From 610393a8fc59fc5bd1bf49c76c799e77325fa470 Mon Sep 17 00:00:00 2001
From: frcojimenez <frco.jimenez@gmail.com>
Date: Mon, 4 Jan 2021 14:58:34 +0000
Subject: [PATCH] results notebook

---
 code_new/Results_notebook_new.ipynb | 1851 +++++++++++++++++++++++++++
 1 file changed, 1851 insertions(+)
 create mode 100644 code_new/Results_notebook_new.ipynb

diff --git a/code_new/Results_notebook_new.ipynb b/code_new/Results_notebook_new.ipynb
new file mode 100644
index 0000000..5213212
--- /dev/null
+++ b/code_new/Results_notebook_new.ipynb
@@ -0,0 +1,1851 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy import interpolate\n",
+    "import corner\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib.ticker import MaxNLocator\n",
+    "from matplotlib import rc\n",
+    "from configparser import ConfigParser\n",
+    "import codecs\n",
+    "from scipy.interpolate import interp1d\n",
+    "\n",
+    "#plt.rcParams['font.family'] = 'DejaVu Sans'\n",
+    "#rc('text', usetex=True)\n",
+    "plt.rcParams.update({'font.size': 16.5})\n",
+    "\n",
+    "import ptemcee\n",
+    "#from pycbc.pool import choose_pool\n",
+    "from multiprocessing import Pool\n",
+    "import h5py\n",
+    "import inspect\n",
+    "import pandas as pd\n",
+    "import json\n",
+    "import qnm\n",
+    "import random\n",
+    "import dynesty\n",
+    "from dynesty import plotting as dyplot\n",
+    "import os\n",
+    "import glob\n",
+    "import csv\n",
+    "import re\n",
+    "from re import match"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f_fpars= [[2.95845, -2.58697, 0.0533469], [2.12539, -1.78054, \n",
+    "  0.0865503], [1.74755, -1.44776, 0.123666], [1.78287, -1.53203, \n",
+    "  0.129475], [2.04028, -1.83224, 0.112497]]\n",
+    "\n",
+    "q_fpars=[[0.584077, 1.52053, -0.480658], [0.00561441, \n",
+    "  0.630715, -0.432664], [-0.197965, 0.515956, -0.369706], [-0.275097, \n",
+    "  0.455691, -0.331543], [-0.287596, 0.398514, -0.309799]]\n",
+    "\n",
+    "def w_fpars_Berti(n):\n",
+    "    return f_fpars[n]\n",
+    "\n",
+    "def tau_qpars_Berti(n):\n",
+    "    return q_fpars[n]\n",
+    "\n",
+    "def mass_from_wtau(n,w,tau):\n",
+    "    f1,f2,f3 = w_fpars_Berti(n)\n",
+    "    q1,q2,q3 = tau_qpars_Berti(n)\n",
+    "    res=(f1 + f2*(2**(-1/q3)*((-2*q1 + w*tau)/q2)**(1/q3))**f3)/w\n",
+    "    return res\n",
+    "\n",
+    "def spin_from_wtau(n,w,tau):\n",
+    "    f1,f2,f3 = w_fpars_Berti(n)\n",
+    "    q1,q2,q3 = tau_qpars_Berti(n)\n",
+    "    res=1 - 2**(-1/q3)*((-2*q1 + w*tau)/q2)**(1/q3)\n",
+    "    return res"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rootpath='/work/francisco.jimenez/sio/git/rdstackingproject/results_new/'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['backup_new', 'backup', '0305', 'RT_0062', '1107', 'GT_0355']\n"
+     ]
+    }
+   ],
+   "source": [
+    "dirs=os.listdir(rootpath)\n",
+    "print(dirs)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax0_False',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax0_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax1_False',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax1_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax2_False',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax2_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax3_False',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax3_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax4_False',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-m-af-nmax4_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-nmax0_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-nmax1_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-nmax2_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-nmax3_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-nmax4_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-fixed-nmax5_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax0_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax1_False',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax1_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax1_True_',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax1_True_0.002',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax2_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax2_True_0.002',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax3_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax3_True_0.002',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax4_True',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax4_True_0.002'],\n",
+       "      dtype='<U95')"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "index=2\n",
+    "case= rootpath+dirs[index]\n",
+    "folders=[x[0] for x in os.walk(case)][1:]\n",
+    "folders=np.sort(folders)\n",
+    "folders"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "regular_list = [glob.glob(x+'/summary*.csv') for x in folders]\n",
+    "sum_files = [item for sublist in regular_list for item in sublist]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['w-tau-fixed-m-af-nmax0_False',\n",
+       " 'w-tau-fixed-m-af-nmax0_True_',\n",
+       " 'w-tau-fixed-m-af-nmax1_False',\n",
+       " 'w-tau-fixed-m-af-nmax1_True_',\n",
+       " 'w-tau-fixed-m-af-nmax2_False',\n",
+       " 'w-tau-fixed-m-af-nmax2_True_',\n",
+       " 'w-tau-fixed-m-af-nmax3_False',\n",
+       " 'w-tau-fixed-m-af-nmax3_True_',\n",
+       " 'w-tau-fixed-m-af-nmax4_False',\n",
+       " 'w-tau-fixed-m-af-nmax4_True_',\n",
+       " 'w-tau-fixed-nmax0_True',\n",
+       " 'w-tau-fixed-nmax1_True',\n",
+       " 'w-tau-fixed-nmax2_True',\n",
+       " 'w-tau-fixed-nmax3_True',\n",
+       " 'w-tau-fixed-nmax4_True',\n",
+       " 'w-tau-fixed-nmax5_True_',\n",
+       " 'w-tau-nmax0_True',\n",
+       " 'w-tau-nmax1_True',\n",
+       " 'w-tau-nmax1_True_0.002',\n",
+       " 'w-tau-nmax2_True',\n",
+       " 'w-tau-nmax2_True_0.002',\n",
+       " 'w-tau-nmax3_True',\n",
+       " 'w-tau-nmax3_True_0.002',\n",
+       " 'w-tau-nmax4_True',\n",
+       " 'w-tau-nmax4_True_0.002']"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tags= [\"\" for x in range(len(sum_files))]\n",
+    "for i in range(len(sum_files)):\n",
+    "    tags[i]=os.path.basename(os.path.dirname(sum_files[i]))\n",
+    "tags"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 153,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "csv_data=[pd.read_csv(x, error_bad_lines=False) for x in sum_files]\n",
+    "csv_data_new_v1=[csv_data[i].sort_values(by=[\"t_shift\"], ascending=True) for i in range(len(csv_data))]\n",
+    "csv_data_new=[csv_data_new_v1[i].reset_index(drop=True) for i in range(len(csv_data))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 154,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "colors=['red','blue','black','orange','cyan','green','purple','pink','gold','olive','red','blue','black','orange','cyan','green']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 155,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "position_fixed = [i for i, s in enumerate(tags) if 'fixed-n' in s]\n",
+    "position_fixed_m_af = [i for i, s in enumerate(tags) if 'fixed-m-af' in s]\n",
+    "\n",
+    "position_var_cte = [i for i, s in enumerate(tags) if '002' in s]\n",
+    "position_aux=np.concatenate((position_fixed,position_var_cte))\n",
+    "\n",
+    "position_var=(set([i for i in range(len(tags))])-set(position_aux))\n",
+    "position_var=np.array(list(position_var))\n",
+    "\n",
+    "tags_fixed=[tags[i] for i in position_fixed]\n",
+    "tags_var=[tags[i] for i in position_var]\n",
+    "tags_var_cte=[tags[i] for i in position_var_cte]\n",
+    "\n",
+    "csv_data_var=[csv_data_new[i] for i in position_var]\n",
+    "csv_data_var_cte=[csv_data_new[i] for i in position_var_cte]\n",
+    "csv_data_fixed=[csv_data_new[i] for i in position_fixed]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 156,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tags_var_m_af = [tags[i] for i in position_fixed_m_af]\n",
+    "position_fixed_m_af_True = [i for i, s in enumerate(tags_var_m_af) if 'True' in s]\n",
+    "csv_data_var_m_af=[csv_data_new[i] for i in position_fixed_m_af_True]\n",
+    "tags_var_m_af=[tags[i] for i in position_fixed_m_af_True]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 157,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "position_var = [i for i, s in enumerate(tags) if '*_True' in s]\n",
+    "position_var = [re.match(s,\"_True\" ) for s in tags]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 158,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "r = re.compile(\"w-tau-n.*_True$\")\n",
+    "tags_var = list(filter(r.match, tags)) # Read Note\n",
+    "position_var = [tags.index(i) for i in tags_var ]\n",
+    "csv_data_var=[csv_data[i] for i in position_var]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 159,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "IndexError",
+     "evalue": "list index out of range",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-159-90c234213a9b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;34m[\u001b[0m\u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0merrorbar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsv_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m't_shift'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mcsv_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dlogz'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myerr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcsv_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dlogz_err'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfmt\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcolors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0mtags\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtags\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0myscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'log'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-159-90c234213a9b>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;34m[\u001b[0m\u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0merrorbar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsv_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m't_shift'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mcsv_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dlogz'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myerr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcsv_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dlogz_err'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfmt\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcolors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0mtags\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtags\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0myscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'log'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mIndexError\u001b[0m: list index out of range"
+     ]
+    },
+    {
+     "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": [
+    "plt.figure(figsize = (12, 8))\n",
+    "\n",
+    "[plt.errorbar(csv_data[i]['t_shift'], -csv_data[i]['dlogz'], yerr=csv_data[i]['dlogz_err'], fmt='o',color=colors[i],label =tags[i]) for i in range(len(tags))] \n",
+    "plt.yscale('log')\n",
+    "\n",
+    "plt.legend(loc ='center right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$|evidence|$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 160,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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j0QitVmtz0eENxo0bhyVLliAlJQX33HMPjh49CpPJhK5du9qs98knn2D9+vVYtmwZ+vbtCwBYv349xowZg5dffhkLFiwAYOk6NWXKFMybNw/FxcW466678NZbb6GoqKhRpzucOXMmli9fjpkzZyI2Nha5ublOB4bW9Zx6hLOpYPho5OkZb4RTNxIReaXbMj1jjYQEy8ODSkpKRCklHTp0sImvXr1aAMjTTz9dp/3s3btXYmNjxd/f32ZavO+++04mTJggbdu2ldDQUJkyZYr88MMPTqdzzMnJkZiYGGndurX07NlTsrOzG3x6xldeeUUAyIcffmiz3smTJ0Wj0cijjz5qjRUXF8vvfvc7iYqKEj8/P4mMjJTRo0dLVlaWzbb5+fmSkJAgAQEB0rlzZ3nxxRflzTffdGt6xtmzZzv9PNOnT7c+rzkW9tMLPvjgg06ntrQ/HhUVFTJnzhyJjIyUwMBAGT58uHzxxReSkJBgnQ6xtLRUoqKiZMiQIXL9+nWb/T3++OPi7+9v82+ivLxcnn32WYmIiBB/f38ZMmSIfPrppzf9zDfianpG+3Nbw2w2y2OPPSahoaHSpk0befjhh+XcuXNOv2N1Paf1cSvTMypxMhiBgNjYWDl48KCn07B0d3F2jpQC3Li7GRERNazjx49bp+1rcCNGWJYebFEnooZRl98VSqlDIhJrH2cfdW/naqR/dDT7rhMRERE1Y+yj7u1czQAwdiz7rhMRNVdsSadmrqys7KY3PoqIiGikbLwXW9S9naubIW3f7hV3ryMiIiJy1+zZsxEZGXnDB7FFvWlwdjOkRx91vm4j372OiIiIyF3288eTcyzUmyovuXsdERERkbv69OlTr7nuWxp2fWmqMjIsfdVr88Dd64iIiIjo9mChbkcpNV4pZSwrK/N0Kjfmqu86B5ISERERNQss1O2IyDYRMYSGhno6lZvT64HCQst86oWFNy/SOZ0jERERUZPBPuothcnE6RyJiIiImhC2qLcUaWmczpGIiIioCWGh3lK4mraR0zkSEREReSUW6i2Fq2kbOZ0jEZHXGTHC8iCilo2FekvB6RyJiKiFunz5MlJSUtCxY0copZCeno5du3ZBKYVdu3Y1ai4bN26EUgqFhYWN+r7UNLFQbyk4nSMRETWyiooKa1HsSS+99BJMJhOeeuopZGVlYeLEiR7Np7krLi7GggULMHLkSLRp06ZeF0Q1F1I3e+h0utvyGbwFZ31pSfR69wpzk8ky2PTsWUsXmYwMFvZERFRnFRUVWLx4MQBghAf78uzatQvDhw/HwoULrbGqqiqUl5ejdevWHsuruTpx4gRWrFiBbt26oX///vj888/d3kfv3r2RlZVlE3viiScwePBgGGpmrQMQHBx8y/l6Mxbq5ByncyQiombi3Llz6N+/v03Mx8cHAQEBHsqoeRs8eDBKSkpwxx134P3338eECRPc3kfHjh0xbdo0m9h//Md/oGvXrg7x2iorK3H9+nX4+/u7/Z7eiF1fyDlO50hE1CIdPnwYSils377dGsvNzYVSCqNGjbJZd8iQIZg0aZLT/RQWFiIsLAwAsHjxYmtXhfT0dABAfn4+kpOT0bVrVwQEBCAiIgIzZszAhQsXbPaTnJzstHtDeno6lFI3/Cw13ScKCgrwwQcfWHMoLCx06KN+/PhxBAQE2LTWAkBOTg6UUli2bJk19u233yIpKQkdOnSAv78/+vfvj7ffftvh/b/++muMGjUKgYGBiIqKwtKlS1FVVXXDnGtTSiE1NRXvvvsu+vbtC39/f/Tt2xf/+Mc/nB6L06dPY+rUqQgJCUHHjh2xYsUKAMDJkyeRmJiIoKAgREdHIzs722b7ixcv4tlnn0W/fv0QHByMkJAQ3H///Thy5IjNeklJSQgKCsLp06etsaqqKsTHxyMyMhIXL14EALRp0wZ33HFHnT/nrag5Rn/729/Qq1cv+Pv744svvnA5BqGwsBBKKWzcuNEm/vXXX2PixIlo164dAgMDMWzYMHz66aeN8hluhIU6OcfpHImIPMJkAvbuBXbv9sxNpAcMGIA2bdogLy/PGsvLy4OPjw/27duHa9euAQB+/vlnfPnll4iLi3O6n/DwcKxbtw4AMGHCBGRlZdn0D//0009x5swZpKSkYM2aNZg6dSreeecdjB07FiLSIJ+lpvtE+/btMXjwYGsO4eHhTtddsmQJ3njjDXzyyScAgLKyMsycORN333035s2bB8DS/3rYsGHIy8vD7NmzkZmZiU6dOuGRRx6xKf5+/PFHjBw5EkeOHMGCBQusxeTq1avd+gy7d+/GrFmz8Mgjj2DlypWoqKjApEmTHC5oAGDy5Mlo1aoVVqxYgf79+2PBggVYt24dEhMTERMTg5UrVyI0NBTJyck2g1nPnDmD999/H+PGjcOf/vQnzJ07F0ePHkVCQgJ++OEH63qvvfYa2rZti5SUFOsFR2ZmJvbs2QOj0Yh27dq59dkaSk5ODubPn49p06YhMzMTkZGRbm1/9OhR3HPPPTh9+jSee+45rFy5EgBw//33Y8eOHbcj5boTET6cPAYPHiwtmlYrAjg+tFpPZ0ZE5BWOHTvW4PvMzhbRaGx/7Wo0lnhjSkxMlOHDh1ufjx49WiZPniwAZO/evSIikpOTIwDkwIEDLvdz6dIlASCLFi1yeM1sNjvE3n77bQEgubm51tj06dNF6+T/nkWLFomljLk5rVYrDz74oE1s586dAkB27txpjV2/fl2GDRsmUVFRUlpaKikpKRIQEGBzrmfMmCFRUVFy6dIlm/2NGTNGIiMjpbKyUkREUlNTRSklhw4dsq5z7tw5CQ0NFQBSUFBw07wBiL+/v5w5c8YaO3LkiACQNWvWWGM1x+LJJ5+0xsrLyyUsLEyUUrJ+/Xpr/JtvvhEAsmTJEmusoqLCmneNgoIC8ff3t1lPROSjjz4SALJq1So5ceKEBAYGSlJSksvPsHXrVofjXF+hoaEyffp0mxgA8fX1lRMnTtjEnZ1fEcvnAiAbNmywxkaNGiWDBg2Sq1evWmPXrl2Tfv36ydChQ28577r8rgBwUJzUo2xRJ+c4nSMRUaPzll6HcXFxOHDgACoqKlBVVYUvvvgCkydPRo8ePbBnzx4Allb24OBgDBw4sF7vERgYaP25oqICJSUlGDZsGABL9xtP8PX1xcaNG3HhwgUkJiZiw4YNWLJkCXr37g3A0rj53nvv4YEHHsD169dRUlJifYwZMwbFxcU4efIkAGD79u0YPnw4Bg0aZN1/eHg49G6O8xo9ejS6dOlifd6/f3+EhITgzJkzDuvOnDnT+nNAQAAGDBgAX19fJCUlWeM9e/ZE27ZtUVBQYI35+/vDx8dSElZWVuLChQsIDg5Gz549Hc7F2LFjkZKSgoULF2LKlClo166d238laGijRo1Cjx496rXtxYsXsXPnTkyZMgVlZWXW81laWorExEQcOHAAZvt/lI2IhTo5x+kciYganbf0OoyPj8fVq1exf/9+HDlyBJcvX0Z8fDzi4uKsXWLy8vIwdOhQtGrVChcvXsSPP/5ofZSVld30PS5evIjZs2ejY8eOCAwMRHh4uLUgrcv2zvbnbg7O9OzZE2lpadi/fz+GDBmCOXPmWF87f/48SktLsXbtWoSHh9s8UlNTresAQFFREbp37+50/7WVlZXZ5F3Tz7tGtJMbE4aFheHSpUsOcft1Q0NDERERAT8/P4d47e2rqqrw6quvonv37vD390f79u0RHh6O/Px8p8fx1VdfRVBQEPLz8/HXv/4Vbdu2dVinMdW+kHHX6dOnISJ47rnnHM7pK6+8gqqqKqfdjBoLZ30h19ydzpGIiG5JdLRlki1n8cY0dOhQ+Pn5IS8vDyEhIejatSs6deqE+Ph4zJ07F1evXsW+ffswf/58AMDEiROxe/du6/bTp093GKxn7+GHH8bnn3+OuXPnYuDAgQgODkZVVRXGjBljM+DS1YDRyspKm+f1ycEZEUFOTg4A4LvvvkNZWZl1UGxNXsnJyS5bxmNiYtx6v9mzZ+Ott96yPk9ISLAZAOnr6+syT3vO1q3L9i+99BL++Mc/YsaMGXjxxRfRrl07+Pj4IDU11eng14MHD1ovKL766iuMGzfO+YdrJLX/OlOjrt+bms83f/583HfffU63cTamobGwUCciIvISGRm2M+MCnul1GBgYiEGDBlkL9fj4eACWLjElJSXIzs5GeXm5dSDpK6+8YtNC26lTJwCui6VLly5hx44dWLx4MV544QVr/NSpUw7rhoWFobS01CFeZHdF4yoHd7322mvIzc3F8uXLkZ6ejlmzZlnn8w4PD0ebNm0gIi6Luhpardbp5zlx4oTN83nz5tlMN1hzUdCYtmzZgpEjR+LNN9+0iZeWlqJ9+/Y2sStXrmDGjBkYPHgwevfujfT0dDzwwAPo06dPY6Z8UzXH0f67Y/+96dq1KwBLV6GbnVNPYKFORETkJWoaaR97DPjlF0uvQ0/day4+Ph7r1q1DUFAQli5dCgDo1q0bIiIisGLFCrRq1crap3zw4MFO9xEYGAillEOxVNPKa98qnJmZ6bCPu+66C2VlZcjPz7fOhV5cXIytW7farOcqB3ecOnUKzz//PPR6PebPn49WrVrh2WefxcMPP4zx48fD19cXEyZMwKZNm/Dcc885dGM5f/68tfV17NixWL16NQ4fPmztp37+/HmY7Kbx6dOnj8eLXF9fX4dzsXnzZnz//ffo1q2bTfyZZ57BTz/9hO3btyMqKgo7d+5ESkoKPv/8c5et956g1Wrh6+uL3NxcPPTQQ9b42rVrbdbr0KED7r33Xrz++uv4wx/+4NB6XvucegILdTtKqfEAxtt/MYmIiBqDXg+88YblZzfvut6g4uLisGrVKly5csXaol4T37JlC4YMGYKgoKAb7qN169bo168fNm3ahB49eqBdu3aIiYlBTEwM7r33XqxcuRLXrl1D586dkZOTYzPAscbUqVMxf/58TJgwAbNmzYLZbMbrr7+OHj16NOig06qqKqSkpCA0NBRr1qwBADz99NPYunUrnnjiCcTFxSEsLAzLly/Hzp07ERsbC4PBgF69eqGkpAQHDhzA4cOHrdMezps3D1lZWUhMTMSsWbOg0WhgNBqh1WqRn5/fYHk3hHHjxmHJkiVISUnBPffcg6NHj8JkMllbm2t88sknWL9+PZYtW4a+ffsCANavX48xY8bg5ZdfxoIFC6zr1lzcHT9+HACQlZWFPXv2oG3btviP//iP2/6ZQkNDMWXKFKxZswZKKdx111347//+b5w7d85h3b/85S+Ij49HTEwMZs6ciS5duqC4uBh5eXmoqKhAbm7ubc/XJWdTwfDB6RmJiOjGbsf0jDUSEiwPTyopKRGllHTo0MEmvnr1agEgTz/9dJ32s3fvXomNjRV/f3+bqRq/++47mTBhgrRt21ZCQ0NlypQp8sMPPzidzjEnJ0diYmKkdevW0rNnT8nOzm7w6RlfeeUVASAffvihzXonT54UjUYjjz76qDVWXFwsv/vd7yQqKkr8/PwkMjJSRo8eLVlZWTbb5ufnS0JCggQEBEjnzp3lxRdflDfffNOt6Rlnz57t9PPUnqaw5ljYTxn54IMPOp3a0v54VFRUyJw5cyQyMlICAwNl+PDh8sUXX0hCQoIkVH8RS0tLJSoqSoYMGSLXr1+32d/jjz8u/v7+Nv8mADh9OMunrlxNz+jsGImInD9/XiZNmiQajUbCwsLkiSeekK+++sphekYRkVOnToler5cOHTpI69at5c4775SHHnpI/vu//7ve+da4lekZlTgZjEBAbGysHDx40NNpEBGRlzp+/Lh12r6GNmKEZenJFnUiahh1+V2hlDokIrH2cU7PSJ5jMlluu+fj45nb7xERERF5MfZRJ88wmWynNigqsjwHOCUkEbV4bEmn5u7ixYu4evWqy9d9fX09OojTW7BQJ8+40e33WKgTERE1a/bz3tvTarXWgbktGQt18gxvuf0eERERNTr7ee/tObuJUUvEQp08w1tuv0dERESNriHmvW8JOJiUPCMjw3K7vdo8cfs9IiIiIi/FQp08Q68HjEbLbfeUsiyNRvZPJyIiIqrGri/kOXo9C3MiIiIiF9iiTk0X52EnIiKiZowt6tQ0cR52IiIiaubYok5N043mYSciIiJqBlioU9PEediJqBkbMWIERowY4ek0mo3Lly8jJSUFHTt2hFIK6enp2LVrF5RS2NXIt4HduHEjlFK8mQ/VCQt1appczbfOediJiLxGRUWFtSj2pJdeegkmkwlPPfUUsrKyMHHiRI/m09wdOHAAf/jDH9CnTx8EBQUhOjoaU6dOxenTp+u8j8LCQiil6vRozthHnZqmjAzbPuoA52EnIvIyFRUVWLx4MQB49C8Eu3btwvDhw7Fw4UJrrKqqCuXl5WjdurXH8mquVqxYgc8++wxTpkxB//798eOPP+LPf/4z/uVf/gX79+9H7969b7qP8PBwZGVl2cTS0tKg0WiQ1oK6ubJQp6apZsBoWpqlu0t0tKVI50BSIiKyc+7cOfTv398m5uPjg4CAAA9l1Lw988wz+Pvf/25zEfTb3/4W/fr1w4oVK7Bx48ab7iMoKAjTpk2zia1atQpt27Z1iNcmIqioqEBgYGC98/cm7PpCTZdeDxQWAlVVliWLdCKiW3b48GEopbB9+3ZrLDc3F0opjBo1ymbdIUOGYNKkSU73U1hYiLCwMADA4sWLrd0U0tPTAQD5+flITk5G165dERAQgIiICMyYMQMXLlyw2U9ycjJ0Op3D/tPT02/a7aGmH3pBQQE++OADaw6FhYUOfdSPHz+OgIAAGGpmEKuWk5MDpRSWLVtmjX377bdISkpChw4d4O/vj/79++Ptt992eP+vv/4ao0aNQmBgIKKiorB06VJUVVXdMOfalFJITU3Fu+++i759+8Lf3x99+/bFP/7xD6fH4vTp05g6dSpCQkLQsWNHrFixAgBw8uRJJCYmWruhZGdn22x/8eJFPPvss+jXrx+Cg4MREhKC+++/H0eOHLFZLykpCUFBQTZdWKqqqhAfH4/IyEhcvHgRAHDPPfc4/KWie/fu6Nu3L44fP17nz18XOp0ODz30ED7++GMMGjQIAQEB2LRpk7XrjLOLgtrfwxp1PaeNjYU6ERGRFzGZTNi7dy92794NnU4HUyPfI2LAgAFo06YN8vLyrLG8vDz4+Phg3759uHbtGgDg559/xpdffom4uDin+wkPD8e6desAABMmTEBWVpZN//BPP/0UZ86cQUpKCtasWYOpU6finXfewdixYyEiDfJZevfujaysLLRv3x6DBw+25hAeHu503SVLluCNN97AJ598AgAoKyvDzJkzcffdd2PevHkAgOLiYgwbNgx5eXmYPXs2MjMz0alTJzzyyCM2ReGPP/6IkSNH4siRI1iwYAFSU1Pxt7/9DatXr3brM+zevRuzZs3CI488gpUrV6KiogKTJk1yuKABgMmTJ6NVq1ZYsWIF+vfvjwULFmDdunVITExETEwMVq5cidDQUCQnJ9sMZj1z5gzef/99jBs3Dn/6058wd+5cHD16FAkJCfjhhx+s67322mto27YtUlJSrBccmZmZ2LNnD4xGI9q1a+fyc4gIfvrpJ7Rv396tz18Xx44dw7Rp0zB27FisXr0avXr1cmv7up5TjxCRZv0AoAAsBPADgCsAvqjLdoMHDxYiIiJXjh071uD7zM7OFo1GIwCsD41GI9nZ2Q3+XjeSmJgow4cPtz4fPXq0TJ48WQDI3r17RUQkJydHAMiBAwdc7ufSpUsCQBYtWuTwmtlsdoi9/fbbAkByc3OtsenTp4tWq3VYd9GiRWIpY25Oq9XKgw8+aBPbuXOnAJCdO3daY9evX5dhw4ZJVFSUlJaWSkpKigQEBNic6xkzZkhUVJRcunTJZn9jxoyRyMhIqaysFBGR1NRUUUrJoUOHrOucO3dOQkNDBYAUFBTcNG8A4u/vL2fOnLHGjhw5IgBkzZo11ljNsXjyySetsfLycgkLCxOllKxfv94a/+abbwSALFmyxBqrqKiw5l2joKBA/P39bdYTEfnoo48EgKxatUpOnDghgYGBkpSUdNPPkpWVJQBk48aNN13XlQEDBkhCQoJNTKvVCgDZsWOHQ/4AZMOGDQ77sf9O1vWc1lddflcAOChO6tGW0KL+FIAEAEMAhAL4D8+mQ0RE5FxaWhrMdveIMJvNjT54Li4uDgcOHEBFRQWqqqrwxRdfYPLkyejRowf27NkDwNLKHhwcjIEDB9brPWr3Ia6oqEBJSQmGDRsGwNL9xhN8fX2xceNGXLhwAYmJidiwYQOWLFliHfwoInjvvffwwAMP4Pr16ygpKbE+xowZg+LiYpw8eRIAsH37dgwfPhyDBg2y7j88PBx6N7tpjh49Gl26dLE+79+/P0JCQnDmzBmHdWfOnGn9OSAgAAMGDICvry+SkpKs8Z49e6Jt27YoKCiwxvz9/eHjYykJKysrceHCBQQHB6Nnz54O52Ls2LFISUnBwoULMWXKFLRr1+6mfyX45ptv8Ic//AFxcXF49NFH3fr8ddG9e3eHbll15c459YRmPZhUKeUL4DkA94jI99XhQx5MiYiIyKWzLu4F4Sp+u8THx+Pq1avYv38/2rRpg8uXLyM+Ph5xcXHIy8vDnDlzkJeXh6FDh6JVq1a4ePEirl69at0+MDAQoaGhN3yPixcvYvHixXjnnXdw7tw5m9fKysrczrk+OTjTs2dPpKWlYeHChRgyZAjmzJljfe38+fMoLS3F2rVrsXbtWqfbnz9/Hr169UJRURGGDx/udP+1lZWVoby83Pq8devWNl1Iop1MOxwWFoZLly45xO3XDQ0NRUREBPz8/BzitbevqqrC6tWrsXbtWhQUFKCystL62h133OHwPq+++io+/PBD5OfnY9u2bWjbtq3DOjV+/PFH/L//9/8QFhaGzZs3Wy8IGlLtCxl3uXNOPcGrCnWlVCSA2QCGAogFEAxgpIjscrKuP4AlAB4FEAbgCIA0EdlRa7U7AQQA+Hel1GwAFwCki8h/3c7PQUREVB/R0dEoKipyGm9MQ4cOhZ+fH/Ly8hASEoKuXbuiU6dOiI+Px9y5c3H16lXs27cP8+fPBwBMnDgRu3fvtm4/ffr0m/btffjhh/H5559j7ty5GDhwIIKDg1FVVYUxY8bYDLh0NWC0djFZ3xycERHk5OQAAL777juUlZVZB8XW5JWcnOyyZTwmJsat95s9ezbeeust6/OEhASbeed9fX1d5mnP2bp12f6ll17CH//4R8yYMQMvvvgi2rVrBx8fH6Smpjod/Hrw4EHrwNGvvvoK48aNc/oeZWVluP/++1FWVobPPvsMERERTte7Vc5meKnr9+Z2nNOG5FWFOoCeAOYDOA0gH8A9N1h3I4BJADKr108G8LFSKkFEvqhepxOAtgC01Y8BAD5RSh0RkRMNnz4REVH9ZWRkwGAw2HR/0Wg0yGjke0QEBgZi0KBB1kI9Pj4egKVLTElJCbKzs1FeXm4dSPrKK6/YtNB26tQJgOti6dKlS9ixYwcWL16MF154wRo/deqUw7phYWEoLS11iNtf0LjKwV2vvfYacnNzsXz5cqSnp2PWrFnW+bzDw8PRpk0biAjuu+++G+5Hq9U6/TwnTtiWH/PmzbOZbrDmoqAxbdmyBSNHjsSbb75pEy8tLXUY/HnlyhXMmDEDgwcPRu/evZGeno4HHngAffr0sVmvoqIC48ePx8mTJ7Fjxw6HvyTcbjXH0f67Y/+9ceeceoK39VE/BKC9iHQH8LKrlZRSdwOYCmCeiMwTESOAUQDOAlhRa9WavyVliEiFiOwDkAPg325L9rfAZAJ0OsDHx7Js5EH+RETkBfR6PYxGI/z9/QFYij2j0eh2v+aGEB8fj88//xx5eXnWQr1bt26IiIjAihUr0KpVK2uf8sGDB+O+++6zPmqKtsDAQCilHIqlmlZe+1bhzMxMhzzuuusulJWVIT8/3xorLi7G1q1bbdZzlYM7Tp06heeffx56vR7z58/H0qVLkZ2djW3btlnznjBhAjZt2uRQcAOWLhI1xo4di88++8ymj/f58+cdZvHp06ePTd6DBw92O+9b5evr63AuNm/ejO+//95h3WeeeQY//fQTNm7ciDVr1iA8PBwpKSk2LdWVlZX47W9/iy+++AKbN2+2fk8aU0hICNq3b4/c3FybuH33FnfOqSd4VYu6iFyp46qTAVwDsL7WthVKqTcBZCilIkWkGMDJ6vW8mslke5PNoiLLc4BTgxMRtTR6vR5vvPEGANh0gWhscXFxWLVqFa5cuWIt1GviW7ZswZAhQxAUFHTDfbRu3Rr9+vXDpk2b0KNHD7Rr1w4xMTGIiYnBvffei5UrV+LatWvo3LkzcnJybAY41pg6dSrmz5+PCRMmYNasWTCbzXj99dfRo0ePBh10WlVVhZSUFISGhmLNmjUAgKeffhpbt27FE088gbi4OISFhWH58uXYuXMnYmNjYTAY0KtXL5SUlODAgQM4fPiwddrDefPmISsrC4mJiZg1axY0Gg2MRiO0Wq3NRYc3GDduHJYsWYKUlBTcc889OHr0KEwmE7p27Wqz3ieffIL169dj2bJl6Nu3LwBg/fr1GDNmDF5++WUsWLAAADBnzhx8+OGHGD9+PC5evGgzb3twcDAeeuihRvlcM2fOxPLlyzFz5kzExsYiNzfX6cDQup5Tj3A2FYw3PAA8BMvUVCOcvPYpgHwn8d9Ub3N/rdg7ANYCaA1gMIBLAHrd7P0bc3pGrVYEcHw4mY2KiIi8xO2YnrFGQkKCwzR0ja2kpESUUtKhQweb+OrVqwWAPP3003Xaz969eyU2Nlb8/f1tpsX77rvvZMKECdK2bVsJDQ2VKVOmyA8//OB0OsecnByJiYmR1q1bS8+ePSU7O7vBp2d85ZVXBIB8+OGHNuudPHlSNBqNPProo9ZYcXGx/O53v5OoqCjx8/OTyMhIGT16tGRlZdlsm5+fLwkJCRIQECCdO3eWF198Ud588023pmecPXu2088zffp06/OaY2E/veCDDz7odGpL++NRUVEhc+bMkcjISAkMDJThw4fLF198YfM9LC0tlaioKBkyZIhcv37dZn+PP/64+Pv7W/9NJCQk2EwxWvvhLJ+6cjU9o/25rWE2m+Wxxx6T0NBQadOmjTz88MNy7tw5p9+xup7T+riV6RmVOBmM4A2UUg8B2Aong0mVUl8B+F5ERtvF+wD4GsBMEXmzOnYHgA2wdI0phmXA6U0Hk8bGxsrBgwcb4JPcnI+PpTS3p5TlpptEROR9jh8/bp22r6GNGDECgGdb1ImoYdTld4VS6pCIxNrHvarrixsCAfziJF5R63UAgIhcAPBAXXaqlDIAMACNO8I+OtrS3cVZnIiIiIhapqZaqJcD8HcSD6j1utvEMijVCFha1OuXmvsyMmz7qAOARmOJExFRy8OWdGru7OePd+Z2TefYlDTVQr0YQKSTeE3sh0bM5ZbVDBhNSwPOnrW0pGdkcCApERERNU/288c7463dsxtTUy3U/wlgtlIqWER+rhUfWr080vgp3Rq9noU5ERERtQz288eTc021UN8C4FkAM2G54VHNnUpTAHwmIvVuUVdKjQcwvlu3bg2QJhERERHZ69OnT73mum9pvK5QV0otrP6xZnjso0qpOAClIvJnABCRfUqpzQBWKqUiAfwvgOmw3H00+VbeX0S2AdgWGxv7+K3sh4iIiIjoVnhdoQ7gRbvnM6qXRQD+XCueVL1uEoAwAPkAxorIZ7c9QyIiIiKi28zrCnURUXVcrwLA3OoHEREREVGz4uPpBIiIiIiIyBELdTtKqfFKKWNZWZmnUyEiIiKiFoyFuh0R2SYihtDQUE+nQkREREQtGAt1IiIib/M/IywPImrRWKgTERFRs3b58mWkpKSgY8eOUEohPT0du3btglIKu3btatRcNm7cCKUUCgsLG/V9qWlioU5ERES3RUVFhbUo9qSXXnoJJpMJTz31FLKysjBx4kSP5tPcHTx4EBMmTIBWq0VgYCAiIiIwZswYfP7553XeR2FhIZRSdXo0Z143PSMRERE1DxUVFVi8eDEAYMSIER7LY9euXRg+fDgWLlxojVVVVaG8vBytW7f2WF7N1f/+7//i+vXrePzxxxEZGYnS0lKYTCbce++9+Pjjj/Fv//ZvN91HeHg4srKybGJpaWnQaDRIS0u7Xal7HRbqdpRS4wGM79atm6dTISIiogZw7tw59O/f3ybm4+ODgIAAD2XUvP32t7/Fb3/7W5vY73//e3Tt2hWrV6+uU6EeFBSEadOm2cRWrVqFtm3bOsRrExFUVFQgMDCwfsl7GXZ9scNZX4iIqCU7fPgwlFLYvn27NZabmwulFEaNGmWz7pAhQzBp0iSn+yksLERYWBgAYPHixdZuCunp6QCA/Px8JCcno2vXrggICEBERARmzJiBCxcu2OwnOTkZOp3OYf/p6ek37fZQ0w+9oKAAH3zwgTWHwsJChz7qx48fR0BAAAwGg80+cnJyoJTCsmXLrLFvv/0WSUlJ6NChA/z9/dG/f3+8/fbbDu//9ddfY9SoUQgMDERUVBSWLl2KqqqqG+Zcm1IKqampePfdd9G3b1/4+/ujb9+++Mc//uH0WJw+fRpTp05FSEgIOnbsiBUrVgAATp48icTERAQFBSE6OhrZ2dk221+8eBHPPvss+vXrh+DgYISEhOD+++/HkSNHbNZLSkpCUFAQTp8+bY1VVVUhPj4ekZGRuHjxosvPotFoEB4ejtLS0jp//rrQ6XR46KGH8PHHH2PQoEEICAjApk2brF1nNm7c6LBN7e9hjbqe08bGFnUiIiJvUmACSvYCVb8A7+uAARlAF32jvf2AAQPQpk0b5OXlYezYsQCAvLw8+Pj4YN++fbh27Rr8/Pzw888/48svv8QjjzzidD/h4eFYt24dnnjiCUyYMMHaL7ymZfvTTz/FmTNnkJKSgoiICHz99dcwGo34+uuvsXfv3gbpe9y7d29kZWXh6aefhlarRWpqqjU3+8GcvXv3xpIlSzB//nxMmjQJo0ePRllZGWbOnIm7774b8+bNAwAUFxdj2LBhaN26NWbPno127drhgw8+wCOPPIJffvkFycnJAIAff/wRI0eORGVlJRYsWICgoCAYjUa3W3p3796NzZs348knn0RwcDBee+01TJo0CWfPnsUdd9xhs+7kyZMRExODFStW4L333sOCBQvQtm1bLFu2DBMnTsSDDz6Iv/71r0hOTkZcXJz1AujMmTN4//33MWXKFHTp0gU//fQT1q1bh4SEBBw7dgydOnUCALz22mvYsWMHUlJSsHv3bvj4+CAzMxN79uzBhx9+iHbt2tnkc+XKFfzyyy+4cOEC3nrrLXz11Vd44YUX3Pr8dXHs2DFMmzYNv//972EwGNCrVy+3tq/rOfUIEeHDyWPw4MHiLbKzRbRaEaUsy+xsT2dERETHjh1r+J2eyRZ5RyNiwq+PdzSWeCNKTEyU4cOHW5+PHj1aJk+eLABk7969IiKSk5MjAOTAgQMu93Pp0iUBIIsWLXJ4zWw2O8TefvttASC5ubnW2PTp00Wr1Tqsu2jRIrGUMTen1WrlwQcftInt3LlTAMjOnTutsevXr8uwYcMkKipKSktLJSUlRQICAmzO9YwZMyQqKkouXbpks78xY8ZIZGSkVFZWiohIamqqKKXk0KFD1nXOnTsnoaGhAkAKCgpumjcA8ff3lzNnzlhjR44cEQCyZs0aa6zmWDz55JPWWHl5uYSFhYlSStavX2+Nf/PNNwJAlixZYo1VVFRY865RUFAg/v7+NuuJiHz00UcCQFatWiUnTpyQwMBASUpKcpr/pEmTBIAAkNatW8vvfvc7qaiouOnndmXAgAGSkJBgE9NqtQJAduzY4ZA/ANmwYYPDfuy/k3U9p/VVl98VAA6Kk3qUXV+8nMkEGAxAUREgYlkaDJY4ERE1M0fSgEqzbazSbIk3ori4OBw4cAAVFRWoqqrCF198gcmTJ6NHjx7Ys2cPAEsre3BwMAYOHFiv96jdslxRUYGSkhIMGzYMgKX7jSf4+vpi48aNuHDhAhITE7FhwwYsWbIEvXv3BmBp3HzvvffwwAMP4Pr16ygpKbE+xowZg+LiYpw8eRIAsH37dgwfPhyDBg2y7j88PBx6vXt/HRk9ejS6dOlifd6/f3+EhITgzJkzDuvOnDnT+nNAQAAGDBgAX19fJCUlWeM9e/ZE27ZtUVBQYI35+/vDx8dSElZWVuLChQsIDg5Gz549Hc7F2LFjkZKSgoULF2LKlClo164dVq9e7TT3RYsWIScnB//5n/+J4cOH45dffsG1a9fc+vx10b17d4duWXXlzjn1BBbqXi4tDTDb/c42my1xIiJqZsxn3YvfJvHx8bh69Sr279+PI0eO4PLly4iPj0dcXBzy8vIAWAr1oUOHolWrVrh48SJ+/PFH66OsrOym73Hx4kXMnj0bHTt2RGBgIMLDw60FaV22d7Y/d3NwpmfPnkhLS8P+/fsxZMgQzJkzx/ra+fPnUVpairVr1yI8PNzmUdOt5vz58wCAoqIidO/e3en+aysrK7PJ276fd3R0tMM+wsLCcOnSJYe4/bqhoaGIiIiAn5+fQ7z29lVVVXj11VfRvXt3+Pv7o3379ggPD0d+fr7T4/jqq68iKCgI+fn5+Otf/4q2bds6rAMA/fr1w7/9278hJSUFn3zyCQ4dOnRbupHUvpBxlzvn1BPYR93LnXXxu9lVnIiImjBNNGAuch5vREOHDoWfnx/y8vIQEhKCrl27olOnToiPj8fcuXNx9epV7Nu3D/PnzwcATJw4Ebt377ZuP336dKeD+Gp7+OGH8fnnn2Pu3LkYOHAggoODUVVVhTFjxtgMuHTVV72ystLmeX1ycEZEkJOTAwD47rvvUFZWZh0UW5NXcnKyy5bxmJgYt95v9uzZeOutt6zPExISbOad9/X1dZmnPWfr1mX7l156CX/84x8xY8YMvPjii2jXrh18fHyQmprqdPDrwYMHrRcUX331FcaNG+f8w9Xi5+eHBx98EEuXLkV5eXmDzsribF91/d7cjnPakFio2/G26Rmjoy3dXZzFiYiomRmQAew32HZ/8dVY4o0oMDAQgwYNshbq8fHxACxdYkpKSpCdnY3y8nLExcUBAF555RWbFtqawYeuiqVLly5hx44dWLx4sc3gwlOnTjmsGxYW5nSmkCK7/xxd5eCu1157Dbm5uVi+fDnS09Mxa9Ys63ze4eHhaNOmDUQE99133w33o9VqnX6eEydO2DyfN2+ezXSDNRcFjWnLli0YOXIk3nzzTZt4aWkp2rdvbxO7cuUKZsyYgcGDB6N3795IT0/HAw88gD59+tz0fcrLyyEiuHLlym2fPrHmONp/d+y/N+6cU09g1xc74mXTM2ZkABqNbUyjscSJiKiZ6aIH7jYCPv6W5xqt5XkjzvpSIz4+Hp9//jny8vKshXq3bt0QERGBFStWoFWrVtY+5YMHD8Z9991nfdQUbYGBgVBKORRLNa289q3CmZmZDnncddddKCsrQ35+vjVWXFyMrVu32qznKgd3nDp1Cs8//zz0ej3mz5+PpUuXIjs7G9u2bbPmPWHCBGzatMmh4AZsu0iMHTsWn332mU0f7/Pnz8NkN8isT58+NnkPHjzY7bxvla+vr8O52Lx5M77//nuHdZ955hn89NNP2LhxI9asWYPw8HCkpKTYtFQ76ypy+fJlbN68GXfeeSc6dOjQ8B/CTkhICNq3b4/c3Fyb+Nq1a22eu3NOPYEt6l6u5q8waWmW7i7R0ZYi3c2xKERE1FR00QP/+4bl5/t2eSyNuLg4rFq1CleuXLEW6jXxLVu2YMiQIQgKCrrhPlq3bo1+/fph06ZN6NGjB9q1a4eYmBjExMTg3nvvxcqVK3Ht2jV07twZOTk5NgMca0ydOhXz58/HhAkTMGvWLJjNZrz++uvo0aNHgw46raqqQkpKCkJDQ7FmzRoAwNNPP42tW7fiiSeeQFxcHMLCwrB8+XLs3LkTsbGx1qkAS0pKcODAARw+fNg67eO8efOQlZWFxMREzJo1CxqNBkajEVqt1uaiwxuMGzcOS5YsQUpKCu655x4cPXoUJpMJXbt2tVnvk08+wfr167Fs2TL07dsXALB+/XqMGTMGL7/8MhYsWADAcsOjgIAA3HPPPYiIiMC3336LDRs24LvvvsM777zTaJ9r5syZWL58OWbOnInY2Fjk5uY6HRha13PqEc6mguHDu6ZnJCIi73Nbpmes8WmC5eFBJSUlopSSDh062MRXr14tAOTpp5+u03727t0rsbGx4u/vbzMt3nfffScTJkyQtm3bSmhoqEyZMkV++OEHp9M55uTkSExMjLRu3Vp69uwp2dnZDT494yuvvCIA5MMPP7RZ7+TJk6LRaOTRRx+1xoqLi+V3v/udREVFiZ+fn0RGRsro0aMlKyvLZtv8/HxJSEiQgIAA6dy5s7z44ovy5ptvujU94+zZs51+nunTp1uf1xwL++kFH3zwQadTW9ofj4qKCpkzZ45ERkZKYGCgDB8+XL744gtJSEiwTodYWloqUVFRMmTIELl+/brN/h5//HHx9/e3/pt48803JSEhQcLDw6VVq1bSvn17GTdunOzateumn/lGXE3PaH9ua5jNZnnsscckNDRU2rRpIw8//LCcO3fO6Xesrue0Pm5lekYlTgYjEBAbGysHDx70dBpEROSljh8/bp22r8H9zwjL0oMt6kTUMOryu0IpdUhEYu3j7KPehJlMgE4H+PhYlpxbnYiIiKj5YB/1JqrmRkg1c6zX3AgJYP91csFk4mAHoqaCLenUzJWVlaG8vPyG60RERDRSNt6Lhbodb5ue0ZUb3QiJtRc54JUdERF5Efv5451h92ywj7or3t5H3ccHcHbqlAKc3JuAWjqdzvmE/Fot4MnR7ERN2G3to07UzB07dgw//PDDDdfxxnnN6+NW+qizRb2J4o2QyC28xS0REXmRPn361Guu+5aGg0mbKN4Iidzi6gqOV3ZERERei4V6E6XXA0ajpeeCUpal0cjuxuQCr+yIiIiaHHZ9acL0ehbmVEe8xS0REVGTw0KdqKXglR0REVGTwq4vREREREReiIU6EREREZEXYqFORETkZUZUP6hhXL58GSkpKejYsSOUUkhPT8euXbuglMKuXbsaNZeNGzdCKYVC3sOC6oCFuh2l1HillLGsrMzTqRARETVpFRUV1qLYk1566SWYTCY89dRTyMrKwsSJEz2aT0uzcuVKKKUwcODAOm9TWFgIpVSdHs0ZB5PaEZFtALbFxsY+7ulciIiImrKKigosXrwYADBixAiP5bFr1y4MHz4cCxcutMaqqqpQXl6O1q1beyyvluDHH3/E0qVLERQU5NZ24eHhyMrKsomlpaVBo9EgLS2tIVP0aizUiYiIqFk7d+4c+vfvbxPz8fFBQECAhzJqORYsWIDY2FhUVVWhtLS0ztsFBQVh2rRpNrFVq1ahbdu2DvHaRAQVFRUIDAysb8pehV1fiIiIyOrw4cNQSmH79u3WWG5uLpRSGDVqlM26Q4YMwaRJk5zup7CwEGFhYQCAxYsXW7sppKenAwDy8/ORnJyMrl27IiAgABEREZgxYwYuXLhgs5/k5GTodDqH/aenp9+020NNP/SCggJ88MEH1hwKCwsd+qgfP34cAQEBMBgMNvvIycmBUgrLli2zxr799lskJSWhQ4cO8Pf3R//+/fH22287vP/XX3+NUaNGITAwEFFRUVi6dCmqqqpumHNtSimkpqbi3XffRd++feHv74++ffviH//4h9Njcfr0aUydOhUhISHo2LEjVqxYAQA4efIkEhMTERQUhOjoaGRnZ9tsf/HiRTz77LPo168fgoODERISgvvvvx9HjhyxWS8pKQlBQUE4ffq0NVZVVYX4+HhERkbi4sWLNuvv378f2dnZ+NOf/lTnz+wunU6Hhx56CB9//DEGDRqEgIAAbNq0ydp1ZuPGjQ7b1P4e1qjrOW1sbFEnIiLyIiYAewH8AkAHIANAY94BYcCAAWjTpg3y8vIwduxYAEBeXh58fHywb98+XLt2DX5+fvj555/x5Zdf4pFHHnG6n/DwcKxbtw5PPPEEJkyYYO0XXtOy/emnn+LMmTNISUlBREQEvv76axiNRnz99dfYu3dvg/Q97t27N7KysvD0009Dq9UiNTXVmpv9YM7evXtjyZIlmD9/PiZNmoTRo0ejrKwMM2fOxN1334158+YBAIqLizFs2DC0bt0as2fPRrt27fDBBx/gkUcewS+//ILk5GQAli4fI0eORGVlJRYsWICgoCAYjUa3W3p3796NzZs348knn0RwcDBee+01TJo0CWfPnsUdd9xhs+7kyZMRExODFStW4L333sOCBQvQtm1bLFu2DBMnTsSDDz6Iv/71r0hOTkZcXJz1AujMmTN4//33MWXKFHTp0gU//fQT1q1bh4SEBBw7dgydOnUCALz22mvYsWMHUlJSsHv3bvj4+CAzMxN79uzBhx9+iHbt2llzERE89dRTmD59ult90+vj2LFjmDZtGn7/+9/DYDCgV69ebm1f13PqESLCh5PH4MGDpbnJzhbRakWUsiyzsz2dERFR03Xs2LEG32e2iGjE9j8kTXW8MSUmJsrw4cOtz0ePHi2TJ08WALJ3714REcnJyREAcuDAAZf7uXTpkgCQRYsWObxmNpsdYm+//bYAkNzcXGts+vTpotVqHdZdtGiRWMqYm9NqtfLggw/axHbu3CkAZOfOndbY9evXZdiwYRIVFSWlpaWSkpIiAQEBNud6xowZEhUVJZcuXbLZ35gxYyQyMlIqKytFRCQ1NVWUUnLo0CHrOufOnZPQ0FABIAUFBTfNG4D4+/vLmTNnrLEjR44IAFmzZo01VnMsnnzySWusvLxcwsLCRCkl69evt8a/+eYbASBLliyxxioqKqx51ygoKBB/f3+b9UREPvroIwEgq1atkhMnTkhgYKAkJSU55L5x40YJDg6WH374QUREEhISZMCAATf9zDcyYMAASUhIsIlptVoBIDt27HDIH4Bs2LDBYT/238m6ntP6qsvvCgAHxUk9yq4vLYTJBBgMQFERIGJZGgyWOBEReYc0AGa7mLk63pji4uJw4MABVFRUoKqqCl988QUmT56MHj16YM+ePQAsrezBwcH1bi2t3bJcUVGBkpISDBs2DICl+40n+Pr6YuPGjbhw4QISExOxYcMGLFmyBL179wZgadx877338MADD+D69esoKSmxPsaMGYPi4mKcPHkSALB9+3YMHz4cgwYNsu4/PDwcejfvED169Gh06dLF+rx///4ICQnBmTNnHNadOXOm9eeAgAAMGDAAvr6+SEpKssZ79uyJtm3boqCgwBrz9/eHj4+lJKysrMSFCxcQHByMnj17OpyLsWPHIiUlBQsXLsSUKVPQrl07rF692madK1euYMGCBViwYAEiIyPd+rz10b17d4duWXXlzjn1BBbqLURaGmC2++1vNlviRETkHc66Gb9d4uPjcfXqVezfvx9HjhzB5cuXER8fj7i4OOTl5QGwFOpDhw5Fq1atcPHiRfz444/WR12mOL548SJmz56Njh07IjAwEOHh4daCtD5TJNcnB2d69uyJtLQ07N+/H0OGDMGcOXOsr50/fx6lpaVYu3YtwsPDbR413WrOnz8PACgqKkL37t2d7r+2srIym7zt+3lHR0c77CMsLAyXLl1yiNuvGxoaioiICPj5+TnEa29fVVWFV199Fd27d4e/vz/at2+P8PBw5OfnOz2Or776KoKCgpCfn4+//vWvaNu2rc3rS5cuRevWrfHMM884bHs71L6QcZc759QT2Ee9hTjr4re8qzgRETW+aABFLuKNaejQofDz80NeXh5CQkLQtWtXdOrUCfHx8Zg7dy6uXr2Kffv2Yf78+QCAiRMnYvfu3dbtp0+f7nQQX20PP/wwPv/8c8ydOxcDBw5EcHAwqqqqMGbMGJsBl676qldWVto8r08OzogIcnJyAADfffcdysrKrINia/JKTk522TIeExPj1vvNnj0bb731lvV5QkKCzbzzvr6+LvO052zdumz/0ksv4Y9//CNmzJiBF198Ee3atYOPjw9SU1OdDn49ePCg9YLiq6++wrhx46yvFRcXIzMzEy+++CJ++ukna7yiogJXr15FYWEhQkNDrce0ITjr91/X783tOKcNiYV6CxEdbenu4ixORETeIQOAAbbdXzTV8cYUGBiIQYMGWQv1+Ph4AJYuMSUlJcjOzkZ5eTni4uIAAK+88opNC23N4ENXxdKlS5ewY8cOLF68GC+88II1furUKYd1w8LCnE7rV2T3n5qrHNz12muvITc3F8uXL0d6ejpmzZplnc87PDwcbdq0gYjgvvvuu+F+tFqt089z4sQJm+fz5s2zmW6wIQvYutqyZQtGjhyJN9980yZeWlqK9u3b28SuXLmCGTNmYPDgwejduzfS09PxwAMPoE+fPgCAn376CVevXsX8+fOtF3K1denSBfPnz8fy5ctv3wfCr8fR/rtj/71x55x6Agv1FiIjw9InvXb3F43GEiciIu9Q0573GCyzvmjR+LO+1IiPj8e6desQFBSEpUuXAgC6deuGiIgIrFixAq1atbL2KR88eLDTfQQGBkIp5VAs1bTy2rcKZ2ZmOuzjrrvuQllZGfLz860zxhQXF2Pr1q0267nKwR2nTp3C888/D71ej/nz56NVq1Z49tln8fDDD2P8+PHw9fXFhAkTsGnTJjz33HMO3VjOnz+P8PBwAJa+3KtXr8bhw4et/dTPnz8Pk93gsD59+liLXE/x9fV1OBebN2/G999/j27dutnEn3nmGfz000/Yvn07oqKisHPnTqSkpODzzz+Hr68vunTp4nBuAGDhwoX4v//7P7z66qvo0aPHbf08ABASEoL27dsjNzfX2oUFANauXWuznjvn1BNYqLcQNX/NSUuzdHeJjrYU6W6OaSEiottMD+CN6p93eTCPuLg4rFq1CleuXLG2qNfEt2zZgiFDhtz0bpOtW7dGv379sGnTJvTo0QPt2rVDTEwMYmJicO+992LlypW4du0aOnfujJycHJsBjjWmTp2K+fPnY8KECZg1axbMZjNef/119OjRo0EHnVZVVSElJQWhoaFYs2YNAODpp5/G1q1b8cQTTyAuLg5hYWFYvnw5du7cidjYWOtUgCUlJThw4AAOHz5snfZx3rx5yMrKQmJiImbNmgWNRgOj0QitVov8/PwGy7shjBs3DkuWLEFKSgruueceHD16FCaTCV27drVZ75NPPsH69euxbNky9O3bFwCwfv16jBkzBi+//DIWLFiA0NBQPPTQQw7vkZmZiVatWjl97XaZOXMmli9fjpkzZyI2Nha5ublOB4bW9Zx6AgeT2lFKjVdKGes7CMWb6fVAYSFQVWVZskgnIiJX4uLioJRChw4dbFpAa3eDqQuj0YioqCg888wz+Pd//3ds2bIFAPD3v/8do0ePxl/+8hc899xz8PPzw8cff+yw/R133IGtW7dCo9Fg3rx5eOutt7Bs2TKMHz++AT7lrzIzM/HZZ59h3bp11m4TPj4+2LBhA8rKyjB79mwAQGRkJPbv349p06bhv/7rv/CHP/wBa9asgdlstv7loWa9nTt3IiYmBsuWLUNmZiaSkpKs+/Emzz//PObMmYNPPvkEs2fPxuHDh/HRRx/hzjvvtK5TM6f8kCFDMHfuXGt89OjRePzxx5Geno7jx497In2XXnjhBTz22GPYsmUL5s2bh8rKSqffsbqeU09QzgYjEBAbGysHDx70dBpEROSljh8/bp22r6GNqF7uui17J6LGVJffFUqpQyISax9nizoRERERkRdiH3UiIiIvs8vTCRDdZmVlZSgvL7/hOhEREY2UjfdioU5EREREjcp+/nhn2D2bhToRERERNTL7+ePJORbqRERERNSovGH++KaAg0mJiIiIiLwQC3VyyWQCdDrAx8eytLuZGhERERHdRuz6Qk6ZTIDBAJjNludFRZbnAG+URERERNQY2KJOTqWl/Vqk1zCbLXEiIiIiuv1YqJNTZ8+6FyciIiKihsVCnZyKjnYvTkREREQNi4U6OZWRAWg0tjGNxhInIqLba8TGERixcYSn0yAiD2OhTk7p9YDRCGi1gFKWpdHIgaRERNT0XL58GSkpKejYsSOUUkhPT8euXbuglMKuXbsaNZeNGzdCKYXCwsJGfV9qmliok0t6PVBYCFRVWZYs0omIyB0VFRXWotiTXnrpJZhMJjz11FPIysrCxIkTPZpPc1dzEeTs8c0339RpH4WFhS73Yf9ozjg9IxEREd0WFRUVWLx4MQBgxIgRHstj165dGD58OBYuXGiNVVVVoby8HK1bt/ZYXs1damoqBg8ebBPr1KlTnbYNDw9HVlaWTSwtLQ0ajQZpLWgKOhbqdpRS4wGM79atm6dTISIiogZw7tw59O/f3ybm4+ODgIAAD2XUMiQkJOChhx6q17ZBQUGYNm2aTWzVqlVo27atQ7w2EUFFRQUCAwPr9b7ehl1f7IjINhExhIaGejoVIiKiRnf48GEopbB9+3ZrLDc3F0opjBo1ymbdIUOGYNKkSU73U1hYiLCwMADA4sWLrd0U0tPTAQD5+flITk5G165dERAQgIiICMyYMQMXLlyw2U9ycjJ0Op3D/tPT02/a7aGmC0ZBQQE++OADaw6FhYUOfdSPHz+OgIAAGGru7lctJycHSiksW7bMGvv222+RlJSEDh06wN/fH/3798fbb7/t8P5ff/01Ro0ahcDAQERFRWHp0qWoqqq6Yc61KaWQmpqKd999F3379oW/vz/69u2Lf/zjH06PxenTpzF16lSEhISgY8eOWLFiBQDg5MmTSExMRFBQEKKjo5GdnW2z/cWLF/Hss8+iX79+CA4ORkhICO6//34cOXLEZr2kpCQEBQXh9OnT1lhVVRXi4+MRGRmJixcvOnyGK1eu4Pr163X+zO7S6XR46KGH8PHHH2PQoEEICAjApk2brF1nNm7c6LBN7e9hjbqe08bGQp2IiMiLmI6asPe7vdhdtBu6TB1MR02N+v4DBgxAmzZtkJeXZ43l5eXBx8cH+/btw7Vr1wAAP//8M7788kvExcU53U94eDjWrVsHAJgwYQKysrJs+od/+umnOHPmDFJSUrBmzRpMnToV77zzDsaOHQsRaZDP0rt3b2RlZaF9+/YYPHiwNYfw8HCn6y5ZsgRvvPEGPvnkEwBAWVkZZs6cibvvvhvz5s0DABQXF2PYsGHIy8vD7NmzkZmZiU6dOuGRRx6xKQp//PFHjBw5EkeOHMGCBQuQmpqKv/3tb1i9erVbn2H37t2YNWsWHnnkEaxcuRIVFRWYNGmSwwUNAEyePBmtWrXCihUr0L9/fyxYsADr1q1DYmIiYmJisHLlSoSGhiI5OdlmMOuZM2fw/vvvY9y4cfjTn/6EuXPn4ujRo0hISMAPP/xgXe+1115D27ZtkZKSYr3gyMzMxJ49e2A0GtGuXTubfB599FGEhIQgMDAQiYmJOHr0qFufva6OHTuGadOmYezYsVi9ejV69erl1vZ1PaceISJ8OHkMHjxYiIiIXDl27FiD7zM7P1s0GRpBOqwPTYZGsvOzG/y9biQxMVGGDx9ufT569GiZPHmyAJC9e/eKiEhOTo4AkAMHDrjcz6VLlwSALFq0yOE1s9nsEHv77bcFgOTm5lpj06dPF61W67DuokWLxFLG3JxWq5UHH3zQJrZz504BIDt37rTGrl+/LsOGDZOoqCgpLS2VlJQUCQgIsDnXM2bMkKioKLl06ZLN/saMGSORkZFSWVkpIiKpqamilJJDhw5Z1zl37pyEhoYKACkoKLhp3gDE399fzpw5Y40dOXJEAMiaNWussZpj8eSTT1pj5eXlEhYWJkopWb9+vTX+zTffCABZsmSJNVZRUWHNu0ZBQYH4+/vbrCci8tFHHwkAWbVqlZw4cUICAwMlKSnJZp3PPvtMJk+eLG+++aZ88MEH8uKLL0poaKiEhITIiRMnbvq5XRkwYIAkJCTYxLRarQCQHTt2OOQPQDZs2OCwH/vvZF3PaX3V5XcFgIPipB5lizoREZGXSNuRBvM1s03MfM2MtB2NO3guLi4OBw4cQEVFBaqqqvDFF19g8uTJ6NGjB/bs2QPA0soeHByMgQMH1us9avchrqioQElJCYYNGwbA0v3GE3x9fbFx40ZcuHABiYmJ2LBhA5YsWYLevXsDsDRuvvfee3jggQdw/fp1lJSUWB9jxoxBcXExTp48CQDYvn07hg8fjkGDBln3Hx4eDr2bU6iNHj0aXbp0sT7v378/QkJCcObMGYd1Z86caf05ICAAAwYMgK+vL5KSkqzxnj17om3btigoKLDG/P394eNjKQkrKytx4cIFBAcHo2fPng7nYuzYsUhJScHChQsxZcoUtGvXzuGvBPfccw82b96MGTNm4IEHHsDChQuxe/dumM1m6+DihtS9e3eHbll15c459QQOJiUiIvISZ8vOuhW/XeLj43H16lXs378fbdq0weXLlxEfH4+4uDjk5eVhzpw5yMvLw9ChQ9GqVStcvHgRV69etW4fGBiIm431unjxIhYvXox33nkH586ds3mtrKzM7Zzrk4MzPXv2RFpaGhYuXIghQ4Zgzpw51tfOnz+P0tJSrF27FmvXrnW6/fnz59GrVy8UFRVh+PDhTvdfW1lZGcrLy63PW7dubdOFJNrJLcHDwsJw6dIlh7j9uqGhoYiIiICfn59DvPb2VVVVWL16NdauXYuCggJUVlZaX7vjjjsc3ufVV1/Fhx9+iPz8fGzbtg1t27Z1WMfegAEDcN9992HHjh03XdddtS9k3OXOOfUEFupEREReIjo0GkVlRU7jjWno0KHw8/NDXl4eQkJC0LVrV3Tq1Anx8fGYO3curl69in379mH+/PkAgIkTJ2L37t3W7adPn37Tvr0PP/wwPv/8c8ydOxcDBw5EcHAwqqqqMGbMGJsBl64GjNYuJuubgzMigpycHADAd999h7KyMuug2Jq8kpOTXbaMx8TEuPV+s2fPxltvvWV9npCQYDPvvK+vr8s87Tlbty7bv/TSS/jjH/+IGTNm4MUXX0S7du3g4+OD1NRUp4NfDx48aB04+tVXX2HcuHHOP5ydO++887YU6s5meKnr9+Z2nNOGxEKdiMgZkwlISwPOngWio4GMDN71i267jN9kwLDNYNP9ReOnQcZvMho1j8DAQAwaNMhaqMfHxwOwdIkpKSlBdnY2ysvLrQNJX3nlFZsW2pq5sl0VS5cuXcKOHTuwePFivPDCC9b4qVOnHNYNCwtDaWmpQ7yoyPaCxlUO7nrttdeQm5uL5cuXIz09HbNmzbLO5x0eHo42bdpARHDffffdcD9ardbp5zlx4oTN83nz5tlMN1hzUdCYtmzZgpEjR+LNN9+0iZeWlqJ9+/Y2sStXrmDGjBkYPHgwevfujfT0dDzwwAPo06fPTd/nzJkzTgfy3g41x9H+u2P/vXHnnHoCC3UiInsmE2AwAObqYqmoyPIcYLFOt5W+n+X79dgHj+GXyl+gDdUi4zcZ1nhjio+Px7p16xAUFISlS5cCALp164aIiAisWLECrVq1svYpt7+pTY3AwEAopRyKpZpWXvtW4czMTId93HXXXSgrK0N+fr51LvTi4mJs3brVZj1XObjj1KlTeP7556HX6zF//ny0atUKzz77LB5++GGMHz8evr6+mDBhAjZt2oTnnnvOoRvL+fPnrYVozQwkhw8ftvZTP3/+PEwm21l8+vTpU6ci93by9fV1OBebN2/G999/D/v7yjzzzDP46aefsH37dkRFRWHnzp1ISUnB559/bj2vtY9DjT179mDnzp2YPn367f0w1UJCQtC+fXvk5uYiNTXVGrfv3uLOOfUEFupERPbS0n4t0muYzZY4C3W6zfT99Hjj0BsAgF3JuzyWR1xcHFatWoUrV65YW9Rr4lu2bMGQIUMQFBR0w320bt0a/fr1w6ZNm9CjRw+0a9cOMTExiImJwb333ouVK1fi2rVr6Ny5M3JycmwGONaYOnUq5s+fjwkTJmDWrFkwm814/fXX0aNHjwYddFpVVYWUlBSEhoZizZo1AICnn34aW7duxRNPPIG4uDiEhYVh+fLl2LlzJ2JjY2EwGNCrVy+UlJTgwIEDOHz4sHXaw3nz5iErKwuJiYmYNWsWNBoNjEYjtFot8vPzGyzvhjBu3DgsWbIEKSkpuOeee3D06FGYTCZ07drVZr1PPvkE69evx7Jly9C3b18AwPr16zFmzBi8/PLLWLBgAQDgt7/9LTQaDe655x60b98eX331FYxGI9q3b+8wf/ntNHPmTCxfvhwzZ85EbGwscnNznQ4Mres59QTO+kJEZO+si4F7ruJEzVBcXByUUujQoQN69OhhjdfuBlMXRqMRUVFReOaZZ/Dv//7v2LJlCwDg73//O0aPHo2//OUveO655+Dn54ePP/7YYfs77rgDW7duhUajwbx58/DWW29h2bJlGD9+fAN8yl9lZmbis88+w7p166zdJnx8fLBhwwaUlZVh9uzZAIDIyEjs378f06ZNw3/913/hD3/4A9asWQOz2Wz9y0PNejt37kRMTAyWLVuGzMxMJCUlWffjTZ5//nnMmTMHn3zyCWbPno3Dhw/jo48+wp133mldp2ZO+SFDhmDu3LnW+OjRo/H4448jPT0dx48fBwA89NBDOH/+PF555RX84Q9/wLvvvotHHnkEBw4ccDo49nZ54YUX8Nhjj2HLli2YN28eKisrnX7H6npOPUE5G4xAQGxsrBw8eNDTaRCRJ+h0lu4u9rRawIMtK+Rdjh8/bp22r6GN2DgCgGdb1ImoYdTld4VS6pCIxNrH2aJORGQvIwPQaGxjGo0lTkRE1EjYR52IyF5NP3TO+kIewpZ0au7s5493JiIiopGyubkff/zxhq/Xd97+m2GhTkTkjF7PwpyI6Daxnz/eGW/qnh0ZGXnD1+s7b//NsFAnIiIiokZlP3+8t/v0009v+Hp95+2/GRbqRERERNSovGH+eHd46mZIHExKREREROSFWKh7CdNRE3SZOvgs9oEuUwfTUdPNNyIiIo/ypj60ROR9bvV3BAt1L2A6aoJhmwFFZUUQCIrKimDYZmj2xbrJZJmu2sfHsjQ1749LRM1M69atbzprBRG1bOXl5fDz86v39izUvUDajjSYr9nertx8zYy0HWkeyuj2M5kAg8FyTxkRy9JgYLFORE1H+/bt8d133+HixYu4du0aW9eJyEpEYDab8f3336NDhw713k+LGEyqlNoFYBiA69WhPBG533MZ2Tpb5vy25K7izUFaGmC2vTaB2WyJc0Y8ImoKQkND4e/vj/Pnz+PChQu4fv36zTciohbDz88PHTt2REhISL330SIK9WrJIvKOp5NwJjo0GkVljrcrjw6N9kA2jeOsi2sQV3EiIm8UEBCAO++809NpEFEzxa4vXiDjNxnQ+Nnerlzjp0HGb5rv7cqjXVyDuIoTERERtTReV6grpSKVUsuVUjuVUleUUqKUGuFiXX+l1Aql1A9KqXKl1F6l1G9c7HqNUuq8UupTpVT/2/YB6kHfTw/jeCO0oVooKGhDtTCON0Lfr/n2AcnIADS21ybQaCxxIiIiIgKUtw1+qS7KdwI4DeAcgHsAjBSRXU7WfRvAJACZ1esnA4gFkCAiX9Ra724AxwBUAngKwCwAvUTkZ1d5xMbGysGDBxvgE5ErJpOlT/rZs5aW9IwM9k8nIiKilkcpdUhEYh3iXliotwHQWkQuKKUeArAVTgr16uJ7H4CnRSSzOhYA4CsAP4jIvTd4j28APCki/5+rdVioExEREVFjcFWoe13XFxG5IiIX6rDqZADXAKyvtW0FgDcBxCmlIm+wbdWtZUlEREREdHt5XaHuhn8B8I2T7iv7ASgAAwFAKdVWKfVv1f3ZWyulngYQBuBAo2ZLREREROSGpjw9YySA753Ei6uXnaqXfgCWAegF4CqALwHcLyJXbnuGRERERET11JQL9UAAvziJV9R6HSJyHpYBpjellDIAMABANOcJJCIiIiIPaspdX8oB+DuJB9R63S0iYhSRWBGJDQ8Pv6XkiIiIiIhuRVMu1Ith6f5iryb2QyPmQkRERETUoJpyof5PAL2UUsF28aHVyyONmw4RERERUcNpyoX6FlgGis6sCSil/AGkAPhMROrVoq6UGq+UMpaVlTVMlkRERERE9eCVhbpSaqFSaiGAKdWhR6tj/1GzjojsA7AZwEql1IrqgaD/HwAtgPn1fW8R2SYihtDQ0Fv4BNQYTCZApwN8fCxLk8nTGRERERE1HG+d9eVFu+czqpdFAP5cK55UvW4SLHOj5wMYKyKf3fYMyaNMJsBgAMxmy/OiIstzANDrPZcXERERUUPxyhZ1EVEuHjq79SpEZK6IRIpIgIjcLSL/46G0b4nJZIJOp4OPjw90Oh1MbB6+obS0X4v0GmazJU5ERETUHHhri3qLYjKZYDAYYK6uPIuKimCobh7Ws3nYqbNn3YsTERERNTVe2aLuSZ4YTJqWlmYt0muYzWaksXnYJVf3o+J9qoiIiKi5YKFuxxODSc+6aAZ2FScgIwPQaGxjGo0lTkRERNQcsFD3AtEumoFdxckyYNRoBLRaQCnL0mjkQFIiIiJqPlioe4GMjAxo7JqHNRoNMtg8fEN6PVBYCFRVWZYs0omIiKg5YaHuBfR6PYxGI7RaLZRS0Gq1MBqNHEhKRERE1IIpEfF0Dl4pNjZWDh486Ok0iIiIiKiZU0odEpFY+zhb1O14YtYXIiIiIiJ7N51HXSn1QkO8kYgsaYj93G4isg3AttjY2Mc9nQsRERERtVx1ueFRSgO8jwBoEoU6EREREZE3uGmhLiJdGiMRIiIiIiL6FfuoExERERF5IbcLdaXUKaXUn5VSdek2Q0RERERE9VCfFvW7APwewFallL/9i0qpvkqpabecGRERERFRC1bfri+vALgbwHalVJDdawMBvHUrSXkSp2ckIiIiIm9Q30L9nwASAPQE8KlSKrTBMvIwEdkmIobQ0GbzkYiIbj+TCdDpAB8fy9Jk8nRGRERNXr0Hk4rINwDiAUQA2KmUuqPBsiIioqbDZAIMBqCoCBCxLA0GFutERLfolmZ9EZECWIr1QAC5SqlODZIVERE1HWlpgNlsGzObLXEiIqq3W56eUUS+B3AvgKsA9gDoeqv7JCKiJuTsWffiRERUJ/Up1PsC2Fk7ICLnAYwA8BOA9FvOioiImo7oaPfiRERUJ24X6iJyXESKncTLANwH4EMA/9cAuRERUVOQkQFoNLYxjcYSJyKienP7pkVKqZ0AjgL4qmYpIlcAQET+D8CEBs2wkSmlxgMY361bN0+nQkTUNOj1lmVamqW7S3S0pUiviRMRUb0oEXFvA6VyAPQGUHvg6LewLd73i8jphkrSE2JjY+XgwYOeToOIiIiImjml1CERibWP16eP+nwACsAWAE8D+COA/wEQB2AegCwAJ5RS/6uUSlVK+dY/bQIAk8kEnU4HHx8f6HQ6mDjlGREREVGz53bXFwBrAXwkIk/UDiqlUgEsAfAAgEUAEgGsAjBOKXW/iFy7xVxbJJPJBIPBAHP11GdFRUUwGAwAAD3/rExERETUbNWnRX0AgP32QRH5WUSegaXrSz8RmQ7gfljuYDrvlrJswdLS0qxFeg2z2Yw0zk9MRERE1KzVp1A/A8vsLq58BEAPACLyKSxdYdj0W09nXcxD7CpORERERM1DfQr1TAC/VUotVEopJ6/HAGhT6/k+AF3q8T4EINrFPMSu4kRERETUPNRnHvX1sPRBTwfwv0qpDKXUb5VSU5RSqwE8CdsbIoUCKG+IZFuijIwMaOzmJ9ZoNMjg/MREREREzVp9BpNCRF5USn0MYAGA2QBqV5L/AGCo9XwKgOP1zrCFqxkwmpaWhrNnzyI6OhoZGRkcSEpERETUzLk9j7rDDpRqDeAuAIEAikTkgt1rowFcFJHPbumNGhnnUSciIiKixuBqHvV6tahX7/AuAL0AXAVwVEQcWs1F5CqAbfV9D0/gnUmJiIiIyBu43UddKRWilHoXwElYivBPAHyvlDqolJrS0Ak2NhHZJiKG0NBQT6dCRERERC1YfWd9uR+W/ulxsHRtear6tXeqB5RSAzIdNUGXqYPPYh/oMnUwHeWdSYmIiIiau/p0fXkQwKsi8nKt2KcA1iqlZgB4o7qfzd8aJMMWznTUBMM2A8zXqu9MWlYEw7bqO5P244BSIiIiouaqPi3qfgAKnL0gIv8Jyw2OnnL2OrkvbUeatUivYb5mRtqONJhMJuh0Ovj4+ECn08FkYks7ERERUXNRn0L9S9z4zqR5AHrXLx2yd7bM+R1Ii8qKYDAYUFRUBBFBUZHlOYt1IiIiouahPoX6KgAPK6Wed/F6DACzi9fITdGhzu9A6vuzL8xmu5Z2sxlpaWmNkRYRERER3Wb1uTPpNgDPA3hRKXVGKbVEKTWt+s6kmQD+AOCdBs6zxcr4TQY0fnZ3JvXToPKTSqfrnz3rvAWeiIiIiJqW+rSoQ0SWA/gNgNOwzP7yNwCbADwJYB2AeQ2VYEun76eHcbwR2lAtFBS0oVrL88tap+tHRztvgSciIiKipqXeNzwSkV0AdimlAgF0ByAA/ldE2O2lgen76R1neMkADAaDTfcXjUaDjIyMRs6OiIiIiG6Hm7aoK6WeUErdo5QKcfa6iJSLSL6IHGWR3nj0ej2MRiO0Wi2UUtBqtTAajdDrOWUjERERUXOgROTGKyhVBUtrOQB8B+ArAEdrLY+LyNXbmaQnxMbGysGDBz2dBhERERE1c9X3IIq1j9el68sdAPpVP2Kql08ACIWlgK9USp2GbfH+lYicbqDcG5VSajyA8d26dfN0KkRERETUgt20Rd3lhkrdiV8L95oivhcAfwAiIr4NlaQnsEWdiIiIiBrDrbSoOyUi3wL4FsDHtd7EF0APWIp2IiIiIiKqp3oX6s6ISCWA49UPIiIiIiKqp5sW6kqpFxrijURkSUPsh4iIiIioJahLi3pKA7yPAGChTkRERERURzct1EWkS2MkQkRE1KSYTEBaGnD2LBAdDWRkALyXBRE1oAbto05ERNQimEyAwQDU3B26qMjyHGCxTkQN5qZ3JiUiIiI7aWm/Fuk1zGZLnIiogbBQ9xYFJuB9HfB3H8uywOTpjIiIyJWzZ92LExHVAwt1b1BgAvYbAHMRALEs9xtYrBMReavoaPfiRET1wELdGxxJAyrt/oRaabbEG5DJZIJOp4OPjw90Oh1MJl4IEBHVS0YGoNHYxjQaS5yIqIGwUPcGZhd/KnUVrweTyQSDwYCioiKICIqKimAwGFisExHVh14PGI2AVgsoZVkajRxISkQNSomIp3PwSrGxsXLw4MHGebP3ddXdXuxotMBDhQ3yFjqdDkVFju+h1WpRWNgw70FERERE7lNKHRKRWPs4W9S9wYAMwNfuT6i+Gku8gZx1McDJVZyIiIiIPIuFujfoogfuNlpa0KEsy7uNlngDiXYxwMlVnIiIiIg8izc88hZd9A1amNvLyMiAwWCAuda8vxqNBhkc+ERERETkldiibkcpNV4pZSwrK/N0Kg1Kr9fDaDRCq9VCKQWtVguj0Qg9Bz4REREReSUOJnWhUQeTEhEREVGLxcGkRERERERNCAt1IiIiIiIvxEKdiIiIiMgLsVAnIiIiIvJCLNSJiIiIiLwQC3UiIiIiIi/EQp2IiIiIyAuxUCciIiIi8kIs1ImIiIiIvBALdXLJZDJBp9PBx8cHOp0OJpPJ0ynRLTCZAJ0O8PGxLHk6iYiIvFsrTydA3slkMsFgMMBsNgMAioqKYDAYAAB6vd6TqVE9mEyAwQBUn04UFVmeAwBPJxERkXdSIuLpHLxSbGysHDx40NNpeIxOp0NRUZFDXKvVorCwsPETolui01mKc3taLcDTSURE5FlKqUMiEmsfZ9cXcurs2bNuxcm7uTptPJ1ERETei4U6ORUdHe1WnLybq9PG00lEROS9WKiTUxkZGdBoNDYxjUaDjIwMD2VEtyIjA7A7ndBoLHEiIiLyTizUySm9Xg+j0QitVgulFLRaLYxGIweSNlF6PWA0WvqkK2VZGo0cSEpEROTNOJjUhZY+mJSIiIiIGgcHkxIRERERNSEs1ImIiIiIvFCLKdSVUv+qlKpSSi3wdC7OmADoYDkhuurnRERERNRytYg7kyqlfAC8CuCAp3NxxgTAAKD6ppEoqn4OABzrR0RERNQytZQWdQOAfQCOezoRZ9Lwa5Few1wdJyIiIqKWyasKdaVUpFJquVJqp1LqilJKlFIjXKzrr5RaoZT6QSlVrpTaq5T6jZP17gCQCmDRbU3+Fri6OSRvGklERETUcnlVoQ6gJ4D5AKIA5N9k3Y0AngaQDWA2gCoAHyul/tVuvQwAmSJS2qCZNiBXN4fkTSOJiIiIWi5vK9QPAWgvIt0BvOxqJaXU3QCmApgnIvNExAhgFCyN0CtqrfcvAIYAeOO2Zn2LMgDY3TQSmuo4EREREbVMXjWYVESu1HHVyQCuAVhfa9sKpdSbADKUUpEiUgwgAZZW+u+VUgAQCuC6UkonIr9r2Ozrr2bAaBosVxrRsBTpHEhKRERE1HJ5VaHuhn8B8I2I/GwX3w9AARgIoBiAEcA7tV5fDeAUbtBa7yl6sDAnIiIiol811UI9EsD3TuLF1ctOACAiZtSaUEUpVQ7gZxEpu+0ZEhERERHdgqZaqAcC+MVJvKLW6w5EJPlGO1VKGVA9hXl0NIdyEhEREZHneNtg0roqB+DvJB5Q63W3iYhRRGJFJDY8PLzeyRERERER3aqmWqgXw9L9xV5N7IdGzIWIiIiIqME11UL9nwB6KaWC7eJDq5dHGjcdIiIiIqKG1VQL9S0A/ADMrAkopfwBpAD4TETq3aKulBqvlDKWlXG8KRERERF5jtcNJlVKLaz+sXf18lGlVByAUhH5MwCIyD6l1GYAK5VSkQD+F8B0AFoAybfy/iKyDcC22NjYx29lP0REREREt8LrCnUAL9o9n1G9LALw51rxpOp1kwCEAcgHMFZEPrvtGRIRERER3WZeV6iLiKrjehUA5lY/iIiIiIialabaR52IiIhaCpMJ0OkAHx/L0mTydEZEjcLrWtQ9TSk1HsD4bt26eToVIiIiMpkAgwEwV99ovKjI8hwA9HrP5UXUCJSIeDoHrxQbGysHDx70dBpEREQtm05nKc7tabVAYWFjZ0N0WyilDolIrH2cXV+IiIjIe509616cqBlhoU5ERETeKzravThRM8JCnTzGZDJBp9PBx8cHOp0OJg4OIiIiexkZgEZjG9NoLHGiZo6FOnmEyWSCwWBAUVERRARFRUUwGAws1omIyJZeDxiNlj7pSlmWRiMHklKLwMGkdmrN+vL4qVOnPJ1Os6XT6VDkZHCQVqtFIQcHERERUQvCwaR1JCLbRMQQGhrq6VSatbMuBgG5ihMRERG1NCzUySOiXQwCchUnIiIiamlYqJNHZGRkQGM3OEij0SCDg4OIiIiIALBQJw/R6/UwGo3QarVQSkGr1cJoNELPwUFEREREADiY1CXemZSIiIiIGgMHk9aRUmq8UspYVlbm6VSIiIiIqAVjoW6Hs74QERERkTdgoU5ERERE5IVYqBMREREReSEW6kREREREXoiFOhERERGRF2KhTkRERETkhVioExERERF5IRbqdjiPOhERERF5AxbqdjiPOhERERF5Axbq1GSZTCbodDr4+PhAp9PBZDJ5OiUiIiKiBtPK0wkQ1YfJZILBYIDZbAYAFBUVwWAwAAD0er0nUyMiIiJqEGxRpyYpLS3NWqTXMJvNSEtL81BGRERERA2LhTo1SWfPnnUrTkRERNTUsFBvCgpMwPs64O8+lmUB+2JHR0e7FSciIiJqalioe7sCE7DfAJiLAIhlud/Q4ov1jIwMaDQam5hGo0FGRoaHMiIiIiJqWCzUvd2RNKDSti82Ks2WeAum1+thNBqh1WqhlIJWq4XRaORAUiIiImo2lIh4OgevFBsbKwcPHvR0GpbuLnB2jhTwSFVjZ0NEREREDUwpdUhEYu3jbFG343V3JtW46HPtKk5EREREzQILdTted2fSARmAr21fbPhqLHEiIiIiarZYqHu7LnrgbiOg0QJQluXdRkuciIiIiJot3pm0KeiiZ2FORERE1MKwRZ2IiIiIyAuxUG/CTEdN0GXq4LPYB7pMHUxHW/bc6kRERETNCbu+NFGmoyYYthlgvmaZY72orAiGbQYAgL4fu8kQERERNXVsUW+i0nakWYv0GuZrZqTtaNk3QiIiIiJqLlioN1Fny4rcihMRERFR08JCvYmK9vN1K05E7jGZAJ0O8PGxLE0cAkJERI2MhXoTldGuEhplG9MoS5yIbo3JBBgMQFERIGJZGgws1omIqHGxUG+i9BFaGDsA2laAgmVp7GCJE9GtSUsDzLZDQGA2W+JERESNhbO+2FFKjQcwvlu3bp5O5cYGZED/iwH6kFrVhK8GGJDhuZyImomzZ92LExER3Q5sUbcjIttExBAaGurpVG6six642whotACUZXm3kXcwJWoA0dHuxYmImg0O0PEqbFFvyrroWZgT3QYZGZY+6bW7v2g0ljgRUbNVM0Cn5pdfzQAdANCz3vAEtqgTEdnR6wGjEdBqAaUsS6OR/08RUTPHATpeR4mIp3PwSrGxsXLw4EFPp0FERETUOHx8LFNd2VMKqKpq/HxaEKXUIRGJtY+zRZ2IiIiIOEDHC7FQJyIiIiLLQByNxjbGAToexUKdiIiIiDhAxwtx1hciIiIistDrWZh7EbaoExERERF5IRbqREREREReiIU6EREREZEXYqFOREREROSFWKi3JAUm4H0d8Hcfy7LA5OmMiIiIiMgFzvrSUhSYgP0GoLL61sDmIstzAOjC0d1ERERE3oYt6i3FkbRfi/QalWZLnIiIiIi8Dgv1lsJ81r04EREREXkUC3U7SqnxSiljWVmZp1NpWJpo9+JERERE5FEs1O2IyDYRMYSGhno6lYY1IAPw1djGfDWWOBERERF5HRbqLUUXPXC3EdBoASjL8m4jB5ISEREReSnO+tKSdNGzMCciIiJqItiiTkRERETkhVioExERERF5IRbqREREREReiIU6EREREZEXYqFOREREROSFWKgTERERUctlMgE6HeDjY1maTJ7OyIrTMxIRERFRy2QyAQYDYDZbnhcVWZ4DgN7zU1qzRZ1cKzAB7+uAv/tYlgXec4VJREREdMvS0n4t0muYzZa4F2Ch3gSYAOhgOVm66ue3XYEJ2G8AzEUAxLLcb2CxTkRERM3H2bPuxRsZC3UvZwJgAFBdLqOo+vltL5ePpAGVdleYlWZLnIiIiKg5iI52L97IWKh7uTQAduUyzNXx28rs4krSVZyIiIioqcnIADQa25hGY4l7ARbqXs5VWXzby2WNiytJV3EiIiKipkavB4xGQKsFlLIsjUavGEgKsFD3eq7K4tteLg/IAHztrjB9NZY4ERERUXOh1wOFhUBVlWXpJUU6wELd62UAsCuXoamO31Zd9MDdRkCjBaAsy7uNljgRERER3XacR93L1ZTFabB0d4mGpUhvlHK5i56FOREREZGHsFBvAvRopMKciIiIiLwGu74QEREREXmhZl+oK6VeV0oVK6UuK6WOKqXGeTonIiIiIqKbafaFOoDVALqISAiAFADZSqkwD+dERERERHRDzb5QF5FvRKSiVsgfQKSn8iEiIiIiqguvKtSVUpFKqeVKqZ1KqStKKVFKjXCxrr9SaoVS6gelVLlSaq9S6jcu1l2rlCoHcADA/wA4fts+BBERERFRA/CqQh1ATwDzAUQByL/JuhsBPA0gG8BsAFUAPlZK/av9iiLyJIBgAP8G4H9ERBowZyIiIiKiBudthfohAO1FpDuAl12tpJS6G8BUAPNEZJ6IGAGMgmWq8RXOthGRShH5HwD3KaVGN3zqREREREQNx6sKdRG5IiIX6rDqZADXAKyvtW0FgDcBxCmlbtQHvRWAu24pUSIiIiKi28yrCnU3/AuAb0TkZ7v4fgAKwEAAUEoFK6WmVS9bKaUmARgJIK9RsyUiIiIiclNTvTNpJIDvncSLq5edqpcCYAaAP8NSwJ8G8O8icvS2Z0hEREREdAuaaqEeCOAXJ/GKWq9DRP4Plr7rdaKUMgAwAEB0dPQtpkhEREREVH9NtetLOSzzodsLqPW620TEKCKxIhIbHh5e7+SIiIiIiG5VUy3Ui+H8pkU1sR8aMRciohbPZAJ0OsDHx7I0mTydERFR09dUC/V/AuillAq2iw+tXh5p3HSoXgpMwPs64O8+lmUB/2e/nUwmE3Q6HXx8fKDT6WBiJUUNxGQCDAagqAgQsSwNBhbrRES3qqkW6lsA+AGYWRNQSvkDSAHwmYjUu0VdKTVeKWUsKyu79SzJtQITsN8AmIsAiGW538Bi/TYxmUwwGAwoKiqCiKCoqAgGg4HFOjWItDTAbLaNmc2WOBER1Z/ytpt0KqUWVv/YG8AjAP4TQAGAUhH5c631/gvAQwBeBfC/AKYDGAJgpIh8dqt5xMbGysGDB291N17FBCANlrtCRQPIAKD3VDLv66qLdDsaLfBQYWNn0+zpdDoUFTkeb61Wi8LCwsZPiJoVHx9LS7o9pYCqqsbPh4ioqVFKHRKRWPu4N8768qLd8xnVyyJYplmskVS9bhKAMAD5AMY2RJHeHJlgmc6mptGrqPo54KFi3XzWvTjdkrNnnR9XV3Eid0RHW7q7OIsTEVH9eV3XFxFRLh46u/UqRGSuiESKSICI3C0i/+OhtL1eGn4t0muYq+MeoXHxP7irON0SV9ONchpSaggZGYBGYxvTaCxxIiKqP68r1On2cNVu6rH21AEZgK/d/+y+GkucGlxGRgY0dpWURqNBBispagB6PWA0AlqtpbuLVmt5rvdY3zoiouaBhbqd5jqY1FW7qcfaU7vogbuNlj7pUJbl3UZLnBqcXq+H0WiEVquFUgparRZGoxF6VlLUQPR6oLDQ0ie9sJBFOhFRQ/C6waTeorkNJrXvow4AGgBGeHBAKRERERG5HEzKFvUmzARAB8tJ1FU/d0UPS1Fe3X4NLVikExEREXkzb5z1heqgPrO46G/wGhERERF5F7aoN1FeN4uLJ/DOpkRERNSMsUW9ifK6WVwaW82dTSurL1dq7mwKcEAqERERNQtsUbfTVGZ98bpZXBrbkbRfi/QalWZLnIiIiKgZYKFuR0S2iYghNDTU06ncUAYss7bUpqmOtwi8sykRERE1cyzUm6gWP4sL72xKREREzRwL9SZMD6AQQFX1ssUU6QDvbEpERETNHgt1app4Z1MiIiJq5jjrCzVdXfQszImIiKjZYou6naYy60t9mI6aoMvUwWexD3SZOpiOct5xIiIiIm/FQt1OU5n1xV2moyYYthlQVFYEgaCorAiGbQYW60REREReioV6C5G2Iw3ma7bzjpuvmZG2w/W84yYAOli+JLrq50REZGEyATod4ONjWZr4S5KIGhj7qLcQZ8uczy/uKm4CYABQU9oXVT8HWtjsMkRETphMgMEAmKt/SRYVWZ4DgJ6/JImogbBFvYWIDnU+v7ireBp+LdJrmKvjREQtXVrar0V6DbPZEiciaigs1FuIjN9kQONnO++4xk+DjN84n3fc1f09ed9PIiLgrItfhq7iRET1wUK9hdD308M43ghtqBYKCtpQLYzjjdD3c/43Wlf392zI+35yFhoiaqqiXfwydBUnIqoP9lFvQfT99C4Lc3sZAFKOmnBtRxpQdhYIjYbfbzKQUcftb8Z01IQZ2wy4Wj3AtaisCDO2Gax5EhF5s4wM2z7qAKDRWOJERA2FLep2mvM86m45aoLaZgDKigAIUFZked5Ard6zd6RZi/QaV6+ZMfsGs9DYe/KoCa0ydVCLfdAqU4cn2SJPDchkMkGn08HHxwc6nQ4mTulBtej1gNEIaLWAUpal0ciBpETUsJSIeDoHrxQbGysHDx70dBoeo8vUoaisyCGuDdWiMLXwlvevFvsAcPbdU5BFVTfd/smjJry+zQDULvb9NPj9eCPWskXeuQITcCQNMJ8FNNHAgAze2dUFk8kEg8EAc63mUo1GA6PRCD0rMSIiamBKqUMiEmsfZ4s6OeXudI5uczHbjMu4HeOONNsiHQCumS1xclRgAvYbAHP1X0jMRZbnBWwldiYtLc2mSAcAs9mMNE7pQUREjYiFOjnl7nSO7rrjNxmA3Sw08NNY4nVQ6eKCwVW8xTuShid9B6DVT52hTim0+qkznvQdYGlhJwdnz57Fv98DFGQCldmW5b/fY4kTUePjzaWopWKhTk65O52ju1b308NvvBEI1QJQQKgWfuONWF3Hbiu+Li4YXMVbuievd8LrJ/6JysvfAxBUXv4er5/4J5683snTqXml/xjfDkGz/hXdqjrD97RCt6rOCJr1r/iP8e08nZrXmrD5cbT6U5RlzMifojBh8+OeTomaiZqbSxUVASK/3lyKxTq1BCzUySl3p3N0e/8ANvTTQ5taCLWoCtrUQmzop6/zXU8NLlrkDQ10IdHcGL89C1wvtw1eL7fEyUH5tP5Yf9r2wmb96X+ifFp/T6fmlSZsfhzvnzSh8kr18bryPd4/aWr2xTovThpHWhrQae7j8H0lCkj3ge8rUeg093HeXOo24V8vvAsHk7rQ0geTNgVPHjXBuCMNlWVn4RsaDcNvMjiQ1IVbHbzb0rR6Naq6SLflG9IZ15/+zgMZebdWf4qqLtJt+bbpjOvPNM/jVXNxYnMB3CoQD/XQY+uUNzyXWDPUPf1xnPZzPNbdrulxKp3HuiGZTMDi04/jTJuPUXnlB/i26YSuV+7Hom5vNOsZjUa+8Tjyrvz6mePb3I+djzfud8vVYFLOo05N1tp+ehbmdeQbGo1KJ7P4sKuQc5WXf3Ar3tJVXnFxvFzEm4Nt337s9K9U27792DMJNWMFIR8DVxyPdUEIj3VDyyh4HKdamazHu/LK9zjVyoSMAkCP5nlRNPKNx7Hr3K8XgpVXvseuchNGvoFGL9adYdcXohaAXYXc4xsS5Va8pfNt43ysg6t4c9ASL048hce68ZzUOL8APalpvhdFeVecf+a8K97xmVmoE7UAa/vp8fvxRvhWD971DdVyzvkbMNy3zPmFzX3LPJOQlxt/5/1Aq0DbYKtAS7yZaokXJ57CY914WuJFkbd/ZhbqdnhnUmqu1vbT43pqIWRRFa6nFrJIvwFe2Lhn65Q38FAPPXzbdAag4Numc7Pvq90SL048hce68bTEiyJv/8wcTOoCB5MSEdGNTNj8OLZ9++sAtPF33t+sL048ice6cbTEQdL2fdQBAK0CMaKDvlH7qLsaTMpC3QUW6kRERNTStMSLIm+e9YWFugss1ImIiIioMbgq1NlHnYiIiIjIC7FQJyIiIiLyQizUiYiIiIi8EAt1IiIiIiIvxEKdiIiIiMgLsVAnIiIiIvJCLNSJiIiIiLwQC3UiIiIiIi/EQt2OUmq8UspYVlbm6VSIiIiIqAVjoW5HRLaJiCE0NNTTqRARERFRC8ZCnYiIiIjIC7FQJyIiIiLyQizUiYiIiIi8EAt1IiIiIiIvxEKdiIiIiMgLKRHxdA5eSSl1HkCRB966PYASD7xvU8Zj5h4eL/fweLmHx8s9PF7u4fFyD4+Xezx5vLQiEm4fZKHuZZRSB0Uk1tN5NCU8Zu7h8XIPj5d7eLzcw+PlHh4v9/B4uccbjxe7vhAREREReSEW6kREREREXoiFuvcxejqBJojHzD08Xu7h8XIPj5d7eLzcw+PlHh4v93jd8WIfdSIiIiIiL8QWdSIiIiIiL8RCnYiIiIjIC7FQbwRKKX+l1Aql1A9KqXKl1F6l1G/quG1npdR/KaVKlVKXlVLvK6W63O6cPUkpNUQp9Rel1DGl1P8ppc4qpd5RSnWrw7bpSilx8vixMXL3BKXUCBefWZRSveqwfYv6jimlNt7geIlSqvMNtm3W3y+lVKRSarlSaqdS6kr1ZxvhYt0HlFKHlVIV1f9GFymlWtXxfXyUUvOUUv9/e/ceLVdZ3nH8+0OICYFEk1JAhGqQGBAiqRQEoUShWrKQy6LIAkyNFaHgZVEFbUuRIGjthRqrKKx6oRGLQCgULGlssCkgtwUlhnCHEg0IKRdDgJAEk6d/vO/IPvvMObPP5AwzZ5/fZ61Zc847+9239czez7z73e9+LNdfJum44dyW10KV/SVpsqQzJd0k6en8PbtV0rEVl/GWQWL1DzuxXZ1SNb4krRhge79ScTm1iC+oHGODnQNC0lktllGLGBtK7iDpAEk3S1or6SlJX5O09RCW9TFJ9+f4ekjSJ4Z3a15V6aBqm+0S4BhgHvAIMAdYKOngiLh1oEqStgH+C9gW+BLwa+DPgCWS9o6IX3V2tbvm88B7gCuBZcAOwCeBuyXtGxH3V5jHKcDawv8vD/ta9p55wF2lsl8OVmGUxtjFwOJSmYCLgBUR8USFedQ1vt5O+v49QvruHdBsIkmHAdcAPwE+BewFfIH0sJBPVVjOl4A/J924dSdwJPBDSRsjYsHmbcJrqsr+2p+0vdcD55O+Y8cAV0j6QkScV3FZlwKLSmU/a2elu6hSfGV3kY5pRcsrLqcu8QXV9tn9wOwm5bOB9wM/rriskR5jlXIHSXsDNwD3Ap8B3gycAUwBPthqIZJOIZ0vrgT+ATgI+IaksRFxwTBvE0SEXx18AfsCAZxeKBtL+tLd2KLu54BNwIxC2TTSgf6L3d62Du6zA4AxpbLdgHXAJS3qzs37+w3d3o7XcH/NzNt8VBt1R2WMNdkPB+Z9+Jctpqt1fJF+sE3Ofx+Vt3Vmk+nuJSVSryuUnQ9sBHZrsYydgA3AvEKZgBuBFcAW3d4Pw7m/gLeSnjhYLBMpUVgLjGuxjLeUzyEj9TWE+FoBXNPmMmoTX0PZZwPUfRh4qMJ0tYixqrkD6Ufz48A2hbKT8j54X4tljCM9ufSaUvmlwBpg4nBvl7u+dN4fAa8A324URMQ64DvAgZJ2bFH3toi4u1D3AdIB/kOdWd3ui4hbImJDqexhUnKwe8XZSNIESRr2Fexhkrat2v0gG5Ux1sQJpIP0v1ScvpbxFREvRMSzg00jaQ9gD+DiiNhY+OibpO6Ux7RYzJHAVnn6xnID+BbwO6TGjRGhyv6KiMci4uelsiBdkRhHSpIqkTRe0pg2VrUnVNlfRUrdRit3R8hqE18w9H3WIGlf4G3AD4ZYb8TGWJXcQdIE4A+A+RHxYmHS+cCLtD7vvReYTCG+sgtJP6oOa3sDBuBEvfNmAA+UAgLgDtKv/L2bVZK0BTCddNmu7A5gahsHsBErJ0Tbk37JVvEL4HngeUnflTSpYyvXO75P+kX/sqQfS9prsIkdY4mkrUgH51siYkXFaqMxvhpm5Pc+cRMRvyS1Us3oV6N//TUR8VCp/I7S/Otuh/xe9Zh2HimRWJf7uP9+Z1arZ7wfeAl4SdKjkk6uWM/xlZyY34eSqNcuxprkDnuRun2Xj18bgKVUO35Rrk+6wripQv0hcx/1ztsRaNbn9cn8/qYB6k0CXl+YrlxXed6Pbu4KjhAnki5pDnpTDPAr4OvAbaTLn+8j9Sf+XUn7RcT6jq5ld2wAFgALSQej6aT+djdL+r0mJ6wGx1jyAVILSZUT2miMr7LGVcCB4magY1qxfrObb1sdE2sj/7A7CVgSEU+3mHwTqd/w1aR7TnYjfb8XSzokIm7q6Mp2xzLgJuAhYDvg48DFkiZFRKsbSh1f0uuA44A7IuKRClXqHGPl3KHV8Wv/FvPbEVgfEc8VCyNig6Rn6UB8OVHvvHFAs5P3usLnA9Wjzbq1ojRyyYXAzaRW4wFFxNdKRQskLc/1/xj4p46sZBdFxC3ALYWiayVdR/rFfw6vtqyUOcaSE0jd065oNeFojK8mWsVNq6sw7R4TayFfyfoBMBH4dKvpI+IXQJ+RNyT9ELgP+Arp5rlaiYgjiv9L+h7p+H+2pG9FxPODVB/V8ZUdQmpF/nKViesaYwPkDq2OX63iYxypkaaZKvWHzF1fOu9lUqtl2djC5wPVo826tSFpB+DfSS2Zx0bEpjZmcxHppq1KQ2LWQUT8jDSyyWDbPOpjLI96cySwqJ1+oNloi69WcdMqZto9JtbF10lXcT4aEfe0M4Pczegy4N2joXtavhdiHulHYKsWz9EeX5AaZzYCl7c7g5EeY4PkDp06flWtP2RO1DvvSV691FLUKBto+LznSL/4BqobNL90UxuSJpK6c0wEPhARbY1Vnb+gT5C6eowmKxl8m0d9jJFGUdiaId5wVTQK46sREwPFzaBDgub6OzQpb3VMHPEknQOcBnwuIi7bzNmtJJ3D37C56zVCrMzvrb5noza+ACSNA44GFkfEqs2c3YiMsRa5w3Acv8aU70vKN+BOrlB/yJyod95SYFpuuSvaL783HaM0n/zvAfZp8vF+wMMRsbbJZ7UgaSxwHTAVODwiHtyMeW0F7Ay06gtaN1MYZJtHe4xlJ5Junrq23RmMwvhamt/7xI2kN5HGI17K4JYCEyRNLZXvV/i8dvIDUeYCX42Ivx+GWU4htZrW8VkHzUzJ762+Z0sZhfFVcARp9JG2Gx8KRlyMVcgdlpOGHy4fv8aQBvdY2mIRjc/L5819SDl1q/pD5kS98xaQhoo6qVEg6fXAR4Gf5stLSNpF/Z8iuYB02WlGoe7bSTewXdnpFe+WfCPM5aRLnMdGxG0DTNdvn0narsmkZ5IuSZUf5FALzbZZ0oGkYaQWFcocYwV5vx0KXN3sB4njq7mIuBd4ADg5f1cbTiXdlHZVo0DSREnTcgtXw7+R7gk4rTCdgD8ljaZzewdXvyuUnor5j6Tk6bODTNdvfw3w/X4bcDzpWRy16sohaVLux18sG0v6nr0A3Food3z1dwKpK97VzT6sc4xVyR3y/Q2LgdmlBtTZwDYUznuSts776rcK0/2EdDX6NPo6ldTos3A4tqXIN5N2WETcLulK4G+Vxkx/FPgIaTzXOYVJ5wMHk0baaPgm6W736yVdQPoV+BnSpZevdn7tu+YCUqvAdcAkSR8ufPZiRFyT/262z36eb4JZTurW8V7SuM43U32M7JHmcklrSTeUPgPsCZyc/55bmM4x1tdxpGPgQC1PozK+JP1V/rPxzILZ+Yff6oj4Ri47k3QVYpGky0kx90nS2OrFUYaOBr5Hapi4BCAiHpc0DzgjJ2B3krogHQQc1+Z9KF3Tan8pjWc9H3iW9HyCE9V3+P3/LHRR6Le/SOeOKbnuk8CupKQT0sgcI0qF+DoCOEvSAtIDiiaTzplTgVNLQx3XPr6g8neyMZrQYcBVTYaEbqhzjFXNHc4inS+XSPo26UrgZ4GFEVF8avW+pCd3n0s+l0bEy5LOBi6UdAXpqa8HAR8GPh8Rq4d9q4b7CUp+NX2S1Vjg70hfgHWk8VwPLU2zhPxchlL5m0m/8J4ntSZcC0zp9jZ1eH8tIfWPbvZaMdg+I426cV/eV+uBB4Ev0uLpfyP5RRo54nZSIvAKqb/0d4FdHGOD7rdbgVUUnq7Zan+Nhviq8t3L0x0F3J2PaStJJ7MtS9PMyXXnlMq3AP6ClIitJ3XBOr7b296J/VXYBwO9Zg62v0itmv9N6vLxCvB/pBGK3tHtbe/Q/noXKdF6PMfGmvxdPLzJvGofX1X2WWG6U3L5BweZV21jjIq5Q572QOCnpJs/V5GueI0vTTMz153bZFkfJ11ZXE960vynO7Vdygs0MzMzM7Me4j7qZmZmZmY9yIm6mZmZmVkPcqJuZmZmZtaDnKibmZmZmfUgJ+pmZmZmZj3IibqZmZmZWQ9yom5mZmZm1oOcqJuZmZmZ9SAn6mZmZmZmPciJupmZ9SFpS0nnSNq/zbqrJX0i/3+kpMivo5pMP1HSM/nzHw3D6puZ1YYTdTMzK3sHMBfYro267wEmAtfn/9+Z39cB05pMfyawTf57WRvLMzOrLSfqZmZW9q78/j9t1J0FPBARj+X/pwOrgDuB3YsTStoeOB1YmIucqJuZFThRNzOz35B0B/Cd/O/K3CXliSHMYhavtqZDStTvAZbTv0X9bOA54Ob8vxN1M7MCJ+pmZlb0N8D9wH3A7Pz6kyoVJe0M7ElO1CVtDexKSsDvpZCoS3orcDJwLjAVWA88OFwbYWZWB07UzczsNyLiKmACcGNEXJpfiypWnwW8ANyU/9+TdJ5ZRmpRnyBpp/zZecCjwCWkVvf7ImLj8GyFmVk9bNntFTAzs94h6Y3ATqTuKkM1C7ghIjbk/6fn92XAyvz3NEmTgOOBDwGbSAn9grZX2sysptyibmZmRY3kuk+iLum3Jf2HpLWSlkt6d+nzMcAh9O2f/k7g16TW8mdIN5XuDvw1cFduvZ9CGvXF/dPNzErcom5mZkV75fdyi/pFwP8CR5Nawq+SNCUi1ufPDwbG0/9G0ocL0ywH5pBGlTm0MA04UTcz68ct6mZmVrQXsDIiVjcKJG0LHA6cGxEvR8Q/k/qizyzUmwUsi4gnSvMqJuDLSUn64oi4IZc5UTczG4Bb1M3MrGgXYEWpbDdgdUSsKpTdA+wBNG40nQX8a+PDPALMG+mbgF8GrAauKJRNB56KiKeHYd3NzGrFibqZmRWtAD4i6QzgKVJCPh5YU5puDfmJopJ2JQ2xWO72AoVEPSJuB24vzWc6bk03M2vKXV/MzKzofNIDiOYC3wf2AV4Cti1NNwF4Mf89i9RSfkvh85ZdWiSNJ91M6kTdzKwJRUS318HMzHpY7qP+LLBzo/uLpPuB0yNikaSFwJqIOK6b62lmVjduUTczs0FFxAvAj4CzJY2VNJvUor4kT7IEmNeVlTMzqzG3qJuZWUuStgfmAwcBjwEfi4jburtWZmb15kTdzMzMzKwHueuLmZmZmVkPcqJuZmZmZtaDnKibmZmZmfUgJ+pmZmZmZj3IibqZmZmZWQ9yom5mZmZm1oOcqJuZmZmZ9SAn6mZmZmZmPej/Af2OjqJQEcwrAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "\n",
+    "[plt.errorbar(csv_data_fixed[i]['t_shift'], -csv_data_fixed[i]['dlogz'], yerr=csv_data_fixed[i]['dlogz_err'], fmt='o',color=colors[i],label =tags_fixed[i]) for i in range(len(csv_data_fixed))] \n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$|logz|$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 161,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import qnm\n",
+    "omegas = [qnm.modes_cache(s=-2,l=2,m=2,n=i)(a=0.692085186818)[0] for i in range (0,6)]\n",
+    "w = (np.real(omegas))/0.952032939704\n",
+    "tau=-1/(np.imag(omegas))*0.952032939704"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 162,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "\n",
+    "[plt.errorbar(csv_data_fixed[i]['t_shift'], -(csv_data_fixed[i]['dlogz']-csv_data_fixed[-1]['dlogz']), yerr=csv_data_fixed[i]['dlogz_err'], fmt='o',color=colors[i],label =tags_fixed[i]) for i in range(len(csv_data_fixed)-1)] \n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.xlim(0,24)\n",
+    "plt.axvline(x=tau[0],color=colors[0],linestyle='--')\n",
+    "plt.axvline(x=tau[1],color=colors[1],linestyle='--')\n",
+    "plt.axvline(x=tau[2],color=colors[2],linestyle='--')\n",
+    "plt.axvline(x=tau[3],color=colors[3],linestyle='--')\n",
+    "plt.axvline(x=tau[4],color=colors[4],linestyle='--')\n",
+    "plt.axvline(x=tau[5],color=colors[5],linestyle='--')\n",
+    "\n",
+    "plt.ylabel(r'$log \\mathcal{B}$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 219,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "[plt.errorbar(csv_data_var_m_af[i]['t_shift'],-csv_data_var_m_af[i]['dlogz'], yerr=csv_data_var_m_af[i]['dlogz_err'], fmt='o',color=colors[i],label =tags_var_m_af[i]) for i in range(len(csv_data_var_m_af))] \n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 229,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/work/francisco.jimenez/local/python-3.7.7/lib/python3.7/site-packages/ipykernel_launcher.py:15: UserWarning: Attempted to set non-positive bottom ylim on a log-scaled axis.\n",
+      "Invalid limit will be ignored.\n",
+      "  from ipykernel import kernelapp as app\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "[plt.errorbar(csv_data_var[i]['t_shift'],-csv_data_var[i]['dlogz'], yerr=csv_data_var[i]['dlogz_err'], fmt='o',color=colors[i],label =tags_var[i]) for i in range(len(csv_data_var))] \n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "[plt.errorbar(csv_data_var[i]['t_shift'],-csv_data_var[i]['dlogz'], yerr=csv_data_var[i]['dlogz_err'], fmt='o',color=colors[i],label =tags_var[i]) for i in range(len(csv_data_var))] \n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.ylim(0,1000)\n",
+    "plt.show()\n",
+    "\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "\n",
+    "[plt.errorbar(csv_data_var[i]['t_shift'], (csv_data_var[i]['dlogz']-csv_data_var[-1]['dlogz']), yerr=csv_data_var[i]['dlogz_err']+csv_data_var[-1]['dlogz_err'], fmt='o',color=colors[i],label =tags_var[i]) for i in range(len(csv_data_var)-1)] \n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.xlim(0,24)\n",
+    "plt.ylim(-50,100)\n",
+    "plt.axvline(x=tau[0],color=colors[0],linestyle='--')\n",
+    "plt.axvline(x=tau[1],color=colors[1],linestyle='--')\n",
+    "plt.axvline(x=tau[2],color=colors[2],linestyle='--')\n",
+    "plt.axvline(x=tau[3],color=colors[3],linestyle='--')\n",
+    "plt.axvline(x=tau[4],color=colors[4],linestyle='--')\n",
+    "plt.axvline(x=tau[5],color=colors[5],linestyle='--')\n",
+    "plt.hlines(0, 0, 20,colors='k', linestyles='solid')\n",
+    "plt.hlines(10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.hlines(-10, 0, 20,colors='k', linestyles='--')\n",
+    "\n",
+    "plt.ylabel(r'$log \\mathcal{B}$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 248,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(0.0, 22.0)"
+      ]
+     },
+     "execution_count": 248,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "index=-1\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "plt.errorbar(csv_data_var_m_af[index]['t_shift'],-csv_data_var_m_af[index]['dlogz'], yerr=csv_data_var_m_af[index]['dlogz_err'], fmt='o',color=colors[index],label =tags_var_m_af[index])\n",
+    "plt.errorbar(csv_data_fixed[index-1]['t_shift'],-csv_data_fixed[index-1]['dlogz'], yerr=csv_data_fixed[index-1]['dlogz_err'], fmt='o',color=colors[index-1],label =tags_fixed[index-1])\n",
+    "plt.errorbar(csv_data_var[index]['t_shift'],-csv_data_var[index]['dlogz'], yerr=csv_data_var[index]['dlogz_err'], fmt='o',color=colors[index-4],label =tags_var[index])\n",
+    "\n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.show()\n",
+    "\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "w_tau_am=interp1d(csv_data_var_m_af[index]['t_shift'], -csv_data_var_m_af[index]['dlogz'], kind='cubic')\n",
+    "w_tau_fixed=interp1d(csv_data_fixed[index-1]['t_shift'], -csv_data_fixed[index-1]['dlogz'], kind='cubic')\n",
+    "w_tau=interp1d(csv_data_var[index]['t_shift'], -csv_data_var[index]['dlogz'], kind='cubic')\n",
+    "t_new = np.linspace(0, 20, num=41, endpoint=True)\n",
+    "#plt.plot(t_new, w_tau_am(t_new)-w_tau(t_new),w_tau_fixed(t_new)-w_tau(t_new))\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_var_m_af[index]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_fixed[index-1]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.hlines(0, 0, 20,colors='k', linestyles='solid')\n",
+    "plt.hlines(10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.hlines(-10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.axvline(x=4*tau[index-1],color=colors[index],linestyle='--')\n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$log \\mathcal{B}$')\n",
+    "nval=int(csv_data_var_m_af[index]['n'][0])\n",
+    "plt.legend(['a-mf-n='+str(nval), 'fixed-n='+str(nval)], loc='best')\n",
+    "plt.ylim(-100,100)\n",
+    "plt.xlim(0,22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 247,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(0.0, 22.0)"
+      ]
+     },
+     "execution_count": 247,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "index=-2\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "plt.errorbar(csv_data_var_m_af[index]['t_shift'],-csv_data_var_m_af[index]['dlogz'], yerr=csv_data_var_m_af[index]['dlogz_err'], fmt='o',color=colors[index],label =tags_var_m_af[index])\n",
+    "plt.errorbar(csv_data_fixed[index-1]['t_shift'],-csv_data_fixed[index-1]['dlogz'], yerr=csv_data_fixed[index-1]['dlogz_err'], fmt='o',color=colors[index-1],label =tags_fixed[index-1])\n",
+    "plt.errorbar(csv_data_var[index]['t_shift'],-csv_data_var[index]['dlogz'], yerr=csv_data_var[index]['dlogz_err'], fmt='o',color=colors[index-4],label =tags_var[index])\n",
+    "\n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "w_tau_am=interp1d(csv_data_var_m_af[index]['t_shift'], -csv_data_var_m_af[index]['dlogz'], kind='cubic')\n",
+    "w_tau_fixed=interp1d(csv_data_fixed[index-1]['t_shift'], -csv_data_fixed[index-1]['dlogz'], kind='cubic')\n",
+    "w_tau=interp1d(csv_data_var[index]['t_shift'], -csv_data_var[index]['dlogz'], kind='cubic')\n",
+    "t_new = np.linspace(0, 20, num=41, endpoint=True)\n",
+    "#plt.plot(t_new, w_tau_am(t_new)-w_tau(t_new),w_tau_fixed(t_new)-w_tau(t_new))\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_var_m_af[index]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_fixed[index-1]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.hlines(0, 0, 20,colors='k', linestyles='solid')\n",
+    "plt.hlines(10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.hlines(-10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.axvline(x=4*tau[index-1],color=colors[index],linestyle='--')\n",
+    "\n",
+    "plt.ylabel(r'$log \\mathcal{B}$')\n",
+    "nval=int(csv_data_var_m_af[index]['n'][0])\n",
+    "plt.legend(['a-mf-n='+str(nval), 'fixed-n='+str(nval)], loc='best')\n",
+    "plt.ylim(-100,100)\n",
+    "plt.xlim(0,22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 246,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(0.0, 22.0)"
+      ]
+     },
+     "execution_count": 246,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "index=-3\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "plt.errorbar(csv_data_var_m_af[index]['t_shift'],-csv_data_var_m_af[index]['dlogz'], yerr=csv_data_var_m_af[index]['dlogz_err'], fmt='o',color=colors[index],label =tags_var_m_af[index])\n",
+    "plt.errorbar(csv_data_fixed[index-1]['t_shift'],-csv_data_fixed[index-1]['dlogz'], yerr=csv_data_fixed[index-1]['dlogz_err'], fmt='o',color=colors[index-1],label =tags_fixed[index-1])\n",
+    "plt.errorbar(csv_data_var[index]['t_shift'],-csv_data_var[index]['dlogz'], yerr=csv_data_var[index]['dlogz_err'], fmt='o',color=colors[index-4],label =tags_var[index])\n",
+    "\n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "w_tau_am=interp1d(csv_data_var_m_af[index]['t_shift'], -csv_data_var_m_af[index]['dlogz'], kind='cubic')\n",
+    "w_tau_fixed=interp1d(csv_data_fixed[index-1]['t_shift'], -csv_data_fixed[index-1]['dlogz'], kind='cubic')\n",
+    "w_tau=interp1d(csv_data_var[index]['t_shift'], -csv_data_var[index]['dlogz'], kind='cubic')\n",
+    "t_new = np.linspace(0, 20, num=41, endpoint=True)\n",
+    "#plt.plot(t_new, w_tau_am(t_new)-w_tau(t_new),w_tau_fixed(t_new)-w_tau(t_new))\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_var_m_af[index]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_fixed[index-1]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.hlines(0, 0, 20,colors='k', linestyles='solid')\n",
+    "plt.hlines(10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.hlines(-10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.axvline(x=4*tau[index-1],color=colors[index],linestyle='--')\n",
+    "\n",
+    "\n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$log \\mathcal{B}$')\n",
+    "nval=int(csv_data_var_m_af[index-1]['n'][0])\n",
+    "plt.legend(['a-mf-n='+str(nval), 'fixed-n='+str(nval)], loc='best')\n",
+    "plt.ylim(-200,100)\n",
+    "plt.xlim(0,22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 245,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(0.0, 22.0)"
+      ]
+     },
+     "execution_count": 245,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "index=-4\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "plt.errorbar(csv_data_var_m_af[index]['t_shift'],-csv_data_var_m_af[index]['dlogz'], yerr=csv_data_var_m_af[index]['dlogz_err'], fmt='o',color=colors[index],label =tags_var_m_af[index])\n",
+    "plt.errorbar(csv_data_fixed[index-1]['t_shift'],-csv_data_fixed[index-1]['dlogz'], yerr=csv_data_fixed[index-1]['dlogz_err'], fmt='o',color=colors[index-1],label =tags_fixed[index-1])\n",
+    "plt.errorbar(csv_data_var[index]['t_shift'],-csv_data_var[index]['dlogz'], yerr=csv_data_var[index]['dlogz_err'], fmt='o',color=colors[index-4],label =tags_var[index])\n",
+    "\n",
+    "plt.yscale('log')\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$logz$')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.figure(figsize = (12, 8))\n",
+    "w_tau_am=interp1d(csv_data_var_m_af[index]['t_shift'], -csv_data_var_m_af[index]['dlogz'], kind='cubic')\n",
+    "w_tau_fixed=interp1d(csv_data_fixed[index-1]['t_shift'], -csv_data_fixed[index-1]['dlogz'], kind='cubic')\n",
+    "w_tau=interp1d(csv_data_var[index]['t_shift'], -csv_data_var[index]['dlogz'], kind='cubic')\n",
+    "t_new = np.linspace(0, 20, num=41, endpoint=True)\n",
+    "#plt.plot(t_new, w_tau_am(t_new)-w_tau(t_new),w_tau_fixed(t_new)-w_tau(t_new))\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_var_m_af[index]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.plot(csv_data_var_m_af[index]['t_shift'], csv_data_fixed[index-1]['dlogz']-csv_data_var[index]['dlogz'],'o')\n",
+    "plt.hlines(0, 0, 20,colors='k', linestyles='solid')\n",
+    "plt.hlines(10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.hlines(-10, 0, 20,colors='k', linestyles='--')\n",
+    "plt.axvline(x=4*tau[index-1],color=colors[index],linestyle='--')\n",
+    "\n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$log \\mathcal{B}$')\n",
+    "nval=int(csv_data_var_m_af[index]['n'][0])\n",
+    "plt.legend(['a-mf-n='+str(nval), 'fixed-n='+str(nval)], loc='best')\n",
+    "plt.ylim(-100,100)\n",
+    "plt.xlim(0,22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "regular_list = np.asarray(sorted(np.asarray([glob.glob(x+'/best*value*.csv') for x in folders])))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "regular_list=(regular_list.flatten())\n",
+    "regular_list_fixed=np.sort(regular_list[position_fixed])\n",
+    "regular_list_var=np.sort(regular_list[position_var])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax0_True/best_values_305_w-tau_nmax_0.csv',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax1_False/best_values_305_w-tau_nmax_1.csv',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax1_True/best_values_305_w-tau_nmax_1.csv',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax2_True/best_values_305_w-tau_nmax_2.csv',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax3_True/best_values_305_w-tau_nmax_3.csv',\n",
+       "       '/work/francisco.jimenez/sio/git/rdstackingproject/results_new/0305/w-tau-nmax4_True/best_values_305_w-tau_nmax_4.csv'],\n",
+       "      dtype='<U128')"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "regular_list_var"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "best_vars_n=[pd.read_csv(x, error_bad_lines=False) for x in regular_list_var]\n",
+    "best_vars_n_fixed=[pd.read_csv(x, error_bad_lines=False) for x in regular_list_fixed]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "index=3\n",
+    "tshift=best_vars_n[index][r'tshift']\n",
+    "best_vars_n_w0=np.asarray([x[r'$\\omega_0$'] for x in best_vars_n[index:index+1]])\n",
+    "err_vars_n_w0_up=np.asarray([x[r'$\\omega_0$'] for x in best_vars_n[index:index+1]])\n",
+    "err_vars_n_w0_low=np.asarray([x[r'$\\omega_0$'] for x in best_vars_n[index:index+1]])\n",
+    "\n",
+    "\n",
+    "best_vars_n_tau0=np.asarray([x[r'$\\tau_0$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a0=np.asarray([x[r'$A_0$'] for x in best_vars_n[index:index+1]])\n",
+    "\n",
+    "\n",
+    "best_vars_n_w1=np.asarray([x[r'$\\omega_1$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_tau1=np.asarray([x[r'$\\tau_1$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a1=np.asarray([x[r'$A_1$'] for x in best_vars_n[index:index+1]])\n",
+    "\n",
+    "best_vars_n_w2=np.asarray([x[r'$\\omega_2$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_tau2=np.asarray([x[r'$\\tau_2$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a2=np.asarray([x[r'$A_2$'] for x in best_vars_n[index:index+1]])\n",
+    "\n",
+    "#best_vars_n_w3=np.asarray([x[r'$\\omega_3$'][0::3] for x in best_vars_n[3:]])\n",
+    "#best_vars_n_tau3=np.asarray([x[r'$\\tau_3$'][0::3] for x in best_vars_n[3:]])\n",
+    "#best_vars_n_a3=np.asarray([x[r'$A_3$'][0::3] for x in best_vars_n[3:]])\n",
+    "\n",
+    "#best_vars_n_w4=np.asarray([x[r'$\\omega_4$'][0::3] for x in best_vars_n[4:]])\n",
+    "#best_vars_n_tau4=np.asarray([x[r'$\\tau_4$'][0::3] for x in best_vars_n[4:]])\n",
+    "#best_vars_n_a4=np.asarray([x[r'$A_4$'][0::3] for x in best_vars_n[4:]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tshift=best_vars_n[2][r'tshift']\n",
+    "best_vars_n_a0_fixed=np.asarray([x[r'$A_0$'] for x in best_vars_n_fixed[2:3]])\n",
+    "best_vars_n_a1_fixed=np.asarray([x[r'$A_1$'] for x in best_vars_n_fixed[2:3]])\n",
+    "best_vars_n_a2_fixed=np.asarray([x[r'$A_2$'] for x in best_vars_n_fixed[2:3]])\n",
+    "#best_vars_n_a3_fixed=np.asarray([x[r'$A_3$'][0::3] for x in best_vars_n_fixed[2:3]])\n",
+    "#best_vars_n_a4_fixed=np.asarray([x[r'$A_4$'][0::3] for x in best_vars_n_fixed[2:3]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "operands could not be broadcast together with shapes (1,78) (1,60) ",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-27-8c17549e8900>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtshift\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbest_vars_n_a0_fixed\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mbest_vars_n_a0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'bo'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtshift\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbest_vars_n_a1_fixed\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mbest_vars_n_a1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'ro'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtshift\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbest_vars_n_a2_fixed\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mbest_vars_n_a2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'go'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mr'$t_0M$'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (1,78) (1,60) "
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 864x576 with 0 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "plt.plot(tshift,(best_vars_n_a0_fixed/best_vars_n_a0)[0],'bo') \n",
+    "plt.plot(tshift,(best_vars_n_a1_fixed/best_vars_n_a1)[0],'ro') \n",
+    "plt.plot(tshift,(best_vars_n_a2_fixed/best_vars_n_a2)[0],'go') \n",
+    "plt.xlabel(r'$t_0M$')\n",
+    "plt.ylabel(r'$A_i/Ap_i$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "plt.plot(tshift,(best_vars_n_a0_fixed/best_vars_n_a0)[0],'bo',label=r'$A_{0}$') \n",
+    "plt.plot(tshift,(best_vars_n_a1_fixed/best_vars_n_a1)[0],'ro',label=r'$A_{1}$') \n",
+    "plt.plot(tshift,(best_vars_n_a2_fixed/best_vars_n_a2)[0],'go',label=r'$A_{2}$') \n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A_i/A_i^{fixed}$')\n",
+    "plt.xlim(0,20)\n",
+    "plt.ylim(0,8)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "omegas = [qnm.modes_cache(s=-2,l=2,m=2,n=i)(a=0.692085186818)[0] for i in range (0,6)]\n",
+    "w = (np.real(omegas))/0.952032939704\n",
+    "tau=-1/(np.imag(omegas))*0.952032939704"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([11.74090006,  3.88312743,  2.29980777,  1.62209641,  1.25654938,\n",
+       "        1.03071732])"
+      ]
+     },
+     "execution_count": 80,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tau"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 147,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w0[0][0::3], yerr=np.abs(best_vars_n_w0[0][1::3]-best_vars_n_w0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_0$')\n",
+    "\n",
+    "plt.axhline(y=w[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 152,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau0[0][0::3], yerr=np.abs(best_vars_n_tau0[0][1::3]-best_vars_n_tau0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_0$')\n",
+    "\n",
+    "plt.axhline(y=tau[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 151,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w1[0][0::3], yerr=np.abs(best_vars_n_w1[0][1::3]-best_vars_n_w1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_1$')\n",
+    "\n",
+    "plt.axhline(y=w[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 161,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau1[0][0::3], yerr=np.abs(best_vars_n_tau1[0][1::3]-best_vars_n_tau1[0][2::3]),fmt='o',label='n=0',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_1$')\n",
+    "\n",
+    "plt.axhline(y=tau[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 158,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w2[0][0::3], yerr=np.abs(best_vars_n_w2[0][1::3]-best_vars_n_w2[0][2::3]),fmt='o',label='n=2',color=colors[3])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_2$')\n",
+    "\n",
+    "plt.axhline(y=w[2], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 159,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau2[0][0::3], yerr=np.abs(best_vars_n_tau2[0][1::3]-best_vars_n_tau2[0][2::3]),fmt='o',label='n=2',color=colors[3])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_2$')\n",
+    "\n",
+    "plt.axhline(y=tau[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 168,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_a0[0][0::3], yerr=np.abs(best_vars_n_a0[0][1::3]-best_vars_n_a0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 171,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_a1[0][0::3], yerr=np.abs(best_vars_n_a1[0][1::3]-best_vars_n_a1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 170,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_a2[0][0::3], yerr=np.abs(best_vars_n_a2[0][1::3]-best_vars_n_a2[0][2::3]),fmt='o',label='n=1',color=colors[3])\n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "index=2\n",
+    "tshift=best_vars_n[index][r'tshift']\n",
+    "best_vars_n_w0=np.asarray([x[r'$\\omega_0$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_tau0=np.asarray([x[r'$\\tau_0$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a0=np.asarray([x[r'$A_0$'] for x in best_vars_n[index:index+1]])\n",
+    "\n",
+    "\n",
+    "best_vars_n_w1=np.asarray([x[r'$\\omega_1$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_tau1=np.asarray([x[r'$\\tau_1$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a1=np.asarray([x[r'$A_1$'] for x in best_vars_n[index:index+1]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w0[0][0::3], yerr=np.abs(best_vars_n_w0[0][1::3]-best_vars_n_w0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_0$')\n",
+    "\n",
+    "plt.axhline(y=w[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau0[0][0::3], yerr=np.abs(best_vars_n_tau0[0][1::3]-best_vars_n_tau0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_0$')\n",
+    "\n",
+    "plt.axhline(y=tau[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w1[0][0::3], yerr=np.abs(best_vars_n_w1[0][1::3]-best_vars_n_w1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_1$')\n",
+    "\n",
+    "plt.axhline(y=w[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau1[0][0::3], yerr=np.abs(best_vars_n_tau1[0][1::3]-best_vars_n_tau1[0][2::3]),fmt='o',label='n=0',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_1$')\n",
+    "\n",
+    "plt.axhline(y=tau[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_a0[0][0::3], yerr=np.abs(best_vars_n_a0[0][1::3]-best_vars_n_a0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.errorbar(tshift[0::3],best_vars_n_a1[0][0::3], yerr=np.abs(best_vars_n_a1[0][1::3]-best_vars_n_a1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "index=1\n",
+    "tshift=best_vars_n[index][r'tshift']\n",
+    "best_vars_n_w0=np.asarray([x[r'$\\omega_0$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_tau0=np.asarray([x[r'$\\tau_0$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a0=np.asarray([x[r'$A_0$'] for x in best_vars_n[index:index+1]])\n",
+    "\n",
+    "\n",
+    "best_vars_n_w1=np.asarray([x[r'$\\omega_1$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_tau1=np.asarray([x[r'$\\tau_1$'] for x in best_vars_n[index:index+1]])\n",
+    "best_vars_n_a1=np.asarray([x[r'$A_1$'] for x in best_vars_n[index:index+1]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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mdTPbaGYvmVkbYdbnUdF+kYpXjnN8aZSWVLqCmtrcfTPwiWhm6fcBhxGWlv5zlqWsRSpSOc/xpeYuqWQ5BR4z+2fgDMLotRpgG2HZgv8L/Mrd3y5ZCUUSkuQKkCIHslxrPN8BdgGbgN2EAPQR4AvAa2b2BXf/aWmKKJKMSnxYUqQS5NrH836gxt1Hu/t73f1dwHuBzxGWm37EzC4qURlFEqE5vkRKI6fA4+4vurtnpP3F3e8BxhFGsd1c/OLJQFGOnfgaPSZSGv2eq83ddxFWE31v/4sjpVaOX/DlOuOxRo+JlEbeo9rMrJqwKujLwHZgBGHl0P8qbtGk2Mp1lFY5d+Jr9JhI8RVS49kLDAFmAnMIz+zcSVh6WspYuU5pr058kYEl78Dj7rvc/e8JNZ0PA8uARsKDo1LGyvULXp34IgNLToHHzG41syHpaR484e4XAz8BmktQvgGjp76XYvbJlOsXvDrxRQaWXPt4Pgt8xszmAQvcfU3G/u3AqUUt2QEkfY36ESNGsGPHDvbs2bNvvXoga9/LsmXLuO+++4rWJ9PU1ERjY+N+zW3l8AWvGY9FBpZcA8+JwLeA64AvRvOyrQE2AnWEh0mfK0UBK92mTZv2Cypbt27dty8VSGpqarL2vTQ3N/P22293S++r0z090KWCW0NDQ1l/wasTX2TgyCnwuHsbcIWZzQZmAH8PnAdUR1lWAleWooCV7tVXX90XdLJpb2/vFnRSMoNOSm99Mn2NXNMXvIgkLa/BBe7e6u5fdfcz3b0WeBdQ6+4fcnfVeLLoLej05eCDD86a3lufTLmOXBMRSenXA6Tu/qa7dxarMAeSVHNXLoYPH561c72xsTHvTvdyHbkmIpLS75kLpLvM5q7e1NbWcvvtt2d9Qv6uu+7K+8n5ch25JiKSUujS19KLbM1dKcOHD983qi2zcz9b30u+fTLlOnJNRCRFgacEemvW2rJlCxMnTgRK07lfziPXRERAgack6uvraW1t7ZaeajIrNY1cE5Fypj6eEsj2JP5BBx3Eu9/97oRKJCJSPlTjKYFszV01NTUcddRRCZdMRCR5qvGUSENDA2effTYTJkxg7dq1CjoiIhEFHhERiZUCj4iIxEqBR0REYqXAIyIisVLgERGRWCnwiIhIrBR4REQkVgo8IiISKwUeERGJlQKPiIjESoFHRERipcAjIiKxUuAREZFYKfCIiEisFHhERCRWiQYeM6syszlmtsHMOsxsuZldkMNxs83Ms7w29pB/hpn9ycw6zewlM/tc8d+NiIjkIukVSBcAU4G5wMvAdGCxmU1w96dyOH4m0J72e0dmBjObCdwDPAT8K3A+8H0zq3b37/an8CIikr/EAo+ZnQlcAlzv7nOjtIXAamAO8OEcTvOgu7/RyzVqgCbgp+7+qSh5npkdBHzNzOa7+47C34WIiOQryaa2i4HdwPxUgrt3AvcC55lZXQ7nMDMbYmbWw/6PAMOBuzLS7wQOB/4h71KLiEi/JBl4TgNecPedGelPAwaMy+Ec64AdwA4z+4GZHZHlGgAtGekrgb1p+0VEJCZJ9vHUAa9nSW+LtqN6OXY78D1gObAL+BtCf8/pZnaWu3elXaPL3belH+zuu8xsa2/XMLNGoBGgvr6+73cjIiI5STLw1ABdWdI70/Zn5e63ZyQ9bGarCU1o04B5aefY1cNpOvu4RjPQDDB+/HjvKZ+IiOQnyaa2DqAqS3p12v583EMY4ZY+HLuna6Suk+81RESkn5IMPG2EprBMqbQN+ZzM3fcSmu7S+3nagEMz+37M7FDCoIO8riEiIv2XZOBZBYw1s8EZ6WdF2+fyOZmZHQIcB2zOuAbA+Izs4wnvfRUiIhKrJAPPw8AhwJWpBDOrAq4Alrn7hiit3szGph9oZiOznO9GQvPZ42lpvwW2AVdn5L0K2Aks7ud7EBGRPCU2uMDdV5jZQ8Ct0TM7rwCXA6MJMxikLAQmEIZYp7Sa2f2Eh027CM/rTAWeAH6cdo0OM/sKcKeZPQj8ijBzwT8BX+rt4VMRESmNpKfMmQZ8I9oOA54HJrn7sj6OWwScC3wSOBRYG53nFnffk57R3e8ys93AF4HJwGvAF9z9jiK+DxERyVGigSeaqeDG6NVTnolZ0j6T53Xm8c4QaxERSZCWRRARkVgp8IiISKwUeEREJFYKPCIiEisFHhERiZUCj4iIxEqBR0REYqXAIyIisVLgERGRWCnwiIhIrBR4REQkVklPEioiIr1YsmRJ0kUoOtV4REQkVqrxiIhIVqWqbanGIyIisVLgERGRWKmpTaRCHYidzjIwKPCISN4qMehVYpkPVGpqExGRWCnwiIhIrBR4REQkVgo8IiISKwUeERGJlQKPiIjESoFHRERipcAjIiKxUuAREZFYaeYCkT7oiXeR4lKNR0REYqXAIyIisVLgERGRWCnwiIhIrDS4QMqGOvFFBgbVeEREJFaq8QxAqlmISJJU4xERkVgp8IiISKwUeEREJFYKPCIiEisFHhERiZUCj4iIxErDqWOiIcwiIoECTxlRcBKRgUCBJwEKMCIykCnwVAAFKhE5kGhwgYiIxCrRwGNmVWY2x8w2mFmHmS03swsKOM8vzczNbG6Wfd7D67NFeRNlasmSJaopiUhZSrqpbQEwFZgLvAxMBxab2QR3fyqXE5jZfwc+3Ee2x4EfZaStyKegIiJSHIkFHjM7E7gEuN7d50ZpC4HVwBz6DiaY2aHAvwG3Ajf3kvUFd88MPCIikoAkm9ouBnYD81MJ7t4J3AucZ2Z1OZzjC0AN8J2+MppZjZlVF1hWEREpkiQDz2mEmsjOjPSnAQPG9XawmR0NfAW4yd3b+7jWlcBbQIeZPW9mFxVW5Pyon0VEpLskA08d0JYlPZU2qo/jbwFepHvfTaYngZuAycDngCrgUTO7tLeDzKzRzFrMrGXz5s19XEJERHKV5OCCGqArS3pn2v6sov6hacAEd/feLuLu52Ycex+hH+lWM7u/p+PdvRloBhg/fnyv1xARkdwlWePpINQ+MlWn7e/GzAy4HXjE3Z/I96Lu/hZwD3AscGK+x4uISP8kWeNpIzS3ZUqlbejhuIuAM4GbzGxMxr4hUdomd88auCKvRdsjciuqiIgUS5I1nlXAWDMbnJF+VrR9rofj6gnl/i3watoL4Iro5wl9XPv4aKvOGxGRmCVZ43kYuIEw4mwuhJkMCMFjmbtviNLqgVp3fyE67ufA2iznewz4BWE49jPRsSPcfUt6JjMbDlwNvOrufy7uWxIRkb4kFnjcfYWZPUTo5K8DXgEuB0YTZjBIWUiowVh03CtR3v2Erh9ecfefpCV/3swmEwLSOuAYoBE4EphS1DckIiI5SXrKnGnAN6LtMOB5YJK7LyvS+Z8EzgU+Q+jP2Qk8BXyriNcQEZE8WB+jkYUwnLqlpSXpYoiIVBQzW+nu47ulK/D0zcw2A60FHj4C2NJnLknR/cqP7ld+dL/y1597NtrdR2YmKvCUmJm1ZIv4kp3uV350v/Kj+5W/UtwzLQQnIiKxUuAREZFYKfCUXnPSBagwul/50f3Kj+5X/op+z9THIyIisVKNR0REYqXAIyIisVLgERGRWCnwlICZVZnZHDPbYGYdZrbczC5IulzlyMwmmpn38BqbdPmSZmZ1ZvZtM/t/ZvbX6L5M7CHvhWb2jJl1mtk6M/uamSU9LVascr1fZra2h8/ct+MvdTLM7ENmdqeZrTGzt6LPzP1m9t4sec8xsyfMrN3MNprZ7WZWW+i1B9SHMkYLgKmEWbdfJkx6utjMJrj7U8kVq6zNBVZmpPW0JtNAciLwJcLn6HngnGyZzOwfgJ8Qlgu5BjgF+CrhqfNr4ihomcjpfkVWEs2Mn2Z1aYpVlr5EmMvyIcK9Ohr4PPCsmZ3p7n8CMLNxwG+APwL/TFhE8wbC8jL/o6Aru7teRXwRFqlz4Lq0tGrCH8Lvki5fub2AidH9mpJ0WcrxBRwODI9+nhLdq4lZ8v2R8EV6cFraN4G3gfcl/T7K8H6tBX6SdHkTvlfnAIdmpL0P6AQWpKX9ElgPDE5LuzK6t39TyLXV1FZ8FwO7gfmpBHfvJKwTdF60BIRkYWaHD7Smob64+1/dfWtveczsJOAk4N/d/e20XXcRmtOnlrCIZSWX+5UuahYvuMmokrn7k+6+KyPtz4T/xLwfwMyGAH8LLHT3nWlZFxJm+/9UIddW4Cm+04AXMv6RAJ4mrCk0LvYSVYYfAm8CHWb2KzM7JekCVZDTou1+U6h7WExxfdp+2d/fAW8Bb5nZK2bWmHSBkmZhYbOjeGdS0FMIXTKZn61dhFWkC/ps6X+XxVcHvJ4lvS3ajoqxLJVgF2E12sWED/uphPbjJ8zsQ+7+UpKFqxCpWnRbln1t6DOXzfPA74GXgJGENbv+3cyOcPcBM8AgiwbCgpmzot/7+mz9t0IuosBTfDVAV5b0zrT9EnH3JwkL9qX8zMx+Tvgf1tcIfwjSu9RnqqfP3YBsSuqNu1+Y/ruZ/QfwBPAVM7vb3XckU7LkRKNI7yTchx9GyX19tgr6PlNTW/F1AFVZ0qvT9ksv3P054NeAhqDnJvWZ6ulzp89cH6K+sbmEIF3Q/+IrmZkdDfxvYDvwSXffG+0qyWdLgaf42ninepoulaYhwrl5jbBcufQt1QzS0+dOn7ncvBZtB9TnzsyGEpq6hwIfc/eNabtL8tlS4Cm+VcBYMxuckX5WtH0u3uJUrOOBzUkXokKsirb7LdZlZqMIz1ysQnJxfLQdMJ87M6sGfg6cAHzc3V/MyLIa2EP3z9ahhIFSqwq5rgJP8T0MHEIY5w6EIZvAFcCyaKSRRMys+7K4ZucBHwEej79Elcfd/wi8ADSa2cFpu64C9gKPJFKwMmVmR5jZQRlp1cCNwF+BAfGQd/RZeYDQtPhJd1+emSfq6/o1cFnGf6YvAwYTHj7NmwYXFJm7rzCzh4Bbo2d2XgEuB0YTZjCQ/T1gZu2EAQZbgJOBxujn2QmWq2yY2ZejH98fbS+LgvMb7v79KO1G4GfA42b2AOE+fp7wbM+AGhmYw/26EJhlZg8THiQdTvgbPQG4KsujEAeq7xLuxc+BI8zsn9L27XT3n0Q/zyL8fS4xs/mEWvQXgcXu/uuCrpz007MH4ovQ6XYboX20k/AMz0eTLlc5voBrgRXAVsKDt68DPwDqky5bubwIT4hne63NyDcFeDb6zL0G3AwMSrr85Xa/gDOiL9v1hNFabwJLCE1NiZc/xvu0JI/P1nnAMsJggk3AHcBhhV5bC8GJiEis1McjIiKxUuAREZFYKfCIiEisFHhERCRWCjwiIhIrBR4REYmVAo+IiMRKgUdERGKlwCMiIrFS4BEpA2Y2yMy+ZmZ5rwUTHfuGmX0u+n2ymXn0mpIl/1Az2xLt/0URii+SFwUekfLwAcKkqN1m687BuYS1VH4Z/f7BaNsJjM2S/0bCzMIQloAWiZUCj0h5OCPaPlPAsZOAF9z91ej3UwkTObbwzgzNAJjZUcB1hIW/QIFHEqDAI5IwM3sauDf69bWoCez1PE4xiXdqOxACzx8Ii3hl1ni+AmwDnoh+V+CR2CnwiCRvDvAnYA1hga3LgP+Zy4Fmdhxh7Z1fRr/XAu8hBJQ/khZ4zOzdhLWObiasPdMFZK44KVJyCjwiCXP3R4AhwO/c/UfRK9fVVycRVs38ffT7yYS/6+cJNZ4hZnZMtO8bhIUJFxBqRWvc/e3ivAuR3GkFUpGEmdkw4BhC81i+JgG/cfdd0e+nRtvnCYvBAYw1syOAS4FPEZbDPpmwTLtI7FTjEUleKljsF3jM7Egz+z9m1m5mq83s7Iz9hwIXsH//zgeBPYTazBbCIIP3A7cAK6Pa1fGEUW3q35FEqMYjkrxTom1mjece4C/ARYSayiNmdry7d0X7JwCH0X1gwZ/T8qwGphNGzX00LQ8o8EhCVOMRSd4pwGvu/kYqwcwOBz4O3OzuHe5+H6EvZ2LacZOA59399YxzpQeU1YSg82t3/02UpsAjiVKNRyR59cDajLT3AW+4+6a0tD8AJwGpgQeTgEdTO6MRbsPYP6D8J/AG8GBa2qnARnffXISyi+RNgUckeWuBy83sBmAjIcAcBryZke9NohkHzOw9hCHRmc1skBZ43H0FsCLjPKei2o4kSE1tIsn7JuGBztnAD4HxwFvA4Rn5hgA7o58nEWoyT6bt77MJzcwOIwwuUOCRxJi7J10GEckQ9fFsBY5LNbeZ2Z+A69z9cTNbDLzp7p9OspwihVCNR6QMuftfgV8AXzGzajO7jFDjWRJlWQLMTaRwIv2kGo9ImYom9FwInA+8Csxw9+XJlkqk/xR4REQkVmpqExGRWCnwiIhIrBR4REQkVgo8IiISKwUeERGJlQKPiIjESoFHRERi9f8BLYzBFQNV3lMAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w0[0][0::3], yerr=np.abs(best_vars_n_w0[0][1::3]-best_vars_n_w0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_0$')\n",
+    "\n",
+    "plt.axhline(y=w[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau0[0][0::3], yerr=np.abs(best_vars_n_tau0[0][1::3]-best_vars_n_tau0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_0$')\n",
+    "\n",
+    "plt.axhline(y=tau[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w1[0][0::3], yerr=np.abs(best_vars_n_w1[0][1::3]-best_vars_n_w1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_1$')\n",
+    "\n",
+    "plt.axhline(y=w[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau1[0][0::3], yerr=np.abs(best_vars_n_tau1[0][1::3]-best_vars_n_tau1[0][2::3]),fmt='o',label='n=0',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_1$')\n",
+    "\n",
+    "plt.axhline(y=tau[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_a0[0][0::3], yerr=np.abs(best_vars_n_a0[0][1::3]-best_vars_n_a0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.errorbar(tshift[0::3],best_vars_n_a1[0][0::3], yerr=np.abs(best_vars_n_a1[0][1::3]-best_vars_n_a1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 190,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tshift_f=best_vars_n_fixed[1][r'tshift']\n",
+    "\n",
+    "best_vars_n_a0_f=np.asarray([x[r'$A_0$'] for x in best_vars_n_fixed[1:2]])\n",
+    "best_vars_n_a1_f=np.asarray([x[r'$A_1$'] for x in best_vars_n_fixed[1:2]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 200,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "\n",
+    "plt.errorbar(tshift_f[0::3],best_vars_n_a0_f[0][0::3], yerr=np.abs(best_vars_n_a0_f[0][1::3]-best_vars_n_a0_f[0][2::3]),fmt='o',label='n=0: fixed',color='gray')\n",
+    "plt.errorbar(tshift[0::3],best_vars_n_a0[0][0::3], yerr=np.abs(best_vars_n_a0[0][1::3]-best_vars_n_a0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "\n",
+    "plt.errorbar(tshift_f[0::3],best_vars_n_a1_f[0][0::3], yerr=np.abs(best_vars_n_a1_f[0][1::3]-best_vars_n_a1_f[0][2::3]),fmt='o',label='n=1: fixed',color='cornflowerblue')\n",
+    "plt.errorbar(tshift[0::3],best_vars_n_a1[0][0::3], yerr=np.abs(best_vars_n_a1[0][1::3]-best_vars_n_a1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "\n",
+    "\n",
+    "plt.legend(loc ='upper left') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 201,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "tshift=best_vars_n[3][r'tshift']\n",
+    "best_vars_n_w0=np.asarray([x[r'$\\omega_0$'] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_tau0=np.asarray([x[r'$\\tau_0$'] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_a0=np.asarray([x[r'$A_0$'] for x in best_vars_n[3:4]])\n",
+    "\n",
+    "\n",
+    "best_vars_n_w1=np.asarray([x[r'$\\omega_1$'] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_tau1=np.asarray([x[r'$\\tau_1$'] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_a1=np.asarray([x[r'$A_1$'] for x in best_vars_n[3:4]])\n",
+    "\n",
+    "best_vars_n_w2=np.asarray([x[r'$\\omega_2$'] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_tau2=np.asarray([x[r'$\\tau_2$'] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_a2=np.asarray([x[r'$A_2$'] for x in best_vars_n[3:4]])\n",
+    "\n",
+    "best_vars_n_w4=np.asarray([x[r'$\\omega_3$'][0::3] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_tau4=np.asarray([x[r'$\\tau_3$'][0::3] for x in best_vars_n[3:4]])\n",
+    "best_vars_n_a4=np.asarray([x[r'$A_3$'][0::3] for x in best_vars_n[3:4]])\n",
+    "\n",
+    "#best_vars_n_w4=np.asarray([x[r'$\\omega_4$'][0::3] for x in best_vars_n[4:]])\n",
+    "#best_vars_n_tau4=np.asarray([x[r'$\\tau_4$'][0::3] for x in best_vars_n[4:]])\n",
+    "#best_vars_n_a4=np.asarray([x[r'$A_4$'][0::3] for x in best_vars_n[4:]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 210,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w0[0][0::3], yerr=np.abs(best_vars_n_w0[0][1::3]-best_vars_n_w0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_0$')\n",
+    "plt.ylim(0.554,0.557)\n",
+    "\n",
+    "plt.axhline(y=w[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 205,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau0[0][0::3], yerr=np.abs(best_vars_n_tau0[0][1::3]-best_vars_n_tau0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_0$')\n",
+    "\n",
+    "plt.axhline(y=tau[0], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 206,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize = (12, 8))\n",
+    "\n",
+    "plt.errorbar(tshift_f[0::3],best_vars_n_a0_f[0][0::3], yerr=np.abs(best_vars_n_a0_f[0][1::3]-best_vars_n_a0_f[0][2::3]),fmt='o',label='n=0: fixed',color='gray')\n",
+    "plt.errorbar(tshift[0::3],best_vars_n_a0[0][0::3], yerr=np.abs(best_vars_n_a0[0][1::3]-best_vars_n_a0[0][2::3]),fmt='o',label='n=0',color=colors[2])\n",
+    "\n",
+    "plt.errorbar(tshift_f[0::3],best_vars_n_a1_f[0][0::3], yerr=np.abs(best_vars_n_a1_f[0][1::3]-best_vars_n_a1_f[0][2::3]),fmt='o',label='n=1: fixed',color='cornflowerblue')\n",
+    "plt.errorbar(tshift[0::3],best_vars_n_a1[0][0::3], yerr=np.abs(best_vars_n_a1[0][1::3]-best_vars_n_a1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "\n",
+    "\n",
+    "plt.legend(loc ='upper left') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$A$')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 207,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEYCAYAAAB7twADAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAdQ0lEQVR4nO3de7hdZX3g8e9PDbmIJ6ImCKnnpF4qOl5gDGAVJYqdC+14Qxmnp9yKk+pYq7a1PmOqxUdSCa1P0Y5VuXQieqoWGJ1iZXR0SqpgQJBLUaGKkGgSQAWJeJKA8ps/1tpyctgnZ+991jprn72/n+fZz9rrXXut/ct61slvv++73ndFZiJJ0lw9oukAJEmDwYQiSaqECUWSVAkTiiSpEiYUSVIlHtV0AE15whOekKtXr246DElaUK699tofZeaKdtuGNqGsXr2aa665pukwJGlBiYitM22zyUuSVAkTiiSpEiYUSVIlGk0oEbE4IjZGxI6I2B0RWyLiuA72uz0icobXd+YjdknSvprulN8EnACcA3wXOBW4LCKOzcyv7We/twIHTisbA84Evlh1kJKk2TWWUCLiKOB1wNsy85yy7ELgJmAj8OKZ9s3Mz7Y53p+WbyeqjlWSNLsmm7xeAzwAnN8qyMw9wAXAMRFxSJfH+23gtsy8sroQJUmdarLJ6wjg5sy8b1r51UAAhwM7OzlQRBwBPAPYUGWAkpq1a9cu7rrrLh544IGmQxl4ixYtYuXKlYyMjPR8jCYTyiHA9jblrSRyaBfHGi+X+23uioh1wDqA0dHRLg4vDb61a4vl5Zc3GcVDdu3axZ133smqVatYunQpEdF0SAMrM9m9ezfbtxf/JfeaVJps8loK7G1TvmfK9llFxCMo+mKuy8xv7++zmXluZq7JzDUrVrSdOUBSn7jrrrtYtWoVy5YtM5nULCJYtmwZq1at4q677ur5OE0mlN3A4jblS6Zs78SxwCrsjJcGygMPPMDSpR39rlRFli5dOqfmxSYTyk6KZq/pWmU7OjzOOPAg8MkqgpLUP6yZzK+5nu8mE8r1wGERMX08ydHl8obZDhARiynGsVyemZ0mIElSDZpMKBcDi4DXtwrKBHEacEUrQUTEaEQcNsMxjgcei81dkjq0du1DNyCoWo3d5ZWZV0XERcDZ5ZiTW4FTKEa8nzrloxdS9JO0q4uNU3TsX1JvtJKk2TQ9OeTJwAfK5QcpaizHZ+YVs+0YESPAbwL/mJn31hqlJC0QH/nIRzjxxBMZGxsjIjj11FPn7bsbncurHBn/9vI102fWzlC+iw5vLZakYXHWWWexa9cujjrqKO644455/e6mJ4eUJFVo8+bNjI6OEhE89rGPndfvbrrJS5LmzcQEbNkCmzfD6tXF+nw744wziAhuu+02Tj75ZJYvX87y5cs57bTTmJycnPPxW01dTbCGImlBu+WWYvn0p+//cxMTsG4d7C3n59i6tVgHGB+feb+6nHDCCTzlKU/hrLPO4hvf+Abnn38+K1euZOPGjQDce++9HQ0yXLJkCQceOH30RTNMKJKGwvr1ML0CMDlZlDeRUI488kg++tGP/nL9xz/+MRdccMEvE8orXvEKNm/ePOtxTjnlFDZt2lRXmF0xoUgaCtu2dVdetze84Q37rL/oRS/iM5/5DLt27WJkZIT3v//93HPPPbMe59BDu5lHt14mFElDYXS0aOZqV96E6TOeH3TQQQDcc889jIyM8LznPa+JsObEhCJpKGzYUPSZTG32WrasKG/CIx/5yLblmQnA3Xffzf333z/rcZYuXcry5csrja1XJhSpz/Tbc0kGRauf5PTTi475sbEimTTRf9KJV7/61fahSFK/Gh+H884r3vd7wrYPRZJUiV77UC699FJuuKGYrH3v3r3ceOONnHnmmQCcdNJJjI2NVRbjdCYUSRogl1xyCR/72Md+uX7ddddx3XXXAXDMMcfUmlAcKS9J8+iMM84gMx82Lcqpp55KZrJ69eo5HX/Tpk1kZtvX2prn7TehSJIqYZOXpKHS753xC5k1FElSJUwokqRKmFAkSZUwoUiSKmFCmQdr1z40nYakzrXmtdL8mOv5NqFI6kuLFi1i9+7dTYcxcG655aGHkk23e/duFi1a1POxTSiS+tLKlSvZvn07k5OT1lRqlplMTk6yfft2Vq5c2fNxHIciqS+NjIwAsGPHjv0+CveOO4rlgw/OR1QL30zna9GiRRx88MG/PO+9MKHUbGICtmwppstevbq/p8uW+s3IyMis/8G98Y3F0gGLnanzfNnkVaOJieKBPnv3FutbtxbrExPNxiVJdTCh1Gj9+n2fDgfF+vr1zcQjSXUyodRo27buyiVpITOh1Gh0tLtySVrITCg12rABli3bt2zZsqJckgaNCaVG4+Nw7rmweHGxPjZWrHuXl6RB5G3DNRsfh/POK957W6OkQWYNRZJUCWso88CaiaRhYA1FklQJE4okqRImFElSJUwokqRKmFAkSZUwoUiSKmFCkSRVwoQiSaqECUWSVAkTiiSpEiYUSVIlTChSH5mYgC1bYPNmWL26WJcWChOK1CcmJmDdOti7t1jfurVYN6looTChSH1i/XqYnNy3bHKyKJcWAhOK1Ce2beuuXOo3JhSpT4yOdlcu9RsTygBZu7Z4aWHasAGWLdu3bNmyolxaCEwoUp8YH4dzz4XFi4v1sbFifXy8/u/27jJVwUcAS31kfBzOO694P1+Pjp7p7rJWPFKnrKEMCH9hqlfeXaaqmFAGgOMXNBfeXaaqNJpQImJxRGyMiB0RsTsitkTEcV3s/9sRcXVE/Cwi7o6IzRFxVJ0x9yN/YWouvLtMVWm6hrIJeBvwCeAtwIPAZRHx67PtGBFnAh8Dbir3fQ9wK/DEuoLtV/7C1Fx4d5mq0linfFmTeB3wtsw8pyy7kCJBbARevJ99XwC8EzghMz9Tf7T9bXS0aOZqVy7NptXxfvrpRbPp2FiRTOyQV7earKG8BngAOL9VkJl7gAuAYyLikP3s+xbg65n5mYh4REQcWG+o/c1fmJqr8XF4/vPh2GPh9ttNJupNkwnlCODmzLxvWvnVQACH72ff44CvR8SfA/cCP42I2yNiKP8Mmhy/IEktTY5DOQTY3qZ8Z7k8tN1OEXEQ8HiK5rJfAO8A7gbeBHwiIiZnagaLiHXAOoDRAWsPamL8giRN1WQNZSmwt035ninb22k1bz0eeHlm/k1mfgp4GfAD4N0zfWFmnpuZazJzzYoVK3oMW5LUTpM1lN3A4jblS6Zsn2k/gNsy86pWYWbujYiLgbdExIFtmtL6TmverapqFNZMJDWpyRrKTopmr+laZTtm2O9uiprNnW223UnR/7J8ztF1yAkZJanQZEK5HjiszR1aR5fLG9rtlJkPlvuuarP5Vyj6Ve6uJkRJqscg/hhtMqFcDCwCXt8qiIjFwGnAFZm5oywbjYjDpu17EfCkiPiNKfuOACcCV2bmTM1lfcO5t6S58++ovzTWh5KZV0XERcDZ5ZiTW4FTgDHg1CkfvRA4lqIpq+XDFInokoj4K+Ae4HTgscB/rz34Uuti3ru3uJiXLoWDD569L6PX2V2r7nORFjJnSe4/TU+9cjLwgXL5QYoay/GZecX+dsrMSeAlwP8G3gy8j2I8ystm27cq7S7mm2/u7JeSc29Jc+ffUffqrtE1+jyUcmT828vXTJ9ZO0P5HcBJ9UQ2u3YXc8tsv5Sce0uaO/+OujMfNbqmaygL1mwX7f5+KfUyu6ttxdK+nCW5O/NRozOh9KiTi3ampNPt3Fs+70R6OOew68581OhMKD1qdzFPN1PS6XbuLduKpYdzDrvuzEeNzmfK92j6lN8RkPnQ9tl+KXUz95ZtxVJ7zmHXuQ0bipaNqT9Oq67RWUOZg/FxWLIEli+Hj3+8+IUU0fkvpcsv7+yPwLZiabA00Sc6HzU6ayhzMDEBu3YVNZP16+t7KNF8/LKQND+aHD9Td43OGkqPWhdFq5mrzo5y24qlwTHIfaImlB7N90XhE/WkwTDIfaI2efWoiYvCTkdp4RsdLVo02pUvdNZQemRHuaReDPL4GRNKjwb5opBUn0HuE7XJq0fTx6GMjdV3l5ekwTKo42dMKHMwqBeFJPXChDJHJhJJKtiHIkmqROUJJQovrvq4kqT+VkcN5QDgn2o4riSpj/XUhxIRJ+5n8wE9xiJJWsB67ZT/JHAVsLfNtoHul5mYKKZX2batGMTorcKqmjd6aKHqNaHcDLwrM788fUNELAFmeNr6wtaaELI1h9d8zhIqSf2u19rERcDBM2z7OfCxHo/b1wZ5llBJ86vT5yEtJD3VUDLzjP1s+zlwWq8B9bNBniVUkuaqo4QSEX8IPA/4VWApcDdwA/B/gS9m5i9qi7CPDPIsoZI0V502ef0lcAKwCngMRXJ5K/A54HsR8YpaouszTggpSTPrNKE8A1iamWOZ+dTMfCzwVOBNwM+ASyLiVTXF2Ddas4R2++x4SRoGHSWUzLwls/Ww21+WfS8zPwIcDnwFeE/14fWf8fHiiYkPPuiTEyVpqjmPGcnM+4GLKWoskqQh1fVdXuU4kwuB7wL3AE8ATgG+Xm1okqSFpJfbhh8ERoDfAw4C7gQ+BHy4wrjqd8stsHZt01FIfeOc68s3axsMogcLNe6m1Hm+um7yysz7M/M/UNRMXgxcAawDDq04NknSAhLT+trbfyjibODMzNw1w/a/Bo7MzOdXHF9t1qxZk9dcc03TYUh9o1VhX2ijtxdq3E2Z6/mKiGszc027bZ3WUN4AbI2IsyPimW223wM8p7fwBsPEBCxZUtxOvHp1sS5Jw6TTPpSnA39OMZjxjyJiJ/At4A7gEOAlFCPnh1Jr0si95dzLThopaRh1Og5lZ2aeBjwN2ADsAI4Bfgc4DrgO+N26gux3ThopSV3e5ZWZW4F3ly8iYgS4PzP31BDbguGkkZI0x4GNmblr2JMJzDw5pJNGShomA/10xfnipJGSZEKphJNGSlLvjwDWNOPjJhBJw80aiiSpEiYUSVIlTCiSpEqYUCRJlTChSJIqYUKRJFXC24YlAU7/rrmzhiJJqoQJRZJUCROKJKkS9qFI0hCps6/MGookqRImFElSJUwokqRKNJpQImJxRGyMiB0RsTsitkTEcR3sd0ZEZJvXHfMRtyTp4ZrulN8EnACcA3wXOBW4LCKOzcyvdbD/7wGTU9Z3VxyfJKlDjSWUiDgKeB3wtsw8pyy7ELgJ2Ai8uIPD/H1m/qSuGCVJnWuyyes1wAPA+a2CzNwDXAAcExGHdHCMiIiRiIiaYpQkdajJhHIEcHNm3jet/GoggMM7OMY24F7g3oj424h4XLUhSpI61WQfyiHA9jblO8vlofvZ9x7gr4EtwP3ASyn6U/5tRBydmXvb7RQR64B1AKOjoz2GLUlqp8kaylKg3X/8e6ZsbyszP5CZf5CZf5eZF2fmfwPeDDwXOHk/+52bmWsyc82KFSvmEvu8m5iAJUsgAlavLtYlqZ80mVB2A4vblC+Zsr0bH6G442vW244XmokJWLcO9pbpd+vWYt2kIqmfNJlQdlI0e03XKtvRzcEy80GKJrSB60dZvx4mJ/ctm5wsyiWpXzSZUK4HDouIA6eVH10ub+jmYBGxCHgS8MO5h9Zftm3rrlySmtBkQrkYWAS8vlUQEYuB04ArMnNHWTYaEYdN3TEi2nWAvJ2iuewLtUXckJnuH/C+AqmYPdenTfaHxu7yysyrIuIi4OxyzMmtwCnAGMWI+ZYLgWMpbiVu2RoRn6IYBLkXeAnFiPuvAn9Xf/Tza8OGos9karPXsmVFuST1i6anXjkZeG+5PAi4ETg+M6+YZb8J4IXAa4EDgNvL47wvM39eW7QNGR8vluvXF81co6NFMmmVS1I/iMxsOoZGrFmzJq+55pqmw5CkBSUirs3MNe22OX29ard2bfGSNNhMKJKkSphQJEmVMKFIkiphQpEkVcKEIkmqhAlFtZqYgC1bYPPm/psl2bvPpGqZUFQbZ0mWhosJRbVxlmRpuJhQVBtnSZaGiwlFtXGWZGm4mFBUmw0bilmRp3KWZGlwmVBUm/FxOPdcWFw+6HlsrFh3lmRpMDU9fb0G3Pg4nHde8d6HIEmDzRqKJKkSJhRJUiVMKJKkSphQNJT6eUoYaaGyU16167fO+JmmhAHvQJPmwhqKho5Twkj1MKFo6DgljFQPE4qGjlPCSPUwoWjoOCWMVA8TioaOU8JI9fAuLw0lp4SRqmcNRZJUCROKJKkSJhRJUiVMKJKkSphQGrR2bfGSpEFgQpEkVcKEIkmqhAmlIU6fLmnQOLCxAU6f3h8c0ChVyxpKA5w+XdIgMqE0wOnTJQ0iE0oDnD5d0iAyoTTA6dMlDSITSgOcPl3SIPIur4Y4fbqkQWMNRZJUCROKJKkSNnk1yKYuSYPEGso8cFZhScPAhCJJqoQJRZJUCRNKzZxVWNKwMKHUaKZZhU0qkgaRCaVGziosaZiYUGrkrMKShokJpUbOKixpmJhQauSswpKGSaMJJSIWR8TGiNgREbsjYktEHNfDcT4fERkR59QQZs+cVVjSMGl66pVNwAnAOcB3gVOByyLi2Mz8WicHiIjfBF5cU3xz5qzCkoZFYzWUiDgKeB3wJ5n5J5l5LvBSYBuwscNjHAD8FXB2bYFKkjrSZJPXa4AHgPNbBZm5B7gAOCYiDungGG8BlgJ/WUuEFbn8cmsnkgZfkwnlCODmzLxvWvnVQACH72/niHgi8C7gnZk5ub/PSpLq12RCOQTY2aa8VXboLPu/D7gF+ESVQUmSetNkp/xSYG+b8j1TtrdV9r+cDBybmdnpF0bEOmAdwKiDQSSpUk3WUHYDi9uUL5my/WEiIoAPAJdk5le7+cLMPDcz12TmmhUrVnQVrCRp/5qsoeykaPaarlW2Y4b9XgUcBbwzIlZP2zZSlt2ZmW0TkiSpHk3WUK4HDouIA6eVH10ub5hhv1GKuP8fcNuUF8Bp5ftjK41UkjSrJmsoFwN/DLyeYmAjEbGYIilckZk7yrJRYFlm3lzudylwe5vjfQb4HMVtx9+oM3BJ0sM1llAy86qIuAg4uxxzcitwCjBGMWK+5UKKGkeU+91afnYfRdcKt2bmZ2sNXJLUVtNTr5wMvLdcHgTcCByfmVc0GpUkqWvRxV23AyUifghsncMhngD8qKJwhoHnqzuer+54vrozl/M1lpltb5Md2oQyVxFxTWauaTqOhcLz1R3PV3c8X92p63z5PBRJUiVMKJKkSphQendu0wEsMJ6v7ni+uuP56k4t58s+FElSJayhSJIqYUKRJFXChCJJqoQJpQsRsTgiNkbEjojYHRFbIuK4puPqRxGxNiJyhtdhTcfXpIg4JCLOioh/ioifludk7QyffXlEfCMi9kTEtoj4s4hoeoaLedXp+YqI22e43s6a/6ibExFHRsSHIuJbEfGz8rr5VEQ8tc1nXxARX42IyYi4IyI+EBHLev3uobowK7AJOIFiMsvvUsw5dllEHJuZX2surL52DnDttLKZHk0wLJ4OvIPiGroReEG7D0XEfwQ+SzGz9puBZwPvphjl/Ob5CLRPdHS+StdSTjY7xU31hNW33gG8ELiI4nw9Efh94LqIOCozvw0QEYcDXwa+Cfwh8CsUE/Y+GfhPPX1zZvrq4EXxDJYE3jqlbAnFRf7PTcfXby9gbXm+Xtl0LP32Ah4DPL58/8ryPK1t87lvUvwH+cgpZWcCvwCe1vS/ow/P1+3AZ5uOt+kXRcI9YFrZ0yiehrtpStnngR8AB04pe315fl/ay3fb5NW51wAPAOe3CjJzD8V0+ceUMyarjYh4zLA10+xPZv40M3+8v89ExDOBZwIfzcxfTNn0NxRN1SfUGGJf6eR8TVU2TffcbLPQZeaVmXn/tLLvUPxAeQZARIwAvwFcmJn3TfnohcB9wIm9fLcJpXNHADdPO/kAV1NMrX/4vEe0MHwc2AXsjogvRsSzmw5ogTiiXF4ztTCL5wT9YMp27evfAT8DfhYRt0bEuqYD6gflo9MP5qEJIZ9N0eUx/fq6n+Lhhz1dX/5q7NwhwPY25TvL5aHzGMtCcD/FQ9Quo7iIn0PRPvvViDgyM/+1yeAWgFaNd2ebbTvxemvnRuArwL8CK4D/Cnw0Ih6XmUPVMd/GOLAKWF+uz3Z9/XovX2JC6dxSYG+b8j1TtquUmVcCV04p+oeIuJTiF9GfUVzgmlnreprpmhvaJp2ZZObLp65HxP8Evgq8KyI+nJn3NhNZs8q7Kj9EcS4+XhbPdn319P+ZTV6d2w0sblO+ZMp27Udm3gB8CfBW69m1rqeZrjmvt1mUfU/nUCTfnn5xL3QR8UTgH4F7gNdm5oPlplquLxNK53byUDVxqlbZsN8K26nvA49rOogFoNUUMdM15/XWme+Xy6G75iJiOUWT83Lg32fmHVM213J9mVA6dz1wWEQcOK386HJ5w/yGs2A9Gfhh00EsANeXy30eghQRh1KMF7gedeLJ5XKorrmIWAJcCvwa8FuZecu0j9wE/JyHX18HUNxgdH0v32tC6dzFwCKK+7SB4vZE4DTgivLuG5Ui4mGPCI2IY4CXAF+Y/4gWlsz8JnAzsC4iHjll0xuBB4FLGgmsT0XE4yLiEdPKlgBvB34KDM3A4/J6+TRFM99rM3PL9M+U/UlfAk6a9iP5JOBAikGRXbNTvkOZeVVEXAScXY45uRU4BRijGDGvfX06IiYpOuZ/BDwLWFe+P6PBuPpCRPxp+fYZ5fKkMuH+JDP/R1n2duAfgC9ExKcpzuHvU4xNGaq75Do4Xy8H1kfExRQDHB9P8ff5a8Ab29zuP8jeT3E+LgUeFxG/M2XbfZn52fL9eoq/z8sj4nyKmu8fAZdl5pd6+uamR3UupBdFZ9VfULQ/7qEYg/KypuPqxxfwB8BVwI8pBoRuB/4WGG06tn54UYxGbve6fdrnXglcV15v3wfeAzyq6fj77XwBzyv/A/0BxZ1Lu4DLKZp7Go9/ns/V5V1cX8cAV1B0wt8JfBB4dK/f7QO2JEmVsA9FklQJE4okqRImFElSJUwokqRKmFAkSZUwoUiSKmFCkSRVwoQiSaqECUWSVAkTilSTiHhURPxZRHT9LI5y359ExJvK9VdERJavV7b5/PKI+FG5/XMVhC91zYQi1effUEyE+bCZlzvwQornWHy+XH9uudwDHNbm82+nmCUWikfhSvPOhCLV53nl8hs97Hs8cHNm3lauP4di8r5reGjGXQAi4mDgrRQPUwITihpiQpFqEBFXAxeUq98vm6K2d3GI43modgJFQvkXigcjTa+hvAu4m+KZ4WBCUUNMKFI9NgLfBr5F8dCik4Df7WTHiHgSxbNPPl+uLwOeQpEovsmUhBIRv0rxnJn3UDz7Yy8w/el80rwwoUg1yMxLgBHgnzPzE+Wr0ydVHk/xlMGvlOvPovhbvZGihjISEavKbe+leNjbJopazLcy8xfV/Cuk7vjERqkGEXEQsIqimapbxwNfzsz7y/XnlMsbKR6yBXBYRDwO+C/AiRSPBX4WxaOqpUZYQ5Hq0UoC+ySUiFgZEf8nIiYj4qaIeP607QcAx7Fv/8lzgZ9T1D5+RNE5/wzgfcC1ZW3oyRR3edl/osZYQ5Hq8exyOb2G8hHge8CrKGoWl0TEkzNzb7n9WODRPLxD/jtTPnMTcCrFXWQvm/IZMKGoQdZQpHo8G/h+Zv6kVRARjwF+C3hPZu7OzI9R9JWsnbLf8cCNmbl92rGmJoqbKJLJlzLzy2WZCUWNs4Yi1WMUuH1a2dOAn2TmnVPK/gV4JtDqsD8e+F+tjeUdXwexb6L4JPAT4O+nlD0HuCMzf1hB7FJPTChSPW4HTomIPwbuoEgcjwZ2TfvcLsoR7hHxFIpbf6c3d8GUhJKZVwFXTTvOc7B2oobZ5CXV40yKgYZnAB8H1gA/Ax4z7XMjwH3l++Mpah5XTtk+a1NWRDyaolPehKJGRWY2HYM0FMo+lB8DT2o1e0XEt4G3ZuYXIuIyYFdm/ucm45R6ZQ1FmieZ+VPgc8C7ImJJRJxEUUO5vPzI5cA5jQQnVcAaijSPyokcLwReBNwGnJ6ZW5qNSqqGCUWSVAmbvCRJlTChSJIqYUKRJFXChCJJqoQJRZJUCROKJKkSJhRJUiX+P3BnZ5G5epJbAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_w1[0][0::3], yerr=np.abs(best_vars_n_w1[0][1::3]-best_vars_n_w1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\omega_1$')\n",
+    "\n",
+    "plt.axhline(y=w[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 209,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.errorbar(tshift[0::3],best_vars_n_tau1[0][0::3], yerr=np.abs(best_vars_n_tau1[0][1::3]-best_vars_n_tau1[0][2::3]),fmt='o',label='n=1',color=colors[1])\n",
+    "plt.legend(loc ='upper right') \n",
+    "plt.xlabel(r'$t_0/M$')\n",
+    "plt.ylabel(r'$\\tau_1$')\n",
+    "\n",
+    "plt.axhline(y=tau[1], color='r', linestyle='-')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
-- 
GitLab