Week0/PrimeNumbers/CalcAndPlotPrimeNumbers_original.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate Prime Numbers and Plot Them\n",
    "\n",
    "### Authors: \n",
    "- Christian Michelsen (Niels Bohr Institute)\n",
    "- Troels C. Petersen (Niels Bohr Institute)\n",
    "- Étienne Bourbeau (Niels Bohr Institute)\n",
    "\n",
    "### Date:    \n",
    "- 07-11-2019 (latest update)\n",
    "- 06-10-2015 (originally)\n",
    "\n",
    "***\n",
    "Script calculating all prime numbers up to 10000 and plots them in a histogram, effectively counting the number of primes in intervals of 100.\n",
    "***\n",
    "\n",
    "First, import the relevant packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np               \n",
    "import matplotlib.pyplot as plt\n",
    "from iminuit import Minuit\n",
    "import sys                                         # Modules to see files and folders in directories\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.path.append('../../External_Functions')\n",
    "from ExternalFunctions import Chi2Regression, nice_string_output, add_text_to_ax # useful functions to print fit results on figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decide whether or not the program should save the plot along with the maxmimum prime number and the starting point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "save_plots = True\n",
    "Nmax = 10000              # Maximum prime number\n",
    "N    = 2                  # Starting value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Main program:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating prime numbers comes down to taking a number (here `N`), and testing if it is prime by dividing it by all numbers up the the square root of it. If no number divides `N` (tested using the `%` operator, which returns the remainder: `6%3 = 0`, `5%2 = 1`, etc.), then `N` is prime!\n",
    "***\n",
    "See if you can follow this in python program form below. There are only 9 lines in total! The central part consists of a While-loop, which loops as long as the statement is true. It is true to begin with (`N=2`, `Nmax = 10000`), but at some point `N` will have increased enough to equal `Nmax`, and the looping stops.\n",
    "***\n",
    "We start by creating empty list for primes. We dont create a numpy array since we don't know the size of it before creation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I got a prime 2\n",
      "I got a prime 3\n",
      "I got a prime 5\n",
      "I got a prime 7\n",
      "I got a prime 11\n",
      "I got a prime 13\n",
      "I got a prime 17\n",
      "I got a prime 19\n",
      "I got a prime 23\n",
      "I got a prime 29\n",
      "I got a prime 31\n",
      "I got a prime 37\n",
      "I got a prime 41\n",
      "I got a prime 43\n",
      "I got a prime 47\n",
      "I got a prime 53\n",
      "I got a prime 59\n",
      "I got a prime 61\n",
      "I got a prime 67\n",
      "I got a prime 71\n",
      "I got a prime 73\n",
      "I got a prime 79\n",
      "I got a prime 83\n",
      "I got a prime 89\n",
      "I got a prime 97\n",
      "I got a prime 101\n",
      "I got a prime 103\n",
      "I got a prime 107\n",
      "I got a prime 109\n",
      "I got a prime 113\n",
      "I got a prime 127\n",
      "I got a prime 131\n",
      "I got a prime 137\n",
      "I got a prime 139\n",
      "I got a prime 149\n",
      "I got a prime 151\n",
      "I got a prime 157\n",
      "I got a prime 163\n",
      "I got a prime 167\n",
      "I got a prime 173\n",
      "I got a prime 179\n",
      "I got a prime 181\n",
      "I got a prime 191\n",
      "I got a prime 193\n",
      "I got a prime 197\n",
      "I got a prime 199\n",
      "I got a prime 211\n",
      "I got a prime 223\n",
      "I got a prime 227\n",
      "I got a prime 229\n",
      "I got a prime 233\n",
      "I got a prime 239\n",
      "I got a prime 241\n",
      "I got a prime 251\n",
      "I got a prime 257\n",
      "I got a prime 263\n",
      "I got a prime 269\n",
      "I got a prime 271\n",
      "I got a prime 277\n",
      "I got a prime 281\n",
      "I got a prime 283\n",
      "I got a prime 293\n",
      "I got a prime 307\n",
      "I got a prime 311\n",
      "I got a prime 313\n",
      "I got a prime 317\n",
      "I got a prime 331\n",
      "I got a prime 337\n",
      "I got a prime 347\n",
      "I got a prime 349\n",
      "I got a prime 353\n",
      "I got a prime 359\n",
      "I got a prime 367\n",
      "I got a prime 373\n",
      "I got a prime 379\n",
      "I got a prime 383\n",
      "I got a prime 389\n",
      "I got a prime 397\n",
      "I got a prime 401\n",
      "I got a prime 409\n",
      "I got a prime 419\n",
      "I got a prime 421\n",
      "I got a prime 431\n",
      "I got a prime 433\n",
      "I got a prime 439\n",
      "I got a prime 443\n",
      "I got a prime 449\n",
      "I got a prime 457\n",
      "I got a prime 461\n",
      "I got a prime 463\n",
      "I got a prime 467\n",
      "I got a prime 479\n",
      "I got a prime 487\n",
      "I got a prime 491\n",
      "I got a prime 499\n",
      "I got a prime 503\n",
      "I got a prime 509\n",
      "I got a prime 521\n",
      "I got a prime 523\n",
      "I got a prime 541\n",
      "I got a prime 547\n",
      "I got a prime 557\n",
      "I got a prime 563\n",
      "I got a prime 569\n",
      "I got a prime 571\n",
      "I got a prime 577\n",
      "I got a prime 587\n",
      "I got a prime 593\n",
      "I got a prime 599\n",
      "I got a prime 601\n",
      "I got a prime 607\n",
      "I got a prime 613\n",
      "I got a prime 617\n",
      "I got a prime 619\n",
      "I got a prime 631\n",
      "I got a prime 641\n",
      "I got a prime 643\n",
      "I got a prime 647\n",
      "I got a prime 653\n",
      "I got a prime 659\n",
      "I got a prime 661\n",
      "I got a prime 673\n",
      "I got a prime 677\n",
      "I got a prime 683\n",
      "I got a prime 691\n",
      "I got a prime 701\n",
      "I got a prime 709\n",
      "I got a prime 719\n",
      "I got a prime 727\n",
      "I got a prime 733\n",
      "I got a prime 739\n",
      "I got a prime 743\n",
      "I got a prime 751\n",
      "I got a prime 757\n",
      "I got a prime 761\n",
      "I got a prime 769\n",
      "I got a prime 773\n",
      "I got a prime 787\n",
      "I got a prime 797\n",
      "I got a prime 809\n",
      "I got a prime 811\n",
      "I got a prime 821\n",
      "I got a prime 823\n",
      "I got a prime 827\n",
      "I got a prime 829\n",
      "I got a prime 839\n",
      "I got a prime 853\n",
      "I got a prime 857\n",
      "I got a prime 859\n",
      "I got a prime 863\n",
      "I got a prime 877\n",
      "I got a prime 881\n",
      "I got a prime 883\n",
      "I got a prime 887\n",
      "I got a prime 907\n",
      "I got a prime 911\n",
      "I got a prime 919\n",
      "I got a prime 929\n",
      "I got a prime 937\n",
      "I got a prime 941\n",
      "I got a prime 947\n",
      "I got a prime 953\n",
      "I got a prime 967\n",
      "I got a prime 971\n",
      "I got a prime 977\n",
      "I got a prime 983\n",
      "I got a prime 991\n",
      "I got a prime 997\n",
      "I got a prime 1009\n",
      "I got a prime 1013\n",
      "I got a prime 1019\n",
      "I got a prime 1021\n",
      "I got a prime 1031\n",
      "I got a prime 1033\n",
      "I got a prime 1039\n",
      "I got a prime 1049\n",
      "I got a prime 1051\n",
      "I got a prime 1061\n",
      "I got a prime 1063\n",
      "I got a prime 1069\n",
      "I got a prime 1087\n",
      "I got a prime 1091\n",
      "I got a prime 1093\n",
      "I got a prime 1097\n",
      "I got a prime 1103\n",
      "I got a prime 1109\n",
      "I got a prime 1117\n",
      "I got a prime 1123\n",
      "I got a prime 1129\n",
      "I got a prime 1151\n",
      "I got a prime 1153\n",
      "I got a prime 1163\n",
      "I got a prime 1171\n",
      "I got a prime 1181\n",
      "I got a prime 1187\n",
      "I got a prime 1193\n",
      "I got a prime 1201\n",
      "I got a prime 1213\n",
      "I got a prime 1217\n",
      "I got a prime 1223\n",
      "I got a prime 1229\n",
      "I got a prime 1231\n",
      "I got a prime 1237\n",
      "I got a prime 1249\n",
      "I got a prime 1259\n",
      "I got a prime 1277\n",
      "I got a prime 1279\n",
      "I got a prime 1283\n",
      "I got a prime 1289\n",
      "I got a prime 1291\n",
      "I got a prime 1297\n",
      "I got a prime 1301\n",
      "I got a prime 1303\n",
      "I got a prime 1307\n",
      "I got a prime 1319\n",
      "I got a prime 1321\n",
      "I got a prime 1327\n",
      "I got a prime 1361\n",
      "I got a prime 1367\n",
      "I got a prime 1373\n",
      "I got a prime 1381\n",
      "I got a prime 1399\n",
      "I got a prime 1409\n",
      "I got a prime 1423\n",
      "I got a prime 1427\n",
      "I got a prime 1429\n",
      "I got a prime 1433\n",
      "I got a prime 1439\n",
      "I got a prime 1447\n",
      "I got a prime 1451\n",
      "I got a prime 1453\n",
      "I got a prime 1459\n",
      "I got a prime 1471\n",
      "I got a prime 1481\n",
      "I got a prime 1483\n",
      "I got a prime 1487\n",
      "I got a prime 1489\n",
      "I got a prime 1493\n",
      "I got a prime 1499\n",
      "I got a prime 1511\n",
      "I got a prime 1523\n",
      "I got a prime 1531\n",
      "I got a prime 1543\n",
      "I got a prime 1549\n",
      "I got a prime 1553\n",
      "I got a prime 1559\n",
      "I got a prime 1567\n",
      "I got a prime 1571\n",
      "I got a prime 1579\n",
      "I got a prime 1583\n",
      "I got a prime 1597\n",
      "I got a prime 1601\n",
      "I got a prime 1607\n",
      "I got a prime 1609\n",
      "I got a prime 1613\n",
      "I got a prime 1619\n",
      "I got a prime 1621\n",
      "I got a prime 1627\n",
      "I got a prime 1637\n",
      "I got a prime 1657\n",
      "I got a prime 1663\n",
      "I got a prime 1667\n",
      "I got a prime 1669\n",
      "I got a prime 1693\n",
      "I got a prime 1697\n",
      "I got a prime 1699\n",
      "I got a prime 1709\n",
      "I got a prime 1721\n",
      "I got a prime 1723\n",
      "I got a prime 1733\n",
      "I got a prime 1741\n",
      "I got a prime 1747\n",
      "I got a prime 1753\n",
      "I got a prime 1759\n",
      "I got a prime 1777\n",
      "I got a prime 1783\n",
      "I got a prime 1787\n",
      "I got a prime 1789\n",
      "I got a prime 1801\n",
      "I got a prime 1811\n",
      "I got a prime 1823\n",
      "I got a prime 1831\n",
      "I got a prime 1847\n",
      "I got a prime 1861\n",
      "I got a prime 1867\n",
      "I got a prime 1871\n",
      "I got a prime 1873\n",
      "I got a prime 1877\n",
      "I got a prime 1879\n",
      "I got a prime 1889\n",
      "I got a prime 1901\n",
      "I got a prime 1907\n",
      "I got a prime 1913\n",
      "I got a prime 1931\n",
      "I got a prime 1933\n",
      "I got a prime 1949\n",
      "I got a prime 1951\n",
      "I got a prime 1973\n",
      "I got a prime 1979\n",
      "I got a prime 1987\n",
      "I got a prime 1993\n",
      "I got a prime 1997\n",
      "I got a prime 1999\n",
      "I got a prime 2003\n",
      "I got a prime 2011\n",
      "I got a prime 2017\n",
      "I got a prime 2027\n",
      "I got a prime 2029\n",
      "I got a prime 2039\n",
      "I got a prime 2053\n",
      "I got a prime 2063\n",
      "I got a prime 2069\n",
      "I got a prime 2081\n",
      "I got a prime 2083\n",
      "I got a prime 2087\n",
      "I got a prime 2089\n",
      "I got a prime 2099\n",
      "I got a prime 2111\n",
      "I got a prime 2113\n",
      "I got a prime 2129\n",
      "I got a prime 2131\n",
      "I got a prime 2137\n",
      "I got a prime 2141\n",
      "I got a prime 2143\n",
      "I got a prime 2153\n",
      "I got a prime 2161\n",
      "I got a prime 2179\n",
      "I got a prime 2203\n",
      "I got a prime 2207\n",
      "I got a prime 2213\n",
      "I got a prime 2221\n",
      "I got a prime 2237\n",
      "I got a prime 2239\n",
      "I got a prime 2243\n",
      "I got a prime 2251\n",
      "I got a prime 2267\n",
      "I got a prime 2269\n",
      "I got a prime 2273\n",
      "I got a prime 2281\n",
      "I got a prime 2287\n",
      "I got a prime 2293\n",
      "I got a prime 2297\n",
      "I got a prime 2309\n",
      "I got a prime 2311\n",
      "I got a prime 2333\n",
      "I got a prime 2339\n",
      "I got a prime 2341\n",
      "I got a prime 2347\n",
      "I got a prime 2351\n",
      "I got a prime 2357\n",
      "I got a prime 2371\n",
      "I got a prime 2377\n",
      "I got a prime 2381\n",
      "I got a prime 2383\n",
      "I got a prime 2389\n",
      "I got a prime 2393\n",
      "I got a prime 2399\n",
      "I got a prime 2411\n",
      "I got a prime 2417\n",
      "I got a prime 2423\n",
      "I got a prime 2437\n",
      "I got a prime 2441\n",
      "I got a prime 2447\n",
      "I got a prime 2459\n",
      "I got a prime 2467\n",
      "I got a prime 2473\n",
      "I got a prime 2477\n",
      "I got a prime 2503\n",
      "I got a prime 2521\n",
      "I got a prime 2531\n",
      "I got a prime 2539\n",
      "I got a prime 2543\n",
      "I got a prime 2549\n",
      "I got a prime 2551\n",
      "I got a prime 2557\n",
      "I got a prime 2579\n",
      "I got a prime 2591\n",
      "I got a prime 2593\n",
      "I got a prime 2609\n",
      "I got a prime 2617\n",
      "I got a prime 2621\n",
      "I got a prime 2633\n",
      "I got a prime 2647\n",
      "I got a prime 2657\n",
      "I got a prime 2659\n",
      "I got a prime 2663\n",
      "I got a prime 2671\n",
      "I got a prime 2677\n",
      "I got a prime 2683\n",
      "I got a prime 2687\n",
      "I got a prime 2689\n",
      "I got a prime 2693\n",
      "I got a prime 2699\n",
      "I got a prime 2707\n",
      "I got a prime 2711\n",
      "I got a prime 2713\n",
      "I got a prime 2719\n",
      "I got a prime 2729\n",
      "I got a prime 2731\n",
      "I got a prime 2741\n",
      "I got a prime 2749\n",
      "I got a prime 2753\n",
      "I got a prime 2767\n",
      "I got a prime 2777\n",
      "I got a prime 2789\n",
      "I got a prime 2791\n",
      "I got a prime 2797\n",
      "I got a prime 2801\n",
      "I got a prime 2803\n",
      "I got a prime 2819\n",
      "I got a prime 2833\n",
      "I got a prime 2837\n",
      "I got a prime 2843\n",
      "I got a prime 2851\n",
      "I got a prime 2857\n",
      "I got a prime 2861\n",
      "I got a prime 2879\n",
      "I got a prime 2887\n",
      "I got a prime 2897\n",
      "I got a prime 2903\n",
      "I got a prime 2909\n",
      "I got a prime 2917\n",
      "I got a prime 2927\n",
      "I got a prime 2939\n",
      "I got a prime 2953\n",
      "I got a prime 2957\n",
      "I got a prime 2963\n",
      "I got a prime 2969\n",
      "I got a prime 2971\n",
      "I got a prime 2999\n",
      "I got a prime 3001\n",
      "I got a prime 3011\n",
      "I got a prime 3019\n",
      "I got a prime 3023\n",
      "I got a prime 3037\n",
      "I got a prime 3041\n",
      "I got a prime 3049\n",
      "I got a prime 3061\n",
      "I got a prime 3067\n",
      "I got a prime 3079\n",
      "I got a prime 3083\n",
      "I got a prime 3089\n",
      "I got a prime 3109\n",
      "I got a prime 3119\n",
      "I got a prime 3121\n",
      "I got a prime 3137\n",
      "I got a prime 3163\n",
      "I got a prime 3167\n",
      "I got a prime 3169\n",
      "I got a prime 3181\n",
      "I got a prime 3187\n",
      "I got a prime 3191\n",
      "I got a prime 3203\n",
      "I got a prime 3209\n",
      "I got a prime 3217\n",
      "I got a prime 3221\n",
      "I got a prime 3229\n",
      "I got a prime 3251\n",
      "I got a prime 3253\n",
      "I got a prime 3257\n",
      "I got a prime 3259\n",
      "I got a prime 3271\n",
      "I got a prime 3299\n",
      "I got a prime 3301\n",
      "I got a prime 3307\n",
      "I got a prime 3313\n",
      "I got a prime 3319\n",
      "I got a prime 3323\n",
      "I got a prime 3329\n",
      "I got a prime 3331\n",
      "I got a prime 3343\n",
      "I got a prime 3347\n",
      "I got a prime 3359\n",
      "I got a prime 3361\n",
      "I got a prime 3371\n",
      "I got a prime 3373\n",
      "I got a prime 3389\n",
      "I got a prime 3391\n",
      "I got a prime 3407\n",
      "I got a prime 3413\n",
      "I got a prime 3433\n",
      "I got a prime 3449\n",
      "I got a prime 3457\n",
      "I got a prime 3461\n",
      "I got a prime 3463\n",
      "I got a prime 3467\n",
      "I got a prime 3469\n",
      "I got a prime 3491\n",
      "I got a prime 3499\n",
      "I got a prime 3511\n",
      "I got a prime 3517\n",
      "I got a prime 3527\n",
      "I got a prime 3529\n",
      "I got a prime 3533\n",
      "I got a prime 3539\n",
      "I got a prime 3541\n",
      "I got a prime 3547\n",
      "I got a prime 3557\n",
      "I got a prime 3559\n",
      "I got a prime 3571\n",
      "I got a prime 3581\n",
      "I got a prime 3583\n",
      "I got a prime 3593\n",
      "I got a prime 3607\n",
      "I got a prime 3613\n",
      "I got a prime 3617\n",
      "I got a prime 3623\n",
      "I got a prime 3631\n",
      "I got a prime 3637\n",
      "I got a prime 3643\n",
      "I got a prime 3659\n",
      "I got a prime 3671\n",
      "I got a prime 3673\n",
      "I got a prime 3677\n",
      "I got a prime 3691\n",
      "I got a prime 3697\n",
      "I got a prime 3701\n",
      "I got a prime 3709\n",
      "I got a prime 3719\n",
      "I got a prime 3727\n",
      "I got a prime 3733\n",
      "I got a prime 3739\n",
      "I got a prime 3761\n",
      "I got a prime 3767\n",
      "I got a prime 3769\n",
      "I got a prime 3779\n",
      "I got a prime 3793\n",
      "I got a prime 3797\n",
      "I got a prime 3803\n",
      "I got a prime 3821\n",
      "I got a prime 3823\n",
      "I got a prime 3833\n",
      "I got a prime 3847\n",
      "I got a prime 3851\n",
      "I got a prime 3853\n",
      "I got a prime 3863\n",
      "I got a prime 3877\n",
      "I got a prime 3881\n",
      "I got a prime 3889\n",
      "I got a prime 3907\n",
      "I got a prime 3911\n",
      "I got a prime 3917\n",
      "I got a prime 3919\n",
      "I got a prime 3923\n",
      "I got a prime 3929\n",
      "I got a prime 3931\n",
      "I got a prime 3943\n",
      "I got a prime 3947\n",
      "I got a prime 3967\n",
      "I got a prime 3989\n",
      "I got a prime 4001\n",
      "I got a prime 4003\n",
      "I got a prime 4007\n",
      "I got a prime 4013\n",
      "I got a prime 4019\n",
      "I got a prime 4021\n",
      "I got a prime 4027\n",
      "I got a prime 4049\n",
      "I got a prime 4051\n",
      "I got a prime 4057\n",
      "I got a prime 4073\n",
      "I got a prime 4079\n",
      "I got a prime 4091\n",
      "I got a prime 4093\n",
      "I got a prime 4099\n",
      "I got a prime 4111\n",
      "I got a prime 4127\n",
      "I got a prime 4129\n",
      "I got a prime 4133\n",
      "I got a prime 4139\n",
      "I got a prime 4153\n",
      "I got a prime 4157\n",
      "I got a prime 4159\n",
      "I got a prime 4177\n",
      "I got a prime 4201\n",
      "I got a prime 4211\n",
      "I got a prime 4217\n",
      "I got a prime 4219\n",
      "I got a prime 4229\n",
      "I got a prime 4231\n",
      "I got a prime 4241\n",
      "I got a prime 4243\n",
      "I got a prime 4253\n",
      "I got a prime 4259\n",
      "I got a prime 4261\n",
      "I got a prime 4271\n",
      "I got a prime 4273\n",
      "I got a prime 4283\n",
      "I got a prime 4289\n",
      "I got a prime 4297\n",
      "I got a prime 4327\n",
      "I got a prime 4337\n",
      "I got a prime 4339\n",
      "I got a prime 4349\n",
      "I got a prime 4357\n",
      "I got a prime 4363\n",
      "I got a prime 4373\n",
      "I got a prime 4391\n",
      "I got a prime 4397\n",
      "I got a prime 4409\n",
      "I got a prime 4421\n",
      "I got a prime 4423\n",
      "I got a prime 4441\n",
      "I got a prime 4447\n",
      "I got a prime 4451\n",
      "I got a prime 4457\n",
      "I got a prime 4463\n",
      "I got a prime 4481\n",
      "I got a prime 4483\n",
      "I got a prime 4493\n",
      "I got a prime 4507\n",
      "I got a prime 4513\n",
      "I got a prime 4517\n",
      "I got a prime 4519\n",
      "I got a prime 4523\n",
      "I got a prime 4547\n",
      "I got a prime 4549\n",
      "I got a prime 4561\n",
      "I got a prime 4567\n",
      "I got a prime 4583\n",
      "I got a prime 4591\n",
      "I got a prime 4597\n",
      "I got a prime 4603\n",
      "I got a prime 4621\n",
      "I got a prime 4637\n",
      "I got a prime 4639\n",
      "I got a prime 4643\n",
      "I got a prime 4649\n",
      "I got a prime 4651\n",
      "I got a prime 4657\n",
      "I got a prime 4663\n",
      "I got a prime 4673\n",
      "I got a prime 4679\n",
      "I got a prime 4691\n",
      "I got a prime 4703\n",
      "I got a prime 4721\n",
      "I got a prime 4723\n",
      "I got a prime 4729\n",
      "I got a prime 4733\n",
      "I got a prime 4751\n",
      "I got a prime 4759\n",
      "I got a prime 4783\n",
      "I got a prime 4787\n",
      "I got a prime 4789\n",
      "I got a prime 4793\n",
      "I got a prime 4799\n",
      "I got a prime 4801\n",
      "I got a prime 4813\n",
      "I got a prime 4817\n",
      "I got a prime 4831\n",
      "I got a prime 4861\n",
      "I got a prime 4871\n",
      "I got a prime 4877\n",
      "I got a prime 4889\n",
      "I got a prime 4903\n",
      "I got a prime 4909\n",
      "I got a prime 4919\n",
      "I got a prime 4931\n",
      "I got a prime 4933\n",
      "I got a prime 4937\n",
      "I got a prime 4943\n",
      "I got a prime 4951\n",
      "I got a prime 4957\n",
      "I got a prime 4967\n",
      "I got a prime 4969\n",
      "I got a prime 4973\n",
      "I got a prime 4987\n",
      "I got a prime 4993\n",
      "I got a prime 4999\n",
      "I got a prime 5003\n",
      "I got a prime 5009\n",
      "I got a prime 5011\n",
      "I got a prime 5021\n",
      "I got a prime 5023\n",
      "I got a prime 5039\n",
      "I got a prime 5051\n",
      "I got a prime 5059\n",
      "I got a prime 5077\n",
      "I got a prime 5081\n",
      "I got a prime 5087\n",
      "I got a prime 5099\n",
      "I got a prime 5101\n",
      "I got a prime 5107\n",
      "I got a prime 5113\n",
      "I got a prime 5119\n",
      "I got a prime 5147\n",
      "I got a prime 5153\n",
      "I got a prime 5167\n",
      "I got a prime 5171\n",
      "I got a prime 5179\n",
      "I got a prime 5189\n",
      "I got a prime 5197\n",
      "I got a prime 5209\n",
      "I got a prime 5227\n",
      "I got a prime 5231\n",
      "I got a prime 5233\n",
      "I got a prime 5237\n",
      "I got a prime 5261\n",
      "I got a prime 5273\n",
      "I got a prime 5279\n",
      "I got a prime 5281\n",
      "I got a prime 5297\n",
      "I got a prime 5303\n",
      "I got a prime 5309\n",
      "I got a prime 5323\n",
      "I got a prime 5333\n",
      "I got a prime 5347\n",
      "I got a prime 5351\n",
      "I got a prime 5381\n",
      "I got a prime 5387\n",
      "I got a prime 5393\n",
      "I got a prime 5399\n",
      "I got a prime 5407\n",
      "I got a prime 5413\n",
      "I got a prime 5417\n",
      "I got a prime 5419\n",
      "I got a prime 5431\n",
      "I got a prime 5437\n",
      "I got a prime 5441\n",
      "I got a prime 5443\n",
      "I got a prime 5449\n",
      "I got a prime 5471\n",
      "I got a prime 5477\n",
      "I got a prime 5479\n",
      "I got a prime 5483\n",
      "I got a prime 5501\n",
      "I got a prime 5503\n",
      "I got a prime 5507\n",
      "I got a prime 5519\n",
      "I got a prime 5521\n",
      "I got a prime 5527\n",
      "I got a prime 5531\n",
      "I got a prime 5557\n",
      "I got a prime 5563\n",
      "I got a prime 5569\n",
      "I got a prime 5573\n",
      "I got a prime 5581\n",
      "I got a prime 5591\n",
      "I got a prime 5623\n",
      "I got a prime 5639\n",
      "I got a prime 5641\n",
      "I got a prime 5647\n",
      "I got a prime 5651\n",
      "I got a prime 5653\n",
      "I got a prime 5657\n",
      "I got a prime 5659\n",
      "I got a prime 5669\n",
      "I got a prime 5683\n",
      "I got a prime 5689\n",
      "I got a prime 5693\n",
      "I got a prime 5701\n",
      "I got a prime 5711\n",
      "I got a prime 5717\n",
      "I got a prime 5737\n",
      "I got a prime 5741\n",
      "I got a prime 5743\n",
      "I got a prime 5749\n",
      "I got a prime 5779\n",
      "I got a prime 5783\n",
      "I got a prime 5791\n",
      "I got a prime 5801\n",
      "I got a prime 5807\n",
      "I got a prime 5813\n",
      "I got a prime 5821\n",
      "I got a prime 5827\n",
      "I got a prime 5839\n",
      "I got a prime 5843\n",
      "I got a prime 5849\n",
      "I got a prime 5851\n",
      "I got a prime 5857\n",
      "I got a prime 5861\n",
      "I got a prime 5867\n",
      "I got a prime 5869\n",
      "I got a prime 5879\n",
      "I got a prime 5881\n",
      "I got a prime 5897\n",
      "I got a prime 5903\n",
      "I got a prime 5923\n",
      "I got a prime 5927\n",
      "I got a prime 5939\n",
      "I got a prime 5953\n",
      "I got a prime 5981\n",
      "I got a prime 5987\n",
      "I got a prime 6007\n",
      "I got a prime 6011\n",
      "I got a prime 6029\n",
      "I got a prime 6037\n",
      "I got a prime 6043\n",
      "I got a prime 6047\n",
      "I got a prime 6053\n",
      "I got a prime 6067\n",
      "I got a prime 6073\n",
      "I got a prime 6079\n",
      "I got a prime 6089\n",
      "I got a prime 6091\n",
      "I got a prime 6101\n",
      "I got a prime 6113\n",
      "I got a prime 6121\n",
      "I got a prime 6131\n",
      "I got a prime 6133\n",
      "I got a prime 6143\n",
      "I got a prime 6151\n",
      "I got a prime 6163\n",
      "I got a prime 6173\n",
      "I got a prime 6197\n",
      "I got a prime 6199\n",
      "I got a prime 6203\n",
      "I got a prime 6211\n",
      "I got a prime 6217\n",
      "I got a prime 6221\n",
      "I got a prime 6229\n",
      "I got a prime 6247\n",
      "I got a prime 6257\n",
      "I got a prime 6263\n",
      "I got a prime 6269\n",
      "I got a prime 6271\n",
      "I got a prime 6277\n",
      "I got a prime 6287\n",
      "I got a prime 6299\n",
      "I got a prime 6301\n",
      "I got a prime 6311\n",
      "I got a prime 6317\n",
      "I got a prime 6323\n",
      "I got a prime 6329\n",
      "I got a prime 6337\n",
      "I got a prime 6343\n",
      "I got a prime 6353\n",
      "I got a prime 6359\n",
      "I got a prime 6361\n",
      "I got a prime 6367\n",
      "I got a prime 6373\n",
      "I got a prime 6379\n",
      "I got a prime 6389\n",
      "I got a prime 6397\n",
      "I got a prime 6421\n",
      "I got a prime 6427\n",
      "I got a prime 6449\n",
      "I got a prime 6451\n",
      "I got a prime 6469\n",
      "I got a prime 6473\n",
      "I got a prime 6481\n",
      "I got a prime 6491\n",
      "I got a prime 6521\n",
      "I got a prime 6529\n",
      "I got a prime 6547\n",
      "I got a prime 6551\n",
      "I got a prime 6553\n",
      "I got a prime 6563\n",
      "I got a prime 6569\n",
      "I got a prime 6571\n",
      "I got a prime 6577\n",
      "I got a prime 6581\n",
      "I got a prime 6599\n",
      "I got a prime 6607\n",
      "I got a prime 6619\n",
      "I got a prime 6637\n",
      "I got a prime 6653\n",
      "I got a prime 6659\n",
      "I got a prime 6661\n",
      "I got a prime 6673\n",
      "I got a prime 6679\n",
      "I got a prime 6689\n",
      "I got a prime 6691\n",
      "I got a prime 6701\n",
      "I got a prime 6703\n",
      "I got a prime 6709\n",
      "I got a prime 6719\n",
      "I got a prime 6733\n",
      "I got a prime 6737\n",
      "I got a prime 6761\n",
      "I got a prime 6763\n",
      "I got a prime 6779\n",
      "I got a prime 6781\n",
      "I got a prime 6791\n",
      "I got a prime 6793\n",
      "I got a prime 6803\n",
      "I got a prime 6823\n",
      "I got a prime 6827\n",
      "I got a prime 6829\n",
      "I got a prime 6833\n",
      "I got a prime 6841\n",
      "I got a prime 6857\n",
      "I got a prime 6863\n",
      "I got a prime 6869\n",
      "I got a prime 6871\n",
      "I got a prime 6883\n",
      "I got a prime 6899\n",
      "I got a prime 6907\n",
      "I got a prime 6911\n",
      "I got a prime 6917\n",
      "I got a prime 6947\n",
      "I got a prime 6949\n",
      "I got a prime 6959\n",
      "I got a prime 6961\n",
      "I got a prime 6967\n",
      "I got a prime 6971\n",
      "I got a prime 6977\n",
      "I got a prime 6983\n",
      "I got a prime 6991\n",
      "I got a prime 6997\n",
      "I got a prime 7001\n",
      "I got a prime 7013\n",
      "I got a prime 7019\n",
      "I got a prime 7027\n",
      "I got a prime 7039\n",
      "I got a prime 7043\n",
      "I got a prime 7057\n",
      "I got a prime 7069\n",
      "I got a prime 7079\n",
      "I got a prime 7103\n",
      "I got a prime 7109\n",
      "I got a prime 7121\n",
      "I got a prime 7127\n",
      "I got a prime 7129\n",
      "I got a prime 7151\n",
      "I got a prime 7159\n",
      "I got a prime 7177\n",
      "I got a prime 7187\n",
      "I got a prime 7193\n",
      "I got a prime 7207\n",
      "I got a prime 7211\n",
      "I got a prime 7213\n",
      "I got a prime 7219\n",
      "I got a prime 7229\n",
      "I got a prime 7237\n",
      "I got a prime 7243\n",
      "I got a prime 7247\n",
      "I got a prime 7253\n",
      "I got a prime 7283\n",
      "I got a prime 7297\n",
      "I got a prime 7307\n",
      "I got a prime 7309\n",
      "I got a prime 7321\n",
      "I got a prime 7331\n",
      "I got a prime 7333\n",
      "I got a prime 7349\n",
      "I got a prime 7351\n",
      "I got a prime 7369\n",
      "I got a prime 7393\n",
      "I got a prime 7411\n",
      "I got a prime 7417\n",
      "I got a prime 7433\n",
      "I got a prime 7451\n",
      "I got a prime 7457\n",
      "I got a prime 7459\n",
      "I got a prime 7477\n",
      "I got a prime 7481\n",
      "I got a prime 7487\n",
      "I got a prime 7489\n",
      "I got a prime 7499\n",
      "I got a prime 7507\n",
      "I got a prime 7517\n",
      "I got a prime 7523\n",
      "I got a prime 7529\n",
      "I got a prime 7537\n",
      "I got a prime 7541\n",
      "I got a prime 7547\n",
      "I got a prime 7549\n",
      "I got a prime 7559\n",
      "I got a prime 7561\n",
      "I got a prime 7573\n",
      "I got a prime 7577\n",
      "I got a prime 7583\n",
      "I got a prime 7589\n",
      "I got a prime 7591\n",
      "I got a prime 7603\n",
      "I got a prime 7607\n",
      "I got a prime 7621\n",
      "I got a prime 7639\n",
      "I got a prime 7643\n",
      "I got a prime 7649\n",
      "I got a prime 7669\n",
      "I got a prime 7673\n",
      "I got a prime 7681\n",
      "I got a prime 7687\n",
      "I got a prime 7691\n",
      "I got a prime 7699\n",
      "I got a prime 7703\n",
      "I got a prime 7717\n",
      "I got a prime 7723\n",
      "I got a prime 7727\n",
      "I got a prime 7741\n",
      "I got a prime 7753\n",
      "I got a prime 7757\n",
      "I got a prime 7759\n",
      "I got a prime 7789\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I got a prime 7793\n",
      "I got a prime 7817\n",
      "I got a prime 7823\n",
      "I got a prime 7829\n",
      "I got a prime 7841\n",
      "I got a prime 7853\n",
      "I got a prime 7867\n",
      "I got a prime 7873\n",
      "I got a prime 7877\n",
      "I got a prime 7879\n",
      "I got a prime 7883\n",
      "I got a prime 7901\n",
      "I got a prime 7907\n",
      "I got a prime 7919\n",
      "I got a prime 7927\n",
      "I got a prime 7933\n",
      "I got a prime 7937\n",
      "I got a prime 7949\n",
      "I got a prime 7951\n",
      "I got a prime 7963\n",
      "I got a prime 7993\n",
      "I got a prime 8009\n",
      "I got a prime 8011\n",
      "I got a prime 8017\n",
      "I got a prime 8039\n",
      "I got a prime 8053\n",
      "I got a prime 8059\n",
      "I got a prime 8069\n",
      "I got a prime 8081\n",
      "I got a prime 8087\n",
      "I got a prime 8089\n",
      "I got a prime 8093\n",
      "I got a prime 8101\n",
      "I got a prime 8111\n",
      "I got a prime 8117\n",
      "I got a prime 8123\n",
      "I got a prime 8147\n",
      "I got a prime 8161\n",
      "I got a prime 8167\n",
      "I got a prime 8171\n",
      "I got a prime 8179\n",
      "I got a prime 8191\n",
      "I got a prime 8209\n",
      "I got a prime 8219\n",
      "I got a prime 8221\n",
      "I got a prime 8231\n",
      "I got a prime 8233\n",
      "I got a prime 8237\n",
      "I got a prime 8243\n",
      "I got a prime 8263\n",
      "I got a prime 8269\n",
      "I got a prime 8273\n",
      "I got a prime 8287\n",
      "I got a prime 8291\n",
      "I got a prime 8293\n",
      "I got a prime 8297\n",
      "I got a prime 8311\n",
      "I got a prime 8317\n",
      "I got a prime 8329\n",
      "I got a prime 8353\n",
      "I got a prime 8363\n",
      "I got a prime 8369\n",
      "I got a prime 8377\n",
      "I got a prime 8387\n",
      "I got a prime 8389\n",
      "I got a prime 8419\n",
      "I got a prime 8423\n",
      "I got a prime 8429\n",
      "I got a prime 8431\n",
      "I got a prime 8443\n",
      "I got a prime 8447\n",
      "I got a prime 8461\n",
      "I got a prime 8467\n",
      "I got a prime 8501\n",
      "I got a prime 8513\n",
      "I got a prime 8521\n",
      "I got a prime 8527\n",
      "I got a prime 8537\n",
      "I got a prime 8539\n",
      "I got a prime 8543\n",
      "I got a prime 8563\n",
      "I got a prime 8573\n",
      "I got a prime 8581\n",
      "I got a prime 8597\n",
      "I got a prime 8599\n",
      "I got a prime 8609\n",
      "I got a prime 8623\n",
      "I got a prime 8627\n",
      "I got a prime 8629\n",
      "I got a prime 8641\n",
      "I got a prime 8647\n",
      "I got a prime 8663\n",
      "I got a prime 8669\n",
      "I got a prime 8677\n",
      "I got a prime 8681\n",
      "I got a prime 8689\n",
      "I got a prime 8693\n",
      "I got a prime 8699\n",
      "I got a prime 8707\n",
      "I got a prime 8713\n",
      "I got a prime 8719\n",
      "I got a prime 8731\n",
      "I got a prime 8737\n",
      "I got a prime 8741\n",
      "I got a prime 8747\n",
      "I got a prime 8753\n",
      "I got a prime 8761\n",
      "I got a prime 8779\n",
      "I got a prime 8783\n",
      "I got a prime 8803\n",
      "I got a prime 8807\n",
      "I got a prime 8819\n",
      "I got a prime 8821\n",
      "I got a prime 8831\n",
      "I got a prime 8837\n",
      "I got a prime 8839\n",
      "I got a prime 8849\n",
      "I got a prime 8861\n",
      "I got a prime 8863\n",
      "I got a prime 8867\n",
      "I got a prime 8887\n",
      "I got a prime 8893\n",
      "I got a prime 8923\n",
      "I got a prime 8929\n",
      "I got a prime 8933\n",
      "I got a prime 8941\n",
      "I got a prime 8951\n",
      "I got a prime 8963\n",
      "I got a prime 8969\n",
      "I got a prime 8971\n",
      "I got a prime 8999\n",
      "I got a prime 9001\n",
      "I got a prime 9007\n",
      "I got a prime 9011\n",
      "I got a prime 9013\n",
      "I got a prime 9029\n",
      "I got a prime 9041\n",
      "I got a prime 9043\n",
      "I got a prime 9049\n",
      "I got a prime 9059\n",
      "I got a prime 9067\n",
      "I got a prime 9091\n",
      "I got a prime 9103\n",
      "I got a prime 9109\n",
      "I got a prime 9127\n",
      "I got a prime 9133\n",
      "I got a prime 9137\n",
      "I got a prime 9151\n",
      "I got a prime 9157\n",
      "I got a prime 9161\n",
      "I got a prime 9173\n",
      "I got a prime 9181\n",
      "I got a prime 9187\n",
      "I got a prime 9199\n",
      "I got a prime 9203\n",
      "I got a prime 9209\n",
      "I got a prime 9221\n",
      "I got a prime 9227\n",
      "I got a prime 9239\n",
      "I got a prime 9241\n",
      "I got a prime 9257\n",
      "I got a prime 9277\n",
      "I got a prime 9281\n",
      "I got a prime 9283\n",
      "I got a prime 9293\n",
      "I got a prime 9311\n",
      "I got a prime 9319\n",
      "I got a prime 9323\n",
      "I got a prime 9337\n",
      "I got a prime 9341\n",
      "I got a prime 9343\n",
      "I got a prime 9349\n",
      "I got a prime 9371\n",
      "I got a prime 9377\n",
      "I got a prime 9391\n",
      "I got a prime 9397\n",
      "I got a prime 9403\n",
      "I got a prime 9413\n",
      "I got a prime 9419\n",
      "I got a prime 9421\n",
      "I got a prime 9431\n",
      "I got a prime 9433\n",
      "I got a prime 9437\n",
      "I got a prime 9439\n",
      "I got a prime 9461\n",
      "I got a prime 9463\n",
      "I got a prime 9467\n",
      "I got a prime 9473\n",
      "I got a prime 9479\n",
      "I got a prime 9491\n",
      "I got a prime 9497\n",
      "I got a prime 9511\n",
      "I got a prime 9521\n",
      "I got a prime 9533\n",
      "I got a prime 9539\n",
      "I got a prime 9547\n",
      "I got a prime 9551\n",
      "I got a prime 9587\n",
      "I got a prime 9601\n",
      "I got a prime 9613\n",
      "I got a prime 9619\n",
      "I got a prime 9623\n",
      "I got a prime 9629\n",
      "I got a prime 9631\n",
      "I got a prime 9643\n",
      "I got a prime 9649\n",
      "I got a prime 9661\n",
      "I got a prime 9677\n",
      "I got a prime 9679\n",
      "I got a prime 9689\n",
      "I got a prime 9697\n",
      "I got a prime 9719\n",
      "I got a prime 9721\n",
      "I got a prime 9733\n",
      "I got a prime 9739\n",
      "I got a prime 9743\n",
      "I got a prime 9749\n",
      "I got a prime 9767\n",
      "I got a prime 9769\n",
      "I got a prime 9781\n",
      "I got a prime 9787\n",
      "I got a prime 9791\n",
      "I got a prime 9803\n",
      "I got a prime 9811\n",
      "I got a prime 9817\n",
      "I got a prime 9829\n",
      "I got a prime 9833\n",
      "I got a prime 9839\n",
      "I got a prime 9851\n",
      "I got a prime 9857\n",
      "I got a prime 9859\n",
      "I got a prime 9871\n",
      "I got a prime 9883\n",
      "I got a prime 9887\n",
      "I got a prime 9901\n",
      "I got a prime 9907\n",
      "I got a prime 9923\n",
      "I got a prime 9929\n",
      "I got a prime 9931\n",
      "I got a prime 9941\n",
      "I got a prime 9949\n",
      "I got a prime 9967\n",
      "I got a prime 9973\n"
     ]
    }
   ],
   "source": [
    "primes = []\n",
    "\n",
    "while (N < Nmax):\n",
    "    # print(\"Potential Prime number I want to test: \", N)\n",
    "    hit = False                # Define a variable \"hit\", with starting value \"False\".\n",
    "\n",
    "    for i in range (2, int(np.sqrt(N)) + 1) :   # Loop over the possible divisors.\n",
    "        # print(\"  I'm testing the first number with the second and get the third: \", N, i, N%i)\n",
    "\n",
    "        if N%i == 0:           # If the remainder of the integer division is 0\n",
    "            hit = True         # hit = \"True\" (i.e. the number being tested had a divisor, and is not a prime)\n",
    "            break              # Skip the rest of the possible divisors.\n",
    "\n",
    "    if not hit:             # If no number gave a perfect integer division (i.e. with remainder 0)...\n",
    "        primes.append(N)\n",
    "        print(\"I got a prime\", N)   # ...the it is a prime number.\n",
    "\n",
    "    N += 1                     # Increase N by one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now convert the Python list into a Numpy array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 10 primes,  [ 2  3  5  7 11 13 17 19 23 29]\n"
     ]
    }
   ],
   "source": [
    "primes = np.array(primes)\n",
    "print(\"First 10 primes, \", primes[:10]) # prints the first 10 primes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that there are no even primes except 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  The even prime numbers are listed here:  [2]\n"
     ]
    }
   ],
   "source": [
    "print(\"  The even prime numbers are listed here: \", primes[(primes % 2) == 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Draw output:\n",
    "\n",
    "Having computed the prime numbers, we now try to plot the distribution of them to see if there are any interesting patterns. \n",
    "\n",
    "We first define the number of bins and the minimum/maximum x value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nbins = 100\n",
    "xmin = 0\n",
    "xmax = Nmax\n",
    "binwidth = int((xmax-xmin)/Nbins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case we want the distribution of prime numbers as graph with error bars and not a regular histogram.  \n",
    "Therefore we don't do `ax.hist(primes, bins=Nbins, ...)`, but rather bin it using Numpy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, bin_edges = np.histogram(primes, bins=Nbins, range=(xmin, xmax))\n",
    "x = bin_edges[:-1] + np.diff(bin_edges)       # Calculate the x-values as the center of the bins.\n",
    "sy = np.sqrt(y)                                  # Assume Poissonian errors (more on that later!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "ax.errorbar(x, y, sy, fmt='.', label='Prime number distribution')\n",
    "ax.set(xlim=(xmin, xmax), \n",
    "       xlabel=\"Prime Number\", \n",
    "       ylabel=f\"Frequency /{binwidth:4d}\",    # To put the bin width in the y-axis label \n",
    "       title=\"Prime number density distribution\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting the data:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The __[Prime Number Theorem](http://en.wikipedia.org/wiki/Prime_number_theorem)__ states, that the number of prime numbers follows roughly the function $f(x) = \\frac{1}{\\ln(x)}$. We have binned our prime numbers, so we must have a function with a few more degrees of freedom: $f(x) = c_0 + \\frac{c_1}{\\ln(x)}$, where $c_0$ and $c_1$ are constants that needs to be fitted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the function to fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "def fit_prime(x, c0, c1) :\n",
    "    return c0 + c1 / np.log(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a chi2-regression object based on the fit function `fit_prime` and the `x`, `y` and `sy` values: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td title=\"Minimum value of function\">FCN = 32.43840310667772</td>\n",
       "        <td title=\"Total number of call to FCN so far\">TOTAL NCALL = 34</td>\n",
       "        <td title=\"Number of call in last migrad\">NCALLS = 34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td title=\"Estimated distance to minimum\">EDM = 1.510727894581261e-20</td>\n",
       "        <td title=\"Maximum EDM definition of convergence\">GOAL EDM = 1e-05</td>\n",
       "        <td title=\"Error def. Amount of increase in FCN to be defined as 1 standard deviation\">\n",
       "        UP = 1.0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table>\n",
       "    <tr>\n",
       "        <td align=\"center\" title=\"Validity of the migrad call\">Valid</td>\n",
       "        <td align=\"center\" title=\"Validity of parameters\">Valid Param</td>\n",
       "        <td align=\"center\" title=\"Is Covariance matrix accurate?\">Accurate Covar</td>\n",
       "        <td align=\"center\" title=\"Positive definiteness of covariance matrix\">PosDef</td>\n",
       "        <td align=\"center\" title=\"Was covariance matrix made posdef by adding diagonal element\">Made PosDef</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td align=\"center\" title=\"Was last hesse call fail?\">Hesse Fail</td>\n",
       "        <td align=\"center\" title=\"Validity of covariance\">HasCov</td>\n",
       "        <td align=\"center\" title=\"Is EDM above goal EDM?\">Above EDM</td>\n",
       "        <td align=\"center\"></td>\n",
       "        <td align=\"center\" title=\"Did last migrad call reach max call limit?\">Reach calllim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "        <td align=\"center\"></td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "    </tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td><a href=\"#\" onclick=\"$('#SfeRaPRNYX').toggle()\">+</a></td>\n",
       "        <td title=\"Variable name\">Name</td>\n",
       "        <td title=\"Value of parameter\">Value</td>\n",
       "        <td title=\"Hesse error\">Hesse Error</td>\n",
       "        <td title=\"Minos lower error\">Minos Error-</td>\n",
       "        <td title=\"Minos upper error\">Minos Error+</td>\n",
       "        <td title=\"Lower limit of the parameter\">Limit-</td>\n",
       "        <td title=\"Upper limit of the parameter\">Limit+</td>\n",
       "        <td title=\"Is the parameter fixed in the fit\">Fixed?</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>0</td>\n",
       "        <td>c0</td>\n",
       "        <td>-1.5844</td>\n",
       "        <td>2.79333</td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>1</td>\n",
       "        <td>c1</td>\n",
       "        <td>109.924</td>\n",
       "        <td>22.8795</td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td>No</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<pre id=\"SfeRaPRNYX\" style=\"display:none;\">\n",
       "<textarea rows=\"10\" cols=\"50\" onclick=\"this.select()\" readonly>\n",
       "\\begin{tabular}{|c|r|r|r|r|r|r|r|c|}\n",
       "\\hline\n",
       " & Name & Value & Hesse Error & Minos Error- & Minos Error+ & Limit- & Limit+ & Fixed?\\\\\n",
       "\\hline\n",
       "0 & c0 & -1.5844 & 2.79333 &  &  &  &  & No\\\\\n",
       "\\hline\n",
       "1 & c1 & 109.924 & 22.8795 &  &  &  &  & No\\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "</textarea>\n",
       "</pre>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi2_object = Chi2Regression(fit_prime, x, y, sy)\n",
    "minuit = Minuit(chi2_object, pedantic=False, c0=0, c1=10) # Initializes the fit with given initial values\n",
    "minuit.migrad(); # Fit the function to the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the fit parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit value: c0 = -1.58440 +/- 2.79333\n",
      "Fit value: c1 = 109.92404 +/- 22.87953\n"
     ]
    }
   ],
   "source": [
    "c0, c1 = minuit.args                    # Get the output arguments\n",
    "for name in minuit.parameters:          # Print the output (parameters of the fit)\n",
    "    print(f\"Fit value: {name} = {minuit.values[name]:.5f} +/- {minuit.errors[name]:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot the fit along with some extra text to the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_fit = np.linspace(xmin, xmax, 1000)[1:]   # Create the x-axis for the plot of the fitted function - Not from x[0] since x[0] is 0, which is not defined for the log!\n",
    "y_fit = fit_prime(x_fit, c0, c1)    \n",
    "\n",
    "ax.plot(x_fit, y_fit, '-', label='Prime number fit result')\n",
    "\n",
    "ax.text(0.5, 0.6, r'Fit function: f(x) = $C_0 + \\frac{C_1}{\\log (x)}$', transform = ax.transAxes, fontdict={'size': 18}); # transform so relative coordinates\n",
    "ax.legend(loc='best')\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "We also want to extract the $\\chi^2$ value (see `IntroToPlottingAndFitting.ipynb` if the command below is unclear):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi2_val = minuit.fval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the number of degrees of freedom:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_NotEmptyBin = len(y > 0)\n",
    "Ndof = N_NotEmptyBin - len(minuit.args)            # Number of degrees-of-freedom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate the $\\chi^2$ probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "chi2_prob =  stats.chi2.sf(chi2_val, Ndof)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And add the fit information to the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4R8AKc76+d+7cSWhoKKNHjyYiIoLt27dTv359tm3bRnp6OikpKXz11VcFtlmhQgWXdWeeyDMSrIw0OO0522iKiIiIyOXlH//4B2fPniUsLIyQkBD+8Y9/FOv88ePHM3z4cNq3b4+3t/dFxZCenk7r1q2ZNm0ar776KgCvvfYacXFxhIWFcd111/HWW29dVNu5YmJiePjhhwvc5OJc5+t76tSphISEcP311+Pv78+dd95J3bp1ue+++wgLCyM6OpoWLVoU2OaQIUOcdTyVyc3Cy7OIq71t3Gdz4Ib+ZR2KiIiIiJzHL7/8km9Nkkh5UNBn0xiz0Vpb8G4eJeAZI1gANqvwOuVU8+bNiY2NLeswRERERESklHlQgpVZotODgoLw9/fH4XA4XytXrizy+cYY5/MGimvr1q3OZx1I2crKyqJ3797UqVMHY4zLzjyQ/fyK4OBgKleuTFRUFCkpKc6y/fv3ExkZSaVKlbjhhhv4+eefL3H0IiIiIlLeeVCCVfIRrE8//ZTU1FTn67bbbnNDYOJpbr75ZhYtWpTv+KlTp+jVqxfjx4/n8OHDGGN4+umnneVDhgwhJCSEo0eP0rt3b5dtSkVEREREwKMSrNJbKxYTE8ODDz5Iu3btCAgIYNCgQc6yO++8E4fDAcD111+Pw+FgxIgRzvKEhASMMSxcuJD69esTEBDASy+9BMDo0aNxOBx4eXnlGy3LzMzk2WefJSgoiNq1a/PXv/7VZceUiRMnctVVVxEYGEhERAQHDhwotev/M/Hy8mL48OEFPjxv1apVVKlShfvvv5/KlSvzt7/9zblbz/Hjx1mxYgVjxozB39+fkSNHsmfPHn766adLfQkiIiIiUo55ToKVVbIpgoVZsWIFCxYsYOvWrSxcuJANGzYA8OWXX5KamgrAjz/+SGpqKlOnTs13/kcffcTGjRs5dOgQnTt3BuCll14iNTWVevXq5av/yiuvsGzZMtauXcuOHTvYtm0br732GpD9pPEXXniBdevWkZyczJtvvunyTAUpHfHx8TRt2pQ1a9bQpUsXgoODOXbsGImJiezYsQM/Pz8cDgft27dn//79NGzYkPj4+LIOW0RERETKEc9JsNwwRTAqKoqqVas6X4cPH3aWdevWjXr16lGvXj1CQ0P59ddfi9X2uHHjuOKKK6hUqdJ5t53M691332X8+PFcc801BAQE8Nhjj7FkyRIge71XZmYm27dvJzMzk1atWnHFFVcU72Kl2E6ePInD4SAxMZH4+Hj8/PwASE1NdZadOHGC3377jaSkJAICApzJt4iIiFyc3jPX03vm+rIOQ8Rt/lQJ1tKlS0lOTna+atWq5SyrXr2683dfX99iP126cePGxaq/b98++vfv70z2BgwYQGJiIgBNmjRh5syZvPDCC1SvXp1evXpx/PjxYrUvxVe5cmVSU1Pp3r07u3fvdk7ZdDgczrK6dety8OBBbrzxRk6cOOGcPioiIiLlg7e3N+Hh4YSEhNCrVy9OnTpVYL277rqL5GTPec5qUFAQR44cKZW2Y2JinOvTH3roIbZt23beunPmzOH3338/b/m4ceOcS2OKG3NCQgILFixwvo+Li+Ovf/1rkc8vLzwowSrdKYKFMcZcsNzHx6dY7dWtW5fly5c7k73jx4+7jJrFxMSwdu1adu7cya+//sq///3vi4pbiq5JkyZs377d+X7btm1Ur16dmjVr0qhRI9LS0ti/fz8AZ86cYefOnQQHB5dVuCIiIlIAf39/Nm/ezM8//4yvr2++B+9aa8nKyuKLL76gatWqZRTlpZWRkVHkuu+++y7XXXfdecsvlGBlZmby3HPPXfRGcucmWBEREc4lNJ7EgxKssn0O1pVXXunWbbkHDRrEuHHj+P3337HW8uuvv7JixQoAdu7cyddff82ZM2fw8fEhKyuLwMBAt/X9Z5eenk56errz99zRyk6dOpGSksKCBQs4efIkU6ZM4b777gMgMDCQzp07M2nSJNLS0nj11Ved00lFRETk4p1IO8uB5NNs3JPk9rbbt2/Pjh07SEhIoFmzZjz66KPccMMN7Nu3zzm6kpCQQNOmTXnooYcICQkhOjqalStX0rZtWxo3buxcl3/y5EkGDRpEy5YtadGiBcuWLcvXX2xsLJGRkfTs2ZOmTZsSHR2NzdmoLe9oTlxcnPMRPhMmTGDAgAF07tyZoKAglixZwlNPPUVoaChdunRx2QTt5ZdfplWrVrRq1cr5+KDExETuvfdeWrZsScuWLVm7dq2z3SFDhtC5c2ceeOABlzittQwbNozrrruOrl27uiybiYyMJC4ujszMTGJiYggJCSE0NJRXX32VRYsWERcXR3R0NOHh4Zw+fZqgoCCee+452rVrx8KFC11Gw84X87l1cmcEjRkzhv/973+Eh4fz6quvEhsby9133w3AsWPHiIqKIiwsjJtuusm50diECRMYNGgQkZGRNGjQoFwkZH+qBKtbt24uz8F67733inzuxIkTGTZsGNdcc43L1t3nk5mZ6exn7969zr5nzZoFwBNPPEH79u1p164dgYGB9OjRw/nhPnPmDGPGjKFGjRo0adKENm3a0L9//4u7aMknODjY+R9y06ZN8ff3B6BSpUosXLiQCRMmULNmTbKyspg0aZLzvJkzZ7JlyxaqVavGBx98wIcffljoyKaIiIic38Y9SWw/eIL9SaeJfvdbtyZZGRkZfPnll85/DI2Pj+eBBx5g06ZN1K9f36Xujh07GD58OD/99BPbt29nwYIFrFmzhilTpjBx4kQAXnzxRTp16sT333/PqlWrePLJJzl58mS+fjdt2sTUqVPZtm0bu3btciY8F7Jz504+//xzli1bRr9+/ejYsSNbtmzB39+fzz//3FkvMDCQDRs2MGzYMOeu1sOHD2fkyJF8//33LF68mIceeshZf+PGjSxbtsxlVAjg448/Jj4+ni1btvDOO++wbt26fDFt3ryZAwcO8PPPP7NlyxYGDhxIz549iYiIYP78+WzevNn5HcrPz481a9bQp0+ffO0UFPP5TJo0ifbt27N582ZGjhzpUjZ+/HhatGjBTz/9xMSJE12Sxu3bt7N8+XI2bNjAs88+65KUloXizWsrS1klS7DOfaBsXnPmzHF5Hxsbm69OTEwMMTEx+Y4HBQU5/2UiL29v7wtugODj48O4ceMYN25cvrJmzZo5/7VE3O9Cn4XIyMjzbnBSt25dVq9eXUpRiYiI/Pl8u+soWTlfo85mZPHtrqPcWL9aido8ffo04eHhQPYI1oMPPsjvv/9O/fr1uemmmwo859prr3UmYs2bN+fWW2/FGENoaKjze8OKFSv45JNPmDJlCgBpaWns3buXZs2aubTVqlUr6tSpA0B4eDgJCQm0a9fugjHfeeedVKhQgdDQUDIzM+nSpQuAS/8Affv2df7MTUBWrlzpsmbq+PHjnDhxAoB77rnHmQTl9c0339C3b1+8vb25+uqr6dSpU746DRo0YNeuXTz++ON07drVuUt2QS70bNCCYr4Ya9asYfHixUD2rKOjR4+SkpICQNeuXalYsSIVK1akVq1aHDp0yPk3KAuek2CV8RRBEREREXGvmxrUwMtAloUKPl7c1KBGidvMXYN1rsqVK5/3nLyPw/Hy8nK+9/Lycq5fstayePHiQtdf523L29vbeX7usg8g32ZqefurUKGCc4ZM3v7BdU+A3N+zsrJYv359gYnUha65sFk41apV48cff2T58uW88cYbfPTRR+fdE6Co/eT+nvdeWGs5c+bMBWPJrXe+ts93z8vKn2qKoIiIiIiUHzfWr0bTKwOoU82f+Q/dVOLRq9J0xx138Prrrzu/6G/atKlY5wcFBbFx40YA50hMcX344YfOn23atAGgc+fOTJ8+3VmnoOTyXLfccgsffPABmZmZ/PHHH6xatSpfnSNHjpCVlcW9997L888/zw8//ABAQECAc4TsYmPOey+WLVvmnNJ3obZvueUW5s+fD2TPNrviiivK7R4FHjKCZcp8F0ERERERcb8AvwoE+FUo18kVwD/+8Q9GjBhBWFgY1lqCgoL47LPPinz++PHjefDBB5k4cSKtW7e+qBjS09Np3bo1WVlZ/Oc//wHgtdde47HHHiMsLIyMjAxuueWWfDsnnqt79+58/fXXhIaG0qRJEzp06JCvzoEDBxg4cKBzpOmf//wnkL1s5uGHH8bf35/16wt/fllBMQ8ePJi//OUvtGrViltvvdU5AhYWFoaPjw/XX389MTExLs+WnTBhAgMHDiQsLIxKlSoVay+FS80UNNxW3kRc7WPj5o2DW/OvVxIRERGR8uGXX37JtyapMLkPGf5waJvSCEkEKPizaYzZaK2NcHdfnjFF0JhSnSIYExPD3//+9wvWmT9//gUX94mIiIhI8X04tI2SK7mseEaCBZBV8imCb775Jg0bNqRy5cqEhoby7bffFvnc6Oho53Oqcv3222906dKF6tWrU6tWLR544AHnbiZSuvr168eVV15JlSpVaN26tcsQ9eTJk2ncuDEBAQGEhIQU+JyKwjz//PMYY5zPa8jrf//7H8YY3n333RJdg4iIiIhcfjwnwSrhCNbChQt57rnneP/99zl+/DizZs3Cy6tkl3/8+HH69u3L7t27SUhIIC0tjSeeeKJEbUrRPPnkk+zevZuUlBSef/55/vKXv5CZmZ2E+/j4sHjxYlJSUpg5cyb9+/dn165dRW47ISGBr776qsCyjIwMxowZQ9OmTd1yHSIiIpcbT1h+In8ul/oz6SEJloES3piJEycyevRo2rRpg7e3t/OJ0rn++OMP2rVrR0BAAIMGDXIeT0lJweFw4Ofnl+8ZBjfeeCMDBgygSpUqVKpUifvvv79Ii/2k5K6//nr8/f2x1nL27FkSExOdT0cfNWoUYWFheHl50bZtWxo0aODcqaYoRowYwYsvvlhg2euvv07Xrl2pXbu2W65DRETkcuLn58fRo0eVZEm5Ya3l6NGj+Pn5XbI+PWMXQUOJdhHMyMhgy5Yt3Hzzzeets2LFCueTtps3b87DDz9Mq1atqFKlCqmpqcyZM6fQKWHr168nLCzsouOU4nn00UeZNWsWZ86coVevXgUmPUlJSfz666+EhIQUqc0vvviCihUr0rZt23xlBw8eZPbs2WzYsCHfdFERERGBOnXqsH//fhITE8s6FBEnPz+/S/rgYc9IsCjZJhdHjhwhMzOT6tWrn7dOt27dqFevHpD91Oxff/3VZYSrMBs3bmT27NmsW7fuouOU4nnzzTeZOnUqixcvpkKFCgXWGTp0KAMGDCjSjkbp6ek89dRT591y9W9/+xtjx469pP8CIiIi4kkqVKjAtddeW9ZhiJQpD0mwKFGCdcUVV+Dt7c2xY8fOWydv8uXr65vvCdsXkpCQwL333svcuXNp1KjRRccpxefr60vfvn257rrraN68uUsiNXbsWI4ePcr7779fpLamTJnC3XffTVBQUL6ytWvXsmvXLvr06eOu0EVERETkMuQ5a7BKsIugj48PISEhpbI+6vDhw9xxxx288MILdOnSxe3tS9FkZmaydetW5/upU6eyfPlyli5diq+vb5Ha+P7773nppZcwxmCMAaBx48YsXbqU77//nvXr1zvLVq9ezeDBgxkxYkSpXI+IiIiIeCbPSLAMJd5FcMyYMbz00kt89913ZGZm8sMPP/D999+XqM2UlBS6dOnCI488Qr9+/UrUlhTdwYMHmTVrFikpKWRkZDBz5kwSEhK48cYbAZg7dy4zZszgyy+/JCAgoMA2Ro8eTWRkpMuxpUuXYq11viB7K/6oqChGjBjhUtahQwfeeecdpk6dWqrXKiIiIiKexTMSrBKuwQLo06cPzzzzDH369CEgIIDo6GgyMjIKPe/555/H4XDw8MMPs379ehwOBw0bNgSyv5Bv2rSJv//97zgcDudLSpe3tzfz58+nYcOGVKtWjRkzZrBw4ULnnO/x48eTkJBAgwYNnH+TiRMnurRx6NAhEhISyiB6EREREbmcGU/YRjOirr+Ne30gRL1Z1qGIiIiIiMhlwBiz0Vob4e52PWQEixKPYImIiIiIiJQ2z0iwTMmnCIqIiIiIiJQ2z0iwoES7CIqIiIiIiFyrB7g5AAAgAElEQVQKHpJgaQRLRERERETKPw9JsLikCVZkZCTvvvuuy7FDhw7Rrl07HA4HnTp1umSxiIiIiIiI5/CQBMuALdspgm+//Ta1atXixIkTfP3112Uai5SemTNnEhQUREBAAFFRUSQlJTnL4uLiaN26NYGBgQQHB/Pxxx+XYaQiIiIiUh55RoJlgDLeTn7Pnj1cd911GGPKNA4pPZs3b+app57i888/59ChQ5w9e5Ynn3zSWd6vXz+6detGcnIy06dPJzo6miNHjpRhxCIiIiJS3nhGggUlniIYFBTE+PHjadSoEdWrV+ett95ylh07doxu3boRGBhI9+7dOXPmjLNs/vz5OBwO3nvvPSZPnqwpgpexb775hg4dOtC8eXMqVarE448/zpIlS5zle/fupWfPnnh5eXH77bfj7+/P7t27yzBiERERESlvPCTBMm7ZRfC7777jp59+YtasWTz11FNkZGQAMHbsWPz8/EhMTKR///6sX7/eeU50dDSpqalER0fz1FNPkZqaqimCl6lzH7ptrSUpKYljx44BMHz4cBYtWkRmZiYrVqwgICCAkJCQsghVRERERMopD0mwcMsmF4MGDaJSpUp07dqVEydOcPDgQQA+//xzhg0bRsWKFenRowcNGjQocV/ieTp06EBsbCxbtmwhNTXVOcp56tQpALp27crs2bOdn5O3334bf3//sgxZRERERMoZz0iw3PSg4erVqwPg6+sLQFpaGgCJiYnUqlXLWa927dol7ks8T3h4OJMnTyYqKorg4GBat24NQEBAAElJSdx1111MnjyZ9PR0/u///o++ffuyZ8+eMo5aRERERMoTz0iwoFR3EaxVqxaHDx92vj906FCp9SXl28MPP8zOnTs5cOAAYWFhBAUFUaVKFX777Td8fHy499578fb2pl27djRo0IB169aVdcgiIiIiUo54SIJVug8avvvuu5k+fTrp6eksWbKEXbt2lVpfUr5t2bKFrKwsduzYwdNPP83DDz8MQJMmTThz5gxLly7FWktcXBy//PILzZo1K+OIRURERKQ88ZAEi1Ldpv3FF18kLS2NmjVrMn/+fNq0aVNqfUn59swzzxAYGMjNN9/M3Xff7dymvWrVqixatIjx48cTGBhI7969eeWVVwgPDy/jiEVERESkPDHn7pxWHkVcW9XG/aMNDPqyrEMREREREZHLgDFmo7U2wt3tetAIVulNERQREREREXEHJVgiIiIiIiJuUuoJljHG2xizyRjzWc77a40x3xljfjPGfGiM8S1CK6W6i6CIiIiIiIg7XIoRrOHAL3nevwS8aq1tDCQBDxbagkEjWCIiIiIiUu6VaoJljKkDdAXezXlvgE7Aopwq7wFRRWipXCZYCQkJGGPIyMgo61BERERERKQcKO0RrKnAU0BudlQDSLbW5mYk+4FrCjrRGDPEGBNnjIk7c+YMZJUswQoKCsLf3x+Hw8E111zDqFGjyMzUtMPLUXx8PF26dKFq1aoEBQUV69zY2FiCg4OpXLkyUVFRpKSkOMv2799PZGQklSpV4oYbbuDnn392c+QiIiIi4ulKLcEyxtwNHLbWbsx7uICqBe4Tb61921obYa2N8PWt6JYRrE8//ZTU1FS++uorFixYwDvvvFPiNqX88fHxoU+fPrz88svFOu/UqVP06tWL8ePHc/jwYYwxPP30087yIUOGEBISwtGjR+nduze9e/d2d+giIiIi4uFKcwSrLXCPMSYB+IDsqYFTgarGGJ+cOnWA3wttyc1rsJo2bUr79u1dRiBiYmIYMWIEPXr0wOFwUL9+fY4fP461lueee446depw5ZVXMnz4cM6ePevS3qRJk6hSpQphYWFs3Ljx3O7kEmvYsCExMTFce+21xTpv1apVVKlShfvvv5/KlSvzt7/9jQ8//BCA48ePs2LFCsaMGYO/vz8jR45kz549/PTTT6VxCSIiIiLioUotwbLWPm2trWOtDQL6AF9ba6OBVUDPnGoDgGWFt+beXQS3bNnC6tWradGihcvxuXPnMnDgQFJSUli6dCkVKlRgyZIlzJ49m3Xr1rFt2zbWrVvHG2+84XLe0aNHSUxMZPDgwdx///1klXA6o5SN+Ph4mjZtypo1a+jSpQvBwcEcO3aMxMREduzYgZ+fHw6Hg/bt27N//34aNmxIfHx8WYctIiIiIuVIWTwHazQwyhizg+w1WbOKdJYbRrCioqKoWrUqUVFRDBkyhIEDB7qUd+zYkW7duuHt7U2LFi3w9/dn2bJl9O/fn3r16lG9enUeeeQRli5d6nLeiBEj8PX15ZFHHmHv3r3s2LGjxLHKpXfy5EkcDgeJiYnEx8fj5+cHQGpqqrPsxIkT/PbbbyQlJREQEEBqamoZRy0iIiIi5YlP4VVKzlobC8Tm/L4LaFW8Ftyzi+DSpUu57bbbzlveuHHjfMcOHz7MTTfd5Hx/5ZVXcvDgQZc6tWrVArLX/lSrVo3Dhw/TpEmTEscrl1blypVJTU2le/fudO/enaSkJAAcDoezrG7dus6//4kTJ3A4HGUZsoiIiIiUM2UxglV8Bsgq/R3/fHzy55u1atVySagOHjxI7dq1XeocOnQIgIyMDJKSkvKVi2do0qQJ27dvd77ftm0b1atXp2bNmjRq1Ii0tDT2798PwJkzZ9i5cyfBwcFlFa6IiIiIlEOekWAB2AI3Gyx199xzD/PmzWPv3r0cO3aMGTNm0K1bN5c606ZN4+zZs8yYMYOgoCAaNWpUJrFKNmstaWlpnD171vn7mTNnXOqMHj2ayMhIl2OdOnUiJSWFBQsWcPLkSaZMmcJ9990HQGBgIJ07d2bSpEmkpaXx6quvUq9ePUJDQy/VZYmIiIiIB7gkUwRLruweNHzvvfeyZcsW2rRpQ0ZGBj179uTxxx93qVOjRg2uuOIKgoKCWLBgAdnPU5aysmfPHpcdBP39/enQoQOxsbHOY4cOHSIhIcHlvEqVKrFw4UKGDBnCQw89xO23386kSZOc5TNnzqRfv35Uq1aNpk2b8uGHH+pvLSIiIiIujC2jkaHiiGhUy8Y9Uh2e2F54ZRERERERkUIYYzZaayPc3a6HTBEsuxEsERERERGRovKMBMvNDxoWEREREREpDZ6RYGEuyS6CIiIiIiIiJeEhCRYawRIRERERkXLPQxIsU2bbtIuIiIiIiBSVZyRYBrCaIigiIiIiIuWbZyRYUKpTBM+ePcuDDz5IQEAA9erV46OPPiq1vkrbsmXLaNOmDRUrViQmJqbI58XGxuLl5YXD4XC+fvnlF2f5+++/T8OGDQkMDKR9+/Zs3brV7bE/88wzDB48uMTtTJ48mcaNGxMQEEBISAjLli0r0nnz5893uf5KlSrh5eVFYmIiAGvWrKFFixY4HA5uvPFGNm/eXOJYRUREROTy4iEJVulu0/7qq6+yZcsW9u3bx9y5cxk0aBD79u0rtf5KU5UqVXjyySd58MEHi33u1VdfTWpqqvPVrFkzAPbv38+gQYOYNWsWycnJdOzYsVjJW1GkpaXxzjvvMGLEiBK35ePjw+LFi0lJSWHmzJn079+fXbt2FXpedHS0y/VPmzaNW265hZo1a5Kenk6vXr0YNWoUKSkpdO/enV69euEJz5ETERERkUvHQxIs3LKL4JtvvklwcLBzFObgwYMALFy4kL/+9a9UrVqVyMhI2rRpw8cff1zi/spCZGQkPXr0oHr16m5r88CBA1SvXp3IyEi8vLzo1asX27ZtK1YbMTExzJkz57zl8+bNIzw8nObNm5cwWhg1ahRhYWF4eXnRtm1bGjRowMaNG4vdzuzZs3nggQcAiI+P5+TJk/Tv3x9vb2+eeOIJduzYwZYtW0ocr4iIiIhcPjwjwTIlH8H6z3/+w8svv8yiRYtISkri2Wef5ezZs0D2l+emTZvSr18/lixZwnXXXUd8fLw7Ivcohw8fpnbt2jRs2JCJEyc6R2ciIiIIDg5m1apVZGZmsnDhQrp27erWvqdNm+aW0atzJSUl8euvvxISElKs8+Lj4/nxxx/p2bMnANZajDH56u3YscMtcYqIiIjI5cGnrAMoshImWLNnz+aJJ54gNDQUgE6dOjnLTp48icPhID4+ngMHDhAQEOCxUwQvVrNmzdi6dSsNGzbkp59+4i9/+QtXXXUVAwcOxNvbm379+tGtWzfS0tKoX78+q1atKrTNNWvWcPfddwNw6tQpPvroI2cSlZyc7Ky3YsUKMjIyuPPOO91+XUOHDmXAgAHO6Y5FNXv2bP7yl78QGBgIQNOmTalUqRJz586lb9++TJkyBR8fH06dOuX2mEVERETEc3nGCFb2NoIl2qp93759BAUFFVhWuXJlUlNT+f7773n88cc5ceIEDofjovsqbXv37nVuxOCOKXUAtWvXpnHjxnh5eREeHs5jjz3Gp59+CsDKlSt55pln+O6770hLS+Pxxx/nrrvuKnT9Ubt27UhOTiY5OZn777+fN9980/k+r6lTpzJ8+PB8I0Qlvc6xY8dy9OhRpk2bVqzzMjMzmTdvnnN6IEDFihVZuHAh06ZN46qrruLQoUM0aNDAmYCJiIiIiIAnjWBB9iiW8b6oU+vWrUtCQkKBZU2aNGH79u1EREQAsG3bNrp163axUZa6evXqkZqaWqp9eHn9/9z7hx9+oF27ds4kZ/DgwYwcOZKDBw9y1VVXlaif+Ph4vvvuOxYtWpSvrCTXOXXqVJYvX05sbCy+vr7FOnf58uVkZWVx++23uxxv166dcy3X0aNHeffddwkLC7uo+ERERETk8uQZI1i5AxslmCYYExPDv/71L37++WcyMzNZvXq1cxrgfffdx2uvvUZycjKrV69m/fr1dO/e3Q2BX3qZmZmkpaWRmZnp/D0jI8OlTmRkJKNHj3Y59vXXX7N3714AfvnlF2bMmOFMMlu0aMHatWuJj4/HWsu8efOoUaMGtWrVKnG8U6dOZfDgwVSqVKnEbeWaO3cuM2bM4MsvvyQgIKDAOqNHjyYyMrLAstmzZxMdHY23t2syv337dtLT00lKSmLYsGF07NjxvKOiIiIiIvInZa0t968bg+tYOz7Q2rNptiRee+0127hxY+twOGzbtm3tH3/8Ya219syZM3bgwIHW4XDYOnXq2A8++KBE/ZSl2bNnW8DlNX78eJc69evXtwMGDHA59vLLL9tatWpZf39/GxQUZP/5z3+6lE+ePNnWq1fPBgQE2IiICPvNN9+UONajR4/awMBAu2/fvhK3lVdQUJD19fW1lStXdr5efPFFlzoDBgyw9evXLzAmX19f++OPP+Yrmzhxoq1atap1OBy2Z8+eNjEx0a1xi4iIiMilA8TZUshdjPWA5/hENK1r4/och7F/gK/7RjqkbE2aNInNmzfzwQcflHUoIiIiIvInY4zZaK2NcHe7njFFMHeOYCk+bFguverVqzNu3LiyDkNERERExG08b5MLuWwMGTKkrEMQEREREXErzxjByt2+22aWbRwiIiIiIiIX4BkJVi4PWC8mIiIiIiJ/Xh6SYGkNloiIiIiIlH8ekmDlyCqdKYLx8fF06dKFqlWrXrLnGhXW52uvvUbt2rWpXr06Tz/9tEvZzJkzCQoKIiAggKioKJKSkorU54EDB7jrrruoUqUK9evXZ8GCBc6yL774gpYtWxIYGEjdunV54YUXSnR959O2bVvmz59fojbOnj3LAw88wFVXXUWVKlXo2LEjW7dudZZPnjyZxo0bExAQQEhICMuWLSty2++//z4NGzYkMDCQ9u3bu7QbFxdH69atCQwMJDg4mI8//rhE1yEiIiIilx/PSLDc8KDhC/Hx8aFPnz68/PLLpdJ+cfvcsGEDEyZM4Ouvv2bLli188MEHfPTRRwBs3ryZp556is8//5xDhw5x9uxZnnzyySL1OWzYMOrWrcuRI0eYM2cOgwYNYvfu3QCkpqbyz3/+k8TERL799lvef/993n//ffddMNkJSkJCAvfdd1+J2snMzKRRo0Z8//33JCUlcc899xAVFeUs9/HxYfHixaSkpDBz5kz69+/Prl27Cm13//79DBo0iFmzZpGcnEzHjh2JiYlxlvfr149u3bqRnJzM9OnTiY6O5siRIyW6FhERERG5vHhGguWmKYJvvvkmwcHBztGJgwcPAtCwYUNiYmK49tprSxpokV2oz4ULF9KjRw+aN2/ONddcw0MPPeR8VtQ333xDhw4daN68OZUqVeLxxx9nyZIlRepz9erVDB06lAoVKtCxY0fCw8P59NNPAbjvvvu47bbbqFixItdccw1dunRh/fr1xbqmoKAgEhISzlv+6quv8thjj1GhQoVitXsuPz8/xo0bR506dfDy8mLgwIHs2LGDxMREAEaNGkVYWBheXl60bduWBg0asHHjxkLbPXDgANWrVycyMhIvLy969erFtm3bnOV79+6lZ8+eeHl5cfvtt+Pv7+9MUEVEREREwGMSrBwl2EXwP//5Dy+//DKLFi0iKSmJZ599lrNnz7oxOPeJj4+nadOmTJs2jaeffprrrruO+Ph4AM59MLS1lqSkJI4dO1ZouwWdu2PHjgLrfvvtt4SFhV3kFeT3+++/89lnnzF06FC3tZlr/fr1XH311dSoUSNfWVJSEr/++ishISGFthMREUFwcDCrVq0iMzOThQsX0rVrV2f58OHDWbRoEZmZmaxYscI5BVFEREREJJeHJFglH8GaPXs2TzzxBKGhoXh7e9OpUyfq1q3rpvjc6+TJkzgcDvbt28dvv/1GQEAAqampAHTo0IHY2Fi2bNlCamoqb731FgCnTp0qtN3IyEhmzpxJeno6X331FZs3by7wvDfeeIO0tDSX6XHnM2nSJKpWrUrVqlXZu3cvYWFhVK1albvvvtul3vTp0+ndu3eBSVBJpKSkMHz4cF555RW8vPJ/nIcOHcqAAQNo1qxZoW15e3s7pwFWrFiR+fPnM2XKFGd5165dmT17NhUrVqRHjx68/fbb+Pv7u/V6RERERMSzeUaC5YY1WPv27btkG1iUVOXKlUlNTWXKlCksWrSIEydO4HA4AAgPD2fy5MlERUURHBxM69atAQgICCi03ddff539+/dTp04dJk2axD333ENgYKBLnS+++IKXX36ZTz75hIoVKxba5pgxY0hOTiY5OZl69erx008/kZyczGeffeasc/r0ad555x1GjBiR7/z58+fjcDhwOBw8/PDDhfaXV3p6Ot27d6d379707t07X/nYsWM5evQo06ZNK1J7K1eu5JlnnuG7774jLS2Nxx9/nLvuuss5SnjXXXcxefJk0tPT+b//+z/69u3Lnj17ihWziIiIiFzePCPBys2wsi4+wapbt+4F1weVJ02aNGH79u3O99u2bSM4ONj5/uGHH2bnzp0cOHCAsLAwgoKCqFKlSqHt1qlTh88//5zExET++9//snv3bq6//npn+bp16xgyZAifffYZ9erVc9v1zJ07lxtuuIHrrrsuX1l0dDSpqakuo3FFkZmZyf3330+jRo14/vnn85VPnTqV5cuXs3TpUnx9fYvU5g8//EC7du1o3rw5Pj4+DB48mK1bt3Lw4EF+++03fHx8uPfee/H29qZdu3Y0aNCAdevWFTlmEREREbn8eUiClaMEI1gxMTH861//4ueffyYzM5PVq1ezb9++7GatJS0tjbNnzzp/P3PmjLuiLtCF+uzVqxdLlixh69atHDhwgFmzZrmM0GzZsoWsrCx27NjB008/nW/k58CBAzRq1Cjf5hf79u3j2LFjpKenM3XqVPbt20f37t0B+Omnn+jVqxcfffSRW9cVWWt57bXXGDlypNvaBJxruWbMmJGvbO7cucyYMYMvv/zyvCN7o0ePJjIy0uVYixYtWLt2LfHx8VhrmTdvHjVq1KBWrVo0adKEM2fOsHTpUqy1xMXF8csvvxRp6qGIiIiI/IlYa8v968brGlo7PtDag1ttSbz22mu2cePG1uFw2LZt29o//vjDWmvt7t27LeDy6tChQ4n6KkxhfU6dOtXWrFnTVq1a1Y4ePdrl3G7dutnKlSvbmjVr2jFjxtjMzMwC2549e7bL8f/+97/2qquusv7+/vamm26yGzdudJbFxMRYb29vW7lyZeerS5cuJb7OL7/80jZt2tRmZWWVuK1cCQkJFrD+/v4u8X7zzTfWWmuDgoKsr6+vS9mLL77o0saAAQNs/fr187U9efJkW69ePRsQEGAjIiKcbeZeS1hYmHU4HLZBgwZ25syZbrsmEREREbm0gDhbCrmLsefsLFceRYQ0tnE9D8PQb+Cq6ws/QcqNLl26EBUVVez1VSIiIiIipckYs9FaG+Hudj1jiqDJWYOVWT63VZeCpaenc/PNN/PAAw+UdSgiIiIiIpeET1kHUDS5CVbprosS96pYsSLjxo0r6zBERERERC4ZDxvBUoIlIiIiIiLll2ckWLlhaoqgiIiIiIiUY56RYOU+aFgjWCIiIiIiUo55RoLlHMFSgiUiIiIiIuWXZyRYzjVYGWUbh4iIiIiIyAV4WIKlESwRERERESm/PCPB0jbtIiIiIiLiATwjwdKDhkVERERExAN4WIKlESwRERERESm/PCPB0hRBERERERHxAJ6RYBk9aFhERERERMo/z0iwIDvJ0giWiIiIiIiUY56TYHn7QpZGsEREREREpPzyrARLUwRFRERERKQc86AEq4KmCIqIiIiISLnmQQmWrxIsEREREREp1zwowaqgKYIiIiIiIlKueU6C5aUpgiIiIiIiUr55ToKlKYIiIiIiIlLOeVCCpSmCIiIiIp7izJkzvPLKK7Ro0YIqVapQu3ZtunTpwldffVXWoYmUKp+yDqDItE27iIiIiEdIS0uja9eupKam8tZbbxEREUFaWhoLFy5k+fLl3HrrrWUdokip8bAES1MERURERMq7Z555ht9//524uDgqV64MQOXKlYmJiSnbwEQuAQ9KsCpARnpZRyEiIiIiF3DkyBHeeOMN5s2b50yuRP5MPGgNlkawRETEvWJjYzHGMGfOnBK3tXv3bqKioqhZsybGGI/4l3p3Xn9puNA9/fnnn/Hx8eG///3vRbW9dOlSfH19+e2339wUreT66quvyMrKIioqqsDy9PR0br75ZqpWrcqiRYsucXQipc/DEiytwRIRkcLlJg7ne3377bfnPXfz5s1MmDCBhISEYvUZExPD6tWrGT16NPPmzWPo0KElvAr3uNjrKQ8udE9HjRpF27Ztuf322y+q7aioKEJDQxk9erS7wi2xU6dOMXXqVDp06MCVV16Jr68vNWvW5M477+T9998nKyurrEMskj/++IOrrrqKChUqFFheoUIFFi9ezIgRIy5xZCKXhgdNEfTRCJaIiBRL3759ueuuu/Idb9SoEQC33HILp0+fdvkiuHnzZp599lkiIyMJCgoqUj/p6en873//Y9iwYfztb39zS+zucqHrKej6y4sL3dP169fz3//+l6VLl5aoj+HDhzNgwAC2bt1K8+bNS9RWSW3YsIGePXuyf/9+7rzzTkaNGkWNGjVISEhg4cKF9O/fn+PHj/Poo4+WaZxFERQUxOHDh0lLS8PPzy9fuZeXF1dddVUZRCZyaXhQgqUpgiIiUjw33HAD/fr1O2+5l5dXgV8Ai+vQoUNYa6levXqJ27qU3HX9peFC9/TNN9+kRo0aBSbPxdGjRw8eeeQR3nrrLV5//fUStVUSmzZt4rbbbqNSpUqsWbOGm2++2aV8woQJvPLKK4SHh7ulv9jYWDp27MiqVauIjIx0S5t5de7cmbp16zJ48GCmTJlCrVq12Lt3L4sXL6Z27dpER0e7vU+R8kRTBEVE5E/r3DVIEyZMYODAgQB07NjROaXwQuupYmJiqF+/PgDPPvus85zY2FgmTJiAMabA6XlBQUEuX27nzJmDMYavv/6aKVOm0LBhQypWrEiTJk147733Cuz7zJkzTJ48mfDwcCpVqkSVKlWIiIhg+vTpRbqe863BOnLkCI899hh169bF19eXunXr8thjj3H06FGXesWNeefOnWzfvv2897Io9zQjI4OlS5dy++23u4y8ZWRk0LZtWxwOR74+3n77bYwxjBs3zuW4w+Ggffv2LFy4sNCYSkt6ejr3338/6enpfPbZZ/mSKwBvb2+efPLJAsvKo0qVKjmfdRUREUFAQAC33HILmzZtom3btmUcnUjp86ARrAqQpQRLRESK7tSpUxw5csTlWMWKFQkICCiwfo8ePfjjjz94++23GTt2LM2aNQOgYcOG5+1j6NChhIeHM3LkSLp3706PHj0AaNasGbGxscWOeezYsZw+fZqhQ4dSsWJFZsyYQUxMDI0aNXL5cnrmzBnuuOMOYmNj6dy5M/369cPPz48tW7awZMkShg0bdlHXk5KSws0338yOHTsYNGgQN9xwA5s2bWLGjBl8/fXXbNiwId/9K2rMt956K3v27MFae8F7cKF7unHjRlJTU2nVqpXLOT4+PixYsIDw8HD69OnDt99+i5+fH1u3bmXEiBG0a9eO8ePH5+urTZs2LF++nO3bt9O0adMLxpWVlcWxY8cuWCev6tWr4+V14X/Lnj17Ntu3b2fkyJFEREQUue3yrm7dusybN6+swxApG9bacv+68cYbrf38b9ZOqm9FREQKs2rVKgsU+Ordu3e+erNnz3Yemz17tgXsqlWritzf7t27LWDHjx/vcnz8+PEWsLt37853Tv369W2HDh3y9RseHm7T09Odx/fv3299fX1tnz59XM5/6aWXLGCffvrpfG1nZmYW6XoKuv6xY8dawL7xxhsudadPn24B+/e///2iY65fv77N/upRuPPd03//+98WsMuWLSvwvMWLF1vAPvbYY/bUqVM2JCTEVqtWze7Zs6fA+vPmzbOAXbRoUZFjKuqroL/7ucLDw60xxv7666+F1nWX3L97cT7j7tajRw977bXX2i8rSRYAACAASURBVNDQUDtq1Kgyi0P+3IA4Wwq5iweNYPlChtZgiYhI0Q0ZMoRevXq5HLvyyivLKJqiefTRR/H19XW+v+aaa2jSpEm+7cTnz59PtWrV8k17AwodNbmQjz/+mJo1azJkyBCX40OHDmXChAl8/PHHPP/88xcVszt2MkxMTAQ473q33HVVb7zxBps2beLnn39m8eLF1KtXr8D6NWrUAODw4cOF9n3llVcWa1v4wj5rR44c4ccffyQ0NJTGjRsXud3iKGjULSUlxfnz3BHeooy6ucPixYtLvQ+RsuI5CZaPH2SkgbVgTFlHIyIiHqBx48bcdtttZR1GsTRo0CDfsRo1arBnzx6XY7/99hvh4eFu36Ri9+7dRERE4OPj+hXBx8eH4OBgfvjhh4uO2R1MzncAe4Fphq+88gorVqxg3bp1DB482DnFsCC57ZgifLfw8/Nz6+cpd7pkcHBwkc/JyMjgiSf+X3t3Hh9Vdf9//HVmJguEAGGXHQTFXQy2WPVbV7TWqrVSUdr6danW1mJr+2uV9ltX2lp3rYpWbetusdbd1g1344JQRAFFFkFAAgSSQLbJnN8f905IyGRmkpmbO8v7+XjMY+7cc5fPuXPnhg/n3nN+wX333UckEuGUU07h1ltvpaioKObyn3/+OWPGjIlZFmucqhUrViTde6aIxJY9CVZBD7DNTk+CodgXERERkUwS7x/t4XA45vxgMBhzfqyEIpmkoDt0JuZUDRw4ECDus1ALFy7k888/B5wBicPhcLuEMSq6neh242lubm5pQUs21o6OTXR7AE1NyT9j/vvf/55XX32VRYsWUVBQwAknnMAll1zC9ddfH3P5WK1u//3vf/nlL3/Jtddey3777ddueRFJjWcJljGmGHgNKHL386i19lJjzBjgYaAf8AHwfWtt4nv/Cno6703blWCJiIhn0pm0RG9j27x5c5tWgfr6etatW9cyHldX7LbbbixevJiGhoYOWy+g8/UZO3YsS5cubZeUhMNhPvnkk5itVd1p7733Bmh3+2FUdXU106ZNY8CAAVxwwQX85je/4dJLL2XWrFkxl1+2bFmb7cazevXqDluDYknUGjRu3DgCgQAffvgh1tqkvqu77rqL66+/nqFDhwJOT5HTpk3j2muvjXlrX6xWt+j3Wl5ennQ37ZmSzO/MiyReJFVe3mTbABxhrd0P2B841hgzGbgauMFaOx6oAs5OamsFPZz3pjovYhUREQGcrrshfgtJsnbbbTcAXnzxxTbzb7jhBiKRSErbnj59OlVVVVx11VXtylr/o7Oz9TnppJOorKzkrrvuajP/L3/5C5WVlXz729/ucszJdtMez8SJE+nduzcVFRUxy8877zxWrVrF/fffz8yZM5k6dSp//OMfmTt3bszlKyoqGDx4cFK36UVbg5J9JWoN6tevH9/85jf57LPPuPnmm2Mus3z5cmbPng3Ali1bWL16NRMnTmwpP+CAA1rme8mLjgDS8RLJRHFbsIwxfYBjgWE4PeKsBf5jrd2SaMNuzxy17scC92WBI4DT3fl/By4Dbk8YaUsLlhIsERHxzoEHHkggEGDWrFlUVVVRUlLCmDFj+OpXv9rpbR111FFMmDCB3/3ud2zatIkxY8bwxhtvUFFRwYABA1KK88ILL+Spp57iqquu4r333mPKlCkt3ZIvXbq0JanrbH1+9atfMWfOHH7yk5/wwQcfMHHiRObPn8/dd9/N7rvvzq9+9asux5xsN+3xBINBTj75ZJ544ol2rXd33303Dz/8MDNnzuSII44AnDGw3n33Xb73ve+xcOHClk4tAGpra3n99dc566yzktp3up/BArj99ttbupJ/7rnnOPzwwxk4cCDr1q3jtdde48UXX+S3v/0tADU1NQD06dOnZf2+ffu2KfPS6NGjufHGG2M+u9UVc+bM4eGHH06qw4sjjjiCmTNnZt0zlZKfOmzBMsb8AOcWvsOAnkAJcDgwzy1LyBgTNMYsADYALwCfAVustdEbz9fgJG+x1j3XGPO+Meb9yspKKGx1i2Arp97xNqfe8XYy4YiIiCQ0cuRI7rnnHurq6jj//PM57bTTuP32xP8PGEswGOSJJ57gsMMO45ZbbuHiiy+msbGRV199lZKSkpTiLCws5Pnnn+eqq65i9erVzJw5k5kzZ/Luu++26dShs/Xp06cPb775Jueddx7PPvssM2bM4Nlnn+VHP/oRb7zxRodjiHWn888/n6qqKp5++umWeUuWLGHGjBl87Wtf4/LLL2+Z37dvXx566CE2bNjQMuhy1D//+U+2b9/Oeeed122x72zYsGF88MEH/O53v2PdunVcccUV/PSnP+Wvf/0rhYWF3HrrrcyYMQOg5dhHewEEp1WrdVm2iEQiXHLJJS3JYyL/93//l1JyL9KdTEf/i2SMWQp8defWKmNMGfCOtXa3pHdiTF/gX8DvgL9aa8e580cAz1pr94m3/qRJk+z7D/8R7v8OnPU8jNzxv27R5OqR8w5KNhwRERHJcsceeyzbtm3j9ddf7/I2ysvLGTVqFI899lgaI/PWyJEjueGGG/jOd74DwPPPP8+pp57Kpk2bPO9ePZ0tWM888wy/+c1vWLBgQVLLW2sZO3Ys999/f5vBq0VSYYyZZ61N+wjf8X6JBueWvp1F3LKkuUnaK8BkoK8xJnpr4nCc2w4TK4jdgiUiIiL557rrruPtt9/m+eef79L6jz/+OB9++CFXX311miPz1jnnnMOsWbNYu3YtlZWVXHbZZZx55pndMnZVaxs2bODUU09l0KBBDB8+nIsuuoj6+vqW8tWrVzNlyhR69+7Nvvvuy3XXXddyOyPAE0880e52v6uvvpr999+/5RbS5557jsGDB/PRRx9hjOGII47gySef7J4KiqQg3q9xFvCBMeZ2Y8xM9zUb57bB2F3xtGKMGei2XGGM6QEcBSwG5gKnuIudATyRVKTq5EJERERce+21F+FwmClTpnRp/ZNOOonGxkbPBvj1ysyZMznkkEPYa6+9GDduHHvuuSe///3vuz2O0047DXA6Lnn33Xd5/fXX2wx6fdpppzFs2DDWr1/PE088wV//+tc26y9YsIA999yzzbwLL7yQTZs2MWfOHN5++23OOOMMnnjiCfbaay8A9txzz6RbvET81GGCZa39OzAJeBWnR8BGnFaoSdbavyWx7V2AucaYhcB7wAvW2qeBXwMXGWOWAf2Bu5OKVC1YIiIikudCoRA333wzVVVVbN26lbvuuivtg00n8sUXX/Dyyy9z4403UlpaytChQ7n88sv529/+BjitV2+++SZ/+tOf6NmzJ2PGjOHCCy9ss42qqip69+7dZl5xcTFXXHEFF198MSeffDL33XcfkydPbinv3bs3VVVVntdPJFVxexG01lYZY+bSqhdBa21SZ7a1diEwMcb85cBXOh2pehEUERER8d2aNWsoKipil112aZk3duxYKisraWxsZO3atRQXF7cZvHnkyJFttlFWVkZ1dXW7bR9wwAGsXLmSGTNmcMwxx7Qpq66upqysLM21EUm/eL0I7m+MqcBptboauAZ41RhTYYw5oJvi20EtWCIiIiK+Gz58OA0NDaxfv75l3ooVKxg4cCCFhYUMHTqU+vp6KisrW8o///zzNtvYf//9+fjjj9vMW7FiBccffzwXXHABDz74YLuu5z/++GP2339/D2okkl7xnsH6G3ChtXYPa+3R1tqjrLUTgJ8Bf42znjdansFSgiUiIiLil2HDhnH44Ydz0UUXUVtby7p167jssss444wzABgxYgQHH3wwF198MXV1daxcuZJbbrmlzTZOOOGENgNwf/nll0yZMoWZM2dy8803s+eee3LNNde0lFtrefnllzn++OO7p5IiKYiXYJVYa9/Zeaa1tgJnTKzuFXLvL9YtgiIiIiK+evDBB2lqamLMmDFMmjSJyZMnc8UVV7SUP/TQQ6xevZrBgwdzwgkncPrpp7cZFPq4446jtraW+fPnU11dzbHHHsv06dM5//zzAZg1axbXX38969atA+CVV16hT58+HHrood1bUZEuiPcM1nPGmGeAe4HV7rwRwA+Af3sdWDuBAIR6qAVLRERExAcrV65smR4yZAhz5szpcNkRI0a06UL/tttua/McViAQ4A9/+ANXXnkljz32GPPnz2+z/sEHH0xtbW3L5yuvvLJNi5ZIJuswwbLWzjDGfAM4EaeTCwOsAW611j7bTfG1VdBDLVgiIiIiGe6DDz6gR48eTJgwgUWLFnHttde2tE5FTZ06lalTpya1vZdfftmLMEU8kagXweeA57oplsQKS6BRLVgiIiIimWzjxo38+Mc/Zt26dfTv35/TTjutXVftIrkqboLVEWPMndbac9MdTEIFukVQREREJNNNmTKFZcuW+R2GiC86TLCMMf06KgKO8yacBHSLoIiIiIiIZLB4LViVwCqchCrKup8HeRlUhwp6qgVLREREREQyVrwEazlwpLX2850LjDGrYyzvvaJSqP3Sl12LiIiIiIgkEm8crBuBsg7K/uRBLIkV9Yb6al92LSIiIiIikki8btpvjVN2S0dlniruDQ1KsEREREREJDPFa8HKPNEWLGv9jkRERERERKSd7EqwivtApAnC9X5HIiIiIiIi0k6HCZYxpktjZHmquLfzXr/V3zhERERERERiiNeCVWGMedwY8yNjzOhuiie+oj7Ouzq6EBERERGRDBSvk4tJxphRwDeAG40xw4A3gOeAV621Dd0U4w7RFix1dCEiIiIiIhko7jNY1tpV1trZ1tqTgK8BTwFHAa8bY57pjgDbKNItgiIiIiIikrmSfs7KWtsEvOy+cFu0ulexe4ugWrBERERERCQDdbkXQWvtF+kMJCktnVwowRIRERERkcyTXd20F+kZLBERERERyVwJEyxjzN7dEUhSCnsBRi1YIiIiIiKSkZJpwZptjHnXGPNjY0xfzyOKJxBwnsOqq/I1DBERERERkVgSJljW2kOA6cAI4H1jzIPGmKM9j6wjJQNg+ybfdi8iIiIiItKRpJ7BstZ+CvwW+DXwdeBmY8wSY8zJXgYXU8/+sH1jt+9WREREREQkkWSewdrXGHMDsBg4AviWtXYPd/oGj+Nrr+cA2KYWLBERERERyTzJtGD9GfgA2M9a+xNr7QcA1tq1OK1a3atnP90iKCIiIiIiGSmZgYaPA+qstc0AxpgAUGyt3W6tvc/T6GKJPoNlLRjT7bsXERERERHpSDItWC8CPVp97unO80fP/hBp0lhYIiIiIiKScZJJsIqttbXRD+50T+9CSqDnAOd9W3IdXZx6x9ucesfbHgYkIiIiIiLiSCbB2maMOSD6wRhTDtR5F1ICPfs779s3+xaCiIiIiIhILMk8g/UzYI4xZq37eRfgVO9CSqAkmmCpq3YREREREcksCRMsa+17xpgJwO6AAZZYa5s8j6wjJYOc99ovAaipb6K6Psy8VVWUjyrzLSwREREREZGkBhoGDgT2BSYCpxljfuBdSAn0Guy816xn3qoqlqyvYU1VHdPvqmDeqirfwhIREREREUnYgmWMuQ/YFVgANLuzLXCvh3F1LFQIJQOhei0VyzcRsc7spnCEiuWb1IolIiIiIiK+SeYZrEnAntZa63UwSSsdAjXrmbxffwIGIhYKQgEmj+3vd2QiIiIiIpLHkkmwFgFDgHUex5K80l2gZh3lo8qYMKSU6vowN02bqNYrERERERHxVTIJ1gDgY2PMu0BDdKa19gTPokqkdBdYO9+ZLC6gtLhAyZWIiIiIiPgumQTrMq+D6LTSXWBbJTT715mhiIiIiIjIzpLppv1VY8woYLy19kVjTE8g6H1ocfTexXmvyZy7FkVERERERBJ2026M+SHwKHCHO2sY8LiXQSXUZ4TzvmW1r2GIiIiIiIi0lsw4WD8BDgaqAay1nwKDvAwqob6jnPctn/sahoiIiIiISGvJJFgN1trG6AdjTAhnHCz/9I22YK3yNQwREREREZHWkkmwXjXGzAR6GGOOBuYAT3kbVgKhIqejC7VgiYiIiIhIBkkmwboYqAQ+BM4DngV+62VQSek7CqrUgiUiIiIiIpkjmV4EI8Bf3FfmKBsFq96Cnn4HIiIiIiIi4kiYYBljVhDjmStr7VhPIkpW2RhY+A8KejTSZAp9DUVERERERASSG2h4UqvpYmAq0M+bcDphwHjAMiT8BasLxvgdjYiIiIiISOJnsKy1m1q9vrDW3ggc0Q2xxdd/HABDw2t8DkRERERERMSRzC2CB7T6GMBp0Sr1LKJkKcESEREREZEMk8wtgte1mg4DK4HvehJNZxT1gt7DGNq02u9IREREREREgOR6ETy8OwLpkoG7M2KVumoXEREREZHMkMwtghfFK7fWXp++cDppyL6M+Ow1grbJtxBERERERESiku1F8EDgSffzt4DXAP/vzdtlX0KEGRFWK5aIiIiIiPgvmQRrAHCAtbYGwBhzGTDHWnuOl4ElZch+AIxu+sznQERERERERJLoph0YCTS2+twIjPYkms7qN5Y604MxTcv8jkRERERERCSpFqz7gHeNMf8CLPBt4F5Po0pWIMDK0FjGqAVLREREREQyQDIDDc8CzgSqgC3Amdba33sdWLJWFuzKqPByiDT7HYqIiIiIiOS5ZG4RBOgJVFtrbwLWGGPGeBhTp6woGEexrYfNy/0ORURERERE8lzCBMsYcynwa+ASd1YBcL+XQXXG8oLxzsSa9/0NRERERERE8l4yLVjfBk4AtgFYa9cCpV4G1RlrQqOoNb1g1Rt+hyIiIiIiInkumQSr0VprcTq4wBhT4m1InWNNgI8L94WVSrBERERERMRfySRY/zDG3AH0Ncb8EHgR+Iu3YXXOx0X7QtVK2OL/2MciIiIiIpK/EnbTbq291hhzNFAN7A78zlr7gueRdcLHhfs6E6vehL7T/A1GRERERETyVtwEyxgTBP5jrT0KyKikqrXPQ6OhuC+sfB32a5tg1dQ3UV0fZt6qKspHlfkToIiIiIiI5IW4twhaa5uB7caYPt0UT5dYE4DRh8Dy18DalvnzVlWxZH0Na6rqmH5XBfNWVaV1v6fe8Tan3vF2WreZT3T8RERERCTXJLxFEKgHPjTGvIDbkyCAtXaGZ1F1xbijYMnTsOFjGLwXABXLNxFx862mcISK5ZvUiiUiIiIiIp5JJsF6xn1ltt2Pg6d/DkueaUmwJo/tT8BAxEJBKMDksf19DlJERERERHJZhwmWMWaktfZza+3fuzOgLisdDMMPdBKsr/8KgPJRZUwYUkp1fZibpk1U65WIiIiIiHgq3jNYj0cnjDH/7IZYUjfhm7BuAWxd0zKrtLiAYX17KLkSERERERHPxUuwTKvpsZ3dsDFmhDFmrjFmsTHmI2PMhe78fsaYF4wxn7rv6ct8JhzvvC9+Om2bFBERERERSVa8BMt2MJ2sMPALa+0ewGTgJ8aYPYGLgZesteOBl9zP6TFgHAzZBxY+nLZNioiIiIiIJCtegrWfMabaGFMD7OtOVxtjaowx1Yk2bK1dZ639wJ2uARYDw4ATgehzXX8HTkqtCjvZfzqsnQ9ffpzWzYqIiIiIiCTSYYJlrQ1aa3tba0uttSF3Ovq5d2d2YowZDUwE3gEGW2vXuftYBwzqevgx7DMVAiFY8EBaNysiIiIiIpJIMt20p8QY0wv4J/Aza221MSbRKtH1zgXOBRg5cmSHyz1y3kFtZ5QMgN2OhYWPwFGXJdxPdKDbdttJsjwVXm47G/YvIt1Pv/v8pe9eRKR7xLtFMGXGmAKc5OoBa+1j7uwvjTG7uOW7ABtirWutvdNaO8laO2ngwIGd2/EBP4BtlfDxE10PXkREREREpJM8S7CM01R1N7DYWnt9q6IngTPc6TOA9GdB446G/uPg7T+D7Ur/HCIiIiIiIp3nZQvWwcD3gSOMMQvc13HAH4GjjTGfAke7n9MrEIDJ58Pa+eze9FHaNy8iIiIiIhKLZ89gWWvfoO1YWq0d6dV+W+x3Grx0JSfUzuGafnt7vjsRERERERFPn8HyVWEJHHQBkxreYdfGpX5HIyIiIiIieSB3EyyAyT+i2vTmu7X3+h2JiIiIiIjkgdxOsIpKearXVPZvmAcr3/A7GhERERERyXG5nWAB/y75FpXBQfDcxRBp9juctDr1jrdbxjXR/rNLoti9rls2H7tEcrlukPv1S4WOTfbSd+cvHX/xQj6fVzmfYDWaYu4vPQe+/BDm/c3vcEREREREJIflfIIFUFF8KIw+FF66HKrX+R2OiIiIiIjkqLxIsDAGvnUThBvhqRkafFhERERERDyRHwkWQP9d4ajL4NPnYf79fkcjIiIiIiI5KH8SLICvnOvcKvjvS2DzCr+jERERERGRHJNfCVYgACfe6rw/8n1o3O53RCIiIiIikkPyK8ECKBsF37kHvlwET12o57FERERERCRt8i/BAhh/FBzxG/jwHxy/7TG/oxERERERkRwR8jsA3xzyC1i/iO9//Be2BMuAg9K+i+jgao+c17Vt+72+dCzXj22u1y+efK67iEiu0TVd/JCfLVjgPIf17Tv4qHBfzt9yHXz6ot8RiYiIiIhIlsvfBAugoJhryi5ldWg0PPI9+Gyu3xGJiIiIiEgWy+8EC6gLlPD7frOg31h48FT45D9+hyQiIiIiIlkq7xMsgOpgX/jfp2HQHvDwdPjw0aTWq6lv4ostdcxbVeVxhLlJx09EREREco0SrKie/eAHT8DwA+GfZ8Nr18btwn3eqiqWrK9hTVUd0++qUJLQSTp+IiIiIpKLlGC11qMv/OBx2GcqvHwlPP5jCm19zEUrlm8i4uZfTeEIFcs3dWOg2U/HT0RERERykRKsnYWK4OS/wGGXwH8f5KqNP2dI+It2i00e25+AcaYLQgEmj+3fzYFmNx0/EREREclFSrBiMQYOuxim/5Oy5k38YeNPYVHbAYnLR5UxYUgpw8t68MA5kykfVeZTsNlJx09EREREcpESrHjGH8XFA29lTWgkPHom/PMc2L65pbi0uIBhfXsoOeiiTD5+p97xdsvghCKt6dyQrkp07uTyuZXLdYPcr590XarnRj6fW9lcdyVYCWwKDuSy/tfCYTPho3/BbZNhybN+hyUiIiIiIhko5HcAXnvkvINS3kazCcFhv4bdvwGPnw8Pnwa7f5OB4alUhoakIUoREREREckFed+ClWgspjblu+wLP5wLR14Ky+dyfeW5nFzzADRu92TfXvN7/yLS/fS7z1/67kVEukdeJ1iJxmKKWR4qhEMvggve44Pir3Bq7X1wywHw/l+hOZy2fXvN7/2LSPfT7z5/6bsXEek+eZ1gJRqLKW55n+HcUPZbLut3DfQZAU//DG79itPbYCSS8r695vf+RaT76Xefv/Tdi4h0n7xOsBKNxZTMWE2Li/aBs5+HaQ9BsNDpbfC2ybDgQYK24xYtv8eB8nv/ItL99LvPX/ruRUS6T853chFPdCym6vowN02b2K678ETlLYyBCcfBbsc4PQ2+cQM8fj43BQfxdMnJ0LA3FJV2bdse8Xv/ItL99LvPX/ruRUS6T163YEHisZg6NVZTIAj7nAI/egNO/webAgM4s3o2XLcHPPNLqFza9W17wO/9i0j30+8+f+m7FxHpHnndguUZY2C3Y7h0QG/GNS5h1rAK+ODv8N5fYPShcOA5TpfvGS46uFs6urr3Y/+J1ve7ftnM6+8mm+Vy3ZKR6u/Oy+OX7d+N3/H7vX8v6e9FfPle/3iy+dhkc+zJ8LN+ed+C5bVlhRPg5Dvg5x/Dkb+DqpUw5wy4bnfO2vpnxjUuAWv9DlNERERERNJACVZ36TUQDv0FzFgA0/8Jux7J4dufZ9amn8GfJ8Fr18DmFZ3apN9jmuT7/lPRqfHXfNh/NsvlukHu1y8VOjbZS9+dv3T8xQv5fF4pwepuwRCMPwpOuZtzBz/E7D4/g16D4eWr4Ob9YfYh8Oo17Z7X2pnfY5rk+/5T0aXx17px/9ksl+sGuV+/VOjYZC99d/7S8Rcv5Pt5pQTLR3WBEub2PBbOfBYuXAhTroJQD5h7Fdz6Fa6rPJfv1vwdVr8HkeY26/o9pkm+7z8VKY2/1g37z2a5XDfI/fqlQscme+m785eOv3gh388rdXKRKcpGwdd+6ryq18Lip9n60r18u/YRuPsh6NEPxh0J46fArke2jGkSsf6Oo5Wv+09Foti9rls2H7tEcrlukPv1S4WOTfbSd+cvHX/xQr6fV0qwMlHvofDVc7liwT70ilRz9yE18OkLsOxF+HAOYCgfVs4FvQ/kzcg+zJx2ZN6No+X3/lORtvHXPNp/NsvlukHu1y8VOjbZS9+dv3T8xQv5fl4pwcpwtYHesM8xzvhakQism+8kW5++wIUNd3AREXiwEIZ/BcYc6nQDP3wShIo8j620uIDS4gJfx/Hyc/+pSBS713XL5mOXSC7XDXK/fqnQscle+u78peMvXsjn80oJVjYJBGBYufM67GLOvv1FJjQu4uIJlbDydXjlj8AfnOe4hpUzrXoYnxTuAdt2g5L8apoVEREREfGDEqwsVhcoYX7xV+EYdwC1uipY9RaseB1Wv8O3tj1KaFszXHMZ9BvrtHKNcF8D9/A1dhERERGRXKQEy0M19U1U14eZt6qqS82jnV6/RxlM+KbzAr5z44sEt1fym322Ur7tdfjsJVj4sLNsqAdXmlEsLxgPHyyDofvDwAkQLOh0nB3J5RHCU/1uvZbqsU+1fl5/96lsP9G6Xn+3ifaf6b+bTI8vFblct+7g5/HL9e8u1fpl8/Hx+++Z17L576Xf55Xf+49H3bR7JNX+/9Ox/odfNvBBdW+mvzuKeQf9GX75qTPQ8cl/gUlnETYF/E/dS/DkBc74W78fBnceDk//HOb9jXGNSyiK1HVqv/kg18d2yPX6xZPPdRcRMutGlgAAIABJREFUyTW6potf1ILlkVj9/3fmf048W7/fGOe173e5fNXbGBvh4VMGw7oF7uu/sOif8P49zIpu7MZRMGhPGLyn8z5oTxgwPulYck2q302my/X6xZPPdRcRyTW6potflGB5JNX+/7trfWsCMGCc89rnFHemhaqV/Om+fzGyaSXThtXAhsWw7AWIhJ1lAgVcExjGmtAomDsZ+o93kq7+46CoV6dizTa5PrZDrtcvnnyuu4hIrtE1XfyiBMsjqfb/7+v6xkC/McwrPoh5xQcxbap7b2u4ATZ+6iRbGz6i8r03Gdv0Cbz2OtjIjvVLh8KA8Zy1tZS1oeGwbBsM2A16D3d6QsxyuT62Q67XL558rruISK7RNV38ogTLQ6n2/+/3+u2EimDI3s6LqfzpM/fhwrMmwublsOlTJwHbtAw2fsIhde9TYrfB/bOd9YNFUDYKysZA2WiO2wbrg7vAhr7QdxQU9kxPnN0g18d2yPX6xZPPdRcRyTW6posflGBJ6gqKneezBu/ZZvZZs9+iT2QLdx7XBzZ+Aps/g6qVzmvVW5zRWOMseNtlznuvIVA22nn1G8Oh25uoDA2BLcOgdJe09nAoIiIiIuIFJVjiHWPYGiyD0QfB6IPbllnLObP/w6Dwen5/WC+oWgGbVzrJ18o3YOEjXID7ZOqNvwQTcJKsPsOhzwjoM5wp25rYGBwE60ud+cV9nNsbRURERER8ogRL/GEMNYE+1BT2gX1ijF/QVM/P73ySAc0b+M3BpbB1jftaDV/Mg8VPcnZzo7Ps7Eud90I30eozHPoM45SaMJuD/eGTGigd4iRoPfsn9RxYpo+bIf7RuSFdlejcyeVzK5frBrlfP+m6bh8TNYdkc92VYElmKihmbWgEa0MjoDxGAhaJcN7sZxnQXMmsI/q2SsDcJGztfKZu3+gs++BNO9YLFLjJ1hAuqipkc6A/vP62k3yVDoHeQ5m3pSdL1tcQsTD9rgoeOGdyp3/YmTxwYDbI1PpFx1RJ5dyQ7JXKoJuJzp10nFv63XTMy2OTy99dMlIdjDaXB1FO9dzIhN+OX7K97kqwJDsFAmwJ9mdLsD/sFfuievrs1+gbqeK2bw2FmnWtXuuhZh3DwsvZu3kBvPRkm/UqwieAnQoEaWpqouJft1I+9ksoGQS9BkHJQPZoqHRuf6ybAMV9dWtintCYKtJVic6dXD63crlukPv1k67ze0zUbJbtdVeClYJM/N+SbOL18Ws2BWwKDoIRB8Ys/0X0f73O3Lcl6aJmPZNXbiL4pgUiFBjLZBbC0vmwfWNLd/SXRTdyNRAshJKBzqvXICgZxGnVjU4CtnA19Ozn3JoYfRVkT2+J0pbGVJGuSnTu5PK5lct1g9yvn3Sd32OiZrNsr7sSLJHCEui/q/MCyveB8ctfazVuxonOcpFmqKuC2g1c+cgr9IlsYcZX+0DtBthW6bzXfgnrF3H8tg2ECMNjd7TfX6iYWyO9qAn0gXtHtE2+3NdeDV9SE+gN1aOdBC1U1H3HQzqkMVWkqxKdO7l8buVy3SD36ydd5/eYqNks2+uuBEskhpjjZgSCUDIASgawqGgrADMOit0KN332W5TYWu757q6wfRNs2+i8u68P5y+hNLKVMY3bYctqZ379lpb1fxeduN59LyyFnmXQowyK+/KzqgjbAr3gxf84tyj2KIMe0fcy+jdvoNaUgrW6fTHNNKaKdFWicyeXz61crhvkfv2k6zJuTNMsks11V4Il4gVj2GZK27SMtTZ7hXt74jmtErTmMNRthu2buOzh1yiNVPOLQ/q7SZkzn7otUFfFyKZ1lNgaeOtFiDS12/5t0YkrQy1JWesk7H+31lEbKIWKBTvKi3tDUW8o7k2PyDbqTQ8PDoyIiIhIblOCJZIpgiHnGa5eg1hc5LZmTYrdQnZR9PmxcydD4zan9auuqiUBm/2fefSK1PC9/fo486PltRugcimH1m2il62Ff8cO5W9ABAN/KHWTrj5tErCzttax3ZTAGxWtyvu0lJc1b3TK1YImIiIieUYJlnTI7/EHvB47wu/6pYUxUNTLefUZ3jJ77usDAfjeUbETtLPveBtjm3n4B3vuSMDqq6GhGuq3cu/chfS02zllr95Qv7VlPrXrYeMn9KztzSeRMcx7/gHKA5+22/7s6MQVQSgqdZKz4j7OrY5FpXyjsg8Lw6OY949XKB9koNCtQ2EvKCplQuPn1JkesHmwu04vCBVnRbKWE+dVClL93Xl5/LL9u/E7fr/376W8+HuRgnyvfzzZfGyyOfZk+Fk/JVgSk9/jD3g9doTf9csE1gTdHg77tSt75j2nheyUb8Qez+eM2W8RsXBrKMADp42nfECzm6Bthfpq7nxhPj0j2/je/mVucuYmaI21zNsY4A+1x9FEkGc/aOaBwlntkrTLoxM3t5oZCLUkYNduCzgJ2H1DW+ZFk7QTaquc2xv/u6pt4lbQEwpLKG3eQn2ghyeta/l+XqX6u/Py+GX7d+N3/H7v30v6exFfvtc/nmw+NtkcezL8rl/eJ1iJugr3sitxv7t5j7d/v8cf8HrsCL/rl83aHLvmCBXroXyP3dss89KbuwDwvSPbn2MVc5fRsG6ps74JUnHYg5R/bTA01EJjLTTUcNVj71Bs6/jl14e586pbldeybslKim2dk7hVr4WGGre8huluV/r8K3b8d0UnLndbzgqdxIuCEigsYeamRhpMMTw2sl0ZhT05dPs6p3zZdndeiZu89aLik42+n1eJBt1MdN1JZdDOVH93Xv4us/03n474U/mbk+3HL57uOC+zefD5XP7uwdtrXnfoavyZELuXkqlf9Nh5Ie8TLInN7/EHvB47wu/6ZbO0fze7DtzxDJfrwyK34479Y//BuC76B+WHO5Vby/fveIUeke3ceeoEJ/FqrIXG7dC0DRq3cc/cjyi2dZw+cYDz/Fr01bQdGmvpabdQFtkMn69x1mvcBuG6ll1cEJ24P0bdIuMpZiZNhCiwzUx+70JYvNlJwAp6QEFPfla1nQZTBE+PapnX+v3gui+c8mXb2pVR0JOiSD2NprBTx7y7pPq78/J3me2/eb/j93v/XtLfi/jyvf7xZPOxyebYk+F3/ZRgSUx+jz/g9dgRftcvm2X0uB7G0GiKaQwWx+y9EeA/7zrJ2elHxE7efhvrfwMjzW4Ctp0Z975Bsa3nTyfs2ioxc5K08sZtnP3aPFY19ebMcXWUFw+HpjJ3uXqo/ZIR4c0U2nr4eAE01TnrY1t2NSM6ESOBA7g3OnFVcdvkK9QDCnrw202NToI2Z1irxKx9ItfyChU7r4JiCPVgcHitk8Bt37yjLBBI6vCn+rvz8tzI9t+83/H7vX8v6e9FfPle/3iy+dhkc+zJ8Lt+SrCkQ36PP+D12BF+1y+b5d24HgG3s46iUr4MDXXmjZwcc9H3FzkJWvnpsRO4X+ycwFkL4Qanlaypjgvve4si28CfThzvJF/RJKzJKb//9cUU2Qam7jegXRlN2ymwtfSK1MD6zW3LW7XCxdPy2NufWs0MFjoJXKiIW+oNTRTC7LI2iRmhIijowS/qt9JoCilfOheW75zAFXO0XU1TcQHlYWBVtMxdP9SDIYX19CsqpHxEn/bBpSjrzrud+B2/3/v3kv5exJfv9Y8nm49NNseeDD/rpwRLRMRPxjjJR0Ex9ChjfWiYM3/EV2Iu/tR8J0GbenTsBO7Sju7HtxbC9W2TrsZtO5K7cAM01XHL84sopJHzvjbMTcyiyV89hOtZ/PFqCmwjw3qXONsL1zvPwrnLTWyoodA2wLvNMZO6n0cn7ot9OO6JTlwBBItaErMdr0LnPVjUatp5P3fLFppMAfznaSdhCxa5iZvz+vr21U754o1ty9z1h4S/cMprK9tuOwt6rxQRkcyhBEtEJB8Ys+O2QNr3HBn1xhuDATjvq7ETuNvWOgnc1zpooTu/dYLX0jpX3/K66IEKCmnkjyfs5iZ89W0SvL++toRC28j08sFuglffarl6aG505zU6iV1zpTMdrmdiQy0h2wTvN0NzA0TCbWL7cXTikdh1vyk6ce1OBW4CdmeToYkCuLl3zATtF5u3ETYF8K9hOyV/znLH1653yuctdea3foUK2aPhU8ImBGt7tJkfnS6K1DnlGl9ORCSjKcESz+T6+AqZzO9j7/X+U9l+ph8bv+NLpFPxtW6dc31RsM6Z6OAWy3/PcxK06Yd1vkev83duvYs0O4lbcwOEG7jg3rcpoIkbvrNHS1IWLSPcwCXPrGBtYw9mlBdT3qfWLWtsSezeWbiKAtvE4cP67Ejyoknf9k0Mbt5MgW2Clcvb7JdwA2D5fjTQp2LHf1l04s7Y5S3P311Oq+SswEn2goXcUNvsJHB39GmZR7DATQIL3M+tptvML4yR1LVetpC9GpY5Cd4XRTETwMa6GjbXG+at3ET56O59oDzTfzep8npcyEyWzbEnI5v/Xvr93fi9/3iUYGWxTO7mvTvGH/C7/qnwcniAZI69l8fO6+8+0fb9Pi/jScd4O36e934fv0TaHZtA0Olqn54AVIaGOPOH7NNu3XmrqnikqoCIhXfeCvDAOSe2q9vdq5wE7vDvxP4OfhXv9szmJs74y+sU0MRdp+/jJGXNTe57AzQ3ccXjCwjZJmYes2vLPKfFzpm+781PKbBNTCsf4s5vdNd3XiuWriVEmJG9eu3YfmMt1G1utWyTu213OtwAkaakju/vohN/aV82LzKexY0zaSTE9Nmv8kDR1ZQXrHKTrxC311snObu5lzMvUOAmb04C90iPkDP/4T87Y961JI8F7rLOdtqtGyhg3paefLKuL80EmH7nmzwwJUL5kNbrFjCucSnNJghf9om53aJIPWETzMjWQa/HhYTM/Xua6decVPn99zKVdf0+rzL93FCCJZ7I9fEVMpnfx97r/aey/Uw/Nn7Hl0imx5cKT+tmDIQKqQ/0pB6gz7CYi31U5AYwIfY/Sp7+r5PATTs8dvnN0QRveif/UeMmgLGSutYJ4GX/mk8BTfzmmHHtlq34uIiGjwuwBGgiQMXwsygftRqaw9DcyPyPviBEmEFD+zrrRMI71o+EnUSwucl5RaL7DbvlTTummxtp3esmQEX4BCJMxWJoam6m4oU5lIeebLPMrOjE7bEPQZvWwUCoXVJ3y/ZmwhTAraVtEjcn4Qvxq83baCYEcwa3XTdQAIEQ06s3OOUvv+yuH3ITSWf6iO2riRCE/37urhdq2UfFwgjWWsA45+aCRZQX92uzjbLmjc7266rarEsgmNW/22yOPRnZ/PfS7+/G7/0nogRLPOH3+AP5zO9j7/X+U9l+ph8bv+NLxO/4vBxM1e+6+cpNAAnFH19tcVGzM7F7++M/eWAVZvFbWAsFBUEmT/kutPrHzp1fON/d10/p2nfX5ruPNLdJziav2gz3LgFrKQiFmHzyz2Dwz90kzmmp+8PTCwnRzP87aoyTrLUkcU5Sd/9bywjZMNPKd2mV1O1I+BYvXkvQhhk6oHeb7TqtgPWUNVcRJAxfbmyfHEaaOaahwSl/rTlm/c6LTsQYIH1yZDxFLePrhZk87+cw/9M2y8yOTly989qGyXZ3ivn1jvH5Ks6H+WudFt5oshgItUkI204X8LOqrTQThH/tslNyWMDp1RucsrmvtEsOCQQ5YvvnhAnBwtVtkkpnmRB7NCyl2YTgi8Id23Zfkwc2EjDW+V0Gg0weVuiMb9h6OY9l83XHy7+Xfl8z/d5/IkqwxBN+jz+Qz/w+9l7vP5XtZ/qx8Tu+RDI9vlTkct26Q7cev0DQebnP9pXv0Y8JQ9bG3feCYvc5wL1i/yP5qYXxWwdvW+eUH3Jq7PJLEvwj/AfR8nMnOwlipGlHK14kzI/ufYeQDfPnafu2mu8kZ+XNTRw1ZzHrGwq55OsDKB9wect60WXvfPUTgjbM2QeNcOe7rX6RMOWRJn787lssa+rPGbs1Ul6yB0R225FEttpOy3S4ESLb3PlhRjZVE6DZeb5wp9i/0djoJI+vRmLWvSV5fCxm8Y5nD2PceloOzCkYT0VkDyYHFlP+4KftlnmIgJPgzYombsE2CdhNtWEiBJzWxxjlv920zSl/YEDM8vO2bCJigvDMo63m71jm5Jq1Tvmb78YsP3T7Cuf21I/W75RABikPhDimfyXrGov5vymjKC/8HL5c22aZ/s2VNBOAbRtbbbdVXePw8u+l39dMv/efiBIs8Uyuj6+Qyfw+9l7vP5XtZ/qx8Tu+RDI9vlTkct26g5/HL2u+O2Pc2w7b/vOrKjjAmehggPTKUgiWQvkhsRO4l95zErizD4pd/uZn7vh8p3WtFeaiOAnk96NlP/wq2OY2ySHNTfz4vncI2Gb+fOo+7ZIzmpu44smFhAgz89jddiR4kbCbiIZ5b+5SCm0z5Yf8z07lzjL/en8lQdvMSfsNblmndfknS9cRtM0MHdg3ZnnINhGkGbZVttlv9LVvw3an/KNAzPJTowfihdjH7oLoxJzY5S13rT4du/y26MQ1scsfbEkwC2MmiPfUNhEhwNCnernzAs67CXL5xu1Ocvj3MjDBtuubAL+t20qEAOUfDIEFwXbLnN/4Jc2BIOXL3oDlIbc82GobwXb73LF+++1hAm0+j29c7NRtXc+Y2xtVsIXmgiDlA5qd22N33p6Pz1R6lmAZY+4Bjgc2WGv3duf1w+kgdzSwEviutbbKqxhEREREpBsEAkDAuQWwlU3Bgc7EgHExV/uoKOBM7BY7+Zv7jpPA/fArscv/sdQpP2lK7PJb3QTw4O/GLr+spXUxdvlP4rVOWsu0O94kSDMPnDUpZgI244H3CNDMjVP3aZc8Eglz5ZMLCdK8I8FsaUl0lrnjlaUEbIQfHjwyZgL6xLyVBGyEk/YdFDOB/HTpOgJEGDoommA2O4lwJEyTCTstk81NEKlrtV1nmdFNNQSIwMrPWtZp2YeNcHRjAwEbgTciTnmaXRWduCN2eUty2kHy+Qg4rX9XhlolaDsSwFu3N/OPtEa8g5ctWH8D/kyrZ0eBi4GXrLV/NMZc7H7+tYcxiIiIiIiknzFYEyRMEApLYi7yZegLZ2LQHjHLFxW5t/l1kGC+/K6bYHYwNuEjn7gJ5jGxy/8cJ8G8Kpo8nhV73Z8nuPX1jJ3HPbSRVglYNCGL7PS5bZLXOmFr+7mZPzy9iAARfj1lXMzt3fHKJzuSzxjbe/S9lQRo5uT9hrjlzW22v/DjtcDymHVLlWcJlrX2NWPM6J1mnwgc5k7/HXiFHE6wUn0g0u/1pWOJjm0mj2uRDL/PHT/HtvC77pK5NCZM9sr0Y5Pp8cWT6u/C6zG+dE3vJsbsaCEifoc5yVpQ3MOZ2KNryeecJU75yUfHLr9j7dvAo6kF2YGAJ1vt2GBr7ToA931QN+9fxHPRsRnWVNUx/a4K5q1K712wXm/fb7leP8lOic5Lv89bv/efyTL92GR6fPGk+rtIte7ZfOwkt3V3gpU0Y8y5xpj3jTHvV1ZW+h2OSNJijc2QTdv3W67XT7JTovPS7/PW7/1nskw/NpkeXzyp/i5SrXs2HzvJbd2dYH1pjNkFwH3f0NGC1to7rbWTrLWTBg4c2G0BiqQqOjYDeDuuhVfb91uu10+yU6Lz0u/z1u/9Z7JMPzaZHl88qf4uUq17Nh87yW3d3U37k8AZwB/d9ye6ef8insvkcaCyQa7XT7JTPowJ4+WAqn7y+7tJJNPjiyfV30Wqdc/mYye5e80Bb7tpfwinQ4sBxpg1wKU4idU/jDFnA58DU73av4ifMnkcqGyQ6/WT7JTpY5j5vf9MlunHJtPjiyfV30Wqdc/mYye5y8teBE/roOhIr/Ypki65+L8pkh46N6SrEp07uXxu5XLdIPfrJ12nHqG7LpvrnrGdXIiIiIiIiGQbJVgiIjmkpr6JL7bUdbm74lTXF5H2vP5d6Xfbddl+7LI9fj/V1DcR7NV/iBfbVoIlIpIjNKaMSObR2IiZK9uPXbbH76fosQuWlA3zYvtKsEREcoTGlBHJPBobMXNl+7HL9vj91HLsjDfbV4IlIpIjNKaMSObR2IiZK9uPXbbH76eWY2et9WL73T0OloiIeERjyohkHo2NmLmy/dhle/x+ih67z7dtWevF9pVgSYf87h7T665N/a5fNlO3sx3zu25+jymT6u/Oy+Pn93eTKr/j93v/XvL6vMz2sRFz+bv3+prntVTi9zt2ryWqX2lxAc21m9Z7sW/dIigiIiIiIpImSrBERCQrqDvi/KXvXvyic0+6QgmWiIhkPHVHnL/03YtfdO5JVynBEhGRjKfuiPOXvnvxi8496SolWCIikvHUHXH+0ncvftG5J12lXgRFRCTjqTvi/KXvXvyic0+6SgmWeCbXu//MZH4fe6/3n8r2M/3Y+B1fIn7Gp66oM5uXxy/Rd5/r310+D43hd+zZft3x8u+l39+N3/uPR7cIioiIiIiIpIkSLBERERERkTRRgiUiIiIa70dEulUuX3OUYImIiOQ5jfcjIt0p1685SrBERETynMb7EZHulOvXHCVYIiIieU7j/YhId8r1a466aRfxQCZ3u5oNcr1+kp1yucviXB/vx+/vJpFMjy+eVH8X+dwFfT7L9WuOEiwRERHxfLwfEZHWcvmao1sERURERERE0kQJloiIiIiISJoowRIREREREUkTJVgiIiIiIiJpok4uRERyiHrkEsk86lk2c2X7scv2+P30yHkH8Y8febNttWCJiIiIiIikiRIsERERERGRNFGCJSIiIiIikiZKsERERERERNJECZaIiIiIiEiaKMESERERERFJE3XTLiIiWUHdEecvfffiF5170hVqwRIREREREUkTJVgiIiIiIiJpogRLREREREQkTZRgiYiIiIiIpIkSLBERERERkTQx1lq/Y0ho0qRJ9v333/c7DBERERERyRHGmHnW2knp3q5asERERERERNJECZaIiIiIiEiaKMESERERERFJEyVYIiIiIiIiaaIES0REREREJE2UYImIiIiIiKSJEiwREREREZE0UYIlIiIiIiKSJkqwRERERERE0kQJloiIiIiISJoowRIREREREUkTJVgiIiIiIiJpogRLREREREQkTZRgiYiIiIiIpIkSLBERERERkTRRgiUiIiIiIpImxlrrdwwJGWNqgKV+xyF5ZwCw0e8gJC/p3BO/6NwTP+i8E7/sbq0tTfdGQ+neoEeWWmsn+R2E5BdjzPs678QPOvfELzr3xA8678Qvxpj3vdiubhEUERERERFJEyVYIiIiIiIiaZItCdadfgcgeUnnnfhF5574Reee+EHnnfjFk3MvKzq5EBERERERyQbZ0oIlIiIiIiKS8ZRgiYiIiIiIpElGJ1jGmGONMUuNMcuMMRf7HY9kP2PMCGPMXGPMYmPMR8aYC935/YwxLxhjPnXfy9z5xhhzs3sOLjTGHNBqW2e4y39qjDnDrzpJ9jDGBI0x840xT7ufxxhj3nHPoUeMMYXu/CL38zK3fHSrbVzizl9qjDnGn5pINjHG9DXGPGqMWeJe+w7SNU+8Zoz5uft3dpEx5iFjTLGueeIFY8w9xpgNxphFreal7RpnjCk3xnzornOzMcYkiiljEyxjTBC4FfgGsCdwmjFmT3+jkhwQBn5hrd0DmAz8xD2vLgZestaOB15yP4Nz/o13X+cCt4PzwwUuBb4KfAW4NPrjFYnjQmBxq89XAze4510VcLY7/2ygylo7DrjBXQ73XJ0G7AUcC9zmXitF4rkJ+Le1dgKwH845qGueeMYYMwyYAUyy1u4NBHGuXbrmiRf+hnN+tJbOa9zt7rLR9XbeVzsZm2DhVG6ZtXa5tbYReBg40eeYJMtZa9dZaz9wp2tw/qExDOfc+ru72N+Bk9zpE4F7raMC6GuM2QU4BnjBWrvZWlsFvEASPzjJX8aY4cA3gbvczwY4AnjUXWTn8y56Pj4KHOkufyLwsLW2wVq7AliGc60UickY0xv4H+BuAGtto7V2C7rmifdCQA9jTAjoCaxD1zzxgLX2NWDzTrPTco1zy3pba9+2Ts+A97baVocyOcEaBqxu9XmNO08kLdxbECYC7wCDrbXrwEnCgEHuYh2dhzo/pbNuBH4FRNzP/YEt1tqw+7n1OdRyfrnlW93ldd5JZ40FKoG/uren3mWMKUHXPPGQtfYL4Frgc5zEaiswD13zpPuk6xo3zJ3eeX5cmZxgxbq/UX3KS1oYY3oB/wR+Zq2tjrdojHk2znyRdowxxwMbrLXzWs+OsahNUKbzTjorBBwA3G6tnQhsY8etMrHo3JOUubdWnQiMAYYCJTi3Zu1M1zzpbp0917p0DmZygrUGGNHq83BgrU+xSA4xxhTgJFcPWGsfc2d/6TYD475vcOd3dB7q/JTOOBg4wRizEud25yNwWrT6urfPQNtzqOX8csv74Nz+oPNOOmsNsMZa+477+VGchEvXPPHSUcAKa22ltbYJeAz4GrrmSfdJ1zVujTu98/y4MjnBeg8Y7/Y4U4jzkOOTPsckWc69p/tuYLG19vpWRU8C0R5jzgCeaDX/B26vM5OBrW5T83+AKcaYMvd/6qa480TasdZeYq0dbq0djXMte9laOx2YC5ziLrbzeRc9H09xl7fu/Gluj1tjcB62fbebqiFZyFq7HlhtjNndnXUk8DG65om3PgcmG2N6un93o+edrnnSXdJyjXPLaowxk91z+QetttWhUKIF/GKtDRtjLsCpcBC4x1r7kc9hSfY7GPg+8KExZoE7bybwR+Afxpizcf4wTHXLngWOw3mwdjtwJoC1drMx5kqc/wgAuMJau/MDliKJ/Bp42BhzFTAftyMC9/0+Y8wynP/FnQZgrf3IGPMPnH+ohIGfWGubuz9syTI/BR5w/7NyOc51LICueeIRa+07xphHgQ9wrlXzgTuBZ9A1T9LMGPMQcBgwwBizBqc3wHT+u+6sj0ndAAADGUlEQVR8nJ4KewDPua/4MTn/QSAiIiIiIiKpyuRbBEVERERERLKKEiwREREREZE0UYIlIiIiIiKSJkqwRERERERE0kQJloiIiIiISJoowRIRkZQYY5qNMQuMMYuMMXOMMT07WO5ZY0zfNO97tDHGGmN+2mren40x/5um7b9ijJmUjm2JiEh+UIIlIiKpqrPW7m+t3RtoBH7UutAd0DFgrT3OWrvFg/1vAC50x3nKGMaYjB1rUkREvKMES0RE0ul1YJzbsrTYGHMbzmCjI4wxK40xA9yyJcaYu9xWrweMMUcZY940xnxqjPkKgDGmxBhzjzHmPWPMfGPMiR3ssxJ4CThj54LWLVDuvle60/9rjHncGPOUMWaFMeYCY8xF7n4qjDH9Wm3me8aYt9xY48bmbneOMeYp4Pm0HFEREckqSrBERCQt3BabbwAfurN2B+611k601q7aafFxwE3AvsAE4HTgEOCXwEx3md8AL1trDwQOB64xxpR0sPs/Ar8wxgQ7EfLe7n6/AswCtltrJwJvAz9otVyJtfZrwI+Be5KI7SDgDGvtEZ2IRUREcoRuXxARkVT1MMYscKdfB+4GhgKrrLUVHayzwlr7IYAx5iPgJWutNcZ8CIx2l5kCnGCM+aX7uRgYCSzeeWPW2hXGmHdxEqZkzbXW1gA1xpitwFPu/A9xEr+oh9x9vGaM6e0+R9ZRbAAvWGs3dyIOERHJIUqwREQkVXXW2v1bzzDGAGyLs05Dq+lIq88RdvxtMsB3rLVLk4zj98CjwGut5oXZcbdGcRdiALA7rWc7is0Y81Xi11tERHKcbhEUEZFM9R/gp8bN1owxE+MtbK1dAnwMHN9q9kqg3J0+pYtxnOru/xBgq7V2a2djExGR/KEES0REMtWVQAGw0BizyP2cyCxgeKvP1wLnG2PeAgZ0MY4qd/3ZwNkpxCYiInnAWLvznQ8iIiIiIiLSFWrBEhERERERSRMlWCIiIiIiImmiBEtERERERCRNlGCJiIiIiIikiRIsERERERGRNFGCJSIiIiIikiZKsERERERERNLk/wO5DZRaqBPPzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = {'Entries':  N_NotEmptyBin,\n",
    "     'Chi2':     chi2_val,\n",
    "     'ndf':      Ndof,\n",
    "     'Prob':     chi2_prob,\n",
    "     'c0':       [minuit.values['c0'], minuit.errors['c0']],\n",
    "     'c1':       [minuit.values['c1'], minuit.errors['c1']]\n",
    "    }\n",
    "\n",
    "text = nice_string_output(d, extra_spacing=-2, decimals=2)\n",
    "add_text_to_ax(0.02, 0.95, text, ax, fontsize=12)\n",
    "fig.tight_layout()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we save the plots if save_plots is True:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "if save_plots:\n",
    "    fig.savefig('PrimeNumberDistribution.pdf', dpi=600)"
   ]
  }
 ],
 "metadata": {
  "executable": "/usr/bin/env python",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "main_language": "python"
 },
 "nbformat": 4,
 "nbformat_minor": 2
}