGNOrHTFREczfoj4VIsFkwbZcurVrSrd2zbyOUmea+iHSiB0oLud/3ljFl5uyuWJ4Z3535ekagikiUgO78ouZ9sJSWsVGMfvWMbRuFu11JAkBZtYWmAL0AgqAN83sRufcnMAu1wHPHevwara5as4xA5gBkJCQQHJyco1zFhUV1eo4gH6t4ZPVOzizZXatjj8ZdcnXEJSvbpSvbo7OV+FzLNhSzPjOUUGRu66PnwoVIo3U2t0HuOuV5ewrLOFXl5/GzeN7aD61iEgN5BWVcvOsJZRV+Jh713g6tW7qdSQJHZOBdOdcDoCZvQ1MAOaYWRwwBv+oiursBpKq/NwVSD56J+fcTGAmQGJioktKSjp6lxNKTk6mNscBbI1I4zcfbWTAiLH19m+nLvkagvLVjfLVzdH5Fm/Po6QyhWuThpEUBMtq1/Xx09QPkUbGOcerqRl895+L8Pkcb9wxnqkTeqpIISJSA4dKK7j1xaVkFhxm1rRE+nZo6XUkCS0ZwDgza2b+/6DPBTYGbrsK+NA5V3KMYz8FzjeztoGRGecHtgWVM/oHlinV9A+RoPDt1hyiIowJfeK8jnJKqFAh0ogcLqvkgTdW8/N31jK+Txzz7juDEd3beh1LRKRRqfA57nplBWv3HOCp60cyqkc7ryNJiHHOpQJvASuAtfhfc88M3HwtMLfq/maWaGbPBY7NB34NLA18PRrYFlQGJLSkfcsmfKtlSkWCwrdbchjZvS0tY0NjCqOmfog0Emk5Rdw1ZwVbsg9y/+T+3HtOX63qISJSQz6fY9a6MhZlFvP7K4dy3mA1H5b64Zx7BP8yo0dvT6pm2zLgtio/zwJm1We+ujIzzugXz1ebsqn0Oa2UI+KhnIOlrM8s5Efn9/c6yimjERUijcBHa7O4/KmFZB8sYfYtY/jB5H4qUoiI1MIfPtnEoswKHjivP9eO6e51HJFG7az+7SkoLmfdngNeRxEJawu2+Uc2ndm/vcdJTh2NqBAJYuWVPn7/8SaeX5DOiO5t+Mf1I+ncRs3eRERq47n5afzr2zTO6R7FPef09TqOSKM3sa+/T8U3W3IY1q2Nx2lEwte3W3Jp1zyGIZ1bex3llNGICpEgtfdACdfOTOH5BencMrEnr88YryKFiEgtvbdqD4/N28hFQzpy46AYNSAWOQXiWzTh9K6tSd5cf0uUisjx+XyO+VtzmNQ3PqRGXHtSqDCz+81svZmtM7O5ZhZrZr3MLNXMtprZ62YW40U2kWCwYGsulzw5n01ZhTx1/Qgeuew0YqJUVxQRqY35W3P40ZurGdurHY9fM5wIFSlETpmkAR1YtauA/YfKvI4iEpY2ZBWSW1QWUtM+wINChZl1Ae4DEp1zQ4BI/N2P/wA87pzrB+wHpjd0NhGv+XyOv3+5lZtmpRLXIob37pnEpad39jqWiEijtXb3Ae58eTl92rdg5s2JxEZHeh1JJKScPaA9PodW/xDxyPyt/iWCz+wX73GSU8urj2ijgKZmFgU0A7KAc/Av4wQwG7jCo2winigoLmP67KX85fMtTBnWmXfvnkjfDi28jiVhyMzamNlbZrbJzDaa2XivM4nUxs68Q9zy4hLaNIth9q1jaN00NJZsEwkmp3dtQ9tm0SRvVqFCxAvfbslhYMeWdGgV63WUU6rBm2k65/aY2Z+BDOAw8BmwHChwzlUEdtsNdGnobCJeWbO7gLvmrCDnYCmPXTGEG8Z21/xp8dITwCfOue8FpuE18zqQSE3lHCzlpueXUOlzzL51DAkh9gJOJFhERhhn9W/PN1ty8PlcSM2RFwl2h0orWLYzn1sn9vI6yinX4IUKM2sLTAF6AQXAm8BF1ezqjnH8DGAGQEJCAsnJyTU6f1FRUY2PCXa6puB3rOtxzvH1rgpe3VhG6ybGg2Oa0LUknW++SW/4kDUUar8jCM1rqikzawWcCUwDcM6VAZp4LI1KUWkFt7y4hOyDJbx6+ziNThOpZ2cP7MC7qzJZs+cAw7X6h0iDSUnLo7zShVx/CvBmedLJQLpzLgfAzN4GJgBtzCwqMKqiK5BZ3cHOuZnATIDExESXlJRUo5MnJydT02OCna4p+FV3PcVlFfz87bW8uyGTpAHtefzq4bRt3nh6yIba7whC85pqoTeQA7xgZsPwj3j7gXPukLexRE5OWYWPO19ezsasgzx78yhGdm/rdSSRkHdGv/aYwdebslWoEGlA327JoWl0JIk9Q+//Oi8KFRnAODNrhn/qx7nAMuBr4HvAa8BU4D0Psok0iO05Rdw1Zzlbs4t44Lz+3H12Xw2VlGARBYwE7nXOpZrZE8CDwENVdwr10W3KVzde5fM5x8w1paRkVTJ9SAwRezeSvHdj0OSriWDP2BjyScNp1zyG4d3akLwlh/vP6+91HJGw4Jzj6805jO8TR5Oo0GsU7UWPilQzewtYAVQAK/GPkJgHvGZmjwW2Pd/Q2UQawodrMvnpW2uIjY7k5VvHMinEOvRKo7cb2O2cSw38/Bb+QsV/CfXRbcpXN17kc87x2LyNpGSl85MLB/D9pL7H3DfYHz8I/oyNIZ80rKT+Hfjbl1vILSolvkUTr+OIhLx9xY6M/MPcfmZvr6PUC09W/XDOPeKcG+icG+Kcu8k5V+qcS3POjXHO9XXOXeWcK/Uim0h9Kavw8b/vr+eeV1cysFMr5t13hooUEnScc3uBXWY2ILDpXGCDh5FETsrMb9N4fkE60yb05K6z+ngdRyTsnD2wPc75h6KLSP1bnVMJQFII9qcAb6Z+iISdvMM+rpm5mJUZBUyf1IsHLxpIdKRXqwOLnNC9wCuBFT/SgFs8ziNyXG+v2M3vPt7EJad34uFLB2vVJBEPDOncmvgWMSRvzuHKkV29jiMS8tbkVNCvQwu6tQvNxdlUqBCpZ/O35vC/iw7jIsp5+oaRXDy0k9eRRI7LObcKSPQ6h8jJ+GZLDj95aw0T+sTx16uHqd+PiEciIowz+7fny43ZVPockfq3KFJvDpVWsCnfx/QzOngdpd7oI12ReuLzOZ74Yis3z1pC6ybG+/dMVJFCROQUWrO7gLvmLKdfQkv+ddOokGwmJtKYnD2gAwcOl7Nq136vo4iEtIXbcql0kDQgNKd9gEZUiNSL/ENl/PD1VXy7JYcrR3Thgrj99G7fwutYIiIhY0fuIW55YSntmscw+5bRtIyN9jqSSNg7s197IiOMrzZlM6pHO6/jiISsrzfnEBsJiSH870wjKkROsVW7Crj0yfmkbM/jt98Zyl+uHkaTKA1/FBE5VXIOljL1hSX4nGP2rWPo0CrW60giArRuFs2oHm35cmO211FEQpZzjuTN2ZwWH0lMVOi+nQ/dKxNpYM45Zi/awVXPLCIiwvj3XRO4fmx3NXUTETmFDpVWcOuLS9lXWMLz00bTR6PVRILK5EEd2LT3ILv3F3sdRSQkbd53kKwDJZzePrSnO6pQIXIKFJVWcO/clTzy/nrO7NeeefeewdCurb2OJSISUsorfdz1ygo2ZBXyj+tHMrJ7W68jichRzh2UAMBXmzSqQqQ+fL3JvwTw6fEqVIjIcWzee5DLn1rAR2uz+OmFA3n25kRaN9NcaRGRU8k5x0/fWsO3W3L47XeG/OfNkIgElz7tW9ArvjlfaPqHSL34enM2gzu1om1saL+VD+2rE6lnb6/YzZR/LOBgSQWv3j6Ou5L6aGk8EZF68IdPNvP2yj38z3n9uWZ0d6/jiMhxnDuwAynb8ygqrfA6ikhIOXC4nOU793P2wNBd7eMIFSpEaqGkvJKfvb2G/3ljNcO7tWHefZMY1zvO61giIiHphYXpPPPNdq4f2517z+nrdRwROYFzBnWgrNLHgq25XkcRCSkLtuZS6XOcPaCD11HqnQoVIjW0M+8Q3/3nIuYu2cXdZ/dhzvSxdGipjvMiIvXhwzWZPPrhBs4fnMCvpwxRg2KRRmB0z3a0jI3iy437vI4iElK+2pRN66bRDO/Wxuso9S7K6wAijcmn6/fyozdXE2HGrGmJnDNQc6RFROrL4u15/M/rqxnVvS1PXjeCSE2tE2kUoiMjSBrQga83Z+PzOU2LFTkFKn2OrzdnkzSgPVGRoT/eIPSvUOQUKK/08duPNnLHy8vpHd+cD++dpCKFiEg92phVyIyXltE9rhnPTU0kNjq0u5uLhJrJgzqQW1TGqt0FXkcRCQmrdu0n/1AZk8OkmbRGVIicwN4DJdw7dwVLd+zn5vE9+MUlg2gSpRfMIiL1ZU/BYaa9sITmTaKYfesY2jSL8TqSiNTQWf3bExlhfLUxW0sJi5wCn2/IJirCOGtA6DfSBI2oEDmuBVtzueTJ+azPLOTJ60bw6JQhKlKIiNSjguIyps5aQnFZJS/eOpoubZp6HUmkVszsfjNbb2brzGyumcWa32/MbIuZbTSz+45xbKWZrQp8vd/Q2U+FNs1iGNWjLV+oT4XIKfHlxn2M7d2OVrHRXkdpEBpRIVINn8/x1NfbePyLLfTr0IKnbxhF3w4tvI4lIhLSSsormT57GRl5xbw0fQwDO7byOpJIrZhZF+A+YLBz7rCZvQFcCxjQDRjonPOZ2bFa9x92zg1voLj1ZvKgDvz2o03s3l9M17bNvI4j0mjtzDvE1uwirhsTPstza0SFyFHyD5Ux7cWl/PXzLXxneBfevXuiihQiIvWsotLHvXNXsiJjP3+7driWfBbPmVmMmdVlSE8U0NTMooBmQCZwF/Coc84H4JzLrnvS4HVuYC79lxtD+jJF6t0XgX9D4dKfAk6iUGFm95iZJpZJWFiRsZ9LnpxPSloev7tyKH+5ehjNYjTwSIKXmQ2uZluSB1FEas05x0PvrefzDft45NLBXDy0k9eRJMyZ2Q+ALGBbYIrGPTU53jm3B/gzkBG4nwPOuc+APsA1ZrbMzD42s37HuIvYwD4pZnZFHS7FU33at6B3++Z8vkHTP0Tq4osN++if0ILuceEzMulk3oF1BJaa2QpgFvCpc87VbyyRhuWc44WFO/jtRxvp1CaWt++awJAurb2OJXIy3jCzl4E/ArGBPxOB8Z6mEqmBJ7/cxtwlGdyV1IdpE3t5HUfCmJn9DVgB/AAY5JzLNrP2wK/M7NfOuYdO8n7aAlOAXkAB8KaZ3Qg0AUqcc4lmdiX+19ZnVHMX3Z1zmWbWG/jKzNY657YfdY4ZwAyAhIQEkpOTa3y9RUVFtTquJga1KOOT7YeY9/nXNI+u2TKlDZGvLpSvbpTv5Bwqd6SmF3Nxr+j/yhMs+Y6lrvlOWKhwzv3SzB4CzgduAZ4KzLN7/ugnTJHG6GBJOT/99xo+WruX8wYn8OerhtG6aXg0qZGQMBb4A7AIaAm8Akz0NJFIDby2JIPHv9jClSO78JMLBngdR+QbYAQQDywys0JgDbAWuNPM/uKcO5n1NicD6c65HAAzexuYAOwG/h3Y5x3gheoOds5lBv5MM7PkQKbtR+0zE5gJkJiY6JKSkk7+KgOSk5OpzXE10br3fuY9vYiy+H5cMqJrjY5tiHx1oXx1o3wn571Ve/C5VdxywWhG9fj/Ex2CJd+x1DXfSfWoCIyg2Bv4qgDaAm+Z2R9rfWaRILAxq5DLn1rIp+v38fOLBzLzplEqUkhjUw4cBpriH1GRfmTus0iw+2LDPn7+zlrO6t+eP3z3dMxq9mmryKnmnHvHOfcwkIJ/RMRkYDb+17/tgGQz23YSd5UBjDOzZub/i30usBF4FzgnsM9ZwJajDzSztmbWJPB9PP7i84Y6XZiHhnVtQ0KrJny6TtM/RGrjy43ZxLeIYXi3Nl5HaVAnHFERWDZpKpALPAf82DlXbmYRwFbgJ/UbUaR+vLlsF798dx2tm0Yz9/ZxjOnVzutIIrWxFHgPGA3EAf8ys+85577nbSyR41uRsZ975q5gSJfWPH3DSKIj1d9bgsrdwBvAKvyjKQYBa51zSWYWc6KDnXOpZvYW/mkkFcBK/KMfmgKvmNn9QBFwG4CZJQJ3OuduC5zrX2bmw/+h4u+dc422UBERYZw3OIF/L99DSXklsdFa5l3kZJVX+vh6czYXDelIZER4FfNPpkdFPHClc25n1Y2BJZUurZ9YIvWnpLySh99bxxvLdjOhTxxPXDuC9i2beB1LpLamO+eWBb7fC0wxs5u8DCRyItuyi7j1xaUktIpl1rTRNG+ipsUSXJxzW81sLHAeMBz/9I+fBG4rO8n7eAR45KjNpcAl1ey7jEDRwjm3CBha6/BB6ILTOjInJYP5W3M5b3D4rFogUldLd+RzsKTiPyvohJOT6VHx8HFu23hq44jUr/TcQ3z/lRVszCrkvnP68oPJ/cOuOimhpUqRouq2l73IInIy9hWWMHXWEqIijJduHUN8CxWKJTgFChLzAl9SB2N7xdEyNorP1u9VoUKkBr7YkE1MVARn9Iv3OkqD00cYEjY+XpvFj99aQ1Sk8cItozl7QAevI4mIhJXCknKmvbCU/cVlvD5jPD3imnsdSUQaQExUBOcO7MAXG/dRUekjSlO9RE7IOcdnG/YyqW88zWLC7227niUk5JVV+Hj0gw3c9coK+nZowbz7zlCRQkSkgZVWVHLny8vZuu8gz9w4iqFdtQS0SDg5/7SO7C8uZ9nO/V5HEWkU1mcWsnv/YS48raPXUTwRfqUZCSuZBYe559UVrMgoYNqEnvz84kHERKk+JyLSkHw+xwNvrGbR9jz+evUwzuzf3utIItLAzurfnpioCD5dv5dxveO8jiMS9D5dv5cIg8lhOl1K79gkZH2zJYdLnpzP5r0H+cf1I/nfy09TkUJEpIE553hs3kY+XJPFgxcN5MqRXb2OJCIeaN4kijP6xvPZ+n0457yOIxL0Plm3l7G94mjX/IQLDYUkvWuTkFPpczz++RamvbCEhFaxfHDvJC45vZPXsUREwtKz89OYtTCdaRN6cseZvb2OIyIeuuC0juwpOMyGrEKvo4gEte05RWzNLuKC08JzNAV4VKgwszZm9paZbTKzjWY23szamdnnZrY18GdbL7JJ45ZXVMrUWUt44sutfHdkV975/kR6t2/hdSwRkbD07so9/PajTVxyeicevnQwZlplSSScnTuoAxHm/6RYRI7t0/X+fyPnh2l/CvBuRMUTwCfOuYHAMGAj8CDwpXOu3/9r777DoyrTN45/n3Q6hBJK6EV6DUVBRbGiKxZUrCyg2EXdXet2dXct66q7NmygoCIIilhZNBaUFlrovYQOoYUkpMz7+yPj/lg2qKnnzMz9ua5cZMqZuc+ZzMuZZ94CzApeFvnZFmzK5IJnv2X+pkwev6wrT17ejSpx0V7HEhGJSN+s3cNvpiyhX6tEnrqiG1FaClok4tWtHk+/VnX5KH2Hhn+I/IjPlu2kW9PaNK5dxesonqn0QoWZ1QROA16FojWqnXMHgCHA+ODdxgMXV3Y2CU3OOV75ZgPDxs4hPjaKqbeewhW9m3odS0QkYm06WLTCR+v61Rl7fQrxMSoai0iRwV0asWHPEdbsyvI6iogvbT+Qw5KMgxE97AO8WfWjFbAHeN3MugFpwBggyTm3A8A5t8PMil0/0sxGA6MBkpKSSE1NLdGTZ2VllXgbv4vkfcrOd7y67ChpuwrplRTNqM6wZ80iUtdUfMaSiOTXKJSE4z6JVLYt+7J5Ku0otasmMG5EH2omxHodSUR85NxODfn9B8v4KH0HJzWs4XUcEd/5PDjsI1KXJf2BF4WKGKAncIdzbq6ZPUMJhnk458YCYwFSUlLcwIEDS/TkqamplHQbv4vUfVq+/SC3TlzItv0BfntBB0YNaOnb8c+R+hqFmnDcJ5HKtC/rKMNfn0ehc4wf2ZuGtRK8jiQiPlO/Rjx9WibycfoO7jm7nddxRHzn0+U7aZdUPeLn2dw04O8AACAASURBVPNijooMIMM5Nzd4eQpFhYtdZtYIIPjvbg+ySQhwzvHOvC1c8vx3HM0PMOmmftxwaivfFilERCJBdl4BI8fNZ/uBHO7qmUCbBvqmVESKd0GXRqzbncWaXYe9jiLiK/uyjjJvYybnRnhvCvCgUOGc2wlsNbOTglcNAlYA04HhweuGAx9Udjbxv5y8Qn49eSn3T02nb8tEPrpzAL2aJ3odS0QkouUXBrht4kLStx3kX1f3pG0dzUkhIid2bueGmMFHS3d4HUXEV2at3E3AoUIF3q36cQcw0cyWAt2BvwB/A842s7XA2cHLIv+xfk8WFz83m6mLMrjrrLaMG9GHutXjvY4lIhLRnHM8MDWdL1fv4ZGLu3B2x8ie/EtEflqDGgn0aVE0/ENE/t8ny3aQXKcKnRrX9DqK57yYowLn3GIgpZibBlV2FgkNM5Zu574pS4mPjWb8iD6c1q6+15FERAT4++drmJKWwZhBbbm6bzOv44hIiLigayN+/8Fy1u46TNskDRUTOZCdxzdr9/p63r3K5FWPCpGfJa8gwB+nL+f2txZxUsMafHTnABUpRER84s3vN/GvL9dxVZ+m3HVWW6/jiEgIOa9TcPiHelWIAPD58l0UBBwXdG3kdRRfUKFCfGvbgRyueOl7xn23iVEDWjLpppNpVKuK17FERAT4dNkOfj99OWd1aMDDQzrr2x8RKZEGNRPo3TyRT9J3eh1FxBc+XLqdZolV6dKkltdRfEGFCvGlpXsKuODZb1i/O4sXrunJ7y7sSGy0/lxFRPxg3sZM7nxnMT2a1uafV/UkRu2ziJTC4C4NWb3rMOt2Z3kdRcRT+7KO8t36fVzQtZEK/0E6sxBfKQw4/v75ap5KO0qjWlX48I4BnN9F3Z9ERPxiza7D3DB+Psl1qvDq8N5UidMKHyJSOud3aYRZ0VxkIpHss+W7KAw4LtSwj/9QoUJ8Y8/ho1z36lz++cU6TkuOYdqtp9CiXjWvY4lEJDOLNrNFZjbD6yziH9sP5DD8tXkkBCc2rlMtzutIIhLCkmom0K9lXaYv2Y5zzus4Ip6ZsXQ7repVo2MjrfbxAxUqxBfmbczkgme/YeGW/TwxtCsjO8eTEKtv6UQ8NAZY6XUI8Y+D2fn88vV5ZOUWMG5EH5omVvU6koiEgSHdG7NhzxGWbz/kdRQRT+w5fJQ5GzTs43gqVIinnHOM/Xo9V708h2rxMbx/W38uT2nqdSyRiGZmycAFwCteZxF/yM0v5MY3FrBpbzYvXd+LjlrfXUTKyfmdGxEbbXyweJvXUUQ88emyHQQcXNi1sddRfEWFCvHModx8bp6Qxl8+XsW5nZKYfnt/2jfUya+IDzwN3AsEvA4i3isMOO56ZzHzNmXy9yu6cUrrel5HEpEwUqtqLKe3a8D0JdspDGj4h0SeGUt30KZBddolVfc6iq/EeB1AItPKHYe4ZUIaGftz+N2FHRnZv4W6Oon4gJldCOx2zqWZ2cAfud9oYDRAUlISqampJXqerKysEm9TmZSviHOOCSvzmLWlgKvbx1Fj/xpSU9f4Jl9p+T0f+D9jKOST0DGke2P+vXIX8zZmcnLrul7HEak0uw7lMm9TJmMGtdVnoeOoUCGVburCDB6clk7NhFjeHt2P3i0SvY4kIv+vP3CRmQ0GEoCaZjbBOXftsXdyzo0FxgKkpKS4gQMHluhJUlNTKek2lUn5ijz35TpmbVnNTae14oHBHX72djp+Zef3jKGQT0LHWR2SqBoXzfQl21SokIjySfoOnEOrfRRDQz+k0uTmF/LgtHTueXcJ3ZvW5qM7T1WRQsRnnHMPOOeSnXMtgGHAF8cXKSQyvLtgK098tpqLuzfmvvPaex1HRMJYlbhozu3UkI/Td3K0oNDrOCKVZvqS7bRvWIM2DWp4HcV3VKiQSrE1M5srXvqet+Zu4ebTWzNhVF/q14j3OpaIiBRj1spdPDA1nVPb1uPxod2IilJ3VJGSMrO7zWy5mS0zs7fNLMGKPGpma8xspZndeYJth5vZ2uDP8MrO7oWLujfmYE4+X6/Z63UUkUqxed8RFm45wMU9mngdxZc09EMqXOrq3dw1aTGFAcfY63pxTqeGXkcSkZ/BOZcKpHocQypZ2uZMbntrIZ0a1+SFa3sRF6PvNERKysyaAHcCHZ1zOWb2LkW91AxoCrR3zgXMrEEx2yYCfwBSAAekmdl059z+ytuDyjegTT0Sq8XxweJtnN0xyes4IhVu2qJtmMFF3bTaR3F09iEVpjDgeGrmGkaMm0+jWlWYcccAFSlERHxs7a7DjBy3gEa1qvDaL3tTPV7fZ4iUQQxQxcxigKrAduAW4M/OuQCAc253MdudC8x0zmUGixMzgfMqKbNnYqOjuKBLI/69chdZRwu8jiNSoZxzvL9oG/1a1qVx7Spex/ElFSqkQmQeyeOXr8/j2VlruaxnMtNuPYXmdat5HUtERE5g+4Ecrn9tHnExUbwxsg/1qmt4nkhpOee2AU8CW4AdwEHn3OdAa+BKM1tgZp+YWdtiNm8CbD3mckbwurA3pHtjcvMDfLZsp9dRRCrU4q0H2LQvm0s07OOE9FWJlLvFWw9w64Q09h7J42+XduHK3k213I6IiI8dyM7j+tfmkZVbwKSbTqZpYlWvI4mENDOrAwwBWgIHgMlmdi0QD+Q651LM7FLgNeDU4zcv5iFdMc9RpmWiwX/LzAaco34V49Uv0ql7eJ3v8h1P+comkvO9ueIosVFQ/cA6UlPXl+oxwv34qVAh5cY5x4Q5m/nzjBUk1Uxg6i2n0LlJLa9jiYjIj8jJK2TkuPlsyczmjZF96Ni4pteRRMLBWcBG59weADObCpxCUe+I94L3mQa8Xsy2GcDAYy4nU8x8QWVdJhr8uczstYVreXrWGtp068O6JfN8l+9Yfjx+x1K+sqmofPmFAe75ZhbndG7E4LN7lvpxwv34aeiHlIvsvALunrSY332wnFPb1mfGHQNUpBAR8bn8wgC3vbWQRVsP8Oyw7vRrVdfrSCLhYgvQz8yqWlG30kHASuB94MzgfU4H1hSz7WfAOWZWJ9gz45zgdRHh0p5NcA6mLdzmdRSRCvH1mj1kHsnjku4a9vFj1KNCymz9nixumZDGut1Z/Obck7jl9NZayk5ExOecczwwNZ0vVu3mkYs7c17nRl5HEgkbzrm5ZjYFWAgUAIso6v1QBZhoZncDWcANAGaWAtzsnLvBOZdpZg8D84MP92fnXGal74RHmiZW5eRWdZmyMIPOKV6nESl/0xZto07VWE5rV9/rKL6mQoWUycfpO7h3ytLg5Gt9GdC2nteRRETkZ3j8s9VMSctgzKC2XNuvuddxRMKOc+4PFC0zeqyjwAXF3HcBwaJF8PJrFM1fEZGG9krmV5OXsPZAAmd4HUakHB3OzWfmil1ckdJUy3//BB0dKZX8wgCPzFjBrRMX0japOjPuGKAihYhIiHj12428kLqeq/s2466zilt0QETEO+d3aUi1uGi+3aZlSiW8fLpsJ0cLAlzSU8M+fop6VEiJ7T6cy+0TFzFvUya/PKUFDw7uoIqgiEiI+GDxNh6esYLzOjXk4SGdtSqTiPhO1bgYBndpxIeLM8jOK6BqnD6ySHh4b2EGzetWpUfT2l5H8T19upQSSdu8n1/881vStx3kmWHd+eNFnVSkEBEJEV+v2cOvJy+hT8tEnh7WnWjNJyQiPjW0VzK5hfDZ8p1eRxEpF5v3HWHOhkwu75WsLwl+Bn3ClJ/FOcebczYzbOz3JMRGM/XWUxiimWpFRELGkq0HuHlCGq3rV+fl61NIiI32OpKIyAn1bpFI/SrG5AUZXkcRKRfvLthKlMHQXk29jhIS1I9KflJufiG/fX8ZU9IyOOOk+jx9ZQ9qVY31OpaIiPxMG/ZkMWLcfBKrxTF+ZB9qVVEbLiL+FhVlDGgSw7R1+8jYn01ynapeRxIptYLCAJMXZHB6u/o0rJXgdZyQoB4V8qMy9mdz+Yvf/2dm+FeH91aRQkQkhOw+lMv1r80D4I2RfUiqqRMkEQkNpzQu+k51Spp6VUho+2rNHnYfPsqVvdWb4udSoUJO6Nu1e/nFP79l074jvDo8hbvPbkeUxjOLiISMQ7n5XP/aPDKP5PH6L3vTqn51ryOJiPxs9atGcWrbekyav5WCwoDXcURKbdL8rdStFseZ7ZO8jhIyVKiQ/+Gc48Wv1nP9a3OpXyOe6bcPYFAHvalEREJJbn4hN45fwLrdWbx4bS+6aYZxEQlB1/Rtxo6DuaSu3uN1FJFS2XP4KF+s2s2lPZtoEYIS8OxImVm0mS0ysxnByy3NbK6ZrTWzSWYW51W2SJZ1tIBbJy7kb5+s4vwujZh2a39a1qvmdSwRESmBgsIAd769iLkbM3ny8m6c1q6+15FEREplUIck6teI5615W7yOIlIqUxdmUBBwGvZRQl6WdMYAK4+5/BjwD+dcW2A/MMqTVBFs/Z4sLn5uNp+v2MVDgzvwr6t6UC1e862KiIQS5xwPTE3n8xW7+P2FHbm4h1ZoEpHQFRsdxbDeTfly9W4y9md7HUekRJxzTFqwlV7N69CmQQ2v44QUTwoVZpYMXAC8ErxswJnAlOBdxgMXe5EtUn22fCdD/jWb/UfyeHNUH248rZXW9xURCTHOOf7y8Uomp2Vw56C2jBzQ0utIIiJl9sM30ZPmb/U4iUjJpG3ez4Y9R7gyRb0pSsqrHhVPA/cCP8yKUxc44JwrCF7OAPQVUCUoDDie/Gw1N72ZRuv61fjwjgGc0rqe17FERKQUnk9dz8vfbGT4yc25+6y2XscRESkXyXWqMrBdfSbN30q+JtWUEPLO/K1Ui4vmgq6NvI4Sciq9X7+ZXQjsds6lmdnAH64u5q7uBNuPBkYDJCUlkZqaWqLnz8rKKvE2flfafTqS73hpyVGW7i3ktOQYru2Qz5rFc1lT/hFLLNxep3DbH9A+ifjNxLmbeeKz1Qzp3pg//KKTesWJSFi5um9zbnxjAbNW7ua8zg29jiPyk/YfyePDJdu5tGeyhtOXghdHrD9wkZkNBhKAmhT1sKhtZjHBXhXJwPbiNnbOjQXGAqSkpLiBAweW6MlTU1Mp6TZ+V5p9Wrc7i9FvLGDr/gCPXtKZa/o2r5hwpRRur1O47Q9on0T85MMl2/nt+8s4s30Dnry8m5aSFpGwc8ZJ9WlYM4G35m1RoUJCwuS0rRwtCHD9yf76nBUqKn3oh3PuAedcsnOuBTAM+MI5dw3wJTA0eLfhwAeVnS1SfLFqF5c8N5tDufm8dWM/3xUpRETk5/tqzR7ueXcxKc3r8NzVPYmN1tJnIhJ+YqKjGNanKd+s3cPWTE2qKf5WGHC8OWczfVok0qFRTa/jhCQ/nc3cB9xjZusomrPiVY/zhB3nHM+nrmPU+AU0r1eVD24fQO8WiV7HEhGRUkrbnMnNb6bRpkENXhnemypx0V5HEhGpMFf2bkqUGRPmbvY6isiP+mrNbrZm5nCdelOUmqeDZZxzqUBq8PcNQB8v84SznLxC7n1vKR8u2c5F3Rrz2GVddUIrIhLCVu08xIjX55NUM543RvahVpVYryOJiFSoRrWqcF6nhrwzbytjBrWlapzG/Ys/vfH9ZurXiOfcThqmVFp+6lEhFWTbgRyGvvgdM5Zu5/7z2/PMsO4qUoiIhLDd2QGue3UeVeKieXNUX+rXiPc6kohIpRjRvwUHc/KZunCb11FEirV53xG+WrOHq/o0Iy5GH7dLS0cuzM3bmMlF//yWLfuyeW14b24+vbVmghcRCWG7D+XyxPxc8gsDTBjVl6aJVb2OJCJSaXo1r0PX5Fq8PnsjgUCxiwSKeGrCnM1Em3FN32ZeRwlpKlSEsYlzN3P1y3OoVSWW92/vzxntG3gdSUREyuBgdj7XvzaPQ3mOcSP60DaphteRREQqlZkxsn9L1u85wtdr93gdR+S/5OQV8u6CDM7t1JCkmglexwlpKlSEobyCAL99P52Hpi1jQNt6TLutP63rV/c6loiIlEF2XgEjx89nw54j3Nkjge5Na3sdSUTEE4O7NKJBjXhen73J6ygi/+XDJds5mJOvSTTLgQoVYSbzSB7XvjqXCXO2cPPprXl1eG9NsCYiEuKOFhRy05tpLNqyn2ev6k6neppnSEQiV1xMFNf1a85Xa/awbvdhr+OIAEUrLL42eyMnJdWgb0utrFhWKlSEkXW7D3Pxc7NZsvUAzwzrzv3ntyc6SvNRiIiEsvzCALdNXMQ3a/fy2GVdOa9zI68jiYh47uq+RRMVqleF+MU3a/eyaudhRp3aUnMClgMVKsLEN2v3cMnz35GdV8g7o/sxpHsTryOJiEgZFQYcd09azL9X7uLhIZ24PKWp15FERHyhbvV4LunehPcWZnAgO8/rOCKM/XoDDWrEM6R7Y6+jhAUVKsLAF1vy+eXr82lSuwrv33YKPZrV8TqSiIiUUSDguP+9pcxYuoMHzm/PdSe38DqSiIivjBjQgtz8ABPnbvE6ikS45dsP8u26vfyyfwviYzQ8szyoUBHCCgOOP324nDdW5HF6u/pMueUUkutomToRkVDnXFH7PjktgzGD2nLT6a29jiQi4jvtG9bktHb1eX32RnLzC72OIxHs5a83UC0ummv6ahLN8qJCRYg6nJvPDePn8/rsTZzbPIaXr0+henyM17FERKSMnHM89ulqxn+/mRtPbcldZ7X1OpKIlIKZ3W1my81smZm9bWYJZjbOzDaa2eLgT/cTbFt4zH2mV3b2UHLbwNbszcrj3QVbvY4iEWr7gRw+XLqDYX2aaRGDcqRPtiFoa2Y2N4xfwLo9WTx6SWea5GzUpJkiImHin1+s48Wv1nNtv2Y8OLiDJuQSCUFm1gS4E+jonMsxs3eBYcGbf+Ocm/ITD5HjnCu2iCH/rU/LRFKa1+GlrzZwVZ9mxEbre1ipXK99uxGAEf1beBskzOidHGIWbtnPJc/PZvvBHMaP6KPuRSIiYeSVbzbw1Mw1XNqzCX++qLOKFCKhLQaoYmYxQFVgu8d5wpKZcdsZbdh2IIcPFusQS+U6mJPP2/O2cGHXRhqCX85UqAghny7bwVVj51AtPoZpt/ZnQNt6XkcSEZFyMnHuZh75aCUXdGnE45d1JUo95URClnNuG/AksAXYARx0zn0evPlRM1tqZv8ws/gTPESCmS0wszlmdnFlZA5lA0+qT4dGNXkhdR2BgPM6jkSQt+Zu4UheITee2srrKGFHQz9CxOuzN/LnGSvo3rQ2rw7vTWK1OK8jiYhIOZm6MIPfvr+MM9s34B9XdidGXZdFQpqZ1QGGAC2BA8BkM7sWeADYCcQBY4H7gD8X8xDNnHPbzawV8IWZpTvn1h/3HKOB0QBJSUmkpqaWOGdWVlaptqssJck3sEEBLyw5ylPvziKlYeV8xAmn4+eFUM93tNDxwlfZdKobxd61i0hdW3nZIPSP309RocLnAgHHXz9ZycvfbOScjkk8M6wHVeK05I2ISLj4aOkOfj15CSe3qsvz1/QkLkZFCpEwcBaw0Tm3B8DMpgKnOOcmBG8/amavA78ubmPn3PbgvxvMLBXoAaw/7j5jKSp2kJKS4gYOHFjikKmpqZRmu8pSknynBhyfZKTy1Z5YfnVl/0oZOhdOx88LoZ7v5a83cChvJX+8vC+9WyRWXrCgUD9+P0VnQz6Wm1/IHe8s4uVvNjL85Oa8cG0vFSlERMLIJ+k7uPOdRfRsVoeXr08hIVZtvEiY2AL0M7OqVvSJeRCw0swaAQSvuxhYdvyGZlbnhyEhZlYP6A+sqLTkISo6yrhlYGvStx3k67V7vY4jYS47r4CXvl7PgDb1PClSRAIVKnzqQHYe1786j4+W7uDBwe3540WdtLKHiFQ4M2tqZl+a2crgsnpjvM4Urj5dtoM73l5E96a1GTeyD9W0xLRI2HDOzQWmAAuBdIrOuccCE80sPXhdPeARADNLMbNXgpt3ABaY2RLgS+BvzjkVKn6GS3ok07hWAv+YuQbnNFeFVJyJc7awNyuPMVpCvMLorMiHMvZn88vX57NlXzbPXtWDi7o19jqSiESOAuBXzrmFZlYDSDOzmTpJLl+fLtvJ7W8tomtyLcaN6E11FSlEwo5z7g/AH467+swT3HcBcEPw9++ALhWbLjzFxUQx5qy23PdeOv9euZuzOyZ5HUnCkHpTVA71qPCZZdsOcsnz37H7UC5vjOqjIoWIVCrn3A7n3MLg74eBlUATb1OFl8+X7+T2txbSJbkW40f2oUZCrNeRRETCxmU9k2lZrxpPfrZaK4BIhZgwZzN7s/K4S70pKpQKFT4ye91ernzpe2KjjCm3nEK/VnW9jiQiEczMWlA0gdtcb5OEj5krdnHbWwvp3ERFChGRihATHcU9Z7dj9a7DfLh0u9dxJMxk5xXw0lcbOLVtPVLUm6JCqa+pT3ySvoMx7yymVf1qjB/Zh6SaCV5HEpEIZmbVgfeAu5xzh4q5vUzL4oX7klrFWbS7gH8tOkrzmlGMbpfHwjmzS/1YkXj8ypPf84H/M4ZCPolcF3RpxPOp63lq5hoGd2lErJZ8lnIyYc5m9h3JY8wg9aaoaCpU+MA787bw4LR0ejSrw2vDe1Orqr5hExHvmFksRUWKic65qcXdp6zL4oX7klrHm7VyF8/PTKNTk1q8OaovtaqUrZ2PtONX3vyeD/yfMRTySeSKijJ+c247Ro5bwOQFGVzdt5nXkSQMHMzO5/nU9epNUUlUXvTYi1+t5/6p6Zzatj5vjuqjIoWIeCq4ZN6rwErn3FNe5wkHX6zaxS0TFtK+YU3eHFn2IoWIiPy0M05qQM9mtXl21lpy8wu9jiNh4LnUdRzMyeeB8zt4HSUiqFDhEeccf/14JX/7ZBUXdWvMy9enUDVOHVxExHP9geuAM81scfBnsNehQtUn6Tu46c00TmpYgwmj+qoYLSJSScyM35zbnp2Hchn33Sav40iI25qZzbjZmxjaM5mOjWt6HSci6JOxBwoDjgenpjNpwVau69ecP13Uiago8zqWiAjOuW8BNUjl4P1F2/jV5CV0b1qb10f0pqYmzhQRqVQnt67Lme0b8K8v1nFZz2Tq14j3OpKEqMc/W01UFPzqnJO8jhIx1KOikuUXBrhr0mImLdjKnWe24c9DVKQQEQk3k+Zv4e53F9O7RR3eGNlHRQoREY/89oIOHC0o5InPVnkdRULUoi37+XDJdkaf2oqGtbTgQWVRoaIS5RUEuOOtRXy4ZDsPnN+ee845iaLh4CIiEi7Gf7eJ+95L57S29Rk3og/V4tV5UUTEK63qV2dE/5ZMTstgacYBr+NIiHHO8ZePV1KvehyjT2/tdZyIokJFJcnNL+SWCWl8unwnf/hFR27SH7qISNh56av1/GH6cs7umMTY63uREBvtdSQRkYh3+5ltqFstjj99uALnnNdxJIR8tnwn8zft5+6z21FdXzxUqkovVJhZUzP70sxWmtlyMxsTvD7RzGaa2drgv3UqO1tFyckr5MY3FjBr1W4evaQzI/q39DqSiIiUI+ccT/97DX/9ZBUXdm3E89f0JD5GRQoRET+omRDLvee2J23zfqYv2e51HAkRRwsdj368krYNqnNlSlOv40QcL3pUFAC/cs51APoBt5lZR+B+YJZzri0wK3g55GXnFTBy3Hy+XbeXx4d25Zq+zb2OJCIi5cg5x2Ofrubpf69laK9knhnWg9hodVgUEfGTob2S6dKkFn/9eBXZeQVex5EQ8OH6fLZm5vDnIZ2J0f/rla7Sj7hzbodzbmHw98PASqAJMAQYH7zbeODiys5W3o4cLWD4a/OYu3Ef/7iiO1eoEiciElYKA47ff7CcF79az7X9mvH4ZV2J1gTJIiK+ExVl/PGijuw8lMuzs9Z5HUd8bs2uw3yyMZ/LeiZzcuu6XseJSJ6WhsysBdADmAskOed2QFExA2jgXbKyy8krZNT4+SzccoBnr+rBxT2aeB1JRETKUV5BgDHvLOLNOZu56bRWPDyks1ZxEhHxsV7NE7kypSkvf7OBZdsOeh1HfCoQcDw0LZ2EGHhwcHuv40Qsz2YEMbPqwHvAXc65Qz939QszGw2MBkhKSiI1NbVEz5uVlVXibUoqr9DxzMJcVuwLMLprPNUz15CauqbCnq8y9qmyhds+hdv+gPZJItuRowXcPCGNb9bu5YHz22uCZBGREPHgBR34cvVufjNlKdNv76+hevI/pqRlMH/TfkZ0jqNu9Xiv40QsTwoVZhZLUZFionNuavDqXWbWyDm3w8waAbuL29Y5NxYYC5CSkuIGDhxYoudOTU2lpNuURF5BgJsnpLF8XzZPDO3K5ZUw3KOi98kL4bZP4bY/oH2SyJV5JI8Rr89j2fZDPD60q4b1iYiEkFpVYnn44s7c9GYaY7/ewG1ntPE6kvhI5pE8/vLJSnq3qMOpTY56HSeiebHqhwGvAiudc08dc9N0YHjw9+HAB5WdrazyCwPc8fZCvgiu7lEZRQoREak82w7kMPTF71i18zAvXttLRQoRkRB0bqeGXNC1Ec/8ey3rdmd5HUd85JEZK8jKLeDRS7oQ9TN7/EvF8KKvU3/gOuBMM1sc/BkM/A0428zWAmcHL4eMwoDj7kmL+Wz5Lv74i45a3UNEJMys3XWYoS98x57DR3ljZB/O7pjkdSQRESmlP/6iE1Xjo7nvvaUUBpzXccQHPknfwdRF27j1jDa0S6rhdZyIV+lDP5xz3wInKk8Nqsws5cU5x2/fT2fG0h08OLg9v+zf0utIIiJSjr5fv4+b3lxAfGw0k0afTMfGNb2OJCIiZVC/Rjy/v7Aj97y7hNdnb+SGU1t5HUk8tOtQLg9MS6dbci3uOFPDgfxAs8eUg6dmruHteVu5/Yw2jD5NE6qJiISTaYsyuP61uSTVTGDaraeoSCEiEiYu6dGEszok8dinq0jP0CogkSoQ4Bzq2QAAGdhJREFUcPx68hJy8wt56srummDVJ/QqlNG42Rv55xfruKpPU351Tjuv44iISDlxzvHPWWu5e9ISUponMuWWU0iuU9XrWCIiUk7MjCeGdqVe9XjueHshWUcLvI4kHnjj+018s3YvD13Qkdb1q3sdR4JUqCiDD5ds508zVnBOxyQeHtKZn7vEqoiI+FtBwHHfe0v5+8w1XNqjCeNH9qFWlVivY4mISDmrUy2Op6/szpbMbH47LR3nNF9FJFm76zB//WQVZ5xUn2v7NvM6jhxDhYpS+nbtXu55dzG9myfy7FU9iFEXIRGRsHA4N59/pOXy7oIM7hzUlr9f0Y24GLXxIiLhqm+ruowZ1I73F2/nvYXbvI4jlSQ7r4A73l5EtfgYHhvaVV86+4zOvEph+faD3PTmAlrXr87Lw1NIiI32OpKIiJSDTXuPcOnz37EqM8DjQ7tyz9ntdOIiIhIBbj+zDX1bJvK795dpydII4Jzj3ilLWbPrMP+4sjsNaiR4HUmOo0JFCe0+lMsN4xdQq0qsugKLiISR2ev2MuS52ezJOsqvUxK4IqWp15FERKSSREcZzwzrQZW4aEa/sYCD2fleR5IKNPbrDcxYuoPfnNue09vV9zqOFEOFihLIzS/kxjcWcDAnn1eG9yappipvIiKhzjnH67M3cv1r82hYM4Hptw2gQ131lBMRiTQNayXw4rW92Lo/m1vfSiO/MOB1JKkA36zdw2OfrmJwl4bcfLqWpfUrFSp+pkDA8avJS1i67SDPDOuh5elERMLA0YJC7n8vnT99uIIz2zfgvVtPoVldrewhImVnZneb2XIzW2Zmb5tZgpmNM7ONZrY4+NP9BNsON7O1wZ/hlZ09kvVpmchfLunC7HX7+OP05ZpcM8xszczmjrcX0bZBDZ4Y2k3DO30sxusAoeLpWWv5aOkOHji/PWd3TPI6joiIlNGew0e5ZUIaCzbv544z23D3We2IitIJi4iUnZk1Ae4EOjrncszsXWBY8ObfOOem/Mi2icAfgBTAAWlmNt05t7+ic0uRy1Oasm5PFi99tYE2Daozon9LryNJOTiYk88N4xcQCDheuq4X1eL1UdjP9Or8DB8s3sazs9Zyea9kRp+m7kEiIqFu3sZMbn9rIYdy8/nX1T24sGtjryOJSPiJAaqYWT5QFdj+M7c7F5jpnMsEMLOZwHnA2xWSUop137nt2bDnCA/PWEGzxKoM6qAvKkPZ0YJCRr+xgA17sxg3og8t6lXzOpL8BA39+Akrth/i3ilL6dMykUcv6aLuQSIiIcw5x0tfreeql+dQNS6aqbf0V5FCRMqdc24b8CSwBdgBHHTOfR68+VEzW2pm/zCz+GI2bwJsPeZyRvA6qURRUcbTV3anU+Na3DJxId+u3et1JCmlwoDjnklLmLsxkyeGdqN/m3peR5KfQT0qfsSh3HxunZhG7aqxPH9NT+JiVNcREQlVB3Py+fXkJcxcsYvzOzfksaFdqZmglZtEpPyZWR1gCNASOABMNrNrgQeAnUAcMBa4D/jz8ZsX85D/M1GCmY0GRgMkJSWRmppa4pxZWVml2q6y+CHfTSc5/nbQMfL1udyTkkD7xP+fbNkP+X6M8kHAOV5Nz2P29gKuPCmO2gfXkpq61jf5yiLc86lQcQLOOe6dvJSt+3N4Z3Q/6lUvruAtIiKhYNm2g9wyMY0dB3L5/YUdGdG/hXrIiUhFOgvY6JzbA2BmU4FTnHMTgrcfNbPXgV8Xs20GMPCYy8lA6vF3cs6NpajYQUpKihs4cODxd/lJqamplGa7yuKXfP1OOcqwsXN4dnEOb47qQa/miYB/8p1IpOcLBBy//WAZs7dv4a6z2nLXWe1KtH2kH7+yKms+dRE4gVe/3ciny3fywPnt6d0i0es4IiJSCs453vx+E5e+8B0FhY5JN53MyAEtVaQQkYq2BehnZlWtqMEZBKw0s0YAwesuBpYVs+1nwDlmVifYM+Oc4HXikXrV43nrhr4k1Uzgl6/NZ9EWzWvqd4UBx/1Tl/LW3C3cfHprxgxq63UkKSEVKooxf1Mmf/1kFed2SmLUAM3yKyISivYcPsrIcfP53QfL6deqLjPuGECv5nW8jiUiEcA5NxeYAiwE0ik65x4LTDSz9OB19YBHAMwsxcxeCW6bCTwMzA/+/PmHiTXFOw1qJvDWjX2pUy2Oq16ew79X7PI6kpxAXkGAuyYt5t0FGYwZ1Jb7zjtJX1CEIA39OE7mkTxuf2shyXWq8MTlWltXRCQUzVq5i3unLOXw0QL++IuOXH9yCy09KiKVyjn3B4qWGT3WmSe47wLghmMuvwa8VnHppDQa1arCe7ecwqjx8xn95gKu7RD3X2N0xHuHc/O5eUIas9ft4/7z23Pz6a29jiSlpELFMZxzPDg1ncwjeUy7tb8mWRMRCTE5eYU88tEKJs7dQodGNXl7WHfaJdXwOpaIiISJ+jXieWd0P+54axFvrNhNtU9X8ZtzTlIx3Ae2ZmZz4xsLWLc7i6eu6MalPZO9jiRloELFMSanZfxnXorOTWp5HUdEREpg8dYD3PPuYjbuPcLo01rxq3PaER8T/dMbioiIlEDVuBheuq4XN744kxdS17N+dxZPDO1Grar6ktMr363fy20TFxJwMG5EHwa01RKkoU5zVARt2ZfNn6Yvp1+rRG44tZXXcURE5GfKzivg4RkruPT52WQfLWTiqL48OLiDihQiIlJhYqKjuL5jHL+7sCNfrt7N4Ge/IW2zJtmsbIUBxz9nreXaV+ZSt3o879/WX0WKMKEeFRQtXfPryUuIijL+fkV3otV1S0QkJHy9Zg8PTksnY38O1/Zrxr3ntdewPRERqRRmxqgBLenVvA53vL2QK176nl+fcxI3ndZKQ0EqwZZ92dz33lK+37CPId0b8+glXager4+34UKvJDBx3hbmbcrk8aFdaVK7itdxRETkJ+w/kscjH63kvYUZtKpfjXdvOpk+LbWUtIiIVL7uTWvz0Z2ncv97S3ns01V8uWo3j1zSWXMkVZDCgGPcd5t48rPVREcZj1/WlctTkrUIQpiJ+ELFtgM5/O3jlZzath6X99KEKyIifuac4/3F23hkxkoO5uRz+xltuP3MNiTEapiHiIh4p2ZCLM9d3ZPJCzL4yycrGfzMN4w6tSVjBrWlalzEf+QqN2t2Hea+95ayaMsBzmzfgEcv6UyjWvqiORxF9LvGOcdD09JxwF8u6aIqnIiIjy3bdpA/TF9O2ub9dGtamwmXdqFDo5pexxIREQGKhoJc0bspZ3VM4m+frOSlrzYwY8kO7j3vJC7s2ljDy8tg24Ecnvn3GqakZVCrSixPX9mdId0b6/NbGIvoQsVny3eSunoPv7uwI00Tq3odR0REirEv6yhPfr6Gd+ZvIbFqHI9f1pWhvZI1/ldERHwpsVocjw/txuUpTfnd+8sY885inp21ljsHtVXBooQyj+Tx/JfreGPOZnAwon9LbjujDYnV4ryOJhUsYgsVOXmFPDxjJe0b1mD4yc29jiMiIsfJySvk1W838OJXG8jJL2TEKS0Zc1ZbalXRZJkiIuJ/vVsk8vGdp/Lp8p088++1jHlnMc/MWssNA1pxUffGmvjxRyzffpDx323ig8XbyS8McFnPZO46u53mE4wgEfvueD51HdsO5PDuTScTE61VWkVE/KKgMMCUtAyemrmG3YePcnbHJO499yTaalIyEREJMVFRxuAujTivU0M+W76TZ79Yx4PT0nnkoxX8omtjhvVpSvemtTWEATicm8+/V+7irblbmL9pPwmxUVzaM5lRA1rQpoHOASJNRBYqtmZm89JXG7i4e2PNEi8i4hMFhQE+WLydf325jo17j9CzWW2eu6YnvVuonRYRkdAWFWWc36UR53VuyKKtB3hn3hamL9nOpAVbaV63Kmd3SOKsjkmkNK8TUV+iHszJ54tVu/ho6U6+XruHvIIATROr8NDgDlyR0pRaVdWLMlJFZKHi75+vJioK7j+/g9dRRER8x8zOA54BooFXnHN/q8jnyy8MMG3RNp77ch2b92XTsVFNXrquF+d0TNI3TCIiElbMjJ7N6tCzWR1+d2FHZizdwWfLd/LG95t55duN1KoSy8mt6pLSog49m9ehc+NaxMWET+HiQHYeaZv3M2fDPmYuyWHLZ58TcNCwZgLX9G3GBV0a0bNZHc1DJf4rVFT0CfLmQ4W8v3g7tw5sTcNaCeX50CIiIc/MooHngLOBDGC+mU13zq0o7+c6lJvPpHlbGffdJrYdyKFzk5q8fH0KZ3VooAKFiIiEvRoJsVzVpxlX9WlG1tECvl27h5krdjN/UyafLt8JQFxMFCcl1aBtg+q0SapO2wY1aJZYlYa1EqiZEOPL/y8LA45dh3LJ2J9Dxv5s1u3OYuWOQ6zaeZgdB3MBiIuOomVNuOPMtpzWrj49mtZWcUL+i68KFZVxgjxlTT61qsRy0+mty+shRUTCSR9gnXNuA4CZvQMMAcqtHc7Yn83bq45y+5dfkHW0gL4tE3n44k6ccZIKFCIiEpmqx8dwXudGnNe5EQC7D+WycMt+0jbvZ9XOw3y/YR9TF237r22qxkXTsFYCiVXjqFkllhoJMdRIiKFmQiw1EmLJ2JTP1u83ER0VRUyUER1lxEQbMVFRx6w84nAOHAT/PfayK7qHg4Bz5BcGyM0PkJNfSE5eIbn5heTkF3IoJ599R/LYn51HZlYeuw8fpSDg/pMzJspo06A6fVsm0r5RTbom16JnszrMmf0NAwe2q/iDKyHJV4UKKvgEecX2Q6TvLeShwe00a7yISPGaAFuPuZwB9C3PJ3j0o5XM3FzAhV0bc+OpreiSXKs8H15ERCTkNaiZ8F+FCyiabHLd7iy2Hchh58FcdhzMZcfBHPYfyWf34VzW7yngcG4Bh3Ly/79QsGp5hWVMiI0iITaamgmx1KkWR/3q8bRLqkGDGgk0TaxCcp2qJNepQnKdKsTHRFdYDglPfitUVOgJcsfGNXmobwLXaTlSEZETKa5Lg/ufO5mNBkYDJCUlkZqa+rOfYGCdACf3cjSrd5B96xaRuq60UStOVlZWifapsilf2fg9H/g/YyjkEwk3NRJi6dGsDj2a1fnR+znnyM0P8MVXX9P35FMoDDgKAo7CQkd+IEBhoKh3BIBhmFH088PvFF0meDnKDANiY6KoEhtNldho4mOiNFRDKpTfChU/eYJclpNjgEaxOcyZ/U1p8/mS308WSiPc9inc9ge0T2EsA2h6zOVkYPvxd3LOjQXGAqSkpLiBAweW6ElSU1Mp6TaVSfnKRvnKzu8ZQyGfSKQyM6rERVMt1qhXPd7rOCKl4rdCxU+eIIf7yXFpaJ/8L9z2B7RPYWw+0NbMWgLbgGHA1d5GEhEREZFI4re1bv5zgmxmcRSdIE/3OJOISMRwzhUAtwOfASuBd51zFTfAVURERETkOL7qUeGcKzCzH06Qo4HXdIIsIlK5nHMfAx97nUNEREREIpOvChWgE2QRERERERGRSOa3oR8iIiIiIiIiEsFUqBARERERERER31ChQkRERERERER8Q4UKEREREREREfENFSpERERERERExDdUqBARERERERER3zDnnNcZSs3M9gCbS7hZPWBvBcTxkvbJ/8Jtf0D79FOaO+fql9Nj+VqYtsXKVzbKV3Z+zxgK+aqpHf5JofA6Kl/pKV/ZKF/Z/JCvVOfEIV2oKA0zW+CcS/E6R3nSPvlfuO0PaJ+kbPx+rJWvbJSv7PyeUfnCg9+Pk/KVjfKVjfKVTVnzaeiHiIiIiIiIiPiGChUiIiIiIiIi4huRWKgY63WACqB98r9w2x/QPknZ+P1YK1/ZKF/Z+T2j8oUHvx8n5Ssb5Ssb5SubMuWLuDkqRERERERERMS/IrFHhYiIiIiIiIj4VMQUKszsPDNbbWbrzOx+r/OUlZk1NbMvzWylmS03szFeZyovZhZtZovMbIbXWcqDmdU2sylmtir4ep3sdaayMrO7g393y8zsbTNL8DpTSZnZa2a228yWHXNdopnNNLO1wX/reJkxXPmtPT5Re+qnv4fj20Uza2lmc4PZJplZnFfZgnn+p53z2fH7nzbLy2NYkvbHijwbfL8sNbOeHuV7Ivj6LjWzaWZW+5jbHgjmW21m53qR75jbfm1mzszqBS9X+vELBWqHS53Tt22x2uFSZVJbXM75jrmtzG1xRBQqzCwaeA44H+gIXGVmHb1NVWYFwK+ccx2AfsBtYbBPPxgDrPQ6RDl6BvjUOdce6EaI75uZNQHuBFKcc52BaGCYt6lKZRxw3nHX3Q/Mcs61BWYFL0s58ml7fKL21E9/D8e3i48B/whm2w+M8iTV/yuunfPF8fuRNsvLYziOn9/+nA+0Df6MBl7wKN9MoLNzriuwBngAIPheGQZ0Cm7zfPB9Xtn5MLOmwNnAlmOu9uL4+Zra4TLxc1usdrjkxqG2uLzzlVtbHBGFCqAPsM45t8E5lwe8AwzxOFOZOOd2OOcWBn8/TFFj1MTbVGVnZsnABcArXmcpD2ZWEzgNeBXAOZfnnDvgbapyEQNUMbMYoCqw3eM8Jeac+xrIPO7qIcD44O/jgYsrNVRk8F17/CPtqS/+Ho5vF83MgDOBKV5nC+Y5UTvni+MXdHybtQMPj2EJ258hwBuuyBygtpk1qux8zrnPnXMFwYtzgORj8r3jnDvqnNsIrKPofV6p+YL+AdwLHDsBW6UfvxCgdrgU/NwWqx0uHbXF5Z8vqFza4kgpVDQBth5zOYMw+FD/AzNrAfQA5nqbpFw8TdEfdsDrIOWkFbAHeD3YVfAVM6vmdaiycM5tA56kqEq6AzjonPvc21TlJsk5twOKTpqABh7nCUe+bo+Pa0/98vdwfLtYFzhwzImK18fwRO2cL45fcW0WkIa/jiGc+Hj58T0zEvgk+Lsv8pnZRcA259yS427yRT6f8fUx8Wk7DP5ui9UOlx+1xWVQnm1xpBQqrJjrwmK5EzOrDrwH3OWcO+R1nrIwswuB3c65NK+zlKMYoCfwgnOuB3AE77stlklwrN4QoCXQGKhmZtd6m0pCiG/bYz+2pydoF/12DH3dzhXXZlHUBfV4vvg7LIavXm8ze4iibvoTf7iqmLtVaj4zqwo8BPy+uJuLuc6vr3Vl8e0x8WM7DCHRFqsdrnh+er0joi2OlEJFBtD0mMvJhGBX9eOZWSxFjflE59xUr/OUg/7ARWa2iaJuiGea2QRvI5VZBpDhnPuht8sUiv4jCWVnARudc3ucc/nAVOAUjzOVl10/dEML/rvb4zzhyJft8QnaUz/8PfxPu0jRt3q1g91nwftjeKJ2zg/HD07cZvnpGMKJj5dv3jNmNhy4ELjG/f/69n7I15qiD0BLgu+VZGChmTX0ST6/8eUx8XE7DP5vi9UOlx+1xaVXrm1xpBQq5gNtrWhm2TiKJhqZ7nGmMgmOi3sVWOmce8rrPOXBOfeAcy7ZOdeCotfoC+dcSH9T75zbCWw1s5OCVw0CVngYqTxsAfqZWdXg3+EgQnyC0GNMB4YHfx8OfOBhlnDlu/b4R9pTz/8eTtAuXgN8CQz1MtsPfqSd8/z4BRXXZq3AR8cw6ETHazpwfXDG9H4UDbfbUdnhzOw84D7gIudc9jE3TQeGmVm8mbWkaKK0eZWZzTmX7pxr4JxrEXyvZAA9g3+bvjh+PqN2uIT83harHS5XaotLqdzbYudcRPwAgymaGXU98JDXecphfwZQ1F1mKbA4+DPY61zluH8DgRle5yinfekOLAi+Vu8DdbzOVA779CdgFbAMeBOI9zpTKfbhbYrGSeYHG9JRFI03nQWsDf6b6HXOcPzxW3t8ovbUb38Px7aLFI1HnkfRZFmTvX4PFtfO+en4FddmeXkMS9L+UNRd9rng+yWdolnzvci3jqLxxT+8R1485v4PBfOtBs73It9xt28C6nl1/ELhR+1wmbL6si1WO1yqTGqLyznfcbeXqS224IYiIiIiIiIiIp6LlKEfIiIiIiIiIhICVKgQEREREREREd9QoUJEREREREREfEOFChERERERERHxDRUqRERERERERMQ3VKgQERGRSmdmd5lZVa9ziIhEMrXF4ldanlREREQqnZltomgd9b1eZxERiVRqi8Wv1KNCIpqZ9TazpWaWYGbVzGy5mXX2OpeISDgJtq8fmdkSM1tmZn8AGgNfmtmXwfucY2bfm9lCM5tsZtWD128ys8fMbF7wp42X+yIiEqrUFksoUaFCIppzbj4wHXgEeByY4Jxb5m0qEZGwcx6w3TnXzTnXGXga2A6c4Zw7w8zqAb8FznLO9QQWAPccs/0h51wf4F/BbUVEpOTUFkvIUKFCBP4MnA2kUFSsEBGR8pUOnBX8Nu5U59zB427vB3QEZpvZYmA40PyY298+5t+TKzytiEh4UlssISPG6wAiPpAIVAdigQTgiLdxRETCi3NujZn1AgYDfzWzz4+7iwEznXNXneghTvC7iIj8TGqLJZSoR4UIjAV+B0wEHvM4i4hI2DGzxkC2c24C8CTQEzgM1AjeZQ7Q/4cxz2ZW1czaHfMQVx7z7/eVk1pEJLyoLZZQoh4VEtHM7HqgwDn3lplFA9+Z2ZnOuS+8ziYiEka6AE+YWQDIB26hqNvwJ2a2Izg2+pfA22YWH9zmt8Ca4O/xZjaXoi9YTvRNn4iI/Di1xRIytDypiIiI+JaWzhMR8Z7aYqlsGvohIiIiIiIiIr6hHhUiIiIiIiIi4hvqUSEiIiIiIiIivqFChYiIiIiIiIj4hgoVIiIiIiIiIuIbKlSIiIiIiIiIiG+oUCEiIiIiIiIivqFChYiIiIiIiIj4xv8BCN6HX6I4yRcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1296x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0\n",
    "x_mem = np.zeros([0])\n",
    "y = 0\n",
    "y_mem = np.zeros([0])\n",
    "phi = 88\n",
    "phi_mem =np.ndarray([0])\n",
    "while ( not np.isclose(x,10,0.02) or not np.isclose(phi,90,0.02)):\n",
    "    theta = fuzzy_controller(x, phi)\n",
    "    x = x + np.cos((phi+theta)*np.pi/180) + np.sin((theta)*np.pi/180)*np.sin((phi)*np.pi/180)\n",
    "    y = y + np.sin((phi+theta)*np.pi/180) - np.sin((theta)*np.pi/180)*np.cos((phi)*np.pi/180)\n",
    "    phi = phi - np.arcsin(2*np.sin(theta*np.pi/180)/4)\n",
    "    x_mem = np.append(x_mem,x)\n",
    "    y_mem = np.append(y_mem,y)\n",
    "    phi_mem = np.append(phi_mem,phi)\n",
    "    \n",
    "print(\"x_final:\"+str(x) +\"    phi_final:\"+str(phi) )\n",
    "    \n",
    "plt.figure(figsize=(18,5))\n",
    "\n",
    "plt.subplot(131)\n",
    "plt.plot(x_mem,y_mem)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title(\"The path of movement\")\n",
    "plt.grid();\n",
    "plt.subplot(132)\n",
    "plt.plot(x_mem)\n",
    "plt.xlabel(\"step\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.grid();\n",
    "plt.subplot(133)\n",
    "plt.plot(phi_mem)\n",
    "plt.xlabel(\"step\")\n",
    "plt.ylabel(\"$\\phi$\")\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation2 : $(x_0, \\phi_0) = (2,94)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_final:9.926300763442171    phi_final:89.15341678929418\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 2\n",
    "x_mem = np.zeros([0])\n",
    "y = 0\n",
    "y_mem = np.zeros([0])\n",
    "phi = 94\n",
    "phi_mem =np.ndarray([0])\n",
    "while ( not np.isclose(x,10,0.01) or not np.isclose(phi,90,0.01)):\n",
    "    theta = fuzzy_controller(x, phi)\n",
    "    x = x + np.cos((phi+theta)*np.pi/180) + np.sin((theta)*np.pi/180)*np.sin((phi)*np.pi/180)\n",
    "    y = y + np.sin((phi+theta)*np.pi/180) - np.sin((theta)*np.pi/180)*np.cos((phi)*np.pi/180)\n",
    "    phi = phi - np.arcsin(2*np.sin(theta*np.pi/180)/4)\n",
    "    x_mem = np.append(x_mem,x)\n",
    "    y_mem = np.append(y_mem,y)\n",
    "    phi_mem = np.append(phi_mem,phi)\n",
    "\n",
    "print(\"x_final:\"+str(x) +\"    phi_final:\"+str(phi) )\n",
    "\n",
    "plt.figure(figsize=(18,5))\n",
    "\n",
    "plt.subplot(131)\n",
    "plt.plot(x_mem,y_mem)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title(\"The path of movement\")\n",
    "plt.grid();\n",
    "plt.subplot(132)\n",
    "plt.plot(x_mem)\n",
    "plt.xlabel(\"step\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.grid();\n",
    "plt.subplot(133)\n",
    "plt.plot(phi_mem)\n",
    "plt.xlabel(\"step\")\n",
    "plt.ylabel(\"$\\phi$\")\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] Type-2 Fuzzy Logic: Theory and Applications ,Publisher: Springer Berlin Heidelbergm"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:env2]",
   "language": "python",
   "name": "conda-env-env2-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}