{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# Lotka-Volterra System" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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 assume that the prey population by itself has a birth rate $\\beta$ and a death rate $\\delta$ per capita, just like in the birth-death process we studied before. The net growth rate will be the difference between the birth and death rates. In addition, the prey are being consumed by the predators, which results in its population loss. Since a predation event requires an encounter between a predator and prey, we may assume that the overall consumption rate is proportional to both the predator and prey abundances, just like in the mass action law, 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 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, $d$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "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}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "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": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Steady states and stability" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "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 and keeping things to first order in the perturbations, we 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{J} \\cdot \\left( \\begin{array}{c} \\delta X \\\\ \\delta Y \\end{array} \\right)\n", "\\end{equation}\n", "The eigenvalues of the Jacobian matrix $\\mathbf{J}$ will determine the stability of the steady states." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "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 jac(X, Y): # calculate Jacobian matrix\n", " J = np.array([[r-f*Y, -f*X],\n", " [g*Y, g*X-d]])\n", " return J\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(jac(X,Y)) # this function calculates all eigenvalues and eigenvectors\n", " print(f'steady state at {(X, Y)}: eigenvalues = {w}')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Closed orbits and oscillations" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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 in the `equations()`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "class LotkaVolterra:\n", " \"\"\"\n", " simulating 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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current time = 10.0, current populations = [0.9741404 0.40914513]\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", "T = 10. # total time to integrate the trajectories\n", "dt = 0.01 # time steps to evaluate the trajectories at\n", "\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}')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "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": 6, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "time_hist = lv.time_hist # time history\n", "num_hist = np.array(lv.abundance_hist) # abundance history of all species\n", "\n", "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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "A heuristic argument 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 a chance to grow again, and so on. The main point is that neither population settles onto an equilibrium value. Indeed, the predator-prey model was historically used to illustrate that, in nature, the dynamics of populations (as many other things in biology) do not have to reach an equilibrium state." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us run the simulation multiple times, and plot the trajectories in the phase space (X-Y plane)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current time = 10.0, current populations = [1.16098739 1.31622079]\n", "current time = 10.0, current populations = [0.10108912 0.63875512]\n", "current time = 10.0, current populations = [0.90350065 0.36854218]\n", "current time = 10.0, current populations = [0.02361728 1.93205747]\n", "current time = 10.0, current populations = [1.84411958 1.38471389]\n", "current time = 10.0, current populations = [0.02378507 0.72741858]\n", "current time = 10.0, current populations = [9.7665736 1.14305527]\n", "current time = 10.0, current populations = [8.38454742 0.64276834]\n", "current time = 10.0, current populations = [0.99211186 1.25093108]\n", "current time = 10.0, current populations = [0.02089249 1.14245964]\n" ] } ], "source": [ "num = 10 # number of trajectories to simulate\n", "lv_list = [] # list of simulations with different initial values\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": 8, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEICAYAAABfz4NwAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABwE0lEQVR4nO2dd3hURduH79lN771QQug19C4dkaaAFaxYEBHsfio25AUV7BUEFRVQEQSUJtKl994hlJAA6b3uZne+PzbspvctSc59XbmyZ06ZZ5Pd8zsz8xQhpURBQUFBQUFlbQMUFBQUFGwDRRAUFBQUFABFEBQUFBQU8lAEQUFBQUEBUARBQUFBQSEPO2sbUFn8/PxkaGiotc1QUFBQqFEcPnw4XkrpX9y+GisIoaGhHDp0yNpmKCgoKNQohBARJe1TpowUFBQUFABFEBQUFBQU8lAEQUFBQUEBUARBQUFBQSEPRRAUFBQUFABFEBQUFBQU8lAEQUFBQUEBqMFxCLaMLkNLzuUUNFFp5MZkkpuUjT5di9TqkDqJUKsQDipUrvaoPRyw83HCzt8F+yAXHBq4o3JS/i0KCgqWR7nzVBGZqyd97w1SN11DanTlO0enQ2p06NO15MZkklPG8Q6NPHBu44tTW1/s/ZyrbrSCgoJCMSiCUAmklKTvvE7KP1eKP8BO4NTMG4dG7tgHuKL2cULtZo9wUCNUAqnXIzV6dOladKk56BKz0cZmoo3OQBuVjtTqC1xOE5GKJiKVlPUF+3Nq7YNrj2CcWngjVMJcb1dBQaGOYHZBEEI4ATsAx7z+lksp3yt0zOPAJ8D1vKZvpZQ/mtu2iiL1kqTlF8g8Elug3bmdLx53hGIf4FKu6whU4AhqdwcIdi29z1w9OVdSyDqdQNbpePRpWuO+7LOJZJ9NLHC8a/cg3PrUL7ctCgoKCrewxAghBxgkpUwXQtgDu4QQ66WU+wodt1RK+ZwF7KkUmSfiSPz9nHHbvp4rfk+0M9zUzYiwU+HU3Bun5t54j2lmbNdrdGSdjCfjQDSaiFRje8aBaDIORBu3HZt64jG4EY5NPM1qp4KCQs3H7IIgDUWb0/M27fN+akwhZyklMZ8eIjchGwD7Bm4ETOqAsLOug5bKQY1rl0BcuwQa23QZWjIORJO2IwqZlQtAzqUU4i6dMB7j2NwLz2GNcajvZnGbFRQUbBuLrCEIIdTAYaAZMEdKub+Yw+4VQvQDLgAvSykji7nORGAiQEhIiBktNiC1Oq6/u8e4HfhyZ+wDS5/isSZqV3s8BjbEY2BDAKROknUyjtRNEUZBy7mYTOzFo8Zz3HrXw31wCGpXe6vYrKCgYDsIwwO8hToTwgv4C3heSnkqX7svkC6lzBFCPAOMlVIOKu1aXbt2leZMf11YDOp/2KfGL9xKnSTzSAwp66+gz8wtsl/t44TXqKY4tfRGiJr9XhUUFIpHCHFYStm12H2WFIQ8Y6YBmVLKT0vYrwYSpZSlTnqbUxCklFx/cxdguEkGv97NLP1YG32mltRtkaTvvF7sfvdBDXEf0BCVg9rClikoKJiL0gTBEl5G/oBWSpkshHAGhgAfFTomWEp5M29zFHDW3HaVRsznh42va6sYAKhc7PEa2QSvkU0AyA5PJnnNJXJjMgFI2xpJ2lbDzJ1TG1+8RjfFztPRavYqKCiYF0usIQQDC/Oe/FXAMinlWiHEDOCQlHI18IIQYhSQCyQCj1vArmLJPB5LblwWYJgmqks4NfMi6OUuAOjSNKT8e5XMwzEAZJ9JIPpMAmDwsPK+rwUO9ZSFaQWF2oTFp4yqC3NMGUm95PpbhqkiW19AtiRSpyd913VS1l8tsk/t44TPuJY4hnhY3jAFBYUKY9Upo5pEwq+GmSrHJp6KGORDqFW492+Ie/+GSCnJOhFH4h/nQYIuMZu4uccBULk74PtwKxxDlZgHBYWaiCIIeUidnuy8KRG/p8KsbI3tIoTApUMALh0CAMg6k0DiH+cNuZnSNMTNM8Q8qH2c8H2oFQ4N3K1proKCQgVQBCGPxD/OA4Y0FEJdOZfLrKwsTpw4wdmzZ7l69WqFz7ezsyMkJISQkBAaNWpE/fr1cXAwbyR0VXFu40v9Gb0ByD6fSMJvZw15mhKzif32GAD29d3webCVkphPQcHGUdYQ8oiauhOA+h/chlCXLwo5NzeXPXv2sHXr1mqzozQaNWpEmzZtaNOmDe7utv3knXU63jAFV+jj5dTaB+97m6N2s22hU1CordhUHEJ1UZ2CkHU6noTFZ1G5O1Dv7R5lHh8VFcWPPxafe699+/aEhYUREhKCo2PFXDSzsrKIjIzk2rVrREREEBlZJFi7CD4+PnTt2pWOHTvi4mJ7Ce2klGQeiiFpxcUi+9z61MdzWKjV04AoKNQlFEEog1ujg4AXOpXqShkbG8vcuXMLtLVp04ahQ4fi6WnehdTc3FwuX77M6dOnOX78eKnHhoWF0bdvXwICAsxqU0WROknaf5Gkboooss/7vha4dAlQIqQVFMyMIgilkD8qucHsviUes2jRIq5cMdUjGD9+PI0bN65y/1VBSsn169c5dOgQx44dK/G4Zs2aMXjwYIKDgy1nXBnos3NJ+jucrGNxBdpVbvb4PdlOiXFQUDATiiCUQtYpw1y3fbArgS92LrI/MzOTjz/+2Lj9wAMP0KZNmyr3ay5ycnI4fPgwO3fuJCsrq9hjevbsSb9+/Wxmikkbn0Xir2fQRmcWaHcO88P73uZKSVEFhWpEEYRSuDn7ALrkHPwnhuHYxKvAvqSkJL766ivA4G75zjvvoFbXrLw+Op2O48ePs2nTpmIFwtnZmZEjR9K2bVubmK7JOp1AwuIzRdq97m6Ga/cgm7BRQaEmowhCKdxaPyg8XZSWlsZnn30GQNu2bbn//vur3JctkJGRwc6dO9m3r3B9IgO33XYb/fr1q/CCeHUjdXpSNlwlfUfBxHtqHyf8nmiLvb9tjG4UFGoaiiCUQP5UFfkFQafTMXPmTAA6d+7MqFGjqtSPLXP9+nXWrVvHjRs3iuxr0qQJI0aMwM/PzwqWmchNyiZh0Rm0NzMKtLvdVg/PEY3L7SasoKCgCEKJ3Fo/cAj1IGBSB2P7zJkz0el0BAQEMHny5KqaWmPIyMhg69atHD58uMg+f39/7rnnHqsvTGceizUGERpRCfwntVfyKSkolANFEEog7vsT5FxOwefhVriE+QNw+vRp/vzzTwDee++9OjtnrdfrOXLkCGvXri2yz8vLi3vvvZeGDRtawTID+pxcklZcJOtEfIF2ly6BeI9phrBXRg0KCsWhCEIJFI5O1uv1zJgxA4ApU6bg7+9fZTtrC6dPn2bFihXo9foC7a6urtx///2EhoZaxzAMdRzifzxZpN1/YnscmyiJ9hQU8qNkOy2DW3PQS5YsAaB+/fqKGBSibdu2tG3bFoALFy6wfPlyNBoNGRkZ/PLLLwD4+fnxwAMPWDwgzqmZFw1m90Vq9SSvvkTGwWjAMAIEcO0ehNeopkpEtIJCGSgjBAwLyvlHB9OmTUOlUm4e5eHy5cssXbqUnJycAu1NmjRhzJgxeHhYZ14/52qKMfOqERUEPNsRh4a2nQdKQcGcKFNGxaBL13Dz/f1gJ2jwfh/WrFnD4cOHadasGY888kg1Wlp3OHnyJCtWrCjS3qFDB4YPH46Tk5PFbZJaHUkrw8k8Glug3X1gQzyGNEKo6uYakULdRZkyKobss4kAOLc1uFTe8qwZO3as1Wyq6YSFhREWFoZer2ffvn1s3LgRgOPHjxvzLw0bNowePXpYbLFe2KvxGdsSn7Etyb6QRPxPpwBI2xZJ2rZI7Hyd8Hs6DDsvy4uVgoKtUWdHCAlLzpF1PA7v+1qQEJDDTz/9hEqlYtq0adVopYJWq2XLli1FAuEcHR159NFHadCggcVt0mdqSfjtLDmXUgq0e9/fAtcugRa3R0HBklh1ykgI4QTsABwxjEiWSynfK3SMI7AI6AIkAGOllFdLu25VBeFWyoqg/+vK5z99Q2ZmJo888gjNmjWr9DUVSiclJYU///yTqKioAu0tWrRgzJgxVsmtlL7/Jsl/hRdocw7zw+eBFgj7mpWmREGhPFh7yigHGCSlTBdC2AO7hBDrpZT5HxmfApKklM2EEOOAjwCzzt3okg2LoGpfJzIzDUnVFDEwL56enkyYMAGA8PBwfv31V8DgtXQrgeAdd9xBr169LDal5NYjGLceweQmZBE77wT6NA1ZJ+O5fjIe7ASBz3XCPkipr61QNzC7IEjDECQ9b9M+76fwsGQ0MD3v9XLgWyGEkBaYz4qJiQGw+VKVtY1mzZoxffp0dDod27dvZ8eOHQBs3LiRjRs34unpyaOPPmqxtBl2vs7Ue7sHUqcnedUlMg5EQ64k5ssjAHiNboprz+A6G6ioUDewyBqCEEINHAaaAXOklG8U2n8KGCaljMrbvgT0kFLGFzpuIjARICQkpEtERNFCK+Xllsvp1jZXuHz5MqNGjaJz56LprxUsR1paGsuWLStSKa5v374MHDjQ4q7AWWcSSFhUMPOqUxtffB9sqUwnKdRYbMbtVAjhBfwFPC+lPJWvvVyCkJ+qriHcEoQfnbYASuyBrVGcC6ujoyNPPPEEQUFBFrVFl5JD7Pcn0CVkG9uEo5qA5zoqWVcVahzWXkMwIqVMFkJsA4YBp/Ltug40BKKEEHaAJ4bFZYuhiIFtccuFNSsri5UrV3Lx4kVycnKYN28eAN27d2fo0KEWqU+h9nQk+LVuSJ0keVU4GQeikTk6Yj4zuCr7PNgKlw5KZLtCzcfsgiCE8Ae0eWLgDAzBsGicn9XAeGAvcB+w1ZzrB3qNDoB0tWFh2c6uzoZj2DzOzs48/PDDAJw/f96YXuTAgQMcOHAABwcHJkyYYJF0GUIt8L6nOd73NCfzeCyJSwxZVxOXnCNxyTnc+tQ3pONWgt0UaiiWcDttDywE1IAKWCalnCGEmAEcklKuznNNXQx0AhKBcVLKy6VdtypTRpob6cR+fZQjnhEcyQmnV69eDB06tFLXUrA8Go2GVatWcfr06QLtQ4YMoXfv3hZd+NXGZRL7zVGkxpT0zyHEHb8n2qFyVh40FGwPm1lDqE6qIgi3nu4Wu+wgR6/lhRdewMfHp5otVLAEZ8+eZenSpQXagoODefjhh3Fzc7OYHfocHQmLz5ATnlygPfClzorbqoJNoQhCIVI2RZC25ZpxQXn69OnVYpPm6lWiP/iQjJ07q3Qd+5AQvMc+gNe996L28qoW22o76enp/P7770Uqv40dO5bWrVtbzA4pJambIkjbWtBTyvfRNji39bWYHQoKJaEIQiESl54n82hslQVBSkn09P+RXOgJ1Zz4v/QiPo8/jsoKieJqAlJK9uzZw6ZNmwq0h4WFMXr0aIuuFxXntupxRyPcBzZU4hkUrIYiCIWI+/Ek2eFJLHDaClRcELQ3bhA+aHCx++zr1yfgtf/DfcgQRAU9YPTZ2WTs3k3K33+Ttmlz+U5Sq6n/5Rd4DBlSob7qAjExMfz0008FUnO7uLgwYcIEi04RamMyiPniSIE25/Z++DzQUqnRoGBxFEEoRPQXh4mOjeFvxwP4+vry/PPPl+s8fXY25zt2KtIe+scSnDt2rJQt5UWXkkLCDz+Q8OOCMo8NfPcdvB96SHkKzSM3N5e1a9dy7NixAu2Wnk7SZWiJ/+EE2uhMY5tdgDP+z3RA7WpvMTsU6jaKIBTixoy9HM65yGH7y+X2MIr/4QfiPvvcuO3avx8h8+dXqv/qQpeSQsys2aT8/Xepx4X8/BOuvXpZxigb5/jx4/z1118F2nr06MHQoUMtFosidXqSll8sWKNBLQh6uQt2fs4WsUGh7qIIQiGipu5kg/0xItUJ5XpKvND7NnSJicbtVmfP2OTTt9TrSfj+B+K+/LLEY9z696f+l1+gcq7bN57Y2Fjmz5+PTqcztgUEBPDYY49ZzDtJSknaf5GkbiiYgsX/2Q44NrJOpTmF2o8iCIWImrqTXx13kC20vPLKK6WWeTzbyiQWDeZ8i/vg4tcObBG9RkP0jBmkLC9axewWTdasxrF5cwtaZVvk5OTw559/Eh5eMAX2448/TmhoqMXsyB/odgufh1rh0l6JgFaoXhRBKETU1J3l8jDKLwZNN2/CwQrFXKqT7PPnuTLmbijhf95w/jzc+ve3sFW2gZSSvXv3Gqu83eLOO++ka9divztmobha0F53NcHttvoWs0GhdqMIQiHKIwhXH3yIrKNHAWixfx9qT89K9WWr6HNyuP7yK6Rv3Vrs/vpffI7H8OEWtso2uHbtGj/99FOBtm7dujF8+HCLrTNo4zKNuZJu4T6gAR5DQ21yulKh5qAIQiHKEoTUTZu4/vwLADRZuwbHWl44R0pJ/Jy5xH/7bbH7G8ydg/ugQRa2yvqkpKTwww8/kJ6ebmxr2LAhDz/8ME4WigPRpWqI+eYo+jSNsc2lcwDe97VQciYpVApFEApRmiBIKTnXug0AgW9OxWf8+CrZWRNJXLSImA9nFbsv9M9lOIeFWdgi66LRaFi6dCmXLl0ytjk4ODBp0iSLxTPos3OJ++Ek2usmcXJs4Y3fY22UWAaFCqEIQiFKE4T86watz52ttH21hYSffiY2r7xlYZrt2I69BbKM2gpSSjZv3szu3bsLtFtyAVrm6kn49SzZ50xebw6NPPB7qh0qB6Voj0LZKIJQiKtT/+MXp/9QqVRMmzbN2K5LS+NCt+4AtDx2VEkPkQ8pJTEzZ5L0+5Ii+9wGDKDBnG8rHJldkykunmH06NF06lQ0cNEcSL0kafkFMo+YYhnsAl0IeLYDKicly6pCySiCUIiTb65nheP+IlHKt0YH9vXq0Wzrlmqxszaiz8kh4uFHyD51qsi+ep9+iuedI61glXWIjIxkwYKC0eO33347ffr0sUj/UkpS1lwmfY8pqZ/ay5GA5zqidlPqhCsURRGEQux+ayWbHE7QvHlzY/EVqdVyLqw9YLuBZ7aIJiKCS0OHFbuv+a6d2Pn5Wdgi65CcnMycOXPQarXGth49ejBs2DCLfJaklKRujCBtmynLqsrVnsCXOyvCoFAARRAK8e/bv7HP/iLdu3dnxIgRAFy680404YZFQ2XtoHIkr1jBzbffKdLu+8wzBLz8kuUNsgIZGRksWLCAxHyR7W3btuWee+6xSLlPgNT/Ikn996pxW+ViR+DLXVC7K8KgoAhCEZa98yNn7KIYNmwYPXv2BEzTRc337sHO27va7KyLSI2Gqw89XOyUUrOtW7CvV88KVlmWnJwcfvvtN65du2ZsCwkJ4ZFHHsHBwTI35rSdUaSsu2LcFs52BL2iCENdRxGEQvz47jdEqRN48MEHadmyJTmXLnF55J2AMjqobjKPHCHioYeLtPtNfhb/F16wgkWWRafTsWLFCs6cMdVF8PHxYcKECbi4uFjEhrRd10lZa6pIKxzVBL3aBbWHo0X6V7AtFEEoxNfTPiVRlc7EiROpV6+ecXTgdvtgGpYQnKVQNaReT+Qzk4qtJtdi395aXxlOr9ezYcMG9u/fb2xzdHRkypQppebSqk7Sdl8nZY1JGFQudgS+0kVZY6hjKIJQiI/fm0WmyOHll1/G09PTKAitThxHWGg4X5fJPHKUiIceKtJe/6uv8Bh6hxUssiw7d+5kyxaTF5u9vT3PP/+8xYQhfc8NklebguzUXo4EvtAJlYtSk6EuYFVBEEI0BBYBgYAEvpdSflXomAHAKuDWhOdKKeWM0q5bFUGY8d7/0AvJ22+/jVpKzrfvAJhnukiXqyXmcjjXz58lOy0VeydnHJydcXByxtHNjaAmzXH3rRueOIWRGg2Xx9yN5vLlAu0uPXoQ8vNPCAvlDbIWBw4c4J9//jFu29nZ8fzzz+NpobxZadujSFlvWmOw83cmYEpHJY6hlmNtQQgGgqWUR4QQ7sBhYIyU8ky+YwYA/yelvLO8162sIEid5H8z/wcYopSjZ75P0m+/AVUThMzUFDZ89yWXjxws2B+Q6exKopc/yR4+aOwdcM1KxyMtGY+0ZFyyM1FJfbHX7DT8LnqMeQBXr9q/yF2Sh1JdiIY+ePAg69atM26r1WpeeOEFiwlD6uYIUjebFr/t67vh/0x7JfK5lmJTU0ZCiFXAt1LKTfnaBmAhQdDn5DJj1vuAQRBuTRdVptZBRnISPz73FLlaDXoh2NHjDg527Fthm4rDQZNNlxN76HZ8N45aU01gN18/Rr3yJsHNWlZLP7aGNiaG8P4DirTXhQR7hw4dYu3atcZtlUrFCy+8gJcF1leklKT+e5W07VHGNqeW3vg+1gahrt0jtbqGzQiCECIU2AG0k1Km5msfAKwAooAbGMThdDHnTwQmAoSEhHSJiIgofEiZ6DK0zPzkA6CgIFRkdJB4I4qfX56ETqVi0X1TiPcJrLAdlaXZlTMM3rUOj4wUY9uwyS/Tpt+gWhVMJ6Xk2vjHyTxwoEC71wMPEDzjf1ayyjIcPnyYNWvWGLeFELz44osWE4bkVZfI2HfT2ObSJRDve5sr2VVrCTYhCEIIN2A78IGUcmWhfR6AXkqZLoQYAXwlpSy1jFdlRwi61Bxmfm7I5FlRQZB6PZ8/OIp0Fze+e2xqscd81SqE+4O8UVXy5iyl5GR6FouuJ/DrzYQyj3fOyuD+db8QGG/6Aj8w7UMatm1fqf5tkaSly4h+770CbWpvb5pv/69WOwEcOXKE1atXF2h76aWXLCMMekni72fJOmX6DCr1GGoHVhcEIYQ9sBbYIKX8vBzHXwW6SinjSzqmsoKQm5jN+1/PBuD1UaON3i5lCcLVY4dZPus9vnnibXIcC9YjPn1bO3wdzLsQJ6VkbVwKUy9EkaDNLfE414xUxq3+CZ8Uw5+u3cAh3D5hCmq7mr9QmHPxIpfvGlWkvbavMxw9epRVq1YZtx0dHXn++ectUvtZavXE/XgSTYRxQI/nnU1w76NUcKupWHtRWQALgUQp5UslHBMExEgppRCiO7AcaCRLMa6ygqCNy+SDOYZ0zuPPniX7+Amc2rWj8fI/Szxn1x+L+WfbVn4a96KxrZuHK6s7N7Pq01KcRsvzZ67xX1JaiccM3rmGzqfzfN+F4Mkv5uEdXLO/zPqMDM53Kfp5Dl36B84dOljBIstQWBh8fX2ZOHEijo7mDzDTZ+cS881RdAnZpv4faY1zu7rpIVeTsbYg9AF2AieBW+40bwEhAFLKeUKI54BngVwgC3hFSrmntOtWWhCiM/hg3icAjP1jKQANv5+PW79+xR6/fs7nLE7MZGsf03p3eN8w3OxszwMjTqPlqVNXOZCSUez+plfPcdemP7DXGUYYE775Ec+AIEuaWK1IKbn22HgyDxb07Kr38Ud4jio6kqgt7N69m02bjD4ZhISE8Nhjj2FngVGgLk3DzY8OQK7pvuE/uQOOIZaJoVCoOlafMjIHlRUEzfV0PvzhU8AkCCVlN93/1zI+O3eFHT2HAtDby42VnWpOOc0lNxN4+Vxksfu8UhJ4dMV3OGmyUantmPDNjzU6HiL2yy9JmDe/QJvfc8/h/9wUK1lkXqSUbNq0iT17TM9NrVu35v7777dI3WdtbCYxnxes+Rz0WlfsfJ1LOEPBVlAEIR8511KZ9ZNhGeOWIBS3fhAfGcHr83/gn8H3AfBm42BeDLWcN1F1czY9i4EHzxe7r1FUOPf+swi1Xo+TmztPfjkfZ/ea+cSXun49119+pUCb5+jR1PtotpUsMi96vZ5Vq1Zx/PhxY1u3bt0YMWKERaYzsy8lE//DSeO2ytWOoFe7KlHPNowiCPnIuZzCrEVfACULgpSS/z31EPMefQOAV0IDeb1xcBUtth0SNLkMPnieaI22yL5Op/YxeNdaBNDhjpEMfnJSjfQqyTx6lIgHC6bHcOnenZCFv9TI91MWOp2OJUuWEB4ebmwbMGAAAwYMsEj/GUdjSVpqeuBwbOGN3/i2CHXt+1vXdBRByEf2xSRm/2bInFGSIHz12L3MeuJdABo42XOoV9sqWmu7RGTl0GNf8R5WI7Ysp+3FYwA8OPNT6rVoZUHLqoecK1e4PHxEgTb7kBCa/ru+VqbG0Gg0/Pzzz9y8aXJDHjVqFJ07d7ZI/ymbIkjbYop6dh/YEM+hoRbpW6F8KIKQj6xziXz0x9dA8YKQGh/LwI17uR7cCIDogR2rbmwN4UhKBiOOXCx235RfPsQlOxOf+g15dPZX2NUw/39tbCzh/foXaFP7+NB8545aWQs6KyuLuXPnkpZm8kB74oknaNSokdn7lnpJwsLTZJ9PMrb5PNQKl/b+Zu9boWwUQchH1ul4PvrTkOJ67B9LcWzViiZ/m4qlf/jIvXz9lGF0cLR3G4Ida9aNr7r442YCLxWzIH3bgc30PvIfAEOffYl2A263sGVVQ5eayoXuPQq0qdzcaLFvL6IWxGoUJjk5mS+//LJA24svvoi3BYpA6bNyif70IPoMU9xMwPOdcKhv/vgJhZJRBCEfmSfi+HjlHMAgCH6TJ+P/wvMApMRG0/J0NAABDnacuK1d9RlcQ9Ho9Yw4fJFT6VlF9k389VM805PxbRDCYx9/g6oGPWkXF8ugcnOjxf59tXLEcO3aNX766SfjtpeXF88++6xFYhi0cZnEfGbySBIOKoKndlcWnq2EIgj5yDgayyer5gIGQQhdsRzntoY1gvyjg5sDOtTKxceqsDspjXuPXSrS3uvQVvoc2grA4599h2+DhpY2rdLoMzM537lLgTa1tzfNd+2slcJQOLjNkq6q2ecTif/ZlKLMqY0vvo+0VnIkWRhFEPKRcSiGT9Z+BxgE4VYMgpSS4P8MrntBDnYcU0YHJaKXkodPXGZbYsEIaXttDlN+mYW9Lpe+Dz1O99H3WcnCilOcMNiHhNB0w7+17sFASsmGDRvYt2+fsW3QoEH0KyE4s7pJ2XiVtK2m6UivUU1x613762zbCoog5CPjQDSf/DMPMAjCrQXlDfO+ZnxLwxcion97HGuhB4o5OJCczqij4UXaxy/7hoDEGFy9fZjwzQLs7GvG9EBxU0kuPXrQaOEv1jHIjOh0OhYtWkT+rMHjxo2jVSvze5NJnZ64+SfQXDM9VCgRz5ZBEYR8pO69zucbfkBIeGCpSRDu/ehTdnc3LJDWJc+i6iJTp6fd7lNk6goW+xm4ex1dT+4F4Mkv59eYPErFLT7X1gC3jIwMvvzyS7RaU1zK888/j6+vr9n71qXmcPNDU4pz4aAi+K0eStU2M6IIQj4Sdlzlm62/YK+De/40CILU6wnefgKAJe2bMNBXeUqpCm9eiOLn6wUT1QbGXefRFfMQyBqVnrs4d1W/55/Df0rtS4kRGxvL3Llzjdv+/v4888wzFsmRlB2eTPyPpohn125BeN1j3eSRtRVFEPJxc+tF5u/4DSctjF5hEIQtv8zn4UaGp0FldFB9bE9MY+zxoovQz/38Ac45WQyd9CLtBg6xgmUVp7gAt9qaRO/EiROsXGkqWdKvXz8GWahaXfL6K6Tnq9rm+2gbnNuaf6RSl1AEIR/XN53nh91LcNFI7lq5jNbnzjL2w9ls7zUMUATBHMRrcmm3+1SR9ltuq13vuof+jzxpBcsqTuaRo8YaGreojWm3pZSsXLmSkydNT+3jx4+ncePGZu9br9ER88VhdEmm0rFBb3bHztP8LrJ1AUUQ8hG54QwL9i7DTSMZmScIQduOAfB5q4Y8FKw8jZgLnZT0P3CO8MycAu23FqAbte/EvW/NqBHTBMUl0Wu2fTv2gbWrUE9WVhaffvopOp3O2Pbaa6/h6upq9r610RnEfHnEuO3Uygff8W1qxOfDllEEIR8R60/x8/7luOdIRvy1jKZHDxOy7wJgvtGBVqflaupVMrQZaHQaJJJ6rvVo4N6gTn64pZSMP3mFjQmpBdrHrl5AyI0ruHh68cx3C2tEoFvsV1+R8N28Am2tThyvdaU9IyMjWbBggXG7RYsWjBs3ziLxC+l7b5C8yjT1qBTmqRqKIOTjyrrjLDz4F57ZkmF/L+PSy5OZ0KIvUHVBiM6I5oWNz3A29XKVrmMnVEzqMJnxbcfjZOdUpWvZOm9fiGJBoQXouzb9QatLp1Db2/PCwuU1QhgiHn+CzHx+/U7t29N42VIrWmQedu3axebNm43bd911F126dCnljOpB6vTEfnsM7U1T8afgt3ugdq9dwmsJFEHIR/iaY/x6+G+8s/QM37GZt8bcw64quJtGZ0QzZLllFkZf7vQij4c9iUrUvhiJOddimXnpRoG2of/9Rftzh2uMMMjcXM61CyvQ5v/Si/hNmmQli8yDTqfj559/JirKtPhrqfxI2pgMYr4wTSM5d/THZ2zLOjnSriyKIOTjwqoj/H50NT6ZekZdv0zPCf8HwKuNAnmtSflrHpyJP83YdeOKtDfWaJmVZUfbgdOh7T1Q3iF1RjwcXczlQz/yuzqDpR7uZZ7yfMcpPN3+mVr1ZVgenchzZ68VaBuyfRUdzx7EztGR539Zhkpl28KQm5DAxdv6FGirjQvPhRPnNW/enIceesgin8e07ZGkrL9q3Paf2B7HJp5m77c2oAhCPs79dYg/jq/FL0PPPfY6Og+5H4Cr/drjpC775p2rz6XT4k4F2npkZfN9n9mo2t1bYXvKJCuZ3G0fsPD8Er70KfkJrL6TH4vuWkqAS+1Y1NwQn8L4k1cKtI3c8idtLh7HKzCYJ7/63uaFMPPQISIeebRAW4tDB1G71a5sn0eOHGH16tXG7YceeogWLVqYvV+p1RP9yUF0qRoAVB4OBL/WDWFf+0bQ1YlVBUEI0RBYBAQCEvheSvlVoWME8BUwAsgEHpdSHil8rfxUVhDOrNjPspPrCUjXcU9oIB3bGp7kyjNdtDtiK5P+e9G4/URyKq9MPAbO5h8qG5ESeWQRy/97kxl+JXtE/T7id8L8w0rcX1PYFJ/Co4WE4d5/FtHk2gVCO3Tm3rdmWMmy8lO43rNjm9Y0yefnXxvQ6XTMmzePuLg4AIQQvPHGGzg5mX8NLOdKCnHzTxi3vcY0xa2nkhupJKwtCMFAsJTyiBDCHTgMjJFSnsl3zAjgeQyC0AP4SkrZo9gL5lFZQTj5515WnN5AYJqOsEAn7us2EihbEL7c8Q4LrpiyRB4f/DOqBsX+TS1LroaEv55iQvIBwkvwbPl79N809WpqYcOql79jkph0JqJA26PL5xIUf4MOQ0Zw+4TJVrKsfEgpudinL7qEBGNb0PTpeI8ba0Wrqp+bN28yf75J/Pr27cvgwYPN3q+UksQ/zpN1PM7YFvxmd9RK7EIRbGrKSAixCvhWSrkpX9t84D8p5ZK87fPAACnlzRIuU2lBOLFsDyvPbCQ4VUe4q57FgwxTRqUJwuytr/BbpMHcB1PSeOuFqxXu11Lojyzmg93vsqyYNQhnlQObHtiKp2PNnWv95Xo8Uy9EFWh7ZvEneGSkMOTp52h/+zArWVY+chMTudj7tgJtzbZtxT649tTsBti4cSN79uwxbj/77LMEBgaavd/c5GyiZx80brv1rofXqJr9MFTd2IwgCCFCgR1AOyllar72tcBsKeWuvO0twBtSykOFzp8ITAQICQnpkj9LY3k5+sdOVp3bQr2UXBZ06khEw2Y0VcPufh2LPX7F8R+ZfswwwzUzUzDm2RPFHmeL5B7+hdf3z2STq0uRfc+2fYrJXV+yvFHVxPuXbvDttdgCbS/9+D/sc7WMm/EJ9Vu2tpJl5SNt6zaiJptGNSpPT0PVNhtfF6kIWVlZfPTRR8bt4OBgJkyYgNoC3mJpO6+Tss7k/h34f12x93M2e781AZsQBCGEG7Ad+EBKubLQvnIJQn4qO0I4vGQ7a85vo0GylndGG0YHX7VqyNhiIpRj0m9y+4o7AHg9TcOjz52vcH+2Qubm6dx/9Q+uFZOGeu3da2nkYf5au+bgweOXCtRlcEtPYdKvnyCAZ+Ytws3bx3rGlYNrT08kY+dO43bQ9PfwHlfUe60mc+7cOf744w/jtqUWnfXZudyYvte47dzeD58HW9Uq0a0MVhcEIYQ9sBbYIKX8vJj9FpsyOvjbf6y7+B8hSVreGmMQhGv92+NQjHto2ELDomxDrZZ/JpyrcF82SU46B+d25Emfok9LL7afxIRONS+Lp15Kmu44QZbe9FnucmI3g/asB+DlJats2lVVl57Bha4Fv5/N9+7BzgJ+/ZZCr9ezePFirlwxOAi4u7vz0ksvWWS0kHE4hqQ/Lxi3A17ohEO92uXpVRGsvagsgIVAopTypRKOGQk8h2lR+WspZffSrltZQTjw61b+Cd9Bo0QNb979AFD8+sGEFXeyP90wJXXykaOgrn352eWZ1fzftpfY6FYwL009J1/W3rcJe3XNKGpzi9RcHS12nizQdu+6hTSJvEjb/rczbPJL1jGsnKRt3UrUZJMgO3foQOjSP0o5o+Zx48YNvv/+e+O2xQryaPXc+GA/MjsXyCvf+WjrOjlasLYg9AF2AieBW9VT3gJCAKSU8/JE41tgGAa30ydKmy6CygvC3kWb2XB5F40TNLxxT/GCkKnNpMfvBienTe1eIqjLUxXup0aRq+Hg3A486VlU9NaMWUOoZ6jlbaoCJ9MyGXLoQoG2yQtn4ZqVwejX3qVZ11Id2KzO5bvuIueiqQpdo18X49LVBjzaqgkpJb///jsXL14EwNXVlZdfftkidReyTieQsNjo4EjgK12wDyi6xlabsfqUkTmorCDsXriBTVf2lioIt6aKXPR69j9xuvAlajVpm96l942/i7T/MOR7etbrZXmDqsCCqDjevnjduO2clcGUhbMQwLM//IaLh+16WxVXmOdW/e/aQmEX1bFjx9K6tfmdAWSunhsz9yFzDBlcXboG4nOf+dc0bIXSBKHOhfTp8+aZs0uYu8zUmJJn7b1ng0VssiXch8zk5PiTnBz4A3emm/4WT2+aSNjCMFZf/MuK1lWMpxr4Ez2wIx3dDU+AWc6ufDrpfQ62v43vnn6Yha89Z2ULS8Y+IIDW587iN/lZY9u51m1I/vtv6xlVzQQHB/Pee+/RsmVLAJYuXcpHH31Ebm6uWfsVdirq/6833mMN/WYeiiFq6k5yk7LN2m9NoMwRghDiESnlrxayp9xUdoSwfcE/bIs8QIpzIEu6G554848Qbo0OvHU6djx5prhL1C0yElg4vwOf+hZc4Hy+/TNM7GS7N9TCpOXqaF5ofeHp3z7DKy2JkS++Tqve/axkWdnoNRrOty+YB6m2pdiOjo5m3jxTGvH777+ftm3bmr1ffY6OG++Z4iU8hjTCY3CI2fu1JlWaMhJCbADOAa9IKXWlHmxBKisI235cy/aoQ+xu2pmTDULw1mk4e7tp/fqWIBwZuRx7v5bVZm+NR5PBxi+b8mqgf4HmyW2f5NmuL1vJqIpTuKynY04Wz//8AQKY8tMfOLnarvdJypo13HjtdeN2wOuv4/vkE1a0qHqRUrJ06VLOnTN49Pn4+PDcc89ZpubC7uskrzHFLdSb0RuVg+16plWFqk4ZDQeygK1CCP+yDrZ19HkCeMXPkASur4vpKWvRng+NrxUxKISDK3e8Hs3JR46yKCHT2Dz39E+ELQxj6RmbG0QWS38fd6IHdmS4n2H9IMfRmU8nvc/p5h2Y8+Q4Vn/+YRlXsB6ed91FqzOmNa3Yjz/mbKvW6DUaK1pVfQghGDduHM8+a5gmS0xMZMaMGcTGxpZxZtVxu60+wW+bnA1uTNtD1rlEs/dra5QpCFJKvZRyKobkczuFEBOFEN2FEDVyaV4vDY5O6XlJt/rUN4XTf3JxCQBfu7W3vGE1BbUdnV65xMnHTrA4w+QV8v7BjwhbGMa/l/+xonHl5+ewxoT3NSX/+2fw/Xwy6X1OHz7IZ2PvJD6y4lHwlkCoVLQ+d5YG874ztp1v34GkpcusaFX1EhgYyLRp0/D1NQSLzp07l40bN5q9X7W7Aw1m98W5g+G5N+GX08R+d5ya6nhTGcrlZSSEuBOYDDQA9gBtgLZAkpSymVktLIHKThltmr+K3TePMq//GAD+696SVq7OSClpv8ggBCcfOwG1yJvDrOhy2flZCJMDC0Z6/zz0J7oGdbOSURVjZUwSk/Mlzut4ah9Ddq3FwdmF53+x3RutlJJzrdsUaGt15jTCAlMsluL48eP89ZfJkeHNN9/E0dH8CetyrqUSN/e4cbs2Jcqr0pSREOIK8CzwhZSyvZRykpSyn5TSFxhQvaaan8IC2MLFMFL4fe9sU6MiBuVHbUff129w8sH9zIo1lcJ8YsOThC0MIz4rvpSTbYN7Ar25OaAD9nn/92PtevLJpPdJRMVnY+/k6omjVraweIQQtD53lnqffWpsO9emLem7d1vRquqlQ4cOvP66ad1k1qxZXLhwoZQzqgfHEA/qf3AbIm8d4easA2QcijF7v9amPIvKraSUNpe3obIjhI3z/mJP9HHjCOGWh9GtxeTpjo25d9zqEs5WKJPMRL6f34FvfLwKNB9/7HiNKP1ZOKitxaVTjN5kiBZ+5Y81NhsHULh8p9rbmxZ795RyRs3jr7/+4vhxw1N7o0aNePzxxy3y/0jdeo3UjYYRpH2QKwEvdrLZz0F5qNIIwRbFoCqUNUF27721rzC6RXHxYeLLkZwctpT22TnG5g6LOvDuf69Z0bDyEebuQvTAjoS5GXI9XWjajk8mvU+aqzufj7uLa6dsM9utsLMzxC288DwAuqQkzrZqjTY62sqWVR933303EyZMACAiIoL//e9/pKSkmL1fj0EhBL7SBQBtdAbX39xFbnJOGWfVTGz/ka26KUYRcnLzBaTYKylyq4XANvz2zAUOtjAFVv0d8S9hC8PYGbXDioaVj03dWrKrhynHzrxH32D9gLv5c+ZbfPnI3Va0rHT8J0+mxT5Ths/wAQOJ++ZbK1pUvTRo0IB3330X+7ysvV988QWnT5s/m4B9gAv1P+iDcDJMIUXPPkDmSdufDq0odU4Qipsim7Ol5vjR1zScek3m5PiTrNKYAtsmb5lC2MIwsnNtOzK0mYsT0QM70sHd8JBwqlUXPpn0PllS8NnYO0mIumZlC4tH7eVF63NnccxLMR0/Zw5nW7WuNd4yarWat99+21iJ7c8//2T58uVm71eoBfWn98ZjiCFVfOJvZ0lYUqsmUOqeIBQ3RPg5ehcArzvUzJoANYEmT+/g5IP7mZpg8u3u9ls3Zu54y4pWlY8NXVuyuasp181XE6ZxpG0Pfnl1Mms+n2VFy0qnyepVNPzhB+P2udZt0FSiqJSt0rdvX55++mkATp06xfTp09HpzB876zE4BP/JhsjxrONxRE3diczVl3FWzaDOCUJpz0gP3rnAYnbUSRxcePiV65zo842xadmVNYQtDONqylXr2VUO2uWtLdxiS9+7+GTS+5zfv5vPxt6JNts2RztuffvQ6oTJffLS0GHEfvml9QyqZurXr8/UqVON2zNnziQx0fwBZY4hHtT7nynZ4/V3dqONzzJ7v+amzglCaYpg527+mq8KIJoO4OT4kyzPMqWJuOvvu+j7u+1nU40e2JEf2oYatz+d9D4JXn58Pf4+zu2xzbUR4eBA63NncelmiAtJmDefs61su8RoRXBycmL69OnUq1cPgK+//trojWROVI521J/VB4cQQ/3ymE8PkXUmwez9mpM6JwgSiS6fy1iOjc9j12ZaTtrLyTH/Mjwvq2qyNp2whWEcjz1mXcPK4K4AL672M0Wz/zTuJTbfNpJ1X33MgheftqJlpdNo8SIa/mAqTnO2VWv0GRmlnFGzmDhxIkOHDgUMLqr5y3aaCyEEAZM74jk8FICERWdI2XDV7P2aizonCABpTqYKYasPfmVFSxTwrM/HUy6zJ3iUsemR9Y8yfNkgKxpVNk5qFdEDO3K7rwcAR8N68cmk90mKvmmYQsqxzQcNt759aXHooHH7fJeuZB4+bEWLqpdevXrxzDPPAIZazpZaV3Dv3xC/CYY4kLRtkcR8c7RGLuLXPUGQkhRnkyD8dMEQdzBAW/f+FLaE+x0fcPLB/TyakgpAVFYcYQvDiEi17UXQX9s3YVUnU/aWTye9T6qbJ18/dh8RJ45Zz7BSULu50frcWeN2xMOPEPv5F1a0qHoJDg7mrbdMzgozZ84kJ8f8cQNOzbwIetOQOVl7PZ3rb+5C6mqWKNS5u6AEUpxNc9dRaAF4svUjVrJIwYiDC6+/EMF2b1OlsDv/upPJ/z5pRaPKpoeXG5H9TfUK5j/yGsdbd2X5B++w/tvPrGhZ6bQ+dxbP0aMBSPj+ey70vs3KFlUfDg4OvPfeezg7G1yGZ82aZZEgNjtPR+q/b/o7Xn97F/oc8xb8qU7qnCAApOaNEJy0prTBHXu8aC1zFArhM+pbTt69kf6ZBq+NnTEHCVsYRqY2s4wzrYe9ShA9sCPNXAwJ0Db2H8Oie57lzM5tfDb2TitbVzL1PppNg7lzANAlJtaqeAUhBG+88QZNmjQBDEFsN2/eNH+/dirqz+qDysWQDfjGe3vRpdSMyOY6JwhSStIcDU8Nfrmmf5Kwqz3Vp2oFHsF8+2w4a3NMdY97/N6DXVE7rWhU2ezq0ZqPWjQAICagPp9Meh8JfDb2TnJttG6B+6BBNPtvm3H7XOs26C0wxWIpHnvsMXr27AnA/PnzOX/+vNn7FEJQb1ovHJsaPr83Zx1AcyPd7P1WlXKlv65SB0L8BNwJxEop2xWzfwCwCriS17RSSjmjrOtWNrndmm+W8naIP7EePnTISeVGzBQATo4/WcaZFSPybCL//XaO1PjyLS6GDWxAl2GNcK0lKXarExl1mPZbHjdu9/TvyA8jFlvPoHJwOTOH3vtN8/Qv/jgDh1wNT3wxH5969a1oWclIjYZz+Up1Nt+5Azv/Gl8Ty8jBgwdZt24dAMOHD6dHjx5lnFE9JK++RPqeGwD4T2qPY6hnGWeYlyqV0KyGzvsB6cCiUgTh/6SUFRpXV1oQvvqDV5o3JM3ZlYG6DE5dnwRUjyBcPhrH+vnVIyx29iruf6sbPsGuZR9cF9Bp+frbpvzgZfoyHX30KHYqu1JOsi4avZ6Q7aZkeE8t+RKflHjunvoeTTrZZq2IwjUWGq9ahVPLFqWcUbO4ePEiv/32GwDdunVj5MiRFuk3bWcUKesMz7x+T4fh1NTLIv0Wh1UFIc+AUGCtLQjC6i9/Z0rb5mjt7Bmac4MjMW8AVROEM7tusO3XojlNQtr6cNu9zfGpV/JNPSM5hxPboji6MYLS/hV3PteBRu18Sz6gjnB5Xk9GO5t851eOWklz7+ZWtKhsgrYdM76+e/2vNIs4R79HnqTbXfdYz6gyyB+41nDBj7jdVnsWnKOjo5k3bx4AnTp1YnTewrq5Sd93g+S/DfW8/Z5sh1ML7zLOMA81QRBWAFHADQziUGz6QiHERGAiQEhISJeISuRlWf3Fb0zs2BaAvnHbOZf1I1A5QdBp9cx7/r8CbQMebknbvlWbEtBk5fLvD6eIPFN8CP74Wbfh5l13p5b0x5fS4dj7xu2pXV/n4baPWtGisum7/ywXMw3z8gN3r6Pryb207NWXO196w8qWlczlUaPJyStG02DOt7jnJZOrDaSkpPDFFwZX2169ehkD2sxNxqEYkpYb/qa+j7XBuY3lH/JsXRA8AL2UMl0IMQL4SkpZ5iNfZUcIq774lWc6GsxoHbmYeLmRgToHvn6yYsE5MVdSWf6Rqf8Rk9vTuL1fhe0pD4f/vcq+vy8XaR/8eGta9Qw2S582T0Y8Ty3uxQFnQ8W7nv6d+GHEIisbVTpvnI9k4Q1DaoMux3czaO96/Bs15rGPvynjTOsR+exk0rcZFpzrf/kFHsOGWdmi6iMxMZGvv/4agIEDB9K/f/8yzqgeMo/HkrjEsLDt/0x7HBtbdk2hSgVyzI2UMlVKmZ73+h/AXghhnjuroRPjyySSAOjtU7G8LpeOxBYQg8nfDTSbGAB0GRbKlHmDeHbuQOo19zK2b/nlLHMmbWVv3jC0TuHqx4JnLvBuvGEUtS/uqLHqna3yUcuGTGtqyLdzuMNtrBt0H3ERV/jxhQlWtqxkGn43F/fhBhG4/tLLpFqg2L2l8PHxYfLkyQBs27aNffv2WaRflw4BeN9vWJeJm38CzU3bSR9idUEQQgSJvHp0QojuGGwyW4Yovd4kCDoMUbFdQss/XIyNSOXf708BUL+FF1PmDbJYOT2VSnD3q52ZMm8Qd0xoa2w/8m8EcyZtZffyixaxw2YQggdevc6y2DRjk62LwuSQAL5pHQLAmRYd+Wvow6TERDPvGdud8mrwxRd43HUXANdfeJH0nbbt+lsRAgICmDhxIgD//vsvR44csUi/rl0C8RzZGIDYr46Qm2AbmVLNLghCiCXAXqClECJKCPGUEGKSEGJS3iH3AaeEEMeBr4Fx0qzzWPkEQRgiF5u2vKtcZ2o1Ov6cZRgZNGztzZhXOle/eeWkeddApswbxH1TTSO/Y5sjmTNpK1dO1L5KTqXR+rWrbHcyCUHYwjD00nbz098f5MMv7Qw3g/DGrVk36D4ykpOY+/TDVrasZOp/8jFugwz5pSKfnkjWyep107Ym9erV44knngBg9erVFqnABuDetwFu/Q0xK9GfHEKfbf2IZrMLgpTyQSllsJTSXkrZQEq5QEo5T0o5L2//t1LKtlLKDlLKnlJK81YGz6c1AsOTpcrZq1ynfv/CduPrUS92qlazKktgqAdT5g1i7DsmN8Z/5p5gzqStpNaC/OzlxWfs7xxucL9xu8OiDuj05k9qVlmG+Xvyc7tQwDBS2NZrGFmpKfz+zqvWNawUGs6dg3Mnw+f+6v0PoI2NtbJF1UejRo145BFD+po///zTIhHNAF7DG+OUt7B8Y/pepN66UeJWnzKyNPn/3EJf/lQIB9aYFnWnzLO9TJx+DdyZMm8QAx5uaWxb/M5e5r+4vZSzahcOg6dxvN1rxu2OizvatCgM9/fi27zpo0Md+nA4rBc3L55n84LvrGxZyYQu+d34Orxff/Q2Gn1dGZo1a8bddxvqZc+fPx+Nhd6b32NtQG2Ydr7xnnmfh8uizglCfkkQpdZPK8jBdVcBuPf1LtVtULXStm/9AoKVm6NjzqStxFxNtaJVlkPV5TFOtDdV0Oq4uKNN5+a5L8iHd5oYPMW23jaSa/Uac3zjOo5tWGdly0omf6bU8/kim2sDHTp0oGVLw0PVhx9+aLF+6880xHlIrd6qdZrrnCBU5taw7ENT/vigJtYNOy8vU+YNYty07sbt5bMP8efsirvp1kREp4c50cGU/rj9ovalHG19nmsUyH2BhiClpaOeIt3ZjS0/fUf0Jdt1Emh19ozxdW2qvgbw4IMPGl8vWmQZV2ahEtR7z1AxMOt4HFnnzV8GtFg7bPnpqTQqG4ew4pOfmdLVMA/qf83g2VFWUNqcSVsBeOrTvji52ZernzM3Uhnxdfm9MbqH+rB4Qncc7dTlPqe8/PjKDnIyTQtWz84diEplGc8oa5K741M6XVlo3K7ufFXVTaPtx8nJm0P+v3nvIpC8uHgldg62mXhRl57Bha4Gpwbvhx4kaNo0K1tUfWi1Wj744AMARo0aRefOlnEgybmaQtw8Q7qTeu/1QuVc/alZbDoOweJUUAD3/hVufF0eMfhkwzlCp66rkBgAHLiaSMt3/iV06jpCp64joxpzqE/4vB8jp5iekr+bvK1OLDjb9fs/9rub6jTf/Vf5vMmsRUS+mgqfTpoJwFeP2m56C7WbK41++xWApN+XkBMeXsYZNQd7e3tjjMLq1auJj7eM555jqCeuPYIAuPG/vRaf7qxzgiArOGl0ZMM1AO57o1hBNRIem07o1HXM2WYKEhsRFsS5mcO4OntkiT9XZo3g9WEti1yv7XsbCJ26jvUnq8fbITTMj2fnDDBuL35nL5eO1B4vkZJwued71t00BCCGp17ll5M/W9mi0rk+wCQKawfdB8B3E223eJNLly64DRgAwOU7bVtwK0pAQIAx+d23335rsX697zYlakj596rF+oW6KAgV0AOd1uTLHtjYo8Tjvtp8kds/N3nzrJpyG1dnj2Tuw11wsi99CkgIweQBzYwCse/Ngvlinv3tCKFT17HuRNWFQaVWFVhw/vf7U+xaZrvz1NVFyNQoZscanvA+O/I519OvW9miklELwaauhijWsy06kuDlR2ZKMlePWyZgqjI0nGfyiqpt6wndunVDpTLcJjdaMEq73jRD/Yb07VHo0iznyVXnBKEirPn2WJnHTFt1ii82G5JVDWzpz9XZI+nQ0AsAnS6T4yeeYcvWpqX+pKadMl4vyNPJKA73dDIlyZvyu0EYEjOq/uGYMm8Qnv6GIkHHt0aye0XtGeqXxMhXo2ibV/Rl2ArbzscT5u7CcD+D88JP414CYMWH02zaW6rlYdN6Xsa+/Va0pPp5/fXXAdizZw/Z2eWrb1JVVC72eAwNBeDmB5b7e9Y5QajIlNH188kAPDyjZ7H7Vx6JYtFeQ8bV2feE8fMTBq+e2Nh/2bK1Kf9tDyM+fnOZ/Rw8ONooDsnJpi/W52M7cnX2SO7r0sDY1nnmJsbO31vu91ASj8zsRUhbQ0DMsU3X2Ffb8yGp1Pwx/DfjZtfFtu0+/HNYY+PrxfcYgvo/H2e7UzIqV1f8X3wBgGuPP25dY6oZJycnevUyrEV98sknFuvXY2BD4+vMY5aZ3q1zglAZvAJcirRl5OTyyrLjALw1ohXjuoeg1+ewZWtTTp6aku9IQefOfzB40KUiP+3aFZ2XPHxkLFu2NuXKFVMGzE/v78CVWSOM2/uvJBI6dV2BvEyV4a7nO1C/pcHd8fC/EYQfruVrCg27sU9rqACWo9dwPO64lQ0qnRO9DfmqogMakJVX9jXu2lUrWlQ6fs8+a3x9/bXXrWhJ9XMrPbZOp+PSJcs9PAW+anhwSfzjvEVGiHVQEAr+UQNyi49kjY8qvf5p2/c2GF9P7NeUjIxLbPvPVGmqdeuP8m784Xh7FV8dKzBguFEcBg0Mx93dlI/n8pUvC4wYhBBcnT2Sn58wXavJW/8QlVS1wvNjXu6Ed5BB8Db8cIq0RMsMia2F64StPJVsyGH1yD+2u1gLEOBoTwsXQ3rvb594G4BFrz1nTZPKpMn6fwBIXbPGpqe4KsOECYastIsXW658q72/CyoXg+tp6uZrZu+vzglC4Y+obwl/gh1/GPKVF1ftbP9lUzLWK7NGkJ0Tzb79dxjbBg0Mp17wfRWySwhB925/M3jQJVo0f9fYfmvEcIuBLQMI/2C4cbvPR9s4dT2lQn0V5qHppimxRW9ZN3TeErx0/2rj69n7Z1nRkrLZ0aOV8XWcdwAAF/btspY5ZeLY2DTVdXnY8FKOrHk0aNDAmNn44kXLOWMEvmrwcEzboghC9VPoqcVbFB/4cTPccJPtN65oPdmx3xvypr8+rCVCCHbvNpUXHDzoUpXTYTds+DiDB13Czc10M9iytSl6vWFR1E6t4upsUy3YO7/ZxYWYtCLXqQj5vY9uBeLVWup1ZHmUwWvrt3O/l3Gw9Xm8vqHWxi9jDXP0a76YbU1zyqTFfsP3Q1OJioa2zq1U2bfqMlsCtas9wslwnzL3WkKdE4TCIwQPVemlKOsXqnua38tn8oBmbN1mEozBg6p3brFH93Xc1tv0NLjtvzZoNKYAmfyicMcXO8jWVi2R2/hZJmGLj6qawNg6LV8xPeH9b+//rGhJ2cxuYXIqyHA2jFgTosz/tFhZ1J6m9C4xFlyEtQTBwaYKhVlZlgvuDJhiiE9JzJu5MBd1ThAKS4KnXdEF49IY+Ol/ADTxc0WrTUJKw014QH/zpEVwcgpm0ECTW+jOXT3Q6UzrBvlFodW7/1apLzdvR1w9DWkSlr5/sIyjazjO3vwddQOA5ReWW9mYsungblhUnjv+TQB+eXWyNc0pk9BlSwFIXPCTlS2pfvr16wfAsmXLLNanvb/pPpWbZL51vjooCAXxcHCv0PEpWVoAVj/fhx07DXN7Li7NUKsrJiwVQQhRYPTx3/aCVcHyeyAN+uy/KvX1+Ed9jK8vH42r0rVsnaYTTesl5xPN++RVVdZ2Ljp1acs4tzelStFn2E6JyOpgQF5k9pUrVyzar32QYXQYN8983nF1TxAKzRm5OxSNQE4vQYHze024OZrWHnr2qNqTeXnJLwr5F5qFEKyc3BuAy3EZ5OqqVi2sZU9DLpX18207GVyV8W/J6DSDN9l9ayrmBGBp7PMlI7y1uHzpsI0HgOWtpV1/4w0rG1K9qFQqY/RySkrVHDoqgt+EdgDoUswXuVznBKHwcq+7Y9F01pePFZ/I6u9jppQHsbEmt1NL1VQG6N3rP+NrrdZU46BziGmto9nb66vUx+2Pm9xndVUUF1tnRkKytU0oNwO8DaPZFfcZ/P3//nimNc0pk1vFdNI3b7GyJdVP17wsr8eOHbNYn2o382e9rXOCUBgX+6JTPXGRhgVVV6+CC84f/2uYVhjaNpCTpwxzuA0bPmFmCwvi7GyKXtyxs2AZz2PThlR7f2u/se3graqieszkgmrrfvNf5lVXS1OXLwW7tXHu2NHaJpiNTnmlRI8ePWqV/jU3So+TqixmFwQhxE9CiFghxKkS9gshxNdCiHAhxAkhhFkTj4tCYwRHVVHVTcgLSvNr4Fag/WaKYSrpidtMvtbNmr5GmXz8MWzbVrBt2zZDeyUY0L/4IuBeLqb3cvZm1Sqk9b63GQBR55KqdB2bp3Ff48u9N6qeEsScBDnWDCGoC9zyNkpOTrZov/Z5cVHJf5sn/5glRgi/AKVlExsONM/7mQhYtKCsnSj6J0i4bhCE4oLSALqF+hhfq8pwWzWc0A0eeMAkCtu2Gba7FR/BXBZqtZPxdf5po/yMmbO7Ute+RachIVU6vybRSGtwFFh2wXJeI3UNWYtqL1sTp9aG/GOaa+ZxCze7IEgpdwCl1YMbDSySBvYBXkKI4FKOr1aKmyTQ6wytDk7FB62pK1ptbOBAWLbMIALTphl+L1tmaK8iN278UWD7ybzRS05u7Z77r066ZBsC/mw9t1FxSH3N+D/nWNgjp7Zi5+tU9kFVwBbWEOoDkfm2o/LaiiCEmCiEOCSEOBQXVzmXyMK3cp200Bdq4EB49lmYOdPwuxrEACA9o6C7ZKif+dxfayueeQvnqTlVm2azChZ0aKgKOgt649RmzFFSs8D1zXr1akZK+b2UsquUsqu/v3+lrlERQajWRcZt2+C77+Dddw2/C68pVJIA/4L5Yv49FV0t161LXLU3fMkauDco40jbw5IeblXBzq9y31eFgpjT5RRsQxCuAw3zbTfIa7MIelH0pu/sbli8S0/KKfac5MwK/lNurRksWwYzZpimj6pBFPz8ClZY23PJkHhvTMd6VbpuVnrdmfPd5moYVfVv2N/KltReHBqHWtuEWkFubF6WAjvzPAjYgiCsBh7L8zbqCaRIKaunkHAxFPYy0hUzB+sfYghWi40ofgph6UHTDFf+gjYlcvBgwTWDW2sKByuXHiLi2g/G1yU9IX72QMdKXfsWdSHrKQA5Jve9x9o8ZkVDysbW3WJLo6aMZMqLTle1vGGVJX2PId2KxyDzOH1Ywu10CbAXaCmEiBJCPCWEmCSEmJR3yD/AZSAc+AGwaJIWrU5bpC2gkSEAKD6yoK/vuG6Ggcys9ecICDCkizh8ZGzZnbz+etE1g4EDDe0VREpJeLgh22XTJq8W2HfPXJNnUYUXvguRqzEI5T3/Z1YvYOuzyvRx83P2s6IhZTM3smalEtGlm8dX3hY4dMjwINisWTOr9O/ev2HZB1UC865QAFLKB8vYL4EppR1TnRR+UsnSFF3sahTmy6F/rhZpf3NEa/7IGx20bfMpsbH/mMXG0ti6zfQBDA013czi03M4ci0ZgKUTiy/5WV4uHowxvg5u5lWla9k6f13bDP6+1jajXMy8ZHg6HL5tBQDtb7ft2tDXnngSAOFS+xwd1q83ZAMYNsxy/wOZL2uAUNfeKSOrkppdNPAqqHHRdBYAns6mwKCcXJOWHj06vvoNK4b8+YsG9DfF+Ukp6fq+qXZzjyZVu8FtXGAIfGvTt2rrEDZP3AWm5YnBx/0qFyRoKbT5yqW2O2+Ijr19gsWeoypF9klDLqyma9dY2RLz4ednuVFl4pJzZu+jzgmCKBSIFp9TsUhcFwc1AN0/3GysVZCYtIv09AvVY2AxZGZeKSAGvXttQ602pEPW6SWN3zSNVPKnw64M+YvjDHy4VSlH1nz2LDBFKQ9vbNvVvTrsKRrob8vz8mlbTQ4T9vVq14PFrl2G7727e8UyJVeVrFMGh5GA5zqarY86KAgFt2O1pafm1RUK8Dr49u0ApGXngjoAHx/DTWX/geFkZlZvhSgpJVu2NmXvvtuNbf37HcPZ2bCgdDkunaZvmcQgf2nNyrD2W1Ng1mMf9q7StWyeE3/yTLAha+gb3Ww7G2eKNpfEvOJHL/44A4CJc3+xokVlEzXZMJ0ZNP09K1tSvej1ejZvNozGJ02aVMbR1UfyP6bAPocG5hOiOicIhSMR4vSlF5s4uLZghKVrvrTXrd79l04dfzFu7903iEuXPquyhVptKlu2Ni2wXgCG9Nd2doYPw8BP/2PQZ9uN+y59OAI7deX/nbuXXyQi7wmk191Ncfcxb0SkVdFm0fvQdOPmI20esZ4t5aDlLsPowD0tGYdcgzuwu6/tLoDfeOtt42vvceOsaEn18+uvvwLQtGlTXF2LT21T3Ui9JH1HFAD+kzuYta86JwiFh9kxovjAtNufMKSAPvxv0af+/AVpBn/2H4MHXcLZyfDUfjViLlu2NuXixQ8r5Cao0cSzdVsLtmxtWiSLab++h421EH7dF0Ho1HVciTeNbK7OHlklr6LF7+7l2GbDYnmTjv50Htqo0teqCfzyTXPS8sRz1zjbLVgP8NQp0wPJpN8+BeDl31dZy5wy0URGkrJyJQCNV9uunZUhKSmJy5cvA/Dwww9brN/rb5k+o44hReu3VCdm9zKyNQoLQmwJT9UtewSx+eczJV5j08v9GPLFDi7FZRA6dR1XZ28jKekAR44anKquRS7gWuSCAuepVM7Y23uRk1O+MIv+/Y4ZRwQf/nOW73dcLrD/r8m96ZSvDkJFkVIy91nTXG/bfvUZ8FDLSl+vJrDjo0A+CzJMFc28bSaexdTDsBVWxyazLs7gBTf+z28BuHvqe6jUamuaVSJSp+PSkDsAcGrfHqcWNavKW2loNBq++uorAIYPH24skGNuUjaZHkjrf3BbKUdWD3VOECqT+2Xnsgv0faDgh7t5oDt/Te7N3XMNAVyhU9ex+KnuDB50iaSk/Rw5+lCR6+j1WeTklF6Yu3u31bi7twXgeGQyo+esK3LMswOa8sawqi34Xj0Zz7o5J4zbQ59uR7MuAVW6pq2z9eMgXswTg7tChzOm2RjrGlQKu5PSmHj6KgC9Dm0lICGapl170qRT5TLkmhspJefatjNuN86rqVwbkFLy4YcfAoapoh49elik3+yLSaRtuQaAz7iWiCpMCZeXOicIhSOVS+OBt7ux7IODnNgaVUQQADqFeHP8vTvo8L+NADy64AAAjf1c2fDSRRzsVEip5+bNlURdX0RamqmOgYd7exqGPElgwAiEMDzxpWZrGf/TAY5cKyoCAB/eHcZDPaoWoZir0TH/he0F2p75uj92Drb51Fkt6PXM+7oRcwIN+XT6BvXgw/6262a6JSGVh08YRoONIsPpc2grzu4ejHntHStbVjxSSs61NlXZa3W2+JF1TeX99983vn700Uct0qcmKo34BYa1I5cugbh0tMzDWt0ThAqMEPwbmlbzN/9ypkBpyVt4OttzdfZIFuy6wsy1hi/ClfgMWryTv4ylM/AM7o52uDiqSc7U5ktPXXo9Zi8Xew68dTsOdlV7OtDrJd9NLpg7KTTMl5FTzLtIZXXiLtB/zRgSvb0AuK/JXbzX90Pr2lQKH1+5yedXDYGBDW5c4YF1v6C2t2fyj79b2bLikbm5nGsXZtxueeyoTbvDVgS9Xs+MGTOM29OmTbNIv5rr6cR+ewwAu0AXfO633NSbIghl8ND0Hvw+fT/n90XTY1STEr1vnurTmKf6NGbf5QTGfb+v2GPScnJJy8kts893RrZmQt8mFbKzJDRZufzw8o4i7c/OHYiqiuktbJ24Px9jUOZRyJtz/6jPbEY0rVqchjlpsfMEqXkPCu3PHGTojlXUa9mGB2fY5mhGExlpXDMAaHniOCoH89f9tQSZmZl8nK+i4VtvvWWRdYO0XddJWWsYHapc7Qh6uYvZ+8xPnROEogmwS8c7yBXvIBeSojNZ9NYenvmmP3b2JU+v9GziWyA4LDolmx93Xubf09FEJZnWD0J9XRjaLogHu4UQ6lf97muXjsTy7/dFg5me+qwvTq61vBRjehwTfu3NfmeTeP/3wH/4OttmioqbORo67TFNs4za8Dstr5yhz7jH6HH3A1a0rGTi5s4l/utvjNutzp6pNSODmzdvMn/+fMAQfPbKK69Y5L1Ff3aI3DjDPcKxhTf+T7Yr44zqp84JglAJkBKEQKJCUHaBnIem9zRG8M5/fnuFbqpBnk68c2cb3rmz6HRTdZMUncHv0/cXu+/pL/uVWAGu1iAlx+Z04FF3CXli0NojlGV3227qhCdPXuGfeFM+red+/gDnnCye+vpHvAKDrGhZ8RSeInJq04bGK1dY0aLqZeXKlZw4YXC26NixI2PGjDF7n3qNjhvTTNmFve9pjmt36/zva/kdojgEDrpcNHb2SBwRZIFeB6rSF1WnzBtkFIUFr+6k191NbcJf//TO6/z32/li9zXvFsgdT7W1sEXWIXrTOwy5sQryBXFuum8TQa62d1MFOJKSwYgjF43bgXHXeWzFdyAEry5da0XLSiZhwQJiP/nUuN1w/jzc+teOGhKxsbHMnTvXuH3PPffQvn17s/eb8u9V0v4zpdMPerM7dp7lqNNuJuqcIAghcMjVorGzRy1dkSKLs8cX07rT42WeO2XeIH54aTuabB17/7rE3r8uMeTJNrSwoJpfORHPP3NPlHyAyPMaKmVaqzaRtO19+l0r6OI4qc14pnT7PytZVDoJmlza7i44lTfh98/xTk1k3P8+pn4r848kK4omIoJLQwtm9Wx1+hTCRuMhKoKUkjlz5hAfHw+Avb09r7/+Ovb25p1WzU3MJvrjgvVQ6s/qY/VptzopCC6abNKdXHCTPqSJeH49/BUflEMQAJ7+sj+RZxNZ/dUxADb9dIZNPxnmf29/vDUtewZXi51SSi4ciCkxOC4/IW19GDmlQ61fJM7Phb+e5N7Ugl+o23zaMu+uP6xkUemk5epovvNkgbaeR/6j74HNtOzVlztfsr18Srq0NC50616greGCH3G7zfwBUpbg119/JTw83Lh933330a6deeftpV4WiDwG8H+2A46NzBuBXF7qnCAgBO7ZmcR6+NDDozub0y+w2j6XDypwiYatfZgybxAXDkQbxQBg8y9n2fzL2SLHu3o5EtzUE3dfJ/Q6iS5XT3aGltirqaTGl55LqTjsHFSMfac7XgG1L898qWQls2RuWz708ynQ3MqtIcvuWWf1p6viiM3R0n7P6QJtAXE3eGzFXASGNBS2FnmsS0/nQteCAXAeI0dS/7NPSzijZrFhwwb27t1boO3NN9/E0dF8UzVSSmK/PYb2uqlokFMrH/wet60p3TonCCJPEABc/fpB+q+VvlaL7kG06B6ETqdnxUeHibuWVuxxGck5hB+OrXQ/d0xoS7MuATZ5w7ME8Xu+ZODFvDQg+cRgbMgdvDOw6skEzUH+4LJbuKcl88xvnyGQvLB4BfYO1psrLg5NVBSXbh9SoM2+Xj2abtlcKz5769evZ//+gk4XL7/8Mp6e5ktfIvWS2K+Poo0umFW5/szbEPa2l0qu7gmCSo17tkGlI7NyTDvyPI8qg1qt4oG3Cj5RZadrObr5GuGHY0mNKzldhZuPIyGtfWjSKYAGrbxRVzEArbagizzAa2seZJNr0VHQt/2/oH/o7cWcZV20esmYoxc5nJpZoL3BjSuMW70AFw9PnvltJWo723L7TVm1ihtvTC3QZhcURLMtm2v8OkFubi5ffPEFGRkFb8jPPPMMwcHVM71bHHqNjhvv7YFC+S2D3+mB2s12YzXqoCAI3PLyCV3XmlxO//lnCiNGzi3ptArj5GZPrzFN6TWmadkHKwCgizrIm6vGst4tLy4jnxiEuTZg4d2rsVfb1s0UYH5kLO+F3yjSPnjXWjqf2kfY4KHcYWOeQ/rMTMLvGIoubzH1Fu5Dbqf+11/X+BFBXFwcc+bMKdJubiHIDk8i/sei8T/B7/ZEXQPif+qeICDwzjBM7Vyzd+LthsP5NHI9b8TvZEQZ5ypUPzH75zD+5Ldct8/7KLoVDNJbNepvmnjbnqhuS0jlwUJTQrd4dtFs3DLTeWT2VwQ2tq38Q7FffknCvPlF2ut//hkeI2r2NyA3N5eff/6Z69evF9lnzjUCmasnds4xtDcLjkKEg4p67/ayyamhkrCIIAghhgFfAWrgRynl7EL7Hwc+AW79J7+VUv5oJmNwzzEM6VMdXRg/8GM+XWjIO6TXZKBysEzRi7qKjA/nj6Wj+dAt35fEvuDHcPmdy2jp29rClpXNXzFJPHum+Kp4d6//lWYR5+g2+j76/Wxbnk5Jy5YRPa1o5TKVhwfNtm5F7VazP/MHDhzgn3/+KdLevn177r77brONdlL/iyT136tF2j2Hh+Lev6FZ+jQ3ZhcEYUjlOQcYAkQBB4UQq6WUhf0pl0opnzO7PZScvGLY4q5sfKqol5BC5ZHpcaxe+RDvyGhTo1vBJ6bmDj78MGalzaWW0Oolr52P5I/oxGL39z64hd6Ht9Gqdz9GzPrIZryFpJTEz51L/DffFru/0eJFuHSzzTTa5WXXrl3GUpaFefXVV81W7zh9/02S/wovdp+trw+UB0uMELoD4VLKywBCiD+A0YBVcuQW97Sw+4Ed3LasHzft7EiK3Id3w55WsKx2oLm2j+/XTWC+S+lPZVM7PMdDHSba3Fz15oRUHilhKghgwJ71dD2xm05D72TQ/72MUL1qQetKJjcpichnJpF9ovigxeDZs/CyQBoGc6HX69m4cSP79hWfOPKBBx6gTZvqD+qTUpK6+ZqxLkFhfB9vi3Mrn2L31UQsIQj1gch821FAcRUm7hVC9AMuAC9LKSMLHyCEmAhMBAgJqWRdgELBW1k6PR7O3oQKJ67KbPptfZqTjxwBG1y8tDnSYti9/nneSj9FYv6n42LEYGLoXTzbdwZ2KttatjqSksEDxy+Rris5p9VDf82nfkwkg5+aTMe337SgdSUj9XoSFiwg7rPPSzymwdw5uA8aZEGrqpfo6Gi+//579Pri/zfmEgFdqoa4H0+QG1u8d6D3/S1w7RJY7f3aArby7VwDLJFS5gghngEWAkU+yVLK74HvAbp27Vr+gsX5uPVE2iImmguBQSy9cIXHWzdlzWMHCVtoSNoV9mtnTjx0EGFfiwvNVxBt1EGWbPk/PqGY6ZNipkr+r93TPNJpCuoyckRZEiklS6MTeelckWeNAnQ8vZ9Bu/+hSbv23PXyVBwHfmchC0tGSknSr78R80HJIZR2/v6E/rEE+/r1LWhZ9ZGTk8OaNWs4daqol84tHnvsMZo0qZ7U8LeQeknatkhSNxW/PgTg83BrXML8qrVfW8QSgnAdyL/C0gDT4jEAUsqEfJs/AmZLAH9LEHpfCudCYBBTo9N4PG/98tDDB+n6m2Futf3v3VjTaSqh7S1XTNsW0ESfZs22qfyQEW7y/CmDAR7NeXvIHILczOfOVxmuZeUw9UIUWxOLDxi8RZOIc4zcspwAT09G/9/bBAx8Bp57xkJWFo8+O5u4L74gceGiUo8Lmj4dr7EP2NzUW3nIyclh7dq1nDx5ssRjWrRowb333lutHkJSStJ33zDWHSgOOz9n/J4Os2qiOWtgCUE4CDQXQjTGIATjgAIFh4UQwVLKW5XnRwFmW9l1yAsKahlTtNC9o50TRx45TOdfDUUp7jo6G47OZtfA7/EM6WUukyyOPukq+3bNZnnUVja5lPCBL0EMHgzsxaT+s/CxsQXgS5nZTA+/waaE1DKP7XJiD30PbKJJi1YMf/5V3Ad2hMfHmd/IUsjYf4Abb7xBbnR0qcf5v/wyvhOeqpEBY9HR0axcuZLY2NKj9sePH0/jxo2rrV+9Rkfqhquk7y4aK5Ifa6adthXMLghSylwhxHPABgxupz9JKU8LIWYAh6SUq4EXhBCjgFwgEXjcXPY42hm8AHT51hLWRycyPMiwMGSvduDk+JO8vvJu1qcZvAn6bJsIwPAcPR/ctxp7H9vzizei15MdsZs9x35gS8wBNjiqySmp0lNJYgAMcGvChNum0SHIshWbykKrlyy5mcCMSzdKnfe/hXt6CsO3rqDRjcvcPmEy7QcPQwzsCEw2u60lkXXyFNEzZ5a4AJyf4Fmz8BwzusaNADQaDdu3b2f37t1lHlvd00DZl5JJXHoefaqm1OM8hoXi3q+BoUaKAgBCykpNxVudrl27ykOHDlX4vFPL97H81L8Epuu43KYpixt3BCB6YMcix+qlnnt/60O4rvgpBw+djifsg7m70yR8W40COzMNL7NTyLpxlJOXN3A05hBH0yM54qAmq4ol/eqpnLi36Wju6TQJP2fbmh/V6PX8HZvM1xExhGfmlH0Chpv/7TvX0DTiHD1G30ePe8bi4ORsZktLRubmkrJqFbEff4IuJaXM41379CFo+nQcGtSsNQCNRsOuXbvYsaNoqdbC1K9fn7vvvhs/v+r5vGmi0kj6OxxtVHqZx3rf1wKXOpwT7BZCiMNSyq7F7qtrghC+9hi/Hvob7yzJgyEBtG9jSOX7lL87H7Qr+cn/zPV9jN38dKXttQa+wp47gnoxov0TdAjsYpNfhBNpmXwfGcfymKQKndfm/FH6HNxCiwB/+j38BCHtzF/MpCSklGTs3kP8t9+SdexYuc5xatOGoP9NxzksrOyDbQQpJREREWzatKnYaODiGDJkCD179kRdxSkuqZdkHo0lZf0V9OnaMo93aumN193NsfOqW2sA5aE0QbAVLyOL4eRk8BzSqAXpGzbycaNGvO7agAVxaXSPTmR0UPE+xW3q9+TkeNPi15XEC/y4811WJ1s+nKKtnQedfNvRuckwuoYMwNvJ2+I2lJcsnZ718Sn8diOB3cllP8UVJvTaBXod2U6L7FS6j7qXsMFDDU/9AzvCpCeq3+BS0Gdmkrx8BQkLFpAbE1Pu8zzuvBP/l17EoUEDM1pXfUgpiYyMZPv27Vy6dKnc5w0aNIjevXtjZ1e120rOtVRSN0aQE55cruPt67vhPaYZDg3NE4xWl6hzI4SEPRF8s/Fn7HVwz59LaX3uLCO+X8iR5h0A6OvuxJ9dW1WbnVJKtHotObocUjWp2Ak7nO2dcVY7Y6eys8mn9opwISOb1bHJrIpN4mI5p3YK45KVTpcTe2h/9hAdOnSk2133Ety8ZTVbWj506emkrl1H0pIl5JwvvjRpSTi1b4//c1Nw7du3RvxftVotx44dY/fu3SQnJ5f7vHr16jFkyBBCQ0Mr/T6lTk/m8TjStkeRG5NZ9gl5OIf54XFHI+z961gtkGpEGSHkwzFvIVWbN4LVpafzz8Tx3Dv3e3a37s7OtGyCth1jYj0fZrSsZPBbPoQQOKgdcFA74O5Qc55g4jRa/ktMY1tiGlvjU0guxwJuaQTGXqfD2YO0Cj9Jt34DaX/7MAKbNDMdMKJPFS0uH1KvJ/PAQVL++ouUVasqdQ33YcPwfepJnNq1s/kbv0aj4dSpUxw8eJCbN4t61pWGn58f/fv3p02bNpWa8pG5ejJPxJGx9yaayNJdfwtjF+CC59BGOLXxtfm/cW2izgmC2rFgBHLU5Ck0WrSQFZMnsnr130x0DwXg+xuJfH/DEIR1t78ns1o2xKucfvm2SFqujiOpmRxKyeBQSjr7ktPJqsbBYbMrZ2l56STtEm7QvnsPWvbqS/2WbRDGhe+OwMjq67AEtLGxpP27gdT168k6erTS13Ht3Qvvhx7CbcAARBWnQMyJlJKbN29y5MgRDh8+TGVG/K1ateK2226jQYMGFb756tI1ZB6OJeNgNLnxJdf9KAnHZl6492uAY3Mv5cZvA9juJ91MqArlJM88cICcy1dwbNKYUaPGMDI3lx8WL2R6qMnd8q+4FP6KK+ol0svDmcF+XvTwcqOtmzMu6upPcyulJF2n52pWDlezNFzNyiE8M4fzaRlczMwhw8wzfh5pyYRGXqTxtQt0yM2gZdswmnTqRkhYh4KFXgZ2BB40mx0yN5esY8dI/+8/0rZuQ3O55KCi8qD288PrnnvwuvceHBo1qiYrq5+cnBzOnTvH6dOnuXDhQqWv06hRI7p160arVq0qNMevjckg82gcmcdj0SVVbkrQoZEHbr2CcW7nh1AKQNk0dW4NQZeSw8wvZgHwYps2xrTAjX77FZcuBX3uk2Oi+XrxQr7rNARZRRdPWyIg7gYNoiNoeOMKLTOTad2iJaEdu9AorCMunl4Ws0PqdGSfPUfmvr1k7NtPxv79oC3bg6Q8OHfpgseI4bgPGYJ9QEC1XLM6kVKSmJjI+fPnuXDhAlevXq3S9RwcHOjcuTOdO3cmoJzvV5eaQ9bpBLJOxpNzuWy32NJwau2DW89gHJt7K379No6yhpAPlYcDQoIUYDd8OA4LfkITEUHEw48A0PLYUVR5nkhegUFM+783mJZ3rjYnmxObN7Dv4D522rtzrll7ogMs7znilpGKb2Isvsmx+CbGEZiRQnMXB0ICA/Gt3xDfBg0JatoCV6+SvI86msWu3IQEsk6cIOvECbKPnyDz2DFkZvkXDMuFELgNHoT7wEG4DeiPna9tRUzn5uYSGRnJxYsXuXjxInFxcdVyXT8/P9q1a0dYWBi+ZbxnXaqGrHMJZJ9NJPts8am7K4pzmB8uHQNwaumtPOXXYurcCAHgr3d+5rhdBO3ateO+++4jesYMkn5fUuAYl549qf/F59h5V92lU0qJXpeLUKlQ2VCyt8JIKcmNjiYn/BI54eHkXLhA9rlz5Jw1f40IpzZtcOnVE9eePXHp3BmVq20UbZFSEh8fT0REBNeuXSMiIoKUcgSZVYQGDRrQokULWrZsSUBA0cApKSW6xGyyw5PJuWT40WfkVlv/9g3dcQnzw7mdH3Y+SkLH2o4SmFaIiKnb+dlpGwDTpk1DpVIhtVou9OyFvlAx7sK49OyJ+8ABOHfujGOLFqjMVJavLKRWS258PLkxMWhv3kR74wba6zcMv/O29WkV8+yoTpzCwnDu1BGXLl1x6dIZu2qKTK0KOp2OuLg4bty4wfXr14mKiiKmAvEEFUGlUtG8eXOaN29Os2bN8PLyMu7TZ2rJiUxDE5GK5loammupSE3VvLiKwy7QBefWPji19sWhobsylaMAKIJQhKipO1njcIgYleFJ79133y3gVpd94QLXxj+OLqli0bO1DbugIJxatcKpbVuc2rbBqXVr7IKCrOoNkpWVRUxMDNHR0cTExBhfl5Qzvzrx9PSkUaNGhISE0LhxY7yc3NFGZ6K9kYEmKg1tVBq5CdlmtUHt64RTUy8cm3nh2MSzxlfoUrA8iiAUIutUPPG/nmGB01ZjW8OGDXn88cdL9LfWXr9O6r8bSP3nH7JPn65Uv+ZG7emJXf162Ncz/TiEhOAQ2hiHBvURDta5eej1epKTk0lISCjyU93TL+XFxcWFev7BBLn4EoAXvhnOqOJz0SWa94ZeGPuG7jiGuOMQ4oFDQ3fU3o6K+6WCWVEEoRiipu5EIguIQn7CwsLo1asXwcHBtf4LKqUkJyeHlJQUUlNTSUlJKfBzq80ST+EVwUXthK/KHW+NCz5aN3ykG17SBRWWX/RU+zjh0MANh4Z5N/d6bgh7ZfFVwfZQBKEY9Jlabsww1GfNJIffnXZV2SZnZ2fc3NxwdHTE3t4etVqNSqVCCIFKpSrwI4RAp9Oh0+nIzc0lNzcXjUaDVqs1/r71Y2s34qriKO3wkC54Shc89S54SBd8pCse0gW1FW7mCLAPdMEuyBWHYFfsg92wD3JF5W5f6x8GFOoeiiCUgNRLEpecI+tkvLFNj+Si+iYH7C6SI6rPk6OmISS44oSbdMJVOub9Nm27SiccsUNgvRumna8Tdn7O2Pm7YOfvjJ2fM/b+zqjcHZQbuYJCCShxCCUgVALfhw31M3MiUkndHEHOxWRa6urRUlevxPMkkiw0pItssoSGLKEhkxzjaw06coUOiUSPLPBbItELw2+1VKFChRqBGjV2Uo0dKuyNrw3bdlJtaEONvVTjiD2O0h5H7HDI+23NG3NJCAc1ak8H7HycUHs5ovZ2ws4777eXEyo3e8XzRUHBhqjTgpAfx0Ye+D9VMDe91EtyE7LQRmeiS8wiNykHXXIOunQNdhlaXDNckBqdlSwuBbVA5WyHyskO4WxneH3rx8kOlZs9ajd7VK72qNwcDK9d7BBmSL2hoKBQc1AEoRSESmDv76Kk2lVQUKgTKI+ECgoKCgqAhQRBCDFMCHFeCBEuhJhazH5HIcTSvP37hRChlrBLQUFBQcGE2QVBCKEG5gDDgTbAg0KINoUOewpIklI2A74APjK3XQoKCgoKBbHECKE7EC6lvCyl1AB/AKMLHTMaWJj3ejkwWCh+gwoKCgoWxRKCUB+IzLcdlddW7DFSylwgBSiS41cIMVEIcUgIcai60gorKCgoKBioUYvKUsrvpZRdpZRd/f39rW2OgoKCQq3CEoJwHWiYb7tBXluxxwgh7ABPIMECtikoKCgo5GEJQTgINBdCNBZCOADjgNWFjlkNjM97fR+wVdbUnBoKCgoKNRSL5DISQowAvgTUwE9Syg+EEDOAQ1LK1UIIJ2Ax0AlIBMZJKUutoi6EiAMiKmmSHxBf5lG1D+V91y2U9123KO/7biSlLHbOvcYmt6sKQohDJSV3qs0o77tuobzvukV1vO8ataisoKCgoGA+FEFQUFBQUADqriB8b20DrITyvusWyvuuW1T5fdfJNQQFBQUFhaLU1RGCgoKCgkIhFEFQUFBQUADqoCCUlYq7NiKEaCiE2CaEOCOEOC2EeNHaNlkSIYRaCHFUCLHW2rZYCiGElxBiuRDinBDirBCil7VtsgRCiJfzPuOnhBBL8mKcah1CiJ+EELFCiFP52nyEEJuEEBfzfntX9Lp1ShDKmYq7NpILvCqlbAP0BKbUkfd9ixeBs9Y2wsJ8BfwrpWwFdKAOvH8hRH3gBaCrlLIdhkDYcda1ymz8Agwr1DYV2CKlbA5syduuEHVKEChfKu5ah5TyppTySN7rNAw3h8IZZ2slQogGwEjgR2vbYimEEJ5AP2ABgJRSI6VMtqpRlsMOcM7LieYC3LCyPWZBSrkDQ1aH/OQvI7AQGFPR69Y1QShPKu5aTV41uk7AfiubYim+BF4H9Fa2w5I0BuKAn/Omyn4UQrha2yhzI6W8DnwKXANuAilSyo3WtcqiBEopb+a9jgYCK3qBuiYIdRohhBuwAnhJSplqbXvMjRDiTiBWSnnY2rZYGDugM/CdlLITkEElpg9qGnlz5qMxCGI9wFUI8Yh1rbIOeclBKxxTUNcEoTypuGslQgh7DGLwm5RypbXtsRC3AaOEEFcxTA8OEkL8al2TLEIUECWlvDUKXI5BIGo7twNXpJRxUkotsBLobWWbLEmMECIYIO93bEUvUNcEoTypuGsdeeVIFwBnpZSfW9seSyGlfFNK2UBKGYrhf71VSlnrnxillNFApBCiZV7TYOCMFU2yFNeAnkIIl7zP/GDqwGJ6PvKXERgPrKroBeyq1RwbR0qZK4R4DtiAKRX3aSubZQluAx4FTgohjuW1vSWl/Md6JimYmeeB3/IefC4DT1jZHrMjpdwvhFgOHMHgWXeUWprGQgixBBgA+AkhooD3gNnAMiHEUxhKAzxQ4esqqSsUFBQUFKDuTRkpKCgoKJSAIggKCgoKCoAiCAoKCgoKeSiCoKCgoKAAKIKgoKCgoJCHIggKCgoKCoAiCAoKCgoKeSiCoKBQTQghJgkhvsu3/b4QYrE1bVJQqAhKYJqCQjUhhHABzgNhQB9gJtBbSpllVcMUFMqJIggKCtWIEOJjwBVDEaYhUspLVjZJQaHcKIKgoFCNCCFaYUioNlpKWesTJyrULpQ1BAWF6mUahuI0dSpxpELtQBEEBYVqQgjxKuCEIcvki1Y2R0GhwihPMQoK1YAQYhCGFNO9pJRpQggPIURHKeUxK5umoFBulBGCgkIVEUKEAD8C90sp0/KavwJesppRCgqVQFlUVlBQUFAAlBGCgoKCgkIeiiAoKCgoKACKICgoKCgo5KEIgoKCgoICoAiCgoKCgkIeiiAoKCgoKACKICgoKCgo5PH/P2Fy8OdNjhQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "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\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.plot([X1], [Y1], 'rx') # plot the neutrally stable steady state\n", "plt.xlabel(r'$X$')\n", "plt.ylabel(r'$Y$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We see a collection of closed orbits going around the neutrally stable point $(X^*, Y^*)$. Notice from the previous plot that the phase of $Y(t)$ is behind that of $X(t)$, which means that the closed orbits go in the counterclockwise direction." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "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 have a symmetry that 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": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Limit Cycle" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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., given 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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "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": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "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": 9, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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): # replacing the equations of the base class\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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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 $C > K(gK+d)/(gK-d)$. Let us run some simulations with parameters in that range." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current time = 20.01, current populations = [2.95975025 0.49488357]\n", "current time = 20.01, current populations = [0.1576071 0.86732205]\n", "current time = 20.01, current populations = [4.47094092 0.59637233]\n", "current time = 20.01, current populations = [4.8468879 1.31874527]\n", "current time = 20.01, current populations = [4.60225864 0.61106926]\n", "current time = 20.01, current populations = [0.80699131 0.48018203]\n", "current time = 20.01, current populations = [4.84761065 0.64414391]\n", "current time = 20.01, current populations = [5.28971701 1.09493367]\n", "current time = 20.01, current populations = [0.16641022 0.82357656]\n", "current time = 20.01, current populations = [0.16565913 1.26570262]\n" ] } ], "source": [ "C = 8 # carrying capacity\n", "K = 3 # consumption capacity\n", "\n", "T = 20. # total time to integrate the trajectories\n", "dt = 0.01 # time steps to evaluate the trajectories at\n", "\n", "num = 10 # number of trajectories to simulate\n", "mlv_list = [] # list of simulations with different initial values\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": 11, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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\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', lw=2) # 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": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "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": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "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." ] } ], "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 }