{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 3, Nonlinear dynamics, stability and bifurcations\n", "\n", "> ordinary differential equations (ODE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "\n", "from ipywidgets import interact, interactive, fixed, interact_manual\n", "import ipywidgets as widgets\n", "\n", "from IPython.display import HTML\n", "from IPython.display import display\n", "\n", "from scipy.integrate import solve_ivp\n", "\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from IPython.display import display, clear_output\n", "\n", "from matplotlib.colors import Normalize\n", "from ipywidgets import interact, FloatSlider\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our last session, we analyzed how the Earth's temperature changed over time, utilizing a simplistic yet surprisingly effective model. Today, we'll build on that foundation, looking at stability.\n", "\n", "Our simple model is based on *ordinary differential equations (ODEs)*, where some variables change in time - with the rate of change as a function of their current values.\n", "\n", "\n", "$$ \\frac{dx(t)}{dt} = f(x(t)) $$\n", "\n", "The simplest numerical method to solve such an equation is the **(forward) Euler method**, in which we convert this equation into an explicit time-stepping routine:\n", "\n", "$$ \\frac{dx(t)}{dt} = \\frac{x(t+\\Delta t) - x(t)}{\\Delta t}$$\n", "\n", "```{prf:assumption}\n", ":label: euler-forward\n", "\n", "$$ x(t+\\Delta t) \\simeq x(t) + \\Delta t f(x(t)) $$\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the ODE: Euler method\n", "\n", "Let's use this to simulate a simple nonlinear ODE that describes the dynamics of a population of bacteria. The bacteria will grow by reproduction at a rate $\\lambda$ when sufficient food is available, in which case we would have $\\dot{x} = \\lambda x$. However, the available food limits the sustainable population to a value of $K$, leading to a modified equation:\n", "\n", "$$\\dot{x} = \\lambda \\, x \\, (K - x).$$\n", "\n", "In this model, when $x$ is close to 0, the growth rate is close to zero and it increases as $x$ increases, reaching a maximum when $x$ is at half of the carrying capacity ($K/2$). Beyond this point as $x$ continues to increase, the growth rate starts to decrease, eventually approaching zero as x gets closer to $K$\n", "\n", "This is sometimes called the [**logistic** differential equation](https://en.wikipedia.org/wiki/Logistic_function#Logistic_differential_equation) (although the name does not seem particularly helpful).\n", "\n", "Our goal is to use computational thinking, but we will only be interested in the exact dynamics in time rather than in the **qualitative** features of the system's behavior. For example, at long times (formally $t \\to \\infty$), does the population get arbitrarily large? Or does it, for example, oscillate around a particular value? Or does it converge to a particular size?\n", "\n", "This forms the subject of **nonlinear dynamics** or **dynamical systems** theory. \n", "\n", "Let's simulate the system using the Euler method to try to guess the answer to this question. We should never use the Euler method in practice. Instead, we should use a tested library (` scipy.integrate import odeint`) that provides much better accuracy in the solutions if we are interested in faithful numerical results.\n", "\n", "```{prf:proof} Analytic solution\n", "In contrast to real world systems we could still solve this system for it's stable points'\n", "\n", "The differential equation given is:\n", "\n", "$$\n", "\\dot{x} = \\lambda x (K - x)\n", "$$\n", "\n", "where:\n", "- $\\dot{x}$ represents the rate of change of $x$ with respect to time,\n", "- $\\lambda$ is a growth rate constant,\n", "- $K$ is the carrying capacity of the environment.\n", "\n", "To find the stable points (or equilibrium points), we set $\\dot{x} = 0$ and solve for $x$. This leads to the equation:\n", "\n", "$$\n", "0 = \\lambda x (K - x)\n", "$$\n", "\n", "Expanding this equation gives:\n", "\n", "$$\n", "0 = \\lambda xK - \\lambda x^2\n", "$$\n", "\n", "This equation can be factored into:\n", "\n", "$$\n", "x(\\lambda K - \\lambda x) = 0\n", "$$\n", "\n", "Setting each factor equal to zero gives the stable points:\n", "\n", "1. $ x = 0 $\n", "2. $ \\lambda K - \\lambda x = 0 $ leading to $ K - x = 0 $ and hence $ x = K $\n", "\n", "Thus, the stable points of this system are $x = 0$ and $x = K$.\n", "```\n", "\n", "\n", "```{exercise} \n", "Implement the forward Euler method as given in {prf:ref}`euler-forward`\n", "\n", "Change the growth rate and see how the model responds. Describe the behavior.\n", "```" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambda_ = 0.01 # Growth rate\n", "K = 20 # Carrying capacity\n", "x0 = 10 # Initial population\n", "\n", "t = np.linspace(1, 200, 10000)\n", "dt = t[1] - t[0] # Time step\n", "\n", "x = np.zeros_like(t)\n", "\n", "x[0] = x0\n", "\n", "for i in range(1, len(t)):\n", " x[i] = x[i-1] + dt * lambda_ * x[i-1] * (K - x[i-1])\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(t, x, label=r'$\\dot{x} = \\lambda x (K - x)$')\n", "plt.xlabel('Time')\n", "plt.ylabel('Population (x)')\n", "plt.title('Logistic Growth Model (Euler Method)')\n", "plt.axhline(y=K, color='r', linestyle='--', label='Carrying Capacity (K)')\n", "plt.legend()\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following, we will rescale the function to its simplest form\n", "\n", "$$ \\dot{x} = x(1-x) $$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def logistic(initial_population, timesteps):\n", " \"\"\"\n", " Computes the logistic growth of a population over given timesteps.\n", " \n", " Parameters:\n", " initial_population (float or array-like): The initial population or an array of population values.\n", " timesteps (array-like): An array of time steps at which to compute the population values.\n", " \n", " Returns:\n", " numpy.ndarray: An array of population values at the given timesteps.\n", " \"\"\"\n", " population = np.asarray(initial_population, dtype=float)\n", " time_differences = np.diff(timesteps)\n", " \n", " for time_step in time_differences:\n", " if population.size == 1:\n", " next_population = population + time_step * population * (1 - population)\n", " else:\n", " next_population = population[-1] + time_step * population[-1] * (1 - population[-1])\n", " population = np.append(population, next_population)\n", " \n", " return population" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "t1 = np.arange(0, 20, 0.01)\n", "dxdt = logistic(0.5, t1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t1, dxdt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{important}\n", "We see that for this particular initial condition, the solution seems to settle down to a fixed value after some time, and then remains at that value thereafter.\n", "\n", "Such a value is called a **fixed point** or a **stationary point** of the ODE.\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Qualitative behaviour: Fixed points and their stability" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But what happens if we have a different initial condition:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "25bb6d78cfd64abebecc02f9ac8de820", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.5, description='Initial Condition:', max=3.0, min=-3.0, style=Slider…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def plot_func(initial_condition):\n", " plt.close(\"all\")\n", " plt.figure(figsize=(10, 6))\n", " plt.plot(t1, logistic(initial_condition, t1), linewidth=2, color='#1f77b4')\n", " plt.title('Dynamics of Bacterial Population Growth', fontsize=16)\n", " plt.xlabel('Time ($t$)', fontsize=14, labelpad=10)\n", " plt.ylabel('Population ($x(t)$)', fontsize=14, labelpad=10)\n", " \n", " plt.xlim([0, 10])\n", " plt.ylim(-3, 3)\n", " \n", " plt.grid(True, linestyle='--', alpha=0.7)\n", " \n", " plt.show()\n", " \n", "interact(plot_func, initial_condition=widgets.FloatSlider(value=0.5, min=-3, max=3, step=0.1, description='Initial Condition:', style={'description_width': 'initial'}))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get an overview, we can draw all graphs in a single plot." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,8))\n", "for initial_condition in np.arange(-1, 2, 0.1):\n", " plt.plot(t1, logistic(initial_condition, t1))\n", "plt.xlabel(\"t\")\n", "plt.ylabel(\"x(t)\")\n", "plt.xlim([0,10])\n", "plt.ylim(-1, 2)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe that trajectories initiating near $x_0=1.0$ appear to converge to 1 as time progresses. In the particular case where the system starts *precisely* at 0, it remains there indefinitely. Conversely, for starting points in close proximity to 0, on either side, the trajectory diverges *away* from 0, maintaining its side of origin. In scenarios where the initial value is negative, $x$ becomes increasingly negative over time. Although negative populations contradict the original interpretation as population dynamics, exploring the dynamics of the equation with negative initial conditions remains valid, as it may represent other systems.\n", "\n", "The distinguished values $x^*_1=1$ and $x^*_2=0$ are termed **stationary points** or **fixed points** of the differential equation. Starting at $x^*_i$, the derivative evaluates to $f'(x^*_i) = 0$, rendering any movement away from $x^*_i$ impossible! We can locate the fixed points by identifying the zeros or **roots** of the function $f$, defined as values $x^*$ such that $f'(x^*) = 0$.\n", "\n", "However, we discern a **qualitative difference** between the two types of fixed points: trajectories near $x^*_1 = 1$ gravitate *towards* $x^*_1$, while those near $x^*_2 = 0$ repel *away* from it. Consequently, $x^*_1$ is classified as a **stable fixed point**, and $x^*_2$ as an **unstable fixed point**.\n", "\n", "Finding analytical expressions for the position and stability of fixed points is generally infeasible; alternatively, numerical **root-finding algorithms**, such as the Newton method, can be employed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## State space: Vector field and phase portrait\n", "\n", "If we want to find the whole trajectory for a given initial condition, then we need to solve the equations, either numerically or analytically.\n", "\n", "However, we may want less information about the system, for example, the **long-time** or **asymptotic** dynamics. It turns out that we can obtain some information about that *without* explicitly solving the ODE! This is the **qualitative approach** to studying nonlinear systems.\n", "\n", "Instead of drawing trajectories $x(t)$ as a function of time $t$, as we did above, let's use a different graphical representation, where we draw **state space** or **phase space**: This is the set (\"space\") of all possible values of the dependent variables (\"states\"). For the above ODE, there is only a single dependent variable, $x$, so the state space is the real line, $\\mathbb{R}$.\n", "\n", "At each possible value of $x$, the ODE gives us information about the rate of change of $x(t)$ at that point. Let's draw an **arrow** at that point, pointing in the direction that a particle placed at that point would move: to the right if $\\dot{x} > 0$ and to the left if $\\dot{x} < 0$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "states = np.array([])\n", "initial_conditions = np.arange(-1, 2, 0.05)\n", "\n", "for initial_condition in initial_conditions:\n", " states = np.append(states, logistic(initial_condition, t1)[-1])\n", "\n", "X = np.ones(len(states))\n", "Y = initial_conditions.copy()\n", "U = np.zeros(len(states))\n", "V = np.ones(len(states))\n", "V[states - initial_conditions < 0] = -1\n", "\n", "states[states == -np.inf] = 2\n", "\n", "# Create the quiver plot\n", "plt.figure(figsize=(2,8))\n", "plt.quiver(X, Y, U, V, scale=10, width=0.02, angles='xy', scale_units='xy')\n", "\n", "# Mark the fixed points\n", "plt.plot([1, 1], 'ro', markersize=12)\n", "plt.plot([1, 0], 'go', markersize=12)\n", "# Set plot limits and remove x-axis labels\n", "plt.xlim([1, 1])\n", "plt.xticks([])\n", "\n", "# Add labels\n", "plt.ylabel('Initial Condition, $x_0$')\n", "plt.title('Stability of Fixed Points')\n", "\n", "# Show the plot\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`````{admonition} Dynamics of the system\n", ":class: tip\n", "\n", "This vector field indeed gives us a *qualitative* picture of the dynamics. It does not tell us how **fast** the dynamics will occur in each region, but it indicates what the **tendency** is.\n", "\n", "We have coded the fixed points according to their stability; this may be calculated using the derivative evaluated at the fixed point, $f'(x^*)$ , since this derivative controls the behavior of nearby initial conditions $x^* + \\delta x$.\n", "\n", "`````" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bifurcations\n", "\n", "Now, suppose that there is a **parameter** $\\mu$ in the system that can be varied. For each value of $\\mu$ we have a *different* ODE.\n", "\n", "$$\\dot{x} = f_\\mu(x).$$\n", "For example, \n", "\n", "$$\\dot{x} = \\mu + x^2.$$\n", "\n", "```{important} Remember\n", "\n", "The focus is not on the evolution of the system over time, but rather on examining how the system's behavior changes as the parameter $\\mu$ varies.\n", "\n", "```\n", "\n", "Let's draw the state space for each different value of $\\mu$:\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "346a257cbe21470280d76c18e03b21a6", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=-1.0, description='mu', max=2.0, min=-2.0), Output()), _dom_classes=('…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def xdot(mu, x):\n", " return mu + x**2\n", "\n", "x = np.arange(-5, 5, 0.001)\n", "\n", "def plot_func(initial_condition):\n", " plt.figure(figsize=(8,8))\n", " a = xdot(mu = initial_condition, x = x)\n", " plt.plot(x, a)\n", " plt.title(\"$\\dot{x} = μ + x^2$\", fontsize=14)\n", " plt.xlabel(\"x\")\n", " plt.ylabel(\"$\\dot{x}$\")\n", " plt.xlim([-5,5])\n", " plt.ylim(-2, 2)\n", " plt.grid()\n", " \n", " try:\n", " zero_crossings = np.where(np.diff(np.signbit(a)))[0]\n", " plt.text(x[zero_crossings[0]]+0.2, 1.8, \"Zero Crossing\", rotation=0, fontsize=10, color='green')\n", " plt.text(x[zero_crossings[1]]+0.2, 1.8, \"Zero Crossing\", rotation=0, fontsize=10, color='green')\n", " plt.vlines(x[zero_crossings+1], ymin=-2,ymax=2, ls = \"--\", color = \"black\")\n", " for arrows in np.arange(-5,x[zero_crossings[0]],0.5):\n", " plt.arrow(arrows, 0, 0.25, 0,shape='full', lw=1, length_includes_head=True, head_width=.05, color =\"blue\")\n", " for arrows in np.arange(x[zero_crossings[0]]+0.5, x[zero_crossings[1]],0.5):\n", " plt.arrow(arrows, 0, -0.25, 0,shape='full', lw=1, length_includes_head=True, head_width=.05, color = \"blue\")\n", " for arrows in np.arange(x[zero_crossings[1]], 5,0.5):\n", " plt.arrow(arrows, 0, +0.25, 0,shape='full', lw=1, length_includes_head=True, head_width=.05, color =\"red\")\n", " plt.plot([x[zero_crossings],x[zero_crossings]],[0,0], marker='o', markersize = 12)\n", " except:\n", " for arrows in np.arange(-5,5,0.5):\n", " plt.arrow(arrows, 0, 0.25, 0,shape='full', \n", " lw=1, length_includes_head=True, head_width=.05, color =\"blue\") \n", " plt.show()\n", " \n", "interact(plot_func, initial_condition = widgets.FloatSlider(value = -1,\n", " min = -2,\n", " max = 2,\n", " step = 0.1, description='mu'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's collect all the vector fields into a single plot. We *rotate* the vector field to now be vertical, thinking of the dynamics of $x$ as occurring along the vertical direction. The horizontal axis now represents the different possible values of the parameter $\\mu$:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, '$\\\\mu$')" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "saddle_points0 = np.array([])\n", "saddle_points1 = np.array([])\n", "\n", "stepsize = 0.1\n", "for mu in np.arange(-2, 2, stepsize):\n", " a = xdot(mu = mu, x = x)\n", " zero_crossings = np.where(np.diff(np.signbit(a)))[0]\n", " if zero_crossings.size > 1:\n", " saddle_points0 = np.append(saddle_points0, x[zero_crossings[0]])\n", " saddle_points1 = np.append(saddle_points1, x[zero_crossings[1]])\n", " for arrows in np.arange(-5,x[zero_crossings[0]],0.25):\n", " plt.arrow(mu, arrows, 0.0, 0.1,shape='full', lw=1, length_includes_head=True, head_width=.025, color =\"blue\")\n", " for arrows in np.arange(x[zero_crossings[0]], x[zero_crossings[1]],0.25):\n", " plt.arrow(mu, arrows, 0.0, -0.1,shape='full', lw=1, length_includes_head=True, head_width=.025, color =\"red\")\n", " for arrows in np.arange(x[zero_crossings[1]],2,0.25):\n", " plt.arrow(mu, arrows, 0.0, 0.1,shape='full', lw=1, length_includes_head=True, head_width=.025, color =\"blue\")\n", "\n", "\n", " elif zero_crossings.size == 1:\n", " saddle_points0 = np.append(saddle_points0, x[zero_crossings])\n", " saddle_points1 = np.append(saddle_points0, np.nan)\n", " else:\n", " saddle_points0 = np.append(saddle_points0, np.nan)\n", " saddle_points1 = np.append(saddle_points1, np.nan) \n", " \n", " for arrows in np.arange(-2,2,0.25):\n", " plt.arrow(mu, arrows, 0.0, 0.1, lw=1.3, length_includes_head=True, head_width=.02, color =\"blue\")\n", " \n", "plt.ylim(-2,2)\n", "plt.xlim(-2,2)\n", "plt.scatter(np.arange(-2,2,stepsize), saddle_points0, color=\"green\", marker='D')\n", "plt.scatter(np.arange(-2,2,stepsize), saddle_points1, color=\"black\", marker='o')\n", "plt.ylabel(\"fixed points and dynamics with given $\\mu$\")\n", "plt.xlabel(\"$\\mu$\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "We see that at the **critical value** $\\mu_c = 0$ there is a **qualitative change in behaviour** in the system: for $\\mu_c < 0$ there are two fixed points, whereas for $\\mu_c > 0$ there are no fixed points at all. In this particular ODE the two fixed points collide in a **saddle--node** or **fold** bifurcation.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bistability and hysteresis\n", "\n", "Now let's look at the dynamics of the following system:\n", "\n", "\n", "$$\\dot{x} = \\mu + x - x^3.$$\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def h(mu, x):\n", " return mu + x - x**3" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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3W/TsSam4AP1YiWT7VapET+g//KDFhEiS5tw50pgxiu+/17ZFMo26ddP0ZcqWBerWNWBQqcTbb1Nsi1GMGUOzH6Kp6hmJggWNq6PGGDmbACWeWBZiTgpFsU5wEXGeS5QAmjen7X79pHRAWnPnDv3ezJ6d1iORjpThfPopxUJYTgunJc+eacGY69dTULEtfHwoe0t9ii5Vil+A2cdHC5QUreQN0PKeiICgq9O8ubhAqF4iI62X24KD+cvMmTLREi5ABbrTc0bkoUPiBYJfvNAKwF68KLY81KoVSTnMmeM8AfOpibrk72h+/pm0sAAgNNR69igpPD1pydTNjWa0Bw0SOx9Tp5KMCm//Ev2Eh4uteKg8f07/8u5hqYB0pIwmJob+dYLpRwAUZ6LGsMTEABMn8tuoT9GMiTtG48ZRMGbnzikbryswcCCwZYu4Pa/IaErw8aEbkslErxo1xNSux4yhgGvRGYd//9W2eTOczsqHH2qzd716iQk7mkw0yyeqKO2smM30IOYsv2svP9yJBGr366cltogmMFSqRIV4CxbUP0ZXQ28ppJYtSQA5HSIdqfTOmjWaYF/37pqXnhxt2lgvnXXsyO9DzZDLk4cE40Tw86N4ENHK367MggXakoGjuXZNm2Fauxb49Vd+m9Gj6UappzROlixA6dJiBU3PnCFblXr1nOeGrIeXA6EtJTwyOp9/TiK9IgHX9nD6tPa7tm4d//qoWxcoU4a23d3FpANy5KBQgu++04qNSxyH3lJIp04ZNxaDkY6UM/H8OVWtVxGpETZ9ura9ahXpqNjCMk7B359+DHmYTHSRX7zoeunX9mCUzIA9bNliXRds5Up+m7p1gTffJPVjI2oG5s6tFUp1cyMnPT0uB/bpowkmFi3qWvUV1VlRdcbd0Vg+sHXsSMt1tlAUzenv2lVcOqBNG+PitjIST57Qsr2eMmGAcaWQnAzpSDkTp06RgriKSE2xgQO1m1DBglrdJVuMGkUzRmPGiM0gALTkowaQS5Jn1y560nWWH5BOnazVkYcM4bdRFJppOH3amMD/3Lkp0FpRaMnYKB2whATKeBNdCv3lF2173Tq+vZ+fJkkwenT6TpL49VeasTQCxjT9JUBsGbtBAy0bN1Mmynjk8d57tJwkM+Qcz2efUVC3UdqDenn8WFNyX7vW+Mx1Hkyii/DwcAaAhYeH842XL2eMfkYY8/ZmbPdu2/YJCYxVqMCYotDr88/5fUREMObjQ33MnSt2EBJxoqIYe/ZM3H7sWDoXu3aJt1GvERG6d9fsc+Rg7No1fpvhw8m+bFm6xpyBs2dpTOXKGTemS5eoj169+LYREYy5u2ufraIwdu8ev93Dh4xt28ZYdHTKx5uW6LkGGdN3ne/bp+0fYMzfn3/Or1yhcwAwNnSo+LgkYnz9NWMzZojbG/27xhhj2bKJ28+bZ31NtWwp1EzX/VsH6fgRKo0RmeI8elTbfvECOH7ctr06Pc0YPYWJBKT6+JBnXqUKZVhJHEuDBsamwz96pG3zUrYB4NIlbfvxYzHh1mHDKA5p+nTnWUIrVYoyWTdsMH5MvLhBgL5HdevSLIibGy1tigTZ58xJ8h6ZMqV4mBmWKlU0EVWTiWZJeee8SBESGnZzkxlyIuiNMRw82DiBXnv45hstJq5FC75+2DvvaOEBQJpLiUhHyl7KlKFUcVsMH679YPj4iAm4dehAKdLTp4tXbh81iqY25dIbn2PH9P3oHDhgXSDZkVy6ZB3kKhJ0bVljsGZNMbmIIkWAv/5yPgX46tXFxFpTizFjKMA+IYHiQdIrkZF0XRi13LF1q7ZUFxzML4/j7q4VX2aMHHsR1qyhh4XAQPvH6go8e0bfo50703okhD2lkCyrIWzezL928+Uj1XiAxFQtY4vTAOlI2cvz5/yYiGLFKHMBoFgmkSKiHh4UrxASkvIxSqy5fZvSl2fMSOuREF5emlCrotCsBu9JvUULurHIGoOOp0EDekAKDEzzH+YUcf8+zYbPm2fM/n/8Udu+dIlK/fDo1YuSW7p1E5cO8PYWf5jMSDCmT9H94UPgyhVgyRLjxqQHe0ohqTp0ADmFIsW5R4yga+nDD9O8uoV0pOylb1/rIN7kmDqVAnwtLxRJ2vDiBf0rUmDWHh4/1tLB//qLn9EUEEAZSWqNQRGpATc3+sGcOtW1ssRU1HNoBIpCCR+XL6f5D7NTY6m55OkpFlLg60sPMt9+a9y4MgpTpzqXlMbXX2szkG+9pdXVTA57SiFZVkcQTdwoW5YEcfv04dsajHSk7EW0gGiFCvRkmF4LrTozd+5YlzNJaz74QEvTnjqV1v15jBxJTlTx4lR+R4T69YFJk1zvZj97tvhsxpEjNPsIUFaPquafHklIoGvdCOLirGsjlijBjymrWFFbuuneXRbj5XH9uj7ZgC+/FIvrsxfLcjhqXJItrlyx/T4p9JZCypQJmDmT4g27duXbOxnSkbIXZ3picFWaNqXAVaOwLGdhuZyRHC8Hpb/5Jr9NUBAFXK9bl77T51ODmTNpGUOEs2etbxL//GPIkFKFIUOME4w0m4Fbt7T3t2+L6aBNmUI3vREjjBlXRqJwYTG9vtTg+XNrMdxixaxrDibFsGHab1O2bNYlpJLDnlJI/fsD27aJrfQ4GfKXW+I8fPqpPqXka9eMG0tkpLVQ3/vv8zPkOncmDSmAHKRatcT6atuW7CWO4733rGdK0vMNX4++E2NacsT16/yEGG9v7UZpMtHNTKQY79tv002vVCnxsbkyInFk9pCQoP1mnj9Pwpm28PB49YHN29t2m0KFKEsOoBAVkQzVjFIKSRDpSEmchzFjgDp1jNn3w4dU/w+gG5Ol2ndS+PhQPICaDl+5Mj8dXr0pAfqKNUscj1qUFqCl0LJl03Y8lhw4YFy9xHXrtNi5vXvFYjMHDKDMOsZkLCeP+HixkjWpxZo19JAHUIIBT3DX3Z2yvBVFk5YQKeM1eTKFEwwalOIhZ0SkIyUxhgsXKOaH94T0MkaVnPj+e+vludmz+W3UmnMJCeI158aMoWBl9QnOVTh1ivSCnKkAcb9+NBM1c2Zaj8SaGjVIs8oIXl4CLFyY3yZ3bpo9WLqUZh8kyfPZZ5QgYpS0xKlT2pL0d9/xHbaSJa3fq/UGbREcTMttHh40AylC6dIU9ymireaCSEdKIgZj5FCIsmwZTf07SyHK996zLocjMuXcsCHwxht0M2rTRqwfb29Kn3e1QPDvvgMOHzZOc+vcOe0G88svYjMCOXJQkLlIrFpqY9T3onZtoHx52vbwECveC9CshojOXUbjr7+orIwo6jWot+acKJZF5Lt0ofHZompVeoAB6LenXz9+H1mzklbT5s1Arlz2j9VJiDOnfW1T6UhJxBg4UBNAcwYmTtR+1CpU4Ach58mjBUkGBopJBygKBSlfvep6jlFsrLFSA3qxnOFr1855xAeNZt8+7TqfM4f/MKMompiozKjjU7++pvXnaBISrIvKi8RJNW6s/dZkziwmuKvOlvfqBWTPLja2OnXE6rI6OcvDlsNnpg+Why1P03FIR8pVEUl7tWThQueSGti8Wds+cUJMG2rECBJ7mzRJZsjxaNXKuOUne1DLtwD05F2hQlqOJvWwnDkdORL43//4bTp0AP780/WK98bEUMKHZRmltOTgQXrgU+nXjz+TOmyYZtO3r5ggaZs2JPdh6bSlU/TMLi0PW47ev/VGrDkWvX/rnabOVLq+m+zevRstW7ZE/vz5oSgKNlqmqyfBzp07oSjKK69z586lzoCdhYcP6cll9eq0Hglx+7b1k1Tz5vwfHLXkhKJQILFlSYLkeP114OLFNK/LlC7Yti3tK6pbEhKizcboefI2muvXKbvTUpvHkbzzjub0+/mJZYJ6eFBWnavFs9y6RYkkU6ak9UiIKlVIdBegh4CuXfkJKKpUgpubeCkdk4k001RBSydCr2MkOrukOlEMdJ9gYGnqTKVrRyoqKgrly5fH119/ravd+fPncefOncRX8eLFDRphKhEfT8Hdoqg/+lu3GjOe2FhNKuDWLb5TFBVlrWUiIj747ruk5aUqgssMOdscPmxcptHz55oUxb//isfSDRoE/PGHmG3RolS2RVGcq4jt/PnATz/xC5IDNGNiqXsmUsJl0CDNkRo8OF1q7KQItYSSHvTEcuphyxZN4bt7d742mZohp8LLqFNZvZp+D4sUsWuYzoI9jpHI7NLLTpRKWjpT6dqRatq0KaZPn4527drpapcnTx7ky5cv8WVytviXkyf5+i+WdO9OisTOwqRJWimITp2AVats2xcvTjFL6g1j7Fi+Y+ThQTei4GBrvSfJq9y6RU/H06YZs/8JE4AffqDtPn0o+0uE+fOBZs3E+1mzBrh7l0QE0yNhYdbL47Nn853bfPloBjVLFtdLPV+yhJI9nIX167Xtq1fJseIRHExq/D17arNTPDw9xeqypjJGLbvpmV1KzolSSStnKl07UvYSFBQEf39/1K9fH6FqSY9kiImJwbNnz6xehlO+PKkGiyLyhU4Jp09r2ydP8u1fXtcX+VEYNYqeJPPnB9q3FxvXu+9SdqCnp5i9q6JKSpw/b8z+Xy5/ZJQKd5Ysxi9Xxccbl5FVtSo5BqqGz5AhYjOpS5bQg5W/vzHjSi2ePtU3WzRmjHHXrNlsHQ5QuTL/vFvOKHl5idUYzJqVln+dpaCwnRi17KZndonnRNlqazQu5Uj5+/tj8eLFWL9+PTZs2ICSJUuifv362L17d7JtZs6cCT8/v8RXQdFaXypxcTQjo3dZ5cABffZGERlJBShVqlblZ8j166ep5RYsKCYdULs2ZSWtXElT4pLkuXWLZmeMwjKgWWTprVcvbcnptdf0zTI5G++8I17zUC9qRh1j5PyL1uvMKBQubOysmjqL//w5f0kwJsb6ofD0aQoxsEWFCiTSC9AsYTqXDhCdYTJq2U3P7FKcOQ4DNg/gOlGWbQdsHpBq0ggu5UiVLFkSffr0QcWKFVG9enXMnz8fzZs3x2effZZsm3HjxiE8PDzxdePGDX2dfvopLb05i2P04oUWZP7nnyQeaYssWUguQH1yzp9fK4OSHDlyaE9ro0aJSQcoCgUUN2jAt3V1mjY1rrBnZCQF+6u0bMkvjePnp+nXiFZud1Y2btQKT/Mwm4GICNoODxd7WHrvPbrGJ01ynoD51OLZM8r+NYI//tD0s375ha5DW2TOTDFnJhO9evcWOx9TptCDQnouOQTxGSajlt30zi6tPrkaC5ovgAKxWFgFChY0XwAPkwff2AGk4188x1CtWjVcsBGo7eXlBV9fX6uXLtSlwPj4FIzSgSxfrmW13LtnHQyZFJZP0YoifqOcNAn4+WeXqbWUImbMoFRpUfQ683rw8aFZR7U0TpkyYlpEEybQTFb37mL9WCreG1np3kg++ojivACSi1i3jt/G0xPYsUMrV5ReYQzYvz+tR6Hx8u+riFM7eDD9piUkaOWEeNStS9IrzhST+h+OnmEyatmt12+90G9TP92zS13LdcXSVku5zpQCBUtbLUVwkMDSq4NweUcqLCwM/uk59mDLFk0T6oMP+JXbGzSwjssQWYZRM+R8fcUqfwNk3769eOVvV+bDD7UlA0dz/772dL52LbBnD7/NmDFaaRyRwH+AZiHr1+cXQAVI5ydfPu19vXrOU7tMDy8/UKTHY7CX+fOBmjUpgN4Irl/XftdshF4k0rw5ZXYCWg05Hv7+wDffAF98obVNpzh6hsnIZTcAYIzZNbsUHBRs05lKCycKSOeOVGRkJI4fP47j/6UeX7lyBcePH8f169cB0LJcN4sb/9y5c7Fx40ZcuHABp0+fxrhx47B+/XoMHjw4LYb/KvHx1jEEK1bw21g+Sc2aRct1tihRQlu6yZ5dTK3cw4PS50+ccL3069TCqADndeuADRu09zaWsRNp1oxinfLlI00bR+PlpcWwKAo5X+lRvmLgQK3skL+/MZ+Vs6LOiqpLm47GMq7yrbeoALMt3Ny0B4b27cVqDAIUpyaq15SKGJEhJzrDlBrLbotbLrZ7dsnKmWK2bVOLdO1IHTlyBEFBQQgKCgIAjBgxAkFBQZg0aRIA4M6dO4lOFQDExsZi1KhRKFeuHGrXro29e/di8+bNuuUTDOPwYW2pAADGj+c/5fbooT0Z58pFT/c81B+cYcPEZhAAChoX/XFyZcLCKDPr3r20HgnRsaN1jcHevflt3Nwo+PbqVeu2jiIggMalKJoOmBEwRg8j0dFi9pazdbwaZwAteapLmSNGGPNZpRb79ompptuLpfivyDJ2pUra75qHh9hSWrduwOLFzlekGmkvTCk6w7T46GK7grrtWXZLyexScIn3sPR5Q2rJAAVIMycKABTGXGk+OuU8e/YMfn5+CA8P58dLbdwItG1L2wUK0Nq6GhCZFAkJQKlSpL6tKMDkyRRrZIvHj2nfL15QSYjx4/kHwRgtAbq7p+/A4NQgPp7Oi6jEwgcf0Mzgrl1Uz0oEdTZG5Ks4bhzwySe0/cYbFBjNi2FStZ1ee40EM53hnIeFARUrkibU+fPGjOnKFVqyGTQI4In2RkbS56jWF3R3p+xIntzCzZvkgLRrR0vf6RU91yCg7zo/dMg68zcggJbubM1Cnj1LlQgAirMU1SZzQpaHLceAzQOwoPkC7o3e0uHhzbDYco4s24rOMKntulfojpXHVwrbW45RdExJHgf7zyOyYZvI118DQ4ZgeRAwoDmw4FYFBC/nLzPrun/rwAl+UTMwlvXgbt0Ctm+3be/mRk/njNEP+YAB/D5y5ACGDgUKFRKr/A3QD5inp3PcUJ2d996jLDlnwfIaOn0aEClvNGIEULKkc9UYDAoigcN164wbk+oUWAa2J4ePD43JzY2+HyVLigXZBwTQrHB6dqKMpkIFIGdO2jaZSHyXt5RbujQV8AXEA8GdkLQWprRnhmntqbVY1GJRqi27BQcFY6l/P212iQFLm3Kczv+uoeAwIHIGEFwvbbMoneRXNR1SvbomdJgclgJu3t5iGWxdupA43KhR4pXbZ82iEh3qj5UkeSyWeoXYsEFsmccebt2yvgE3bsyfEVCzLBWFZjdFaq+VLk0Ol2iiQGrRrh3NSjkLo0fT7GN6Lzv04gV9tkbVED10CPjyS9oeN04rD5QcXl5aHJKeDLk1a+gYnEndHPqz49JSmLL/pv7oVLaT7sDuPpX62L/s9npnLL3zpq5lt+A5oVj6G+BpBpb+BgQ/KWJ7oEWK0DUOwCNXHnrgTUOkI2Uvly9rywDJUa4cFQ8FSFeJp78EkMN1+LDrVW5PDe7dozgvnbUZDeP5c+tSQI8e8dt06EBB4On9Zu+MtGpF10eePBTDlV65fZu0lKZPN2b/33yj/fbt3w989x2/zYABNAvevLm4dECuXDQz6ETYmx2nkhbClPbOMNkd1B0WhuBFf2uO0a5sCK7Q0/ZA+/ZF8HGFZpfu5acMYB6jR5OTPnJkmle3kBLS9tKjx6ulUJJi6lSyS8fT0xkGVbn4wAHSkDFi/6om2alTlB5uS4y0WDG6ef/+u7jUgIcHOYLbt5MKt6uh6pkZgclE501VHk/vGBX+2qePFjxuMonNdObKRQ8NzrK0bEGcOU5IuNHS4en9GyVtJOVMiDpGKnoy5ABgQfMFumKe1Ngsk5tJd/xScFAwcPAget9bAjWEaWmZcbaX3f4rhRR8/Ay6ngI8pn/A/8727g1MnAiP6GgKRRCpblG1Kn8yI5Vwvqs6vTBwoJhdrVq0PJReC606M+HhfLmH1GT8eE1qYPBgyiDiodYYLFBAS0zg0b49sGhR+s4Ss4eVKyneRoRz57RSL2vXUlsRsmZ1zngnPUXM9ZCQoMUiASQ1wBMPrlWL4skA0pgTLcbr4SFW5SAVSW39JZW0EKa0d4Yp+KTJetntBqc0joWIs4e7l1gpJF9fWiYuW1Yss9jJkI6UvUgpgLSnZUtjS8rs26dt79zJt39Z1K9IEX6bmjWBr76iJ3xZY9A2w4eLFc0GSMrAsmKB0YW9jWTaNOMKFj9/bq1QfuiQVo0hOdSM4rJl+ZUR0oC0UvhOD8KUwW90wdKDeawDu5t8Y3uGadgwLaj7fGaxYs32lEKaMIG+3yIrPU6GdKQkzsPq1ZSeL8qpU8aNJTLS2klr2JBfcy44mLK/AIoDESl+qyg0eyWi/yURp1Mn6x/k9Ly0PmeOvhkpNdbu2TN+pYMsWSh+yWQiR75HD7FYztat6aZnYLJAZCRw9664PWPAnNC0U/j2MHmkvjBlyyWJTpEtW23ADMFHzNoM03ZvBL/BqdtZqhQSmjSDRwKQ0LefmKPj6Yn73+1AxGDxUkj2nO/bt51jdU86UhLnoVs3oEYNY/YdEUGlIAAKxOU5YT4+tIykpsOXKMHPosyaVVvylYHgaUuWLFqVgCpVrHWM0ppz58RFQvXy++90vACwaZNYcd2hQ+nf+HinKsbbpQvVSL94Ucx+5JrlGLmrN2Lj00bhe3nYcu5MkYrDhCmvZMPSX2E9w2QrENzLCwlDh6N7mBvCZ7ihW81h2sOfDVYETsVSBGNLieFcW4AcnAIFyN8WRe/53r6d+lBLx6Yl0pGSGMOdO7TWrQZ4iyKSuWYPK1Zo2XrPn9M0Mo8xY7R0eNGac+PGUTkLkdI7GYlr1yijkLcslJoMHkwxPM6mdF26tFamydG8vDwsUrkgIIBKB82Y4TTFeC9dAn77DWBKXOLzjy2Why3HF5d6Q823TyuF7zhzXLKxSCrC+ktMIEMue3YEhyFxhmlhbAuu6Ofmgv0RBw+4JyjYkH+ITVuAVH7G/lQZfbAMU5cX4toD9FMbH096wSKr8Ynnm0HofAPA7Nn07/z5xoUQiiIdKYkxzJsHLFsGHD2a1iMhWre2zhgS0R1R0+Fz5xZPh8+WjeKevLzsGma6ZcECEtj8r+6lw7l9Wytie+iQWBt/fxL8VCVInAmRmDt7aNwYKF6ctk0m8Tpyw4fTQ4CT8MUXAIKWA+N9sPjIcjx+nLzt8rDl6PWb5kSppGSGyV79JTX7LzgoGN80XgrocIyCg4Ix+88AK/2lr4qMsekYncpVD//gDfQMA57MMMGUZQl3rNPm50RnrEVXrMaUJQW4yZ3ffw88fEjbR45Yh9QlRVQUKWQAdAl+/jl3SPjiC+3nefly2DzfAC0oqPJ+ERHAt9/y+zAS6UhJxJg2TV9gqdGVh775RruxtmjBL55aqBDNTgCkwyQiHWAy0ePUhQsZIx1eDwkJWmFhZ6BVK227WjX+r3lG4Z9/tOv8++/53yu1OgJA17hoRl0qIRoIvvHacrCWvQFTLOKb9sYn22wv073sRKmklcI3AFRx74mav3W3imFa0tK2MGXhf5pg0W8KPM3Agt9MqOA30mbfBw4qmI0xUACsS+iKrcfz2bSPjCQnZAPa4Qe8j4sXNScpOSxzbgD+V+/cOW1i2mymKkK8y3b3bu3n5sUL/izWgQOvtk9LpCPlqsTG6rOfNEns0SK1sCzuvHmz2CzFyJEUxzRmjLh0gK9vuswiSTG9ejmXTlW5ctojq7v7qxmSGRXLmdNOncRU9rt0ocQNtSajk6BHauB2ZQvnSGH47N+USQ2khcJ3pfhD2Bu2InHZbXFoNvQKsi1MWfm7EegTxhAxA2icOxg129iOy+zZE6g6pyNa4DcsKTIjUXA+OXx8aLlN5a+/+KGfM2ZoBRTGj+dL8FWqZJ0ku3kzPyri55+17V9/BerWtW3fsyctegCkLMQ7bqORjpQr8vQpZeZs2pTWIyGePKFizSoiOiJqgCxAxXhFlm8qV6ZHpfScwZVarFhBQfnOwogRNEsGkKOQz/aTd6rx6BGNzajUoUaNNO2lTJnoLsXD25s+I4MlWkRnlwA7pQZsLNOlC4XvoCAgVy4EhwFPZrihzxvvcz2KwKalsMO9KTwTgCJz+b9THh5A09ae2IyWCKzhj/z5uU2s8i5EKkzlzk3RCgCtHIuE3VmWJxWp8FOiBEVFANaTz8nh4aGFGVapAqHjNhLpSGUEGOOn5lvy+DEtZH//vXHjUdOueenXAHDzJnD+vPZ+717+XHC3bto3b/Rop1RMdiquXDFu3/HxJI4K0LUluqw7c6Z4vFOZMpochRNllmHOHArw+Ptvvq3ZTNeqisj3b9gwzYHs21e75tMY0dkl1dYZpAZSMsMUHBSMpa9/YJ0dV32m7cBuLy+KPQPgncCEH+D6Zl6D13CRkhIk6QJ593FGrl/Xt/Q2fDiQN69hw9HNzJl0gwHo5seb2ShbluZyVWdo9Gj+XHCmTNRPo0ZAV44Oiqtz7x4thalz4Y7mo4+AhQtpu21bcQd9/HigTh3xftasoeCJsmX1j9Eo9MSRHTpE2XEqI0fync4iRUjJ3s1NPHDcYERnlyxtnUVqAEiBwvfvN60Vvo8InPv+/fECXtiEFloSAIenbjlwGa8J2UqcA+lIOSOFC1MquSirVhk3FoAyplRu3uTbv6yRwwsEBzSpgRw5gM6dxcbVvz+wbRuQObOYvauiSlCIzv7o5eWUez2zg3oeGPLmNd6JYkybAXI01appsV1ubrSELSKpsWYNzfQFBhozrv8QWaoTnV1KyvZlHC41kATJzjBV6ImltytZzzC1XGx7hqlfv0SF754nTED37vzB5syJTHiO1vhV6Ngk6RPpSBlNQgLwv//pb/f7744fiz1ERQHly2vv33iDn5s6aJB2cxWVDmjShJ7QFy4UW4R3ZZ48ITU6o7CUMDhyhG8/YICW1Zg/v76HAGdj0CDjZjjd3LSlPTc3TTCUh5eX4QkPIkt1orNLtmxfxlFSA7pnmKKiELzqH22GaZMbggu1sd1xjRp4VrwiPBKAqFYdSQ1SgNdeUzBxorg474cfAnnyCJsje3b6udWTG/Lee9YlFnk0akR96Am7e+01YOJEcfvUOG6jkI6U0cybR+VFRG5IqUF8vHYTPnaMln1skSmT9Y945syU+WYLf39tVikkREw6QFFo2cMZvhXOTsuW+n4F9RAZaR2BWqsW8OCB7Ta5c2tP56KV252VBQuoyLFRdOtGDyNDhzrNcrzIUp2e+KXUDARXCY4uiaWbTVYaTDYDwX18gD590POkCRGzTQgu2w3IxS/G6/v5FCSUD4LPZHEpmH/+AaZOFTbHqFGkbytK9uw06d+mjXib777T96z+9tvUhx5HyhmP2yikI2U0avEgo0pC6GXFCppBAEjwYwhH2dbyKVpRaNZIRDpg8mRyIvv3T9FwXYIVK+hciHL6tGFDQZYslEKjKPQqVAjImZPfbvJkYOVKoE8f48bmbMydC8yaRdtvvQX88Qe/TebMdIdJBSkRRy3V6Y1fWn1ydaoGggMAbtxA8OF4bYbpcW2uwjdCQqAkJMAz1ky/ayK0bAm348eofJQg3t76q0XpnZTXa28yiSvA2NuHMx63UUhHKr1z4IAm2DdvHj++4803rd+L1Lbr1o1mpby9xW+UgYHkpIlW/nZlevY0rsbgs2dagPP69cCJE7btFYXi1Rijl2hGZIECdJ34+vJtb9+2nuVs0sR4AVcjsIwdBMTiB1MJRy3V2TO7NGDzAHQt1zVVA8HRvj3g758YwxQ8YDF/sIGBNGUydixlhUokdiIdKWciIQGYPl17LzL3GmzxwzJsGD8eq3x5Te3Mx4eEF3lkykTytHv2uKY4ZWrw5Ikx+125kparACqaNWkSv02HDhTrlD27MTUDo6OtExB4S4fOypAhmsZT9uxOkz3qyKU6e2eXPEwe9geCBwVj6T9FrQPBy02wPcPk4ZEoi+HRuKm1Lp0tJk50OuFSSfpDOlLOxMGD1tF5/frxn9TbtdN+zH19NeU0W6hLdf378+OdVMqXFxMDdHUuXQKaNdNmCdOatm216wMA3n+f38bdneLnTp8mJ9rRFCtGcV7qTJdoQWh72LqV4gJFOHNG2xaptFqwoBbTN2yYU6wzGLFUB8Cu2SXAcoYJ+qQG3N/E0t+pVMrS3xUEVxIQ6e3Th5aYna1ItSTDIx0pI9mzR4uhGD4cuHjRtn2VKlptLJOJnnB5N5jBgzWbwYMpxoVHkyYk0KgnEtBVUZe4RFmyhGJlRG7E9vDll5qT1rixVtQqOQICtJu9noy6vHkpacAoRo+mGdgCBehhwAhu3CCJ5Q8/5NtGRlpLPletyi9CBgBTplAdyoED7R6mCPbEO6mkxlKdzWK8rAKW/oqXpAaW2J5hGjkSwccYImcCwSXeo1g9Hn5+dD4ss4wlklRAOlJGsnSpth0WBvz0k217d3frwsC8QHCAbnZdu9LTsGg6tZsbCf1J/SU+Q4Y4zZINAGCxRezH9u3A4cP8NqNG0dLT2LHOk1FXsyY5hatWGTcmVVVfJHYpSxb6TqgPJf7+pGnGo2RJYMIEfsGyFJCSeCcVhy/V6YlfKlECwRd8tEDw+9UQXJETUlC5MlCzJjzMEA8El0jSCOlI2UvbtnxVYzU7DqCbRY8e/P0GB9OSQc+e4pXbly8Hnj9P+4JD6QG1lIko33xDucJG8PixtdpxT9sFTQEklpwAQEtk9erx21SqRH1Z1idMaxSFxiNSIzE1sAyyVxTDyw6J1qlzRLyTisOW6ip/ZD27VHeO7dklHx9g4EAtELzvApv9JrJmDbBzJzlVEokTIx0pe9m9mx8HU62aliXXqZPYUknWrFQiZsmSFA9R8hKPHlGtMqMcI73cvm293HvwIH8ZsUsXLRNS1hh0LO++S0uavr5iqtV2IlqnTiTeKU2W6n44b10qZW8Uv+P/AvM9ar8lLh1QpAjJSkgkTo78FbaXTp3E9HWmTKF4i1HiAm4Sg1Bno7ZsMWb/cXFaXM3du3ynqEwZmpFRnaExY8RqDH7yCZU+d6Ylx4yApycVHz5+3LBlb9E6daIq4vYW703RUl2nTtrs0nGFHFAeAQH0gLhxo9A4JZL0hHSk7GXwYDG7Zs1opsGZCq1mFF68sC5nktZMngwsW0bb770HrF7Nb6PWGMyZk5xzEfr2BTZtMiajzpnZsgVo1UrM9sYNTRpk7Vpg82axdoUK0UyIASQ6R8x2nTo9KuIAuDIDKkku1VXoiaWPa+mrOdekCVCiBDwSALQQL8aL/PlpRlgiyWBIR8peSpZM6xFI3n0XCAoybv9nz2rbp07x7X18rN+LzGo0akRB4IsWUU01SfJ06yZe1+L330n7TMUy8SMNsHKiLPydl50ivfFOos5UsrNMUVEIXvS3tlT3u4Lggq1tH4yiUCZk7tyalIpE4sIojKVHSeG049mzZ/Dz80N4eDh8RVScJeJs2waUKyeedp89O8WpiV7Cly9TJc1OnfhxUpGR9AStCkd6e9Msh616XI8fUzr/ixeUMHDlirWGkyRl6DnfT5/S+Xv+nN7/739A/fqGDCvOHJdYQDcpRJwjBQoWtliIIX8MQaw5VrhvT5MnIsdFJvaflMPGXaobOBBYvBhxJsDj3ffFZlIlknSIUfdvOSMlcR6aNBETFLWHmBitGG1oKDk5tsiShSp0qjFL+fLx0+Fz5NAy70aOlE5UWpItm1bO6I03hLMDFy2iEnqi8ALH9cww9d/UH53KdrIr3kkl+NlrWPKyZpMtJwoAGx6CBHMCPGLNiB8mJjXw5Zf01RApLwhQnoe3N9CaM9llSdeulOwsWnln714ak2VxCFswRgLoBQuKa7bK4xazd8bjNhQm0UV4eDgDwMLDw9N6KM7N06eMTZzIWGyseBtV/lKUbNnE7efP1/YPMNa2Lb/NqlVkqyiMffONWD937jD244+MRUSI2WcUHjxgbOhQxp4/N64PPeebMcYuX2asdm3GNmwQMr91izF3dzrdFy/y7ZcdW8aUKQrDFDBlisKWHVtm9f+x8bHMc5onwxQIvzynebLFRxYn7je5V1L9Mcbo2gPYsiAwzwlgi4fV5R7HH38wNgNj2ZcYzH78kX/ccXGMBQTQqajL3z1jjLHp07Wv0r//8u1v3mTMZKI2Y8eK9dG6NdnnzCl2Gf7xh/ZzII87eTLKcTNm3P1bOlI6kY6UIBMm0FW+a5d4GyMdqfPnrR2pxYv5bWJiGMuThzE/P8YiI8XH5YqMG6f/fOvh6VPt3F25YkgX48fTj7nJxNjgwbZtLZ0oW85NUnYizpGtdsk6UYyxi+fi2HUEsASAvXAD+3km/y729tt0zG5ujFWuzP+cfvrJ+qt0/Lht+xcvGMuVi2xNJsYGDuT38cEH2o01a1b+c8nFi3TTVse0fDm/D3ncrnXcjBl3/5ZLexIxFi8GPv9c3D5OTHDQbn76SdPx6t+flu5sUaIESQYA4sV41XT4sDCx0juuTEKCsftv2VLbfu01qgXoQKKjga+/Jo1dM4vD0qXJ15EWlSYA7M+os1eaYOv/3PE5RkIBsC2hJdYcsp1RFxlJlazMZjqFx44B9+/bbIJNm6zf89REwsI0VRCzGfj1V36Y26+/anrHERHAgQO27bdutd7nb7/ZtpfH7VrHbTgOdctcAJedkdI7WzR2rLEzUiVLWj8mbd3KbxMaSraTJ4uPyVUZP56xQYPE7e0533p45x16hFbXCxw8KxUfT6uACFrGMMGTFW6zjMXEvGonMsOkd2bK1gzTstaFmDIZDJPBlMlgy9Z9YPM4oqMZ+2hUOBuDT1jNbP8ILav8/rv2NVq/nm9/9Spjb7xB9r17M8b7KUxIYGzZMq2PvXv5ffz9t2a/YAHtwxbR0Yx9+CHZ58oltpwkj9u1jpsxubSXJLt27WItWrRg/v7+DAD75ZdfuG127tzJKlasyLy8vFhgYCBbsGCBrj4zhCP17BljpUsztmePeBsjHanISMbq19f6mDiR3+bzz7W53fz5aSGfR0ICfQPj4/m2rk5qOM56OHRIc6Latzeki2XHljFMVshpceAy3SvtJ4s5UYwxxnr3ZssqKsxzAtiyyibG7t3jHselS/RRdeokfuzO9pzEmP6QOHncxo0poxy3XNpLgqioKJQvXx5ff/21kP2VK1fQrFkz1K5dG2FhYRg/fjyGDh2K9evXGzzSVCA6Wtz2wQPSSFogWPPKaM6eBf78U3u/ahV/Lrh3b02QcsQIscK3ikJtXDGbLrl1qrRk5Urg/Hkx2ypVqOQSY4ZoF6nLdQADraZZL9PZW4rFsqZecIWeWOr9jpZRB35GHUaORPAxRiriFXoCefLYfYwSicQY0rUj1bRpU0yfPh3t2rUTsl+4cCEKFSqEuXPnonTp0ujduzeCg4Px2WefGTxSnTx+rC/mZMYM5ypYvGgRMGsWbb/9NvDXX7btK1eml5sbOTsjRvBLpfj6AuPGkWJ8796OGXdG5eFDkmZYtcqY/c+Zo53vt94SVxHv0QOoUUO8n9WrKTiialXdQ7SFVcxTMmKZKSnFksjBgwj+4EdN/HKnHzlHtihVCmjalFTEQ0L0H5xEIjGcdO1I6eXAgQNo1KiR1d8aN26MI0eOIM7o4Gg9FCoE9Osnbv/pp1odOSOwnO2KEihQaqkIbjYD587x26ilUrJk0bSYeEyYAJw8Cfj5idm7Ks+e0b/bthmz/3v3rN/fvSve9vFjcdtixYDGjcXt/8NyVuhl9JRjSUkpFgD0sJAvH9Wpm+VGThTvgQHA069W4/r//gVef51rK5FIUh+XcqTu3r2LvHnzWv0tb968iI+Px0M1zeAlYmJi8OzZM6uXbk6e1GcfFZXmJS0Sef6cnopVihbVbszJMWyYdoPw8wO6d+f307Yt0LEjMHs2kDWr/eN1BZ4/d3jWmhXXrmnbly/z7YcM0ZZLc+QAOnc2Zlx2YEsw055yLHaXYgEADw8SagXgYQYwfLjQMXQemhOFGxQXeh4BaLIWABo0ELMHgNq1qaiAKNWq0b+iRQgAqpjUq5e4vR5bQB63PO40xKERV2kIBILNixcvzmbMmGH1t7179zIA7M6dO0m2mTx5MgMlIFu9hIPVliyhiLgTJ8TsGTM2Si8hgVI1AMaqVuWnYMTFUTC3Oqbs2cXUz9q1I/vx48XGJRGneXPjojIjIugcq+fbx4exR4/47Tp1IvupU8XHpfc614ktwUx7xTJj42Ot960GjicToP4KT59SmlHnzkLHcO6c9jH16SN+7A8fitsyRl9pvVJpevt49Igxs1ncPiFBfx/yuMVw1eOWweYOIF++fLj70rLD/fv34e7ujpw5cybZZty4cQgPD0983bhxQ1+nFy/Sv6rmUVrz3XdA+/a0fegQzSbYwt2dnqIVhWKYhg0j7X8eU6fSch1v/xISZrl1S9x+3z7jxpIlCxWjtZxRFKlJNWUKMHMm1W1zAl6ebXo5eDylMU/BQcH4xjfYKnB8camxtgPHAfo8HzwA1qwR6nfOHG2yb+VKaipCMj9nyeLtrV8qTW8fOXLQT4goiqK/D3ncYrjqcRuFSzlS1atXx44dO6z+tn37dlSuXBkeHkkXHfXy8oKvr6/Vy6k4c0Zz0n76iZ/tVrSo9fsSJfh99OqlZbsNGCA2rjJlKAA5Xz4xe1emeXPjagy+eKEVof3zT/5SnaKQA8wYbY8aJZYRWbw48MEHtos6qzx+bH3dicbECSIqmJnSmKdqP3tpgeO/AVX/p2PdQ5BDhzShwthYsXBDiUSSuqRrRyoyMhLHjx/H8ePHAZC8wfHjx3H9+nUANJvUrVu3RPv+/fvj2rVrGDFiBM6ePYvly5dj2bJlGDVqVFoM/1UYA5ZbxHKIzDy8+671dmiobfvq1YFKlWjby4tUwXn4+ZF07G+/yfRro7CMS3Iky5fTbBFAQeEi13rnzvQ4mTkzEMyZYbGH27eBCxe09wcP8h8ABNETPA7wnSlbMU9bSw5HjzAFkTOAd8J8cLScYx1CAPjlF217xw6KbZFIJM5Funakjhw5gqCgIAQFBQEARowYgaCgIEyaNAkAcOfOnUSnCgACAwOxZcsW7Ny5ExUqVMC0adMwb948tFeXutKaQ4esI+7ee49/g6lfX5v79/YGKla0ba/OOAA0EyA6N1q/PtCkiZitK3PvHmVc6tH1MpKGDa0zw9QyObbw9qbS6gcOiC3r6aVMGZLFUOf9x4wRyl4DUpaBp2LTmbJoyivHEjK/OMIKtIBHAnC1SX90G+T4JInAQCBbNtp2iqBaiUTyCgpjDnoUdBGePXsGPz8/hIeH85f5TpygG8bjx0CjRsC339rWe4qJAQICSPfHZAL69gXmz7fdx5UrVHuMMYpHmjePfxDx8VRDrmRJ51lkziiMGwd88gmwaxdQp45YG9WJEPkq/vAD8P77tN2rFxWI48WstWoF/P47zTLduiUW42Y0W7cCTZvS9XfrFs2OclgethwDNg/AguYLXnFu4sxx8Jnpg1hzrPAQPE2eiBwXSXFPUVFY3jQfer8dCYb/xDIbzENwLdsxfvN6HIP7yqWo+NN4VOsQINy3HrJnp9V7+UstkaQMXfdvHaTrGSmn57PPNJ2c7dvJkbKFl5eWEp2QICbAFxhI0gFubsLp1HB3JyFE6UTx+fhjYOxYcXuj73bqMh0ALFsG7N7Nb6Mu54kmCqQGjRvTTNSiRcJOVO/feiPWHPtKYWAg5cHjyJQJwbfzWohl+iK4Kn/Z+3a+ihiE+YjNY4wTJZFInB/pSNnL4MH8m6alfpKiAJ068ffbvz/dWFq0oABeEdasoXSelwPJJa+iV3h1wgTStjKCyEhSAlcZP57fpn9/bQarQAGa8eRRuzZFKk+YYN84jUBRKBlBYFmdl4GnkqLgcTc3YPRoBB9XEDkTCG4xkXSfJBKJhIN0pOxlzRpagrNF/fqaGnHbtjR7xCNnThJc/PVX8bFkykTLNhLbPH1KWWVbtqT1SIjz561nlL7/nu+c9+pFQeAAyVKI1hj08NCXi+wkiGbgqSQX76RiM+6pa1fA1xcenpmcquzQxx8DRYqk9SgkEklypL9fVmehXTvS27GFogATJwKFC+srtKoowsG3Eh08fkyq7N99Z8z+GdNy1dV/bVGpEhXjVWsMqnpdtsiaFfjwQyAoSL8UcDpDbwaeSqIzpegLHkfmzMDOneTcqhHeHLp2pURYPdVbHj0Sq7SkMnCgdZKjRCJxLmSwuU4Sg9VCQ+Fbt25aD8e1MZuBmzfJURXh8mUKzO/USdyZ0hMI/sknFGyu8ssvQJs2ttusXw906EAO0u3bgI+P2LgyOKIZeEAyDtLDh5g/sikGBx6h4HEFWNpqGV8w02Du3KFSmm+9Bfzvf2k6FInE5ZDB5s4GT2ZAYjx9+hi75mGpgn/7Nt8+IsL6vUgh6TZtgC5dKDFBOlEAKANvwOYBQk4UQDNTAzYPsJZG+P57DFx1RAsev1YhzZ0ogJIs4+NJG/XUqbQejUQicQTSkZI4D0eOiDkfKpZqhY4mKsq6qufrrwNPnthuM2iQFrOUKxcVYeZhMpHyeN++9o81g5HiDDwAeO89MHcPBIcBkTOA4DZTDRqtOFFR5EgBdNrnzEnb8UgkEscgHSmJ8/Dmm2JZaPZgNmtrKWFhwP37tu0zZaLlNsv3vBmj/Pm1zMyQEKG0flcnOYHNlJZvQZ48iGxPVQ2e+QRSFqwAGzcC69YJmerm7FkK0QPocgwNNUYtIyyMwje/+UbMnjGgbl2gcmVSXRFh5UrqY88eMfuICFrS1PO8MGIE4O8vXl9QHreYvaset6E4tASyC2BU9egMx4sXjC1cSCW9RVHL3IuSLZu4/dKl2v4Bxt59l99mwQLGFIVes2eL9XPpEmNffEGlz12JyEjGZs1iLD5euMmyY8uY5zRPtuzYMps2yhSFYQpeeSlTFJtt2enTLCLfayxuybdC43n0iDEvL8ZMJsZu3hQ+DF38+qt2CZ44YUwfnTvT/gsUYCwujm+/Z482pi1b+PYJCYwVL072LVuKjWnuXLI3mRi7cYNv/+ABnQuAsY8+EutDHrc8bh5G3b+lI6UT6UgJ8tFHdJXv3SvexkhH6tgxa0dqzhx+m6goxvz8GMuUibEnT8TH5YpMmkSf6+7dQuaWDhLPIUq0nazDibKDjz9mzM2Nfvw/+MChu7ZC72Wuh5s3afxqH+vW8du0akVtTCbG6tbl22/Zou1fURj791/b9nFxjAUEaDfWMWP4fUybRucCYCxHDsaeP7dtL49bHrcIRt2/5dKeRIxff9UnG6Dmd4vIANjDn3+SLhQAfPQRv5+gIK1kS5YsYtIBmTPT+suuXcLp8C5LTAz9K7BWJSqwqRIcFIyll8vQIh8DFAYsrfyRQ4PHY2KAL76gpQ6zmZYLIiMdtvtUY8MG668C7ysbGQls3kxtzGZSf+Cteq9dq20zBvz4o237v/+m5FqA+li9mn+ZrF6tLTs9fkxfQVvI4ybkcacRDnXLXACXnZHS+xg9dizZ79plTB8lSljPMG3dym+zaRPZjhghPiZX5auvGJs+Xdxe8HzbvVTXtClbGgTmOQFsWRAYO3NGx8HwiYnRli8AxgoWpNVKIzByRurpU8b69KH9u7szdvQov82yZdqY5s/n258+zZi/P9m3bs3YvXu27c1mmnFQ+/jtN34f27Zp9pMm8Zdu5HHL4xZBLu05CRnCkYqOZqxJE8ZOnRJvY6QjFRPDWI8eWh8LFvDbfPSRvrlgxugbfvGicXfIjIQB59uWE8VzpqJ+/5MxgL1wA7tSqrE9R8QlIUE7bD2hfXox0pFijML0AMY6dTJuTEY/JzGmb+WeMXnc8rj5GHX/FqgvkTwvXrzAyZMncf/+fSS8FP7fqlWrlOxaopeEBPESIHfuAFu3UlmZNJ8TBXDsGLBihfZ+2jSgXz/bKt/9+wPTp1MNOdFivG5uJMjpisTGAp6eada9qMCmuswHwGrpbsnFengbZVA24R988HA01sSLVcfRg+XlZmRhgcKFxcpuSiSS9IHdP0Vbt25Ft27d8DCJenOKosBsVGyMKxATQzc90V/z5cuBzz8HTp82dlyi/PgjFaQFqJTO1q2Ua5scVasCpUsD587RMQ8ezD/23LnJmfrhB2DAAMeNPSPy9CkVOP7hB6BlS8fvf8UK7Xw3bgzs2AHUqpX43/YKbHYt1zVRG2rBQgWrsALlcALrHr6N4L+ARo0cfSCpw9mzYn6/RCJJH9gdbD548GC88847uHPnDhISEqxe0olKIWXKAJMni9uPHAmcOWPcePTy55/a9qNH/MhBRQHGjKGZYA8Pmo0S4csvgXv3+DUPXZ3Hj4HoaHKkjODIEW37xQuaYbTAEQKbkyYBx1AJKxCMnj2VxLyB9EimTPpmvOLi6PRJJBLnxG5H6v79+xgxYgTy5s3ryPFkTETKi1hy8SItbzkDcXFA2bLa+2LFgOfPbbcZNkzbzpRJLEPu/fcpq+7DD2nJUZI88fFUN9AoLNXl1cxIWwwbpnkGPj5Az56vmKRUYLNTJy1xcvly55nRiYykUi9xSeuKOoSuXUkb9to1MfvMmelfW5PAL1OsmL7nkTfeoH9z5hRvA+ibENUbHSKPW7yNqx63YdgbXNWzZ0+2dOlSR8ZrpQt0B6utW0cRcefOiXdidJTe3r1k37gxCWfa4vlzCuZWx5QlC2Mix96oEdkPHSo+LokYXbsaF5UZHc1Y/vza+c6Zk1JkeLRsSfajR9s0S4nApt7L3B5++IG0W0WZMIHGtGqVMeO5dk3LqQgJEW934YK+gPknTxi7f1/f2C5c0Gd/9SrllYgSH8/Y5cv6xySPm4+rHrdRweYKYwLCL0kQHR2Nd955B7lz50bZsmXh4eFh9f9Dhw51gJvnfOiuHv3BBxQ/smsXhNcj1Kd70VOTPTvNHIjYb9wItG2rvR8wAJg/33abjz4Cpk6lcQ0fTgV2eRw8SIXFpk83trBwRuDQIaBECTqPIug53wDNXr32Gk3r8JILzGYgMBC4cYPe58wJ3LrFL3cTFgYsWwaMG0fxWDZIDDxnDOoEVbKlXizQe9hGEx1NVYHCw+mJ/dQpxwepjxxJK9hmMz2B37kDOLBovUTiUui+fwtid7D52rVrsW3bNmTKlAk7d+6EYvELoihKhnWknI6bN7Xll337gJo1bdtnyWL9XkRocsAA4OOPaUnJctnOFtWq0UvCp1o1oHx54Phxx+87Pp6C/QGKZbp7F8iXL3l7k4nu3iEhmuMsUjMwKEiryMshuMR7wNlZ6F3qX6i+1NLWtp0oZ2TVKm0V9PRp0m51dKnIrVs14cHoaODwYaB+fcf2IZFIUobdMVITJkzARx99hPDwcFy9ehVXrlxJfF02Mn4jo/PHH9q2SBZe69badq1a5EzZokEDoFQp2nZ3pww5HrlzU9XKZcuAggX59hL9nDhhzH5XrAAGDaLtf/8FRB5wgoPJ4fbwMCYj8tw5BK/7F0t/AzzNwNJ9ORFc4dW4qpepXt3xQ0kJJ09av//nH8f3YakqvWqVcTW9JRKJ/djtSMXGxuK9996Dm6h2kYTP0aNAs2ba++bN+esYQUGafpSHB0UR2kLNkAMowDt/frGxdewI9OghZuvKPHtGS6Hx8Wk9EuLNN63f82YsAYps/uMPeumNLhWhUiXgzTcRfMINkTOB4FaThdbE1q+nGRlR7t+nuHfRivV6mTkTaNKEtj/5xBifs3x5bdK4a1dj9a0kEol92O0Fde/eHevWrXPkWDIeFy8CP/9M24sXA0+e2LYvVUoLgDCZgLfe4v9yjhihFSnq2hUQyaLs1An46Sdgxgy+rUQfn35K0hX79xuz/+3btaXcSZP4Dlv58kDdurTt40OzTSLUqgXUq2fvKLnEjRwLJCQgwT1rkll+SZEpk74MnW++oQm5cePsGyMPPz/6eAGaLXspTFQikbgIdsdImc1mzJ49G9u2bUO5cuVeCTafM2dOigeX7vnoI+DSJdr+7jvg9deB8eOTt8+SBRg4kB5vzWZykni8/jopE27fLmYPUMxLhw5itq7OsmVARATFColgZB48AAwZom1Pm0YzTI0b224zejRVJx0wgGabnIAfY9qAoTMOmmtjerwPsjl4/8+fA/Pm0fa+fRQe5hRp0hKJJMNh94zUqVOnEBQUBDc3N/zzzz8ICwtLfB03ImjW2Zg5k2/Tvr31e8t4puQYMoRil+rV0x53eaxZQ4KcqtiHxHH07k2B10YQGwt066a9/+YbfpuuXbWl3Jw5tdkmWzRpAly9SpmXTgBjwCefmtBNWYMFCf2weLHj+1i71loCSz7XSSQSo7B7Rio0NNSR40h/fPIJ3WDz5EnepkULSv2/ehVo2FDM0cmfnzLxMmUSH0vu3FLdW4TISMqQW7wYqFEjrUdDCuCrV2vvZ86kGUlby7kDBpCkREyMeEadmxsVeHMS/v5bC8xmjGaORo92bPxP1apAoULA9ev0XsTfdFaGDAFmz07rUUgkkuSQkeL20rixbScKoDinsWNJhlkN8BYhb14pFmME9+9TJqTIzE9qULUqLc0qCjk7IjUGc+akLDx/f6o1mA6pUAF47z3t/ahRjg+iLlOG5AgACgns29ex+1dp04aefXg5Hilh6lS6dCUSiXOSIkdqz5496NKlC6pXr45bt24BAFavXo29e/c6ZHBOjahOVv/+FLDRoIGx43FFGOMH8KcmS5ZoxXvffpvikmyhKORoM0ZFqkVrDH7+OZUdypUrRcNNK7y8rMv+iYafOSPVqpF2qWjy6+PHFPPfrp14H4oin6skEmfGbkdq/fr1aNy4MTJlyoSwsDDExMQAACIiIjDDFbLBRNLIJcYybpyxdfksawry6gsCJG2tYjaL6YB17EhO18SJ4srmEqdCjwLMokVAVBQVGFDzUCQSSfrGbkdq+vTpWLhwIZYsWWKVsVejRg0ce6n6e4ZECro4nosXgRcvxO0XLTJuLC9eaMKlAJVNiYiw3Wb4cO268PUV093y9AT+/NN2NqckQxAbC3zxBW27uQFz56bpcCQSiYOw25E6f/486iRRO87X1xdPRSrGSyQvU7y4/hLgojCmzRhduULCmbYwmaylDGJiKJvSFkWLUtAMQHFML5fjkaQJepbF9u7VYqsczbFjwIMHtG02A7/8YkzdwPPngbJl+WUVLenUib56ouPZuJH6EH1mfvECqFIFmDBBfEwzZpDeMO+rqiKPW7wPVz1uw7C32nHRokXZjh07GGOM+fj4sEuXLjHGGFu5ciUrXbq0A+opOydGVY/OcMTHM/brr/ra0Pda3D5bNnH7NWu0/QOMde/Ob/Ppp4wpCmNuboxNmiTWz8mTjI0cydjt22L2GYXYWMZWr9ZVih1grEwZ44aUkMDY/PmMRUSI2T97xpiPD2NeXow9fGjMeBYt0i7BXbsc3wdjjPXrR/svVowxs5lvf+yYvjElJDBWoQLZd+woNqYlS8je05Ox+/f59uHhjGXJQm3mzBHrQx63PG5+P8bcv+12pGbNmsVef/11dvDgQZY1a1a2Z88etmbNGpY7d2721VdfOXKMToV0pAT59FO6yg8dEm9jpCO1d6+1IzVtGr/N06eMZc7MmIcHY/fuiY/LFfn4Y/pc9+0TbrJvH2OPHhk4Jp3Mnav5zSKXh73ovcz18OAB3bzUPjZv5rfp3Jkxk4leLVvy7Xfv1vZvMjF2/bpt+4QExooX1z7bjz7i9/HFF2QPMFagAGNxcbbt5XHL4xbB6RwpxhgbP348y5QpE1MUhSmKwry9vdmECRMcNTanxGUdqT17GPtvBlKIsWP1P3brucMcOaLZL17MnwlJSGCsYkWy9/Kib6II27cztmmTmK0rY8/5diLi4xkLCNAuqZw5GXvxwpi+jHSkvvrK+nmhVSvb9hERjLm7a/aKwn9m6NrVuo+PP7Ztv3+/tX3+/Pyva8mS1m22brVtL49bHrcITudIXbt2jZnNZhYVFcUOHz7MDh06xCIiIlhCQgK7du2aI8foVLisI6X3199oR6p0aetvkoiT98MPZNuvn/iYXJV16xhbtkzcPhUcqSVL6Ak6Otrx+46Oph98S0fq6VPH98OYsY7U3buMtW6t9REaym8zY4ZmL7KCffAgY97eZF+zJmNXr9q2j4tjbOBArY/ly/l9qF9VgLHevRl7/ty2vTxuedwiOJ0j5ebmxu4l4co+fPiQubm5pWhQzkyGcKRiYhjr25cxPQ6vkY6U2czY+PFaHz//zG8zZgzNMwMU2PLsGb9NXBzNrBkRAJPRSA3HWQfPnzOWPbs2AWkET55oh/34sTF9MGasI8UYY5cu0f47dTJuTEY/JzGmb+WeMXnc8rj5GHX/tjtrjzGW5N8jIyPh7e1t7251M3/+fAQGBsLb2xuVKlXCnj17krXduXMnFEV55XXu3LlUG69TcPMmlUnRk1JhJAcPUsqGypAh9B20hWXxXtFivO7uQK1apA4uSVesWaNpr376KZCQ4Pg+smXTto2U9PL0BLp3N27/EokkddFda2/EiBEAAEVRMGnSJGTOnDnx/8xmMw4dOoQKFSo4bIC2WLduHYYPH4758+ejZs2aWLRoEZo2bYozZ86gUKFCybY7f/48fC1yonM7W506xvTpVP3+O7BgAbBli75+zGZ99qL873+awnf//sCGDdaaTC9TtSrVgrt2jWQHevbkH39AANUZWbfO2qmSvEpEBPDmm6S8Xru24/f/66/a+e7cGdi0SbzgtiCWmksXLpBEQf36Du0i1bh1y1gdWYlEkrronpEKCwtDWFgYGGM4depU4vuwsDCcO3cO5cuXx4oVKwwY6qvMmTMHvXr1Qu/evVG6dGnMnTsXBQsWxIIFC2y2y5MnD/Lly5f4MplMqTJeYd56C5g/X9y+Z0/gjz+MG49eLIU9zp4lERJbmExUtRYgB2rwYLF+Vq8mwZKCBe0apsvw4AGJrixcaMz+N23Stm/eBLZvd3gXvXpp2w0akF+YXsmVS58aukQicW50f51DQ0MRGhqK7t27448//kh8Hxoaim3btmHRokUoXry4EWO1IjY2FkePHkWjRo2s/t6oUSPs37/fZtugoCD4+/ujfv36COWo78XExODZs2dWL91ERuqz37OHBB1FMWpmCaA1FMvPuHZtID7edhvLsXt4AMHB/H569CBBzv79qSCvCG5ufJHMjAhjwKNHxu4/qe3ksJwR9Pa29nocREiItvS2Y4fz1J6Li6NTYcRSo8qAAXTs9+6J2Xt50b96foZ9fPSNSX12EVlRt6RaNXFbvVW45HGLt3HV4zYMe4OroqOjWVRUVOL7q1evsi+++IJt27bNAaFbfG7dusUAsH0v6dZ8/PHHrESJEkm2OXfuHFu8eDE7evQo279/PxswYABTFIXtshFBN3nyZAbglZdwsNqWLRQRd/my8LEZHqV37hzZv/suPy81MpKCudUxeXmJif/UrEn2vXqJj0sixsiRxkVlxsSQCIx6vgsWpGuAR716ZD9ggPi4dKL3MreHr75ibPp0cfuZM2lM69cbM567d0nGDGBs4kTxdvv3i4sUMsbYzZuMXbkibp+QoEsyjDHG2IkTYjkhKtHRjB09qq8PedxiuOpxO13WXsOGDdmCBQsYY4w9efKE5cmThwUEBDBvb282f/58hw0wOVRHav/+/VZ/nz59OitZsqTwflq0aMFa2lAle/HiBQsPD0983bhxQ9+JcLZ0hx07rGUDxozht1Ez5Ewmxvr3F++nXj3GzpwRs3dlzp/Xl9NvZHrLixeM5cqlXR9Zs4pJg+/ezVibNoxduCA+Lp2khiOlh5gYxvLkoTFVq2ZMH5MmkaghwJifnzHSDxKJq+B0WXvHjh1D7f8CV3/++Wfky5cP165dw6pVqzBv3rwUzpPxyZUrF0wmE+7evWv19/v37yNv3rzC+6lWrRouXLiQ7P97eXnB19fX6uVUPH1KL0CsnPzLhXejo/lt1KWbhARaYxGhQQPgr7+A0qXF7F2ZkiWBFi2M2TdjQFgYbV+8CISH27b38qJz7OZGsWuDBomtA9SuTcXjihVL+ZjTCevWAffv0/bBg8ChQ8b0oS4bhocDu3c7vg+JRJIy7HakoqOjkfW/BdPt27ejXbt2cHNzQ7Vq1XDt2jWHDTA5PD09UalSJezYscPq7zt27ECNGjWE9xMWFgZ/0Zic1EC96QEUuMvD8gZcvDhw9Kht+1atKEMOoMBuEccoIAD4/HNg5kygRAm+vUQ/f/1lzH6/+w7o0IG2//4bGDqU36ZfP4ptA8QD/1OB119P6xFYs3On9ftduxzfx+LF2vYnnwANGzq+D4lEkjLsdqSKFSuGjRs34saNG9i2bVti0Pf9+/dTbdZmxIgRWLp0KZYvX46zZ88iJCQE169fR//+/QEA48aNQ7du3RLt586di40bN+LChQs4ffo0xo0bh/Xr12Ows9wsTp4EKlXS3jdowA/2DQjQUoAUhVKCbGEyAaNG0Xbr1kDRomJjGzYMGDtWzNaViYkhmQGRIO3U4LXXrN+XLMlvkzMn8P33JN5UoIAx47KDTZv0Jac+fQpMnAgcP27MeGbMIOUOgL5SRvyM1KmjBdmPHSuz/SQSp8TeNcGffvqJeXh4MDc3N9awYcPEv8+YMYM1adLEIeuOInzzzTescOHCzNPTk1WsWNEqcLx79+7srbfeSnw/a9Ys9tprrzFvb2+WPXt2VqtWLbZZtNrhf+haY719m7HKlSnAYfhwftDu48eaFr+bG2Nt2/L7OHyY7BWFgsdFiIigCq3nzonZS8SZNo3Ox9694m30xMQdOqTZz5/PTxZgTLsGvbycRtU9Pp6xnj31VaHRy+zZdNiNGxvXR2qUGHS22DCJJL3idMHmjDF2584dduzYMWa2CJs/dOgQO3v2bIoH5qzoOhE9e1oHdn/yCb/N4MGa/UuB9MlSowbZHzokZi8R57ffqBCUKEYnF5QqZX1Nbd/Ob/Pjj4Zn1OllwwYakq+vWFKgXmJjGcuXT/uYjMp5kI6URJJ+cLpg8x49euDff/9FUFAQ3Czmm6tUqYJStlSsMwrLl/NtXpZefvttfpuQEFqie/NNoHp1sbGsXg38+SdQpYqYvUScVq2Ajh2N2bfZbL1cum4dv02bNrQ8C5Coi8g10rYtcOAAMH26XcM0gk8/pWWqiAhg5UrH7//nnwHLPJTPP3d8HxKJRAKkIEYqIiICjRo1QvHixTFjxgzcunXLkeNyfkJCtJSd5Hj3XSBfPtquUUNMjrloUeDECcqAEqVoUTEnzdV5/pyC88+cSeuREIcOAbNna+9DQvixVZaBOAMHimXUubuTMp6T1CU5doz8uoQEOtzPP3d8SFmRIoBF9SrhUEBn5N1303oEEonEFnY7UuvXr8etW7cwePBg/PTTTyhSpAiaNm2Kn376CXFxcY4co3NSsyaQJ49tGw8P4L/ahBgzRnzfZcs6VZBvhuHOHWDzZuDjj9N6JES1anTHB2h6plcvfo3BAgWA99+nWSlnSZLQSfHi9Fyh0q6dvtKSIlSvDpw6RdudOgHjxzt2/yrq84uN0p4pZsECsQReiUSSNqQoByRnzpwYNmwYwsLC8Pfff6NYsWLo1q0b8ufPj5CQEJv6TOme4cPF7EJCSACmZUtDh+OyxMSk9Qg01q/Xivd26MCXonBz02oMurmJlwVavZrK9AQE2D/WNCRrVmD3bjOAnQC+R/PmO2E2ssyRgTRqBERFaf4wj8hIIDCQyr6I4uYmn6skEmfGIcm0d+7cwfbt27F9+3aYTCY0a9YMp0+fxuuvv44vvvjCEV04Hw0aiNm5u1NhMJm37Hi++ILuSs7Ctm3a9oMHrwoNJUWPHiRaOniwtgycwdmwYQOKFCkCoB6ATqhXrx6KFCmCDRs2pPHI7MNyCZHH8uXA1aukkOFq0RASSUbF7rt7XFwc1q9fjxYtWqBw4cL46aefEBISgjt37mDlypXYvn07Vq9ejY8++siR43UepGPkeO7f11eA+aOPaLnOCOLigPLltfclSwIvXthuM2yYtu3tLVasOXNmitnKqA8cL7FhwwZ06NABN19aq7p16xY6dOiQbp0pEcxm4LPPtPdff512Y5FIJI7Dbm/A398fffr0QeHChfH333/jyJEj6N+/f6LaOQA0btwY2VQ1OYmER968QPfuxu1fTeN6/Ji/JGg2AzduaO9v3QJiY223eeMNTXq6Tx8ge3b7x5oBMZvNGDZsGFgSkeXq34YPH+7wZT61SrwIZ88C//zj0O4TOXRIu6TMZspWNEK39fp1WnLctEm8zYgRJGgvyl9/UR/nzonZx8WR/q+e54XFi4HmzSlHRAR53OJ9uOpxG4a9ugmrVq1iz58/d5wQQzrBKB2KDEdCAmN//62vjZHFmjdutNZfEtFUmjKFhFFNJsZGjBDrZ/9+xt5/n7HLl8XsMwpmM2P/+59Nk9DQUAaA+woNDXXIkOLjGZswgbF798Tsnz9nLEcOxrJk0Ve1XhSzmbHJk7VL8JdfHN8HY3SpAoyVKyem13r2rDamI0fE+qhVi+x79xazX7uW7DNnZuzpU759dLT29V60SKwPedzyuHk4pSCnKyIdKUEWLKCrPCxMvI2RjtTWrdaO1Nix/Db37jHm4UHO1LVr4uNyRb74gj7Xw4eTNVm7dq2QI7V27drUG7cFS5dqRQK++MK4fvRe5noIDydHUO1j505+m7596VnB3Z2xjh359keOaPv38GDs/n3b9gkJjFWoQJ+rojD2+ef8PhYv1vooVoycUFvI45bHLYLTOVLR0dEsKioq8f3Vq1fZF198wbZt2+aQgTkrLutInTol/vjCmPEK3xcuaPabNvHtExIYK1mS7E0mxm7eFOtnzRq6w0psI3C+U3tGSg8JCYyVKEE//ABjBQowFhdnTF9GOlLz51s/L7RrZ9s+IoIxT0/N3s2Nf6PUW7DBsqoRwFjBgvwZhNdft27DmeyUxy2PWwinUzZv3bo1Vq1aBQB4+vQpqlatis8//xytW7fGggUL7N2txFkpWxaoXDmtR6HRvr223aIFsGuXbXtF0bS8OnYUzyfv3Jn0nVyN0FBgyxaH7rJ27doICAiAkoxolKIoKFiwIGrXrp3k/2/YQLIBRsjURUdToqUasxQeDjx75vh+jKZpU+sCB50727bPkoXC+VS6d+fXPbcUCC1WjK/sUrastc2AAXzdMMv4ncaN+UUb5HET8rjTCHs9sJw5c7J//vmHMcbYkiVLWLly5ZjZbGY//vgjK1WqlMM8PWcjQ8xIxccz9tFH+grY6n2M1jMjlZDA2FdfaX38+Se/zcCBNLMEUDHeR4/4bZ4/p7p516/zbV0dg873+vXrmaIoTFEUq1ko9W/r169Psl1sLGP+/tSFUSt/V69qh33pkjF9MGbsjBRjNHaAsU6djBuT0RPOjOmvMSiP27gxZZTjdroZqejo6MQMve3bt6Ndu3Zwc3NDtWrVcO3aNUf4eBKjuHYNmDRJn9q6kRw8CAwZor3v2lWbGkiOkBCqMQKQzIBI+RNvb+C994CCBe0fqyRFtGvXDj///DMKvDQjGBAQgJ9//hnt2rVLst369aR0oShUVYd3edhD4cLattElZZo2NXb/Eokk9bDbkSpWrBg2btyIGzduYNu2bWjUqBEA4P79+/D19XXYACUC7NsH9O+vvx1PF8lejhzRRHImTrSWEUiKSpVI+gCg0icdOvDngtU5ZkUhp0qSPNHRQJMmWs0UR7N3L1UhBiiv+tIlm+bt2rXD1atXERoairVr1yI0NBRXrlxJ1okCNP0lxoDjx+mST69cvqyvlKZEInFu7HakJk2ahFGjRqFIkSKoWrUqqv9XhX779u0ICgpy2ABdki5d6BFclA4dgEWLjBuPXubNo7oZALB7N/BfLF2yeHpqzlBCgnj5nTVrqAhZ8eJ2D9UluHuXVNc/+cSY/S9Zos0OHj0KrFvHbWIymVC3bl28//77qFu3Lkwmk037+vW17dKlgRIlUjLgtCUwUJ+2lUQicW7sdqQ6dOiA69ev48iRI9i6dWvi3+vXr59xy8LYi16Bwe++I+dIFKNmlgCaArBU6O7USbtpJoelvZsbLdXx6NuXSul06CBe9iVrViB/fjHbjIaR51wvlrOh7u5U9sbBzJhhRpYsOwF8j/nzdyJnzvRZm88eJk0iYf0nT8TsVZ/UyIpD6kq6XoewZElx2zfe0Ldvedz62unBVY9bGIdGXLkAuoPV9u5lLFcu8XR7xpwrSi8igoK51TGZTGJCIuXKkf1774mPSyLG7NmM5c4tbq/nfMfHM1a7tna+K1dmLCaG3+7NN8m+WzfxcQmyfv16FhAQYBWcHhAQkGxgekoYN47yGET5+mvS4zFK9eXJE8YyZaKPdtYs8XYbN4qdNpVz5xg7cULcPj6esfXrxYUQGWMsNFRcHJUxOvbt28XtGZPHLYqrHrfT6Ui5KrpPhLOlOxw6xJivr9bH7Nn8NgMGaApuXbqI9fPzz6TbZEOgUfIfd+7oEy0y0nGOirK+Pry9GXv8mN9u82bGqlTR9+ssgJrlZ+lEQSDLLzWIj2esUCH6mOrXN6aP2bNJ6wdgLG9efTcNiURijdNl7UmchNhYrTiRiPDNv/9a2509y28zYgQt58XHA6NGiY2rfXsqzORM2lPOir8/xcUZAWNUJxAAHj7k1xjMnBkYPJjmzU0moHdvsZqBzZpRMbly5VI+5v9Iq9p8ovz6K9X7AoA//zQmln/pUm0l/d49qnkmkUicC+lIORs3b2rbT5/y7Vu31m6OOXMCZ87Ytn/3XSBPHu39iBH8PooVA8aOBYYOBcqX59tL9CMQoG0XGzcCderQ9vbtYoH8gwZRNqSewH8D2LNnD25afh9egjGGGzduYM+ePak4Ko1ff7V+//vvju9j9mxte9gw4O23Hd+HRCJJGdKRcibOn7cOtK5Xjy+Y4+amSQXEx9N7W1hmyDVoAJQpIza2mTOBL78Us3VlEhKAzZvTehQaPj7W70Vml/LnJ/mKOXOA114zZlwC3LlzJ0V2UVHAggXAhQuOHJXGlCla9mD37sDAgY7vo3VrIFs22p47l76+EonEuUiRI7Vnzx506dIF1atXx63/lg9Wr16NvXv3OmRw6Z6nT4Fjx2h7715ahrOFn5+2rShA7tx8PaXRo8nZUhRaXilVij+ufv2onVHp8K7MF19QyZq//zZm/+fPazOVL0+JJEWDBqQXAFBG3eDBYv3065ems1EA4O/vnyK7lSvJuRk3zpGj0ggMBNq2pe3gYM3hkUgkroXdjtT69evRuHFjZMqUCWFhYYj5b3kpIiICM2bMcNgA0zXjxgE7dtD2hx8C8+fbts+Xj2JlFIWco9Gj+X289RbFpTAmHr+UPTutGVSqJGbvyuzfTwEwojx4QP8aJU9gKYvRpg3VxLOFZY3B999PV3IRKanNl5CgaYRu2ABcuWLkSCUSiStjtyM1ffp0LFy4EEuWLIGHh0fi32vUqIFj6ixMRmbTJr7Ny8KkFSrw24wcSU7R66/TbAIPRaFH71WrgLp1+fYSfdSsKXYe7IEx6+XS//2P36ZuXU1AxdtbLGbt/feBn38G0tkDjslkwpf/fT4vO1Pq+7lz5yYp5rlpE3D1Km2//DFLJBKJI7HbkTp//jzqqEGsFvj6+uKpSJB0eqdLF+D+fds2Xbtq8/1ly9LsEY8yZUiF+qef+Mt6KhUqUF+i9q5KbCwFUvNK1qQWBw9aL591786PiRs+XEvj6tVLrMaglxdlUQYE2DvSNMPe2nze3tbvOcLpTo2lqrtEInE+7Hak/P39cfHixVf+vnfvXhQ1uuKnM1C+PMUw2SJTJsp0AyjrTdTRadSIZqQkjuXmTVpe/fDDtB4JUbmyJstrMlFGJe8aee01ikBWlDSPYUotEmvzZc+OtYBQbb5GjYATJ8wAdqJKle/RrNlOQ2QS3nyT/jVSXXntWuCff4zbv0QiSSH2ClDNmjWLvf766+zgwYMsa9asbM+ePWzNmjUsd+7c7KuvvnKY0JWzkSjo9e23Yg2iohg7e1af4KJEHD1Su3qEKVX0iKP++adm//rrJB/MY/ZsslcUxq5cEesnMpKxu3fFbJ2Z+Hh99jqESNevX8/y5UsdNXQ9p+L5c8aqV2ds0iSHD0MikXBwOkHOMWPGoE2bNqhXrx4iIyNRp04d9O7dG/369cNg0cyg9EyrVmJ2mTNTJp27u7HjcUXWrgWqVk3rUWhYFmc+cwb45Rd+mz59aHmuY0egSBGxfrJkAfLmtWuITsWbb2oR4Q5kw4YN6NChA+7etdagunXrFjp06IANGzY4tD89p2LtWuDAAWDWLODRI4cOQyKRpBEKY7ygDNtER0fjzJkzSEhIwOuvvw6fl3VrMhjPnj2Dn58fwsPD4evrm9bDyVhERZHjKboEmiMHVXIVvYQvX6alsU6dqDC0LRISgObNAbUgd926lIFpyyH++2/NsXN3p6XEjODwGIV6nkXPX/bsJP1gw95sNqNIkSLJCnkqioKAgABcuXIlySB1I2GMlCj+/ZcOfepUYMKEVB2CROLSGHX/TpGO1J9//pmYvbdw4UIMHToUwcHBCA4OdtT4JK5EyZJaqr4Iep8B1CDthAR+2+fPSftL5cABfgmeKlWA6tVpu2tX6UQ5EsFSSClVQ793DxDUAdXNwYMkA8YYXYILFui/hEW4fx/o2RPQI/j+6afk2Ily+DD1ce2amH1CAuV5rFkj3sfPPwN9+wJxcWL28rjF+3DV4zYMe9cEp0yZwtzc3FiVKlVY69atWZs2baxeGRWj1lgzJKIxPypGFmu2jF8CGPvgA36bUaOoWLPJxFi/fmL9bNvGWJ06jP3zj5h9RuLUKX32es53kyaavbs7Y6dPJ2m2du3aVwocJ/Vau3btK23j4hjLn5+x7NkZi47WdygixMYy1revdhhLlji+D8Yo/gpgrGZNMftr17TCyGfOiLVp2pTshw8Xs//tN7LPlk3ss42NZSxfPmqzZo1YH/K4xexd9bgZM+7+bbcjlS9fPrZq1SpHjiVdIB0pQdasoas8mRtekhjpSK1fb+1IDRrEb3P9OjlRgFjguCuzdCl9TidPirfRc76bNaOAfLXN2bNJmoWGhgo5UqGhoa+0/eEH450cxvRf5nqIjta+FgBjhw/z24SEaM8LvXvz7c+c0fafOTNjT5/y29Sqpd28Fy7k23/3nZaDUa4cP6dEHrc8bhGczpHKkSMHu3jxoiPHki5wWUfq2jXGLlwQtx87lq7wXbvE2+i5w9y5o9kfOcK3j49nrFAh7dsqeu3OmcPYxx+L2boyes/3nj3a+RM5F6Gh2rlr1ixZs/j4eBYQEMAURUnSgVIUhRUsWJDFv5QxmJDAWFAQ7V5RGCtenDGzWexQ9GKkI6X6s+rr/fdt20dE0M1RtffwYOzhQ9tt+vWz7mPOHNv2YWHW9sWK8W+UQUHWbXbvtm0vj1setwhOl7XXu3dvrF271t7mkvRG8eL0chYssyYrV6YYJluYTFoJnVatxIvxhoQA48fbN8b0zPHj/M80Jfu2LOvSuDH9HtpCsBSSvWroUVEUBK7+NF+/nj6z6qpWBQoV0t7zih1kyWIt3F+3Lr9moKWucPbsJP5vi8BA6yIPTZrw80kaN9a2y5ThlxCVx03I404j9HhdISEhia9hw4axbNmysTp16rDBgwdb/V9ISIhDvT1nIkPMSCUkkEsfGSneRu9jtN4ZCsult7Awvn23btrcsbs7Y7du8dtERNDjVDLLQhILjDzf4eHaY7HJxFjHjmJ9hIUxtmqVkHbY+vXrWUCAtY5UwYIFbepIHT4cz4BQBqxlCxaEvjJr5SiMnJFizHi5NMaMn3BmTN/KPWPyuOVx83GKGamwsLDE14kTJ1ChQgW4ubnhn3/+sfq/48ePO97jS4b58+cjMDAQ3t7eqFSpUrLZOCq7du1CpUqV4O3tjaJFi2LhwoWpNFIn4upVoHdvfRlyRnL4MJUwUWndmj9DMXKkloUnWozXx4dmmHiPOxJj8fUF+vWjbbOZzqUIOkohJaqhh4Zi7dq1XDX0DRs2oG3bIgDqAeiEAQPqoUiRIg7XnFJRFdElEkn6R5dKZCiv0nwqs27dOgwfPhzz589HzZo1sWjRIjRt2hRnzpxBIct5v/+4cuUKmjVrhj59+mDNmjXYt28fBg4ciNy5c6O95Y08vXH6NLBxo3jpE9VJMaom4rlzmk7TvHlU7iZXruTt33gD8PMDwsNpCa5BA/7Nslw5oF49IDRU/Ebsqqg1BidMAAoXdvz+T5wAliyh7RkzaAnY3992m+HDqZJw9eq0NGsAJpMJdQXm/FUBT/aS864KeNqq6WcPx46JryxLJBLnx+4YqevXr7/yw2P5f6nBnDlz0KtXL/Tu3RulS5fG3LlzUbBgQSxYsCBJ+4ULF6JQoUKYO3cuSpcujd69eyM4OBifffZZqoxXmHHjgJ07xe1btHAuZb+PPyYxSgBYvx5YtMi2febMWk1CsxkYMUKsnzVrgCNHqO6hJHlu3gSWLgUmTjRm/599Bjx+TNvbtgHLl/PbFCoEXLhADwBpiNlsxrBhw5L8LVP/Nnz4cIfW6QsKokk5iUSSMbDbkQoMDMSDBw9e+fujR48QGBiYokGJEBsbi6NHj6JRo0ZWf2/UqBH279+fZJsDBw68Yt+4cWMcOXIEccmogMXExODZs2dWL8P55BPg7bfF7Y2aWVKZMkXbHjuWv+zWsaP1+w4d+H0MHAh4eAANG9IMlQj58wOVKonZZjR45yApDCjaCwDo1k3bVhRaahWhaFHbM5WpQEoFPFODefMomDYqSl87I521zJnpXzeddxA9xZ0LFtS3bxV53I7HVY9bFLsdKcbYK1kxABAZGQlvb+8UDUqEhw8fwmw2I+9L6tF58+bF3bt3k2xz9+7dJO3j4+Px8OHDJNvMnDkTfn5+ia+Ces/2qVO0dJGE02kTe26URhAZSTNMKp9+yj+Wpk2BYsVou3lzUiznkS8f8PAh8Ouv9o/VVVi1CqhY0Zh9M0YldFTattVi0ZKjQQNavgWANm3IQUon3BGUMU/O7rvvgAIFgGSe3VJMVBRNJO7aBaxYIdYmMBCYP19fGcODB/VNgo8ZA3z1FVCjhnibH38E9u0Tt//jD33K2PK4xdu46nEbht7odDUrz83NjfXr188qU2/o0KGsatWqrEaNGg6NiE+KW7duMQBs//79Vn+fPn06K1myZJJtihcvzmbMmGH1t7179zIA7M6dO0m2efHiBQsPD0983bhxQ1/Uv7OlO5w5Q8Ieah/Ll/PbdOtGmXHu7oyJqtYvW0YS0Tt3itm7Ms+eCWWiJWJkektEBGPe3tr14e7O2IMH/HZr1zJWsCBjL30fnZ2UCHgmJDBWqhR9TEYVc/jmG02HtEgRkkOTSCT24RRZe4CWuccYw6lTp6yy9c6dO4fy5ctjheijUwrIlSsXTCbTK7NP9+/ff2XWSSVfvnxJ2ru7uyNnzpxJtvHy8oKvr6/VK12zdy9w8aL2fts2fpsRI4D4eHrZ0PCxIjiY4mYsRUgkSVOsmHhcmD2oy9bx8fzZJR8foE8fCvp3dwe6dBFbfnv/fRJfUmsNphNq166NgICAJGfXAdKeKliwIGpb6l79x44dlFcB0ETqpUuOH9/XX2uT01evAn/95fg+JBJJCrHXA+vRo0eaaylVqVKFDRgwwOpvpUuXZh8kU0dtzJgxrHTp0lZ/69+/P6tWrZpwn7o9Wr0zUs+fa7MBcXF8+06dNHtfX8YuX7ZtHxXFmJ+f1ubQIbFx9ejBWIcO+mZOJGIYOQO5Y4e1BPDo0fw2ly5p0yB66+c5G8ePc6/Z9evXM0VRXlFDV/+WnPZUly7WH+306Y4f/pIl2v7feUef9JtEIrHG6UrEOAM//PAD8/DwYMuWLWNnzpxhw4cPZ1myZGFXr15ljDH2wQcfsK5duybaX758mWXOnJmFhISwM2fOsGXLljEPDw/2888/C/dpqCN19SpjmTJpv5x16vAdlzp1rH/Njx7l9zNhAtnqcCAlgiQkiJWsscRIR+qXX6yvjyFDxNpNncrYmDHiY3JGbt2iYxYo8WOPgOfJk4zlzk1dNGtGVYuMQO9KrkQiSRrpSCXDN998wwoXLsw8PT1ZxYoV2S4Lh6V79+7srbfesrLfuXMnCwoKYp6enqxIkSJswYIFuvrTdSKioxl79136FVy0iF+86+pVbSZAURirXp3fx6ZNmn3t2mIHcecOzWT99ZeYvUSchQvpfBw/Lt5GjyOlOgeis4nx8YwVLqxdI5cuiY8rvaNT+jj+yBEWCrC1AAtduJCrbB4fH8/ef5+U0OfONU4JXTpSEoljkI6Uk6DrRISEWM8GiJTB7tBBK33yyy98e7OZsddeI/vff+fbS/Rx+jRjx46J2xudXFCpkvU1JRLc/dVXZNu2rfiYMgJ6g+yzZNE+Vy8vxu7fT9Y8qRmsgIAAmzNY9iIdKYnEMThFsPnJkyeRwAtWdRUOHuTbBARYvy9QgN9m9GgKCC5SBGjZkm/v5gYsWwbMnAk0a8a3l+jjjTeMkxoAgJ9+0raPHuXbly2ribm4u1MOMI+ePUmM6JNP7BujK5AlC1CiBOlgKQoJhiaTgKIqob+sP6UqoRtVVkYikTgnuhypoKCgRL2lokWL4lF6LI/uKJo35+sp9e6tKZm99pqYo1OlCgnGrF1LmVMivPUW8MEH+tXSXI2EBCphoqpwpzV//w28+672vm1bfTUGO3cWU7zLkgUYMoQchfTM6dPWmmaORFFILEedkxo9OsnvU1oooRvpx0skkpSj686bLVs2XLlyBQBw9epV156dCgzkp4VbFmdN5oc5Sbp3T3dp5OmCq1epHqGzFGsuWxbInp22TSagcWN+jcEyZYD69WnbSMkEZ0RPKaSHD7Xak2vXiilmduhAavnZs5PsQxKkhRL6xo3A7t0O251EInEwuhyp9u3b46233kJgYCAURUHlypVRtGjRJF8ZnuHDharQY8IE4M8/yTmSOAfPnxuz36NHSWoXACZP1uoNJkemTPbXGDx+nAo3uxJ6SiF9/z3www/a+1mz+G3c3ami8OnTdG6SIKVK6PHxQPv2pBItStasQBIyVhKJxElw12O8ePFitGvXDhcvXsTQoUPRp08fZM2a1aixOTfvvCNmlyOHvrp5EnG2bweWLLGOM0pL5s4FIiJoe+dOYOVKbVYkOQYOpPi2evWA0qXF+smXT18RK2elVSv6HnXt6vh9v/suLYOqYqTBwWLtkhHzVfH39xfaTXJ269cDGzaQDm737s5RJ0wikaQMhSW12C9Az549MW/ePJdzpJ49ewY/Pz+Eh4enf5VzZ8NsFo8LA4DcuWkJR/QSvnyZYtU6daIiabZgDOjbF1i6lN537gysXm17FjI0VHOa3dyov8KF+eOKiqLZEC8vsePIKKifpej5y56dZqVE7Xv1ApYvp8SNixf1XVvJYDabUaRIEdy6dSvJOClFURAQEIArV67A9FJ/jFGN7ePH6f2cOTSxLZFIUgej7t92Ryd/++23LudESQymWjW6u4gSH2/cWKKiyHFS+eEHctpsUbcuxT0BFG8j4kQBFAzuak5UajBiBMUyTpzoECcKAEwmE7788ksAeKWsjPp+7ty5rzhRAHDkCBAWpsWzf/GFMbXJnz6lQ1YdNhFWrQIWLxa3P3uW+rh3T8yeMcrz2LJFvI8//wQ++oier0SQxy3eh6set2GkRDvhyZMn7LPPPmO9evVivXv3Zp9//jl7+vRpykUZnBijdCgyJI8f67M3UuH78GHNHmDss8/4bfr3Z8xkosK9nTuL9fPTT4wVL87Y33+L2Wckbt3SZ6/nfOsthWQw9iihR0Ux1qSJdhjTphkzttmzaf+NG4vZ373LmIcH6bVeuSLWRtUZnjhRzP6vv8g+b17GYmP59mYzY4GB1GbjRrE+5HGL2bvqcTPmhIKchw8fZjly5GAFChRgbdu2ZW3atGEBAQEsZ86c7KhImZJ0inSkBPn1V7rKL1wQb2OkI7VqlbWQZY8e/Dbnz2tK83pEOV2RH3+kz+ncOfE2es63PaWQDCY+Pp6FhoaytWvXstBQMWXz+Ph4BpAaumgbPcTGMpYvn/YxnTnDbzNpEmkAm0yMDR/Ot796VdMM9vMjB5FHkyZamzVr+Pbqz4eiMFazJt9eHrc8bhGczpGqVasW69GjB4uzKKwbFxfHunfvzmqLlipJh7isI/Xwob5iYkYrfEdEaPY3bvDtY2K0wmgAFUoTYcwYxgYNErN1ZfSe7/PntXNhQ0E8EXtKITkZqaGGvnattb/Zq5dt++ho64nazJkZ4y0qvFywgVdl6+xZa/uyZfklRGvVsm5z+LBte3nc8rhFcAplc0uOHDmCsWPHwt1dS/xzd3fHmDFjcOTIEbuXGiVOSlCQcwk6Wqq+Fy7MXyj39ARCQmi7fn0tlonHrFnA11/bNcR0zeXLFBhhBGfOWGco1qvHDxZq2pQSBRhzHh0wgOL01q3jjj+11NCLFNE0gAGAp0Tj4UEfq0pgIODtbbuNpX1S718me3brJNPixfnKMcWKads5cwJ58ti2l8dNyONOI+z1wPLkycO2bdv2yt+3bt3K8uTJkyLvzpnJMDNSmzeLLV6r6F120ztDsW+f1odIYd127awLPIu0efSIsREjXDN+SS9Gnu/79xnz9CR7NzfGmjcX62PnTsZmzuQX/05NZs6k4zhwIFmT+Pj4V2aiLF+KorCCBQs6bJlPZ61mxpjxX297+tBbY1Aet3FjyijH7XQzUu+99x569eqFdevW4caNG7h58yZ++OEH9O7dG++//74jfDyJUVy/TiVueBpHqcXx40DNmtr7xo35MxSjR5ONogBt2og9kuTIAXz+OfDmmykZrSSl5M4N9OhB5y4hgc6lCM5YCkkVCY2NTdYkLdTQJRJJ6mH3L9Jnn32Gdu3aoVu3bihSpAgKFy6MHj16oEOHDpgloiIscRzXrwPffitur8oG3LplzHhu3AD++IO2v/9eE6lMjsBAbZ7WZCKxHd5ccLVq5BAxBowalfIxZ2TMZmDqVL58g71cukRKkwAJpD55wm8TEkLnrlw5oE4dY8blJKRUDV0ikTg3djtSnp6e+PLLL/HkyRMcP34cYWFhePz4Mb744gt4SU2clPH118CJE+L2zZqJKzenBhMnAidP0vbChcA339i29/Mj8UuAbvojR4r1s3o18PvvQI0a9o/VFbh2DZgyBRg71pj9T51KgpcAla9ZsIDfplQpqn+3YYNYqaV0TErV0CUSiXOT4jnyzJkzo2zZsihXrhwyW0Z/SexnyBDrpS4eRs0sqSxcqG3Pncu3b9bM+n3jxvw2w4fTkk316uJLbyVLUiFbiRgvXhiz33btrN+3bi3Wrnp1fuRqBqB27doICAh4RcBTRVEUFCxYELWTKaj33Xckxh8To69fI59n3XUVF9PIkkXcNkcO+/qQx+14XPW4hXFoxJULoDtY7coVxtq25eeYWuJMUXoRESQ4Yplreu+e7TZxcYwVKEC2deqIj+vff/n7ljC2ZQtjrVuL2+uNyhwzRjvXQ4bwc5fj4xkrUoTsGzYUH5czMn68uNzF5s3a51SkCGOnTiVrun79eqYoClMU5ZVAc0VRkpVAsFTtWLFCbFjx8YxNmKDvq7R5M2nJivLkCWPjxtH4RJk3j7GwMHH7c+dIdFEUedzibVz1uJ1OR8pV0X0inC3d4epVa9GOX3/lt2nXjtS9TSbGGjQQ62fOHNr/pk1i9q6MhRabELlyGec4P3tG51q9PhRF7Jdq/nzGvLwY275dfFzOiJ7vXnCw9QPGrFk2ze1RQ1+xQjsNpUvzfVqJRJI8Tpe1F8ELIJY4J5s3A3v3au9XrOC3GTWKAtTNZvEMq2HDKJPp5WU+yau8+SYwe7a4vZE1BrNmBbp2pbl8d3datuOJugDAgAG0dNiwoXFjczaGDNG2vby4cYrt2rXD1atXERoairVr1yI0NBRXrlxBu5eXRi1QS08yRrJeu3Y5YuASicSR2O1I1a5dG3fv3nXkWCT2MGqUloJdogS/qmTnzkCmTNr7wYP5fVSvTnFONWuK3yjd3Ej9LYMHEjuE48eNCwT/+2+gQgXaXrtWzGEbOZKctfh4ccfZWbEhO5BiKlQgSQaA5Bxy5eI2MZlMqFu3Lt5//33UrVs3yeLGlnTooG1XqQKUL2//cCUSiTHY7UhVrlwZVatWxblz56z+HhYWhmZyFsI+7t8H8ufX3lv+iibHzp3a9oULWvZUclhmyJUpQ6rSImzdSjNZ0jHic+1aWo9A48IFa/mJl76vSfLGG0D//kCXLkDVqsaNzWju3wcKFgTmzzeujylTaNZ1xAhDdj9+vBlZsuwE8D1mzdoJX1+zIf1IJBL7sduRWrp0KYKDg1GrVi3s3bsX//77L959911UrlxZyh+oxMcD4eG0/fgxX2Ty8WPAUkvm33/FhCkBcnCCgsSkAIYPpyfp6dOlY+Ro1q6l+gVGlVd59kybgRRx2N55B8ibV3svKi2xYAHJS6RnIiPp3337xOwtP8/Ll8Xa1K1Ly+UGlE/asGEDihQpgqioegA6oV69eihSpIjDyslIJBLHkCL5g8mTJ2PkyJFo2LAhypQpg+fPn+Pw4cP45ZdfHDW+9M3UqZp0QNu2JE5pi1KlqKaYqtw8dizf0Wnfnmax1BpkIo5RkSI0kyWapu7K3LhBgpOiqPpZDx4YMx7LGoNFiwJhYbbtLWsMNmhAs02SV4mMpAcRlfLl6cEmjUit2nwSiSTl2O1I3blzB0OHDsW0adPw+uuvw8PDAx07dkTFihUdOT7n5d9/+TaentbvOfEQACjmKSGBZhHefZdv7+5OgpeDBpFTJXEsJUpYV9R0NLt3a9u8ZVmAAr9VZ5kxqhDKo29fcrI/+cS+MboCWbJQ6Rr1s/XzA3x902QoZrMZw4YNA0tiNlr92/Dhw2E2y2U+icQZsNuRKlq0KPbs2YOffvoJR48exYYNGzBw4EDXKQ9Tpw7w6JFtmwEDNGcqf34xR6dePeDjj4HlyylYW4Q2bUgNXdTeVWGMshSjo8XbGCViCdBskhqsDIjVGBw1Sqsx2K4dzS7yyJ4dmDWLSu+kZ/SWQtKDopCzqX62o0bZr0KYQmRtPokkfWG3I/Xtt98iLCwMzZs3BwA0btwYoaGh+PLLLzFw4ECHDdBpyZULyJaNb9OjB22PHCn2w6wowPjxUjbACK5eBXr2pBumM/Daa5r0r8lEaVm8pdmqVenlijUG9ZRCiowE5s2j7V9/Bf75h9+mc2eSV86cOU1LLsnafBJJ+sJuR6pjx46v/K1ixYrYv38/dlpmkmVUhgwRW6qbNImCdvv0MX5MEtuosz0iRXXt4d9/tTi4b77hz1j6+gL9+tG23hqDf/xBhZtdCT2lkFasAL78krajooAPP+S38famzNQDB9JsWQ+QtfkkkvRGimvtvUyRIkWwTzRLJj3TubOYXYEClEaeNaux43FFDh8Wdz5Sg+nTafkJAH780bpGYXIMG0bJBTVrApUri/VTvDjQpIn943QWBg0ih9AIWrbUkjYAsXhDAChdGihb1pgxCZLS2nwSiSR1cbgjBQDZRQJg0zs+Pmk9Aknbtpr0sxFMm6Ztjx/Pj196+WYtEhNXqBAFmW/cqHt46Z75841bwi5cWNNhE03cSC0aNACWLEn2v00mE778bzbtZWdKfT937lyumKdEIkkdDHGkJBK7aNsWWLNG3D4qyrixREYCH32kvf/kE76kQbNmFPcEkIxFqVJifQUGCqliS3QyciTFoI0e7VyJGH/+qYniJkO7du3w888/o0CBAlZ/DwgIwM8//2yzrExUFMmAXbggPqQ//tDny1+7Rn2okmYirFxJq6aiHDkCLF3Kf35Rkcct3oerHrdhOLRynwtgVNHDDImeUuGMGVus+exZxooX1/pYsYLfpmtXrVhz69Zi/SxZwpivL2N//SVmn5GIiNBnr+d8jxyp2Rcvztjdu/rH5yzoOO74+HgWGhrK1q5dy0JDQ1l8fDy3zTff0O7btxcbzpMnjHl706V+545Ym549qY9PPhGzP3iQ7IsUYUzgEFhCAmNvvEFtduwQ60Met5i9qx43Y8bdv6UjpRPpSAkSGspY5syMXb8u3sZIR2rxYm3/AGPvvstvc/y4Zr9nj/i4XJE//qDP6fJl8TZ6znelStbnb+9e+8bpDOi9znVgNtPNC2BMUcROx6xZjLm50WvCBL79nTt0EwYYy5NH7HmpQwfaP8DYL7/w7f/3P+0YGjXi28vjlsctglM6Urt372adO3dm1apVYzdv3mSMMbZq1Sq2JwPfdFzWkYqKYkzPMY8dS1f5rl3ibfTcYOLjGfPxIXuRb3ZkJGN+flofBw6I9dO1K2Pt2tEjkyR59J7vx4+1cxEdzbf/4QftVzMoKH2fDwMdqV9/tfY3hw2zbR8by1jevJq9nx991W0xcaJ1H6tX27a/coVOm3r6qlfnH0fjxlobgLHTp23by+OWxy2CUfdvu2Ok1q9fj8aNGyNTpkwICwtDTEwMACAiIgIzZsxwwKKjxKmoV490jpyFdu20WmpZswLnz9u2z5KFssQAOg5R6YBVq4D1612vJuH9+4ANUcgUcekSkC+f9r5ePX5ghD2lkFIDxqzV6XmcOqVt377t8OF4e1u/58Wjm81Apkza+0yZqLCCLV4ON3u5z5dRFM2GMWrPO93u7pqNh4d1AmZSyOMm5HGnEfZ6YBUqVGArV65kjDHm4+PDLl26xBhjLCwsjOXNm9cxbp4TkmFmpA4f1vdUr/cpWu8MxYULWh8PHvDtGza0foT55x9+m9u3aUnvzz/FxuTK5M7NmKenuL2e833jBsWdqY+sb70l1scvvzA2aBA9VjsL8+bRcRw9yrc9eVJb7wAYK1XKkJm1f/7RYkdE4lNiYrQhvXjBtzebaQYAYGzrVrFDiI7W+hA5fXFxFBkgOmHJmDxuedx8nG5G6vz586hTp84rf/f19cVTPaH9dvLkyRN07doVfn5+8PPzQ9euXbn99ujRA4qiWL2quZqoIUBPwm++SbpHzsCZM9YZbiIzFJblPBo2FCvG6+8PrFsHvP12ysbrCjx4AMTGGrPvgACgY0c6d+oMkwjOWApJFQlVZ0dtUaCANnY3N6BkSUNm1tQZBy8vsSd1y5KgXl58ezc3bUYgUyaxQ7CcBRE5fe7u2rgs24r0IY/bNq563EZityPl7++Pi0kUWd27dy+KFi2aokGJ0KlTJxw/fhxbt27F1q1bcfz4cXTt2pXbrkmTJrhz507ia8uWLYaP1XAePwb0HIdaP+7cOWPG8+gRcPAgbf/vf8B/y77Jkju39k1wcyNtJd63tX594PXX6UY8enTKx5yRYYzyio2Si7hzB/jrL9reuFGsluHIkTSuYsUyhrioCDlyAL160bWdkCCvW4kkg2C3I9WvXz8MGzYMhw4dgqIouH37Nr777juMGjXK8Fp7Z8+exdatW7F06VJUr14d1atXx5IlS7Bp0yac58TKeHl5IV++fImvHDlyGDpWu/j5Z+DKFXH7Zs2A/2oeOgXjxgG7dtH2tGk0i2CL3LmB7t313WAUhcqALFxIAoeS5Ll6lUoUGVVj8MMPSWUeAL74gn++ASAoiGLP1q3jB0RkJEJC6N+KFYEaNdJ2LBKJxCHY/Qs2ZswYtGnTBvXq1UNkZCTq1KmD3r17o1+/fhg8eLAjx/gKBw4cgJ+fH6pWrZr4t2rVqsHPzw/79++32Xbnzp3IkycPSpQogT59+uD+/fs27WNiYvDs2TOrl+G8846+H1leoHVKWb9e21Zrydni5eVSi/OULCNG0AxF2bLAW2+JjevNN6lWnbMEHjsr6jKpUUvu9etbv69bV6xdu3bkULgSxYqR8uAvvxh+3Tqjf6rnkDNntq8PedzOg8scd0qDrKKiotjhw4fZoUOHWIReQT47+fjjj1nx4sVf+Xvx4sXZjBkzkm33ww8/sE2bNrFTp06x3377jZUvX5698cYb7IWNiLvJkyczAK+8hIPVHjxgbMgQxp4/F7NnTH9gtx49JcYYu3SJ7Dt14ttGRGgiImpw8L17tts8f85YjhxkrydVfe9eCjqX2ObgQbqmRNFzvhljbO5c7XyLKPBZ5lSL5Do7M199xdj06WK2+/Yx5uFBx121qj4NLQN58YKx7t31DWfFCsa+/lrc/tYtxrp106fB+sEH+nRqDx1ibOhQcXt53OJtXPW4nU5H6tq1aywhmRvktWvX7Npnck6L5evw4cPs448/ZiVKlHilfbFixdjMmTOF+7t9+zbz8PBg69evT9bmxYsXLDw8PPF148YNfSdi3Dhj9ZQY0+dI3b9PamlqHyKaXw0bUpaVmxtj1aqJ9fPRR7T/H34Qs5eIkz+/sY6zmlGnvniOM2Ok8geIqe85M3q+e127Wn9OH39s7NgkEkmKcLqsvcDAQDxIovbYo0ePEBgYaNc+Bw8ejLNnz9p8lSlTBvny5cO9e/deaf/gwQPkzZtXuD9/f38ULlwYF2wU6/Hy8oKvr6/VSxc8kY7U5ocfKAZL5dNP+W1GjyYBEj0BsqNHU2yOWjhWkjwtWlBhKlFEgrntxceHltzc3SkBoHFjIE8efrsRI4AnT4BWrYwbm7PRr5+2bTJRnJ9RiGQFSiSSNMFuR4ox9kplcgCIjIyEN0+xKxly5cqFUqVK2Xx5e3ujevXqCA8Px99//53Y9tChQwgPD0cNHbFFjx49wo0bN+Dv72/XeJ2Czz7TYl/q1QPCw23bd+xonY/auze/jwYNgHLlgKJFgdatxcbl7Q0ULpz2eanpgc2bgR49jNn3mTMkDwEAa9cCy5fz24waBcTHk/MsGqDu7g5ky+YkAQsWREQYt+8aNbQYr44dSd7ACKZNI+kOiUTilLjrbTBixAgAgKIomDhxIjJbRIiZzWYcOnQIFSpUcNgAk6J06dJo0qQJ+vTpg0WLFgEA+vbtixYtWqBkyZKJdqVKlcLMmTPRtm1bREZGYsqUKWjfvj38/f1x9epVjB8/Hrly5ULbtm0NHa8w4eHkDKkMHQrMm2e7jeVMxs6dwNGjtnWS1Ay5pUvJMRLJ9lMU4MQJvp2ECA8H/PzSehTE/v3A5cva++3bgeBg222qVCGHOTLS+npMbzx6BOTKRQ7k++87fv+KAkyZAkyeTM6nUcyZI2ekJBInRvfjY1hYGMLCwsAYw6lTpxLfh4WF4dy5cyhfvjxWrFhhwFCt+e6771C2bFk0atQIjRo1Qrly5bB69Worm/PnzyP8vxkak8mEU6dOoXXr1ihRogS6d++OEiVK4MCBA8iaNavh4xXiyhUgLEx7/8cffGFKNZ1aUYASJcRufCNGkO3kyc43g5De2bSJZmYuXTJm//HxmlDm8+d8+06drJ26/x6EuGzcSBpg6TkjUp2d3bRJnz0gnuHYsiVw7Bhg8MOjRCJxYuwNrurRo0f6L5NiB7qC1T77zDoY9fff+W1q1dLKSCxcyLe3zJBbupRvL9HHo0eM3b0rbm90sebmzTV7Dw/Gzp7lt5kwIWNk1OlFT5B9dLQWxA8wljMnY0+fGj9GEfRm5UokkiQxKthc99KeyrfffgsAOHPmDK5fv47Yl8pJtMroQacPHgC8wPOXNaqSCJB/hTFjKGDXzw/o1o1v7+1NcVK//w507sy3l+ijYkWaqXjyxJj9W2qA3b/PD+w2m7XSKnFxYskMgwbRbKdIPJyr4un5ajyfnbGeEonEtbDbkbpy5QratGmDU6dOQVEUsP+WoNQAdLPZ7JgROiuVK9PNKVu25G2GDAE+/5xufjlyiDk6zZsDAwYA1auLFx3q2ZNeEj5bt1LwvLvgpX/tmnFjOX2agvhV3n4bOHXK9nLa6NF0DGqNwddf5/eTLx+wZk3Kx5vWPH5MpYeaNXP8vk0mKlsTEkKf7fDhYoXIjOaff7Rlxu+/12oUSiQSp8HuAJmhQ4ciMDAQ9+7dQ+bMmXH69Gns3r0blStXxs6dOx04RCfF3Z0vxaoWZwXoh1nkCdfNDZg/HxCoGyjRyY0bQNOmVNLEGcib17qIbWAg/yZZrx4VaNZT7DejoKcUUkwMSX0AVK7o6lV+m+BgIEsWOicDBtg9TIfy3nvadqdOWk1DiUTiNNjtSB04cAAfffQRcufODTc3N7i5uaFWrVqYOXMmhg4d6sgxOieDBlmX0U6OyZOBTz5xnh9mVyYujv69edOY/d+8SbNFANWQ42Va5cpFsgd6awyuXElZl7ayMzMiekohLV+uOcy3btFsE4+sWSnB448/gJw57Rujo2nUSFtyzJQJqFQpbccjkUhewW5Hymw2w8fHBwDpP92+fRsAULhwYW7h4AyB6FJa8eLA2LF005Q4lgsXqEiuszBxoiYTMX++WPHekBCaXSpfHqhdW6yfSpWAXr3S/xLPzJnAoUPG7Pvl7NVGjcTa1arlXJIPw4ZpcXB9+9oOJZBIJGmC3Y5UmTJlcPLkSQBA1apVMXv2bOzbtw8fffQRihYt6rABOi3Zs6f1CCTNmomn89vDkiXa9ldf8e0bN7Z+L3LzLlkSOHAgVYrYOh3jxwN16hiz71KltFiqbNnEEjdSi+Bg4NdfxWyLFAHat6el32HDDB2WRCKxD7sdqQkTJiDhvyel6dOn49q1a6hduza2bNmCeTwRSYkkKYYNA7ZtE7d/+NC4sURGWi/HDh36ahbmy3ToAOTPT9u1a2uq1zyqVaP4KFfkpWxfh6KKZA4dKp64kRp8+y3Qpo24/Zo1FGgveI3ExgK//Qb8t0ggxJEj5M+Lcv8+9aGnWtGOHcDZs+L2Fy7QKqso8rjF27jqcRuGI7UUHj16lGwh44yCUToUEmZssebr1xl76y2tj02b+G3atGHM3Z2K+L79tlg/qnbYb7+J2Wck4uP12es5359+qtnXrSum8ZSQQEWY4+L0jcto9F7nOlm5knbfvbuYfWQkY76+jHl7M/b4sVibwYOpj6++ErM/dYrsS5em0yJClSrUZv9+MXt53GL2rnrcjBl3/7b723zt2rVknaZr167ZPSBnRzpSghw9yljJkvrELI10pL75xloctU0bfpt9+zT7rVvF+jGbSSQ1gz9QvMK+fYzlzs3YzZvibfSc7zJlrM/fn3/aN05nwEBHKiGBsTfeoN27uzN2+za/zTffMKYopAP8ySd8+8eP6SYMMFa4sJj/3LMn9QEwtmMH3/7AAbJVFMbat+fby+OWxy2C0zlSbm5u7N69e6/8/eHDh8zNzS1Fg3JmXNaRio1lLCZG3N5ohW/G9DlST54wlimT1sf//sdvk5DAWIMGjFWr5nqOkV6MPt/Llmm/tCVKpO/zYaAj9b//WfubH35o2z4+nrEiRTT7PHn4X/NPPrHuY8MG2/Z37tDNTj19DRvyj6N9e+1GrCiMXb5s214etzxuEYy6f9sdI8UYSxTftCQyMhLeUhE449Ghg3jmU2rQu7cmVJg3L2lE2SJbNqBPH9p+4w0x6QBFoYX+AwdcLxA8IsI4Nffbt63r/zVpwq8p2akTidqq+lnOdD7OnRO3taxuEBHh8KG8XCLwwQPb9jEx1iUbY2OBqCjbbR49st3ny1iWMGSMxsQ73ZY2isLvQx631t4WrnrchqPX8woJCWEhISHMzc2N9evXL/F9SEgIGzp0KKtatSqrUaOGQ709ZyLDzEhduaLPXu9TtN4ZiqdPtT6eP+fb16hh/Uhy6BC/zeXLjNWuzX+kkjBWrhzN44ui53xfuKA9fgKMVawoNsO0fDljbduKXR+pxbff0jGcOsW3/fdfqo+oHnelSg6fWUtIYOyvv2j39etTCUEe9+9rQxJZiX/xgrFu3ch+9WqxQ7hxQ+vjyRO+fXi4Zi8SKSKPWx63CE5Tay8sLEx1wHDq1Cl4WohSenp6onz58hilZstInJN79ygDaN48KmOT1ly+bF3q5O23gX37+KVS2rYlm2rVgCpV+P0EBgK7d6d8vK7Af9ImhlCsGNCyJbBpE2kkjR0rNsPkjKWQ1Nmox4/5tj4+1o/d2bI5fGZNUYDChWk7b16xZMXcubXtvHn59l5egL8/bRcqJHYIAQHatogUlq8v2T19Sn3wkMctjzst0e1IhYaGAgB69uyJL7/8Er68wr0S44mOphptVauK2atzuQcPGuNIRUZqKtQnTgA1a75aENYST08gPp62FYVKdPC+rS1bksbO1atiiuCuzqZNpHOllqRxJE+fAv89YGHfPqoTyetn9GjKXS5QAGjXzvFjckb8/WmJcvVqcqh0XLdx5jh4mAw4dxKJJMXojpE6dOgQ/vjjD3z77beJTtSqVasQGBiIPHnyoG/fvoiJiXH4QF2KnTv5mkWWtGtHszLOwvjxwMaNtD10KLBokW37gADgnXfIeRK9wZhMtN8JE4BWrVI85AzN9evkeI4fb8z+x40Dtm+n7fHjSdWdR82awJdfAqtWiReQzgiMHEnXeMmSwjGHy8OWw2emD5aHLTd4cBKJxB50O1JTpkxJVDQHgFOnTqFXr15o0KABPvjgA/z++++YOXOmQwfpctSrp0/x2agyGyqWy2F//sm3L17c+v1rr/HbjBpFN5jXXtMUqXk0agRMm2Z7tkuizfYZpVxXoYL1+3Ll+G0UhZxsV6sXWK4csHkz8NNPQmsky8OWo/dvvRFrjkXv33q7lDPlSv61JfK40yF6g6ry5cvHDh8+nPh+/PjxrGbNmonvf/zxR1a6dGmHBHA5I7qD1SIiKH9Uj1ihkTIAjDF26RLZd+rEt42I0EREVNGO+/f5bbJmJfuSJcUDan/8kTGLa0uSDGfPMjZ7tri9nvPNGGNr12rn+9tv+fbR0do1WLZs+pYmWLeOpBZEOHWK8scBxlq00KeZJsCyY8uYMkVhmILElzJFYcuO2R5fVBRj9eoxdvy4eF+ffCKeQs4YY+fOUR+PHom36dSJsZ9+Erf/4w/GWrcWt5fHLd7GVY/baXSkvLy82PXr1xPf16xZk02bNi3x/ZUrV5iPj49jRueE6D4RkybRD+3u3eKdGOlIhYczNnAg2Xt5MXbiBL9N9eqk3qYoJIwocqNUs7hEb0oScYoWNdZxVkVgVFGXJPTiXkG9ztesER+XM6Lnu9eli3Xm6PTpDhtGUk6UHmdKIpG8itPoSOXNmxdXrlwBAMTGxuLYsWOoXr164v9HRETAw4iA1vSKGi/GE9JILVau1GJYYmKAiRP5bcaMoewqPRo+48aR/lLnzikbryswcCCwZYu4vUiGmL34+AANG9JyqckE1KgB5MnDbzdmDHDmDPDuu8aNzdno0kXbVhTgvfccslt1OY8h6d8MBuZyy3wSiTOj25Fq0qQJPvjgA+zZswfjxo1D5syZUbt27cT/P3nyJF4TiYmROIY1azR1su7drdXWkqJNG6okr9KxI78PNUMuTx7xm4WfHwXAe3mJ2bsyCxYAzZsbs+9r14Bu3Wh77Vrg11/5bUaPBsxmeo0ZI9ZPlixA6dLGZAWmBDU+zAgaNaKgcYASHooVS/EueU6UinSmJBLnQbcjNX36dJhMJrz11ltYsmQJlixZYqUltXz5cjRyJgXs9MTz50Dr1tr7Tz7ht5k+XdtetQrYs8e2fcGC2qyBvz8plvMwmUhe4eJFkiqQ2CYuLq1HoLFlC0kSqKxcyW9Tty7w5puk7dWihWFDM5ynT0k0R09JeT0oCmWN5svnEAmOOHMcBmwewHWiVBgYBmwegDizE11vEokLotuRyp07N/bs2YMnT57gyZMnaNu2rdX///TTT5g8ebLDBuhSnDpF2joq8+fzlwQHDtSW2goWBOrX5/czahTNGI0ZIz6D4OMDZM0qZuvK7NpFpUx4JWtSi06dgMyZtfciumGKAvz9N3D6tPXsZXrj8WNyptasEbO3/K6JLsV36QLcuUNyDinEw+SBBc0XQIGYSKcCBQuaL5D6UhJJGmP3r6Sfnx9MSaSd58iRw2qGyqX59ltg1izabtyYP1v05puUSq4o9Bo+nB+PFBxMyyoAadSISAFUqkQ3mOHD+bauTnS0vppof/xBgqT/xRE6nB49tKXcnDlJI8oWfn5A3760XbYszTZJXiU2VlumA0g2mVeELAUkN4sUHBSMpa2Wcp0pBQqWtlqK4KBgI4YnkUh0kI4fN9OY2Fi+zdGj2vaLF8Dx47btFYVmiRgjzftevfh9+PgAkydTiZRg+aPqcBo0EFeMtwfLiqDR0Xz7S5e07cePxYRbhw0jbbLp052r2K8zwZh1keanTw1LEOEJbPKcKelESSTOhXSk7KVMGZp5sIXljJKPj1idsA4dKHB1+nSaTRBh1CgS5ZRLb3yOHdN3gzxwADh71pixXLoE5M+vva9Xjz82NRZHUWg5qXJlfj9FigB//ZX+FeCjo40Tn/XyAkJCaCnTZAIGDaLvrIMRFdi0cqYsLgnpREkkzod0pOzl+XN+/IhanBWgWCaRH2YPD8qsCglJ+Rgl1ty+TcuaM2ak9UgILy/KjAPIMcqUiT9j1KIFFV/WWastQ6CnFJLZTM4jQPUeHzzgt+nXT4sZHDzYvjHa4OWMPF7mXXBQMJaGFaR5KQYoDFhaeqx0oiQSJ0M6UvbSt691EG9yTJ1KAb5Dhxo/JoltXrygf8+cMWb/jx9TkDZAN3FezcmAAJKfUGsMikgNuLkBS5bQdZWeM+rsQc9s1IoVQJ8+tH36tFiQfc6cwPffU3B6gQJ2DTE5kpM14DpTuRth6e8KPM3A0s0mBNeVD1gSibMhHSl7UQN4eVSoAMyb5/AfZgkoW+r779N6FBoffACEhtL21KnAN9/w26hFbIsXB5o0Eeunfn1g0qT0X2Nw5Urg/Hlj9h0UZP2+ShWxdm3bimmrWcCTH0iRwObIkQg+xhA5Awiu0FNMHFUikaQq0pGyl7x503oEkqZNKb3fKDZu1LZ//JFv/3JQ+ptv8tsEBQEbNgDr1qVvqQF76NGDlNONoGJFQBUKzpwZ6N3bkG54geMpFtgsVQpo2hQeCZDL/RKJk+Jiv9wSp+bTT7WlMRGuXTNuLJGR1uVO3n+fnyHXuTNpSAHkINWqJdZX27avzqC4CkaWu1GXSvv1A3x9Hb57XuC4owQ27322Gmc2/ksCqQKYzcCRI5pKhgiXLwMXLojbP3tGfYgkL6ucOgXcuiVuf/cuP9HZEnnc4m1c9biNQjpSEudhzBigTh1j9v3wIdX/A6hUiqXad1L4+ABvvUXLZ25ulB3HW1bx9iapAUC8JqFEDL2lkACgWTPg33+BadMcPpzEmSaWfOC4owQ2Ow/NiTfaFMfJk2Jj27iRJkMnTBCzj4mhydRKlfiJyCqffEJ9rF0rZn/pElC+PD0ziNKlCz1fyOO2jTxu8T4Mw6ElkF0Ao6pHZzj+/Zexxo0Ze/xYvA1FC4nbZ8smbj9vnrZ/gLFWrfhttm3T7H/+Wayf588Zu3yZsfh4MfuMwsmTjL35JmP374u30XO+S5a0Pn/bttk3Tgew7NgypkxRGKbglZcyRWHLji0TtrfVjjH6WNVD7t5dbHxVqpC9tzdjjx7x7VesIHtFYeyrr/j2kZGM+fpSm9KlGUtI4LcZPFg7jv37+fbyuOVx89B73IwZd/+WjpROXNaRSkhgzGwWtx87lq7yXbvE2xjpSN27x5iHh9bHr7/y2yQkMPbGG4wVLux6jpFejD7fX35Jv/wAYwULptn5sNcpSmw3WdyJYoxuKm5udNju7ozdvm17fAcOWPubM2bYtk9IoJuj+tEWKsT/aL/6Sp9P+/gx3ewAOpa2bW3bMyaPWx63bXu9x61i1P1bLu1JxBg4kOZenYWJE7WlngoVaOnOFnnyAN260XZgoJh0gKIA//wDXL2a/jPk9BIbq8lFOJrHj4ESJbT3IkK19pRCspPksvBSEjgeHBSMyUFLAUuBTcYX2Dx9GkhIoO34eLoUbfHvv6+2t0VUFMmrqTqwDx/yY07OnbPd58vcuKEpgSQkkPoIT3dWHrc8blvoPW7Dcahb5gJkmBmpJ0/02eudLTJ6hiIoyPqRRKSf06cZe+01xr79VnxMrkrjxoxVrSpur+d8nzplfe5KlRJbL/j0U5rPf/ZMfFw6WXZsGfOc5vnKDFFsfCzznOZpcybq5ZfnNE8WGx+r7eT6dbakiidTJoNhMpgyGWzZ0aU2x3P7tvYxHTrEH7/ZzNgPP5B9pUpiX/Pz57U+zpzh2z97xljLlmQ/Zw5jcXH8NkePan1cv863l8ctj9sW9hw3Y3JG6hU+/vhj1KhRA5kzZ0a2bNmE2jDGMGXKFOTPnx+ZMmVC3bp1cTrNXdk04OFDIHt2YPXqtB4Jcfs2jUeleXP+I8zIkfSvolAxXjXV3Ravvw5cvEhp9xLbbNtmXDmWMmWAt9/W5B5EA/MNLoVkKwvPIYHj8fHofTgOS38DCWyeCkRwRdv1NP39AfXnTUQKy81NU90oWVJrawvLycHSpfn2WbNqCYSVKgHu7vw2FStq2wUL8u3lccvjtoU9x20k6daRio2NxTvvvIMBAwYIt5k9ezbmzJmDr7/+GocPH0a+fPnQsGFDREREGDjSVCA+Xn8uKwBs3WrMeGJjNamAW7f4TlFUFBAerr2/c4ffx7vvkpYXYzJDToTDh/nnwV6eP9ekKP79V5ujt8Xo0WSXM6exWmCCiJRv4RUTVkl2uS4wEGjbFt3D3Ehgs/NnDj8OiUSS+qRbR2rq1KkICQlB2bJlhewZY5g7dy4+/PBDtGvXDmXKlMHKlSsRHR2NtaI5nanFyZPieakApYNbPmakNZMmAd9+S9udOgGrVtm2L16cYpbUGYqxY/mOkYcHKcYHB1vrPUle5dYteswzQAYAAOUf//ADbffpAyxdym/TuDE5wIsWUc1BA7FXedweZ4pbVHjUKJiQgNsJhYDWrfUdiEQicUrSrSOllytXruDu3bto1KhR4t+8vLzw1ltvYf/+/cm2i4mJwbNnz6xehlO+PGAxTi5bthg3FsA6kk9E5MPPz/q9SLHmUaNohiJ/fqB9e7FxvfsusGwZ4OkpZu+qqJGfRpVjebn8Uf78/DaKAsyaJX6u7SSlyuNcZ8qiGdeJAoDq1dEHi9EFa1wvgUEiyaC4jCN19+5dAEDel0q75M2bN/H/kmLmzJnw8/NLfBUUWfC1JC6OZmT0LqscOKDP3igiI4Fq1bT3VavyM+T69SNxSoAWyNu04fdTuzYwZw7VXxNZhHdlbt0igUqj+N//tO0//uDb9+qlFfB+7TUSwnQCeMrjKc3CW1p9Js1LMUBhwNKG82w7Uf9xvnYfvP+NQEzff3z1lT7h+1y5gKJFxcuBAsDw4fpCB9u3pz70TITXri1WflJFHrcY8rjF2xiGQ0PXU8jkyZMZ6Bkv2dfhw4et2nz77bfMz8+Pu+99+/YxAOz2SwIVvXv3Zo0bN0623YsXL1h4eHji68aNG/qi/j/+mFIL9u0Ts2fMWD2l588ZmzKF7PPmZezSJdv2CQmMlS2rCY8ULSqmJzVwINl/+aXYuCTilC2r7/q4dInsO3Xi20ZEMObpqV2DJhNpcPEICSH7hQvFx2UgSek9Weo1OSQLr1s3tiwIzHMC2LIgcTEbkQTFlLaxxz41+tCLPG7j7F3xuI3K2nOqR//BgwejI6fyepEiRezad758+QDQzJS/v3/i3+/fv//KLJUlXl5e8EpJDIe6FBgfb/8+HMny5cCUKbR97x4tqW3YkLy9olDMUpcutD16tFhx3UmTKDOrSROHDDtDM2MGfVaWM3+2uHHDuLH4+NCs4/795EqVKQPkzs1vN2ECZVvWrGnc2EDxTi+XUHkZXswTQDNKC5ovEJqRApLJwmvdGsGrVqHrCVBR4ZUC2mSwLy9Cbxuj7TNKH844ptTowxnHlFp9GIFTLe3lypULpUqVsvnyVpeMdBIYGIh8+fJhx44diX+LjY3Frl27UMOoCvSpwZYtmqLaBx/QUqItGjSwvvpElmHUDDlfX03UkkfevDQfrIooSpLnww+prp8R3L9Pzi9AhbL27OG3GTOGKoImJIgF/gNUrLl+fW1J1wB48U6qjWjMU4qz8Fq3BgoVIifq7bdJhkMikbgcTuVI6eH69es4fvw4rl+/DrPZjOPHj+P48eOItMh2K1WqFH755RcAgKIoGD58OGbMmIFffvkF//zzD3r06IHMmTOjkxOkXwOgWatBg7T3K1bw24SEaNuzZgF//mnbvkQJmjkASLtJRK3cw4PS50+c0GJhJI5FT1l1PaxbZz3j+JlAyn2zZhTrlC8f0KGDMePSCS/eydJGT8xTirLwTCZyUk0mcj4lEolLkm4dqUmTJiEoKAiTJ09GZGQkgoKCEBQUhCNHjiTanD9/HuEW+kRjxozB8OHDMXDgQFSuXBm3bt3C9u3bkdUggT/dHD4MzJ+vvR8/nh+k3qOHttSWKxdQrx6/H3WGYtgw8RmEggWBwoXFbF2ZsDDgjTdo2dQZ6NiRHGGV3r35bdzcKFPz6lXrtgbAkyYAxDSe4sxxGLB5gNAynbqPAZsHIM4cl7IsvMGD6QGocWOhfiUSScYj3TpSK1asAKOiy1avunXrJtowxtDDIjVBURRMmTIFd+7cwYsXL7Br1y6UKVPGuEFu3EizRADpKZ04Ydu+alXSVFIUupn1789fVunXT0v/DwkR0+SpXZtS4idO5Nu6OvHx+maL1q2j4lJGSQ2MG6ct5ZYpAzx4YNs+d27SGQNolkmdjeTh5WW4vlNKlupedqZSqjweXK47lp4pZp2F12yhUBaeRCJxbdKtI5Uu2LxZ2751C9i+3ba9mxstETBGEgAiqu05cgBDhwKFCpFTJYKikPMlEjTu6rz3HtC0aVqPQsPyGjp9+tWKokkxYgTVUZg0yWnOuSOW6l52plIU8xQTg+Ct97TyLX+4I7jYO/YfoEQicRmc41c1PVK9uiZ0mBxDhmjb3t6kt8OjSxegcmXKphPJlgJo1uvaNSq3IbHN9ev67DdsAP76y5ix3LpFAfwqjRvzl3JHjaJ/FYWEW2vV4vdTujQ5XKKJAgYjslRnr8aT3TFPmTMDgwcj+KQJkbPcEFylv3X9R4lEIkkG6UjZy+XLwIsXtm3Klft/e3cfF2WV/g/8MyAgGmKKCj6TprZZiZJJ2aa2Eq6pa7t+a3URQ8x8KtdKzR7ArSzb1L5lPqP5tXbb3dKyUtP9raAmbpqgZiulq5IimaYIKg/C9fvjOAyjcN/nHmZggM/79ZqXw3jd3OfijM7Fuc99jrqbB1BbmTRrZv59GzZUc6VeeaXqbSRnP/6o5nktXFjTLVEuX3beCujsWfNjfvc7NQncC/cYdGW+k135gqgq852Aq8XUkOVll+nsTOc8TZoE2GzwuyJqxUIiIg0spFw1Zsz1W6FUZPZsYPhw57vrqGZcvKj+9NSq8RcvOjaPPnBALSFgpHNnYOhQ63sMLlyolvMd4T2Xnty5NMGa/WuqNN8JAOIzG2HFJ3Ce82Q2cbx1a/WznT9fzScjItJgE/HUlvB104ULFxAcHIzc/fvRhOvG1KzcXGDPHrV+kY7//ld9QI4cCbz/vt4x9sJG55/Jk0+qjZTtFi0yn+e2Y4ea/N+mjbpLrhZuj1O+QKps1Ef3Uh3gGDkCYHpMpaNMV3+uKyOACYOBxX6/QfyL66wnR0R1Rtnnd24umpSfVlFFte9/bW/BpQBq3pAhaoFJT/0u8OWXjucpKUC5O0IrdNNNzl/rrMJ/zz1qk6lbb/W6IsqVVcSvXT3c/n1cuVSX/6y67FlZMWV4qe6ee4CICMSnpyP2P37wy1qmdW4iIqt4aY+8x5o1wHff6ccfOOC5tuTnq1Xg7QYOVKuEG4mPV1usAGrhU53tcWw2tRaRzvpfLhIBsrPNp/SV9/aOlbhhTs0vTeDyGk82G+QZtUimbdSj2jdunDsH/PyzVigAtTJGdrb5VdzyTp8G8vL04/PzAYN91a/jSn8zbz3MW/8Yb8zbU1hIkfcYPRrw1HY9eXnAggXq+bp15kXYDTcAPXqo+Us2myqMzD6Mg4KAiRPVcy+aCL55s7py+EKS+WRwAFjx9Uo88U/vWZogPiIeKzo+4TzfafBS0zWetjT5Le5DCuY00rtxo6RE3QjZtav5Dbl2f/6z+tkabVdZXna2ih82TC8eUDfytm4NHD6sF2/vb/uWmmaYN/M2Uxfy9ii3boFcD3hq9+g6JztbZOxYkfx8/WPULxn68U2b6se/9Zbj+wMiQ4eaH7N2rSN+9Wq985w7J7Jjh0hBgV58NRgwQAQRyYLn/eWdncmGscl7kwVJNkEiBEnqYUuySfLeZKcYW5Kt7O+NHpUem2geW15heBdJjoD4Pw9JjoDIxo16eUMkKEgkL8/85/Thh47uXrXKPL6gQCQkRMVHRprHi4g8+6zjHPv2mccfPixis6n4iRP1zsG8mbeR+pq3iOc+v1lIWcRCStPMmepdnpqqf4wnC6njx0V8fBzneP9982OuXBHp0EGkRQuRwkL9dnmR/fuvFlGJ9uKl8mJFp8gpulIk/i/5axVR9of/S/5SdKWo7DyL0sq3B4JE4yJKROSTPnPkCnykyAdyGiFyNtu4UN2/37lufust85/VnXeqt4jNJnLLLSKlpcbxq1Y5n+PLL43j8/NFmjRRsb6+IqNHm7dp0iQVC4g0bChy9qxxPPNm3mbqa94invv85qU90vPSS47FIHV4+mbQd95xbJXy4IPmF+Pbtwf+53/U89BQvaUDfH2B/fvVkgb2bXi8hM6aTQDwxv9bCQxNgLomBkCuX/wSuOZSXQVX39y5NEGfKw/jmfU3O63ztHyI8dIEr+eORxH84VcKLMAfsT/TePuaa1e42LbNuJ35+epqb2mpeusePgycOWN8TPl7EQBg507j+EOHgAsX1POSEiA11fyfybZtjnkpBQXq7WiEeTuON8K861feHufWsqweqDMjUlZHWKyOFs2Y4dkRqV/8wvlXki1bzI/ZvVuNA8+fr98mL5S8N1n8X/I3HMGxx1V2Ca78CJArl+p0jql0lGnPHhGg7FLd0v7NTX8tzswUeRXT5Rjay4Y1Z0x/RkVFjqu5nTuLnDxpeoikpTneTtu3m8efPi3St6+KnzVL5PJl82M2bHCc45tvzOMzMx3xn3xiHs+8mbeZ+pq3CEekyJ3On1errH/2WU23RDl3DujWzfF1QoL5MU884XjeqZNjBXkjkZHqVyUvXBxVd4RJZ4+68nFmk8GXfb3MpaUJYm+PdW0rFgDo1Qu4807EpfvgwhzgseGJphPzu3QB5jadi444jkF/MN8Kyc/PsT9z795qEquZPn0cz3V23mnRQq2yAKjdfRo2ND+m/LaNt95qHt+lC9C0qXo+dKh5PPNm3mbqa96exEKqLhAxvzW/vJ9/Vqtw//WvnmtP8dXCoFijQDhxAsjMdHy9Y4f5WPDo0Y5/ec884zWb8bpCZ1Vwe5zZHnUVxVVGIHj8s8cx8raR1bs0AQDMmAFflKKwNAh49FGtcxMReaPa++lTl2VlqYU7dE2dCrRq5bHmWPbqq2qbDUCtxbRunXH8bbepxS7txdAzz5gvHRAYqM4THQ3Exla5yTWlqiNM1xZTrix++ZcDf8HSB5e6vjRB6YPOSxO0TDBdmgC/+Q3ewyg8gz871t4iIqqFWEh5ow4d1Oa0uv7v/zzXFkAtCmJ34oR5/KVLzl/rrMo2fbqaAdmsGTBqlF67Hn8c+OILoFEjvfhqYvUyXVVHmMof5+ril+N6jXP5Ul28byRWrAf8S4AV64H4GzUus/r6IhbvYRnGa7WTiMhbsZDytNJS4J//tH7cp5+6vy2uuHhRrd5md+ut5kviTprk2O6kRQvgkUfMzxMTAzz1FLBkid5FeC/l6mU6u2uLKSuX6ezHubr4peM4WLtUN2ECxhzwR94cYHR2a+1fAjp1Al54QSsUAPDcc0DLlvrxN96o3oZW9nZ++GE1D0RXdLQ6h5Udo5i3Huath3nrH+Mp3LTYIsubHr75pprcvHu3muysw8pGuYB6R50/rxd/5QqwYoXaTLdbN7WHnNFlwdJSNRPwyBH1dWiouvToZ7wHG8aMAVavBubMAZ59Vi8PL6Wz5xygt3nvtXGVscGGJQ8uwZSNU1BUon+Z19/XH/nP5sPP18/wPJW2Lz8fK3/VHAkxRRColRBWDHgT8b980vjEjz0GLF8OvPGGKog1FBQAAQHWFoAvKLBWZ1uNLylRb3mzt3dV28S8PXcO5m2uvubtqU2LOSLlafbNg6693FVT3n1XFVGAWvBjyhTjeB8fNWcJUP8innpK719fYiLw1lvq8lstVlsnggNwbTJ448aIL7rVcaluV0vE9zV5jwCqv1evBsaN02oroP4DtLqLjtXBSqvxvr7WPlxcOQfz9uw5rGDenjuHN+btKSykaru0NMfClG+9pX7NMHLnnc5f6+xtN3o0EBys3rW6H5Th4apIu/FGvfhqVF1LDdT0RHAAiO/0O6zIvc8xGRww3ewX06cjPh3InwPE//ZlvTsi27RR7xM3/pZHRFQbsJDyJqWlwMsvO77WmScVX+4D8cknzedj3XGHukMOUHdLjR1rfo7AQLU87fbtqqCqxap7hKmmJ4Jj9WrEL0hxjDAd72F+R93vfge0bg2/4BvVTqJERFQpFlLeZNcu59l548ebz3t66CE1Tguo0QD7ymlG7JfqHn8cCArSa9sdd6iFFL2M7ugS4P4RppqZCG5xzabhwwFfX8cIU/QMw/MCUDM49+4FDh5URTQREVWKhZQnbd8OzJ2rnk+dqjY2MtK7N9C2rXru66vWRzK7yDx5siNm8mSgcWPzdsXEAEePArNnm8d6Md3RJXusO0eYXF0RvLik2LSYqvQyXUQ8VgQ+7Lxm08C3jUeY2rYtu63FL1T/jjq0agWEhenFEhHVYyykPGnFCsfz9HTgH/8wjm/QwHljYLOJ4ID6sIuNVfOXJk3Sa5ePD9Cxo9etvwS4f/5S+Vh3jjDVyERwAPGr9zuv2XS5W4VxTp5+Ws1VmzHDsSwFERG5BZc/sKjs9skBA9Bk82bHZbWK7NoFREWp5w0aqGUDzH7Lz8tTazU98IC6nbweWZm+EhM+n4DFgxcbjrJUVPBUVoB4eqmBhYMWYvxn402/f4XF0c8/Y+XIW5DQ57RjqYFhycYjTMuXA489hmIfwO+mzmprnVq8PQ4RUXXh8gfeZts2x91ylenTx3GX3MiRepdKgoJUwVUHiqianL9kFHutqowwVWkieHY24r847Rhh+ioU8T1M9p37wx+AG2+EXylq/R6DRER1Af8XdtXIkUBz813okZQE3HWX8yW7eqAm5y+tTF9ZrUsNuDwRvHt3YMAAxO/zURPBR8zR22PwtdfU1ue1eI9BIqK6gpf2LCobGvzqKzS5dk2mOs7dK3xfG3ut8sfqji6VPw6A5WPMzmW4Yvnzg5HQYIPjMl2LsYiftOK6OCdffKEm/zdvDpw8qZYCJiIit+OlPW/TtWtNt6BauXv9pYpir1XVO+Rib4+t1qUG4hvd4zwRvFWMeWOjo9Uk8KVLWUQREdVCHJGyyFMVbU2ozj3krj3O6ghTXI84rM5YbXl0yWq7yuTnY2V0CyREF+jvOffzz0CbNiguKoBfm3ZqiQmjmxGIiKjacESqnjh7Vq1kMGyY/jGxseqmwBMn9OJ37ABsPVci8GULI0xSO+cvAVdHmAYthk1gac+5R/M6Y9nVEablXzY333OuWTPs6/Uo/EqBbwc9pVVEVVt/25wXzTciovazbtdO7XGt43//V51j40a9eOatFw8wb+ZtjHnrn8NjhCzJzc0VAJKbm+uR7//yyyKACHyL5LvvzONPnBDx9RWBT5HMmKF3jh6PJgsSbYJEiC3JJsl7kyuMS96bLLYkmyAJ1z3KH2cUV9lxrhxjpU3XWbRIkiMgtkSovBNReexV+57+PxFACnwgX499x/TnWlwsEhF2Sn6Lv0tM3zzTeBFHf9tsYq2/Idr9PWyYim/eXOTyZfP4jRuvvgch8ve/m8cXF4u0bavi+/XTaxPzZt5GmDfzNmM1bxHPfX6zkLLIk4VUQYFISIgIIpIFz/tL/2nGH/QiIjNnith6qviGUcmSZ/L5/eomRxFlVIDoFDq2JJss3bNU/F/y1yqI7A//l/yl6EqR9jkqaptTDiYFoYjI8S2ZIoAkR0D8n4fMnDTa9Gcb3a9QctBSziNY+kbkm8b/4x+O/6AAkYwM4/iy/ob6T2TiRNNTyMyZjv9wgoLEtL8PH1b/mdnbtHKl+TkGDFDn8PERiYw0j2fezNsI82beZqojbxHPfX7z0l410F1PKT0dONNuJTA0AfAtwtagBCTvNb70tnr/SsgQFV8QnYDEj41X+H52VwIAQfkrZDW1wrd9UjeumdRdPrayrVIGbhtftlUKAEzraLyI56eZXfAZBiM+Hcia0xT/zVpi2M78fGDrl/7oja/QA+nYua8xTp82zu2zz5y/3rDBOD49HThzRj0vKQE++QSmWyt+8omKBdTarWlpxvGbNjl/z/XrjePz89XORiUlag/tvXvBvCvBvBXmXTHm7T15e5xby7J6wGpFm7w3Wfxf8je9jCQisuLrZEGS+WhR+e+tG+/pEaZle5a5NLrkSt4iIpc6dC0bXUqOgJRu3GT4s710SWTFH7aKADI3MFFruPnTTx2/8Xz0kXn8sWMit96q4hMSRMzeIqWlIsnJjnPs2GF+jq++csQvXqy+h5FLl0See07Fh4ToDbMzb+ZthHkzbyPemrcIL+1d5+WXX5aoqCgJDAyU4OBgrWPi4uIEagyj7HHXXXdZOq+VjihfvJgVBlbn/liJtzofaczHY6p3/lJ+viSPvMXS/CWZN09KYJNCH4i0bq0u5Js4crhUGuKSjHrkimmsnf0ft64ZM1R8aqr+MVbP0bSptfgjR1T8yJGeaxPz9tw5mLce5u25NtWVvHlp7xpFRUUYMWIEJkyYYOm4mJgYnDp1quyxwWycshJr9q0x/HtPrKeke+mt1q3w/Z//IP4v/3GswfRlc/OtUhISUIBA+JcCmDZNbzNemw0FCIT4cEkCIiJyj1q7Ffzs2bMBAO+++66l4wICAhAaGlrl80/eMBmBNwRaWk/JXuAAsLyekv3Y7VnbtdZTKn+uxYMXW1qzyb5psK+Pr+X1l+Ij4oGUFCTkroHI1fWXujxlvBFvZCQQGYm4PXsxal8pAha8aL5VSpMmmB/wLIYU/h13JCSY5kVEROQJtXZEylUpKSlo2bIlunTpgnHjxuG02Uw7AzWxntK7Ge9aiq+RFb6PN3Ne4ft8uHljp0+HL0pRVHoD8KjJaNRV8wKfRw/sB4KDteKJiIjcrV4VUoMGDcL777+Pf/3rX5g3bx52796NAQMGoLCwsNJjCgsLceHCBaeHXVXudktYn4A1+9dg8eDFlu54G9NjTJXukKvs2EpHmLr9Hiu2NS27Q84mwIqBbxuPMD35JB7NsCF/DhD3fTAQF2fe2OHD8Q/fR/DJ3a8DQUFa+Y0dqxVWxr6Q7a9+pX/MvfcCt9+uH9+nj/ozLEz/mEaNrOXCvPUwb/1jmLce5q1/jDfm7SletUVMUlJS2SW7yuzevRuRkZFlX7/77ruYOnUqzp8/b/l8p06dQocOHfDBBx/goYcestammQAaqqc22LDkwSWYsnEKikqKtM/v7+uP/GfzsWb/GtMCzOoGvpUVRiv3JiPh0wR166jNOBaAWvq2Qwckt8rGxMHA4q2NEP/Pq8vWGvntb4G1a4FZs4BXXjGOvernn4GmTQEfzfJeRB3TvLlePKBW3LUSX1Cgbstt3Nhz52DeevHM23NtYt6eOwfz1ouvjrw9tUWMVxVSZ86cwRn7AhSV6NixIxqW+xCvSiEFADfffDMSEhIwY8aMCv++sLDQacTqwoULaNeunVMhBVT/fnAu7R8HAO+9h5XzY5EwVF2tswFYMSzZeIRp/nzg6adR7Av4PZ8IJCaa5odvvgHWrAH++EfADXPSiIiIqsJThZRXTTYPCQlBSEhItZ3v7Nmz+OGHHxBmMF4ZEBCAgIAA0+9V/m638Z+NtzxaZH9etq+dyWiRI36s/ugSANx0E+LT1dMJg4HF/sONiyhAjbm+8AL8iosB3bsku3cH5s7ViyUiIqqlau0cqaysLGRkZCArKwslJSXIyMhARkYG8vPzy2K6deuGdevWAQDy8/Px9NNPIy0tDceOHUNKSgqGDBmCkJAQDB8+vMrtsc9HGtdrnEtzkQAgvsejWHFjnGM+EmA8qTsiHit2t3aev3SzyR1yUVFAr16ITwfy5/kjfuJy8+SCg9XSsevXAy1bmscTERHVE7W2kHrxxRcRERGBxMRE5OfnIyIiAhEREdizZ09ZTGZmJnJzcwEAvr6+OHDgAIYNG4YuXbogLi4OXbp0QVpaGoI0JzdXxm3rKf3734h/8l3HHW+pTU3XU4rv9Dus+NSm4jc2QPyvnzNprA2YPh0A4BcXr3+B+f77gZgYvVgiIqJ6wqvmSNUG9mus9jlSRsXRyvWzkbA3yTEX6b55iO8/rfJvXlgItG0LnDmDYj8f+CWMBxYtMm7Q0aNAp04otgn8Jk0B3nrLPIkrV4CvvgK6drU2U4+IiKiW8tQcqVo7IuUNTNdT+sdh5/WUdl42/oYBAcDUqQAAvyuiJmqbCQ8Hhg+HH3zKjjXVoAFw990sooiIiKqII1IWlR+RSh6xAvE9DRa/+Oc/gYEDUewD+IkNOHJEFT5Gzp4F2rQBoqP1t7S+fFk9mjXTT4SIiKgeqRd37dUmCzcC8dOGGgfdfz/wi1/A79tvgYeGmxdRgBolumwycnWtwED1ICIiomrFS3suiu38W6BFC+Mgmw144QWgQwfgmWf0v7nNZr7XHBEREdU4XtqzqGxocOtWNOnXr6abQ0RERBo42dzb9OxZ0y0gIiKiGsZCioiIiMhFLKRcVFqqF7d6tZpKtX27XnxeHtC+PfDYY/ptmTZN7cr900968enpqk3vvKMXLwL06wdERjJvM8xbL55568UDzJt5G2Pe+ufwGCFLcnNzBYB8+GGuaWxpqcjNN4sAIkOG6H3/N99U8b6+Ij/8YB7/008iAQHqmD/9Se8co0ap+DZtRIqLzeO3b1fxgMiGDebxzJt5m2HezNsI82beZqzmLeL4/M7NNf/8toKFlEX2jujb17wjNmxwvGFtNpHvvjOOLy4WadvW8QacPt28PS+9JOLjo45p1kzk8mXj+BMn1Pe2t+tvfzM/x9Ch6hhfX5F+/czjmTfzNsK8mbcZ5s28jbiStwgLKa9h7wggV3780Tj2D39wdDQg8vLLxvFffukcHxamfhsw0qWL8zGbNhnHv/WWc/zQocbxeXnOb1hAmHclmDfzNsK8mTfzrpin87ZjIeUl7B0xb555Rxw8qN5EgMiwYeZv2JISVZnb3xzr15u354svHPEvvmg+xHn+vMi4cSq+QQORr782P0dysuMcixaZxzNv5m2EeTNvM8ybeRtxJW8RFlJew2pHzJihOjs1Vf8c9jeUrqZNrcUfOaLiR470XJuYt+fOwbz1MG/PtYl5e+4czFuPK3l7qpDiXXtERERELmIhRUREROQiFlJERERELmIh5WG33qr+bN7c2nFDhujHDh1q7Xs3aqT+jIzUP6ZzZ/M9mstj3vrHAMxbB/PWw7z1j2HeeupK3p7CTYstcmXTw8OH1RtX1/HjaoVXf3+9+JISICsLCA/XP8fhw0CnToDNphd//jxQXGztHx/z1sO89eKZt7U2MW9zzNvaOWp73p7atJiFlEWe6ggiIiLyHE99fvPSHhEREZGLWEgRERERuYiFFBEREZGLWEgRERERuYiFFBEREZGLWEgRERERuYiFFBEREZGLWEgRERERuYiFFBEREZGLWEgRERERuYiFFBEREZGLWEi5SHeHwo8/Bm67Ddi7Vy++oADo3Rt4/nn9tsyZA0REABcu6MVnZqo2vf++/jlGjlS7czNvY8xbL55567eJeevFM2/9c9TXvD1GyJLc3FwBIBs25JrGlpaK9OghAog88oje91++XMX7+4ucPq3THpHGjdUx8+frnWP8eBXfubNISYl5/N69Kh4QSU01j2fezNsM82beRpg38zZjNW91HvX5nZtr/vltBQspi+wdERNj3hHbtjnesL6+IllZxvGlpSI33yxis4n4+Ij86U/m7VmwQMUDIm3aiBQXG8f/9JN6c9vb9fnn5ucYNUq139dXZMgQ83jmzbyNMG/mbYZ5M28jruQtwkLKa9g7AsiVH380jo2NdXQ0IPLKK8bxO3c6x7durd6URrp2dT5m0ybj+Lffdo4fOtQ4Pi9PpEEDR7zNJsy7EsybeRth3sybeVfM03nbsZDyEvaOmDHDvCN27RJp2FB19D33iBw7ZhxfXCwycaLjzbFypXl7PvjAEZ+QIHL5snF8To7IsGGOY7ZuNT/HnDmO+BdfNI9n3szbCPNm3maYN/M24kreIiykvIbVjpgxQ3W0zrVoO/ubQ1fTptbijxxR8SNHeq5NzNtz52Deepi359rEvD13Duatx5W8PVVI1cq79o4dO4axY8ciPDwcgYGB6NSpExITE1FUVGR4nIggKSkJrVu3RmBgIPr164eDBw9WU6uJiIiorqmVhdShQ4dQWlqKpUuX4uDBg1iwYAGWLFmCWbNmGR73+uuvY/78+Vi4cCF2796N0NBQDBw4EHl5edXUciIiIqpLGtR0A1wRExODmJiYsq9vuukmZGZmYvHixXjjjTcqPEZE8Oabb+K5557DQw89BABYvXo1WrVqhb/85S8YP358tbSdiIiI6o5aWUhVJDc3F82aNav0748ePYqcnBxER0eXvRYQEID77rsPO3furLSQKiwsRGFhodN5AOCC5qphISHqT5tNf6ExAIiM1I/v3RvYvFk/3n4FtH17/WMaNwYuXtSPZ97MWwfzNse89eKZN/M2Y//cFhG9A3S5dcZVDTl8+LA0adJEli9fXmnMl19+KQDk5MmTTq+PGzdOoqOjKz0uMTFRAPDBBx988MEHH3XgceTIEbfVHyIiXjUilZSUhNmzZxvG7N69G5GRkWVfZ2dnIyYmBiNGjEBCQoLpOWw2m9PXInLda+U9++yzmDZtWtnX58+fR4cOHZCVlYXg4GDT89UVFy5cQLt27fDDDz+gSZMmNd2casO8mXd9wLyZd32Qm5uL9u3bG169coVXFVKTJ0/GI488YhjTsWPHsufZ2dno378/oqKisGzZMsPjQkNDAQA5OTkICwsre/306dNo1apVpccFBAQgICDguteDg4Pr1RvQrkmTJsy7HmHe9Qvzrl/qa94+Pu69z86rCqmQkBCE2C/Gmjh58iT69++PXr16YdWqVaY/mPDwcISGhmLLli2IiIgAABQVFSE1NRVz586tctuJiIio/qmVyx9kZ2ejX79+aNeuHd544w389NNPyMnJQU5OjlNct27dsG7dOgDqkt7UqVMxZ84crFu3Dt988w3GjBmDRo0aYeTIkTWRBhEREdVyXjUipWvz5s04fPgwDh8+jLZt2zr9nZSbjZ+ZmVl2lx0ATJ8+HZcvX8bEiRNx7tw53HXXXdi8eTOCgoK0zx0QEIDExMQKL/fVZcybedcHzJt51wfM271520TcfR8gERERUf1QKy/tEREREXkDFlJERERELmIhRUREROQiFlJERERELmIhZeLYsWMYO3YswsPDERgYiE6dOiExMRFF9o1+KiEiSEpKQuvWrREYGIh+/frh4MGD1dRq93jllVdw9913o1GjRmjatKnWMWPGjIHNZnN69OnTx7MNdTNX8q4L/X3u3DnExsYiODgYwcHBiI2Nxfnz5w2PqY39vWjRIoSHh6Nhw4bo1asXtm/fbhifmpqKXr16oWHDhrjpppuwZMmSamqpe1nJOyUl5bp+tdlsOHToUDW2uOq2bduGIUOGoHXr1rDZbPj4449Nj6kL/W0177rQ36+++iruvPNOBAUFoWXLlvjNb36DzMxM0+Pc0d8spEwcOnQIpaWlWLp0KQ4ePIgFCxZgyZIlmDVrluFxr7/+OubPn4+FCxdi9+7dCA0NxcCBA5GXl1dNLa+6oqIijBgxAhMmTLB0XExMDE6dOlX22LBhg4da6Bmu5F0X+nvkyJHIyMjApk2bsGnTJmRkZCA2Ntb0uNrU33/7298wdepUPPfcc0hPT8e9996LQYMGISsrq8L4o0eP4te//jXuvfdepKenY9asWXjiiSfw0UcfVXPLq8Zq3naZmZlOfXvzzTdXU4vd4+LFi7jjjjuwcOFCrfi60t9W87arzf2dmpqKSZMmYdeuXdiyZQuuXLmC6OhoXLx4sdJj3Nbfbt25r554/fXXJTw8vNK/Ly0tldDQUHnttdfKXisoKJDg4GBZsmRJdTTRrVatWiXBwcFasXFxcTJs2DCPtqe66OZdF/r722+/FQCya9eustfS0tIEgBw6dKjS42pbf/fu3Vsef/xxp9e6desmM2fOrDB++vTp0q1bN6fXxo8fL3369PFYGz3Bat5bt24VAHLu3LlqaF31ACDr1q0zjKkr/V2eTt51sb9Pnz4tACQ1NbXSGHf1N0ekXJCbm2u46eHRo0eRk5OD6OjostcCAgJw3333YefOndXRxBqVkpKCli1bokuXLhg3bhxOnz5d003yqLrQ32lpaQgODsZdd91V9lqfPn0QHBxsmkNt6e+ioiJ8/fXXTv0EANHR0ZXmmJaWdl38Aw88gD179qC4uNhjbXUnV/K2i4iIQFhYGO6//35s3brVk830CnWhv6uiLvW3fTFuo89qd/U3CymLjhw5grfffhuPP/54pTH2rWqu3Qy5VatW121jU9cMGjQI77//Pv71r39h3rx52L17NwYMGIDCwsKabprH1IX+zsnJQcuWLa97vWXLloY51Kb+PnPmDEpKSiz1U05OToXxV65cwZkzZzzWVndyJe+wsDAsW7YMH330EdauXYuuXbvi/vvvx7Zt26qjyTWmLvS3K+paf4sIpk2bhr59+6J79+6Vxrmrv+ttIZWUlFTh5Lryjz179jgdk52djZiYGIwYMQIJCQmm57DZbE5fi8h1r1U3V/K24uGHH8bgwYPRvXt3DBkyBBs3bsR3332Hzz//3I1ZWOfpvIHa398VtdUsB2/tbyNW+6mi+Ipe93ZW8u7atSvGjRuHnj17IioqCosWLcLgwYPxxhtvVEdTa1Rd6W8r6lp/T548Gfv378df//pX01h39Het3GvPHSZPnoxHHnnEMKZjx45lz7Ozs9G/f39ERUVh2bJlhseFhoYCUNVuWFhY2eunT5++rvqtblbzrqqwsDB06NAB33//vdu+pys8mXdd6O/9+/fjxx9/vO7vfvrpJ0s5eEt/VyQkJAS+vr7XjcIY9VNoaGiF8Q0aNEDz5s091lZ3ciXvivTp0wfvvfeeu5vnVepCf7tLbe3vKVOmYP369di2bdt1e/Fey139XW8LqZCQEISEhGjFnjx5Ev3790evXr2watUq+PgYD+SFh4cjNDQUW7ZsQUREBAA1TyE1NRVz586tcturwkre7nD27Fn88MMPTgVGTfBk3nWhv6OiopCbm4uvvvoKvXv3BgD8+9//Rm5uLu6++27t83lLf1fE398fvXr1wpYtWzB8+PCy17ds2YJhw4ZVeExUVBQ+/fRTp9c2b96MyMhI+Pn5ebS97uJK3hVJT0/3yn51p7rQ3+5S2/pbRDBlyhSsW7cOKSkpCA8PNz3Gbf1taWp6PXTy5Enp3LmzDBgwQE6cOCGnTp0qe5TXtWtXWbt2bdnXr732mgQHB8vatWvlwIED8vvf/17CwsLkwoUL1Z2Cy44fPy7p6ekye/ZsueGGGyQ9PV3S09MlLy+vLKZ83nl5efLUU0/Jzp075ejRo7J161aJioqSNm3a1Om8RepGf8fExMjtt98uaWlpkpaWJrfddps8+OCDTjG1vb8/+OAD8fPzk+TkZPn2229l6tSp0rhxYzl27JiIiMycOVNiY2PL4v/73/9Ko0aN5I9//KN8++23kpycLH5+fvLhhx/WVAousZr3ggULZN26dfLdd9/JN998IzNnzhQA8tFHH9VUCi7Jy8sr+/cLQObPny/p6ely/PhxEam7/W0177rQ3xMmTJDg4GBJSUlx+py+dOlSWYyn+puFlIlVq1YJgAof5QGQVatWlX1dWloqiYmJEhoaKgEBAfLLX/5SDhw4UM2tr5q4uLgK8966dWtZTPm8L126JNHR0dKiRQvx8/OT9u3bS1xcnGRlZdVMAi6ymrdI3ejvs2fPyqhRoyQoKEiCgoJk1KhR190OXRf6+5133pEOHTqIv7+/9OzZ0+n26Li4OLnvvvuc4lNSUiQiIkL8/f2lY8eOsnjx4mpusXtYyXvu3LnSqVMnadiwodx4443St29f+fzzz2ug1VVjv63/2kdcXJyI1N3+tpp3Xejvyj6ny/8/7an+tl1tABERERFZVG/v2iMiIiKqKhZSRERERC5iIUVERETkIhZSRERERC5iIUVERETkIhZSRERERC5iIUVERETkIhZSRERERC5iIUVERETkIhZSRFTv7dixA35+figsLCx77ejRo7DZbDh+/HgNtoyIvB0LKSKq9zIyMnDLLbcgICDA6bWmTZuiQ4cONdgyIvJ2LKSIqN7bt28fIiIinF7LyMjAHXfcUUMtIqLagoUUEdV7GRkZ6NGjh9Nr6enpLKSIyBQLKSKq10pKSnDw4MHrRqT27t17XXFFRHQtFlJEVK9lZmbi8uXLaN26ddlraWlpOHnyJEekiMgUCykiqtcyMjIAAG+//Ta+//57bNy4EaNHjwYAp7v4iIgqwkKKiOq1jIwMDBw4EEePHkX37t0xa9YsvPbaa2jSpAneeeedmm4eEXk5m4hITTeCiKimPPDAA+jZsydeffXVmm4KEdVCHJEionpt3759uP3222u6GURUS7GQIqJ6KycnBz/++CMLKSJyGS/tEREREbmII1JERERELmIhRUREROQiFlJERERELmIhRUREROQiFlJERERELmIhRUREROQiFlJERERELmIhRUREROQiFlJERERELmIhRUREROQiFlJERERELvr/2d/8tUKbBSEAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Variables for storing equilibrium points for different mu values\n", "saddle_points0 = np.array([])\n", "saddle_points1 = np.array([])\n", "saddle_points2 = np.array([])\n", "\n", "# Range of state variable values\n", "x = np.linspace(-2, 2, 400)\n", "\n", "# Parameters for plotting arrows\n", "stepsize = 0.1\n", "arrow_length = 0.1\n", "arrow_head_width = 0.025\n", "arrow_lw = 1\n", "\n", "# Loop over a range of mu values to analyze bifurcations\n", "for mu in np.arange(-2, 2, stepsize):\n", " a = h(mu, x)\n", " zero_crossings = np.where(np.diff(np.signbit(a)))[0]\n", " \n", " if zero_crossings.size > 2:\n", " saddle_points0 = np.append(saddle_points0, x[zero_crossings[0]])\n", " saddle_points1 = np.append(saddle_points1, x[zero_crossings[1]])\n", " saddle_points2 = np.append(saddle_points2, x[zero_crossings[2]])\n", "\n", " for arrows in np.arange(-2, x[zero_crossings[0]], 0.25):\n", " plt.arrow(mu, arrows, 0.0, arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"blue\")\n", " for arrows in np.arange(x[zero_crossings[0]], x[zero_crossings[1]], 0.25):\n", " plt.arrow(mu, arrows, 0.0, -arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"red\")\n", " for arrows in np.arange(x[zero_crossings[1]], x[zero_crossings[2]], 0.25):\n", " plt.arrow(mu, arrows, 0.0, arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"blue\")\n", " for arrows in np.arange(x[zero_crossings[2]], 2, 0.25):\n", " plt.arrow(mu, arrows, 0.0, -arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"red\")\n", " \n", " elif zero_crossings.size == 2:\n", " saddle_points0 = np.append(saddle_points0, x[zero_crossings[0]])\n", " saddle_points1 = np.append(saddle_points1, x[zero_crossings[1]])\n", " saddle_points2 = np.append(saddle_points2, np.nan)\n", " for arrows in np.arange(-2, t[zero_crossings[0]], 0.25):\n", " plt.arrow(mu, arrows, 0.0, arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"blue\")\n", " for arrows in np.arange(x[zero_crossings[0]], x[zero_crossings[1]], 0.25):\n", " plt.arrow(mu, arrows, 0.0, -arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"red\")\n", " for arrows in np.arange(x[zero_crossings[1]], 2, 0.25):\n", " plt.arrow(mu, arrows, 0.0, arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"blue\")\n", " \n", " elif zero_crossings.size == 1:\n", " saddle_points0 = np.append(saddle_points0, x[zero_crossings])\n", " saddle_points1 = np.append(saddle_points1, np.nan)\n", " saddle_points2 = np.append(saddle_points2, np.nan)\n", " \n", " for arrows in np.arange(-2, x[zero_crossings[0]], 0.25):\n", " plt.arrow(mu, arrows, 0.0, arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"blue\")\n", " for arrows in np.arange(x[zero_crossings[0]], 2, 0.25):\n", " plt.arrow(mu, arrows, 0.0, -arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"red\")\n", " else:\n", " saddle_points0 = np.append(saddle_points0, np.nan)\n", " saddle_points1 = np.append(saddle_points1, np.nan) \n", " saddle_points2 = np.append(saddle_points2, np.nan) \n", " \n", " for arrows in np.arange(-2, 2, 0.25):\n", " plt.arrow(mu, arrows, 0.0, arrow_length, shape='full', lw=arrow_lw, length_includes_head=True, head_width=arrow_head_width, color=\"blue\")\n", "\n", "# Set plot limits\n", "plt.ylim(-2, 2)\n", "plt.xlim(-2, 2)\n", "\n", "# Scatter plot to show equilibrium points\n", "# Green 'D' markers for the first type, black 'o' for the second, etc.\n", "plt.scatter(np.arange(-2, 2, stepsize), saddle_points0, color=\"green\", marker='D')\n", "plt.scatter(np.arange(-2, 2, stepsize), saddle_points1, color=\"black\", marker='o')\n", "plt.scatter(np.arange(-2, 2, stepsize), saddle_points2, color=\"green\", marker='D')\n", "\n", "# Adding labels and legend\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"State $x$ of the system\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that there is a range of values of $\\mu$ for which there are *three coexisting fixed points*, two stable and one unstable. Since there are two stable fixed points in which the system can remain, we say that the system is **bistable**.\n", "\n", "\n", "Now that we understand what the plots mean and the dynamics, let's plot just the fixed points $x^*(\\mu)$ as a function of $\\mu$. Such a plot is called a **bifurcation diagram**:\n", "\n", "The pieces of curve are called **branches**.\n", "\n", "\n", "\n", "## Hysteresis\n", "\n", "\n", "\n", "Suppose we now think about slowly varying the parameter $\\mu$. If we change the parameter $\\mu$ by a little, the system is no longer at a fixed point, since the position of the fixed point moves when $\\mu$ changes. However, the system will then **relax** by following the dynamics at the new value of $\\mu$, and will rapidly converge to the new fixed point nearby.\n", "For example, starting at $\\mu=-2$, the system will stay on the lower black (stable) **branch** until $\\mu=0.4$ or so. At that point, two fixed points collide and annihilate each other! After that there is no longer a fixed point nearby. However, there is another fixed point much further up that will now attract all trajectories, so the system rapidly transitions to that fixed point.\n", "Now suppose we decrease the parameter again. The system will now track the *upper* branch until $\\mu=-0.4$ or so, when again it will jump back down.\n", "For each parameter value $\\mu$ in the interval $[-0.4, 0.4]$ there is **bistability**, i.e. **coexistence** of *two* fixed points with the same value of $\\mu$ (together with a third, unstable fixed point that is not observable).\n", "The fact that the system tracks different stable branches depending on where we started, i.e. on the history, is known as **hysteresis**.\n", "\n", "\n", "Hysteretic behaviour like this is found in many scientific and engineering contexts, including switches in biology, for example genetic switches, and in the historical dynamics of the earth's climate.\n", "\n", "\n", "\n", "## Slow--fast systems\n", "\n", "What are we actually doing when we let the parameter $\\mu$ vary? Effectively we now have a system with *two* equations, for example\n", "\n", "$$\\dot{x} = \\mu + x - x^3;$$\n", "$$\\dot{\\mu} = \\epsilon,$$\n", "\n", "where $\\mu$ varies at some slow speed $\\epsilon$. On a time scale much shorter than $1 / \\epsilon$, the dynamics of $x$ \"does not know\" that $\\mu$ is changing, so it will converge to a fixed point $x^*(\\mu)$ for the current value of $\\mu$. [An associated term is **adiabatic approximation**.] However, $\\mu$ does gradually change, so the value of $x$ will effectively \"slide along\" the curve $x(t) \\simeq x^*(\\mu(t))$, tracking the curve of fixed points as $\\mu$ changes.\n", "Once $\\mu$ reaches a critical value $\\mu_c$, however, there is no longer a nearby fixed point, and the dynamics will rapidly transition to the far away alternative fixed point.\n", "If we now reverse the dynamics of $\\mu$, we slide back along the upper branch." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-Dimensions - one step closer to chaos\n", "\n", "Shifting from one-dimensional to two-dimensional analysis in dynamical systems, as illustrated by the Brusselator model\n", ", marks a significant advance in the complexity and understanding of these systems.\n", "\n", "The Brusselator is used for modeling chemical oscillations, capturing the interactions between different chemical species. The differential equations for the Brusselator model are given by:\n", "\n", "$$\n", "\\dot{x} = A - (B + 1) \\cdot x + x^2 \\cdot y\n", "$$\n", "\n", "and\n", "\n", "$$\n", "\\dot{y} = B \\cdot x - x^2 \\cdot y\n", "$$\n", "\n", "This represents a step towards representing real-world systems, like chemical oscillations, where interactions between components are essential. The 2D Brusselator model, unlike its 1D counterpart, can exhibit a vast range of dynamical behaviors, including oscillations, chaos, and complex attractors. These phenomena, which are invisible in simpler 1D systems, are pivotal for understanding the intricate interactions between variables in a system, where the state of one directly influences the rate of change of another.\n", "\n", "This interplay is captured in phase portraits, a tool unique to 2D analysis, allowing for comprehensive visualization of how systems evolve from different initial conditions. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ea1e8dbff359448a828f2afa93152a0a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=1.0, description='A', max=5.0, min=0.1), FloatSlider(value=1.0, descri…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def brusselator(A, B, X, Y):\n", " dxdt = A - (B + 1) * X + X**2 * Y\n", " dydt = B * X - X**2 * Y\n", " return dxdt, dydt\n", "\n", "@interact\n", "def interactive_brusselator(A=FloatSlider(value=1.0, min=0.1, max=5.0, step=0.1),\n", " B=FloatSlider(value=1.0, min=0.1, max=5.0, step=0.1)):\n", " X = np.linspace(-2, 2, 20)\n", " Y = np.linspace(-2, 2, 20)\n", "\n", " X, Y = np.meshgrid(X, Y)\n", " U, V = brusselator(A, B, X, Y)\n", "\n", " speed = np.sqrt(U**2 + V**2)\n", "\n", " fig, ax = plt.subplots(figsize=(8, 8))\n", " strm = ax.streamplot(X, Y, U, V, density=1.5, color=speed, cmap='viridis', linewidth=1.5, norm=Normalize(vmin=speed.min(), vmax=speed.max()))\n", " cbar = fig.colorbar(strm.lines)\n", " cbar.set_label('Speed')\n", "\n", " ax.set_xlim([-2, 2])\n", " ax.set_ylim([-2, 2])\n", " plt.xlabel('X')\n", " plt.ylabel('Y')\n", " plt.title('Brusselator Model Phase Portrait\\n(A={:.2}, B={:.2})'.format(A, B))\n", " plt.grid(True)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3D: Chaos in the Lorenz equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [Lorenz equations](https://en.wikipedia.org/wiki/Lorenz_system) is a (very) simplified model of convection in a layer of fluid representing the atmosphere, first investigated in a famous paper by Edward Lorenz, published in 1963, about work done at MIT. They represent a pioneering numerical investigation of **chaotic behaviour**.\n", "\n", "The Lorenz equations are a set of three coupled ODEs. They have an apparently simple form, with only two nonlinear terms:\n", "\n", "$$\\begin{align}\n", "\\dot{x} &= \\sigma (y - x) \\\\[6pt]\n", "\\dot{y} &= x (\\rho - z) - y \\\\[6pt]\n", "\\dot{z} &= x y - \\beta z\n", "\\end{align}$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "5844a461ebd0419c80b001fd321b3f60", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=1.0, description='Rho:', max=50.0), Output()), _dom_classes=('widget-i…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parameters\n", "sigma = 10.0\n", "beta = 8.0 / 3.0\n", "\n", "# Lorenz equations\n", "def lorenz(t, state, rho):\n", " x, y, z = state\n", " dxdt = sigma * (y - x)\n", " dydt = x * (rho - z) - y\n", " dzdt = x * y - beta * z\n", " return [dxdt, dydt, dzdt]\n", "\n", "@interact\n", "def interactive_lorenz(rho=widgets.FloatSlider(value=1.0, min=0.0, max=50.0, step=0.1, description='Rho:')):\n", " # Initial conditions and time span\n", " initial_state = [0.0, 1.0, 0.0]\n", " t_span = (0, 50)\n", " t_eval = np.linspace(*t_span, 5000)\n", " sol = solve_ivp(lorenz, t_span, initial_state, args=(rho,), t_eval=t_eval)\n", " x, y, z = sol.y\n", " # Create a 3D plot\n", " fig = plt.figure()\n", " \n", " ax = fig.add_subplot(111, projection='3d')\n", " ax.view_init(elev=15, azim=80) # elev=90 makes Z vertical, azim=0 sets the view angle\n", " \n", " ax.clear()\n", " ax.plot(x, y, z, lw=0.5)\n", " ax.set_xlabel('X')\n", " ax.set_ylabel('Y')\n", " ax.set_zlabel('Z')\n", " ax.set_title(f'Lorenz Attractor (Rho={rho})')\n", " plt.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deterministic chaos occurs when nearby initial conditions separate exponentially fast in state space. This has been given the name **butterfly effect**: the perturbation to the atmosphere's state caused by a butterfly flapping its wings could end up being magnified to modify the direction in which a tornado moves. \n", "\n", "We can see this in a simple way by perturbing the initial condition slightly and calculating the distance between the two systems as a function of $t$:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ad383f9d3bad441ca97780cfd967ce05", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.01, description='Time:', min=0.01), Output()), _dom_classes=('widget…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parameters\n", "sigma = 10.0\n", "beta = 8.0 / 3.0\n", "rho = 28\n", "# Lorenz equations\n", "def lorenz(t, state, rho):\n", " x, y, z = state\n", " dxdt = sigma * (y - x)\n", " dydt = x * (rho - z) - y\n", " dzdt = x * y - beta * z\n", " return [dxdt, dydt, dzdt]\n", "\n", "@interact\n", "def interactive_lorenz(tmax=widgets.FloatSlider(value=0.01, min=0.01, max=100.0, step=0.1, description='Time:')):\n", "\n", " initial_state = (0.01, 0.01, 0.01)\n", " epsilon = 1e-10\n", " peturbed_state = (0.01+epsilon, 0.01+epsilon, 0.01+epsilon)\n", " \n", " t_span = (0, tmax)\n", " t_eval = np.linspace(*t_span, 5000)\n", "\n", " solution1 = solve_ivp(lorenz, t_span, initial_state, args=(rho,), t_eval=t_eval)\n", " solution2 = solve_ivp(lorenz, t_span, peturbed_state, args=(rho,), t_eval=t_eval)\n", " \n", " x1, y1, z1 = solution1.y\n", " x2, y2, z2 = solution2.y \n", " # Create a 3D plot\n", " fig = plt.figure(figsize=(12,8))\n", " \n", " ax = fig.add_subplot(111, projection='3d')\n", " ax.view_init(elev=15, azim=150) # elev=90 makes Z vertical, azim=0 sets the view angle\n", " \n", " ax.clear()\n", " ax.plot(x1, y1, z1, lw=0.25, color=\"orange\", alpha=1)\n", " ax.plot(x2, y2, z2, lw=0.25, color=\"blue\", alpha=1)\n", "\n", " ax.set_xlabel('X')\n", " ax.set_ylabel('Y')\n", " ax.set_zlabel('Z')\n", " ax.set_title(f'Lorenz Attractor')\n", " plt.draw()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "initial_state = (0.01, 0.01, 0.01)\n", "epsilon = 1e-10\n", "peturbed_state = (0.01+epsilon, 0.01+epsilon, 0.01+epsilon)\n", "\n", "# Parameters\n", "sigma = 10.0\n", "beta = 8.0 / 3.0\n", "rho = 28." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "t_span = (0, 100)\n", "t_eval = np.linspace(*t_span, 50000)\n", "\n", "solution1 = solve_ivp(lorenz, t_span, initial_state, args=(rho,), t_eval=t_eval)\n", "solution2 = solve_ivp(lorenz, t_span, peturbed_state, args=(rho,), t_eval=t_eval)\n", "\n", "distances = np.sqrt(np.sum((solution2.y - solution1.y)**2, axis=0))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Distance between two initial conditions')" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(distances)\n", "plt.ylabel(\"Distance between two initial conditions\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We indeed see a significant window over which the distance grows exponentially (straight line on the semi-logarithmic graph) for large enough values of $\\rho$, before it saturates at a value of the order of the diameter of the attractor. \n", "\n", "Since the Lorenz equations model the atmosphere, we could expect that the dynamics of the atmosphere are at least as complicated.\n", "\n", "We can also plot the $x$ coordinate of each trajectory for comparison:\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 't')" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(solution2.y[0], alpha=0.5)\n", "plt.plot(solution1.y[0], alpha=0.5)\n", "plt.ylabel(\"x(t)\")\n", "plt.xlabel(\"t\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{important}\n", "Now let's look at the \"climate\" in this model, namely the average value of each coordinate over a long time.\n", "```" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 6.49853417 6.9047668 23.62573919]\n", "[ 6.50016063 6.93978189 23.62765838]\n" ] } ], "source": [ "t_span = (0, 1000)\n", "t_eval = np.linspace(*t_span, 5000)\n", "\n", "solution3 = solve_ivp(lorenz, t_span, initial_state, args=(rho,), t_eval=t_eval)\n", "solution4 = solve_ivp(lorenz, t_span, peturbed_state, args=(rho,), t_eval=t_eval)\n", "\n", "print(np.mean(np.abs(solution3.y), axis=1))\n", "print(np.mean(np.abs(solution4.y), axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the average mean value of each component is approximately the same, even though the individual trajectories are wildly different. This is an example of how statistical properties can be the same, even if individual behaviour is very different, and motivates the idea that climate -- i.e. \"average weather\" -- can be stable, even if day-to-day variations differ a lot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{note}\n", "Thanks a lot to [David P. Sanders](https://github.com/dpsanders) for providing the lecture. The original lecture is part of the MIT class [Introduction to Computational Thinking](https://computationalthinking.mit.edu/Fall20/lecture20/).\n", "\n", "This class uses the [Julia programming language](http://www.julialang.org/). The orignal code can be found under [github.com](https://github.com/mitmath/18S191/blob/master/lecture_notebooks/week11/nonlinear_dynamics_bifurcations.jl)\n", "````" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" } }, "nbformat": 4, "nbformat_minor": 4 }