{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lotka-Volterra System\n", "> BingKan Xue, PHZ4710 - Introduction to Biological Physics, University of Florida" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider an ecological system involving a predator species and a prey species. We would like to study the population dynamics of this ecosystem. In particular, we are interested in whether one species goes extinct, or both species can coexist at some equilibrium population sizes, or something else." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first model the dynamics of the system. Imagine that the prey species lives on external food sources, such as plants, which are not explicitly modeled. We will assume that the prey population grows at a constant per capita growth rate, $r$. This will be the net growth rate, i.e., the difference between birth and death rates, like in the birth-death process we learned before. In addition, the prey are being consumed by the predators, which results in population loss. Since a predation event requires an encounter between a predator and prey, we may assume that the overall consumption rate of prey is proportional to both the predator and prey abundances, with a rate constant given by a \"feeding rate\", $f$. On the other hand, the predator population will grow at a rate proportional to the consumption rate of prey; we will assume a proportionality constant $\\eta$, which represents the efficiency of converting the biomass of prey to predators. Finally, we assume a constant per capita death rate of the predator, $d$.\n", "\n", "We may represent the processes described above by chemical reactions like we did before in class. Denote the predator and prey by P and Q respectively, we have:\n", "\\begin{align}\n", "Q &\\xrightarrow{\\beta} 2 Q \\\\\n", "Q &\\xrightarrow{\\delta} \\emptyset \\\\\n", "Q + P &\\xrightarrow{f} (1 + \\eta) P \\\\\n", "P &\\xrightarrow{d} \\emptyset\n", "\\end{align}\n", "The third reaction is central --- it describes the trophic interaction (predation) between the two species. Here $\\eta$ is not really a stoichiometric coefficient as it does not have to be an integer. So we will not make stochastic simulations, but only study the rate equations. You should be able to derive:\n", "\\begin{align}\n", "\\dot{N}_Q &= (\\beta - \\delta) N_Q - f N_Q N_P \\\\\n", "\\dot{N}_P &= \\eta f N_Q N_P - d N_P\n", "\\end{align}\n", "For simplicity of notations, let us denote the abundances of the predator and prey by $Y$ and $X$ instead of $N_P$ and $N_Q$, and also let $r \\equiv (\\beta - \\delta)$ and $g \\equiv \\eta f$. Then our equations become:\n", "\\begin{align}\n", "\\dot{X} &= r X - f X Y \\\\\n", "\\dot{Y} &= g X Y - d Y\n", "\\end{align}\n", "These are known as the \"Lotka-Volterra equations\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Steady states and stability" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first find the steady states of the dynamical equations above. They would be solutions to the equations:\n", "\\begin{align}\n", "\\dot{X} &= X (r - f Y) = 0 \\\\\n", "\\dot{Y} &= Y (g X - d) = 0\n", "\\end{align}\n", "We have two such states: $(X^*, Y^*) = (0, 0)$ and $(d/g, r/f)$. The first steady state simply means both species go extinct. The second steady state is where they coexist in equilibrium." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To check the stability of these steady states, we expand $X, Y$ around their equilibrium values, $X = X^* + \\delta X$ and $Y = Y^* + \\delta Y$. Inserting these into the original dynamical equations, you should find:\n", "\\begin{equation}\n", "\\frac{d}{dt} \\left( \\begin{array}{c} \\delta X \\\\ \\delta Y \\end{array} \\right) = \n", "\\left( \\begin{array}{cc} r - f Y^* & -f X^* \\\\ g Y^* & g X^* -d \\end{array} \\right)\n", "\\left( \\begin{array}{c} \\delta X \\\\ \\delta Y \\end{array} \\right)\n", "\\equiv \\mathbf{M} \\cdot \\left( \\begin{array}{c} \\delta X \\\\ \\delta Y \\end{array} \\right)\n", "\\end{equation}\n", "The eigenvalues of the Jacobian matrix $\\mathbf{M}$ will determine the stability of the steady states." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will evaluate the matrix at both steady states and find their eigenvalues. Eigenvalues of a matrix can be numerically computed using the linear algebra module `numpy.linalg`, as follows." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.integrate as intgr\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "steady state at (0, 0): eigenvalues = [ 1. -1.]\n", "steady state at (1.0, 1.0): eigenvalues = [0.+1.j 0.-1.j]\n" ] } ], "source": [ "r = f = g = d = 1. # simple values just for illustration\n", "\n", "def mat(X, Y): # calculate Jacobian matrix\n", " M = np.array([[r-f*Y, -f*X],\n", " [g*Y, g*X-d]])\n", " return M\n", "\n", "X0, Y0 = 0, 0 # steady state at (0, 0)\n", "X1, Y1 = d/g, r/f # the other steady state\n", "\n", "for (X,Y) in [(X0,Y0), (X1,Y1)]:\n", " w, v = np.linalg.eig(mat(X,Y)) # this function calculates all eigenvalues and eigenvectors\n", " print(f'steady state at {(X, Y)}: eigenvalues = {w}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, one can calculate analytically that, for $(X^*, Y^*) = (0, 0)$, the eigenvalues of $\\mathbf{M}$ are $\\lambda_1 = r > 0$ and $\\lambda_2 = -d < 0$. The presence of the positive eigenvalue means this steady state is unstable. Indeed, if both species are absent, then adding a few preys would allow them to start growing.\n", "\n", "On the other hand, for $(X^*, Y^*) = (d/g, r/f)$, the eigenvalues are $\\lambda = \\pm i \\sqrt{r d}$. It may look strange that the eigenvalues are *imaginary*; they actually imply that the flow around the steady state is rotating around this point. The absence of a real part in the eigenvalues implies that this point is *neutrally stable*, such that $(X,Y)$ will circle around this point indefinitely (see below). Were there a positive real part, the flow would be spiraling out; or if the real part were negative, then the flow would be spiraling in. We can plot the flow using `streamplot()` as before." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_points = np.arange(0.1, 2., 0.2) # grid lines for x-axis\n", "y_points = np.arange(0.1, 2., 0.2) # grid lines for y-axis\n", "x_grid, y_grid = np.meshgrid(x_points, y_points) # generate a grid of x, y values\n", "\n", "x_flow = x_grid * (r - f * y_grid)\n", "y_flow = y_grid * (g * x_grid - d)\n", "\n", "plt.figure()\n", "plt.streamplot(x_grid, y_grid, x_flow, y_flow)\n", "plt.xlim(0, 2)\n", "plt.ylim(0, 2)\n", "plt.xlabel(r'$X$')\n", "plt.ylabel(r'$Y$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Closed orbits and oscillations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us visualize the population dynamics by plotting the trajectories in the $X$-$Y$ plane. As before, we will have to numerically solve the dynamical equations. We will define a Python class for the simulation, so that we can easily change parameters and initial values later. You will notice that the class below is written very similarly to the `RateEquations` class we had before. The main difference is that the `equations()` are different." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class LotkaVolterra:\n", " \"\"\"\n", " simulation the Lotka-Volterra system.\n", " \"\"\"\n", " \n", " def __init__(self, param, init, record=True):\n", " \"\"\"\n", " initialize by assigning parameter values and initial values.\n", " inputs:\n", " param: list, parameters of the model: r, f, c, d (in this order)\n", " init: list, initial abundance of prey and predator species (in this order)\n", " record: boolean, whether to record history of abundances at time points\n", " \"\"\"\n", " self.param = param # list of parameters\n", " self.abundance = np.asarray(init) # current abundance of each species\n", " self.time = 0. # time since beginning of simulation\n", " self.record = record # whether to record time series\n", " if self.record:\n", " self.time_hist = [0.] # list of time points\n", " self.abundance_hist = [self.abundance.copy()] # list of abundances at time points\n", " \n", " def equations(self, x, t):\n", " \"\"\"\n", " calculate time derivatives of abundances in the Lotka-Volterra system.\n", " inputs:\n", " x: 1-d array, current abundances of both species.\n", " t: float, current time.\n", " outputs:\n", " dxdt: 1-d array, time derivatives of abundances.\n", " \"\"\"\n", " X, Y = x # parse variables, X is prey and Y is predator\n", " dXdt = self.param[0] * X - self.param[1] * X * Y\n", " dYdt = self.param[2] * X * Y - self.param[3] * Y\n", " return [dXdt, dYdt]\n", " \n", " def run(self, tmax, dt):\n", " \"\"\"\n", " solve equations until time `tmax` since the beginning of the simulation.\n", " inputs:\n", " tmax: float, time since the beginning of the simulation.\n", " dt: float, time step by which solution is calculated\n", " \"\"\"\n", " T = tmax - self.time # time remaining to be solved\n", " new_times = np.arange(0, T+dt, dt) # new time points at every step dt\n", " x0 = self.abundance # current abundances as initial values to the solver\n", " sol = intgr.odeint(self.equations, x0, new_times) # solve equations using integrator\n", " if self.record:\n", " self.time_hist.extend(self.time + new_times[1:]) # save time points\n", " self.abundance_hist.extend(sol[1:]) # save abundances at given time points\n", " self.time += new_times[-1] # update time to latest\n", " self.abundance = sol[-1] # update abundances to latest" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us choose some appropriate parameter values. Without loss of generality, we can set $d = 1$ by rescaling time. Similarly, by using $X^* = d/g$ and $Y^* = r/f$ as units for the population sizes $X$ and $Y$, we effectively set $X^* = Y^* = 1$, which then means $g = 1$ and $f = r$. Therefore, we are left with only one free parameter, $r$, which controls the growth rate of the prey relative to the lifespan of the predator, i.e., the \"turnover\" rate. Consider the case of a large $r$, e.g., $r=5$, so that the prey grows fast and there is plenty food for the predator." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current time = 10.0, current populations = [0.87452859 1.2575456 ]\n", "current time = 10.0, current populations = [0.02309464 2.21439176]\n", "current time = 10.0, current populations = [2.88186798 0.7367846 ]\n", "current time = 10.0, current populations = [0.00853583 1.36676582]\n", "current time = 10.0, current populations = [0.19213035 0.51763606]\n", "current time = 10.0, current populations = [0.24346762 0.44547826]\n", "current time = 10.0, current populations = [0.35949967 0.42082286]\n", "current time = 10.0, current populations = [0.99448009 0.51700546]\n", "current time = 10.0, current populations = [1.17020256 0.38491816]\n", "current time = 10.0, current populations = [1.07941808 1.44391077]\n" ] } ], "source": [ "r = 5 # growth rate of the prey\n", "f = r # feeding rate of the predator\n", "g = 1 # growth rate of the predator per prey available\n", "d = 1 # death rate of the predator\n", "\n", "num = 10 # number of trajectories to simulate\n", "lv_list = [] # list of simulations with different initial values\n", "\n", "T = 10. # total time to integrate the trajectories\n", "dt = 0.01 # time steps to evaluate the trajectories at\n", "\n", "for i in range(num):\n", " X0, Y0 = np.random.rand(2) # random initial values between 0 and 1\n", " lv = LotkaVolterra([r, f, g, d], [X0, Y0])\n", " lv.run(T, dt)\n", " print(f'current time = {lv.time}, current populations = {lv.abundance}')\n", " lv_list.append(lv)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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BWzJSJTIVBeSnpXGscxeb9rovvUTNe8bqYFExnNoI8wt5azfqC+OWaR5MCkUhdN9DuBaoMXy43iYonARXPz+T62r1EebPxYU33yQqPIKYMWNxmgepRn20paTH/zW3ndqgFX6a3Uq5rCquCiUIRoSrq94mKJyQkDfeIOJIFA2+/MLUlrlrF0ciWhIVHmHKf6U7gS00YXj6iLktJRam19Rmw7mZ+tmmuGaomoKQrVXjkk6WJFPhvPj17UvEkSiabdxg1X6sew+iwiPIOny4iDMdjH+wJgzPn7FufzNIE4bMK7qYpbg2qJqCcEGLeUs776WzIYprDbfAQM076dBBPBo3NrWfumM4UeERXPn1V/2Ms8SruiYML18EN4vP+TsNNWFIu6ifbQqnpWoKwqWjACQe9QXAq6UK8lFcHcLVlSYr/iDiSBQ1LTyT4p5/gajwCOJee63okx2Jmwe8fAFeTYKaZgHjvaaaMKTG62ebwumomoJgTDWccVFLdBYw1sk8RxTXFHWff46II1HU++ADU9uVRT8QFR7ByWG3OUcBHxcXeGIPTLsC9SwcTGa10IQhJU430xTOQxUVhGirQ/+bB+lkiOK/hP+gm4g4EkWjZb+Z2rKPHjUV8DFkZelonREh4KHVmjCE9TG3zw5XwqBQggDg4u2tkyGK/yJezbXSn822WsdWHm3fgajwCKvsurohBNy7XAmDwgolCApFJVGQijt8/z6ExUPH8R49iQqPIKc82XorigJhiEzWAtoKUMJQJamagmDI09sCRRVCeHgQvmc34VGH8WrVytR+4qZBRIVHkHngoI7WWTD+d6MwXGduKxAG5ZVUJaiaggDk56qwfoVjEULQaMnPRByJskqoF3PnnUSFR5C+bbuO1lkwfpm2lGQ5YyjwSspK1s0sReVTZQUh/YKTlVJUVCnqvTeTiCNR1HrInL30zL33EhUeQeq6dfoZVoAQ2oyhsFfSjFBNGPKydTNNUXlUXUE4rwmCa4CqQKXQjzpTphBxJIo6U6ea2mIfeVQThtWriznTQVh6JVUPNbe/UQfeaWRThU5xbVNlBSEtTove9Ovbt4SRCkXlU1C4Jygy0tQW+/hEosIjSPlrpX6GFSAEPHUAXrlkbstMhOkB8NUN4CzJ/hTlosoKQl6mlszO7zolCArnIWD0KCKORBH85humtnNPPqkJw8q/dbTMiKu7tvH8wjlzW+wOLbvq0gm6maWoGKqsIBTg29NOMXOFQmdqDB9OxJEoQt6ZYWo7N3mytpS0Zq2Olhnx9NOE4Znj5rb9i7X9hbVv62eXolxUeUFwrVFDbxPIzsggIyWZjJRkMtNSyc5Id558+wpdqT5smDZjmGG+ycY+9pjmlbR1q46WGfGrownDpN3mtvUzNGE48LN+dinKRNWsmBZZ3VQpzRFlM1MvX2Ldgq84tm1ThVzPq5o/7QfeTJsBg/CvHVgh11RcGyT99BPxr7xq1Rb28894t25VxBkO5sx2mHujdduE9RDSXhdzFLaoEpqFcYAgbPrhW7b/srhSrl0U7l7eDLj/EVr26YdwqfKTv/80l7+ZR8I771i1NfnrTzzCwvQxqDD7f4SlD1m3PXsKfGrqY4/ChBKEwlSSICSeP8c3Tz1st8+7mj+9R4+j1fUDcHVzR0pJblw6uXHp5KfkYEjNIT8jF+Hmgqu/B241vXGr6YVbXR9cfd0BkFISH32MfatWcGh96VwS64W34pbJz+JXs1aF/ZwK5yFh1iwuz/nKqq3Zpo241a6tk0WFWPkSbP3Yuu3VRHBRFQr1QglCYSpYEJLizzN3sq2HxfCXXqdh6/akbTpH8opT5X6fwlTr34Bqvevh4uNO6uVLbPx+HlGb1hV7TmDDRtw29RX8A+tUuD0K/Tj/3HMk/7bMqq3F7l24+PjoZJEFUsIn3Ux1SAAIvwVGf6efTVUYJQiFqUBB+Pj+UWSnp5uOI3pfz433PcHFj/aQn5JT6usIT1dcfNyQeRJDaunPK4x7PT9qjmyOe11fEmJO8uu7r5N6ueg8NP3vf4QON91SZL/i2iLm7jFk7jZv8Lr4+NB85w7nWELMzdRKeVoy6B3o/og+9lRRlCAUQk6rzpHF5ROExPOxfPOU+YPcvFsvBtzwIInfH7E73rtnCMdzDBzY/i8BzdZQPWwLLm6lu/FnJYWSkdCc1NhOhDTsQav2gfhdSCd98/lSnV9jWBN8uwdzJf48v733Jpdjz9gdF9S0OcNfmI6Xn1+prqtwTqTBwLGu3TCkpZnafK/rS+gXX+holQVJp+HDttZtD66B+p30saeKoQShELnPBRD9m/akUhZB2L3iN9bOn2M6njDta5IXHLMa4xrgyR6fXHJqzKJavX1lsrO0XDp0C65ZI+l1XWNctsaRG5de7PjACW3xbFyd/f/8xao5H9sd41O9BuPf+wQf/+qVYbLCARgyMjja0fomG/jkZGo/4iRP5NH/wMLh1m3Pn9HqQSsqDSUIhUh/JJAz67RNt6sVhHUL5rDrD60iVkjzlvTJvdWqP6VVACfcp+JT55i90wEQwoN69UYTUKM71apF4OVVHyHMU3opJQZDJqmph7lyZQdJV7aTlLQNKXNLbWfC3jsJCRpHu0Bf0lbbnxEAeLUIoOaYCFKvXOL7l6eQkXzFZky1WoHc8+5HePtVK/X7K5yH3Lg4ovv1t2qr//lnVLv+en0MKsw/r8Gm2ebjmk1g0i4tXYaiwtFVEIQQDYAFQF1AAl9KKT8sNEYAHwKDgQzgXinl7sLXsqQ8gpA0Jpj4XTWAqxMESzG48fbHCNhrvkEmNnThYotxNucI4U7HDgupUcPu779c5OamcObMHGJOf1ri2IsHb6W2z3209/Mka6/9PQWXau7UndSRPLdcvn9pConnY23G1Kofypi338fdQ2WLvdbI2LmT02PvsWpr8s8qPOrX18kiC6SE2RGQalGQ5+aZ0E2lw6ho9BaEYCBYSrlbCFEN2AXcJqU8bDFmMDAJTRC6AR9KKbsVd93yCMKFYQ1IPOqH8PYmfE+xumPi+PYtLJv9FgBDBz6Nd7TRFRTJwZ7P4OF32Wp8r56b8PIKLpN95cFgyOH0mTmcPDm72HGnVz/HTcOGIpceL3JM3SmdyPc2sPDFJ0m+EG/T33fs/XS59Y5y26xwLEmLFhH/2nSrthb79+Hi4aGTRRZkJMK7jazbJu2GWk30sec/iFMtGQkhfgM+llKusmj7AlgnpVxkPD4KXC+lLLJ+X3kEIfaGMFJjvfFo2oQmy5eXOD4jJZnPHhoDwM2dHsU/0R+AuJoxpHSONI1zcw2kb98tVss/eiOl5Pz5xRw5+lKRYxKPDqR+7adodC6NvPgMm37h6UrQs13Izkvny8fvIz/Xdunq3lmfUqt+qE27wnmJfWIyqX+bE+b5dO1KwwXzdbTIgmN/w/d3Wrep+IUKwWkEQQgRBmwAWkspUyzalwMzpJSbjMergeeklDsLnT8BmAAQGhra6XQZa9Ke6tGErCSPUntezBqluWV2CrqJpt7tATgU8SluDf41jenbZw/u7v5lsseRGAy5REW9TPwF+3lmUmM7UstzOhFZBrKiEm36PZsHUHt8K2L272LpjEib/nrhrRg57S1c1D/uNYHMz+dIq9ZWbUGvTyfgzjuLOMPB/HQvHPrFfNx1AgyeqZs5/wWcQhCEEH7AeuBNKeXSQn2lEgRLyjNDONa2Bfk5LgTcfTdBr75S7Nglb71KzL7dBHs3pm+Q9k9ypN8jCPcsAAJr3knb9jOKu4RTc/nyevbuu99uX3JMd+p4v0zT8+nkXcy06a9xW1N8uwXx5yezidpom4Fz3MyPCQwNq2iTFZVA7oUEoq+7zqqt8Z8r8GzUqIgzHEheDrxRKGeXclMtM7oLghDCHVgOrJRS2ixuO3rJKCo8AoA6zz5LrfvvK3JcblYWH40fgZvwYHjYUwAcvfFeU3/H9j8QULNLmWxwRtLSj7N9+yC7fRcPDKN7l2dwW3bCbn/wK93JyE7my0fvtenretud9LlrfEWaqqgkUv/5h9iJk6zawg8eQLi56WSRBfEH4PPe1m2vXNJqNChKjd6bygKYDyRKKZ8sYswQYCLmTeWPpJRdi7tuRQhCvY8+xP/GG4scV7BUNKrRcwCc6PM0ed7aMkrPHhvw9q5Xpve/FkhNPcy/O26123fq71cYfsdNpC+NtumrPqQR1frUZ9Wcj9n/z182/RO/WYynj2+F26uoWM5NfZaU3383HVcffgchb76po0UWrJoGmz8wH/eaDAOnFzlcYY3egtAb2AgcAAoKsL4IhAJIKT83isbHwCA0t9P7ilsugnIIgpRERbQEIGzJz3i3sp82ODkhnq8mPUjHmjfQrHonLjX5hctNNJfTbt3+xs+36ng9JCZuZs9eW5farKT6eKd9RMukPLub0SGRPYg/E82iV56x6Rs9fSb1WkRUir2KikHm5XGkdRurtobff4dPx446WWSBIR+mF8qc+uQBqKEcG0pC9yWjyqDMgpCXQ1TrdgA027oFt4AAu8NmjboFgWBko2fJ9brEyb7aTS2ixSeE1LO/rPJfR0rJkahXOB+/yKbv7MaJDLvlbtJ/sg3IC5zQFtcGPsx9cgKpl6xjIG585Ana9Ct6lqbQn+wTJzg5xDrfVfj+fQhncFON3QlfDTAf12wMT+zRz55rACUIlmSlENVeC3EIjzqMsBMNmZmawqcP3m1aKirYN/Byb0+vPkvKbPN/iZycS2zcZBsqkhbXioZ1/0fdXRfIT8q26qs2IJTqAxuy9edFbPnJOtNl+5uGMOD+RyvVZkX5uPjR/7j0qTkIssZdowmeNk1Hiyz49nY4scZ8fPdP0Fw9aNhDCYIl6ZeI6tQHKDpKedaoW3AV7owIe5rY9h+QXmcvAAP6299QreqcPTOfY9G2a7ixa2cyrG8nm9QZbrW8qPt0Z6J3b2PZe9br0oENG3HPjA+dIzunwgZpMHCkpfUya6PffsWrRQudLLLAXlDbyxfBzQlmMk6EEgRLks8R1e0GoHhBGNXoOaTI49jABwHo3m01vr5hZTW3SpCVdZ7NW/rYtJ/f9gC33PoQ6d/ZZoINebU7ly+dY8HUiTZ9kxf+gpu78iBxRrKOHuXUsNus2oqacTucbZ/DX8+Zj697Hvq9oJ89TkZxglD1HsPysortPrjWFEBtEgNAiUEp8PIKYUD/E/TvF03NAHMytZDuX7P7Yne2NZoPd4VbnXN++jayPz3L5C+W8NhX31v1fTj2dmaNuoX8vNIn9VM4Bq8WLYg4EkWNUaNMbUciWpL04486WmWk+yPwapL5eP0MiKwOmUlFn6MAquIMISGKqL5a/h17M4RZo26hT93h1K1Wj+gB2pp2v+uP4OKinlTLQnz87xw6/KRVW2ZiQ0L85xJy4JJNwFvdpzshAtz5cOzt1hcSgicX/oKrM/jDK6wwZGVxtH0Hq7YWu3bi4usE7sUxm2HeYPNxp/vg1g90M8cZUDMES0qYIQCE+DQ1iYGQNZUYlIOgoFsZ0P8EXbv+YWrzrnmaJLcBHOowiqOtfPFqYfb0ujB7F/GvbGPSe4uYvNAiZYGUfDDmNj4YezuG/HxH/giKEnDx8iLiSBT1PvjA1Ha0U2fi33pLP6MKCOsFkcngZ6zUtusbNVsohqo3QzizjagbtejkwjOEk7t3sGrWRwxu8BDHjGPU7KBiycm5zMZNdmIOzy6mg68/GTsvWDXXebw9LnU9+fAe66yq7l7eTPzmB5UzycmQUnKkbTuwSIDYbNNG3GrX1tEqI3H74Iu+5uMeE+EmJwm2cyBqU9mSk+uIGqw9/RcWhILN5LjWX5ISsgWoWM8igzTw16m/+Hjvx5xNPXtV57at3ZaRLUZyU9hNeLl5VZhNemEw5LB+QycMBuuANsOZxXQNqk3qOuvfT90pnaC6Kx/dY11hK7hZC+5+Y1al26u4OjIPHCDmzpGmY78bBtDgY/vV+RzOu00g45L5+IVY8Kw6xZ+UIFhyfBVRtz4BFC0IBXEHXTr/ib9/83LZufDwQt7Z8U65rlEcjas3JrJnJB3qdCh5sBMipYGNG/uQm2ddbyE/5ie6hdS0EYbgl7thcDPw0fgRVu3dh4+m18ixlW6v4uo4eetQso+ba240XbsG92DH1wmx4ewO+PoG83HfZ6F/0Sni/0soQbDkyAqibpsCWAuCwZDPp2NGc2uTB4nu/xhQ9tnBmZQzDPllSJH919W/jpEtRtI9uDsersX7SJ9LO8fmc5v54+Qf7E4oXTGf13u9zm1Nb7sak3VHSgMbNnQjL9865bbbhV9o4+JJxp4Eq/aQ6T3JzEjh84etK4Dd9uyrNOlUbBoshYPJiYnhxKCbTcfVBg6k/v8+0tEiC16vA/kWAZQvJ4Dbf7saoBIES6J+J+r2ZwFrQdj843fU2ObN5X7vket7AfJrMGDgrqu69OmU09zyyy027W/1fotbm9hPFFceoi5H8c6Od9h1oWg7g32DmT9oPsF+TvBUVgqkzGfd+g4YDOmmtrysajSo/ge19l4k92yqqV24uxDyWk/ioo+w6JWpVte5/8MvCQgKcZjdipKJGTOWzF3mz2qzLZtxq1mzmDMcxKmNMN/i//aOr6Ctk9SDqASUIFhy+Dei7ngesBaEwstFvXttx9Oz9BthHb7tQJ4hz3R8c6Obebfvu1dvXznIM+Tx+b7P+WJ/0UV/Fg1ZROvarYvsdxYMhlzWrotAK8OtkXy6Gz36fIrh28PIbLOnkU/HOtQc2YJ9q1bwz1fW9aWfWPAz7p7X/p7Lf4Xsk6c4OdjsBlrroYeoM+VpHS0yIiW8VsO6LTJZF1MqGyUIlhxcStQIba2wsCCMbDSVYzdqxWJKu1x0LOkYw5eZNzqHNB7CjD62BXPy8vLYsGEDGzZsuHqbLWjevDl9+/alfikKo1/OvMyj/zxKVKL9iOyfb/2ZFjWdIOVAMeTlpbF+Qzurtrgd47jt/qlcmWU9M6o1viXeEbVY/uG7HN1i/j2HtevI8BdVemRnIrr/AHLPnzcdO02yvJ1zYflT5uOnDkH1kv/XriWUIFhy4Gei7tSqpFkKwpyx4+nU35eksJVA6QTh1+hfeWWzueLatru34etuDsZJSUlh9uzii91XBMHBwdx5553ULGb6nW/I57Wtr/FL9C82fUG+Qfw67Fcr252NjIxTbN12g1VbzKqXGDt5JBc/sM5uGfxyN1x83GxiFka89AYN27Z3hLmKUpCxYwen7zGnVa/3/mz8b765mDMcRFYKzGhgPu7zDAwovrLitYQSBEv2LSZqVCRgFoS0pEROv76O+Fu0dehmjT4mtFHxH8yZO2ay4PACALoFdeOrm74y9e3cuZPly5fbPe/GG2+ka9euuF1lxG1OTg779u1jy5YtJCUVH1RTr149xowZg4+Pj91+KSWvbnmVX6N/tel7qdtLjA4ffVW2OZKLF1ex/8Aj1o1nF9OtRT2u/Gou2CM8XQmJ7EHq5YvMedy6ROgT3y7B3eO/vXF4rSCl5IixPgkAbm5EHDygn0GWfNFXi10oYNoVcIZcTeVECYIle78navTrgFkQ/vr0fVqf6WzaPyhpdjD/0Hze2/keAJM7TubBNlrOo9OnT/PNN99YjQ0NDWXcuHFXLQCl5cKFCyxZsoSEhIQix4wfP55GRdTGTclJ4dZfbiUxy9q7x9fdlzV3rsHH3b6o6M2xY29zNtYswhkJzenceREuf50iNzbN1O5/Uxj+/RqwY9kSNnxn/tuE97qOIU9Yb0Qr9CNx4XdceOMN03HTdWtxDwrS0SIjJ9fBgmHm44c3QHC7IodfC5RLEIQQY6WUCyvFsnJQZkHYs5Cou7ToxAJBmDXqFkY2nmJKZlecIGw9v5UJqyYAMLXzVMa10qa8kZGRVuNGjx5NeHh44dMrncTERObOnUtaWprd/uLEYd3ZdUxaM8mm/YchP9Cqtv3KcnoipWT9+o7kG1JMbWfXT+buqY+Q8MZ2q7HBL3bFpZoHs0dbe3vd9fp7hDR3/N9JYUt+airHuphdhgMnP0HtR52gRkZ+Lrxu4WDScRwM/Z9+9pST8grCSuAI8LSU0mmSyJRZEHbNJ2qMtulrKQg39I/gUrOlQNGCkJWXRZfvugAwovkIpvWYRlJSEh9++KFpTP/+/enbt6/d8x2NwWDg77//Ztu2bXb7n3nmGfz8/GzaM/MyGfjzQJKzrb0spvWYxojmI2zG601WVhybt1gXX8879SPXXd+ES3PMyw8eYf7UeaQdiedj+eYp62Wnp3/43TlSNytsgtmKSlPvcH6+Hw5aFMi6RpeQyisILsBbQA9ghJTyYrEnOIgyC8LOuUSNnQmYP2jzxk2gwb2rAajl9zDtuz5r99Q28831ZQ+MP0BMTAzz5s0ztb344ot4OIOnhB2klPzzzz9s3rzZpq979+4MGmS/LOjsXbP55qD1MtjYiLE81/U5u+P15PTpr4k+YU6olny6K737fwF/nCTnjDl+oc7E9njUr8bGRfP599efTO1DnphKeK/rHGqzwj6pa9YQ+9jjpuOm69fjXreOjhYZKVyy85lo8AvUz54yUCF7CEKIO9CEYTawFzgopbStrO4gyiwI/84hapzm+VMgCLsnf0fSsFcB6Hd9FC4utjf1T/Z+wuf7Pgdg/7j9nDhxgoULtZU0Hx8fnn3Wvog4I3l5eXz99dfExcXZ9E2dOhVfO2mL155ZyxNrn7BqG95sOJE9IyvLzDIhpWTN2qZWbbHrZzD26aHEvf2vVXu9t3tjyM/jgzHWqbaf+v43XFxV0jy9MaSnc7ST+b4VNP01AkaOLOYMB5GXDW9YiNNdi6HFtVNnvdyCIIS4BXgMqA9sAVoCrYAkKWXT4s6tLMosCNu/IGr8B4AmCNkZGVycvqvYDeV8Qz7tv20PwPxB86kv6vOpsbZss2bNGDNmTFl+BKfg3LlzzJkzx6a9qL2Go4lHGfG79bKRMwpDevpJtm0faDrOTGxIpw6/4B11mbRN50zttcZG4N26NgfXrmLl5+alv8FPTCVCzRacAsuYBfcGDWi66m+dLTLyRhDkGet5tBkJw23/j5yR8i4ZnQIOAx9IKVcV6qsvpYytMEuvgjILwtZPibpP2xCKOBLFrj9+o86m6hwb+ABgXxB6ft+T1FxtyWHv2L28/rrmpVSrVi0mTbLdhL0Wyc/P58svv+TCBev004MHD6ZrV9vcQCeunOC2326zanuq01Pc3/p+m7F6snfvo1xONN9ATv31Jve/MYLzr261Glfv7d5IaeD9u4ZZtau9Becg6ccfiX91muk4/NBBhDPM4lZPh40W2Xavgejm8gpCuJTSthiuzpRZELb8j6j7taf7iCNRfD35Ibo3bkJ8G03dCwtCbn4uHRd2BGD73dt5901zOorCnkX/FTZt2sQ///xj1da3b1/69+9vM/bklZMM+836JvrJgE/oW985NtYBsrMvsGlzT9NxRkJzOrT/jhpJWVz5zfz3rv1QG7ya1GD/6r9Y9aU5VfNdr88kpHmEQ21W2JIbF0d0P/Nn0GkypxbeV3jxPHg4b5BnuSqmOaMYlAuDtaPUlfg4LjdeBoBLru2TcIEYAKz/Z73p9bRp02zG/lfo3bs3kZGRVkthGzZsIDIykrVr11qNbVyjMQfGH2DuTXNNbY+vfpw289twLu0czoCnZ10G9D9hqvPsU+cYR893YfGvW6j3Ri/TuEtzDhD37g7aDhjE5G+XmtoXvTKVxZHPO9xuhTXuwcGEHz5kOo7u15/UQg8uulC/M7xg8Vl/KwQSnMQz6iqp9BKaQoi5QogEIcTBIvqvF0IkCyH2Gr9erVSDCnnOugkPLbspENF6cpGn/Tv6X7Zv13zbH3rooSqxjNCsWTMiIyN58MEHTW3r168nMjKSHTt2WI3tEtSFA+MP8Ep3c4j/oCWDaDO/DQZpcJjNxdGhwxx69dxoOg676TmWzruPalM6U62/lqogPzGL2Oc3InJgyuLldLhZi1uIjTrIrFG3kJtVcglWReUhXFyIOBKFa6AWFxA7cRLnX3KCOgaefpobagGfdofDv+lmTllxRE3leUBJW/AbpZTtjV+VmoVMFqrHW8+3mel13ZBuVn1vb3/b9Pqdt81FburVq1dJ1jkn9evXJzIykgceeMDU9scffxAZGcmZM2esxo5sMZID4w/Qr0E/U1u7Be34aLdz5L/38gphQP8T+FfTZsw1Gm9i54HW7L6UTvDL5r9/3BvbSd0QS/97H+aBj8wR0R+NH8Gx7bauuwrH0nzjRmo99BAAyUuWcrRrtxLOcABCaHsIQW214x/HWe8vXANUuiBIKTcAiSUOdBAyN8/quIGvOUq18FP/90e+B2BB/wWmtldfrdwJjDPToEEDIiMjufvuu01tc+fOJTIykvT0dKuxH/X/iJ1jzXs8cw7Moc38NlddOrSy6NJlMV06/2o6NgQNZcE7X1Hv7d64VtfyHCWvOEXs8xupUTeIKYvNual+n/023788xdEmKwpRZ8rThM79GgBDSgpR4U6yz/PIRuiuFdli9XRY+rC+9lwFjpghlIYeQoh9Qog/hRBF5kgQQkwQQuwUQuy8eLFs8XEyJ8fquJ6Pfa9Zyyjd377Wpn6hoaG4uDjLr0w/mjdvTmRkJNdff72pbebMmXxcqGaup6snB8YfYOFgc+aTwUsHM/J3J/AlB/z929C/nzkhXmi/WSz77nY8x7ei5hjzzSX2+Y0YMnKZsng5fe6+F4C440eZNeoWq2yqCsfj27MnTdeZ97WiwiNsVgF0YdDbMMSY6Xj/D/Bpz+LHOwnOcHfbDTSUUrYD/gf8WtRAKeWXUsrOUsrOgYFliw40ZGVbHUuRZ3dcga99fW9zLvT77ruvTO/5X+X6668nMjKSOnW0IJ1Lly4RGRnJ/v37rca1C2zHgfEHTJ5HUYlRtJnfhkOXD9lc09EIIRjQ/wQN6mvusn4hB9hzpC37Y64QEtnDNO789G1kHr5M12EjeOBDs7/5+3cPIyn+vM11FY7DPSiIFnvNKdCPtGqNwRn2ero8AGONqS4SDkFkdX3tKQW6C4KUMkVKmWZ8vQJwF0KUvlTZ1b6fxQwhIyWZtNr77I6LT9eKvvc6pnmheHp6VomN5LLw2GOPWUVqL126lMjISHJzc63GfTLgE9aOND/NjV4+mkFLnCPCs3nzl+jWdYXpON33Jr6Z9jv1Z/QB45/98oLDXP7hCDWCgnn6h99NY+dOnsDhjWsLX1LhQFy8vKw8kI6270BeCWniHULTG+ARiz0nJxcFh6S/FkKEAcullDa1G4UQQcAFKaUUQnQFfkabMRRrWFnjELLmPcGpGVp8nfvCeSQd+ZiUkC0YcgMYeJN2vTxDHh2+7QDA8FNaNbSXXnoJd3f3q36/wmQbDLwfc4EPTl8oebAFjzWow7ONgvBy1V3Di2X//v0sXWp22ezXrx/XXWcb8fvGtjdYfHSx6fifEf9Q17euQ2wsDinzWbO2uen43JaHGfvCM6SuOkPqOvP+R/0ZfQBYMHUiF8/EANCsa0+GTnnRofYqbLHcS3CaNNopcTDbIquujgFs5YpDqIA3XwRsBVoIIWKFEA8IIR4RQhSkmxwBHBRC7AM+AkaXJAblQeaYn1rPH4siLXAvAL4efUzt7+7Qgs+C081BL+URg7jsHILW7iVo7V4art9/1WIA8OnZBMI27DddJ2jtXqIznGBaXIi2bdtaxWisXbuWyMhIcgrt3bzc/WXWjVxnOr7h5xt4f9f7jjKzSIRwZUD/E3h4aH/7ej2/4Nf59+DWI5jAR8158GOf34g0SMbN/Ni0r3D83y3MGnWLvcsqHIhldtTo6/uRE+sE8TD+wfBcjPnYSWcKVa5ATsYnD3H6f5sA2DdqKIHX/QxAs7BPCG2sLV8UZDUtmB0MHDiQXr162bla8exKTmfI7uN2+15pEsI9IbXwdys6/F5KyZYraUyKOsP57NwixwG8H96Au4JrXbWNlcnJkydZsMDsoXXbbbfRvn17m3F3LLuD40nm39P+cfudYnnu5MmPOBWj5TfKz/GmdZNNBDXw43ykOe1FyKvdcfFxJ+74USvPI0uvJIU+WM0UnCWqOTMJ3gkzH+swU1AV0yxIe/8+zn6h1Qf4q2Nz2j6oxctd1/cAbm5adbDCgnC1KSrS8/JpstG6DGD36r782L4JHhXgpXQoLZMBO44W2b+6Swta+XmX+30qAiklr732mlWbvd/njvgd3L/SnAdp1YhVBPnqP9VPTNrKnj1jTcd1XdfTqm89zr2wydw2pRPugT6kX0ni84fvMbU/teg3XFycIN9OFcZSFJpt3YJbQICO1hhJvQCzjMuSnv7wgmNdsXVdMnI2ZJ75SVsYzE+hBWKQa9D662SWLff6orjLVmLwVMO6xPdrz68dm1WIGAC08vMmvl974vu1J+76dtxWp4ZV/4AdRwlau5epR/X3+RdCEBkZydChQ01tkZGRpKamWo3rEtSF3ffsNh0P/Hmg3ZrPjqZmQA+r6OYL+dex9ddo0x4CwIVZu8g+k4JvjQCrlBfv3zWMvNziZ3aKysVy+eh4j54YMjN1tMZItbowyfhZz06Bz/sUP96BVD1ByDX7KNf0tJ1Czjs4D4A+8dofqUuXLqW+9l37TvDUEfNNOL5fe55rXLnTVCEEn7cKI75fe2Kva0d1iyWob89fJmjtXpps2F/MFRxDx44def55cz6gWbNmceCA9SzK3cWdA+MPUN9Pc/V9ZfMrjP9zvEPttIeXVwjXX2fOvJJZfRArv9pH/Rl9cPHT9pYufrqPrONJuHl4WHkgfTj2dnJzsm2uqXAclqJwtENH54hTqNUEJqzTXsfv16qxOQFVThAwmPPqBHo1sOn+aI91ioWiKokVptOWQ6xN1J56Z7doQHy/9mW3sYy4uQiO9mlDfL/2fNqyoak9Pd9g2ojWc4nQy8uLyMhIU9nOJUuW8O2339qM+3P4n7zQ9QUAdifstqpUpxeurt7073fMdOzW+A6Wf7yLkJe7496gGgCXvj5I5tFEhBBWewgf3TOc3GzncwCoSliKwpFWNs6O+hDSAcYaZ5QHl8C/+tdTqHKC4OavVUPzahJMbc8ichJZ3DNdS5FzffyBk5wzbvr+3rEZd4fov7l7R90A4vu1Z0s363D+4HX7GLPvpE5WaTzzzDPccMMNAJw4ccLunsLdEXfzy9BfTMdt5rfRVcxA80CyjGz2bjmSP7/YS93H2+PZXFubvvzNIbJOXAGsN5Y/GjdCRTXrjGWcgtOkuWg6AAYZ86SteAYS9E0uXeUEoQDh4mJ3yQigQbrtzKEoFsclsvJSCqCJQZfqzpUHvbGPJ/H92rO7R0tT2+rEFILW7uXXC/oF7vTu3ZtHH33UdBwZGYnBYJ0VtWlAUzaNNm/etl3Qltx8fdfkhRBWouDRbDirFxwm8P7WeDbRXAkvzTlAzvk0wFoU3r97mO6iVpURLi40t3BEOfOwk+QY6v4INDR6MX7azSZFvyOpeoJQ8A8pwMPNo1CX1tflorZv0LFjR4ojPS+fyUe0bJ9vN6/vdGJgSYiXB/H92rO4XRNT2yOHTxO0di8GnW5SdevW5YUXXjAdT58+3Sa6ubpndfbcY05L0HFhR7Ly9F1+KSwK1L+VPavOEPhQW9zqas4JCR/tIT9Vi72w3FOYPfpWh9qqsMbVz5dGv2jLNOnrN5CyalUJZziI+8xR8kyvqZsZVVAQjN+FIMfXusj8zgva04Mw5ioYOHAgxWHpTXRfvUrLtlGhXFezGvH92jOirtn9LmTdPj6IidfFHk9PT6sMsm+++SZZhfLQuLm4sX+ceWO8y3ddnGSmYN5TSHTtx+mDlwl6qpOpLe7N7ch8A0IInvrenBtfBa/pi1dEBLUnTgTg3KQnnCPFBcCrFnbM0+czUuUEoWAWIFwEWdVOW/V9sf8Lq2Nv76J9+VdeMgeU6LGBXF4+btmQmL5tTcczTsUTtHavLra4uLhY7SPMmDHDJrJZCMGB8WYB7riwI3kG+4kJHYUQrlzX1yxUh44PIy0py8ol9dxLWh4bF1dXHp/7g6n99/dnOM5QhQ2BEx8HY/aB4z2cJBOpiwtMNC5pxWyE446fvVQ5QTBvGAuy/WK1JoMbANvjtlttKBfH+AOnAHinef0SRtoxQUo+WRtN2PN/lPjV/a3VnLqUXvJFy4CXqwvx/dozKdQccxG0di9nMvVxk7QUhbfeeou8PNsbvuVMocO3HXRfk3dz86VHd62Mo2f1OJbNnY6Uknpv9zaNiX1ei2Pw8vXjrtffA+DYtk1E79jmeIMVJiIOmD9LJ25yjiSL1G4G1xnds78b4fD9hKorCAJyqhkFITvM1F0ru2QPoZ/izfV+xl/FUtH6YxcJe/4PGr2wgpkri440tiQ+JYt+760zCcRdX26r8JvgS01CONDLXIai67Yo3TacLUXhjTfesPlZhRBWotB2QVv0xsenES0jtPxXdTssZs6UnxBCEDLNnD47ZbW21xTSPJyed2q1qn977w3ljqozzTZpYp1z+jSZh/RPxw5AP/O+mqP3E6qeIBQoghBk+2pJrzzcwky9La60AKBWraKFYVKU9s/9ZauwIsdYciA2mbDn/2D83H+t2tvWr87GZ/sRM2OIzdfh6TfxRH/b4j1bT16m0QsrCHv+DzYcK1uRIHsEerhbLX09cvg0Dx+KqbDrXw2WyfEKp70ATRR2jd1lOh6zYoxD7CqO4ODh+PlpnlxNbnmBNd9G4eLtRq1xWlvKqtPkp2gzrx4j7jKd99G4EY43VmHCrXZtatw1GoCY4U70t3jlkvl17K6ix1UwVU4QpMUMIc9be9L39gk19Qdnaq6ovXv3LnwqAOezzGvbQwuljLBH73fWcOvHZtfJabe2NN30l03sTYOaPnbP8/Fw4+kbW1iJxCd3W3s9jZv7L2HP/8HiHWfsXqMsxPdrT4SvFwC/JVyh9/aoEs6oeIQQvPLKK6bjwpXYADxcPfjtNm2jdv/F/Sw5tsRh9hVFt65mbyJD8FCSL2bi3bIW7kHa3zjuLfMDgVVJzg/M9boVjifY4gHk9Nh7ihnpQFzdoddk7fVX/R32tlVOEAomCHkW2TT9qtnGHbRpYz86tuPWw4CWrK7Yt5GSsOf/IDZJy51yf69GxMwYwn29GpXFagCGtA02iUPf5uaKcc8tOUDY839w/EJqMWeXnrVdw3nRmHIjOiObXtscLwqurq5Mnqz9Q1y6dIldu2yfkhpXb8wr3TXhiNwaSVpOmkNttMd1fbWCS8LFwNL/zQWg7pNmz6OLc80pMO6d/RkAx7ZuJDOtYv52irLRdO0aADJ27iQ/rXL27K6agdPNr5dNcshbVkFB0BQh20IQ/Gs0xCCtg6Lc3NyKvcxP7e3XYi6g0Qtmv+LtLw7g1VtbFjP66llwf1diZgzh4b6NTW0D399A2PN/VMj1n2hYl2lNQgA4kZnN4F3HSjij4gkICDAlxfv9999tYhQARrYYiZuL9rfqsaiHTb+jcXPzo3HjpwEIvX42q+drDxBBz2qxLdnHkjBkapvlteo1oFptTdg/feAuO1dTOAr34GBcqmkpSI51tpsIVB8eNaZa373AKu1OZVHlBKFgySjHQhCqB4RyLKnkG94Fi5oE7i5F5+u3vCkfe+Nm6vp7lcHS0vHC4AhiZgzB18OcYiPs+T9ISC3/ZuWjoXWINIrC7pQMvj1/qYQzKh7L4MA333zT7hjLwLV3/tV/+aVR2OOm12muL5KfZ8Ctpheu1T0BOP+auZ7ChE++Mb0+vsPcrnA8zbebvb7yEhOLGelA6lo8SP6vQ6W/XZUThAJFyMF8Q/fxC2Zvwt4STx2+V4tOberjWeSYuZtOmV4ffO0mPNwc8ys+NH0QG6b2Mx13fXM1v+8rf/H3R0Lr0L+m9uQ09WgsMTq4pFpuMm/ZssXumO8GfwfAwqiFZOfrn120IGW2X8gBPp+oLUcEPW/OnJsTa14iuvGRJwBY9p59wVM4BuHigmdLLcfR8Z5XXxCr0njOGC+VFFPpb1V1BcHiAd/V1Yt9F/eVGIMQnaHdaJYUsVwkpWT6cm2JYM64zvh5Fr/sVNGE1vIhZsYQ0/GkRXv4aLX9im1Xw/cW6S6667CfIIRg7FitSM3ff/9td0zbQLP7aeeF+k/5vbxCTK+b3PIcuTn5CCHw66slVEz4eK+pv02/G02v963602E2KmxptMTsnGAoFBypG941zK83zqrUt6qCgqB9yy5UonH/xf1UzyldndO6nvbrK/ecscb0emBL/QrGx8wYQoOaWpT17FXHrGYtZcXSJVWPiOamTc0i/N1339kds/eevabXydn6FTEvoGCD2d3nCl8+sR6AGoPNez55ieZlvdue1dJ3/PPVJw60UFEYy9Ktp24dWsxIBzNumfZ99fTix5WTKicI0rRkZD0dOJN6hoCcosvrZeYXv6EjpSQuWfsHP/jaTeW0svxsfLY/7eprAjd9+WGOxKeU+5o7LDKmJpRQ47kyePLJJwE4ftz+rMfVxZXQapoLce8f7LsNOxI3Nz/T67odzSLmFaEFG8W/u8PU1qRTV9PrpPjyL/Upyk7zbdpeTs7p0yWMdCCNrzO/vlJ5lRCrnCAUYLmHUECN7BqA/RxG38VdLvZ6b60wL6U4eqmoKH6baL4pDvpgY7kjnBt4mbPDtt3i+KjOGjVqmF5v2LDB7phlty1zkDWlo2sXLd4goOk69qzS4kUKgtUK06RzdwDmTp7gGOMUdnG1+JzlXay44M9yE2J0sPhf8VmYy0PVEwRDwQzBloIlo6Ag2+Lu885pHjY31PK3e9k5G7VlmSWP6u/6aInlnoKlK2xZsVw6upTj+ORy48aNA2DNmjV2+10titp/tvczh9hUHNWqmQuxbP1Fe2iwXJbI2Jdgej10ikXKAoWueDTUKg7G3K1/FLyJ8cbAx/zK29uoeoJQEJhmp6tGTg1Ay9NfmIIN5XtLyF3UqaF+ucyLYtfLN5heJ6VX3Iep9eaDJQ+qYBo3Nq/BFy6oU8DnN3wOwKf7PnWITaUlqJO5XKj/DdrSVuIic04rFwsxy0i+4jC7FLaEfrsAgNyzlbc8c9V4+pU8ppxUPUEwYm/xxE1qSz01axZ9U+9ndMG0pCLW5yuTWn5mN9kOr5c/pe7xPvrXOAbYutW+336vek7kMgh06LAQgOqNtpKerD1YVOsfanesu5e2XLl2vv71dasy7nXqlDxIT5JjK+WyVU4QSrOO7utbdFoKV2G79/C60dW0SaDzVkw79sbNFXatam7mJ9kcB0RPFqZ/fy23y6pSVLvSu7oaQM0A8zLitl9OAFo9DnsMfPAxAI5sXl/5hilKhdThM14kvsaUNX8+VymXr3RBEELMFUIkCCHsri8IjY+EENFCiP1CiMrbMYFS1Tvw9Cw68Mwem6O1Defy5CmqbCwD5OKSMyvsui8eO1dh1yotvXqVfgbw+8nfSx7kQI5ss61MJ/PNH8rwXtfZ9Cv0JfuY49O2FEm/F7XvR5YXP66MOGKGMA8orvrEzUAz49cEoHJ3Ao0zBGnnSb+AqxWEAm6I0C/24Gp45dfyr/37GwVmYQneV5WBq6triWMiamqbuatPr65sc8qNZdSycKlyk3anJ23tWr1NMBNaudXdKv3TJ6XcABSXGGQYsEBqbANqCCGCK88e4/dixpRVEOr6l+08R+FqXKb4JyqhhJElM7BW6YL49KJRdW22djrFiXzJiyA/Wf9UGwpb3AK15Zmcs5WzXl8mXEp+GCrX5Sv16qWjHmC5lR9rbLNBCDFBCLFTCLHzYiX6B4tiZg/FkW/Qt5xjSRTY5+Ve/j97ap5jS/tdLTlG1zxPV+cWaQA7ITEKJ8CQkQGAi4/9miW6kFO5qbmdQRBKjZTySyllZyll58DAwJJPsH8R7VsxQ7Kzy/bEdjjOub2NCpjYr/jU3aXh78vaz1rdrXKfWMrKngQtA2rr2q11tqRkPOrZeq4p9MeQrt18vdvpX6bVRNaVSr28MwjCOcCyQk19Y1vlUIqnsfT0q1PhgqWYpbsdv8FaFh67vvyCUMDscNviQpVNYilSE1/O0vY2RjR3orKIgG91D5s2t5rm9OipiY5PMa4oHp8uXUoe5CiOrazUyzuDICwDxhm9jboDyVLKOD0NSku7uspbTw5oBsC8LTGVYE3FYJngzqWYWg5Xy5DAGhV2rdLy66+/AlCtWslP1u3rtK9cY0pBXp7589T11sbFjITNP2gxC64lFGhSOA53O5kLdGObMdhywKuVcnlHuJ0uArYCLYQQsUKIB4QQjwghHjEOWQGcBKKBOcBjlWuP9r24f7fU1KLLGcZm2Ub6PnJ9EzsjnYuCtNxP3dC83NeadlzfmdCZM1pOoHvvvddu/5VKnlZfLQcPafUOpMGViF6av0TOOfsPHYfW/wPAkCcrx89cUTpkvnPvkdHryUq5bKU/hkgpi60NKLVIsceLG1OhGBXBduIOqW6pVMurRkKCrReOQNt3+OxMAm82r2/V5+5q1tWE1CzqVKu8CmllwbKC2+QbmpX7el/Eahv6M1vUL2FkxWO5nFerVi27Y/r9pBUKCvMPc4RJJXL5shZkdurvVxE3aJ+/hP9pexw+He1HxDbr4lw5saoaF96eobcJthgsRKqSvI2cYcnIoRREiNoThMte2rrzWTv5S55sqMUYfH3O/hpvuwY1AK1SmTPR+x1zErjtLw4o9/XCNx4wvb4npPi8TpXBzJkzAQgOtu+ZLKUkz6Blqvrp1p8cZldRZGaaZ1MNW2glEC2j5QNGmGdsa+d96TjDFMWStFBbugudN09fQyz5rfKfm6ucIGAUBE87fkaXvLSbvb0lo0dDi89tsvRRc8BIQor+6RJAmxnEJmlRye/d2a7ctZ13JKdzxehu+nfn8i89XS2XLpnFeMIE+ymiu3xn3gD0ctN/prZla18AUs+1Y+D9WtrrS3PMomqZwmL3n1rq7nve+ciBFioKk3veXI/Ct3s3HS0pxL5F2vdHNlfaW1Q5QSj4B3QvpAdh/mFc9Co6tsG/BPdKVxdB54ZagZ2ub+k7S8jMybdaJnptaCtGdCrf8k5Cdi637tYK09R2d6NtNcf7Zn/88ccAtG3b1m6sSHRStKme8va7tzvUNnskJ+81vU47/gxCCGSegeyTWjW34BfNRXFWfm4WgTphxW88KyqX6P7aTNrvOidKI7Jhpvl1UOW5Ulc5QTDtIVhM26WU9K7Xmwy3jFJd4pcLSXbbf7aYJVjekB3JmK+2EfHqX6bjXx/vxfieYeW65qWcPKuCOAd7O963f/p0c+nAO+64w6bfIA3cvux2AIY2GYqPu/7BRDt3DQfgUtTNjHlN2xM497L56c7VGNmem53FwbVarejx76kSmnqSecA8e2vwxec6WlKINW9o3+/7q/hx5aTKCYIw/sSWgpCVlUC/Bv1KjFF4r4Xmc//o4aLTIex71VwwPez5P8pdpay0vL78MGHP/2FKtAdw6u3BtDfubZSV3cnpVnUPLAvkOIpff/3VVPvguefse9+0W9DO9PrN3m86xK7iWL3G7HnWvtNLCCFIXmX+3NR7y1zN7qNx5liJ2g0aOsZAhV1i7hwJQM3779fZEgu+GWx+3bBynQ2qnCCY9hAsUtpeij9Gh7odSjx1bIjZqyW9CLe06j7ubH6+v+m40QsrWHuk/LmD7JGVqy0NhT3/B19bxBksfKAbMTOGlDkFRwEPHYxh8G5z/WI9xGDdunXs3bsXgLvvvttuedM28831Gfbes9dBlhXN0WOvm14fW/o/WnQPJudcGqmrjSU0721lWrr8atIDprFTFldOBktF6YiKMJc2rfvsVB0tsSBmE5w2zion76/0t6ty0S8F/4h+BknBjkHihaM0aNTHalxqaqrdwKdqri6k5htosuFAkTfIejW8OfbGzTR/+U8A7punFVN/d0RbRnYuX2RvXHImPd62Xz5y5oi23FnO64NW4yB0vfWHTw8x+OWXX9i3bx8AQ4YMoXlz241sSzFYNWKVVQlNPTh37gdiY+cBcHbDEzz68WDykrNNbqZeLQLwDtcKMP312QckJ1wA4KFP5upir0Lj8tdfm9LaNN++TWdrjORmwjxjCdyuD0NA5c8eq5wgFOwhuBokLnleGNyySEk9YjPs22+/5bHHbGPkonq3of567SZ1OjObht72k6d5uLkQM2MI8zafIvJ3LSjs2Z/38+zP2o22cW1fnh0UzoCIOlZxDAVIKdl79grv/HWEbSeLT9Ww9YX+BFe3fXIuC/fsP8mqy+acTB+GhzIq2PFlQWfMmEFWluatNWjQILoUSh8gpaTtAnOOmRW3ryDIV9+I0vPnf+TI0ZcAuHR4CPe8NIm8K9nEz/jXNKb2fdr+y5p5X3BonRaEdscLr+Ff28krdP2HSd+6lYSZ7wEQ8u47uFZ3kky+b1p8nge/65C3rHKCUDBDkAYDnikNyax5lOzcKFP//pr7aZvY1m5wGoCbi+CGWv78czmFbtuiSnxyvrdXI+7t1Yhl+87zxKI9pvaTl9J5ZOGuMv8c/zzdl6Z1Ki4p2qdnEph+4rxVW+x17XCrwDQXpSErK4sZM8xBQffccw9NmlhHgidkJDDgJ3NMxZo71xDoU8ZkhxXE0aOvE3tuHgBJx/tx+4OzyU/IMM0MAOrP0Gahv733JtE7tPKfNzz4GI3ad3K4vQqNjF27OHOftl9QbdAgqg8dqrNFRiItRGnaFYe9bZUTBFPuinwDPoktyax5FOFlniEc9z9O28TisxsubNuYoLV7AQhau7dUyylD24UwtF0IANEJabz864ESn/wL6NOsNrNGtquUCOgPYuKZccq6itfCto25oZZ/hb9XSWzbto2//jJ7UUyZMsVm2e7rA1/zwe4PTMe7xu7Cw9VemKHjWLeuPfkGLXbl0qFbuePhWWRtjyP5D/O+ToEYzBp1i6lt8BNTiVAV0nQjbeMmzj70EABerVtT/4P3dbYIbdnqtRrm4xfPm+9ZDqDKCUKBl5E0SHwvt+Ry019MfU92fNLqZpOZmWl3ExPgSO/WhG/SvG/abD7IgV6ld8VsWsePHybol5ogX0rqrdtn0/5S42AmNXR81bfCswKAyMhIq+OM3Ay6fW8OEgrxDWHliMrN/FgSeXmprN/Q3nQcu+lxxr38FOcjtyJzNKcDz2Y1CHygDVnpaXxy/2jT2NGvvUu98JaFL6lwEJe+nMPF2bMB8GrThkY//aizRUB+LrxuEf3/Ujy4V8xScGmpcoJQ4GWEwYBXinUN5Htb3WslCO+8847NjamAGu5u/N25OTfuPMbFnDyC1u4l7vp25fbsqUzszQYAXmkSwuMlRGJXBlJKPv74Yy5fNrvK3nXXXbRo0cJq3B3L7uB4ktnb6bMbPqN3vd7oyalTn3Ly1CzT8cXtnzFmYl/OvbjJ1BYwqgW+HeqwZ+Vy1sw1+7Q/PvcHvHz9HGqvwsyx3n3IN0a9+w+9lXrvOmZ9vlgun4D/WZSTf+UyuDr+9lzlBEEYvVCkwUBipvU+QYGHyqp6qxh4bmCJ12pbzYcNXcPp+6+25BS8bh//iwjlziDHb8IWxYvHYplbRP6lrd0iaOSjT0WxZcuWsXv3btOxn58fzzzzjNWY+Yfm897O96za9o/br6vo5uYmsWFjZ9OxNLjQpM5WWvvHEv/uDlN7yKvdMbhJqyUiN3cPJi9c6lB7FWby09I51tn8twuZOZPqt95SzBkOYsWz8O8X5uNpVxy6TGRJlRME3Ny17wYDZ9OPYG9CluJh9rKJjY2lfv2i0z409/Ui9rp2Js+jSVFnmBR1hs9aNuT2ugEVaXmpWJZwhQmHYorsf6phXZ5rXGklq4tFSsmPP/5IVFSUVfuzzz6Lj0WZwt9P/M6Lm160GvPd4O9oG6hv5aotW4aQmWXebzq7fjJ3jriLpO+iyDW2eTYPIPD+1vz9xUccWPO3aeytT79A8269HGyxooBLX3zJxffNewRNN6zHvY7Onl2GfJhu8fDYqC+M/10/e6iCgiBcNUGQRkEo7Nn+860/M+L3EVzxuEKNnBp89dVXRS4bFeDmIojv155fLyTxiDGK+dHDp00RzfPbNOKm2hXvynYoLZO7953gQk5eseOmhgUxpZF+Lpk5OTm8/fbbNlHbjz/+OJalUBccWsDMnTOtxkxsP5GH2z3sEDuLIupwJOfjvzUd56TVpk3dX2mRHU3Sd2aBCH6xG6ej97FglPVT59M//O7US4n/ZfJTUznWpatVW3jUYf3/Hnu+g98s3NrvXwmh3fWzx0iVEwTcjTOEfAP5XuZo5ZQrMfjXCKNFTW39enW91Qw/peWiOXnyJI0bl5xw7La6AdxWN4ClF5J4zCK9xfgDp2zGtvXz5s6gmtwcWJ16nu5WH1ApJSl5+Wy9ks7Ky8ksT7hCar7B5hpFUc/TnZWdW1DbQ98/b3R0NAuNaYQteeKJJ6hZU3syklIyeOlgYtNircaMiRjD812fd4idRXH69DyiT7xu3XhyPm2iJVo9J42A4c1IrZnKBw9Z51i6d9an1Kof6gBLFfY4fc84MnaYl/FC536Nb8+exZzhANIS4L1CNUl02i+wh3NY4UCEm+aiKPPzad69NyJ/L9I1j/0736f3DR8C0D24O9vitnHB+wJ1M+uyYMGCEmcJltxRN4A76gaQLyWvHD9ndw1/f1om+6PP8Up0+auPvdIkhEcbBOKi91MPWgGb2bNnk18otYeXlxdTpkzB3SjIO+N3ct/K+2zOd4YZweFDrxB34XurtqTNr9M9vQFYpE337RpEYsNEPn/3QauxAx54jPY3DkahD5e/mUfCO++Yjl1r1aLZpo36zgqkhNkRkGpRHXjEXGg9XD+b7CAclXytouncubPcuXPnVZ+Xu+Rlol9aglsNH2ot/Y1zv8whIUJ7ih3Q/wRgHQVbMEsAW1fIshCVlsmr0efYmHR1dZuvC6jGpIZ16FXDT//pbiGys7OZN28ecXG2pbBvvPFGehqfyjLzMun6XVebMaAVswmvGV6pdhaHlPls2ngDOXlnrNrTtzxJx7T2Vm2ezWpwMiCKTYsXWLV3GTaCvnffW8mWKooiZdUqzk16wqqt6fr1uNfVea/g5wfg4M/m45COMGGtbuYIIXZJKTvb66tyMwQXHy24y5CdS82Q+qSf7W8ShAKEEAxsOJBVp1exosEKBp/Vnva+/PLLIguzlJYIP29+at+0XNdwBpKSkvj888/Jzs626QsMDOShhx7Cw8ODrLwsen7fk9Rc26JDETUjWHzLYl0FLinpX3bvsa3yGrDlTeqk1bNq82pfm+U7/sflv61FY+BDE2l7w6BKtVNRNFd++ZW4F16wagud9w2+3XVek/9xHBz+zbrt+TPg5SSpMexQ9QTBGGhmyNY2YmPTj9sdN/v62bSZ34ZMt0ziGsYRfDqY8+fPM3PmTKZOdZJMiA7EYDCwYcMG1q1bZ7ffy8uLxx57DH9/fy5nXqbToqLTMawasUrXvEMGQw5bNg8lO9f2b990zSe45vlatWV3gF+XvgOFtoJGTZtB/ZaOrw2h0Ljw7kwS51onBQx+6y1q3HG7ThahLQ3NuwVOb7Jun7QbajWxf44TUeUEQXgaHU0N2lLZzkt/URAvemT/QsLbjjWNXXHHCgYvHcwWly3c0+IeMo5mkJ6eTmRkJK+++iouLv/d7OEGg4HNmzezenXR1d8aNGjAmDFj8PLy4pO9n9Drl6LdKn8Y8gOtareqDFNLhZSSgwdeJOGSbURqrRNDqX3CtujO8tjPSc9NthGCR+d8h4+/8z7l/ZcxZGRwvO91GNKsl1zrffQh/jfeWMRZDiD1AsyyU1Z28j4ICHO4OWWlyu0h8O8cosZpIesRR6KYN+UxOjWuTULEd4B5H6GAn4/9zGtbXwNgVMAo8nabXTxbtGjBXXfZLjdciyQlJbFixQqOH7c/Yyrg9ttvp127diw7sYyXNr1U7Ng/bv+DUH/9vGyklEQdmkFcwld2+5us/Qi3XOucTVEZ29l/YZ3N2IETJtF2wE2VYaaiFKT8/Tfnnphs0x728894t9bvQYN9P8AvdpwgphyFavpm3y2K4vYQqp4g7PyGqLFaqHrEkSgSz58j46OTHL3xXsBWEMA6YlZIwR0x1k+Tfn5+TJkyxek2e4vi/Pnz/P3338TExJQ4dtCgQXTs0pG3tr/FkuNLih07vNlwpvWYpuvvIS8vlX+3jycz2zZXE0DotlfxTrF2IU7Ku8A/sd9ikNaeUXUbN2PUazNw99Anmruqk3fxIsf79LVpd6lenWZr1+Dio1OZ1PRLmsdQfo51e4NucN+foHNNjpJQgmDJnoVE3aWVWIw4okXM/nDfUwTeswwAl+yB9LvZtpbqlvNbeHiV+Ung4ZCHubTZ1p20du3aTJgwAQ8PfTNw5uXlERUVxY4dOzhz5kzJJwDVqlXj9ttvZ2PmRpuUEfYI8w9j4eCFVPfUd/nkQsI/HDxYtKtq/Z1T8U20fopMzrnE6vPfkiut/6kDgkMY89b7ePpY7yMoHIMhJ4ezDzxoFT9QQFBkJAGjR+lgFVpU8eKxcHSFbd/wr6HNCNt2J0V3QRBCDAI+BFyBr6SUMwr13wvMBAqc8j+WUtqf5xspsyDsW0zUqEjALAizRt3Cba3uIaa3li7B3iwBIDs/m84LrX+Pg2oNwndn8TePOnXqcNNNN9G4ceMKeXrOzc3l9OnTnDhxghMnThRZu6E4atWqReterZkVM4vTqUXXiLZkYMOBvN3nbTxd9X1iTks7zo5/x2HA/s/tkutNw22v4ZFp7W54Lv04Wy7+ZjMTqBPWhBGvvIG3X8XVl1CUHkN2NmcfeYSMrbaVyrxataLh99/h4qnDZ05KWPUqbPnIti8wQnMddXA20opAV0EQQrgCx4CBQCywA7hLSnnYYsy9QGcp5cTSXrfMgnBwCVEjXgbMgnD+2BESPz/MhVs07yFDZmMGDllV5CV2xO/g/pW2Rbj7efaj5hHnSWwHEFg3kPOB5/k97XekKP3fur5ffebcOIf61YrO4+QorlzZw+5dDyLFlSLH1Dg9kDrHRiOk9XT934srOJV2wGZ8z5Fj6H7H6Gtmme+/Rt7Fi8TcdTe5sbF2+5uu/gf3evXs9lUq+bmwdAIcKiIJ4TXiLVQceschdAWipZQnjcb8AAwDDhd7VmVhp5hKSPNwFp17huHrPuDE9U/i4n2Si/G7CQzqaOcC0CWoCwfGHyAmOYZbf73V1L42ey1YZNT2yvOia0pXApMrp5qXcBHIWpL9cj+x3rFkumXaH5gOFHPfu6flPTzR4Qm83Cq+AM/VYjDkcTL6a07HFkpJXMh+rytNqbd3Im45NazaY9OPsv3iCvIKLQX5B9Zh+IuvUzNEh5uMAoCUlX9zbrLtxnABTf5eiUeoDk4IKXHwzSBIirHfP345FKq5/l/FEYJQDzhrcRwLdLMzbrgQoi/abOIpKeXZwgOEEBOACQChZf3guLjbbR48cQrHv9tFQGwfkutvZP/hO+lVYzteXrXtjgcIqx7GgfHa0+ehy4cYvXy0VX+WWxYbam4AJ5g01POrx9QuU+nfoL/TPBVLKYmP+4PDUS+CSC92rM+l1gQffAi3HOv9ivMZJ/j34gqyDRk25wx/cTph7eyLuqLyyY2L4+zDj5B97Jjdfo/GjWm48Fvcajr4H0RK2PoJ/F2Ml9wjmyCojeNschKcJQ7hd2CRlDJbCPEwMB/oX3iQlPJL4EvQlozK9E5FrPlF9OnHio9nMerwcyTX3wjA5i3d6NxhJdUDSo4sblWrlUkcQKvwNXvXbBYfXVwmM6+WGxveyOjw0XSu29lpbviW5OdnEX1sDrFxH9h22jG35slbqX1iGEJaf0SPJu/gQNIG8qV1hle/gJoMe+Zlgpra8QVXOIT81FTiXnyR1FX/FDmm9uOPU3vi447/jJ7eAt8MxjIXlRWB4VrqaT+d01zojCP2EHoAkVLKm4zHLwBIKd8uYrwrkCilLNZ1pcx7CPEHibr+TsC8h1BATmYGH987ipGNnjW5oQL4e46mS683r/69qiAGQw5nTi/h5InPkC6lS9xXLa4rgcdG455t/aR4JTuBHZf/IjHbNkdSx8HD6DVyDB7eOrkeKsi9kMD5554jY5vtZnABHo0aEfrVHMfvB5zdAd/eBjnF5Ay79SPoNN5hJjkLeu8h7ACaCSEaoXkRjQbuthwghAiWUhb81w8FrO/UFYlv0UtAHt4+jHjlDX5+Yxoj/p7H6W7Tyap+kpTsH1i95gcimn5NSOj1lWbatURa2nGOHv6SK2lFbL4VEcQdcHogNU8OxS3X2qMnJecymy4vIiHL1kW2aZfu9Lv3YfxrV85ejKJkpJSk/LGC84Wq2hVGuLsTOn8ePh0duFQnJexeAL8/Ufy4VrfD0P+Bp/ImK4pKFwQpZZ4QYiKwEs3tdK6U8pAQYjqwU0q5DHhCCDEUyAMSgXsrzSCfWggXiTQIDOnpuPhau4yGtm7Hbc+/wuK3pzGKV8msfoIz3bSc+FHRDxAVDd6u/ejR9wu0ycx/k/z8DM6fW8Gp6EXksveqz/e92JZaJ2/FO7mZTd+x5J0cvrLV7rp/19vupMvQ4armsM5k7NlD3MuvkHPCvgt2AW6BgdT/9FO82zgwp1PyOfhjChz7s/hxzW+G2z8Db8dXLrxWqXqBaUBM78ZkXvIk9Ju5+PboYXdMVloanzwwmsbV2tGl9iASQ1dyMXyRzTgp3Wgd8QVBIdeXyRY9yMlJ5EL8GmJP/016znqEKL7iWlGIfA9qxtxEjbMDbLx9DNLA0eR/OZ6yi8x822l7445d6HrbSOq1iCjTeysqjqyjx7jw5ptk/PtviWOrD7+DulOn4lqjRuUbBpCVDKtfhx1zSh7bcxL0exnc9feWc2b0XjJyOnzr5pB5yZP0rduKFAQvPz+mLF7Ojt+XsnjhO/TLupsWZ+aR7XuemF7mer9C5HHoyAMcOmJ9vshvSN06Q2nQ+Eaq+YUjROUkwsvNTSY19RiXLxwk8fIBMjIPYnAt/qnOys4S9vY8UxpSI/Y6qsV3xzXPdr3+bPpR9iX/waVsW39yD29vuowYQbsbB6ugLydA5uSQ9PPPXJw1G0N68V5dAN6dOhEcOQ3PZrazvEoh4Qj8Mw2O/VXyWJ/aMPwraNKv8u2qQlTJGULGY4GcXlMbr9atafTzTyWOl1Lyy4xITu3dhZ9bAEMaaDUR8t0yiG85l7SgstmhN+4ZgfgldMQvoTPeV5og7Cz8J2SeISbtIGfTj9r49gPUqh9K2wE3EdGnH97V/G36FY5HSknmzp0kfPghmTt3leocj8aNCZo2Dd9u9gsYVSg56bDtM1jzesljC7jlfeh4L/yHMww7CjVDKIR3be3GlnXwYKnGCyG44wUt42lS3DnmPqnlzREIml3oRIda5gBrKfJIrbOblJDNpAfaT7BWWbhm++OVEob3laZ4JTfFO7kJLvn2Q/6z8tOJzzhFdOZJ4jOW2+T0KSC0dVuaDe7NjV2ewa9mrco0X3GVyJwckv9YweWvvipxrd+S6rfdRu2JE/GoX8meP/l5cPhXWPsWJJbSvuqhcOPr0HJYydNXRYVTJQWhPKs3AcH1mLJ4uen4+I6t/Dn/K1IuXjC1uZ5yI9i7CfV8b6SuVyjebpW7XJKSc5mU3MtcyblIfM4FknLOkZFXtKOWm4cnoa3bEtq6Hde3uonA0DCEevJyWrKiokj8diHJS4vw6CoCzxYtqDPlaXz79Klcv//kWNj+OWz5mCL9/O3R7VHo83SV9/13JqqkIFiSffIkno0blzywCJp16UGzLrb7ELnZWZzau4vTB/eTEHOChFMnyM/NLY+pVri5e1Ctdm0CgutROzSMwIbNaB52EzWCgnFx8vS7Cmtkfj5p6zeQ9MMi0jdsvOrzfXv1otaDD+DTvXvl3fiz02D/D7D109I/7RfQ9Abo9yLUK7qKnsI5qJqCIFwI7pZE3PYAzk15hsa/XN2TV2lw9/SiebdeNO9WdBUxRdVA5uWRvm07KcuXk7x8OeRdvVeXi78/Ne8dT8Do0ZWX6iH+oObPv+dbyLV1CS6Rbo9C90euqQphCmuqpiC0uZPqhsXEbQ8gOyoKmZOD0Ll+geLaJTchgdQ//yT59+Wl3peyh0fjxgSMHk31YUNxrV4JNSYuRcOBn2DfIrhSupTnNjS7CXpOhLA+ao3/P0jVFIR2dyH2L8a/uQcpx3I4Mehmmq4punawomoi8/PJ3LuX1DVrSFu7jpyTJ8t1Pdfatak+ZAjVhw3FMyKiYpd3MpMg6nc4uBROri37ddy8oMM90PEeCGqrbvpVjKopCI2vByCkQwwpx0LIPX+ehPfeo04JYfmK/wb5aelk7PiX9C1bSd+8udw3+gJ8unen+i1DqHbjjbj6V5ALriEfYnfC8ZVwbCVcKPsMxETLYdB+DDQZAK5V8xagsE/V/DQYn3qEgCYLZnFi3BQuf/U1aRs20ujXX5THzTWGzM0l88BBMv7dTvr27WRs267lt6koXFzw69ePav374de3L26BFZBTKSsFTm2A6FUQvRqSbbK9l42gttD6Dmh5G9RsVOJwhcKSKhmYBmj/jPO14jbZ4/dy8ubBpq6Au++i7vPPq30FHchPSSFz/wEy9+8ja/8BMg8cIP/y5Up5L+Hjg2/PHvj17oPfdX1xDw4u+8WkhItH4NRGiNkAMZu0ZZyKpOlACB+s5ejxL4etiiqNCkyzR6O+ppee6ycRfvAAZ+67n4wdO0j6fhFJ32t5i2qMHkXtRx/Dva7ylS4NhsxMsqNPkH3sGNnHj5N97BhZx4+Rf/GSQ97fq11bfLt2w6d7N3w6dMDFpwzpsaWElHPaUk3sDji7XfteGXgHaG6ZTW+Axv2gWt3KeR+FohRU3RkCQHYqvG1RM/i5GAwGD+KmRZKyfHnR5wG+1/XFf9DNVLthAK7Vrs08PVJKDGlp5J49S86Zs+TGniXnbCy5Z88Yv1fQMkYZ8WzRAu+2bfBq2xbvtm3xbNIE4XYVzzDZadqae9w+iNuvfb9gW1+5wqnVTCu5GNYHGvZSN3mFU1HcDKFqCwJARiK8a7HW6h0AY5ZA/U7kp6Rwee5cLn/+RfnfpwoivLzwbN4cz2ZN8WreXHvdtCmutWuX7GGTmwmXo+HiUbh0TPueEAWXjjrG+AJcPaFBVwjtDg26Q/1OKp2y4ppGCUJpWPcOrHvLtr3lMGg9ApoNBHdvcs6cIWXFClJW/FlkrdhrGdeaNXFvUB+P+g1wD22gfW9QH4/QUNwCAxGudqKg8/Mg9TxcOQNJp7XvV85A0ilIPAVp8Y7/QQpTLQSC20FwWwhuDyEdoFqQcqtUVDmUIFwNx1fBD2MgP7v05/gGajebuq2hZmPwD9FuNtWCwbsm0mAgPymJvIsXybt0CUNGBjI3D5mXh8zLhbw8i2MtilW4u+Pi7Y2LjzfC2xsXL29cvL20194+uPh44+LlhYuvr7aMkp+jLYFlJUPmFchMhIzL2lf6JfPrjMvarCg9oeI3PSuTWs2gToTFV0uo2US5TSoUV4kShLKSlWwM9lkCJ9ZU7nv91/Cvr7k91mwEAY2gVlOo3UxLa+Durbd1CkWVRXkZlRWv6tBhrPZVmLxsuHAI4vbC+T3ahmX8QZD5DjezRFzcwKeWxVdNbVbjV9f4vY722q8O+NZRFacUiiqKEoSy4uYJ9TpqXwqFQvEfQIXkKhQKhQJQgqBQKBQKI0oQFAqFQgEoQVAoFAqFESUICoVCoQCUICgUCoXCiBIEhUKhUABKEBQKhUJh5JpNXSGEuAiUsVI4tQHHJOi/epzVNmXX1eGsdoHz2qbsujrKaldDKaXdsn/XrCCUByHEzqJyeeiNs9qm7Lo6nNUucF7blF1XR2XYpZaMFAqFQgEoQVAoFAqFkaoqCF/qbUAxOKttyq6rw1ntAue1Tdl1dVS4XVVyD0GhUCgUtlTVGYJCoVAoCqEEQaFQKBRAFRQEIcQgIcRRIUS0EOJ5ve0BEELMFUIkCCEO6m2LJUKIBkKItUKIw0KIQ0KIyXrbVIAQwksI8a8QYp/Rttf0tskSIYSrEGKPEGK53rYUIISIEUIcEELsFUJUcv3Z0iOEqCGE+FkIcUQIESWE6KG3TQBCiBbG31XBV4oQ4km97QIQQjxl/NwfFEIsEkJUSJnDKrWHIIRwBY4BA4FYYAdwl5TysM529QXSgAVSytZ62mKJECIYCJZS7hZCVAN2Abfp/fsCEEIIwFdKmSaEcAc2AZOllNt0Ng0AIcTTQGfAX0p5i972gCYIQGcppVMFWQkh5gMbpZRfCSE8AB8p5RWdzbLCeO84B3STUpY1ILaibKmH9nlvKaXMFEL8CKyQUs4r77Wr2gyhKxAtpTwppcwBfgCG6WwTUsoNQKLedhRGShknpdxtfJ0KRAH19LVKQ2qkGQ/djV9O8XQjhKgPDAG+0tsWZ0cIUR3oC3wNIKXMcTYxMDIAOKG3GFjgBngLIdwAH+B8RVy0qglCPeCsxXEsTnKDc3aEEGFAB2C7zqaYMC7L7AUSgFVSSmex7QPgWcCgsx2FkcDfQohdQogJehtjpBFwEfjGuMT2lRDCV2+j7DAaWKS3EQBSynPAe8AZIA5IllL+XRHXrmqCoCgDQgg/YAnwpJQyRW97CpBS5ksp2wP1ga5CCN2X24QQtwAJUspdettih95Syo7AzcDjxqVKvXEDOgKfSSk7AOmAU+ztFWBcxhoK/KS3LQBCiAC0lY1GQAjgK4QYWxHXrmqCcA5oYHFc39imKALj+vwS4Dsp5VK97bGHcYlhLTBIZ1MAegFDjev1PwD9hRAL9TVJw/hkiZQyAfgFbQlVb2KBWIvZ3c9oAuFM3AzsllJe0NsQIzcAp6SUF6WUucBSoGdFXLiqCcIOoJkQopFR9UcDy3S2yWkxbtx+DURJKWfrbY8lQohAIUQN42tvNEeBI7oaBUgpX5BS1pdShqF9vtZIKSvk6a08CCF8jY4BGJdkbgR092qTUsYDZ4UQLYxNAwDdnRYKcRdOslxk5AzQXQjhY/wfHYC2v1du3CriItcKUso8IcREYCXgCsyVUh7S2SyEEIuA64HaQohYYJqU8mt9rQK0p917gAPGtXqAF6WUK/QzyUQwMN/o/eEC/CildBoXTyekLvCLdv/ADfheSvmXviaZmAR8Z3xIOwncp7M9JoziORB4WG9bCpBSbhdC/AzsBvKAPVRQGosq5XaqUCgUiqKpaktGCoVCoSgCJQgKhUKhAJQgKBQKhcKIEgSFQqFQAEoQFAqFQmFECYJCoVAoACUICoVCoTCiBEGhqCCEEI8IIT6zOH5DCPGtnjYpFFeDCkxTKCoIIYQPcBRoA/QGXgd6SikzdTVMoSglShAUigpECPEu4IuWEG2glPKEziYpFKVGCYJCUYEIIcLREo0Nk1KqxImKawq1h6BQVCyvohV8qVKJIxX/DZQgKBQVhBBiCuAFjAQm62yOQnHVqKcYhaICEEL0R0vb3ENKmSqE8BdCtJdS7tXZNIWi1KgZgkJRToQQocBXwJ1SylRj84fAk7oZpVCUAbWprFAoFApAzRAUCoVCYUQJgkKhUCgAJQgKhUKhMKIEQaFQKBSAEgSFQqFQGFGCoFAoFApACYJCoVAojPwfRLIW0ph0n5MAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "for lv in lv_list:\n", " time_hist = lv.time_hist # time history, excluding t=0\n", " num_hist = np.array(lv.abundance_hist) # abundance history of all species\n", " plt.plot(num_hist[:,0], num_hist[:,1]) # plot prey vs predator abundances\n", "plt.xlabel(r'$X$')\n", "plt.ylabel(r'$Y$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see a collection of closed orbits going around the neutrally stable point $(X^*, Y^*)$. If we plot $X$ and $Y$ as functions of time, we will see that they undergo some kind of \"nonlinear oscillations\"." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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T81JCW3nlGCGCevUVDEdDiBIzMMIwq1t7rBBpQmGEuIY6xpOzkmntGaRnILax+uMBV4iBFgax9ldqBREhlc3dQTv2DHQESPAYIa6h+B/ALwxTj/GYhBrialCiQ12DprLZ50cLwVcJaq6o7+xjIEbNg7SCiIBBj5fq1t6QFUS6M4G0JAd17X0WSTZxCHflVZSpTHd6jMemMgw/GkBxplIQx/QYj0k4vkpQCkJK1Y89FmgFEQF17X14vDKkYloGhRlJMftPH09U+1anoY5xXmoSDpugTo/xmBimzik+02ewFPuUcL1WEGNS2dxDqi9JNhQKjYWOVhDjD8O+bWy1Q6Eo00mtfrDGxBXmGNtsgsIMp568gsDV2kOSw0Z+iHWrCjLU+VoJj01lczelIQZawHElHKudsFYQEWCsvEqyQ99BFGUk6x1EENS09uLwTfahUpiRpJVwENS09TI5OznkySvJYScnNVEriCBwtfZSGuIODRj63msT0zjE1dqLTRy3d4dCUWYSDZ39eLw6WW40XK29FGc5gy5W5k9xplbCweBq7R0KnAgVvUsbGymlb4xDX0hmOB0kJ9j1DmI84mrtoSjDGXTxLX+KMpx4vJKmrn4LJJs4uFp7KAnjwQI1edV19OmM9TFwtfaGtQsGKNK7tDFp7Rmkd9ATlilaCKHM0XoHMf6I6MHyRYDoKJvRqWnrDevBArVL6xnw0Nmv4/RHomfATUv3QARjrHdpY2H40SaHOcaFGUkx26VpBREBNa0RTF4ZsY1OGA/0uz3Ud/SH/WAZSlibQEamZsiPFv73uLl7gP4Ydz6LZ8wYYx3FNM4Y9HipbQ9fQRRm+iJA9OQ1Isfa1NiEb/5QSlibQEbGFenk5fseN3RoU+lIDI1xmKbSosxkGjr68cbAX2mZghBCPCiEaBBC7Bzh+DeFEFt9r51CCI8QIsd37KgQYofv2CarZIyEuvY+vDL8yUvH6Y+NGSsv0Lu00XC1hR+JB7GPshkPuFp7SE9ykJEcXum7oowkBjxeWnoGTJZsbKzcQTwErB7poJTyZ1LKRVLKRcC3gLeklC1+p1zgO15hoYxhE0kOBOg4/WAYst2GGWFjxOnrMR4ZV2sPifbQcyAMjAg+vUsbmXDDiA1iWRXAMgUhpXwbaBnzRMX1wKNWyWIFkeRAGOhkudFxtfZit4mhZKFQcSboOP2xcLX2MinLiS2MMGKA4gyfn0eP8Yi4IvBVQmx3aTH3QQghUlA7jSf93pbAGiHEZiHE7bGRbHQiyYEwKMpw6gdrFGraeinKcAbdgSsQhRlO7ecZhZoIIvEAMpIdOBNseoxHQEoZ8RgXxbDcRswVBHAl8N4w89JKKeUS4DLgi0KIc0f6sBDidiHEJiHEptGadZhNJDkQBjpOf3RcrT1hRzAZFGfGLgJkPBDp6lYIEdMom3ino9dNZ787bDMpQH5aEjYRG1NpPCiI6xhmXpJS1vh+NgBPA8tG+rCU8j4pZYWUsiI/P99SQf2JJAfCoDjTSc+Ah44+HacfiEgnL/Bl+urJKyB9gx6auvojmrxAj/FouNoi81UCOOw28tNjk5AYUwUhhMgEzgOe8XsvVQiRbvwbWAUEjISKJZHkQBgYlRr1w3UyA24v9R19ESvhogwnTV0DMaunH88YvTJKwqgR5E+x9qWNiOGrjHQnHKtdmpVhro8C64DZQgiXEOJWIcTnhRCf9zvtKmCNlLLb771C4F0hxDZgA/CClPJlq+QMh0hzIAyGwjD1w3USQ2HEEa5ui7USHhEzAi1ALXRiFacf79SYNcYx2qVZ1pNaSnl9EOc8hAqH9X/vMBCbBqxBEmkOhEGRjiEfkXDLfA/HCHVt6OxjShh9OyYykYYRGxRlOBnweGnrHSQnxH4HEx1Xay/JCXayI+yLXpTpZP3hZpOkCp548EGMOyLNgTA4PnnpLNThRJrAZXA8RFCP8XBcEZRS90cny41MTVsPJRHkQBgUZjjp6HPTNxjdkiZaQYSBWVtzZ4KdzOQE/WAFwNXai4gwjBj0Lm00alp7mZSVHFYpdX8KjYREPcYnYUagBUBBemxKmmgFEQZm5EAY6NajgTEjjBggKyWBRLtN7yAC4GrtMWnyUs+Brsd0Mq7W3ogd1OC3S+uM7lyhFUQYmDV5geF80g/WcMyIEgMVp1+QkUSDVsInEUmjIH8K9A4iIJ19g7T3DkZsaYDYmfG0gggDM3IgDArSnXryCoCZY1yY4Yz6yive6Xd7aOjsN2WMkxzKCavH+ESMMGIzlPBxM542McU9Zq1uQf3HN3TqEEF/3B4vdR19pjxYYJjx9C7Nn+Ol1M0aY70THk6k1Yj9yUxOINFhi/piUiuIEDErB8KgMMOJ2ytjUso3Xqnr6MPjlaaNcUG6zvQdTqRdzoZTkKF3wsMxK0kOlKk0Fv5KrSBCxMiBMOvB0hEgJ2NWlJhBYYaTzj43PQO6pImBmatbgMJ0vUsbTk1bL0mO8EupD6cwPfq7NK0gQsTsyasgQ0eADMfMlRccV8J6jI9jlFIvijAHwqAww0ljVz8ebSodwtXaw+SsyHMgDGLhS9MKIkTMyj410ElGJ2OsbidlmTd5gR5jf4xIvEhKqftTmJGExytp7tJK2KDGpBBXAxWNp3cQcY0RmVBs0uRlbD/19vw4rtYeCjOSSHLYTbnekBlPZ6wPUdNmnh8Nju+E9ff4OGZG4oHypXX1u+nqj56pVCuIEKlp7TV18kp02MhNTdQhgn6YFZ9vcNyMp8fYwOzJS+/STqR3wENz94CpSvi4qTR6Y6wVRIjUtJk7eYGOABmOWt2aN3mlJzlITrDrycvHgNsXRmzi5FUUo0zfeKXGhD4QwzGUcDRrt2kFESIqdd7cqqA6Tv84Hq/kmMnmj+MhgnqMQUXiSWnu5JWXlogQ2sRkMBRoYeJiMhYRj1pBhIDXK6ltN38HUajj9Ieo7+jD7ZWmrm5B7dL0GCvMKqXuj8NuIy9NlzQxMDvaEWIT8agVRAg0dPYz6DF/8irMSKKpqx+3R3c9qzGpzPdwCjOcuqy6D2PymmLJTlgrCFBjnGAXQ1VYzSAWplKtIELACrsiqJWBV0Jzt86mtmJ1C0YiVx9S6jh9V5t51Yj9iUUiV7xS09ZLcWYytghLqfszZCrVPoj4ZGjbaLaJSUeADOFqMd92C2qMewY8UQ0RjFdUGLGTBJNyIAwKMpw0aCc1YF4p9eFE21SqFUQImJ3haxCrSo3xSE1bL3lpSTgTzAkjNijQYzyEWU1shqNMpQMMalOpqQU9/SmMcsSjZQpCCPGgEKJBCLFzhOPnCyHahRBbfa/v+R1bLYTYJ4Q4KIS4yyoZQ6WmrZfslARSEs1t5a13EMexbvLSuRAGNSbnQBgYY9x4ivt6+gbNK6U+HKPmVbRMpVbuIB4CVo9xzjtSykW+1w8AhBB24LfAZcA84HohxDwL5Qwaqx6s3NREbEJPXuDLM7FQQZzqcfpGKXWrdhCgFzq17ervN9tMCup73DvooTNKplLLFISU8m2gJYyPLgMOSikPSykHgMeAj5gqXJhYkSQHx0MET3Xzh9crLduaG9Ekp/oY17arUupWfI+N1qOn+hhbFWgBx02l0VpMxtoHcaYQYpsQ4iUhxHzfe5OBar9zXL73AiKEuF0IsUkIsamxsdEyQaWUqjqjBf/poLueATR29TPg8ZoeBACQmuQgPclxyq9urQojBv9M31N7jK3yVUL0lXAsFcQWYKqUciHwa+Cf4VxESnmflLJCSlmRn59vpnwn0NI9QN+g15KVF+hsarAmucifWFTDjDdcJveB8Cc3NRG7TWglbHIpdX+ibcYLSUEIIUx7cqWUHVLKLt+/XwQShBB5QA0wxe/UEt97MeX4yssaBaHrMVm7NQe1wq07xcfYKKVuVjVif2w2lRimFzo9FGeaV0rdn2hXzQ3qLxBCnCWE2A3s9f2+UAjxu0huLIQoEr5OGkKIZT5ZmoGNwEwhRLkQIhG4Dng2knuZQY2F20ZQxc6auwcYcJ+6IYJWbs3B6Jt8aisIs0upD0eXNDG/GrE/aUkO0pIcUTPjBRuv+X/ApfgmainlNiHEuaN9QAjxKHA+kCeEcAF3Awm+z98LfBy4QwjhBnqB66SK3XILIb4EvALYgQellLtC/cPM5niSnDXmD2Pr2NjVb9mXK96paeslJzXR9DBiA8PEJKU0rcvXeMPKyQtUGGZlc49l1x8P1LT1ctb0PMuuH01TadBPopSyethD5Rnj/OvHOP4b4DcjHHsReDFY2aJBTVsvaUkOMpKtmryO50JMzkqG3jbY8meo3QrpxbDoBiiMi2hfy7AqB8KgMN3JgMdLW88g2amJ0FkPmx6ApgOQOx2W3ARZU8a+0Dimpq2XRVOyLLt+YYaTDUf9ghebDsKWh6DjGBQtUGOckmPZ/WONFaXUh3NScc/qjVCzCVbcYfq9gjWSVQshzgKkECJBCHEnsMd0aeIYY/KyauVZmO6XyNWwF/5wDrz6XXBtgg33wb0r4Z2fwwSuJWT08LWKE3IhjrwDvzkD3v4ZHNsC7/wCfrsMtv/DsvvHGitKqQ+nMCOJtp5B+gY9sO3v8Psz4f0/qO/xa99XY3zkbcvuH2usKKU+HFWPyacg3voZPHAxrP0NDHSbfq9gFcTngS+iwk1rgEW+308ZrMqBMDBMTO2NNfDXq8HdD7esga9uh2/sg3kfgdd/AG/+j2UyxBIprcuBMDDGuLNqB/ztGkgvgi9uhK9sg69shUlL4KnbYOvfLJMhllhVSt0fYyfcseMlePpzMGU5fHWn+h5/7h1IyYVHPqEU9ATE6kALMHxp/cj374M3fgQLroEvrofEVNPvFZSCkFI2SSlvkFIWSikLpJQ3SimbTZcmjrEyBwIgOyWRBLtg0Y4fQk8T3PA4lC5XB1Ny4OoHYPGN8NZPYedTlskRK5q6Buh3WxdGDOrBcuBm5jtfhYQUuOlZyJuhDmaVwo1PQvl58NxXoGaLZXLECitzIAwKM5xk0Un2mq9AwVz45D8gvVAdLD4dbn4Rssvg8ZugPebBiaZjta8SlBKe4qmGNf8JM1fBVfdCUrol9wo2iulhIUSW3+/ZQogHLZEoDunoG6Szz23p5GWzCT6UsofZLW/C+XdB8cLhJ8AV/6dWZM99ZcI9XNGYvAoykrjG/hZZnfvhynvUDsKfBCd84iFIK4THb7Zkyx5LjNWt1TvhLzqewdHXAh+7DxKH/X+m5sK1f1U75Cc/C96JFbVnVSl1fwozkrjL8SheexJ85HdgsyYiDYI3MZ0upWwzfpFStgKLLZEoDqmxOIELACn5nHycJnsBrBjBeudIVKsFrxue/9qE8kcMbc1zrJu8kuQAX014isrUBTDnQ4FPSsmBj/0R2irhrf9nmSyxoMbCJDmDItnMp+2vcqD4SuWUDkTeTFj9E6haC1sfsUyWWGCUUk90WJeDPK13J5fYt1A19zZIsy45GIJXEDYhRLbxixAihxAioMY7VudAAHDkLea49/BIwseUIhiJnGlw4X/CgVfgwKvWyRNlrOjhexJbH6GAVh7PuBlGCzaYeqYy5637DdTvtk6eKONqtaaUuj+Z2+7DhpdXC24e/cRFN0DpWSoQo3viWKut9qMBlO35A40ygw+Kr7X0PhC8gvg5sE4I8UMhxI+AtcDEWl6NQjS25mz4I12ObP7St3Lsc8+4DXKmq4fLMzEa4NS09pKZnEC6M8GaG0gJGx/kaMIM3hmcM/b5F/8AEtPgtbutkScGuFqtqZQ7xEAPYuvfeMtxJgf6s0c/12aDD/0C+jrgnf+1TqYo47Ko4vMQrZUkH32dRz0XUttrnaI3CNZJ/WfgaqAeqAM+JqX8i5WCxRM1bb0kOWzkpY2yso+EznrY9xL7i66kqc9G78CoKSZqh3HJf0HjXtj6V2tkijJWdeAaovp9aNjFxryrgutNnZoLK78GB9ZA5Trr5IoiNRaHuLLrKehr4+2MK4MrBVEwFxZ9EjbeD23VY58f5xil1C1dSG7+E0IInnOsikrGeiiGsr3AU6hs6i4hRKk1IsUfRoirZdm32x4F6aFh5jVAkNUw53wIJleo3AjPoDVyRRGrM3z54K+QmM6xKR+iobMfrzcI/82y25XD+l8/tE6uKDFUSt1SE97fIG8WzblnBF+Z+Lz/UD/f+ql1ckWJug5VSt0yJez1wrbHYNZqyCiJHwUhhPg31O7hVeB54AXfz1MCy7fmOx6HKctJnaRMH0GtvoSAc78JbVXq8+MYKaVvdWvR1twzCHufh9mXkZOdhccrae4eGPtziSlwzjeg8r1xv4toMkqpW/U97qiFyrVw2scpyHQGXwoiawos/YxaJI3zyDyra4lR/T501sJpVw/lQlhNsDuIrwCzpZTzpZSnSykXSClPt1KweKKqpYfSHIsmr+ZDUL8T5n009Najsy6FwgVqF+EdwywVx7T2DNIz4LHuwTryFvS2wvyrTihpEhSLPwXJOfDeL62RLUpUWx2Jt+dZQMJ89T3u6nfTFWzXs7O+pHxE6yOq/xlzLI923PUUOJwwa7WvHlOc7CBQDXzarRQkXunoG6StZ5ApVimIvb6N2NwPDZXbCHryEgLOvROaD/oe0PGJ5eGXu56GxHSYfmHoTW0SU2D552D/S6oEyjhlKNDCsjH+JxTMg/zZQxnrQU9gWaVw2tWw+SFVg2ycYuwgJllQSh2vB3Y/AzMvgaQ0CjOcNHYFaSqNgGAVxGHgTSHEt4QQXzdeVgoWL1S3qAfLsh3EnuegeBFklZKR7CDJYQvOiWow90rImgrrf2+NfFHA0vIEHjfsfQHmXA4JTr+GKyGM8bLbVeb12l+bL1+UMBIRLfHzdNZB1TqYfxWA30InhDE++8sw0AWbxm/+rau1h4J0i0qpV62HrnqY91FAVc0d9Ehae4IwlUZAsAqiCuV/SATS/V4TnuoW9WBZoiA6joFro5rkASFE6D0LbHa1wq1+f9yWh7C0PIFrgzIvzbkCgLy0JIQIsSNXSo4yNW3/u7K1j0Ncrb1kpySQmmRB+tLB1wAJsy8HjtdjCqlnQdECmH6RWui4x2fDIUt9lQdfBZtDldbAr/CkxX6IYMNc/yvQy1LJ4gRjBzHFCrviwdfUz9mXDb2lWo+GaFtcfKOK2X//XhOFix5VLT1kOB1kpliQA3HwNRB2mHY+AAl2G7mpYXQ9W/F58A7ClofNlzEKVFvpRzv4OqQVQaFqKx92W8wzvwDdDbB7fJpLq1p6mGrZGL+myuw4MwC/9gAWNw4KNoopXwjxMyHEi0KIfxkvSyWLEyydvA69ocIoC473eVCtR0OcvJyZKp5851Nquz/OqGrpoTTX6gcrc+itwnAcfDnTYMbFsOlP4zKsWI2x+dU+8Xrg0L9gxkVD2elpSQ5SEu2hK+FpF6px3vhH8+W0mAG3l9r2XmuUcGc91O1QY+yjID1EP0+YBGtiegSVB1EO/BdwFNUadMJT3dpjjYPa61XRNdMuOKHsw0nNQIJl2efUCncc2nAtW912NUDtthMeLPCVSw5n5XXGbdBVdzywYJzg9nipae2l1Io6V8c+gL42mH7h0FthmUpBZVef8VllLq3dbq6cFnOsrRevxBolfMi3Fp/upyDC8aWFQbAKIldK+QAwKKV8S0p5C3DhWB+aCFgW4lq3HXqaT3iwQK1uuwc8wYcIGuTNUPbJzQ+NqxWuxytxtfZao4SNB2vGxSe8rcx4YTxYMy9RETcb7jdBuOhR2676QFjyPT74GiBO+h4XpIfZFnPRJ8GRPO52EZVWBrMceh1S86HoeGZBksNOdkqC5clywSoIY8apFUJcIYRYDIzaN1AI8aAQokEIsXOE4zcIIbYLIXYIIdYKIRb6HTvqe3+rEGJTkDKajjcak5fPNm4Qci6EPxW3qEiHfS9FKFz0qOvoY8DjZWqOBSuvw2+qBjVFJ6bsFKQ7aerqx+0JsdS0zQ4Vt0Llu+OqiF/V0ORlwRgffB0mLzmpjWjYu7TkbDj9E7D9cRVcME6oskpBeL1qrph+kdph+RGNZLlgFcSPhBCZwDeAO4H7ga+N8ZmHgNWjHD8CnCelXAD8ELhv2PELpJSLpJQVQcpoOg2d/Qy4vdYoiMNvQMH8481UfBSE6+ADmHEJpE9Su4hxQlWzhSuvqnVQembAB0tK1aQoZBZ/CuxJ42qFW2mMsdl+nv5O1Qt5+snGBCPYQoZTkv6M28DdO646+1W39JDosA35BkyjYZfP0nDBSYcKMpyhRYqFQbBRTM9LKdullDullBdIKZdKKUcNNZBSvg20jHJ8ra+vBMB6oCRoqaNEdasRwWSy7XawV8U1B/hPH0rkCmdlYHfAkk+rFUfr0QiFjA6W5Zl01KoxKD3zpENhR9mAKuJ32tWqd3V/V4RCRoeqlh4S7IKiDJMTuFwbQXph6lknHSrMcNI36KWjN4xqw8Wnq8CCTQ+Om54nVc3KFG2zmVyvrWq9+hlojNPDiHgMkVEVhBDi10KIX430MlGOWwF/u4gE1gghNgshbjfxPiFh2eq2ZjN4BqDsnJMORWRiAljyKeX03jw+wjErW7qx24T52afVxoMVSEFEOMZLb1ZJXTufDFO46FLd0kNJdgp2KyYvYYOSM046FHEY5pKbVIWAyrWRSBg1Kq3yVVatg4zJkDnlpEOFGU4aO/vxWJhNPdYOYhOwGXACS4ADvtciVNJcxAghLkApiP/we3ullHIJcBnwRSHEuaN8/nYhxCYhxKbGxkYzRBqiqqUHISwoT2AUfpuy7KRDaUkOUsMJETTILFHO6g/+Oi6c1VUtqoqrw25yB66q9Sr7uejkkmERmfFA/b/lzxk3ORGWBVpUrVMJbgH6IRemRzjG8z8KSRnjYoyllNZE4kmp5orSFQEbXBVmJOGV0NxlnR9i1KdSSvmwlPJh4HTgfCnlr6WUvwYuQimJiBBCnI7yZ3xESjnUVkpKWeP72QA8DZw8kx4/9z4pZYWUsiI/39z2e9WtPRRlOM1Pna9ap3IfUgL7+cN28Bks/YxKONr3YvjXiBKWTl4lFWA/OX8lNzUJu02Er4SFUCvcms1QFzAGI66obO42f4w9g+DaFNCEByZk+iamwoJPqPpDce6sbu0ZpKvfbf4Yt1dD5zGYsiLg4YIoZFMHu2zLBjL8fk/zvRc2vn4STwGfklLu93s/VQiRbvwbWAXE5CmsbrEgB8LrgeoNalUwAhFXapx5CWSUqKSuOKequdv8Me7rUIlFI0xedpsgPy1C++3C68CeGPcr3PaeQTr6LJi86rbDYM+I3+OId2kAS28Cd5/y98QxlkUwGf6HEcY45MKTYRCsgvgJ8IEQ4iEhxMPAFuC/R/uAEOJRYB0wWwjhEkLcKoT4vBDi875TvgfkAr8bFs5aCLwrhNgGbABekFK+HOLfZQrVLb3ml9io3wkDnaof7whEHL5msytn9eE3oOVw+NexmI6+QVp7BplqdnSN4TwdRQkXZiRRH0pRxOGk5MDcD6v6TIO94V/HYoYmL7PH2Ji8RljdpiQ6SHc6IlvoFC9UhSw3PxzXzurK5m7AijFep6oQ+0qYDCeswpMhEmwU05+A5Shzz1PAmT7T02ifuV5KWSylTJBSlkgpH5BS3iulvNd3/LNSymxfKOtQOKuU8rCUcqHvNV9K+ePI/sTw6Bv0UNfRZ/6qwPA/jDp5OcMPETRYfKNyIMaxs9qyCKZRnKcGqqRJhCuvpTdBX7syg8QplS2+ycv0MV6nqghnFI94iilx+ktvUqGeNZsju46FWFavrWq98nfZApu4wyo8GSKheAbtQCPQCswazXE8ETAqjE4xuzxB1ToVkZB1clSCQUF6Ev3uMEMEDTInq9aEWx8Bt7UlgcPFsiixqnXKOR3AeWoQVlHE4ZSdo2oHxbESNnYQpprxpFST1wgmPAO1S4twjE/7uAo2iOPcnqoWVeY7OdFEX2VvKzTsGXWMVeHJxNibmIQQPwXeA74DfNP3utMyqeIAY9s41czaKlL6krdG3j2An4Mv0v/4pTdDd6NqdhOHWGL+GMN5alCY7qS1Z5B+dwSd+IRQpryqtdB0IPzrWEh1Sw95aYmkmVnmu+Ww+l6N9T1OD6Pw5HCcGXDax1Qhyv7OyK5lEZYEWlRvBOSYY1yQbm02dbA7iI+iWo5eIaW80vf6sGVSxQFHmpSCKM8zUUG0HlGlMMZceUUYp28w42IVQx2nq6+qlh6yUhLIcJpYKbd2u8rCDVIJRzyBLbpB1emPU2d1lRWBFkPO0zG+x5kq0zfirmdLbobB7rjNOzGS5My96Dr1vZq8dNTTTNkJj0IoHeUsqHcdvxxt7ibD6SDbzDLfQ/6HsbfmYILzyXBWH3ojLjOrLVl5VY3t44HjUTYRb8/TClQ/j62PxqUpr9KqySs5G/JmjXqaaV3PSipUWHgcmvL63R5qO/qsCQIoXqha3o6C1fWYglUQPcBWIcQfLMqkjjuONvVQnpeKCJCgEjZV68CZpZKsRqEg1N7Uo7H4RmUK2fKXyK9lMtasbtdBdjmkF416mqkduZbcBD1NsO+FyK9lIoMeL8faLOhRULVeRS/ZRp8+TBtjI+/k2BYVvhxHuFp7kdJkB7W7Xznlx1hIggq2aO7uZzDUwpNBEqyCeBZVUG8tKrPaeE1YjjR1m+t/gOP+hzEerOREOxmRhggaZJaoIn5xllk96PHiau01twPXkI9n7AeryCwzHqhidZlT4m6FW93Sg1dCmZnf4+4maD4ApcvHPNXUrmenX6OKJMbZGB81TNH5Jo7xsa3g6R9zFwzK2qAKT1qziwg2zPXhQC9LJIoD+gY9HGvvpcxM/0NXo6otE8R/Opi8dVx6s2p0s/8Vc65nAtUtPXi8kmn5aeZdtPmgqnwZxBhnpSSQaLeZM8Y2u9qpHY4vU94RKyavIP0PcNxUaspCJyUH5n1EJc0N9ER+PZMwxniamXOFYSYdIcfEn8J0E3fCAQg2iumIEOLw8JclEsUB1S09SAnleSaubqvfVz+DeLDAhHIb/sxcBenFceWstiQIwHiwAlS+HI4QIvKMdX/iMO/EssnLngSTFo95an66yYlcS2+C/nbY/U9zrmcCh5u6yU5JICvFlNJ0iur3IXcGpI1dOsi0gJYRCNbEVAGc4XudA/wK+KslEsUBxoNl6ta8er0qzVC8KKjT1eRl0oNld6g+Bgdfg7Yqc64ZIYcbrZi81qsGQbkzgjrdVCWcWQIzL40rU54lk1fVetUgyDF234Mkh52c1ETzJq+pZyvHeByVkDnS2G3uIsfr9eWYBGtpsLY3dbAmpma/V42U8h7gCkskigOONluxun1frboSgitrXZhhUoigwZJPqZ9x4qw2Jq/sVDMnL5//IcjAgrBbj45Eha9I4t74cFabPnkN9EDt1qAnL1BJn6aNsRCqEKVrQ9wUSTzS1E15nplm0gPQ2xKUeQkgNy0Jm4i9iWmJ36vCV0/JxMyb+OJIk4rPN23lNdinHqwA5b1HwrQQQYOsUpUX8cFfwBNBhrZJHGnqMnfy6qxXCVwhTV5Oc7fmMy72OavjY4Vr+uRVsxm87qDNpHB8oWMaC6/zOatjP8bd/W7qOvqYZqqPJ7hQeAO7TZCXlmRZNnWwJqaf+73+B1gKXGOJRHHA0aZuc81LtVtVg6AgVwVgchimwdKbobMWDqwx75phYvrkVR2889SgMMNJZ5+bngGTFKbNrsIxD78JzYfMuWaYWDJ5GWMcykLH7ESulByYfxVs+3vMO/pZY2lYDyl5kDs96I9YmQsRrInpAr/XJVLK26SU+yyRKA442mzy1nyo8uXYoYEGpoYIGsy6FNKKYu6s7u53U9/Rb+7kVbkOHMkBGwSNxHH7rYkP1+IbQdhjPsaWTV4F81SSXJBY0vWs4hZVETnGmdVHm1Q0lemBFiM0CBoJK7OpgzUx5fqS47b42oD+UgiRa4lEMaZv0ENte5/JDur3IWd6UFEJBkWZRikIE//j7QlqAjv4KrRVm3fdELEsgqmkAhzBmwUtiQDJKIY5l/uKJFqX4ToWpo+x0cckhEUOqIWO1+w4/SnLfJnVsTUzHWlSOxjT5opR+qiPRkGGk4ZIStePQrAmpsdQlVyvBj7u+/ffLZEoxlT6KoyWmRXiKqVSECE+WPlpFtV6X/IpJdMHsQtCM33y6u9UDWxCfLCGSpqY/XAt/YzKx9jznLnXDYEjjSZH4jXshv6O0Mc40tajgTCc1cc+UK8Ycbipm+JMp3lVXMMwkwJ88YIZPP2FsUO7wyFYBVEspfyhlPKI7/UjVGOfCYexKjBt8mo+5EveCk1BJDpUKd/adpO3jtllKvM3hs5q08OIXZvGbBAUCMOMV9ducsOfaReocY5hOOaRpm4mmTl5jdHdbCQKh8bY5O/xwmtVGfAYj7HpkY6OZCgO3kwKMDkr2fyqDz6CVRBrhBDXCSFsvtc1QPyk5ZrIwQalIEzL8B1y7IX2YAFMzk6mps2CbmVLb4aOGpUXEQMsmbzGaBAUiPQkB+lJDo61mTx52WzKWV35LjTuH/t8Czjc1G1yBvU6SJ+kouFCYFKW6qdi+kLHmanKgO94QrWYjQHmK4iR+6jHilEVhBCiUwjRAdwG/A3o970eA263Xrzoc7Chi+JMp3n186vWqwJ9Y1S+DERJdjKuVgvKCsy+DFILYmbDNX/yWguFp6neASEghGCyVWO8+EawJcTEWS2l5HCjiWHEUqoggBCdpwB5aYkkOWzWjHHFLaoM+I7o96xu7R6grWfQAjNp6AtJKxlVQUgp06WUGVLKdCAPWAlcDFwAXBkF+aLOwcYuZhSYGX65wdc2MJTmfYqS7BRqWnsjaz0aCHuC2kXsfyXqPaullBwxc/JyD6jmKlPPDuvjJdkpQ90DTSWtAOZ+SDmrB7rNv/4otPYM0tHnNi+MuK0SOo8FVcJkOEII30LHgjGetERFrW18MOo9qw8bZUzMWuhUv6/MpGGMsZUEG8X0WeAt4GXg+76f3wvicw8KIRqEEAHTHoXiV0KIg0KI7UKIJX7HbhJCHPC9bgpGzkjxeiWHGrqZbpZ5qacFmvaF7KA2KMlOpt/tpdGKSo0Vt6i4/Q33m3/tUWjuHjB38qrdphoEhflgTclJ9pVstmCCWfY56GtTBeaiyKFGn5nULCVcuVb9DHOMLVPCQsCy21XP6qPvmH/9UThkmKLN+h5XrlPh0SXB55hEg2CXtV9B1WGqlFJeACwG2oP43EPA6lGOXwbM9L1uB34PIITIAe4GlgPLgLuFEMEHX4dJbUcfvYMe83YQ1RvUzzC3jSXZyn5rycOVUQzzPqqc1VFs5bi/Xt1rplljXPme+hli5IdBSXYKXf1u2nstqJ9UukKtcN//Q1RXuAfq1eQ1s9DEMXZmQf7csD5umakUYMEnVP2t9/9gzfVH4EBDJ0kOm3n9TCrXqgZBSSZaL0wgWAXRJ6XsAxBCJEkp9wKzx/qQlPJtoGWUUz4C/Fkq1gNZQohi4FLgVSlli5SyFXiV0RWNKRgOatMURNVaZYeetGTscwNQ4mtCYomCAFj+eRW6uO0xa64fAGOMZxWmm3PByrXKvxNCjok/liphIWDFHdC4B468Zf71R+BAQycpiXYmZSabc8FKX42rMMykoL7HrT2DdPVbEDWX4FTm0r0vRLXU+oGGLqbnp2G3mdBQbLBPlTGJM/MSBK8gXEKILOCfwKtCiGeAShPuPxnwz9hy+d4b6f2TEELcLoTYJITY1NjYGJEwpiuIo++pnrJjtA0ciclZxuRl0eqrpEIpr/f/oKpIRoED9V2kJzmGchAiwutRQQARPFjHFYRFYzz/Y6p0wvp7rbl+AA7UdzGzIA2bGZNXZz20HIrvMT7jsyqKbcMfrbl+AA7Ud5m3Qzu2RTUIGq8KQkp5lZSyTUr5feC7wAPARy2UK2iklPdJKSuklBX5+eGtIg0ONnSRlZJArhkVRvs7VRJP2cqwL5Ga5CAnNdG6HYQQahfRfAAO/8uaewzjQEMnMwrTzGnl2rBb9QcojWTysniXluBU/p79L0ctIOBAQyczCkzaoVUZ/ofwggDAT0G0WDTGGZNUM6Etf4lKfabufjc1bb0mmkl9YxymmdRKQt4zSinfklI+K6U0o8xoDTDF7/cS33sjvW8phxq6mJFv0uRV9T5IT0QKArAuAsRg/kdVyGuUbLgH6ruYZdbkFaHzFCAzOYF0p8PaMY5iQEB77yD1Hf0m+h/WqoS0EJO3/DmuhC3sBLfiDrVY2G69udSwNMw000xaME8VIowzwjMqmsezwKd90UwrgHYpZS0qCW+VECLb55xeRRQS80wNca18F2yOkCpfBsJSBx+oxi9n3KoqvDYdtO4+QHNXP83dA+Y6TzNLIWvK2OeOgoqysXCMM4pVBdIoBAQcbDA7CGCd+g5HkLyVl5aIM8FmrRIuOUP1W4mCufSAoSDMGGOPWwWzxOHuASxWEEKIR4F1wGwhhEsIcasQ4vO+fhIALwKHgYPAH4EvAEgpW4AfAht9rx/43rOMlu4BWroHTPQ/vOvzP0QWamhZLoQ/Sz+jut2t/61198BkH4+RvDU18gfL8l0awPI7VEDAlj9behsjgsmUIIDeNqjfGZF5CYxcCItCXY/fBFZ8AZr2q2KUFnKgoZNEu41SMyKY6neoyrRx6H8AixWElPJ6KWWxlDJBSlkipXxASnmvlPJe33EppfyilHK6lHKBlHKT32cflFLO8L0sT/ndV+dbeZnxYPV3Qc2WiM1LYHEuhEF6ISy8Hj54BLoaLLvNfjMjmJr2q+5tJjxYhoKwVAmXLIWpK2Hdb1Vyn0UcaOjCmWAbCnCIiMq1gDRvjNss3KWB2qVlToF377H0Ngfru5iWn4rDbsL0ecSXvxGhEraKWJuY4oa9daqey9wiEyav6vWm+B/A4jBMf876smpqtP73lt3iYH0nqYl2ijODa7s6KoffVD+nnR/xpSzNhfBn5VdVDaydT1h2iwMNykxqSgTT4TeU/yHEGleBiMouzZ4AZ35JOdar3rfsNvsbOs3zPxx+E/LnKDNkHKIVhI99dZ1kpySQn25C+OVRw/8QXga1P4aDr7rF4tVX3gyYeyVsfMCy4mcHGrqYUZhuThDAoTcgu1xVTY2QqCnhGRermlHv3mOZnfxAfSczzQoCOPym2j04In8mSrJTaOsZpLPPYiW85FOQnAPv3WPJ5XsHPLhaTYpgGuxTuzQTFjlWoRWEjz11ncwpyjBp8vqXSpmP0P8AxycvyxUEqBVuf7slBeaklOyv7zTJsTeolLBJD9YUnxI2eoFYhhBw9ldV+ZX9L5t++fbeQWrb+8wJAmivUWa8aRdEfi38v8cWK+HEVFj+Odj3IjTsMf3y++s7kRJmmTHGrg2qTIxJY2wFWkGgajDtr+tkTrEJK6+uBlUfaMZFkV8LSElUSWVHmqKgICYvhfJzYf3vTO+G1tjZT1PXAPOKQ6u4GpCazcqxN92cB2tqrlIQRptOS5l/lSqZ/e7/mV5+Y2+tz0xqxhibaMKD470/KqMxxstuV6ax935l+qX3mD3Gwg5l8el/AK0gAKhq6aF30MMcM/wPh95QP01SEABTc1Oj82ABrPwadNbCtkdNvexu0ycvAWXnRH4tVEJiQXoSR5uiMMZ2h/L3uDYcryNlEsYYzzdrjFPzoXB+5NcCynyFA49E43uckqP6cez4B7RVmXrpPbUdpCbah3adEXHoDeXfSTLJJGgBWkFw3EE9p8iEB+vQ66q0QtHCyK/lozw3NTqrW1Db3clL4e2fmxpts6dWRYmZsoM49IaKeTcxsagsN9V6E5PB4hshrRDe+G9TdxF7ajvITU2M3I8mpVIQ084Puf/DSKQlOchLi5ISBjjr31T5jbf/19TL7q7tYE5xRuRBAL2tqtKCSbtgq9AKAthb14kQJoRfer1w8HXV0jPMwmaBmJqXQlPXgPUOPlATwgXfhvYq2Gpe3+o9tR1MzkomMyXCblk9LeDaqMbYRMryUqKzugVISIZzvqF2EEfeNu2ye2o7mVtsgh+tdqsKIZ5u3i4YoDwvhaPRUsKZk1URv62PQMsRUy4ppWRvbSdzzTBFH3wdkKZ/j81GKwhgb20nZbmpkbfArNsOPU2mmpdA7SAgCk5Ug+kXqQist//XNF/EntoOkx6s11QI8ezLI7+WH1NzU2ns7KfbioqjgVhyk2rhadIuwu3xsq/epMlr30tq9T1zVeTX8mNqbmr0dhAAK7+uoglN2kW4Wnvp7Hczrzgz8ovte1GZ8CZXRH4tC9EKAthX32mO/+HAGkBYsLpVCiJqZiZjF9FRY0rmb9+gh0ONXeaYl/a9qMwzkxZHfi0/yqM9xglOOPcbKmfmUOSFEg83dTPg9prj49n3ologpOZGfi0/yvNSaYimEs4ohopblT+t+VDElzvuR4twrvAMwoHXYNalploarCC+pYsCgx4vA24vs81QEHueU3Vr0goiv5YfQ1E20Vx9lZ+nsjvf/l8YjCw0cX99J15pgoPaPWDZg2VE2RyNRrSYweJPqcxfE3YRRnTNvEkRjnG7C+p2qL7lJlMW7Z0wqNBteyK8+ZOIL7WntgMhiHyuqFyrwslN3gVbwSmvIBLsNt6760K+fOHMyC7UWqlMTHM+ZI5gfkQ11NVACLjgO9BVp8pDRIBpoYGV76nwVgserKiGuho4kuDcb0LNJtjzbESX2l3bQaLdFnm73H0vqZ8WjHFZXgzGOK0Alt8OOx6H2u0RXWpPbQfluamkJDoik2nfS2BPiusEOYNTXkEYRByVsPcF9XPOFZELE4CohroalJ0Ns69QMfsR1GjaU6tKbERc3GzfS+Bwqt2NyUQ11NWfRTeoUs+vfi8if8+e2k5mFKSREGl9oH0vQe4MyItwwRSAqb4dxJFoj/HKr0NyNqz5TkQ7td21HZEvcqSE/S8p5WBCIq3VaAVhFntfUA967nRLLl+emxr9Bwvgkh+Au0+ZQcJkZ007cyMNDfR61Cp7+kVhd+gbi7K8KIYTG9gdsOpHql1mmB3RpJTsrGlnfqTmpZ4W1RrVItNHWpKD/Fgo4eQsOP9bKmIszAz2tp4Bqlt6Izfh1W5V/9cWLSTNRisIM+g4pswfcz9s2S2mF6TS3D1AW491lUADkjdDtXTc8nBYpQvcHi87j7VzeklWZHJUvqcS+BZ8PLLrjML0/FQONcZACc+4SNVpevv/qUk6RFytvbR0D3D6lKzI5Nj9T/C6YcEnIrvOKEzLS+VwLBY6FZ+B3Jmw5rvKSRwi213tACyM9Hu84wnVp36edXOFmWgFYQY7HgcknH6NZbcwCrAZPRWiynn/obI9Xwl9i76/vou+QS8Lp0QYGrjjcUhMg1mrI7vOKMwoSKele4BmK0urj8SqH6lmQmE4U49PXpGO8ZOQNwuKFkR2nVGYWZjGgfpOa0urB8KeAKt+qNrrbnow5I9vd7UBsCCSMfZ6YOeTMPMSZfIaB2gFYQbb/q5S5i0yL8HxJjsHYqEgUnLgvLtUlvjuZ0L6qPFgRbTycvfD7mfVttwi8xIc7xAWkzEumKtak278IxzbGtJHt7vaSLTbIqsE0F6jdmkLPmFa9nQgZhak09HnprEzBkp41mpl+//Xj6GzLqSPbnO1My0vlczkCBI9K9eqXfBpV4d/jSijFUSk1O2Ehl1w+rWW3mZyVjLJCfahjmFRZ9ntamX50n9AX3vQH9vmaiczOWEoSigs9r8MfW2Wmj6AoSqoMVEQABd+V5Vpef6rarUZJNtcbcwtTifREcHjvP3vgLR88oqpEhYCLv+58qm9/K2QPrrd1cbpke7Qtj0KCamWhBBbhVYQkbLlz8qmOP9jlt7GZhNML0jlQIO1PY1HxO6AK38JXfXwrx8F/bFt1erBiqj8w6YHIaPE8rIERRlO0pIcHKyP0RgnZ8FlP1E1ejbeH9RHPF7JDlc7CyPxP3g9sPlPqvihhbtggBmGEo7VGOfNgHPvhF1PwYHgWpPWd/RR39EfmR+tt1WZl06/ZlxELxloBREJ/Z2w9W+qhLPJWaeBmFmQHhsfhMHkpbDsNhVtU71xzNP7Bj3sq++MbOXVfEgVjlt6M9giLIUyBkIIZhSkxW4HAWqhMf0ieP2H0FY95umHG7voHvBENnkd+peqelpxS/jXCJL8tCSyUhJiO8Znf0X5Wl74umoPPAbbqtsAIvOjbXtM7VwqPhP+NWKApQpCCLFaCLFPCHFQCHFXgOP/J4TY6nvtF0K0+R3z+B2LLIvIKrY9phK3ln8uKrebUZBGbXtfdIr2jcSF34XMEnj69jEfrl3H2vF4ZWT+h00Pqno6Sz4d/jVCYGasFYQQ8KFfABL+eceYnee2meGg3vgApBZYkuQ5HCGEGuNYmUpBJShe+SulgF8Z29S03dWO3SbCr8EkpfoeT66AYvOqPEcDyxSEEMIO/Ba4DJgHXC+EmOd/jpTya1LKRVLKRcCvgaf8Dvcax6SU8RcT5vWqlfSkxWplHQUM+21MQjENnBlw1b2qQuYr3x711G3VvskrXPNHb5sy4c39MKQXhneNEJlZmEZjZ3/0w4n9yS6Dy34KR9+Bdb8Z9dTtrjZSE+1MCzeDutHX3W7pTeBIDO8aITKjIJ39DTGIZPJn6pmqDMeWP8Oe50c9dZurjVmF6eEX89z/iurOt+y28D4fQ6zcQSwDDkopD0spB4DHgI+Mcv71gLldaqxkzzOqdeSKL1oa9eGP0Sh9f6zstwZlK9U2fcvDxzPIA7C5qpXiTCeFGc7w7rPhj9DfAed8PUxBQyem4cT+LLpB9Qh//QejlojYdLSVhVOysIebhPjOL1T58eWfD1PQ0JlZkEZbzyDN3TFUwgDnfxuKTodn/23EqCaPV/JBVRtLSrPCu4eU8PbPVBfBcRS9ZGClgpgM+BtRXb73TkIIMRUoB/zLWjqFEJuEEOuFEB8d6SZCiNt9521qbGw0Qewg8HrhzZ9C3mw4zVrntD+lOSk4E2zsq4uxggBVp6nodPjnF6Dl8EmHpZRsPNLCGWVhNvXp74L1v4VZl1kalz8cI5JpT6zHWAhlBknJhcdvUrupYXT0DbK3riP8MW45ovJLKm6B1LzI5A0Bo+9KzL/HjkS4+n5VjPKJWwIm0O2p7aCr382y8jDH+MhbqtbW2V9VuRjjjHhxUl8HPCGl9I/tmyqlrAA+CdwjhAgYXiGlvE9KWSGlrMjPz4+GrCoConEPnP8fljtO/bHbBLOLMth1LPgwU8twJMI1vlLgj91wkj+iuqWXhs5+zgj3wVr7axX5ce6dEQoaGpOzkslMTmD3sY6o3jcgKTlwzcPKVv7krSeFvm6pbMUrCX/y+tcP1aR15pdMEDZ4jHLZcTHG+bPhw79SOSABQl83HlWZ7RXhKGGvF177vur7seiGCAWNDVYqiBpgit/vJb73AnEdw8xLUsoa38/DwJuAuQ0AwqW/U6XrFy2AeVdF/fbzJ2Ww+1hHbO23Bjnl8Ik/QeNeePpzJ0xgG3wP1rJwHqy2anjvHrUlL4luQxUhBPOKM9gdD0oYoHQFXP4z1SjptbtPOLTpaCt2m2BROD6eqvUq7PKsL6u+CVEkNy2JogxnfCx0QIWenvkllaS46U8nHNp0tJXJWclMzkoO/brbH1Mhyxd/X/X/GIdYqSA2AjOFEOVCiESUEjgpGkkIMQfIBtb5vZcthEjy/TsPOBvYbaGswfPmT6DzGFzxi5g0+5g/KYOOPjeu1sh6NJjG9Avh0v+Gvc+rBC+f4tp4pIXM5IQhx3rQSAkvfAMQcPF/mS5uMMyflMHeuk7cntEjiKJGxWdUPay1v4Z37xl6e8PRFk6blEFqUojlp9398PzX1Mp25VdNFTVY5k/KYFc87CAMLv4vVQ/rha/Drn8Cyky64WgLFWVhlMXoalQLyZIzLE/wtBLLZjgppRv4EvAKsAf4h5RylxDiB0II/6ik64DH5IlL4rnAJiHENuAN4CdSytgriENvqKiSiltUY6AYYHRlM7pbxQUr7oBz7lQRIWv+E6RkY2ULFVOzQ6/guuVhOPCKWnVlTRnzdCuYPzmDfrc3NkXlRuKy/6d2VK/dDRvvp9/tYVt1W3imj3/9CBp2K9NKjJK25k/K4FBjF70DwWeMW4rdoUymJWfAk5+FA69S1dJDY2d/6D4eKeG5ryhrw4d/Hfdd40Yjws4XoyOlfBF4cdh73xv2+/cDfG4tED3PZDC0HoWnblOO6VU/jpkYc4oysAnYdayDS+cXxUyOk7jwP9UDse439HW1Utm4mmsqQpzgqzfAi/+u6uUsu90SMYPBiHffdax9yKEac2x2uOoPMNADL3yDptpa+t2LQ5+8dj4Fa3+lFjkzL7FG1iCYNykDr4S9dR0sLo2TwnWJqfDJf8DDV8Kj11O78EfAlNDH+J3/hX0vqJ11wVxLRI0W41e1RZOOY/DXq1WUw7V/sbRg3Fgk+2Le48ZGbiCEit0/999x7niEPyX8P84sDGF1WLcDHr0eMibBx/8U01XX9PxUkhw2dtXE0S4NlEP5mj/DgmuYvOV/+ZnjD1RMCiF34eBrKvmu9ExYHXkLzkiYP0kp4bjaCYMqd3LTc1C6ghUf/Affcj7JzLwQ/Aeb/qR2aKdfCyu+YJmY0UIriLGo2QL3X6LipK9/TEU9xJi4s98aCAEXfoenSu5iuW0vpz93uarCOpZDfd/L8NAVKsP1hidU9E4McdhtzClKj7/JC1T02Mfu46n0T3K14x3yHrkEKteN/hkjk/fR61WnuGsfUWMdQ0qyk8lwOuLze5ychbzhCZ63XcDneBLbQ5dDw97RP+NxK8Xw/Fdh5ioVohyl/Cgr0QoC1APW3Xz8dymhcb9ylt5/MUgv3PyCyr6MAxZMzqS2vY+Gzr5YixKQX7au4Mclv0OkFcI/PgUPrILtj58YCisluDbD4zfDo9eqRKLPvKSKqcUBp03OZIerHa83DqLFhtE76OWulg/zyKxfqxj+P62Gv12rMnb925Z63KqO1Z8/rJzSZSvV6jgKdcPGQgjB/ElqjOORQ61uvtRzG+8u/KnKNv/9mfDU5+Doe2pcDQb71CLovvNVQtyiG5UCHqdRS8Ox1AcxLvAMwl8/BoM9apJKyoTuBlW11JagagBd/H219YwTDJvtlso2Vp8WR34IoKq5h8rmHqaddQaseAs++IvK1n3qs4BQobEJKdDuUiW8E1Lh3H9X+Q4xXtX6s7g0m0fer+JgY1f8+CF8bDjawoDHS2nFaii7Gtb/Tr32v6y+sznl6mdbJQx0qRLil/1MRULFkcN0cWkW9719mN4BT/hlLCzi3QMq6XbqeZ+GVZ+Ad36uAii2PwaOZDXG0qt8k+4+VR7lEw+pwp0TCK0ghA0+9TRUrVO9HQa6VEGtyYth9hVRjxEPhvmTMkiwCz6obo07BfHOQfVgnTMrX0WGVHwGltykEpEq31NtS939Klqk5AyYc3lcdtcySitsqWyNOwXxzv5GEu02lWOSaFfK9awvq6qs1euh+aBK0ipbCVPPUiaPGPrNRmLp1GzcXsl2VxvLp8V+V+PPuwebmJqbwpScFCAFVv83XPgdpYRdm5XyBRUaO/0CKD9vXGZKj4VWEDa7SkYqXRFrSYLGmWBn/qRMPqhsi7UoJ/HO/iYmZTqZlucXPmmzQfk56jVOKM9LJTslgS1VrVy3rDTW4pzAuwebqCjLPnHV7UiE2avVa5wwtBOuii8FMejxsu5QMx9dPKwyUGKqCjUehzWVwiV+9puakFhSms32mjYG4yWZC1XYbO2hJlbOzIusQVAcIIRgcWk2W6raYi3KCTR09LG3rpOVM6NXO8kqclITKc9LZUtVa6xFOYEPqtroHvBwzswole6JY7SCGKcsmZpF36CXPXEUafNBVSsdfe4J82AtKc3iYEMX7T0x7L8xjLf2KxPeuRNkjBeXZvFBVWt8lI7x8ea+Buw2wZnT42dXEyu0ghinLBlyVMfP6uvV3fUk2AXnzZ4ok5ca4w+q42eM1+yupzjTyfxJGbEWxRSWlGbT1DVAVUtPrEUZYs3uelZMyyEzeeL5FEJFK4hxyiRfAbH1h1tiLQqg6ta8squOM6fnkeGcGA/WoilZOGyC94/Exxj3Dnh450Ajq+YVjnsTnoGRpRwvY3yosYuDDV1cMjc6DariHa0gxjFnTc9l3eFmPHEQq3+woYujzT2smjdxHqzUJAeLpmSx9mBTrEUB4O0DjfQNelkVTyVWImRWYRp5aUlxM8av7q4H4JIJNMaRoBXEOObsGXm09w7GRV39NcaDNYEUBKgx3l7THhd+iDW76slwOsLv/xCHCCE4a3ou7x1qjgs/xJpddZw2OSO88t4TEK0gxjFn+Zxo7x2K/eprza46Fk3JCr+9aJxy9ow8pIR1h5vHPtlC3B4v/9pbz0VzC0mwT6zH9uwZuTR29nMgxm1eGzr7+KC6jUvm6t2DwcT6pp1iFGQ4mVmQxnsx3p5Xt/SwzdUeX9VlTWLRlCySE+ysjbESXnuomdaeQS6dP7F2aABnTVchu7H+Hr+0ow4pibvk01iiFcQ45+wZeWw82kLfYOzq6v/zA9Uo8MOLJsVMBqtIdNhYVp7DuzGevP65tYZ0p4PzZxfEVA4rmJKTwtTclJgriKc/qGFOUTqzi+Ircz6WaAUxzjl/dj59g96YrXCllDy9tYZl5TkT1m57/ux8Djd2c7gxNiaQngE3r+ys44oFxTgT4qtmkVmcNyufdw82xayB0NGmbrZWt3HV8OzpUxytIMY5Z07PJS3JwZpd9TG5/46adg43dk/oB8twvBsRLtHm1d31dA94Ti79MIFYNa+IvkEv7/iK5EWbZ7YeQ4iJuQuOBK0gxjlJDjvnzc7ntT0NMSlN/eRmF4l2G5efFn9FDc2iJDuF+ZMyhiK1os0Tm11MynSq4nwTlOXTcshwOmIyxl6v5MktLlaU51KcOTF3weFiqYIQQqwWQuwTQhwUQtwV4PjNQohGIcRW3+uzfsduEkIc8L1uslLO8c6qeYU0dfXzQXVbVO/bM+DmqS01XL6giMyUiZEcNxKr5hWxpaqVxs7+sU82kcrmbt450MS1Z5SG3t97HJFgt3HR3EJe31OPO8r1xd452ERVSw/XL4+voozxgGUKQghhB34LXAbMA64XQswLcOrfpZSLfK/7fZ/NAe4GlgPLgLuFEPFXEzpOuGBOAQl2wcs7a6N632e3HqOz380NK6ZG9b6xYNX8QqSENbvronrfv22owm4TXHtGiP29xyGr5hXS2jPIhqPRzap+ZH0luamJrJ6AUXiRYuUOYhlwUEp5WEo5ADwGfCTIz14KvCqlbJFStgKvAuOnjnGUyXAmcP7sAv659VjUVl9SSv76fiWzC9OpmDrxdfeconRmFKTx9JaaqN2z3+3h8U0uLplbSFHmxMovCcT5swtIS3JEdYxr23t5fW8D15wxhUSHtrgPx8oRmQxU+/3u8r03nKuFENuFEE8IIYxlUrCfRQhxuxBikxBiU2NjbBxc8cDVS0po7OznnSiFCm440sLOmg5uPHPqhKkLNBpCCK5eUsKmylaONHVH5Z5Pb6mhpXuAG0+BHRpAcqKdKxYU8+KOWnoG3GN/wAQeeu8oUko+GWc9P+KFWKvM54AyKeXpqF3Cw6FeQEp5n5SyQkpZkZ8/MaqIhsOFcwrITkngic2uqNzv928dIjc1kY8vKYnK/eKBqxZPxibgqS3Wj7HHK7nv7cOcNjmDs2ecOmWnr15aQveAh5d3Wm/Ka+8d5JH3q/jQ6ZN8neM0w7FSQdQA/obTEt97Q0gpm6WUhtfvfmBpsJ/VnEiiw8ZHFk3m1d31tHQPWHqv3cc6eHNfI585uyzueglbSVGmk5Uz83lis8tyU96aXXUcburmjvNmnBI7NIMzyrIpzUnh7xurxz45Qv66vpKufjefO2+a5fcar1ipIDYCM4UQ5UKIROA64Fn/E4QQ/rGRHwb2+P79CrBKCJHtc06v8r2nGYUblpcy4PbyyPpKS+/zq9cPkJbk4FMryiy9Tzxyw/JSatv7eMnCFa7HK/nl6wcoy0055co+CCH45PJS3j/Sws6adsvu09k3yAPvHuG8WfnMn5Rp2X3GO5YpCCmlG/gSamLfA/xDSrlLCPEDIcSHfad9WQixSwixDfgycLPvsy3AD1FKZiPwA997mlGYWZjO+bPzeXjdUctKb2yubOXlXXXcds60CR/aGoiL5xZSnpfK/e8ctqz66DNba9hb18nXV83GPoFDW0fi+mWlpCbauf+dw5bd4763D9PSPcCdq2Zbdo+JgKU+CCnli1LKWVLK6VLKH/ve+56U8lnfv78lpZwvpVwopbxASrnX77MPSiln+F5/slLOicRt50yjqWtgqD6SmUgp+clLe8hLS+Kz55Sbfv3xgN0muHVlOdtc7ZY0uekb9PDzNftZMDmTDy2YuMmHo5GZnMB1y0p5bnstNW29pl+/oaOP+985wpULJ7GgRO8eRiPWTmqNyZw1PZcFkzP59b8Omr6LeGbrMTYebeVrl8wkNclh6rXHE1cvKSEvLYmfr9ln+i7id28eoqatl29dPmdCJ8aNxS0ry7EJ+NVrB0y/9g9f2IPHK7lz1SzTrz3R0ApigiGE4FuXzaGmrZeH1x417bqt3QP84PndLC7N4rozTu2QwOREO1+9eCYbj7aaWhriQH0nv3/zIFctnjxUAvtUZXJWMjedWcY/Nlezp9a8hlhv7G3guW3H+OIFM5iam2radScqWkFMQM6akccFs/P5zRsHTSkNIaXku8/spKN3kP/52IJT0i4+nOvOmML0/FR+8tJeU3ZqA24vdz6xndQkB/95xVwTJBz/fOnCGaQnOfjxC3tM2am19Qzwnad3MKMgjc+fryOXgkEriAnKd66YR7/by7ee2h7xw/W3DVU8v72Wr10yizlFGSZJOL5x2G3cfeV8jjR18/M1+yK+3k9f3su26jb++6oF5KYlmSDh+CcrJZE7L53NuwebeHRDZGGvUkrufHwbjV39/OKahSQ5Tp3w7EjQCmKCMqMgjX+/dDav7WmIKKZ8w5EW/uu53Zw3K587zptuooTjn3Nn5XPD8lLuf/cI6w6F35L06Q9cPPDuEW46cyqXn6KO6ZG4cflUzp6Ry49e2B1RBvs9rx3gtT0NfOfyuZxekmWegBMcrSAmMLecXc7ZM3L53jO72BRGAbTdxzq49eGNlGQnc8+1i05pp+lIfPvyuZTnpfLFv22hsjn0CeyNfQ188/HtrJiWw7e1aekkbDbBzz6+kESHjVsf3kh7z2DI1/jL+kp++foBPr60hJvOKjNfyAmMVhATGJtN8NtPLmFydjK3PLSRzZWtQX92/eFmrrtvHamJDv5y63KyUxMtlHT8kprk4IGbzsArJTfc/35ISuKZrTXc/udNzCpM575PV2izxwhMykrmDzcupbqlh08/+D6tQVYKkFLy2zcO8t1/7uSiOQX85GMLTqmsdDPQCmKCk5WSyF9uXUZOaiI33v8+j2+qHtUn4fZ4+d2bB/n0AxvIT0/i8c+fOWFbiZpFeV4qf7llOd39bq7+/Vre3j960cieATfff3YXX3lsK0tKs3n0thVkOE+9pMNQWD4tl9/fsJQ9dZ1c/fu17Do2epZ1c1c/X/zbFn72yj4+smgSv7txCQ67nu5CRViVDRoLKioq5KZNm2ItRlzS0NnHlx/9gPWHW1hWnsPnzp3Gypl5Q6vWtp4B1uyq54/vHOZAQxeXnVbE/3xsAVkpeucQLAcbuvjCI5vZX6/G7+azyqgoyxmK+qrv6OO5bcd44N0j1Lb3cfNZZXzr8jl65xACG4608G+PbqG5a4BrzpjCJ5eVMn9SBkIIpJRUNvfw1Ac1PPTeEfoGvXz1kpl8/tzp2jw6CkKIzVLKioDHtII4dfB4JY+8X8mvXj9AU9cADpugKNOJ2yOp6+gDYFZhGl+/ZBarJ3ALUSvpHfBw71uHuP+dw3QPeEhy2CjMcNIz4KGpS4UcV0zN5t9Xz2FZ+cRtIWolLd0D/PK1/fxtQxWDHklakoPctETaewdp8/koLplXyDcvnc2swvQYSxv/aAWhOYEBt2oOv6mylbr2Puw2QVluCitn5nP65Ey92jKBngE3r+9pYFt1G01d/SQ57MwoSOP82fnM1JOWKbR0D/Da7np2HWunvXeQlCQHc4vSuXBuoTaLhoBWEBqNRqMJyGgKQnttNBqNRhMQrSA0Go1GExCtIDQajUYTEK0gNBqNRhMQrSA0Go1GExCtIDQajUYTEK0gNBqNRhMQrSA0Go1GE5AJlSgnhGgEKsP8eB7QZKI44wH9N098TrW/F/TfHCpTpZT5gQ5MKAURCUKITSNlE05U9N888TnV/l7Qf7OZaBOTRqPRaAKiFYRGo9FoAqIVxHHui7UAMUD/zROfU+3vBf03m4b2QWg0Go0mIHoHodFoNJqAaAWh0Wg0moCc8gpCCLFaCLFPCHFQCHFXrOWxGiHEFCHEG0KI3UKIXUKIr8RapmghhLALIT4QQjwfa1migRAiSwjxhBBirxBijxDizFjLZDVCiK/5vtc7hRCPCiGcsZbJbIQQDwohGoQQO/3eyxFCvCqEOOD7mW3GvU5pBSGEsAO/BS4D5gHXCyHmxVYqy3ED35BSzgNWAF88Bf5mg68Ae2ItRBT5JfCylHIOsJAJ/rcLISYDXwYqpJSnAXbguthKZQkPAauHvXcX8LqUcibwuu/3iDmlFQSwDDgopTwspRwAHgM+EmOZLEVKWSul3OL7dydq0pgcW6msRwhRAlwB3B9rWaKBECITOBd4AEBKOSClbIupUNHBASQLIRxACnAsxvKYjpTybaBl2NsfAR72/fth4KNm3OtUVxCTgWq/312cApOlgRCiDFgMvB9jUaLBPcC/A94YyxEtyoFG4E8+s9r9QojUWAtlJVLKGuB/gSqgFmiXUq6JrVRRo1BKWev7dx1QaMZFT3UFccoihEgDngS+KqXsiLU8ViKE+BDQIKXcHGtZoogDWAL8Xkq5GOjGJLNDvOKzu38EpRwnAalCiBtjK1X0kSp3wZT8hVNdQdQAU/x+L/G9N6ERQiSglMMjUsqnYi1PFDgb+LAQ4ijKjHihEOKvsRXJclyAS0pp7A6fQCmMiczFwBEpZaOUchB4CjgrxjJFi3ohRDGA72eDGRc91RXERmCmEKJcCJGIcmg9G2OZLEUIIVB26T1Syl/EWp5oIKX8lpSyREpZhvo//peUckKvLKWUdUC1EGK2762LgN0xFCkaVAErhBApvu/5RUxwx7wfzwI3+f59E/CMGRd1mHGR8YqU0i2E+BLwCiri4UEp5a4Yi2U1ZwOfAnYIIbb63vu2lPLF2ImksYh/Ax7xLX4OA5+JsTyWIqV8XwjxBLAFFa33AROw7IYQ4lHgfCBPCOEC7gZ+AvxDCHErquXBNabcS5fa0Gg0Gk0gTnUTk0aj0WhGQCsIjUaj0QREKwiNRqPRBEQrCI1Go9EERCsIjUaj0QREKwiNJkx81VK/4Pv3JF+IpUYzYdBhrhpNmPhqWT3vqxyq0Uw4TulEOY0mQn4CTPclHB4A5kopTxNC3IyqppkKzEQVkEtEJSj2A5dLKVuEENNR5ebzgR7gNinl3mj/ERrNSGgTk0YTPncBh6SUi4BvDjt2GvAx4Azgx0CPr2jeOuDTvnPuA/5NSrkUuBP4XTSE1miCRe8gNBpreMPXb6NTCNEOPOd7fwdwuq+a7lnA46psEABJ0RdToxkZrSA0Gmvo9/u31+93L+q5swFtvt2HRhOXaBOTRhM+nUB6OB/09eA4IoT4BKgqu0KIhWYKp9FEilYQGk2YSCmbgfd8zeN/FsYlbgBuFUJsA3YxwdvdasYfOsxVo9FoNAHROwiNRqPRBEQrCI1Go9EERCsIjUaj0QREKwiNRqPRBEQrCI1Go9EERCsIjUaj0QREKwiNRqPRBOT/A95TO9uoc643AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(time_hist, num_hist[:,0], label='X') # plot prey abundance vs time\n", "plt.plot(time_hist, num_hist[:,1], label='Y') # plot predator abundance vs time\n", "plt.xlabel('time')\n", "plt.ylabel('abundance')\n", "plt.legend(loc='upper right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the phase of $Y(t)$ is behind that of $X(t)$, which means that the closed orbits in the previous plot go in the counterclockwise direction. This can be explained by the intuitive argument that goes like: first the prey grows in number, then the predator has more food to eat and grows in number, then the prey is consumed fast and reduces in number, then the predator runs out of food and reduces in number, and finally the prey gets the chance to grow again, etc. Indeed, a main point that the predator-prey model was used to illustrate is that, in nature, the dynamics of populations (and many other things in biology) do not have to reach an equilibrium state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The existence of closed orbits in a dynamical system is a nontrivial result. Here we even have a family of closed orbits as the distance from the neutrally stable point varies. This is in fact because the particular equations of the Lotka-Volterra system has a symmetry, which leads to a conservation law, like in classical mechanics. The conserved quantity (or \"integral of motion\") here is $I = g x - d \\log(x) + f y - r \\log(y)$.\n", "\n", "**Exercise**: Check that $dI/dt = 0$ using the dynamical equations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Limit Cycle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The closed orbits found above share one property in common with the steady states. Once the system is on a particular orbit, it never leaves the orbit. This is similar to a steady state, as once the system is at a particular steady state, it never leaves there. For steady states, we studied their stability, i.e., if there is a small perturbation away from the steady state, whether the system will return to it. We can ask a similar question for the closed orbits, i.e., if the system is perturbed away from an orbit, will it settle back on it.\n", "\n", "This is not true for the simple model above. As we have seen, there is a family of closed orbits around the steady state $(X^*, Y^*)$, distinguished by their distance from the steady state. If we push the system a little bit off one orbit to a nearby point, it will simply settle on another orbit that passes through the new point. Therefore, under perturbations, the system will drift from one orbit to another, instead of staying close to a particular orbit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, small modifications of the original Lotka-Volterra equations would lead to a different behavior. To motivate the modifications, notice that in the original model, the constant per capita growth rate of the prey means that the prey abundance can grow exponentially and indefinitely in the absence of the predator. In reality, there is limited amount of resources that can only support a finite population size. To address this problem, we may introduce *competition* between the prey individuals (recall the birth-death-competition process in [homework3](../Unit3-Stochastic-Processes/homework3.ipynb)). This will amount to changing the overall growth rate of the prey abundance from $r X$ to $r X \\cdot (1-X/C)$, where the new parameter $C$ represents the \"carrying capacity\" for the prey. The factor $(1-X/C)$ guarantees that the growth rate reduces to $0$ when $X$ approaches $C$, so that the prey abundance can never exceed the carrying capacity.\n", "\n", "Similarly, consider the consumption rate of the prey by the predator. We assumed above that the overall consumption rate is proportional to both the predator and prey abundances. That means if the prey abundance becomes very large somehow, the consumption rate may in principle increase without bound (besides the limit coming from the carrying capacity above). This is not realistic, because beyond a certain point the predators would be \"satiated\", unable to consume the prey any faster. Therefore, let us modify the consumption rate from $f X Y$ to $f X Y \\cdot K/(X+K)$. The new factor $K/(X+K)$ makes sure that, when $X$ is large, the consumption rate saturates at a level $f K Y$; on the other hand, when $X$ is small, the factor goes to $1$ and we recover $f X Y$. This modified consumption rate is called a \"type II functional response\" in ecology, whereas the original mass-action form is called \"type I\". The new parameter $K$ can be viewed as the \"consumption capacity\" for the prey by the predator.\n", "\n", "After these modifications, our dynamical equations become:\n", "\\begin{align}\n", "\\dot{X} &= r X \\Big( 1 - \\frac{X}{C} \\Big) - f X Y \\Big( \\frac{K}{X + K} \\Big) \\\\\n", "\\dot{Y} &= g X Y \\Big( \\frac{K}{X + K} \\Big) - d Y\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To simulate the modified model, we can define a derived class of the original `LotkaVolterra` class. All we need is to decorate the `equations()` method." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "class ModifiedLotkaVolterra(LotkaVolterra):\n", " \"\"\"\n", " modify the predator-prey model by adding prey carrying capacity and predator satiation.\n", " \"\"\"\n", " \n", " def equations(self, x, t):\n", " \"\"\"\n", " calculate time derivatives of abundances in modified Lotka-Volterra equations.\n", " inputs:\n", " x: 1-d array, current abundances of both species.\n", " t: float, current time.\n", " outputs:\n", " dxdt: 1-d array, time derivatives of abundances.\n", " \"\"\"\n", " X, Y = x # parse variables, X is prey and Y is predator\n", " factor1 = (1 - X / self.param[4]) # param[4] is C\n", " factor2 = (self.param[5] / (X + self.param[5])) # param[5] is K\n", " dXdt = self.param[0] * X * factor1 - self.param[1] * X * Y * factor2\n", " dYdt = self.param[2] * X * Y * factor2 - self.param[3] * Y\n", " return [dXdt, dYdt]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we now have two new parameters $C$ and $K$. The new behavior that we will look for happens when $K > d/g$ and $C > K(gK+d)/(gK-d)$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current time = 20.01, current populations = [4.40982046 1.4849132 ]\n", "current time = 20.01, current populations = [4.97191148 1.26379635]\n", "current time = 20.01, current populations = [3.70453114 0.53408085]\n", "current time = 20.01, current populations = [4.34069083 0.58346939]\n", "current time = 20.01, current populations = [5.46204342 0.88250225]\n", "current time = 20.01, current populations = [1.53938635 0.45896019]\n", "current time = 20.01, current populations = [5.14479312 0.70098578]\n", "current time = 20.01, current populations = [4.80874892 0.63805994]\n", "current time = 20.01, current populations = [1.38262881 0.45931313]\n", "current time = 20.01, current populations = [5.40494704 1.00357746]\n" ] } ], "source": [ "r = 5 # growth rate of the prey\n", "f = r # feeding rate of the predator\n", "g = 1 # growth rate of the predator per prey available\n", "d = 1 # death rate of the predator\n", "C = 8 # carrying capacity\n", "K = 3 # consumption capacity\n", "\n", "num = 10 # number of trajectories to simulate\n", "mlv_list = [] # list of simulations with different initial values\n", "\n", "T = 20. # total time to integrate the trajectories\n", "dt = 0.01 # time steps to evaluate the trajectories at\n", "\n", "for i in range(num):\n", " X0, Y0 = np.random.rand(2) # random initial values between 0 and 1\n", " mlv = ModifiedLotkaVolterra([r, f, g, d, C, K], [X0, Y0])\n", " mlv.run(T, dt)\n", " print(f'current time = {mlv.time}, current populations = {mlv.abundance}')\n", " mlv_list.append(mlv)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "for mlv in mlv_list:\n", " time_hist = mlv.time_hist # time history, excluding t=0\n", " num_hist = np.array(mlv.abundance_hist) # abundance history of all species\n", " plt.plot(num_hist[:,0], num_hist[:,1]) # plot prey vs predator abundances\n", " plt.plot([num_hist[0,0]], [num_hist[0,1]], 'b^') # blue trianble labels starting point of each trajectory\n", " plt.plot(num_hist[-500:,0], num_hist[-500:,1], 'k') # black line labels last period of each trajectory\n", "plt.xlabel(r'$X$')\n", "plt.ylabel(r'$Y$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that all trajectories converge to a single closed orbit, marked black in the above figure. If a trajectory starts outside that orbit, it will spiral inward and asymptotically approach the orbit from outside. And if a trajectory starts inside that orbit, it will spiral outward and asymptotically approach the orbit from inside. Such an isolated closed orbit (i.e., having no other closed orbits in its neighborhood) is called a \"limit cycle\". What we have here is a *stable* limit cycle because it \"attracts\" nearby trajectories. (One could also have unstable limit cycles from which a small perturbation leads to the trajectory spiraling away.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Steady states and limit cycles are common features of dynamical systems. They share the property that once the system is on such a state or trajectory, it will remain so indefinitely. Stable steady states and limit cycles both belong to a class of objects called \"attractors\" in dynamical systems." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }