{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Ordinary differential equations\n", "\n", "An ordinary differential equation is an equation of a type\n", "$$\n", "\\frac{dx}{dt} = f(x,t),\n", "$$\n", "where $f(x,t)$ is some function.\n", "Together with the initial condition $x(t=0) = x_0$ it defines\n", "the $x(t)$ dependence at $t>0$.\n", "\n", "In many physical applications $t$ plays the role of the time variable (classical mechanics problems),\n", "although this is not always the case.\n", "\n", "Some differential equations can be solved explicitly, the solution to\n", "$$\n", "\\frac{dx}{dt} = \\sin t,\n", "$$\n", "reads\n", "$$\n", "x(t) = x_0 + \\int_0^t \\sin t' dt' = x_0 + 1 - \\cos t.\n", "$$\n", "\n", "In general case, however, the solution cannot be obtained analytically.\n", "Let us consider for example\n", "$$\n", "\\frac{dx}{dt} = -x^3 + \\sin t.\n", "$$\n", "\n", "In this case one resorts to numerical methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Euler's method\n", "\n", "Suppose we have an ODE:\n", "$$\n", "\\frac{dx}{dt} = f(x,t).\n", "$$\n", "\n", "Let us apply the Taylor expansion to express $x(t+h)$ in terms of $x(t)$:\n", "$$\n", "x(t+h) = x(t) + h \\, \\frac{dx}{dt} + \\mathcal{O}(h^2)~.\n", "$$\n", "\n", "Given that $dx/dt = f(x,t)$ and neglecting the high-order terms in $h$ we have\n", "$$\n", "x(t+h) \\approx x(t) + h \\, f[x(t),t]~.\n", "$$\n", "We can iteratively apply this relation starting from $t = 0$ to evaluate $x(t)$ at $t > 0$.\n", "\n", "This is the essence of the *Euler's method* -- the simplest method for solving ODEs numerically." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def ode_euler_step(f, x, t, h):\n", " \"\"\"Perform a single step h using Euler's scheme.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x: the value of the dependent variable at the present step.\n", " t: the present value of the time variable.\n", " h: the time step\n", "\n", " Returns:\n", " xnew: the value of the dependent variable at the step t+h\n", " \"\"\"\n", " return x + h * f(x,t)\n", "\n", "def ode_euler(f, x0, t0, h, nsteps):\n", " \"\"\"Solve an ODE dx/dt = f(x,t) from t = t0 to t = t0 + h*steps using Euler's method.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x0: the initial value of the dependent variable.\n", " t0: the initial value of the time variable.\n", " h: the time step\n", " nsteps: the total number of Euler steps\n", "\n", " Returns:\n", " t,x: the pair of arrays corresponding to the time and dependent variables\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros(nsteps + 1)\n", " x[0] = x0\n", " t[0] = t0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1] = ode_euler_step(f, x[i], t[i], h)\n", " return t,x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us apply the Euler's method to solve the differential equation\n", "$$\n", "\\frac{dx}{dt} = -x^3 + \\sin t.\n", "$$\n", "with the initial condition $x_0 = 0$ at $t_0 = 0$ from $t = 0$ to $t = 10$ in 1000 steps." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define the ODE\n", "def f(x, t):\n", " return -x**3 + np.sin(t)\n", "\n", "t0 = 0.\n", "tend = 10.0\n", "N = 1000\n", "h = (tend - t0) / N\n", "x0 = 0.\n", "\n", "ODEsol = ode_euler(f,x0,t0,h,N)\n", "\n", "# Plot the solution\n", "import matplotlib.pyplot as plt\n", "params = {'legend.fontsize': 'large',\n", " 'axes.labelsize': 'x-large',\n", " 'axes.titlesize':'x-large',\n", " 'xtick.labelsize':'x-large',\n", " 'ytick.labelsize':'x-large',\n", " 'xtick.direction':'in',\n", " 'ytick.direction':'in',\n", " }\n", "plt.rcParams.update(params)\n", "\n", "plt.plot(ODEsol[0], ODEsol[1])\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.title(\"Solution of ODE using Euler's method\")\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "h = (tend - t0) / N\n", "ODEsolN10 = ode_euler(f,x0,t0,h,N)\n", "\n", "N = 20\n", "h = (tend - t0) / N\n", "ODEsolN20 = ode_euler(f,x0,t0,h,N)\n", "\n", "N = 50\n", "h = (tend - t0) / N\n", "ODEsolN50 = ode_euler(f,x0,t0,h,N)\n", "\n", "N = 1000\n", "h = (tend - t0) / N\n", "ODEsolN1000 = ode_euler(f,x0,t0,h,N)\n", "\n", "plt.plot(ODEsolN10[0], ODEsolN10[1], 'o', label='N = 10')\n", "plt.plot(ODEsolN20[0], ODEsolN20[1], 'o', label='N = 20')\n", "plt.plot(ODEsolN50[0], ODEsolN50[1], 'o', label='N = 50')\n", "plt.plot(ODEsolN1000[0], ODEsolN1000[1], label='N = 1000')\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of ODE using Euler's method\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The error of Euler's scheme is proportional to $h^2$ at each step. Since the total number of steps is $N = (t_{\\rm end} - t_0)/h$, the total accumulated error is linear in $h$, i.e. of order $\\mathcal{O}(h)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Midpoint (second-order Runge-Kutta) method\n", "\n", "Better schemes with a smaller error can be achieved with little extra work.\n", "\n", "Euler's method essentially corresponds to approximating the derivative $dx/dt$ with a forward difference\n", "$$\n", "\\frac{dx}{dt} = f(x,t) \\approx \\frac{x(t+h) - x(t)}{h} + \\mathcal{O}(h).\n", "$$\n", "\n", "Recall that better accuracy in numerical differentiation can be obtained if one uses central (midpoint) difference, \n", "$$\n", "f(x,t+h/2) \\approx \\frac{x(t+h) - x(t)}{h} + \\mathcal{O}(h^2).\n", "$$\n", "\n", "Let us exploit this idea applied to ODEs.\n", "Consider Taylor expansions of $x(t+h)$ and $x(t)$ around $x(t+h/2)$:\n", "\\begin{align}\n", "x(t+h) = x(t + h/2) + \\frac{1}{2} h \\left( \\frac{dx}{dt} \\right)_{t+h/2} + \\frac{1}{8} h^2 \\left( \\frac{d^2x}{dt^2} \\right)_{t+h/2} + \\mathcal{O}(h^3),\\\\\n", "x(t) = x(t + h/2) - \\frac{1}{2} h \\left( \\frac{dx}{dt} \\right)_{t+h/2} + \\frac{1}{8} h^2 \\left( \\frac{d^2x}{dt^2} \\right)_{t+h/2} + \\mathcal{O}(h^3),\\\\\n", "\\end{align}\n", "\n", "Subtracting the second equation from the first one we get\n", "\\begin{align}\n", "x(t+h) & = x(t) + h \\left( \\frac{dx}{dt} \\right)_{t+h/2} + \\mathcal{O}(h^3),\\\\\n", "& = x(t) + h f[x(t+h/2),t+h/2)] + \\mathcal{O}(h^3)\n", "\\end{align}\n", "\n", "How to calculate $x(t+h/2)$? Use Euler's scheme\n", "$$\n", "x(t+h/2) = x(t) + \\frac{1}{2}h f(x,t) + \\mathcal{O}(h^2)\n", "$$\n", "\n", "It can be shown using Taylor expansion that\n", "$$\n", "f[x(t+h/2),t+h/2)] = f\\left[x(t) + \\frac{1}{2}h f(x,t), t + \\frac{1}{2}h\\right] + \\mathcal{O}(h^2).\n", "$$\n", "\n", "Therefore, \n", "$$\n", "x(t+h) = x(t) + h f\\left[x(t) + \\frac{1}{2}h f(x,t), t + \\frac{1}{2}h\\right] + \\mathcal{O}(h^3),\\\\\n", "$$\n", "which can iteratively be written as\n", "\\begin{align}\n", "k_1 & = h \\, f(x,t), \\\\\n", "k_2 & = h \\, f(x+k_1/2,t+h/2), \\\\\n", "x(t+h) & = x(t) + k_2~.\n", "\\end{align}\n", "\n", "This is the midpoint (or second-order Runge-Kutta method) which has a local (per one step) error of order $\\mathcal{O}(h^3)$.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def ode_rk2_step(f, x, t, h):\n", " \"\"\"Perform a single step h using 2nd order Runge-Kutta scheme.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x: the value of the dependent variable at the present step.\n", " t: the present value of the time variable.\n", " h: the time step\n", "\n", " Returns:\n", " xnew: the value of the dependent variable at the step t+h\n", " \"\"\"\n", " k1 = h * f(x,t)\n", " k2 = h * f(x + k1/2., t + h /2.)\n", " return x + k2\n", "\n", "def ode_rk2(f, x0, t0, h, nsteps):\n", " \"\"\"Solve an ODE dx/dt = f(x,t) from t = t0 to t = t0 + h*steps using Euler's method.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x0: the initial value of the dependent variable.\n", " t0: the initial value of the time variable.\n", " h: the time step\n", " nsteps: the total number of Euler steps\n", "\n", " Returns:\n", " t,x: the pair of arrays corresponding to the time and dependent variables\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros(nsteps + 1)\n", " x[0] = x0\n", " t[0] = t0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1] = ode_rk2_step(f, x[i], t[i], h)\n", " return t,x" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "h = (tend - t0) / N\n", "ODEsolN10 = ode_rk2(f,x0,t0,h,N)\n", "\n", "N = 20\n", "h = (tend - t0) / N\n", "ODEsolN20 = ode_rk2(f,x0,t0,h,N)\n", "\n", "N = 50\n", "h = (tend - t0) / N\n", "ODEsolN50 = ode_rk2(f,x0,t0,h,N)\n", "\n", "N = 1000\n", "h = (tend - t0) / N\n", "ODEsolN1000 = ode_rk2(f,x0,t0,h,N)\n", "\n", "plt.plot(ODEsolN10[0], ODEsolN10[1], 'o', label='N = 10')\n", "plt.plot(ODEsolN20[0], ODEsolN20[1], 'o', label='N = 20')\n", "plt.plot(ODEsolN50[0], ODEsolN50[1], 'o', label='N = 50')\n", "plt.plot(ODEsolN1000[0], ODEsolN1000[1], label='N = 1000')\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of ODE using RK2 method\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Compare Euler and RK2 schemes\n", "\n", "N = 20\n", "h = (tend - t0) / N\n", "ODEsolN10Euler = ode_euler(f,x0,t0,h,N)\n", "ODEsolN10RK2 = ode_rk2(f,x0,t0,h,N)\n", "\n", "N = 1000\n", "h = (tend - t0) / N\n", "ODEsolN1000 = ode_rk2(f,x0,t0,h,N)\n", "\n", "plt.plot(ODEsolN10Euler[0], ODEsolN10Euler[1], 'o', label='N = 20 (Euler)')\n", "plt.plot(ODEsolN10RK2[0], ODEsolN10RK2[1], 'o', label='N = 20 (RK2)')\n", "plt.plot(ODEsolN1000[0], ODEsolN1000[1], label='N = 1000 (RK2)')\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of ODE using Euler and RK2 methods\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Fourth-Order Runge-Kutta method\n", "\n", "The above logic can be generalized to cancel high-order error terms in various powers in $h$.\n", "This will require more evaluations of function $f(x,t)$ at intermediate steps.\n", "The following classical 4th order Runge-Kutta method is often considered to be a sweet spot.\n", "It corresponds to the following scheme:\n", "\\begin{align}\n", "k_1 & = h \\, f(x,t), \\\\\n", "k_2 & = h \\, f(x+k_1/2,t+h/2), \\\\\n", "k_3 & = h \\, f(x+k_2/2,t+h/2), \\\\\n", "k_4 & = h \\, f(x+k_3,t+h), \\\\\n", "x(t+h) & = x(t) + \\frac{1}{6} (k_1 + 2k_2 + 2k_3 + k_4)~.\n", "\\end{align}\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def ode_rk4_step(f, x, t, h):\n", " \"\"\"Perform a single step h using 4th order Runge-Kutta method.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x: the value of the dependent variable at the present step.\n", " t: the present value of the time variable.\n", " h: the time step\n", "\n", " Returns:\n", " xnew: the value of the dependent variable at the step t+h\n", " \"\"\"\n", " k1 = h * f(x,t)\n", " k2 = h * f(x + k1/2., t + h /2.)\n", " k3 = h * f(x + k2/2., t + h /2.)\n", " k4 = h * f(x + k3, t + h)\n", " return x + (k1 + 2. * k2 + 2. * k3 + k4) / 6.\n", "\n", "def ode_rk4(f, x0, t0, h, nsteps):\n", " \"\"\"Solve an ODE dx/dt = f(x,t) from t = t0 to t = t0 + h*steps using 4th order Runge-Kutta method.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x0: the initial value of the dependent variable.\n", " t0: the initial value of the time variable.\n", " h: the time step\n", " nsteps: the total number of Euler steps\n", "\n", " Returns:\n", " t,x: the pair of arrays corresponding to the time and dependent variables\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros(nsteps + 1)\n", " x[0] = x0\n", " t[0] = t0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1] = ode_rk4_step(f, x[i], t[i], h)\n", " return t,x" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 20\n", "h = (tend - t0) / N\n", "ODEsolN10Euler = ode_euler(f,x0,t0,h,N)\n", "ODEsolN10RK2 = ode_rk2(f,x0,t0,h,N)\n", "ODEsolN10RK4 = ode_rk4(f,x0,t0,h,N)\n", "\n", "N = 1000\n", "h = (tend - t0) / N\n", "ODEsolN1000 = ode_rk4(f,x0,t0,h,N)\n", "\n", "plt.plot(ODEsolN10Euler[0], ODEsolN10Euler[1], 'o', label='N = 20 (Euler)')\n", "plt.plot(ODEsolN10RK2[0], ODEsolN10RK2[1], 'o', label='N = 20 (RK2)')\n", "plt.plot(ODEsolN10RK4[0], ODEsolN10RK4[1], 'o', label='N = 20 (RK4)')\n", "plt.plot(ODEsolN1000[0], ODEsolN1000[1], label='N = 1000 (RK4)')\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of ODE using Euler, RK2, and RK4 methods\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adaptive time step\n", "\n", "It can be useful to control the time step $h$ adaptively, such that it corresponds to the desired accuracy of calculations.\n", "If $h$ is too small, we waste computing resources by making too many calculations.\n", "On the other hand, if $h$ is too large, we will not achieve the desired accuracy.\n", "\n", "To solve this problem we can introduce error estimate at each step, and adjust the time step accordingly to reduce the error.\n", "One way to do so is to use a combination of two Runge-Kutta methods of different order.\n", "The difference between the two gives an error estimate for the present step size, which can then be adjusted as necessary.\n", "The [Runge-Kutta-Fehlberg method](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%E2%80%93Fehlberg_method) is one popular example combining 4th and 5th order Runge-Kutta methods.\n", "\n", "Here we consider another approach applied to 4th order Runge-Kutta method. Recall that the error for one time step $h$ is of order $ch^5$. Let us take two RK4 steps h to approximate $x(t+2h) \\approx x_1$. Then, the error estimate is\n", "$$\n", "x(t+2h) = x_1 + 2 c h^5. \n", "$$\n", "On the other hand, $x(t+2h)$ can also be approximated by a single RK4 step of size 2h, $x(t+2h) \\approx x_2$ with\n", "$$\n", "x(t+2h) = x_2 + 32 c h^5. \n", "$$\n", "The error $\\epsilon c h^5$ for a single RK4 step of size $h$ is thus\n", "$$\n", "\\epsilon = |c h^5| = \\frac{|x_1 - x_2|}{30}.\n", "$$\n", "\n", "If the desired accuracy per unit time is $\\delta$, the desired accuracy per time step is $h' \\delta$, and $h'$ should therefore be equal to\n", "$$\n", "h' = h \\left( \\frac{30 h \\delta}{|x_1 - x_2|} \\right)^{1/4}~.\n", "$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def ode_rk4_adaptive(f, x0, t0, h0, tmax, delta = 1.e-6):\n", " \"\"\"Solve an ODE dx/dt = f(x,t) from t = t0 to t = t0 + h*steps \n", " using 4th order Runge-Kutta method with adaptive time step.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x0: the initial value of the dependent variable.\n", " t0: the initial value of the time variable.\n", " h0: the initial time step\n", " tmax: the maximum time\n", " delta: the desired accuracy per unit time\n", "\n", " Returns:\n", " t,x: the pair of arrays corresponding to the time and dependent variables\n", " \"\"\"\n", " \n", " ts = [t0]\n", " xs = [x0]\n", " h = h0\n", " t = t0\n", " i = 0\n", " while (t < tmax):\n", " if (t + h >= tmax):\n", " ts.append(tmax)\n", " h = tmax - t\n", " xs.append(ode_rk4_step(f, xs[i], ts[i], h))\n", " t = tmax\n", " break\n", " \n", " x1 = ode_rk4_step(f, xs[i], ts[i], h)\n", " x1 = ode_rk4_step(f, x1, ts[i] + h, h)\n", " x2 = ode_rk4_step(f, xs[i], ts[i], 2*h)\n", " \n", " rho = 30. * h * delta / np.abs(x1 - x2)\n", " if rho < 1.:\n", " h *= rho**(1/4.)\n", " else:\n", " if (t + 2.*h) < tmax:\n", " xs.append(x1)\n", " ts.append(t + 2*h)\n", " t += 2*h\n", " else:\n", " xs.append(ode_rk4_step(f, xs[i], ts[i], h))\n", " ts.append(t + h)\n", " t += h\n", " i += 1\n", " h = min(2.*h, h * rho**(1/4.))\n", " \n", " return ts,xs" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "h = (tend - t0) / N\n", "delta = 1.e-2\n", "ODEsolN10RK4adaptive = ode_rk4_adaptive(f,x0,t0,h,tend, delta)\n", "\n", "delta2 = 1.e-3\n", "ODEsolN10RK4adaptive2 = ode_rk4_adaptive(f,x0,t0,h,tend, delta2)\n", "\n", "plt.plot(ODEsolN10RK4adaptive[0], ODEsolN10RK4adaptive[1], 'o', label='RK4 adaptive (${\\delta}=$' + str(delta) + ')')\n", "plt.plot(ODEsolN10RK4adaptive2[0], ODEsolN10RK4adaptive2[1], 'o', label='RK4 adaptive (${\\delta}=$' + str(delta2) + ')')\n", "plt.plot(ODEsolN1000[0], ODEsolN1000[1], label='N = 1000 (RK4)')\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of ODE using Euler and RK2 schemes\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implicit methods and stiff equations\n", "\n", "Consider the following ODE\n", "$$\n", "\\frac{dx}{dt} = -15x,\n", "$$\n", "with $x(0) = 1$.\n", "\n", "The solution is \n", "$$\n", "x(t) = e^{-15t},\n", "$$\n", "which tends to zero as $t \\to \\infty$.\n", "\n", "If you apply Euler's scheme with $h = 1/4$ we have" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f_stiff(x,t):\n", " return -15.*x\n", "\n", "def x_stiff_sol(x,t):\n", " return np.exp(-15.*t)\n", "\n", "h1 = 1./4.\n", "t0 = 0.\n", "tend = 1.0\n", "N = round((tend - t0) / h1)\n", "x0 = 1.\n", "\n", "ODEsol_stiff1 = ode_euler(f_stiff,x0,t0,h1,N)\n", "\n", "h2 = 1./8.\n", "N = round((tend - t0) / h2)\n", "ODEsol_stiff2 = ode_euler(f_stiff,x0,t0,h2,N)\n", "\n", "h3 = 1./16.\n", "N = round((tend - t0) / h3)\n", "ODEsol_stiff3 = ode_euler(f_stiff,x0,t0,h3,N)\n", "\n", "tref = np.linspace(0,1,100)\n", "xref = x_stiff_sol(0., tref)\n", "\n", "plt.plot(ODEsol_stiff1[0], ODEsol_stiff1[1], 'o', label='Euler (h = ' + str(h1) +')')\n", "#plt.plot(ODEsol_stiff[0], ODEsol_stiff[1], label='Euler (h = 1/4)')\n", "plt.plot(ODEsol_stiff2[0], ODEsol_stiff2[1], 'o', label='Euler (h = ' + str(h2) +')')\n", "plt.plot(ODEsol_stiff3[0], ODEsol_stiff3[1], 'o', label='Euler (h = ' + str(h3) +')')\n", "plt.plot(tref, xref, label='exact')\n", "plt.ylim(-3.,8.)\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of stiff ODE using Euler's scheme\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Euler's scheme gives\n", "$$\n", "x_{n+1} = x_n - 15 h x_n = (1 - 15 h) x_n = (1-15h)^n x_0\n", "$$\n", "where $x_n \\equiv x(t+nh)$.\n", "\n", "For $h > 2/15$ we have $|x_{n+1}| \\to \\infty$ as $n \\to \\infty$ (equivalent to $t \\to \\infty$), although the true solution exhibits $x \\to \\infty$ as $t \\to \\infty$.\n", "\n", "This is an example of instability of ODE solver, which is typical for explicit solvers. The same for Runge-Kutta 4th order method." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f_stiff(x,t):\n", " return -15.*x\n", "\n", "def x_stiff_sol(x,t):\n", " return np.exp(-15.*t)\n", "\n", "h1 = 1./4.\n", "t0 = 0.\n", "tend = 1.0\n", "N = round((tend - t0) / h1)\n", "x0 = 1.\n", "\n", "ODEsol_stiff1 = ode_rk4(f_stiff,x0,t0,h1,N)\n", "\n", "h2 = 1./8.\n", "N = round((tend - t0) / h2)\n", "ODEsol_stiff2 = ode_rk4(f_stiff,x0,t0,h2,N)\n", "\n", "h3 = 1./16.\n", "N = round((tend - t0) / h3)\n", "ODEsol_stiff3 = ode_rk4(f_stiff,x0,t0,h3,N)\n", "\n", "tref = np.linspace(0,1,100)\n", "xref = x_stiff_sol(0., tref)\n", "\n", "plt.plot(ODEsol_stiff1[0], ODEsol_stiff1[1], 'o', label='RK4 (h = ' + str(h1) +')')\n", "#plt.plot(ODEsol_stiff[0], ODEsol_stiff[1], label='Euler (h = 1/4)')\n", "plt.plot(ODEsol_stiff2[0], ODEsol_stiff2[1], 'o', label='RK4 (h = ' + str(h2) +')')\n", "plt.plot(ODEsol_stiff3[0], ODEsol_stiff3[1], 'o', label='RK4 (h = ' + str(h3) +')')\n", "plt.plot(tref, xref, label='exact')\n", "plt.ylim(-3.,8.)\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of stiff ODE using Euler's scheme\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implicit methods\n", "\n", "In implicit methods, the value of the variable at the next time step itself enters the r.h.s.\n", "For example, implicit Euler's method reads\n", "$$\n", "x(t+h) = x(t) + h f[x(t+h),t+h].\n", "$$\n", "\n", "Applied to the stiff equation above we have\n", "$$\n", "x_{n+1} = x_n - 15 h x_{n+1},\n", "$$\n", "thus\n", "$$\n", "x_{n+1} = \\frac{x_n}{1+15h} = \\frac{x_0}{(1+15h)^n}.\n", "$$\n", "Here $x_{n+1} \\to 0$ as $n \\to \\infty$ for any $h>0$, i.e. the method is stable.\n", "\n", "Great stability, especially for stiff equations is the main advantage of implicity methods.\n", "The drawback, is that one has to solve an algebraic equation at each time step to determine $x_{n+1}$ [or $x(t+h)$]." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def stiff_implicit(x0,t0,h,nsteps,k=-15.):\n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros(nsteps + 1)\n", " x[0] = x0\n", " t[0] = t0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1] = x[i] / (1 - k*h)\n", " return t,x\n", "\n", "t0 = 0.\n", "tend = 1.0\n", "h1 = 1./4.\n", "N = round((tend - t0) / h1)\n", "ODEsol_stiff1 = stiff_implicit(x0,t0,h1,N)\n", "\n", "h2 = 1./8.\n", "N = round((tend - t0) / h2)\n", "ODEsol_stiff2 = stiff_implicit(x0,t0,h2,N)\n", "\n", "h3 = 1./16.\n", "N = round((tend - t0) / h3)\n", "ODEsol_stiff3 = stiff_implicit(x0,t0,h3,N)\n", "\n", "tref = np.linspace(0,1,100)\n", "xref = x_stiff_sol(0., tref)\n", "\n", "plt.plot(ODEsol_stiff1[0], ODEsol_stiff1[1], 'o', label='Implicit Euler (h = ' + str(h1) +')')\n", "#plt.plot(ODEsol_stiff[0], ODEsol_stiff[1], label='Euler (h = 1/4)')\n", "plt.plot(ODEsol_stiff2[0], ODEsol_stiff2[1], 'o', label='Implicit Euler (h = ' + str(h2) +')')\n", "plt.plot(ODEsol_stiff3[0], ODEsol_stiff3[1], 'o', label='Implicit Euler (h = ' + str(h3) +')')\n", "plt.plot(tref, xref, label='exact')\n", "plt.ylim(-1.,3.)\n", "plt.xlabel('t')\n", "plt.ylabel('x')\n", "plt.legend()\n", "plt.title(\"Solution of stiff ODE using implicit Euler's scheme\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Systems of ODE\n", "\n", "System of $N$ first-order ODEs\n", "$$\n", "\\frac{d x_1}{dt} = f_1(x_1,\\ldots,x_N,t),\\\\\n", "\\frac{d x_2}{dt} = f_2(x_1,\\ldots,x_N,t),\\\\\n", "\\ldots \\\\\n", "\\frac{d x_N}{dt} = f_N(x_1,\\ldots,x_N,t).\n", "$$\n", "\n", "In vector notation:\n", "$$\n", "\\frac{d \\mathbf{x}}{dt} = \\mathbf{f}(\\mathbf{x},t).\n", "$$\n", "\n", "All the methods we covered have exactly the same structure for systems of ODEs, applied to vectors:\n", "- Euler method\n", "$$\n", "\\mathbf{x}(t+h) = \\mathbf{x}(t) + h \\, \\mathbf{f}[\\mathbf{x}(t),t]~.\n", "$$\n", "\n", "\n", "- RK2\n", "\\begin{align}\n", "\\mathbf {k_1} & = h \\, \\mathbf{f}(\\mathbf{x},t), \\\\\n", "\\mathbf {k_2} & = h \\, \\mathbf {f}(\\mathbf {x}+\\mathbf {k_1}/2,t+h/2), \\\\\n", "\\mathbf{x}(t+h) & = \\mathbf {x}(t) + \\mathbf {k_2}~.\n", "\\end{align}\n", "\n", "\n", "- RK4\n", "\\begin{align}\n", "\\mathbf{k_1} & = h \\, \\mathbf{f}(\\mathbf{x},t), \\\\\n", "\\mathbf{k_2} & = h \\, \\mathbf{f}(\\mathbf{x}+\\mathbf{k_1}/2,t+h/2), \\\\\n", "\\mathbf{k_3} & = h \\, \\mathbf{f}(\\mathbf{x}+\\mathbf{k_2}/2,t+h/2), \\\\\n", "\\mathbf{k_4} & = h \\, \\mathbf{f}(\\mathbf{x}+\\mathbf{k_3},t+h), \\\\\n", "\\mathbf{x}(t+h) & = \\mathbf{x}(t) + \\frac{1}{6} (\\mathbf{k_1} + 2\\mathbf{k_2} + 2\\mathbf{k_3} + \\mathbf{k_4})~.\n", "\\end{align}\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def ode_euler_multi(f, x0, t0, h, nsteps):\n", " \"\"\"Multi-dimensional version of the Euler method.\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros((len(t), len(x0)))\n", " t[0] = t0\n", " x[0,:] = x0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1,:] = ode_euler_step(f, x[i], t[i], h)\n", " return t,x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example: System of equations\n", "\\begin{align}\n", "\\frac{dx}{dt} & = xy - x,\\\\\n", "\\frac{dy}{dt} & = y - xy + (\\sin t)^2\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ff(xin, t):\n", " x = xin[0]\n", " y = xin[1]\n", " return np.array([x*y-x,y-x*y+np.sin(t)**2])\n", "\n", "a = 0.\n", "b = 10.0\n", "N = 100\n", "h = (b-a)/N\n", "\n", "tpoints = np.arange(a,b,h)\n", "xpoints = []\n", "ypoints = []\n", "\n", "sol = ode_euler_multi(ff,[1.0,1.0], a, h, N)\n", "tpoints = sol[0]\n", "xpoints = sol[1][:,0]\n", "ypoints = sol[1][:,1]\n", "plt.title(\"ODE system solution using Euler's method\")\n", "plt.xlabel('t')\n", "plt.ylabel('x,y')\n", "plt.plot(tpoints,xpoints,label='x')\n", "plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def ode_rk2_multi(f, x0, t0, h, nsteps):\n", " \"\"\"Multi-dimensional version of the RK2 method.\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros((len(t), len(x0)))\n", " t[0] = t0\n", " x[0,:] = x0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1] = ode_rk2_step(f, x[i], t[i], h)\n", " return t,x" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ff(xin, t):\n", " x = xin[0]\n", " y = xin[1]\n", " return np.array([x*y-x,y-x*y+np.sin(t)**2])\n", "\n", "a = 0.\n", "b = 10.0\n", "N = 100\n", "h = (b-a)/N\n", "\n", "tpoints = np.arange(a,b,h)\n", "xpoints = []\n", "ypoints = []\n", "\n", "sol = ode_rk2_multi(ff,[1.0,1.0], a, h, N)\n", "tpoints = sol[0]\n", "xpoints = sol[1][:,0]\n", "ypoints = sol[1][:,1]\n", "plt.title(\"ODE system solution using RK2 method\")\n", "plt.xlabel('t')\n", "plt.ylabel('x,y')\n", "plt.plot(tpoints,xpoints,label='x')\n", "plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def ode_rk4_multi(f, x0, t0, h, nsteps):\n", " \"\"\"Multi-dimensional version of the RK4 method.\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros((len(t), len(x0)))\n", " t[0] = t0\n", " x[0] = x0\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1] = ode_rk4_step(f, x[i], t[i], h)\n", " return t,x" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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ysuLXX38t8zqG1cVJSUlVmm41KOt7HW7/v6amphZ//sSJE6jV6uI6sjsNGDAAjUbD8ePHix8z3C/r+c2bN8fPz48rV65UOdb6QiRNQine3t6Eh4cTGxtb6XMNv4SNWeZsKCa8+xexqTz44INs2rSJjz76iG+++YYvv/wSkH/5ffjhhwwaNKj4uU5OTkyaNIkvv/ySXbt20a9fP9atW8fNmzeZPXs2tra2xc8NCAjg8OHDzJs3j82bN7NmzRpA/kH18ssvl7sE+m6GIt7Lly+Xqim5U1nLpcuqJzD8Miuv1kCr1VJQUFCl2F566SXc3d1ZsmQJixYt4pNPPkGlUjFgwAD+97//0bFjRwDS0tIA8PLyKvM8hveF4XlKq0m8FX3NdTqdqUIswVTvtYreE1AyfsNrb9KkSannazSaav1Sv5Phj6Dc3FyOHz/Oc889x7x58wgKCuKRRx4p97gNGzbw0EMPsXHjRgYOHMiWLVtwd3cv9bwnn3wSOzs7lixZYlR8Zans61bRe+LO77WkpCQKCwsr/D4H+Xu9Ol/f6v6/Nm7cuMx6NK1WW1y3eOfzoez3AcjfQw0xaRKr54RSDH9h/vPPPxU+T6fTsWPHDgB69epV7esYju3evXu1j62qe++9l+3bt5OSksK2bduYPXs2Z8+e5d577+XChQslnvv8888Dtwu/7y4Av1NoaCi//PILSUlJHD16lA8//BC9Xs+MGTP47rvvqhSb4QfemDFjkOSp8jI/oqOjjX79NfHYY49x8ODB4rYQTz31FDt37mTo0KHcunWrxGu4fv16mee4du1aieeVR62WfxSV1+iwOivUKmKqeI1V0ess7zWa4r1WHc7OzoC8AvNuOp2uxIo9Y9ja2tKzZ0/+/vtvnJycePbZZ4u/7mWxsbHht99+46GHHuLEiRP079+/zP+/48ePc/PmTTw8PEqsODMUQ7/33nuoVKriRQR1ycXFhUaNGlX4fS5JUqnRTVPHkJycXOYfToWFhSQmJhb/3xueD2W/D6D876H6TiRNQilTpkxBo9Gwdu1azp8/X+7zvv32WxISEggJCSlzCLciN2/eLE5KHn300RrFWxUODg4MHDiQjz/+mNdff528vDz++uuvEs9p27YtvXv3Zu3atezfv5+dO3fSr1+/ChtparVaOnXqxCuvvMLKlSsBeam+gWEKrayRiFatWuHq6srBgwerPAKkBFdXV0aOHMnXX3/NlClTSEpKYs+ePQB06NABoNx2BobHDSNT5WnUqBFAmaOb6enpZbYuqOhrW56K4i0sLGTv3r1VitdYFb3Oo0ePVnhsZe81UzF8jQxfizsdPHiw3MS2ury9vXn99dfJzMysdIpOq9Xy888/8/jjj3Pu3Dn69etXaqr5scce46mnnir1YZgWDgsL46mnnmLIkCEmib86unfvTkpKCufOnavyMRqNxqQjmB06dECv15fZWmX37t3odLoS73vD/bJWhkZFRVVpJqI+EkmTUErz5s15/fXXi5fDl5U4rV+/nhdffBGNRsOSJUuK/4KuilOnTjFkyBASExMZOXJkrbQbANi2bRs5OTmlHjf85XTnlJvB888/T15eHuPGjUOSJJ577rlSzzl8+HCZf32VdV7DUHtZP2C0Wi0zZszg2rVrzJw5s8xYr127VmHiWls2b95c5i9Hw/C94TX26tWLkJAQ9u7dWzx1ZLBmzRp2795Ny5Yty6yPuZOTkxOhoaHs27evxOvV6XS89NJLZX5tKvralmf06NE0btyYlStXcvDgwRKfW7hwIVFRUQwePLhKbRmMYWi98PXXX5d4/MyZM2XW/FTnvWYqjz32GCCPzNw5TZmfn1/hliXGmDFjBk2aNOH777/n8uXLFT5Xo9Hw3Xff8eyzz3Lp0iX69u1bot/Vp59+yrJly0p9GEaa7r33XpYtW1aiXUZdmT17NgBPP/10mT2OsrKySr0f3dzcuHXrFrm5uSaJ4cknnwTgtddeIzs7u/jx7OxsXn31VQCeeuqp4scfffRRrKys+Oyzz0p8nfV6PXPmzKlWb776RNQ0CWWaN28eWVlZfPzxx7Rv355hw4bRunVrCgoK2L9/P4cOHcLOzo6VK1eW2Q0c5MJMQy+kgoICEhMTOXbsGMeOHQPkb0rDaFNZFi5cWG7RZ//+/SvdrPJf//oXMTEx9O/fn8DAQKytrTl27Bjbt2/H39+fiRMnljpm7NixeHp6cu3aNTw8PHjwwQdLPefnn39m8eLF9OvXj6CgIBo1akRkZCS///47NjY2vPjii8XP7dGjB/b29ixcuJCkpKTi+oAZM2bg4uLCW2+9xalTp/jyyy/5/fffGThwID4+Pty8eZPLly+zb98+3nvvPe65554KX6upTZw4EVtbW3r37k1gYCCSJLFnzx6OHDlCx44dGTx4MCAvAFi+fDlDhgxhwoQJjBo1ilatWnHx4kXWr1+Pk5MTP/zwQ5WS6ldeeYUpU6bQq1cvxo8fX9yvqqCggPbt23Pq1KkSzw8JCcHHx4dVq1ZhZWWFv78/KpWKyZMnlzvN4ejoyLfffsv48ePp168f48ePx9/fn2PHjrFlyxa8vLwqfE/W1KhRowgJCWHlypXExcXRrVs3rl69WtzL6+5C4eq810ylX79+PPPMM3z11Ve0bt2asWPHYmVlxe+//46LiwtNmzat1h9JFbG3t+fVV19l9uzZvP3228UjaOVRqVR8+eWX2NnZsXDhQvr06cP27dsJDg42STy1ZdCgQXz44Ye89tprBAcHM3LkSJo1a0ZmZiZXrlxh165d9O7dm82bN5c45siRI4wYMYI+ffpgbW1N+/btuf/++42K4ZFHHmHDhg38+uuvtG7dmtGjRxfv4xkdHc1DDz1UYtQ/MDCQDz/8kH/961906NCBCRMm4OLiwt9//01qairt2rWrcA/Requul+sJluXQoUPSY489JgUGBkq2traSg4OD1Lp1a+lf//qXFBsbW+YxhqXTd37Y2tpKXl5eUp8+faR///vfZfZOMqhKy4Hylpnf6ZdffpEmTpwoBQUFSQ4ODpKTk5PUunVr6fXXX5du3rxZ7nGzZ8+WAOnll18u8/MHDx6UnnvuOaldu3ZSo0aNJFtbW6lFixbSlClTSizdNvjrr7+k7t27F/ek4a4l53q9Xvrhhx+kgQMHSo0aNZKsrKykpk2bSr169ZLee+896erVq8XPrWxpPhW0eqhsCfOdvvjiC2n06NFSs2bNJDs7O6lRo0ZSWFiY9H//939lLnEODw+XJk2aJHl5eUlarVby8vKSHn30USk8PLzUc8tqOWDw7bffSvfcc49kbW0tNWnSRHrmmWekxMTEMlsOSJIkHT58WBo4cKDk7OwsqVSqEuetqN3D4cOHpdGjR0vu7u6SlZWV5OfnJz333HNSfHx8qedWt01AZeLi4qQJEyYUv3c6d+4s/fbbb2WeqzrvtYpaDpT3/17e/4VOp5M+/vhjKSQkRLK2tpa8vb2l559/XkpNTZUcHR1L9SGqSHl9mgxycnKkpk2bSiqVSjp16lTx44bvlfK8/vrrEiB5eXlJZ8+eLfd5NWk5UN7Xrbz3oyRV/H7Zs2ePNH78eMnb21uysrKS3N3dpfbt20uzZ88u1asqMzNTeu655yQfHx9Jo9GU+r6v6Hu9vBh0Op20ePFiqVOnTpKdnZ1kZ2cndezYUfr8889L9FK7088//yx16NBBsrGxkdzd3aVHH31Uio+Pr/BrUJ+pJKmMHvqC0ID17duXvXv3cunSJYKCgpQORxDMxuXLl2nZsiUTJ06sdFRIEOojUdMkCHc4ePAge/bsYfjw4SJhEhqs69evl6pZyc7OLt7SY+zYsQpEJQjKEzVNggB8/vnnxMXFsXz5cjQaDe+8847SIQmCYhYuXMjKlSvp378/3t7eXL9+nW3bthEXF8e9994rkiahwRLTc4KAXPQYFxdHUFAQ77zzjsk6CguCJdq2bRuffPIJJ0+eJDExEY1GQ0hICI888ggvvviiyTbsFQRLI5ImQRAEQRCEKhA1TYIgCIIgCFUgkiZBEARBEIQqEIXgJqTX60lISMDJyalaO5ALgiAIgqAcSZLIyMiotHmrSJpMKCEhAT8/P6XDEARBEATBCLGxsfj6+pb7eZE0mZCTkxMgf9Hv3C1aEARBEATzlZ6ejp+fX/Hv8fKIpMmEDFNyzs7OImkSBEEQBAtTWWmNKAQXBEEQBEGoApE0CYIgCIIgVIFImgRBEARBEKpAJE2CIAiCIAhVIArBBUEQBKEe0ul0FBQUKB2GojQajUn3ShRJkyAIgiDUI5Ikcf36ddLS0hDby4KNjQ3u7u4mWdUukiZBEARBqEfS0tJITU3Fw8MDBweHBrtDhSRJFBQUkJaWRnx8PECNEyezS5qSkpJYt24df/zxB2fOnCE+Ph5ra2vatm3LE088wRNPPFFhi/OanCcmJoZmzZqVe84JEyawatWqGr9GQRAEQagNkiRx8+ZNnJ2dcXd3VzocxdnZ2eHk5ERcXByJiYn1L2lavXo106ZNw8vLi4EDB+Lv78+NGzdYu3YtU6dO5c8//2TNmjWVZs41OU/79u0ZPXp0qcfbtGljqpcpCIIgCCan0+nQ6XSiwfIdVCoVLi4uxMfHU1BQUKMaJ5VkZhOe27dvJyMjg/vuuw+NRlP8+PXr1+natSuxsbGsXr2acePGmfw8hpGmxx9/nO+//77asaenp+Pi4kJaWpp4wwqCIAh1Ljc3l+joaAIDA7Gzs1M6HLORk5NT/Dve1ta21Oer+vvb7FoODBw4kFGjRpVIdAC8vLx47rnnANi5c2ednUcQBEEQLE1DrWMqj6m+HmY3PVcRa2trgBovH6zsPAkJCSxdupSkpCTc3Nzo0aMH7dq1q9E1BUEQBEGwbBaTNBUWFrJ8+XIAhg8fXqvn2bp1K1u3bi3xWP/+/Vm+fDn+/v6VXiM9Pb3Ev21sbLCxsTEyYqEhSMspID4lB0cbLf5u9kqHIwiCIJTBYpKmV199lbNnzzJixAiGDRtWK+ext7fnrbfeYvTo0TRv3hyA06dPM2/ePHbs2MGgQYM4efIkDg4OFV7Dz8+vxL/nzp3LvHnzjI5ZqH9uZeTxwV8XOJ+QTnxqDhm5hcWfmzEwiNmDW6JWi+F1QRAEc2J2heBlWbhwIbNnzyYkJIS9e/cavYzS2PMUFhbSu3dvDh06xMKFC3nxxRfLfJ6hkCw2NrZEIZkYaRLulJ5bwISlB7lwreSIpKu9FanZcvfewaGefDIhDCdb03WyFQSh/jMUgpdX8NxQVfZ1sdhC8LstWrSI2bNnExoays6dO41OmGpyHq1Wy9SpUwHYvXt3pc93dnYu8SESJsEgt0DH1OVHuXAtHXdHG76a3Imts/ty/p1hnHx7KB+Nb4+1Vs0/F24yZsl+ohOzlA5ZEATBLOTm5tKhQweCgoJIS0srfvz69et4eXnRv39/dDpdrcZg1tNzCxYsYM6cObRp04Zt27bh6emp2HkMx2RliV9ignEKdXqm/3yCw9HJONloWf5kF1o3dSnxnLGdfAnydOTZH48RcTOTUZ/v5cvJnejZQjSpEwTBOJIkkVNQu8lEddlZaaq9os3W1pZff/2VTp068eSTT/Lbb7+h1+t59NFHkSSJlStXlloxb2pmmzR98MEHvP7664SFhbF161ajR5hMdZ5Dhw4BFNc6CUJ1SJLEa2vP8M+FG1hr1Xz9eOdSCZNBez9XNs7oxbQVxzl2JYWZK0+w7V/9cbETU3WCIFRfToGOe97+W+kwSjj/zjDsraufggQHB7Ns2TImTJjAokWLSE5OZufOnWzevBlvb+9aiLQks5yemz9/Pq+//jqdOnVi27ZtFSY6BQUFhIeHExkZWaPzgJwY5efnl3p8165dfPzxxwBMmjSpmq9GEOCTrZdYfSwOtQo+f7gD3Zu7Vfh8TydbfprajeYeDiRm5vPJ1kt1FKkgCIJ5e+ihh5g2bRpz5szh3Xff5fXXX2fIkCF1cm2zKwRfvnw5U6ZMQaPRMGPGDFxcSv81HhgYyJQpU4DbXbwDAgKIiYkx+jwgtxU4d+4c/fv3x9fXF4AzZ86wbds2QE7C3nzzzXJjFx3BhbLEpWQzYMFOCnQS/x3bjoe6+FV+UJF9EYk8uuwQahVsnN6bNj5lj04JgiBA2QXP9WV67k5Hjx6lS5cuWFtbExcXh4eHR4XPN1UhuNlNz0VHRwPy/jkLFy4s8zn9+vUrkeyY6jyTJ09m3bp1HDlyhL/++ouCggKaNGnCQw89xPTp0+nTp091X44g8OWuSAp0Er2C3KqVMAH0CnLnvnbebDp9jbc3nGXNcz1FKwJBEKpFpVIZNRVmrrKyspg8eTItW7bkxo0bTJ06lQ0bNtTJtc1upMmSiZEm4W7X0nLo99+d5Ov0/PJMd7pVMi1XlutpuQz6aCdZ+Tr+O64dD3WuXuIlCELD0RBaDkyePJm1a9dy+PBhwsPDGTduHB9//DGzZ88u95gG03JAECzZ0l1R5Ov0dGvW2KiECcDLxZZZg1sC8OFf4aRml667EwRBaAiWLVvGihUrWLx4Ma1bt2bs2LFMnz6dV155hcOHD9f69UXSJAi15GZ6Lj8fvgrAzEHBNTrXlF6BBHs6kpyVz4ItF00RniAIgkU5c+YMM2fO5PHHHy9RWrNgwQLatWvHhAkTSE1NrdUY6s8kpyCYmaW7o8gv1NMpoBE9Wxg3ymRgpVHzzqg2PPz1QX46dJVJ3QNo5SWmgAVBaDjatm1LdnZ2qcdtbGw4evRoncQgRpoEoRbcysjjp0NXAHmUqSarRAx6tHBjeGsvJAmW74+p8fkEQRCE6hFJkyDUgmV7osgt0NPez5W+wabr5v1Er0AA1p9IIK1onzpBEAShboikSRBMLDkrnx8PyqNMLw4KMskok0HXZo0JaeJEToGO1cdiTXZeQRAEoXIiaRIEE1tzLJbsfB2tmzozIMS4/RLLo1KpmNwjAIAVB6+g14uOIYIgCHVFJE2CYGIbTyUAMLGrv0lHmQzGdPDByUZLTFI2eyISTX5+QRAEoWwiaRIEE4q6lcnZ+HQ0ahUj23jVyjUcbLSM7SRv8/ODKAgXBEGoMyJpEgQTMowy9Q5yx83RptauY5ii237xJrHJpZfgCoIgCKYnkiZBMBFJkoqTpgfaN63Va7XwcKRPsDuSJNc2CYIgCLVPJE2CYCLnEtKJupWFjVbN0NZNav16k7vLo02/HI0l18x2MBcEQaiPRNIkCCby+2l5lGlgK0+cbK1q/XqDQpvg42pHanYBvxeNcAmCIAi1RyRNgmACer3EplPXgNqfmjPQqFU82t0foHiPO0EQBKH2iKRJEEzg+NUU4lNzcLTRMqCVaXszVWRcR19UKjhxNZW4FFEQLgiCUJtE0iQIJmAoAB/augm2Vpo6u66nsy1dAxsD8OeZa3V2XUEQhIZIJE2CUEOFOn1xwlJXU3N3uq+dNwB/nBZJkyAIQm0SSZMg1ND+yCQSM/NpZG9FryDTbc5bVcPbeKNWwam4NNGzSRCE0iQJ8rPM60Oq/hZQe/bsQaVSsXLlylKf++GHH1CpVBw5csQUX7FyaWv17ILQABhWro1s642Vpu7/DvFwsqF7czf2Ryax6fQ1pvVvUecxCIJgxgqy4f26HwWv0OsJYO1QrUP69OlDhw4dWLx4MQ8//HCJz33++ed06dKFLl26mDLKUsRIkyDUgE4vsfXCDQDuV2BqzuBewxTdGdF6QBCE+mvmzJns27ePkydPFj925MgRjhw5wvTp02v9+mKkSRBq4FRcKqnZBTjbaukc0EixOIa39uLtDec4G59OTGIWge7V+wtOEIR6zMpeHtkxJ1b2Rh328MMP88orr7B48WK+/vprAD777DM8PDyYMGGCKSMskxhpEoQa2H3pFgC9g93RKjA1Z+DmaEPPFm4A/CFW0QmCcCeVSp4KM6cPlcqol2JjY8Ozzz7Lzz//TGpqKrdu3eLXX39l6tSp2NjU3n6fBiJpEoQa2FWUNPVr6aFwJHBvW3mKbpNYRScIQj02bdo0CgoK+Pbbb/n6668pLCzkueeeq5Nri6RJEIyUmp3PqdhUAPqaQdI0rLUXWrWKC9fSibyVqXQ4giAItcLb25vx48ezZMkSvvzyS+6//378/f3r5NoiaRIEI+2NSEQvQcsmjni72CkdDo0crItbHvwpRpsEQajHXnzxRSIjI4mNja2TAnADkTQJgpEM9Ux9g5UfZTIwrKITU3SCINRnXbt2JTAwkNDQUAYNGlRn1xVJkyAYQZKk2/VMIeaTNA27xwsrjYqLNzKIuJmhdDiCIAi14vTp08TExNTpKBOIpEkQjHLpRiY30vOwtVLTpWjvN3PgckdX8q3nbyocjSAIgmlFRkayfft2nnnmGby9vZkyZUqdXl8kTYJghF2X5ISke3O3Ot2gtyoGtfIEYEe4SJoEQahf5s+fz5AhQ8jMzGT16tXY2xvX78lYImkSBCPsvpQImEergbsNKEqajl5JJjU7X+FoBEEQTOf7779Hp9Nx9uxZevXqVefXF0mTIFRTdn4hh6OTAfNoNXA330b2tGziiF663UdKEARBqDmzS5qSkpJYtmwZY8aMISgoCDs7O1xcXOjduzfffPMNer2+WueLi4vjySefpGnTptjY2BAYGMisWbNISUkp95j9+/czcuRIGjdujL29Pe3atWPhwoXodLqavjyhHjgUlUy+To9vIzuam+l2JQPEFJ0gCILJmV3StHr1ap5++mkOHjxIt27dmDVrFmPHjuXs2bNMnTqV8ePHI0lSlc4VGRlJp06d+O677+jatSuzZ8+mefPmLFq0iB49epCUlFTqmA0bNtC3b192797NmDFjeOGFF8jPz2f27NlMnDjR1C9XsECG0Zu+LT1QGbkVQG0b1KoJADsv3UKnr9r3iyAI9UdVf082FCb7ekhmZtu2bdL69eulwsLCEo9fu3ZN8vPzkwBp9erVVTrX0KFDJUD69NNPSzw+e/ZsCZCeffbZEo+npaVJ7u7ukrW1tXTkyJHix3NycqQePXpIgLRy5cpyr5eWliYBUlpaWpXiEyzTgP/tkAJe2SRtPntN6VDKVVCok9rN+1sKeGWTdCQ6SelwBEGoI4WFhdL58+elxMREpUMxK7du3ZIuXLhQKrcwqOrvb5UkWU46+v777/PGG2/wwgsv8Pnnn1f43MjISIKCgmjWrBkRERGo1bcH1TIyMvD29kav13Pz5k0cHR0B+Oabb5g6dSqPP/4433//fYnzbd++nUGDBtGnTx92795d5jXT09NxcXEhLS0NZ2fnmr1YwSzFJmfT57870KpVnHh7CE62VkqHVK4ZK0/w+6kEnu/fgpeHt1I6HEEQ6si1a9dITU3F09MTe3t7sx0Rr22SJFFYWEh6ejrp6em4urri7e1d5nOr+vtbW1vB1gZra2sArKwq/0W1Y8cOAIYOHVoiYQJwcnKiV69ebNmyhUOHDhV3EzUcM3z48FLn69u3L/b29hw4cIC8vLw62U1ZMD97Lsur5jr6NzLrhAnk1gO/n0pge/hNkTQJQgPi5eUFwM2boqYRQKPR4O3tjYuLS43PZTFJU2FhIcuXLwfKTmrudvHiRQCCg4PL/HxwcDBbtmzh0qVLxUlTRcdotVqaNWvGuXPniIqKIjQ0tNxrp6enl/i3jY2NSLLqiUPRch1cjxZuCkdSuX4tPVCrIPx6BgmpOTR1VX5/PEEQap9KpcLb2xtPT08KCgqUDkdRWq0WjUZjstE2i0maXn31Vc6ePcuIESMYNmxYpc9PS0sDKDezNDyemppao2PK4ufnV+Lfc+fOZd68eZWFLJg5SZI4FCW3GujW3Hy6gJenkYM1HfwbcexKCtvDbzKpe4DSIQmCUIc0Gg0ajXk137V0FpE0LVy4kI8++oiQkBB++OEHk5zTUMpVneyzqsfExsaWmBMVo0z1Q2xyDtfTc7HSqOjg10jpcKpkYCtPjl1JYYdImgRBEGrM7FoO3G3RokXMnj2b0NBQdu7cibu7e5WOM4wKGUaP7maYQrtzVMmYY8ri7Oxc4kMkTfXDwaKpufa+rthZW8ZfbwOL+jXti0wkt0D0GRMEQagJs06aFixYwKxZs2jTpg07d+4sLm6ripCQEAAuXbpU5ucvX74MQMuWLat0TGFhIdHR0Wi1Wpo3b17lOIT6w5Km5gxaeTnh7WJLboGeA5Gl+5IJgiAIVWe2SdMHH3zAnDlzCAsLY8eOHXh6elbr+AEDBgCwZcuWUl3EMzIy2LdvH3Z2dnTv3r348YEDBwKwefPmUufbvXs32dnZ9OzZU4wcNVCHY+Sko2sz8y8CN1CpVMXdwbeL7uCCIAg1YpZJ0/z583n99dfp1KkT27Ztq3BKrqCggPDwcCIjI0s83qJFC4YOHUpMTAyLFy8u8bm5c+eSlZXFY489hoPD7W0wxo0bh7u7O6tWreLo0aPFj+fm5vLmm28CMG3aNFO8RMHCJKTmEJucg0atolOAZdQzGQwMkZOmnZdE0iQIglATZlcIvnz5ct5++200Gg19+vTh008/LfWcwMBApkyZAkB8fDyhoaEEBAQQExNT4nlLliyhZ8+ezJw5k23bthEaGsqhQ4fYsWMHLVu25L333ivxfGdnZ77++mvGjRtH//79mThxIo0bN2bjxo1cvHiRcePGMWHChNp66YIZM7QaaOPjgqON2X3bVKhHCzesNCpik3O4kpRFgJt57pcnCIJg7szup390dDQAOp2OhQsXlvmcfv36FSdNFWnRogVHjx7l7bffZvPmzfz55594e3szc+ZM5s6dS+PGpWtTRo8eza5du3jvvff47bffyM3NJSgoiI8//piZM2c22M6qDV1xPVMzy6lnMnCw0dLRvxGHopPZfTmRySJpEgRBMIpFbaNi7sQ2KvXXwAU7iUrM4pvHOzMotInS4VTb59svs2DLJYa1bsLSyZ2VDkcQBMGsVPX3t1nWNAmCObmZnktUYhYqFXQOtLyRJoDewR4A7I9IolCnr+TZgiAIQllE0iQIlTgULU/NhXo542Jn3vvNlaetjwsudlZk5BVyKq7sPmSCIAhCxUTSJAiVMBSBW1J/prtp1Cp6BcmtEvZcvqVwNIIgCJZJJE2CUInD0YYicMvpz1SWPkVTdHsvJyociSAIgmUSSZMgVCA5K59LNzIB6GqBK+fu1DtI7nd2IjaV9NyGvfO5IAiCMUTSJAgVOFw0NdeyiSONHawVjqZm/Brb08zdAZ1e4qDYUkUQBKHaRNIkCBU4VE+m5gwMo017xBSdIAhCtYmkSRAqYGhqaelTcwZ9guWkaW+ESJoEQRCqSyRNglCOjNwCwq+nA/Unaerewg2NWkV0YhaxydlKhyMIgmBRRNIkCOU4GZuKXgLfRnY0cbZVOhyTcLa1ooOfKyBGmwRBEKpLJE2CUI6jMSkAdA5opHAkptU72FDXJPo1CYIgVIdImgShHMevyklTJwvdOqU8hrqmfRFJ6PRi60lBEISqEkmTIJRBp5c4cTUVgE7+9Wukqb2vK042WtJyCjgTL7ZUEQRBqCqRNAlCGS5ezyAzrxBHGy0hXk5Kh2NSWo2a7i3kFgr7RF2TIAhClYmkSRDKcOyK3Gqgg78rGrVK4WhMr1dR0rQ/UiRNgiAIVSWSJkEow9ErRfVM9awI3KBXUZPLozEp5BboFI5GEATBMoikSRDKcOyKYeVc/SoCNwjydMTTyYa8Qn1xwbsgCIJQMZE0CcJdbqTnEpeSg1oFYf6uSodTK1QqFT0NU3QRYh86QRCEqhBJkyDcxTDK1MrLGUcbrcLR1J6eLYpaD4i6JkEQhCoRSZMg3MXQ1LK+1jMZ9AySR5pOx6WRkVugcDSCIAjmTyRNgnAXw8q5zoH1O2nybWRPgJs9Or1UvDGxIAiCUD6RNAnCHXLydZxLkDfpre8jTXB7im5/pKhrEgRBqIxImgThDqfiUinUSzRxtsHH1U7pcGpdT9GvSRAEocpE0iQId7iz1YBKVf+aWt7NkDSFX88gMTNP4WgEQRDMm0iaBOEOhqSpYwOYmgNwc7ShVdE2MWKKThAEoWIiaRKEInq9dMdIU8NImuB2d/D9Yh86QRCEComkSRCKRCVmkpZTgK2VmnuaOisdTp25XdckRpoEQRAqIpImQShiGGVq7+uKlabhfGt0bdYYjVrF1eRsYpOzlQ5HEATBbDWc3wyCUIlj9XyT3vI42VrR3tcFEKvoBEEQKiKSJkEo0lCTJrhd17RP7EMnCIJQLpE0CQKQmp1P5K0sADr4N7yk6c4ml5IkKRyNIAiCeRJJkyAAJ66mAtDc3YHGDtbKBqOADv6u2GjVJGbmEXEzU+lwBEEQzJJZJk1r1qxhxowZ9OnTB2dnZ1QqFZMmTarWOb7//ntUKlWFHxqNpsQxMTExFT5/4sSJpnyZghk5flWemmuIo0wAtlaa4r32xCo6QWh4cvJ1HIxK4nxCOoU6vdLhmC2t0gGU5d133+XUqVM4Ojri6+tLeHh4tc8RFhbG3Llzy/zcnj172L59OyNGjCjz8+3bt2f06NGlHm/Tpk214xAsQ0OuZzLo2cKdfRFJ7ItI5PGegUqHIwhCLZIkiXMJ6eyNSGTP5VsciUkhv1BOluysNLTzdaGDfyO6NWtM/xCPBrFDQlWYZdL0ySef4OvrS1BQELt27WLAgAHVPkdYWBhhYWFlfq5Hjx4APPPMM+UeO2/evGpfU7BMhTo9p2JTAegY4KpoLEoy9Gs6GJWETi+hUYsfkoJQHyWk5jDrl5Mcjk4u8XgTZxuy8nRk5hVyKDqZQ9HJfLkrkr4tPfjfuHY0cbZVKGLzYZZJkzFJUlWdPXuWgwcP4uPjw7333ltr1xEsx8UbGWTl63Cy0RLs6aR0OIpp6+OCk42W9NxCziek07aoDYEgCPXH1vM3mLPmFKnZciPf3kHu8kewBy08HNBLEHkrk5NXUzl2JYX1J+PZfekWwxbu5v0xbRnZ1lvpl6Aos0yaatPSpUsBeOqpp0rVNBkkJCSwdOlSkpKScHNzo0ePHrRr164uwxTq0PGiIvAwf9cGPbqi1ajp1rwx/1y4yf7IRJE0CUI9kleo48O/wvluXwwA7Xxd+OzhDgS4OZR4nkYFLZs40bKJEw918WNqn2bM+uUk5xLSef6n4zzY0Yd5D7TG2dZKgVehvAaVNOXk5LBixQrUajVTp04t93lbt25l69atJR7r378/y5cvx9/fv9LrpKenl/i3jY0NNjY2xgUt1Lrjhk16G2gR+J16tHDnnws32ReZxLP9WigdjlDHUrLyORKTzKUbGbRu6kL35m7YWZf9x6VgOZIy85jy3RHOxKcB8FTvZrwyvBXW2srXggU3cWLd871Y+M8lvtwVydrj8ZxPSOfX53o0yMSpQSVNv/76K6mpqdx77734+fmV+ry9vT1vvfUWo0ePpnnz5gCcPn2aefPmsWPHDgYNGsTJkydxcHAodeyd7j733LlzRY2UGRNF4LcZ6pqORCeTX6iv0g9VwbIdiEzizzPXOBydzMUbGSU+Z6NV06OFGwNCPBnaugneLnYKRSkYK7dAx9QfjnImPo1G9lYsGN+eQaFNqnUOa62al4e3YkArT6atOE749QyeX3Gc757o0qC2nAIzbTlQW7766isAnn322TI/7+npyTvvvEPHjh1xdXXF1dWVvn37smXLFrp160ZERATLli2r9DqxsbGkpaUVf7z22msmfR2C6dzKyONqcjYqlTw919CFNHHCzcGanAIdp+JSlQ5HqEV6vcRHWy7y8NcH+fHgleKEKcjTkXvbedPUxZa8Qj07L95i7sZz9P/fTlYfjVU4aqE69HqJ2b+c5MTVVFzsrFj9XM9qJ0x36hLYmO+mdMHeWsPeiEReW3umwTXDbTAjTefPn2f//v34+voycuTIah2r1WqZOnUqhw4dYvfu3bz44osVPt/Z2RlnZ+eahCvUEUN/ppaeTg1yqPluarWK7i3c+OP0NfZFJNIlsLHSIQm1IC2ngFmrTrDj4i0AHuzow9B7vOgS2Ag3R7mUQJIkLt/MZEf4Tf48c41TcWnMWXOaIzHJvDOqDbZWYtrO3H3w1wX+Onsda42aryZ3IsjTscbnbOvrwuJHOvLU8iOsORaHbyM7Zg1uaYJoLUODGWmqSgF4RTw9PQHIysoyaVyCsgxJU0NuNXA3wxSdaHJZP126kcGoz/ey4+ItbLRqPpnQno8fCmN4G6/ihAlApVLRsokTz/Zrwbrne/HvoS1Rq+DXo3GMWbKf6ETxs9Cc/XAghq/3RAPwv/Ht6NbczWTnHtDKk/mj5b6FC/+5zJpjcSY7t7lrEElTbm4uP/74I2q1mqeeesqocxw6dAiguNZJqB9EEXhphn3oTlxNISdfp3A0gikdiExizOJ9xCRl4+Nqx2/TejKmg2+lx6nVKqYPDObHp7rh7mjNhWvpPPDZXvZeTqyDqIXq2h5+g3kbzwEwZ1gIo8J8TH6NR7sFMK2/vFjk1d9OF9eG1ncWnzQVFBQQHh5OZGRkuc9ZvXo1KSkpjBw5sswCcINDhw6Rn59f6vFdu3bx8ccfA1R7OxfBfOUX6jkdJ68m6SiKwIsFutnT1MWWAp3E0SvJlR8gWISbGbnMWHmcrHwdPZq7sXF6L9r4VK+tRK8gd/6Y2YcugY3IyCvk2R+Pcj4hvfIDhTpzMz2X2b+cQi/BxC5+PN+/9lbBzhkawr1tvSnUS7y85hS5BfX/jyyzrGlav34969evB+D69esAHDhwgClTpgDg7u7OggULAIiPjyc0NJSAgABiYmLKPJ+hALy8DuAGr7zyCufOnaN///74+sp/fZ05c4Zt27YBMH/+fHr27FmTlyaYkfPX0skr1ONqb0Vz94pXRDYkKpWKHi3c+e14HPsikugT7KF0SEIN6fQSs1adJDEzn1ZeTnz3RBeja5KaONvy09TuTPnuMPsjk3jy+yOsf6EXXi6iW7TSJEni9XVnSMspoI2PM/NHt6nV7U/UahXvj2nL4ZhkIm9l8em2y7w8vFWtXc8cmGXSdPLkSZYvX17isaioKKKiogAICAgoTpoqc+HCBfbu3VulAvDJkyezbt06jhw5wl9//UVBQQFNmjThoYceYvr06fTp08e4FySYpTun5sS+SiX1bOHGb8fjOBAppl/qg8U7ItgfmYSdlYbPH+lY4yJua62aLyZ1YuwX+4m4mckT3x9h9XM9cLQxy18pDca6E/H8c+EmVhoVH40Pq5N2AC72Vswf1YbnVhxj6e4oRrb1rvYIpiVRSQ1tvWAtSk9Px8XFhbS0NLF6zgK88PNx/jh9jTnDQnhhQJDS4ZiVa2k59PhgO2oVnHh7KC52YmWhpToYlcQjXx9EL8FH49sztlPlNUxVFZuczZgl+0jMzKd/iAfLHuuMtoH17TEX19NyGfrJLtJzCxX5mfbCT8f548w17vF2ZsP0XhbXv6mqv78t61UJggkZRpo6iP5MpXi72NHcXd6H6lCUWEVnqZIy83hx1Qn0Eozr5GvShAnAr7E9yx7vgq2Vmp0XbzHv93MmPb9QNZIk8dra06TnFtLe14Vn+9b9gqV5D7TG1d6K89fSWbqr/BpjSyeSJqFBik/N4VpaLhq1ijA/V6XDMUs9g0TrAUsmSRL/Xn2KG+l5tPBw4J1RrWvlOmF+riyc0AGVClYcvMqm0wm1ch2hfKuPxrHj4i2stWoWjG+vyGifh5MNc++/B4BPt0Vw+a7u8vWFSJqEBulojLwq7B5vZ+ytRR1GWXoHya0H9kaIuiZLtO3CzeJfpIsf7Vir7/PhbbyYXjQd9Ob6s9xMz621awklXUvLYf6m8wD8a0hLgps4KRbL6DAfBoR4kK/T82o97RYukiahQRL7zVWue3M3VCqIuJnJDfFL0KIU6vR8uDkckDdnbeVV+zWWMwYG08bHmdTsAl757XS9/IVpjj78K5yMvELC/FyZ2kfZPoIqlYr3xrTFzkrDsSsp/H3uuqLx1AaRNAkN0tEYOWnqHCiSpvK42lvTtmgVzD4x2mRR1hyLI+JmJo3srYobENY2a62ajx8Kw1qrZsfFW6w6Ivapq21HY5LZcDIBlQrmj2qDRq38KuCmrnY81bsZAP/dfJFCnV7hiExLJE1Cg5OZV0j4dbkhX+cAsbdaRQzdwcUUneXIydfxyT+XAJg+MLhO91Rs2cSJl4eFADB/03muJmXX2bUbGr1e4j+/y9NyD3Xyo62v+Szzf7Zfcxo7WBOVmMUv9WyTZ5E0CQ3Oiasp6CXwcbUTDfkqYahr2h+RJKZbLMS3+6K5kZ6HbyM7JnX3r/PrP9mrGd2aNSY7X8e/Vp9Epxfvm9qw5ngcZ+LTcLTR8u+iRNVcONlaMWOgXOO28J/LZOcXKhyR6YikSWhwxNRc1XUObIS1Vs319Fwib4kNWs1dUmYeX+yUl3vPGRaCjbZmTSyNoVarWDC+PQ7WGo7EpPDdvug6j6G+y8gt4L+bLwIwc1AQHk42lRxR9x7tFoBfYztuZeTxzZ768x4QSZPQ4BiKwDuLIvBK2Vppir9O+0V3cLP32fYIMvMKaePjzP3tmioWh19je966T15+/vHWS1xLy1Eslvro8x0RJGbm0czdgSk9mykdTpmstWr+PVQeAVu6O4qkzDyFIzINkTQJ9ZteB1f2w+bX4OtB6Le8TcTVOAA6iXqmKullaD0gdrQ3a1eTsvnp0BUAXh0eilrhouCHOvvRKaAR2fk63t10QdFY6pPoxCy+3SuP3Lx5byjWWvP9NX5/u6a09XEhM6+Qz7ZHKB2OSZjvV1sQauL6Gfh9FnzUCr4bAQeXQPxR1PsX8ZdqJs/bbCbE3VrpKC2Coa7pQFRSvVsJU598vuMyBTqJPsHu9A52Vzoc1GoV80e1Qa2CP85cY/elW0qHVC988OcFCnQSfVt6MLCVp9LhVEitVvHqCHkD358OXeFKkuVP8YukSah/Yo/AsiFw7DvIugk2LtBuIoxcQKpDcxqpMnlZ9QOaJV3g3HqlozV7bXxccLbVkpFbyNmEdKXDEcpwKyOP9SfkTtyzBgcrHM1t9zR15vGegQDM3XiOvEKdsgFZuKMxyWw5fwO1Ct66N9QiNhrvFeROn2B3CnQSS3ZY/vYqImkS6pdbF+Hn8VCYAwG9YdJvMCcCHlwKXZ9mrs9XvFzwNJnWHpB6FVY/DuF/KB21WdOoVfRoIW+pIvo1macfD14hX6eng7+r2U07zx7SEg8nG6ITs1hWjwqC65okSfxfUcPShzr7Kdr5u7pmDW4JwG/H44hPtez6NpE0CfVHWjz8+CDkpIBPJ3j0VwgaDNrb03BHrqTzq24AZx7cAR0fkx/cOBMyxdRBRQx1TSJpMj+5BTpWHJRrmab2VrYjdFmcba14895QAD7bfpnYZNG7yRjbw29yJCYFG626OAmxFJ0CGtGjuRuFeomvLHwzX5E0CfVDdjKseBDS48AtGB5ZDdYOJZ6SkJpDQtEmve2aecPIBeDZGrIT4fcXQfQhKpchaToak0JOvphiMSfrTsSTnJWPj6sdw1o3UTqcMj3Qvik9mruRW6DnnaJ90oSq0+ml4hYDU3oFWmR/OUPfppVHYrmZYbnbMomkSbB8BTmw8mG4FQ5OTWHyOnBwK/W0o0WtBkK9nXCw0YLWRp62U1vBxT/gxIq6jtxiNHd3wNvFlnydnqNXkpUORygiSRLfFK2keqJXoCK721eFSqXinVGt0apVbD1/g12iKLxa1p+I5+KNDJxttTzfL0jpcIzSo4UbHfxdyS/UW3TfJvP8DhOE6tjxPsQeBFsXuYbJ1a/Mpx2LkX/Zl9g6xastDHxDvr/5VUiJqeVgLZNKpSreUmVfRJLC0QgGuy7dIuJmJo42Wh7qUvb73lwEN3FiSlFR+LubzouVmFWUV6jj463ytjjT+gfhYl932+KYkkqlKh5t+vHgFVKy8hWOyDgiaRIsW1IkHPxCvj/6S2hyT7lPNYw0dbq7qWXPmeDfA/IzYd00ubeTUErvYHn0bm+EGCUwF4ZRpgld/Op0jzljzRgUTCN7Ky7fzOTnw1eVDscirDh4lfjUHJo42xQnnZZqQIgn93g7k52v47v9MUqHYxSRNAmWbevboC+AFgMhZES5T8vMK+TCtaJNeu/ePkWtgTFfgrUjXN0Ph76szYgtlqGu6VxCer3p7mvJwq+ns+dyImoVFvPL1MXOipeKukR/vPUSadkFCkdk3jJyC1i8Q24KOXtwS+ys635bHFNSqVRMLxpt+n5fNOm5lvf/L5ImwXJF74bwTaDSwLD3oYKeJSevphZv0uvtYlf6CY0CYei78v29C6FQJAV383SypZWXE5IEe8UqOsUZ6kJGtPHGr7G9wtFU3cNd/GjZxJHU7AIWbbusdDhm7es90SRn5dPcw4FxnXyVDsckhrf2IsjTkfTcQn48cEXpcKpNJE2CZdLrYPPr8v3OT4JnaIVPP1JUz1Rqau5OHSaBk7fcEPPcOlNFWq/0a+kBwO5LImlSUnJWPhtOys0sn+pjnnuPlUerURfvS/fDgRgibmYqHJF5SsrM45s9UQD8e2iI2Rb5V5dareL5/i0A+HZvNLkFllUOUT/+F4SG58QKuHFGLv7u/1qlTz8ULRcvd2teQeM/jRV0eUq+f/AL0YKgDH2LkqY9l28hia+PYtYejyNfp6etjwsd/S1v4+k+wR4MauVJoV7i/T/FvnRlWbwjkqx8HW19XBjRxkvpcEzqgfZN8XG1Iykrn3Un4pUOp1pE0iRYntx02D5fvt/v1TLbC9wpr1DHiaupAHRrVvFz6fQEaGzg2kmIPVzzWOuZTgGNsLVSczMjj4s3MpQOp0GSJIlVR2IBmNjVvFfMVeT1e0PRqlVsD78pWhDcJT41p7hh6ZxhIRaxXUp1aDVqnugVCMDXe6LQ6y3nDzCRNAmWZ89HkHVLbmLZ9elKn346Lo28Qj3ujta08HCo+MkO7tBuvHz/0BcmCLZ+sbXS0L25nHiKDViVcexKChE3M7Gz0vBA+6ZKh2O0Fh6OPNYjEBAtCO626J9L5Ov0dG/emD5msPlybZjY1R8nWy1Rt7LYHn5T6XCqTCRNgmXJSry9um3ou/KUWiUOR8v1TF2bNa7aX2zdpsm35zdCWpyxkdZbfYINU3SirkkJKw/Lo0z3tfPGyQLaDFTkxUHBuBa1IFgpWhAAEHEzkzXH5J87Lw9vVe9GmQwcbbQ80tUfkEebLIVImgTLcvRbKMyFph2h5bAqHXIwqqieqbKpOQOvNhDYByQdHFlmbKT1Vr+W8l++h6KTxZYqdSw9t4A/zsgF4BOLfuFYMhd7K14aIu+j9vHWS6TlWN4SdFP7ZOsl9BIMDm1ikfVq1TGlVyBatYpD0cmcik1VOpwqEUmTYDkKcuHwV/L9Hi9U2GKg+BCdnmNFTS27NqvG7u/dnpVvj30P+WKD0Tu18HCkqYst+YV6DseILVXq0oaTCeQW6An2dKSjv6vS4ZjEI139CfJ0JCW7gM8aeAuCs/Fp/HHmGiqVXMtU33m72BVPMVvKaJNImgTLcWa1XMvk7Av3jKrSIecS0snO1+Fqb0VIE6eqXytkJLj6Q06KfF2hmEqlKp6iE3VNdeuXI/IU1sSu/vVm2karUfPmvXLLkOUHYohOzFI4IuX83+ZwAEaH+RDiVY2fVxZsap/mAPx55hqxyeb/B6pImgTLIElwYLF8v9uzVaplAjhUNDXXJbAxanU1fsmoNdD1maKTfCnaD9ylb0uRNNW1s/FpnI1Px1qjZkwHH6XDMan+IZ70D/GgQNdwWxDsuXyLPZcTsdKomD24pdLh1Jl7mjrTO8gdvQTf7YtROpxKiaRJsAyR2+HWBXmrk06PV/mwQ0VF4N2qMzVn0GEyWDnAzfOi/cBdegW5oVbB5ZuZXEvLUTqcBmFV0SjTsDZeNHawVjga03vz3lA0ahVbz99gfwPrOK/XS3zwpzzKNKl7AP5ultPh3RSe7iuPNq06ctXst9YRSZNgGQyjTB0fkxtaVoFOLxV3Aq9yEfid7Fyh1Uj5/oWN1T++HnO1t6adrysAe0R38FqXnV/IhhNyAfjDXSy3N1NFgjydmNRNLm5/Z9N5dBbUu6emNpyK5/y1dJxstMwYGKx0OHWub7A7rbycyM7XsfKIea+iNMukac2aNcyYMYM+ffrg7OyMSqVi0qRJ1T5PYGAgKpWqzA8vr/I7rO7fv5+RI0fSuHFj7O3tadeuHQsXLkSnEyuFFHHjPERuA5X6doF2FVy4lk5GbiGONlruaeps3LVDH5Bvz28UU3R3KZ6iuyym6Grbn2euk5FXiH9j++I+WfXRrMEtcbbVEn49g58bSAuC3AIdC/6+BMC0AS3q5ShiZVQqFU/2lrcDWr4/hgIz7tmlVTqAsrz77rucOnUKR0dHfH19CQ8PN/pcLi4uzJo1q9Tjjo6OZT5/w4YNjB07FltbWyZMmEDjxo35/fffmT17Nvv27WP1alEUXOcOLpFvQ++XN9atIkN/ps6BjdBUp57pTkGDwcoe0q5Cwgnw6WjceeqhvsHufLrtMnsjEtHpJeO/xkKlVh+VezNN6OJXvdo8C9PIwZp/DQ1h7sZzLPj7Ive29a73ScSPB64Qn5qDl7MtT/ayrH0ETemB9k357+ZwrqXl8tfZ62bbuNUsk6ZPPvkEX19fgoKC2LVrFwMGDDD6XK6ursybN69Kz01PT2fq1KloNBp27txJ586dAZg/fz4DBw5kzZo1rFq1iokTJxodj1BNmTfh9K/y/R7Tq3Vo8X5zxkzNGVjbQ/AQOL9BnqITSVOxMD9XnGy0pGYXcCY+jTA/V6VDqpdik7M5FJ2MSkW9KwAvy6Pd/Fl1JJYL19L5398X+eDBtkqHVGtSs/P5bLvcZuGloS2xtdIoHJFybK00TOoewMJ/LvPN3mjub+dtlitEzXJ6bsCAAQQHB9f5F2z16tUkJiby8MMPFydMALa2trz77rsALFmypE5javCOLQddHvh2Ab+uVT5Mr5eKR5oq3KS3KsQUXZm0GjW9guRGlzsvWs42CJZmfdGGpj1buNHU1U7haGqfVqPmnVGtAbkw+HRcqrIB1aIlOyNJzy0kpIkTYzv6Kh2O4iZ1D8Baq+ZUbCrHr6YoHU6ZzDJpMqW8vDxWrFjB+++/z6JFi9ixY0e5tUk7duwAYPjw4aU+17dvX+zt7Tlw4AB5eXm1GrNQRK+HEz/I97tMrdahEbcySckuwM5KQ1ufqhWOl6vlMHkT3+RIeSWdUGxgK08Ai9o7ypJIksTaoqTpwQ4N55dql8DGjOnggyTB2xvOWdSGrlUVl5LN9/tjAHh1ZCsxvQ24O9owOkyelvtmb7TC0ZSt3idN169fZ/LkybzxxhvMmjWLgQMHEhwczK5du0o99+LFiwAEB5devaDVamnWrBmFhYVERVXcuTQ9Pb3Eh0iyjBS9C1Kvgo1LlZtZGhj6M3UKaISVpoZvcxsnCBok3z+/oWbnqmf6t5KLwU/HpXEzI1fhaOqf41dTiU7Mwt5aw/A25S9eqY9eG9EKB2sNJ2NTWXO8/u0B+d4fF8gv1NOzhRv9ixZVCBQXhG8+e524FPNrdlmvk6YnnniCbdu2cf36dbKysjhz5gzPPvssMTExjBgxglOnTpV4flpaGiAXj5fF8HhqamqF1/Xz88PFxaX444MPPqj5i2mIjheNMrUbD1bVm5Y4WJP+TGW5c4pOKObpZEs7X/n7Yme4WEVnamuLkoXhbbxwsDHLEtRa4+lsy6yiJo//91e42ffvqY49l2/x19nraNQq5t7f2ixrd5TSyut2s8vlRSNx5qReJ01z585l4MCBNGnSBHt7e9q0acOXX37JSy+9RE5OTpULxA2konqWyt7gsbGxpKWlFX+89tprxr6Ehis7GcI3yfc7PlatQyVJ4lCUnDRVa7+5ioQMB7WV3GAzsWHvj3U3MUVXO3ILdPx+Su7N1FDrXab0CiTI05GkrHwWbLmodDgmkV+oZ+7GcwA83iOwwWyXUh1PFY02rTocS2ZeocLRlFSvk6byPPfccwDs3r27xOOGkSTDiNPd0tPTSzyvPM7OziU+bGxsahpyw3P6F9Dlg3d7+aMaLt3IJDEzDzsrDWGm2tTUrhE07yffF1N0JRiSpj2Xb5FXKHqZmcr28Juk5xbi7WJbr3szVcRKo+adB+Si8B8PXile3GHJvt0XTdStLNwdrZk1pOE1sqyKfi09aO7hQEZeYXG7DXPRIJMmT0/5h3xWVsmNIUNC5F2lL126VOqYwsJCoqOj0Wq1NG/evPaDbMgk6fbUXIfJ1T58T1Gzxa7NGmOjNeES3uIpOpE03alNUxfcHW3IytdxJNo8V7yYHV2hvBl0yhW4flZu4HrXykzD1NyYDj4Nuki4Z5A7EzrLXdBf/e00uQWWm5hfT8vl023ySPWrI0Jxtq3aHpoNjVqtKu5Z9d2+GLPqDt8gk6ZDhw4BlEp+Bg4cCMDmzZtLHbN7926ys7Pp2bOnGDmqbfHH5FVqWltoO77ah+8r2reqd9FyeJNpdR+oNHD9NCSb58oOJajVKgYWFYRvC7+hcDRmLikSlvaF+W7wf4GwqB182Qu+6AE/jYcs+b2bmJnHzoty8v9gx/rfm6kyr98biqeTDVGJWSzaZrnT4+//eYHsfB0d/V15sAH03KqJsR19cbW34mpyNlvPm8/PFYtPmgoKCggPDycyMrLE4+fOnSM5ufRQbmxsLNOny00S796aZdy4cbi7u7Nq1SqOHj1a/Hhubi5vvvkmANOmTTP1SxDuZhhlume0vP9bNeQX6os36e0dbOKkycENAnvJ9y/8btpzW7g765ok0cuqbDH7YNkguHbHAhStLTh4gMYaIrbCl70hZh8bTyZQqJdo7+tCkKeoeXGxs+Ld0W0A+Gp3FGfjyy6hMGcHIpPYeCoBlQreGdWmXnd2NwU7aw2TugUAsGxPxSvW65JZLsdYv34969evB+SWAQAHDhxgypQpALi7u7NgwQIA4uPjCQ0NJSAggJiYmOJzrF69mg8//JABAwbQrFkznJyciIqKYtOmTeTm5jJy5Ej+/e9/l7ius7MzX3/9NePGjaN///5MnDiRxo0bs3HjRi5evMi4ceOYMGFCrb/+Bi0vE87+Jt/vWP2pueNXU8jO1+HuaE2r2iiwDH0AonfDxT+h10zTn99C9Q72wEqj4kpSNlGJWbTwKHubogbr5ErYOAP0BeDTCcZ9C05NQVu0RciNc7B6CiReguX3obV9BDXDGdupYRaAl2Voay/ua+fNptPXmLPmNBun96p5O5E6klug460NZwG543mbmvaOayAe6xHA0t2RHL2SwomrKXTwb6R0SOaZNJ08eZLly5eXeCwqKqq4P1JAQEBx0lSeAQMGcPHiRU6cOMGBAwfIysrC1dWV3r17M3nyZCZPnlzmKrjRo0eza9cu3nvvPX777Tdyc3MJCgri448/ZubMmWJpaG07tw7yM6FxcwjoVe3DDVNzvYLca+f/KniIfBt3BPIy5B5OAo42Wro1c2NvRCI7wm+KpMlAkmDH+7D7v/K/7xkNY74s3UKjSWt4egf8OQdO/cxjOSvwsz5H+zZ/1XnI5mzeA63ZF5HIhWvpLN0VyfSBllFIveDvi0TczMTd0YZ/Dw1ROhyL4elsywPtffjteBzf7I3m80eUT5pUkhhLN5n09HRcXFxIS0vD2dlZ6XAs07IhEHcYBs+D3rOrffjoxfs4GZvK/8a1Y3xR8ajJLQqDlGh4eBWEjKida1igb/dG886m8/Rs4cbPT3dXOhzzsP1d2P0/+X7vl2DgW6CueHTk9x8+YnDkh9ip8mHou9BzRh0EajnWn4hn1i8nsdaoWft8T7MftTkYlcTDXx9EkuCbxzszKLSJ0iFZlAvX0hmxaA8atYpdc/rj28i+Vq5T1d/fljG2KTQMiRFywqTSQPuHq314WnZB8T5VJq9nulMLecEAkdtr7xoWyFDXdDg6mfTc+tOI0Gg3zsPeT+T7930Cg+dWmjDp9RLvxYUxt/Bx+YFt8+FW6dW8DdmosKYMDm1Cvk7P9J+Pk2HG77XMvEL+vfoUkgQTOvuJhMkIod5ys0udXuL7fTFKhyOSJsGMnF4l3wYNAqfqbxlxICoJvQQtPBzwdqnFjU1bDJBvI3fU3jUsUKC7A809HCjUS+y9nKh0OMrS62HTLNAXyqsuOz9ZpcMORiVxPT2XzVaD0bcYJG9WvX4a6C13mb2pqVQqFoxvh4+rHTFJ2by29ozZLj54d9N54lJy8HG14837QpUOx2I91aeo2eWRWMWTZJE0CeZBr4dTv8j32xlXbL83Ql6ibfJWA3cL7COPhiVdhlTzarymtIEh8mjTtgsNvDv4iR8g9hBYO8KI/1b5MMPmvPe280H9wGfyvovxR2H/Z7UVqUVytbfms0c6oFWr2HT6Gj8duqp0SKVsD7/BqiPyz4cF49vjJHoyGa1fsAdBno5k5hXyyxFlf+aKpEkwD1cPQNpVsHGGVvcadQrD6Ebv4Fre/NLOVV4BBRAlRpvuNDBUTpp2XLxJoU6vcDQKybwFW+fK9we8AS5V68eTk6/jrzPXgKLeTC4+MPx9+ZM73oeb4bURrcXq6N+IV0e0AuCdTefNqg1BclY+r/x2BoAnezWjR4uG2dHdVNRqFVN73252qeTPFpE0Cebh1Er59p5R1d6cFyA2OZuYpGw0ahXdm5tov7mKiLqmMnUJbIyrvRXJWfkciWmg3cG3vAG5qeDVDro+U/XDzl8nK1+HbyM7OhmWVoc9CsFDb0/T6cxrHy6lPdW7GYNDPckvNJ/6pvxCPc+tOMatjDxaeDjw8nCxWs4URnfwwc3BmvjUHDafu65YHCJpEpRXkAPn1sv3jSgAh9utBsL8XOtmGNxQ1xS1S55aFAB5r7AhRcWum89eUzgaBUTtlPdNRAX3LwRN1bu6rCuamhvTwed240OVCu5fJE/TJRyHI1+bPGRLJtc3tS+ub3px1UkKFByFkCSJN9ad4XB0Mo42Wr6Y1AlbKxNu5dSA2VppmNQ9ABc7KzJylfvjQSRNgvLC/4D8DHDxB/8eRp1iT21tnVIen07yVGJOMlw/VfnzG5DhbeQi/r/P3UBvRntG1TpdAWx6Sb7f9enbU7hVcCsjjz1F08tj7t5ew7kpDJkn39/3KRTmmyDY+sPV3prPH+mAjVbN9vCbvLzmtGLvu6W7o1h9LA61Cj5/pAMtm4g+bqb0dN/mHHhtIA939VcsBpE0Cco7XVQA3n5CpUuyy6LXS+w3JE212WrgThoruSAcxBTdXXoFueNgreF6ei6nilpANAjn1kNypLwtysA3q3XoxlMJ6PQS7f1caV5WY9CwR8HJGzIS4Myvpom3Hung34gvJnVEq1ax7kQ872w6X+cr6v4+d53/2yzXnb193z30L1oUIZiOo40We2tle3IbnTStW7cOnU4sgxVqKOMGRGyT77ebaNQpzl9LJyW7AEcbLWF+rqaLrTKi9UCZbK00DCyeolOu9qBOSRIcXCzf7/oM2Fav4eK6E3EA5W/iqrWB7kX7Xu5bJKaEyzCwVRMWjG8PwPf7Y/h0W0SdXftsfBqzVp1EkmBy9wAe7xlYZ9cW6pbRSdPYsWMJCAjg7bff5upV81vuKViIs2tA0oFPZ3APMuoUuy7JrQa6N29ct3tRGYrBrx6E/Ky6u64FGN5anqLbfO662fbQManYw5BwAjQ2Ve7JZHD5RgZn49PRqlXc375p+U/s9IRc25R4Sd77UChldAcf/vNAawA++ecS3++LrvVrHr+awmPfHianQEefYHfm3n+P2G6rHjP6N8zzzz9PVlYW7777Li1atOD+++/njz/+aBg/IAXTMayaa2/cKBPAtgs3AOp+OLxxc3D1lzdhvbK/bq9t5vqHeGCjVXMlKZvw6xlKh1P7Di6Rb9s9BA7VmyI29GbqH+JBYwfr8p9o6wxdnpLv71soj24JpTzeM5DZg1sCMO/38/x3czi6Wqpx2nz2Og9/dZDkrHza+rjw+SMd0VrIJsKCcYz+3/38889JSEhg2bJldOzYkT/++IMHHniAgIAA5s+fT0JCginjFOqjG+fg+hlQW0GbsUadIjEzjxOxqQAMCq3jpEmlguaGKTpR13QnBxstfVvK/bL+qu9TdKlX4cJG+b5hCq2KdHqJdcflpOnBjr6VH9B9mjyaFXdEJOoVmDkoiOf7twBgyc5Ipnx3mJQs0xbQf78vmmk/HSOvUM+AEA9WPdMdFzvRwLK+q1FKbGdnx5NPPsmhQ4c4ceIEzzzzDGlpacydO5fAwEAefPBBtmzZYqpYhfrmVNG2KS2Hgb1xvZV2hN9EkqB1U+fa3TqlPMX9mkRd090MU3R/1/ek6fDXIOmhWT9o0rpah+6LSOR6ei4udlZVS/odPSHskaKDF1Y/1gZCpVLx8vBWfPpwB+ysNOy5nMj9n+81SQPMAp2e9/44z7zfzyNJ8HBXf75+rDMONsoWKAt1w2TjiO3bt+eLL77g2rVrfPXVV3h4eLBhwwZGjBhB8+bN+eijj8jOzjbV5QRLp9fBmdXy/RpNzcnbdQxWaiPMZn0BFdy6AOlidPVOg0OboFWruHgjg6hbmUqHUzvyMuH4cvl+9+erffiaY3IB+Kiwpthoq9jPp+cMUKnh8hZ5tFYo1wPtm7L2+Z4EuNkTl5LD2C/2s2RnhFFNMCVJ4u9z1xm2cDdf75FrpeYMC+H9MW3ElFwDYtL/6ezsbH7++WeWLl3KtWvXkCSJsLAwEhMTmTNnDqGhoZw+fdqUlxQsVfQuyLgGtq5yx2Mj5Bbo2H1ZLgJXLGmybwxNw+T7MfuUicFMudhbFW8foWQH31p1aiXkpkHjFtV+H6fnFvB30ddlbFWm5gzcWsid80FeSSdUKNTbmY0v9GZAiAd5hXr+u/kivT7czsdbLpJcxSm7Y1dSGP/lAZ798RhRt7Jo7GDNoolhvDAgSBR9NzAmSZpOnjzJtGnT8Pb25plnniE8PJxnnnmGkydPcuzYMeLj43n//fe5ceMGM2fONMUlBUtn2Jy3zYPycmojHIxKIjtfRxNnG9r4OJswuGoK6CXfXhFJ092KG13Wxyk6vR4OfSnf7z6t2j3G/jh9jbxCPcGejrTzrV6LAnrNkm/PrIHMBr45chW42FvxzeNdWDC+Pc09HEjPLeTT7RH0+nA7r6w5zbd7o9kefoPIW5nk5Ou4eD2D1UdjeXvDWUZ9vpexX+zn6JUUbK3UTB8QxK45/RkVVrU9BYX6xehJ2OzsbFauXMnSpUs5duwYkiQRGhrKtGnTePzxx3Fyut0J1cnJiVdffZUrV67www8/mCRwwYLlZ8GF3+X7Rm6bAren5ga2aqLsX3sBveDA56IwtwxD7/HizfVnORWXRnxqDj6uCtSd1ZaIfyApQm4DYMT72DA1N66Tb/Xfv03DwLeLXBB++lfoOb3a129o1GoV4zr5MqaDD1vOXWfJzkjOxKfxy9HYyo9VwfhOfswe0hIvF9s6iFYwV0YnTU2bNiUjIwOtVsu4ceN4/vnn6devX4XH+Pj4kJOTY+wlhfriwiYoyJKX7Pt2MeoUkiQVtxoYXNer5u7m312+Tbwo73Dv6KFsPGbEw8mGLgGNORyTzJ+nr/F03+ZKh2Q6x76TbztOBpsyunhXIOpWJseupKBWlbFtSlWFPSInTSd/gh4vyKs5hUpp1CpGtPVmeBsv9kUksTcikavJWcQkZnMlKYusfB0O1hpa+7jQzseFtr4udA5sXL8SfsFoRidNTk5O/Otf/+Lpp5/Gy8urSsfMnDmTyZMnG3tJob4w9GZqN8HoH/QXrmWQkJaLrZWaXnW131x57BuDZ2u4eQ6u7r9dbyIA8EBYUw7HJLP+ZHz9SZqyk+HyVvl+h+r/TPvtuDzK1LelB57ORo5ctH4Q/noVbp6Ha6du19YJVaJSqegd7F5i6yVJkkjNLsDZzgqNWiShQmlG1zRduXKFt956q8oJE4CzszMBAQHGXlKoD9KvyUXgIDcCNNI/RaNMvYM8zGMX8YCe8q2Yoivl3rbeaNUqziWkc+lGPWl0eWGj3NS0SVvwbFWtQ3V6ibVFvZnGdapGAfjd7Fyh1b3y/ZM/G38eoZhKpaKRg7VImIRyGZ00qY3YWFUQOLNa7mnj112enjOS2UzNGQSKYvDyNHKwLu7Wvr6o+7XFO7NGvm07rtqHHohM4lpaLs622pqv+gx7tCie1VBo2uaNgiCUVmuZz+7du9m/fz96sbGkcKfTRavm2k8w+hQ303M5FSc3qRvYykySJv+ikabrZyEnRdlYzJChbmfDyQT0tbSlRZ1Ji4eYvfJ9IzrZrzkmFx4/ENa05qOkLQaAkzfkJMPlv2t2LkEQKlVrSVP//v3p06cPwcHBLF26lPx88VdQg3f9DNw4CxpraD3G6NNsD5dXzbX3czW+HsTUnJqAWxAgwdVDSkdjdgaFeuJkoyU+NYcjMclKh1Mz59YCkpwou/pV69D03ILinlXV6s1UHrVGrg0EMUUnCHWg1pKmvn370rt3b9LS0pg2bRqBgYG1dSnBUty5bYpdI6NP84+hC7i5jDIZFNc1iSm6u9laaRjRVq5/XH/SwqfoDJ3sjZiaW38intwCPUGejoT5uZomHsO2Kpf+Fj2bBKGW1VrStHPnTnbt2kViYiInT57k9ddfr61LCZZAV3i7DqQGvZky8wrZGyF3AR+kVBfw8gT0lm9F0lSm0UVTdHJTR53C0Rgp8bK8Uk2thXtGV+tQSZL4+dBVAB7p6m+63mIeIeDTCaQ7tiYSBKFW1Ho1t06no127dkyfLpqvNWiR2yHzOtg1hqAhRp9m6/nr5BboaebuQKi3U+UH1CXDSFPCSXlPMqGE7s3c8HaxJT23kB3ht5QOxziGxL/FQHBwq9ahJ2JTCb+egY1WbZqpuTsZRpvEFJ0g1Cqjk6Zp06aRl5dX4XOuXLlCnz59jL2EUJ+cXCHftpsAWmujT7PxpLwp7v3tm5rfnk+ufuDiL//FH3dY6WjMjlqt4oGwpoCFrqKTpDum5sZX+3DDKNO97bxxsbcyZWRyQbrGWq4ZvCb29xSE2mJ00rR06VK6devGxYsXy/z82rVr6dChA4cOiaLYBi8rCcL/lO93eNTo06Rk5bPnciIg715ulkS/pgqNLtqva3v4TdKyq7/TvKISTkByJGjtIGRktQ5Nyylg02k54X+0m7/pY7NrdLtnk6F2UBAEkzM6aXrjjTc4e/YsnTt3Zvny5cWP5+fn88ILLzB+/HjUajXr1q0zSaCCBTuzWm4E6NUOvNoafZo/z16jUC/RuqkzQZ7V27aizhj6NcWIuqayhHo708rLiXydnj/PXlM6nOoxTM21GlntbVMMBeAtmzjS0d/4RRAValNUmH5+gzwqJliWvEx5enX7exD+h/zHpmB2jN5GZf78+fTv359Jkybx5JNP8s8///Diiy/y9NNPc+rUKXr16sXKlSvx9TXx3L1geQxTcx0m1eg0hqk5sx1lAnnzXoD4o1CQC1Zm0hLBjIzu4MOHf4Wz9ngcD3ethVGX2qDXwdnf5PvVnJqrtQLwuwUNAmtHSI+D+OPg26l2riOYjiTB1QNw4ic4vx7y76qFdAsG/27Q+Um52F9QXI0KwQcNGsSpU6cYPHgwP//8M926dePs2bO8+eab7Nq1SyRMglxfcf2MXG9hRB1I8WnScjhc1N/nPnNOmho3B8cmoMuH+GNKR2OWRof5oFGrOBKTwmVL2VYl9rC8kMHWBVoMqtahx6+mcPFGBrZWasaYugD8TlZ2cjsPkH8BC+btxjlY3BW+GyH/YZmfKf/8aP8weBRtzZN0GU6sgG+Hw8mVysYrACZYPefo6IiHhweSJCFJEi4uLvTr109ssyLITv4k34aMlDe2NdKmU9eQJOgS2Mi8dxtXqURdUyW8XGwZVNRj66eiERizd7GoJi94WLUXMhhe433tmuJiZ+IC8LsZNos+v15M0Zmz+OPw3UhIvCSPDnaYBE9shhnHYcyX8MIheDkaHv5F/tmpy4f1z8E/80DssqGoGmU2p06domPHjqxcuZJhw4bx5Zdfkp+fz7Bhw3jzzTeN3kJlzZo1zJgxgz59+uDs7IxKpWLSpOpN7SQlJbFs2TLGjBlDUFAQdnZ2uLi40Lt3b7755psyY4uJiUGlUpX7MXHiRKNeT4NVmAenf5Xv13Rq7pQFTM0ZBIh96Cozqbu8cfdvx+LIzi9UOJoquLRZvg0ZUa3D0rIL+OO0XLv1SG0UgN8taAhY2UPqVbh2svavJ1Tf1YPwwyjITQXfLjDrDIxaDAE95D+6DOwbQ8hwmPAT9Pm3/NjeT+DXyaKliYKMrmlavHgxc+bMobCwkPfff59XXnkFgAEDBjBhwgQ++OADdu3aZVRd07vvvsupU6dwdHTE19eX8PDwase3evVqpk2bhpeXFwMHDsTf358bN26wdu1apk6dyp9//smaNWvKrC9o3749o0ePLvV4mzZtqh1Hg3bxL3lPLCdvua+NkaITszgTn4ZGrWJkW28TBlhL/LvLt3FH5VoYdQ33F6uHege5E+Bmz5WkbDacTDDv2qbECHlEQG0l1w1Vw9oTceQV6mnl5UQHU3UAr4i1PQQPlUeazm+Aph1q/5pC1UXthJUPQ0E2BPaBh1eCTSX95tRqGPSW3MR0w3QI3yRP1z2+sUaj94JxjE6aZsyYgb+/PytXrqRHjx7FjwcHB3Pw4EH+9a9/sXjxYsLCwkhMTKzWuT/55BN8fX0JCgpi165dDBgwoNrxtWzZkvXr13Pfffeh0dz+pfX+++/TtWtX1q5dy2+//ca4caW3QggLC2PevHnVvqZwF8PUXPuJNUocDAXgvYLccXO0MUVktcvzHrBxhrx0uW7Bu53SEZkdtVrFpG4BvPfnBVYcvMLELn7m13fL4NJf8m1gb7mmqYp0eonv98cAcpuBOnt994y6nTQNmlty9EJQzuWtsOpR0OXJdXETVshJblW1ewgaBcKqR+DGGfj9RXjoB/H/W8eMnp4bNWoUJ06cKJEwGVhbW/PZZ5+xdu1aJCPm1QcMGEBwcHCNfsgMHDiQUaNGlUiYALy8vHjuuecAeasXoZakX4OIf+T7YcZPzUmSxMZTciPEUZYwNQdygujbWb4fK/qUlWdcJ1+stWrOJaRzMjZV6XDKd7Eoaarm1NzW8ze4kpSNi50VYzvV4aKY4KGgtYXkKHkRhqC81FhY86ScMLW6Tx5hqk7CZODXFR5dLW/jc2GjXCQu1Cmjk6Z169bRqFHF/UZGjx7NyZMnjb1ErbG2lgs5razKLspMSEhg6dKlvP/++yxdupTTp0WH3Wo79TNIevDrBu5BRp/m/LV0Im9lYaNVM7S1me01VxG/oim6qweVjcOMNXKw5r528nTrjwevKBxNObKT5SXhAC2HV+vQZXuiAHmUyd7a6EH96rNxhKDB8v3zG+ruukLZJAk2TpdHnn27wvjvQVuDEfOmHWDgm/L9v16BpEiThClUTa0vcfPz86vtS1RLYWFhcTPO4cPL/iG4detWnnvuOd544w2ee+452rdvz4ABA7h6tWorfdLT00t8VLbdTL2j18HR7+X7HR+r0anWHIsDYGArT5xsa3nlkSn5d5NvxUhThSYXFYRvOn2NlKx8haMpw+UtcvLfpA00CqjyYSeupnD0SgpWGhWP9wysvfjK03qMfCtW0Snv6DdyLZPWDkZ/ARoT/BzrOVOuiSrIgt+eAp2Fdde3YA2uL8Crr77K2bNnGTFiBMOGDSvxOXt7e9566y2OHTtGSkoKKSkpxTVVO3fuZNCgQWRlZVV6DT8/P1xcXIo/Pvjgg9p6OeYp4h9Iuwq2rvKeWEbKzi8sTpomdDGv5LtSPp1BpYG0WEizwH3W6kiYnyutmzqTX6gv/r82K4ZWA9Wcmlu2JxqAB9r70MRZgQanwUNBYwNJEXDzQt1fX5AlR8GWt+T7g+fVaNS9BLVGbk1g6ypv77Ozgf2OUVCDSpoWLlzIRx99REhICD/88EOpz3t6evLOO+/QsWNHXF1dcXV1pW/fvmzZsoVu3boRERHBsmXLKr1ObGwsaWlpxR+vvfZabbwc83Wk6GvUYZLccM9Iv59KICO3EP/G9vQN9jBRcHXExhG8ilZbxoopuvKoVKri9gMrDl1BrzejUZHCPIjYJt+vRtIUm5zNX0VbxEzt06w2IqucrfPtlX6i0aUy9DpY/8LtlXJdnzHt+V184f5F8v09H0PMXtOeXyhTg0maFi1axOzZswkNDWXnzp24u7tX+VitVsvUqVMB2L17d6XPd3Z2LvFhY2MBK75MJTlaXiUCcuv/GlhxsGjriW7+qNUWuEKkuK5JTNFVZFRYU5xstFxJymb35VtKh3NbzB65S7OjF3hXfen+t/ui0UvQJ9idUG/nWgywEsWNLkVdkyIOfgFX98vNK0d9LrcOMLXWo4t64EmwcaaYpqsDDSJpWrBgAbNmzaJNmzbs3LkTLy+vap/D01PuYFyV6bkG7dh3gCT3ZXJrYfRpTsWmciY+DWuNmvF1ufLIlIrrmsRIU0XsrbU8VDT9umSHGRW1XjQ0tBxe5V94aTkF/HokFoCpfZrXVmRVEzJC7i11KxwSLysbS0OTFAnb3pHvD31XbhVQW4Z/CPbukBx5u82LUGvqfdL0wQcfMGfOHMLCwtixY0dx8lNdhw7JowXNmyv8g9CcFeTeXgLbZWqNTrWiaDXVyLZeltGbqSyGkabrZ0UH30o83ac51ho1h2OSORRlBru7S9IdrQZGVvmwVYevkpWvI6SJE32Dqz6aXStsXaBZH/l++B/KxtLQbJ8vtxdoPgA6Tanda9k4QZ9/yfd3/h8U5NTu9Ro4i0+aCgoKCA8PJzKy9F+o8+fP5/XXX6dTp05s27at0im5Q4cOkZ9fegXPrl27+PjjjwGqvZ1Lg3J+A2QngbOvvEeXkdKyC/j9tNzQ0lDvYpFcfMDFDySd2Ly3El4utozvLI8ofrY9QuFokPsbpcfJK56a9a3SIfmF+uJmlk/1aWYezToNCZ+hoF2ofQkn4dw6QAXD3qub5pOdn5R/7mYk3K4pFWpFHTYPqbr169ezfv16AK5fvw7AgQMHmDJlCgDu7u4sWLAAgPj4eEJDQwkICCAmJqb4HMuXL+ftt99Go9HQp08fPv3001LXCQwMLD4nwCuvvMK5c+fo379/8dYvZ86cYds2uRh0/vz59OzZ08Svth4xfLN2ngIa499aa47HkVsgbz3RKaDiXmBmz6+bvIIu9hA076d0NGbtuX4t+OVILHsjEjl+NYWO/gr+3xtGmVoMrPJihl+OXOVaWi6eTjaMCjOTRqwhI+HPf0PsYci8CY7GjbQL1bD9Xfm27Xho0rpurmllC/1flftB7fkYOj4uLwYQTM4sk6aTJ08W91IyiIqKIipKbhYXEBBQnDSVJzpaXvKr0+lYuHBhmc/p169fiaRp8uTJrFu3jiNHjvDXX39RUFBAkyZNeOihh5g+fTp9+vQx/kXVd9dOQ9xhuYaig/G9mSRJ4qeiqblHuweYx1/rNeHXDc6uEU0uq8CvsT1jOviw+lgci7dH8M2ULsoFc3mLfNuyaiOmOfk6Pi0aIZsxMAgbrZnsN+jiA95h8ua9lzbXuG+aUIkr+yFiq9yxe0Adr5pu/zDs/1TeJ/HA5zDg9bq9fgNhltNz8+bNQ5Kkcj/uHFEKDAws9VhVziFJUqltVJ566ik2bdpETEwMmZmZ5OXlcfXqVX755ReRMFXm6Dfybej94GR85+79kUlEJWbhYK1hTAcfEwWnIEMxeNwReQmyUKHnBwShVsG28JucjU9TJojsZEg4Lt83dNauxPf7Y7iVkYdvIzsmdDGzzYdb3SvfhospulolSbeLvzs+Bo3ruP5Vo4UBb8j3DyyGrOrt+SpUjVkmTYKFyU6G07/K901UAD6mow+ONmY5EFo9nq3lJcd56aLJYBU0c3fg/qI9BhfvUKi2KWqn3AXcI1QeqalEWk4BX+6SaypnD26JtdbMfqwa6pqidkC+WP1bayL+kbfc0dpC3znKxHDPKHlkMT8T9nykTAz1nJl9dwsW6fDXcgM3r3YQYHzNV0xiFlvO3wDg0W4WXAB+J432js17xRRdVbwwQO6a/NfZ61y6kVH3ARgaWhqaQ1Zi2Z4o0nIKCPZ0ZLQ5jo42aQ2u/lCYC5E7lI6mftLrb48ydX0GnBWqaVOpYNDb8v0jyyDNDLvsWziRNAk1k58Fh76U7/eeVaOVIp/viECnl+gf4qFsU0BTE00uq6VlEyeGt5Z7qdX5SjpJgsiqJ02JmXl8s1eun/zX0BA05tiEVaWCkKIpOrGKrnacXw/XT4O1E/SerWwsLQZCQG/Q5cOhpcrGUg+JpEmomeM/Qk4yNGoGoaOMPs2VpCzWnZD3aHtxULCpojMPoslltU0fKI82/X4qgWNXUuruwjcvQMY1udWAf+Wjpot3RJCdr6O9rwvDWhtfy1frWhVN0V3aLGrrTE2vh50fyvd7zgD7xsrGo1LJcQAcXy56xJmYSJoE4+kKYP9n8v1eM2vUZmBx0ShT35YedFByqXlt8O0CKjWkXoX0a0pHYxHa+LgUd4J/e8NZdHW1J13EP/JtYC95GXcF4lNz+Kloq585w1qZ90pP/57y5q7ZSXL7C8F0IrZC4kWwcYbu05SORhY8VC5Ez02DUyuVjqZeEUmTYLwza+QGgA6e0P4Ro08Tm5zN2uP1dJQJ5I69hn4t4hdWlb0yohXOtlrOJaTz86ErdXPR4qm5ylfN/XdzOPk6PT2au9EryK2WA6shjfZ2+wTRHdy0DH84djKj3khqNXR7Tr5/aKk8GiaYhEiaBOPo9bBvoXy/x/OV/lVekSU7IyjUS/QJdrf8ZpblMdQ1xR5WNg4L4u5ow7+GhgDwv78vkpSZV7sXzM+GKwfk+y0qrmfaHn6DDScTUKvgtZFmPspkEDJCvr34p1y7JdTctVPyxs5q7e0kxVyEPSKPfiVdvv3HgFBjImkSjHNps7wRqI2z3MLfSHEp2aw+Kq/wqJejTAZ+hromMdJUHY928+ceb2fScwv57+aLtXuxK/vk/cJc/MC9/PdiRm4Bb6w7C8ib8rbzda3duEwlaDBorCE5Cm7V8teyodj/uXzbegy4mNnG4jZO0GGyfP/gF8rGUo+IpEmoPkmCvfJefHR+Ut4Y1EhLdkZSqJfoFeRG50CFCyhrk19X+fbaKbGhZjVoNWrmj5anNn85Gsvxq7VYFG6oZwoaVOEq0P/bHM61tFwC3OyZPbhl7cVjajZOt/fRuyim6GosLR7OrZXv95iubCzl6faMXE8ZuU0kyiYikiah+q7slztca2xqVPgYn5rD6qOxALw4yIJ++RjD1R8cvUBfAAknlI7GonQKaMzYjnVQFG7oz1TB1NyhqCRWFBV/f/BgW+yszWS7lKoq3sB3s7Jx1AeHl4K+EAL7QNMwpaMpW6PA2//nhtYwQo2IpEmonju3Cgh7BJy8jD7VfzeHU6CT6NHcja7N6vEoE8gjF4bWA2Ifump7dUQrnGy1nI1PZ+nuSNNfIPWqXPuh0pS7sXJugY5X154B4OGu/vRs4W76OGqboa4p7oi8ga9gnLwMOPq9fL/HC4qGUinDH7YnV8q7Nwg1IpImoXou/C73G9LaQb+XjT7NvohENpxMQFVUSNsgFNc1iWLw6vJwsuGNkaEALPj7IvsiTLyvlmGUya9rudPNC/+5THRiFk2cbSz3PevcFJp2ACS5LlEwzokVkJcGbsEQXLVNnRUT0AuatIXCHDj+g9LRWDyRNAlVV5gP/8yV7/ecYfRWAXmFOt5aLxfSTu4eYDmFtDV1ZzG4WL1UbRO6+DGuky96CWasPEF8qglrwwz1TOVMze24eJOvika43hvdFmdbK9Ndu64VT9H9pWwclkpXCAeXyPd7PC8v7zdnKtXt0aYj34j2AzVk5v/bglk5+q288sbBU25maaSvdkURlZhVYkl5g+DVTt7MMycZkhTajNaCqVQq3h3dhtZNnUnOyuf5FcfIKzRBd2tdAUTvlu8HDSz16bPxabzw03H0Ekzo7Mfge8y483dVGKboInfIbRaE6rn4hzyda+8G7R9WOpqqafMg2LhA2lWI3ql0NBZNJE1C1eSkwq6irQIGvC6vxDHC1aRsPi/avf6t+0JxsbPgv9irS2sNTTvK90XrAaPYWmn4clInXOysOBWXxn9+P1/zk8Yfh7x0sGss7xB/h2tpOTy1/AjZ+Tp6Bbkxf3Sbml9PaU3ayG0VCnMgepfS0VieI8vk205TwMpO0VCqzMoO2j0k3z/+o7KxWDiRNAlVs+cjyEkBj1a3e39UkyRJvL3xLHmFenoFufFAe4V2AleSofWASJqM5tfYnkUTw1Cp4OdDV/nlyNWanTBqh3zbvB+ob6+Gy8gt4InvjnAjPY9gT0eWPNoJa209+JGpUpVsdClUXeJleVRSpYZOTygdTfV0LPq5Hb5JFITXQD34CSDUupQrt5erDplv9B5zm89eZ+fFW1hr1Lwzqo1ldFE2NUNd01WRNNVE/xDP4h5Jr649w/L9McafLGqnfNu8f/FDBTo9L/x8gvDrGXg42fDdE13q16jona0HRI1L1R39Vr4NHgaufsrGUl3e7eUPXT6c/kXpaCyWSJqEym37j/yN1qwfBA8x6hSJmXnM+/0cAM/2a04LD0dTRmg5DElT4kXx114NTR8QxMNd/ZEkmLvxHO/9cR59dXs45WXIy+8Bmg8AIDU7n+d+PMbuS7ews9LwzeOd8W1kb+LoFRbQS+7mn3UTEo4rHY1lyM+Gkz/J97s8pWwsxjLMEhz/QSxGMZJImoSKXfobzv4GqGDo/Ao7JZenUKdn5soT3EjPo4WHAy8MCDJ9nJbCwQ3cil5/3FFlY7FwarWK98e0Yc4weTHB13uimbHyBLkF1SgOv7JfblDYqBk0CuDE1RTu/XQv28JvYq1R89nDHern6k6t9e1NicUUXdWcWwu5aeAaUOnehGar7Xh5McrN83Itn1BtImkSypeVBBuKtgfo/rw8tGuEj7ZeYn9kEvbWGpZO7oStlYV1UTa14tYDosllTalUKl4YEMTCCWFYaVT8ceYak5YdIvJWZtVOUDQ1JzXvzzd7o3lo6QHiU3MIcLNn7fM9LX+lXEVE64HqOfKNfNv5CfNvM1AeO1e4Z5R8/4To2WQMC/2fF2qdJMGmWfLwvUcrGPS2Uaf5+9x1vtgp97f577h2BHkat+quXhFNLk1udAcflj/ZFSdbLUevpDD4411MW3GM03GpFR6nj9wOwOIrvszfdJ4CncTItl78PqM3bXyM31PRIgQPljug3zwPydFKR2PeEk7I05gaa6MXwpgNQ/xnfoP8LGVjsUDGVfQK9d/pX+DCRlBr4cGvwMq22qeITszi37+eAuDJXs24r10DXC1XFkPSFH9M7hGkqUcFxgrq2cKddc/34v82h7P1/A3+Onudv85ep3eQO8PaeOFiZ4WzrRZnOyuy8grZfewMb9wKRy+pWBbni7VGzRv3hvJYj4CGsUjBrhEE9ISYPfJoU4/nlY7IfBlGme4ZBQ4WuH3OnQJ7y9PRKdFwbj10eFTpiCyKSJqE0lJj4c858v3+rxo1LZedX8hzPx4jI6+QLoGNLHfbidrg3lLeqiM3Da6fAZ+OSkdUbwR5OvL1Y525dCODL3dGsuFUAnsjEtlbxrYro9V7wRrC1c0Z06stD3f1p2WTBjYSGjKyKGn6UyRN5clJhTNr5PudLbQA/E4qldx+YNs7cOJHkTRVk5ieE0rS62H9NLnZn28X6DW72qfIydfxzA/HuHgjA3dHGxY/0hErjXirFVOrwdfQr0lM0dWGlk2c+HhCGLvm9OfZfs0Z1roJPZq70bqpM36N7WjqYsvkJlEAtOr5AHPvb93wEia43a/pyn6xmrM8p1bJjUA97wH/7kpHYxrtH5F7TV09ALcuKR2NRREjTUJJexbIf3la2cOYpdXuyZSdX8hT3x/lQJSh8Lsjns7Vn9qr9/y7QcRWuRi8+3NKR1Nv+Tay57URoaU/IUnwsbzIQd2if90GZU4aNwPP1nDznLxSNsxCtgWpK5J0uzdT5yeNWj1slpy9IXiovGnzqZUweK7SEVkM8ee/cNux72HHe/L94R+AW4tqHZ6VV8iU745wICoJB2sNPzzZlU4BjU0fZ31wZ5NL0S+l7iVehowEefm1Xz0ZPTBW6H3ybfgmZeMwR1cPyj3VrOyh3QSlozGt9hPl29O/igan1SCSJkF2fiNsKpqK6/NveV+lasjMK+Txbw9zODoZJxstP07tRudAkTCVy6eTXGSfkQBpsUpH0/AYtk7x727UIod6pVVR0hSxTWzge7fjy+XbNmPB1lnZWEyt5Qh5E9/0OLiyV+loLIZImgSI3gO/PQWSHjo+DgPfrNbhscnZPPL1QY5eScHZVsuKqd3o6N+oloKtJ6wdbhfYXxX9mupcGVunNFhebcHVX67bKWrBICDvtXlunXy/mn9EWgQrW2g9Wr5/apWioVgSkTQ1dNdOwcqH5W1SWt0H935crXn7TacTGPnpHk7HpeFiZ8VPU7vT3s+19uKtT/x7yLdXDygbR0OjK5T/UIDirVMaNJXq9miTmKK77fRqKMyFJm3kkeH6qH1RDdv5DWKUsYpE0tSQRWyDH0ZDfgYE9Iax31S58Ds7v5BXfzvN9J9PkJFbSAd/VzbN6E1b33reENCUDCtxxEhT3Uo4Lr/n7RqBVzulozEPhqTp4l9y77CGTpLkGk+QR9/rSwH43fy7y9vC5GdC+B9KR2MRRNLUEOl1sPNDWDEWcpKhaUd4+Ocq13YciEzi/s/2supILCqVvHHqr8/2wK9xPdvUtLYZisFvXpCnAoS6YZiaa9bPcrfDMDX/7mDvDrmpcGWf0tEoL/6YvKJQawvtHlI6mtqjUt0uCD+1UtlYLIRZ/sRYs2YNM2bMoE+fPjg7O6NSqZg0aZJR54qLi+PJJ5+kadOm2NjYEBgYyKxZs0hJKf+X1P79+xk5ciSNGzfG3t6edu3asXDhQnS6amwEaq6ykuCncbDzA0CS5+qf+EtutliJY1dSeOTrgzz89UEib2Xh6WTDT09149/DQkQfJmM4ekLjFoAEsUeUjqbhKK5n6qdoGGZFrbnds+mCmKLj2Hfybesx8n5t9ZlhVWDUDsi4rmwsFsAsf9O9++67fP7555w8eRIfHx+jzxMZGUmnTp347rvv6Nq1K7Nnz6Z58+YsWrSIHj16kJSUVOqYDRs20LdvX3bv3s2YMWN44YUXyM/PZ/bs2UycOLEmL0tZer08b720r1zsqbWD0V/C/YsqHGGSJIljV5J54rvDjP1iP/sjk7DSqHi8RwCbZ/WlZ5CFbymgNFHXVLfys243FBVF4CWF3i/fhv/RsJeg56bD2bXy/Y6PKxtLXXBrITfblfRwZrXS0Zg9s2xu+cknn+Dr60tQUBC7du1iwADjijWff/55bt68yaeffsqMGTOKH3/ppZf45JNPeOONN/jyyy+LH09PT2fq1KloNBp27txJ586dAZg/fz4DBw5kzZo1rFq1yrKSJ10hnFsLez6CW+HyY41bwIQfoUnrMg+RJImLNzLYeDKB308nEJucA4BGrWJ8J1+mDwzCt5GYijMJ/+5wcoWoa6orVw6AvkBeLdaomdLRmJdm/cDaUW6DkXACfOtp8XNlzqyGgmxwD6k/HcAr034ixB2WV9H1nFH58xswsxxpGjBgAMHBwTXaNDMyMpItW7bQrFkzXnjhhRKf+89//oODgwM//PADmZmZxY+vXr2axMREHn744eKECcDW1pZ3330XgCVLlhgdU52RJLlO5sAS+LwTrH1aTphsXKDvHHhmZ4mESa+XiLiZyW/H4nhr/VmGfLKb4Qv3sGRnJLHJOdhZaRjb0ZdtL/Xjw7HtRMJkSoaRpoTjUJinbCwNgaE/U/P+9be411hWthA8RL4f/ruysSjJ0JupUz0uAL9b6zGgsYYbZ+X9MIVymeVIkyns2CH/cBw6dCjqu4o9nZyc6NWrF1u2bOHQoUMMGjSoxDHDhw8vdb6+fftib2/PgQMHyMvLw8bGppZfQRXodZCdJM9DZ96Ud62O2St/ZN/eoFRv50ZKu6kktJxEss6OhNOpxKdcIz41h/iUHMKvp5OeW1ji1NZaNQNCPLi/fVMGtvLE3rrevlWU5dZCLsDNTpTbP/h1VTqi+i16l3zbTNQzlanVfXJvogubYPA8paOpewkn5O9DjfXt5fgNgX1jaDkMLvwujzZ5tVU6IrNVb38TXrx4EYDg4OAyPx8cHMyWLVu4dOlScdJU0TFarZZmzZpx7tw5oqKiCA0tYz+rIunp6SX+bWNjU6Mk6+CyWQTG/Y4GPWr0aNChRo8DOWgou/YgR7LmqBTCP7qO/Jrbj5xdtrCr/L8gbLRq2vq4EObnSgf/RvRp6Y6zrZXRMQtVpFLJUwDhm+S6JpE01Z6sxNt/RYukqWzBQ+WEIeky3LoIHiFKR1S3DG0GQh+QE4mGpP3DctJ0ZjUMeUdeHCCUUm+TprS0NABcXMpeFWZ4PDU1tUbHlMXPz6/Ev+fOncu8efMqC7lcqtw0vEgs83N6SUUSztySXLkhuXJcH8wB/T2ckoIoKPrvVanAyUaLs60VTrZavF1s8Wlkh4+rPT6N7Gju7kCIl5NYAaeU4qTpIPR6Uelo6i/DKFOTNuDooWws5srWWU4oI7bChY3gMUfpiOpOXgacWSPf7/yEsrEoIWiI3Lss84a8wjRokNIRmaV6mzRVRiraJLU6dVNVPSY2NhZn59v7FNV0Ks///le5lDQFVBoktQZJpQGVBr21Izo7d1QaLSoVNEHFKK2KcRo1Vho1Wo0KOysNDtZa1OoGMjdviYpX0B2U69EaSh1FXYsqSprEqrmK3fOAnDSd2yDXQDYUZ9bITR7dgiGgl9LR1D2tNbR+EI5+I2/iK5KmMtXbpMkwKmQYPbqbYQrtzlElY44pi7Ozc4mkqaa8A0LwDmhgw+QNiVc7uQVETjIkXgaPlkpHVD/d2dRSKF+r++TNu2+caVhTdIbeTJ2mNNw/XNpNkJOmC79D/sfyHplCCfV2PiYkRP5Gv3TpUpmfv3z5MgAtW7as0jGFhYVER0ej1Wpp3ry5qcMVGjKt9e29rUS/ptqRHA2pV0CthYCeSkdj3uwbQ4uiUQZDv6L6Lv54wywAv5tfV2gUCAVZYluVctTbpMnQ22nLli3o72rUlpGRwb59+7Czs6N799t9OAYOHAjA5s2bS51v9+7dZGdn07NnT/NYOSfUL2IfutplqGfy7QI2jsrGYgnajJVvz62Vp4zrO0MB+D2jwMFN0VAUpVLd7hB++hdlYzFTFp80FRQUEB4eTmRkZInHW7RowdChQ4mJiWHx4sUlPjd37lyysrJ47LHHcHC4Pfw4btw43N3dWbVqFUePHi1+PDc3lzfffBOAadOm1eKrERosQ11TrEiaaoWoZ6qekBHyvmuJl+TePfVZbvrtAvBODbAA/G6GpClyu9zKRijBLGua1q9fz/r16wG4fl3eC+fAgQNMmTIFAHd3dxYsWABAfHw8oaGhBAQEEBMTU+I8S5YsoWfPnsycOZNt27YRGhrKoUOH2LFjBy1btuS9994r8XxnZ2e+/vprxo0bR//+/Zk4cSKNGzdm48aNXLx4kXHjxjFhwoRafe1CA+XXBVBBchRk3ACnJkpHVH/o9aI/U3XZOsuNLi/8Dmd/q999e86ukaej3FuKqVuQe8f5dIb4o/L/fXcxUHAnsxxpOnnyJMuXL2f58uX8/fffAERFRRU/tmbNmiqdp0WLFhw9epQpU6Zw6NAhPvroIyIjI5k5cyYHDhzAza30MOzo0aPZtWsXffv25bfffuOzzz7DysqKjz/+mFWrVtWoS7kglMvWRV4KD3B1v7Kx1Dc3z8lNYK0dwbdz5c8XZIYpurO/1d8pOkmCo6IAvBTDaNOpVcrGYYZUklRfvxvqXnp6Oi4uLqSlpZl09ZzQQPz5MhxeCl2ehnsXKB1N/bH/M9jypty48VGxIWmV5WfD/4LkUZip2+vnXnTxx+DrgaCxgX+FN7yGluXJSoSPQkBfCC8cbhArKKv6+9ssR5oEoUEK7C3fXtmnbBz1jahnMo61vVzbBPJoU310ZwG4SJhuc3CHoMHy/dO/KhuLmRFJkyCYC0NDvZvnIStJ2Vjqi8L820moqGeqvjtX0enL3rLJYuWk3FEAPkXRUMxSu4fk29O/1r//+xoQSZMgmAsHN/Ao2tNQjDaZRtwRKMiWN0X2vEfpaCxP0CCwcYGMa/Wvh9iJn+T3huc9ogC8LCEjwdoJ0q7Wv//7GhBJkyCYk8Ci0SaRNJlG5Hb5tsUAUIsfd9WmtYHQ++T75+pRo0u9Do58Ld/v+owoAC+LlZ08bQlwaqWysZgR8VNEEMyJoa4pZq+ycdQXUTvk2+YDlI3DkrV5UL49tx50hYqGYjKXt0JKjLxq1TANJZQWVtQd/dx6eWGAIJImQTArhrqmG+cgO1nZWCxdTgoknJDvtxBJk9Ga9ZOnN7MT5Y1864PDX8m3HSaL/dUq4t8TXP0hPwMu/ql0NGZBJE2CYE4cPeUme0iijqCmoneDpAf3EHBuqnQ0lktjBe0nyveP/6BsLKaQeBkitwEq6DJV6WjMm1p9ey++kz8rG4uZEEmTIJgbw2hTjKhrqpHIoqk5McpUcx0fk28v/Q0Z15WNpaYOF9UytRwGjZspG4slMCTMUTsg/ZqysZgBkTQJgrkprmvao2wclk7UM5mORwj4dQNJZ9kjDnkZt+Pv+oyysViKxs3Br7s8ais28RVJkyCYHcNI0/UzkJOqaCgWKzlKLvRVa2+vSBRqxjDadOJHy91W5eRKuT7HLVgk09VhKAg/tdJy/+9NRCRNgmBunL2hcQvkuqaDSkdjmQxTc75dwcZJ2Vjqi3tGy/v3JUdZZksMSbpdAN71GdGCojpajwGtLdwKv724ooES7xpBMEeG0RExRWccw9Rci4HKxlGf2Dje7hBuiQXhkdsh6bKc+BnqdISqsXWBVvfK9xt4zyaRNAmCOQoQ+9AZTa+TV86BKAI3NcMU3fkNljd1vG+hfNthEtiKDdWrrf0j8u2ZNfL2RA2USJoEwRwZRpqunYLcdGVjsTQJJyA3Tf7ruGkHpaOpX3w6yduOFObCmdVKR1N1ccfkRFqthR7TlY7GMjXvD45ekJMMl7coHY1iRNIkCObIxRcaBcorVmIPKR2NZTHUMzXrC2qNsrHUNyqV3BAS5IJwS7H3Y/m27UPg6qdsLJZKo4V24+X7lryCsoZE0iQI5ipAtB4wimg1ULvaTQCNtTwKeu2U0tFU7mY4hG8CVNB7ltLRWLawR+Xby39Dxg1lY1GISJoEwVwZ+jVFi6SpyvIybo/MiXqm2uHgdrso+Oi3ysZSFYZaplb3yv2mBON5hsorUvWFcPInpaNRhEiaBMFcNesr3147Ke+jJlQuZp/8A901QG7KJ9SOLk/LtydXmveIQ+rV27VXvV9SNpb6otPj8u3xH0CvVzYWBYikSRDMlYuPvA+dpL+9GkyoWJTYOqVOBPQE3y6gy4NDXyodTfn2fyYn0c36gm8npaOpH1qPARtnSImGmIb3c0kkTYJgzgx1OVE7FQ3DYkT8I9+K/ky1S6WCXrPk+0e+Mc8Vnpm3bveTEqNMpmPtAG2LCsKPLVc2FgWIpEkQzJlhxMSwIkwoX3I0JEXIy8qb91c6mvovZKQ8EpqXBse+Uzqa0g59IbdGaNpBvB9MzTBFd+F3yEpUNpY6JpImQTBnAb1ApZGHwlNilI7GvBlGmfy6yT2ahNqlVkOvF+X7B5ZAYZ6y8dwp8xYcKtoypfdL8siYYDre7eVkVF/Q4DqEi6RJEMyZrbNcOwJiiq4yl7fKt0GDlY2jIWn7EDg1hczrcGqV0tHctvMDeWNe7/bQ6j6lo6mfOhaNNh1b3qA28RVJkyCYOzFFV7mC3Nv9rIKHKBtLQ6K1hh7Py/f3fypvYaO0Wxfh2Pfy/aHviY15a0vbcWDlIO/nd2W/0tHUGfFuEgRzZygGj95lHr+UzNHV/VCQDU7e0KSN0tE0LJ2myNOhSREQ/ofS0cCWt0DSyTVXzfooHU39ZeMEbQ0bODecgnCRNAmCufPpCNZOcq+m66eVjsY8XS6qZwoaJOpX6pqN0+2+TXs/UXaqJmqn3K1arYUh7ygXR0PRcYp8e249ZCcrGUmdEUmTIJg7jdXtv5jFFF3ZIgz1TGJqThHdngOtLSQch/PrlYlBr4O/35Tvd34S3IOViaMh+f/27jw+qur+//hrspCdhLDvSSABFCFfQNmjAQ0QrEDBChUQwRbQoona1ooWUAr2p6zfilCxKlq1gmUREKISQJIQkPJFQBaJRoMCEQwJhCyE3N8fl0ADAQaczJ2ZvJ+Pxzzmeu/Mve+MDzKfnHPuOU07QcNbzPm6asgM4SqaRNzBhfmaVDRdJu9bOH7QvMtQt5ZbI7j+xTvp1k+GktPOz7DrPTi2G/xC4fannH/9mshmg9vOtzJmLoJzZdbmcQIVTSLuoKIY+G4rlJ6xNIrLqWhlat4VAsIsjVKj9UqGsBZQ8D1sftG51y4thA3Pm9txT5jr44lzdPgVBNaF/BzY/6HVaaqdiiYRd1AvGmo3hXOl8F2G1WlcS8V4pmhNNWAp3wAY8P/M7Yy/mXexOcuG6XDqiFm03TbeedcV8/97l3HmdsYCa7M4gYomEXdgs6mLriplJRfX5dN4Juu1GQAx/c313tb+3jmDwr/6BLae/7JOfAl8/av/mlLZrQ+Bdy04vA1ytludplq5bNF0+PBhxo4dS5MmTfDz8yMiIoKkpCTy8uxb7f2NN97AZrNd9eHt7V3pPdnZ2Vd9/fDhw6vjRxWxz4X5mjZaGsOlfJsOZwshuCE0usXqNALQ/wXw9jOnyNi7vHqvdToXVkwwt2/7LcT0q97rSdVCGl5cj27ry9ZmqWY+VgeoSlZWFj169CA3N5dBgwbRtm1btm3bxrx581i3bh1paWnUrXv1PuvY2FimTJlS5bHPPvuMDRs2MGDAgCqPd+zYkcGDB1+2v317zf8iFoq83Xw+tttcJiK4vrV5XEHF0imt79RUA64iPBJ6P27Oyr1+MkQngF+w469jGLDiYSj8ERrcpCkGrNZtonkH3Zer4GQOhDW3OlG1cMmi6eGHHyY3N5f58+czadKkC/sff/xx5syZw+TJk1m4cOFVzxEbG0tsbGyVx7p37w7Ab3/72yu+d+rUqTeUXaTaBNc3W1OO7oasT6GjWj61dIqL6vmYuSZZXjas/xP8Yr7ji9rMReZNAN5+MPQ1c2yNWKfRLRAZZ3aXb1sECdOtTlQtXK57Lisri5SUFCIjI3nkkUcqHZs2bRpBQUEsWbKE06dv7JbWPXv2sHXrVpo2bcrAgQMdEVnEeaLPdz8cXGdtDldw8js4fgBsXhe7LsU1+AbAwNmADf6zBNLmOvb8R/fAx382txOmQ8ObHHt+uTHdzn9n71hizbQTTuByRVNqqjnINSEhAa9L1gwKCQmhZ8+eFBUVkZmZeUPnX7RoEQDjxo27bExThR9++IFFixYxY8YMFi1axBdfaBZmcREx/c3nQ59CWam1Wax24CPzuXk3CKhjbRa5XOu+5vgmgE+mwu5ljjlv/vfw/mhzQsXofhfnCRLrRSdA3dZQku+xk126XNF04IB5m2p0dNWzuVbsP3jw4HWfu6ioiLfffhsvLy8eeuihK77u448/ZsKECUyePJkJEybQsWNH4uPj+e677677miIO1bQzBNWHkgJzvbWabP9q87mtWoxdVrcJ0O38gr4rJv78hV1PZME/+sNPWRDaHAa9rLFsrsTLy5wdHsxpJzzwDzuXK5ry8/MBCA0NrfJ4xf6TJ09e97nff/99Tp48yYABA2je/PJBaoGBgTz77LPs2LGDvLw88vLy2LRpE/Hx8WzcuJG+fftSWFh4zesUFBRUepSUlFx3VpEqeXn9VxfdemuzWKkoD7LTzO22idZmkatLmA5t7zbnGHt3BBz/6sbOc+xLeH0A5H8H4a3gwY90M4Qrir0fghqY3ec737I6jcO5XNF0Lcb5eT9sN/DXxd///ncAxo+vevKzBg0a8Nxzz9GpUyfCwsIICwsjLi6OlJQUunbtyqFDh1i8ePE1r9O8eXNCQ0MvPGbOnHndWUWuqOK26gMfWbs4qpW++thcyb5+OwiPsjqNXI2XN/zyVWh2KxSfhCWDIWvD9Z3j8A54IxFOH4OG7WHsOo+9O8vt1QqEuCfN7c0vwtkia/M4mMsVTRUtSRUtTpcqKCio9Dp7ffnll6Snp9OsWTMSE6/vL1MfH58L3XmbN2++5utzcnLIz8+/8PjTn/50XdcTuapWfcyJ5PK+Mddcq4nUNedeagXCiPfMFqKCw/DWEFj6IBQcufr7zvwEn82CJfeYrYvNboUxqyG4gXNyy43pPAZqNzNnaf/8H1ancSiXK5ratGkDXHnM0ldfmU27MTEx13VeewaAX02DBuY/Unu652rXrl3p4efnd93XE7kiv2CI6G1u18S76MpKzIHwoK45dxJUD367EbpONO943Ptv+NutsPUV+OkbKC642HJ6IgvWPAFzboZPn4PS0+Y8ZaNWaNC/O/Dxg9v/YG5/Ntuj7qRzuXma4uPNW4dTUlIoLy+vdAfdqVOnSEtLIyAggG7dutl9zuLiYt566y28vLwYN27cDeWquFsvKkpdAeICYvqbczUdWHdxdfma4pvN5pdoSGNo/D9Wp5Hr4V8bBrwAsSNg9ePw/eew7inzAeDlaxZFhT8C5wuoRrdA999B+6Hg7WtZdLlOsb82p5r46WvIXHixy87NuVxLU6tWrUhISCA7O5uXX648HfuUKVMoLCxk9OjRBAUFAXD27Fn2799PVlbWFc+5dOlS8vLySExMrHIAeIXMzExKSy8f7b9p0yZmz54NwMiRI2/kxxJxrDbnpx7I2Wp2YdQkFV1zbRLNgfHifhp3hHEfw91zzS4730Bzf/lZKMwFDPOGhwc+hPGfmRO5qmByL96+cMfT5nb6fCg6aWkcR7EZhuuNJL10GZV27dqRmZlJamoqMTExpKenX1hGJTs7m8jISFq2bEl2dnaV5+vduzdbtmxh1apV/OIXv7jide+44w727t3LHXfcQbNmzQDYvXs3n35qdgU8//zzPPPMM1d8f0FBAaGhoeTn51O7du0b/OlF7LSgB+TuNQfZdviV1Wmco7wcZrc1BwSP/EAzgXuSs0XmHwBnTkBAGIS1sDqR/Fzl5+CVnvDjPoj7PfS58ven1ez9/nbJP9NatWrF559/zpgxY8jMzGTWrFlkZWXx6KOPkpGRcc115/7bvn372LJli10DwEeNGkXXrl3Zvn07r776KgsWLODgwYP86le/YvPmzVctmESc7r/voqspvt9hFky1Qi6O6xLP4BsAoU2hcQcVTJ7Cyxv6TDa3t75irpnp5lyypcldqaVJnCpnG7x2F/iFwh+yakb3xSdTYcscuPmXcO/rVqcRkWsxDHg1Hn7YCR1HwJCrrxtrFbduaRIROzTtDIH1zCULvsuwOo1z7F9rPmuqARH3YLPBgBcBm7mIc8Ui225KRZOIu/LyNtd6AvMuOk93/JC5QK+Xj8YyibiT5rdeXE7nwyQoOWVpnJ9DRZOIO2szwHze/6Hnzw5+YI35HNHbHCgsIu6jz2QIa2lObvrJVKvT3DAVTSLurPWd4BtkrvP0/Q6r01SvL1eaz+qaE3E/tYLgnvnm9vbFF9eOdDMqmkTcWa3Ai7Ni7/nA2izV6aevzaLQ5gU3DbI6jYjciKg7oNNoc3vVJLdcl05Fk4i7u/mX5vPe5eY8Rp6ooiCMjNO6YyLu7K7nzdn8f8qCDdOtTnPdVDSJuLvWfc1pB04d8cy76AwDdi8zt9sPszaLiPw8AWEw0Fxhg4y/wY43LY1zvVQ0ibg7Hz9od36me0/soju2F37cD961Lv6cIuK+2iZC7yfM7dVJsG+1pXGuh4omEU/Q/nwX3Zcr4VyZtVkcbc/5VqboBN01J+Ip+jwL/zMKjHJYNtZtBoaraBLxBJG3Q2BdOHMcsjdbncZxDONi61n7odZmERHHsdnMBZvbDIRzJfDuCDi6x+pU16SiScQTePvATYPNbU/qoju83ZxOoVYwxPS3Oo2IOJK3Dwx7DVp0N1c2eHsoHHbtqVNUNIl4ioouun0fQlmJtVkcZfdS87ntQHN6BRHxLL4BMOJdaHATnD4Ki/vC2t9DcYHVyaqkoknEU7Tobt7KW5wPWRusTvPznSszp1EA3TUn4skC6sCYNdBhOGDAtr/Dy13NPwBdjI/VAUTEQby84eYhsHWB2UVXscSKu8reDIU/QkA4tIq3Oo2IVKfAcPjlIug4HFYnQ9438K+RUK8N1G0FdSIuPhp1gNqNLYmpoknEk7QfahZNBz6C0jPu3aW1+/zYrJsHg7evpVFExElaxcPDGbD5JUibay7SffxA5dfc9Tz0fNSSeCqaRDxJ084Q1sIcPL1/DXS41+pEN+ZsMexbZW6ra06kZvENgL7Pwm2/gWN7IC+78qN+G8uiqWgS8SQ2G8SOhI0zYMfr7ls07V8NJQVQu6k5VktEap6QRubDhWgguIin6TQKbN7wbRrk7rc6zY35/B/mc6fR4KVfUyLiGvTbSMTT1G5ycRD4jtetzXIjcveZBZ/N++KK6CIiLkBFk4gn6vKg+bzrXXNAuDupaGVqM8AsAEVEXISKJhFPFNUHwlqaczZVzHXkDkoLYdd75naXsdZmERG5hIomEU/k5XWxtami5cYd7F5mDgCvEwlRmptJRFyLiiYRTxU7Erx84fvP4cgXVqexT0WB1+VBDQAXEZej30oiniq4PrT7hbntDgPCv98BR/4PvP3Mgk9ExMWoaBLxZBXjgr54H0pOWZvlWipamW4eDEF1LY0iIlIVFU0iniyiF9SNhtLTsHup1WmurCjv4rIpGgAuIi5KRZOIJ7PZLg4Iz1wE5eXW5rmSXf+CsiJocDM072p1GhGRKqloEvF0sfeDXyj8uB/2rbQ6zeXKSmHry+Z2lwfNQk9ExAWpaBLxdAFh0P1hc3vjX12vtWnXO+YCw0ENzAJPRMRFqWgSqQm6Tjjf2rTPtVqbykph80vmdq9kqBVobR4RkatQ0SRSE7hqa9P//RPycyC44cWxVyIiLkpFk0hNUam1aZXVacxWps9mmdu9ksE3wNo8IiLX4LJF0+HDhxk7dixNmjTBz8+PiIgIkpKSyMvLs/scERER2Gy2Kh+NGjW64vvS09NJTEwkPDycwMBAOnTowNy5czl37pwjfjQRawSEQbeJ5vYmF2ht2vnW+VamRtB5jLVZRETs4GN1gKpkZWXRo0cPcnNzGTRoEG3btmXbtm3MmzePdevWkZaWRt269k1+FxoaSlJS0mX7g4ODq3z9ypUrGTp0KP7+/tx3332Eh4fz4YcfkpycTFpaGkuXuvBcNyLX0m0ibH0Fcr80W5tuHmxNjrIStTKJiNuxGYZhWB3iUv369SMlJYX58+czadKkC/sff/xx5syZw/jx41m4cOE1zxMREQFAdna2XdctKCigVatWFBQUkJaWRpcuXQAoLi6mT58+ZGRk8O677zJ8+PArvj80NJT8/Hxq165t1zVFnC51Jmx6ARrcBBPSrFnjbftiWPMEhDSGR/8PfP2dn0FE5Dx7v79drnsuKyuLlJQUIiMjeeSRRyodmzZtGkFBQSxZsoTTp087/NpLly7l+PHjjBgx4kLBBODv78/06dMBWLBggcOvK+JU3SaaY5tyvzQHYjvb2WL4bLa53etxFUwi4jZcrmhKTU0FICEhAa9L/gIOCQmhZ8+eFBUVkZmZadf5SkpKePvtt5kxYwbz5s0jNTX1imOTKq7dv3//y47FxcURGBhIRkYGJSUl1/MjibiWgDCIe9LcXj8ZCo449/qbXoCC7yGkCXQa7dxri4j8DC5XNB04cACA6OjoKo9X7D948KBd5zt69CijRo1i8uTJJCUl0adPH6Kjo9m0adN1XdvHx4fIyEjKysr4+uuvr3rNgoKCSg8VWeJyuj0MTTpBST6sTgZn9dJ/vwPS5pnbiS+qlUlE3IrLFU35+fmAOYC7KhX7T548ec1zPfjgg3z66accPXqUwsJCdu/ezfjx48nOzmbAgAHs2rWrWq7dvHlzQkNDLzxmzpx5zawiTuXtA4NeBi9fOPgR7Pmg+q95thhWPAxGObQfBu3urv5riog4kEvePXc1FePWbXasTzVlypRK/92+fXsWLlxIcHAws2bNYurUqSxfvtzh187Jyak0kMzPz8/ua4g4TcOb4PY/QOpfYO3vIfJ2CK5ffdfb9Fdz/bugBmYrk4iIm3G5lqaK1pyKVp9LFRQUVHrdjZgwYQIAmzdvrpZr165du9JDRZO4rF7J0PAWKPoJ1j5Zfdf5fgekzTW3754DgeHVdy0RkWrickVTmzZtgCuPWfrqq68AiImJueFrNGjQAIDCwkK7r11WVsY333yDj48PUVFRN3xtEZfi7QuD/gY2b/hyBXxZDevSqVtORDyEyxVN8fHxAKSkpFB+yYzFp06dIi0tjYCAALp163bD16i48+7S4qdPnz4ArFu37rL3bN68mTNnztCjRw+1HIlnaRILvZLM7RUPw+HPHXduw4CPnz3fLVdf3XIi4tZcrmhq1aoVCQkJZGdn8/LLL1c6NmXKFAoLCxk9ejRBQUEAnD17lv3795OVlVXptXv37uWnn3667Pw5OTn87ne/A2DkyJGVjg0bNox69erx3nvv8fnnF784iouLeeaZZwCYOHHiz/8hRVzN7X+EiN5Qehre/iUc2XXt91xLRcG07e/mf989V91yIuLWXHJG8EuXUWnXrh2ZmZmkpqYSExNDenr6hWVUsrOziYyMpGXLlpVm/p46dSovvPAC8fHxREZGEhISwtdff83q1aspLi4mMTGR5cuXU6tWrUrXXrFiBcOGDcPf35/hw4cTHh7OqlWrOHDgAMOGDeP999+/4kBwzQgubq3kNLw9FHK2QkA4jFljDha/EYYBKc9Axt/M/x44C259yHFZRUQcyN7vb5csmsBsEfrzn//MunXrOHHiBI0bN2bw4MFMmTKF8PCLf61eqWjatGkTCxcuZOfOnRemHAgLCyM2NpZRo0YxatSoKxY/aWlp/OUvfyEjI4Pi4mJat27N2LFjefTRR/H29r5iZhVN4vaK82HJYPjhP2Z32oMfQb2q50y7IsMwJ83cer6leOBsuHWcw6OKiDiK2xdN7khFk3iEMz/Bm/fAsd3m2nB3z4WYfmDHNB+UlcDHf4bM82tD3j0Huoyt1rgiIj+X2649JyIWCwyH0Sugfls4dQTevQ9eHwDfXWXpotJCyHgZ5nX8r4JprgomEfEoamlyILU0iUcpzoctc2DrK1BWbO5rkwht7wYfv/MPf3PQ+NYFcOaE+ZqQJpDwPNwyzLrsIiLXQd1zFlDRJB6p4AfY+ALsfMuca+lK6kSYk2V2HGEWVCIibsLe72+3W0ZFRJysdhO4Zz50/x1k/C8UHDFbns6Vms++QdB5DLQfaq5pJyLiofQbTkTsUz8G7vlfq1OIiFhGA8FFRERE7KCiSURERMQOKppERERE7KCiSURERMQOKppERERE7KCiSURERMQOKppERERE7KCiSURERMQOKppERERE7KCiSURERMQOKprcQElJCVOnTqWkpMTqKB5Pn7Vz6HN2Dn3OzqHP2Tlc4XO2GYZhWHZ1D2PvKsmucl65nD5r59Dn7Bz6nJ1Dn7NzVOfnbO+51dIkIiIiYgcVTSIiIiJ28LE6gCep6OksKChw6Hkrzufo88rl9Fk7hz5n59Dn7Bz6nJ2jOj/ninNea8SSxjQ50OHDh2nevLnVMUREROQG5OTk0KxZsyseV9HkQOXl5fzwww+EhIRgs9msjiMiIiJ2MAyDU6dO0aRJE7y8rjxySUWTiIiIiB00EFxERETEDiqaREREROygoklERETEDiqaXNjhw4cZO3YsTZo0wc/Pj4iICJKSksjLy7M6msc4ceIEixcvZsiQIbRu3ZqAgABCQ0Pp1asXr732GuXl5VZH9FhvvfUWNpsNm83G4sWLrY7jcT777DOGDh1K48aN8fPzo3HjxiQkJLB27Vqro3mMVatWceedd9KsWTMCAgKIiori3nvvJSMjw+pobmfZsmVMmjSJ3r17U7t2bWw2GyNHjrzqe9LT00lMTCQ8PJzAwEA6dOjA3LlzOXfuXLXl1DxNLiorK4sePXqQm5vLoEGDaNu2Ldu2bWPevHmsW7eOtLQ06tata3VMt7d06VImTpxIo0aN6NOnDy1atODYsWP8+9//5qGHHmLt2rUsW7ZMd0M6WE5ODpMmTSI4OJjTp09bHcfjTJ8+nWeffZZ69epx991307hxY44fP87OnTvZuHEjiYmJVkd0e08++SSzZs2ibt26DB48mHr16nHo0CFWrlzJBx98wBtvvMHo0aOtjuk2pk+fzq5duwgODqZZs2bs37//qq9fuXIlQ4cOxd/fn/vuu4/w8HA+/PBDkpOTSUtLY+nSpdUT1BCXlJCQYADG/PnzK+1PTk42AGP8+PEWJfMsn376qbFixQqjrKys0v4jR44YzZs3NwBj6dKlFqXzTOXl5Ubfvn2NqKgo48knnzQA49VXX7U6lsf417/+ZQDGnXfeaRQUFFx2vLS01IJUnuXIkSOGl5eX0bBhQ+PYsWOVjm3YsMEAjIiICIvSuacNGzYYBw8eNMrLy43U1FQDMO6///4qX5ufn2/Uq1fPqFWrlrF9+/YL+4uKiozu3bsbgPHuu+9WS051z7mgrKwsUlJSiIyM5JFHHql0bNq0aQQFBbFkyRL9he4Affr0YdCgQXh7e1fa36hRIyZMmADAxo0bLUjmuebPn8+GDRt4/fXXCQoKsjqORykvL+ePf/wjAQEBvPPOO4SEhFz2Gl9fXwuSeZZvv/2W8vJyunbtSoMGDSodi4+PJyQkhOPHj1uUzj3Fx8cTHR1tV6v+0qVLOX78OCNGjKBLly4X9vv7+zN9+nQAFixYUC05VTS5oNTUVAASEhIum2QrJCSEnj17UlRURGZmphXxaoxatWoB+pJxpH379vHUU0/x2GOPERcXZ3Ucj5Oenk52djYDBw6kTp06rFmzhr/+9a/MmzdP42wcKDo6Gj8/PzIzM8nNza10LDU1lVOnTnHXXXdZlM7zVXxH9u/f/7JjcXFxBAYGkpGRQUlJicOvrTFNLujAgQOA+Q+zKtHR0aSkpHDw4EH69u3rzGg1RllZGW+++SZQ9T9MuX5lZWWMGjWKFi1aMGPGDKvjeKTt27cDZktp586d+eKLLyodj4uLY9myZdSvX9+KeB4jPDycF198kaSkJG666SaGDBlyYUzTqlWrSEhIYOHChVbH9FhX+4708fEhMjKSvXv38vXXX9OuXTuHXltFkwvKz88HIDQ0tMrjFftPnjzprEg1zlNPPcWePXsYMGAA/fr1szqOR3juuefYuXMnW7ZsISAgwOo4Hqmi1eOVV14hKiqKDRs2cOutt/Ltt9/yxBNPsH79eu699151OTvApEmTaNmyJWPGjKl092fr1q154IEHLuu2E8ex8jtS3XNuyDi/8o3u6Koec+fOZdasWbRp04YlS5ZYHccjbNu2jRkzZvDEE0/QvXt3q+N4rIpbrQ3D4IMPPiA+Pp7g4GBuvvlmli9fTrNmzdi0aZO66hxg5syZDBkyhDFjxpCVlUVhYSE7duwgKiqK+++/nz/84Q9WR6yxqvM7UkWTC6qokiuq6UsVFBRUep04zrx580hOTqZdu3Zs3LiRevXqWR3J7VV0y8XExPD8889bHcej1alTB4CoqChuueWWSscCAgIutJpu27bN6dk8yYYNG3j66acZNGgQs2fPJioqisDAQDp16sTy5ctp2rQps2bNIisry+qoHsnK70gVTS6oTZs2ABw8eLDK41999RUAMTExTstUE7z00kskJSXRvn17Nm7cSKNGjayO5BFOnz7NwYMH2bdvH/7+/hcmtLTZbEybNg2A3/zmN9hsNpKSkqwN6+YqfneEhYVVebyiqCoqKnJWJI+0Zs0awLzj61KBgYHcdtttlJeXs3PnTmdHqxGu9h1ZVlbGN998g4+PD1FRUQ6/tsY0uaCKf4gpKSmUl5dXuoPu1KlTpKWlERAQQLdu3ayK6HFmzpzJ008/TWxsLB9//LFamBzIz8+PcePGVXnsP//5Dzt37qRXr160adNGXXc/U1xcHD4+Phw6dIjS0tILd4BW2LNnDwAREREWpPMcpaWlAPz4449VHq/Y7+fn57RMNUmfPn345z//ybp16xgxYkSlY5s3b+bMmTPExcVVz+dfLbM/yc+myS2d57nnnjMAo3PnzsaJEyesjlOjTJkyRZNbOtj9999vAMaUKVMq7U9JSTFsNpsRGhpq5OXlWZLNU1RMINqwYUPj8OHDlY6tXbvWsNlshr+/v3H8+HGLEro3V57c0mYY50dMiUu5dBmVdu3akZmZSWpqKjExMaSnp2sZFQd48803GTNmDN7e3kyaNKnKPvCIiAjGjBnj/HA1wNSpU5k2bRqvvvoqDz30kNVxPEJubi49e/bk0KFDxMXFXbh7bvny5dhsNt555x3uvfdeq2O6tfLycvr168cnn3xCSEgIQ4YMoVGjRuzbt4/Vq1djGAZz587lscceszqq21ixYgUrVqwA4OjRo6xfv56oqCh69+4NQL169XjppZcqvX7YsGH4+/szfPhwwsPDWbVqFQcOHGDYsGG8//771XOzVLWUYuIQ3333nTFmzBijUaNGhq+vr9GiRQvj0UcfVWuIA1W0dFztcfvtt1sd02Oppal6nDhxwkhOTjYiIiIMX19fIzw83LjnnnuMjIwMq6N5jNLSUmPOnDlG165djZCQEMPb29uoX7++MXDgQGP9+vVWx3M71/pd3LJly8ves2XLFmPAgAFGWFiY4e/vb7Rv396YPXv2ZctiOZJamkRERETsoLvnREREROygoklERETEDiqaREREROygoklERETEDiqaREREROygoklERETEDiqaREREROygoklERETEDiqaREREROygoklE5Cqys7Ox2Wxaf1BEVDSJiIiI2ENFk4iIiIgdVDSJiFzB1KlTiYyMBODNN9/EZrNdeLzxxhvWhhMRp/OxOoCIiKu64447OHnyJPPmzaNjx44MHjz4wrHY2FjLcomINWyGYRhWhxARcVXZ2dlERkbywAMPqHVJpIZT95yIiIiIHVQ0iYiIiNhBRZOIiIiIHVQ0iYiIiNhBRZOIyFV4e3sDcO7cOYuTiIjVVDSJiFxFnTp1sNls5OTkWB1FRCymKQdERK6he/fuZGZm8utf/5ro6Gi8vb2555576NChg9XRRMSJVDSJiFzDoUOHSE5OJj09nby8PAzD4PXXX9civiI1jIomERERETtoTJOIiIiIHVQ0iYiIiNhBRZOIiIiIHVQ0iYiIiNhBRZOIiIiIHVQ0iYiIiNhBRZOIiIiIHVQ0iYiIiNhBRZOIiIiIHVQ0iYiIiNhBRZOIiIiIHVQ0iYiIiNhBRZOIiIiIHf4/vC401Gtd3akAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ff(xin, t):\n", " x = xin[0]\n", " y = xin[1]\n", " return np.array([x*y-x,y-x*y+np.sin(t)**2])\n", "\n", "a = 0.\n", "b = 10.0\n", "N = 100\n", "h = (b-a)/N\n", "\n", "tpoints = np.arange(a,b,h)\n", "xpoints = []\n", "ypoints = []\n", "\n", "sol = ode_rk4_multi(ff,[1.0,1.0], a, h, N)\n", "tpoints = sol[0]\n", "xpoints = sol[1][:,0]\n", "ypoints = sol[1][:,1]\n", "plt.title(\"ODE system solution using RK4 method\")\n", "plt.xlabel('t')\n", "plt.ylabel('x,y')\n", "plt.plot(tpoints,xpoints,label='x')\n", "plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Second-order ODEs\n", "\n", "A system of $N$ 2nd-order ODEs\n", "\n", "$$\n", "\\frac{d^2 \\mathbf{x}}{dt^2} = \\mathbf{f}(\\mathbf{x}, d\\mathbf{x}/dt,t),\n", "$$\n", "\n", "can be written as a system of $2N$ 1-st order ODEs by denoting $d\\mathbf{x}/dt = \\mathbf{v}$:\n", "\n", "\\begin{align*}\n", "\\frac{d \\mathbf{x}}{dt} &= \\mathbf{v},\\\\\n", "\\frac{d \\mathbf{v}}{dt} &= \\mathbf{f}(\\mathbf{x}, \\mathbf{v},t),\n", "\\end{align*}\n", "\n", "and solved using standard methods.\n", "\n", "This is particularly relevant for classical mechanics problems since Newton/Lagrange equations of motion correspond to a system of 2nd order ODEs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple pendulum in non-linear regime\n", "\n", "![pendulum](pendulum.gif)\n", "\n", "The equation of motion for non-linear pendulum reads\n", "$$\n", "m L \\frac{d^2 \\theta}{dt^2} = - m g L \\sin \\theta.\n", "$$\n", "\n", "Denoting $d\\theta / d t = \\omega$, one can rewrite this 2nd-order differential equation as a system of two 1st-order equations\n", "\\begin{align}\n", "\\frac{d \\theta}{dt} & = \\omega, \\\\\n", "\\frac{d \\omega}{dt} & = -\\frac{g}{L} \\sin \\theta~,\n", "\\end{align}\n", "which can be solved using standard first-order ODE methods.\n", "\n", "For small angles $\\theta$ one can approximate $\\sin \\theta \\approx \\theta$ and solved the equation\n", "$$\n", "m L \\frac{d^2 \\theta}{dt^2} \\approx - m g \\theta.\n", "$$\n", "For a pendulum initially at angle $\\theta_0$, the analytic solution for small angles reads\n", "$$\n", "\\theta(t) \\approx \\theta_0 \\cos\\left( \\sqrt{\\frac{g}{L}} t + \\phi\\right),\n", "$$\n", "where $\\phi = 0$ if the pendulum is initially at rest." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = 9.81\n", "L = 0.1\n", "\n", "def fpendulum(xin, t):\n", " theta = xin[0]\n", " omega = xin[1]\n", " return np.array([omega,-g/L * np.sin(theta)])\n", "\n", "\n", "theta0 = (20./180.) * np.pi\n", "omega0 = 0.\n", "\n", "x0 = np.array([theta0,omega0])\n", "a = 0.\n", "b = 2.0\n", "N = 5000\n", "h = (b-a)/N\n", "\n", "sol = ode_rk4_multi(fpendulum, x0, a, h, N)\n", "tpoints = sol[0]\n", "xpoints = sol[1][:,0]\n", "ypoints = sol[1][:,1]\n", "\n", "\n", "def theta_small_angles(t):\n", " return theta0 * np.cos(np.sqrt(g/L) * t)\n", "\n", "xpoints_small = theta_small_angles(tpoints)\n", "\n", "\n", "plt.title(\"Solving non-linear pendulum using RK4 method, ${\\\\theta_0 = \" + str(theta0/np.pi) + \"\\pi}$\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('${\\\\theta}$')\n", "plt.plot(tpoints,xpoints,label='RK4')\n", "plt.plot(tpoints,xpoints_small,label='${\\\\theta_0 cos(\\sqrt{g/L}t)}$')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = 9.81\n", "L = 0.1\n", "\n", "def fpendulum(xin, t):\n", " theta = xin[0]\n", " omega = xin[1]\n", " return np.array([omega,-g/L * np.sin(theta)])\n", "\n", "\n", "theta0 = (179./180.) * np.pi\n", "omega0 = 0.\n", "\n", "x0 = np.array([theta0,omega0])\n", "a = 0.\n", "b = 5.0\n", "N = 5000\n", "h = (b-a)/N\n", "\n", "sol = ode_rk4_multi(fpendulum, x0, a, h, N)\n", "tpoints = sol[0]\n", "xpoints = sol[1][:,0]\n", "ypoints = sol[1][:,1]\n", "\n", "\n", "def theta_small_angles(t):\n", " return theta0 * np.cos(np.sqrt(g/L) * t)\n", "\n", "xpoints_small = theta_small_angles(tpoints)\n", "\n", "plt.title(\"Solving non-linear pendulum using RK4 method, ${\\\\theta_0 = \" + str(theta0/np.pi) + \"\\pi}$\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('${\\\\theta}$')\n", "plt.plot(tpoints,xpoints,label='RK4')\n", "plt.plot(tpoints,xpoints_small,label='${\\\\theta_0 cos(\\sqrt{g/L}t)}$')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adaptive time step for system of ODEs\n", "\n", "The adaptive 4th-order Runge-Kutta method for single first-order ODE can be generalized to a system of ODEs.\n", "One has to generalize the notion of the difference $|x_1 - x_2|$ between two estimates of the independent variable to the case of vectors $\\mathbf{x}_1$ and $\\mathbf{x}_2$ of variables.\n", "\n", "The simplest choice would be to evaluate the modulus of the difference vector $|\\mathbf{x}_1 - \\mathbf{x}_2|$, which would be the default choice. Alternatively, in some cases we may only be interested in the accuracy of a single variable from the vector, for example of coordinate $x$ but not of velocity $v$ in case of a second-order ODE cast as system of two first-order ODEs. In this case one can generalize the definition of the distance between $\\mathbf{x}_1$ and $\\mathbf{x}_2$ as appropriate for the problem at hand.\n", "\n", "The implementation of the RK4 scheme with adaptive time step for a system of ODEs can be implemented as follows." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# The default definition of the error (distance) between two state vectors \n", "# Default: the magnitude of the difference vector\n", "def distance_definition_default(x1, x2):\n", " diff = x1 - x2\n", " diffnorm = np.sqrt(np.dot(diff, diff))\n", " return diffnorm\n", "\n", "def ode_rk4_adaptive_multi(f, x0, t0, h0, tmax, delta = 1.e-6, distance_definition = distance_definition_default):\n", " \"\"\"Solve an ODE dx/dt = f(x,t) from t = t0 to t = t0 + h*steps \n", " using 4th order Runge-Kutta method with adaptive time step.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x0: the initial value of the dependent variable.\n", " t0: the initial value of the time variable.\n", " h0: the initial time step\n", " tmax: the maximum time\n", " delta: the desired accuracy per unit time\n", "\n", " Returns:\n", " t,x: the pair of arrays corresponding to the time and dependent variables\n", " \"\"\"\n", " \n", " ts = [t0]\n", " xs = [x0]\n", " \n", " h = h0\n", " t = t0\n", " i = 0\n", " \n", " while (t < tmax):\n", " if (t + h >= tmax):\n", " ts.append(tmax)\n", " h = tmax - t\n", " xs.append(ode_rk4_step(f, xs[i], ts[i], h))\n", " t = tmax\n", " break\n", " \n", " x1 = ode_rk4_step(f, xs[i], ts[i], h)\n", " x1 = ode_rk4_step(f, x1, ts[i] + h, h)\n", " x2 = ode_rk4_step(f, xs[i], ts[i], 2*h)\n", " \n", " diffnorm = distance_definition(x1, x2)\n", " if diffnorm == 0.: # To avoid the division by zero\n", " rho = 2.**4\n", " else:\n", " rho = 30. * h * delta / diffnorm\n", " if rho < 1.:\n", " h *= rho**(1/4.)\n", " else:\n", " if (t + 2.*h) < tmax:\n", " xs.append(x1)\n", " ts.append(t + 2*h)\n", " t += 2*h\n", " else:\n", " xs.append(ode_rk4_step(f, xs[i], ts[i], h))\n", " ts.append(t + h)\n", " t += h\n", " i += 1\n", " h = min(2.*h, h * rho**(1/4.))\n", " \n", " return ts,xs" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = 9.81\n", "L = 0.1\n", "\n", "def fpendulum(xin, t):\n", " theta = xin[0]\n", " omega = xin[1]\n", " return np.array([omega,-g/L * np.sin(theta)])\n", "\n", "def error_definition_pendulum(x1, x2):\n", " return np.abs(x1[0] - x2[0])\n", "\n", "theta0 = (179./180.) * np.pi\n", "omega0 = 0.\n", "\n", "x0 = np.array([theta0,omega0])\n", "a = 0.\n", "b = 3.0\n", "N = 500\n", "h0 = (b-a)/N\n", "eps = 1.e-3 # accuracy in theta\n", "sol = ode_rk4_adaptive_multi(fpendulum, x0, a, h0, b, eps, error_definition_pendulum)\n", "\n", "tpoints = [t for t in sol[0]]\n", "xpoints = [x[0] for x in sol[1]]\n", "ypoints = [x[1] for x in sol[1]]\n", "\n", "\n", "plt.title(\"Solving non-linear pendulum using adaptive RK4 method, ${\\\\theta_0 = \" + str(theta0/np.pi) + \"\\pi}$\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('${\\\\theta}$')\n", "plt.plot(tpoints,xpoints,'.',label='Adaptive RK4, ${\\\\theta}$ accuracy = ' + str(eps) + ' ${s^{-1}}$')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "thpoints = []\n", "hpoints = []\n", "for i in range(len(tpoints) - 1):\n", " thpoints.append(0.5*(tpoints[i] + tpoints[i+1]))\n", " hpoints.append(tpoints[i+1] - tpoints[i])\n", " \n", "plt.title(\"Time step lenghts\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('h [s]')\n", "plt.plot(thpoints,hpoints,'.',label='Adaptive RK4, ${\\\\theta}$ accuracy = ' + str(eps) + ' ${s^{-1}}$')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comet motion (Exercise 8.10 from M. Newman *Computational Physics*)\n", "\n", "\n", "\n", "Many comets travel in highly elongated orbits around the Sun. For\n", "much of their lives they are far out in the solar system, moving very\n", "slowly, but on rare occasions their orbit brings them close to the Sun for\n", "a fly-by and for a brief period of time they move very fast indeed:\n", "\n", "\"Comet\" \n", "\n", "This is a classic example of a system for which an adaptive\n", "step size method is useful, because for the large periods of time when the\n", "comet is moving slowly we can use long time-steps, so that the program runs\n", "quickly, but short time-steps are crucial in the brief but fast-moving\n", "period close to the Sun.\n", "\n", "The differential equation obeyed by a comet is straightforward to\n", "derive. The force between the Sun, with mass $M$ at the origin, and a\n", "comet of mass $m$ with position vector $\\vec{r}$ is $GMm/r^2$ in direction\n", "$-\\vec{r}/r$ (i.e., the direction towards the Sun), and hence Newton's\n", "second law tells us that\n", "$$\n", "m {d^2\\vec{r}\\over d t^2} = -\\biggl({GMm\\over r^2}\\biggr)\\,{\\vec{r}\\over r}.\n", "$$\n", "Canceling the mass $m$ and taking the $x$ component we have\n", "$$\n", "{d^2 x\\over d t^2} = -GM {x\\over r^3}\\,,\n", "$$\n", "and similarly for the other two coordinates. We can, however, throw out\n", "one of the coordinates because the comet stays in a single plane as it\n", "orbits. If we orient our axes so that this plane is perpendicular to\n", "the $z$-axis, we can forget about the $z$ coordinate and we are left with\n", "just two second-order equations to solve:\n", "\\begin{align*}\n", "{d^2 x\\over d t^2} & = -GM {x\\over r^3}\\,, \\\\\n", "{d^2 y\\over d t^2} & = -GM {y\\over r^3}\\,,\n", "\\end{align*}\n", "where $r=\\sqrt{x^2+y^2}$.\n", "\n", "We will write a program to the equations using the fourth-order\n", "Runge--Kutta method with a *fixed* step size. \n", "As an initial condition, we take a comet at coordinates $x=4$ billion kilometers\n", "and $y=0$ (which is somewhere out around the orbit of Neptune) with\n", "initial velocity $v_x=0$ and $v_y = 500\\,\\mathrm{m\\,s}^{-1}$. The trajectory of the comet will be a plot of $y$\n", "against $x$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G = 6.67430e-11 # m^3 / kg / s^2\n", "Msun = 1.9885e30 # kg\n", "\n", "def fcomet(xin, t):\n", " x = xin[0]\n", " y = xin[1]\n", " vx = xin[2]\n", " vy = xin[3]\n", " r = np.sqrt(x*x+y*y)\n", " return np.array([vx,vy,-G*Msun*x/r**3,-G*Msun*y/r**3])\n", "\n", "x0 = [4.e12,0.,0.,500.]\n", "\n", "a = 0.\n", "b = 50. * 365. * 24. * 60. * 60. # 50 years\n", "N = 100000 # 100 thousand RK4 steps\n", "h = (b - a) / N # Time step: around 1/5th of a day\n", "sol = ode_rk4_multi(fcomet, x0, a, h, N)\n", "\n", "tpoints_rk4_ref = sol[0]\n", "xpoints_rk4_ref = sol[1][:,0]\n", "ypoints_rk4_ref = sol[1][:,1]\n", "vxpoints_rk4_ref = sol[1][:,2]\n", "vypoints_rk4_ref = sol[1][:,3]\n", "vpoints_rk4_ref = [np.sqrt(x[2]*x[2] + x[3]*x[3]) for x in sol[1]]\n", "\n", "\n", "plt.title(\"Solving the comet motion using RK4 method\")\n", "plt.xlabel('x [m]')\n", "plt.ylabel('y [m]')\n", "plt.plot(xpoints_rk4_ref,ypoints_rk4_ref,label='RK4 (h = ' + str(h) + ' s)')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now use the RK4 method with an adaptive time step. We expect to have a smaller step near the sun, where the comet motion is faster, and a larger step away from the sun" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G = 6.67430e-11\n", "Msun = 1.9885e30\n", "\n", "def fcomet(xin, t):\n", " x = xin[0]\n", " y = xin[1]\n", " vx = xin[2]\n", " vy = xin[3]\n", " r = np.sqrt(x*x+y*y)\n", " return np.array([vx,vy,-G*Msun*x/r**3,-G*Msun*y/r**3])\n", "\n", "def error_definition_comet(x1, x2):\n", " return np.sqrt((x1[0]-x2[0])**2 + (x1[1]-x2[1])**2)\n", "\n", "x0 = [4.e12,0.,0.,500.]\n", "\n", "a = 0.\n", "b = 50. * 365. * 24. * 60. * 60. # 50 years\n", "h0 = 1. * 365. * 24. * 60. * 60. # Initial time step: 1 year\n", "delta = 1000. * 1.e3 / (365. * 24. * 60. * 60.)\n", "sol = ode_rk4_adaptive_multi(fcomet, x0, a, h0, b, delta, error_definition_comet)\n", "\n", "tpoints = [t for t in sol[0]]\n", "xpoints = [x[0] for x in sol[1]]\n", "ypoints = [x[1] for x in sol[1]]\n", "vxpoints = [x[2] for x in sol[1]]\n", "vypoints = [x[3] for x in sol[1]]\n", "vpoints = [np.sqrt(x[2]*x[2] + x[3]*x[3]) for x in sol[1]]\n", "\n", "plt.title(\"Solving the comet motion using adaptive RK4 method\")\n", "plt.xlabel('x [m]')\n", "plt.ylabel('y [m]')\n", "plt.plot(xpoints_rk4_ref,ypoints_rk4_ref,label='RK4 fixed')\n", "plt.plot(xpoints,ypoints,'.',label='RK4 adaptive')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.title(\"Coordinates\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('x,y [m]')\n", "plt.plot(tpoints_rk4_ref,xpoints_rk4_ref,label='x (RK4 fixed)')\n", "plt.plot(tpoints_rk4_ref,ypoints_rk4_ref,label='y (RK4 fixed)')\n", "plt.plot(tpoints,xpoints,'.',label='x (RK4 adaptive)')\n", "plt.plot(tpoints,ypoints,'.',label='y (RK4 adaptive)')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.title(\"Velocity\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('v [m/s]')\n", "plt.plot(tpoints_rk4_ref,vpoints_rk4_ref,label='v (RK4 fixed)')\n", "plt.plot(tpoints,vpoints,'.',label='v (RK4 adaptive)')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "thpoints = []\n", "hpoints = []\n", "for i in range(len(tpoints) - 1):\n", " thpoints.append(0.5*(tpoints[i] + tpoints[i+1]))\n", " hpoints.append(tpoints[i+1] - tpoints[i])\n", " \n", "plt.title(\"Time steps\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('h [s]')\n", "plt.plot(thpoints,hpoints,'.',label='Adaptive RK4')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Leapfrog method\n", "\n", "\"Leapfrog\" \n", "
\n", " (a) 2nd-order Runge-Kutta
\n", " (b) Leapfrog
\n", " Source: M. Newman \"Computational Physics\"\n", "
\n", "\n", "Recall the 2nd order Runge-Kutta (midpoint) method.\n", "\n", "The full step proceeds by evaluating\n", "$$\n", "x(t+h) = x(t) + h f[x(t+h/2),t+h/2],\n", "$$\n", "where the midpoint value $x(t+h/2)$ is estimated using Euler's method\n", "$$\n", "x(t+h/2) = x(t) + \\frac{1}{2} h f(x,t)~.\n", "$$\n", "\n", "The idea of the leapfrog method is to use the last equation (Euler half-step) only in the first iteration, and then use the first equation to estimate both $x(t+h)$ and $x(t+3h/2)$, i.e., given the values of $x(t)$ and $x(t+h/2)$ at each step the algorithm calculates a pair of values\n", "\\begin{align*}\n", "x(t+h) &= x(t) + h f[x(t+h/2),t+h/2], \\\\\n", "x(t+3h/2) &= x(t+h/2) + h f[x(t+h),t+h].\n", "\\end{align*}\n", "\n", "The attractive features of this algorithm is that it is time reversible. By changing $h \\to -h$ one gets\n", "\\begin{align*}\n", "x(t-h) &= x(t) - h f[x(t-h/2),t-h/2], \\\\\n", "x(t-3h/2) &= x(t-h/2) - h f[x(t-h),t-h],\n", "\\end{align*}\n", "i.e. the same steps are performed in reverse.\n", "Changing $t \\to t + 3h/2$ one gets\n", "\\begin{align*}\n", "x(t+h/2) &= x(t+3h/2) - h f[x(t+h),t+h], \\\\\n", "x(t) &= x(t+h) - h f[x(t+h/2),t+h/2],\n", "\\end{align*}\n", "\n", "The time reversal symmetry is important since the microscopic equations are typically time-reversal, so it is good to have this feature built-in by construction in the numerical scheme." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def ode_leapfrog_step(f, x, x2, t, h):\n", " \"\"\"Perform a single step h using the leapfrog method.\n", "\n", " Args:\n", " f: the function that defines the ODE.\n", " x: the value of x(t)\n", " x2: the value of x(t+h/2)\n", " t: the present value of the time variable.\n", " h: the time step\n", "\n", " Returns:\n", " xnew, xnew2: the value of the dependent variable at the steps t+h, t+3h/2\n", " \"\"\"\n", " \n", " xnew = x + h * f(x2,t+h/2.)\n", " xnew2 = x2 + h * f(xnew, t + h)\n", " return xnew, xnew2\n", "\n", "def ode_leapfrog_multi(f, x0, t0, h, nsteps):\n", " \"\"\"Multi-dimensional version of the leapfrog method.\n", " \"\"\"\n", " \n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros((len(t), len(x0)))\n", " x2 = np.zeros(len(x0))\n", " t[0] = t0\n", " x[0,:] = x0\n", " x2[:] = ode_euler_step(f, x0, t0, h/2.)\n", " for i in range(0, nsteps):\n", " t[i + 1] = t[i] + h\n", " x[i + 1], x2 = ode_leapfrog_step(f, x[i], x2, t[i], h)\n", " return t,x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us return to the problem of a non-linear pendulum and apply the leap-frog method.\n", "We can monitor the behavior of energy\n", "$$\n", "E = m L^2 \\dot{\\theta}^2/2 - mgL \\cos(\\theta)\n", "$$\n", "as a function of time.\n", "\n", "If $\\theta_0 = \\pi/2$ and $\\dot{\\theta}_0 = 0$ the total energy is zero." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = 9.81 # m/s^2\n", "L = 0.1 # m\n", "\n", "def fpendulum(xin, t):\n", " theta = xin[0]\n", " omega = xin[1]\n", " return np.array([omega,-g/L * np.sin(theta)])\n", " #return np.array([omega,-g/L * theta])\n", "\n", "# The energy of a pendulum\n", "def pendulum_energy(x):\n", " return L*L*x[1]**2/2. - g*L*np.cos(x[0])\n", " #return L*L*x[1]**2/2. - g*L*x[0]**2/2.\n", "\n", "\n", "theta0 = (90./180.) * np.pi\n", "omega0 = 0.\n", "\n", "x0 = np.array([theta0,omega0])\n", "a = 0.\n", "b = 10.\n", "N = 500\n", "h = (b-a)/N\n", "\n", "sol_leapfrog = ode_leapfrog_multi(fpendulum, x0, a, h, N)\n", "sol_rk2 = ode_rk2_multi(fpendulum, x0, a, h, N)\n", "tpoints = sol_leapfrog[0]\n", "xpoints = sol_leapfrog[1][:,0]\n", "ypoints = sol_leapfrog[1][:,1]\n", "\n", "xpoints_rk2 = sol_rk2[1][:,0]\n", "\n", "def theta_small_angles(t):\n", " return theta0 * np.cos(np.sqrt(g/L) * t)\n", "\n", "xpoints_small = theta_small_angles(tpoints)\n", "\n", "plt.title(\"Non-linear pendulum ${\\\\theta_0 = \" + str(theta0/np.pi) + \"\\pi}$\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('${\\\\theta}$')\n", "plt.plot(tpoints,xpoints,label='Leapfrog')\n", "plt.plot(tpoints,xpoints_rk2,label='RK2')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "energies_leapfrog = [pendulum_energy(x) for x in sol_leapfrog[1]]\n", "energies_rk2 = [pendulum_energy(x) for x in sol_rk2[1]]\n", "\n", "plt.title(\"Non-linear pendulum ${\\\\theta_0 = \" + str(theta0/np.pi) + \"\\pi}$\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('Total energy')\n", "#plt.ylim(-2,2)\n", "plt.ylim(-0.05,0.05)\n", "plt.plot(tpoints,energies_leapfrog,label='Leapfrog')\n", "plt.plot(tpoints,energies_rk2,label='RK2')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The leapfrog method shows greater stability as the average energy is conserved.\n", "Such a method is thus particularly suitable for long simulations of periodic systems." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Exercise 8.11\n", "\n", "def fpendulum(xin, t):\n", " theta = xin[0]\n", " omega = xin[1]\n", " return np.array([omega,omega**2 - theta - 5])\n", " #return np.array([omega,-g/L * theta])\n", "\n", "theta0 = 1.\n", "omega0 = 0.\n", "\n", "x0 = np.array([theta0,omega0])\n", "a = 0.\n", "b = 50.\n", "N = 50000\n", "h = (b-a)/N\n", "h = 0.001\n", "\n", "sol_leapfrog = ode_leapfrog_multi(fpendulum, x0, a, h, N)\n", "sol_rk2 = ode_rk2_multi(fpendulum, x0, a, h, N)\n", "tpoints = sol_leapfrog[0]\n", "xpoints = sol_leapfrog[1][:,0]\n", "ypoints = sol_leapfrog[1][:,1]\n", "\n", "xpoints_rk2 = sol_rk2[1][:,0]\n", "\n", "def theta_small_angles(t):\n", " return theta0 * np.cos(np.sqrt(g/L) * t)\n", "\n", "xpoints_small = theta_small_angles(tpoints)\n", "\n", "plt.xlabel('t [s]')\n", "plt.ylabel('${\\\\theta}$')\n", "plt.plot(tpoints,xpoints,label='Leapfrog')\n", "#plt.plot(tpoints,xpoints_rk2,label='RK2')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Verlet method\n", "\n", "Suppose we are solving Newton's equations of motion\n", "$$\n", "\\frac{d^2 x}{dt^2} = f(x,t).\n", "$$\n", "These are rewritten as\n", "\\begin{align*}\n", "\\frac{dx}{dt} &= v, \\\\\n", "\\frac{dv}{dt} &= f(x,t).\n", "\\end{align*}\n", "\n", "If we apply the leapfrog scheme to this system of equations, it will look like\n", "\\begin{align*}\n", "x(t+h) & = x(t) + h v(t + h/2), \\\\\n", "v(t+3h/2) &= v(t+h/2) + h f[x(t+h), t+h)],\n", "\\end{align*}\n", "i.e. the coordinates are evaluated are full steps using velocity estimates at half-steps,\n", "and vice versa.\n", "\n", "This is the essence of the Verlet method.\n", "It's feature is that we do not need to keep track of coordinates at half-steps (only the velocities) and of velocities at full steps. In case we are interested in velocity values also at full step, these can be estimated as $v(t+h) = v(t+h/2) + (h/2) f[x(t+h),t+h].\n", "\n", "The full algorithm is as follows. Given initial values $x(t)$ and $v(t)$ one first computes\n", "$$\n", "v(t+h/2) = v(t) + \\frac{h}{2} f[x(t),t].\n", "$$\n", "Then each step of the Verlet algorith corresponds to\n", "\\begin{align*}\n", "x(t+h) & = x(t) + h v(t+h/2), \\\\\n", "k & = h f[x(t+h),t+h), \\\\\n", "v(t+h) & = v(t+h/2) + k/2, \\\\\n", "v(t+3h/2) & = v(t+h/2) + k.\n", "\\end{align*}\n", "\n", "The algorith is straightforwardly generalizable to more than one variable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modified midpoint method\n", "\n", "Recall that steps in the leapfrog method are time-reversible ($h \\to -h$).\n", "For this reason the local error (per one step) contains only odd powers of $h$,\n", "while the global error integrating from $t$ to $t+H$ would have only even powers of $h$.\n", "The only issue is the first Euler half-step $x(t+h/2) = x(t) + hf(x,t)$ which is not symmetric in $h$.\n", "This half-step ruins the desired property of the global error containing only even powers of $h$.\n", "\n", "To fix this issue one uses an extra step at the very end,\n", "which is called the modified midpoint method.\n", "Let $y_n = x(t+H-h/2)$ and $x_n = x(t+H)$ be the estimates of the solution resulting from the leapfrog method.\n", "One then re-evaluates $x(t+H)$ as an average of $x_n$ and the $x(t+H)$ evaluted usinf Euler half-step from $y_n$:\n", "$$\n", "x(t+H) = \\frac{1}{2} [x_n + y_n + \\frac{h}{2} f(x_n,t+H)].\n", "$$\n", "\n", "This modification cancels all odd terms in the global error for $x(t+H)$." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "def ode_MMM_multi(f, x0, t0, H, nsteps):\n", " \"\"\"Multi-dimensional version of the modified midpoint method.\n", " \"\"\"\n", " \n", " h = H / nsteps\n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros((len(t), len(x0)))\n", " x2 = np.zeros(len(x0))\n", " t = t0\n", " x = x0\n", " y = ode_euler_step(f, x0, t0, h/2.)\n", " for i in range(0, nsteps):\n", " yprev = y\n", " x, y = ode_leapfrog_step(f, x, y, t, h)\n", " t = t + h\n", " \n", " return 0.5 * (x + yprev + 0.5 * h * f(x,t))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bulirsch-Stoer method\n", "\n", "Bulirsch-Stoer method is an analogue of Romberg integration applied to ODE.\n", "The method allows one to integrate a (system) of ODE for $t$ to $t+H$ to desired accuracy.\n", "To achieve that one uses the modified midpoint method with increasing number of steps,\n", "and the difference between the subsequent steps to cancel out higher and higher-order error terms in $h$.\n", "\n", "The iterative procedure is as follows.\n", "Let $R_{n,1}$ be an estimate of $x(t+H)$ from the modified midpoint method using $n$ steps of size $h_n = H/n$.\n", "Then\n", "$$\n", "x(t+H) = R_{n,1} + O(h_n^2).\n", "$$\n", "One constructs high-order approximations $R_{n,m}$ such that\n", "$$\n", "x(t+H) = R_{n,m} + O(h_n^{2m}),\n", "$$\n", "from the following iterative procedure\n", "$$\n", "R_{n,m+1} = R_{n,m} + \\frac{R_{n,m} - R_{n-1,m}}{[n/(n-1)]^{2m} - 1}~.\n", "$$\n", "\n", "The procedure goes one in incremental steps of $n$ until the distane between the solution estimates $R_{n,n}$ and $R_{n,n-1}$ reaches the desired accuracy.\n", "\n", "In practice, if the desired accuracy is not reached after $n \\sim 10$ steps, it may indicate that $H$ is too large, and one has to split it into two subintervals of width $H/2$ and apply the Bulirsch-Stoer method recursively." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "def bulirsch_stoer_step(f, x0, t0, H, delta = 1.e-6, distance_definition = distance_definition_default, maxsteps = 10):\n", " \"\"\"Use Bulirsch-Stoer method to integrate for t to t+H.\n", " \"\"\"\n", " n = 1\n", " R1 = np.empty([1,len(x0)],float)\n", " R1[0] = ode_MMM_multi(f, x0, t0, H, 1)\n", " error = 2. * H * delta\n", " while error > H*delta and n < maxsteps:\n", " n += 1\n", " R2 = R1\n", " R1 = np.empty([n,len(x0)],float)\n", " R1[0] = ode_MMM_multi(f, x0, t0, H, n)\n", " for m in range(1,n):\n", " epsilon = (R1[m-1]-R2[m-1])/((n/(n-1))**(2*m)-1)\n", " R1[m] = R1[m-1] + epsilon\n", " error = distance_definition(R1[n-2],R1[n-1])\n", " \n", " if n == maxsteps:\n", " # Reached maximum number of substeps in Bulirsch-Stoer method\n", " # reducing the time step and applying the method recursively\n", " sol1 = bulirsch_stoer_step(f, x0, t0, H/2., delta, distance_definition, maxsteps)\n", " sol2 = bulirsch_stoer_step(f, sol1[-1][1], t0 + H/2., H/2., delta, distance_definition, maxsteps)\n", " return sol1 + sol2\n", " \n", " return [[t0+H, R1[n - 1]]]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def bulirsch_stoer(f, x0, t0, nsteps, tmax, delta = 1.e-6, distance_definition = distance_definition_default, maxsubsteps = 10):\n", " \"\"\"Use Bulirsch-Stoer method to integrate for t to tmax using nsteps Bulirsch-Stoer steps\n", " \"\"\"\n", " H = (tmax - t0) / nsteps\n", " t = np.zeros(nsteps + 1)\n", " x = np.zeros((len(t), len(x0)))\n", " t = [t0]\n", " x = [x0]\n", " for i in range(0, nsteps):\n", " bst = bulirsch_stoer_step(f, x[-1], t[-1], H, delta, distance_definition, maxsubsteps)\n", " [t.append(el[0]) for el in bst]\n", " [x.append(el[1]) for el in bst]\n", " return t,x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us apply the Bulirsch-Stoer method to solve the motion of non-linear pendulum.\n", "Due to the fact that the method dynamically adjust $H$ to reach the desired accuracy, we can start with just one step." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = 9.81\n", "L = 0.1\n", "\n", "def fpendulum(xin, t):\n", " theta = xin[0]\n", " omega = xin[1]\n", " return np.array([omega,-g/L * np.sin(theta)])\n", "\n", "def error_definition_pendulum(x1, x2):\n", " return np.abs(x1[0] - x2[0])\n", "\n", "theta0 = 179. * np.pi / 180.\n", "omega0 = 0.\n", "x0 = np.array([theta0,omega0])\n", "a = 0.\n", "b = 10.0\n", "N = 1\n", "eps = 1.e-8\n", "maxsubsteps = 10\n", "\n", "sol = bulirsch_stoer(fpendulum, x0, a, N, b, eps, error_definition_pendulum, maxsubsteps)\n", "\n", "tpoints = [t for t in sol[0]]\n", "xpoints = [x[0] for x in sol[1]]\n", "ypoints = [x[1] for x in sol[1]]\n", "\n", "\n", "plt.title(\"Solving non-linear pendulum using Bulirsch-Stoer method, ${\\\\theta_0 = \" + str(theta0/np.pi) + \"\\pi}$\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('${\\\\theta}$')\n", "plt.plot(tpoints,xpoints)\n", "plt.plot(tpoints,xpoints,'b.',label='Bulirsch-Stoer method')\n", "plt.ylim(-np.pi,np.pi)\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "thpoints = []\n", "hpoints = []\n", "for i in range(len(tpoints) - 1):\n", " thpoints.append(0.5*(tpoints[i] + tpoints[i+1]))\n", " hpoints.append(tpoints[i+1] - tpoints[i])\n", " \n", "plt.title(\"Time steps H\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('H [s]')\n", "plt.plot(thpoints,hpoints,'.',label='Bulirsch-Stoer method')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now apply the Bulirch-Stoer method to analyze the comet motion.\n", "Again, we can use a single step $H$ initially" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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YCwQHBysfH58bHudqt1rmXO97tuDau7q6Fvt+e+mllxSgpk+fbtk2ZMgQBagjR44UG1/z5s1VtWrVrLZd79xfz/XOX2Rk5DU/p3l5ecre3l5169bNss1kMikfHx8VEBBQ7LVISkpSOp1ODR8+vMjz3yjRutXP2q2c7169eilArVu3rsj+Bdf2VhOtCtV0CDB8+HAGDx7M+vXr2bx5M/v27WPz5s38/PPP/Pzzz0yYMIEvv/wSnU5HWloap0+fpmbNmtStW7fIsQra1vfu3XvD5x03bhxffvklCxYs4K677rJs/+abb7C3t2f06NE3/Rpat25dZJu9vT3Vq1cnKSnJsu348eNkZmbSunVr3NzcijymU6dOfPnllzf9vLcTX1BQEIBVfNu2bQPym3yKa/sv6BNy7NixGz7n9u3bAejXr98N9923bx8A3bt3L3Kft7c3LVu25O+//+aff/4pUuV8dXNEgRo1atzwvujoaEJCQoB/X/eGDRvYuXNnkcdcunQJs9nMyZMniz1mSdxO3AWud97s7e3p2rUrCxcuZN++fZbXWhL79u1Dr9fTtWvXIvd1794dg8FQ7Geubt26xb7PC957ycnJxd5/u+677z6eeeYZGjVqxL333kuXLl3o2LGjpdnoZmn9ue7atatVP5mEhAS2bt3Kk08+SdeuXVm2bJnVd1d5MBqNNGvWrMj2hg0b0qJFCxYtWkRUVBSDBg2iY8eOtG7dGgcHB6t9b+W7oUDz5s0xGAxFtgcFBVk+v5DfRFZc/5+rv89upcy5kYJr36lTp2K7NvTq1Ys333zT6vOxbds27O3tr9kXLScnh7i4OBISEvDx8bFsv9a5vxnFnb+C75TiPqcGgwE/Pz+r75sTJ06QkJBAnTp1eP3114t9Hicnp5sqHwq71c/arZzvvXv3otfr6dSpU5H9b3X+rAIVLtGC/BPau3dvS18Gk8nETz/9xIQJE/j6668ZNGgQgwcPJiUlBQB/f/9ij1MwHLlgv+vp2LEjtWvXZuXKlSQlJeHl5cXu3bs5cuQIQ4YMwdfX96bjv9YIHTs7O0wmk+XvgriqV69e7P7X2n67iovPzi7/rXJ1fAkJCUB+R+zrdeK8fPnyDZ+zoENnYGDgDfe9net6vdd2vftyc3Mt2wpe97vvvnvdOG/mdd+s0oi7ND8P15OSkmKZb6i4uAr6QBV2vc8FWL/3StPTTz+Nr68vc+fOZfbs2XzwwQfodDq6d+/Ou+++S8uWLW/qOLb2ufbx8WHgwIE4OTlx55138vTTT5d7olW9evViExCDwcDatWuZMWMGS5cu5fnnnwfA3d2dcePG8eabb+Li4gLc2ndDgetdi6s7YEdERDB9+vQi+xX+4XizZc6NlOQzmJCQQF5eXrFxXu3y5ctWida1zv3NuNXvm4L7i/uePHny5HVjL8n35K1+1m7lfF/v++tax7mRCjXq8FoMBgP33HMPTz31FABr164F/r0YsbGxxT7uwoULVvvdyJgxY8jOzmbx4sXArXeCv1Xu7u5A/giP4lxre3kpOG+zZ89G5TdDF3ubN2/eDY9V0FE0Jibmpp+3tK7rrSo4bkpKynVfd3E1Oloqr/Pm4eFBYmKi1Zdugby8POLj4y3v7bKg0+nIy8sr9r7iRmhB/md7+/btJCQk8OuvvzJx4kQ2bNhA7969i4zWu13l/blu27YtkF/DcHWBotfnf/0Xd66udZ5u1fUKei8vLz744AOioqIsA0nq1avHhx9+aNU5+Va+G25Vt27div3s3si1ypwbKcln0MPDAy8vr+t+1yilitRCaz1BcsFrGDp06HXjPnv2bJnHcKvn+1rfX9c6zo1UikSrQEF1ZsEHxc3NjfDwcGJiYjh58mSR/devXw9w079Yx4wZYxnynpuby6JFi/D19S2zX4n169fHycmJgwcPkpaWVuT+zZs339LxCqqCS6tmoF27dgBs2rSp1I61Zs2aG+7bokULgGKHEycnJ7N//34cHR2tRp6UppK87tI+9yVxvfOWl5dneT9d/XkoSdwtWrTAbDbz999/F7nv77//xmQy3fRnriS8vLyIiooqst1kMrF///7rPtbT05P+/fvzxRdfMG7cOBISEkrl/X210v5c38jVTSlX1+YUNKUUd652795dqjHcSO3atZk4cSIbN27E1dWVZcuWWe67le+G8la4zIHrf2bq1auHs7Mz+/fvt7ouBYork9q1a0dSUhJHjhwp1djLWv369fH09GT79u3FJi3FKe3vyZKc75YtW2I2m4v9HJZ0eboKlWgtWrSIP//8s9h5eGJjYy3zIXXp0sWyfcKECSileO6556wuXnx8vKXdeMKECTf1/CEhIXTr1o3t27cza9Ys4uPjGT16dLFVjKXBwcGBkSNHkpKSwsyZM63uO3DggKVG7WYVVCsX98VaEq1bt6Zz5878/PPPfP3118Xuc+jQoWKbiQobO3Ys7u7uzJ07t9i5UK5u+7///vuxt7fno48+4tSpU1b7vfrqq6SmpnL//fdbTUNRmh5//HHs7e156qmnih32nZOTU6RwLu1zXxJDhgzB29ubRYsWWfq9FJg1axZnzpyhV69eVsOzSxJ3wefpxRdftJpFPSMjgxdeeAGAiRMnlvh13Ejbtm05d+5ckXncZs6cSWRkZJH9V69eXWytTsH71tHRsVTjK+3P9Y3873//A6Bp06ZW/VQKarqunkcO8mtnFi1aVKoxFHb27NliE4ekpCSys7Otzvmjjz6KnZ0dM2bMKLY/z7Xm9ysNJSlzrveZcXBw4L777uPy5cu89tprVvedPn2aDz/8EHt7ex544AHL9oJas4ceeqjIXHcA6enpRT7PtsDOzo4nnniCCxcu8OSTT5KZmVlknwsXLnD06FHL315eXuh0ulL7nizJ+S6YRubll18mKyvLsj0xMbHI5/VmVag+Wjt27GD27NmWyQQLJjc7e/Ysv/76K5mZmQwePJjhw4dbHvPss8/y+++/s2LFCpo1a0b//v0t82hdunSJ559/vthOb9cyduxY1q9fz8svv2z5uyy9/fbbrFu3jnfeeYcdO3bQoUMHLly4wJIlS+jfvz/Lly+3NAHcSPv27XF2dmbWrFkkJCRY+oI88cQTJW4u+v777+nRowcTJ07kww8/pG3btnh6ehIdHc3Bgwc5fPgw27Ztw8/P77rH8fX15fvvv2f48OF06dKF/v3706RJE1JSUjh48CDR0dGWKubQ0FBmzZrFpEmTaNmypWUerY0bN7Jt2zbq169/w7nRbkf9+vX5+uuvmTBhAo0aNaJv377UrVuX3Nxczp07x6ZNm6hWrZpVodCzZ09+/PFHhg0bRr9+/XByciIkJMTqA17WXF1d+frrrxkxYgRdu3ZlxIgRBAcHs2fPHv744w/8/f357LPPrB7Ts2dP3n33XR566CHuvvtuXF1d8fT05PHHH7/m84wePZoVK1awZMkSGjVqxJAhQ9DpdCxfvpyzZ89yzz33cN9995XZ63z22WdZs2YNgwcPZuTIkXh7e7N161bOnj1Lt27divwqvffee3F0dKRTp06WOZ42bdrErl27aNmyZbGTIN+u0vxcF4iIiLDqW5SYmMjWrVvZs2cPTk5OzJkzx2r/8ePH89577/HWW29x4MABGjZsyIkTJ/j9998ZOnQoP/30U2m81GIdOHCAoUOH0qpVKxo3bkyNGjWIi4tjxYoV5ObmWs1b17BhQ+bOnct//vMfmjdvbplHKz4+nl27duHh4WGpmShtJSlzbvQ9+/bbb7Np0ybmzJnDrl276N69u2Vep7S0NObMmWN5Hsj/DL799tu8+OKL1KlTh/79+xMWFsbly5eJjIxk48aNdOrUidWrV5fJObgdr776KgcOHODTTz9l1apV9OjRg8DAQC5dusTJkyfZsmULb7zxBg0bNgTyv6Patm3L33//zf3330+dOnUsc6c1bdq0RDHc6vkeNWoUixcvZuXKlTRu3JjBgweTm5vL0qVLueOOOzh9+vStB3FLYxQ1du7cOTVnzhw1ZMgQVbduXcscGP7+/qpfv37qm2++sZrbo0BmZqZ64403VKNGjZSjo6NydXVVHTt2VN9//32RfW80vDQtLU25uLgoQDVu3PiasV5vGPi1hm0XN3Raqfy5usaMGaN8fX2Vo6OjatasmZo/f7768ccfFaBmzZp1zTgK+/3331W7du0sr4GrhroXTCWwfv36Io+73nlJTU1Vb7zxhmrZsqVycXFRjo6OKjQ0VPXv31999tlntzSPy+HDh9UDDzygatSooezt7ZWfn5/q0qWL+uyzz4rsu2bNGnXnnXcqT09P5eDgoMLDw9Vzzz1nNU9WgesNZb/eFAbXOycHDx5UY8eOVcHBwcrBwUF5eXmpRo0aqYcffrjINBJ5eXnqxRdfVGFhYcrOzu6mhwhf7/mvN4z8eu+1nTt3qiFDhihfX19lb2+vgoKC1H/+8x8VExNTbAzvv/++ql+/vmV+p6vfo9c6ryaTSX388ceqVatWysnJSTk5OamWLVuqOXPmFPsZvd75uNEUE8VZuXKlatWqlTIajcrb21uNHDlSRUREFHusTz75RA0ZMkSFhYUpJycn5eXlpZo3b67+7//+r8gwdlv8XF9regcHBwcVFhamJk6cqI4dO1bsY48cOaL69++vXF1dlYuLi+ratavasGFDqU3vUNzrVkqpqKgo9eKLL6oOHTqo6tWrKwcHBxUYGKj69u2rfvvtt2Ifs3XrVjVs2DBVrVo1ZW9vrwICAlSfPn3Ujz/+aNnnRt/ftzrNSknLnOt9zyqVP7XB888/r2rXrq0cHByUh4eH6tWrl1qzZs01Y9m0aZMaMWKECggIUPb29srX11c1a9ZMPfXUU2rXrl1W+17v3F/Pjc7f9T6n13pOs9msFi5cqHr06KG8vLyUvb29qlGjhurYsaN64403rOZBU0qpkydPqgEDBihvb2+l0+ms3lsl/azd6vnOzs5W06dPV2FhYcrBwUGFhISol156SWVlZZVoegedUjfR80/YpJdffpk333yT1atX06dPH63DEUKUAvlcC1G5SKJVAZw/f94yh0mBQ4cO0aFDB4xGI9HR0aXej0QIUbbkcy1E1VCh+mhVVa1bt6Z27do0btwYFxcXTp48ya+//orZbOaLL76QL2MhKiD5XAtRNUiNVgUwY8YMVq5cSUREBCkpKXh4eNC+fXueffZZm5urSQhxc+RzLUTVIImWEEIIIUQZqVDzaAkhhBBCVCSSaAkhhBBClBFJtIQQQgghyogkWkIIIYQQZUQSretYunQpTzzxBJ07d8bd3R2dTsf9999fasf/888/eeaZZ+jZsyfe3t7odLobLgf01Vdf8cgjj9C2bVucnZ3R6XS88sorpRaTEEIIIUqPzKN1HTNnzuTAgQO4urpSs2bNYhc0vR0ff/wxK1aswNHRkdq1axe7unhhzzzzDCkpKXh5eVGjRo2SrbskhBBCiHIhNVrX8cEHH3DixAlSU1P55JNPSv34//3vfzl8+DCXL19m1apVN/WYH374gYiICBITE6UmSwghhLBxkmhdR/fu3alTpw46ne6mH7No0SK6d++Ol5cXjo6ONGjQgJkzZ5KdnV1k3/bt29OoUSMMBsNNH79v376EhITc9P5CCCGE0I4kWqVo4sSJjB49mtOnT3P33XczadIkvL29efXVV+nbty+5ublahyiEEEKIciR9tErJ/Pnz+frrrxk+fDjffPON1Tpl06ZNY/r06Xz88cdMmTJFuyCFEEIIUa6kRquUzJ49G3t7+2IXg3311Vfx8fHhu+++0yg6IYQQQmhBarRKQUZGBgcOHMDX15dZs2YVu4/RaCz1UYtCCCGEsG2SaJWCpKQklFLExcUxffp0rcMRQgghhI2QpsNS4OHhAUCLFi1QSl33JoQQQoiqQxKtUuDq6kqjRo04cuQIiYmJWocjhBBCCBshiVYpefrpp8nJyWHChAkkJycXuT8pKYm9e/eWf2BCCCGE0Iz00bqO5cuXs3z5cgBiY2MB2LZtG+PGjQPA19eX9957D4AJEyawZ88e5s6dS3h4OH369CE4OJjExETOnj3L33//zfjx4/n0008tx9+8eTNffvklAJcvXwbg5MmTluND/rQRV/vyyy/ZvHkzAKdOnQJg1apVREdHA1C/fn1eeOGF0jsJQgghhCgxnZKOQ9dUMP/VtYSEhBAREWG17ZdffuHTTz9l586dJCcn4+3tTXBwML179+b++++nfv36ln3nz5/P+PHjrxtD4cszbtw4FixYcM39u3btyoYNG657TCGEEEKUD0m0hBBCCCHKiPTREkIIIYQoI5JoCSGEEEKUEekMX4jZbOb8+fO4ubmh0+m0DkcIIYQQN0EpRVpaGjVq1ECvt516JEm0Cjl//jxBQUFahyGEEEKIEoiKiqJmzZpah2EhiVYhbm5uQP6Fcnd31zgaIYQQQtyM1NRUgoKCLOW4rZBEq5CC5kJ3d3dJtIQQQogKxta6/dhOI6YQQgghRCUjiZYQQgghRBmRREsIIYQQooxIoiWEEEIIUUYk0RJCCCGEKCOSaAkhhBBClBFJtIQQQgghyogkWkIIIYQQZUQSLSGEEEKIMiKJlhBCCCFEGZFESwghhBCijEiiJYQQQghRRmRRaSFEhaWUIsdkJjvPTE5e/r/Zuab8f/PMmMyqYE+UAgX5/6r87Qa9DnuDHnuDHge7f/9vb9DjYNBjtNdjtNPb3CK1QoiKQxItIYSmzGZFcmYuCZezib+cQ0J6NonpOSRcziEtK4+0rNz8f7Ov/Hvldjk7l6xcc5nHZ9DrcHEw4Gq0w8VyM+DiYIeboz1ezvZ4uTjg7eKAl3P+v94u9ng5O+Dp7IBBf40kLSUGEk+Ddzh4BJb56xBCaEMSLSFEmUnPzuNCSiYXUrK4kJzF+ZRMy7+XUrMtSZWl4uk2Ge30ONjpMdoZMNrpMeh1FFRG6QCdTofuyh86wKwgJ89MrqngpsjJM5Nj+jeBM5kVqVl5pGbl3XI8Oh34uhoJ8HCkursj/u6O+Hs40jb5V1odmIYOM0qnRzdwNrQcUxqnQAhhYyTREkKUmFKKS2nZRMSnE5mQQUTCv/9GJWbcUnLi6WyPj4sDPi5GfFwd8HJxwN3RHjdHO9wd82uP3BztcDX++39He4Olec/BUHpNfEop8syKrFwT6dkmLmfnkZGTx+XsPNKzTaRn5/8/LSuP5IwcEtNzSLL8m0tieg4pmbkoBXFp2cSlZQMpAPiTwH+MU9Hp8rNLnTJjWjmZR7d64OoXQrC3s9WtmptRmi6FqMAk0RJC3FCuyUxEfDonLl7mxMU0TlxM40xcOpGJ6TdsvnMz2hHg6UiAhxM1rvwb4JFfs+PreiWpcnbA3mA7Y3N0Oh32hvw+W26O9iU6Rp7JTGJGDpdSs4lNySI2NYuLqVm4nL+EIcK6Cs+AmdTzJ/gjuuhXspvRjlp+rtTxc6W2nyu1q+X/G+TtfO1mSSGEzdCpgl6hAoDU1FQ8PDxISUnB3d1d63CEKHtX9RVS7jWITc3icEwq/1xI5fjFNE5eTONsfDq5puK/Kgx6HTW9nAjxcSHUJ78WJtTHhWAfZwI8HEucqFRaKTEwqzGofxNUpTOwts9fnMhyJyoxg3NXbueTs67q0G/NwU5PLV8XGga407BG/q1RgAceznK+RdVkq+W3JFqF2OqFEqK0KaVI2vwVXmufQ4cZM3re0D/CVxmdi93fxcFAnepu1K3uSt3qboT7uRLm40Kgl5NN1UZVCHsXwqopoEygM8DAWcX20crJMxOZkM7JS5c5deV28tJlzsRdJjuv+JrEQE8nGhUkXjU8aBbkgZ+bY9m+HiFsgK2W35JoFWKrF0qI25WenceBqGT2RCax51wSF86d5jfzoxh0/34F5Ck9XXM/xM0vhIYB7tTzd6NudTfqVHcl0NNJ+gqVppQYSDwD3rVuedShyayIScrkxMU0jl5I5ej5VI5cSCEqMbPY/Wt6OdEi2IvmQZ60CPakUQ13jHaG0ngVQtgMWy2/JdEqxFYvlBC3QilFdFIme88l5SdWkUn8cyHVanRfe/0RFjm8UeSxOfevxKF213KMVpSWlMxc/ilIvM6ncjgmhROX0ij8Le9g0NOwhjstg71oW8ubNqHeeLk4aBO0EKXEVstvSbQKsdULJcSNXEjJZOupBLadSWDb6QRikovWbgR6OtEyxItWwZ608cmiweIO6K7qK4TOAFMOybxOlUhaVi6HolPYF5XMvnNJ7DuXTEJ6TpH96vu70a6WD+1qedMmzAdvSbxEBWOr5bckWoXY6oUSorD4y9lsO53A1tMJbDsdT0RChtX9dnodjQI9aBXsRasQL1qGeBLg4WR9kJvsKyQqD6UUUYn5tZ27IxPZcSaRk5cuF9mvXnU32of70LVuNdrW8sbZQQapC9tmq+W3JFqF2OqFEsJkVuyPSmbD8UtsOB7HoZgUq/v1OmgS6EH7cF/ah/vQOsQLF+NNFI630VdIVA7xl7PZeTaR7WcS2HEmkeMX06zudzDouSPMiy51qtGlbjXq+7tJfz1hc2y1/JZEqxBbvVCiaoq/nM3fJ+JYfzyOTSfjSM7Itbq/QYA7HcJ9aF/Lhza1vHGXqRREKUhMz2HHmQQ2nYrn7xNxRCdZN0P7uRnpUrcaPev70aVutZtL6IUoY7ZafkuiVYitXihRdZyNT2fNkVjWHIllf1SyVUdmd0c7OtetRvd6fnSp6yvD9kWZU0pxNj6dv0/EsfFEHNvPJJKZa7Lc72Cnp2O4D3c29KdXAz/83OU9KbRhq+W3JFqF2OqFEpWXUooj51P540gsa45cLNJs06iGO93r+dGtXjWaB3liJ3NWCQ1l55nYHZHE+mOX+POfi0QW6hvYPMiTOxtWp29jf8KruWoUpaiKbLX8lkSrEFu9UKJyUUpxKCaFlfvPs/pIrFXTjJ1eR/twH3o38qd3w+pUlxoCYaOUUpy8dJk/j17kj6MXORCVbHV/fX83BjarwcCmNQj2cdYmSFFl2Gr5LYlWIbZ6oUTlcOpSGiv3n2flgfNWowQd7fV0rVuNPo386Vm/uiyjIiqki6lZ/PXPRf44cpEtp+LJu2ritqY1PRjQNIC7mtYg0NPpOkcRomRstfyWRKsQW71QouI6n5zJqgPnWbH/PEcvpFq2O9rr6dWgOgOa1qBr3Wo4OchM3aLySErPYc2RWH45eIGtp+OtJsttFeLFsJaBDGhaAw8n+VEhSoetlt+SaBViqxdKVCxZuSbWHIllye4otpxKsGy30+voUrcag5rV4M6G1WW0lqgS4i9n8/vhWH45cJ6dEYmWAR4Odnp6N6zO8FY16VynGga9TBkhSs5Wy29JtAqx1QslbF9Bv6slu6NYsf88aVl5lvvahnkzqHkN+jcOkKVORJUWm5LFygMxLN0TzYmL/06U6udmZGjLQIa3rEmd6m4aRigqKlstvyXRKsRWL5SwXUnpOfy8L4Yfd0dxLPbfEYOBnk6MaF2Tu1vWJMhbOgILcTWlFIdjUvlpbzTL98dYzRF3R6gX97UNoW9jfxztpUld3BxbLb8l0SrEVi+UsD0HopL5Znskqw6cJzsvf71Ao52evo39uad1EO1r+aCXphAhbignz8y6Y5dYuiea9ccvYbrSocvL2Z4RrYMY1SaYMF8XjaMUts5Wy29JtAqx1QslbENWrolVB87z7fZIDkT/uwROwwB3RrcNZmAz6dwrxO24mJrF4l1R/LDzHOdTsizbO9X25b62wdzZsLrMJSeKZavltyRahdjqhRLaik7K4JttkSzeHWVp4nAw6LmraQAPtA+hRZCnrP0mRCkymRUbjl/iux3nWH/8kqUDfaCnE2M7hDDyjmD5USOs2Gr5LYlWIbZ6oYQ2DkYn88Wms/x26IKlOSPQ04n72gUzsnUQPq5GjSMUovKLSszgh13n+GFnFAnpOQA4Oxi4p3UQ4zuGEuIjzYrCdstvSbQKsdULJcqP2axYd+wSX2w6w46ziZbtHWv7ML5DGN3r+8kwdCE0kJVrYsX+GL7afNYyYlGng14NqvNgpzDahHlLzXIVZqvltyRahdjqhRJlLzvPxM97Y/hi0xnOxKUD+fNeDWpWg4mdw2hUw0PjCIUQkD9icfOpeL7afJYNx+Ms21uFeDGpezjd6/lJwlUF2Wr5XSkTrYSEBJYtW8avv/7KoUOHiImJwcHBgSZNmjB+/HjGjx+PXl98Z0pbvVCi7GTlmli08xyfbTxDbGp+51s3ox2j2wUzrkMoAR6yXIgQturUpTS+3hLB0j3R5FwZ/dsgwJ3HuoXTv0mA1D5XIbZaflfKROvTTz/l0Ucfxd/fnx49ehAcHMzFixf5+eefSUlJYdiwYSxdurTYXzy2eqFE6UvPzuO7HZF8/vdZ4i9nA+Dv7siDncMYeUcQbo7S0VaIiuJSWhZfbTrLt9sjSc8xARDm68KjXcMZ0iIQBzsZqVjZ2Wr5XSkTrXXr1pGWlsaAAQMwGP6d7C42NpY2bdoQFRXFjz/+yPDhw4s81lYvlCgFKTGQeJrLLiEsOJLLl5vOkHRlBGGgpxOPdgtnROuaGO1kgkQhKqrkjBwWbI1k3tazlhHCgZ5OTO5Zh2EtA2VqiErMVsvvSploXc+bb77Jyy+/zKRJk5gzZ06R+231QonbtHchatVkdMqMCR0v5j7IElN3Qn2ceax7bYa2CMRevoCFqDTSs/P4fsc5Pt90hri0/BrrUB9npvSqy8BmNaRJsRKy1fK7ypUsDg7568zZ20uzUFWRmxSFWpmfZAEYULxl/xWfDvLnr6e7ck/rIEmyhKhkXIx2PNSlFpue784rdzXA28WBiIQMpizeT99Zf/P7oQuYzVWqnkFopEqVLnl5eSxYsACAvn37Xnff1NRUq1t2dnZ5hChKkdmsWLE/huc+W4YOs9V9Bsz0DciQZgQhKjlHewMPds5PuJ7rUw93RztOXrrMo9/tZeCczWw6GXfjgwhxG6pUKfPCCy9w+PBh+vXrR58+fa67b1BQEB4eHpbbW2+9VU5RitKw6WQc/T/cxOQf9rM92RMThZoJdAbwrqVNcEKIcuditGNS99ps+m8PnuxZB1ejHUfOp/LAVzsZ+/VOjl+1ILwQpanK9NGaNWsWTz31FPXq1WPz5s34+voWu19BG29UVJRVG6/RaMRolFnAbd2pS2m88es/rL8yt46box2PdKnFQ65bMP7+NChTfpI1cBa0HKNtsEIIzSSm5zBn3Sm+2R5Brkmh18E9rYN4+s66+Lk7ah2eKAFb7aNVJRKt2bNnM2XKFBo0aMC6devw9/e/5r62eqHE9SWm5zD7rxN8u+McJrPCTq9jTPtQnuxZG0/n/H55+aMOz+TXZHkEahuwEMImRMSn886aY/x2KBbIX9rn4S61eLhLLZwd7DSOTtwKWy2/K32i9d577/Hcc8/RuHFj1q5di5+f33X3t9ULJYqXk2dm4bYIPlx7ktSsPCB/OY6X+tenVjVXjaMTQlQUeyITmfnrP+w7lwxADQ9HXhnQkH6N/WWW+QrCVsvvSp1ovfXWW7z00ks0b96cP//885rNhVez1Qslitp6Kp5XVxzm9JXlcur7u/HagIZ0qH3j6yyEEIUppfjtUCxv/f4P0UmZAHSq7cu0QQ2p7eemcXTiRmy1/K60idbrr7/Oa6+9RqtWrfjjjz/w9va+qcfZ6oUS/7qUlsWbv/7D8v3nAfBxceC5PvUY0TpI5sYRQty2rFwTn2w4zScbT5OTZ8ZOr2NCpzBLJ3phm2y1/K6UidaCBQsYN24cBoOBJ554Ag+PoosBh4aGMm7cuCLbbfVCCcgzmfl2eyTv/3GCtOw8dDq4v20Iz/auh4ezzIsmhChd5xIymPHLUf765yIAfm5GXh3QkAFNA6Q50QbZavldKROtadOmMX369Ovu07VrVzZs2FBku61eqKruQFQyLy07xJHzqQA0q+nB60Ma07Smp7aBCSEqvfXHLjF91REiEjIA6FHfj9eHNCbQUxactyW2Wn5XykTrdtjqhaqqMnNMfPDXCb7cdAazAndHO57vW59RbYKlmVAIUW6y80x8uuEMH68/RY7JjIuDgef61OOBRvYYks6Ad7iMZtaYrZbf0tgsbNb2Mwm88NNBy6/Iwc1r8OqAhvi6ynxmQojyZbQzMLlXHe5q6s8LPx1id2QSR3/7GN2fXwIKdHoYOFvm5xNFSI1WIbaaEVclaVm5vP37Mb7bcQ4Af3dH3hzWmB71q2scmRBC5C/vtfzvnQxe3weD7t8iVOkM6KYckpotjdhq+S01WsKmbDoZx3+XHuR8ShYAo9oE82L/+rg7Smd3IYRt0Ot1DAvJBp11PYVOmYg5c5jAFpJoiX9JoiVsQlauibd/P8b8rREABHs78/bdTegQLnNiCSFskHd4fnOh+nfB+jylZ9RPcYxNP8v4DqHopR+poIotKi1s0+GYFAZ+tNmSZD3QLoTVUzpLkiWEsF0egfl9snQGIL/ZcL7PFM7lefH6L0cZ/eV2ohIzNA5S2ALpo1WIrbbxVkYms+Kzv0/zwZ8nyDUpqrkZeWd4U7rXu/4ySUIIYTOuWkNVudfg+53nmPnLP2TmmnA12jFzSGOGSFNiubDV8lsSrUJs9UJVNueTM5nyw352RiQC0KdRdd4a1hRvFweNIxNCiNsTmZDOM0sOsDsyCYDhrWoyfVAjXGRW+TJlq+W3JFqF2OqFqkzWH7vE00v2k5SRi4uDgamDGjGiVU2ZaVkIUWmYzIqP1p3kw7UnMSuoVc2Fj0a1oFGNoiuViNJhq+W3JFqF2OqFqgxyTWbe++M4n208A0DjQHc+Ht2SEB8XjSMTQoiysf1MAlN+2E9sahYOdnpe7t+AMe1D5IdlGbDV8ls6w4tycT45k3s/325JssZ1COWnRztIkiWEqNTa1fLht8md6Vnfj5w8M1NXHuHRb/eSlpWrdWiinEiNViG2mhFXZBuOX2LK4v0kZ+TiZrTjneFN6dckQOuwhBCi3CilmL81grd+O0aOyUytai58dn8r6lR30zq0SsNWy2+p0RJlRinFx+tPMX7+LpIzcmkS6MEvT3aSJEsIUeXodDrGdwxjyX/aE+DhyJm4dAZ/vIVfD17QOjRRxiTREmUiPTuPSd/v5d01x1EKRrUJYumj7aWpUAhRpTUP8mTVE51oX8uHjBwTk77fy5u//UOeyXzjB4sKSRItUeoiE9IZNncrvx2Kxd6g482hTXhrWFOMdgatQxNCCM35uhr5ZmIbHulSC4DP/z7DA1/tJCk9R+PIRFmQREuUqk0n4xg0ZwvHL6ZRzc3IDw+3Y3TbYK3DEkIIm2Jn0PNi/wbMva8lLg4Gtp1JYMjcLZy6dFnr0EQpk0RLlJrvdkQybt4uUjJzaR7kyS9PdKJViLfWYQkhhM3q3ySAnx/rSKCnE5EJGQydu4XNJ+O1DkuUIkm0xG0zmxVv/vYPLy87jMmsuLtlTRY/0o7q7o5ahyaEEDavnr8bKx7vSKsQL9Ky8hg7byffbo/UOixRSiTRErclM8fEY9/t5fO/8+fHerZ3Xd4bIf2xhBDiVvi6GvnuwbYMbRGIyax4Zflhpq08gsksMzBVdJJoiRK7lJbFvZ9vY/WRWBwMembf25zHe9SRGY+FEKIEHO0N/O+eZjzXpx4A87dGMOm7vWTlmjSOTNwOSbREiUTE548sPBCdgpezPd891JbBzWWFeiGEuB06nY5J3WszZ3QLHAx6Vh+JZczXO0nJlJnkKypJtMQtOxyTwvBPtxKdlEmojzPLHuvIHaHS6V0IIUrLgKY1mD/hDtyMduw8m8g9n24jNiVL67BECUiiJW7J9jMJjPp8O/GXc2hUw50f/9OBUF+ZhFQIIUpbh3BfFj/SHj83I8cvpjFs7hZOXUrTOixxiyTREjftz6MXGfP1TtKy82gb5s2ih9tRzc2odVhCCFFpNazhzk+PdqBWNRfOp2Qx4tNtHI5J0ToscQsk0RI35ee90fzn2z3k5Jm5s2F1Fkxog7ujvdZhCSFEpRfk7czS/3SgWZAnSRm5jPpiO3vPJWkdlrhJkmiJ60uJYf3vP/Huj+swmRXDW9Xkk/ta4mgv0zcIIUR58XZx4NuJbbgjNH+urQe+3MH2MwlahyVugiRa4tr2LkR90JjuOyaw2eFJZtU9yLvDm2JnkLeNEEKUNzdHexZMaEPH2j6k55gYN28nf5+I0zoscQNSYoripcRgXjkZHfkryht0isFR76JLPa9xYEIIUXU5O9jx1dg76F6vGlm5Zh5csJt1xy5qHZa4Dkm0RLHWbNqC/kqSVUCnTJB4RqOIhBBCQP7Epp890Jq+jfzJMZn5z7d72XRSarZslSRaoojvdkQydXMWJlVohnedAbxraROUEEIICwc7PR+NbkHvhtXJyTPz0MLd0mfLRkmiJaws3xfDK8sPE4sPq2u9iNJd6fSuM8DAWeAhs78LIYQtsDfkJ1sFzYgT5u9iT6SMRrQ1OqWUrFh5ldTUVDw8PEhJScHd3V3rcMrVH0diefS7vZjMigfahTBjcKP8PlmJZ/JrsiTJEkIIm5OVa+LBBbvZfCoeN6Md3z3UlqY1PbUOq9zZavktNVoCgM0n43n8+32YzIphLQKZPqhR/uLQHoEQ1lmSLCGEsFGO9gY+H9OKNmHepGXnMebrnZy6dFnrsMQVkmgJ9p5L4qGFu8kxmenTqDrvDG+KXq+78QOFEELYBGcHO74edwfNgjxJzshl7Nc7ZW1EGyGJVhV3Ju4yE+fvIjPXROc6vnw4qoXMkyWEEBWQq9GOeePuoJavCzHJmYz9eicpmblah1XlSYlahcVfzmbcvF0kZeTStKYHnz3QCqOdzPguhBAVlbeLAwsmtLEsRP3Qwt1k5Zq0DqtKk0SrisrIyWPi/F2cS8wg2NuZr8begbODndZhCSGEuE1B3s4smNAGN6MdO88mMuWH/ZjMMu5NK5JoVUF5JjNPfL+PA9EpeDnbM3/8HVRzM2odlhBCiFLSIMCdz8e0xsGgZ/WRWN5ZfUzrkKosSbSqoNd/OcraY5cw2un5cmxralVz1TokIYQQpax9uA/vjmgKwGd/n2HJ7iiNI6qaJNGqYr7fcY4F2yIBmDWyOa1CvDWOSAghRFkZ3DyQJ3vWAeDlZYfYIbPHlztJtKqQnWcTeW3FYQCe7V2Xfk0CNI5ICCFEWZvSsw53NQkg16T4z7d7iExI1zqkKkUSrSoiOimDR7/dQ55ZcVfTACZ1r611SEIIIcqBXq/jvRHNaFrTg6SMXCYu2M3l7Dytw6oyJNGqAjJy8nh44R4S0nNoVMOdd4c3zZ/1XQghRJXg5GDgizGtqe5u5NSlyzy/9ACyAl/5kESrklNK8dLPhzh6IRVfVwc+H9NapnEQQogqqLq7I3Pva4W9Qcdvh2L5ctNZrUOqEiTRquQW7Yxi+f7zGPQ65t7XikBPJ61DEkIIoZFWIV68OqAhAG+vPiad48uBJFqV2OGYFKatOgLA833q0SZMRhgKIURV90C7EIa2CMRkVkz6fh8XU2VNxLIkiVZllBJD+vF1TP3mD3LyzPRq4MdDnWtpHZUQQggboNPpeHNoE+r7uxF/OZsnvt8nM8eXIUm0Kpu9C1GzGuOyaChLMh/iEbctvD+iOXq9dH4XQgiRz8nBwKf3t8LVaMfOiETmrDuldUiVliRalUlKDKyajE6ZATDoFC/kfYpH7iWNAxNCCGFrQn1deH1IIwBmrz3B7ohEjSOqnCTRqkwST8OVJKuATpkg8YxGAQkhhLBlQ1vUZGiLQMwKJv+wn5TMXK1DqnQk0apEcj3DMFOoiVBnAG/pnyWEEKJ4MwY3ItjbmZjkTF5edkjm1yplkmhVIh/tzuSF3AcxFVxWnQEGzgKPQE3jEkIIYbvcHO2ZfW9zDHodvxy8wIr957UOqVKRRKuS2HsuiY/Xn2KJqTvr+q6Fsb/AlEPQcozWoQkhhLBxLYK9mHxl8empK49wKU2mfCgtkmhVAlm5Jp798QAms2JI8xrc2a4lhHWWmiwhhBA37dFu4TSq4U5KZi4vLzssTYilRBKtSmDOulOciUunmpuR6YMaax2OEEKICsjeoOe9Ec2wN+j48+hFVh6QJsTSUCkTraVLl/LEE0/QuXNn3N3d0el03H///VqHVSaOnE/h042nAXh9cGM8nO01jkgIIURF1SDAnSd6SBNiaaqUidbMmTOZM2cO+/fvJzCw8jaf5ZnM/Peng+SZFf0a+9O3sb/WIQkhhKjgCpoQkzNymb7qqNbhVHiVMtH64IMPOHHiBKmpqXzyySdah1Nmvtp8lsMxqbg72jF9cCOtwxFCCFEJ2Bv0/N/dTdHr4NeDF9h0Mk7rkCq0Splode/enTp16qDTVd5lZ84nZzLrr5MAvDKgIX5ujhpHJIQQorJoHOjBmPahALy6/DBZuSZtA6rAKmWiVRpSU1OtbtnZ2VqHZOWN3/4hM9fEHaFejGhVU+twhBBCVDLP9K6Ln5uRiIQMPtsoK4yUlCRa1xAUFISHh4fl9tZbb2kdksXWU/H8evACeh1MH9S4UtfcCSGE0Iaboz2vDmgIwMcbThERn65xRBWTndYB2KqoqCjc3d0tfxuNRg2j+VeuyczUlUcAeKBdCA1ruN/gEUIIIUTJDGgawOJdUWw+Fc/MX//hy7GttQ6pwpEarWtwd3e3utlKorVgawQnL13G28WBp++sp3U4QgghKjGdTse0QY0w6HX89c9Ftp6O1zqkCkcSrQokOSOHD9fmd4B/vk89mTNLCCFEmavt58p9bYMBmPnLP5jMMmP8rZBEqwKZu+E0qVl51Pd3Y0TrIK3DEUIIUUVM7lkHN6MdRy+k8vPeaK3DqVAk0aogYpIzmb81AoD/9q2PQS8d4IUQQpQPH1cjj/eoDcB7fxwnIydP44gqDkm0KoKUGFYsW4R3XhztannTrV41rSMSQghRxYztEEpNLycupmYzb0uE1uFUGJVy1OHy5ctZvnw5ALGxsQBs27aNcePGAeDr68t7772nUXS3aO9C1KrJPKbMPGLUcb7W2+h07bWOSgghRBXjaG/g6Tvr8vSSA3z+9xkeaB+Cu6P0Fb4RnVKq0vVqmzZtGtOnT7/m/SEhIURERBR7X2pqKh4eHqSkpFhN76CJlBiY1RiU+d9tOgNMOQQelXcNRyGEELbJZFb0/mAjp+PSeapXXSb3qqN1SBY2VX5fpVI2HU6bNg2l1DVv10qybE7iaeskC0CZIFFm6BVCCFH+DHodU3rVBeDLzWdIycjVOCLbVykTrUrDOxxz4UukM4B3LW3iEUIIUeXd1SSA+v5upGXl8eVm+eF/I5Jo2bDjme68kDuRPHXlMukMMHCWNBsKIYTQjP6qWq15WyJIyZRareuplJ3hK4uP1p3kF1N37Or04s2uLvk1WZJkCSGE0FifRtWpV92N4xfT+H7HOR7tFq51SDZLarRs1LmEDH47dAGA+3t3gLDOkmQJIYSwCTqdjoe75Hdj+XrLWbJyTRpHZLsk0bJR87aexaygS91qsnC0EEIImzOwWQ0CPByJS8tm+b4YrcOxWZJo2aCUzFyW7IoC4KHOYRpHI4QQQhTlYKdnYqf8Murzv8/IGojXIImWDVq86xzpOSbqVXejU21frcMRQgghinVvm2DcHe04E5/OumOXtA7HJkmiZWNyTWbmX1naYGLnMHQ6WdNQCCGEbXI12jGqTTAA32yP1Dga2ySJlo1Z+89Fzqdk4evqwKBmNbQORwghhLiu0W2D0eng7xNxRMSnax2OzZFEy8Z8vzO/b9Y9rYNwtDdoHI0QQghxfSE+LnStWw2A73ZIrVZhkmjZkKjEDDadjAPg3juCNY5GCCGEuDkPtAsBYMnuaJnqoRBJtGzI4l1RKAWd6/gS7OOsdThCCCHETelWz49ATydSMnP55eAFrcOxKZJo2Yhck5nFu/ObDUe3kdosIYQQFYdBr+PeO4IA+HlvtMbR2BZJtGzEjv2HqJ2+l4YuafRsUF3rcIQQQohbMqRF/uol284kEJOcqXE0tkMSLVuwdyEdVnVjkcMb/GJ6FIeD32odkRBCCHFLgrydaVfLG6WQmeKvIomW1lJiUKsmo8cMkP/vqimQIm9SIYQQFcuwljUB+GlvNErJTPEgiZb2Ek+jU2brbcoEiWe0iUcIIYQooX6N/XG013MmLp2D0Slah2MTJNHSmnc45sKXQWcA71raxCOEEEKUkJujPb2u9DP+7bCMPgRJtDSXbF+Nl/IeJE9duRQ6AwycBR6BmsYlhBBClES/xgEArD4cK82HgJ3WAVR1645d4oe8bkR7t+fbodXya7IkyRJCCFFBdatXDaOdnsiEDP65kEbDGu5ah6QpqdHS2J9HLwLQonEjCOssSZYQQogKzcVoZ1mSZ/WRWI2j0Z4kWhrKSjhH5on1+JPAnQ1l7iwhhBCVQ9/G/gCsln5a0nSomb0LMa6czHy9GZOjDv1FBTXHah2VEEIIcdt6NqiOQa/jxMXLRCdlUNOr6i4rJzVaWkiJgVWT0V2ZO8uAQvfLUzJ3lhBCiErBw8meFkGeAPx9Il7bYDQmiZYWEk+DzJ0lhBCiEutypZ/W3yfiNI5EW5JoacE7HKWTubOEEEJUXgWJ1pZT8eSazDfYu/KSREsLHoHsajxV5s4SQghRaTUJ9MDT2Z607Dz2RyVrHY5mJNHSyDc5XemUPZsljT+FKYeg5RitQxJCCCFKjUGvo2NtXwC2nkrQOBrtSKKlAaUUW0/FE4sPIS17S02WEEKISqltmDcAuyMTNY5EO5JoaSAiIYOE9BwcDHqaB3tqHY4QQghRJlqH5CdaeyOTyKui/bQk0dLA3sgkABoHumO0M2gcjRBCCFE26vm74Wa0Iz3HxLHYNK3D0YQkWhrYF5WfaLUM9tI4EiGEEKLsGPQ6WoXml3W7Iqpm86HMDK+ByLOnaK8/SYdqNbQOpUozmUzk5uZqHYYQoozZ2dlhMBjQ6XRah1IltQ7xYsPxOPZEJjG+Y5jW4ZQ7SbTKWfbO+cxPnoLBQaFWvwX2s2XEYTlTShEbG0tycrLWoQghyonBYMDPzw8PDw9JuMpZ40APAI5eSNU4Em1IolWeUmJw+P0pdDoFgE6ZYdUUCO8pIw/LUUGS5efnh7Ozs3zpClGJKaXIy8sjNTWVCxcukJmZSUBAgNZhVSmNauQnWmfj00nPzsPFWLVSj5t6tRMmTLjtJxoyZAiDBg267eNUaImn85OrqxUsvSOJVrkwmUyWJMvHx0frcIQQ5cTNzQ2j0Uh8fDx+fn4YDDIQqbxUczPi52bkUlo2x2JTaXVlJGJVcVOJ1vz582/rSXQ6HaGhoZJoeYdjRo+eq5ItWXqnXBX0yXJ2rroryQtRVbm4uBAXF0dubq4kWuWsUQ13Lh2P48h5SbSuacqUKUyePPmWn0ApRa1akkgA4BHIZx5P8lDyh9jpzLL0joakuVCIqkc+99ppVMOD9cfjOHq+6vXTuulEy9PTk5CQkLKMpdJTSvFJSgcWZIfzw/DqhNZpLEmWEEKISq9OdVcAzsSlaxxJ+bupROvdd9+lY8eOJX6S2318ZRF3OZvUrDwu63wIaN4LZLJSIYQQVUAt3yuJVnzVS7RuasLSZ555hnbt2pX4SW738ZXFuYQMAAI8nGRGeFEm5s+fj06ns9zs7OwICAjg3nvv5eTJkyU65tq1a2ndujUuLi7odDqWL19eukELISq9UN/8frHxl7NJzapa8xdWrTGWGrsYfYb2+iP4eDbQOhRRyc2bN4/69euTlZXFli1beOONN1i/fj3Hjh3Dy+vmVyRQSnHPPfdQt25dVq5ciYuLC/Xq1SvDyIUQlZGboz3V3IzEpWUTEZ9O05qeWodUbiTRKi97F9Lvr8nc5WDGHKuHvTJRqSg7jRs3pnXr1gB069YNk8nE1KlTWb58OePHj7/p45w/f57ExESGDh1Kz549SyW23NxcS22bEKLqCPN1IS4tmzNxVSvRKvFah9HR0TzzzDP07NmTevXqUatWrSK38PDw0oy14kqJgVWTLdM66LkyUWlKjLZxiSqjIOm6ePGiZdvu3bsZNGgQ3t7eODo60qJFC5YsWWK5f9q0adSsWROA//73v5ZpWgqcPHmS0aNH4+fnh9FopEGDBnz88cdWz7thwwZ0Oh3ffPMNzzzzDIGBgRiNRk6dOgXAX3/9Rc+ePXF3d8fZ2ZmOHTuydu1aq2NMmzYNnU7HkSNHGDVqFB4eHlSvXp0JEyaQkpJita/ZbOajjz6iefPmODk54enpSbt27Vi5cqXVfosXL6Z9+/a4uLjg6upKnz592LdvXwnPrhDiZgR55TcfxiRnahxJ+SrRT8qNGzfSr18/srKysLe3x8/Pr9hfp0qp2w6wUkg8DTJRqU1TSpGZa9I6DAsn+9Jdl+3s2bMA1K1bF4D169fTt29f2rZty6effoqHhwc//PADI0eOJCMjg3HjxvHggw/SrFkzhg0bxhNPPMHo0aMxGo0AHD16lA4dOhAcHMz777+Pv78/a9as4cknnyQ+Pp6pU6daPf+LL75I+/bt+fTTT9Hr9fj5+fHtt98yZswYBg8ezIIFC7C3t+ezzz6jT58+rFmzpkgN2t13383IkSOZOHEihw4d4sUXXwTg66+/tuwzbtw4vv32WyZOnMiMGTNwcHBg7969REREWPZ58803eeWVVxg/fjyvvPIKOTk5vPvuu3Tu3JmdO3fSsGHDUjvvQoh/+Xvkf39cTM3SOJLyVaJE67nnnsNkMvHdd98xcuRI9PoSV4xVDd7hoNNbJ1syUalNycw10fC1NVqHYXF0Rh+cHUretGYymcjLy7P00Zo5cyZdunSxTBr82GOP0ahRI9atW2f5kdSnTx/i4+N56aWXGDNmDDVr1iQvLw+A4OBgqwEtTz/9NG5ubmzevBl3d3cA7rzzTrKzs3n77bd58sknrfqChYeH8+OPP1r+zsjIYPLkyQwYMIBly5ZZtvfv35+WLVvy0ksvsWPHDqvXNHHiRJ577jkAevXqxalTp/j666/56quv0Ol0bNq0iW+++YaXX36ZmTNnWh7Xt29fy/+joqKYOnUqjz/+OB9++KFl+5133kmdOnWYPn06ixcvLuFZF0Jcj7+7IwCxKVUr0SpRhnTo0CFGjx7NqFGjJMm6GR6BMHA2JpV/rpRMVCrKWLt27bC3t8fNzY2+ffvi5eXFihUrsLOz49SpUxw7doz77rsPgLy8PMutf//+XLhwgePHj1/z2FlZWaxdu5ahQ4fi7Oxc5PFZWVls377d6jF333231d9bt24lMTGRsWPHWj3ebDbTt29fdu3aRXq69TDwwitLNG3alKysLC5dugTA77//DsCkSZOuGfuaNWvIy8tjzJgxVs/r6OhI165d2bBhw/VPrBCixKpfSbSkRusmeHl53dLIJQGXG42m1xII1V/k66fuwbmaTP5qS5zsDRyd0UfrMCyc7G9v+o+FCxfSoEED0tLSWLx4MZ999hmjRo3i999/t/TTevbZZ3n22WeLfXx8fPw1j52QkEBeXh4fffQRH3300U09vvAivgUxDB8+/JrPk5iYiIuLi+XvwmtTFjRjZmbm9/eIi4vDYDDg7+9/zWMWPO8dd9xR7P3yw1GIsuPv4Yg/CQQmn4CUsCpT2VCiRKtfv35s3LixtGOp1OLSsgFwstPdVpOQKBs6XeW6Lg0aNLB0gO/evTsmk4kvv/ySpUuX0qRJEyC/39SwYcOKffz1pnDw8vLCYDDwwAMPXLP2KCwszOrvwv3NfH19Afjoo4+uOcde9erVrxlDcapVq4bJZCI2NrZIYlf4eZcuXSorXQhRzkIif2KL8RkMeQo1awa6gVVj9H2JSpa33nqLdu3aMWnSJN555x2rX53iGvYuZIvxRQw6BbPegCryBhO24Z133uGnn37itdde4/Dhw9SpU4cDBw7w5ptv3vKxnJ2d6d69O/v27aNp06Y4ODjc8jE6duyIp6cnR48e5fHHH7/lxxenX79+vPXWW3zyySfMmDGj2H369OmDnZ0dp0+fLtKcKYQoQykxuP/1LDpd/iA5nboy+j68Z6Wv2SpRouXn58fq1atp27YtCxcupG7dunh4eBTZT6fTFRmqXSWlxBC69SXLG4wq9AYTtsHLy4sXX3yR559/nu+//57PPvuMfv360adPH8aNG0dgYCCJiYn8888/7N2716rjenFmz55Np06d6Ny5M48++iihoaGkpaVx6tQpVq1axbp16677eFdXVz766CPGjh1LYmIiw4cPx8/Pj7i4OA4cOEBcXByffPLJLb3Gzp0788ADDzBz5kwuXrzIgAEDMBqN7Nu3D2dnZ5544glCQ0OZMWMGL7/8MmfOnLH0X7t48SI7d+7ExcWF6dOn39LzCiFuQuLp/OTqalVk9H2JEq0jR47QvXt3yxw215p/RlZKvyLxNDqq5htM2I4nnniCOXPmMGPGDP755x927tzJG2+8wZQpU0hKSsLHx4eGDRtyzz333PBYDRs2ZO/evbz++uu88sorXLp0CU9PT+rUqUP//v1vKp7777+f4OBg3nnnHR555BHS0tLw8/OjefPmjBs3rkSvcf78+bRs2ZKvvvqK+fPn4+TkRMOGDXnppZcs+7z44os0bNiQ2bNns2jRIrKzs/H39+eOO+7gP//5T4meVwhxA1V49L1OlWCyqz59+vDXX38xffp0xo4dS40aNTAYKsfafampqXh4eJCSkmIZtn7bUmJQHzS2TrZ0BphySBKtcpaVlcXZs2cJCwvD0dFR63CEEOVIPv8a27uQvBWTsdOZMaNHP6h0u9CUSfldCko0xGbbtm0MGzaMV155haCgIJtNsqKjo5kwYQI1atTAaDQSGhpq+fVerjwCOeF/F1YpbdORkmQJIYSoOlqOoVP2bO7NeYVPWyyvMv2US5RoOTg4WC3FYYtOnz5Nq1atmDdvHm3atOGpp56iVq1azJ49m/bt25OQkFB+waTEUCf2V6xaUg8uliV4hBBCVCmx+LDd3JCL+Nx450qiRIlWt27d2LlzZ2nHUqoee+wxLl26xIcffsjy5ct5++23WbduHU899RTHjx/n5ZdfLr9gEk9b1jm0KOijJYQQQlQx6Tm2s+RZWStRovXOO+9w9OhR3n77bZtcz/D06dP88ccfhIWFFZnnZ/r06bi4uLBw4UIuX75cPgF5h2Om0MCAKtIJUAghhCjgTwLt9UcwZsRqHUq5KdGow5kzZ9K4cWNefvllvvjiC5o3b37N6R2++uqr2w7yVq1fvx6A3r17F5np2c3NjY4dO/LHH3+wY8eOIgvXlonTawulWTpZgkcIIUTVsnchW4xPYtApzGf1sLdqzCdZokRr/vz5lv+fPXuWs2fPFrufVolWwTptderUKfb+OnXq8Mcff3DixIlrJlqpqalWfxuNRsuSH7ckJQZWTUbHVTV/Ol3+HFpCCCFEVXClLDRcmU9ST9WZT7JEida1EitbUTC/V3G1bFdvT05OvuYxgoKCrP6eOnUq06ZNu/VgEk9bzxsC+X/LHFpCCCGqimLLwqoxn2SJEq2KvkZYQb+y602oGhUVZTUPR4lqs6BKT9ImhBBCAFW6LKyUS9UX1FgV1GwVVtAseK0aLwB3d3erW4kTLY9AGDgb85VTbUYHvaZW+gxeCCGEsLhSFpqulIVKp68yfZVvKtG6dOkSGRkZJX6S2338rapXrx4AJ06cKPb+kydPAlC3bt3yCajlGDaHPI5Z6dCj4K9psHdh+Ty3EEIIYQtajmGs+1fcm/MKO4dsrBId4eEmE62AgADee++9Ej9JQEAA77//fokff6u6d+8OwB9//IHZbN0mnJaWxpYtW3BycqJdu3blE1BKDJ0i56AvvKi0TFgqStH8+fPR6XRWt2rVqtGtWzd++eWXEh932rRpRZrZu3XrRrdu3W4z4ltT8Pp2795d4mMopfjhhx/o3Lkzfn5+ODo6UrNmTfr06cOXX35p2S8jI4Np06axYcOGUojc9pTH9Tt69CjTpk0jIiKiyH3jxo2z+UmvRdkomLDU7Fr5a7IK3FSidbtzZSmlynW+rfDwcHr37k1ERAQff/yx1X1Tp04lPT2dMWPG4OLiUj4ByYSlohzNmzePbdu2sXXrVj7//HMMBgMDBw5k1apVpfYcc+fOZe7cuaV2vPLy4osvMmrUKBo0aMCXX37J77//zsyZM6levTorVqyw7JeRkcH06dMrbaJVHo4ePcr06dOLTbReffVVli1bVv5BCc1lZOcB4Oxgm0v3lYWb7gw/f/78En/pXK/TeVmZO3cuHTp04Mknn2Tt2rU0aNCAHTt2sH79eurWrcsbb7xRfsF4h6PQF11Uugp0AhTlr3HjxrRu3dryd9++ffHy8mLRokUMHDiwVJ6jYcOGN9zHZDKRl5dX8v6NpSwzM5NZs2YxZswYPv/8c6v7xo0bV6T2W0u2du5KW3h4uNYhCI2kZuUnWu5O9hpHUn5uujN8REQEGzZsKNFNi9njw8PD2b17N+PGjWPHjh28//77nD59mieffJJt27bh41OO6yx5BBIdPEgWla7sUmLg7N821yTs6OiIg4MD9vb/frFt2LABnU5X5MdTREQEOp3Oaq684hRueip43DvvvMPMmTMJCwvDaDSyfv16zGYzM2fOpF69ejg5OeHp6UnTpk2ZPXu21TGPHTvGqFGjqF69OkajkeDgYMaMGUN2drbVfmlpaTz66KP4+vri4+PDsGHDOH/+/A3PQ3p6OtnZ2QQEBBR7f8HkxhEREVSrVg3IX0mioBl23Lhxln03b95Mz549cXNzw9nZmQ4dOvDrr78WOWZsbCyPPPIINWvWxMHBgbCwMKZPn05eXt5Nnbtr+fjjj+nSpQt+fn64uLjQpEkT3nnnHXJzc632U0rxzjvvEBISgqOjIy1btuT3338vcrysrCyeeeYZy+TT3t7etG/f3qqWr4BOp+Pxxx/ns88+o27duhiNRho2bMgPP/xg2Wf+/PmMGDECyO/KUXAOC95XhZsOW7RoQefOnYs8l8lkIjAwkGHDhlm25eTkMHPmTOrXr4/RaKRatWqMHz+euLi4a54vYRtMZsXlKzVa7o4lmvSgQrqpV2pLv/RuRVBQEPPmzdM6DEiJoea5lUUXle7xiiRblcXehbBqcn7/O50eBmo343FBbYhSiosXL/Luu++Snp7O6NGjy/y5P/zwQ+rWrct7772Hu7s7derU4Z133mHatGm88sordOnShdzcXI4dO2Y1j92BAwfo1KkTvr6+zJgxgzp16nDhwgVWrlxJTk6OVc3Ogw8+yF133cX3339PVFQUzz33HPfffz/r1q27bmy+vr7Url2buXPn4ufnR//+/alXr16RGveAgABWr15N3759mThxIg8++CCAJfnauHEjd955J02bNuWrr77CaDQyd+5cBg4cyKJFixg5ciSQn2S1adMGvV7Pa6+9Rnh4ONu2bWPmzJlEREQU+W4q7txdy+nTpxk9ejRhYWE4ODhw4MAB3njjDY4dO8bXX39t2W/69OlMnz6diRMnMnz4cKKionjooYcwmUyWQUMA2dnZJCYm8uyzzxIYGEhOTg5//fUXw4YNY968eYwZY/1eXrlyJevXr2fGjBm4uLgwd+5cRo0ahZ2dHcOHD+euu+7izTff5KWXXuLjjz+mZcuWwLVrssaPH8/kyZM5efKk1ev+448/OH/+POPHjwfyy6LBgwezadMmnn/+eTp06EBkZCRTp06lW7du7N69Gycnp2ueN6Gty1n//sBwc6w6NVooYSUlJUUBKiUlpfQOemajUlPdi97O/F16zyFuSmZmpjp69KjKzMwsvYMmRys1zdP62k7zyt9ejubNm6eAIjej0ajmzp1rte/69esVoNavX2+1/ezZswpQ8+bNs2ybOnWqKvxV0bVrV9W1a9cijwsPD1c5OTlW+w4YMEA1b978urH36NFDeXp6qkuXLt3w9T322GNW29955x0FqAsXLlz3OZRSaufOnSo4ONhybtzc3NSAAQPUwoULldlstuwXFxenADV16tQix2jXrp3y8/NTaWlplm15eXmqcePGqmbNmpbjPPLII8rV1VVFRkZaPf69995TgDpy5IhS6vrn7maYTCaVm5urFi5cqAwGg0pMTFRKKZWUlKQcHR3V0KFDrfbfsmWLAqyuX2F5eXkqNzdXTZw4UbVo0cLqPkA5OTmp2NhYq/3r16+vateubdn2448/FvseU0qpsWPHqpCQEMvf8fHxysHBQb300ktW+91zzz2qevXqKjc3Vyml1KJFixSgfvrpJ6v9du3apYAi7/PCyuTzL27auYR0FfLfX1S9V34rk+OXSfldCirlPFo2xzs8f86Qq0kfrcrjejMea2DhwoXs2rWLXbt28fvvvzN27FgmTZrEnDlzyvy5Bw0aZNVECdCmTRsOHDjAY489xpo1a4osb5WRkcHGjRu55557LLVGN3qOqzVt2hSAyMhIIL/WIy8vz3IzmUyWfe+44w5OnTrF6tWreemll2jfvj1r165lzJgxDBo06IbdHNLT09mxYwfDhw/H1dXVst1gMPDAAw8QHR1tWQLsl19+oXv37tSoUcMqnn79+gH5NWM3OnfXsm/fPgYNGoSPjw8GgwF7e3vGjBmDyWSyTGuzbds2srKyuO+++6we26FDh2Innf7xxx/p2LEjrq6u2NnZYW9vz1dffcU///xTZN+ePXtSvXp1q9c/cuRITp06RXR09E29hqv5+PgwcOBAFixYYGlBSUpKYsWKFYwZMwY7u/zGl19++QVPT08GDhxodU6bN2+Ov7+/DF6wcQnpOQB4OjloHEn5kkSrPHgEYrprFnmqYKI2Q5WZqK1KKJjx+GoaJtINGjSgdevWtG7dmr59+/LZZ5/Ru3dvnn/++esuO1Uaiuv/9OKLL/Lee++xfft2+vXrh4+PDz179rRM05CUlITJZKJmzZo39RyF+1cWNCtmZmYCMGPGDOzt7S23ws1V9vb29OnThzfeeIM1a9YQFRVlmQKjuP5LV0tKSkIpVezrrFGjBgAJCQkAXLx4kVWrVlnFYm9vT6NGjQCIj4+3evy1+o4Vdu7cOTp37kxMTAyzZ89m06ZN7Nq1yzLCuuA8FMTh7+9f5BiFt/3888/cc889BAYG8u2337Jt2zZ27drFhAkTyMrKuuHjr95W8Ly3asKECcTExPDnn38CsGjRIrKzs636xl28eJHk5GRLn8Orb7GxsUXOqbAtsSn576XqHo4aR1K+qk5vNI3ZtR7Lvb9cpmHuUcaNHElw0y5ahyRKy5UZj1k1Jb8mywYT6aZNm7JmzRpOnDhBmzZtcHTM/6Ir3NH8dguq4kYY29nZ8fTTT/P000+TnJzMX3/9xUsvvUSfPn2IiorC29sbg8FQopqQ4jz88MMMGDDA8veNRu75+PgwZcoUNmzYwOHDh+nfv/819/Xy8kKv13PhwoUi9xV0yPf19bX827Rp02uOcC5IzArc7Ojs5cuXk56ezs8//2xVM7V///4irwvy+4oVFhsba9UZ/dtvvyUsLIzFixdbxVH4/XH146+1raQDjfr06UONGjWYN28effr0Yd68ebRt29ZqhGvBAIjVq1cXeww3N7cSPbcoHxdT8xMtf/fKOZr2WiTRKi97F/IdL2OwV6ifv4c87TpLizLQckz+KvSJZ/JrsmwoyYJ/C+GCprmCQvbgwYP06dPHst/KlSvLNA5PT0+GDx9OTEwMU6ZMISIigoYNG9K1a1d+/PFH3njjDUuiUlI1atQoksQA5ObmkpqaWmwiUNA8VvC4wrVkBVxcXGjbti0///wz7733nqXjtdls5ttvv6VmzZqWFScGDBjAb7/9Rnh4OF5eXrf1mq5WkAhdnUAqpfjiiy+s9mvXrh2Ojo5899133H333ZbtW7duJTIy0irR0ul0ODg4WCVZsbGxxY46BFi7di0XL160NB+aTCYWL15MeHi4pWbyWufwWgqaX2fNmsWmTZvYvXs3n332mdU+AwYM4IcffsBkMtG2bdubOq6wHf8mWlKjJUpbSgysmoyBK4tZc2Vm+PCeNlcgi9vgEWgT1/Pw4cOW6QMSEhL4+eef+fPPPxk6dChhYWFAfjNPr169eOutt/Dy8iIkJIS1a9fy888/l3o8AwcOtMztVa1aNSIjI5k1axYhISGWEWb/+9//6NSpE23btuWFF16gdu3aXLx4kZUrV/LZZ5+VSk1FSkoKoaGhjBgxgl69ehEUFMTly5fZsGEDs2fPpkGDBpZpBNzc3AgJCWHFihX07NkTb29vfH19CQ0N5a233uLOO++ke/fuPPvsszg4ODB37lwOHz7MokWLLMnKjBkz+PPPPy3z+dWrV4+srCwiIiL47bff+PTTT2+6ufRqd955Jw4ODowaNYrnn3+erKwsPvnkE5KSkqz28/Ly4tlnn2XmzJk8+OCDjBgxgqioKKZNm1ak6W/AgAH8/PPPPPbYY5bRia+//joBAQGWJcuu5uvrS48ePXj11Vctow6PHTtmNcVD48aNAfj8889xc3PD0dGRsLCw69Z4TZgwgf/7v/9j9OjRODk5WUZwFrj33nv57rvv6N+/P5MnT6ZNmzbY29sTHR3N+vXrGTx4MEOHDr3lcyrKR2xq1Ww6lFGHhciow8qtMo86Km7UoYeHh2revLn63//+p7Kysqz2v3Dhgho+fLjy9vZWHh4e6v7771e7d+++rVGH7777bpG43n//fdWhQwfl6+urHBwcVHBwsJo4caKKiIiw2u/o0aNqxIgRysfHx7LfuHHjLHEXvL5du3ZZPe5aIygLy87OVu+9957q16+fCg4OVkajUTk6OqoGDRqo559/XiUkJFjt/9dff6kWLVooo9GoADV27FjLfZs2bVI9evRQLi4uysnJSbVr106tWrWqyHPGxcWpJ598UoWFhSl7e3vl7e2tWrVqpV5++WV1+fLlG567a1m1apVq1qyZcnR0VIGBgeq5555Tv//+e5HzYDab1VtvvaWCgoKUg4ODatq0qVq1alWR66eUUm+//bYKDQ1VRqNRNWjQQH3xxRfFXntATZo0Sc2dO1eFh4cre3t7Vb9+ffXdd98ViXPWrFkqLCxMGQwGq/dV4VGHV+vQoYMC1H333Vfs/bm5ueq9996zvH5XV1dVv3599cgjj6iTJ09e97xV5s9/RXDvZ9tUyH9/UT/tiSqT49vqqEOdUrc+m+ilS5fw8/O7/SzPBqWmpuLh4UFKSgru7u6lc9CUGJjV2Hpkms4AUw7ZRA1IVZKVlcXZs2cJCwuz9FMSQtw8nU5XbqNYS5t8/rXV/q21XEjJ4qdHO9AqpPSa0wuUSfldCko06jAoKIiRI0fecIJAccWVztIFUzyY0NtcZ2khhBCirGTmmLhwZdRhLd9yWmfYRpQo0apbty4//vgjd955J3Xr1uX9998v8ZDeKqPlGE6O2s69Oa/Ql49RLR7QOiIhhBCiXEQkpAPg6WyPl4vMo3VDhw4dYtOmTdx3331ER0fz3HPPUbNmTe6//342bdpU2jFWGsFhtdmpGnIyy4NLacUPmxZCCFumlKqQzYZCW2fj8xOtsCpWmwW3MWFpx44dWbhwIefPn+d///sfYWFhfP/993Tr1o2GDRvy4YcflvnkiBWNo72BUJ/8N9mJi2kaRyOEEEKUjzNxlwEI85FE65Z5enoyZcoUjh49yoYNGxg1ahRnz57lqaeeIjAwkPHjx1tmgBZQp7or/iSQ9s/6/E7yQgghRCX3z4X8yoV6/lVvUtlSXYInICAAf39/XFxcUEqRnZ3NggULaNu2LXfffbfUcAF3s44txifpv/eh/JGIexdqHVKVVILBtkKICk4+99o5cj4FgIY1bGc0YHm57UQrNzeXxYsX07NnT+rXr8///vc/qlWrxgcffEB8fDx//fUXd955J8uWLWPSpEmlEXPFlRLDnaffwqC78mFXVyYulZqtclOwOG3BhJ5CiKojNzcXyJ+FXpSfy9l5RCRkANAwoOolWiWeGf7UqVN8/vnnLFiwgPj4eAwGA0OHDuWxxx6jR48elv169OhBjx49GDJkCL/99lupBF1hJZ7OnxX+asqUv2yLTPVQLgwGAwaDgdTUVFkXTYgqRClFSkoKRqMRe3t7rcOpUv65kArkL73j41q11jmEEiZavXr1Yv369SilqFGjBq+99hoPPfRQseuLFWjVqhWrVq0qcaCVgnc4SqdHV3jiUu9a2sVUxeh0Ovz8/Lhw4QJGoxEXF5ebXsxXCFHxKKXIzc0lJSWFy5cvExgoP2rL25GY/GbDRlWw2RBKmGitW7eO7t2789hjjzFkyJCbqoYdMmQIwcHBJXm6ysMjEN3A2ZhWTsaAGTN69DJxabnz8PAgMzOT+Ph44uLitA5HCFEOjEYjgYGBNjVjeFWxLyoZgCY1PbQNRCMlSrT++ecf6tWrd0uPadKkCU2aNCnJ01UuLccw70IYf23ZToOGzZjasrfWEVU5Op2OgIAA/Pz8LH02hBCVl8FgkOZCDe2OyF/w/I5Qb40j0UaJEq1bTbKEtfDa9Zi5KZWLsQ5M1TqYKqygv5YQQoiyEZOcSUxyJga9juZBnlqHo4lSnd5B3JyWwV7odfkz5cZeWftJCCGEqGx2RyQC+aMNXYwlHn9XoUmipQEPJ3saB+a3VW87E69xNEIIIUTZ2BOZ32zYOtRL40i0I4mWRtqH+wCw9ZQsxi2EEKJy2nIqvzKhTRXtnwWSaGmmQ7gvAFtPJ8hsxUIIISqdmORMTselo9f9W+ZVRZJoaeSOUC/s9DpikjM5l5ihdThCCCFEqfr7RP70Oc2DPPFwrrqjPiXR0oizgx0tg/PbrDeekLmchBBCVC4FiVaXutU0jkRbkmhpqGcDPwD+PHpR40iEEEKI0pNnMrP5Sv8sSbSEZno1rA7A9jMJpGXJxJlCCCEqhz2RSaRl5eHhZE+zmp5ah6MpSbQ0FF7NlTBfF3JNik0nZZoHIYQQlcPqI7EA9GpQHYO+aq8nK4mWxnpdaT78S5oPhRBCVAJKKdYczk+0+jb21zga7UmipbFeDfKbDw/98w+5pzZCSozGEQkhhBAldzA6hfMpWTg7GOhcp+pO61BAEi2NtQ715kGXTaxWj2L/7SCY1Rj2LtQ6LCGEEKJEfr9Sm9W9vh+O9rKerCRaGjOknecl02cYdFcmLVVmWDVFaraEEEJUOEopfjt0AYB+0mwISKKlvcTT6DFbb1MmSDyjTTxCCCFECe2JTOJcYgYuDgZ61PfTOhybIImW1rzDUbpCl0FnAO9a2sQjhBBClNBPe6MB6N8kAGcHO42jsQ2SaGnNIxDdwNmYr1wKE3oYOAs8ArWNSwghhLgFWbkmfjmY32w4rGVNjaOxHZJu2oKWY4j2bs/zny/nnKrO0lojqKF1TEIIIcQt+Oufi6Rl5RHo6UTbMG+tw7EZUqNlI4JD60BoJ84rH5bsjtI6HCGEEOKW/Lg7v9lwaItA9FV8ktKrSaJlQ0a1CQZgya4oTGalcTRCCCHEzYlMSOfvk/mLSA9vJc2GV5NEy4b0aeSPp7M951OyLG9YIYQQwtZ9v+McSuUvIB3q66J1ODZFEi0b4mhvYGiL/E7w3+84p3E0QgghxI1l5ZosXV7GtAvROBrbI4mWjbmvbf6b9PA/R4k98IdMXCqEEMKm/XboAkkZuQR6OtFd5s4qQkYd2pjafq68VmM3YxM+wLBMgU4PA2dDyzFahyaEEEJYUUqxYFskAKPbBmOQTvBFSI2WrUmJYXziLFmSRwghhM3beTaRA1HJONjpGXlHkNbh2CRJtGxN4ml0siSPEEKICuDTjacBGNGqJr6uRo2jsU2SaNka7/D85sKrKFmSRwghhI05FpvK+uNx6HXwUGcpo65FEi1b4xEIA2fnJ1dAntKzq/FrsiSPEEIIm/L53/ktLf0aB8iUDtchneFtUcsx6MJ78uvGLby+NQuH00GsM5mxM0heLIQQQnsxyZms3H8egIe7SG3W9UjJbas8AunR925yXQI4l5jBiitvaCGEEEJrc9adJM+s6BDuQ7MgT63DsWmSaNkwJwcDD135pTBn/SlZlkcIIYTmziVkWNY1fPrOuhpHY/sk0bJxD7QLwcvZnrPx6aw8IFM8CCGE0Nbstfm1WV3qVqN1qLfW4dg8SbRsnIvRjgevjOb4358nyMkz3+ARQgghRNk4E3eZZfukNutWSKJVAYzvGIqfm5GoxEy+2xGpdThCCCGqqFl/ncSsoGd9P5pL36ybUukSrdzcXGbPns348eNp3rw5Dg4O6HQ6vvzyS61DKzFnBzum9Mr/5fDRulOkZeVqHJEQQoiqZn9UMisP5A/Mekpqs25apUu00tPTmTJlCvPnzyc2NhZ/f3+tQyoV97SuSS1fFxLTc1j05zY4+7csyyOEEKJcKKV449ejAAxrGUjjQA+NI6o4Kl2i5ezszG+//cb58+eJjY1lwoQJWodUKuwMep7vW497DOuZuHsQLBgIsxrD3oVahyaEEKKSW304ll0RSTja63muTz2tw6lQKt2EpQ4ODvTr10/rMMpEnyATve2/RE+hBafDe8rM8UIIIcpEdp6Jt1cfA+DhzrUI8HDSOKKKpdLVaFVmusQz/yZZBWTBaSGEEGVo4dZIIhMyqOZm5JGu4VqHU+FUuhqt0pKammr1t9FoxGjUeGXyggWn1b9TPCidAZ0sOC2EEKIMXEjJZNZfJwB4rnc9XIySNtwqqdG6hqCgIDw8PCy3t956S+uQil1wenvDV6TZUAghRJl4/ZejpOeYaBnsyfBWNbUOp0KyydQ0NDSUyMibny9q7NixzJ8/v1RjiIqKwt3d3fK35rVZBa4sOP3H5q28timTzKP+rL2cja+rjcQnhBCiUthw/BK/HYrFoNcxc0gT9Hqd1iFVSDaZaIWHh+Po6HjT+wcEBJR6DO7u7laJlk3xCKRnv+HMOrWZoxdSmbHqKB+OaqF1VEIIISqJrFwTr604AsC4DqE0rGGj5WEFYJOJ1tq1a7UOweYZ9Dr+7+6mDP54MysPnGdIixr0qF9d67CEEEJUAnPWneJcYgb+7o4yOeltkj5aFViTmh6WdRBfXnZYZowXQghx2w7HpPDJxtMATB3YEFfpAH9bJNGq4J7qVZcQH2cupGTxzurjWocjhBCiAsvJM/PsjwcwmRX9m/jTr0npd82paiplmvr2229z7Fj+5Gr79+8HYN68eWzevBmATp068eCDD2oVXqlycjDw1tAmjP5yB99sj+SupgG0q+WjdVhCCCEqoDnrTnIsNg1vFwdmDG6sdTiVQqVMtFavXs3GjRuttm3dupWtW7da/q4siRZAh9q+jGoTxKKdUTyz5AC/T+mMu6O91mEJIYSoQA7HpPDxhvwmwxmDG8lo9lJSKZsON2zYgFLqmrfSngrCFrx8V0OCvZ2JSc5k2pWRIkIIIcTNyMo18cySf5sMBzStoXVIlUalTLSqIlejHR+MbIZeBz/vi+HXgxe0DkkIIUQF8fbvxzh+MQ0faTIsdZJoVSKtQryZ1L02AC8tO0RsSpbGEQkhhLB1645dZP7WCADeu6eZNBmWMkm0Kpkne9ahaU0PUjJzeXrJfkxmdeMHCSGEqJIupWbx7I8HAZjQMYzu9fw0jqjykUSrkrE36PlgZHOcHQxsPZ3A179thrN/Q0qM1qEJIYSwIWaz4uklB0hMz6FhgDv/7VdP65AqJUm0KqHwaq68ObQJ9xjWM2HXQFgwEGY1hr0LtQ5NCCGEjfhk42k2n4rH0V7Ph6NaYLQzaB1SpSSJViU1pBa8bf8VBt2VpkNlhlVTpGZLCCEEm07G8f4f+ZNczxjUmNp+rhpHVHlJolVZJZ5Gj9l6mzJB4hlt4hFCCGETYpIzeXLRPswKRrYO4p47grQOqVKTRKuy8g4HnfXlNaMH71oaBSSEEEJr2XkmHvt2D0kZuTQJ9GD64EZah1TpSaJVWXkEwsDZoMtvc89Tel7IncjSUzIKUQghqqrpq45yIDoFT2d75t7XEkd76ZdV1irlEjziipZjILwnJJ7h68OKJVvSWL7sEOHVXGgR7KV1dEIIIcrRN9sj+X7HOXQ6mH1vC4K8nbUOqUqQGq3KziMQwjrz4F2d6d2wOjl5Zh75Zg8XU2UyUyGEqCo2nYxj2sr85dme7V2PrnWraRxR1SGJVhWh1+v438jm1K3uyqW0bB7+Zg9ZuSatwxJCCFHGTl26zGPf7cVkVgxrGchj3cK1DqlKkUSrCnE12vHFmNZ4OttzICqZKT/IzPFCCFGZJaXnMHHBLtKy8mgd4sVbw5qg0+m0DqtKkUSrignxceGz+1vhYNCz+kgsb/72j9YhCSGEKAPZeSb+8+0eIhMyqOnlxGcPtJJJSTUgiVYV1LaWD+/d0wyArzaf5evNZzWOSAghRGkymRVPLz7AjrOJuBrt+GrsHfjIYtGakESrihrUrAYv9KsPwOu/HmX14QsaRySEEKI0KKWYseoIvx66gL1Bx6f3t6Kev5vWYVVZkmhVYY90qcX97YJRCib/sJ+dZxO1DkkIIcRtmrvhNAu2RQLw/j3N6VTHV+OIqjZJtKownU7HtIGN6NWgOtl5ZibM38Wh6BStwxJCCFFCi3ed4901+WsYvjagIYOa1dA4IiGJVhVnZ9AzZ3QL2tXy5nJ2HmO+3sHJi2lahyWEEOIWrT58gRd/PgTAo93CmdApTOOIBEiiJQBHewNfjr2DZjU9SMrI5f6vdhCVmKF1WEIIIW7SX0cv8vj3+QtFj2hVk+f71NM6JHGFJFoCyJ9ja/74NtSr7sbF1GxGf7md2BSZPV4IIWzd3yfieOy7veSZFQOb1eDtu5vKXFk2RBItYeHl4sA3E9sQ4uNMVGImo76QZEsIIWzZttMJPLRwNzkmM30aVed/9zTDoJcky5ZIoiWs+Lk78u3EtgR6OnE2Pp17P9/GhZRMrcMSQghRyK6IRCYu2EV2npke9f34aFRL7A1SrNsauSKiiCBvZ354uB01vZyISMjg3s+3Ext1Gs7+DSkxWocnhBBV3tbT8Yz9eicZOSY61/Fl7n0tcbCTIt0WyVURxQrydmbxI+0J9nambfKvVPuqFSwYCLMaw96FWocnhBBV1objlxg/b5clyfr8gdY42svSOrZKEi1xTYGeTiwZFcxb9l9i4Mri08oMq6ZIzZYQQmhg9eFYHlq4m+w8M70a+PHFmNY4OUiSZcsk0RLX5Z8X82+SVUCZIPGMNgEJIUQVtfLAeSZ9v5dck+KuJgF8cn8rqcmqACTREtfnHQ4667eJSenZl+6tUUBCCFH1fLcjksk/7MNkVgxrGcjse5tLx/cKQq6SuD6PQBg4G3T5v5pM6HkxbyL3/nCOtf9c1Dg4IYSo3JRS/O+P47y87DBKwX1tg3lveDPsJMmqMOy0DkBUAC3HQHhPSDxDrnsICasukn3sEg9/s4d3hzdlWMuaWkcohBCVTp7JzMvLDrN4dxQAU3rVYXLPOjIZaQUjKbG4OR6BENYZR59gPn2gFUNbBGIyK55ecoAP155EKXXjYwghhLgpGTl5PPzNHhbvjkKvgzeHNmFKr7qSZFVAkmiJW2Zv0PP+iGY80qUWAP/78wTP/niQnDyzxpEJIUTFF385m9Ff7GDdsUsY7fR89kBrRrcN1josUUKSaIkS0et1vNi/AW8MbYxBr+OnvdGM/XonKZm5WocmhBAV1rHYVAbP2cL+qGQ8nOz5/qG23NmwutZhidsgiZa4Lfe1DeGrsa1xcTCw7UwCd3+ylajEDK3DEkKICmftPxe5e+5WYpIzCfVx5qdHO9AqREZ4V3SSaInb1q2eHz/+pwP+7o6cunSZwR9vYdvpBK3DEkKICkEpxZebzvDgwt2k55hoV8ubZY91pLafq9ahiVIgiZYoFQ1ruLN8UkeaBHqQmJ7D/V/tYP6Ws9JJXgghriMnz8yLPx9i5q//oBSMahPEwglt8XJx0Do0UUok0RKlxt/DkR//094yInHaqqM8t/QgWbkmrUMTQgibcyElk5Gfb+OHXfkjC18d0JA3hzaRxaErGbmaolQ52hv43z3NeOWuBuh1sHRPNCM/305sSpbWoQkhhM3YdjqBgR9tZt+5ZNwd7fhq3B1M7BQm0zdUQpJoiVKn0+l4sHMtFk5oi6ezPQeikhnw0Sa2nIrXOjQhhNCUUorP/z7N/V/tIP5yDg0C3Pnlic50r+endWiijOiUdKKxkpqaioeHBykpKbi7u2sdToV3LiGDh7/ZzbHYNHQ6mNyzDk/0qINBL7/ahBBVSEoMmRdP8PrWbL4/lt+dYljLQN4Y0gQnB1kYujTYavktiVYhtnqhKrKsXBPTVh7hh135y0h0rO3DrJEtqOZm1DgyIYQoB3sXolZNRqfMmJSOV0wP0XDA49zfNliaCkuRrZbfkmgVYqsXqjJYti+al34+TGauiWpuRj68twXtw320DksIIcqMSolGfdAEPf+unKF0BnRTDuUvbSZKja2W39JHS5SboS1qsuqJjtSt7kpcWjb3fbmd9/84Tq5Jlu4RQlQ+8Zezeef736ySLACdMkHiGY2iEuVNEi1Rrmr7ubFiUidGtKqJWcFH604x/JOtnIm7rHVoQghRaraciqff7E0si3TEpAo1D+oM4F1Lm8BEuZNES5Q7JwcD745oxpzRLfBwsudAdAp3fbiZ73eckwlOhRAVWlauiRmrjnLflzuIS8vG1S+ES93eyU+uIP/fgbOk2bAKkT5ahdhqG29ldSElk2d/PMCWU/lL9vRq4MfbdzfF11U6ygshKpb9Uck8vWQ/Z+LSARjVJpjXBjTMH1WYEpPfXOhdS5KsMmKr5bckWoXY6oWqzMxmxddbzvLO6uPkmMz4uDgwY3Bj+jfxlxE5Qgibl5Nn5qN1J5m74TQms8LPzcj/3d2U7vVlbqzyZKvltyRahdjqhaoK/rmQylOL93MsNg2Avo38mTGkEX5ujhpHJoQQxTsWm8rTiw9w9EIqAIOa1WDG4EZ4OstaheXNVstvSbQKsdULVVXk5Jn5eP0pPl5/ijyzwsPJnqkDGzK0RaDUbgkhbEZWrok5607x6cbT5JkVXs72zBzShLuaBmgdWpVlq+W3JFqF2OqFqmqOnk/luaUHOHI+/1di93rVeGNoE2p4OmkcmRCiqtt2OoGXlh3ibHx+X6zeDaszc2hjqX3XmK2W35JoFWKrF6oqyjWZ+fzvM8z+6yQ5JjMuDgaeurMu4zqEYmeQAbNCiPKVnJHDW78dY/Hu/FUu/NyMzBjcmL6N/TWOTIDtlt+SaBViqxeqKjt1KY3//nSIPZFJANT3d+ONoY1pFeKtcWRCiKpAKcXKA+d5/ZejxF/OAeC+tsH8t1993B3tNY5OFLDV8lsSrUJs9UJVdWaz4sc9Ubz1+zGSM3IBGNk6iBf61cfLRTqdCiHKxrHYVKauOMKOs4kA1PZz5a1hTbgjVH7o2RpbLb8rXaJ18uRJfv75Z9asWcPJkye5ePEiXl5etG3blqeeeoru3btf9/G2eqFEvsT0HN7+/R+W7I4GwMvZnuf71uee1kEY9NJZXghROlIyc/ngzxN8sz0Sk1nhaK/nsW61eaRrLYx2Bq3DE8Ww1fK70iVa9957L4sXL6ZBgwZ07twZb29vjh8/zsqVKzGZTMyaNYvJkydf8/G2eqGEtd0Ribyy/LBlKogGAe68NqChLFIthLgtZrNi6Z5o/m/1MRLS85sJ+zX25+W7GlDTy1nj6MT12Gr5XekSrXnz5tG0aVNatWpltX3jxo3ceeedAERGRhIQUPwQXFu9UKKoXJOZhdsimf3XCVKz8gDo06g6L/VvQIiPi8bRCSEqmh1nEnjzt384EJ0CQHg1F6YPakynOr4aRyZuhq2W35Uu0bqe3r178+eff/Ljjz8yfPjwYvex1Qslri0xPYdZf53gux3nMJkVDgY94zuGMqlHbemoKoS4oVOXLvP278f465+LALg4GJjSqy5jO4TiYCcjnCsKWy2/7bQOoDw5OOR3mra3l8K3MvG+smTP/e1CeP2Xo2w6Gc9nf5/hxz3RTOpem/vaBuNoL30qhBDW4tKymb32BIt2RmEyKwx6HffeEcSUXnWp5ibrrYrSUWVqtCIjI6lXrx4Gg4Ho6Gi8vLyK3a8gI46KirLKiI1GI0ajfPBsnVKKDcfjmPnrUU5fWdg10NOJyb3qMKxFIHaXL0DiafAOl4Vdhaii0rPz+HrzWT7deJr0HBMAvRpU54V+9ajt56ZxdKKkpEZLQ9nZ2dx3331kZ2fzf//3f9dMsq4WFBRk9ffUqVOZNm1aGUUoSotOp6N7fT861/Fl6Z5oZv11kpjkTJ5fepBzf33KM1lz0WEGnR4GzoaWY7QOWQhRTjJzTHy7PZJPN562dHRvVtODF/s3oF0tGUgjyoZN1miFhoYSGRl50/uPHTuW+fPnF3tfXl4e9957Lz/99BPDhw9nyZIl110zT2q0KpesXBMLt0WwdP1Ofjc/ikH379td6QzophySmi0hKrnsPBOLdpzj4w2niUvLBiDUx5mn7qzLwKY10MvUMJWC1GjdgvDwcBwdb37NqGuNIMzLy2P06NH89NNPjBgxgu+///6mFyZ2d3e3qQslSsbR3sDDXcK5r3okhkXWvyl0ysTe/Xto0aWGLFgtRCWUk2fmxz1RzFl3igspWQDU9HLiyZ5XuhLIUl6iHNhkorV27drbPkZubi4jR45k2bJljB49moULF2IwSIfoqsrFv15+c6EyW7blKT2P/Z6M78HNPNGjDnc2qC6/bIWoBDJzTCzedY4vNp0lJjkTgAAPRx7vUZsRrYJkJKEoVzaZaN2unJwchg8fzqpVqxgzZgzz5s1Dr5cPVpXmEZjfJ2vVFFAmlM7AmrD/knraj9iYVB75Zg/1/d14vEdt+jUOkFnmhaiAUjJz+WZbBPO2RFj6YFVzM/JYt3BGtZHRx0IbNtlH63ZkZ2czbNgwfvvtNyZOnMjnn39+S0mWrbbxilKSEgOJZ8C7FngEkpiew1ebz7BgaySXs/MnPQ32dubBzmEMb1UTZ4dK+VtEiEolLi2brzaf5dvt/36Og7ydeKRLOMNb1ZQEq4qw1fK70iVa48ePZ/78+fj6+vLYY48V2/emW7dudOvWrdjH2+qFEmUrOSOHeVsiWLAtwrJotaezPWPahfBA+1CZU0cIG3TiYhrztpzl570xZOfldwuoV92Nx7qHc1eTAOmDVcXYavld6RKtbt26sXHjxuvuc72pGmz1QonykZGTx9I90Xy56SznEjMAcLDTc3fLQCZ2CpM5doTQmNms2Hgijq+3nGXTyXjL9hbBnkzqVpse9f2kr2UVZavld6VLtG6XrV4oUb5MZsWaI7F89vcZDkQlW7Z3rO3DA+1C6dXAT34tC1GOMnLy+GlvDPO2nOXMlcmI9Tro08if8R3DuCPUS0YPV3G2Wn5LolWIrV4ooQ2lFLsikvhi0xnW/nMR85VPSw0PR+5rF8LIO4LwdZVmRSHKyqlLaXy34xw/7Ym2LB7vZrTj3jZBjGkfSpC3s8YRClthq+W3JFqF2OqFEtqLTsrgux3nWLwrisQrI5ocDHruahrAfW2DaRUiv6iFKA3ZeSZWH47lu+3n2BmRaNke6uPM+I5h3N2qJq5GGagirNlq+S2JViG2eqGE7cjKNfHrwQss3B5p1axYq5oL97QOYljLQPzcbn7CXSFEvjNxl1m08xxL90STdGVQikGvo2d9P0a3DaZLnWrS/0pck62W35JoFWKrF0rYpgNRyXyzPZJfD14gMzd/cVqDXkeP+n6MbB1Et3rVpC+XENeRkpnLb4cu8NOeaHZHJlm2B3g4cu8dwYy8Iwh/D/nhIm7MVstvSbQKsdULJWzb5ew8fjlwnsW7o9h3LtmyvZqbkWEtAhncPJAGAW7StCgEkGcys+lkPD/tjeaPoxfJuTI1g14H3er5MbpNsPxIEbfMVstvSbQKsdULJSqOExfTWLIrimX7YiyzUwPU8XNlcPMaDG4eKB14RZWjlOLI+VRW7I9h+f7zlsWdIf+zcXermgxpHii1V6LEbLX8lkSrEFu9UKLiyckzs+7YJVbsj2HtsUuWX+0ALYM9Gdw8kLuaBuSPWkyJgcTT4B2ev1yQEJWAUoqjF1L59eAFfj10gciEDMt93i4ODGpWg7tb1qRxoLvU9orbZqvltyRahdjqhRIVW2pWLmsOx7Ji/3m2no63TBOh18Hzfjt5OOVD9JjzF74eOBtajtE2YCFKSCnF8Ytp+cnVwQuciU+33Odor6dHfT+GtqhJ17rVZHFnUapstfyWRKsQW71QovK4lJrFLwcvsGJ/DBejz7DF+CQG3b8fQzN6osbuICSsroZRCnHzTGbF3nNJ/HX0In8evWiVXBnt9HSv58ddTQPo2cBP1g8VZcZWy295xwtRzvzcHZnQKYwJncKIO5iJ4Wfr3zp6zPz3ixUkVmtDj/rV6V6vGq1CvKRjsLAp6dl5bDoZx59HL7H++CXL3HKQP79c13rVGNA0gJ4NqsucV6JKk3e/EBqqFtIwv7lQ/dt/y4SeaPyJvniZExcv8+nG07g52tGlbjW61/Oja91qssi1KHdKKc7Ep7PpRBwbTsSx9XSCVb9Dd0c7etT3o1fD6nSpWw13R3sNoxXCdkjTYSG2WvUoKrG9C2HVFFAm0Blg4CxS6o9iw4lLrD92iY0n4iyTNxZoVtODLnWr0SHcl5YhnhjtDNrELiq1lIxctpyO5+8TcWw6GU9McqbV/UHeTtzZwJ87G1andagX9lLrKjRkq+W3JFqF2OqFEpVcSgwkngHvWkVGHZrMigPRyWw4don1x+M4FJNidb/RTs8dod60D/ehY21fGtdwl2ZGUSIZOXnsiUxix5lENp+K52B0smXgBuQ3Cd4R5kWn2tXo2cCPOn6uMlpQ2AxbLb8l0SrEVi+UEAUupWWx4XgcW07Fs/V0gtV8RJC/4G7bWj60CfOiVYg3jQPdpcZLFCs1K5fdEYnsOJvIjjOJHI5JIc9sXSTU9nOlS51qdK7rS9swb+nMLmyWrZbfkmgVYqsXSojiKKU4dekyW08nsOVUPNvPJJCalWe1j4OdnqaBHrQK9aJ1iDetQrzwdnHQKGKhFaUUEQkZ7I9KYv+5ZPacS+Lo+VQK5VXU8HCkbS0f2tXypnOdatTwdNImYCFuka2W35JoFWKrF0qIm2EyK46eT2Xr6Xh2RyaxJzLJajRYgVq+LjSp6UGTwPxbo0APGRlWkRUz4W1yRg77o5IttwNRyUX6+gGE+jjTJsybtmE+tAnzllULRIVlq+W3JFqF2OqFEqIklFKcjU9nz5Wka3dkEqcuXS6yn053JfkK9KDxleSrnr8bns5S82Xr1J4F8MsUdMqMGT3f+D7FF+mdiE7KLLKvg52eRjXcaR7kSYtgL9qEesuSN6LSsNXyWxKtQmz1QglRWpLSc9gfnczh6BQOxeTfLqRkFbtvdXcjdau7Ua+6G3X98/+tU91V+uloQClF3OVsTl9K51TcZU5fukxs9Gk+vjQGA/9+jecpPZ2yZxOLD6E+zrQI9qJ5kCfNgzxpEOAus7GLSstWy2/5thSiivFycaB7PT+61/OzbIu/nJ2fdF1Jvo6eTyUmOZOLqdlcTM1m08l4q2PU9HLi/9u7/6Cq6vyP48/Dz3v5IQqsGQFCJKZbO9julpK/WVH+2DHLWdrF0sVKm0YS09HaETTTdmYpf7C6zEKutj+cnRy/TLs1LaZCq2s5LuB8a1QK5CtWYqIgvwXu+f5BsBKo1HI4F309Zpx77znXz+c9noLX/ZzP/XyiQ/2JCvEnKtSf6FA/Rof4EzHC7+a/yLWv4w01XW2n6lIz/1fTSMXFRj670ED518Hqm/PvJnmcwtOn52dlL8PFGz8NIXxCIkF+WstKxG4a0foGd03EIoOtvqWNTy80UHa+ntPV9ZRV13P6fAMXG1qv+3c8PQzuGu5kdIgfYUFOwoY7CRvu+PrRSfiZt/B+N71zgdbbcF9H0zSpb23nwpUWzte1UnW5iapLTVRdbubspSbOXWqipo85dV08DIgI9iPmewHEfM+fCUFNJB2YhXHNgrcYnrD8fxVi5bbjrr+/NaIlIn0KdHjzQOQIHogc0eN4TUMr5V81UnmxkTM1jfxfTSNnLjZRebGR5rYOzl5q4uylpl7tjaKGI77LoWtfR9OF6+3n2XF2NI6QCEICfAgN8CU0wJcQfx+GOb1xeLv/shQul0l9SzuXm67+509jG5ebrlJ9peXrUcEWLtR3PjZd7bhpm0FObyKCndwdGkDM9wK4Z2QAMSM7RxB7/Zv4be214K1Cloj7UNASkW8lJMCXkABfHowO7nHcNE0u1Ldy5mIjZy818WVtC1/WNfN5bTNf1DYTXnuyx+bZ0Lmv4+Fjx/jQ1XuCPnQukDnM6cUwhzeBDi+GOTsfA329cfp44uvtgcPrP48Ob098vTxweHvi6WFgGOBhGHh8/cg1rztcJu0dJu0uF20dJm0dLto7TNpcnY+t7R00tnbQdLWdxqsdNLW203DN6/qWNmqb2qhtutpriYSbCXR4cccwB+EjnESM8CMy2I+IYCfhI/yICPYjyPktbvk98CTEJFx3wVsRsZduHX6Duw49igx1Zt052HJ/j9tcLjzYev//UNkWxMWGVi7WX6WmsZVLjd8+vNjNz8eTEX4+DPfzJtjfh+F+PtwR6MsdwxyMHObLqGGO7uf6MoHIwHPX39/6v11EBoURFN45J+ua21weP91C+gPTe73X5TJpvNrOlZZ26lvauNLczpXmNupb//O8pb2D1jYXLe0dtLS5aG130dLWQUtbB63tLlwuE5dpYgIus3PEzWWamGbnaJanh4GXpwfeHgZengbenh54e3rg5dH53MfLA39fT/x9vPDz8ep87uuFn0/nMX9fL0b4e3eHK62+LyJ9UdASkcHTz9tcHh4GgQ5vAh3egFYmF5GhS0FLRAZX0F2aRyQitw2tXCciIiJiEQUtEREREYsoaImIiIhYREFLRERExCIKWiIiIiIWUdASERERsYiCloiIiIhFFLRERERELKKgJSIiImIRBa1B1trayrp162htbbW7FPkOdP2GPl3DoU3Xb2i7Ha+fYZqmaXcR7sTq3b/ddXdx6R9dv6FP13Bo0/Ub2qy8fu7634ZGtEREREQsoqAlIiIiYhEvuwtwN113Uq9cuWJJ+13tWtW+WEvXb+jTNRzadP2GNiuvX1eb7jYjSnO0vuHcuXNERETYXYaIiIh8B1VVVYSHh9tdRjcFrW9wuVx88cUXBAYGYhiG3eWIiIhIP5imSX19PWFhYXh4uM/MKAUtEREREYu4T+QTERERucUoaImIiIhYREFLRERExCIKWoPk3LlzpKamEhYWhq+vL1FRUSxfvpzLly/bXZrcxN69e1m2bBlTpkxh2LBhGIbBggUL7C5L+qmmpoa8vDzmzZvHPffcg9PpJCgoiMmTJ/PGG2/gcrnsLlFuYvXq1SQkJBAREYHT6SQ4OJgJEyawfv16ampq7C5PvoM//vGPGIaBYRjk5eXZXY6lNBl+EJSXlxMfH8+FCxeYO3cu9957L8eOHePQoUOMHTuWI0eOEBISYneZch1xcXGcOHGCgIAAwsPDOXXqFCkpKfzpT3+yuzTph5ycHJ599llGjRrFzJkziYyMpLq6mn379lFXV8ejjz7K3r179S1jN+bj48MDDzzA+PHjGTlyJI2NjXz44YccP36csLAwjh49SmRkpN1lSj9VVVVx//3309HRQUNDA7m5uTz11FN2l2UdUyyXmJhoAua2bdt6HE9PTzcBc8mSJTZVJv1x8OBBs6yszHS5XOahQ4dMwExJSbG7LOmnAwcOmPn5+WZ7e3uP419++aUZERFhAuZbb71lU3XSH83NzX0ef+mll0zAXLp06SBXJN+Vy+UyExISzLvvvttcuXKlCZi5ubl2l2Up3Tq0WHl5OQUFBURHR/Pcc8/1OLd+/Xr8/f158803aWhosKlCuZkZM2YwZswYjXgMUTNnzmTu3Ll4enr2OD5q1CiWLl0KQGFhoQ2VSX85HI4+j//sZz8DOn/OytCwbds2Dh48yB/+8Af8/f3tLmdQKGhZ7NChQwAkJib2WkAtMDCQhx9+mObmZj766CM7yhO5rfn4+ADg7e1tcyXyXfztb38D4Ac/+IHNlUh/nDx5kjVr1vD8888zdepUu8sZNNrr0GKnT58GYMyYMX2eHzNmDAUFBZSVlZGQkDCYpYnc1trb29m9ezcAc+bMsbka6Y+srCwaGhqoq6vj+PHjHD58mAkTJvDiiy/aXZrcRHt7O0888QSRkZFs2rTJ7nIGlYKWxerq6gAICgrq83zX8dra2sEqSUSANWvW8PHHH5OUlMTs2bPtLkf6ISsri+rq6u7XSUlJ7Nq1S18mGgJefvllSkpKOHz4ME6n0+5yBpVuHdrM/PpLn5r/IzJ4tmzZwmuvvcbYsWN588037S5H+un8+fOYpsn58+fZt28f5eXlxMXFUVxcbHdpcgPHjh1j06ZNvPDCC0yaNMnucgadgpbFukasuka2vunKlSs93ici1tq6dSvp6emMGzeOwsJCQkND7S5JvqU77riDefPmsX//fmpqanjyySftLkmuo+uWYWxsLBs2bLC7HFsoaFls7NixAJSVlfV5/tNPPwUgNjZ20GoSuV1lZWWxfPly7rvvPgoLCxk1apTdJcl/ITIykvHjx/PJJ59w8eJFu8uRPjQ0NFBWVsbJkydxOBzdi5QahsH69esBePrppzEMg+XLl9tbrEU0R8tiM2bMAKCgoACXy9Xjm4f19fUcOXIEp9PJxIkT7SpR5Lbw6quv8tJLLxEXF8f+/fs1knWL+OKLLwB6Ld8h7sHX15fFixf3ea64uJiSkhImT57M2LFjb9nbigpaFouJiSExMZGCggK2b9/OsmXLus9lZmbS2NjIkiVLbpv1RETssGHDBjIyMvjhD39IQUEBwcHBdpck/XTq1CmGDx/ea/TR5XKxdu1aLly4QHx8PCNGjLCpQrkRp9N53S121q1bR0lJCQsXLrylV4ZX0BoEO3bsID4+nrS0NA4cOMC4ceP46KOPOHToELGxsWzcuNHuEuUG8vPzyc/PBzon4wIcPXqURYsWARAaGkpWVpZN1cnN7N69m4yMDDw9PZkyZQrbtm3r9Z6oqKju6ynu5b333mPVqlVMnTqVmJgYQkJCqK6upqioiIqKCkaNGkVubq7dZYpcl4LWIIiJieH48eNkZGTw3nvv8e6773LnnXeSlpZGZmamPl27udLS0u71lrpUVFRQUVEBwOjRoxW03NiZM2cA6OjoYMuWLX2+Z9q0aQpabuonP/kJzzzzDEeOHOHEiRPU1tbi7+9PbGwsTzzxBGlpafoZKm5Nm0qLiIiIWETfOhQRERGxiIKWiIiIiEUUtEREREQsoqAlIiIiYhEFLRERERGLKGiJiIiIWERBS0RERMQiCloiIiIiFlHQEhEREfbu3cuyZcuYMmUKw4YNwzAMFixYMGDt79+/nxdeeIGEhASCg4MxDIPJkydf9/2ff/452dnZJCUlER0dja+vLyEhIcyaNYt9+/YNWF1WU9ASkVuOYRg9/nTtUWmFrKysHn1pKx8Zql555RV++9vfUlpayl133TXg7W/fvp3XX3+df/3rX/1qPzs7m7S0NE6dOsX06dNZsWIFs2fP5p///CePPfYY6enpA16jFbTXoYjckkaPHt0degICAizrJz4+nszMTGpra9m6datl/YhYbfPmzYSHh3PPPfdQVFTEjBkzBrT91atXs3HjRu69916qqqqIjo6+4fsffPBBDh48yPTp0zEMo/v4yZMnmThxIlu2bCElJYUf/ehHA1rnQFPQEpFbUlRUFOvWrbO8n/j4eOLj46msrFTQkiHtuwSrPXv28Pvf/57S0lKam5uJjo4mJSWFVatW4evr2+O9kyZN+lZtP/roo30eHzduHMnJyeTm5lJYWOj2QUu3DkVERORbW7x4Mb/4xS8oLy/nscce47nnniM4OJi1a9cyZ84c2traLOvbx8cHAG9vb8v6GCgKWiLiFh555BEMwyA7O7vXubVr12IYBkuWLPmv+6msrOyeS1VeXs78+fMJCQkhMDCQxMREPv74YwCqq6tZvHgxd955Jw6Hgx//+McUFhb+1/2L3Ap27drFzp07mT9/PmVlZeTl5fHaa69x5MgRMjMzKSwsZPv27Zb0feXKFfbu3YthGCQmJlrSx0BS0BIRt7Bz504iIyNZtWoVJSUl3ccPHDjApk2buO+++9iyZcuA9VdZWclDDz1EdXU1ixYtIjExkffff5/p06dz+vRpJk6cSHFxMcnJySQnJ3PixAnmzJnD2bNnB6wGkaFq69ateHt7k5ubi8Ph6HFu7dq1hISE8Oc//3nA+zVNk6eeeorq6mqWLl3KuHHjBryPgaY5WiLiFoKDg9mzZw/Tpk0jOTmZ4uJimpqaWLBgAQ6Hg7/+9a84nc4B66+oqIhXXnmFX/3qV93HNmzYQEZGBg899BCPP/44O3bswMOj8/Po7NmzSUlJYfPmzWzevHnA6hAZapqamjhx4gShoaHX/fDj6+vLqVOnBrzv9PR03nrrLR5++GFef/31AW/fCgpaIuI24uPj2bBhAy+++CJLlizhq6++4vz587zxxhuMHz9+QPuKiopizZo1PY4tXLiQjIwM2tra+M1vftMdsgCSk5NZtGgRpaWlA1qHyFBz+fJlTNPkq6++Yv369YPW74oVK9i6dStTp07lnXfe6TWS5q4UtETEraxevZrCwkL+8pe/APDzn/+c1NTUAe8nLi4OT0/PHsfCwsIAiI2NJTAwsMc5T09PRo4cyblz5wa8FpGhJCgoCIAJEyZQXFw8KH2mpaWRnZ3NjBkz+Pvf/46fn9+g9DsQNEdLRNyKYRjMmzev+/Xy5cst6afrl8W1vLy8rnuu67yV36QSGQoCAgL4/ve/zyeffMKlS5cs7cs0TZ599lmys7OZNWsW77zzzpAKWaCgJSJu5tNPP2XlypWMGDECDw8Pnn76aVpaWuwuS0SusWLFCq5evUpqaiq1tbW9zl++fPm/Hu0yTZNnnnmGnJwckpKSePvttwd0nuZg0a1DEXEbra2tJCcn09jYyD/+8Q+KiorYuHEj6enp/O53v7O7PJFbWn5+Pvn5+QDd21YdPXq0e4eF0NBQsrKyAEhNTeXf//43O3bsICYmhtmzZxMZGcmlS5c4c+YMH3zwAb/85S/Jycnpbv/w4cPk5eUB0NDQAHR+sLp226pdu3Z1P3/55ZfJy8vD6XQSFxfHr3/96141x8XF8cgjjwzQv4A1FLRExG2sXLmSkpIS1qxZw6xZs5g5cyaFhYXk5OSQkJDA/Pnz7S5R5JZVWlrK7t27exyrqKigoqIC6NzWqitoQefehUlJSeTk5PD+++9TW1tLcHBw9zIt39yQ+rPPPuvV/oULF3ocuzZonTlzBoDm5mZeffXVPmteuHCh2wctwzRN0+4iRETy8/OZN28ekyZN4oMPPuieL1VVVUVcXBwdHR2UlpYSFRV107YMw2DatGl9LjBaWVlJdHQ0Cxcu7PFDvT9/t6vvysrKb92uiNyeNEdLRGx39uxZUlNTGT58OHv27OkOWQARERHs3LmTuro6Hn/8cU1GF5EhRbcORcR2XXM7rmfu3LkM1OB7VFTUDdu60bm+RrJERG5EI1oicksqKirCMAwMw+ie2GuFrKwsDMMgOjrasj5EZOjSiJaI3HIyMzN7vA4ICLCsr/j4+B79xcXFWdaXiAw9mgwvIiIiYhHdOhQRERGxiIKWiIiIiEUUtEREREQsoqAlIiIiYhEFLRERERGLKGiJiIiIWERBS0RERMQiCloiIiIiFlHQEhEREbHI/wOvgQL4tcMZUgAAAABJRU5ErkJggg==", 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G = 6.67430e-11\n", "Msun = 1.9885e30\n", "\n", "def fcomet(xin, t):\n", " x = xin[0]\n", " y = xin[1]\n", " vx = xin[2]\n", " vy = xin[3]\n", " r = np.sqrt(x*x+y*y)\n", " return np.array([vx,vy,-G*Msun*x/r**3,-G*Msun*y/r**3])\n", "\n", "def error_definition_comet(x1, x2):\n", " return np.sqrt((x1[0]-x2[0])**2 + (x1[1]-x2[1])**2)\n", "\n", "x0 = [4.e12,0.,0.,500.]\n", "a = 0.\n", "b = 50. * 365. * 24. * 60. * 60.\n", "N = 1\n", "delta = 1. * 1.e3 / (365. * 24. * 60. * 60.)\n", "sol = bulirsch_stoer(fcomet, x0, a, N, b, delta, error_definition_comet)\n", "\n", "tpoints = [t for t in sol[0]]\n", "xpoints = [x[0] for x in sol[1]]\n", "ypoints = [x[1] for x in sol[1]]\n", "vxpoints = [x[2] for x in sol[1]]\n", "vypoints = [x[3] for x in sol[1]]\n", "vpoints = [np.sqrt(x[2]*x[2] + x[3]*x[3]) for x in sol[1]]\n", "\n", "plt.title(\"Solving the comet motion using Bulirsch-Stoer method\")\n", "plt.xlabel('x [m]')\n", "plt.ylabel('y [m]')\n", "plt.plot(xpoints_rk4_ref,ypoints_rk4_ref,label='Reference')\n", "plt.plot(xpoints,ypoints,'.',label='Bulirsch-Stoer adaptive')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.title(\"Coordinates\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('x,y [m]')\n", "plt.plot(tpoints_rk4_ref,xpoints_rk4_ref,label='x (Reference)')\n", "plt.plot(tpoints_rk4_ref,ypoints_rk4_ref,label='y (Reference)')\n", "plt.plot(tpoints,xpoints,'.',label='x (Bulirsch-Stoer adaptive)')\n", "plt.plot(tpoints,ypoints,'.',label='y (Bulirsch-Stoer adaptive)')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.title(\"Velocity\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('v [m/s]')\n", "plt.plot(tpoints_rk4_ref,vpoints_rk4_ref,label='v (Reference)')\n", "plt.plot(tpoints,vpoints,'.',label='v (Bulirsch-Stoer adaptive)')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()\n", "\n", "thpoints = []\n", "hpoints = []\n", "for i in range(len(tpoints) - 1):\n", " thpoints.append(0.5*(tpoints[i] + tpoints[i+1]))\n", " hpoints.append(tpoints[i+1] - tpoints[i])\n", " \n", "plt.title(\"Time steps H\")\n", "plt.xlabel('t [s]')\n", "plt.ylabel('H [s]')\n", "plt.plot(thpoints,hpoints,'.',label='Bulirsch-Stoer method')\n", "#plt.plot(tpoints,ypoints,label='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SIR model\n", "\n", "The SIR model is the simplest model for infection disease dynamics in the population.\n", "The population is split into susceptible ($S$), infected ($I$), and recovered/immune ($R$) parts.\n", "The SIR equations read\n", "\\begin{align*}\n", "\\frac{dS}{dt} & = -\\beta S I, \\\\\n", "\\frac{dI}{dt} & = \\beta S I - \\gamma I, \\\\\n", "\\frac{dR}{dt} & = \\gamma I.\n", "\\end{align*}\n", "\n", "Here $\\beta$ is the infection rate and $\\gamma$ is the recovery rate.\n", "They are inversely proportional to the average time each infected person spreads the disease to (when all of population is susceptible, $S \\approx 1$) and that it takes to recover. The ratio $R_0 = \\beta / \\gamma$ is basic reproduction number.\n", "\n", "Given that $S + I + R = 1 = \\rm const$ at all times, one only needs to solve two ODEs, e.g. $dS/dt$ and $dI/dt$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gam = 1./10. # 10 days recovery rate\n", "beta = 1./4. # 4 days to infect other person\n", "# R0 = beta/gam # basic reproduction factor\n", "kappa = 1. / 90. # immunity lasts for 90 days\n", "\n", "def fSIR(xin, t):\n", " S = xin[0]\n", " I = xin[1]\n", " R = 1. - S - I\n", " return np.array([-beta * S * I, beta * I * S - gam * I])\n", "\n", "t0 = 0.\n", "tend = 365.\n", "\n", "I0 = 1.e-5 # Initial fraction of infected\n", "x0 = [1. - I0, I0] # Initial conditions\n", "\n", "delta = 1.e-9 # The desired accuracy per day\n", "N = 50 # Minimum number of steps\n", "sol = bulirsch_stoer(fSIR, x0, t0, N, tend, delta)\n", "\n", "tpoints = [t for t in sol[0]]\n", "Spoints = [x[0] for x in sol[1]]\n", "Ipoints = [x[1] for x in sol[1]]\n", "Rpoints = [1. - x[0] - x[1] for x in sol[1]]\n", "\n", "\n", "\n", "#Nrk4 = 1000\n", "#hrk4 = (tend - t0) / Nrk4\n", "#sol = ode_rk4_multi(fSIR, x0, t0, hrk4, Nrk4)\n", "\n", "# Exponential phase\n", "texpon = np.linspace(0.,90.,50)\n", "def fIexp(t):\n", " R0 = beta / gam\n", " return x0[1] * np.exp(gam*(R0-1.)*t)\n", "Iexpon = fIexp(texpon)\n", "\n", "plt.title(\"Solving the SIR model using Bulirsch-Stoer method\")\n", "plt.xlabel('t [days]')\n", "plt.ylabel('Population fraction')\n", "plt.ylim(0,1)\n", "plt.plot(tpoints,Spoints,'.',label='Susceptible')\n", "plt.plot(tpoints,Ipoints,'.',label='Infected',color='red')\n", "plt.plot(tpoints,Rpoints,'.',label='Immune',color='green')\n", "plt.plot(texpon,Iexpon,label='Infected (Exponential phase)',color='red')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can clearly see the initial exponential phase of the epidemic, and its end once a sufficient amount of population obtained immunity.\n", "\n", "What if the immunity does not last forever but lost after some time (e.g. three months)?\n", "One can add this effect into the equations through the corresponds loss of immunity rate $\\kappa$:\n", "\n", "\\begin{align*}\n", "\\frac{dS}{dt} & = -\\beta S I + \\kappa R, \\\\\n", "\\frac{dI}{dt} & = \\beta S I - \\gamma I, \\\\\n", "\\frac{dR}{dt} & = \\gamma I - \\kappa R.\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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LvXv3YuTIkVi3bh04HA4KCgqQnJwMFxcX+Pj4yOUl6b905cqVCo8bERGBdevWYdOmTTJ9Y7Zs2QIej4fBgwer/BrerrIGAB6Ph7p16+LZs2fSbXfu3EFRURHatm2rsPq2U6dOWLduncrHrUz5XF1dAUCmfBcuXAAgboZS1DdF0jfj9u3bKh03KCgId+7cQXx8PE6fPo2rV68iPj4eR48exdGjR7Fx40YcPHhQYdOSIkKhEPPnz5fZxufzcfDgQbWaKiV8fHzkrgOXy0XdunVRWFiIhg0byj2nXr16SEhIkD7W5D0p+TsoKEgufWBgoFyz4YsXL/D333/D0dERy5cvV/ha+Hy+ytdFG2xsbNCnTx/88ccfaNWqFd5//3106tQJ77zzjtqj2FR9f0qGjHfq1EkuvYmJCfz9/TVq3o2KipK+30UiETIzM7F//35MnTpV2gQqKY+utGjRQqbpQ6Jv376YNWsWxo8fjxMnTqBbt24ICAhA48aNZfr+FBYW4vr166hbt65aI8hUvRZxcXFy/XTc3d1l5oJasGABpk6diuPHj+PixYu4cuUKEhISsHbtWqxfvx6//PILRo0apVK5JNc+JCRE4f53330X58+fx5UrV9C5c2fcvXsXubm58Pb2xoIFCxQ+x8LCQuFnprxzr4o2bdrIbatXr16F+8r2CdL293BZ6n7WVD3ft2/fxosXLxAYGKiwf3FwcLDclC+qoCDpPzweD6GhodIfutLSUvz+++8YOXIk1q9fj759+6Jfv37STq1OTk4K85GMFKmo8ysABAQEwMvLCwcPHsSzZ89gZ2eHy5cv48aNG+jfvz8cHR1VLr+iNwUg7iNTWloqfSwpV926dRWmL297ZSkqn+SHuGz5JJ0+T5w4Idfxtqznz5+rfGwTExMEBgYiMDAQAMAYw4kTJzB8+HAcP34cP//8Mz7//HOV8nJzc5N2RMzPz8fx48cxevRoDBo0CBcuXFC774iy66ZsX9m5czR5Typ7H3C5XGmfEolnz56BMYYnT57IBYn6tGvXLnz77bfYvn075s6dCwAwNzfHhx9+iO+//17l/iuqvj918fkxMTGRdqLPzMzEokWLsHDhQqxZs6bSeaujvPeTm5sbLl26hHnz5uHYsWPSgQSurq748ssvMWHCBACQdhRWd3oBVa9FXFyc3HsxKChIbsLMWrVqYdCgQRg0aBAAcfC2ZMkSLFy4EOPHj0fv3r1Vum7qfs4k32X37t1T+plR9F1W3jFUoez8KdtXXFws3VYV38OqlE/RZ03V813RZ1PTc1rjR7eVh8vl4sMPP5TOe3Py5EkAby5wVlaWwudlZmbKpKtIeHg4Xr16hV27dgFQv8O2umxtbQGIRwAoUt52XZGctxUrVoCJm4MV3jZs2KDxMTgcDkJDQ7Fw4UIAb66tumxtbfHBBx9g27ZtyMvLw7Bhw6QduHVJk/ek5G9F17u0tFRuhJIkfatWrZRel8q8fkmn0fImT1T0j4eFhQXmzZuHu3fvIi0tDVu3bkWnTp2wefNmDBw4UOOylEfXnx9Jp9RLly7JbOdwOOWeJ0lwUlnKZvf38/PDrl27kJubi8uXL2PJkiUQiUSYOHGi9LMp6bCbkZGhlfK8bd68eXLvPVVGFVpZWWHBggXo1KkTXr16Ve4I4Lep+zmT3A8YMEDp5yUlJUUuL32vrKCL72FVy6Du+S7vM1hePhWhIKkCkqYQyZe/jY0NPD09kZGRgXv37smlj42NBQC0bt1apfzDw8OlQ0+Li4uxY8cOODo6amVouiKNGjWChYUF/vnnHxQUFMjtP3funFr5cblcALL/AVSGZMSWZAh8VXr72mqqV69e6N69Oy5fvozt27dro2hq0eQ9Kfn79OnTcunPnj0r9wNsbW2NJk2a4MaNG1U2t4ydnR0A8aiutyUlJVX44+/q6oohQ4bg+PHj8Pb2xpkzZ7ReVkmzkaLPiUgkwvnz57V6PEnzw9tDxe3s7BSep9LSUly7dk2rZVDG1NQUbdq0wfTp07Fjxw4AwL59+wCIg5GmTZvi8ePHOi2TqhR9/pV9n0mufXmBmGS75LPVqFEj1KpVCxcvXpSppTEGmnwPa/u3QJPzbWlpiWvXrin8h0rTaTlqfJC0Y8cOnDhxQu5LCBBHnr/++isAoHPnztLtI0eOBGMMX3zxhcwbIicnR9r2PHLkSJWO7+bmhuDgYFy8eBHLly9HTk4OBg8eXGXDqM3MzDBo0CAIhUJpTYrE33//La3JUpWkWUbRF7Ym2rZti8DAQOzduxfr169XmObff/9FdnZ2hXkdO3YMe/fuVfgF9fz5c2nfmrLXVlOS6x4VFaWXZSTUfU9KmiQWLVokE0i8fPkSM2fOVHiMKVOm4PXr1xg5cqTCgOXZs2cq9cUrT6NGjWBra4sDBw7IXN+ioiJMmjRJLv2TJ09k+mZJFBYWoqCgAFwuV+0pGSoSEBAAT09PxMbG4ujRozL71q5dq9XpJl69eoXVq1cDgNycSO+88w7S0tLk5qtZuHBhuXPeaMulS5cU/rcu2WZubi7dJrlun332GfLz82XSl5aWSmsDqsL//ve/cudWOnfuHGJjY2FqaoqOHTtKtyv7PgsICICvry/OnTsnN1fZnj17cObMGfj4+Ej7q5mammLixInIzMzEpEmTUFRUJJdnZmYmbt68qfFrrCqafA9r+7dA3fPN4/EwZMgQFBQUyPWjunz5ssaz1tf4PkkJCQlYsWIFnJyc0KlTJ3h4eAAAUlJScPjwYRQVFaFfv34yVffTpk3D0aNHceDAAbRo0QI9e/aUzkmTnZ2NL7/8UmHHzvIMHz4csbGxmD17tvRxVVqyZAlOnTqF7777DgkJCfD390dmZiZ2796Nnj17Yv/+/TLzZSjTsWNHWFpaYvny5cjNzZW2B0+cOFHlJse3bd++HV26dMGoUaOwcuVKvPPOO6hVqxbS09Pxzz//4Pr167hw4QLq1KmjNJ/bt29j8uTJsLOzQ2BgILy9vWFqaor09HQcPnwYeXl5eOedd6R9KCqjbdu26NevHw4cOIDo6GiMHTu20nmqQ933ZEBAACZOnIhVq1ahadOmGDhwoHSeJDs7O4WzMI8cORJ//fUXVq9eDU9PT4SFhaFBgwZ4+vQpUlJScObMGYwYMQK//PKLRq+Bx+NhypQpmDdvHlq1aoUBAwagpKQEJ06cQL169aQdTCUyMjLQoUMH+Pn5oXXr1nB1dUV+fj4OHTqErKwsTJgwQdo8pi0mJiZYt24dunfvjr59+0rnSfrnn39w4sQJ9OjRA0ePHlX58yMRFxcn/WJnjCEzMxNHjx5Feno6GjZsKP1ukJg2bRqOHz+Ofv36YdCgQbC3t8f58+eRkpKC4ODgKl1EdPv27fjpp58QFBQELy8v2NnZITk5GX/88Qf4fL5M/75PPvkE586dw+bNm+Hl5YV+/fqhdu3ayMjIQGxsLEaOHKn2gqOq2rZtG7788ks0atQIHTp0gLOzMwoLC3Hjxg2cOnUKjDH88MMPMu+rrl274n//+x9Gjx6N999/H9bW1qhVqxYmTJggrfHv1q0bBg0ahH79+qFRo0a4c+cO9u/fDxsbG2zevFnm2s+ZMwd///03fvnlF/zxxx/o0qUL6tevj+zsbNy7dw/x8fFYtGgRGjduXCXnoDLU/R7W9m+BJuf7m2++wcmTJ7F8+XJcvnxZOk/Srl270LNnT83WYVVrLFw1lJaWxn788UfWv39/5uPjw2xsbBiPx2NOTk6sR48ebMuWLQrn1SkqKmKLFi1iTZo0Yebm5sza2poFBASw7du3y6Utb/itREFBAbOysmIAWNOmTcstq7IpAFQdNi2Rnp7OwsPDmaOjIzM3N2ctWrRgGzduZL/99hsDwJYvX15uOd529OhR1qFDB+lrQJkhtJJhn4qGRCs7L/n5+WzRokWsdevWzMrKipmbmzN3d3fWs2dPtmbNGvb8+fMKy/XkyRMWHR3NPvroI+bn58dq1arFTE1NmaOjIwsODmY//fQTe/XqlcIyqTNPksS1a9cYh8Nh9evXV2m+JCgZxl3edWNM8fuAMfXek4wxJhKJ2KpVq1ijRo2YmZkZc3Z2ZuPGjWN5eXlKj//HH3+wXr16sdq1azMej8fq1q3L2rVrx2bPns1u3bql8mssr0zffvsta9iwIePxeMzV1ZV98cUXrLCwUK5Mz549Y/Pnz2chISGsXr16zMzMjDk5ObGgoCC2fft2uWkBFJVF0/fnxYsX2bvvvsusra2ZtbU169q1Kzt//jwbP348A8CuXbum0ustbwoAS0tL1rx5czZ79myFUy4wxtjBgwdZmzZtGJ/PZ/b29mzQoEEsNTVVa1MAlPd9dfHiRfbpp5+y5s2bMzs7O2Zubs48PT1ZRESEwmH1jDG2detW1rlzZ2Zra8v4fD5zd3dngwcPZn/99Zc0TUVDyNV9L125coUtWLCAhYSEMHd3d2Zubs74fD5r2LAhGzx4sMy8YWX98MMP0s+Eos/87du32dChQ5mTkxMzNTVlTk5ObMiQIez27dsK8xOJRGzz5s2sS5cuzM7OjvF4PFavXj0WEBDAFi1aJDPFQ0XnXhll50/Z74Q2v4er4rdA3fOdmZnJRowYIfPbtmHDhgp/K8vDYUwPPU2JwZo9eza++eYbHDt2DGFhYfouDiFGJSAgAAkJCRAKhbCystJ3cQghlVTj+yTVVI8ePZLb9u+//2LlypVwcHBQOH8OIUQ8Z5SiPlkbN27E+fPn0b17dwqQCKkmDLJP0p49e3D69Glcu3YNf//9NwoKCjBkyBCFa9xUJD09HXPnzsWxY8eQm5sLZ2dn9O/fH1FRUdLRNDVR27Zt4eXlhaZNm8LKygr37t3D4cOHIRKJ8Ouvv8p0viSEvJGWloZWrVqhW7du8PLyQklJiXQCWjs7O4VrMRJCjJNBNre1bNkSf//9N6ytreHi4oLbt29rFCQlJyfD398f2dnZ0k5fly5dki6sGB8fLzdpXk3x9ddf4+DBg0hNTYVQKIRAIEDHjh0xbdo0qkUiRIlnz55h+vTpOHv2LB49eoSioiI4OTmhW7dumD17tsJZ0gkhxskgg6TY2Fi4uLjAy8sLp0+fRkhIiEZBUlhYGGJiYrBy5UpMnDhRun3KlClYtmwZxo4dq/FIHEIIIYRUbwYZJJUVFxenUZCUnJwMLy8veHh4ICkpSWaYYEFBAZydnSESiZCdnQ1ra+uqKDohhBBCjFi17bgtmWU4NDRUbs4SGxsbBAQEoKioSOFkdIQQQgghBtlxWxvu3LkDAPD29la439vbGzExMbh79y66du0qt18kEiE1NRU8Hk9mHR0+n6/x6syEEEIIqVqMMRQUFKBevXpqT+z6tmobJEnWbilvpk/J9vLWg3r06BE8PT2rpGyEEEIIqVoPHz6Ei4tLpfKotkFSRSRdscpbbVmy+OHNmzelfwOVq0nKEhYhdNkZiMr0AuNyODg+ORBOAguDTJNwPxejNl2Wey3rh7dD+4b2cq/vQe4LuDlYSp9vUCZOBDZvBr76CvjiC32XhhBCSBXIz8+Hq6urzG+3pqptkCSpKVK0GjAA6WKL5dU0SYKn+vXra239J1tbW3z78TuYtfc6ShkDl8PBN+81hY9rXYNN09SDB1NzS7lAqolHXdjavgmEdiWmYebefyFigAkHWPxeMwxq10Ar503rbG3FN0IIIdVWeZUg6qi2QZKvry8AlLsq97179wAAPj4+OisTAAxq1wCdfWojNecF3B0t4aygxsWQ0jgLLLD4vWZygVTZdJnCImmABAAiBszaex2dfWorPKbevH4tvjcz0285CCGEGIVqGySFhIQAAGJiYiASieSmAIiPj4eFhQU6dOig87I5CywqDB4MKU1FgVRKTqFMTRMAlDKG1JwXFCQRQggxWkY/BUBxcTFu376N5ORkme2enp4IDQ1FamoqfvrpJ5l9UVFRKCwsRHh4OK2xpCJngQU6ejooDHo8HK1g8latJpfDgbujpY5KpyIKkgghhKjBIGuS9u/fj/379wMAsrKyAAAXLlxAREQEAMDR0RHff/89ACAjIwN+fn5wc3NDamqqTD6rV6+Gv78/Jk2ahJMnT8LPzw8JCQmIjY2Fj48PFi1apKuXVK2p0iRnEF69Et9TkEQIIUQFBhkkXbt2DZs2bZLZdv/+fdy/fx8A4ObmJg2SlPH09MTly5elC9weOXIEzs7OmDRpEqKiomBvb19hHkQ1qvR/0jtJTRLNc6VUcXExSktL9V0MQgiRweVywePxdHpMg1+WRF/y8/MhEAggFAq1NrqN6Jm/P3DhArBvH9C/v75LY3Dy8/ORk5ODV5IaN0IIMTB8Ph+Ojo5Kf5e1+fttkDVJpPrKFBYhJacQHo5Wuq9toj5J5crPz0dGRgasra3h6OgoN9M8IYToE2MMxcXFEAqFyMjIAACdVGBQkER0Ru9zKVGQVK6cnBxYW1vDxcWFgiNCiEGysLCAjY0N0tPTkZOTo5MgyehHtxHjUN5cSpnCIt0VgoIkhYqLi/Hq1SsIBAIKkAghBo3D4UAgEODVq1coLi6u8uNRkER0QtlcSjpDQZJCkk7auu4QSQghmpB8V+ligAkFSUQnDGIuJUmHZBrdphDVIhFCjIEuv6soSCI6IZlLifvfm1svcylRTRIhhBA1UJBEdGZQuwY4NyMEO0Z3wLkZIbpfAJeCpBorISEBAwYMQIMGDcDn81G3bl107NgRU6dO1XfRtOrIkSOYN2+ewn3u7u7SCXkBIC4uDhwOB3v27Kkw33nz5lFNI6mRKEgiOqVseZMqR0FSjXT48GH4+/sjPz8f3333HWJiYrBixQoEBARg165d+i6eVh05cgTz589XuG/fvn2YM2eOjktEiHGjKQBIzUFBUo303XffwcPDA8ePH4ep6ZuvvI8++gjfffedHkumW61atdJ3EQgxOlSTRGqG0lJAJBL/TUGSTmUKi3A+OUe30z2UkZubC0dHR5kAScLE5M1XIIfDUdhU9XYz1YsXLzBt2jR4eHjA3Nwc9vb2aNu2LXbs2CHzvISEBPTp0wcODg4wNzeHp6cnIiMjZdLcu3cPgwcPRp06dcDn8+Hn5ye3ILekWWzr1q2YMmUKnJycYGFhgaCgIFy9elWaLiIiQvpcDocjvUnWtHz7dUi8fPlSab7K7Nq1Cx07doSVlRWsra0RFham8nMJMQYUJJGaQVKLBFCQpEO7EtMQsOQUBv+agIAlp7ArMU3nZejYsSMSEhIwadIkJCQkVHpulSlTpuDnn3/GpEmTcOzYMWzZsgUffPABcnNzpWmOHz+OwMBApKWlYenSpTh69Ci++uorPH78WJrm5s2baNeuHa5fv44ffvgBhw4dQq9evTBp0iSFTWazZs3C/fv3sW7dOqxbtw6PHj1CcHCwdE3LOXPmYODAgQDEC4JLbs7OzkpfT0X5luebb77Bxx9/jMaNG2P37t3YsmULCgoKEBgYiJs3b6p8PgkxaIwoJBQKGQAmFAr1XRSiDc+eMQaIb69e6bs0BqWoqIjdvHmTFRUVaTXfR3kvmMeMQ8xt+ptbwxmH2aO8F1o9TkVycnJYp06dGAAGgPF4PObv788WL17MCgoKpOkAsKioKLnnu7m5seHDh0sfN23alPXv31/pMT09PZmnp6fScxoWFsZcXFzkvmMmTJjAzM3N2dOnTxljjMXGxjIArHXr1kwkEknTpaamMh6Pxz755BPptvHjx7Pyvtbffh3q5BsVFSWTb1paGjM1NWUTJ06UOUZBQQFzcnJiH374Ybmvm5DKqug7S5u/31STRGqGsjVJNGmiThjEBKIAHBwccPbsWSQmJmLJkiXo168f7t69i5kzZ6JZs2bIyclRK7/27dvj6NGjmDFjBuLi4lBUJNuMePfuXSQnJ2PUqFEwNzdXmMfLly9x8uRJDBgwAJaWligpKZHeevbsiZcvX+LixYsyzxk8eLDMCDM3Nzf4+/sjNjZWrfK/TZN8jx8/jpKSEoSHh8uU3dzcHEFBQYiLi6tUmQgxFBQkkZpBEiTxeAANZdYJg5hAtIy2bdti+vTp+O233/Do0SNMnjwZqampanfeXrlyJaZPn479+/cjJCQE9vb26N+/P+7duwcAePLkCQDAxcWl3Dxyc3NRUlKCVatWgcfjydx69uwJAHLBm5OTk1w+Tk5OMs18mtAkX0mzYbt27eTKv2vXLrUDT0IMFY1uIzUDjWzTOckEorP2XkcpY/qZQLQcPB4PUVFRWLZsGa5fvw4A4PP5eCWZlb2Mt4MFKysrzJ8/H/Pnz8fjx4+ltUp9+vTB7du3Ubt2bQBAenp6uce3s7MDl8vFsGHDMH78eIVpPDw8ZB5nZWXJpcnKyoKDg4PyF1sBTfJ1dHQEAOzZswdubm6VOj4hhoyCJFIzUJCkF4PaNUBnn9pIzXkBd0dLvQRImZmZCjsv37p1CwBQr149AOLRX//8849MmlOnTuH58+fl5l23bl1ERETg77//xvLly/HixQv4+PjA09MT69evx5QpU8BXsAyOpaUlQkJCcPXqVTRv3hxmKrwvd+zYgSlTpkibxh48eIDz588jPDxcmkZyrKKiIlhYqHauVcn3bWFhYTA1NUVycjLef/99lY5DiDGiIInUDBQk6Y2zwEKvtUdhYWFwcXFBnz590KhRI4hEIly7dg0//PADrK2t8fnnnwMAhg0bhjlz5mDu3LkICgrCzZs38eOPP0IgEMjk984776B3795o3rw57OzscOvWLWzZsgUdO3aEpaW4KfGnn35Cnz590KFDB0yePBkNGjRAWloajh8/jm3btgEAVqxYgU6dOiEwMBCfffYZ3N3dUVBQgKSkJPzxxx84deqUzHGzs7MxYMAAjB49GkKhEFFRUTA3N8fMmTOlaZo1awYA+Pbbb9GjRw9wudwKgzBV8n2bu7s7vv76a8yePRv3799H9+7dYWdnh8ePH+PSpUvS2jZCjF6lu35XUzS6rZpJTBSPbGvQQN8lMThVNbrNUOzatYsNHjyYeXt7M2tra8bj8ViDBg3YsGHD2M2bN6XpXr16xb788kvm6urKLCwsWFBQELt27ZrcqLAZM2awtm3bMjs7O8bn81nDhg3Z5MmTWU5OjsxxL1y4wHr06MEEAgHj8/nM09OTTZ48WSZNSkoKGzlyJKtfvz7j8Xisdu3azN/fny1cuFCaRjIKbcuWLWzSpEmsdu3ajM/ns8DAQHb58mWZ/F69esU++eQTVrt2bcbhcBgAlpKSwhgrf3SbKvm+PbpNYv/+/SwkJITZ2toyPp/P3Nzc2MCBA9mff/6p0rUhRBO6HN3GYYwxZUFUTZWfnw+BQAChUAhbW1t9F4dUVnw80KkT4OUF/NfBloi9fPkSKSkp0skRiWGJi4tDSEgIfvvtN+k8SITUZBV9Z2nz95tGt5GagZrbCCGEqImCJFIzUJBECCFETdRxmxicTGERUnIK4eFopb0OvxQkESMVHBwM6hVBiH5QkEQMyq7ENMzc+y9EDDDhAIvfa4ZB7RpUPmMKkgghhKiJmtuIwcgUFkkDJAAQMWDW3uvaWT1eEiQpmLOGEEIIUYSCJGIwqnStL8lMylSTRAghREUUJBGDUaVrfVFzGyGEEDVRkEQMhmStL+5/yyNoda0vCpIIIYSoiTpuE4NSZWt9UZBECCFETRQkEYNTJWt9UZBECCFETdTcRmoGCpIIIYSoiYIkUjPQFAA11saNG8HhcHD58mW1n5uamopevXrB3t4eHA4HkZGRWi/f6tWrsXHjRq3nCwAcDgfz5s2rkrwJqQmouY3UDDQFANHA5MmTkZCQgPXr18PJyQnOzs5aP8bq1avh6OiIiIgIredNCKkcCpJIzUDNbfqTng7cuwd4ewMuLvoujVquX7+O9u3bo3///vouCiFED6i5jdQMFCTpR3Q04OYGdOkivo+O1neJEBERAWtrayQlJaFnz56wtraGq6srpk6dilf/1TjGxcWBw+EgKSkJR48eBYfDAYfDQWpqKgAgPz8f06ZNg4eHB8zMzFC/fn1ERkaisLBQ5lgikQirVq1Cy5YtYWFhgVq1aqFDhw44ePAgAMDd3R03btzA6dOnpcdwd3eXPl/V4+Tn52P06NFwcHCAtbU1unfvjrt371bdSSSkhqCaJFIzUJCke+npwJgxgEgkfiwSAWPHAmFheq9RKi4uRt++fTFq1ChMnToVZ86cwYIFCyAQCDB37ly0bt0aFy5cwIABA+Dp6Ynvv/8eAODs7IwXL14gKCgI6enpmDVrFpo3b44bN25g7ty5+Pfff/Hnn3+C899cXxEREdi6dStGjRqFr7/+GmZmZrhy5Yo02Nq3bx8GDhwIgUCA1atXAwD4//WbU/U4jDH0798f58+fx9y5c9GuXTvEx8ejR48euj+xhFQ3jCgkFAoZACYUCvVdFKINQ4cyBjD2/ff6LonBKSoqYjdv3mRFRUXazfjUKfE5f/sWG6vd41Rgw4YNDABLTExkjDE2fPhwBoDt3r1bJl3Pnj2Zr6+vzDY3NzfWq1cvmW2LFy9mJiYm0vwk9uzZwwCwI0eOMMYYO3PmDAPAZs+erbR8TZo0YUFBQXLbVT3O0aNHGQC2YsUKmXSLFi1iAFhUVJTS4xNibCr6ztLm7zc1t5GagUa36Z63N2Dy1lcMlwt4eemnPGVwOBz06dNHZlvz5s3x4MGDCp976NAhNG3aFC1btkRJSYn0FhYWBg6Hg7i4OADA0aNHAQDjx4/XqIyqHic2NhYAMGTIEJnnDx48WKPjEkLeoOY2UjNQc5vuubgAa9eKm9hKS8UB0po1em9qAwBLS0uYm5vLbOPz+Xj58mWFz338+DGSkpLA4/EU7s/JyQEAPHnyBFwuF05OThqVUdXj5ObmwtTUFA4ODjL7NT0uIeQNCpJIzUBTAOjHqFHiPkhJSeIaJAMIkCrL0dERFhYWWL9+fbn7AaB27dooLS1FVlaWRlMHqHocBwcHlJSUIDc3VyZQysrKUvuYhBBZ1NxGagaqSdIfFxcgOLhaBEgA0Lt3byQnJ8PBwQFt27aVu0lGp0k6Tv/8889K8+Pz+SgqKtL4OCEhIQCAbdu2yTx/+/btlXylhBCqSSI1AwVJREsiIyPx+++/o3Pnzpg8eTKaN28OkUiEtLQ0xMTEYOrUqXjnnXcQGBiIYcOGYeHChXj8+DF69+4NPp+Pq1evwtLSEhMnTgQANGvWDDt37sSuXbvQsGFDmJubo1mzZiofJzQ0FJ07d8aXX36JwsJCtG3bFvHx8diyZYuezxQhxo+CJFIzUJBEtMTKygpnz57FkiVLsHbtWqSkpMDCwgINGjTAu+++KzPP0caNG9G6dWtER0dj48aNsLCwQOPGjTFr1ixpmvnz5yMzMxOjR49GQUEB3NzckJqaqvJxTExMcPDgQUyZMgXfffcdXr9+jYCAABw5cgSNGjXS8dkhpHrhMMaYvgthiPLz8yEQCCAUCmFra6vv4pDKat0auHoVOHZM3EeGSL18+RIpKSnw8PCQ68xMCCGGpqLvLG3+flOfJFIzUE0SIYQQNVGQRGoGCpIIIYSoiYIkUjPQFACEEELUREESqRmoJokQQoiaKEgiNQMFSYQQQtREQRKpGShIIoQQoiYKkkjNQAvcEkIIURMFSaT6Y4xqkgghhKiNgiRS/RUXv/mbgiRCCCEqoiCJVH+SWiSAgiRCCCEqoyCJVH8UJNVoGzduBIfDweXLl/VdFEKIkaEgiVR/kiCJwwG4XP2WhRBCiNGgIIlUf2VHtnE4+i0LIYQQo0FBEqn+aGSbXqXnpyM2JRbp+en6LgoAICIiAtbW1rh9+zbCwsJgZWUFZ2dnLFmyBABw8eJFdOrUCVZWVvDx8cGmTZtkni9pvjt16hRGjx4NBwcH2NraIjw8HIWFhcjKysKHH36IWrVqwdnZGdOmTUNxmcEDcXFx4HA4iIuLk8k3NTUVHA4HGzdulCtrUlISevbsCWtra7i6umLq1Kl4JVlq5z+vX7/GwoUL0ahRI/D5fNSuXRsjRozAkydPtHsCCalBKEgi1R8FSXoTfSUabsvd0GVzF7gtd0P0lWh9FwkAUFxcjPfeew+9evXCgQMH0KNHD8ycOROzZs3C8OHDMXLkSOzbtw++vr6IiIjAX3/9JZfHJ598AoFAgJ07d+Krr77C9u3bMXr0aPTq1QstWrTAnj17MHz4cPzwww9YtWpVpcrat29fdO3aFQcOHMDIkSOxbNkyfPvtt9I0IpEI/fr1w5IlSzB48GAcPnwYS5YswYkTJxAcHIyioiKNj09IjcaIQkKhkAFgQqFQ30UhlXXlCmMAY/Xq6bskBqmoqIjdvHmTFRUVaTXfh8KHzGS+CcM8SG/c+Vz2UPhQq8epyIYNGxgAlpiYyBhjbPjw4QwA+/3336VpiouLWe3atRkAduXKFen23NxcxuVy2ZQpU+Tymzhxosxx+vfvzwCwpUuXymxv2bIla926tfRxbGwsA8BiY2Nl0qWkpDAAbMOGDdJtkrLu3r1bJm3Pnj2Zr6+v9PGOHTvkXhNjjCUmJjIAbPXq1cpOESFGpaLvLG3+fhtsTVJ6ejpGjhyJevXqgc/nw93dHZGRkXj27Jla+Rw8eBDvvvsuXFxcYGFhgYYNG+KDDz7AhQsXqqjkxOBQTZJe3Mu9BxETyWwrZaVIepqkpxK9weFw0LNnT+ljU1NTeHl5wdnZGa1atZJut7e3R506dfDgwQO5PHr37i3z2M/PDwDQq1cvue2Knq9OWfv06SOzrXnz5jJ5Hjp0CLVq1UKfPn1QUlIivbVs2RJOTk5yTXuEENWY6rsAiiQnJ8Pf3x/Z2dno168fGjVqhEuXLmHFihU4duwY4uPj4eDgUGE+06ZNww8//AAHBwf0798fjo6OSEpKwoEDB/D7779j48aNCA8P18ErInpFQZJeeDt4w4RjIhMocTlceNl76bFUYpaWljA3N5fZZmZmBnt7e7m0ZmZmePnypdz2t9Oa/ff+UrRd0fMrU1Y+ny+T5+PHj5GXlyctw9tycnI0Pj4hNZlBBknjxo1DdnY2Vq5ciYkTJ0q3T5kyBcuWLcPs2bPxyy+/KM0jKysLy5YtQ926dfHPP/+gTp060n2xsbHo0qULoqKiKEiqCShI0gsXWxes7b0WYw+NRSkrBZfDxZrea+Bi66LvoumVJOB5u+N1ZQIZR0dHODg44NixYwr329jYaJw3ITWZwQVJycnJiImJgYeHB8aPHy+zb/78+Vi7di02b96M77//HtbW1uXm8+DBA4hEIrzzzjsyARIAhISEwMbGhv67qilocVu9GdV6FMK8wpD0NAle9l41PkACAHd3dwDAP//8g7CwMOn2gwcPapxn7969sXPnTpSWluKdd96pbBEJIf8xuCApNjYWABAaGgoTE9kuUzY2NggICEBMTAwSEhLQtWvXcvPx9vYGn89HQkICsrOz5WqSCgoKMGDAgKp5EcSwSP5jp5okvXCxdaHgqAwnJye8++67WLx4Mezs7ODm5oaTJ09i7969Guf50UcfYdu2bejZsyc+//xztG/fHjweD+np6YiNjUW/fv3o+44QDRhcx+07d+4AEAc5iki23717V2k+9vb2+N///ocnT56gcePGGD16NGbOnIkPPvgA3bt3R2hoaIVNdgCQn58vc3u7ipwYAUnfDQsL/ZaDkP9s2bIFXbt2xfTp0/HBBx8gIyMDO3bs0Dg/LpeLgwcPYtasWdi7dy8GDBiA/v37Y8mSJTA3N0ezZs20WHpCapBKj4/TstGjRzMA7Ndff1W4f9asWQwA++abb1TK78CBA8zOzo4BkN68vLzYtm3blD5PMoTw7VtUVJS6L4no24YN4ikAevbUd0kMUlVNAUAIIVWBpgBQgjEGQDwstiKLFy/GgAEDEBERgeTkZBQWFuKvv/5Cw4YNMWTIEHz55ZcV5vHw4UMIhULpbebMmZV+DUTHJDVJb40QIoQQQpQxuCBJIBAAAIRCocL9+fn5MunKc+rUKcyaNQv9+vXD0qVL0bBhQ1haWqJ169bYt28f6tevjx9++AHJyclK87G1tZW58anzr/GRzDZMQRIhhBA1GFyQ5OvrC6D8Pkf37t0DAPj4+CjN5/DhwwDEI9neZmlpifbt20MkEuHq1auVKS4xBlSTRAghRAMGFyRJgpqYmBiIRLKz9RYUFCA+Ph4WFhbo0KGD0nxe/zfsu7zFHSXbqWbIOGUKi3A+OQeZQhXWpKIgiRBCiAYMLkjy9PREaGgoUlNT8dNPP8nsi4qKQmFhIcLDw2FlZQVAvPjj7du35ZrNAgMDAQBr165FRkaGzL6jR48iPj4e5ubm8Pf3r8JXQ6rCrsQ0BCw5hcG/JiBgySnsSkxT/gQKkgghhGjA4OZJAoDVq1fD398fkyZNwsmTJ+Hn54eEhATExsbCx8cHixYtkqbNyMiAn58f3NzckJqaKt0+cOBAvPvuu/jzzz/h5+eHAQMGwMnJCbdu3cKhQ4fAGMOSJUtUWt6EGI5MYRFm7v0XInH/fYgYMGvvdXT2qQ1nQTlD/ClIIoQQogGDDJI8PT1x+fJlzJ07F8eOHcORI0fg7OyMSZMmISoqSuH6Sm8zMTHBkSNH8NNPP2Hnzp3Yt28fXrx4AXt7e/Ts2ROTJk1CaGioDl4N0aaUnEJpgCRRyhhSc15UHCTRPEmEEELUYJBBEgC4urpiw4YNFaZzd3eXTgvwNh6Ph8jISERGRmq5dERfPBytYMKBTKDE5XDg7mhZ/pOoJokQQogGDK5PEiHKOAsssPi9ZuD+N08Wl8PBN+81Lb8WCaAgiRBCiEYMtiaJkPIMatcAnX1qIzXnBdwdLZUHSAAFSYQQQjRCNUnEKDkLLNDR06HiAAmgySRruI0bN4LD4eDy5csaPT81NRW9evWCvb09OBxOlTTfr169Ghs3btR6voB4dYJ58+aplPbs2bPg8/l48OCBdFtwcDA4HI7Cm7u7e5WU2ZicP38e8+bNQ15enty+4OBgBAcHa5RvZZ6rSFxcHDgcDvbs2aO1PLUpOjoa9evXR2Fhob6LIoNqkkj1RzVJpBImT56MhIQErF+/Hk5OTnB2dtb6MVavXg1HR0dERERoPW9VMcYQGRmJ0aNHw83NTWZfw4YNsW3bNrnn0Dxz4iBp/vz5iIiIQK1atWT2rV69Wj+FMkLDhw/Ht99+i++++w7z58/Xd3GkKEgi1R8FSaQSrl+/jvbt26N///76LkqVOnbsGK5cuYLt27fL7VNlAl8ir3HjxvougtEwNTXF2LFjsWDBAkyfPh2WlkoG4+gQNbeR6o+CJPKWiIgIWFtbIykpCT179oS1tTVcXV0xdepUvHr1CsCb5omkpCQcPXpU2sQkmY8tPz8f06ZNg4eHB8zMzFC/fn1ERkbKNReIRCKsWrUKLVu2hIWFBWrVqoUOHTrg4MGDAMQjdG/cuIHTp08rbMZS9Tj5+fkYPXo0HBwcYG1tje7du5e7vJMiP//8M9q1ayddGkodjDH07NkTDg4OSEt7M7nrixcv0KRJE/j5+UnLO2/ePHA4HFy9ehXvvfcebG1tIRAIMHToULkVEkQiEb777js0atQIfD4fderUQXh4ONLT02XSBQcHo2nTpkhMTERgYCAsLS3RsGFDLFmyRG7lBlXPJ4fDwYQJE7Blyxb4+fnB0tISLVq0wKFDh6Rp5s2bhy+++AIA4OHhIb1+cXFx0nK93WQ2f/58vPPOO7C3t4etrS1at26N6OjockdpV8Td3R29e/fGvn370Lx5c5ibm6Nhw4ZYuXKlwvTFxcWYPXs26tWrB1tbW7z77ru4c+eOTJoTJ06gX79+cHFxgbm5Oby8vDB27Fjk5OTIpHvy5AnGjBkDV1dX8Pl81K5dGwEBAfjzzz9l0v3555/o2rUrbG1tYWlpiYCAAJw8eVKubEOGDEF+fj527typ0bmoClSTRKo/CpI0wxjw4oW+S/GGpSXw36hGbSguLkbfvn0xatQoTJ06FWfOnMGCBQsgEAgwd+5ctG7dGhcuXMCAAQPg6emJ77//HgDg7OyMFy9eICgoCOnp6Zg1axaaN2+OGzduYO7cufj333/x559/gvNfWSMiIrB161aMGjUKX3/9NczMzHDlyhVpsLVv3z4MHDgQAoFA2jwjacZS9TiMMfTv3x/nz5/H3Llz0a5dO8THx6NHjx4qnYvXr1/jzz//xMSJE8tNU1JSIrfNxMQEJiYm4HA42LJlC1q2bIkPP/wQZ8+eBY/Hw7hx45CSkoKEhATpKgkSAwYMwIcffohPP/0UN27cwJw5c3Dz5k0kJCSAx+MBAD777DOsXbsWEyZMQO/evZGamoo5c+YgLi4OV65cgaOjozS/rKwsDBkyBFOnTkVUVBT27duHmTNnol69eggPD1frfEocPnwYiYmJ+Prrr2FtbY3vvvsOAwYMwJ07d9CwYUN88sknePr0KVatWoW9e/dKm2KV1SClpqZi7NixaNCgAQDg4sWLmDhxIjIyMjB37tyKLpVC165dQ2RkJObNmwcnJyds27YNn3/+OV6/fo1p06bJpJ01axYCAgKwbt065OfnY/r06ejTpw9u3boFLpcLAEhOTkbHjh3xySefQCAQIDU1FUuXLkWnTp3w77//Sq/PsGHDcOXKFSxatAg+Pj7Iy8vDlStXkJubKz3e1q1bER4ejn79+mHTpk3g8XhYs2YNwsLCcPz4cXTt2lWa1snJCY0aNcLhw4cxcuRIjc6F1jGikFAoZACYUCjUd1FIZbm6MgYwdvmyvktikIqKitjNmzdZUVGR7I7nz8XnzVBuz59r9Po2bNjAALDExETptuHDhzMAbPfu3TJpe/bsyXx9fWW2ubm5sV69eslsW7x4MTMxMZHJkzHG9uzZwwCwI0eOMMYYO3PmDAPAZs+erbSMTZo0YUFBQXLbVT3O0aNHGQC2YsUKmXSLFi1iAFhUVJTS4yckJDAAbOfOnXL7goKCGACFt1GjRsmkPXfuHDM1NWWRkZFs/fr1DABbt26dTJqoqCgGgE2ePFlm+7Zt2xgAtnXrVsYYY7du3WIA2Lhx4xSWddasWXJlTEhIkEnbuHFjFhYWJn2s6vlkjDEArG7duiw/P1+6LSsri5mYmLDFixdLt/3vf/9jAFhKSorCc6foukqUlpay4uJi9vXXXzMHBwcmEolUfq6Em5sb43A47Nq1azLbu3XrxmxtbVlhYSFjjLHY2FgGgPXs2VMm3e7duxkAduHCBYX5i0QiVlxczB48eMAAsAMHDkj3WVtbs8jIyHLLVlhYyOzt7VmfPn3kXneLFi1Y+/bt5Z4zZMgQVrduXaWvudzvrP9o8/ebmttI9Uc1SUQBDoeDPn36yGxr3ry5zMiu8hw6dAhNmzZFy5YtUVJSIr2FhYXJNLccPXoUADB+/HiNyqjqcWJjYwGImyvKGjx4sErHefToEQCgTp06Cvd7enoiMTFR7jZnzhyZdAEBAVi0aBGWL1+Ozz77DEOHDsWoUaMU5vl2WT/88EOYmppKX4vk/u3O7O3bt4efn59cc42TkxPat28vs+3t66nq+ZQICQmBjY2N9HHdunVRp04dld4j5Tl16hTeffddCAQCcLlc8Hg8zJ07F7m5ucjOztYozyZNmqBFixYy2wYPHoz8/HxcuXJFZnvfvn1lHjdv3hwAZF5TdnY2Pv30U7i6usLU1BQ8Hk/amf/WrVvSdO3bt8fGjRuxcOFCXLx4EcXFxTJ5nz9/Hk+fPsXw4cNlzrdIJEL37t2RmJgo18xZp04dZGdnK6y51AdqbiPVHwVJmrG0BJ4/13cp3tByR05LS0uYv/We4PP5eCl5vyjx+PFjJCUlSZsd3ibpu/HkyRNwuVw4OTlpVEZVj5ObmwtTU1O5tShVPW7Rf9NkvH0+JMzNzdG2bVuV8hoyZAjmzJmDV69eSfvrKPJ22STllzTVSO4VjSasV6+eXKCiaB1OPp8vfW2A6udTnTzVcenSJYSGhiI4OBi//vorXFxcYGZmhv3792PRokUa56voOku2lW36AuRfk6RpV3JskUiE0NBQPHr0CHPmzEGzZs1gZWUFkUiEDh06yJRx165dWLhwIdatW4c5c+bA2toaAwYMwHfffQcnJyc8fvwYgHgt1fI8ffpUpinW3NwcjDG8fPkS1tbW6pyGKlHpIKmwsBB5eXkoLS1VuF/S7kqI3lCQpBkOB3irHwkRc3R0hIWFBdavX1/ufgCoXbs2SktLkZWVpdHUAaoex8HBASUlJcjNzZX5EczKylL5OID4B6sySktLMWTIENjZ2YHP52PUqFGIj4+HmZmZXNqsrCzUr19f+vjt8kvuMzMz4eLiIvPcR48eyfRHUpWq57Oq7Ny5EzweD4cOHZIJSPfv31+pfBVdZ8k2dRdxv379Ov7++29s3LgRw4cPl25PSkqSS+vo6Ijly5dj+fLlSEtLw8GDBzFjxgxkZ2fj2LFj0vO5atWqckdH1q1bV+bx06dPwefzDSJAAioRJG3atAnfffcdbt++XW4aDodjMFVmpIYqLQUkVcAUJBEt6d27N7755hs4ODjAw8Oj3HQ9evTA4sWL8fPPP+Prr78uN115tROqHickJATfffcdtm3bhkmTJkm3KxrOr4ifnx8AcYfdyoiKisLZs2cRExMDKysrdO7cGV988QVWrFghl3bbtm1o06aN9PHu3btRUlIiHQ3WpUsXAOKOv+3atZOmS0xMxK1btzB79my1y6fq+VTH2zUxynA4HJiamko7SEuet2XLlkqV4caNG/j7779lmty2b98OGxsbtG7dWq28JB3X354Da82aNUqf16BBA0yYMAEnT55EfHw8AHHza61atXDz5k1MmDBBpePfv3/foKZO0ChIWr9+PT755BNwuVwEBgZK2y0JMThlm04oSCJaEhkZid9//x2dO3fG5MmT0bx5c4hEIqSlpSEmJgZTp07FO++8g8DAQAwbNgwLFy7E48eP0bt3b/D5fFy9ehWWlpbS0WTNmjXDzp07sWvXLjRs2BDm5uZo1qyZyscJDQ1F586d8eWXX6KwsBBt27ZFfHy8yj++Li4uaNiwIS5evCgTZEkUFRXh4sWLCp8rqSE4ceIEFi9ejDlz5khHLC1evBjTpk1DcHAwBgwYIPO8vXv3wtTUFN26dZOObmvRogU+/PBDAICvry/GjBmDVatWwcTEBD169JCObnN1dcXkyZNVu1hlqHo+1dGsWTMAwIoVKzB8+HDweDz4+vrK9GWS6NWrF5YuXYrBgwdjzJgxyM3Nxffff1/pSTnr1auHvn37Yt68eXB2dsbWrVtx4sQJfPvtt2rPN9SoUSN4enpixowZYIzB3t4ef/zxB06cOCGTTigUIiQkBIMHD0ajRo1gY2ODxMREHDt2DO+99x4AwNraGqtWrcLw4cPx9OlTDBw4EHXq1MGTJ0/w999/48mTJ/j555+leYpEIly6dKncfmx6oUlv7yZNmjB7e3t28+bNSvccN1Q0uq2ayMl5MzqquFjfpTFIFY0UMXbljW6zsrKSSysZeVWWotFtjDH2/Plz9tVXXzFfX19mZmbGBAIBa9asGZs8eTLLysqSpistLWXLli1jTZs2labr2LEj++OPP6RpUlNTWWhoKLOxsWEAmJubm9rHycvLYyNHjmS1atVilpaWrFu3buz27dsqjW5jjLE5c+YwOzs79vLlS5ntyka3AWDFxcXs0aNHrE6dOqxLly6stLRU+lyRSMT69OnDatWqJR39JTnHf/31F+vTpw+ztrZmNjY27OOPP2aPHz+WOXZpaSn79ttvmY+PD+PxeMzR0ZENHTqUPXz4UK6MTZo0kXtNw4cPlzmX6pxPAGz8+PFyebq5ubHhw4fLbJs5cyarV68eMzExYQBYbGystFxvj1Bbv3498/X1ZXw+nzVs2JAtXryYRUdHy42QU2d0W69evdiePXtYkyZNmJmZGXN3d2dLly6VSScZ3fbbb7/JbE9JSWEA2IYNG6Tbbt68ybp168ZsbGyYnZ0d++CDD1haWprMe+nly5fs008/Zc2bN2e2trbMwsKC+fr6sqioKOmIOonTp0+zXr16MXt7e8bj8Vj9+vVZr1695Mpy8uRJ6XtDGV2ObuMwpv4MVubm5hg+fHiF1W/GLD8/HwKBAEKhELa2tvouDtFURgbg4gKYmr5pdiMyXr58iZSUFHh4eJTbcZdUf48ePYKHhwc2b96MQYMGVdlx5s2bh/nz5+PJkydV3geoJnB3d0fTpk1lJrk0VsOGDcP9+/elzXXlqeg7S5u/3xpNAWBvb09fpsQ4UKdtQlRSr149REZGYtGiRXKzVBNS1ZKTk7Fr1y58++23+i6KDI06EvXu3RtxcXFgjMnMTkqIwZEESRYW+i0HIUbgq6++gqWlJTIyMuDq6qrv4pAaJC0tDT/++CM6deqk76LI0Ki5LTc3FwEBAQgKCsLSpUvlppuvDqi5rZr46y+gbVvA1RUos6YUeYOa2wghxkSXzW0a1SR98MEHsLS0xLp167B9+3b4+PhAIBDIpeNwOAoXsSNEZ6i5jRBCiIY0CpLKTt1eWFiIq1evKkxHTXFE7yhIIoQQoiGNgiTq1EeMhmSCNwqSKqRByzshhOicLr+raIFbUr1RTVKFJLP/vr04JSGEGCLJd1XZmcurCgVJpHqjIKlCPB4PfD4fQqGQapMIIQaNMQahUAg+n1/uQsXaVKm1RHbs2IHo6GhcuXIF+fn5sLW1RZs2bTBq1Ch89NFH2iojIZqjIEkljo6OyMjIQHp6OgQCAXg8HvUpJIQYDMYYiouLIRQK8fz5c5nFkauSRkESYwxDhgzBrl27wBgDl8tF7dq1kZOTg5MnT+LUqVM4ePCgyosrElJlKEhSiWSYbE5ODjIyMvRcGkIIUYzP56N+/fo6m5pHoyDpl19+wc6dO9G6dWssWbIEISEh4HK5KC0txenTpzFjxgzs2rULnTt3xqeffqrtMhOiOgqSVGZrawtbW1sUFxejtLRU38UhhBAZXC5XJ01sZWkUJK1fvx7u7u44e/YsLMrMZMzlctGlSxecPn0aTZs2RXR0NAVJRL9oxm218Xg8nX8REUKIIdKo4/atW7cwYMAAmQCpLAsLC/Tv3x+3bt2qVOEIqTSqSSKEEKIhjYIkDodT4SgYGiVDDAIFSYQQQjSkUZDk5+eHffv24aXkB+gtRUVF2L9/Pxo3blypwhFSaTSZJCGEEA1pFCRFRETgwYMHCA4ORmxsrLSTZ2lpKWJjYxESEoIHDx5g5MiRWi0sIWqjmiRCCCEa0qjj9meffYYzZ85g9+7dePfdd2FiYgJ7e3s8ffoUIpEIjDF8+OGH1Gmb6B8FSYQQQjSkcZ+knTt3YuvWrQgJCYFAIMDTp08hEAjQpUsXbNu2DTt37tR2WQlRHwVJhBBCNFSpGbcHDx6MwYMHa6sshGgfBUmEEEI0RGu3keqtGgZJ6fnpiE2JRXp+ur6LQggh1RoFSaR6M7LJJCsKgKKvRMNtuRu6bO4Ct+VuiL4SreMSEkJIzaFSkGRiYgJTU1PcvXtX+pjL5VZ4MzWtVGseIZVnRDVJFQVA6fnpGHNoDERMBAAQMRHGHhpLNUqEEFJFVIpiOnfuDA6HA0tLS5nHhBg8IwmSyguAwrzC4GLrAgC4l3tPul+ilJUi6WmSNA0hhBDtUSlIiouLU/qYEINlJJNJqhIAeTt4w4RjIpOOy+HCy95LLr/0/HTcy70HbwdvCqAIIURD1CeJVG9GUpMkCYDKejsAcrF1wdrea8HlcKX71/ReIxcEUb8lQgjRDo2CpIYNG2LlypVK0/z0009o2LChRoUiRGuMJEhSNQAa1XoUUiNTETs8FqmRqRjVepTMfuq3RAgh2qNRz+rU1FTk5eUpTZOXl4cHDx5okj0h2mMkQRIgDoDCvMKQ9DQJXvZe5TaTudi6lLuP+i0RQoj2VNnws+fPn8PMzKyqsiekYowZVZAEKA+AVKFOvyVCCCHKqRwkpaWlyTzOy8uT2waIF7l9+PAhfv/9d2puI/pVXCwOlACjCZIqS9JsN/bQWJSy0nKb7QghhFSMw5jkV0Q5ExMT6bB/xliFUwAwxrB06VJERkZWupD6kJ+fD4FAAKFQCFtbW30Xh2giPx8QCMR/v3wJ8Pn6LY8OpeenV9hsRyPgCCHVkTZ/v1WuSQoPDweHwwFjDJs3b0bz5s3RsmVLuXRcLhcODg7o2rUrQkNDK1U4QipF0tQGAAbQ9KvLoKSiZrvoK9HSDt4mHBOs7b1WrhM4IYTUdCrXJJVlYmKCefPmYe7cuVVRJoNANUnVQFoa4OYmbmqTzJekJ4YUlKTnp8NtuZtcv6XUyFSqUSKEGD291CSVJRKJKk5EiL4ZyESSqsymrUs0Ao4QQlSj0TxJT548wZkzZ5Cfn69wf35+Ps6cOYOcnJxKFY6QSjGQkW3KghJ9UGXiSkIIIRoGSQsXLkTv3r3B5XIV7udyuejTpw8WL15cqcIRUikGEiQZWlCi6sSVhBBS02kUJJ04cQLdunWDlZWVwv1WVlYIDQ3F8ePHK1U4QirFQIIkQwxKKpq5mxBCiIZ9kh4+fIg+ffooTdOwYUPExMRoVChCtMJAgiRA9dm0damyE1cSQkh1p1GQxOFw8Pr1a6VpXr9+jdLSUo0KRYhWGFCQBBhnUEJzKRFCajKNgiRfX98Ka4liYmLg5UUdQYkeSYIkCwv9lsNIGdK0BYQQog8a9UkaOHAgbt26hQkTJuBl2Qn7ALx8+RKff/45bt++jUGDBmmlkIRoxMBqkoxJedMWpOen67lkhBCiOxrVJE2aNAk7duzAzz//jP3796Nz586oX78+MjIycPbsWWRkZKBFixZGuyQJqSYoSNIYzaVECCEaBkkWFhaIi4vDuHHjsHv3buzcuVO6z8TEBIMHD8aPP/4IC2rmIPpkIJNJGiPJtAVvz8pNcykRQmoSjYIkAKhVqxa2b9+OFStWIDExEXl5eahVqxbat28PR0dHbZaREM1QTZLGJNMWjD00FqWs1CCmLSCEEF3TOEiSqF27Nnr27KmNshCiXRQkVYohTltACCG6pFHHbV1IT0/HyJEjUa9ePfD5fLi7uyMyMhLPnj1TO6+zZ8/i/fffh7OzM/h8PpydnREaGoojR45UQcmJwaAgqdJcbF0Q7B5MARIhpEaqVE3SpUuXEBMTg4yMDLx69UpuP4fDQXR0tNr5Jicnw9/fH9nZ2ejXrx8aNWqES5cuYcWKFTh27Bji4+Ph4OCgUl4LFy7EnDlz4OjoiN69e8PZ2Rk5OTm4evUq4uLiqBasOqMgSSdoLiVCSHWlUZAkEokQHh6OHTt2gDEGDocDxph0v+SxpkHSuHHjkJ2djZUrV2LixInS7VOmTMGyZcswe/Zs/PLLLxXms3v3bsyZMwfvvvsu9u7dCxsbG5n9xcXFapeNGJHCQvG9paV+y1GN0VxKhJDqTKPmtlWrVmH79u0YPHgwEhMTwRhDZGQkzp8/j2+++QY2Njb46KOPcP/+fbXzTk5ORkxMDDw8PDB+/HiZffPnz4eVlRU2b96M58+fK81HJBJh+vTpsLCwwPbt2+UCJADg8Xhql48YkRcvxPflrDFIKofmUiKEVHcaBUmbN2+Gt7c3tmzZgjZt2gAQj3br0KEDZsyYgdjYWPz+++84deqU2nnHxsYCAEJDQ2FiIls8GxsbBAQEoKioCAkJCUrzOX/+PFJTU9GrVy/Y2dnh8OHD+Pbbb7FixQpcuHBB7XIRI0Q1SVVK2VxKhBBSHWjU3Hb37l0MGzZMZltJSYn071atWqF3795YvXo1RowYoVbed+7cAQB4e3sr3O/t7Y2YmBjcvXsXXbt2LTefxMREAICTkxPatGmDf/75R2Z/586dsWfPHtSuXVtpefLz82Ue8/l88Pn8Cl8HMQCSIIlqkqoEzaVECKnuNKpJYoyhVq1a0sdWVlZ4+vSpTBpvb2/cvn1b7byFQiEAQCAQKNwv2Z6Xl6c0n+zsbADAzz//jKKiIpw6dQoFBQW4fv06wsLCcObMGXzwwQcVlsfV1RUCgUB6W7x4sRqvhugVNbdVKclcSlwOFwBoLiVCSLWjUU2SZAkSiYYNG+Kvv/6SSXPv3j1YVcGPk6SDOIfDUZqutLRUmv73339Hs2bNAABNmjTBvn374OPjg9OnT+PChQvo2LFjufk8fPgQtra20sdUi2REdNjcVlNHeNFcSoSQ6kyjmqT27dvLBEU9evTApUuXsGDBAty4cQM//vgjDhw4gA4dOqidt6SmSFKj9DZJ81d5NU0SdnZ2AMQBnCRAkrCwsEBYWBgA8TQGytja2srcKEgyHiUF4s79OazSc6YqFX0lGm7L3dBlcxe4LXdD9BX1R3QaM5pLiRBSXWkUJL3//vsoLS1FSkoKAODLL7+Em5sboqKi0Lx5c0yaNAm1atXCkiVL1M7b19cXgLjfkyL37t0DAPj4+KiUT9lmwbIkQVSRZH0vUq3sSkxDTrZ44tGIXTewKzGtSo5DI7wIIaT60uhf7P79+6N///7Sx/b29rh69Sp+/fVXJCcnw93dHeHh4XB2dlY775CQEABATEwMRCKRzAi3goICxMfHw8LCosJaqs6dO8PU1BRJSUl4/fo1zMzMZPZfv34dAODu7q52GYlhyxQWYebef3GtWDzB6QtTPmbtvY7OPrXhLNDuosvKRnhRzcobNbU5khBi3LS2LIlAIMC0adPw888/Y/r06RoFSADg6emJ0NBQpKam4qeffpLZFxUVhcLCQoSHh0v7OxUXF+P27dtITk6WSevo6IhBgwYhLy8P33zzjcy+EydO4Pjx4xAIBOjevbtG5SSGKyWnECIGWBSLZ9x+wTNHKWNIzXmh9WNJRniVRSO8ZNX05khCiPHSKEjicrn46KOPtF0WqdWrV6NOnTqYNGkS+vfvj5kzZ6JLly5YtmwZfHx8sGjRImnajIwM+Pn5KZwOYOnSpfDy8sL8+fMRFBSEadOm4YMPPkCPHj3A5XLx66+/ltscR4yXh6MVzEQl4InEnfdfmJmDy+HA3VH7HbhphJdy1BxJCDFmGjW3WVtbV2kzlaenJy5fvoy5c+fi2LFjOHLkCJydnTFp0iRERUXB3t5epXzq1KmDhIQELFy4EPv27cOFCxdgY2ODXr16YebMmRp1LCeGz1lggSXdGwL/Ez8u5pnjm/eaar2pTYJGeJWPmiMJIcaMw8ouuqaioKAg1KpVCwcOHKiKMhmE/Px8CAQCCIVCmSkAiJHIyABcXMC4XGTl5MO5Fs26rQ/p+elwW+4mN+FkamQqBUmEkCqhzd9vjZrbvvzySxw+fBgnTpyo1MEJqTL/TSTJsbKiAEmPqDmSEGLMNGpuy83NRffu3dGjRw/069cP7du3h5OTk8IJHsPDwytdSELURkuSGAxqjiSEGCuNmttMTEzA4XDw9lPLBkmMMXA4HOnM18aGmtuMXHw80KkT4OkJJNGCq4QQUlNo8/dbo5qk9evXV7gsCCF6Reu2GR2aS4kQYmhUCpLy8/Nhbm4unZAxIiKiKstESOVRc5tRib4SLZ0qwIRjgrW912JU61H6LhYxIqoE2dpKQ2oOlTpu29nZ4dtvv5U+HjlyJA4ePFhlhSKk0nS4uC2pHJpLiVQkPT8dsSmx5b4nVJmwVFtpVCkPqT5UCpI4HA5EojdDeDdu3Ihr165VVZkIqTyqSTIayuZSItVfZQMgVYJsbaVRpTyqvi5iHFQKkurVq4ck6vxKjAn1STIatLRLzaWNAEiVIFtbaSiQqnlU6pPUtWtXbNmyBTk5OdI12fbv34/U1FSlz+NwOIiOpnWaiB5Qc5vRkMylNPbQWJSyUppLqYYoL+AI8wqTXntVZmyXBNlvT1haNsjWVhpVyqPK6wLU64dH/aT0R6Ug6dtvv8Xjx48RExMDkUgEDoeDa9euVdjkRkES0RtqbjMqNJdS9aTsx11bAZAqQba20ug6kAJUD6YokKoaKgVJderUwZEjR1BcXIzMzEy4u7sjMjISn3/+eVWXjxDNUHOb0XGxdanwy51+CIxHRT/u2gqAANWCbG2k0WUgBWi/Voo+P+pTa54kHo+HBg0awM3NDe7u7nBzc6uqchFSOdTcVu3QNAHGQ5Ufd20GQJL8Kvrh10YaXQVSgH6a9yiQkqXRZJIpKSnaLgch2kXNbdWKOs0TRDcq25QGaDcA0iVdBFKA4faTqklzUmkUJBFi8Ki5rVpR9UeX6IY2mtIkDC0A0pbKBlKSPAytn5QqgZS20hgClaYAIMToUHNbtULTBBgOVYbBS37cuRwuANCIxXK42Log2D24wmAqNTIVscNjkRqZKhdIqHKuVfn8aGsKBG3OSWUIqCaJVE/U3Fat0DQBuqXLpjRSMUPpJ6XKtddWGkNBQRKpnqi5rdqhH13doKY042QogZS20hgKam4j1RM1t1VLqjRP0CzGmqOmtOqtos+PNpr2tJXGUHAYY0zfhTBE+fn5EAgEEAqFsLW11XdxiLrq1QMyM4ErV4BWrfRdGqIjxtIZ1FDFpsSiy+Yu8tuHxyLYPVhmW3p+OtXq1VCqXHttpdGENn+/KUgqBwVJRq5WLUAoBO7cAXx89F0aogPp+elwW+4mV4WfGplKP+JlKOtvROeQVAfa/P2uVJ+kxMREJCYm4tmzZygtLZXbz+FwMGfOnMocghDNUHNbjWNMnUH1paKaNuogT4gsjWqShEIh+vfvjzNnzkDZ0zkcjsLgyRhQTZIRe/0a4PPFfz99CtjZ6bc8RCeoFkQ5dc4PNaURY6b3mqQvvvgCp0+fRmBgIEaMGAFXV1eYmtJAOWIgJCPbABrdVoOoUwtiDDP9aps6NW00Ko0QMY0im4MHD6J169aIjY2FiQkNkCMGRtLUxuUCPJ5+y0J0SpVpAqpz525lwZ8xDbsmxFBoFOEIhUKEhIRQgEQMU9mJJDkc/ZaF6JyyYc7GNNOvuqKvRMNtuRu6bO4Ct+VuiL4SLbPfmIZdE2IoNKpJ8vb2xuPHj7VdFkK0g2bbJuWorp27VV13iybkJEQ9GlUFjR8/Hn/88QcyMjK0XR5CKo9m2yblUGcNOEOblFJZeVRZd0tClQk5CSFiGtUk9ejRA6dOnUKnTp0QFRWFNm3aQCAQKEzboEGDShWQELXR8H9SDlU7dxtavyVtLhVCCFGdRlMAmJiYgMPhgDEGjpI+HxwOByUlJZUqoL7QFABGbN8+4L33gI4dgfPnK51dTRwJVd0pG+Ku7lD5it4blU2janmir0TLBX/VpUM6IerQ+xQA4eHhSoMjQvRKi81thlajQLRD2RB3VfstqfLe0EYaVctD/Y0I0T5alqQcVJNkxNauBcaOBfr2BQ4c0DgbmpywZlLluhtaGkLIG9r8/aYx/KT60dLoNnU6w5LqQ5Wh8qq8N7SVhobuE6I/lZ4m++HDh7h69SqEQiEEAgFat24NFxf68BI90lJzG3WGrbkqarpS5b2hrTSqlIcQUjU0rklKTU1FWFgY3N3dMWDAAERERGDAgAFwc3ND9+7dkZqaqsViEqIGLY1uo//gazZlQ+VVeW9oK40q5SGEVA2N+iRlZmaiXbt2ePToEdzc3BAUFARnZ2dkZmbi3LlzuH//PurVq4fLly/DycmpKspd5ahPkhH7/HNg5Upg5kzgm28qnR0t9knKo8p7Q1tpCCGq0fvotgULFuDRo0dYvHgxpk6dKrO4bWlpKZYtW4Yvv/wSCxcuxI8//lipAhKiNi1PJkmLfZLyqPLe0FYaQojuadTcduTIEXTr1g3Tp0+XCZAAgMvlYtq0aQgNDcWhQ4e0UkhC1EKTSRJCCNECjYKkrKwstG3bVmmaNm3aICsrS6NCEVIptHYbIYQQLdAoSBIIBEhLS1OaJi0trdylSgipUrR2GyGEEC3QKEgKCAjAnj17kJCQoHB/QkICfvvtN3Tq1KlShSNEI9TcRgghRAs06rg9e/ZsHD58GIGBgfj4448RHBwMJycnZGVlIS4uDjt27ICJiQlmzZql7fISUjFqbiNakCksQkpOITwcreAssNA4DSHEeGkUJLVp0wa7d+/GyJEjsWXLFmzdulW6jzEGe3t7rF+/Hm3atNFaQQlR2fPn4nsKkoiGdiWmYebefyFigAkHWPxeMwxq10DtNAAFUoQYM41n3O7Xrx/S0tKwf/9+mRm3W7Vqhf79+8OKfqCIvuTni++pTxzRQKawSBr8AICIAbP2Xkdnn9rSIEeVNIDqgRQhxDBValkSKysrDBkyBEOGDNFWeQipPEmQRJOAknIoq91JySmUBj8SpYwhNeeFNK0qaVQNpAghhqvSa7cRYlBevQJevxb/TUESUaCi2h0PRyuYcCATBHE5HLg7WqqVRpVASoKa5AgxTCoFSZs3bwYADBgwADY2NtLHqggPD9esZIRoQlKLBAA2NvorBzFIqtTuOAsssPi9Zpi19zpKGQOXw8E37zWVCV5USaNKIAVQkxwhhkyltdtMTEzA4XBw69Yt+Pj4SB8rwxgDh8NBaWmp1gqrS7R2m5FKTga8vMSdtiUduEmNoqxW5nxyDgb/Kj91yY7RHdDR00Eun9ScF3B3tFQ6uk1Zml2JaXKBVNkAKFNYhIAlp+QCqXMzQqhGiRAN6XzttvXr14PD4cDZ2RkAsGHDhkodlJAqQ522azRtNKVJOAssKgxUKkozqF0DdPapXW4gpU6THCFE91QKkiIiImQeDx8+vCrKQkjlUaftGktbTWnapiyQUidoo35LhOieRh23z5w5A3d3dzRoUH67+cOHD5GSkoLOnTtrXDhC1EZBUo2laq1MRbU7uqRq0Eb9lgjRD42WJQkJCcHGjRuVptm8eTNCQkI0yZ4QzVGQVGNJamXKUtaU1tHTwSBqZAa1a4BzM0KwY3QHnJsRIhf8lFdDliks0kNpCalZNAqSVOjrLe24TYhOUZBUY0lqZbj/fe/ooilNW5QFbcpqyAghVavK5klKS0uDDQ3BJrpGQVK1VlG/HENqStMW6rdEiP6oHCR9/fXXMo/j4uIUpistLcXDhw+xc+dOBAQEVKpwhKhNKBTfU5BU7ajaL0eVUWnGhPotEaI/KgdJ8+bNk/7N4XAQFxdXbqAEAPXr18eSJUsqUzZC1Ec1SdVSTV/io6Iaspp+fgipKioHSbGxsQDEfY26dOmCiIgIhVMBcLlcODg4wNfXFyYmGnV5IkRzFCRVSzSfkPIaMjo/hFQNlYOkoKAg6d/Dhw9H//79ZbYRYhAoSKqW1OmXUxPR+SGkamhU1bNhwwb07dtX22UhpPIoSKqWjHnkmi6oc34yhUU4n5xDUwgQooIqG91GiF5QkFRtVceRa9qkyvmhzt2EqEfjTkOPHj3CuHHj4OXlBQsLC3C5XLmbqanmMVh6ejpGjhyJevXqgc/nw93dHZGRkXj27JnGeW7ZsgUcDgccDgfr1q3TOB9iwChIMlqq1HAY0iSQhkjZ+aFJKYkqVPkc6jKNvmkUxTx8+BDt27fHkydP0LhxY7x69Qpubm7g8/m4f/8+SkpK0LJlSwg0XGQ0OTkZ/v7+yM7ORr9+/dCoUSNcunQJK1aswLFjxxAfHw8HB4eKM3qrzBMnToS1tTWe0+rw1RcFSUaJajiqHnXuJhXNo6XK51CXaQyBRjVJCxYsQHZ2Ng4fPox//vkHADBixAjcvn0b9+/fR1hYGIqKirB3716NCjVu3DhkZ2dj5cqV2L9/P5YsWYJTp05h8uTJuHPnDmbPnq1WfowxjBgxAg4ODvj00081KhMxEmoGScbwn0x1RzUcuqHOsi30uTA+FV2zXYlpCFhyCoN/TUDAklPYlZgm9/yKPoe6TGMoNAqSYmJiEBYWhrCwMLl9Li4u+O2331BUVISoqCi1805OTkZMTAw8PDwwfvx4mX3z58+HlZUVNm/erFZt0MqVK3Hq1Cls2LABVlZWapeJGIniYqDovw+ZCrWYFX1pEN2gZTd0Q9XO3fS5MDy6CIBU+RzqMo2h0ChIysrKQtOmTaWPuVwuiorenGxra2t069YNBw4cUDtvyXxMoaGhcvMs2djYICAgAEVFRUhISFApv1u3bmHGjBn4/PPP0blzZ7XLQ4xIQcGbvytYEseY/pOp7tSp4SCVQ4vpGhZVaux0FQCp8jnUZRpDoVGQZGtri9evX0sf29nZISMjQyaNQCDAkydP1M77zp07AABvb2+F+yXb7969W2FeJSUlGDZsGBo0aIBvvvlG7bIAQH5+vszt1atXGuVDdEDS1GZhAfB4SpMa038y1R0N79ctbS2mS01ylaNKjZ0uAyBVPoe6TGMoNOq47ebmhocPH0oft2jRAqdOncKLFy9gaWkJkUiEmJgYuLi4qJ238L+1t8rr9C3ZnpeXV2FeX3/9Na5evYpz587BwkKzk+/q6irzOCoqSmaJFmJA1OiPRJPvGRYa3m8YVP1cGEunW31S1kla1WVkVOlsr8o1U3X9P1U+h7pMYwg0CpK6du2KtWvXori4GDweD8OHD0d4eDj8/f3RrVs3nDt3Djdu3MCsWbO0XV4wJn4ncDgcpekuXbqEb775BlOnTkXHjh01Pt7Dhw9hW+ZHl8/na5wXqWJqLG6r6pcG0Z3qtjCtMVLlc0HrxFV+lJiqIw11HQBJ8qvoOuoyjb5pFCSNGjUKdnZ2yMnJgbOzM4YOHYq//voLq1atko52++ijj9QehQa8qSmS1Ci9Lf+/2gJl0wtImtl8fHywYMECtctQlq2trUyQRAyYmiPbjOU/meqgoh8VYjgq+lyoM5WAMV73ygZAqgSRqtbY6SMAIrI0CpK8vb0xffp0mW3Lli3DrFmzcP/+fbi7u6Nu3boaFcjX1xdA+X2O7t27BwDw8fEpN4/nz59Ln29ubq4wzejRozF69Gh8/vnnWL58uUZlJQZGgzmS6Euj6lHTjPFR9rnQdpOcLgMpXQRAqgSR6tRkUwCkX1pdlqR27dqoXbt2pfIICQkBIJ5mQCQSyYxwKygoQHx8PCwsLNChQ4dy8+Dz+Rg1apTCfVeuXMHVq1fRqVMn+Pr6VqopjhgYmkjS4FDTTPWjzSY5bQZShhIAqRpEqlOTTQGQ/hjc2m2enp4IDQ1FTEwMfvrpJ0ycOFG6LyoqCoWFhRg7dqx0vqPi4mIkJyeDx+PB09MTAGBhYVHusiPz5s3D1atXMXz4cHzyySdV/4KI7lCQZHBolufqSRtNctoMpAwpAFKnloiCH8OnUpA0cuRIjTLncDiIjo5W+3mrV6+Gv78/Jk2ahJMnT8LPzw8JCQmIjY2Fj48PFi1aJE2bkZEBPz8/uLm5ITU1VaNykmqCgiSDQ6MIq6/KNslpK5AyxACI+jtWHyoFSRs3btQoc02DJE9PT1y+fBlz587FsWPHcOTIETg7O2PSpEmIioqCvb29RuUh1RwFSQaHRhHWTKpcd20FUoYaAFEtUfWgUpCUkpJS1eWQ4+rqig0bNlSYzt3dXTotgCrmzZtH8xxVVxQkGST6r7pmqui6ayuQogCIVCWVgiQ3N7eqLgchlUdBksGiH5WaqaLrro1AigIgUpUMruM2IRqjIIkQo1PZQErVNKoci5C3aRQkpaWpvip0gwY0HwrREQqS9MIYJwwkxqW6zN5MjI9GQZK7u3uFy4IA4o7bJSUlmhyCEPVJgiQls7ET7aKJIgkh1ZlGQVJ4eLjCICkvLw/Xrl3DgwcPEBwcTH2ZiG5RTZJO0USRhJDqTqMgSdmUACKRCAsWLMAvv/yCTZs2aVouQtSnxgK3Eun56biXew/eDt5wsXWpooJVTzRRJCGkujOpOImaGZqYICoqCu7u7pgxY4a2sydEsdJSoLBQ/LeKQVL0lWi4LXdDl81d4LbcDdFX1J/TqyaTDL0uiyaKJIRUJ1oPkiT8/f0RExNTVdkTIqug4M3fKgRJ6fnpGHNoDERMBAAQMRHGHhqL9Pz0qiphtSMZes39r+mdJookhFQ3VTYFwNOnT1Eo+c+ekKomaWozMwP4/AqT38u9Jw2QJEpZKZKeJlGzmxpookhCSHVWJUHSn3/+iV27dqFp06ZVkT0h8p4+Fd+ruGSNt4M3TDgmMoESl8OFl71XVZSuWqOh14SQ6kqjIKlLly4Kt5eUlODhw4dIS0sDh8NBVFRUpQpHiMpyc8X3Dg4qJXexdcHa3msx9tBYlLJScDlcrOm9hmqRCCGESGkUJMXFxSnczuFwYGdnh+7du2PatGkICQmpTNkIUZ2aNUkAMKr1KIR5hSHpaRK87L0oQCKEECJDoyBJJBJVnIgQXVKzJknCxdaFgiMlaDZtQkhNRmu3kepBg5okohzNpk0Iqem0MgVAfn4+Hj58iHzJjMeE6JqGNUlEsfJm084UFum3YIQQokMaB0mvX7/GokWL4OnpCTs7O7i7u8POzg6enp5YtGgRXr9+rc1yEqKcpCaJgiStUDabNiGE1BQaNbcVFBSga9eu+Ouvv8DhcNCgQQM4OTkhKysLDx48wNy5c3Hw4EGcPHkS1tbW2i4zIfIkNUnU3KYVktm0ywZKNJs2IaSm0agmKSoqCpcvX8aAAQNw7949pKSk4MKFC0hJScG9e/fQv39/JCYm0hQARHeoJkmraDZtQggBOIwxVnEyWa6urqhduzauXLmicD9jDK1bt0ZOTg4ePnxY6ULqQ35+PgQCAYRCIWxpVXnD16gRcOcOEBsLBAfruzTVRqawiGbTJoQYFW3+fmtUk5STk4OwsLBy93M4HISFhSFX0gRCSFWjmqQq4SywQEdPBwqQCCE1kkZBkru7O/Ly8pSmEQqFcHd31yR7QtTDGE0BQAghROs0CpJGjx6N3bt3Iz1d8YrpaWlp2LVrF0aPHl2pwhGikvx8oLRU/DcFSYQQQrREo9Ft7733Hs6cOYPWrVsjMjISnTt3Rt26dfH48WOcPn0aK1asQHBwMAYMGIC0tDSZ5zZoQJPRES2TNOtaWIhvRCU0mzYhhCinUcdtExMTcDgcMMbA+W/0S1nlbedwOCgpKdGspDpGHbeNyOXLQLt2gIsLYKQDBXSNZtMmhFRX2vz91qgmKTw8XGEQRIhe0GzbailvNu3OPrWpRokQQsrQKEjauHGjlotBSCVQp221KJtNm4IkQgh5QytrtxGiV1STpBbJbNpl0WzahBAiT6OapLIePnyIq1evQigUQiAQoHXr1nBxcdFG2QhRDdUkqUUym/asvddRyhjNpk0IIeXQOEhKTU3F2LFj8eeff8rt69atG3755ReaJ4noBtUkqW1Quwbo7FObZtMmhBAlNAqSMjMz0alTJzx69Ahubm4ICgqCs7MzMjMzce7cOcTExKBTp064fPkynJyctF1mQmRV8eK21XWovLPAolq9HkII0TaNgqQFCxbg0aNHWLx4MaZOnQpT0zfZlJaWYtmyZfjyyy+xcOFC/Pjjj1orLCEKVeGSJDRUnhBCai6NOm4fOXIE3bp1w/Tp02UCJADgcrmYNm0aQkNDcejQIa0UkhClqqgmqbyh8pnCIq0ehxBCiGHSKEjKyspC27ZtlaZp06YNsrKyNCoUIWqpopokZUPlDV2msAjnk3MooCOEkErQqLlNIBDILTfytrS0NAgEAo0KRYhaqqjjtmSofNlAyRiGylMTISGEaIdGNUkBAQHYs2cPEhISFO5PSEjAb7/9hk6dOlWqcIRUqLQUyMsT/63l5jbJUHnuf7PLG8NQeWoiJIQQ7dGoJmn27Nk4fPgwAgMD8fHHHyM4OBhOTk7IyspCXFwcduzYARMTE8yaNUvb5SVEVl4eIFl+sApGtxnbUHmaTZsQQrRHoyCpTZs22L17N0aOHIktW7Zg69at0n2MMdjb22P9+vVo06aN1gpKiEKS/kg2NgCPVyWHMKah8sbaREgIIYZI48kk+/Xrh7S0NOzbtw/Xrl2TzrjdqlUr9O/fH1ZWVtosJyGK0USSMmg2bUII0R61g6SHDx8iMTERANC2bVsMHToUQ4cO1XrBCFEJLUkix9iaCAkhxFCpFSRNnz4dS5cuhUgkAgBwOBxMnjwZ//vf/6qkcIRUqIpn2zZWxtRESAghhkrl0W27du3C//73P4hEIjRq1Ai+vr4AgKVLl2LHjh1VVkBClHr8WHxft65+y0EIIaTaUTlI+vXXX2Fqaoo///wTN27cwM2bN3HixAlwuVxER0dXZRkJKZ9kwlJnZ/2WQ4dookhCCNENlZvb/v77b/Tv3x8hISHSbSEhIejXrx9iY2OrpHCEVCgzU3xfQxZSpokiCSFEd1SuSXr27Jm0ia0sX19f5Ekm8yNE1yQ1STUgSKKJIgkhRLdUDpJEIhF4Cuah4fF4YIwpeAYhOiCpSaoBzW3GvJYcIYQYI7WWJeH8tzwDIQajsjVJ6elAbKz43sBJJoosiyaKJISQqsNhKlYDmZiYqB0kcTgclJSUaFQwfcvPz4dAIIBQKIStra2+i0MUefUKMDcX//30KWBnp97zo6OBMWMAkQgwMQHWrgVGjdJ+ObVoV2Ka3ESR1CeJEELe0Obvt1pBkiYkcyoZGwqSjMCDB4C7O2BmBrx8CagTxKenA25u4gBJgssFUlMBFxe1i5IpLEJKTiE8HK2qfH6iTGERTRRJCCHl0Obvt8qj24w12CHVWNmmNnWbgu/dkw2QAKC0FEhKUjtI0uaIM1WCLZookhBCdEPjtdsI0bvKdNr29hY3sb1dk+TlpV4Ryhlx1tmnttqBDA3vJ4QQw6JZGxohhqAynbZdXMR9kLhc8WMuF1izRu1aJG2NOKPh/YQQYnioJokYr8rOtj1qFBAWJm5i8/LSqC+SZMRZ2UCpvBFnyprSlAVb1LRGCCH6QUESMV7amG3bxUWj4EjCWWCBxe81kxtx9nZgU1FTmjrBFiGEEN2gIIkYLwOZbXtQuwbo7FO73BFnqvRbUjXYIoQQojsUJBHjpavZttPTxaPhvL3LrXVSNuJM1aa0ioItQgghukUdt4nx0kVNUnS0eD6lLl3E99HRamehzkzZzgILdPR0oACJEEIMAAVJxDgxVvmO2xVJT38zIzcgvh87Vu0lTCRNadz/5nKipjRCCDEO1NxGjNPTp0BxsfjvOnWq5hhanHCSmtIIIcT4UJBEjJOkFsneHuDzFadRoS+RUlqacFKCZsomhBDjYrDNbenp6Rg5ciTq1asHPp8Pd3d3REZG4tmzZyo9Pzc3F+vWrcOAAQPg5eUFCwsLCAQCdOrUCdHR0bTMirGrqNO2FvoSaWvCSUIIIcZJ5QVudSk5ORn+/v7Izs5Gv3790KhRI1y6dAmxsbHw9fVFfHw8HBwclObxyy+/4LPPPoOTkxO6dOmCBg0a4PHjx9i7dy+EQiHee+897NmzB5xy1vyiBW4N3NatwLBhQNeuwJ9/yu77b/HadGsR7tkD3k8Bl0LNF69FenqlJpwkhBCiO3pZ4FaXxo0bh+zsbKxcuRITJ06Ubp8yZQqWLVuG2bNn45dfflGah4+PD/bv34/evXuDK6kJAPDNN9+gffv22Lt3L37//XcMHDiwyl4HqULKRrbdu4foFiKM6QOITAATEbD2j1KM0qAvEYBKTzhJCCHEOBlcc1tycjJiYmLg4eGB8ePHy+ybP38+rKyssHnzZjx//lxpPl26dEG/fv1kAiQAcHJywqeffgoAiIuL02rZiQ4paW5Lr2ctDZAA8f3YPkC6s5UOC0gIIcTYGVyQFBsbCwAIDQ2FiYls8WxsbBAQEICioiIkJCRofAwzMzMAAI/H07ygRL+ULElyz+y5NECSKDUBkviFOigYIYSQ6sLggqQ7d+4AALy9vRXul2y/e/euRvmXlJRg06ZNAIDu3btXmD4/P1/m9urVK42OS7QsNVV87+Ymt8vbwRsmHNm3NpfDhZe9ZqPSCCGE1EwGFyQJhUIAgEAgULhfsj0vL0+j/GfMmIHr16+jR48eCAsLqzC9q6srBAKB9LZ48WKNjku0TBIkubvL7XKxdcHa3mvB5YibWrkcLtb0XgMXW+pXRAghRHUG2XFbGclgvPJGpSmzfPly/PDDD/D19cXmzZtVes7Dhw9lesfzy5uTh+jOy5dvmtsUBEkAMKr1KIR5hSHpaRK87L0oQCKEEKI2gwuSJDVFkhqlt+Xn58ukU9WKFSswefJk+Pn54dSpU3B0dFTpeba2tjQFgKFJSxPfW1sDSqaCcLF1oeCIEEKIxgyuuc3X1xdA+X2O7t27B0A8xF9V33//PSIjI9G0aVPExcXBqSoXRCVVr2xTmwY1ioQQQogqDC5ICgkJAQDExMTIzYpdUFCA+Ph4WFhYoEOHDirlt3jxYnzxxRdo2bIlYmNjUaeq1vkiuqOkPxIhhBCiLQYXJHl6eiI0NBSpqan46aefZPZFRUWhsLAQ4eHhsLISz3lTXFyM27dvIzk5WS6vBQsWYNasWWjTpg1OnjypchMbMXApKeJ7CpIIIYRUIYPrkwQAq1evhr+/PyZNmoSTJ0/Cz88PCQkJiI2NhY+PDxYtWiRNm5GRAT8/P7i5uSFVUsMAYNOmTZg7dy64XC4CAwOxcuVKueO4u7sjIiJCB6+IaBXVJBFCCNEBgwySPD09cfnyZcydOxfHjh3DkSNH4OzsjEmTJiEqKgr29vYV5pHyX21DaWkpli9frjBNUFAQBUnGiIIkQgghOmCQC9waAlrg1oA5O4vXbrt8GWjTRt+lEUtPB+7dA7y9aZ03QgjRI23+fhtcnyRClCoqerO4rYeHfssiER0tnvm7SxfxfXS0vktECCFECyhIIsZFMkeSjQ1gZ6ffsgDiGqQxYwDJSEyRCBg7VrydEEKIUaMgiRiXsiPbDGGOpHv33gRIEqWlQFKSfspDCCFEayhIIsbF0Dpte3sDJm99jLhcwIsW0yWEEGNHQRIxLoYWJLm4AGvXigMjQHy/Zg113iaEkGrAIKcAIKRchhYkAcCoUUBYmLiJzcuLAiRCCKkmKEgixsUQgyRAHBhRcEQIIdUKNbcR43L/vvje0IIkQggh1Q4FScR45OQAT56I//bx0W9ZCCGEVHsUJBHjcfOm+N7NDbC21m9ZCCGEVHsUJBHjIQmSmjTRbzkIIYTUCBQkEeMhCZIaN9ZvOQghhNQIFCQR43HjhvieapIIIYToAAVJxHhQTRIhhBAdoiCJGIenT4GsLPHffn76LQshhJAagYIkYhwktUgNGgA2Nvoti6bS04HYWPE9IYQQg0dBEjEObze1GVvAER0tnrqgSxfxfXS0vktECCGkAhQkEeNQNkgytoAjPR0YMwYQicSPRSJg7FjjCfAIIaSGoiCJGAfJyDZnZ+MLOO7de1NeidJS8YK4hBBCDBYFScQ4SGqSLCyML+Dw9gZM3vqocbmAl5d+ykMIIUQlFCQRw5eXBzx6JP47JMT4Ag4XF2DtWnE5AfH9mjXi7YQQQgwWBUnE8P39t/je1VXcJ8kYA45Ro4DUVHFn89RU8WNCCCEGzVTfBSCkQgkJ4vv27cX3o0YBYWHiJjYvL8MPkCRcXIynrIQQQihIIkbg4kXxfYcOb7ZRwEEIIaSKUXMbMWyMARcuiP8uGyQRQgghVYyCJGLYHj4UL0fC5QKtW+u7NIQQQmoQCpKIYZM0tbVoAVha6rcshBBCahQKkohhk3TafqupLT0/HbEpsUjPN+BJJAkhhBg1CpKIYVPQaTv6SjTclruhy+YucFvuhugrBr4siTqMbU06QgipxihIIobr9Wvgr7/Ef/8XJKXnp2PMoTEQMfGs2yImwthDY6tHjZKxrUlHCCHVHAVJxHD9/Tfw6hVgby+dUfte7j1pgCRRykqR9NSAlyVRBS2CSwghBoeCJGK4zp8X37/zDsDhAAC8HbxhwpF923I5XHjZG/CyJKqgRXAJIcTgUJBEDNfx4+L74GDpJhdbF6ztvRZcjnhZEi6HizW918DF1sgnlqRFcAkhxODQjNvEMBUViTswA0DPnjK7RrUehTCvMCQ9TYKXvZfxB0jAm0Vwx44V1yAZy5p0hBBSjVGQRAxTXBzw8qU4SGjSRG63i61L9QiOyjLWNekIIaSaoiCJGKajR8X3PXtK+yPVCLQmHalq6eniPnDe3uW/17SVhhAjR32SiGE6ckR836OHfsthiGguJVKeit4bqkwzoa00qpRH1TSE6AkFScTw3LsHJCcDPB7Qtau+S2NYaC4lUp6K3huqTDOhrTSqlEfVNJJjUiBF9ICCJGJ4JLVIgYGAjY1+y2JIaC6lmk1ZoKDKe0OVaSa0lUbXwZYkPwqkiJZRkEQMz8GD4ntqapNFcylVX5VtJlPlvaHKNBPaSqPLYAugQIpUGQqSiGF58ODN0P+BA/VbFkNDcylVT9poJlPlvSGZZoLLfbP/7WkmtJVGl8GWPgKp6hxsaev1V5fzyIhCQqGQAWBCoVDfRalZ5s9nDGAsJETfJTFM69YxxuWKzxGXK36syMOHjJ06Jb4n+qXsWjx8yJiJifh6Sm5crmzaU6dk90tusbGyeanz3oiNVf7e0EYaVcpTURptnR9V8pGUR5LOxKT8MleURnLMij6Dqn5OtZVXRWm09fq1eR41oM3fbwqSykFBkh6UljLm4SH+0MyYQT/w5VHlx6mKvnyImiq6Ftr8gZekrSi40SVdBFu6DKT0EWzpKijR1uvX5nnUEAVJOkBBkh7Excl+aOgHXn1V/OVD3lLZWiJ1fnRVqSWqrgwlkNJ1sKXLoERbr19baSpBm7/f1CeJGI4ff5R9TKO31Eedu3VHG52pVenfA4hnY09NFfffSE0VP65JXFzEaziWN2llRefH0PpRqfo51eWIRF127Dem/pVaCNqqJapJ0rHsbMbMzav0v4saQd2mGeq3VD5d1RJJ0hpSM1l1ZSj9qAyxJklbr1+baTREzW06QEGSjk2frjhAoqYi9an6BUX9lsqnjb5EknxqcjOZMTKUTuvazsvQOvarmkYD2vz95jDGmH7rsgxTfn4+BAIBhEIhbG1t9V2c6i0nB3B3BwoLgQkTgJ9/FlcFS6rEa1rTgjakp5e/UG56urh5qGz1O5crbqZQlLY6rs+l7HWpcn7UPYe0aHHNo8p1V/W9oa28ash7UZu/37TALdG/H34QB0itWwMrVyJ9Qjju3TwH78ad4OLbTt+lM07KFspV1j+h7HOio9/MP2NiIu7TYQwBa0WBXUWvS5XzI+njMnasbECv6Hi0aHHNpMp1V/W9oa286L2oNqpJKgfVJOnIkydAw4bA8+fAgQOIdnmCMYfGQMREMOGYYG3vtRjV2gh+mI1JVdSU6GpV+coGQFRLREi1p83fbxrdRvTr88/FAVLr1kgPaiUNkABAxEQYe2gs0vNpdJtWqTLSR9XRN7pcVV4bM1Nrc8SZJK2yUVeEEKNGNUnloJokHThwAOjfX/wff0ICYh0K0GVzF7lkscNjEewerPPiVXuV7bdkaGliY8UB1NtiY8WBjKr5qHJ+CCEGi2qSiPF79gz47DPx3198AbRtC28Hb5hwZN+SXA4XXvYGOHdGdaCsFkRbtU2GNs8L1RIRQtRAQRLRvZISYNgwIDMT8PUFoqIAAC62Lljbey24HPEPGJfDxZrea+BiSz9SelHRBH2GNvkcTcxICNEyam4rBzW3VZGHD4GJE8VNbebmwJkzQDvZEWzp+elIepoEL3svCpAMXXS0/Aivt4MOXaYBqJmMkBpOm7/fFCSVg4KkKhAdDYweLZ52DxA3t61erd8ykcrT5RwuFAARQipAQZIOUJCkZWlp4g6zZZXXYZYQQgjREHXcJsbl6VNgyBDpw2Q7IN0GtPAqIYQQg2awQVJ6ejpGjhyJevXqgc/nw93dHZGRkXj27Jle8iEaOnAAaNwYOHcOpRxg6ADA63PAbTIQ3YZjmKs+E0IIITDQ5rbk5GT4+/sjOzsb/fr1Q6NGjXDp0iXExsbC19cX8fHxcHBwqNJ8qLlNA2VnQ75/H5g7Fzh9GgBQ7OOFwM5JSCjTssaFCVInP6DO2YQQQrSm2je3jRs3DtnZ2Vi5ciX279+PJUuW4NSpU5g8eTLu3LmD2bNn6zQfbXv16hXmzZuHV69e6eX4VSI6Go8au+LOwC547e4KBAWJAyQzM2D6dJw/8KNMgAQApRAh6Wn1bm6rltealIuud81B17pmMLiapOTkZHh5ecHDwwNJSUkwKTM3SkFBAZydnSESiZCdnQ1ra+sqy6cqa5J0WkulwnpY6XcSce/mWXg3Dix3QVmFafLzgUuXgGPH8PiXH+D4AuD+924q5QDcIUOBb74BXF2Rnp8Ot+Vu0iVHAPE8SKmRqdW6JolqJGsWut41B11rw1Wta5JiY2MBAKGhoTKBDQDY2NggICAARUVFSEhI0Ek+VeHRvb/Qwl18X570O4mI3bcU6XcSNU8THY30pg0QO7IL0ps2ULgeVvTKCLhtb48u/0yF2/b2iF4ZId7BGJCXByQn44/JPTF5TnscWDMVe8PbI62JK+DhAQgEQLduwA8/oG6hOEC6VheIDAPqTQXSh/YFXF0B0ESRhBBCjI+pvgvwtjt37gAAvL29Fe739vZGTEwM7t69i65du1Z5Ptq2Z/YAXE7YjzAvYOP0LnjfsjXaBXz4JgFjSIz/DfteXAHjACcY8J5FK7T1HygOXP67/XVhL/54cQ0AcJYBfSyao1XbPuL9IhEgFOLf33/GyUaACQNuOTJ0mfEJGsXEiJvAXr9G0dPHqJ9yGidLAIsSwOo1YP16E0Rz98HkeaF49BmAPv/d3iizYKi7Ox771EcULx5HvIGHtd7sSrIHyoZAo1qPQphXGE0USQghxCgYXJAkFAoBAAKBQOF+yfa8vLwqzUfSCpmRkYH8/Hzpdj6fDz6fr/TY5cm49xe239iPjSfLbr2C/D+uyKTzBTBDZstV5B++KrPFG8AUmS3/IP/4PzJb3ACMzJYtQ/7u3TKP/RWU8znevN5SMx7SLIqRbQU8sgEeCIAHtYCI9mPQYtRMwN4eT/MzsPanxmAA8FL8PBNwUNe5qcy5AwBb2KK1fWtxWd7aVx1JXmNNeK2ErndNQtfacEmuiTZ6ExlckFQRyYvmcDhVmk9BQQEAoHHjxpU6jiL7tJ5jFXpdDLwGIJTdvD5mLbBwbblPE4Gh8RLtnztj5fpfsyOpGeh61xx0rQ1XQUFBuRUlqjK4IEnygiQ1QW+TRIgVvfDK5lOvXj0kJyeDx+PJBFKVqUkihBBCSNVijKGgoAD16tWrdF4GFyT5+voCAO7evatw/7179wAAPj4+VZqPiYkJGjZsWHGBCSGEEGJQKluDJGGwUwC4u7sjOTm53KH7T548gZWVVZXnQwghhJCayeCmAPD09ERoaChSU1Px008/yeyLiopCYWEhwsPDpYFNcXExbt++jeTk5ErlQwghhBBSlsHVJAHyy4n4+fkhISEBsbGx8PHxwfnz56XLiaSmpsLDwwNubm5ITU3VOB9CCCGEkLIMriYJENcCXb58GREREUhISMAPP/yA5ORkTJo0CRcuXFA5sNFWPtpCi+0anz179mDixIkIDAyEra0tOBwOhg4dqvQ558+fR8+ePWFvbw9LS0s0b94cy5cvR+l/804psmnTJrRv3x7W1tYQCAQIDg7GoUOHtP1yiBK5ublYt24dBgwYAC8vL1hYWEAgEKBTp06Ijo6GSCRS+Dy63sZr+vTp6Nq1K1xdXWFhYQF7e3u0atUK8+fPR25ursLn0PWuYRjRiaSkJFanTh0GgPXr149Nnz6dhYSEMADM19eX5eTk6LuIRIEWLVowAMza2po1atSIAWBDhgwpN/3+/fsZl8tlVlZWbOTIkWzatGnM19eXAWADBw5U+JypU6cyAMzFxYVFRkaycePGMXt7ewaArVq1qqpeGnnLzz//zAAwJycnNnjwYDZjxgw2YsQIJhAIGAD23nvvMZFIJPMcut7GjcfjsXfeeYeNGDGCTZ8+nU2YMIG1bduWAWD16tVjDx48kElP17vmoSBJR0JDQxkAtnLlSpntkydPZgDY2LFj9VQyosypU6fY3bt3mUgkYrGxsUqDJKFQyBwdHZmZmRlLTEyUbi8qKmIdO3ZkANiOHTtknhMfH88AME9PT/b06VPp9pSUFGZvb8/4fD5LSUmpktdGZJ08eZLt37+flZSUyGzPzMxkrq6uDAD77bffpNvpehu/oqIihdtnzZrFALBPP/1Uuo2ud81EQZIOJCUlMQDMw8ODlZaWyuzLz89nVlZWzMLCghUUFOiphEQVFQVJ69atYwDY8OHD5fadPHmSAWCBgYEy24cOHcoAsA0bNsg9Z86cOQwAmzNnjjaKTyph0aJFDAAbP368dBtd7+rr2rVrDADr1q2bdBtd75rJIPskVTeGvNgu0R7Jde7evbvcvs6dO8PS0hIXLlzAq1evVHpOjx49ZNIQ/TEzMwMA8Hg86Ta63tXXH3/8AQBo3ry5dBtd75qJgiQdUGWxXaD8iS+JcVB2nU1NTeHh4YGSkhLcv38fAFBYWIiMjAxYW1vDyclJ7jn0vjAMJSUl2LRpEwDZHzu63tXH999/j3nz5mHy5MkIDAzEnDlz0KpVK8ycOVOahq53zWRwM25XR9patJcYNnWvM70vjMOMGTNw/fp19OjRA2FhYdLtdL2rj++//x6PHz+WPu7Rowc2btwoMwKarnfNRDVJBoBpadFeYtg0vc70vtCf5cuX44cffoCvry82b96s1nPpehuPrKwsMMaQlZWFvXv3Ijk5GS1btsSVK1dUzoOud/VEQZIOaGvRXmLY1L3OFaWv6D9RUrVWrFiByZMnw8/PD3FxcXB0dJTZT9e7+qlbty4GDBiAEydOIDc3F+Hh4dJ9dL1rJgqSdEBbi/YSw6bsOpeUlCAlJQWmpqbShZOtrKxQv359PH/+HJmZmXLPofeF/nz//feIjIxE06ZNERcXp7BPCV3v6qtBgwZo3Lgxbty4gZycHAB0vWsqCpJ0ICQkBAAQExMjN2tvQUEB4uPjYWFhgQ4dOuijeERLunTpAgA4duyY3L4zZ87gxYsX8Pf3B5/PV+k5R48elUlDdGPx4sX44osv0LJlS8TGxqJOnToK09H1rt4ePXoEAOByuQDoetdYep2AoAahySSNH00mWf19/fXXDABr06YNy83NVZqWrrdxu3XrFsvMzJTbXlpaKp1M0t/fX7qdrnfNZJAL3FZHtNiucdq/fz/2798PQNy58/jx42jYsCECAwMBAI6Ojvj+++9l0g8cOBDm5ub46KOPYG9vj4MHD+LOnTsYOHAgdu/eLddRc+rUqVi6dClcXFwwcOBAvH79Grt27UJubi5WrVqFCRMm6Oz11mSbNm1CREQEuFwuJk6cqLCviLu7OyIiIqSP6Xobr+XLl+OLL75A586d4enpCQcHBzx+/BinT5/G/fv34eTkhJMnT6Jx48bS59D1roH0HaXVJGlpaSwiIoI5OTkxHo/HGjRowCZNmlThf6xEf6KiohiAcm9ubm5yzzl37hzr0aMHq1WrFjM3N2dNmzZlS5culVvuoqyNGzeytm3bMktLS2Ztbc06d+7M/vjjjyp8ZeRtFV1rACwoKEjueXS9jdO///7Lxo0bx1q0aMEcHBwYl8tltra2rG3btiwqKqrc72W63jUL1SQRQgghhChAHbcJIYQQQhSgIIkQQgghRAEKkgghhBBCFKAgiRBCCCFEAQqSCCGEEEIUoCCJEEIIIUQBCpIIIYQQQhSgIIkQQgghRAEKkgghBo3D4cjcsrKyVH6uu7s73N3dq65wldS7d2+Z17Zx40Z9F4kQUoapvgtACKn+UlNT4eHhgeHDh2sUCLi5uUnXTLO2ttZu4fRo8ODBaNu2La5du4YDBw7ouziEkLdQkEQIMXju7u6YN2+evouhdYMHDwYAbNy4kYIkQgwQNbcRQgghhChAQRIhpErNmzcPHh4eAIBNmzZpvQ8OYww//vgjmjRpAnNzc9SvXx/jx4+HUChUmF4oFOJ///sfunTpAhcXF5iZmaF27dro27cvzp8/L5P22bNnsLS0hKenJ8pbC1zSr+ivv/6Sbtu3bx9CQkLg5OQEPp8PJycndOrUCT/99FOlXy8hRHeouY0QUqWCg4ORl5eHFStWoEWLFujfv790X8uWLSudf2RkJFauXAlnZ2eMGTMGPB4PBw4cwKVLl/D69WuYmZnJpL916xZmz56Nzp07o1evXrCzs8ODBw9w4MABHDlyBAcPHkTPnj0BAHZ2dvjoo4+wYcMG/Pnnn+jWrZtMXg8fPsTRo0fRpk0btGnTBgDw888/Y9y4cXByckLfvn3h6OiI7Oxs/PPPP9i4cSPGjx9f6ddMCNERRgghVSwlJYUBYMOHD1f7uQBYUFCQwn3x8fEMAPP09GS5ubnS7UVFRaxDhw4MAHNzc5N5Tl5eHnvy5IlcXqmpqaxu3brM19dXZvvly5cZAPb+++/LPWfOnDkMAFu7dq10W6tWrZiZmRl7/PixXHpFx2WMsQ0bNjAAbMOGDQr3E0L0g5rbCCFGa8OGDQCA2bNnw97eXrrd3NwcixcvVvgcgUAAR0dHue1ubm744IMPcOfOHaSlpUm3t2nTBu3atcPBgwfx+PFj6fbS0lJER0fDxsZG2gEbEE9ZYGpqCh6PJ3cMRcclhBguCpIIIUbrypUrAICgoCC5fYGBgTA1VdyjID4+Hh9++CFcXV3B5/OlfaR+/PFHAEBGRoZM+nHjxqG4uBjr16+Xbvvjjz/w6NEjDB06FFZWVtLtQ4YMwYsXL9CkSRNMmTIF+/fvx5MnTyr9WgkhukdBEiHEaEk6Z9etW1duH5fLhYODg9z2ffv2oXPnzjh8+DDatGmDCRMmYM6cOYiKipIGW69evZJ5zqBBg2Bvb49169ZJO3CvWbMGAPDpp5/KpJ0yZQo2bdqEBg0aYMWKFRgwYADq1q2Lrl27SoM6QohxoI7bhBCjJRAIAACPHz9Gw4YNZfaVlpYiNzcX9evXl9k+Z84cmJmZ4fLly/Dz85PZN3bsWJw+fVruOBYWFoiIiMDSpUtx4sQJ+Pj4ICYmBh06dEDz5s3l0oeHhyM8PBx5eXk4f/489u3bh/Xr1yM0NBS3bt1C7f+3d/8gjYNxGMefUATFgu3g0EHIYBdxsQgiVkRQBKUuFhRxsJMWVHB0EOkgKE5SUGqHKkXcdVDEobY6iODYpTqIi4g6C0pzg1zhaHocd7H24PvZEpL3z/aQ95f3bW7+16kDqAK+JAH4ci6XS9JncHFSIBCQJNtgk8vl9PHxUXb/9vZWbW1tZQGpWCzq4uKiYl/RaFSGYSiRSCiZTKpYLGpmZua34/N4PBoeHlYymdT09LReXl6Uy+X+ZGoAagAhCcCX83q9MgxDDw8Pjrb786iS1dVVvb6+lu6/vb1paWnJ9h3TNFUoFH6pO7IsS7FYTPl8vmJfra2tGhwc1OHhoXZ2duTxeDQ+Pl723MnJiW04e3p6kvRZVA7g/8ByG4Av53a71dXVpWw2q6mpKfn9frlcLo2OjtouV/2pnp4ezc/PKx6Pq729XeFwuLRPktfrlc/nK3tncXFRs7OzCgQCGhsbU11dnS4vL5XP5xUKhXR0dFSxv2g0qtPTUz0/P2thYUENDQ1lz0xMTKi+vl7BYFCmacqyLOVyOV1fXysQCGhgYOCv5wuguviSBKAq0um0RkZGdHx8rFgspuXlZUcKmTc3NxWPx9XU1KREIqGDgwMNDQ3p7OysbCNJ6bPuKJVKyefzaW9vT/v7+2ppadHV1VVp+a6SUChU+o2/0lLb2tqauru7dXNzo62tLaVSKb2/v2t9fV2ZTMZ2TABqk2FZFfbaB4AaYBiG+vr6lMlkvnsouru7k9/vVzAYVDabdazd3d1dRSIRpVKp0hIigO/HlyQANe/8/Ly0l9Hj4+O3jWNjY0OWZWlubs6R9n6e+xaJRBxpD4CzqEkCUNNWVlZ+uXa73VXt//7+Xul0WoVCQel0Wh0dHQqHw460PTk5qc7OztK1E2fZAXAOy20A8BuZTEb9/f1qbGxUb2+vtre3ZZrmdw8LQBUQkgAAAGxQkwQAAGCDkAQAAGCDkAQAAGCDkAQAAGCDkAQAAGCDkAQAAGCDkAQAAGCDkAQAAGCDkAQAAGDjBz9LeVXUyadvAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gam = 1./10. # 10 days recovery rate\n", "beta = 1./4. # 4 days to infect other person\n", "# R0 = beta/gam # basic reproduction factor\n", "immu = 1. / 90. # immunity lasts for 90 days\n", "\n", "def fSIR(xin, t):\n", " S = xin[0]\n", " I = xin[1]\n", " R = 1. - S - I\n", " # print(xin)\n", " return np.array([-beta * S * I + immu * (1. - S - I), beta * I * S - gam * I])\n", "\n", "t0 = 0.\n", "tend = 365.\n", "\n", "I0 = 1.e-5\n", "x0 = [1. - I0, I0]\n", "\n", "delta = 1.e-9 # The desired accuracy per day\n", "N = 50\n", "sol = bulirsch_stoer(fSIR, x0, t0, N, tend, delta)\n", "\n", "tpoints = [t for t in sol[0]]\n", "Spoints = [x[0] for x in sol[1]]\n", "Ipoints = [x[1] for x in sol[1]]\n", "Rpoints = [1. - x[0] - x[1] for x in sol[1]]\n", "\n", "\n", "#Nrk4 = 1000\n", "#hrk4 = (tend - t0) / Nrk4\n", "#sol = ode_rk4_multi(fSIR, x0, t0, hrk4, Nrk4)\n", "\n", "# Exponential phase\n", "texpon = np.linspace(0.,90.,50)\n", "def fIexp(t):\n", " R0 = beta / gam\n", " return x0[1] * np.exp(gam*(R0-1.)*t)\n", "Iexpon = fIexp(texpon)\n", "\n", "plt.title(\"Solving the SIR model using Bulirsch-Stoer method\")\n", "plt.xlabel('t [days]')\n", "plt.ylabel('Population fraction')\n", "plt.ylim(0,1)\n", "plt.plot(tpoints,Spoints,'.',label='Susceptible')\n", "plt.plot(tpoints,Ipoints,'.',label='Infected',color='red')\n", "plt.plot(tpoints,Rpoints,'.',label='Immune',color='green')\n", "plt.plot(texpon,Iexpon,label='Infected (Exponential phase)',color='red')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shooting method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us solve the problem of a vertically thrown ball at $t = 0$ which lands back on the ground at $t = 10$. We want to find the initial velocity. The equations of motion are\n", "\\begin{align}\n", "\\frac{dx}{dt} & = v, \\\\\n", "\\frac{dv}{dt} & = -g,\n", "\\end{align}\n", "$x(0) = 0$ and $v(0) = v_0$.\n", "\n", "We shall find the value of $v_0$ using the bisection method and solving the ODEs with 4th order Runge-Kutta method." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "last_bisection_iterations = 0 # Count how many interactions it took\n", "bisection_verbose = False\n", "\n", "def bisection_method(\n", " f, # The function whose root we are trying to find\n", " a, # The left boundary\n", " b, # The right boundary\n", " tolerance = 1.e-10, # The desired accuracy of the solution\n", " ):\n", " fa = f(a) # The value of the function at the left boundary\n", " fb = f(b) # The value of the function at the right boundary\n", " if (fa * fb > 0.):\n", " return None # Bisection method is not applicable\n", " \n", " global last_bisection_iterations\n", " last_bisection_iterations = 0\n", " \n", " \n", " while ((b-a) > tolerance):\n", " last_bisection_iterations += 1\n", " c = (a + b) / 2. # Take the midpoint\n", " fc = f(c) # Calculate the function at midpoint\n", " \n", " \n", " if bisection_verbose:\n", " print(\"Iteration: {0:5}, c = {1:20.15f}, f(c) = {2:10.15f}\".format(last_bisection_iterations, c, fc))\n", " \n", " if (fc * fa < 0.): \n", " b = c # The midpoint is the new right boundary\n", " fb = fc\n", " else: \n", " a = c # The midpoint is the new left boundary\n", " fa = fc\n", "\n", " return (a+b) / 2. " ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The required initial velocity is 49.0500000000017 m/s\n" ] } ], "source": [ "g = 9.81 # m/s^2\n", "# ODEs\n", "def fball(xin,t):\n", " x = xin[0]\n", " v = xin[1]\n", " return np.array([v,-g])\n", "\n", "# Initial and final times\n", "t0 = 0.\n", "tend = 10.\n", "# Number of RK4 steps\n", "Nrk4 = 100\n", "hrk4 = (tend - t0) / Nrk4\n", "\n", "# Desired accuracy for v0\n", "accuracy_v0 = 1.e-10 # m/s\n", "\n", "v0min = 0.01 # m/s\n", "v0max = 1000.0 # m/s\n", "\n", "def fbisection(v0):\n", " x0 = [0., v0]\n", " return ode_rk4_multi(fball, x0, t0, hrk4, Nrk4)[1][-1][0]\n", "\n", "v0sol = bisection_method(fbisection, v0min, v0max, accuracy_v0)\n", "print(\"The required initial velocity is\",v0sol,\"m/s\")" ] } ], "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": "3.10.16" } }, "nbformat": 4, "nbformat_minor": 4 }