notebooks/metric_stability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploring metric stability\n",
    "\n",
    "In this notebook, we show that:\n",
    "\n",
    "1. With the standard set of agreement metrics (correlation, RMSE, $R^2$, QWK), the evaluation for a single automated score can give very different results depending on the pair of human raters that are used as the reference against which the system score is evaluated.\n",
    "\n",
    "2. The PRMSE metric, on the other hand, yields stable evaluation results across different pairs of human raters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from pathlib import Path\n",
    "from simulation.dataset import Dataset\n",
    "from simulation.utils import (compute_agreement_one_system_multiple_rater_pairs,\n",
    "                               compute_prmse_one_system_multiple_rater_pairs,\n",
    "                               get_rater_pairs)\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Setup\n",
    "\n",
    "To set up the experiment, we do the following:\n",
    "\n",
    "1. We load the dataset we have already created and saved in the `validation_and_analyses.ipynb` notebook and use that for this experiment.\n",
    "\n",
    "2. We choose one of the simulated systems with high performance from this dataset as the source of our single automated score. \n",
    "\n",
    "3. We create a fixed number of randomly chosen human-rater pairs from our simulated raters, for each category.\n",
    "\n",
    "For convenience and replicability, we have pre-computed many of the parameters that are used in our notebooks and saved them in the file `settings.json`. We load this file below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset (10000 responses, scores in [1, 6], 4 rater categories, 50 raters/category, 5 system categories, 5 systems/category)\n"
     ]
    }
   ],
   "source": [
    "# load the dataset file\n",
    "dataset = Dataset.from_file('../data/default.dataset')\n",
    "\n",
    "# let's remind ourselves what the dataset looks like\n",
    "print(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the experimental settings file\n",
    "experiment_settings = json.load(open('settings.json', 'r'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now get the data frames for our loaded dataset\n",
    "df_scores, df_rater_metadata, df_system_metadata = dataset.to_frames()\n",
    "\n",
    "# next let's get the ID of the simulated system that we have chosen\n",
    "# as the source of our single automated score; this was pre-determined\n",
    "# and saved in the settings file\n",
    "chosen_system = experiment_settings['sample_system']\n",
    "\n",
    "# finally, get the number of fixed human-rater pairs \n",
    "# per category that we want to use\n",
    "rater_pairs_per_category = experiment_settings['rater_pairs_per_category']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now let's get the pre-determined number of randomly-sampled pairs of raters in each rater category\n",
    "rater_category_pairs = df_rater_metadata.groupby('rater_category').apply(lambda row: get_rater_pairs(row['rater_id'], rater_pairs_per_category))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Compute conventional agreement metrics\n",
    "\n",
    "Next, we compute various conventional agreement metrics to measure the chosen system's performance against each pair of human raters in each category. Ideally, with a stable metric, one would not expect the estimate of performance of the **same** system to vary widely depending on which two _specific_ human raters were being used to evaluate it. For this experiment, we focus on the following agreement metrics that are commonly used for evaluating automated scoring systems:\n",
    "\n",
    "1. Quadratically-weighted kappa (denoted by `QWK`)\n",
    "2. Pearson's correlation (denoted by `r`)\n",
    "3. $R^2$ (denoted by `R2`)\n",
    "4. The difference between the human-human Pearson correlation and the human-machine Pearson correlation (denoted by `degradation`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize a list that will hold the dataframe of metrics computed for each rater category\n",
    "category_dfs = []\n",
    "\n",
    "# now iterate over each rater category\n",
    "for rater_category in rater_category_pairs.index:\n",
    "    \n",
    "    # compute the data frame containing the conventional agreement metrics\n",
    "    # this dataframe contains `N_r` * 2 rows, where `N_r` is the number of\n",
    "    # rater pairs we sampled earlier in each category. There are 2 rows\n",
    "    # because for each pair of raters, we compute the chosen system's performance\n",
    "    # against: (a) the score assigned by the first human rater in the pair and\n",
    "    # (b) the average of the scores assigned by both raters in the pair\n",
    "    df_metrics_for_category = compute_agreement_one_system_multiple_rater_pairs(df_scores,\n",
    "                                                                                chosen_system,\n",
    "                                                                                rater_category_pairs[rater_category],\n",
    "                                                                                include_mean=True)\n",
    "    \n",
    "    # save the category itself for later use\n",
    "    df_metrics_for_category['rater_category'] = rater_category\n",
    "    \n",
    "    # save the data frame in the list\n",
    "    category_dfs.append(df_metrics_for_category)\n",
    "\n",
    "# create a single data frame by concatenating all of these frames\n",
    "df_metrics_with_categories = pd.concat(category_dfs)\n",
    "\n",
    "# now create a longer version of this data frame more amenable to plotting\n",
    "df_metrics_with_categories_long =  df_metrics_with_categories.melt(id_vars=['reference', 'rater_category'], var_name='metric')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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2fZ8eJ1gHPosg6fRgjGaLCRJUItKINK5ViedZMzuV4M6H3xC8rgkEkwlej6pbambHEUxWOA+4JTy1nCD5+3hE3RIzO4xgpvFJBEnhjwmSyA8D7eoQ5h0Es3t/QJCgXknwgdtjRG2c5+5bzOyIsM1Ygg1EpxMkte8EBkXUzTezo4A/AT8leN89Azg2vFZ0crhOPwvu/omZjSb4Pv2EYHm3BQQfDtxVh9ffLFjyM+9FREREWh4z24Vg5ooDB2tzOBERERHJVGaWDawFPnb3WGsGSzOVVXsVEREREYkWrvN7OMFMhrfMbGiaQxIRERERqVW4fnO0SwnupnijkcORNNPMYRERERERERERkRbCzP4F5AIfACXA/gRrBX8L7BWx6Z+0AEoOi4iIiIiIiIiItBDhxn+XAzsCHYBVBGsr/8rdV6UzNml8Sg4nyMxaAf2Bpe5elu54RERaGo3DIiLpozFYRCR9NAaLSENqVXsVCfUHFi5cuDDdcYhIZrN0B5DBNA6LSLI0BtefxmARSZbG4PrTGCwiyYo7BmtDOhEREREREREREZEWSMlhEREREREREWlRzKyDmd1jZivMrMjMPjGzExNsO9TMXjCzDWa2ycwmmdkucer+n5l9ZWYlZvatmV1rZsrFiEiToQFJRERERERERFqaicA5wE3AccBcYKKZHVtTIzPrBbwHDAIuAM4CugHvmFn/qLo3AXcD/waOAh4BbgNuT+ULERFJhtYcFhEREREREZEWI0wAHw6c7O4Tw7LJwBDgLmBSDc2vAboCe7v78rDth8BC4EbgsrCse/j8Xnf/ddh2ipm1B641s3vdfWnKX5yISB1p5rCIiIiIiIiItCTjgA3Ai5UF7u7A48DO8ZaIiGj7RmViOGybB7wEnBxR72ggN+wz0gSCiXoJLWEhItLQlBwWERERERERkZZkJDDX3SuiymdGnK/GzNoCQ4HZMU7PBHqFy05U9uHAnMhK7v41UFTDNbqY2aDIA+gfq66ISCpoWQkRERERERERaUm6A1/FKF8XcT6WroBF1IvXdnX4WOjuJTHqrq/hGlcCN8c5JyKSckoOi4iIiIiIiEhL4/U8V5e29bnGeIKlJyL1J9gET0Qk5ZQcFpEWp7S8gn98uJgZi9ex14CuXDB6EDnZWmVHRCSVZi3dwD8/WkR2lnHB6EHs3KdTukMSERGgcEsZj76/kHkrNnHgsB6cuc/2mFm6w2psecSeudstfIw1MxiCGb+eYNs8oL2ZtYkxe7hrvGu4ez6QH1nWAv99RDLTppVQUgA9doB5L8Hs56HLABj9U2jfA758ZVvZ/pdDu26199kIlBwWkWZh0drNAAzq0b7auYKSMm57eR7vf7OGXfp2ol3rVkz8bBkAk2atZOHazdw2btdGjVdEpDkpr3De/2Yt7s6BO/RgUV4hY//2PuXhSo7Pz1jKlGsPoW/ntkCQmGibk60/dkVEUuzV2St4bOoiWrfK4rIxQxk9tEe1Olf++3Nen7sKgJdnrWDNphL+77BhjR1qus0BTjGzrKh1hyv/KIi1pjDuXmRmC4i9XvCuwBp3Xx1xDQNGAJ9WVjKzHYC28a4hIhlo7TfwzHmwem7wvF0PKFy77fysZ2DML+G/V2wr+/h+GHQAHPBzGLh/48YbRclhEcloZeUVXPHkZ7w6ZyUAfTq1Ya+BXbnogMG0b92KP7w6n08Xr6egpAyAJeuKiE5FPDtjiZLDIiL1VFxazhkPfMgXSzcAkNvKKCnzKvfKlpQ7P3r8E9YUlFBcWs6GojIGdm/Hnaftzj6DmsaMCRGRTDdj8Toue+JTPByAP/g2j9vHjeSUvfqTX1RKjw5t2FhcyhvzVlVp99ynS1ticngi8APgBODFiPLzgS/dfW4tba8wsz7uvhLAzLqFfT0VUe8VoAQ4j4jkMHABUAa8lOyLEJE0W/oJTLwU8r6uWh6ZGAbYuBwmXVO1bEsBfPUaLHgXfjoDOm/XsLHWQMlhEclor85ZuTUxDLByYwmTZq3ktdkr6dw2h3WFpdXaRC/uVVLmTFu4jn0HK0EhIlJX//xw0dbEMEBxWewlFGcv31jl+eK8Qn74+HTev+5QOubmNGSIIiLNWnFpOR8vXMeTHy/emhiG4K6O656bxfXPzQrWQWjfmtvGjSDbjLKIit3bt278oNNvEjAZeMTMugMLCZK2BwInVVYysynAwe4eOb/kToKE7yQzu4Ug0XtT+Hh7ZSV3zzOz3wO/MrMN4fX2B64Dxrv7koZ7eSLS4Coq4NmLIX9xYvXLiuOUF8HXr8PeF6UutjrSIpsiktE+WRh7ObByJ2ZiOJ5bXpqTqpBERFqUe976pt5tNxSVsd/v32JhuDSQiIjUzbdrCvj+HydzwaPTeG3Oqph1KtPAeZu3cOm/PqOsYltiOLdVFtcevXMjRNq0uLsDY4F/EyR0XwF2A0529xpn9Lr7KuD7wBLgn8DTBGsEH+Tu30VV/y1wDXAO8DrwY+BmggSxiGSyonWJJ4Zr021IavqpJyWHRSSjrdoUvbdD/cyJmtEmIiKJ2RQu21Nfm0vKueLJT2uv2IKZWQczu8fMVphZkZl9YmYnJtBukZl5nGN+Y8QuIg3rvre/YU1B/d8PHza8F/sNibW3WvPn7hvd/Qp37+Puue6+l7u/EFVnTNSs4cryr939JHfv5O4d3P0Yd68228QD4919mLu3cffB7v77qHWORSQTte8BPYcn389Ox8Lgg5LvJwlKDotIRjtwWPVNNuprbRJvrEVEpP7mrdhIWbn+Tq7BRIJZZzcBxwFzgYlmdmwt7cYR3MIceVwSnnshXiMRyRzJJIYBpn6Tx6qNcW51FhGRmg0/Ifk+DrwK0rxJc1qTw/WdBRG2PcXMPjCz9eHxoZmdHqNevNkSl6b+FYlIYzvnewNpnZ38QJpl0LVdi1xvTUQkKYN7tE+6D3eq3OYs24QJ4MOBH7r7I+7+NsG6mB8Cd9XU1t0/c/ePIg+gcgfWRxs0cBFpFCfs3jep9vlFpfzxFd1IICJSL1+/lnwfH96bfB9JSvfM4XrNgjCzC4BngeXA2eGxDHjazC6O0eRpqs+aeD5Fr0FE0uzWsbvWXqkWfz1rL7Kz0vtpnYhIJrrztN3p1TG5D9fO2Gd7cnOyUxRRszMO2AC8WFkQrpX5OLCzme2SaEdm1prgffP77v5VqgMVkca3YE3ya7bPXaHl1URE6iU7BRPMFr6TfB9JapWuC0fMgjjZ3SeGZZOBIQSzICbV0PwiYDFweuVaPWb2GrAAOJ/qMyFWhjMlRKQZOnVUfx6bupB5KzfVuW239jk89cP92KlvpwaITESk+Rs1sCsfXH8Yy/OL6douh589/Tlvz1+dcPuz9t0+JR/yNWMjgbkx1qecGXk+wb7GAt2pZdawmXUBukQV90/wGiLSiF74bFnSfXw/hcu0iYi0KJ36A9OT66Nd+sfgdM4cTmYWRClQEPkmOfy6ANCioSItTFaWMfHyAzhmZJ/a6xoct2sfDtu5F784aic+vOEwJYZFRJLUKjuLAd3b0bFtDn84ZVcO3bkXrVtlseeALlx39E7sO7gbO/buwNg9+jFqQNet7cbtuR23jd1Vd27UrDuwLkb5uojzibqY4P3yM7XUuxJYGHW8V4friEgjadcmufleY3bswdVH7pSiaEREWpiyFKzZvu+Pku8jSWmbOUxysyDuBZ43sxuBBwAj2FxjJ+CaGPXPN7Mfh/W+AO5y97hvijVbQiTz5OZk8/dzR/HVqk18vaqAgd3b8q+PvmNZfhEn7N6PYb06sHDtZg7buTed2+WkO1wRkWarV8dcHr1wnypll43ZocrzRWs3k51lbN+tXWOGlslqWpA5ocWazaw/cATwmLvXdh/6eGBCVFl/lCAWaXIuO3gov3h2Zu0VYzh6RB/uO0dLq4mI1NuIsfDVK/Vv33Nn2DvW6riNK53J4e5ArLXOap0F4e4vhhvX/Qu4NSzeDJzm7q9GVX+CYImKJUBf4CcEaxP3dfe/xLnElcDNCb0KEWlSduzdkR17dwTgD6dU/Yxnz4jZaiIikj6DUrCJXQuSR+z3xd3Cx1izimO5kOCuwVo3onP3fCA/sszSvIu2iMR22t7b0zE3h9+/Mo/FeYW11j9qRG9+fNBQurTLYUjPDo0QoYhIM7b7mVBRBjOfgbZdobwUVs6C9j1h4Gj48K/b6lo2ePm259mt4YwnIDv9k9fSmRyGes6CMLMjgCeBp4DngGyCje2eMrNT3f3lrZ24nxvV9llgCnCrmT3o7kUxLqHZEiIiIiLSFMwBTjGzrKg77ioXap5dWwcWZHYvBOa7+wepD1FE0unokX34aEEeEz5YFLfO/kO6Mv7MvejdKbfxAhMRaQn2PDc4Yhk5Dr6dDH12hWFHBonjjx8IksT7/gh67BC7XSNLZ3K4XrMgwje3jwNvu/ulEadeDW+X+yvwcqy2EKxNbGb/Ar5PsHRFtZWjNVtCRERERJqIicAPgBOI2KuDYBPmL909kc3oDgaGAtemPjwRaQrO238gz326lE3FZdXO5WQb9549iu4d2qQhMhGRFmy7UcFRqe9uMPa+9MUTRzqTw/WdBdGbYHmIT2Kc+wQYY2a57l7TqtCVG/FFr3csIiIiItKUTAImA4+YWXeCzeEuAA4ETqqsZGZTgIPdPdaMhouBMuAfDR6tiKTF0J4dePOqg3ll1go6tc1h+qJ1vPj5cnp2bMMvjx2uxLCIiMSVzuRwfWdBrAeKgX1jnNsPyKspMWxmWQRLUGwiSFCLiIiIiDRJ7u5mNha4PTy6EGzafLK7v1RbezPrCJwCTHL3VQ0arIikVe9OuVx4wGAATt6rP78/ebc0RyQiIpkgncnhes2CcPcSM7sfuNLMHgaeJVhz+Pyw7U0Rba8BdgLeBlYAfYDLwnqX1zK7WEREREQk7dx9I3BFeMSrMyZO+SZAOwCKiIiISExpSw4nOQviGmA+cAlwKsHyEF8B5wFPRNT7kiDRPDbsfzMwAzgxkZkWIiIiIiIiIiIiIs1VOmcO13sWhLuXAw+ER039vwQoCSwiIiIiIiIiIiISJav2KiIiIiIiIiIiIiLS3Cg5LCIiIiIiIiIiItICKTksIiIiIiIiIiIi0gIpOSwiIiIiIiIiIiLSAik5LCIiIiIiIiIiItICKTksIiIiIiIiIiIi0gIpOSwiIiIiIiIiIiLSAik5LCIiIiIiIiIiItICKTksIiIiIiIiIiIi0gIpOSwiIiIiIiIiIiLSAik5LCIiIiIiIiIiItICtUp3ACIiIiKS4QrXwZs3w5LpMOB70LojfPs29BgGh/8Gug1Od4QiIiIiIhKDksMiIiIikpzHjoE184Ov18zbVr56Dsx9AbJbQ6u20LYbtOu6rU77njDsKDj0RmjbtfHjFhGRFsnMegN/Ao4D2gKfAte5+wcJth8Vtt8P2AK8Blzt7ssi6gwCFsbp4hh3f7W+8YuIpJKSwyIiIiJSf7MnbksMx1O+JThKNkB+xN/J+d/B9IdgwxI4++mGjVNERAQws1zgLaAD8FMgD7gSeMvMRrv7Z7W0Hw5MAaYDpwLtgduAKWa2p7sXRDUZD0T/kpuHiDRrazaVMGnWCjq0acVxu/UlNyc73SHFpeSwiDQ/pUWwbAZ0GwKd+gVl5WWwdDp07KPbm0UkKa/OXsnrc1cyqHt7LjpgEK2yslhfuIV+XdoC8M3qTbw1bzWDerTniOG9ycqyNEfcwN7/c/J9fPUalG2BVq2T70tERKRmFwMjgFHu/imAmb1DkLC9HTimlva3AJuAE9x9c9h+NjAHuBz4Y1T9xe7+UerCF5Gm5suVm3jgnW/o1yWXKw7dkdUbiznpvqmsLywF4NGpC3nh8gPIyQ62fpu/ciNFW8rZY/sumKX/bwUlh0WkeVjzJXz9OmTlwLt3QOFawOCQX8LAA2Dij4OZaQC7nwWjLoJ+eyoRISJ18swnS7j22Zlbnz/6/gI2bymntNwZ0a8Tlx48lCv//RnlHpxv0yqL0vIKsrOMo0f04faTd6Vjbk6aom8gq1Mw+alNR43HIiLSWMYBsyoTwwDuXmJmTwHXmVlHd98Uq6GZ5QDHAw9XJobD9vPN7CPgFKonh0WkGbvtf3N46JxHAaAAACAASURBVP1FW5/fO3lBtTpzlm/ktdkrOW63vlzx5Ge8PGsFALtv34Unfvg9OrRJb3pWyWERyXxfvwFPnQkVZVEnHCbfVr3+F08FR8e+cP6L0HOnRglTRDLffz5ZUuV5ftG2cWfO8o389Kmqd6KWlFUAUFHuvDRzBbk52dxx2u4NH2hjqjb21sOWzVBaDDm5yfclIiJSs5HA5BjlM4FsYDgwLU7bIQRrFM+O0/6CGOU3mtmfgNKw31vd/a14wZlZF6BLVHH/ePVFJH1Wbiiukhiuyd+nfMtD7y3gi6UbtpZ9sSSff0/7jh9+f0gDRZiYrLReXUQkWe7w4uX1S05sWgFPnwcV5amPS0SapcKS5MaLFz5fRuGWFCRTm4rSIsCT78fLoSTmJC0REZFU6w6si1G+LuJ8TW0j60a3b2tmbcPnJcBDwGXAocClQFfgDTMbV8M1riTYyC7yeK+G+iKSJp9+tz7huvNXbqySGK60amNxKkOqF80cFslQqzYW87fJ3/D5knzKKpx2rbM5cpc+/ODAwc1/fctI37wJBavq337tlzD1L/D9q1IXk4g0W8s2FCXVvrTc+ceHi7j04B1SE1C6tcqFzv1hw9Lk+snKhg49UxOTiIi0GGY2htizgGPp6e5rw69r+mQzkU89a23v7iuASyLK3zez54DPgTuAiXHajwcmRJX1RwlikSZnWK8OCdctjzNqHL9bvxRFU39KDotkIHfnjAc+ZFFeYZXy6YvWM31RHovzilieX8TA7u0oq3AKS8ro2bENew/qyri9+rNzn05pirwB5H2bfB8f36/ksIgkpLg0+TsNXvx8efNJDpvBuAfgyTNhSxIzf7PapC4mERFpSeYDFyVYt/IXVR6xZwd3Cx9jzQqulBc+xmtf5O5xpwG6e6GZPQvcYGY93X1NjDr5QH5kWVPYsEpEqpvyVbX/wjF1zm3FhuLqdw8O6dmO3bePXkWm8Sk5LJKBbnt5XrXEcKXX567e+vXs5Ru3fv3d+iJmfJfPA+8u5E+n7sbpe2/f4HE2ih2PhFdvACrq30fBKph6DxzwfykLS0Sap2G92jNrWXLLH+QVbElRNE3EoAPhukUw97/wyrVQmNib5Cp2Pz3lYYmItEhF62HxB9BjR/CKYCLFoAMgt/O2OqVFQXmPYdAqsz+cc/eVVJ9lW5s5BOsOR9sVKCdIOMezACiqoX2stYijVS7vmcQfMCLSFDw3I7G752IlhgHKm8gooOSwSIbZUFTKPz5cnFQfN78wu/kkh7sNgd3Pgi+eSK6fj+9XcrgGZtYBuB04jWCDjDnAb939vwm0PQW4mmBzDwjecN/t7s80ULgiDWafQd2TTg7v0q8Z3b1RKbsV7HpycLz6S/jovup1LAt2OBI2LIHVcyoLYfez4Wht7C4iUi8rZ8P/roTV86B1eyjKh/KSqnVat4d2PYLEceftYf1CKC2E9j3hjCdgwPfSE3v6TATuNbM93P1zADNrDZwFvOnuG+M1dPdSM3sZOMXMrnf3wrD9jsD+wI01XdjM2gGnAN+4e15NdUWk6SsoLk2q/eK8Qhat3cygHu1TFFH9KDkskmHyC7ewJcmPl4rKKpi7fGPzSVAs+TD5PjavgYoKyNI+nXFMBPYCriXYFONCYKKZneDuk+I1MrMLCGZzPAf8Liz+AfC0mXVw90cbMmiRVDtznwE8OnVRvdt3bJPNjccOr71iJjv6dtjzXJj/v2At4dLiYD3hkadCu27BRqIL34WClTD8JMjJTXfEIiKZqbQIHj8BisJVELYUxK63ZXNwQMSHcwTvf1/5Bfz43YaNs+l5BLgceN7MbiBYRuJnQD+gyq0sZrYIwN0HRRTfDEwD/mtmdwLtgduARcB9EW3vIpgl/AGwBhgE/BwYAoxN9YsSkcZ3wA49ePqT5PbeWFe4hUEoOSwidTCwe3v2HNCFz77Lr71yDb5dU9B8ksPrFiTfR/mW4A11bjP5nqSQmR0LHA6c7O4Tw7LJBG9s7wLiJocJ1oBbDJzu7hVh29cIbsk7H1ByWDLKjn06cslBQ3j4vQVURGwqkZ1llFfUvn/NP3/4PYb17tiAETYRvXcJjljMYMjBjRuPiDRLqzYWs6Wsgu27tUt3KOmxdPq2xHB9rVuYmlgyiLsXm9mhBJvC/R3IBT4FjnD3GQm0n2tmhwB/JJgAUQq8Dlzt7pG3F80BfgxcAHQENgAfAj9x96kpfEkikia3nDSS/81cweYt9d+XZN6Kjew1oGsKo6o7JYdFMtCdp+7OEXe/QwJ5iLiW5xelLqC0MxLbVLgGA/ZXYji+cQRvZl+sLHB3N7PHgQfNbBd3nxunbSlQUJkYDttWmFkBUBKnjUiT9stjh3Pd0TtTWl7B0vWFzFq2gX0GdWNxXiG/+M8XbCwuZcxOvejdKZdnPlnCpuIysoFLDxnKHtun942fiEhzUFJazg8en87Ub/Jw4PDhvbjvnL1o0yobCDYP/fe071iUV8iRu/Rm9A490htwQ+k2hKTfB+90bKqiySjhWsXnJVBvUJzy6cChtbR9FE2EEGnWcnOyqfDkchG3/HcuJ+2xHR3apC9Fq+SwSAbaUl6RVGIYoGNuTmqCaQp2OQnmvhD7XL89g3Uul1VOAjA4fjwM2A+mPwwL34E+u8GRtzZauBloJDA3MsEbmhl5Pk7bewlu2bsReIDgL5hLgJ2Aa+Jd0My6EKxtHKl/HeMWaTDZWUZ2VjY79OrIDr2CmcD9u7bjgxsOq1LvV8fvwuqNxbRplU3nds1o3BURSZOSsnKOGv9ulc2Z35y3mu/d9ia9OrZhQ3EZ+YVbKCkL3ixP+GARVx2xI2P32I4B3ZvZDOOOfUk6Oby5HpuIiojIVuVJ5ma2lFewbH0RO/VJ392FaU0ON9YGR2b2f8AVwEBgKUGC4s4YiQ6RjNC1fXIJhvatszlxj34piqYJOPUxmHFwsL5lWQlsXA6tWsOIcTD6p1BRDjMegw3LYOTJQWIY4Lg70xt35ugOfBWjfF3E+Zjc/UUzOxH4F1CZgd8MnObur9ZwzSsJ1nMTyXi9OmlNXRGRVHl9zqoqieFK+UVl5BfF3g3+z298xd1vfMVFBwzm1yfEWfImE2VlQ25nKF5f/z6+fQvmvAgjTkpdXCIiLcjRI/rw3y+Wb31uBmfvsz2lFc7b81azdvOWref6dc5lQ1FplWUo+nTKZYdeHRo15mjpnjnc4BscmdlNwC0EC8S/DYwOv+4GXJ/i1yPSKEpKk/tc4yeH7JDWWxZSLisL9rk4OOI54GeNF0/zVNPnoXHPmdkRwJPAUwRjdjZwDvCUmZ3q7i/HaTqeYJyP1B94L9GARUREpPmZ+s3aerVz4NGpCzlz3+3Zsbms/e6ems2Un/sB7Hgk5LRNvi8RkRbmL2fuQZd2ObwyayV9OrfhnjP3YnDPYIM5d+eNuat47+s1dO/QhnO+NxDH+fm/P2feyk3s3KcjvzlxBNlZltbXkLbsUGNscGRm3YEbgXvd/ddh2ylm1h641szudffkthUUSYOB3dtz4A49eD/qzXH39q05ZOeerNxQwqqNRSzPL2bzlnJaZ2expTxIKO87qBsXjB6Uhqglg+URe3Zwt/Ax5k4oZmbA48Db7n5pxKlXzaw/8FcgZnLY3fOBKrsuBt2JiIhIS+XuvPj5sqT6WJ5f1HySw+WlUJjkhnQAFaXw3Ucw9JDk+xIRaWHMjN+eNJLfnjQy5rkjR/ThyBF9qpQ/8aP9Giu8hKRz6mBjbHB0NMHOo49HtZ8A/BI4Efhbsi9EJB0ePH8UT378HQvXFjCwe3uG9+3E6KE9qn3itKGolM5tc1ieX0ThlrKta2OK1MEc4BQzy4pajmfX8HF2nHa9gb7AJzHOfQKMMbNcdy9OXagiIiLSXM1ZvpGiJO+g+3pVAWN26pWiiNKsVWvY8Wj46pXk++o2OPk+REQkI6UzOdwYGxyNJLiDaE5kY3f/2syKwvPVaCMkyQTtWrfih98fUmu9zm2D9Yn7ddFtYlJvEwmW7jmBiA/0CO7U+LKGD/LWA8XAvjHO7QfkKTEsIiIiieqSgo09f//KPE4Z1Z9u7VunIKImYNz9MPl2WDoNVnwB9dlWZ/T/QddBKQ9NREQyQzqTw42xwVF3oNDdS6L7IEhaxLuGNkISEdlmEjAZeCRcrmchcAFwILB19xIzmwIc7O4G4O4lZnY/cKWZPQw8S7Dm8Plh25sa80WIiIhIZlu5IfnPlCscHnj3W244ZnjtlTNB2y5w4M/hnj3qnhjuuB1c9j6061Z7XRERabbSvSNVY2xwVJ9raCMkEZFQuOTPWOD28OhCcGfHye7+Ui3NrwHmE9zdcSpQQfDB4HnAEw0WtIiIiDQ7364pSEk/XyzJr71SJnn8RCiLkTjPagWWFWw0V7yh+vnO/ZQYFhGRtCaHG2ODozygvZm1iTF7uGu8a2gjJBGRqtx9I3BFeMSrMyZGWTnB8j8PNFhwIiIi0iJ8f1hPWrfKYktZcusOj+zXOUURNRHrFsQu3+kYOONfMOcF+M8F1c8vnQ5lW4K1i0VEpMXKSuO15wDDzSw6hmQ3OBpsZrkR1zBgRGQlM9sBaFvDNURERERERKQJ6delLRMu3IdhvTrUu4/endrwi6N3SmFUTUDnONvj9NszeOy7ezCDOFqvEUoMi0hqVFRAeVm6o5B6SmdyeCLBrcknRJWncoOjV4ASgtuXI10AlAG13Q4tIiIiIiIiTcToHXrwxlUH07Nj4knNLIODduzBPWfuzgfXH0abVtkNGGEanPkk5Ebtp77rabDf5cHX3QbD8XdDm4gZ0z13DjazExFJ1kf3w58Gw+39YNK1QaJYMko6l5Vo8A2O3D3PzH4P/MrMNoTX2x+4Dhjv7ksa/FWKiIiIiIhISt103C787N+fJ1T3b+eM4uiRfRo4ojTqMwKuXwxF66F1J/AyaNWmap1RF8Ke50FFOXh5sA6xiEh9lJfBpuXQvmewrM2r1207N+0B6DYE9rs0fntpctKWHG7EDY5+C2wALgduAJYDNwN/TM0rERERERERkcZ00h7b0Sk3h1dnr2T7bm15fe5KZi7dWK1ejw6tGbNTzzREmAZtu4ZfxJkZnZUdHCIi9bVoKjx9TvBhFECbTtXrTH9YyeEMk86Zw42ywZG7OzA+PERERERERKQZOGTnXhyycy8Ajtm1LxdPmM7ivEJyso1endqw78Bu/OzwHcnNUUJURCQlXrhsW2IYoKT6h3KUFgaPFRWwciZ07AsdezdOfFIvaU0Oi4iIiIiIiCRraM8OTL56DN+uKaBvl7Z0aKM/dUVEUqq0GPIX115v5+Nh43J4/CTI+wqyWsGYG+Cgaxo+RqmXdG5IJyIiIiIiIpISWVnGsN4dlRgWEWkIObkw6MDa6y3+EP62f5AYBqgog7dvgw3LGjY+qTclh0VEREREmjAz62Bm95jZCjMrMrNPzOzEBNuamV1iZjPMrNDM8s3sIzMb3dBxi4iISDNz6mOQ067mOqtmQnF+VGEFTDge3rkj2NBOmhR9pCoiIiJ1smBNAZO/XMPgHu0Ys2MvsrIs3SGJNHcTgb2Aa4GFwIXARDM7wd0n1dL2YeAU4E/AB0B7YFT4KCIiIpK4dj2gbbdt6wrXxfoFMPnWoO3hN6c+Nqk3JYdFREQkYe9/vZaLJkyjtNwBOG1Uf+44bfc0RyXSfJnZscDhwMnuPjEsmwwMAe4C4iaHzewUgkTyge7+YcSplxssYBEREWmeSovgoUNh49Lk+pn1jJLDTYySwyIiIhJXeYVz3+Sv+ey7fPYd3I13vlqzNTEM8J8ZSymvcG48bjjdO7TB3SkqLadd61YUlJRp3UeR5I0DNgAvVha4u5vZ48CDZraLu8+N0/anwLtRiWERERGRupvzAqyO95ajDtp2T74PSSn9xSYiIiJxHXX3u3yzpgCAyV+uiVnn+c+W8b+Zy6lwp6wiKMvOMsornB16dWD8GXswcrvOjRWySHMzEpjr7hVR5TMjz0c3MrMcYD+CBPLtwA+A7sCXwJ/c/fF4FzSzLkCXqOL+9QtfREREmoXCtanp5/i7UtOPpIw2pBMREZGY5q/cuDUxXJst5dsSwxDMOAb4ZnUB1/zni4YIT6Sl6A6si1G+LuJ8vHZtgAuAk4ArgGOAWcAEM/tRDde8kmBt48jjvTpHLiIiIs3HLidBdpvk+jjgSui/T2rikZRRclhERERiilw+IhnzV26irDx60qOI1EFN/xnjnat8n58LHOvu/3H3N4CzgOnAr2voczwwOOr4fp0iFhERkealywDY6dj6t7dsOOia1MUjKaPksGSsp6d/x/F/fY/TH/iQ979O0e0NIiKy1a7bdSY3JzVvFWYu25CSfkRaoDxizw7uFj7GmlUMsJ4gcTzf3RdXFrq7A68C/c2sV6yG7p7v7osiDyDJ3WdEREQko5WVwLwXa68XS8e+cM4z0KZjamOSlFByWDLSq7NXct1zs5i9bCPTFq7j4gnTWZ5flO6wRESalaIt5RSXpmbG74ai0pT0I9ICzQGGm1n0+/Zdw8fZsRq5exHwTZw+LXzUlH4RERFJzKznoNoWCAnotydcPR92ODz1MUlKKDksGcXduev1L7n8yU+rlG8pr+DMBz/i3re/Jq+ghLtf/5Ixd0zmyLvfYdKsFWmKVkQks5VVpCZvNKBbOw4Y2iMlfYm0QBMJNoc7Iar8fOBLd69p2/DnCRLLgyoLzMwI1h5e4O669UpEREQS021IApWs6tNWbeGwX0NFeYOEJKnRKt0BiCTiwXe/5W+TvyG/qCxune/WFXLn61/xyPsLWV+4bYbaT574lOuP2YlLD96hMUIVEWk2crKzyKL+Uwvbt87m4gMHc97+A2ndSp9Hi9TTJGAy8IiZdSfYHO4C4ECCjeYAMLMpwMHuHvlX2R3AOcCrZnYLkA/8ABgFnNko0YuINEFm1hv4E3Ac0Bb4FLjO3T9IoO0JwBkEY+mOwBJ3HxSnbg5wE3Ah0Ifgjo4/u/sjyb8KkUa2aVn1sqGHwfqFkL8Ehp8I3QbDmi9hu72gx46Q2wVeux5WzoIBo+HkB4K1i6VJUXJYmrwPv83j9knzE64fmRiu9PB7C5UcFhGpo9ycbMbutR3PfxrjjWAC+ndtx9VH7pTiqERaFnd3MxsL3B4eXYC5wMnu/lItbfPM7PsESeK/ESRAZgHj3P2Fho1cRKRpMrNc4C2gA/BTgrXdrwTeMrPR7v5ZLV2MBfYGZhDcjd2mhrp/B84GbgQ+A44HHjazHHe/P6kXItLYykqql/XfB857Pvj6uR/Be3cGX89/CSwLcjtD0fqg7LsP4H9XwbnPNk68kjAlh6XJm7YwL+k+Sstr2uRbRETi+fPpe5BfWMrb81fXWvecfQfwxLTvtj6/5KBEbj0Tkdq4+0bgivCIV2dMnPJFwGkNEpiISGa6GBgBjHL3TwHM7B1gHsGHcMfU0v5H7sHCq2b2ArBHrEpmNoLgbo2r3P3usHiKmfUFbjezCe5enPSrEWksOx8HnfrDxnCP2jadYY+zgq9Li2D2c1Xre8W2xHClZZ80fJxSZ0oOS5OXk538rcjZKYhDRKSlevTCffgur5CNxaU8/N4CXvh8ebU63xvcjVvHjeSQnXsxb8VGDhzWgz0HdE1DtCIiIiI1GgfMqkwMA7h7iZk9BVxnZh3dfVO8xpWJ4QSMBRz4Z1T5BILZxIcSLB0kkhlyO8Mlk+GzfwaziHc/C7oOCs5l5UCbjlCcX3MfAw9o8DCl7pQcliZvv6Hdk+6jsFSLn4uIJGNA93YA/OnU3dmpTyc++249Fe5sKi7lwGE9ueKQHTAzDt+lN4fv0jvN0YqIiIjENZJgLfdoMwnmFQ0HpqXoOitjbP45M+J8teSwmXUhWEIoUv8UxCOSvA694PtXVy/PbgWH/wZeviqYMRyp21AoWAWDD4Lj767eVtJOyWFp8nbp2ympDZEAissqWLR2M4N6tE9VWCIiLVLrVllcNmZousMQERERqa/uwLoY5esizqfzOlcCN6coBpHGs/dFMPQQ+OQxmPsCFOXDnufCEb+FLN3P3ZQpOSxN3vwVG5NKDFfKL6q+UZ2IiIiISKZYt3kLE6YuZOXGYk7aYzsO2KFHukMSSSszG0PsWcCx9IyYxVvTpjSp3LAmVl9ewzmA8QRLT0TqD7yXophEGk7XQXDELcEhGUPJYWny/vzGVzHLjcR/a+/cpyO79++csphERERERBpTRYUz9r73+W5dEQDPfLKU+87ek+N265fmyETSaj5wUYJ1K9cRziP2rN1u4WOs2b71kUewdES0ymvHvI675wNVFm41sxSFJCJSnZLD0uTNXrYxZvmUX4yhoKSM0+7/kMItwZrCp43qT8fcHB6dunBrvYN37MndZ+yhX6giIiIikrGu/s/nWxPDlS5/8jP+PuVbxp+5B4N7dODbNQX07tSG975ey5pNJRw1og/9urRNU8QiDc/dV1J9lm1t5hA7absrUE6QcE6FOcAZZtbd3fOirgMwO0XXERFJipLD0uTtOaALb81fXaVst/6dGdg9WD946nWH8u7Xa9iuS1v2HtQNd2fvQV2ZtWwDBwztwYHDdLudiIiIiGSmsvIK3p6/mv9+vjzm+dnLN3L4n9+Nee5Pr37J8z8ZzfC+nRoyRJFMMxG418z2cPfPAcysNXAW8Ka7x56dVHcvAL8DzgX+ElF+AcHM4ESXwxARaVBKDkuT96dTd2PsfVNZsj6YKdGzQ2vuO3uvree7tm/NSXtst/W5mXHsrn05dte+jR6riIiIiEiqrC0o4fT7P2TB2s31al9UWs7973zLX87cM8WRiWS0R4DLgefN7AaC5R1+BvQDTo+saGaLANx9UETZQGCf8Gk/oJ2ZnRo+n+vuc8M2s81sAvB7C25j/Qw4niBZfIW7V70VQEQkTZQcliave4c2vHfdoWwqLqWwpIzenXVrnIiIiIg0f49/sKjeieFKy9Yr/yQSyd2LzexQ4A7g70Au8ClwhLvPSKCLQ4DHosr+Ez7eAvwmovzHwFLgKqA3sAC4xN0fqvcLkPQpWA1eAR16g5atlGZEyWHJGB1zc+iYm5PuMEREREREGkUqErujh8bad0ukZQvXKj4vgXqDYpRNIMF1jt19C/Cr8JBMVVoET58L37wZPM/tDGf8CwYftK3OshnwyvWwbgEMPx6O/gPkaGKbZIasdAcgIiIiIiIi1bVtnZ10Hy9+EXutYhERSdAnj21LDAMUb4BnLoDy0uB5eSk8dTYsnQaFa2HGBHj2YticF7M7kaZGyWEREREREZEmaPrCdUn3sTivkEVJLk0hItKirZlXvaxoHWxaEXy99isoWFn1/JeT4C+7wdJPGj4+kSSlNTlsZh3M7B4zW2FmRWb2iZmdmEC7RWbmcY75UXXj1bu04V6ZiIiIiIhIcr5dU5CSfhblKTksIlJvw46qXtZlAHTePvi6bVdo06l6nS0F8O4dDRubSAqke+bwROAc4CbgOGAuMNHMjq2l3Thg/6jjkvDcCzHqPx2j/vPJBi8iIiKyVf4SWDUn+LqiApZ/DgVr0huTiGS04f1iJBvq4dPF61PSj4hIizT8eDjq9iAJnJUDvXeFs56GLZvhletg/G5QshGyWldvW7yh8eMVqaO0bUgXJoAPB05294lh2WRgCHAXMCleW3f/LEZ/Z4dfPhqjyUp3/yjpoEVERERimfQLmPYQ4NB3dyjaAPmLgj8gDr8ZRv803RGKSAb6w8m7ceaDH1FQUpZUP21bax9yEZGk7H95cFSa9hDcfyB4+bayii3QZSDkL95WNuqixotRpJ7SOXN4HLABeLGywN0deBzY2cx2SbQjM2sNnA287+5fpTpQERERkbiWzYBpDwIePF/xRZAYBqgohTduhpVzg3qVG5eIiCRg5HadmfiT0bTNqf+fbf27tuX0vfunMCoRkRYmfwlM/St88TSUFgeTACb9ompiuNJ2o+CI38JeF8DZ/4Hdz2j8eEXqKJ0fIY8E5rp7RVT5zMjzCfY1FuhO7FnDAOeb2Y8BA74A7nL3Z+J1ZmZdgC5RxXpHJSIiItVNvKzm814O9+8ffN1pOzj3eei1c8PHJSLNwrDeHRm5XWemL0psaYhsg6wso2/ntpy2d39+cOBg2mnmsIhI/bx8DUx/aNvzKbfDmF+ydVJAtD4j4YCfNUpoIqmSzpnD3YFY2++uizifqIuBAiBWwvcJ4ArgSOB8oAh42sxq+t96JbAw6nivDvGIiIhIS7DwXVj7ZeL1Ny6Dt3/XcPGISLO0vjD+XQfbdckly4KvDSh3KC13vltXyL+nLSG3VXbjBCki0tysnF01MQywfhH87+r4bd69S3tOSMZJ90fIcT5qqfXcVmbWHzgCeMzdq23D6+7nRtV/FpgC3GpmD7p7UYxuxwMTosr6owSxiIiIRPr6zbq3iVyHTv6fvfuOj7JK+z/+udJDEgg1IISqCFIsiBUEFETZVUEedS2rrGLZ1VVWV13Fwrq7+IjrLo8/dW0gdldUmqIoClhRBAHpRXoNLRAgpJ3fH/cEUibJJJnJpHzfr9f9msy5zzn3NYjD5JpzX0dEAnD5aS0Z80nxL6IiDP53aHe6t0zmp017eXTKUjbsOXT0/JZ9h9m2P5OWyfFVGa6ISO0wZ4z/9uwDJY/JPggrPoTIaO9550shLjibi4qESjiTw7vxvzq4ke/R36pif4bhrYAuqaREIc65PDN7A+iNV7pinp8++4B9BdvMLMBwRKrQzhXw7f+DrAw4/XfQvm/JfVdMh0VvQb0m3m0ujdpVVZQiIrXTkQPFV5MEovOlwY9FRGq13/fpQOOEGGavTKNNo3rUi41iz8EsLjm5BT3aeL8+9T2xGT3bbSuUHD6uQRzN68eFK2wRkZotuoJfrM15Ag5s837+8p9wy2yIL1q5VKT6CGdyeCkw1MwiitQdUDQfCAAAIABJREFU7uZ7XFLWBOZlbIcBK5xz35bj2vnlNIrWOxapOQ7tgfEDIdP3PcbyqXDjDEg9o3jf1Z/BO1cfe77qE7hzIUTrlwURkQrb8C1kHyq7X1E7lwc/FhGp1cyMq3q25qqerUvtN3JQZ/YdymLWyjROaJbI45d3IzJCi1xERCqkxzBY/E75xjTvDtsXH3u+dx0seR963hTU0ESCKZw1hyfhbfp2SZH264GVzrlANqPrA3QgwFXDAGYWAVwLHMBLUIvUTKs/O5YYBnB5sPAt7+eMnbB4olcjCWBxkXLcB7bBelVJERGplPQtFRu3dJL3BZ+ISJA1TIjh5Rt6snb0ID4ZcR6ntm4Y7pBERGquNmfDadcH3j8uGU6+unh7Xk7wYhIJgXCuHJ4OzALGmVljvE3fbgB6AZfldzKz2UAf55y/r7xvBHKA1/xdwMz+DJwIfAFsA5oDv/dd43bnXGawXoxIlfO3Wm3+K7Dobcgp8Fe795+hfovifV1u6GITEanN9m6Aj++FVTMqNj4iCiJjghuTiIiIiATfcafBAr8pp+IsEpZN9T7n5WZ5bYnNoevQ0MUnEgQVSg6bWQJwNpACzHTO7SjvHM45Z2aDgdG+IxlYBlzunJsWQAxJwFBgeinXX4mXaB7sm/8gMB+4NJBriFRr3z3jvz2nyHceX/0LrnqjeL/VM6HjRcGPS0SkNnMO3rwCdhXfGCpgEVEQXS94MYmIiIhIaDgXeN/Du2HTd8een3kb9LobEpoEPy6RICp3ctjMfg88DtQHHDAA2GFmTYFNwJ3OuRcDmcs5tx+4w3eU1KdvCe0HgIQy5p8GKAkstdOB7QF2zIN9G4o3q+aliEj57VpVucQwQM5hSFsBKScFJyYRERERCY20SvzeHNcAklKCF4tIiJSr5rCZDQWexSsHMRw4WurBOZcGfEKBkhAiEkJtzgm877f/r3ibaXMSEZFyWzY1CJMY1D8uCPOIiIiISEit/qziY5OaBy8OkRAq74Z09wKznHNDgCl+zv8IdK10VCJSuoVvwZb5gfc/sLV4W4uTgxePiEhdkbai8nPEJ3uHiIiIiFRvjdpVfOwnD8APLwUvFpEQKW9yuBswqZTz24BmFQ9HRMq0YylM/gMc2l3xORq1h7NLrOYiIiIlKc+O1QB97oc2vQu39fhd8OIRERHPnnWQkVa47cB22LcxPPGISO1w4d8hIrpiY3My4eP7y1ESUiQ8yltzOJfSE8rH4W36JiKhsuFbvHLfFdSwPdw+DyIrtB+liEjd1r4PDPgbzHkCsjJ8jQaJKZCxg6Pvz007Qc/h3pF1EL4ZC9sWQ/u+cOat4YldRKQ2OpIB71wD6+Z4G36efQf0HwUf3Q3zJ4DLgxMHwRUTICo2vLGKSM2T0gVOGAArpx9ri4qHhq0hLYB9KFwu7F6rEhNSrZU3O7QIGAg8XfSEmUUAVwDzghCXiJSk5WmVG7/3F1gxDboMCU48IiJ1zbl3ekfGTtg4F1p0h4Zt4eBu2PgtNDsJGnc41j82Ec5/KGzhiojUavNe9hLDAHk53pdxyW3gx/HH+qycDovehh7DwhKiiNRwFzwKWxd65RojY2Dg36HHjfD98/D5Y95mwxbhfRlVlEVAyx5VH7NIOZS3rMQzwMVm9jegUf4cZnYiMBHogp/EsYgEUcsekFjJbx1XTC+7j4iIlC6xGZx0qZcYBkhoDJ0vKZwYFhGR0Nqztnjb1gXF23b76SciEohmnWDEYrhpJvzPBG+TureugCYdvbsS4huCc/7LT3T/DUTHVXXEIuVSrpXDzrn/mlk3YCTwgK/5E8B8x6POuY+DG6KIFJJ1CPKyKjfHms8gNxsiK1g7SUREREQkXBa+BbNGw6Fd3u3dBUUnwBm3wOJ3vM+7+Za873327fugyquJSPlFRnsLASYMglzf7+NrvvDac494z/OyvQRx/Zbez6dcA30fKHlOkWqi3P8qOuceMrMPgGuBTnhJ4dXA6865H4Mcn4gUtfpTOLSncnMc3gtrZ0HHC4MTk4iIiIhIVVj/DUz+/bHn2YcLn885DK9dCrm5hdv3b4GvnoKYBOh9T+jjFJHaZ9WMY4lhAPKOJYaPNmXD5S9C6zOrNDSRyqjQV6bOuQWAn3t1RCTkoipwS0pUnLdTakG6tUVEREREapo1M0s/7/K8hRAlmfcKnPsniChvhUURqfPyS4kVVLTWsEWoxJjUOPoXUaSmOb4/tOoZeP+mneDmL6Be42NtbXp5h4iIiIhITZLSpXLj92+Cuc8FJxYRqVtOGAjdrjj2vONF8Kt/e5vUAUREwaAnIaFJeOITqaByrRw2s/Fl98I5526qYDwiUpbIKBg2HT4cAQvfPNYenQDZB/M7wanXQod+cOIgb5XwHT96OzXHJXv/iGm1hIiIiIjUNF2GwC+z4afXKz7H8qlwzh1BC0lqHjNLAcYAvwLi8e6Mvt85920AYy8BrgJ6AB2BTc65tn76tQXWlTDNxc65TyoSu4RRRAQMfRnOfwjyco+tED7teti/1UsK6w5dqYHKW1ZiWAB9HKDksEgoRcXA4Oeg06/hl1nQvBt06A8L34AjB+CUa70dVQuq1whOvS488YqIiIiIBENEJPR7EPZthA3fevU9y6tR++DHJTWGmcUBnwOJwB+B3cAI4HMzO8c591MZUwwGTgfm492NHVtG/7HAf4u0LS9v3FKNFC0vEREBya3CEopIMJQrOeycK7bU0MwigfbAn4FuwEXBCU1EytRpkHfk63Nf+GIREREREakKL/aDjO0VGxtbH/rcH9x4pKa5EegC9PDtp4SZzcFL2I4GLi5j/M3OeUVmzWwycEoZ/Tc45+ZWLmQRkdCp9H3lzrlc59xq59yteN+4PVH5sERERERERESK2DK/4olhgCP7YcM3wYtHaqIhwM/5iWEA59wR4G1ggJkllTY4PzEsIlJbBLvo6MfA0CDPKSIiYWZmiWb2tJltM7PDZvajmV0awLj1ZuZKOFZURewiIiJSi+RWoIxEUVvLqhogtVxXYImf9sVAJNA5yNcbaWZZZnbQzGaZ2QWldTazZDNrW/AAVLNAqoXs3Dze+WEjj01bxper0gCYtWInvx33PdeP/4Fv1uwKc4RSEeWtOVyWxnh1e0REpHaZBJwG3Ie3scYwYJKZXeKcm17KuCEUr8PWDXgRmByCOEVERKQ2a3UGJKZAxo6Kz9HuvODFIzVRY2CPn/Y9Bc4HwxHgJeBTYDvQDrgH+MzMhjrnJpUwbgTwaJBiEAmqe95dxNRFWwEY/8062jWux7rdh46e/27tLmaMOI/2TRPJzM7l7R82sjYtgws6p9DvxGbhClvKEJTksJklA/2BP+EVZRcRkVrCzAbhvcdfnv8h1sxm4dWbfwooMTnsb0MPM7vG9+P44EcrIiIitVpEBNw8C774Gyx5H3Kzyje+fkvoWFZJWakpzKwvMCvA7k2dc/nLGl0p/Uo7FzDn3DbglgJNX5vZ+8BC4Em8xRf+jAUmFGlrBXwVjLhEKmrvwSymLd5aqK1gYhggO9fx+fKdtG+ayB1vLWDm8p0AvDF3I7/u3oKnf3MqERFWZTFLYMqVHDazPEp+ozS8b9rurmxQIiJSrQwB0oEp+Q3OOWdmrwIvmtlJzrllgUxkZjHANcDXzrlVIYlWREREarcGLWHI89CgFXz5ZPnG7t8CK6dDl8GhiU2q2grgdwH2PeB73I3/1cGNfI/+VhUHhXPukJm9BzxgZk2dc2l++uwD9hVsM1MyTcIvKtKIjoggK7f0stsxUca/Plt1NDGc78PF2+jUPIk7zj8hlGFKBZR35fBrFE8OO7w3z1XA2865A8VGiYhITdYVWOZn843FBc8HONdgvA/jpa4a9t2RklykWbXWRKROMrNEYDRwBd5741LgMefc1DLGjcL/rck7nHPNgx2nSJU79y745v/Kv3o4KyM08UiVc85tp/gq27Isxfv8WlQ3IBcv4RxK+Xs/aWM7qVGS4qIZ3rsdz81eW2Kf1IbxPDZtObnO/7rSDxdvU3K4GipXctg5NyxEcYiISPXVGO8LwKIqUpftRiADeLeMfqq1JiJyTEXrvucbgPfem6+cmTSRaio2Cc6+Hb7+d+BjYpKg069CF5PUBJOAZ8zsFOfcQjh6d9vVwEzn3P5QXdjM6gFDgTXOud2huo5IqNx3USe++2U3P23c5/d8cr0YNu09XOL4xNhgb30mwaD/KiIiEohK12Uzs1Z4CYpXnHMHy+iuWmsiIlSu7nsBP/puUxapffrcD3P/AzmZx9osElxu8b4WAbd9BfENqy4+qY7GAbcDH5jZA3gLHu4CjgOuLNjRzNYDOOfaFmhrA/T0PT0OqGdm/+N7viy/3JqZPYW3SvhbIA1oi7dPU3u8u+lqrpwj8N2zsHketD4bzvo9REaHOyqpIk//5lT6/2sOR3KKL37flXGk1LELN+5l9Y4DnJCSFKrwpAJKTQ6bWeuKTOqc21ixcEREpBoKVl22YXgfkMvciK461VrLzs1jy97DtGoYT1RkRNkDRESCK2h130Vqpeh4uPDv8PF94PK8BLC/xHBKN7j8BWjUrupjlGrFOZdpZufjbQr3HyAOWAAMcM7ND2CKfsArRdom+h7/Cozy/bwUuBW4AUjCey//DviDc+6byryGKrFvE2QfgqYnFj/34d2w8A3v55XTYd8G+NVTVRufhMWP6/dw59s/+U0MA2Tl+Hn/LSDHwdRFW7nnQj9/ryRsylo5vJ6K7dQZWYExIiJSPS0FhppZRJG6w918j0vKmsC8zO4wYIVz7tvghxgaP67fwx/eXMDOA0doXj+O/1x3Gqe21mojEalSwaj7vtzMmgE7gQ+Bkc65nWWMEak5zrgZOg6E9d/A5Nv89+n/KKR0qdq4pNry1Sr+bQD92vppm0AAdY6dc+MJYFFEtfThn+DHVwAHbXrBNf+F2ETvnHPwc5EKcYvfVXK4jrjvvcVsTc8s8fzug9llzrFmp+q+VzdlJYcfo2LJYRERqT0mATcBl1Bg5RpwPbAywBVrfYAOePUya4wHJ/3MzgPerVHb92fy0OQlfHRn7zBHJSJ1TGXqvq8FHgR+wqszfC7e+/AFZtbDObfX3yBtCio1UnJr6NYCZo6CjO2Fz0VEKTEsEqiNc+HHAjntDV/D/Alwzh3eczNITIH0Tcf6JKZUaYgSHlk5efyyq6zqgGXLyVOasbopNTnsnBtVRXGIiEj1NR2YBYwzs8Z4myHdAPQCLsvvZGazgT7OOX/1H24EcoDXQh5tEK1NK/zhR99yi0iYVKjuu3Pu9SJNX5jZXOBTvHqbfy9hqDYFlZopMtorHTH5dti/2WuLawAX/gPqHxfe2ERqil/mFG9LW1n4+cDR8P5wyD0CUfEw8B9VE5uEVUxUBKekJrNwU+W2MTirfXn2M5eqoA3pRESkVL7aloOB0b4jGe8W5sudc9PKGm9mSXi7Mk93zu0IabBB5Jzj/E7N+GzZsZAjI4y/TlvK/Rd1AiDPOerFRLFl32G+XJVGuyYJ+rAjIsEWrLrvADjnPjOzbcDZpXTTpqBSc7XvCyN+hqwMr/5wVBxE6tdekYBsWwxfPlm8ff/Wws879IMhz0NeDhzfH+o1Kj5Gap28PFfmhnOBOKVVgyBEI8FU4X8lzSwRL0FQbHeeQDek880xGrjCN9dS4DHn3NQyxq0H2pRweqVzrlOR/ncCd/jGbAZeAP7pp3abiIj44Zzbj/c+ekcpffqW0H4ASAhNZMGXk5vHqGlLeffHzdSPiyIhJoKDWd4/F4eycnnlm/Us3pzOsq37yc7No9cJTfh6dRr5ezIM7JLCC789PYyvQERqmUrXffcjAijxc3B12hRUpEIiIiCufrijEKl5Fr0DeX5qxqYXSPFs+gHe/B/ITAeLhEFj4ORrvJX7kdFVF6tUuV92ZbB57+GA+6c2jGfz3sPFbnEaO3MVrw8/K7jBSaWUe9t1M/uNmS3B22lzA97txUWPQE0CrgUeAn6FtxJtkpkNKmPcELzVDgWPW3znJheJ9yHg38A7wEBgHPAPvKS0iIhIIW//sJE35m4kKyePXRlZRxPDBc3fsJfD2bnk5DlmrzyWGAaYsXQHr31Xnn8KRURKNQlvEcUlRdrLU/f9KDO7EEgB5gYnPBERqTXyN50ryiKP/fz5Y15iGMDlwvT7YPRx3vHxX0Ifo4TNccnxxEdHlt3R56Ze7YiMKP7lcsaRnGCGJUFQrpXDvtuK38LbFOMF4Dbf8yhgMPAz3g7Igcw1COiPd1vyJF/bLKA98BRejUu/nHM/+ZnvGt+P4wu0NQZGAs845x7xNc82swTgPjN7xjm3OZB4q4Nt6Yd5+at17Mo4wuWntaJPx6bhDklEpNb5clVaped4c+5Grj+7XRCiERGpeN13M/sJr9b7SiAbOAf4M7AGeLaK4hcRkZoiuYQbtLMK7LuRUaRKnMv1HnOz4Pv/QKMOcObNoYlPwio+OpJ6MZEczs4tdi4pNpKE2Ci27z9WdmLMjJWk1I9ly77MQn37ntgs5LFK+ZR35fCfgeXAKUB+snW8c+43wOlAR2BhgHMNwVt9PCW/wTnngFeBTmZ2UqBBmVkMcA3wtXOu4G7OFwFxvjkLmoCX0L400GuEW1ZOHlc8/x3jvl7HlIVbGfbKD8xeuTPcYYmI1DqLNqdXeo6dBzLL7iQiEgDf5+PBeHfBjQY+BroTWN33FcAfgInAR3irjV8GzvSVjhARETkmooRVoVGxsHutV1IiqUXpcyyYEPSwpHrYdyib3Qez/J47cCS3UGIYvJJ8CbGF16TGR0dwa58OIYtRKqa8NYe7A393zmWaWT1fWySAc26Jmb0IPECBhG8pugLL/NT9XVzwfIBxDcbbqGN8kfaueDs4Ly3Y6JxbbWaHfeeLMbNkvNv3CmoVYCwh8cO6PYVquzgHHyzYom9cRESCbN8h/x94yuNItkrai0jwVLTuu3Pu6hCGJSIitU3R4rD5dq+BZ88sXI84uQ1kH4KDRe66q39cyMKT8GqYEEOn5kms2H4g4DG7MrJ45NcnMWXhFprVj+PuAR2JK0dpCqka5U0OR+LtmAyQn6ksuM3gSuD3Ac7VGK88RVF7CpwP1I1ABvCun2sccs75205xbynXGAE8Wo7rh1zjxJhibTv3Z/L49OUM7Nqc01o3DENUIiK1y8bdh8jOLelTceCaJ8cHIRoRERERkSq0ekbJ54puVJe+CYqu9bMIOOePwY9Lqo1nrz2NhycvYdm2/ZySmkxcdASfLNlRYv92TRK4sVc7buylknvVWXmTw5uBNgDOucNmthOvnMR7vvMnAgfLMV9pv4EH9Nu5mbUCBgCvOOf8Xbsi1xiLV3qioFbAV4HEFGyb9x5i0aZ99O/UjJkrjpWSmLtuD3PX7eGlr37hhd/2YMBJzcMRnohIrTF54ZbA/vEpw5ih3YMwi4iIiIhIFUpuHXjfYjeB+9rWfwPtzgteTFKtdGiayFs3n3X0+Z6DWew/vIBv1+6mcUIMA7s0590fN5GT52gQH82DgzqHMVoJVHmTw9/ibSKXX294KnCXmR3Cq198O1BW7bN8u/G/creR73GPn3P+DPNdu2hJifxrJJhZrJ/Vww1LuoavBluhOmxmxXdYrApfrU7jpgk/kpXrvfFGGhRd1JbnYMR/F/LJnefRrEEssVFaoi8iUhFr0zLK7hSAr1bt4vS2jcruKCIiIiJSXZzzR1gzE3YsqfgcC9+Cfg8ELyap1holxPDWzWeRfiibhNhIoiIjuOfCjqzZmUG3Vg2oF1PetKOEQ3k3pHsOmG1m+ffLjsQrJTEKL2G8Fm/TukAsBTqbWdEYuvkey3w3Mi9jOwxY4Zz7toRrGNClyLjjgfhArhEuy7bu59lZa3h0ytKjiWEonhjOd/BILr2fnMWpf/2U179bXyUxiojUNs3qx5Z47rgGcURFBPZF4eRFW4IVUvWzdz1k+O5iyc2Gncsh+3CpQ0RERESkBkhoArd9DbfMgcSUis2RsT24MUmN0KBeNFGRXnqvcWIsZ7ZvrMRwDVLe/1ILnHPz8p8459KAU8ysO5ALLPezwVxJJgE3AZdQeAO764GVzrlANqPrA3QA7ivh/MfAEeC3wIIC7TcAOQS+yrlKjflkBc/NXluhsYey83h4ylL6dmxGauN6ZQ8QEZGjruiRyqvfrCeryDdxp7ZOpnn9OD5eEtiH3ZzcWrghXdYh+O+1sPYLsEjoMgQ2fAMHtkFcMgwdByf0D3eUIiIiIlIZZpCXC4cCvZm7iIjo4MYjIiFX3uTwVjN7E3jNObcwv9E5t7gC154OzALGmVljYB1e0rYXcFl+JzObDfRxzvlbrnUjXpL3NX8XcM7tNrPHgYfNLN13vbOB+4GxzrlNFYg7pFbtOFDhxHBBYz9fxVNXnhKEiERE6o6OKUlMvr0X/523kd0Hs4iMMDqmJPHbs9tw7uNfBDzPsHNr2YYLO1bAe7+DNN/3ti4Xlrx37HzmPnj/Jrj0Gdi51Ks317w7dLwIIrViQERERKRGyMuDt6+G1Z9UfI4IffYTqWnK+3/tL8AIvDrDS/A2bXvLOVfy1oQlcM45MxsMjPYdycAy4HLnXJkres0sCRgKTC/j+o8B6Xj1kB8AtgKPAk+UN+aq8OWqtKDMs2RLelDmERGpa046rj5/vayr3/bv1xVeQdGtZQOaJMQwq8B794DOzbi5d/uQx1lldiyD58/1v+lIQZn74N3rCrd1vAiu+W/oYhMRERGR4Jn/SuUSwwAnXhScWESkypQrOeycO9tXr/cG4FrgKeAJM/sUeBWY6mfjt9Lm2w/c4TtK6tO3hPYDQEIA13DAWN9R7R3fLDEo83Q+rn5Q5qmWsg5BZEzh1WiZ+yGuFr9mEQm7fwzpxh1vLWDF9gO0bVyPUZd2oe+JzQDYlXGExZv20T01mSaJJdctrpFmjio7MVySVZ/AtkXQ4uSghiQiIiIiITBvXMXHJjSFjgNh4OjgxSMiVaLc6/2dc2uAh/FKNfTBqxE8FBgE7DOzd51ztwU3zLojOb7y9Xnqx0by2KXFV73VeFmHYPLvYflUr77lwH9Ayx7w3o3ebqpNO8PQl6F5LXztIhJ2xzdL5JMR57HvUBYN4qPx9kT1NEmM5fzOFdy0o7qzwDbhK9Gk38Mf/O0ZKyIiIiLVSvahio9NPQMuezZ4sYhIlYmozGDn3Bzn3E1Ac+Bm33w3ByOwuuqbtbsrPDY2KoKRgzrx48MXUj8ISeZq57tnYdlkbwXb4T0w+XaYdKuXGAZIWw5T/hDeGEWk1kuuF1MoMVzrnf9I5cbvXAqL3w1OLCJS6321Oo3Lnv2Gvk/O4rnZa8IdjohI3dLm7OJtgW4wt+pTb0GXiNQ4lUoOA5jZ+cDzwL+B+kAFt7QUgDznKjz2SE4eS7fuJyaq0v9Zq6f1XxVpyIOtPxVu2rYYdiyFd2+AaSNg38YqC09EpFZq3gX6PlC5OdbNCU4sIlKrpR04wvBXf2TRpn2s332IMZ+sZNJPm8MdlohI3THwfyGqSIm0vOxjPyc0gyYn+B+blw279aWeSE1UoSyimXUys9FmtgH4DLga+AKvvMRxQYyvzqlsrcp562txbv7w3gA6OfjPOd4K4/mvwDM9Yf+2kIcmIlJr5WbDge0Q36jic6R0C148IlJrzVu/hyM5hWucf758Z5iiERGpg+IbQEopZRpTToLda0sY2wianhiauEQkpMqVHDazO8zsB2Ap8BdgF/AnoKVzbrBzbpJzLrvUSaRUF3RqRnRkxW9XLvqButZY9M6x8hHlkZMJn/8t+PGIiNQVL/bzvmw7XIkvH7cvDl48IlJrdWqeVKzM+YeLt3HJ//uaTXuK36q892AW7/64ic+X7yA3r+J334mISAG5OSWf27Xaz0bFBk06Qv9RgZegEJFqpbwrh58GWgJPAd2ccz2cc08753YFP7S6qVn9ONo2SQiob1x0BJ1b1C/U1qdjs1CEFV57NsCk2/z8IxSg5VNL/wdORET8y0yHHT9Xfp7F/4Wsg5WfR0RqtfZNE3nk1yeREBNZqP3nLek8OnVpobZ1uw5y/lOzue+9xdz06o8Me+WHqgxVRKT2SulSwgmDhKbFm0/9rZc0nnYnPHeWd8eZiNQo5U0ODwJSnXP3OeeWltlbKuSUVsmFnhsQG2WckJJYqP1P/U/g+etOo0/HpjRNiuXy01ryyCUnVWGkVWTey0AlVoNkHfDqEIuISPnk5QZnnshYsMiy+4lInfe7c9sx696+xdqXbNnHvz5bRf+n5jBw7Jf86Z2f2Hvo2A2LX63exY+1ubyaiEhV6X5lCSccnHNH4aYO58NPr3H09/VdK+Gbp0MZnYiEQFR5OjvnPglVIHLMnweeyKodB1i0OZ0G8dH8bXBXLj35OPLyHFMWbWHx5nTO6dCEASelAPDqjWeEOeIQi00su09ZfngRBj9b+XlEROqSeo0gKs4r0VMZve+G6LjgxCQitV6zpDi6tWzAz1vSj7alHcji6c9Xlzpu1NQl3HNhJ/p1qoV30hWVmwPZhyCufsl9Du+D2PoQUUs3qxaR0OjQz397qzOg2xVQvyWs/NgrJZF0HKz9onC/9E2hj1FEgqpcyWGpGin145hyRy+2p2eSXC+auGhvtVVEhDHk1FYMObVVmCOsYidfBXOehMqUs974XfDiERGpSyqbHG7UAc77c/DiEZE64ZLuLdi85yB7D3ulwQK5h2zJ1gPc9Oo8PvjDuZySmlz2gJpq8UT45H44tBtOuBCGjiucJN67ASbeAFt/guTWMOQFaHNO+OIVkZqnTS/Y8PWx53HJcPmLvnPnHHtPyTniJYv3bznWt+vlVReniASFvkauxpo3iDuaGK7TImMgOqZyczSoYwl1EZFg6Tq0cuMbHx+cOESkTsg4kkOvJ75g9McrjiaGyyPPwcdLtoUgsjDLzYYq8pflAAAgAElEQVRti2HvRpjyBy8xDLD6U/j4fjhywHuethI+HOElhgH2bYQPboW8WrpptYiExuDnoF0fiIqH9n3htq+hUbvi/aJiYdiHcOp1cPwAuPxl6DKkqqMVkUrSymGp/j4bVbmNjCKi4PyHghaOiEidcvEYiEmCxe9ARoENRmIbQIcLvA3rGraBlmdAvWSY8SDkFUjodL6k6mMWkRrrre83sHnv4UrNkdqwXpCiqSa2/wxvXgkHtnqfa/OKJM0XveVtwJx0HOxeVXx8+kbI3OeVChIRAMwsBRgD/AqIBxYA9zvnvi1jXCQwAhgIdAEaAhuAicCTzrkDRfpHAw8Bw4DmwBrgX865ccF8PUHXsA3cMDWwvrtWQ3YmND0R2vYKbVwiEhJKDkv1t7OCm8lF14OUrnDJ/0FKLdyoT0SkKkRGwYV/9Y4jGfDjK5DQBLpf5b+OZXIb+PwxOLzHW0Vy6nVVH7OI1FiV3VQuLjqCgV1SghRNNfHpQ15iGIonhvNlZfhPDAM0767EsEgBZhYHfA4kAn8EduMlfD83s3Occz+VMjweeBR4G3gR2AX0BB4GLjazs51zBf9H/Q9wDTAS+An4NfCymUU7554P7isLgxXT4Z2rjz1f+THc/oP3+VFEagz9HyvVX+fLYMeS8o/LPgSbf4DJt8Etc8As+LGJiNQlsYlw7h9L73PiRd4hIlIBG3ZXbtVwZnYeny3byTVntg5SRNXAnnWVG696wyJF3Yi36reHc24BgJnNAZYDo4GLSxl7GGjnnNtdoG22me0EJvjGTvPN2QW4CbjbOffvAn1bAKPNbIJzrpK7/obZorcLP9+zFjZ9D23PDU88IlIhqjks1V9C48qN37YIfpkdlFBEREREJHQSYiu/30Z2bi2qr5ubA/VbVG6OH16CjLTgxCNSOwwBfs5PDAM4547grQYeYGZJJQ10zuUWSQznm+d7LLjZzWC8/TRfL9J3Al45ivPLH3o1k9A0sDYRqdaUHJbq78j+ys+xb0Pl5xARERGRkDqldXKl50iIrUU3R345BjbO9X/OAkyku9xjG9iJCEBXwN+tqYuBSKBzBebMT/QWnLcrsN05t8vPdfLPF2NmyWbWtuBB4aRz9XHuXVC/5bHnPYdD047hiydMNu05xL0TF3H1i3N5Y65yD1Lz1KJPTlJrdR0Kn//N+2Drj0WAK2WFSFQcnDAwNLGJiIiISNA0Toit9ByvfLOO/+lRPfMo5bZ8WsnnSvpsXFSLU6BZp+DEI1I7NAb8FTjfU+B8wMysPfAYMMc591UQrjMCr65x9dewDdz5E6z/GpJa1Mm9fnLzHNeN+54Nuw8B8N0vuzGDa89sE+bIRAKnlcNS/SW39nZKbdvL21Dj9OHQIBXik+GkIXDvWji+f+Exx/f3+p74Kxj2UeVvxxMRERGRkIuKqPweEXsPZQUhkmoiJrFy40++Bq77IDixiFRDZtbXzFyAR5MCQ10p05Z2ruj1mwIfAQcBf7vw+pvLlXIOYCzQrsjRO9CYqlxULBx/QZ1MDAMs3Zp+NDGc7x8fLWdtWkaYIhIpP60clpqhbS8vyXvUU4XPX/maV09t1yroeBGcdGmVhiciIiIilbd576FibREGdw84kTe/38C29LL3bupzQi2qdxkZU7nxg8ZAbInlU0VqgxXA7wLse8D3uBv/q3Yb+R79rfYtxswaAzOBZKCPc25zkS678V86Iv/afq/jnNsH7CtyrUBCkhA5nJXLjKXbycrJY2DX5jSIjz56rkWDeKIijJy8Y7n+Q1m5PDx5CW/dfFY4whUpNyWHpXaISYBeI8IdhYiIiIhUwmltGvL63I2F2to3SWDF9v3cPeAE/vL+z+SWsqavU/Mk/jKoIuVCq6G8XNj2U8nno2Ih50gZkyihJLWbc2473gZv5bEU/0nbbkAuXsK5VGbWCPgcaAH0c86tKuE6V5lZ4yKb2HXzPfqreyzVTGZ2LkOe+4YV273vFv49cxVT7+hF0ySvDFLTpFhG9D+Bf35a+K/Asm1B2DtJpIooOSwiIiIiItXCZSe3ZOGmfbw5dyMOyMtzrEk7yJq0g3y4eBtntmvE9+uKL7aLNOP1m87gnOObFJ+0pnJ5kJtT8vmcI5B0HGRsh4gYyM3Gy2v5JLcBrTYU8WcS8IyZneKcWwhgZjHA1cBM51ypWT0za4i3YjgVLzG8tISuk4G/4ZWb+L8C7TfgrQyeValXIVVixtLtRxPDANvSM3lkyhJioiJonBBD06RYTm/biFNSk1m46diC7+4tG4QjXJEKUXJYRERERESqhYgI46+XduW+gZ048x8zycgqvOlarnPc3q8Dz81aW6hY5+39OtSuxDBAZDScdj3Me6nkPge2eo+5fspt7NsAY9rDzbPqbC1QkRKMA24HPjCzB/DKO9wFHAdcWbCjma0HcM619T2PB2YAJwN/BOqZWcHaAZvzy0s455aY2QTgcfPqQvwE/BovWXyHc+5wiF6fBFG2n9tVPl6yvVjb1T1T+XlLOrm+8hJzf9nNL2kZtG9aydrxIlVAG9KJiIiIiEi1sjsjq1hiGKBZUiz3DuzEe78/h191a855HZsw4Xenc/eFJ4Yhyipwzp2VG5+TCZ8+FJxYRGoJ51wmcD7wDfAfYApe3eABzrn5ZQxPAXri5VKeBb4rcgwv0v9WvA1z7gY+xUsO3+KcezYoL0ZCbmCXFFLqxx59XtINGe8t2Hw0MQyQlev4cPG2UIcnEhRaOSwiIiIiItVKaqN42jdN4Je0g0fb4qIjuPOCEwDo0aYhPdr0CFd4VSd9Y9l9ynKg+Ao3kbrOV6v4twH0a1vk+XrKUczbOZcFPOw7pAb6v5mr2bHfq+/eJCGGfYezyXHFVxP7aeKHdXtYsX0/nZrXD3WYIpWilcMiIiIiIlKtmBnjbuhJ/84ptGoYz8AuKcx94IK69wv29pJKmZZDs06Vn0NEpA5asX0/L3+97ujzXQezyMkreVfUZkkxhZ5/vWYXlz3zDcu1OZ1Uc1o5LCIiIiIi1U67Jgm8fMPp4Q4jvPJrCleGy6v8HCIiddDmPYGXhc7Jc+w8kFWs/UhOHhN/3Mwjl6j2u1RfWjksIiIiIiJSHbU+q+w+ZWlZxxPsIiIVVD8+OOspE2MjgzKPSKgoOSwiIiIiIlIdnXgx9P4zfkucRkSB+fl17tw/QdJxEBkDp10PZ94a8jBFRGqjd3/cXOk5WjSI49qz2gQhGpHQCWtZCTNLBEYDV+DtDroUeMw5NzWAsQbcjLf7Z2cgC1gB3O2c+7ZAv5IKwvzeOfd85V6BVFeZmZmkpaWRmZlJTk5OuMORWi4qKoq4uDiaNm1KXFxcuMMRERGR2uSCh6HV6TDpVshMh/qt4Oq3oUV3SFsFU/4AO5ZAbBL0HQmnD4MBo7zdkSzgfbNERCTI4qIiePuWM0mpr98RpXoLd83hScBpwH3AOmAYMMnMLnHOTS9j7MvAUGAM8C2QAPTwPRb1X2BskbZfKh62VGfp6ens2LGDpk2b0rx5c6KiojB9MJYQcc6Rk5NDRkYGGzduJCUlhQYNGoQ7LBEREalNTrwY7l4B+zZC4+Mh0vdrXNOOMHym/zH6/CsiUik9Wifz3vyKrx7OzMnjy1W7aHt2YhCjEgm+sCWHzWwQ0B+43Dk3ydc2C2gPPAWUmBw2s6F4ieRezrnvCpz6qIQh251zc4MRt1R/u3btolWrVtSrVy/coUgdYGZER0fTsGFDYmNj2b59u5LDIiIiEnwx9aBZp3BHISJSZ7z1w6ZKz1E/LjoIkYiEVjhrDg8B0oEp+Q3OOQe8CnQys9K2cvwj8GWRxLAIAFlZWcTHx4c7DKmD4uPjOXLkSLjDEBERERERkUrafbByv9s1Sojmoq7NgxSNSOiEMzncFVjmnMsr0r64wPlizCwaOAv42cxGm9kOM8sxs6VmdkMJ17rezA6bWaaZfW9mV5YWmJklm1nbggfQKuBXJmGnMhISDvp7JyIiIiIiUjv0PbFZpcYfyc4lLjoySNGIhE44aw43Blb5ad9T4HxJ42KBG4DNwB3APuAmYIKZxTjnXirQ/028EhWbgBbAH4D/mlkL59z/lXCNEcCj5XgtIiIiIiIiIiJSS9x/USd2HTjCzOU7SIyNYn9m+Ta7z8xxZCpBLDVAuDekcxU4l7/aOQ4Y5JzbAGBmM/HqFT8CHE0OO+euKzjYzN4DZgN/N7MXnXOH/VxjLDChSFsr4KtS4hURERERERERkVqgQXw0L15/OvsOZXHemFnlHp+b59i67zDtm2pDOqnewllWYjf+Vwc38j3u8XMOYC9e4nhFfmIYjtYr/gRoZWYlrv33lbF4A0ikhNIVzrl9zrn1BQ+8Vcoi1dqOHTs477zzSEpK4p577gl3OCIiIiIiIiI12qfLdpR71TBAm8b1aNs4IQQRiQRXOFcOLwWGmllEkbrD3XyPS/wNcs4dNrM1JcyZX/CzaB3jovKT4mX1E6lRXnzxRZo0acL+/ftV/1ZERERERESkkqIjy/+7dXx0JC9ffzoREfq9XKq/cK4cngQkA5cUab8eWOmcW1bK2A+Azr6N4gAwLxN2MfCLc25XSQPNLAK4FjiAl6AWqTFyckr/tnLDhg2cdNJJFUoMlzW3iIiIhIeZJZrZ02a2zbfJ8o9mdmk55zAz+8LMnJmNDVWsIiIitc1FXVrQMaV8pSGycvM4ISUpRBGJBFc4k8PTgVnAODO70cz6mdkEoBdwb34nM5ttZkXrDz8J7AA+MbOrzexiYCLQA3iwwNg/m9lLvj59zew3vmv2Av7inMsM5QsUCYa2bdvyxBNP0L17dxISEvj6668555xzSE5O5uSTT2b27NkADBs2jFdffZUxY8aQmJjIzJkzycvL43//93/p0KEDjRs35sorr2TPHq9iy/r16zEzxo0bR+vWrTn//PMBGD9+PJ07d6Zhw4YMHDiQDRuOVm/BzHj++ec54YQTaNiwIbfffjteRRfPSy+9ROfOnUlKSuKkk05iwYIFAGzdupWhQ4fStGlT2rVrx9NPP11Ff3oiIiK1wiS8xQ0PAb8ClgGTzGxQOea4GegUgthERERqtfiYSCbffi7/uvJkAl1E7JwjL6+0bbZEqo+wJYd9NYIHA+8Ao4GPge7A5c65aWWM3Q30Bn4GnsP7wNwGGOKc+2+BrivxPgQ/DXwGPA/kAJc6554L6gsSCaG3336bjz76iF9++YXLLruMhx56iD179vDPf/6ToUOHkpaWxoQJE7j22mu57777yMjIoH///jz99NNMnjyZOXPmsHXr1qMJ3YLmzJnD8uXLmTFjBpMnT2b06NF88MEHpKWl0bt3b66++upC/T/88EPmzZvHokWLePfdd5kxYwYAEydOZNSoUbz22mvs37+fqVOn0rhxY/Ly8rjkkks4+eST2bJlC59//jljx449Ok5ERERK5ksA9weGO+fGOee+AG4AvgOeCnCOlsAY4I8hC1RERKQWqxcTxeWnteLWPu0D6n/5aa1UUkJqjHCuHMY5t985d4dzrrlzLs45d5pzbnKRPn2dc8X+j/JtFHeFc66hb2xPP2OnOed6O+eaOueinXPJzrkLyko+i1Q3d955J6mpqbzxxhsMGjSIQYMGERERwYABAzj99NOZPn2633EvvPAC//jHP2jVqhWxsbGMGjWK9957r1AJiVGjRpGQkEB8fDwvvPACDzzwAJ07dyYqKooHH3yQhQsXFlo9/Je//IXk5GRat25Nv379WLhwIQAvv/wy9913Hz179sTMOP7442nTpg3z5s0jLS2NRx55hJiYGNq3b8/NN9/MO++8E9o/NBERkdphCJAOTMlv8C2yeBXoZGYnBTDHf4AvnXPvhyZEERGRuuHegZ0Ye9Up/KZnKqe1TiYywmiaFMud5x9Pn45NOTU1mfsvOpF/DOka7lBFAhbODelEJECpqamAV1N44sSJTJt27PuN7Oxs+vXr53fchg0bGDJkCBERx74HioyMZMeOHcXmzu9/1113cc899xxtc86xZcsW2rRpA0Dz5s2PnqtXrx4ZGRkAbNq0iQ4dOviNYevWrSQnJx9ty83NpXfv3oG9eBERkbqtK7CsyAbOAIsLni9psJldDfQDAkki549JxtsbpKBWgY4XERGprcyMwae2ZPCpLQHIzs0jKsK0IbzUaEoOi9QA+f/QpKam8tvf/paXXnopoHGpqamMHz+ec889t9i59evXF5o7v//IkSO59tpryx1jamoqa9eu9dverl07Vq9eXe45RUREhMbAKj/tewqc98vMmgD/B4x0zm0qxzVHAI+Wo7+IiEidFB0Z1hvyRYJCf4tFapDrrruOadOmMWPGDHJzc8nMzGT27Nls3rzZb//bbruNkSNHHi0LkZaWxpQpU/z2ze//+OOPs3TpUgDS09OZOHFiQLENHz6cf/7zn8yfPx/nHGvWrGHDhg2cccYZ1K9fnyeeeILDhw+Tm5vLkiVLmDdvXjlfvYiISJ1V2o42pZ17GlgHPFPO640F2hU5dMuPiIiISC2k5LBIDZKamsqUKVMYPXo0TZs2JTU1lSeffJK8vKJ3mnruuusuLr30Ui688EKSkpI466yz+P7770ucf8iQIdx///385je/oX79+nTt2pWPP/44oNiuuOIKRo4cyTXXXENSUhKDBw9mz549REZGMm3aNBYuXEi7du1o0qQJw4cPJz09vUJ/BiIiInXMbvyvDm7ke9zj5xxmNgC4CrgPqG9myb5yEQCxvud+7yJ0zu3z7e9x9AD8fxMtIiIiIjWaeftZSFnMrC2wbt26dbRt2za8wUipli9fTufOncMdhtRRAfz9UzGqCtL7sIgEQY17Dzazl4GhQOOCdYfNbDjwEtDFOVes5rCZjQD+Xcb0FzvnPgkwjrboPVhEKqfGvQdXF3oPFpEgKPE9WDWHRURERESqr0nATcAlQMHaUNcDK/0lhn3eAxb6aZ8FvI9XamKxn/MiIiIiUocoOSwiImUys0RgNHAF3g72S4HHnHNTAxhrwM3ArUBnIAtYAdztnPs2ZEGLiNQO0/ESuuPMrDFeDeEbgF7AZfmdzGw20Mc5ZwDOuc34KQXh24h2s3NudqgDFxEREZHqT8lhEREJxCTgNLzaleuAYcAkM7vEOTe9jLH5t0SPAb4FEoAevkcRESmFc86Z2WC8L+hG431Btwy43Dk3LazBiYiIiEiNp+SwiIiUyswGAf3xEhGTfG2zgPbAU3ir2koaOxQvkdzLOfddgVMfhSxgEZFaxjm3H7jDd5TUp2+Ac6nmp4iIiIgcFRHuAEREpNobAqRToNal83YzfRXoZGYnlTL2j8CXRRLDIiIiIiJhY2YpZvaqme0ys4Nm9pWZnRPAuEgzu8fMPjWzLWZ2yMyWm9ljZpZUpG9bM3MlHBeF7tWJiJSPksMiIlKWrsAy51xekfbFBc4XY2bRwFnAz2Y22sx2mFmOmS01sxtKu6CZJfs+UB89gFaVexkiIiIiUteZWRzwOdAHbyHDEOAA8LmZnVrG8HjgUbwya3cBg4DxwAjgCzPzd3f2WODsIocWTohItaGyEiIiUpbGwCo/7XsKnC9pXCzexkmb8W6H3gfcBEwwsxjn3EsljB2B98FbRERERCSYbgS6AD2ccwsAzGwOsByvtvvFpYw9DLRzzu0u0DbbzHYCE3xji9aD3+Ccmxuk2EVEgk7JYRERCYSrwLn8u1PigEHOuQ0AZjYTr17xI0BJyeGxeB+wC2oFfBVIsCIiIiIiJRgC/JyfGAZwzh0xs7eB+80syTl3wN9A51wusNvPqXm+R93pJiI1jspKiIhIWXbjf3VwI9/jHj/nAPbiJY5X5CeG4Wi94k+AVmbWzN9A59w+59z6ggfe6mMRERERkcroCizx074YiAQ6V2DO832P/uYdaWZZvtrGs8zsgtImUnk1EalqSg6LiEhZlgKdzazovxndfI/+PgTjnDsMrClhTvM9Fq1jLCIiIiISSo3xv7ihrJJpfplZe+AxYI5zruBdbkfw7pL7PV7y+DagIfCZmQ0pZcoReDWNCx66e05EQkbJYRERKcskIBm4pEj79cBK59yyUsZ+gJdYbpvfYGaGV4/tF+fcruCGKiIiIiJ1hZn1NTMX4NGkwNCKlEzzd/2mwEfAQeC6QpM4t805d4tz7j3n3NfOudeBc/AWTzxZyrRjgXZFjt6BxiQiUl5KDovUEKNGjcLM2LdvX5l9X3vtNa688ko6dOiAmdG3b99yXWvYsGEkJyeX2W/btm2MHDmSs846i8aNG9OgQQN69uzJq6++Sl6eFoTWItOBWcA4M7vRzPqZ2QSgF3Bvficzm21mRT9MPwnsAD4xs6vN7GJgItADeLBKohcRERGR2moF8LsAj/w6whUtmVaImTUGZuItorjAOVdmCTTn3CHgPaCDL7Hsr4/Kq4lIldKGdCK10Ouvv87OnTs577zzOHjwYMiuM3/+fF5//XWuv/56Hn30USIjI5k2bRrDhg3jp59+YuzYsSG7tlQd55wzs8F4uzePxvsAvAy43DlXdDfmomN3m1lvvCTxc0A88DMwxDk3ObSRi4iIiEht5pzbTvFNjMuyFK/ucFHdgFy8hHOpzKwR8DnQAujnnFtVjuvnL9LTahoRqRaUHBYpQ16eY+qirYz7eh3b0g/TokE8N/Vqx6UnH0dEhJU9QRjMmDGDiAjvM8cpp5wSsuuce+65rF27lujo6KNtF154IRkZGTzzzDOMGjUqoBXIUv055/YDd/iOkvr0LaF9PXBFSAITERERESmfScAzZnaKc24hgJnFAFcDM32fe0tkZg3xVgyn4iWGlwZ6YTOrBwwF1jjndlf0BYiIBJPKSoiUIi/Pcdsb83lw0s/8vCWdXRlZ/LwlnQc++Jnb3phPXl7A5aiCZtu2bVx11VXUr1+flJQUbrzxRtLT0wv1yU8MV9bKlSu56KKLSExMJDU1lXvuuYcjR44cPd+wYcNCieF8PXv2JDc3l23btpU6/4QJEzAzvvjiC66//noaNmxIgwYNGD58OJmZmfzyyy/8+te/JikpiTZt2vDkk8VLc+3du5cRI0bQpk0bYmJiaNOmDQ8//DDZ2dmF+o0aNYqePXsevcYZZ5zBu+++W2w+M2PEiBFMmDCBTp06Ua9ePU4++WQ+/PDDQP/YRERERESk+hoHLAc+MLOrzGwA3j4ZxwEjC3Y0s/Vmtr7A83hgBnAy8DBQz8zOKnC0KtD3KTP7t5ld4auNPAz4DmgP3B3alygiEjitHBYpxdRFW/l6zS4OZeUWaj+cnctXq3cxbfFWLjulZZXGdPnll3PVVVdx8803s3jxYh580CvbOn78+KBe58iRI1x22WXccsst3HvvvcyZM4e///3vNGjQgEceeaTUsV988QUJCQm0bds2oGsNHz6cq666iokTJ/Ldd9/xyCOP4Jxj7ty5DB8+nBEjRvD2229z33330bFjRy677DIAMjIy6N27N3v27GHkyJF06tSJH374gccee4z169fz+uuvH73Gxo0buf3220lNTSUnJ4dZs2ZxzTXXcODAAW666aZC8UyZMoW5c+fyt7/9jcTERMaMGcOQIUNYuXIl7du3L98fpIiIiIiIVBvOuUwzOx+v7Nl/gDhgATDAOTe/jOEpQE/fz8/6Of9XYJTv56XArcANQBKQjpcc/oNz7pvKvAYRkWBSclikFOO+XlcsMZzvcHYuL3+1rsqTw7fccgt/+tOfAOjfvz9r165l/PjxjBs3DrPglbnIzMzk8ccfZ8iQIQBccMEFzJ8/nzfffLPU5PCkSZN4//33eeSRR4iPjw/oWkOGDOHxxx8HvNf0xRdfMH78eF5//XWuu87b9Ldv375MmzaNt95662hy+Omnn2bFihUsWLCA7t27H42zXr16jBgxgr/85S906dIFKJw8z8vL44ILLmDXrl0888z/Z+++46Sq7v+Pvz67Sy/SFMUGBAuIiC12sSH2jsaokYhRY+y/aKyJGktiSYyxfO3EXjBGjTX2bpRoULAQARULCFKks7uf3x/nLjszO7s7uzszd8r7+Xicx+7cNueenX0vnHPvudc16Bxevnw5zz//PF26dAFgs802o1+/fjzwwAOcc845GZ2TiIiIiIgUpmiu4qMy2K5/yuvpQEb/6XL324HsXsEjIpIDmlZCpAnfzF/SpvW5sN9++yW9HjZsGEuXLmXmzJktOo67U11dnVQSVVZWsvfeezd4r88//7zRY7711lscddRR7LbbblxwwQUZ1yX1fQYPHgzAXnvttXJZVVUVgwYNSnr/J598kuHDhzNkyJCk89hzzz0BePnll1du++KLLzJq1Cj69u1LVVUV7dq147bbbuPjjxs+b2KXXXZZ2TEM0LdvX1ZbbbUmz11EREREREREpNioc1ikCWus0vSVr82tz4XevXsnve7QoQMQrvRtiZdffpl27dollenTp69c37VrV9q3b9/gvRLnHE70zjvvsMcee7Dpppvy6KOPUlWV+Y0JvXr1Snpd977pliee58yZM5kwYUKD89hggw0AmD17NhA6rUeOHIm7c/311/P666/zzjvvcMwxx6Rtt9Q2rjv3lraxiIiIiIiIiEgh07QSIk0Yu/0Azvn7ByxZ0XBqiU7tKjl2hwEx1Co7Nt98c955552kZf369WvVsSZMmMDuu+/O4MGDefLJJ+ncuXM2qtisPn360LVrV2655Za06+vO54EHHqBdu3Y8/vjjKzvTIUwfISIiIiIiIiJSrtQ5LNKE/Tbpx5MffMOrU2YndRB3alfJDuv1Yd9hretMLQTdunVjiy22aPNx3nvvPUaOHMmPfvQjnn76abp165aF2mVmzz335Morr6Rv376svfbajW5nZlRVVVFRUX+zxKxZs3j00UfzUU0RERERERERkYIUa+ewmXUFLgNGAz0IT/O82N0fy2BfA35BePrnYPL78l8AACAASURBVGA58DFwhru/kbLtKcBJwLrADOAm4Cp3r83e2Ugpqqgw/u/IzXl84tfc+uo0vpm/hDVW6cSxOwxg32H9qKjI3gPgsmny5MlMnjwZgPnz57NixQrGjx8PwJZbbsm6666blff55JNPGDlyJBUVFVx88cV89NFHSeuHDBlC9+7ds/Je6Zx++umMHz+eHXbYgdNPP52hQ4eyfPlypk+fzpNPPsl1113Huuuuy957782f//xnjjjiCI477ji+/fZbfv/739O3b19++OGHnNVPRERERERERKSQxX3l8CPAZsBZwDRgDPCIme3r7k82s++twMHAFcAbQBdg8+jrSmZ2PnARcCnwArBt9H0v4OxsnYiUrooKY//ha7L/8DXjrkrGHnzwQS666KKkZaNHjwbgjjvuYMyYMVl5nzfffJM5c+YADR8qB+EhcDvttFNW3iudbt268frrr3PppZdy3XXX8cUXX9ClSxcGDBjAqFGjVs4dvOuuu3LzzTdzxRVXsM8++7Duuuty2mmnMXPmzAbtJCIiIiIiIiJSLszd43ljs72AJ4CD3P2RaJkBrwK93X1wE/seDDwIbO/ubzaxXW/ClcI3u/upCcsvJXRID3D3GRnWtz8wbdq0afTv3z+TXSQmH330EYMHN/rxEcmpDD5/hXm5eRFQDotIFiiDW0kZLCJZoAxuJWWwiGRBoxlc0diKPDgQmA+snPTTQ0/134ANzWxIE/ueDLzSVMdwZA+gY3TMROMIV03v18I6i4iIiIiIiIiIiJSEODuHhwKT08z7OzFhfQNm1g7YGvjAzC4zs5lmVm1mk8zs6DTv4YS5jFdy9ynAkibeo4eZ9U8swFotODcRERERERERERGRghbnnMO9gU/TLP8+YX1j+3UAjiZMGXESMA8YC4wzs/bufkvCtovdfVma48xt4j1OA37X7BmIiIiIiIiIiJSYmlrn7Wlz6NK+ik3W7hF3dUQkh+J+IF1TEx43tq7uaueOwF7u/jmAmT0HDAR+C9ySsH1r3uMawtQTidYizIcsIiIiIiIiIlKS7n/nCy56bDJLVtQAsNvg1bj5qC2oqGg4ZencRcs5++8TeXXKbDZcvRuXHbQxG67ePd9VFpE2iHNaiTmkv3K3V/T1+zTrIFzx68DHdR3DsHK+4qeBtcxstYT36GJmHdIcp2dj7+Hu89x9emIhXKUsIiIiIiIiIlKSXp3yHWc//MHKjmGA5z6axQbnP8XZD0+ktjb5Grvf/3Myz0yayeLlNfzni3mceM9/CN0zIlIs4uwcngQMNrPUOmwcff0w3U7uvgT4XyPHrBvGqpvHeFK0bKOkjcwGAZ0ae4+CtmwhPHch3HkAvHs71KZO2SwiIiIiUuS+fAfGj4WHj4UZE6B6GbxyJdwzOnytTjdrnIiItNUzk75Nu3xFrXP/O19y0j0TAJi3eDkzFyzl7WnJ19xN/W4Rsxcuz3k9RSR74pxW4hHCPMH7Ao8mLP8Z8Im7T25i378DZ5hZ/+iqXszMgD2Bqe4+O9ruKWAZcBTwn4T9jwaqgcezcB75U1MNN2wN878Mr6e+CNNfg0Nuj7deIiIiIiLZMvt/MG5vqIk6gD96HNbfAyb/I7ye8izM/Rz2vy6+OoqIlKj+vbs0uf7JSTMZ+aeXmfrdQmocOrWvTFq/Tq/O9O7SPpdVFJEsi/PK4SeBF4HbzOwYM9vZzMYB2wNn1m1kZi+ZWeo9CVcCM4GnzexwM9sTeAjYHDi3biN3nwNcDpxsZhea2QgzOxv4DXCNu3+Zw/PLvqkv1XcM1/nw77B0fizVEREpG0vmwqI5TW9TWwPzvgxfRUSk9T56tL5jGKB6KXz8z+RtPngov3USESkTP91qHbYf1KfJbabMCh3DAEuWJ//bd8y2/dPOTSwihSu2zuFojuADgPuBywhX+Q4DDnL3Jq/ojTp9dwA+AG4gXIW8LnCguz+QsvnFwK+BI4BngeOB3xE6iIuLpQtYo342DRERybqnz4UrB8FVg+Dvx4e7OFJ9NQH+MhyuGQp/2QRmvJv/eoqIlIpu/Rou69Qr+XX3NNuIiEibdW5fxe1jtmT42qu0av9l1Zr6UqTYxHnlMO6+wN1PcvfV3b2ju2/m7v9I2WYnd2/Q+xk9KG60u/eM9t0ydd9oO3f3a9x9PXfv4O4D3P1ydy++xBq4E/QckLxs2GHQUU8CFRHJiakvw1vXQ201eC1MvB8+fLjhdo+fBvO/CN/P/xIePzW/9RQRKSVDD4IBO9a//tEusPefoV3n8LpdZxh1eTx1ExEpcbN+WMqOV7zA+1+2/A5lM9hhvaavOhaRwhPnnMPSlOpl8K/fhVvoeg2Enc+FmZNg8zGweA589wl06AYLZ8L4Y6HPerDh3rD60LhrLjl04YUXctFFFzF37lx69OjR6HZ33nkn//znP5kwYQJTp05lxIgRvPTSS/mrqEip+O7jNMs+SrPsk+TXs9JsIyIimanqAIfdA2/dAMuXhGkl/nU+WAWssw0M2i38O7jOl/+Gb/4bOpRX3SC+eouIlICf3PwW3y7I7KGfVRVGt45VdOvUji7tqzhhxECGrtm6K45FJD7qHC5UL18Bb98Yvp//JXz+erhyDcJtdT3WhSnPpOzzRzj8flh/9/zWVQrOXXfdxaxZs9hxxx1ZtGhR3NURKV4/2hUqqurzF6DP+rBoNnTqCRXRAzjWG5k8H+b6o/JbTxGRUrJwFty8Eyz4quG6L94MBWC7U6F9V3jx0vDaKuDg28KVxyIi0mJ3vD6Nqd9l/v/H6lpn7uIVzF28goGrduaHpWmmXxORgqfO4UI0+38wYVzyssSOiSXfh5LKa+D5C9U5LDzzzDNUVIRZY4YPHx5zbUSKWJ9B4eq11/4ES+bDnCnwj1/Wr++7Mex1JdQsD68rqsKVa/tfH099RURKwX/uTN8xnOqN66EiYZY8r4VXrlLnsIhIK/3pX59mtF2FQa0nL5v63WLO/8eHLF1Rw7E7DMxB7UQkV2Kdc1jSWPw93LITLJ7duv1nToKP/tn8dpK52lqY+CDcNCI8lOqmEeF1bXzTVn/zzTccdthhdO/enb59+3LMMccwf379nFAVFfrVFmmzmmr44VvYYA84+FZY8GUYhEs08wO4Yw+Y8mx4XVsNn78JVR3zX18RkVJRndntzHh1/eDcyn2XZL8+IiJlYNLX85u88rdbx/prC1M7hhNd8fQnLFqmK4hFiomuHC40nzwFy35o2zH+ex8M3ic79Sl3tbXwwJEw9UVYsTgsW/RdeNjU5Efh0LuSr1jJk4MOOojDDjuMX/ziF0ycOJFzzz0XgNtvvz3vdREpSVOeh/FHhzzuuErIguUZ3mJXvSQ8oO7gm3NbRxGRUrRsYcN53Fui6+qwdH7IbhERydgXcxY3uT7TKSOW19Ty/pfz2G6QHkwnUix0eWGh6dC17cfoohDOmg/HJ3cM11mxGD57AT58OJZqHXfccVx44YXstttunHHGGYwdO5b77rsP9yaGcEUkMzXV8OCR9QN1S+fD8hYO2n04HmpWZL9uIiKl7vFT4aNHW7//F2/AY6dkrz4iImVi20F96NK+Mu26bQb2oirD3qOqCmPQalno1xCRvFHncKHZcN/wkKPWat8Vtjste/Upd29e37BjuM6KxfDmdfmtT2S//fZLej1s2DCWLl3KzJkzY6mPSElZ8n3jv/eZssrwYCQREWmZjx/PwjGeaPsxRETKzCqd2nHJAUPTrlurVyfW7tUlo+Ocv/dg+nbXFGsixUT/cy00FRXh4Uetdehd0GtA9upT7pp7GEomD0vJgd69eye97tChAwBLly6NozoipcXSXzHRIj3WgYosHEdEpNz0WKftx6jQzHkiIq1x4GZrpV3+0LtfMW1281OsmcGhW66d7WqJSI6pc7gQffZ86/brv314GJJkT/c127ZeRIrPghltP8ZCXcUvItIqe15Jm/+LUr0E5mchy0WkZJlZXzP7m5nNNrNFZvaqmW2b4b7nmtm7ZjbHzJaZ2TQzu9nMGvSKmlk7M7vIzD6Ptp1kZmOzf0bZMX32ooynj0jHHd7/cl72KiQieaHO4ULUuXf65d37wZpbNL7f9Nfg3tHwypW5qVc52uZX0K5z+nXtOsM2J+W3PiKSe32HZjDwY02vrtV8wyIirTLjXaC2BTsYdOmbvKhDd+jUK5u1EpESYmYdgeeBEcDJwIHAD8DzZrZpBofoAYwHxgCjgCuAvYG3zSx1jsgbgTOBa6JtnwJuNbMT2n4m2XfTK59R3ZIITmPy1wuyUxkRyRt1Dhei4UfAaoMbLl80B77+T/P7vxHPPLglaeghMHDnhh3E7TrDj3aBoQfHU69mTJ48mfHjxzN+/Hjmz5/Pd999t/L1559/Hnf1RApbRSWsN7Lx9R17wAWzw90ajVl94+zXS0SkHHz9XsNlO51Do/9tGXow7HA6VEXzW1a2hz0uh/aNDO6LiMAxwEbAQe5+n7s/S+gg/ga4rLmd3f0sd/+Duz/u7i+5+43AWGANYN+67cxso2j5ee7+52jbXwP3ApdFndQFZc7C5W0+xrY/6pOFmohIPqlzuBB16gHHvVL/j9w6NcvAMxjGq2yXm3qVo4oKOOxu2PdaWGM4dFk1fN332jC/c0Vh/go9+OCDjB49mtGjRzN9+nQmT5688vWLL74Yd/VECt9H/2x83dJ5cM8h4W6Nxmz2s+zXSUSkHAzYoeGyly6n0auJ+6wPT58N1dFzFzr1CoP7IiKNOxD4wN1XXnnl7suA+4CRZtatFcecHX1NvH3sAMCBu1K2HQf0BHZpxfvk1MGbp59zOBMG/OGgoQzp1z17FRKRvCjMni2Bqvaw3amt23fbk7Nbl3JXUQHDRsPxL8OZ/wtfh42OpWP4wgsvxN3p0aNH0vIxY8bg7vTv3z9pu3RlzJgxea+3SNFpbHqfOlObGWQx/XkVEWmVNYa3bPsJtye/XvgtfP569uojIqVoKPBhmuUTgUogzW28DZlZlZl1MrPhhGkjPgYeS3mfb919dsquExPWpztuDzPrn1iA1vfatsCojVbn9jFb0K6y6SnUKoAu7esfvmzAeXsP5ic/Xje3FRSRnND/XgvZwJ2hy2ot32+jg7JfFxGRcrLbhVDR2rswrPG5ykVEWsHMuprZtWb2jZktiR6EtF8G+401s9fN7DszW25mX5rZfWY2JB/1bpXFqX0ozfjh24bLuvfLTl1EpFT1Br5Ps/z7hPVNMrOuhKuEFwPvAVXALu6+KAvvcxowLaW82lydsmWXDfuyUb9VkpZ1SHlK3Xbr9WHSxXvw/m9Hctpu63HOXhtySBuuOhaReKlzuFDNnwHj9oJFs1q236qDoUeDh6SKiEhLDBwBPVt75YPDs+dDbRuf5iEiUu8R4AjgfMJDjyYDj5jZXs3s1wd4DvgFMBK4ABhOeGjSoNxVtw0G7gxd+za/XWN+fHz6Z3eISEkys53MzDMsiZPhehOHbWpdncXAlsB2hHmFewIvmdkaGRzLm1gH4SrkASklzZw7uXPx/huxevcwzWWvLu258pBh7LzBqnTvWMWuG67GlYdswpyFyxj7t3e55rkpXPbkx+xy9ct8PmdRM0cWkUJUFXcFJI25X8C1m2Y2v3AqTSkhItI2/3sOHhoDy35o/TEWfAUrFkGH1kxZJyJSL+oA3o3w4KRHomUvAgOBq4EnG9vX3f+YsuhlM3sL+Aj4KXBxTirdFtXLoKpT6/at7Bju/BCRcvIx8PMMt637x90c0l+12yv6mu5q3yTuXgu8G718w8yeJlzhezZQNz/kHNJPHVH33mnfx93nAfMSl5k1Pc1Dtg1bqwev/WZnps9ZzNq9OtGhqpL9hq+5cv3Nr3zGH5/+mJqELovvFy3njtenc+F+G+W1riLSduocLkSP/Qq8unX7Dtk/u3URESk3T/y/xjuGVxsKs9JNUZei/w7qGBaRbDkQmA88WrfA3d3M/gbcbGZD3H1yC46X7qFJhePNv8K86a3bt2YpTH0JNmzugmoRKRXu/i3hAW8tMYn0nbYbAzWEDueW1uNrM5sBrJ/yPoeZWW93n5PyPpB+3uOCUVVZwaDVujZYPmvBUq54+pOkjuE6S5bX5KFmIpJtmlaiEM2f0br9hv0EOjQM73LknsmdQCLZpc9dCaithXlfpF834mw48XX45Rvpr2rrsyH0HQrDj4RD7shtPUWknAwFJkdXqSVq8oFGicys0sw6mNkGwK3ATOBvTWwf28OQmDu9bft3a8OUFCJSLh4BNo4eJAeAmbUHDgeec/cFLT2gmQ0E1gX+l7D4H4RntR2ZsvnRhCuDm3nCcWH6at4Sqmsb/r+nfWUFh2+1Tgw1EpG20pXDhWjj0fByyl2Ah9wOX/4brAJ6rAtP/6Z+XUUl7HYRbH1ifutZoCorK1mxYgXt27ePuypSZlasWEFlZWXzG0rhqqiADfeBjx5LXt59Ldjx1+H7vhvB1r+E1/5Uv37trWHsM/mrp4iUk97Ap2mWZ/zgJEJncN12nwI7u/vXTWx/GvC7jGuYTUP2h0mPNFxe2T7Mzlm7vPF91xsFa26es6qJSMm4DfgV8HczO4eQp6cC/YBDEzc0s+kA7t4/er0ucDfwAKEjuJowSHcGMJcw3Q/RPh+a2TjgcgvzQrwH7EPoLD7J3Zfk6gRzaeM1V2Gtnp2YMbe++jus14dz9hzMkH7dY6yZiLSWOocL0c7nwpK5MPFBaN8ZRl4CQw8OpU6nnvDeXdClD+x4ZuisEAC6devGggUL6NOnT/Mbi2TRggUL6NZNUwkUvf2vhx7rwMdPQM0KWGcr2Pk8qGxXv83O50H7LmF+4tWGwE7nxFdfESkHbX1w0q5AJ8I8xacBL5rZru4+qZHtr6HhbdprAa9m8F5ts9GBsGIJTPgb/PAN1K4ID1wedWn49+9TZ8HX70O3frDpUfD1hJDVw0bDgB1zXj0RKX7uvtTMdgGuBG4EOgL/AUa6+4Rmdp8HfAacQuhMbgd8BTwFXObun6dsfzwwg9B53BeYChzn7rdk6XTyrqqygnuO3Yq/PDeFGfOWsO8m/Thq69Y+yFlECoHpNujMRLfTTZs2bRr9+/ePtzLSpGXLlvHFF1/Qs2dPunfvTrt27fI+gb+UD3dnxYoVLFiwgLlz57LOOuvQoUOHpnbRh7GVlMMikgVFl8Fm9iZhmuFtU5ZvBbwFHObuD7bgeF2BKcC/3T3jh1Uog0UkC4ougwuFMlhEsqDRDNaVw1JyOnTowDrrrMP333/P9OnTqanRpPiSW5WVlXTr1i2TjmEREZGWmgQcbGYVKfMOt+qBRu6+0Mwmk/zQJBEREREpU+oclpLUoUMH1lhjDdZYY424qyIiIiLSFo8AY4F9gUcTlv8M+MTdJ7fkYGbWC9gEeDNrNRQRERGRoqXOYRERERGRwvUk4Yn2t5lZb2Aa4Un32wMrp4Uws5eAEe5uCcveB+4CPgEWEa4WPgXoDPw+T/UXERERkQKmzmERERERkQLl7m5mBwCXRaUHMBk4yN0fb2b3t4CfA+sQHkg3E3iZME9xi6ajEBEREZHSpM5hEREREZEC5u4LgJOi0tg2O6VZdkIOqyUiIiIiJaAi7gqIiIiIiIiIiIiISP6pc1hERERERERERESkDGlaicxVAsyYMSPueohIERswYEB/YIa7V8dbk6KkHBaRNlEGt4kyWETaRBncJspgEWmTpjLY3D3f9SlKZrY98Grc9RCRkjDA3afHXYlioxwWkSxRBreCMlhEskQZ3ArKYBHJkrQZrM7hDJlZB2BL4BugJubqrEX4w7ADoKFDtUcqtUdDhdYmumKiFQoohwvt8xQ3tUdDapNkhdYeyuBWUAYXLLVHQ2qTZIXWHsrgVlAGFyy1R0Nqk2SF1h5pM1jTSmTI3ZcBr8VdDwAzq/t2hkZd1R6p1B4NqU1KQ6HksD5PydQeDalNkqk9SoMyuDCpPRpSmyRTe5QGZXBhUns0pDZJViztoQfSiYiIiIiIiIiIiJQhdQ6LiIiIiIiIiIiIlCF1DouIiIiIiIiIiIiUIXUOF6d5wEXRV1F7pFJ7NKQ2kWzS5ymZ2qMhtUkytYdkkz5PydQeDalNkqk9JJv0eUqm9mhIbZKsKNrD3D3uOoiIiIiIiIiIiIhInunKYREREREREREREZEypM5hERERERERERERkTKkzmERERERERERERGRMqTOYREREREREREREZEypM5hERERERERERERkTKkzmERERERERERERGRMqTO4SJnZvoZSs6ZmcVdh1xIPa9SPU/JLeWw5FqpZpMyWLJBGSy5VqrZpAyWbFAGS66VajYVWgbrF7nIuXstgJn9ycw2jL7Xz7WN1IaBmVWZWTdgYNx1ySYLqtzdzazSzHrXva5bH3cdpXgoh7NP7Rcog0WapwzODbWhMlgkE8rg3FAbKoPzrew/cKXAzPoBPwWuhvqAltYxs8qEP3Kbmtm2ZrZNyjYl/4+mKIgfAt4FPjGzF8zs2GL+Q2Vm3QE8qI7OcTzwEvC+mZ1oZqtHQV3yP2PJHuVw9iiDA2Vw6f+MJXuUwdmlHFYGl/rPV7JLGZxdymBlcBw/36Jt2HJmZpUpi2YBfwaGmNnhMVSpZJhZhbvXRN+PAx4EXgReMrMHzWwXCL/Q8dUy98ysC/BvoBfwN2As0A24Frg8xqq1mpltBjxnZgdEr6uAt4G1gBeA74ArgAvMbG39w1iaohzODWVwoAxWBkvTlMG5oxxWBiuDpTnK4NxRBiuD48rgqny+mbRdSlgMAGa6+2IzuxU4CjjOzB6KRiIqNGrXMgkjdHcBOwG/AeYTflfuB/qb2bHuPjG2SuZYFEIXE877OGCKu9eaWUfgRmBKnPVrgw7AFsBvzWw5sByYCpzg7jMAzOw6wqh3lZld4u5fmpmV8h9faTnlcO4og5XBKIOlGcrg3Cr3HFYGK4Olacrg3FIGK4OJKYN15XCRSQiLO4F3gHPMbDN3nwOcCGwPnJm4rbSMme0KbA2cADzk7k8AE6LV7wOfxlW3fIjCZzPgU3f/JArjI4EbgPPc/VYz6xaNfhWF6B8mbxJ+PzYCfgscDSx09xnRyB3ufhJwFzAaOK9u1C6uekthUg7nljJYGYwyWJqgDM69cs5hZbAyWJqmDM49ZbAymBgyWJ3DRcjC3CQbEi6zHwz83czGEEYebgaOMrPt46thcUlzuf46wCrAx+6+wszWAyYCjwGnuftSM9sjze00Rc/CpO89gTWAOdGyI4E7CWF8uZm1I4xg7mNmneKrbeaiPyqV7v4GsCswHDiCMCJJNLLdPvr+VML5HgRcZWarxVRtKWDK4exRBtdTBiuDJTPK4OxSDgfKYGWwZEYZnF3K4EAZHG8Gq3O4CKT+0rv7D4R5VxYCM4A/AbcAvwM6Ax2B3S08+VBzRTUh+iVNHY3pAXRz98/MrC9hLphngbHRLTOjgAuBYfmtbe7Ufcbcvdrd5xLO+TAzOwEYB/zW3f8Qbb4hMCLafkkM1W2RhJG4mujra4T6LwV+ZtG8P+6+PCGUTwOeBLoDs+OotxQW5XBuKIMDZbAyWJqmDM4d5bAyOFquDJZGKYNzRxmsDI6Wx57B6hwuAl4/p8/+Ccs+AK4jjDrcR/iAdQf6R+VcYEPdCtSQmVWY2Wgz2z+hbR83s/OjTd4EFpjZeOAj4CngOHdfGIXzTwijPF/GUf9si0JogpkdnbD4bmAF4faNy9z9kmjbTYCbom0uzWtFW8HMLBqJ62Jml9Qtd/e3gV0AAy4ys72i5YmhPAbYOxrpU1aWOeVw9iiDkymDlcHSPGVwdimH6ymDlcHSPGVwdimD6ymDCyiD3V2lCArwK6CW8CTDLYH2wCbAh8Cp0TbrAnsR5qOpBdaLu96FWIC+wO3AIkKwPkgI1h9H6zsSAqmWEMZ9ouXrA3cAM4EhcZ9HltqiivCH/JPofPeLlrcHzgKmRed7PmH+mwnAu0C7aLvKuM+hiXOrjL4aYU6fWuCvKdtsSxi1m0gI35XtkvB9RdznolIYRTmctXZUBte3hTJYGaySYVEGZ7UtlcOuDFYGq7SkKIOz2pbKYFcGF1oGW/SGUuDMbG3C0yrPAvoBDxAmsj4M+AOwgbt/nbB9v8TXkszCHEh/JEx2vgjY0t2nRbd11FiYR+lOYDvgW+ArwpxKfYED3P39mKqeNdE53kt4cuYahMnRAY5w9/uiUaudgCOBjQl/sN4BLvcwAlbl7tX5r3nz6upmZl2BUwj/gNkO6APc7O4nJGy7LfA88DFwibs/HEedpfAph7NHGawMTthWGSwZUQZnV7nnsDJ45bbKYMmIMji7lMHK4GjbgslgdQ4XoLpASHhd4fVPBW0P/AUYBXQlzDVzOuEX5Vh3X5z/GhcnM3uGEDhLCaOd46Ll7T1c0t8ZOJjwi9wV+DfwmLtPj6XCWWRh8va3gO+Ay4DXgX2Ak4EdiUI5YftuHuaWqnud9BktRFEYTwCmA68Ck4GTCD/zv7n7zxO23YbQBne7+8/yXlkpOMrh3FMGK4MTtlUGSxJlcH6Uaw4rg5XB0jRlcH4og5XB0baFkcH5ukRZpWWXn0ffjwWuAu4HDgH6J6zblXArQi2wGPgeGBV3/YuhEF2aD5wHHAu8EbXfzxO2aRd3PXPcBgcQngC6W+K5AlsBL0efq/0Tllflu45ZOMerCWG8PvW3daxNGNmuBW5M2X5oMZ6nSvaLcjjn7asMVgYrg1UaLcrgvLRxWeewMlgZrNJ4UQbnpY2Vwcrggsvg2BtNJekDUZHw/UOES+enAFOjD9CjwA4p++xLmKNkVmJYqzTetmnW7UyY9D01kDsBBye8trjPI4vt8cvoM9Ujep0YyqOjdbWJ51+oBdgAGJyyrBJ4DHg59TMQhfIr0fndkPrzjTuUVeItyuHct2uadcpgZbAyWCXpcxJ9rwzOUdumWVdWNhJhdwAAHThJREFUOawMVgarpC/K4Py0bZp1yuD6dcrguM4l7sZUSf4wRN9fFQXxLkBvwi0Ep0YfoGfSfPgGAn3jPodCLSSPfm4EbE002XvC8l2pH7E7ljAfzI3AEqBf3OeQgzbZO/o8nZQQVHUTu3cDJhFubfguta0KpRAmd18jOo8xKesqCE/NnQqskrB93bkeTpjcfgXw57jPRaUwinI4Z+2qDG7YJspgZbBKSlEG57RtlcPJ56oMVgarpBRlcE7bVhmcfK7K4ALM4AokNmbW1cz2A3B3N7NKM+tJCOF73P0Fd5/j7gvd/S+EEZaRhMvvMbPKaN+p7j4zptMoaInz0ZjZ/wH3AE8Az5vZRWa2GoC7P094CuYHwM2E+XxGA9t6aU6k/y7wBXA8sEs0j9QKM2sHbEOY9P6vhLDbMb5qNs6Db4AR7j7OzNqb2cBoXS3wX6A/cGw0T5G7e230ezOYMPfPTcBBZrZRI28jJU45nFvK4EYpg5XBgjI4H5TDaSmDlcGCMjgflMFpKYMLMYPz3RutkjSicCXhA390wrKBhNGhC6PXlYSRh7rLzJ8lTPbenhK5rSCH7Zs4+nkvIYAOjtr46ajtbyBhlBPYlPBH7zJgvbjPIUvt0B4YRPgj34n6UbmtgfnAh4SnaK4G7EUYsbw/2mYqcEfc59DIeSXe9lRFuJ3pKWCjhOUvROf4a+pH7YYQwviEqA1qgT3jPh+V2D5HyuHcta0y2JXBymCVpooyOOftW/Y5rAxWBqs0+TlSBue2fZXByuCiyeDYK1DOhXAZ+v0kXIoOdAA+Bp5N2C5xDpbHgTfjrnsxFeCsKHS2i17/OvqDN45wKf8NlNitGgnn3i36zEyJznk64cECfaL1W0WhWxN9DucR5jvqAKwVrTsj7vNowc+5ljAaOyxatkoUyrXRH+M3ga+B94B2hFHvWcDWcddfJbbPjXI4922sDFYGK4NVGvvcKIPz085lmcPKYGWwSrOfG2VwftpZGawMLvgMjr0C5V6AvoTJ3muBY6Nlp0ev/5Sy7erA88BthNEJjdSlb9PEUZwuwJ+Ak6LXpwDLgEOBHsAdUVtfUWqBTJgbanL0mdk9Ot+5USifCfSOtlstWv8LwlxHdXPh3BmF18C4zyXNuVU2svyU6Od5LzA0Yfn/A/4GPAJcRDTRe/S7NxFYNe5zUomvKIez3p7KYFcGK4NVMi3K4Jy0adnnsDJYGaySWVEG56RNlcHK4KLL4NgroNIgkA8n3LZxV/T6QcLl9YcRRiHmAhvGXedCLSlBvFf0R2sHwsjTxsBnwIkJv5AHAkujtr6OJp4iWkyFMBJ1L/Av6kfmHojC+FXCyN2Z6YIIOCLa9ztgeNznku7coq9dgEuAa4GLqb/V6VcJoTyskWMMi/5RM6+xbVTKqyiHs9aOymBXBiuDVVpalMFZbcuyz2FlsDJYpWVFGZzVtlQGK4OLMoOrkNi5+0wzO4nwBMN7CCNJxxB+eY4DDgFmE54YOsLdP46pqgXNzMzD5N+Y2T+AVYFp7v5qtGx7oDPwtrtXR7utBjwJjAf+U7d/CVib8EfmWnefbWb3AtsS5vqZTpjg/lQAM7vd3eck7LsW4R8II9x9cl5r3Qgz2wLY0t1v9DBZfXfgLcI/XDoSfo4Hmtne7n69mUGYxN7N7DJ3n5RwrA0IT37tDuzo7hPzfT5SeJTDbacMTqIMVgZLCyiDs0M5vJIyWBksLaAMzg5l8ErK4GLM4Lh7p1XqC+GX4GHCSMNhCcv2BzahQC43L8RCwqX9hAnP3yY82bIqYfmpUdtuHL3uQbhd4SagfdznkKV26EkIGQi3Z1QBRxFGKHemfqTrmqgtaoGfRssSJ8zvHve5JNSlCrg7qmvd7Th/JoxErgf0ITzJ9X/AJ8CAaJsTo32eAvqnHHM4sFbc56ZSeEU53Op2Uwa7MlgZrNLWogxuU9uVfQ4rg5XBKm0ryuA2tZ0yWBlc1BmsK4cLiIcRuxMBB+4zs87ufgfwaMxVK3juXgNgZn8A+gGLgP96/YgchFsZfgY8bWavEf7QbUKYGH55nqucdWbWmXCbxkdm9p67Pxst34ZwW8a77r4iYZezCJPEPwjg7h6Ndrq7L8hz9Rvl7tVmdibhSbnXmtliws/3HnefAmBmjwE/EEbonjazPdz9BjPrSngi7Bcpx3w/rychRUM53DrKYGUwymDJAmVw65V7DiuDlcHSdsrg1lMGK4Mp8gyuiLsCkszdZxLmKXkQuM3MfhpzlYqGmW1OuP1lD2CRu8+Pltd9zmcRJjp/FdgAWABs7wVyu0IWHE643edcYCGAmbUj3NbRnTCSh5mtD2wDfOvuv4sCrwpCKMdR8ea4+zfAaYSR7FsJk7rPAjCzSndfBjwHnEy4HeoJM1vP3a8gPP2zNuFzINIk5XDrKIOVwSiDJQuUwa1X5jmsDFYGSxYog1tPGawMpogz2Aq0/cuema0BXA5cUSJhkRdmdhBwGbA+cIS73xctr6wbzYtedwGqo1/kohady9WEid0XuvsF0XKLRuBGEW5neB34ivCHqIYQVNWNHLYgmdnqwB+BIwlPzz0zWl4RhW4VYS6j8cAT7n64RZP+FOofGylcyuGWUwYrg1EGS5Yog1un3HJYGawMltxQBreOMlgZTJFmsDqHC1hqgEi9ptrGzA4ArgTaA6e6+z+i5RWE38uS+tCb2eGEBwcAXOruF9S1T0Io7w1cSpgYfgrw82iUrug+Y1EoXwMcSvj5/jVaXhfK7YDNCLeuFNW5SeEpxt+RfFAG11MGK4Mld4rxdyRflMOBMlgZLLlTjL8j+aIMDpTBpZPB6hyWopMYIma2D7AmUA186O5vR8sPBS4COgBnJASylVIYA5hZD8LcRb8mzHWzs7vPSgioulDuBiz1aK4fM6sqttG6OmbWlzCnzyGkCeWE7YruD45IoVMGJ1MGK4NF8k05XE8ZrAwWyTdlcD1lcOlksDqHpagk/sKZ2QOEJ4BWEp4SOQ14zN1Pj9YfSLilowK4wN0fjKfWuWdmPQmh/Hvgv8Du7r4kNaASti/6P0opoXyyu18fc5VESp4yOD1lsDJYJF+Uww0pg5XBIvmiDG5IGVwaGazOYSlKZnYjsBcwFpgELCY8RXVH4HB3fyDa7kDgRuAbYAfCxPBF/aE3s07ArsBA4HPgfXf/3MxWAY4m3LLxHjCqqVAuBVEo/4VwW8eh7j4+5iqJlAVlsDIYlMEicSrXHFYG11MGi8RHGawMLrUMroq7AiItZWaDgK0IwfOauy81sz7ApsBtwON127r7I2ZWDUx294WxVDiLotsxXgF6AKsTbl+Zb2bHuPuzZnZHtOnvgafMbC93XxxTdXPO3Wea2RmEuYv+EXd9RMqBMlgZXEcZLBKPcs1hZXAyZbBIPJTBymAovQyuiLsCIo0xsy4WJi9PtSowDJgRBfF6wKfAM4Q5Xxab2c/NbCcAd3/c3T/LW8VzxMw6As8BswlPyOwF7EOY6P4BM+vv7j8AdwDnE0Ytr4qpunnj7l+7+wUeJrXXgJdIliiDkymD01MGi+SOcrieMjg9ZbBI7iiD6ymD0yulDFbnsBSy84HHzeyIlOVVwHJgiZn1B94G/gWMjYJ4K+AwoKeZWR7rm2s7E0L4EmCCuy8B+gGrAH9w9+kWJnb/Abib0AanxFbbGBTrpPYiBUoZnEwZ3AxlsEjWKYfrKYOboQwWyTplcD1lcDOKPYOLumdbSt7dwDrAOAtPerwTwN1fNbMPCLds9AKeAI5x92Vm1gs4DugJ/LuY5/NJY2NgNeBVD0/+PAK4CzjP3f9oZt2BX5vZDe7+LfAQFPeTQEUkVsrgZMpgEck35XA9ZbCI5JsyuJ4yuMTpymEpWO4+CbiQELq3mdmhCav/CCwkDHBcD3SIRuj+AhwEHOvuX+W3xtlnZpVmVhm9nA0YsLaZ/YT6ML48GpEcBWxOGMFbSWEsIq2hDFYGi0i8yj2HlcEiEidlsDK4nOjKYSk40ahcTfRyY2BW9P1dFp52eT/wNNAN+A3hFo55wJxouxHu/kE+65wLCfP6nAm8CXwAdCIE8dYkh/Eg4FRgKuHpoCIiraIMDpTBIhIX5bAyWETiowxWBpcjK52r3KUUmJnV3XphZn8nBM3/CKNyexHmtBnr7ndGo1idgYOBrsBHwKToNoaiZ+EpqG8CTwG/iG5TOR24GvgPMBaYBOxKGNHsAPw4mgy9wt1r46m5iBQrZXA9ZbCIxEE5HCiDRSQOyuBAGVx+dOWwFJSEID4fGAHsDfzH3Zeb2TbArwm3dFS7+73AD8C4uOqbY58BjwO7EZ6IOoP6c70SeIzwR+gb4GtgxyiME0c6RUQypgxOogwWkbxTDq+kDBaRvFMGr6QMLjO6clgKkpndD6wFjASW1wWMmW0K3AmsDxzu7n+Pr5a5Uzdxe/T008nAte5+dsL6zYHBhInu3wPeiCaG14TvItJmymBlsIjEq5xzWBksInFTBiuDy406h6XgRPPWPA/0cPfNomUrg8bMfku4dQHgp9GcP0XPzKqALu4+P3pdQZjX5yZgU+Bgd/+4sds0dPuGiGSDMlgZLCLxKsccVgaLSKFQBiuDy1FF3BWQ8hYFb9Lr6FaOl4EhZnY0hKdcRoEFsAJ4gvAk0P/ms765YmbtgXeA+8xsTLTY3X0RcB9hZHKbpo6hMBaRllIGB8pgEYmLclgZLCLxUQYrgyVQ57DEJpqPpm5OnyoLT8RsF61+GJgL/MbMDoWVgdyL8MTQicDZ7v5RDFXPhSrCnD6rAbea2SvAmWbWxd2fAB4AzjWzNRW8IpINyuAkymARyTvl8ErKYBHJO2XwSspg0bQSEo/EicrN7Dxgc2Ad4AvgMnd/18y2Ap4GaoB/ESZB3wzYgvAkzE9iqXwOmdkAYEPCbSrrAfMII5KDCJPBn+Pu/4itgiJSEpTB6SmDRSRflMMNKYNFJF+UwQ0pg8ubOocl7xJu1cDMHga2A94COhPms+kInOzu48xsOHAGsCPgwPRo3Ydx1D2bzKwdYRL3NYEP3X1FwrouwE7AmOjrMqAf8Cd3/3W+6yoipUMZHCiDRSQuymFlsIjERxmsDJaG1DkssTGz3wCnAIcAb0dPuNwWOBfYGdjX3V+Ibu+oJNzisdzdF8dW6Swxs67A3YT5ezYEXgFuc/e70my7D/Bjwjw/eyUGt4hIaymDlcEiEq9yzWFlsIgUAmWwMljqqXNYYmNmDwC9gP2AZXXz15jZpsC9wFJg+2gi9JIRhfE7wNfAtcAU4F3gM+Amd78u2q69uy9Ps387hbKItJUyWBksIvEqxxxWBotIoVAGK4Olnh5IJ7GInoi5AYC7L4lG6Sqj1+8B/wTWJtzqUDKi8x4HfAkc5u6PAmcDCwkjkReY2QkA7r484YmoKymMRaStlMHKYBGJVznmsDJYRAqFMlgZLMnUOSw5VxeyiaJRqFeAbcxs32hZTcK2swkhVZ23iubHIMAI8/XMNrN7CbesbAbsSgjlM83sZAhPRI2tpiJSEpTBSZTBIpJ3yuGVlMEiknfK4JWUwdIodQ5LTqU8BfRQMzvVzLaPJjm/jRBO55jZSFgZyL2BHYBPgR/iqnuOTAVuAp4zs+MJc/ccCcxy96+A8cBqwO/M7OD4qikipUAZ3IAyWETySjmcRBksInmlDE6iDJZGac5hyYtoPp89CaNRHYCHgF8Bw4GngW+BBwnhuykwAtiu2J8Cmk7d01GjkboewD4J8xvdA8wnDNz8qu4PmYhIWyiD6ymDRSQOyuFAGSwicVAGB8pgaYyuHJacM7MjCfP5jAYGAhcB+xImeZ9IGLH6L3As8DNCYJdcENeJwrgK6AP0JoQyZjYEGAA85O4npNzWIiLSKsrgZMpgEck35XA9ZbCI5JsyuJ4yWBqjK4cl6xJv3YhenwKsC5yZMCp1FvBb4E3gOHefZmZ9gBpgqbsviaHqeWVmWwNvECa7/4LwR6kG2Fbz+4hIaymDM6MMFpFcUQ43TxksIrmiDG6eMlhS6cphyaqUOX0Ojuaq2RiYET0BtBOAu18BXEwIoevNbGt3n+3uc0s9iOu4+1vAjsCPCBPATyEKY43SiUhrKIMzpwwWkVxQDmdGGSwiuaAMzowyWFLpymHJCTN7EBgFdCVM8v6Ou28Vrevg7sui738NXAE8Avy0bnk5iSbDrwIW1N3modE6EWkLZXDmlMEikgvK4cwog0UkF5TBmVEGS52quCsgpSExRMzsTGAT4OfAV8AZwCHRJPA/cfdldYHs7leZ2XLgmXIL4jruvqjuezOrUBiLSEspg1tPGSwi2aAcbh1lsIhkgzK4dZTBUkdXDktWmdlWwGaEJ4BeG9260Rv4PXAE8JS7/yTatqO7L42vtiIipUUZLCISL+WwiEh8lMEiraM5hyVrzOxXhAndrwZ+iIK4yt3nAOcTnga6l5ndDaAgFhHJHmWwiEi8lMMiIvFRBou0nqaVkGx6BNgS+AnhNg6iCc2r3P17MzsPqAZ+ZWbL3H1sjHUVESk1ymARkXgph0VE4qMMFmkldQ5L1rj712Z2NtAROMnMprj7X1MC+UJgOXBzrJUVESkxymARkXgph0VE4qMMFmk9zTksWWdmfYG/AocAp7r7X6PlVVEwV7h7bayVFBEpUcpgEZF4KYdFROKjDBZpOV05LFnn7jPN7OTo5V/MrMbdb6h78qWCWEQkd5TBIiLxUg6LiMRHGSzScuoclpxICOQa4Dozq3Z33bohIpIHymARkXgph0VE4qMMFmkZdQ5LzkSBfAawFHgt7vqIiJQTZbCISLyUwyIi8VEGi2ROcw5LzplZpbvXxF0PEZFypAwWEYmXclhEJD7KYJHmqXNYREREREREREREpAxVxF0BEREREREREREREck/dQ6LiIiIiIiIiIiIlCF1DouIiIiIiIiIiIiUIXUOi4iIiIiIiIiIiJQhdQ6LiIiIiIiIiIiIlCF1DkvBMrMxZnZa3PXIFjMbbmYXmln/uOsiIpIJ5bCISHyUwSIi8VEGSzlR57AUsjFAyYQxMBz4HdA/5nqIiGRqDMphEZG4jEEZLCISlzEog6VMqHNYcs7MKs2sc9z1SGRmncysKu56FAMz6xZ3HUSkbZTDxU05LFLclMHFTRksUtyUwcVNGZwf6hyWrIpuvXAz283MLjCzz4ClwKHR+t3N7AEzm2pmS8xsnpk9a2YjUo4zHRgBrBsdr67slLDNemZ2l5l9Y2bLzWy6mV1pZl1SjjUu2ndVM7vdzGYCi4C1mjmX9mZ2lpm9b2aLzWy+mb1rZiclbNPPzK6OtplrZkvNbLKZ/cbMKhO2uxC4I3r5YsL5jEvYpoOZnWtmk6LjzDOzx81s0zR16x2dyxwzW2hmL5jZpmb2UtR2qdsfYGavR9sujL7fP81206NjbGpmz5jZfGCimR0U1ffYRtpqkpn9z8ysqTYVkdxTDiuHm2pTEcktZbAyuKk2FZHcUgYrg5tqU2mcRiokV64C2gG3AAuAT6LlY4BewJ3ADGBN4FjgeTPb2d1fjbY7Dbgc6AOcnnDcjwDMbHPgBWAecBPwFbAJcAqwnZmNcPcVKXX6F/At8HugC7CwscqbWXvgGWAn4FngbsIflY2Bg4Drok2HRa8fAT6LznlP4A/AQOD4aLu/A2sAxwGX1Z1HtA9m1g54GtgWuCs6/irAL4DXzWxHd383oW7PEW4LGQf8O6rHc8D3ac7lROB64GPgEsAJP4d/mNnx7n5zyi7rENr2IeBhoCvwWNR2Y4FbU46/NTAEOM/dPW2DikgclMPKYRGJjzJYGSwi8VEGK4OlJdxdRSVrhfBL7oTw7ZxmfZc0y/oCs4EnU5a/BExv5H3+SwiXbinLD4zef0zCsnHRsrtbcB5nRftclmZdRcL3nQBLs81dQA2wRpq22SnN9qdH60alLO8OfAG8lLDsxGjb81K2rVs+PWFZT8Ifnf8B3VOO+xnwA9AjYfn06BjHpqnjZdG6ISnLbwGqgX5xf/5UVFSUwwnLlcMqKip5L8rglcuVwSoqKnkvyuCVy5XBKi0qmlZCcuVGd1+cutDdF9V9b2Zdzaw3IbTeBrbK5MBmtjFhZOpeoIOZ9akrwGuEWzR2T7PrVS2o/xHAXODiNOdQm/D9Eo8SKbrto1dUj2cI07ZskeH7HUn44zIh5XzaE0YYtzezTtG2+xLa7C8px7gFmJ+ybCRhVPJad1+QUO8FwF8Jo3C7pezzPfW3nKQe3wmjdQBEt8wcBjzl7l9neK4ikh/KYeWwiMRHGawMFpH4KIOVwdICmlZCcuXTdAvN7EfApcAooEfKas/w2IOjrxdFJZ2+mdapEesB77v70qY2sjCJ/NnAz4BBQOocNz0zfL/BhFG/75rYpg/wJTAA+Nrdk25DcfcVZjYt5T0HRF8npTneh9HXgSnLP3P3mtSN3X2amT0HHGVmZ3u4TeZQoBspt3aISEFQDgfKYRGJgzI4UAaLSByUwYEyWDKizmHJlQajdGbWFXiFMHJ0DfAB4TaCWuAcYJcMj10XeFcT5sVJZ27qgnQjh83I5I/Dn4CTgQcIf2RmASuAzYA/kvlDH43QHmc0sc13CdtmqjUTsjfVTjcT5v7ZjzD/z1jC3D9PtOJ9RCS3lMPKYRGJjzJYGSwi8VEGK4OlBdQ5LPm0K9APOMbdk24TMLNL0mzfWBhOib7WuPtzWaxfok+BwWbWwd2XNbHdUcAr7v6TxIVmNijNtk2F+xRgVeCFxNtEGjEN2M3MuiaO1kWTyA8gTIpf57Po60bA8ynHGRJ9ndrM+yV6lPAHZ6yZfQhsB/zR3atbcAwRiY9yuHHKYRHJNWVw45TBIpJryuDGKYPLnOYclnyquzUgafTIzHYn/fw+C4GeZpY62vQe4RaEE8ws9RYEzKzKzHq1sa73EG6HOD/N8RPrU0PD8+lC8hNN69QFZ7q63QmsTiMjdWaWeFvK40AlcGrKZr8gPFE00b8Icx6dbGbdEo7XjTDCuDDaJiPRrRvjCLfh/C5afFum+4tI7JTDgXJYROKgDA6UwSISB2VwoAyWBnTlsOTTa4RL/q82s/7ADGA4YbTrA2DjlO3fAvYBrjOzNwjB94K7zzKzo4AXgIlmdjthDpvOhHl2DiLcFjKuDXX9C2Gi9fPNbEvgWWApYcRrA+onTR8PHG9mDwDPEeYWOgaYk+aY7xBuWTnPzHoSQnKau78dvd9I4Eoz2yU6twXAOoQRzqXAztFxbgWOBy6JRgT/TZgQ/1DCU0BX/l67+zwzOwu4HnjbzOraZAyhrY5399RJ45tzC3AmcDjwsrtPaWZ7ESkcymHlsIjERxmsDBaR+CiDlcHSGHdXUclaIfySO7BTI+uHEeblmUuY3+clYAdCcHrKtl0Io0AzCUGcdFxgXeD/gOnAckIATgAuB9ZO2K7BsTM8l47AeYSgX0q4PeId4MSEbToDVwKfR9tMIUwIv2tU3zEpxzwamBzV14FxCeuqgFOi91gUlSmEUcPdU46zanRe30fbvUD4w/YuMDnNuRwIvJFw3DeAA9JsNx14KYO2eT6q/1Fxf+ZUVFSSi3JYOayiohJfUQYrg1VUVOIrymBlsErrikUNKyJFzswqgdnA2+6+R47f60lgG6Cfuy/J5XuJiBQL5bCISHyUwSIi8VEGFzfNOSxShMysU5rFJwA9aMGcPa1870GEOX7uUhCLSLlSDouIxEcZLCISH2Vw6dGVwyJFyMzuJtxm8gawjDBq9lPC00A3c/cfcvCeWwGDCbeaDAYGu/v0bL+PiEgxUA6LiMRHGSwiEh9lcOnRlcMixelZYG3gAuAaYCfCxPDb5yKII78Ebge6A0coiEWkzCmHRUTiowwWEYmPMrjE6MphERERERERERERkTKkK4dFREREREREREREypA6h0VERERERERERETKkDqHRURERERERERERMqQOodFREREREREREREypA6h0VE5P+3BwcEAAAAAEL+v25IAAAAAIYCU+Yoq3equdoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1440x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now create a plot of the these convenational metrics by rater category\n",
    "with sns.plotting_context('notebook', font_scale=1.5):\n",
    "    g = sns.catplot(x='rater_category', \n",
    "                    y='value',\n",
    "                    kind='strip',\n",
    "                    hue='reference',\n",
    "                    col=\"metric\",\n",
    "                    data=df_metrics_with_categories_long,\n",
    "                    col_order=['r', 'QWK', 'R2', 'degradation'],\n",
    "                    order=dataset.rater_categories,\n",
    "                    legend_out=False,\n",
    "                    sharey=False)\n",
    "    g.set_axis_labels(\"rater category\", \"value\")\n",
    "    g.set_xticklabels(dataset.rater_categories, rotation=45)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see from the plot that the behavior of the conventional agreement metrics is actually far from ideal. Their estimates of the same system's performance vary depending not only on the category from which the two simulated raters are chosen but also, to a lesser extent, on _which_ two specific raters are chosen from that category. Note that the plots will be a little different each time the above cell is run because of the random jitter added to make the dots not overlap with each other. However, this does not impact our interpretation.\n",
    "\n",
    "We can also look at average values in tabular format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rater_category</th>\n",
       "      <th>low</th>\n",
       "      <th>moderate</th>\n",
       "      <th>average</th>\n",
       "      <th>high</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>metric</th>\n",
       "      <th>reference</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">QWK</th>\n",
       "      <th>h1</th>\n",
       "      <td>0.547853</td>\n",
       "      <td>0.666112</td>\n",
       "      <td>0.730357</td>\n",
       "      <td>0.813188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h1-h2 mean</th>\n",
       "      <td>0.682284</td>\n",
       "      <td>0.767889</td>\n",
       "      <td>0.809369</td>\n",
       "      <td>0.856459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">R2</th>\n",
       "      <th>h1</th>\n",
       "      <td>0.315704</td>\n",
       "      <td>0.439609</td>\n",
       "      <td>0.516935</td>\n",
       "      <td>0.632639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h1-h2 mean</th>\n",
       "      <td>0.449658</td>\n",
       "      <td>0.565152</td>\n",
       "      <td>0.626349</td>\n",
       "      <td>0.702588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">degradation</th>\n",
       "      <th>h1</th>\n",
       "      <td>-0.177214</td>\n",
       "      <td>-0.126635</td>\n",
       "      <td>-0.086549</td>\n",
       "      <td>-0.011377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h1-h2 mean</th>\n",
       "      <td>-0.289228</td>\n",
       "      <td>-0.217583</td>\n",
       "      <td>-0.160722</td>\n",
       "      <td>-0.055033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">r</th>\n",
       "      <th>h1</th>\n",
       "      <td>0.578681</td>\n",
       "      <td>0.678744</td>\n",
       "      <td>0.735397</td>\n",
       "      <td>0.813347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h1-h2 mean</th>\n",
       "      <td>0.690695</td>\n",
       "      <td>0.769692</td>\n",
       "      <td>0.809570</td>\n",
       "      <td>0.857004</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "rater_category               low  moderate   average      high\n",
       "metric      reference                                         \n",
       "QWK         h1          0.547853  0.666112  0.730357  0.813188\n",
       "            h1-h2 mean  0.682284  0.767889  0.809369  0.856459\n",
       "R2          h1          0.315704  0.439609  0.516935  0.632639\n",
       "            h1-h2 mean  0.449658  0.565152  0.626349  0.702588\n",
       "degradation h1         -0.177214 -0.126635 -0.086549 -0.011377\n",
       "            h1-h2 mean -0.289228 -0.217583 -0.160722 -0.055033\n",
       "r           h1          0.578681  0.678744  0.735397  0.813347\n",
       "            h1-h2 mean  0.690695  0.769692  0.809570  0.857004"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# group by metric, the evaluation reference, and the rater category\n",
    "grouper = df_metrics_with_categories_long.groupby(['metric',\n",
    "                                                   'reference',\n",
    "                                                   'rater_category'])['value']\n",
    "# compute the mean, reformat, and reorder\n",
    "grouper.mean().unstack()[dataset.rater_categories]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Compute PRMSE metric\n",
    "\n",
    "Next, we compute the proposed PRMSE metric for the same system against the same set of raters in each cateogry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize an empty dataframe\n",
    "df_prmse_with_categories = pd.DataFrame()\n",
    "\n",
    "# iterate over all rater categories and compute the PRMSE values for all rater pairs in that category\n",
    "for rater_category in rater_category_pairs.index:\n",
    "    prmse_values_for_category = compute_prmse_one_system_multiple_rater_pairs(df_scores, chosen_system, rater_category_pairs[rater_category])\n",
    "    df_prmse_with_categories[rater_category] = prmse_values_for_category\n",
    "\n",
    "# now create a longer version of this data frame more amenable to plotting\n",
    "df_prmse_with_categories_long = df_prmse_with_categories.melt(var_name='rater_category')\n",
    "df_prmse_with_categories_long['metric'] = 'PRMSE'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now combine this data frame with the previous long data frame containing the other metrics\n",
    "# except we only want to keep those metric values computed against the rater1-rater2 average scores\n",
    "df_metrics_with_categories_long_only_average = df_metrics_with_categories_long[df_metrics_with_categories_long['reference'] == 'h1-h2 mean']\n",
    "\n",
    "# and now we don't need the reference column anymore\n",
    "df_metrics_with_categories_long_only_average = df_metrics_with_categories_long_only_average.drop('reference', axis=1)\n",
    "\n",
    "# combine the metrics into a single data frame\n",
    "df_all_metrics_long = pd.concat([df_metrics_with_categories_long_only_average, df_prmse_with_categories_long])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first thing we can do is to compute some descriptive statistics for all of the metrics across all rater categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>metric</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PRMSE</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.791218</td>\n",
       "      <td>0.009080</td>\n",
       "      <td>0.762230</td>\n",
       "      <td>0.787005</td>\n",
       "      <td>0.791126</td>\n",
       "      <td>0.796642</td>\n",
       "      <td>0.822187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>QWK</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.779000</td>\n",
       "      <td>0.064242</td>\n",
       "      <td>0.675206</td>\n",
       "      <td>0.744972</td>\n",
       "      <td>0.789610</td>\n",
       "      <td>0.823241</td>\n",
       "      <td>0.861024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R2</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.585937</td>\n",
       "      <td>0.092898</td>\n",
       "      <td>0.434688</td>\n",
       "      <td>0.531423</td>\n",
       "      <td>0.596121</td>\n",
       "      <td>0.649570</td>\n",
       "      <td>0.712106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degradation</th>\n",
       "      <td>200.0</td>\n",
       "      <td>-0.180642</td>\n",
       "      <td>0.086026</td>\n",
       "      <td>-0.304916</td>\n",
       "      <td>-0.240833</td>\n",
       "      <td>-0.185949</td>\n",
       "      <td>-0.128914</td>\n",
       "      <td>-0.048654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.781740</td>\n",
       "      <td>0.061186</td>\n",
       "      <td>0.683164</td>\n",
       "      <td>0.748357</td>\n",
       "      <td>0.790528</td>\n",
       "      <td>0.823504</td>\n",
       "      <td>0.861549</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             count      mean       std       min       25%       50%  \\\n",
       "metric                                                                 \n",
       "PRMSE        200.0  0.791218  0.009080  0.762230  0.787005  0.791126   \n",
       "QWK          200.0  0.779000  0.064242  0.675206  0.744972  0.789610   \n",
       "R2           200.0  0.585937  0.092898  0.434688  0.531423  0.596121   \n",
       "degradation  200.0 -0.180642  0.086026 -0.304916 -0.240833 -0.185949   \n",
       "r            200.0  0.781740  0.061186  0.683164  0.748357  0.790528   \n",
       "\n",
       "                  75%       max  \n",
       "metric                           \n",
       "PRMSE        0.796642  0.822187  \n",
       "QWK          0.823241  0.861024  \n",
       "R2           0.649570  0.712106  \n",
       "degradation -0.128914 -0.048654  \n",
       "r            0.823504  0.861549  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_all_metrics_long.groupby('metric')['value'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table shows that the variation in the PRMSE metric is significantly lower than the other, conventional agreement metrics. We can also look at this graphically by comparing PRMSE to one of the other metrics in detail, say, $R^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now plot the values of the PRMSE and R^2 metrics by rater category\n",
    "with sns.plotting_context('notebook', font_scale=1.3):\n",
    "    ax = sns.stripplot(x='rater_category',\n",
    "                       y='value', \n",
    "                       hue=\"metric\",\n",
    "                       order=dataset.rater_categories,\n",
    "                       jitter=True,\n",
    "                       data=df_all_metrics_long[df_all_metrics_long['metric'].isin(['R2', 'PRMSE'])])\n",
    "\n",
    "    # we also add a line for the R^2 metric for the system scores\n",
    "    # against the simulated true/gold-standard scores\n",
    "    true_r2 = r2_score(df_scores['true'], df_scores[chosen_system])\n",
    "    ax.axhline(true_r2, color='red')\n",
    "\n",
    "    # set axis labels\n",
    "    ax.set_title(\"R2 and PRMSE with pairs of raters for the same system\")\n",
    "    ax.set_xlabel(\"rater category\");\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot and the table that the PRMSE metric is much more stable and helps keep the evaluation consistent across rater pairs. Note that the plot will be a little different each time the above cell is run because of the random jitter added to make the dots not overlap with each other. However, this does not impact our interpretation."
   ]
  }
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