hawk_dove_dynamics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hawk-Dove Dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# Plotting libraries\n",
    "import matplotlib.pylab as plt\n",
    "# Magic function to make matplotlib inline; other style specs must come AFTER\n",
    "%matplotlib inline\n",
    "# This enables high resolution PNGs.\n",
    "%config InlineBackend.figure_formats = {'png', 'svg'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evolutionary Dynamics of the Haw-Dove Game in Infinite populations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Replicator equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The replicator equation represents the dynamics of competing individuals in a population. It normally found in the following form:\n",
    "\n",
    "$\\dot{x}_i = x_i\\left[f_i(x)-\\sum_{j=1}^{n}x_jf_j(x)\\right]$,\n",
    "\n",
    "where $x_i$ represents the frequency of strategy $i$ in the population, and $f(x_i)$ is the fitness of strategy $i$. This differencial equation, gives the gradient of selection, i.e., the strength with which the frequency of a certain strategy will increase or decrease. It may also be expressed in a more convenient matrix form:\n",
    "\n",
    "$G(x_i) = \\dot{x}_i = x_i[(Ax)_i - x^TAx]$\n",
    "\n",
    "Where the matrix $A$ is a payoff matrix with element $A_{ij}$ representing the fitness of strategy $i$ over strategy $j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from egttools.analytical import replicator_equation\n",
    "from egttools.analytical.utils import (calculate_gradients, find_roots, check_replicator_stability_pairwise_games,)\n",
    "from egttools.plotting import plot_gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Payoff matrix\n",
    "V = 2; D = 3; T = 1\n",
    "A = np.array([\n",
    "        [ (V-D)/2, V],\n",
    "        [ 0      , (V/2) - T],\n",
    "    ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can calculate the gradient of selection of the replicator equation and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_points = 101\n",
    "strategy_i = np.linspace(0, 1, num=nb_points, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate gradient\n",
    "gradient_function = lambda x: replicator_equation(x, A)\n",
    "gradients = calculate_gradients(np.array((strategy_i, 1 - strategy_i)).T, gradient_function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we are analysing a pairwise game with the replicator equation, we can also calculate the roots of the system and their stability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "roots = find_roots(gradient_function, 2, nb_initial_random_points=10, method=\"hybr\")\n",
    "stability = check_replicator_stability_pairwise_games(roots, A, atol_neg=1e-4, atol_pos=1e-4, atol_zero=1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rXFtbW4SEhMDFxQV79uzB2bNnKZES0wsLC4NYLMZHH32ESZMmITs7Gz/99BNevHihcvvQ0FAsWbIE9vb2aNmyJQDp3WO1atWwd+9edO3aVeWzP5kFCxagbNmyGDVqFF6/fq3xQArJyck4ceIEJBIJXr58yQ/IcO/ePSxYsAAdOnTgt50+fTr/XHPatGlwdXXFunXrsGvXLsybN0+penvIkCEYPnw4Hj16hBYtWqB27dqC9bNmzcK+ffvQokULfP7556hduzays7Nx9+5d/P333/j555/VVisGBATgo48+woIFC2BlZYV27drh8uXLWLBgAZydnQV/hXfu3BnffPMNpk+fjpCQEFy7dg2zZs1CtWrVDNpC0cfHB7NmzcLUqVNx+/ZtvP/++yhXrhyePHmC//77D46OjvyABMY8rlgsxoIFC/D69Ws0btwYx44dw7fffouIiAiVz/ILEx0djVatWqFp06aYMmUKatSogSdPnmD79u1YsWIFypYtq/H5LVu2LLy9vbFt2zaEhobC1dUV7u7u8PHxwZw5cxAWFoa2bdtiwoQJEIvFWL58OS5duoT169frnMy++OILrFq1Cp06dcK3336LChUqYN26dbh69arK7a2srPDZZ59h8uTJcHR0FHTP0VZxfe9U+eijjxATE4MRI0bg2rVraNu2LSQSCU6ePAk/Pz/07dsX06ZNw4MHDxAaGorKlSsjPT0dixYtgo2NDUJCQowan9GYtq0TKYqsteCpU6dUru/UqZNSq90dO3awBg0aMDs7O+bl5cUmTpzIdu/erdRakDHGtm3bxgCwsLAwQfknn3zCALDFixcLytW1uv3hhx8YADZt2rRCP49sf9nLysqKlStXjgUGBrIvvvhCbYvZixcvsi5dujBnZ2cmFotZgwYNBK085b18+ZLZ29sX2nrw6dOn7PPPP2fVqlVjNjY2zNXVlQUGBrKpU6fyLZTVyc7OZlFRUax8+fLMzs6ONWvWjB0/fpw5OzuzcePG8dvl5OSwCRMmMC8vL2ZnZ8caNWrEtm7dyiIjIwW/M3XnND4+ngFgf/75p6Bc3Xdi69atrG3btszJyYnZ2toyb29v1rNnT7Z///5CP09R3zFNjhsZGckcHR3ZhQsXWJs2bZi9vT1zdXVlI0eOVDqfmrTaZYyxpKQk1qtXL+bm5sbEYjGrWrUqGzRoEMvOztbq/DLG2P79+1nDhg2Zra2tUuvqf//9l7Vr1445Ojoye3t71qxZM7Zjxw6tzpEqSUlJLCwsjNnZ2TFXV1c2dOhQ/v+b4v9Dxhi7e/cuA8BGjBih8nje3t6sU6dOSuWKLWeL83un+N6MSVsST5s2jdWsWZOJxWLm5ubG2rVrx44dO8YYY2znzp0sIiKCeXl5MbFYzMqXL886duzI/v33X5Wf2xJwjGnRnJIQotKxY8fQsmVLrFu3TmXLzJJu0KBB2LRpE16/fm3qUCzWkiVL8Pnnn+PSpUt8wzdiGahqlxAt7du3D8ePH0dgYCDs7e1x/vx5zJ07FzVr1sSHH35o6vCIhTl79izu3LmDWbNmoVu3bpRELRAlUkK05OTkhL1792LhwoV49eoV3N3dERERgTlz5ghGoSFEE927d8fjx4/RunVr/Pzzz6YOh+iAqnYJIYQQPdCADIQQQogeKJESQggheqBESgghhOiBGhuZGUdHR2RnZ8PKygrly5c3dTiEEGISqampKCgogJ2dHd68eWPqcApFjY3MjEgk0mqmFEIIKck4jlOaY9jc0B2pmSksiZYtWxZOTk7FGI2ylJQUfkBqTWfCKG7mHiPFpz9zj9Hc4wPMK8aMjAy1g+pbwo0FJVIzIxKJ+L++5GcXAYCoqChERUWZIixe5cqV8fDhQ3h6ehY5O4epmHuMFJ/+zD1Gc48PMK8Yo6OjER0dLSiTzVNa2Cwy5oISqZkSiUQm/3ITQkhxUHWTYGVlZfZVujLmn+oJIYQQM0aJlBBCCNEDVe0SrURFRSEjI8PkjZ4sGZ1D/dE51B+dQ8Oh7i9mRvZcQCQSoaCgwNThWCRZIwovLy96zqwDOn/6o3OoP0u6FlLVLiGEEKIHSqSEEEKIHugZqZkpU6YMMjIyUKZMGVOHYrHo2Y9+6Pzpj86h/izpWkjPSM0MPVspHgUFwL17wO3bwK1bwP37gEQCiETSl5sbULOm9OXjA9jYmDpiQkoXS7oW0h0pKTWePAH++Uf62rsXSEvTbD87OyA4GAgPl778/QGOM26shBDLoVMiTU1Nxd9//41Dhw4hMTERT548QXp6OlxcXODh4YGGDRsiJCQEHTt2NPkYjqR0Yww4cgRYvBjYskV6J6qt7Gxp4t27Fxg/HqhbFxg+HBgwAHB2NnzMhBDLolXVbnx8PJYtW4YdO3YgPz+fL5c/BCf3p7qVlRW6dOmC0aNHo23btgYKuWSzpOoMc8YYsGMHMGMGcPascd7D3h6IjASmTgUqVzbOexBSWlnStVCjRHru3DlMmjQJBw4cACBNnBzHFToqv2y9LLGGhoZi3rx5eO+99wwTeQllSV8ec3X1KvDFF8CePUVv6+QEVK8OVKsmrcKVSID8fOkz05s3gefPiz6GnR0wejQwZYr02SohRH+WdC3UKJFaWVkBEN55Wltbo27duggICICrqyucnJzw8uVLpKWlISkpCZcuXRLctcqOk5eXZ+CPULJY0pfH3OTlSe9A582TJkNVHB2lzznffx/o0AGoWrXw553PngEJCdJq3X/+kSZYdZycgO+/Bz79VNpgiRCiO0u6Fmr0jFSWQF1dXfHhhx+id+/eaN26NWxtbdXuk52djX///RdxcXHYunUr0tLSLGYkf2J57t0D+vYFTpxQvd7XFxgzBhg8WLvnmu7uQM+e0pdEAhw4AKxYAWzbppysMzKAkSOB9euBlSuBWrV0/zyEEAvCNFCjRg22YsUKlp2drcnmSrKzs9ny5ctZ9erVddq/NPHy8mIAmJeXl6lDsRjbtjFWrhxj0iejwpenJ2Nr1zKWn2/Y93zwgLGRIxmztlb9vra2jC1axJhEYtj3JaS0sKRroUYVUNeuXcOnn35a6B1oYWxtbTFy5Ehcv35dq/0kEgl+/fVXhISEwM3NDfb29vD19cXw4cNx8+ZNnWI5efIk5s6di44dO8LPzw+urq4Qi8WoVKkSunTpgr/++kvtvj4+PuA4rtCXu7u7TnER3fzwA9CtG/DihbDcxkb6zPLaNaB/f+Dt0wmD8fICli+XPo/96CPl9Tk5wNixQK9ewMuXhn1vQoiZMXUmV+fNmzesXbt2DIDKl62tLdu6davWx3V0dFR7TNmrb9++LF/FLYy3t3eR+7q5uen1uS3przBTKihgbPx41XeD1aszdvp08cazdy9jPj6q46lRg7Fz54o3HkIsnSVdC812QIZRo0bh4MGD/LK/vz+8vb2RkJCArKws5OTkoE+fPjh//jxq166t9fGtra0RGBgIV1dXnD9/Ho8ePeLXbdiwAU2aNMG4cePU7h8cHAwPDw+lchoSzPjy8oChQ4G1a5XX9e4tfT5Z3L+GsDDg0iXgq6+AhQuF627eBFq0AOLigM6dizcuQojxadyP9NKlS3xjoYCAAL4lb7t27dTuU7t2bfz0009aB3Xx4kXUr1+fX+7Vqxfi4uLAcRzOnj2LJk2a8C2Ce/TogU2bNml8bE9PT4wYMQKfffYZXw2bnZ2NAQMGCI5Tr149XLhwQbCvj48P7t27B0Dap7ZNmzZaf7aiWFJLNVMoKAA+/hjYuFF53bx5wIQJph91aNcu6WANitXNIhGwZAkwapRp4iLEkljUtVCT29bz588zkUjERCIRa9KkiWAdx3H8OvmXrPzmzZta3yZPnDhRUF164sQJwfrw8HB+nVgsZi9evND42CkpKSrLb926JXhPOzs7pW3kq3bj4+O1+Ugas6TqjOImkTD26afKVadWVoytXm3q6ITu3mWsaVPVVb0TJkirpgkh6lnStVCjxkZbtmzhu8CMHz9eq0S9bds2rbYHgGPHjvE/cxyHhg0bCtYHBgbyP+fm5uLMmTMaH7tixYoalRdVRbt69WpERkaif//+mDBhArZu3arUb5YY1tSpwC+/CMvs7YHt24GBA00Tkzre3sDhw9I7U0Xz50uHGKTeYISUDBo9Iz169CgAQCwWo1u3biq3YWpqiA8fPoyoqCitgrpx4wb/s5ubG8RisWC9YtK7fv06QkNDtXoPRXsUhsEJCQkpdPvY2FjB8oIFC+Dr64u4uDgEBQXpFQsApKSkoHIR485FRUVpfW4t1Y8/AnPmCMvEYmkSbd/eNDEVRSwGVq+W9mGdOVO47tdfpc96f/vN8C2KCTF30dHRiI6OLnSblJSUYopGfxol0uvXr4PjONSrV09tF5iePXtio9yDKx8fHyQnJ+PKlStaB5Wens7/bG9vr7TewcFBsPxSz/4FqampgoRkZWWFyZMna32c27dvo0OHDkhMTISPj49eMUkkEjx8+LDQbTIyMvR6D0vxzz/SweLliUTSgQ/MNYnKcJx0tKVq1YBhw4SDOKxeDeTmAmvWANZm2+yPEMPLyMgo8vpmSTT67/v06VMAUDuTi6q70bp16yI5ORmPHz/WIzzVx1Z396uLJ0+eICwsDHfv3uXLFi1aJKg+lmnUqBFGjBiBsLAwVKtWDRzH4ciRI/jiiy9w+/ZtAMCLFy/w3Xff4RfFOkgtiUSiImfOKQ0thG/dkvbTVPyVr1wJfPihaWLSRWQk4OIi7VcqP0rm+vXSJBobS8MKktLDyckJXl5ehW6TkpJiMaPhaZRIZc/+cnNzldatXLkSAFCtWjVBuWyw+qysLK2DcnZ25pO3qv0Vy5x1nMvq/v37CA0NFVQlz5kzB5999pnK7VUN1tClSxf4+PgIWhkrVhPrwtPT0/xbqhnZ69fABx8AchUUAIBvvwWGDDFFRPrp1g3YulX6B0BOzrvytWulSXbRItO3OCakOGjyWErWatcSaJRIy5Urh9TUVFy8eFFp3dChQ1Xuc/XqVQC63TXVqlWLT6RpaWnIyckRVCnL9/mUba+tmzdvIjQ0FMnJyQCkiX/RokUYM2aM1seqV68eXF1dkfZ2pmh978KJ9A506FBp30x5PXsCX35pmpgMoWNH6XPdbt2k85zKLFkCuLpKq4EJIZZFo8ok2d1mSkoKduzYUeT2Bw8exK1bt8BxHKpWrap1UM2bN+d/ZozhrMKEkvKtdG1sbFRWwxbm8uXLaN26NZ9Era2tsXbt2kKTaGEtcjMyMgTPdUtDlaux/fqrcl/RgAAgJsby79o6dAD++kv5uejMmcDSpaaJiRCiO40SaXBwMABpUhsyZAhOnz6tdtsLFy5ggFybf9m+2ujfv79gef78+fxz0cTERMTHx/PrOnfuDBcXF345NjZWMPZtQkKC4FinT59GSEgIf9dob2+PrVu3ol+/foXGNHfuXAwZMgTnzp0TlL9+/RqffvqpoC6/RYsWmn5UosLNm4DioFIuLtJq0TJlTBGR4UVESKt0Ff8oGDsW2LnTNDERQnSjUdXukCFDMH/+fADA8+fP0aJFC3zwwQcIDw/n7zjv37+Pffv2YcuWLYI5RwcPHqx1UA0aNED//v3x+++/AwA2b96MunXr8kMEyu4OxWIxZs+erdWxQ0NDBa1dq1atipiYGMTExChtKz/SUX5+Pr9d1apV4e/vj7y8PJw9e5av0gWkjYR0afFLpPLzpYPMv3kjLF+9GqhRwzQxGUvfvtIB7UeMeFcmkUjLjxwB3nvPZKERQrSh6cgNw4YN40crUjeakeK6/v376zxSxOvXr1lISEihg9Zv3rxZab+YmBjBdoojEKk7nqqXvBkzZhS5vZ2dHYuNjdX5MzNmWaN5GMOsWcojAX36qamjMi5Vn9nLSzpVGyGllSVdCzVucL9kyRK0aNECjDG+RS5jTPACpI12GGNo3LgxVqxYoWt+h6OjIw4cOIAVK1agVatWcHFxgVgsho+PD4YNG4YLFy7gw2Ls/zBp0iTExcVh0KBBCAwMRKVKlWBjY4OyZcuiQYMGGDduHC5duoTIyMhii6mkOXNGeeCCGjWABQtME09x+eor5RGQHj4EunYFdGj0TggpZhoPWg9Iu79MmjQJP//8s8quMIC08c+nn36KH374AXZ2dgYLtLSwqIGaDSg/H2jaFEhMfFdmZQUcPSotL+lycqSNkA4fFpYPHCjtY2rpDawI0ZYlXQu1Gk9FLBZj4cKFmDhxInbs2IGTJ08iNTUVjDFUqFABTZo0QdeuXYvsaEuIomXLhEkUkI6tWxqSKADY2kpb8jZvDsh1a8aaNUDjxsDo0aaLjRBSOK3uSInxWdJfYYby8CFQp450AAYZf3/g7FnpeLWlydWrQJMmwKtX78qsrYGDB4HWrU0XFyHFzZKuhTQoGTG5sWOFSRQAfvqp9CVRQPoHxZo1wrL8fOnQghY0hjchpYpGiXTt2rUoKCjQ640KCgqwRvEKQUq9XbuAzZuFZYMHAzp0Py4xPvhAWq0t78kTabcgPf8bEkKMQKNEGhkZiRo1amDhwoVaD3+XkpKC6OhoVK9eXac+paTkys1VHnjBzQ2YN8808ZiTmTOB998Xlh08CHz3nWniIYSop9EzUpFIxHd5EYlEaN26Ndq0aYOgoCD4+fnB1dUVZcuWxatXr5CWloakpCScPn0a8fHxOHLkCN89huM4ve9sSzpLei6gryVLgM8/F5atWiW9IyVAWpp0UIb799+ViUTShFrEdLmEWDxLuhZq1Gq3c+fO2Pl23LKCggIcOnQIhw4d0ugN5PN0ly5ddAiRlETp6cp9Rhs3lk43RqRcXaXTrIWEvKvSlUiAjz8Gzp0DPDxMGh4h5C2Nqna3b9+OhIQEfgxZxYEYCnsB0rFnDx06hK1btxrtgxDLMmcO8Py5sGzBApqTU1HLlsA33wjLHj2SThJO7e0JMQ8aX7aCg4Nx5MgRnD17FsOHD0elSpUK3b5SpUoYMWIEEhMTceTIEbSmtvvkrbt3pXNvyuvenbp3qDN5MhAWJizbvh347TfTxEMIEdKrH+mtW7dw9uxZpKamIj09HS4uLihfvjzee+891ChpI4wXE0t6LqCrfv2AP/54t2xtDVy+DOgwrWyp8eQJUK8e8HaaXgCAo6O0ipf+q5GSyJKuhVqNbKSoevXqqF69uqFiIaXApUvS537yRo2iJFqUChWkd6Bdu74re/NGOoTg4cPKc5sSQooPPZEixWrWLOGzPScn4OuvTRePJenSBfj0U2HZ8ePA99+bJh5CiBQlUlJsLl0C/vxTWDZuHODubpp4LNGCBcpVuTNnAhcvmiYeQgglUrOVkpKCypUrC17R0dGmDksvit1dnJ2BL74wSSgWq0wZ4PffpTPjyOTlAYMGSf8lxBJFR0crXe9SLGhMTHqyYqYkEgkePnwoKMvIyDBRNPq7eBHYtElYNm4c4OJiknAsWtOmwKRJ0i5EMomJwA8/AF9+abq4CNFVRkaG0vXOklAiNVMikQienp6CMicnJxNFoz/Fu1EXF+lg9UQ306cD27YBSUnvymbMkDZGqlvXZGERohMnJyel6TdTUlIgkUhMFJF2aBo1M2NJTb41lZQEBAQIy2bOBKZNM008JcV//0nnL5W/1jRuLG2AJF/1S4glsqRrIT0jJUY3f75wme5GDaNJE2DiRGHZqVPA0qWmiYeQ0ooSKTGqR4+kjWPkjRkjbWhE9DdjhnQOU3lTpwLJySYJh5BSiRIpMarFi4WtSe3sgNGjTRdPSWNnB/zyi7DszRvpIBf00IaQ4qFzY6Nnz55h6dKlOHz4MFJSUpCTk6NyO47jcOvWLZ0DJJbr1Svg55+FZZGRQPnypomnpGrdWjpQg3xC3bVL2kq6Vy/TxUVIaaFTIr1+/TqCg4Px9O3An4W1V5LNY0pKn5UrgZcv3y1zHDB+vOniKcnmzpW24n3y5F3ZmDHSwe6pixEhxqVT1e7EiRORmppaaAIlpVteHrBwobDsgw+AmjVNEU3JV66ctBpd3pMnNPwiIcVBpzvSQ4cOgeM4MMZga2uLOnXqoEyZMrCiNvfkrT//BO7fF5YptjAlhtWrF7BmjbRaV2b5cmDwYKBRI9PFRUhJp1MiLSgoAAC4ubnh1KlT8PHxMWRMpARQ7ILRsqW0zyMxHo4DliwBDhwAsrOlZRKJtOHRsWM0aTohxqLTf60GDRoAABo1akRJlCg5e1Y6KIA8GlO3eFSrJu3+Iu/kSWDVKtPEQ0hpoFMiHT9+PBhjSExMRFpamqFjIhZu2TLhcqVKQLdupomlNJo4UflZ9OTJwLNnpomHkJJOp0QaGBiI3r174/nz52jVqhViY2Nx/vx5JCcnq3yR0iMtDfjjD2HZ8OGAjY1p4imNbG2Vq9bT0oCvvjJNPISUdDqNtSsSifjGRkDhXVw4jkN+fr7uEZYyljS+pCoLFgATJrxbtrGRjrJTsaLpYiqtevcWzv/KccCZM0DDhqaLiRBNWdK1UK/mBxzH8Qm1sBcpHSQS4KefhGU9elASNZXoaMDB4d0yY8Dnn9OIR4QYms6JlBIlUbRnD6A4iNVnn5kmFgJUrqw8P+mRI0BcnGniIaSk0qn7y/Tp0w0dBykBFIcDrF9f2u2FmM748cBvvwF37rwrmzAB6NIFcHQ0XVyElCRmnUglEglWrVqFtWvX4tKlS8jMzISnpyfCwsIwceJE1KhRQ+tjnjx5EvHx8Th8+DDu3LmDJ0+e4PXr13B3d0dgYCAGDx6MDz/8UO3+OTk5WLp0KeLi4nD9+nXk5uaiatWq6NixIyZNmoSKpbQeMyVFOBAAIO2/SCNEmpadnbSKt3v3d2UPH0qHFPzmG9PFRUiJwszUmzdvWLt27RgAlS9bW1u2detWrY/r6Oio9piyV9++fVl+fr7SvqmpqaxevXpq93NxcWHHjx/X63N7eXkxAMzLy0uv4xS3779nTPr0TfpycGDs5UtTR0UYY0wiYax9e+Hvx86OsXv3TB0ZIepZ0rVQr8ZGEokEGzZswKBBg9C2bVu0bdsWkZGRWL9+PT/6ka5GjRqFgwcP8sv+/v6IiIiAvb09AOmdYZ8+fXDt2jWdjm9tbY2mTZsiIiIClSpVEqzbsGEDFisOXAqgd+/euHjxIr8cFBSE9u3bw9paemOfnp6OLl264Pnz5zrFZKkYk1YfyuvdG3ByMk08RIjjgEWLAPkRPLOzlZ+fEkJ0pGsGvnv3Lqtfvz4TiUQqX/Xq1WO3b9/W6dgXLlwQ3On16tWLSSQSxhhjiYmJzNraml/Xo0cPrY5dsWJFNmPGDPb06VO+LCsri/Xs2VPwnvXq1RPst337dsH68ePH8+t27Nihdp22LOmvMJl//xXe7QDSMmJePvtM+fd08qSpoyJENUu6FuqUSDMzM1mdOnUYx3GM4zilJCorr1OnDnvz5o3Wx584caIgMZ04cUKwPjw8nF8nFovZixcvND52SkqKyvJbt24J3tPOzk6wvlevXoL1jx8/FqyvXbs2v65ChQp84teWJX15ZAYNEl6ca9WSVicS85Kaypizs/B31bIl/a6IebKka6FOVbu//PILrl27xg/EwNT0G71+/TpWrlyp9fGPHTvG/8xxHBoq9CAPDAzkf87NzcWZM2c0Pra6xkCK5U4K9ZLyMXl5eaFChQpqY3ry5Alu376tcUyW7NUrYONGYdmQIdTIyBx5eCiPbnT0qHQCcEKI7nRKpH/99Rf/c1hYGI4dO4aXL1/i5cuXOHr0KDp06MCv37x5s9bHv3HjBv+zm5sbxGKxYL1i0rt+/brW76Foz549guWQkBD+58zMTDx8+JBf9vT0VNrf0DGlpKSgcuXKhb6io6P1eg9DiIsDMjPfLVtZAZGRpouHFG7MGMDXV1g2eTKQk2OaeEjpFB0dXeT1LSUlxdRhakyn7i+XL18Gx3GoXLkyduzYIUh0zZs3x/bt21GzZk3cv38fSUlJWh8/PT2d/1nWuEieg/xwLQBevnyp9XvIS01NRVRUFL9sZWWFyZMnqz1+ccQkkUgEyVuVjIwMvd7DEBRnFenUiUYyMme2tsC8eUDPnu/K7tyRjkhFM/SQ4pKRkVHk9c2S6JRIZRdwf39/pbtFABCLxfD398f9+/fx6tUrvQJkKkZOUlWmqydPniAsLAx3797lyxYtWiSoqi3umADpeMaq7nzlKVY/F7dbt5SnSxs61DSxEM19+CHQqpV0lCOZb74BBg0CXFxMFRUpTZycnODl5VXoNikpKZBIJMUUkX50SqTOzs54/vw5Lly4gKysLKU7tKysLFy4cAGAbhd7Z2dnPH36lD+WIsUyZ2dnrd8DAO7fv4/Q0FBBVfKcOXPwmcK4dorHN2ZMMp6enmY/UPO6dcJld3cgIsI0sRDNcRzwww/CidbT0oA5c4DvvzddXKT0iIqKEtQCqiIbtN4S6PSMtH79+gCAx48fIyIiAgcOHMDjx4/x5MkTHDx4EB07dkRKSgo4jkO9evW0Pn6tWrX4n9PS0pCj8ADn0aNHarfX1M2bN9GqVSs+iXIch8WLF2PKlClK2zo4OAj+elJ8f0PFZEkYU06kffrQdGmWolkzYfUuIO1rSrMeEqI9nRJpjx49+J///fdfdOjQAV5eXqhUqRLCwsJw+PBhfn1Pxf+tGmgu96cyYwxnz54VrJdvpWtjY1NoNawqly9fRuvWrfm5Uq2trbF27VqMGTNGo5hSUlKUHoQnJibyP5cvXx6+ii06SpgzZwDF9lT9+pkmFqKb774DrOXqpHJygK+/Nl08hFgqnRLp0KFDUbduXf65oLruLwEBARiqw0Oz/v37C5bnz5/PHzcxMRHx8fH8us6dO8NF7sFObGwsP70bx3FISEgQHOv06dMICQnB48ePAUgbDm3duhX9isgCAwYMUIpJZvv27YJWuv369St0jtaS4Pffhcu+vtK7HGI5atYERowQlq1dC5w/b5p4CLFUOk3sDQAPHz5E9+7dcfr0aZXrGzVqhC1btqBKlSo6BTZgwAD8Lne19vf3h7e3NxISEvjnkWKxGOfOnYOfnx+/XWxsLAYPHswvx8fHo02bNvyys7OzoLVr7dq1UbduXZUxbJLrYMcYQ5s2bQR320FBQXBxcUFCQgI/ebmrqyuuXr0KDw8PnT63JUxmm58vnaLryZN3ZV9/DcyaZbqYiG5SU4EaNaT9gWU6dQJ27jRdTIQAlnEtlNGpsREgHZTgv//+w/bt27F7924kJyeDMQZvb2+8//776Nq1q153ZT///DPu37+PQ4cOAQCSkpIEXWlsbW3xxx9/CJKoJhS7jFy7dk2j8Xo5jsPGjRsRGhqKy5cvA4DSHxHOzs7YsWOHzknUUhw8KEyiAFXrWqry5YGJE4Fp096V7doF/Psv0Lq16eIixJLonEhlunbtiq5duxoiFgFHR0ccOHAAv/32m2AatUqVKqF9+/aYOHFisTfoqVChAk6fPo0lS5Zg48aNuHbtGvLy8lC1alVERERg8uTJRXZZKQkUq3UDA4HatU0TC9HfuHHA0qXSu1OZKVOk3WNK+BMKQgxC56pdYhzmXp2RmQlUqAC8fv2uLDpaejEmlmvpUumoR/K2b5dOAE6IKZj7tVCeRnekQ4YMAQA0btwYI0eO5Jc1wXEcflOcY4tYrN27hUlUJAL69jVdPMQwPv1U+gfRnTvvyr78EujYUTj9GiFEmUaJVNYS9vXr1xg5ciS/XBTGGCXSEubPP4XLbdoApaA2u8QTi6WjG8k3mL90CfjjD0ChwTohRIFeE3uT0iUrS7k1Z69epomFGN5HHwFvx1rhzZgB5OWZJBxCLIbGiVTxUapi31FVL1Ky/PMP8ObNu2WRCOje3XTxEMMSiaSDNMi7fVt5YgJCiJBGVbuKAwdbykDCxLAUq3WDg6UNj0jJ0bGjdAxe+ckIvvkGGDgQUDHpESEEVLVLNJSVBezYISyjat2Sh+OA2bOFZQ8fSqdZI4SoplMibdeuHdq1a4eZM2eq3Wb37t1YvHgxFi9erHNwxHzs2SNsrctx0um4SMnTti0QGiosmzNHOPoRIeQdnRJpQkICDh06xI/wo8qqVavwxRdfYBx1MCwR5EZLBCCt1qUJvEsuxbvSZ8+ks8MQQpQZrWq3oKDAWIcmxSw7W9o5Xx5V65ZsTZsqD8awYAGQnm6ScAgxa0ZJpI8fP8a5c+eMcWhiAvv2Cav1qFq3dPj2W+FyejqwcKEpIiHEvGmcSK2srPgXIO3+snnzZkG57OXl5YV79+4BAJycnIwTOSk2W7cKl1u1okEYSoP69ZVrHn78EUhLM008hJgrrfqRKvYPLaoPKcdxCAoKMnzUpNgUFCi31qW+o6XH9OnCgeszMqRVvISQd7Sq2tVmWjTGGOzs7DBjxgxtYyJm5MQJ4OlTYVm3bqaJhRS/gADlsZQXLZI2PiKESGk8jdrAgQP5RLp69WpwHAdvb2+EhIQItuM4Dvb29qhRowZ69uyp88TexDxs2yZcrlsX8PU1TSzENKZPB+LiANk4LG/eAPPmSV+EEB2nUROJpDeyPXv2xMaNGw0eVGkmmzpIJBIpzW0aFRWFqKioYo2ndm3g+vV3y1OnKjdCISVfZCSwZs27ZQcH6Uwx5cubLiZSckRHRyM6OlpQlpKSAolEUnKmUVM0ffp0AIC/v79BgyHvSCQSPHz4UFCWkZFRrDFcvSpMogBV65ZWX38NrFsnfWYOSOelnT+f7kqJYWRkZChd7yyJXomUGI+qO9LibgGtWK1bqRIQGFisIRAzUaOGdDq12Nh3ZcuWARMm0F0p0Z+TkxO8vLwEZbI7UkugUz/S2NhYNGrUCI0aNcKfiiOZA1izZg2/Plb+fx7RmKenJx48eCB4FXe1rmK3l65dpTOEkNJp6lThJN+yu1JC9BUVFaV0vVO8kTBnOl0WN2zYgHPnzuHGjRvo1KmT0vru3bvj5s2bOH/+PDZs2KB3kKT4PX4MnDwpLKNq3dJNdlcqb9kyIDXVNPEQYi50SqSXL18Gx3Hw9/eHg4OD0vqyZcsiICAAjLFCx+Ml5mvHDkC+GVrZstLBzEnpRnelhCjTKZE+fdux0NXVVe02Li4ugm2JZdm5U7j8/vuAra1pYiHmg+5KCVGmUyK1s7MDYwwXL15U+TC4oKAAFy9e5LclliUnBzhwQFimOIA5Kb1U3ZUq9FwgpFTRKZFWq1YNgLRV1dSpU5XWT506FY8ePQLHcfy2xHL8+6+0070Mx0nvSAkBpHel/fsLy5YupdGOSOml88TeMvPmzUNAQACGDh2KYcOGISAgAD/88AO/PlRxhmBi9v7+W7jcpAng4WGaWIh5mjpV2IL7zRuaGYaUXjol0jFjxvBVtowxXLlyBbGxsYiJicGVK1f4QettbW0xatQow0VLioViIu3Y0TRxEPNVsybw8cfCsiVLgBcvTBMPIaakUyL18fHB8uXLwXEc/5KR/cxxHJYuXQpfGpjVoty6BVy7JiyjREpUmTpVeWaYxYtNFw8hpqJz9/pBgwbhn3/+QWBgoNIUakFBQfjnn38wZMgQQ8ZKisHu3cLl8uWBRo1MEwsxb3XqAH36CMsWLgRevjRJOISYjE5DBMq0b98e7du3x9OnT3H37l0AgLe3N8rTmGEWS7FaNyKCRjMi6n31FSA/5kp6urQ7zJdfmiwkQoqdQS6RHh4eaNy4MRo3bkxJ1IJlZgLx8cIyqtYlhQkIAHr2FJZFRwOvX5smHkJMQa9EmpWVhSVLlqBjx46oW7cuqlevDgDYvn071qxZg3Xr1hkkSFI8EhKA7Ox3y1ZWQFiYycIhFuKrr4TLz58DK1aYJhZCTEHnqt3Lly+jS5cuuHfvHgBp611ZQ6MjR45gwYIFAKR9Tlu0aGGAUImxKVbrtmgBlCtnmliI5WjQQDpgx44d78rmzwdGjQLs7U0XFyHFRac70hcvXiAiIoJ/Lqqof//+fBeYrYpTiBCzpdjQiKp1iaYUx2V5/BhYtco0sRBS3HRKpAsXLsSDBw/AcRwYYxAptEapX78+/6z02LFjOgcnkUjw66+/IiQkBG5ubrC3t4evry+GDx+Omzdv6nTMZ8+eYcWKFYiMjESNGjUEXXh8fHwK3dfHx0ewvaqXu7u7TnGZ2u3b0pc8Gs2IaKppU+XHAN9/D+TmmiYeQoqTTol029sZn0UiEQ4ePIgPPvhAaRvZ7C83btzQKbDMzEyEhYXhk08+weHDh5GWlobs7GzcuXMHv/zyC+rWrcvHoY0jR45gxIgRWLNmDW7duqVTbCXRvn3C5fLlgfr1TRMLsUyKz0rv3wfWrDFNLIQUJ52ekd66dQscx6Fly5Zo06YNli1bprRN2bJlAQDp6ek6BTZq1CgcPHiQX/b394e3tzcSEhKQlZWFnJwc9OnTB+fPn0ft2rV1eg9HR0fk5OQgPz9f632Dg4PhoWLcPCcnJ51iMbW9e4XL7dtTtxeineBgoHVr6VjNMnPnAoMGAdZ6dbQjxLzp9PUuKCgAIE1E6qSkpACQDhOorYsXL2L16tX8cq9evRAXFweO43D27Fk0adIE+fn5yMnJwdSpU7Fp0yaNj12jRg0sW7YMzZs3R/369VG9enW+wZQ2Zs6ciTZt2mi9nznKzwfk/mYBQK11iW6++goID3+3fOsWsHGj8nCChJQkOt1zeHp6gjGG//77D1lZWUrrL1++jDNnzoDjOFSuXFnr469du1awPH78eL5FcMOGDQUD4e/YsUOru966deti1KhRaNiwIazk54IqxU6flnakl0eJlOgiLAwIChKWffcdoGK2RUJKDJ0SaevWrQEAaWlpCAsLw225Virff/892rdvz89T2qpVK62PL99AieM4NGzYULA+MDCQ/zk3NxdnzpzR+j30tXr1akRGRqJ///6YMGECtm7dqlMVsTlQfD7q7w94eZkmFmLZOE65Be/ly8D27aaJh5DioFPV7meffcbfNR4/fpwvZ4zhyy+/5Lu+cByHESNGaH18+QZKbm5uEIvFgvUVK1YULF+/fr3Yp2uLjY0VLC9YsAC+vr6Ii4tDkOKf5DpISUkp8m4+KioKUVFRer+XYiLt0EHvQ5JSrGtX6YhHly+/K5s9G+jWTTjIPSm9oqOjEV3EbPCyx4OWQKdE2rhxY3z55ZeYPXu2YLYXGVm3mClTpqCRDiOey1fV2qvo0e3g4CBYfmkmo2Tfvn0bHTp0QGJiYpFdaYoikUjw8OHDQrfJyMjQ6z0A4NUrQO5vIQBUrUv0IxJJx9rt1+9d2enT0j/Y6I80AkivXUVd3yyJzu0yv/nmG6xYsQIVKlRQmv3F3d0dy5Ytw7fffqt3gLK726LKikOjRo0wZ84cnD59Gs+fP0daWhq2b98umCruxYsX+O677/R+L5FIBC8vr0JfhmghnJAgbWwkY2MDhITofVhSyvXuDbwdMZQ3e7ZpYiHmx8nJqcjrm+L4BOZMr0bpn3zyCYYOHYozZ87g7t27YIzBx8cHgYGBejXkcXZ2xtOnTwFAZWMmxTJnZ2ed30sbf/31l1JZly5d4OPjg/pynS737Nmj93t5enriwYMHeh+nKIrdXlq2BAppjE2IRqytgSlTgE8+eVd2+DBw9Kj0O0ZKN00eS1WuXNli7lr1TvkikQiNGzdGr1690Lt3bzRp0kTv1rC1atXif05LS0NOTo5g/aNHj9Rubwr16tWDq6srv/z48WMTRqMdxeejVK1LDGXgQOVGa3PmmCYWQozJLO+dmzdvzv/MGMPZs2cF6+Vb6drY2Aha8RpLYS1yMzIyBM91LWVQhgcPgGvXhGWUSImhiMXAhAnCsl27gPPnTRMPIcaiUSK1srLS+WWtw5Am/fv3FyzPnz+ffy6amJiIeLlJMzt37gwXFxd+OTY2VjD2bUJCgtbvr8rcuXMxZMgQnDt3TlD++vVrfPrpp3x3HwAWM9uN4tyjLi6ADm3DCFHrk08ANzdh2dy5pomFEGPRKJEqNibS9qWtBg0aCJLp5s2bUbduXXTs2BGtWrXi7w7FYjFma9mCITExEc2aNeNf8k2sU1JSBOt27drFr8vPz0dMTAwaNmwIb29vREREoH379vD29kZcXBy/nUgkwuTJk7X+zKagmEjbtJHOQUqIoTg6Al98ISzbuBHQcQhuQsySxreLsi4txeXnn3/G/fv3cejQIQBAUlISkpKS+PW2trb4448/4Ofnp9VxMzIycPLkSZXrcnNzBetkDZ4AYfee5ORkJCcnK+1vZ2eHn3/+2WLuSBWHBWzb1jRxkJLts8+AefOkXa0A6ShH8+YBK1eaNi5CDEWjRBoZGWnsOJQ4OjriwIED+O2337B27VpcunQJmZmZqFSpEtq3b4+JEycWayOjSZMmwc/PD7t378bFixeRkpKCp0+fws7ODr6+vmjXrh0+++wzVFds82+m7twBFIcYpkRKjKFcOWDkSGnylFm9Gpg+HdBhBFFCzA7HTNUpk6gka/Lt5eVl1O4vq1YBQ4e+W3Z3B548oRlfiHE8fgz4+ADyDfDHjQOKGNyGlGLFdS00BLpsllKqqnUpiRJjqVgRGDJEWPbLL8Dz56aJhxBD0vvSefHiRcybNw+jR4/G0Le3OI8ePUJycrLFdKYtbRhTbmhE1brE2CZOFDZme/MGWLLEdPEQYig6J9LXr1+jT58+eO+99/C///0Py5cv5wdynzhxIqpVqwZvb2/cunXLULESA7lxA1AY04ISKTG6atWAvn2FZYsXA69fmyYeQgxFp0RaUFCATp06YdOmTSq7uAwdOpQv//PPPw0SKDEcxWpdT0+gdm3TxEJKlylThMsvXkireAmxZDol0lWrVuHff/9Vuz4kJARlypQBAIMNiEAMR1W1Lk1vRYpD3bpAly7CsgULhI2QCLE0OiXS33//nf952rRpaNeunWC9lZUV6tWrB8YYrly5ol+ExKAYk874Io+qdUlx+t//hMuPHgFvpzcmxCLplEgvXrwIjuNQr149zJgxA+XKlVPaxsPDAwCQmpqqX4TEoJKSAMVfCSVSUpyaN1eeqm/ePKCgwDTxEKIvnRLpmzdvAABVq1ZVu41sEHeO6gzNytuBonhVqgBy06kSUiwU70pv3ABUzFJIiEXQKZG6ubmBMSYYsk/eixcvcPr0aXAcx9+ZEvNw+LBwuU0bej5Kil+HDkDDhsKyuXOljx4IsTQ6JdKgoCAAwJ07dxAVFYWMjAx+3cmTJ9GtWzdkZmYCABo3bmyAMIkhMAYothFr3do0sZDSjeOUW/AmJirPj0uIJdApkQ4YMID/edGiRdi/fz8A6SwxLVq0wNGjR1VuS0zr9m3l/qPBwaaJhZAePYCaNYVlNMUasUQ6JdJevXohPDxc0H9UNv+nfFl4eDi6deumf5TEIBTvRsuXB4px3H9CBKysgEmThGXx8cCJE6aJhxBd6Tyy0V9//YWPPvpI5dyjjDH06tWLBmMwM4rPR1u3puejxLQGDAAqVRKWff+9aWIhRFcaz0eqyN7eHuvWrcPUqVOxa9cu3L17F4wx+Pj4ICIiAvXq1TNknMQA6PkoMTe2tkBUFDBhwruyrVuBK1cALacaJsRkaBo1MyObOkgkEsHT01OwLioqClFRUTodNyVF+S//xETllpOEFLdXr4CqVYG3PeYAAIMGATExpoqIFLfo6GhEK8ypl5KSAolEYhHTqOl8R6rK69ev8ffff+PevXuoUaMGunXrBhHNzaUTiUSiNHuOfOtobSnejTo5AfXr63w4QgymbFlg9Gjg22/flf3+OzBzpjTBkpIvIyPDomcL0ymR7tu3Dz/88AMAYNiwYejduzfu37+PNm3a4O7du/x2wcHB2Lt3L2xsbAwSbGmi6o7UyclJ5+MpPh9t2VI4pRUhpvT559Ixd7OypMv5+dJJvxcuNGlYpJg4OTnBy8tLUCa7I7UITAfjxo1jHMcxkUjE/vvvP8YYYyNGjODLRCIR//PSpUt1eYtSy8vLiwFgXl5eBj1u/fqMSXuSSl/ffWfQwxOitzFjhN9RBwfGnj41dVTEVIx1LTQGnepdT506BQBwdXXlB1zYsWMH3/2FyT123bRpk97JnujnxQvg4kVhGfUfJeZm/HjAWq6OLDMTWLrUdPEQoimdEmlycjI4jkO1atUAAI8fP8ajtz39Z82ahZs3b8LJyanQYQRJ8Tl6VDj0mq0t8HZwKkLMhrc38PHHwjKa+JtYAp0S6dOnTwEAld42A7169Sq/7sMPP4Svry+aNWsG4N3g9cR0FBsaNWsmTaaEmBvFARpevABWrjRNLIRoSq8mtWlpaQDAzznKcRx8304lYvW2JYudnZ0+b0EM4Ngx4XKrVqaJg5CiBAQAXbsKyxYsAHJzTRMPIZrQKZF6enqCMYYTJ05g7ty5WPr2QYa3tzefOGVNmd3d3Q0UKtFFbi7w9pE2r2VL08RCiCYUp1h7+FDaHYYQc6VTIm3evDkAoKCgAFOnTsXVq1fBcRzatWsHQNoH8u7du4LnqMQ0zp4FcnKEZW9r3QkxS82a0cTfxLLolEi/+OILWL9tXidrpWtlZYXPPvsMAHDo0CF+8IBWVI9oUnIT8QAA/P2BcuVMEwshmlKcYu3aNWDbNtPEQkhRdJ6PdNeuXWjXrh3q1KmDzp07IyEhAe+99x4A4N69e+jUqRM6duyIzp07GzJeoiXF56MtWpgmDkK0ER4ONGggLJszhyb+JuaJxto1M7Kxdg0xviRj0vF1Hz9+VxYTIx3HlBBzt2ED8NFHwrL9+4HQUNPEQ4qXIa+FxkYD4ZZg9+4JkyhAd6TEcvTsCVSvLiybM8c0sRBSGEqkJZhita6bG1CzpmliIURb1tbAxInCsgMHlFuhE2JqlEhLMFXPR2kib2JJIiOBihWFZXPnmiYWQtShRFqCKbbYpWpdYmns7IBx44RlW7YAcoOpEWJylEhLqFevgAsXhGWUSIklGjECcHZ+t8yYtF8pIebCrBOpRCLBr7/+ipCQELi5ucHe3h6+vr4YPnw4bt68qdMxnz17hhUrViAyMhI1atQAx3H8y8fHp8j9c3JysGDBAjRp0gQuLi5wcHBAnTp1EBUVhceKLXtM6L//APmp/KytgbcT9RBiUZycgLdd1Hlr1wL375smHkKUmG4Gt8K9efOGtWvXjgFQ+bK1tWVbt27V+rhbtmxRe0xvb+9C901NTWX16tVTu7+Liws7fvy4jp9YylBz8M2aJZzbsUkTvQ5HiEk9ecKYnZ3wOz12rKmjIsZU4uYj9fX1ha+vL8aMGQMAGDJkCIYMGYKffvrJYAld0ahRo3Dw4EF+2d/fHxEREbC3twcgvTPs06cPrl27pvN7ODo68iM0aaJ37964KDexZ1BQENq3b88fIz09HV26dMHz5891jslQaCAGUpKULw8MHSosW7kSePbMNPEQIk+jRHr37l3cu3cPT548AQDExsZi9erViI+PN0pQFy9exOrVq/nlXr164dKlS/j7779x9OhRPnHl5ORg6tSpWh27Ro0aWLZsGRITE/Hy5Ut4eXlptN+OHTuQkJDAL48fPx6nTp3Cvn37sGXLFr782bNnmGPizm6MASdPCsveDo9MiMWaMAF4O6kUAOnE34sXmy4eQmS0ekaanZ1trDgE1q5dK1geP348uLf9Nho2bIhQuaFNduzYodWcp3Xr1sWoUaPQsGFDfqo3XWKaKNfBrXPnzqhduza//Pvvv4OZcMCoGzek8zjKa9rUNLEQYig+PsoTfy9ZIm1YR4gpaVSvaWdnh5ycHCQkJOCrr77iy5OSkjBr1qwi9582bZpWQR2Tq5fkOA4NGzYUrA8MDMSePXsAALm5uThz5owguRqDfExeXl6oUKGCUkyyauYnT57g9u3bqK44LEsxUbwbrVgRqFrVJKEQYlCTJ0sbGsmkpwMrVkjvVgkxFY0SabVq1XD16lW8efOGr7ZkjOHKlSuYOXNmkftrm0hv3LjB/+zm5gaxWCxYX1Ghh/b169eNmkgzMzP5+VUB6XysilTFpE8iTUlJQeXKlQvdJioqClFRUUrliom0aVMaiIGUDAEBQLduwplgoqOBMWMAW1vTxUW0Ex0djejo6EK3SUlJKaZo9KdRIv3www8xe/ZsvnpVU4wxrfcBIKiqlTUukufg4CBYfvnypdbvoQ3F4xdHTBKJRJC8VZFNVadIVSIlpKT43/+EiTQlBYiNBYYPN1lIREsZGRlFXt8siUaJdOrUqbh+/To2b94MiUQCjuP4eUiNTdV7mPL5o7r3N3RMIpFI5Z2vPCcnJ6Wy7Gzg/HlhGSVSUpI0bQq0bQvIt3WcN0/aqleLRvjEhJycnIps6JmSkgKJfGd4M6bxM9K4uDi8efMGz549Q7Vq1cBxHCIiIrBs2TKDB+Xs7IynT58CALKyspTWK5Y5yw97YgSKxy+OmDw9PXWaOujsWSAv790yxwFBQXqFQojZ+fJLYSK9fRvYuFG5MRIxT+oeS8mTTaNmCbT6+83R0RGOjo4ApHdgDg4O8Pb2NnhQtWrV4hNpWloacnJyYCv3AOTRo0dK2xuTg4MDvLy8+F+q4vubIiZ1FKt1/f2lI8MQUpKEhkpH6pKfCWbOHKBvX0Bk1uO1kZJIp6+cRCKBRCLBxo0bDR0PAKC5XKdHxhjOnj0rWH/mzBn+ZxsbGwQGBholDnUxpaSkKD0IT0xM5H8uX748fH19jR6TKvR8lJQGHCe9K5V36RKwa5dp4iGlm95/u504cQIzZszA4MGDMXjwYEyfPh3Hjx/X65j9+/cXLM+fP59/BpmYmCgYCKJz585wcXHhl2NjYwXj58oPoqCPAQMGKMUks337dly/fp1f7tevn06NrAyBEikpLbp2lda4yJs9WzogCSHFStexBV+8eME6duzIRCKRyld4eDh7/vy5zmMX9u/fXzCOrb+/P4uIiGD29vZ8mVgsZklJSYL9YmJiBPvFx8cL1p85c4Y1bdqUf4nFYsHx5Nft3LmT308ikbDg4GDBsYOCglj79u2ZtbU1X+bq6spSU1N1/tz6jC/55IlwLFKAsfPndQ6FELO3Zo3yd/7gQVNHRQzBksba1SmR5uXlsebNmzORSMQ4jlNKorKyZs2asfz8fJ0Ce/36NQsJCSl00PrNmzcr7VdUIo2Pj1d7TMVXTEyMYN/Hjx+zgIAAtds7Ozuzo0eP6vR5ZfT58mzfLrygODoypuPpJ8Qi5OYy5uMj/N6Hhpo6KmIIlpRIdaraXbt2LU6cOAEAgq4wspes7L///sOaNWt0eQs4OjriwIEDWLFiBVq1agUXFxeIxWL4+Phg2LBhuHDhAj788EOdjq2rChUq4PTp05g3bx6CgoJQtmxZ2NnZoVatWhg7diyuXLmCFiYcHV6xWjcoSDg2KSEljY0NMGmSsOzAAeX/C4QYE8eY9k8UwsPDsW/fPnAch3r16mHKlCkICAgAYwxJSUmYN28ezp07B47jEBoair179xoj9hJJ1uTby8tL6+4vYWHA/v3vlidNAr7/3sABEmJmsrOBatUA+emAu3YVDtpALI8+18LiplP35XPnzgEAPDw8cOjQIUGfyfr16+P9999HnTp1kJqaivOKowMQo5BIhF0BAGpoREoHOztg/HhAbh4JbN8OXLwI1KtnurhI6aFT1W56ejo/mLyqgQdcXFz4gea1mZmF6O7mTUBxVMImTUwTCyHFbcQIwNVVWPbdd6aJhZQ+OiXSMmXKAACuXbumcgingoICfiYU2bbEuE6fFi5XrAhoONUqIRavTBlg7Fhh2caN0ikFCTE2nRJpnTp1wBjDvXv30K9fP9y6dYtfd/v2bQwYMAB3794Fx3GCeTqJ8Sgm0saNacYXUrqMGQOULftuWSIB5s41XTyk9NApkXbt2pX/eePGjahVqxbs7e3h4OCAmjVrIi4ujl/frVs3/aMkRVJ8Pkrj65LSplw5YNQoYdmaNUBysmniIaWHTol05MiRqFKlCr/MGENOTg6ys7MFs6BUrlwZI0eO1D9KUqiCAkBuhEIAlEhJ6TRunLTxkUx+PrVcJ8anUyJ1cnLCzp07UblyZT5xyobkA6SJtXLlytixY4fKqb6IYV29CmRmCsuKYfhhQsxOhQrAp58Ky377DVAxzwQhBqPzWLv16tXDlStX8OOPPyI8PBx16tRB7dq1ER4ejh9//BFXrlxB/fr1DRkrUUOxWrdKFekFhZDSaOJEQCx+t5yTAyxYYLp4SMmn1zS4Dg4OGDt2LMYqNpcjxUpVQyNCSqvKlYHBg4EVK96V/fwzMGUK4OFhurhIyUUz95UAiomUno+S0m7yZOHwmJmZwI8/mi4eUrJRIrVweXnA24GmeJRISWlXrRqgMPMhli4F0tJMEw8p2SiRWrhLl6TPgORRQyNCgP/9T9iX+tUrYPFi08VDSi5KpBZOsVq3enXlodIIKY1q1QL69hWWLVyoPJQmIfqiRGrh6PkoIepNnSq8K335EliyxHTxkJKJEqmZSklJQeXKlQWv6Ohope1oRCNC1AsIAHr2FJZFR0ureYn5iI6OVrrepaSkmDosjenV/YUYj0QiwcOHDwVlGRkZguXsbOlUUfIokRIi9NVXwJ9/vlt+8QJYtkzaHYaYh4yMDKXrnSXRKZHOmjULAODv74+ein/uvZWcnMxPoUYDM2hPJBLB09NTUKY4StSFC9Ih0GQ4DmjUqDiiI8Ry1K8PfPABsHXru7IFC4DRo6WzxhDTc3JygpfCdFUpKSkqZxczRxyTHxxXQyKRCBzHoUePHti4caPKbXr16oW//voLHMchX/5qTwqlzazwK1ZI52GUqVULeDt7HSFETmKicmv2efOEk4ET86LNtdDUjPaMlDHGv4hxKA5UT91eCFGtUSOgc2dh2bx5wJs3pomHlCxGS6R379411qHJW4qJtGFD08RBiCWYNk24/OwZsHy5aWIhJYvGz0jbtWunVHbo0CGV5Y8ePcKNt1PT28nPaUQMJi9PuaERPR8lRL3GjYFOnYBdu96VzZsnncPU0dF0cRHLp3EiTUhI4KdJA6RVt8+ePcOhQ4eUtmWM8dOq1a5d2zCREoErV5RHNKI7UkIKN326MJHK7krpWSnRh1GqdjmO45+Pjh492hhvUeopVut6e9OIRoQURXZXKo+elRJ9aXxHWrVqVf6O9N69e+A4Dvb29vBQmJdIVl6jRg0MHDgQPXr0MGzEBABw9qxwmap1CdGMqrvSZcuASZNMFxOxbBonUvnGQyKR9Ea2Y8eOaru/EONSvCOlREqIZtQ9Kx05Eihb1nRxEculU9VucHAwgoODERAQYOh4iAYkEuWp0+j5KCGamzFDuPz8OY3BS3Sn08hGCQkJBg6DaOPmTeD1a2EZ3ZESormgIKBrV2D79ndl8+cDn30GODubLi5imfQaazczMxOnT59GSkoKchSbkMoZOHCgPm9DFChW61asCCiMJkgIKcLMmcJE+uIFsGiRcn9TQoqicyKdOXMm5s+fj8zMzCK3pURqWIoNjahalxDtvfce0KMHsHnzu7LoaGDMGKBcOZOFRSyQTs9IFyxYgJkzZ+LNmzeCoQAVhwWk4QGNgxoaEWIYM2Yoz1e6YIHJwiEWSqdE+ssvvwCAYIAGRZREjYMxSqSEGErdukCfPsKyRYuAp09NEw+xTDpV7cr6kQLAp59+io4dO6JMmTKwsrIyaHBE2f37QFqasIyqdgnR3fTpwMaN0tbwgLQh39y5dGdKNKdTIvXw8MCjR4/QuHFj/Pzzz4aOiSeRSLBq1SqsXbsWly5dQmZmJjw9PREWFoaJEyeiRo0aOh/7zJkz+PHHH3Ho0CGkpqbC2dkZjRo1wrBhw9TOserj44N79+4Velw3Nzc8e/ZM57iKong36uIC+PgY7e0IKfHq1AEGDABWr35XtmwZEBUFKEyRSYhKOlXtfvDBB2CMGXXS1czMTISFheGTTz7B4cOHkZaWhuzsbNy5cwe//PIL6tati23btul07OXLl6NJkyZYt24dHjx4gNzcXDx9+hR79uxBr1690L9/fxQUFBj4ExmGqoZGhdSwE0I0MH06YGPzbjknB/j2W9PFQyyLTnek06dPx5YtW3DmzBksX74co0aNMnRcGDVqFA4ePMgv+/v7w9vbGwkJCcjKykJOTg769OmD8+fPazUwfkJCAkaPHs0/w3VxcUHLli2RlJSEO3fuAADWrVuHmjVrYvr06WqPExwcrDQ8IiCd6d2Yzp8XLlO1LiH6q1YNGDYM+Omnd2W//iodzN7X13RxEcvAMR1aBQ0ZMgQ3btzA0aNHwXEcvL290aBBA5RT0Wac4zj89ttvWh3/4sWLqF+/Pr/cq1cvxMXFgeM4nD17Fk2aNEF+fj4AoEePHti0aZPGxw4MDETi2/pRFxcXXLhwAVWqVEFubi7atm2LY8eOAQBsbW3x4MEDuLu78/vKV+3Gx8ejTZs2Wn0uTRQ1K3y1aoD8VK+rVwPUu4gQ/T16BFSvDmRnvysbOFBY5UuKT1HXQrPCdMBxHBOJREwkEjGO4wTL8i9ZubYmTpzIAPCvEydOCNaHh4fz68RiMXvx4oVGx718+bLguCNGjBCsX79+vWD9smXLBOu9vb35dfHx8Vp/Lk14eXkxAMzLy0tp3YsXjEnb7b57nTtnlDAIKZXGjxf+/xKJGLt0ydRRlU6FXQvNjd7TqMnmHTUk2V2h7PgNFeovAwMD+Z9zc3Nx5swZrY+reBxVy8ePH1d7rNWrVyMyMhL9+/fHhAkTsHXrVv4u2VguXBAu29gAfn5GfUtCSpUpU4AyZd4tSyTA1Kmmi4dYBp1HNmJG7Cd648YN/mc3NzeIxWLB+ooVKwqWr1+/jtDQUK2OCwCeCuPqqTquOrGxsYLlBQsWwNfXF3FxcQgKCioylqKkpKSgcuXKgjLF8XU9PKIgFkfp/V6EECl3d2D8eOnwgTLbtgHHjwPNm5surpImOjoa0dHRhW6TkpJSTNHoT6dEaszWugCQnp7O/2xvb6+03sHBQbD88uVLrY+r6ti6Hlfm9u3b6NChAxITE+GjZ58UiUSChw8fFrqNu3uGXu9BCFE2fry0+4t8L7YpU4CEBGohbygZGRlFXt8sid5Vu8am6s7XUHfDiscp6riNGjXCnDlzcPr0aTx//hxpaWnYvn07fOWa9b148QLfffed3rGJRCJ4eXkJXjY2XgDevXx8jNtCmJDSqGxZ4KuvhGWHDwP//GOaeEoiJycnpeub4ks277Ul0Gv2F5nU1FQkJycjMzMTwcHBeh/P2dkZT9+O0ZWVlaW0XrHMWcN5jxS3UzxOUcf966+/lI7ZpUsX+Pj4CFoZ79mzR6N4CuPp6SloqZafL3x2AwBjx+r9NoQQFUaMAH78EZAff+V//wPCwwELur6braioKERFFf5YStZq1xLo9ZX4+++/ERgYCE9PTzRt2hTt2rUDAHzxxRdo164dOnTooNHsMIpq1arF/5yWlqY0RdujR4/Ubq/pcVUdR9fj1qtXD66urvzy48ePNdpPG9evSzuJy2vQwOBvQwgBYGsLzJolLDt/HvjjD9PEQ8ybzon0xx9/RJcuXXDu3DmlWV8CAgKQkJCAAwcOYMuWLVofu7ncU33GGM4qDOcj30rXxsZGqbWtJscFwPcnVXVcxe0La5GbkZEheP5qjEEZzp0TLnt5AW5uBn8bQshb/foBAQHCsqlThf1MCQF0TKSnTp3CxIkT+eSp2P2lR48efP22LtWc/fv3FyzPnz+fT9KJiYmIj4/n13Xu3BkuLi78cmxsLN8lh+M4JCQk8OsCAgIEXWni4uJw//59AEBOTg6WLFnCrxOLxejVqxe/PHfuXAwZMgTnFDLa69ev8emnnwoaYLVo0ULrz1wUxRGN3nvP4G9BCJFjZQV8/72wLDkZWLrUNPEQ86VTIl24cCEkEgk4jkNAQACqVasmWO/q6oratWuDMaZ016eJBg0aCJLp5s2bUbduXXTs2BGtWrXi7w7FYjFmz56t1bHnzZvH/5yeno769eujc+fO8PPzw4kTJ/h1kydPFgwBmJ+fj5iYGDRs2BDe3t6IiIhA+/bt4e3tjbi4OH47kUiEyZMna/2Zi6KYSKlalxDj69gRUBzAbPZs5RmYSOmmUyI9fPgwAMDd3R0nTpxQGjABAN/9Q3bHp62ff/4ZISEh/HJSUhJ2797NNwiytbXF+vXr4afliATt27fHokWL+Dvm9PR07Nq1ix9nFwD69u2rNM6u/F13cnIy/vnnHxw4cABpcv+j7OzssGrVKqPckSpW7VIiJcT4OA6Q+9sbAJCeLk2mhMjolEhTU1PBcRyaNGkCR0dHldvIqmJVtbrVhKOjIw4cOIAVK1agVatWcHFxgVgsho+PD4YNG4YLFy7gww8/1OnYn3/+OU6ePImPPvrobbcSG7i5uSEsLAxxcXFYv3690tyqkyZNQlxcHAYNGoTAwEBUqlQJNjY2KFu2LBo0aIBx48bh0qVLiIyM1Cmmwjx5In3Jo0RKSPFo3Bjo21dYtnQpIPe3NynldBq0vly5csjIyEDz5s1x5MgR9OrVC5s3bwbHcSgoKABjDNWqVUNycjJcXV2NOj9nSaNqoOa9e6XN7mUcHICMDOkzHEKI8d2+LZ23NC/vXVmfPsCGDaaLqaSzpEHrdbojrVmzJhhjOHnyJE6dOqW0Pjo6GsnJyeA4TuuqV6JMsVq3Xj1KooQUJ19f4LPPhGVxcdKhAwnRKZF26tQJgHQYu9atWwvmDfXz88OkSZOUtiW6o4ZGhJje118DijNFjhsnHdielG46JdIxY8agfPnyAKSzr6Snp/ONca5du8Y/Hy1fvjxGjBhhoFBLr4sXhcuUSAkpfq6ugEIbRJw8Kb0zJaWbTonU1dUVW7ZsEYzmIyNLqC4uLti8ebOgjyfRXl4ecPWqsKxePdPEQkhpN3IkULOmsGzyZEDHNpWkhNB5ZKPmzZvj0qVLGD9+POrUqQM7OzvY2dmhdu3aGDduHC5fvmyUbiClzbVrwgYOAFC3rmliIaS0E4uBH34Qlt2/DxQxIxgp4XRqtUuMR7Gl2vr1wMcfy6+X/sclhJgGY0BoKCA3wBocHKR/9CpMIUz0UOJb7ZLio/h8lKp1CTEtjpPegcqPjJqZKa3iJaWTRtOorVmzBoB0tKLg4GB+WVMDBw7UPjICgBIpIebovfeATz4BfvnlXdkff0ifobZqZbKwiIloVLUrEonAcRx69uyJuLg4fllTBQUFegVZmihWZ3h7SwfKllm7FlAY058QYgJPn0obHr18+a6sYUPg1Cnq520IJbZqVzHnyk+fpvhStT3RzsuXwiQKAHLzhxNCTMjDQ3nO0rNngd9+M008xHQ0TqSqkqg22xPtXbokXLa2lg5TRggxDyNHAv7+wrIvvwSePzdNPMQ0NHpGKpv/UzatmPx8oMR4FJ+P1q4tbX5PCDEPNjbAokVAWNi7sufPpcl0xQrTxUWKl0aJVH46M1XLxDiooREh5q99e6BHD2Dz5ndlK1cCQ4cCTZqYLi5SfKj7ixmjREqIZfjxR0B+RknGpNW+1M6ydNDojlQ2kbeugoOD9dq/NEpJScGjR8Le3bduRQGIMk1AhBC1qlQBpk0T9iVNTJRW744aZbq4LEV0dDSiFYaHSklJMVE02tMokbZp00ar7i7yOI5Dfn6+TvuWZhKJBMBDQVnZshmmCYYQUqQvvgBiY4ErV96Vffkl8OGHQMWKporKMmRkZODhw4dFb2imtO7+osuLaE8kcgDgxb84zgtVqjiZOCpCiDpiMbB8ubDs5UtpgiWFc3JygpeXl+AlElnOk0eNB2RQufPbu1TFQ8iXcxxHAzJoQdYJ2cnpW2RkTOXLmzcHjh0zYWCEEI307w+sWycs27kToKmZtWNJAzJoVLUbExOjVHb06FH8+uuvKFOmDD7++GMEBAQAAK5cuYJ169bh9evX6Nu3L8LDww0bcSmRlyfsMEoNjQixDNHRwN9/Ay9evCsbNQq4fBkoU8Z0cRHj0Wn2l2vXriEwMBAcx+G///6Dn5+fYP3Vq1fRuHFj5OXl4cSJE3jvvfcMFW+JJ/srzMbmEvLyAvjyJUuA0aNNGBghRGMxMcCQIcKyceNoujVtWNIdqU6V0FOnTkVmZiaaNm2qlEQBoE6dOmjatClyc3MxXXFKeaIBK+Tl1RCU0B0pIZZj0CCgTRth2aJF0nF4ScmjUyJNSEgAx3F4+vSp2m1k644cOaJbZKVadQC2ghKazJsQy8Fx0q4vtnL/jSUSYPBgICfHdHER49ApkWZnZwMALl26hK+//hpZWVn8uqysLEyfPh0X344mkEPfGh0ECJYqVADc3EwUCiFEJ7VqSfuWyrt8GfjmG9PEQ4xHp0TaoEED/ufvvvsO7u7u8PPzg5+fH9zd3fHtt98CkLberU/TlehAmEgDAtRsRggxaxMnSqdWkzd3LnDmjGniIcahUyKdOHGiYKq0rKwsXLt2DdeuXRPcnQLApEmT9I+y1KFESkhJYGMjbXhkLdc/oqBA+gw1N9dkYRED0ymRfvDBB4iOjobV29lrOY4TvBhjsLKywrx58/DBBx8YMt5SghIpISVFgwbAV18Jyy5dAmbONE08xPB0Hjriiy++QGJiIj755BNUr14dYrEYYrEYvr6+GDZsGBITEzF+/HhDxloqMGYNoLagjBIpIZbtf/+TJlR5c+cCR4+aJh5iWDr1IyXGU6FCW6SmCud7TUsDypUzUUCEEIM4dw5o3BiQH3q8WjVpuRON/qmkxPcjJcaTn19LsOzpSUmUkJLgvfeAWbOEZXfu0Fi8JYFGQwSqk5WVhYSEBFy/fh0ZGRlqB6ifptgGnKiVl0fVuoSUVJMmSYcPlO9eHxMDdO4snSWGWCadE+nmzZsxYsQIpKWlFbktJdLCMcZw7NgxHDhwAJmZpwDcA1ABQAQCAhoWsTchxFJYWQFr1kifl7569a582DAgKAgQiR5g8+bNSE5ORnZ2NlxcXNC4cWN06tQJNjY2pgu8mEgkEsTHx+Pff/9Feno6AODVq1e4cuWKylH0zAbTwfnz55lYLGYcxym9RCKR0jJRLTc3l/3yyy+sfv36DIDKl69vM/bHH3+wgoICU4dLCDGQmBjGAPnXEebq2p2JRCKV1wFPT082ffp0lpaWZurQjSIrK4v9+OOPrGbNmmqvhW3btmXbtm1jEonE1OEq0SmRDhs2TJA0RSKRygSqbyItKChgK1euZMHBwczV1ZXZ2dmxatWqsU8//ZTduHFD5+Myxtjp06dZv379WOXKlZlYLGYeHh4sPDyc/fnnn4Xul52dzebPn88aN27MnJ2dmb29PatduzYbN24cS0lJ0fj909LSWHBwsNovjeKre/fu7M2bN3p9ZkKIeZBIGOvVizFAwoBZGl8HqlSpwi5dumTq8A3q0aNHrGHDhhqfg8GDB7Pc3FxThy2gUyKtU6cO4ziO2djYsN27d/MJs1OnTuzEiROsQ4cOzMrKin377bfs7t27OgX25s0b1q5dO7Un09bWlm3dulWnYy9btkztX34AWL9+/Vh+fr7SfqmpqaxevXpq93NxcWHHjx8v8v1fvXrFAgMDNf7iyF7h4eFm9wUihOgmPZ0xF5dpWl8H3Nzc2LVr10wdvkE8ffqU1apVS+tz8NFHH5lVLZ1OibRMmTJMJBKxxo0bM8YYn0h79erFGJMmQU9PT2ZlZcX27t2rU2CRkZGCE+fv788iIiKYvb29IJlevXpVq+PGx8czjuMEya9Tp06sWrVqgvebMWOG0r5t2rQRbBMUFMTat2/PrK2t+TJ3d3f27NkzrT6b7FWtWjU2ePBgNnDgQFapUiWV23z55ZdafV5CSPGRSCRs37597M8//2Tp6emFbrtz506tE4js5efnV+Qf1RcuXGBr1qxhycnJhvyIBtWxY0eVn69OnTps6NCh7OOPP2bu7u4qt/nxxx9NHT5Pp0QqFouZSCRi3bp1Y4wxZm1tzd+RynTq1IlxHMfatGmj9fEvXLggOGG9evXi68UTExMFiatHjx5aHbtRo0aCJCr7kuXk5LAWLVoIkvTTp0/5/bZv3y6Iafz48fy6HTt2qF2n6N69e0p3w56enmzbtm2Cv7Byc3PZ2rVrmbOzs2DbsmXLsoyMDK0+MyGkePzvf/8TXF9mzZqlNqG2bNlS50QKQO1jqBMnTrCIiAhBHNevXzfmx9bJ2bNnlT6Tr68v279/v+A5aHZ2Nvvpp58EN1EAWKVKlcymhk6nRFqhQgUmEolYREQEY4yxcuXKMY7jmJeXF18lKqv+dXJy0vr4EydOFJywEydOCNaHh4fz68RiMXvx4oVGx718+bLguCNGjBCsX79+vWD9smXL+HW9evUSrHv8+LFg39q1a/PrKlSooPaB+NSpUwXHKequ+siRI0pftuXLl2v0eQkhxatChQpK/19VJdRz587plUQBaeMbeYoJVP41d+7c4j4VRfrkk08EMZYrV449ePBA7fbbtm3T+I+J4qZT9xd3d3ekpqbi2bNnAABfX18kJiYiJSUFzZo1g1gsxrVr1wBImzNr69ixY/zPHMehocL0CYGBgdizZw8AIDc3F2fOnEFoaKhWx5Udp7Dl48ePY9SoUUr7enl5oUKFCkr7yj7zkydPcPv2bVSvXl0phrVr1wqWhw4ditq1ayttJ9OyZUt069YN27Zt48u+/vprHD58WO0+hBDTkF0T5aWnp2PatGn49ttv0a1bN6xfv17pOqCL+Ph43L9/H7dv38aQIUNw+/ZttduuWbMG586d0/s9DUUikeCvv/4SlI0dOxZeXl5q9+natStatGghuBavWbMGPXv2NFqcmtIpkdatWxdJSUm4c+cOAKBt27ZITEwEAJw5cwYcxwGQJsEmTZpoffwbN27wP7u5uUEsFgvWV6xYUbB8/fp1jRKp/HEBwNPTs8jjAkBmZiYePnyodj91+yom0pycHCQnJwvK+vfvX2Tc/fr1EyTS58+fY8OGDUXuRwgxH7m5ufjzzz8NOkfzpUuX0LVrV+TLjzuoQlJSEpKSkgz2vsag6bVQPpHevHnTmCFpTKchAoOCggBIL+gXLlzA2LFj4eTkBMYYn0QBwNraGt/oMIutrCMuANjb2yutd3BwECy/fPlS6+OqOra64yoeX9eYMjMzlcoqV66sPuC3qlatWuQ2hBDLcPr0abx588Ygx7p8+XKRSdRS6HItNNR51JdOiXTChAnIy8tDXl4e6tevj8qVKyMhIQEdOnRAmTJlYGtri9atW2P//v1o0aKFXgEyFcMOqiozxLE1Pa6uMZUpU0apTHbXW5irV69qFBchxPx17doVTgYapb5Ro0ZKf8RbKl2uhYY6j/rSqWo3IyOD/1n2Qd577z38888/BgnK2dkZT58+BQClicJVlTk7O2t83MKOo+64Re2naUw2NjaoU6eO4MsQExNTZLV0bGysYNnHxwf9+vUrdB9CSPH7/vvv1d4huru74/PPP8fXX3+NadOmYcuWLXq9l0gkQr169XDp0iUMGzYMhw4dQkFBgcptW7RogbZt2+r1fobEGMPChQsFtXQxMTGIjo4udB/Fa2HdunWNFaJ2dGmhJOs3WrFiRaN0ipVvFs5xHMvOzhasnzJliqDl1v79+zU67sqVKwX7rVixQrD+6tWrgvX9+/fn13l5eQm6qyjq27evYN+bN2+qjGHevHmC7TiOY//++6/amDdt2qTUUm3dunUafV5CSPGqUqWK0v/XOnXqsD/++EMwyMvNmzcF/dl1eX3wwQeC937w4AEbM2YMs7W1Vdo2Ojq6uE9FkSZMmCCI0c7Ojl24cEHt9suXL1f6XLqOU2BoOiVSJycnxnEc69ixo6HjYYwpn2DF0YLCwsL4dTY2Nhp3f7l06ZLguMOHDxesX7dundruLz179hSse/TokWBf+dE5ypcvr7b7y9OnT5W+6A4ODmzBggXs5cuXgu2mT58u6DMLgHl4eCj9YUEIMQ9Lly4tNIHKU9dVRdPXnj17VB5XMaF6e3uzhw8fGvNj6+TmzZtKn6lcuXLs559/FgyH+vDhQzZ+/HilPzxq1qxpNqMb6ZRIg4ODmUgkYoGBgYaOhzGm3MeqR48efGI6c+aMILl0795dsG9MTIxg3/j4eMF6+TEd5QdkyM7OZs2aNePXicVilpqayu+n2IcpKipK7bpx48YV+vkmTZqk8j+Gg4MDa926NWvRogUTi8Uqt1m0aJE+p5YQYmS3b99miYmJahOozPHjx5mVlZVOSdTLqzXLzy88iTx//pwdPXqUZWZmGvLjGdTgwYNVfr6yZcuyNm3asCZNmqg9R3/88Yepw+fplEh37NjBOI5j1tbWLCEhwdAxMcYY69+/v+CkqRoiUCwWs6SkJMF+RSXSffv2CdarGyLw66+/FuwnkUiUBplXNUSgq6urIAGrkpeXxzp37qz1f55hw4aZ5cwHhBDd/Prrrzok0uoMeMK+/FI6+L0li4/PZByn/QhPU6ZMMXXoAjol0kOHDrG+ffsyjuOYvb09GzVqFFu/fj2Lj49nhw4dUnrp4vXr1ywkJETtibS1tWWbN29W2q+oRMoYY4sWLSp00Pq+ffuq/Gvy8ePHLCAgQO1+zs7O7OjRoxp9vpycHDZw4ECNvzjjx483m2oMQojh/P777yqfa6p+BTEgheHt9GsTJ1puMn30iLFKlRgDXjGgi0afn+M4Nnv2bLO7odCrsZHiNGqqXlZWVjoHl5+fz1asWMFatWrFXFxcmFgsZj4+PmzYsGFqZz/QJJEyxtipU6fYRx99xLy8vJiNjQ1zc3NjYWFhLC4urtCYsrKy2Lx581hQUBArW7Yss7OzY7Vq1WJjx45Vem6qiQMHDrDu3VXPQygWi1n//v3ZyZMntT4uIcRy3Llzh02cOJG5urqqTCDNmzdnI0euZUAun0Rlr7FjLS+ZpqUxVreu/OeQMGAH8/F5X+Xnd3BwYJ988gk7f/68qUNXiWNM+06ZIpFIMPACALX9KDmOU9skm7zz4MEDHD58GKNGjcLLly9Rrlw5XLt2DR4eHqYOjRBSTLKysnDgwAHcv38f2dnZcHFxQePGjfluHr/9BnzyiTT1yBs6FPjpJ8DGxgRBa+nNGyAsDDh+XFjerh2wZw+QnHwbR48exZgxY/Dy5Uu4urri1q1bcHFxMUm8mtA5kWr8BpRItVK5cmU8fPgQXl5eePDgganDIYSYmTVrgMGDAcVhzMPDgT//BMqWNU1cmsjNBbp2lSZMedWrAydOAO7u78os6Vqo04AMMTExho6DEEKIBgYOBMRioH9/QP4eZc8eoHVrYOdOQIPR9opdZibQp49yEq1UCdi3T5hELY1OiTQyMtLQcRBCCNFQ376AnR3w0UdAdva78vPngcaNgfXrgTZtTBaekrQ06Z3o0aPCcldXYO9eoFo108RlKDqNtUsIIcS0PvgAiI8HFJtRPH4MhIYC332nXP1rCg8fAsHByknU0RH4+28gIMA0cRmSTnekilOBqSMWi+Hu7g5ra53ehhBCSCGaNZM22unYEZAf810iAaZOBQ4fBlauBKpUMU18+/cD/foBqanCchcXYMcOoGlTk4RlcDplOB8fH6VWu2rfwNoarVq1wldffWVWgyYTQkhJUL06cOyY9Jmp4rwhe/ZI7/i+/x4YPhzQop2oXvLzgZkzgdmzlVsYV6okjctcxps3BL1OK5P2Qy30lZeXh/j4eISFheG3334zVNyEEELecnMDdu0Cvv1WOVm+egWMGiWtXj1xwvixnDkjbfT07bfKSbR2bWnSL0lJFNAjkbK3k3irujNVLOc4DhKJBGPGjMGdO3d0fUtCCCFqiETS6tz9+4GKFZXXHz0KNG8ufbZ66ZLh3//pU+DTT6WNnVQl7I4dpTF4exv+vU1Np0Q6ffp0dO/enR+EITQ0FF988QXGjRuH9u3b89v17t0bAwYMgKOjIwAgJycHK1asMEDYhBBCVGnbFkhKAoYMUb1+2zagXj1pv9O//gLy8vR7v6QkYMQIwMdH+jxW8S7U2hr44QfpM1E3N/3ey1zpNCDDnTt3EBgYiDdv3mDXrl2C5AkA+/btQ6dOnVCuXDmcOXMGr169QsOGDZGXl4egoCCcPHnSYB+gpLGkTsiEEPO2f7/0LrGwisCKFYEuXYAOHaStfcuVK/yYjAEXL0qfc+7cKW3QpE716sDvv0sbRWnLkq6FOiXSjz/+GBs2bEDr1q1x6NAhldsEBwfj6NGj6NevH9asWYNevXph8+bNKFeuHJ4/f6534CWVJX15CCHmLzsbWL5c2h2mqEsvx0mrXmvUkL4cHd89c334ELh9G7hxo+jjODgAX30FREUBtra6xW1J10KdWu0eOHAAHMchKytL7TY5OTlgjGHv3r0AgOrVqwMAXr9+rctbEkII0YGdnTShDRsGREcDixYB6emqt2UMuHtX+tq/X/v3sraWDhLx3XfmObqSsej0jPTVq1cAgDNnzuCnn35SWr9q1SqcPn0aAJCRkSFYV9acB4IkhJASyskJmDEDePQIWL1a2vDIUNzdpQ2d7t6VjgVcmpIooOMdaZ06dXD+/HkwxjB69GjMnTsXfn5+EIlEuHr1Ku7du8e36vXz8wMAPHr0CABQoUIFw0VPCCFEK/b20vF6Bw4Erl6Vji60Z4/0Waf8cINF8fEB3n9f+urQQXrc0kqnRPr5559jyJAh4DgOjDHcv3+fr8OWPXKVdX/5/PPPAQCHDx8Gx3Fo0qSJIeIu8VJSUlBZ4c+6qKgoREVFmSgiQkhJU6eO9BUVBWRlSVvg3rwpfd27J23RK5FIX66u0sZDvr6An5/0Xw3H5SlSdHQ0oqOjBWUpKSmGOXgx0CmRDho0CJcuXeI/uGKfUdlgDBMmTEBkZCTu378PPz8/+Pn5oU+fPoaJvISTSCR4+PChoEyxmpwQQgzF3h4IDJS+iltGRobS9c6S6DwI7vz58xEeHo4FCxbg33//5Rse2dvbIzg4GOPHj+e7xVSpUgW7d+82TMSlhEgkgqenp6DMycnJRNEQQojxODk5wcvLS1CWkpICiTmMuq8Bnbq/KCo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   ],
   "source": [
    "plot_gradients(gradients[:, 0], figsize=(5,4), fig_title=\"Hawk-Dove game replicator dynamics\", \n",
    "               xlabel=\"frequency of hawks\", roots=roots, stability=stability)\n",
    "plt.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evolutionary Dynamics of the Hawk-Dove Game in Finite populations"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "Now we are going to study the effect of having Finite populations. In general, finite populations introduce stochastic effects in the dynamics, also known as random drift $~ 1/Z$, where $Z$ is the size of the population. We can represent these dynamics, by adapting the replicator equation, which considers that individuals are sampled from an infinite population, and therefore selecting a member of strategy $j$ does not reduce its frequency in the population. When the population is finite, we make no longer assume a sampling with replacement, i.e., when an individual of strategy $j$ is sampled, the fraction of members of that strategy is reduced, instead we must sample without replacement.\n",
    "\n",
    "Here the fitness of an strategy $i$ against strategy $j$ directly depends on the size of the population:\n",
    "\n",
    "$f_i(x_i, Z) = \\frac{x_i - 1}{Z-1} * A_{ii} + \\frac{Z - x_i}{Z-1} * A_{ij}$\n",
    "\n",
    "For the selection dynamics, we use a Moran process (or birth-death process) with pair-wise comparison: at each step, 2 individuals, $a$ and $b$, are randomly sampled (without replacement) from the population, and their payoff is compared. The fermi equation gives the probability that individual $a$ (selected for death) will copy the strategy of individual $b$ (selected for birth):\n",
    "\n",
    "$p=[1 + e^{\\beta(f_a-f_b)}]^{-1}$\n",
    "\n",
    "$a$ will imitate $b$ with probability $p$, in any other case, the population state will not change. $\\beta$ indicates the selection strength and on the limit $\\beta \\xrightarrow{} 0$ all strategies are immitated with equal probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from egttools.analytical import StochDynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters and evolver\n",
    "nb_strategies = 2; Z = 100; N = 2;\n",
    "beta = 1\n",
    "pop_states = np.arange(0, Z + 1, 1)\n",
    "strategy_i = np.linspace(0, 1, num=Z + 1, dtype=np.float64)\n",
    "evolver = StochDynamics(nb_strategies, A, Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "gradients = np.array([evolver.gradient_selection(x, 0, 1, beta) \n",
    "                      for x in pop_states])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Hawk-Dove game stochastic dynamics'}, xlabel='frequency of hawks (k/Z)', ylabel='gradient of selection (G)'>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "<Figure size 400x400 with 1 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "plot_gradients(gradients, figsize=(4,4), fig_title=\"Hawk-Dove game stochastic dynamics\", \n",
    "               marker_facecolor='white',\n",
    "               xlabel=\"frequency of hawks (k/Z)\", marker=\"o\", marker_size=20, marker_plot_freq=2)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now let's calculate the stationary distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from egttools.utils import calculate_stationary_distribution\n",
    "from egttools.plotting import draw_stationary_distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/eliasfernandez/PycharmProjects/EGTtools/egttools/utils.py:208: RuntimeWarning: Some of the entries in the transition matrix are close to 1 (with a tolerance of 1e-11). This could result in more than one eigenvalue of magnitute 1 (the Markov Chain is degenerate), so please be careful when analysing the results.\n",
      "  warn(\n"
     ]
    }
   ],
   "source": [
    "#calculate stationary distributions using eigenvalues and eigenvectors\n",
    "evolver.mu = 0\n",
    "t,f = evolver.transition_and_fixation_matrix(beta)\n",
    "sd = calculate_stationary_distribution(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "fig, ax = plt.subplots(figsize=(10, 2), dpi=150)\n",
    "\n",
    "G = draw_stationary_distribution(['Hawk', 'Dove'],\n",
    "                                 1/Z, f, sd, max_displayed_label_letters=6,\n",
    "                                 node_size=5000, \n",
    "                                 min_strategy_frequency=-0.1, \n",
    "                                 font_size_node_labels=14,\n",
    "                                 font_size_edge_labels=14,\n",
    "                                 font_size_sd_labels=14,\n",
    "                                 edge_width=3,\n",
    "                                 node_linewidth=3,\n",
    "                                 node_edgecolors='black',\n",
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    "                                 node_labels_bottom_separation=-0.01,\n",
    "                                 ax=ax)\n",
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    "plt.axis('off')\n",
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Introducing mutations"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "If we introduce mutations, i.e., there is a probability that individuals make an error, and adopt a different strategy instead of imitating the best, the dynamics may change. In this case, at each time step, players are selected for death/birth and their fitness is compared. \n",
    "\n",
    "However, now, with probability $\\mu$ agent $a$ will adopt a random strategy from the strategy space, and with probability $1-\\mu$ it will immitate $b$ with probability $p$. Therefore the probability of immitating $b$ is $p_{eff} = (1-\\mu)*p$. On the limit $\\mu \\xrightarrow{} 1$, all strategies are taken with equal probability. When $\\mu \\xrightarrow{} 0$ we go back to the previous case, also known as small mutation limit (SML). \n",
    "\n",
    "When mutation is small, we may assume that only the the states in which all population adopts a single strategy, also known as monomorphic states, are absorbing and stable. This is because, since there are no mutations, once the population reaches a monomorphic state, it will never leave. Such a simplification, allows us to reduce the number of states of the system, taking the Hawk-Dove game as an example, from Z + 1, to only 2.\n",
    "\n",
    "Moreover, mixed equilibria are no longer stable in the SML. This occurs, since random drift, even if it takes an infinite ammount of time (please note that we are not looking at fixation times), will drive the population to one of the monomorphic states. For this reason, the SML assumption is only reasonable when we know that there are no mixed stable attractors in the studied system, which is not the case in the Hawk-Dove game. This explains why the results of the stationary distribution differ from the previously calculated Nash equilibria.\n",
    "\n",
    "Now we are going to calculate the stationary distribution again, but taking mutations into account."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "evolver.mu = 1e-3\n",
    "stationary_with_mu = evolver.calculate_stationary_distribution(beta)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
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       "<Figure size 500x400 with 1 Axes>"
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   "source": [
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "fig.patch.set_facecolor('white')\n",
    "lines = ax.plot(np.arange(0, Z+1)/Z, stationary_with_mu[::-1])\n",
    "plt.setp(lines, linewidth=2.0)\n",
    "ax.set_ylabel('stationary distribution',size=16)\n",
    "ax.set_xlabel('$k/Z$',size=16)\n",
    "ax.set_xlim(0, 1)\n",
    "plt.show()"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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