Declan-thejoker-velocity-offsets.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07cbe3b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import astropy.table as at\n",
    "from astropy.time import Time\n",
    "import astropy.units as u\n",
    "import numpy as np\n",
    "import corner\n",
    "import pymc as pm\n",
    "import thejoker.units as xu\n",
    "import arviz as az\n",
    "\n",
    "import thejoker as tj\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cb308f02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9Kxsjd/jhh5c9/q1QRGXixIkdcK8BAKD6DW7HObQAV+FeeOGFbPLtCHKDBg3KxqVF4OqIgBghLipTRuXLCGzrrLPOXHPRlUOAAwCA1GXn0PrIVbhVV101++loiy66aPrGN77R4fsFAAA6jzFwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAANSMQw89NPvJKwEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOAAAAByQoADAADICQEOAACoWIceemj2w5cEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOAAAAByQoADAADICQEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOAAAAByQoADAADICQEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAKAyzZqWNpv/v2mHBZ9O6dFLs8u1ToADAAAqz/gzUvrV6umAhR9JOy30VEo3HZFdzq6vYb26+wAAAADmEiHtn2MaX//ZjP+7fstjUi3SAgcAAFSO6CZ576+bX+feX6c0a3qqRQIcAABQOZ7565ctbc35bEa6ZNRu6dBDD021RoADAAAqx0dvl7Va/54za7IoigAHAABUjoWWKmu1aXPmr8miKIqYVLCnn346XXnllWnq1KmpZ8+e2XVbbbVVGj58eP3l9pgyZUq65ppr0osvvpjmm2++9Pnnn6dVV101HXDAAWmhhRbqgHsAAACttMZOKd02qvlulPP2TY/OWq4mi6JogatQN954Yxo1alQaMWJEOu+889I555yTTjjhhPTPf/4zu3727Nnt2v/999+fjjzyyLT66qtn+/7Vr36V/Y7g9qMf/Sh9+umnHXZfAACgbH36p7TF0c2vs8XRaVbdvDVZFEWAq0D33XdfuuCCC9K+++6bhgwZUn/9Yostlo477rj05JNPplNPPTXV1dW1af+PPfZYGjNmTDr44IPTsGHD0jzz/N/L4JNPPkmvvvpq+ve//90h9wUAAFotWsO+MTpraZvLvH2/vL41rWVlFkXJ1ssBAa7CzJgxI5111llZONtuu+0aLV9qqaXS+uuvn+6999501113tXr/0XL361//Og0YMCBtu+22cy277rrrsp/w/vvvt+NeAABAO0VI+8lz6ZIPN0o3frR2SiPOyy63uqtjmUVR0sdvpTwQ4CrM9ddfnz766KM0aNCgtPDCC5dcZ5111sl+X3755WnOnDmt2v+tt96ajX37+te/nnr06DHXsi+++CL7veiii6bNN9+8zfcBAACixH+7y/z36ZcemLlSuu3jNVPaYP/scmcVRUkLLp3yQBGTCnPLLbdkv5dffvkm11lxxRWz32+88UZ6/PHH0+DBg8ve/+233579XmONNRot22OPPdImm2ySddWcf/5WVvUBAIAcF0VJsV4OCHAV5OWXX67vurj00k1/AxDdHwsmTJhQdoB77733soqTYbnlSlftWXbZZVt51CnbZ4yla6s77rijzdsCAEBZRVFKVaEsiOWtbN1rz/lvnD+vssoqbdpWgKsgTz31VP3fTXWfbLhs0qRJZe//+eefr/97kUUWSe+88042TcHkyZOzaQkiGO60005p5ZVXbtPxAwBARdrymP+rNlncEhctbxHecjKFQBDgKkhx4ZDmujAusMACJbdpSQS1gpdeeimNHTs2HXHEEdl0AlHcJCpfHnbYYVlf5d13373s/ca3B1rRAACoaFsek9JGh6ZLRu2W+vecmXbe99Avu022ZVxdO3uRtWYIVEOKmFSQadOm1f/dq1fT2bp42Ycfflj2/qdP/7+5LWJOue9///tpo402yi7HRN4/+MEPsgImF154YTZVAQAAVJU+HVAUpZsJcBWkd+/ejSpCllK8rE+fPmXvf+bMmXN1odx0003nWj7vvPOmr33ta/UVLgEAgMoiwFWQCFUFn332WZPrRXfHcsbKNdf1csMNNyy5zle/+tXs9xNPPJFN6g0AAFQOAa6CFFeALO7u2FDxsqaqSZay0EILzTUheCn9+/evb+WLIicAAFCNDm3vHHXdRICrIOuvv35WDbKl4iTFy1ozALI4IMaYt1KKr59nHi8PAACoJM7QK0jfvn3TuuuuWz9Jd1Nee+21+oC18cYbl73/2HePHj2abeGbOnVqfaGUJZdcslXHDwAAdC4BrsLss88+9ZP7NVXI5LnnnqufPLA1ISvGy6211lrZ32+//XbJdV5//fXs9wYbbNCqAikAAEDnE+AqTLSSRavajBkz5prYu2DOnDnp4Ycfzlrr9ttvv7mWTZkyJR1yyCFpxIgR6Yorrii5//333z/7PWHChJLLH3jggez3Xnvt1QH3BgAA6EgCXAUaNWpUWmGFFdJll12WBbZit956a9bNMeZxW3rppedadt9992WTdcd0AVdffXWT4+x22mmn9OabbzYKcY888kh65ZVX0m677ZbWXnvtTrhnAABAezQ9WzTdJlrXTjvttHT66aenY445Ju24447ZFACPPfZYevDBB9PJJ5+cdXFsaPPNN0+333571j1yjz32aHL/P/zhD7M53375y1+mvffeOwuLL7/8crr22mvTd77znUYtewAAQGUQ4CrUoosumk499dT0wgsvpEmTJqV33303rbfeemnkyJFNVpAcMGBAuvjii1vcdxQyibKpu+yyS9YK99///jcbS/e73/0uu10AAKAyCXAVbtVVV81+OkOEth122KFT9g0AAHQ8Y+AAAAByQoADAADICQEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHKiV2fs9NJLL02V5oADDujuQwAAAKi8APfd73439ejRI1USAQ4AAKrErGlps/n/m/r3nJXSo5emtMZOKfXpn2pBpwS4grq6ulQJKi1MAgAA5bnwwgvnvmL8GSnd++t0wMIzvrx80xEp3TYqpS2OTmnLY1K167QAt8QSS6S99torLbLIIqm7vPrqq+nyyy9Pn3/+ebcdAwAA1JzOaiEbf0ZK/xzT+PrPZvzf9VUe4jotwB177LHpqKOOSt1t2rRp6YYbbujuwwAAgNrQWS1ks6Zl+21WLN/o0JT69EvVqtOqUK699tqpEqy77rrdfQgAAFAbCi1k0SJWqoUslrfVM39tvN+GYnmsV8Xm6awxZ2uuuWaqBGuttVZ3HwIAAFS/clvIZk1v2/4/eru89T5+K1WzTglwCy+8cFpqqaVSJYggWSnFVAAAoGp1dgvZQmXmiwWXTtWsUwLc448/nirFKquskv7zn/9092EAAEB16+wWsiiEMm/f5teJ5bFeFeuUALfccsulShHdOVdaaaXuPgwAAKhund1CFlUstzi6+XVieRUXMOnUIiYAAEAN6YoWsi2PSekboxvfTlyO66t8CoEgwAEAAO3XVS1kWx6T0k+eS5d8uFG68aO1UxpxXna5FsJbp84DBwAA1JhCiIpqk8UFTaKFrL3zwBXr0y89MPPLYVI7b7B/qiUCHAAA0HEipG10aLpk1G6pf8+Zaed9D/2y22SFjE3r02N2GtzntdS/56yUHr30/x9b/5QXAhwAANCxKrWFbPwZ6bQlb0p95vn8y8s3HZHSbaM6tnWwkwlwAABA9Rt/Rkr/HJP6NKwCEl09/znmy79zEOIqpojJ9ttv392HAAAAVKNZ074cl9ecWD5reqp0FRPgXnjhhe4+BAAAoBo989e5i6qUEstjvQpXEQFu1qxZ6fXXX+/uwwAAAKrRR2+Xt97Hb6WqHgN31VVXpU8//bTdB3H//fenzz///wMJAQAAOtJCS5W33oJLp6oOcNdcc026/vrrU48ePTruiAAAADrSGjt9WW2yuW6UMVddrFfNAe7aa69NJ5xwQhozZkxafPHFU9++fdu0n/fffz/NmNFCn1QAAIC2iHneYqqAQrXJUmJ5hcxV16nTCJx88snp4YcfTptttlk6/vjj27SPZ599Nq211lrtPRQAAIDS/v8UAbPuPPX/5oErtLzV2jxwxxxzTDrttNPavP3qq6+eFl100Y44FAAAgNK2PCb9z5+fTRv0eS317zkz7bzvoV92m8xBy1uHVqHcfPPN05QpU9q1jyWWWKIjDgUAAKBJs+rmTQ/MXCnd9vGaKW2wf67CW4cFuN69e6eRI0e2ax/tacEDAAAox4UXXpjyrMPmgTvqqKPatf3w4cM76lAAAACqUkVM5A0AAEDLBDgAAICcEOAAAAByoksD3COPPNKVNwcAAFBVujTAHX744V15cwAAAFWlSwPcF1980ZU3BwAAUFW6NMD16NGjK28OAACgqihiAgAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkRK/uPgAAAKD6XHjhhd19CFVJCxwAAEBOCHAAAAA5oQslAACQOxfWaBfNLm2Bq6ur68qbAwAAqCpdGuBGjhzZlTcHAABQVbo0wB166KFdeXMAAABVRRETAACAnBDgAAAAckKAAwAAyIncTCPwxRdfpNtuuy09++yzqW/fvmmzzTZL66yzTncfFgAAQO0EuOeffz499NBDc13Xo0ePtOOOO6ZFF100uzxp0qS02267pf/85z9zrfetb30rXXbZZalfv35deswAAAA1GeBef/31dMghh6TPP/88u7zQQgulNdZYI62//vpZgIvlX//619PUqVOzeeSWW2659LWvfS29+eab6eabb0677LJLuuuuu7r7bgAAADlxYY4nAe/2MXDf/OY308knn5z69OmTLrjggvT++++nBx54IK211lrZ8qOPPjp98MEH2d977713evHFF9PVV1+d7rvvvnTDDTek8ePHp7/+9a/dfC8AAAA6X4+6aNbqRnHza665ZjrppJPSHnvsMdeyV155Ja200krZ3yussEJ6+umns6BXbM8998x+X3XVVV141BQMHjw4+z1x4sTuPhQAAKj6c+hub4H717/+lebMmdMovIVbbrklC3hh5MiRjcJb2G+//dKECRO65FgBAAC6U7cHuMcff7w+gTb0yCOPzNXVspRooZsyZUqnHR8AAECl6PYAN3v27NSzZ8+Sy5566qns9zzzzNPklAHRKtfU9gAAANWk2wPcYostllWUbGjmzJnZmLeYUmC11VYr2X0yPPPMM2mVVVbpgiMFAACo8QC37rrrZvPARWArFpUlP/300+zvrbbaqsntL7744myOOAAAgGrX7QEu5nuLud8uuuii+uumTZuWTjzxxPrL++yzT8ltzzrrrGyS76OOOqpLjhUAAKCmJ/Lu1atX+vGPf5x+8pOfpH//+99p4MCB6aabbkr//e9/s+6T22+/fdpkk03m2uaFF17IAl7MBxeTgC+44ILddvwAAAA1E+DCMccck7WkXXbZZVloK0wdsMEGG6RLLrmkfr1zzjknW+exxx6rXye6UMb4uLPPPrvbjh8AAKBmAlyIoHbggQemu+66K+tCueGGG2ZdJ6OFrmDWrFlp7bXXzn6KFcbKAQAAVLMedYWmLOjiWeQBAKAWDW7HOXS3FzEBAACgPAIcAABATghwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE4IcAAAADmR+wD3wQcfpIMOOqi7DwMAAKDT5T7AvfXWW+mSSy7p7sMAAADodLkPcJMmTeruQwAAAOgSvVIFeffdd9Odd96Z3nzzzTRjxowW1589e3a6/PLLu+TYAAAAultFBLgIYj/5yU/ShRdemObMmdOqbevq6lKPHj067dgAAAAqRUUEuJ/97Gfp/PPPz8IYAAAAFRrg3n///fTb3/42zTPPPGmzzTZLQ4cOTUsssURaaKGFymq5i22feuqpLjlWAACAmg5wMeatZ8+e6V//+lfaeOONW739gAED0k477ZSq0dNPP52uvPLKNHXq1OwxCltttVUaPnx4/eWOEmH4Bz/4Qdpyyy3TAQcc0KH7BgAAqiTAvfHGG2nrrbduU3gLq666alV2vbzxxhvTuHHj0gknnJCGDBlS31p50kknpfvvvz+NHTs2zTfffB12e5deeml65ZVXOmx/AABAFU4j8Pnnn6dFF120zdsvvfTS6cQTT0zV5L777ksXXHBB2nfffevDW1hsscXScccdl5588sl06qmndlhwff7559M111zTIfsCAACqOMCtscYa6T//+U+bt+/Xr19VBbiYPuGss87Kwtl2223XaPlSSy2V1l9//XTvvfemu+66q92399lnn6UzzzwzffHFF+3eFwAAUOUBbtiwYemll15Kzz77bJu2nz59ejr55JNTtbj++uvTRx99lAYNGpQWXnjhkuuss8462e+YA6+10y6U6joZ498AAIDK1+0Brnfv3lmL03777ZeFsdZ66623snFh1eKWW27Jfi+//PJNrrPiiivWjx98/PHH23xbL7zwQrrpppvSUUcd1eZ9AAAANRTgwj777JP22GOPtMkmm6SHH364Vdu++OKLqVq8/PLLWaGSwti+5ipvFkyYMKHNXSfPOOOMrOLkMsss06Z9AAAANVaFsmDUqFFpo402ysZ9rbXWWlllymWXXTb16tX0IUbXv/POOy9Vi+L57JrqPtlw2aRJk9p0W9H9sm/fvmmXXXZJ77zzTmqPCNHRFbat7rjjjnbdPgAAdLX2nP/G+fMqq6yS7wAXJfN/8YtfpA8//DArkx8/5YhiHz169EjVoND6Fuaff/4m11tggQVKbtOaF0xMU1CYQB0AAMiHighwv/nNb9LRRx9df7ka53Urx7Rp0+r/bq7lsXhZBN7WTtsQVSdjzGG0cHaE+PZAKxoAALXkjnac/w4ePDi/Ae6TTz7JipBEaItAMXTo0KxU/kILLdTittGF8oorrkivvfZaqgZR0KWgubL+xcv69OnT6q6Tsc1uu+3WxqMEAAC6S7cHuLvvvjtreYogtvfee7d6+/XWWy/ttddeqRosssgicxUZaUpx2f/mxso1FPPt3XDDDencc8/VdRIAAHKo28/iX3nllazVrS3hLUTBk2pR3KWxuSkVipctt9xyZXedjKqTUfEz5pgDAADyp9tb4GLS6nJDSCnR3TJK4VeD9ddfP/Xs2TObnLu54iTFy8rtPxutbzNmzEgPPfRQo6kailv0br/99vTEE09kfy+66KLpuOOOa8M9AQAAqjLArbzyyukf//hHm7ePkPHHP/4xVYMo67/uuuumRx99NJukuymFMX/RDXLjjTcua99f/epXs/FvTU2Gvv/++2d/b7PNNlUTiAEAoNp0exfKmPftySefTFOmTGlzEZRLL700VYvo4lgo9d9UIZPnnnuufu6JJZdcskuPDwAAqOEAt+CCC6YTTzwxHXjggdk4rdZ68803s22rRbTARatadHcsnti7ILpXRhfIaK2LqQCKRQg+5JBD0ogRI7KiMAAAQHXp9gAXjjjiiLTaaqulbbfdttmug00VQak2o0aNSiussEK67LLLssBW7NZbb01Tp05NJ5xwQlp66aXnWnbfffelyZMnp5kzZ6arr7667Nv79NNPS46HAwAAKku3j4ErOOecc7KxbJtssknaaqut0tZbb50GDhzY7ITWETZ++ctfpmoTrWunnXZaOv3009MxxxyTdtxxx7TAAgukxx57LD344IPp5JNPThtssEGj7TbffPOsCMnbb7+d9thjj2ZvIwJeFDQJ77zzTv31N910U3rmmWdSjx49snnpqvHxBQCAvOpRFzNod6Mzzzwz/c///E/95TicCA/lKqzfsKWqWrzwwgtp0qRJWViN8v8bbrhhmm+++VKlKFTBnDhxYncfCgAA5EJ7zqG7vQVu8cUXz0JYsW7OlBVl1VVXzX4AAAAqIsCFaEVbe+21s4m555133rK2jVapv//97+nDDz/s5KMEAADofhUT4HbYYYf0t7/9rdXbx7i5kSNHdsKRAQAAVJZ5KiXAbbHFFm3afsiQIR18RAAAAJWp2wPcUkstlYYOHdrmcV5LLLFE2nLLLTv8uAAAACpNt3ehXGihhdLdd9/drgDYnu0BAADyottb4Nrrk08+SZdeeml3HwYAAEBtBLiYmHratGlt2vall15KBx54YIcfEwAAQKWpiAB30kknpeeee65N2z7yyCMdfjwAAACVqCICXEzcfc8997R6u8mTJ6f//d//7ZRjAgAAqDQVEeAK87l98cUXZa9/8803p4022ii99tprnXpcAAAAlaJiAtwLL7yQzjvvvBbXmzFjRjrkkEPSTjvtlN5///0uOTYAAIBKUDEBLowaNSo99thjTS4fP358WmedddIf/vCHrNtl/AAAANSKiglwEcZmzZqVRowYkd544425ls2ePTv95Cc/Sd/4xjeycW+x7sCBA9NFF12UhT4AAIBa0O0TeRePaVtvvfXSvvvum7bddtt0//33p/79+6dHH300HXDAAenZZ5+tb3Hbb7/9su6W/fr1S++9916aMmVKdx8+AABAp+tRV2H9EGfOnJm22mqr1Lt376zF7Ze//GX6/PPPs/C2+OKLp9/97ndp11137e7D5P8bPHhw9nvixIndfSgAAFD159AV04WyYP7550+33nprevvtt7MJvj/77LMsvA0fPjxNmjRJeAMAAGpWxQW4sOiii6Z//OMfaemll069evVK48aNS3/961/Tkksu2WjdGC+30kordctxAgAApFoPcGH55ZdPt912W+rbt2+zY9zefffd9Morr3TpsQEAANR0EZNSYsqAG2+8Me2www5pueWWS/vvv3+jde65555uOTYAAICqCXAx0fZTTz3VYfsbOXJkuvjiixtNL9DcvHEAAADVpNMCXMzpFnO29ejRI7vcnmKXsY/YPqYWaCiuL9wGAABANevVmYVICgFrwQUXzC53dNCKFjhzwAEAALWi0wLcYostlgW2X/ziF2nUqFFpnnk6p17KSSedlE03AAAAUO3m6ewWuB/84AedFt7Cjjvu2Gn7BgAAqCSdlqwWWWSRrPtk//79U2dafPHF2zW+DgAAINV6gDv66KPTF1980ekFRlZYYYXsdgAAAKpdxU7kDQAAwNwEOAAAgFoOcA899FCqJJV2PAAAABUT4LbZZptUSSrteAAAAComwH300UfptddeS5XglVdeSR9//HF3HwYAAEDljoF75plnUiWYNGlSdx8CAABAZQe4xx9/PFWCxx57rLsPAQAAoEP0Sp3k5JNPTv/+97+zCb27y9SpU9Ptt9/ebbcPAACQiwA3a9asdNNNN6XuVldX1+mTiQMAAOQ6wEVwAgAAoMID3N13390ZuwUAAKhpnRLghg4d2hm7BQAAqGmdVoUSAACAjiXAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAUMsBbvXVV++M3QIAANS0TglwL730UmfsFgAAoKZ1SoD77LPP0quvvtoZuwYAAKhZnTYG7vjjj++sXQMAANSkTgtwl19+efrmN7+Z7r///s66CQAAgJrSqVUo77777rTlllumr3zlK+lnP/tZeuCBBzrz5gAAAKpapwW4urq6NHjw4DRs2LDUu3fv9Ktf/SptscUWaZlllkk/+MEP0h133JE+//zzzrp5AACAqtNpAe6Pf/xjeuSRR9Lf//739PTTT6f3338/61a5+eabZ7+32267tOSSS6YDDjgg3XDDDWnmzJmddSgAAABVoUddNJV1sHnnnTcLZL169Sq5/NNPP03/+Mc/suB28803Z+Fu/vnnT9tss03adddd0/Dhw9PCCy/c0YdFJ4hW1jBx4sTuPhQAAKj6c+jSCasDAlxT4S1El8oRI0ZkP3PmzEn33HNPuv7669Nf//rX7Ce2j7FzEeZ23nnnNGDAgM44TAAAgFzplC6UgwYNKnvdnj17pm984xvpvPPOS6+99lp68MEH09FHH539/cMf/jAtt9xyaZNNNklnnHFG+s9//tMZhwsAAFC7XSg7Soydi5a56Gr5+OOPpx49eqQ11lgja5nbZZdd0nrrrdfdh1jzdKHMp2nTpmUt4J988kk67LDD0u6775769+/f3YcFAFATBrfjHLqiA1yxm266KTvRfOutt7IgF5ZffvksyMXPZpttVn89XUeAy5+xY8emU045Jc2YMaP+ur59+6Zjjz02HXfccd16bAAAtWBwO86hO3UeuPaaPHly+uUvf5nWXnvtLKS9/fbb2fWROePnlVdeSWeffXYaOnRoNk0B0HJ4Gz169FzhLcTluD6WAwBQuSquBe6dd95JV111VfrLX/6SHnrooey6wiEWt7DFdXF50003Tfvss0/ac88906KLLtptx12r8t4CF10Jr7322jRlypSsWE41dyWM+zpw4MBG4a1YtMS9+eabqV+/fl16bAAAtWRwpVWhjFazn//852Wv/9FHH6Xrrrsu/fnPf07/+te/ssqUpYJb4XKMfdt7773TXnvtlRU5gY7qSnjUUUdVbVfCCKrNhbcQy2O9gw46qMuOCwCAbg5wY8aMaTHAxVxwMQdchLbbbrstu9wwtMVPobvkKquskoW2+FlttdU647Cpwa6EDRW6EoZqC3HRytiR6wEAUCUBrqlemV988UW68847s9B24403Zi1vzYW26O4VXSOji+QGG2zQGYdKDVZXjHWi5a05sfyII46oqq6E5c6naN5FAIDK1SlFTD777LO5umo98MAD2cnwMsssk7bffvt02WWXpenTp5fsIhnj2A499NCsK+Wrr76azjzzTOGNslvVIvSPHz8+TZgwIY0cOTK73LAwR2u6EpYSATAK5wwZMiSNGzcuu5wHEWZjjFtzYnmsBwBADQW4aGmLVpBoAVlppZXSFltskc4///ysQEmp0BYnjfvtt1+65ZZbsu5bF1xwQdpyyy1NC0CnVFdsT1fCckNiJYqWyBjf15xYXk2tjgAA1aZTulCGaEGLn6a6R/bu3TtrjYsxbcOHD099+vTprEOhyrW2S2RbuxJWw7i5wvHV+jxwtVR9FACoLp0yjcA888zTqOR/6NmzZ/rGN76RhbZdd93VN/1VoBKmEYhujNESVs56UV2xLeX0q60Ef3Rhbhhg8nDcHcFE5gBAd6u4aQRKzdUWoW2PPfZISy65ZGfeJDWotV0iC10JS7WmNdWVsNpK8Md9y8NxdrS8tKJqIQQAujzAxTfaP/7xj9OBBx6Yll9++c66GWhTl8jWdiVUgj//8lJ9tNbmJwQAKiTAXXXVVdkYN+hs0ToRJ7gtdW9sWF0xTobjZL2croRK8OdfHlpR89JCCABUWRXKXr16pe22264zdg0dWl2x0JUwTorjd1MtL0rw51+lt6KW20IY4xcBgNrVaQHOFAB0pQhgY8aMaRSy4nJc395WCyX486/SW1HbOz8hAFAbOqULZScUtoQWtaZLZFv3H1QwrK2utl2l0lsIAYAqDnC33357Z+wWur26YmeHRDrPeeedl2bPnl2xraiV3kIIAFTxPHDUjkqYBw7aWhykYL755ksnnHBCyVbUGJs2YsSI9Mknn6TDDjus00r6V9tcgwBA55xDd8oYuM4wefLk9Le//S3df//96dVXX+3uwwFyopziIDFuN1pWSwW/CFXjx49PEyZMyCaMj8txfUczzhIAqKoAF93VrrzyynTSSSelr33ta2m55ZZL+++/v5YfoN3FQaJ1rWFxkEKrXcNtCyX9OyPEdXYxHgAg/3LbhfKaa65Je++9d+rZs2e6+eab07Bhw7r7kGqSLpRUugg+xx9/fFnrFQJSd3dnjKkCjLMEgOo1uB3n0J02kXfB559/nu6444704osvZn+vssoqadttt83GnLTHHnvskY4++ujsBOrEE08U4IAOKw7S3ZN+d3YxHgAgvzo1wN1yyy3p4IMPTu++++5c1y+22GLpt7/9bRbC2uKFF15IF110URbewlNPPdUhxwtUn7ZMH6CkPwBQcwHu3nvvTTvvvHOaM2dOo2Xvvfde1v1x5syZ6YADDmhyH88880zWrPjss8+ml156KfuJ8PbRRx/Ntd68887bKfcByL9CcZDmqlA2LA6ipD8AUHNj4NZZZ500adKk1KNHj+xy4WaKLy+wwALpySefTCuttFL9dh988EE666yz0p/+9KdG3243PNTCvrbeeuv0j3/8ozPuBi0wBo68iKIj5U7C3t1j4ACA6ja40sbA3XPPPfXhLUJXdJmMkDbPPPOkN954I73++uvZetECF+PXLrvssuzyQw89lLXavfPOOyXDWiGwFcQ6MZbu5JNPTtXo6aefzipvTp06NSvWErbaaqs0fPjw+stt8fbbb6ebbrope5wjMEdQXmihhdJGG22U7XvJJZfswHsBlaE1k7C3pdUOACC3LXA//elPs1a01VZbLRvr9o1vfGOu5a+88ko6++yz07nnnpsFkQgUUXVtvfXWy775Di0dVu/evdOOO+6YBcC11147VZsbb7wxjRs3LptceMiQIdl177//fjaNQtz3aE1oSyGYBx98MJtLL8YmLrLIItl1s2fPzqp6XnLJJdm+jzzyyLKLwmiBo5q1ptUOAKBc7TmH7pQAF61EEdLigAohoZQbbrghK2Tyl7/8Jfs7WptCbBNdMJdaaqmsNSi6WkZYievjW/OoZBmhrb2VLCvVfffdl37xi1+kAw88MO21115zLYuwG+MGN9tss6w0esNWyea89dZbWWiOfUdraEMXXHBBuv7667Nlp556alp//fVb3KcAR7VT0h8AqPoulDFlQHxr3Vx4C7vsskvac889sy6XcYL0zW9+M/34xz/OWn969er0GQ4qUnzTH62Xkau32267Rssj1EawiiIxd911Vzb+r1x/+9vfsm6SpcJb2G233bIA98UXX2TdWssJcFDtlPQHACpJ6TP5dvrwww/T9ttvX9a6+++/f7r44ovTt7/97Wy+uNiuVsNbiAAVVTYHDRqUFl544ZLrROtkuPzyy0tW+WxKtIo+9thj6eOPPy65PFo7YyxcYfxda/YNAADkNMDFhN2LL7542c2Hn332WTa2iy/nzgvLL798k+usuOKK2e8oCPP444+Xve8YuxPj3yIsn3766SUDWqE4SrTCFcYjAgAAVRzgmuqiV0pUqIzQsPLKK7f59kp1Ncyjl19+OStUEpZeeumy5p6aMGFC2fsfOnRo9jsCc7R2NpwAPa4vhLYFF1wwq8QHAABUjm7vqxhhr70TcY8fPz5Vg+JA1VT3yYbLYrqGcm266abp+9//frr55puzrpLF8+8VwmChps2IESPKnqogxjyWW7WylAiTAACQJ8Pacf4b589RmDGXAY7/U2h9C/PPP3+T60VVzlLblGPXXXfNfhqKLpNXX3119ndMWxBjEwEAgMoiwFWQ4jFnzRVyKV4WBWM6wqWXXpq15m2xxRbZHFetKSQT3x5oRQMAoJbc0Y7z38I0AhUT4GbNmpUV4yhngu3oshc/r732WouTd5cSVRU//fTTVA1iEu3iFrGmFC/r06dPu24zHvM//OEP2UTe3/ve97J5+aBWvjCJrsKffPJJOuyww7L53Yz7BABqtgUuToxaY4UVVki1rnjevCgo0pTZs2eXNVauJRF8zzjjjPTcc89lc8+tscYabd4X5MnYsWOzuSpj3sUwcuTIdNRRR2Wtz8cdd1x3Hx4AQPd0oSy3Ra1Hjx5tan0r3r4aLLvssvV/T58+vcn1ipctt9xybbqtGDt34oknpiWWWCL97ne/y6pOQq2Et9GjRze6PsJc4XohDgCoqWkEWqs94a2arL/++vWVH5srTlK8rC39Z2P+uJ/+9KdZ5ZwIcaXC25133tnq/UIeuk1Gy1tzYnlzX6AAAFRlC9zOO++c1llnndTZYiLrm266KVWDmGh73XXXTY8++mgWspoS4wULUzBsvPHGrT6B/fnPf56OPPLIJsNfdK184okn0tZbb93KewCV7dprr63vNtmUWB7rHXTQQV12XAAA3RrgYl63OAHqiq6Nc+bMmausft7ts88+WYCLuSGiWEmpSdFjzFqIFrQll1yyVfu/4IIL0pprrtlsy93EiROzxxWqzZQpUzp0PQCAqghw0Q2wq8alxW2VO+F0HkQLXLSq/fvf/84m9o7LxSJYPfzww1lr3X777dfopPOEE05Ib7/9dtpzzz3TvvvuO9fy6BZ29913ZwHuoYceahQOoytrbPvnP/85684J1WbAgAEduh4AQFUEuK4e01ZtY+hGjRqVfvSjH6XLLrssrbXWWnMF1FtvvTVNnTo1K8Sw9NJLz7XdfffdlyZPnpz9HZNyNwxw0d00WvUiGMYP1JqYKiCqTTbXjTK+HIn1AABqpohJqQpvnamrb6+zxQnkaaedlk2mfcwxx6S77rorPfjgg+n888/PgtnJJ5+cNthgg0bbbb755tl0DPPPP3/J+dyidQ1qWczzFlMFNCeW9+vXr8uOCQCgNXrUVVvzVZV54YUX0qRJk7K53wYNGpQ23HDDNN9886VKURhLF+PmIK/zwBW+ODEPHABQ6efQAhztIsDlT1QiHTFiRPrkk0/SYYcdlnUXjJapWhNjQqPYUowdjTFv8ThoeQMAuoIAR7cR4PJFyxMAQL7PoTttHjig8sJbqfGiEeYK1wtxAAA1WMQEqLxuk9Hy1pxYHt0KAQCoXAIc1IAY69Vc6fwQy2M9AAAqlwAHOW9ZGzp0aBoyZEgaN25cdrmUKNRRjnLXAwCgewhwkOMxbQMHDkzjx49PEyZMSCNHjswux/UNRZXFcpS7HgAA3UOAgxwXJGnYLbJQkKRhiIsS+VFtsjmxPNYDAKByCXBQAwVJYp63mCqgObHcPGgAAJVNgIMaKUgSUwSMGTOmUUtcXI7rTSEAAFD5zAMHOdOegiQR0o444ogs3MXyGPMW3Sa1vAEA5IMABznT3oIkEdYOOuigDj4qAAC6gi6UkDMKkgAA1C4BDnJGQRIAgNqlCyXkUKHgSFSbLC5oEi1vEd4UJAEAqE496urq6rr7IMivwYMHZ78nTpzY3YdSk2KqAAVJAABq5xxaCxzkmIIkAAC1xRg4AACAnBDgAAAAckKAAwAAyAkBDkjTpk1LQ4cOTUOGDEnjxo3LLgMAUHkEOKhxY8eOTQMHDkzjx49PEyZMSCNHjswux/UAAFQWVSihhkVIGz16dKPrY265wvXmlAMAqBxa4KBGRTfJmAi8ObE85poDAKAyCHBQo2IC8Ghpa04sj/UAAKgMAhzUqClTpnToegAAdD4BDmrUgAEDOnQ9AAA6nwAHNWr33XdPffv2bXadWB7rAQBQGQQ4qFH9+/dPxx57bLPrxPJ+/fp12TEBANA80whADStMERDVJosLmkTLW4Q3UwgAAFSWHnV1dXXdfRDk1+DBg7PfEydO7O5DoR1iqoCoNhkFS2LMW3Sb1PIGAFB559Ba4IAsrB100EHdfRgAALTAGDgAAICcEOAAAAByQoADAADICQEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOGrCtGnT0tChQ9OQIUPSuHHjsssAAJA3AhxVb+zYsWngwIFp/PjxacKECWnkyJHZ5bgeAADypFd3HwB0pghpo0ePbnT9jBkz6q8/7rjjuuHIAACg9bTAUbWim+Qpp5zS7DqxfPr06V12TAAA0B4CHFXr2muvzVramhPLYz0AAMgDAY6qNWXKlA5dDwAAupsAR9UaMGBAh64HAADdTYCjau2+++6pb9++za4Ty2M9AADIAwGOqtW/f/907LHHNrtOLO/Xr1+XHRMAALSHaQSoaoUpAqLaZHFBk2h5i/BmCgFaqmQaRW5inGR0tY3W2vhiAACgu/Soq6ur67ZbJ/cGDx6c/Z44cWKqZDFVQMMTcS1vHR92RowYkT755JN02GGH5T7sxByCgj8AUGnn0AIcNRHg6FzVFnaamgC+YMyYMbm8XwBA/s+hjYEDOiTsNJxzLy7H9bE8T0wADwBUMgEOaLNqDDsmgAcAKpkAB7RZNYYdE8ADAJVMgAParBrDjgngAYBKJsABbVaNYccE8ABAJRPggDarxrBjAngAoJIJcECbVWvYiSkCYqqAhuE0LptCAADoTuaBo13MA0c1zgNXYAJ4AKAzmMibbiPANS6r3/CEP1qpaoGwAwBQHgGOblONAS5C2IgRI9Inn3ySDjvssLJDWLW2QgEAUDnn0MbAQYMQNnDgwDR+/Pg0YcKENHLkyOxyXN/SdqNHj240J1pcjutb2h4AAMohwEE7Q1i02EXLW3NieXQxBACA9hDgoJ0hLMZ9NQx9DcXyWA8AANpDgIN2hrAo2lGOctcDAICmCHDQzhAWFRfLUe56AADQFAEO2hnCokplwwmfG4rlsR4AALSHAAftDGExxUBMFdCcWG5ONAAA2kuAgw4IYTHP25gxYxqFwLgc15sHDgCAjmAib9ql2ibybu9k3FGlMgqdxFi56G4ZLXZa3gAA6KhzaAGOdqm2ABeEMAAAKvUculcnHA/kWoS1gw46qLsPAwAAGjEGDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJRUygRk2bNq1Rtc2YDw8AgMolwEENKjXf3VFHHVX2fHcAAHQPAQ5qTIS30aNHN7o+wlzheiEOAKAyGQMHNdZtMlremhPLYzJzAAAqjwAHNSTGvBV3mywllsd6AABUHgEOakgULOnI9QAA6FoCHNSQqDbZkesBANC1BDioITFVQN++fZtdJ5bHegAAVB4BDmpIzPMWUwU0J5b369evy44JAIDymUYAakxhioCG88BFy5t54AAAKluPurq6uu4+CPJr8ODB2e+JEyd296HQSjFVQFSbjIIlMeYtuk1qeQMAqOxzaC1wUKMirB100EHdfRgAALSCMXAAAAA5IcABAADkhC6UABVk2rRpjcYmRvVQAIAgwFWwp59+Ol155ZVp6tSpqWfPntl1W221VRo+fHj95baaPHly+vOf/5xef/31NN9886U5c+akjTfeODtZ7N27dwfdA6A1xo4d26g66FFHHaU6KABQT4CrUDfeeGMaN25cOuGEE9KQIUOy695///100kknpfvvvz870Yvg1Rb33ntvOv3009MRRxyRfv7zn2fXffzxx+mMM87IrovfvvGHrhX/p0ePHt3o+ghzheuFOADAGLgKdN9996ULLrgg7bvvvvXhLSy22GLZCdyTTz6ZTj311NSWGSCeeeaZbNutt946bbPNNvXXL7jggmnUqFHp3XffTSeeeGKaPXt2h90foOVuk9Hy1pxYHlM/AAC1TYCrMPFt+1lnnZWFs+22267R8qWWWiqtv/76WSvaXXfd1ap9RzfJaHmLcLb99ts3Wj7//POnoUOHZl03r7nmmnbdD6B8MeatuNtkKbE81gMAapsAV2Guv/769NFHH6VBgwalhRdeuOQ666yzTvb78ssvz0JZuSLwvfHGG2mBBRZIK6+8crP7vu6661o8oQQ6RhQs6cj1AIDqJcBVmFtuuSX7vfzyyze5zoorrpj9jjD2+OOPt3rfyy23XJNFUAr7jhB5zz33tOrYgbaJapMduR4AUL0EuAry8ssvZ4VKwtJLL13WSdyECRPK2ncUKXnuueda3HfxsnL3DbRPVH/t27dvs+vE8lgPAKhtqlBWkKeeeqr+76a6TzZcNmnSpLL2HePavvjiixb3HePg+vTpk2bNmjXX8TTnxRdfTMOGDUttdccdd7R5W6gGUfU1pgooVYWyIJb369evS48LAGhae85/4/x5lVVWadO2WuAqSKH1rRCkmhJj2Ept0xH7Ll4elfFaM8YOaLuoMDtmzJhGLXFxOa43hQAAELTAVZAITAW9ejX91BQv+/DDDzt038XLoxJmbLfooos2u358e6AVDdovQlrMxRjVJqNgSXSXjm6TWt4AoPLc0Y7z38GDB7d5WwGugvTu3bv+70J3x1KKl0V3x47cd8PlxdsBnS/C2kEHHdTdhwEAVChdKCvIIossUv/3Z5991uR6xZNsNzeerS37Lt7/fPPN12JhBQAAoOsIcBVk2WWXrf97+vTpTa5XvCymBChH8XrN7Tta3wrzvxUfDwAA0P0EuAqy/vrr18/P1lxxkuJl5fafjYm7C611ze37gw8+qO9CueGGG5Z97AAAQOcT4CpIdFdcd9116yfpbsprr72W/Z5nnnnSxhtvXNa+e/TokTbZZJMW9/3666/X/73pppuWfewAAEDnE+AqzD777FM/N0RTxUYKE3LH3BNLLrlk2fvec889sxa+t956a66qlKX2vd5666U111yzDfcAAADoLAJchYkWuGhVi3FopSbSjnnZHn744ay1br/99ptrWZQdP+SQQ9KIESPSFVdc0WjbgQMHpuHDh2fTAzz00EMlb//BBx/MphE4+OCDO/BeAQAAHUGAq0CjRo1KK6ywQrrssssaTaR96623pqlTp6YTTjghLb300nMtu++++9LkyZPTzJkz09VXX11y34ceemjWunbllVdm6xV75JFH0jPPPJOOPvro9NWvfrUT7hkAANAePeqiOYaKE8VETj/99Kyk/4477pgWWGCB9Nhjj2UtZEceeWQaMmRIo22iBS6C3dtvv52+/e1vN2qhK/jkk0/SOeeck4W9XXbZJZti4Nlnn0233357OvDAA7OumeUqFFGZOHFiO+4tAADUjsHtOIcW4CrcCy+8kCZNmpQFuUGDBmWVIWN+to7w6quvpscffzzrrjlgwIAsFLZ23jcBDgAAUpedQ/dq9RZ0qVVXXTX76QwRCOMHAADIB2PgAAAAckKAAwAAyAkBDqgIMTfh0KFDs7GY48aNa3KuQgCAWibAAd1u7Nix2TyF48ePTxMmTEgjR47MLsf1AAD8H0VMgG4VIW306NGNro/qqIXrjzvuuFQLotXx2muvzaYEicqwu+++e+rfv393HxYAUEFMI0C7mEaA9gaWaGmLsNaUmNrizTffTP369UvVHmRPOeWUuR6LuO/HHntszQRYAKgVg9txDq0LJdBtorWpufAWYnmsVwutkA0fi0IrpK6kAECBAAd0m+gq2JHr5bUVMlremhPLp0+f3mXHBABULmPggG4T47w6cr08jnFrTSvkQQcd1GXHCgBUJgEO6DYRYI466qgWx8DFetU4xi3u+8Ybb5xqvRUSACifLpRAt4kKi1GkozmxPO8FTJob43bXXXfVVCskANA+WuCAblWosFitFRjLGePWkmpphQQA2k+AI9fMm1UdIqQdccQRjZ7LvLe8hXLGuLWkGlohAYCOIcBRdWOKqqHVphZFQKnGIh3ljl3beuut04MPPliVrZAAQMcR4Mj1mKKGCvNmBSe9VIJyx67tvffe6brrrqvKVkgAoOP0qKurq+vA/VFj2jOLfHu6TQ4cOLDFyoVvvvmmk1+6ndcrANCR59CqUJI7rZk3C7pbrVTaBAC6hi6UVO2YIvNmUSmqvdImANB1BDiqdkyRebOoJNVcaRMA6DrGwNEuxsABAEDrGANHTTGmCACAWqULJblkTBEAALVIF0py14Wy2PTp040pAgCgZs6htcCRaxHWDjrooO4+DAAA6BLGwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcUNOmTZuWhg4dmoYMGZLGjRuXXQYAqFQCHFCzxo4dmwYOHJjGjx+fJkyYkEaOHJldjusBACqRibyBmhQhbfTo0Y2unzFjRv31xx13XDccGQBA07TAATUnukmecsopza4Ty6dPn95lxwQAUA4BDqg51157bdbS1pxYHusBAFQSAQ6oOVOmTOnQ9QAAuooAB9ScAQMGdOh6AABdRYADas7uu++e+vbt2+w6sTzWAwCoJAIcUHP69++fjj322GbXieX9+vXrsmMCACiHaQSA3FWQjOIiMT4tujhGK1kEstYqTBEQ1SaLC5pEy1uEN1MIAACVqEddXV1ddx8E+TV48ODs98SJE7v7UKiRuds6OnDFVAENA6GWNwCgUs+htcABNT3xdoS1gw46qEOOEQCgsxkDB1Q8E28DAHxJgAMqnom3AQC+JMABFc/E2wAAXxLggIpn4m0AgC8JcEDFM/E2AMCXBDig4pl4GwDgS6YRAHLBxNsAACbypp1M5E1XM/E2AJB3JvIGaoaJtwGAWmYMHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE706u4DAOgK06ZNS9dee22aMmVKGjBgQNp9991T//79u/uwAABaRQsckNtANnTo0DRkyJA0bty47HJTxo4dmwYOHJhGjhyZjj/++Ox3XI7rAQDyRIADcqcQyMaPH58mTJjQbCCL60aPHp1mzJgx1/VxOa4X4gCAPBHggFxpTSCLVrlTTjml2f3F8unTp3fa8QIAdCQBDsiN1gayGPPWMOg1FMtjPQCAPBDggNxobSCLgiXlKHc9AIDuJsABudHaQBbVJstR7noAAN1NgANyo7WBLKYK6Nu3b7PrxvJYDwAgDwQ4IDdaG8hinrdjjz222fVjeb9+/Tr0OAEAOosAB+RGWwLZcccdl8aMGdMo+MXluD6WAwDkRY+6urq67j4I8mvw4MHZ74kTJ3b3oVBDYqqAqDZZXNAkAlmEt6YCWVSmjOImMT4uulhGK52WNwAgb+fQAhztIsDRXQQyAKAWz6F7dcLxAHS6CGsHHXRQdx8GAECXMgYOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOAAAAByQoADAADICQEOAAAgJ3p19wFQ2rRp09KVV16ZnnjiiTTffPOl2bNnp1VXXTXtu+++aYkllmjXvufMmZNuvfXW9PTTT6cZM2ak119/PX3++edpjTXWSMOGDUsbbrhhh90PAACg4whwFSgC1THHHJM22WSTdPbZZ2cBLkLXX/7yl3TooYemMWPGZGGrLaZPn57OOuustPPOO6fhw4fXX//kk0+mU089Nf3zn/9MW2yxRTr22GPTvPPO24H3CgAAaC9dKCtMBKzjjjsuLbjggunwww/Pwlvo2bNn2m+//dIqq6ySTjzxxDRlypQ27f/MM89MBx98cFpvvfXmun6dddZJJ598curRo0e699570znnnNMh9wcAAOg4AlyFueiii9Kbb76ZttlmmzTPPI2fnm233TZ9+OGH6de//nWr9/3KK6+k999/Py233HIll3/lK19J6667bvb3HXfckd5444023AMAAKCzCHAVJILbnXfeWd8iVkrh+sceeyzr9tjaABe38Z///KfJdVZeeeXs9xdffJGeeuqpVu0fAADoXAJcBfn73/+ejXWLboyDBg0quc7iiy+eFlpooezvW265pVX779u3b/r444/T97///Wws3csvv9xoneiqWRAtfQAAQOUQ4CrIhAkTst/9+/dP888/f5PrDRgwIPv96KOPprq6urL3v+aaa6bFFlss+/ull15K11xzTaN1ootlwcCBA1t1/AAAQOdShbJCzJw5s75r48ILL9zsuoXl0UL26quvpuWXX76s2+jTp09WwfKCCy5I77zzTtp8883nWh6tfxMnTqwPiRtvvHFZ+33xxRez6QfaKsbbAQBAngxrx/lvnD9HccK2EOAqxAcffFDfmtZc61tYYIEF5moxKzfAFQqV/OpXv2qyC2eEwuiiecIJJ5hGANoxj+O1116bVYuNL0N23333rGUdAKC9BLgKOuEr6NWr+aeleHnxdu0RrX8XXnhhNsbul7/8ZVpxxRXL3ja+PdCKBl8aO3ZsOuWUU9KMGTPqrzvqqKOyuRVjihAAoDrc0Y7z38GDB7d5WwGuQvTu3bv+76gA2Zzi5cXbtdUzzzyTRo8enVZfffXsJLOlLpxA0+Et/i81FGGucL0QBwC0hwBXhtNPP71TW5hi34ssskj95c8++6zZ9WfPnl3/d/F2bfHPf/4zm1Nur732SnvvvXfJueeAlkVreLS8NSeWH3HEEalfv35ddlwAQHUR4MoQJfcPOOCATr2NaPWKsWcfffRRmj59erPrFpZH2GprpcgYb3fJJZdk4TFOKtdaa6027Qf4Uox5K+42WUosj/UOOuigLjsuAKC6CHBliOIDnV2AIMLYeuutl+699940derULGDFfHClFEr9x9iztnyTH10wzzzzzCwsRkXKUvuICcW33nrrNtwTqM0CIHG8HbkeAEAp+stVkM022yz7/emnn6Z333235DrRvfKtt97K/t50003bdDvnnXdeFg5PPvnkJgPgww8/3KZ9Q3vHkEWr8siRI9Pxxx+f/Y7LcX2lK8zP2FHrAQCUIsBVkK9//etpmWWWyf5+/vnnm5wzIuZri+6WO+20U6tvIyb/vv3227NxOE218EVIfOKJJ1q9b+iIAiANuyEWCoBUeoiLlsK+ffs2u04sj/UAANpKgKsgPXv2zFocwr///e+S6xSu32+//UqeLJ511llp+PDh6eijj04ff/xxo+U33XRT1j3zgQceSI888kijn3vuuSeddNJJ2bx0UGkFQFoaH9qdoptnVHFtTixXwAQAaA9j4CrMFltskfbdd990zTXXZN/UF8/HFt0qb7nllrTtttumXXfdtdG2cXJ72223ZX9PmjQpPfbYY9n+GrbARRXLlk6WoStVSwGQwhQBDeeBiy9bzAMHAHQEAa4Cffe7383md4tuY9FNcoUVVsgKH1x//fVpm222qW+layi+2d9+++3T3Xffnb7yla+k9ddfv1HAmzlzZhfdC6jNAiAR0qKLcsNCLFreAICO0KMu+tNRkaIaZXRrfO+997JpBjbccMO05JJLpkpSmEV+4sSJ3X0o5Ni4ceOa/GKi4XqV3AIHANDZ59ACHO0iwNFRY+Ci2mRz3SijG+Kbb76pJQsAqOlzaEVMgG6nAAgAQHmMgQMqggIgAAAt04WSdtGFko4WxXYUAAEAqtngdpxDa4EDKkqENYVKAABKMwYOAAAgJ7TAAVVf4bJhl8womgIAkEcCHFC1xo4d26goylFHHaUoCgCQWwIcULXhbfTo0Y2ujzBXuF6IAwDyxhg4oCq7TUbLW3NieVS8BADIEy1wkCPGc5UnHqPibpOlxPJYT8VLACBPBDjICeO5yhcBtyPXAwCoFAIc5IDxXK0TrZMduV4pWkMBgO7Qo66urq5bbplU67PIU35QGDhwYLNdAvv27ZvefPPNbBJsOv8xK9UaGvvTGgoAdPY5tCImUEXjufhStIRFmGpOLG9reItWz4bPSaE1NJYDAHQWAQ4qnPFcbRMtYWPGjMlaxorF5bi+LS1lqlsCAN3NGDiocF0xnqtaRUg74ogjGo1Va2tXU9UtAYDuJsBBhYvAEdUmWxrPFevRWIS1jgpTWkMBgO6mCyXU8HguWkdrKADQ3QQ4qNHxXLRetHI2fA4a0hoKAHQmXSihRsdz0fbW0FJz8hVoDQUAOpMABzU6nou2KbR2mgcOAOgOJvKmXUzkTa2KqQK0hgIAXX0OrQUOoA20hgIA3UEREwAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOAAAAByQoADAADICQEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOCgggwbNiz7gYa8NmiK1wZN8dqgKV4b+SbAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAAAAA5IcABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAkBM96urq6rr7IMivRRddNM2aNSutvvrq3X0oVeHFF1/Mfq+yyirdfShUGK8NmuK1QVO8NmiK10b3e/bZZ1OfPn3SBx980OptBTjaZYUVVkjTp09PK664YncfCgAA5MLLL7+c+vXrlyZPntzqbQU4AACAnDAGDgAAICcEOAAAgJwQ4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOCoaTNmzMh+mvPuu+922fFQObw2aIrXBk3x2gC6Qq8uuRWoUBdddFH697//nbbddtu0/vrrp6WXXjp98cUX6YMPPkjPPfdc+uc//5l22GGHNHz48Gb38+GHH6ZrrrkmPfnkk2m++eZLc+bMSQMHDkzf+c530pJLLtnstjNnzkzXXntteuihh1KvXr3S7Nmz06BBg9Lee++dll9++bLuR2x7/fXXp08++ST16NEj28+3vvWt9I1vfKOs7d955510xRVXpBdffDE7/jiGeDz23HPPbJLJWtSe18awYcPKuo14rG+55ZYml8fr6K9//Wv617/+lT2vcXmxxRbLnpc11lijrNt4+umn05VXXpmmTp2aevbsmV231VZbZcdduNycadOmZds/8cQT9a+NVVddNe27775piSWWSLWove8bn332Wfr73/+exo8fn/2f7d27d/Z72WWXTdtvv30aPHhwlzwvd9xxR7rtttuy11Uc/wILLJB23333NGTIkLK2j8ln//znP6fXX3+9/n1v4403zvYR96kWdcRnyqOPPpquvvrq7HUSj2n83mabbbL39HL+z/pMqXwvvfRSds7w5ptvZo9tPM/rrbde2meffbLHq7MeV58pVSQm8oZaddppp9VtvfXWJX9GjBhR9/e//73FfUyaNKnu29/+dt3VV19d99lnn9VfH9vG9R988EGT206dOrXu4IMPrjvxxBPrPv744/rrb7vttrpvfetbdffff3+Lt3/RRRfV7b777nXPP/98/XWvvfZa3QEHHFB3yimn1H3xxRfNbv/UU0/V7bzzznVXXHFF3eeff55d9+mnn9b9+te/rtt7773r3njjjbpa1J7XRlPbNfyJx7cps2bNqjv66KPrjjzyyLr333+//vqHHnooe23cdNNNLd6HG264IVv34Ycfrr/uvffeqzviiCPqfvrTn2bPc3PidbTXXnvVnXPOOfXrxmvksssuq9tll13qnn766bpa1J7XRjymBx54YN1xxx1X9/rrr9dfP3v27Lobb7yxbocddqg788wzm/1/297nZc6cOXVjxoyp++53vzvXMTz33HN1u+22W93vf//7Fh+D8ePHZ6+tf/zjH/XXffTRR3UnnHBC3SGHHFL34Ycf1tWi9n6mXHzxxXXbbbdd3b///e/661599dW6Pffcs2706NH179FN8ZlS+eK9O84N4r28+P/kGWeckb0vN/X4tvdx9ZlSXQQ4alp82I4aNapu5MiRddtvv33djjvumH34xQnMO++80+L2L7/8cvah/Mc//rHRsuuvvz770L7yyitLbhtvXvFGuuuuu9bNnDmz0fI4iYvjefbZZ5u8/euuuy67jbvvvrvkm30s+93vftfk9vGGHydsxx57bKNl8aYaJ5pxkjdt2rS6WtOe10Y87vFh/Mwzz9S98sorJX9++9vflnzcQ3yA/+///m92Ilfqti6//PK6bbbZptmTsXvvvTdb5y9/+UujZW+99Va27KSTTmryZCGe8zhhi/sfJxcN/exnP8tO8t588826WtPW10Y8pnHy8uMf/7jkY1o40W7ufaMjnpfzzz8/u414fTZ0xx13ZMviRK0pcZIVQfPss89utOyTTz7JTjKPOuqoFk/mqlF73jf+9re/ZY/9b37zm0bLbrnllmxZnPg2xWdK5bv99tvrhg0bVvfoo482emxOPvnk7PEt9fy093H1mVJ9jIGj5n39619PF198cbr11lvTzTffnH7/+9+ngw8+uMWm/PgC5Ne//nWaZ555sq4pxe677750/vnnZ3+///77Jbe/6qqr0jPPPJN1PejTp0+j5dGV6tNPP02nn3561s2hoSlTpmTddRZccMG0xRZbNFq+1lprZV2yoivNpEmTSh5DHH90Z4jbaii6QkRXwOgeFY9PLWrrayOWH3300Wn11VfPui6V+omutbG8lDvvvDN7DW244YYlb2u77bbLumWdeeaZJcfbxHVnnXVW9hqNdRtaaqmlsm439957b7rrrrtKHkO8tqJ7T3Tditd4Q9FFLLoOx2uoFrXltRH/599777204447lnxMC4/rMsssk/2/7YznJbp5R9e4FVZYoeTrb+jQoVlXygsvvDB7j2ko3oviPSm6PZV635h//vmzfUQ3q+giVova8tqYNWtWGjduXPb3N7/5zUbLN9988+w9Ofb5xhtvlNyHz5TKFl0O47wgukjH+2+x3/3ud1mX6qbOGdr7uPpMqT4CHLRRjHOID8tNNtmk0XiPeCMsnMyUGg8Vb4ZxEhXWXnvtkvtfbbXVsg/h1157LRs30dDll1+efQhHv/Wm+p2vs8462e9LLrmk0bLof/744483ewyF7WOsTKmTOUqLx7OlsQAxxqTUSVI8p/HcFvZTSoxZiDGWH330Uf3rqFhcF8siKC688MLNPreF11Gx+JCND/zi9Zra/rHHHstCAS2L/3MhTpCbEuNSvvKVr2QnMnHC1tHPy6WXXtrsa2veeedNX/3qV9Pnn3+ejbVpKE7OIkBEyFt55ZWbPYbrrruuxYIe/N/nyccff5y9b8Tj31CMb4oT7/i/+re//a3Rcp8plS8CdjzHEfAbKpwzxHt2jIXryMfVZ0p1EuCgjeKNMqy55pqNlm255ZbZiVIM8F9llVUaLb/nnnuyN/IQ34SXEh+gyy23XPZ3fIvbcJD63Xff3ez2YcUVV8x+x5t/fDtXLL7JDfFm3NQbcmH7eDOOYgeUZ9NNN212eTwf8YFd6rmLZfFhF5orOFB4bgrPY7FCYZRyto+T8cLJQUEU2IjnPMJEfGCXsvjii6eFFlportujeRGKQhSzaE60bsXg/oZBr73PS7wHFEJkOe8bcZIf7zXFCvuM96amTvIL28cJX7zX0bIoShEWWWSRJltnY1nhBLchnymVLe5vITSXOmf44Q9/mLXARktc3759O/Rx9ZlSnVShhJTSI488klVlim+933rrraybSXxTtcsuu2TVkRqKN6KHH344+zu6lJQyYMCAZm+vIKqUNSWWxQd7nPDFh3PhhC7eHKMyWUvbFx/DhAkT6o81wsPEiRNb3D6+Ze/fv3/WEhDbH3TQQanWtPa1EaILWVPitRNdSY466qgmb6+gnOc2uuS9/PLL9R+e8XehC05rXhvFlQ/jcojnPlqRm9tHnKRH1bzoWhMfzrWkta+NaLH673//m3VBi9aQr33tayVfH/H/Par9NQxI7X1eCtuX+9qI95gIfFFZMsR7UCF8tvS+VXzMUXWx1rT2tVFoqSzn/1D8H4/qkPH+XHx7BT5TKk883oWqjaXODSK0lwo2HfG4+kypTgIcNS9OpuJk6cc//nH9CVOctJx00klZd6FDDjkk7bHHHnNtE29o8YEcFl100TR9+vSs7HN0qYx9RHeEGOfSVHeFwviBeCNrrtx24du2eBOPfW+00UZzbV+8TnPbF7bZeeeds7+jC02he1Zz2xeWx7r/+c9/sm9pm3vzrTZteW205LLLLsu6isQJfCnFz23hG/dyntvCh+1TTz1Vcp2Wti+I5zie65a2L14eJ6mvvvpq2SXKa/W1ESfv0Y0oHuPRo0enDTbYIHufiG7Y0XUxxPtIdJWL7Yt1xPPSltdGbFMIcDGurdDVq7nt4z0iuurFuK7i26wVbXltFMYlNew2W2r+uDixjee2OMD5TKlszz//fH2AidfEK6+8knWpjHAf0wjE/9Fdd921UbjriMfVZ0p10oWSmhdvEFGEpPjb7nXXXTfr0hAflNFa8uCDD861Tbz5FsS3VUcccUS2n1/96lfp1FNPzbqpxId3oZBJw25UhTfklj64ij+giwc2F/9darB6QfH+27J98T7isYhvEGtJW14bzYkTphhIfuCBBza5Tkc+t829vpp6bcV8VXHfWtq+uX3Ugra8NmJs2zHHHFMf1uJb5l/84hfZHEznnntuOu+887Ivg+J9pOGcTh3xvLT3tVHu9sXL472uVMGMataW10YhSEX32ThxLTXnXnzWFMTrpMBnSuWL5y/E//147iPMx7x6URjkxBNPzOZ3i1azaLUt1hGPq8+U6iTAUdNinElT45UK1dhCVBErVvwt6SmnnJJ9CxnFSqK5Pz60Y0LKGPt2ww031I+VK9628GYW37w1p3h58W3Gt1MFhZPBUoqXtWX7hsuLt6t2bX1tNCW+hTzttNOysN/cN+TFz1O5z23x81K8fXOvr+Jlbdm+4fLmWg6qTXteG1tvvXU21qXw7XaILkM33XRTNsFuhLpSY5w64nlpy2ujLdsXL4/3Oq+Nll8b8XlR6FIbX/I0FAVlCuODGvKZUvkKgTuC1RlnnJF+/vOf10+cHWPefvKTn2TnD1EhtLjKaEc8rj5TqpMAR02LriylKkIV3kgKVdbiG9HoylBQPLA/uqLEN2kNbbbZZtnvQvWnUt+AFbojNaV4efFJf7n7KP7muy3bN9xHS98AVpO2vjaaElXboptUfBPfnOLnqbnnpnhZ8fPSVds3XN5cKK027XltROv9mDFjspP5KLMf001EV+vCWI+XXnop+0b+7LPPbvLxbevz0pbXRlu2b24f1a49r42f/vSn2fi46EZb6LYW3VCjsEW00BS33BcXuPGZUvkK5wzRwhrTMURrfLFocY/3gRiHeOWVV3bo4+ozpToJcNS0+OarqYpfhfFtBcUftsXN/HFCXupbrcIcS1H9qbjLZdxmYf3CoPGmxJt9qb7rxf3Im9tH8bKmti++jdbso9q19bVRSvT/j9bYUkUrGip+jJt7boqXFT+fxds399po7/YN9+G10fJrI8bBRAtsnKhFK3087lHgI7pRxdjIb3/72/UnPlGF7fbbb+/Q56Utr422bF+8j2iRalhVr5q1530jXg/nnHNOOuyww7IQF91tjzvuuGyOrehWW9hv/I5x1sW36TOlshV3HYy52EopTB8RU0p05OPqM6U6CXDUtOi69MADD6S333675PLiCkjFbyzF41OaqspUvE4MVC5WKOUct1/o+lJK8TiH4mqXhe0brlPu9vF34WQgjqE5hX1E950YgF0r2vraKCW6S8U3izF5d0uKn6fmnpvi57b49VC8fbmvjeLt44O30FWrue2Ll8drKeYQqhVtfW389re/zb6J32mnnRptEyfp0Xrzm9/8pv7xL54QtyOel/a+Nsp934nXeqGqYlNVeqtVe983opUuJkqOsZHR1S6CWxS/iesL3dLieWg4lshnSmUrPh+I/+ulFB6LeJ4LLXYd8bj6TKlOAhw1KwbWjhw5Muuu9L3vfa/kG0txP+5ClbCGb2hN9Skvbv5v+I1sobxunOg0N4i7MIg3vokqnjS3uDxvcwN9i5cVbxMfJoUuHM1tH8cXj1NYf/31m/1muZq057VRqnx0oQx0cydWpZ6n4qIFDRWetxhzWTzxazxPheIJbXltxHNc2F+8Nps75sI+YvxOw6Ib1aqtr40o+x6vhWhha26KkRgbt9tuu9XfVkc+L8Xf/LfltRHvQYVv1pvbPo670BWqqdaGatQR7xvRQlGYL7ChwgTN0QWvIZ8pla34nCFapUspvr7wuHTE4+ozpTrVxv8cKCG6KBXe8OLkqtQ3poUPwnhjLZ7cNN5QC90om/pGqfjka5lllplrWfEg9+IByw0VJkqNMuPF39zGsRS+nWpu+0IXnehi03DsVeEYonWwqSpx8ZgUujwUxvTVgva8NhoqLmJT/JpoSjzXhQ/fcp7beF6Lu6gVP9flbB+3VSgTX1B4rmOqjELp8obidVFoWW5p4vJq0tbXRjyWceJSTnfClVZaqX5i2458XopfK+W878R7THEZ73gPitdnuduXOoZq1t73jeg6F6Xko3ttqRBWKEUfUxQ05DOlshU/Vk2dMxSe8/h/X/wFcHsfV58p1UmAo2YVf0Buu+22jQYVxwdx4Q0pCg4Uv6HFt1GFN5gYXF5K4Y0uToAadgWIb1BjLrBQmBi3obj92HfcVpQZbyjKVDe3ffGy+Ea/4WDx6MYVA+HjTTMmF25u+zj+5ianrjbteW00VFxRsHgsZFOim+U3v/nNuU7YGooP8ZiMN8TJXkP77LNP9jvWaWrQeOG5jeqpDbt2RhGGwpcOTR1D7DuOI7rGlOoSWK3a+tqIFo/o9hZdmJpqYSkozDHZsPWqvc9LvAdEQGhu++LXRqnXVrwXxXtSnGg1VSWusH18677mmmumWtHe942oNBlFS2I/Dbu6xeMd7x/RQltqflGfKZUtWpQKwy2aOmcoDtcd+bj6TKlOAhw1a9CgQdnvmEg3qn8VfxtZKOUcb1TxZvKd73yn0fbxJhffNMUEraXGMtx///3Z77322qvk7UdXmxjX8NBDD5VcXhjIPGLEiEYteIVy5HGCEB/qha41xWIMSkymGd10CidtxeIDofBG3dIxxLEWz2lU7dr72ihW/G1jqfmdStl///2zFt6HH364ZHeTxx9/PDvRiy8RCidtxeLb0vgGNF4DpSZSjg/J2HecQO63336NlsdzHc95wwH1xQrXx/a1VKSiPa+NbbbZJnuviMe+OTEXVHRVjBDQ0c9LnHjHe8KTTz45VzXd4pPICBlxwlmqpSdOEIcPH569Lpt634h5ruK97eCDD061pL3vG/GYxjZHHnlk/b4KoqhJOOqooxrtt8BnSuWKc4XCY1Pq/398qRPXx5CMQhfqjnxcfaZUHwGOmlX4lqhU+IouDldddVX2hhfztZQadBx92uMNKd70Gs719vLLL2fjnrbYYovsQ7GUqFIZH9QRAGPup2LR/SY+sDfYYIN06KGHltw+3hBPPvnkrKpZlKhv6C9/+Uv2oTF27Ngm3wx333337PhiDqqGfePjm7577703HXDAAWnzzTdPtaS9r41ixcUGyp20NsZIHX/88dk3tbfddlujD8qYmiK62f3P//xPk/sYNWpU1i0qqhs27HZz6623ZsdywgknNFmEJ167cdIQYSJezw1DaXQXi4BR6kSumrXntREn7fG8xYTdTVUujedmwoQJ2falxoC093mJ94IokBEnccXlyhtOdxHvLU2dYMd7UrSuxfYNQ+AjjzySTVgf0yMUqurViva+b0TLSRSf2H777ee6fvz48dnzevjhhzfboukzpfJfHxGQIgA17I3x97//PX388cdZIaNSxTva+7j6TKk+PerKGVUPVSq+bY6JM6ObY3RXig+lKPt/3XXXZR/E8YFZPAaklJjLKd784k0nJuaMby7jxCa6QfzgBz9o8VvGeOO+9NJLszeuOOGJN8Hrr78++yY0So43rDZW6j7EZOJRVjq6ScQ3sFEF7dlnn83ejFdbbbVmt49v/i666KLsm7345i/efOPNNT4oohtDlDavRR3x2ihUoIwTtxD7ieeqXPGcRFXC+FCOE+Y4Cbv55puzk8D4hr+lMsvRZSruQ5xQRqtAbBddOqOFJE70hgwZ0uIxxElb3Ga8FuLDO17f8fqME5Fa+xa9I14b0TUuJvK+++6701ZbbZUVCIjt46QsWu3jC6FyXlvtfV6iu1NMLB+BIN6r4n3gzjvvzIpsHHvssSVbaIrFazFK3k+ePDmrkhivxXjPiakPYr6yOFmtRe15bUQXudg2CjnE//kIS9EyEo9rbBcnwOXwmVK54r04pg2JkB3dEuOxefrpp7PwEv9vYlqRznxcfaZUDwEOUkovvPBC1i87ugfEh1ZMplrOyXlBnPRE94H44I0ByDEeoblKcw3F7cb2Mc4hPvDjW9LWlN+O/8bxrV7ch+iiE9XFiitHlSO+mYtv/uO+xDfw8UZcPJdLrWrvayOem/gGPb5hjC5pxfNAlSPGQ8XzEi02Ufggurc0HFtTzn2Irk/xoRtds+LEsqlKaKXECWC0rETIiNdEbF/OlAjVrj2vjWiRiZPzQqGL2D6+AGrq2+vOeF7iW/RoqYnJwyMsRAtOqQqHzYluwXE/4jGI97x439D9qX2vjdg23s/jvTzKsUdFv6aqHTfFZ0plK/y/iQAVX5bE81M8OXtnPq4+U6qDAAcAAJATxsABAADkhAAHAACQEwIcAABATghwAAAAOSHAAQAA5IQABwAAkBMCHAAAQE4IcAAAADkhwAEAAOSEAAcAAJATAhwAAEBOCHAA0I1WWGGF1KNHj0Y/vXr1Sj/60Y8arT9t2rTUp0+f+p9S284777xzrTP//POnhRdeOK222mppp512SuPGjUvvvfdeWcc3ZsyY+v3Efkvd3uTJk1t1n4899thG+5hnnnnqbyeOs1zbbLNN/XY9e/Zs1X7PO++8Fu9b8eNY/NO7d+80YMCAtPXWW6exY8emV199NbXW4MGDS95m/Hz3u99t9f6A2iDAAdAp/vOf/6QNN9wwLbTQQul73/teqqur6+5Dqni77757+vOf/5wef/zxNGPGjHT22Wc3Wqd///5p1qxZ9T/XX3/9XMt32WWXuZbHz8yZM7PAdu2116ZBgwalQw89NK244opZOIvlzRk9evRc+4r9N3Tbbbe16n7ecccdc12OgPnaa6/V38bzzz9f9r5uv/32+u0+/PDD7P4VLLDAAumNN95ocr+HH354s/ctHtuGj2Xxbf3zn//MAtzvfve77PE85JBD0jvvvFP2sU+cODHbzwMPPJAuvvjiLNABtESAA6As0coSLQPlOvHEE7MT1I8//jg7OW140k5jF110Udp7773Tuuuum7XwlGP99def6/I666yTtUQ1FC16a6+9djr33HPTjTfemIWQ448/Pn3zm9/MWvXKEfuN/Td06623pnK9//776bHHHkuLLbZY/XVLLrlkGjhwYGqv+LIgglTBEksskbWStfW+NXxsG4bO1VdfPY0aNSo9/fTT2eP4+9//Pnvuxo8fX/YxRyDfZJNN0siRI9Nxxx1X9nZA7RLgACjLF1980ar1G4a91oS/WrXIIot0ye1861vfygJ2iNaf7bffPn3++eet2ke/fv3q/7777rvTp59+WtZ2d955ZxbY1lxzzVQt4rG45ZZb0gYbbJDeeuuttO2226Z//OMfFfv8A/kmwAFQlo8++qhV65988slZF8oFF1ww67IXXc2oHEcffXTWxTA8+OCD6U9/+lOrto+xZwXR3fOee+4pa7toiR02bFjVBfoYQ/fHP/4xa+mM1s3ddtstPfvss919WEAVEuAAKHtMW2ustNJK6ZFHHsmCX4wRqrYT9rzr27dv+trXvlZ/+aqrrmrV9sOHD2/TOLgIcNFCVY2iC2ZhHF2E2r322ivNmTOnuw8LqDICHABl+de//tXdh0AHKx4f9tJLL7Vq2ygWEmPqWjMO7oUXXsiKlUQLXLX64Q9/WP/3k08+mS688MJuPR6g+ghwALQoxje1toWGylc8bi1a5FqruBUuwllLITAqRq633nrZGLhqteWWW6bFF1+8/vJpp52mFQ7oUAIcAC0644wz0rvvvtvdh0EHixL7BVE9sbUadqNsqRUuuk8Wj52rRtFVuHi8Z8wP15oqnQAtEeAAaNIHH3yQTj311PqKhVSPTz75JOviV/Cd73yn1fvYaKON5mpNa24cXFS5jG641Tr+rdimm2461+Wbbrqp244FqD4CHAAlrbbaammZZZZJ//u//zvXFAJ9+vSZ6yfWKxYFS+L6mFcrWiMKP6Ucc8wx2brzzDNP/XorrLDCXF3uosT90ksvXX9b//M//9OoImYEzR//+MfZtrFejO369re/nU2I3Vp//etfszL7EUxiLrallloqa2n629/+lqrJ1VdfnYW4sN9++7WpSmg8bzvssMNc0wk0NTH4Qw89lHUl3GyzzVK1W2WVVea6HBN+A3QUAQ6Akp5//vnsZDx+ll9++frrC9cVfmK9Yocddlh2/YcffphNUtxS18xY95VXXmm0LIJahMeTTjopvf7661lFywhUp59+ejZp8uzZs+u7qEUoiLA5YcKELMxFifxrrrkmayEq9+R55syZWVDbeeedswmao3UqKgleccUV2X5HjBiRDjrooFbPh1eJ4jErTBq95557ZhNQt1VxN8p4DJsqdhNhfOjQoWm++eZL1W7llVee6/LkyZOzxwagIwhwAHSKhRZaKC288MJlrbvccsvNdTkq98XcZBEGIoTF3FpR8TBajaKVLsJcBLtoQYoWugiCP/3pT7PiETG32c9+9rOshPtnn32Wvvvd77Y4yXTsJ1qSbr755qwlL/YXrX5xu9Ey9Ze//CVbL+b5OvLII1MeRYB47rnn0q9+9as0ZMiQ7L7F3G9XXnllFozbKsa0FYeypsZ7VfP0AQ01fN1H6C/1JQVAWwhwAFSUKJZy/PHHpz//+c+NWmu++tWvZq04hZB31llnpa9//etZl8eGoiUwRNn6G264odnbjNaoCIsROqPVr6G4jTXWWCP7+/zzz0+PPvpoqlRjxoxp1M01fiLYRsti3L/DDz88TZo0qU3j3hqKidrj8WluHNy0adPSww8/XPUFTIofk4YadvsFaCsBDoCKEq1hu+22W1p22WVLLl9zzTWz3++//34WRgpdAZtar6XiGhFkzjvvvOzvmIQ5Qlwphdajurq6NHbs2FSpRo8e3aiba/zE4xohKkLbySefnD2+MQZx6tSp7b7N4m6UMeH7iy++ONfyGBs3cODALIDXgnnnnbfRdYUuvwDtJcABUHEiSDWleI6t6F4ZY99aWu+ZZ55pcn/RohYVEkNxS1JDxcU3ojtgdM/Mk/nnnz/rOhlhtXD8Z555Zlp//fWzMX7t0XA6gYaBOca/1UrrW6HFsZxWOYC2EOAAqDibb755WettscUWZa3XVCtTjE26/vrr6y+vuuqqTe5jiSWWmKs7XHEJ/ryJoPrLX/4y+zvGZkXrYkuTcDcnitystdZaTY6Dq6Xxb00FuMUWW6xbjgWoPgIcABWlX79+2XitckShkXIUWtgaigqab7/9dv3lRRZZpMl9NDwBf/PNN1OeHXLIIfWtQlG5M6ZdaE+FzeJWuHvuuae+6mJUYHz55ZezyqG1IiqwFovHObqQAnQEAQ6AilJu5crWrlvKG2+8Mdfl6E5YqgBI/AwePDib2y5++vbtm12XZ3EfNtxww/rLEydObLKCZGsDXIy5K0zfEK1v0XWzuXBcbaLaZ8PXVVNzIQK0lgAHQEVpzYlue0+K33nnnbkuP/HEEyULgBR+oiUvfj7++OM0bNiwlHcNi4rccsstbd7X1772tbm6mRbGwXXk+LdoIYyWz0off9hwAvlaGv8HdD4BDoCa1bCrZq1NttywBTO6OrbVPPPMk82lVxzgInBFS1xHjH+L/a244opZV8Tozhpz9rWku1q9Gga43XffvVuOA6hOAhwANau4UmVhDrpaFt1D26O4G2UURbniiivSnDlzsta59njqqaeyyqSvvvpqfRGZUvP1laq82dWipTYmoS/Yaqutamb6BKBrCHAAtHscWUyonUfrrLNO1nLU2haoCA+/+c1vUrVVSxw0aFC79hddBYsnX485+qJ4SXuDYUza/umnn7a6LP+AAQNSV4uWwuhiWxBz7gF0JAEOgHaPI8try1VUvNxggw3mKuRRjn/9619p5ZVXTtVWbCNai9ojJkEfOnRo/eXXXnutQ8Z/xeTgxWL+v9/+9rcl140Jy4uLh3S1c889t/7vvfbaq+wpMQDKJcAB0KLevXvX/z179uy5lr344otzFa/Im8MOO6z+7zvvvDPV1dU1u/7rr7+eHn300XaHne4WQad4Au9ll1027bTTTi1uV3h8mnqcGk7q3RHj3wqtbTH+7ZFHHkkPPfRQWnPNNUuu+9///rf+71133TV1pSgCc/fdd9fPjXfBBRd06e0DtUGAA6BFcTJaHNiK3XTTTXOVo8+b/fffP+tKWehCWSh/35TRo0dnc6iVO1ddpfrDH/6QjSULvXr1ShdffPFcQb0phfnviufPK/atb32r/u9VVlklrbDCCu0+1mhxC9Ga1dxr7d57783mtAvRErjpppumrvLWW2+l733ve9nfSy65ZPrHP/7R7mkuAEoR4ABo0YgRI+r//sUvfpEVpghXX311+tvf/pY22WSTlFcxZuuqq66qb0U86qij5hrDVOy0005L9913XzrxxBNTnj3wwANp1KhR2d8xBvCPf/xj2m677VrcLqZQuOuuu+pbK0uJSpGF1rGOaH0L3/3ud1P//v3T+PHjG02SXRCvyRhzFyI4XXLJJamrRKiN+xq/11hjjew1stpqq3XZ7QO1RYADoEXR4lRo+YiwEyfIUSBizz33zFod5p133kbbzJgxY66T7ULLTVPdEgtim9i2nMm3G07E3dR6UayjuX1GlcAINeutt156+umn05ZbbpkFlJhWIOYcixPyaFkaN25cNq9ZjJ2rFNGds2EJ+0LALhb3I+a5+/GPf5x1/4zHIybYju6I++23X1ljHeN1UCj0cumll6Y//elPjYqLFHejbGr8WzwfxV0dY9/Fr4GGokXr8ssvT++//37WCnfttdfONRdcjMHcZ599sha4COI33njjXK3G5YjHLB6f5h7bYnH7zz//fBo7dmwWWOPvCMUPP/xw1vII0GnqAKAMH374Yd0PfvCDuiWXXLKud+/edauuumrdmDFj6j7//PO51rvggguy5fPMM08Mkqr/ictx/ejRo+vX/elPf5pd16NHj5LrnnvuufW3HZfnnXfeudaLn/nmm69uqaWWavU+S5kzZ07dlVdeWbfbbrvVDRo0qG7++eev69evX92GG25Yd/rpp9d98sknHf64Lr/88vXHWI7CY1H4afh4xE+vXr3mWqfw2C2zzDLZfTn66KPr7rnnnuz+tuQXv/hFk7cTPz179syWF7v//vuz2/voo4/qrxs2bFj9sTR8bcRPPF+F5fHaKuWxxx6r23LLLbP1+/TpU7fyyivXrb766tn9je132mmnuldffbWuXPFaKNxm7KPU/Wv4OBb/DBgwoG7bbbetO/PMM+veeeeduva6++6762/3O9/5Trv3B1SnHvFP58VDAKA5MUbslVdeyf72kVyemGPu/vvvz1p1Y7LwmP7g61//elbkJM+iummhOM53vvOdrIUToKFeja4BAKhgK620UvYDUIuMgQMAAMgJAQ4AACAnBDgAAICcEOAAoEJMnTq1uw+BbvTqq6929yEAOaCICQBUiJhTb6eddkprrbVWNjddnz59uvuQ6EQx992kSZOyuQfj980339zdhwTkgAAHABUiJqiOn9CzZ890+OGHp7PPPru7D4tOsskmmzQ7gTlAKeaBAwAAyAlj4AAAAHJCgAMAAMgJAQ4AACAnBDgAAICcEOAAAAByQoADAADICQEOAAAgJwQ4AACAnBDgAAAAckKAAwAAyAkBDgAAICcEOAAAgJwQ4AAAAHJCgAMAAEj58P8A8Xx/uVzi3XgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t1_lim = (55555, 57000)\n",
    "t2_lim = (60000, 61000)\n",
    "\n",
    "rng = np.random.default_rng(42)\n",
    "fake_t1 = Time(rng.uniform(*t1_lim, size=32), format=\"mjd\")\n",
    "fake_t2 = Time(rng.uniform(*t2_lim, size=6), format=\"mjd\")\n",
    "t0 = Time(58000, format=\"mjd\")\n",
    "\n",
    "# Generate fake data:\n",
    "P = 3.1 * u.day\n",
    "K = 0.25 * u.km / u.s\n",
    "offset = 0.7 * u.km / u.s\n",
    "\n",
    "fake_rv1 = K * np.cos(2 * np.pi * (fake_t1 - t0).jd / P.to_value(u.day))\n",
    "fake_rv2 = K * np.cos(2 * np.pi * (fake_t2 - t0).jd / P.to_value(u.day)) + offset\n",
    "\n",
    "fake_err1 = rng.uniform(0.005, 0.01, size=len(fake_t1)) * u.km / u.s\n",
    "fake_err2 = rng.uniform(0.05, 0.1, size=len(fake_t2)) * u.km / u.s\n",
    "fake_rv1 += rng.normal(0, 1, size=len(fake_t1)) * fake_err1\n",
    "fake_rv2 += rng.normal(0, 1, size=len(fake_t2)) * fake_err2\n",
    "\n",
    "data1 = tj.RVData(fake_t1, fake_rv1, fake_err1)\n",
    "data2 = tj.RVData(fake_t2, fake_rv2, fake_err2)\n",
    "data = [data1, data2]\n",
    "\n",
    "ax = data1.plot()\n",
    "data2.plot(ax=ax, color=\"C2\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8596c537",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_prior(**additional_pars):\n",
    "    dv0_1 = xu.with_unit(\n",
    "        pm.Normal(\n",
    "            \"dv0_1\", (np.average(data2.rv.value) - np.average(data1.rv.value)), 0.01\n",
    "        ),\n",
    "        u.km / u.s,\n",
    "    )\n",
    "    offset_list = [dv0_1]\n",
    "\n",
    "    p = pm.Normal(\"P\", 3.0, 0.2)\n",
    "    P = xu.with_unit(p, u.day)\n",
    "\n",
    "    # I would add an \"extra variance\" or jitter parameter here:\n",
    "    s = xu.with_unit(pm.Lognormal(\"s\", -2, 0.5), u.km / u.s)\n",
    "\n",
    "    return tj.JokerPrior.default(\n",
    "        P_min=None,\n",
    "        P_max=None,\n",
    "        sigma_K0=30 * u.km / u.s,\n",
    "        sigma_v=100 * u.km / u.s,\n",
    "        P0=3.0 * u.day,\n",
    "        pars={\"P\": P, \"s\": s, **additional_pars},\n",
    "        v0_offsets=offset_list,\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d9549f9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(12345)\n",
    "\n",
    "with pm.Model() as model:\n",
    "    prior = make_prior()\n",
    "    prior_samples = prior.sample(size=1_000_000, rng=rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e2a7be78",
   "metadata": {},
   "outputs": [],
   "source": [
    "joker = tj.TheJoker(prior)\n",
    "joker_samples = joker.rejection_sample(data, prior_samples, max_posterior_samples=256)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "480e96cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[0.61202981] \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity [0.61202981] km / s>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joker_samples[\"dv0_1\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "95c1de63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = tj.plot_rv_curves(joker_samples, data=data, apply_mean_v0_offset=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b446c96c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = tj.plot_phase_fold(joker_samples, data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5bbf7e35",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_69681/572976532.py:9: FutureWarning: The `start` kwarg was renamed to `initvals` and can now do more. Please check the docstring.\n",
      "  trace = pm.sample(\n",
      "Initializing NUTS using jitter+adapt_full...\n",
      "/Users/aprice-whelan/projects/thejoker/.venv/lib/python3.12/site-packages/pymc/step_methods/hmc/quadpotential.py:760: UserWarning: QuadPotentialFullAdapt is an experimental feature\n",
      "  warnings.warn(\"QuadPotentialFullAdapt is an experimental feature\")\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [dv0_1, P, s, e, __omega_angle1, __omega_angle2, __M0_angle1, __M0_angle2, K, v0]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">/Users/aprice-whelan/projects/thejoker/.venv/lib/python3.12/site-packages/rich/live.py:256: UserWarning: install \n",
       "\"ipywidgets\" for Jupyter support\n",
       "  warnings.warn('install \"ipywidgets\" for Jupyter support')\n",
       "</pre>\n"
      ],
      "text/plain": [
       "/Users/aprice-whelan/projects/thejoker/.venv/lib/python3.12/site-packages/rich/live.py:256: UserWarning: install \n",
       "\"ipywidgets\" for Jupyter support\n",
       "  warnings.warn('install \"ipywidgets\" for Jupyter support')\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 8_000 tune and 500 draw iterations (32_000 + 2_000 draws total) took 215 seconds.\n",
      "There were 19 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
     ]
    }
   ],
   "source": [
    "from pymc_ext.distributions import angle\n",
    "\n",
    "with pm.Model() as model_mcmc:\n",
    "    prior_mcmc = make_prior()\n",
    "\n",
    "    joker_mcmc = tj.TheJoker(prior_mcmc, rng=rng)\n",
    "    mcmc_init = joker_mcmc.setup_mcmc(data, joker_samples)\n",
    "\n",
    "    trace = pm.sample(\n",
    "        tune=8000,\n",
    "        draws=500,\n",
    "        start=mcmc_init,\n",
    "        random_seed=123,\n",
    "        cores=4,\n",
    "        chains=4,\n",
    "        init=\"jitter+adapt_full\",\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c39396e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P</th>\n",
       "      <td>3.100</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3.100</td>\n",
       "      <td>3.100</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1586.0</td>\n",
       "      <td>1231.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e</th>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>583.0</td>\n",
       "      <td>560.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>omega</th>\n",
       "      <td>-0.051</td>\n",
       "      <td>1.872</td>\n",
       "      <td>-3.139</td>\n",
       "      <td>2.719</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.136</td>\n",
       "      <td>470.0</td>\n",
       "      <td>342.0</td>\n",
       "      <td>1.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M0</th>\n",
       "      <td>-0.483</td>\n",
       "      <td>1.565</td>\n",
       "      <td>-3.068</td>\n",
       "      <td>2.529</td>\n",
       "      <td>0.078</td>\n",
       "      <td>0.046</td>\n",
       "      <td>442.0</td>\n",
       "      <td>589.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s</th>\n",
       "      <td>0.008</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1036.0</td>\n",
       "      <td>1054.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.252</td>\n",
       "      <td>-0.256</td>\n",
       "      <td>0.256</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.000</td>\n",
       "      <td>6.0</td>\n",
       "      <td>149.0</td>\n",
       "      <td>1.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v0</th>\n",
       "      <td>-0.001</td>\n",
       "      <td>0.002</td>\n",
       "      <td>-0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>902.0</td>\n",
       "      <td>621.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dv0_1</th>\n",
       "      <td>0.607</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.591</td>\n",
       "      <td>0.626</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1185.0</td>\n",
       "      <td>1057.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "P      3.100  0.000   3.100    3.100      0.000    0.000    1586.0    1231.0   \n",
       "e      0.009  0.007   0.000    0.022      0.000    0.000     583.0     560.0   \n",
       "omega -0.051  1.872  -3.139    2.719      0.094    0.136     470.0     342.0   \n",
       "M0    -0.483  1.565  -3.068    2.529      0.078    0.046     442.0     589.0   \n",
       "s      0.008  0.002   0.005    0.012      0.000    0.000    1036.0    1054.0   \n",
       "K      0.000  0.252  -0.256    0.256      0.125    0.000       6.0     149.0   \n",
       "v0    -0.001  0.002  -0.005    0.003      0.000    0.000     902.0     621.0   \n",
       "dv0_1  0.607  0.009   0.591    0.626      0.000    0.000    1185.0    1057.0   \n",
       "\n",
       "       r_hat  \n",
       "P       1.00  \n",
       "e       1.01  \n",
       "omega   1.09  \n",
       "M0      1.01  \n",
       "s       1.00  \n",
       "K       1.73  \n",
       "v0      1.00  \n",
       "dv0_1   1.00  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(trace, var_names=prior_mcmc.par_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9a03378b",
   "metadata": {},
   "outputs": [
    {
     "data": {