Population_evolution_OwWu17__04_06-2020.ipynb 1.66 MB
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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# last worked on 4.6.2020"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 20,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Number of processors:  4\n"
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     ]
    }
   ],
   "source": [
    "import sys\n",
    "import importlib\n",
    "sys.path.append('../platypos_package/')\n",
    "# Planet Class\n",
    "from Planet_class_LoFo14 import planet_LoFo14\n",
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    "importlib.reload(sys.modules['Planet_class_LoFo14'])\n",
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    "from Planet_class_Ot20 import planet_Ot20\n",
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    "from Lx_evo_and_flux import Lx_evo, flux_at_planet_earth, L_xuv_all\n",
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    "import keplers_3rd_law as kepler3\n",
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    "import notify\n",
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    "\n",
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    "#importlib.reload(sys.modules['Mass_evolution_function'])\n",
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    "from Lx_evo_and_flux import undo_what_Lxuv_all_does\n",
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    "importlib.reload(sys.modules['Lx_evo_and_flux'])\n",
    "\n",
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    "\n",
    "sys.path.append('../platypos_package/population_evolution/')\n",
    "\n",
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    "\n",
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    "\n",
    "from evolve_planet import evolve_one_planet, evolve_ensamble\n",
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    "importlib.reload(sys.modules['evolve_planet'])\n",
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    "from create_planet_chunks import create_planet_chunks\n",
    "from create_summary_files import create_summary_files_with_final_planet_parameters\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import matplotlib\n",
    "matplotlib.rcParams.update({'font.size': 18, 'legend.fontsize': 14})\n",
    "mpl.rcParams['axes.linewidth'] = 1.1 #set the value globally\n",
    "from matplotlib.ticker import ScalarFormatter, FormatStrFormatter, FuncFormatter\n",
    "import matplotlib.ticker as ticker\n",
    "import os\n",
    "import math\n",
    "from astroquery.nasa_exoplanet_archive import NasaExoplanetArchive\n",
    "from PyAstronomy import pyasl\n",
    "from astropy import constants as const\n",
    "# Use multiple cores for parallel processing\n",
    "import multiprocessing\n",
    "import multiprocessing as mp\n",
    "print(\"Number of processors: \", mp.cpu_count())\n",
    "import time\n",
    "import scipy\n",
    "from scipy import stats\n",
    "from sklearn.neighbors import KernelDensity\n",
    "import seaborn as sns\n",
    "import scipy.optimize as optimize\n",
    "from scipy.optimize import fsolve\n",
    "\n",
    "import random\n",
    "random.seed(42)\n",
    "\n",
    "#################################################################################################\n",
    "p = \"../supplementary_files/\"\n",
    "# Tu et al. (2015) model tracks\n",
    "blue = pd.read_csv(p+'Lx_blue_track.csv', header=None).sort_values(0)\n",
    "red = pd.read_csv(p+'Lx_red_track.csv', header=None).sort_values(0)\n",
    "green = pd.read_csv(p+'Lx_green_track.csv', header=None).sort_values(0).reset_index(drop=True)\n",
    "# Lx sample Jackson et al. (2012)\n",
    "jack = pd.read_csv(p+\"Jackson2012_Lx_clean.csv\")\n",
    "\n",
    "def read_results_file(path, filename):\n",
    "    # read in results files\n",
    "    df = pd.read_csv(path+filename)\n",
    "    t, M, R, Lx = df[\"Time\"].values, df[\"Mass\"].values, df[\"Radius\"].values, df[\"Lx\"].values\n",
    "    return t, M, R, Lx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tu evolutionary tracks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "# stellar parameters\n",
    "mass_star = 1.0  # M_sun\n",
    "radius_star = 1.0  # R_sun\n",
    "age_star = 10.\n",
    "L_bol = 1.0  # L_sun\n",
    "Lx_age = 2.*10**30  # calculate_Lx_sat(L_bol) # erg/s\n",
    "\n",
    "# use dictionary to store star-parameters\n",
    "star = {'star_id': \"dummySun\", 'mass': mass_star, 'radius': radius_star, 'age': age_star,\n",
    "        'L_bol': L_bol, 'Lx_age': Lx_age}\n",
    "age = star['age']\n",
    "Lx_age = star[\"Lx_age\"]\n",
    "\n",
    "# create dictionaries with all the values necessary to create the evolutionary paths\n",
    "Lx_1Gyr = 2.10*10**28  # Lx value at 1 Gyr from Tu et al. (2015) model tracks\n",
    "Lx_5Gyr = 1.65*10**27  # Lx value at 5 Gyr from Tu et al. (2015) model tracks\n",
    "\n",
    "track1 = {\"t_start\": age, \"t_sat\": 240., \"t_curr\": 1000., \"t_5Gyr\": 5000., \"Lx_max\": Lx_age, \"Lx_curr\": Lx_1Gyr, \"Lx_5Gyr\": Lx_5Gyr, \"dt_drop\": 0., \"Lx_drop_factor\": 0.}\n",
    "track2 = {\"t_start\": age, \"t_sat\": 40., \"t_curr\": 1000., \"t_5Gyr\": 5000., \"Lx_max\": Lx_age, \"Lx_curr\": Lx_1Gyr, \"Lx_5Gyr\": Lx_5Gyr, \"dt_drop\": 20., \"Lx_drop_factor\": 7.}\n",
    "track2_2 = {\"t_start\": age, \"t_sat\": 70., \"t_curr\": 1000., \"t_5Gyr\": 5000., \"Lx_max\": Lx_age, \"Lx_curr\": Lx_1Gyr, \"Lx_5Gyr\": Lx_5Gyr, \"dt_drop\": 20., \"Lx_drop_factor\": 5.}\n",
    "track2_3 = {\"t_start\": age, \"t_sat\": 100., \"t_curr\": 1000., \"t_5Gyr\": 5000., \"Lx_max\": Lx_age, \"Lx_curr\": Lx_1Gyr, \"Lx_5Gyr\": Lx_5Gyr, \"dt_drop\": 0., \"Lx_drop_factor\": 0.}\n",
    "track3 = {\"t_start\": age, \"t_sat\": age, \"t_curr\": 1000., \"t_5Gyr\": 5000., \"Lx_max\": Lx_age, \"Lx_curr\": Lx_1Gyr, \"Lx_5Gyr\": Lx_5Gyr, \"dt_drop\": 20., \"Lx_drop_factor\": 18.}\n",
    "track3_1 = {\"t_start\": age, \"t_sat\": 20, \"t_curr\": 1000., \"t_5Gyr\": 5000., \"Lx_max\": Lx_age, \"Lx_curr\": Lx_1Gyr, \"Lx_5Gyr\": Lx_5Gyr, \"dt_drop\": 20., \"Lx_drop_factor\": 10.}\n",
    "track_list = [track1, track2, track2_2, track2_3, track3, track3_1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PLOT\n",
    "########################################################################################################\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.set_title('$L_x$ evolution evolutionary tracks')\n",
    "\n",
    "ax.plot(blue[0], blue[1], marker=\"None\", linestyle=\":\", color=\"blue\", linewidth=2.5, alpha=0.6, label='_nolegend_')#, label=\"fast rot. (solar model)\")\n",
    "ax.plot(red[0], red[1], marker=\"None\", linestyle=\":\", color=\"red\", linewidth=2.5, alpha=0.6, label='_nolegend_')#, label=\"slow rot. (solar model)\")\n",
    "ax.plot(green[0], green[1], marker=\"None\", linestyle=\":\", color=\"green\", linewidth=2.5, alpha=0.5, label='_nolegend_')#, label=\"interm. rot. (solar model)\")\n",
    "ax.plot(jack[\"age\"]/1e6, 10**jack[\"logLx_cgs\"], ls=\"None\", marker=\"o\", color=\"grey\", mec=\"k\", alpha=0.3, zorder=1)\n",
    "#####################################################################\n",
    "step_size = 1.\n",
    "t_track_start = 10.\n",
    "t_track_end = 10000.\n",
    "t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "Lx_arr = np.array([Lx_evo(t=t_i, track_dict=track1) for t_i in t_arr])\n",
    "ax.plot(t_arr, Lx_arr, color=\"xkcd:royal blue\", ls=\"-\", zorder=2, label=\"fast activity track\", lw=2.2)\n",
    "#####\n",
    "t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "Lx_arr = np.array([Lx_evo(t=t_i, track_dict=track2) for t_i in t_arr])\n",
    "ax.plot(t_arr, Lx_arr, color=\"xkcd:green\", zorder=3, lw=2.2, alpha=1., label=\"medium activity track 1\")\n",
    "#####\n",
    "t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "Lx_arr = np.array([Lx_evo(t=t_i, track_dict=track2_2) for t_i in t_arr])\n",
    "ax.plot(t_arr, Lx_arr, color=\"green\", zorder=3, lw=2.2, alpha=1., label=\"medium activity track 2\")\n",
    "#####\n",
    "t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "Lx_arr = np.array([Lx_evo(t=t_i, track_dict=track2_3) for t_i in t_arr])\n",
    "ax.plot(t_arr, Lx_arr, color=\"xkcd:orange\", zorder=1, lw=2.2, alpha=1., label=\"100 Myr saturation\")\n",
    "#####\n",
    "t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "Lx_arr = np.array([Lx_evo(t=t_i, track_dict=track3_1) for t_i in t_arr])\n",
    "ax.plot(t_arr, Lx_arr, color=\"xkcd:dark red\", zorder=2, label=\"lower activity track\", alpha=0.9, ls=\"-\", lw=2.2)\n",
    "#####\n",
    "t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "Lx_arr = np.array([Lx_evo(t=t_i, track_dict=track3) for t_i in t_arr])\n",
    "ax.plot(t_arr, Lx_arr, color=\"xkcd:red\", zorder=2, label=\"low activity track\", alpha=0.9, ls=\"-\", lw=2.2)\n",
    "#####################################################################\n",
    "\n",
    "ax.loglog()\n",
    "ax.set_xlabel(\"Time [Myr]\")\n",
    "ax.set_ylabel(\"L$_\\mathrm{x}$ [erg/s]\")\n",
    "ax.set_xticks([5, 10, 20, 50, 100, 300, 1000, 5000])\n",
    "ax.set_yticks([10**27., 10**28., 10**29., 10**30., 10**31.])\n",
    "ax.xaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.0f}'))\n",
    "ax.set_xlim(left=4.9, right=11000)\n",
    "ylim = ax.get_ylim()\n",
    "ax.set_ylim(abs(ylim[0]), ylim[1])\n",
    "ax.legend(loc=\"best\", fontsize=12)\n",
    "#plt.savefig(\"./tracks_v1298Tau.png\", dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create a Planet Population\n",
    "Valley detected in Kepler (also K2) sample -> choose stellar & planetary population such that it matches the observed\n",
    "- orbital period distro similar to Kepler targets\n",
    "\n",
    "<font color=red> NEED: </font>\n",
    "- distribution of semi-major axes/orbital periods/equilibrium temperatures\n",
    "- core mass distribution\n",
    "- initial envelope mass fraction distribution <br>\n",
    "\n",
    "\n",
    "**Lopez & Fortney 2014**\n",
    "- f_env = envelope mass in % of total planet mass  ->  the planet models I use! Take different definition into account when creating the underlying distributions\n",
    "\n",
    "**Owen & Wu 2017**\n",
    "- orbital period distro similar to Kepler targets (from fitting Kepler planet sample & correcting for transit probabilities): <br>\n",
    "<font color=blue> dN/dlogP = const. (P>7.6 days) & P^1.9 (P<=7.6 days) </font>\n",
    "- logarithmically flat initial envelope mass fraction [f=M_env/M_c] distribution (<font color=blue>f=10^(-5) to 1 </font>) <br>\n",
    "(NOTE: f<1, such that core mass dominates & self-gravity of envelope can be neglected!)\n",
    "- Rayleigh distro for core masses (1 to 11 M_earth cores): <br>\n",
    "<font color=blue> dN/dM_c ~ M_c*exp(-M_c^2/(2*sig_M^2), where sig_M = 3 M_earth  </font>\n",
    "\n",
    "-> models which fall into the gap (R=1.8 +/-0.2 R_earth) after a few Gyr (due to cooling contraction & photoevaporation) are disvavored by observations and thus flagged! <br>\n",
    "**Note**: Their final models DO include many planets within the gap! They just exclude them and conclude the initial population must exist of either planets with M_pl >2 M_earth and envelopes of several %, or lower mass planets with essentially no atmospheres\n",
    "    \n",
    "**Ginzburg et al. 2018**\n",
    "- orbital period distibution: <br>\n",
    "<font color=blue> dN/dlog(T_eq) = const. (500<T_eq [K]<1000) & T_eq^(-6) (1000<T_eq [K]<2000)  </font>\n",
    "- correlate f_env [f=M_atm/M_c] with core mass according to theoretical planet formation models: <br>\n",
    "<font color=blue> f ~ M_c^(-1/2)  </font>\n",
    "- broken power-law core mass distro (reason: matches high mass tail of observed M_c distro (RV mass measurements) better <br>\n",
    "<font color=blue> dN/dM_c = const. (for M_c <= 5 M_earth) & M_c^(-2) (for M_c > 5 M_earth)  </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**--------------------------------------------------------------------------------------------------------------------------------------------------------------**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Population based on **Owen & Wu (2017)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stellar Parameters & Evo Tracks\n",
    "- Gaussian distribution in stellar mass with center at 1.3 M$_\\oplus$ and variance $\\sigma$ of 0.3 M$_\\oplus$ <br>\n",
    "- L$_{XUV}$ = L$_{sat}$ for t<100 Myr & L$_{sat}$*(t/t$_{sat}$)$^{-1-a_0}$ for t>=100 Myr\n",
    "- $a_0=0.5$, t$_{sat}=100$ Myr, L$_{sat}=10^{-3.5}L_{\\oplus}(M_{*}/M_\\oplus$)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 3,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2025\n",
      "1298\n",
      "1290\n",
      "1074\n",
      "1017\n",
      "983\n",
      "921\n"
     ]
    }
   ],
   "source": [
    "# get dataset from CKS (California-Kepler-Survey): https://california-planet-search.github.io/cks-website/ \n",
    "# column explanations: https://www.astro.caltech.edu/~howard/cks/column-definitions.txt)\n",
    "df_cks_orig = pd.read_csv(\"../supplementary_files/cks_physical_merged.csv\")\n",
    "print(len(df_cks_orig))\n",
    "df_cks = df_cks_orig.copy()\n",
    "# sample selection based on Fulton 2017\n",
    "mask_confirmed = df_cks[\"koi_disposition\"] == \"CONFIRMED\" # only select confirmed planets\n",
    "df_cks = df_cks[mask_confirmed]\n",
    "print(len(df_cks))\n",
    "# restrict sample to only the magnitudelimited portion of the larger CKS sample (Kp <14.2):\n",
    "mask_magnitude = df_cks[\"kic_kmag\"] < 14.2\n",
    "df_cks = df_cks[mask_magnitude]\n",
    "print(len(df_cks))\n",
    "# planet-to-star radius ratio (R_pl/R_star) becomes uncertain at high impact parameters (b) due to degeneracies with limbdarkening. \n",
    "# excluded KOIs with b > 0.7 to minimize the impact of grazing geometries.\n",
    "mask_impactparam = df_cks[\"koi_impact\"] <= 0.7\n",
    "df_cks = df_cks[mask_impactparam]\n",
    "print(len(df_cks))\n",
    "# remove planets with orbital periods longer than 100 days in order to avoid domains of low completeness \n",
    "# (especially for planets smaller than about 4 R_earth) and low transit probability.\n",
    "mask_period = df_cks[\"koi_period\"] <= 100.\n",
    "df_cks = df_cks[mask_period]\n",
    "print(len(df_cks))\n",
    "# also excised planets orbiting evolved stars since they have somewhat lower detectability and less certain radii. \n",
    "# implemented using an ad hoc temperature-dependent stellar radius filter:\n",
    "mask_evolved = df_cks[\"koi_srad\"] <= 10**(0.00025*(df_cks[\"koi_steff\"]-5500)+0.20)\n",
    "df_cks = df_cks[mask_evolved]\n",
    "print(len(df_cks))\n",
    "# also restrict sample to planets orbiting stars within the temperature range where we can extract precise stellar parameters \n",
    "# from our high-resolution optical spectra (6500–4700 K).\n",
    "mask_temperature = (df_cks[\"koi_steff\"] >= 4700) & (df_cks[\"koi_steff\"] <= 6500)\n",
    "df_cks = df_cks[mask_temperature]\n",
    "print(len(df_cks))\n",
    "\n",
    "# drop columns which have missing stellar mass, planetary radius, semi-major axis or period\n",
    "df_cks = df_cks.dropna(axis=0, how=\"any\", subset=[\"koi_sma\", \"koi_period\", \"koi_smass\", \"koi_prad\"])\n",
    "df_cks.reset_index(inplace=True)\n",
    "\n",
    "\n",
    "# Gaussian kernel density estimation\n",
    "# actual data -> transform to log space\n",
    "log3P = np.log(df_cks[\"koi_period\"])/np.log(3)\n",
    "log2R = np.log(df_cks[\"koi_prad\"])/np.log(2)\n",
    "\n",
    "# make a grid (in log space - to match the data)\n",
    "n = np.arange(log3P.min(),log3P.max()+1,1)\n",
    "m = np.arange(log2R.min(),log2R.max()+1,1)\n",
    "nn, mm = np.mgrid[n.min():n.max():200j, m.min():m.max():200j] \n",
    "\n",
    "nm_sample = np.vstack([nn.ravel(), mm.ravel()]).T # now I have a grid of points covering my radii and periods\n",
    "nm_train  = np.vstack([log3P, log2R]).T # this is my data in grid-form\n",
    "\n",
    "# construct a Gaussian kernel density estimate of the distribution\n",
    "kde = KernelDensity(bandwidth=0.25, kernel='gaussian')\n",
    "kde.fit(nm_train) # fit/load real dataset\n",
    "\n",
    "# score_samples() returns the log-likelihood of the samples\n",
    "prob_density = np.exp(kde.score_samples(nm_sample))\n",
    "# nm_sample is the range/grid over which I compute the density based on the data (2-D)\n",
    "prob_density = np.reshape(prob_density, nn.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "ax.set_facecolor('xkcd:off white')\n",
    "ax.plot(df_cks_orig[\"koi_period\"], df_cks_orig[\"koi_prad\"], ls=\"None\", marker=\".\", color=\"k\", alpha=0.1)\n",
    "ax.plot(df_cks[\"koi_period\"], df_cks[\"koi_prad\"], ls=\"None\", marker=\".\", ms=12, color=\"k\", mec=\"white\")\n",
    "\n",
    "# plot gaussian kernel density of known exoplanet population\n",
    "ax.contourf(3**nn, 2**mm, prob_density, cmap=\"YlOrBr\", levels=15, alpha=0.5)\n",
    "\n",
    "ax.set(xlabel=\"Period [d]\", ylabel=\"Radius [R$_\\oplus$]\", xlim=(1,100), ylim=(0.3,20), title=\"Planets in CKS sample\")\n",
    "ax.set_ylim(1,10)\n",
    "ax.set_xlim(0.7,100)\n",
    "ax.loglog(basex=3, basey=2)\n",
    "ax.set_yticks([1,2,4,6,10])\n",
    "ax.set_xticks([1,3,10,30,100])\n",
    "ax.xaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.0f}'))\n",
    "ax.yaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.0f}'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(7,6))\n",
    "mask_radius = df_cks[\"koi_prad\"] <= 20.\n",
    "hist, bins, _ = ax1.hist(df_cks[\"koi_prad\"][mask_radius], bins=18, range=(0.5, 6.5), histtype=\"step\", density=True)\n",
    "\n",
    "# histogram on log scale. \n",
    "# Use non-equal bin sizes, such that they look equal on log scale.\n",
    "logbins = np.logspace(np.log10(bins[0]), np.log10(bins[-1]), len(bins))\n",
    "ax2.hist(df_cks[\"koi_prad\"][mask_radius], bins=logbins, histtype=\"step\", density=True)\n",
    "\n",
    "ax2.vlines(1.8, ax2.get_ylim()[0], ax2.get_ylim()[1], color=\"k\", linestyle=\"--\")\n",
    "ax2.set_xscale('log')\n",
    "ax2.xaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.0f}'))\n",
    "ax2.set_xticks([1,2,4,6])\n",
    "ax1.set_title(\"Radius Histogram\")\n",
    "ax2.set_xlabel(\"Radius [R$_\\oplus$]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "#hist, bins, _ = ax.hist(df_cks[\"koi_smass\"][mask_radius], bins=10, histtype=\"step\", density=True)\n",
    "\n",
    "# 1D KDE\n",
    "sns.distplot(df_cks[\"koi_smass\"], hist=True, kde=True, \n",
    "             norm_hist = True,\n",
    "             color = 'darkblue', \n",
    "             hist_kws={'edgecolor':'black'},\n",
    "             kde_kws={'linewidth': 4})\n",
    "\n",
    "ax.xaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.1f}'))\n",
    "ax.set_title(\"Stellar Mass Histogram & KDE\", fontsize=15)\n",
    "ax.set_xlabel(\"Stellar Mass [M$_\\odot$]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "#hist, bins, _ = ax.hist(df_cks[\"koi_smass\"][mask_radius], bins=10, histtype=\"step\", density=True)\n",
    "\n",
    "# 1D KDE\n",
    "sns.distplot(df_cks[\"koi_srad\"], hist=True, kde=True, \n",
    "             norm_hist = True,\n",
    "             color = 'darkblue', \n",
    "             hist_kws={'edgecolor':'black'},\n",
    "             kde_kws={'linewidth': 4})\n",
    "\n",
    "ax.xaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.1f}'))\n",
    "ax.set_title(\"Stellar Radius Histogram & KDE\", fontsize=15)\n",
    "ax.set_xlabel(\"Stellar Radius [R$_\\odot$]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# HR-diagram\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_yscale(\"log\", basey=1.2)\n",
    "ax.plot(df_cks_orig[\"koi_steff\"], df_cks_orig[\"koi_srad\"], ls=\"None\", marker=\".\", color=\"k\", alpha=0.2)\n",
    "ax.plot(df_cks[\"koi_steff\"], df_cks[\"koi_srad\"], ls=\"None\", marker=\".\")\n",
    "ax.set(ylim=(0.5, 6.0), xlim=(6600, 4500))\n",
    "ax.yaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.1f}'))\n",
    "ax.set_yticks([0.5, 0.7, 1.0, 1.5, 2.1, 2.9, 4.2, 6.0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
534
   "execution_count": 4,
535
536
537
538
   "metadata": {},
   "outputs": [
    {
     "data": {
539
      "image/png": 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pDB48uPr70NBQQkNDm63r6NGjQP2NNbXWzW62+e677/J///d/REVF4e3tzdChQ7nllltIT09vsPzcuXM555xzasXZnIKCAlavXs3y5ctrHQ8MDKwVn63XW5Mj19yUrKwsJk+ezNq1a/H19XW4HmeyZWSrB7BAKeWNsaD+f1rrz5VSLwBpWutPgXnAu0qpbIwRrXEui1gI0ayEhAROnTqFt7e32aF4LOkjD2bnCJMZLBYLW7ZsYdq0abWOp6Wl8eCDD1Z/n5qaSmpqapN1ffHFF4wYMQJvb28OHjxY67NDhw7VG/mpq0+fPqxevZqysjKKi4vp0aMHY8eOJS4url7ZQ4cO8cknn/Dmm282d4m1bNiwgcrKSgYNGlTreFpaGuecc07197Ze7/nnn0+3bt0cvuamrFu3joKCApKTz6x4qqysZM2aNbz11luUlZXh5+fncP2OaDbZ0lpvAoY0cPzZGu9PADc5NzQhhKOUUnToYNcqgXZH+ki0RFZWFsePH6dnz57VxzZv3sz27dtrjRjZOq3m6+vLsGHDWLFiBTfddOaf0xUrVtQbPWtMYGAggYGBHD16lOXLl/PXv/61Xpn58+fj5+fHuHH2jYlUVlYCUF5eXn0sOzub5cuXs2TJkupj9kwjOuOaG3Lttddy9tln1zp21113kZCQwOTJk80Z7XJkVX1LX8jdiEK41O7du/VZZ52ld+/ebXYoHkv6yDO01rsR//Of/2hAP/DAA3r79u36q6++0v369dOAXr58uUN1Llq0SPv4+Oi5c+fqrVu36kceeUQHBgbqnJyc6jIzZ87USUlJtc778ssv9bJly/SuXbv0V199pQcNGqSHDx+uT548WaucxWLRCQkJ9e7+s0VBQYEOCAjQ48aN01u3btVffvmlTkxM1OPHj3foWqs4cs0lJSU6IyNDZ2RkaH9/f/3888/rjIwMvWfPnkbbMftuRPlvnRBtUEhICAcjzuX8137E2/8Xm8/Ledn8DQ7dJSQkhLvuukt2kBcOyczMrN6nLTk5mcTERFJTU7nrrruYOXNmvTvsbDF27FgKCwuZOnUqBw4cIDk5mWXLlhETE1NdpqCggKysrFrnFRUV8dRTT5Gbm0toaCg33HAD06ZNq7dh76pVq9ixYwcLFy6s1/b8+fO566672L17N7GxsfU+79q1Kx988AGPPfYYgwYNIjIykrvvvptJkybZfZ0tvea0tDQuvPDC6u+nTJnClClTuPPOO5vd4NQsSpuwjr3qbsTi4mKCg4Pd3r4Q7UHspKV2n9Oeki3hGbZt20bfvn3NDsNul112GUOHDuWll14yOxSnmDJlCosXL2bjxo3tenq9sd/HkpKSqv+YhWitS+ytt/32qBBtWFFRESWZXxLY93z2vtb8DtGOJGatXVFREf/73/+4+eab6dTJpK0GRKu1ceNGxo8fb3YYTrNs2TJmzZrVrhMtV7JpU1MhROtSUFDAse8WUnlctrNrTEFBAc888wwFBQVmhyJamfz8fPLz881/BIwTrV+/vtbUnHAuSWGFaIP69OlD9MP112WIM/r06VPvlnMhbBEeHo4ZS3BE6yUjW0IIIYQQLiTJlhBt0I4dO9j72k2cOpJndigea8eOHQQHB7Njxw6zQxFCtHGSbAnRBoWHh9P1sofwDuxidigeKzw8nLfffrtFO1ULIYQtZM2WEG1QSEgIgf1Gmx2GRwsJCeHWW281OwwhRDsgI1tCtDUVpRRt+JABW2aQWPELVJ42OyKPVFBQwJQpU+RuRCGEy0myJURbcfwIfP0ivNaPTp/9H5+d/RNfdZoGc0ZC9tdmR+dxysrKWLp0KWVlZWaHIoRo42QaUYi24NhemH8VHNtjfN9jED/mnSRG5dOjYDssvB4GjoVrZoO3/LEHiImJIS0tzewwhBDtgPytK0Rrd2Q3LLgaivZCj0GQ8lcqI8/h5j99iK9PB7Kv2Qer/wqb3ocOfvC7N0Aps6M2XWVlJaWlpQQFBeHt7W12OEKINkySLSFakbqP1QmhjGV+TxGlCthgSWD87j9QMruQU0fmsX/u/fS89204byL0GmkkZOn/hsAwuPgZk67Ac+zcuZOkpCSysrJITEw0OxwhRBsma7aEaMWe6fAuUaqATZY4fn9yEiUEAOAd3JXwW1/GO7irUTB6ONw0H5Q3rH0FdqwwL2gPERUVxZo1a4iKijI7FCFEGyfJlhCtUM7LV5Jzlzc3dVgDHToy8JEP+OXlG43jL1/J3r/fwMH3nmTv3284c1LS5WdGtJY+BiePmxO8hwgICOD8888nICDA7FCEAGDNmjVcffXVREZGopRi/vz5Np335ptvMnDgQEJCQggJCWHkyJEsXeoZD5efPXs2cXFxdOzYkWHDhrF27domyz/33HMopWq9IiIi7C7jaSTZEqI1Kj8Gn0003l/0DHRLqPXxwYMHufvuu+s/+2/kwxCebCyoXz3dTcF6pkb7SAiTlJaWkpyczIwZM/D397f5vKioKKZPn056ejppaWlcdNFFXHvttWzatMmF0Tbv/fffZ+LEiUyePJmMjAxGjRpFSkoKe/fubfK8pKQkDhw4UP3avHmzQ2U8iSRbQrRG62ZB6UGIHgHnPlDvY4vFwpEjR7BYLLU/8PaBq14HlFHHoW3uidcDNdpHQtho3bp1eHl5UVpaWn3s6NGjKKXYuHGj3fVdccUVpKamcuONN+LlZfs/z9dccw0pKSnEx8eTmJjItGnTCA4OZt26dXa1//PPP3PppZfSvXv3eiNHO3futPdyePXVVxk/fjz33nsvffv2ZebMmfTo0YM5c+Y0eV6HDh2IiIiofnXv3t2hMp5Eki0hWpnOlMCP1r+sLn0RvOrfSdezZ0+WLFlCz54961cQfQ4MGw+W07DqZdcG68Ga7CMhbJCZmUlCQgJBQUHVxzIyMvD19aVfv34ApKamEhQU1OSruak1e1RWVrJo0SJKS0sZNWqUzedt2bKF0aNH07dvX1atWsU333xDREQEw4cPZ+HChfTu3duuazl58iQbNmxgzJgxtdoZM2YMP/zwQ5Ox7Nq1i8jISOLi4hg3bhy7du1yqIwnkbsRhWhl7uuwFE6WQvwl0GtEg2UqKirYsWMHCQkJ+Pn51S9wwROQ+R5s/QQOb3dxxJ6p2T4Sppn+83R+PfKrW9s8K/Qsnhz+pF3nZGZmMnTo0FrHMjIy6NevHz4+PgBMmDCBm2++ucl6IiMj7Qu2AZs3b2bkyJGcOHGCoKAglixZwoABA2w+f+LEiaSkpPDGG28A0L9/f8aPH8/ixYu57bbbAPuupaCggMrKynrPHg0PD2flypWNnj9ixAjmz5/PWWedxaFDh5g6dSqjRo3il19+oWvXrjaX8TSSbAnRinSliPHey41vRk9utNyePXsYMGBA49sadIqEwbfChvnw3avA71wSrydrto+EaEZmZiY33HBDrWPp6ekMHjy4+vvQ0FBCQ0NdHktSUhKZmZkcO3aMDz/8kDvvvJNVq1aRnJzc7LkFBQWsXr2a5cuX1zoeGBiIqrEnnyPXours6ae1rnesppSUlFrfn3vuufTu3ZsFCxbw2GOP2VzG00iyJUQrcleHLwlQFZCYAlHDGi0XFxfHrl27mt7W4LxHIf1d2PQ/otQIcnWYCyL2XDb1kTCFvSNMZrBYLGzZsoVp06bVOp6WlsaDDz5Y/X1qaiqpqalN1vXFF19w/vnntygeX19f4uPjATj77LNZv349r732GvPmzWv23A0bNlBZWcmgQYNqHU9LS+Occ86p/t6ea+nWrRve3t71bkA5dOhQvdGupgQFBdG/f3927NjRojJmk2RLiNbi9EnGen9rvD9vYpNFfXx8iIuLa7q+0DgYcBNsWsS93kuZcvouJwXaOtjUR0I0Iisri+PHj9da87d582a2b99ea2TLXdOIdVksFioqKmwqW1lZCUB5eXn1sezsbJYvX86SJUuqj9lzLb6+vgwbNowVK1Zw0003VX++YsWKeqOBTTlx4gS//vorF154YYvKmE5r7fYXEAzo4uJiLYSw0aYPtJ4Sorc+k6y1xdJk0X379ulLL71U79u3r+k6D27RekqILno2XJ/15GInBuv5bO4j4VJbt241OwSH/Oc//9GAfuCBB/T27dv1V199pfv166cBvXz5cofqLCkp0RkZGTojI0P7+/vr559/XmdkZOg9e/ZUl5k5c6ZOSkqqdd6TTz6p16xZo3fv3q03bdqkJ02apJVSetmyZTa1W1BQoAMCAvS4ceP01q1b9ZdffqkTExP1+PHjHbqOKosWLdI+Pj567ty5euvWrfqRRx7RgYGBOicnp9Hrefzxx/WqVav0rl279I8//qivvPJKHRwcXOscW8o4qrHfx+LiYg1oIFg7kPfI3YhCtBbrjemAhZWXNPtsQ19fX5KSkvD19W26zvD+EHUOIaqcK71/clakrYLNfSREAzIzM7n00kvJzc0lOTmZxx57jNTUVLp06cLMmTMdqjMtLY0hQ4YwZMgQysvLmTJlCkOGDOHZZ5+tLlNQUEBWVlat8w4ePMjtt99OUlISF198MevXr+eLL76otbZp/vz5KKXIycmp127Xrl354IMPyMjIYNCgQUyYMIE77riDuXPnOnQdVcaOHcvrr7/O1KlTGTx4MN999x3Lli0jJiam0evJzc3llltuISkpieuvvx4/Pz9+/PHHWufYUsbTKG2MNLm3UaWCgeLi4mKCg4Pd3r4QrU7+LzBnFCXan3MrZvHLyzc6r+6MhfDJQ2ywJDDshTTn1SuEDbZt20bfvn3NDsNul112GUOHDuWll14yOxSbTJkyhcWLF7Nx40Y6dJAVRI1p7PexpKSEkJAQgBCtdYm99crIlhCtQdo/Afio8jeU0fzO0mVlZXz55ZeUlZU1X3f/6yjW/gzz2tGuNjm1q4+EqGPjxo0MHDjQ7DBstmzZMmbNmiWJlkkk2RLC050+CZsXA/DfyottOiUvL4+UlBTy8vKaL+wbyCeV5xnvNyxwNMpWx64+EqKG/Px88vPzW1WytX79es9eQN7GSbIlhKfb+TWcOAZh/flV97LplISEBE6ePElCQkLzhYFFlRcZbza9D5WnHI20VbG3j4SoEh4ejtaa/v37mx2KaCUk2RLC023+wPg6wPZ1WkopfHx8mtw8sKZfdCzbLZFQfgR2rXYkylbH3j4SQghHSbIlhCerKIFflxnvk23fmyYnJ4d+/fo1eOdRYz6vHGm8+eUjOwJsvRzpIyGEcIQkW0J4sl+XwelyiD4Xuth+W3NISAh33nln1d0zNvnccq7xZtvncNq2zRBbM0f6SAghHNFssqWUilZKfauU2qaU+kUpVW/raqXUaKVUkVIq0/p6tqG6hBB2cmAKEYxnmD355JN2Pcdsl+4JEQOgogiyv7arvdbIkT4SQghH2DKydRp4XGvdFzgXeEgp1a+Bcmu11oOtrxecGqUQ7VH5Udj1LShv6H+dXacWFRXxj3/8g6KiIvva7H+98bUdTCU63EdCCGGnZpMtrfUBrXW69X0JsA1w/oOchBC1bf8KLKchZhQEdrPr1IKCAp5++mkKCgrsa7Mqqft1GZwqb7psK+dwHwkhhJ3sWrOllIoFhgANPddjpFJqo1LqC6WU3A8rREtlLTW+nnWV3af26dOH/Px8+vTpY9+JoXHQYzCcKmvzdyU63EdCCGEnm5MtpVQQ8CHwqNa6uM7H6UCM1noQMBP4uJE67lNKpQFt+29xIVrq1AnYsdJ4f9YV7m07ydpe1jL3tiuEEG2UTcmWUsoHI9F6T2tdbzGH1rpYa11qfb8M8FFK1Zv30Fq/o7U+G/hty8IWoo3bvcYYXYoYAJ1t28i0puzsbEJCQsjOzra/7STrw2u3LweLxf7zW4kW9ZEQQtjBlrsRFTAP2Ka1frWRMhHWciilhlvrLXRmoEK0K79+bnx1YAoRICwsjDlz5hAWFmb/yREDICQKSg/CgQyH2m8NWtRHQghhB1tGts4D7gAuqrG1wxVKqQlKqQnWMjcCW5RSG4E3gHFaa+2imIVo2ywWyPrCeJ/k2BRiSEgIt912m2N7SCkFSZcb77O+dKj91qBFfSSEC6xZs4arr76ayMhIlFLMnz/fpvPefPNSTW0TAAAgAElEQVRNBg4cSEhICCEhIYwcOZKlS5e6NlgbzZ49m7i4ODp27MiwYcNYu3Ztk+U9+Vpawpa7Eb/TWiut9cAaWzss01q/pbV+y1pmlta6v9Z6kNb6XK31D64PXYg2an86lB2CTr2MUSYHFBYW8txzz1FY6OAAc6J1KrEq6WuDWtxHQjhZaWkpycnJzJgxA39/f5vPi4qKYvr06aSnp5OWlsZFF13Etddey6ZNm1wYbfPef/99Jk6cyOTJk8nIyGDUqFGkpKSwd+/eRs/x1GtpKdlBXghPk21dGJ84xhhlckBpaSmfffYZpaWljsUQdz74BkH+Zji2z7E6PFyL+0i0e+vWrcPLy6vW79DRo0dRSrFx40a767viiitITU3lxhtvxMvL9n+er7nmGlJSUoiPjycxMZFp06YRHBzMunXr7Gr/559/5tJLL6V79+4opWq9du7cae/l8OqrrzJ+/Hjuvfde+vbty8yZM+nRowdz5sxx+bV4Gkm2hPA0VclW/CUOVxETE8OGDRuIibH9ET+1dPCDPhca73csdzgOT9biPhLtXmZmJgkJCQQFBVUfy8jIwNfXl379jL2/U1NTCQoKavLV3NSaPSorK1m0aBGlpaWMGjXK5vO2bNnC6NGj6du3L6tWreKbb74hIiKC4cOHs3DhQnr37m3XtZw8eZINGzYwZsyYWu2MGTOGH36wbfLL0WvxRB3MDkAIUcPxI5C3Abx8IPZ8h6uprKykrKyMwMBAvL29Hask/hLY9hns/BbOucfhWDyVU/pIuMTB1FQqtv3q1jb9+p5FxOTJdp2TmZnJ0KFDax3LyMigX79++Pj4ADBhwgRuvvnmJuuJjGz5PuGbN29m5MiRnDhxgqCgIJYsWcKAAbYvQ5g4cSIpKSm88cYbAPTv35/x48ezePFibrvtNsC+aykoKKCyspLw8PBan4eHh7Ny5UqXXosnkmRLCE+y61vQFoj9DfgFNV++ETt37iQpKYmsrCwSExMdq6TPRdaYVkPlKfD2cTgeT+SUPhLtWmZmJjfccEOtY+np6QwePLj6+9DQULc8fzMpKYnMzEyOHTvGhx9+yJ133smqVatITk5u9tyCggJWr17N8uW1R7EDAwNRNZYyOHItqs5SCK11vWN1teRaPJUkW0KYLHbSmTtt/tZhPjd1gNTtkbwzyfE7cKKioli1ahVRUVGOB9a5F3RNgMIdkJsGMSMdr8sDOaWPhEvYO8JkBovFwpYtW5g2bVqt42lpaTz44IPV36emppKamtpkXV988QXnn+/4SDaAr68v8fHxAJx99tmsX7+e1157jXnz5jV77oYNG6isrGTQoEG1jqelpXHOOedUf2/PtXTr1g1vb28OHjxY6/NDhw7VG+1y5rV4Kkm2hPAYmt96G3fcrLYMaqZs0wICAvjtb52wd3D8xUaytfPrNpdsOa2PRLuUlZXF8ePH6dmzZ/WxzZs3s3379lojW+6aRqzLYrFQUVFhU9nKykoAysvPPA81Ozub5cuXs2TJkupj9lyLr68vw4YNY8WKFdx0003Vn69YsaLeaGBz7LkWTyXJlhAeIufRGHjrGAT3ZPmUCQ7fiQhw8OBB/vKXvzB16lQiIiIcD6rPxfDTW7DzG7joL47X44Gc1keiXcrMzARg1qxZ/PGPfyQnJ4dHH30UoFZiYM/UW2lpafUTDSwWC3v37iUzM5PQ0FB69epV3d6sWbP49dcza9omTZrElVdeSXR0NCUlJfznP/9h1apVNu9PNWLECAICAvjzn//Ms88+y969e3nkkUcYN24cl19+uUPXAvDYY49xxx13MHz4cM477zzeeust9u/fz4QJE6rL1L2ell6Lp5K7EYXwFNlfG1/jL2pRogXG/1QPHz5c/T9Wh8WeB96+kJduLN5vQ5zWR6JdyszM5NJLLyU3N5fk5GQee+wxUlNT6dKlCzNnznSozrS0NIYMGcKQIUMoLy9nypQpDBkyhGeffba6TEFBAVlZWbXOO3jwILfffjtJSUlcfPHFrF+/ni+++IKUlJTqMvPnz0cpRU5OTr12u3btygcffEBGRgaDBg1iwoQJ3HHHHcydO9eh66gyduxYXn/9daZOncrgwYP57rvvWLZsWa07gOtejy3X0hopMzZ6V0oFA8XFxcUEBwe7vX0hPEnVmq2c/v8wRpBumAcDbjQnhpevrP/hgt8Zz2q88V+QfL1b4xJt37Zt2+jbt6/ZYdjtsssuY+jQobz00ktmh2KTKVOmsHjxYjZu3EiHDjKp1ZjGfh9LSkqqnjYRorUusbdeGdkSwgP4cBr2WDfti7ugxfVVVFSwdetW56xzqLorcec3La/Lgzi1j0S7s3HjRgYOHGh2GDZbtmwZs2bNkkTLJJJsCeEBhqgdcLocwvpBUMsfjLxnzx769+/Pnj17Wh5cnHUReY7zNl70BE7tI9Gu5Ofnk5+f36qSrfXr13PhhReaHUa7JSmuEB7gPO9fjDdOGNUCiI2NJTs7m+jo6JZX1mMQ+HWCozlwdA90aRs7rju1j0S7Eh4ejhlLcETrJSNbQniAkV5VyZZztiLw9fWlT58++Pr6trwyL29jk1VoU6NbTu0jIYRogiRbQpgsgBMMUdmgvCDGOc//ys3N5fLLLyc3N9cp9RFn3XBxd9tJtpzeR0II0QhJtoQw2TleWfioSug5BPw7O6XOqh2YnTZqUzW9uXsNtJHpE6f3kRBCNELWbAlhslFeW4w3TppCBAgLC2PWrFlOq4/ufSGgG5Tsh8Kd0C3eeXWbxOl9JIQQjZCRLSFMdq7XNuNNXMuejVZTWVkZX331FWVlZc6p0MurxrqtNc6p02RO7yMhhGiEjGwJYaYTxSSr3ZzS3vhEj3BatXl5eVx22WVkZWWRmJjonErjLoCtH/P5J+/z8OKmHyRbV4ObpZrMJX0khBANkGRLCDPt+wlvpdloiWOob6DTqk1ISKCiogIfHx+n1Vm1bmuE11ZAAy17pJDZXNJHQgjRAEm2hDBTzncA/GTpy1AnVquUcv7C767xEBhG97JD9FYH+Oale5s9peoxQJ7IJX0khBANkGRLCDPt+QEwkq0HnFhtTk4OV111FZ9//jmxsbHOqVQpY2uKrR8z3OtX59RpIpf0kXAKs5J0e6a7R48eTXJyssM3WSil+OCDD7jxRvc+B1WYQ5ItIcxysgz2p1OpFWkW564ZCgkJ4fbbb696cKrzxJzXZpItl/WREDY4cOAAXbp0MTsM4SaSbAlhln0/g+U0v+g4SglwatWhoaFMmjTJqXUC1ZuutoVky2V9JJzGXTdWmDGSFhER4fY2hXlk6wchzLLne8CYQnS2oqIi5s2bR1FRkXMrDutHkQ4gShXAsb3OrdvNXNZHol36+uuv6dy5M2+//TYWi4UXX3yR6Oho/Pz8GDBgAJ988kmt8kopFi9ebFPdL7zwAjExMfj5+REREcHvf//76s9Gjx7NAw88wOOPP05oaCjdu3dnxowZVFRU8NBDD9G5c2d69erFu+++W6vOSZMmkZSUhL+/P7Gxsfz5z3/mxIkT1Z/v27ePa665htDQUAICAjjrrLNYtGiRTTGJ+iTZEsIsOa5LtgoKCnjqqacoKChwbsVeXvxsOct4b11v1lq5rI9Eu/Phhx9y3XXX8c4773D//fczY8YM/va3vzF9+nQ2b97Mddddx/XXX09mZqZDdb/yyivMnj2bHTt28PnnnzN8+PBaZd577z2Cg4P56aefmDRpEo8++ijXXnstiYmJpKWlceedd3LPPfewf//+6nMCAwP55z//ybZt25g9ezaLFi1i2rRp1Z8/+OCDHD9+nG+//ZZffvmF119/nc6dO9sck6hNphGFMMPpCsjbAMB6S5LTq+/Tpw+HDh1yer0AP1vO4lLvdGNkbtA4l7ThDq7sI9F+vPPOOzzxxBMsXryYMWPGAPDKK6/wpz/9iVtvvRUwRoHWrFnDK6+8wsKFC+2qf8+ePfTo0YMxY8bg4+NDr169OPvss2uV6d+/P8899xwAjz32GC+//DI+Pj5MnDgRgGeffZbp06fzww8/VC/If+aZZ6rPj42NZfLkybzyyiu8+OKL1e3ecMMNDBo0CIC4uDi7YhK1SbIlhBn2Z0BlhTEttzfI7Giq2bJ2ZZBqGyNbQrTUJ598wttvv82aNWsYOXIkAMXFxezfv5/zzjuvVtnf/OY3LFu2zO42brrpJmbMmEFcXByXXXYZl19+OVdffTV+fn7VZQYOHFj9XilFWFgYAwYMqD7m4+NDly5dav3nYvHixbz++utkZ2dTWlpKZWUllZWV1Z9PnDiRCRMm8OWXX3LxxRdz3XXXMWzYMJtjErXJNKIQZti7zvja61yXVJ+dnU2nTp3Izs52et2/6FjKtB8UZkNp6x0ZcmUfifZh4MCB9OjRg3nz5qHrPKBdqfqb/jZ0rDnR0dFkZWXx9ttvExISwuOPP86wYcNqPWaq7sa8SqkGj1ksFgB+/PFHxo0bx2WXXcZnn31GRkYGU6dO5dSpU9Xl7777bnbv3s1dd93F9u3bGTVqVPXomS0xidpkZEsIM+z90fjaa6RLqg8LC+PNN98kLCzMpvJ23/W1YB7sXm1cR7+rHYjQfPb2kRB1xcXFMXPmTEaPHs19993HO++8Q0hICD179uS7777joosuqi773Xff0a9fP4fa6dixI1deeSVXXnklkyZNIiIigu+//7562tJe33//PZGRkbWmEvfs2VOvXFRUFPfddx/33Xcf06dPZ8aMGdUJl7Njausk2RLC3SyWGsnWucBmpzdRtYeUy/Q610i29v3UapMtl/eRaBd69+7Nt99+WyvheuKJJ3j22WdJSEhg2LBhLFy4kLVr17Jhwwa7658/fz6nT59mxIgRBAUF8f777+Pj40NCQoLDMScmJpKXl8d7773HyJEjWb58Of/9739rlZk4cSIpKSkkJiZSXFzMl19+WZ0suiKmtk6SLSHcrSALThyDkEjoFI0rkq3CwkJmzZrFww8/TNeuXZ1ef/X0Z9V0aCvk8j4SLebJj3uqqU+fPqxatYrRo0dz//33M2fOHEpKSvjzn/9Mfn4+SUlJfPjhhwwePNjuujt37sz06dP505/+xKlTp+jXrx8fffRRrQXr9vrd737HE088waOPPkp5eTljxozhhRde4MEHH6wuY7FY+MMf/sC+ffsIDg7m4osv5u9//7vLYmrrVN15Zrc0qlQwUFxcXExwcLDb2xfCVGn/hM//CMk3wI3/rP4HxZkbOO7Zs4frrruOJUuWEBMT47R6q1WUwMu9QHnBpH3g2/CmrK64NmdxeR8Jm2zbto2+fWtvf9IaHtcj2qaGfh8BSkpKqp42EaK1LrG3XhnZEsLdXLxeCyAmJob09HSX1Y9fMIT3h4ObYX86xP7GdW25iMv7SDhMkh7R1sjdiEK4m4vvRARjCqCkpKT67iOXqEoWW+lUolv6SIhmpKamEhQU1OArJSXF7PCEkzQ7sqWUigb+DUQAFuAdrfWMOmUUMAO4AjgOjNday38ZhaireL/xmBu/EAhz7M4kW2RnZ5OUlERWVhaJic59yHW16BHw8zuw9yfX1O9ibukjIZoxYcIEbr755gY/8/f3d3M0wlVsmUY8DTyutU63rrXaoJRaobXeWqNMCpBgfY0A5li/CiFq2mdNTKLOBi9vlzUTFRXFt99+S1RUlMvaqB7Z2vezcYelV+saKHdLHwnRjNDQUEJDQ80OQ7hYs387aq0PVI1SWReFbQMi6xS7Bvi3NvwIdFZK9XB6tEK0dvt+Nr5Gu24KESAgIIDRo0cTENDwwnWn6GS9m7KiCA5tbb68h3FLHwkhBHau2VJKxQJDgLrzBpHAvhrf51I/IRNCVI1sRbv2oa0HDx7k3nvv5eDBgy5th2jrAPa+1jeV6LY+Es0y4654Iepy5e+hzcmWUioI+BB4VGtdXPfjBk6pF7VS6j6lVBqw2q4ohWgLTpXDgY3GdgmRw1zaVGVlJfn5+bWedeYSVclW7nrXtuMCbusj0SQfHx/Ky8vNDkMIysvL6z3myFls2vpBKeWDkWi9p7X+qIEiuUB0je+jgP11C2mt3wHeqdpny/5whWjF8tLBchrCB0DHEJc2FRkZyaeffurSNoAzI3StcGTLbX0kmhQWFkZeXh6RkZH4+/s79PxAIVpCa015eTl5eXmEh4e7pA1b7kZUwDxgm9b61UaKfQo8rJRahLEwvkhrfcB5YQrRBrhpChGgoqKCXbt20bt3b/z8/FzXUHgy+ATAkV1QehiCuruuLSdzWx+JJlk3imT//v21HoQshDv5+PgQHh5e/fvobLaMbJ0H3AFsVkplWo9NBnoBaK3fApZhbPuQjbH1w13OD1WIVq56cbzrb9Tds2cP/fr1c/22Bt4djCnRnLWQ+zOc1Xo2o3RbH4lmhYSEuOwfOSE8QbPJltb6Oxpek1WzjAYeclZQQrQ5Wrt1ZCs2NpYdO3bQq1cvl7dF9HAj2dr3U6tKttzaR0KIdk0e1yOEOxTuhPIjEBQOXWJd3pyvry/x8fEubweocUfiz+5pz0nc2kdCiHatde1CKERrVb2Z6TnghgXAubm5pKSkkJub6/K2iDrH+Lo/A06fdH17TuLWPhJCtGuSbAnhDrnuW68FxmLPuLg4l93GXEtAKHRLhNMnjAdTtxJu7SMhRLsm04hCuMM+6z5UblivBRAeHs7s2bPd0hZgXFfBdtj3I0S5dg8xZ3F7Hwkh2i0Z2RLC1U4UG4+z8fKBHoPd0mRZWRkrVqygrKzMLe0RZU0iW9Hmpm7vIyFEuyXJlhCulrcB0NBjIPh0dE+TeXmMGTOGvLw8t7R3ZnPT1pNsub2PhBDtlkwjCuFqVaM9Ue6ZQgSIj4+nvLwcX19f9zTYLQn8QqA4F4r3Q0hP97TbAm7vIyFEuyUjW0K4WvVmpue4rUkvLy86duyIl5eb/oh71XjeYyvZAsLtfSSEaLfkbxkhXMliqTGy5b5kKycnhwEDBpCTk+O2NqunElvJui1T+kgI0S5JsiWEKxVmw4ljEBQBnaKbL+8kwcHB3HLLLQQHB7utzda2SN6UPhJCtEuyZksIV8qtMYXohs1Mq3Tt2pXJkye7rT3gzJYP+zONzU07ePZaKFP6SAjRLkmyJYSTxU5aWv0+tcNibu0A0zYFMzdjaRNnOVdRUREfffQR119/PZ06dXJPo/5djM1NC7bDwU0QdbZ72nWQKX0khGiXZBpRCBca4pUNQLolwa3tHj58mCeeeILDhw+7td3WNJVoWh8JIdodGdkSwkVynjsfXs4FLx8+fOFBt+2xBca2BgUFBW5rr1r0OZC50Lgj8dwH3N++HUzrIyFEuyMjW0K4yv503L2Zqela0ciWEEK4iyRbQrjKPvdv+VAlOzubLl26kJ2d7d6GuyeBbzAU7YPiA+5t206m9ZEQot2RZEsIV6m6E9GEZCssLIw33niDsLAw9zbs5X3mrkQPH90yrY+EEO2OJFtCuIQ2ZTPTKiEhIdxxxx2EhIS4ve3q6/XwZMvUPhJCtCuSbAnhAnHqIJQfhaBw6NzL7e0XFhby4osvUlhY6Pa2W8u6LVP7SAjRrkiyJYQLDFE7jDdR7t3MtEppaSkfffQRpaWlbm+7en+t/Rl04LT727eRqX0khGhXZOsHIVxgqFeNZMsEMTExZGRkmNI2AaHQNR4Ks+mr9rJZ9zYnjmaY2kdCiHZFRraEcIGqzUzNSrYsFgulpaVYLBZT2q+aSqxOOj2Q6X0khGg3JNkSwskCOMFZai94dYCeQ0yJITs7m+DgYPO2NbBOJQ7x4GTL9D4SQrQbkmwJ4WSDvHbirTSEJ4NvgCkxREVF8c033xAVFWVK+0RbR7aU5yZbpveREKLdkDVbQjjZEGXuFCJAQEAAF154oWnt070v+ATS69RhulFkXhxNML2PhBDthoxsCeFk1VNn1tEdM+Tn53PfffeRn59vTgDeHSByKOC5U4mm95EQot2QZEsIZ9La9MXxAKdPn+bAgQOcPm3i1gvRnr1I3iP6SAjRLsg0ohDOdHQ33VQxBTqEbl1iTQsjMjKSzz77zLT2gepkszr59DAe0UdCiHZBRraEcKbcNAAyLAmmbGZa5eTJk/z666+cPHnStBiqkq2BahdUet7okUf0kRCiXZBkSwhn2mc8fDrdkmBqGDk5OfTt25ecnBzzggjsxm5LOAGqAvK3mBdHIzyij4QQ7YIkW0I4U66RbGXoeFPDiI2NZfv27cTGxpoaR7q2Jp0e+JxET+kjIUTbJ8mWEM5y8jgc3MJp7cVGi7mPqPH19SUhIQFfX19T48iweG6y5Sl9JIRo+yTZEsJZ9meAruRX3YtyOpoaSm5uLldccQW5ubmmxlGdbFmnVz2Jp/SREKLtazbZUkr9Uyl1SCnV4KILpdRopVSRUirT+nrW+WEK0Qrs+wkwf70WgI+PDzExMfj4+Jgax686mjLtB0d3Q+lhU2Opy1P6SAjR9tkysjUfuLyZMmu11oOtrxdaHpYQrZB1qswTkq3w8HDmzJlDeHi4qXFU4s0mSx/jGw+bSvSUPhJCtH3NJlta6zXAETfEIkTrpfWZOxG1+clWWVkZK1eupKyszOxQSK+6WSDXs6YSPamPhBBtm7PWbI1USm1USn2hlOrvpDqFaD2O7ILjBRDQjb06zOxoyMvL49JLLyUvL8/sUNhgSTTeeNi6LU/qIyFE2+aMHeTTgRitdalS6grgY6DB/9orpe4D7kMW5otWJnbS0iY/v85rLa/5wlclMYB5m5lWiY+P5/jx4/j5+ZkdChkW68hWXjpUngJvz1gj5Ul9JIRo21qc9Giti7XWpdb3ywAfpVS3Rsq+o7U+G/htS9sVwpNUPf/PE9ZrAXh5eeHv74+Xl/n/rzlKCIT2gdPlcHCz2eFU86Q+EkK0bS0e2VJKRQD5WmutlBqOkcAVtjgyITxQzstXNvzBnJcgHybd+3smxZ7n3qAakJOTw9VXX82nn37qGZt2Ro+AIzuNRfKRQ82OBvDAPhJCtFm2bP3wX2AdkKSUylVK3a2UmqCUmmAtciOwRSm1EXgDGKe11q4LWQgPU1ECh34Brw7Qc4jZ0QAQHBzM2LFjCQ4ONjsUQ7TxnMSq7TE8gcf1kRCizWp2ZEtrfUszn88CZjktIiFam7x00BaIGAi+AWZHA0DXrl15+umnzQ7jjOgRxtd9nrP9g8f1kRCizZLFCkK0VNVddlUJhQcoKipi/vz5FBUVmR2KoftZ4BsMRXuh+IDZ0QAe2EdCiDZLki0hWmrfj8bXXp6TbB0+fJjHH3+cw4c9ZNd2L2+IOtt47yH7bXlcHwkh2ixJtoRoCYvlzNSYB41sxcfHU1hYSHx8vNmhnBE93Pi61zPWbXlkHwkh2iRJtoRoicO/QkURhERCpyizo/Fs1eu2PCPZEkIId5FkS4iWqEocPGhUCyA7O5vQ0FCys7PNDuWMqLMBBQc2wqlys6PxzD4SQrRJkmwJ0RIeuDgeoHv37rz22mt0797d7FDO6NgJwvuD5ZRxB6fJPLKPhBBtkiRbQrSEBy6OB+jUqRN33nknnTp1MjuU2qqnEn80Nw48uI+EEG2OJFtCOKr0sPEAap8ACE82O5paCgsLmTp1KoWFHvYwh17nGl894KHUHttHQog2R5ItIRxVtV4rcpjHPFy5SklJCR988AElJSVmh1JbzUXyFoupoRQfO8ay//2PoqwsyjdvpnzjRizl5q8lE0K0PS1+NqIQ7ZaHLo4HiI2NZePGjWaHUV/nXhAUAaUHoXAHdE9ySTOVpaWUfvMNFTt2UFlUTGVREZXFRViq3xdjKSlhHlDxf3eTU3Witzd+iYn4DxyI/8AB+A8ciG/v3ihvb5fEKYRoHyTZEsJRe6vWa400N44GWCwWTpw4QceOHfHy8qABbKWM9W1bPzH6z4nJluX4cUpXr6Z42TJKV69BnzyJ8vHBq1MnvDt1wjskhA7du+OXEI9XSCe8goOxBAbg17UrHTp1gspKyrds4cSmzRQvW8ax998HwCswkI7JyfgPHEDHgQPxHzgQn/Bwp8UthGj7JNkSwhGnymF/BqDOPGTZg2RnZ5OUlERWVhaJiYlmh1Nb9LlGsrXvJxh2Z4uqspw8SdnatRQvXUbJt9+iy8vp0L07nceOJeSKFPwHDUI1kmxu3769Xh8FX3IJANpi4WTOHso3beTEps2Ub9pE4fwFcOoUAB0iIuh8ww10uf02OnTp0qJrEEK0fZJsCeGIvHRjC4PwAcaWBh4mKiqKlStXEhXlgRutVi2S3+vYHYn61CnK1q2jeNkXlKxciaW0FO8uXeh0zdWEpFxBwNnDbJr2a6qPlJcXfr3j8OsdB9deC4ClooKKbdso37SZsu+/p+DNNyn817/oMnYsoePH4xMe5tD1CCHaPkm2hHDE3nXG16rEwcMEBARw8cUXmx1GwyIGgk8gHNkJJfkQbNuU3OmCAgrmvEXx0qVUHjuGV3AwwWPGEJKSQuC5I1A+9t2kYG8fefn54T94MP6DBxP6+zs4sX07hXP/wZEFCzi6cCGdrruOrvfcjW+vXnbFIYRo+zxoMYcQrUj1ei3PTLby8/OZMGEC+fn5ZodSn3eHM1OvVUlrE/SpUxTOn8/Oy1M4+r//EXjeeUTNnk3C99/RM3UaQef/xu5EC1reRx0TE4n821/ps/xLOt1wPUVLlrDz8hTyHv8TJ7K2O1SnEKJtkpEt0W7FTlrq2ImWyjP7RHng4niA06dPk5uby+nTp80OpWG9RsKuVUbS2v/aRouVrVvHwWnTOJm9k8Dzzyf8qaeMqT0ncFYf+UZH0+O55+j2wIMcWbCAY4sWUbx0KUEXXki3++/Df/Bgp8QrhGi9JNkSwl6HthkPn+7UCzpFmh1NgyIjI/n888/NDqNxVUnq3h8a/PhUXh750/9KyVdf4RMdTdTsN9+5+5sAACAASURBVAm68EKUUk4Lwdl95BMeRvifn6Dbffdy5L33OPrvd8kZdwsBw4cT9vhj+A8a5LS2hBCtiyRbot3LeflK+07w8PVaACdPniQnJ4fY2Fh8fX3NDqe+qLPBqwMc3AwVJeAXDIDlxAkK/zGPwrlzwcuL7o9OJPSuu/Dy83N6CK7qI+/Onen+0EN0HT+eox98wJF5/yTnllvpNuF+uj3wgENTnkKI1k3WbAlhr6pkK8YzpxABcnJySEpKIicnx+xQGuYbCD0GgbbAvp/RWlO8YgW7rryKglmzCLroQvosW0q3CRNckmiB6/vIKzCQruPH03vZUjr97ncUzJ5Dzq23UbFrt0vaE0J4Lkm2hLCH1rDHmmxFe+7IVmxsLFlZWcTGxpodSuOsU4kVPy1n3913k/eHR/AKCKDXggVEvfYaPj16uLR5d/WRd3AwPae/TOTrr3Nq7152X389R//7X7TWLm1XCOE5JNkSwh5Hc6BkP/iHQvezzI6mUb6+viQmJnrmFKKVjj6XwqxAdk37jPItvxD+9NPELfmIwBHD3dK+u/so5PLLiPv0UwKGDePg8y+wb8IETh8+7Ja2hRDmkmRLCHvs+d74GjMKPOkxOHXk5eVx1VVXkZeXZ3YoDbIcP87+t5ZzKKMTQZEn6fP5J4TecTuqg/uWkZrRRz7hYUT/Yy7hf/kLx3/8iV1XX0PJypVua18IYQ7P/ddCCE+0x3r3XMx55sbRjA4dOhAVFUUHNyYvtjqZk0PO2HEUr/yW7iP9iBpVQIcTOW6Pw6w+UkoRevttxH30IR16RJD78B/Y//TTVJaWuTUOIYT7SLIlhD1yvjO+xowyN45mhIeH89ZbbxHuYQ9MLvn2W3bfdDOnDx0ieu47dLvhIpTiTL+6kdl95NenD3GLFtH1/vspWvIxu6+9luPp6abEIoRwLUm2hLBVUS4c2wN+IRAxwOxomnT8+HG+/vprjh8/bnYogPFg58NvzCT3gQfxjY4m9sMPCTrvPIi1jhBWTc+6kSf0kfL1JeyPjxKz8F0A9tx+B4dnzkJbLKbFJIRwPkm2hLDVnhr7a3k1/6BjM+Xm5nLJJZeQm5trdigEnTzOvgceoGD2bDpddx0x/3kP3yjrZrAxvzG+7v0JKk+5NS5P6qOAoUOJ+3iJsUXEm2+y/09PYKmoMDssIYSTeN6CDiE81Z7WMYUIEB8fT1lZGR07djQ1jtii/Tz70wLKThUT8dwUOo8dW3sX+OBw6BoPhdlwYKOx2ambeEofVfEOCqLHyy/hlxDPoVf+zqn8fKJmzaRDly5mhyaEaCEZ2RLCVq1kcTyAl5cXAQEBeJl4x2TRZ5/z2pqZ+FhOEfPvBXQZN67hx+1U9aeb1215Qh/VpZSi6z33EPnaq5zYvJk9427h5N69ZoclhGghz/lbRghPVnoICraDTwD08PwHC+fk5DBo0CBTdpDXp05xMDWV/U88wY7O0Twy+lEChgxp/IRY61Sim9dtmdlHzQlJSaHX/H9RWVREzthxlGdmmh2SEKIFJNkSwha71xhfo0fw/+zdd3hb1fnA8e/R8JT33s62s6eTEDIYTaFAoAVKgBbSMhNGS/trgbL33iMkYSWsQqGUsAoFMsnew5lOPOS9tzXP749rO07ieEWyPM7nefTcK+nq3tfnSvKrc8/A0HMHCm0SEBDA5ZdfTkBAQLce11lXR87N8ylf9h6h117D3dNuotwnsO0XNdVsZW8Ap8P9QTbyVBl1lN/48ST/8yN0AQFkXTuPqu++93RIiqJ0kWqzpSgdkblGWw6Y4dk4OigsLIx77723W4/pqKgg5+b51O/aRcyjjxB82WU47vq6/RcGxUFIMpRnctE9r7NbDuzwMTs9iXgLniijzvJKTib5nx9hXnALuX/+M7a//53Qede2fjlWUZQeS9VsKUpHHO1dyVZlZSVLly6lsrKyW45nKyoi6/fX0LB3L3EvvkDwZZd1bgfJ0wGYqtvrhuha191l1FWG0FAS332HgNmzKXrqKQofeRRpt3s6LEVROkHVbClKe6ryoCwDvAJ6RXstgOLiYu644w6mTZtGUFCQW49lzc4m+4/XYS8rI2HxIvynTu38TgbMhO3vcYYunX889ka7myd3pMasHd1ZRqdL5+ND3AvPU/Tcc5S99Ta2vDzinnsWnb+/p0NTFKUD2q3ZEkK8LYQoEkLsOcXzQgjxshDisBBilxBivOvDVBQPaqrVSjoD9L3j98ngwYMpKytj8ODBbj1Ow4GDZF59Nc7qapLefadriRbAAK1ma5JuP9itLozw1LqrjFxF6HRE/e1vRN1/HzWrV5P1+2uwFRV5OixFUTqgI5cR3wXOa+P584EhjbcbgYWnH5ai9CBNjeMbEwJFU7dtO1m//z1Cpyfpg/fxHT266zsLiOaQMw5/YYE8NWVNW0Kvuor411/DkplJ5ty5WHtgb0pFUY7XbrIlpVwNlLWxycXAMqnZAAQLIWJcFaCieFxmY7KV3HuSrcOHDxMWFsbhw4fdsv+aNWvJvu469CHBJH3wAd4uqB1a5xyurTQlt27m7jJyp4BZs0hatgxZ30DW76/BcuSIp0NSFKUNrmggHwfktLhvbnxMUXq/8iyoyAafoB4/H2JLERERPPfcc0RERLh831XffkvOggVaT7kPWky9c5rWOUdoK92UbLmzjLqD78gRJC1bipRS65xw8KCnQ1IU5RRckWy11gdZtrqhEDcKIbYAq1xwXEVxv6ONb9Xk6T1+PsSWgoKCmDdvnssbfpd//Am5f/krvqNHk7T0XQzh4S7b90ZnKk4pIGcj2Opdtt9TcVcZdSfvIUNIWrYModeTfc21NOzb5+mQFEVphSuSLTOQ0OJ+PJDX2oZSysVSyonATBccV1HcL2OFthw4y5NRdFppaSmPPfYYpaWlLtmflJKSxUsoeOAB/GdMJ/HNJegD2xmstJMqCCBdJoHDqg1w6mauLiNP8R44gKT3liF8fcma9wfqd7fal0lRFA9yRbK1HLimsVfiFKBSSpnvgv0qimc5ncdqtgae5dlYOqm6upqPP/6Y6urq096XlJLi556j+PnnCbzwQhJefRWdr68LojzZz82XEt1f+e3KMvI0r6Qkkt57D73JRPYf/qCm91GUHqYjQz98BKwHhgkhzEKI64QQNwshbm7c5BvgCHAYWAIscFu0itKdCndDXSkEJUDYIE9H0ynJycns2rWL5OTk09qPlJKiZ56l9M23CL5yLrFPP4UwGl0TZCvWOhvbxWX85LZjNHFVGfUUXvFxJL3/HvrQULL/eB11W7d6OiRFURq1O2iQlPLKdp6XwC0ui0hReormS4gzoZdNj+J0OrFYLHh7e6PTda0CuynRKnv7bUKuuoqo++51+zQxm5wpoPeG/F1QWwL+rmsTdiJXlFFPY4yJIem998ieN4/s628gYeFC/KdM9nRYitLv9Y1vGEVxhyMrtWUvu4QI2rAGfn5+XR7WQEpJ0bPdm2gBWPCCpKmAPFb+bnK6ZdRTGaMiSXpvGV7xceTcdBM1a3/2dEiK0u+pZEtRWmNrgOz12vqA3tefIy4ujv/973/ExXV+WIamNlplb71NyFVXdlui1awpuT2ywq2HOZ0y6ukM4eEkLl2K14ABmOfPp3rlSk+HpCj9mkq2FKU1ORvA3qCNrWXqfeMw+fv7c+655+LfybnzmhKtpjZaUffd172JFsCgs7VlxgqQrY4i4xJdLaPewhAaStK77+A9dCjm226n+ocfPB2SovRbKtlSlNY0NdAeOMuTUXRZYWEh8+fPp7CwsMOvkVJS/PzzzYlW9P33d3+iBRA1EvwjoCoXStw3UGdXyqi30QcHk/jO2/gOH475z3dQ9d33ng5JUfollWwpSmsONdYCDD7Xs3F0kc1mIysrC5vN1qHtmxOtJW9qiZYnarSa6HTHktwM911K7GwZ9Vb6wEAS3noL31GjyP3rX1UNl6J4gEq2FOVElblQtBeM/pA41dPRdEl8fDzffPMN8fHx7W6rJVovaInW3Cu0RMvTvfOaLiUedl9i0Jky6u30Jn8SlizGZ8RwzHf8heqf3NseTlGU46lkS1FO1PQPfuBMMHh7NpYuslqtHDp0CKvV2uZ2UkqKX3iR0iVLCL7iCu3SoacTLYBB52jLzDVum7qno2XUV+hNJhLffBOflBRy//QnalZ3zxyUiqKoZEtRTnb4f9qyl15CBMjMzGTo0KFkZmaecpvmRGvxYi3ReqCHJFoAAVEQM1brpJC51i2H6EgZ9TX6gAAS31yC95AhmG+9TQ0LoSjdpId8sypKD+GwwZHGqWJ6cbKVnJzMvn37Tjk6upSS4hdf0hKt3/62ZyVaTYbM1paH3NOou70y6qv0QUEkvv0WXgMHYr7lFmrXr/d0SIrS57U7gryi9Cs5G8FSBeFDISTJ09F0mZeXFykpKad8vuSVVyhdtIjgyy8n+sEH3J5oJd/1dedfNGQ2rH5aS7bk0y4fxb+9MurLmnopZl87j5z5C0hYtAj/yWmeDktR+qwe9lNWUTzsUNMlxF94No7TlJuby0UXXURubu5JzxW/9holry8k6LJLiX7owZ5Xo9Ukbjz4hkJ5JpS6fpT3tsqoPzCEhJD4ztsY4+PIuflm6rZs8XRIitJnqZotRWmpKdka0nsvIQIYDAZiYmIwGI7/iJe88QYlr7xK0K9/TczDD7s90cp88oKuv1in1y7l7v5Eq90KH+K6wDh1GfUnhrAwkt59l6xrriX7xptIfPNN/MaP83RYitLn9NCftIriAeWZ2pAPXgGQdKanozktUVFRLF68mKioqObHSpYsofjFlwi6eA4xjz7Sc2u0Wmpqt3XwO5fvurUy6o8M4eEkvvsOxshIcm64gfqdOz0dkqL0Ob3g21ZRusmB/2rLweeAwcuzsZymuro6VqxYQV1dHQClb71N8XPPE3jhhcQ8/jhCr/dwhB00+BwQOshaBw2VLt31iWXUnxkjI0lc+i76sDCyr7ue+t27PR2SovQpKtlSlCYHv9WWw37l2ThcwGw2c/bZZ2M2mylbupSiZ54h4PzziH3yid6TaAH4hWoDyzptxy7xukjLMlLAGBVF0tJ30QcHawnX3r2eDklR+gyVbCkKaLUmmWtB6GFI724cDzB48GCqq6sJ27iRwieeJGD2bOKefhrRG9snNSW/B75x6W6bymjw4MEu3W9vZoyJ0RIuk4nsP16nEi5FcRGVbCkKaKPGO+1aLYpfqKejOW06nQ7bl19S9NjjmM49h7jnnkUYjZ4Oq2tSGpOtQ/8Du+tGe9fpdJhMJnS9oe1aNzLGxZG4bBl6f3+VcCmKi/TCn7mK4gYHmi4hnu/ZOFwkY+EbWF96Cf2UycQ//3zvTbQAQgdCRCoU74OstcfmTWxBSkmDo4Eaaw01thpqrDVU26qxOqw4pAOndGpLp7P5flFJEa++9io3z7+Z4NBgBAJvvbd2M3jjo/fBW++Nj6FxqffB26A972vwxUvfu9v1tcUrXku4sq+5huw/Xkfi22/hO2KEp8NSlF5LSCm7/6BCBABVVVVVBAQEdPvxFQWODbSZ+dhseGaQdinxtm0QNsjDkZ2eis8+I/+ee8mPjWX0B+8THhPj6ZA6zeqwUlJfQlFdEcX1xRTtWEZR5ipKolKpjBjCjweyEfoGEsN11NhqqLXWYpf2bo3R1+BLiHcIIT6NtxbroT6hBHsHE+oTSohPCBG+EfgZ/bo1PlewmnPJvuYaHLW1KuFS+rXq6moCAwMBAqWU1Z19varZUpSjq7REKyKl9ydan/+H/Hvvw//MM5n12qvovHveRNpSSsoaysiuzia7Kpuc6hyK6oooqi+iuK6Y4rpiyi3lJ73OEBRIeF0uwbWBADhtwYyLHITJaMLkZcJkNBHgFYC/0b956aP3QSd06IQOvdCj0zUu0R1bb3wewOKwYLFbaHA0YHFYaLA3Lh0NWOyW5scaHA1UWCoobyin3FJOWUMZGRUZVFgqqLe3PnF2qE8osf6xxJhiiDPFEWuKJc4UR4y/dr8nJmOqhktRXEMlW4qS/oW2HH6JZ+M4TZVffEH+P/6B/9QpBD3+GB988gkXX3xx06+xbiWlpMJS0ZxQZVVlactqbVljq2neVid0hPmEEeEXQax/LGMixhDpF0mkXyQRvhHa0ieM4IVnoqvOh18uJXldAQBP3Nr1QVOrqqr44osvXF5G9fb65iSsvEG7FdYVkluTS15NHofKD7EqZxVW5/Htz4K9g4k1xZIQkMCgoEEMDB7IoKBBJAUmYdR77jKwSrgU5fSpZEvp1/Q4YH/jvH3D53g2mNNQ8emn5N93P35TJhP/2mscyc3l9ttvZ+rUqW5PtupsdRyqOMTB8oMcKDvAwfKDZFRkUGWtat5GJ3TE+MeQFJjE6IGjSQxMJCkwicSAROJMcR1LJlLnwKZFsPc/wJTTjruoqMgtZeRr8MXX5EusKfaU2zilk7KGsuYErGmZV5PH3pK9fJ/5PRKtiYde6EkMTGxOwAYHD2Zg0ECSg5Lx1ndPzaVKuBTl9Kg2W0q/lXzX10zV7eUjr8cgbDDcusXlkx13h7IPP6Tw4Ufwnz6d+FdeRufj45bjSCnJr83nQNkBDpRrSdXB8oNkV2U3JwYmo4mhIUMZHDxYS6YCE0kMTCTeFH/6Dcqz1sE750NwIskFTwDi9KYD6sHq7fVkVmaSUZnBkYojZFRkcKTyCNnV2TilE9AS2MSARFJDUxkeNpwR4SNIDU3F5GVyW1yqDZfSX6k2W4pyGn6l26itDL+4dyZaS5dS+MSTmM4+m7gXX0Dn5boecsV1xewq2cWu4l3sLtnN/tL9VNuOfcckBCQwLGQYFwy8gGEhwxgaMpQ4UxzCXeWYMAVM0VCRzWhxhF2yd7eva4uvwZfUsFRSw1KPe9zqsJJZlaklYJUZHCo/xI7iHXyb+W3zNsmByaSGpTIibATDw4a7NAFTNVyK0jUq2VL6LR1OztNv1u4Mv9izwXRByZIlFD/3vDZg6bPPIFokWocPH2bKlCls2LChQ4N2Ntgb2Fe2j13Fx5Kr/Np8AAzCwLDQYZw/4HyGhWpJ1ZCQIfgb/d32t7VKp9PO06ZF/Eq/kV3200u2OltGPYGX3ouhIUMZGjL0uMfLGspIL01nb8le0kvT2Va4jW+PagmYQJAUmMTwsOGMiRjD+KjxDAkegl7XtZkEVMKlKJ2nki2l35okDhAhKiE4CaJHezqcDpNSUvL665S88iqBF1xA7FNPnjQyfEREBM888wwRERGt7iO/Jp8thVu05KpkFwfLDjYPndDUSP13qb9jdMRoUsNSu61tULtGXAKbFnGBbiNPcuVp7aq9MupNQn1COTPuTM6MOzaBekl9Ceml6VoSVrqXzQWb+eaoNgq/v9GfMRFjGBs5lvGR4xkVPqpTvSFVwqUonaPabCn91of3XsJVhhVw5l/g3Ac8HU6HSCkpfvElShctIujii4l5/LF25zqUUmKuNrOlcAtbCrewtXAruTW5APgZ/BgZPpLREaMZFT6K0RGjCfcN744/pWucTng+FWoKmGN5hOVP3O7piHoNKSV5tXlsL9rOjqIdbCvaxuHyw0gkeqEnJTSFcZHjmm8Rfu0noc1tuKqrSVi0CL/x47rhL1GU7ne6bbZUsqX0T3YLlY8kEyTqYMEGiExt/zUeJqWk6OlnKHvnHYIvv4zohx5CtDLVjJSSHdk7eOXzVwgaEcSuil0U1RUBEOIdwoSoCUyMnsiEqAmndTnJY769Eza+wZv287n+0X92eTelpaUsWrSIm266ibCwMBcG2HtUWavYWbST7UXb2V60nT0le2hwNACQFJhEWnQaaTFppEWnEerT+jRWttxcsv94HbaiIuJfeQXTmdO6809QlG6hki1F6Yr9X8M/r2KfM5HUh3d7Opp2SSkpfOxxyt9/n5CrriTq3nuPS7TM1WbW569nY/5GthZupaS+BIBgYzCT4yYzMWoiE6MmMjB4YPMAnr1W7lZYcjbFMoiI+4+AvmutITIzM7nooov48ssvSU5Odm2MvZTNYWNf2T62F21nS8EWNhduptZWC8DQkKGkRacxOUZ7P7VsdG8vKSH7+huwZGQQ9+yzBP5ytqf+BEVxC5VsKUpXfHItpP+HJ2xXcvdjb3g6mjZJp5OCBx+i4pNPCL32WiLvupMqaxWbCjaxIW8D6/PXk1OdA0CkXySToidptVdRE0kOTHZf70BPkZKMB1IZpMuH330Gg8/1dER9lt1pJ700XXuv5W9gR9EOLA4LeqFnRNiI5lqvcZHjMNZZybnpZup37iTmkUcIvvQ3ng5fUVxGJVuK0lkNVfDsEJw2C9MsL7P+yWs8HdEpSYeD/Hvvo/Lzz7FedSGrLohnQ8FG9pbuxSmd+Bn8SItOY0rsFKbGTGVA0ACEEDidTqxWK15eXuhaudTY2z13z3X81fgpjPotXLqkS/vo62XkDhaHhV3Fu9iQv4FN+ZvYU7IHu7TjpfNiQtQEpodNYtLLK5AbtxN5152EzZvn6ZAVxSXUOFuK0ln7vgR7A5tkKvn03LY6mSWHyL3rLkLXpvP5DC8+SvwW/V4DI8NHcuPoG5kaM5VREaMw6k4eff3w4cMMGzaMAwcOMHTo0Fb23rv9xzmNv/Ip7P8KLDXg3flxpPp6GbmDt96bSdGTmBQ9CcZBra2WbYXbWJe3jnV563g6/2UMMyR/q/Fh3JNPcSh7B6l3PkSQd5CnQ1cUj1LJltL/bH8fgM8dZ7azYfdqsDewpXALa8xr2HJ4FXOXZjMyW/L1eaE4557Pi7FTSYtOI8Cr/drguLg4vv/+e+Li4roh8u6XI6PY7BzKJNtBLeEaM7fT++jrZdQd/I3+TI+fzvT46YA2pMjPeT+zfsDPVC/5iRkffsfbB39g29yxnJEwjTNjz2R42PDe1ylDUU6Tuoyo9C8lh+HVCWD0Z0T1y9Ti69EpX3Kqc1hjXsPa3LVsLthMg6OBmFov7vtUEFZYj8/9/8fAK/7gsfh6quS7vuYq/Y88bnwLkqfDvK88HZJyApvDxv6H78bw8dfsnBDCk+dW49BpE25Pi5vGjLgZTIubpmq9lF7hdC8jdqihghDiPCHEASHEYSHEXa08P08IUSyE2NF4u76zgShKt9j+nrYc8Wtq8e32w1sdVtblreOpTU9x0ecX8at//4onNj1BVlUWlw69lMWD7+XVTwKJrJAkLl7c5USrsLCQBQsWUFhY6OK/oOf40jEVjH6QuQZKMzr9+v5QRp5k1BsZ+eAzRPz5T4zZWs6/N07l6cmPMj1uOuty13HnmjuZ8fEMrv32Wt7c/SaHyg/hiR//itId2r2MKITQA68BvwDMwGYhxHIpZfoJm34spbzVDTEqims47LDzI219/O9hQ2m3HLa0vpQ1uWtYbV7Nz7k/U2evw1vvzcToicxNmcv0uOkkBiZSt2ULOXfcAt5eJL3/Hj7Dh3f5mDabjaNHj2Kz2Vz4l/Qs1fjBiF/Djg9g2zL4xUOden1/KCNPE0IQfvPN6AICKHzkUYY32Jj96qswzYc9pXtYbV7NGvMaXtr2Ei9te4kY/xhmxM9gRvwM0qLT8DG4Z1J1Relu7V5GFEJMBR6UUv6y8f7dAFLKJ1psMw+Y2NFkS11GVDxi/zfwzyshbAjcupnku7WpS1x9GVFKycHyg6wyr2KVeRW7i3cjkUT6RTIzfiYz42eSFpOGr+FYzVrVf78j7+9/xxgXR8KSJXjFq3ZEbUm+62sAMheEw9uzwT8C7kgHg+sm4lZcq3L5cvLu/gc+I0aQ8MZCDKHHBkktrC1s/kGyIX8D9fZ6vPXepEWnMSthFjPjZxLlH+XB6JX+rjt6I8YBOS3um4HJrWx3qRBiBnAQuENKmdPKNoriOduWastxvwMXjz1lcVjYlL+JVeZVrDavbp7EeWTYSBaMXcDM+JmkhKa0OuZV2XvvU/j44/iOHUv8669hCAk57XisVivZ2dkkJibi5dWHE5CENIhIgeL9cPDbTk0o3m/KqIcImjMHnclE7h1/IfPy3xK/8HV8GnuBRvlHcdnQy7hs6GVYHVa2FGxhde5qVuWsYk3uGh7hEVJDUzkr4SxmJswkNTS1740fp/RpHUm2WntHn1gd9iXwkZTSIoS4GVgKnH3SjoS4EbiRDrYVUxSXKc+Eg9+B3gvGXu2SXZY1lLHavJqVOStZl7eOens9vgZfpsRM4eYxNzM9bnqb88tJp5Oi556j7K23MZ17DnHPPovOxzWXTTIzM/vHsAZCwPhr4bu7Yeu7nUq2+k0Z9SABZ59N0vvvYV5wC1lzryT2+ecImDXruG289F6cEXcGZ8SdwZ2T7uRI5RFW5qxkZc5KFu5cyOs7XyfKL4qZ8TOZlTCLtJi0njNRuqKcQkeSLTOQ0OJ+PJDXcgMpZcvGL0uAp1rbkZRyMbC46TJi50JVlNOw+U1AwojfgKn9CXZbI6XkaNXR5i/+HUU7kEii/KKYM2hO8+XBjnzxS6uVvH/cQ9VXX2nT79xzT7sTSndGUlIS6enpJCUluWyfPdaYufDjw5DxExQfhIiOJU79qox6EN9Ro0j+9F+Y5y/APH8BkX//O6Hzrm21pkoIwaDgQQwKHsR1o65rbv+4KmcVXx75kk8OfoKvwZczYs9gZvxMZsTPIMy3546dp/RfHUm2NgNDhBADgFxgLnBVyw2EEDFSyvzGu3OAfS6NUlFOh7UOtjX2Qky7sVMvtTvt7CjaoSVY5pVkVWUBkBqayvwx85mVMOuUlwdPxVFTg/m226hbv4GIO+4g7MYbXH5JxNvbm9TUnj+5tkv4hcLo32qXiTctggue69DL+lUZ9TDGqCiS3n+PvLv/QdFTT2E5fIiYBx5AtHM5N8w3jEsGX8Ilgy/B4rCwuWBz84+fH7N/RCAYEzGGsxLPYlbCLAYEDlCXG5UeoUPjbAkhFkrOrgAAIABJREFUfgW8COiBt6WUjwkhHga2SCmXCyGeQEuy7EAZMF9Kub+N/akG8kr32boUvrwd4ibADT81P9zcyPqEBvK1tlp+zv2ZlTkrWZ27mkpLJUadkbSYNM6K19qMRPtHdykUa3Y25ltvw3LkCDGPPkLwJZd0/e9qQ25uLvPnz2fhwoV9ctDOk85d4V5YeAYY/eEv6eAb3O4++noZ9QbS6aTk1VcpeX0hfhMnEvfKy11qsyilZH/ZflaaV7IiewX7yrTf+0mBScyKn8VZiWcxJmIMBp0ax1vpmm6ZrkdK+Q3wzQmP3d9i/W7g7s4eXFHcTkrYtFhbT7vplJsV1BY0/0LeVLAJm9NGkHdQc7uQM2LPwN/of1qhVP+0grw77wSdjoRFb2CaNu209tcWvV5PVFQUehdemuzRokbAgBlwdLU2ltoZt7X7kn5XRj2Q0OmIuP12vAYMJP+ee8j87RUkLHwd78GDO7cfIUgNSyU1TKtxLqgtYFXOKlaYV/Dh/g9Zmr6UYO9gZsTPYFbCLKbFTsPP6Oemv0pRTqZGkFf6tsM/wPuXgikK/rwbDFp7Kiklgx5cgiFgH2OH5Tb/Ek4MSOSsBO0SxNjIsS75JSwdDopfeYXSNxbhM3w4cS+/hFd8/Gnvtz9rtVayaWiP4ES4bTvoVS1Gb1K/cyc5t9yKbGgg7vnnMM2Y4ZL91lhrWJe37qSa6skxkzkr4SxmxM/ock210n+cbs2WSraUvu3dC7URxs99EOvUW9hSsIUVOStYaV5JQW0BUgrGRbqvjYe9vJy8v/4ftevWEXTpb4i+/3503u7vOVVXV8emTZtIS0vDz6/v/YJvNdlyOuDViVB2BC59C0Zd1uY++noZ9Ua2/HxyFtyC5cABou78OyHXXOPaz6PTzvai7azMWcmKnBXkVGsjFKlhJZT2qGRLUU7FvIWyt3/BmsAQVo26gJ8LNlFnr8PX4MvUmKl8vTEUR00KRx+7wi2Hr9+9B/OfbsdRXELU/fcRcvnlbjlOaw4ePNinhzU4VXs7tr4LX/4JIofDzT+D7tSjzPT1MuqtnHV15N15J9X/+4Hgyy8n+r5722043xVSSo5WHmWl+eTexU0DqaphJZQmKtlSlBaklM3j8qzavpgdzlqkEET6RjIjYQYz42cyJWYKPgafU//DdkEMFf/6F4WPPIo+Ipz4l17Gd9RIlx6jPU6nk9raWvz9/dG1kXD0Vqc8d3YLvDQWqvNg7oeQcupz29fLqDeTTifFL71M6aJF+IweTdyzz+CVmOjWYzYNK3HiuHnTYqcxM2Em0+Omq2El+jGVbCn9ns1pY2vhVlblrGLZzm/QeZUBkGKxMr3OwtKK2yhtGMqpxtJ1ZbLlbGig4JFHqPzs3/hPm0bss8+4ZER45XhtJsobFsJ/74LY8VrvU3VJqNeq+u935N9/P9jtRN13H0GXXNwtl/iaZoRo6jRTVF+EQDAqYlTzlFtDQ4aqy439iEq2lH6prKGMtblrmyd3rrHV4KXzoq5qAPbqVB5pWMtctvGufTYP2ue1uS9XJVtWsxnz7bdjSd9H2Pybibj1VpcOVNoZWVlZ/PrXv+bzzz/vk4N2tplsWevgxZFQVwpXfwZDzm11H329jPoKW14eeX+/k7otWwj81flEP/ggeu2fXreQUpJels5q82pW56xmT+keAKL9o5sHUlWTZvd93TL0g6J4mlM62Ve2j9Xm1awxr2FPyR4kknDfcGYnz26+PDj8vhWMEkeY670NDL7M++urzAtw/wS2NatXk/u3v4PTSfzrrxNw9lluP2ZbTCYTF198MSaTyaNxeISXH5xxO/zwAPz4EAw6u9W2W/26jHoRY2wsiUvfpXTJmxS/8gp1O3YQ98wz+E2Y0C3HF0IwImwEI8JGMH/MfErqS1hjXsMq8yqWZyzn4wMf46P3YUrMFGYkzGBG3Aw1abZyElWzpfRYNdYa1uevZ7V5NWtz11JSX6JV5YePYnr8dKbHTyc1NBWdOPaPNPmur1lqfJKZ+l0w7U/wi4fdGqOztpai51+g/IMP8E5JIf7ll9zetkRpp2YLtNqtV8ZDdX6HeiYqvUP9zp3k/t/fsOXmEn7zTYQvWIAweK7OoGnS7FXmVawyryK3JheAYSHDmB4/nTPjzlSDqfYR6jKi0mc0NW5fm7uWNeY1bC3ait1pJ8ArgGmx05geP51psdPabKR6xd3P8rH3I+AdCH/aqU3l4ia169aRf9/92PLyCLn6aiL/+hd0vr5uO15nVFVVsXz5cubMmdP0BdGndKhzQ1PPxJABcOtm0BuPe7qvl1Ff5aippfDRR6n8z3/wHTOG2GefwSshof0XulnLzjlrc9eyo2gHdmknwBjAlNgpTI/Tkq+2JqdXei6VbCm9WpW1io35G/k592fW5q6lsK4QgMHBg5keP50ZcTM6Prio08HeB8cxQpcFZ90DM//ulpgd1dUUPf00Ff/6FK/kZGIee7TbLml01OHDh5kwYQJbt25lcCdH4+4NOpRsOezw+hQoPQS/ehbSbjju6b5eRn1d1TffkP/Ag+B0Ev3A/QTNmePpkI5Tba1mQ/4G1uauZa15LUX1RQCkhKZwZtyZTI+bzuiI0arWq5dQyZbSqzilk/TSdNbmrmVd3jp2Fe/CIR2YjCamxExhWtw0psVOI8YU0/mdb3kHvvozZhlO/D27tbY7Lla9ciUFDzyIvbiYsD/+gfBbb0XnoxrGdrcOD9ux70v4+HfgEwy3bQN/1XW/L7Hl5pL79zup37qVwAsvJPqB+9H3wP8pUkoOlh/Uau1z17CjaAcO6SDAK4ApMVM4I/YMpsZOJc6k5ujsqVSypfR4xXXFrM9fz9rctWzI20C5pRyAEWEjmpOrURGjMOqM7eypDfXl8MoEqCvlFuvtvPb4Iy6KXmMvL6fwiSeoWv4l3kMGE/P44/iOGuXSYygd1+FkS0p47xI4shLGXwNzXnF/cEq3knY7JYsXU/La6xjCw4n8298IvOBXPXpYhpa1Xj/n/txco58UmMTUmKlMjZ1KWnQaJi/VeaOnUMmW0uNUW6vZUrCFjQUb2ZC3gYzKDABCfUKZFjuNaXHTmBo7lVAfF7an+vr/YPMSNjhTmWu9l8wnL3TZrqu++56Chx/GUVlJ+I03EnbzTejcMKK1K2VkZDB16lTWr1/PoEGDPB2OyzUlWx0xSOTyrdddeAknXP8jxGuXfPt6GfU39bt2UfDgQzSkp+M3cSJR992Lz7Bhng6rXU0j2a/PX8+6vHVsLthMvb0evdAzOmI0U2OnMjVmKiPDR6pLjh6kki3F46wOKzuLd7IhfwMb8zeyp2QPDunAR+/D+KjxTImZwpSYKQwLHXZcz0GXyVoP75wHOgPn1T/KfpnokrGz7CUlFDzyKNXffYfP8OHEPP4YPikpLgjY/SorK/n000+57LLLCAoK8nQ4LteZZAvgLsNH3Gz4EqJHwQ0rQG/s82XUH0mHg4pPP6P4hRdwVFURcuWVRNx+G/pedH5tDhs7inewPk9LvtJL05FIAowBpMWkkRat3QYFD+rRtXd9jUq2lG7ncDo4UH6ATfmb2JC/gW1F26i316MTOkaGj2Ry9GSmxk5lTMQYvPRurgGy1cMbZ0LpYZjxN5K/Hwec3kCl0maj4rPPKH7hRZx1dYTfdhthf/yDR7uYK12XfNfX+NFAetSDUJkNs/4Bs+70dFiKGzkqKih++WXK//kx+qAgIv5yB8GXXorohdMyVTRUsKFgA+vz1rMhbwN5tXmAdqUgLTqNSdGTSItOIykwSSVfbqSSLcXt7E47+0r3saVwC1sKt7C9cDvVNu29NjBoIFNipjA5ZjIToycS6NXNXej/dz/8/BJEpMBNq0m+9wega8mWdDqp+vZbil96GVt2Nr4TJxDz0EN498JLTGVlZSxevJgbb7yR0FD3DX/RGzS377opAJZeBDoD3PATZd4Jqoz6uIb9+yl45FHqt27FZ+RIou+7F98xYzwd1mkxV5vZVLCJTQWb2Jy/ubmXY6RfZHOt16ToScQHxHs40r5FjSCvuJzNYWNv6V4tuSrYwvai7dTZ6wBIDkxmdvJsJkZPZFLUJM+OlHxkJfz8MggdzHkVDN5d2o2Uktq1P1P0wvNY0vfhPXQo8W8sxDRzZq/9pVhVVcX777/P3LlzVSLRZMAMSLsRNi2Gz+dTPfttVUZ9nE9KCknvv0fVV19T9PTTZF4xl6Df/IbIv9yBITzc0+F1SXxAPPEB8fxmyG+QUpJVldWcfK3LW8dXR74CINY/lonRExkXOY7xUeMZEDig136f9QWqZkuh1lbL7pLdbC/aztbCrews2kmDowHQxruaEDWBiVETmRA1oecMyFdTBAunQW0RzLwLzrob6EQvtUb1O3ZQ9PwL1G3ahDE+nog/3U7gBRf0yssNSuuOe09Ya+GN6VCWoXon9jOOmlpK31hI6dJl6Ly9Cb/lFkLmXtFjBiJ2BSklGRUZWq1XwWa2FW2jrKEMgBDvkObEa3zkeFLCUk6vB3g/oy4jKp0ipSS3JpcdxTvYUbSDncU7OVh+EKd0IhAMCRnCxKiJTIqexPio8a7tMegqTge8fykcWQHJ0+GaL0CnTfjc0WTLcvgwRS++SM0PP6IPCyN8wXxCLr8c0cN7GXaUlBKbzYbRaOz3v2ZPek/k74I3zwWHBftFr6If/7t+X0b9ieXIUQqfeILaNWvQh4YSes3vCbnyyl7ViL6jmmq+thVtY1vhNrYXbSe7OhsAX4Mvo8NHMy5qHOMixzEmYgz+Rn8PR9xzqWRLaZPVYSW9NJ2dxTvZUbSDHcU7KKkvAcDP4MfoiNGMjRzL2IixjIoY1f1trrriu3tg/avgFwY3/wyBxwZAbS/ZsuXmUvzqa1R+8QU6Pz/Crr+O0N//Hp1/3/qSOXjwIMOGDePAgQMMHTrU0+F4VKvvia1L4cvbqbNJii96n6Qpc47btjNc0fNV6V5SSuq3bqVkyRJqV61G5+9P8NwrCL3mWoxRkZ4Oz62K64rZXrS9OQE7UH6g+cf2oOBBjI4Yzejw0YyKGMWgoEHoG3/I9neqzZbSzOF0kFmVyZ6SPewp2cPe0r0cKDuA1WkFIM4Ux+SYyYyNGMvYyLEMDh7c+8Zt2fqulmjpjPDbZcclWm2xHDpE2YcfUvnpZyAEoddeS9iNN2AICXFvvB4SFxfHd999R1ycGpG6VeOvwXb0Z/z2fEzCmv+DlHEQ7Pn59ZTuIYTAb+JEEidOpGH/fkqXvEnZO+9Svuw9gi65hLDr/ohXcrKnw3SLCL8IZifPZnbybABqrDXsLN7JruJd7CrZxY/ZP/LvQ/8GtB/kI8NHMip8FKMiRjEmYgzhvr2zrZunqZqtXkpKibnGzN6SvVpyVbqHfaX7mhuy+xp8GR42nJFhIxkbOZYxEWN6Tnurrjr0P/hoLjjtcPFrMO53J23SshZDWq1U//gj5R9+RN3mzQgvL4IunkP4ggUYY7owHZDSK52qtsqInWXGJ5mqT+eAM57LrQ9QhVbD2ZHaqs62D1R6NmtODqVvv03lZ/9G2u0E/HI2Yddfj++IEZ4OrVtJKcmuztaSr+Jd7C7ZzYGyA9ilHYAY/xhGho9keNhwhocOJyUspWc2N3ExdRmxH3A4HWRXZ3Og/AAHyg6wr3Qfe0v3UmGpAMBL50VKaIqWXIWPZGT4SJIDk/tW9e+RlfDhFWBvgGl/hl881OpmyXd9TXh9Bd8OKqX8X//CUVyCMT6ekCu1Xkh9tSbrREVFRTz88MPcf//9REb27csi7TlVsuWorUBsXsYP52Yy1FDANudgrrHeRQ1+Ktnqx+wlJZQte4/yDz/EWVOD/7RphN1wA36T0/pt274GewP7y/Y3J1+7S3aTW5Pb/Hy0fzSpoamkhqUyPHQ4qWGpRPhG9KnyUpcR+5g6Wx0Hyw9yoOwA+8v3c7DsIIcqDlFvrwfAIAwMCh7EOYnnMCJ8BCPCRjAkeAhGfR/uVZK5Fj66Uku0Jv4Rzn3wpE2klNRt2MA9G5cytWAvJUhMM2YQctWV+J95JkLfhxLPDrBarRw+fBir1erpUDzuVMmQ2Wzm+uvfI+Dq9+C/1zG+8jB7Bi+C3/27myNUehJDeDiRf7mDsBuup/yf/6Rs6TKy583DmJRI0EVzCJpzEV6JiZ4Os1v5GHy0tr2RY5sfq7RUaj/+y/aRXprOvrJ9rMxZiUSrwAnzCSM1LJXU0FSGhgxlSMgQEgMT+20PSFWz5SE2p42c6hwyKjLIqMhoTrByqnOa36yBXoEMCx3GsJBhDAsdRkpoCgODBrp/VPaeJH05fHY9OCww9mptPK0WwzI4qqqo/M8XlH/0EdajR6n08uP7pDTuWngPXvFqUD+lg8qz4N0LoDIHYsbCVZ9AQNtjyKmarf7BabFQ9dXXVC5fTt2mTSAlvmPHEjjnIgLPP7/f1JZ3RJ2tjv1l+49LwI5UHMEhHQAYdUYGBA1gSMgQhgQPaV5G+0f3+FowdRmxh7M5bGRVZZFRmcGRiiMcrjjMkcojZFZlYnfam7dLCEg4LqkaFjKsV7wB3UZK2LgI/nsXIGHidfCrZ0Cnx15aSs2KFVT/8CO169YhrVZ8x4wh5KormbhWYtMb+/0/QKvVSk5ODgkJCXj1keEsXO2kMirPhGUXa8ugRLj6XxB56rkwVbLV/9jy86n6+msqv1iO5dAhMBgwTZ9O0JyLMJ11FjofH0+H2ONYHBaOVh7lUPkh7VahLQvrCpu3CTAGMDhkMEOChzAweCADAgcwIGgAUf5R7plPtwtUstUDSCkpbSglqyqL7KpssqqyyKrK4kjlEbKrspsbFgoE8QHxDAoaxMDggQwOHtz8xvIz+nn4r+hBrLXw1R2w62Pt/tn3Yk2+guoff6L6hx+o37YNpMQYG4vp3HMImnMxviO1RqzqH6BGDf3QvlbLqKZY64SRuwW8AmDOSzDy0lZfr95r/VvDgQNUfrGcqq++wl5UhM5kIuCXswm6aA5+kyb2u6YLnVVpqSSjIuO4BOxQxSGqrcfyGB+9D8lByQwIHKAtgwaQHJhMUmBSt//PVMlWN5FSUmmpJLMqk+zq7OMSq+zqbGpttc3bGoSB+IB4BgYNZFDwscQqOTAZH4P65QOnbrQ8QhzleeNChgozleV+fJk9hbC8SgZU5QPgnZJCwDnnEHDuOXinpJxU86f+AWosFgsZGRkMGjQIb++uTWPU152yjKx18MUtsLex7dbEP8IvHgFv03GvV+81BUA6HNRt2kTl8i+p/u47nHV16IOC8JsyBf+pU/GfdgZeCWpYkY5oqrg4WnmUo5VHyazK1JaVmeTW5DY3sQGtV2RiYCIJAQnEm+K1ZYC2DPByfV6hki0XqrZWk1eTR25NLrk1ueTV5GGuMZNXk0deTR41tprmbXVCR6x/LEmBSSQGJpIUmKTdApKIMcX0vvGrutmJyZY3Vu6w/4u55T/RUGSkPNcf6gQOBOlhA1gXM5KnX7i13S8t9Q9QcQkpYctb8N+7wWGF4ES48AUYfG7zJuq9ppzIWV9PzcqV1KxZS+26ddgLCgAwxsc3J15+kyerdl5dYHFYyKrKIrNSS8COVh0lpyqHnOocyi3lx20b5B1EginhuAQszhRHjCmGaL/oLnUoU70RO8jmsFFcX0xhXSGFtYUU1hVSUFtAQW1Bc3JVZa067jW+Bl/iTHHEmeKYGDWRWFNsc1IVb4rv2z0A3UwnnSRWFfL5TBP1P31B3Y4d2KognxCEUYfpjDMJmD0b01lnceHT6wF4Uf067LDc3FwWLFjA66+/rgY2PYU2y0gImHQ9xKdptVwFu7QpolIu1HrDhg/xRMhKD6fz9SXw/PMJPP98pJRYj2ZSu24dtevXU/Xtt1T8618gBD6pqfhPOwP/qVPxHT9etfXqAG+9N0NDhjI05ORmETXWGsw1ZszVZnKqtQTMXG1md8luvs/6vrmBPmjNecJ9w4nxjyHaP5oY/xgtCWta948h2DvY5e2le32y5ZROKiwVlNSXUFJfQml9aXNCVVRXpK3XFVJaX3pcFSRoyVS0fzRxpjhGR4xuTqziTHHEmmLdUuD9laOmlobdu6jbto367Tv4ZMMW/O0NFKwAvbcDvwgrIWNC8f3Nn/E5Zy66Vhp1d2Uqlf5Kr9cTERGBXrUbOaUOlVHMaLhhhTZrwaqnYP9XcOBbGDOXwWIMh6Xq8aq0TgiB98ABeA8cQOjvrkba7dTv3k3t+vXUrltH6TvvUrrkTdDr8R44EJ/hqXinpuKTOhyf1BT0gb1g6rQewuRlIiU0hZTQkzu02J128mvzya3JJb8mn4LaAvJr88mvzedg+UFWmVdhcViOe42P3ocIvwgifCOI9Iskwi+CAOfpXYXrkZcRLQ4LFQ0VVFgqKLeUU95QTml9aXNCVdJQQll9GSX1JZQ1lB2XtTYJ8Aogyi+KKP8oov2im9ej/KKa101Gk0qmXMxZV4flyFGsRzKwHM7AciQDa8YRrFlZ4HSCEHjHhuDwLiYyogrfcCvG6AjE2f/QRoRvZSBWNV+d0iNUF8DKJ2HbMmj8zlnhGMNZV/0Nhp4HqqZb6QRnbS21mzdTv2MHDfv2YUnfh724uPl5Y3w8PqmpxyVhhsi+NVBoTyClpNxSTn5tPgU1xxKx4rpiiuqLKKkvoaiuiJrqGvbN3we9sc3WQz89RL2hnnJL+bHkqqG8ecqZExmEgTDfMMJ9w48tfU6+H+kXqXr3uZF0OnGUlWHNysKSoSVTliNHsGQcxp6Xf2xDgwGvxES8E2PxDnHi652Fr20beqP2jyrbGUHiRXdr42cZVTW6K9XV1bF582YmTZqEn5/6LLSmy2VUdgTWvUrD5mX4CBsAJTKQ7x0T+daZxiZnChZaH25D/QhQ2mIvKaFh3z4a0vdpy33p2LKym5/Xh4TglZiIMSEBY0I8XvGNy4QEDFFRCF3PGCahr5FSUlBWQGx4LLgz2RJCnAe8BOiBN6WUT57wvDewDJgAlAJXSCkz29hfAFA18c2JhAWHEeIdQrBPcOtL72BCfEII8wkj0Duwx4y50VdJpxN7SQn2wkJsBQXYCwqxFxZgyy/AVth0vxBpszW/Rvj44DVgAN6DBuE9cCBe0UF4+1fjZT2MMK+Dwj3HDqAzwJDZzNs9ktXO0Rx58iIP/JV9nxr6oX2nW0bj7vqI3+jXcoV+BUN1x6YuqZdebHSmssmZwlbnUHbLAdSh/ZhQyZbSWY6aGiz799OQvg/LoYNYc8zYcnKw5edrVwsaCaMRY1wcxoQEvBLiMcYnYIiIwBAehj4sDEN4OPrgYJWQdZHbeyMKIfTAQeAXgBnYDFwppUxvsc0CYLSU8mYhxFzg11LKK9rYZ4/sjdiXSCmRNhvO2loc5RU4KitwVFTgqKhssV6Bo7Ly2OMVFVo1tt1+3L6E0YghOhpjVJS2jI7CEB2DMT4O78GDMcbGIuz1rH7kl4zUHSVU1Bz3+jrpzTrncP7nnMh/HZOo5FgXevXPxz0cDge1tbX4+/urdlun4LIykhIK90L6F3Dgm+N/XAAgyHBGc0AmcETGcNQZQ46MwCwjKCIYuwuazqrPUf8jbTZs+fnYzGYtATPnNCdiVrMZZ2XlyS/S6dCHhmIIC8MQFoY+PAxDaJiWkAUHozMFoDOZ0AeY0AU0rQcgfHz6/eXL7uiNmAYcllIeARBC/BO4GEhvsc3FwION658CrwohhPTENcoeQDqd4HAgHQ6k3QF2W+O6Hex2pN1+/H2HA2m1Iq1WnBaLtm6xNj5maXzcemybhnpkfT3O2jqcdae+nZg0HUenQx8UpN2CgzFGRuIzdCiGyEgMMdEYo6MxREVhjI5GHxLS/q8hox+puixCRQ3l0sRu5wC2OIexWQ5jm3PIKS+rKO6h1+ubvhiUU3BZGQkB0SO129n3QHUhHF0NORu1W9E+BpHPIPJPeqlTCkoJoEQGUS4DKCOAKulHFf7USF9q8aEOH+qlNw0YseCFFQMWacSGofGmh7oy8As9/b9F6TWE0YhXYiJeiYn4t/K8o6pKu0pRUoKjtBR7SSn2slIcJaXYS0uxl5ZgzcrCXlqKbGho+2AGA3qTCZ1JS8L0/v4IHx90vj4Ibx+Ejzc6H190Pt6IpqV3i+eNRoSXEWEwaOtGbZ2m9ZY3vR70eu1/jt6A0OuaH0On67VJX0eSrTggp8V9MzD5VNtIKe1CiEogDChpa8fpV12Nv/FYo9ITewu2eKJxKY9ftvKYRJ6w/cn3pTzhMacTZOPjzetObZvW7judzQkVUmqJVeMSeaxa1y30BoS3Nzo/P+3m64vOzw8RYEIXFYnO1xe9rx/Gpsf9/NAHBaIPDkYfGNicYOlMpnYTKHvjjdraNrdrcl31fAplKD88dBXjhGAccEM7r6mu7vQPBKUDsrOzufrqq/nggw9I7GeT5naU+8rIDwacp90A7FYoOQglh6AsQ2vzVWmGCjPUFeMjK4mnktPp11i9phjOuN0l0St9hBAQEQEREQjA2Hg7kZRS++FeXYWjugZnbQ2OmhqcjevOmlqcNU2P12KrrtZ+0DcmaU6LpXlJQwPSZnXv36VrSsS05KvpJoRoXBcgBELomu8LodPKo/nGKR4TNK5Ac06nrdQ6Tu6I1xkduYx4OfBLKeX1jfd/D6RJKW9rsc3exm3MjfczGrcpPWFfNwI3oiV5Y04rckVRFEVRlO4VK6U8uZq6HR2p2TIDLUeTjAfyTrGNWQhhAIKAshN3JKVcDCwWWvq4HZje2YCVHmMVMNPTQShdos5d76bOX++mzl/vtQYo6MoLO5JsbQaGCCEGALnAXOCqE7ZZDlwLrAcuA35qq72WlFIKIexdaWSm9AxCCKc6f72TOne9mzp/vZs6f71XY97Spbbo7SZbjW2wbgW+Qxv64W0p5V4hxMPAFinlcuAt4D0hxGG0Gq25XQmR04JUAAAHNUlEQVRGURRFURSlr+lQn2Mp5TfANyc8dn+L9Qbg8k4ee3Ent1d6FnX+ei917no3df56N3X+eq8unzuPjCCvKIqiKIrSX6ihZBVFURRFUdzI7cmWEOI8IcQBIcRhIcRdrTzvLYT4uPH5jUKIZHfHpHRMB87dPCFEsRBiR+Ptek/EqbROCPG2EKJICHHikOZNzwshxMuN53eXEGJ8d8eotK4D526WEKKyxWfv/ta2U7qfECJBCLFCCLFPCLFXCPGnVrZRn70eqoPnr9Ofv9OfJ6INjVP9vEaLqX6EEMtbTvUDXAeUSykHN0718xRwyql+lO7RwXMH8LGU8tZuD1DpiHeBV9HmLW3N+cCQxttkYCEnD1iseMa7tH3uANZIKS/snnCUTrADf5VSbmucmm6rEOJ/J3x3qs9ez9WR8wed/Py5u2areaofKaUVaJrqp6WLgaWN658C54jeOh5/39KRc6f0YFLK1bQy3l0LFwPLpGYDECyEiOme6JS2dODcKT2UlDJfSrmtcb0a2Ic2y0pL6rPXQ3Xw/HWau5Ot1qb6OTHo46b6AZqm+lE8qyPnDuDSxmrwT4UQCa08r/RcHT3HSs80VQixUwjxrRBihKeDUU7W2CxmHLDxhKfUZ68XaOP8QSc/f+5OtlqroTqx+2NHtlG6X0fOy5dAspRyNPADx2oold5BffZ6r21AkpRyDPAK8B8Px6OcQAhhAj4D/iylrDrx6VZeoj57PUg756/Tnz93J1udmeqHtqb6Ubpdu+dOSlkqpbQ03l0CTOim2BTX6MjnU+mBpJRVUsqaxvVvAKMQItzDYSmNhBBGtH/UH0gp/93KJuqz14O1d/668vlzd7LVPNWPEMILbWT55Sds0zTVD3Rgqh+l27R77k5oYzAH7dq20nssB65p7Bk1BajsygSrSvcTQkQ3tW0VQqShfZeXejYqBbSehmizquyTUj5/is3UZ6+H6sj568rnz629EdVUP71XB8/d7UKIOWi9N8qAeR4LWDmJEOIjYBYQLoQwAw8ARgAp5Rtos0L8CjgM1AF/8Eykyok6cO4uA+YLIexAPTBX/UjtMaYBvwd2CyF2ND72DyAR1GevF+jI+ev050+NIK8oiqIoiuJGagR5RVEURVEUN1LJlqIoiqIoihupZEtRFEVRFMWNVLKlKIqiKIriRirZUhRFURRFcSOVbCmKoiiKoriRSrYURVEURVHcSCVbiqK0SwhxjxBib+Ok4zuEEJOFEMFCiAUdfH1Na+tdjEUKId5rcd8ghCgWQnx1Ovs9xbGShRD1LQY3dMnxhRC+jeVoVdPsKErfp5ItRVHaJISYClwIjG+cdPxcIAcIBjqUbJ3GsYUQ4sTvqVpgpBDCt/H+L4BcN4aRIaUc68rjSynrG/ep5sNTlH5AJVuKorQnBihpmnRcSlkipcwDngQGNdbQPAMghPidEGJT42OLhBD6U+1UCPEfIcTWxhqzG1s8niyE2CeEeB3YxvET9jb5Frigcf1K4KP29i2E8BdCfC2E2CmE2COEuKK1xzpYJm0eX1EUpSWVbCmK0p7vgQQhxEEhxOtCiJmNj99FY62PlPJvQohU4ApgWmOtjQO4uo39/lFKOQGYiDbPZliL54YBy6SU46SUWa289p/AXCGEDzAa2NiBfZ8H5Ekpx0gpRwL/PcVjHdHe8RVFUZqpZEtRlDZJKWuACcCNQDHwsRBiXiubntO43ebGNk7nAAPb2PXtQoidwAa02qshLZ7LklJuaCOmXUAyWq3SNx3c927gXCHEU0KI6VLKylM81q4OHB8hxLDG5PQ5IURsR/arKErfZPB0AIqi9HxSSgewElgphNgNXNt4vyUBLJVS3t3e/oQQ/9/O3bpIFUdhHP8+TUVRxJckGgVZEDVokU0Gm+AfYBJfuiCYthhcg9hNW7eIoCwIGtSuFl+CgtHVIG5Q8RjuRYZlRu84e3EYvp/4497zO/Hh3DMzT7P7daKq1pI8AjYNPPK1Q1t3gUVgHvg9FRtVu6peJzkKnAauJ1mpqoVhZx3uHnl/28Mu4CpwBdgCLCY5V1XfOtaWNEOcbEn6o3ZCMzh1Ogy8B74A2wbOHwJnk+xp39uZZP+IstuBz20YOggc/4fW7gALVfWiS+12urRWVUs0IenIsLMNuB/gJHALOAPsBZaBQ2PUljRDnGxJ+putwO0kO4AfwFvgfFWtJnmS5CVwv93bugastL8g/A5cpglm6z0ALiR5Dryi+dw3lqr6QBNoutaeA24k+dn2dnHE2aT3A7wBTlXVTYB28f5x19qSZkuq6n/3IElTKckB4F67PD/uu5doPmcGWKqq5SHPvAOOVdXHyTqVNM0MW5I0QpJ9wFNgdd1/bU1adzPwDNgNzFXVp42qLWn6GLYkSZJ65IK8JElSjwxbkiRJPTJsSZIk9ciwJUmS1CPDliRJUo8MW5IkST0ybEmSJPXIsCVJktSjXzNhTxK94v+zAAAAAElFTkSuQmCC\n",
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      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# creating a distribution for the stellar mass\n",
    "# info: df_cks is the \n",
    "cks_mean = df_cks[\"koi_smass\"].mean()\n",
    "cks_std = df_cks[\"koi_smass\"].std()\n",
    "from scipy.stats import norm\n",
    "smass_dist_cks = norm(cks_mean, cks_std) # Gaussian\n",
    "\n",
    "# sample probabilities for a range of outcomes\n",
    "starmass_arr = np.linspace(df_cks[\"koi_smass\"].min(), df_cks[\"koi_smass\"].max(), 100)\n",
    "probabilities = [smass_dist_cks.pdf(value) for value in starmass_arr]\n",
    "\n",
    "# Owen & Wu 2017 paper:\n",
    "# Section 3.2. \"We adopt host star masses similar to those in the CKS sample (Fulton et al. 2017), \n",
    "# a Gaussian distribution in mass, centered at 1.3 M_sun with a variance of 0.3 M_sun.\"\n",
    "mean_OW17, variance_OW17 = 1.3, 0.3\n",
    "std_OW17 = np.sqrt(variance_OW17)\n",
    "smass_dist_OW17 = norm(mean_OW17, std_OW17)\n",
    "smass_dist_OW17_2 = norm(mean_OW17, variance_OW17)\n",
    "\n",
    "starmass_arr_OW17 = np.linspace(0,5,100)\n",
    "probabilities_OW17 = [smass_dist_OW17.pdf(value) for value in starmass_arr_OW17]\n",
    "probabilities_OW17_2 = [smass_dist_OW17_2.pdf(value) for value in starmass_arr_OW17]\n",
    "\n",
    "#plot \n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "ax.hist(df_cks[\"koi_smass\"], bins=20, histtype=\"step\", density=True, lw=2)\n",
    "\n",
    "ax.plot(starmass_arr, probabilities, ls=\"-\", lw=2, label=r\"$\\mu$={:.2f}, $\\sigma$={:.2f}\".format(cks_mean, cks_std))\n",
    "ax.plot(starmass_arr_OW17, probabilities_OW17, ls=\"-\", label=r\"$\\mu$={}, $\\sigma$={:.2f}\".format(mean_OW17, std_OW17))\n",
    "ax.plot(starmass_arr_OW17, probabilities_OW17_2, ls=\"-\", label=r\"$\\mu$={}, $\\sigma$={}\".format(mean_OW17, variance_OW17))\n",
    "ylim = ax.get_ylim()\n",
    "ax.vlines(cks_mean, ylim[0], ylim[1], linestyle=\":\", color=\"k\", lw=1.3)\n",
    "ax.vlines(mean_OW17, ylim[0], ylim[1], linestyle=\":\", color=\"k\", lw=1.3)\n",
    "ax.set_xlim(0,2.5)\n",
    "ax.xaxis.set_major_formatter(ticker.StrMethodFormatter('{x:.1f}'))\n",
    "ax.set_title(\"Stellar Mass Histogram\", fontsize=15)\n",
    "ax.set_xlabel(\"Stellar Mass [M$_\\odot$]\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 5,
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   "metadata": {},
   "outputs": [
    {
     "data": {
599
      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def L_high_energy(t_i, mass_star):\n",
    "    \"\"\" L_HE (UV to X-ray) in Owen & Wu (2017).\n",
    "    @param t_i - in Myr\n",
    "    @param mass_star - in solar masses\n",
    "    \"\"\"\n",
    "    t_sat = 100. # Myr\n",
    "    L_sat = 10**(-3.5)*(mass_star) * (const.L_sun.cgs).value\n",
    "    a_0 = 0.5\n",
    "    if t_i < t_sat:\n",
    "        L_HE = L_sat\n",
    "    elif t_i >= t_sat:\n",
    "        L_HE = L_sat*(t_i/t_sat)**(-1-a_0)\n",
    "    return L_HE # in erg/s\n",
    "\n",
    "# make test plot\n",
    "step_size, t_track_start, t_track_end = 1., 1., 3000.\n",
    "fig, ax = plt.subplots()\n",
    "for m in [0.7, 1.0, 1.3]:\n",
    "    t_arr = np.arange(t_track_start, t_track_end+step_size, step_size)\n",
    "    Lx_arr = np.array([L_high_energy(t_i, m) for t_i in t_arr])\n",
    "    ax.plot(t_arr, Lx_arr, label=\"{} M$_\\odot$\".format(m))\n",
    "ax.loglog()\n",
    "ax.legend()\n",
    "ax.set(xlabel=\"Time [Myr]\", ylabel=\"L$_{\\, \\mathrm{high\\ energy}}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# draw N times out of pre-defined distribution of stellar masses which resembles the observed data\n",
    "N = 1000\n",
    "masses_cks = dist_cks.rvs(N)\n",
    "# calculate corresonding saturation luminosity\n",
    "L_HE_cks = L_high_energy(1., masses_cks)\n",
    "\n",
    "# plot L_HE distro\n",
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "# 1D KDE\n",
    "sns.distplot(L_HE_cks, hist=True, kde=True, \n",
    "             norm_hist = True,\n",
    "             color = 'darkblue', \n",
    "             hist_kws={'edgecolor':'black'},\n",
    "             kde_kws={'linewidth': 4})\n",
    "\n",
    "ax.set_xticks([6*10**29, 10**30, 2*10**30])\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_xlabel(\"L$_{HE}$ [erg/s]\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Planetary Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- orbital period distro similar to Kepler targets (from fitting Kepler planet sample & correcting for transit probabilities): <br>\n",
    "<font color=blue> dN/dlogP = const. (P>7.6 days) & P^1.9 (P<=7.6 days) </font>\n",
    "- logarithmically flat initial envelope mass fraction [f=M_env/M_c] distribution (<font color=blue>f=10^(-5) to 1 </font>) <br>\n",
    "(NOTE: f<1, such that core mass dominates & self-gravity of envelope can be neglected!)\n",
    "- Rayleigh distro for core masses (1 to 11 M_earth cores): <br>\n",
    "<font color=blue> dN/dM_c ~ M_c*exp(-M_c^2/(2*sig_M^2), where sig_M = 3 M_earth  </font>\n",
    "\n",
    "-> models which fall into the gap (R=1.8 +/-0.2 R_earth) after a few Gyr (due to cooling contraction & photoevaporation) are disvavored by observations and thus flagged! <br>\n",
    "**Note**: Their final models DO include many planets within the gap! They just exclude them and conclude the initial population must exist of either planets with M_pl >2 M_earth and envelopes of several %, or lower mass planets with essentially no atmospheres\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Semi-major axis distribution"
   ]
  },
  {
   "cell_type": "code",
711
   "execution_count": 6,
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   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000\n",
    "deltaP = 0.01\n",
    "period_values = np.arange(0.01, 100, deltaP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MjIhNq3QrT6Xobq7VOjjQ82tdt/saPXWXVeuuHvHm5basYywzR5kwSpLUKRoZw3gaRWviP9WRLJKZ12fm4X1Uu7WM4YDKwogYRzE+8rYWn19VZj5CkRAeVOVwd1m/rt3p7s5ywostjJIkdYxGEsaJPD0Z5FkiYs+IOL3B978cSOCUHuXvo+jy/k7F9WdExO79Pb8fLgNmRMRrK2IYTbHu4zLgxwO4dsea0zWNsaxnRizqu7IkSRoWGumSPoOim/muXo6/oKzzyXovmJmzI+LLwEkRcSVFErYHxU4tN/LMRbevA6bB01sTN3g+EXEocGj58sXl80kRsay83qcrqp8FvBn4bkScQ9HieAzFcjrHV9s2RzAnp7NrLGCT2NjuUCRJUpM0kjD2MeWVcUC9i2JXOgWYB5wAHAUsoZhUc3pmdjX5/CMoktpKp1V8/beEMTOXlguRnwWcSLGX9BzgbZl5eT0fbKTJLFoYXz769naHIkmSmqhmwhgRk4DJFUVbR8QOVapuRbHUzsONBlDunnJ2+ahVb/pAzi/rzgJmNRDbQuCd9dYf6R5jMkvZwvGLkiR1mL5aGE8FusclJsUWfD234esWFMvsaIS6u3uHF2dIS5LUUfpKGG8on4MicfwBcGePOgmsAn6XmTc3NToNK3PKGdK7x0NtjkSSJDVTzYSxXD7nRoCImAZ8NTN/PxiBafiZ0zWdHeJRJsWadociSZKaqO5JL5l5XCsD0fA3J6c5flGSpA7Ua8LYPbklMx+qfN2X7voaWVblOObl8zh69E3tDkWSJDVZrRbGeUBXRIwvt9ebRzFesS+jmxCXhpl7c3uSUbYwSpLUgWoljJ+kSBA39HgtPcvdXdMBZ0hLktSJek0YyzULe30tVZqT09iKFWzL4+0ORZIkNVkje0lLvZrTNY2Zo+YTfe0HJEmShh0TRg3YhhzFPbm94xclSepQtWZJd9H4mMXMzEb2p1YHeCCn8BRjHb8oSVKHqpXcXYqTXFSH7h1e9ox57Q1EkiS1RK1JL8cOYhwaxuZ0TWNTnmLHeKTdoUiSpBZwDKMGbE5OZ/d4mDHR1e5QJElSC5gwakAyk7vLGdKSJKkz1Zr0MhfoAnbPzPUR8WAd18vMnNG06DTkPbJ8LcuYyEzHL0qS1LFqTXqZTzHppXviy0M4CUY93L1oBeAOL5IkdbJak14Oq/VaApi9cDmj6HINRkmSOphjGDUgsxcsY9dYwGbxVLtDkSRJLdLwItsRsSlwGLBTWfQgcGNmrm1iXBoGMpPZC5dz+Kh6hrdKkqThqqGEMSLeBZwDbAl07xqcwLKIOC0zL2lueBrKHlm+liWrnmLvMSaMkiR1sroTxoh4K3AJxeSXLwBzKJLGmcA/AxdHxJrMvLwFcWoIunPBcgD2GjW3zZFIkqRWaqSF8ePAPcBBmbmiovyHEfEV4PfAvwEmjCPE7IXLGDMq2D0eancokiSphRqZ9LIb8I0eySIAmbkc+AawS7MC09B354Ll7LbtRMbF+naHIkmSWqiRhHExT49brKYLeHRg4Wi4yEzuXLCcvZ+/RbtDkSRJLdZIwngJcGxETOh5ICImAe+haGXUCPDw42tYvmY9ez9/crtDkSRJLVZra8BDexT9CngNMLscs3gPxQzpmcAHgCXATS2KU0PMnQuXAbDXVFsYJUnqdLUmvdzAs7cC7O6S/s+KY91l04CfA6ObFZyGrtkLljN2zCh2fd7EdociSZJarFbCeNygRaFh584Fy9lju0mMHeNmQZIkdbpae0l/czAD0fDR1ZXctXA5b3jR1HaHIkmSBoHNQ2rYg0tWsXLdBvZyhrQkSSNCf/aSfh7wYortAZ+VcGbmpU2IS0PY7Q8VE1723WHLNkciSZIGQyNbA44CvgwcT+2WSRPGDvfHh55gi802YadtNm93KJIkaRA00iX9EeD9wGXAuylmR38MOBG4D7gN+PtmB6ih548PLWOf7SczalStddwlSVKnaCRhfDdwbWa+C/hJWfaHzPwqsB+wTfmsDrZy7XrufXSl3dGSJI0gjSSMO/F0othVPm8CkJlPUuzycnzzQtNQdOeC5WTCi3ZwhxdJkkaKRhLGNcD68utVFAt3P7fi+GJg+ybFpSHq9vlPEAH7mDBKkjRiNJIwzgdmAGTmeuB+4JUVx48EHm1eaBqK/vjwMnZ+zgQmjduk3aFIkqRB0kjC+EvgjRWvvwUcExHXR8QNwJuB7zUxNg0xmckfH3rC8YuSJI0wjazD+AXgZxGxaWauA86k6JJ+B7ARuAA4o/khaqiYt3Q1T6xe7/hFSZJGmLoTxsx8BHik4vVG4EPlQyPA7fOfAGDfabYwSpI0krg1oOr2x4efYOKmY9j5ORPaHYokSRpE/dka8C0UYxl3KoseBH6QmY5f7HC3zXuCfXZwwW5JkkaaulsYI2J8RPycYqeXtwK7ALuWX18WEddFREN7xUXEqIg4NSLuiYi1EfFwRJxd73UaPT8iXh0RN0fEkxHxeERcERE7Vqk3KyKyl8dHGvmMnWL56mLB7gOmb9XuUCRJ0iBrpEv6s8DLgfOBKZm5VWZuCUwpyw4HPtPg+58LnAPMAU4GrqAYE3lNuXd1086PiKOB/wU2A/4v8HngUOA3ETGll+ufCryzx+NHDXy+jnHb/MfJhP13NGGUJGmkaaRL+q3AFZl5SmVhZi4GTomIqWWdU6qd3FNE7EmR5F2ZmW+qKJ8LfBF4G/DdZpwfEZtQJLUPAy/NzFVl+U+APwCzgBOqvM1VmTmvns/T6W6Z+zhjR49in+2dIS1J0kjTSAvjJOD6Gsd/Wdap1zFAAOf1KL8QWE2xXE+zzn8ZRUvoRd3JIkBm3gHcALy1TCqfJSImRUTDYz07zS3zHmfv52/BuE1GtzsUSZI0yBpJGO+kGLfYm12A2Q1cb3+KPalvqSzMzLXAHeXxZp3f/fVvq1zndxSJ7q5Vjt0JLAfWlmMfX9VHTB1p9VMbmL1gOQfYHS1J0ojUSML4CeB9EfHangci4vXA8cDHG7jeFGBJuQh4TwuBbSJibJPOn1JRXq0uwNSKsmUUC5GfDLwe+FdgGvCjiDi2RkxExAkRcRtwY616w8kdDy1jQ1c6flGSpBGq167WiPh6leK5wFURcS/wZyCBmcBuFK2L/0TRNV2P8UC1ZA9gbUWdp5pw/vjydbX6lXUByMye3dzd34+7gHMj4n8qu7YrZeYFwAURMRFY0Ut8w8rv5z7OqID9XLBbkqQRqdbYvGNrHNu9fFTaG9gLeG+d772aYmvBasZV1GnG+d3Pm/bzvcjMpRHxVYoJMgcDP6tVv5PcOu9x9thuEpPGVR3mKUmSOlyvXdKZOaofj0ZmRCyi6DaulsRNpehu7q11sdHzF1WUV6sL1bure5pXPm9TR92O8NSGLm5/6AnHL0qSNIK1c2vAW8v3P6CyMCLGAfsAtzXx/FvL55dUuc5BFF3Hf6kj5u5JP4/WUbcjzF64nLXru1ywW5KkEazhhDEK+0bEP5aPfSOiP3vFXU4xBrLnuo3voxhP+J2K95wRET27wOs+n2ICyiPA8RHxt42QI+KFwGEU60uuL8vGRMQWPYONiO2BDwBLgZvr+4jD328fWALAgTtt3eZIJElSuzS0vmBEvBL4CsWM4UrzIuKDmXltvdfKzNkR8WXgpIi4EvgxsAfFTi038sxFu68r3zP6c35mro+ID1MkmTdFxIUUS+mcCjwGnFHxXhOAuRFxFcXEnicoJvUcXx47JjPX1Ps5h7tf37+EmdtNYqvNa01YlyRJnazuhDEiDgGuBp6k2EnlrvLQnhQTZK6OiMMzs5HWt1MoxgWeABwFLKHYkeX0zOxq5vmZeUVErKFYHugLFDOmrwM+mpmV4xfXAN8HDgTeQJEkLgF+AXwuM5+x7mMnW/PURm6fv4x3H9zz/weSJGkkaaSF8XRgMXBgZj5SeSAiPg/8vqzzynovmJkbgbPLR6160wdyfkX9/6XYT7pWnXUUrYkj3m3zH+epjV0csvOImeMjSZKqaGQM44HABT2TRYCy7EKKCSTqEL++fwmbjA5nSEuSNMI1kjCOBVbWOL6irKMOcfP9S3nR9lsyfuyI30pbkqQRrZGE8c/A2yLiWdlDWfbWso6Gk1lbPP2osGz1U9y1aLnd0ZIkqaGE8b8ouqWvi4ijImLH8vEaiskjB1LMoFYH+N2DS8mEQ3Z2OR1Jkka6uvsaM/OiiNgF+Ajwd1WqfD4zL25aZGqrX9+/hM3HjuaF209udyiSJKnNGhqclpkfjYiLgdcDO1Ksi/gAcHVm1rNTioaBzOSGex/jJTO2ZpPR7dwMSJIkDQV1JYzlfs0HAo+UieHnWxqV2uqBx55kwRNr+MBhM9odiiRJGgLqbT7aSDFO8VUtjEVDxA33/hWAw3Z7bpsjkSRJQ0FdLYyZuSEiFlOxNZ861/X3/pVdnzeBqZM3e/bBHrOpmbV8cIKSJElt08gAtSuAt0SEg9o62Kp1G7hl7uMcbuuiJEkqNTLp5SLgcODnEXEecB+wumelzHyoSbGpDX5z/xLWb0xetttz2h2KJEkaIhpJGO8CkqJb+rAa9UYPJCC11w33PsaETcfw4mluByhJkgqNJIyfpEgY1aEyk+vv+SuH7Lw1Y8c48kCSJBUaWbh7Vgvj0BBw54LlLF6xlo/M3K3doUiSpCGk3nUYnwPsBCzJzAdaG5La5ad3L2b0qODIPZzwIkmSnlaz3zEiRkXEV4FHgJuBv0TEr8sEUh0kE669azEH7bQVk8ePbXc4kiRpCOlroNpJwAnAYuBKYDZwMPC1FselQXZ/TuXBJU/yyj23bXcokiRpiOmrS/pdwJ+BgzJzJUBEXAgcGxGTM3NZqwPU4Li268UAvMKEUZIk9dBXC+NuwCXdyWLpfIqlc3ZtWVQadD/deAAv2mEyz5s0rt2hSJKkIaavhHFzYFGPskUVx9QBHu56DnfljvyDrYuSJKmKehbb67n2Yvdr95XuED/sOhiA1+y9XZsjkSRJQ1E9y+q8OiIqm57GUySNb46IfXrUzcw8t2nRqeUy4aqNh7B/3MPztzyq3eFIkqQhqJ6E8e3lo6f3VylLwIRxGJmT07g/n8+nx1wMnNbucCRJ0hDUV8J4+KBEobb54cZDGMMGXj36lnaHIkmShqiaCWNm3jhYgWjwdXUlV298CS8bdSdbxcq+T5AkSSNSPZNe1KFufmApi9ma143+TbtDkSRJQ5gJ4wh22a0PsQWr+IdRt7U7FEmSNISZMI5QS1et42d3L+ZNo3/FuFjf7nAkSdIQZsI4Qn3/9gWs35gcM/r6dociSZKGuHqW1VGHyUz++5aHefG0Ldnl0YVPH5i1xTMrzlo+uIFJkqQhyRbGEeim+5bw4JInOeaAHdodiiRJGgZMGEegi349l+dM3JTXvNCtACVJUt9MGEeYexev5Fd/eYxjD57OpmNGtzscSZI0DJgwjjAX3fQg4zYZxdvtjpYkSXUyYRxBFi5bw1V3LOTN+23PlpuPbXc4kiRpmDBhHEG+9Mv7CIIPHDaj3aFIkqRhxIRxhHho6WquuG0BxxywPVMmb9bucCRJ0jBiwjhCnPeLvzB6VPDBw3dudyiSJGmYMWEcAf4w/3Gu/ONC3vt3O/K8SePaHY4kSRpmTBg73Mau5Iyr72bbSeM40dZFSZLUDyaMHe6Sm+dx18IV/Ourd2fzTd0JUpIkNc6EsYPd9+hK/vOn93DkHs/ldS+c0u5wJEnSMGXC2KFWP7WBky/7IxM2HcOZR+9NRLQ7JEmSNEy1PWGMiFERcWpE3BMRayPi4Yg4OyI2b8X5EfHqiLg5Ip6MiMcj4oqI2LGXurtFxFUR8URZ/6aIOGIgn3cwdHUl/+fyP/GXR1dyzlteyHMmbtrukCRJ0jDW9oQROBc4B5gDnAxcAXwIuCYi6omv7vMj4mjgf4HNgP8LfB44FPhNREzpUXcGcDPwEuBzZf0JwLURcWS/Pukg2NiVfPT7d/LTuxfzb0fN5LDdntvukCRJ0jDX1lkQEbEnRZJ3ZWa+qaJ8LvBF4G3Ad5txfkRsApwPPAy8NDNXleU/Af4AzAJOqLj8mcBkYL/MvKOseylwN/DliNg9M3Mgn7/Zlq9Zzxo0CfgAAA1/SURBVGnf+xO/+POjnHLkLrznkOntDkmSJHWAdrcwHgMEcF6P8guB1cA7mnj+y4ApwEXdySJAmQzeALy1TCopu7NfB9zQnSyWdVcBFwG7Avv3/fEGx5JV6/jmzfM48pwbueHev3LGa2dyypG7Om5RkiQ1RbvXWdkf6AJuqSzMzLURcQd9J2WNnN/99W+rXOd3wBEUieDdwN7ApjXqdl/vlirHn2HlypV9Vem3pavW8eov3sSqtRsA2GeHyXzxTXvxgqmT63/fdTUaSatdo2f9lSt7v0atY/Vq5Br9eb/uz9jfOAd6fquvV+3arbp+u9+vnjigvbFUU8/P2VDX2++b4fY56jGSPmsjWvi3ToOjz7whM9v2AGYDj/Zy7HtAAmObcT5Fd3QCe1Sp+8Hy2CvK128qX3+gSt2Z5bHP9vK+JwC3AXeU9Xz48OHDhw8fPobLY7tq+U27WxjHA+t6Oba2os5TTTh/fPm6Wv3KujRY9xky8wLggij6g7cFVlWr12Q3UnS5a+jwngxN3pehx3syNHlfhp7BuCcTgMXVDrQ7YVwN9DaNd1xFnWac3/1cbY2ZgdStqpwQ80itOs0SEV2ZaX/AEOI9GZq8L0OP92Ro8r4MPYN0T3q9frsnvSwCtomIaonZVGBJZvbWutjo+YsqyqvVBVjYj7qSJEkdrd0J461lDAdUFkbEOGAfirGAzTr/1vL5JVWucxCwAvhL+Xo2RXd0b3WpI7bBdEG7A9CzeE+GJu/L0OM9GZq8L0NPW+9JtHMpwYjYC/gT8IMe6yieTLGO4jsz89tl2Qxgk8y8p5/nbwLMB9YDe1asw/hC4HbgG5l5fMU1rgCOBvbNzD+VZRMoZlGvA3YbauswSpIktUJbE0aAiDgfOAn4AfBjYA+KnVp+AxyRmV1lvXnAtMyM/pxf1n0zcDlFknkhMAk4lWJW0H6ZubCi7s4Uy+asp9hNZgXwPmAv4KjMvLaZ3wdJkqShaigkjKOBUyiWo5kOLKFI6k6vXGC7RsJY1/kV9V8DfIJircV1wHXARzPzgSp19wDOopiVNJaiJXJWZv5iIJ9ZkiRpOGl7wihJkqShrd2TXtQPETEqIk6NiHsiYm1EPBwRZ5dbGqqFImLXiPhkRPwuIh6LiJURcUdE/Fu1739E7BYRV0XEExHxZETcFBFHtCP2kSQixkfE3IjIiPhSlePel0ESEVtFxBci4v7y99VjEXF9RLy0R70DI+IX5c/Uioj4aUTs0664O1VETIiIj0fE7PJ7vSQibo6IY6PHfrLek+aLiH+NiCsi4sHy99O8PurXfQ8iYkpEXFr+jK2JiNvKoXjNid0WxuEnIv4fxTjNHwA/oRi3eTJwE3Bk5bhNNVdEnAWcCFxNsU3keuBw4C3AncBBmbmmrDuDYhzsBor9zpdTjIN9AfAqhza0TkR8AXg/xSK0X87MkyqOeV8GSURMA26guA8XU6xEsQXFkKBrM/O/y3oHlfUWAt0J/kkU6+wenJmzBzXwDhURoygWfz4Y+CbF77DxwDEUq418LjM/Wtb1nrRARCTwOMUQt/2AFZk5vZe6dd+DiNiKYvWW5wLnAAuAt1MMqXtPZn5jwMG3c2tAH40/gD0p9s/+fo/ykykm77y93TF28gN4MbBFlfJPl9//kyrKvgdsBPapKJtAMVv/Xsr/sPlo+j3alyIZ/D/lPflSj+Pel8G7FzcBD9PLVmMV9W6hmFg4taJsaln2s3Z/jk55UCwVl8C5PcrHAg8Cy7wnLb8HO1V8fRcwr0bduu8B8Lny3r62omx0eY2lwISBxm6X9PBzDBAULSOVLqTYfeYdgx7RCJKZt2Xm8iqHLi+fXwBQdk+/DrghM++oOH8VcBGwK7B/i8MdccpJcBcCPwWurHLc+zJIIuJQ4O8oWq0eiYhNIuJZW6qWK1LsD1yRFStVlF9fARwZEdsOVtwdblL5vKiyMIsNLpYAT4L3pJUy88F66vXjHrwdeCAzr6mouxE4H9gKePVAYzdhHH72p2hhvKWyMDPXAnfgH7t2eX75/Gj5vDfF1pK/rVL3d+Wz96r5TgV2p+i2qcb7Mni6/0A9FBHXAGuAJyPiLxFR+R/b7u93b/ckKLruNHC3AMuAf4mIN0fEDuV43jMpvsezynrek/ar+x5ExHYULY+/66Vu5fX6zYRx+JlCseXhuirHFlJslTh2kGMa0cpWrdMpukG/WxZPKZ+rbSHZXVZt60n1U0TsCPwH8MnMnNdLNe/L4NmtfL6QooXj3cB7gaeAb0XEceVx78kgycwnKFrYH6cYmjEfuIdiXPabMvPCsqr3pP0auQeDcr/GDPQCGnTjKdaPrGZtRZ1ae3Cruc6j2DLy45l5b1nW3fVW7V6t7VFHzfFfwFyKAd+98b4Mnonl80rg8LLbk4j4AcV4uc9GxDfxngy2VRRj564GbqZI5k8EvhsRr8/Mn+M9GQoauQeDcr9MGIef1RSzoKoZV1FHgyAiPkXR/XlBZp5Zcaj7Hmxa5TTvU5OVXZyvAA7NzPU1qnpfBs+a8vmy7mQRilauiLgaeBdFK6T3ZJBEsZ3uzcCpmfnVivLLKJLIC8tVBLwn7dfIPRiU+2WX9PCziKLbudo/jKkU3dW2Lg6CiJhFsWvQN4B/7nG4e1B5tW6A7rJq3QdqUPmzcA7F1qCLI2LncsD4tLLKFmXZZLwvg2lB+by4yrFHyuct8Z4MplMpEogrKgszczXwI4qfmel4T4aCRu7BoNwvE8bh51aK+3ZAZWFEjAP2oViHSS0WEWcAZwCXAsdnuYZBhdkU3QMvqXL6QeWz96o5NgOeAxwF3FfxuKE8/o7y9fF4XwZT98S851c51l32V4rfadD7PUngD80NbcTqTh5GVzk2puLZe9J+dd+DzHyEIiE8qJe60ITfayaMw8/lFP9QTulR/j6KMQrfGfSIRpiIOJ1iNuG3gOOyykLp5TIt1wCHRcQLK86dQJG43EePme7qtyeBN1d5fLA8/tPy9dXel0F1FcX4xXeU31/gbzM63wDcl5n3Z+b9FH/M3hwRUyrqTaG4b7/MzGqtlGrcnPL52MrCsvX99cATFEuzeE/arB/34DJgRkS8tqLuaIo1mpdR9MAMiDu9DEMRcT7FuLkfUPwj2INi55ffAEdUS2DUHBFxIsWK+w8B/06xxFGlR8tB493raN1CsRvMuRSLrb4P2As4KjOvHay4R6KImE4xCabnTi/el0ESEScAXwPuBr5OsUD0B4DtgNdk5s/KegcD11N0Y59fnn4y8DzgkMz80yCH3pHKnXdupxgK8B2KvxlbUfz7nw6cmJlfKet6T1ogIt7J08NlTqb4mTi7fD0/M79VUbfuexARW1O0OG5NMURnIcW6zYdR9IJdPODg273quY/GHxTdCadR7EqxrvyHcQ5NWMndR5/f+0soWnh7e9zQo/4ewA8p/oe3Gvg1xfaNbf8snf6g+AP4rJ1evC+Dfh+OplgL7kmKFseflX/setZ7CXAdxSzelcC1wL7tjr/THsAMim0BF1D8p2kF8CvgaO/JoHz/b6j370ej94BiyMG3KBZhX0vxn4O3Nit2WxglSZJUk2MYJUmSVJMJoyRJkmoyYZQkSVJNJoySJEmqyYRRkiRJNZkwSpIkqSYTRkmSJNVkwihJgygiDouIjIhj2x2LJNXLhFGSOlRE3FAmp92P9RGxMCIui4g92x2fpOFjTLsDkCS11Drg+PLrzYADgXcDR0XE/pl5b9sikzRsmDBKUmfbkJnfrnh9YUT8GfgC8CHgxPaEJWk4sUtaktosIjaPiDMj4oGIWBcRiyPi0oiYVqXu1hHx9YhYGhGrIuKXEfGisvt5Xp1veW35vHPTPoSkjmYLoyS1UUSMoUjgDgH+Bzgb2AX4APCKiHhxZi4o644FfgHsA1wC3ALsXZY93sDb7lI+L2nCR5A0ApgwSlJ7HUeRLH4+M/+luzAifgH8L3Am8M6y+HiKZPETmfmZirqzgS8D86u9QURsU37ZPYbx3PL1pc37GJI6mQmjJLXXG4EuisTwbzLzRxFxB/D6iBiVmV3Aa4GNwP/rcY0Lgc/2cv3Ngcd6lC0Gjs3Ma6vUl6RnMWGUpPbaEViUmU9UOXY3RYviNsBfK+quqqyUmesjYi6wZZVrrKVINAE2AI8C95YJqCTVxYRRktorWlS328bM/EU/zpOkv3GWtCS11wPAlIiYXOXYTGAFT09OmVvWnVBZKSI2oWh9lKSWMGGUpPa6iuJ38ccqCyPiVcCLgKsruo+vAUYDH+5xjfcBW7Q4TkkjmF3SktRel1DsvPLRiJgO/IpifcQPUow3/HhF3YuA9wOfjoideXpZnbcA9+PvdEktYgujJLVRZq4H/gE4CzgAOA94B3AFcGBmPlxRdx3wcuCbwOspdmvZrSxbDqwZ1OAljRiRme2OQZI0ABExmmKc4+8z85XtjkdS57GFUZKGkYjYrErxPwOTgZ8PcjiSRghbGCVpGImIbwPjgJuBdcBLgLdTzLbeNzNXtjE8SR3KhFGShpGIeBdwIrArMIFiYsyPgX/PzEfbGZukzmXCKEmSpJocwyhJkqSaTBglSZJUkwmjJEmSajJhlCRJUk0mjJIkSarp/wNiP+90FkekJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this is dN/dlogP\n",
    "\n",
    "class logP_pdf_unnormalized(stats.rv_continuous):\n",
    "    def _pdf(self, P):\n",
    "        if P < 7.6:\n",
    "            return P**1.9\n",
    "        elif P >= 7.6:\n",
    "            return float(7.6**1.9)\n",
    "\n",
    "rv_logP = logP_pdf_unnormalized(a=0, b=100, name='logP_pdf')\n",
    "pdfs = np.array([rv_logP.pdf(p) for p in period_values])\n",
    "area_under_curve_logP = scipy.integrate.trapz(pdfs, period_values)\n",
    "\n",
    "class logP_pdf_normalized(stats.rv_continuous):\n",
    "    def _pdf(self, P):\n",
    "        if P < 7.6:\n",
    "            return (P**1.9)/area_under_curve_logP\n",
    "        elif P >= 7.6:\n",
    "            return float(7.6**1.9)/area_under_curve_logP\n",
    "\n",
    "rv_logP = logP_pdf_normalized(a=0, b=100, name='logP_pdf')        \n",
    "pdfs = np.array([rv_logP.pdf(p) for p in period_values])\n",
    "print(scipy.integrate.trapz(pdfs, dx=deltaP))\n",
    "\n",
    "rvs = rv_logP.rvs(size=N)\n",
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(period_values, pdfs)\n",
    "ax.hist(rvs, bins=10**np.linspace(np.log10(np.min(period_values)), np.log10(np.max(period_values)), 50, endpoint=False), density=True, rwidth=0.9)\n",
    "ax.set(xlabel=\"logP\", ylabel=\"Probability density\")\n",
    "ax.set_xscale(\"log\")\n",
    "plt.show()\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(period_values, pdfs)\n",
    "ax.hist(rvs, bins=10**np.linspace(np.log10(np.min(period_values)), np.log10(np.max(period_values)), 50, endpoint=False), density=True, rwidth=0.9)\n",
    "ax.set(xlabel=\"logP\", ylabel=\"Probability density\")\n",
    "plt.show()\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(period_values, pdfs/period_values)\n",
    "#ax.hist(rvs, bins=10**np.linspace(np.log10(np.min(period_values)), np.log10(np.max(period_values)), 50, endpoint=False), density=True, rwidth=0.9)\n",
    "ax.set(xlabel=\"Period\", ylabel=\"Probability density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
817
   "execution_count": 7,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    },
    {
     "data": {
829
      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
841
      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this is dN/dP (dN/dlogP*dP/dP = dN/dP*dlogP/dP = dN/dP*P)\n",
    "\n",
    "class P_pdf_unnormalized(stats.rv_continuous):\n",
    "    def _pdf(self, P):\n",
    "        if P < 7.6:\n",
    "            return P**1.9/P\n",
    "        elif P >= 7.6:\n",
    "            return float(7.6**1.9)/P\n",
    "\n",
    "rv_P = P_pdf_unnormalized(a=0, b=100, name='P_pdf')\n",
    "pdfs = np.array([rv_P.pdf(p) for p in period_values])\n",
    "area_under_curve_P = scipy.integrate.trapz(pdfs, period_values)\n",
    "\n",
    "class P_pdf_normalized(stats.rv_continuous):\n",
    "    def _pdf(self, P):\n",
    "        if P < 7.6:\n",
    "            return (P**1.9)/P/area_under_curve_P\n",
    "        elif P >= 7.6:\n",
    "            return float(7.6**1.9)/P/area_under_curve_P\n",
    "\n",
    "rv_P = P_pdf_normalized(a=0, b=100, name='P_pdf')        \n",
    "pdfs = np.array([rv_P.pdf(p) for p in period_values])\n",
    "print(scipy.integrate.trapz(pdfs, dx=deltaP))\n",
    "\n",
    "rvs = rv_P.rvs(size=N)\n",
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(period_values, pdfs)\n",
    "ax.hist(rvs, bins=10**np.linspace(np.log10(np.min(period_values)), np.log10(np.max(period_values)), 50, endpoint=False), density=True, rwidth=0.9)\n",
    "ax.set(xlabel=\"Period [d]\", ylabel=\"Probability density\")\n",
    "plt.show()\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(period_values, pdfs)\n",
    "ax.hist(rvs, bins=10**np.linspace(np.log10(np.min(period_values)), np.log10(np.max(period_values)), 50, endpoint=False), density=True, rwidth=0.9)\n",
    "ax.set(xlabel=\"Period [d]\", ylabel=\"Probability density\")\n",
    "ax.set_xscale(\"log\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "# if P <= 7.6, probability density is distributed like P^1.9\n",
    "\n",
    "class my_pdf_unnormalized(stats.rv_continuous):\n",
    "    def _pdf(self,P):\n",
    "        return P**1.9\n",
    "    \n",
    "my_rv_unnormalized = my_pdf_unnormalized(a=0, b=7.6, name='my_pdf')\n",
    "area_under_unnormalized_pdf = scipy.integrate.trapz(my_rv_unnormalized.pdf(period_values), period_values)\n",
    "\n",
    "class my_pdf_normalized(stats.rv_continuous):\n",
    "    def _pdf(self,P):\n",
    "        return P**1.9/area_under_unnormalized_pdf\n",
    "\n",
    "my_rv_normalized = my_pdf_normalized(a=0, b=7.6, name='my_pdf')\n",
    "\n",
    "# PLOT\n",
    "fig, axs = plt.subplots(1,2, figsize=(14,4))\n",
    "axs[0].set_title(\"PDF\")\n",
    "axs[0].plot(period_values, my_rv_normalized.pdf(period_values), label=\"PDF\")\n",
    "axs[1].set_title(\"CDF\")\n",
    "axs[1].plot(period_values, my_rv_normalized.cdf(period_values), label=\"CDF\")\n",
    "\n",
    "for ax in axs:\n",
    "    ax.set_xlim(0,25)\n",
    "    ylim = ax.get_ylim()\n",
    "    ax.vlines(7.6, ylim[0], ylim[1], linestyle=\"--\", color=\"k\")\n",
    "\n",
    "plt.tight_layout()\n",
    "#plt.show()\n",
    "plt.close()\n",
    "\n",
    "print(scipy.integrate.trapz(my_rv_normalized.pdf(period_values), period_values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n"
     ]
    }
   ],
   "source": [
    "#if P > 7.6, probability density is const. (uniformly distributed)\n",
    "\n",
    "rv_uniform = stats.uniform(loc=7.6, scale=100)\n",
    "\n",
    "# PLOT\n",
    "fig, axs = plt.subplots(1,2, figsize=(10,4))\n",
    "axs[0].set_title(\"PDF\")\n",
    "axs[0].plot(np.log10(period_values), rv_uniform.pdf(np.log10(period_values)), label=\"PDF\")\n",
    "axs[1].set_title(\"CDF\")\n",
    "axs[1].plot(np.log10(period_values), rv_uniform.cdf(np.log10(period_values)), label=\"CDF\")\n",
    "# for ax in axs:\n",
    "#     ax.set_xlim(0,120)\n",
    "#     ax.set_xlabel(\"Period [d]\")\n",
    "#     ylim = ax.get_ylim()\n",
    "#     ax.vlines(7.6, ylim[0], ylim[1], linestyle=\"--\", color=\"k\")\n",
    "plt.tight_layout()\n",
    "#plt.show()\n",
    "plt.close()\n",
    "\n",
    "print(scipy.integrate.trapz(rv_uniform.pdf(period_values), dx=0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Core-mass distribution"
   ]
  },
  {
   "cell_type": "code",
995
   "execution_count": 8,
996
997
998
999
   "metadata": {},
   "outputs": [
    {
     "data": {
1000
      "image/png": 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\n",
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