docs/examples/hawk_dove_dynamics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evolutionary dynamics of Hawk-Dove"
   ]
  },
  {
   "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 Hawk-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",
    "$\\dot{x}_i = x_i[f(x_i)-\\sum_{i=1}^{n}x_if(x_i)]$,\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": {
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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/vvv1d4hurm54fPPP8e0adMwbdo0bNmyRa/3EolEqFevHi5duoRhw4bh0KFDKCgoULltixYt0LZtW73ez5AYY1i4cKGgli4mJgbR0dGF7qN4Laxbt66xQtSOLi2UZP1GK1asaJROsfLNwjmOY9nZ2YL1U6ZMEbTc2r9/v0bHXblypWC/FStWCNZfvXpVsL5///78Oi8vL0F3FUV9+/YV7Hvz5k2VMcybN0+wHcdx7N9//1Ub86ZNm5Raqq1bt06jz0sIKV5VqlRR+v9au3Zttm7dOsEgLzdv3hT0Z9fl9cEHHwje+8GDB2zMmDHM1tZWadvo6OjiPhVFmjBhgiBGOzs7duHCBbXbL1++XOlz6TpOgaHplEidnJwYx3GsY8eOho6HMaZ8ghVHCwoLC+PX2djYaNz95dKlS4LjDh8+XLB+3bp1aru/9OzZU7Du0aNHgn3lR+coX7682u4vT58+VfqiOzg4sAULFrCXL18Ktps+fbqgzywA5uHhofSHBSHEPCxdurTQBCpPXVcVTV979uxReVzFhOrt7c0ePnxozI+tk5s3byp9pnLlyrGff/5ZMBzqw4cP2fjx45X+8KhZs6bZjG6kUyINDg5mIpGIBQYGGjoexphyH6sePXrwienMmTOC5NK9e3fBvjExMYJ94+PjBevlx3SUH5AhOzubNWvWjF8nFotZamoqv59iH6aoqCi168aNG1fo55s0aZLK/xgODg6sdevWrEWLFkwsFqvcZtGiRfqcWkKIkd2+fZslJiaqTaAyx48fZ1ZWVjolUS+v1iw/v/Ak8vz5c3b06FGWmZlpyI9nUIMHD1b5+cqWLcvatGnDmjRpovYc/fHHH6YOn6dTIt2xYwfjOI5ZW1uzhIQEQ8fEGGOsf//+gpOmaohAsVjMkpKSBPsVlUj37dsnWK9uiMCvv/5asJ9EIlEaZF7VEIGurq6CBKxKXl4e69y5s9b/eYYNG2aWMx8QQnTz66+/6pBIqzPgCfvyS+ng95YsPj6TcZz2IzxNmTLF1KEL6JRIDx06xPr27cs4jmP29vZs1KhRbP369Sw+Pp4dOnRI6aWL169fs5CQELUn0tbWlm3evFlpv6ISKWOMLVq0qNBB6/v27avyr8nHjx+zgIAAtfs5Ozuzo0ePavT5cnJy2MCBAzX+4owfP95sqjEIIYbz+++/q3yuqfoVxIAUhrfTr02caLnJ9NEjxipVYgx4xYAuGn1+juPY7Nmzze6GQq/GRorTqKl6WVlZ6Rxcfn4+W7FiBWvVqhVzcXFhYrGY+fj4sGHDhqmd/UCTRMoYY6dOnWIfffQR8/LyYjY2NszNzY2FhYWxuLi4QmPKyspi8+bNY0FBQaxs2bLMzs6O1apVi40dO1bpuakmDhw4wLp3Vz0PoVgsZv3792cnT57U+riEEMtx584dNnHiRObq6qoygTRv3pyNHLmWAbl8EpW9xo61vGSalsZY3bryn0PCgB3Mx+d9lZ/fwcGBffLJJ+z8+fOmDl0ljjHtO2WKRCLBwAsA1Paj5DhObZNs8s6DBw9w+PBhjBo1Ci9fvkS5cuVw7do1eHh4mDo0QkgxycrKwoEDB3D//n1kZ2fDxcUFjRs35rt5/PYb8Mkn0tQjb+hQ4KefABsbEwStpTdvgLAw4PhxYXm7dsCePUBy8m0cPXoUY8aMwcuXL+Hq6opbt27BxcXFJPFqQudEqvEbUCLVSuXKlfHw4UN4eXnhwYMHpg6HEGJm1qwBBg8GFIcxDw8H/vwTKFvWNHFpIjcX6NpVmjDlVa8OnDgBuLu/K7Oka6FOAzLExMQYOg5CCCEaGDgQEIuB/v0B+XuUPXuA1q2BnTsBDUbbK3aZmUCfPspJtFIlYN8+YRK1NDol0sjISEPHQQghREN9+wJ2dsBHHwHZ2e/Kz58HGjcG1q8H2rQxWXhK0tKkd6JHjwrLXV2BvXuBatVME5eh6DTWLiGEENP64AMgPh5QbEbx+DEQGgp8951y9a8pPHwIBAcrJ1FHR+Dvv4GAANPEZUg63ZEqTgWmjlgshru7O6ytdXobQgghhWjWTNpop2NHQH7Md4kEmDoVOHwYWLkSqFLFNPHt3w/06wekpgrLXVyAHTuApk1NEpbB6ZThfHx8lFrtqn0Da2u0atUKX331lVkNmkwIISVB9erAsWPSZ6aK84bs2SO94/v+e2D4cECLdqJ6yc8HZs4EZs9WbmFcqZI0LnMZb94Q9DqtTNoPtdBXXl4e4uPjERYWht9++81QcRNCCHnLzQ3YtQv49lvlZPnqFTBqlLR69cQJ48dy5oy00dO33yon0dq1pUm/JCVRQI9Eyt5O4q3qzlSxnOM4SCQSjBkzBnfu3NH1LQkhhKghEkmrc/fvBypWVF5/9CjQvLn02eqlS4Z//6dPgU8/lTZ2UpWwO3aUxuDtbfj3NjWdEun06dPRvXt3fhCG0NBQfPHFFxg3bhzat2/Pb9e7d28MGDAAjo6OAICcnBysWLHCAGETQghRpW1bICkJGDJE9fpt24B69aT9Tv/6C8jL0+/9kpKAESMAHx/p81jFu1Bra+CHH6TPRN3c9Hsvc6XTgAx37txBYGAg3rx5g127dgmSJwDs27cPnTp1Qrly5XDmzBm8evUKDRs2RF5eHoKCgnDy5EmDfYCSxpI6IRNCzNv+/dK7xMIqAitWBLp0ATp0kLb2LVeu8GMyBly8KH3OuXOntEGTOtWrA7//Lm0UpS1LuhbqlEg//vhjbNiwAa1bt8ahQ4dUbhMcHIyjR4+iX79+WLNmDXr16oXNmzejXLlyeP78ud6Bl1SW9OUhhJi/7Gxg+XJpd5iiLr0cJ616rVFD+nJ0fPfM9eFD4PZt4MaNoo/j4AB89RUQFQXY2uoWtyVdC3VqtXvgwAFwHIesrCy12+Tk5IAxhr179wIAqlevDgB4/fq1Lm9JCCFEB3Z20oQ2bBgQHQ0sWgSkp6veljHg7l3pa/9+7d/L2lo6SMR335nn6ErGotMz0levXgEAzpw5g59++klp/apVq3D69GkAQEZGhmBdWXMeCJIQQkooJydgxgzg0SNg9WppwyNDcXeXNnS6e1c6FnBpSqKAjnekderUwfnz58EYw+jRozF37lz4+flBJBLh6tWruHfvHt+q18/PDwDw6NEjAECFChUMFz0hhBCt2NtLx+sdOBC4elU6utCePdJnnfLDDRbFxwd4/33pq0MH6XFLK50S6eeff44hQ4aA4zgwxnD//n2+Dlv2yFXW/eXzzz8HABw+fBgcx6FJkyaGiLvES0lJQWWFP+uioqIQFRVloogIISVNnTrSV1QUkJUlbYF786b0de+etEWvRCJ9ubpKGw/5+gJ+ftJ/NRyXp0jR0dGIjo4WlKWkpBjm4MVAp0Q6aNAgXLp0if/gin1GZYMxTJgwAZGRkbh//z78/Pzg5+eHPn36GCbyEk4ikeDhw4eCMsVqckIIMRR7eyAwUPoqbhkZGUrXO0ui8yC48+fPR3h4OBYsWIB///2Xb3hkb2+P4OBgjB8/nu8WU6VKFezevdswEZcSIpEInp6egjInJycTRUMIIcbj5OQELy8vQVlKSgok5jDqvgZ06v6iqKC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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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-9-0ef21391ac1a>:6: DeprecationWarning: This class will soon be deprecated in favour of egttools.analytical.PairwiseComparison, which is implemented in c++ and runs faster, as well as, avoids precision issues that appeared in some limit cases.\n",
      "  evolver = StochDynamics(nb_strategies, A, Z)\n"
     ]
    }
   ],
   "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": {
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      "text/plain": [
       "<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)\n",
    "plt.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now let's calculate the stationary distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time spent as Hawk: 1.0 & time spent as Dove: 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/eliasfernandez/PycharmProjects/EGTtools/src/egttools/analytical/sed_analytical.py:687: 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 magnitude 1 (the Markov Chain is degenerate), so please be careful when analysing the results.\n",
      "  warn(\n"
     ]
    }
   ],
   "source": [
    "evolver.mu = 0\n",
    "stationary_SML = evolver.calculate_stationary_distribution(beta)\n",
    "print(\"time spent as Hawk: {} & time spent as Dove: {}\".format(*stationary_SML))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Introducing mutations"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "evolver.mu = 1e-3\n",
    "stationary_with_mu = evolver.calculate_stationary_distribution(beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
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\n",
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      "text/plain": [
       "<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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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