Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Μια επίδειξη των δυνατοτήτων της Python με εφαρμογές στον επιστημονικό προγραμματισμό και την ανάλυση δεδομένων\n",
    "\n",
    "Η γλώσσα προγραμματισμού Python είναι μια πολύ υψηλού επιπέδου Interpreted γλώσσα (δηλαδή δεν χρειάζεται Compilation αλλά τρέχει \"γραμμή-γραμμή\" (Script)).\n",
    "\n",
    "Μπορεί να χρησιμοποιηθεί και για Συναρτησιακό αλλα και για Αντικειμενοστραφή προγραμματισμό ενώ η ευκολοδιάβαστει δομή της είναι ιδανική για code reading.\n",
    "\n",
    "Είναι απολύτως δωρεάν και ανοιχτού κώδικα (open source) και υποστηρίζεται από μια μεγάλη κοινότητα προγραμματιστών και χρηστών (Community) δίνοντας της μεγαλύτερη ευελιξία/προσαρμοστικότητα και ταχύτητα ανάπτυξης σε σχέση με \"ανταγωνιστικές γλώσσες\".\n",
    "\n",
    "Λόγω της απουσίας compilation ο ίδιος κώδικας λειτουργεί πανομοιότυπα σε κάθε μηχάνημα ανεξαρτητώς αρχιτεκτονικής και λειτουργικού συστήματος. Βέβαια ακριβώς για τον ίδιο λόγο είναι αρκετά πιο άργη από compiled γλώσσες (C, Fortran κλπ)\n",
    "\n",
    "Παρακάτω θα παρουσιάσουμε "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Τύποι αριθμητικών μεταβλητών\n",
    "* Ακέραιος **int**\n",
    "* Floating-point number **float** (αντίστοιχως της **double** στη C)\n",
    "* Μιγαδικός **complex**\n",
    "* Λογικός **boolean**\n",
    "\n",
    ">Στη Python δεν χρειάζεται να δηλώσουμε προηγουμένως τις μεταβλητές μας (με εξαίρεση τις **global**). Για να δηλώσουμε οτι μια μεταβλητή ειναι ακέραια απλά της δίνουμε μια αρχική ακέραια τιμή (βλ. παρακάτω τη μεταβλητή **a**)\n",
    "\n",
    ">Για να δηλώσουμε μια float μεταβλητή δίνουμε μια αρχική τιμή σε δεκαδική μορφή (βλ. παρακάτω τη μεταβλητή **b**).\n",
    "\n",
    ">Ο φανταστικός αριθμός i συμβολίζεται με **J**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "2.0\n",
      "(1+3j)\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "a=2 #integer\n",
    "b=2. #float\n",
    "c=1.+3.J\n",
    "d= 3>2\n",
    "print(a)\n",
    "print(b)\n",
    "print(c)\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Containers\n",
    "Επίσης υπάρχουν και \"συνδυαστικές(?!)\" δομές δεδομένων (sequences). Η βασική δομή δεδομένων είναι η λίστα (**List**) δηλαδή η συλλογή διαφορετικών (και είδους) μεταβλητών. Η λίστα δηλώνεται μέσω του συμβολισμού **[ ]**.\n",
    "Μία λέξιλογική προταση (**string**) είναι ουσιαστικά μια λίστα γραμμάτων. \n",
    "\n",
    "Μπορούμε να ανατρέξουμε σε μια λίστα μέσω του αριθμου **index** δηλαδή ζητώντας το σημείο εκείνο όπου είναι αποθηκευμένη μεταβλητή μας ξεκινώντας απο το **0**. Δηλαδή αν η λίστα είναι η L, ζητάμε τη μεταβλητή που έχει αποθηκευθεί εντός της λίστα στο σημείο 4 μέσω της εντολής ```L[4]```. (*βλ. παράδειγμα παρακάτω*)\n",
    "\n",
    "Ένα \"λεξικό\" (**Dictionary**) είναι μία λίστα όπου αντί για index χρησιμοποιούμε ένα string. Αυτό είναι πολύ χρησίμο όταν καταχωρούμε πολλά (και διαφορετικά) δεδομένα σε μια λίστα και θέλουμε να τα καλέσουμε μέσω μιας λέξης κλειδί. πχ: ```H['time']```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 'a string', 0.0001, 'a string', [301.0, 2, 'a string'])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = [1.,301.,a,'a string',1.e-4]\n",
    "L[0],L[3],L[-1],L[-2],L[1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a string\n"
     ]
    }
   ],
   "source": [
    "print L[-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1.0, 301.0], [2, 'a string', 0.0001]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G=[L[:2],L[2:]]\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'str'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[3][2:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "P=[2.]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0, 2.0]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*P\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Προσοχή** Μία λίστα δεν είναι ένας \"πίνακας\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 4, 5, 6, 7, 2, 4, 5, 6, 7]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K=[2,4,5,6,7]\n",
    "2*K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ένα *string* είναι μια λίστα."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ig'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s='a bigger string'\n",
    "s[3:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = {'a':1,'b':2,'c':3}\n",
    "D['b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D['a']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'tuple' object does not support item assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m-------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                   Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-50dd93f869da>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mtup\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2.\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3.\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mtup\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "tup =(2.,3.,5.)\n",
    "tup[2]=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 4, 5, 6, 7]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "K[1:4]=[2,3,9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.0, 2, 3, 9, 7]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K[0]=9.\n",
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.0, 2, 3, 9, 7]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "K[:2]=[0,'a']\n",
    "K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Control Flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d=10 if a>4 else 4\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "if a == 1:\n",
    "    print(a)\n",
    "elif a==2:\n",
    "    print(a**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.0, 2.0, 3, 9, 7]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K[1]=2.\n",
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 9.0\n",
      "1 2\n",
      "2 3\n",
      "3 9\n",
      "4 7\n"
     ]
    }
   ],
   "source": [
    "for i,k in enumerate(K):\n",
    "    print i,k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(len(K))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 9.0\n",
      "1 2.0\n",
      "2 3\n",
      "3 9\n",
      "4 7\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(K)): \n",
    "    print i,K[i]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<enumerate at 0x7f26d467ffa0>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enumerate(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 9.0\n",
      "1 2.0\n",
      "2 3\n",
      "3 9\n",
      "4 7\n"
     ]
    }
   ],
   "source": [
    "for index,value in enumerate(K):\n",
    "    print index,value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List Comprehensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[81.0, 4, 9, 81, 49]\n"
     ]
    }
   ],
   "source": [
    "lc=[i**2 for i in range(len(K))]\n",
    "lc=[i**2 for i in K]\n",
    "print(lc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 3.*x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[243.0, 12.0, 27.0, 243.0, 147.0]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[f(i) for i in K]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for ** or pow(): 'list' and 'int'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m-------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                   Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-34-4e3cedb8da84>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;34m[\u001b[0m\u001b[0;36m0.\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3.\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for ** or pow(): 'list' and 'int'"
     ]
    }
   ],
   "source": [
    "[0.,3.]**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for ** or pow(): 'list' and 'int'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m-------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                   Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-35-49021c67dd39>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m488\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-32-027f9c22a0cc>\u001b[0m in \u001b[0;36mf\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0;36m3.\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for ** or pow(): 'list' and 'int'"
     ]
    }
   ],
   "source": [
    "f([488,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for ** or pow(): 'list' and 'int'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m-------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                   Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-36-b5c5e8ba1e6d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-32-027f9c22a0cc>\u001b[0m in \u001b[0;36mf\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0;36m3.\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for ** or pow(): 'list' and 'int'"
     ]
    }
   ],
   "source": [
    "f(K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Βιβλιοθήκες/Πακέτα της Python\n",
    "\n",
    "\n",
    "## Εγκατάσταση Πακέτων\n",
    "### Package manager\n",
    "* Παράδειγμα για debian based systems (ubuntu, mint, elementary κλπ)\n",
    "``` bash\n",
    "sudo apt-get install numpy\n",
    "```\n",
    "\n",
    "### pip (Linux)\n",
    "* The PyPA (Python Packaging User Guide) recommended tool for installing Python packages.\n",
    "* Ανεξάρτητο σύστημα άρα και ανεξάρτητο από τους package manager της εκάστοτε διανομής.\n",
    "* Latest version\n",
    "* Compile from source\n",
    "* Παράδειγμα:\n",
    "``` bash\n",
    "sudo pip install numpy\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy  (http://www.numpy.org/)\n",
    "\n",
    "NumPy is the fundamental package for scientific computing with Python. It contains among other things:\n",
    "* a powerful N-dimensional array object\n",
    "* sophisticated (broadcasting) functions\n",
    "* tools for integrating C/C++ and Fortran code\n",
    "* useful linear algebra, Fourier transform, and random number capabilities\n",
    "\n",
    "Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.\n",
    "``` python\n",
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.,  2.,  3.,  9.,  7.])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "a= np.array(K)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "could not convert string to float: string",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m-------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-39-6fb3c2026c86>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'string'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: could not convert string to float: string"
     ]
    }
   ],
   "source": [
    "a[0]='string'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 18.,   4.,   6.,  18.,  14.])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.*a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    \"\"\"\n",
    "    Docstring\n",
    "    Usage\n",
    "    Description of the function (Input and Output)\n",
    "    \"\"\"\n",
    "    return x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 81.,   4.,   9.,  81.,  49.])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import tan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.0, 2, 3, 9, 7]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.2246467991473532e-16"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.46013911,  1.10714872,  1.24904577,  1.46013911,  1.42889927])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 1.,  1.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=np.ones((4,2))\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 2)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 1.,  4.],\n",
       "       [ 1.,  1.]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2,1]=4.\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.58305839,  0.06789145],\n",
       "       [ 0.08276288,  0.83649712],\n",
       "       [ 0.45219536,  0.41127844],\n",
       "       [ 0.51657028,  0.3546244 ]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g=np.random.rand(4,2)\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.58305839,  0.08276288,  0.45219536,  0.51657028])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[:,0]=[0.,0.,0.,0.]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.],\n",
       "       [ 0.,  1.],\n",
       "       [ 0.,  4.],\n",
       "       [ 0.,  1.]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.  2.  2.]\n",
      " [ 2.  2.  2.]\n",
      " [ 2.  2.  2.]\n",
      " [ 2.  2.  2.]]\n",
      "[ 2.  2.]\n"
     ]
    }
   ],
   "source": [
    "aa=np.ones((4,3))*2.\n",
    "print aa\n",
    "print aa[1:3,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "aa[1]=np.array([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  2.,  2.],\n",
       "       [ 1.,  2.,  3.],\n",
       "       [ 2.,  2.,  2.],\n",
       "       [ 2.,  2.,  2.]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "bnVtcHlfaW5kZXhpbmcucG5n\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image('numpy_indexing.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  2.,  2.],\n",
       "       [ 1.,  2.,  3.],\n",
       "       [ 2.,  2.,  2.],\n",
       "       [ 0.,  1.,  3.]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa[3]=np.array([0,1,3])\n",
    "aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False],\n",
       "       [False, False,  True],\n",
       "       [False, False, False],\n",
       "       [False, False,  True]], dtype=bool)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa>2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.,  3.])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa[aa>2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  2.,  2.],\n",
       "       [ 1.,  2.,  0.],\n",
       "       [ 2.,  2.,  2.],\n",
       "       [ 0.,  1.,  0.]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa[aa>2]=0\n",
    "aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "aa>2 && aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False],\n",
       "       [False, False, False],\n",
       "       [False, False, False],\n",
       "       [False, False, False]], dtype=bool)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_and(aa>2,aa<1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa[np.logical_or(aa>2,aa<1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 81.,   4.,   9.,  81.,  49.])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(np.array(K))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 81.,   4.,   9.,  81.,  49.])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vectorized_f=np.vectorize(f)\n",
    "vectorized_f(K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scipy (http://www.scipy.org/)\n",
    "\n",
    "It provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization.\n",
    "\n",
    "```python\n",
    "from scipy.optimize import curve_fit\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib (http://matplotlib.org/)\n",
    "matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. matplotlib can be used in python scripts, the python and ipython shell (ala MATLAB®* or Mathematica®†), web application servers, and six graphical user interface toolkits.\n",
    "\n",
    "* http://www.labri.fr/perso/nrougier/teaching/matplotlib/matplotlib.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "#%matplotlib notebook\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. ,\n",
       "        1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ,  2.1,\n",
       "        2.2,  2.3,  2.4,  2.5,  2.6,  2.7,  2.8,  2.9,  3. ,  3.1,  3.2,\n",
       "        3.3,  3.4,  3.5,  3.6,  3.7,  3.8,  3.9,  4. ,  4.1,  4.2,  4.3,\n",
       "        4.4,  4.5,  4.6,  4.7,  4.8,  4.9,  5. ,  5.1,  5.2,  5.3,  5.4,\n",
       "        5.5,  5.6,  5.7,  5.8,  5.9,  6. ,  6.1,  6.2,  6.3,  6.4,  6.5,\n",
       "        6.6,  6.7,  6.8,  6.9])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(0,7,0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  2.33333333,  4.66666667,  7.        ])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=np.linspace(0,7,4)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f43fd63f810>]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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X5bp9R6moqlkbnNKxDRmpidwyLo2M1ERG9OpEfJsI+Ws5dVPLmQI7kE0t3Udq\nU4vIGURIcoSOorJK1vhPXB6f/84vrlkz3DYuhhG9OjH5vPSa0XdaYvhdweekTS1naFla7D956KpP\nfw9tahEJCgX6Waj2OTYfLKpZdeIffW/JLcb5F0D0S4rns4OSyUirmToZ3L0DcaG65ru8+MzNlmoH\n9hk3tSRrU4uIRxTojZB7tOzTE5Yrdx8hO6eQkoqaEWhi+zgyUxO5ckRPMtISyeidSKf2Hk8BBHtT\nS3wSdOiuTS0iIUKBXo+yymrW7i38dMngqj0F7C2oaVbVKsYY1rMjN4zp7R99d6ZP1/Yts+a7uTe1\n9BoTEVdqEREFOlBz4nJHfslJ4b1h/1Gq/Gu+eyW2IzMtkSnnp5OZ1plhPTvSNq4Zg65ZN7VE55Va\nRCRKA72gtOKk3ZarcwooKK0EIL51LKNSE5l2Yb9P+50kdWjCmu+ArtQSwKYWXalFRAIU8YFeWe1j\n4/4iVu058unoe3t+zXyxGQxO6cDlw7r7V510ZkByArFnWvPd7FdqGa4rtYhIszirQDezy4EngVhg\npnPu0Wapqomcc+wrLKtZceJfMpi9t5By/5rvbgltyExL5PoxvclMS2Rk70QS2rQ6caWW4i2wtZ6t\n4cfvVxTVffD23U4E8vErtdS1+7BdF21qEZGgaHKgm1ks8H/AZUAOsNTM3nTOrW+u4hpSUl7FmpzC\nmkuk+UffuUXlALRtBed1h3tGVjOqczmD4kvo7CvASvLg8EHYXSuw69vU0qbTiTDuMaqe6Y4UbWoR\nkZBwNiP0ccBW59x2ADN7GbgGCEqg+3yOrblFrNu+mx07t3Ng727KC/bTlUKSrIDr2pZwd5tiUpIK\n6VB1mFZlh7B8H+Sf8kat2p1ottR1APQ5v+7pDm1qEZEwczaB3gvYU+t+DjD+7Mqp25L/vY3U/I/p\nQyGDrNbJQ/+g2MXEYe2PB3JfSBhff7Ol1gmalxaRiBT0k6JmNg2YBpCWltak96ju2JsDvrEc7dKT\nrt1T6ZKSSkytoDZtahEROatA3wuk1rrf2//YSZxzM4AZAFlZWXUsoG7YhEm/aMrLRESiytkst1gK\nDDSzvmbWGrgZeLN5yhIRkcZq8gjdOVdlZt8G/kbNssXZzrl1zVaZiIg0ylnNoTvn3gbebqZaRETk\nLGiHi4hIhFCgi4hECAW6iEiEUKCLiEQIBbqISIQw55q016dpBzPLA3Y18eXdOL0zSygLp3pVa/CE\nU73hVCuEV71nW2sf51xSQ09q0UA/G2a2zDmX5XUdgQqnelVr8IRTveFUK4RXvS1Vq6ZcREQihAJd\nRCRChFOgz/C6gEYKp3pVa/CWkIxjAAADSElEQVSEU73hVCuEV70tUmvYzKGLiMiZhdMIXUREziAs\nAt3MLjezTWa21cyme11Pfcxstpnlmtlar2sJhJmlmtn7ZrbezNaZ2fe8rqk+ZtbWzJaY2Wp/rQ95\nXVNDzCzWzFaa2Vte19IQM9tpZtlmtsrMlnldz5mYWaKZvW5mG81sg5lN8Lqm+pjZYP+f6fGPo2Z2\nV9COF+pTLv6LUW+m1sWogVta8mLUgTKzC4FiYJ5zbrjX9TTEzHoAPZxzK8ysA7AcuDZE/2wNiHfO\nFZtZHPAx8D3n3Ccel1YvM7sHyAI6Oueu8rqeMzGznUCWcy7k13Wb2VzgI+fcTP+1GNo75wq8rqsh\n/izbC4x3zjV1P84ZhcMI/dOLUTvnKoDjF6MOOc65D4HDXtcRKOfcfufcCv/tImADNdeKDTmuRrH/\nbpz/I2RHI2bWG7gSmOl1LZHEzDoBFwKzAJxzFeEQ5n6XANuCFeYQHoFe18WoQzJ0wpmZpQOZwGJv\nK6mffwpjFZALvOecC9lagSeAewGf14UEyAHvmtly/3WAQ1VfIA+Y45/Ommlm8V4XFaCbgZeCeYBw\nCHQJMjNLAOYDdznnjnpdT32cc9XOuQxqrl87zsxCclrLzK4Ccp1zy72upREucM6NBq4AvuWfPgxF\nrYDRwNPOuUygBAjZ82rH+aeGrgZeC+ZxwiHQA7oYtTSNfz56PvCCc26B1/UEwv8r9vvA5V7XUo/z\ngav989IvAxeb2fPelnRmzrm9/s+5wBvUTHWGohwgp9ZvZ69TE/Ch7gpghXPuYDAPEg6BrotRB4n/\nROMsYINz7rde13MmZpZkZon+2+2oOUm+0duq6uac+6FzrrdzLp2af6//cM7d6nFZ9TKzeP9JcfzT\nF58HQnKllnPuALDHzAb7H7oECLmT+HW4hSBPt8BZXlO0JYTTxajN7CXgIqCbmeUADzrnZnlb1Rmd\nD0wEsv1z0wD3+68VG2p6AHP9KwVigFedcyG/HDBMpABv1Px8pxXwonPuHW9LOqPvAC/4B3jbgSke\n13NG/h+SlwFfD/qxQn3ZooiIBCYcplxERCQACnQRkQihQBcRiRAKdBGRCKFAFxGJEAp0EZEIoUAX\nEYkQCnQRkQjx/4l0DwGbT3UkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f43fd63f790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#fig = plt.figure(figsize=(10,10))\n",
    "plt.plot(X,X**2)\n",
    "plt.plot(X,X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/ipykernel/__main__.py:9: RuntimeWarning: overflow encountered in square\n",
      "/usr/local/lib/python2.7/dist-packages/ipykernel/__main__.py:9: RuntimeWarning: invalid value encountered in square\n",
      "/usr/local/lib/python2.7/dist-packages/ipykernel/__main__.py:10: RuntimeWarning: overflow encountered in absolute\n",
      "/usr/local/lib/python2.7/dist-packages/ipykernel/__main__.py:10: RuntimeWarning: invalid value encountered in less\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f26ad9e54d0>"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LNRV9Kr6+xzbSN1wk3SPppKSjpbK7JJ2Q9GT+sVj63p2Sjks6Jun6UvmipGclPS/pjup3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\ncLiYWRIOFzNL4v8BNgjRKAgq1n8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f26adbb6c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.linspace(-1.5,1.5,2000)\n",
    "Y=np.linspace(-2,2,2000)\n",
    "X,Y=np.meshgrid(X,Y)\n",
    "c=X+1J*Y\n",
    "ms=c*0.\n",
    "z=ms\n",
    "\n",
    "for i in range(20):\n",
    "    z=z**2+c\n",
    "ms=np.abs(z)<50\n",
    "fig = plt.figure()\n",
    "plt.imshow(np.abs(ms),cmap='viridis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pandas (http://pandas.pydata.org/)\n",
    "pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language.\n",
    "\n",
    "```python\n",
    "import pandas as pd\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sympy (http://www.sympy.org/)\n",
    "SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python. \n",
    "```python\n",
    "import sympy as sm\n",
    "sm.init_printing()\n",
    "```\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jupyter Notebook (iPython)\n",
    "The Jupyter Notebook is a web application that allows you to create and share documents that contain live code, equations, visualizations and explanatory text. \n",
    "\n",
    "### Code cell\n",
    "παρακάτω\n",
    "### Markdown Cell\n",
    "* Latex support\n",
    "$$\n",
    "    \\begin{equation} \n",
    "    \\rho \\left(\\frac{\\partial u_x}{\\partial t} + u_x \\frac{\\partial u_x}{\\partial x} + u_y \\frac{\\partial u_x}{\\partial y} + u_z \\frac{\\partial u_x}{\\partial z}\\right) = -\\frac{\\partial p}{\\partial x} + \\mu \\left(\\frac{\\partial^2 u_x}{\\partial x^2} + \\frac{\\partial^2 u_x}{\\partial y^2} + \\frac{\\partial^2 u_x}{\\partial z^2}\\right) - \\mu \\frac{\\partial}{\\partial x} \\left( \\frac{\\partial u_x}{\\partial x} + \\frac{\\partial u_y}{\\partial y} + \\frac{\\partial u_z}{\\partial z} \\right) + \\rho g_x \n",
    "    \\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "    \\begin{equation} \n",
    "    \\rho \\left(\\frac{\\partial u_y}{\\partial t} + u_x \\frac{\\partial u_y}{\\partial x} + u_y \\frac{\\partial u_y}{\\partial y} + u_z \\frac{\\partial u_y}{\\partial z}\\right) = -\\frac{\\partial p}{\\partial y} + \\mu \\left(\\frac{\\partial^2 u_y}{\\partial x^2} + \\frac{\\partial^2 u_y}{\\partial y^2} + \\frac{\\partial^2 u_y}{\\partial z^2}\\right) - \\mu \\frac{\\partial}{\\partial y} \\left( \\frac{\\partial u_x}{\\partial x} + \\frac{\\partial u_y}{\\partial y} + \\frac{\\partial u_z}{\\partial z} \\right) + \\rho g_y \n",
    "    \\end{equation}\n",
    "$$\n",
    "\n",
    "### Rich Display System\n",
    "```python\n",
    "from IPython.display import display, Image,YouTubeVideo\n",
    "\n",
    "```\n",
    "### Magic\n",
    "``` python\n",
    "%magic\n",
    "%lsmagic\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.gridspec as gridspec\n",
    "import seaborn\n",
    "from tqdm import tqdm,tqdm_gui\n",
    "import sympy as sm\n",
    "import sympy.physics.vector as vc\n",
    "sm.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "%magic\n",
    "#%lsmagic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython will make a temporary file named: /tmp/ipython_edit_x1i0yK/ipython_edit_zvHx__.py\n"
     ]
    }
   ],
   "source": [
    "%edit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANoAAAAyBAMAAADIJNgHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$- \\frac{G M_\\odot}{r} + \\frac{0.5 p_\\phi^{2}}{r^{2}} + 0.5 p_{r}^{2}$$"
      ],
      "text/plain": [
       "                      2          \n",
       "  G⋅M_\\ȯ   0.5⋅p_\\phi          2\n",
       "- ─────── + ─────────── + 0.5⋅pᵣ \n",
       "     r            2              \n",
       "                 r               "
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r,u,pr,pu,G,Ms,a,e=sm.symbols('r,\\phi,p_r,p_\\phi,G,M_\\odot,a,e')\n",
    "H=pr**2/2.+pu**2/(2.*r**2)-G*Ms/r\n",
    "H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAAyBAMAAAC39cr2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3ZJhZfb/POBHGT12eyVFC5P+A/aPXhm1UDq4AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- \\frac{M_\\odot \\phi^{2}}{r} + \\frac{0.5 p_\\phi^{2}}{r^{2}} + 0.5 p_{r}^{2}$$"
      ],
      "text/plain": [
       "            2             2          \n",
       "  M_\\ȯ⋅\\phi    0.5⋅p_\\phi          2\n",
       "- ─────────── + ─────────── + 0.5⋅pᵣ \n",
       "       r              2              \n",
       "                     r               "
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.subs({G:u**2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAA/BAMAAADtZ0VFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nY2+dG5RtlqnVtoTPHz3yHBBTBUryX635RPwY0AGwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( 1.0 p_{r}, \\quad \\frac{1.0 p_\\phi}{r^{2}}, \\quad - \\frac{G M_\\odot}{r^{2}} + \\frac{1.0 p_\\phi^{2}}{r^{3}}, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "⎛                                          2   ⎞\n",
       "⎜        1.0⋅p_\\phi    G⋅M_\\ȯ   1.0⋅p_\\phi    ⎟\n",
       "⎜1.0⋅pᵣ, ──────────, - ─────── + ───────────, 0⎟\n",
       "⎜             2            2           3       ⎟\n",
       "⎝            r            r           r        ⎠"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dotr=H.diff(pr)\n",
    "dotu=H.diff(pu)\n",
    "dotpr=-H.diff(r)\n",
    "dotpu=-H.diff(u)\n",
    "dotr,dotu,dotpr,dotpu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAc0AAAAmBAMAAABUn93bAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nOwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left ( a \\left(- e + 1.0\\right), \\quad 0.0, \\quad 0.0, \\quad \\sqrt{G M_\\odot a \\left(- e^{2} + 1.0\\right)}\\right )$$"
      ],
      "text/plain": [
       "⎛                           ________________________⎞\n",
       "⎜                          ╱           ⎛   2      ⎞ ⎟\n",
       "⎝a⋅(-e + 1.0), 0.0, 0.0, ╲╱  G⋅M_\\ȯ⋅a⋅⎝- e  + 1.0⎠ ⎠"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr0=sm.Float(0)\n",
    "u0=sm.Float(0)\n",
    "pu0=sm.sqrt(Ms*G*a*(1.-e**2))\n",
    "r0=a*(1.-e)\n",
    "r0,u0,pr0,pu0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "sub1={G*Ms:0.0172**2,a:1.0,e:0.0167}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.9833   ,  0.       ,  0.       ,  0.0171976])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y0=np.array([r0.subs(sub),\n",
    "             u0.subs(sub),\n",
    "             pr0.subs(sub),\n",
    "             pu0.subs(sub)\n",
    "            ]).astype('float')\n",
    "Y0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "dr = sm.lambdify((r,u,pr,pu),dotr.subs(sub1),\"numpy\")\n",
    "du = sm.lambdify((r,u,pr,pu),dotu.subs(sub1),\"numpy\")\n",
    "dpr = sm.lambdify((r,u,pr,pu),dotpr.subs(sub1),\"numpy\")\n",
    "dpu = sm.lambdify((r,u,pr,pu),dotpu.subs(sub1),\"numpy\")\n",
    "def dY(y,t):\n",
    "    a= np.array([\n",
    "            dr(y[0],y[1],y[2],y[3]),\n",
    "            du(y[0],y[1],y[2],y[3]),\n",
    "            dpr(y[0],y[1],y[2],y[3]),\n",
    "            dpu(y[0],y[1],y[2],y[3])\n",
    "        ])\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAOBAMAAAAoFKpzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAoElEQVQIHWNgVDJ2YAACVvXnQDqMgf0HiMd9\ngXUhA0MqA8NMEO8lA0M1A8MsBoZ8ByDPjIHhfgDD/gAI7xsDQ/8FkKL1AUBDPgF5B4Acju9AghFI\n+BcAGVwJIB5QDsxTAnLgKnkUQDwGoCn3gaZcYmAUAPKMGRjeBzCwKDDwgHhA27UZGKTKi7IY4jcw\ncF1gncLAsP///18gY1lrjjkwAABIUyhz5oYQCQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$2.0$$"
      ],
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dr(0,1,2,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 844 ms, sys: 44 ms, total: 888 ms\n",
      "Wall time: 891 ms\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/scipy/integrate/odepack.py:221: ODEintWarning: Integration successful.\n",
      "  warnings.warn(warning_msg, ODEintWarning)\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "t=np.arange(0.,50.*365.,3./365.)\n",
    "sol=odeint(dY,Y0,t,rtol=1e-12,atol=1e-13,printmessg=True)\n",
    "rt,ut=sol[:,0],sol[:,1]\n",
    "prt,put=sol[:,2],sol[:,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f43e92c98d0>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WaOHChUfNWBtjxozRmjVr6vWcAAAgMVGAASBO+f1+rVixovqWl5d3zK+NRCKHFOBjEQqF\nNGLECOXl5enrr7/WypUr9f777+uhhx6q8T2O5P3335d09AJ833336cYbb5R05AJ8tPc7nJ///Oe6\n++676/RaAADQtFCAASDBTJs2Tf3791fPnj110003VY/ODh48WL/61a/Ur18/zZkzR/Pnz9dtt92m\n3NxcrVu3TpL03HPPacCAAerWrZvefffdQ8795JNPatCgQbroooskSWlpaXrwwQerR5+nTJmisWPH\natCgQRo7dqwkaePGjRo8eLC6du2qqVOnVp8rIyNDkpSXl6d3331Xubm5uv/++w95zxdeeEFDhgxR\nRUWFJk+erGeeeUa5ubl65plnDnm/g0echw0bprfeekuS9Prrr2vgwIHq27evrrzyShUXF0uSzjrr\nLC1atKjOBRoAADQdHqcDAEAiuPbVaw85dnHgYo35wRiFIiHdvOjmQx6/tMuluqzLZdpVtku3vnXr\nAY89OuTRo75nKBRSbm5u9f2JEydq9OjRGj9+vCZPnixJGjt2rBYsWKDhw4dLkioqKqqnOa9Zs0bD\nhg3TFVdcUX2OSCSipUuXauHChZo6daoWLVp0wHuuWrVKp59++gHHOnfurOLiYu3du1eStHr1ai1Z\nskR+v19z587V0qVL9cUXXygtLU39+/fX0KFD1a9fv+rX5+fn695779WCBQsO+RoLCgrUsmVLpaam\nSqos98uWLdODDz4oqbJwH/x+Ndm+fbtmzJihRYsWKT09XXPmzNF9992nyZMny+VyqUuXLlq5cuUh\nXxsAAEguFGAAiFP7pkAfbPHixbr77rtVWlqqnTt36tRTT60uwKNHjz7iOS+//HJJ0umnn65gMFin\nXCNGjJDf76++f+GFF6p169bV51+yZMkBBfhICgsL1aZNm1q9X00+/PBDrV69WoMGDZJU+YuAgQMH\nVj/etm1bbdmyhQIMAECSi6sCbIz5q6Rhkr631vas4XEj6QFJl0gqlTTOWvtJ46YEkIyONGLr9/iP\n+HhLX8tjGvE9FmVlZbr55pu1bNkyderUSVOmTFFZWVn14+np6Ud8/b6RVrfbXeOU4B49euidd945\n4Nj69euVkZGhZs2a1fgelf80H/7+kfj9/gPy12T/9/N4PIrFYtX3973WWqsLL7xQTz31VI3nKCsr\nO2qJBgAATV+8XQM8V9KQIzz+Y0ldq243SfrfRsgEAHFjX+HLyspScXGxnn/++cM+NzMzU0VFRbU6\n/zXXXKMlS5ZUT40OhUKaMGGCfv3rXx/2NW+88YZ27typUCikefPmVY/CHkuObt26HTASfbTMgUBA\nK1asUCwW08aNG7V06VJJ0hlnnKH33ntPa9eulSSVlJTom2++qX7dN998o549D/m9KgAASDJxVYCt\nte9I2nmEp1wq6W+20oeSWhhj2jdOOgBoXPuuAd53y8vLU4sWLXTjjTeqZ8+euvjii9W/f//Dvn7M\nmDG65557dNppp1UvgnU0fr9fL730kmbMmKHu3burV69e6t+//2G3OpKkAQMGaNSoUerdu7dGjRp1\nyPTn3r17y+12q0+fPocsgpWenq7OnTtXF9dzzz1Xq1evrl4E62CDBg1Sdna2evTooQkTJqhv376S\npDZt2mju3Lm6+uqr1bt3bw0cOFBfffWVJOm7776T3+/XCSeccEzfAwAA0HSZw+3t6BRjTEDSgsNM\ngV4gKd9au6Tq/r8k/cZae8SNLfv162ePZe9LIBlYa5U9caEkK1fKNhl3qeQulXFVSCasWEVbxUIn\nSyaslKzFkvZNN62c1hotyVG0tKtkwvK2/ECKpcharxTzysZSFKtoKxtuVfU6q2D+CGe+0OP05Zdf\n6pRTTnE6RlJ48cUXtXz5cs2YMaNBzn///ferWbNmuv766xvk/HVR098vY8xya+2xXTwNAADqJK6u\nAa5PxpibVDlNWieddJLDaYDGEaqI6JS7FkjWK0nytnxPLu8uGe9eGc8euTx7FSk+RVJlKU3L+Z2M\niR1wjoqdZ6o8dLIkKaX1YlVOFPn3L8oqrEvR0q4y7pB87Q7dr7Xsux8rvPMcGe9OZXS5Vz3/Ol02\nmi4byVAs3Fzh3WcoWpojmXK5UrfJhltq7bQr5HbH1YQUNKKRI0dqx44dDXb+Fi1aVG/ZBAAAklui\nFeDNkjrtd79j1bFDWGsflvSwVDkC3PDRgMYTyHtFkuTJ/EKu1EK5UrbLlbJDrpTt8p8YUGjTOElS\nSut3ZNylsuHmikWaKRo6WdGyDlVnMSrbfLVsLFU26pdiqbIxr2ysaqEg69HTF76jnie2OOT9l3+7\nS6P+9z0VfT1VxlRIrrCMCUuuCtlI88onxVJVvu18GXdp5c1TJLd/syJFpZIkt3+T0k7+iySpz2P3\nKlbeRrGKLFXsPFux8hMkE9HQnh30x2sOP8UXTccNN9zQYOe+9tpDt7ACAADJKdEK8HxJ440xT0v6\noaQ91tpChzMBDSpw+z/k9m2Sy7dF7tRCycQkjZEkeVstkdv/rWy4hWIVWQrvyVU09O8ZDyXrbtU3\n0y9Visd9mLMPrVOm009uqWD+sGN45phDjuwsqVDf6W8oWn6CQhvHyqTsrCrw2+ROXyvtqty6xpP5\nud6umKIefzpB0bL2ipV3UKysvaJlHRWcfWmdcteWtbZWKxoDxyLeLj0CACCZxFUBNsY8JWmwpCxj\nzCZJd0nySpK19k+SFqpyC6S1qtwGiV/ro0lZt61IF/zhBdmKyn1RU9u+rIxu78uYyh+YY+FMRcs6\nqXJKslHZpmtkY/5GK4T1oVV6ioL5hy/e+0a3YxVtFN41UC5fobyZq2RafixJKl5zuwJ5r8idtk7G\ns1fR0Mn6cvLV8nnr958zn8+nHTt2qHXr1pRg1BtrrXbs2CGfz+d0FAAAklLcLYLVEFgEC/Fqw44S\nDX7gWbnT18mdtlaetAIZT6mKv7lDNpopT+bncqV+p2iok2JlJ6pg5minIzuiPBzVD6Y+I1dqoaIl\n3SUZ+To8I2/zTyVJsUimoqUBRUu6Kry7v9bMvETe47ymOBwOa9OmTUfdoxaoLZ/Pp44dO8rr9R5w\nnEWwAABoeBRgoJFl3/GMrPVIMZ88zZfL3+E5SVKsooWipZ0VKc1WpKinXr75AvXq2NzhtPHrz2+v\n0Zw335Lbv0HutG/lTlsnG81QacEESZK35RLZSKYipV0UnHmVw2mBo6MAAwDQ8CjAQAPbWVyufvc8\nLk/GV/JkfCmXf6PKt16m8O4fynj2ypPxlSIlnbVu6n/I5WIl5LraE6pQn+kvSbE0STGld8mXy7tX\n1hpFSwOKFJ+iSNGpWj9tLFOaEZcowAAANLy4ugYYaCpe+axQv3jyE8lVrvTs+5Wes1uSFA11VMX2\n8xUpzdEDY3J1ae6JDidtOpr7UxScdWX1/XGPZumdghXyZH4lT8Zq+dotVLmrXNkTW0smIldqoT68\ndZzaNuNaTAAAgGTBCDBQTzbtKtXZDzwmb7PPJFdY5VtHSpJS2y5UrLyNIiXdVTDjaodTJq/sSX+X\n5JaNNJM7Y7XSOv1NsYpWCu/to8jePlp713VyuRgZhnMYAQYAoOFRgIHjlH3n3+RtsVzeZp/KlbJL\nNuZWpLiHyjb/RJI54orHcEbg9hfkyfxC3mYr5U5fJ2Niipa1U2jj9bKRZvyZwREUYAAAGh4FGKiD\nwMQXJeuW5FZK1htKyXqzcgXivX0UKeqh4KwrnI6IY5R9xzPyNPtc7rT1Ktt8tSSXvC2WykZ9ihT3\nSKgtppDYKMAAADQ8CjBwjKy16jzlL/K2/FDeZitVtmW0IsWnyriLJRNVwYyfOB0Rx6lyD2KrtOw/\nyO3bolgkTZE9pym8e4DWT7vO6Xho4ijAAAA0PBbBAo4ikPeyPM0+U0rLD5Se861szKvI3t6KhVtr\n6e3ns4hSE7Jv6vNzy3op758vyNtimbytPlRK6/fU7Z7Vqthxrq7q11F3X9HH4aQAAACoC0aAgcMI\nTHxJsh5JMaV3vleSUcXOgQrvOZ0pzkkk+45n5G2xTJHiroqVnyhX6la5079ReHe/A1adBo4XI8AA\nADQ8CjBwkOw7H1NK63fkyfhaJev+R7IpMp7devaGi9U/kOV0PDjk1mdX6B+fbFZK67eU2vZV2ZhX\n4d39VbHjbBXMuMbpeGgCKMAAADQ8CjBQJWfKn5XS+m15Mr+QrFvhPaerfNtFCs68yuloiDM5d/1F\nKa2WyNN8hSQpvGuAyr+7jNWjcVwowAAANDwKMJJeIO8VuVK3KD3n97JRnyp2naHwzkEqmDnG6WiI\nc9mTnlBK63dkYymq2DZEkpUr5XsWzEKdUIABAGh4FGAkrZwpf5LbV6jw7gGSrDzNP1Gk6FQFZ41y\nOhoSTOXq0ZI7ba3STn5E4b2nqmL7hVo/9XqHkyGRUIABAGh4FGAknZy7/qLUNm/Ik/mlYuHmKll3\nm2Q9TF/FcQvc/oJSWi1RSqt3JVeFInv7qHzbBSqY/jOnoyEBUIABAGh4bIOEpJE96Qmltv2n0nNW\nykZ9Kv/+IlXsGqTg7EudjoYmonL2wCgF7nhWKa3eUUqr9+VOK1Agr6UkN79kAQAAcBgFGE3evump\nrpRyeTK+Uvn281Sx4yy2MkKDqVw47Spl3/G0XKnbJLklRdV1zh0K7+6v4OzLHE4IAACQnJgCjSbr\nv/7+kf61+WW5Ur9T+daqwuEqV3DW5c4GQ9IJ5L0id/rXSjvpUcXCzVX+/Y/1j7G/UO9OLZyOhjjC\nFGgAABoeI8BokjpP+71ST3hJvhO+V6QkRzJhRt3gmMqpz0PVeZpXqW1fkf/EpzXmlfdUtnWE1k/5\nL6fjAQAAJA1GgNGkZN/xjFLbvSJv808Vq2ip8u+GacX/+29l+LxORwMkSfNXbtKtC/9PqW1ek42m\nq7RggiQX1weDEWAAABqBy+kAQH14+J11/96KJn2Nyrefp5L1/621k35N+UVcGdGno9ZOvEsl6/9H\noc3XSHJJrjJ1mTlb24rKnI4HAADQpDECjISXc9cj8rb8oOo6X5dkKhScPdLpWMAxCeS9Im+rd+Rr\nt1CRki4qK7yMbZOSFCPAAAA0PK4BRsIK5L2klKzFSsteLBtNU8WOc7Ti9qvV3M+ILxJHMH+o/v5h\nD01926vUNq8pPed36nr3l/pF33H61QU/cDoeAABAk8IIMBJSzpSH5Wv/nNy+rQrvyVXZd8Ortp4B\nElf2pKfkO+FFeTK/VMWOH6n8+2FcG5xEGAEGAKDhUYCRUM65Z7G+3VGs9Jz7JFe5yraO1LpJtzkd\nC6g3oYqIev12lqKl2bLhVpKrTI/+7Ec6t3s7p6OhgVGAAQBoeBRgJIzsO/8mG2kmWa9cqVsVCzdT\ncNaVTscCGkTlom5W/o6PVf6yZ8toFcy4xulYaEAUYAAAGh6rQCPulZSH1WX2FKXnPKCUrEWSpPVT\nr6f8okkL5g/VsjsuULiop9z+zUrPeUBdZs5xOhYAAEBCowAjrgVuf06nP/xT+Tu8oGioo8K7zuSa\nSCSNrExf1ZZJExSraCV/x7+r++9uUGDii05HAwAASEgUYMStnCl/VnrOA/Jkrlb590P027MeUsGM\nnzgdC2h0BdN/JrNlvCp2nC1PxpcyrnD1vtcAAAA4dhRgxJ3dpRWVP9zHvLJRv0qDN+ub2+7RJb1O\ndDoa4JhV04bp61v/qJL1t8pG0yVF1Xn6fU7HAgAASCgsgoW4Epj4D3mbr1B49wBJRlJMwfzhTscC\n4kog7xV5W34g3wkvqWLnQJV/N1TB/EudjoXjxCJYAAA0PI/TAYB9ciY/qrTsv8uVsk3RUCfNu/FK\n9e7YwulYQNwJ5g/VqP9tpi927FBK6yVy+zYre1IJlwgAAAAcBVOgERc6T79PaYE/yrhLFNpwvdZP\nvZHyCxzBCz8/S1/f+r8KbfqJXL6tSsv+g3KmPuR0LAAAgLhGAYajQhVRdZ0zSf5OcxULt1JpwS1a\nN/mXTscCEsbaOyaqtOAXspFMybpZHAsAAOAImAINx+z7Qd2d0VyRop4q23KlgrNHOpwKSDzrp12n\nQF4b7fudZufpv9W9w67SyNM6ORsMAAAgzjACDEcE7nhWnswvJEnR4h56YsSDlF/gOATzhysnK11u\nf4HSTpqriUtuY79gAACAgzACjEaXfefjSjv5Ubm8e1SyNqCCmaOdjgQ0CW/+v8GKRs/WD367Salt\nFyrt5D8r+45yFcwc43Q0AAAAqXbsAAAgAElEQVSAuMAIMBpVzl1/UVrgf+XyFCm04VrKL1DP3G6X\n1vw6X6FNY+VK/V5pgT8p+86/OR0LAAAgLlCA0Wg6T3tAaSf/WbIulQZ/rnV3jXc6EtBkrZt0m0q/\nvVFyheT2b2JxLAAAAFGA0UgCea/I7d+oWLiFSoM3a/2065yOBDR566f8XCXrblNkbx9JUuD25xxO\nBAAA4CwKMBrcvh+6K3YMVmnwFyqY8ROHEwHJIzjrCkmS2x9URpc56jLjbocTAQAAOIcCjAbVdc4k\npXe+VyZlmyTDSs+AA4L5QxUtb6tYeTv5Oj6hLjNnOx0JAADAERRgNJiud+fJd8JLioZOlg23VDB/\nqNORgKQVnHWlSjder2joJPlOfEpdZs1wOhIAAECjowCjQXS753/ka/eKwnt7Kav0RgVnX+p0JCDp\nBWddrtCG6xQtzZavw7PKmfqQ05EAAAAaFQUY9a7LrJlKbfu6wrtP0/mtb9WSX1/odCQAVYKzRyq0\ncZzKvxuqWKgTq0MDAICkQgFGvQrkvaJI0akq2zpMl3W8VX/8ST+nIwE4SHD2SIV3/UiSS8a7U11m\nznE6EgAAQKOgAKPedJmZL7lKJevVOSeMUv6oXKcjATiMfdfkp7Z5Q74Tn6QEAwCApEABRr3oMnua\n/B2fUGrWm8pM9eiRnzHyC8S7YP5QlRVeplioo3wnPqXO0+9zOhIAAECDogDjuHWZOUe+9s8rUtxF\n5dsu1udTL3Y6EoBjFJx9uUo3XqtYeVv5Oz6uztP+4HQkAACABkMBxnHpPPVB+To8rViok0Kbfqrg\n7MucjgSgloKzrlBow/WKhVspJWuRAnkLnI4EAADQICjAqLNA3gKlnvCyYuGWKt30MwVnj3Q6EoA6\nKpg5WqENNyi06WeSDKtDAwCAJokCjDqp/OHYKLRxnEIbrlNw5lVORwJwnApmXC3FUiVTodR28xW4\n/TmnIwEAANQrCjBqLXD780rJ+pekqGykmQpm/IfTkQDUk2D+ULl8hfK2/Ej+jo8rMPElpyMBAADU\nGwowauWnf/1A/hOfVErWm3L5tlZvpQKg6Vh/180q23KlPOkF8rV/Tlv3hJyOBAAAUC8owDhm1lp9\ntGeuPBlrVF54mdZPucnpSAAayNrb71D59xfL23ylzn54ktNxAAAA6gUFGMes25y7lNLqfVXs+JHW\nTJzidBwADezNG6YpvCdX3lbvK3D7C07HAQAAOG4UYByTwO3PK7XtPxUp7qabe//S6TgAGkHHlmkq\nKxyl0oLxUszHytAAACDhUYBxVIG8V6SYX6Xf3qTQ5p/olxf8wOlIABpJcPZlspEWkmLytnpHgTue\ndToSAABAnVGAcUSBifPkyfxCkhQr76DgrFEOJwLQ2IL5Q+VK2a7UNq/L3+Ep/eXdtU5HAgAAqBMK\nMA7LWqvUdgvk7/h3uVI3s+IzkMTWT7tW5VsvlSdjre756EGn4wAAANQJBRiH1XX2DKW0/Ejl28/R\n+qms+Awku69+PVnh3X2VkvWmOk//ndNxAAAAao0CjBrl3PV/8rV/UZGSbI046Tqn4wCIA263S2Vb\nL1OsvK187Z9TYOI8pyMBAADUCgUYhwjkvSTfiU/Ixnwq2/wT3XtlX6cjAYgTwdkjVbb5GoU2XyNZ\nryY89anTkQAAAI4ZBRg18Khi28Uq2zxGBTPHOB0GQJxZP+1axUInS5JeXv25w2kAAACOHQUYBwhM\nfFGSFCnqqXWTJzicBkC8Kph9iTzNVii982/VeeofnY4DAABwTCjAqJY96Smld75XnmYrZIzTaQDE\nM2OMIsU/kA23kK/Dswrc/oLTkQAAAI6KAgxJ0qotu+Vr/5yMO6RYWQcVzGbLIwBHFpw1SmVbrpLx\n7pKv3ctOxwEAADgqCjAkSZc9frc8GWtU/t0wrZ92rdNxACSIdXf9QhU7zpW3xXJ1mZnvdBwAAIAj\nogBD2Xc+rtS2rypS3E0Lr73N6TgAEs3OCxUpyZFc5QrkveJ0GgAAgMPyOB0Azvpw/Q6509ZJ1qOy\nwsvVtV2m05EAJJhvZg5TIE+SWDwAAADEN0aAk9yYhz9UZE9/Fa+9TQUzrnE6DoAEFcwfJsnK03yZ\nOk+/z+k4AAAANaIAJ7HsSU/InbZWkrT41kscTgMg0aWlSCmt3pWv/QusCg0AAOISBThJWWvlO+El\n+Tv9TXKVKjsr3elIABLc6mnDVFZ4hYynSKltFzodBwAA4BAU4CTVZea98mR+qfJtFyg460qn4wBo\nItZP+S+Fd/5IKS2XKmfqQ07HAQAAOEBcFWBjzBBjzNfGmLXGmLwaHh9njNlmjFlRdbvBiZyJLjDx\nRfnazVe0rJ0yys91Og6AJqZ82wWKhZvLd8I8/ffTnzgdBwAAoFrcFGBjjFvSHyX9WFIPSVcbY3rU\n8NRnrLW5VbdHGjVkE5GS9ZZcKbtV/t2l+vTOIU7HAdDEBGdfrrLCkSrfdpFeXFHodBwAAIBqcVOA\nJQ2QtNZau95aWyHpaUmXOpypyQnkvSIbbqaKnWdo3eRbnI4DoIlalfcrRYtPkST2BgYAAHEjnvYB\nPlHSxv3ub5L0wxqeN8oYc7akbyT9t7V2Yw3PkTHmJkk3SdJJJ51Uz1ETk7VWkhTefYbDSQA0dT6v\nW5KUkvUvGXexpKHOBgIAAFB8jQAfi5clBay1vSW9Iemxwz3RWvuwtbaftbZfmzZtGi1gPOsy/Q/y\nNF8mKaZgPj+MAmhYwfyhMq5ypbT6QDlTHnY6DgAAQFwV4M2SOu13v2PVsWrW2h3W2vKqu49IOr2R\nsiW8Xz39iVLbvazUrDclE3M6DoAkUb79PMUi6Uptu1Bl4YjTcQAAQJKLpwL8saSuxphsY0yKpDGS\n5u//BGNM+/3ujpD0ZSPmS2ivFMyX27dV5d8PUXA2l1YDaBzBWaNUsf08edLX6dT8B5yOAwAAklzc\nFGBrbUTSeEmvqbLYPmutXWWMmWaMGVH1tAnGmFXGmJWSJkga50zaxBKY+A+ltHld0dKT9P4t/+10\nHABJpmX0bMUqWiu17av69XMrnY4DAACSWDwtgiVr7UJJCw86Nnm/zydKmtjYuRJdSut35fIWqWTz\nf6htM5/TcQAkmaW3D1HnqWtkYz49W7BJd1/Zx+lIAAAgScXNCDAaRiDvFUXLOqhix9laf9fNTscB\nkKQWj79esfIOktgWCQAAOCeuRoDRMKLFPRQt7uF0DABJ7KTWaZIJy9f+BUVDJ4ltkQAAgBMYAW7C\nsu94Vimt/yW5ytj2CIDjCmZdKuPZq5SsxQpMnOd0HAAAkIQowE1YSuu3ldJmkVyevU5HAQAZY1Sx\n/Xy5PEXytvjI6TgAACAJUYCbqOw7npa35QeK7M3V+mnXOh0HACRJ6yZPUKQkRylZbzMKDAAAGh0F\nuInytloimYjKt5/ndBQAOEDF9gsYBQYAAI6gADdBgdtfUErLDxUp6qWCaeOcjgMAB1h753iVbb1U\nkaJeypnIitAAAKDxsAp0E2TcpYqGAqrYcbbTUQDgEMYYhXcNlCRZh7MAAIDkwghwExPIe0U23Eqh\njddq/ZT/dDoOANRo0a1ny+0PKvWEf2jV5j1OxwEAAEmCAtzEuPzfynh3Oh0DAI6oS9tMmZTtSmm5\nVCP++len4wAAgCRBAW5CCneH5Gv/gvwnPqmlt5/vdBwAOKLInlzFws2U0uodp6MAAIAkQQFuQn70\n+4flTv1eFbsGqm0zn9NxAOCIgvmXKrzrTHky1irnrkecjgMAAJIABbgJ8bb8QLFIuiJ7ezsdBQCO\nScWuAbIxj7wtP3Q6CgAASAIU4CYie9IT8mSuVnh3PwVnX+Z0HAA4JsFZV6pi51mKlbdVII8tkQAA\nQMNiG6Qmwu3fIFm3wrt/6HQUAKiVim0XOx0BAAAkCUaAm4Af3PlPRYp6q3jNJBVMH+t0HAColYLZ\nl0gmIk/GKhWXhZ2OAwAAmjAKcBNQFqmo/CTGwlcAEo8xRp5mK+Tv9Lj6zPmz03EAAEATRgFuAvwd\nH5fvxCc09oyTnY4CAHUS2dtbNpoqb4tlTkcBAABNGAU4wWVPekru9G8Uq8jS9Mt6Oh0HAOokOHuk\nwkW95Mn8XIGJLzodBwAANFEU4ATnafapjLEK7+nrdBQAOC6R3X1l3BXyZK5yOgoAAGiiKMAJLByJ\nyttiuaKlJ6tg2jin4wDAcfnnf/1UsYqWcqevczoKAABooijACaz7jEfkTv1e4T2nOx0FAI5bt3bN\nVRq8WeWFo9gTGAAANAj2AU5gsYpWKiscqfDeXk5HAYB6YaOZTkcAAABNGCPACerj4E4plqbw7h8q\nOOsKp+MAQL0I5g9VSuvF8nf6q9NRAABAE0QBTlCj/zpP3hYfSqbc6SgAUL+sS56Mb5Q96e9OJwEA\nAE0MBThBeVssU+oJL0sm5nQUAKhX4aLKLd08zb5wOAkAAGhqKMAJ6Ls9IXmafa5ocVemPwNocgqm\n/1TRsg7yZn7udBQAANDEUIAT0MD7H5PLu1vhIha/AtA0Rfb2lDttg7InPel0FAAA0ISwCnQC8mR8\nJWuNosU/cDoKADSI8N7eMp4SSVzmAQAA6g8jwAnI5d2laOgkFcy8yukoANAgvrrrP1T+3XDZSEun\nowAAgCaEApxgAnmvqKzwKoU23Oh0FABoMKket6So3P6gAhPnOR0HAAA0ERTghGOrPjB7HUDT5k5f\nq7TAn+ROK3A6CgAAaCJoUQnG1/5ZWbm1aOwfnY4CAA0qWpotG/PIk/G101EAAEATwQhwAvnz22vk\nyfxSktSpVZrDaQCgYQVnj1S0NEeedAowAACoHxTgBDJn8Zsy7jJFS7o4HQUAGkWkuJtcqduVPekJ\np6MAAIAmgAKcQNxp6yVJ0dIch5MAQOPY9+8d1wEDAID6QAFOIJ70dYqWt1HBjKudjgIAjeKByy9R\n6bc3KVLU0+koAACgCaAAJ4j/eny5IiU5Cu8e4HQUAGg0w/ucWDkKbL1ORwEAAE0ABThBvLpqq8I7\nz1F451lORwGARmW8O5XS5lVlT3rK6SgAACDBsQ1SgjCePbIxnxRLdToKADQq4y5VatZbipWf4HQU\nAACQ4CjACSK17UK5/Rv0xQ1vOx0FABpVc3dA4ZhXbv8Gp6MAAIAExxToBGCtldu/UdGyjjLGOB0H\nABrVp3derGjZiXL7NjkdBQAAJLhaF2BjzEBjzB+NMZ8ZY7YZYzYYYxYaY35hjGneECGTXc6kZ+VK\n2aloqJPTUQDAEbFQR7l8WxTIm+90FAAAkMBqVYCNMf+UdIOk1yQNkdReUg9JkyT5JL1kjBlR3yGT\nnctfOeoRC3V0OAkAOCNa1kmyHhnvLqejAACABFbba4DHWmu3H3SsWNInVbffGmOy6iUZqrl9G2Wt\nUbSMAgwgOUX29lTx3l7iyh0AAHA8avWTRA3lt07PQe1E9vZW2ZbRCs4e6XQUAHDEG/99rii/AADg\neNVpFWhjTJEkW3U3RZJXUom1tll9BcO/xSraKVbRzukYAOCYru0yldL6LblSvpc01Ok4AAAgQdXp\n1+nW2kxrbbOqwuuXNErSQ/WaDJKkwMQX5cn8XMZd7HQUAHCU8eyRJ/MLLf7qO6ejAACABHXc88ls\npXmSLq6HPDiIK3Wr/B2fkIv9LwEkuVj5CTLuCl339zecjgIAABJUXadAX77fXZekfpLK6iURDuD2\nbZVU+YMfACSzWHnlpSCuVEaAAQBA3dSpAEsavt/nEUlBSZcedxocwpW6VTaaogeuONfpKADgqGh5\nW0mSmwIMAADqqE4F2Fp7bX0HQc1cKdsVq2ijEX3YAglAcgvOulKnPPSkrK3r724BAECyq+sUaJ+k\n6yWdKsm377i19rp6yoUqLu9ORcvbOx0DAOJCaMMNTkcAAAAJrK6LYD0u6QRVLnz1tqSOkorqKxQq\nXfmn91W6cZzKt13kdBQAAAAASHh1LcBdrLV3qnLv38dUuSnjD+svFiTp4+Au2XCWbEUbp6MAQFzw\nNP9Y6V1mKTBxntNRAABAAqprAQ5XfdxtjOkpqbmktvUTCfu4Ur6Xt9W7Mu4Sp6MAQHywHrm8e+Xy\n7nI6CQAASEB1LcAPG2NaSpokab6k1ZLm1FsqSJLcaUH52r0imQqnowBAXIiFW0mSDAUYAADUQV1X\ngX6k6tN3JOXUXxzsz3j2yFojG2nmdBQAiAs23FKS5ErZ6XASAACQiGo1AmyM+Q9jzGFfY4zpbIz5\n0fHHgiQZT5FsNF3B/BFORwGAuHBB186y1sh4WHcRAADUXm1HgFtL+tQYs1zScknbVLkNUhdJ50ja\nLimvXhMmMZdnr2wk0+kYABA3/vKzAfrBA6cpVs7igAAAoPZqVYCttQ8YYx6UdJ6kQZJ6SwpJ+lLS\nWGvthvqPmLyMp4jpzwBwkLLCq5yOAAAAElStrwG21kYlvVF1QwMq/fY/ZVwsgAUAh4o5HQAAACSg\nOi2ChYa39vtiyabIRlOcjgIAcSW13Xx5MlZLGu50FAAAkGDqug0SGtgF97+u1LYL5fIxqxwA9mdj\nXhlvkSJRRoEBAEDtUIDjlPGUKKX1O3Klfu90FACILzG/jImqy6T5TicBAAAJpk5ToI0xqZJGSQrs\nfw5r7bT6iQXjKqv8JOZzNggAxBkbrfx3sfrfSQAAgGNU12uAX5K0R5VbIZXXXxzsY9whSZKN+h1O\nAgDxxcZSKz9xU4ABAEDt1LUAd7TWDqnXJDjAvpENywgwABwgVt5WFTsHSjEWCQQAALVT1wL8vjGm\nl7X283pNg3+rGtnYN9UPAFApVn6iyr870ekYAAAgAdW1AP9I0jhjTIEqp0AbSdZa27vekiW5yJ6+\nKtqTK9YpA4CDWclEJWucDgIAABJMXQvwj+s1BWpgJLmdDgEAcceV8r3SO9+v0KafSBrhdBwAAJBA\n6jS8aK39VlILScOrbi2qjqGeuNO/UeoJ8yQTcToKAMQVu++/LhN1NggAAEg4dSrAxphfSnpCUtuq\n29+NMbfURyBjzBBjzNfGmLXGmLwaHk81xjxT9fhHxphAfbxvvHH7Niul5YdOxwCA+GOrZsdQgAEA\nQC3VdQr09ZJ+aK0tkSRjzBxJH0j6w/GEMca4Jf1R0oWSNkn62Bgz31q7+qD33mWt7WKMGSNpjqTR\nx/O+calq5PfeK05zOAiwn8+elf41TdqzSWreUTp/stT7KqdTIdlUFWBjYg4HAQAAiaauKywZSfv/\n6j1adex4DZC01lq73lpbIelpSZce9JxLJT1W9fnzks43xjS9lVBMTNa6NLh7O6eTAJU+e1Z6eYK0\nZ6MkW/nx5QmVx4HGZPf910UBBgAAtVPXAvyopI+MMVOMMVMkfSjp/+ohz4mSNu53f1PVsRqfY62N\nSNojqXU9vHccsspIresgPVDP/jVNCocOPBYOVR4HGpG1HkXL2stG/U5HAQAACaZO7cpae58x5i1V\nbockSddaaz+tt1T1wBhzk6SbJOmkk05yOE0dxDyS9ai0PCKfl9WgEQf2bKrdcaChxPwqLfil0ykA\nAEACqtUIsDGmWdXHVpKCkv5edfu26tjx2iyp0373O1Ydq/E5xhiPpOaSdhx8Imvtw9baftbafm3a\ntKmHaI2rYsf5Kv56upasO+RLA5zRvGPtjgMAAABxprZToJ+s+rhc0rL9bvvuH6+PJXU1xmQbY1Ik\njZE0/6DnzJf0s6rPr5D0prXW1sN7x6UJT8XVwDqS2fmTJe9BU069/srjQCMynr1Ky/693Bmrj/5k\nAACA/dRqCrS1dljVx+yGCGOtjRhjxkt6TZJb0l+ttauMMdMkLbPWzlfltcaPG2PWStqpypLc5Lgz\nvpK32QqVFY5yOgpQad9qz6wCDae5yuX2bZFxlTudBAAAJJg6XQNsjPmXtfb8ox2rC2vtQkkLDzo2\neb/PyyRdebzvE+9cKdvkbb5CZVsvczoK8G+9r6LwwnGmaps4WRYJBAAAtVOrnx6MMT5JaZKyjDEt\n9e+tj5rp0NWacTxiXkmScVU4HAQA4kxVAbYUYAAAUEu1/enhPyX9SlIHSZ/sd3yvpAfrKxQkG0ut\n/IQpfgBwgOoR4BgFGAAA1E5trwF+QNIDxphbrLV/aKBM0L8LMNe4AcCBbCxFkZJs2Wi601EAAECC\nqe0U6POstW9K2myMufzgx621/6i3ZMku6lcskiEp5nQSAIgrsfITFdrwn07HAAAACai288fOkfSm\npOE1PGYlUYDrSTSUrZI1k5yOAQAAAABNRm2nQN9V9fHahokDAMCReVu+J2/LD1W6/ldORwEAAAnG\nVZcXGWN+aYxpZio9Yoz5xBhzUX2HS2omLF/Hv8mTudLpJAAQV1ze3XJ5d2vNzGFORwEAAAmmTgVY\n0nXW2r2SLpLUWtJYSfn1lgqa9/Nz5Mn4Si5fodNRACC+uEOyUb+87rr+FwYAAJJVXX962Lf/7yWS\n/matXbXfMdSD3JNaykYy5PIUOR0FAOKKcZfIRtOcjgEAABJQXQvwcmPM66oswK8ZYzLFcsX1zkYz\nZNwlTscAgLji8uyVjTRzOgYAAEhAtV0Fep/rJeVKWm+tLTXGtJbEwlj1zEYyZDzFTscAgLgSDZ2s\nWLiF0zEAAEACqlMBttbGjDEdJf3EGCNJb1trX67XZFCsvI1Myk6nYwBA3Jgyf5XKvxvhdAwAAJCg\n6roKdL6kX0paXXWbYIyZVZ/BIJV/P1xlm36m3lNeczoKAMSFue8XqHLbeQAAgNqr6xToSyTlWmtj\nkmSMeUzSp5Jur69g+Le9ZRGnIwBAXHD5Nirt5EcU2vhTp6MAAIAEdDx7SOx/AVbz4w2CQ7lStyot\n8Ae5/UGnowBAXHB5d8u4KlgFGgAA1EldR4BnS/rUGLNYldsfnS0pr95SQZJkYyly+zfLpGxzOgoA\nxAVXyg5JUqwiy+EkAAAgEdV1EaynjDFvSepfdeg31tqt9ZYKkqRMT5Zi1sjl3eV0FACIC66U7YqF\nmyk4e6TTUQAAQAKq1RRoY0xbY8zvjDELJE2Q9Ja1dj7lt2F8dtePZcPN5WIlaACQJJmUHYpVtHY6\nBgAASFC1vQb4b5JKJP1BUoak39d7IhwgVtFWLqZAA4AkKVLUQ5G9uU7HAAAACaq2U6DbW2vvqPr8\nNWPMJ/UdCAeKlHSRO/U7fRzcqf6BVk7HAQDHBPJeUeWSEwAAAHVT61WgjTEtjTGtjDGtJLkPuo96\nFt55tsoKr9SVf/rA6SgA4CxXmeQqdToFAABIYLUdAW4uabkqV37eZ98osJWUUx+hUJOY0wEAwFHe\nzM/l6/CCitfe5nQUAACQoGpVgK21gQbKgcMxFUrvcrcqdpwtabjTaQDAMS5foWwsRbOHMw0aAADU\nTa2nQKNxBWePlKyRO7XQ6SgA4ChXaqFiZSdozICA01EAAECCogAngFjZiXL5NzsdAwAc8/3eMrl9\nWxUtP8HpKAAAIIHVdh/ghcaYQMNEweFEy06UK2WbAhP/4XQUAHDED+9+QcYdUqy8vdNRAABAAqvt\nCPCjkl43xtxhjPE2RCAcKlrWUcZYuX1MgwaQnGwsVWWFlytS3NXpKAAAIIHVdhGs54wx/5R0p6Rl\nxpjHtd/yxNba++o5HyTFQp1UseNHstE0p6MAgDNifoV3D3A6BQAASHB1uQa4QlKJpFRJmQfd0ADW\nz7hK5d8PU6yirdNRAMAR7vSvZbw7Fcwf6nQUAACQwGo1AmyMGaL/z959x8lZl/v/f1/Td7ak00Jg\nd5MAUhQwdvTYOCp4KDZAz7F3PT896vmeFEroUbEcuyiColJUEDQcqSoqUgJCkBLSlvSe3c3uzE79\n/P6Ymd1JSGDvO7t778y8no9HHruzO/fMtZOZ+/5cn3J9pK9LulXSic651KhEhd2YmaSCQolNQYcC\nAGPug9f8XU2H/rw8AvwfQYcDAABqmNcR4AWS3u2cm0vyO7aik+9Tc8e31XHudUGHAgBj6t6ux2Wh\nnArpw4IOBQAA1Diva4BfO1qB4PkVUh2SpHDT6oAjAYCxFW5aI0kqpGcEHAkAAKh17ANcIw6Md8gV\nYgonSYABNJZwcpWKuQlaeeH7gg4FAADUOBLgGvH3ef+qQvpwEmAADeXRNTsVTq5SoX+mQiEuWQAA\nYP/QmqghhVSHwonNal9wY9ChAMCYOON79ym16vPKbHtz0KEAAIA64GkNMIKV631JqQhMIRF0KAAw\nZlyhVSoEHQUAAKgHjADXkDOPfbEKqVmSwkGHAgBjIjblbkXa/qHVl58SdCgAAKAOkADXkK+fdbxC\n8U2KTb1Lvels0OEAwKhqn3uLYlPuVTjZVd4PHQAAYP+QANeYcGKt4tPu0vGLrg06FAAYVeFklyyc\nUb7vyKBDAQAAdYIEuMbk+4+QJIWbnwk4EgAYXZGWp+SKERX6ZwUdCgAAqBMkwDVm9SXvVWHgQEVa\nlgUdCgCMmmKxqEjr0yqkZqrr8jODDgcAANQJEuAalO97kcLJ1Wqf/6ugQwGAUdF57s1y+Wbldx0d\ndCgAAKCOsA1SDcrvOlaxSfcrHN8UdCgAMDqKCaWe/bQkF3QkAACgjjACXINu+ehZ6nvmXBXSnUGH\nAgCjwzKSpK5Fbw84EAAAUE9IgGvQcYdOVGXwvn3u74INBgBGWMe5v1DLERcr0vpY0KEAAIA6QwJc\noyzSrWTn1xRp/WfQoQDAiIq0LZWF8ioMHBp0KAAAoM6QANeoy057tSycVqRtadChAMCIirYtVSE9\nXasvfn/QoQAAgDpDAlyjznl5h/K9L1ak5Sm1z/910OEAwIjoOO9nCjetU673xUGHAgAA6hAJcA3L\n9ZwoCxUUbXs86FAAYERUzmd5EmAAADAKSIBr2CP//SEVMtMUmfBI0KEAwH7rSeWU632xBjaeqdWX\n/HvQ4QAAgDpEAlzDJjbHlN36r8rteLXa5y4OOhwA2C8vuegOudxk5bpfEXQoAACgTkWCDgD7J7/r\nuKBDAIAREZ14v4q5SXmTSYEAACAASURBVCr0Hxl0KAAAoE4xAlzjuhadKov0Kjr5Xt3w0LNBhwMA\nvrTPu1nxA/5P0bal6lp0atDhAACAOkUCXAfCTauVOPA2zf/DTUGHAgC+RNoel4UzynW/NOhQAABA\nHSMBrgP5XceomG9WdNL9QYcCAL5EJz6kYnaK/vjZDwcdCgAAqGMkwHWga9HpynW/TJGWp9Vx7i+D\nDgcAPOm84EeKJLuU3fkKHTalOehwAABAHSMBrhO57pfJrKjoxIeCDgUAPLHILhUyByjXPSfoUAAA\nQJ0jAa4Tqy9+v/J9R8rC/WyJBKBmtM9drEL/kUqt+i91XfbuoMMBAAB1jm2Q6kh67fslhYMOAwCG\nLRTbomJusuS4HAEAgNHHCHAd+fUnT5IkWXS7BnL5gKMBgOd35vf+oqYZVytxyHVsfQQAAMYECXAd\nmdM+WeHmZWqZ9VUdc/n3gg4HAJ7X4zv/qlBsp/K9JwQdCgAAaBAkwHWmkOpUMd+i2OS/BB0KAOxT\nTzqr2NQ/qZCZpq+d+r6gwwEAAA2CBLjOdF1+hnI7X6lI69PqPP/qoMMBgL068YrvKpzYoOz21+n0\n4w8NOhwAANAgSIDrUG7nq+SKUcWm/jHoUABgryKtT6iYa2P6MwAAGFMkwHVo9aXvUW7nqxRpeVLt\n838VdDgAsJv2uYuV2XSGUl2fVtflpwcdDgAAaCDsO1GnMtter+z210nFZNChAMDuQhmpGJfLTww6\nEgAA0GAYAa5TXZe9W67QIsmpfd5vgw4HACRJnQu/r5ZZlyqcXMXWRwAAYMwxAlzXimo67Mcq5iZL\nOiPoYABA8Wl3yrmoCunpQYcCAAAaECPAdaxr0b+pmDlI0QmPqOP8a4IOB0CDm3nRtxVpWa7s9ter\n6/J3BB0OAABoQCTAdS677Q2Siyg+7Y6gQwHQwFKZvGLT7lAx16rczlcGHQ4AAGhQJMB1bvWlZyu7\n/bWKtj2uzoXfDzocAA3q2MuuUSTZpez2N6rrcpZkAACAYJAAN4DsjtepmG9RbPJflS8Ugw4HQIOZ\nd9PjKmYOVv/qz6ot95qgwwEAAA1s3CTAZjbZzO40s+Xlr5P2cb+CmT1a/nfrWMdZi7oue4fSaz6k\ngY3v1qwF/xd0OAAazHVLnpEkFQcO1cPnvi3gaAAAQCMbNwmwpLmS7nbOzZZ0d/n23qSdc8eX/502\nduHVtiZ3mOSikuX0mi/fGXQ4ABpE+/zfqHnm1xSdfK8emP+moMMBAAANbjwlwKdL+mn5+5+KfXtG\n1BMXvVUW3qXmzq9ri+4JOhwADSI25U8KRXapkOrUgW2JoMMBAAANbjwlwAc65zaWv98k6cB93C9h\nZkvM7H4zI0n24JkL361idqri0+5Sx4Ibgg4HQJ3rOO9axSb/VbnuE7Rq4SeCDgcAAGBsE2Azu8vM\n/rmXf6dX38855yS5fTzM4c65OZLeK+mbZjZzH8/18XKivGTr1q0j+4fUqGgkrMzmf5NCWcUO+EPQ\n4QCoY845JQ78nSRTZutbgg4HAABA0hgnwM65Nzvnjt3Lv1skbTazgyWp/HXLPh5jffnrKkl/knTC\nPu53pXNujnNuzrRp00bl76lFqy76kHI7XqPohIfVufAHQYcDoE51nn+tws0rlNn6Zq2+5H1BhwMA\nACBpfE2BvlXSB8rff0DSLXvewcwmmVm8/P1USa+R9OSYRVgnMtveJFdoUXTCI1pw8+NBhwOgzrTP\nXSyXm6L+lV9UqPd1QYcDAAAwaDwlwIsknWxmyyW9uXxbZjbHzH5cvs+LJC0xs8ck/VHSIuccCbBH\nXZe9U6muTyqz+d/0iwfWBB0OgDoTim+S5OTyE7XskrcHHQ4AAMAgKy23rW9z5sxxS5YsCTqMcSWT\nL+jIc/8gi/RKclp9yXuDDglAHeg8/ydKdv6vMlvepuX/b1HQ4dQUM3u4XOMCAACMkvE0AowxFI+E\nJeWVbP+uEgffpHQ2H3RIAGrcF298RIlDfi1XSCjfc2LQ4QAAADwHCXAD61p0urLbX6dIyzIddwUj\nNQD2z++6rle4aa0ym07X6kvfE3Q4AAAAz0EC3OA+9/IPqJA6TPEDf8fewAB86zz/asWm3alc7zF6\neu7coMMBAADYKxLgBvfZNxypgY3vlIWyih/8G/VnckGHBKDGfPHGx2SRXSpmpyiz6QxFwlxaAADA\n+EQrBVp10YeV2foWqZDQMQtvCzocADXmN4+sUyE1U6nVn9PqS88OOhwAAIB9IgGGJOmSN3xaAxvP\nklxE7XMXBx0OgBrRecGVik25W1JRqy9nyyMAADC+kQBDknTWyw6TVNq/M37QTfr89Y8EHBGA8a59\n3s1KTL9e0UkPSKEBmVnQIQEAADwvEmAM6lp0qkLxjYpNelC3rf1F0OEAGOfiB/5eodg2DWx4j7ou\ne3fQ4QAAALwgEmDs5pm585XreYli0+7UzAu/E3Q4AMapWZcuUmzSg8pu/xetPP9zQYcDAAAwLCTA\n2E0oFNLApnfIZacoMf06tkYC8Bzt836r+EG3qJA+VNmtJwcdDgAAwLCRAOM5ui57h9Lr3ysLpxSb\n8kctXrox6JAAjBPtcxdLLqr0uv9Qev3Z6lp0WtAhAQAADBsJMPZq1YUfU3rNR5XZ+jZ95pcUxAJQ\nEoqvlyQV04dr9cUfCDgaAAAAb0iAsU9PLfiU5CJSKKXOhT8IOhwAAZt1+UVq7vy2ws1Pq2vRqUGH\nAwAA4BkJMPYpFim9PRKH/FrJGVer47yfBRwRgKB0XvAjJQ66Wfn+Tp047RVBhwMAAOALCTCeV9ei\nU5XZfKpkTk2H/kzt824KOiQAY6xjwY1qOvTncoWkBta/V7/65ElBhwQAAOALCTBe0OqL36/0+vcq\nFN+ixCE36oHV24IOCcAYaZ/7OyWm/1wW6VV63b9r9aVnBR0SAACAbyTAGJaV531emS2nKNr2hP79\nV18NOhwAYyBXKEoKKd9zogY2vkurFn4q6JAAAAD2Cwkwhu2xz12izJa3Kt9zQmkrFAB17YjzfyVJ\nyvW8TCvmLwg4GgAAgP1HAoxhS8Yjym5/vVyhVVJBnedfHXRIAEbJzEu+quZZX1G4qUtXf+hlQYcD\nAAAwIkiA4Ull65P4gb9Xsv17JMFAHepc+H01Tb9OxcwBKgwcojcceUDQIQEAAIwIEmB41rXoVGV3\nvFbORdQ042p1LLg+6JAAjJCO869R04xr5PKtSq/9gLouPzPokAAAAEYMCTB8WX3xfyi99oOySJ+a\nZlyj9vm/CTokAPupY8ENSs64SlJIqTUf1upLzw46JAAAgBFFAgzfVi38hNLr3qdQYqOaDrmBwlhA\nDWufu1iukFR+14uVXvtBrb74A0GHBAAAMOJIgLFfVp73RQ2sP0eZbW+SJL144e0BRwTAq/Z5N8si\n3ZJCymw5RasWfiLokAAAAEYFCTD224oFc1UcOFSS1B9ZqksWPxFwRACGq33eb9U042dKHv5DyXKD\nhe4AAADqEQkwRkTXolMVanpWyRk/07UrrtBNj6wNOiQAL6B93i1qOvRahZMrldl6srouPyPokAAA\nAEYVCTBGzKoLPq3M1jcqNnGJ5t27UHc9tTHokADsQ/vcW5SY/gtFWp5RZuM7tGL+eUGHBAAAMOpI\ngDGinv7CN5TZ9gbFJj2oz9wxX79fuj7okADsoX3uYsWm3aNo61Ma2HS6ls9bGHRIAAAAY4IEGCMq\nFArpyc9/U5mtb1Js4hJ97rc36bt/XBF0WADKKtXas9tfp/T6c7T8fy4JOCIAAICxQwKMERcJh/T0\nF76h/lX/qUKqU1+9fZlO+85fgw4LaHjt825WbNofJMtKxYRWzJ8fdEgAAABjigQYoyIUMq1c+DFJ\nUji5XM8Uf6D2eb8NOCqgcbXP/42aDrtKsSl/VjjZRbVnAADQkEiAMWrMrFQdOr5N0QmPqWnG1Wqf\n/5ugwwIaTvuCG5U87McKN63VwPpztPK8/wo6JAAAgECQAGPULf+fS5Ref5bCyS4lD/uROhbcEHRI\nQMPoOO9aJQ//gULxTUqve79WLJgXdEgAAACBIQHGmFgx/1yl135AofgWJdu/r44FNwYdElD32ucu\nlqwgk1N6zUe18twvBh0SAABAoEiAMWZWnvcFpdZ8VPm+I+UKycFqtABGXucFV0lyctlp6l/1X1p5\nwWeCDgkAACBwJMAYU6su+LQym0+TZLLoNs269MtBhwTUnVmXX6hkx7cUnfiAJKlr0WkBRwQAADA+\nkABjzFWqz8an3q2mQ3+uI776Je0ayAUcFVD7fvSXFTry659R0yG/VqG/U7ne46n2DAAAUCUSdABo\nTF2LTlX7vJxkRcUPuF0v++E2DWw8U12LTg86NKAmtc//jZqmX6fYlGXK7nilXj7hQ7r2slcHHRYA\nAMC4QgKMwHRdfoaWrn293nXDQsWn3a1QbKs6Fgxo9aVnBR0aUFPa5y5WuGmjwsmVGth4hp75n4tk\nZkGHBQAAMO4wBRqBevGMiXrmS99Uet175VxErhinOBbgQcd5P5MkFdId6l/xP1o+92KSXwAAgH0g\nAca4sGLBPKXXfExyUSmU1qzLL1Q6mw86LGDcunHJszriis+reebXFE6ukCStvvTsgKMCAAAY30iA\nMW50LXq7JCk26QE1HfJrnfD9D6t93s0BRwWMPx0LbtAFD/yX4tPuVr7neBXSh1HsCgAAYBhYA4xx\npWvRqbr76ZfqU7/PKzb1biWb1qnzgm1adeHHgg4NGBdmXvhdJTt+KQunNLDxHXryS+crGgkHHRYA\nAEBNYAQY486bjjpIz3zpG0qv+YgsNKBk+3c165KvaHtfJujQgMB8++7lap+7WKHERslFler6tJbP\nvZDkFwAAwANzzgUdw6ibM2eOW7JkSdBhwIeOBTcofuBiZba8TS7fJklM9UTD6Tj35wrFt6rQf4Qk\nJ1lOXZefGXRYGGFm9rBzbk7QcQAAUM8YAca4tvrSs/Tz075ZTn6LShxyg2Ze/I2gwwLGhHNOsy67\nVM2d/6vEwb+WLK9Vl51K8gsAAOATCTDGvTntk9W16FRZpE+hxHolD/uJjvzmR9Q+/6agQwNGTfv8\nX+lF336/mqZfr2LmQKWe/aS6Lj9doRBbHAEAAPhFAoyasfqSc5Ra/Z/KbPsXRSc+pOaOb2rmRd8K\nOixgxLUvuFHNnd9QpG2pMltO1hvaLtDqi/8j6LAAAABqHmuAUZM6L/yemg65UZJT/8ovSgqzNhg1\nr33eb0t7YUuKTblb+b6jtOrCjwccFcYKa4ABABh9jACjJq264NPqX/U5pdd+UFJYspxmXnKFGqFD\nB/VnQ3dKsy67RM2zvqJQfIMkyXW/meQXAABghLEPMGpWpRBQ+9zFik58QImDfq8XffdBZTadrtWX\nvC/g6IDh6Tz/asUPvFVN01eokDpMzkWZzQAAADBKSIBR87oWnarjLjANbC4qPu1ORWZ+XbO/8rhy\nO16trkWnBR0esFftcxcrNvVOJTv/JBWjGth0mq54yyd1+vEzgg4NAACgbpEAoy48fuEpkk5Rx3nH\nKnHQLUocuFjh+Ca1z2VtMMaXHX0ZnXjJXYO38z3HK7PlrVp96dkBRgUAANAYKIKFulMsFjX7sq/J\n5SapmDlYFumVhQa06qIPBR0aGlznwisVP+A2ZXe8VoW+oyQ5dS16e9BhYZygCBYAAKOPEWDUnVAo\npJXn/rfa5y6WJMWm3qnoxId15NcfUGb7G9V16XsCjhCNpuPcXyh+wO1q7viHivmkLDSgD766XQtP\nOybo0AAAABoKCTDqVmXqc8eCPkmm6OT7FJ24REd89X5ld5ykrsvfEWyAqHvtcxcrOvleNc+8Q5KU\n2fZ6Zbe/Xl2XvTPgyAAAABoTCTDq3upLz5J0ljovuEqxaXcofsCdskhK7XPjksQaYYy49vk3SS4s\nKSJXSCrfe5wyW99CdXIAAICAsQYYDadz4ffl8hPk8hMUSqxTOLFBue4T1bXo9KBDQ41rn3eTYpP/\nrujke5Xd9ibldr5GEp0sGB7WAAMAMPoYAUbDWbXwUyoWnTrn36bohEcUm3yfYlPv1uwvP6Bc98sG\n9xcGhqt93k2KTrpfzbPuVSjSr3zfkSqkDyfxBQAAGGcYAUZDS2fzOvbL31Zs6j2KJLtUzDcru+3N\nyu18FckLXlCl0FrTjKsVaVmmfN9sZbaerFULPxVwZKhFjAADADD6SIABScWi0+yLv6vY1D+qkGpX\ndvsbJRVkkV6tvuTfgw4P40zH+dcoNvmvym59s1yhVaHEGkki8cV+IQEGAGD0kQADe2if+ztJIUVa\nlyox/Trldx2j3I6T9PSCTyoaCQcdHgLy+PqdOuMnP1V00t8VaXlKcmENrD9H+b5jmC2AEUECDADA\n6CMBBvah49xfKjrpPsUmPSgLp1VIT1d256uU7zlRXYv+LejwMEba5y6WLKdkx7cVjm9RMd+sXPcr\nlNvxKq2+9Oygw0MdIQEGAGD0kQADL6B93s2KTviHopP/JlNR/au+KMnK06PPCTo8jIKedFYnfPkq\nhZvWKLfzJElSbNofVMwcqPyu49R1ORXDMfJIgAEAGH0kwMAwdaeyOuGy38jl2yTLqWX2pSpmpyjX\n/TLlel+srsveHXSI2E8d5/5S0Qn/UGTCwwrHt8oVY+pbPlcqJrX68lNkZkGHiDpGAgwAwOgjAQZ8\naJ/3W0UnLlF04oMKJzbKubDyfUcou+1NKg4cyprQGlKp5FxZ823mlE+1K9/9UuV2Haeuy94ZcIRo\nFCTAAACMPvYBBnzouvwMSWeoWCxq1kU/UrTtUUXalkoqSpI6z/+JLLpThdQspsuOQ+3zb1Kk5SlF\nWh9XpO1Y5XtPUCHVoez2NyjXfaJWX/yBoEMEAADAKCABBvZDKBTSqoWfkCRdetsT+tGK1ZKk6KQH\nFJt8n1whrqO+faPyu45Wvu9IdV32riDDbWjtc3+vSNtjirQ+rpbZy2ShvIq5VhX6j5Ak3fqpt+m4\nQylqBQAAUM+YAg2MgiPO+50K8WcUaXlSkdYnFYr0qZhrU/+KeZJMFu7T0wvfpXiUbZVGy/LNu/SW\n712vUGyr8rteIklKdnxLFt6l/K7jlO89Tv/56pP1+ZOPDDhSoIQp0AAAjD4SYGCUffePz+hr996l\nUKRX+V3HSXJqnrVIkpTvn61C/2wV+mdq9aVnBRtoHeg49zqFkysUaV6pcPNyhaK9pUJWy86XFJFF\nerX4M2/T0QdPDDpU4DlIgAEAGH0kwMAYa597q6ITlyjcvFyR5hWy8IAkKbPlZGW3v0lSURbp1aqL\n30vV4eeRzuZ19MXXKdy0RvldL5JcXLGpdyk+7S65fFL51Ezl+45Uoe9I9utFTSABBgBg9JEAAwH6\n9C+W6A/LH1KkebkK6XYVUjMVim9Qc+e3VMxNUCHVrkJ6hoqZQ1RIH6quy88MOuTAtM9dLIt0Kzrh\nEYWb1irUtFahSJ8kKbXmQyr0HymLdMvCKX3nXafolOOmBxwx4A0JMAAAo2/cJMBm9m5JCyW9SNLL\nnXN7zVjN7K2S/ldSWNKPnXOLXuixSYBRK977o/v1964uRdoeV7ipS+HkswpFeyRJqTUfUaF/tkKJ\n9Yo0P6NC5iAVM9P0xTe+Up99Q/2sYz3je/dq6aaVCsU3lf4lNinfc6Lyu45VKL5ezZ3fViEzTcX0\nDBUGZqiQPkyXnfKvOvvl7UGHDuwXEmAAAEbfeEqAX6TSHjI/lPSlvSXAZhaW9IykkyWtk/SQpHOc\nc08+32OTAKOWdSy4XqHEBhXSh0vFhKKT/qbEQb8b/L0rhlXMTlV67Ufk8m0KxTfJwn0q5ibK5SeU\nt2waX9rn3SKL9CgU265QdIeKucmlasyhAbXMvkQWykuSnDMVs1OV3f565XteKqkohQbUddm7g/0D\ngFFAAgwAwOgbN9sgOeeekvRCax5fLmmFc25V+b7XSzpd0vMmwEAte+761VPVPv9EheJbFIptLf2L\nb5XLN0uSohMfVGzyfYP3PuaqL8tlJyv17KckmSItT8hiO+TyzXKFZrlCk1RMqJg9oHxEXjd8/CS9\nonPKC8b2+6Xr9NnrHpLMScW4JCmUWCOL9MnCaVkoLYuk5HITlOt+hSSpeeZX1HrUjt0eJ9d9QikB\nLiaU3fFaFbNTVcwcpGLmgHGZwAMAAKA2jZsEeJimS1pbdXudpFcEFAsQmH3tJ/yFGx/VzUtfr/yu\nY2TRboWi3eV1sWlJpc6lyIRHFW17fLfjSls0zZckNc24Vh+59zzpz2FJIcmZitkDlOr6TPn3Vymc\n7JKsILOiWo+SCqnDlHr205KkxMG/UTixefCxnTPldx09mADnek6QFFIxN0EuO1nF3BR95YyT9O45\nh5WPOHVEXiMAAABgT2OaAJvZXZIO2suvFjjnbhnh5/q4pI9L0mGHHfYC9wbqw9ffc7y+/p7jn/c+\nv3/sBH32hvtk4X5ZpF8WGtjt97meE1QYmC6zvCQnyckVWgZ/n+87UsXMQXIuIrmIVIyomJ8w+PuB\nje+SZHKFJrlCk2751Jv0khmTq56BBBcAAADBGNME2Dn35v18iPWSZlTdPrT8s70915WSrpRKa4D3\n83mBuvH2lxyit79k7yPIJS+UoJLAAgAAoDaFgg7Ao4ckzTazDjOLSTpb0q0BxwQAAAAAqAHjJgE2\nszPNbJ2kV0labGa3l39+iJndJknOubykz0q6XdJTkm50zj0RVMwAAAAAgNoxbopgOedulnTzXn6+\nQdIpVbdvk3TbGIYGAAAAAKgD42YEGAAAAACA0UQCDAAAAABoCCTAAAAAAICGQAIMAAAAAGgIJMAA\nAAAAgIZAAgwAAAAAaAgkwAAAAACAhkACDAAAAABoCCTAAAAAAICGQAIMAAAAAGgIJMAAAAAAgIZA\nAgwAAAAAaAgkwAAAAACAhkACDAAAAABoCCTAAAAAAICGQAIMAAAAAGgIJMAAAAAAgIZAAgwAAAAA\naAgkwAAAAACAhkACDAAAAABoCCTAAAAAAICGQAIMAAAAAGgIJMAAAAAAgIZAAgwAAAAAaAgkwAAA\nAACAhkACDAAAAABoCCTAAAAAAICGQAIMAAAAAGgIJMAAAAAAgIZAAgwAAAAAaAgkwAAAAACAhkAC\nDAAAAABoCCTAAAAAAICGQAIMAAAAAGgIJMAAAAAAgIZAAgwAAAAAaAgkwAAAAACAhkACDAAAAABo\nCCTAAAAAAICGQAIMAAAAAGgIJMAAAAAAgIZAAgwAAAAAaAgkwAAAAACAhkACDAAAAABoCOacCzqG\nUWdmWyU9G3Qc+2mqpG1BB1EHeB1HBq/jyOB1HBn18joe7pybFnQQAADUs4ZIgOuBmS1xzs0JOo5a\nx+s4MngdRwav48jgdQQAAMPFFGgAAAAAQEMgAQYAAAAANAQS4NpxZdAB1Alex5HB6zgyeB1HBq8j\nAAAYFtYAAwAAAAAaAiPAAAAAAICGQAI8TpnZu83sCTMrmtk+q5ua2VvNbJmZrTCzuWMZYy0ws8lm\ndqeZLS9/nbSP+xXM7NHyv1vHOs7x6oXeX2YWN7Mbyr9/wMzaxz7K8W8Yr+MHzWxr1Xvwo0HEOd6Z\n2U/MbIuZ/XMfvzcz+1b5dV5qZieOdYwAAGB8IwEev/4p6R2S7t3XHcwsLOm7kt4m6WhJ55jZ0WMT\nXs2YK+lu59xsSXeXb+9N2jl3fPnfaWMX3vg1zPfXRyTtdM7NkvQNSV8e2yjHPw+f0xuq3oM/HtMg\na8c1kt76PL9/m6TZ5X8fl/T9MYgJAADUEBLgcco595RzbtkL3O3lklY451Y557KSrpd0+uhHV1NO\nl/TT8vc/lXRGgLHUmuG8v6pf319LepOZ2RjGWAv4nI4Q59y9knY8z11Ol/QzV3K/pIlmdvDYRAcA\nAGoBCXBtmy5pbdXtdeWfYciBzrmN5e83STpwH/dLmNkSM7vfzEiSS4bz/hq8j3MuL6lH0pQxia52\nDPdz+s7ytN1fm9mMsQmt7nBOBAAAzysSdACNzMzuknTQXn61wDl3y1jHU6ue73WsvuGcc2a2r7Ln\nhzvn1ptZp6R7zOxx59zKkY4V2IffSbrOOZcxs0+oNKr+xoBjAgAAqDskwAFyzr15Px9ivaTqkaJD\nyz9rKM/3OprZZjM72Dm3sTwVcss+HmN9+esqM/uTpBMkNXoCPJz3V+U+68wsImmCpO1jE17NeMHX\n0TlX/Zr9WNJXxiCuesQ5EQAAPC+mQNe2hyTNNrMOM4tJOlsSFYx3d6ukD5S//4Ck54ysm9kkM4uX\nv58q6TWSnhyzCMev4by/ql/fd0m6x7G5+J5e8HXcY53qaZKeGsP46smtkt5frgb9Skk9VUsgAAAA\nGAEer8zsTEnfljRN0mIze9Q59xYzO0TSj51zpzjn8mb2WUm3SwpL+olz7okAwx6PFkm60cw+IulZ\nSe+RpPLWUp90zn1U0osk/dDMiip1Ci1yzjV8Aryv95eZXSRpiXPuVklXSbrWzFaoVJzo7OAiHp+G\n+Tr+f2Z2mqS8Sq/jBwMLeBwzs+skvV7SVDNbJ+kCSVFJcs79QNJtkk6RtEJSStKHgokUAACMV8Zg\nDQAAAACgETAFGgAAAADQEEiAAQAAAAANgQQYAAAAANAQSIABAAAAAA2BBBgAAAAA0BBIgIEaYGYz\nzGy1mU0u355Uvt2+l/sWzOxRM/unmf3KzJI+nu/HZnZ0+fv5e/zuPn9/xV6f55tm9jqfxx5nZteM\nVCwAAACof2yDBNQIM/t/kmY55z5uZj+U1OWcu3wv9+tzzrWUv/+FpIedc1/fj+cdfLyRZGZTJC12\nzr1yPx7jLkkfds6tGbnIAAAAUK8YAQZqxzckvdLMPi/pJElXDOOYv0iaJUlm9oXyqPA/y48hM2s2\ns8Vm9lj552eVf/4nM5tjZoskNZVHlH9R/l1f+auZ2VfLxz1edezry8f/2syeNrNfmJntJbZ3SvpD\n5YaZnW9mD5Uf8HpPOwAAIABJREFU78rKMZVYyt9PNbOuqsf4naSzh/0KAgAAoKGRAAM1wjmXk/Tf\nKiXCny/f3iczi0h6m6THzeylkj4k6RWSXinpY2Z2gqS3StrgnHuJc+5YVSWk5eecKyntnDveOfe+\nPZ7iHZKOl/QSSW+W9FUzO7j8uxMkfV7S0ZI6Jb1mLyG+RtLDVbe/45x7WTmOJklvf76/r2yJpNcO\n434AAAAACTBQY94maaOkY5/nPk1m9qhKyeEaSVepNGJ8s3Ou3znXJ+kmlRLHxyWdbGZfNrPXOud6\nPMRykqTrnHMF59xmSX+W9LLy7x50zq1zzhUlPSqpfS/HHyxpa9XtN5jZA2b2uKQ3SjpmGDFskXSI\nh5gBAADQwCJBBwBgeMzseEknqzSC+1czu945t3Evd007547f49i9PqZz7hkzO1HSKZIuMbO7nXMX\njUC4marvC9r7uSYtKVGOLyHpe5LmOOfWmtnCyu8k5TXUWZfY4zES5ccBAAAAXhAjwEANKK+H/b5K\nU5/XSPqqhrcGuOIvks4ws6SZNUs6U9JfzOwQSSnn3M/Lj3niXo7NmVl0H495lpmFzWyapNdJetBD\nTE+pvD5ZQ4ntNjNrkfSuqvt1SXpp+fvqn0vSEZL+6eE5AQAA0MBIgIHa8DFJa5xzd5Zvf0/Si8zs\nX4ZzsHPuEUnXqJSgPiDpx865f0g6TtKD5SnTF0i6ZC+HXylpaaUIVpWbJS2V9JikeyT9P+fcJg9/\n02JJry/H1y3pRyols7dLeqjqfldI+pSZ/UPS1D0e4w3lxwEAAABeENsgAQiMmf1V0tvLCbDXY+Mq\nrTs+yTmXH/HgAAAAUHdIgAEExsxeodKa5aU+jp0tabpz7k8jHhgAAADqEgkwAAAAAKAhsAYYAAAA\nANAQSIABAAAAAA2BBBgAAAAA0BBGNQE2s7ea2TIzW2Fmc/fy+7iZ3VD+/QNm1l7++cvN7NHyv8fM\n7MyqY7rM7PHy75aMZvwAAAAAgPoxakWwzCws6RlJJ0tap9K+nuc4556sus+nJb3YOfdJMztb0pnO\nubPMLCkp65zLm9nBKu0zekj5dpekOc65baMSOAAAAACgLo3mCPDLJa1wzq1yzmUlXS/p9D3uc7qk\nn5a//7WkN5mZOedSVft6JiRRqhoAAAAAsF8io/jY0yWtrbq9TtIr9nWf8uhuj6QpkraV9wf9iaTD\nJf1HVULsJN1hZk7SD51zV+7tyc3s45I+LknNzc0vPeqoo0bmrwIAAAAAjCsPP/zwNufctBe632gm\nwPvFOfeApGPM7EWSfmpm/+ecG5B0knNuvZkdIOlOM3vaOXfvXo6/UtKVkjRnzhy3ZAnLhQEAAACg\nHpnZs8O532hOgV4vaUbV7UPLP9vrfcwsImmCpO3Vd3DOPSWpT9Kx5dvry1+3SLpZpanWAAAAAAA8\nr9FMgB+SNNvMOswsJulsSbfucZ9bJX2g/P27JN3jnHPlYyKSZGaHSzpKUpeZNZtZa/nnzZL+VdI/\nR/FvAAAAAADUiVGbAl1e0/tZSbdLCkv6iXPuCTO7SNIS59ytkq6SdK2ZrZC0Q6UkWZJOkjTXzHKS\nipI+7ZzbZmadkm42s0rsv3TO/WG0/gYAAAAAQP0YtW2QxhPWAAMAAABA/TKzh51zc17ofqM5BRoA\nAAAAgHGDBBgAgDqTLxSDDgEAgHGJBHic+9uKbTrlf/+irm39QYcCABgDW3oH9PCzO30ff/sTm3T0\n+bfrkTX+H2NJ1w5l8gXfxwMAascja3bqDVf8SU9u6A06lDFBAjzOXf23Lj25sVe/X7rB1/HZfFHf\nuWe51u5IjXBkAIDR8MVfPaZ3fv8+3+ftmx5Zp2yhqNv/ucnX8Y+u7da7fvB3zb+JTRYAoBY8uHqH\nvn7HMhWL/mo7/fKBNVq9rV+/enjtCEc2PpEAj3PPbN4lSVq2uc/X8X94YpOuuOMZXXDrEyMZFgBg\nHzb2pLV1V8bXscWi01+Wb5MkLXl2h6/HWLsjLWno+uHVfStLz/+3Fdt8HS9JPemc+jN538cDAIbv\nS796TN+6Z4Ue7PJ33Vi1tZRnLNvk77pRa0iAxzHnnDb1DEiSVm/zlwA/vq5bkrRyq7/jAQDDVyg6\nnfHdv+nM7/3N1/Hb+oYS52e3ex8Bds6pa3tpyczG8vXDqzXl592RyvoaTSgUnU7537/oQ1c/5Ov5\nAaDR7M+uPMWi05ryjKHH1nb7eoyVW0vXjfXdad9x1BIS4HFsR39W2XIhk829/kYTVmwpJb7rd6ZV\n8NGQKRad/v3HD+hrdyzz9fwA0Eie3tSrzb0ZrduZHuzA9GJD1TGVkVwvetN5pbKltbt+E+BK4p3N\nF7W9P+v5+Cc29Gh9d1oPdu1QH6PAAPCCzvnR/XrPD/7u69jqpHXtTu8dp+lsQT3pnKTSdcPvNOpa\nQgI8jlUaL0cc2KLtfRlfCezanaUPRb7ofE3Je2JDr/66Ypu+fc8KX88PAI1kTdWo7bPbvRcv3FBu\nyMQiIW3Z5T2B3ZkqJawzpzWrJ53TQM57IatNvQOKR0K7xePFqq1Df7ef1wAAGsm6nSndv2qHHuza\n4avjtDrp3dDt/fjt/aX84OiD25TNF7Uj5b3js9aQAI9jlQ/BsYdMUNGVRoS92t6X0fSJTZL8TWtY\nvmVoLUAXDRkAdS6dLehDVz+ou57c7Ov43XvivZ9zK+f9ow9u83XO3zGYALdIkrpTOe+P0Z/VkQe1\nDn7v1YaeqtfAZyGvvy7fph/8eeV+TQsEgFpQma255/fDtb2vdJ4+fErSV6dl5fjZB5auGzt9nPdr\nDQnwOFbpya80RLyO4OYLRXWnc4PHb+/zPgJcvf3Seh+NOam0roFGDIBa8MdlW/THZVs17+bHfR2/\noXtA4ZBJkjb1eD9ndpenoXVOa/aVfFYaLp3lBHinx578QtGpdyCnjqnNvo6XpI1VIxB+RjMk6TO/\nfESL/u9p6lcAqAlbegeU87n/+rqq9vWzO7wPNlWuFUcc2Oqv47R8zKxKx2nae8dprSEBHscq8/EP\nn1JqiHSnvb2pd6Zyck6adYD/kYDqEQy/C+PPu+Wfeus3/+L7xAAAY6VSOXlHf9ZXx93m3gEdPiWp\n5lhYO/q9n3N70zm1JiKa1hLXdh8xVBoyneUE1ut5vyddum4MJcDe/4aNPWnNPqBFZv5GkPsy+cHr\n39J1PZ6PB4CxtL47rZO+/Eed91t/W8et706r3G/qcwQ3I7PSeXtnyvt1o1J8ceYBjABjHOgdyMtM\nOnRSaQpzb9pbMZFKw2PmNP89+dv7szr64DZJ0hYfhbgKRaef379Gyzbv0tJ1/irTAcBYqcx6KRSd\nr07D7nRWk5IxTW6J+Trn9qRzmtAU1aTmmLL54mBBq+GqPGdH+bzf47njtHT/wyYnFTKp28ffsKM/\nqwPbEprYFPW1lqy6AeinEBgAjKW/r9yubKGo6x/yt4fuxu60DpnYpKktcX/LHfuzmtgU1ZTmmHIF\np36P143BEeD9GDCrNSTA41hvOqeWeEQTmqKl2wPe3pCVRe0zJicVDZuvnvyd/Vkd0BZXayLiqzFX\nXQDlqY2NsbcYgNpVPRVtg48pzD3pnNoSEU1OxnxVUO6tJMDJ0nnf61S0Hf05xcKhwdoPXs/7lYR3\ncnNME5qivpP4tqaIJjfH/K0hrkqA1/moaAoAY+nJDb2D3+/y2FaXSufpyc0xTW2JaVufv07Hyc0x\nTWqOlR7P43l3ZyqnaNh0yOB1gxFgBKg3nVNbIqq2SgLsuSFUegNPaY5rYjLmuyd/cjKmyc3+RjOq\n97FslL3FAATnvpXb9OKFt+v+Vdt9Hb+jPzuYPPpZv1oZwZ3cHPM1jaxyfEu8dN7vG/A286d3oJR8\nTkqWGkJee/Ir07YnJWOalIz56jjtHchrQlNUU5rjg8VVvKhUMZ3S7K8TQZIeWbNTH77mIV+VtAHA\ni829+7d9XXfVdcNPvZ7t/VlNaY77Pu/3ZXJqTUTVHAsrFg75Ou/XGhLgcax3oPSBaI1HZFZqVHhR\naTiVGkP+evJ3psq9Skl/PfnVhbs2+yyGAgDDdfMj69U7kNfipRt9Hb8zlR1aB+WjEdCTqozg+jtn\n9pQ7PlsSEUmlhokX/Zm8muMRJaIhhUPm+fhKR+nEZFStiYh2ebzuSJUR4KgmJqO+ptJVrhtHHtTq\nOwH+wZ9W6p6nt+jWRzf4Oh5AY+nfjz3LN/UOKBYupVRbfSSwPamsJiZjmuJzCnRv+ZxbmTnktb3f\nN5BXczwsM1NLIuL5ulGLSIDHsd50Xm1NEYVCppZ4xPMIcF/5w9xcnkbtdQ3xQK6gVLagSc3+R4Ar\nJ4KjD27TZp898X9ctkWnf+ev2uhjOiKAxlKpGrx6m/dKmoWiU3c6V1VAyts5r1h02pUpjX62JiKD\n52AvKiPAreUE2GvHZ3+moGQsIjNTcyys/oy3tWCVRmBrIqrmeMRzo3AgV1A2XxxM4v28Bt3prFri\nER3QGteOfu+NSUlaU95+6cmNvS9wTwCN7o/LtuiYC2733XG6uXdAx06v1MvxN3NoYjmB9dPx2p/N\nqyUeVmuiPHPI43m3L1MYnHXUHPd+3ahFJMDjWKUhJEltiajnNcCVnvvmWKTUkMl6+0DsrFoLNjEZ\n1U4fFU237sqoNR7RYZOTvopoSdKVf16lx9b1+D4xAWgclemza32sHe0tV0CeMVgAyvs51zmprWko\n+fNajbN3IKcJydLMH8n7FOj+TKkhJEktce8JaKV4SjIWVouPBLjSUTuhKaq2RNTXerjedL48HTDu\n67rjnBvcf9hPRVUAjeW2cvvy9ic2eT7WOactvRkdN32CJGmLxy1Li0VXSoCTQx2nXq8bfQN5tSQi\nai6f+71eN/oyuarrRtTXzJ9aM6oJsJm91cyWmdkKM5u7l9/HzeyG8u8fMLP28s9fbmaPlv89ZmZn\nDvcx60nvQGkqnCS1JiKeR3D7M3k1x8IKh0zNPhpCOwfXgkV9JeBSaQR4Wmtck5qjg9taeLWiPKJT\n2Z4EAPYmVygOrvnc0J32voVQudNvakusVDfBYwXlnqrkryUeVaHoNJAb/vZvmXxBA7mi2hKRqinQ\nXhPY0hRoSb5GcPszeUVCpngk5CuBrrwGbU3RweO9/j9UplBPbo6qL5PXQM57RdNKIr+hm6U3AJ5f\nV7lgq5+ZQ32ZvLKFoqZPalIyFvZc92BXJq+iU3nmT+m64bX6f3+moOZ4RK1xvyPAebWUrxst8fB+\nTQevFaOWAJtZWNJ3Jb1N0tGSzjGzo/e420ck7XTOzZL0DUlfLv/8n5LmOOeOl/RWST80s8gwH7Nu\n7BrIDxbA8tOT3pcZagi1xiM+eoRK92+Jl3ql+n00ZLbtymhqS1xtTVF1p3Oej8/kC4PrwfycmAA0\nji27Miq60tZvuUJpOrIXQ+tfY5rY5H396m4JcDmB3eVhLVWqPO2sOR4ZbIz4OW83x4YSYK8NoVS2\noGSstBbMTwJd6SitvAZFJ6U9JrClSthDOyB4HY2oVFGdPrFJm3oGfO3nDKBxVAq2+po5VD4/TWiK\nlpYbemyr96SGzpmVpS9eznmZfEHZQlGt8aoRYM8dnwW1lAfc/HR81qLRHAF+uaQVzrlVzrmspOsl\nnb7HfU6X9NPy97+W9CYzM+dcyjlXefUTkipXr+E8Zl1wzpV68mOlN3MyHvbciNiVyQ82wvyOBJSO\nLU2F89WQKSfxE5tKe1p6GQ2Rdt972Ou0EgC154d/XqmTvnyPr6r1larLsw9olSTt8NgTXz3rxU8B\np0onZWvC3xTmVG5o+nFzrFT80GvHZypTGGwEtcQjPkYS9hxB9nZ8dSeAn8Zc5TGqOxE8z14qv3c6\npzUrW/C+l7JUSuQ/+8tH9PCzOz0fC6B2DOQK2rIro+ZYWN2pnO9lH22JcgLscbZjZaZRZQRY8lb8\nsL+q4zQSDikRDXn+G3YNDC2d8ZMv1KLRTICnS6reEXpd+Wd7vU854e2RNEWSzOwVZvaEpMclfbL8\n++E8psrHf9zMlpjZkq1bt47AnzO2BnJFOSc1lXvykzHvUxL6M/nBRlhpDXBBxeLwe8KHRoCrpuN5\nbMjsGsipNRHRxHJlOq/ToCul5Wcf0LJbRWkA9emKO5Zp3c607lvpfRujyvmlY1qpiNUOj0l0pU5C\n6ZwX9TyCXJl221I9guvhMdLl52+KlYsfxiLeY6hKYH1dN6qmULfEw8oWisrkh59AVpLd6tfAbwLc\n6nMrqErnSaWYmZ8Cjrf/c5N+v3SjvnHnM56PBVA7KlWXjzq4bbfbw1U5v7Um/C0XHNqxxV/xw/6q\ntnrlq5/rxv4cX4vGbREs59wDzrljJL1M0jwzS3g8/krn3Bzn3Jxp06aNTpCjKFVuCCUrI8CxiNIe\ne7FLZc2HpkBL8lQIa2gEuKoh42NdQWtiaCqb1zV1m8oJ8HHTJyiVLfjqlRrIFfTNu55RF1OogXEt\nmy8qVyh10i3f3Of5+MEEuJz4eB0B7tvtnOc9eUwNJrBhX52GlZHKZLQ8gutxG6KhmUNDDRk/U+Eq\nM48q1w8vo8CV61RzPDzYmPOzjtjvNHJpaPuqjsFq3t7rTzy2rluStM7HlEgAY+vmf6zTmd/7m69a\nM5UOspnljlOvW68NjgA3RdTWFFWP13o9lXNmLKI2H7NmqjsdK1+9XHfyhaLSuaEq0H6KH9ai0UyA\n10uaUXX70PLP9nofM4tImiBpt25/59xTkvokHTvMx6wLlYZQU6UhEgsPfkiGq3pRu5+GTHVjsNVH\nY845V55WEdHESgLssSEy1DNXmtLoZxr0b/+xXt+8a7m+escyz8cCGDubqvYK95N4dO+R+HgeAa46\n5zXHvDcCUntUUJa8dRpWzs/J8lS0ppi3pS8DuaKKTvtVBCuVzSsZ2/O64SeJjww2qLxM487mS42x\nCeUiWqXj/U2B7phW2s/ZTwK8fmepevT67rTyBW9LdwCMrctve1r/WNOtPy3b4vnYytKXzvL5YqfX\nBHhgaAp0W5P3LUsHB7yqtjHycs6sDGwNztxJeDvvD02hHur4TGULKniYMVqLRjMBfkjSbDPrMLOY\npLMl3brHfW6V9IHy9++SdI9zzpWPiUiSmR0u6ShJXcN8zLqQrloLJpWmxHkeAd5tDXBlYbyPdQWx\n8GBDxtN0vlzpA9SaiA4W8/J6Yqjc/7DJpQatn969f6wp9eSv3OJ9RAnA2FlftWXNeh/b11TOD4dO\napLkZwuhoRFYvwWkpFJPvp9Ow3SuMvNnaAqzl/P+0LKV6rVc/qqJlh7H+whu9Si4nzXAlYZfi8+O\nV6mU8MYjIR0yoTRxzM8U6M3l+hO5gvM8IgRg7JSq/5c+r8s2ed8tZGgEuJQA+x8B9lcEq7rj1M85\ns3J+HGzve1w605etTOHe/bzvdevUWjNqCXB5ze5nJd0u6SlJNzrnnjCzi8zstPLdrpI0xcxWSPqC\npMq2RidJeszMHpV0s6RPO+e27esxR+tvCFL1B0IqJaHZQlHZ/PB7oqtHgIemog2/MdSfzSsRDSkS\nDg0m0H4+lK2JyGCDymsxkt6BvJqiYU1tiZVu+0iAK1X91uxIUQ0UGMc29pSS3pnTmj2vw5JKCXA0\nbJrWEpfkpxJmXslYuLT+Nu698n26Kvlr9pU87tHxGfWWAFePYEtDa3i9XDdKa4D3nALt7W+IhEyx\nSGjw7/DyNwy+Bj7XUUulEZxJyVjV0hvv143NvQOa0ly67mzro/4EMF5V14epbGfkRfceU6B39Hv7\nvO+qauuWdmzJexo9rZxfkzF/1f+r6/VU4vByzq48V/UIstcYalFkNB/cOXebpNv2+Nn5Vd8PSHr3\nXo67VtK1w33MejS0Brj0X9RU1ZCIRV6438I5t9ui9sqaMK8fqsEPVHkE2MuHqrc6AY75K83em84N\nrqsoPab/BDiVLWhHf1ZTyo1jAONLZarqzGktenRtt+fjK2tHI+GQmqJhzxWU+7OF3ab/Fl1pWnHl\n/Duc45+T/HmYwjy49CU6NPPHy6yXvszu143K11Q2r1gkNqzH6M9UvQblv8FLx2UqWxh8vSp/R8rD\na1B5vZpj/vdCrrwP/CTwUmka9vb+rF47e6r+snyb5309AYydSrFUafedQ4arUjPg0ElJhUOmXo9r\neHsHckrGwoqGQ4ODTf3ZvNrK05lfSHXHZ8hst58Nx55FsLzOXtpzCrWfa1ctGrdFsBpdes8R4MoI\nam54b+pMuZhM9VowyXsRrOf0CHnpVco8dwTYa0OkJ50bLC0vyfOJqVh02tg9oPYpSUlspQSMtot/\n/6QW3upvYk5lpK59arN2prKeZ2z0ls8XUumc5WcEuGVwCyHvnXbp8h66kpSIeB/93PO83xQNacDH\n6GmlIVRJRL1sP5fKDr0Giaj3hlD1azD4/D4ac8lYWPFIWLFwyPMa4FS2oJZEpLyfsffrTmVK5JEH\nlmpPbPc4IlSxeOlGPdS1w9exAIanslxh1gEtvtp4O1NZtcQjikVCvgoH9qbzg4nvYKejx9mWsUhI\n0XBI4XIH6nDb+tLu9XpKMXibOTRQPr9XrlmD530f28fVEhLgcWrPqXCVr8Ndz5UpN3iGRhIqDSFv\nDZHmwdEQ743B6j0xK3F4LeTVO5BTW1N0sFHrdQR410Be+aLT7HJDxs+0SgDD05PK6aq/rtY193X5\nWq/fmy5tmza1JaZcwXlviJTPF1Kp8r33xGl/C0ANHR8KmRLRkK8R4OoRXC8Nof6qYirS0Pl/uDEU\ni06pqlFwP9eNVK7q+Kj3EeRKo6vy3KVK2F5H8vPl5Le0lZSfmUfS0HZa23Z5v25s3ZXRZ375iN5/\n1YOejwUwfFt2lUaAjz2kTVt2DXjuOK3MGJFKnYee25mZXNXoa6Wt6+G6UVV5X/KewFbX65FKCayX\n606mvEQmHi2lhJXztpfzfi0iAR6nUlX7QUpDDaLhfigq+zbu+Yb2WlCl8qGOhUMKmbcPRHVp9lDI\nSpWsffSstSUiSkRDiobN9wbjfosbVKze1j+4TgTA3i3bPFSAZPlm78VIKg2Ryc2lZQpeO6yqz1l+\nRoD3Vjnf6xreZFVDxusa3lQ2LzMpUT5vJ6JhpbPDH73NPKcnv/Q4wz1vV6YqN++RQHs576ez+cHj\nIuGQYmFvoxl7XQftsSG2e+et90rYleU7h0xokpm/pTePrNkpqdT5wLUDeH6Ll27Ub//hb1OXLb0Z\nhUw68qA2DeSKngdaSrMdS+eb1oS3LYSk0jlraPTVW1tdqnTYDa1ITUbDnjoNM/mComFTJDzU3vdy\nzt7zutHEFGgEac/9ICs9O8PtVapMeRt8Q/uYylaqBlo6zszU5PFDWV0ESyoVNfHeECmN6JiZ2hJR\nz6NKlTWFnZXiBj6KmXSnsnrDFX/SJ6592POxQCOpFLGShtbee9GTzmliMuprL0Sp1OioXLz9NGT6\nM4XB0dMWXyPAQ8dL5RFcj1OYk9HSyGXp+PBgYa3h2LMn3+sU5tQeU+n8dJyWGoNVnQCxsLcp0HvU\nv/A6GiLt/v/YHA/7mkkgSROSpa2YvL4PJWlDVRXztTu8VzQHGkUmX9BnfvmIPn/Do55ne0hD7cRJ\nydIortd2YnUC2+qj4zSdLQyeKwfb6h6Xzux5zvQ2hbmoeGT3jtdcwSk3zO3b9jUCzBRoBGLPfYAr\nX1PDbAw9ZwTYR49O9Rrg0mNEPB0/uC4hNlRa3fMU6Ko1fW1N0cGe+eEa3A9yarPM/E2Bfqir1JP/\nwOodnqqpAo1mt22Mdnpv9HensqX9X30mwKns0FQyP2u5ShWQ/ddNSGXzSkaHzpmJaMjb9OFsYXDW\njzQ0+jncKX2VpS/xyB5T2YZ53k3vay2YpzXEz/0b/EyBrl5H7HUkorSOuTITIOpp9wOpaluTRGn5\njZ8R4Or3v5/OIKBRPLt96PPxxIZez8f3PqdWjLfPa1/VjBE/HV7p3FDHa9LHjifVxRelSsepl47P\nwuA5X/K+dGXP64af2g+1iAR4nEpnCwrZ0BvS6zZClR6dSkOm8jheeuKrTwqS1BTzVpBlIL97Et8c\n9zYF2jmn3oG82pqG1lakPDZoKz2Bk5tjvkaQJWn5lqGpnDRkgH3b0J3WxGRUrfGItvmonFuZAt3q\nY99xaffkqyUe9dyQKU2d3b0n30vylN7LCLC3AlL53adQx8IquqHz+QupdHwm9qj9MNwYBq8b0d2v\nG56LYEX3WM/max30UBLudfu86krWLR6vO9JQx0tbU8TXTAJJ2tBT+ixIu2/TAmB3q7b2DX6/Zof3\nNlalnVip/+B5BLhqtmOpw8z7dSe5x3XD2xrg/HNGgL1NgS7ulgB7LWK1r+sGa4ARiNJIRmRwKtxg\nMZFhNsYqb9zKCHBlCrOXhshAVa+WJCWj3qbzVXqVYuV1CcmYtynQ6VxBhaJTS7kxnIxFPG/MvbM8\n4juxKarWhL+pbJt6hkrsr9lOAgzsy47+rKa2xDWpOTY4+8KLnnReE5piVVXnvU5lG0ogW3xMfS01\nhErPnfCx/rV/L2uAvfTk720NsZcYBvbRkz/cKtCVc3Zl7XClkJe31+C5SbzXddDS7lOgvTx/Nl9U\ntlCs6sj4/9l702hJrqtM9DuZEZHTHWqS0FCSJQ9gy0MbUPtB9zML7KaxlycaDIblZ3BD42bx3EDT\nNM9uwH6Aux/DasANboyNMViYhTG0h8aiBTQYYzBGki1sGclYs6ok1XDrjjlH5nk/TpyIyIgz7B1R\nt1S3KvdaterevHEiTmZGnLP3/r797WqlN4BCgKvuG2d2x/jyK5fii0tbms/yCHC+dIBqu6MpVlsZ\nAswNgPNgT5XnXVGgs1I/gKsCXUSA+SJW7ULSEaAnLov7RndJgV7ak2nDabwQfKYZmZiXyV+oC2A+\nVKN4ngbQANBmj1c9ixsNFcQrCnR1MZQeMysGZG1V1jtJLRfTEQJUAKydqTMVaoiXtrTLxTIRq6iS\n0787mmLpS/C4AAAgAElEQVStHaT0VQ7yJqXEcJpvwcNDX6WU6Oeos3rNHTPRz06YZ800WfThYTHp\nyOzDm5a+VNR+KI7X5+C2cuoUgnguAqx7KVe9PpA5olUojTvDGFGzgVbSFmWXmYgB1LNwpBfhUDdc\nBsBLW5rDNvoTtIIGrlxtVQqAd4YKAa5KgR7kSl9WW0GtxKsOHrmlM71S4pQHVkV5CnTNdT9jDl3a\nJX/LAPgitSISwEUj0r5e4eJDQVUUlVJiEhcL63ktPcbTRVpGN2qS2zgB5XYYXAQZUCJYq+0AQbOB\ntXZYSWDhiZ0RnnPtOoAllW1pl7bFszl+/EOfx1996Uyl8XUC4NlcYhzP0Y2CVDiPk7AaTeeQMkMO\nO2ETk3iO2ZxYPxvPMZfZWlulDko5UsXgkdd7vYiecuYwjucQAgibKunIfQ8pElDcN5gBbPE9cIXA\nislfXj2d7j6gS2/4zKHd0RRrHcXAWm3zqfSA2nvWOyGOdCOcq6gC/djWEHc9ulVp7NKWdlBsY2+C\no70IR1daONevKILVDitToIvih6PpnCwgBSyuefo8rDVrPEsTdgCfNTOO52jlEOC23jcYJZON3L5R\npfTlINoyAL5IrT9eFBJp6xpeKpXNgABzqGzZ+HwAGzAfytkCLWOFqQJt6oXMVwONsZpri1LFkTm9\nM8ZTjnax2gqWAfDSLmn79IPn8P5PP4J//4G7Ko3PB8CbzAA4o7420QoaCBqChQD3c+Pz/5ODx+li\n/ateczltiIrBW5X61wUEmV3LpZKOunQmbYPERpCrMX/mc5mg2AUhLyaCW6SBc/vXA1kipNcKWHRE\nIKkpTMQXq1Kgt4dTrHerPQvavv937sQ3v+OvK2lXLG1pB8U2BxMc7kU43A0rlc7sjmKsdZT2hBA8\nBFiXTKxE1SjMOnGr1/2oqfYubv/4Yh9glgjWtCCCxU58ztAKsu4DumRyWQO8tCfFhtNFJCBIHip6\nAFt2ZDgU6KIYCsBHAooIcJv5QA0KDm2vgoq0aktSXd4e0K1ZIhxbbeFsDQo0tzn70pZ2oe2ex5UC\n59m9CeZE5DRv2wnqtVYBNcuoq2oj5vbxLTJGdBacq5yvg0bdw5a65qUIdl4FukIm31T6Qg/iF5OO\nXOaQsXQmpLcx0iU63RpJgP5kUXyxy0aA1bH5XsaTGZ0JAAB7o2muLQqfOTSazjCO51jvhDjUDbE5\n4Aewg0mMz53YBoAlCry0i95uf+gcTu+O/AcabKM/wZFeVEk7Ip7NsTeOsdoO0GgIrES8UrdiyQS/\nfjbZd8KsZShnzdKlO52SCjSvXLHoqwPMxGm4GA52mEH4QbRlAHyRWjELDugAkoZGjKaWAJb6QEzL\nAXSbmckfxWVnjDp/IOfQhllNHveB3MupulapBZvEcwynM6y1VX1J1Uz8j3zgLnzLr/0Nywlb2tIu\ntOUVOM/2ecme+Vxid6wy8SvtAHuTmBVE9wuMj5UWT31XOww6eNK1WCMigluXNZM6QlGONcNcM4uZ\nfG4N8KiQdAybDYRNwa4FK5XOUPsIp99BdQqzrYaYmkAcFBBg/X1wkq+j6Tz9DLoRr6cmkCFQWnuC\nW7oDAA+e7ac/P5T7eWlLu9js4Y0+vu2dn8Ib3//ZSuPP9cc42otwpMtnS+gkqWZsdFtNFuNjr1Ay\n0WUmTotMRSABa4jP/DhWpTvFNXfMKd8pIsAV2E/tYDHe4JRMHlRbBsAXqY0L9bdA4oxRRbBsAWwt\nCnQ9BJibiTeJYE1nktWLd0HcoB2y21mkaqCdsFIfYkA5Xv/jsyfx2Ue2UoRtaUu7GC0fAHP7+O6O\nYkiJpI1RACn5QiBAlvDiitYVGSNp7/Qps3d6wZHgoqcLSceI2cfX2s6C/h5K+0bAWPen9cQTdbC/\nmHgN2L2QF2uI1f1ATZ5qhzgVM6tQy50v3+EmIYCsBlH3tK7CPDq9kyWgTizb7y3tIrZPP3AOAPB3\nD52rxBza7E9xpNfC4a4CGThAgQY1tG5Ej9ktpJgw08899XnPmEfVWCtp6U1uzeWi0JO47Gvn5+az\nUTwrIcBc9f+DaMsA+CK10bR8Q7YCvjNWFDNhU6iLzhwTAV505niZ+MG0WAOsFhjOHPL9IFfbASaz\nOeuhzjsya+2gkohWXuL/H0/tOo5c2tKeXDu9M8bV620AwKkdHp2t6PQDvD6+wwJ1lVvzP0gdkYKS\nJQM9BeokDc0BNK+P77yAQDfT1+njC44MI4gfWRKndO2Jxe8AyOrZyAjuJC7UEPMEWYqJ0xbTGQQ0\nkl7tPgIKz0KLn3gFkNJJhUClntpLW9qFsvtzfXyfYO4b04TCfKgb4lA3wlyC5WcVE17dFo9xUhrP\n7IGrE6xF0VoyhTr1tU3MHzqKXEy8AozSl2l53+B2jTmItgyAL1IzOjJhI80W+WxUM5OfUqiDMhWO\nmuEbT80PJR1NiBfG6UWBLS+fU/cDeE65prKpfpAhdoZ8R+ahjYy+xkXVlra0C2lbgwmeekUPANh1\ni1nv1EzFmSdiVU54cXvo5sdXbgVRuWzEXD8LcGpwFxOfVWp482uungNbPLFi4tS278wlMCFSiAeT\nWYlCrV6n3QuZGNoiAsxJfOa/B64zCigFaCBhQySJ1zGRvaXtVIIAP+uqtVraE0tb2n7b49tZ0Pvo\nOR5boZ8LQHXilFOqVkx8cruF2PYNahBdvL4+B7tjy8KambBeiBTkUU0RrKJgrT7Hsg/w0p4UMzky\nHBGpcTxD2BRoJj14AR6iYkOA9dwoVkaAeZn0bGEqqPNx2orkGozXyeQrCnSQOvkc0xtC1GzgxDIA\nXtpFbJuDKW48pgJgbhujNJOe6+PLEyNZpECrLDqv3AHIrRfcVhC1EeDyeI4zNZtLTGdyYbz+mY4A\nz4yJU44YCqDWKm2sJIABBee+h+F0ln5uQJ4CzaUkVkuEqGtlNXH6fqzUiqliT2tAMTAOd0Ncc6i9\nRICXdlHbEzsjrCXBK/dezSOwqxVAitF00U/sMTUH9LV0qRwfqFkUwQK4vnq5dCZlS1JLHi3Moara\nEfocSwR4aU+KFTM6QPJQVXwg9Hh+LViNrFIBAc7ofNWobL2I91ADKrvYKyDInPG65ne9E2CtHWIS\n8yjUgFI4DBoCT79yZZnJX9pFa6PpDMPpDFevd9AKGthiqnHmA9BKCPC4TIHmPGvD2giwec3jl42U\nk36U4G9iEOFKg0cG86ek5smkcQcNgaC5SOOus2+0mAiseg8mRVOumJmaQ5XEZ14VlUuJBBYF2XQA\n3Ge2YtoaTnG4F+HYSr3uA0tb2n7bqZ0Rnnt8HQBwhqkEna37GQJcBcHV60SX2fe7uG9wS+2K4wFd\nP0tHb/UYbXoPoK77ReZQsyEQBfQOBibtiGUbpJomhHiJEOKLQoj7hBBvMvy9JYT4QPL3Twshbkhe\n/0YhxJ1CiM8n/78oN+bjyTnvSv5duZ/v4ckyqwgW46FqGxwhshOSqoFWp6IVadxcR2Y4mUGIsiND\ndSTmc6nodBXl7YEiAqxUBrlK0ltJj7ujKxHOVehxt7SlUe307gg/+sG/rySak69bPNKL2BTofMJq\npaWeFU4mX9f855E7LttDXz9/HrIYiWXN45aNGANYQtLPpMDMp0AbRLCYiU8T84iLIOcDWG4QX0Sx\nq9TD5a/broAAj6ezFAGukjjVDnwnama0zjGzpGA4xWo7xHonZPU1zdtoOsPdJ7eXLfiWtq92emeM\nr/iyNTQbAmeYyZoMgW2mvloV8cNODijhqEAX1302BXpaDoBbFcpGqiLAmjlkUnGm93+fl+MFJpJ+\nEG3fAmAhRBPAOwC8FMBNAL5TCHFT4bDvBbAppXw6gF8C8HPJ62cBvEJK+VwA3w3glsK410opn5/8\nO71f7+HJsvlcKR0Xb8g2UwTLlNGhtnNwIsBkWkWxDRKP1jGYzNANs+bcur0J1RHSDk/WD5JPoc7X\nAGuKD7cV0rn+BIe7IQ5XkPhf2tI49nt/9yj+4M4TuOVTD7PH6rrFw90Ih7pRBQQ4FwCntVz0Z0Wr\ncfZyJQsc1K6oGcCvv7UhwDwBKFPZB+UcpjZMQUOgIRgUaIuYyZiR+DRRqCezOUn7wfUZUJk/xZ6U\nKZ2PlQRopPtGlRrgvCoqN5ECLKJCqxUp0LujOK2nH8f8GmIA+NU/vw8v/5VP4lMPbLDHLm1pFBvH\nijl0pKcSp2d3zwMFmvGsmBBcDgJcFD+srlWTF+6rLzyY/5vLTMwjPQcO+8nUPaDKmnOQbD8R4BcA\nuE9K+YCUcgLg9wC8qnDMqwD8dvLzHwB4sRBCSCk/K6V8LHn9CwA6QojWPs71ojItFmLK5HMeKhOF\nWv/NZyZnsK4iKTeAHk4LaqDMhakohsKtCQTU4hw2BdphM6WycXsRb/anONyNcKQXYWMZAC9tH+2u\nR7cAAPc+wVcb30wC3kPdEOudgJ3oyRyRXA1wFTETnYlnqlAOJjNF/Wpq6iqvdjNN+uXRS079rAsB\npqy5hqSjEIJdT1ZCcJltkIr7hn4/FBErUz2bPh8lCSClTFp6lBOnZAS52H6PuW8UEZWMSs9jI0TN\nBsJmo5IiOqBE5bT4IsBnHgHAn91zCgDwt/cvA+Cl2U1KiTsfPsfqda1N35drHcVW4DId+nntiCrd\nAwoIbC9Rgaa3nlvUu8n8VGYf4ALYM6Jq5aQU6GqsGdO+Aai9i6zXY4gXOOMPqu1nAHwtgEdzv59I\nXjMeI6WMAWwDOFo45lsBfEZKmedVvDehP/+k0GneS8hcNzRHzbNVcIR0hohyU5vogNw2RmUEmOeI\nFPtBaoeE+hkMCjWFVTP5RREtbi3XucEER3oRDncj7I7iSpvMH33uMbzklz/Bbk2ztMvLtMr4I0wl\nTmBRuXalFWCPeZ/3c314qySbhknZRqORIXdUxgqg1rVOjjGi109OL8T8OD2HOq3nqqy55fZ39R0Z\nau90475R0xnjJE6zANpQD0dGkGfGGmIukt8OqyVSAOU8p5TMCsI+gAosVnOK6lUC4DO7ym16cGPZ\nR3hpdvvo3z+Gb/21T+E9n3yQPXa7wJLjdsrYyzF/eq3qNcBZ3+4As7lksWaAbM2KggaChmC3XesU\nfFW+CJYBASaVzpSTjkCyb7DiBcO+wxChPIh2UYtgCSGeDUWL/re5l1+bUKNfmPx7nWXsG4QQdwgh\n7jhz5sz+T/Y8mqn+Vv/OopGVMvl0Z8zUEzNzRGiZ/OIcuPVspQCYGYDb2mFwUKX+OM6JcCXiCAwk\nAFA1wIe6EQ73wuR3fj3XO/7iftz7xC7+5AtPsMcu7fIx3YPx5OaQXfenHZEsAOYjwLpmP2w2EDbp\nTgSgBesyxgdXfKgY/DUagkcDs5R91OkD3Aro78FEgQbOz7pfR0U6C+L9czAlEVgouOEzqI0AM5lH\nxfugiohWP9fKqQoFG1DlA2udEGspAsxH1jTj6GQFTYClXT72qYQh8KkKTIGdnHbEeidkd8rIt0HS\n6z8n2TOczNDIacVwxVLH8RwNocpNtHHqX8fTRa0aIGNrUvbgjAJdDewxUaj1+cj7xtSsHTGO6Uj6\nQbT9DIBPArgu9/vx5DXjMUKIAMA6gI3k9+MAPgTgu6SU9+sBUsqTyf+7AH4XimpdMinlu6SUN0sp\nb77iiivOyxu6UGZDgFVWqboIVpqJZ9UVVBV0KdMJuc25h5PZQlaNqyaqkdpig3OOIzOYZnPoVkCA\npZTYHExxuBummXxOdlObFjX6x1N7niOXdrnacDLD9lDda5PZnCUkAuRVnJUYCZfpoPq3BikC2w55\nIhrF553bNs0U/HHqiLMAtiyCRXECnMEbBwE2BLAc9LKM4DZ5ZSuG8fpv3vEmGjkj8epKInCSAAvM\noyhhAlQUgKwigpW/l7kBOICk28Acq60MAeYiaye3FBskChoLfVqXtrSiffGUKpl54Czfv9hJKdAB\n1ioItul6314rQLMh0IuaPPHEhKWn950uE0XWwoF5Mimv9dt8QXMA4PU+HzmYQ/USpwzmkAUBnksg\nJmg/HFTbzwD4dgDPEELcKISIAHwHgI8WjvkolMgVALwawJ9LKaUQ4hCAjwF4k5Tyr/XBQohACHEs\n+TkE8HIAd+/je3hSzEaFUyrQ1YvaWY6IVqarLehSzsSTKcyT2IgAUx/qPCVT/V+Fypah0FX6EA8m\nM8zmEmudsJIyLqAy/zoj+uDZPmvs0i4f0/T4Z1+j2lFsMPsxFttRcO/TQSGA5bYx6heed65qe7Hk\nAtBK0vQ1UwggbGaOTDtsQhIdmbEhE89CgG2lL8RMvmbdtE0IcA3tiCpK1pUFXYxtlHjrfvE9RM0G\nGoLXhil/Xc1m4Owbg0lc6itKFfECMrR3rZOvAeYFFvr5f+ZVqzjXn1zSSM7S6tmpJEHy2NaIJHaX\nt0Wh0DANiKm2N4kRNRuIkmd2pR3wRLCmi/tOj6v9YBCc7XJavzl8bZKvbKgBbnOSjtbEKW3/Neku\n6PEAn7lykGzfAuCkpveNAG4DcA+A35dSfkEI8dNCiFcmh70HwFEhxH0AfgSAbpX0RgBPB/CWQruj\nFoDbhBCfA3AXFIL87v16D0+WpbLoBhXneC4RE50xm5gJiQIdK0GZfD9IliNkeqhDXiZ+MJmlys2A\ncmQEw5HRNcA68OVeX80hRjeZgxY5qNIOo9eqJgwEYKHud1kDvDSbaRGrp1+5AgA41+e1oxhM4pRK\nthIFmMRzcu2oHp8PYDnBpxo/KylpArw+vlFxzQsbPOSwgARwUOi6NcAjA+tGzYGGAE9nElKWx3PE\nTFylM9TEZ5FOWAkBNjiDvORvWUiMywTI778KEeKJYOn7V6FDILckATJUrU4N8PZQrQc3HuthHM9Z\n+97SLh+bzyVO747Ri5qYzWW6j1BtZ5RvFRlgZzhlJVv64zgVvwJUALvH6uMbp88awPfzVMlEwdeO\nAlb7PJvgLKfsI7/eVEGAjTXAFXUX8nO4lIWwAv8h1U1KeSuAWwuvvSX38wjAtxnGvQ3A2yyn/erz\nOceL0ewIsC6Mn2Ol6c5dmNRAM0eGlom31oJVRID1A85po5TP7AkhlKIpYzyQOdJCCLYjM5zMcKgb\nAQC6LX4AnEn8N1NHhousafraM69aXQbAS7OadpqfekUPAHC2AgKsKcwrObp+FESk8YOc0w8oJ4LV\nezWeo5MXAqlQy1UKHhllI+PpzMi60eemXB9AqkINVKQPV0SATfW3erxOnAa+fWM6x9FeMYCmU5A1\nGmJKIpDeg+EzCJsCgtMKytALmVPLXUSAAZVE5dzLw8kMx1bUc6P3Hc6+odHe1XZWOsMtadBaEzcc\nVevBuf4kTQYvbWnaNvoTxHOJr752HZ9+8BzO7I1xdIXedGW7gADHc4nhdEa+1/rjWSpUCiS1p0z1\n/2LiFWAwPuLyut/hsC2nZfowhy05mqoa5jzziKObkNYAG+bA23eqM0YPql3UIliXq7k4/QA1gHWJ\nmdCcOVMNMnW8Sdq90RCIgga5D7CJzqfk5XnqeouODB+V0otr1Gyg2RBsCjSgsporqRooj8qmA+Bn\nX7OOzcG0kor00i5901S06490AaBCH984TfJUUa4dTmbpOEA5EZy6xyKVTDMuqMjZaDor03+ZCLCV\nNUNK+s0QFFgzrDXbkDQE6Or/9gBa/U5rY1R2Bnkq0PbxVUtndOKTg2Kb9C/oiJABAWbuG/1JnJbM\nADxKJZDVRa60gpwIFzMATtYDnRDb7PPFF5d26ZtOqj/3WlU6c3qHxxzaGepWkY2Urs+pV98dlcUP\nWWVq03paMbbe6bwa4HLCDaCpOI+m5RpkIQQdwXWs+1XLVgAein1QbRkAX4RmVXVj9vEtOyL0G9pU\nT1etML+YWWuSHVpjT8uQgeiY2powFjYgE1gA1KLUjZoscaC9PAVaI8BMKpsOZL7iKkVtPbvH26CW\ndnDs929/FC99+19hu4JSuKaiXXuoA4BPmewnIlYAcskaTrKnQIFmOv3FpB23f6uthQ+vdtSWBa/G\nmtFocFX6r5oDMZNvEPFSv/OYO8XSGx6F2TCehSCXE6fqHHRExvQ9dhj16EZRGsZ9BCTaEYUWgJxn\nQTvOnaiJqKnasnCCAkAhwFGzgWuS9YBLbQWAeDbH+z/98JJ5dAmbZgro0pkNZunM7miK1XYIIUSK\n5PYZyZpxPKu1bxSZR1nSsTpjpBU0GUCLiQKd0LAJz+xoWk7YqXPQ1iwbYEZOnDoo1Pm/X4rmDYCF\nEMeFED8qhPiIEOJ2IcQnhBD/XQjxMiHEMoDeB7PdkFxaRdER4dL5atUQGxBggEtFM9dW8PurLQrr\nsGuACwILrHYYphpgJpVtZ6hqM687rJG9ZSb/UrWfv+1e3PP4Dv7yS/zWbZqKdnXi8HLFSAbjDAFe\nqdiPcYECHdLrqAClfNsqPKv6vBQzsV44dDoj64XZw7YYvGaZ/OpJwzYRxTYxXtTvnHXbkTilUqCL\n6GtNBFj/XqenZZvBRsjEzBZRJY4jmG+fByT7DuNZSHVAQqUuy0WgAVUDvN4NcaiTtN9jqvMCwK13\nP4Ef/9Dd+IXbvsgeu7SDYTpxel3CHOImToe5dT8VGmWABMWEFadeX19/USy1nmaAOgdzvbHsG5Q5\nmMAmPQfamql9bUPpDIdCXcPfP6jmDGCFEO8F8JsAJlD9eL8TwA8A+DMALwHwSSHE1+33JC83s1IS\nODW8LgSYiCYUM0rNhkDYFLWdOXpmzizNzmkFBSzW5HHEDYByfUk3arKym/3kWiutJlR/VMFGgLeH\nST/IjqYXVQuAuf35lnZhLZ7N076d9yVtKTimqWi9qKn6+LIR4Dh1YHoVkjWDIgWaqQJt6xvOQYCr\nCoGk17fRf4noZXG9A3QQXrMGmNUPsgaK7ewDTJtDcXyQlI5QUXQ153Lyl97T0py8pVDAgQwBXlRl\npSPQgLpnu61FQTdePfzid8kNoAGVKD3UCdNnskr7vdsfPAcAuPeJHfbYpV04u+/0Ht7zyQcxq9Cy\nRvsTxw+rxCmXfaTW/aR0Jk1achDgealMjVVvPzWLJ3IC4PK+wUCADSJaKQpNZc0YAmCy9oOthpco\nfuhKOqrzX7oUaF+V+n+VUpraDN0N4H8k7Y2uP//TurzNJMIB0MVE4tkc8VzWdITMtIwWUVTGhgBT\nqWDxbI6Z4T2wHKF4rlpg5BucM5CA2Vy1FVlo7dJi1oLlEGAhhApMuAjwaIr1jhKYUL/zHZk7Hz6H\n1/z63+Ktr3w2Xvc1T2GPX9r+29m9CbR45kMbA/b4ndEUawkVbaUVsNumDCYzHO0p4R7t0HDLBRae\nlbDJdIQKFGhuH+DajBEHBZqIXpoCYH4tlsmRqYEAsxKfjvZ55M/AgGYQEVybACS3F3J536EjOiZE\npB02yTX1k3iO6UyWKdAVEWBAIWucNkpAEgB3wwVBO67p/vMnNofssUu7cPaTH74bn3pgAzce6+JF\nz/wy1lidGD+60kInbLIT5YNcAJq1iuSUvsxL6z5v34lLzxrACYBnKUsiOwcHAZ7hcG9RKJKLAJsT\npzwE2CyeOIeUcqG+2Da+XHZymSPAluA3//eJlPK+8zulpZlEOAA6Bdoqax7Qxqtjys6gOkd9Oh6l\ntYrtPbB6IZvEDUJ6Zk8H6gsIcBiwnPp8AAzwe9wBCQLcVi0GgGoI8Mc+9wTiucQff/5x9tilXRg7\nszs2/ky1nYQpAKj2Kewa4HEm3MMNPtWxi44It96+mEnnqAer48wtfMgIsKEWi+MEmJAAdQ56LVax\nDzFAV7L2iWD5HLqsH2QdCrTZmWsR1926SthqDub3wGECAIsOIec+0vd8HRGsIg2b270AUPX7q+0w\nrevnrgdAJsC4NZiyE2pLu3B2T4LQf/aRLfZYXWLVi5pY6wRpKQ3V8uu+9pW4NcDtYrKIWwO8QIFO\n6m/J6v9mtmQ9CjUjADaUzuhzkNbMmjW8/n3j0kWASTW8QogHhRAPFP/t9+QuV7MFj7rHpS+AdBXF\nq79Xo1ADdDrfyBLE8+vhyjXELHEDo4gW7YEeJMFrnl7DRYBTESydIWXWRQI6sAlyCDDfEXnw7B4A\n4OTWMpN/sdqZPeVsXrPexpkKQmc7oxhrCdqz2uYzDQaTWUph4/bglVJiMK0nZlJcczjII2AR7mM7\nMvXow0YxE2LwZupDDHAQYLuAVP7vruvnj9fG0o4wOJMAvYbXhoJT0RAppVXMjE6hLqPQrH1jqp67\n0rPAQYALCWCuMi6gSxqaaDa0eCM/AD65NUzbMHHbqi3twthgEqe6II+cq8gc6ijm0HonZCk4q+tn\n636q28CoAS4GkNzSmWK7TG7f8JGJ+cPunW4Dq4g1wDbmEMPXjmwBrOd9uPrPU8YfZKOKWN0M4J8m\n/14I4L8B+J39mtTlblZOP9EZsxW1p4qkRDTBhgBT6xoAM5WNI6JVh9I4MtaC0Rc27XAsoFrMfo6D\niXKKmwkNu80MCgCFAK93sn6Q3A0KAB5NKGwnN4eV6oSWtv+mUd+brlmrhABrNU5A9Q/lIjZKuEfd\nY7oHL/VZm8zmkHJxE+2ETUxnktS2az6XmMwWn9cgUb/ltD0zC0hx1ECrORHZ9c0IcNUWQoBy6KYz\n6X1u7bVcNBRbz7GctKxHoQY0mlFn36AlEeK5xFzaWoIwEeC8CBZLe6LMXmKrQBcR4AoB8GCcqbr3\nKpTeDCcz7I5iPOvqNQDAOaY68NIujD2cK5c5WYGqvjuK0+T6WjtkJ9iHOQRW328cllwxYdVl7Bvx\nTJUb5MUX2e02DX6ibrsmpd9XMpbecIT/rCJYdAQ4bIrUx8yPV3/3JD4N6xWwFMFKTUq5kft3Ukr5\nywBets9zu2xtHM+MNzSZ0mChROiFgRSAGvpBAirLxFGWMzlT1FoywFwHzZKnN42nZvJ1D99Ck3ZO\ndnJvHKeKugC/Nyqgkb0QQbOBXsSv0ZFS4sTmAL2oiXgucXp32dLiYjTdf/GZV61hezgllQrkbTDO\nMl2fBs8AACAASURBVPErTAq0lHJBzIRLgc6c/rKKM8Xx1wJFRuSOsF5o3QMTAkxvg2RImKW9EKkq\n0BbdBCrrxkgf5iY+qyVObfW3YVNACBoVzkqBJu4bpuAzHV83gGYwCYpUdJ72RPl74IpYFZ3aKiJY\n/Vxf79UKAbCmwj4t6SN8btlH+KI03Rbx+iNdPFaB4aUZZgCw3gnZFOg8AtxJKdD1EGCAu2+UA9A6\nKs4c4T/Tut9hJJDt2hH00hcbWKX/7ru+vp5p/KUsgkWlQH9V7t/NQojvh19Aa2kVzY4kEDP5lqJ4\n/VrVnpaAdgTqIsDVBWHYKtIVHSkAGE7LFGjO9QGFqvUWasECNgK8kyDAALDWCdk1wLvjGKPpHDdd\nozL5G0sq20Vpm4MpelETV6y2AIAvYjXNWq+stgKWgvMkCSA1Ahwm6CtdgdksHASA1PfbWofEXW8M\nCPBsTkMTnCJYtVSgqfTf8+XIWJy5io5Q1sqphqIp9Xs0BJ8AoyemRXyRSiMHzFR01r5juJe5KtDF\nNoa9KGDVVaYJrRoIsA6EbjymA+AlAnwx2rmkc8AzrlzBuQq9nrV4IpBolLBLZzLmUCtQbLc6KtDn\nY9/giM4ZS+UCZuKz6Kcy9XbMayY1aWguvaH2X7e2QboMRLCoQex/zf0cA3gIwLef99ksDYBdFS6l\nMPs4/RYVaYCOiLicMWpdg75ecTy1lgww0zLoFOjywlAFAc7XclF7q2nrj+PUCQE0hZonEDGO5yn9\nWan78jaorb7O5K/g9oc20w1zaReX7Y0VhTkVOxvFOLrSIo9XVLRExIqJGOmarao1vDanH6ApgtrQ\nR2r7GQr9N2y6872uNkg0R8a2ZjZJZQuuNkoAvChyXRVod+KUtm/Y9i7qvqHRkFIdNJm5ZBd0oTMB\nyvuGpmD7FFUBMwOrkyQ+KeP1OfLfI1tQLlZdFDQStdIK2DXAOgC+4agKgDeW+8ZFaXo/f+oVPfzv\ne08vUJIptjOMccMx1QO4y2wTCeg2ROp6Quh6c9o5TN0+OP3fszWvoBUT0Vg3Usok4WVDgGcAQsPI\n/BzKa16jIRA1aTTskUF8Echo2JTxrsQpXTS3evL3oBopAJZSfsN+T2Rpmdmz6DRVNpuKNMBwRAxO\ngJpDk4RA2uoSqOICtgCaKsKl52ByhEZTvzQ8gHQRz9eXcCjY+hx5CrUSeKBn1LLAJGszwG2HsZlk\nhZ92xQoALAPgfbSP3HUSUgLf/JXXssfujmKstnNiZ2w1zkUxEo7Dre/p/L3eYbYQAopOPy1wU+Nt\nwn3UhJ1bAGo0nS2UIhjPYekfmz+/bw61gj+HgJT+u3u85TMga0eYg0f9Glk80TKekrhzsZ+oCLK6\nnlkMjfI8mES02mEDcwlMZxJR4B+vrplHtRqQ0r63++bAFcFKy3dyJRGPMgWSdAB81XobUdCopD0B\nABt7Y/RaAel9L41vm/0JhABu0Ej9YIJrow55/F6OpdaLmqn4J8Wms3LLLw5d39TtgyPAaEvatYlA\nyXQmS9oVejzgDx4Vu6jcrlPPiVLGNDK0bQPoHU98idOqiU+uCOVBNDKNWQjxMgDPBtDWr0kpf3o/\nJnW5myuLDtBrgI3OFKM5tq2f4xliAGsOwGkIqovSOEmyhsXg2nSOYn83vdApwR33hqwXhqLEvhak\n8V0fUIvbYg0wDwHWwW4a2IS8DQoAthJH5qlXLDP5+2njeIYf+r27AAD/8tlfliYtqLY3jrHSDtJW\nRpxa76IKczcKMEuFpfyO59jAGuGgTqbgidc/1r4JUwIva+90IvqpkICyI5LWv9ZQQOaUjdgEpAAG\nAlxRyMuWRAA4Ql72lh4UYbfaSQTHZzCXSiSrSK82ncPaQjCeldRW7XMoK9OqVluE57GEACsEeT6X\nC33tbabRXt2KaaXFo1ADWQJuvRMmNcT8GuDd0RQv/sW/xFdedwjv/dcvYI9fmt/ODSY41AlxLGEL\nbfYnuPYQPQAe5veNJMFOvc90oiXvI3Ho+sZnhVEDbEuctsMGqQ2Sdd8hK+ebmUv6tTrlhlS24zie\nG9ckahsjW+JTCLpm0EE1ag3wOwG8BsC/AyAAfBuAp+zjvC5rs93QmgLtyyrZ0FP9ms+RMSmypuND\negBrbYfBqukrI8Dq7zQU2+YMVu2ryW6yXqCncPtB6t6P2pHpMdswAcBWggA/5WgXzYZY1nLtkz2S\nU+P8h8d22ON3RqpvZ4YA8+qopMzuT/0/NxOfv1c5dYsmKho1Aw3YN+EWse2ZTTOAypqxqQdz61/r\nlI24gj+AjgBHzfJnSBvvQoD9zBedRLC9BxIaYkPBGYlbwNUKikrjLjvUADOZk2/pxWhBqK6zmEDu\nMtgUQB4BzpdE8BzZ7VwAXKV/PQB8/uQ2tgZT/MUXzyy7DzhsY2/MRui1bfanONyLcKQXAeAzvPI1\nvL2oCSnp91na87piq0gTW0KjyXVrgGmlejYRLRoC7Fozo6Y/aSildCLA1PXKmLRkJD6DhkBgKBGi\nliAdVCMFwAD+mZTyuwBsSil/CsDXAvjy/ZvW5W02mhQ1I2OilWijICpaWc/2UFV1IvLjffLyGRpR\nrglU568myMIJoEcGRCS7Pp0aWmyHMZrOMSc6A8VWTJ0oYCHIANIegYe7EVZa1RyZ2Vzi395yB37n\nbx9mj71cLN+O4kSldhRTRYFOa4DpiEuxXp1TRwWYM+GqdQtV+EeXXZQRYBZyZ6DvUrPoas7VEl62\nhJt+rbYCMrmWqw6VzV4/q+fnGw+UvwN9Dp8zZ0siABwU3MwcagdNTAj7hlXQJUVgafdi6T5iJD5N\n7aS4LUWKdYGpojrxeR6kidNk3wibaTKVajoAXm2HlbQnAODex3fTn6sGeJeDve49f4eX/8on2cr/\ngAp4D3ejlO22xSidmc8lRtN5SjvWiXZqDW96n+UQ4G5Irzc3sRU7rBpgi3YEGahxJ07prJtqZRu6\nfaCtDVI8l4g9Ao4uFWn1d1/JpHk8QC89OahGDYC1NzcQQlwDYArg6v2Z0tJsFGiA5hC6HkpKVsnm\nRGTjayDAyYM+nXkCYEsv5BTZItYx16lrcCLADEfGJPBAzbD2C+JEvQr9IHUNsO4lXMWRueOhc7jt\nC6fwEx++mz32crFHcg7eyQrtKPZGMVZb1WqA9fNQPQA2I8CULPzC+LCa0++iQFOVNPPXTMdzlTAr\nsla0mIo9+KMG0C4xE/+6b3KkgoZAg0Dj9ncPqJNEqFkHTURwXd0HKOMBc/KWM940Bx3MchKnJgo1\ndd8pIcBhpglAte2hSsg1G0IFwMzSG2AxEfj49rL9nslO747wD4/vYHs4xRce22aP3x1PsdYOsNLW\nwSv9eyruG71036Cdw0SBbke0nt+AOQDl1QDbKdBUkAQwB9AAgTVTs+OKS3chXTMoiU8Lgqz/7pyD\nQQVbGzUBfVCNGgD/kRDiEIBfAPAZKBXo392vSV3uZruhgQSNoAawFVWgnTXE5N5kthpgoiCLI7MH\nMPqr2Ra2iq2Y2BRog5onQA9MslZMzfR/PgVaOTJBs1HZkfniqSyTv1Wh1cLlYKd2RwibAuudEI9v\nV0GAlQhWN2qi2RAsBFijO52cw6tep1P1AUMNcK02SBUQYAOVrU4bJD4CXI1+axNT0efUwnu+OdjW\nXIASAJsTp4rGTdk33BRoP5JQb98BXDRyKo3bQ4WnzqHGvmNKINdFgFvMADqtAc7tG3OZsbsotpv0\nnweA1YoUaN2jFsCy/7zF7j/dT39+8GzfcaTZlNBmkGqNcL4nG3OIigAXA2ggoc0y950iSw6g7V1W\nESxi+Y61/R4j6QhUT5xma6ZrzfOvu0UV6/w5ve9hWlbBzuawrAGGlPJnpJRbUso/hKr9faaU8i2+\ncUKIlwghviiEuE8I8SbD31tCiA8kf/+0EOKG5PVvFELcKYT4fPL/i3Jjvjp5/T4hxH8TFInTA2a2\nGxqg1VL5MvH+B6pM4VoYXwcBptYlWGs7aHXQ6Ryszb1plMRGoSdllUx+2xBA06lsizU2vYQCzcnk\nFx0Zbn9ZoD6993Kw7cEUh7oRjvYibA54n3E8m2M4nWGlFapWEmE11VdNldf3S50AlhMAj1JHpiIC\nbGF8cNab4vXzv5ODNwv9liyG4nBEfMGHvfd6gzTeVj+r5kBY930iWF4kwY1m1FM05dG4bSJWVEG1\nOqUzpv2X21KkiABTEwDaUgQ4CYqy3qp0Z1bVhqpxKxX6CAPARn+MZ1ypug+c3llqT5gsnyzN77NU\n2xvHWGkFKdrPSXDrZ1InTvW+wUWAFwJgRqcMowgWS+fFHIBSOxhkFGrb8071U80BLNVXN/n7VATX\nBphxRHOdgNslrALtDICFEP9n8TUp5VhKuZ38fU0I8RzL2CaAdwB4KYCbAHynEOKmwmHfC1VX/HQA\nvwTg55LXzwJ4hZTyuQC+G8AtuTG/BuD7ADwj+fcS5zs8gOa+IetRmCmcfhv6CqiFQasg++ZgU4EG\n6FS2oiMSER/qdA41EeBW0FyoqcuyatTayEWntMtQOAQMGdqWyuRzsnKDSZy2Ylpth5UcmWUA7LfN\nRI3zUDdko+T6O9H9nrutZtoCi2JFKlqHSWWzimDVqiHmIMDmNYe6AdtrP88TAlxnPEOMxIV++t+D\nebyeA53CbEEzKrZhUuPPTz1b1VpulohV3dIZSz09QN83ighwRockIsCF2kwOrVTbYDJLa0Kr7htn\ndye44VgPraCBM3vLANhkmhrejZqVPqN+0sao0RDoRc1KCLC+P7Sf0Kcy1DTzKMxEsKjJLsDClmCy\nNdT4cgBbVzU+Pz/7eJevTVlz/QiwH8GtKZ5oSToC9JLHg2o+BPhbhRB/I4R4ixDiZUKIFwghvk4I\n8T1CiFsA/BEAm976CwDcJ6V8QEo5AfB7AF5VOOZVAH47+fkPALxYCCGklJ+VUj6WvP4FAJ0ELb4a\nwJqU8m+lgsDeB+CbeW/54jfbDQ2oANCfyfc5MjQE2FWPRsnEO2u5iAtLSdGUSAuJZ3PE83J/NpYK\ntEEMpU28PmBW0+ZSU4fFADjkUagBFVzpzG5VMZMze2M886rV9OellW1zMMXhboTD3Qjn+jwEWH8n\naQDMaCUBZPdJp0BlqxPAclSgzW2QODXAdsZHVdRtcQ5U5NDsiNSqf6VS0WzBHxX9dImZUN5DiqaY\n6skoKLg7iQBQUfAapTM+ESzivWhDgKk9raNmY6GNzPlCgKmBxaCgHdGJ1PV5AXCc7jdVVaA3+mMc\nW2lhvRNim8mKuVzsie0R1jshrjvcxVlCq7C8zecSg8ksRfpX2rx2VUURqxQBJiY7TBToDlG5H/Cx\nJWpoR3BrgK3dRqonDaNmvRpgFoLrFE/0z8G5b1yuCLCU8t8DeDmAx6FaH/0MgB+BQl5/XUr5dVLK\n2y3DrwXwaO73E8lrxmOklDGAbQBHC8d8K4DPSCnHyfEnPOc88GYKvLRREFyd0TGxw2lIgLuwH6DU\nYtky+cTC/GnZiciP9zlS+u+m2hB1fVotlxVJYDj1eWeKWwNcpEBnKo28LO9Kmsmv5shsDSZ42hWK\nynZub1kDbLKtwQSHuiEOdSM2AqyDXf09dRk9eIGyI9JhJkrq9gE20Wc5rV9cASwHdSszPqglF+41\nr179KzUT7ykbIYy39ZiliSf6PoN6pTeA/z0oQRa7M1cVAeYEoCYRSq54oskhp45XczAjwFTmT4YA\na02ApCSCWVaRp0BPZnNWS5T5XOJcf4JjK5EKgBmifpeTndkd48rVFo6tRuzkcrZvVKOqFxOnvZQC\nzfNPOkUKNLf0JnevR80GhKinHdEJm5jM5iSmomk8GwGu2Dvd5qcCvCDcJX5IYg7Z9o1LHAEOfAdI\nKc8BeHfy74KaEOLZULTof1lh7BsAvAEArr/++vM8s/01WwshAGg1CTXAjowORVTGVM+XHw8QAlhL\nbzM6BdqMgkeMAFxdz+yIULOD9US4zKgadTygKEZCZA4Ql0INqGD5aNIjcKVdTQTrXH+CK1ZbWG0H\nqar00hZtazDF4euiSp9R8ZnrRk0WApzVAGcBNAAMuH18C7VYWjnWJ7Vget5YbAtLANkKGyTULcuk\nWxDgmmImPqfShQRQ1sw4cdbqlI04uwcQnDGteRA0TIlTCoJsD6A5NXV1xBNdVHp9fp/VRYBNQXyK\n4DIQ4IX2eyHtPtY2mKh7oZl8l50K+8YwR4FOuxdYeo6abG8SYy5V94H1TsgS9bucbHs4xXonxBUr\nLdz5yCZrbDFBvtIOsVehdCZfYqVeJ5bOmFp+JT4mZ9/Ij2f1XrewVvTzNonnC8F5abxFM4BfA2wu\n26COjyxJR8DvK9rW/Uz80L/36cS7aQ6XvQhWRTsJ4Lrc78eT14zHCCECAOsANpLfjwP4EIDvklLe\nnzv+uOecAAAp5buklDdLKW++4oorar6VC2s2SgNAy8gUN8+F8XWRAGJdny0IzwLYihRqqjNoEXRp\nM6hkpjpmLhUuP2cgLzJBreWaoRNmdcg6Q8tBgPuTOKVIrbYCTOI5K6s3nc2xO4pxOBF42uhfmgHw\ncDLDq371k3jXJ+73H1wwKSW2BlMc6qka4NGUh5YUg4duFPAQ4FQFerEGmNr705WsIdXbxzMEDYEg\nV7KQ9S2vnslvBzTNAXs/SCrjRL9/CwW6Vh9hf/DmC8B94/U5alGgk33DyhyqmUTQ1/DNoRYC7El8\nUrUjbOKLtGROmcbNqUGWUpZoiZxkkrrOog/ALb0B1L6R9p+vUnqTK+tYq4EA//2jW/jze09VGnsQ\nbGekAmDFHOJ9Rjoxt5Lb3/c4/eMt7fOoQXSKYFZkK9jWDE7vdXW8hbFRUfxQl96RVaCrMocsfYgB\n2pplK/XTRmt7ai47UeOXfYCr2u0AniGEuFEIEQH4DgAfLRzzUSiRKwB4NYA/l1LKpOXSxwC8SUr5\n1/pgKeXjAHaEEF+TqD9/F4CP7ON7uOCmb2h3AEtAgG0UaoJD6XZk6iLAVEqiuxZsMiPWMRsQJcr1\n9TE2h5rTm9QoZsLI5C/U1zBrOwFVD6bFLXrMRvcA0k35cC/E4V6Ec/1Lswb40w9u4O9PbOO/3Hov\ne+xwOsNkNsehTpQ6I5wkRfGZUwgwP5PfKdRyDYmqr+ae1/Von4BSt6SiboCh5p9Io7bVUtFbCLnr\nV+mOlCuTb/8cXAF0oyGSejIKa6ZO4tOXeK2TBKDT+VyfoW/dH8UzRIbyH6pDbNt/qUwCfY26NcjA\nIqrFKd3R5zBqTzBFsEoJNcb4LDirjgBLKfF977sD3/Nbd1yy7fc0ArzWUUJjc0+yL296j0lrgNkU\n6MX2eTrhT+4eMC2v2+k5arUxotfwmlgrqeZAxRreRkMnb4nlghZf13f9iTOA9q85pgRE8RwUESxr\nySUh8XmQbd8C4KSm940AbgNwD4Dfl1J+QQjx00KIVyaHvQfAUSHEfVC1xbpV0hsBPB3AW4QQdyX/\nrkz+9gMAfgPAfQDuB/DH+/UengxzOWLqdZqKs9URIjiUaT2dIwCtigBzAmjTQ02mQNvEDRgIsOk9\nsMYbBR7ojhCgNqg8hSdFgJmZ/F60SGXjODLa8dACT5tMgSdtk3heSUn0Qtk9j2e9jrl1L6mz1w6w\nkrSc4iQZivcKGwHW7SySjbiZbOCDKV0FullAcDmtY2zK9S2CeJK+hkm3gKNkaQp8wqaAELTAS13P\nvOaRxzuThv41177u+5VVXdoRlEy+Lemoru9XcXZ2HyDX1FkSn8RkTN19x06JTOZPTpxWr0E2+QBc\nFekijZsrgiWlVBToooo0Y03Swn4r7aCyCNbmYIrTiTDU505ss8dfKLvlUw/hzod59GVt28Mp1joh\n1toBpOS1MdpLA+CkBpip8VFUgW40BCvoGcezklYLq1zAUbpC3neCMmuF+7zb+7dXT5zSAmjzepN/\nzbXmpKVTjsSl73vwrfuUNe+gmrcGGACEEF0A/wHA9VLK7xNCPAPAV0gp/8g1Tkp5K4BbC6+9Jffz\nCEpcqzjubQDeZjnnHQCMrZcuBfMFwBEhqzSeOkS0cg5lNzKPH1nQUyBb3FwiVFJKOwLMUjStjiDb\nnDFqbQegFvBibQTHEXGiasQAazCZpcFrfjwVQZ7NFZ0uFUNJkUH6JnmunwXAq+0A952uFsR+z2/d\njoc2+vjL//gNaW3axWT5fownN4d4aiL6RTGtutqLmjkaGb8fY3sBAeaJmeRr/gBeGyOX8A+V7WDr\nZUinjdarHbXVQbWJ9F/AHsDWU4H2r1k2xkr+HPUCWEorJ3PSUY8H1LofNM3H1P0MdB20K4D1OnO2\nAJpRT5e/XvH6VDZDnWfJ1E6KOn9txec56wNMp7bGc5kii9y+4sAiPXetE2I3QTeLwpYue/Rc1n7v\nkXP8HrkXwr74xC5+8iNfwOFuiM++hSdXM59L7I3jJABWidPdhBJNMZ1kzYsnUnUfALOKM0/Eqnyv\n62QLDcG1U5hpNcDmNYutGWDZe/a9BjhlPjlYM47vwoVA63nVXfc5pVwHzagI8HsBjAF8bfL7SVgC\n1KXVM5Oaat7oVDZ7RgdwOxK2ugh9fXWM/aGaziSkdCMBVXuTtYhUMJMCc/76VRFgznhTHTK1n6W2\n4XRWUlikXh/IVCJ1hrhKGyVdu3WoG7IpVtq2BhN88r6zOLE5xD2P77DHXwh7bGuU/nxyi9frOK+6\nqp1GzudUQoBbTdZ3VKTKA0n9DwMxstdN1kCAOZl8R8kERY3TumYS+lKaxFjyc6jTD7JNCJ5cwaN+\nvaqCsp5XvXYYFBp3ueQjG8/4DGopYZvpfNTSFxsi02wIhE1BRLXKe1fQbCBoiNoIMJU5VCzf4VKg\nhwVkMEWQK9YAr7SakJIXQAOLQS93Tb5Q9tlEuGpzMGUHC7ujGDIRClvrqH1jZ8jQ9yhQoDlJT0B9\nn0KUk/R0pkF5zeGy5EzdPjh9fKuWnQC+AJaie+D2lWce1owz8cpJnDoZo/69z7Tv6Tn4ALeDbNQA\n+GlSyp8HMAUAKeUAwMUH4VwCph9YkyocQMuMudRA9cbuuqldtAwKnc8mQLU43u+ImK9Pre0wO6TU\nejp9jqJTrmtDSCJYBlSHQ4UDyoFNKkJGXJRSZFJvkMw2TEA+iA4q94O87/Re+vP9Z/YcRz559sTO\nENcf6QLIUG+q6c+z12pWrAFevF+7oRIrc22eeTO37GqyVGftPXRpCLA5i06tAbaNr4cAA8ohI5dM\nWBwROhJQjfXipUCT6pDri2DZS2cINO6a/eNtScvF8dVqiHWNol8J2+7QtgOGU255D5RnYWRAgNMA\nnEFNNYkvUgPQojqwbqPE6z+vEqcrrSC9PofVAmSsnPVOiMcv0gD4wbP99OeHN3gota6LXmsHKQLM\nqZUuimB1IvWc+0QDtQ0mM3QLwnda/Z9iZsG3emVmAAMBtoA9EXG9sGkGAEQEOJ5DCFVqUzRKAEup\nAXZ9jq41U71Oo2G7aoh9pS8H2agB8EQI0QEgAUAI8TQoRHhp59m8CHBIc+bsCLLfoUyDcAPVrW5W\niqdoWn4PQYNY0+dxxmgq0HWFfcpOLScAB1QQpZ0PgN8Oo19odF9NzCQL7laTfpDcGtnHtjN0lesk\nXCg7szvGM69aBQBsMHsd62C3GwWpM8KjQC/WImnEntPGqJgw4tCXXIJvdRFgqmJ6/fWiRh1U8nfj\nmhc0CZl8AnpJSDo6EWDHeCmlJ4ClOUKU0hnXeH2tolESGc4aYirzx9JCkIrAOpO/hM8wm4P5PXC6\nB5iEuOgq0IvfpZ4PFR3UbXC6hcQpB+HM1wCn6xlDFwFQqGrQEHjK0S7OVaghvhB2aifb2/JlNBTT\n7Kr1TohVHQAz1LJNCDDAE9nsRItlXp2aFGheq0kLhZn6rNmYgkT9CnfSkFYDbNKuWJyDf810tUGq\numbqObjGz+YSk5mrbWpW+nIpGqkGGMBbAfwvANcJId4P4J8DeP1+TepC2HQ6xYkTJzAajfwHX0Cb\nxHO8+5VX45jcwD33bJX+/uKrpnjBS6/EPffcYz3Hf3hBD0GjkR7Tbrdx/PhxhGFIdGTKLU20USiJ\n6UPpqAH21zHP0FptlV6n9ojLUGizI1Inu0il59j6KXMCk9F0EQHm0IuA3AZZFMFiqUhnWWa9Se+N\nYrRWzM62yXT2PmwKnN69uJ45bTvDGNcf6aLZELUQ4N55QIBTpH48S5EB33hTJp5MmTTS/Rn17lZH\nhJgsstb80+bg6k9KmcNoaqbi6fGAWg9s9a9uASh/0ipbM6sxf+K5xFya17t0PMGZ69RInLqTCHQE\nuGrpjT5H1c8QqN8OC1B7m+lepCZO7foVtJZigNr/1nJ1pI2GSKitTAS40AapSg1wL6qOAG8Npjik\nxRcvUhXoUztjXLnawundMc7s8nAhHeyu5SjQuwyGVVH8MJ/g7ll6uy6Mn8Sl0hmVqKFToIvBGwcB\ntrXgaQdNUksoW8cTTsmDqwWQX0DKve8AHralC2w6L4nTBraG9udmYkm2ZeOz0hWbZtBBNlIALKX8\nUyHEZwB8DRT1+YeklGf3dWb7bCdOnMDq6ipuuOEGb7PuC2n9cQxxZg83HuulwUbeTu2McGpnhGde\nu26dt3hiB90owPVHupBSYmNjAydOnMCNN95IpOPVQ5CdynhNxsLkmANFCCw/38XxNEdALW5mNING\nhbMIPBCzm+oci5n8sCnQEPQa4n6BAt2tQGXrj2MIoTbZPLp5dKWcoLDZ49sjrLYCfNl6G2d3Lz5H\nZhLPMZzOcKgb4nA3ZPc6zjt7K+0KNcAF1kSP6TAaEVwiZVONN1Gg6QjwaDrHaru8nbTDJonSZ+//\neh4QYEodlCWAV+OzNatnueXPmwhWRTSCgiD7nNpxPMMhi/gONYC1JhEIKs4uGnjYVAJvdajwFEVy\nH5JPexbsCDCtnOD8IMAlcaKQritQokBXKJ3ZG6ngqtkQ6XrGGQ8o7YjDyZr8wNmLs3Tm1O4IeBsa\nrQAAIABJREFUz712Hf/73tOpYjXVdDeHfHKZQ4Eex3OETZGKH3LVuofTWSnp1WYzh4rjOTXAtmel\nHgW6rtaMPgcp4WYZHxHWzMnMDjalYA9JBMvBfqq45uZfp/qrB81IFGghxL8CEEspP5YoP8dCiG/e\n36ntr41GIxw9evSiCn4BYC5V7UbDMi/tW7hKPKTMjhNC4OjRoynSTaNAE5xBApphCqLJVDSLqiyg\n5eWrOzKUugh9DjMCTO9RB5SdUiqSYJqDEIKl0jgoiGC1me0wAEWB7kUBhBBpcMfJUgOKXnzFagvH\nViJsXIR9hNNarE6Iw92I3XNykKOiaWePK4KVr0Xiqn0bEVxmosUqgkW81221m1WVc9V4v3iSGm/P\nxNeug6LUvzocifOSyfcETxQE2UfjHrn6xxODeFcSIj9P2/j8tcrnoKz7dZkADgSYxRwy3wd1E6f0\nmn5DCz9iSzLAQIFmUmsBtf6l6sTJ/sNhxQAaAVb956u239tvO70zxvVHu1htBWwEeJD24c26B3CS\nBEUBI26J08jQMYSlAj2do1UI3lK6/AURT6xJgfaUfdRBkElg0XRu1fuhzMEl3qjnUJV1A4AEmB1k\no9YAv1VKmTZhk1JuQdGiD7RdbMEvoIJXALBNTc9ZSnsEPJdy4b3lf6Zm8l31dPoY1/j8tUrnoGbW\nnHQ+v0Nsm4MKQN0P9NxRG0FdnIutbdLxDEfGlIzgiBv100x+oZ0Fg4o2mMRpAL1aob4VyHodHltp\n4SyzvpZjrufCZYu1WAE7wO/nEJNmQ6g2Rsw2SPmETyt1OOlUNFOihdM3tPi8cUSwXCJWtTL5qeib\n+353KxjX7YFLq3+1oZ9Rs6F0CyiZfOeaSXFk3Ou2q5bLWUNMSET4VKjz8zRf30/n81OYXfVs/vsg\nQ19tCHCde7keAtwm7FvZHMqJAOr8gTICHAUqcT1g7Bu74zhNmFZFgDcHk5QCvTeOLzpF2ulM9bY/\n0o1wqBfyE6e5z7kVNNAQvPKkInOGG0SbnnleDbBBBZpVA2xrf1c3cUottXNToM8Lc8izb9jGU+ag\n98WqvrLNR83G8/yQg2bUANh0HLV+eGkWazabeP7zn5/++9mf/dnUgbfSm5OXXX5+HgEuGo2K5qYf\n62Os4x0IsJoDxRFxOWMNjD1F+TYnQr3mR3Bd6nocR0gdb3JkqgcmiqJEGz/MZZiBLJPPU/OMUwcm\npfcyA8TtoepteLQXYWNvfxDgux7dwnP/3z/BX3zxNHtsWovVDrHSVj0rOTaYxGg2RLqZdaMgFQ+j\nWPGZy1rn1EF8/HWf2XhTDTEdhXb17aaWG5gF5+gIsEs5n9LGyOZEUAScXOgnRbfAxVjRc3DXknnW\nXEobIgMalI0nJE4pSQRCDbEzkUGiNLoCaJoYmm3dJ9M6a1Coz0fpjCkRwGEeDQptkPTPwwndEe7n\n9g0dmHER4O3hFIc6IQ51+fRgbSc2B3j3Jx7AdB+EfHZzrZ7WO2GaSKVaVmutGFa9KGDVSReTLfq+\npQbRNvFDVuK0uO9wKNC2cgGq4rpt3yHXAPt64BICaC9rxp34tK1X+hxOCjOhdKZu0lHP81I0ahB7\nhxDiFwG8I/n9/wZw5/5M6fKxTqeDu+66a+E1LfSgb+fZbIZmrkn2PLkR5zBHwFJKzKXEzHLDUgNY\n2wOl2zHQaBV1qGyu2gqaIwTYVV2rtlFS16f1RrMtTpSWJgAQz1Q7A2N7GwbFCUCKLuogjUOB7o/j\ntIa4So9bQDkyNx7rYa0TYm8cYz6XRrSsjn3sc49hbxzjw589iW/4iivZ8wMUBXq1HeDkJk+puj9W\nYmU6cdWN6N8RUM4kt4nIZzbejOCeDxEsKgJsq5enjJ/YqHDEz8EmPKTPUY/KRnRkLI6QOof7c3D1\nXtdzqMu6yR9nO4cLDfGPt38GQVrD66dAu7/HOrXgnHZW5hpeX4Azm0tMZ9LaT5rCLHEhwDxkrihu\nRGceDQsIMAC0I3p7HGAxoVKF3gsof+hwL8o0EcYxjjG0JwDg//vje/Gxzz2O64508JLnXM0a67Pd\nXOnMWjvEDjMxXEpQR7w+vkWGWCZWRtSOmM5xtFfdvzCtGZkIFg0kWDPoDtBBBkvfb2q7TS9ziLLe\nVAeLJg6mI2UOLqBGv05rXedGgC/rGmAA/w7ABMAHkn9jqCB4aefZpJR46dc+Dz/+n96Mr/qqr8IH\nP/hBfP3Xfz1++Id/GDfffDN+/b//Ck4++gi+6Rv/BZ73vOfhxS9+MR555BEAwOtf/3p8//d/P177\nin+Bt731PxnPr290p4qzAwFW53AHoK4aYD0Hp6LpbI7YEPgtjvcvTC5BFn9blPoI8CieGefAqYtU\nc1h8TCMGAmz6LribbH8ySynQ3QptlIAkk99VweVc8tVAAXVfnHT0grz3iV0AwEMV2ixpx2W9E2C1\nxadADyYZ2gFotISHAOe/I44TocabEdxa7SwY2V+bmicdNXNT2SiMDVOyS52D6shUp4G5HCF1DqqI\nVTUU21W7CnDQiBoIsOcz8KkgjxxJR/065T5woeDUxKm9np2GIJsRYGo5gJmWSEXmVEss8/NMRYBN\n+0Y3arJKZ0Y5GnaqjM8YP4nnGE3nWGsHlbUnAOCuR1Q3jbse3Tb+fWswwVs+cvdCP1+q7QzVfNba\nYSUEuD+ZIWyKlL3SawVpOQ3FtHaEtqzEibFvGGqAyX2ADWsGxcfU5hOM85U0eUWwSBTmOolT+5qp\nvxcnc8exbwF+Kri/DVLD+TmOHOsdQGOMHmSjqkD3Abxpn+fypNlP/c8v4B8e2zmv57zpmjW89RXP\ndh4zHA7x/Oc/P/39zW9+M178MqUtdvToUXzmM58BALzzne/EZDLBHXfcgZ3hFK945Svw2v/rdXjD\n934PfvM3fxM/+IM/iA9/+MMAgBMnTuB9H74Nx4+sGK9JQgIcCLA+Rx00IvJsxLpOzUXH8yGwPiEv\nuhhKNQQZsGcX22ETmwSVYZtTyxEzMaEJXYYaKKCy7lettZOx/Fqu+VxiZ6Qo0Lqlz+4oNqqcu+zn\nb/si3vWJB/DHP/RCPOvqtdLfH096DT+ywXdk8gjwSitgI9z9ySwVegGqoCVFBJgnOmNDcOkiWA4V\n6Dr9HHMbsEtzwVVDDBBquRyZdEo9mXO9ILRu89Vy+ZwpfwDsQZAJ4/PHFU1K6a6jppbOOD8DHwru\no+P51z3f9+h7rkcORMRHQwfciAq1jdHI8jlQtSemMwkpzSrS1Bpe0/3UYQRGgEYXG+l5GoLXBzgT\ncMx6q3Mp1PO5xJmk5ObRc+bE6B/ceQLv+9TDGE5m+IVv+yes82tKtqZAc3r4AgppL9PMmRTowniA\nnqC2iqVx1MYL626jIZIkvX8OE0/i05XQ0n83rftpt5EaKs6Uz2Ecz9N7s2jkpKEHAXaBNRTxRCnV\nmhAF5f2XIjyornMZU6CFEF8O4EcB3JAfI6V80f5M6/IwEwVaqwi+5jXfvvD6a17zGgCqBvhzd96O\nj3zoQwCA173udfixH/ux9LhvefWr0Ww2HTXAFEVTMy0lPYcHgfUjwJ7Cfg8tIyJQyXx1zHVUpCkq\n1Ooc7qDAP978OXCQvVE8W2iTACQIcEUKtFaR5tB7d8cxpNQCU1kAzLU/vPMEAOCvvnTGGACfSgLg\nzcHUW1tTmuMoqwFebYcYTGaIZ/a+r0Xr5xRPAaAT8mjmxY2YIyRiGq/PwWtnsTg+ILaecdI+c9RZ\npyNjQZCztml+CrSzBRChB+56nRZAU3sNMpDU/XvQV1s7DMBP//XVEPtQGZ10rKv94E+c1nsPJCq7\nY/y5fk0EmHB9daxF2ZaYTNLXyxsVAbYh6a2ggc0BHQEu3o+diJc4HeVo2FXqWzUS2ouCyqU3G/1J\nmrR41FLWctejCiH+0ml+m6UFCnSlGuA4RW0B1a2hz9GOKFKgNUOL0z7PwByaJOVXTU+Zkg2BpbZS\nsu0L5ADYsuY0GgJRk7pe2JmGo3jmTN7W1T1w7Vv6HFVbxy3Owbw/UXQX1HGXMQIM4IMA3gngNwBc\ncqkAH1J7IU1TFVZWFhHcXq8HwK8C3esuHlc0Cqozms5wxaq9zsabySfVABMeaoczdjZ2I6iu2g5K\nW5Q0iLfQa6hqnjZHiLo5AGWHsB02sUFUUlbqwotz6EZBBQq0WiqiJCjiqIHuDPNOgjoPV8wkns3T\n+vgHzpQR3r1xjN1xjKcc7eLhjQHO9Se4er1DPv9gPENDqO9W0+364xnWu7QAeJDUAGvrhE1WL+Hi\nRsoREgHMNX/tsIk4aX3jC+StbAWCI+OmfdbL5GtHxk999TA+vMjdDC3LmkemQLvKRjwotGu9UnNo\nYDqTVqfUX0PsdmToNcT1Eqe1elJ6AkCbZkJ2fZoKdEMAgal0hvEsGOsSGQiwqXSG3H/ekkCm1uMD\nloQag1Gi55E/R7fFU8bXreW6rcX+8xx7LCmZWe+EOGtpUfRIggzff4YfAKcU6I6iQI/judpzHWtB\n3gaTwr4RBawgehwv9l/nt0Eyd5lQ554tBOfm65vX3U5E60DgY/6o58W+pvi0G+q022wFDSd6ms7f\n1z7Ps+a5KdBNJ1jgKvUDFkuIVtvlv7vEYtXrlzYCTK0BjqWUvyal/Dsp5Z36377O7DI13d/Xlndr\nCOCffPUL8MHf/wAA4P3vfz9e+MIXlsbbEndBQ6AhKFkptzNGqUerKkrjLcwPG5hQajsc0u7kTL7F\nkSFRoC1zoPchNgfhHDEU1dtzcXwnpFPhAK3mmWXyuWqgiy2GNALMC4DP7k3Se/thQ43vqR2F/t6U\nIMPUBIE25YgoJU7tUOyO6XMcFpwetphJQcwjpUATNh5XzR/gz96q8WbEnKLY7qZ9+hknrpZj+ry+\n8cpJqVYHBbjXPFrw50M//UlDVwDto4Lb9ALS63sozBkVzoNmeBKn/s+gBp2PLAhT7T4CkAYvpgQy\na98womI0BHg0rcscMidDKO8/f44ShZqhKq/OsZj0Uu116PtGHgHOKNA8R/x0EvQ+86pVnLO0KNJ7\nx+4oZu2LwCIFWu8bnOTucDJLg1YA6EXNNPCnmOkzBjhtkMxdJgA/+8i27wD0Vo2u7gH67zbLtGJc\nrJk6jBEaW7K2boKTAu33tX1rrmsOZAT4Eq0BpgbA/1MI8QNCiKuFEEf0v32d2WVgugZY/3vTm94E\nCU8bJAi86Wd+Dr9zy/vwvOc9D7fccgve/va3547wtVESJEfClcGsWwNcV9mO4gjY0Fc93pvJd9Sj\nRU16P0crFY44HjAhwHQ1z/G0rJLIaacxn0sMcggwoCnUDAQ45ySsVRQzeXxbZfJbQSOt6cqbDrKf\ndoViTpxltloaTuPUEdG9jjlzHMeLSDtHSAQoOwItohMCZDV/tky+716P5xJz6ep9Wk8wDnBvoCn9\ntqIYiX98c+E4kznFk4i9z+vRf/30YX2cybwiWJ7xPkeIQof3Jk5rJj59tdz+ejha//k6KtRO7Qji\num2llVIRYEvylvL+tZnbKNH3DaBMT+WoCwM5BDhqpiKMe4ykJJDtC0+9YgWj6bwU4M7mEmd2x7hm\nXcFjp3d4+8bOKIYQwEoUpCKIPHZVQTyRSTMvrhvNpP6WsvdIKY0U3LSVkucc6b5jWfcpIIGtdzil\nVC8r27D7mSTtCKvyPXXdN4+PAv94CtjkT5y611zXHPxJR1oS/aAalQL93cn//zH3mgTw1PM7ncvL\nZrPyw/3Y1hB/8unP49ix9fS1j3/84+nPQgDXHL8eH731NhzqRgtjf+u3fgv9cYz7z+xZEWDAj0CS\nMvkeJMBZz3Ye6hoo6nwuNIRMga5BZbNL9NN7o6rjyxsUWQXakMlvh02cJSKkehPs5QSeuArHWvik\nFwUpAswVC9FZ+udeu26s1dLnu+GYKgE4x6AfA4tUtG5LC31xxUhytVhMZ6/IFtBCIhTExYX46Ln5\n5m4ar89BfVZcCLBTAZnQisFHH3aPzz4H20bvCkApPZlN7USKc/BR2SiZfNtzX1cEy6e7oP9WRwWa\nsu676XzuxKFfEZXaf95+H7ho6ICHOeShsafnMCQt9XjNZHAJytmSIdTSG/0+Sm2UuBTowv3QCpsY\nMcanCHArCy45vdWBXACc7AsbexN0j2Ru78beGHMJPOfadTy2PcLp3XG6h1BsZzjFaitAoyHSPZKD\nUg8nswU/rhcFtRKnQLL3EPZnG2NCJ4LJpS+mZA/hXtPaEbbSGzUHyrpfByhxlc5Q9i6Kcr47gI1c\nyvmENka+NVcfZx7vLzsBeJovB8lICLCU8kbDv2Xwuw8292xuet+cW9h8mubnOofXofQ5MgRBljpZ\nLZsKZja+SWhH4W5rMktqI13jbXPQjszc9iV45kCtxbKLYPEo0CUEmEGFs7XD4GSpB7kgOqvl4i2o\nTyQCV8+5dh3bw2lp/jq4uO6wqvvlBtiDnBpn2uqJQfMu1rtVaYNUrrmjC4kAJqYA0ZHRm6CldQtF\nQEofWx5PcQLs19ev+9BTAHYKNDEI97cQcr+HWv0cqY6MFcF1r5m+Wi5bEqU4B18Nry3pqObgZ/7U\nDcABFyJEYzP4mABONXDH3qVfo6BSRjYFgcmgx+fnm12fjuCaHHuOqN4sKWtYKOsIGqTATJtOQHaj\npgowI14NMZAFwNcf7QIoJ0ZPJYjvc65VgMPp3RHr/Hs58UNdL8tJnBZrgLl10qZ1h7o/29YMSuC3\nOL4aXX+SBuD2e90pluoBSnwJZG+7TSoCbFlvMgFH13rhZ/741lw3Auz+HEeO7wCgvYeDbKQAWAjR\nFUL8hBDiXcnvzxBCvJww7iVCiC8KIe4TQpTaKAkhWkKIDyR//7QQ4obk9aNCiL8QQuwJIX61MObj\nyTnvSv5dSXkPB8WkdH8pPhGstAbYcQ6KQ+l35tyZeDeF2k1N8TrEQYPkBNShdbjETNL+br45TC11\nlUHDG4Dn52euxaJS2coiWKw2B4ZNjkvv1VS2ThSgHTYghF2lcmr5TLYTsZGnXakozsUaX02zvjYJ\ngLkU62HOEcnqqJiOSO5z1krbvj6G2kzPDBXptydKaDRqlyNDqVd3C//Q6qjU9e0JL58AlTrOk4n3\n9KCt5ch4gjff5+h3ZHxUNt+a6a7l8gWP+hx1g3gv88hTD0dKpHgQIdcz6Wufp4/xzcGG4OaP4c5B\nv1a1FRPl/adzqIkATwzPNLUuVJtGUnX5Ta8VYI+5ru8Mp1htBzjSUyhrsT53a6j2kRsT1Jer4pyv\n4c16HXOC/MUa4G4YYBwrMTeKmdvfcWvF6+4bpgCWvm+47nUS88chQkUqnam4ZvoCaFVuWBMs8iQN\nXaV+gN/X1e/NljwOmg0EDUEGTA6akQJgAO8FMAHwz5LfTwJ4m2uAEKIJ4B0AXgrgJgDfKYS4qXDY\n9wLYlFI+HcAvAfi55PURgJ+Ear1kstdKKZ+f/DtNfA8HwnwIsPAhwJ4aYMC9QLpamqTjCT0t/bVg\n1SmREWEjd2XWMmGeaig0VRhAZfIdtNCK1NJ20EzbFPjMFFhRKdiAeZPrMgWeBqmYiRKXsfUhftcn\n7sdX/vSfpvW+edseTrHSCnDU4shoNc6jvRbaYQO7TKQg346Cq6QJlO/5dtjEXPqTJLbx+hw0IRE7\n5VGduw6C60+WuJ8VgiNDKnmgIH/VEl4uKh6QOQHuwMfniFBYN44A2rPm+CjMVEeo7rrvagVFEgJz\nXt/NRkjfg8Mh1qquNjMFful4QksQ17NE2Xf0332tYdzjy6wdgI4gAzCq47aIJRmAuYSIWxbSz9UA\nAyrAHDDGA2rfWE96uwMoBdApc+iIQoj1PpK34WSGt//Zl4x9hPP7hqZAc0Ss1Pjse0rPUauNUX21\ncKAec8jX9g2o/6x4E6fNen5mlnQ0nyPTnvAk7Vz6F541r+3xdSnii+o4e+K02CazfA464HLQjBoA\nP01K+fMApgAgpRzALlSs7QUA7pNSPiClnAD4PQCvKhzzKgC/nfz8BwBeLIQQUsq+lPKTUIHwvhkV\nnbmQJmUW5JqskXzsOtA1jQcWVaCL79PliPiQBDXe3wf4fIhouUSwfI6Mk8pGyMSTspOGGu7iHGzZ\nUQBeZ8K2wPsUYfNmokBz2mHYHBlOcKiP1YFlJwqMWfLf+KsHsTeO8Yl/PFP6285oirV2gLW0hjgu\n/T1sCrTDBlZaIVtlOp+JzyjQzAC48BkBwIhIozY7MkwKdNFhJWfyHfc6od7dtWbwkk2uANgfQNva\nSfiUqE1oFXsOPiqb53McWdgi+fGAm8IcBQ17+zsqBdq37lvupbmB8moa708i+BFg275dVwgMcH+P\nlPFOESxCMkifw1ZXqa5PTUiVA1jKeMCcCGgzanhNexe1j7G2fkqBDtLrc9ZkIAuAM2X/wr6RIL5X\nrLYQNRtGBPgjd53EL/3ZP+KX/+xLpb8NpzkEOKqGAOdFsKgCVIBdPZ+OAJsThx1qAOyiQFME5xzr\nPodt4Qpg6/qZag7upKEfwa2RNEySdraklQ1kScd7PsfRdO5Meuo5XNYUaAATIUQHicSwEOJpAHxy\nedcCeDT3+4nkNeMxUsoYwDaAo4T5vDehP/+kcEGdDmu329jY2LjogmAJoEFAgG3TnhdqgKWU2NjY\nQLudNQFzBbCkh5qAZviQgJGDHkoRMwE8qq4uR4YQGLj6o0W1HRleJt+kAq3P7zNF7Ty/CDC3xU9/\nHCNI+rkCGkFedESklGmf3/sNfX63h9PFPsLDIgI8xVo7hBACa+0AOwaqnJQSd5/cNiLnw6mJAk17\nj6b+oxwUORu/+D1T24bYa/4008CXybdTwXw1SAvjnfd6dQTXl7CZWN5/eQ6epF8NKpqrFkyfuxZr\nxieC5ekjnNK4KyLIeg5+NKQGgjydefYNd+KTTIV3JWMciVMWKmURT1THeCjQBuHChfFkcSIzAkxB\nc0z7J7V0BzAnTtkq0BNVU67RqY4lIfjZRzbxpj/8nBE1TQPglkqcFhFgzSRaawdY65h78H7mkU0A\nwH2GPsFDg3YEFb2dzVUboTwFus34jvQzZ0L6Sb6BjWEWutcabT7mkG/fGTmSbrQyNQ8C7EEuyS2A\nfLoLDrAncqDQvvZ/+bnZmTvuxKlPydpXeqPncKlSoKkq0G8F8L8AXCeEeD+Afw7g9fs1KY+9Vkp5\nUgixCuAPAbwOwPuKBwkh3gDgDQBw/fXXl05y/PhxnDhxAmfOlNGmJ9POJH3rphst6zGnt4YYtAKc\n65QbhO+NY2wNpmhst9ONo91u4/jx4+kxruycLysG+J05CgI8l6r9StgsB/u+hS0LQGcptak0B4dD\nSuvv5s/kU+qQTZ8DnWJkpiVyesSODRm+dthEnDgyNqXubHz5c+AiwBpd1UkZk0jHuf4kdWwfMfT5\n3dEBsEaAixToUYy15HlYbQfGGuA//YdTeMMtd+InXvYs/JsXPnXhb/1xLgBmUqBNjneHkcm3CVFQ\nHRkbgplufjUdmXoUan+yiUSB9iCH7vHu54285lneQ9YP002B1kk/U87WnzT0Ibju1nVZLZcvCVBt\n3acnTt3fo087Qs/V9FlRasnzxxnnMJ2hvWree2l1ifbPkYrgjg2sHYAuSGNlhBBrkAG1ppi0J/T5\nvfuGrQaYSYEutggyraf/+WP34I6HN/E1Tz2Kb/7KRYxlezjFM65cybVRKlOgG0Kht2ud0NjD9+SW\nKsk5YaRAz3DNoYyireZNe4/6vXQXAmB6cttV603RwLBqjBDvk4lj3aXQZl1lF5T+8d4aYJ9mgWe9\noASParyb+WNj6vlqkNXfcgmRdvnv1MSpbd317VvqHLz2ZwfJvAFwgrDeC+BbAHwNFPX5h6SUZz1D\nTwK4Lvf78eQ10zEnhBABgHUAG66TSilPJv/vCiF+F4pqXQqApZTvAvAuALj55ptLKeMwDHHjjTd6\n3sKFtze/46+x2g5wy/c+33rMt7/1Nrz65uN46yueVfrbuz/xAP7zrffg7p/6Jmtw2AqaxloXwI++\nAuqBrUVlyy0soWEjpTjEerx1Do7MGK0ucW5tyUGuAa6NAJsXSKpIhTrG0Ac4oDsyo3QOizXALBXo\nQq9D0/jHt0e5n8s1wDujGNce6qRBrgkB1jS31baZAv3xhFr9iS+dLQXAw0mMTqjGR0nPUyrKbXIk\nUiobRY3TUkvVDpskURa7mAm1BthHgXbfZ5OZazwl2eSrxfLTyNzjfVl0f/DmQqF911fjfUk/T9KQ\nksl3XF/Pz68i7Vv3Pc5gTREr6r6x6piDq/0d4EZQx64aYL3uEu7lWiJYsUU8kaBKuzgHc2BD3TfK\ngVWWSOpZfIv8eDWH7Byu+8dkg8kM3UL7vc1+eT28P0Fm/+HxnVIAvDtSzKCg2UAnbJYC4J1EW6LR\nEFjvhMbuAY9vqb1poz9RQXnuvedLZ1pBAw1BR4D1Z9TJ7xsBPXFqe+ZaQRNnY38bQNu6T7/P3Ahu\n3fFA/cSpC6SgMg396747aecbbyvdyc/NtW67EGifr+kTHgR4oqkHzbwUaKl4qrdKKTeklB+TUv4R\nIfgFgNsBPEMIcaMQIgLwHQA+Wjjmo8h6DL8awJ9LBydZCBEIIY4lP4cAXg7gbsJcDoyRMjKOrBIp\ngHVQYDkPtb0wn5jJ983B48i4laTttRGUTDxFDdTvyJhRaHotl7m2se1BtIrnMKkLU64PmBHgtiUT\nb7NSq4coKDkJOgB+6hU9bBh6+CoEOEiD3CLFeXeUBcArFrXQ+5L+wY9sLFKspZQY5CjQQgh0LEJd\nJjNtxBmKTM/ElwJYD/KZjreIUFFrDn2tWyiIFWBWkmx7NmDf9dXr7s/BV8Pr+xzq6h6QgkefM+Wh\nMHvpeJ7xgGYU1GH+2BEV2r7hE3RxO3Ntz2fob59HS5wWxZ+y8f7Ep8up5TyP5gDavW9m4+2BkZoj\nTVegrB1BC4zyxywgwAzxRqCMAJsQ5OFkhs2BClofMFCU80H0ioEZlGcOrbXLAbCUEicq/yPPAAAg\nAElEQVS3hjjcVccUuw+MphkFWgiBXhSQEWAbSq7OS0lS2Jk/tP7xNgSZep/pe92UrKnJHDof3QM8\ndcheP9NTP0tjvThYM+m+4w9g7aUv9vUqf25XEE5DgC9NCrQ3AE7sM0KIf8o5cVLT+0YAtwG4B8Dv\nSym/IIT4aSHEK5PD3gPgqBDiPgA/AiBtlSSEeAjALwJ4vRDiRKIg3QJwmxDicwDugkKQ382Z18Vu\nNE6+O6vUEEDgU3XzPJSUwnprYT6ht5meq3m8hwLddD/UPnl6X09MfW7fwugKwHVdp4newxHBMqHQ\nEeH62kYGR4YiMJGfA7B4P3TDAJOY7siUMvkGBPjsnqL+P+uqtVKvRkAFwOudEGGzgW7ULDkqKsjW\nCLCZAq2R5Uc3hwtzV045FmqxFN2OqMRpoGKlFGiCCJZNvIes5mllChBrgF11i4Qg3BUAUuoOfQEo\npYWQ7fpqvNuZ8gVO+ty1HBnPM+9jzfjo7MU2XMY5uIJ4h6Jrfg7eJALBGbPtG6Pp3I2GeD9D93sg\nJT4J675PBCtoCCOzxueM5s/hVFSvSoFmBrB2VXn6mrYgnhjRA3CgnDg1ld48sTMy/gwkic3cOVZb\ngYECPU3LahQFuhwgj+M5nnX1GgBgo78ofWPq40tWcDY8cywKtA3BJSQt1fXdidOq/aYBv3qxGm9f\nM9qEZBGlhrdW4rVm6zk9N9t65aKQa/PuXY71Kn9uJ4LsZQ7RtEgOolFrgP8PAK8VQjwMoA9Fg5ZS\nyue5BkkpbwVwa+G1t+R+HgH4NsvYGyyn/WrinA+kTQg3ZORxxtph09MGyZ6dozqD6lrm7JGXlkFY\nWFzS7JSHOn9ceTzBKXf0V6M2SM8fa7q+T1HTRgmkOiJTSxDOQYBNwVknUnMaTGKstst16EUbTGJ0\nw0UKdNGR0VTfG4/18LHPzxaQ69lcYnccp47Kajso1WoNc5n4XitIFUS1zecSp7bHqRO1OZjg2Eor\nmV+5FotD8zZlojk1wDbaJFU11UeB9qt5uinQvvtUb+QmBJiSbKE8rxRHxlZDS0aAPQhsXSRAXcsR\nwJLqXx2ZfJKYSXUat+t7oIlo+faNcrmGbbzJvG1N0vvAHcDaVFGpIlh1mUO27zIVf/QyMmYQooxC\nUxFowEaB5idOFxHgDM3qRt5TLLQYAsw1wE8kzKHrjnRS/RRtGm3W51hpB9gztM/TzKFeVA5ed3L7\n0t/cv5EKNQJqT1Eq0Nkce5YOByYzPXPUNds2Xp2D2j3AxhQgMhWc+0bWciwKzH7cyJA41hYkZUik\nANaRsKqq8wLkBcmqs16iwF6PTVtzfWuep3uA57s0lciVzhE20pZkl5pREeBvAvA0AC8C8Aoo6vEr\n9mtSl7NRKQkTRwDrp8JR0AwCrcL1UNWh83k+Ax8FmloT6ELGRg4k3odAA+6WHBRHTJ/f5BRTKOD5\nOdhrwaqhi5wAGigjwF0DTWxnOEXQEDh+uAMgQ4SBTLkzdVRa5fHDyaKIVbH2dqM/wWQ2x3OPrwPA\ngrM0SNttFNCGWhRo9TMnADYiwES6omk83ZFxU6An5Ex+eXzQEGgIYrLIQV113as+BWKymqen/rRu\n8AiYnzktouVeM/10PG87C4d6v16LfPVo/jZKrnXbvW+4ko7q+rSaPGtbE2Lisg4C7EpkUBBcl6Aa\npwa4FZRbYlE1ATSDqk7pjE0FOv83nxVp2KY1+Ykdxep57rXrOLs3wTzH7BkWEpsrLRMFeppSoLtR\ngEFhX8knZoFFCrRem4sIMDVYMFOgtW/CSHyW9nciAmxZtyjB5+J4u4/jrpdP7pGK675v39BAkavk\nAvC3QfL5ylV7n1OFAwG3gKNrvBDCA5hd3iJYpABYSvkwlFjVi5KfB9SxS+OZjz4M+DL5RCpcjd5m\nbY8j4EMjKIiM6/o+NcyMxl2tJlD/zYcA+2qQ1RwM9J6UmkqhwpXHZ+/fU4M8Nc+hmiOTfRZUKp62\nYq9DUxuknZGiOB9KoIG8+NMgoSJr8ZGeoYZ4mO/jm6hc578fHfDelFDZ8gG2dpQ6BMVRk5k2Ymod\nVf4YE4JLUwM1jw8TR8bfBslBRSM43ZN4DiFgFHcSQjgZJwvXd1BXY0f7Fdf88+etW4vlR5Ad9auO\nOUxnElL6r28bD7gTduk5QncdsyloKs6hnjPnCeLJ+4Y7CLcF8b4A2saYSccTxAdVIsJ2H9JriGuJ\naNWkUGcJJRsyWBEBZgbAxfehhejyQa4OSJ911Rpmc7mA0PYLAbCJ1bM7irGq95VWE/1JvBAwFQPg\nfHlOum/kBSLDgJ44NaxbvoBncXxyrxgQYFKdtydJ72UqONZdqo8F+BDcOhRoX9s09/isdZyb+eNk\nrYR2sKruvmFLVJXm4Egk0OKNy7wPsBDirQD+HwBvTl4KAfzOfk3qcjYKJz9yOmPuxtiAvqHNfXh9\nWTEgt5Fb6XB2Gpm+vmu8VxDGk8mmyOO7rq/PbRfRoiAB/uyol8pmo8IRkYAUhT4fCDCBprU9nGJr\nUK7fHYzjhfrabtTEYDorOBpx0uZIOSN5ESuN9uYdmTzNrChilQpQ5Y7RlOmnX7kCYDEATinQFZWu\nTfcbJ0lgUtoGlGMzmrrR1/w17DW8xEx+RcG2caxqN23Bk7+Gl8bYsGoOOOYP+MWTaI6MXwDKTd+1\nz4FCwc5QGfua59s32h7tCK8j5VADPS90vtizb3jQMV1DbFLuX7y+73v0MAmqqkhT9g1HaxhyGyWL\nD0EXX7QEwKwaYhMCTGfF6Osssmp04ji3rg+naAjg+qNdAMUANU7GBen/xT1rNM0lTqMAc7n4/nQA\nfM2hDpoNsVB6M0gTp7nEZ9ggsXb0+wMWEUQf7dY03oQAT2fSq9HhS7aQEWDnvlEdwfUnTj37BkE4\nELDvGyp5S2H+eBKnlvGUGmBXuR5lzdXncM2BEkBf7iJY/wrAK6HqfyGlfAwwdiJYWg2T0t8YG3Av\nDLbs7+L4rCWHafz/z96bBs2SpeVhT1Zl1vp93116maVBszADqIHAIY2xA2HLCjkkCFvgUIgQyBJC\nRhCyRIQtLDnQD2GFwtiBQRohSzLC7ChsGIFkRgEChoFBDDAzPQPTw8z0LD293u6evuu31ZaZVekf\nJ9+z5Vnek9W3uff2PREd/d2qOpmnsjLPuzzP+7z0mdB8IITgRjL5ERGqkBOhn9+rhB3JrLFEsAIO\n5YgR3ISuI7sWzINCU2YyHkB7KNApKtAtuqejKr7f/1t+7EP4L//xb3YM77LaYm4JTDWNiaScrioc\nTXIctAGwTlWzM+0zi+JMtV7qfXEM3dEiR+bND4hM/vGy68i8khToFMEYXyad+ztJR8qjPLvvfH2N\nvvl962dj5wfigihlZH4xzJBlIeRwP0cmJqZC88Vnu2vgOjKTCArN6R4QZg5xmEe+xGkczWCVvnCS\nCAEEuK8zCegJw1jiM7zvx2uAA/MDJUgjxrNIxw+1lonP95XO8NFJl5bIWCZOeWiS7QdMHfNP10KH\n4gK1x9PsBu3rZHumxaATfOsiVtQrWKcwk924MC063QXcfXy7dqNpGvxP73oc//rDz3e+H2Cj5HGW\ngZrvsxtM/yKw74VAFnu+026wyg3CviYncTr0CM5x1hAqU1NrCCUNOb4yow1SpPRGP5drPnffdo3Q\nfqWv4TXbBqkdZdueqAGALMvmt29Jr93BocIB4oYOoSExBDhEgeU6g+Kz3YcqRiMz5vekQMeFAbiZ\nwfDmHKsp5FGgA5l8hsiEMzvLrOWSFGgPlY1Lr7WpkS5H9urZGo8/f4zr5yU+e/XMOIbolWgKhYjX\nlTNBtVgkqqWrdaoaXTFvZolcrVulZToHOST68cmReaStMdb7YCunUw/S8/0o0EwnRJ8f6tccnu9X\nnp0w2lEElWsZa4gmrBgqziH6LaeVQ8gRoky+Dznc35EJB076e333XHGMGIK7jyPEE9HyJU5jKLz+\nnus7NE0TFYCMI8jcxGvYIQ3VJIbmyzXsY3eCCDB/Pwh1H4iX3rh/y7Q2SN1nYpqAbop1mH6AS1jw\npG2PJ/vDawgtMYd0hFdn9UgRKytxqn/GDoDPNt0Ae2oF6fb1+fgLp/j537uCv/tzHzNed12jFJq4\nD6nXxcZCg8TSXKUrMfQVCNsdrtCoa/36McKJU56f2Fcrht7br/2dXwWas+8rRoCfORRn7kRqgFmM\n0dd2APyuLMv+JYCLWZZ9O4Bfwz3WfuhOGLEaJhqhjAwLAQ60k+C1QfJnclmOEEfRNFQDzECgAf/G\nEJsfWwOPyhZAgCOUTnUMH5WNhwD7RLCS+gDXjnYYjiz1czeW8u9nrqs+u/V2h7LemQiw15ERTgYg\n2lPQWFaWI2Nl2alG2KZA644MqXleno9EGyXt+C4K7LQYONtZ/M6T143vCvgQ4Pg9pua7DSE30RFi\nK3ARYD/9OO6QbeptXDwpWm8fd2T8taPMOibPfK6Ccbx3er89j9OCiI7fVziQ1hBKOkbtTvA7xK/B\nJOAU8xKvnNKZfolbII4A58MB8gANnY7tSwYREyH0LIUQYG4A7EtmcHUJfOJEaW2QuveDry3bO9/z\nGfztn/1oh1lgO+cTV2nLSrQxog4Benu8VWUmTidWGyX6HpQ4JRt1biHA+SDDbDTE4cRCgB0UaJcC\n8xOfPzWOJ8/vuEZc3Qaxfk+JE9du1P66f5bdCNkdRgJ4HQig6Rh9k00Az88Unwsnzfw9eMnX3ZMC\n3bONUUhFWx+T4L7PEU98jVKgsywbA0DTND8A4OcA/DyALwHwPU3T/J+3f3mvrcEJHgERIO+X0fEb\nUlYbpMDm5gu63OcP1bPtQ6ULIzrDQYZiGDYyIVSL04d3HfgtlbhCPJPvoyfRGkNDiWDZjkwCAuwI\nLlzX/4Xjlfz7yi3196rqOgmuAPp0JdockdKznmknR4MoakIFupuJlwGwI8A+XVXIMtEL8mhSGAG2\ni77poj49e2OBv/QjH8Tf/H8+YrzuqiUi9UWOI+NzvLlBdLju0G/81Hy/0z5h3GuxPSeGQsdLHsKO\nTFnvgjQycYz9+/juWwsGuJ+5FCqbzxljUdkiNG4OkkDn6sznUKBDdD5OEiLiVMeEwGL3EYcSGfoN\n6Ni+7xCrKQTCCHCsDlytYc8+wh7Huo/d0IMrF713U2/xg+/9LP7t77+Ap7XEqWIEuCjQ2r7eiidK\nCvSqW9oy17Qj9P71tvr/bNxlJp20/eezLBMBsG6XrABbfMeueOKVmyph+oJmG337xiRyj3Xnu5H6\nKAIcSJrFgk85P1LvHhOMi6Onsfl7+Jn1NsgcEscIaT/EASt63kNlI7H5gA9siu9XAP2WAQo0I17g\naJHcjSOGAP8uAGRZ9tNN07ynaZq/2zTN32ma5j2vwtpecyOtqL1f8Ejz9fOZa+DQATl0vn2oaBFH\nJlrbwUMTwpur36FktXYJOFODNgDnZmi7a+cGwG40P00FuusYu6hwFPQOMuDF47XxHQAzuHAF0IIC\nnWOcD1AMM6MGWIlUKYqz7mS4aoT1eUCLME8KDAYZjqa5QYF23bMuBeYPPHUDgKC06YrEXgSXUUcV\nm6+/758fqDtkKIKGM/nxe6Wsd1EjHg4auCUPIfQzkgUP0YeZ7Sh87aA4ugn7lp3Q+33rZ4GII1Rv\n4wEwZ99noRkBuxNKpERolTHbx2UOxVoABlEtRvI22Ic4ch3G+YDRB/iVsRt+RgpjT3OsgX4/fV99\n6poKej/9eVU64yoLcSc2zcSpUQNsUaDt+TaFmQJlvcXe2Vr1CT4Y51Zpjpl4Fevt2g09Iawnin2+\nFl/9371vcQSo6P0Q/ZijMRKn+/dPfMYTp0w/MbBfhFrPiTWEBWd9FHK1BvH9XErUnP0m1LqMY7fo\nfdczSyrSnNIbIM5YvBtHLAAeZVn2lwB8dZZlf97+79VY4GtplFxHqPAbQVY7jIBDuanDSpr6+twI\nMgcBDlOxNhGHmt8GKZaZi2zOwUx+uC5i7TDg5vnjdRWirs+BAEe+v1qD+7cIUeC7a/AjwLqRvnq6\nxtEkxyOXpkYrCldwYGeoFU06bzPthUE1W0o1TxXgVlvV5shGmZUKtJnJP5oKR+ZwUuBsoyPAXUPk\nytw+p2XyXzrRg3y3I8OtnQnNB5hq4beLAp3H7xUOgtv3WQPiCRse/TdMHx5kIrEVmu9bQ1rw53Jk\n4gE0Hd/nyGw5jkyojpmhIh3at1No4GEUnIMgBxKngfMPI4lHabtiYmixZE7U7jAQ4ACy1tduKAQ6\nnngVa/AwUpj0XF/pjR7AvqgFhM9q+6tLWE72VrcTm9Mck2KIcT6wEGCLAm1RqNeW3Zg5tClWZS1f\nP+jYJTOApu9oo2Uvnqxkf3u9/7xv36BjxIavBnQSCfzk/ADrg3ufxMvE9kt8xphHYT+RYTeiSb+w\n7oKPQq7mt75OcN/3ryEEtsRK/dQa3Ek3Cmg52hH6+e6lEQuA/waA/wzARQB/zvrvv769S3vtDQ76\nSu+H6hI4jhR91h5cKp2Y3y8rFRPTiKEZsQeSo8oaQoTkGiJoQlAEK7K5cTL5vt9CNTcPGyglgmVT\nrBIz+QxxppNVhYuzES7PRrihtaLwoavi2G0m3lLTPBjnZg1wp59jq/JcboPvGzXA61rS5I4mFgLs\n+K0mhVCq1rOeOn1ND4a9YiQM9DU0n63mGUCdYkIidPzQfSo+E0KA93RkYqhZxKFjUaBDtVytsx5y\nZIIILos660cvQ+USxho8rJVYsk2tIVzHvBcCXPHpfH2ZR7H+5+I7cNhT/RHgqN2I0Toj1NJYEM4p\naYgpUbPbonkYKZzgzFWH7KLm6oioSQ92JU4dCPC6kvW/R9PCbFNk2RVqc+ezG0oFWh1/WW7l67YI\nlh1A699R/42PlxXe+pBov6cnh+l3sJ8ZbislX+KOq9a9DiK43BpgT+kMgy0QS3xyugeE23XG9gue\nrxvuocvcMx3PjK/ftj4IbHGtgcM8ovf7ljsCGvPjHlSCziPvv6Fpmv8+y7Lfb5rmh1+VFb2Gh9wQ\nmRTopmk6ThvPkQnT8aKOWGBzcynq2oOD4IYeSgoAo22Q9sjEl4wgPIZqhdbAzrCG5jMcIaDrGHPE\nWOQxHIqirt//eFXh4qzA5fkI18+7Rt5QSLayoraYiI9qJqlq5KiUNS7MCtXvsTBVoO0aYHKUDieF\nUW/mMkS6s05rf+F4hYcPx7h6trEy+e5aIo4TQfNdmeQkCnTgPrm1ZCDAAaYCnSM0n8TLXCOebIqj\nZsArIIK1B4XaRL+Kznwg1kc4HjxymD967XvyfI3VYN9r3HYYQMBuxNCQwHyOENlgkEX1Ly5OC+d7\ncg0hJgAXAY48CzH2U0wYCAjYDU5JQwiZizyLgN+x5iZexRq6dsPFaHnheIXRcIAvuDTFjUUXHZ1Y\n6Cqg7EW13WFZbqUC9OEk71CgB5n6HlPLLth2xYUAL8qtTJz6RLCMNWrBJ71+sqrwFY9cwGw0NPoU\n+1SUJxGavH6Nxnk3cce2GwHld752xB7MoYjuAMtH45TOeHUTeKUzejmWcX5Oy9KAiCTX3/e1g2KX\nznie+RTATf/8vTRiCPDfa///N273Qu6PhBs6D7SjSEFwPXUFbBVppzMXd2RiaposFHsYcmTiaxgF\nMnu7Xbwfc6w3WkxQZcTKsIZbMcVqMpS4knmMLMuEke2LADso1CQWcmk+6hh5wAwOVKsHcf4ugjs0\n0NtVWWNaDCUtf2o5KnY/xqlFdQOEsud8TBTo3DBqrvvFZbiunm3w6BuPAADXzzfGfHfNHdORCcwH\nOAFwWI2Tl8l3z+e0PmGJmexBgd5XNV6uoWftKM2nz7rOD4TRzxB6yaEP0/su9I2NALesBl892r4U\n6FeCQs1Bof2/I1MILNo9IHwv71vPzmkN4wvCQwkAcw0BaiujjzDg/i1Cvaj14UKARw6/4/pZiQcO\nRnjwcGwkTt2lM2YATckgSr7Z/eFFj99cBoiqO0BtnGNqIcDnG9P2EHJ8MBat8Uj/QV4nbY10LP0e\nOWmTw5dmIxMB9jwzkwBbRR8+ASNuK6UQy23/REvcboQQaLWGfRKnMbvBQ3CDfuoe9GFO6Y04hjsZ\nwSn1ozUE2ZqvYQp0DAG+kWXZrwJ4S5Zl77bfbJrm62/Psl6bgyOLDpgbXGE5Xbx6uO4mTWPfGmJf\n3anrGCFHpG89HM2PrSGUCVeIYBjF3gQC0JhTy8uw+il9KVQ2dy9hfwJAH+taZdj1c+vHB4SRf+PF\nKS5bRt5Fs7GFHZYWgjsdDTsIsC40MrdErpYWgkwZfSOIrrYa1c3sB7lpKbRmr+NuwHO8rPCmyzPk\ng6xD83YGsIzgU8539ouOZ9Fp/tRzr8cQJzF/ayiZGvMZzpRIFoWpaDHl3BByF8tAb6o4BTqUyWft\neSExEg+Cr4/BoFUFDwTQfUWwUhBgWq99vXTEKj7f7YzF5oeSKSl10D56KKumL7Dv+xKGxvxYPTtD\nmTYWFIg17JHQitmNWPu9ADIUEwHTj2Ffh+EgQz7IDASYEqcPHYzxKa1dkMt+2vuAq/RlYak063bD\nJ4Ila4Qd1GHd9ujMosOhYKDZzB+67nSOTb3FstyK8qD5CLc0u1F67tcUESx34jSBOeR53niJlrDd\nASLt8/YUjIsxj6J2g8F2DD2vHF87lIwguxmyG4B/z+OU+on3PRRo8tW5ormvQQr0fwXgjwH4aQD/\n6PYv57U9uJQEvZbmcKJeJ+QyjgTshwCH2viwlelCqqy1vy2LnB9QKWTL03trO+LfIaoiHQuAIxnW\nmEIfi0JdiUb3ruswsepKmqbB//qLT+BPfcnD+Jq3P6gdo3s/jYaDDoX6ZFnh4rTA0bTAshRZ8lxD\n6Y1+jlYt2MqBAOsU41W5NeqsyGGhWi2bQl0MhZL00oEGAMIRWlVb7HYNBi0ToVu/awY8210jWm7M\nRnjgYISb5ybK7Ws7wlKB9iBXHPSVzu8LIEMqlmr+DpdmESpbJBMfCkCjjky1xfhw7H0/KoK13eHi\nKE599ddy8SnQzgCWMZ+O4QugAV4mPkQfThEzOeysIQHB9TB/OO37vPNl8peRBAggwDFV19C+qTQT\nwqjUuYOGDjCZQ4wAWqyhf0JLIIM+5hGnhtj/W3D3tLXDbsj52u9/2gbADxxYpTOORLq9F9nih/PR\n0DiGnTi12yipxKt4XSapastutMiwTsE+nBRuu2EFftT398K0wMVZgZtLs/2ee983+9QDgnG0qXd4\n5OLUmu8OoPXr5BuhAJKXaPHbHa7dmIcC2GIg2S3O+UztCK+fyBT+26/0Jpz0iyVugZD2A89u+EqQ\n2AgwU4vkbhzBb940Tdk0zQcAfHXTNL9p//cqrfE1MySVju2ImDdkCoUa8ASwjIc61M/Qp0zoWoPr\ngWqahumM+R3adcVRsub0BQ1TqMOOTBgVGueDIIU5FkDHRLjoGCJYdTS6twzc7z9/jB99/9P4tp98\nrHMM+36yf/+maWQmnwwqBaeu72E7Ca4+vnrwuiitTP7InC8D6MJ0dnQV6OWmdmbyfd/RDnjO1hWa\nBrg4LXB5Pu7Uq7nuFY6zSvNdzwubAh2r5eJQqKO1XHtQoCPOlA8JsdcQFiPZJ5OfIGbiCd5igZs4\nRsQR6cl6UYnTOPpJ63Udg4/g+ijQ4fkhFeKUejRvAFu/Cv2gAwGkZA4FRbT2RIAjAWjMfrISp4Hf\nIlbPrx/DmRS0EOTjVYmLswIXWwGrXVvW5aoJt/fDlYXgzkY5FqXJHJpqzBa7PZ5TxCofYG0kTmvt\n+C674U6cygB4qQLgo0lhINQpFOj/7icew3/x/b9h7IFe5lFkv5TzgyrQ8fKdsN3hBMDxZJGv9ZyY\nvz8FmrPn7VN6Ywt+ps4H/GBJWhukUOlNf9t3t4/glcuy7J+0f/5YlmXvtv97Fdb3mhp8R8aNRvCd\niJAjxEczQoX9fR3SatugaeLzQwEgJ4gP9gVlbAzjSAAau46jiCMTp1Dv197GRoCfeOlUztE3S584\nzqRQBnJRblHvGlycqQCY2gy56Oj2/duhMI/yDnqrOzIKQW4D6GqL0XBgUNGmI9VKomkaLDUK9Gxs\nqkQ7e1ZaCPBx68hcnBW4YPcR9gSAMWdXzvfcrzEKl5ofUoHmObxxNc8YBTqGeoUcmXgATZ9znp8V\n+OwnghXsx8jYb8Qa3M98EgXaqQaaWMtlHaNpGpYgTIgK98pdg/i+7923WTRufwDLRYC9FOwIehs7\nv36M0L4fSpzG7GfMbsXW4LL7f3DlxFDtB8IIsIsCfTQt0DTAeRvAupIRtnijSztiZZW2uLQnfCrQ\ngGk3tjvxXBBCbFOoXQikrVR9vFJ2Yz4eGiJaPgRzkg87+hUfu3KCatvgEy+aNHFf4pXeD43QM8v1\nL3wsO07LrVjSLBZ4sUWw9hE/LEKME17Cjc5lj5jQqn6MUOkMZ8+rtg22lmYQv4Y4Tme/W0eMAv3T\n7f9/4HYv5P7gB4++uoJkR8hTT3ZxNoqu1Udh5tcAhwv7+yrbiWNw+ruF+oLGEwnjYmj0HHQdI6YG\nqgdRvjUEM7ScwMY33wrOnr2h2vq8fLLBH3lg1h7Dh06qTVmneR1MxJZCNEGnmInFYFhVJhVNODKm\n2qaO7koEmeaX284mPimG8n0RfGlIgawRrgGMnZlkG/nUHZmDcYErt7SelV4KdPce/Qfv/gRO1xX+\n0Td+pUTm/Zl8Xu0Nx5FxKf/K+YHgJ9SHUJ8fpkArJ8B1L8WCp1DJBR03Xovld+jWlb8GmkaYyrZn\nJp+buNwXAfY4xgq55CVe90qcempIFR1vjxremlf+41LSBsR1dKm5G/MDiUsOcyhW+kLCQH7mUKz0\nJmw3RvnAWwvPWYMdgF872+DP/bP34yu/4AJ+4Tu/xliH6360ExjHS9E+77C1G2frGkeTwukL2cwj\nuz/8fGzWANvJWxvBpQDYVpqWdqX9HIljTS0E2WU37B68xxoCfDAuDPq8D8G0nzgc0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VTUeA3QiycqRc15ucCJ+hmEQCWP37uRFgIYYSul/EZ0RLjXrXGPVms/Y7hii4esCjMvlDHI5F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\nRERERKRbUAAsIiIiIiIi3cL/Azi4el2SJI4HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f43e94489d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=rt*np.cos(ut)\n",
    "y=rt*np.sin(ut)\n",
    "\n",
    "#True Orbit\n",
    "ee=0.0167\n",
    "phi=np.linspace(0.,2.*np.pi,len(x))\n",
    "rr=(1.-ee**2)/(1.+ee*np.cos(phi))\n",
    "xx=rr*np.cos(phi)\n",
    "yy=rr*np.sin(phi)\n",
    "\n",
    "fig=plt.figure(figsize=(16,12))\n",
    "gs=gridspec.GridSpec(3,4)\n",
    "ax1=plt.subplot(gs[0:2,0:2])\n",
    "ax1.plot(x,y,label='Earth Orbit (numerical)')\n",
    "ax1.plot([0],[0],'o',label='Sun Position')\n",
    "ax1.axis(xmin=-1.3,xmax=1.3,ymin=-1.3,ymax=1.3)\n",
    "ax1.set_ylabel('Y Position (au)')\n",
    "ax1.set_xlabel('X Position (au)')\n",
    "ax1.plot(xx,yy,label='Earth Orbit (true)',linestyle='--')\n",
    "ax1.legend(loc='best')\n",
    "ax2=plt.subplot(gs[2,:])\n",
    "#ax2.plot(T,vx,label='X Velocity')\n",
    "#ax2.plot(T,vy,label='Y Velocity')\n",
    "ax2.plot(t,np.abs(rt-rr),label='Error')\n",
    "ax2.set_ylabel('Difference (au)')\n",
    "ax2.set_xlabel('Time (days)')\n",
    "ax2.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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