Week2/original/TableMeasurements/TableMeasurement_original.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table Length Measurements\n",
    "\n",
    "Python program for analysing measurements of the length of the lecture table in Auditorium A at NBI.  \n",
    "There are two measurements each with estimated error of the table length:\n",
    "1. Measurement with a 30cm ruler.\n",
    "2. Measurement with a 2m folding ruler.\n",
    "\n",
    "Each person was asked not only to state the measurement, but also their estimated uncertainty. None of the persons could see others measurements in order to get the largest degree of independence. Also, the 30cm ruler measurement was asked to be done first. Finally, those measuring were asked to try to measure to the mm, even if precision was less than this.\n",
    "\n",
    "### Authors: \n",
    "- Troels C. Petersen (Niels Bohr Institute)\n",
    "\n",
    "### Date:    \n",
    "- 19-11-2020 (latest update)\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                                     # Matlab like syntax for linear algebra and functions\n",
    "import matplotlib.pyplot as plt                        # Plots and figures like you know them from Matlab\n",
    "from iminuit import Minuit                             # The actual fitting tool, better than scipy's\n",
    "import sys\n",
    "from scipy import stats\n",
    "from scipy.special import erfc                         # Error function, to get integral of Gaussian\n",
    "\n",
    "sys.path.append('../../../External_Functions')\n",
    "from ExternalFunctions import Chi2Regression, BinnedLH, UnbinnedLH\n",
    "from ExternalFunctions import nice_string_output, add_text_to_ax # useful functions to print fit results on figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Options for the program: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "blinded = True            # Add a random (but fixed) offset to the 30cm and 2m data seperately\n",
    "save_plots = False\n",
    "\n",
    "r = np.random             # Random generator\n",
    "r.seed(42)                # Set a random seed (but a fixed one)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Gaussian PDF (unit integral):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define your PDF / model \n",
    "def gauss_pdf(x, mu, sigma):\n",
    "    \"\"\"Normalized Gaussian\"\"\"\n",
    "    return 1 / np.sqrt(2 * np.pi) / sigma * np.exp(-(x - mu) ** 2 / 2. / sigma ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extended Gaussian PDF (including normalisation, which enables fit to histograms):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "def gauss_extended(x, N, mu, sigma) :\n",
    "    \"\"\"Non-normalized Gaussian\"\"\"\n",
    "    return N * gauss_pdf(x, mu, sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial data analysis:\n",
    "\n",
    "Before we even look at the look at the data, we decide whether or not we want to blind the analysis by adding a constant to all measurements:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "if blinded:\n",
    "    blinding30cm = r.normal(0, 0.1)      # I add a constant (Gaussian with +-10cm) to remain \"blind\"\n",
    "    blinding2m   = r.normal(0, 0.1)      # I add a constant (Gaussian with +-10cm) to remain \"blind\"\n",
    "else:\n",
    "    blinding30cm = 0\n",
    "    blinding2m = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define what datafiles we want to look at. Extend it to suit your analysis: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "infiles = [\"data_TableMeasurements2020.txt\",\n",
    "           \"data_TableMeasurements2019.txt\",\n",
    "           \"data_TableMeasurements2018.txt\",\n",
    "           \"data_TableMeasurements2017.txt\",\n",
    "           \"data_TableMeasurements2016.txt\",\n",
    "           \"data_TableMeasurements2015.txt\",\n",
    "           \"data_TableMeasurements2014.txt\",\n",
    "           \"data_TableMeasurements2013.txt\",\n",
    "           \"data_TableMeasurements2012.txt\",\n",
    "           \"data_TableMeasurements2011.txt\",\n",
    "           \"data_TableMeasurements2010.txt\",\n",
    "           \"data_TableMeasurements2009.txt\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We read in all the data from the `infiles` files:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "  3.35017357  3.34617357  3.34617357  3.04617357  3.35117357  3.33617357\n",
      "  3.35617357  3.35117357  3.34617357  3.34617357  3.35617357  3.33617357\n",
      "  3.35017357  3.35617357  3.33617357  3.34617357  3.73617357  3.35017357\n",
      "  3.34917357  3.34617357  3.34617357  3.35117357  3.35117357  3.35117357\n",
      "  1.35217357  3.34917357  3.34917357  1.35117357  3.35117357  3.34717357\n",
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      "  3.34917357  3.34917357  3.34217357]\n",
      "\n",
      "\n",
      "Read all 12 file(s) which included 711 measurements. \n",
      "\n"
     ]
    }
   ],
   "source": [
    "L30cm = np.array([])\n",
    "eL30cm = np.array([])\n",
    "L2m = np.array([])\n",
    "eL2m = np.array([])\n",
    "\n",
    "# Loop over files and open them\n",
    "for infile in infiles:\n",
    "    \n",
    "    tmp_L30cm, tmp_eL30cm, tmp_L2m, tmp_eL2m = np.loadtxt(infile, skiprows=2, unpack=True)\n",
    "    \n",
    "    L30cm = np.append(L30cm, tmp_L30cm + blinding30cm)\n",
    "    eL30cm = np.append(eL30cm, tmp_eL30cm)\n",
    "    L2m = np.append(L2m, tmp_L2m + blinding2m)\n",
    "    eL2m = np.append(eL2m, tmp_eL2m)\n",
    "    \n",
    "N_read  = len(L30cm)       # Number of measurements read in total\n",
    "\n",
    "print(L2m)\n",
    "\n",
    "print(f\"\\n\\nRead all {len(infiles)} file(s) which included {N_read} measurements. \\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we plot the data. Using an interactive plotting style could be useful here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:21: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1008 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Carefully consider binning - this might have to be changed, and subplots are defintely worth considering!\n",
    "Nbins = 1000\n",
    "minL = 2.2\n",
    "maxL = 3.2\n",
    "binwidth = (maxL-minL)/Nbins\n",
    "\n",
    "# Define two histograms with all the lengths recorded:\n",
    "fig_raw, ax = plt.subplots(nrows=2, figsize=(16,14), gridspec_kw={'hspace':0.5})\n",
    "ax_L30cm, ax_L2m = ax\n",
    "\n",
    "hist_L30cm = ax_L30cm.hist(L30cm, bins=Nbins, range=(minL, maxL), histtype='step', label='30cm data')\n",
    "ax_L30cm.set_title('Length estimates by 30cm ruler',fontsize=15)\n",
    "ax_L30cm.set_ylabel('Frequency',fontsize=15)\n",
    "ax_L30cm.set_xlabel('Table length (m)',fontsize=15)\n",
    "\n",
    "hist_L2m = ax_L2m.hist(L2m, bins=Nbins, range=(minL, maxL), histtype='step', label='2m data')\n",
    "ax_L2m.set_title('Length estimates by 2m ruler',fontsize=15)\n",
    "ax_L2m.set_ylabel('Frequency',fontsize=15)\n",
    "ax_L2m.set_xlabel('Table length (m)',fontsize=15)\n",
    "\n",
    "fig_raw.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 30 cm ruler:\n",
    "\n",
    "We consider the measurements for the 30cm ruler and focus on that for now. Below is a mean and RMS calculation along with a general Gaussian fit to all the data. Somehow, it doesn't seem optimal/right..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Initial estimate of raw data (30 cm ruler):  3.379 +- 0.008 m     (RMS = 0.203)\n"
     ]
    }
   ],
   "source": [
    "print(f\"  Initial estimate of raw data (30 cm ruler):  {L30cm.mean():.3f} +- {L30cm.std(ddof=1)/np.sqrt(len(L30cm)):.3f} m     (RMS = {L30cm.std(ddof=1):.3f})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting the data:\n",
    "Then we set up an __unbinned likelihood fit__, and fit the full data set (note that we set the initial step size, called error_mu and error_sigma, and fix the normalisation):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  The unbinned LH fitted estimate (30cm ruler): 3.379 +- 0.008 m     RMS = 0.203\n"
     ]
    }
   ],
   "source": [
    "ullh_L30cm = UnbinnedLH(gauss_extended, L30cm, weights=None)\n",
    "minuit_L30cm = Minuit(ullh_L30cm, pedantic=False, N=len(L30cm)*binwidth, fix_N=True,\n",
    "                      mu=L30cm.mean(), error_mu=0.01,\n",
    "                      sigma=L30cm.std(ddof=1), error_sigma=0.01, print_level=0) \n",
    "minuit_L30cm.migrad();\n",
    "\n",
    "# The fitted values of the parameters and their uncertainties:\n",
    "L30cm_fit_mu = minuit_L30cm.values[\"mu\"]\n",
    "L30cm_fit_mu_error = minuit_L30cm.errors[\"mu\"]\n",
    "L30cm_fit_sigma = minuit_L30cm.values[\"sigma\"]\n",
    "print(f\"  The unbinned LH fitted estimate (30cm ruler): {L30cm_fit_mu:.3f} +- {L30cm_fit_mu_error:.3f} m     RMS = {L30cm_fit_sigma:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note on fit result:\n",
    "\n",
    "Surprised to see the same numbers come out of the unbinned likelihood fit as those of the mean, standard deviation, and uncertainty on the mean?\n",
    "\n",
    "Well, the reason for this is, that the calculation of these three quantities can actually be *derived* from the principle of maximum likelihood (see Barlow 5.2.1 and 5.2.2)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting:\n",
    "\n",
    "Now we plot the fit on the figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dQeso2asfS5IkSVKpO+M7o5m3Yn2Hre/AAb145stva3N+jx49GD16NH379qWuro4zzzyTc889l9NPP50vfelLfO5zn+Oiiy7iiiuu4JZbbuHKK6/ssNp2xg033MDFF19M7969C7YNQ60kSZIk7aR5K9Yz+zvnd9j6hnz5/m3Ojwj69u0LQF1dHXV1dUQEKSVGjx7N7bffDsDHP/5xrr32Wq688koWLVrEFVdcweuvvw7AjTfeyAEHHMC73vUuzjzzTMaOHcsJJ5zAZZddxjXXXMPixYu57bbbOPXUU7fY9vr167nsssuYNm0axxxzDOvXbw7zV155JePGjWP9+vVceOGFXHfddfzkJz9h/vz5jBo1ioEDB/L444+32m5XGWolSZIkqYw0NDRw8sknM3PmTD796U9z2mmnsWTJEgYMGEC3blnEGzx4MPPmzQPgqquu4q1vfSv33HMPDQ0NrFmzhuXLlzNz5kzuvPNObrrpJk455RRuv/12nn76ae677z6+9a1vce+9926x3RtvvJHevXszefJkJk+ezEknnbRp3je/+U322msvGhoaOPvss5k8eTJXXXUVP/zhD3n88ccZOHBgm+2GDx++S5+H59RKkiRJUhmprKxk0qRJVFdX8/zzzzNlyhRSSlu1iwgARo8evWkYcmVlJXvssQcAQ4cOZdiwYVRUVHDcccdx9tlnExEMGzaM2bNnb7W+J598kosvvhiA4cOHbxFG77jjDk466SROPPFEpk6dyrRp01qtvb3tdoShVpIkSZLK0IABAzjrrLN46KGHGDhwICtWrKC+vh6A6upqDjjggG0u36NHj02vKyoqNr2vqKjYtJ6WmoJyc7NmzeL73/8+jz32GJMnT+b888+ntrZ2p9vtKEOtJEmSJJWJmpoaVqxYAWTnuD766KMcffTRRASjRo3irrvuAuDWW2/lggsuAODss8/mxhtvBLKhy6tWrdqpbb/lLW/htttuA2DKlClMnjwZgFWrVtGnTx/22GMPFi1axIMPPrhpmX79+rF69ertttsVhlpJkiRJKhMLFixg1KhRDB8+nFNOOYW3v/3tvPvd7wbgu9/9Lj/84Q85/PDDWbp0KZ/85CcB+PGPf8zjjz/OsGHDOPnkk5k6depObfvKK69kzZo1DB8+nO9973ubLiR1wgkncOKJJ3LcccfxiU98gjPOOGPTMpdffjnnnnsuo0aN2ma7XRGtjb0uNyNHjkzbuz+SJEmSpK7t2K8/xLqNDbt0teLp06dzzDHHbHrf2bf06QpafsYAETEhpTSytfZe/ViSJEmSdlJXD6ClwOHHkiRJkqSyZaiVJEmSJJUtQ60kSZIk7YDd4bpEpWpnPltDrSRJkiS1U8+ePVm6dKnBtgBSSixdupSePXvu0HJeKEqSJEmS2mnw4MFUV1dTU1NT7FJ2Sz179mTw4ME7tIyhVpIkSZLaqaqqiqFDhxa7DDXj8GNJkiRJUtky1EqSJEmSypahVpIkSZJUtgy1kiRJkqSyZaiVJEmSJJUtQ60kSZIkqWwZaiVJkiRJZctQK0mSJEkqW4ZaSZIkSVLZMtRKkiRJksqWoVaSJEmSVLYMtZIkSZKkslWyoTYiBkTEXRHxckRMj4g3FbsmSZIkSVJp6VbsArbhx8BDKaULI6I70LvYBUmSJEmSSktJhtqI6A+8BbgUIKW0EdhYzJokSZIkSaWnVIcfHwrUAL+OiBci4uaI6FPsoiRJkiRJpaVUQ2034CTgxpTSicBa4MvNG0TE5RExPiLG19TUFKNGSZIkSVKRlWqorQaqU0rP5e/vIgu5m6SUbkopjUwpjRw0aFCnFyhJkiRJKr6SDLUppYXAGxFxVD7pbGBaEUuSJEmSJJWgkrxQVO5fgdvyKx+/DlxW5HokSZIkSSWmZENtSmkSMLLYdUiSJEmSSldJDj+WJEmSJKk9DLWSJEmSpLJlqJUkSZIklS1DrSRJkiSpbBlqJUmSJElly1ArSZIkSSpbhlpJkiRJUtky1EqSJEmSypahVpIkSZJUtgy1kiRJkqSyZaiVJEmSJJUtQ60kSZIkqWwZaiVJkiRJZctQK0mSJEkqW4ZaSZIkSVLZMtRKkiRJksqWoVaSJEmSVLYMtZIkSZKksmWolSRJkiSVLUOtJEmSJKlsGWolSZIkSWXLUCtJkiRJKluGWkmSJElS2TLUSpIkSZLKlqFWkiRJklS2DLWSJEmSpLJlqJUkSZIklS1DrSRJkiSpbBlqJUmSJElly1ArSZIkSSpbhlpJkiRJUtky1EqSJEmSypahVpIkSZJUtroVu4C2RMRsYDXQANSnlEYWtyJJkiRJUqkp2VCbG5VSWlLsIiRJkiRJpcnhx5IkSZKkslXKoTYBf4uICRFxecuZEXF5RIyPiPE1NTVFKE+SJEmSVGylHGrPSCmdBJwLfDoi3tJ8ZkrpppTSyJTSyEGDBhWnQkmSJElSUZVsqE0pzc+fFwP3AKcWtyJJkiRJUqkpyVAbEX0iol/Ta+AdwJTiViVJkiRJKjWlevXjfYF7IgKyGm9PKT1U3JIkSZIkSaWmJENtSul14IRi1yFJkiRJKm0lOfxYkiRJkqT2MNRKkiRJksqWoVaSJEmSVLYMtZIkSZKksmWolSRJkiSVLUOtJEmSJKlsGWolSZIkSWXLUCtJkiRJKluGWkmSJElS2TLUSpIkSZLKlqFWkiRJklS2DLWSJEmSpLJlqJUkSZIkla0OD7UR8ceIeEdEREevW5IkSZKk5grRU3sQ8BAwNyL+OyIOL8A2JEmSJEnq+FCbUjoDOAr4HfAx4JWIeDIiLo2IPh29PUmSJElS11WQc2pTSjNSSl8FDgHOA6qBnwMLIuKWiDizENuVJEmSJHUtBb1QVEopAU8CDwJTgb5kIffJiJgQEScUcvuSJEmSpN1bwUJtRJwREb8EFgI/BSYBb0op7Q+MAFaRDVGWJEmSJGmndOvoFUbEV4BLgcOBvwOfBf6UUlrX1CalNDki/pOsF1eSJEmSpJ3S4aEWuBr4LXBLSumVbbR7Gbi8ANuXJEmSJHURhQi1g1NK9dtrlFJaCtxSgO1LkiRJkrqIQpxTe2ZEfKy1GRFxSUS8tQDblCRJkiR1QYUItd8CDmhj3n75fEmSJEmSdlkhQu3xwPg25k0EjivANiVJkiRJXVAhQm0jsGcb8/Yu0DYlSZIkSV1QIQLmM8AXIqKq+cT8/eeApwuwTUmSJElSF1SIqx9/lSy4zoiIPwALgP2Bi4C9gH8owDYlSZIkSV1Qh4falNKLEXE6cC3wz2RDkZcDjwHXpJRe7uhtSpIkSZK6pkL01JJSmgp8oBDrliRJkiSpiRdtkiRJkiSVrYL01EbE+4B/AgYDPVvOTym9uRDblSRJkiR1LR0eaiPia8B1wFRgGrBxJ9dTSXa/23kppXd3XIWSJEmSpN1FIXpqLweuTyl9aRfXczUwHei/6yVJkiRJknZHhTinth/wt11ZQUQMBs4Hbu6QiiRJkiRJu6VChNo7gHfs4jpuAP4daNz1ciRJkiTtqB/87RWGXfMwi1bVFruUVtXWNXDqNx/lC3e82K721943lXUbGwpclYqhEMOPHwK+HxF7AY8AK1o2SCm12ZMbEe8GFqeUJkTEWdtodznZUGcOPvjgXa1ZkiRJUjNvLFvH6g31rFhXx779t7r2a9FtbGhk8eoNvLF8XbvaVy9fx/cuHM43759e4MrU2QoRau/Knz+ZP1pKQOU2lj8DeG9EnEd25eT+EfH7lNLFW6wkpZuAmwBGjhyZdrlqSZIkSbu1KHYBKohChNojdmXhlNJXgK8A5D21X2wZaCVJkiRJggKE2pTSax29TkmSJEmSWlOIC0UREVUR8c8R8b8R8UBEHJ5PvzAijmrvelJKY7xHrSRJkiSpLR3eU5sH2L8BA4GJwD+w+V6zo4D3AB/v6O1KkiRJkrqeQvTU/gRYCAwBzmHL87GfIAu5kiRJkiTtskJcKOqtwAdTSssiouVVjhcC+xdgm5IkSZKkLqgQPbUbgB5tzDuAVu5bK0mSJEnSzihEqH0E+EpE9Gs2LUVEFfAZ4KECbFOSJEmS1AUVYvjxvwHPAjOBh4EE/AdwHNAH+GABtilJkiRJ6oI6vKc2pTQXOAH4FXA0MIfsolH3ASenlOZ39DYlSZIkSV1TIXpqSSktBb5SiHVLkiRJktSkEOfUSpIkSZLUKTq8pzYiFpCdR9umlNIBHb1dSZIkSVLXU4jhx7ewdajdC3gb0Bu4tQDblCRJkiR1QR0ealNK/9na9IioAO4E1nX0NiVJkiRJXVOnnVObUmoEfglc1VnblCRJkiTt3jr7QlGHAN07eZuSJEmSpN1UIS4UdXkrk7sDxwAfA+7u6G1KkiRJkrqmQlwo6hetTKsH5pENP/56AbYpSZIkSeqCChFqq1pOSCk1FGA7kiRJkqQurhBXPzbASpIkSZI6RSHOqf3IjrRPKd3e0TVIkiRJkrqGQgw//j2Q8tfRbHpb0wy1kiRJkqSdUohb+pwGzAGuA4YD++XP38innwbsmT/2KsD2JUmSJEldRCF6ar8L3JhSur7ZtMXAlIhYB3wvpTSqANuVJEmSJHUxheipPR14sY15k8l6aiVJkiRJ2mWFCLXVwKVtzLuU7H61kiRJkiTtskIMP/5P4PaIOBa4j2zo8T7Ae4FhwIcLsE1JkiRJUhdUiPvU3hERs4EvA5cB+wKLgHHAv6SUnuvobUqSJEmSuqZC9NSSUnoe+KdCrFuSJEmSpCaFOKcWgIjYIyLeFBEfjIgB+bSqQm1PkiRJktT1dHiojYiKiPgW2QWhngH+AByaz74vIq7p6G1KkiRJkrqmQvTUfhP4NPA54Eggms27l+yCUZIkSZIk7bJCnFP7ceDLKaVfRkRli3mvAYcVYJuSJEmSpC6oED21ewIz2phXBbQMupIkSZIk7ZRChNqpwHvamPdO4IXtrSAiekbE8xHxYkRMjYjrOrRCSZIkSdJuoRDDj78F3BERPYA7gQQcHxHvAa4E3teOdWwA3pZSWpNfMfnpiHgwpTS2APVKkiRJkspUh4falNLdEfEx4LvA5fnk3wALgctSSg+2Yx0JWJO/rcofqaNrlSRJkiSVt4LcpzaldDtwMHA8cBYwHBicT2+XiKiMiEnAYuCRlNJzhahVkiRJ0u7hl0++zn0vzm93+5QS//vEa/zf5PYvo9LToaE2Pxd2WkS8M2WmpZSeTClNSSk17si6UkoNKaURwGDg1Ig4vsW2Lo+I8RExvqampiN3Q5IkSVIZ+uYD07lxzGvtbt+Y4NsPvswvnmj/Mio9HRpqU0q1wEA6cKhwSmkFMAZ4V4vpN6WURqaURg4aNKijNidJkiRJKiOFGH78B+Bju7KCiBgUEQPy172Ac4CXO6A2SZIkSdJupBBXP34NuDAixgIPAIvYsuc2pZR+uZ117A/cGhGVZMH7jpTS/xWgVkmSJElSGStEqL0hf94fOLWV+QnYZqhNKU0GTuzguiRJkiRJu5lChNqqAqxTkiRJkqStdMg5tRHxt4g4CjZdtbgBeCvQs+l980dHbFOSJEmSpI66UNQ5wB5Nb/JzYR8Bjuqg9UuSJEmStJVCXP24SRRw3ZIkSZIkFTTUSpIkSZJUUB0ZalM7p0mSJEmS1CE68urHD0dEfYtpj7UyjZTSPh24XUmSJElSF9VRofa6DlqPJEmSJEnt1iGhNqVkqJUkSZIkdTovFCVJkiRJKluGWkmSJElS2TLUSpIkSZLKlqFWkiRJklS2DLWSJEmSpLJlqJUkSZIklS1DrSRJkiSpbBlqJUmSJElly1ArSZIkSSpbhlpJkiRJUtky1EqSJEmSypahVpIkSZJUtgy1kiRJkqSyZaiVJEmSJJUtQ60kSZIkqWwZaiVJkiRJZctQK0mSJEkqW4ZaSZIkSVLZMtRKkiRJksqWoVaSJEmSVLYMtZIkSZKksmWolSRJkiSVLUOtJEmSJKlsGWolSZIkSWWrJENtRBwUEY9HxPSImBoRVxe7JkmSJElS6elW7ALaUA98IaU0MSL6ARMi4pGU0rRiFyZJkiRJKh0l2VObUlqQUpqYv14NTAcOLG5VkiRJkopp/or1zFy8mvqGxk3TUkq8VnYq9FgAACAASURBVLOGlNJW7Zes2cDMxauzZRo3z5+zdC0b6xtZub6uU+pWYZVqT+0mETEEOBF4rsX0y4HLAQ4++OBOr0uSJElS51myZgNn/+AJelZVcOVZh3HRqVkGGDd7OWf/4Alu/OhJWy3znp8+Tc+qSlas28jydXWcP2x/Vq6v463Xj+Gz5xzBUzOW0L9nyUcibUdJ9tQ2iYi+wJ+Bz6aUVjWfl1K6KaU0MqU0ctCgQcUpUJIkSVKn2FDfyJ69q7j0zUNZU1u/1fzVG7aetqa2nr985gwuedOQVuetqa3na+8+thDlqhOVbKiNiCqyQHtbSunuYtcjSZIkSSo9JRlqIyKAW4DpKaUfFrseSZIkSVJpKslQC5wBXAK8LSIm5Y/zil2UJEmSJKm0lORZ0Smlp4Eodh2SJEmSpNJWqj21kiRJkiRtl6FWkiRJklS2DLWSJEmSpLJlqJUkSZIklS1DrSRJkiSpbBlqJUmSJElly1ArSZIkSSpbhlpJkiRJUtky1EqSJEmSypahVpIkSZJUtgy1kiRJkqSyZaiVJEmSJJUtQ60kSZIkqWwZaiVJkiRJZctQK0mSJEkqW4ZaSZIkSVLZMtRKkiRJksqWoVaSJEmSVLYMtZIkSZKksmWolSRJkiSVLUOtJEmSJKlsGWolSZIkSWXLUCtJkiRJKluGWkmSJElS2TLUSpIkSZLKlqFWkiRJklS2DLWSJEmSpLJlqJUkSZIklS1DrSRJkiSpbBlqJUmSJElly1ArSZIkSSpbhlpJkiRJUtkqyVAbEb+KiMURMaXYtUiSJEmSSldJhlrgN8C7il2EJEmSJKm0lWSoTSk9CSwrdh2SJEmSpNJWkqFWUtv+7c4X+dnoGcUuQyqouUvXcfHNz/H8LL/fbOn3Y+fw6dsmUlvXsFPLj5u9jItvfo45S9d2cGWZdRvrueJ3E7hj3BsFWf+OmjJvJR+9eSwvL1y1adqYVxbz8V89z+JVtVu0rW9o5Oo/vsCHbxrLo9MWtbq+a/4yhQ/fNLZk9k+FdcvTs7j6jy9Q39BY7FLaNHPxGj5681hefGPFLq3n2deWcMktz1G9fF27l3l6RrbM/BXrd2qb81es55JbnuPpGUtanb+qto7/d+t4/jJp3lbz7hhfzZW/n9DqcnOWruXzf5rEpb9+ntUb6gHo0S2LPd27bY4/97+0gDeWr9s07ZFpi7js188zd+k6/uV347lrQjUA335gOp++fSIf+9XzPPFqzRbbemjKQj5801g+/6dJNDSmTdNr6xr49G0T+dyfJnHxzc8xe0n2O7e130nNVS9fxyW3PMfn/zSJK343gXUb67eY/293vshPH2v978A/Pj+XK38/gfUbt///w5ylazf9P/vtB6bzjb9O2+4ypaxsQ21EXB4R4yNifE1NzfYXkHYTd06o5v6XFha7DKmgps5fydMzlzD29aXFLqXkPDp9Efe/tICV6+t2avnnXl/K0zOXMGVe639Q7aqlazby0NSFPDq99VDY2SbOXc4zM5fywtzNf/A/M3MJT7xaw4zFa7Zou76ugYenLuSIffvy9MzW/8i++4V5DB+8R8nsnwrr4SkL+cuk+azfyS+ROsPk6hU8M3Mp42bv2peAY19bylMzljB9wep2L/Psa0t4asYSXlnY/mWae2Xhap6asYRnX2v939uCFbU8On0RY17Z+m/9hatqeWZm9n/En698E+cev9+mef/ylsO4+4V5Wyz3yTOH8qfLT+ctRwwCYOQhe/KDD5zA7f98OocO7AvAUzNqePyVGsbOWsrDUxcx+uXs3/mtf5/N/ZMX8OSrNTzb4nfDUzNqOHr/ftz34nzqmn35sWp9Hfe/tIB7XpiX/c6dvxJo/XdScy8vyD6Tu1+Yx0NTF7Jk9cYt5md/By5oddlHpy/mwSkLWbp2Q6vzm5s6fxVPz1zCc68v5bd/n8Ovnpm13WVKWdmG2pTSTSmlkSmlkYMGDSp2OZIkaTfQraKCoQP7bLPNYfv07aRqJLXHyYfsRZ8e3Ta9P2BAz63a9Kyq5LRD9yYie19VWcGbDx/IiIMGbHf99Q1pm/MPHdSXiorYsaKLLSUOpIbDax7hC/yWP3X/Bqwr39FR3bbfRJIkSZJUttYtg/kTYd5EmDeBs+eM47yeS+Fl2FBRxdR0CKytgd57FbvSnVKSoTYi/gCcBQyMiGrgmpTSLcWtSpIkSZJKXH0tvDEV5k3Y/Fj2Wj4zYOCR1Oz3D/xi5p4MO2UU140L1jVUMnvQUUUte1eUZKhNKX242DVIkiRJUklrbISlM2DeBD665EGu6v4SB974BjTmF5jqux8MHgknXgwHngwHjICeezD5pQX8/pWJfKHfkdQxA9j2EOtSV5KhVpIkSZK0pX1Yzps3ToFHR2c9sPMnwYbswn+nR28mpqGsPukK+h92ehZi+x9Q5Io7h6FWkiRJkkpMX9bR442nYdqUfBjxRJ7vOR/WAc92g32Ph2EfyMLrgSdz1QMreeTlJTx9xij679m72OV3KkOtJEmSJBVT/UZYPJUDZ47h+m6jGVHxGofFfCruzYcF73UoDDmDayf2YsWew7jh6o9B1ZZXeU4xvgiFlwZDrSRJkiR1mkTftXNh8nMwb3zWC7tgMjRs4BhgUGV/JjUexn0Nb+KS9/8T+xz9pk1XJf7NuPs5ulu/rQJtV2eolSRJkqQC2Yfl7Dv/MVgyh7OnPsN7e7zIgCfWZjOresP+I+DUf4YDT+bp9Ydw8Z8XANl9bz9wyCjo3bWGEu8MQ60kSZIkdYT8frC9X3+eX1Y9yrCK19kvlsNYICrp1ecwHmw4lcNGvIVTz3wHDDoaKjdHstppi4CFRSu/XBlqJUmSJGlHbVjN0DUTOXbWLG6o+Dvdf/4lWDEHgL7AobE/zzYex0uNQznnnHM544xR/N+ExXz9L1P59sHDOHW/g4tb/27EUCtJkiRJ29CDjRwbczh54Xi4ez7MfwGWvMr/y+/v+kYMIu33Jhj5CTjwJGr6Hs3ZPxi3afmT9z4RujuMuFAMtZIkSZKUi8Y6jovZnLFyPNx3K/d1G8MRUU1VNMBcYNm+cMBJMOxCbp09gF5DT+E//7aQye9/B5VVlQCkVbXF3YkuxlArSZIkqWuqW0+vxZM4t/YhTptbzYXdX+K4h6r5QI86WAysGsBSDmZ0wwgmNx7KsFNH8a8XvAUiu5DTq8te4uju/fE82OIy1EqSJEna/W1YTWX1C1xa+RCjli+A/5kPNS9zeGrgcGBdbX8mpIOZMfQSfj69N3secRrfuPQ9XPYfD1LfmA0zHtp9n02BVqXDUCtJkiRpt9KfNRxXMYfjYxa97rsLFr0ES2fSj8S1VbBiw54w+BQ4+jzmdD+Ca8d346AhR/LbsXP53jHD+evUyZzXfT8DbJkw1EqSJEkqUwlWvMExq5/lmBnz+J+q53jL6Pl8oGf1phaN1YPhgBEw/IOs2etYRt22gsMPPZw/fPR0AFZVr6TmhckcZIAtW4ZaSZIkSaWvfj1HN87kuIUTuabbOI6pmMvRMRduWMsn8yZ9Y1+W7zGCn608kylpKFMbD+GJL19I/55V2SrWbaSGRzi8eHuhAjDUSpIkSSodKcGq+fSZM45PVT7AOfNq4GfVHLB0Jr9KjTAT1lb24JV0EPc3nM5HLziPn07ryYFHnszn//I61588nF/MmlzsvVAnMtRKkiRJKoo+rGf/1VNg4jhYNBUWTcke65czGPj3Kli6fj/Y/2RWH3Y+35nQjSNPeDPXPbOWRAUAHz3lfObMfpF9q/oWd2dUNIZaSZIkSYW1cR0seQUWvwyLp0HNy5w+bypTe86DqWSPbr1g32PhmPfCvsczt/uhnP+n5ZxzzBH86EMjWL1iPWMmPcu+vQ4i8Wqx90glxFArSZIkqWPU1cLSGVuEVxZPh+Wzgey2OFR2h72PYNXAEfzstTM47LiR/NM7z4E9h0BF5aZVrV+4mtU8WYy9UJkx1EqSJEnaMetXsP/qKby/YhyHvvgkTKqGmldg2WuQGrM2Fd1g78Nh/xPghItg0NGwz7Gw16FQ2Y1pLy/m56+O41N7HQZ7H1bc/VFZM9RKkiRJ2kqkBgbHYvrMHQ2zqmHJjPzxKqxdzCXAJd2h8eVusPehMOgoOO4fYZ+jYdAxWaDt1r3Yu6EuwFArSZIkdWXrlrHf6qlcUDGOw6Y8A1PmwZIZfK/mVap61MEDebtee8LAI+HId8DAI7l7Ti9++lIF11xyLmcde2BRd0Fdm6FWkiRJ2p2lBGuXwLLXW3/UruAjwEe6Q5pekZ3bOvBInqo/nocX9efTF57LwUeOgD57b7HamatfZlZ6jVRRVZTdkpoYaiVJkqRylxph5bzsgkxbBddZsHH15rZRAXsclJ3bevz7Ya9DuXduD372YiNf/sh5nDPsIADu++ML3Dt/Pp/Y/1To0684+yW1g6FWkiRJKnWNjbBmEayYmz9mw4q5nDF3Bo93f52DH18Ko+s3t6/olvW47nUoHPLm7HnPodnzgIO3Otf19TWvMDPNJFV6DqzKj6FWkiRJKrbGBli9EFbNy0PrnOx5ef688g1o2LjlMn32oar7fkxJQ1l58HmMOH4Y7JUH1/6DodI/9dU1eKRLkiRJhdTYkPWyrpyXhdZV82DVfFhZnT2vmpcF2tSw5XK9B2a9qvsNg6PPhz0PgQGHZNP2OAi692bMxGo+f8eL/OfhxzDilEOLs39SkRlqJUmSpJ21YTWsXgRrFmbBdM2izUF11fwsyK5esHVg7dYL9jgQ+h8AQ9+aPfc/APYYvDm09uhbnH2SyoyhVpIkSWqusRHWL+PgutfpWTGHbi8tg9qaLLA2BdfVC2HNYqhbu/XyWwTWt2wZWPsfAP0PzG6PE9H5+ybthgy1kiRJ2r2llPWorluS3dpm7ZL8dQ2sXdrsddP8xdBYz/cBugP35+vp3g/67Qt994MDT8qem943f+45wMAqdSJDrSRJkspHU0Bdv7z1x7plW4bUdUuz1y0vstSkqk92/9XeA6Hf/tn5q333gb778cOxK3l2UTd+c9V76Lv3gdC9T+fuq6R2MdRKkiSpc6UEG9dA7SrYsCoLqbWr2g6qLR8tz09trqo39Bm4ZUjtvTf0GbR5ep+Bm193793mqsZO+jvj0zLSnkOhe1UBPghJHcFQK0mSpPZpbIC6dbBxbf5YszmQblidBdTalVsG1Q2rWszPp5G2va0e/aHXgOzc0157ZueoNr1u69FzAFT17JSPQlLpMNRKkiTtLlLKhtnWrYf62tafN67Ng+maZuG0xaOujen169tXR2X3LJT27A89+mWv9xqaPffol09vPn+P7PWmcLoHVNozKql9SjbURsS7gB8DlcDNKaXvFLkkSZKktjU2QP2GLFQ2Peo3QEMdNOTP7Z1fvyELkHW1rTy3EVabnrfXA9qaqt7Z+aLd+2TnmHbvA937Qt99N0/fYl4+v3vvzaG15x6bX9tbKqkTlWSojYhK4OfA24FqYFxE3JdSmlbcyiRJEinljwZIjVmYS42QGojatezJKvo1dM9uedJiPim1eN98fmMr7Zvet9xeQxYCGxugsR4a6/Lnpun10FjP8DlL+Hy3BZzw8mOwvBc0NvDOOYsZ2m05h//9Hnip26b2Pevr+BkLOHxiLzZs3Ai/7rFpPdn6G7iX5ewzuoJzNtTC9UB9U0DdkNXWkSp7ZOGwW6+tn3v2h277tpjeE6p6tfLcY3ObpvBa1TsPpfnrioqOrV2SOlFJhlrgVGBmSul1gIj4I3ABUJahtvav/86i5as7YUs78c0sEGlnluusZcj+kNlBO38R/c7Zr537zLNtXd9tKb1XdaP617e0e5kd38xOHks7tVRnHhelfdzujJ3bJ3ayvp09LnZ8uaHrNnJj1Vr2f6EnC18rdI/Pzv4bzh6bXqeU72vz1+Sf9eZ50RR8mk/f9LppemOzbWy5vWvWbODL3RvoeVN31gSbtrd5XTR73dhivYmP1tVzYY8G+vy1ktoHIq8nbbENEpuWDxqzNil7jnxaWwYDL/QE5gA/2OGPtsONAIZVBmlWN+rndCNVdOOohuCQyqDnGz1Y162KFNn0BirZhzp61G1k/cZGlq1NNEYVqaInKfrQWFnFjNSHbnsOZMaSjRy5z140VnSnsaKKxsrupIqqze9beU55u1anN1tP03Sig4JmAuryxxYagdX5Q61ZunYDAI9MW0SvqsoiV9O6ydUrAZi2YBUPvrRgp9czs2YNABPmLKe+Ifs3Pn9FLQBPzajh9Xx+c6/l08bNXkZt3TYu3tWGl+at3LSe1mqftyIb7j5v+XoefGkBS9e2cQXrpvXln8XOWLm+jtlL122xngUra3nwpQXUN27+f+K1mrVb1Dp32TqO3r8/AA9PXUj3yopN62vuhbkrqIxg6rxV2TbmrWRAK/v8Yot9eOLVxQzs22OLaavW17X6eS1enf28xrxSw959um9zf1+YuxyAVxevoa6hc/5mKaRInfSH146IiAuBd6WU/l/+/hLgtJTSZ5q1uRy4PH97FPBKpxe6YwYCS4pdhLo8j0OVAo9DlQqPRZUCj0OVgnI4Dg9JKQ1qbUap9tS21uGzRfpOKd0E3NQ55ey6iBifUhpZ7DrUtXkcqhR4HKpUeCyqFHgcqhSU+3FYqidQVAMHNXs/GJhfpFokSZIkSSWqVEPtOOCIiBgaEd2Bi4D7ilyTJEmSJKnElOTw45RSfUR8BniY7JY+v0opTS1yWbuqbIZKa7fmcahS4HGoUuGxqFLgcahSUNbHYUleKEqSJEmSpPYo1eHHkiRJkiRtl6FWkiRJklS2DLUdKCIOiojHI2J6REyNiKtbafPRiJicP56NiBOKUat2X+05Dpu1PSUiGvJ7Q0sdpr3HYUScFRGT8jZPdHad2v218//mPSLirxHxYt7msmLUqt1XRPSMiOebHWPXtdKmR0T8KSJmRsRzETGk8yvV7qydx+HnI2JanlUei4hDilHrjvKc2g4UEfsD+6eUJkZEP2AC8L6U0rRmbd4MTE8pLY+Ic4FrU0qnFalk7Ybacxzm7SqBR4Basoux3dX51Wp31c7fhwOAZ4F3pZTmRsQ+KaXFRSpZu6l2HotfBfZIKX0pIgYBrwD7pZQ2Fqdq7W4iIoA+KaU1EVEFPA1cnVIa26zNp4DhKaUrIuIi4B9TSh8qUsnaDbXzOBwFPJdSWhcRVwJnlcNxaE9tB0opLUgpTcxfrwamAwe2aPNsSml5/nYs2T14pQ7TnuMw96/AnwFDhDpcO4/DjwB3p5Tm5u08FtXh2nksJqBf/gdfX2AZUN+phWq3ljJr8rdV+aNlz9IFwK3567uAs/NjUuoQ7TkOU0qPp5TW5W/LJqsYagskHzJyIvDcNpp9EniwM+pR19TWcRgRBwL/CPyi86tSV7ON34dHAntGxJiImBARH+vs2tS1bONY/BlwDDAfeIms56KxU4vTbi8iKiNiEtmXyY+klFoehwcCb0B2e0tgJbB351ap3V07jsPmyiarlOR9astdRPQl6wH7bEppVRttRpEdKGd2Zm3qOrZzHN4AfCml1OCXwCqk7RyH3YCTgbOBXsDfI2JsSunVTi5TXcB2jsV3ApOAtwGHAY9ExFNt/R8u7YyUUgMwIj/14p6IOD6lNKVZk9b+Q/Y8QXWodhyHAETExcBI4K2dXePOsKe2g+Xj0/8M3JZSuruNNsOBm4ELUkpLO7M+dQ3tOA5HAn+MiNnAhcD/RMT7OrFEdQHtOA6rgYdSSmtTSkuAJwEvnqcO145j8TKyofAppTQTmAUc3Zk1qutIKa0AxgDvajGrGjgIICK6AXuQDYWXOtw2jkMi4hzgP4D3ppQ2dHJpO8VQ24Hy8x5uIbsQ1A/baHMwcDdwib0RKoT2HIcppaEppSEppSFk5+18KqV0byeWqd1ce45D4C/AP0REt4joDZxGdr6j1GHaeSzOJRsxQETsCxwFvN45FaoriIhBec8YEdELOAd4uUWz+4CP568vBEYnr+iqDtSe4zAiTgT+lyzQls21Lhx+3LHOAC4BXsrHqgN8FTgYIKX0C+DrZOdH/E8+7LM+pTSyCLVq99We41AqtO0ehyml6RHxEDAZaARubm0IlLSL2vM78b+A30TES2RDQL+Ujx6QOsr+wK35nQcqgDtSSv8XEd8AxqeU7iP78uV3ETGTrIf2ouKVq91Ue47D68kumHdnnlXmppTeW7SK28lb+kiSJEmSypbDjyVJkiRJZctQK0mSJEkqW4ZaSZIkSVLZMtRKkiRJksqWoVaSJEmSVLYMtZKkshURqR2Ps9q5rqPz9udsp913IqK6A2p/V769w3d1XbtQw3kR8ZlWpv8xIp7ehfX+R0Q8uGvVQURURMSrEfH/2bvzMF3K8k7Av0fAJdG4gQGRxUSHuEzccDfjxkRjJm7RDNGoGBOi0YxGk7gkrnEcHY0al4xRUdzihpjgLqK4gwIRlE0PAnpU5AgCIpvAM39UtbZN9zndnO7vnDrnvq+rr/6q6v3eeurrOsuv37eqHrm5fQGw7fKcWgCm7O7zXl8nyaeTvDjJR+atP2mmFU3Lg5Lsl+R1q9VhVV0/yTOSPGxz++ruK6vq5UleUFUf6O4rN7tAALY5Qi0Ak9XdR829rqrrji9Pm7+emXtskh9392dXqb93J3lNkvsnOXyV+gRgG2L6MQDbvKrao6reVlWnV9XFVXVqVT2/qnZapPkNx+m3F1bVWVX17GX0v0tVHVRVZ4/9f76q7nQ16tyhqp5bVd+uqkur6pSqetSCNkdV1Tur6nFjuwuq6kNVteuCdr9RVYeP9ZxWVY+qqg9X1cfH7S9N8uQk+8ybqv2GBX08qKpOHD+Lz1bVPss4jMclOWRBPy+tqvVVda+q+s+quqiqjhx/LruNdV047ute89/b3Rcm+WSGsAwAV2GkFoDtwU2SnJXkaUnOS3KrJC9IcqMkT13Q9tVJPpjkD5PcL8lLqurs7j5osY6r6jpJPpPkWkmenuScJH+V5IiqukV3/2gFdb4xySOTvDDJ8RmmB7+zqjZ09/xRyv+WZM/xeH5trPlfkjx8rOkaST6c5JpJDkhyeZLnj8f7jbGP1yf5zSR3TrL/uO6H8/ZxiwxTuV+Q5GdJXplh1PSOSxVfVTcYt//jIpt/bdznS5NclmH09eAkO2X4vF+b5DlJDqmqvbr70nnv/dJ4rABwFUItANu87j42ybFJUlWV5IsZgtU/V9XTu/uKec2P7e65myd9oqpumuQfkiwaapP8aYZweKvuPmPcx6eTrMsQmJ+7nBqr6jZjX/t393vH1Z+qqpsleV5+eertryb5/e7+yfjemyV5cVXt2N2XZ7ie9VZJbtfdJ4xtjhtr+sb4mXy3qn6Y5JIlpmvfKMldu/vM8f3XTvLuqtp77jgXcccklV8E5/mul+TA7j567G+vJP+U5Jnd/apx3YYMP6d7ZPhFwZzjk+xaVXt093eX2DcA2ynTjwHY5o130f3bqjolycUZRh4PSnLdJLstaP7BBcuHJtm7qm6yRPf7JTk6yfqq2rGqdkxyRZLPJ9l3BWXul+TSJB+a62fs64gkC6cyf3ku0I5OSrJDkrkpyHdOcsZcoE2S7j49yddXUM835wLtvH0kyc028p65/S82On3hXKAdrRu/f3qRdbsveO9cf7sGABYwUgvA9uCZSV6U5CVJvpBhCvI9k7wqybUXtD17ieXdFtmWJDsnuVeGoLzQiSuocecMU5h/utjGqtp53lTm8xZsvmz8PncsuybZsEg3i61byqb2sZi5bZcusu38Jfo7b5F1C/dx6RLrAUCoBWC78Mgk7+ru58+tqKqlrg1dOCI7t/yDJdqfm2E682LXfF68ghrPTXJJkt9ZYvvCkLkxZyW59yLrdxm3rZVzx+83WOX93GBB/wDwc0ItANuD6+Sqo4ePXqLtw5K8dd7yw5Oc2d2LjdImw/Tg5yb5dndvTuj6dIaRyOt09+c3o58k+WqSZ1bVb8+7pvbmSf5rfjlsXpbVHf08dfx+86xuqN07w82uTl/FPgHYRgi1AGwPDk/yhPFmSWdmeOzMUteG3qmqXpvkQxmejfonSQ7cSN9vTvLnSY6sqldmCF47J7l7ktO7+/XLKbC7j6+qtyY5tKpeluS4JL+S5LZJ9uruJy2nn9EHk5wy9vWcDIHwBRmC5pXz2p2SZI+qenSGQHp2d39nBftZ6JQMo6l3SvLlzehnoX2T/Gd3X7SKfQKwjXCjKAC2B/+Q4YZPL03yrgzXd/7NEm2fluGa1EMzPA7nud39pqU6HoPWvTPcGOp/ZwjQr06yV4YR05X4syQvS/KEJB/LMGL8gCSfW0kn3X1lkt9PckaSt2d4HM+rkpyW5IJ5Td+V5N/Ger+a4ZE6V1t3d4ZA/Xub088iHpjkA6vcJwDbiBr+/QEAtmVVdeMk307y0u7+P2u4n7sn+WySXTdzOvZcf7fLELj37u7vb25/AGx7hFoA2AZV1VMy3HhqXZJfT/K3SW6Z4Xm6axoOq+qIJJ/p7hevQl8HZ3iW7hM3uzAAtkmuqQWAbdNlGYLsnhmem3t0kvvPaLTzqVn87ssrUlXXSPLNJAdvbl8AbLuM1AIAADBZbhQFAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQTtvnCwAAIABJREFUCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1AAAATJZQCwAAwGQJtQAAAEyWUAsAAMBkCbUAAABMllALAADAZAm1ANuxqnpBVf1oS9cxX1UdWFUPXWT9GVX1ii1U012q6gWLrJ/p57dUHWu4v4Or6pg16vvOVfXWqlpXVRdV1alV9fyquvZa7G81rOXnAcDVJ9QCsLU5MMlVQu0Wdpckz19k/ZuTPGArqGOK/meS30zysiQPSvL6JE9P8q4tWRQA07Pjli4AAKaqu9cnWb+l65iol3X3hnnLR1bVJUn+tar26u4zZ1FEVV27uy+Zxb7m7fM63X3xLPcJsC0zUgvARlXVjarqX6vqh1V1SVV9qaruuqBNV9VTq+olVbWhqs6uqtdX1bUWtLtPVZ0w9vPVcTrtj+am1FbVkUnulORxY59dVQcs6OOvq2p9Vf24qt5TVTdYxjHctqo+UlU/Gb/eX1W7ztu+U1W9oqq+U1WXVtX3q+qDVXXNcf+vnXecPdZ5lenH4/F1Vd2/qv6jqn5aVd+qqt+tqh2q6uXj8X6vqp6+oMa7V9Vh475/WlVfq6pHz9u+ZB2be4zL+PweWlWnjD+3L1TVredte39VfWaR97xwPGd2WqzPBYF2zn+O328yr58jq+qQqnp8VZ1eVRdW1Tuq6lrj+fOVcd2RVbXnJo7jgPFzu8vY/uIkfzvv53bbBe2PrKpDNtHnnuN5eG4N06g/UVX7zNu+99j3o6vq7VV1XpIPbaxPAFZGqAVgSWMo/VSS/57kbzNMC96Q5FPzA9PoGUlumuRPkrw8yV8keeq8vnZP8tEkZyd5RJJ/zTDV9Drz+vjLJKeM7e4+fn1k3vY/SnL/DFOUn5nkfyR5ySaO4RZJvpjk2kkek+SAJLdJ8qGqqrHZs5M8Oslzx2N9WpLzk+ww7v+fxnZzNf3lxvY5HtsXkjwsyZlJDknyuiTXS/Kocfmfqupu896z11jnnyX5gyQfSPLWqvrjcfuSdazCMW7MXklemeQfx9qvn+QT9YtrX9+c5N5VdfO5N4z7fGySd3b3zzbR/3z3SHJlklMXrL9bkscl+askf5fhPHhtkjcl+ecM59xvJHnjMvfz7iQfzjDt+cMrqO+XVNWNMvyc90nyxLGuX83w5+M6C5q/IslPkjwymzhnAVgZ048B2Jg/SXLbJLfp7m8lSVV9KkPoeEaGoDvnjO4+YHz9iaq6Z5KHJ/m/47qnJbkoyR/MTb2sqguSvHeug+4+qap+mmRDdx+1SD0/S/LQ7r58fP+tk+yfjYfM5yc5K8nvdfdl4/tOyBCeH5QhLN4lyb9199vmve994/eLq+qMsb7FalrMO7r75eO+1ic5Mck+3X2/cd2nMlxT+rAkR419v2fuzWMo/FySmyX58yTv7u4NG6ljc49xY3ZO8pDu/tLY77FJTssQnN+Q5PAk3x2X5673vW+SvZO8dRn9Z+x31yR/n+Gzu2DB5uuONZw/tr1Phs/l3t39uXHdTZO8vqp+pbsv2sTuXtPd/zxv3/dZbp0L/HWGEHv77j537OuLSc5I8qcZrhOec1R3P/lq7geAjTBSC8DG7Jfk2CSnV9WOVTX3y9DPJtl3QdtPLlg+KUMom3PnJIcvuJbwsBXW85m5QDtvHzfZxBTa/ZJ8MMmV847h9AzBY+4YvpbkgKr6u6r67Xmjm1fXEfNerxu/f3puRXdfmeTbSXafW1dVN6yq11TVmRnC+88yjEj/l2Xsby2P8ey5QDvWfmaGc+Iu847l4CSPndfnAUmO6e5vLGcH48/vfUkuzBAUFzpmLtCO1iW5LMMo6fx1yTBbYFM+sukmy7JfhlB/wbzP/ScZPp+Ffz5Wa58ALCDUArAxO2eY+vmzBV+PT7LHgrbnLVi+LMN02Dm7Zpi6/HPjDXouXEE9i+2jkmws1O6cYarywmP4jfziGF6cYVTtL5Mcn+S7VfXUq3a18jrnRk6XqH3+53NwhtHblyf53Qy/BHjLgjZLWctjPHuJdbvNW35rhmnK962q6yX5w7H2TRqD8NszTJd+UHf/eJFmi312PxkD9fx1yfI+rx8up7Zl2DnDz2zh537fXPXPx2rtE4AFTD8GYGPOTXJMkictsu3SFfZ1VpJd5q8Yr8u87tUrbdnOzTCK+eZFtv0o+Xm4fl6S51XVLTNcH/nqqjq1uz++xvXNfQ6/n+Qp3f2GeeuX+8vntTzGmyyx7sS5he4+Y5xSfUCSm2f4pfm7l1n7q5I8JMl/7+5TlvmezdULlufufrzwlyM3yvj5LeHcDLMN/nGRbT/ZxD4BWCVCLQAbc0SGUcPvdPdiI3Yr8dUkj69ffpzJgxdpt3AEc3MdkeG64GO7e5PBoru/VVV/k+TJSW6d5ONjTWv5+JdrZbhh089/UTCOeD44vxyGlqpjNY5xKTepqnvMu6Z2zyR3zFWvlz0ow+jsbZL8e3cvHF29iqp6doabP/1Rd39hU+3X0NxjmW6V5Lgkqao9MtwA6psbed8RGW4OdaJH9ABsOUItANesqkcssv6zGaaFPjHDM0RfkeE60BtnuJ7yrO5+1Qr28+oMIepDVfWqDNORn5Xh5lHzp5GekuQBVfWAJOckOb27z1nhMc33giRfSfKRqnpLhpG33TPcAfjg7j6yqj6Y4TrI/0xycYa7M++Y4WZNczUlyVOr6tNJLujuhXfovdq6+/yq+mqGUdQLMnwez8pwd+Jfm9d0qTpW4xiX8qMk76iq547ve1GG6ccHL2j370n+JUPgffamjrmqHpXhLsAHJ/negjtBn7bEI3/WRHevHz//f6yqizKMND8nw0jsxrwyw83UPl1Vr03yvSS/nuTeSb7Q3csdrQZgM7imFoDrJXn/Il+3GUcD75vhZjgvzHAzqH9OcssMIWrZuvt7GabY3iTJoRlG6P40wwjl/LvdvjjJyRluHPTVDI+3udq6+5sZrgu+KMMjXz6W4VguzS9uLvSlDI8r+rck/5HhWbl/2N3HjNs/n+Fa16cmOTrDI3tW26My3Nzp7Rk+4w+Mr+dbtI5VOsalnJnhLtcvSPKeDD+rBywcse7uS8f9fjfDY6A25XfH7wck+fKCr99fxvtX26OSfCfJOzOE7Rflqo8W+iXd/aMMn/spGaZRfzLD3b6vn+SEtSwWgF+oZcxSAoA1UVX3yhDU7tfdn9nS9XD1jXf+PTPJW7r7uVu6HgC2H6YfAzAzVfWyDNNfz8pwveJzM4xofXZL1sXVNz6O53YZRjpvnLUZxQaAJQm1AMzStTJMn/31DHeH/WSSpy94NAvTctMMU9HPTvIX3b1+E+0BYFWZfgwAAMBkuVEUAAAAk7VNTD/eeeede++9997SZQAAALAGjj322B919y6LbdsmQu3ee++dY47Z1BMJAAAAmKKqOnOpbaYfAwAAMFlCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZMw21VXXtqvpKVR1fVSdW1QsXaXOtqnpvVa2rqqOrau9Z1ggAAMB0zHqk9tIk9+vu2yW5fZIHVtXdFrR5QpIfd/ctkrwqyctmXCMAAAATMdNQ24MLx8Wdxq9e0OwhSd42vj4kyf2rqmZUIgAAABMy82tqq2qHqvpakrOTHN7dRy9osnuS7yZJd1+e5PwkN55tlQAAQHfnlYd/M4ccu35LlwJLmnmo7e4ruvv2SW6W5C5VddsFTRYblV04mpuqOrCqjqmqYzZs2LAWpQIAwHbtiis7rzniW3nbl87Y0qXAkrbY3Y+7+7wkRyZ54IJN65PskSRVtWOS6yc5d5H3v7G79+3ufXfZZZc1rhYAAICt0azvfrxLVd1gfH2dJPslOWVBs8OSPG58/Ygkn+7uq4zUAgAAwI4z3t9uSd5WVTtkCNTv6+4PV9WLkhzT3YclOSjJO6pqXYYR2v1nXCMAAAATMdNQ290nJLnDIuufN+/1JUkeOcu6AAAAmKYtdk0tAAAAbC6hFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJmmmorao9quozVXVyVZ1YVU9dpM19qur8qvra+PW8WdYIAADAdOw44/1dnuQZ3X1cVV0vybFVdXh3n7Sg3ee7+3/MuDYAAAAmZqYjtd39g+4+bnz9kyQnJ9l9ljUAAACw7dhi19RW1d5J7pDk6EU2372qjq+qj1XVbZZ4/4FVdUxVHbNhw4Y1rBQAAICt1RYJtVV13SQfSPK07r5gwebjkuzV3bdL8tok/75YH939xu7et7v33WWXXda2YAAAALZKMw+1VbVThkD7ru4+dOH27r6guy8cX380yU5VtfOMywQAAGACZn3340pyUJKTu/uVS7TZdWyXqrpLhhrPmV2VAAAATMWs7358zySPSfL1qvrauO45SfZMku5+Q5JHJHlSVV2e5OIk+3d3z7hOAAAAJmCmoba7v5CkNtHmdUleN5uKAAAAmLItdvdjAAAA2FxCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZQi0AAACTJdQCAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZMw21VbVHVX2mqk6uqhOr6qmLtKmqek1VrauqE6rqjrOsEQAAgOnYccb7uzzJM7r7uKq6XpJjq+rw7j5pXpvfS3LL8euuSf7f+B0AAAB+yUxHarv7B9193Pj6J0lOTrL7gmYPSfL2HhyV5AZVtdss6wQAAGAattg1tVW1d5I7JDl6wabdk3x33vL6XDX4wlZnw08uze1f9Mm84hOnbulSAIDtyNu+dEZu/byPZ93ZP9nsvi6+7Irc7SVH5NmHnrAKlcFsbJFQW1XXTfKBJE/r7gsWbl7kLb1IHwdW1TFVdcyGDRvWokxYkfMvviznXfSznHnuRVu6FABgO/Kdcy/KRZddkbMvuHSz+7rkZ1fkrAsuyZnn+P8M0zHzUFtVO2UItO/q7kMXabI+yR7zlm+W5PsLG3X3G7t73+7ed5dddlmbYgEAANiqzfrux5XkoCQnd/crl2h2WJLHjndBvluS87v7BzMrEgAAgMmY9d2P75nkMUm+XlVfG9c9J8meSdLdb0jy0SQPSrIuyUVJHj/jGgEAAJiImYba7v5CFr9mdn6bTvLk2VQEAADAlK1o+nFVvaeqfnecRgwAAABb1Eqvqd0jyceTfKeqXlxVt1iDmgAAAGBZVhRqu/ueSfZJ8o4kj01yalV9rqoOqKpfXYsCAQAAYCkrvvtxd3+ru5+TZK8MN3Ran+T1SX5QVQdV1b1WuUYAAABY1NV+pM94Q6fPJflYkhOTXDdDyP1cVR1bVbdbnRIBAABgcVcr1FbVPavqTUnOSvLaJF9Lcvfu3i3J7ZNckGGKMgAAAKyZFT3Sp6qeneSAJLdI8uUkT0vy3u6+aK5Nd59QVf+QYRQXAAAA1sxKn1P71CRvT3JQd5+6kXanJDnwalcFAAAAy7DSUHuz7r58U426+5wkB129kgAAAGB5VnpN7b2q6rGLbaiqx1TVvVehJgAAAFiWlYbalyS56RLbdh23AwAAwEysNNTeNskxS2w7LsltNq8cAAAAWL6Vhtork9xwiW03vhr9AQAAwNW20hD6xSTPqKqd5q8cl/86yRdWqzAAAADYlJXe/fg5GYLrt6rq3Ul+kGS3JPsnuVGS31nd8gAAAGBpKwq13X18Vd0tyQuS/HmGqcg/TnJEkud39ymrXiEAAAAsYaUjtenuE5M8cg1qAQAAgBVxYycAAAAma8UjtVX10CQPT3KzJNdeuL2777EKdQEAAMAmrSjUVtVzk7wwyYlJTkpy2VoUBQAAAMux0pHaA5O8vLufuRbFAAAAwEqs9Jra6yX55FoUAgAAACu10lD7viS/uxaFAAAAwEqtdPrxx5O8oqpulOTwJOctbNDdRnIBAACYiZWG2kPG708YvxbqJDtsVkUAAACwTCsNtbdckyoAAADgalhRqO3u09aqEAAAAFipld4oKlW1U1X9eVX9a1V9tKpuMa5/RFXts/olAgAAwOJWNFI7BthPJtk5yXFJfifJr42b75vkD5I8bjULBAAAgKWsdKT2NUnOSrJ3kv2S1Lxtn80QcgEAAGAmVnqjqHsn+aPuPreqFt7l+Kwku61OWQAAALBpKx2pvTTJtZbYdtMs8txaAAAAWCsrDbWHJ3l2VV1v3rquqp2SPCXJx1etMgAAANiElU4//tskX0qyLsknknSSv09ymyS/muSPVrU6AAAA2IgVjdR293eS3C7JW5L8VpIzM9w06rAkd+ru7692gQAAALCUlY7UprvPSfLsNagFAAAAVmSl19QCAADAVmNFI7VV9YMM19EuqbtvulkVAQAAwDKtdPrxQblqqL1Rkvsl+ZUkb1uNogAAAGA5VhRqu/sfFltfVddI8v4kF23s/VX1liT/I8nZ3X3bRbbfJ8l/JDl9XHVod79oJTUCAACw/ViVa2q7+8okb0ryvzbR9OAkD9xEm8939+3HL4EWAACAJa3mjaL2SnLNjTXo7s8lOXcV9wkAAMB2bKU3ijpwkdXXTHKrJI9Ncugq1HT3qjo+yfeT/E13n7gKfQIAALANWumNot6wyLrLk3wvw/Tj521mPccl2au7L6yqByX59yS3XKzhGLAPTJI999xzM3cLAADAFK10+vFOC7+6+5rdffPufnp3X7g5xXT3BXN9dPdHk+xUVTsv0faN3b1vd++7yy67bM5uAQAAmKiV3v34irUqJEmqatckP+zurqq7ZAjd56zlPgEAAJiulV5T+6iVtO/uf1vw/ncnuU+SnatqfZLnZxjxTXe/Ickjkjypqi5PcnGS/bt74XNxAQAAIMnKr6l9Z5K5kFnz1i+17pdCbXf/8cY67+7XJXndCmsCAABgO7XSa2rvmuTMJC9M8ttJdh2/v2hcf9ckNxy/brR6ZQIAAMBVrXSk9mVJ/l93v3zeurOTfKOqLkryf7v7vqtWHQAAAGzESkdq75bk+CW2nZBhpBYAAABmYqWhdn2SA5bYdkCG59UCAADATKx0+vE/JPm3qrp1ksMyTD2+SZIHJ/mvSTZ6IygAAABYTSt9Tu37quqMJM9K8vgkv57kh0m+muQvuvvoVa8QAAAAlrDSkdp091eSPHwNagEAAIAVWek1tUmSqrp+Vd29qv6oqm4wrttpdUsDAACAjVtRqK2qa1TVSzLcEOqLSd6d5DfGzYdV1fNXuT4AAABY0kpHav93kicn+esk/yVJzdv27xluGAUAAAAzsdJrah+X5Fnd/aaq2mHBttOS/ObqlAUAAACbttKR2hsm+dYS23ZKsjDoAgAAwJpZaag9MckfLLHtAUn+c/PKAQAAgOVb6fTjlyR5X1VdK8n7k3SS21bVHyR5UpKHrnJ9AAAAsKQVjdR296FJHpvk95McnuFGUQcn+Yskj+/uj612gQAAALCUlY7Uprv/rareneRWSXZOcm6Sk7r7ytUuDgAAADZm2aG2qq6d5Lgkf93dn0hy0ppVBQAAAMuw7OnH3X1JhpHZXrtyAAAAYPlWevfjd2e4phYAAAC2uJVeU3takkdU1VFJPprkh/nlkdvu7jetVnEAAACwMSsNta8ev++W5C6LbO8kQi0AAAAzsdJQu9OaVAEAAABXwyavqa2qT1bVPknS3Vd09xVJ7p3k2nPL87/WumAAAACYs5wbRe2X5PpzC1W1Q5LDk+yzVkUBAADAcqz07sdzalWrAAAAgKvh6oZaAAAA2OKWG2p7mesAAABgZpZ79+NPVNXlC9Ydsci6dPdNNr8sAAAA2LTlhNoXrnkVAAAAcDVsMtR2t1ALAADAVsmNogAAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyZppqK2qt1TV2VX1jSW2V1W9pqrWVdUJVXXHWdYHAADAtMx6pPbgJA/cyPbfS3LL8evAJP9vBjUBAAAwUTMNtd39uSTnbqTJQ5K8vQdHJblBVe02m+pg4668svPxb5yV8y667Crb1p19YT5zyoYtUBWwmG987/x8ff35P18+5awLctx3frwm+7riys7Hvv6DnH/xz9akf7Yd51/0s3z8Gz/IFVf2li6FNXTahgtz9LfPyZGnnp3vnXfxz9d/cd2PcuY5P92ClV093zr7wiTJeRdflrMvuGQLV7P1+Mrp52bd+NmsxCU/uyIfOv77+dRJP0y3vwtWy9Z2Te3uSb47b3n9uO4qqurAqjqmqo7ZsEGYYO196bRz8sR3Hps3fu7bV9n2d4ccnyO/eXbusOcNtkBlwEKPOejoPPrNR/18+S/fdVwe/i9fWpN9HXnq2XnSu47LwV88Y036Z9tx0BdPzxPfeVw+/y3/b9mWPesDJ+R/vvGoHPDWr+alHzslSXLOhZfm0W8+Os8/7MQtXN3K/fV7v5aH3WH33PT618mrPvWtLV3OVuGyy6/MH/3rl/N3hxy/4vcecuz6vOKTp+YZ7z8+J37/gjWobvu0tYXaWmTdor/C6O43dve+3b3vLrvsssZlQXLF+Nu0Kxb5rdoVnfzN7+6TA+6x94yrAhZz3sU/ywWXXP7z5Ut/duWa7Wtu1G2xvxtgvivHc+VK58o2bf5I/C9+5lfdNhVXdueJ9/7NPOwOu//8eLZ3nbm/91f+3iu7899uuUv2uvGvTPJ82FptbaF2fZI95i3fLMn3t1AtAAAAbOW2tlB7WJLHjndBvluS87v7B1u6KAAAALZOO85yZ1X17iT3SbJzVa1P8vwkOyVJd78hyUeTPCjJuiQXJXn8LOsDAABgWmYaarv7jzexvZM8eUblAAAAMHFb2/RjAAAAWDahFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJismYfaqnpgVZ1aVeuq6lmLbD+gqjZU1dfGrz+bdY0AAABMw46z3FlV7ZDk9Un+e5L1Sb5aVYd190kLmr63u58yy9oAAACYnlmP1N4lybru/nZ3X5bkPUkeMuMaAAAA2EbMOtTunuS785bXj+sW+sOqOqGqDqmqPRbrqKoOrKpjquqYDRs2rEWtAAAAbOVmHWprkXW9YPlDSfbu7t9O8qkkb1uso+5+Y3fv29377rLLLqtcJgAAAFMw61C7Psn8kdebJfn+/AbdfU53XzouvinJnWZUGwAAABMz61D71SS3rKqbV9U1k+yf5LD5Dapqt3mLD05y8gzrAwAAYEJmevfj7r68qp6S5BNJdkjylu4+sapelOSY7j4syf+qqgcnuTzJuUkOmGWNAAAATMdMQ22SdPdHk3x0wbrnzXv97CTPnnVdAAAATM+spx8DAADAqhFqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMkSagEAAJgsoRYAAIDJEmoBAACYLKEWAACAyRJqAQAAmCyhFgAAgMmaeaitqgdW1alVta6qnrX7HpFqAAANvUlEQVTI9mtV1XvH7UdX1d6zrhEAAIBpmGmoraodkrw+ye8luXWSP66qWy9o9oQkP+7uWyR5VZKXzbJGAAAApmPWI7V3SbKuu7/d3ZcleU+Shyxo85AkbxtfH5Lk/lVVM6wRAACAidhxxvvbPcl35y2vT3LXpdp09+VVdX6SGyf50UwqXAPrzr4w/+ejJ2/pMthMP/rpZUmSj339rKz74YW/tO3bGy7MTjtcIzvtcI0c/e1z8oSDv7olSgRG3cP3uT+LP7zgkl9aXk0bLrw0SfKh47+fE793/qr3z7bjtA3Dvx3//Klv5V1HfWcLV8NaWXf2L/6P8JUzzs0TDv5qLrviyiTJid+/YE3+Hvrm2T9Jkrz8k6fmRl84fbP6mqv15B8MtX7vxxdnh2tUdtzhGvn8tzb4P06SK8Z/ZL694cIVfx7f/fFFuectds6O16i8+CMn5deuvdNalLhij77bnrnfb/36li7jaque+5d/FjuremSSB3T3n43Lj0lyl+7+q3ltThzbrB+XTxvbnLOgrwOTHDgu7pPk1BkcwubYORMO5mwznIdsDZyHbC2ci2wNnIdsDaZwHu7V3bsstmHWI7Xrk+wxb/lmSb6/RJv1VbVjkusnOXdhR939xiRvXKM6V11VHdPd+27pOti+OQ/ZGjgP2Vo4F9kaOA/ZGkz9PJz1NbVfTXLLqrp5VV0zyf5JDlvQ5rAkjxtfPyLJp3uWw8kAAABMxkxHasdrZJ+S5BNJdkjylu4+sapelOSY7j4syUFJ3lFV6zKM0O4/yxoBAACYjllPP053fzTJRxese96815ckeeSs65qByUyVZpvmPGRr4Dxka+FcZGvgPGRrMOnzcKY3igIAAIDVNOtragEAAGDVCLWrqKr2qKrPVNXJVXViVT11kTaPrqoTxq8vVdXttkStbLuWcx7Oa3vnqrqiqh4xyxrZ9i33PKyq+1TV18Y2n511nWz7lvlv8/Wr6kNVdfzY5vFbola2XVV17ar6yrxz7IWLtLlWVb23qtZV1dFVtffsK2Vbtszz8OlVddKYVY6oqr22RK0rZfrxKqqq3ZLs1t3HVdX1khyb5KHdfdK8NvdIcnJ3/7iqfi/JC7r7rluoZLZByzkPx3Y7JDk8ySUZbtp2yOyrZVu1zL8Pb5DkS0ke2N3fqaqbdPfZW6hktlHLPBefk+T63f3MqtolyalJdu3uy7ZM1WxrqqqS/Gp3X1hVOyX5QpKndvdR89r8ZZLf7u4nVtX+SR7W3f9zC5XMNmiZ5+F9kxzd3RdV1ZOS3GcK56GR2lXU3T/o7uPG1z9JcnKS3Re0+VJ3/3hcPCrDs3ph1SznPBz9VZIPJBEiWHXLPA8fleTQ7v7O2M65yKpb5rnYSa43/ofvuhmevnD5TAtlm9aDC8fFncavhSNLD0nytvH1IUnuP56TsCqWcx5292e6+6JxcTJZRahdI+OUkTskOXojzZ6Q5GOzqIft01LnYVXtnuRhSd4w+6rY3mzk78P/kuSGVXVkVR1bVY+ddW1sXzZyLr4uya2SfD/J1zOMXFw50+LY5lXVDlX1tQy/TD68uxeeh7sn+W4yPAYzyflJbjzbKtnWLeM8nG8yWWXmj/TZHlTVdTOMgD2tuy9Yos19M5wo95plbWw/NnEevjrJM7v7Cr8EZi1t4jzcMcmdktw/yXWSfLmqjurub864TLYDmzgXH5Dka0nul+Q3kxxeVZ9f6t9wuDq6+4oktx8vvfhgVd22u78xr8li/yC7TpBVtYzzMElSVX+SZN8k9551jVeHkdpVNs5P/0CSd3X3oUu0+e0kb07ykO4+Z5b1sX1Yxnm4b5L3VNUZSR6R5F+q6qEzLJHtwDLOw/VJPt7dP+3uHyX5XBI3z2PVLeNcfHyGqfDd3euSnJ7kt2ZZI9uP7j4vyZFJHrhg0/okeyRJVe2Y5PoZpsLDqtvIeZiq2i/J3yd5cHdfOuPSrhahdhWN1z0clOFGUK9cos2eSQ5N8hijEayF5ZyH3X3z7t67u/fOcN3OX3b3v8+wTLZxyzkPk/xHkt+pqh2r6leS3DXD9Y6wapZ5Ln4nw4yBVNWvJ9knybdnUyHbg6raZRwZS1VdJ8l+SU5Z0OywJI8bXz8iyafbHV1ZRcs5D6vqDkn+NUOgncy9Lkw/Xl33TPKYJF8f56onyXOS7Jkk3f2GJM/LcH3Ev4zTPi/v7n23QK1su5ZzHsJa2+R52N0nV9XHk5yQ5Mokb15sChRspuX8nfiPSQ6uqq9nmAL6zHH2AKyW3ZK8bXzywDWSvK+7P1xVL0pyTHcfluGXL++oqnUZRmj333Llso1aznn48gw3zHv/mFW+090P3mIVL5NH+gAAADBZph8DAAAwWUItAAAAkyXUAgAAMFlCLQAAAJMl1AIAADBZQi0Ak1VVvYyv+yyzr98a2++3iXYvrar1q1D7A8f93WJz+9qMGh5UVU9ZZP17quoLm9Hv31fVxzavuqSqrlFV36yqR25uXwBsuzynFoApu/u819dJ8ukkL07ykXnrT5ppRdPyoCT7JXndanVYVddP8owkD9vcvrr7yqp6eZIXVNUHuvvKzS4QgG2OUAvAZHX3UXOvq+q648vT5q9n5h6b5Mfd/dlV6u/dSV6T5P5JDl+lPgHYhph+DMA2r6r2qKq3VdXpVXVxVZ1aVc+vqp0WaX7DcfrthVV1VlU9exn971JVB1XV2WP/n6+qO12NOneoqudW1ber6tKqOqWqHrWgzVFV9c6qetzY7oKq+lBV7bqg3W9U1eFjPadV1aOq6sNV9fFx+0uTPDnJPvOmar9hQR8PqqoTx8/is1W1zzIO43FJDlnQz0uran1V3auq/rOqLqqqI8efy25jXReO+7rX/Pd294VJPpkhLAPAVRipBWB7cJMkZyV5WpLzktwqyQuS3CjJUxe0fXWSDyb5wyT3S/KSqjq7uw9arOOquk6SzyS5VpKnJzknyV8lOaKqbtHdP1pBnW9M8sgkL0xyfIbpwe+sqg3dPX+U8r8l2XM8nl8ba/6XJA8fa7pGkg8nuWaSA5JcnuT54/F+Y+zj9Ul+M8mdk+w/rvvhvH3cIsNU7hck+VmSV2YYNb3jUsVX1Q3G7f+4yOZfG/f50iSXZRh9PTjJThk+79cmeU6SQ6pqr+6+dN57vzQeKwBchVALwDavu49NcmySVFUl+WKGYPXPVfX07r5iXvNju3vu5kmfqKqbJvmHJIuG2iR/miEc3qq7zxj38ekk6zIE5ucup8aqus3Y1/7d/d5x9aeq6mZJnpdfnnr7q0l+v7t/Mr73ZkleXFU7dvflGa5nvVWS23X3CWOb48aavjF+Jt+tqh8muWSJ6do3SnLX7j5zfP+1k7y7qvaeO85F3DFJ5RfBeb7rJTmwu48e+9sryT8leWZ3v2pctyHDz+keGX5RMOf4JLtW1R7d/d0l9g3Adsr0YwC2eeNddP+2qk5JcnGGkceDklw3yW4Lmn9wwfKhSfauqpss0f1+SY5Osr6qdqyqHZNckeTzSfZdQZn7Jbk0yYfm+hn7OiLJwqnMX54LtKOTkuyQZG4K8p2TnDEXaJOku09P8vUV1PPNuUA7bx9JcrONvGdu/4uNTl84F2hH68bvn15k3e4L3jvX364BgAWM1AKwPXhmkhcleUmSL2SYgnzPJK9Kcu0Fbc9eYnm3RbYlyc5J7pUhKC904gpq3DnDFOafLraxqnaeN5X5vAWbLxu/zx3Lrv+/vTsGrauK4zj+/bu1U8BKu7Rphm7VDnXJUDI4qDhZcIpbq1go6KAI0lAHxWRRQZwqJAhxMw4dOpS22g4igRa3KNoYh7a0EKqDbTLk73Be5Pm8N+b1vRTefd/PcnnnXv7nbo8f/3vOAe5VlKkaq/N/c1TZvLdWce+Pmnr3K8Y651irGZckyVArSRoKrwDzmXl2cyAi6taGdnZkN3/frnl+lfI5c9WazwddvOMq8BA4VnO/M2Ru5Q4wUTH+VOveTlltXUf6PM9IR31Jkv5hqJUkDYNd/Ld7OFnz7MvAbNvv48BKZlZ1aaF8HjwF3MzMXkLXZUoncldmXuuhDsAi8G5EPNO2pnYMeJp/h811+tv9/Kl1HaO/ofYgZbOr5T7WlCQ1hKFWkjQMLgInWpslrVCOnalbG3o0Ij4DzlPORn0VeH2L2l8ArwHfRsTHlOC1BxgHljPz8+28YGb+GBGzwEJEzADXgd3AYWA0M09tp07LN8BSq9Z7lED4PiVobrQ9twTsj4hJSiC9m5m/dzFPpyVKN/Uo8H0PdTo9C9zIzL/6WFOS1BBuFCVJGgZnKBs+TQPzlPWdb9c8+xZlTeoC5Ticqcw8V1e4FbQmKBtDfUgJ0J8Co5SOaTdOAjPACeACpWP8PHC1myKZuQG8BPwGfEk5jucT4Ffgz7ZH54GvWu+7SDlS55FlZlIC9Yu91KnwAvB1n2tKkhoiyv+PJElqsoh4ErgJTGfmRzs4zzjwHbCvx8+xN+sdoQTug5l5q9d6kqTmMdRKktRAEXGasvHUL8Be4B3gEOU83R0NhxFxCbiSmR/0odYc5SzdN3p+MUlSI7mmVpKkZlqnBNkDlHNzfwCee0zdzjep3n25KxHxBPAzMNdrLUlSc9mplSRJkiQNLDeKkiRJkiQNLEOtJEmSJGlgGWolSZIkSQPLUCtJkiRJGliGWkmSJEnSwDLUSpIkSZIG1t8wOWuSj5UXNQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x1008 with 2 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the x-axis for the plot of the fitted function\n",
    "xaxis = np.linspace(minL, maxL, 10000) \n",
    "\n",
    "# Compute the fitted function for x_fit\n",
    "yaxis = gauss_extended(xaxis, *minuit_L30cm.args) \n",
    "\n",
    "# Plot the fitted function\n",
    "ax_L30cm.plot(xaxis, yaxis, '-', label='Fit')\n",
    "ax_L30cm.legend()\n",
    "\n",
    "# Show the actual fit and fit results:\n",
    "fig_raw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Next steps:\n",
    "\n",
    "For the above, you should by now be aware, that there is definitely room for improvement. It is now up to you to select in (based on solid **quantified** arguments) and/or correct the data, and subsequently produce a better estimate of the length of the table in world famous Auditorium A. Good luck..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  The number of measurements used before and after is: 711 and 711\n"
     ]
    }
   ],
   "source": [
    "# Clean up in the data:\n",
    "L30cm = np.sort(L30cm)\n",
    "\n",
    "# For your data analysis, you can consider either throwing away measurements or correcting them.\n",
    "# This is question 2 below.\n",
    "mask = (L30cm>=np.percentile(L30cm,0))*(L30cm<=np.percentile(L30cm,100))      # Write your own data selection!!!\n",
    "\n",
    "# But remember, you should be able to argue for each an every point you remove or correct!!!\n",
    "# Barlow 4.2.3 (and the note above this very short section) along with Chauvenet's Criterion might serve as guidelines\n",
    "\n",
    "L30cm_subset = L30cm[mask]\n",
    "print(f\"  The number of measurements used before and after is: {len(L30cm):d} and {len(L30cm_subset):d}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "Start by taking a close look at the data, first by inspecting the numbers in the data file (yeps, open the damn thing, and look over the numbers!), and then by considering the histograms produced by running the notebook. To begin with, only consider the 30cm ruler measurements, and disregard the estimated/guessed uncertainties. You can then expand from there, as guided below by questions.\n",
    "\n",
    "When you're done, please fill in your results here: https://docs.google.com/forms/d/1cqql58JThj7O2O3cKxaRyCe5zRJ0UWv5VllbL0nn8Us/ (anonymous). The purpose is to see, how large variation one can get in answers, even when asking the same data the same questions.\n",
    "\n",
    "\n",
    "# Questions:\n",
    "\n",
    "1. Consider the mean, standard deviation, and uncertainty on the mean. Is the result as you would expect it? And do you think that it is close to the best possible (i.e. most accurate and precise) estimate? NOTE: Make sure that you know the difference between accuracy and precision!!! See \"Common definition\" in: http://en.wikipedia.org/wiki/Accuracy_and_precision\n",
    "\n",
    "2. Do any of the measurements looks wrong/bad/suspicious? Do you see any repeated mistakes done for obvious reasons? Would you correct or exclude any of the measurements and how would you justify this? This problem requires that you discuss with your peers, and then each do what you think most justified/best. It somehow boils down to how far away a measurement is from the expectation.\n",
    "Apply the criterion you find fitting to the list of measurements, and perhaps produce a new list with your accepted and possibly corrected measurements in (to save the original data). How many measurements did you throw away in the end?\n",
    "\n",
    "3. Fit your accepted length measurements with a Gaussian distribution, possibly in a (small?) range around what you believe is the true value. What would be your strategy for choosing a range? Is the Gaussian distribution justified? Also, do you see any \"human\" effects? Did any of your class mates (or you?) not read to mm precision and rounded the result?\n",
    "\n",
    "4. Once you have selected the measurements you want to use, calculate the mean, RMS and uncertainty on the mean. How much did your result improve in precision from the raw data in Q1?\n",
    "\n",
    "5. The \"Pull\" distribution is defined as the plot of $z_i = \\left(x_i - \\mu \\right)/\\sigma_i$ where $\\mu$ is the *sample* mean of $x$, and $x_i$ and $\\sigma_i$ are the *single measurements* and their corresponding uncertainties. If the measurements and uncertainties are good, then it should give a unit Gaussian. Is that the case? And thus, were the uncertainty estimates/guesses reasonable? If not, then the pull distribution is often used to remove overly precise measurements (those far out on the tails), and afterwards to scale the errors on the remaining measurements to a reasonable level. Consider the pull distribution, and see if any measurements have suspicious uncertainties.\n",
    "\n",
    "6. Try to calculate the weighted mean. Did you get a good Chi2 probability, when doing so? Do you need to discard more dubious measurements? Did the result improve further in precision?\n",
    "\n",
    "7. Is the number of mismeasurements 30cm below the actual length more common than those 30cm above? Determine the ratio $r_{mis} = N_{30cm~high} / N_{30cm~low}$ including both its statistical uncertainty, and if possible a systematic uncertainty from defining exactly when a measurement is 30cm off.\n",
    "\n",
    "\n",
    "\n",
    "#### Now repeat the above for the 2m folding rule\n",
    "...and consider all the questions below as optional problems, where you might just try to solve selected problems.\n",
    " \n",
    "***\n",
    "\n",
    "8. How much better/worse is the single measurement uncertainty from the 30cm ruler case to the 2m folding rule?\n",
    "\n",
    "9. Does the length of the table seems to be different when measured with a 30cm and a 2m ruler? Quantify this statement! I.e. what is the difference, and what is the uncertainty on that difference? Is this significantly away from 0?\n",
    "\n",
    "10. If you were asked for the best estimate of the length of the table, what would you do? (If posssible, read Bevington page 58 bottom!)\n",
    "\n",
    "\n",
    "### Advanced questions:\n",
    "\n",
    "11. Consider the 2020 data files with additional information about which day the measurements were done, and find out if the day has an impact on the quality of the measurements.\n",
    "\n",
    "12. Is there any correlation between the errors on the measurements and the distance value? I.e. do you see any effect of those measuring e.g. too long having a smaller/larger uncertainty? What would the effect of this be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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