Altruism-invasion-plots-SI6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the code used for plots in Electronic Supplementary Material 6 of \"Oblique Transmission, Conformity, and Preference in the Evolution of Altruism.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "sns.set_context('paper', font_scale=1.3) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Inequality 10\n",
    "def f(β, γ, ρ, b, c, m_v, m_o):\n",
    "    return b * (ρ * (1 - γ + (m_v * β)) + (1 - ρ) * c * (1 - γ + (m_o * β)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [0.2, 1, 1.2, 1.5] \n",
    "b = [0.8, 0.9, 1]\n",
    "ρ = np.linspace(0, 1, 51)\n",
    "β = np.linspace(0.1, 2.5) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additive Model I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter γ:  0.01\n"
     ]
    },
    {
     "data": {
      "image/png": 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/e1o4VxvF59Ype1IMTHfXGJdzF8WTExZSbO/JIxfv6D37X6f4Xvq7hvl/TXGf/bpeZBExMSJeEhEvGO0yJKmbbNmXquMgitaOfx2hzGUUoz4fR9EScTpwBHBuROwO3EExqNZePPe4tCHtlB3OTygeT3RqRMyguLf7/sz874287wKK0aLPpLgX+aqG1/8PxQndGRHxeuA/KZLTFwD7UwyQ9LoW67hOZj5Isb9acTrF86Y/X0u8fkbxeLPjKE5kT28o2+q+HJdta0etl8PlwJuH6abaqm9SJKT/VlveNIr98Ls2lzOe+2Q0x+hI72nnuBhWFo+BexPFIweviYjLgOsoRk/fg6LXxJPAWzJzpMRmYzYDlkTEt2p1XUrRKnoCxb3bVzeUXw78d0R8heIizrEUn8O7xmkQumY+RXEcnRcRe1AM3vgailHel7Px1vbRfHcOZ7Tfcd+v1fu02qME769tw5609v3a7uc2ZhExleIRhxsMXBoRi4AdM7PV2y2GLha8juIJEQ+OVLiT9+xn5m0R8XmKx/9dDnyHonfKeykuWF1cV3w7inEq/i91A1C2uQwi4iieG3diK2BSRHyo9vcDmbmwE9smST1/HICTk1NnJp4bHG3XjZS7i6LV7fm1v19AkYStAp6gOCl8Ec0f99RO2f1o8hg44BiKAbzW1F4/f6TytdcmUQzKlcC5w2zXBIoTq59QnGA/RdHd+yLgoBb239D6W3kU3QaP3qvN3wo4G1hMkcAupnj29cwmZdvZly1t20j7cCzbWyu/B00esdXmfnsexW0Rv6IYufoBimT3pTQ8Bo6NPAKvjX0y7HIokuVFTeY3PUY3sm3Dvqed46KF9UyneMzhLbXj8GmKJPGfgW2alJ/TuG83Mn8SxQWZGyli7pnaMfkVYG6T/XoARe+XB2tlbweOaFKPkT6HDY7bdj83isT2copYWkVxQXAnikR5Y4+jG+135wb1HulYGGmbaq+/mOJizuraei6lSC4XsZHv11F8bs32a9NjnWI8jRzmmE/gZU1eWw78uo3j+iU89yjH57f6vk5NFN9NJ9U+42coxmv5NLVHWDaJm+tGu4y6YziHmTZYtpOTk9Nop8gc9QCqkqQBEhHfBTbNzH16XRf1VkS8g+KJFa/LzOt6W5vmai3ky4EvZubxva5P1UTETRSt0G9rmP9yao/fzMzzWlzWiyguAn4oM/+x45WVpAHlPfuSpFadBOwVEQf1uiJSvYh4fpPZQ2NgfK+bdRkEEfEWYFeajzPyZxTJfuPYKiPZrfbz5jFWTZJUx3v2JUktycw78P+GyunfIuIB4KcU3an3Bw4BfkwxSKI6KDOvpLh1oNlrZ9D+IJFDyf7PRiwlSWqLJ22SJKnfXU3xdIu3AM+nGBfhTOCjOfzz1VUer6QY1X8sg0tKkhp4z74kSZIkSRXjPfuSJEmSJFWMyb4kSZIkSRVjsi9JkiRJUsWY7EuSJEmSVDEm+5IkSZIkVYzJviRJkiRJFWOyL0mSJElSxZjsS5IkSZJUMSb7kiRJkiRVjMm+JEmSJEkVY7IvSZIkSVLFmOxLkiRJklQxJvuSJEmSJFWMyb4kSZIkSRVjsi9JkiRJUsWY7EuSJEmSVDEm++q5iJgYEWdFxKO16XMRMWGYspMj4tyIuD8inoiIX0bEO7tdZ0kQEe+OiJ9GxDMRcWWv6yMNqnZi0f+jUne1+78yIs6PiDUR8WTdtFc36qrqMdlXGXwIeA2wS23aBzhlmLITgCXAAcA04B3AmRFx0PhXU1KDh4GPA+f2uiLSgGsnFv0/KnXXaP5Xnp2ZU+umG8apbqo4k321JSL+PCKur7XAPxIRf9eBxb4T+HhmLsnMJcA/Asc1K5iZT2XmRzLz3iz8F/ADiosFkoYxHrGbmZdn5pXA8g5UURoIvY5F/49Kw+t1fEqdZrKvlkXEccA5wIeBWcAfAz9uKHN2RDw+wvSChvIzgO2BW+pm3wK8ICKmt1CnKcAewK1j2jipwsYjdiW1r4yx6P9RqVCy+DymdsHhjoh4f0SYs2lUIjN7XQf1gYiYBjwEvDUz/7ODy90BeBDYKjOX1+ZtBSwFdsjMxSO8N4CFwHbA/pm5tlP1kqpivGK3YR0LgN0y8y3jsXypCsoYi/4flQplis+I+ONaXR4F/gS4FPhMZn5mPOqlavMqkVr1euDhcfgCfLL2s74Vf+j3J4Z7U+0E5fPAHwFv8QRFGtZ4xa6k9pQqFv0/Kq2nNPGZmTdn5rLM/H3tNptPAv+j1/VSfzLZV6u2BB7bWKGIOKdh9NDGab3uTZn5GLAY2K1u9m7AQ5m5cph1DJ2g7AkcNFw5ScA4xa6ktpUmFv0/Km2gNPHZhBfiNGom+2rVz4BXRsRrACJidjR5DEhmHt8wemjj9GCTZZ8HnBoR20TENhQj8X95hLqcBbwaOLB2sUDS8MYtdiNiQu1+3wnAJhExJSImjfsWSf2pTLHo/1FpfaWJz4h4e0RMi8KrgP8NXNaxLdVAMdlXSzLzZuADwMKIeAr4EdCpq5cfA24AflGbfgx8YujF2lXUc2q/7wicSNHt8IG6K6nndKguUqWMc+x+CHgaOBX4i9rv/96hZUuV0stY9P+oNLKyxGfNuynGs3oCuAg4GzizQ3XRgHGAPkmSJEmSKsaWfUmSJEmSKsZkX5IkSZKkijHZlyRJkiSpYkz2JUmSJEmqGJN9SZIkSZIqxmRfkiRJkqSKMdmXJEmSJKliTPYlSZIkSaoYk31JkiRJkirGZF+SJEmSpIopXbIfER+NiDsjYm1EHDZCuT+NiNsjYnVEXBsRs7pZT0mSJEmSyqp0yT5wD/A+4MbhCkTEFOBy4JPAlsC9wBe6UjtJkiRJkkqudMl+Zl6Ymd8DfjtCsf2Ax2plnwYWAIdExNQuVFGSJEmSpFKb0OsKjNLOwK1Df2Tm0oh4FJgL/Ky+YEQsAOZ3tXZSn8jM6HUdjFFpeMaoVG7GqFRuZYjRXorM7HUdmoqI64CzMvObTV77MLBdZh5fN+8u4F2Z+cMWll2qjS7rZ6Bqi4jSfgGWKUaNT/WKMbpxxqd6yRjdOGNUvVTmGO2W0nXjb9FTwLSGedOAJ3tQlzGLGOhjUJKkUfH/pyRJw+vXZP9OYNehP2oj8c+gGNyvL3nCIkmSJEnqlNIl+xExsTba/ibAxIiYEhtmwtcBW0bEEbWyHwGuycy+bNkfYsIvlY9xKUlS++zCL/Ve6ZJ94FzgaWAf4OLa7ztGxDkRcQpAZv4WeBtwKvAo8GLgxN5Ut7NMLCRJkiRJY1XaAfrGU1kGLRnJIH4u6q4yD1pSthg1HtULxmhrjE/1ijE6MmNTvVbmGO2WMrbsC1v4JUmSJEmjZ7JfYib8UjkYi5IkSeo3JvslZ5IhSZKkfmIXfqkcTPb7gAm/JEmSJKkdJvt9woRfkiRJktQqk/0+YsLfebvssgvf/va3B3b9ap3x1xu9jpFer18qs17HR6/XL5Vdr2Ok1+uXj97rS4P4manzyvw4krLGqLGnbjJGW2NcqleM0eaMSZVFmWO0W2zZ70O2MEqSJEmSRmKy36dM+Dtjzpw5XHnllZx//vnstttunHbaacyaNYutt96az372swAsXbqUyZMn88ADD6x739NPP8306dP56U9/CsC8efOYPXs206ZNY/fdd+cHP/jBurL33Xcf+++/P9OnT2fGjBnstdderF69er31Q3El/Mwzz+RFL3oRW2yxBQcffDD33XffenX91Kc+xZ577slmm23Gvvvuy0MPPTTu+0jqJWNUKi/jUyo3Y1Qm+33MhL+z7rjjDjbddFN+/etf8/Wvf52TTz6Ze++9l1mzZnHggQdy0UUXrSt71VVXMXv2bF71qlcBsP/++/OLX/yCFStWcPjhh3PYYYfxxBNPAHDqqacyd+5cli9fztKlSznzzDOZMGHCButfuHAhn/70p7nyyitZsmQJL3/5yznkkEN49tln15W56KKLuOSSS1i2bBmbbropH/7wh8d5r6ieMddbxqhUXsanVG7G6GAy2e9zJh+dM3PmTE466SQmTpzIfvvtx5w5c7jlllsAOOqoo1i4cOG6sgsXLuToo49e9/exxx7L9OnTmThxIieffDJr167l1ltvBWDSpEksWbKERYsWMXHiRPbee28mTZq0wfoXLlzIe9/7XnbddVcmT57Mxz/+cRYvXsyNN964rsyJJ57ITjvtxJQpUzjyyCO56aabxmt3SKVjjErlZXxK5WaMDiaT/Qow4e+Mrbfeer2/N91003VXLd/85jfz8MMPc9NNN7F06VK+//3vM2/ePADWrl277qrmtGnT2HzzzVm5ciXLly8H4IwzzmC77bbjgAMOYM6cOSxYsIC1a9dusP7FixczZ86cdX9PmjSJ2bNns3jx4nXzttlmm6b1kwaBMSqVl/EpcHC+MjNGB9OGfSzUl2qjTfa6GpU1ZcoUDjvsMBYuXMicOXN49atfzQ477ADAxRdfzMUXX8y1117L3LlziQhmzJix7vOYNWsWZ599NgC33norBx54ILvuuiuHHnroeuvYfvvtWbRo0bq/16xZw5IlS9h+++27s5FSHzNGB5f//8rP+JTKzRitLlv2K8QW/vF11FFH8bWvfY0LLrhgva5Nq1atYtKkScycOZM1a9Ywf/58Vq1ate71Sy+9lAcffJDMZMaMGUyYMKHpvUzz5s3jrLPO4s477+SZZ55h/vz5zJ49mz322KMr26fWGGflZYxK5WV8SuVmjFaTyX7FRITJyDjZd999mTx5Mnffffd6VyuPOeYYdtllF3bccUde+MIXMnXq1HVXQwFuuukm9t57b6ZOncpee+3Fcccdx5ve9KYNln/00Ufznve8h0MOOYRtttmGm2++mauvvrrpF6akDRmjUnkZn1K5GaPVFIPY9S0iBmKjB/GzVetqXV9LeWWo7DFqbKkbjNHWGZPqBWN0fcahyqbMMdottuxXmC38kiRJkjSYTPYrzoRf6jzjSpIkSWVnsj8ATEwkSZIkabCY7A8IE35JkiSNB+/Xl8rJZH+AOFK/1DnGkiRJksrMZH8AmaRIkiRJUrWZ7A8oE35JkiSNlV34pfIy2R9gJvzS2BhDkiRJKiuT/QHnffySJEmSVD0m+wJsoZQkSZKkKjHZ1zom/FL7jBup94xDqTe8X18qN5N9rcdu/ZIkSZLU/0qX7EfErIj4bkSsjojbI2LPYcodGBG3RcSqiLglIvbpdl2rzIRfkiRJkvpX6ZJ94BzgPmBL4JPAZRExub5ARDwPuBT4ODAdOB34ZkSUcXv6lgm/1BpjRZI0aOzCL5VflClQI2IzYDmwQ2Yurc27HTgpM6+tK7cl8BtgYmZmLclfA2ybmctaWE95NrpPlOk4UWdEBJlZyiy1H2PUGFGnGaPtMQbVbYMeo8acyq7MMdotZWsJnwusGEr0a24Ddq4vlJkrgG8CR9Ra+ecBP2+W6EfEgojI+mkc619ZtlxqvBijUrkZo1K5GaOShlO2lv19gHMz8yV1874ILM7MjzWUfSvwr8A04Eng4Mz8rxbXU56N7jNlOl40NmW+2tmvMWp8qJOM0fYYf+q2QY9RY05lV+YY7Zaytew/RZG81xtK5teJiJcC5wFvBCYBbwGuiIitulHJQeZo/ZIkSYPNRF/qD2VL9u8BtmxI2l8G3NlQ7mXAzzLzhsxcm5nXAb8GXtWdasqEX5IkSZLKq1TJfmY+AVwDzI+IKRFxBLAFcF1D0VuA3SLiTwAi4rXAS4BfdrG6A89Wfml9xoMkSZLKYkKvK9DECcBXgUeB+4FDM/OZiDgFeEFmHp+Z90TEe4ALI2I2sAQ4ITPv7121B1ftfpheV0OSJEnjzHM+qX+UaoC+binjwEJVMYjHU78q86Al/RyjxoA6xRhtj7GnbhvUGDXW1C/KHKPdUqpu/Op/dmPWoDMGpN4w9iRJWp/JvjrOe/klSZKqx1Z9qb+Y7GvcmPBLkiRJUm+Y7Gtc2cqvQeQxL0mSpF4z2VdXmPRLkiT1L7vwS/3HZF9dZcKvQeGxLkmSpF4y2VfX2covSZLUP2zVl/qTyb56xqRfVefxLUmSpF4x2VfPmRBJkiRJUmeZ7KsUbOWXJEkqH7vwS/3LZA5hvv4AACAASURBVF+lYtKvqvF4lrrHeJMk6Tkm+yolT9gkSZIkafRM9lVatvKrKjyOJUn9yC78Un8z2VfpmfRLkiRJUntM9tU3TPrVzzx2JUn9xFZ9qf+Z7KvvmPRLkiRJ0shM9tW3TPrVbzxeJUmS1C0m++p7Jv2SJEmdYxd+qRpM9lUZJv3qBx6jkiRJ6gaTfVWOSb8kDS6//6WxsVVfqg6TfVWWSb/KyuNSkiRJ481kX5Vn0i9JkrRxtupL1WKyr4Fh0q8y8ViUJEnSeDLZ18Ax6ZckSVqfrfpS9Zjsa2CZ9KvXPP4kSZI0Xib0ugJSr9UnXF7VliRJg8bzH6mabNmX6tjar27zeJMkSdJ4MNmXmjDpl6T+5fe31Dpb9aXqKl2yHxGzIuK7EbE6Im6PiD2HKTcpIj4TEcsiYmVEXNrtuqr6TPrVDR5jkiRJ6rQy3rN/DnAf8FbgUOCyiHhhZj7TUO6TwFbAHwGrgF27WksNFO/rlyRJVeM5jVRtUaYgj4jNgOXADpm5tDbvduCkzLy2rtyWwC+BF2bmE6NYT3k2Wn2rTLEzGhFBZpaySXlQY7Tfjyl1ljE6NsaTxlsVYtQ4UZWVOUa7pWzd+OcCK4YS/ZrbgJ0byu0KLAH+KSJWRMTPImL/blVSgue6+NsFW53isSRJ6hYTfan6ypbsb0rRJb/eKmBqw7zZFAn/I8C2wIeAb0TEzMYFRsSCiMj6aRzqrQFn0j96xqhUbsaoVG7GqKThlK0b/x8D387M2XXzLgFuzMzP1M17K/B14A8y89navB8Dn8jMb7ewnvJstCqrTLHVTJm7Ng16jJb92FF3GKNjYxxpvPVzjBofGgRljtFuKVvL/j3AlhGxVd28lwF3NpS7A8jaJJWSrf0aLY8baeyMI0nSoCtVsl8bbO8aYH5ETImII4AtgOsayt0N/Az4h4h4XkQcRDEq/w1drrK0Ud7bL0mSysJWfWlwlCrZrzmBYqC+R4FTgUMz85mIOCUizqkr91fAGyju6f9n4LDMXNH12kptMPFXqzxGJEmdZqIvDZZS3bPfLf1wr6EGR69isMz3MRmjzxnE72gVjNGxM340nvoxRo0JDZIyx2i3TOh1BaRBV9+C6z9hSZI0HjzHkAZPGbvxSwPLbv5q5LEgSZLUGxHx04j4y17XY7RM9qWSMvHXEI8BaXSMHalgq77Uvoh4HrALcNs4LHtiRJwVEY/Wps9FxLC97iNiu4i4MiJWRMTyiLi04Ql2TZnsS33AxF+SJI2Gib40an8EBMXj4TvtQ8BrKC4m7ALsA5wyQvnP137uCOwETAH+ZWMrMdmX+oyJ/2Dy85YkSeqqVwC/AN4fEUsi4jcR8TcdWvY7gY9n5pLMXAL8I3DcCOVfBFyamU/WHlf/dWDXja3EZF/qYyb+g8XPWZLUDlv1pTHZjaJ1fyUwBzgW+FxE7FBfKCLOjojHR5he0FB+BrA9cEvd7FuAF0TE9GHq8mngLyNiekRsTvEY+qs3tgEm+1JFmPgPBj9fSVIrTPSlMXsF8NXM/FJmPpOZ3wF+DexcXygzT8zMzUeYHmxY7tTaz8fr5g39vtkwdbkemAU8Wps2p+gNMCKTfamCTPwlSZKkMXkFRXd5AKI4sZ4JLBvjcp+s/axvxR/6/YnGwhGxCfA94IcUFwOmUwwaeOXGVmSyL1WciX/1+FlKrTNeJEntiohZwDbAI3Wz/5yiBf6WhrLnRMSTI0zrdePPzMeAxRS3CQzZDXgoM1c2qc4WFAPznZWZq2v37J8NvD4iJo60HSb70gAx8a8OP0NJkqRx8wrgWeCoiNgkIl4JnAV8IDPX1hfMzOMzc+oIU2M3foDzgFMjYpuI2IZiJP4vN6tIZi4H7gVOiIjJEfEHwPHAHZn5u5E2Ythn+UmSyi0ivCdTkiSp814BXE7Rbf9Rihb+D2bm10d8V+s+BmxJMdo/wEXAJ4ZejIhzoLiQUJv1FuAzwJLa3z8B3r6xlcQgnihGxOBttNREZpayedgYbc8gfo8PgtrFHGO0A4wRjYeyx6jHvQZdmWO0W+zGL0l9zi79kiRJamSyL0mSKs0LYpKkQWSyL0kVYDIjSZKkeib7klQRJvySJEkaYrIvSRViwi9JkiQw2ZekyjHhlzZkXEiSBo3JviRVkImNJEnSYDPZl6SKMuGXJEkaXCb7klRhJvySJEmDyWRfkirOhF8qGAuSpEFisi9JA8AkR5IkabCY7EvSgDDhlyRJGhwm+5I0QCLCpF+SJGkAmOxL0gAy4deg8tiXJA0Kk31JGlAmPZIkSdVlsi9JA8yEX5IkqZpM9iVpwJnwS5IkVU8pk/2ImBUR342I1RFxe0TsuZHy/ysiMiJe1a06SlKVOHCfBonHuiRpEJQy2QfOAe4DtgQ+CVwWEZObFYyIbYG/ApZ0r3qSVE0mQZIkSdVQumQ/IjYD3ggsyMynM/NC4DFgv2HecjpwGrCmOzWUpGoz4ZckSep/pUv2gbnAisxcWjfvNmDnxoIRsRewXWZePtzCImJBrYv/uqnzVZY0WsZoOdmtX0OqGqMe36qKqsaopLErY7K/KbCqYd4qYGr9jIjYBPgs8P6RFpaZCzIz6qeO1lbSmBij5WZCJGNUKjdjVNJwypjsPwVMa5g3DXiyYd47gNsy85ZuVEqSBpWt/JIkSf2njMn+PcCWEbFV3byXAXc2lHst8PaIWB4Ry4EdgO9HxDFdqqckDRQTflWNx7Qkqcois3y39UTE5cDDwAeAtwFnAC/MzGfqysyg6PI/5Abgb4D/m5lPbWT55dtoqQfK2tXPGC2/Mv7vqJqIMEa7wGNZo1X2GPXY1qArc4x2y4ReV2AYJwBfBR4F7gcOzcxnIuIU4AWZeXxmPkYxSj8AEfF7YOnGEn1J0tjV/oH2uhrSmHksS5KqqpQt++OtSi0S0liU9WqnMdpfBvH/SDeUuUWiajHqMazRKHuMelxr0JU5RruljPfsS5L6iAP4SZIklY/JviSpI0z41a88diVJVWSyL0nqGFv5JUmSysFkX5LUcSb96jcer5KkqjHZlySNG5N+SZKk3jDZlySNO5N+SZKk7jLZlyR1jUm/ysxjU5JUJSb7kqSuM+mXJEkaXyb7kqSeMelX2Xg8SpKqwmRfktRzJv0qE49FSVIVTOh1BSRJGlKfZGVmD2siSZLU32zZlySVkq396iWPPUlSvzPZlySVmkm/JElS+0z2JUl9YSjpN/FXt3isSZL6mcm+JKnvmPRLkiSNzGRfktS3bO3XePPYkiT1K5N9SVIlmPhrvHhMSZL6kY/ekyRVjo/wkyRJg86WfUlSpdnir07w+JEk9RuTfUnSwDDx11h43EiS+ond+CVJA6kxcbO7v1oRER4rkqS+YMu+JEnY6q/WeYxIkvqBLfuSJDWw1V+SJPU7W/YlSdoIW/3VyGNBklR2tuxLktQGW/01xPv3JUllZrIvSdIYmPwPNhN+SVJZmexLktRBzbp3mwxWmwm/JKmMTPYlSRpntv5Xnwm/JKlsSjdAX0TMiojvRsTqiLg9IvYcpsw3ImJpRKyIiCsiYpte1FeSpHbVD/jnwH/V4ecoSSqT0iX7wDnAfcCWwCeByyJickOZTYH/B+wMzAaWAF/sZiUlSeokk/9q8POTJJVFlKnLWURsBiwHdsjMpbV5twMnZea1I7xvV+DfM3PbFtdTno2WeigzS3lGaoxKBWO0v5XpHEudV7t1o7Qx6vGnQVfmGO2WsrXszwVWDCX6NbdRtOCP5NXAL5u9EBELIiLrpw7VVVIHGKNSuRmjo2cLv7rBGJU0nLK17O8DnJuZL6mb90VgcWZ+bJj37AT8N3BoZv6wxfWUZ6OlHirr1U5jVCoYo9VRpvMtdUaZWw1t2ZfKHaPdUraW/aeAaQ3zpgFPNiscETOBfwM+1GqiL0mS1G228kuSuq1syf49wJYRsVXdvJcBdzYWjIipFIn+JZn5pS7VT5IkaVQcvE+S1E2lSvYz8wngGmB+REyJiCOALYDr6stFxCTgCuCmzPxo1ysqSZI0Sib8kqRuKNU9+wARsTXwVWAf4H7guMz8r4g4BXhBZh4fEftSXABYDazbgMyc2uI6yrXRUo+U9T4mY1QqGKPVV7bzMLWuzPcDe8++VO4Y7ZbSJfvd4EmKVCjrF6AxKhWM0cExiOdj/a7MiYTJvlTuGO2WUnXjlyRJGkTezy9J6jSTfUmSpJIw6ZckdYrJviRJUsmY9EuSxspkX5IkqaRM+iVJozWh1xWQJEnSyOoTfgdekyS1wmRfkiSpj5j4S5JaYbIvSZLUp0z8JUnDMdmXJEmqABN/SVI9k31JkqSKaRzUz+RfkgaPo/H32Ac/+EEuvvjiga+DVFZliI8y1EEqqzLERxnqsDFDo/o7sr8kDY4YxCu9ETF4Gy01kZmlPOszRqWCMapuGcTzwbGKiFLHqJ+pBl2ZY7Rb7MYvSZI04Oz2L0nVYzf+Ubj//vv5h3/4B2644QZWrVrFddddx/bbb7/u9d13353rr7+exx57jDvuuIPDDz982GXNnz+fK664Yt3fmcnxxx/PbbfdxsqVK7nqqquYNm0aAFdddRUf+tCH1nv/l770JT73uc8BcMQRR3DbbbexatUqHnjgAU477bT1yp5++uksWbKEVatW8atf/Yo3vvGNTeswUv3nz5/Pt771LT73uc/x2GOP8cADD/D2t7+93V0ojStj1BhVuRmj5Y/R+m7/dv+XpD6VmQM3ATmW6f7778+f//znOWfOnJw8eXJec801ed555yWQ06dPz2XLluW73/3unDBhQr7mNa/JlStX5t577910WfPnz88rrrhi3d+Zmf/xH/+RW221VU6fPj1vuummnD9/fgJ56KGH5l133bWu7KRJk/Kxxx7LPfbYI4E8+OCDc+7cuQnkK17xinzkkUfyiCOOSCAPOuigfPDBB3PbbbdNIHfYYYd1ZevrsLH6z58/P5955pl8+9vfnptsskkeddRRuWrVqpw6deqY9qlTb6Zex6Ixaow6jTz1OhaNUWO0xeN0IJU9RqVBV+YY7dZky/4onX322SxatIhnnnmGiy66iN133x2AN77xjSxbtoyzzjqLZ599luuvv56LL76YY445puVln3766SxbtoyVK1dy2WWXrVv21VdfzVZbbcUee+wBwJve9CZ+85vfcOONNwLw3e9+l3vuuQeAn//851xyySXst99+AKxZs4YpU6awyy67MGHCBB566KF1Zeu1Uv+bb76ZSy+9lLVr17Jw4UImTZrEi1/84vZ3ojSOjFFjVOVmjFYnRpv1ArA3gCT1nsn+KD3yyCPrfn/qqafYbLPNANh+++1ZtGjRemUXLVq0XvfE0S57zZo1fOMb32DevHkAHH300Xz1q19dV/aggw7iRz/6EcuWLePxxx/n+OOPZ+bMmQBcd911zJ8/n4997GMsX76cb37zm8yZM2eDdbdS//r6ATz99NPr6iiVhTH6HGNUZWSMPqfKMeqFAEnqHZP9Dlu8ePEG//znzJnD4sWLO7L8hQsXcvjhh7Ptttty0EEHceGFFwIwceJELr/8cr74xS+y3Xbbsfnmm3POOees98/0C1/4AnvttRc77rgjv/vd7/iXf/mXrtdf6jVjVCo3Y3RwjHQhwIsBkjR2Jvsd9p3vfIdZs2Zxwgkn8LznPY+9996bI444Yr2Wg7G4/vrrefLJJ/nKV77CDTfcwIMPPgjA5MmTmTJlCitWrGDNmjXsueeeHHnkkeve96pXvYq99tqLiRMnsnr1ap544gmeffbZrtdf6jVjVCo3Y1RDNnYxwAsCkjQyk/0Oe/zxx3nDG97AvHnzWLFiBV/+8pc58cQT+dGPftSxdVx44YUcfPDB6504PPnkk/zt3/4tX/rSl1i5ciUf/OAH+drXvrbu9WnTpnH22WezYsUKHnnkEWbPns373ve+ntRf6iVjVCo3Y1TtaOWCgBcGJA2qKAYqHCwRMXgbLTWRmaU8+zFGpYIxKvXWSOfJEVHqGB3Ec3ypXpljtFsm9LoCkiRJUhnZI0BSP7MbvyRJkiRJFWOyL0mSJElSxZjsS5IkSZJUMSb7kiRJkiRVjMm+JEmSJEkVY7IvSZIkSVLFmOxLkiRJklQxJvuSJEmSJFVM6ZL9iJgVEd+NiNURcXtE7DlMubkRcUOt3H9FxNxu11WSJEmSpDIqXbIPnAPcB2wJfBK4LCImNyn3deBqYAvgW8DXulZDSZIkSZJKLDKz13VYJyI2A5YDO2Tm0tq824GTMvPaunIvAW4AtsrMZyNiArAM2DMz72phPeXZaKmHMjN6XYdmjFGpYIxK5VbmGC3TOb7UCxFR2hjtlgm9rkCDucCKoUS/5jZgZ+Daunk7A7/IzGcBagn/L2vz10v2I2IBMH88Ky1p9IxRqdyMUanchovRiIHOcSRRvpb9fYBzM/MldfO+CCzOzI/VzTsKODIzD66bdy1wYWYu7GadR6N2tbXU38Blr2PZ6wflr2PZ69dL/bBvyl7HstcPyl/Hstevl/ph35S9jmWvH5S/jmWvXy/1w74pex3LXj8ofx3LXr9uKNs9+08B0xrmTQOeHGU5SZIkSZIGTtmS/XuALSNiq7p5LwPubCh3J/DS2r361H6+pEk5SZIkSZIGTqmS/cx8ArgGmB8RUyLiCIrR9q9rKPdL4H7gA7WR+j8A3NfK4HySJEmSJFVdqZL9mhMoBup7FDgVODQzn4mIUyLinLpyhwNvAR4H3gr8VddrOnof7XUFWlD2Opa9flD+Opa9fr3UD/um7HUse/2g/HUse/16qR/2TdnrWPb6QfnrWPb69VI/7Juy17Hs9YPy17Hs9Rt3pRqgT5IkSZIkjV0ZW/YlSZIkSdIYmOxLkiRJklQxJvuSJEmSJFWMyb4kSZIkSRVjsi9JkiRJUsWY7EuSJEmSVDEm+5IkSZIkVYzJviRJkiRJFWOyL0mSJElSxZjsS5IkSZJUMSb7kiRJkiRVjMm+JEmSJEkVY7IvSZIkSVLFmOxLkiRJklQxJvuSJEmSJFWMyb4kSZIkSRVjsi9JkiRJUsWY7EuSJEmSVDEm+5IkSZIkVYzJviRJkiRJFWOyL0mSJElSxZjsS5IkSZJUMSb7kiRJkiRVzKiS/Yj4g4iY2enKSJIkSZKksWsr2Y+IHSPiP4FVwG8iYmVEfD0i9h+f6kmSJEmSpHZFZrZeOOJ6YGfgdOBeYFvgYOAg4FzgxGxngZIkSZIkqePaTfZ/C/x1Zi5smL838G3gM5n5sc5WUZIkSZIktaPde/afBB5vnJmZPwbmA3/TiUpJkiRJkqTRazfZvwp4T0REk9fuBjYfa4Ui4qMRcWdErI2Iw0Yo96cRcXtErI6IayNi1ljXLUmSJElSFbSb7H8A2AG4ISL+PCImA0TENODdwL91oE73AO8DbhyuQERMAS4HPglsSTF+wBc6sG5JkiRJkvpeW8l+Zj4GvAa4k6KV/8mIWAasAHYDLoiI6WOpUGZemJnfA347QrH9gMdqZZ8GFgCHRMTUsaxbkiRJkqQqmNDuGzJzBfDOiHg/cCCwO0Wi/wrgW0BGxAPAzzLz0E5Wts7OwK11dVoaEY8Cc4Gf1ReMiAUU4wlIapCZzW7J6SpjVBqeMSqVmzEqlVsZYrSX2hqNf6MLi9iGIvF/JfDyzPyrMSzrOuCszPxmk9c+DGyXmcfXzbsLeFdm/rCFZbe90T5RUFUTEaX9Amw3Ro1PVZExKpWbMSqVW5ljtFvabtkfSWY+Any3No2np4BpDfOmUTwtYFzUDpbxWrwkSZLUdZ7fStXV7gB9ZXEnsOvQH7WR+GdQDO43bpo/hECSJEmSpHIpXbIfERNro+1vAkyMiClNHvV3HbBlRBxRK/sR4JrMHLeW/br6jfcqJLXJuJQkSZLWV7pkHzgXeBrYB7i49vuOEXFORJwCkJm/Bd4GnAo8CrwYOLFbFTSxkCRJUr+zC79UbR0doK9fjGaAvkaDuN9ULWUetMRBNKVqxajxqSqqQowam6qyMsdot3SsZT8iXhsRL+nU8srO1n1JkjbOZEKSpN7oZDf+64A7IuI/IuKNHVxuaZnwS5IkqR95IU6qvk4m+68DDgF+CLy3g8stNRN+SZIkSVLZeM9+hwziflR/K/N9TN6zL1UnRo1NVVW/x6ixqaorc4x2SxlH4+9LtvBLkiSpH5joS4NhVMl+ROwcEUdFxCkRsU1t3h9GxGadrV5/MeHvP7vssgvf/va3B3b9Utn1OkZ6vX6pzHodH71ev1R2vY6RXq9fbXbjj4ipwFeAQ4FngQnAn2TmzRFxKfBgZn5gXGraQePRjb+eV0vVD8rctWm0MWrsqUqqEqPGpaqqX2PUmNSgKHOMdku7LfufBvYGDgA2A+p33neAgztUL0mSJEmSNErtJvtvA/5XZv4A+H3Daw8AO3akVn3O7vz9Y86cOVx55ZWcf/757Lbbbpx22mnMmjWLrbfems9+9rMALF26lMmTJ/PAAw+se9/TTz/N9OnT+elPfwrAvHnzmD17NtOmTWP33XfnBz/4wbqy9913H/vvvz/Tp09nxowZ7LXXXqxevXq99UNxpf3MM8/kRS96EVtssQUHH3ww991333p1/dSnPsWee+7JZpttxr777stDDz007vtI6iVjVCov41MqN2NU7Sb7zwdWDPPaZmx4AWBgmfD3nzvuuINNN92UX//613z961/n5JNP5t5772XWrFkceOCBXHTRRevKXnXVVcyePZtXvepVAOy///784he/YMWKFRx++OEcdthhPPHEEwCceuqpzJ07l+XLl7N06VLOPPNMJkyYsMH6Fy5cyKc//WmuvPJKlixZwstf/nIOOeQQnn322XVlLrroIi655BKWLVvGpptuyoc//OFx3itSeRijUnkZn/3BLvyDyxgdTO0m+z8Bjh7mtcOAH4+tOtViwt9fZs6cyUknncTEiRPZb7/9mDNnDrfccgsARx11FAsXLlxXduHChRx99HOhcOyxxzJ9+nQmTpzIySefzNq1a7n11lsBmDRpEkuWLGHRokVMnDiRvffem0mTJm2w/oULF/Le976XXXfdlcmTJ/Pxj3+cxYsXc+ONN64rc+KJJ7LTTjsxZcoUjjzySG666abx2h1S6RijUnkZn1K5GaODqd1k/0PA2yLi+8C7gAT+PCIWAm8H5ne4fn3PhL9/bL311uv9vemmm667avnmN7+Zhx9+mJtuuomlS5fy/e9/n3nz5gGwdu3adVc1p02bxuabb87KlStZvnw5AGeccQbbbbcdBxxwAHPmzGHBggWsXbt2g/UvXryYOXPmrPt70qRJzJ49m8WLF6+bt8022zStnzQIjFGpvIxPqdyM0cG0YR+LEWTm9RGxP/BJ4CyKAfo+CvwXsH9m/qTzVex/tZEge10NjcGUKVM47LDDWLhwIXPmzOHVr341O+ywAwAXX3wxF198Mddeey1z584lIpgxY8a6z3zWrFmcffbZANx6660ceOCB7Lrrrhx66KHrrWP77bdn0aJF6/5es2YNS5YsYfvtt+/ORkp9zBiVysv4LAfPRTUcY7S62mrZj4iPAPdn5j7ANGB7YLPMfDVwX+11NWELf/876qij+NrXvsYFF1ywXtemVatWMWnSJGbOnMmaNWuYP38+q1atWvf6pZdeyoMPPkhmMmPGDCZMmND0XqZ58+Zx1llnceedd/LMM88wf/58Zs+ezR577NGV7ZP6nTFaPiYXGmJ8SuVmjFZTu93451Mk+GTm05n5cGaurr02G7vxj8iEv7/tu+++TJ48mbvvvnu9q5XHHHMMu+yyCzvuuCMvfOELmTp16rqroQA33XQTe++9N1OnTmWvvfbiuOOO401vetMGyz/66KN5z3vewyGHHMI222zDzTffzNVXX930C1PNGWODzRiVysv47C0vvGljjNFqinaCPyLWAn/arLt+RLwZ+NfMnNnB+o2LiOjpN55fuCqD2u0lpcyOxxKjxpeqogoxajyqyvopRo1FDaIyx2i3bPRSSkQcAxxT+zOBL0TEqoZiU4BdgX/vbPWqyXv4JUmSJEnjqZV+E6uBFbXfA1gJPNpQZg3wb8DZnatatZnwS5Ikabx5vikNrna78Z8HnJaZ949flcZfr7vx1/MLWL1S5q5NduOXqhGjxqOqrF9i1DjUoCpzjHZLW8l+VZQp2Qe/hNUbZf4CNNmXqhGjxqOqrB9i1BjUICtzjHZLu6Pxaxw4grgkSZIkqZPaftZBRPwP4K+BF1MMzLeezJzVgXoNHO/hlyRJkiR1Slst+xFxBHAB8Ctge+BbwLdry1kFnNXpCg4SW/ilsTOOJEmyC7+k9rvxnwx8DPjb2t9nZ+Y7gZ2A5RQj92sMTFQkSZIkSWPVbrI/F/hRZv4e+D0wDSAznwA+Bby7s9UbTCb8kiRJkqSxaDfZXwlMrv3+a+Clda8FsGUnKqUi4TfplyT1K7sQS5LUW+0O0PdT4OXAtRT3638kIp4F1gAfAf67s9WTA/dJkiRJktrVbrL/T8COtd8/Uvv9bOB5wE+A/9m5qmmICb8kSZIkqR0td+OPiIkUSf0PATLz8cx8MzAV2Dwz/zQz7xtrhSJiVkR8NyJWR8TtEbHnMOUOjIjbImJVRNwSEfuMdd1lZpd+qXX/n717D5ezLu/9/77JsT9COIRECQEi3XgAERVKCVbFohTFTVtRiiGA9qABT1eLsn8caiL420Vaa3/ARqBuD4STHAUFobU23UJjQRQM4AElAYIJSVZCAoQmQO79x0xWJ4u1kjVrzeE7M+/Xdc3Fmme+88y9VtY9rM98n+f72C+SJEnqdfWcs/8S8H22Pk+fzNyYmesbWNOlwKNUzv8/H7gxIibUDoiIMcB1wOeBnYELgBsiot41CDqKAUaSJEmSNBzDDseZuRl4BHhFs4qJiJ2AY4D5mfl8Zl4JrAWOGDB0F2AnIlNPNAAAIABJREFU4LqsHN9+LZUPB7p+gUADvyRJkiRpe+qdCT+byqJ8BzajGCqX9uvLzJU12xYD+9cOysw+4AZgdnWWfw7wQGaualJdRTHwS5IkSZK2pd6wfw6V2fP7I+LxiLg3Iu6pvY2ynh2BgacErKeyLsBA3wQuAjYCFwIfG2yHETE/IrL2Nsoai+Cl+dQturVHpW5hj0pls0clDSXqWeU9Ir62vTGZ+eERFxPxZuA7mTm9Zts1wD2Z+aWaba8DFgHvpnK5v7cB1wBvGM7sfre9CbpSv0aiepWHIj8xakSP2hfqdJ3eo/agul3pPWoPqteV3KOtUtel90YT5IfpEWBKREytCe2vB74+YNzrgZ9k5qLq/YUR8SRwCPDdJtdYHC/NJ0mSJEmqVdTq9Zn5DHAbMC8iJkbEbGA3YOGAofcDb4yI3wGIiLcBrwV+3sJyi+Ih/dLW7AmpffwAWpKk9qtrZr9FTgWuANYAS4DjMnNjRJwF7J2ZczPzkYj4BHBlREwHlgOnZuaS9pXdflvCjX9kSZIkSVJvq+uc/W7RbefsD6YX/11Vn5LPY2pUj9oH6mSd3KP2nnpB6T1qH6rXldyjrVLUYfxqHA9hliRJkqTeZdjvYl6eT5IkSZJ604jO2Y+IVwMzgIkDH8vM20dblBrL1frVq/zdlyRJUq+qK+xHxP7AN4H9gcGmjBMY04C61GCGHkmSJEnqHfXO7F8GjAfeBzwMbGp4RWoaV+uXJEmSpN5Qb9h/E3BCZn6nGcWoNZzllyRJkqTuVu8Cfb9mkPP01XlcvE+S1Ax+mCxJUhnqDfunA2dFxL7NKEatZ+CXJEmSpO4T9XwCHxH3AnsDuwJLgacHjsnMQxtVXLNEhNMOg3A2prdUT+co8tOeRveov9vqRJ3ao/abekXpPWovqteV3KOtUu85+w9Wb+pCnssvSZIkSd2hrpn9buHM/vb14u9Fryn5005n9qXO7VH7Tb2i9B61F9XrSu7RVql3Zh+AiJgOzAJ2A/qAH2bmbxpZmNrLWX5JkiRJ6lx1hf2IGANcBPwFMKbmoZci4nLgE5m5uYH1qY22LN5n6JckSZKkzlLvavyfA/4UOAuYCfxW9b9nVbfPb1xpKoUr9qvT+TssSZKkXlPvavyPAxdm5t8N8tingU9m5t4NrK8pPGd/5Jzl7x4ln8fUjB71d1edphN71D5TLym9R+1H9bqSe7RV6p3Znwb8dIjHflp9XF0sIpwllSRJkqTC1Rv2fwmcMMRjJwC/GF056hQGfkmSJEkqV72r8X8euDYi9gZuAJ6iMpv/AeAdDP1BgLqQC/ipk3iFCUmSJPWSusJ+Zl4XEU9TWajv/wfGAS8A9wFHZ+Y/N75Elc7QL0mSJEllqWuBvq2eGLEDsDuwutMut+cCfc1j4O8cJS9a0qwe9fdTnaQTe9QeUy8pvUftR/W6knu0Veo9jL9fNeCvbGAt6gLO8kuSJElS+2037EfEPcCHMvPhiLgX2GaKy8xDG1WcOpehX5J6i+/3kiSVZTgz+w8Bz9d87f/NNWyGfpXERfokSZLUK0Z8zn4n85z99unF37dSlXweUzN71N9BdYpO61F7S72m9B61J9XrSu7RVtmhETuJiF0asR91v4jon+2XJEmSJDVHXWE/Ik6NiDNq7r8xIpYBfRFxX0TMaHiF6koGfkmSJElqnnpn9j8BrK+5fyHwG+DE6r7Ob1Bd6gHO8qsd/J2TJElSL6j30nt7A78AiIipwFuAIzNzYURsAi5ucH3qAS7iJ0mdzfdvSZLKU+/M/kZgfPXrdwAbgB9U768BPHdfI+ZMvyRJkiQ1Rr1h/x7gYxFxAPBJ4I7MfKn62L5UDukflYiYFhF3RMSGiHgwIg4bYtz4iPhSRKyKiHURcd1oX1tlMPSr2fz9kiRJUrer9zD+04FbgcXAE8Cf1jz2J8DdDajpUuBR4I+B44AbI2LfzNw4YNz5wFTgNVTWETiwAa+tgnh4vyRJkiSNTIwkSEXEFGBN7QU8I+JAYEVmrhpxMRE7AauBvTJzZXXbg8DpmXnngNf/ObBvZj4zgtcxPXYog3/jlHzt0Vb0qL9LKl0n9aj9pF5Ueo/al+p1Jfdoq9R7GD8Amdk3IOjvkpmLRxP0q/YD+rYE/arFwP4Dxh0ILAf+JiL6IuInEXHkYDuMiPkRkbW3UdaoNvIQ/+5jj0pls0elstmjkoZSV9iPiFMj4oya+2+MiGVAX0TcFxEzRlnPjmx9aT+q9ycN2DadSuBfAewBnANcHxG7D9xhZs7PzKi9jbJGFcDQ3z3a1aP+/kjDs70edfZQai//1pU0lHpn9j/B1mH8QiqL8p1Y3df5o6znOWDygG2TgWcHbHseeAE4PzM3ZeZtVA7rH3QxP3UvQ78kSZIkvVy9C/TtDfwCICKmAm8BjszMhRGxCbh4lPU8AkyJiKk1pwS8Hvj6gHEPAVm9SS7mJ0mSJEk16p3Z3wiMr379DmAD8IPq/TXALqMpprrY3m3AvIiYGBGzgd2AhQPG/RL4CXBGRIyJiKOorMq/aDSvr863Zabf2X4Nh78nkiRJ6lb1hv17gI9FxAHAJ4E7MvOl6mP7Ujmkf7ROpbJQ3xrgbOC4zNwYEWdFxKU14z4IvJvKaQV/B7w/M/sa8PrqEoZ+SZIkSb2qrkvvRcT+wK1Ugv0TwLuqs+xExJ1ULr13SjMKbSRXKe1dHub/X0q+HEkre9TfCZWqE3rU/lEvK71H7U/1upJ7tFXqCvv9T6pc537NgMvvHUgl7I/28ntNZ9iX/wMs+w2w1T3q74NK1Ak9au+ol5Xeo/anel0jejQifgR8ITOvb1BZLVXvYfwAZGbfwHeQzFzcCUFfAg/xlyRJkjS0iBgDHAAsbsK+x0XExRGxpnq7KCKGXDw/In47Ir4bEWsj4smIOGM4r7Pd1fgj4h7gQ5n5cETcy3ZWwM/MQ4fzwlIJagO/n4BLkiRJqnoNEFSuGNdo5wC/R+XDBIDvAmcB5w4cWP3Q4VbgW8CxVE6p/+eIWJaZV2/rRYYzs/8Qlevab/l6ezepI7mSf+/y31ySJEkDHAT8DPiriFgeEU9FxEcbtO8/BT6fmcszcznw/wF/NsTY11Rvn8vMFzLzF8D/Bj6yvRfZ7sx+Zn645usPDaNwqeNtCX/O9kvS4Hx/lCR1uTdSCdnrgJnAkcC3IuL2zHxiy6CIuASYvY39vCEzH68ZvyswA7i/Zsz9wN4RsXNmrhvw/C0T9DFg2xu29w2MaIG+TucCfRqJbuuV0hcWavVrdtu/rzpf6T1qz6jX2aNS2UbboxFxB7A0M+fWbFsCzM3MO0ex372Ax4Gpmbm6um0qsBLYKzOXDRg/jsoRBjcCnwX+G3AHsEdmbnPyfrsz+0MU+BpgT2DiwMcy8/aR7FMqnef3d7fq/xDaXYYkSZLKcBDwhS13ohIGdgdGuyj9s9X/7gysrvka4JmBgzPzhYj4Q+BLwJPAMuBrwHZPKagr7Fcvr3cN8Dq2PoygvxZgTD37lDqRwV+SJEnqThExDXglsKJm83uAp9n68Hsi4lJgzjZ2t3/tYfyZuTYillE5TeDX1c1vBJ4Y5BD+Lc95CDiq5jW/APzb9r6Pemf2vwq8ALwX+BWwqc7nS13H8/slSZKkrnIQ8CJwUkScU71/MfDpzNxcO7B6mP/cl+9im74GnB0Rd1fvnwV8ZajBEfEGKh8MbMnif0plDYFtqjfsvw44bjTnKEjdytn+zueh/JIkSaIS7m+ictj+Gioz/Gdm5jcbtP/zgClUzsUHuAr4n1serB4tQM16AccDpwETgAeAP8rMn27vRepaoC8ivg9ck5n/OOwnFcgF+tRKpYbH0hcWatdrl/rvpd5Teo/aK+p19qhUtpJ7tFXqndn/CHBNRGwA/pXKOQtbycwNjShM6hbO+HcWZ/clSZLUDeoN+6uBpcAV2xjjAn3SEAz+kiRJklqh3rB/JTAL+DtcoE8aldrgD4Z/SZIkSY1T7zn7zwF/kZlXN6+k5vOcfZWuFcG/5POYSuhRP3xRu5Xeo/aIep09KpWt5B5tlXpn9pcCnpMvNZmH+0uSJEkajR3qHP8ZKtcDnNn4UiQNJiL6b2odf96SJEnqZPUexn8vsDewK5VZ/sFW4z+0UcU1SwmHCEuNMJpZ/5IPbSqlRz2qQu1Ueo/aH+p19qhUtpJ7tFXqPYz/wepNUgE83L+5vAyfJEmSOlVdM/vdopRZQ6mZttfbJX/aWVKP9uJ7pMpQeo/aG+p19qhUtpJ7tFXqPWd/UBGxSyP2I6lxas/19/zzkfNnJ0mSpE5UV9iPiFMj4oya+2+MiGVAX0TcFxEzGl6hpIYw/EuSJEm9o96Z/U8A62vuXwj8Bjixuq/zG1SXJBXDD0ckSZLUaepdoG9v4BcAETEVeAtwZGYujIhNwMUNrk+SJEmSJNWp3pn9jcD46tfvADYAP6jeXwN47r6kruTsviRJkjpJvTP79wAfq56n/0ngjsx8qfrYvlQO6ZckSZIkSW1U78z+6cD+wGJgL+Dsmsf+BLi7QXVJUnGc3ZckSVKniJFcgzMipgBrai/gGREHAisyc1UD62uKkq7hLbVTqdceLblHvW6xWqXk6wN7DW/JHpVKV3KPtkq9M/tbTAHeERHv2XKjMtP/O40oKiKmRcQdEbEhIh6MiMO2M/5/RERGxCGNeH1JGoqz+5IkSeoEdZ2zHxH7A9+kcij/YH/xJjCmAXVdCjwK/DFwHHBjROybmRsHqWkP4IPA8ga8riRtV/WT4naXIUmSJA2p3pn9y6isxv8+4DXAqwbc9h1tQRGxE3AMMD8zn8/MK4G1wBFDPOUC4Fxg02hfW5IkSZKkblBv2H8TcHpm3pKZj2TmYwNvDahpP6AvM1fWbFtM5WiCrUTELGDPzLxpqJ1FxPzqIf79twbUKKlBOrVHPZxfvaJTe1TqFfaopKHUG/Z/DUxsRiE1dgTWD9i2HphUuyEidgD+Afirbe0sM+dnZtTeGlqtpFGxR6Wy2aNS2exRSUMZyaX3zoqIUR+uvw3PAZMHbJsMPDtg24eAxZl5fxNrkaQhObsvSZKkUtV16b2IuBfYG9gVWAo8PXBMZh46qoIq5+yvBmZsuYxfRCwGPp2Zd9aM+zqVtQO2nKu/K/AM8KnM/MZ2XsPDmyS89F6juFifmqHkSwZ5WS/JHpVKV3KPtkq9Yf9r2xuTmR8eVUWV17kJ+A3waSqB/m+BrVbjj4hdqRzyv8Ui4KPAv2Xmc9vZv+9+Eob9RvKPKjVayX+kGCQke1QqXck92ip1XXqvEUF+mE4FrgDWAEuA4zJzY0ScBeydmXMzcy2VVfoBiIiXgJXbC/qSJEmSJHW7umb2u0UnzhpKzVDqp52d2qO9+H6q5il5RsJZQ8kelUpXco+2Sl0z+wAR8SfAXwCvZpCV+TNzWgPqkqSOU/2fSrvLkCRJkupbjT8iZgPfAH4FzABuBb5T3c964OJGFyhJncQV+iVJklSCei+99xngPOBj1fuXZOafAq+isoL+hgbWJkmSJEmSRqDesL8fcHdmvgS8BEwGyMxngC8AH29seZLUeZzdlyRJUrvVG/bXAROqXz8JvK7msQCmNKIoSep0Bn5JkiS1U70L9P0IeANwJ5Xz9T8bES8Cm4DPAv/R2PIkqXO5YJ8kSZLapd6w/zfAPtWvP1v9+hJgDHAv8JHGlSZJnc/AL0mSpHaI0f4RGhETgAmZub4xJTVfp17DW2q0Uq892o09auBXvUq+PrDX8JbsUal0Jfdoqwz7nP2IGBcRb4mI6bXbM3NjJwV9SWoHz+GXJElSK9WzQN9LwPfZelE+SdIwGfglSZLUKsMO+5m5GXgEeEXzypGk7mbglyRJUivUe+m9s6mswH9gM4qRpF5g4JckSVKz1bVAX0TcC8wEdgOeBJ4CttpBZh7awPqaohsX/5JGotRFS3qlR108SdtS8sJCLv4l2aNS6Uru0Vap99J7D1ZvQ/FdRZKGycvySZIkqVnqDftLgK9k5m8GPhARewB/0ZCqJKlHbDmk39AvSZKkRqr3MP6XgFmZec8gjx0M3JOZYxpYX1P0yiHC0vaUemhTr/aogV+1Sj780EOEJXtUKl3JPdoq9S7QFwx9qP4MYO3oypGk3uXCfZIkSWqU7R7GHxGnAKdU7ybw5YhYP2DYROBA4J8aW54k9RYP65ckSVIjDOec/Q1AX/XrANYBawaM2QR8F7ikcaVJUu9y8T5JkiSNRr3n7H8NODczlzSvpObr1fOBpYFKPY/JHv0vBv7eVfK5hp4PLNmjUulK7tFWqSvsdwuDhFRR6hugPfpyvfhe3etK/iPFICHZo1LpSu7RVql3gT5JUhtEhAv4SZIkadgM+5LUQQz8kiRJGg7DviR1GGf5JUmStD2GfUnqUIZ+SZIkDcWwL0kdztAvSZKkgcZub0BE3AsMeznPzDx0VBVJkkZkS+B3BWZJkiRtN+wDD1FH2JcktZehX5IkSVHaH4MRMQ24Angb8Cjw55n5w0HG/C/g7cAY4P8Ap2bmimG+RlnftNQmpV571B5trNLe5zU8JV8f2Gt4S/aoVLqSe7RVSjxn/1IqIX8KcD5wY0RMGDBmRyoBf39gOrAcuKyVRUpSp/CcfkmSpN5T1Mx+ROwErAb2ysyV1W0PAqdn5p3beN6BwD9l5h7DfJ1yvmmpjUr9tNMebb6S3vs1uJJnJJw1lOxRqXQl92ir1D2zHxF/EhHfi4jHI2LlwNso69kP6NsS9KsWU5nB35a3AD8f5WtLUs9wtl+SJKm71RX2I2I28A3gV8AM4FbgO9X9rAcuHmU9O1b3U2s9MGkbNb0KOBf47BCPz4+IrL2NskZJDWSPtteW0G/w11DsUals9qikodR1GH9E/AS4gcq59C8Ah2Tmj6uH3/8zcENm/t2Ii4l4M/CdzJxes+0a4J7M/NIg43cH7gL+PjMvr+N1fBOU8DB+Dc3DP9uv5MMPPURYskel0pXco61S72H8+wF3Z+ZLwEvAZIDMfAb4AvDxUdbzCDAlIqbWbHs98PDAgRExCfgucE09QV+StH3O+EuSJHW2esP+OmDLyvhPAq+reSyorKA/YtUPDW4D5kXExOppA7sBC2vHRcR44Gbgvsz83GheU5K0bQZ/SZKkzjO2zvE/At4A3EnlfP3PRsSLwCYq58z/RwNqOhW4AlgDLAGOy8yNEXEWsHdmzgVmAe8EDo+IOVuemJlDntsvSRq92sDvIaKSJEnlqvec/cOAfTLzmxGxC5XF+t4DjAHuBT6YmY82pdIG8nxgqaLU85js0c5k+G+sks819HxgyR6VSldyj7ZKXWF/0B1ETAAmZObAVfSLZZCQKkp9A7RHO59/ZI5eyX+kGCQke1QqXck92ir1XnrvoIh4T+22zNyYmesj4j0R8YbGlidJ6kS15/l7rr8kSVLr1btA35eA3x3isd+pPi5J0lYGhn8/AJAkSWquesP+m4G7h3hsEfCm0ZUjSeoVhn9JkqTmqXc1/jHAjkM8tiMwfnTlSJJ61WCB33NOJUmSRqbemf17gY8M8dhHqFyaT5Kkhhjs8H+PApAkSdq+emf25wPfi4j/oHLZvRXAHsDJwEHAuxpanSRJg/AoAEmSpG2r+9J7EXEE8DfAoUAAm4H/AP7fzPxBowtsBi/rJVWUejkSe1SN1okfBJR8ySAv6yXZo1LpSu7RVqk77Pc/MeL/AXYF1mbmhoZW1WQGCami1DdAe1StUvIfwyX/kWKQkOxRqXQl92ir1HvOfr/M3JCZT3Za0C/NmWeeydVXX93zNUilKqE/SqihWw21JoBrA0iSpE633Zn9iLgH+FBmPhwR9wLbfEJmHtrA+prCWUOpotRPO+1RdYpmzpyVPCPhrKFkj0qlK7lHW2U4C/Q9BDxf87XvHJIkMfhCgQP5B7ckSWqH7R7Gn5kfzswl1a8/VL0/5K35JbffkiVLOOOMM1i0aBHr169n4cKFzJgxo//xgw8+mLvuuou1a9fy0EMPccIJJwy5r3nz5nHzzTf3389M5s6dy+LFi1m3bh233HILkydPBuCWW27hnHPO2er5l19+ORdddBEAs2fPZvHixaxfv57HHnuMc889d6uxF1xwAcuXL2f9+vX86le/4phjjhm0hm3VP2/ePG699VYuuugi1q5dy2OPPcbxxx9f749Qaip71B4tyfZOFfB0AUmS1BSZOewb8Flg+hCP7QF8tp79tetG5eiEEd+WLFmSDzzwQM6cOTMnTJiQt912W37ta19LIHfeeedctWpVfvzjH8+xY8fm7/3e7+W6devy8MMPH3Rf8+bNy5tvvrn/fmbmv/zLv+TUqVNz5513zvvuuy/nzZuXQB533HH5i1/8on/s+PHjc+3atXnooYcmkEcffXTut99+CeRBBx2UK1asyNmzZyeQRx11VD7++OO5xx57JJB77bVX/9jaGrZX/7x583Ljxo15/PHH5w477JAnnXRSrl+/PidNmjSqn6m39tza3Yv2qD3qbdu3dvfitnpU6nX2qFS2knu0Vbd6F+ibB8wY4rHp1cd7wiWXXMLSpUvZuHEjV111FQcffDAAxxxzDKtWreLiiy/mxRdf5K677uLqq6/mlFNOGfa+L7jgAlatWsW6deu48cYb+/f97W9/m6lTp3LooZVlEY499lieeuop7rnnHgDuuOMOHnnkEQAeeOABrrnmGo444ggANm3axMSJEznggAMYO3YsTzzxRP/YWsOp/8c//jHXXXcdmzdvZsGCBYwfP55Xv/rV9f8QpSayR+1RSZKkXlZv2A8qsw2DmQGsHV05nWPFihX9Xz/33HPstNNOAMyYMYOlS5duNXbp0qVbHUI80n1v2rSJ66+/njlz5gBw8sknc8UVV/SPPeqoo7j77rtZtWoVTz/9NHPnzmX33XcHYOHChcybN4/zzjuP1atXc8MNNzBz5syXvfZw6q+tD+D555/vr1EqhT36X+xRSZKk3rPdsB8Rp0TE9yPi+1SC/pe33K+5/TtwJfBvzS64dMuWLXvZH+gzZ85k2bJlDdn/ggULOOGEE9hjjz046qijuPLKKwEYN24cN910E5dddhl77rknu+yyC5deeulW54J++ctfZtasWeyzzz688MILXHjhhS2vX2o3e1SSJEm9YDgz+xuAvuotgHU197fclgAXAB9pTpmd4/bbb2fatGmceuqpjBkzhsMPP5zZs2dvNbs3GnfddRfPPvssX/3qV1m0aBGPP/44ABMmTGDixIn09fWxadMmDjvsME488cT+5x1yyCHMmjWLcePGsWHDBp555hlefPHFltcvtZs9KkmSpF4wnNX4r8/MDwCzge8D8zPzAwNuJ2bmeZnZ1/SKC/f000/z7ne/mzlz5tDX18dXvvIVTjvtNO6+++6GvcaVV17J0UcfvdUf988++ywf+9jHuPzyy1m3bh1nnnkm1157bf/jkydP5pJLLqGvr48VK1Ywffp0PvWpT7Wlfqmd7FFJkiT1gqgsVDiMgRE7AP8JvDsz/6WpVTVZRAzvm5a6XGYWec0ve1SqKLlHh/v3g9StIsIelQpWco+2yrAX6MvMzcAvgVc0rxxJkiRJkjRa9a7Gfzbw2Yg4sBnFSJIkSZKk0Rv2YfwAEXEvMBPYDXgSeIoBl+LLzEMbWF9TeIiwVFHqoU32qFRRco96iLB6XcmHCNujUtk92ipj6xz/YPUmSZIkSZIKVdfMfrdw1lCqKPXTTntUqii5R3vx7wepVsmzhvaoVHaPtkq9M/sARMT+wMHAXsBXM3NFRPw34KnMfKaRBUqSJEmSpPrUFfYjYhLwVeD9wAvV598BrAD+J/A48OkG1yhJkiRJkupQ72r8fw8cDhwJ7ATUHhZxO3B0g+qSJEmSJEkjVO9h/O8DPpWZ/xoRYwY89hiwT2PKkiRJkiRJI1XvzP5vAX1DPLYT8NLoyoGImBYRd0TEhoh4MCIOG2LcfhGxqDruhxGx32hfW5IkSZKkblBv2L8XOHmIx94P/PvoygHgUuBRYApwPnBjREwYZNw3gW8DuwG3Atc24LUlSZIkSep4dV16LyJ+D/gecBdwPXAJMA94DZWw/7bMvHfExUTsBKwG9srMldVtDwKnZ+adNeNeCywCpmbmixExFlgFHJaZvxjG63gtEomyL+vV7hqkEpTco17WS72u5Mt62aNS2T3aKnWds5+Zd0XEkVRm3C+mskDf54AfAu8cTdCv2g/o2xL0qxYD+wN31mzbH/hZZr5YrevFiPh5dftWYT8i5lP5QEJSgexRqWxD9WhET//9JBXDHpU0lO3O7EfEuMx8YZDtvwXsCjydmRsaUkzEW4F/zMzX1my7DFiWmefVbDsJODEzj67ZdidwZWYuaEQtzVT9tLXod+DSayy9Pii/xtLra6dO+NmUXmPp9UH5NZZeXzt1ws+m9BpLrw/Kr7H0+tqpE342pddYen1Qfo2l19cKwzlnf0VEXB4R74iajwgz8/nM/E2jgn7Vc8DkAdsmA8+OcJwkSZIkST1nOGH/GuC/UzlX/8mI+FJE/G6T6nkEmBIRU2u2vR54eMC4h4HXVc/Vp/rf1w4yTpIkSZKknrPdsJ+ZHwf2BP4AuB04Cfj3iHg0Ij4fEa9vVDGZ+QxwGzAvIiZGxGwqq+0vHDDu58AS4NPVlfo/DTw6nMX5JEmSJEnqdsO69F5mbs7M72XmnwOvBP4QuBv4BPBARDwYEWdGxL4NqOlUKgv1rQHOBo7LzI0RcVZEXFoz7gTgj4CngT8GPtiA126Vz7W7gGEovcbS64Pyayy9vnbqhJ9N6TWWXh+UX2Pp9bVTJ/xsSq+x9Pqg/BpLr6+dOuFnU3qNpdcH5ddYen1NV9el91725Mqs+jHAbCrBm8ysa4V/SZIkSZLUWMOa2d+GNwFvAw6v7uvxUVckSZIkSZJGpe5Z+Ih4E5VD6I8H9gZWAtcxbtXeAAAgAElEQVQD12TmosaWJ0mSJEmS6jWssB8Rr6MS8P+Eyvn064CbqazU//3M3Ny0CiVJkiRJUl22e85+RPwUOAB4HvgOlYD/3czc1PzyJEmSJElSvYYzs/8YcD5wS2Y+1+R6JEmSJEnSKI1qNX5JkiRJklSe0a7GL0mSJEmSCmPYlyRJkiSpyxj2JUmSJEnqMoZ9SZIkSZK6jGFfkiRJkqQuY9iXJEmSJKnLGPYlSZIkSeoyhn1JkiRJkrqMYV+SJEmSpC5j2JckSZIkqcsY9iVJkiRJ6jKGfUmSJEmSuoxhX5IkSZKkLmPYlyRJkiSpyxj2JUmSJEnqMoZ9SZIkSZK6jGFfkiRJkqQuY9iXJEmSJKnLGPYlSZIkSeoyhn1JkiRJkrqMYV+SJEmSpC5j2JckSZIkqcsUF/Yj4nMR8XBEbI6I929j3O9GxIMRsSEi7oyIaa2sU5IkSZKkUhUX9oFHgE8B9ww1ICImAjcB5wNTgF8DX25JdZIkSZIkFa64sJ+ZV2bmPwP/uY1hRwBrq2OfB+YD742ISS0oUZIkSZKkoo1tdwEjtD/w0y13MnNlRKwB9gN+UjswIuYD81pandQhMjPaXYM9Kg3NHpXKZo9KZSuhR9spMrPdNQwqIhYCF2fmDYM89tfAnpk5t2bbL4A/z8wfDGPfWer3LbVKRBT7BmiPSvaoVDp7VCpbyT3aKsUdxj9MzwGTB2ybDDzbhlokSZIkSSpKp4b9h4EDt9yprsS/K5XF/SRJkiRJ6mnFhf2IGFddbX8HYFxETIyIgYdfLASmRMTs6tjPArdlpjP7kiRJkqSeV1zYB/4ReB54K3B19et9IuLSiDgLIDP/E3gfcDawBng1cFp7ypUkSZIkqSzFLtDXTC5aIpW9aIk9KtmjUunsUalsJfdoq5Q4sy9JkiRJkkbBsC9JkiRJUpcx7EuSJEmS1GV6Nuy/fIF/SZIkSZK6Q8+GfUmSJEmSulVPh31n93XAAQfwne98p2dfXypdu3uk3a8vlazd/dHu15dK1+4eaffrq4cvvVd7vxd/BlLJlyPxkkGSPSqVzh6VylZyj7ZKT8/sb+EMvyRJkiSpmxj2qwz8vWnmzJl861vf4utf/zpvfOMbOffcc5k2bRqveMUr+Id/+AcAVq5cyYQJE3jsscf6n/f888+z884786Mf/QiAOXPmMH36dCZPnszBBx/Mv/7rv/aPffTRRznyyCPZeeed2XXXXZk1axYbNmzY6vWhcoTJF7/4RX77t3+b3XbbjaOPPppHH310q1q/8IUvcNhhh7HTTjvx9re/nSeeeKLpPyOpnexRqVz2p1Q2e1SGfanqoYceYscdd+TJJ5/km9/8Jp/5zGf49a9/zbRp03jXu97FVVdd1T/2lltuYfr06RxyyCEAHHnkkfzsZz+jr6+PE044gfe///0888wzAJx99tnst99+rF69mpUrV/LFL36RsWPHvuz1FyxYwN///d/zrW99i+XLl/OGN7yB9773vbz44ov9Y6666iquueYaVq1axY477shf//VfN/mnIpXDHpXKZX9KZbNHe5Nhv4az+71t99135/TTT2fcuHEcccQRzJw5k/vvvx+Ak046iQULFvSPXbBgASeffHL//Q9/+MPsvPPOjBs3js985jNs3ryZn/70pwCMHz+e5cuXs3TpUsaNG8fhhx/O+PHjX/b6CxYs4JOf/CQHHnggEyZM4POf/zzLli3jnnvu6R9z2mmn8apXvYqJEydy4oknct999zXrxyEVxx6VymV/SmWzR3uTYX8AA3/vesUrXrHV/R133LH/U8s//MM/5De/+Q333XcfK1eu5Hvf+x5z5swBYPPmzf2fak6ePJlddtmFdevWsXr1agD+9m//lj333JN3vvOdzJw5k/nz57N58+aXvf6yZcuYOXNm//3x48czffp0li1b1r/tla985aD1Sb3AHpXKZX9KZbNHe9PLj7HQlpUb212GCjJx4kTe//73s2DBAmbOnMlb3vIW9tprLwCuvvpqrr76au688072228/IoJdd921/3do2rRpXHLJJQD89Kc/5V3vehcHHnggxx133FavMWPGDJYuXdp/f9OmTSxfvpwZM2a05puUOpg9KpXL/pTKZo92L2f2h+AMvwY66aSTuPbaa/nGN76x1aFN69evZ/z48ey+++5s2rSJefPmsX79+v7Hr7vuOh5//HEyk1133ZWxY8cOei7TnDlzuPjii3n44YfZuHEj8+bNY/r06Rx66KEt+f6kTmePSuWyP6Wy2aPdybC/DQZ+1Xr729/OhAkT+OUvf7nVp5WnnHIKBxxwAPvssw/77rsvkyZN6v80FOC+++7j8MMPZ9KkScyaNYs/+7M/49hjj33Z/k8++WQ+8YlP8N73vpdXvvKV/PjHP+bb3/72oG+Ykl7OHpXKZX9KZbNHu1P04uHqETHsb7oXfz7qDdXTVYr8RCsi0t5Tr7NHpbLZo1LZSu7RVnFmfzuc3ZckSZIkdRrD/jAY+CVJkiRJncSwP0wGfkmSJElSpzDs18HAL0mSJEnqBIb9Ohn4JUmSJEmlM+yPgIFfkiRJklQyw/4IGfglSZIkSaUy7I+CgV+SJEmSVCLD/igZ+CVJkiRJpTHsN4CBX5IkSZJUEsN+gxj4JUmSJEmlMOw3kIFfkiRJklQCw36DGfglSZIkSe1WXNiPiGkRcUdEbIiIByPisCHGvSsiFkfE+oi4PyLe2upah2LglyRJkiS1U3FhH7gUeBSYApwP3BgRE2oHRMQY4Drg88DOwAXADRFRzPdj4JckSZIktUtkZrtr6BcROwGrgb0yc2V124PA6Zl5Z824KcBTwLjMzGrI3wTskZmrhvE6LfumS/r5SrUigsws8lOpiEh7R73OHpXKZo9KZSu5R1ulmJnwqv2Avi1Bv2oxsH/toMzsA24AZldn+ecADwwW9CNifkRk7a2J9b+MM/zStrW7RyVtmz0qlc0elTSU0mb23wr8Y2a+tmbbZcCyzDxvwNg/Bv43MBl4Fjg6M384zNdp+Tdd0s9ZgrI/7XRGQrJHpdLZo1LZSu7RViltZv85KuG91pYw3y8iXgd8DTgGGA/8EXBzRExtRZEj4Qy/JEmSJKlVSgv7jwBTBoT21wMPDxj3euAnmbkoMzdn5kLgSeCQ1pQ5MgZ+SZIkSVIrFBX2M/MZ4DZgXkRMjIjZwG7AwgFD7wfeGBG/AxARbwNeC/y8heWOiIFfkiRJktRsY9tdwCBOBa4A1gBLgOMyc2NEnAXsnZlzM/ORiPgEcGVETAeWA6dm5pL2lT181fNH2l2GJEmSJKlLFbVAX6uUskppL/7sVY6SFy1xYSHJHpVKZ49KZSu5R1ulqMP4e01EeFi/JEmSJKnhDPsFMPBLkiRJkhrJsF8IA78kSZIkqVEM+wUx8EuSJEmSGsGwXxjP45ckSZIkjZZhv1AGfkmSJEnSSBn2C2bglyRJkiSNhGG/cAZ+SZIkSVK9DPsdwPP4JUmSJEn1MOx3EAO/JEmSJGk4DPsdxsAvSZIkSdoew34H8rB+SZIkSdK2GPY7mIFfkiRJkjQYw36HM/BLkiRJkgYy7HcBD+uXJEmSJNUy7HcRA78kSZIkCQz7XcdZfkmSJEmSYb9LGfglSZIkqXcZ9ruYs/ySJEmS1JsM+z3AwC9JkiRJvcWw3yOc5ZckSZKk3mHY7zGGfkmSJEnqfob9HmXglyRJkqTuZdjvYc7yS5IkSVJ3MuzL0C9JkiRJXcawr34GfkmSJEnqDoZ9bcVZfkmSJEnqfIZ9DcrQL0mSJEmdq7iwHxHTIuKOiNgQEQ9GxGFDjBsfEV+KiFURsS4irmt1rb3A0C9JkiRJnWdsuwsYxKXAo8AfA8cBN0bEvpm5ccC484GpwGuA9cCBLa2yx0QEmdnuMiRJkiRJwxAlBbiI2AlYDeyVmSur2x4ETs/MO2vGTQF+Duybmc+M4HXK+aY7UEm/Mxq56gc4RR62ERHp75l6nT0qlc0elcpWco+2SmmH8e8H9G0J+lWLgf0HjDsQWA78TUT0RcRPIuLIwXYYEfMjImtvzSm9d3hovxrJHpXKZo9KZbNHJQ2ltLC/I5VD8mutByYN2DadSuBfAewBnANcHxG7D9xhZs7PzKi9NaHunmToVyPYo1LZ7FGpbPaopKGUFvafAyYP2DYZeHbAtueBF4DzM3NTZt5G5bD+QRfzU3MZ+iVJkiSpLKWF/UeAKRExtWbb64GHB4x7CMjqTYUw9EuSJElSGYoK+9XF9m4D5kXExIiYDewGLBww7pfAT4AzImJMRBxFZVX+RS0uWYMw9EuSJElSexUV9qtOpbJQ3xrgbOC4zNwYEWdFxKU14z4IvJvKOf1/B7w/M/taXq2GZOiXJEmSpPYo6tJ7reIqpe3Ri79rJSv5ciReMkiyR6XS2aNS2Uru0VYpcWZfXcqZfkmSJEmdJCJ+FBEfaHcdI2HYV8sZ+iVJkiSVLiLGAAcAi5uw749XP0jYGBHfavT+AcY2Y6fScNQGfg81kyRJklSY1wBB5apxjfYb4PPAO4EZTdi/M/sqg7P9kiRJkgpzEPAz4K8iYnlEPBURH23EjjPzpsz8FrC6EfsbjGFfRTH0S5IkSSrEG6nM7q8DZgIfBi6KiL1qB0XEJRHx9DZue7e+dA/jV6E8xF+SJElSmx0EXJGZl1fv3x4RTwL7A09sGZSZpwGntaG+bXJmX8Vztl+SJElSGxwEfHPLnaiEkt2BVW2rqA6GfXUMQ78kSZKkVoiIacArgRU1m98DPA3cP2DspRHx7DZubTmM37CvjrMl9Bv8JUmSJDXJQcCLwEkRsUNEvAm4GPh0Zm6uHZiZczNz0jZujw/ceUSMjYiJVE6t3yEiJkbE+EZ+A56zr47muf2SJEmSmuAg4CYqh+2voTLDf2ZmfnObzxq+c4B5NfefB/4NOKJB+yd6MSBFRO990z2kF3+nRyIiyMwiD4+IiPTfUb3OHpXKZo9KZSu5R1vFmX11HWf7JUmSJPU6w766msFfkiRJUi9ygT71DBf1kyRJktQrnNlXz3G2X5IkSVK3M+yrpxn8JUmSJHUjw75UZfCXJEmS1C0M+9IgDP6SJEmSOplhX9oOg78kSZKkTmPYl+pg8JckSZLUCQz70ggZ/CVJkiSVyrAvNUBt8AfDvyRJkqT2MuxLTeCsvyRJkqR2MuxLTeasvyRJkqRWM+xLLeasvyRJkqRmM+xLbeSsvyRJkqRmMOxLBXHWX5IkSVIjGPalQjnrL0mSJGmkdmh3AYOJiGkRcUdEbIiIByPisO2M/x8RkRFxSKtqlFotIra6SZIkSdJQigz7wKXAo8AU4HzgxoiYMNjAiNgD+CCwvHXlSe1n+JckSZI0lOLCfkTsBBwDzM/M5zPzSmAtcMQQT7kAOBfY1JoKpTIZ/iVJkiRtUVzYB/YD+jJzZc22xcD+AwdGxCxgz8y8qVXFSZ1iYPj3AwBJkiSpd5QY9ncE1g/Yth6YVLshInYA/gH4q23tLCLmV8/n7781tFqpg5QY/O1RqWz2qFQ2e1TSUEoM+88Bkwdsmww8O2Dbh4DFmXn/tnaWmfMzM2pvjStV0mjZo1LZ7FGpbPaopKGUGPYfAaZExNSaba8HHh4w7m3A8RGxOiJWA3sB34uIU1pUpyRJkiRJRYoSr90dETcBvwE+DbwP+Ftg38zcWDNmVyqH/G+xCPgo8G+Z+dx29l/eNy21Qamf/kdElvjeJLVSRNijUsHsUalsJfdoq4xtdwFDOBW4AlgDLAGOy8yNEXEWsHdmzs3MtVRW6QcgIl4CVm4v6EuSJEmS1O2KnNlvNmf2pYpSP+10RkIqe0bCHpXsUal0Jfdoq5R4zr4kSZIkSRoFw74kSZIkSV3GsC9JkiRJUpcx7EuSJEmS1GUM+5IkSZIkdRnDviRJkiRJXcawL0mSJElSlzHsS5IkSZLUZQz7kiRJkiR1GcO+JEmSJEldxrAvSZIkSVKXMexLkiRJktRlDPuSJEmSJHUZw74kSZIkSV3GsC9JkiRJUpcx7EuSJEmS1GUM+5IkSZIkdRnDviRJkiRJXcawL0mSJElSlzHsS5IkSZLUZQz7kiRJkiR1GcO+JEmSJEldxrAvSZIkSVKXMexLkiRJktRlDPuSJEmSJHUZw74kSZIkSV3GsC9JkiRJUpcx7EuSJEmS1GUM+5IkSZIkdZniwn5ETIuIOyJiQ0Q8GBGHDTHm+ohYGRF9EXFzRLyyHfVKkiRJklSa4sI+cCnwKDAFOB+4MSImDBizI/B/gP2B6cBy4LJWFilJkiRJUqkiM9tdQ7+I2AlYDeyVmSur2x4ETs/MO7fxvAOBf8rMPYb5OuV801IbZWa0u4bBRESW9N4ktUNE2KNSwexRqWwl92irlDazvx/QtyXoVy2mMoO/LW8Bfj7YAxExPyKy9tagWiU1gD0qlc0elcpmj0oaSmkz+28F/jEzX1uz7TJgWWaeN8RzXgX8B3BcZv5gmK9TzjcttVGpn3Y6IyGVPSNhj0r2qFS6knu0VUqb2X8OmDxg22Tg2cEGR8TuwHeBc4Yb9CVJkiRJ6nalhf1HgCkRMbVm2+uBhwcOjIhJVIL+NZl5eYvqkyRJkiSpeEWF/cx8BrgNmBcREyNiNrAbsLB2XESMB24G7svMz7W8UElNF9HTR11JkiRJo1LUOfsAEfEK4ArgrcAS4M8y84cRcRawd2bOjYi3U/kAYAPQ/w1k5qRhvkZZ37TUJqWex7SlR0t7f5JaqeRzDT0fWLJHpdKV3KOtUlzYbwXDvlRR6hugYV8q+48Ug4Rkj0qlK7lHW6Wow/glqZaH8kuSJEkjY9iXJEmSJKnLGPYlSZIkSeoyhn1JRfNQfkmSJKl+hn1JkiRJkrqMYV9S8ZzdlyRJkupj2JckSZIkqcsY9iV1BGf3JUmSpOEz7EuSJEmS1GUM+2125plncvXVV/d8DdJwOLsvSZIkDU9kZrtraLmI6L1vWhpEZhaZnrfXo734vqXeExFF96h9qF5nj0plK7lHW8WZfUmSJEmSuoxhfwSWLFnCGWecwaJFi1i/fj0LFy5kxowZ/Y8ffPDB3HXXXaxdu5aHHnqIE044Ych9zZs3j5tvvrn/fmYyd+5cFi9ezLp167jllluYPHkyALfccgvnnHPOVs+//PLLueiiiwCYPXs2ixcvZv369Tz22GOce+65W4294IILWL58OevXr+dXv/oVxxxzzKA1bKv+efPmceutt3LRRRexdu1aHnvsMY4//vh6f4TSqHg4vyRJkrRthv0ROvHEE/ngBz/I1KlTee655zjvvPMA2Hnnnbnjjju49tprmTp1Kh/96Ee57LLLOPzww4e97w984AP8/u//PnvvvTczZszgL//yLwG44oorOOmkk/rHjR8/ng984AMsWLAAgDVr1vC+972PyZMnc+yxx/KRj3yE2bNnA3DUUUdxwgkn8OY3v5nJkyfzjne8g1/+8pcve+3h1P8Hf/AH/OAHP2DKlCmcc845fOUrX2HSpEn1/xClUYgIQ78kSZI0BMP+CF1yySUsXbqUjRs3ctVVV3HwwQcDcMwxx7Bq1SouvvhiXnzxRe666y6uvvpqTjnllGHv+4ILLmDVqlWsW7eOG2+8sX/f3/72t5k6dSqHHnooAMceeyxPPfUU99xzDwB33HEHjzzyCAAPPPAA11xzDUcccQQAmzZtYuLEiRxwwAGMHTuWJ554on9sreHU/+Mf/5jrrruOzZs3s2DBAsaPH8+rX/3q+n+IUgMY+CVJkqSXM+yP0IoVK/q/fu6559hpp50AmDFjBkuXLt1q7NKlS7c6zH+k+960aRPXX389c+bMAeDkk0/miiuu6B971FFHcffdd7Nq1Sqefvpp5s6dy+677w7AwoULmTdvHueddx6rV6/mhhtuYObMmS977eHUX1sfwPPPP99fo9QOBn5JkiRpa4b9Blu2bNnLQvTMmTNZtmxZQ/a/YMECTjjhBPbYYw+OOuoorrzySgDGjRvHTTfdxGWXXcaee+7JLrvswqWXXrpVCPryl7/MrFmz2GeffXjhhRe48MILW16/1CwGfkmSJOm/GPYb7Pbbb2fatGmceuqpjBkzhsMPP5zZs2dvNQM/GnfddRfPPvssX/3qV1m0aBGPP/44ABMmTGDixIn09fWxadMmDjvsME488cT+5x1yyCHMmjWLcePGsWHDBp555hlefPHFltcvNZPn8UuSJEkVhv0Ge/rpp3n3u9/NnDlz6Ovr4ytf+QqnnXYad999d8Ne48orr+Too4/eKoA/++yzfOxjH+Pyyy9n3bp1nHnmmVx77bX9j0+ePJlLLrmEvr4+VqxYwfTp0/nUpz7VlvqlZjP0S5IkqddFZra7hpaLiN77pqVBZGaRibjRPdqL73PqfBFRdI/aV+p19qhUtpJ7tFXGtrsASWq22ll+//iRJElSLzDsS+opBn9JkiT1AsO+pJ71f9u7+1jJ6ruO4+8PXQIU2AgLi9V2aUy2LAu0oFjXUiht0krSxKKQ1oImjUZjNbExYo2ghS1qMDTEf9ouqdZNaBpoRAwPDWugrEp4sDSNsF22RZ4iEFzLysPuli0rX/8458o4vQ9zH2bmzOz7lZzMzjm/e+Zzzj1fLt8zZ870f67f5l+SJEnTwmZfklqz3dTPEwCSJEmaRDb7kjSP+e7q74kASZIkdZXNviQt0SBf7+cJAUmSJI2Dzb4kDdEgJwRm40kCSZIkLYfNviR10FJPEizEkwiSJEmHhsPGHaBfkrVJ7kyyP8mOJJvmGLc+yf3tuAeSrB91VkmaNEk6P0mSJGn5OtfsA1uAJ4A1wDXAzUmOmGXcTcBtwPHArcCNI0soSRqacZ9s6MokSZK0HOnSJZ1JjgW+D7ytqna383YAf1BV23rGbQDuB06sqoNJVgH/BWyqqu8O8Drd2WhpjKqqkx2FNSo1ulyjXfr/B2kcklijUod1uUZHpWuf2V8PvDDT6LceATYC23rmbQQeraqDAG3Dv6ud//+a/SRXAVcOM7SkpbNGpW6bq0a9+kDqBmtU0ly69s7+ucCXqmpDz7zrgWeq6uqeeb8GXFpVF/TM2wZ8papuGGXmpWjPtnb6v8Bdz9j1fND9jF3PN06TsG+6nrHr+aD7Gbueb5wmYd90PWPX80H3M3Y93zhNwr7pesau54PuZ+x6vlHo2mf29wGr++atBvYucZwkSZIkSYecrjX7jwFrkpzYM+90YGffuJ3Aqe1n9WkfN8wyTpIkSZKkQ06nmv2qegW4A7gyyZFJLqG52/72vnG7gCeBy9o79V8GPDHIzfkkSZIkSZp2nWr2W5+kuVHfHuAK4KKqOpDk8iRbesb9CnAh8CLwS8DHR5506TaPO8AAup6x6/mg+xm7nm+cJmHfdD1j1/NB9zN2Pd84TcK+6XrGrueD7mfser5xmoR90/WMXc8H3c/Y9XxD16kb9EmSJEmSpOXr4jv7kiRJkiRpGWz2JUmSJEmaMjb7kiRJkiRNGZv9IUmyNsmdSfYn2ZFk0xzjnmrH7G2nkdxIIsnmJDuTvJ7k4nnG/Vybf3+SbUnWjiLfIjNWz/7bm+Q3RpTviCRbkzyb5MUkdyc5ZY6x65Pc3+7HB5Ks71i+sRyH42SNjizfWOqzfW1rdIJZoyPL59/QlclojVqjw8pnja5MxkOuRsFmf5i2AE8Aa4BrgJvTfE3gbM6rqmPa6coR5XsM+BTwr3MNSHIk8Pc0+dcAjwNfHEm6xoIZe7y9Zx/+zZBzzVgF/Dvwbpr9cxfwtTnG3gTcRvNVkrcCN3YsH4znOBwna3R5ul6fYI1OOmt0ebpeo12vT7BGF2KNLo81unzW6EKqymmFJ+BY4ACwtmfeDuAXZhn7FHD2GLNuBy6eY9kFwI6e52vb7TqmKxnb5QWc0JHfewFH9s3fAPw3sKp9vqp9fkoX8rXLxnocjul3ZY0OOV+7vBP12fN7t0YnYLJGR5OvXd6JGu16fc6XsV1mjVqjK56vXW6NLjNju+yQqtGZyXf2h2M98EJV7e6Z9wiwcY7xtyd5PsmNSU4afryBbQQennnSbs8emu3rmoeTPJNkS5Jjx5ThHOCpqnq1b/5G4NGqOgjQPu5i7uNh1PlmdPU4HAZrdLS6UJ9gjU4Sa3S0ulCjXa9PsEZ7WaOjZY0OxhrtY7M/HEcDL/fNexk4ZpaxlwAn05wV2w98ZbjRFmUx2zFO59Lsw7OBdcB1ow6Q5Hjg88AVsywe+35cIB90+zgcBmt0dMZen2CNTiBrdHTGXqNdr0+wRmdhjY6ONToAa3R2q8YdYErtA1b3zVsN7O0fWFX3tf88kORTwItJjq6qfUPOOIiBt2Ocqure9p/PJ/lD4B7gN0f1+kmOov18UlV9dZYhY92PA+Tr+nE4DNboiIy7PsEanVDW6IiMu0a7Xp9gjc7BGh0Ra3Rh1ujcfGd/OB4D1iQ5sWfe6cDOBX6u2inDCrZIO4EzZp60dyc9jmb7uqpG+WJJVtHcCOR7VTXXmcSdwKnt2Jmf2cDCx8Oo8vXr2nE4DNboeIy0PsEanWDW6Hj4N3RpGft17TgcBmt0PKzRpWXs17XjcGhs9oegql4B7gCuTHJkkkto7k65vXdcknVJNiVZ1X7+5q+Af66qoZ8JS3J4ewfSw4DD25z9B/x2mv+QX9KO/QxwxyjyDZoxyWlJzkhyWPsH51rg9lHka/11m++35hpQVbuAJ4HL2rvUXgY8UVXf7UK+cR6H42KNjiZfB+oTrNGJZI2OJl8HarTr9QnW6Kys0dHks0YHYo3OZ9x3CJzWCTgJ2EbzmZDvAJva+ZcDW9p/n0Zz59K9wG6ar614y4jybeWNs1oz09tpvkbl8p5xm9r8+4F/BE4a4T5cMCPwAZqzr/uA54DrgdUjyndym+kH7e9wZlrX+3tux74DeKAd+yDwjq7kG+dxOM7JGn5ngfAAAAXWSURBVB1+vnHWZ/v61ugET9bo8PONs0a7Xp+LyWiNWqPDymeNrkzGQ7VGq4q0O0CSJEmSJE0JL+OXJEmSJGnK2OxLkiRJkjRlbPYlSZIkSZoyNvuSJEmSJE0Zm31JkiRJkqaMzb4kSZIkSVPGZl+SJEmSpCljsy9JkiRJ0pSx2ZckSZIkacrY7EuSJEmSNGVs9iVJkiRJmjI2+5IkSZIkTRmbfUnS1EpyVZKaZbqrXb41yUM94z+a5BNjC7wE/dvQJUk+k+TZJK+3OYeyv5OckeTrSV5op1uSrF3ueiVJmmSrxh1AkqQhewm4YJZ5AFcDR/XM/yhwArB1+LGmW5Kzgc3A5cB2YHe7aEX3d5KfBO4BHgQuBVYDXwR+H/jjpa5XkqRJZ7MvSZp2B6vqgdkWVNXjow5zCNnQPn6+ql4e4uv8HvAy8MtVdQAgya8Dxw7xNSVJ6jwv45ckHbJ6LytPshW4CHhfz+X+V/WOS/LBJA8n2Zfk3iSnzbLO9yb5pyT720vKv5Tk2J7lpyW5M8medj2PJvndQZfPsy0XJtmV5NU228YlZFuR7Wz35Q3t0JfafXn+oPt7kT4M3NLT6B8HvBf45hLWJUnS1PCdfUnS1EvS//fuf6qq+uZdDawDfgz4nXbeMz3L1wHXAn8O/AD4HPC1JKfPrCvJOcDdwD8AFwNrgGuA49rnALcCu4BfBQ4Ap9Bces6Ay2dzMnAd8Kdtts3AtiTrq+rVRWRbqe28GvgP4E+AD7Tr2Ql8oud1FtrfC0pyNHAq8GftiYYz27zPADctZl2SJE0bm31J0rRbA7zWN++DwF29M6rq8SR7gMPmuOz/eOCcqnoMIMlhwC00zfiudsw1wH1V9bGZH0ryLHB3ktOB54GfAi6sqkfaIXf3jD1hvuXzOAH4SFXd167nW8DjNM31lkGyVdWOldrOqtqRZOYjEt+sqr3tmP8LPMD+HsQ7aa5S/DbwNM3JhgPA+TMnOSRJOlR5Gb8kadq9BPxs3/TgEtbz1EwD3NrZPr4VIMmbgZ+neRd81cwE3EtzsuFngD0073hvSfKxWe4Yv9DyueyeafQBqupp4FvAuxeRbSW3c1TOBPYCT9BcUfDbwJPAHUl+fIQ5JEnqHJt9SdK0O1hVD/VNryxhPS/2Pf9h+3hk+3gc8CbgCzRN78x0ADgceFtVvQ58iOYd/i8Dzyf5lyRnASy0fB6755j3lkGzreR2LpB1JZ0F/FtVvVZV36iq64FfpLk64X0jzCFJUud4Gb8kSSvjRaCAq4Cvz7L8OYCq2gVclORw4FzgL2neiX5rVb2+0PI5Xnu2KwDWAt9ZTLYBreS6lutMfvQqjZnL9/9zhDkkSeocm31Jkt7wQ954B3tRqmpfkgeAU6rqswOMfw34RpLrgK/S3Khuz6DL+6xN8p6ez+yvA34a+NulZFsg94qti2Xs7yRvAk4HbutbdCnNfrp3edEkSZpsNvuSJL1hF/CRJBfS3NH9uapazDvVn6a5Sd3rwN8Br9Dccf7DwBU0je3naO4U/wTNJfF/RHMp+p4k75xv+Tyv+33ghiQzd+P/LM1l/FsHzVZV31up7VzEumbd30nOB+4B3l9V2+f42Q3AUcCnk7wAPErzlXtXAJ+sqoOL2B5JkqaOzb4kSW/4As3nwL9M02hvprlcfSBVdW+S89qfu4Hms+1PA3fSXFZ+RPt4BfATNJfE30PT0EPzWf35ls/laeAvaO6SfzLwEPDx3jvSD5BtYCu4rrn295vb5bPdi2DGmTT3CriFZruLpuG/tKpuXkQGSZKmUn70a4YlSZLGJ8lm4Lyqev88Y64FPlRV7xpdMkmSJod345ckSV3zHuC6BcacBXx7BFkkSZpIXsYvSZI6pao+OMCwdwG3DzuLJEmTysv4JUmSJEmaMl7GL0mSJEnSlLHZlyRJkiRpytjsS5IkSZI0ZWz2JUmSJEmaMjb7kiRJkiRNGZt9SZIkSZKmjM2+JEmSJElT5n8BqShBqFvCZTEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x864 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Additive Model I\n",
    "γ = float(input(\"Enter γ: \"))\n",
    "m_v1 = 1/2\n",
    "m_o1 = 0\n",
    "\n",
    "fig, axes = plt.subplots(3, 4, figsize=(16, 12), sharex=True, sharey=True)\n",
    "fig.suptitle(r'Additive Model I (Parent-to-Offspring Altruism), $\\gamma = $'+str(γ), \n",
    "             x=0.5, y=0.95, horizontalalignment='center', verticalalignment='top', fontsize = 18)\n",
    "axes[1,0].yaxis.set_label_coords(-0.18,0.5)\n",
    "axes[1,0].set_ylabel(r'Vertical transmission rate, $\\rho$', fontsize = 15) \n",
    "fig.text(0.51, 0.07, r'Fitness benefit, $\\beta$', horizontalalignment='center', \n",
    "         verticalalignment='bottom', fontsize = 15)\n",
    "\n",
    "for i in range(3):\n",
    "    for j in range(4):\n",
    "        b_, c_ = b[i], c[j]\n",
    "        ax = axes[i,j]\n",
    "        β_, ρ_ = np.meshgrid(β, ρ)\n",
    "        z = f(β_, γ, ρ_, b_, c_, m_v1, m_o1)\n",
    "        ax.contourf(β_, ρ_, z, levels=[0, 1], colors=['k', 'w'])\n",
    "        \n",
    "        if j == 3: #Label b values \n",
    "            if i == 2:\n",
    "                ax.yaxis.set_label_coords(1.24,0.5)\n",
    "            else:\n",
    "                ax.yaxis.set_label_coords(1.3,0.5)\n",
    "            ax.set_ylabel(r'$b = $'+str(b_), horizontalalignment='right', rotation=0)        \n",
    "        if i == 0: #Label c values\n",
    "            ax.title.set_position([0.5, 1.045])\n",
    "            ax.title.set_text(r'$c = $'+str(c_))              \n",
    "        \n",
    "        #Label the light and dark regions of the plots\n",
    "        if γ == 0.01:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 0 or (j == 1 and i != 2) or (j == 2 and i == 0):\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.1:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 0 or j == 1 or (j == 2 and i == 0):\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 2 and i == 1:\n",
    "                ax.text(0.15, 0.04, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.3:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j != 3 or i != 2:\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.7:\n",
    "            ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            if i == 1:\n",
    "                ax.text(1.83, 0.92, 'invasion')\n",
    "            elif i == 2:\n",
    "                ax.text(1.8, 0.89, 'invasion')\n",
    "        elif γ == 0.99:\n",
    "            ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            \n",
    "#plt.savefig('dec9_mI_g01.pdf') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additive Model II"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter γ:  0.99\n"
     ]
    },
    {
     "data": {
      "image/png": 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/vG5aO+tyuJ7b+vo51Smlu63nfP5AVQz1H5WtFbwDFa+DGa511fR9m9V3mv+w4Xbnuh5X09L7ZR3L+DpVsfd3zXaORPV1cf9EdYT15Mb7WxXV976vURxnZt9AebD28zum9m0DfY+fRnWZxhPAfw21H0NwFVVB/M6G6R9t5cFD3KY20/Z2r07f2QT7Nkz/O9bxuW0Ir1un7EY1uN36fqPAXVTfmrCA6rkeN3hzoHPX7F9MtV3624bpf0113Xz9mWVExPiI2C4iXjRY52rvqS9TfevBP67rybTbXpIG45F9aXTbn+qoxr8O0uZSqtGdj6I6cnEScBjwtYjYheq6wL2B3Xn+q9H6tNN2ID+lGoDohIiYTnUd9/2Z+b/reNy5VCNDn0J13fGVDff/C9UHt5Mj4g3Af1IVoi8C9qEaUOn1LfaxX2Y+RLW+WnES1XdLf6VWZP2c6mjMUVQfWk9qaNvquhyW57a+amc+XAa8ZYBTXVv1LaqC9N9r85tKtW5+P+ijmhuudTXU9+1gj2vn/dJUVl8BdxDV1w1eHRGXAtdSne67K9VZE08Bb83MgYqaVkwBFkXEt2v9XEx1RPQYqmu3r2povxT434j4N6qdOO+heg3eN8JHJj9P9V46OyJ2pRq88bVUI70vZd1H3IeyTW1mqO8fqC5d+hXVV91tQnXU+rVUBfW6trvtvm7rLSImU3294VqDmUbEA8A2mdnq5RZ9OwteT/XtEA+t6wGdumY/M2+LiK9Qff3fZcB3qc5O+SDVDqsLGh6yJdVYFf9FbRDK2rq4kWrH3f1UZ229k+prS0/IzB/Vz6Dd9pLULot9aXQ7qvZzwNN1awPe3Q0cGhF/VxsEaU/gC1RHmYOqWHg98B8Nj2257SDLfygi3kt1BPsMqu+VPhdY14fe71Cdzrox8PXMfLZhvr+PiDcDx1IVOJ+q3fUI1YenxjMBOi4zl0fEa2rLPoiqwPkt1dkB87LuO9PbXO9df26DOIPqyOeBVEXPUJxM9fyPoirWH6U6qnY2zw/q1pLhWldDfd8O9rh23i/rWMYvI+LlwIeozn55E9VRwAeBU6m+LnJ9Cn2orif/EtUOk32ByVSj3H8b+KfMfKSh/T9QFXzvpzqD5R6qr79rLJCGVWYurQ2weQrVIJtJNUDd66kK8GcHeTgMYZs6QJuhbvf6dqq9hero7geoxrP4PtX199ev4+Htvm6dcDDVke+zmtw3mTUvc1mXvmL/IVrY+TUM/pbqFP//A7yZaufKqcAnW7xMaBVwK9UOpy2oXo+fAgdk5jUdaC9JbYnq7C5JkloTEd8DNszMPbvdF3VXRLybaifN6zPz2u72ZmC1I+RLgbMy8+hu96eXRMRNwIOZ+faG6S+n9vWbmXl2i/N6CdVlKh/PTE9hl6T15DX7kqR2fQTYPSL273ZHpEYR8UdNJveNjfGDkexLr4uIt1KNIt9s7JE/pyr22zm7Zufaz5vXs2uSJDyNX5LUpsy8A/9/qFz/HhEPAj+jurxhH6rLTn5CNUiiOiQzr6D65odm951M+4NE9hX7Px+0lSSpJX5YkyRJveQqqnEx3gr8EbCQ6hr+Tw3w/eoqxyupRvVf3zEnJEl4zb4kSZIkST3Ha/YlSZIkSeoxFvuSJEmSJPUYi31JkiRJknqMxb4kSZIkST3GYl+SJEmSpB5jsS9JkiRJUo+x2JckSZIkqcdY7EuSJEmS1GMs9iVJkiRJ6jEW+5IkSZIk9RiLfUmSJEmSeozFviRJkiRJPcZiX5IkSZKkHmOxL0mSJElSj7HYlyRJkiSpx1jsS5IkSZLUYyz21XURMT4iTouIx2q3UyNi3ABtJ0bE1yLi/oh4MiJ+FRHvHek+S4KIeH9E/CwiVkbEFd3ujzRWtZNF/49KI6vd/5URcU5ErIqIp+puu49EX9V7LPZVgo8DrwV2qN32BI4foO04YBGwLzAVeDdwSkTsP/zdlNTgEeCzwNe63RFpjGsni/4flUbWUP5Xnp6Zk+tuNwxT39TjLPbVloh4U0RcVzsC/2hE/G0HZvte4LOZuSgzFwH/CBzVrGFmPp2Zn8zMe7PyP8CPqHYWSBrAcGQ3My/LzCuApR3oojQmdDuL/h+VBtbtfEqdZrGvlkXEUcCZwCeAGcCrgJ80tDk9Ip4Y5PaihvbTga2AW+om3wK8KCKmtdCnScCuwK3r9eSkHjYc2ZXUvhKz6P9RqVJYPo+s7XC4IyI+HBHWbBqSyMxu90GjQERMBR4G3paZ/9nB+W4NPARslplLa9M2AxYDW2fmwkEeG8ACYEtgn8xc3al+Sb1iuLLbsIz5wM6Z+dbhmL/UC0rMov9HpUpJ+YyIV9X68hjwp8AlwBcz84vD0S/1NvcSqVVvAB4Zhg3gU7Wf9Ufx+35/cqAH1T6gfAX4Y+CtfkCRBjRc2ZXUnqKy6P9RaQ3F5DMzb87MJZn5h9plNicCf9Xtfml0sthXqzYBHl9Xo4g4s2H00MbbGqc3ZebjwEJg57rJOwMPZ+byAZbR9wFlN2D/gdpJAoYpu5LaVkwW/T8qraWYfDbhjjgNmcW+WvVz4JUR8VqAiJgVTb4GJDOPbhg9tPH2UJN5nw2cEBEzI2Im1Uj8Xx+kL6cBrwH2q+0skDSwYctuRIyrXe87DtggIiZFxIRhf0bS6FRSFv0/Kq2pmHxGxDsiYmpUXg38P+DSjj1TjSkW+2pJZt4MfBRYEBFPA9cDndp7+RngBuCXtdtPgM/13Vnbi3pm7fdtgGOpTjt8sG5P6pkd6ovUU4Y5ux8HngVOAP6i9vv3OzRvqad0M4v+H5UGV0o+a95PNZ7Vk8D5wOnAKR3qi8YYB+iTJEmSJKnHeGRfkiRJkqQeY7EvSZIkSVKPsdiXJEmSJKnHWOxLkiRJktRjLPYlSZIkSeoxFvuSJEmSJPUYi31JkiRJknqMxb4kSZIkST3GYl+SJEmSpB5jsS9JkiRJUo8prtiPiE9FxJ0RsToiDhmk3Z9FxO0R8UxEXBMRM0ayn5IkSZIklaq4Yh+4B/gQcONADSJiEnAZcCKwCXAvcMaI9E6SJEmSpMIVV+xn5nmZ+QPgd4M02xt4vNb2WWA+cGBETB6BLkqSJEmSVLRx3e7AEG0P3Nr3R2YujojHgDnAz+sbRsR8YN6I9k4aJTIzut0HMyoNzIxKZTOjUtlKyGg3RWZ2uw9NRcS1wGmZ+a0m930C2DIzj66bdhfwvsz8cQvzLvNJ97hS32tjVUQUuwE0o91hRstiRtXIjJbFjKqRGS1LyRkdKcWdxt+ip4GpDdOmAk91oS+SJEmSJBVltBb7dwI79f1RG4l/OtXgfipUxJjesSYVz4xKZTOjUtnMqEpTXLEfEeNro+1vAIyPiEmxdnKuBTaJiMNqbT8JXJ2ZHtmXJEmSJI15xRX7wNeAZ4E9gQtqv28TEWdGxPEAmfk74O3ACcBjwMuAY7vTXbXDPZ5S2cyoVDYzKpXNjKokxQ7QN5wctKT7xuL7rjQlD1piRrvLfJbBjGogZrQMZlQDMaNlKDmjI6XEI/uSpC7yqIRUNjMqlc2MqhQW++oKN4JS2cyoVDYzKklaF4t9SZIkSeogd8ipBBb76ho3glLZzKhUNjMqlc2Mqtss9tVVbgQlSZIkqfMs9qVB7LDDDnznO98Zs8uXSt8h1+2MdHv5khkte/lSyRntdj66vfyxwK/eUxHG4vuw20r+OhIzWh4zOvLMqFplPrvDjKpVZrQ7Ss7oSPHIviRJ0ihW8pFDSWZU3WOxryKUuhGcPXs2V1xxBeeccw4777wzn/70p5kxYwabb745X/rSlwBYvHgxEydO5MEHH+x/3LPPPsu0adP42c9+BsDcuXOZNWsWU6dOZZddduFHP/pRf9v77ruPffbZh2nTpjF9+nR23313nnnmmTWWD9Ve4VNOOYWXvOQlbLzxxhxwwAHcd999a/T185//PLvtthtTpkxhr7324uGHHx72daSxwYyaUZXNjJpRla3EjJrP3mexr2KUuBGsd8cdd7Dhhhvym9/8hosvvpjjjjuOe++9lxkzZrDffvtx/vnn97e98sormTVrFq9+9asB2GefffjlL3/JsmXLOPTQQznkkEN48sknATjhhBOYM2cOS5cuZfHixZxyyimMGzdureUvWLCAL3zhC1xxxRUsWrSIl7/85Rx44IE899xz/W3OP/98LrzwQpYsWcKGG27IJz7xiWFeK1I5zKhUNjMqlct89qjMHHM3IL2VeSvNNttsk5dffnmeffbZOXPmzDXue+lLX5rf+ta3MjPzoosuyu22267/vje96U35uc99bsD5brTRRnnddddlZuYRRxyRBx10UN59990DLj8zc999980TTzyx/76VK1fmlClT8vrrr+9ve8YZZ/Tff9555+WOO+44YB9q67vreWx26/b70JsZNaNmdLTeSmNGzai3cjPay/nMLDujI3XzyL6KUvLR/c0333yNvzfccMP+vZZvectbeOSRR7jppptYvHgxP/zhD5k7dy4Aq1ev7t+rOXXqVDbaaCOWL1/O0qVLATj55JPZcsst2XfffZk9ezbz589n9erVay1/4cKFzJ49u//vCRMmMGvWLBYuXNg/bebMmU37J3WKGTWjKpsZNaPSUJjP3rT2ORRSl9VGzux2N9oyadIkDjnkEBYsWMDs2bN5zWtew9Zbbw3ABRdcwAUXXMA111zDnDlziAimT5/e/xxnzJjB6aefDsCtt97Kfvvtx0477cTBBx+8xjK22morHnjggf6/V61axaJFi9hqq61G5klKo5gZlcpmRjVW+DnXfI4kj+xLHXL44Ydz0UUXce6553LEEUf0T1+xYgUTJkxg0003ZdWqVcybN48VK1b033/JJZfw0EMPkZlMnz6dcePGNb2Wae7cuZx22mnceeedrFy5knnz5jFr1ix23XXXEXl+Up+SjxwOxoxqrDCjZlRlG40ZNZ+jk8W+ijQaN4J77bUXEydO5O67715jb+WRRx7JDjvswDbbbMO2227L5MmT+/eGAtx0003sscceTJ48md13352jjjqKgw46aK35H3HEEXzgAx/gwAMPZObMmdx8881cddVVTTeY0nAzo2ZUZTOjZlTqJPM5OsVoO42kEyJi7D3pUWosvj9HSu00siI/DZrR0cF8Di8zqvVlRoeXGdX6MqPDq+SMjhSP7EuShmQ0HjmUxhIzKpXNjGq4WeyraG4EpbKZUalsZlSSxi6LfRXPDyqSJEnqRX7O1XCy2JckrRc/qEhlM6NS2cyohovFvkYFN4JS2cyoVDYzKpXNjGo4WOxr1HAjKJXNjEqSJJXDYl+SJGkMcIecVDYzqk6z2Neo4kZQKpsZlcpmRqWymVF1ksW+Rh03glLZzKhUNjMqlc2MqlMs9jUquRGUymZGJUmSustiX6OWxYQkSUPj/1CpbGZUnWCxL0kaFn5QkcpmRqWymVGtr+KK/YiYERHfi4hnIuL2iNhtgHb7RcRtEbEiIm6JiD1Huq/qPjeCUtnMqFQ2MyqVzYxqfRRX7ANnAvcBmwAnApdGxMT6BhHxAuAS4LPANOAk4FsRUeLz0TBzIyiVzYxKZTOjktSbIjO73Yd+ETEFWApsnZmLa9NuBz6SmdfUtdsE+C0wPjOzVuSvArbIzCUtLKecJ62OKem9PBpEBJlZ5Cc8M9p7zGf7zKhGkhltnxnVSDKj7Ss5oyOltCPhc4BlfYV+zW3A9vWNMnMZ8C3gsNpR/rnAL5oV+hExPyKy/jaM/VcXeWRidDKjY4P5HL3M6NhgRkcvMzo2mFENRWlH9vcEvpaZ29VNOwtYmJmfaWj7NuBfganAU8ABmfk/LS6nnCetjirp/Vy6kvd2mtHeZUZbZ0bVDWa0dWZU3WBGW1dyRkdKaUf2n6Yq3uv1FfP9IuJPgLOBNwMTgLcCl0fEZiPRSZXLvZ5S2cyoVDYzKpXNjKodpRX79wCbNBTtOwJ3NrTbEfh5Zt6Qmasz81rgN8CrR6abKpkbQalsZlQqmxmVpN5QVLGfmU8CVwPzImJSRBwGbAxc29D0FmDniPhTgIh4HbAd8KsR7K4K5gcVqWxmVCqbGZXKZT7VqnHd7kATxwDfAB4D7gcOzsyVEXE88KLMPDoz74+23J0AACAASURBVImIDwDnRcQsYBFwTGbe371uqzS163S63Q1JAzCjkiQNjf9D1YqiBugbKQ5aMraMxfd4K0oetMSMjh3mc2BmVCUwowMzoyqBGR1YyRkdKUWdxi8NB091ksplPqWymVGpbGZUg7HY15jghlAql/mUymZGpbKZUQ3EYl+S1HV+UJHKZkalsplRNWOxrzHDjaBUNjMqlc2MSmUzo2pksa8xxY2gVDYzKpXNjEplM6OqZ7GvMceNoFQ2MyqVzYxKZTOj6mOxrzHJjaBUNjMqlc2MSmUzowKLfY1hbgSlsplRqWxmVCqbGZXFvsY0N4JS2cyoVDYzKpXNjI5tFvsa89wISmUzo1LZzKhUNjM6dlnsS7gRlEpnRqWymVGpbGZ0bLLYl2rcCEplM6NS2cyoVDYzOvZY7Et1IsINoVQw8ymVzYxKZTOjY4vFvtSEG0KpXOZTKpsZlcpmRscOi31pAG4IpXKZT6lsZlQqmxkdGyz2pUG4IZTKZT6lsplRqWxmtPdZ7Evr4IZQKpfjbEhlM59S2cxob7PYl1rghlAqmxmVyuVOOals5rN3WexLLXJDKJXNjEplM6NSucxnb7LYl9rghlAqmxmVymZGpXJ5Fk7vsdiX2uSGUCqb+ZTKZkalspnR3mGxLw2RG0KpXO6Uk8pmPqWymdHeYLEvrQc3hFLZzKhULnfKSWUzn6Ofxb60ntwQSmUzo1LZzKhULnfKjW4W+1IHuCGUymY+pbKZUalsZnR0stiXOsgNoVQud8pJZTOfUtnM6OhjsS91mBtCqWxmVCqXO+WkspnP0cViXxoGfliRymY+pbKZUalcfs4dPYor9iNiRkR8LyKeiYjbI2K3AdpNiIgvRsSSiFgeEZeMdF+ldXFDKJXLDytS2cynVDYzWr5x3e5AE2cC9wFvAw4GLo2IbTNzZUO7E4HNgD8GVgA7jWgvpRb1bQgzs8s9kdRMRJhPqVD+D5XKZkbLFiW9MBExBVgKbJ2Zi2vTbgc+kpnX1LXbBPgVsG1mPjmE5ZTzpDWmFJY3MrPIXbJmVN1QUj7BjEqNzGjrzKi6wYyWp7TT+OcAy/oK/ZrbgO0b2u0ELAL+KSKWRcTPI2KfkeqkNFSe7iSVy9P6pbKZUals5rM8pRX7G1Kdkl9vBTC5YdosqoL/UWAL4OPANyNi08YZRsT8iMj62zD0W2qZH1bWZEZVGvO5JjOq0pjRNZlRlcTPuWUp7TT+VwHfycxZddMuBG7MzC/WTXsbcDHwwsx8rjbtJ8DnMvM7LSynnCetMa2b+Sv51CYzqlKY0ebMqEphRpszoypBt+vMkjM6Uko7sn8PsElEbFY3bUfgzoZ2dwBZu0mjlns/pbKZT6lsZlQql59zu6+oYr822N7VwLyImBQRhwEbA9c2tLsb+Dnw9xHxgojYn2pU/htGuMtSR7gxlMplPqWymVGpbOaze4oq9muOoRqo7zHgBODgzFwZEcdHxJl17d4JvJHqmv5/Bg7JzGUj3lupg9wYSuWyoJDKZj6lcvk/tDuKumZ/pHgdk0aD4c5mydcxmVGVbiT+d5pRaejMqBlV2cZ6RkdKiUf2JeERCqlkHqGQymZGpbKZz5FhsS8VzA8rUtnMp1Q2MyqVazR8zo2In0XEX3a7H0NlsS+NAqNhYyiNVeZTKpsZlcpWakYj4gXADsBtwzDv8RFxWkQ8VrudGhHjBmm/ZURcERHLImJpRFzS8A12TVnsS6NIqRtDSeZTKp0ZlcpWYD7/GAiqr4fvtI8Dr6XambADsCdw/CDtv1L7uQ3wYmAS8OV1LcRiXxqFCtwYSqqxoJDKZj6lchX2P/QVwC+BD0fEooj4bUT83w7N+73AZzNzUWYuAv4ROGqQ9i8BLsnMp2pfV38xsNO6FmKxL41ShW0MJTUwn1K5/B8qla2QjO5MdXR/OTAbeA9wakRsXd8oIk6PiCcGub2oof10YCvglrrJtwAviohpA/TlC8BfRsS0iNiI6mvor1rXE7DYl0a5QjaGkpown1LZzKhUti5n9BXANzLzq5m5MjO/C/wG2L6+UWYem5kbDXJ7qGG+k2s/n6ib1vf7lAH6ch0wA3isdtuI6myAQVnsSz3CDyxSucynVDYzKpWtSxl9BdXp8n19CGBTYMl6zvep2s/6o/h9vz/Z2DgiNgB+APyYamfANKpBA69Y14Is9qUe4wcWqVzmUyqbGZXKNlIZjYgZwEzg0brJb6I6An9LQ9szI+KpQW5rnMafmY8DC6kuE+izM/BwZi5v0p2NqQbmOy0zn6lds3868IaIGD/Y87DYl3qUH1ikcplPqWxmVCrbCOTzFcBzwOERsUFEvBI4DfhoZq6ub5iZR2fm5EFujafxA5wNnBARMyNiJtVI/F9v1pHMXArcCxwTERMj4oXA0cAdmfn7wZ7EgN/lJ6k39G0MM7PLPZHUyHxKZTOjUrmGOZ+vAC6jOm3/Maoj/B/LzIsHfVTrPgNsQjXaP8D5wOf67oyIM6HakVCb9Fbgi8Ci2t8/Bd6xroXEWNx4RcTYe9JSTV/mI4LMLPKwhRnVWFX/P9mMSuUxo1K5GuvakjM6UjyyL40xnpYolcujiFLZzKhUrvrPuGa04jX7kiQVxp1yUtnMqFQ2M1qx2JckSZIkqcdY7EuSJEmS1GMs9iVJkiRJ6jEW+5IkSZIk9RiLfUmSJEmSeozFviRJkiRJPcZiX5IkSZKkHmOxL0mSJElSj7HYlyRJkiSpx1jsS5IkSZLUYyz2JUmSJEnqMRb7kiRJkiT1GIt9SZIkSZJ6jMW+JEmSJEk9xmJfkiRJkqQeU2SxHxEzIuJ7EfFMRNweEbuto/0/RERGxKtHqo+SJEmSJJWqyGIfOBO4D9gEOBG4NCImNmsYEVsA7wQWjVz3JEmSJEkqV3HFfkRMAd4MzM/MZzPzPOBxYO8BHnIS8Glg1cj0UJIkSZKkshVX7ANzgGWZubhu2m3A9o0NI2J3YMvMvGygmUXE/Nop/v23zndZ0lCZUalsZlQqmxmVNJASi/0NgRUN01YAk+snRMQGwJeADw82s8ycn5lRf+tobyWtFzMqlc2MSmUzo5IGUmKx/zQwtWHaVOCphmnvBm7LzFtGolOSJEmSJI0WJRb79wCbRMRmddN2BO5saPc64B0RsTQilgJbAz+MiCNHqJ+SJEmSJBUpMsu7rCciLgMeAT4KvB04Gdg2M1fWtZlOdcp/nxuA/wv8V2Y+vY75l/ekpS4o9VQ/MypVzKhUNjMqla3UjI6Ucd3uwACOAb4BPAbcDxycmSsj4njgRZl5dGY+TjVKPwAR8Qdg8boKfUmSJEmSel2RR/aHm3s7pUqpezvNqFQxo1LZzKhUtlIzOlJKvGZfkiRJkiStB4t9SZIkSZJ6jMW+JEmSJEk9xmJfkiRJkqQeY7EvSZIkSVKPsdiXJEmSJKnHWOxLkiRJktRjLPYlSZIkSeoxFvuSJEmSJPUYi31JkiRJknqMxb4kSZIkST3GYl+SJEmSpB5jsS9JkiRJUo+x2JckSZIkqcdY7EuSJEmS1GMs9iVJkiRJ6jEW+5IkSZIk9RiLfUmSJEmSeozFviRJkiRJPcZiX5IkSZKkHmOxL0mSJElSj7HYlyRJkiSpx1jsS5IkSZLUYyz2JUmSJEnqMRb7kiRJkiT1GIt9SZIkSZJ6jMW+JEmSJEk9xmJfkiRJkqQeU1yxHxEzIuJ7EfFMRNweEbsN0OabEbE4IpZFxOURMbMb/ZUkSZIkqTTFFfvAmcB9wCbAicClETGxoc2GwH8D2wOzgEXAWSPZSUmSJEmSShWZ2e0+9IuIKcBSYOvMXFybdjvwkcy8ZpDH7QR8PzO3aHE55TxpqYsyM7rdh2bMqFQxo1LZzKhUtlIzOlJKO7I/B1jWV+jX3EZ1BH8wrwF+1eyOiJgfEVl/61BfJXWAGZXKZkalsplRSQMp7cj+nsDXMnO7umlnAQsz8zMDPObFwP8CB2fmj1tcTjlPWuqiUvd2mlGpYkalsplRqWylZnSklHZk/2lgasO0qcBTzRpHxKbAvwMfb7XQlyRJkiSp15VW7N8DbBIRm9VN2xG4s7FhREymKvQvzMyvjlD/JEmSJEkqXlHFfmY+CVwNzIuISRFxGLAxcG19u4iYAFwO3JSZnxrxjkqSJEmSVLCirtkHiIjNgW8AewL3A0dl5v9ExPHAizLz6IjYi2oHwDNA/xPIzMktLqOsJy11SanXMZlRqWJGpbKZUalspWZ0pBRX7I8EN4BSpdQNoBmVKmZUKpsZlcpWakZHSlGn8UuSJEmSpPVnsS9JkiRJUo+x2JckSZIkqcdY7EuSJEmS1GMs9iVJkiRJ6jEW+5IkSZIk9RiLfUmSJEmSeozFviRJkiRJPcZiX5IkSZKkHmOx32Uf+9jHuOCCC8Z8H6RSlZCPEvoglaqEfJTQB6lEJWSjhD5I3RKZ2e0+jLiIGHtPWmoiM6PbfWjGjEoVMyqVzYxKZSs1oyPFI/uSJEmSJPUYi/0huP/++/n7v/97brjhBlasWMG1117LVltt1X//LrvswnXXXcfjjz/OHXfcwaGHHjrgvObNm8fll1/e/3dmcvTRR3PbbbexfPlyrrzySqZOnQrAlVdeycc//vE1Hv/Vr36VU089FYDDDjuM2267jRUrVvDggw/y6U9/eo22J510EosWLWLFihX8+te/5s1vfnPTPgzW/3nz5vHtb3+bU089lccff5wHH3yQd7zjHe2uQmlYmVEzqrKZUTOqcplP86kekplj7gbk+tzuv//+/MUvfpGzZ8/OiRMn5tVXX51nn312Ajlt2rRcsmRJvv/9789x48bla1/72ly+fHnuscceTec1b968vPzyy/v/zsz8j//4j9xss81y2rRpedNNN+W8efMSyIMPPjjvuuuu/rYTJkzIxx9/PHfdddcE8oADDsg5c+YkkK94xSvy0UcfzcMOOyyB3H///fOhhx7KLbbYIoHceuut+9vW92Fd/Z83b16uXLky3/GOd+QGG2yQhx9+eK5YsSInT568XuvUW3du3c6iGTWj3ga/dTuLZtSMehv81u0sDkdGzaf57KVbt7PY7ZtH9ofo9NNP54EHHmDlypWcf/757LLLLgC8+c1vZsmSJZx22mk899xzXHfddVxwwQUceeSRLc/7pJNOYsmSJSxfvpxLL720f95XXXUVm222GbvuuisABx10EL/97W+58cYbAfje977HPffcA8AvfvELLrzwQvbee28AVq1axaRJk9hhhx0YN24cDz/8cH/beq30/+abb+aSSy5h9erVLFiwgAkTJvCyl72s/ZUoDSMzakZVNjNqRlUu82k+1Rss9ofo0Ucf7f/96aefZsqUKQBstdVWPPDAA2u0feCBB9Y4/Wmo8161ahXf/OY3mTt3LgBHHHEE3/jGN/rb7r///lx//fUsWbKEJ554gqOPPppNN90UgGuvvZZ58+bxmc98hqVLl/Ktb32L2bNnr7XsVvpf3z+AZ599tr+PUinM6PPMqEpkRp9nRlUa8/k886nRzGK/wxYuXLjWxmX27NksXLiwI/NfsGABhx56KFtssQX7778/5513HgDjx4/nsssu46yzzmLLLbdko4024swzzyTi+QEozzjjDHbffXe22WYbfv/73/PlL395xPsvdZsZlcpmRqVymU9pdLHY77Dvfve7zJgxg2OOOYYXvOAF7LHHHhx22GFr7JlcH9dddx1PPfUU//Zv/8YNN9zAQw89BMDEiROZNGkSy5YtY9WqVey22268613v6n/cq1/9anbffXfGjx/PM888w5NPPslzzz034v2Xus2MSmUzo1K5zKc0uljsd9gTTzzBG9/4RubOncuyZcv4+te/zrHHHsv111/fsWWcd955HHDAAWtsmJ566in+5m/+hq9+9assX76cj33sY1x00UX990+dOpXTTz+dZcuW8eijjzJr1iw+9KEPdaX/UjeZUalsZlQql/mURpeojdg5pkTE2HvSUhOZGetuNfLMqFQxo1LZzKhUtlIzOlI8si9JkiRJUo+x2JckSZIkqcdY7EuSJEmS1GMs9iVJkiRJ6jEW+5IkSZIk9RiLfUmSJEmSeozFviRJkiRJPcZiX5IkSZKkHmOxL0mSJElSjymu2I+IGRHxvYh4JiJuj4jdBmg3JyJuqLX7n4iYM9J9lSRJkiSpRMUV+8CZwH3AJsCJwKURMbFJu4uBq4CNgW8DF41YDyVJkiRJKlhkZrf70C8ipgBLga0zc3Ft2u3ARzLzmrp22wE3AJtl5nMRMQ5YAuyWmXe1sJxynrTURZkZ3e5DM2ZUqphRqWxmVCpbqRkdKaUd2Z8DLOsr9GtuA7ZvaLc98MvMfA6g9vNXTdoREfMjIutvw9R3SUNgRqWymVGpbGZU0kBKO7K/J/C1zNyubtpZwMLM/EzdtMOBd2XmAXXTrgHOy8wFI9nnoYiILH0vU+l9LL1/UH4fS+9fN42GdVN6H0vvH5Tfx9L7102jYd2U3sfS+wfl97H0/nXTaFg3pfex9P5B+X0svX8jobQj+08DUxumTQWeGmI7SZIkSZLGnNKK/XuATSJis7ppOwJ3NrS7E/iT2rX61H5u16SdJEmSJEljTlHFfmY+CVwNzIuISRFxGNVo+9c2tPsVcD/w0dpI/R8F7mtlcD5JkiRJknpdUcV+zTFUA/U9BpwAHJyZKyPi+Ig4s67docBbgSeAtwHvHPGeDt2nut2BFpTex9L7B+X3sfT+ddNoWDel97H0/kH5fSy9f900GtZN6X0svX9Qfh9L7183jYZ1U3ofS+8flN/H0vs37IoaoE+SJEmSJK2/Eo/sS5IkSZKk9WCxL0mSJElSj7HYlyRJkiSpx1jsS5IkSZLUYyz2JUmSJEnqMRb7kiRJkiT1GIt9SZIkSZJ6jMW+JEmSJEk9xmJfkiRJkqQeY7EvSZIkSVKPsdiXJEmSJKnHWOxLkiRJktRjLPYlSZIkSeoxFvuSJEmSJPUYi31JkiRJknqMxb4kSZIkST3GYl+SJEmSpB5jsS9JkiRJUo+x2JckSZIkqcdY7EuSJEmS1GMs9iVJkiRJ6jEW+5IkSZIk9RiLfUmSJEmSesyQiv2IeGFEbNrpzkiSJEmSpPXXVrEfEdtExH8CK4DfRsTyiLg4IvYZnu5JkiRJkqR2RWa23jjiOmB74CTgXmAL4ABgf+BrwLHZzgwlSZIkSVLHtVvs/w7468xc0DB9D+A7wBcz8zOd7aIkSZIkSWpHu9fsPwU80TgxM38CzAP+byc6JUmSJEmShq7dYv9K4AMREU3uuxvYaH07FBGfiog7I2J1RBwySLs/i4jbI+KZiLgmImas77IlSZIkSeoF7Rb7HwW2Bm6IiDdFxESAiJgKvB/49w706R7gQ8CNAzWIiEnAZcCJwCZU4wec0YFlS5IkSZI06rVV7Gfm48BrgTupjvI/FRFLgGXAzsC5ETFtfTqUmedl5g+A3w3SbG/g8VrbZ4H5wIERMXl9li1JkiRJUi8Y1+4DMnMZ8N6I+DCwH7ALVaH/CuDbQEbEg8DPM/PgTna2zvbArXV9WhwRjwFzgJ/XN4yI+VTjCUhqkJnNLskZUWZUGpgZlcpmRqWylZDRbmprNP51zixiJlXh/0rg5Zn5zvWY17XAaZn5rSb3fQLYMjOPrpt2F/C+zPxxC/P26wE7wG9ZHN0iotgNoBntDDM6upnR3mdGRzcz2vvM6OhWckZHSttH9geTmY8C36vdhtPTwNSGaVOpvi1AI6QWoG53Q9IAzKhUNjMqlc2MarRrd4C+UtwJ7NT3R20k/ulUg/tJkiRJkjSmFVfsR8T42mj7GwDjI2JSk6/6uxbYJCIOq7X9JHB1Znpkf4Q1/xZGSaUwo1LZzKhUNjOq0ay4Yh/4GvAssCdwQe33bSLizIg4HiAzfwe8HTgBeAx4GXBsd7orSZIkSVJZOjpA32jhoCWdNxbfR6NdyYOWmNHOM6OjjxkdW8zo6GNGxxYzOvqUnNGR0rEj+xHxuojYrlPzkyRJkiRJQ9PJ0/ivBe6IiP+IiDd3cL4aBbyeSSqbGZXKZkalsplRjUadLPZfDxwI/Bj4YAfnK0mSJEmS2uA1++qosfh+Gq1Kvo7JjA4fMzp6mNGxyYyOHmZ0bDKjo0fJGR0pJY7GL0mSJEmS1sOQiv2I2D4iDo+I4yNiZm3aSyNiSme7p9Gm165n2mGHHfjOd74zZpev3mNGe2v56j1mtLeWr97TSxntdj66vfyxoK3T+CNiMvBvwMHAc8A44E8z8+aIuAR4KDM/Oiw97SBPbRpent40OpR8apMZHV5mdHQwo2OXGR0dzOjYZUZHh5IzOlLaPbL/BWAPYF9gClC/8r4LHNChfmkU66U9nlIvMqNS2cyoVDYzqtGi3WL/7cA/ZOaPgD803PcgsE1HeqVRr1c2grNnz+aKK67gnHPOYeedd+bTn/40M2bMYPPNN+dLX/oSAIsXL2bixIk8+OCD/Y979tlnmTZtGj/72c8AmDt3LrNmzWLq1Knssssu/OhHP+pve99997HPPvswbdo0pk+fzu67784zzzyzxvKh2ot8yimn8JKXvISNN96YAw44gPvuu2+Nvn7+859nt912Y8qUKey11148/PDDw76OpG4yo1LZzKhULvPZ+9ot9v8IWDbAfVNYeweA1DPuuOMONtxwQ37zm99w8cUXc9xxx3HvvfcyY8YM9ttvP84///z+tldeeSWzZs3i1a9+NQD77LMPv/zlL1m2bBmHHnoohxxyCE8++SQAJ5xwAnPmzGHp0qUsXryYU045hXHjxq21/AULFvCFL3yBK664gkWLFvHyl7+cAw88kOeee66/zfnnn8+FF17IkiVL2HDDDfnEJz4xzGtFo1Wv7JCrZ0bVS8yoGVXZei2j5rM3tVvs/xQ4YoD7DgF+sn7dUS/ptY3gpptuykc+8hHGjx/P3nvvzezZs7nlllsAOPzww1mwYEF/2wULFnDEEc9H5T3veQ/Tpk1j/PjxHHfccaxevZpbb70VgAkTJrBo0SIeeOABxo8fzx577MGECRPWWv6CBQv44Ac/yE477cTEiRP57Gc/y8KFC7nxxhv72xx77LG8+MUvZtKkSbzrXe/ipptuGq7VoR5gRs2oNJLMqFQu89mb2i32Pw68PSJ+CLwPSOBNEbEAeAcwr8P9k4qx+eabr/H3hhtu2L/X8i1veQuPPPIIN910E4sXL+aHP/whc+fOBWD16tX9ezWnTp3KRhttxPLly1m6dCkAJ598MltuuSX77rsvs2fPZv78+axevXqt5S9cuJDZs2f3/z1hwgRmzZrFwoUL+6fNnDmzaf+kscCMqtf02g45M6pe00sZNZ+9ae1zKAaRmddFxD7AicBpVAP0fQr4H2CfzPxp57uo0aw2Cma3uzHsJk2axCGHHMKCBQuYPXs2r3nNa9h6660BuOCCC7jgggu45pprmDNnDhHB9OnT+9fLjBkzOP300wG49dZb2W+//dhpp504+OCD11jGVlttxQMPPND/96pVq1i0aBFbbbXVyDxJ9SQzakZVNjNqRqVuM5+jV1tH9iPik8D9mbknMBXYCpiSma8B7qvdL41Jhx9+OBdddBHnnnvuGqc2rVixggkTJrDpppuyatUq5s2bx4oVK/rvv+SSS3jooYfITKZPn864ceOaXss0d+5cTjvtNO68805WrlzJvHnzmDVrFrvuuuuIPD9ptDOjUtnMqEajXjq6PxjzOTq1exr/PKoCn8x8NjMfycxnavfNwtP41cRY2QjutddeTJw4kbvvvnuNvZVHHnkkO+ywA9tssw3bbrstkydP7t8bCnDTTTexxx57MHnyZHbffXeOOuooDjrooLXmf8QRR/CBD3yAAw88kJkzZ3LzzTdz1VVXNd1gSu0wo2ZUZTOjZlRlGwsZNZ+jU7RzalhErAb+rNnp+hHxFuBfM3PTDvZvWERE758PV6CxcBriaFI7NbTI/05mdOSZz/KYUdUzo+Uxo6pnRstTckZHyjp3lUTEkcCRtT8TOCMiVjQ0mwTsBHy/s92TJI2EsXJdsDRamVGpbGZUJWrlvIhngGW13wNYDjzW0GYV8O/A6Z3rmnqNG0GpbGZUKpsZlSS1o93T+M8GPp2Z9w9fl4afpzZ1jx9SylHyqU1mtHvMaDnMqJoxo+Uwo2rGjJaj5IyOlLaK/V7hBrC7xuJ7rkQlbwDNaHeZ0TKYUQ3EjJbBjGogZrQMJWd0pLQ7Gr+03sbCiKXSaGZGJUmSRr+2v8sgIv4K+GvgZVQD860hM2d0oF+SJElqwmv3pbKZUZWirSP7EXEYcC7wa2Ar4NvAd2rzWQGc1ukOqjd55FAqmxmVymZGpbKZUZWg3dP4jwM+A/xN7e/TM/O9wIuBpVQj90stcSMoSZIkScOj3WJ/DnB9Zv4B+AMwFSAznwQ+D7y/s92TJHWLO+SksplRqWxmVN3WbrG/HJhY+/03wJ/U3RfAJp3olMYON4JS2cyoVDYzKpXNjKqb2h2g72fAy4FrqK7X/2REPAesAj4J/G9nu6exwEFMJEmSJKmz2i32/wnYpvb7J2u/nw684P+zd+/Rctfl3fffF+TUh5AAIdGEAJHe8cBBsNAU8ISLyoPio22hFEMA7cEGj2sV5X441B3B+y7SWruEBwF7ixIOchYUhVZtegulBVEggCJKAgQTciBkA+FOgFzPHzPZTDZ7Z+/Zew7fmf1+rfVb7Jn5zsy1N/n8Zq7f4fsD7gE+1rjSJEklcIOcVDYzKpXNjKpdhn0Yf0SMp9LU/wQgM5/NzA8Bk4FdMvMPMvOx0RYUETMi4raI2BgRD0bEoYOMe29ELI2I3oi4LyLeOdr3Vvt4iJNUNjMqlc2MSmUzo2qHes7ZfwX4Mduep09mbsrM3gbWdDHwGJXz/88DboiIibUDImJH4Frgi8BU4Hzg+oiodw4CieSsuQAAIABJREFUFcSVoFQ2MypJktQ5ht0cZ+YW4FHgdc0qJiJ2Bo4BFmXmi5l5BbAeOKLf0F2AnYFrs3JMzLepbBxwgsAOZzMhSdLI+Bkqlc2MqtXq3RN+FpVJ+Q5oRjFULu23LjNX19y3FNi3dlBmrgOuB+ZX9/IvAO7PzDVNqkuShF9UpNKZUalsZlStVG+zfzaVvef3RcQTEXFPRNxdu4yynp2A/qcE9FKZF6C/a4ALgE3AV4FPDPSCEbEoIrJ2GWWNajJXgmOLGe08ZnRsMaOdx4yOLWZU0mCinpkhI+KyocZk5kdHXEzE7wHfy8xZNfddDdydmV+pue8twF3A+6hc7u9dwNXAW4ezd9+VYGdw1tLmqs4MW+Q3QjNaPvPZfGZUo2FGm8+MajTMaPOVnNFWqevSe6Np5IfpUWBaREyvadr3B77Zb9z+wM8z867q7SUR8RRwCPCDJteoFvEyJVK5zKdUNjMqlc2MqhWKmr0+M58DbgV6ImJSRMwHdgOW9Bt6H3BQRPw+QES8C3gz8MsWlitJY5qHCktlM6NS2cyomq2uPfstcipwOfAMsAw4NjM3RcSZwF6ZuTAzH42ITwFXRMQsYCVwamYua1/Zaga3ekplM6NS2cyoJI1ddZ2z3y08j6nzjMV/p81W8nlMZrTzmNHGM6NqFPPZHGZUjWJGm6PkjLZKUYfxS4PxMCdJkkbGz1CpbGZUzWKzL0kaNb+oSGUzo1LZzKiaYUTn7EfEG4HZwKT+j2Xm90dblDQQzzuUymZGpbKZUalsZlSNVlezHxH7AtcA+wIDbX5KYMcG1CUNyJWgVDYzKpXNjErS2FHvnv1LgAnAnwAPA5sbXpE0BL+oSGUzo5IkjYyfoWqkepv9twEnZOb3mlGMNFyuCKWymVGpXOZTKpsZVaPUO0HfbxjgPH2pHZzIRJKkkfEzVCqbGVUj1NvsnwacGRH7NKMYqV6uCKVymU+pbGZUKpsZ1WhFPYeIRMQ9wF7ArsBy4Nn+YzJzXqOKa5aI8LiYLuJhTiNTPUSsyE8RM9pdzOjImFG1ihkdGTOqVjGjI1NyRlul3nP2H6wuUjE8r0kqmxmVymZGpbKZUY1UXXv2u4VbO7vTWPy3PBolb+00o93JjNbHjKrVzGh9zKhazYzWp+SMtkq9e/YBiIhZwGHAbsA64D8z87eNLEyql1s9pbKZUalsZlQqmxlVvepq9iNiR+AC4K+AHWseeiUiLgU+lZlbGlifVBdXglLZzKhUNjMqSd2j3tn4vwD8OXAmMAf4nep/z6zev6hxpUkj48ylUtnMqFQ2MyqVy3yqHvXOxv8E8NXM/IcBHvss8OnM3KuB9TWF5zGNDe6Z2L6Sz2Myo2ODGd0+M6p2M6PbZ0bVTuZzaCVntFXq3bM/A3hgkMceqD4uFcEtn1LZzKhUNjMqlct8ajjqbfZ/BZwwyGMnAI+MrhypsVwRSmUzo1LZzKhULvOpodQ7G/8XgW9HxF7A9cDTVPbm/ynwHgbfECC1jZMNSWUzo1LZzKhULvOp7anrnH2AiDiKykR9vweMB14C7gV6MvNfG15hE3ge09jkinBbJZ/HZEbHJjO6LTOq0pjRbZlRlcR8vlbJGW2Vupv9vidG7ADsDqzttMvtuQIcu1wRvqrkFaAZHbvM6KvMqEpkRl9lRlUa87mtkjPaKvWes98nM7dk5upOa/Q1tnluk1Q2MyqVzYxK5YoIM6ptDHnOfkTcDXwkMx+OiHuA7W4yysx5jSpOagbPbZLKZkalsplRqWxmVFsNZ4K+h4AXa372X4463tatnq4IpTL5RUUqmxmVymZGBaM4Z7+TeR6Tao3FDEDZ5zGZUW01VvMJZlSdwYyaUZXNjJaZ0VYZ8Tn7tSJil0a8jtQOntsklct8SmUzo1LZzOjYVlezHxGnRsTpNbcPiogVwLqIuDciZje8QqkFXBFK5XLCIals5lMqmxkdu+rds/8poLfm9leB3wInVl/rvAbVJbWcK0KpbGZUKpf5lMpmRsem4UzQV2sv4BGAiJgOvB04MjOXRMRm4MIG1ye1lJOZSGUzo1K5nPxWKpufoWNPvXv2NwETqj+/B9gI/KR6+xnAc/fV8TxkWCqb+ZTKZkalcvk9d2ypt9m/G/hEROwHfBq4LTNfqT62D5VD+kclImZExG0RsTEiHoyIQwcZNyEivhIRayJiQ0RcO9r3lmq5IpTKZT6lsplRqWxmdGyot9k/DdgXWArsCZxV89ifAXc2oKaLgceAaVTmALghIiYOMO48YDrwpurYv2vAe0vbcEUolcu9E1LZzKdUNjPa/WIk521ExDTgmax5ckQcAKzKzDUjLiZiZ2AtsGdmrq7e9yBwWmbe3u/9fwnsk5nPjeB9PFlFdenG85tKvvaoGVW9zGhrmVHVy4y2lhlVPboxn1B2Rlul3j37AGTmun6N/i6ZuXQ0jX7VXGDd1ka/aimVowlqHQCsBP4uItZFxM8j4siBXjAiFkVE1i6jrFFjkHsQm8eMqhHMZ/OYUTWCGW0eM6rR8ntu96qr2Y+IUyPi9JrbB0XECmBdRNwbEbNHWc9ObHtpP6q3J/e7bxaVhn8VMBM4G7guInbv/4KZuSgzo3YZZY0aw1wRNp4ZVaOYz+Ywo2oUM9ocZlSNYka7T7179j/Fts34V6lMyndi9bXOG2U9LwBT+t03BXi+330vAi8B52Xm5sy8lcph/QNO5ic1kitCqVzunZDKZkalspnP7jKuzvF7AY8ARMR04O3AkZm5JCI2AxeOsp5HgWkRMb3mlID9gW/2G/cQkNVFajmvJSyVzWsJS2Uzo1K5/J7bPerds78JmFD9+T3ARuAn1dvPALuMppjqZHu3Aj0RMSki5gO7AUv6jfsV8HPg9IjYMSKOojIr/12jeX+pXm79lMrlHkSpbOZTKpsZ7Xz1Nvt3A5+IiP2ATwO3ZeYr1cf2oXJI/2idSmWivmeoXNrv2MzcFBFnRsTFNeM+DLyPymkF/wAcl5nrGvD+Ul1sKKSymU+pXH6GSmUzo52trkvvRcS+wC1UGvsngfdW97ITEbdTufTeKc0otJGcpVTN0kmHO5V8ORIzqmbopHyCGdXYY0Ybx4yqGcxo56mr2e97UuU698/0u/zeAVSa/dFefq/pXAGq2TphZVjyCtCMqpk6IZ9gRjV2mdHRM6Nqlk7JJzQmoxHxU+BLmXldg8pqqXoP4wcgM9dlv//Tmbm0Exp9qRU83Ekql/mUymZGpXKNpcP6I2JHYD9gaRNee3xEXBgRz1SXCyJi0MnzI+J3I+IHEbE+Ip6KiNOH8z5DzsYfEXcDH8nMhyPiHoaYAT8z5w3njaVu50ymUrnMp1Q2MyqVbYxcUeNNQFC5YlyjnQ28g8rGBIAfAGcC5/QfWN3ocAvwHeCDVE6p/9eIWJGZV23vTYazZ/8hKte13/rzUIukGmNl66fUicbSHgqpE5lPqVxj4DP0QOAXwN9ExMqIeDoi/rpBr/3nwBczc2VmrgT+B/AXg4x9U3X5Qma+lJmPAP8L+NhQbzLknv3M/GjNzx8ZRuGS+nEPhVS2MbKHQupIfoZKZevijB5EpcneAMwBjgS+ExHfz8wntw6KiIuA+dt5nbdm5hM143cFZgP31Yy5D9grIqZm5oZ+z9+6gz763ffWoX6BEU3Q1+mctETtVErmnFhIGpgZHZoZVTuZ0aGZUbVLKfmE0Wc0Im4Dlmfmwpr7lgELM/P2UbzunsATwPTMXFu9bzqwGtgzM1f0Gz+eyhEGNwCfB/4bcBswMzO3u/N+yD37gxT4JmAPYFL/xzLz+yN5TWms6OKtn1JXcC+/VDYzKpWry77nHgh8aeuNqPxyuwOjnZT++ep/pwJra34GeK7/4Mx8KSI+BHwFeApYAVwGDHlKQV3NfvXyelcDb2Hbwwj6agF2rOc1pbGqy1aGUlcxn1LZzKhUtk7PaETMAF4PrKq5+/3As2x7+D0RcTGwYDsvt2/tYfyZuT4iVlA5TeA31bsPAp4c4BD+rc95CDiq5j2/BPz7UL9HvXv2vwG8BHwA+DWwuc7nS+qn01eGUjczn1LZzKhUtg4+EudA4GXgpIg4u3r7QuCzmbmldmD1MP+Fr32J7boMOCsi7qzePhP458EGR8RbqWwY2NqL/zmVOQS2q95m/y3AsaM5R0HSwDp4ZSh1PRsKqWx+hkrl6tDP0AOBG6kctv8MlT38Z2TmNQ16/XOBaVTOxQe4EvifWx+sHi1AzXwBxwMfByYC9wN/lJkPDPUmdU3QFxE/Bq7OzK8P+0kFctISla4VK0MnFpJGplVfVsyoNDJm1IyqbGa0derds/8x4OqI2Aj8G5VzFraRmRsbUZg0lnXoFlBpTDCfUtnMqFQ2M9o69Tb7a4HlwOXbGeMEfVKDuDKUymU+pbKZUalsnn7TfPU2+1cAhwH/gBP0SS3jFxapXOZTKpsZlcplPpur3nP2XwD+KjOval5Jzed5TOp0jVghlnwekxlVJ2vUFxYzKjWHGZXK1cimv+SMtsoOdY5fDnhOvtRmEdG3JVRSWcynVDYzKpXLfDZWvc3+56hcD3BO40uRVC9XiFK5zKdUNjMqlct8Nka9h/HfA+wF7EplL/9As/HPa1RxzeKhTepWdea52EObzKi6Ub2HJppRqbXMqFSukRzeX3JGW6XeCfoerC6SCuQkJ1K5zKdUNjMqlat2L78ZHb669ux3C7d2aqzYXr5L3tppRjUWDPX5a0al9jKjUtk6OaOtUu85+wOKiF0a8TqSGsvznaRybc2nGZXKZD6lspnRodXV7EfEqRFxes3tgyJiBbAuIu6NiNkNr1DSqNlUSGUzn1K5/AyVymY+B1fvnv1PAb01t78K/BY4sfpa5zWoLklN4gpRKpf5lMpmRqVyuWHuteqdoG8v4BGAiJgOvB04MjOXRMRm4MIG1ydJ0pjjFxWpbGZUKpsZrah3z/4mYEL15/cAG4GfVG8/A3juviRJkiRJbVbvnv27gU9Uz9P/NHBbZr5SfWwfKof0S5IkSZKkNqp3z/5pwL7AUmBP4Kyax/4MuLNBdUmSJEmSpBGKoa5POOCTIqYBz2TNkyPiAGBVZq5pYH1N4bVHpYpSrz1qRqUKMyqVzYxKZSs1o61S7579raYB74mI929dqOzp//1GFBURMyLitojYGBEPRsShQ4z/7xGREXFII95fkiRJkqROVtc5+xGxL3ANlUP5B9pKksCODajrYuAx4I+BY4EbImKfzNw0QE0zgQ8DKxvwvpIkSZIkdbx69+xfQmU2/j8B3gS8od+yz2gLioidgWOARZn5YmZeAawHjhjkKecD5wCbR/vekiRJkiR1g3qb/bcBp2XmzZn5aGY+3n9pQE1zgXWZubrmvqVUjibYRkQcBuyRmTcO9mIRsah6iH/f0oAaJTWIGZXKZkalsplRSYOpt9n/DTCpGYXU2Ano7XdfLzC59o6I2AH4J+BvtvdimbkoM6N2aWi1kkbFjEplM6NS2cyopMGM5NJ7Z0bEqA/X344XgCn97psCPN/vvo8ASzPzvibWIkmSJElSx6nr0nsRcQ+wF7ArsBx4tv+YzJw3qoIq5+yvBWZvvYxfRCwFPpuZt9eM+yaVuQO2nqu/K/Ac8JnM/NYQ7+HhTRLlXo7EjEoVZlQqmxmVylZqRlul3mb/sqHGZOZHR1VR5X1uBH4LfJZKQ//3wDaz8UfErlQO+d/qLuCvgX/PzBeGeH1XgBLlrgDNqFRhRqWymVGpbKVmtFXquvReIxr5YToVuBx4BlgGHJuZmyLiTGCvzFyYmeupzNIPQES8AqweqtGXJEmSJKnb1bVnv1u4tVOqKHVrpxmVKsyoVDYzKpWt1Iy2Sl179gEi4s+AvwLeyAAz82fmjAbUJUmSJEmSRqiu2fgjYj7wLeDXwGzgFuB71dfpBS5sdIGSJEmSJKk+9V5673PAucAnqrcvysw/B95AZQb9jQ2sTZIkSZIkjUC9zf5c4M7MfAV4BZgCkJnPAV8CPtnY8iRJkiRJUr3qbfY3ABOrPz8FvKXmsQCmNaIoSZIkSZI0cvVO0PdT4K3A7VTO1/98RLwMbAY+D/xXY8uTJEmSJEn1qrfZ/ztg7+rPn6/+fBGwI3AP8LHGlSZJkiRJkkYiMkd3Gc6ImAhMzMzexpTUfF57VKoo9dqjZlSqMKNS2cyoVLZSM9oqwz5nPyLGR8TbI2JW7f2ZuamTGn1JkiRJkrpdPRP0vQL8mG0n5ZMkSZIkSYUZdrOfmVuAR4HXNa8cSZIkSZI0WvVeeu8sKjPwH9CMYiRJkiRJ0ujVNUFfRNwDzAF2A54Cnga2eYHMnNfA+prCSUukilInLTGjUoUZlcpmRqWylZrRVqn30nsPVpfBuGKRJEmSJKnN6m32lwH/nJm/7f9ARMwE/qohVUmSJEmSpBGr9zD+V4DDMvPuAR47GLg7M3dsYH1N4aFNUkWphzaZUanCjEplM6NS2UrNaKvUO0FfMPih+rOB9aMrR5IkSZIkjdaQh/FHxCnAKdWbCXwtInr7DZsEHAD8S2PLkyRJkiRJ9RrOOfsbgXXVnwPYADzTb8xm4AfARY0rTZIkSZIkjUS95+xfBpyTmcuaV1LzeR6TVFHqeUxmVKowo1LZzKhUtlIz2ip1NfvdwhWgVFHqCtCMShVmVCqbGZXKVmpGW6XeCfokSZIkSVLhbPYlSZIkSeoyNvuSJEmSJHUZm31JkiRJkrqMzb4kSZIkSV1m3FADIuIeYNgzembmvFFVJEmSJEmSRmXIZh94iDqafUmSJEmS1F6RWVYfHxEzgMuBdwGPAX+Zmf85wJj/D3g3sCPwv4FTM3PVMN+jrF9aapNSrz1qRqUKMyqVzYxKZSs1o61S4jn7F1Np8qcB5wE3RMTEfmN2otLg7wvMAlYCl7SySEmSJEmSSlXUnv2I2BlYC+yZmaur9z0InJaZt2/neQcA/5KZM4f5PuX80lIblbq104xKFWZUKpsZlcpWakZbpe49+xHxZxHxw4h4IiJW919GWc9cYN3WRr9qKZU9+NvzduCXo3xvSZIkSZK6Ql3NfkTMB74F/BqYDdwCfK/6Or3AhaOsZ6fq69TqBSZvp6Y3AOcAnx/k8UURkbXLKGuU1EBmVCqbGZXKZkYlDaauw/gj4ufA9VTOpX8JOCQzf1Y9/P5fgesz8x9GXEzE7wHfy8xZNfddDdydmV8ZYPzuwB3AP2bmpXW8jytBiXIPbTKjUoUZlcpmRqWylZrRVqn3MP65wJ2Z+QrwCjAFIDOfA74EfHKU9TwKTIuI6TX37Q883H9gREwGfgBcXU+jL0mSJElSt6u32d8AbJ0Z/yngLTWPBZUZ9EesutHgVqAnIiZVTxvYDVhSOy4iJgA3Afdm5hdG856SJEmSJHWbcXWO/ynwVuB2Kufrfz4iXgY2Uzln/r8aUNOpwOXAM8Ay4NjM3BQRZwJ7ZeZC4DDgD4HDI2LB1idm5qDn9kuSJEmSNFbUe87+ocDemXlNROxCZbK+9wM7AvcAH87Mx5pSaQN5HpNUUep5TGZUqjCjUtnMqFS2UjPaKnU1+wO+QMREYGJm9p9Fv1iuAKWKUleAZlSqMKNS2cyoVLZSM9oq9V5678CIeH/tfZm5KTN7I+L9EfHWxpYnSZIkSZLqVe8EfV8B/mCQx36/+rgkSZIkSWqjepv93wPuHOSxu4C3ja4cSZIkSZI0WvU2+zsCOw3y2E7AhNGVI0mSJEmSRqveZv8e4GODPPYxKpfmkyRJkiRJbTSuzvGLgB9GxH9RuezeKmAmcDJwIPDehlYnSZIkSZLqVvel9yLiCODvgHlAAFuA/wL+38z8SaMLbAYvRyJVlHo5EjMqVZhRqWxmVCpbqRltlbqb/b4nRvxfwK7A+szc2NCqmswVoFRR6grQjEoVZlQqmxmVylZqRlul3nP2+2Tmxsx8qtMa/dKcccYZXHXVVWO+BqlUJeSjhBqkUpWQjxJqkEpUQjZKqEFqlyH37EfE3cBHMvPhiLgH2O4TMnNeA+trCrd2ShWlbu00o1KFGZXKZkalspWa0VYZzgR9DwEv1vzsykOSJEmSpIINeRh/Zn40M5dVf/5I9fagS/NLbr9ly5Zx+umnc9ddd9Hb28uSJUuYPXt23+MHH3wwd9xxB+vXr+ehhx7ihBNOGPS1enp6uOmmm/puZyYLFy5k6dKlbNiwgZtvvpkpU6YAcPPNN3P22Wdv8/xLL72UCy64AID58+ezdOlSent7efzxxznnnHO2GXv++eezcuVKent7+fWvf80xxxwzYA3bq7+np4dbbrmFCy64gPXr1/P4449z/PHH1/snlJrKjJpRlc2MmlGVy3yaT3WRzBz2AnwemDXIYzOBz9fzeu1aqBydMOJl2bJlef/99+ecOXNy4sSJeeutt+Zll12WQE6dOjXXrFmTn/zkJ3PcuHH5jne8Izds2JCHH374gK/V09OTN910U9/tzMwf/ehHOX369Jw6dWree++92dPTk0Aee+yx+cgjj/SNnTBhQq5fvz7nzZuXQB599NE5d+7cBPLAAw/MVatW5fz58xPIo446Kp944omcOXNmArnnnnv2ja2tYaj6e3p6ctOmTXn88cfnDjvskCeddFL29vbm5MmTR/U3dWnP0u4smlEz6rL9pd1ZNKNm1GX7S7uz2IyMmk/z2U1Lu7PY7qXeCfp6gNmDPDar+viYcNFFF7F8+XI2bdrElVdeycEHHwzAMcccw5o1a7jwwgt5+eWXueOOO7jqqqs45ZRThv3a559/PmvWrGHDhg3ccMMNfa/93e9+l+nTpzNvXmVahA9+8IM8/fTT3H333QDcdtttPProowDcf//9XH311RxxxBEAbN68mUmTJrHffvsxbtw4nnzyyb6xtYZT/89+9jOuvfZatmzZwuLFi5kwYQJvfOMb6/8jSk1kRs2oymZGzajKZT7Np7pDvc1+UNlKMpDZwPrRldM5Vq1a1ffzCy+8wM477wzA7NmzWb58+TZjly9fvs3hTyN97c2bN3PdddexYMECAE4++WQuv/zyvrFHHXUUd955J2vWrOHZZ59l4cKF7L777gAsWbKEnp4ezj33XNauXcv111/PnDlzXvPew6m/tj6AF198sa9GqRRm9FVmVCUyo68yoyqN+XyV+VQnG7LZj4hTIuLHEfFjKo3+17berln+A7gC+PdmF1y6FStWvGblMmfOHFasWNGQ11+8eDEnnHACM2fO5KijjuKKK64AYPz48dx4441ccskl7LHHHuyyyy5cfPHFRLw6AeXXvvY1DjvsMPbee29eeuklvvrVr7a8fqndzKhUNjMqlct8Sp1lOHv2NwLrqksAG2pub12WAecDH2tOmZ3j+9//PjNmzODUU09lxx135PDDD2f+/PnbbJkcjTvuuIPnn3+eb3zjG9x111088cQTAEycOJFJkyaxbt06Nm/ezKGHHsqJJ57Y97xDDjmEww47jPHjx7Nx40aee+45Xn755ZbXL7WbGZXKZkalcplPqbMMZzb+6zLzT4H5wI+BRZn5p/2WEzPz3Mxc1/SKC/fss8/yvve9jwULFrBu3Tr++Z//mY9//OPceeedDXuPK664gqOPPnqbFdPzzz/PJz7xCS699FI2bNjAGWecwbe//e2+x6dMmcJFF13EunXrWLVqFbNmzeIzn/lMW+qX2smMSmUzo1K5zKfUWaI6Y+fQAyN2AP4P8L7M/FFTq2qyiBjeLy11ucyMoUe1nhmVKsyoVDYzKpWt1Iy2yrAn6MvMLcCvgNc1rxxJkiRJkjRa9c7Gfxbw+Yg4oBnFSJIkSZKk0Rv2YfwAEXEPMAfYDXgKeJp+l+LLzHkNrK8pPLRJqij10CYzKlWYUalsZlQqW6kZbZVxdY5/sLpIkiRJkqRC1bVnv1u4tVOqKHVrpxmVKsyoVDYzKpWt1Iy2Sr179gGIiH2Bg4E9gW9k5qqI+G/A05n5XCMLlCRJkiRJ9amr2Y+IycA3gOOAl6rPvw1YBfxP4Angsw2uUZIkSZIk1aHe2fj/ETgcOBLYGag9LOL7wNENqkuSJEmSJI1QvYfx/wnwmcz8t4jYsd9jjwN7N6YsSZIkSZI0UvXu2f8dYN0gj+0MvDK6ciAiZkTEbRGxMSIejIhDBxk3NyLuqo77z4iYO9r3liRJkiSpG9Tb7N8DnDzIY8cB/zG6cgC4GHgMmAacB9wQERMHGHcN8F1gN+AW4NsNeG9JkiRJkjpeXZfei4h3AD8E7gCuAy4CeoA3UWn235WZ94y4mIidgbXAnpm5unrfg8BpmXl7zbg3A3cB0zPz5YgYB6wBDs3MR4bxPl6ORKLcy5GYUanCjEplM6NS2UrNaKvUtWc/M++gMjnfROBCKhP0fQHYB/jD0TT6VXOBdVsb/aqlwL79xu0L/CIzX67W9TLwywHGERGLIiJrl1HWKKmBzKhUNjMqlc2MShrMkHv2I2J8Zr40wP2/A+wKPJuZGxtSTMQ7ga9n5ptr7rsEWJGZ59bcdxJwYmYeXXPf7cAVmbm4EbU0U0Rk6VuZSq+x9Pqg/BpLr6+dOuFvU3qNpdcH5ddYen3t1Al/m9JrLL0+KL/G0utrp07425ReY+n1Qfk1ll5fKwxnz/6qiLg0It4TEX1/rMx8MTN/26hGv+oFYEq/+6YAz49wnCRJkiRJY85wmv2rgf+Hyrn6T0XEVyLiD5pUz6PAtIiYXnPf/sDD/cY9DLyleq4+1f++eYBxkiRJkiSNOUM2+5n5SWAP4P8Gvg+cBPxHRDwWEV+MiP0bVUxmPgfcCvRExKSImE9ltv0l/cb9ElgGfLY6U/9ngceGMzmfJEmSJEndblgT9GXmlsz8YWb+JfB64EPAncCngPsj4sGIOCMi9mlATadSmajvGeAs4NjM3BQRZ0bExTXjTgD+CHgW+GPgww1471b5QrsLGIbSayy9Pii/xtLra6dO+Nv+sF1GAAAgAElEQVSUXmPp9UH5NZZeXzt1wt+m9BpLrw/Kr7H0+tqpE/42pddYen1Qfo2l19d0dV167zVPruxVPwaYT6XxJjPHNaY0SZIkSZI0EnVdem8AbwPeBRxefa0nRl2RJEmSJEkalbr3wkfE26gcQn88sBewGrgOuDoz72pseZIkSZIkqV7DavYj4i1UGvw/o3I+/QbgJioz9f84M7c0rUJJkiRJklSXIc/Zj4gHgP2AF4HvUWnwf5CZm5tfniRJkiRJqtdw9uw/DpwH3JyZLzS5HkmSJEmSNEqjmo1fkiRJkiSVZ7Sz8UuSJEmSpMLY7EuSJEmS1GVs9iVJkiRJ6jI2+5IkSZIkdRmbfUmSJEmSuozNviRJkiRJXcZmX5IkSZKkLmOzL0mSJElSl7HZlyRJkiSpy9jsS5IkSZLUZWz2JUmSJEnqMjb7kiRJkiR1GZt9SZIkSZK6jM2+JEmSJEldxmZfkiRJkqQuY7MvSZIkSVKXsdmXJEmSJKnL2OxLkiRJktRlbPYlSZIkSeoyNvuSJEmSJHUZm31JkiRJkrqMzb4kSZIkSV2muGY/Ir4QEQ9HxJaIOG474/4gIh6MiI0RcXtEzGhlnZIkSZIklaq4Zh94FPgMcPdgAyJiEnAjcB4wDfgN8LWWVCdJkiRJUuGKa/Yz84rM/Ffg/2xn2BHA+urYF4FFwAciYnILSpQkSZIkqWjj2l3ACO0LPLD1RmaujohngLnAz2sHRsQioKel1UkdIjOj3TWYUWlwZlQqmxmVylZCRtspMrPdNQwoIpYAF2bm9QM89rfAHpm5sOa+R4C/zMyfDOO1y/ylC1Lqvws1TkQUuwI0o0Mzo93PjHY2M9r9zGhnM6Pdr+SMtkpxh/EP0wvAlH73TQGeb0MtXSliTOdCKp4ZlSRJ0vZ0arP/MHDA1hvVmfh3pTK5nyRJUlu5QU4qmxnVWFBcsx8R46uz7e8AjI+ISfHaNC4BpkXE/OrYzwO3ZqZ79hvIlaAkSZIkdabimn3g68CLwDuBq6o/7x0RF0fEmQCZ+X+APwHOAp4B3gh8vD3lSlJ7uEFOKpsZlcpmRtXtip2gr5mctGT4xuK/j7Gi5ElLzOjwmdHuZUa7gxntXma0O5jR7lVyRlulxD37KohbPKWymVGpbGZUKpsZVTez2ZckSZIkqcvY7GtIbvGUymZGpbKZUUlSO9jsS5IkSRqz3CCnbmWzr2FxJSiVzYxKkiSpls2+tB377bcf3/ve98bs+0ula3dG2v3+6hxjdYNcuzPS7vdX5xiLGW13Ptr9/mOBl95TXcbiv5duVfLlSMzoyJnR7mFGu4/57C5mtPuY0e5SckZbxT37kiRJLTAW9xxKncSMqtvY7KsuY20lOGfOHL7zne/wzW9+k4MOOohzzjmHGTNm8LrXvY5/+qd/AmD16tVMnDiRxx9/vO95L774IlOnTuWnP/0pAAsWLGDWrFlMmTKFgw8+mH/7t3/rG/vYY49x5JFHMnXqVHbddVcOO+wwNm7cuM37Q2Vr85e//GV+93d/l912242jjz6axx57bJtav/SlL3HooYey88478+53v5snn3yy6X8jlcWMmlGpJGZUKpf57H42+9IwPfTQQ+y000489dRTXHPNNXzuc5/jN7/5DTNmzOC9730vV155Zd/Ym2++mVmzZnHIIYcAcOSRR/KLX/yCdevWccIJJ3Dcccfx3HPPAXDWWWcxd+5c1q5dy+rVq/nyl7/MuHHjXvP+ixcv5h//8R/5zne+w8qVK3nrW9/KBz7wAV5++eW+MVdeeSVXX301a9asYaedduJv//Zvm/xXkcphRtUJxtoGuVpmVJ1grGbUfHYnm33VbayuBHfffXdOO+00xo8fzxFHHMGcOXO47777ADjppJNYvHhx39jFixdz8skn993+6Ec/ytSpUxk/fjyf+9zn2LJlCw888AAAEyZMYOXKlSxfvpzx48dz+OGHM2HChNe8/+LFi/n0pz/NAQccwMSJE/niF7/IihUruPvuu/vGfPzjH+cNb3gDkyZN4sQTT+Tee+9t1p9DBTOjZlQqkRmVymU+u5PNvjRMr3vd67a5vdNOO/VttfzQhz7Eb3/7W+69915Wr17ND3/4QxYsWADAli1b+rZqTpkyhV122YUNGzawdu1aAP7+7/+ePfbYgz/8wz9kzpw5LFq0iC1btrzm/VesWMGcOXP6bk+YMIFZs2axYsWKvvte//rXD1ifNBaYUXWKsbpBzoyqU4zFjJrP7vTaYyikYajObtnuMooxadIkjjvuOBYvXsycOXN4+9vfzp577gnAVVddxVVXXcXtt9/O3LlziQh23XXXvr/fjBkzuOiiiwB44IEHeO9738sBBxzAscceu817zJ49m+XLl/fd3rx5MytXrmT27Nmt+SXVUczotsyoVDYzKpXLfHYu9+xLDXLSSSfx7W9/m29961vbHNrU29vLhAkT2H333dm8eTM9PT309vb2PX7ttdfyxBNPkJnsuuuujBs3bsBzmRYsWMCFF17Iww8/zKZNm+jp6WHWrFnMmzevJb+f1OnMqEoyFvccDsWMqiRmdFvmszPZ7GvEXAlu693vfjcTJ07kV7/61TZbK0855RT2228/9t57b/bZZx8mT57ctzUU4N577+Xwww9n8uTJHHbYYfzFX/wFH/zgB1/z+ieffDKf+tSn+MAHPsDrX/96fvazn/Hd7353wBWmBGa0PzMqlc2MSuUyn50pxuJhnhEx9n7pJhmL/366RfUw7yK7QTPaOGa0c5nRscGMdi4zOjaY0c5VckZbxT37GhX3HEplM6NS2cyoJKlZbPYlSZIkaQBukFMns9nXqLkSlMpmRqWymVGpbGZUncpmXw3hSlCSJEmSymGzL0ljgBvkpLKZUalsZlSdyGZfDeNKUJIkSZLKYLMvSWOEG+SksplRqWxmVJ3GZl8N5UpQKpsZlSRJGhts9iVJkgrhBjmpbGZUncRmXw3nSlAqmxmVymZGpbKZUXUKm301hStBSZIkSWofm31JGoPcICeVzYxKZTOj6gQ2+2oaV4JS2cyoVDYzKkkajeKa/YiYERG3RcTGiHgwIg4dZNx7I2JpRPRGxH0R8c5W16qh+UVFkiRJ3cjvuSpdcc0+cDHwGDANOA+4ISIm1g6IiB2Ba4EvAlOB84HrI6LE30eSiuUXFalsZlQqmxlVySIz211Dn4jYGVgL7JmZq6v3PQiclpm314ybBjwNjM/MrDb5m4GZmblmGO9Tzi89RpT070wVEUFmFvkJZUZbz4yWx4xqK/NZJjOqrcxomUrOaKuUtid8LrBua6NftRTYt3ZQZq4DrgfmV/fyLwDuH6jRj4hFEZG1SxPr1yDc6qnBmFGpbGa0/fwM1faY0fYzoypVaXv23wl8PTPfXHPfJcCKzDy339g/Bv4XMAV4Hjg6M/9zmO9Tzi89hpT0b01lb+00o+1hRstiRtWfGS2LGVV/ZrQsJWe0VUrbs/8Clea91tZmvk9EvAW4DDgGmAD8EXBTRExvRZEaGbd6SmUzo5IkSd2jtGb/UWBav6Z9f+DhfuP2B36emXdl5pbMXAI8BRzSmjI1UjYTkiSNjJ+hUtnMqEpTVLOfmc8BtwI9ETEpIuYDuwFL+g29DzgoIn4fICLeBbwZ+GULy5WkruMXFalsZlQqmxlVSca1u4ABnApcDjwDLAOOzcxNEXEmsFdmLszMRyPiU8AVETELWAmcmpnL2le2hqt6/ky7y5A0CDMqlc2MSpKGo6gJ+lrFSUvKMBb/7ZWk5ElLzGj7mc/2M6PaHjPafmZU22NG26/kjLZKUYfxS5LK4GGIUtnMqFQ2M6oS2OyrbVwJSmUzo1LZzKhUNjOqdrPZV1u5EpTKZkYlSZI6k82+2s5mQpKkkfEzVCqbGVU72exLkrbLLypS2cyoVDYzqnax2VcRXAlKZTOjUtnMqFQ2M6p2sNlXMVwJSmUzo1LZzKgkqZbNvoriFxVJkiR1I7/nqtVs9lUcV4RSucynVDYzKpXNjKqVbPYlSXXxi4pUNjMqlc2MqlVs9lUkV4JS2cyoVDYzKpXNjKoVbPZVLFeCUtnMqFQ2MypJY5vNvormFxWpbGZUkqSR8TNUzWazr+K5IpTKZkalcplPqWxmVM1ks6+O4IpQkqSR8TNUKpsZVbPY7KtjuCKUymU+pbKZUalsZlTNYLOvjuKKUCqX+ZTKZkalsplRNZrNvjqOK0KpXOZTKpsZlcpmRtVINvuSpIbyi4pUNjMqlc2MqlFs9tWRXAlKZTOjUtnMqFQ2M6pGsNlXx3IlKJXNjEplM6NS2cyoRstmXx3NlaBUNjMqlc2MSmUzoxoNm311PFeCUtnMqFQ2MyqVzYxqpGz21RVcCUplM6NS2cyoVDYzqpGw2VfXcCUolc2MSmUzo1LZzKjqZbOvrhIRrgilgplPqWxmVCqbGVU9bPbVlVwRSuUyn1LZzKhUNjOq4bLZV9dyRSiVy3xKZTOjUtnMqIajuGY/ImZExG0RsTEiHoyIQwcZNyEivhIRayJiQ0Rc2+paVT5XhFK5zKdUNjMqlc2Maijj2l3AAC4GHgP+GDgWuCEi9snMTf3GnQdMB94E9AIHtLRKdYyIIDPbXYakAZhPqWxmVCqbGdX2REn/OCJiZ2AtsGdmrq7e9yBwWmbeXjNuGvBLYJ/MfG4E71POL62WKenfegmqHw5FbhI2o2OTGd2WGVVJzOdrmVGVxIy+VskZbZXSDuOfC6zb2uhXLQX27TfuAGAl8HcRsS4ifh4RRw70ghGxKCKydmlO6SqdhzqVyYxqKzNaJjMq8Go3JTOjAj9DNbDSmv2dqBySX6sXmNzvvllUGv5VwEzgbOC6iNi9/wtm5qLMjNqlCXWrQ/hlpTxmVLXMZ3nMqGqZ0fKYUW1lPtVfac3+C8CUfvdNAZ7vd9+LwEvAeZm5OTNvpXJY/4CT+Un9uTKUymU+pbKZUalc7thSrdKa/UeBaRExvea+/YGH+417CMjqIo2IK0KpXOZTKpsZlcpmRgWFNfvVyfZuBXoiYlJEzAd2A5b0G/cr4OfA6RGxY0QcRWVW/rtaXLI6nCtCqVzunZDKZj6lsplRFdXsV51KZaK+Z4CzgGMzc1NEnBkRF9eM+zDwPirn9P8DcFxmrmt5tep4NhRS2cynVC4/Q6Wymc+xrahL77WKs5RqMGMpDyVfjsSMaiBjKZ9gRtV5zGg5zKgGYkbHnhL37Ett49ZPqVzuQZTKZj6lspnRkYmIn0bEn7a7jpGw2Zf6saGQymY+pXL5GSqVzXzWJyJ2BPYDljbhtT9Z3ZCwKSK+0+jXB5t9aVCuDKVymU+pbGZUKpcb5eryJiCoXDWu0X4LfBH4ehNeG7DZl7bLFaFULr+sSGUzn1LZzOiwHAj8AvibiFgZEU9HxF834oUz88bM/A6wthGvNxCbfWkINhRS2cynVC4/Q6WymdEhHURl7/4GYA7wUeCCiNizdlBEXBQRz25n2av1pcO4dryp1ImqM3q2uwxJA9j6RcWMSmXyM1Qqmxkd1IHA5Zl5afX29yPiKWBf4MmtgzLz48DH21DfdrlnX6qDWz+lsplPqVx+hkplM58DOhC4ZuuNqPyRdgfWtK2iOtjsSyPgylAqlw2FVDbzKZXLz9BXRcQM4PXAqpq73w88C9zXb+zFEfH8dpa2HMZvsy+NkCtDqWzmUyqXn6FS2cwnUNmr/zJwUkTsEBFvAy4EPpuZW2oHZubCzJy8neWJ/i8eEeMiYhKVU+t3iIhJETGhkb+A5+xLo+Q5TlK5PJdfKpufoVK5/AzlQOBGKoftP0NlD/8ZmXnNdp81fGcDPTW3XwT+HTiiQa9PjMX/eREx9n5ptUQn5an6BavIzbZmVM3QSfkEM6qxx4w2jhlVM5jRzuNh/FIDeViiVC7zKZXNjEplM5+dx2ZfagJXhlK5bCiksplPqVx+hnYWm32pSVwZSmUzn1K5/AyVymZGO4PNvtRkrgylcplPqWxmVCqb+Sybzb7UIn5hkcplPqWymVGpXOazXDb7Uou5MpTK5RcWqWzmUyqXn6HlsdmX2sCVoVQ28ymVy89QqWxmtBw2+1IbuTKUymU+pbKZUalsZrT9bPalArgylMplPqWymVGpbGa0fWz2pYK4MpTKZT6lsplRqWxmtPVs9qUCuTKUymU+pbKZUalsZrR1bPalgrkylMplPqWymVGpbGa0+ca1uwBJQ9u6IszMNlciqb/aLypmVCqPn6FS2cxo89jsSx3EpkIqm19YpHKZT6lsZrTxbPalDuUKUSqX+ZTK5YZzqWx+hjaOzb7U4VwhSuUyn1LZzKhULjfMjZ7NvtQlXCFK5TKfUtls+qWymdGRKXI2/oiYERG3RcTGiHgwIg4dYvx/j4iMiENaVaNUMmc3lcplPqVybc2nGZXKZD7rU2SzD1wMPAZMA84DboiIiQMNjIiZwIeBla0rT+oMfmmRymU+pbKZT6lcfoYOT3HNfkTsDBwDLMrMFzPzCmA9cMQgTzkfOAfY3JoKpc7kClEql/mUymVTIZXNfA6uuGYfmAusy8zVNfctBfbtPzAiDgP2yMwbW1Wc1OlcIUrlsqmQymY+pXL5GfpaJTb7OwG9/e7rBSbX3hEROwD/BPzN9l4sIhZVz+fvWxparaRRMaNS2cyo9FolNRNmVHqtkjLaTiU2+y8AU/rdNwV4vt99HwGWZuZ923uxzFyUmVG7NK5USaNlRqWymVGpbGZU0mBKbPYfBaZFxPSa+/YHHu437l3A8RGxNiLWAnsCP4yIU1pUpyRJkiRJRYoSr1UYETcCvwU+C/wJ8PfAPpm5qWbMrlQO+d/qLuCvgX/PzBeGeP3yfmmpDUrd+m9GpQozKpXNjEplKzWjrTKu3QUM4lTgcuAZYBlwbGZuiogzgb0yc2FmrqcySz8AEfEKsHqoRl+SJEmSpG5X5J79ZnNrp1RR6tZOMypVmFGpbGZUKlupGW2VEs/ZlyRJkiRJo2CzL0mSJElSl7HZlyRJkiSpy9jsS5IkSZLUZWz2JUmSJEnqMjb7kiRJkiR1GZt9SZIkSZK6jM2+JEmSJEldxmZfkiRJkqQuY7MvSZIkSVKXsdmXJEmSJKnL2OxLkiRJktRlbPYlSZIkSeoyNvuSJEmSJHUZm31JkiRJkrqMzb4kSZIkSV3GZl+SJEmSpC5jsy9JkiRJUpex2ZckSZIkqcvY7EuSJEmS1GVs9iVJkiRJ6jI2+5IkSZIkdRmbfUmSJEmSuozNviRJkiRJXcZmX5IkSZKkLmOzL0mSJElSl7HZlyRJkiSpy9jsS5IkSZLUZWz2JUmSJEnqMsU1+xExIyJui4iNEfFgRBw6yJjrImJ1RKyLiJsi4vXtqFeSJEmSpNIU1+wDFwOPAdOA84AbImJivzE7Af8b2BeYBawELmllkZIkSZIklSoys9019ImInYG1wJ6Zubp634PAaZl5+3aedwDwL5k5c5jvU84vLbVRZka7axiIGZUqzKhUNjMqla3UjLZKaXv25wLrtjb6VUup7MHfnrcDvxzogYhYFBFZuzSoVkkNYEalsplRqWxmVNJgStuz/07g65n55pr7LgFWZOa5gzznDcB/Acdm5k+G+T7l/NJSG5W6tdOMShVmVCqbGZXKVmpGW6W0PfsvAFP63TcFeH6gwRGxO/AD4OzhNvqSJEmSJHW70pr9R4FpETG95r79gYf7D4yIyVQa/asz89IW1SdJkiRJUvGKavYz8zngVqAnIiZFxHxgN2BJ7biImADcBNybmV9oeaGSJEmSJBWsqHP2ASLidcDlwDuBZcBfZOZ/RsSZwF6ZuTAi3k1lA8BGoO8XyMzJw3yPsn5pqU1KPY/JjEoVZlQqmxmVylZqRluluGa/FVwBShWlrgDNqFRhRqWymVGpbKVmtFWKOoxfkiRJkiSNns2+JEmSJEldxmZfkiRJkqQuY7MvSZIkSVKXsdmXJEmSJKnL2OxLkiRJktRlbPYlSZIkSeoyNvuSJEmSJHUZm31JkiRJkrqMzX6bnXHGGVx11VVjvgapVCXko4QapFKVkI8SapBKVEI2SqhBapfIzHbX0HIRMfZ+aWkAmRntrmEgZlSqMKNS2cyoVLZSM9oq7tmXJEmSJKnL2OyPwLJlyzj99NO566676O3tZcmSJcyePbvv8YMPPpg77riD9evX89BDD3HCCScM+lo9PT3cdNNNfbczk4ULF7J06VI2bNjAzTffzJQpUwC4+eabOfvss7d5/qWXXsoFF1wAwPz581m6dCm9vb08/vjjnHPOOduMPf/881m5ciW9vb38+te/5phjjhmwhu3V39PTwy233MIFF1zA+vXrefzxxzn++OPr/RNKTWVGzajKZkbNqMplPs2nukhmjrkFyNEsy5Yty/vvvz/nzJmTEydOzFtvvTUvu+yyBHLq1Km5Zs2a/OQnP5njxo3Ld7zjHblhw4Y8/PDDB3ytnp6evOmmm/puZ2b+6Ec/yunTp+fUqVPz3nvvzZ6engTy2GOPzUceeaRv7IQJE3L9+vU5b968BPLoo4/OuXPnJpAHHnhgrlq1KufPn59AHnXUUfnEE0/kzJkzE8g999yzb2xtDUPV39PTk5s2bcrjjz8+d9hhhzzppJOyt7c3J0+ePKq/qUt7lnZn0YyaUZftL+3Oohk1oy7bX9qdxWZk1Hyaz25a2p3Fdi/u2R+hiy66iOXLl7Np0yauvPJKDj74YACOOeYY1qxZw4UXXsjLL7/MHXfcwVVXXcUpp5wy7Nc+//zzWbNmDRs2bOCGG27oe+3vfve7TJ8+nXnz5gHwwQ9+kKeffpq7774bgNtuu41HH30UgPvvv5+rr76aI444AoDNmzczadIk9ttvP8aNG8eTTz7ZN7bWcOr/2c9+xrXXXsuWLVtYvHgxEyZM4I1vfGP9f0SpicyoGVXZzKgZVbnMp/lUd7DZH6FVq1b1/fzCCy+w8847AzB79myWL1++zdjly5dvc/jTSF978+bNXHfddSxYsACAk08+mcsvv7xv7FFHHcWdd97JmjVrePbZZ1m4cCG77747AEuWLKGnp4dzzz2XtWvXcv311zNnzpzXvPdw6q+tD+DFF1/sq1EqhRl9lRlViczoq8yoSmM+X2U+1cls9htsxYoVr1m5zJkzhxUrVjTk9RcvXswJJ5zAzJkzOeqoo7jiiisAGD9+PDfeeCOXXHIJe+yxB7vssgsXX3wxEa9OQPm1r32Nww47jL333puXXnrp/2/v/mPkqM87jr8fsGUTwCoYjoYmJqrkYAwk0LqpgUBIJFKjSA0tKGlsKkWtWhWQiqrSVEAbcGgrKiJUIYUYQqglUGSiECp+CSoIbmswNERRwTFOKOZHAbluzrXx2cHg8vSPmYPNZs+392Nnv7t+v6TReme+O/uZuXl8enZm57jpppsazy/1mzUqlc0alcplfUqDxWZ/lj344IOMjIxwySWXcOihh3LmmWeycuXKn/tkciY2bNjA2NgYt99+Oxs3buSVV14BYN68ecyfP5/R0VHeeustli9fzqpVq9593bJlyzjjjDOYO3cue/fuZffu3ezfv7/x/FK/WaNS2axRqVzWpzRYbPZn2c6dOzn//PO5+OKLGR0d5bbbbuPSSy/l8ccfn7X3uPPOO1mxYsXP/cc0NjbGZZddxq233squXbu48sorWbdu3bvLFyxYwM0338zo6Cjbtm3j+OOP5/LLL+9LfqmfrFGpbNaoVC7rUxosUd+x86ASEQffRksdZGZMPqp51qhUsUalslmjUtlKrdGmeGZfkiRJkqQhY7MvSZIkSdKQsdmXJEmSJGnI2OxLkiRJkjRkbPYlSZIkSRoyNvuSJEmSJA0Zm31JkiRJkoaMzb4kSZIkSUOmuGY/IkYi4qGI2BsRmyJi+QTjFkfExnrckxGxuOmskiRJkiSVqLhmH1gDbAUWAtcDd0fEvA7j7gLuA44G7gXWNZZQkiRJkqSCRWb2O8O7IuJI4KfABzNzez1vE/Dnmflwy7glwEbg2MzcHxFzgP8Blmfmj7t4n3I2WuqjzIx+Z+jEGpUq1qhUNmtUKlupNdqU0s7sLwZGxxv92rPA0rZxS4HnMnM/QP24pcM4IuLaiMjWqUfZJU2DNSqVzRqVymaNSppIaWf2zwa+kZlLWubdAryamde1zPt9YFVmrmiZ9zBwZ2be0WTm6YiILP1TptIzlp4Pys9Yer5+GoR9U3rG0vNB+RlLz9dPg7BvSs9Yej4oP2Pp+fppEPZN6RlLzwflZyw9XxNKO7O/B1jQNm8BMDbNcZIkSZIkHXRKa/afBxZGxLEt804BNreN2wycVH9Xn/pxSYdxkiRJkiQddIpq9jNzN/AAcE1EzI+IlVR321/fNm4L8CJwRX2n/iuArd3cnE+SJEmSpGFXVLNfu4TqRn07gKuBCzNzX0RcFRFrWsb9HnABsBP4HeALjSedvtX9DtCF0jOWng/Kz1h6vn4ahH1TesbS80H5GUvP10+DsG9Kz1h6Pig/Y+n5+mkQ9k3pGUvPB+VnLD1fzxV1gz5JkiRJkjRzJZ7ZlyRJkiRJM2CzL0mSJEnSkLHZlyRJkiRpyNjs90hEjETEQxGxNyI2RcTyCca9VI8Zq6dGbiQREasjYnNEvBMRFx1g3G/W+fdGxMMRMdJEvilmzJb9NxYRf9hQvnkRsTYiXouInRHxaEScOMHYxRGxsd6PT0bE4sLy9eU47CdrtLF8fanP+r2t0QFmjTaWz9+hs5PRGrVGe5XPGp2djAddjYLNfi+tAbYCC4Hrgbuj+jOBnZyTmUfU0zUN5XseuBz494kGRMR84LtU+RcCLwBfbyRdZdKMLT7Usg+/2eNc4+YA/wl8jGr/PAJ8e4KxdwH3Uf0pyXuBdYXlg/4ch/1kjc5M6fUJ1uigs0ZnpvQaLb0+wRqdjDU6M9bozFmjk8lMp1megJcPyPoAAAkOSURBVCOBfcBIy7xNwG91GPsSsKyPWdcDF02wbAWwqeX5SL1dR5SSsV6ewDGF/NwTmN82fwnwv8Cc+vmc+vmJJeSrl/X1OOzTz8oa7XG+enkR9dnyc7dGB2CyRpvJVy8vokZLr88DZayXWaPW6Kznq5dbozPMWC87qGp0fPLMfm8sBkYzc3vLvGeBpROMvz8itkXEuog4rvfxurYUeGb8Sb09O6i2rzTPRMSrEbEmIo7sU4azgJcy8822+UuB5zJzP0D9uIWJj4em840r9TjsBWu0WSXUJ1ijg8QabVYJNVp6fYI12soabZY12h1rtI3Nfm8cDrzRNu8N4IgOY1cCJ1B9KrYXuLO30aZkKtvRT2dT7cNlwCLgxqYDRMTRwNeAqzss7vt+nCQflH0c9oI12py+1ydYowPIGm1O32u09PoEa7QDa7Q51mgXrNHO5vQ7wJDaAyxom7cAGGsfmJlP1P/cFxGXAzsj4vDM3NPjjN3oejv6KTM31P/cFhF/ATwG/FFT7x8Rh1F/Pykzv9VhSF/3Yxf5Sj8Oe8EabUi/6xOs0QFljTak3zVaen2CNToBa7Qh1ujkrNGJeWa/N54HFkbEsS3zTgE2T/K6rKfoVbAp2gycOv6kvjvpUVTbV6ps8s0iYg7VjUB+kpkTfZK4GTipHjv+miVMfjw0la9dacdhL1ij/dFofYI1OsCs0f7wd+j0MrYr7TjsBWu0P6zR6WVsV9px2DM2+z2QmbuBB4BrImJ+RKykujvl+tZxEbEoIpZHxJz6+zf/APxrZvb8k7CImFvfgfQQYG6ds/2AX0/1H/nKeuyXgQeayNdtxog4OSJOjYhD6l84NwD3N5Gvdlud748nGpCZW4AXgSvqu9ReAWzNzB+XkK+fx2G/WKPN5CugPsEaHUjWaDP5CqjR0usTrNGOrNFm8lmjXbFGD6Tfdwgc1gk4DniY6jshPwKW1/OvAtbU/z6Z6s6lY8B2qj9b8f6G8q3lvU+1xqcPUf0Zlataxi2v8+8F/hk4rsF9OGlG4FNUn77uAV4HbgEWNJTvhDrTz+qf4fi0qPXnXI/9MPBkPfYp4MOl5OvncdjPyRrtfb5+1mf9/tboAE/WaO/z9bNGS6/PqWS0Rq3RXuWzRmcn48Fao5lJ1DtAkiRJkiQNCS/jlyRJkiRpyNjsS5IkSZI0ZGz2JUmSJEkaMjb7kiRJkiQNGZt9SZIkSZKGjM2+JEmSJElDxmZfkiRJkqQhY7MvSZIkSdKQsdmXJEmSJGnI2OxLkiRJkjRkbPYlSZIkSRoyNvuSJEmSJA0Zm31J0tCKiGsjIjtMj9TL10bE0y3jPxcRX+xb4Glo34aSRMSXI+K1iHinztmT/R0Rp0bEgxExWk/3RMTITNcrSdIgm9PvAJIk9dguYEWHeQDXAYe1zP8ccAywtvexhltELANWA1cB64Ht9aJZ3d8R8SvAY8BTwCpgAfB14M+AK6e7XkmSBp3NviRp2O3PzCc7LcjMF5oOcxBZUj9+LTPf6OH7/CnwBvC7mbkPICL+ADiyh+8pSVLxvIxfknTQar2sPCLWAhcCn2i53P/a1nERcV5EPBMReyJiQ0Sc3GGdH4+If4mIvfUl5d+IiCNblp8cEQ9FxI56Pc9FxGXdLj/AtlwQEVsi4s0629JpZJuV7az35R310F31vjy32/09RZ8B7mlp9I8CPg58fxrrkiRpaHhmX5I09CKi/ffd/2Vmts27DlgE/BJwaT3v1Zbli4AbgL8FfgZ8Ffh2RJwyvq6IOAt4FPgn4CJgIXA9cFT9HOBeYAtwMbAPOJHq0nO6XN7JCcCNwF/X2VYDD0fE4sx8cwrZZms7rwP+C/gr4FP1ejYDX2x5n8n296Qi4nDgJOBv6g8aTqvzvgrcNZV1SZI0bGz2JUnDbiHwdtu884BHWmdk5gsRsQM4ZILL/o8GzsrM5wEi4hDgHqpmfEs95nrgicz8/PiLIuI14NGIOAXYBvwqcEFmPlsPebRl7DEHWn4AxwCfzcwn6vX8AHiBqrle0022zNw0W9uZmZsiYvwrEt/PzLF6zLuBu9jf3fgI1VWKPwRepvqwYR9w7viHHJIkHay8jF+SNOx2Ab/RNj01jfW8NN4A1zbXjx8AiIj3AWdQnQWfMz4BG6g+bPh1YAfVGe81EfH5DneMn2z5RLaPN/oAmfky8APgY1PINpvb2ZTTgDFgK9UVBX8CvAg8EBG/3GAOSZKKY7MvSRp2+zPz6bZp9zTWs7Pt+Vv14/z68SjgUOBmqqZ3fNoHzAU+mJnvAJ+mOsN/O7AtIv4tIk4HmGz5AWyfYN77u802m9s5SdbZdDrwH5n5dmZ+LzNvAX6b6uqETzSYQ5Kk4ngZvyRJs2MnkMC1wIMdlr8OkJlbgAsjYi5wNvD3VGeiP5CZ70y2fIL37nQFwAjwo6lk69JsrmumTuMXr9IYv3z/vxvMIUlScWz2JUl6z1u8dwZ7SjJzT0Q8CZyYmV/pYvzbwPci4kbgW1Q3qtvR7fI2IxFxZst39hcBvwb843SyTZJ71tbFDPZ3RBwKnALc17ZoFdV+2jCzaJIkDTabfUmS3rMF+GxEXEB1R/fXM3MqZ6q/RHWTuneA7wC7qe44/xngaqrG9qtUd4rfSnVJ/F9SXYq+IyI+cqDlB3jfnwJ3RMT43fi/QnUZ/9pus2XmT2ZrO6ewro77OyLOBR4DPpmZ6yd47RLgMOBLETEKPEf1J/euBi7JzP1T2B5JkoaOzb4kSe+5mep74LdTNdqrqS5X70pmboiIc+rX3UH13faXgYeoLiufVz9eDRxPdUn8Y1QNPVTf1T/Q8om8DPwd1V3yTwCeBr7Qekf6LrJ1bRbXNdH+fl+9vNO9CMadRnWvgHuotjupGv5VmXn3FDJIkjSU4hf/zLAkSVL/RMRq4JzM/OQBxtwAfDozP9pcMkmSBod345ckSaU5E7hxkjGnAz9sIIskSQPJy/glSVJRMvO8LoZ9FLi/11kkSRpUXsYvSZIkSdKQ8TJ+SZIkSZKGjM2+JEmSJElDxmZfkiRJkqQhY7MvSZIkSdKQsdmXJEmSJGnI2OxLkiRJkjRkbPYlSZIkSRoy/w/VFisvQlN2kAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x864 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Additive Model II\n",
    "γ = float(input(\"Enter γ: \"))\n",
    "m_v1 = 1\n",
    "m_o1 = 0\n",
    "\n",
    "fig, axes = plt.subplots(3, 4, figsize=(16, 12), sharex=True, sharey=True)\n",
    "fig.suptitle(r'Additive Model II (Parent-to-Offspring Altruism), $\\gamma = $'+str(γ), \n",
    "             x=0.5, y=0.95, horizontalalignment='center', verticalalignment='top', fontsize = 18)\n",
    "axes[1,0].yaxis.set_label_coords(-0.18,0.5)\n",
    "axes[1,0].set_ylabel(r'Vertical transmission rate, $\\rho$', fontsize = 15) \n",
    "fig.text(0.51, 0.07, r'Fitness benefit, $\\beta$', horizontalalignment='center', \n",
    "         verticalalignment='bottom', fontsize = 15)\n",
    "\n",
    "for i in range(3):\n",
    "    for j in range(4):\n",
    "        b_, c_ = b[i], c[j]\n",
    "        ax = axes[i,j]\n",
    "        β_, ρ_ = np.meshgrid(β, ρ)\n",
    "        z = f(β_, γ, ρ_, b_, c_, m_v1, m_o1)\n",
    "        ax.contourf(β_, ρ_, z, levels=[0, 1], colors=['k', 'w'])\n",
    "        \n",
    "        if j == 3: #Label b values \n",
    "            if i == 2:\n",
    "                ax.yaxis.set_label_coords(1.24,0.5)\n",
    "            else:\n",
    "                ax.yaxis.set_label_coords(1.3,0.5)\n",
    "            ax.set_ylabel(r'$b = $'+str(b_), horizontalalignment='right', rotation=0)        \n",
    "        if i == 0: #Label c values\n",
    "            ax.title.set_position([0.5, 1.045])\n",
    "            ax.title.set_text(r'$c = $'+str(c_))              \n",
    "        \n",
    "        #Label the light and dark regions of the plots\n",
    "        if γ == 0.01:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 0 or (j == 1 and i == 0):\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j == 1 and i == 1:\n",
    "                ax.text(0.2, 0.05, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j==2 and i == 0:\n",
    "                ax.text(0.16, 0.02, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.1:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 0 or (j == 1 and i != 2):\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j == 1 and i == 2: \n",
    "                ax.text(0.18, 0.04, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j==2 and i == 0:\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.3:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 3 and i == 1:\n",
    "                ax.text(0.17, 0.04, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            else:\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.7:\n",
    "            ax.text(1.8, 0.89, 'invasion')\n",
    "            ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.99:\n",
    "            ax.text(1.8, 0.89, 'invasion')\n",
    "            ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            \n",
    "#plt.savefig('dec9_mII_g01.pdf') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additive Model III"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter γ:  0.99\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Additive Model III\n",
    "γ = float(input(\"Enter γ: \"))\n",
    "m_o1 = 0\n",
    "\n",
    "fig, axes = plt.subplots(3, 4, figsize=(16, 12), sharex=True, sharey=True)\n",
    "fig.suptitle(r'Additive Model III (Sibling-to-Sibling Altruism), $\\gamma = $'+str(γ), \n",
    "             x=0.5, y=0.95, horizontalalignment='center', verticalalignment='top', fontsize = 18)\n",
    "axes[1,0].yaxis.set_label_coords(-0.18,0.5)\n",
    "axes[1,0].set_ylabel(r'Vertical transmission rate, $\\rho$', fontsize = 15) \n",
    "fig.text(0.51, 0.07, r'Fitness benefit, $\\beta$', horizontalalignment='center', \n",
    "         verticalalignment='bottom', fontsize = 15)\n",
    "\n",
    "for i in range(3):\n",
    "    for j in range(4):\n",
    "        b_, c_ = b[i], c[j]\n",
    "        m_v1 = b_\n",
    "        ax = axes[i,j]\n",
    "        β_, ρ_ = np.meshgrid(β, ρ)\n",
    "        z = f(β_, γ, ρ_, b_, c_, m_v1, m_o1)\n",
    "        ax.contourf(β_, ρ_, z, levels=[0, 1], colors=['k', 'w'])\n",
    "        \n",
    "        if j == 3: #Label b values \n",
    "            if i == 2:\n",
    "                ax.yaxis.set_label_coords(1.24,0.5)\n",
    "            else:\n",
    "                ax.yaxis.set_label_coords(1.3,0.5)\n",
    "            ax.set_ylabel(r'$b = $'+str(b_), horizontalalignment='right', rotation=0)        \n",
    "        if i == 0: #Label c values\n",
    "            ax.title.set_position([0.5, 1.045])\n",
    "            ax.title.set_text(r'$c = $'+str(c_))              \n",
    "        \n",
    "        #Label the light and dark regions of the plots\n",
    "        if γ == 0.01:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 0 or (j == 1 and i == 0):\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j == 1 and i == 1:\n",
    "                ax.text(0.2, 0.05, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j==2 and i == 0:\n",
    "                ax.text(0.16, 0.02, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.1:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j == 0 or (j == 1 and i != 2) or (j == 2 and i == 0):\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            elif j == 1 and i == 2: \n",
    "                ax.text(0.18, 0.04, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.3:\n",
    "            ax.text(1.7, 0.89, 'invasion')\n",
    "            if j==3 and i==1:\n",
    "                ax.text(0.17, 0.04, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            else:\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.7:\n",
    "            ax.text(1.8, 0.89, 'invasion')\n",
    "            ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        elif γ == 0.99:\n",
    "            ax.text(1.8, 0.89, 'invasion')\n",
    "            ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            \n",
    "#plt.savefig('dec9_mIII_g01.pdf') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additive Model IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter γ:  0.7\n",
      "Enter m:  0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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FhEd/0sc2dsnMxRTHqy/Op3jO9neieIb8ryi+wJ9I8YXy/Jq6fT2Wg7JvffBPwEUUj4mbm5l9ebQZ0NUDfAvw0Zphqv05R7cBlkbEHRTHdBlFb9nJFBOX3dnHOlDf32hzejuXbwL+N/DPleMwluLv/Vqd6+nN5mICBuHcqTMm6tl+PXX7e8z66usUf6+rIuJAiokDD6KYvX0FNSMLonj++wfoZk6LiFgI7JGZPd4qEBHbU+znjd28/F6KId21cxX01uMPDOw9+5k5PyK+Q/GouluAH1HMGfBF4P9SjDaptivFIwv/L8X/bV0iYiIwnWJehPm9bPasiJhCMf/GYorHef45xXnwHxT/P1WvdyGbOdbd6Lw48yfA2ZXzu0cDdUybdDwlqXtZgkcCuLi49L5QDFNOYL/N1HuSYvj071V+fxtFcrIWeIkiMdqLYujh3Jr31lP3ELp5DBxwPMUsyB2V16/urX7ltZEUE2kl8N0e9quN4ovSLym+/L9MMTT4+8BhfTh+ndv/ch/qvukxY5XyHYFLKO5vf63y8zt087i6Oo9ln/att2NY7/5STCL3SqXOrH6cjwdS8yiy/pyjlb/9/6Z4HvVKihmsF1IkVntXnR+91qn3b0Qvj3frw7m8NcVQ92cqbVlEcSHhnZV6ZzciJrY0LjZ3jvQxJvq8/Trr9vmY9fa3BOYCC7sp35NissqXKGL09krZCmoe8VhpSwLv6mY9K4D/2syxO7Ty/k9189pS4MfdlHc+anH3emOzv0vlvD6VIj43UMzf8I908wg83nhEXXfnxBmV1/56M9v7KG/ME/Fq5Xx4uPL+0f051t28Z59KWxZR+Uxs1ePp4uLi0tMSmYN9e5wkqdVExD3AWzPzA81ui7SlKsPKVwCXZ+ZJVeXzgEWZ+Yma+n8IPELxyLx6boNRnfp7rCNiL4qLcmdlZr9n9pekocx79iVJ/XEqMDUiDmt2Q6R6RMTvdVPcOafGT6rqfYzime/dzbfxZxQJaHfzKWhg9fdY71/52dvcB5LU0uzZlyRJw0ZEzKUY2v0gxXDrQ4GPUMx+/8Hs+5MpVGIRcS5wFrBL9vAIQ0lqdU7QJ0mShpM7KZ6W8TGKuSOWUEyG+Pcm+i3lPRRPUTDRlzRs2bMvSZIkSVKL8Z59SZIkSZJajMm+JEmSJEktxmRfkiRJkqQWY7IvSZIkSVKLMdmXJEmSJKnFmOxLkiRJktRiTPYlSZIkSWoxJvuSJEmSJLUYk31JkiRJklqMyb4kSZIkSS3GZF+SJEmSpBZjsi9JkiRJUosx2ZckSZIkqcWY7EuSJEmS1GJM9iVJkiRJajEm+5IkSZIktRiTfTVdRIyIiIsj4sXKclFEtPVQd1REfDcino2IlyLi1xHxmUa3WRJExOcj4sGI2BARtzW7PdJwVU8s+jkqNVa9n5URcXVEdETEuqplaiPaqtZjsq8yOAs4CJhcWT4AnNFD3TZgKfBhYCzwaeCCiDhs8JspqcbzwHnAd5vdEGmYqycW/RyVGqs/n5WXZOaYquWBQWqbWpzJvuoSEX8eEfdVeuBfiIj/PgCr/QxwXmYuzcylwFeBE7urmJkvZ+bfZeZvsvDvwL0UFwsk9WAwYjczb8nM24AVA9BEaVhodiz6OSr1rNnxKQ00k331WUScCFwG/C0wAXgv8G81dS6JiNW9LG+rqb8dsBvwcFXxw8DbImJcH9o0GjgQeHSLdk5qYYMRu5LqV8ZY9HNUKpQsPo+vXHB4PCL+JiLM2dQvkZnNboOGgIgYCzwHfDwz/3UA17s7sBjYMTNXVMp2BJYBu2fmkl7eG8BsYFfg0MzcOFDtklrFYMVuzTbOBvbPzI8NxvqlVlDGWPRzVCqUKT4j4r2VtrwI/BFwI/CtzPzWYLRLrc2rROqrDwHPD8J/gOsqP6t78Tv//VJPb6p8QfkO8AfAx/yCIvVosGJXUn1KFYt+jkqbKE18ZuZDmbk8M39Xuc3ma8BfNrtdGppM9tVXOwCrNlcpIi6rmT20dtlkeFNmrgKWAPtXFe8PPJeZa3rYRucXlCnAYT3VkwQMUuxKqltpYtHPUelNShOf3fBCnPrNZF999SvgPRFxEEBETIxuHgOSmSfVzB5auyzuZt1XAWdGxM4RsTPFTPzf66UtFwPvB/60crFAUs8GLXYjoq1yv28bsFVEjI6IkYO+R9LQVKZY9HNU2lRp4jMijo6IsVF4H/C/gJsHbE81rJjsq08y8yHgy8DsiHgZuB8YqKuX5wIPAP9ZWf4N+IfOFytXUS+r/HsP4BSKYYeLqq6kXjZAbZFayiDH7lnAK8CZwH+r/PtfBmjdUktpZiz6OSr1rizxWfF5ivmsXgK+D1wCXDBAbdEw4wR9kiRJkiS1GHv2JUmSJElqMSb7kiRJkiS1GJN9SZIkSZJajMm+JEmSJEktxmRfkiRJkqQWY7IvSZIkSVKLMdmXJEmSJKnFmOxLkiRJktRiTPYlSZIkSWoxJvuSJEmSJLWY0iX7EfH3EfFERGyMiE/2Uu+PI+KxiFgfET+OiAmNbKckSZIkSWVVumQfeBr4EvCLnipExGjgFuBrwA7Ab4BLG9I6SZIkSZJKrnTJfmZel5k/AV7tpdohwKpK3VeAs4GPRMSYBjRRkiRJkqRSa2t2A/ppX+DRzl8yc1lEvAjsDfyqumJEnA20N7R10hCRmdHsNhijUs+MUancjFGp3MoQo80UmdnsNnQrIuYCF2fmTd289rfArpl5UlXZk8BfZebP+7Ducu70MFHWc264iYjS/gdojDaHsVkuxqi6Y5yWhzGqWsZnuZQ5RhuldMP4++hlYGxN2VhgXRPaojpFDOuYkySpX0wkJEn1GKrJ/hPAfp2/VGbi345icj9JkiRJkoa10iX7ETGiMtv+VsCIiBgdb+4KngvsEBEzKnX/Drg7M+3ZHyLs3ZckSVKrcOSNyqh0yT7wXeAV4APAnMq/94iIyyLiDIDMfBX4BHAm8CLwDuCU5jRXkiRJkqRyKe0EfYPJSUvKYzief2VR5klLjNHmMB7LxRhVLWO0XIxRVTM+y6fMMdooZezZ1zDicH5JkiQNZSb6KiuTfUmSJEmSWozJvprO3n1Jknpnz6EkqV4m+5IkSZLUD16IU5mZ7KsU7N2XJEmSpIFjsq/SaEbCP3nyZO66666Gb7cs25fKrtkx0uzta1Onn346c+bMGfZtkMqqDPFRhjZIZeGj91Qqw/F8bJYyP47EGG0O469cjFFVMz7LxxiVcVluZY7RRrFnX6XicH5JkiRJ2nIm+yqdRib8kyZN4rbbbuPqq69m//3355xzzmHChAnstNNOXHjhhQAsW7aMUaNGsWjRoq73vfLKK4wbN44HH3wQgJkzZzJx4kTGjh3LAQccwL333ttVd8GCBRx66KGMGzeO7bbbjqlTp7J+/fpNtg/F1eELLriAvfbai+23357p06ezYMGCTdr69a9/nSlTprDNNttw8MEH89xzzw36MZKayRgd+p599lm+8pWv8MADD7B27Vrmzp3Lbrvt1vX6AQccwH333ceqVat4/PHHOeaYY3pcV3t7O7feemvX75nJSSedxPz581mzZg233347Y8eOBeD222/nrLPO2uT9V1xxBRdddBEAM2bMYP78+axdu5ZFixZxzjnnbFL3/PPPZ+nSpaxdu5ZnnnmGI444ots29Nb+9vZ27rjjDi666CJWrVrFokWLOProo+s9hNKgMkaNUbWwzBx2C5Au5V4aZY899shbb701r7rqqmxra8tvfvOb2dHRkffee2+2tbXlM888k5mZRxxxRH71q1/tet/111+f++yzT9fvV155Za5evTo7Ojry/PPPz+233z7Xrl2bmZnHHHNMfvazn82Ojo7s6OjI+++/Pzds2LDJ9jMzr7nmmpw4cWI++uij+eqrr+Zpp52W73znO/O1117rqrvffvvlggUL8pVXXsnDDz88jz/++H7ve+U4Nz0eu1uaff4N16WMjNHmx2N3Sz3n1bPPPpuPPPJITpo0KUeNGpV33313XnXVVQnkuHHjcvny5fn5z38+29ra8qCDDso1a9bktGnTul1Xe3t73nrrrZucsz/72c9yxx13zHHjxuW8efOyvb09gTzqqKPyySef7Ko7cuTIXLVqVR544IEJ5PTp03PvvfdOIN/97nfnCy+8kDNmzEggDzvssFy8eHHusssuCeTuu+/eVbe6DZtrf3t7e27YsCGPPvro3GqrrXLWrFm5du3aHDNmTEvE53BnjA7vGFX5lTlGG7XYs69SasZw/vHjx3PqqacyYsQIDjnkECZNmsTDDz8MwKxZs5g9e3ZX3dmzZ3Pcccd1/X7CCScwbtw4RowYwWmnncbGjRt59NFHARg5ciRLly5l4cKFjBgxgmnTpjFy5Mg3bX/27Nl88YtfZL/99mPUqFGcd955LFmyhF/84hdddU455RT23HNPRo8ezbHHHsu8efMG63BIpWOMDl2XXHIJCxcuZMOGDXz/+9/ngAMOAOCII45g+fLlXHzxxbz++uvcd999zJkzh+OPP77P6z7//PNZvnw5a9as4eabb+5a95133smOO+7IgQceCMCRRx7Jb3/7266/1z333MPTTz8NwCOPPML111/PIYccAkBHRwejR49m8uTJtLW18dxzz3XVrdaX9j/00EPceOONbNy4kdmzZzNy5Eje8Y531HX8iu+s0uAxRrcsRqWyMtlXaTU64d9pp502+f2tb30rL730EgAf/ehHef7555k3bx7Lli3jpz/9KTNnzgRg48aNnHnmmey9996MHTuWbbfdljVr1rBixQoAvvGNb7Drrrvy4Q9/mEmTJnH22WezcePGN21/yZIlTJo0qev3kSNHMnHiRJYsWdJVtvPOO3fbPmk4MEaHrhdeeKHr3y+//DLbbLMNALvtthsLFy7cpO7ChQs3GULc33V3dHTwwx/+sOs8OO6447j22mu76h522GHcf//9LF++nNWrV3PSSScxfvx4AObOnUt7ezvnnnsuK1as4Kabbtrkb9+pL+2vbh8Ut5h0tlEqC2P0DcaoWonJvtQHo0eP5pOf/CSzZ89mzpw5vP/972f33XcHYM6cOcyZM4e7776bNWvWsHr1asaNG9fVEzNhwgQuueQSFi1axB133MGll166yb1knWo/kDo6Oli6dGldH6jScGWMDk21F1CgmPug+gLKlpg9ezbHHHMMu+yyC4cddhjXXXcdACNGjOCWW27h8ssvZ9ddd2Xbbbflsssu2+Qi86WXXsrUqVPZY489eO211/j2t7/d8PZLzWaMds/RNhoqTPZVamWanX/WrFnccMMNXHPNNZsMD167di0jR45k/PjxdHR00N7eztq1a7tev/HGG1m8eDGZyXbbbUdbWxttbW1vWv/MmTO5+OKLeeKJJ9iwYQPt7e1MnDixa3ibpN4Zo0PPj370IyZMmMDJJ5/M1ltvzbRp05gxY8YmvXtb4r777mPdunVceeWVPPDAAyxevBiAUaNGMXr0aFauXElHRwdTpkzh2GOP7Xrf+973PqZOncqIESNYv349L730Eq+//nrD2y81mzEqDW0m+yq9siT8Bx98MKNGjeKpp57iqKOO6io//vjjmTx5MnvssQdvf/vbGTNmTFePIsC8efOYNm0aY8aMYerUqZx44okceeSRb1r/cccdxxe+8AU+8pGPsPPOO/PQQw9x5513dpt0SHozY3ToWb16NYcffjgzZ85k5cqVfO973+OUU07h/vvvH7BtXHfddUyfPn2TL/fr1q3jc5/7HFdccQVr1qzh9NNP54Ybbuh6fezYsVxyySWsXLmSF154gYkTJ/KlL32pKe2XmskYlYa2GI7DUCJi+O30EDccz9PBFhFkZjmupNQwRpvDOCsXY1SdjM1yMkaHJ+Nx6ChzjDaKPfsaEsrSuy9JkiRJQ4HJvoYME35J0nBjL6Ikqb9M9iVJkiRpM7z4pqHGZF9Dir37kiRJkrR5Jvsackz4JUmSJKl3JvuSJEmS1AuH8GsoMtnXkGTvviRJkiT1zGRfQ5YJvyRJkiR1z2RfQ5oJvyRJkiS9mcm+JElSCXmPsFQOxqKGKpN9DXn27kuSJEnSpkz21RJM+CVJkiTpDaVL9l6znyMAACAASURBVCNiQkTcExHrI+KxiJjSQ70/jYj5EbE2Ih6OiA80uq0qFxN+SZIkDSSH8GsoK12yD1wGLAB2AL4G3BwRo6orRMTWwI3AecA44Hzgpogo4/6ogUz4JUmSJAmiTFerImIbYAWwe2Yuq5Q9BpyamT+uqrcD8FtgRGZmJcnvAHbJzOV92E55dloDrkzndJlFBJlZyqsjxmhzGDvlYozKmCw3Y3R4MA6HrjLHaKOUrSd8b2BlZ6JfMR/Yt7pSZq4EbgJmVHr5ZwKPdJfoR8TZEZHVyyC2XyVg7/7QYoxK5WaMSuVmjA4eE30NdWXr2f8A8N3M3Keq7HJgSWaeW1P348A/AWOBdcD0zPz3Pm6nPDutQVOmc7uMyny10xhtDmOmXIzR4c14LD9jtPUZh0NbmWO0UcrWs/8yRfJerTOZ7xIR7wSuAo4ARgIfA26NiB0b0UgNDfbwS5IkSRquypbsPw3sUJO0vwt4oqbeu4BfZeYDmbkxM+cC/wW8rzHN1FBhwi9JkiRpOCpVsp+ZLwF3A+0RMToiZgDbA3Nrqj4M7B8RfwQQER8E9gF+3cDmSpIkSWpBDuFXK2hrdgO6cTJwLfAi8CxwVGZuiIgzgLdl5kmZ+XREfAG4LiImAkuBkzPz2eY1W2VVuV+n2c2QJEmSpIYp1QR9jeKkJcPTcDzXe1PmSUuM0eYwRsrFGB3ejMfyM0ZbmzE49JU5RhulVMP4pcHk/fuSJEnaHBN9tQqTfQ0rJvySJEmShgOTfQ07JvySpDKzV1GSNBBM9jUsmfBLkiRJamUm+5IkSZKEI2vUWkz2NWzZuy9JkiSpVZnsa1gz4ZckSZLUikz2NeyZ8EuSJElqNSb7Eib8kiRJw53366vVmOxLFSb8kiRJklqFyb5UxYRfktRM9ixKkgaKyb5Uw4RfkiRpePFCm1qRyb7UDRN+SZIkSUOZyb7UAxN+SZIkSUOVyb7UCxN+SZIkSUORyb60GSb8kiRJrcv79dWqTPalPjDhlyRJkjSUmOxLfWTCL0mSJGmoMNmX6mDCL0kaLA4lliQNJJN9qU4m/JIkSa3Bi2xqZSb7Uj+Y8EuSJEkqM5N9qZ9M+CVJkiSVlcm+tAVM+CVJkiSVkcm+tIVM+CVJkoYe79dXqzPZlwaACb8kSZKkMjHZlwZIRJj0S5IkSSoFk31pgJnwS5Lq5XBiSdJAM9mXBoEJvyRJUnl5gU3DQemS/YiYEBH3RMT6iHgsIqb0UG9kRHwrIpZHxJqIuLHRbZV6Y8IvSZIkqVnamt2AblwGLAA+DhwF3BwRb8/MDTX1vgbsCPwBsBbYr6GtlPogIrxyLEmSJKnhokyJSERsA6wAds/MZZWyx4BTM/PHVfV2AH4NvD0zX+rHdsqz0xoWyhRnnSoXIko5/MAYbY4ynqfDmTE6vBh/Q48xOrQZc62vzDHaKGUbxr83sLIz0a+YD+xbU28/YCnwvyNiZUT8KiIObVQjpXo5U78kSVI5mOhruChbsv9WiiH51dYCY2rKJlIk/C8AuwBnAT+MiPG1K4yIsyMiq5dBaLfUJyb8b2aMSuVmjErlZoxK6knZhvG/F7grMydWlV0P/CIzv1VV9nHgB8BbMvP1Stm/Af+QmXf1YTvl2WkNS2WIuzIPbTJGm6MM56XeYIwOL8bf0GOMDl3G2/BQ5hhtlLL17D8N7BARO1aVvQt4oqbe40BWFmnIsYdfkiRJ0mAqVbJfmWzvbqA9IkZHxAxge2BuTb2ngF8BX4mIrSPiMIpZ+R9ocJOlfvM+fkkS2MsoNZLxpuGkVMl+xckUE/W9CJwJHJWZGyLijIi4rKrep4DDKe7p/ybwycxc2fDWSlvIhF+SJEnSQCvVPfuN4n1MKqNGx2KZ72MyRptjOH4elJkxOnwYe0OTMTo0GW/DR5ljtFHK2LMvDUsO65ckSZI0UEz2pZIx4ZckSRp49uqrXhHxYET8RbPb0V8m+1IJmfBLkiRJzRMRWwOTgfmDsO4REXFxRLxYWS6KiLZe6u8aEbdFxMqIWBERN9Y8wa5bJvtSSTmsX5IkSWqaPwCC4vHwA+0s4CCKiwmTgQ8AZ/RS/zuVn3sAewKjgW9vbiMm+1LJmfBLkiRJDfdu4D+Bv4mIpRHx24j47ACt+zPAeZm5NDOXAl8FTuyl/l7AjZm5rvK4+h8A+21uIyb70hBgwi9Jrcl7iKXGMNbUD/tT9O6vASYBJwAXRcTu1ZUi4pKIWN3L8raa+tsBuwEPVxU/DLwtIsb10JZ/BP4iIsZFxLYUj6G/c3M7YLIvDREO65ckSZIa5t3AtZl5RWZuyMwfAf8F7FtdKTNPycxte1kW16x3TOXn6qqyzn9v00Nb7gMmAC9Wlm0pRgP0ymRfGmJM+CVJkqRB926K4fIARPElfDywfAvXu67ys7oXv/PfL9VWjoitgJ8AP6e4GDCOYtLA2za3IZN9aQiyl1+SJEkaHBExAdgZeKGq+M8peuAfrql7WUSs62XZZBh/Zq4CllDcJtBpf+C5zFzTTXO2p5iY7+LMXF+5Z/8S4EMRMaK3/TDZl4YwE35JkiRpwL0beB2YFRFbRcR7gIuBL2fmxuqKmXlSZo7pZakdxg9wFXBmROwcETtTzMT/ve4akpkrgN8AJ0fEqIh4C3AS8HhmvtbbTvT4LD9JQ0Nnwu/EM5IkSW/mdyT1w7uBWyiG7b9I0cN/emb+oNd39d25wA4Us/0DfB/4h84XI+IyKC4kVIo+BnwLWFr5/ZfA0ZvbSAzHkz8iht9Oa1ioJ54jgsws5dAAY7Q5huPnQZkZo8ODcTd0GaNDh3E2PJU5RhvFYfxSC/FefkmSJElgsi+1JBN+SSo/exslSYPJZF9qUfbyS5Kk4c6LahrOTPalFmfSL0mSJA0/JvvSMGHCL0mSJA0fJvvSMGIvvyRJkjQ8mOxLw5AJvyRJktTaTPYlSZIktRwn59NwZ7IvSZIkSVKLMdmXJEmSJKnFmOxLkiQ1mMOLJUmDzWRfkiRJUkvxgppksi9JkiRJUssx2ZckSZIkqcWY7EuSJEmS1GJM9iVJkiRJajEm+5IkSZJahpPzSYVSJvsRMSEi7omI9RHxWERM2Uz9/xkRGRHva1QbJUmSJEkqq1Im+8BlwAJgB+BrwM0RMaq7ihGxC/ApYGnjmidJkiRJUnmVLtmPiG2AI4CzM/OVzLwOWAUc0sNbzgfOAToa00JJkqT+c4ixJKkRSpfsA3sDKzNzWVXZfGDf2ooRMRXYNTNv6WllEXF2ZYh/1zLwTZbUX8aoVG7GqFRuxqiknpQx2X8rsLambC0wprogIrYCLgT+preVZebZmRnVy4C2VtIWMUalcjNGpXIzRjflyBnpDWVM9l8GxtaUjQXW1ZR9GpifmQ83olGSJEmSJA0VZUz2nwZ2iIgdq8reBTxRU++DwNERsSIiVgC7Az+NiOMb1E5JkiRJkkopyjjUJSJuAZ4Hvgx8AvgG8PbM3FBVZzuKIf+dHgA+C/zfzHx5M+sv305LTVDWoX7GaHOU8fNgOIsIY7RFGWutwRgtJ+NLncoco43S1uwG9OBk4FrgReBZ4KjM3BARZwBvy8yTMnMVxSz9AETE74Blm0v0JUmSJElqdaXs2R9sw/lqp1StrFc7jdHmGI6fB2VW5h4JY3TLGGutwRgtH2NL1coco41Sxnv2JUmSJEnSFjDZlyRJahB7HiVJjWKyL0mSJElSizHZlyRJkiSpxZjsS5IkSRrSvEVGejOTfUmSJEmSWozJviRJkiRJLcZkX5IkSZKkFmOyL0mSJElSizHZlyRJkjRkOTmf1D2TfUmSpAYwIZEkNZLJviRJkiRJLcZkX5IkSZKkFmOyL0mSJElSizHZlyRJkjQkOReG1DOTfUmSJEmSWozJviRJkiRJLcZkX5IkSZKkFmOyL0mSJElSizHZlyRJGmROIiYNPONK6p3JviRJkiRJLcZkX5IkSZKkFmOyL0mSJElSizHZlyRJkiSpxZjsS5IkSZLUYkz2JUmSJA0pzsQvbZ7JviRJkiRJLcZkX5IkSZKkFlO6ZD8iJkTEPRGxPiIei4gpPdT5YUQsi4iVEXFrROzcjPZKkiRJklQ2pUv2gcuABcAOwNeAmyNiVE2dtwL/D9gXmAgsBS5vZCMlSZL6wnuLJUnNEGX6AIqIbYAVwO6ZuaxS9hhwamb+uJf37Qf8S2bu0sftlGenpSbKzGh2G7pjjDZHmT4PBBFhjLYIY6s1GaPNY0ypL8oco41Stp79vYGVnYl+xXyKHvzevB/4dXcvRMTZEZHVywC1VdIAMEalcjNGpXIzRiX1pGw9+x8AvpuZ+1SVXQ4sycxze3jPnsB/AEdl5s/7uJ3y7LTURGW92mmMNkeZPg9U7h4JY7Q+xlZrMkabx5hSX5Q5RhulbD37LwNja8rGAuu6qxwR44F/Bs7qa6IvSZIkSVKrK1uy/zSwQ0TsWFX2LuCJ2ooRMYYi0b8+M69oUPskSZIkSSq9UiX7mfkScDfQHhGjI2IGsD0wt7peRIwEbgXmZebfN7yhkiRJkiSVWKnu2QeIiJ2Aa4EPAM8CJ2bmv0fEGcDbMvOkiDiY4gLAeqBrBzJzTB+3Ua6dlpqkrPcxGaPNUbbPg+GuzPcaGqP1MbZakzHaHMaT+qrMMdoopUv2G6GV/wOU6lHW/wCN0eYYjp8HZVbmLynGaH2MrdZkjDaH8aS+KnOMNkqphvFLkiS1EhMTSVKzmOxLkiRJktRiTPYlSZIkSWoxJvuSJEmSSs/bYqT6mOxLkiRJktRiTPYlSZIkSWoxJvuSJEmSJLUYk31JkiRJklqMyb4kSZIkSS3GZL/JTj/9dObMmTPs2yCVVRniowxtkKRakydP5q677hq221djORN//ZodI83eviCGY+BExPDbaakbmRnNbkN3jNHmGI6fB2UWEcboEGdMtTZjtLGMJ9WrzDHaKPbsS5IkSZLUYkz2++HZZ5/lK1/5Cg888ABr165l7ty57Lbbbl2vH3DAAdx3332sWrWKxx9/nGOOOabHdbW3t3Prrbd2/Z6ZnHTSScyfP581a9Zw++23M3bsWABuv/12zjrrrE3ef8UVV3DRRRcBMGPGDObPn8/atWtZtGgR55xzziZ1zz//fJYuXcratWt55plnOOKII7ptQ2/tb29v54477uCiiy5i1apVLFq0iKOPPrreQygNKmPUGJU0+CZNmsRtt93G1Vdfzf77788555zDhAkT2GmnnbjwwgsBWLZsGaNGjWLRokVd73vllVcYN24cDz74IAAzZ85k4sSJjB07lgMOOIB77723q+6CBQs49NBDGTduHNtttx1Tp05l/fr1m2wfiv+bL7jgAvbaay+23357pk+fzoIFCzZp69e//nWmTJnCNttsw8EHH8xzzz036MdIaiZjVGTmsFuA3JLl2WefzUceeSQnTZqUo0aNyrvvvjuvuuqqBHLcuHG5fPny/PznP59tbW150EEH5Zo1a3LatGndrqu9vT1vvfXWrt8zM3/2s5/ljjvumOPGjct58+Zle3t7AnnUUUflk08+2VV35MiRuWrVqjzwwAMTyOnTp+fee++dQL773e/OF154IWfMmJFAHnbYYbl48eLcZZddEsjdd9+9q251GzbX/vb29tywYUMeffTRudVWW+WsWbNy7dq1OWbMmC06pi7NWZodi8ZouWJU5dLKMTpclla3xx575K233ppXXXVVtrW15Te/+c3s6OjIe++9N9va2vKZZ57JzMwjjjgiv/rVr3a97/rrr8999tmn6/crr7wyV69enR0dHXn++efn9ttvn2vXrs3MzGOOOSY/+9nPZkdHR3Z0dOT999+fGzZs2GT7mZnXXHNNTpw4MR999NF89dVX87TTTst3vvOd+dprr3XV3W+//XLBggX5yiuv5OGHH57HH3/8Fu2/MWo8lZ0xWt4YbdRiz34/XXLJJSxcuJANGzbw/e9/nwMOOACAI444guXLl3PxxRfz+uuvc9999zFnzhyOP/74Pq/7/PPPZ/ny5axZs4abb765a9133nknO+64IwceeCAARx55JL/97W/5xS9+AcA999zD008/DcAjjzzC9ddfzyGHHAJAR0cHo0ePZvLkybS1tfHcc8911a3Wl/Y/9NBD3HjjjWzcuJHZs2czcuRI3vGOd9R/EKVBZIwao5IaZ/z48Zx66qmMGDGCQw45hEmTJvHwww8DMGvWLGbPnt1Vd/bs2Rx33HFdv59wwgmMGzeOESNGcNppp7Fx40YeffRRAEaOHMnSpUtZuHAhI0aMYNq0aYwcOfJN2589ezZf/OIX2W+//Rg1ahTnnXceS5Ys6fr/F+CUU05hzz33ZPTo0Rx77LHMmzdvsA6HVDrG6PBkst9PL7zwQte/X375ZbbZZhsAdtttNxYuXLhJ3YULF24yhLi/6+7o6OCHP/whM2fOBOC4447j2muv7ap72GGHcf/997N8+XJWr17NSSedxPjx4wGYO3cu7e3tnHvuuaxYsYKbbrqJSZMmvWnbfWl/dfugGOrT2UapLIzRNxijkgbbTjvttMnvb33rW3nppZcA+OhHP8rzzz/PvHnzWLZsGT/96U+7/p/cuHEjZ555JnvvvTdjx45l2223Zc2aNaxYsQKAb3zjG+y66658+MMfZtKkSZx99tls3LjxTdtfsmTJJv9njhw5kokTJ7JkyZKusp133rnb9qn8ik5abQljdHgy2R9gtScyFPegVJ/IW2L27Nkcc8wx7LLLLhx22GFcd911AIwYMYJbbrmFyy+/nF133ZVtt92Wyy67jIg3JqC89NJLmTp1KnvssQevvfYa3/72txvefqnZjFFJaqzRo0fzyU9+ktmzZzNnzhze//73s/vuuwMwZ84c5syZw913382aNWtYvXo148aN60ruJkyYwCWXXMKiRYu44447uPTSSzeZw6RT7YXQjo4Oli5dWteFXGm4MkZbl8n+APvRj37EhAkTOPnkk9l6662ZNm0aM2bM2KR3b0vcd999rFu3jiuvvJIHHniAxYsXAzBq1ChGjx7NypUr6ejoYMqUKRx77LFd73vf+97H1KlTGTFiBOvXr+ell17i9ddfb3j7pWYzRiWp8WbNmsUNN9zANddcs8nw4LVr1zJy5EjGjx9PR0cH7e3trF27tuv1G2+8kcWLF5OZbLfddrS1tdHW1vam9c+cOZOLL76YJ554gg0bNtDe3s7EiRO7bquS1DtjtDWZ7A+w1atXc/jhhzNz5kxWrlzJ9773PU455RTuv//+AdvGddddx/Tp0zf5cr9u3To+97nPccUVV7BmzRpOP/10brjhhq7Xx44dyyWXXMLKlSt54YUXmDhxIl/60pea0n6pmYxRSWq8gw8+mFGjRvHUU09x1FFHdZUff/zxTJ48mT322IO3v/3tjBkzpqtHEWDevHlMmzaNMWPGMHXqVE488USOPPLIN63/uOOO4wtf+AIf+chH2HnnnXnooYe48847u006JL2ZMdqaYjjeAxMRw2+npW5kZmy+VuMZo80xHD8PyiwijNEhzphqbcZo4xhL6o8yx2ij2LMvSZI0wExOJEnNZrIvSZIkqZS8cCb1n8m+JEmSJEktxmRfkiRJkqQWY7IvSZIkSVKLMdmXJEmSJKnFmOxLkiRJktRiTPYlSZIklY4z8UtbxmRfkiRJkqQWU7pkPyImRMQ9EbE+Ih6LiCk91Ns7Ih6o1Pv3iNi70W2VJEmSJKmMSpfsA5cBC4AdgK8BN0fEqG7q/QC4E9geuAO4oWEtlCRJ6oFDjyVJZRBl+kCKiG2AFcDumbmsUvYYcGpm/riq3j7AA8COmfl6RLQBy4EpmflkH7ZTnp2Wmigzo9lt6I4x2hxl+jwQRIQxOkQZS8ODMTr4jCVtiTLHaKO0NbsBNfYGVnYm+hXzgX2BH1eV7Qv8Z2a+DlBJ+H9dKd8k2Y+Is4H2wWy0pP4zRssjYlh/HqoHxmj9jCU1UivHqLEkbZmy9ex/APhuZu5TVXY5sCQzz60qmwUcm5nTq8p+DFyXmbMb2eb+iIgs+1Wmsrex7O2D8rex7O1rpqFwbMrexrK3D8rfxrK3r5mGwrEpexvL3j4ofxvL3r5mGgrHpuxtLHv7oPxtLHv7GqFs9+y/DIytKRsLrOtnPUmSJEmShp2yJftPAztExI5VZe8Cnqip9wTwzsq9+lR+7tNNPUmSJEmShp1SJfuZ+RJwN9AeEaMjYgbFbPtza+r9GngW+HJlpv4vAwv6MjmfJEmSJEmtrlTJfsXJFBP1vQicCRyVmRsi4oyIuKyq3jHAx4DVwMeBTzW8pf33981uQB+UvY1lbx+Uv41lb18zDYVjU/Y2lr19UP42lr19zTQUjk3Z21j29kH521j29jXTUDg2ZW9j2dsH5W9j2ds36Eo1QZ8kSZIkSdpyZezZlyRJkiRJW8BkX5IkSZKkFmOyL0mSJElSizHZlyRJkiSpxZjsS5IkSZLUYkz2JUmSJElqMSb7kiRJkiS1GJN9SZIkSZJajMm+JEmSJEktxmRfkiRJkqQWY7IvSZIkSVKLMdmXJEmSJKnFmOxLkiRJktRiTPYlSZIkSWoxJvuSJEmSJLUYk31JkiRJklqMyb4kSZIkSS3GZF+SJEmSpBZjsi9JkiRJUosx2ZckSZIkqcWY7EuSJEmS1GJM9iVJkiRJajEm+5IkSZIktZh+JfsR8ZaIGD/QjZEkSZIkSVuurmQ/IvaIiH8F1gK/jYg1EfGDiDh0cJonSZIkSZLqFZnZ98oR9wH7AucDvwF2AaYDhwHfBU7JelYoSZIkSZIGXL3J/qvAX2fm7JryacBdwLcy89yBbaIkSZIkSapHvffsrwNW1xZm5r8B7cBnB6JRkiRJkiSp/+pN9m8HvhAR0c1rTwHbbmmDIuLvI+KJiNgYEZ/spd4fR8RjEbE+In4cERO2dNuSJEmSJLWCepP9LwO7Aw9ExJ9HxCiAiBgLfB745wFo09PAl4Bf9FQhIkYDtwBfA3agmD/g0gHYtiRJkiRJQ15dyX5mrgIOAp6g6OVfFxHLgZXA/sA1ETFuSxqUmddl5k+AV3updgiwqlL3FeBs4CMRMWZLti1JkiRJUitoq/cNmbkS+ExE/A3wp8ABFIn+u4E7gIyIRcCvMvOogWxslX2BR6vatCwiXgT2Bn5VXTEizqaYT0BSjczs7pachjJGpZ4Zo1K5GaNSuZUhRpuprtn4N7uyiJ0pEv/3AH+YmZ/agnXNBS7OzJu6ee1vgV0z86SqsieBv8rMn/dh3T4ecAv5hMWhLyJK+x+gMdp/xmbrMEZbl3HaGozR1mR8to4yx2ij1N2z35vMfAG4p7IMppeBsTVlYymeFiBJkiRJ0rBW7wR9ZfEEsF/nL5WZ+LejmNxPDdD9AxkkSVJv7DWUJDVK6ZL9iBhRmW1/K2BERIzu5lF/c4EdImJGpe7fAXdnpj37kiRJkurmxTi1mtIl+8B3gVeADwBzKv/eIyIui4gzADLzVeATwJnAi8A7gFOa09zhy959SZIkSSqnAZ2gb6hw0pKBMxzPn1ZR5klLjNH+MyZbhzHamozR1mGMth7js7WUOUYbZcB69iPigxGxz0CtT0ODvfuSJEmSVD4DOYx/LvB4RPwsIo4YwPWq5Ez4JUmSNJTZq69WNJDJ/p8AHwF+DnxxANcrSZIkSZLq4D37GjDD8Vwaysp8H5Mx2n/GYeswRluTMdo6jNHWYmy2njLHaKOUcTZ+SZKklmMyIZWTsalW1a9kPyL2jYhZEXFGROxcKfv9iNhmYJunoWQo3rs/efJk7rrrrmG7fansmh0jzd6+VGbNjo9mb18qu2bHSLO3rzqH8UfEGOBK4CjgdaAN+KPMfCgibgQWZ+aXB6WlA8ihTYPHK6NDR5mHNhmj/WcMtg5jtPUYn63FGG0dxmZrKnOMNkq9Pfv/CEwDPgxsA1QfvB8B0weoXRqihmLvviRJkiS1mnqT/U8A/zMz7wV+V/PaImCPAWmV1CCTJk3itttu4+qrr2b//ffnnHPOYcKECey0005ceOGFACxbtoxRo0axaNGirve98sorjBs3jgcffBCAmTNnMnHiRMaOHcsBBxzAvffe21V3wYIFHHrooYwbN47tttuOqVOnsn79+k22D8VV5QsuuIC99tqL7bffnunTp7NgwYJN2vr1r3+dKVOmsM0223DwwQfz3HPPDfoxkprJGJXKy/hUK2jlXn1jVPUm+78HrOzhtf+fvXsPk6uu833//kpucxICISRACBBxxwsYvDEMl63iIIwXDs4IKnL1MqOAg/PMIO4zgCQCZ4s6qEc5CM6MF8JdUfAKMxyH2cKgYBQJoIJCwEAwN0iAsBMg3/NHVZpKpzvd1V1V/atV79fz1JOuVaurvt1PfSr9Xb/f+q1t2fIAgHpQt47u33PPPUyePJlHHnmEq6++mtNPP53f//73zJw5k0MPPZTLL7+8b9/rr7+eWbNmse+++wJwyCGH8Otf/5pVq1Zx9NFHc9RRR/Hkk08CcOaZZzJ37lxWrlzJ8uXLueCCCxg3btwWr79w4UI+97nPcd1117Fs2TL22WcfDj/8cJ577rm+fS6//HKuvPJKVqxYweTJk/nEJz7R5t+KVA4zKpXLfEplM6O9qdlm/w7ghEEeOwr4r9GVo6roxoZ/xx135LTTTmP8+PEcfPDBzJkzhzvvvBOA448/noULF/btu3DhQk444YUovP/972e77bZj/PjxnH766WzcuJG77roLgAkTJrBs2TKWLFnC+PHjOfDAA5kwYcIWr79w4UI++tGPMm/ePCZOnMh5553H0qVLuf322/v2OeWUU3jxi1/MpEmTOPbYY1m0aFG7fh1SccyoVC7zKZXNjPamZpv9s4B3RsRNwF8DCbwtIhYC7wbmt7g+qWN22mmnze5Pnjy576jlO97xDh599FEWLVrE8uXLuemmKtc5jgAAIABJREFUmzjuuOMA2LhxY99RzalTp7L99tuzZs0aVq5cCcBnP/tZdt11V9785jczZ84cFixYwMaNG7d4/aVLlzJnzpy++xMmTGDWrFksXbq0b9vOO+88YH1SLzCjUrnMp7pRlafw92dGe9OWcyy2IjNviYhDgPOBC6kt0PdJ4KfAIZl5R+tLVLeqr4A51mW0xKRJkzjqqKNYuHAhc+bM4aCDDmK33XYD4IorruCKK67gxhtvZO7cuUQE06ZN6/vZZ86cyUUXXQTAXXfdxaGHHsq8efM48sgjN3uN2bNns2TJkr77GzZsYNmyZcyePbszP6TUxcyoSleV/w9HwnxKZTOj1dXUyH5EnA08mJmvB6YCs4FtM/Mg4IH641IlHX/88Vx11VV84xvf2Gxq09q1a5kwYQI77rgjGzZsYP78+axdu7bv8WuuuYaHH36YzGTatGmMGzduwHOZjjvuOC688ELuvfde1q9fz/z585k1axb77bdfR34+qduZUalc5lMqmxmtpman8c+n1uCTmc9k5qOZua7+2Cycxq9+uvHc/cG88Y1vZOLEidx3332bHa088cQT2Xvvvdljjz3Yc889mTJlSt/RUIBFixZx4IEHMmXKFA444AA++MEPcsQRR2zx/CeccAKnnnoqhx9+ODvvvDO/+MUv+N73vjfgB6akLZlRqVzmUyqbGa2maGZaWURsBP5soOn6EfEO4F8zc8cW1tcWEdG7c+nGSC9PXyxV/TSLIo/GmNGRM2vVYUarxWxWjxntbmay+krOaKcMeSglIk4ETqzfTeDLEbG2326TgHnAv7W2PEmSJEmS1KzhzJtYB6yqfx3AGmB1v302AD8CLmpdaaqSKi3WJ0mSJEmla3Ya/9eAczLzwfaV1H5ObRobNvtlKXlqkxkdOXNWHWa0Wsxm9ZjR7mUee0PJGe2Uppr9qvADcOz04vutVCV/AJrRkTNj1WFGq8VsVo8Z7V7msTeUnNFOaXY1fmlUqrQ6vyRJkiSVqulrHUTEe4C/AV5KbWG+zWTmzBbUJUmSVAmOIkqSxkJTI/sRcQzwDeB3wGzgu8D368+zFriw1QWqehzdlyRJ0ljw4Jt6SbPT+E8HzgU+Ur9/UWZ+AHgxsJLayv3SkGz4JUmSJKl9mm325wK3ZubzwPPAVIDMfBL4NPC3rS1PkiRJkiQ1q9lmfw0wsf71I8ArGh4LYHorilJvcHRfkiRJktqj2QX6fg7sA9xI7Xz9syPiOWADcDbws9aWp6qrXxJjrMuQJElSxfk3p3pNs83+p4A96l+fXf/6ImAb4A7gQ60rTZIkSZIkjcSwp/FHxHhqTf1PADLzicx8BzAF2D4z/ywzHxhtQRExMyJuiIh1EXF3ROw/yH6HRsTiiFgbEXdGxOtH+9oaG07nlyRJkqTWauac/eeBH7P5efpk5vrMXNvCmi4GHqB2/v/5wLURMbFxh4jYBrgGOA/YDvgM8K2IaHYNAhXChl+SVEVOG5bKYBbVi4bdHGfmRuB+YKd2FRMR2wJvBxZk5jOZeRnwOHBwv123B7YFrslacq+idnDABQIlSZIkST2v2ZHwM6ktyjevHcVQu7Tfqsxc3rBtMbBX406ZuQr4FnBMfZT/OOBXmbmiTXWpAxzdlyRJkqTWaLbZP4va6PmdEfFwRNwREbc33kZZz2Sg/ykBa6mtC9Df1cCXgPXAF4GPDPSEEbEgIrLxNsoa1UY2/L3HjEplM6NS2cyopMFEM+evRMTXhtonM98/4mIiXgt8PzNnNWy7Erg9Mz/fsO0VwG3AW6ld7u8NwJXAPsMZ3fdDsHyeV9V+9cseFnl0xYyOnNmpDjNaDWayusxo9zCHvankjHZKU5feG00jP0z3A9MjYkZD0/5K4Ov99nsl8MvMvK1+/+aIeATYF/hRm2uUJEmSJKloRa1en5lPAj8A5kfEpIg4BtgBuLnfrncCr46IPwWIiDcALwd+08Fy1UZO55ckSZKkkWtqZL9DTgYuBVYDDwJHZub6iDgD2D0zT8rM+yPiVOCyiJgFLANOzswHx65stVp96s1YlyFJkiRJXaepc/arwvOYukcvvj87peTzmMzoyJmZ6jCj1WAmq8uMdgcz2LtKzminFDWNX+rP6fySpG5lkyFJGks2+yqeDb8kSZIkNWdE5+xHxEuB2cCk/o9l5g9HW5TUn+fvS5IkSdLwNdXsR8RewNXAXsBAw60JbNOCuqQt2PBLkiRpuPy7Ub2u2ZH9S4AJwDuBe4ENLa9IkiRJkiSNSrPN/muAozPz++0oRhqKo/uSJEmSNLRmF+j7PQOcpy91kgv2SZIkSdLWNdvsnwacERF7tqMYabhs+CVJkjQYZ4JKEM0EISLuAHYHpgFLgCf675OZ+7WquHaJCNNfEX6Qj1z9lIgij5qY0ZEzE9VhRrufeaw2M1o286eSM9opzZ6zf3f9JkmSpEHYaEiSxlpTI/tV4dHOaunF93ArlHy004yOnHmoDjPa3cxi9ZnRsplBlZzRTml2ZB+AiJgFHADsAKwCfpqZj7ayMGm4XKFfkiRJm/h3oVTTVLMfEdsAXwL+Btim4aHnI+IrwKmZubGF9UnDYsMvSZIkSS9odjX+TwIfAM4A5gB/Uv/3jPr2Ba0rTWqOK/RLkiRJUk2zq/E/DHwxM/9pgMc+Bnw0M3dvYX1t4XlM1eYI//CUfB6TGR053//VYUa7m1msPjNaLvMnKDujndLsyP5M4K5BHrur/rg0phzhlyRJktTrmm327wOOHuSxo4Hfjq4cqTVs+CVJknqPo/rSC5pdjf884KqI2B34FvBHaqP57wLexOAHAiRJkiRJUoc01exn5jUR8QS1hfr+H2A88CywCHhLZv5760uURsYV+iVJY8H/eyRJJWhqgb7NvjHiRcCOwMpuu9xery9a0mv8o2tgJS9aYkZHzvd7dZjR7mUOe4MZLZP50yYlZ7RTmp3G36fe4C9vYS1SWzjCL0mSVH3+vSdtbshmPyJuB96XmfdGxB3AVlOUmfu1qjipVWz4JUmSJPWS4Yzs3wM80/C1HZO6kg2/JEmSpF4x4nP2u1kvn8ckp3htUvJ5TGZ05Hx/V4cZ7V7msDeY0fKYPTUqOaOd8qJWPElEbN+K55E6IaKnMy9JklQ5NvrSlppq9iPi5Ij4eMP9V0fEUmBVRCyKiNktr1BqAxt+SZIkSVXW7Mj+qcDahvtfBB4Fjq0/1/ktqktqOxt+SZIkSVXV7KX3dgd+CxARM4CDgEMy8+aI2ABc2OL6pLZy0T5JUiv5f4okqRTNjuyvBybUv34TsA74Sf3+asBz99V1HOGXJEmSVDXNNvu3Ax+JiL2BjwI3ZObz9cf2pDalf1QiYmZE3BAR6yLi7ojYf5D9JkTE5yNiRUSsiYhrRvva6l02/JIkSd3JGTXSwJqdxn8a8F1gMfAH4AMNj70HuLUFNV0MPAD8FXAkcG1E7JmZ6/vtdz4wA3gZtXUE5rXgtdXDnNIvSZIkqSpiJM1NREwHVmfDN0fEPOCxzFwx4mIitgVWArtl5vL6truB0zLzxn6v/xtgz8x8cgSvY0enQfVKw1/ytUfN6Mj1yvu3F5jR7mQGe4cZLYe500BKzminNDuNH4DMXNWv0d8+MxePptGvmwus2tTo1y0G9uq33zxgGfCpiFgVEb+MiEMGesKIWBAR2XgbZY2qOKf0d5YZlcpmRqWymVFJg2mq2Y+IkyPi4w33Xx0RS4FVEbEoImaPsp7JbH5pP+r3p/TbNotaw/8YsAtwFvDNiNix/xNm5oLMjMbbKGtUD4gIm/4OMaNS2cyoVLZez6ij+tLgmh3ZP5XNm/EvUluU79j6c50/ynqeBqb22zYVeKrftmeAZ4HzM3NDZv6A2rT+ARfzk0bKhl+SJElSN2p2gb7dgd8CRMQM4CDgkMy8OSI2ABeOsp77gekRMaPhlIBXAl/vt989QNZvUlu5cJ8kSZKkbtPsyP56YEL96zcB64Cf1O+vBrYfTTH1xfZ+AMyPiEkRcQywA3Bzv/3uA34JfDwitomIw6ityn/baF5fGowj/JKkoXhgWJJUkmab/duBj0TE3sBHgRsy8/n6Y3tSm9I/WidTW6hvNXAmcGRmro+IMyLi4ob93gu8ldppBf8EHJWZq1rw+tKAbPglSZIkdYumLr0XEXsB36XW2P8BOLQ+yk5E3Ejt0nsntqPQVnKVUo1GVUZuSr4ciRkduaq8P2VGu5H56y1mdOyZOW1NyRntlKaa/b5vql3nfnW/y+/No9bsj/bye23XKx+Aap8q/OdS8gegGR25Krw3VWNGu4/56y1mdOyZOW1NKzIaET8HPp2Z32xRWR3V7DR+ADJzVfZLV2Yu7oZGX2oFL80nSZIkVVdEbAPsDSxuw3OPj4gLI2J1/faliBh08fyIeElE/CgiHo+IRyLi48N5nSFX44+I24H3Zea9EXEHQ6yAn5n7DeeFpSpwpX5JkiSpkl4GBLUrxrXaWcB/p3YwAeBHwBnAOf13rB90+C5wHXAEtVPq/z0ilmbmFVt7keGM7N9D7br2m74e6ib1FEf4JUmSpMp5FfBr4B8iYllE/DEiPtyi5/4AcF5mLsvMZcD/DXxwkH1fVr99MjOfzczfAv8KfGioFxlyZD8z39/w9fuGUbjUcxzhlyRJ6hz/7lIHvJpak70GmAMcAlwXET/MzD9s2ikiLgKO2crz7JOZDzfsPw2YDdzZsM+dwO4RsV1mrun3/ZsG6KPftn2G+gFGtEBft+uVRUs0NrolUy4sVE3d8v7T0Mxo9zF/vcWMji3zpqGMNqMRcQOwJDNPatj2IHBSZt44iufdDXgYmJGZK+vbZgDLgd0yc2m//cdTm2FwLXA28N+AG4BdMnOrg/dDjuwPUuDLgF2BSf0fy8wfjuQ5papwlF+SJEnqeq8CPr3pTtTO3d0RGO2i9E/V/90OWNnwNcCT/XfOzGcj4h3A54FHgKXA14AhTyloqtmvX17vSuAVbD6NoK8WYJtmnlOqIht+SeotfuZLUnVExExgZ+Cxhs1vA55g8+n3RMTFwHFbebq9GqfxZ+bjEbGU2mkCv69vfjXwhwGm8G/6nnuAwxpe89PAfw71czQ7sv9V4FngcOB3wIYmv1/qGZsW7vMPQEmSJKmrvAp4Djg+Is6q378Q+FhmbmzcsT7N/6Qtn2KrvgacGRG31u+fAfzLYDtHxD7UDgxs6sU/QG0Nga1qttl/BXDkaM5RkHqNo/ySJEmt499V6oBXAd+mNm1/NbUR/n/MzKtb9PznAtOpnYsPcDnwPzc9WJ8tQMN6Ae8GTgEmAr8C/jIz7xrqRZpaoC8ifgxcmZn/POxvKlAvLFqi8pT2H5MLC1VTae8zjZwZ7S5mr/eY0bFj3jQcJWe0U5od2f8QcGVErAP+g9o5C5vJzHWtKEyqGqf1S5IkSeqUZpv9lcAS4NKt7OMCfdJWOK1fkiRJUrs12+xfBhwA/BMu0CeNmA2/JEmSpHZq9pz9p4G/ycwr2ldS+1X9PCZ1l7Fq+ks+j8mMjpwHkarDjHYXs9d7zOjYMGsarpIz2ikvanL/JYDn5EsttOlcfkmSJElqlWab/dOpXQ9wTutLkXpXRNj0S1KXcqRRklSiZqfx3wHsDkyjNso/0Gr8+7WquHap8tQmdb9O/dFY8tQmMzpyNh3VYUa7h7nrTWZ0bJg3DVfJGe2UZhfou7t+k9QmXqJPkiRJ0mg1NbJfFVU+2qlqaWc+Sz7aaUZHrhc/06vKjHYPc9ebzGjnmTU1o+SMdkqz5+wPKCK2b8XzSNqc5/JLkiRJGommmv2IODkiPt5w/9URsRRYFRGLImJ2yyuUZMMvSZIkqSnNjuyfCqxtuP9F4FHg2Ppznd+iuiT14yi/JEmSpOFqdoG+3YHfAkTEDOAg4JDMvDkiNgAXtrg+Sf24gJ8kSZKkoTQ7sr8emFD/+k3AOuAn9furAc/dlzrEUX5JktQrHOSQmtfsyP7twEfq5+l/FLghM5+vP7YntSn9kjrEUX5JkiRJA2l2ZP80YC9gMbAbcGbDY+8Bbm1RXZKa4Pn8kjQ2PNgqSSpVjOQ/qYiYDqzOhm+OiHnAY5m5ooX1tUVVrz0qbTKcXJd87VEzOnI2HtVhRruDmetdZrSzzJqaVXJGO6XZkf1NpgNvioi3bbpRG+n/01YUFREzI+KGiFgXEXdHxP5D7P8/IiIjYt9WvL7U7RzllyRJknpbU+fsR8RewNXUpvIP1E0ksE0L6roYeAD4K+BI4NqI2DMz1w9Q0y7Ae4FlLXhdqTI8n1+SJFWBf8tII9PsyP4l1FbjfyfwMuDF/W57jragiNgWeDuwIDOfyczLgMeBgwf5ls8A5wAbRvvaUhV5Pr8kSZLUe5pt9l8DnJaZ12fm/Zn5UP9bC2qaC6zKzOUN2xZTm02wmYg4ANg1M7892JNFxIL6FP++WwtqlLpOqU2/GZXKZkalsplRSYNpttn/PTCpHYU0mAys7bdtLTClcUNEvAj4AvAPW3uyzFyQmdF4a2m1Upcprek3o1LZzKhUNjMqaTAjufTeGREx6un6W/E0MLXftqnAU/22vQ9YnJl3trEWSZIkSZK6TlOX3ouIO4DdgWnAEuCJ/vtk5n6jKqh2zv5KYPamy/hFxGLgY5l5Y8N+X6e2dsCmc/WnAU8Cf5eZ3xjiNZzeJEGxlyMxoyPnIkbVUfIlg8zoC8xc7zKjnWPONBIlZ7RTmm32vzbUPpn5/lFVVHudbwOPAh+j1tB/FthsNf6ImEZtyv8mtwEfBv4zM58e4vn9xJCw2a8i/yCqjpL/SDGjLzBzvcuMdoYZ00iVnNFOaerSe61o5IfpZOBSYDXwIHBkZq6PiDOA3TPzpMx8nNoq/QBExPPA8qEafUmSpFawCZEklaypkf2qqNLRTmk0Sj3aaUZHrhc/06uq5BEJM1pj3nqbGe0Mc6aRKjmjndLUyD5ARLwH+BvgpQywMn9mzmxBXZIkSZIkaYSaWo0/Io4BvgH8DpgNfBf4fv151gIXtrpASZIkSZLUnGYvvXc6cC7wkfr9izLzA8CLqa2gv66FtUmSJEnqUU7hl0an2WZ/LnBrZj4PPA9MBcjMJ4FPA3/b2vIkSZIkSVKzmm321wAT618/Aryi4bEApreiKEmSJEmSNHLNLtD3c2Af4EZq5+ufHRHPARuAs4GftbY8SZIkSZLUrGab/U8Be9S/Prv+9UXANsAdwIdaV5okSZIkSRqJGO3CFxExEZiYmWtbU1L7Venao9JolHrtUTM6ci5mVB0lXx/YjNaYt95mRtvPjGk0Ss5opwz7nP2IGB8RB0XErMbtmbm+mxp9SZIkSWWz0ZdGr5kF+p4Hfszmi/JJkiT1HBsRSVLpht3sZ+ZG4H5gp/aVI0mSJEmSRqvZS++dSW0F/nntKEaSJEmSJI1eUwv0RcQdwBxgB+AR4I/AZk+Qmfu1sL62qMqiJdJolbpoiRkdOacWV0fJCwuZUbMmM9puZkyjVXJGO6XZS+/dXb8NxlRKkiRJkjTGmm32HwT+JTMf7f9AROwC/E1LqpIkSZLUkxzVl1qj2Wn8zwMHZObtAzz2OuD2zNymhfW1RRWmNkmtUOrUJjM6cv6BVB0lTz80o2ZNZrSdzJdaoeSMdkqzC/QFg0/Vnw08PrpyJEmSJEnSaA05jT8iTgROrN9N4MsRsbbfbpOAecC/tbY8SZIkSZLUrOGcs78OWFX/OoA1wOp++2wAfgRc1LrSJEmSJEnSSDR7zv7XgHMy88H2ldR+3X4ek9QqpZ7HZEZHzvMcq6Pkcw17PaPmTGBG28mMqRVKzminNNXsV0W3fwBKrVLqB6AZHble/EyvqpL/SOn1jJozgRltF/OlVik5o53S7AJ9kiRJkiSpcDb7kiRJkiRVjM2+JEmSJEkVY7MvSZIkSVLF2OxLkiRJklQx44baISLuAIa9LGZm7jeqiiRJkiT1HFfil1pryGYfuIcmmn1JkiRJkjS2orQjaBExE7gUeAPwAPDXmfnTAfb5f4E3AtsA/ws4OTMfG+ZrlPVDS2Ok1GuPmtGRK+0zXSNX8vWBez2j5kxgRtvBbKmVSs5op5R4zv7F1Jr86cD5wLURMbHfPpOpNfh7AbOAZcAlnSxSkiRJkqRSFTWyHxHbAiuB3TJzeX3b3cBpmXnjVr5vHvBvmbnLMF+nnB9aGkOlHu00oyNX0me6RqfkEYlezqgZ0yZmtPXMl1qp5Ix2StMj+xHxnoi4KSIejojl/W+jrGcusGpTo1+3mNoI/tYcBPxmlK8tSZIkSVIlNNXsR8QxwDeA3wGzge8C368/z1rgwlHWM7n+PI3WAlO2UtOLgXOAswd5fEFEZONtlDVKaiEzKpXNjEplq0pGHdWXWq+pafwR8UvgW9TOpX8W2Dczf1Gffv/vwLcy859GXEzEa4HvZ+ashm1XArdn5ucH2H9H4Bbgc5n5lSZex08TCafxV5F/LFVHydMPezmjZkybmNHWMltqtZIz2inNTuOfC9yamc8DzwNTATLzSeDTwN+Osp77gekRMaNh2yuBe/vvGBFTgB8BVzbT6EuSJEmSVHXNNvtrgE0r4z8CvKLhsaC2gv6I1Q8a/ACYHxGT6qcN7ADc3LhfREwAvgMsysxPjuY1JUmSJEmqmnFN7v9zYB/gRmrn658dEc8BG6idM/+zFtR0MnApsBp4EDgyM9dHxBnA7pl5EnAA8GbgwIg4btM3Zuag5/ZLkiRJktQrmj1nf39gj8y8OiK2p7ZY39uAbYA7gPdm5gNtqbSFuvE8JqkdSj2PyYyOnOc8VkfJ5xr2ckbNmDYxo61lttRqJWe0U5pq9gd8goiJwMTM7L+KfrG68QNQaodSPwDN6Mj5x1J1lPxHSi9n1IxpEzPaOuZK7VByRjul2UvvvSoi3ta4LTPXZ+baiHhbROzT2vIkSZIkSVKzml2g7/PAnw3y2J/WH5ckSaocRx8lSd2k2Wb/tcCtgzx2G/Ca0ZUjSZIkSZJGq9lmfxtg8iCPTQYmjK4cSZIkSZI0Ws02+3cAHxrksQ9RuzSfJEmSJEkaQ+Oa3H8BcFNE/IzaZfceA3YBTgBeBRza0uokSZIkSVLTmr70XkQcDHwK2A8IYCPwM+D/ysyftLrAdui2y5FI7VLq5UjM6Mi5gFh1lHzJoF7NqPlSIzPaGuZK7VJyRjul6Wa/7xsj/g9gGvB4Zq5raVVt1k0fgFI7lfoBaEZHzj+aqqPkP1J6NaPmS43MaGuYK7VLyRntlGbP2e+Tmesy85Fua/RL84//+I9cccUVPV+DJEmSJKl1hhzZj4jbgfdl5r0RcQew1W/IzP1aWF9bdNPRTqmdSj3aaUZHzhGS6ih5RKJXM2q+1MiMtoa5UruUnNFOGc4CffcAzzR8bSIlSZIkSSrYkNP4M/P9mflg/ev31e8Pemt/yWPvwQcf5OMf/zi33XYba9eu5eabb2b27Nl9j7/uda/jlltu4fHHH+eee+7h6KOPHvS55s+fz3e+852++5nJSSedxOLFi1mzZg3XX389U6dOBeD666/nrLPO2uz7v/KVr/ClL30JgGOOOYbFixezdu1aHnroIc4555zN9v3MZz7DsmXLWLt2Lb/73e94+9vfPmANW6t//vz5fPe73+VLX/oSjz/+OA899BDvfve7m/0VSpIkSZLaqKlz9iPi7IiYNchju0TE2a0pq3zHHnss733ve5kxYwZPP/005557LgDbbbcdN9xwA1dddRUzZszgwx/+MJdccgkHHnjgsJ/7Xe96F3/+53/O7rvvzuzZs/n7v/97AC699FKOP/74vv0mTJjAu971LhYuXAjA6tWreec738nUqVM54ogj+NCHPsQxxxwDwGGHHcbRRx/Na1/7WqZOncqb3vQm7rvvvi1eezj1/8Vf/AU/+clPmD59OmeddRb/8i//wpQpU5r/JUqS1CWcaiy1nrmS2qvZBfrmA7MHeWxW/fGecNFFF7FkyRLWr1/P5Zdfzute9zoA3v72t7NixQouvPBCnnvuOW655RauuOIKTjzxxGE/92c+8xlWrFjBmjVruPbaa/ue+3vf+x4zZsxgv/1qyyIcccQR/PGPf+T2228H4IYbbuD+++8H4Fe/+hVXXnklBx98MAAbNmxg0qRJ7L333owbN44//OEPffs2Gk79v/jFL7jmmmvYuHEjCxcuZMKECbz0pS9t/pcoSZIkSWqLZpv9YPBz9mcDj4+unO7x2GOP9X399NNPs+222wIwe/ZslixZstm+S5Ys2Wya/0ife8OGDXzzm9/kuOOOA+CEE07g0ksv7dv3sMMO49Zbb2XFihU88cQTnHTSSey4444A3HzzzcyfP59zzz2XlStX8q1vfYs5c+Zs8drDqb+xPoBnnnmmr0ZJkiRJ0tgbstmPiBMj4scR8WNqjf6XN91vuP0XcBnwn+0uuHRLly7doomeM2cOS5cubcnzL1y4kKOPPppddtmFww47jMsuuwyA8ePH8+1vf5tLLrmEXXfdle23356LL76YiBcWoPzyl7/MAQccwB577MGzzz7LF7/4xY7XL0mSJElqv+GM7K8DVtVvAaxpuL/p9iDwGeBD7Smze/zwhz9k5syZnHzyyWyzzTYceOCBHHPMMZuNwI/GLbfcwlNPPcVXv/pVbrvtNh5++GEAJk6cyKRJk1i1ahUbNmxg//3359hjj+37vn333ZcDDjiA8ePHs27dOp588kmee+65jtcvSZIkSWq/IS+9l5nfBL4ZEeOBHwGfzMyftL2yLvXEE0/w1re+lS984Qt86lOf4tFHH+WUU07h1ltvbdlrXHbZZXziE5/gAx/4QN+2p556io985CN85StfYcqUKdx8881cddVV7LbbbgBMnTqVCy64gJe85CU8++yz3HbbbZx88sljUr8kSZIkqb1iuKtgRsSLgP8NvDUz/7+2VtVmEeHSnxKQmTH0Xp3oVjAFAAAgAElEQVRnRkfOlY2rIyLMaEHMlvozo6NnrtROJWe0U4a9QF9mbgTuA3ZqXzmSJEmSqs5GX2q/ZlfjPxM4OyLmtaMYSZIkSZI0esOexg8QEXcAc4AdgEeAP9LvUnyZuV8L62uLbpnaJLVbqVObzOjIOVJSHSVPP+zFjJot9WdGR8dMqd1KzminDLlAXz9312+SJEmSJKlQTY3sV0U3HO2UOqHUo51mdOR68TO9qkoekejFjJot9WdGR8dMqd1KzminNDuyD0BE7AW8DtgN+GpmPhYR/w34Y2Y+2coCJUmSxpJNiSSpGzXV7EfEFOCrwFHAs/XvvwF4DPifwMPAx1pcoyRJkiRJakKzq/F/DjgQOATYFmicFvFD4C0tqkuSJElSBTlbRuqMZqfxvxP4u8z8j4jYpt9jDwF7tKYsSZIkSZI0Us2O7P8JsGqQx7YFnh9dORARMyPihohYFxF3R8T+g+w3NyJuq+/304iYO9rXliRJkiSpCppt9u8AThjksaOA/xpdOQBcDDwATAfOB66NiIkD7Hc18D1gB+C7wFUteG1JkiRJkrpeU5fei4j/DtwE3AJ8E7gImA+8jFqz/4bMvGPExURsC6wEdsvM5fVtdwOnZeaNDfu9HLgNmJGZz0XEOGAFsH9m/nYYr+OJQhJeeq+KPA+yOkq+ZFCvZdRcaSBmdOTMlDqh5Ix2SlPn7GfmLRFxCLUR9wupLdD3SeCnwJtH0+jXzQVWbWr06xYDewE3NmzbC/h1Zj5Xr+u5iPhNfftmzX5ELKB2QEJSgcxoa0X09P9pagMzaq5Utm7MqJmSOmPIkf2IGJ+Zzw6w/U+AacATmbmuJcVEvB7458x8ecO2S4ClmXluw7bjgWMz8y0N224ELsvMha2opZ0iIks/ylR6jaXXB+XXWHp9Y6kbfjel11h6fVB+jaXXN5a64XdTeo2l1wfl11h6fWOpG343pddYen1Qfo2l19cJwzln/7GI+EpEvCkaDsNl5jOZ+WirGv26p4Gp/bZNBZ4a4X6SJEmSJPWc4TT7VwL/J7Vz9R+JiM9HxJ+1qZ77gekRMaNh2yuBe/vtdy/wivq5+tT/ffkA+0mSJEmS1HOGbPYz82+BXYG/AH4IHA/8V0Q8EBHnRcQrW1VMZj4J/ACYHxGTIuIYaqvt39xvv98ADwIfq6/U/zHggeEszidJkiRJUtUN69J7mbkxM2/KzL8GdgbeAdwKnAr8KiLujoh/jIg9W1DTydQW6lsNnAkcmZnrI+KMiLi4Yb+jgb8EngD+CnhvC167Uz451gUMQ+k1ll4flF9j6fWNpW743ZReY+n1Qfk1ll7fWOqG303pNZZeH5RfY+n1jaVu+N2UXmPp9UH5NZZeX9s1dem9Lb65Nqr+duAYao03mdnUCv+SJEmSJKm1hjWyvxWvAd4AHFh/rodHXZEkSZIkSRqVpkfhI+I11KbQvxvYHVgOfBO4MjNva215kiRJkiSpWcNq9iPiFdQa/PdQO59+DfAdaiv1/zgzN7atQkmSJEmS1JQhz9mPiLuAvYFngO9Ta/B/lJkb2l+eJEmSJElq1nBG9h8Czgeuz8yn21yPJEmSJEkapVGtxi9JkiRJksoz2tX4JUmSJElSYWz2JUmSJEmqGJt9SZIkSZIqxmZfkiRJkqSKsdmXJEmSJKlibPYlSZIkSaoYm31JkiRJkirGZl+SJEmSpIqx2ZckSZIkqWJs9iVJkiRJqhibfUmSJEmSKsZmX5IkSZKkirHZlyRJkiSpYmz2JUmSJEmqGJt9SZIkSZIqxmZfkiRJkqSKsdmXJEmSJKlibPYlSZIkSaoYm31JkiRJkirGZl+SJEmSpIqx2ZckSZIkqWJs9iVJkiRJqpjimv2I+GRE3BsRGyPiqK3s92cRcXdErIuIGyNiZifrlCRJkiSpVMU1+8D9wN8Btw+2Q0RMAr4NnA9MB34PfLkj1UmSJEmSVLjimv3MvCwz/x3431vZ7WDg8fq+zwALgMMjYkoHSpQkSZIkqWjjxrqAEdoLuGvTncxcHhGrgbnALxt3jIgFwPyOVid1icyMsa7BjEqDM6NS2cyoVLYSMjqWIjPHuoYBRcTNwIWZ+a0BHvsEsGtmntSw7bfAX2fmT4bx3GX+0GOo1PeB2iciiv0ANKMvMJu9y4x2D3Pam8xo9zCjvankjHZKcdP4h+lpYGq/bVOBp8agFkmSJEkFstFXL+vWZv9eYN6mO/WV+KdRW9xPIxDR0we9JEmSJKlSimv2I2J8fbX9FwHjI2JSbNmJ3gxMj4hj6vueDfwgMx3ZlyRJHeOooSSpVMU1+8A/A88ArweuqH+9R0RcHBFnAGTm/wbeCZwJrAZeCpwyNuVWh6P7kiRJqgoPxqnXFbtAXzu5aMngevH90KtKXrTEjL7ATPYuM9odzGjvMqPlM5+9reSMdkqJI/uSJEmSJGkUbPa1GafyS5IkSVL3s9mXJEmSVClO4Zds9jUAR/clSZIkqbvZ7EuSJEmSVDE2+xpQr4zu77333nz/+9/v2deXSjfWGRnr15dKNtb5GOvXl0o31hkZ69eXl97TVvTie6OXlHw5EjP6AnPYu8xo+cxnbzOj5TKbgrIz2imO7GtQvTK6L0mSJElVY7OvnjZnzhyuu+46vv71r/PqV7+ac845h5kzZ7LTTjvxhS98AYDly5czceJEHnroob7ve+aZZ9huu+34+c9/DsBxxx3HrFmzmDp1Kq973ev4j//4j759H3jgAQ455BC22247pk2bxgEHHMC6des2e32oHYW+4IILeMlLXsIOO+zAW97yFh544IHNav30pz/N/vvvz7bbbssb3/hG/vCHP7T9dySNJTMqlct8SmUzo7LZ11b10uj+Pffcw+TJk3nkkUe4+uqrOf300/n973/PzJkzOfTQQ7n88sv79r3++uuZNWsW++67LwCHHHIIv/71r1m1ahVHH300Rx11FE8++SQAZ555JnPnzmXlypUsX76cCy64gHHjxm3x+gsXLuRzn/sc1113HcuWLWOfffbh8MMP57nnnuvb5/LLL+fKK69kxYoVTJ48mU984hNt/q1I5TCjUrnMp0rhFP6BmdHeZLMv1e24446cdtppjB8/noMPPpg5c+Zw5513AnD88cezcOHCvn0XLlzICSec0Hf//e9/P9tttx3jx4/n9NNPZ+PGjdx1110ATJgwgWXLlrFkyRLGjx/PgQceyIQJE7Z4/YULF/LRj36UefPmMXHiRM477zyWLl3K7bff3rfPKaecwotf/GImTZrEsccey6JFi9r165CKY0alcplPqWxmtDfZ7GtIvTK6v9NOO212f/LkyX1HLd/xjnfw6KOPsmjRIpYvX85NN93EcccdB8DGjRv7jmpOnTqV7bffnjVr1rBy5UoAPvvZz7Lrrrvy5je/mTlz5rBgwQI2bty4xesvXbqUOXPm9N2fMGECs2bNYunSpX3bdt555wHrk3qBGZXKZT6lspnR3rTlHAtpAPXVLMe6jDEzadIkjjrqKBYuXMicOXM46KCD2G233QC44ooruOKKK7jxxhuZO3cuEcG0adP6fl8zZ87koosuAuCuu+7i0EMPZd68eRx55JGbvcbs2bNZsmRJ3/0NGzawbNkyZs+e3ZkfUupiZlQql/mUymZGq8uRfWmYjj/+eK666iq+8Y1vbDa1ae3atUyYMIEdd9yRDRs2MH/+fNauXdv3+DXXXMPDDz9MZjJt2jTGjRs34LlMxx13HBdeeCH33nsv69evZ/78+cyaNYv99tuvIz+f1O3MqFQu86lO6OWBqdEyo9Vks69h65Xp/IN54xvfyMSJE7nvvvs2O1p54oknsvfee7PHHnuw5557MmXKlL6joQCLFi3iwAMPZMqUKRxwwAF88IMf5Igjjtji+U844QROPfVUDj/8cHbeeWd+8Ytf8L3vfW/AD0xJWzKjUrnMp1Q2M1pN0YtHwCKi937oFunF90tV1U/NKPIIjhl9gZnrXWa0bGZTZrQ85lKNSs5opziyr6b0+ui+JEmSJHUDm31JkiRJXc1RfWlLNvtqmqP7kiRJklQ2m31JkiRJkirGZl8j4ui+JEmSJJXLZl8jZsMvSZKkseb5+tLAbPYlSZIkSaoYm32NiqP7kiRJklQem31JkqQmOGVYktQNbPY1ao7uS5IkaSx48E0anM2+WsKGX5IkSZLKYbMvSZIkSVLF2OyrZRzdlyRJkqQyFNfsR8TMiLghItZFxN0Rsf8g+x0aEYsjYm1E3BkRr+90rZIkSZIklai4Zh+4GHgAmA6cD1wbERMbd4iIbYBrgPOA7YDPAN+KiBJ/np7i6L4kSZI6wcX5pK2LkkISEdsCK4HdMnN5fdvdwGmZeWPDftOBPwLjMzPrTf4GYJfMXDGM1ynnh66okt5XGlhEkJlFHp0xoy8wS73LjJbLXArMaAnMoram5Ix2Smkj4XOBVZsa/brFwF6NO2XmKuBbwDH1Uf7jgF8N1OhHxIKIyMZbG+uX1CQzKpXNjEplM6OSBlPayP7rgX/OzJc3bLsEWJqZ5/bb96+AfwWmAk8Bb8nMnw7zdcr5oSuspPeWtlTy0U4z+gJz1LvMaLnMpcCMlsAsamtKzminlDay/zS15r3Rpma+T0S8Avga8HZgAvCXwHciYkYnitTweP6+JKlqbC6kMphFaWilNfv3A9P7Ne2vBO7tt98rgV9m5m2ZuTEzbwYeAfbtTJmSJEmSJJWrqGY/M58EfgDMj4hJEXEMsANwc79d7wReHRF/ChARbwBeDvymg+VqGBzdlyRJkqTOGzfWBQzgZOBSYDXwIHBkZq6PiDOA3TPzpMy8PyJOBS6LiFnAMuDkzHxw7MrWYOrny4x1GZIkSZLUM4paoK9TemXRkpL04vusdCUvWmJGX2B2epcZLZOZ1CZmdOyYQw1HyRntlKKm8au6nM4vSZIkSZ1js6+OseGXJEmSpM6w2ZckSZIkqWJs9tVRju5LkiRJUvvZ7KvjbPglSZI0Ei7OJw2fzb7GhA2/JKnb2GRIkrqJzb4kSZIkSRVjs68x4+i+JEmSJLWHzb7GlA2/JEmShsNTaaTm2OxLkiRJklQxNvsac47uS5IkSVJr2eyrCDb8kiRJktQ6Nvsqhg2/JEmSJLWGzb6KYsMvSZKk/lycT2qezb4kSdIQbDQkSd3GZl/FcXRfkiRJkkbHZl9FsuGXJEmSpJGz2VexbPglSZIkaWRs9lU0G35JkqTe5poZ0sjY7Kt4NvySJEmS1BybfUmSJEmSKsZmX13B0X1JkiRJGj6bfXUNG35JkiRJGh6bfXUVG35JkqTe4eJ80sjZ7Kvr2PBLkiRJ0tbZ7Ksr2fBLkjrFkUVJUjey2VfXsuGXJEmSpIHZ7Kur2fBLkiRJ0paKa/YjYmZE3BAR6yLi7ojYf5D9JkTE5yNiRUSsiYhrOl2rymDDL0mSVD2eQiONzrixLmAAFwMPAH8FHAlcGxF7Zub6fvudD8wAXgasBeZ1tEoVJSL8D0GSJEmS6qKkBikitgVWArtl5vL6truB0zLzxob9pgO/AfbMzCdH8Drl/NBqqZLez6WrHyApclqEGX2B7+neZUbLYQ41EDPafmZPo1FyRjultGn8c4FVmxr9usXAXv32mwcsAz4VEasi4pcRcchATxgRCyIiG2/tKV3SSJhRqWxmVCqbGZU0mNKa/cnUpuQ3WgtM6bdtFrWG/zFgF+As4JsRsWP/J8zMBZkZjbc21K1CeP5+9zGjUtnMqFQ2MyppMKU1+08DU/ttmwo81W/bM8CzwPmZuSEzf0BtWv+Ai/mpt9jwS5IkdTen8EujV1qzfz8wPSJmNGx7JXBvv/3uAbJ+k7YQETb9kiRJknpWUc1+fbG9HwDzI2JSRBwD7ADc3G+/+4BfAh+PiG0i4jBqq/Lf1uGSVTgbfknSaDi6KEnqVkU1+3UnU1uobzVwJnBkZq6PiDMi4uKG/d4LvJXaOf3/BByVmas6Xq2KZ8MvSZIkqdcUdem9TnGV0t7Ui+/1rSn5ciRm9AW+b3uXGS2DGdRgzGh7mT2NVskZ7ZQSR/altnCEX5IkqXw2+ipJRPw8It411nWMhM2+eooNvyRJkqThiIhtgL2BxW147r+tH0hYHxHXtfr5Aca140mlktWn9Ix1GZIkSZLK9jIgqF01rtUeBc4D3gzMbsPzO7Kv3uQIvyRJkqQhvAr4NfAPEbEsIv4YER9uxRNn5rcz8zpgZSuebyA2++pZNvySJEmStuLV1Eb31wBzgPcDX4qI3Rp3ioiLIuKJrdx273zpTuNXj3NKvyRJUjn8u0yFeRVwaWZ+pX7/hxHxCLAX8IdNO2XmKcApY1DfVjmyr57nCL8kSZKkAbwKuHrTnag1DjsCK8asoibY7EvUGn6bfkmSJEkAETET2Bl4rGHz24AngDv77XtxRDy1lduYTOO32Zca2PBLkjZxOrEk9bRXAc8Bx0fEiyLiNcCFwMcyc2Pjjpl5UmZO2crt4f5PHhHjImIStVPrXxQRkyJiQit/AM/Zl/rxPH5JkiSp570K+Da1afurqY3w/2NmXr3V7xq+s4D5DfefAf4TOLhFz0/0YlMTEb33Q6tpVc9G/aBGkVMZzOgLqv4+1ODM6Ngzf9oaM9oe5k6tUnJGO8Vp/NIgnNIvSZLUOTb6UmvZ7Etb4cJ9kiRJkrqRzb40DDb8kiRJkrqJzb40TDb8kiRJkrqFzb7UBBt+SZIkSd3AZl9qkufxS5IktZaL80mtZ7MvjZANvyRJkqRS2exLo+AovyRVk6OMkqRuZ7MvtYANvyRJkqSS2OxLLWLDL0mSJKkUNvtSCzmtX5IkSVIJbPalNrDhlyRJGh7XyJDaw2ZfahNH+SVJkiSNFZt9qc1s+CVJkiR1ms2+1AGO8kuSJEnqJJt9qYNs+CVJkiR1gs2+1GGO8kuSJElqtyKb/YiYGRE3RMS6iLg7IvYfYv//EREZEft2qkZptGz4JUlSr3Mlfql9imz2gYuBB4DpwPnAtRExcaAdI2IX4L3Ass6VJ7WGo/ySVB6bD0lSFRTX7EfEtsDbgQWZ+UxmXgY8Dhw8yLd8BjgH2NCZCqXWs+mXJEmS1ErFNfvAXGBVZi5v2LYY2Kv/jhFxALBrZn67U8VJ7WTDL0mSJKkVSmz2JwNr+21bC0xp3BARLwK+APzD1p4sIhbUz+fvu7W0WqnFem2U34xKZTOjUtnMqKTBlNjsPw1M7bdtKvBUv23vAxZn5p1be7LMXJCZ0XhrXalS+/RK029GpbKZUalsZlTSYEps9u8HpkfEjIZtrwTu7bffG4B3R8TKiFgJ7AbcFBEndqhOqSN6oeGXJEm9x8UwpfaKEkMWEd8GHgU+BrwT+CywZ2aub9hnGrUp/5vcBnwY+M/MfHqI5y/vh5aGoZV5jQhKPfpvRl9Q4me0OsOMjh1zp+Ewo6Nn1tROJWe0U8aNdQGDOBm4FFgNPAgcmZnrI+IMYPfMPCkzH6e2Sj8AEfE8sHyoRl/qZptG+f3PUZIkSdLWFDmy327dcrRTGspo8lvy0U4z+oJe/IxWjRkdO+ZOw2FGR8+sqZ1KzminlHjOvqRh6pVF/CRJkiQ1x2ZfqgCbfkmSJEmNbPalCrHhlyRJ3cAp/FL72exLFeMovySNnA2IJKkqbPalirLplyRJknqXzb5UcTb9kiRJUu8ZN9YFSOqMxobfaaqSJElStTmyL/UgR/olSZKkarPZlyRJktQxzjCUOsNmX5IkSZKkirHZlyRJkiSpYmz2JUmSJEmqGJt9SZIkSZIqxmZfkiRJkqSKsdmXJEnCFcIlSdVisy9JkiSpIzyoJnWOzb4kSZIkSRVjsy9JkiRJUsXY7EuSJEmSVDE2+5IkSZIkVYzNviRJkiRJFWOzL0mSJKntXIlf6iybfUmSJEmSKsZmX5IkSZKkirHZlyRJkiSpYmz2JUmSJEmqGJt9SZLU81w4TJJUNTb7kiRJkiRVjM2+JEmSpLZy9ozUecU1+xExMyJuiIh1EXF3ROw/yD7fjIjlEbEqIr4TETuPRb2SJEmSJJWmuGYfuBh4AJgOnA9cGxET++0zGfhfwF7ALGAZcEkni5QkSZIkqVRR0pSaiNgWWAnslpnL69vuBk7LzBu38n3zgH/LzF2G+Trl/NDSGMrMGOsaBmJGX1DSZ7Q6KyLMaAeZNTXLjDbHjKnTSs5op5Q2sj8XWLWp0a9bTG0Ef2sOAn4z0AMRsSAisvHWololtYAZlcpmRqWymVFJgyltZP/1wD9n5ssbtl0CLM3Mcwf5nhcDPwOOzMyfDPN1yvmhpTFU6tFOM/qCkj6j1Vklj0hUMaNmTc0yo80xY+q0kjPaKaWN7D8NTO23bSrw1EA7R/z/7d1/kBf1fcfx51tBSQIXlR9WJch0RiViEiPWIomJOhM0wwyxJhoETTLN1KDO1HFq7ag0qLQdazJORxMEY60DBIlRqRotdmKkFYMxv8agSEQFIklQBPltQMqnf+wefDnvuO8d993v3t7zMbNzfHc/3/2+du/7/h7v73d3vzEE+C9gWr2NviRJkiRJVVe2Zn8lMDgihtbMOwVY3nZgRAwka/TvTyndXVA+SZIkSV3gp/pSc5Sq2U8pbQUeB6ZHxICImAwcBSyuHRcRhwELgV+mlG4uPKgkSZIkSSVWqnP2ASLiaGAOcBawCvh6Sum5iLgBGJFSmhoRnyV7A2AHsHcDUkoD63yMcm201CRlPY/JGt2nbK/RKk6ZzzWsYo1aa+oqa7R+1peaocw1WpTSNftFKNsLoNQsZX0BtEb36Yuv0cqU+T8pVatR60zdYY3WzxpTM5S5RotSqsP4JUmSJEnSwbPZlyRJkiSpYmz2JUmSJEmqGJt9SZIkSQ3h+fpS89jsS5IkSZJUMTb7kiRJkiRVjM2+JEmSJEkVY7MvSZIkSVLF2OxLkiRJklQxNvtNdv311zN//vw+n0GSJEmS1HOiL34dRkT0vY2W2pFSimZnaI81uk9ffI1WJiKs0YJYZ+oOa7Q+1peapcw1WhQ/2ZckSX2WjYjUONaX1Fw2+92watUqrrvuOpYuXcqWLVtYvHgxw4cP37t8zJgxLFmyhHfeeYeXXnqJSZMmdbiu6dOns3Dhwr23U0pMnTqVZcuWsXnzZh555BFaWloAeOSRR5g2bdp+97/77ru58847AZg8eTLLli1jy5YtrFmzhltuuWW/sbfddht//OMf2bJlC6+++ioTJkxoN8OB8k+fPp1HH32UO++8k3feeYc1a9Zw8cUXd3UXSpIkSZIayGa/m6ZMmcIll1zC0KFD2b59OzNmzADgwx/+MIsWLWLBggUMHTqUb3zjG8yePZtx48bVve6LLrqIc889lxEjRjB8+HCuueYaAObMmcNll122d9xhhx3GRRddxNy5cwHYuHEjF154IS0tLUycOJHLL7+cyZMnAzB+/HgmTZrEaaedRktLC+eccw6vvPLK+x67nvznnXcezzzzDIMHD2batGncc889DBw4sOs7UZIkSZLUEDb73TRz5kxWr17Nzp07+f73v8+YMWMAmDBhAuvXr+c73/kOu3fvZsmSJcyfP5+vfvWrda/7tttuY/369WzevJmHHnpo77ofe+wxhg4dyhlnnAHAxIkTefPNN3n++ecBWLRoEStXrgTghRde4P777+fss88GYNeuXQwYMIDRo0fTr18/3njjjb1ja9WT/1e/+hUPPPAAe/bsYe7cuRx22GGceOKJXd+JkiRJkqSGsNnvpnXr1u399/bt2xk0aBAAw4cPZ/Xq1fuNXb169X6H+Xd33bt27eKHP/whl156KQBf+cpXmDNnzt6x48eP59lnn2X9+vVs2rSJqVOnMmTIEAAWL17M9OnTmTFjBm+//TYPPvggI0eOfN9j15O/Nh/Au+++uzejJEmSJKn5bPZ72Nq1a9/XRI8cOZK1a9f2yPrnzp3LpEmTOOaYYxg/fjzz5s0DoH///jz88MPMnj2b4447jiOOOIJZs2YRse8ClHfddRdnnnkmxx9/PO+99x533HFH4fklSZIkSY1ns9/DnnjiCYYNG8YVV1zBoYceyrhx45g8efJ+n8AfjCVLlrBt2zbuvfdeli5dyu9+9zsADj/8cAYMGMCGDRvYtWsXY8eOZcqUKXvvd/rpp3PmmWfSv39/duzYwdatW9m9e3fh+SVJkiRJjWez38M2bdrE5z//eS699FI2bNjAPffcw5VXXsmzzz7bY48xb948zj///P0a8G3btnHVVVdx9913s3nzZq6//noWLFiwd3lLSwszZ85kw4YNrFu3jmOPPZarr766KfklSZJUbX7tntR80RcLMSL63kZL7UgpReejimeN7tMXX6OViQhrtADWmLrLGj0wa0vNVuYaLYqf7EuSJEmSVDE2+5IkSZIkVYzNviRJkiRJFWOzL0mS+iTPKZYkVZnNviRJkiRJFWOzL0mSJElSxdjsS5IkSeoxniIjlYPNviRJkiRJFVO6Zj8ihkXEoojYEREvRsTYDsadEBFL83HPRcQJRWeVJEmSJKmMStfsA7OA14HBwK3AQxFxeDvjfgA8BhwFPAosKCyhJEmSJEklFmU6pyYiBgFvAx9JKb2Vz3sR+LuU0pM140YBS4GhKaXdEdEPWA+MTSn9to7HKc9GS02UUopmZ2iPNbpPmV6jVayIsEYbzPrSwbBGO2ZtqQzKXKNF6dfsAG2cAGxobfRzy4CTgSdr5p0MvJxS2g2QN/wr8vn7NfsRcRMwvZGhJXWfNXpgEX36b5RKoMo1an2pCspYo9aWVA5l+2T/LOB7KaVRNfNmA2tTSjNq5l0GTEkpnV8z70lgXkppbpGZuyMiUtnfZSp7xrLng/JnLHu+ZuoN+6bsGcueD8qfsez5mqk37JuyZyx7Pih/xrLna6besG/KnrHs+aD8GcuerwhlO2d/O9DSZl4LsK2b4yRJkiRJ6mIg2PUAAAsKSURBVHPK1uyvBAZHxNCaeacAy9uMWw58ND9Xn/znqHbGSZIkSZLU55Sq2U8pbQUeB6ZHxICImEx2tf3FbcatAFYB1+ZX6r8WeL2ei/NJkiRJklR1pWr2c1eQXahvI3Aj8MWU0s6IuCEiZtWMmwRcAGwC/gq4pPCk3XdzswPUoewZy54Pyp+x7PmaqTfsm7JnLHs+KH/Gsudrpt6wb8qesez5oPwZy56vmXrDvil7xrLng/JnLHu+hivVBfokSZIkSdLBK+Mn+5IkSZIk6SDY7EuSJEmSVDE2+5IkSZIkVYzNfoNExLCIWBQROyLixYgY28G41fmYbflUyIUkIuLmiFgeEXsi4ksHGPeXef4dEfFkRAwrIl8XM6aa/bctIr5eUL7DI+K+iPh9RGyKiKci4qQOxp4QEUvz/fhcRJxQsnxNeR42kzVaWL6m1Gf+2NZoL2aNFpbPv6E9k9EatUYblc8a7ZmMfa5GwWa/kWYBrwODgVuBhyL7msD2fCalNDCfpheUbyVwNfB8RwMiYgDwMFn+wcBrwF2FpMt0mrHGyJp9+O8NztWqH/AqcAbZ/vkx8EAHY38APEb2VZKPAgtKlg+a8zxsJmv04JS9PsEa7e2s0YNT9hote32CNdoZa/TgWKMHzxrtTErJqYcnYBCwExhWM+9F4Lx2xq4GTm9i1sXAlzpYdj7wYs3tYfl2DSxLxnx5AoaU5PeegAFt5o8C3gH65bf75bdPKkO+fFlTn4dN+l1Zow3Oly8vRX3W/N6t0V4wWaPF5MuXl6JGy16fB8qYL7NGrdEez5cvt0YPMmO+rE/VaOvkJ/uNcQKwIaX0Vs28ZcDJHYz/UUSsi4gFEXF04+PV7WTgN6038u3ZSLZ9ZfObiFgbEbMiYlCTMnwKWJ1S+lOb+ScDL6eUdgPkP1fQ8fOh6Hytyvo8bARrtFhlqE+wRnsTa7RYZajRstcnWKO1rNFiWaP1sUbbsNlvjA8BW9rM2wIMbGfsZOB4snfFdgDzGhutS7qyHc10Ftk+PB0YAdxedICIOAr4LnBjO4ubvh87yQflfh42gjVanKbXJ1ijvZA1Wpym12jZ6xOs0XZYo8WxRutgjbavX7MDVNR2oKXNvBZgW9uBKaWf5v/cGRFXA5si4kMppe0NzliPurejmVJKS/J/rouIvweeBv6mqMePiA+Qn5+UUprfzpCm7sc68pX9edgI1mhBml2fYI32UtZoQZpdo2WvT7BGO2CNFsQa7Zw12jE/2W+MlcDgiBhaM+8UYHkn90v5FI0K1kXLgY+13sivTnok2faVVSrywSKiH9mFQF5JKXX0TuJy4KP52Nb7jKLz50NR+doq2/OwEazR5ii0PsEa7cWs0ebwb2j3MrZVtudhI1ijzWGNdi9jW2V7HjaMzX4DpJS2Ao8D0yNiQERMJrs65eLacRExIiLGRkS//PybfwP+N6XU8HfCIqJ/fgXSQ4D+ec62T/jFZC/kk/Ox3wQeLyJfvRkjYnREfCwiDsn/4HwL+FER+XL35Pku72hASmkFsAq4Nr9K7bXA6yml35YhXzOfh81ijRaTrwT1CdZor2SNFpOvBDVa9voEa7Rd1mgx+azRulijB9LsKwRWdQKOBp4kOyfkJWBsPv8GYFb+79FkVy7dBrxF9rUVxxSU7z72vavVOo0k+xqVG2rGjc3z7wD+Gzi6wH3YaUbgXLJ3X7cDfwBmAy0F5Ts+z/Ru/jtsnUbU/p7zsScCz+VjfwacWJZ8zXweNnOyRhufr5n1mT++NdqLJ2u08fmaWaNlr8+uZLRGrdFG5bNGeyZjX63RlBKR7wBJkiRJklQRHsYvSZIkSVLF2OxLkiRJklQxNvuSJEmSJFWMzb4kSZIkSRVjsy9JkiRJUsXY7EuSJEmSVDE2+5IkSZIkVYzNviRJkiRJFWOzL0mSJElSxdjsS5IkSZJUMTb7kiRJkiRVjM2+JEmSJEkVY7MvSaqsiLgpIlI704/z5fdFxC9qxl8cEV9rWuBuaLsNZRIR34yI30fEnjxnQ/Z3RHwsIp6IiA35tDAihh3seiVJ6s36NTuAJEkNthk4v515ADOAD9TMvxgYAtzX+FjVFhGnAzcDNwCLgbfyRT26vyPiOOBp4GfAFKAFuAu4Bri+u+uVJKm3s9mXJFXd7pTSc+0tSCm9VnSYPmRU/vO7KaUtDXycvwW2ABemlHYCRMRfA4Ma+JiSJJWeh/FLkvqs2sPKI+I+4IvAZ2sO97+pdlxEfC4ifhMR2yNiSUSMbmedn46I/4mIHfkh5d+LiEE1y0dHxKKI2Jiv5+WIuKre5QfYlgsiYkVE/CnPdnI3svXIdub7cm4+dHO+L8+ud3930QRgYU2jfyTwaeDn3ViXJEmV4Sf7kqTKi4i2f+/+L6WU2sybAYwAjgCuzOetrVk+AvgW8M/Au8C3gQci4pTWdUXEp4CngP8EvgQMBm4FjsxvAzwKrAAuBXYCJ5Edek6dy9tzPHA78I95tpuBJyPihJTSn7qQrae2cwbwBjANODdfz3LgazWP09n+7lREfAj4KPBP+RsNp+Z51wI/6Mq6JEmqGpt9SVLVDQbeazPvc8CPa2eklF6LiI3AIR0c9n8U8KmU0kqAiDgEWEjWjK/Ix9wK/DSl9OXWO0XE74GnIuIUYB3w58AFKaVl+ZCnasYOOdDyAxgCfCGl9NN8Pb8EXiNrrmfVky2l9GJPbWdK6cWIaD1F4ucppW35mL2B69jf9fg42VGKvwbWkL3ZsBM4u/VNDkmS+ioP45ckVd1m4C/aTD/rxnpWtzbAueX5z+EAEfFB4EyyT8H7tU7AErI3G8YAG8k+8Z4VEV9u54rxnS3vyFutjT5ASmkN8EvgjC5k68ntLMqpwDbgdbIjCqYCq4DHI+LPCswhSVLp2OxLkqpud0rpF22mrd1Yz6Y2t3flPwfkP48EDgVmkjW9rdNOoD/wkZTSHmA82Sf89wLrIuKZiPgkQGfLD+CtDuYdU2+2ntzOTrL2pE8CL6SU3ksp/SSlNBuYSHZ0wmcLzCFJUul4GL8kST1jE5CAm4An2ln+B4CU0grgixHRHzgL+FeyT6KHp5T2dLa8g8du7wiAYcBLXclWp55c18E6lfcfpdF6+P6bBeaQJKl0bPYlSdpnF/s+we6SlNL2iHgOOCmldEsd498DfhIRtwPzyS5Ut7He5W0Mi4hxNefsjwBOA/6jO9k6yd1j6+Ig9ndEHAqcAjzWZtEUsv205OCiSZLUu9nsS5K0zwrgCxFxAdkV3f+QUurKJ9XXkV2kbg/wILCV7IrzE4AbyRrbb5NdKf51skPi/4HsUPSNEfHxAy0/wOO+DcyNiNar8d9Cdhj/ffVmSym90lPb2YV1tbu/I+Js4GngnJTS4g7uOwr4AHBdRGwAXib7yr0bgStSSru7sD2SJFWOzb4kSfvMJDsP/F6yRvtmssPV65JSWhIRn8nvN5fs3PY1wCKyw8oPz3/eCBxLdkj802QNPWTn6h9oeUfWAP9CdpX844FfAJfUXpG+jmx168F1dbS/P5gvb+9aBK1OJbtWwEKy7U5kDf+UlNJDXcggSVIlxfu/ZliSJKl5IuJm4DMppXMOMOZbwPiU0ieKSyZJUu/h1fglSVLZjANu72TMJ4FfF5BFkqReycP4JUlSqaSUPlfHsE8AP2p0FkmSeisP45ckSZIkqWI8jF+SJEmSpIqx2ZckSZIkqWJs9iVJkiRJqhibfUmSJEmSKsZmX5IkSZKkirHZlyRJkiSpYmz2JUmSJEmqmP8HFkyvC7XvRycAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x864 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Additive Model IV\n",
    "γ = float(input(\"Enter γ: \"))\n",
    "m = float(input(\"Enter m: \"))\n",
    "m_v1 = m\n",
    "m_o1 = m\n",
    "\n",
    "fig, axes = plt.subplots(3, 4, figsize=(16, 12), sharex=True, sharey=True)\n",
    "fig.suptitle(r'Additive Model IV (Assortative Meeting), $m = $'+str(m)+r', $\\gamma = $'+str(γ), \n",
    "             x=0.5, y=0.95, horizontalalignment='center', verticalalignment='top', fontsize = 18)\n",
    "axes[1,0].yaxis.set_label_coords(-0.18,0.5)\n",
    "axes[1,0].set_ylabel(r'Vertical transmission rate, $\\rho$', fontsize = 15) \n",
    "fig.text(0.51, 0.07, r'Fitness benefit, $\\beta$', horizontalalignment='center', \n",
    "         verticalalignment='bottom', fontsize = 15)\n",
    "\n",
    "for i in range(3):\n",
    "    for j in range(4):\n",
    "        b_, c_ = b[i], c[j]\n",
    "        ax = axes[i,j]\n",
    "        β_, ρ_ = np.meshgrid(β, ρ)\n",
    "        z = f(β_, γ, ρ_, b_, c_, m_v1, m_o1)\n",
    "        ax.contourf(β_, ρ_, z, levels=[0, 1], colors=['k', 'w'])\n",
    "        \n",
    "        if j == 3: #Label b values \n",
    "            if i == 2:\n",
    "                ax.yaxis.set_label_coords(1.24,0.5)\n",
    "            else:\n",
    "                ax.yaxis.set_label_coords(1.3,0.5)\n",
    "            ax.set_ylabel(r'$b = $'+str(b_), horizontalalignment='right', rotation=0)        \n",
    "        if i == 0: #Label c values\n",
    "            ax.title.set_position([0.5, 1.045])\n",
    "            ax.title.set_text(r'$c = $'+str(c_))              \n",
    "        \n",
    "        #Label the light and dark regions of the plots\n",
    "        if γ == 0.1:\n",
    "            if m == 0.25:\n",
    "                if j == 0 and i == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 0 or (j == 1 and i == 0):\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                elif i == 0 and (j == 2 or j == 3):\n",
    "                    ax.text(0.21, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                else: \n",
    "                    ax.text(1.7, 0.89, 'invasion') \n",
    "            if m == 0.5:\n",
    "                ax.text(1.7, 0.89, 'invasion')\n",
    "                if j == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            if m == 0.75:\n",
    "                ax.text(1.7, 0.89, 'invasion')\n",
    "                if j == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        if γ == 0.3:\n",
    "            if m == 0.25:\n",
    "                if (j == 0 and (i == 0 or i == 1)) or (j == 1 and i == 0):\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                elif j == 1 and i == 1:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.75, 0.89, 'invasion')\n",
    "                elif j == 1:\n",
    "                    ax.text(0.21, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                elif j == 2 and (i == 0 or i == 1):\n",
    "                    ax.text(0.21, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                elif j == 2:\n",
    "                    ax.text(0.18, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                elif j == 3 and i == 2:\n",
    "                    ax.text(0.16, 0.92, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                else:\n",
    "                    ax.text(0.18, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "            if m == 0.5:\n",
    "                ax.text(1.7, 0.89, 'invasion')\n",
    "                if j == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            if m == 0.75:\n",
    "                ax.text(1.7, 0.89, 'invasion')\n",
    "                if j == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "        if γ == 0.7:\n",
    "            if m == 0.25:\n",
    "                ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                if j == 3 and i == 2:\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "            if m == 0.5:\n",
    "                if j == 0 and (i == 0 or i == 1):\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 0:\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 1 and i == 0:\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 1:\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                else: \n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                    ax.text(0.28, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "            if m == 0.75: \n",
    "                if j == 0 and (i ==0 or i==1):\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                elif j == 0:\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 1 and i == 0:\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                    ax.text(0.28, 0.07, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j == 1:\n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "                elif j==2 and i==0:\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                    ax.text(0.23, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                elif j==3 and i==0:\n",
    "                    ax.text(1.7, 0.07, 'invasion')\n",
    "                    ax.text(0.23, 0.89, 'no invasion', fontdict = dict(color = 'w'))\n",
    "                else: \n",
    "                    ax.text(1.7, 0.89, 'invasion')\n",
    "            \n",
    "#plt.savefig('dec9_mIV_m25_g01.pdf') "
   ]
  }
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