contacts_vs_distance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contacts vs distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Welcome to the cooltools expected & contacts-vs-distance notebook!\n",
    "\n",
    "In Hi-C maps, contact frequency decreases very strongly with **genomic separation** (also referred to as **genomic distance**). In the Hi-C field, this decay is often interchangeably referred to as the: \n",
    "\n",
    "* **expected** because one \"expects\" a certain average contact frequency at a given genomic separation\n",
    "* **scaling** which is borrowed from the polymer physics literature\n",
    "* **P(s) curve** contact *probability*, *P*, as a function of genomic *separation*, *s*. \n",
    "\n",
    "The rate of decay of contacts with genomic separation reflects the polymeric nature of chromosomes and can tell us about the global folding patterns of the genome. \n",
    "\n",
    "This decay has been observed to vary through the cell cycle, across cell types, and after degredation of structural maintenance of chromosomes complexes (SMCs) in both interphase and mitosis. \n",
    "\n",
    "The goals of this notebook are to:\n",
    "\n",
    "* calculate the P(s) of a given cooler\n",
    "* plot the P(s) curve\n",
    "* smooth the P(s) curve with logarithmic binning\n",
    "* plot the derivative of P(s)\n",
    "* plot the P(s) between two different genomic regions\n",
    "* plot the matrix of average contact frequencies between different chromosomes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import core packages\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "from itertools import combinations\n",
    "\n",
    "# import semi-core packages\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import colors\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-poster')\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# import open2c libraries\n",
    "import bioframe\n",
    "\n",
    "import cooler\n",
    "import cooltools\n",
    "\n",
    "from packaging import version\n",
    "if version.parse(cooltools.__version__) < version.parse('0.5.1'):\n",
    "    raise AssertionError(\"tutorials rely on cooltools version 0.5.1 or higher,\"+\n",
    "                         \"please check your cooltools version and update to the latest\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "./test.mcool\n"
     ]
    }
   ],
   "source": [
    "# download test data\n",
    "# this file is 145 Mb, and may take a few seconds to download\n",
    "cool_file = cooltools.download_data(\"HFF_MicroC\", cache=True, data_dir='./')    \n",
    "print(cool_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load a Hi-C map at a 1kb resolution from a cooler file.\n",
    "resolution = 1000 # note this might be slightly slow on a laptop\n",
    "                  # and could be lowered to 10kb for increased speed\n",
    "clr = cooler.Cooler('./test.mcool::/resolutions/'+str(resolution))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to data stored in a cooler, the analyses below make use\n",
    "of where chromosomal arms start and stop to calculate contact frequency versus distance curves\n",
    "within arms. For commonly-used genomes, bioframe can be used to fetch these \n",
    "annotations directly from UCSC. For less commonly-used genomes, a table of arms, or chromosomes \n",
    "can be loaded in directly with pandas, e.g.  \n",
    "\n",
    "`chromsizes = pd.read_csv('chrom.sizes', sep='\\t')`\n",
    "\n",
    "Regions for calculating expected should be provided as a [viewFrame](https://bioframe.readthedocs.io/en/latest/guide-intervalops.html#genomic-views), i.e. a dataframe with four columns, chrom, start, stop, name,\n",
    "where entries in the name column are unique and the intervals are non-overlapping. If the chromsizes table does not have a name column, it can be created with  `bioframe.core.construction.add_ucsc_name_column(bioframe.make_viewframe(chromsizes))`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>chrom</th>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>chr2</td>\n",
       "      <td>0</td>\n",
       "      <td>93139351</td>\n",
       "      <td>chr2_p</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>chr2</td>\n",
       "      <td>93139351</td>\n",
       "      <td>242193529</td>\n",
       "      <td>chr2_q</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>chr17</td>\n",
       "      <td>0</td>\n",
       "      <td>24714921</td>\n",
       "      <td>chr17_p</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>chr17</td>\n",
       "      <td>24714921</td>\n",
       "      <td>83257441</td>\n",
       "      <td>chr17_q</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   chrom     start        end     name\n",
       "0   chr2         0   93139351   chr2_p\n",
       "1   chr2  93139351  242193529   chr2_q\n",
       "2  chr17         0   24714921  chr17_p\n",
       "3  chr17  24714921   83257441  chr17_q"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use bioframe to fetch the genomic features from the UCSC.\n",
    "hg38_chromsizes = bioframe.fetch_chromsizes('hg38')\n",
    "hg38_cens = bioframe.fetch_centromeres('hg38')\n",
    "# create a view with chromosome arms using chromosome sizes and definition of centromeres\n",
    "hg38_arms = bioframe.make_chromarms(hg38_chromsizes,  hg38_cens)\n",
    "\n",
    "# select only those chromosomes available in cooler\n",
    "hg38_arms = hg38_arms[hg38_arms.chrom.isin(clr.chromnames)].reset_index(drop=True)\n",
    "hg38_arms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the P(s) curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the average contact frequency as a function of genomic separation, we use the fact that each diagonal of a Hi-C map records contacts between loci separated by the same genomic distance. For example, the 3rd diagonal of our matrix contains contacts between loci separated by 3-4kb (note that diagonals are 0-indexed). Thus, we calculate the average contact frequency, *P(s)*, at a given genomic distance, *s*, as the average value of all pixels of the corresponding diagonal. This operation is performed by `cooltools.expected_cis`.\n",
    "\n",
    "Note that we calculate the *P(s)* separately for each chromosomal **arm**, by providing  `hg38_arms` as a `view_df`. This way we will ignore contacts accross the centromere, which is generally a good idea, since such contacts have a slightly different decay versus genomic separation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cvd == contacts-vs-distance\n",
    "cvd = cooltools.expected_cis(\n",
    "    clr=clr,\n",
    "    view_df=hg38_arms,\n",
    "    smooth=False,\n",
    "    aggregate_smoothed=False,\n",
    "    nproc=4 #if you do not have multiple cores available, set to 1\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function calculates average contact frequency for raw and normalized interactions ( `count.avg` and `balanced.avg`) for each diagonal and each regions in the `hg38_arms` of a Hi-C map. It aslo keeps the sum of raw and normalized interaction counts (`count.sum` and `balanced.sum`) as well as the number of valid (i.e. non-masked) pixels at each diagonal, `n_valid`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>region1</th>\n",
       "      <th>region2</th>\n",
       "      <th>dist</th>\n",
       "      <th>n_valid</th>\n",
       "      <th>count.sum</th>\n",
       "      <th>balanced.sum</th>\n",
       "      <th>count.avg</th>\n",
       "      <th>balanced.avg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>chr2_p</td>\n",
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       "      <td>0</td>\n",
       "      <td>86055</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>1</td>\n",
       "      <td>85282</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>2</td>\n",
       "      <td>84918</td>\n",
       "      <td>10842540.0</td>\n",
       "      <td>8344.916674</td>\n",
       "      <td>127.682470</td>\n",
       "      <td>0.098270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>3</td>\n",
       "      <td>84649</td>\n",
       "      <td>4733321.0</td>\n",
       "      <td>3623.417357</td>\n",
       "      <td>55.917034</td>\n",
       "      <td>0.042805</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  region1 region2  dist  n_valid   count.sum  balanced.sum   count.avg  \\\n",
       "0  chr2_p  chr2_p     0    86055         NaN           NaN         NaN   \n",
       "1  chr2_p  chr2_p     1    85282         NaN           NaN         NaN   \n",
       "2  chr2_p  chr2_p     2    84918  10842540.0   8344.916674  127.682470   \n",
       "3  chr2_p  chr2_p     3    84649   4733321.0   3623.417357   55.917034   \n",
       "\n",
       "   balanced.avg  \n",
       "0           NaN  \n",
       "1           NaN  \n",
       "2      0.098270  \n",
       "3      0.042805  "
      ]
     },
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       "      <th></th>\n",
       "      <th>region1</th>\n",
       "      <th>region2</th>\n",
       "      <th>dist</th>\n",
       "      <th>n_valid</th>\n",
       "      <th>count.sum</th>\n",
       "      <th>balanced.sum</th>\n",
       "      <th>count.avg</th>\n",
       "      <th>balanced.avg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>325450</th>\n",
       "      <td>chr17_q</td>\n",
       "      <td>chr17_q</td>\n",
       "      <td>58540</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>325451</th>\n",
       "      <td>chr17_q</td>\n",
       "      <td>chr17_q</td>\n",
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       "      <th>325452</th>\n",
       "      <td>chr17_q</td>\n",
       "      <td>chr17_q</td>\n",
       "      <td>58542</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>325453</th>\n",
       "      <td>chr17_q</td>\n",
       "      <td>chr17_q</td>\n",
       "      <td>58543</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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      "text/plain": [
       "        region1  region2   dist  n_valid  count.sum  balanced.sum  count.avg  \\\n",
       "325450  chr17_q  chr17_q  58540        0        0.0           0.0        NaN   \n",
       "325451  chr17_q  chr17_q  58541        0        0.0           0.0        NaN   \n",
       "325452  chr17_q  chr17_q  58542        0        0.0           0.0        NaN   \n",
       "325453  chr17_q  chr17_q  58543        0        0.0           0.0        NaN   \n",
       "\n",
       "        balanced.avg  \n",
       "325450           NaN  \n",
       "325451           NaN  \n",
       "325452           NaN  \n",
       "325453           NaN  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(cvd.head(4))\n",
    "display(cvd.tail(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the data from the first couple of diagonals are masked. This is done intentionally, since interactions at these diagonals (very short-ranged) are contaminated by non-informative Hi-C byproducts - dangling ends and self-circles. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the P(s) curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time to plot *P(s)* !\n",
    "\n",
    "The first challenge  is that Hi-C has a very wide dynamic range. Hi-C probes genomic separations ranging from 100s to 100,000,000s of basepairs and contact frequencies also tend to span many orders of magnitude.\n",
    "\n",
    "Plotting such data in the linear scale would reveal only a part of the whole picture. Instead, we typically switch to double logarithmic (aka log-log) plots, where the x and y coordinates vary by orders of magnitude."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the flags used above, `expected_cis()` does not smooth or aggregate across regions. This can lead to noisy P(s) curves for each region:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lStdZuX4jjmBq71PJznUG7baE0shvyAGfrOeNl6/UQmkiEjUlGtnC9iffxHdNhtKy40babbeyonz08wt48K3rQ4xMRNKREo1sISunCe1OfowVtKT7oNWU9AhmCWi1Hra+8Uk+mvt+uAGKSFpRoolRJt2jqaxLz4Es2PNmzGDozksq7tcMWghTrvg9i9csDjlCEUkXSjQxyrR7NJVts98v+WLrY8lu6gwasel+zYEfr+O+e8ZpSQERqRclGqnV8NNuZ26TAbTstJE2wzfdrzlo/AweevfGECMTkXShRCO1ys5tRtuTH2cNzek5eNP9mtbrYavrH+fj+R+GHKGIpDolGqlT+55DWDTqJsxgyM5LWd8yuF8z+Efn0ysu4Oe1P4ccoYikMiWaGGXqYICq+o86if91HE1O0zIGjlhKWWRJgYMmr+Xeu3W/RkRqpkQTo0weDFBV633+wNymg2nVuZjW262qKD/w8e94UPdrRKQGSjRSfzlN6XjaU6yiJT0Hr6Kke3C/ps062OqGx5k8f1LIAYpIKlKikai07tqfZQf+o+J+zYYWwf2avB+cT6+8QM/XiMgWlGgkar12P4aCfqeS06yM/pXu1xzy0Truue8syrws3ABFJKUo0UiD5J1wM3Oab0PrrYppPXzT/ZqDH/uOZz/4Z4iRiUiqUaKJUWMZdbaF7CZ0Pf0pVlhreuatYmO3TfdrWl15D7MLZ4QcoIikCiWaGDWmUWdVNe/Ui7WH34tjDN11KWsi86H1X1jGR386lXUl60KOUERSgRKNxGTrnQ5j1rDfkNO0jP67L6UkOyjf+ZNlPH7z6bh7uAGKSOiUaCRmg46+gpltdqd9h2Jydt50v2aXx7/gqZevDTEyEUkFSjQSu6wsep/5OIuzupDXexWrBm4AILcEul33OP/+4qmQAxSRMCnRSFzktu5I1nHjKbYm5G+3hFUdSwHoshxWXXI10wunhRugiIRGiUbipvOgXZm76xVk5cB2uxWxoWlwf2aH78t484ozWbNxTcgRikgYlGgkrgYfch5fbzWapq1K6T1iKeWPbh7wzjL+efcZmnxTpBFSoolRo32OphZDT7+HuU0G0H7rDTQZHrRisoB9HprKna9dGm5wIpJ0SjQxaszP0dQku2kL2p7yFCtoxcAhKyiOTL7Zaj0MvPlF3vzu5ZAjFJFkUqKRhGjfYxCFB9yBY2yzyxI2RB7m7LcI5l52Cd8WaXCASGOhRCMJM2Dk/zFt0LlkN3UG776EkuxgcMBeUzfy1NUnM3PZzJAjFJFkUKKRhNr2+KuZ3mYPmnfYSOf8FRXlx725lrvuPoMVG1bUcrSIZAIlGkmsrCz6j3uchdnd6dp3La3yVgfFDic+/TM3PH0epWWlIQcpIomkRCMJl9uqPc1Oepq1NKPH8JVkdw9mDmhRDAfdNYV73r8h5AhFJJGUaCQpOvQZzs/73YplwYARSylpHzxPs9UK6H7NeN6Y8e+QIxSRRFGikaTps+cvmT7oHLKaOHl7LKG4eTA4YPCP8ONFF/Hd0u9CjlBEEkGJRpJqyHHX8k2bvWjSspSBexRVLCuw+zclvHrpqRocIJKBlGhipJkBopSVRb9x45mT1ZsWHTfSdcSyil0Hvbuc2x8Yp8EBIhlGiSZGmhkgei1atSP3+MdYS1M691xHk20jI9GA/R76igdeuSLcAEUkrpRoJBTdB27PD3v9HYD+Q1aysctGANqvgW2ufI7737leq3OKZAglGgnNoH1P4qu832FZMHTEEta2D7rMOqyGblc/yj2f/iPkCEUkHpRoJFTDj72MqZ2PIKd5GdvtVci6lkF5v0XQ7Pr7mLro83ADFJGYKdFIuMzY9sz7+aFJX3KalzF0j58pyQl2jShw/nPxWSxavSjcGEUkJko0Errs3Oa0O+1pllsbmrUvoceIpRX79pm8mud/N5ofV/8YYoQiEgslGkkJrbrlseHoJ9lALu17rKd5/sqKfft+uJK7/36inrERSVNKNJIyugzbk5WH3UspRp8Bq2m246qKfUdNWMQtd53MhtINIUYoIg2hRCMppfPO/8f8XS4HoM/AVWT1Xg9As43wfw/M4O8PnsHGso0hRigi0VKikZTT99ALmN73VMxg4M7LKO0eJJbcUjj09s+4/Z5fafYAkTTS6BKNmT1jZl+Z2Rdm9l8z2y/smGRLQ066hYK2e5KV4wzdvZB1XYKloJuWwD73fMZDL1yiBzpF0kSjSzTAWe4+3N13AM4CnjOzxvjvkNqyshlw3gS+yx1GVjZsv+ciVvQwAJoXw7DrXuSBd64POUgRqY9QP2DNrIeZ3WFmH5vZWjNzM+tTQ92eZjbBzFaY2Uoze8HMekX7nu6+vNLLtg0MXZIgJ7cZW5/+JEVZHcnKgV1GLKRwqyDZtF8Dva94jBcm3hVylCJSl7D/kh8AjAWWAR/WVMnMWgDvAXnAKcBJwEBgopm1jPZNzexWM5sNPA8c5e5lDYhdkqBNlz5kn/ISy2lNVo6z2+4/saJNkGx6FsHWf7iDVybeS0lZSciRikhNwk40k9y9i7sfCjxXS70zgX7AGHd/0d1fAo4EehN0fwFgZu+YWVEN28jyeu7+O3fvB5wA3GhmuQm5OomL9r23Zc0xz7KWZjRpVsa2eyxiResg2bRbC23/chvXvnlhyFGKSE1CTTRRtCSOBD5x91mVjp0DTAZGVyrb39071bBNrub93wDaA9vGdiWSaN2H7c7yg+6g1I2WbUrZfv+fWNwx+PXttBK2u+lVXv3fEyFHKSLVCbtFU1/DgG+qKZ8GDK3vScysuZn1rfR6N6AjMLshQZnZlPKtIcdLdLrtNpbv9g7uyTRrWsYuuy9kXdOgZTNoIeRecDWPf3pvmCGKSDVywg6gnjoQ3MepailBi6S+mgNPmllroARYQ3CPprpzR6W4uJiCgoJYT5PSioqKQr/GrG478km/89nl+zto0bKMQXv+zPSPu9BqTRk9lkCT397GXWdMZ989zo75vVLhepNJ15vZwrzedEk0ceHuS4Hd4ni+ncq/z8/P97y8vHidOiUVFBSQEteYdxXTX+7IkM8vo1WnjWy71yIK3u1K0+IyuiyHDre+ydRi57hzY1vPJmWuN0l0vZktzOtNl66zZVTfcqmppSMZbsiRF/Bl3gUANGtbwtADfuKnrk0BaFIK297+Flfd9n+sK1kXYpQiAumTaKYR3KepaijwbZJj2YyZjTOzzwoLC8MMo1Ha7rgr+LrfmQDkti5lrz3m8FOPFkDwi33ow9M5/5J8itYVhRiliNQ70ZjZDokMpA4vAyPMrF+lePoAIyP7QuPu97l7fufOncMMo9Ha9qSb+H7QGQDk5MDeu89ibp/g0aoWG+D3L5Zx6d/2pri0OMwwRRq1aFo0U8zsczP7tZlFcwO+VmZ2tJkdDZTf7zgkUrZ3pWr3A3OBl8xstJkdCbwELAA0zKgxM6P/8TfzZc+TAMjOglE7zOGn7psmfTj31TJevvp0zY0mjcqcojVMW5gaazhFk2j+BrQGbgcWmtnTZnagmVmMMTwX2cqHCd0VeX1FeQV3XwPsC8wAxgNPAHOAfd19dYzvHxN1naUAM7b71R3M2voIAJo3LWHkyBnMGNwGgJwyGPbUZzx56VgtniaNwvwla9n37+9z2O0f8d85S+s+IMHqnWjc/Wp3HwjsDTwFHAK8Dswzs6vMrH9DAnB3q2EbVaXefHc/yt3buHtrdx/j7nMb8p7xpK6zFGHGgDMeZmH3gwFomlXKEcML+HSn1hVVdpzwDRNOHcW0+f8LK0qRpLju9emUN+DPfSL8x/yiHgzg7h+6+6+ArsBpwPfARcAMM5toZieZWfM4xylSt+wmdDttPN/1HAtAVjacPPA7vt61U0WV3b9YT+Fxp/JpwdthRSmScGWVuolLy8LvMm7wqDN3X+fujxHMQ/Y0YAStnUeBH83sisYwh5i6zlJMTi6DT7+fgkHBFHhZwDF9vmLxPt0pbhL08nZZWsaSs87nqomXaGlokSRoUKIxs5ZmdpqZTQK+A44huDl/BHAg8AFwKY3gRr26zlJT3vE38G3P4wEwg1Fd/seqQ3pQ3DT4le+7GIZf9TxXvq3JOEUSLapEY2Z7mdnDwCLgQaAL8Fegp7v/wt1fdfd33P0XwE3AL+IesUh9mDH0V3fzvyGbEskeLT6lZFQbinODX/tBC2HfK97g0kdOCitKkUYhmudoZgETCdaP+Rcwyt0Hu/uN7r64mkO+ANrEJ0yRBjBj52P/yrSdr2edB724O7X/lo2jWrG+eTD7Urdl8MvrP+Pymw5nY9nGMKMVyVjRtGhWAr8Burn7ye4+qY76LwN966iT9nSPJvUNO+wcPt/zftZ7EwDyOxTQfLcSVjXbVOfYB7/n/fOO1bM2IgkQzfDmHd39Lnev14MI7r7W3ec1PLT0oHs06WHk/mP46YjxrPBg1oC8rRbS9MD1m9XpMXE6Tx86jPlF34cRokjGiqbrbIiZnVjL/hPNrPFMhSppp2/+Icz/v5eZXxb8UbBdi6V0O2opi3q0qqiz/RxnzR6Hs2heqFPoiWSUaLrOrgZqu2t6AnBlbOGIJNa22+XT4tyJfJc1AIC2Tdaz2y6zqbrU67KDjmLFF/9JfoAiGSiaRDMCeK+W/e8Rx7VeRBKlU9eedP/de3zdYlcAmuWWMOy4hUzap91m9dpccRMLn9Hy0JJ+1mworfh+2drwB7lEk2g6UvvaLyuARnejQoMB0lOr1m3Z9g+vMW3rTSPwz+ryLV8f2mKzeisuu5qZD9ye7PBEYvLRrNRaGiOaRLMYGF7L/uFAal1dEmgwQBrLzmHYuIeZOuDciqKxbWZxx5lllFaaKrbk5ruZc8WlIQQokhmiSTRvAKeb2a5Vd5jZLsDpkToi6cOM7U+4lvndD6sounPVIu49o4yVlWbsW//UBKae8H94sda1EYlWNInmSoJnaT4ys2fM7OLI9izwUWTfFbWeQSQVmdHrzCeZn38REPynuGPVIuadsJIp/Tc1bZpOmc6TY7bnp5U/hhSoSHqK5jmaHwlu9r8HHA1cFdmOipSNdPcFiQhSJBl6Hf4XFhz9WsXrsatXM2jkEqYM2JRsdpztPPabAygpKwkjRJG0FNVcZ+4+290PIrjpPyKydXb3g919ViICFEmmntuMZO2Zkyte71K8np8PWMP9B236r3Lkp867B+0cRngiaalBsze7+1J3/29kC3/5thBp1FnmadF9G0r/soBvCdby+/Wy5XTpv5qve29q2fRasJ4vzjgeLy2t6TQiEhF1ooksETDUzPaMzOa82ZaIIFOZRp1lpuzmbfCjHmF+Vg9ygb8sXc4ROy/crE6zj6byv7GHVX8CEakQzRQ0rczsfmAp8DXwPsFszuVb+WuRjJDdJJdef5vGN4PPB6B5jrP6xCXM7rqpTutp83jg7L0o86pzC4hIuZwo6t4BnAK8QpBQGnWXmTQe2xx/FTO/Gc3ACfuxc8kGZh5QyNcTOzPkh2D/yPcL+c/BI9njzY/DDVQkRUWTaEYDj7v7yYkKRiRVDdwmn4Wt/0e3h3dm4MaNzDhwOZ9Mbs+I74JlBTrOW84TFx3NL695DjOr42wijUs092iaEDwvI9Iodes9iB/Pmk6pG4etXctuu/zMonab9u/4wjQ+23d3rWkjUkU0iWYyMCxRgYikg+5bdyP7wrkA5G3cSM/Df+bzfptaMK1+Ws67h40IKTqR1BRNorkAONrMRicolrSk4c2NUPN28LelLOu+NwNKSmi9z3J+7LBpd/fZK/nl5cM0QEAkIppEcxewBnjBzOab2Qdm9l6V7d0ExZmyNLy5kcrKpv2ZLzNrj1s4cs0aph+zZrPdlz5dxthrhvPfn/4bUoAiqSOaRNOP4D7NfKAU6AX0rbL1i3eAIqlswP6nU3zCS/xmxQpmHL9ys31XPV7KC1efRmmZHuqUxi2auc76uHvfurZEBiuSinIHjqLk9PcY7atptc/mSzad8m4Zfz1/OKuLV4cUnUj4GjQFjYhsLqfnTvD7Anp2WYc32/zezGnvlPH7p2tbBV0kszVkCpphZnaBmV1nZv0jZc3MbJCZNa/reJGM1WZryi5azNAxi8jtu26zXb+7toBnC54JKTCRcEWVaMzsn8BXwC3An4HekV05wGfAuTUcKtIoZOU2g99+Rf9dl1HWevN7M9uOuZyZy2aGFJlIeKKZ6+wC4BzgNuBAoOLhAXdfDbwIHBnX6ETSUfvecNFChh22mPVbb9xs16N/HcMT058IKTCRcETTojkTmODufwC+qGb/N8DAuEQlku5yW8JFC9l+j82frzrh/TLuffc6Hp32aEiBiSRfNImmP1DbczJLgA617BdpXHJbYpcX0eeAzZPNvXeWcveHN/H2vLdDCkwkuaJJNKuB1rXs70+QbESkXHYTmt9eSNs+azcrfvi2Uv4w8XdMWTwFQPOjSUaLdq6z46vbYWZtgNMI1qRpVDQFjdTJjG5vzKPZgM2TzTPXl3LqG6dy1ttncdDzB/Hd0u9CClAksaJJNFcDw8zsdWD/SNkQMzuFYMRZW+C6OMeX8jQFjdRX31fmbVF25uul/Gfhf/hpzU/8duJvQ4hKJPGimRngf8BRwPbAk5Hi24GHgXbAUe7+TZzjE8koeV9P3ez1AVMdi3Sb/bj6xxAiEkm8qJ6jcfdXgT4Ei6D9BbgIOBro4+6vxz06kQxjTZrS68EHNit75vrSimQjkominhnA3Te4+yvufpO73+DuL7j72rqPFBGAliNH0mzP3Tcre+b6Ulqsd/79+ZbdayLpTnOdiYSg7/0PblH2yK2lFL29B5NnFYUQkUji5NS3opnNrkc1d/f+McQj0mgM+uwzZuTnb1ZW+klrdlvXH7+0CMtuElJkIvEVTYtmPjCvyvYDwRo1fYCSSB0RqYfsVi3p/87mD22OnO7s0LsndlUn0H0byRDRjDob5e77VNn2cveewHFAK+C8hEUqkoFye/Rgq2cf36zs6RtK2aFnT9Zc0SWkqETiKy73aNz9WWACwazOIhKFjsN32qLsyZtKGdG3C1zeNoSIROIrnoMBvgFGxvF8Io1G/7ff2qKsR6GzKDtbyUbSXjwTzR5AcRzPl1BmdpqZuZmNCTsWkdyePel65RWbld3yQClHdezGRlCykbQWzaizk2vY1R7YFzgcSIu5z82sD8GyB5+EHIpIhfZjx7LqzbdYM3lyRdkDt5ey5wU9+WTRAkpuyiPnTwUhRijSMNG0aB4hmG7mkSrbrcAhkX1RTdZkZj3M7A4z+9jM1kZaGH1qqNvTzCaY2QozW2lmL5hZr2jeL3KeLOAB4DfAhmiPF0mkHnfftUXZw7eVMql5M3LW/ETJh7clPyiRGEWTaPYhaLnsU2kbBQwHOrj7Ge6+Ksr3HwCMBZYBH9ZUycxaAO8BecApwEkEi6xNNLOWUb7n74HJ7j4lyuNEEi4rN5feTz65RfmTSzqx1oycdy+D5QtCiEyk4erddebuHyTg/Se5excAMzuDYIno6pwJ9AMGu/usSP2vgJnAWURGu5nZOwSTflZnNLCCYGLQveIUv0jctdhxB9be/Gda/PHGirLfvlzGAef3YOLPC8i9bRu4bDmY1XwSkRQS6hQ07l5Wz6pHAp+UJ5nIsXMI1sgZXalsf3fvVMM2GdiT4OHSmWY2FxgB3Gdmv47TJYnExU6Hn8b7226eSB64vZQRPXrydW4uT9zag9++91vmrJgTUoQi9RfNYICHGnB+d/fTG3BcVcOAl6opnwYcE0UwdwN3l782s/eB29z9xYYEZWYV3W877bTlsxAisdjlzvGw94mblT1xcym/ObsLi9sbLHiPGctm8PpRmjhdUlu9Ew1wKlA+J0bVNntt5fFINB0I7uNUtZRg1FvoiouLKSjI7BFBRUVFGX+NlYV9vS28BdPPOpQh9762Wfkd95Qy9sJsMOOH1T/ELcawrzfZGtP1FhQUhHq90SSarsDrwGzgZmB6pHwo8EeCLqlD3D1t1jR291ExHl/RjMnPz/e8vLyYY0plBQUFZPo1VpYK1ztkyN95rE0ZO9/0xmblf5lQxg3HZAPQa8UntNj11JjfKxWuN5ky+3q/3+xVXl5eqNcbzT2aW4Gf3P0Yd//U3VdGtk/c/WhgcaROIiyj+pZLTS0dkYxx8um3cvFJ2ZuV7TTLOfONUgBavP5bmP9pGKGJ1Es0ieYQ4NVa9r8aqZMI0wju01Q1FPg2Qe9ZL2Y2zsw+KyxMm4acpKHrz32B53ffvGf6gC+c/b6IjKd56EBYoaWgJTVFk2hyCIYY16Q/wZIBifAyMMLMKt4/8mDnyMi+0Lj7fe6e37lz5zDDkAw3qP0gnttzy/+uZ71RxrycSA/4rUNhqUahSeqJJtG8C/zazP6v6g4zO4pgiYB3ow3AzI42s6OB8vsdh0TK9q5U7X5gLvCSmY02syMJRqEtAO6N9j1F0tGTRz7Df4Zs+ezMmK23ZlaTyN94t28PxWuSG5hIHaJJNL8FCoHnzGyOmb0R2eYAzwI/Axc0IIbnItvZkdd3RV5XzDDo7msIZiWYAYwHngDmAPu6++oGvGfcqOtMkmVYx2Gc/q9veWzfzf/bPnlTKb/osTXflSeba7uFEJ1IzaJZ+Gw+wXQzNwHrgL0j27pI2fbuPi/aANzdathGVX1/dz/K3du4e2t3H+Puc6N9v3hT15kk29V3frVF2WlvlXJ0j60pzI78l37+zCRHJVKzqGYGcPfl7n6huw919+aRbWikbGmighSRTbKzsun20P2blR0yxem0wtm3V4/gobavn4USzRkrqaHBU9CYWVMzTbakrjMJQ9vd99ii7K67SmlS4hzSoxsrswyu3iqEyES2FFWiMbOBZvasmS0H1hDM4IyZdTazJ81stwTEmNLUdSZh6f/GllPPPHFTKT/mZDOyd8+g4I78JEclsqV6JxozGwx8SjDD8qdUmm4mMhtAHnBGvAMUkerl9ulDs+HDtyi/cnwp5s5/mjWDJTMpfePiEKIT2SSaFs01BDf+hwEnsOW8Zm8QPNciIknS+/HxW5Tl/Qi/+I9z1tZbMS03l+xP7tSQZwlVtAuf3eXuP7JpEs3K5gGNblyl7tFImLJyc+l2881blB83qYzcjc5x3bsyqXmzYMjzOs3WJOGIJtG0IHhWprb9jW5wgO7RSNjaHn4YXS/72xblNzxUCu6c13UrfsrOhhv6JD84EaJLNLOpefVKCJ6p+S6maESkQdoff/wWZd2XQv7MoPPhwF7dg0JNvikhiCbRPAWcamaVx1U6gJmdCxxB8NS+iIRg0Ccfb1H25+c3LWJ7SI+tg8k3y0qTGZZIVInmRuC/wETgLYIkc4OZzQbuAN4D7ox7hCJSL9nt2tH/zTe2KO/7U9Cq+aFJE9aawZUdwKu7zSqSGNFMQVMMHAD8mSDJrAe2BVYDFwKHunuj+1NJgwEkleT27g05m69neMMjpexaELRsdu3Tk1VmcO9eYYQnjVS9Ek1kFoC9gL7ufqu757t7y8gUNMPd/SZ335jgWFOSBgNIqsn7esu50P7wrzKyyoJWzO59erJh8VcUv3d9skOTRqq+LZpSgiUADk5gLCISB2a2RasG4PyXN92vOWnrruROug5+DmcNeWlc6pVo3L0E+BHITWw4IhIP1bVqdp/udFkWtGqmN81latNcuGvXZIcmDVC2fj1Lxz/Oqvcmhh1Kg0QzGGA8cIKZJWoVTRGJEzMjb9o3W5Tfcc+m26gndesafHN5Wyhem6zQpAGW3Hc/i6+5hh/OPZf1380IO5yoRZNoJkXqf25m55nZwWa2V9UtQXGKSJQsO5uuV11Za52KtPPh3xMejzRc0V13VXy/8vXXQoykYaJJNG8SLHw2jGA486sEQ53Lt/cjXxsVjTqTVNb+mGO2KHv07yUV31/cuWPwzYdbTmMjEi9b3jGs2a+ofo6zRs3d7wPuy8/P17+NpKTBX3zOdzvsWPG6eTHsNLOMKQOzeLVVS64vXAJAxy/vhrx/hBVmWistK+V/i//HgHYD6NS8U9jhpJwaE42ZnQxMKl8u2d0fSVJMIhJHWc2bb1H2lwllHPsXw7OM2U1y6LexhM7TH6H4423I3U3LQEfrsW8f45Ypt9C5eWfePPpNmmTpVnZltXWdPQzsXv7CzErN7JeJD0lE4q3n/fdvUfbMDcGkm6N7bJp0PffNPyYzrIxxy5RbAChcV8jniz8POZrUU1uiWQ20qfS60c3MLJIpWu255dLPAKe+Ezxbs1m/7/Nq0cRi9cbVYYeQcmq7RzMV+LOZ5QLLI2V7mlmt93Xc/bH4hCYi8TTggw+Ytffem5Ud+pnz6P7O8L69+HrO/KDw62ehz0jY6dTkB5kBbv/8dvbrtV/YYaSU2lo0FxC0Ym4DHiH4o+esyPc1bQ/HP0QRiYcmXbaqdpG0f0Serdm2by+KsiMfCf/+LazWSMqGmL1idtghpJwaE427fwEMAPKAUQRJ5xqClTZr2vZNbLipR8ObJZ20PfywLcq6LoftZgddaPv06kHFpIU3D4Cysi3qi0Sr1udo3L3U3We4+yTgA+B9d/+gti05YacOTaop6abnffduUXbxM2W0XxXcqZnarOmmHVe2T1ZYksGiWSZgH3d/N5HBiEjitdqr+gk87r0z6EK7v12bzXd883yiQ5IMF83MACKSIQa8X/0kHj0KnY+bN+fW9m03FU74FcydnKTIJBMp0Yg0Qk26dq22/JYHglbNQ+3ass4qPdHwyKGw+NtkhCYZSIlGpJEa/NWX1Zb/4fkg2ezSpyfb9u3Fl00jq4PcvVuyQpMMo0Qj0khl5eYy8MNJW5TvOsPZ85tNo81O7Fap9fPlM8kILa2UlJXUXamRU6IRacRyOnem29+3fLbmN//efFjz+VtFJor81zjYENuT7/NXzufeL+9l7oq5MZ0nVbw97+2kvl/Z2vRbO6jeicbMZpvZkbXsP9zM9KSSSJppc8gh1Zaf9+9SBv8QDHme2LIFc8uXh76ue0zvd+JrJ3Ln1Ds5/tXjYzpPqkj2lDOlS5Ym5sTrlsG7V8LXE+J+6mhaNH2AVrXsbwn0jikaEUk6y8qi1yNbTuqx9zfOVeNLyS4Nks0RPTdNvsmC/zb4/ZZtWAZoTrCU8/qFwQJ4z58OPxfE9dTx7DrrSTARp4ikmZYjRtS476YHSzEPkk3FrAEPHpD4oCS5vnp60/dztrx3F4taJ8g0s9HA6EpF48xs/2qqtgf2Bz6JY2xpwczGAeN69eoVdigiMbEX/4WP+cUW5T2WwKivnInbGTv27cVXc+YHU7m/dB6M/mfS45T0U9cKm9sDp0a+d2CvyFbVaoIkc168AksXWmFTGoNzXivjg22Nsizj+dYtOXrVGvjicTYedCNNmrUMOzxJcXXNdXaFu2e5exbBpJonlr+usrVx9wPcfUZywhaRROhx91017ns6slDaFZ06VpQ1ub5bjfVFykVzj6Yv8K9EBSIi4Wu9zz70eb7mUUfPXh88zHlr+7YV92u++ui1JEQm6SyaRFMM5Ne008z2NLPq57UQkbTRfNgwWu1b84ofTYudh9q1Zce+vXBg+DuZMUxZEieaRHNDZKvJdZFNRNJcz7tqvsk//u+lFd9/HZme5o2330x4TJK+okk0ewOv1rL/NYIF0kQkA7Q54oga9z17XQlNi50zum4FwMGTxzKvqHE+3eCe3HFAXpJ+U95Ek2i6AItr2f8zoK4zkQyx9VVX1rp//N9LWZeVxYTWwaiz3nfGNmNAunp1dm1/f8ffqjfTr/UYTaJZCgyqZf9gYGVs4YhIqshq1owhBdNrrZNdGoxC269nN25r35Z/P3RVkqJLHZ///HnYIaS8aBLN+8CZZtan6o5I2ZmROiKSQQa8+06N+566MRjy/HNODg+2a8tF2c9SUlpWY31pnKJJNFcA2cCXZnaDmZ0Q2W4Epkb2XZGAGEUkRE26d6fn/ffXuL9vlQ71x/4+NMERSbqpd6Jx9++Ag4CFwJ+Ax4DxwB8jZQe6e8ovwWdm75vZHDObGtn+FnZMIqmu1Z574Nf8qdp9Nzy8aS40gDu2yuHL959PVmiSBqKaVNPdP3b3IcBOwPHAccCO7j7U3T9ORIAJ8jt33z6y1X7HU0QAGHrUr3g136rd98z1m4Y8l5hhH5/NnB8WJis0SXENmr3Z3b9w92cj29SGvrmZ9TCzO8zsYzNba2Ze3T2gSN2eZjbBzFaY2Uoze8HMNJOlSBI9ekB2jfv2+nrTvZkTunWl7wNDkhGSpIGwV9gcAIwFlgEf1lTJzFoA7wF5wCnAScBAYKKZNWRGv+vN7OtI4hrcgONFGqVD+x5a475fv1LGo38vIatsUzda6Ye3JiMsSXFRJRoz29vMXjezIjMrMbPSKlu0TxJNcvcu7n4o8Fwt9c4E+gFj3P1Fd38JOJJgobWzKsX3TiS26raRkWonu3seMJzgIdO3zKzmP9NEpML1e15PmzdrnguteTH88v2gZfPfZk3Jfvdy1iz5MVnhSYqKZinnA4B3gB2BjyPHTgQ+jVSZRjA4oN7cvb7jII8EPnH3WZWOnQNMptJ6Oe6+v7t3qmGbHKkzP/LV3f0hglVDtTKoSD2YGd17D6PPKy/XWOfIT4MWzelbd+GHnGxa3qFRaI1dNC2ai4H5wBDgtEjZte6+O8HUM70IRqIlwjDgm2rKpwH1/i02s2Zm1qnS60OBUmBBQ4IysynlW0OOF0lXzQcMrHX/KW8HgwMO6xEsI7DozVvqPOfiNYv5YMEHbCzbWGddSS91LXxW2Y7Ade6+1Mw6RMqyANz9QzN7CLgK2CPOMQJ0ILiPU9VSgtU966sN8LqZ5QJlkXMe7u4x/2YXFxdTUBDfdbZTTVFRUcZfY2W63trNHn8j/U76c7X7DvvM+XAbZ/bWxpSmTdnp4yt4MSufvJ5bbVav/P1Kyko4Z+o5LN+4nKO7H82xPY5t+IXUUyJ/von+vYn2/AUFBXVeb16l7xctXszyOF5DNIkmCyiMfL8u8rXyh/y3BPdSUpa7/0wwNDte56s4V35+vufl5dVWPe0VFBSQ6ddYma63dnnk8cnfZtH2yvuq3X/9I6Uce2E2p3brwvU/F3Hk5CNYsPfmgwPK3++rwq9YvnE5ABN+nMBl+1/WsIuIQtx+vp9uWRTv35uqEwHVff7vt6gfzfV27dKFrnG8hmi6zhYQuZfh7uuARcDulfZvD6yJW2SbW0b1LZeaWjoikgQjfvm7Wvf/455gipoLt+rEdn170fuD6us7Wgk9tcT35xFNovkAOKzS6wnAr83sATN7mGD0V6KmFZ1GcJ+mqqEELanQmNk4M/ussLCw7soiGajfq6/UuK/rcjjwc6f9KsfKnF901wTvaWHOpLieLppEcytwr5k1i7y+GHiLYGDAyQQTav4xrtFt8jIwwsz6lRdEHuwcGdkXGne/z93zO3fuHGYYIqFp2r9/rfvPeKuMe+8s5bpHS5nVpEmSopKYLJsX19NFNdeZu9/r7usjr1e5+2EE3Vdt3f0Ad4/6z3ozO9rMjmbTvZNDImV7V6p2PzAXeMnMRpvZkcBLBN1590b7niISX/1ef63uOovgoM+dJiWbumXKR5gle/EwSa5onqP5m5ltU7Xc3Ve4+2ozG9bACSqfi2xnR17fFXldMRO0u68B9gVmEDyr8wQwB9jX3UNd1k9dZyLQtG9f6Nmtznqnv1XGGW9uenzurx/+NZFhJVwqJsglqzdEf1Bxom6vB6LpOruc4Gn6mmwDRD1UxN2thm1UlXrz3f0od2/j7q3dfYy7z432/eJNXWcigbzX63eLdp+vNn04vzn3TQrXpu8fabOWz6q7UpLNW7o2+oPKSuuuE4N4znXWAki/xaxFJC4sJ4e86fUbm9Ni/aZks+9z+yYqpIRbX7I+7BDSQq3P0URmR+5TqSjPzPaqpmp7glFns+MXWnows3HAuF69NJG0iFn1ywhU9citpYz966aPn1TsgpL4qeuBzdMIusM8sl0c2aoygiftz4hrdGnA3e8D7svPz9f/FBFg6+ee5KdjfllnvebrnfVNoeU6OPmNk5MQmYSlrkTzIsFoLwMeAu4jmFCzMgdWA5+VT1gpIo1Xu2134MZ9sjhpYu1z5j56a3BfoCQL/jE6i0/zwl61JHp60LR+ak007v4l8CWAmfUGnnf36ia3FBGp8O8RWfzQCf76XN0TtOeUwR/+VcbYv25KNNOKpjGsU3XPaIdrZfFKflj1A0M6DMHMOOG1E8IOaQsbS+o7KX7yRPMczRVKMlvS8GaRLd1/4P180b9+92vKXf54CUTu1bw+53XK6r2KSHJsLN3ImBfHcOwrx/LCN0+zek1qzn718OS5YYewhWgXPjMzO9DMzjWzSyPP1lTeLk1UoKlKw5tFtjRi6xH8Y9/bOfbCbKb3qN8xQxfATrOCRPPot4+yw/gdWLMxsc93RGPSj5MoXFdIl2VOr5OuZNpeI2mzJvW6zt6Ytij2kxSviv0clUTzwGYewSSirwN3EjxQeXk1m4gI+/bal2eOeI7LTqr/JPF/mVCGRVo1ZV7GPV/eA8C789/llNdP4a25byUk1voob2Gd82oprdZDmzXOSe+lVqsrbpbNjevpolkm4E6C2Zv/RLCy5tK4RiIiGWdIxyFcvOvFnHPe1dz9z/o9FLjX184Hw4Nut0emPcIj0x6p2Pf5z59z8LyD+csuf6FT8041nCGxOq3c9H27UOclSR/RdJ3tDtzi7re4+xfuPq+6LVGBikh6Oi7vOA4bcQrz69m7vOe02ruj3pj7Bvs8uw9/m/w3NpQ2YLqVStaXrOfFWS/y7ZLgQdPi0mJ+XvtztXWNIPlZ6vWWpbxoEs0aGrjkcSbTYACRuv1p5z9xwDtT61V3+Fyv172Pf836F/mP5zNvZcP+vv1i+Rfs/MTOXDr5Uo595ViWrFvC6BdHc8CEA3hv/nv1OodHN96h0Yom0fwLOCBRgaQrDQYQqZ+spk154xf1Gxlw7aP1n3vrko8u4eFvHub6/17PqihuYl/73bWbvR717Ch+WP0DZV7Gbyf+dov6XxV+Ve9zy+aiSTR/Arqb2a1m1s/qO9eEiEjEaZc9x/h96v7Y2WoFdF5evz6qqYVTuWXKLTwx/QlunXJr3QcAs1dEP1vWO/PfAUAffNGLJtEsA3YGzgdmAiVmVlpl06SaIlKjds3aceb1Na/IWdk/7y6ly7Lobog8N+O5OuuUeRmjXxwd1XlXbFjBglW6c9BQ0Yw6e4x4LyQtIo1O37Z92f7P2fzy/TKO+G/tHyl33FPKOedls6RN/dsR2z66LU8f9jSDOgzi1im3Mqj9IMYMGFOx/7U5dS/SVlV1XWlSf/VONO5+agLjEJFG5C+7X8y12ddyxH/r7gS5+5+l3Px/Wfx3cNAB03aNM3S+80U/Y33T6hPQca8eR7ZlU+rBvZ7urbqzc9edgfovtvZMwTMcm3cs05ZMY8riKZt26M/tqKXfLHYpRqPORKJ3fN7xfHDsBzy9V/0+gv74Qhk9CoPRaPffXsrvXizjrNdrf1iyPMkA/OrNX1FSVsKKDSvqHePVn14NwHGvHFdjnYwZdbbyx4SePpquMwDMbD9gDNAvUjQbeNHd341jXGlDywSINEyHZh1oM+5X3Nr+IX73Ut1P2N/ywOYj0UZOd/4xpv7vt8P4HaKMECbOnxj1MWmpdGNCTx/NFDTZZvYU8BZwHrBfZDsPeMvMnjQztZBEpN7O2e4cPhmSus2C8yeev0VZ6kabuqJJDH8GjgUeB/KA5pFtMDA+su9P8Q5QRDJXiyYtePuYhneGDJ23aW60MKgbo36iSTQnA6+4+ynuPsM3mRkZKPAacGoighSRzGVmPFXPezVVXf5kGU/cWMroj8totiE5H/vJnoKmrLg4uW+YANH8dPsSzNxck9cjdURE6s0w/rW78ddTsht0fE4ZnPB+GY/dUsoZb5RWrGmTFEnoR1szaVLi3yTBgwGiSTQrCWZvrkmvSB0RkXozMzDj+26xf2of+IXz7PVJTjYJtvSx8Yl/k6KZCT19NInmHeA8M9uj6g4zGwn8Gng7XoGlCw1vFolNjm0a/DruNw1r1VS15zeZkWhKV69h7X//m/g3Wr88oaePJtFcDGwAPjCzD83s3sj2ITAJWAdckoggU5km1RSJTbtm7di92+4ALG8Vn76o37xSRu7GxCebRL/D4muvrbtSPKxPbGdUvRONu88B8oFnge2AMyPbdsAzwM6ROiIiUbln/3u4cvcrAbjj8Pg8JXHx0+nfhbbihRfCDiEuonpg093nAsdHnpcp/xO+0N0zdD1TEUkGM+MXA39B4bpC7uAOZnUz/nFf/ZcKqM6QHwju1wC3jc7iP0Pjk8C08Fn0GvQv7+5l7r44sinJiEhcjBs+js9P+pxRI3/JH86Iz/0agAteKktM60ZPb9ZLNDMD/MrMamzHmdnzZnZyfMISkcaqSVYTtmqxFQs6GzO6xe+8z15fyt5fxf53sXJL9KJp0ZwF1Da0ajFwTmzhiIjAiUNOBOCDbeM7q9V5r5aRPyN+nTDqRaufaH6Kg4Ava9n/daSOiEhMmuU04/RtTuedHYyFHYKyl0bEpy3x5+fL6LhSKSKZokk0uQRzm9WkRR37RUTq7ZjBx+BmXHBWDmP/msMT+2Rz1XHxaeHc/c/IQAN39v6qjMP+W0Z2aT2TTwrnqE9mLwk7hGpF81MrAA6tZf8hBEs8i4jErHur7luUfd03i2P/Ep9BAs9eV8L2s53zXi3jlHfLOHhKzRnEyoK1cKpK5Ho0ZevXR33MpBkNfHB86eyGHVdP0SSaR4B9zOwOM2tTXmhmbczsH8A+wMNxjk9EGrGpJ03ln/v9k7GDxlaUeVb8Pt0venbT/ZqjP6rh3o071zxayn13lLL7t2WbDQZouT5xzZuf/35L1Md8s7CBD15+n9jlxKJJNHcCzxOsP1NkZjPNbCbBAIHfAC8Ct8c9whSnKWhEEic7K5u9euzFpbtdyk173VRR/vs4Dn0u17SGtb+OnVTGgEWQ5cEw6bZrN+0buiBYWjoRlo2Pfo6zBrdoEiyamQHc3Y8BTgDeADZGtteBX7r7UY3xmRpNQSOSHFu12Kri+x86G2P/msMj+8VvVFpONZ9e5s5R/6k9kRz3Qfgfe+6esvdnoAEPbLr7U+5+pLsPjWxj3P3pRAQnIlJueOfhm70+Z7tzmDa4WVzfY7+pm5KGuXP8+3UnkWa1LBfj7pSUJj4RvfXtYo6775OEv09DRTUFjYhIWHKycpg4diIzl81kl667kJ2VzdjBY3n8k7046PP4dF+d9XoZ8zsZs7rDyGnOmE/qPm9Nd4xKy5yx937MnKI1PHzqzmzXsx0LL/wra7/4nO4330zzbbeNS8wAZ42fErdzJYISjYikjU7NO9GpeaeK181zmvPgQdkc9HlJ3N7jmvHRzbG2+3SnJKuUp0ZlsaTNprTz0tQfmTJvGQAnPvApn47uzIoXXwRg3oknkffl1HiFnPLi+9itiEgSNcsOus7GXhj/wQHR2Guac9kTmyeowlUbKr5ftaGEtT/+VPHaN2ygMVGiEZG0lZ2VzYQjJnDG8DP5w+nhJpuuy6FJyaautuyixeyz4HOalQRJ5ZWvFlZ73NLHHmN63hC+y98Zd2f1Bx8w+4gjkxFy0qjrTETS2uAOgxncYTDn73A+w7cazhXjSxjyQzix7DTT+WSI4WVl7HTNBYxcu4p3e+zIzfm/5N2Cn9m1mmMWX3sdAGWrV7Pob5ex/Lnnkht0EqhFIyIZwczYrvN23HxUeC2b3j8HLZrSFStotnYVAPv98DkAQ5fM3azuyjfepPDOf25WlolJBupINGaWZWYXmtkpddQ71cz+HN/QRESic8NeN7CqhfHbceEkm4pnbopXb7FvzOyPNnv94wUXUHTnnTG/58Ll62I+R6LV1aI5DrgGmFFHvRnAdWZ2dFyiEhFpgO6tujPhiAn81NFYHd9HbOrNyhxu23zocp8VP9VQO3bnP/VFws4dL3UlmuOBie7+cW2V3P0/wDvASfEKLFHMLNfMbotMofO1mb0cdkwiEn8XnRJOq6a6Bzj7rExcovksMoQ6ldWVaPKBN+t5rreBXWILJymuJVjyYLC7bwuMCzkeEUmARR2ML/olfz3M3Goe6dnHpyY9jlRSV6LpQO2ralZWFKlfb2bWIzIb9MdmttbM3Mz61FC3p5lNMLMVZrbSzF4ws15Rvl8LgsRyYfm8bO6+KJpziEj6uOmo5I93uu7RUua8sdVmZXvMqm3NyIYrWh2H53HWJb5FVNdPYRWwVR11ynWO1I/GAGAssAz4sKZKkQTxHpAHnELQRTcQmGhmLaN8v2XAhWb2PzObbGaHRxmziKSwnq17VnxfkmNxW5mzvjqthJJ1m3fbFa9skpD3uv71gthPsjH6dW+iVVei+ZraFzur7FDgmyjff5K7d3H3Q4HaxvWdCfQDxrj7i+7+EnAk0Bs4q7ySmb1jZkU1bCMJnhvqBcxy952B04GHzKxflHGLSIpq0aQFjx3yWMXrsuT3niXNsjW1zOhZX9+9Gvs56lBXonkW2NPMflVbJTM7FdgLiGoW5yiWFTgS+MTdZ1U6dg4wGRhdqWx/d+9UwzYZmE+wEOvjkfoFwJfAjtHELSKpbYetdgg7hKSIy1Sir/4hHmepVV2J5gGCD+L7zewRM9vLzNpaoE3k9SORelOBBxMU5zCqby1NA4bW9yTuXkQwuOFgADPbGtiWoOUWNTObUr415HgRSbzCtpnbpHmv4OewQ6iXWqegcfeNZnYowcqaJ1P98GUDPgaOcvca1qiLWQeCeytVLQXaR3muc4AHzewagj8I/uDu38UYH8XFxRQUxKG/NIUVFRVl/DVWpuvNDO9tZ+z+rdFtVQ5XHV3GrfdHNztzKor251RQUFDjzzcvTu9RmzrnOouMyhppZmOAXxC0LtoAK4FvgReAl9w9cYtnx5G7zwX2i9O5dir/Pj8/3/PyavqRZYaCggIy/Ror0/WmuU+DL2VZRvv7b2f3Xvvx42PDueSkbK6OcimAVNO5R186tmoKfF+v+nl5eVH/fOP5uxDNUs4vuvsp7p7v7oMiX0+OlCc6ySyj+pZLTS0dEZEKZoZZ0IU2o4fx3Mj07k7b6ep3SJO/7YH0mVRzGkFLqqqhBK2q0JjZODP7rLCwvo8biUgyXLzrxQB0aNaBPbvvCUDr3NYAvDwii6WtQgstLlaui99ib4lWa9eZmZ0b7Qnd/a6Gh1Ojl4Gbzayfu88GiDzYORK4MAHvV2/ufh9wX35+fvr8eSHSCBw7+FgGdxhM7za9yc3OBeCe/e/hhNdOYEOu8etzsjnt7TIOmJqe/3W3u/Kt2E+yfkXs56iHuu7RRDu1qANRJZpKE3GW3+84xMwKgUJ3/yBSdj/wa+AlM7sk8j5XAQuAe6OMUUQaATPbYpjz8M7DK74vyTFe2zmLA6am9/2amDx3alLepq5Es08SYqj6oGZ5ovoAGAXg7mvMbF/gVmA8wUi3d4EL3H3L+biTyMzGAeN69YpqNhwRSQErWoQdQYjKyuD795LyVnUNb/6gtv3x4O71uivn7vOBoxIcTtTUdSaSvnr2GMorO3/D4f9rhP99k5RkIH0GA4iIxN2zRzzLhINbhx1GONYvT9pbKdHESKPORNLbDXvdwKUnhrf8c2OgRBMjd7/P3fM7d+4cdigi0gCjeo7iu57p/VxNqlOiEREBvusedgRJloR1aMop0YhIo3L0oOCJirzWm0+xcvVx2czoFkZEIfh5Orz2x6S9XZ1znUntNLxZJL1ctMtFHNj7QJota7ZZ+YZc45JTcrj+4RL6ZeC6uznrCmHGfOi/L7xwZlLfWy2aGOkejUh6aZLdhN267Ubz7ObV7r/shGwWt4MfOsIZ52fzY1QL1CfHdjar7kqVlZbQ+63T4Mlj4MO/Q1GUx8dIiUZEpJINucZvzsnh9+NyWNnSuP6YbCYP2XywwAu7hzt44JDs/2GUkU0wq0EuGzkm+332yfqi+gMWfk6TdZGRse9fCyXrkhNohLrORERqsbiD8Y8x2YycvmkSy7VNjTitb9kgZ+f8mwOyPqN/1k+s9aa0sA0V+w7bcA3TvG9osVVHLRoRkTTUP+sngM2SDMDx2cl74r++lGhipAc2RRqf/wzRczfRUKKJkQYDiDQ+RW3TLNHM+0+ob697NCIiGaRyCuzMMn6R/RG881Ro8YASjYhIRjkh510mlw2jiy3j1zkv0tFWhR2Sus5ERJ45/Bna5LaJ6ph3t0vd7rO7cm/nsibjUyLJgBKNiAhDOw7lzzv/udY6D++fxYoW8OCBwcfmwwfo47O+1HUWI01BI9I4vL5zFq/nG1jQkiluYpQaZDfCNdOipZQcI406E2lEbPPusvqtDyxKNCIiBOvSRGvKQGWa+lCiEREB2jZty4ujX4zqmPsPymJqXyWbuijRiIhE9G/XP6r6K1sa1x6nZaDrokQjIhKjJa3DjiC1KdGIiMTo+ZH6KK2N/nVipEk1RSSVH95MBUo0MdLwZhHxLCWa2ijRiIhIQinRiIhIQinRiIhIQinRiIhIQinRiIhIQinRiIhIQinRiIjEwZ2H6+O0JvqXERGJg0/y9CxNTZRoREQquWDHCxp0XHETJZqaKNHESFPQiGSWU4adEnYIGUeJJkaagkYks+RkaYX7eFOiERGJkzd2VPdZdZRoRETi5MlR+kitjv5VRETiZH1TtWiqo0QjIiIJpUQjIiIJpUQjIhJHJfpU3YL+SUREqrhp75safOwfzsiOYySZQYlGRKSKg/sc3OBjf+qoAQFVKdGIiEhCNapEY2bZZja10jbNzNzMhocdm4iklrOGn9XgY7vddGOddZrvsEODz59uGtVcC+5eCmxf/trMjgcudPevQgtKRFJS7za9G3xss7y8GvcN/nwKaz7+mBb5+czYdUSD3yOdhNqiMbMeZnaHmX1sZmsjrYs+NdTtaWYTzGyFma00sxfMrFeMIZwBPBDjOURE6i2rRQta77cf2W3bhh1K0oTddTYAGAssAz6sqZKZtQDeA/KAU4CTgIHARDNr2ZA3NrP+wG7A4w05XkRE6ifsrrNJ7t4FwMzOAA6sod6ZQD9gsLvPitT/CpgJnAXcEil7h0pdY1WMdvfJlV6fDjzv7stivQgRkYZo0r07G3/8MewwEi7UFo27l9Wz6pHAJ+VJJnLsHGAyMLpS2f7u3qmGrSLJmFk2QctI3WYiUq1WTVo1/OCszT9aszt1AqDLXy/crLzXQw82/D3SSNgtmvoaBrxUTfk04JgGnO8wYLW7fxBLUGY2pfz7nXbaKZZTiUiK2bvn3g0+NrdfP3L796f4++/pfMEFtDv6KDZ8P5sWO+dvXq93wwccpJN0STQdCO7jVLUUaN+A850BxPVPieLiYgoKCuJ5ypRTVFSU8ddYma43syXyer/77jv86qtgwQIKBw6kqKgI2raBGTO2rLzfvvDuewmJIxbx/LdJl0QTV+5+ZJzOU9GMyc/P97xahjRmgoKCAjL9GivT9Wa2el3vpw07d8V56/GsTOGwYRSlYKKJ5+9C2KPO6msZ1bdcamrpiIhIikiXRDON4D5NVUOBb5Mcy2bMbJyZfVZYWBhmGCIiKStdEs3LwAgz61deEHmwc2RkX2jc/T53z+/cuXOYYYiIpKzQ79GY2dGRb8vvdxxiZoVAYaVRYfcDvwZeMrNLAAeuAhYA9yYzXhGRuHIPO4KECz3RAM9VeX1X5OsHwCgAd19jZvsCtwLjAQPeBS5w99VJirNaZjYOGNerV6yz4YiIZKbQu87c3WrYRlWpN9/dj3L3Nu7e2t3HuPvccKLeLC51nYlkqG07bQtA85zmIUeS3kJPNCIiqer2fW/nwl0uZMIRExL3Jpnfc6ZEEyuNOhPJXJ2ad+KEISfQq426xmOhRBMjdZ2JiNROiUZEJEQ5HTuEHULCKdGIiISo2TbbhB1CwinRxEj3aEQkJo3gORolmhjpHo2IJNsSbx12CFFRohERCZNF/zH879LdEhBI4ijRiIiEqNmwoVEfc3PJ2AREkjhKNCIiIbKs6D+GV9MiAZEkjhJNjDQYQETCcH7xr8MOod6UaGKkwQAiEoaXy3ZnQVl6fO4o0YiIpKl0GRitRCMiIgmlRCMikqZ+pn3YIdSLEo2ISJp6smTfsEOoFyWaGGnUmYiEZWNKLJJcNyWaGGnUmYhI7ZRoRETS1LfeO+wQ6kWJRkQkTX3v3cMOoV6UaEREJKGUaEREJKGUaEREJKGUaGKk4c0iIrVToomRhjeLiNROiUZERBJKiUZERBJKiUZERBJKiUZERBJKiUZERBJKiUZERBJKiUZERBJKiUZERBJKiUZEJI2lwyqbSjQx0hQ0IhKm60uODzuEOinRxEhT0IhImFbSMuwQ6qREIyIiCaVEIyIiCaVEIyIiCaVEIyIiCaVEIyIiCaVEIyKS5o7Z8LewQ6iVEo2ISJr7n+dxxcaTwg6jRko0IiKSUEo0IiKSUI0u0ZjZoWb2uZlNNbNpZnZ22DGJiGSynLADSCYzywKeBPZy96/MrBsw08xedveFIYcnIpKRQm3RmFkPM7vDzD42s7Vm5mbWp4a6Pc1sgpmtMLOVZvaCmfWK9i0jX9tFvrYGVgGrG3QBIiJSp7C7zgYAY4FlwIc1VTKzFsB7QB5wCnASMBCYaGb1nlHO3UuBY4DnzWweMAU4291XNvgKRERSgNVdJTRhd51NcvcuAGZ2BnBgDfXOBPoBg919VqT+V8BM4CzglkjZO8D2NZxjNPApcDEw1t0nmtk2wNtm9rm7z4/PJYmISGWhJhp3L6tn1SOBT8qTTOTYOWY2mSCB3BIp27+2k5hZPtDN3SdG6n9jZt8AuwJKNCIiCRB211l9DQO+qaZ8GjA0ivMsALpFWjKYWQ9geOQ8UTOzKeVbQ44XEWkMwu46q68OBPdxqloKtK/vSdx9caSL7kkzcyAbuMjdv401wOLiYgoKCmI9TUorKirK+GusTNeb2RJ5vZnw7xjPa0iXRBM37v408HSczrVT+ff5+fmel5cXj9OmrIKCAjL9GivT9Wa2qK/30/pXjfbfcXpUtZMjnr8L6dJ1tozqWy41tXRERBoVDzuAWqRLoplGcJ+mqqFAzN1esTCzcWb2WWFhYZhhiIikrHRJNC8DI8ysX3lB5MHOkZF9oXH3+9w9v3PnzmGGISKSskK/R2NmR0e+Lb/fcYiZFQKF7v5BpOx+4NfAS2Z2CUEr8SqCUWT3JjNeERGJTuiJBniuyuu7Il8/AEYBuPsaM9sXuBUYT/AQ7LvABe4e6vQxZjYOGNerV7Sz4YiINA6hJxp3r9fMCZEn949KcDhRc/f7gPvy8/NT+V6ciEho0uUejYiI1CKV5zpToomRRp2JiNROiSZGGnUmIlI7JRoREUkoJRoREUkoJZoY6R6NiEjtlGhipHs0IiK1U6IREZGEUqIREZGEUqIREZGEUqKJkQYDiEgqSOU5sJRoYqTBACIitVOiERGRhFKiERHJAJpUU0REGi0lGhERSSglmhhp1JmISO2UaGKkUWciIrVTohERkYRSohERkYRSohERkYRSohERkYRSohERkYRSoomRhjeLiNROiSZGGt4sIlI7JRoREUkoc0/lVQzSh5kVAvMaeHgnoCgO9WraX1151bLKr6v7fkjk9fR6xFmXZF9vXdef6ddbn5+1rrfhdL2b9Hb3Lbt33F1byBvwWTzq1bS/uvKqZZVfV/c9MAWYko7XW9f1Z/r11udnrevV9cb7eitv6jpLDffFqV5N+6srr1p2Xz2+j5dkX29d15/p11vfn3W86HobVi/TrreCus6kXsxsCoC77xR2LMmg681sut4kv78SjYiIJJK6zkREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaEREJKGUaCSuzOw0M3MzGxN2LIlkZu+b2RwzmxrZ/hZ2TIlkZrlmdpuZzTSzr83s5bBjShQzy670c51qZtMiv9PDw44tUczsUDP7vNL1nh3P8+fE82TSuJlZH+BM4JOQQ0mW37n7i2EHkSTXArnAYHcvM7OuYQeUKO5eCmxf/trMjgcudPevQgsqgcwsC3gS2MvdvzKzbsBMM3vZ3RfG4z3UommkzKyHmd1hZh+b2drIX2x9aqjb08wmmNkKM1tpZi+YWa8qdbKAB4DfABsSfwXRiff1prp4Xq+ZtQDGEXzYlgG4+6KkXEg9JfjnewbB73bKiPP1WuRru8jX1sAqYHW84lWiabwGAGOBZcCHNVWKfMi8B+QBpwAnAQOBiWbWslLV3wOT3X1KwiKOTbyvF+D6SDfSBDMbnJiwGyye1zsgcp4Lzex/ZjbZzA5PZPANkIifL2bWH9gNeDwBMccibtcbacEdAzxvZvMIVuM8291Xxi3aeCztqS39NiCr0vdnAA70qabeb4FSYEClsr5ACfD7yOttgI+BJpHX7wNjwr7GRF1vpKxX5KsBvwLmAdlhX2eCfr47Ro7/VeR1HvAz0C/s60zUz7fSvmuB8WFfX4J/vjmR/7P7RF5vA/xU/jsej00tmkbKI10g9XAk8Im7z6p07BxgMjA6UrQn0IegX3cuMAK4z8x+HbeAYxTn68Xd50e+urs/BLQCescv4tjE+XrnE3yQPR7ZXwB8SZCAUkK8f74QDAogaAWkVLcZxP16twe6ufvEyP5vgG+AXeMVrxKN1GUYwS9dVdOAoQDufre7b+3ufdy9D8FggHHufmfywoybOq/XzJqZWafyHWZ2KMFfjQuSEmF81efnWwS8CRwMYGZbA9sCXycpxniq83orOQxY7e4fJDyqxKnP9S4AupnZNhDc/wGGR+rEhUadSV06EPQDV7UUaJ/kWJKhPtfbBnjdzHKBskj9w919Y3JCjKv6/nzPAR40s2sIWjd/cPfvkhBfvEXz+3wG8GDCI0qsOq/X3Reb2RnAk2bmQDZwkbt/G68glGgk7tx9VNgxJJK7/wzsFHYcyeTuc4H9wo4jmdz9yLBjSBZ3fxp4OlHnV9eZ1GUZ1bdcavpLKd3pegO63syQEterRCN1mUbQz1vVUCBuTesUousN6HozQ0pcrxKN1OVlYISZ9SsviDwYNjKyL9PoenW9mSQlrtci46alETKzoyPf7gecDZwLFAKF5SNtIg91fQmsAy4huBF8FcHTw8PdPW5PDyearlfXq+sN6XrDfvBIW3hb5Jeuuu39KvV6Ac8DKwmmpniRah4OS/VN16vr1fWGc71q0YiISELpHo2IiCSUEo2IiCSUEo2IiCSUEo2IiCSUEo2IiCSUEo2IiCSUEo2IiCSUEo1IhjKzUZG15E8NO5aqzGyumb0fdhySHEo0ImnMzNqZ2eVmNirsWERqovVoRNJbO+CyyPfvV9k3CWgOpOOCbJJBlGhEUkRkjfqm7r42HufzYF359fE4l0gs1HUmGcXMWpjZNWY208zWmdlSM5tiZhdUqZdlZueZ2RdmttbMVprZm2Y2okq98vscp5nZH8xstpmtN7OvzOyoat7/XDN718x+MrNiM5tnZreZWetaznuBmc0gSApjI/uPM7NXzOyHyHkWmtlDZta18jmAOZGXl0XO5+X3Pmq6R2NmW5nZvWb2Y+Tcc8zshshMv5XrXR45fnBk/8LItX9qZrtH8WOpkZntYmYfRn4Gi8zsVjNrXqXOI5E4uprZ02a23MxWmdkLZtY7HnFIYqlFI5nmLuAE4B6C6dFbEizytDdwW6V6jwHHAU8B9wOtCNaI/8DMDnD3SVXOez7BSoX3A8XA6cBzZjbW3SdUqvcHYDLwOrCGYN2P3wDbAftUE+8FBFO2P0iwjvt3kfJzgZ+BOyPlOwC/AnYzs+3dfQMwHfgdcCvwL+CFyLGLa/rHMbN2wH+APsB9wNeRGP8MjDSzUe5eUuWwxyLXcj3QJnKNr5hZX3dfUdN71UMP4E2Cn8FTBP8+FwD9geqWUX4dWAhcDAwAzgN2ivx7ZOLqmJkj7KmutWmL50awPO1dddT5BcF06idWKW8NzAM+q1Q2KlJ3BdC1Unl74CdgAZBdqbxFNe93WeQcu1Vz3kKgQzXHVHeeUyLHHF+prE+k7PJq6pe/x6mVyq6LlJ1Spe5VkfIzK5VdHil7icjaVZHyoyLlZ8fwc5obOcc5VcrvjZQfVKnskUjZ01XqHh8pvy7s3ztttW/qOpNMsxzYNbKKYE1OBJYAb5hZp/INaAq8TfBXcocqxzzh7ovKX3jwF/SDBH+V71SpfC0E91siI8I6ARMju3euJpbx7r60amGl82SZWdvIecpbWdWdp77GAD8A46uU30jQUhtTzTF3eOSTPaL8egbEEAcEyfuBKmU3Rb6Orqb+LVVeP02Q6KurKylEiUYyzR+AwcAcM/vGzG6vZujvEKAjkdUIq2ynR+p0qXJMQTXvNT3ytW95gZkdZGb/IVjRcFnknB9Edrer5hyzqruIyL2Ltwm6rJZHzjO7lvPUV1+gwIOBAhXcfRXBh3a/ao6ZU6VueWLsGEMcALPdveqIuO8JEl7faupv9jOIJL/vaqgrKUT3aCSjuPsLZjYJOIyg6+ho4Ddm9pi7nxKplgX8CJxay6nmR/vekYEEr7Lp3sk8ghv83Qm6f6r7w26LEWaRG9wTgSKC5XdnRuplA2/UcJ5EKq2h3JIahaQtJRrJOO5eBDwKPBoZMjweONnMbnb3rwk+uA8EPnL3+g7/zaumbEjka/lf/McSJIPD3X1eeSUzOzDKSxgDtABO9sja75HzDKqmbrRL5M4G8szMKneHmVkroCfwTpTni0U/M2tSpVXTH8ilSisqIg/4b/kLMzMirdeERikxU9eZZIzy+yKVy9y9FPgq8rK8q2c8wYfZVTWcp2q3GcAJVYYWtyfoZvsRmBIpLv/LP6tSvSyC7rxobHGeiD9VU3d15Gv7ep77JYL7SidWKf8jwb/Ji/U8Tzy0JRjpVzUOgJerqf/7Kq+PI0iO1dWVFKIWjWSS1sBCM3sJmErQ9TSYYBjs98DHAO7+rJkdDvzRzHYmGDa7jOBDa2+gCbBblXPPBj4xs/sInrQ/neA+zvGRZAbBh/jvgVfN7F6CRDGW4AM8Gm8QdLk9ZmZ3EHSbHQ50rlrR3ZeY2ffAcWY2i+Bezs/u/l4N574BOAZ4yMx2BaYBuxMknsnAw1HGWiHy/M7eQF93n1uPQ2YD15rZtsA3BMObjwZec/c3qqk/2MxeBV4jaPn8mmBgw40NjVmSJOxhb9q0xWsj+EC/HvgfwbMn6wkSzO3A1lXqGnAawYfrKoKb97MJRjIdVqneKILuqdMI/tqeDWwg+GA8ppoYjiVoQa0jaO3cBgyjyhBkqhl6XOU8+wGfEgwGKCS4x9M5cswjVeruRpBE10b2v1/bexAkyPsInkkpJhhqfCPQskq9yyPH96kmvurimBKJt109flZzCabM2QX4MBL7z8A/qDK0m03Dm7sCzxAMjlhN0PrqG/bvnba6N4v8IEWkGpERaxOB09z9kVCDSWGRLssi4Bp3v6yO6tGe+xGC5340+CBN6R6NiMTDvgQtL3VjyRaUaEQkZu7+grtv7e5rwo5FUo8SjYiIJJTu0YiISEKpRSMiIgmlRCMiIgmlRCMiIgmlRCMiIgmlRCMiIgmlRCMiIgn1/99Sl67MyiqIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 921.6x633.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cvd['s_bp'] = cvd['dist']* resolution\n",
    "f, ax = plt.subplots(1,1)\n",
    "\n",
    "for region in hg38_arms['name']:\n",
    "    ax.loglog(\n",
    "        cvd['s_bp'].loc[cvd['region1']==region],\n",
    "        cvd['balanced.avg'].loc[cvd['region1']==region],\n",
    "    )\n",
    "    ax.set(\n",
    "        xlabel='separation, bp', \n",
    "        ylabel='IC contact frequency')\n",
    "    ax.set_aspect(1.0)\n",
    "    ax.grid(lw=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The non-smoothed curves plotted above form characteristic \"fans\" at longer separations. This happens for two reasons: (a) we plot values of **each** diagonal separately and thus each decade of s contains 10x more points, and (b) due to the polymer nature of chromosomes, contact frequency at large genomic separations are lower and thus more affected by sequencing depth.\n",
    "\n",
    "This issue is more that just cosmetic, as this noise would prevent us from doing finer analyses of *P(s)* and propagate into data derived from *P(s)*. However, there is a simple solution: we can smooth *P(s)* over multiple diagonals. This works because *P(s)* changes very gradually with *s*, so that consecutive diagonals have similar values. Furthermore, we can make each subsequent smoothing window wider than the previous one, so that each order of magnitude of genomic separation contains the same number of windows. Such aggregation is a little tricky to perform, so `cooltools.expected` implements this operation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Smoothing & aggregating P(s) curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of the flags above, we can pass flags to `expected_cis()` that return smoothed and aggregated columns for futher analysis (which are on by default)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "cvd_smooth_agg = cooltools.expected_cis(\n",
    "    clr=clr,\n",
    "    view_df=hg38_arms,\n",
    "    smooth=True,\n",
    "    aggregate_smoothed=True,\n",
    "    nproc=4\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>region1</th>\n",
       "      <th>region2</th>\n",
       "      <th>dist</th>\n",
       "      <th>n_valid</th>\n",
       "      <th>count.sum</th>\n",
       "      <th>balanced.sum</th>\n",
       "      <th>count.avg</th>\n",
       "      <th>balanced.avg</th>\n",
       "      <th>balanced.avg.smoothed</th>\n",
       "      <th>balanced.avg.smoothed.agg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>0</td>\n",
       "      <td>86055</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>1</td>\n",
       "      <td>85282</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.001043</td>\n",
       "      <td>0.001060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>2</td>\n",
       "      <td>84918</td>\n",
       "      <td>10842540.0</td>\n",
       "      <td>8344.916674</td>\n",
       "      <td>127.682470</td>\n",
       "      <td>0.098270</td>\n",
       "      <td>0.087228</td>\n",
       "      <td>0.088615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>chr2_p</td>\n",
       "      <td>chr2_p</td>\n",
       "      <td>3</td>\n",
       "      <td>84649</td>\n",
       "      <td>4733321.0</td>\n",
       "      <td>3623.417357</td>\n",
       "      <td>55.917034</td>\n",
       "      <td>0.042805</td>\n",
       "      <td>0.043116</td>\n",
       "      <td>0.043947</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  region1 region2  dist  n_valid   count.sum  balanced.sum   count.avg  \\\n",
       "0  chr2_p  chr2_p     0    86055         NaN           NaN         NaN   \n",
       "1  chr2_p  chr2_p     1    85282         NaN           NaN         NaN   \n",
       "2  chr2_p  chr2_p     2    84918  10842540.0   8344.916674  127.682470   \n",
       "3  chr2_p  chr2_p     3    84649   4733321.0   3623.417357   55.917034   \n",
       "\n",
       "   balanced.avg  balanced.avg.smoothed  balanced.avg.smoothed.agg  \n",
       "0           NaN                    NaN                        NaN  \n",
       "1           NaN               0.001043                   0.001060  \n",
       "2      0.098270               0.087228                   0.088615  \n",
       "3      0.042805               0.043116                   0.043947  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(cvd_smooth_agg.head(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 921.6x633.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cvd_smooth_agg['s_bp'] = cvd_smooth_agg['dist']* resolution\n",
    "cvd_smooth_agg['balanced.avg.smoothed'].loc[cvd_smooth_agg['dist'] < 2] = np.nan\n",
    "f, ax = plt.subplots(1,1)\n",
    "\n",
    "for region in hg38_arms['name']:\n",
    "    ax.loglog(\n",
    "        cvd_smooth_agg['s_bp'].loc[cvd_smooth_agg['region1']==region],\n",
    "        cvd_smooth_agg['balanced.avg.smoothed'].loc[cvd_smooth_agg['region1']==region],\n",
    "    )\n",
    "    ax.set(\n",
    "        xlabel='separation, bp', \n",
    "        ylabel='IC contact frequency')\n",
    "    ax.set_aspect(1.0)\n",
    "    ax.grid(lw=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `balanced.avg.smoothed.agg` is averaged across regions, and shows the same exact curve for each."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3QPbDz7Dq14URpxIRST8qzpJQPR56iwXhEf7tlsPcBy6NNpCISBpScS4nXRD2R3Xrb0etq68gL3xSeMcZGxhx++mRZhIRSTcqzuWkC8L+bL9jz+Kb7gUPD6PFsM/4ctyICBOJiKQXFWdJin73jOLb1sHuc80NsOSm61mzclnEqURE0oOKsyRFVnY2uw9+kV/rBu2dfnHeueCoaEOJiKQJFWdJmuZtOrPob8eyKfwp6zhlDSPvOCvaUCIiaUDFuZx0QVjpOhx1FjMP27Gg3fzVj/ly/OsRJhIRSX0qzuWkC8K2rt/gd/m2VRYQDO+55MbrdP5ZRKQUKs6SdFnZ2ez+wPO/n39e5Lyt888iIiVScZYK0bztHqy74G8F5587TVnDyDvPjjaUiEiKUnGWCtP99H8w47AdCtrNh07S+WcRkWKoOEuF6j/4PWYXOv+8WOefRUT+RMVZKlRWdjZdHnieZeH55+Y6/ywi8icqzlLhmrfdgzXnDfjD+WeNvy0i8jsV53LSfc5lc9SZN/zh/HPLVz/js/eejzCRiEjqUHEuJ93nXHb9B7/HrF2C8bdr5MHa2+5k6cI5EacSEYmeirNEJis7m30eGc7i+kG72VKYcH5vNm/aFG0wEZGIqThLpJrtnEOVqy5hQ9WgvVtuHsOvOC7aUCIiEVNxlsgdePz5fNu7c0G7/Zi5jHn21ggTiYhES8VZUkL/W4cyvUstALK3QO1HXub76R9HnEpEJBoqzpIyjh4yhnlNDYD6qyH38nPYsH5dxKlERCqeirOkjNr1GtDsjntZXSNot5q3hdcvOCLaUCIiEVBxlpTSaf9jWHzm0WwJdqDp/MlyXr/nvGhDiYhUMBXnctIgJIl37MX38dWB2xW0d3ppPJPHDo0wkYhIxVJxLicNQpIcfR8e84cHZKy86WYNUCIilYaKs6SkqtWq0+VfL7G0XtDefglMPK+XBigRkUpBxVlSVvM2neHqiwoGKMmZtZHhl3SPNpSISAVQcZaUduAJF/Jdnz0L2h3HLeTNfw2KLpCISAVQcZaU1/emF/lq7+D4dhWHZs+8z5SxwyNOJSKSPCrOkhZ6D/mQ73cOflxr/QYrb7xBF4iJSMZScZa0UL1GTTo9+ELBBWLNlsLEc3WBmIhkJhVnSRvN2+4BV1/Eb/kXiH27kWEXHRltKBGRJFBxlrRy4AkX8n2/vQranT5axOgHLokwkYhI4qk4S9rpe8PzTNtnWyD4Ad7+2f9oBDERySgqzpKWjn9sLN+1CC8Q2wCrb7iZhT/mRpxKRCQxVJwlLVWvUZPOD71ccIFY01/hi/P66hGTIpIRVJzLSQ++iE7zNp2xay9lfbWg3WbOZt4YeGi0oUREEkDFuZz04ItoHdBrIPNOOZgtYbvTF6t49ZoTIs0kIlJeKs6S9npf+RjTD9++oL3bm9/w/pM3RphIRKR8VJwlI/T71/vMbF8dgKqbYdtHh/Hl+NcjTiUiUjYxF2cz2z2ZQUTKIys7m+5PjmHuDgZA3XWw/LprWTRvdsTJRETiF8+e8xQz+5+ZXWRm9ZOWSKSM6tbfjl0HP8mvdYN2s6Xw2XnHszFvQ7TBRETiFE9xvgGoAzwI/GxmQ82su5lZcqKJxK91x/3x/7uk4AruXX/YzMgzD4o2lIhInGIuzu5+m7u3AQ4GXgF6AO8CP5rZrWbWOkkZReJy4PHn8+PJha7gnryKoZceHWkmEZF4xH1BmLtPdPczgabAGcD3wLXAt2Y2zsxOMbMaCc4pEpfjr3qM6UfuVNDu+N4cXr/nvAgTiYjErsxXa7v7end/HjgHGAoYwV71c8ACM7vZzKolJqZI/E56aAzT96gNQBWHli+M58OX/xlxKhGRrStTcTazWmZ2hplNAGYB/YBRwHFAd2A8cD0wJFFBRcqi11Pj+bZ1NgDVN0LN+55i6sRREacSESldXMXZzA4ys2eARcBTQBPg/4Cd3P14d3/b3T9w9+OBe4HjE55YJA7Va9TkwKffYX7T4LrFemth+TXXMP/7GREnExEpWTz3OX8HjAP6A68Dh7h7W3e/x91/KeYtXwJ1ExNTpOwaNNmJlv964g8PyZh+3omsWbks2mAiIiWIZ895FXAxsL27n+ruE7ay/migZZmTiSRQm87dqHrTNazdJmi3nL+F908/VPdAi0hKiudWqj3c/VF3Xxnj+uvc/ceyRxNJrH17nMaSC05gY1bQbvdNHiPPPJDNmzZFG0xEpIh4DmvvZmYnl7L8ZDPLSUys5DGzV83sKzP70sw+N7PDo84kFafHwNv5tt8ehe6BXs2wi46MNJOISFHxHNa+DTillOV/A24pX5wKca67d3L33YFzgeFmpgeAVCJ9b3qJ6X/ZuaDd5aNFvHpV7+gCiYgUEU9R2hf4sJTlHwL7xfPhZrajmT1kZp+Y2TozczNrUcK6O5nZa2a20sxWmdlIM2sez+cBuPuKQs168b5fMsNJg99j2v4NCtod3pzFyDvOijCRiMjv4inODYHlpSxfCTSO8/N3Ibj6ezkwsaSVzKwmQfHPAU4j2INvA4wzs1pxfiZm9oCZ/QCMAPq4+5atvUcyT7/HxzOjc00gGKSk9Usf8/ajV0ecSkQkvuL8C9CplOWdgKVxfv4Ed2/i7kcDw0tZ7xygFdDb3d9w91FAT2BngkPTAJjZB2a2tISpW/567n6pu7ciOBR/j0Yyq5yysrPp+exEcttWBaDaZmj22GjGDb0/4mQiUtnFU5zfA84ys32KLjCzvYGzwnViFscea0/gU3f/rtB75wCTgF6F5h3h7o1KmCYV8/nvAfWBjvHklsxRvUZNjnz+I75vHvxXqJEHNe95go/ffibiZCJSmcVTnG8huNf5v+EVz9eF0zDgv+Gym5MREmgPFDek00ygXawbMbMaZtayUHs/gsP1P5QllJlNyZ/K8n5JDbXrNWDvZ0YXjCJWdx3YjffwxZhXIk4mIpVVdqwruvuCsJj9G+hLMJ42gAP/AS5y9/mJjwhAA4o/372MYM83VjWAl82sDrAJWEtwzrm0c+kxycvLIzc3t7ybyThLly5Nm36pce3tLLzlWpothW3XwLJ/3ML7K1axc6eDk/7Z6dRPUVNfxUb9FJtU7aeYizOAu/8AHGVmDQgu5gL4zt3TYhzEMGdcV5RvZXt75r/u2rWr5+Sk/G3eFS43N5d06ZecnBxmbdeQhRecS5Nl0GAVbLlvMJv+1ZwO+/ZI6menUz9FTX0VG/VTbFK1n8p0f6+7L3P3z8OpIgrzcorfQy5pj1qkTNp2OYjGD/yLJdsG7UYr4ddLLyN3Sml3EYqIJFbcxTl8XGQ7MzswfErVH6ZkhCQ4t9y+mPntgK+T9JlSSbXfpzvb3ncPv4aPbdluOSy8+EJmT/vTNYUiIkkRz/Cdtc3sCYLzvNOBjwieUpU/5beTYTSwr5m1KpSnBdAtXBYZMxtoZpOXLFkSZQxJsE7djqPGnbewvHbQbroM5l94Nt9P/zjaYCJSKcRzzvkhggFA3iIowgk5nG1mfcOX+edve5jZEmCJu48P5z0BXASMMrN/EFyEdiswHxiSiBxl5e6PA4937drVo8whibfn4f347Lb1rLzuTuqthWZLYd55Z7HpkSG07ZKsg0QiIvEV517Ai+5+aoIzFB185NHw63jgEAB3X2tmhwEPAC8ABowFBrn7mgTnESmwz19O5eO8Day86X7qrQueBb3wgnPxhx4hZ8/Doo4nIhkqnnPOVQnuZ04od7cSpkOKrDfP3fu4e113r+Puvd19bqLzxEuHtTPf/j3PgduvYUV4iLvJMvjloguZ8em70QYTkYwVT3GeRPEXZVVq7v64u3dt3DjeYcUlnezb4zSy77iBZXWC9nbLYfnfL2PqxFHRBhORjBRPcR4E9DWzXltbUSQT7dV9ADXvua3gKu5GK2HN5dcwZWxpw8KLiMQvnuL8KMGIWiPNbJ6ZjTezD4tMY5OUUyQl7H5oH2rfdxdLw4eNNlwFeVfdwMTX/x1tMBHJKPEU51YE553nAZuB5kDLIlOrEt8tkiG6HNiL+v+6n8XhsDjbroUaNz/ImGdvjTaYiGSMmIuzu7dw95Zbm5IZNhXpgrDKqcO+PWj67yEsCC81qPUbNL7vZd588LJog4lIRijT8J3yO10QVnm17XIQuz0/gh93CJ5mtc1G2HnIu4y49bSIk4lIuivL8J3tzWyQmd1pZq3DeduY2a5mViPxEUVS1w4t27H3y+/zXYvgv1LVzZDz8ucMu/r4iJOJSDqLqzib2SPAV8D9wFXAzuGibGAycEFC04mkgQZNduLQVyfyTduqAFRx6Dgql6EXHB5xMhFJV/GMrT0IOB8YDHQnGKULgHCUrjeAnglNJ5ImatdrwHHDv2BG598PHnX+8GdePXUfNuZtiDCZiKSjePaczwFec/fLgS+LWT4DaJOQVGlEF4RJvqrVqnPCS58zbb/fn27a6fNVvNl/b9asTItHnotIioinOLcmGM+6JL8SPF+5UtEFYVJYVnY2Jz3zMdOO3Klg3m65eYzvdyAL5ujppiISm3iK8xqgTinLWxMUaJFK76SHxjDzpD3ZmBW0W83bQu6pffjmiw+iDSYiaSHesbUHFLfAzOoCZxA801lEgL43vcj8i3qzrnrQ3n4JLLvgYj4e/US0wUQk5cVTnG8D2pvZu8AR4bzdzOw0giu16wF3JjifSFo75vw7WX/LpSwPjzk1WA3Vrr+fdx67NtpgIpLS4hkh7AugD9AFeDmc/SDwDLAt0MfdZyQ4n0jaO6DXQOo9/C8WNgratTbAjg+9zmu3JPrR6CKSKeK6z9nd3wZaAL2Aq4Frgb5AC3evlA+31dXaEov2+3Sn7QsjmLPT74OV7PbyFwy9uHvEyUQkFcU9Qpi7b3D3t9z9Xne/291Huvu6ZIRLB7paW2K1Q8t2HDBs3O+DlQCd/zOfV/+2N5s26l5oEfmdxtYWqUB162/HccO/4Ku96xbM6zRlNbOvPZkVvy6MMJmIpJJ4Rgj7IYbp+2SGFckEVatV58TnP2PaX3ZmSzgvZ/YmPul/OPNm/S/SbCKSGuLZc54H/Fhk+ongGc8tgE3hOiISg5MGv0fuKfuRlx20Wyxwvj/jb0ydOCraYCISuXiu1j7E3Q8tMh3k7jsBJwG1gQuTllQkA/W57mkWXTaA1eGQ3E2XwW+DrmHc0PujDSYikUrIOWd3Hwa8RvC0KhGJw1Fn3sDiy85mab2gXW8t1LvjCUYP/nu0wUQkMom8IGwG0C2B20sLupVKEmGXvY5huyFD+KlJ8LC3GnnQ8vExvHrNCREnE5EoJLI4HwDkJXB7aUG3UkmitO1yELsPfZvZLYMBubO3QKc3vmHoOQexedOmiNOJSEXKjnVFMytpOKP6wGHAscBziQglUlk1ataSI1/7mLdPP5j2038DoPPEJbw+YC+OeXY8NWrV3coWRCQTxFycgWcBB6yYZZsIhvG8NAGZRCq1GrXqcvwrXzDsgsPoMiE4XdJ++m980Hd/9nlyFNvt0DrihCKSbPEc1j6UYA/50ELTIUAnoIG7n+3uqxOeUKQSysrOZsDjE5h+fDs2hf9Ld5mzmWl/PY5ZUydEG05Eki6eW6nGFzNNcPcZ7r4mmSFFKqv+d45g7rlHsb5a0N7xF2fxuefy2XvPRxtMRJJKw3eKpLjj/j6YVdedy4paQbvRSrD/u5P3n7op0lwikjzxXBD2dBm27+5+VhneJyKFHHLiIL7asTWLrrqKpr9CnfVQ7YFXGb1qGT0vfTDqeCKSYPFcEHY6wQVh8OeLwkqbr+IskgCduh3HvGebM/O8AbRY4FTfBC2f+A8jVp9Knxt0mFskk8RzWLspMBUYCewHbBtO+wOvA18CTdy9SqEpK6FpU5AGIZGK1LxNZ/YbNpbZrX6/FzrnlS8YdvXxEScTkUSKpzg/ACx0937u/pm7rwqnT929L/BLuE6lokFIpKJt27AZh786iW9ygqvEqjh0HJXL0Iu7R5xMRBIlnuLcA3i7lOVvh+uISJLVqlOP44Z9zozONQrmdf7PfIaedYBGExPJAPEU52ygVSnLWxM8PlJEKkDVatU54aXPmbbPtgXzOk/6lRGn7sfGvA3RBRORcounOI8FLjKzP43Eb2Z9CB4XOTZRwURk67KysznpuU+YekjTgnkd/7eGN05RgRZJZ/EU578DS4DhZjbHzN4LpznAMGAxMCgJGUVkKwY8No6vjmnNlrDdYdp63vibCrRIuopnhLB5BEN13gusBw4Op/XhvC7u/mMyQorI1p1431vM6L3b7wV6+npG/W1fFWiRNBTXCGHuvsLdr3H3du5eI5zahfOWJSukiMTmxLtGMvP4dgUFuv303xj1VxVokXRT5uE7zay6mRX3hCoRiVD/O0cws0+H3wv0jN8YNWAfFWiRNBJXcTazNmY2zMxWAGsJnkyFmTU2s5fNbL8kZBSROPW/fTgz+3RkS/jnc/uZGxg9YB82rF8XbTARiUnMxdnM2gKfAd3DrwV7ze6+BMgBzk50QBEpm/63D+PrPp0KCnS7mRt485Ru2oMWSQPx7DnfTnDxV3vgb/x5HO33gG4JyiUiCdDvtleZ2bfz73vQM37j9dO6aaASkRQXT3E+FHjU3Rfw+4MuCvsR2D4hqUQkYfrfOpSZJ3QsOAfd8cu1DD/noEgziUjp4inONQnuZS5teaW7QEwPvpB00P/2Ycw4pnVBu/Mnyxl67iHRBRKRUsVTnH8AupSy/GBgVrnSpCE9+ELSxYn3vcXUI3YoaHce/wtDLzkqwkQiUpJ4ivMrwOlmdkCheQ5gZhcAxwEvJDCbiCTYgIc/YNoBjQrancfM49WrekcXSESKFU9xvgf4HBgHjCEozHeb2Q/AQ8CHwMMJTygiCdXvsXF8tVfdgnaH0bMYccupESYSkaLiGb4zDzgSuIqgMP8GdATWANcAR7v75mSEFJHEycrOpu8zk5jRuSYQ/BJo8+oXvP3o1dEGE5ECMRXncDSwg4CW7v6Au3d191rh8J2d3P1ed9+Y5KwikiBZ2dn0fuFjvmkbPOW16mZo+thoPnp1cLTBRASIfc95M8HjIP+SxCwiUoGqVqtO9+c/4vvmwa+BmnmwzT1DmDJ2eMTJRCSm4uzum4AFQLXkxhGRilS7XgO6PvkGPzUJ7oKstxbWXncDs6dNijiZSOUWzwVhLwB/M7OqyQojIhWvafM2tHjwCZZsG7Qbr4C5l5zDonmzo4wlUqnFU5wnhOv/z8wuNLO/mNlBRack5RSRJGrTuRt17ryNlbWC9o6/OFPO7s3a1SujDSZSSWXHse77hV4/xJ+H8LRwXlZ5Q4lIxdv90D58dNV8qt4+hJp50GreFt49/WCOf3UyWdnx/KoQkfKK53/cmRQ/praIZIhDThzEW0sXsPMjb5G9JXjU5LALDmPA4xOijiZSqZRYnM3sVGCCu88FcPdnKyiTiETo2AvvZdiCOXQcOROALhOWMPyGAfS75ZWIk4lUHqWdc34G2D+/YWabzeyvyY8kIlHrf8drTOvWsKDddsRU3n38uggTiVQupRXnNUDdQu1K98Qpkcqs35CP+Hq34O7Jqpuh0aMj+ey95yNOJVI5lHbOeSpwlZlVA1aE8w40s1LPU7t7WvzvNbMzgKeB4939jYjjiKScrOxsjnp2HBP6HEjLn7ZQ+zdYctOdfL/DLrTuuP/WNyAiZVZaoR0EjAQGh20Hzg2nkjiQ8sXZzFoA5wCfRhxFJKXVrteADv9+mR9OO4kmy4J7oGf//Wwaj/iIuvW3izqeSMYq8bC2u38J7ALkAIcQHNa+HTi0lOmweD7czHY0s4fM7BMzW2dmHhbO4tbdycxeM7OVZrbKzEaaWfN4Pi/cThXgSeBiYEO87xepbJq36Uy9229jVfCcDHb+2Rlzdnc2b9oUbTCRDFbqICTuvtndv3X3CcB44CN3H1/aFOfn7wL0B5YDE0taycxqEjySMgc4DTgFaAOMM7NacX7mZcAkd58S5/tEKq3dD+3DiosGsDEcxaD9zA0MH9Qj2lAiGSyeR0Ye6u5jE/z5E9y9ibsfDZQ22v45QCugt7u/4e6jgJ7AzhQ6zG5mH5jZ0hKmbmbWAegD3Jbg70Mk4x115g3k9mxX0O449idG3XdhhIlEMlc8w3cmnLtviXHVnsCn7v5doffOASYBvQrNO8LdG5UwTQIOBFoAs81sLrAv8LiZXZSgb0kko/W/cwRfdQ1u4qjisONzH/Lx289EnEok80RanOPQHphRzPyZQLti5hfL3f/t7s3cvYW7tyC4IGyguz9cllBmNiV/Ksv7RdJR7yfG8V3L4Ph2zTzYdOs9zJv1v4hTiWSWdBkwtwHBeemilgH1KzhLsfLy8sjNzY06RspZunSp+iUG6dZPDa++h0XXXk7T8Arury4+hRX3PE+1beK9BCR+6dZXUVE/xSZV+yldinNSuPsh5Xz/nvmvu3bt6jk5OeXOlGlyc3NRv2xd2vVTTg5f3LSStVfdQq3foPW8LUy/+1z6vzI56R+ddn0VEfVTbFK1n9LlsPZyit9DLmmPWkSSbK/uA1h09jFsDscO7PjlWoZdfXy0oUQyRMzF2cx+MLOepSw/1sx+SEysP5lJcN65qHbA10n6TBHZimMv+icz/tKyoN32rVzGvnRPhIlEMkM8e84tgNqlLK9FcGtTMowG9jWzVvkzwsFKuoXLImNmA81s8pIlS6KMIRKZfveOZmaHbQCothm2GfwM30//OOJUIuktkYe1dyJ4WEZczKyvmfUF8s/f9gjnHVxotSeAucAoM+sV7sGPAuYDQ8oXu3zc/XF379q4ceMoY4hEJis7myOGvMNPTYLj2w1WQ+7l57B+7aqIk4mkr1IvCDOzXhS6jxgYaGZHFLNqfeAIyjZWddHBRx4Nv44nGDYUd19rZocBDwAvEAwlOhYY5O5x/0EgIom1bcNmNLnjblZfdBV11kOreVsYff6RnPj8Z1FHE0lLW7tauwtwevjagYPCqag1BIU57uGC3D2mR1G6+zyC0b1EJAV16nYcb535EbUefYcqDp0+X8WIW06lzw0p/ywckZSztbG1b3b3Ku5ehWBv9eT8dpGprrsf6e7fVkzs1KFzziK/O/bi+5h+aLOCdsvXvuDj0U9EmEgkPcVzzrkl8HqygqQrnXMW+aN+D45hVpvgoFyNPNh45/0s/DH1BnkQSWXxFOc8oGtJC83sQDNrWv5IIpLOsrKz2feRkSxqGLS3Ww6fXtJfj5gUiUM8xfnucCrJneEkIpVc0+ZtqPGPa1hfLWjnzNrI8Kt6lf4mESkQT3E+GHi7lOXvEF5dXZnonLNI8fbtcRrfH797Qbvd+z8wbuj9ESYSSR/xFOcmwC+lLF8MVLrD2jrnLFKyfje/zIzONQCouhmyBj+h888iMYinOC8Ddi1leVtAow6IyB8c+ejb/Bz+7dp4BXx6kc4/i2xNPMX5I+CccNjMPwjnnROuIyJSYNuGzahz/XW/n3+evZHhV5Y4TL+IEF9xvhnIAqaZ2d1m9rdwugeYGi67OQkZRSTN7d39ZH44YY+Cdrsxc/jwlfsiTCSS2mIuzu4+CzgK+Bm4EnieYCjNK8J53d290j0hSheEicSm700v/eH8c9XBT+r8s0gJ4nrwhbt/4u67ETykYgBwErCHu7dz90+SETDV6YIwkdgd+ejbLAj/qzRaCZ8MOjHaQCIpqkxPpXL3L919WDhNTXAmEclQ2zZsRt3rr+O3qkF7t2/yGP4PFWiRohL5yEgRka3au/vJfHvMbgXt1qO/YsrYog+nE6nc4irOZnawmb1rZkvNbJOZbS4y6f4IEdmqvrcNI3fXYPe5Rh4sve1GPf9ZpJCYi7OZHQl8AOwBfBK+dxyQ/8DWmQQXiImIlCorO5s973uBZXWDdvOFzqiLe0QbSiSFxLPnfB0wD9gNOCOcd4e7708wbGdzgiu4KxVdrS1SNs3bdGbV2SewJXyie8dPlvHeE9dHG0okRcRTnPcAnnT3ZcCWwu9394nA08CtiY2X+nS1tkjZ9Rh4O9P3bQBAFYc6T7zG/O9nRJxKJHrxFOcqQP7u4frwa/1Cy78GOicilIhUHsc9+A7zmgW7zw1WweTL/qrhPaXSi6c4zwd2BnD39cAiYP9Cy7sAaxOWTEQqhVp16tHoHzf/4fGSI67X7VVSucVTnMcDxxRqvwZcZGZPmtkzwLnA+4kMJyKVw56H9+O74zoWtHd5+2u+HDciwkQi0YqnOD8ADDGzbcL2dcAYgovDTiV46MUVCU0nIpVG/9uH8U1OsPtcIw8W3XY9G9aviziVSDTiGlvb3Ye4+29he7W7HwM0AOq5+5HurkuWRaTMut77PMvrBK9bLHBev/zYaAOJRCSe+5xvMLMORee7+0p3X2Nm7c3shsTGS326lUokcZq36cyyU48uaLcbv5AJrz0cYSKRaMRzWPsmoFMpyzsAN5YrTRrSrVQiiXXsxfcxffdaQPD0qk2DH2HV8sURpxKpWIkcW7smoPsfRKTcjnxwFL8Etz/TbCm8e8lx0QYSqWClFmcza25mB5nZQeGsnPx2kakXwdXaPyQ9sYhkvPqNd2DLRWexKfwN1eGLVbzz2LXRhhKpQNlbWX4GwaFqD6frwqkoIxg17OyEphORSuuwv17B0HGj6TxxCVWAuk+/zsIep0YdS6RCbK04vwHMJSi+TwOPEzz0ojAH1gCT3X1egvOJSCXWa/BbTDh2X5ovdBqugkmXnUSH24dGHUsk6Uotzu4+DZgGYGY7AyPcXQPfikiFqFGrLvX/71o2XH471TdC+5kbmPLSLeTc+nLU0USSKp77nG9WYRaRirZ395PJPbJVQbvNW18ya+qECBOJJN/WDmv/gZkZcCSwC9CQ4HB3Ye7ule7JVCKSXP3uGcU7X3dml7lbqLMeZl17AbuMnkpWdly/wkTSRsw/2WaWQ3AOug1/Lsr5nEr22EgzGwgMbN68edRRRDJWVnY2bW5/iNVnXUjt36DND5t57f/6cOK9o6KOJpIU8dzn/DDBU6muBPYEWhYztSrx3RlKg5CIVIycPQ9j3gl7FbTbvP+tHo4hGSue4rw/cL+73+/uX7r7j8VNyQoqItLnhuf5OqcqEDwcY+Ht17Mxb0PEqUQSL57ivJbgmc4iIpFpcvFtLK8dvG75kzPico0eJpknnuL8OsHFYCIikWm0w64s/dvvv4p2GzefT999LsJEIokXT3G+EtjBzB4ws1bhldsiIhWu56UPMqNTDQCqbYKVd9/N+rWrIk4lkjjxFOflwF7AJcBsYJOZbS4y6cEXIlIhDvznqyytF7xuvsgZdVnPaAOJJFA8Nwk+T3CrlIhI5Jo2b8OU03vT4F9vUAVoP/EXJrz2MAf1vSjqaCLlFnNxdvfTk5hDRCRux5x/J6/+9wM6TVlD9hbY+K9HWHPkX6ldr0HU0UTKJZHPcxYRqXDdB79R8Ozn7ZfAW4N09bakv7iLs5kdbmYPmdnb4fSQmR2ejHAiIltTv/EObDrvFLaEl6h2+HQZH7xwV7ShRMop5uJsZllm9gowBrgQODycLgTGmNnLZqY9cRGpcEecei3T960PQJZD1r+fY/mSBRGnEim7eIrpVcCJwItADlAjnNoCL4TLrkx0QBGRWBw7+C1+DkfRbboMxlx6fLSBRMohnuJ8KvCWu5/m7t/672aHF4u9A5yejJCpzMwGmtnkJUuWRB1FpFKrXa8BWZdcwKbwt1qHyat59/Hrog0lUkbxFOeWwLulLH83XKdS0YMvRFLHIf0uZsYB2wHBL7faT41k8YLvow0lUgbxFOdVBE+lKknzcB0Rkcj0fuBN5jcNrg5rtBLGX9Yv4kQi8YunOH8AXGhmBxRdYGbdgIuA/yQqmIhIWdSoVZfaV15JXjiKQ4dp6xk9+O/RhhKJUzzF+TpgAzDezCaa2ZBwmghMANYD/0hGSBGReOx/zBl8c8iOBe2GL41h4Y+5ESYSiU/Mxdnd5wBdgWFAZ+CccOoMvArsFa4jIhK5Pve/xdwdgsPbDVbDf6/6a8SJRGIX133J7j7X3QcA2wLNwmlbd/+ru89NfDwRkbKpWq06Da++9g+Ht99+9OpoQ4nEqEyDhrj7Fnf/JZy2JDqUiEgi7N39ZL45ePuCdt3nRrN0oQ7wSeqLZ4SwM81sZCnLR5jZqYmJJSKSGMf/849Xb4+9on/EiUS2Lp4953OB0kba+AU4v3xxREQSq3qNmtS8dBAbs4J2hylreP+pmyLNJLI18RTnXYFppSyfHq4jIpJSDug1kJndgoGCqgDVn3qVFb8ujDaUSCniKc7VCMbSLknNrSwXEYlMz/veZEE4kF+TZfDeZSdEG0ikFPEU51zg6FKW9wBmly+OiEhy1KpTj+yLzv197O3PVzD2pXuiDSVSgniK87PAoeHzm+vmzzSzumb2L+BQ4JkE5xMRSZhDThzEzH0aAMGjJe3fz7Bm5bKIU4n8WTzF+WFgBMHzm5ea2Wwzm01wkdjFwBvAgwlPKCKSQEff/zqLGgavmy2Fty7rFW0gkWLEM0KYu3s/4G/Ae8DGcHoX+Ku799E9zyKS6urW347N557CluDuKtp/spQJrz0cbSiRIuIehMTdX3H3nu7eLpx6u/vQZIRLBjP7yMzmmNnUcLoh6kwiUrGOOPVaZnQNzs5lb4ENDz3K+rV6qJ6kjjKNEJYBLnX3LuF0S9RhRKTidb9/JIvrB693/MUZdVnPaAOJFBJpcTazHcMLzD4xs3Vm5mbWooR1dzKz18xspZmtMrORZta8giOLSIao33gH1p/Zl/xzce3++wv/HfV4pJlE8kW957wL0B9YDkwsaSUzqwl8COQApwGnAG2AcWZWqwyfe5eZTQ+LfdsyvF9EMsBfzrmVmXvUBqDqZlh3/2Ad3paUEHVxnuDuTdz9aGB4KeudA7QCerv7G+4+CugJ7EwwrCgAZvaBmS0tYeoWrnaqu+cAnYB3gDFmlpWU705EUt5h9w1jybbB651+cd64XIe3JXqRFuc4ru7uCXzq7t8Veu8cYBLQq9C8I9y9UQnTpHCdeeFXd/engdoERV5EKqFGzVqy9swTCg5vt5+ow9sSvaj3nGPVHphRzPyZQLtYN2Jm25hZo0Lto4HNwPyyhDKzKflTWd4vIqmhx8Dbmbl7cIZMh7clFWSXttDMqgBXAQvd/blS1jsd2M7dkzUWXgOC89JFLQPqx7GdusC7ZlYN2BJu81h331jegHl5eeTm5pZ3Mxln6dKl6pcYqJ9il6y+anHRvSy5/AIarwgOb4/4+zF0veKJhH9ORdHPVGxStZ9KLc7AScDtwAFbWe9b4Ckz+8HdX0tIsiRw98XAngncXsG2unbt6jk5OYnadMbIzc1F/bJ16qfYJa+vcnj3zBNoeP9IqgCdPlnKsm8nsn/Pc5LwWcmnn6nYpGo/be2w9gBgnLt/UtpK7v4x8AHBVdTJsJzi95BL2qMWEYlb0cPba+57QIe3JRJbK85dgfdj3NZ/gL3LF6dEMwnOOxfVDvg6SZ8ZEzMbaGaTlyxZEmUMEUmQw+4fXuTqbY29LRVva8W5AcGDLWKxNFw/GUYD+5pZq/wZ4WAl3cJlkXH3x929a+PGjaOMISIJ0qhZS9acfnxBu/3ERXw8On3PPUt62lpxXg1sF+O2Gofrx8XM+ppZX34/F9wjnHdwodWeAOYCo8ysl5n1BEYRXGU9JN7PFBEpzdHn3cH0Ioe3165eGXEqqUy2VpynA0fHuK2jKf52p60ZHk7nhe1Hw/bN+Su4+1rgMIILz14AXgLmAIe5+5oyfKaISKmKHt5+8++x/ioUKb+tFedhwIFmdmZpK4W3Uh0ExP10Kne3EqZDiqw3L3wsZV13rxM+DWtuvJ+XaDrnLJKZGjVryfqz+xc8WrLDJ8sY8+yt0YaSSmNrxflJYBrwhJk9a2YHmVk9C9QN28+G600Fnkpu3NSjc84imeuos29m+r7BjSJZDts89jKLF3wfcSqpDEotzuHgHEcDnwKnAuMIBv7YRHAL07hw/mfAMYkYzENEJJUc9+C7/NQk2H1uvAImDOobbSCpFLY6fKe7L3L3bsAJwIvAl8D34deXwvkHuPuiZAYVEYlCrTr1qHXVlWwIh2xqP/03Xr9rYLShJOPFPLZ2+DSo09y9q7vvGn49NZzvyQyZynTOWSTz7X/MGeQe0aKgvf2wicyaOiG6QJLx0uXBFylL55xFKod+/3yT71oEvzLrroNZ/3cBmzdtijiVZKqtPfjigng36O6Plj2OiEhqysrOps3tD7Hq7Aupsx7azNnM8Ct7ctID70QdTTLQ1h588XCc23OC+5RFRDJOzp6HMaLvPrR74TMAdhszh49eHcwhJw6KNphknK0V50MrJIWISJroc92zDJ+2Bx2+Wk+1zWCDh7D4gOPYbofWUUeTDFJqcXb38RUVJF2Z2UBgYPPmzaOOIiIV5IhH3uTL44+g2VLYbjlMvLgPfUZOjTqWZBBdEFZOuiBMpPKp33gHalxzBRuqBu12X29g2LW6/1kSR8VZRKQM9jv2LGYdk1PQbvPmTD5997kIE0kmUXEWESmjvrcN55ucagBssxHW3X4XSxfOiTiVZAIVZxGRMsrKzmb/B19jcTD8Ns2WwsTzeun+Zyk3FWcRkXJo2rwNVa66pOD8c86sjQwb9JdoQ0naU3EuJw3fKSIHHn8+3/XZo6DdcewC3nrkyggTSbpTcS4nXa0tIgB9b3qJr7rWAYLHSzZ+6i2mThwVcSpJVyrOIiIJ0nPIB8zZ6ffxt5dfcw0L5nwdcSpJRyrOIiIJUqNWXdre/wRL6wXtpr/Cl+f2Y+3qldEGk7Sj4iwikkCtO+5P9vVXsLZ62J63hXfPOERXcEtcVJxFRBJsv2PPYtHAY9kU/oZtP+M3hp97SKSZJL2oOIuIJMGxF97LN73aFbQ7T/qVVy46IsJEkk5UnMtJt1KJSEn63zmCqYc0LWh3+WABQ684LsJEki5UnMtJt1KJSGkGPDaOaftuW9Du/NZ3DB3UI7pAkhZUnEVEkqzfkxOZvnutgnbn9+byysCDdZGYlEjFWUQkybKys+nzwqcFg5QAdJmwmNdO358N69dFmExSlYqziEgFyMrOpu+zHzPtgEYF8zpNXs37ffZm0bzZESaTVKTiLCJSQbKysznpyYlMPWpntoTz2vywmW8G9GTK2OGRZpPUouIsIlLBBvzrPWafdTDrg0dB0/RX8MtuYMStp0UbTFKGirOISAR6X/kYv912WcFQn7U2QLuXPmd4/z1Y9sv8aMNJ5FScRUQisn/Pc9jp2Rf4tnVWwbwOX61n2gndGfvSPREmk6ipOJeTBiERkfJosVtXjh01lWl/aUFeWKOb/gpNbnuGoaftx4pfF0YbUCKh4lxOGoRERMorKzubkwa/y8qbL2RheDF3lkPnz1bw5XGHMebZW6MNKBVOxVlEJEUc1Pciur45nmn7NWCzBfOaLoMd7n6ZV0/eR3vRlYiKs4hICqlbfztOemYSS248h5/DA3JVHDpNXsWXxx3GBy/cFW1AqRAqziIiKejQky5j33c+ZdoBjQoePdl0GTS94zmGnr4fq5YvjjagJJWKs4hIiqpVpx4nPTmRX2++oGAvOsuh86crmHzcwYwben+0ASVpVJxFRFLcIf0uZp+3Jv3hXHSzpdDolicYeslReoBGBlJxFhFJA7XrNeCkZyax6NrTWNQgmJe9BTqPmcebvXdn3uxp0QaUhFJxFhFJI0eccg27v/kh07v8/gjKtt9tYt7fTtLAJRlExVlEJM1s27AZ/YdO5uu/7sW6cHzuhqug0R3PMOy6ftGGk4RQcRYRSVN9bngeHriFn5oEJ6KrbYaOI2bw6t/2Iu+3tRGnk/JQcRYRSWN7Ht6PvUaO5et21QvmdZqyhvlXnsrcbyZHmEzKQ8VZRCTNbduwGb2HTWbakTsVXM3dav4W5p1xCp+PeTHacFImKs7lpAdfiEgqyMrO5qSHxjD3wmNYXSOY13gFcPXtvPfE9VFGkzJQcS4nPfhCRFLJsRf9k6x/3sIv9YN2nfWw/eDXGH7jX6MNJnFRcRYRyTB7Ht6PrFvvYs6OwTHuqpuhw6tfMvTcQzRgSZpQcRYRyUCNd2zLAcM/4pvdqhXM6zz+F14/aS/Wrl4ZYTKJhYqziEiGqlt/O3oNn8K0/RsUzGs/4zfG9u/Gsl/mR5hMtkbFWUQkg2VlZ3PS05OYfny7gqdbtZmzmc//ehTzv58RbTgpkYqziEgl0P/OEcw550g2VA3aOy9wvj29H7O+/CjSXFI8FWcRkUqi56UPsvjyv7Jmm6C9/RJYfN75TB47NNpg8icqziIilUj3069n4y2Xsbx20G60EjZddTOfvPVUtMHkD1ScRUQqmf17nkPNB+5icXgvdL21YDf8k49HPxFtMCmg4iwiUgl1ObAX2z/2JAsbBe166yDrpvv576jHow0mgIqziEil1aZzN3b+91P8HA5wWHcdVL35ASa+/u9og4mKs4hIZda64/60HPIcCwoV6Oq3PMjEkY9EG6ySU3EWEankWrXbm10ef4EF2wXtOuuh2m0P89l7z0cbrBJTcRYREVrs1pVdn3iJn8ICXXcdbLr+TqZOHBVtsEpKxVlERABo3nYPWj/2HIsaBu0Gq2HVldeQO+XDaINVQpWuOJtZNTMbbGazzWy6mY2OOpOISKpo1W5vmg5+iCXbBu3GK2DhJRcy95vJUcaqdCpdcQbuAKoBbd29IzAw4jwiIillt72OoM7ddxQMVNL0V5h93qks/DE32mCVSKTF2cx2NLOHzOwTM1tnZm5mLUpYdycze83MVprZKjMbaWbN4/y8mgTF+Bp33wLg7ovK/Y2IiGSY3Q8+Hm6+ilU1g/aOvzhTzzxBT7OqIFHvOe8C9AeWAxNLWiksqh8COcBpwClAG2CcmdWK8/OWA9eY2RdmNsnMji1reBGRTLb/MWew/upzWVs9aLdY4Hx86l9YtXxxtMEqgaiL8wR3b+LuRwPDS1nvHKAV0Nvd33D3UUBPYGfg3PyVzOwDM1tawtQNyAaaA9+5+17AWcDTZtYqWd+giEg6O+TEQfz69wH8Fj7NqvWPWxh38uGsXb0y2mAZLtLinH9oOQY9gU/d/btC750DTAJ6FZp3hLs3KmGaBMwDHHgxXD8XmAbskaBvSUQk4xx15g0sOO9Y8rKD9q7fb+L9kw9kw/p10QbLYFHvOceqPVDcU8FnAu1i3Yi7LwXeB/4CYGbNgI7A9LKEMrMp+VNZ3i8iki6OvfBe5px+KJvCqrHbrI28eUo3NuZtiDZYhsqOOkCMGhCcKy5qGVA/zm2dDzxlZrcT7EVf7u6zypmPvLw8cnN1JWNRS5cuVb/EQP0UO/VVbJLRTznHXsLk5b+y+8ivqOLQfsZvjDx1fzr+4zmqZKdLOfmjVP15Ss/eLAd3nwscnqBt7Zn/umvXrp6Tk5OIzWaU3Nxc1C9bp36KnfoqNsnqp5zbX2UY/Wk/YjpVgE5T1zHt3nM46blPEv5ZFSFVf57S5bD2corfQy5pj1pERJKk/+3DmHFM64J2589W8MrAgyJMlHnSpTjPJDjvXFQ74OsKzvIHZjbQzCYvWbIkyhgiIhXqxPveYtoROxa0u0xYwtCLu0eYKLOkS3EeDexb+JancLCSbuGyyLj74+7etXHjxlHGEBGpcCc9/B+mHvj7777O/5nPK5cfF2GizBF5cTazvmbWF8g/f9sjnHdwodWeAOYCo8ysl5n1BEYB84EhFRpYREQK9P/3h0zbp15Bu/Pbs/nypr9HmCgzRF6cCQYfGQ6cF7YfDds356/g7muBw4BvgReAl4A5wGHuvqZC04qISIGs7Gz6PfVfZuweDMRtGNu8+j7T7rk24mTpLfLi7O5WwnRIkfXmuXsfd6/r7nXcvXd45XWkdM5ZRCq7rOxsTnj+Y/JywmdNulHt2ZF89eBt0QZLY5EX53Snc84iIpBVtSrtXx3Lpl3qBjO2GNWGvMiMpx6INliaUnEWEZGEyK5enbavjmVz8+BRVr7ZyH5gCN+8pEuD4qXiLCIiCVOtVm12eW0sW3YIHmXlmwy76wFmv/5SxMnSi4pzOemcs4jIH21Td1tavPofvEkwCKVvNDbfeAs/vP9GtMHSiIpzOemcs4jIn9Vq1Jgdh74LjbIA8LwqbLzmGhZ++VnEydKDirOIiCRF3WY70vTlN7H6BsCW9cbK805nxU8/Rpws9ak4i4hI0tRv3pL6j7+I1XQAfCX8fPJx/LZqRbTBUpyKs4iIJFWTjntQ/e57sWpbALBFG5k94Cg2b9wYcbLUpeJcTrogTERk61oeeRx+5SCsSrAHnf39Kr46Q+Nwl0TFuZx0QZiISGx2O+V8fjvteCAo0NtM/pEvr7842lApSsVZREQqTJer72T9kbsXtLcZ8R++GfpkhIlSk4qziIhUqC6DX2Rj2wZBY4thd/1Tt1gVoeIsIiIVqkpWFru+8DY0Du+B/s1YceEZrF2qa3fyqTiLiEiF26butjQc8nLBLVYsc3445Wi2bN4cbbAUoeJcTrpaW0SkbLZr14msm27CssIruOesYerFf404VWpQcS4nXa0tIlJ2bXqexG+nHl/QrjFuGl8/+3CEiVKDirOIiESqy9V3smHPnYKGG1mDH2bxzKmRZoqairOIiESu/ZNv4NsFT7Ha8pux9IJT2bh+XcSpoqPiLCIikataoyYNH3kO2yY4/2y/bGTGwD4Rp4qOirOIiKSEJh33YPPF54OFI4h9MZev7r8x4lTRUHEWEZGU0f6sv7P+4A4F7WrPDq2UA5SoOJeTbqUSEUmszg+9wpYdtwHA86qwfNA5bNqwIeJUFUvFuZx0K5WISGJlVa1Kk0dfpEqh88/TK9n9zyrOIiKSchrt2p6N551NwROsJs4kd+hT0YaqQCrOIiKSkjqcdwUb9tw5aLjBvfeycsH8aENVEBVnERFJWbsNeQ0aBKXK1xrzzu0XcaKKoeIsIiIpq3rtOtS88wEsOxx/+7uVfHnjJRGnSj4VZxERSWk7H9yddb0PL2jXGDGG+R9/FF2gCqDiLCIiKa/LzQ+yqXUdAHyTsebqi9j42/qIUyWPirOIiKS8KllZ7Pjoq78//3nJZqZfPCDaUEmk4iwiImmh/s4t2XLxheTfXlXjv7l8M/TJaEMliYpzOWmEMBGRitPujIv5rWtLALK32UKt/97NqhW/Rpwq8VScy0kjhImIVKz2jw3D2lelVY/FNG+0mG+fHhh1pIRTcRYRkbRSrXYdat/9MhuqVgOg66oPmDz6sYhTJZaKs4iIpJ0dd+nAjC7/KGi3nXITP8+dFWGixFJxFhGRtLRXr4v4X+2DAahj61n50uls2pgXcarEUHEWEZG0ZFWq0PqMJ/iFhgDstvFrvnjx+ohTJYaKs4iIpK16DZuw9MiH2OIGwF5zHyd38tiIU5WfirOIiKS19t2O4bMdTgEg27ZQ5+3zWb1yWcSpykfFWURE0t6ep93L7KxdANjBfyH36fMjTlQ+Ks4iIpL2qlXfhm1Oepp1Xh2AvVa+x5S303f0MBVnERHJCDu16cyMTv9X0G7zxfUsmjc7wkRlp+IsIiIZY6/j/86XtQ4AoC7rWPbiGWzetCniVPFTcRYRkYxhVarQ8oynWEwDANrlTeeLF2+IOFX8VJzLSQ++EBFJLds2asriwwcXtLvO+TczJ70dXaAyUHEuJz34QkQk9XQ4sBefNDsZCG6vavqf8/nlp+8jThU7FWcREclIe535ADOrdQKgIStZ8ewANvy2LuJUsVFxFhGRjJRdtRpNz3ql4Pxz202zmPpEetz/rOIsIiIZq2GTHVl+7FPkeTYA+/z6Bp8PuyfiVFun4iwiIhmtbdfDmNrh9/uf95x5B9PHvhxhoq1TcRYRkYy3V5/L+KRxPwCyzGkz4RLmfjku4lQlU3EWEZGMZ1WqsNe5j/FFzYMA2MY2suN7p1N9+bcRJyueirOIiFQK2dnZtLvwFb6rEVzBnb1hBc3HXQgL/hdxsj9TcRYRkUqjVq3a7HLJaNh+dwCy8lbBcz3h2/cjTvZHKs4iIlK51KgPp46CHfcO2nmr4eUTYeL9sGVLtNlCKs4iIlL5bFMPThnJ6u0PDGc4jL0ZnukBS7+LNBqoOIuISGVVvQ4LDrwHDrjs93nzP4V/7wdvDoLlP0YWTcVZREQqL6sCR9wIp7wO9ZoH8zbnwZRn4MEu8Nxx8MVTsGQWbNlcYbGyK+yTREREUlXrw+CCj2H8PfDFk7BxHfgWmDMhmACq1oLGu0K9neCgK6BZ56TFqVR7zmaWZWZTC00zzczNrFPU2UREJGLV60D3W2HQdDjwiqAIF7ZxLfz8JXwzGjZtSGqUSrXn7O6bgS75bTMbAFzj7l9FFkpERFJLrUZw+PVw2D9gwRSY/R9YOBUWToPVC4N1tm2e1AiRFmcz2xG4GugKdAZqAC3dfW4x6+4EPAAcCRjwATDI3eeVI8LZwJPleL+IiGQqM9ixazDl27geVv4EtbZL6kdHfVh7F6A/sByYWNJKZlYT+BDIAU4DTgHaAOPMrFZZPtjMWgP7AS+W5f0iIlIJVa0BjdpAleSWz6gPa09w9yYAZnY20L2E9c4BWgFt3f27cP2vgNnAucD94bwPKHTYuohe7j6pUPssYIS7Ly/vNyEiIpJIkRZnd491KJaewKf5hTl87xwzmwT0IizO7n5ELBszsyyCPfC/xpdYREQk+aI+rB2r9sCMYubPBNqVYXvHAGvcfXx5QpnZlPypPNsREREpLOrD2rFqQHBeuqhlQP0ybO9s4KlyJSoiLy+P3NzcRG4yIyxdulT9EgP1U+zUV7FRP8UmVfspXYpzQrl7zwRtZ8/81127dvWcnJxEbDaj5Obmon7ZOvVT7NRXsVE/xSZV+yldDmsvp/g95JL2qEVERNJWuhTnmQTnnYtqB3xdwVn+wMwGmtnkJUuWRBlDREQySLoU59HAvmbWKn+GmbUAuoXLIuPuj7t718aNG0cZQ0REMkjk55zNrG/4Mv/8bQ8zWwIsKXQ19RPARcAoM/sH4MCtwHxgSEXmFRERSbbIizMwvEj70fDreOAQAHdfa2aHEQzf+QLB8J1jCYbvXFNBOUVERCpE5MXZ3S3G9eYBfZIcJ25mNhAY2Lx5cgdBFxGRyiNdzjmnLJ1zFhGRRFNxFhERSTEqziIiIilGxbmcdJ+ziIgkmopzOemcs4iIJJqKs4iISIpRcRYREUkx5u5RZ8gI4ahmPyZgU42ApUl6T2nrlbSsuPlF55XU3i1sfxNDtrJIVl+pn1KznyC5fZVu/VR0Xib3U0nLyzqvIv7vxfI97+zuxZ8TdXdNKTQBk5P1ntLWK2lZcfOLziupDUwBpqRbX6mfUrOfkt1X6dZPxfRNxvZTWfukpHkV8X+vLP1UeNJh7dTzeBLfU9p6JS0rbn7ReVtrJ0uy+kr9pH5K5HuS1U9F52VyP5W0vKzzKqKvyvUZOqwtSWNmUwDcfc+trVuZqZ9ip76KjfopNqncTyrOIiIiKUaHtUVERFKMirOIiEiKUXEWERFJMSrOIiIiKUbFWUREJMWoOIuIiKQYFWcREZEUo+IsIiKSYlScRUREUoyKs4iISIpRcRYREUkxKs6SEszsDDNzM+sddZZUZGYfmdkcM5saTjdEnSkVmVk1MxtsZrPNbLqZjY46U6oxs6xCP0dTzWxm+H+vU9TZUo2ZHW1m/yvUT+dV1GdnV9QHiZTEzFoA5wCfRhwl1V3q7m9EHSLF3QFUA9q6+xYzaxp1oFTj7puBLvltMxsAXOPuX0UWKgWZWRXgZeAgd//KzLYHZpvZaHf/Odmfrz1niYuZ7WhmD5nZJ2a2LvyLu0UJ6+5kZq+Z2UozW2VmI82seZF1qgBPAhcDG5L/HVSMRPdTpkpkP5lZTWAgQaHZAuDuiyrkG0myJP88nU3wfzDtJbifLPy6bfi1DrAaWJO0b6AQFWeJ1y5Af2A5MLGklcJflB8COcBpwClAG2CcmdUqtOplwCR3n5K0xNFIdD8B3BUeqn3NzNomJ3aFS2Q/7RJu5xoz+8LMJpnZsckMX4GS8fOEmbUG9gNeTELmKCSsn8IjDP2AEWb2IzAFOM/dVyX1O8jn7po0xTwBVQq9PhtwoEUx6/0d2AzsUmheS2ATcFnY7gB8AlQN2x8BvaP+HlOtn8J5zcOvBpwJ/AhkRf19plI/AXuE7z8zbOcAi4FWUX+fqdRPRda/A3gh6u8vFfuJ4LTvR8ChYbsDsDD//2KyJ+05S1w8PFwYg57Ap+7+XaH3zgEmAb3CWQcCLQjO48wF9gUeN7OLEhY4IgnuJ9x9XvjV3f1poDawc+ISRyPB/TSP4Jfxi+HyXGAaQdFOa4n+eYLgwjCCvcaMOKQNCe+nLsD27j4uXD4DmAHsk7DApVBxlmRpT/CDXNRMoB2Au//b3Zu5ewt3b0FwQdhAd3+44mJGbqv9ZGbbmFmj/AVmdjTBX/3zKyRhaojl52kp8D7wFwAzawZ0BKZXUMZUsNV+KuQYYI27j096qtQTSz/NB7Y3sw4QnM8GOoXrJJ2u1pZkaUBw3qeoZUD9Cs6SymLpp7rAu2ZWDdgSrn+su2+smIgpIdafp/OBp8zsdoK96MvdfVYF5EsV8fy/Oxt4KumJUtNW+8ndfzGzs4GXzcyBLOBad/+6IgKqOEvKcPdDos6Qitx9MbBn1DnSgbvPBQ6POkc6cPeeUWdIde4+FBgaxWfrsLYky3KK30Mu6S/Wykr9FBv1U2zUT7FJ+X5ScZZkmUlwXqeodkCFHBZKE+qn2KifYqN+ik3K95OKsyTLaGBfM2uVPyMcDKBbuEwC6qfYqJ9io36KTcr3k4X3b4nEzMz6hi8PB84DLgCWAEvyr/wMb+SfBqwH/kFwcc6tBKPsdHL3ChllJ0rqp9ion2KjfopNpvSTirPELbxysTjjC1/UFQ6F9wBwJMHgGWOBQeFFOxlP/RQb9VNs1E+xyZR+UnEWERFJMTrnLCIikmJUnEVERFKMirOIiEiKUXEWERFJMSrOIiIiKUbFWUREJMWoOIuIiKQYFWcRqVBmdoiZuZmdHnWWosxsrpl9FHUOERVnEUk4M9vWzG4ys0OiziKSjvQ8ZxFJhm2BG8PXHxVZNgGoAWyswDwiaUXFWURKZWZZQHV3X5eI7bn7FuC3RGxLJFPpsLZIBTCzmmZ2u5nNNrP1ZrbMzKaY2aAi61UxswvN7EszW2dmq8zsfTPbt8h6+edtzzCzy83sBzP7zcy+MrM+xXz+BWY21swWmlmemf1oZoPNrE4p2x1kZt8SFNL+4fKTzOwtM/sp3M7PZva0mTUtvA1gTti8Mdye55/LLemcs5ltZ2ZDzGxBuO05ZnZ3+AShwuvdFL6/bbj85/B7/8zM9o/jn6VEZra3mU0M/w0WmdkDZlajyDrPhjmamtlQM1thZqvNbKSZ7ZyIHFJ5ac9ZpGI8CvwNeIzgUXW1CB7sfjAwuNB6zwMnAa8ATwC1gbOB8WZ2pLtPKLLdS4D64bp5wFnAcDPr7+6vFVrvcmAS8C6wluC5tRcDnYFDi8k7iODxeU8By4BZ4fwLgMXAw+H83YEzgf3MrIu7bwC+AS4leOLP68DI8L2/lNQ5ZrYt8DHQAngcmB5mvAroZmaHuPumIm97Pvxe7gLqht/jW2bW0t1XlvRZMdgReJ/g3+AVgv4ZBLQGehaz/rvAz8B1wC7AhcCeYX8sL0cOqczcXZMmTUmegOXAo1tZ53iC58qeXGR+HeBHYHKheYeE664EmhaaXx9YCMwHsgrNr1nM590YbmO/Yra7BGhQzHuK285p4XsGFJrXIpx3UzHr53/G6YXm3RnOO63IureG888pNO+mcN4owifrhfP7hPPPK8e/09xwG+cXmT8knH9UoXnPhvOGFll3QDj/zqh/7jSl76TD2iIVYwWwj5m1KGWdk4FfgffMrFH+BFQH/kOwN9agyHtecvdF+Q0P9tSeItj727PQ/HUQnD8Or6RuBIwLF+9VTJYX3H1Z0ZmFtlPFzOqF28nfmy9uO7HqDfwEvFBk/j0ERwR6F/Oeh9y98DNv87+fXcqRA4I/eJ4sMu/e8GuvYta/v0h7KMEfR8WtKxITFWeRinE50BaYY2YzzOzBYm4z2g1oSLDXWnQ6K1ynSZH35BbzWd+EX1vmzzCzo8zsY2A9wV78EmB8uHjbYrbxXXHfRHgu9j8Eh5NXhNv5oZTtxKolkOvBxWIF3H01QaFrVcx75hRZN/+PiYblyAHwg7sXvZL8e4I/EloWs/4f/g3CPxhmlbCuSEx0zlmkArj7SDObABxDcFi3L3CxmT3v7qeFq1UBFgCnl7KpefF+dngx2dv8fi74R4KLvHYgODRb3B/pf7oyO7zIaRywFPgHMDtcLwt4r4TtJNPmEuZbhaYQSQIVZ5EK4u5LgeeA58Lbk14ATjWzf7r7dIJi1x34r7vHeqtRTjHzdgu/5u9ZnkhQQI919x/zVzKz7nF+C72BmsCp7p6/142Z7VrMul7MvNL8AOSYmRU+VG1mtYGdgA/i3F55tDKzqkX2nlsD1Siytx7KAT7Pb5iZER4lSWpKyWg6rC2SZPnneQvPc/fNwFdhM/8w7AsEBeDWErZT9JA2wN+K3MZUn+AQ+AJgSjg7fw+zSqH1qhAcao/Hn7YTurKYddeEX+vHuO1RBOfJTy4y/wqCPnkjxu0kQj2CK+SL5gAYXcz6lxVpn0TwB0Vx64rERHvOIslXB/jZzEYBUwkOC7cluOXme+ATAHcfZmbHAleY2V4Et+gsJ/hFfzBQFdivyLZ/AD41s8cJRtw6i+C89IDwDwAICt9lwNtmNoSguPYnKHrxeI/gcPjzZvYQwSHtY4HGRVd091/N7HvgJDP7juDc9GJ3/7CEbd8N9AOeNrN9gJnA/gTFehLwTJxZC4T3Vx8MtHT3uTG85QfgDjPrCMwguJWqL/COu79XzPptzext4B2CPeyLCC5uu6esmUVUnEWSbx3wIHA4cBTBoeEFBFdV3+nBvcH5TiM4r3s2wXndbIJboz7nz1cyE263IcH9xzsQHBo/0d2H56/g7hPNbADBfbh3EdyfPJzg3ugZsX4T7v5d+MfDHQS3Ya0jOJd9CsG9z0WdQnAl890Ew3WOB4otzu6+wsy6ERw1OAEYSHDv8L3Azf7ne5zjUSfMuiLG9ecT3A51H8H5/zUE/fx/JazfA/gXcDvBv9c7wKXFXe0uEiv7450IIpIOwiu9xwFnuPuzkYZJYeHphKXA7e5+41ZWj3fbzxLcl60L0CThdM5ZRDLZYQSH1HWIWdKKirOIZCx3H+nuzdx9bdRZROKh4iwiIpJidM5ZREQkxWjPWUREJMWoOIuIiKQYFWcREZEUo+IsIiKSYlScRUREUoyKs4iISIr5fwRNMABxYfSIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 921.6x633.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cvd_smooth_agg['s_bp'] = cvd_smooth_agg['dist']* resolution\n",
    "cvd_smooth_agg['balanced.avg.smoothed.agg'].loc[cvd_smooth_agg['dist'] < 2] = np.nan\n",
    "f, ax = plt.subplots(1,1)\n",
    "\n",
    "for region in hg38_arms['name']:\n",
    "    ax.loglog(\n",
    "        cvd_smooth_agg['s_bp'].loc[cvd_smooth_agg['region1']==region],\n",
    "        cvd_smooth_agg['balanced.avg.smoothed.agg'].loc[cvd_smooth_agg['region1']==region],\n",
    "    )\n",
    "    ax.set(\n",
    "        xlabel='separation, bp', \n",
    "        ylabel='IC contact frequency')\n",
    "    ax.set_aspect(1.0)\n",
    "    ax.grid(lw=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the smoothed P(s) curve and its derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logbin-smoothing of P(s) reduces the \"fanning\" at longer s and enables us to plot the derivative of the P(s) curve in the log-log space. This derivative is extremely informative, as it can be compared to predictions from various polymer models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Just take a single value for each genomic separation\n",
    "cvd_merged = cvd_smooth_agg.drop_duplicates(subset=['dist'])[['s_bp', 'balanced.avg.smoothed.agg']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate derivative in log-log space\n",
    "der = np.gradient(np.log(cvd_merged['balanced.avg.smoothed.agg']),\n",
    "                  np.log(cvd_merged['s_bp']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3O/h2e2/ueu79QLPLiEjToTCVRtGjXUt+cGiX8vU/vTmXyUvUIElEmgaFqTSag3q34prDg7ndS0qd7zwxVc9PRaRJUJjGgVrz1t8PvjaU/fu0A2D1lt18X89PRaQJUJjGgVrz1l9mehp3X7A/7XIyAZgwdz33fajnpyKS2hSm0uh6tmvJn88eVb7+x//p+amIpDaFqYTimOFdubrK89NNen4qIilKYSqh+eHXhrJfxeenz0zX81MRSUkKUwlNZnoaf7tgf9q2DJ6fvpu/Ts9PRSQlKUwlVNU9P9X4vSKSahSmcaCuMbE5dkTl56fffmIq67buDrkqEZH6U5jGgbrGxO6HXxvK2H4dAFi/rZDr//MFe0pKQ65KRKR+FKaSFILnp/vROTcbgM+XbOL2N/JDrkpEpH4UppI0urRpwd8v2L98/tP7P1zMazNXh1yViEjdFKaSVMb278BPTxxWvv7DZ6azcP32ECsSEambwlSSzhWH9uekfboBsKOohGsfncKOwuKQqxIRqZnCVJKOmfGHM/dlQOdWAMxft52fPj8Tdw3oICLJSWEqSSm3RSb//OYYWmamA/Dy9FU8MmlpyFWJiFRPYSpJa0jXXH5/5j7l6795dQ5Tlqovr4gkH4VpHGjQhsQ5fXRPLj2kHwB7SpzrH/+Cgu2F4RYlIlKFwjQONGhDYv3fScPLJxRfs3U31z2uAR1EJLkoTCXpZWWk8fcL96dT6ywAPlu8kdte/TLkqkRE9lKYSkro3rYl91w4hozIgA4Pf7yEZyYvD7kqEZGAwlRSxtj+HfjFqSPK129+cRbTl28OryARkQiFqaSUiw7uy9ljegFQVFzKtY9NYf02NUgSkXApTCWlmBm/PiOPUb3bAbB6y27NMCMioVOYSsppkZnOP79ZuUHSb16ZE3JVItKcKUwlJVVtkPTvSUvVIElEQqMwlZSlBkkikiwUppLSqjZIuuZRNUgSkcanMJWUVrVB0pqtu7n2sSns3lMSbmEi0qwoTONAY/OGa2+DpGwApizdxP9pyjYRaUQK0zjQ2Lzh6962JfdfPIasjOBb+vmpK/nH+wtDrkpEmguFqTQZ+/Vpzx/P2rd8/fY35vLGrDUhViQizUVUYWpm+yWqEJF4OH10T75z9KDy9ZuemsaslVtCrEhEmoNor0ynmNkXZvZtM9M9TUlKNx07hBPzugGwa08JVz0ymXXbdodclYg0ZdGG6S+AXOAuYJWZPWlmx5uZxb80kYZJSzP+fM4o8nq2AYIhB69+RC18RSRxogpTd/+Nuw8GjgCeAE4EXgeWmtmvzWxgAmoUiVpOVgb3X3wAXXKDFr7Tlm/mx8/NUAtfEUmIBjVAcvcP3f1yoBtwGbAQ+D9gnplNMLOLzKxlHOsUiVr3ti257+IDyI608H1p2ir+9u6CkKsSkaYopta87r7L3R8BrgKeBIzgqvXfwEozu9XMsmIvU6RhRvdux5/OHlW+/ue35vHStJUhViQiTVGDw9TMWpnZZWb2ATAXOBt4CTgVOB54H/g5cG88ChVpqFNH9eCGYwaXr//gmelMWrghxIpEpKmJOkzN7HAz+xewBngQ6Ar8FOjt7l9391fd/W13/zrwR+Drca1YpAFuPHYw39i/JwB7SpyrH53MvLXbQq5KRJqKaPuZLgAmAOcALwBHuvtQd7/d3ddW85apQJvYyxSJjZnx+2/sy/hBHQHYtruYy/71OWu3qsuMiMQu2ivTrcB3gB7ufrG7f1DH/i8D/RtUmUicZWWk8Y9vjmFYt1wAVm7exeUPf872wuKQKxORVBdt15j93f0ed6/XkDLuvtPdlzasNJH4a9Mik39ddiDd2rQAYPaqrVz/+BfsKSkNuTIRSWXR3uYdbmbfrOX1b5rZsNjLEkmc7m1b8q/LDiQ3OwOA9+et52cvzFIfVBFpsGhv8/4GuKiW1y8EftXwckQax/DubfjnRWPISAsG73pq8nL+/Oa8kKsSkVQVbZgeDLxby+vvAuMaXk7jMLOnzGyGmU01s8/M7Jiwa5LGN35QJ/5w5t5ZZv42YQEPfLgoxIpEJFVlRLl/R6C2GbC3AJ0bXk6jucbdN0P5TDjvmFknd9eDs2bmzDG92LijiNte+xKA37z6Je1ysjhrTK+QKxORVBLtlelaYN9aXt8XKIjmgGbWy8zuNrNJZrbTzNzM+tWwb28ze9bMtpjZVjN73sz6RPN5AGVBGtE22vdL03LV4QO47si9w0r/+LkZvDlb86CKSP1FG6ZvAFeY2UFVXzCzscAVkX2iMYig3+om4MOadjKzHILbyMOASwie3Q4GJphZqyg/EzO7w8wWAc8BZ+qqtHn74deGcv7Y4PeyklLn209M1ShJIlJv0Ybprwj6mn4Uee54c2R5Gvgo8tqtUR7zA3fv6u4nAc/Ust9VwADgDHd/0d1fAk4D+gLXlO1kZm+bWUENy/iy/dz9JncfQNBo6naNIdy8mRm/OSOPk/fpDkBRcSlXPTKZmSs0sbiI1C3afqYrCRoYvQucBfw6spwZ2Tbe3ZdHecz6XhGeBnzi7uXTfrj7YmAicHqFbce6e6calonVfP4bQHtgn2jqLmNmU8qWhrxfkkd6mvGXc0dx2OBOAGwvLOaSf32mYQdFpE7RNkDC3RcBXzOzDgS3aAEWuPvGuFb2VSMJBtKvajbBIPv1EpkarlskiDGzcQQNq2JuxllSUkJ+fn6sh2myCgoKUuL8fG9sLus3bSO/oJCNO4o49x8Tuf2EHvRul/ibF6lyjsKi81M3naNwRB2mZSLh+Vkca6lLB6pvSbyR4MqyvloC/zGzXKAY2EHwzLS2Vso1cvcxZV/n5eX5sGEas6Im+fn5pMr5eXLgIM6//1O+XL2VTbtLuPmddTx1zTj6d4r68XxUUukchUHnp246R+FoUJhGGvz0Jbiis6qv12PM3tBEfglI+r6wEq52OVk8dsVYzr//E+at3c66bYVccP8nPHX1OPp0zAm7PBFJMtEOJ9jazO4nuBqcCbxHMItM2VK2ngibqP4KtKYrVpGYdGydzeNXHszAzsHV6Ootuzn//k9YsWlnyJWJSLKJ9sr0boJuKa8QhGain5NWNJvguWlVI4A5jVjHV5jZ1cDVPXr0CLMMSYDOudk8cdXBnHvfJywu2MHKzbu44P5Peeqag+netmXY5YlIkoi2a8zpwGPufpq73+Hu/65uSUShBNO5HWxmA8o2RAZ3GB95LTTufp+7H9C+fTSPbiVVdGnTgv9cdRB9OgS3d5dt3Mm59+oKVUT2ijZMMwn6k8aVmZ1lZmcBZY15ToxsO6LCbvcDS4CXzOx0MzuNoHXvcuDeeNckUlH3ti35z1UH0bNdcDVaFqhLN+wIuTIRSQbRhulEqr/VGqtnIsu1kfV7IuvlA0C4+w7gaGAe8CjwOLAYONrdtyegpnozs6vNbPKmTXp025T1ap/DU9ccXH6FunLzLs65dxIL14f67SciSSDaML0ROMvMTq9rx2i4u9WwHFllv2Xufqa7t3H3XHc/w92XxLOWhtBt3uajV/scnr5mHAMiXWTWbi3k3Hs/Ye4aDewg0pxFG6b3EPTLfN7MlpnZ+2b2bpXlnQTUKZI0urVtwZPXHMyQrq0BKNheyHn3TWLWSg09KNJcRRumAwiemy4DSoA+QP8qy4Aa3y3SRHTJbcGTV49jRPc2AGzauYcL7v+Eacs3h1uYiIQi2rF5+7l7/7qWRBUrkkw6tMriP1cdxKhewSx+W3cXc+H9n/DxwqhmIRSRJiDaK1OphhogNV/tcrJ49MqDGNM3eF6+o6iESx/6nDdmaT5UkeakQWFqZiPN7EYz+52ZDYxsa2FmQyIDyTcraoDUvLVpkckjl48tn22mqKSU6x6fwlOfLwu5MhFpLFGHqZn9HZgB/AX4EcEYvRCMpjQZuC5u1YmkiFbZGTx4yYGcsm8wH2qpw4+fm8k/318YcmUi0hiiHZv3RuBbwJ3A8VQY5D7S1/NFgnlHRZqdrIw0/nrefnzz4D7l237/ej6/fe1L3D3EykQk0aK9Mr0KeNbdvw9Mreb1WcDgmKtKMXpmKmXS04xfn57Hd4/Z+9/gvg8W8cNnZ1BcUhpiZSKSSNGG6UCgtn6kGwhmcWlW9MxUKjIzvnfcEG45dUT5tmenrOCaR6ews6g4xMpEJFGiDdPtQG4trw8kCFSRZu/S8f3563mjyUgLnoa8k7+O8+/7hILthSFXJiLx1pCxec+v7gUzawNcRjCnqYgAp4/uyYOXHkirrHQApq/Ywjfu+ZjFBRogX6QpiTZMfwOMNLPXgWMj24ab2SUELXnbAr+LY30iKe+IIZ156ppxdM7NBoIZZ75xz0S+WKZn7CJNRbQjIH0OnAmMBv4T2XwX8C+gHXCmu8+KY30iTUJez7Y8/61DGNg5GCB/0849nH/fJ7w5W4M7iDQFUfczdfdXgX4EE4X/GPg/4Cygn7u/HtfqUoRa80p99O6Qw3PfOoQD+wUN1QqLS7n2sSk8MmlJuIWJSMwaNAKSuxe6+yvu/kd3/4O7P+/uO+NdXKpQa16pr3Y5WTx6xUGctE83IBjc4Rcvzeb3r+dTWqq+qCKpSmPzijSyFpnp/O38/bni0L1zQvzz/YXc+NQ0ikoUqCKpKCOanc1sUT12c3cf2MB6RJqFtDTj56eMoEe7lvzm1Tm4w8vTV7F0bQseGTCIti0zwy5RRKIQ7ZXpMmBplWUFwRyn/YDiyD4iUg9XHNqfv1+wP1kZwX/F6Wt2c84/J7Fq866QKxORaETbmvdIdz+qynK4u/cGzgNaA9cnpFKRJuqkfbrz+JUHlV+Nzl27jW/c8zFfrt4acmUiUl9xe2bq7k8DzxLMJiMiUTiwXwee+9YhdGkVPHlZszW4Qp24QBONi6SCeDdAmgWMj/Mxk566xkg8DOrSmjtP7klezzYAbCss5tJ/fcYLU1eEXJmI1CXeYXooUBTnYyY9dY2ReOmQk8GTV4/jiCGdAdhT4tz01HT+PmGBpnETSWLRtua9uIaX2gNHA6cA/461KJHmrHV2Bg9ccgA3vzCTpycHV6V//N9cVm3exa2njSQjXT3aRJJNVGEKPAw4FSYFr6CYYFjBm2KsSaTZy0xP4w9n7kuPdi258+35ADz+6TLWbt3NXefvR05WtP91RSSRov0feVQ12xzYCCxx9+2xlyQiEMyLeuOxQ+jRtiU/fWEmJaXO21+u4/z7P+XBSw6gU+vssEsUkYiowtTd309UISJSvXMO7E2XNtlc9/gX7CwqYfryzZz5j495+LKx9O/UKuzyRAQNJyiSEo4c2oWnrxlXfjW6dMNOzvzHx0zVNG4iSSHaBkgPNeAz3N2vaMD7RKSCvJ5teeG6Q7jkX5+xaP0ONu4o4sIHPuX+iw9g/KBOYZcn0qxF+8z0UoJnpPDVRki1bVeYisRB7w45PHftIVz1yGQmL93EzqISLvvX59x1/n6ckNct7PJEmq1ob/N2A6YBzwPjCCYEbwccArwATAW6untahSU9btUmKQ3aII2pfatgGreyvqhFJaVc9/gUnpm8POTKRJqvaMP0DmC1u5/t7p+6+9bI8om7nwWsjezTrGjQBmlsLbPSuf/iAzh53+5AMC/qD5+dwUMfLQ65MpHmKdowPRF4tZbXX43sIyIJlpWRxl3n7cf5Y/uUb/vVK3O44615Gi1JpJFFG6YZwIBaXh9IMB2biDSC9DTjt1/P49oj9k4h/Nd35nPbq18qUEUaUbRh+g7wbTP7RtUXzOxMgunX3olHYSJSP2bGT04cxo9OGFq+7YGPFnPrf+coUEUaSbSteW8APgKeMbNlwNzI9qFAH2AlcGPcqhORervuyEHkZmfw85dmA/Dwx0soKXVuPW0kaWnVjQAqIvES7eTgy4B9gT8Cu4AjIsuuyLbR7r403kWKSP1cNK4ft309r3z90U+W8rOXZlFaqitUkUSKerRsd98M/CSyiEiSufCgvqSb8dMXZuIO//l0GaWlzm+/vo+uUEUSJKbhBM0s28z0v1MkyZw3tg9/OHNfyv53Pvn5cn703AxKdIUqkhBRh6mZDTazp81sM7CDyEwyZtbZzP5jZuPiXKOINMA5B/Tmz2ePouxi9NkpK/jJczN0y1ckAaIKUzMbCnwKHB/5s/yq1N3XA8OAK+NZoIg03Df278Ud544uD9Rnpqzglv/OVitfkTiL9pnpbQSNjcYChcC6Kq+/AXyl24yIhOf00T1xh5uenoY7PDJpKS0y0/npicPQUxqR+Ij2Nu9RwD3uvpK9A9tXtBToEXNVIhJXZ+zXk99+fZ/y9fs+WMSdb88PsSKRpiXaMM3hq1ejVV9vdr/qaqB7SQXnj+3DL08dUb7+13fm84/3FoZYkUjTEW2YLgJG1/L6EewdyKHZ0ED3kiouG9+fH58wrHz9D2/k8/BEDY4vEqtow/QJ4FIzO7TCNgcws+uAU4FH41SbiCTAt44cyHePGVy+fst/5/DclBUhViSS+qJtgHQ7cAwwAZhBEKR/MLNOQF/gXeBvca1QROLupmMHs3tPCfd9sAiAHz03g/atMjl6WNeQKxNJTdEOJ1gEHAf8iCBIdwP7ANsJRkQ6yd1L4l2kiMSXmfHTE4dx3oG9ASgpda57/AumLN0YcmUiqaneYRoZ7ehwoL+73+HuB7h7K3dv6e77uvsf3X1PAmsVkTgyM35zRh7HjwiuRnfvKeWyf33O3DXbQq5MJPVEc2VaQjC92gkJqkVEGllGehp3nb8fY/t3AGDr7mIufuhTVmzaGXJlIqml3mHq7sUEU6xlJa4cEWlsLTLTeeCSAxjevQ0Aa7cWcvGDn7Fhe2HIlYmkjmhb8z4KXGhmmYkoRkTC0aZFJv++/ED6dMgBYFHBDi5/+HN2FhWHXJlIaog2TD+IvOcLM7vezE4ws8OrLgmoU0QSrEtuCx69YiydWgc3n6av2MINT07TTDMi9RBtmP6PYHLwkcDdwKsE3WTKlvcif4pICurbsRUPXzaWnKx0AN6as5ZfvzIn5KpEkl+0/Uwvp/oxeUWkicjr2Za7z9+Pqx6ZTKnDwx8voXeHHK44tH/YpYkkrVrD1MwuBj5w9yUA7v5wI9QkIiE7ZnhXbj09j5+/OAuA37w6h57tWnJCXreQKxNJTnXd5v0XcEjZipmVmNkFiS1JRJLBRQf35ZrDBwDgDjc8OZWpyzSZg0h16grT7UCbCuvNbkYYkebsxycM4+R9ugNQWFzKlf+ezLIN6oMqUlVdz0ynAT8ysyxgc2TbYWZW6/vc/ZHYS0s8M7sMeAj4uru/GHI5IkknLc348zmjWLN1N1OWbmLDjiKu+PfnPH/dIeS2UA85kTJ1hemNwPPAnZF1B66JLDVxIOnD1Mz6AVcBn4RcikhSa5GZzv0XH8DX75nI0g07mb9uO999YioPXHIg6Wm6WSUCddzmdfepwCBgGHAkwW3e24CjalmOjqYAM+tlZneb2SQz22lmHgm66vbtbWbPmtkWM9tqZs+bWZ9oPi9ynDTgAeA7gIZ5EalDh1ZZPHjJAeRmB79/T5i7nt+//mXIVYkkjzq7xkRmgZkHzDOz94H33P39ONYwCDgHmAJ8CBxf3U5mlkMwxVshcAnBFfBvgAlmtq+774jiM78HTHT3KWb6zVqkPgZ1yeXuC/bj8oc/p9Th/g8XM7hrLucc0Dvs0kRCF+0UbEe5+ztxruEDd+/q7icBz9Sy31XAAOAMd3/R3V8CTiOYR7X8trOZvW1mBTUs480sDziTIIhFJApHDu3CzSePKF+/+YWZfL5E07aJRDsCUty5e2k9dz0N+MTdF1R472JgInB6hW3HununGpaJwGFAP2C+mS0BDgbuM7Nvx+mvJNKkXT6+X/k8qHtKnGsencLyjWrhK81b6GEahZHArGq2zwZGVLO9Wu7+D3fv7u793L0fQQOkq939bw0pysymlC0Neb9IqjEzfnV6Xvm0bRt3FHHVI5PZXqhB8aX5inY4wTB1AKrrMb4RaN/ItVSrpKSE/Pz8sMtIWgUFBTo/dUilc/T9g9pww/qtrNleTP6abVz5wIf84uhupCWwHUIqnZ+w6ByFI5XCNCHc/cgY3z+m7Ou8vDwfNmxYzDU1Vfn5+ej81C7VztEj3fvw9b9PZEdRCZ8s38mbK9O58dghCfu8VDs/YdA5Ckcq3ebdRPVXoDVdsYpIgg3pmstd5+9Xvn7n2/N558u1IVYkEo6owtTMFpnZabW8foqZLYq9rGrNJnhuWtUIINQ5oszsajObvGmTMl2an2OGd+XGYweXr9/41DQWF0TTU00k9UV7ZdoPaF3L660IuqokwsvAwWY2oGxDZHCH8ZHXQuPu97n7Ae3bJ8WjW5FG992jB3PMsC4AbNtdzDWPTmaHGiRJMxLv27y9CQbHj4qZnWVmZwFlzx9PjGw7osJu9wNLgJfM7PTIFfJLwHLg3tjKFpFYpKUZfzl3NP07tQJg3trt/Oi5Gbhr+mNpHupsgGRmp1OhHydwtZkdW82u7YFjadhYt1UHa7gn8uf7BMMY4u47zOxo4A7gUYKhDd8BbnT3qANcROKrbctM7r1oDGf8fSI7i0p4dcZq9u3ZlmuOGBh2aSIJV5/WvKOBSyNfO3B4ZKlqO0GQXh9tEe5er7b07r6MYPSipGJmVwNX9+jRI+xSREI1pGsufzxrFNf/5wsA/vBGPiN7tOXQwZ1Crkwkseq8zevut7p7mrunEVwNfrNsvcrSxt2Pc/d5iS87ueiZqcheJ+/bnWuOCJo2lDp898mprN6yK+SqRBIr2mem/YEXElGIiDQdP/raMA4dFFyNbtxRxHf+M5U9JfUdOVQk9UQbpkXAATW9aGaHmVm32EoSkVSXnmb89bzRdG2TDcDkpZv405tzQ65KJHGiDdM/RJaa/C6yNCvqZyryVR1bZ3P3+fuXTyB+7/uLNKCDNFnRhukRwKu1vP4akda3zYmemYpUb2z/Dvzg+KHl6997ejorNmmGGWl6og3TrkBtv1quA3SbV0TKXXP4AI6ODOiwZdcerv/PVIqK9fxUmpZow3QjUNso1kOBrQ0vR0SamrQ0489nj6JH2xYATF++md+/rllNpGmJNkzfA66KDONXSWTbVZF9RETKtW+Vxd8u3J+MyPPThyYu5o1Za0KuSiR+og3TW4F0YLqZ/cHMLowstwPTIq/dGucak54aIInUbf8+7fnJiXunBvvxczNYtVn9T6VpiCpM3X0u8DVgFfBD4BGCof1+ENl2vLuHOoNLGNQASaR+rji0P8cO7woEz09vemoaJaUav1dSX9QD3bv7JHcfTjAo/fnAecD+7j7C3SfFu0ARaTrMjNvP2pcuuUH/008Xb+Qf7y0IuSqR2DV41hh3n+ruT0eWaXGsSUSasA6tsrjj3NFYZETuO96ez5SlekQiqS3eU7CJiNRp/KBOXHN4MJtMSalzw5NT2bp7T8hViTRc1GFqZkeY2etmVmBmxWZWUmXRjMAiUqfvHTeEfXu1BWDFpl384sVZIVck0nBRhamZHQe8DewPTIq8fwLwaWSX2QQNkpoVteYViV5WRhp/PW8/crLSAXhx2iqe/2JFyFWJNEy0V6Y3A8uA4cBlkW2/dfdDCIYR7EPQwrdZUWtekYbp36kVvzo9r3z95y/OYumGHSFWJNIw0Ybp/sAD7r4RKBsPLA3A3T8EHgJ+Hb/yRKSpO3P/npw6qgcAO4pK+O6T0zRdm6ScaMM0DVgf+bqst3XFy7E5wKhYixKR5sPM+M0ZefRs1xIIhhv8+wR1l5HUEm2YLgf6Arj7LmANcEiF10cDukcjIlFp2zKTO8/b213m7ncXMG355lBrEolGtGH6PnByhfVngW+b2QNm9i/gGuB/8SpORJqPA/t14Noj9naXuempaewsUucASQ3RhukdwL1m1iKyfjPwJkFjpIsJBrn/QdyqE5Fm5aZjhzC8exsAFhfs4HevaXYZSQ1Rj83r7ve6++7I+jZ3PxnoALR19+PcfX3tR2l61DVGJD6yMtK489zRZGUEP5oe/WQp781dF3JVInWLtp/pL8wsr+p2d9/i7tvNbKSZ/SJ+5aUGdY0RiZ+h3XL50deGlq//6NkZbNpRFGJFInWL9jbvLcC+tbyeB/yywdWIiACXj+/PuAEdAVi3rZCbX5yJu2aXkeQV77F5cwC1GBCRmKSlGX86ZxS5LTIAeG3mGl6ctjLkqkRqVmeYmlkfMzvczA6PbBpWtl5lOZ2gNe+ihFYsIs1Cz3Yt+XWF0ZF+8eJs1m3XYPiSnDLqsc9lBLduPbLcHFmqMoJRka6MW3Ui0qydProHb325lldnrGZbYTF/+mgdh+7vpKVZ2KWJVFKfMH0RWEIQlg8B9xEMcl+RA9uBye6+LI71iUgzZmbcdkYeny/eyLpthcxYs5uHJi7mysMGhF2aSCV1hqm7TwemA5hZX+A5d9dcSSLSKNrlZPHHs0dxyUOfAXD7G3M5bHBnhnbLDbkykb2i7Wd6q4JURBrbEUM6c/G4vgAUlZTyvac1GL4kl/rc5q3EzAw4DhgEdCS4/VuRu3uzmjnGzK4Gru7Ro0fYpYg0WT89cTjvzF7Fyq17mL1qK3e/u4DvHTck7LJEgCjD1MyGETxDHcxXQ7SM08ymYXP3+4D78vLy1BFOJEFaZqXzg0O78P3XV1Lq8PcJCzh2eBf27dUu7NJEou5n+jeCWWN+CIwB+lezqGWAiCTE8C4tKg2G/72np7N7T0nIVYlEH6aHAH9x97+4+1R3X1rdkohCRUQAbjh2MMMijY8WrNvOX96aF3JFItGH6Q6COU1FREKRnZHOn88ZRUakr+n9Hy7i8yUbQ65Kmrtow/QFgsZHIiKhGdmjLTccMxgAd/j+09PZUaiRTCU80YbpD4GeZnaHmQ2ItOwVEWl03zpyIKN6tQVg2cad/O71L0OuSJqzaMN0E3Ag8F1gPlBsZiVVFv16KCIJl5Gexp/PGU12ZO7Txz5Zxgfzmt10ypIkou1n+ghB1xcRkdAN6tKaH35tKL95Nbgq/fFzM3jjxsNp2zIz5MqkuYkqTN390gTVISLSIJeP78+bc9by2eKNrN6ym1/9dw5/PmdU2GVJMxPv+UxFRBpVWprxp7NGkZOVDsBzX6zgzdlrQq5KmpsGhamZHWNmd5vZq5HlbjM7Jt7FiYjUR5+OOdx88vDy9f97YSYbdxSFWJE0N1GFqZmlm9kTwJvA9cAxkeV64E0z+4+Z6WpXRBrdBWP7cPiQzgAUbC/iZy/OxF1NPKRxRBt8PwLOBR4DhgEtI8tQ4NHIaz+MZ4GpwMyuNrPJmzZtCrsUkWbLzLj9zH1p0yJoCvLazDW8PH1VyFVJcxFtmF4MvOLul7j7PN9rfqRx0mvApfEuMtm5+33ufkD79u3DLkWkWevWtgW3nj6yfP0XL81m7dbdIVYkzUW0YdofeL2W11+P7CMiEoozRvfkayO7ArBl1x5+8twM3e6VhIs2TLcSzBpTkz6RfUREQmFm3Pb1fejYKguACXPX89wXK0OuSpq6aMP0beB6Mzu06gtmNh74NvBWPAoTEWmoTq2z+c0ZeeXrv/rvbNbpdq8kULRhejNQCLxvZh+a2b2R5UPgA2AX8LN4FykiEq0T9+nOyft0B2Dr7mJufnGWbvdKwkQVpu6+GDgAeBoYBVwVWUYBTwEHRvYREQndLaeNpH1OMLTgW3PW8sqM1SFXJE1V1H1C3X2Ju58PtAO6R5Z27n6Buy+Jb3kiIg3XOTebW07b27r3ly/PZsP2whArkqaqwQMsuHupu6+NLKXxLEpEJF5OG9WDY4d3AWDjjiJ++fLskCuSpijaEZAuN7Pna3n9OTO7OPayRETiw8z4zRn7kBsZzOGVGat5Y5bG7pX4ivbK9BqgtgkD1wLfang5IiLx161tC35+yojy9Z+/NIvNOzV2r8RPtGE6BJhey+szI/uIiCSVs8f04rDBnQBYv62QX7/yZcgVSVMSbZhmEYzFW5OcOl4XEQmFmfG7b+xDqwpTtU2Yuy7kqqSpiDZM84GTann9RGB+w8sREUmcXu1z+MlJFaZqe34m23bvCbEiaSqiDdOHgaMi85e2KdtoZm3M7K/AUcC/4lifiEhcXTi2Dwf17wDA6i27+e1r+SFXJE1BtGH6N+A5gvlLC8xsvpnNJ2iU9B3gReCuuFaYAGb2npktNrNpkeUXYdckIo0jLc34w5n70iIz+PH3xGfLmLigIOSqJNVFOwKSu/vZwIXAG8CeyPI6cIG7n5lCfU5vcvfRkeVXYRcjIo2nX6dW/OD4oeXrP35uBjsKi0OsSFJdgwZtcPcn3P00dx8RWc5w9ycbciwz6xW5bTzJzHaamZtZvxr27W1mz5rZFjPbambPm1mfhnyuiDRvl43vz/592gGwYtMufv+6bvdKwzV4BKQ4GgScA2wCPqxpJzPLAd4FhgGXABcBg4EJZtaqAZ/7ezObGQnnoXXvLiJNSXqacftZo8jKCH4MPvrJUj5eqNu90jDJEKYfuHtXdz8JeKaW/a4CBgBnuPuL7v4ScBrB/KrXlO1kZm+bWUENy/jIbhe7+zBgX+A14E0zS0/I305EktagLq35wfF7u8b/6Fnd7pWGCT1Mo3jGehrwibsvqPDexcBE4PQK24519041LBMj+yyL/Onu/hDQmtonPa+RmU0pWxryfhEJ1xWHDmA/3e6VGGWEXUAURgIvVbN9NnB2fQ9iZi2A1u5eEFk/CSgBlsdaYElJCfn5+o9Yk4KCAp2fOugc1S5R5+e6/XO5bsUW9pQ6j36ylLy2exjVPTXHn9H3UDhSKUw7EDxXrWoj0D6K47QBXjezLKA0csxT3L1BPbfdfUzZ13l5eT5s2LCGHKZZyM/PR+endjpHtUvU+RkG/LCoVXmf07s/28T/btyHVtmp9CMyoO+hcIR+m7exufs6dx/j7vu4+yh3P9LdPwu7LhEJl273SizqDFMzSzOzn5jZJXXsd6mZ/Sh+pX3FJqq/Aq3pilVEpN7S04w/qnWvNFB9rkzPA24D5tWx3zzgd2Z2VsxVVW82wXPTqkYAcxL0mfViZleb2eRNm5TpIqlsUJfWfP84te6V6NUnTM8HJrj7pNp2cvePgbcJ+n8mwsvAwWY2oGxDZHCH8ZHXQuPu97n7Ae3bR/PoVkSS0ZWH6XavRK8+YXoA8L96Hu8tYGy0RZjZWZEr2rLGPCdGth1RYbf7gSXAS2Z2upmdRtC6dzlwb7SfKSJSnepu9344f33IVUmyq0+YdiAYyL4+CiL7R+uZyHJtZP2eyPqtZTu4+w7gaILbyY8CjwOLgaPdfXsDPjNudJtXpGmpOpjDD56ZzuadRSFWJMmuPmG6DehSz+N1juwfFXe3GpYjq+y3LDKYfht3z42MCbwk2s+LN93mFWl6rjh0AGMjU7Wt3VrIzS/Mwt1DrkqSVX3CdCa1Twhe0UnArIaXIyKSHNLTjL+cM4rcSF/TV2eu5oWpK0OuSpJVfcL0aeAwM7u8tp3M7FLgcKBBs8eIiCSbXu1z+NUZezsR/PKl2azYtDPEiiRZ1SdMHwCmA/eb2cNmdriZtbVAm8j6w5H9pgEPJq5cEZHGdcbonpy8b3cAthUW872np1NSqtu9UlmdYRoZZu8k4BPgYmACwRB+xQSDJUyIbP8UOLmhw/KlMjVAEmm6zIzbzsijW5sWAHy2eCP3f7go5Kok2dRrOEF3X+Pu44FvAI8BU4GFkT8fj2w/1N3XJKrQZKYGSCJNW7ucLP509qjy9T+/OZdZK7eEWJEkm6jG5o3MI3qJux/g7kMif14c2a77HiLSZB06uBOXj+8PwJ4S57tPTGW7RkeSiGY30L2ISEP96IShDOuWC8Cigh387IWZ6i4jQD2mYDOz66I9qLvf07ByUpOZXQ1c3aNHj7BLEZEEapGZzt8u2J9T7/6IXXtKeHHaKg4Z1IlzDugddmkSsvpM1ve3KI/pBCMYNRvufh9wX15enn5FFWniBnVpzW/OyOP7z0wH4BcvzWK/3u0Y3DU35MokTPUJ06MSXoWISAo5c0wvPl64gee+WMHuPaVc/58veOn6Q2mZlR52aRKSOsPU3d9vjEJERFLJr88YybTlm1i4fgfz1m7n1v/O5vdn7ht2WRISNUASEWmAnKwM/n7h/mRHZpd58vPlPDtlRchVSVgUpiIiDTSsWxtuOW3vcIP/98JMZqzYHF5BEhqFaRxoBCSR5uu8A3tz1pheABQVl3LNo1NYv60w5KqksSlM40AjIIk0X2bGb87IY1SvtgCs3rKb6//zBXtKSkOuTBqTwlREJEYtMtP550Vj6NQ6CwjG7731v7M1oEMzojAVEYmD7m1bcs+FY8hIMwAe+2QZD3y4OOSqpLEoTEVE4mRs/w78+oy88vXbXvuSV2asCrEiaSwKUxGRODp/bB+uO3Jg+fr3nprOZ4s3hliRNAaFqYhInP3wa0M5Y3QwVndRSSlX/PtzZq7QlG1NmcI0DtQ1RkQqMjNuP2sUhwzsCMC23cV888FPmbNqa8iVSaIoTONAXWNEpKqsjDTuu/gA9u/TDoAtu/Zw4QOf8OVqBWpTpDAVEUmQ1tkZPHz5WPaN9EHdtHMP5947ic+X6BlqU6MwFRFJoDYtMnn08oPI69kGgK27i/nmA5/y1py1IVcm8aQwFRFJsLY5mTxx1cGMGxA8Qy0sLuXax6bw0EeLNbBDE6EwFRFpBLktMvnXZQdyYl43AEpKnV+9MofvPz2d3XtKQq5OYqUwFRFpJC0y0/nbBftz5aH9y7c9P3UlZ/7jY5YU7AixMomVwlREpBGlpxk/O2UEd547unwu1NmrtnLSXR/y1OfLdNs3RSlMRURCcMZ+PXnuW4fQq31LAHYWlfDj52Zy7WNT2LijKOTqJFoK0zjQoA0i0hB5Pdvy2g2H8Y39e5Zv+9/stRx/xwdq7ZtiFKZxoEEbRKSh2rTI5C/njOZvF+xH25aZABRsL+SqRybz/aens2XXnpArlPpQmIqIJIFT9u3BGzcexmGDO5Vve+6LFZxw5wd8MG99iJVJfShMRUSSRPe2LXnk8rHc9vU8crLSAVi9ZTcXP/QZN78wkx2FxSFXKDVRmIqIJBEz48KD+vLGDYcztn+H8u2Pf7qME/76AZ8u2hBidVIThamISBLq0zGHJ686mJ+fMqK8C83yjbs47/5P+PUrczTQQ5JRmIqIJKm0NOOKQ/vz2g2HMbp3OwDc4cGPFnPSXR8ydZl6ECQLhamISJIb2Lk1z147jh9+bSiZ6QbAovU7OOufk7j/g0Ua6CEJKExFRFJARnoa1x81iJe/fSjDuwcz0JSUOre99iXffmKqGieFTGEqIpJChndvw0vXj680vu+rM1Zz+t8nsnD99hAra94UpiIiKSYrI42fnTKCv1+wf3kXmgXrtnP63yby2QoNmB8GhamISIo6ed/uvHT9eAZ0agXA9sJibnlnjeZJDYHCVEQkhQ3umstL3x7PscO7AFDq8KtX5vCzF2exp6Q05OqaD4VpHGigexEJU26LTO696ACuOmzvc9THP13Gpf/6jC07NbZvY1CYxoEGuheRsKWnGTefPIIbD+lMRlrQfWbigg2c+c+PWbl5V8jVNX0KUxGRJuSEIW149IqDaJcTzECzYN12vnHPRPLXbA25sqZNYSoi0sSMG9iR5ytMPL52ayFn/2MSkxZqXN9EUZiKiDRBAzq35vnrDmFkj2CAh22FxVzy0Ge8MmNVyJU1TQpTEZEmqktuC566Zlz5HKlFJaV854mpPPTR4pAra3oUpiIiTVjr7AwevORAzhjdAwgGyv/VK3P4y5tz1Rc1jhSmIiJNXFZGGn85ZzTXHDGgfNtd7y7gd6/nK1DjRGEqItIMpKUZPz1xOD85cVj5tvs+WMQvXppNaakCNVYKUxGRZuTaIwZy62kjy9cf/WQpP35uBiUK1JgoTEVEmplLDunHH87cBwvGduCZKSv44bPTdYUaA4WpiEgzdO6Bfbjz3NGkR0ZLev6Lldz84kwFagMpTEVEmqnTR/fkznNHE8lTnvhsObf8d7YaJTWAwlREpBk7dVQP/njWqPJbvo9MWsptr36pQI2SwlREpJk7c0wvfvf1fcrXH/hoMX/839wQK0o9zTJMzSzLzO40s/lmNtPMXg67JhGRMJ03tg+/On1vK9973lvIPe8tCLGi1JIRdgEh+S2QBQx191Iz6xZ2QSIiYbt4XD+Kikv5zatfAnD7G3PJzc7gonH9wi0sBYR+ZWpmvczsbjObZGY7zczNrF8N+/Y2s2fNbIuZbTWz582sT5SflwNcDfzE3UsB3H1NzH8REZEm4MrDBnDDMYPL13/+0mxemLoixIpSQ+hhCgwCzgE2AR/WtFMkBN8FhgGXABcBg4EJZtYqys/bBPzEzD43s4lmdkpDixcRaWpuPHYwl4/vX77+g2dm8OZsXXPUJhnC9AN37+ruJwHP1LLfVcAA4Ax3f9HdXwJOA/oC15TtZGZvm1lBDct4glvbfYAF7n4gcAXwkJkN+OpHiog0P2bGz08ZzjkH9AKgpNT59n+mMnFBQciVJa/Qw7TsVms9nAZ84u7lT8TdfTEwETi9wrZj3b1TDctEYBngwGOR/fOB6cD+cforiYikPDPjd9/Yl5P36Q4E07dd9chkpizdFHJlySn0MI3CSGBWNdtnAyPqexB3LwD+B5wAYGbdgX2AmQ0pysymlC0Neb+ISLJKTzPuOHc0RwzpDMDOohIu+9dnzFm1NeTKkk8qtebtQPCss6qNQPsoj/Ut4EEzu43gKvX77h5zp6qSkhLy8/NjPUyTVVBQoPNTB52j2un81C0R5+imsa3ZsGUbs9buZuvuYi6472P+dGIPerXNiuvnpLJUCtO4cfclwDFxOtaYsq/z8vJ82LBhte3erOXn56PzUzudo9rp/NQtUefoP4MGc8H9nzBr5VY27y7hF++u55lvHULPdi3j/lmpKJVu826i+ivQmq5YRUQkTtq0yOSRyw9iUJfWAKzaspuLHviU9dsKQ64sOaRSmM4meG5a1QhgTiPXUomZXW1mkzdtUqaLSNPVoVUWj11xEL07BFejiwp2cPFDn7Fl556QKwtfKoXpy8DBFbuwRAZ3GB95LTTufp+7H9C+fbSPbkVEUku3ti14/IqD6ZKbDcCXq7dy2cOfsaOwOOTKwpUUYWpmZ5nZWUDZ88cTI9uOqLDb/cAS4CUzO93MTgNeApYD9zZqwSIizVifjjk8duVBtMvJBOCLZZu55tEp7N5TEnJl4UmKMCUYrOEZ4NrI+j2R9VvLdnD3HcDRwDzgUeBxYDFwtLtvb9RqRUSauSFdc/n3ZWNpnR20Y/1oQQHffWIqxSX1HTqgaUmKMHV3q2E5ssp+y9z9THdv4+657n5GpGVuqPTMVESao1G92/HAJQeQnRFEyZtz1vKjZ2dQWtr85kJNijBNdXpmKiLN1cEDOvLPb44hIy2YXfz5qSu55b+zm93k4gpTERGJyVHDunDHuaOxIE95ZNJS/vRm85pcXGEqIiIxO3VUD3739X3K1/8+YSH/fH9hiBU1LoVpHOiZqYgInDe2Dz87eXj5+u9fz+fxT5eGWFHjUZjGgZ6ZiogErjxsAN89elD5+s9enMVL01aGWFHjUJiKiEhc3XTcEC49pB8A7vC9p6fz9py14RaVYApTERGJKzPjF6eM4KwxeycXv+4/X/BxE55cXGEqIiJxl5Zm/P4b+3BiXjcAiopLufKRyUxd1jTblihM40ANkEREviojPY07zxvN4RUmF7/84c9ZvnFnyJXFn8I0DtQASUSketkZ6dz7zTEc2C/4+bhp5x6u+PfnbNvdtGaaUZiKiEhCtcxK576LDqBvxxwA5q3dzo1PTqOkCQ07qDAVEZGEa98qiwcvOYDcyMD47+Sv4/Y38kOuKn4UpiIi0igGdcnlrgv2IzKML/d+sIhnp6wIt6g4UZiKiEijOWpoF/7vpL2jJP3fCzOZtXJLiBXFh8I0DtSaV0Sk/q44tH95H9Si4lK+9fgUtuxM7QZJCtM4UGteEZH6MzN+c0YeI3u0AWD5xl3c+NTUlJ4HVWEqIiKNrkVmOv+4cAxtWgQNkibMXc/fJywIuaqGU5iKiEgo+nTM4c7zRpev/+XteXwwb314BcVAYSoiIqE5eljX8llm3OGGJ6eyesuukKuKnsJURERCdcOxQzhscCcgGCEpFQd0UJiKiEio0tOMO88dTZfcbAA+Xbwx5Z6fKkzjQF1jRERi07F1NnecOxqLDOhw59vzmLxkY7hFRUFhGgfqGiMiErvxgzrxrSMGAlDqcMOT01Km/6nCVEREksZNxw1hvz7tAFi5eRc/eX4G7sn//FRhKiIiSSMzPY27ztuvfED812et4YnPlodcVd0UpiIiklR6d8jht9/Yp3z91v/OZv7abSFWVDeFqYiIJJ1TR/XgnAOC8XsLi0v57pPTKCwuCbmqmilMRUQkKf3y1JEM6NQKgC9Xb+X2N+aGXFHNFKYiIpKUWmVn8Nfz9iMzPegv8+BHi3lv7rqQq6qewlRERJLWPr3a8oPjh5av/+CZ6azfVhhiRdVTmMaBBm0QEUmcqw4bwPhBHQEo2F7Ej56dnnTdZRSmcaBBG0REEictzfjLOaNpn5MJBNO1/fvjJeEWVYXCVEREkl7XNi24/axR5eu/fT2fL1dvDbGiyhSmIiKSEo4b0ZWLDu4LQFFxKd99Yiq79yRHdxmFqYiIpIybTx7O4C6tAZi/bju3vfplyBUFFKYiIpIyWmSmc9f5+5GVEcTXo58s5a05a0OuSmEqIiIpZnj3Nvz0xGHl6z96djprt+4OsSKFqYiIpKBLD+nHkUM7A7Bp5x6+//R0SkvD6y6jMBURkZRjZvzp7FF0ap0NwEcLCnjgo0Wh1aMwFRGRlNSpdTZ/Onvf8vU//m8us1ZuCaUWhamIiKSsI4d24fLx/QHYU+J894mp7CwqbvQ6FKYiIpLSfnziUIZ3bwPAooId/Oq/cxq9BoWpiIiktOyMdO46bzQtMoNIe/Lz5bw2c3Wj1qAwjQMNdC8iEq7BXXP5+Skjytd/8twMVm3e1WifrzCNAw10LyISvgvG9uG4EV0B2Lq7mJuemkZJI3WXUZiKiEiTYGb84cx96dom6C7z6eKN3P6//Eb5bIWpiIg0GR1aZXHHOaNJs2D93vcX8fwXKxL+uQpTERFpUg4Z1In/O2l4+fpPnp/J1GWJbdOiMBURkSbnikP7c9aYXkAwXdtVj0xh2YadCfs8hamIiDQ5ZsZtX89j/z7tACjYXsiFD36SsM9TmIqISJOUnZHOfRcfwIBOrQBYvjFxXWUUpiIi0mR1ap3No1ceRPe2LRL6OQpTERFp0nq2a8mjVxxEp9ZZCfsMhamIiDR5g7q05plrD0nY8RWmIiLSLPSPPDtNBIWpiIhIjBSmIiIiMVKYioiIxCgj7AIam5mlA1MqbMoERgCj3H1GOFWJiEgqa3Zh6u4lwOiydTM7H/iJglRERBoq9Nu8ZtbLzO42s0lmttPM3Mz61bBvbzN71sy2mNlWM3vezPrEWMKVwAMxHkNERJqx0MMUGAScA2wCPqxpJzPLAd4FhgGXABcBg4EJZtag9s5mNhAYBzzWkPeLiIhActzm/cDduwKY2ZXA8TXsdxUwABjq7gsi+88A5gPXAH+JbHubCrdxqzjd3SdWWL8CeM7dEzs3j4iINGmhh6m7l9Zz19OAT8qCNPLexWY2ETidSJi6+7H1OVikIdIlwAXRVfyV45Q3Zho5cmQshxIRkRQVephGYSTwUjXbZwNnN+B4JwPb3f39mKqqoKSkhPz8/HgdrskpKCjQ+amDzlHtdH7qpnMUjlQK0w4Ez1Wr2gi0b8DxrgQejKkiwN3HlH2dl5fnw4YNi/WQTVZ+fj46P7XTOaqdzk/ddI7CkUphGlfuflrYNYiISNOQDK1562sT1V+B1nTFKiIi0ihSKUxnEzw3rWoEMKeRa6nEzK42s8mbNinTRUSao1QK05eBg81sQNmGyOAO4yOvhcbd73P3A9q3b8ijWxERSXVJ8czUzM6KfFnWmOdEM1sPrK/Q2vZ+4NvAS2b2M8CBXwPLgXsbs14REZGKkiJMgWeqrN8T+fN94EgAd99hZkcDdwCPAga8A9zo7tsbqc5qmdnVwNU9evQIswwREQlJUoSpu1s991sGnJngcqLm7vcB9+Xl5XnYtYiISONLpWemIiIiSUlhKiIiEiOFqYiISIwUpnGgfqYiIs2bwjQO1M9URKR5U5iKiIjESGEqIiISo6ToZ9oURCYJLzaz6Qk4fCegIM7717ZPTa9Vt73qtprWh0fWv6yjroaI9vzU9z3N+RzVd/9oz1FTOT/1fU9z/h6q73sa+3toVB31NIy7a4nDAkwBpiTo2JPjvX9t+9T0WnXbq26raT2Zzo/OUfz2j/YcNZXzo++h8M5Rsp4f3eZNDfclYP/a9qnpteq2V91W13oiNOQzdI7is3+056ipnJ/6vqc5fw/V9z1N4nvIImktMYrc5sXdx9S1b3Ok81M3naPa6fzUTeeodok8PwpTERGRGOk2r4iISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxygi7gKakQ4cOPmDAgLDLSFpFRUVkZWWFXUZS0zmqnc5P3XSOajdlypQCd+8c7+MqTOOoR48eTJ48OewyklZ+fj7Dhg0Lu4ykpnNUO52fuukc1c7MlibiuLrNKyIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxUpiKiIjESGEqIiISI4WpiIhIjBSmIiIiMVKYioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiIiIxSrkwNbM0M/upmS0xs91mNt3Mzqznex82M69muTPBZYuISBOWEXYBDfBr4AfAzcAU4DzgGTM7xd1fq8f71wOnVdm2Or4liohIc5JSYWpmXQiC9Pfu/qfI5glmNgj4PVCfMC1y908SVaOIiDQ/qXab92tAFvBYle2PAfuYWf/GL0lERJq7VAvTkUAhsKDK9tmRP0fU4xhdzKzAzIrNbJ6Z/djM0uNapYiINCspdZsX6ABsdnevsn1jhddrM43gOetsoAXwdeB3wGDgyoYUZGZTyr4eOXJkQw4hIiIpLtQwNbNjgbfqsev77n5krJ/n7ndW2fSamW0HbjSzP7j7/FiOX1JSQn5+fiyHaNIKCgp0fuqgc1Q7nZ+66RyFI+wr04+B4fXYb2fkz01AOzOzKlenZVekG4neE8CNwAFA1GHq7mPKvs7Ly/Nhw4Y1oITmIT8/H52f2ukc1U7np246R+EINUzdfScQza9Qs4FsYCCVn5uWPSudE0s5MbxXRESasVRrgPQGsAe4sMr2bwKz3H1xA455IUGQfh5jbSIi0kyFfZs3Ku6+zsz+AvzUzLYBXwDnAkdTZSAGM3sH6OvugyLrfYFHgScJrmqzCRogXQrc6+4LG+vvISIiTUtKhWnEzcB24AagGzAXOMfdX6myXzqV/37bCJ6p/hjoCpQS3GL+LnBPgmsWEZEmLOXC1N1LgN9Eltr2O7LK+kbgjIQVJiIizVaqPTMVERFJOgpTERGRGClMRUREYpRyz0xFRJq6wuISlm/chRm0zs6gc+ts0tIs7LKkFgpTEZEkMmnhBj5ZtOEr248b0ZW8nm1DqEjqQ7d5RUSSxHtz11UbpABvzVnLW3PWNnJFUl8KUxGRJLB8406mLttcaVun3OxK67NWbuHTGsJWwqXbvCIiIdtTUsqzU1ZU2nb14QNolZ3Bll17eOijvSOlfrxwA3065tC9bcvGLlNqoStTEZGQvfPlukrr5xzYm1bZwbVO25aZXD6+f6XXn/xsOUXFpY1Wn9RNYSoiEqKSUufL1VvL13u1b0nPdpWvOtvmZPL1/XpW2vbitJWNUp/Uj8JURCREH85fX2n91FE9qt2vX6dW9OuUU76+ctMulm3YWe2+0vgUpiIiISkt9UqNjsb0bU+LzPQa9z99VOWr0+e+WEFpqaZiTgYKUxGRkMxft73S+kEDOtS6f1qacd7Y3pW2vT5rTdzrkug1OEzNrJ2ZDTUzNSkTEWmA9+bubXjUOjuD7Iyar0rLdG/bkgGdW5Wvz1u7jTVbdiekPqm/qMPUzA41s8+ADcAcYFxkexczm2hmJ8a5RhGRJmfLzj3sLCopXz9lVPd6v/ekfSrv+8RnyyjR7d5QRRWmZnYQ8DbQBXio4mvuvg4oBi6KW3UiIk3U3LXbKq13zW1R7/dmpqdxRpXWvQ9/vCQeZUkDRXtleiuwBBgJ/BSoOvLy+8DY2MsSEWnaJi3cO5LRIQM7Rj2Qff9OrejdYW/r3q279jBl6ca41SfRiTZMxwEPuPsOoLp7CsuB+t+rEBFphgqLSyj1vT9CB3fNbdBxzhhduRvNB/MKWL65KKbapGGiDdMMYHstr7cnuNUrIiI1+HTR3ivIrm1a0KFVVoOOk5GexuWHVh4d6b3F21m5eVdM9Un0og3TuUQaHNXgRGBGw8sREWn6lm3cO9hC93b1f1ZanbYtM/nG/pWfnz79+XLmV3kmK4kVbZg+CJxvZudX2OZmlmVmtwOHAw/ErToRkSZm444i1m8rLF8/ZGDHmI/Zt2MrTtynW6Vtr8xYzYT8dTW8Q+It2llj7iG4Mn0cKCB4bvpvoDOQDTzq7v+Oa4UiTVhxSSk7CkvYVriHwuJSVmwpotXGnWRnptE+J4vMdI2r0tQs31h5CMCsOP0bD+vWhow041/vFJRvm7Z8M7NWbuG6owaRHmUDJ4lOVGHq7g5808yeAy4EhhNc3U4jCNJn4l6hSBNSWuqs3LyLxQU7WLV5F+u2FVbqH1hQsJ2ZW4OpuMyCW3idc7MZ0Kk1Azq3qnWoOUkN71a4WjxkYEfM4hdyg7rkcsKQNkyu0Ki3uNS56535XD6+P21zMuP2WVJZg+YzdfcXgBfiXItIk7Vu225mrdzC3DXb2b2npO43AO6weeceNu/cw/y12zGDfh1bkdezLYO6tE5wxZII2wsrt8/s0S7+A8h1bpXBtfsM5J/vL6y0/aGJizlz/1706ZhTwzslFjFNDm5mnQHcfX1d+4o0N+7OooIdTF6ykVWbqx/urW3LTDrlZpObnUF2ZhrLM3bQrWd7dhYWs2FHERt3FJVfubrD4oIdLC7YQZuWmRzUvwMje7SJ65WNJFZBhWelEEy3lggts9K58djBPPbpskqf+dwXK/jayG6M6NEmIZ+b7AqL6/eLbENEHaZm1h/4DXAK0DqybTvwCvALd19Yy9tFmjx3Z+H67UxatPErPzwz0oy+nVoxsHMr+nZsRevsyv8F8/cUMGxI5/L1klJn5aZdzFm9tdKcl1t37eGtOWv5aEEBJ+V119VGiphQYSze0b3bJfQXITPjooP78sWyTbw/d+/1zv9mryE7M42BnZvf3Y11Wwvr3qmBogpTM9sHeI+gP+lE4MvIS8OB84ETzewId58ZzyJFUsW6rbt5b956Vm6q3M+vQ6ss9unVlhHd20T13DM9zejTMYc+HXM4alhnpizZxKeL9z4Q21VUwnNfrKBPhxxOHdWDrAw1WEpmRcWl5V/369Sqlj3jZ/8+7emQk8ULU/dOJv7ytFVceFAfurSJrVtOqknk+MXRXpn+haDB0SHu/knFF8xsHPA68Gfg+PiUJ5Iadu8p4cP5BcxetYUKA9vQOTebg/p3YFCX1jFfhWRnpHPIoE6M7d+BjxduYMrSTeWvLdu4k79PWMBpo3s0yyuOVLB6y65KA9v3b6QwhSC4zz6gF89MXlG+7fFPl/GtIwc2q0ZtJZ64MI3219hDgLurBimAu08C/gaMj0dhNTGz75nZf81stZm5md0S5fsPNbOPzWyXma0xs79oGjmJxYJ123hk0hJmrdwbpG1aZnLyvt258KA+DO6aG9fbeRnpaRw+pDNXHtafdlVaZ748bRWvz1yNJ/CHhjRM/uq9gyi0D6FVba/2OZxaZWaaf7y3sFl9ryRyIItow3QHUFtjo7XUPtxgPFxFMGvNi9G+0cz2Bd4C1hE88/0ZcBnwcPzKk+ZiV1EJr85YzX+nr2ZHYXDFkZWRxqGDO3HJuL4MiXOIVpXbIpPLxvfnmOFdKm3PX7ONO9+eT8H2xD0fkuhNW765/OuD4zBQQ0MM6pLL6N7tKm17debqUGoJw5erkydMnwfONrOvvM/M0oFzIvsk0kh3Pwj4TgPeeyuwAjjb3d9x9weAG4BzzGz/eBYpTdvyjTt5/NOlzKvwm27fjjl88+C+HNivAxmNONjCvr3acc0RA8jOrPyZj05aWukHuIRn3bbKrbkT0SWmvo4c2pmcrL23duev3c6Sgh2h1dNYEn0FHu3/+L8RtOCdYGZnmlleZDkLmADkAH8zsz4Vl3gW7O6lde/1VWaWCZwAPO3ueyq89DRQBJweh/KkiSspdSYuKOC5L1awbXfQZzA7M43jR3bl6/v1pG3LcDrF52Rl8K0jBjKySpeHCfnr+M+nmjg6bJt27Km0npsdU6/EmJgZl47vV2nbC1NXJrTbSDJI9H+BaP9FZxAMIWjAoVVeswr7VJUMT7gHAi2AWRU3uvtuM1sIjAilKkkZ2wuLeXXGqkp9Rnu2b8kJed1o0yL8kWXMjONHdmNI19xKLTfXbt3NXe/M57Lx/WiX07DZSSQ2r1W4lXrUsC6h9w3Ozkjn3AN789Tny8u33TNhITcdNyTEqhIr0b8sRBumv6L6eUxTQYfIn5uqeW1jhdejYmZTyr4eOXJkQw4hKWDFpp28NnPvs1EzOHhAR8b26xD1pM6J1q9TK647aiAPfLi4UleMf01cwgl53RjevXl22A9LxX8DgHYh3b2oqke7luzbqy0zVmwp3/bh/PUcNrhzLe9KXRWnvUuEaMfmvSWeH25mxxI0CKrL++5+ZDw/OxFKSkrIz88Pu4ykVVBQkHLnx92ZW1DIlJU7y28T5WSmcVi/VrQrWs+8efEd/Cue5+jobs7EpTtYvGnvZNGPvVdAr7aZHNk/9q46YUjF76H1O4opKNg74Mau9SXkFyTu3EdzjrrjvFuw9/rijYICCjeuplfb2u9g7ClxJi3fwbbCEnbtcYxgDOD2LdM5emAuGUn2CybAnIXbKNi6p+4dGyi8G/eBjwkGfKjLzrp3qVPZd0z7al7rAMxuyEHdfUzZ13l5eT5s2LCGHKZZyM/PJ5XOz56SUt75ch2Ld2+lQ2SEoZ7tW3LyPt1plaBnXvE+R8OHw4J12/nv9FXl23YDb6wgJfsYptr3EMCsKSvo1CkIp6Hdchk+vHsd74hNtOfo5oHF3Pv+ovL1mVth9Mi+dGqdXe3+H80v4PPlGyG9DWk5ULG3bAnw1ko498DeoTayqs6sHSsoyopHlFQv6iaHZpZmZldE+nrOjiz/NbPLq2vlWxt33+nu+fVYlkVbZzUWAoVApXuxZtYCGADMicNnSBOxZdcenvp8eaUh/Eb3aceZ+/dKWJAmyqAurbnmiAFf2f6P9xayavOuat4h8bR55947A0O65oZYSfVysjI4c/9elbY9OmkpK6t8b2zaUcQdb83j8yV13y596vPlSddCeO3W6sfHjpeows/McgiGE7wPOA7IiizHAfcTtPJNrl9HIty9CHiDoBtMxZ+GZxHMxfpyKIVJ0lm+cSdPfLasfALnzHTjhLxuHDW0S8rOCZmTlcF3jh5Ep9aVb9899flyPl5QUMO7JFZrtuwub/UNJO1sP3065nDk0MrPSp/+fDmPTlrCF8s2ccdb83j44yVfed/w7rl895jB3Hjs4K/83V6YurLSJOhhWrNl91eeXcdbtFemvyBoxXsb0MndB7v7YKAj8GvgsMg+CWNmB0S64nwjsmmEmZ0VWXIq7PegmRVXefstQB/gaTM7xsyuAO4CnnX3KUiz5u5MXbaJ579Yya7IsG9tWmZyzoG9m0SjnYz0NC4a149DB3eqtP3TxRt5dNKSZjUSTmNZtH7vGDaZ6cn9i9h+fdpzWJXvjYLtRZUGya/oW0cO5IS87qSnGWbGqaN6cNroHpX2eeyTpQkPsfpYtSXxd2CiDdNzgMfc/RfuXv5d4u47Io2THgfOjWN91fk28AzwVGT97Mj6MwQjI5VJp0qXHHefRjBucHfgVeC3wCPAJQmtWJJecUkpb81Zy3tz11MaCZXeHXK4YGwfuuQ2rcHAD+zXgfPG9q60rWB7EXe+PZ+tuxPXQKM5qjgpwRFDutSyZ3I4oF8HzhrTq9Z9Tt63OzcdN6Ta5+0DO7fmqGGV/55PfLYs9F/UGqOfdbQPf3oSzBZTk4kE4ZYw7n4pcGlD93P3D4BxcS5LUlh1/Uf369OOwwd3TrpuL/HSvW1LvnXkQP7xXuUZEx/8cDFn7NezUQdhb6qqDufYvV1q/FLWu0MONx47mBWbdrFu225KIheW3dq0oHeHlnW2Ah/dux1LN+xg0frgmenGHUXkr9kW6t2dZRsS1/CoTLRXpuuBvFpeHwnoAYykjDVbdvPEp8vKgzQ9zThuRFeOHNqlyQZpmRaZwQTSVRvFvDh1JR/EuctPc7RmS+UGLx1bpc6AGWZG7w45jOnbgbH9g6VPx5x6d6c6bVTl271vzFoT2u3e3XtKWLYx+cL0VeAaM/tm1RfM7ELgaoJJwkWSmrszc8UWnpm8nO2FwaP11tkZnH1AL/J6tg25usZjZpy8b3dOyOtWafuUpZu474OFTX6IuUR6a87a8q8PGdgxJfv1NpSZcfG4vpW2PfV5PDplRK/s/3eiRRumPwOWAf82s6Vm9r/IspTg2eMy4OfxLlIknoqKS/nf7DW8/eVaiiPPUrq3bcH5B/Whe9ukbIyecMO7t+HyQ/tX2rajsIR7JizU7DMNUPUZYZ+OOTXs2XR1bJ3NqN57fzEt2F7E8ka4Qqyq4vPSYd0S1zUp2n6h64ExwO0E07EdHlm2A38ADojsI5KUCrYX8sRnyypNxZTXsy1njelF6xTrPxpvbVtm8t1jBn/lPDw6aSmT69G3UPaaWmG2npys9Gb7S1rVRlfPTllBcUnj3u6dvGTvCE8tshI3SEnUgza4+xZ3/6m7j3D3lpFlpLv/n7tvqfsIIo3P3ZmxYjNPfraMjTuCTvSZ6cbXRnbjuBFdG3XKtGSWnmZceVj/r8x5+eH8Av41cXGj/yBMVUs37B2woFf75ndVWiY9zTjnwMotxxt7/tSVm/deDSfyF2b9BJEmb9vuPbw4bSXvfLmOPSXBLZ+OrbM4f2wfRvRI/f6j8WZmHDWsy1d+CG7euYe7312gUZPqsL2wmCUFe3+AV+3X29z0bNeSrm32tmRetH5Hoz46qHjHPa9H4tpD1BrTZnZxQw7q7o80rByR+HF3vly9jffnrWf3nr0NaUb2aMORQ7uQlaHfJWvTs11LrjtqIPe+v6jSc6enPl9OXs+2HDs8/KnEktHCddsrrbdp0bwfHwCcOaYn90zY2w3r0UlLufHYwQn//tmycw87IwOwtMvJpGUCb/PW9a/8MHvnL60vJ2iMJBKaDdsLeTd/HSs27b2KyslK55jhXZN2SLdklJ2RzneOHsRbc9Yye9XecYpnrdzCrJVbUnKw/ERyd97NX1e+vm+vtvqFg+D76NRRPSpNuDBz5Rb27dUuoZ87fcXm8q/TEvzvUFeYHpXQTxeJs6LiUj5dvIEvlm4uH8kIYGCX1hw7vAs5WbpKiFbZpOMje7bl6QqTSUMwWP5J+3RnaAJbSaaSrbsqd8NoTt2s6jKoS2uyMtLK+5u+8+U6hnTNTegvYzuL9v57JHqSgVp/srj7+/U5iJmNJBifd5K7azwyaXQlpc7MlVv4dNGG8ts6ALktMjhyaGcGdk7N+TuTSc92LfnO0YN4ZNJStuza+9/8tZmrmb5iM2eP6dXsz/EH8yt3ZuiSW/00Zs3VxeP68sCHi8vXn5m8nIvG9UvIZ5WUeqVW+yMSPAJTtLPG3GBmz1XZ9i9gBjABmGVmXeNYn0it9pSUMmPFZv798RIm5K8rD9L0NOPAfh24eFw/BnXJbfY/5OMlIz2Nyw/tz+FDKs8wsnLTLu58e36lkG2OFlR4XnrY4E76vqsit0Um+/aq3Pc0UQ3aKraoBsjOTGwbiWiPfhFQ/kDAzI4gGCT+SeBmgrF7fxK36kRqsKuohE8WbeChjxbzzpfrKv0QH9ilNd88uC+HDu6kRkYJMqZve644rP9Xtj/00WLmrd1WzTuavvlV/t66xVu9I6r8IvbU58sTMhD95go/E9q0zEz4s/1of9L0p/Ik2t8AVgHfdPffA/cAp8SpNpGv2LC9kAn563jwo0VMWlj5lm6v9i05b2xvThvVgw4pNA5qqmrTIpMbjhlM5yq3Ml+dsZo3Zq0JqarwvPXl3uEDu7VtoYZZNchIT/vKzDQfL4zvkO7uXmnquIP6d4jr8asTbWuMlgQjH5U5Gvif7x07K5/g6lQkboqKS5m3dhuzV22pNLMLgFkw7dMB/do321FmwpSWZnzz4L7MXLGFtyuEyZert/Ll6q185+hBzWJAjHXbdlO4Z++AFkcNTf7p1sLUu0MObVpmsjVy9Th5ySYO7Nchbr+A7N5TeXCRLm0S/+w62u/yFcC+AGbWl2CWmPcqvN4JaPzBF6XJcXfWbt3NO1+u5f4PF/HWnLWVgjQjzdi3V1suGdePU0f1UJCGbJ9ebbl8/Fdv+9797oJKfXybqlemVx7Vp2sj/PBOdReM7VNp/dkpK+J27GkVhnNslZ3eKHMSR3tl+gzwAzPLAA4iGJP31QqvjwYWVvM+kXopLC4hf/U2Zq7cwvptXx0lpUOrLPJ6tmF49zbq5pJk2uZk8p2jB3H3uwsqbf/Hewu5eFxfOrZumgGzvbC40jP7k/bproZH9dAyK53xgzoxcUFwi3f9tkJWbt5Fz3ax/2K8YP3ehmCJ7hJTJtor098ATwAXEHSFucTdNwKYWVvgdOCduFYozUIwyMJaHvhwMe/mr6sUpBlpxvDubTjnwN5cPK4vY/p2UJAmqYz0NG489qvPUR+ZtJTVW5rmMIRvzan8fFiDgtTfmL7tK60//flySmNsjLRheyEFFX5+VP2MRInqJ5K77wIureHlbUAPdJtX6sndWbh+B9OWb652aqbOudns07MtQ7sltmO3xJdZ8Bx1wtx1TFu2uXz7k58t52sjuzWp8ZA3bC+sNA7v0cO6kN7EJ5WPp/Q04xv79+T5L1aWb/tg/nqOjOGZ8xcVvucy043cFpmxlFhvcfv13t1LAc0aI3Vyd5Zu2MnEhQWs21r5Vm5GmjGkWy6jerWja5ts3S5LYUcN7UKHnKxKw+v9b/YadhYVc0C/xLeubAyPTFpaab1iH0qpn74dW5GTlV7eMn/qss0c2K8DrRoww8vuPSXMWrk3hg4e0DFuddZF98qkUW3ZtYe356xlWZUr0TYtMxnVqy0je7RN6GDU0rhG9W5H59xsnqowDOGH8wvYuKOI40Z0TelfluZUGKsY4BgN/N9gF43ry73vLypff/zTpVx12ICoz+eH8yt3sWnMvr5Nv826JAV3Z17Bbh77ZGmlIO3UOotT9u3OZYf044B+HRSkTVCPdi258ODKLTdnr9oa19abja2ouJT/za78rHQfDdLQYDlZGRw1bO+t3R2FJcyNcvCPqlelI3u0adTHQwpTSbjC4hJemraKT5fvLB/kunV2BifkdePCg/oyuGsuaXrO1KR1yW3BVYcPqLRtxaZd3PHWvISMfpNI7s6Tny+rtO3icX11VRqjUVVukb8+c01U3aqeqfLL2fhBjTuPrMJUEmpHYTHPTlnB4oK9Y30M796Gi8b1ZXj3NgrRZqR1dgbXHjHwK9vvemd+SvVFnbp8Mxu2F5Wvj+7drsl2+2lMZsbF4/pW2vaP9xbiXvcvW9OWb67Ugveg/g175hoLhakkzMYdRTz5+fLyRkaZ6capo3pwQl43tc5tplpmpXPDMYO/sv0f7y2stkV3slm3dXelYeoAjhzauYa9JVodW2ezf5WuLE98trzWQF2xaScTKjRyAxg3sPEaHpVRmEpCFGwv5OnJy8uHC2udncHXBueqD56QlmbccMxgOlXpi/rslBW8PH1Vva5EwrCzqJjHP618e/fyQ/vr9m6cHT64U6XuRWu37uaxKue9zKyVW3hmcuXbu5ce0i+UfxOFqcTdjsJiXpq2il2Rpu4dW2dx7tjetG+pxuMSSEszLjq471cGIF+4bjt3vj2fZRuS6yq1pNQrtTYFOHGfbrRt2Th9GJsTM/vK44CCbYXc8dY8Vm7ehbuzanPwvP2tOWsr7XfqqB60D2mSC/10k7jaU1LKf6evKr8i7ZSbzdljetEiM51VIdcmyeeQQZ3o16lVpa4zAM99EVxtnLRPd4Z0DXdid3fnrnfmV9q2T8+2DOvWdAafSDZZGWlcd9RA7plQeXTap6t8n1R06qjuod750pWpxI278+bstazeEgxI3yo7ndNH99DzUalVj3Yt+fbRg2iX89WrvNdmruae9xby0fwCFq7fzpbdJRSXlFZzlMQoLXX+VmWs4XY5mRw7omuj1dBcZWekc/1Rg+o1J/Glh/RjUJfGGYO3Jil3ZWpm3wOOAg4AugG3uvst9XzvLcAvq3npJXc/I04lNluTFm4onxg6M904bVRP2jTSUF6S2jLT07hsfH/Wbt3Nf6o8HysqLuXzJRsBKCjYwsfrF9AqO522LTNpn5NFj3Yt6dmuJe1yMuN6BevuPDRxMcUVuu6YBT+4pXFkZaRx/VGDWL5xJx/MX0+aGSWlTma6UVhcyrgBHRnUJdw7F2VSLkyBq4CtwIvAtQ08xqFAxbb4G2OsqdlbtmEnny7eexpPyOtGt7aJn/ZImpaubVpw03FDWL8tmAR+/fbC8r7JFe0oLGFHYQmrNu9mdoWRiNq0zOTkfbrH/L1XWur8fcKCSkEKcP1Rg5LiB3dz07tDDhce1LfuHUOUimE60t1LI9PANTRMP3X34ngW1ZwVFpfwZoWZMw4Z2DH0Wy6S2jrnZnPOgb2BoGX46s27KdhRyNw9W2jVOostu/awp+SrrX637trDE58FV7bfPLjvV2avqY/SUufudxdQWqVV8XePGaxB7KVGKRemkQH1JYl8OK+AbbuD3016tGvBgU1kEHNJDp1aZ9MpMihCd9/IsGH9cHd27Slh9ZbdLN+4k6kVZgop89gnS8nKSOOKQ/vX+7n97j0l/OO9r07J/J2jBylIpVbNtQHScjMrMbOlZvYHM2vwbLRmNqVsiWeBqWLphh3MjIyHmZluHD+im0Y1koQzM3KyMhjYuTVHDu3CTccN4bTRPb6yX1FxKf94byGvzVxd57CFi9ZvrzZIrz9qEBnpzfVHpdRXyl2ZxmgB8BNgKuDA8cBNwP7AcbEevKSkhPz8/FgPkzKKikt5Ze5WdhQFNwsO6JnD2uWLWFvD/gUFBc3q/DSEzlHt6jo/J/aGNdv28NaCyoOkFxQUMHHWYgZ1zGZsr5xKV5nbCkt4cc5XZ49skWmcndeeRQvmxe8v0Aj0PRQOC3O0ETM7FnirHru+7+5HVnlvBrCHKFrz1lDDDcCdwHHu/nZDjwOQl5fns2bNiuUQKeWtOWvLZ2no2b4lZ4/pVWvjjPz8fIYNG9ZY5aUknaPa1ff8uDuTFm3g00XVty3s2zEI1EXrd1T7+uje7ThyaOeUbGyk76HamdkUdz8g3scN+8r0Y2B4PfZL5HAoTxCE6YFATGHanCzfuLM8SIPbu6k9N6U0LWbGIQM7MbZfB577YgWrNu+u9PrSWkZYumhc3/JntCL1FWqYuvtOIFnuRyTngKBJqLTUeW/e3sG+xw/qRLuccIbwEqlNRnoa5x7Yh6LiUt6YvYZ1W3ezvbCYqjfkMtKMo4Z1YWSPNvqlUBok7CvTZHBh5M/PQq0ihcxZvbV8uqNOudmM6tUu3IJE6pCVkcZpo4IGSsUlpewoLCEtDdLMaJmZrkZzErOUC1MzOwDox96WyCPM7KzI169FrnYxsweBS9w9o8J7pwKPAHMJrkSPA74DvOHu7zbO3yC1FRaXMHFBQfn6EYM76weRpJSM9DTa5qh1rsRXyoUp8G3gkgrrZ0cWgP7AksjX6ZGlormR93cnCONFwK+A2xNUa5Pz+eJN7IzMBjOgcyv6dMwJuSIRkfClXJi6+6XApQ3Zz93PS0RNzcWWnXuYumwTENweO3ywJkUWEYHmO2iDNMBHCwrKxyod1bttaPMGiogkG4Wp1MvKzbvKZ4RpkZnOwQM6hlyRiEjyUJhKndyd9+fu7QozbmBHzVEqIlKBwlTqNHftNtZuDTq9d2iVxT4924ZckYhIclGYSq1KSp2PF2woXz9scCfNniEiUoXCVGo1Y8VmtuzaAwTj7/bv1CrkikREko/CVGpUWFzCp4v3DhR+2OBOGmpNRKQaClOp0ZSlm9gVGaBhcNfWdG/b4GlfRUSaNIWpVGtHYTFfLN07QMMhAzuFXJGISPJSmEq1Plm0gT0lwQANeT3b0EEDNIiI1EhhKl+xaUcRs1ZuBYK5Sg/SAA0iIrVSmMpXTFxYQGlkwsf9+7SndXbKDeEsItKoFKZSyeotu5i/djsALbPSGdOvfcgViYgkP4WplHN3Ppy/d67Ssf07kJ2hYQNFROqiMJVys1ZuZeWmXQC0aZnJvho2UESkXhSmAsD2wmI+mL93MPujhnYmI13fHiIi9aGfloK7827+OoqKSwEY1i2XAZ1bh1yViEjqUJgKC9ZtZ+G6vY2OjhjaOeSKRERSi8K0mdu9p4QJc9eVrx8xpDM5WeoKIyISDYVpM/fBvPXsKAzG3+3fqRXDuuWGXJGISOpRmDYxJaVe732XbdjJ7FXBSEdZGWkcNayLZoUREWkA3c9rYp77YgVFxaX07ZhDv46t6N62RbWtcveUlPL2l2vL1w8Z2JG2LTMbs1QRkSZDYdqEFBaXsHrzbkrdWb+tkMlLNpGZbvRqn0Ofjjn07ZBDh1ZZmBmTFm4on/S7e9sWjOrVLtziRURSmMK0Cdm2u5gOrTIp2F5Uvm1PibO4YAeLC3YAkNsig17tW5K/ZhsA6WnGsSO6kpam27siIg2lMG1COrXO5qJx/di2ew/LNu5k2YadLN24s3yCbwgC98vV28rXD+zXgU6ts8MoV0SkyVCYNkG5LTIZ2aMtI3u0xSO3fJdu3MnSDTtZtXlXeSOlTq2zGNu/Q8jVioikPoVpE2dmdGnTgi5tWnBgvw4UFZeycvMuNu8sYmi3XNJ1e1dEJGYK02YmKyON/p1aAa3CLkVEpMlQP1MREZEYKUxFRERipDAVERGJkcJUREQkRmqAFCdmNgUoNrPpCTh8J6AgzvvXtk9Nr1W3veq2mtaHR9a/rKOuhoj2/NT3Pc35HNV3/2jPUVM5P/V9T3P+Hqrvexr7e2hUHfU0jLtricMCTAGmJOjYk+O9f2371PRaddurbqtpPZnOj85R/PaP9hw1lfOj76HwzlGynh/d5k0N9yVg/9r2qem16rZX3VbXeiI05DN0juKzf7TnqKmcn/q+pzl/D9X3PU3ie8giaS0xitzmxd3HhF1LMtL5qZvOUe10fuqmc1S7RJ4fhamIiEiMdJtXREQkRgpTERGRGClMRUREYqQwFRERiZHCVEREJEYKUxERkRgpTEVERGKkMBUREYmRwlRERCRGClMREZEYKUxFRERipDBtJGb2lJnNMLOpZvaZmR0Tdk3JyswuMzM3szPCriXZmNl7ZrbYzKZFll+EXVMyMbMsM7vTzOab2UwzeznsmpKJmaVX+N6ZZmazI//X9g27tmRhZieZ2RcVzs+19XmfJgdvPNe4+2YAM9sPeMfMOrl7abhlJRcz6wdcBXwScinJ7CZ3fzHsIpLUb4EsYKi7l5pZt7ALSibuXgKMLls3s/OBn7j7jNCKSiJmlgb8Bzjc3WeYWQ9gvpm97O6ranuvrkxrYGa9zOxuM5tkZjsjv731q2Hf3mb2rJltMbOtZva8mfWpuE9ZkEa0TWDpjSbe5yjyjfwA8B2gMPF/g8SL9zlqauJ5fswsB7iaIBxKAdx9TaP8RRIowd9DVxL8n0tZcT4/FvmzXeTPXGAbsL2uOhSmNRsEnANsAj6saafIf+B3gWHAJcBFwGBggpm1qrLvHWa2CHgOOLMJXJXG+xx9D5jo7lMSVnHji/v3EfD7yC3MZ81saGLKbjTxPD+DIsf5iZl9bmYTzeyURBbfSBLxPYSZDQTGAY8loObGFLfzE7lyPxt4zsyWAlOAa919a51VuLuWahYgrcLXVwIO9KtmvxuAEmBQhW39gWLgezUc+wTgcyAr7L9nspwjIA+YBGRG1t8Dzgj775hM5yiyrU/kTwMuB5YC6WH/PZPh/AD7R95/eWR9GLAOGBD23zNZzlGV/X8LPBr23y+Zzg/Bo8/3gKMi63nA6rL/d7UtujKtgdf/qvE04BN3X1DhvYuBicDpNRz7DaA9sE+sdYYpzufoMKAfwfOJJcDBwH1m9u24FRyCeH8fufuyyJ/u7g8BrYG+8au4ccX5/Cwj+EH6WOT1fGA6QcimrET8LDKzdIKrs5S+xQtxPz+jgR7uPiHy+ixgFnBQXQdXmMZuJMHJrmo2MALAzFqaWf+yF8xsHNARWNQoFYavznPk7v9w9+7u3s/d+xE0QLra3f/WeGWGqj7fRy3MrFPZC2Z2EsFv2ssbpcJw1ed7qAD4H8GdH8ysO8EvrDMbqcaw1XmOKjgZ2O7u7ye8quRRn/OzHOhhZnkQPI8F9o3sUyu15o1dB4J79VVtJLj6BGgJ/MfMcgluKewgeGZa3fuaovqco+auPueoDfC6mWUBpZH9T3H3PY1TYqjq+z30LeBBM7uN4Cr1++4+txHqSwbR/D+7Engw4RUllzrPj7uvNbMrCX5eO5AO/J+7z6nr4ArTRuDuGwke9Es9ufuRYdeQbNx9HTAm7DqSmbsvAdSHuw7uflrYNSQrd38SeDLa9+k2b+w2Uf3VVU2/BTVHOkd10zmqnc5P3XSOapfQ86Mwjd1sgnvxVY0A6rw10EzoHNVN56h2Oj910zmqXULPj8I0di8DB5vZgLINkQ7D4yOvic5Rfegc1U7np246R7VL6PmxSF8aqYaZnRX58hjgWuA6YD2wvqwVXKSz73RgF/AzgkYPvyYYOWNfd69z5IxUpnNUN52j2un81E3nqHZJcX7C7nCbzEvkZFe3vFdlvz4EoxptJRh66kWq6TTcFBedI50jnR+do7CXZDg/ujIVERGJkZ6ZioiIxEhhKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiMFKYiUm9mdqSZuZldGnYtVZnZEjN7L+w6pHlSmIpIJWbWzsxuMbMjw65FJFVoPlMRqaod8MvI1+9Vee0Dgsnum8OE5CL1pjAVacLMLB3Idved8Tieu5cCu+NxLJGmRLd5RepgZjlmdpuZzTezXWa20cymmNmNVfZLM7PrzWyqme00s61m9j8zO7jKfmXPHS8zs++b2SIz221mM8zszGo+/zoze8fMVptZkZktNbM7zSy3luPeaGbzCILvnMjr55nZK2a2InKcVWb2kJl1q3gMYHFk9ZeR43nZs8ianpmaWRczu9fMVkaOvdjM/hCZqaPifrdE3j808vqqyN/9UzM7JIp/lhqZ2Vgz+zDyb7DGzO4ws5ZV9nk4Ukc3M3vSzDab2TYze97M+sajDmledGUqUrd7gAuBfxJM4dSKYELhI4A7K+z3CHAe8ARwP9AauBJ438yOc/cPqhz3u0D7yL5FwBXAM2Z2jrs/W2G/7wMTgdeBHQTzL34HGAUcVU29NxJMK/UgsBGYG9l+HbAO+Ftk+37A5cA4Mxvt7oXAl8BNwB3AC8DzkfeurenkmFk74GOgH3AfMDNS44+A8WZ2pLsXV3nbI5G/y++BNpG/4ytm1t/dt9T0WfXQC/gfwb/BEwTn50ZgIHBaNfu/DqwCbgYGAdcDYyLnY1MMdUhzE/bUOVq0JPsCbALuqWOfrxNM+fTNKttzgaXA5ArbjozsuwXoVmF7e2A1sBxIr7A9p5rP+2XkGOOqOe56oEM176nuOJdE3nN+hW39IttuqWb/ss+4tMK230W2XVJl319Htl9VYdstkW0vEZlPObL9zMj2a2P4d1oSOca3qmy/N7L9axW2PRzZ9mSVfc+PbP9d2N93WlJr0W1ekbptBg4ys3617PNNYAPwhpl1KluAbOAtgqudDlXe87i7rylb8eBK6EGCq6sxFbbvhOD5Z6SlbSdgQuTlA6up5VF331h1Y4XjpJlZ28hxyq6WqztOfZ0BrAAerbL9doIr7jOqec/d7l5x/seyv8+gGOqA4BeUB6ps+2Pkz9Or2f8vVdafJPhlprp9RWqkMBWp2/eBocBiM5tlZndV021kONCR4Kqw6nJFZJ+uVd6TX81nfRn5s3/ZBjP7mpl9DOwiuEpeD7wfebldNcdYUN1fIvIs8S2C26ubI8dZVMtx6qs/kO9B46Ry7r6NIJgGVPOexVX2LQv/jjHUAbDI3au2NF5IEOr9q9m/0r9BJODn1rCvSI30zFSkDu7+vJl9AJxMcJvzLOA7ZvaIu18S2S0NWAlcWsuhlkX72ZHGS6+y91nmUoJGRT0JblVW9wvxV1ruRhrVTAAKgJ8B8yP7pQNv1HCcRCqpYbs1ahUicaIwFakHdy8A/g38O9Ld5FHgYjP7k7vPJAin44GP3L2+XUeGVbNteOTPsiu3cwkC7xR3X1q2k5kdH+Vf4QwgB7jY3cuuajGzIdXs69Vsq80iYJiZWcVbt2bWGugNvB3l8WIxwMwyq1ydDgSyqHI1HDEM+KxsxcyMyF2IhFYpTY5u84rUouw5ZcVt7l4CzIislt2WfJTgB/avazhO1Vu8ABdW6ZbSnuCW8EpgSmRz2RVcWoX90ghuPUfjK8eJ+GE1+26P/Nm+nsd+ieA57zerbP8BwTl5sZ7HiYe2BC2oq9YB8HI1+3+vyvp5BL8AVLevSI10ZSpSu1xglZm9BEwjuE06lKALxUJgEoC7P21mpwA/MLMDCbpcbCL4wXwEkAmMq3LsRcAnZnYfwYhCVxA8Vz0/EtgQBNX3gFfN7F6CMDyHIKSi8QbB7eFHzOxuglu8pwCdq+7o7hvMbCFwnpktIHi2us7d363h2H8AzgYeMrODgNnAIQThOhH4V5S1lov0bz0C6O/uS+rxlkXAb81sH2AWQdeYs4DX3P2NavYfamavAq8RXMF+m6Ax1e0NrVmaJ4WpSO12AncBxwBfI7hVupKg1e3vPOibWeYSgueSVxI8l8wg6OryGV9t6UrkuB0J+n/2JLhVfK67P1O2g7t/aGbnE/SD/D1B/9BnCPqmzqrvX8LdF0TC/rcE3Wp2EjyLvYig72lVFxG0dP0DwfCB7wPVhqm7bzaz8QRX5d8Aribou/lH4Fb/ah/TaORGat1cz/2XE3Rv+TPB8+vtBOf5pzXsfyLwV+A2gn+v14CbqmsNLVIbq9w6XUQSLdISeAJwmbs/HGoxSSxye70AuM3df1nH7tEe+2GCfrFq8CRxoWemIpKsjia4xaxbrpL0FKYikpTc/Xl37+7uO8KuRaQuClMREZEY6ZmpiIhIjHRlKiIiEiOFqYiISIwUpiIiIjFSmIqIiMRIYSoiIhIjhamIiEiM/h/latirtzYjOgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 468x936 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axs = plt.subplots(\n",
    "    figsize=(6.5,13),\n",
    "    nrows=2, \n",
    "    gridspec_kw={'height_ratios':[6,2]}, \n",
    "    sharex=True)\n",
    "ax = axs[0]\n",
    "ax.loglog(\n",
    "    cvd_merged['s_bp'],\n",
    "    cvd_merged['balanced.avg.smoothed.agg'],\n",
    "    '-',\n",
    "    markersize=5,\n",
    ")\n",
    "\n",
    "ax.set(\n",
    "    ylabel='IC contact frequency',\n",
    "    xlim=(1e3,1e8)\n",
    ")\n",
    "ax.set_aspect(1.0)\n",
    "ax.grid(lw=0.5)\n",
    "\n",
    "\n",
    "ax = axs[1]\n",
    "ax.semilogx(\n",
    "    cvd_merged['s_bp'],\n",
    "    der,\n",
    "    alpha=0.5\n",
    ")\n",
    "\n",
    "ax.set(\n",
    "    xlabel='separation, bp', \n",
    "    ylabel='slope')\n",
    "\n",
    "ax.grid(lw=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the P(s) curve for interactions between different regions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can plot P(s) curves for contacts between loci that belong to different regions. \n",
    "\n",
    "A commonly considered situation is for trans-arm interactions, i.e. contacts between loci on the opposite side of a centromere. Such P(s) can be calculated via `cooltools.expected_cis` by passing `intra_only=False`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cvd_inter == contacts-vs-distance between chromosomal arms\n",
    "cvd_inter = cooltools.expected_cis(\n",
    "    clr=clr,\n",
    "    view_df=hg38_arms,\n",
    "    intra_only=False,\n",
    ")\n",
    "# select only inter-arm interactions:\n",
    "cvd_inter = cvd_inter[ cvd_inter[\"region1\"] != cvd_inter[\"region2\"] ].reset_index(drop=True)\n",
    "cvd_inter['s_bp'] = cvd_inter['dist']* resolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(1,1,\n",
    "    figsize=(5,5),)\n",
    "\n",
    "ax.loglog(\n",
    "    cvd_inter['s_bp'],\n",
    "    cvd_inter['balanced.avg.smoothed.agg'],\n",
    "#     marker\n",
    "    markersize=5,\n",
    ")\n",
    "\n",
    "\n",
    "ax.set(\n",
    "    xlabel='separation, bp', \n",
    "    ylabel='IC contact frequency',\n",
    "    title=\"average interactions between chromosomal arms\")\n",
    "ax.grid(lw=0.5)\n",
    "ax.set_aspect(1.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Averaging interaction frequencies in blocks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For *trans* (i.e. inter-chromosomal) interactions, the notion of \"genomic separation\" becomes irrelevant, as loci on different chromosomes are not connected by any polymer chain. Thus, the \"expected\" level of trans interactions is a scalar, the average interaction frequency for a given pair of chromosomes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# average contacts, in this case between pairs of chromosomal arms:\n",
    "ac = cooltools.expected_trans(\n",
    "    clr,\n",
    "    view_df = None  # full chromosomes as the view\n",
    ")\n",
    "\n",
    "# average raw interaction counts and normalized contact frequencies are already in the result\n",
    "ac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pivot a table to generate a pair-wise average interaction heatmap:\n",
    "acp = (ac \n",
    "    .pivot_table(values=\"balanced.avg\",\n",
    "                 index=\"region1\",\n",
    "                 columns=\"region2\",\n",
    "                 observed=True) \n",
    "    .reindex(index=clr.chromnames,\n",
    "             columns=clr.chromnames)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = 14\n",
    "\n",
    "f, axs = plt.subplots(\n",
    "    figsize=(6.0,5.5),\n",
    "    ncols=2,\n",
    "    gridspec_kw={'width_ratios':[20,1],\"wspace\":0.1},\n",
    ")\n",
    "# assign heatmap and colobar axis:\n",
    "ax, cax = axs\n",
    "# draw a heatmap, using log-scale for interaction freq-s:\n",
    "acpm = ax.imshow(\n",
    "    acp,\n",
    "    cmap=\"YlOrRd\",\n",
    "    norm=colors.LogNorm(),\n",
    "    aspect=1.0\n",
    ")\n",
    "# assign ticks and labels (ordered names of chromosome arms):\n",
    "ax.set(\n",
    "    xticks=range(len(clr.chromnames)),\n",
    "    yticks=range(len(clr.chromnames)),\n",
    "    title=\"average interactions\\nbetween chromosomes\",\n",
    ")\n",
    "ax.set_xticklabels(\n",
    "    clr.chromnames,\n",
    "    rotation=30,\n",
    "    horizontalalignment='right',\n",
    "    fontsize=fs\n",
    ")\n",
    "ax.set_yticklabels(\n",
    "    clr.chromnames,\n",
    "    fontsize=fs\n",
    ")\n",
    "# draw a colorbar of interaction frequencies for the heatmap:\n",
    "f.colorbar(\n",
    "    acpm,\n",
    "    cax=cax,\n",
    "    label='IC contact frequency'\n",
    ")\n",
    "\n",
    "# draw a grid around values:\n",
    "ax.set_xticks(\n",
    "    [x-0.5 for x in range(1,len(clr.chromnames))],\n",
    "    minor=True\n",
    ")\n",
    "ax.set_yticks(\n",
    "    [y-0.5 for y in range(1,len(clr.chromnames))],\n",
    "    minor=True\n",
    ")\n",
    "ax.grid(which=\"minor\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
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 },
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}