floquet_mfd_path.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to check the variation of floquet quasi energy vs $(4h/\\omega)$.\n",
    "So there are two options here, either we can change the frequency or we can change the symmetry breaking field's amplitude. \n",
    "We will do both of the options."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. when frequency varies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken 0.49684786796569824 sec\n"
     ]
    },
    {
     "data": {
      "image/png": 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SsHcDOMkY20lEbwHwFwDeTETnAXgLgOcC2ALgRiLaxRhr+nsWfeJLXwK+/GVgaAhYtw5YWACOHwc2bADOOw/YvRu47z5gdhbYtMn6GODbfu3XgD17gL17gWuuAS6+GPjbv7WOB/g4gI+xzwfw7+fngfXr+depKb59etq6bc8evn3vXuu+dl+7eY7TGPn4vezvhPx88bq1m89tbDePnY7XzZrctvcydjXbT2VfJzo991Req9WssZdz8WrsqeDXccJy3HZrmZ3lX/uxljCdW6/4ufYov079IMznH+a1xYE4vf5xOtde6ffvJh8gxlgwBybaA+BKxtjP6o+vAADG2J9LY67Xx+wlohSAWQAbAPyRPFYe53bMiy++mN19991enM6qYV/8Eu75+N+gkM057t+8fAKbCydw79bnAAB2HX8G+XoZ9205xzLmOctHgc98Bo9e9deYy47ioXe/B+d/+R8tc104sx/jzQoemNyJhYzz8TiEoXoVl8w8hmQqiWfGNuKpsUlk61VccuQxpDJp4KabAADzr/0FPDi+DWAMAAFo/bpz4Qi2VZeAm24CYwx3v/0DKFLS8pzTl47hrJUTxrylV/887t5wFrRUCqQxvODwIxhF09hff+WrcOfGs1HLZAHGsGXpGM5ZnuX7u7hhn3/tL+DBdacDqRTwm78JfPGLQKMBJPV1aVrrvtU8/nP97XzFFbjomUewhtUta5yensbU1BSwdy+0l78Cd284C6XcCH/euecCjz0GXHGF43yWbe3GrmY70HFf7vd/Dy889CAS4r3QQ0C+703vxMzwmtZ5Ox2332O6HPfQgw/i/Oc/v/s5pXk3LJ3A8xYP9/Ya9cLevZh73RsxtFJseW95yt69OPSLv4ot8zPIpBL+HbfNWo68/s349w9+GOd/7Rr369IN+rU7Z/YAtlSXgz23Xtm7Fw+/5d04nhnp/B49VfTXyelzzQ3jMy/q6J/Zd0yejcpQztvXulf0a7Nt/gh2Fo/3/B4emGsUFHv34t5ffR+WkllPfw6N301B0svvxbihvzYLv/5m/NKVV4TudwkR3cMYu7hle4CB4RsBvJox9h798dsBXMoY+4A05mF9zGH98VMALgVwJYDbGWNf17d/GcB1jLF/czjOewG8FwAmJydf8K1vfcvT8+qVpx8+iI8e3th2fwoafmpoCTdXxgEAO1JlbE1V8ZPKWsuYL0zshzY6ht86uBlNkONcL8ku4o354/jgwtldre1Da57F+ZkSPrywHTPNLADgd8YOY3e2CGzdCgD4+8cY7qiOuc6zLVnBx9cdArZuxaGVBK7cn28ZM0YN/N3Ek8a8/76/iv+3MmHs/7nhefzyyHFj/96nCvhiYYuxP62/BsnTtnIV1I3ZWXzuMYa7Oqy737x86CTePjrHz0FfY7FYxMjICDA7iycOLeATi2f4uqZT4Yo1T+OcTNlyPp1oHp3Fbz6QRyMm5c0Ehs+sfwIj2zZ3/Rr1xOws/uThNHakynin7b3lJdUjs/jAQ3m8deQYfnp40bfjOjI7i489nMLBxnBfpz0rVcZHxp8O9tx6pHR4Fh94eASsze8AL5gaOtnTe8/4zIs6s7N48MAirl7eFvRK2pKjJj67/gkkuvm9KDEw1yggjhw6hj9+vPU+RxFP3rytgtdUDoXud8lP//RPOwaGgaWS+gVj7EsAvgRwxTBsfwW784FDAIDfv+UaXHbofsu+z7/oTbhh1x6M3vMA8NwpbF06hkS9grETTwPPeSm+e83v4bvP/Rlc84LX4rKPXonap65GE4Rfv/u/cNorLsBFf/d3xlz/63V/iLHZJ3HBbd8A3vV5fPB//gUvO3CP45qeGd+C37n897Hzmq9j6uDdwLu+gOdUinh843bs+Ma3MHXgDkO5+9p3f4gdY5vw1/99NUDE1Tbp699c9is4sO40TH36I8BNN2HviTqwv4CrbvwCzp/ZDxDhqxe9FtefvQdTH/mIMe+P/+lrGH7ey/GNf78Sv/aGj2Dd/Xdg6pZ/MvYfufrPgZ/5TXzlPz+Bm7e/AF+/4NW47GNXYeiHP+hKMfzKf92Ms/Pr8Jc3/T3wu78LfPrTQL0BpHTFsKkB6ZR132oef/ZzAID3XXcIax55AFM3fb6tYsg+9hng9R/GX97wOZx91RXA+c8DHnoY+MBvt8zXsq3d2NVsB1z3Hdj7AD50Xwk7/vnrmHr2/p7+Cla85TY0HjiJd977fbz+iVutx+xw3L6P6XLcvffei4suuqj7OfV5pz/1j/jbS38Z51/9dzjjP77hmWK4cusBpI7ux9S1n/LtL5JHb74V9YcWseaGH2Pqrn8LXDH8o/95Aheua+CjX/sz9+vSDQ89jM999WY8MnEmpq7+SOj+yuvG/ut/AoZl/MFPvoYXzzx66q+FGw89jCu++xCaxQVMfe/PYqkYHvzbfwVe9i5c858fx+hf/5V3r3WvPPQwbrz6n/G5F/4izv3LT2Pzf/2rUgx95LvfmQZQwue+9xfYUl707OfQ+N0UJL38Xowb+mvzzPvfhamPRud3SZCB4REA8p/aTtO3OY05rKeSrgEw3+Vzo8HrXgd8cS92jxF2n73JUmO4O1vDDQC0Sy7BlkIZFySK2D++AeyMDdi5XMDuS8/DHeu42sh+cD3wghcCV/0Qpz13J87aMITdl55n1BDmnsiB5c8C++1/AW5awvaLzsXuDWXHGsPcsSJQBLRfeSvwyr+Cdv1JjNWHgSagvemXgVf9mfHm1m4vYOTEEnZf+SHH2sL1zZ14qpQyfiDYUyeAW+/Arte/ErsnLwfm5/EDbIe2lLH80LBfLCF9sITd3/wSsj84Ce2SS4GPvs087gd/F3hwBef//V9h/7NV4NEy2LXXdfdDt2cPtNuWMbqwhN3f+CJ/zguf077GUN63mscAcvcW0Ri/EPhwmw+GPXvQ+MSfAXcWcd6fXoHnvealfPvpLwXWfbE1f99pW7uxvW7vsC+ffQFw3y2o/erbgFf+dU8fdLUXXAxcewPOfPFu7P7Yr7U+121N/R7T5bilA0nsPn28+zn1eWcrGnBXESv/dI13vwz27EH5+wtYGTsP+JB/v3SKz30+8MNbsPyylwOf/K1gf9nt2YPl7y/ggjU18+f5VDj9pdg+U8P/PLUSmV/kgvmd5wE/uh27X/1i7H7F73i79tNfijOeLOPgXCFyr1Nf2LMHR9/9fmSfXMFLv3I16MUvDnpFJqe/FOUmw+duK+DAP34Dm+N2bQJm3+gmpOkpvOptr0H6p6c8+9kwfjcFSS+/F+OG/tosPf10pD4jgwwM7wJwNhFtBw/q3gLgrbYx3wPwDgB7AbwRwM2MMUZE3wPwDSK6Gtx85mwAd/q28j5ipPJ+9rPAzgnLPpp+CvjB42BnnQV6ZhF0wQ6w2WWwyVHQsSLwV98F/fgp4LrHwS65BKyp8ee96U1A42ngu9815/r0LWATebALzwFu+jHwrncBF37EcU00VwA+fQvYG94APH8L2I9uRHLLGcCBebDLLwcuOs0Yq61ZC8rkgfe+yXGuxL8+APbUvBnw6aebeNvbgO3r+Pc/eBzsJwctPzTapk1IzM0Ae/YgcfON0J5zIbDHzKXXztwOPPgIkpe8EInks8Cjj6N5ySXdvOQAgOboGiTzo+Yx9+yx/tDavz+VxwCS+RyaOyaBPe3/utc4exdw571I7b7AusNhPsdt/dzusi+d5Gmg9ctfD+ze6vzcNtT192jmNa8GLj29p+N6MqaXcT2OHXreucBdd6F8nnd/PWWMYUUDSltP8/WXTrHaAAAUnnchsOeCDqO9pdHUsNIEcmvyfXsN1u48A5Wn9qFy8SUY6suM/rBQqgEA1v3GO4FN3qfKT565BbcvzkTmhqffHMmNY8tEMlxBoc6Ol10C3HYTDmw8A5cFvZiYsX+ugLMmR5H+4BVBL8UfevkdGjf27AGq1Ui9PoEV+jDGGgA+AOB6AI8B+A5j7BEiuoqIXqcP+zKA9UT0JIDfg2k68wiA7wB4FMAPAPx2VB1JRYWnW0WIUQUqDSKyfmUwgy5ymIwI0BgzAlFyGqSTEHPq82kMSOobNVtJKpPGt5tLk+pYxffyc+xjxLikvsYEUcv+pmbOkyAyntMtTcaM5/lBKkFoaJrrmIZ+Tim3FzQEpJN8fbWG+/k4IZ4j5hhkcukkAKBc8+6jqVLXwBhQ8vAYTpSq/HjFat3X4zpRqPAgNZfu33tqPJcBAJxcqfVtTj+YL1UBAOvyGV+ONzk2hKVyHZV6JH/9njJHF8vYvCacfzqYHMtiOJ3EweOloJcSO/bNFrBrcjToZSgUqyLQGkPG2LUArrVt+xPp+woARymKMfYJAJ/wdIF+0iaYAyRVEdYAkD+NjDGdgkxL8NjFYkSgJcoG7WsRj93mIpAtMNS3S0FZ0jHwM8ckiD+WMQLMBJmBoT1qdUHTGHdT9Ilkgoxgth1NIzAMtzGLeN1q9ovSBVU9MPTztQ+KXIZ/vK54GLSVajwoWtEVPL8QAaEIyoJkucLXkuvjb7PxXBoAcLJUx+Y1/TW18ZL5oq4Y5vwLDAFgbrmCM9bHz2xjZrGCl5w90XlgABARtk/kcfBEMeilxIpCpY4ji2W8tV1GjEIRcgb/7izkuIlcInTSNB6YEQAwgIEZAaFVMWyvBhIRGJMUyg4qn22VhmJoXy9jcFXeEgmryuikGBJRqxLJmDEmkSCHgFSslYy1dQq8ZIJRDN3XJ/YnQ64YZkQq6SoCQ6EYZmMQGA5n+DmWPVRThBpZ9D0wDOa4TiyX+68YrtUDq8WIKYYLpRrW5tJIJf35+Zoc427Vc8tVX44XJupNDccKFWwJqWIIANs35HHghFIM/eSJYzwQP0cphoqIMvh3ZyFH6HzkoLuJuEVjjAeGRIbqZ49pOgV9JI5mKIbtb6LIlpqpMRhpnaYuaV2b21wWxdMIDM0nOSl+mhS4OaaS6o+TREi0SXN1Q2MwnucH3SiGDT3QSoU8zVLUGK4mldSoMYxFYMglrHLNu+DJUAxrzZY/nnhJSdQYhkox7GMqaV5XDFeCT5XthYVSzbc0UsCqGMaNueUKNAZsWRteRfmsiTyeXVhZ1We1YnXsny0AAM7ZpAJDRTQZ/LuziOAWXPE28DyUk1NG+fNMydAtTVR0kBDPdouJxC4xH2OsbfDFA0P3ekWLYqiJ7WQZI+Yy5zW3JwhoOhxXnJfT8zuhaQx+xl+pRAIN+0nYiIximDoFxbApagwH/6PHjxpDkaba0NiqUntXSzFMgWFZDww9qDFciJhiOF+qYr0KDH3h6BI/580hDgy3b8hDY8AzCytBLyU2PD5bQC6TxNYQvy8UCjcG/+4s7LimklrTN4kgKYZ6KqkxDTPVPIdALaGrjSIwc08ltQaBsmJoD74Y62Q+Y1UM5YDOGOMQdGpSMJpItCqGmmE+Q23X5kZTY74GYL3UGKZDXmMozHFqHQJdJ8RfrjMxCAyHMzwwXPEhlRQwDWH8wAwMg1fUvKgxXKvXGC6WohUY+q0Yjg2lMJROxDIwnFksAwC2rg1xKukEb1J/UKWT+sb+uQLOnhz1NSNJoegng393FnLcDGNkwxejxlB/FrWMMSdrN5fGpODRNZXUPK746lZj6JaWmrDVD2oOsaucMmuM06yppPY0OTFPUjKf6aXGUE5V9YNUsntX0mTIU0mJCJlk4pRcSeOQSppNJUDkrWJYkmr8Sj7W+xV1pbDa0AJPU/OixjCbSiKfSUY0lTTr2/GICJNjQ7GsMTyiB4ZhNifaPsENgQ4cVwY0frF/roBzJkeCXoZCsWoG/+4sIrilY2q686dhICPVGJqKYecaQ/HcdmPMtZhzQn9ewggMW2sM3QQuEZAK3GoMmS2AtKSS2oI+S7sKoTj2cH8aRsXQqDGMwF8aM6nEKaWSxiEwJCIMp5OeBoaysY2X7qd25CA0aAOaQqWOBAHZZH/nXZvLRMp8RtMYFko1X1NJAWBydCiWiuHRxQrWDKeRzwZq7u7KmuE0JkYySjH0iRPFKk4Ua6pVhSLSDP7dWchxdSWVUjrF90LzM/sYSu0q3Ixl9FRS46HLmuQ5+THNYMW+XIYOrqR6MCsQsVHnGkO7+YztuJIhj8hK7LmPoY8B2CC5knYJJ0MAACAASURBVAK8D+EpKYYxSCUFgFwm6WkqqZw+6meAJh+rGHCd4XKlgdGhdN8zAMbz6Uj1MVws16Ex/3oYCjaOZXGsED/FcCbEPQxltk8oZ1K/2D+njGcU0Sced2chxnAldbmnMRRDoCX4s7SrcJnLMK5xCMycxkI6lhyk2XsFdgrGCK0BHz++OcapQb2sirZLJZUDR8B0Ku0Gbj4TLsUwKjWGwCkohjFKJQV4naG35jMNx++9Rg4MlwOuM1wu1zE61H/VZjyXiVQq6YLe3H79iL+B4aaxIcwuVXx1xQ0DM0uVSBiM8F6GKjD0A8ORVCmGiggTj7uzCOBYF+iwgaeDMscxnVxJge4CUbv5jGww06IYsg6KYcLe4F4c36Fdhc18JmmYzzikkjIzsEvYFM5uaDJ/U0lTic6BVEPjKmgUitbTycSqXDDjlEoKwPNU0hWL+Yx/gWGp2jCuYdDOpMuVOsaG0n2fN2qppKK5/XofawwB7kxarjdRCEFPSz+ZWSxjc4iNZwTbJ0ZwvFANhVHUoLNvrojxXBobRv39GVQo+kk87s5CjHsqqTSGJJdSaR+MoMi9xlCkdDqZv7Q9LpjxNengHMqP26mPofU5pmIpr41/ldXIpmQ+k3RIJZX7J5rmM+3XYUfT3APaftOdYqhFor4QwKrNZ4w+hjFJJR3OpDxNJV0JyJW0UG1gk96qIOgaw+VyA2PDXiiG6YgphjwwDCKVFACOxajOsFRtYKlcD3UPQ8GODdyARqmG3rN/roBdk6OunhEKRdiJx91ZiOlkGAPI5jNmOijZxjAwQzFzqjGkLsYYY+WAFNZm8G4pnU7Y00DNPoqSYmgEnbKyKLXkcGhwL7uWihijF1dSbj7T9fBTpqsaw6a/KuapcKqppOmYKIa5dBKVAUwlLVUb2KTXVwWtRHipGC6V64YpVNiZ1wNDv1NJzV6G8akzPLrEHUm3hNiRVLBjQgWGfsAYw/7ZgqovVESeeNydRQKHYE6qvSMiiwMpjKDJ3GjETs7eM9A0KRXUTeWDLQiU+hi2tKsA69DH0OY26tDgXjbZMeZl5rxJpz6GzDRpcapR7ITfqaRduZJqDKkI1BcCPJW0voo+htWYmc8MZ5JYqXsXsK3UmhjXe+4VfVQMS9WmYbwRvGJYx9hw/wND8boulaOhGgrFcDznf40hAMwuxUcxnFnk5xoFxfD09TkQAQeOq8DQS2aWKihUG8qRVBF54nF3FmK6qYvTdIXQbHAv9TGU0kthbGuFQLpi2H6MwF5PKNf7MdiVO/fZEtSuxtDheG1dSVtbUTS11lTSXgJDTWO+pnukkomOimFTY0iFvIehQLmSdsdwJulpG4lyrYl1+QwS5J9iqGkMRYtiGHS7ioYniqFIyYxKOulCqYbRoZTv9bsilXSuEKfAUPQwDH+NYTaVxGnjw0ox9BjDeEYphoqIE4+7sxDjmkoqqYH29E6zXYW53dznnJfK97emcrYe1+pAKrekaKkxBFwVQ7LVBxo1htKTnM1nzDFOqaRMClbF114b3PvpSprqSjGMUI1hanXmM/WmhnSSImGw0w+GPU4lLdUayGdTyGdSvtUYiprJ9fkMMslEoIFhU2MoVL2pMVyrK29RMaCZD6CHIQDkMimMDqVwLEappDNLFRDB+ONI2Nk+MYIDJ1STey/Zp7eq2LVRBYaKaKMCw5Dg5kpqOIlKqp9jjaExznkurjbqj11TScWcHK4Y6tt6NJ+xq4HO7Spg2Se+N1JJnWoMpdpGInNbtwTR4L5TrVKUagzTqzSfqTU0pGOiFgLe9zFcqTWRyySRyyZ9cyUVx8lnUxgZSgVaYyh6KI56oBiKVNKoKIbzxSrWjwTjhjg5Fq8m9zOLZUyODkXms2zHRB4Hj5di11LET/bPFrBpbAhrcv3/LFIo/CQan2qDjNvntNzgHqSbz4hd1gDCqhi2mUp2Je2Q/inmFF+dDGLEY/eeiFY10LnBvZP5jJRKmmgN+ppMNp9ZRSppB9OcftOdYhidGsPsas1nmlpsWlUA3qeSrtQayGVSyGdTKPmUSioUwpEsV4qCrDEUPRTHPOpjCCAyTe4XSjXfHUkFm2IWGB5dikarCsGODXmUak0cL8RH1fWbfXMF7FJppIoBID53aCHF7Cvo7CQKmK0ZjBpDKZq0Nri3bpNJkFAbO/cxhKTgifHt0i479jG0qYHONYatxja8nYS53ymVVFYU+XPC60qaTHZ2JY1WjeHqXUnjUl8I8FTSWkPrKc25F1ZqTQxnkshnUp4GoDJCMRzJpjCSTQWaSiqMYbwwn1mr/+VfpZJ2ZuNYNlaupDOLlUgYzwi2686kB1SdoSc0NYYnjhVxzuRI0EtRKE6Z+NyhhRy3cMC8pyRDGWwxn2Ed2lWQrdehy/HkbEYRjxmqnNaqGLpNZlcandaYcGg3IZxY+Xqo5bhyn0MxrtmjK6mfdW7dKoYDn0oaM8Uwl0kCAMoepZOuVJvIZ5LIZZK+KXdFKZV0dChlpHMGgakY9j8wHMmmkEpQJFJJGWM4GaBiODk2hGOFSk9/nIsqjDHMLJaxJSL1hYAUGCpnUk94er6EWkPDOZvGgl6KQnHKxOcOLaR00+Aeol2FZDRjNrg3t7n3RCRdAbQ+z/m4ZjAnhhuqnsP63Y1szHF8TjGfOcYplZTPa45tbXCPFvMZu3OpG5rmr/lMMsFdSd1qPBrNaJnPrKZdRRwVQ4C7h3qBSCUdyaZ8cyUtVuVU0rQRnAXBcpmvxQvzGSLC2lwGJ0vhVwyXyw00NBZcYDiaRb3JIpN2eyoslGqoNrRIKYZb1gwjm0rgoDKg8YT9uvHMOapVhWIAiM8dWkhxrQu01eeZDSOYsU9+WqcgU05Dda8LNOcTwVq7Oj6GTuqjNU3UNJ8xn+XUx1BukeGUSqpJ7SpEnBHmPoapROs52uGKYTR+JNPJ1bmS1hrxUgyHMzxg8S4wFOYzKaz45Eoqp5KOBpxK6qViCHADmigEO/Mlnsbpd3N7gXDnjEM66VG9X+PmCDS3FyQShO0TedWywiMeny2ACNi5UaWSKqJPfO7QQk679E8AeiCofy9MZox2FXLg1b5e0fJcdBnMwRxv1gpax8ruoc5zmePk51vNZ8T6zMllc5mEQxqmHDj2mkrKdOXUT/MZsdaGi6zZ1BjSEakxzKy2j2FMU0m9aHJfa2hoaAy5TBL5IFNJAzSfEUGpFzWGADCez0QilVQ0t1+XD8aVdOOYCAwH34DmiN7DcGuEFEOAp5OqGkNv2D9XwBnrchjWP+8ViigTnzu0kOJqSqp/1TTYzGfatKtwCfqIyNauonP6p8aYZBZjywmF+dDdfKZNjWHCaYy5TWOQagxb1VDZVTRpBMfdBYYiyAxCMXSrM4xSjWFmla6k9aZKJe0XYk7hSuqX+YwIBEeHeLuKYrURmA3+crkOImA02/9UUoArhlEwn5nXA8OgzGcmYxQYHhXN7SPkSgrwwPCZ+ZVVfW4r3Nk3W8AulUaqGBDic4cWUrpxCTVcSUF8vFRjaGlwD+s2mQTxQaYLavvjOcWACaI2tX7u5jP2NFGnVFKnPoay66hTKmnTth8Auv19J5RFv/sYAnB1Jo1SjaHqY9gd4i/IXgSGoj2FUAxLNX8CtFK1gWSCkE0lMDqURlNjnpnrdGK5UsdIJuWZkdR4LhqK4XxRDwwDSiXdoPdPjEMq6cxSBZlUIrAgfLXs2DCChsZw+GQ56KUMFJV6E4fmV3COalWhGBDic4cWQeTgzehjKD2Wx1jUQKe01JYxLseVnE7l9hKkt7yQ6Wg+Y4yzp5JKYzr2MaSWNFFm63MIuKtxMiKb08dMUlMxdDFsiZpi2NBYzy6Ecasx9NKVVCiEw3qNIWPeuZ/KFCsN5DNJEBFGdKUuqDrD5XLDszRSAFiby2BxpRb6xuALeo1hUOYzmVQCEyMZzBUGXzEUjqRuWTdhRDiTKgOa/nLgeAlNjSnFUDEwxOcOLaS4p5KaARNXDIUyyFrGsA5qIOmqG5Metz2urEJKgZyTYigre07YaxPN+cwnmamg5vN4H0PTfMZ+Xya3qxDBVNeppB16M3pBUlfJ3BRDXmMYjR9Jsc56L1awAKoxCwxFKqkXaZ7ChTSvp5ICQMkHA5pitYlR3exldCjgwLBSN9bgBeO5NOpNhpJPabqrZb5Uw0g2hWwquBqnjaNDmFuKSWAYsfpCANihWlZ4guFIqhRDxYAQnzu0kOLmSiq3ouBjzACqJZUU7mqgEVR2kboqm88YiiGIK4YOtX5OCqUxl83N1LHBfZs+hnK7ilbzGXNuI5W0y8DQ7rTqBwNXY6gHhr2mk8auxtDDVNIVo8aQp5ICpmOolxSrdeSz/HhmYBhMuuVyue6pYjie4wpc2FtWLATYw1AwOZaNhWJ4dKkSKUdSwXg+g7W5tHIm7TP75gpIJ8lQZBWKqBOfO7SQ0y79E9AVQ/17pqt+9sDO4jjqqBh270oqH1euWyS0qnIMDG4dFuxpouL5zu0qnFNJk23aVdhrDLvNahTpj0G4kroV/kepxlCofr32MoybK6lhPuNJKqleY5hNIae3xSj50MuwVG0aKaRCOQzKmXS50vCsVQUArM3xuRdDXmcYjsBwaOBrDBtNDXPLFWyNmPGMYMdEXimGfWb/bAFnbRiJTLaPQtEJ9U4OnM431kyKBLkyKPUxNIIbJqWYOmuGDJDSTXtLJSUintJpG8tjLDdXUmN50ni7+YyzK6kIOJ2VSrnPob6ty8gwrK6kzQgphkYqaY8Od3FrcC8CNm9SSU3FUARqfjiTFqsNI3U18FTSct2T5vaCcT3YWgi5M+l8sRa4GcrGsSGcKFbRGGDXy7lCFRoDNkcwlRQAtk+MKMWwz+ybU46kisEiPndoIcVd5TODQRJjdPdRI5VUmqezYuje0qLluIyZqaf6HPbgq3ONYTtXUnmMOZeA11WagZ9TKqnYn+wi6JIRKadeORk60ZUrqcaQikjQJPot9ppKGjfzmaE0P9eyB0qeHBjm9NROP5S7YrVhBKKm+UwwilqhUvdUMRw3FMNwB4ZhUAw3jQ2BMeB4cXBVwxm9VUUUawwBYMeGPGaXK76knMeBYrWBwyfLqr5QMVDE5w4t5DgGc/pXS7sKWE1a5BpD+/NkzOCr/fHs65GPxc1nWhXDzn0MzXPgX8X87oohY6Y5TDLhkErKGEQveHuvxE4IvxQ/zWdSuvzZSTGMWipprUd1oN6MjsFOPyAiDKeT3qSSVkW7ihTyQpn0wXymJAWGIpU0CMVQ0xgK1QbGPDWfCX+NIWMM86Uq1gXUqkIwOTb4LSuMwHBNNFNJRR3coXmlGvYDYTyjFEPFIBGfO7SQ4upKaguqDNUPZmBlupK6N6/nPRDN43WqrxO9A+UG94TW4EsEre3PobXG0B772M8TEK6j5hxO/RPldhb257th9jHsanhfSCWFYtg+kKo3tcikkq7WfCZuiiHAFT1PUknrkvmMrhj6UWMop5IG2a6iWGuAMXhqPrNGnzvMvQwL1QbqTYaJfDbQdcShyf3MIj+36KaSKmfSfrJ/VnckVYGhYoCI1x1aCHHtPSipfASzFyEkMxpTMZTaVTgch0g3k+kyeDJcTPXHCTINbGS0DoqhnOrKx7OW8U6KnyXwo9agz9KuIgLmM93WGEZNMeylxpAxFjvzGYA7k3qjGDaRICCbShiKodcpYowxlKoNo7YwmSDkM8lAzGeWyzxY8zKVNJVMYGwoFepU0gW9uX3QqaQbdcXw2EAHhmWMDaWMP4hEDbOXoQoM+8G+uQKG00mcNh7NPxQoFE7E6w4txLjFKEyvp7M0vF9NjSHkVE739Yi0UU2alJvAtNYYdpoHsKaS2o9t9iGU57XWELYqlaY5jYiluq4xDMB8ZvBqDHsPDEXaaTZugWE66Vm7ilwmBSIyagy9Np8p15vQGAzFEABGhlKB1Bgul3kw6qX5DMANaMKsGM7raa5Bp5JO5LNIJgizAxwYHl2KZg9DwVA6ia1rh1Vg2Cf2zxWwa3LEV78ChcJr4nWHFkKYSzKp3Lyem79Y00EBa5DFHLbJc/EgjhmPXREqnaXGsDX1tWONof4Ok81n7KmuToGdtY8htZjeaFo/UklVjeFqEYFhtYdUUtHaQhjXxAXPUklrDeT0/oXZVBLpJHmuGBb1lFE5MBwdSgejGFa8VwwBYG0ug5NhVgz1wDBoV9JEgrBxNDvQNYZHFiuRDgwBrhoeUIFhX9g3W1T1hYqBQwWGAePalN6ovbOljDJ5vFxj6BL02cxkOprP8IOZCqPe4N4efDGgpWZQxq4Y8kDSdqw2qaRmOwrnGkOx30gl7VIxDLKPYcOl71+kagxX0cdQ1CPGqV0FwP9K700fw6YRGALchMbzwFCff1RWDLOpQGoMjVRSD2sMAe5MGuY+hgslHogFnUoK8JYVg1xjyBXDaBrPCLZP5HHgeLHrshKFM/PFKk4Uq8qRVDFwxOsOLcS4xSiGAQxE3Z+pullrDMVkrXMk9FxSN1XRPp43uDfbSyQcawy7M58xagy19jWG8txNzXyuU42h3K5CPL/bGMVoV+FnjWFywGoMRSppD4qhERimkh1GDha5jFeppA2jTyLAA7SSx6mkJd311KoYBhMYimN6rRiO5zKGKhdG5g3FMFjzGQCYHM3i2IAqhiu1BhZX6ti8JtqK4Y4NeRQqDeN9o1gd++eKAKACQ8XAoQLDgHF3JTVNVQhkUf0M8xkxD+ugPsLefsI9ABFGM1aF0d0d1Al7j0Insxp7Swsx3kgl7dSuQqSrdq0Y8q9+CldmjWH7QCpSNYYpfj69tKswA8NonGO/yGVSWPGoj6FVMUx6chyZQpUrZ8IFFRCBYQA1hiKV1OMaw7W5dOjNZ4bTSQxngv+Dy6Y1Q5grDKZiKBxJtw5AKimgDGhOlX2zywCUI6li8IjXHVoIMdM53AI1HgmSHhkyKbXUWq/HHLaJcbC2n+iwLrv5DIF0xdBuPuN8PHkewF5j6D5GjEtIiqA9nrLvF9u6QQtCMRw0V9JTMJ+JW43hUDqJSr23th7dsFJrIicpd7lsCkWP+xgKxXA0a6p0o9mAagx18xmvHSLX5TIo1Zo9t2bxi/kQNLcXTI4NYXGljooHqdNBI3oYbo5oD0PBjokRAMBB1bLilNg3V8TaXBobRoNX6hWKfqICw5Dg1uDeaFdBcsootYzpqBj2kEpKEO0tzPFO7SrkINUJJzXQHpA59THUpFpE53YVpumMUOOaXQaGYXQlZYyhqbHI1BiuxnxG3FjHzZXUKyVvpdZALm2qRCPZpNH03iuKbRXDYMxn8pmk5yr7Wj3oCqtqOF+qYSJgR1LBxlHRsmLw0kmPLunN7SOuGG4dH0YmmcBTJ4pBLyXScEfSUdc/jCsUUSRed2gRQw6YiOQgkEmKob5NqjF0bldBunFNNwol321NJSWj7lCGobVhfctEkNtVtI43awxtrqQW85nWNhmyaynf5n5KAqPGMESupCJgjIpimF1FH0OhGMYtldSzPoZO5jMe1xgKRXJkyNquYqXWRKOH90I/WC7XPTeeAbj5DBDeJvcLpWqoFEMAA5lOemSxAiKeLhtlkgnCGetzSjE8BRhj2D9bUGmkioEkXndoIcRd5bPWGMqKnVFjaNTwyfscUklhDZy66mNoM58RdYoyRv1j23nM9fHxrTWJQiWzpJLa2lFozBo4yg3ue+1jKGoRkz7+pa+TYijWHpkaw1Mxn0kGXwvlJ8N6Kmm3NbDdwlNJzdcyn0l67koq5h+xtavg+/xNH1yu1D03ngG4+QyA0LasWCjWsC4ExjOAGTQNojPp0cUyNo5mjc++KLN9Iq9qDE+Bo0sVFKoN7FLGM4oBJPqfcANCu7pAwFrn1+7WkhvLMMvzrJNZg8euzGcgtasgOLarcFIAZZwb3Dubz1j7GFpTSQFrYCsrisku6vdkgkglNWsMnQOpqCmGaV3168V8ph7TGkOh6vVbNbS7kuaz3pjcyBQrDSSIB7sC0bpi2WcDmuVyw3PjGYCbzwDhTCVljGG+VMP6kKSSTo7ywHB2afACw5mIN7eX2b4hj6fnV7r+namwsm+uAEAZzygGExUYBoxbg3tpkKQMMqv5jNHHUEoldZjCSLe0VCi2hyuGZrCZIOLun441hi6KYcIcJ9bZbR9DN3MZJrmbkkMqqhtBtKvo1MdQpOFFpcbQNJ9ZRR/DGKaSAv0NDJsaQ6WuWVJJ89mU5yYwxWoD+WzK8jM/qqeV+m1A479iGL5U0pVaE9WGFppU0rHhFLKpBI4VBrDGcLGCLRFvVSHYMZFHrakZhjqK3tg/qwJDxeASrzu0ENLJMAbgsZhh/gK9jyHIMkhuRdGmvz0YY4a7Z7fmM/IfFAkEe0uJTnPZgz5Nc2pX0VojKAecTuYyTaldhRjTrfmM2a7CR8WwQx/DyCmG+vn04tRYjWtgqKtr/exlKIJMe7uKSl3zVAUoVRstLqCi3tBvA5pCpeFTjWF4U0lFf8WwBIZEhMkBbHLPGMORxeg3txds151JnzquDGhWw765AjaNDWFNzvvPH4XCb+J1hxZinA1j+FeN8UDQcBa1KIYc0fieb3NOS9VkV9IOmiGRSFuVFEOyCobi/tO9j6G1ftDZfMbcZ87NjD6Dch2lvF8+bpJaeyy2QwSQQfQxrA9IjSERIZ2k3voYNuPqSsoDp34qhsJ91N7gHoCn6aRCMZQRNYbCsdQvuGLofSrpcCaJbCqBkyFsCG42tw9HYAgAmwYwMDy5Uke1oUW+ub1gxwbVy/BU2D9XUPWFioElXndoIcRd5DLVNiIYERKDFBgawZEZ9Tm3vrC6knZUDMlMWxWPyRZ8GXO5zOPU4L61xtDBfKZDKqkmtasQ6+u+wb3/qaSGK2mbQKoRQN3jqZJJJnoynxFjB8G8oReGM/x8V/qoGIq57K6kgLcmMEUnxTDrv2LIGMNyuW4EpV6zLp8JZSrpfJGnbIZFMQSAjWNZzA1YuwqRcjkoNYbr8xmMDqVUYLgKmhrDE3NFnDM5EvRSFApPiNcdWghxU/BMxVCM0Z/DzFRSq2JoHWefSx7TCaFOmscmI1gUGIqhSzAjO6saa2+pMRTzMWOMHEAK91CrOY1VeUwmKNTmMx1dSZvRSiUFuAHNahTD+KWS9l/JMwND2XyGB4kljxVDe2A4FkAqaanWhMbgi/kMAKzNZUJpPiMUw4mRcLiSAjBSSbut+Y4CZmA4GKmkRIQdypl0VTw9X0K1oWGXqi9UDCiB3KER0ToiuoGIntC/jrcZ9w59zBNE9A59W46I/puIHieiR4jok/6u3htcxSubEsgAI/qTt8k9B53mZ9JcnXr4GeYz9nYVsmIoUlddXUn5V2sfw3Y1hiIwtD7XHiAD1nYVYo5eU0n9VQzdawzrWrTMZwBdMewlMDTaVcQsMNRVvUo/U0lrIpVUblehB6AeKoZhqTFcLnP1zg/zGYD3MgyjYhi2GkMAmBzLYqXW9N2MyEsGTTEEeMuKA6qXYc/sF46kKpVUMaAEdYf2RwBuYoydDeAm/bEFIloH4KMALgVwCYCPSgHkpxhjzwGwG8BlRPQaf5bdf9z+qmomiTIQEUwHUqmPobTNLVAjW6DXKfzgNYlWs5oEkcVF1a1vonxcwNquwh772PsYarbAzR44GvMk5MDQmmrqBgsgMOy6j2EiOkFTOplAraFcSTshgjfPU0l1xdDLG/JStdlSYzicTiKZIF9rDEVrDD/MZwBuQBNW85lsKmF5HwSN0eR+gNJJjy5VkEklQlXLears2DCCI4vlvv7BKg7smy2CCNi5UaWSKgaToO7QXg/gq/r3XwXwBocxPwvgBsbYAmPsJIAbALyaMbbCGPsRADDGagDuBXCaD2v2BLfbajOosgZyPB1TtGowt3V2ODVdRrtqcA852CS9js8cYwZwbvOI9ZnPsQdk4qEIjsQaRTDl1KfQ3vYimWjtsdiOZgCupKKurq0rqUgljVCPv8wqU0ljV2OY9iIwbDWfMRRDD1NJC5U6RrLWIISIMDqU8lkx5MfySzFcm0tjMYSK4XyxhvX5jGvLIL8xA8PBMaA5sljGljVDoXqdT5XtE9yA5tC8Ug17Yf9cAaevy1k+exWKQSKoO7RJxthR/ftZAJMOY7YCeFZ6fFjfZkBEawFcDq46RhpnwxiOMJ9xSqmUrGfMGsM2Dqca607lE2i2YLOtYugWGCbIMlZ2VDXG2BRBEeCJcQmH8+btKqyppF3XGAbgSirOobNiGJ0bj17NZ1QqqbeKoVDySn0MQGUYYyjVmkbqqMxI1t/AsGAohv7cnI3rNYbdGlz5xUKpinUhaW4vGMTA8OhSZWAcSQUiMDyo0kl7Yt9cQdUXKgYaz36rEtGNADY57Ppj+QFjjBFRz79tiSgF4JsA/o4xdsBl3HsBvBcAJicnMT093euhPOXxw/wG5/bbb8fEsPWG+aFj/EaLMWBhfgGHtEUAwEq5jOPHqpiensZj8/wm8L777jdaIdx3733YlC5bznVmpoparYF9+/YBAPbuvQ3jQ+1v0KvVCmZn53D33fMAgEceeRilUh3HtBVj3rKeRnjgqQOY1p51nOeJk3x99z9wPxpHUpg7VkG5rFnWVqjxefbtfwLT1UOo6vMeOnAA0ziMJ57hr9H/3HqrseZarY6ZmSOYnj4BAGg06jh8ZAbT0/Ntz0nw8Ax/Xe++6y4czvsXpCQJOHDwEKanZ4xtxWIR09PTeHKRv06PPPwQknOP+bamU6FSLuPosZWuf6aePFBDkoBbbvmxtwvrM+IarRbxfn74sf2Yrh7qy5ru138m7r/nDhzK8vfwQoUH3vc++AjGTu7vy3Fkak2GpsYwd+QZTE/PWvZRo4pDR2Z9+3y9Q/8ZfuyBe7HwJD//U71ObswfrUNjwHU3TSOfDs8fbw7NlpFPU6h+r1X09/ve+x/F/j8TrAAAIABJREFUuuUnW/Z7eZ284uDcCs5dl4zcut0Q1+nGOx/C8Pw+y74oXiM/qGsMB46v4NyRaiheH3WdokHUrpNngSFj7BXt9hHRHBFtZowdJaLNAI45DDsCYEp6fBqAaenxlwA8wRj7mw7r+JI+FhdffDGbmppyG+47c3c9Azz8EPbs2YOttsL25mNzwL13AwDWr1+HHWeMA0/sRzY7hMnJcUxN7Ub2qXngrttxwYUX8Abi99yFi15wEZYPPAD5XG9eehj3npjB2bt2AY8+jMte/GJsHGvvsJa780eYnBzH7ovOBPbeiueffz5uOLof69cOY2rqYgB6nc+NP8TZZ+/E1Eu2O84z9sxJ4I7b8Lzzn4+pczbiW8/egwJKmJr6KWPM4koNuPkGnLVzJ6Yu285rpG68Hjt3noWpnzoLR+98Bnj0Ibxozx7jr7aJH12P07dtw9TUeQCA4dtuwqZNGzA19fyOr/n8PYeBBx/AnhddijPW5zuO7xepG6/D1m3bMDV1rrFtenoaU1NTyB9aAG7fi4suvBAvOXvCtzWdCusevRUj2RSmpi7tavxPio9i6MgzCNvPYCfENVotmsaAG6/F5m1nYmpqV1/WtP+Wp4BHH8crpn7KMINZrtSB6R/itDPPwtRLd/TlODLHC1Xghhtxwbm7MLXnTMu+zY/vBREwNbWn78d14unbDgEPPoJXvOwyrNcdOU/1Orkxf89hfPPxB3De7ksMpSUM/N87bsbZ29ZhaurCoJdiYfQn1yM/sRVTU89t2efldfKCRlPD4vXX4aLnnImpqXOCXk5f2XTnTcDoBKamLrBsj9o18ovHji5D++FP8KpLn4epC7YEvRx1nSJC1K5TUDld3wPwDv37dwD4L4cx1wN4FRGN66Yzr9K3gYj+FMAaAB/0Ya2+0K7FhPk9GfUNvF2FbYyUS9quxtDS0qJDrYQwnxHjE9TaroIJYxqXecw0Uf7Y6MloOVYn8xlY9osxctZlgswU0U4E4UoK8DRR0ZbCTiRrDJMJIz20G+pNDemYGc8APJ16KJ3ob4N7PV1U1C8CQM6DWkaZkm5qYzefAYDRoZSvLpTCldSvPobjeX6csBnQzBdroXIkFUyuGZwm93OFKjQ2WI6kgu0TeRw8UQx6GZFBOZIq4kBQd2mfBPBKInoCwCv0xyCii4noHwGAMbYA4OMA7tL/XcUYWyCi08DTUc8DcC8R3U9E7wniJPqBWywj1wHK4YLc488aF5pGMS1zEekGNZ1bTABSuwqpyFAY0pjr6Gw+Q7ax3JXU3q5CPwfRrsJwQiXLV7m+p6VdRYJ6bnDvd2uIZIIGq8awV/OZhha7+kJBLpPqex/DoXTC8h5OJRPIphJGANdvii6B4Yjf5jOVOobTSd8cbsdzPPgKUy/Dcq2Jcr2J9SGrMQR4y4pBCQxFq4rNawajh6HM9g2ql2EvPD5bQDpJONPHTCOFwm8CsVVijM0DeLnD9rsBvEd6/BUAX7GNOYzO3RYig5thjHyWVvMZWTGU2lW4KYZk63XYYV2kH0eTxgsV0b52t56ICZsayBiDvSODOcZqPiPEs6RtP/TzsLar6MGVlAUTGKaSidj3MYxbqwrBcDqJcq3716oTK7WGoyveSDblWYN7ERiOhkIxbPhmPAOYgeHJUnicSedLvB1EGFsoTI4O4Y6DC0Evoy+IwNBe6jEI7JjI4+RKHSdLNYyH8H0UNvbPFrBjYiS2v8cU8UC9u0NCZ5dQc7/GzIdmg3vm6hJK4JGhqRh2OB6JwM9MuyRbE3nDPdRtGrKOdWpXYe9jaKR66ttFIOmWSppMENpkabYgFEO/U0ldFUORShqxPob1HvoYVpsxDgwzSZTrfVQMq03H3nW5bBIljxrcu6WSjmTTKFTqrn1Z+8lype5bqwpACgxDpBiaze2zAa+klY1jQzhWqPj2fvCSmUWufG4ewMBQ1MseUKphV+ybK2CXSiNVDDjxvEsLEe6ppPbHco2hLZVUrh90CNXsNYOdQqKEnnoq9z0k2JvMdw4yW1tRtI5v7WNonVfMIattre0qum9w3wwolTSVIDQ1Z9VIBIxRqjFM95hKWo91Kmmy7w3unQLDfCYVSCrp6FAK9SbjBlg+sFyp+9bcHuDnlyCEqpfhvBEYhk/p2TSWRb3JcDJEr9dqObpUxthQyjB5GiR2bOBN2lU6aWeK1QYOnyzjnEnV2F4x2MTzLi1EmHWBrfvkAEpOJWWWMdJcLvWDBGsqaSe1zDCrkcYnyBbIdtXHUKyNf7UrffJajBpD45jt9jO9H6ItlbTrPobW+f1i4GoMezSfqcVYMRxKJ1HuY2BYapNKms+mPDOfMVJJHfoYjunb/KozLFQaxjH9IJEgrM1lwqUYFvlaQplKqjtezy5Fv85wZrE8kMYzAHDa+DBSCVIGNF3whG48o3oYKgadeN6lhZAOJYa8xk//3ursqQdNsAaMLXORVVXsJBkK8xk5XdTe4F7rIshsrTF0Mp/p5Epq38+/yopfMtF9g3sjlTQQxbCNK2kUawxT1HuNYYwVw366kpbbKIa5TNKzWr9ixd18BoBvdYbLZX8VQwBYm0uHSjE0UklDaD4jWiHNFQYhMKwMbGCYTiZw+rocDqgm9x1RjqSKuBDPu7QQ4ZpK2sZ8hjFI5jNiW4caQz2o69aV1Eg9Nebk7SrkTEhm1B+2n8dsNSHXGHYawx+LVFERS9hTTROW18da/+iGaW4TnhrDRkRrDHt2JY2pYjjcd8Ww6awY9tn91HLMagNEZlsMmdEsD9IKFX8Cp+VKw1G59JLxXMYIxsLAiVIV6SQ5mgEFzeQYr3s8NgDOpDNL5YF0JBXwlhUqMOzEvtkihtNJbBvPBb0UhcJT4nmXFiK6VfBI/w+wKoZyuwrx/3Y1hp2cS53WJgeS1EYxdDPOMXsUmkGdfXxLH0PNGrza52ga+2XFsIcaw6BcSROJtn0MmxGsMcwkE6j32scwporhcJ9rDMu1hnONYTblmflMsdpEPpNyVNpHfEwlZYxxxdBH8xkAGM+lQ5dKuj6f7WwkFgAbR3XFcLka8EpOjZVaA4sr9YFVDAFgh96yottSjLiyf66AXZMjvmcaKRR+E8+7tBDiGMy1BFD8K1cMdfMZqfCwkyspTzftzpVUmM8w6TFvYWGOsQdwTsjmOIAwn3E6nmxQ45xKKuYQXy2ppD20qwjWlbSD+UyEfun0aj5TjbFi2O9U0pVaE/msU2CY9LBdRd3xmIBZd+hHYFiuN9HQmO+ppOO5TOhSScNoPAPwHqfr8xnMRlwxFI6kW9YOsmI4gmpDw9GIXyuveXy2oOoLFbEgnndpYcIlmLGnkgqcFUPJcdQxldSWbtphWS0KI+mBlMNyu3ElFUEbc2hXIcbZU0lFVqWRStoSOFrX0G2NoYhl/O9j6JJKGsEaw3QygXrTTE/uRJzNZ/qdSrpSa2I43ZpCmMuksOJZu4pmW2dGP1NJl8s8+PRdMcyHy3xmvlQLZXN7wcaxocinkh5d4j0Mt6wZXMVQtKw4qOoM2zJfrOJEsarqCxWxIJ53aSHCNZiTv28XGEoqohn0OamPVvOZTmoZN5qxms/YG9w7BWhO8/CxML46ldElEoR25jMtqaSsVfFLJnpvcB+EK2lb85kI1hhm9SCv3mUDyXpTQza2qaQplOvNvqRrMcb0Bvet6t1INolaU+vJLbZbitVG+8DQR/OZZT349LPBPcDNZ6oNra8B/qkQZsUQ4HWGUU8lFc3tBz2VFAAOKGfStuyf46+NUgwVcSCed2khxDFGkRUxkK0Wj4ztgAj63FpfWNtVdG0+YzwmI1gUdONK2k2Dez6HVVWU521pV6G1HjdhM8ZxQ9O4AY7ftTmpBBkBoJ0o1him9bV2m05aa8S3xlAEcf3o81dtaNAYb2bfehweLHlhQFOsNhwdSQF/awyFKul/jWG4mtyHPjAcHcJcxBXDmcUKiMz2G4PIxtEs8pmkciZ1QTmSKuJEPO/SQkSXIhdAUpzo8BxL0Of4dNGwvrsDCoXRbDbfqhh243BqFGpL9YFOAZnch7BpC/yEe6jY7mQekyAytneiyVggKZuuiqEWjCHOqSBaT3RrQBN3V1KgPwGbMLFxcgcVNYAlD1StkotimE4mMJRO+KMYilRS32sM+fHCEBhWG00Uq41Q9jAUTK4ZwoliFY0e6pDDxsxiGRtHswP9uUVE2L5BOZO6sW+ugDXDaWwczQa9FIXCcwb30y4imMFVD+YzcEol7aLG0GGudpCo+ZNUQdJ7GwoMV1LXGkMxVq4xdBrnlErqPIdTCmsyQV3XunHF0P8ALJ1MtDef0W+eomY+A6DrXoaxDgwzIjA89YCtpAdfOYcgTSh6Kx4EaIVK+8AQAEayaX9qDPVj+N2uYq2uGIbBgMboYZgP743q5FgWGgNOFIMPpFfL0aUKNg9wfaFg+8SICgxd2D9bwDmTo6F0AFYo+k0879JCiKPKR9b94qHGWsfLrSWcZhNBnRGIdrCfsaeAiuNbgy9zXzscawydgmBqDfzEh3BLywuHdhWJnsxnlGLYD0RaaLfpkfUmi29gqKt7lT44kwp3U8d2FRnvav1KtYaRMurE2FDKl1TS5bJKJZ0visAwxIqh0bIiuumkM4tlbB3g+kLB9ok8Dp9cQbURjvrZMMEYw765AnZtGgl6KQqFL8TzLi1EuIUyVvMZsgRITuYz5tj2c3VbY5gwAknzccKmOq6+xrD98eQ1inEiWBJimziuJZU0QejSA4Wnkgbwl7+US4P7psaQSlCk/iKZ7UExZIyhFuM+hjkPFMO8Q4P7fh5HhjGGkkuNIcAVPF8CQ/0Y/je411NJQ9Dkfl5fw0SIXUlFXV5UA0PG2MA3txectSEPjQHPzK8EvZTQMbtcQaHSwDmbxoJeikLhC/G8SwsRrr0HpY3ybksfQ7lhhVuNob7RydHTCQIP4qw1hlbnz25cSU1zHLMVhXONYatiKAK/blJJ5T6IndA01jEw9oJOimGU1ELAVAy7MZ8RY7JxVQz7GLAJV8zhNg3uATN47BfVhoZ6k7mnkg6lfKoxrCObSmDIocbSS9YaimEYUkm522eoFcM1PM01qoHhyZU6KnVtoB1JBaJlxQGVTtrCvlndeEY5kipiQjzv0kJIN6mdTn0NLe0qXJrXi/k1l+BRxlAMpePx4Msc0436aAZ14jluNYa2Pobt2lU4NKhP9pBKqrFgUjZTiUT7PoZNLVL1hYAZGNYbnV930T4hE1PFsJ+ppCK4dFIMjcCwz66kItB0CwxHfawx9Nt4BuBN20eyqVClkq4PcY3h+nwWyQRFtmWF2api8BXDM0UvQxUYtiACw12TKpVUEQ/ieZcWIlxTSdvUGEL63jSk6eBKKpnU2Od2PrjersKYk69AjmvstYBO2Bvct21XIfUxbGrWNRqppIaBjXVu8fyuawxD6koaNcVQ1At2oxiKXodxrTE020j0IZVUD/qcFUPdlbTPTe7FfG6ppCO+1Rg2MOZzGqlgbS4dGvOZVIJ87+XYC8kEYcNINrKKYRx6GArGhtKYGMniwHHVy9DOvrkCJseyRsaAQjHoxPMuLUQwl2iuZZOcWirUNLmPoVtaqv61m2BOjJcNbRKJ1nRNpwDNTrfmM/LcrX0M9ee6tqvovvVHUK6kvMbQOYhqaixy9XdGH8MuzGfEmKidY78QtX/lfpjP1Dqbz/Q7lbRQ5cGQq2I4lELRlxrDYBRDgBvQhEExXCjVMJ7PhL4meXIsi7lCNBXDo0s8oI2DKykA7JhQLSuc2D9XUI3tFbEinndpIaRdiwnze+dkU7mFhelJ6uz6CQBdimo8cJJTSUG85YVTKqnLPJQQY03F0OlcZVdReyqpk+oonxOgq3Hd9jEM0pW0jUNOFBXDXsxnjFTSmCqGoh6u3IcUz5JLKqlIWe13H0OhGLqnkqZQrDUM12CvWK40fHckFazNpUNRYzhfqoW6h6FgcmwIc0vRVQwzqUQkXud+sEP1MmyhqTE8MVdU9YWKWBHPu7TIYDWf6eQ26pYmatTpac41fq3jW81n5DpAQDKBcXkXiaBOdhxt2+De3scwYZ3D3q4iYVNQtW4DwzbprF6TSrZ3JY10jWFX5jM8sIhrYNhPt9CySyppIkHIZ5J972NY1BVDkarqxOhQGoz1v77RTqFc992RVDCey2AxJIphmI1nBJNjQ5grRDQwXKpg85ohJCL2ubxatk/kcaJYw1I5+D98hIVnFlZQbWjYtUkFhor4EM+7tBDRjeomBshKYIv5DLqrV2xqrKv0owSRpW4xoZvftHYxdDfOcXIUdfo969TH0FAME2IO61dZYUsSda1UaCHsY9jUGJLJaN2AGK6kXaWS6jWGMU0lNRTDPqSSlmpNpJPUNsjOZVN9D86KumLoFpCJHode1xkGm0qaDke7imI1IoFhFosr9b6YLvnNzGIZW2KSRgqYzqRKNTRRjqSKOBLPu7QQ4ugkajGfse43H0vtIFxrDM1av27CD7tiCFDbdhXurqT2GsM25jNSH0NRhmdPJTVTTVvbVfSUShpGV1KNIe0mvYaQXsxnxJhMKlrBb79IJgjZVMKoDzwVyrWmkTLqRD6T9MB8Ru+d2KHGEICnLSsYY7r5TFCppBksVxpodPGe95L5Ug0TI+F1JBVs1HsZHo9gneHRxTI2x8CRVLBjgwgMlQGNYP9cAUTA2cqRVBEjonUnOoAwF53Pfgvt1q5CnsstyGxX4+e4NmlpCTLrDs393fVEFMcFeNDnXGPYvk+hPZXUqV0FkRlQdlxLl+m0/aajYhixlKVMT4qhaFfhb++5MJHLJPuSSrpSc280n8+msNJvxbDSOTAU9YdetqyoNjTUmlpgbpyiyf1igOl2tYaGQqURCcVwU0Sb3DeaGmaXK9gaA0dSwenr8kgQcPC4UgwF++YKOH1dznCVVijigAoMA8a9xYQ18HFsVyHN4zqXMY517JkImKmksospSY8ta+9CMZQdR9sphvYaQzIUQ+vxnNxQk73UGAYUhLm5ktabWuQCQ7PGsIc+hjGtMQS4MUy/Ukmd6gsF+Uz/G82L+ZwMbwSjuornZSrpsh6QBaUYjuvBWJB1hsIVNQqB4aQeGM5GLDCcK1Shsfg4kgL8s3nbupxqci+xb1Y5kiriR3zv0kKGm7GM+N5ZMdQDL9mV1MXhVGPoKpeU9PYRco1hwlZjaHcPdaKlwT3gqNbxPobWPoUiULKnkjq1q0gmwm8+k0wQGm2CqKbGkIpYjWGmB1fSelMFhsOZZN9SSZ1aVQhy2f4okzLFagO5TNL1jxdjPtQYLutzB9muAkCgzqRmc/soBIY83TVqTe6Pxqi5vcx21bLCoNpo4uCJkqovVMSO+N6lhYRujd2pxXyGf++sGDorckB78xen8fY57TWGhgtqh3nEcc3jO63P2tJCbANaG9w71TYSEbot+wnKfIYrhszSC1LA21VE68exlz6GVaOPYbSC334ynOmTYlhtuKY25bOpvvcxLFUbrq0qAH/MZ5YrQjEMzpUUQKAGNAul6CiGa4bTyKQSOBYxxfBIjJrby4jA0Ol3VNw4cLyEpsaUI6kidkTrTnQAcQvmWsxnLI+tY7j3TGczGK3LVFKRNioHYfY+hkIFdHM5ldcnntOuXYWhCNpqCFvmcKgxTCYQAcWQ/7g5lRk2NYZ0xFJJV2M+k42xYphL96f2r1x3Vwy9MJ8pdhEYilRS0drCC4xU0oAUw7WixjBIxbDE1bf1I+EPDIkIm8aGIldjaDa3j5diuGPDCFZqTSxWVWC4f045kiriSXzv0kKGm5Oo+dh9TDf1irxdRXfrkYxODcXS2uC+1R3U6bgiLVU8x7ldhVxjaB6Tz6+v3VAM+XZZ9bP3WHRDYwikN5VIFXWqM4xkjWFCmc/0Qr9SSUvVhmutXy7jRbsKd8MbAMilkyDyKZU0KMUwL1JJw6AYht+VFODppFGrMZxZLGN0KGX8sSMu7NBbVsyWVGC4b7aAVIKMNh4KRVxQgWHAuLqSOtQUmhus2y19DF3qFbtvVyH6GJpGMHK6pzim2OdGwhb0dUoltbuddpNKKiuOndA0hiAyGsV5OK0zijWGiQQhlSBVY9gl/TKfKXcwnxnJprBSa/Y1HaybVNJEgjCSTQ20+Uw+k0Q6SYHXGCYIWBuQatorG8eGcCxiNYYzi/FyJBVsNwLDYNuxhIH9cwXs2JCP9e8sRTxR7/iA6fbejadySjWGtvCOSQWBbmmpvF1Fd6mkdvMZ3tvQHOPUT9AJeysKR/MZB8VQBFIW4xyYqaRJSyopdf1aBulKCsCxl2EUawwBHuh1ExjWVI1h39pVlGpN5DuYzzQ1ZtR19oNitdlRMQSAUa8Dw0qwqaREhLW5TKCupPOlGtblM4FkPayGydHopZLOLJZjl0YK8PYiQ+mECgzBW1UoR1JFHIneneiA0jlWs4Z79j6GsmLo5nDKulQMhfmMkdYJ0ltYOLWrcJ+RQJagzrnGsH0fQxEAioDQcEO1pJI6K3FOBFVjKALDpoMzaRRrDAHesqKnVNIY//V1OJNEpW+KoYv5jL6vnwY0xWrdaGDvxuhQ2uMawwYyyUSgtarjubSRzhkEC6VqJIxnBJNjWZT+P3tvHiRJdp+HfS+zrq6jZ3qmZ3pm757F7uAiQAlLXATBhkBSdDgs0ZQtBy2bkC0GQyFRsk2bYSoYFhSiaUm2LIdMSZRhmg6SYdMSTTJIWjTg5QK92MVB4lwci+0e7Mzuzk4fM9M93V13VWY+//Hy5VV5vKzKrMyset/GRl15vO6e7sqvvu/3fSM98QqVNLF/2l+64BmAvac+cbGBg95yW0m7Qw23j/tyvlBiKbG8V2kFgNdK6g6j4c/bzDDpGUOD2iUYYYph1PHcM4b+VlL3jKG3x9BtJdU9VlOAvaHpojOGGSmGqtn7F6wYFpQYivQYSispVsqzK4ZjnRW8hymGXNlLsrKiO9TRqEbPhzZr6SuGqyslIddDWlirVzINnzk2FcOi4IqpvB2cFkM17I90POiNl5IYAsCTl5pLrxjeuNsBAFyXiaQSS4jlvUrLCWiY/dNZT4GAHkN+HFDXPKAXnHPoolZSArPg3l4AId7wGX5skRnDcCsps4J6FUMvMYTndfc5RGeqdJqtldRP2dR0o3AzhgBLGY1jJa2oy/snp27WVcwy+8fJXnjBPXstSYWmM4gOnwGAVq2UqjLUHmiZzRdyrNUrmYbPHHVHuFiQ4BkAuNxixLAolRV7p8vZYcixud7AvT4V+ru+qNg5OAMgiaHEcmJ5r9JyhrBSeuuxiyhOVjk4OFzgwSgVVQxNMucgaXzukMOqx4g4lkK8dRX+21jk0bCfAwA+emdZSf3qKmKGz2RVcA/4p5LqBZ0xLKtEzEqqGyirJFOlJ2vUKiooxUyzfzzVNKzHsG4phskQtJHGVMqWEDEspx4+08o4dGWtUc40fKZoiqFVct8uCDE0OwyvnltOxXBzvQGDAm8c97JeSmbYOeigVlbw6Fo966VISMwdxbsSXTCEiQehVlJLMTQJH5wzfz7HMm8NQzCV1Dyok2x6KyFsAhcnldSflBEHsQtWDEPqKhQCQV6YT8WwoDOGccJnllktBFidAzCbxZPXUITZOptVrhgmYyXls4oiimHqqaSDcWZVFRw8fCaLEnBNN3DSGxeMGDLl7bAgyaT7J4zALmMqKQBsXmLJpLfudTNeSXbYNYNnihLwJCGRJJb7Si0HCFX5HIgqpXcrhrOnkipmXYVTneP2Uo44M4Z8W0qDra6cL1kWVSXcSuquqzBfE2CHuhFNZtOAGpJKmlVS6qyIEz6zzPOFgK3yzaLkccVwpRySSsrPk5ClsxODGK7WSmgP0i24z95KWoZm0EzCVI5NC2sRyu05GtUSWtVSYWYM75z0QYhNaJcNvMvw1v3lJYYykVRimbHcV2o5gh9ZcllHJ2yl7uedM4b+PYY2uRLhH3b4jP1YIcRFvMJSUJ1QPPODQXUVfBvdM0NoWUktq6lZV+E4EE8uFQmgYeEzkZsljpL5hfgphuOCzhiy8BmxHsNlJ4Y1c/ZvlmRSEfWO9w12Ewqf4QRIxErarJYw1AyhDwumwdlAw+pK9oohgEwCaOxy++IQQwC4vFrF3YJYSfdP+7jUrC7t36vz9QpaZeDmkhLD4+4I99pDmUgqsbRYzr98OYKwlRQe8mjed9ZQ+O3nfY6RK4HwGfOYzroKwK0YeovogyBiJfVu4zyupRh66yo8qaTOfcOQVV2FpRgG1FUUUTGMYyUtSyspgNmspL1xdPhM3XwtqbqKOFZSXmmRlpqWD8WQkbIsAmiOO6ZiWKDwGYCpb0Wxku6dDJY2kZRjo6Hg5r1O1svIBLuHbQDA0zJ4RmJJsdxXajlAWICL9znid99SDMPrKhQHMRThRHye0Eo6VexuQ2vtITON3nVbVlL4K5ZOu6nhOa7XSupbV2GRx+ivzTBoJrMDUTOGpQKGz1QEraRDqRhahK0/CzE05wYbYT2GlmKYDDlrmySvKTDb1zRJWxp20sFYx1AzMiu351irs/Nn0WV41C2elRTgxLAYiuHeaX9pE0k5rjSUpbWScmIoFUOJZcVyX6nlCFGppMSc8fO+ZtlNHZ2DYbZU3aBC4TMwk0SdZJOlizrCZwTrKnhHIaU0ZMaQOGYMvYohe54TQuqxmgKwrKFCVlJKLevpPKGq4amkpQIqhmWVYCzSYyjDZywraW8GKymfT6yHKIbVkgJVIRaJnBVcMWzGUAzTCKDhx8w6fGatIa2kcbGxWsPds2EmgT1xQCnF3kkfDy1pIinHlQbB3fYwkznarLFz0Ma5lbKVpishsWxY7iu1HCDO+2RoXQXCFUMHfxRWDNlx3eEzfgX3UXyGE8qw3kMn6bRmCLldlgff8BlEnxlDb3JpGPKYSjrWDYs4FgmiVtKxbqAqFUMAsyn7nffLAAAgAElEQVSGfQErKSEE9Yqa2EVdZxDDSlpNkxgyIpa9YpidlfSoOwIh9hqKgo3VKka6kWnNhwhOemMMxgauLrmV9Eqd/a1+bQlVw93DNq5vtJa6WkliubHcV2o5gB3gEm4mDa6rMI9Dw8Ng+FMGpZEJp3x7g1KXrZMllU6Gz0TNLHILahiRVBUyYSX1WkWjXgfEUkmNnKaSFlMxFE8lXfYZQ54kOgsx7ApYSfnrSfUYdmIphmXXPknizFIMsyWG51bKIASZkJzj7hDnV8qFm0e2KyvybSe9Y3YYPiytpACWL4CGUopXDtp4+koz66VISGSG5b5Syznc4TPEd8aQE0qnIudfV2EraqKppE4rqUII4FEM/SydfuDl9Rah89mB9RjCWiPA5ho5VL/XHYexZyijvzY941RSb/gMpbS4M4YlsVRSWVdhq3yzWEn7Iw2EALVy+PeyUVUTSyW1yWiwSsnRtKykyZOmsz47ZitjK6mqEKzWyjjJInymYOX2HFbJfc6J4b5ZqbGs5fYcl+vMpbNsATQHZwO0B5qcL5RYaiz3lVoeEGJ9DONbE4ohHEE2YYqhEaROumGFzzh0QcVTZGiHz4jNGIb1HrqspD7hMk4rqW9dRYhN04usrKS2YugmUnzJRVQMRcNnRjJ8xuoX7M+g5HVHOuplNfJ3rlEtJZZK2hmOUSsrKAl8mpJmKulZTqykAAugyUIxvN8ZFS6RFLAVw7s5TybdMxXDZU8lragED59fWboAmp0DM5FUEkOJJcZyX6nlABRiM39eK6nzecCt7gXtD4jN4PHtnXOLCiGudFHnsSIVQ0VkxtDPKhr1usNKGqOuwjCyqasImjHkM3pFnDEsq+J1FcsePmNbSafv+OuNdKxE2EgBNs+YVPhMZ6ijWRUjY2mGz5z182ElBVjXm1QMxXGpxcjsQc4Vw73TPiqqgosF/B4njc31xtIRQ6uqQhJDiSXGcl+p5QRBdMCpChDPlvw1v35Bf0XOJCWCdRXEnAukDpWPzRjaEE0l5aQujEiG9RgCTG3j/CO0riLH4TNBM4acKBZSMSwpYqmkuoHykiuGqkJQKSnojacnTb2RhkZVwNJZLSVWV9EdamgKnBMAqiUVFVVJhxhaimG2VlKAK4bZEMOiVVUA7N/FhUYl91bSvZMBrp6vZVJnlDdcW2/g1r1u7pNkk8TOQQeXW1UreVhCYhmx3FdqOUCoyue8H6AY2mmjjs5B3xlDdmsIppIS85h2wb27a5CfUwTEPK8f4XOuz+o69CGc7td96io48RWxkmalGKr+a9QsYli8X8c44TPVJVcMAaYaDmbpMRzplvIYhnolSSupJtRhyNGqlVKbMSwpROjrTxtr9QoedOdrJdUNige9UWHVrMutau5L7vdP+rh6brmDZzg21xtoDzXc6+T7Z5Ykdg/buC6L7SWWHPJKLWNQ0MB5oYkeQ5/XnNuIFM5TwVRSrg66rKQBBfdRn67aiqH9tfiejxfYG5PEz2kl9aurcFpqo2AY2dZVBCqGBbSSVlSCkW5Efkggw2cY6hUVvVnqKka6UG1EkuEznaEWmYLqRLNWSq3HcHWlnIsY+fP1ytwVw5PeCJQWr8OQ48q5Gu62864Y9pd+vpBj8xJL5rx1bznspLpBceNuW9pIJZYemVypEUIuEEKeJYTcMG/XArb7mLnNDULIx3xe/wNCyLfSX3G6CLSSunoLvdZSt7nUVVfhd6wpUkmd9k8zlNQ8lzckJvpYLluqzzY8udR9XLeV1DtjSDyvA3kPn2G/bronfEbjM4YFtC9xsudXweHEWIbPAGDJpLOkknZHWmi5PUcjScVwoAlVVXC0aqXUwmeyLrfnuNAoozfSMdSSId8isMrtm8ULnwGAjVYNB6f5JYaabuDgbLD05fYc19YbALA0c4a3j3sYjA2pGEosPbK6Uvt5AM9RSp8C8Jz52AVCyAUAHwfwPgDvBfBxJ4EkhPw4gMJnKccruHfctxRDPmPoJHE+Vk3zVhdMJSXwdiMSu/TefNImotGKIVsff+yzjS/xcx7Dft7XSsqJoVD4jJidNmlYiqFnJk8r8Iwh7yaMspPKHkOGWa2kfVErabWE3kgX6vWMQncUz0rarKZnJc1DIinAFEOAFaLPC0cmMSyqlXRjtYr7naHQh3dZ4G57CIPKRFKOh86voFJSloYYvmImksqqCollR1ZXan8RwK+b938dwI/5bPPnATxLKT2mlD4A8CyAHwUAQkgTwM8C+G/nsNZUEZZK6nresw3x3DpTSf0VQ74dFTCS8vAZNrfota1OKnvhx1IIgWE4tvfZgW/D16gQj0JKiHWR628lJda+UdAptWYS54mgGUO9wDOGXAWMSiaVdRUMs1pJuyNNzEpqqor9GdRJ65xDsXNytGrllMJntMw7DDnWTGI4TzuppRgWlBheXq3BoMDZKJ/EkFdVXF3ycnsOVSF44mIdry6JlZQnkj61IcvtJZYbQu+yhJAPAnjCuT2l9DdmOO8GpXTfvH8AYMNnm4cB3HY8ftN8DgB+EcD/CKAXdSJCyE8D+GkA2NjYwPb29pRLTgevvz4CNajvuu717Ivt22/cxkr7jvX45s2b2Ka3MdTYm+yrr74Knk7//PPb6Ha7rmN+54BdqLU7HegUkd+HO3eGGGsaXnvtdRCw7V97jV2YbD//PEoKwc4b7NPyz3/h8zhfDb7o7/X6uHuvhxc/9zkAwHdv3MD28DXXNocHQ/QHOra3t3HrtZF1Tg5tNMKdvX1sbx/juzfZOl584QVUTLL1ivn1ffFPvoQ3W+EExDAobt9+A9vbB6HbJY2TIft5vvzKDrZ7NwEAnU4Hn/vCFwEAuzuvYLv93bmuaVbcMv8NbH/2RZyv+X/fDUox1in2MvieJ4FOp5PY341+Z4De2P/3XQSnnT4e3D+M/v01fy7PfuazgT8X4XP2Rnhwdx/b20dC23dPhrh3oif+t3b/qIeHGkrgcZP8OUXh9SP2x/Yzn/sSDi7OJwznC+bPdOelL+Nwp3gfsty7y/5G7z3o5e59GAC+uG+ub/db2N4v3vc3SfDfpRYG+PYb3Vz+vJLGi98c4NIKwZ9+/sWslyKMef7Nk5geRfs5RRJDQshvAngSwNcB8I+fKYBQYkgI+WMAV3xe+gXnA0opJYQIf4RICPleAE9SSv8LQsgTUdtTSj8B4BMA8Mwzz9CtrS3RU80FX+y/AuX2Lfit680HPeCznwEAPP74Y3jXE2vAV78MAHjyyWvY+vCT6I904I8/iWtPPoneUANe/S4+8pGPYHt723XM/jf3ga9/FbWVOgD4ns+JFzovQz24jccefwzKazextbWFb9PvAjd28AMf/jCqJRW3v/Aa8PK38aHv/36sh8y9tF56ARfOr+CDH3gn8JnncP3609h63+OubT559A3stu9ia2sLX+y/AvV19/dk5QvPYePKOra23s3WsbuDrR/8QUuFGnyLfX3veeYZvO3qauBaKKWgn/wjXHviCWxtPR36PUgax90R8Jln8eRbnsLWB58AwMjv9be9B3jhs/ied74dW+96aK5rmhV3v3QbePkbeOZ978cja3XfbYaaDnzqk3j6LdewtfWWOa9wdnh/l2bBb93+Ml6738PW1oen2n/83Cfx1BOPYmvr7aHbPfjam/iNl1/Cu595HzbNWaGpzqcbGH/y/8Xb3rKJra2nhPb5zOm38O0He4l9zzj0z/8xnnz0Mra23uX7epI/pyhc3jvDf/+lF/DE02/H1vdcncs5v/7Hu8DLN/Bv//BWIW3ZF988xT/96osYKrW5/Zzi4JXnXwVeegV/4Yd/AK0cdGVmCf679CeDV/CrL9zEh37gwygV8N9cHPzSV5/Hu59oYGvrmayXIox5/s2TmB5F+zmJKIbPAHg7jVlmQyn9oaDXCCGHhJCrlNJ9QshVAHd9NrsDYMvx+BEA2wA+AOAZQshrYOu/TAjZppRuoYCgCP62ensM3WE0ZviMI40z7Afk3E4k5IRVTLC5QD5b6E3+FO4xVNzVF/51FcQ1Q+jdxGklNXxSS/n3Kmp+xc+GOi8E9RgWecbQtpIGf9/5/OGyF9wDrEZi2h5Dw6Doj8UK7nmK6KwBNHz/OFbSphk+w36Pk/s3fdbXctFhCABrDUYcHsxxxvC4O8K5lXIhSSHAZgwB4GSYTyvp/kkfrVpp6UmhE5vrDYx1ijsnfTx+cfoPmPKOoabj1v0ufuQdfuY1CYnlgsg7zLfgr/zNgj8AwFNGPwbg9322+RSAHyGErJmhMz8C4FOU0l+hlD5EKX0CwIcA7BaVFAIAaHAq6QRcRMh7GAoa2lFoh7OIFdw75hb5jCE84TMhKaPuM4sU3LvTTr3k0ZlKygNmnOSOzwxGFdz77TsvlKzkVPc8XpFnDEXCZyxiKGcMUSur6I+iex/9wOcFGyKppNVkiCFPF23FnDHUTRKbFMa6gf5Yx2pOLtqzmDE86ha3wxAALjarUAjwIKfE8M6JTCT1gieT3lzwOcNb97vQDCqrKiQkIKYYrgN4mRDypwCsplNK6V+Y4bz/EMC/JoT8NQCvA/jLAEAIeQbAX6eU/hSl9JgQ8osAvmTu8/cppccznDO3CAyf8WwTHipjdiJGnMOI1WNIrSAY9px9DHZrbxt+LHfBfVCPIT+e4aNqOlNJ/eoqOKeKCrzjnCyLgvsoxVAtYI9h2VxzWPjMSJfEkKNeUdEfTUfWeGiNSF0F32aWoBsA6JqDy/HCZ9i27YGGeoz+wzDwMJu8pJLWyipqZQUPunMMn+mMChs8A7C/f5daVZwM5lfxEQf7p308JINnXOA29Jv3u/hIxmtJEzs8kVRWVUhICBHDv5f0SSmlRwA+6vP8lwH8lOPxrwH4tZDjvAbgnUmvb54QsX8CTHXzpnTy561j0eAqCv6scFWDScSo4xxWXYV37ZE9hkztoyFE0ttj6N1EUYil9jnJqr2/oJXUUgzD15wGLMXQW1dhEqciW0lHIcRwbAYkSSupmUo61qeyWfZNkidiJeW9g90pSShHZ8isko2qeMAKP3d7oGEjeNw3Fs76bB15sZICwIV6Ze5W0scv+s/xFgVXVmt4MMhny9TeSR/vfvR81svIFS40Kji3Usat+/n8mSWF3cM2SgrBtXWZSCohEXmlRil9HsArAFrm/98xn5NIADREwXPNFAbVVThqKByuz8ljxahzAEyiRdlcU1BdhV+foP+x3PsF9hg6Zgi95FEx6zMARv68iiJ/HGklteYTc6gYFpEYilhJdUZoylIxRK2sglJgGNH76AdO8kSspPXErKTsZxenJoLbPZPsMjwzj9Wq5kMxBFiX4cm8raTN4iqGAKusOBlMZ6VOE/2Rjge9MR6WHYYuEEKwud5Y+C7DnYMOrl1qSFeLhAQEiCEh5C8D+FMA/z6Y5fNPCCH/XtoLWyaI9BgSBBTcm4/5PGDQsTjn0AWVCh4+Q+EMn3HPGNpEL8pKSqwgm6DtvVbSSUXQtoEaPsooP2ZUobeRIQkjhEBVSGCPYRFDJUR6DIcyfMYCt3j2p7B49izFUGDG0NyGW0GnxbThMwAS7TI86+fLSgqwAJp5zRgaBsWDXrGtpAALoMlj+MzeqdlheE5aSb24tt5Y+BnDncMzOV8oIWFC5ErtFwB8H6X0Y5TSnwTwXgD/TbrLWh7EyXr1EkX2nG3vZDOGAeqjpdpFK3x8ewo+k+g+J7UUw8l1+cFbcO+3vddK6qcY6o7XvQX1lpU0x+Ez/LyLpBjGCZ+pyk9jbWI4RTBLbyRO0vhsX29WK6lJ7ppTzBh2ZlQrneCKYZ6spEwxnI+V9LQ/hm5QXGgE1wIVARutGjpjs8ImR9g/GQAAHpKK4QQ21xvYPx3M/Lckr+gONdw+7uO6JIYSEgDEiKFCKXXWSRwJ7ichgFD7p+sBCQ2NoTT8YHxfpzU0DFzlc6qQnLfErasgJumjIQojPx8/rjIRPmNbSZnV1Lu/e21BMDK0kgJsjlDzqGtFnjHkxDBMMeRVFtKmw6ykwHShMJZiWI5WDCslBRVVsayg04KTuzjE0J4xTNBKymcMc5JKCgBr9fkphkdmyM16wa2kG6Yid/dsGLHlfLF3whRDmUo6ic1LLIDmtfu9jFeSDm7cZfOTT8vgGQkJAGIE75OEkE8RQv4qIeSvAvg3AP4o3WUtFwKtnV4rqfOxFT7DQBE+Y8hfEE0lJXAqgm4rqVPZA6IVQ159EafHcIL4Kfb+OqUTxJGrbaLhM1kRw0VTDO3wmegewyJaZZMGV/Kms5LGs3XWq+rsiuEUVtKWNWOYhmKYJ2JYwWl/HGlfTwLHJjEsvpWUEcPDs0HGK3Fj77QPQoCNc8VWZNMAD2RZ1DnDXZ5IKhVDCQkAAqmklNKfI4T8JQDfbz71CUrp76W7rOVBmMLlDZ/xnTF0KGV+xfD2sRiM0K5D5/FtEuitq/AuOYpoKoRAo0akldQZLjPRY0js2TxKJ4kdJ4pRVlJ+DZcVRymFzBgWsccwTviMVAxttW86K6l4XQXASu6TmDGslpRYpN6ZSpoU2gMNChEL3pkXztcrMCgjrefr6RK24y5T2IpPDBnxOsyhYnipWUW1lJ9/X3nBE+ssCXdRk0l3DtuolRU8eqHYib8SEklB6GNgSunvAPidlNeylBDpHgRM8hU1Y0iDSZqT6InoUvzcuuEIq/EqhpYtM/xYVviM1SEYtA3M408SP155wdcUVFcRlbqatZVUVZRAxbBUxB7DEltzaI+hDJ+xsGL1C8YnTf24xLCqJlJwH8dGCjDlu1FRk50x7I+xulKOXfGRJtbqTL087o5SJ4bcSnpxAWYMgfwphvunA1yV84W+qFdKuHqutrABNLuHbTx1uVVIx46ERBoIvFIjhLxo3rYJIWeO/9uEkLP5LXEJIBgGE/oEr6uISCUN6zp0LylYMeSSIac3UcdjM4ZRBffuGoyJHkPiTkOdqKuwegzDvy49Y9smUwwXZ8awIjBjOJIzhhZmSSXl6p9oaXy9Ukqgx1CLZSPlaNXKCddVaLmaLwSANVO9m0eX4XFnZJ4zX9+DuDhfL6OkAIftfBHDOyd9PCzL7QOxud7AzQW1ku4ctGUiqYSEA4FXapTSD5m3LUrpquP/FqU0odpiiXArqfcx8X2NJ4gyxTDoWPYMnlj4DKzt+VFtsgjzVlwx5Ovjjye2UYhlh/Ulfg4Lpl9dhbdjMQgylTRZ8G5CkVRSqRjOaCUda6iUFOF/J81qaWbFsDuFYgiwyoqkFcM4XYrzwJqpEs6jy/CoO0KrWiq81ZEQgrUqweFpfoghpRT7JwNclcEzgbh2qYGb9zrCPchFwYPuCHfbQ1y/IovtJSQ4RHoMf1PkOYnpEWwldRNBd/iMe39KTVtqAOuzrKExraTOmUR7xtAmaN51+oHPD/L9gqyk/JhRVlLDmKyrsAruBXsMM0slVRd0xlDESioVQ0sxnCqVdKjHmrGrV9SpzuPENFZSgFVWJB0+kzvF0LSSzkMxPOqOcKHgiaQc56skVzOGJ70x+mNdVlWEYHO9ibOBNpd/6/PEzqEZPHNFah0SEhwiV2rvcD4ghJQAvCed5SwnAsmcaxvPY1cwDWGppKGKIQMVLbh3FMZzIucki+bBYlVfhBfc82MzxTDKSuoll1Yqac4Vw1KIYljIGUOhHkMZPsNRM4ndYMrwGVEbKcCSRJOwkjanUOqa1YSJYV/LVYchAGuucB6K4XF3WPjgGY7zNZIrKykvt39IltsH4to6q6y4eW+xAmh2D2UiqYSEF2Ezhn+HENIG8C7nfCGAQwC/P7cVLjjCrBneegqXguijGFoPfA/GbowQ8uh3bt1Rb2EF3Tj7BgVJZlTBvTMcx6/gXlXsgnu/ugrFS1oDoGetGCoKdE+1Q5FnDFWFQFWI7DEURH2mHkNNOHgG4OEzs6aS6lPNGK4mPmOYP8VwtVaCqpC5dBkedUaFD57hWKuSXPUY7sly+0hscmK4YHOGOwdtrNZKVlquhIRE+IzhP6CUtgD8D575wouU0r8zxzUuNMICY7wIrKKwZgxDEk4dYTJCdRWOmURLMeRrtsJnxG2pIgX3/NiGMWk3VRxWUt+6CofCGQae+5KnGcOsA3FmRUVVLPLnB24zLRdQEU0aJZUVz09bcB+LGFZmnzFsDzQ0q/Hn2pJXDMe56jAE2IdZ51fK8wmf6Y5wcYEUw85QS3QGdRbsm4rhVRk+E4hH1lZQVsnCdRnuHrZx/UorV2nHEhJZQ+Qj/D8lhJzjDwgh5wkhP5bimpYOUWTObzuvrZTNGIbYUmOmkjqtnXx7xaHqsVsx5Y3bQONYSf1nDNn9sLoK8fCZyGWnAjZj6EklLfCMIcAIX5iVdCjDZ1yolZUpraRaLCtpvVLCUDMsRXoaTBs+00owfEbTDXRHeu4UQ4ClbKZtJaWU4kFvkWYM2d+BvFRW3Dnpo6IqWF8QRTYNlFQFj12o49YCVVZQSmUiqYSED0Su1D5OKT3lDyilJwA+nt6SlguhPCYgbGbiMYE9YxjA05xEK1b4jGHfd5JLQFx9tHsMpw+fUYmtBho+VlJrxjBCMczaShqmGBZxxhBgFtGo8JmKqshPZU3UK6WpegxjK4am0tedMoBGNyj64+mspM1aCb2RPhMp5eAEM28zhgBLJn3QTVcxPBtoGOt0YRTDtSr7O5AXYrh/MsCVc7WJ9xQJNzbXm7i5QCX3h2dDnA00XL8iiaGEhBMixNBvm/y9QxcUIkmiAFMFJwrvrfsAaLi1MyjRNAicOOkO8jehyoUQUe+xKMJTTJ11E5RSeMWzSCup4llbAIwQO+s8UFImU0k104bpTVotCiqqgnGIYjjWDTlf6EC9oqI/jk+Y+iMdK7GIIfszPQ0JBWxCNp1iyNS9WWccARY84zxmnnC+Xkl9xvDYLLdfmPAZkxjmZc5w76SPh6SNNBLXLjXw2lEv8sPXooAnkkrFUELCDZGrtS8TQv4JIeRJ8/9/AuAraS9smRCVJApw4kR8X3T1GIoknApphgwslZSHz7Dn+NuCn+XT99wTM4aT23DFjxpmuIyPlZS/Iek+dRVxw2fyNGOoGQYUgsJ+Yl0WUAzlfKGNWllFfwqy1h1paMRMJQWmJ2fdWYihuc9ZAgE0/BirOesxBIALjfIciOHQPNeCEMMa+1twkBPFcO+kj4dkh2EkNtcbGGkG9k76WS8lEeweyERSCQk/iBDDvwVgBOBfmf8PAfzNNBe1TBDtiyWYTCK17xOzJzCsE9H/fuD5nIqh5zlnKqnI5b5CiHvG0IcAORVKvwJ7VQm3sHKiGPVpZvaKoTKpGBq0sPOFAKusCEslHWlSMXRi2n7BXlzF0Nx22gAarhhOYyXlZfRJzBme9U1imLPwGcC0kvbGqRZ/3+8w4rkoqaQrJYJmtZQLK6mmGzhsD2UiqQB4ZcWiBNDsHLZxuVXF2oJ84CIhkRQi3/EppV0APz+HtSwlwlJJveSIBLxGzHCXsBlD595i9k92qxvO8BlzzdS+FQ2f4aEyzuP4nc+ykoakkhqUTih+zrqLMOQ1lbSo84UAs5KG9hhKK6kLKxU1NmGilKI30q25QRHwoJppuwwtK+kUSh23fSaRTGorhvkjhufrFYw0A/1xvI7JOLCspAsSPgMAl1erubCS3m0PoRtUJpIKYPOS3WX44acvZbya2bFz0JbzhRISPoh8JyOEPA3gvwLwhHN7SumfS29ZywYB+yfxkEHPdub0XfCxHE8L2T/NW6c6Z1deTL4WBrvgnvcY+s0Y2sTOoH5WUbvH0Dechs8YRoXPZJ1KqvikkuqTRLdIYFbS8LoKmUhqY6Ws4l473kXxSDegGzQW+eAW0F4GVtKmpRgmYCXt5zl8hpHVB71x6sRwUcJnAGCjVcuFYsirKqRiGI1LzSqa1dJCKIa6QXHjbht/5X2PZ70UCYncQeSd7LcB/EsAvwpg9iQBCRfCBK6J8JnA7bjFUyyVVASKI+WT72kphrAXLZQ0SZhSx79Wvz0mewwnw2X4/n51FZaVNMLRZeQhldRbcG8YhSy356hGhM+wGUNJDDmmsZJychcnlbRupZJOqRiaal+cuUYObiVNVDHMoZX0fJ2RtQfdER5OiVwcdUZoVFTUyvH7JPOKK+dq+NJrx1kvA3d4ub2cMYwEIQSb642FKLm/fdzDYGzI+UIJCR+IvONrlNJfSX0lS4tg1Y2E2D+984aWlTTgLEE21CDYiiEmwme44GX4WD79wGYMaeh8n9NKqvsokdyOap3XayU1eUfUrE/W4TMl1S98hkIt8oxhiWAQkrI50gxUpZXUwkpFRT9mj2FvHJ8YckI3bfgMt5K2prGSVpMkhhoIAZopKXKzgCuGJymW3B93hwtlIwVsKymlwanc88D+CVcMpZVUBNcuNfCV1x9kvYyZYSWSSiuphMQERK7W/pAQ8jcIIVcJIRf4/6mvbIkg+rYYGCBDzB7DMJIZEFwTfC7bmmn3GJqqHhwETXjGMKrg3rapUp/jKo5UUr/ZRtHwGT2EnM4Dqk/4jK7TQqd2RoXPyLoKN1bKJfRjK4aMYMWxK/J5xGnrKrozhc8kOGPYH6NVLeUytZcHV6SZTHrUHeHCggTPcGy0ahjpRqqEWgR7J320qqVcVqHkEZvrDdw56WMQ84OtvIEnkj51uZnxSiQk8geRd/yPmbc/53iOAriW/HKWD8JWUuI2k3p7DG3FMGheMV74DN/GWR3Bd3OGz4j3GNp1FX772GokSyX16zF0Wkn9ZhD5esNgZK0YKgSad8bQKPaMYWT4jGagWpbEkKNuKoZx1BJuPY1lJa3Mlgxqp5LGtzDWygpUhaCdUF1FXi/cz1szhukRw+PuCBuri6Vo8a/nsD3INBVy73Qg5wtjYHO9AUqB1496hQ5u2Tls49ELK1N96CUhseiIvFqjlG76/C9JYUIQJVdAsGJoK3lhCaf2fbHwmWTyGZAAACAASURBVMkwF+ccIADfWgn/c5NIxdDqMaT+SqTXSjphNbWspOFrscNnspsx1BdsxjCyx1CXM4ZOrFRU6AYN/Z55wYlhnLoKVSGolZWpqjEAoDPUUVEVVEvxiSEhBK1aKaG6Ci2X84UAq6sAgAfdNK2ko4XpMOS4co4poAen2QbQ7J30ZSJpDFxbZwrbrfudjFcyG3YP23K+UEIiACKppD/p9zyl9DeSX85yIlDlE7R/sroKGjpj6D5fNKy6CjpZcG9XQlDhY1Fnwb0PR/D2GPqljnILpkHpBNEQtpJmHD5T8i24L75iGNljKImhhRUzRKQ/0oVJF7eDxg2CaVanJ2ed4XgqtdB57qTCZ/JYbg8wG3WrWkpNMaSU4qgzWqhEUgC43GJkLOvKiv3TAd796PlM11AkWJUVBQ6gGWkGbt7r4ofetpH1UiQkcgmRd9vvc9yvAfgogK8CkMQwATgTPr3w2j/9VEK2HVML2YyhAMmMYyU1bJKoOJRJwD891A+KgGLoJJ2GT+ooVx3ZNj6ppaI9hnlQDH1nDItLnGSPYTxw1a8/1iF6STqNlZRtX7LmE+OiO9Sn6jDkaNXKic0YPnqhPvNx0sL5RhknKRHDzlDDSDcWTjG8vMoUwywrK/ojHcfdER46JxVDUTSrJVxuVXHrXnGJ4a37XWgGLbQVVkIiTYgU3P8t52NCyHkA/1dqK1oyiFpJCSbnCq37fP4uhBO5iZSY/RNgVlK1xNNn2I0rHVRoxlCk4J5bSWmglZQrjrrhZyWdtL76gQtbWQl0i6gYlksE47AeQ00SQyc4uYtj8eSKYT3mTEy9oqI7tZVUm6qqgqNVLSUyY9geaLkst+dYq1fwIKUQFavDsLlY4TPVkoq1ehmH7eyIoewwnA5Fr6x45eAMACQxlJAIwDRXa10Am0kvZJkRWDHhDZ8J4Q7U1B6FUkkFiSjgtpJ6ZwwpYswYGuEF985UUr/ZRVWxC+4p9SdSzm2CkH2P4WQqadFnDCuqGtljKK2kNpxWUlFYimHMLrtmtWSli8ZFZ6BNVW7PkdiM4WCcy3J7jvP1SmqK4dEClttzbKzWcJihlXTP7DC8KjsMY+HapUahS+53D9soKcSal5SQkHBDZMbwD2FrUQqAtwP412kuapkQRmOi5gqd21Gz5kGoE1FgXa66Cs9+1KEYitpSeWoqEN1jyIif93VikTo/Kyk/RoRgmLmVtKxOppLqC6AYDiPCZ6RiaMNpJRWFRQxjzvzVqyWc9qdTs7ojbSYLY6tWwo27sxFDw6DoDPOuGJbxWkoXyscdRgwXzUoKcGKYnWK4ZyqGD0vFMBaurTdx3L2Nk94I5+vF+3e5c9DB5npDvidJSAQgkBgSQqqU0iGAf+x4WgPwOqX0zdRXtiSgIcmerjlC74yhZ/6QO0lFgmxEuwcBTv7ciiEnX3HqKqKspDYR9U8l5eQSYEQqqAsx0kqawxlDTacoFVhR4+EzQfULY6kYujCtlVRVSOzvY6OiWiXecdEZajPN9jUTUAzbQw2UIreppAC3kqajGHIr6WISw6pl68sCe+bvxca5xbLppo3NdRZAc+t+F3/mseL9u9w9bON7HjmX9TIkJHKLsKuML5i3P0Upfd78/3OSFM4P3qnA4C5CYvcYBiqGjvtxwmeos+Ce3VKHpVOUZFJEFdyzW4NSX+KnEtsmGjTbyAloGLK2kvrNGOoGLbiVVAGlwYmwUjF0ozallbReVoV7DzkaM1pJWzNZSctoD8bW34tpcGaqna2cppICrMuwPdBCk3mnhWUlbRbvAjwKG6s13GsPI5Ok08L+yQCXWtWp6liWGVYyaQEDaHojDW8c92RVhYRECMLebSuEkP8QwAcJIT/ufZFS+rvpLWt5EJZK6oJnxnCS6JkzhsG7+94PguJQ8CbrKuxb8VRS54zh5DbOHkM/gqsoxBV6EzhjGHFtxi9CslMMGYkyDGoF5owNA9Vyfi98o1A2Sd9INyaUT8OgGBc8dTVp8OL5/licsPWGemwbKcAUw2nDZ7pDbaYC6Ga1hLFOMdQMiwzHxZkZXpNnKylX8056Y1xqJas+HXeHqJUV69/MIuHyag0GBY46Q1xenX8y6N5pXwbPTIFH1+pQFVLIOcMbh6x/8WlJDCUkAhH2bvPXAfwVAOcB/Due1ygASQyTQJjK5yGCQaqfe8ZQwJYqNGXIoLtmDHldBeVLF55XNKitNAbZQAHeY+hvJY0ipDz9NPTrMV9Ws1IMVXZezaComMSw6IohJ31jjQIeYYOXuEvF0MZUVtKxPhU5qFdLVqJpHBgGRXekz0QMefdge6BNTwz7bO15D58BgJPeKHFiyDoMF9PqeMUkgwdng2yI4UlfEoQpUCkpeHRtpZDEcOewDUAmkkpIhCHw3ZZS+iKAFwkhX6aU/m9zXNPSIZgYTpIjxyPX85SGE7WAXUPWZBM1O5WUvUYtgiYWPsOrJjix89vH1WNIJxU91Rk+41NXAbhVxSBYVtKMeIrqIIMchZ8xNEnfUNcBuJUdbq+rSmJoYSor6VCL3WEIOFU7PZZlrmuSyVmspE2LGE6vpBVBMVyrs7WlUVlx1B0t5HwhwGYMAWSSTEopxd7JAFvXL8/93IuAa5eahays2D1oo1ZW8FiOe1ElJLJG5NWaJIXpQnS6ghEh/xlDAsJUvBBm6FYMo2HN/BnU2kFx2D3ZreiMIS+4j1YMeY/hhJWUCFhJyWSwixdZh89wZdCZTFp0xbBiqqB+XYa8+F4qhjY4wYs9YzgFMbTUyWE8O2nX3H4WxbBVZYRplgCa9oDtey7n4TMAUgmgOe6OFnK+EGAzhkA2Jfen/TH6Yx1XZbn9VNhcb+DW/U5k2FvesHPYxlOXW4VOAZeQSBvyai1jUEqFrJ3ebby2UqYYUiHFUITM8fMZdLKughM00VRSQngNhf3YC2fiKfWxijqrKIKspNyyGgZOHLPrMZxUDMeGUeg3Kk76/LoMuZVUzhjaKKsKyiqJWVehTWUl5cSuG9NO2hky9as5Q+hL02ElnRY8fCbPiuF5UzFMo8vweIEVw4uNChQC3M2AGN45kVUVs2BzvYHB2MBBhnUj02DnoC3twxISEZBXazlAGEdxJoKGJY5SRFVfiJ2Pg/MUZ0IoPzanNH6zgP7nZqmp4YqheUyDp5J6XleI53W/8BlEfoLJX89eMbTXWXTFkJO+kU/yj6UYSmLoQq2sxqyrmE4xbJhkshtTMeyY2zenCLzhaCVBDAezE9S0YSuGaVhJhwtZbg8AJVXBpVY1E3Kxz8vtJTGcCtcclRVFwYPuCHfbQ1y/IovtJSTCEHm1Rhj+I0LI3zUfP0YIeW/6S1sORBkxnGqdWyUkrvtWmmfgceJZSZ0JpN66CqdiKAInyWSP/dU+fj4/wmkritS0sE6ex1lpEQTLSpqZYsh+5TSH7bLoM4YWMfRRDMcyfMYX9Yo6hZV0mvAZRuxiK4YmmWvMkIbJVb72YHrCdNbX0KyWcq2o1ysqKqqSuJW0N9IwGBu4sKDhMwAvuZ//jCEvt3/ovLSSToNrlxi5KtKc4a4ZPCMVQwmJcIhcrf0LAB8A8BPm4zaAf57aipYMYWQOsAkTUwyDyR01/xNKOBUiRbbl0Q6f4ekz7CZOXQU/Fnvst415aDN8RlG8xNA+px4wY0hi9BhmxAsXc8aQW0l9FMOhnDH0xUpZncJKOl34DIDYXYZ8LnAmK6l57llmDM8GYyvdNK8ghOB8vYyTbrKK4VHH7DBcUMUQAC63apnMGO6dDFBWCdYXmHSniY3VKlbKKm4VqMtwVyaSSkgIQeRq7X2U0r8JYAAAlNIHmAill5gFYUSNBN33WkMtxVDASiqwJkvlcxbcm6/ZiiEVSvf0KoZ+Xy8nerzWItBKahLHoGNEWkkpW0/covCk4JtKWvQZwxDFUFpJ/bFSKc3FSsr3iWsl5USymUgq6Wwzhqs5Dp7hWKtXcJywYnhsltsv6owhwAjG3XYGiuFJH1fPrUx8ACkhBkIINtcbuHm/k/VShLFz2EarVrJqUiQkJPwhcrU2JoSoMHUiQsglABE14hKiEE4lBQmcEyTEnDFEsBLmtZ5Gns+REko8iqGVSgqxTkS+vxaiGDrrMaKspIZB4cczFGL3FAYhSG2cF5w9hhxawRVDq8dQppIKo15RhQvudYOVxE8VPmPuE7fLkKt8s6SSllUFtbKSgGJYAGLYKCcePnPUZYTpwoKmkgKsy/C4O8JQi/fBxaxgxFAShFmwealRqBnD3YMOrm+0MvtQWEKiKBC5WvufAfwegMuEkF8C8CKA/y7VVS0RKA1OEgUcRI945wTd96kj9dP3OH7HDIFT5bOW4JkxNAJm/SaP5bWShoTPUP9wGed6gkJvRHsMs0okBfwVQ12n1uxhEcFJ30ifvLjjZFESQzdWyuIzhpzUTRU+M6uVdAZiCACtWnnmGcM8l9tzrNUriYfPcCvpItsdeWXF3TnPGe6fDmQi6Yx4cr2B28c9X6dI3kApxc5hG09LG6mERCQi33Eppf8HIeQrAD4Kxi9+jFL6ndRXtkwISyU1M0cnNvFRDAEa+GlYXCupM3yGkzLPiCGrhhCaMWS3WigxtBVKvxoMZ51F0GyjSqKtpLqRsWLIZwx1t2JYVov7KSZf+0jzUQxNsiitpG6sVFTc74hdDHPLaX2KhNCGFT4T30paUgiqMxL6VrWEsxmspO3hGKu1/F/Mna9XElcMLSvpAiuGl82S+7vtAR6dU+m4blAcnA1wVQbPzITNSw0YFHjjuIe3XM530ufd9hCn/THeKomhhEQkRFJJnwRwi1L6zwF8C8APE0LOp76yJUGkldQiZSSQ3BEgXiqpAAdxb09cz1HnjKHIsSy1zwg8v0X8DLPAPsBKSk0raRC5jFIMdZ9jzxNcGVykGcNqSPgM/zRZ9hi6Ua+oGAiGz1jEcArFcKWsghCgN4Vi2KyVZrZdtWolK+F0GjDFsABW0noZJ72x9bcxCRx3R6iUFDSm+LkXBXbJ/fwUw7vtAXSD4iGpGM6EzXUzmfRe/ucMXzmQiaQSEqIQuVr7HQA6IeQtAP4XAI8C+D9TXdUyISqVVOAQzn5BoVRSoblA+z7nLNztaM0YxkwlDVMMnTbVsFRS20rqcx6FwIebuGAYNNPAAb9U0kWZMfSzFMlUUn+sxOgx5DbQaWYMCSFoVEpWL6EoOkNtpqoKjmatNLWV1DAo2gVIJQWYlVQzKNozzFN6cdQd4WKjstAzUTwI5OB0fsmke2a5/UPnJDGcBZsXi9NluCuJoYSEMESu1gxKqQbgxwH8M0rpzwG4mu6ylgtCYTAIrpwwQ0nNoJjg/e19467JrRhysYv6WVxDjqXrYXUVTqvo5NfhTC0NCpBRCMQUwwxJmHfG0DCts0WeMbTDZ/x6DNnXOaslcdGwEqPHkNdaTKMY8v1ih88MtJnnCwGgVS1PHT7THWkwKJtTzDvO19kak6ysOO6OFjqRFGDft4qq4LA9T2LIziUVw9lwrl7GxUalEMRw57CNS63qwv8+SUgkAdFU0p8A8JMA/h/zuZneqQkhFwghzxJCbpi3awHbfczc5gYh5GOO5yuEkE8QQnYJIa8QQv7SLOvJEjTCTOoslw/sMSTmbB7C6iripZIqLhLqfo6v2TBEFUN2y8vl/YNjzGMHpJI6U1JD6yqiiKHgmtOCN5WUk+xSgWcMw3oMZSqpP+L0GNqK4XTEsFEtxZ8xHGkzdRhyMMVwOmLIZxOLEj4DINGS+6MlIIaEEFxerc41fIYrhnLGcHZcu9QoRMn97mEb16VaKCEhBJGrtf8ErOD+lyiltwghmwB+c8bz/jyA5yilTwF4znzsAiHkAoCPA3gfgPcC+LiDQP4CgLuU0qcBvB3A8zOuJzNEFtxztY6E9BiCK4aCVtKYM4be8BlOZoyoxVv7u1Uyv/OrLsVwUlW0lLbQugrimt3zQ9C+80LJM2PIudQiWEmHvj2GumsbCYZ6RYVmUKFEv741YzgdQWpU1SlSSfWZqio4ZpkxPOsz9a0odRUAEu0yPOoMF7rcnmNjdb4l9/unA7SqpUL8u8o7NtcbuJnzknvDoNg9bEsbqYSEICKv1iilL1NK/zal9LfMx7copf9oxvP+RQC/bt7/dQA/5rPNnwfwLKX0mFL6AMCzAH7UfO0/BfAPzPUYlNL7M64nU4QRNbtc3hs+41EAKe8VDDhOwH2RNdnk1BM+A39bqBfeVFI/tS+6x5DdcqtpUOVFVPZD9uEzbsWQh5MWOXymEtZjqEvF0A8rJskTsZPOEj7D9ivFJ4aDMVqJEMMyOiMtMi3YDxYxLET4DCNwSSaTMivp4lZVcFyZMzG8c9KXamFC2Fxv4n5niLMZKmnSxu0HPQzGBq5fyXdyqoREXhD5zk8IeQqMhL0dgPXXlFJ6bYbzblBK9837BwA2fLZ5GMBtx+M3ATzsSET9RULIFoBXAfwMpfQwYP0/DeCnAWBjYwPb29szLDt53L03QLdrBK7LMOP+X/7Od2Ac2hfX3/jGS9DusAvFXq+Hw7t9DDSgp1Fsb2+j0+m4jtke2Rdm+3t72N4+Cl3Xd47sC9b79+9he3sbB112kf/tl7+Dcyc3cHLSh0oQ+T298QZ703jzzh4I/Lfnx/7Wt18GpcAbr7+O7e196/XdN9kxPv/5L7CIbM/rANBp99GPWM/e/hDDoZ7Zv4Obp+z7+rWvvwS6V8JZpwuA4NbNV7Gtv5HJmmYFt+/ufvdVbLt+ZYGdV9mF8hc/90JhVVHv71ISuH2b/Xv+9GdfwFotnDR/3fz9+fqX/xS3qvG/h4POAGdDGutrOD7r4awynPnrPnxzDEqBT316GyuleGv/2l1GZm98+yWM34wmxWn8nETRMf++fuml72Dt9LszH2+kU/RGOs7uvont7bszHy9P8P6cRmdD3DnW5vaz232zj3MVkrtrgTxB9Hepd8h+R3/nU5/F5rl8pud+1Vxj584NbHdvZryaZJHl3zwJcRTt5yTykfD/Dmbp/J8AfATMWipSc/HHAK74vPQLzgeUUkoIifNxcgnAIwA+Tyn9WULIzwL4xwD+Y7+NKaWfAPAJAHjmmWfo1tZWjFOlj9+6/WV00MPW1od9X1c//UlA1/GOt78N79u8CGw/BwD43ne/Gx98yzoAoPm153HpUhOdoYbSQMPW1vdje3sbzq/1QXcEfPpZAMDDDz+Mra13hq6r+uoR8KUvAgA2Ll/G1tafxWv3u8AL23jrW9+KrT/7CH75O59Hraxga+v9ocfa+5M3gJe/icsbV6Du3YHfz4Af+/r1twLfeAnXNjextfWU9frRV94EvvUSvu+97wM+uz3xOgD8i50vAAC2tj4QuJbfO/ga3hyc+K5hHli/cwp84UW8/R3vxNY7ruD3P/UZAD287frT2Hr/45msKQko/9+/wcOPPo6treuu57863gVu3MBHP7JV2HRF7+9SEjj52h3g21/Hu9/zXly7FP5J9s7zrwIvv4If2vqBqeyd//feV/Hy3lmsr0H7zKfwlicewdbWO2Kfz4mD+hv4VzvfxLufeX/ssI/jr74JfPUlfORD78fjZgJiGNL4OYlCNyjIZ/4I6w89NvE7MA3unPSBZz+NZ77nrdh672MJrDA/8P6cXiGv4tnXX8EzH/hQIoFHUWi/8Cw+eO0Ktra+J/VzFRWiv0sPH7bxy1/7LC48/lZsfe/D6S9sCnzr0zcA7OI/+Ld+cC7/vuaJLP/mSYijaD8nkd+SFUrpc4QQQil9HcDfMwvv/27YTpTSHwp6jRBySAi5SindJ4RcBeD3kegdAFuOx48A2AZwBKAH4HfN538bwF8T+Dpyi3ArKfHfzmP1tHoME5ox9A+f4VZSmLf+ls6gc+sB/YPOY/MaB6+4xMNpgl4H2JyiswbCDwbN1rbJQ2asGUPzm1lUNY2jUlICw2cqqlJYUpgWamX26bpIAA0PjlkpTxk+UymhGyOVlFKKzkhLxErKA2ymSSYt0oyhqhCcWynjQS8ZS91xxyy3X4oZQ7Pk/myAZsSHJLNiMNZx3B3hYWklTQSPXayDEODVHM8ZvnLQxqMXVhaOFEpIpAWRwZ8hIUQBcIMQ8jOEkH8XwKx/vf8AAE8Z/RiA3/fZ5lMAfoQQsmaGzvwIgE9RNuD2h7BJ40cBvDzjejJD1Ewcv5wmJLx9kJr/Bc4YOi7MxcjcZIqps2uQ3cZLONWMkDoNzxziZI8he8zn2Py6CFVFLHwmSw5W8s4YmlyqyDOGAAuX8Q+fMeR8oQ/4vKDIjGF/pGGlrE7dv9moltCL0WPYG+mgFAmFzzBSN02XIU8lTSIddR5Yq1cSSyU96rKUzovNJSCGrfmV3FuJpLLDMBFUSyoeWVvJdWWFTCSVkIgHkSu2/wxAHcDfBvAeMMvmx0L3iMY/BPDDhJAbAH7IfAxCyDOEkF8FAErpMYBfBPAl8/+/bz4HAP81mHL5DXM9/+WM68kMkR5a4rgJDJ+BQzEMqquIty7nNag3lZSvOSzsxn1urpIZwYqhp9/Pu5mlKFpdiH4BNnZiahB0I+seQ3cq6SLUVQAsgMa/x1ASQz9wYihSct8d6WhUp5/faVRVdEeaFRoVBa7uJUEM+af0Z1Mkk571x6hX1MIk2p6vl3GSlGLY5Yrh4ofPbJzjxDD9AJr9U9lhmDQ215u4db+T9TJ8MdIM3LzXlYmkEhIxEPnOTyn9knm3AzZfODMopUdgSp/3+S8D+CnH418D8Gs+270OwH8or4AIU91sxXCSDDph1VVEHMdvX/81+a3Bk0pKxdQ3Z11F0PaWqmgSP29yqKUYmlZRv2tFoR5DQftrWphQDDkxLHDBPRBuJS0XnPSmgThW0v5Ix8qUiaQASyU1KDAYG0LH4cSwlYBSt8qtpNMQw8G4EDZSjrV6JTFyYxPDJVAMV+dHDO+YiuFD0kqaGK6tN/CV145BKc3dyMCt+11oBsX1K5IYSkiIQiSV9GkAPwfgcef2lNI/l+K6lgaCH+ID8Cdr7HlzxhBhVk0HqRTT+Sb2tQruHT2GcaykIjOGXEkLqqsIeh1gZFKsxzAHdRUmibIUwwWwkvp18o2kYuiLOFbS3khDvTw9SWuaamNnqAkRQ15t0ZiyN9F1bpMYTlNyf9bXClFuz3G+XsbOQTuRY93vjFBWiUWsFxnNagmNijoXK+n+CSOfV85JYpgUrl1qoDvScbc9tEh+XrBzyH4fpWIoISEOkXed3wbwLwH8rwDEB1UkBBE8Fwg45vs8W7mJHjsOUwwDrKSufaNX5Rc+w4/NyQz1KaL3P5atkgWd26sITlhJFT5jyF/3s5KSaCspzZYYTiqGpkJaeGJI/HsMzfAZCTd4Wb2IYtgb6ajPYCXl5+qNNADR1sROgrN9fMawM5xmxrBYiuGFesVS+mbFcXeItXoldwpMWthYreGwnb5iuHfSx3qzimopn9UKRcTmOksMvnmvmztiuHvQhqoQXLsUnWosISHBIPLOr1FKfyX1lSwxhAruSTC5s2YMgUAvqXN7EQ7ipzBaiiHihc+4UkkDTu61kk4qhu4ZQz93oqogskg7TLWcB1TPLKVlJS243bJSUv3DZ3QDFXkRNgGeMCoyY9gb6VOX2wOw5hO7ggE03EqaRIpfvayCkOkUw/ZAw6VWcWbs1hoV9Mc6BmPdsgpPi+PuCBebxfnaZ8XGag2Hp3Mghqd9mUiaMDgxvHW/iw88eTHj1bixc9jG5npDfhAgIREDgR/lE0IuEEIuAPhDQsjfIIRc5c+Zz0skAOFUUviphOZ9YpLC0BnDSWtoGPzCZ/ghbMUwXO2097dJXXRdBSeG/uvRA1JL+TH0iG+okbliyH7l+NfJ2zUKP2OokpC6imKT3jSwYllJowlTd6hZqt804CEyopUVfLskwmcUhaBZLU1nJR2MC2WlPF9n6mYSATRH3REuLsF8IcfGanVuiqEMnkkWD51bQbWk5DKARiaSSkjER9i77lfgDp78OcdrFMC1tBa1TKAQ6zEMVQxBQCmrqwgiXkHziYHn9Qm6sY5thc+IVl+w2/DwGa6k8XAZj2LosZL6nVcRCZ8x6ESwzTyhqu6vU1+QGcPQHkM5YziBskqgKkQsfGY8m2LISWVXsEvQspIm1Pu1WitPOWM4xupKcayka3VG5B70RjPPsB13R3h0rZ7EsgqBjdUaDs+GqQaYUEqxfzrADz59OZXjLysUhWBzvZG7yoreSMMbxz38+J95JOulSEgUCoHv/JTSzXkuZJkhFgbjJZBu4mankkYTQ5HTua2nfM6RgSuGLHwm+ljO8vrAOg2rwJ7XVQRYSSPCZ6KspIYBZCnOBaWSFn/GMDh8plaWxNALQgjqZVWsrmKoz6gYittWAaBjWk6TIobNain2jCGlFGcDLZFk1HmBK4ZJdBked0ZLkUjKcXm1hpFm4LQ/xvl6Ol/3aX+M3kiXiaQpYHO9kVjwUlK4cdgBpZCJpBISMRF5xUYIqRFCfpYQ8ruEkN8hhPznhBD5lzUhRHWLuSf9goNl+IxhYCqp50hR8M4wAjYZs+oqIKYYWjbQkLAaSzEMnDFkt1yV8sszUYhAj2HGdRXWjKHO5zTZbdFnDMthPYYyfMYXKxVVuOB+phlDk1R2RBXD4RgKQWKEvlWLbyXtjXToBi1U+AxXDGe1kg41He2htlRW0itmaMlBipUVeyeywzAtbK438MZxz/c9ICvwRFJJDCUk4kHknf83ALwDwC8D+Gfm/d9Mc1HLhGgrqePWh6zxB0wxDKurCNg36Lw+M4l8v7iKobPgPoiUWuEzATOG3P7Jw2f8lEdFia6ryLzg3qN8LlKP4SgglbQoBeXzxkpFjbSSUkrRm9FKymcFe4LEsDvU0ayWErP0NWslYVLKcTZg5KqoVtJZ8KDLvvYLzeUhhhurLGgnzcqKPavDUBLDpLG53oBmULz5oJ/1UizsHrRRk/hncwAAIABJREFULSl47MLyWLIlJJKAiE/nnZTStzsef4YQ8nJaC1pGhF9+Ed9tvM5QNmMoVlchVDHhuJa3sme4Ymg+poKppPb8YLRiqBn+M4Q2uQy2kiokesaQZqwYKgqBQuyvw1gQK2lFVTDSJkmOnDEMxoqAlXQwNkApZrKSclLZFbaSaonZSAFWWfH6US/WPmd9RiSLpBgmFT5zv8PI0TIphvMoud8/NYmh7DBMHNcuNQEAt+53rJTSrLFz2MZTG83Cv7dKSMwbIldsXyWEvJ8/IIS8D8CX01vSciEyldRSDIlH9ZsMh2FELeg4Ma2kPuEz9nmodSvWY8hu9ZAZQ28dhTd11LKSGsFWUlWAGGbdYwgwdZArhnwsr/hWUv8ew6EkhoGoV1QMIhTDnpkQOotiWC0pKCkkVvhMEh2GHCyVNB5ZshXD4swY1soqVsrqzF2GfP8LjeWpq+C1JHdTJIZ3TgYoqwTrS1QDMi9cc3QZ5gW7h21ZbC8hMQVE3nXfA+DzhJA3zMePAdghhHwTAKWUviu11S0BWPegYPhMyH2rxzAAfoX1oefyCZ/ht5x8GYKppM7gmCDHZKSVVPEQx0ArafhamGqZMTFUiZVKalhW0mITw0rJP3xmrBuoSmLoi5VKtGLIX5+FGBJCUBc4F0d3pCVSVcGxOsWMISeSRVIMAeBCozKzlZQTw4tLZCWtlVWs1cspzxj2ceVcLbBLV2J6rDUqOF8v42ZOkklPeiMcng1lVYWExBQQeff/0dRXseQIe5sijls/lRDm8xQUCIn6DupADIKLSHpuuShHIdZjyDcKK5dXIqyifP2hdRUkOszHMKiv2jhPqApZuBnDoPCZkS5nDIOwUi7huBs+k2MTw9mIWqNaElYM2wmngTarJQw1I5at2LKSFmjGEGB20lmtpEecGC6RlRSwKyvSwv5pHw+dk/OFaWFzvYFbOVEMdw9Zp+LTMnhGQiI2It/9KaWvz2Mhy4rIVFKHjdOtErqJnpVKKnJSIcVsMnzGVgzZ84YRb8ZQ02nghSE/DCcX3sNOKoqT51WV6IL7fFhJiWPGkN1mvaZZwcJnggruJTH0w4qAlZSXzder0yuGgEkMRQvuhxquJjiHxUlmZ6jhQkmM7FhW0gLVVQAsgGZ2xXAIVSGFU0tnxeXVWqpW0r2TAd67eSG14y87rq038bnv3s96GQAciaRSMZSQiA15xZYDhKaS8vAZEpwsSohJDENmDJ37xFYMvTOGsGcMxXoM2a1uhKWmshnKIMXQtpKG1VVEp5IaIarlvKA6Zgz1BZkxrAT1GMoZw0CwHsNwssbrLOrlGYlhRUV3KGglHSZrJW2ZBCfOnOFZf+zatyhIQjE87o6wVq8sneVxo1VNTTHUDYqDs4HsMEwR1y41cHA2EHYmpIndgzZatVKiH3BJSCwL5BVbDhBqJbXIXFiPIbOSRlk7+WsixMipBFoF946QG4D3GEYeyraJRiSCKsS2WHoVNG/BvW9dBSGRYT65UQz1xSu491pJDYNCM4JV4mWHyIwhv8ialajVK6VIEsrRTjiVlAfZxJkzPBtoqJWVwv3bSUIxPOqMls5GCgBXztVwrzOM/HBvGtxtD6AbFFellTQ18DTSWzmYM9w5aOP6Riuxyh0JiWVCsd51FxBRRMaCAOOLqo/w9hGKns5LKCm1bZBiJJPdshnD4O2cNQ7e7fgxwsJnVAViPYaZK4Y2AebLLRd8xrBSUmBQ9/efW0vljKE/RKykvOdwZYbwGYARy46AYkgpRTfxuoopiGF/XEgr5Vq9jNP+eCZyc9wd4cISEsPLqzXoBsVRJ3nVkJfbPyw7DFNDXoghpRQ7h205XyghMSXkFVvGoAgOjAE8BC3ISgqHlTTkXN4QmTA4iRe3NPFn+DVPlHXVeyxNN0KJJHEoht7vCVfUwuoqRHoMDYNmbtFyppJaimHBraSc/DntpJwYylRSf9TLKsY69Q3t4eD2z1lSSQGgUY22rQKsN9GgsyuUTrSqjODFKbk/G4wLFzwDAOfrFVBqW2GnwVF3tFTl9hwbrfRK7nm5/VVpJU0NeSGGd9tDnPbHcr5QQmJKyCu2HCDcSkp8t/H2DFKY4TOhilwMxdAnldRWDNljI3bBfTgJVgmxZgi9BNI6hh5iJVUEewxzpBjysJyi11WUTWLrDKDhJLFodsB5gauA/RDV0O4xnE8qaXvICE2SPYa2YihOltoDrXDBMwCw1mBk9ngGO+lRZ7iUVtI0S+6tcnupGKaGWlnFw+dXcPNeJ9N17Byw4BnZYSghMR3kFVvGELWSThbcO+6DMUNm8QxNsrGOFX0+v/3YLSdflIrVVTgTRaOspLZV1Puae8bQj9w5rahB0A0EdinOCyWFWF+nKRwWfsaQq4JOxZArYTKV1B8WMQyZM+wn0GMIiIfP8G2aM6agOtF0pJKK4qxfTMVwrc4I3cmUxHCsGzgbaLi4ROX2HBYxbCdPDPdOBmhWS4W0JxcJm+uNzBXD3UNODJuZrkNCoqiQV2wZI06SqFcldN7nSaHhCaeT+waf1y98xlQM+drhP+s3eSx2G9ZjyM+jmUzJa/fkD8N6DFVCEDXaQwXnItOEK5V0QWYMuZV07KMYyhlDf3CyFxZA0x3pqKjKzN/DeqWE/liP/OCkY84BNmZUKJ2YasZwoBXyIp4Twwfd6aykD8wOw2W0kq43K1AIcHiaBjHsy0TSOWBzvYGb97uRNVxpYuegjfVmFReby/fhioREEpBXbDlAUNqoaxvioxI6XhOaMXQknEavKeA+8YbPRB7KIpRRimFYXYWzCxHwV/04mTRCLn5zk0pqEmDD/GAg67nHWcHton7EUFpJ/bFSFlEMtZmDZwBYYTJRc4Zc1UvSSlotqaioitVNKIKz/tgilEWCRQynVAyXtdweAEqqgvVmOpUVe6d9mUg6B2yuN9AeaNa/4yywe9jG9StSLZSQmBbyii1jUIR/suY36zf5PDFnDMN7BZ2diFFQfBRDft+aMYyYGfTbP+zkimP2zsuTvOEzfqqfsxYjCFGq5TzgnjEs/nwh4B8+M5TEMBQrpirXHweTte5IRyMBYlivRquTgF2PkWQqKcBUw46gYkgpLW74jDljOG2X4TFXDJeQGALMTpqGlXT/ZCDnC+eAa5eyDaAxDIrdw46cL5SQmAHyii1jRI8FEus2jIRRSk3FMCz1kx8zGmEJqNaMIURJpv/9ye1IYB2F047q9zpgk8ewABrDyItiaBPDrNeTBCxiqPvMGEpi6Iu6NWMYnEraH+mJKIbcGhoVQNNJiRg2ayVhK+lgbGCs00JaSVvVEkoKkYrhlNhYTV4xHIx1HHVHeEiWnaeOa+tMqcsqgOb2gx76Yx1vlVUVEhJTQ16x5QBC9k/PRhP2TqSYSupVDM37UUTUe17v/cntYM0YejfzWkn9Rq6scJzg6+xcWEldPYYGRang84WAHT4z1m1SbllJ5YyhL7iVNMze2R1pMyeSAnb9RFQATVrEsFUrCYfPcMvp6krxrKSEEJyvl/FgSsWQd/gttWKYcCrpvjmzKBXD9PHw2grKKsHNjBRDmUgqITE75BVbxoga0SaO2yArKcBnDKOspPxWZMbQMcPoOYgzlVRsxtC+Hz5jaCtp3tRRy0qqG9a2XvB9whVDscCcNMF6DB1W0oJ3GALhPYZSMfSHWF2FPnMiKQDLjtqNmDHkimKSPYYA6zIUravgHYBFVAwB1mU4bSrpcXcEQtgxlhEbqzUcd0cYatEJuqKQHYbzg6oQPH6xgVv3siGGPJH0KUkMJSSmhrxiyxqCJfEg3u2c4TPEVgyF6iqiT+e2fxL3844eQ5HQFOf+UT2GYytcxt9KGlZXwclj6Iwhpb5q4zzhTSVdjBlDN3EHpGIYBbHwmWSIYT1G+Awhs9djeBHHSnpmblfEGUMAWKuXZ7KSrtUrmbsassLGKkuSvNdOzk7KieHDUjGcC65lWFmxc9jBI2sriTseJCSWCfKKLQcInwv0J1UToTSUcmYYcp7J44id171Ww5FKKnL5MkEsA7dzzhD6H0MLmTHkaw5NJTWyL7h3ppIuyoxhJazHUCqGvhCrq9AsUjcLeC9hR8BK2qyUhP5GxEErFjHkimExL+7W6pWp6yqOO6OlnS8EgMtWyX2SxJBZSa/IGcO5YPNSA68f9SKrcdLA7kEb16VaKCExE+QVW8aITCW1bonv84BnxjDsWHzGUGBdzm284TH87z2FKMl07h9Ogjnx8x6XkzmN9xj6/Mvljsyg9yNOGLOuhlCdBfcUCzFj6Bc+M5Q9hqEQsZL2Rzrq5QQUQ3NOsRcVPjPQEreRAiyURXjGkFtJC6sYVqZWDI+7o6WdLwSAKxYxTG7OcP+0j/VmFdVSsiq4hD+urTcw0g3cedCf63lHmoFX73XwtAyekZCYCfKKLWNEFdx77Z/2rXsG0J4xFEglFbKSBimVdl2F6IxhkC11YjvFDp+J7DEMs5IGMENuMc2HYsitpHQhZgzDegyrUjH0RUVVoJBwK2l3mAxRs1JJo+oqRlqiHYYcrVoZnaEmVHzNraRF7DEEWGXFSW88Vcn3UXeIi0tYbs+xkQIxvHPSx8NyvnBu2OTJpPfnm0z62lEXmkGlYighMSPkFVsOIJQSGnDL9iegpvYowDGFFMOgjYgrfEY04dTfluqFQgh03d9KSsx/qUHE0XmeoAsyPSeKYUlVbGJoLIiVVIbPxAYhBPVKKdRK2h8nU1fBewyj6yr0VBTDZq0E3aCRPYpA8cNn1uoVjHRD6Gv1YtkVw7V6GWWVJGol3T8dyHL7OSKrLkOZSCohkQzkFVvGEE4lDej149swxVC0rkIkMGZyP+d6AEYQRRI+xesqSOAMoWUl5eEzflbSiPAZTmgzTyV11lUsSviMj2I4luEzkVipqIFW0pHG+vySKLgvqwoqJSUylbQzGKOVhpXUVP9E7KRngzEqJQW1BCy0WWCtzghtXDupphs46Y9xoVFNY1mFACEEl1s13E1IMaSUYu+kL6sq5oiLjQpatRJuzjmZdPewDVUhePJyY67nlZBYNMgrtoxBKRUKn/GzkNrb8OyZ8DAYvqtYxYS/yqcozvAZMfVRtOCekOACe/6Yp5b6fR/4sYOspPzprHmKOlFwX/xfwzDFsCwVw0CslFX0A8gat5iuJNBjCLDKiijFsDvU0agmT8h4SqBIZcVZXyusWgjYVRMnMbsMH/TGoHR5y+05rpyr4SAhYnjW19Ab6XhIWknnBkJIJsmkrxy0sbnekLOkEhIzQl6x5QAi3YPex24yadZV0Cg1UHzIMDh8hljzjOxQSSuG/uEyVl2FSTb85gT5sYNGe4JI57zBFEP2dRjUrnooMixiKAvuY6FeUQMth1zdS6o6olEtoSeQSpqGlZQTPZFk0vZgXMhye441kxjGVQyPu2z7ZbaSAqyyIqkZwztmVYVUDOeLzQyI4e6hTCSVkEgC8ootY0RaSTmX8z4m7m0opYwYxjhWGNz2UbeV1DDP5d0u6rzsfvD2KiGWqjdhJVXcVtJpwmcMy4aafSrpos0Ylktc0Z0Mn1kE4psWauVgKyknjIkRw0op2ko61FKxkvJAGxFieDYotmJoW0njKYZHXTZXt8zhMwBMK2kyM4b7p2a5vayqmCs215u4c9LHICRxOUn0RhreOO7J+UIJiQQgiWHGEA2us0mdj5U08IH/dmKBMUH3mTppWIph9LFEewzdtRb+xxiH1FXwbYyg8BmaD2LonDHUKV2IGUN/KylFpaQk3om3SKhX1MBU0r5FDJMhavWqim6IYkgpTSwF1YtYM4b9cWGrKgDbSvqgO51ieHGJZwwBlkzaHmqRtmcRyHL7bDDvAJrv3u2AUuD6leZczichsciQxDAHCK2Y8GaJBiqGIvOK3mOGrcl/fZY6aT4Wm1e070dZSYO2884P+h2Hp40GEUMjJ1ZSVVGs9FVjQQruVYWAkEnFUNpIwyFiJU0ifAZgc35hiuFQM6AZNLW6CkBwxnAwLmxVBQCcnzJ8RlpJGa6cY8T4bnt21fDOyQBllWC9udxke97YXJ8vMZSJpBISyUFetWUMYSvphKXUbfW06ioEUkmFyBycJA2u+5Q6FcN4M4ah63P8a/SSN0I48QghhhZ59D9+bhRDlWBszhjqdDEK4AkhKKuKq+B+pOuyqiICtbIaaLeyw2eSIYb1iho6Y8jVvGYaVtJqDCtpwcNnyqqCVq0UO3zmqMOIIbeiLis2Wsz2eXA6+5zh/mkfV87VMq8oWjbMmxjuHrZRKSl4/KJMJJWQmBXyqi1r0PAk0SC4omeIo65CYJ/YVlLXMYhrxjDusaZVDPlzQeE0gB1IE2gl5TOGmSuG3lTSxbhoqaqKy0o61qhUDCMgpBgmRNQa1VKolZNb9xoJWVediEUMCx4+A7AAmmkUw/P1MkpL/jtz2Sy5v9uenRjunfRlh2EGaFRL2Fitzq2yYuewg6cuNxfmvVRCIkss9ztQThCaSsrrKjzbTlhJYdZVCB0rrsrnVg85CfVuJ3as6PUFbacQQAtTDCPDZ9zbZYVF7DEEWC2Fy0qqG1IxjMCKQPjMSkJ9fo1KCb0QKyknbWlYSVWFoFFRI2cMB2MdI80otGIIMNUvbvjMspfbc2ysMttnEsmkeycDOV+YEa6tN3Hzfmcu59o9kImkEhJJQV61ZQzB7JlQUkdAHKmkQj7RWJsoLhLKkkMtK2n0oWLUVTju+5AlhRCLeExVV2FZSSOXnCpUhVV+GAaFbtCF+ZSz4lEMR5ohE0kjsFIpBYbP9IbJKob1qopuwLkAWzFMw0oKsDnDqBnDM/P1IofPACyA5iSmYni/M1z6DkOA/furV1QczphMqhsUB2cDmUiaETYvzaey4rQ3xsHZAE9fkcRQQiIJSGKYMYTtn/zWL0DGvBs1YxinrsJ1HG/4DJzhMyKKof/9ye3sF4OIX1j4DCd8eoSVNOvwGa4QagZlimHWTDUhlEvEmgEFWJhJRZYNh6JeUTHSDauf04neONm6imalhJFmuFRdJzoJE9GJ89dKkVZS/vpqgcNnAK4YxreSSsWQffh4ZXX2kvt77SF0g8oOw4xwbb2Bk944djpvXOwcsuCZ65IYSkgkgsW4Ii04QlNJA8NnHNsAjoL7sPNEn89vTW7F0Bs+E3koz7GCd1ADzul8zuox9PmXy88TaCWl+SCGqrl43aDQF8lK6gmfGUsraSS4TdTPTtob6iAEqCb0PaybhC8ogCbN8BmAVVZEWUnP+gukGHbjW0kvyvRMAMDl1SruzkgM7XJ7qRhmAR5AczNl1dAihtJKKiGRCORVW8agEWZSL4fxzhxaz1F2tDA9kKuMojzET51UiG1bda4nDF4ratT5grZz2kt9FUPLShoRPpODGUMA0AxjocJn/Kyk1QVRQ9MCTxz1s5P2RjoalVJiPZC89iKosoJ3HKZFDJvVEs4iFMMzSzEsNjFcq1fQHmqB6qwXhkHxoDeSVlITG6u1ma2kvNxeKobZ4Nol1imYtp1096CNVrUkLcMSEglBXrVljGgrKfHcWi/AeVdEMeT8Q/Q606/egoAFplBLfYs+TpD6GHS+oO1cVlOfDdSo8JncKIb2OhcpfKbiEz5TLi3G15YWuE3UTzHsj7XEqioA2yIaVBzeGTKFK43wGYCRvU7UjCFXDAtuJb3QiNdleNIfw6Cyw5CDEcNB4Id8IuDl9jKVNBs8sraCkkJw8166ATQ7h208faWV2AdoEhLLDkkMc4C4lQ+AW8Vzls6HkswYqaRwHMtbN0HByKFzmzAonv0DtwvpMQTcZNDvMPy5oBlDnkqatUJXUu0ZQ32RZgxVRRbcxwS3kvpVVnSHemLl9gDQqHLFMMhKas40JpSC6kVLYMZwkcJnAAh3GR53mTomiSHDxmoNQ83AaT+eHdeJvZMBmtVS4T9kKCrKqoLHLtRTVQwppdg9bMtiewmJBCGv2jJG1AeiEwTIR/WzFcOIuoqgYwaAkzPiORnrMeSzfiJWUocSGPIvzr2dX/iM/7YctpXU//h5SiUFTMXQoIujGHp7DOWMYSS4IuhHDHsjHSsJdgrWK3zGMMhKqqFRUVOrc2lG9CgCrNweWAwrKQDh4A1ebn+xIWcMAWdlxfR2UtZhWJNKUobYXE83mfRee4iT3hjXN5qpnUNCYtkgr9oyRlTpw2QaqfuWvcbqD5hiKMAMReGTYspnDI0YM4ZRs4N+r/ldmzpf900tjbCS5jGVVFugGcNyScHIkUo6kqmkkeCK4cAvfGakJaoY8tnBIHLWGWip2UgBVlfRG+m+CawcZ4MxyipBrVzst6bzdW4lFVUMGTGUiiHDhllyP0uX4f7pQM4XZoxrZmWFEfCePCt48IysqpCQSA6ZvPsSQi4QQp4lhNwwb9cCtvuYuc0NQsjHHM//BCHkm4SQbxBCPkkIWZ/f6pNHKE/x2D+Jj4rHFEManUpqHTKuldRzLseMoZiVVHTG0H8fDicZ9PsS+D5GkJXUUgyzJoZmKqm+YDOGHsVwKHsMI2GpeIGKYXLEsB6iTgJAZ6SlVlUB2LOL3YBUVABoD8ZYrZULr/KsNbiVVEwxvG8Sw4tNSQwBYKM1OzHcO+nLRNKMsbnexFAzsGcGASWNnQOZSCohkTSy+lj25wE8Ryl9CsBz5mMXCCEXAHwcwPsAvBfAxwkha4SQEoB/CuAjlNJ3AfgGgJ+Z28oTRtRw/YSTNOB6iZM1kRlDUR7iFz6jEMKspJ5tRI4TtX3UdnwdCvEnt5zwBRFDK5U0a8XQmjE0FmrGsFIiE+EzSVUtLCpsK+mkitcbaYl1GOL/b+/Mg+Q4z/P+vHPuzuwurgUWAC8sSBE0qcsiLIkxFa5EipYURYfjUiTHjnxFkRO77HK5fKmS+EgsObbiOK6KZEVSmbYVW7JpxTItiaJIrkiB4AHeBHESBIhjD2AXe8zs7Jxf/ujumZ6evmYxPd0z8/yqtubob77+ZnqOfvd93udFw3zGNWMYYGA4qgeGKy4GNCuFSs/XFwJaH0OgjYyhLiU1JKiDzo66lHRjgeF6uYqFfAm7aTwTKkbLiqDkpMdmVzE+kmabF0I6SFhnbR8EcI9+/R4AH7IZ8yMAHlBKLSqlLgN4AMB7oMVKAiArWnQwBuBC8EsODj9hipuUFIKGlNQ18DKG+8wY2tUzSvt9DH2bz3hkBBuBrf0cxn6clGq1mv+6yCDpV1dSq/lMuUrzGS+MwNBeSqq1q+gURmBoF4QCWo1hoIGhR2AKaEFjP5iFDCfjSCVivjOGi/kixoYSrMnVGUrGsTmT3HCN4cyyFlDuopQ0VPZuDzYwPD63in07WV9ISCcJ61doQik1o1+fBTBhM+YqAGdNt88BuEopVQbw8wBehBYQ3gzgSwGuNXD8NaU3LqXpNmAK9LyMbND6WDdiNoGYiOjtKowx3vP4lYWZ53JrR+EU2HlJSauRkZJq+y/rUtKw19Mp7PoY8kTXnYyLK2mhw1JSo57RScqZKwYrJR3VDWXcnElXCuW+yBiKCLZkkr7bVSywuX0LE6NDG84YzrC5fSTYMZpGNhXHqYudDwxrNYXjczk6khLSYQI7CxCR7wLYabPpU+YbSiklIr4rk0UkCS0w/EEApwD8KYDfBPBfHcZ/AsAnAGBiYgLT09N+d9UVcrk1XFJrjutaXdF+4A49dQizozGUS9qJxoEDB5BNagHF3FwRhfUqyhWF8+fPYXr6InK5XMuc+fwaAODw4cPILBzzXFu1qp3AHXn5CDYtnQAArOULuFTJ47GDBwEAx48dw3T+lOdchnPqBX19diwsNE4CHn3key2ZweK6XqdQq9m+Xq+taCe8L7z4EtIXj7Zsf+Gi9nyef/ZZ5E+HZ4pyZF5bx8EnnwIAvHbmNKanezrpDQC4OF9EvlCpH5tiuYqZ8+cwPT0f7sKuELvPUqcwzHoOHzuB6fKZpm2rhRIW5mYwPb3Qsf2l4sDRV17FdLL1/XZpeQ1bY4XAnuupJe3z+dhTz2DtjP1Pz+zCGnaPxDa0hiCP00ZIqTJOvDaD6enLnmNfOVdAvIZIrT8o/B6nZGUdJ8/nN/SaPHpOk/CePfoCps/yn1Pt0snP0viQwqHjZx1/9zfK/FpN6/+6dKHjc/cKUfvOI/b02nEKLDBUSt3ltE1E5kRkl1JqRkR2AbA7czwPYMp0+2oA0wDerM//ij7X12BTo2haxxcAfAEA9u/fr6amppyGhkLm2e9h+/gIpqZutd3+p0ceA5Yu461v/SHcODGK1KMPAOUSbr/9dmzS/7P+Txefxyu5SyjWyrjm6mswNXUzpqenYX2uI889AuRW8YbX34Kp1+/yXFti+n6gUsEtt9yMqTftBgCMvvgoto4O4W1vuwX43sO46aabMLX/Gs+5Yt/5Jqo1hWuv0dZnx9fOPw3MzQIA3jk11ZJpzB6aBtbySCTiLc8N0AvRH3sEN998C6be2Pr8akfngKcPYf/+W/HmazZ7rjko1NF54JmncMsb3ww8/jhuvOF6TN1xfWjr6RTTK4fxzMVzmJqaQq2mUP32N3HD3j2Ymrox7KVdEXafpU6hlIJ895vYdfV1mJraV7+/WlMoffub2Hd9Z1+/se9/F1t3TGBq6g0t26qPfAfXX7sbU1Ov79j+zFxzMQc8/j1M3vgDmHrzVbZjKge+ixuu3YGpqTe2PX+Qx2kjXH38cZSrNUxN/TPPsZ957hFMbs1gamp/F1YWLn6P0z9dfB6Pnri0oWP6woMngJeO44N334GhgPpy9jOd/Cy9ceZZPHf2csc/mw+8PAc8cgj/8o79eMu1tv6FfU/UvvOIPb12nML6V9o3ABguox8H8A82Y+4HcLduOLMFwN36fecB3Cwi2/Vx7wZwJOD1BoofJ1HrWLu6P+U1l11fQhdiNrJVo11FQ0rankzUrb5PLJLVljn0xzqZxxjlbE4N7o3yt7D/qtogAAAgAElEQVSVm4Z0tKjLLvulxjCViKGkv8jGJaWk7ogIMsl4i5S0oNccGk3pO0U2HXepMawGKyVNG+YzHjWGfSAlBYAt2TalpGxV0cTE2BAu5oqO7YfcuLBUwPhIikFhBJgcz+Lc5QKKFWc34o1wXG9V8bodrDEkpJOEddb2GQDvFpETAO7Sb0NE9ovIFwFAKbUI4PcAPKX//a5uRHMBwO8AeEREXoCWQfz9EJ5DR/BqcG8glmvStE0a7Sp8zOE3DDHir6YaQwC1Ns1ntHHe9Y12LqjN25vX5bQPp55Jxpqj0sfQMBzplxrDZFxQ1qWR9cCQ5jOeDKfi9UDQwAjeOtngHgCyqQTyNuYvxUoVpWqt7hwaBEaNYc4hMCxValgv1/rCfAYANmdSWPLhSlqrKSzmS+xhaGFiLI1qTWEh374BzQX2MIwMe8ezUAp4bWGto/Mem13FVZuH698rhJDOEMovsFJqAcCdNvcfAvBzpttfBvBlm3GfB/D5INfYLbyzfE6XzQ6eWsZQ+ZyrzYxh0xwCBbTVrkIb5z3eGOMUKBmPddpuZBId+xjWomE+E7cEhn2TMYzHUa0pTQZZYcbQL8OpOAqWjOGabhDTyQb3gJYxtDOfyQe0PzNDyRgSMcGqQ7sK4/6+yRhmklgqlDW5sMv33sp6GdWaYmBoYYfe5H5+pYgdo+2ZyFxYKuCG7cwkRQHDmfSVi3m8roNGMZojKY1nCOk0PGsLGa33oIu80pLnsxspogVqWoN773YQvjOGpvmb9qVU2xlDr2xg0/oc21G4t6swt4GwIzKupHGLlLRPsmrJhOG2WmsEhn3y3IIkk0y0yDsNaWkn+xhq87XuC2hk8UYC/O+7iGBkKOHYrsKQmI71SQZgSyaFak25SmcBTUYKsLm9lYmxjTW5V0phZqmAXXQkjQR7AuhlWK7W8MpFOpISEgQ8a4s6ThlDy6B6jaHbVB5SzNbxrYGaVmOo/fhat7nhFdQ1j3HYHjMu7QcYUzvJc42AMWwpaVx/IkZgGHag2imMILBUrdX7GTJj6M1QKo5Cubn5ZlBS0pG0fWBm3DfS4ZpGK6NDCcd2FSsFI2PYP1JSAJ69DBeNwDDLdhVmduqB4WybgeFKoYJ8qYqrKCWNBGNDSYyPpPHqpVzH5nz1Uh7lqsJNzBgS0nF41hYyCnCN5pzqAq1ZPMA7MrTLALphF4RqNYaqrT6GTXP5kJI6N7B3DxzrGUMnKWlUMoaG+Uy/SUn1ILBUqVFK2gaZZBwFh4xhp6WdmVSr0Q0A5PX9B2k+AwAj6aRzYKhLSfulZmhLRnselz3qDBdyWmBIKWkz4yMpiKDtJvcXlrW2Rrs2MTCMCnvHsx3NGB6b1YxnmDEkpPPwrC1sPAxjrNSb1FvsaOo1hq6RYXuupMaomE3GsKZat/mby3mMV1bR73ZHKamelHFyNe0WVlfSsAPVTpHUM4blaq3+3JKUknpibz5TrW/rJNm0vflMXUoacGCoZQztA6WVQn9JSY2M4eW8z4whpaRNJOIxjI+kMd9mxvACm9tHjr3bOxsYHp9bRTwm9fpFQkjn4FlbBHAL1KyZNsd2FTBqDF32Y7n0wq5dBUTLvNVrDP3OFfMhJdXfjU5D/GYUlYf5TCzkd31rxrA/Pob1wLCi2K6iDYZtsniGlDTbaVfSdBz5UrXlM9KQkgYcGDpIWYFGxrBfpKRGBtCrZcWi7rrJjGErE2PptmsMG4EhM4ZRYXI8i0u5EpYL3i69fjg2u4o92zJsR0JIAPCsLWS8ulWIxXTG1nwGem9Bh+31cW26ktq1q4iZgtB25vJjPmPM5eVK6hRH9Yr5TEsfw3h/ZAzrUtJqFWX9uaWZMfREk5LaZwyDMJ+p1lT9vWdgBGtBS0l91Rj2ScbQt5Q0X8JIOoF0gie5VnaODWG2bSnpOpJxwfYR1mxGhckOG9DQkZSQ4OBZW8horqTOOLWpsM8YureraNeVtB4QmvelB6Htu5Iaa72CGkOPBvfG46se5jNhS0mNDGH/tavQnkeJGcO2cOtjmOlwoGbULFozlIa8dCTgHoIjblLS9TLiMel4MBwWY0NJxMTbfGYhxx6GTuwYG9qQlHRibMjRpIx0H0Py2QkDmkKpijOLa6wvJCQgeNYWAXz1HmzxIbWrMWwd1/wY7/3Z0ZQxjDXqC63b3JB6xvAKXEl9Bo6OUlKjwX3YGUNLu4qwM5idopExbJjPsMbQG3spqV5j2GGplJERtNYZ1jOGHZauWhkdSiJXrNh+RlfXKxgbSvhWIUSdWEywaTjpQ0rKwNCJidEhLORL9e8TP8wssbl91LhmawYxAV69eOUZw5PzOSgF7GNgSEgg8KwtZLykpFbszplEdCmpV42hQ5DpPd50nyVj6DemaWQM3ca4m+M0pKQbNZ+JSsbQIiXttxrDKl1J2yGTTKBUqTW9b9dKVaQTsY7/06AeGFpcUHPrFWRS8cD/STGSTqBcbZWyApqUtF+a2xtsyaR8SUm3MTC0ZWJMk4NezPmXk55fKmD3JhrPRIl0Io5rtmbwSgekpMfmdEdSSkkJCQSetYWM8nAlrdcYWgY5xTZ+5vIfzNnLVmsmV9IgGtx7taNw3K4/3iEujFAfQyMw1KWkfVJj2DCfqVFK2gbDKe01MstJ10qVQOr9DJmmNWOYD2h/VsZ0qapdneHKeqVv6gsNNmeSPvoYFulI6sCEHuDNLvuTk1ZrCnMrzBhGkcnxbEcyhsdmV5BKxHDd1kwHVkUIscKztgjgx5XUelss9ymnBzQ92HLpuS7t0hxIiUi9ntG47Qd/De61S6eMnpcc1Ui81RykpPXeiyG/65P1GkMjY9gfgaERBBbNGUNKST0xmtivmbJ4a6Vqx2WkQMN1NF9slq7mitXAHUmBRo9CuzrDlUIZowHXOHabLZkULuedM4ZKKV1KSqMUOyZGtcDQb53hxdUiKjWFXQwMI8ek3svQqdTDL8fmcnjdjhEk+NtCSCDwkxUyyqeY1CoDNQdkmrzTuO4yh2m8H+zMamICXUrqvT/bNbi2q/CSkjavq3V7j7iS1msMtZPzsNfTKVLMGG4IIwBcLzXklWvFKrLpzgeGGZsgFABy6+WuBIbGPuxaVqysl/swY5hyzRiuFisoVxWlpA4YUlK/LSuM5vZXsYdh5Ng7nkWhXMVcmy6zVo7PrrK+kJAA4VlbyHhKSS11d04ZQz8uoXY9EN1omNWYzGfECELbk2UaWTr3dhXNY60YmUSv7U4Zw6hISRt9DPu1xlAxY9gGhrxzrWzKGJar9UxiJzGCzVzR6koaTCBqZdRNSlqo9E0PQ4Ot2SQWXQLDxVxJH8fA0I4tmRSSccHcqr9gwuhhuGsTM4ZRY+/2EQDAqYsbdyZdXitjdmWd9YWEBAjP2qJAG3GKnbOowBQYukzWbrsK2ASSxr6MpJzvwLAtV1J3Kamz1FS7rDlkDI37w87QDUQfQ2YMfTNs00JirVipt5boJEYdoTVjuFqsYCQdfLZuxLXGsD8zhuvlWr01jZWFvB4YssbQllhMsGN0CHM+awxnlrRxrDGMHkYvw1NXYEBzfF4znmHGkJDg4FlbyHjJ7a1lgdYMonbdnxlMIyO38WBO9IyhEWR11nymeawVI/nkJDUVEcTExXzGkJKGbT6j77/f+hgm9QC3XFF0JW2DhpTUbD5TDaSfn9GOwlpjmC9WMNKFjOGYQ41hpVrDWqnal66kABxbVizobpuUkjozMZbG3Kq/wPD8UgHZVLxuckSiw86xIQwlY1fU5P7YLB1JCQkanrVFANfeg5asnd1Io12F03brfvyGIbbZSV22qmy2uc5Vfx5+Mobu290yfvGY1ANAK0YwG3Yfw1hMC2D7tY+h2XymX4LeIMnYZQxLlXo9YCcZSsYQExtX0mJ3XEmdagyNDGK/ndBvyWiBrpMBzWKeUlIvJsaGfNelzSwXsHvzcN/0wuwnYjHBnm3ZKwoMj8+tYiSdYDsSQgKEgWEE8Gck2ogMW5xK0V7G8EqyfMb1Rh/DzklJPV1HfWQdRcRRSlpVKjJBWCIWM2UM++NjaDafKVZrSCViPEHzgREYNrerCCZjKCLIphItfQxXi5W6zDNInKSkK3oGsd8yhpv1jKGTAY0hJd1GV1JHtMDQp/nM0jodSSPM9dtHrqjG8NjsKm6cGOHvCiEB0h9npD2Ml3Wz1XTGiVpb7SP8fak2pmp2QK0p5csF1UxDJupnjENg6OFaCmgyTWfzmfBlpAbxmPRdjaG5wX25opCm8YwvhnQpacEiJR0OIDAEgEw6jjWTlLSsZ3hHAshQWknGYxhKxlqkpCsFLVAc7bMawy1ZPWPo0OR+MV9CJhUP7Fj3AxNjQ1hdr7TUxdoxs1ygI2mEmRzP4uzlQl1R0g5KKRyfW8U+ykgJCRSeuYWMgr/gylxr2DJevGsVAf9BppWmjGFM21ejJ2DnMoZxj/V59Tk0xlQdfnNqSoXew9AgEZO+qzGsm89UaihVq6wv9Im1hYRSSmtwH1Cglk0nkDOdZBuy0m5ISQEt+LNKSesZw76TkrrXGGo9DCkjdaPRssJdTrperuJSrkRH0ggzOZ5FtaZw9vJa24+9uFrE5bUyjWcICRieuUUAP1LSxlhpyZiZaxQ72N++4WJq6ZmouZJ61zTarsEtYxjzKSV1edfGYm4ZQxWdjGFc+q7G0AhwjQxUkhlDXxjmMwW9fUmxUkNNIbAsUjaVwJopMDNknd2QkgJay4oVq5S00K9SUu35uElJaTzjzsSYlgH0kpPOLtORNOpMbtecSV+92H6d4bE5Gs8Q0g145hYynq6klmjOLmPY3E7CPZumXbYnJRXLfQowmc90ssZQu3QKlHxlHT0Cw7B7GBqYs4T9UmMoIkjFYyjpfQyZMfTHUDIGEaCgZ/EME5og2lUAWk1j3iRbNeoNu9HgHgBG0wnkBqTGMJ2II5uKY9HRfKbIjKEHfpvcGz0MaUwSXfbqLSs2YkBjOJIyY0hIsPDMLWQUlGswZ4RldUdRB/OZ+nUPYxavMWZc21XUzWd8zhVrvnTfn9P25nFOc1Sd+hgqFbojqYE5+O2XGkNAk5OWKjWUq4qBoU9EBMPJeD0gNCSlQbiSAloAaHYlNYK0rgWGQ0nHGsN+k5ICmgGNU8ZwMVfCVhrPuLJDzxjOe0hJLzBjGHk2Z1LYmk3h1KX2DWiOz61ifCSFbSP8vBASJDxziwB+ArVG9k5aAklrA3rHOeqXbWYMLa6kSqlGe4yONrg39ueeMXSTXsZEHPsY1iLmSmoQlTV1gmRcUK7WUKzU6i6lxJvhZLzuSmoEiJmA+gpm0omm1hi5LtcYjqQTNu0qyogJAqurDJMt2aRtjaFSCpfyJWxjc3tXRtMJZFJxzPrMGO5kxjDSTI5ncWpDUtIcbmS2kJDA4ZlbyPiVkor5dkvG0GeNoU2g57pvmzkFWmuMuvmM37l87NQzYxhz325sc2xXUfMvow2apoxhHwWGRsawVK0hyYyhb4ZT8boraT0wDKzGMN4UmBnN7ruXMUzYtKuoYHQoGZmMfifZkknZupLmS1WUKjVKST0QEV8tK2aWCxgfSdVdfkk0mRxvv5dhraZwYm6VgSEhXYBnbiGj0J75jN19fmsM27WKqUtPTY+LiWE+42d/DfzIQL37GDaPs8OrwX1UkljmYLC/MoYx3XymynYVbdCUMdSDtuFkcK6kZvOZXFELWrplPjMyZFNjWChjbLj/soWAs5R0MWf0MGRg6MWO0bSnlPT80jodSXuAyfEs5leLLaoBN84vFbBWqrJVBSFdgGdukcDbkMUtGPJfY+g9xm58U12gGO0qVNMYL9qRkjplDepSUo8aQ0fzGRUhV9KY8Vz8y3F7Ac18hjWG7ZJJmWsMdfOZgKSk2VQca+VqPbOeMzKGXZJxjg4lkStVmjL7K+tljKb7y3jGYEsmaZsxXMhrgQ6lpN5MjA1hbtUjY7hUwG72MIw812/AmdQwnmHGkJDg4ZlbyHhKSevmM/ptkdZgzHedn3HZXl2gNWOoTBlD3w6nljXYEfeQita3u7arcJaS1mrRM5+JyHI6Rl1KSlfStjBLSfN185ngagyVQj1DaWTvggpErYzq+zf3UlwpVPo6Y7iyXm4xxVrMaxlDms94s3PTEGaX1+v/kLSilMKFpQKNZ3qAyfERAGjLgKbeqmJiJJA1EUIa8MwtdFSb5jOt8s3mjKFbZrE9V1K7YE6gt6vYYMbQdX0eWUXxEdjGXcxnqlEyn4k3Mob9RENKWkOy355cgJilpIV6jWFwUlKgEYDmSxUMJWNIdEn6O6pLVs1y0pX1MsaG+jdjqBSwXGjOGi7kKSX1y47RNIqVWt291srKegX5UhW7KSWNPNdty0CkvZYVx2ZXcdXmYYz26XcEIVGCgWEEcK0KNLmRGrdb2lX4dSW1zOW5LltXUk2qqUy325nLyzjGbU5/clTnGsMoNbg3XEkjEqd2DM2VVKFUrSGVoAmEXzKpRL1NRTfMZwBgTZeQ5oqVrhnPAI1aRrMBjVZj2J8nfVsyWuBndSZtZAwZGHpRb3LvICet9zBkxjDyDCXj2L1puK3A8PjcKusLCekSDAxDxneDe9PtFiVpUK6k9YEmKWkMTX0MO1tj6J7RrNflubWriImzlDRCfQwT9ecS8kI6TJOUtN+eXIA0u5IG28fQmNcwf8itdzcwNP7rb5jeAFqQ2LcZQz3wu5xvDgwXckWkE7HA/gHQT9QDQwdnUiMw3MUaw55g73b/LSvK1RpeuchWFYR0C565hYy3K6lJQ6rftsox/fcxFM8xzeM1mmMpTapZa7Ndhb8G99qlU+DnJ7CNu5nPRChj2DCficZ6OkVSN5/RMob8evGLtY9hIiaBvX5GEGhkJvPFStd6GAINKemKnjGs1hRWi/1bY7glowW8VgOahXwJ27KpvjKfCoqdemA4u+wQGOr3X8WMYU+wV29Z4VQzaub0pTzKVYV9O1lfSEg34JlbBHCVdtoEQ60ZQ9N1H70v2m1Kbx6vxTMbb3B/JTWGfrKOIlq/QjuqNWfH025j1BhGZDkdIxU3Zwz77MkFiNWVNMgsUkY3mTFqDHPdDgzTzTWGxmXfZgxdpKRb6Ujqix1jmkHP/Kp9y4oLSwUkYoLxERr59AKT41nkihVczLm3IAHMxjPMGBLSDRgYhoyf/5gBHg3uxf666xx+9mlTFyjS3ODed/axDSmpoyupj3YV8Zg4vqY1pSITiMX11Gm/xU6pRMN8hhlD/wwl4yhWaqjVFNZKlcBkpACQ1efOFxuB4WgIUlKjxnBlXcuk9WuN4WY9Y2jtZbiYL2EbHUl9MZSMY9Nw0lFKOrNUwM5NQ5ExFyPuTG7Xsn9+WlYcn11FTIDrtzNjSEg34JlbyPhtcN9oNm8zxjSB289izGUO9/HSdJ9SCob9jP/WF82XbmOcsoqNPofOc7g1uK/WIuRKaupj2E8YrqRlSknbwsgQFspV5APOGBptKQzzmW5LSQ3zGaPG0HDrNCSm/cZIOoFETFqlpLkSHUnbYGIs7VJjuE5H0h5i77jWy/CUDwOaY3Or2DOexVCStbiEdAOeuUUAdydRSzAnHp6iHjJL85ye63KQsdYUUNPlmu33MXTP9mljnNbjR0oqLf3CDLSMYTQiMT89GXuRVCKG9XINlZpCKs4fcr8YgeBaqYpCqVqXewZBPWNokpKOdDEoy6biELHJGPaplFREsDmTss0Y0pHUPxNjQ5hdcZCSLrO5fS+xe/MwUomYL2fS43M57KOMlJCu0Wenpb2Hd4P71tsbN5/xHmP7uCYpqdHgfqN9DN324+462ggcXYJLcX5Na1HqY9jH5jOGRDGZ6K/nFiTGf8PXy1VNSpoMLlCr1xiapKTddCUVEYykE43AUO9N16/mM4BmQHM538gYFkpVFMpV1hi2wcTYEOZtMobVmsLs8jp20XimZ4jHBHu2ZTydSQulKk4v5FlfSEgXYWAYMkopD0OW1suWFhYWqafzXN7BmRk7sxfRAy9luu0HfzWGzWOdtru2q3DJGEbRlTQicWrHSMWlnoliuwr/GDWFa6WqZj4TYMYwnYgjGRfkS1VUqjWsl2v1LGK3GBtKDkzGENAMaMzmMwt5LfNFKal/JsbSmF8ttrQjupQrolJT7GHYY0yOZ/HqpZzrmJPzOSgF3MQehoR0DZ659QjmVhMtWcQ2zWfabUpvbXCvgA24kjavwX6Me/DoJ7CNxZzbVdRq0ZFu9muNYSoRq7cySbPG0DfmGsOgXUm1/SWwVqwgr9cZdlNKCkDPGGoBoREg9qv5DABsySabA8Oc0dye5jN+mRgbQrWmsGDpB3neaG6/iVLSXmJyfASvLa6h4mQjDpMjKQNDQroGz9xCxsuT1M5JtEVK6nDdcTKf2JnPaDWGqv0+hkbQ55rtc5/Tn5TUpY9hhKSk/epKmjRlCWk+4x9DSrpWqmCtGKwrKaAFZrliFTk9uzsSYIbSjtGhBHJFQ0pahgi66ozabbSMYUNKupg3AkNmDP3i1OR+Zkm7zYxhb7F3exblqsK5ywXHMcfnVpFKxHDd1kwXV0bIYMMzt7BR/uruzLc3mjH0U+fXNG/9caY5YqJJSeuBoc+ModHg3sdzde5jqF26SkljcJWSRsV8JtGnUlJzYJiklNQ39YxhqYq1cjcyhnGslSr1OsNuupICWobSLCUdSSci02M0CAzzGUNpYWS9KCX1j1NgeKGeMWRg2EsYzqRuBjTHZldxw/YRJPhbQkjX4KctArj5jNqbzzg/3s9c7bqSmqdsZAyV7fqc55KmSzu8Alc/gW1MBA5xYaTMZ+Jxw2gn5IV0GHOWkBlD/wybpaTFav12UGTSWsbOCM66aT4DaL0MGxnDSl/XFwKa+Uy5qpAvadLdRaPGkOYzvpnQm9zPWZxJLywXkE3F+9q8qB+Z9NGy4vjcKvZRRkpIV+GZW8h4tre3MZ+xhmNNgZJrRs5ziGW8nfmMXmNoGeOFV/2gtk27dDKIMR7rZiATc5OSRsh8JuFDFtuLmA1naD7jn2FdSrq6XkGpGrwZzEg6jrVStZ4x7H5g2KgxXFkv920PQ4MtGS0AvKxnChfyJaTisa6/7r3M+EgaIvYZw12bh33/FpFosDWbwthQwtGAZrlQxszyOh1JCekyPHMLGc2V1Htcw3zGfbDb1vocbUpJm+JO0das2mxXYSdLtRLzCJYaNYguNYYu5jPVmoqMXC3ex+YzdteJO4Z0dCFXbLod3P4SyBcr9axdt81nRpvaVZT72ngGADZntOe3pNcZLua0HoYMZvyTjMewLZvG/KqlxnB5nfWFPYiIYO/2EceWFSd045l9O0e6uSxCBh6euUWAtoI5aa8msXmbdum7LtAmyxcTo8G9anMu7303DGrstzeawrvP4WRyVlPRyxj2W2CYZMZwQxjS0Uu6W2XQ5jPZVBz5UiMw7Ha7itGhBIqVGkqVGlbWB0BKqtcSGs6kbG6/MXZuSmN2uTVjSEfS3mTveNaxxrDuSMqMISFdhWduIePpSmqRfwpaA0lzMOgaZLYtJW2+1B6rNbg31t2uK6l7faCxP/tBDWmr+xzWPlcGWsbQe63dwHAljUgCs2MkTZEuM4b+GUroGcO8ERgGmzHMphNYK4YnJTX2p9U5lvu+PmyLnjE0AsOFfIn1hRtgYnSoqcZwvVzFpVyJGcMeZXI8i5nldazp7shmjs2uYiSdwFU8toR0FZ65hYzyciW1u6/FfMZ5m+1Iv/JPm0CtnjFUxlR+jWz81Bi6B35+6hTdpKRKRaemr18zhpSSboxYTDCUjHVNSppNJ7SM4Xo4rqSjeoZwdb2sSUn7PWOo1xgaUtKFfJEZww2wY2yoSUpqZA93MWPYk0xu1wxoTl9aa9l2bHYVN06MUG5NSJfhmVsE8CP/NDd3twZj/ttV6GPaDObEJvKs1xj6fAf5kZIam5zknoYy0bVdhQiqPdHHUJou+4UU+xhumEwqUW98HrSUNJOKY71cw3KhjFQi1vVjZdQ0rhQqWC1W+r7GcJP+/Iz+hUaNIWmPibE0LuVKKOv1AheWtVYVzCr1JnvHtfrBUxYDGqUUHUkJCQmeuYWM8vYlBWCWkop7xtCtXYWNNNTfPhsYcUy17RpDPzJQIxB1l5K6Br8xcZWSRqXG0JBc9lvGkH0MN85wMo4FvY1BJuCG84aUc361GIozpuFCOrNcgFLAWJ+7kibiMYwNJbC0VsJ6uYp8qcoehhtgp97LcH5V+5xc0Jvb72Jg2JPsGdca179qMaC5mCvi8lqZ9YWEhEAoZ24islVEHhCRE/rlFodx3xaRJRG5z3L/pIg8ISInReSrItKzv7BKtWc+o2UMLWOa2kl4z3Vl5jPa9WqbfQyN2j4/fQydXUmNYMpFSipw7mMYKVfS/qwxbJKSMjBsi+FUvJ5R6oYrKQDMr66HEximtQzaeb05eb9LSQHNgObyWrl+jLeNpENeUe9hbXI/o79/KCXtTTKpBHZtGmoxoDk+q2UQ9zEwJKTrhHXm9hsAHlRKvQ7Ag/ptO/4QwE/a3P8HAP5YKXUDgMsAfjaQVXYLV5dR49IkJbUERr4zgB0xn9Fo15XUr3GM2xgjzvCqU6w6ZQzpSho45ixhmlLStsik4vV/amSSAbuS6hnJ+ZVi1+sLgUbG8IIRGPa5+QwAbM6kcHmtVA8MKSVtnx16k/t5PTC8sFzAtmwKQ8lg/5FCgmNyPNvS5L7uSEopKSFdJ6wztw8CuEe/fg+AD9kNUko9CGDVfJ9oEca7APyd1+N7Ab+upPXbNmFdcwmgi5TUYU6v8U0ZQz2gMVpCXMlcVmIe7Sga7Szc51COfQzdH9tNGjWGIS+kw9B8ZuMMm05ug5aSGu0p5lbWMRpCYGjUGA5UxjCTxNJaue48Sylp+zQyhg0pKR1Je5vJ8SxOXcw1/W4fn13FtmwK48yqE9J1wvF0tpEAABacSURBVPo37YRSaka/Pgtgoo3HbgOwpJQy/I3PAbjKabCIfALAJwBgYmIC09PT7a82QGrVGs6+dhbT03O222cuaD+AxrovXy5gfV01PY8Tr5Xr14+8/DLGLh9HLpdrea7nz2tzHThwANmkd4A0P6+Nf+SRR5DSU1uvntJOak69+ioA4NFHH0HSR7A1M6PN9eSTT+B0xj5gOLVUBQCcO2v/ehyZ0Q75qZMnMV05YzvH3GwRa+tV2+NcLBYxN3MB09MLnusNmlNntGNWLZcj9568Ek4vV+vXH3/sAIYS0QjErwS7z1IQFExui08//hjSAb52Jxa045QvVbGeX+76e7Csp0aPvjYPADh++HmUzl1ZMNyt47RRiqvrmLlcw4FDzwMATh5+DrnTg/fPkys5TlovWuDJF4/jutJpnLiwhl3ZWKSPey/Szc9SbbmMlfUK/vGBaYyltO+8p04UsCMNHlcPov6dRzR67TgFFhiKyHcB7LTZ9CnzDaWUEhF/DiwbQCn1BQBfAID9+/erqampoHa1IWIPfAvXXXctpqZust1+/+KLkPOvwVj3l155Asu1PMzP49zjZ4CXXwIA3HLLzZh6425MT0/D+ly/t3oYeO00br/99rpLnhvfmH8OuHAeU3fcUc/+HMErwImjuOba64BXTmLqjjt8mYw8vPwS8NoZ3Pb2t+OarRnbMVvPLQGPH8Aeh9cj/8IM8Pwz2LfvdZi6bY/tHPcvvoAjy/Mtzx0AYt/7Dq65ejempl7vud6gOf/EGeDISxhKp2zX2qscnV0BDj4KALjznf7eG1HH7rMUBF87/zReuDQLEeDd75oKNLu95ewS8NQBAMC1u3Zgauotge3LidRD38JqLQmgiHfdfhuu3Wb/veCXbh2njfK91cN4ceEcdlyzF3jhCN77zndgU6b/M6VWrvQ47XziIaS3bMUdd7wJyw/dj7vfeA2mpm7p3AJJVz9L6ug8/vroU9h945uwf89W1GoKsw/dj4/s53H1IurfeUSj145TYIGhUuoup20iMiciu5RSMyKyC8B8G1MvANgsIgk9a3g1gPNXuNzQ8HIltTebcb7t6kpqMbLxwq4pvXG9XfMZX46inuYzzXM5zeEkJY2S+YxRYxiR5XQMw3BGpPEciT+MOqnhZDzw96m5rnA0JEfQ0XQCF3V3yUGoMdySSSFXrGB2eR2JmAzEcw6CHWNpzK8UsbJeQb5UZauKHmdyXOtleOpSHvv3bMX5pQLWSlW2qiAkJML6d/43AHxcv/5xAP/g94FKO+t/GMCPbeTxUcPbldTqOiqtfQxh3u4yV93cxadhDFrHG+er7ZrP+GlO31if03Z/LS9c+xhGxHzGcCXtV/OZVDzGxsRtYjiRBt3DEGiYzwCNesNuYw5Iw3BG7TZb9JrCU5fy2JJN8fOxQSZGhzC3sl43Ltq1mY6kvczVW4aRjAtO6S0rjs3qxjN0JCUkFMIKDD8D4N0icgLAXfptiMh+EfmiMUhEHgXwtwDuFJFzIvIj+qZfB/ArInISWs3hl7q6+g7jFcw1mcvYjLdzDbWdy8cYu3mb96/dquiBof/so3Hp3a7C6YSpbtji1q7Co49h1DKGfaC0bMKQHLNVRfsYAWHQrSrM+wIaRjDdxtjvSDqBxAC8X7bostFXLuZoPHMF7Nw0hNmVdczoze1pPtPbJOIxXLs1g1f1Jvd1R9KJkTCXRcjAEsoZgVJqAcCdNvcfAvBzptvvcHj8KQBvDWyBXcTTldSaHbSTllq2O85l037CDVcpaT0w9Jkx9CGdrPcpdHQlbR5nh4hLH0OlfGc4gybe51JSOpK2jyEl7UZgmDXtI6xsndHLMCwpa7fZktGCwbOLa7jt+m0hr6Z32TGWxup6Ba/Maxmm3ZsYGPY6k+Mj9V6Gx+dWcdXmYYwOgFMxIVGEZ28ho5RyrQsEWjOC7n0M3YImPdDzmTO09lA0X9eCLF/TOM5lxauPoZ92FXGXPoY1FZ0MXcJH9rMXSSYYGG6UhpQ0+MAwEY/V+0yG0ccQaGQMB6FVBQBs1jOGNQVszdKGf6NMjGrS0efOLiERE2wf5WvZ6+zdnsXphTVUawrHZleZLSQkRHj2FgG8paStgVnTGL81hj7GNO9bWsYaMVm1ptqqkTHW6JoxjLlLSf1kHeMxQc2xj2GUagyNwDDkhXQYZgw3TjdrDIFGpjC0jKERGA6ICYuRMQTYw/BKMHoZPvvaZUyMDTkqTEjvMDmeRalSw2uLazh1Mc/G9oSECM/eQsZbSoqmJKDAJifot8awzaBI0CrbNG61mzFsp8bQy5XU7URAxD4wrJvlROQkIhHvTylpUn9e/dCmott0U0oKABndgCY8KelgZQzNgeFWBoYbZucmLUN4YXmdjqR9wl7dmfSho/MoVWvYR+MZQkKDZ28h4+lKKjbCT6v5jGW881zaZTtOotaRRmBVqXpLYK1zee3br5TU7TnGY/Y1hoZTaXQyhv3pSioiSMaF5jMboJtSUqDhRhqWlNSoIRrz0VO1HxhOxevyXQaGG2fHWMOFlI6k/cHkdi0wvP+lWQB0JCUkTHj2FgXakWTamc+YawDdHtvm7kScM4ZVpdpZdqMHocs7ztt8xoeU1KHGsBq1jKEhi+3DT2AqHqOUdAMMGxnDLgVq2ahISQfEfAZoZA0pJd04o+lE/bNCR9L+YPtIGiPpBJ46s4iYADfsYI0hIWHBs7cewGou02I+4zjWfh6/oZFVxqrNoZvP1Npz+BQfGUMvg5q6lNR1jsb6zBjy0qjUoxjrSERjOR0lmWBguBGGjYxhsktS0lS4UtK6+cyAZAyBRi9DZgw3johgYkyTk+7exIxhPyAimBzPQilgz3i2LqsnhHQfnr2FiNKDFXcpaau5TGvG0P56y1zwlmI2zyst2bl6uwrVVqLTV7bPa0zcw5zGPMZaZ2hkDKMiJa1nDCOynk6SjMcoJd0A9T6G3coY6vsLq4+hISUdlHYVQKOX4bYROmleCYaclBnD/mGvLidlfSEh4cKztwgg338UOHjQftvMDKRcqm+XxUXIpUtN4+Xkycb1r/2t81znz2mXj9tvbxk/OwMpV5rmi506BQConTyJWKnkuC8rsXNntcsnn3QeYwSGDzxgO68REMb//l7H/cbOavupHnxcG/PpTwMHD6JW07c/9KDvNQdJ3ZV0eSkS6+kkqUoZqdOn+u55BU1dSnrgka68dtmVRe3y2UOB78uOuvnMw98dmPfKloLWvHvbkedDXklvs7OkNUPfdeZ4yCshnWKycBkAcGN5KeSVEDLYMDAMEWWcDD30EHDnna0nRwcPQu69F1Iqadu/8AXI978PmZttjD94EPLp32885i/u0bbl861z/eVfAgDkrru8T8QOHkTs3nshpWLTvmKf/SwA4PuXqpDiuv267eb68pe06+99r3NQ98zT2uV9/2g7b+yll7TLv/pLx9cr9qUvAgA+8sUn8OHPHcSHj6Tw4c8/jp/4zH0AgPg/3edvzQGTOKw/l8sLkVhPxzh4EKkL55B6+aX+el5dIPOSFixk7vtG8K/dwYPI3vcNJKtlpO/28X0QAKMnjwIAxr76lcF4rxw8iM3fvg/xWhWb3nt3/z/foDh4EBP/+HcAgKs+9qN8HfuBgwcx+SefBgDs++P/xmNKSIgMjoYnikx/D+94tYrrFi8ApRIwPQ3cdptp+zTed+RRbF1Z0Lbfey9+7PQqLg2PNcYDuPXMS7jrxOOI12p4w8wJbdvqqmVf07j72GNApawFmtZ9tazNsm99X289/TzuOvEEiokk3jRz3H7dNnPdefxxrCGOdCHvOH784CP4mUOn8c9fOWQ77w88fwAfe/48bj17GCjbv153nHwKT+28EZWYuUZBgEszeNfFefzwq8/6W3PAvO7ZA/jx585j353XR2I9HWN6Gj976AB2Lc/31/PqAruffBQ/9fQZvPPkk8G/dtPT+MDhh7EjxOP0+hcew8eeP4+3n35+MN4r09P48EsPYmJ5HrFSsf+fb1BMT+MDh6eRKBYxtnqZr2M/oP92/+vn78ftJw/xmBISJkqpgfm79dZbVaR47DGlhoeVise1y8cec9/+Z3/WOt4YE4spBWiXw8Pq4fvua29fftbmsK8NzdWJ18NtezqtVCrl/tqFib7Wh//oj6Kxnk7R7vusB3j44Ye7s6NuvnZROE4dXkPXjtNGicJrHgGu+DjxdQycrn+WeEw3ROS/84hSKrrHCcAhZRMrMWMYJrfdBjz4oPbfsamp1v+Q2W1/wxtaxxtjtm0DFha0bcVie/vyuza7fW10rk68Hm7bAe/XLiyMtZ45o12GvZ5O0e77jDTo5msXheMUhTV0k0F7vkHB17H/4DElJDKIUjbdwPuU/fv3q0OHwjFa6DbT09OYMoIjEll4nKIPj1FvwOPUG/A4RR8eo96Ax6k3iOpxEpGnlVL7rffTfIYQQgghhBBCBhwGhoQQQgghhBAy4DAwJIQQQgghhJABh4EhIYQQQgghhAw4DAwJIYQQQgghZMBhYEgIIYQQQgghAw4DQ0IIIYQQQggZcBgYEkIIIYQQQsiAw8CQEEIIIYQQQgYcBoaEEEIIIYQQMuAwMCSEEEIIIYSQAUeUUmGvoWuIyEUAZ8JeR5cYB3Ap7EUQT3icog+PUW/A49Qb8DhFHx6j3oDHqTeI6nG6Tim13XrnQAWGg4SIHFJK7Q97HcQdHqfow2PUG/A49QY8TtGHx6g34HHqDXrtOFFKSgghhBBCCCEDDgNDQgghhBBCCBlwGBj2L18IewHEFzxO0YfHqDfgceoNeJyiD49Rb8Dj1Bv01HFijSEhhBBCCCGEDDjMGBJCCCGEEELIgMPAsIcRkWtE5GEReVlEDovIL9mMmRKRZRF5Tv/7z2GsdZARkdMi8qL++h+y2S4i8r9E5KSIvCAibwljnYOMiOwzfUaeE5EVEfllyxh+lkJARL4sIvMi8pLpvq0i8oCInNAvtzg89uP6mBMi8vHurXrwcDhOfygiR/Xvta+LyGaHx7p+R5LO4HCMfltEzpu+197n8Nj3iMgx/XfqN7q36sHD4Th91XSMTovIcw6P5WepCzidf/fDbxOlpD2MiOwCsEsp9YyIjAJ4GsCHlFIvm8ZMAfhVpdT7Q1rmwCMipwHsV0rZ9rHRf4h/EcD7ALwNwJ8opd7WvRUSMyISB3AewNuUUmdM90+Bn6WuIyL/HEAOwF8opV6v3/ffASwqpT6jn6RuUUr9uuVxWwEcArAfgIL2/XirUupyV5/AgOBwnO4G8JBSqiIifwAA1uOkjzsNl+9I0hkcjtFvA8gppf7I5XFxAMcBvBvAOQBPAfiY+VyDdA6742TZ/lkAy0qp37XZdhr8LAWO0/k3gJ9Cj/82MWPYwyilZpRSz+jXVwEcAXBVuKsiG+CD0H4AlFLqcQCb9S8dEg53AnjFHBSS8FBKPQJg0XL3BwHco1+/B9oPspUfAfCAUmpR/8F9AMB7AlvogGN3nJRS31FKVfSbjwO4uusLI3UcPkt+eCuAk0qpU0qpEoC/gfYZJAHgdpxERAB8BMBfd3VRpAmX8++e/21iYNgniMgeAD8I4AmbzbeJyPMi8i0RuaWrCyOA9h+h74jI0yLyCZvtVwE4a7p9Dgzww+SjcP7R5WcpGkwopWb067MAJmzG8HMVLX4GwLcctnl9R5Jg+QVd7vtlB+kbP0vR4R0A5pRSJxy287PUZSzn3z3/28TAsA8QkREA9wL4ZaXUimXzMwCuU0q9CcCfAvh/3V4fwe1KqbcAeC+A/6jLREgEEZEUgA8A+FubzfwsRRCl1UOwJiLCiMinAFQAfMVhCL8jw+NzAK4H8GYAMwA+G+5yiAcfg3u2kJ+lLuJ2/t2rv00MDHscEUlCe1N+RSn199btSqkVpVROv/5NAEkRGe/yMgcapdR5/XIewNehyXLMnAdwjen21fp9pPu8F8AzSqk56wZ+liLFnCG31i/nbcbwcxUBROSnALwfwL9RDqYGPr4jSUAopeaUUlWlVA3A/4H9a8/PUgQQkQSAHwXwVacx/Cx1D4fz757/bWJg2MPoWvMvATiilPofDmN26uMgIm+FdswXurfKwUZEsnphMkQkC+BuAC9Zhn0DwL8VjbdDKyqfAQkDx//G8rMUKb4BwHBy+ziAf7AZcz+Au0Vkiy6Pu1u/j3QJEXkPgF8D8AGl1JrDGD/fkSQgLPXsH4b9a/8UgNeJyKSuqvgotM8g6S53ATiqlDpnt5Gfpe7hcv7d879NibAXQK6IHwbwkwBeNFkX/xaAawFAKfV5AD8G4OdFpAKgAOCjTv+1JYEwAeDrejyRAPB/lVLfFpFPAvVj9E1ojqQnAawB+OmQ1jrQ6D+k7wbw7033mY8TP0shICJ/DWAKwLiInAPwXwB8BsDXRORnAZyBZsYAEdkP4JNKqZ9TSi2KyO9BO6kFgN9VSm3EeIP4wOE4/SaANIAH9O/Ax5VSnxSR3QC+qJR6Hxy+I0N4Cn2PwzGaEpE3Q5O8nYb+/Wc+Rrqr7C9AO3mNA/iyUupwCE9hILA7TkqpL8Gm/p2fpdBwOv/u+d8mtqsghBBCCCGEkAGHUlJCCCGEEEIIGXAYGBJCCCGEEELIgMPAkBBCCCGEEEIGHAaGhBBCCCGEEDLgMDAkhBBCCCGEkAGHgSEhhBBiQUTiIvKsiNyn3z4tIuMOY5Mi8kx3V0gIIYR0FgaGhBBCSCu/BOCIz7G3AzgQ4FoIIYSQwGFgSAghhJgQkasB/AsAX7Rs+kUReUZEXhSRm0z3vwfAt/TH/oqIvKT//bJ+3x4ROSoify4ix0XkKyJyl4gcEJETIvJWfVxWRL4sIk/q2coP6vdnRORrIvKyiHxdRJ7QGyZDRD4nIodE5LCI/E7ALw0hhJA+hoEhIYQQ0sz/BPBrAGqW+y8ppd4C4HMAftV0/zsBTIvIrQB+GsDbALwdwL8TkR/Ux9wA4LMAbtL/fhxapvFXAfyWPuZTAB5SSr1Vn/MPRSQL4D8AuKyUuhnAfwJwq2nfn1JK7QfwRgB3iMgbr/TJE0IIGUwYGBJCCCE6IvJ+APNKqadtNv+9fvk0gD36+KsALCql1qAFel9XSuWVUjl9/Dv0x7yqlHpRKVUDcBjAg0opBeBFYy4AdwP4DRF5DsA0gCEA1+rz/g0AKKVeAvCCaU0f0esbnwVwC4Cbr+gFIIQQMrAkwl4AIYQQEiF+GMAHROR90AKzMRH5K31bUb+sovH7+R4A9/uYt2i6XjPdrpnmEgD/Sil1zPxAEbGdUEQmoWUcf0gpdVlE/lxfMyGEENI2zBgSQgghOkqp31RKXa2U2gPgo9CknT/h8pB6fSGARwF8SK8JzAL4sH6fX+6HVscoAGCSoR4A8BH9vpsBvEG/fwxAHsCyiEwAeG8b+yKEEEKaYMaQEEII2QAiEgdwg1LqKAAopZ7Rs3ZP6kO+qJR6VkT2+Jzy96DVN74gIjEArwJ4P4D/DeAeEXkZwFFoUtRlpdQJEXlWv+8s6IxKCCHkChCtxIEQQggh7SAitwP4CaXUJwPeTxxAUim1LiLXA/gugH1KqVKQ+yWEEDJYMDAkhBBCIoyIjAJ4GEASWh3iryulvuX+KEIIIaQ9GBgSQgghhBBCyIBD8xlCCCGEEEIIGXAYGBJCCCGEEELIgMPAkBBCCCGEEEIGHAaGhBBCCCGEEDLgMDAkhBBCCCGEkAGHgSEhhBBCCCGEDDj/H2VVUGYWr7QaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from odeintw import odeintw\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import multi_dot, norm, eig\n",
    "import math\n",
    "import time\n",
    "from array import *\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "    \n",
    "N = 2\n",
    "h = 25.0\n",
    "h0 = 0.1\n",
    "nn = 1   # this is the 'th column of the inital floquet evolution matrix \n",
    "         # for which the path we shall follow\n",
    "tsteps = 20\n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "omega_range = np.linspace(5.0,50.0,100)\n",
    "omegas = omega_range\n",
    "#omegas = np.hstack((omega_range,41.5831))   # inlcude the frequency coresponidng to Bessel's root\n",
    "omegas.sort()                                # arrange the omegas in ascendng order\n",
    "\n",
    "psi = np.eye(N) + (1j) * np.zeros((N,N))\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "phasefunc_path = np.zeros(len(omegas))\n",
    "prob = np.zeros(N)\n",
    "\n",
    "title = \"mf floquet dynamics in path mode: n \" + str(N) + \"_bessel 4th root\"\n",
    "photoname = \"n_\" + str(N) + \"_mfd_bessel_floquet_path_bessel4.jpeg\"\n",
    "filename = \"n_\" + str(N) + \"_mfd.txt\"\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "class Periodic_Lattice(np.ndarray):\n",
    "    def __new__(cls, input_array, lattice_spacing=None):\n",
    "        obj = np.asarray(input_array).view(cls)\n",
    "        obj.lattice_shape = input_array.shape\n",
    "        obj.lattice_dim = len(input_array.shape)\n",
    "        obj.lattice_spacing = lattice_spacing\n",
    "        return obj\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__getitem__(index)\n",
    "    \n",
    "    def __setitem__(self, index, item):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__setitem__(index, item)\n",
    "    \n",
    "    def __array_finalize__(self, obj):\n",
    "        if obj is None: return\n",
    "        self.lattice_shape = getattr(obj, 'lattice_shape', obj.shape)\n",
    "        self.lattice_dim = getattr(obj, 'lattice_dim', len(obj.shape))\n",
    "        self.lattice_spacing = getattr(obj, 'lattice_spacing', None)\n",
    "        pass\n",
    "    \n",
    "    def latticeWrapIdx(self, index):\n",
    "        if not hasattr(index, '__iter__'): return index         # handle integer slices\n",
    "        if len(index) != len(self.lattice_shape): return index  # must reference a scalar\n",
    "        if any(type(i) == slice for i in index): return index   # slices not supported\n",
    "        if len(index) == len(self.lattice_shape):               # periodic indexing of scalars\n",
    "            mod_index = tuple(( (i%s + s)%s for i,s in zip(index, self.lattice_shape)))\n",
    "            return mod_index\n",
    "        raise ValueError('Unexpected index: {}'.format(index))\n",
    "\n",
    "\n",
    "def floq_jac(psi0,t, h, h0, w, cosp, N):\n",
    "    drive = h0 + h * np.cos(w * t)\n",
    "    jac = (- 1j) * N * (-2.0 * q * q - drive * np.sqrt(1.0 - 4.0 * q *q) * cosp)\n",
    "    return jac\n",
    "\n",
    "def floq_func(psi0,t,h,h0,w,cosp,N):\n",
    "    return np.dot(floq_jac(psi0,t, h0, h, w, cosp, N), psi0)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    periodic_psi  = Periodic_Lattice(psi)       \n",
    "    cospinit = 0.0\n",
    "    for k in np.arange(N):\n",
    "        for m in np.arange(N):\n",
    "            for l in np.arange(N+1):\n",
    "                for j in np.arange(l+1):\n",
    "                    cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* \\\n",
    "                                          math.comb(l,j)* periodic_psi[(k+(l-j),(m))]])\n",
    "            cosp[k,m] = cospinit\n",
    "            cospinit = 0.0\n",
    "    \n",
    "    # calculate for first frequency\n",
    "    w = omegas[0]\n",
    "    T = 2 * np.pi/w                            \n",
    "    t = np.linspace(0,2 * np.pi/w,tsteps)           \n",
    "    floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "    \n",
    "    for mm in np.arange(N):\n",
    "        psi0 = periodic_psi[mm]       \n",
    "        psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "        floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "        #print('np.linalg.norm(psi_t[N-1])',np.linalg.norm(psi_t[N-1]))\n",
    "        #print('psi_t[N-1]',psi_t[N-1])\n",
    "        \n",
    "    #print('floqEvolution_mat',floqEvolution_mat)\n",
    "    evals, evecs = eig(floqEvolution_mat)\n",
    "    phasefunc = (1j * np.log(evals[nn]))/T\n",
    "    evecs_path = evecs[nn]\n",
    "    phasefunc_path[0] = phasefunc.real\n",
    "    \n",
    "    # calculate for rest of the frequencies\n",
    "    for cc, w in enumerate(omegas[1:len(omegas)]):\n",
    "        T = 2 * np.pi/w                      \n",
    "        t = np.linspace(0,2 * np.pi/w,tsteps)    \n",
    "        floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))        \n",
    "        \n",
    "        for mm in np.arange(N):\n",
    "            psi0 = periodic_psi[mm]       \n",
    "            psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "            #print('np.linalg.norm(psi_t[N-1])',np.linalg.norm(psi_t[N-1]))\n",
    "            #print('psi_t[N-1]',psi_t[N-1])\n",
    "            floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "        evals, evecs = eig(floqEvolution_mat)    \n",
    "        prob = np.asarray(list(map(lambda x:np.dot(np.conjugate(evecs_path).T,x),evecs))) \n",
    "        #print('prob',prob.real)\n",
    "        \n",
    "        for i,pr in enumerate(prob):\n",
    "            if (pr >= (0.99 + 1j * 0)):\n",
    "                pp = i\n",
    "                break\n",
    "        evecs_path = evecs[pp]\n",
    "        phasefunc = (1j * np.log(evals[pp]))/T\n",
    "        phasefunc_path[cc+1] = phasefunc.real\n",
    "                \n",
    "    print('time taken',time.time()-start,'sec')\n",
    "    plt.figure(figsize=(15,6))\n",
    "    plt.title(title)\n",
    "    plt.xlabel(\"4h/omega\")\n",
    "    plt.ylabel(\"phase function\")\n",
    "    plt.plot(4*h/(omegas),phasefunc_path)\n",
    "    plt.scatter(4*h/(omegas),phasefunc_path,marker='.',color='r')\n",
    "    plt.grid()\n",
    "    #plt.savefig(photoname,dpi = 300)\n",
    "    plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. when h varies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "floqEvolution_mat [[ 9.99848431e-01-0.01123361j -6.29592630e-03-0.00641517j\n",
      "  -2.85547625e-04-0.00980034j]\n",
      " [ 3.25271261e-01+0.33495439j  3.50642990e-02-0.88288529j\n",
      "  -2.33019833e-02-0.02729929j]\n",
      " [ 2.26499400e-03-0.01126224j -6.31197057e-03-0.00643152j\n",
      "   9.99845133e-01-0.00982531j]]\n",
      "time taken 3.139286994934082 sec\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from odeintw import odeintw\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import multi_dot, norm, eig\n",
    "import math\n",
    "import time\n",
    "from array import *\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "    \n",
    "N = 3\n",
    "\n",
    "h0 = 0.1\n",
    "nn = 1   # this is the 'th column of the inital floquet evolution matrix \n",
    "pp = nn  # for which the path we shall follow\n",
    "tsteps = 20\n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "w = 100.0  # omega frequency\n",
    "T = 2 * np.pi/w                            \n",
    "t = np.linspace(0,2 * np.pi/w,tsteps)   \n",
    "hs = np.linspace(50.0,70.0,2)\n",
    "\n",
    "psi = np.eye(N) + (1j) * np.zeros((N,N))\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "phasefunc_path = np.zeros(len(hs))\n",
    "prob = np.zeros(N)\n",
    "\n",
    "title = \"mf floquet dynamics in path mode: n \" + str(N) + \"_bessel 4th root\"\n",
    "photoname = \"n_\" + str(N) + \"_mfd_bessel_floquet_path_bessel4.jpeg\"\n",
    "filename = \"n_\" + str(N) + \"_mfd.txt\"\n",
    "\n",
    "class Periodic_Lattice(np.ndarray):\n",
    "    def __new__(cls, input_array, lattice_spacing=None):\n",
    "        obj = np.asarray(input_array).view(cls)\n",
    "        obj.lattice_shape = input_array.shape\n",
    "        obj.lattice_dim = len(input_array.shape)\n",
    "        obj.lattice_spacing = lattice_spacing\n",
    "        return obj\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__getitem__(index)\n",
    "    \n",
    "    def __setitem__(self, index, item):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__setitem__(index, item)\n",
    "    \n",
    "    def __array_finalize__(self, obj):\n",
    "        if obj is None: return\n",
    "        self.lattice_shape = getattr(obj, 'lattice_shape', obj.shape)\n",
    "        self.lattice_dim = getattr(obj, 'lattice_dim', len(obj.shape))\n",
    "        self.lattice_spacing = getattr(obj, 'lattice_spacing', None)\n",
    "        pass\n",
    "    \n",
    "    def latticeWrapIdx(self, index):\n",
    "        if not hasattr(index, '__iter__'): return index         # handle integer slices\n",
    "        if len(index) != len(self.lattice_shape): return index  # must reference a scalar\n",
    "        if any(type(i) == slice for i in index): return index   # slices not supported\n",
    "        if len(index) == len(self.lattice_shape):               # periodic indexing of scalars\n",
    "            mod_index = tuple(( (i%s + s)%s for i,s in zip(index, self.lattice_shape)))\n",
    "            return mod_index\n",
    "        raise ValueError('Unexpected index: {}'.format(index))\n",
    "\n",
    "\n",
    "def floq_jac(psi0,t, h, h0, w, cosp, N):\n",
    "    drive = h0 + h * np.cos(w * t)\n",
    "    jac = (1j) * N * (-2.0 * q * q - drive * np.sqrt(1.0 - 4.0 * q *q) * cosp)\n",
    "    return jac\n",
    "\n",
    "def floq_func(psi0,t,h,h0,w,cosp,N):\n",
    "    return np.dot(floq_jac(psi0,t, h0, h, w, cosp, N), psi0)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    periodic_psi  = Periodic_Lattice(psi)       \n",
    "    cospinit = 0.0\n",
    "    for k in np.arange(N):\n",
    "        for m in np.arange(N):\n",
    "            for l in np.arange(N+1):\n",
    "                for j in np.arange(l+1):\n",
    "                    cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* \\\n",
    "                                          math.comb(l,j)* periodic_psi[(k+(l-j),(m))]])\n",
    "            cosp[k,m] = cospinit\n",
    "            cospinit = 0.0\n",
    "    \n",
    "    # calculate for first h\n",
    "    h = hs[0]        \n",
    "    floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "    \n",
    "    for mm in np.arange(N):\n",
    "        psi0 = periodic_psi[mm]       \n",
    "        psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "        floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "    \n",
    "    evals, evecs = eig(floqEvolution_mat)\n",
    "    phasefunc = (1j * np.log(evals[nn]))/T\n",
    "    evecs_path = evecs[nn]\n",
    "    phasefunc_path[0] = phasefunc.real\n",
    "    \n",
    "    # calculate for rest of h\n",
    "    #for cc, h in enumerate(hs[1:len(hs)]):\n",
    "    for cc, h in enumerate(hs[1:len(hs)]):\n",
    "        floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))        \n",
    "        \n",
    "        for mm in np.arange(N):\n",
    "            psi0 = periodic_psi[mm]       \n",
    "            psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "            floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "        evals, evecs = eig(floqEvolution_mat)\n",
    "        prob = np.asarray(list(map(lambda x:np.dot(np.conjugate(evecs_path).T,x),evecs))) \n",
    "        \n",
    "        for i,pr in enumerate(prob):\n",
    "            if (pr >= (0.9 + 1j * 0)):\n",
    "                pp = i\n",
    "                break\n",
    "        evecs_path = evecs[pp]\n",
    "        phasefunc = (1j * np.log(evals[pp]))/T\n",
    "        phasefunc_path[cc+1] = phasefunc.real\n",
    "                \n",
    "    print('time taken',time.time()-start,'sec')\n",
    "    plt.figure(figsize=(15,6))\n",
    "    plt.title(title)\n",
    "    plt.xlabel(\"4h/omega\")\n",
    "    plt.ylabel(\"phase function\")\n",
    "    plt.plot(4*hs/w,phasefunc_path)\n",
    "    plt.scatter(4*hs/w,phasefunc_path,marker='.',color='r')\n",
    "    plt.grid()\n",
    "    #plt.savefig(photoname,dpi = 300)\n",
    "    plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-1-5j)\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1 + 1j*1])\n",
    "b = np.array([2 - 1j*3])\n",
    "print(np.dot(np.conjugate(a),b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot prod (1+0j)\n",
      "dot prod (1+0j)\n",
      "dot prod (1+0j)\n",
      "dot prod (1+0j)\n",
      "dot prod (1+0j)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-3-06483c87cf96>:108: RuntimeWarning: divide by zero encountered in log\n",
      "  phasefunc = (1j * np.log(evals[nn]))/T\n",
      "<ipython-input-3-06483c87cf96>:108: RuntimeWarning: invalid value encountered in cdouble_scalars\n",
      "  phasefunc = (1j * np.log(evals[nn]))/T\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'pp' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-06483c87cf96>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    130\u001b[0m                 \u001b[0mpp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    131\u001b[0m                 \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 132\u001b[0;31m         \u001b[0mevecs_path\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevecs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpp\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    133\u001b[0m         \u001b[0mphasefunc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1j\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevals\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m         \u001b[0mphasefunc_path\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcc\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mphasefunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'pp' is not defined"
     ]
    }
   ],
   "source": [
    "## frequency experiment\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "from odeintw import odeintw\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import multi_dot, norm, eig\n",
    "import math\n",
    "import time\n",
    "from array import *\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "    \n",
    "N = 5\n",
    "h = 25.0\n",
    "h0 = 0.1\n",
    "nn = 1   # this is the 'th column of the inital floquet evolution matrix \n",
    "         # for which the path we shall follow\n",
    "tsteps = 20\n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "omega_range = np.linspace(5.0,50.0,100)\n",
    "omegas = omega_range\n",
    "#omegas = np.hstack((omega_range,41.5831))   # inlcude the frequency coresponidng to Bessel's root\n",
    "omegas.sort()                               # arrange the omegas in ascendng order\n",
    "\n",
    "psi = np.eye(N) + (1j) * np.zeros((N,N))\n",
    "psis = np.eye(N) + (1j) * np.zeros((N,N))\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "phasefunc_path = np.zeros(len(omegas))\n",
    "prob = np.zeros(N)\n",
    "\n",
    "title = \"mf floquet dynamics in path mode: n \" + str(N) + \"_bessel 4th root\"\n",
    "photoname = \"n_\" + str(N) + \"_mfd_bessel_floquet_path_bessel4.jpeg\"\n",
    "filename = \"n_\" + str(N) + \"_mfd.txt\"\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "class Periodic_Lattice(np.ndarray):\n",
    "    def __new__(cls, input_array, lattice_spacing=None):\n",
    "        obj = np.asarray(input_array).view(cls)\n",
    "        obj.lattice_shape = input_array.shape\n",
    "        obj.lattice_dim = len(input_array.shape)\n",
    "        obj.lattice_spacing = lattice_spacing\n",
    "        return obj\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__getitem__(index)\n",
    "    \n",
    "    def __setitem__(self, index, item):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__setitem__(index, item)\n",
    "    \n",
    "    def __array_finalize__(self, obj):\n",
    "        if obj is None: return\n",
    "        self.lattice_shape = getattr(obj, 'lattice_shape', obj.shape)\n",
    "        self.lattice_dim = getattr(obj, 'lattice_dim', len(obj.shape))\n",
    "        self.lattice_spacing = getattr(obj, 'lattice_spacing', None)\n",
    "        pass\n",
    "    \n",
    "    def latticeWrapIdx(self, index):\n",
    "        if not hasattr(index, '__iter__'): return index         # handle integer slices\n",
    "        if len(index) != len(self.lattice_shape): return index  # must reference a scalar\n",
    "        if any(type(i) == slice for i in index): return index   # slices not supported\n",
    "        if len(index) == len(self.lattice_shape):               # periodic indexing of scalars\n",
    "            mod_index = tuple(( (i%s + s)%s for i,s in zip(index, self.lattice_shape)))\n",
    "            return mod_index\n",
    "        raise ValueError('Unexpected index: {}'.format(index))\n",
    "\n",
    "\n",
    "def floq_jac(psi0,t, h, h0, w, cosp, N):\n",
    "    drive = h0 + h * np.cos(w * t)\n",
    "    jac = (- 1j) * N * (-2.0 * q * q - drive * np.sqrt(1.0 - 4.0 * q *q) * cosp)\n",
    "    return jac\n",
    "\n",
    "def floq_func(psi0,t,h,h0,w,cosp,N):\n",
    "    return np.dot(floq_jac(psi0,t, h0, h, w, cosp, N), psi0)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    periodic_psi  = Periodic_Lattice(psi)       \n",
    "    cospinit = 0.0\n",
    "    for k in np.arange(N):\n",
    "        for m in np.arange(N):\n",
    "            for l in np.arange(N+1):\n",
    "                for j in np.arange(l+1):\n",
    "                    cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* \\\n",
    "                                          math.comb(l,j)* periodic_psi[(k+(l-j),(m))]])\n",
    "            cosp[k,m] = cospinit\n",
    "            cospinit = 0.0\n",
    "    \n",
    "    # calculate for first frequency\n",
    "    w = omegas[0]\n",
    "    T = 2 * np.pi/w                            \n",
    "    t = np.linspace(0,2 * np.pi/w,tsteps)           \n",
    "    floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "    \n",
    "    for mm in np.arange(N):\n",
    "        psi0 = periodic_psi[mm]       \n",
    "        psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "        #floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "        psis[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "        print('dot prod',np.dot(psi0,psi[mm]))\n",
    "        \n",
    "    #print('floqEvolution_mat',floqEvolution_mat)\n",
    "    evals, evecs = eig(floqEvolution_mat)\n",
    "    phasefunc = (1j * np.log(evals[nn]))/T\n",
    "    evecs_path = evecs[nn]\n",
    "    phasefunc_path[0] = phasefunc.real\n",
    "    \n",
    "    # calculate for rest of the frequencies\n",
    "    for cc, w in enumerate(omegas[1:len(omegas)]):\n",
    "        T = 2 * np.pi/w                      \n",
    "        t = np.linspace(0,2 * np.pi/w,tsteps)    \n",
    "        floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))        \n",
    "        \n",
    "        for mm in np.arange(N):\n",
    "            psi0 = periodic_psi[mm]       \n",
    "            psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "            #print('np.linalg.norm(psi_t[N-1])',np.linalg.norm(psi_t[N-1]))\n",
    "            #print('psi_t[N-1]',psi_t[N-1])\n",
    "            floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "        evals, evecs = eig(floqEvolution_mat)    \n",
    "        prob = np.asarray(list(map(lambda x:np.dot(np.conjugate(evecs_path).T,x),evecs))) \n",
    "        #print('prob',prob.real)\n",
    "        \n",
    "        for i,pr in enumerate(prob):\n",
    "            if (pr >= (0.99 + 1j * 0)):\n",
    "                pp = i\n",
    "                break\n",
    "        evecs_path = evecs[pp]\n",
    "        phasefunc = (1j * np.log(evals[pp]))/T\n",
    "        phasefunc_path[cc+1] = phasefunc.real\n",
    "                \n",
    "    print('time taken',time.time()-start,'sec')\n",
    "    plt.figure(figsize=(15,6))\n",
    "    plt.title(title)\n",
    "    plt.xlabel(\"4h/omega\")\n",
    "    plt.ylabel(\"phase function\")\n",
    "    plt.plot(4*h/(omegas),phasefunc_path)\n",
    "    plt.scatter(4*h/(omegas),phasefunc_path,marker='.',color='r')\n",
    "    plt.grid()\n",
    "    #plt.savefig(photoname,dpi = 300)\n",
    "    plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken 209.4754719734192 sec\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# h experiment\n",
    "\n",
    "import numpy as np\n",
    "from odeintw import odeintw\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import multi_dot, norm, eig\n",
    "import math\n",
    "import time\n",
    "from array import *\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "    \n",
    "N = 5\n",
    "\n",
    "h0 = 0.1\n",
    "nn = 1   # this is the 'th column of the inital floquet evolution matrix \n",
    "pp = nn  # for which the path we shall follow\n",
    "tsteps = 100\n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "w = 100.0  # omega frequency\n",
    "T = 2 * np.pi/w                            \n",
    "t = np.linspace(0,2 * np.pi/w,tsteps)   \n",
    "hs = np.linspace(50.0,500.0,500)\n",
    "\n",
    "psi = np.eye(N) + (1j) * np.zeros((N,N))\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "phasefunc_path = np.zeros(len(hs))\n",
    "prob = np.zeros(N)\n",
    "\n",
    "title = \"mf floquet dynamics in path mode: n \" + str(N) + \"_bessel 4th root\"\n",
    "photoname = \"n_\" + str(N) + \"_mfd_bessel_floquet_path_bessel4.jpeg\"\n",
    "filename = \"n_\" + str(N) + \"_mfd.txt\"\n",
    "\n",
    "class Periodic_Lattice(np.ndarray):\n",
    "    def __new__(cls, input_array, lattice_spacing=None):\n",
    "        obj = np.asarray(input_array).view(cls)\n",
    "        obj.lattice_shape = input_array.shape\n",
    "        obj.lattice_dim = len(input_array.shape)\n",
    "        obj.lattice_spacing = lattice_spacing\n",
    "        return obj\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__getitem__(index)\n",
    "    \n",
    "    def __setitem__(self, index, item):\n",
    "        index = self.latticeWrapIdx(index)\n",
    "        return super(Periodic_Lattice, self).__setitem__(index, item)\n",
    "    \n",
    "    def __array_finalize__(self, obj):\n",
    "        if obj is None: return\n",
    "        self.lattice_shape = getattr(obj, 'lattice_shape', obj.shape)\n",
    "        self.lattice_dim = getattr(obj, 'lattice_dim', len(obj.shape))\n",
    "        self.lattice_spacing = getattr(obj, 'lattice_spacing', None)\n",
    "        pass\n",
    "    \n",
    "    def latticeWrapIdx(self, index):\n",
    "        if not hasattr(index, '__iter__'): return index         # handle integer slices\n",
    "        if len(index) != len(self.lattice_shape): return index  # must reference a scalar\n",
    "        if any(type(i) == slice for i in index): return index   # slices not supported\n",
    "        if len(index) == len(self.lattice_shape):               # periodic indexing of scalars\n",
    "            mod_index = tuple(( (i%s + s)%s for i,s in zip(index, self.lattice_shape)))\n",
    "            return mod_index\n",
    "        raise ValueError('Unexpected index: {}'.format(index))\n",
    "\n",
    "\n",
    "def floq_jac(psi0,t, h, h0, w, cosp, N):\n",
    "    drive = h0 + h * np.cos(w * t)\n",
    "    jac = (1j) * N * (-2.0 * q * q - drive * np.sqrt(1.0 - 4.0 * q *q) * cosp)\n",
    "    return jac\n",
    "\n",
    "def floq_func(psi0,t,h,h0,w,cosp,N):\n",
    "    return np.dot(floq_jac(psi0,t, h0, h, w, cosp, N), psi0)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    periodic_psi  = Periodic_Lattice(psi)       \n",
    "    cospinit = 0.0\n",
    "    for k in np.arange(N):\n",
    "        for m in np.arange(N):\n",
    "            for l in np.arange(N+1):\n",
    "                for j in np.arange(l+1):\n",
    "                    cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* \\\n",
    "                                          math.comb(l,j)* periodic_psi[(k+(l-j),(m))]])\n",
    "            cosp[k,m] = cospinit\n",
    "            cospinit = 0.0\n",
    "    \n",
    "    # calculate for first h\n",
    "    h = hs[0]        \n",
    "    floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "    \n",
    "    for mm in np.arange(N):\n",
    "        psi0 = periodic_psi[mm]  \n",
    "        psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "        floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "    \n",
    "    evals, evecs = eig(floqEvolution_mat)\n",
    "    phasefunc = (1j * np.log(evals[nn]))/T\n",
    "    evecs_path = evecs[nn]\n",
    "    phasefunc_path[0] = phasefunc.real\n",
    "    \n",
    "    # calculate for rest of h\n",
    "    for cc, h in enumerate(hs[1:len(hs)]):\n",
    "        floqEvolution_mat = np.zeros((N,N)) + (1j) * np.zeros((N,N))        \n",
    "        for mm in np.arange(N):\n",
    "            psi0 = periodic_psi[mm]\n",
    "            psi_t = odeintw(floq_func,psi0,t,args=(h,h0,w,cosp,N), Dfun=floq_jac)\n",
    "            floqEvolution_mat[mm] = psi_t[N-1]/np.linalg.norm(psi_t[N-1])\n",
    "                  \n",
    "        evals, evecs = eig(floqEvolution_mat)\n",
    "        prob = np.asarray(list(map(lambda x:np.dot(np.conjugate(evecs_path).T,x/np.linalg.norm(x)),evecs))) \n",
    "        #print('prob',prob)\n",
    "        \n",
    "        for i,pr in enumerate(prob):\n",
    "            if (pr >= (0.9 + 1j * 0)):\n",
    "                pp = i\n",
    "                break\n",
    "        #print('pp',pp)\n",
    "        evecs_path = evecs[pp]\n",
    "        phasefunc = (1j * np.log(evals[pp]))/T\n",
    "        phasefunc_path[cc+1] = phasefunc.real\n",
    "                \n",
    "    print('time taken',time.time()-start,'sec')\n",
    "    plt.figure(figsize=(15,6))\n",
    "    plt.title(title)\n",
    "    plt.xlabel(\"4h/omega\")\n",
    "    plt.ylabel(\"phase function\")\n",
    "    plt.plot(4*hs/w,phasefunc_path)\n",
    "    plt.scatter(4*hs/w,phasefunc_path,marker='.',color='r')\n",
    "    plt.grid()\n",
    "    #plt.savefig(photoname,dpi = 300)\n",
    "    plt.show()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.05691986821726593+0.19959655777600374j)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "aa = np.array([ 9.99971012e-01-3.84824527e-03j, -6.73816911e-04-3.75660345e-03j,-1.04441583e-03-3.61156125e-03j, -4.64017086e-05-3.80316366e-03j])\n",
    "bb = np.array([ 5.62367233e-02+1.95927165e-01j,  8.31713471e-01-5.16173263e-01j,3.91700546e-04-3.73533508e-05j, -4.14192101e-03-1.58282061e-02j])\n",
    "#bb = np.array([-2.46321722e-02-7.91034349e-03j,  1.08808167e-01+1.75353822e-01j,8.31049920e-01-5.15844601e-01j,  1.62381803e-03-4.94077519e-04j])\n",
    "#bb = np.array([ 3.53049992e-04-3.84978225e-03j, -6.74086032e-04-3.75810383e-03j,-1.04483297e-03-3.61300370e-03j,  9.99970927e-01-3.80468263e-03j])\n",
    "np.dot(np.conjugate(aa).T,bb/np.linalg.norm(bb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6126115153165423+0.0806637366497684j)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ccc = np.array([ 0.99920143-0.02574689j,-0.01698867-0.00934755j,-0.01362533-0.00144682, -0.00107483-0.01920185j])\n",
    "ddd = np.array([ 0.59962343+0.0697886j ,-0.7698387 -0.20199748j,-0.00236293-0.00627001j,-0.04424615-0.01113837j])\n",
    "np.dot(np.conjugate(ccc).T,ddd)"
   ]
  }
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