Buckets:
| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "###### Content under Creative Commons Attribution license CC-BY 4.0, code under MIT license (c)2014 L.A. Barba, G.F. Forsyth. Partly based on David Ketcheson's pendulum lesson, also under CC-BY." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Phugoid Oscillation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Welcome back! This is the second Jupyter Notebook of the series _\"The phugoid model of glider flight\"_, the first learning module of the course [**\"Practical Numerical Methods with Python.\"**](https://openedx.seas.gwu.edu/courses/course-v1:MAE+MAE6286+2017/info)\n", | |
| "\n", | |
| "In the [first notebook](https://nbviewer.jupyter.org/github/numerical-mooc/numerical-mooc/blob/master/lessons/01_phugoid/01_01_Phugoid_Theory.ipynb), _\"Phugoid Motion\"_, we described the physics of an aircraft's oscillatory trajectory, seen as an exchange of kinetic and potential energy. This analysis goes back to Frederick Lanchester, who published his book _\"Aerodonetics\"_ on aircraft stability in 1909. We concluded that first exposure to our problem of interest by plotting the flight paths predicted by Lanchester's analysis, known as _phugoids_.\n", | |
| "\n", | |
| "Here, we will look at the situation when an aircraft is initially moving on the straight-line phugoid (obtained with the parameters $C=2/3$, $\\cos\\theta=1$, and $z=z_t$ in the previous analysis), and experiences a small upset, a wind gust that slightly perturbs its path. It will then enter into a gentle oscillation around the previous straight-line path: a _phugoid oscillation_.\n", | |
| "\n", | |
| "If the aircraft experiences an upward acceleration of $-d^2z/dt^2$, and we assume that the perturbation is small, then $\\cos\\theta=1$ is a good approximation and Newton's second law in the vertical direction is:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "L - W = - \\frac{W}{g}\\frac{d^2 z}{dt^2}\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "In the previous notebook, we saw that the following relation holds for the ratio of lift to weight, in terms of the trim velocity $v_t$:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "\\frac{L}{W}=\\frac{v^2}{v_t^2}\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "This will be useful: we can divide Equation (1) by the weight and use Equation (2) to replace $L/W$. Another useful relation from the previous notebook expressed the conservation of energy (per unit mass) as $v^2 = 2 gz$. With this, Equation (1) is rearranged as:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "\\frac{d^2z}{dt^2} + \\frac{gz}{z_t} = g\n", | |
| "\\end{equation}\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Look at Equation (3) for a moment. Does it ring a bell? Do you recognize it?\n", | |
| "\n", | |
| "If you remember from your physics courses the equation for _simple harmonic motion_, you should see the similarity! \n", | |
| "\n", | |
| "Take the case of a simple spring. Hooke's law is $F=-kx$, where $F$ is a restoring force, $x$ the displacement from a position of equilibrium and $k$ the spring constant. This results in the following ordinary differential equation for the displacement:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| " \\frac{d^2 x}{dt^2}= -\\frac{k}{m}x\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "which has the solution $x(t) = A \\cos(\\omega t- \\phi)$, representing simple harmonic motion with an angular frequency $\\omega=\\sqrt{k/m}=2\\pi f$ and phase angle $\\phi$.\n", | |
| "\n", | |
| "Now look back at Equation (3): it has nearly the same form and it represents simple harmonic motion with angular frequency $\\omega=\\sqrt{g/z_t}$ around mean height $z_t$. \n", | |
| "\n", | |
| "Think about this for a moment ... we can immediately say what the period of the oscillation is: exactly $2 \\pi \\sqrt{z_t/g}$ — or, in terms of the trim velocity, $\\pi \\sqrt{2} v_t/g$.\n", | |
| "\n", | |
| "_This is a remarkable result!_ Think about it: we know nothing about the aircraft, or the flight altitude, yet we can obtain the period of the phugoid oscillation simply as a function of the trim velocity. For example, if trim velocity is 200 knots, we get a phugoid period of about 47 seconds—over that time, you really would not notice anything if you were flying in that aircraft.\n", | |
| "\n", | |
| "Next, we want to be able to compute the trajectory of the aircraft for a given initial perturbation. We will do this by numerically integrating the equation of motion." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Prepare to integrate" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We want to integrate the differential equation and plot the trajectory of the aircraft. Are you ready?\n", | |
| "\n", | |
| "The equation for the phugoid oscillation is a second-order, ordinary differential equation (ODE). Let's represent the time derivative with a prime, and write it like this:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "z(t)'' + \\frac{g \\,z(t)}{z_t}=g\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "There's a convenient trick when we work with ODEs: we can turn this 2nd-order equation into a system of two 1st-order equations. Like this:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{eqnarray}\n", | |
| "z'(t) &=& b(t)\\\\\n", | |
| "b'(t) &=& g\\left(1-\\frac{z(t)}{z_t}\\right)\n", | |
| "\\end{eqnarray}\n", | |
| "$$\n", | |
| "\n", | |
| "Are you following? Make sure you are following the derivations, even if it means writing the equations down in your own notes! (Yes, the old-fashioned paper way.)\n", | |
| "\n", | |
| "Another way to look at a system of two 1st-order ODEs is by using vectors. You can make a vector with your two independent variables, \n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "\\vec{u} = \\begin{pmatrix} z \\\\ b \\end{pmatrix}\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "and write the differential system as a single vector equation:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "\\vec{u}'(t) = \\begin{pmatrix} b\\\\ g-g\\frac{z(t)}{z_t} \\end{pmatrix}\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "If you call the right-hand-side $\\vec{f}(\\vec{u})$, then the equation is very short: $\\vec{u}'(t) = \\vec{f}(\\vec{u})$—but let's drop those arrows to denote vectors from now on, as they are a bit cumbersome: just remember that $u$ and $f$ are vectors in the phugoid equation of motion.\n", | |
| "\n", | |
| "Next, we'll prepare to solve this problem numerically." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Initial value problems" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Let's step back for a moment. Suppose we have a first-order ODE $u'=f(u)$. You know that if we were to integrate this, there would be an arbitrary constant of integration. To find its value, we do need to know one point on the curve $(t, u)$. When the derivative in the ODE is with respect to time, we call that point the _initial value_ and write something like this:\n", | |
| "\n", | |
| "$$\n", | |
| "u(t=0)=u_0\n", | |
| "$$\n", | |
| "\n", | |
| "In the case of a second-order ODE, we already saw how to write it as a system of first-order ODEs, and we would need an initial value for each equation: two conditions are needed to determine our constants of integration. The same applies for higher-order ODEs: if it is of order $n$, we can write it as $n$ first-order equations, and we need $n$ known values. If we have that data, we call the problem an _initial value problem_.\n", | |
| "\n", | |
| "Remember the definition of a derivative? The derivative represents the slope of the tangent at a point of the curve $u=u(t)$, and the definition of the derivative $u'$ for a function is:\n", | |
| "\n", | |
| "$$\n", | |
| "u'(t) = \\lim_{\\Delta t\\rightarrow 0} \\frac{u(t+\\Delta t)-u(t)}{\\Delta t}\n", | |
| "$$\n", | |
| "\n", | |
| "If the step $\\Delta t$ is already very small, we can _approximate_ the derivative by dropping the limit. We can write:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "u(t+\\Delta t) \\approx u(t) + u'(t) \\Delta t\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "With this equation, and because we know $u'(t)=f(u)$, if we have an initial value, we can step by $\\Delta t$ and find the value of $u(t+\\Delta t)$, then we can take this value, and find $u(t+2\\Delta t)$, and so on: we say that we _step in time_, numerically finding the solution $u(t)$ for a range of values: $t_1, t_2, t_3 \\cdots$, each separated by $\\Delta t$. The numerical solution of the ODE is simply the table of values $t_i, u_i$ that results from this process." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Discretization" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "In order to execute the process described above and find the numerical solution of the ODE, we start by choosing the values $t_1,t_2,t_3 \\cdots t_n$—we call these values our *grid* in time. The first point of the grid is given by our _initial value_, and the small difference between two consecutive times is called the _time step_, denoted by $\\Delta t$. The solution value at time $t_n$ is denoted by $u_n$.\n", | |
| "\n", | |
| "Let's build a time grid for our problem. We first choose a final time $T$ and the time step $\\Delta t$. In code, we'll use readily identifiable variable names: `T` and `dt`, respectively. With those values set, we can calculate the number of time steps that will be needed to reach the final time; we call that variable `N`. \n", | |
| "\n", | |
| "Let's write some code. The first thing we do in Python is load our favorite libraries: NumPy for array operations, and the Pyplot module in Matplotlib, to later on be able to plot the numerical solution. The line `%matplotlib inline` tells Jupyter Notebook to show the plots inline." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy \n", | |
| "from matplotlib import pyplot\n", | |
| "%matplotlib inline" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now, initialize `T` and `dt`, calculate `N` and build a NumPy array with all the values of time that make up the grid." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Create the time grid.\n", | |
| "T = 100.0 # length of the time-interval\n", | |
| "dt = 0.02 # time-step size\n", | |
| "N = int(T / dt) + 1 # number of time steps\n", | |
| "t = numpy.linspace(0.0, T, num=N) # time grid" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We have our grid! Now it's time to apply the numerical time stepping represented by Equation (10)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### Challenge!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "* Write the code above using the NumPy function `arange()` instead of `linspace()`. If you need to, read the documentation for these functions." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### Pro tip:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Enter a question mark followed by any function, e.g., `?numpy.linspace`, into a code cell and execute it, to get a help pane on the notebook." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Euler's method" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The approximate solution at time $t_n$ is $u_n$, and the numerical solution of the differential equation consists of computing a sequence of approximate solutions by the following formula, based on Equation (10):\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "u_{n+1} = u_n + \\Delta t \\,f(u_n)\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "This formula is called **Euler's method**.\n", | |
| "\n", | |
| "For the equations of the phugoid oscillation, Euler's method gives the following algorithm that we need to implement in code:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{align}\n", | |
| "z_{n+1} & = z_n + \\Delta t \\, b_n \\\\\n", | |
| "b_{n+1} & = b_n + \\Delta t \\left(g - \\frac{g}{z_t} \\, z_n \\right)\n", | |
| "\\end{align}\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### And solve!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "To apply the numerical solution method, we need to set things up in code: define the parameter values needed in the model, initialize a NumPy array to hold the discrete solution values, and initialize another array for the elevation values." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Set the initial conditions.\n", | |
| "z0 = 100.0 # altitude\n", | |
| "b0 = 10.0 # upward velocity resulting from gust\n", | |
| "zt = 100.0 # trim altitude\n", | |
| "g = 9.81 # acceleration due to gravity\n", | |
| "\n", | |
| "# Set the initial value of the numerical solution.\n", | |
| "u = numpy.array([z0, b0])\n", | |
| "\n", | |
| "# Create an array to store the elevation value at each time step.\n", | |
| "z = numpy.zeros(N)\n", | |
| "z[0] = z0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "You should pay attention to a couple of things: (1) See how there is a dot after the numbers used to define our parameters? We just want to be explicit (as a good habit) that these variables are real numbers, called \"floats.\" (2) We both _created_ and _initialized_ with zeros everywhere the solution vector `z`. Look up the documentation for the handy NumPy function `zeros()`, if you need to. (3) In the last line above, we assign the _initial value_ to the first element of the solution vector: `z[0]`.\n", | |
| "\n", | |
| "Now we can step in time using Euler's method. Notice how we are time stepping the two independent variables at once in the time iterations." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Temporal integration using Euler's method.\n", | |
| "for n in range(1, N):\n", | |
| " rhs = numpy.array([u[1], g * (1 - u[0] / zt)])\n", | |
| " u = u + dt * rhs\n", | |
| " z[n] = u[0]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Make sure you understand what this code is doing. This is a basic pattern in numerical methods: iterations in a time variable that apply a numerical scheme at each step." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Plot the solution" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "If the code is correct, we have stored in the array `z` the position of the glider at each time. Let's use Matplotlib to examine the flight path of the aircraft.\n", | |
| "\n", | |
| "You should explore the [Matplotlib tutorial](https://matplotlib.org/users/pyplot_tutorial.html) (if you need to) and familiarize yourself with the command-style functions that control the size, labels, line style, and so on. Creating good plots is a useful skill: it is about communicating your results effectively. \n", | |
| "\n", | |
| "Here, we set the figure size, the limits of the vertical axis, the format of tick-marks, and axis labels. The final line actually produces the plot, with our chosen line style (continuous black line)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 900x400 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Set the font family and size to use for Matplotlib figures.\n", | |
| "pyplot.rcParams['font.family'] = 'serif'\n", | |
| "pyplot.rcParams['font.size'] = 16\n", | |
| "\n", | |
| "# Plot the solution of the elevation.\n", | |
| "pyplot.figure(figsize=(9.0, 4.0)) # set the size of the figure\n", | |
| "pyplot.title('Elevation of the phugoid over the time') # set the title\n", | |
| "pyplot.xlabel('Time [s]') # set the x-axis label\n", | |
| "pyplot.ylabel('Elevation [m]') # set the y-axis label\n", | |
| "pyplot.xlim(t[0], t[-1]) # set the x-axis limits\n", | |
| "pyplot.ylim(40.0, 160.0) # set the y-axis limits\n", | |
| "pyplot.grid() # set a background grid to improve readability\n", | |
| "pyplot.plot(t, z, color='C0', linestyle='-', linewidth=2);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### Explore and think" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Try changing the value of `v` in the initial conditions. \n", | |
| "\n", | |
| "* What happens when you have a larger gust? \n", | |
| "* What about a smaller gust? \n", | |
| "* What happens if there isn't a gust (`v = 0`)?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Exact solution" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The equation for phugoid oscillations is a 2nd-order, linear ODE and it has an exact solution of the following form:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "z(t) = A \\sin \\left(\\sqrt{\\frac{g}{z_t}} t \\right) + B \\cos \\left(\\sqrt{\\frac{g}{z_t}} t \\right) + z_t\n", | |
| "\\end{equation}\n", | |
| "$$\n", | |
| "\n", | |
| "where $A$ and $B$ are constants that we solve for using initial conditions. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Our numerical solution used the initial conditions:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{eqnarray}\n", | |
| "z(0) = z_0 \\\\\n", | |
| "b(0) = b_0\n", | |
| "\\end{eqnarray}\n", | |
| "$$\n", | |
| "\n", | |
| "Applying these to the exact solution and solving for $A$ and $B$, we get:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{equation}\n", | |
| "z(t) = b_0 \\sqrt{\\frac{z_t}{g}} \\sin \\left(\\sqrt{\\frac{g}{z_t}} t \\right) + (z_0-z_t) \\cos \\left(\\sqrt{\\frac{g}{z_t}} t \\right) + z_t\n", | |
| "\\end{equation}\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We already defined all of these variables for our numerical solution, so we can immediately compute the exact solution. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### Pro tip:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The expression is a bit long —if you don't feel like scrolling left and right, you can cast the value of the variable between parenthesis and insert line breaks and Python will treat the next line as a continuation of the first." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "z_exact = (b0 * (zt / g)**0.5 * numpy.sin((g / zt)**0.5 * t) +\n", | |
| " (z0 - zt) * numpy.cos((g / zt)**0.5 * t) + zt)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Plot the exact solution" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now we can plot our exact solution! Even better, we can plot _both_ the numerical solution *and* the exact solution to see how well Euler's method approximated the phugoid oscillations.\n", | |
| "\n", | |
| "To add another curve to a plot, simply type a second `pyplot.plot()` statement. We also add a legend using `pyplot.legend()`." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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HNc2YMQN3d/d60wcPHgxAZmYmxcXFdebl5+fz9ddfA3Dttdei1Wob3LbpOI2Pj29X2V9nZ+dGB8q77rrrzH2AmutTZPo/WHN0dCQsLAyA06dPtznGpnzxxRfU1NQAxngbMmbMmCb7VXT0Z6Ihpn4NTcV5+eWX4+Tk1KrtWhNC8L///Q+AiRMnNvi5BMtr1Ov1fPDBB3XmXXvttbi5uQEN/89LS0v5/vvvuemmm9Dp6tYfMu17zJgxjVYENB23er2eb7/9ttHX4urqal7W2nXXXcc///nPRtfrKFFRUQ0eM6bPbkPfa0II8/t5ySWXNFpZ0/S6CgoKWL9+fQdG3T4LFixosM/foEGDAHBxcWHSpEn15pvek/T0dEpKSurMa+/vrmR/ZCIj2bWgoCBzVbKL/9pry5Yt5schISHk5OQ0+Gf68RFCcPDgwTrbMHV8zc3N5Zdffqkzr6kfeIDg4GA8PDzMz0tKSsjNzTXv19XVFTB2iOxMv//+u/nxmDFjGl3Oet7FnXmtDRw4sMHp3t7e5seFhYUtD7BWa+OsqqrqsOICHaUt782uXbuorq4GICwsrNHj1DpBOnDgQJtjjIiIwNHRscF5AQEBBAUFAbBz584mt9Pca23LMdAS1h3XTRcDGhIdHd3ovI7+TDTEFKe3tzchISENLuPk5ERERESrtmstNjaWzMxMoOnXMXDgQHM5cuvvRWj+gs2qVasoKSnhtttuqzO9sLDQnFAPGjSo0ePWOlFr6rgdOHBgg9+jXaUtn93Y2FiysrIA4+eqsffA9F0P7fvsdrTGXrPpdys8PLzBRMf6d+3ii0kd8bsr2RdZflmS2sj66lljV6AvZjopMJkxYwahoaGkpqayfPlyrrnmGvO8H374gZKSEpYuXdrgtoQQrFy5kk8//ZQDBw40WG0LoKKiokWxtZX1+9CnT59Gl7Oe19QdFesfMWvWJ8emK+atYdqnqUpZY1oapxra8t5Yv4b777+f+++/v9n9XHyctob1iVlDgoODSU9PN1dta0xzr7Utx0BLmKpOubi4NDm2VFPHUEd/JhpiitOUGDamqTib09LXAcb/a1FRUYOv47bbbmPFihXmCzbW33MrVqxg2LBh9ZLG1NRUc3W6L774gi+++KLZeJs6bhsa96krtfez++qrr/Lqq682u5/2fHY7WkN3jwFz8tLYfI3Gco29qfekrb+7kn2RiYzUYwkh2rW+9S3vDz74oNFmF9YiIyPrPFcUhaVLl/LSSy+xfv16srKyCAgIAIw/8EOHDmX06NH1tlNTU8M111zDzz//jIODA3feeSeTJ08mKCjI/CPxf//3f2zYsKE9L7FFrN8HZ2fnRpeznmdq4tUQ6x+xjmSKs6kYL57fVJxqaMt7Y/3/eemllxpsynGxlpajbUhjTddMTO9vTU0NlZWVjTZ96qzjoDmmCwLNHSdNvc6O/kw0pCPibE5LX4f1/IZex8yZMwkJCSEtLY0VK1aYE5kzZ86wZcsW/u///q/JfS9evJj77ruv2XibSjzVOp7as3/r9+D+++/n6quvbnad3r17t3o/naW5UvLNzW9IR/zuSvZFJjKS1EbWV9iGDx/OxIkT27SdpUuX8vLLL1NTU8MXX3zBo48+ytmzZ9myZQuvvfZag+u8++67/Pzzz4CxucbixYvrLfP555+3KZ7Wsn4fKioqGr3yaX1nqKkTjs5iirO5O1Rqx9nRrP8/AwcO7PTBX/V6fZPzTe+vg4NDu/pvtEdTg5qarhI3d5w09Tq74jPh7u5OYWFhu+JszsWvoymm+Q29DtMFm5dffpn169eTnZ1Nr169WLlyJRqNpsF+RNb79vf375GDFlu/B/369euR78HFOup3V7Ifso+MJLWRddvzM2fOtHk74eHhTJ06FbB04F25ciWKojTaUfi7774DjM05GkpiupL1+5Cent7ocufPnzc/bqzjbmcyxVleXt5kJ3614+xoHXWctlRzBRJMx0h77vo0xdQPoqmmZ03d/TDFVV5e3mQ/nPz8/EbndcVnwhTnhQsXmlyuqTib09LXYT2/sddx2223oSgK1dXV5mZin332GfPmzSMwMLDe8mFhYea7GF1x3HZHXf3ZtQXyPZEuJhMZqcc7fvw4l19+OZs3b27VerNmzTI/3rdvX5PLRkdH4+jo2GhbXVOn/5iYGGJiYlixYgVz584lODi4weVNHUCbard+cbWXi7Xltn5DrN+HQ4cONbqcdSWsi0eF7gqtjdPR0ZHJkyd3Wjwd9f43Z/LkyeZ2+M0dpwsXLkSn07Wrw3BiYmKDFfjA2FbddMJrSt47munuR2MJVVZWVpMJinVcR44caXS5pqqMdcVnwhRnQUFBo6PJV1VVtauf15AhQ8xJRlOvIzEx0ZwcWr92axdfsNmzZw8JCQn1OvmbeHh4MHbsWMDYgb2pu2ivv/46Op2uS6qPQdd9dq3f/+Y+u/fffz86nY7vv/++1fvpqtfTETryd1eyDzKRkXq83Nxc1q5dy9mzZ1u13pAhQ8xfql9//XWjTS927drFyZMnmTFjRqPtl5csWWKuPPPAAw+QkJDQaCd/sHTwTUpKavAHXgjB0aNHm4zftD9TRSuT6667juHDhze5rrUFCxaYr8J++eWXDS6j1+v55ptvAJg9e7a5lHJXuvnmm83NXhqLs6ioyFw97pZbbunUpmUNvf9JSUlERkby/PPPd9h+vL29zXf2fv3110Z/1NPS0tiwYQPh4eHmE8i2qKioYN26dQ3Osy6Pa0reO5qptGtpaWmdOx4mF1cHvJh1lUDTnc+LHTlyhJSUlEa30RWfCesEoLE4165d265iH4qi8Mc//hGAPXv2NPqaTa9Rq9Vyzz33NLo9U8xHjx7lz3/+M56enixatKjR5f/0pz8BkJOTw9q1axtcpqamhhUrVqAoCkuWLGn2NXWEhj67FRUVREZGcvfdd3fYfqzf/8OHD3Ps2LEGlysqKuKbb77Bw8OjwRLTzWnst2DKlCkNlv5XU0f+7kr2QSYyktQO7777Lq6urqSnp/Pwww/XSyoyMzO5/fbb0el0vPLKK41ux8PDw9wBdufOnXh6ejbZsdPUnCwvL6/BsWTefPPNZq/EmkpjZmVlmX8MKisr2bRpE5WVlU2ua02j0bBs2TI0Gg2///47n376ab1lXn75ZRITE3F1deXdd99t8bY7kqenJ//5z38AY5OWi8cSMhgMPPLIIxQWFtK7d+8WVQhqD9P7b9084tChQ8THxzfbsbq1Xn31VXr37k1ZWRl33XVXvf9vcXExN910E3q9nldffbVdV2j9/Pz4y1/+Qm5ubp3pZ86c4e9//zsAV111FdOnT2/zPpoybdo087glF/cTy8vL46233mqyglVwcDBPPPEEAB9//HG9q74VFRU8+OCD5qIcDemKz8S4ceO44YYbAHjttddITk6uMz83N5ennnqq3SWHn3zySYYMGYJer+e+++6rd7ft+PHj5jshf/vb35rsfH3dddeZT5p37tzJdddd1+SxfssttzB79mwAHnzwwXqJqcFg4IknnuDUqVPcf//9jZah7mgNfXaPHTtGfHx8u4orNMT0/gPceeed9e4mVlVVceedd5KXl8ff/va3RiuBNcX0eqwv5mVkZLB3794m74SppaN+dyX7IDv7S3Zj//79bN++vc602NjYZpsbNHTCv3HjRjIzM81XwEpLS80nRfPmzTNf4RkyZAhr167lmmuuYdmyZRw6dIjrr78eLy8v4uLi+OSTTygvL+ejjz5i/PjxTcZx2223mfdx7bXX4uLi0uiyf/zjH/nll1/YuHEjf/3rX9m5cydz585FURQ2bdrExo0bzWWdMzMz+fzzz3F3d69z9dP0OjIzM7nllluYP38+a9asIT8/nz//+c+teh9mz57Nl19+ye23386dd97J+vXrmTNnDjU1Nfz0009s2LABb29vVq9eXa+CzI8//khJSYn5TkFycjKff/45vXv3Zt68eZSWlrJ69eo6g5pt3LiRc+fOMXz48FbdPbrtttvIzc3lz3/+MwsXLuS2225j4sSJlJSU8PXXX7Nv3z769evHunXr6pyommIwPQbjiYvpvQgPD29RNTBrt956K2vWrGHVqlUMHjwYd3d3/u///g8XFxfzCapp+xfv07S/zMxMNm7cyKlTp+q8n/7+/kyePNl8Utm7d282bdrEwoULWbt2LcOHD+fWW28lMDCQpKQkVqxYQUZGBq+88kqd0rhtMXToUGbPns3w4cO56667CA0NJSkpiWXLlpGTk8OYMWPqDOZoel3Hjh1jz5495mmm13711Vfj5uZmPhYvPk4uPq7d3Nx44YUXePLJJ3n22WdJTU1l3LhxZGRk8PHHH/PSSy/xzDPPUFRUZH4/AwICmD9/vnkbL7/8MqdOnWLNmjXMmjWLP/zhDwwfPpysrCyWL1/O1KlTiYiIqPc6rLXnM2F67Re/VjCe3JssW7aM1NRU9u7dy7hx47j33nuJiIggLS2Njz76iOnTpxMUFMT27dvN23B2djaP69ISLi4ubNiwgUsvvZQNGzYwatQoli5dir+/P8ePH+ejjz6itLSURx99lOeee67JbXl4eHD11Veb+8g0ddcZjAnhDz/8wKJFi9i6dSvDhg3jzjvvJDIykoyMDH788UcOHTrElVdeyRtvvFFnXdPxYkrwTN+D0LbPq7Wbb76Zt99+m927d/PUU0/Rv39/3n33XTQajfmuU0d9r5ne/4ULF3Lo0CGio6O54447CA0N5cyZM3z99dckJCRw33338cgjj7Tp9SxevJi//vWvnD17lnvuuYfRo0fz2WefYTAYuOOOO+q8nobeT9NFN9N3pMmePXvQ6XTm17Nnzx6SkpLqbcP0GU5OTmb37t0Nfp911u+uZAeEJNmJV199VQBt/vv000/N25oxY0ajy23ZsqXevrOzs8Vf//pXMWzYMOHm5iYcHR3FgAEDxN133y1iY2NbFL9erxf9+vUTgNi6dWuzy1dXV4u33npLjB07Vri6ugpHR0cREhIili5dKo4dOyZuu+22OnGHhITU20ZMTIxYsGCB8PT0FC4uLiI6Olq88847Qq/Xt+l9SE1NFQ899JAYNGiQcHFxEW5ubmLo0KHi6aefFllZWQ2+jpCQkAa3P2PGDCGEECkpKY3G8Pzzz7fovb3Y8ePHxV133SVCQ0OFk5OT8PT0FGPHjhX/+Mc/RHFxcb3lm4oBELfddlub4vjf//4noqKihKOjo/D39xfz5s0TBw4cMM9vbn9btmxp0fFsUlxcLF599VUxbtw44enpKRwcHETfvn3FjTfeKPbs2dOm12BiOt5M/7fVq1eL2bNnC19fX+Hs7CyioqLEK6+8IioqKuqt+/zzzzf6OlJSUoQQjR+LDR3XQgjxySefiNGjRwsXFxfh7e0t5s2bZ/5cXXzMTZkypd76BoNBLFu2zPz58vLyEhMnThQff/yxEEKIpUuXCkDMmTOnyfelLZ+Jpo61i1VWVorXX39dDB06VDg7Owtvb28xadIk8cEHHwiDwVDvffPz82sy3sZUVlaK//73v2LatGnCx8dHODo6ij59+ogbbrhB7Ny5s8Xb2bhxowBEWFiYMBgMLVrHYDCIzz//XMyfP1/06tVL6HQ64e/vL+bPny++/PLLBtdp6rurrZ9Xa99//70YM2aM+T2fPHmy2LBhg3l+R3+vVVVViXfffdf8/ut0OhEYGCiuuuoqsX79+na/ni1btoipU6cKV1dX4e7uLkaPHl3nvW3s9Zg+oy15PRf/Jl38Gf7000+7/HdXsn2KEO0cTKML7d69mzvuuIOEhARSUlI6reqNJEmS1Dq33347K1asYMaMGa0epd4WXXPNNaxevZolS5bU6fsjSZIkdR2b6CNTXl7O448/zvTp00lISGjxetXV1bz77rtMmzYNPz8/nJ2dCQkJ4ZJLLuHVV19tdEDE+Ph4brnlFoKCgnB2diY8PJwnn3yyyUo3kiRJkn04f/58s781p0+fBoxN6SRJkiR1dPtEJikpiZEjR7Jq1SrWr1/f4vWys7MZP348//nPf7j33nvZt28fJ06c4Pnnn2ffvn389a9/bXCgsK1btzJq1CgOHjzI8uXLOXXqFM8++yzvv/8+o0ePbrZmvyRJkmTb3nnnHaZMmdJoR+fk5GRiY2MBuPLKK7syNEmSJMlKt+/sHxsby5w5c3jjjTdaXI3DYDBwxRVXUFBQwKFDh/D19TXPi4iIwMHBgSeffLJeZZ6CggKWLFmCEIJ169aZO8qGhYXh5OTEzTffzNKlS+tVO5IkSZLsS05ODv/5z3949NFH60yvrKzkvvvuQwjBkiVLGDlypDoBSpIkSd0/kbnssstafcXrk08+Yd++fXzwwQd1khiTW2+9lVtvvbXe9HfeeYecnByuv/76eiUkb7jhBp588kk2bdrErl27mDJlSuteiCRJkh1qrpqRqRSyLTFd5HrsscfYvHkzM2fOxNfXlzNnzvDFF1+QmJjI9OnT+fDDD1WOVJIkqWezqc7+YPmBaaqz//jx4zlw4ABnzpyhX79+Ld728OHDOX78OMuWLeMPf/hDvfm33norn3/+OQ8++CBvv/12m+KXJEmyJ6GhoaSlpTU4z1aLslRUVLBq1Sp++eUXDh8+zPnz56moqMDHx4eRI0dy0003ceutt7Z7jBZJkiSpfezuW7iwsJCDBw/i7OyMn58fr7zyCt999x1nz57F3d2dCRMm8MgjjzB58uQ665WWlprbPF9c09/ENP3AgQOd+yIkSZJsRGpqqtohdDhnZ2duvvlmbr75ZrVDkSRJkppgd4nMsWPHEEKg0+mYOnUqLi4uvP766/Tr148jR47w1FNPsWrVKt59913uu+8+83opKSnmjp2BgYENbjsoKAhoeABFa5WVlXVGzjYYDOTl5eHn59euEbMlSZIkSZIkqbsQQlBcXExwcDAaTdfXELO7RCY7OxuAkpISMjIySExMxNXVFYCoqCiGDx/OqFGjePDBB5k2bRrR0dEAFBUVmbfR2Ijqpu00V4b51Vdf5cUXX2z3a5EkSZIkSZKk7u7s2bP07du3y/drd4lMWVmZ+fHdd99tTj5Mhg0bxpw5c9iwYQPvv/8+77zzTofH8PTTT/PYY4+ZnxcWFtK/f38SEhIaLD4gSSbV1dVs2bKFWbNm4eDgoHY4UjcnjxeppeSxIrWGPF6klsrLy2PQoEF4eHiosn+7S2Ss76ZERUU1uMyYMWPYsGED+/fvN0/z9PQ0Py4vL29wPVOS5OXl1WQMTk5OODk51Zvu6+uLn59fk+tKPVt1dTWurq74+fnJHw+pWfJ4kVpKHitSa8jjRWottbpOdPsBMVvL1I8FaPTuhylrzM/PN08LCwsz/xMyMjIaXM80GGZ4eHiHxCpJkiRJkiRJUtvYXSIzbNgwtFotYBzPoCGm6T4+PuZpbm5u5v4ycXFxDa5nmj5u3LgOi1eSJEmSJEmSpNazu0TGw8ODOXPmABATE9PgMqYyyxeXYF6yZAkAmzdvrreOwWDg999/r7OcJEmSJEmSJEnqsLtEBuCvf/0rAMuXL6e4uLjOvBMnTrB582acnJz405/+VGfegw8+iJ+fH2vWrCElJaXOvK+//pr09HRmz57NtGnTOvcFSJIkSZIkSZLUJJtIZLKzs8nIyKjTd6WhaSYzZszg73//O7m5uVxyySXs2LGDM2fOsGbNGq688kocHBxYvnw5ERERddbz8fHh22+/BeDSSy9lw4YNpKSk8Omnn3LvvfcSGhrKypUrO/fFSpIkSZIkSZLULJuoWjZu3DjS0tLqTBs/frz5sRCi3jrPPPMM48eP59///jdXX301RUVFBAQEMHv2bJ544gmGDx/e4L5mz57NkSNHeOmll1i6dCn5+fn06dOHe+65h+eeew5vb+8OfW2SJEmSJEmSJLWeTSQyqampbVpv3rx5zJs3r9XrRUZG8uWXX7Zpn5IkSZIkSZIkdT6baFomSZIkSZIkSZJkTSYykiRJkiRJkiTZHJnISJIkSZIkSZJkc2QiI0mSJEmSJEmSzZGJjCRJkiRJkiRJNkcmMpIkSZIkSZIk2RyZyEiSJEmSJEmSZHNkIiNJkiRJkiRJks2RiYwkSZIkSZIkSTZHJjKSJEmSJEmSJNkcmchIkiRJkiRJkmRzZCIjSZIkSZIkSZLNkYmMJEmSJEmSJEk2RyYykiRJkiRJkiTZHJnISJIkSZIkSZJkc2QiI0mSJEmSJEmSzZGJjCRJkiRJkiRJNkcmMpIkSZIkSZIk2RyZyEiSJEmSJEmSZHNkIiNJkiRJkiRJks2RiYwkSZIkSZIkSTZHJjKSJEmSJEmSJNkcmchIkiRJkiRJkmRzZCIjSZIkSZIkSZLNkYmMJEmSJEmSJEk2RyYykiRJkiRJkiTZHJnISJIkSZIkSZJkc2QiI0mSJEmSJEmSzZGJjCRJkiRJkiRJNkcmMpIkSZIkSZIk2RyZyEiSJEmSJEmSZHNkIiNJkiRJkiRJks2RiYwkSZIkSZIkSTbHphKZ3bt3M3jwYBRFITU1tVXr/uc//0FRFBRF6ZzgJEmSJEmSJEnqMjaRyJSXl/P4448zffp0EhISWr1+amoqzzzzTIuXj4+P55ZbbiEoKAhnZ2fCw8N58sknKSwsbPW+JUmSJEmSJEnqeN0+kUlKSmLkyJGsWrWK9evXt2kb99xzD35+fi1aduvWrYwaNYqDBw+yfPlyTp06xbPPPsv777/P6NGjuXDhQptikCRJkiRJkiSp4+jUDqA5sbGxzJkzhzfeeAN3d/dWr798+XK2bt3KqlWruPLKK5tctqCggCVLliCEYN26dQwYMACAsLAwnJycuPnmm1m6dCkbN25s02uRJEmSJEmSJKljdPs7Mpdddhnvvfdem5KYzMxMHnvsMZ566imGDRvW7PLvvPMOOTk5XHXVVeYkxuSGG24gODiYTZs2sWvXrlbHIkmSJEmSJElSx+n2iYxWq23zun/605/o3bs3zz77bIuW/+677wCYM2dOvXkajYbZs2cD8M0337Q5JkmSJEmSJEmS2q/bNy1rq9WrV/PDDz+wY8cOnJycml2+tLSU2NhYACIjIxtcxjT9wIEDHReoJEmSJEmSJEmtZpeJTEFBAX/605+4//77mTJlSovWSUlJwWAwABAYGNjgMkFBQYCxAEFTKisrqaysND8vKioCoLq6murq6hbFI/VMpuNDHidSS8jjRWopeaxIrSGPF6ml1D5G7DKRefzxx9HpdLz66qstXseUbAC4uLg0uIyrqytAs2WYX331VV588cV607ds2WLehiQ1RRaUkFpDHi9SS8ljRWoNebxIzSkrK1N1/3aXyGzevJlPPvmEtWvX4uHhoUoMTz/9NI899pj5eVFREf369WPWrFktLgMt9UzV1dVs3LiRefPm4eDgoHY4UjcnjxeppeSxIrWGPF6klsrNzVV1/3aVyJSVlXHPPfdw0003sXDhwlat6+npaX5cXl7e6PYBvLy8mtyWk5NTg/1yHBwc5BeC1CLyWJFaQx4vUkvJY0VqDXm8SM1R+/iwq0TmwIEDJCcnk56eXq9csxDC/Nh63smTJ+nfvz9hYWEoioIQgoyMDAYOHFhv+6bBMMPDwzvpFUiSJEmSJEmS1BJ2lciMHz+e06dPNzjv/PnzzJw5E4CjR4+apwcHBwPg5uZGdHQ0J06cIC4ujmnTptXbRlxcHADjxo3r2MAlSZIkSZIkSWoVu0pkXFxciIiIaHCeTmd5qY0ts2TJEk6cOMHmzZv5wx/+UGeewWDg999/Ny8nSZIkSZIkSZJ6uv2AmF3pwQcfxM/PjzVr1pCSklJn3tdff016ejqzZ89u8G6NJEmSJEmSJEldxybuyGRnZ6PX6+tNc3Z2Bhof9wUgLy+PqqoqsrOzzdMyMjIA4x0c6477Pj4+fPvtt1x22WVceumlvP322wwcOJCtW7fy0EMPERoaysqVKzvypUmSJEmSJEmS1AY2kciMGzeOtLS0OtPGjx9vfmzdkf9i11xzDdu2baszzTSw5W233cby5cvrzJs9ezZHjhzhpZdeYunSpeTn59OnTx/uuecennvuOby9vdv3YiRJkiRJkiRJajebSGRSU1PbvO7WrVtbvU5kZCRffvllm/cpSZIkSZIkSVLnkn1kJEmSJEmSJEmyOTKRkSRJkiRJkiTJ5thE0zJJkiRJkiSpZyksq+anY+kcTM0jp6QSFwctQ/t4cfnwYCIC3JvfgGT3ZCIjSZIkSVKXMxXqURRF5Uik7qaqxsCHO5L57++JlFfXrVq76VQWb206zWXDg3jusigCvZxVilLqDmQiI0mSJElSpxNCsCcpl68OnGVfci5ZxZU46TREBnmycGggN4zrj5erg9phSirLLank3pWHOJiW3+Rya49dYG9SLu/ePJqJA/y6KDqpu5GJjCRJktQuNXoDCZklXCgsx0GrYVBvD3mVVKrjfEE5f/3hONsSsutMr6wxEHO2gJizBXywPZlnFg5h8Zi+KkUpqS2zqILrPthDWm4ZABoFbhjfn+vH9iM8wJ380ip+i83gf1uTyC2tIre0iqUf7+eDpWOYNThA5eglNchERpIkSWqT/NIq3t+exHcHz5FXWlVn3oi+Xtw9bQCXDw+STYd6uMNn8vnDioPkWh0jHk46BvRyo7iihuScUgDySqt4/LsYjpzN54UrotFpZT2inqSwvJrbPtlvTmJ6ezrxwa1jGdnP27yMu5OOu6cNYPHovjz8zVG2J2RTpTdw78pDfPWHCYwJ8VUpekktMpGRJKkOIQT7UvLYk5TLufxytBqICHBndmQAEQEeaocndRO/xWbw9A/H6yUwJjHnCnnwqyN8ue8M/7lxJAEe8g5NT7Q/JY9bP95HZY0BgEBPZ/5yaSQLhwXhqDMmKik5pby5IZ5fjl0A4PO9Zyir1PPPJSPQaGQS3BMYDIJHvzlKXEYxAP18XfjmnkkEe7s0uLyPmyOf3DaWh78+ytrjF6iqMXDf54f55cGp9PaU3zU9iUxkJEky+z0uk7+vPUVydmm9ef9YF8e0gf48c9kQIgM9VYhO6i7e35bEa+vjzM8dtRpmRwYQGeRBeZWeHadzOHmhCIA9yblc8c5OPrtzAoMDZSLck8RnFHPXigPmJGbSAD/ev2VMvX4wYf5u/Pem0cwcfI6nfzhGtV7ww5HzeLk68PwV0WqELnWxj3em8HtcFgC+bo58dueERpMYE51Ww1s3jCSvtIo9yblkF1fy4FdH+PoPE2UC3IPIRKYHOHGugB3bfkOTtgu38vMY0FDgFgYR81g4faK8yi5RWaPnbz/G8s3Bs4BgnBLPeE0cgUoeNWhJFH3YrB/FjtNwxTs7+dvlUdwyMUQ2GeqBLk5iLony5x+jCvHN3QQlGaBz4S9TB7NTO5Yn12WQUVRBZlElN3+0l6/vkd83PUVxRTX3rjxIcUUNADMG9eLDpWNxVPRweiOcOwCl2eDgCr2HwqAFXDumLx7OOu7/4jB6g+DTXakM7+vF1aNknxl7Fp9RzOu/Wr5T3rp+JGH+bsYnNZWQuBnSD0NZLji6Q9AIGLQAnDxw0Gr4702juPK/uzhfUM7+lDxW7EnljilhKr0aqavJRMaO5ZdW8c3Xy5mR9g5/1JwxTtTWzqwATnzAlpiRrI96nLsWL8TVUR4OPVFZVQ13fHqAfSm5XKI5wJO6bwjXXKi33MsOCuv043mj5gaeWyM4V1DOXy6JlMlMD7L6yDmrJEbw4fDTzM18CmXV2TrLKcA0RcvWqGv5Y/pCtlxwIKekits+OcDPD07F182xy2OXuo4QgmdWnyC1tq/D0D6e/O+mETge/hi2/9OY8F5M4wBjbmfBzL/w90VDefqH4wA8/cNxRvbzsZzYSnbFYBA8s/o4NQZjKe77ZoQzfVAvqKmCve/B7reNCczFHFxh7J0w4yn83D35vyXDuenDfQC8/msccyJ709/PtStfiqQS2ZPOTsWdy2bHv27kvrNPMsSUxDRglvYo98bdzif/epq0nJIujFDqDiqq9fzhs4McT0nnvw5v877jWw0mMQAaBJdr9/Gr41+4RrOdD7Yl888N8V0csaSW+Ixi88mlJyVsC/ov8xJeQCk82/AKQo9z7Dd8UvYQd/nHAsbKVQ98abzaLtmvX09k8FNMOmDs1P/+Vf1w/eIKWPdEw0kMgKEaDnwI703iRv9krh/bD4CKagNPfX8Mgzxm7NJ3h86ayyyH+bvxyNyBkJ8KH86GTc83nMQAVJfBnv/CexPh3CEmh/uzdFIIYDxmXl1/qotegaQ2eQneDp1MOUf58sVcqVhu1WZ7RuEx+W6c+44EfRUVSbuo3rcMj8pMHBU9D1Qs45v3zqG/bxkDZNOPHkEIwXM/nuBUYgrfOb5KtCbNMrP/ZBh1MwREGX8wUnfCgY+gNBtXpZJ/Ob5P3+oc3t5yNeG93LlmtGz6Yc8qqvXc/8UhKqoNBJPDGs836JV/zrJA+BwYcQP4D4SKIkjeCgc/hopClMpCnqt8BSfXu3ivbA67k3L5aEcy984IV+31SJ2nqKKa53+KNT//zzw3+n6/EIrOWxaKvByGXQs+YVCeB6c3waHlUF0KpVmw8hpeuuJd9iQHciavjP2peXy+L42lk0K7/PVInae0soY3frVcDHv5qqE4Z8XA54uNxwWAooHoqyFqEfiEQEkWxK+Do19CTYXxuPr0ErjuM55cMJd1xy+QU1LF+hMZ7EvOZYIcX8buyUTGziSdz6J8xbWMqU1iKnGkfN5r9Jp8J1g1AXIOmYTztD9R8Mvf8I5ZBsD1hnV8+8E9uD/0CQFeTXeyk2zfNwfO8tuheL50fM2SxDh5wpVvG380rJuMhU6FSX+C3/4Khz8D4DGH71EQ/OUHLZGBnkQFywIA9urtzadJyi6lFwV85/oavaqMV9tx9YOrl8HAuXVXGDADJj8IvzwKJ38E4M+GjynV1rBCv4A3NyYwOzKAgb3lRRN7868NCWQVVwJwXbieWfv+AMW1x4tnX1j8EYRMqrtS+GyY8jCsuR8SN4HQ4/TTH/l46r+Yt6k3AG9uSODKEcF4u8pmifbik50p5pLcC4cFMtUzC5ZfA+W1A2H6RcDijyF4ZN0VB86DKY/A6nvhzB7QV8E3t+Jxw5c8MT+Sv9TeOf772lP89MAU2fzZzsmmZXakuLyKc5/cxhiMt1SLFQ/EHevwnnJX3ZNSEwcXvK/+P0oueRt97aFwnX4da5Y9T0W1vitDl7pYSk4pL/10jP85vMVQTapxokcw3L3JePWroePFyQOufAcW/MM86VGHVSw0bOexb49SWSOPGXt06kIRy7Yn40QVnzj+kz6G2pNS33C4Z2v9JMbE1ReWLIdpT5gnPe+wklmaI1TVGHj6h+MIIZsL2ZPk7BJW7jVeFOnlUMkrpS+gmJKYwGFwz5b6SYyJR2+46TsYe1ftBMHAPU/xWKTxynxheTVvbTrdya9A6ioFZVUs254MgFaj8NRUX/jcKonpP9n4e3RxEmPiEwJLf4Kh1xqfG6rh+ztY0r+EIUHGi2rHzxey+VRWJ78SSW0ykbETQgh+++hvzNDvBqAMFzRLf8A5ZFyz67pPvI3SBW+Zn99Zsoyvvvu6s0KVVGYwCP6y6hgP8A1TtLVNQFz9Yeka6DW4+Q1M+hPM/7v56esOy1AyT/AfeZJhd4QQPPvjCWoMgud1KximMZ544NXPeLx49296A4oCc56DqY8BoMHAfx3/S18li4Np+fx8rOH+WJJtenNjQm3/J8FXAZ/hUJBknOE/GG79EdybGXldo4HL3oTRtxmf66v4U9YLBDsYxxb5fG8aydmyL6c9WLY9meJKY0W760cHErLlQSiu/T4IHgU3fQMuPk1vROcIV38AUVcZn1eVoP3mJv48I9C8yNu/n5YXTOycTGTsxJYtv7Eo5wPz85LLP8AtbHyL1/ecdBvZI/8EgFYRzIv/G7tjkzo8Tkl9Xx04g0PaNu7X/QSAULRw/efQa1DLNzLpARhzOwBOSg1vObzLiu1xJGbJkwx78ltsJofS8rlcs4ebdFuME3UucOPX4N2v5Rua/Zz5ZMONct5yeA8tel5dd4ryKnknzx4cP1fI2trE9D6X34nIrT1enL3g5m/Bzb9lG1IUYzIzYCYA2rIcPvdfCQhqDIL//p7Y8cFLXaq4opqVe4x37hy1Gv7ivg5SdxhnugfCTd+CcwubKmt1sOh9CBxufJ6fwsyUf5rvyhw7V8jWhOyOfglSNyITGTuQXVBM3+1PolOMg44lRd5HwNirWr2dXle+zAXvMQD0VXIoWPUYpbVXTCT7UFhezbu/HuU1hw/N05R5LzXe3KMxigKXvmEc/wEYrDnHI5pvePHnWHn1y07U6A288VscvhTxosNyy4zL/w2BQ1u3MY0GrvwveBurCo3VJHCv9hcuFFbw6e6UjgtaUs2/NyUA0IdsHtd8aZlx9TLwCW3dxrQOcM1H4NYLgAH5O7nLZRsAa2LSScutP2CvZDu+3n/WfDfmviGVeO5/yzhD0RqbozZ35+5ijq5wwxfGPp6AEvM1r0Smmme/K5NfuyYTGTuwf+XfGISxxPJZpwjCl/y9mTUaodHS+7bllCrGev0LDVv5cc13HRWm1A38b2sSf6j+gr5KjnFC6DSYeH/bNqZzgsUfIXTOANyh/ZXsxMOyTbKd+PbgOZKzS/mbw2f4KcamPQy5Ekbe2LYNOnsaO3orxp+dB3Wr6atk8+H2ZErkBRObFp9RXDsqu+BNl09x0JcbZ4y5HQZf0raNuveCq94zP31S+zW+FKE3CN7bIlsL2KqqGgMf7zRevNBg4P6ifxn7twBMfbT1F9VMvPvDpa+bn446/jLDexm/aw6m5XP8XGG74pa6L5nI2LgTJ48zN2clADVo8LjuA+PVrDbS+PSnfMZz5ufjYv9OUkZ+u+OU1Hcuv4ydu7axVLsBAIPOGa74j/FqeVsFDEGp7cytUwz83eET3vztlBzzwcbV6A28tzWR8copFmmN/e5w9oaF/2zfhvuNhwn3AeCiVPG87jPyy6r5bE9q+7YrqeqD7cbEYoHmIBPFUeNEj2CY91L7NjxoPgy/HgDnmiKeczb23Vx1+BzpBeXt27akip9j0skoqgDg+T6HjOWWAfwHwfQn27fxETfCIGPirJRk8mqvDeZZ8s6v/WrRGYxWq+2wP51OR3Jycme/rh5BCEHumudwUoxXM+JDb8E7fGy7t+s//R4uuA0BYJByjgPf/V+7tymp753NiTypfI5WMSYZmhlPgV8HjOUx5SGEr3E7YzUJDMr+jfUnGhn0TrIJvxy7wPn8Up5x+MIycd6LxspS7TXzaWM7eGCe9hDTNTF8uD1ZNmO1UekF5fx0NB0Havir41eWGZe+buwf017zXgYn43auZivDlGRqDILP96Y1s6LUHX1W+39zpYIbS1daZlz+Fjg4t2/jigKXvApaY4nuqLTPGeZsbH3wS8wFsmvLgkv2pUWJjBCiQ/+kjrF7+0ZmVBo7VBYqHgxe0s6rXyYaLT5L3jY/nZOzkuPJ55tYQeruzheUk3VkLTO0xwAwePZre5Oyi+mcUBa+YX76mO573t54Uo7ebqMMBsH/tiZxpWY3I0xVygKiYdStHbMDZ0+Y/7L56ZO6b8gvq+K7g2c7ZvtSl/p0Vwo1BsHN2k2EUHsBI2QKDLmiY3bg0Rtm/dX89CmHbwD4av8ZOUyAjTlxvpCYswUAPOu9AceK2ibOQ66A0CkdsxPfAcYxrABFX8XrvmsAqNIb+HLfmY7Zh9SttLhNyYEDB0hJSWnXX3JyMi4ucqDFjmAwCFy2W/rCZI56GJ1bM6UKW8E5dDypgQsA6KUUEbfmjWbWkLqzZVsTeUJruVqqmfdC+69+WYuYiwibDkCIJouxeb+w/oQsrWuLfo/LIikznyd0Vv3j5r8MGm3H7WTotcZxRYBhmlQu1ezn092pMvm1MRXVer49eA5XKnhYt9oyY/7fGx6Lqq3G3mkuFDFVc5xJmljyy6pZc1ReYLMlX+43JhJ+FHJd1Y/GiRodzH2xY3c09TFzoYiovM1EaYz7/ebAGfkdY4dalMgoikK/fv0ICQlp119oaCia9rTHl8z271jPaL2xbekFbRADFz7U4fsIvvrv1NQeIgsKvuFQnGwSaIuyiyvJOLSGaI3xln5N7xEQfU2H70eZ87z58UO6H1ixPU7egbVBn+xKYZF2F/00tSVLB8yCiDkduxONBmb/zfz0Cd23nM0tYfOpzI7dj9Spfjl2gcLyam7WbsLHVBBi6LXQZ3TH7kjnWOeuzBO6bwHBp7tS5XeMjSiprGHNEWPieZ/Tr+gMxn4yjL2rY5o4W3NyNxYOqPWy9y8ApBdWsDMxp2P3JamuxU3LOor80mk/IQTanW+anxeOeRBF59Th+3HsPYiz/a8GwFMpJ+3X/3T4PqTOt2JXCn9UfjA/1836S/s6+Dem71hE5GUA9FYKGHzhJw6lyUIRtiQxq5i9Sdncr11jmTjz6c7Z2cB50N9YoShcc4EFmgN8skt2yLUlX+xLw4kq7tGtrZ2iwIw/d87Ohi2BXsa+m2M0p5mkOUlcRjGHz8jvGFvw09F0Sqv0eFFiLjiD1hGmPtI5Oxx7J3gEATCmbCfRSioA38omrHanRWczFy5cICCglXW9G5GcnExoaGiHbKunOrjnd8ZVHwQgS9OLwfPv7rR99b3yWfS1h8n0/B9IPC9L69qSimo9Sft/YaTGWFWo2j/KXNWlMyjTLScxf9Cu5aPtpzttX1LH+3zvGS7X7GWApravQ+g06D+hc3am1D3pvU/3M3uTczl1oahz9id1qNj0Qo6cKeAG7RZ6KbWlbaOugl6DO2eHGi1Mf8L89F6t8Sr7NwfkiaktMCUQd+h+xclQW3Fu1K3gGdw5O3RwgWmPm58+6LwOgI2xmeSXVnXOPiVVtCiR6d27AyrV1OrVq5dsXtZO+u3/Nj/OGXl/p9yNMXHwH0Bq73kA+CtFHPvlf522L6nj/XLsArdWrzI/d5j5ZOfcjTEJHokhbCZg7Cuji/9FDl5nI0ora1h16Cx/1FndjWlvOdTmDJhlHpF7hCaZSZqT8sTURnyx7wxa9Nyj+8Uy0SrR6BRRi8x9ZWZqYxiipPHLsQtyHKJuLiWnlKNnC3ChgrscfjNO1OhgysOdu+NRt4CrHwDzxR6CyaFKb+BH2bfKrnR6RlFaWspLL3VQNS2JxNOnGFu+C4A8xZvIS/7Y6fsMWvgX8+Ox6Z+TWVDS6fuU2k8IwbbtW5isPQlAhWeo8YppJ9NMtfw43aP9mS/3yTKptmD1kfMMrT7GEE1tItFnLNQWcOg0ilLnZOY+7c/8cPicrEbVzVVU6/k5Jp35moP0UXKNEwcuMBdw6DRanbkiFcC9up8pq9Kz9lh65+5Xapcfa/vGXKPdiYeovbA17DrwCencHTu4wPh7ANCg5w7drwB8d/Bc5+5X6lKdnsiUlJTw4osdXJGiBzu34R10igGAMwNuROPY+VXgXENGk+I1HoD+Shb7fv2imTWk7uDI2QIm51ruxjhNub9jK081ZsAsagKMJzTDNSkkHtxIVY2h8/crtcs3B85yu/Y3y4SJf+zYylONsbrKPkN7jIDKVFnxrpvbfCqL4ooabtdddLx0hZE3m6+yX6bZRwD58i5eNyaEqL0DIi76frmvawIYdzfojBU6b3bYgielnLxQRGKWvCBrL9qVyFy4cIHXXnuN6667jnnz5jF79ux6f4sXL+6oWHu8/IJCRmQZm31UCy0DFz7YzBodx2u2pQJIQPwXVOvliWl398POY1yt3QlAlc4dZeRNXbNjRUE3xXJsXln9KxtOygEyu7P4jGLy008zV3PIOMEjqEvu3gHGq+wTLCc1N2s38/V+eWLanf1w+BzRSioTNHHGCf6DYcDMrtm5o6uxIzfgoOi5QbuFw2cK5IlpN3XkbAFpuWVM0ZxgoKa2SVf/yRA0omsCcPOHETcC4CrKWazdDsDPMfIunr1ocyKzb98+IiMjeeaZZ/j+++/ZvHkzW7durfe3e/fujoy3Rzu6/iN8FOOX9Um/ubj59emyffsOu4RsnbECyEQRw579+7ps31LrFVdU4xP3Nc5KNQCa0beAk0fXBRB1FdVOvgBcqtnHL7tjum7fUqutOnyOW7Ub0Sq1VSXH3gVah64LYOSNCJ3x7vJi7XaOp6STnC1PTLujnJJKtiVkc5v11fUJ93bN3TuTMbeDYjx9uUm3GR01/CRPTLslU7Oy2y8+XrqS1YWSm7S/A4KfY9JlFV070eZE5oknnkAIwV/+8hdWr17N77//zpYtW+r9ff/99x0Zb48lhKDP6c/Nz3vN6eROchfTaCgeutT8tGTXh127f6lV1sac53rFWOLSgIJuwj1dG4CDM7oxxpHgHRU9A86uJiVHdvrvjmr0BtYeTuF67VYAhNYJxt7RtUG4+KAMuxYwlnq/UrvbfAIkdS8/x6TjaijmKm3tRUonLxhxQ9cG4dUXBl0KQKCSzxzNYX46el6emHYz1XoDP8ek04ds5miOGCd69oHIy7s2kIBI410gYKDmPOOUeJJzSolNlxUS7UGbE5lDhw7x/vvv88orr3DVVVcxc+ZMZsyYUe9vypQp8sulAxw/uINBBuOAlEkOgwiOntLlMYTOvYdKjFdpJxf/SuqF7C6PQWqZ+D1r6asYB/4q6Tu94wccawFl7B0IjFdpb9Jt5oeDstN/d7QjMYfRZbvwVoyJphK9yNgco6uNs5SRv1W7kTXyxLRbWn3kPFdpd+NUe7eXUTeDo1vXBzLuLvPDW7UbSc0t4/j5wq6PQ2rU3uRc8suquVa7HY35bu8dxuakXa22OSLAzbpNgGxeZi/anMh4e3szefLkZpfr3bs3BkPH9KfYvXs3gwcPRlEUUlNTO2SbtqJw9yfmx8VRN6oSg8bdn9TABQB4K6Uc37hSlTikpiVllzAq92fzc49JdzaxdCfyDaMqzDgifF8lhwuH12IwyBPT7mbVoXNcp91qmTDqVnUCCR4JfcYAEK1Jwzv/OEfPFqgTi9Sg5OwSjp0rNN+9A9Q7XgbMAt8BAEzVxtJfyeSno/LEtDtZdzwDBQNLdNuMExSNsViDGqKuBBdTc+f9+FDEzzHp8jfJDrQ5kbnuuuuIiWm+3XtHlF8uLy/n8ccfZ/r06SQkJDS7fHZ2Nv/617+YM2cO/v7+ODg44Ofnx6xZs/j444+bTazi4+O55ZZbCAoKwtnZmfDwcJ588kkKC9W52lNUUsywPGMzoXIciZzbxc0+rPSeZWnbGpiyGr38Euh2ftkXywKNccDUcgdvlMELVYvFaYIliZpRvomDaXIU7u6kuKKa2JPHmaKJBUD4hEHoVPUCGnO7+eFi7Q7WyBPTbmX9iQyilVSGalKNE4JHQ+8odYLRaGC0pbnzYu0Ofjl2QZ6YdhN6g2DjyQwma2LNrQOImNt5A2A2R+dkvHsIOCk1XKPdSXphBcfkXTyb1+ZE5h//+Afff/89q1evbjIxaG/55aSkJEaOHMmqVatYv359s8snJiYSGhrKE088wZAhQ/jll1+Ij4/n888/p6SkhLvvvpu5c+dSVlbW4Ppbt25l1KhRHDx4kOXLl3Pq1CmeffZZ3n//fUaPHs2FC11fFvTYxs/NzT7ifWbj7OHT5TGYeA+aRqbOWGRgjOE4h48dVy0WqT69QVB15DtLs4/h14POUb2AIuZR6Wg8XudrDrH+wCn1YpHq2XQqkyvFNnOzD2XUzV3baftiUYvMnf6v1O7mt5g0amSFxG5j7bELLNFutUwYrdLdGJPh15s7/V+j2UFmURn7UvLUjUkC4EBqHjklVRfdvbtFrXCMRt9mfmiq6PlbrKyoaevanMi4urryyiuv8MILL+Dn58eIESOYNWtWh5dfjo2NZc6cOZw4cYJ58+Y1u3xJSQllZWU8+uij/Pe//2XixIkMGDCASy+9lG3bttG/f3+2bNnCK6+8Um/dgoIClixZghCCdevWsWDBAsLCwrjjjjv44IMPSE5OZunSpQ3stXO5n/za/Nhrsnp3YwBQFAoHGf+nGkWQvWuFuvFIdRxIzePS6o3m5y7jb1cvGACdI5oR1wHgpFSjnFwtBzvsRtbFnDc3+xCKBkZ0UYnuxjh7ogy5AjA2Xx1Rvo9dSbnqxiQBkJpTStKFHBZpjQMyo3OGoSoPr+AZbGxiBvTTZDNeiZdjEHUTv57IwIsSc+sAXP3MBRpU4z/Q3Hx1qCaVwcoZmcjYgTYnMjExMYwaNYrjx49TWFjI8ePH2bZtW4eXX77ssst47733cHd3b9V6d911V71prq6u3HKL8YrAt99+W2/+O++8Q05ODldddRUDBgyoM++GG24gODiYTZs2sWvXrlbF0h5pyfEMrzI24UvXBBE2dkGX7bsx/Wdb3tuorLWUVFSrGI1k7cDebeZmH/k+w9Vr9mHFYbSlTfRlhq1sjc9SMRrJpLC8mqrEbZZmH+FzwKvrSro3aqSlD+C12m2sOSqrl3UH609kME9zyNw6gKirwNlL3aAArMbHula7jQ2xmbJ5mcoMBsGvJzK4Qrun+7QOMBlh+X65WruT5OxSOQaRjWtzIvPnP/+ZmpoannnmGX788cdOK7+s1bZuJPJhw4aRn59PVFTDJ3B9+/YFIC+v/u3n7777DoA5c+bUm6fRaJg9ezYA33zzTatiao8z21aam32khyxSt9lHLWf/UJLcRwMQqlxg/47fmllD6go1egMep380P3cdr3KzD5PA4ZR4DwZgjOY0u/ftVTkgCWDTyUwWYrko02UDpjYnbAbCwzhm1UxNDIdPxlNVI5uXqW39iQuWksugXqfti0VeBk6eAFyq3U9hUQEx5wrUjamHO3qugIyiCsvdO+g+x0v0NaAxVl+9WrsTDQZ5V8bGtbkG3r59+3j//fe58camK2hlZmZ2aQlNrVaLt7d3o/NNfVyGDRtWZ3ppaSmxscYOr5GRkQ2ua5p+4MCBDoi0eUIIAs/+Yn7ef2bXN2trjGbkTbDzMACGI1/AvC6uCy/Vszsxm7mGXaCAHi1Ow1Vu9mGiKLiOuwU2PgdAYNoaSiqvwN1JhRKcktlvx9L4p3Y/AHqdG9rBKjf7MNFoUUbcCDv/hU4xMKd6O3uSZzNjUC+1I+uxzuaVkXruPDOcjhonuAeqWxTCmoMLRF8Nh1fgrlRwieYAv8VGM6q/en1Je7pfT2TQh2zGamqLM/UaAoFD1Q3KxM0PBs6H+LX0VgqYojnBhlgf/jQrQu3IpDZq85mEo6MjkyZNana5jiy/3BHWrVsHwJ/+9Kc601NSUsxxBgYGNrhuUJDxKmFSUlKT+6isrKSystL8vKjIOOhSdXU11dUtb4aVePIIQwwpxscOgwgJHtiq9TtTn4mLKd/5DC5UMrp0Oxdy8vH3al3zP6k+0/+3Lf/nmD2/Mb22mVBu78n4OHpCNzleiLoGNj6PBgML2c2mE+lcNjxI7ahsXluPl8LyajRJm/HU1RY9GbyQanTd53iJXoLDzn8BcIV2D18dS2dymLe6Mdm49ny3/BJznku0B3BUjP3b9FFXYdAboJsUYlCGLkF32Nhf8wrtHl46sYDH5gxA6QYtGGxVe46XDbHGZmUm+qirMXSX7xZqj5f4tQBco93Bo+eGcyanmCAvZ5Ujs01qn5e2OZFZtGgRMTExhIaGNrlcaWkpb775Jn/729/auqsOs2HDBg4dOsTChQu59tpr68wzJRsALi4uDa7v6uoK0GwZ5ldffbXBSm1btmwxb6NFTq1miOmhy1hia5Ow7iLYcSTjqvbhq5Sw7Mt36R0yrPmVpBbZuHFj8wtZqTGAb9JPUNsSM9Uxij3d7HgZ6RxJSMVJQjWZvLPxR5RzIWqHZDdae7zsy1K4TLE0+9hf3p+sbna8zHDuh3fFWUZqkvhzzGF+0aWikeel7dbaYwXgm+Na/q6xNCvbWRBIQXc6XoSB+Q6+uFTnMU1znPzcLD5ZtZ6gVvzcSg1r7fGSVQ6puTqudLQkMr9n+1DWjY4XjUHPAq0bjvpS5mkO4UQVb6/awrRA2beqLRqrAtxV2pzIvPHGG9x0000IIbjyyivRaBrubmMqv6x2IpOTk8Pdd9/NwIEDWbFiRadeqXn66ad57LHHzM+Lioro168fs2bNws/Pr0XbMOgNZB55yvhYKEy6/gm8Avp3Srxtdd6nFH7fB8DA8qNMXfiUyhHZvurqajZu3Mi8efNwcHBo8Xq/x6Yz/egDAFQpjoy6/i+McvLorDDbRPTOgl+fAGBI2X5mzv0Dro6yeVl7tPV4WbtiF3M1xqah1U4+jL3uCdC2fP2uoPGKh63G6pKzDPvoFfUiE8J8VY7KdrX1WMktqaR07xomOZ4EjGMNTb72gW7RX9Oaxmkf7PsfDoqeBdoDlPvdzcJZ4WqHZbPaerx8ujuN8JjfidKkAWAIHs3Mq1WuttoArdgMx77EXalghiaGTO0lLFw4Ru2wbFJurrqVJdt8FnHNNddQUVHB4sWL8fT0pH///vj6+tZLEKqqqtodZHuVlJSwcOFCNBoNmzdvxt/fv94ynp6e5sfl5eUNbseUdXp5NV2pxcnJCScnp3rTHRwcWvyFcCJmG0Mx9ueJdx7BkD7d7ws5ZOIiyn5/FFcqGF22i/yScgJ8PJtfUWpWa44VgJRDG1igGO8qFvSdTYB7NzzhG3YN+l+fQoueS5Q97ErKZ+FwlQZHszOtOV5KK2twT9uIi9b43awbugjFuRteuh5+rTmRuVy7h1VxOUwd1FvloGxfa79btidlcJlmL1rTWENDF+Pg2A2qT11s2BLY9z8ALtfs5fW4q3h0fsP9XaWWa+3xsjUhhyutikJohi1B04r1u8ywxXDsSwAu0+7jydQJVAtFXlxrg9YcH52hzVXLtm7dyt69exFCdGr55fYqLi5m4cKF5Ofns337dvr169fgcmFhYeYkLCOj4QoWpkIB4eGdn1QU7PvK/LgiclGn768tFEdXUv1nAuCllHF8+2p1A+qhqvWGOkUhfCZ0k+pTF3PzozBoMgB9lRxOHvhd5YB6ph2ns+tWKxt2bRNLq8h3APrAEQAM06QSe+KILKurgk0nM+ucmNJdj5c+o8Hb2Fx1siaWC+nnuFDY8EVJqXMUVVSzPyWXK2ubIQoUYyGG7mjADHD2BmCO5jBKTQW7E+WYVbaozYkMwKpVqxosudyR5ZfbIz8/n7lz55KXl8eOHTvo37/xpllubm5ER0cDEBcX1+Aypunjxo3r+GCtGPQGwrON7VKrhZaBs1QeDbcJnmOvMz92OPWjeoH0YPtPZzBbGKtPlWvccBis/lhDjfEce735ca8za+XgmCrYfjyJ6ZpjAFS69Ib+k1WOqHHaYZbKe+NLt3H8fNP9E6WOVVGtJ/F0HKM1iQCIgCgIGNLMWipRLCfNOsXApdr9/B4nx6zqSjsSchgsUgnTZAKghE4Fz25a1EXrAEOM1VbdlQpmamLYIsc4s0ntSmSmTJnCjBkzmvybMmVKl5ZfNsnKymLmzJlUV1ezdevWOpXIMjMzueSSS8jMzKyzzpIlSwDYvHlzve0ZDAZ+//33Ost1lvijOwnCWH0qznU07t7dt+xonzGXUYIbAKPK95CRm69yRD1P0oH1eCrGZo95fWaDQ/etvKKLupwaxXjrfgF72B6f2cwaUkeq0RsQCb+Zq09ph14FjfRv7BasruZert3DZnli2qX2JOcy3bDP/FzprlfXTYZeY354uWYvW+Tx0qU2x2UyX2s1PEX0ItViaRGr43mhdh9b47NVOV+V2qfNv2Bnz54lICCg2eXUKL+cnp7OjBkzcHV15ffff6/XJ6a8vJzffvutXl+YBx98ED8/P9asWUNKSkqdeV9//TXp6enMnj2badOmdWr8eYdWmR9XRizs1H21l+LgTGrALAA8lHJid6xROaKexWAQuKf8an7uO66bjB3TGBcfCoKMn59AJZ+Ew1tUDqhnOZSWz7Qay4CkuuirVIymBbz7UxVk7IA7RHOWUycOqxxQz7L5VCYLNActE4ZcoV4wLRE4HOFrbPo9XnOKk4kp8q5vF9EbBFvjs+seL4MvUy+glgibAS7G8Ybmag6RU1BIQmaJykFJrdXmRKZPnz4dGUeTsrOzycjIqNN3paFpAOfPn2fatGnExcVRUFDA3LlzGTt2bJ2/K6+8ssH9+Pj48O233wJw6aWXsmHDBlJSUvj000+59957CQ0NZeXKlZ33QjEOgtnnwibAWK0sYtp1zayhPs9RlpNnbUL3KbHYExw/m8c0vfGKaZXiiEvkfJUjap7XaMvx4pHym+z30IW2nEhjpiYGgEpHH+jf/FhganMcusj8OCxnKxmFFeoF04MIITh08jTjNacAMPiEQ69u3nleUVBqky2tIphiOMDeZNnvoSscPVuAZ1kakZqzxgl9x3ffZmUmWgeINDYvc1MqZfMyG9WiRObLL7/ssOpj3333XatrTo8bN46goCDzgJQA48ePrzcN4MCBAyQnJwPGPi2HDh2q93f8+PFG9zV79myOHDnC6NGjWbp0KZGRkbz88svcc889HDlyhODgzq2ylBJ3hFBxDoAEpyi8A/p26v46Qr8xl1CGsTnT8NLdFJbKE42uErt/E70UY7+BrICp4OimckTNcxiyEEPtV880/T6OnpXNEbuCEILC2I24KrWD9Q5eCBqtukG1RKTlqu4C7UHZ76GLxKYXMbR0j7lamSbq8m5XcrlBtSemAPM1B2Xzsi7ye9zFd+8ub3zh7sSq+dt87QF5vNigFiUyt956KwUFBR2yw7vuuqvRqmCNSU1NRQjR6J+1RYsWNbms9V9jg3lGRkby5ZdfkpGRQWVlJcnJybz55pt4e3u38VW33IW935kfF4de0un76wiKoyup3hMB8FWKObbnN5Uj6jkcTq81P/Yc1c3br5u4+ZHjOxqAAZoMjhza28wKUkdIzCphTNlO83OnYd28WZmJXzjlPoMBGKUkcvD4SZUD6hk2n8riEo1Vf4chDbdk6Hb6jMHgbizTPV1znD1xabLfQxfYlpDNAuv+MZE2ksiETgNH45hrszVHOZKWQ2G5uiPVS63TokSmI78E5BdK0/zPWUbRDZna/ZuVmThEW37kqk78pGIkPUdSVjETKoxlLvVo8BxuIz8cgOsIy0m0Er+2iSWljrLpxDnm1A6CWaV1M7YPtxHOQ43NhTSKwC1tI+VVst9DZ9tzKpWpGmPrBb1bIASPVjmiFtJo0NTexXNSqgkr3E9iluz30JlySyrJPp9qrm5HQDT4db+x7xqkc4KB8wDwUUoYTRw7T+eoHJTUGi0e+efbb7+tM2hkW+n18geoMedTTzNYfxqAZN0ABvTv5u2RrYRNupqaXU+gw8Cg/O1UVtfg5CAHlupMh/fvYIkmG4ALPuPo69oNB8FshPvwq2DLcwCMLt9NWm4pIX7dv1mcLcs6/js+ivGErnrAXBy7cXW7iylDLocd/wRgNgfYnZTDnCFycMzOkl9ahX/GdpwcagDQRl3RvavbXSzyMjj4CQDza5sjDuztoXJQ9mtnYg7ztIcsE2ylWZlJ5GUQ+wMA8zSH2HF6AZcN7+b9eySzFp9pPvzww50ZhwSk7foWUwmFnL7zGKBqNK2jc/clwW0Ug0oP0U/J4sCh3YybOF3tsOxbnGUQTOfhNtJMyMQnhGz3wfQqiWekJpmvjhwnZO5EtaOyW4Vl1YTlboHaLjFuIxapGk+rBY2k3DUIl7ILTNbE8lpsikxkOtHOxBwWaPZbJtjaiWnodAyOHmiqipmrOcwfT6Vz7wwbuUNgg7Yn5LCoTjPEbl7d7mIRcxEaHYqhhvmag3ySYCzDrNhCnzCpZYnM9OnTO/Qf6uLi0mHbsieeaZYyukETbadZmUnNwIVw1HhVpvDIjyATmU5TWFbNsKLt5sah/mNspH+MFU3kZXAwHoDy4z+DTGQ6zY7TWczTGD+bNYojutqmFDZDUdBFXQ4HP8RJqaH61G8IMUGeaHSSnXHneba2ul21oxcOIVNUjqiVdI5oBi2AE9/jpZShPbuHkspJuDvJVgIdTQhBTEIyr2uMfdeEdwhK76EqR9VKLt7GwTuTt9JPk41HUQIpORMY0Mtd7cikFmjRp3rr1q2dHIZUmJdFZOUJUOC8Eki/wWPUDqnVwqYugaMvA9A383cMBoFGI080OsPBmKPMqS1zec4tmr6enVtNrzP4jrkaDv4LgEH5Wyksq8bL1UHlqOzT6ZhdXK7kAVAYNAU/J9trZuMQdQUc/BCA8VV7OHWhmKjg9jd3luoSQlCWsA0PxTjOmmbwpcYytbYm8jI48T0Ac5QD7EnKZV6UvIvX0eIzi4kqO4DO0TheoDLkCtuobnexwZdB8lYA5mkOsjPxUpnI2AgbavRq3xJ2/4ROMX4RnAuYYZNfBC7+IaQ4DgIgkhROxcWqHJH9KoyxNCuriVigYiRtpwQOI9/R2A55gnKK3bFJKkdknwwGgWvqJvNzzxE21uzDJGQylTpj4jJTc5Sd8ekqB2Sf4jKKGV1paVamjbxUxWjaIWIuBo0xAZunPcSOBFlWtzPsSMhhjvaIZcIg26i2Ws9gy3E+T3uIHbLDv82QiUx3kWBpVuYxrJuPhtuE4hBLk5WMg7J6WWcwGAS9M7eZnwePs7H+MSaKQlmYcQBPB0VPVsyvzawgtcXJC0VMqLGM7+AQaZuJL1oHqgfMBcBTKScrdqu68dip7fFZ5up2BkUH4bNUjqiNnD0xhEwDoI+Sy/n4Q82sILXFzoQMZtQ2Q9Q7ekJ/G20i7N0PETgcgOGaFFKS4qnWG1QOSmoJmch0AzXV1UQUGcfSKMWZgeNt9EQDCB63yPzY8+zv6gVix2JTLzDWcAKAfK0/jn1GqBxR2/Uabbk74Ht+CwaDLM/e0fafiGOkxni3K89jMHh1/0F2G+M2dKH5cWDmdkora1SMxj6dPnmY/rXVECuDJ4Czl8oRtZ0u0nJ3YHDRbs7mtW4wbqlpFdV6qlL34a2UAqAZOMc2myHWUqwG351Yc4CYswXqBSO1mExkuoGEI9vwodj42G0cDo62Uxb1Yv4Dx5GrGMsAD62KITuvQN2A7FDygXU4KcYBu3KDZ9pkM0QTx/DpVCjG432i4TAn0wvUDcgOlcda7nRpB9vuRRIAJWIOhtqfrZnKEfYm56ockX0prazB/8JW83PnaBttVmYycL754SztEdlcqIPtT8ljOpY7XcpA2/5+sW4WN1NzlO3yeLEJMpHpBgqO/mx+rLfR/g5misJ5/6kAuChVJOxdp3JA9scpxTJoqu8oG+3vYKJzIqvXJAB6KUWcOrStmRWk1igsr2ZAwU7zcy8bGjS1Qa6+FPqPAiBCk87x40fVjcfO7E3OZaZy2PxcGWTjiYxvGBVexrLLo5XTHDqVqHJA9mV7QjazNEcBECjmgSVtVuBw9K4BAEzRxLIv4bzKAUktIROZbqB3huXkbcBkG+3vYMV1qOXHryb+NxUjsT/ZRRUMLzd2xK3CAd+hNv7DAbhFW5oLkbBBvUDs0K74dKYqxtHZy7Re0HesyhG1n6vV8aIkyuOlI+0/mcxYxVgSvdQ9BPwjVI6o/RyHGH+PtIpAm7qFGtnvocPEx58ksrZ6pj54DLj5qxxRO2k0aAcZ7+K5KFW4pO+lsLxa5aCk5shERmUXziQSbkgB4LRuIL69+6scUfuFjruM6tqR9yIKd1FTo1c5IvsRc3AnwbVldM95jQVHN5Ujaj+/UZa7BIOL98gfjg509shmcxnd4n4zQaNVN6AO4BRluVAysnw/Z3Jlv4eOUpWwyVw90yHSRqtPXURj1Zxykv4QMecKVYzGfmQWVRCSZ7nbqxtsH8eL9V2lGcoR9iTJ5qvdnUxkVJa2d7X5cV6wjVaHuYjO1YskV2MH9D5kc+rEwWbWkFqqLNbSVE9rJycaeAZzwWUgAMM1yRw4cUrlgOyDEAKPs5vNz31svRmiSUAUxU7G8UAmak6x61SaygHZhzO5ZQwt22t+brqTYfP6T6JKZxwPZIYmhp0JGSoHZB/2JOWaq9sBMMjGm8WbhM/CoBgv+MzUHGXH6WyVA5Ka0+mJTFFREXfeeWdn78ZmOaVYxnfwH2MnJxpAVdhc8+Ocw7IMc0eo0Rvon7vD/LzP+EXqBdPBqgZYjpf8o2tVjMR+nLpQzMTasst6NDgOsv1miAAoivn7xUmpJufYxmZWkFpi5+kMZtaW0a3SukLIFJUj6iBaB/RhMwHwVUrIOLmzycWlljl4+hyTNScBqHQNhMBhKkfUQZy9EP2MJaTDNJmcOX1c5YCk5nR6IlNeXs6KFSs6ezc2qby0hMgy4xWNHLwZMMxOfjiAvhOuNj/2O79VvUDsyInTyQwXpwG44BiCzi9U3YA6UOBYS98wv/StCCHLMLfXiWOHGKAxXn3O9h4FLt7qBtSBfEZYmiP2ztxKVY3s99Be6Sd24acYq2eW9ZsOOkeVI+o4LlGWflV9s3fI5qsdoDpxq7l6pnbwApuunnkxUz8ZgIjC3WQUVqgYjdScdiUyhw8f5p577mH8+PEMHDiQAQMG1PsbP358R8Vqd+L3rcNFqQIgxWcKih20Xzfx7R9FujYYgKiak2Rkytv57XXh0C9oFOMJfmG/OSpH07GcQsZTpDGOVzHOEEN8umyX3F41cZayy7ohdtIMsZYmfAbVinG8iqkc4XBansoR2TaDQeB1zjLuly0PytygCMsd31mao7LfQzudyy9jeNk+83O76R9jYl22W3OUPcmyDHN31uZEZv369UycOJGPPvqIgwcPkpSURGpqar2/s2fPdmS8dqXypOVEw146VlrL7D0dAJ1iIHHvz80sLTXH7YzlRKPX6CtVjKQTaLRk9zaW7fZQykk4IJsLtUdljZ6Q/N3m53720j/GxNGN3F4TAAhW8jh5dHczK0hNicsoZpLB0t9Bay/9HUw8elPkMxSAKE0asadOqhyQbduTmMNM7VEAahRHGDBD3YA6WsAQKt2MF2InaE5xMF6ex3ZnbU5k/va3v+Hp6cl//vMf9u7dS0JCAikpKfX+9u3b1/zGeqig3D0A1AgN4RNtfHyHBnhaXdXTnJZlUtujqLyS6ArjiUYprvhFTlU5oo7nMczS/EOTKBOZ9ohJvsBYjEUT8hx6o/SKVDmijuc21PL9okva1MSSUnOOnIxnqCYVgFyPSPDorW5AncC62p0ij5d2SYo7TB/FeFerNHC8XVTPrENRzIMHOyk11CTL8c26szYnMrGxsSxbtowHH3yQ8ePHExERQUhISL2/sLAw+ve3/ZLCHS09NZ7+Ih2A045D8PDyVTmijhc2Zj7lOAEQUXyAalmGuc1iD243t18/4z0WtA4qR9TxAkYuRF/7lTSweD/lVfJ4aauzRzaZ268XBk21q/brJh5DLXexB5Xsp7BM9ntoq9I4S3U7JcK+mq2aOFk1r4wsPUBWkez30BZCCJxSLSf2btHzm1jadumsynYPL9vP2TxZ5r27anMi4+bmxpgxY5pdzt/fn5SUlLbuxm6dPWBpalXYZ7qKkXQejaMzyW7GUbgDlHzij+1tZg2pMSUnLXe07PVEA1dfzrsa7xwMVs5y9KRs/tFWDqlbzI99httJGd2L+Q4gz6kPAGOUBPbHp6obj42q1hvonW2p5OUz3P6aOQMQPIpynScAUzUn2JuYqXJAtiktt4yRVYfMz3UD7aQa4sXCpqOv7Yc3U3uUPYmyn0x31eZEZv78+ZxswYlGRUUFn332WVt3Y7ccrU40/EbY6YkGUB1qGRsnL2a9ipHYtl6Zu8yP+4+zs/4OVir6zzQ/zjkqj5e2KKqoJrL0AGAsu+wdPbeZNWxXWT9j23wHRU/WMdlcqC2Onc1nMscAqFScUWpLz9odjZbSPsYmuZ5KGWdP7GhmBakh+06nM1FjbLZa4tgLAoaoHFEncXSjJMjYD6+PkkvSqcPNrCCppc2JzBtvvMGrr77abB+YwsJC7rjjjrbuxi5VV1cRUWK8opGPB+F2VHb5Yn3HWfr+eKXLH462OHchk2h9HAAXtMG49g5XOaLOEzja0u/B4/x2FSOxXUeOn2CQ5jwA6W5DwMVH5Yg6j99IS78qt3OyHXtbJMTspZdiHO0+p9cEuyq7fDEvq+aILmfk8dIWWbHbzNVWK0Nm2GWzVRO3KEvzMqc0OSxAd6Vr64rPPfccXl5eTJ48mcGDBxMREYGfnx/KRQd1eXl5u4O0N0mHtxKpGN+XZI+xjNG1+d/Q7fmHRJOhBBAosoisOkFBQT7e3vZ7YtUZkg+up69i7C+S3XsKQSrH05k8wydSorjhLkoZUXWE7MIyenm5qh2WTSk4bmmGWBUyq4klbZ/LwJnUoEWHnpGVh0kvKCfY20XtsGyKIdHSP8Z1iH32dzBxGDQXasfbHVV1mDO5ZfT3k98vLSWEwMvqApN1YmiPdAPnwqbnABhVfZjknFLCe7mrHJV0sTafQS9fvhxFURBCEBcXR1xcXKPLXpzc9HQFxy1llw0DZqsYSRdQFNL9JxGYvQYnpYaY/b8xfv4NakdlU0Sipeyye7R9/3Cg1XHeZzyD87bgo5Sw9dA2Zs6236aXncEr3XKiETh6YRNL2gEnDy54jqBf0WFCNZmsizlM8Az7vcPd0Sqq9Qwo3Gtum+EzzM6/X7z6kOs6AL+yZIYrSaw5lUT/qXYyIn0XSMouYaz+KGjAgIIuws7PXwKGUOrYC7eqbCZqTvFDQjrhvQapHZV0kXbdCvj3v/+Nl5dXk8sUFBTw2GOPtWc3dsc3w9LEKnS8/fZ3MHGKnA/ZawCojt8IMpFpMb1BEFZoLJJQjZaQ0fZ9xRRAN3AO7DP2ISs/tRFkItNiGfmljKw+AgqUKm64hU1QO6TOFzEHDhvbr5ed3AAykWmxw4nnGaPEA5DnEISvn/02WzWpCZsNscloFUFB7EaQiUyLHTkZzxJNGgA5HkMIcPNTOaJOpihUhszE7fR3uChV5J7cBlNkItPdtCuRueGGGwgICGhymczMTB599NH27MauFORkElF9GhRI0YQQ1idM7ZA6Xfj4y6jZ/iA6xUDfvD0IIeRduhZKOHWMIRir66Q4D2WQi6fKEXW+vuOugH3PAhCcs0seL61w8tA2ZiulAJz3mcAgrf02WzUJHHUZHP4/AHplyeOlNdKPbmSyUgNAYZ9p+PaA981/xKUQ+xEAfhk7EOJReby0UOlJq/G97L01SS3vYQvg9HeAsZ+vwXA3Go08XrqTNnf237FjB35+zWfjvXr1kuWXrSTt/wWNYuwwltlrssrRdA1nDx+SnIyVTULEedKS41WOyHZkHl1nflxmVdHLnjn5h5Ku6wdAtCGB5LPpKkdkOyrjLCcaukF2Wqb7Ig59RlCk8QZgjOE4iRfy1A3IhjhadXj3tdeyyxfRhk2hSjEWNBhvOEpCRrHKEdkGg0HQK8tSPdNvZM+4U64Jn40BY+IyXn+EhCx5vHQ3bU5kpkyZglarbX4HGg0hISFt3Y3d0SdYSoTa60BSDSm2Givn/MGfm1hSsuZmdaIROLpn/HAA5AUay6TqFAOpB2UZ5pYQQhCUu9v8vO/Yy5tY2o5oNGQFGC8KuSsVnD70ezMrSGAs0x1lVabbK8p+y3TX4eBCps9YAIKUPE4ea7ryqmQUn1HIBBEDQIXigrZ/D2i2CuDmR66H8ULsEM0ZjsQ23h9cUkebExmTiooKli1bxuLFixk7dixjx45l8eLFfPjhh1RUyJFzrQmDgdACY3+HCuHAwLE9J5Hxt7p645S2Vb1AbEhpWTlDKo4CkI8XgYN6yA8H4GXV6VibLE9MWyL5bDpDDQkApOv64egfqm5AXcjFqtqWsKrCJTUu5vgJIjTGu53n3YaCc9P9Xe2JwyBL0lYdL8cfaon4o7vxV4oAyPSbAFoHlSPqOopVUYPyOHm8dDftSmRiYmKIiorij3/8I6tXr+bw4cMcPnyY1atXc9999xEdHc2xY8c6KlabdzbpOAEYmz0kuIzA2bXnlPELGTqFQoyvd1DpYSqrKlWOqPuLP/g77rVlutO8x4Om3dcdbEbfkXOpqu3CN7B4P1XVepUj6v5SD/2KTjEAkBfYszq8B42yVGcLLdhLjd6gYjS2Id+qemZV6AwVI+l6AVbHS5+8PfJ4aQH9acsFAqfIHnL3rpbvcMuF2IDsXegNcjyZ7qTNZ0aZmZksWLCA1NRUoqOjufPOO3n66ad5+umnufPOO4mOjiYlJYUFCxaQmZnZkTHbrNzjlvbrZf2mN7Gk/VG0OpI9xwPGUZUTDm1ROaLur/SkZTwQjb2XubyI4uROiutwAPoo2Zw6IUdVbo71nStPOx/f4WIaz96cdYoAIFpJIfZ0ksoRdX/eVgMUB47uIc0Qa2kCIsnX9QJgjDjJyTNZKkfUvekNgn75e8zPA0Ze1sTS9kfTbzwVinF8qoniGCfPF6gbkFRHmxOZ1157Db1ez8aNGzl27BgfffQRr7zyCq+88gofffQRx44dY8OGDdTU1PDGG290ZMw2y/WcpaNc0Oie9UUAQLjlZLzoxG8qBmIbArJ3mh+HTrD/Mt0Xq7QazDH3mOwn05SaGj0RRca2/tXo6DtynsoRdb2SvpaLQxlH5PHSlOzCUkZUHwGgWHHHPWycyhF1MUUht7YfnrNSTdqRDc2s0LOdSktnpDD2Dcl2CELjP0DliLqYzpFsf2PTbn+liIRju5tZQepKbU5k1q5dy5tvvsmcOY1Xxpk7dy7//Oc/+fln2bkbIKLyBABZ+NJ/8GiVo+l6IVZj5vhn7GxiSSkrM52BNcaryim6MDx79VM5oq4XPMaS7HtajSYt1ZcQd5y+SjYAKa7D0Dj3nGarJn5WzT9czmxVLxAbEHd4G15KGWAs042m+cI99sbD6q6lLlm2EGjK2cMbcFSMzXvzAqepHI06nK2a0xlOy3543UmbE5mzZ88yc+bMZpebOXMmZ8+ebetu7Ipzbb3+VO+JKD2ov4OJb1AoqVpjBbuBNafJzb6gckTdV9rBdeYy3bkBPau/g4l/+GhyFV8AoiqPUVhconJE3VfuMUt/h/L+Pau/g0lA9AzKcQJgSNlByiqrVI6o+6o4ZWnmrBnYM8p0Xyxg+AL0tadAEcX7qayR/fAa45BqSfQ8hy5QMRL1+I+09Kvqny/74XUnbT6bdnFxIS+v+Xr9eXl5uLi4tHU3dezevZvBgwejKAqpqakdsk01aHvI+A4Nyao9KdcoguR9a1WOpvvSJG81P3aP7pk/HCgKZ30nAuCqVBK/f2MzK/RcnnX6O/TAZqsAOifSPMYA0Esp5OTRPc2s0HMF5liaxvQf17P6x5gorj6cdYkEYKByjpOnTqocUfdUrTcQXrQfgBq0BI7oec1WARTfAeQ4BAEwijhiU+X4Zt1FmxOZkSNH8tZbbzW73JtvvsmoUaPauhsAysvLefzxx5k+fToJCQktXm/fvn0sWrSIXr164eLiQnR0NH//+9+prGy6YtaFCxe477776N+/P05OTvTv35/77ruP9PT2H7gGoRAxoWf+cAC4RVlOyg2yTGqDDAbBgNofjnLhSPjYnlUhxpp1mdSKeNmOvSHV1TVEVhjHd8jDi94RY1WOSD36AZZ+VbIfXsPSMzIYojf+jp7T9cfZv+eO81bWb6b5cXbMr40v2IMlxJ8kTDG2nkh1iUbpQWW661AU8/hmjoqec0dlGebuos2JzB/+8Ac+++wzLr/8cn777Tfy8/PN8/Ly8li/fj2XXHIJX331Fffcc0+bA0xKSmLkyJGsWrWK9etb3oHzyy+/ZMqUKWRmZvLDDz9w4sQJ7rzzTl588UWmTZtGSUnDzVROnjzJsGHDWLNmDf/+97+Ji4vj3//+Nz/++CPDhw/n5Mn2XbVJdBiIl19gu7ZhyyLGzaNCGOvPhxbsRRjk7dmLVRacN5fpTnQdgYOTq8oRqSd0/OUYhHFU5eAceYW9IZXZibgrxjG70nwm9qgy3RfrM9bSD8/vwo4mluy5zhz6zVymO7uHNls16WU1vpn7OdkPryF5Vs1WS/v1zGarJtbN6hxSZL+q7kLX1hVvvPFGfvnlF7766itzgqGp/QE11J6cCiG46aabuP7669scYGxsLHPmzOGNN97A3b1lHViTkpK488478fPzY/369Xh7ewPw+OOPU1lZyTPPPMOjjz7Khx9+WGe9mpoaFi9eTG5uLrt27WLyZONo0WFhYQQGBjJ16lSuvfZajh07hk7Xtreup3aUM3FyduO4ywiGVRykN3mkxB0hLGqM2mF1K865x82Py3v4D4ebT28SHSKIqDlNhCGF9HOpBPcNVTusbsWz0HK8KBE9t9kqgHffSDI0vQk0ZBJZfZL8/Hx8fHzUDqtbUaxOwNyje86gzA3pNXgyJbjiThlR5Ycoq6jE1dlJ7bC6FffzlgsCAVaJX0/Ue/g8atZr0GFgYPE+qvUGHLQ998JRd9Gu/8Dnn3/Oa6+9hq+vL0II9Ho9er0eIQS+vr68/vrrrFy5sl0BXnbZZbz33nstTmIA/vGPf1BZWckdd9xhTmJM/vSnP+Hk5MQnn3zCmTNn6sz76quviIuLY8KECeYkxmTKlClMnDiRU6dO8c0337T59XgP66H9HayUWZ2cZx6R/WQu1q/0hPlx7x42vkND8oOmmh+fOSCPl4sNrLAkMqHjemj/GBNFId3P2K/KSakh8YBsXmZNGAQDCo1luiuFA6FjenYig1ZHipdxfDNvpZT4w/IunjW9Xk9kubFMdwEeBA6eoHJE6lJcvDnjEgVAmHKBuFMnmllD6grtSmQUReHPf/4zFy5cYM+ePXz99dd8/fXX7NmzhwsXLvDkk0+iKEq7AtRqW1cWUq/X88MPPwA0WBray8uLcePGYTAY+P777+vM++677xpdD4zlpIE2JzLFwpnwUTPbtK49CRpjqf7henabipF0P5VlJUQbjPX6M/Gj/6ARKkekPuvBHTVWgz5KkJ91nkhSAUjSDsA7oK+6AXUDjoMtnZGrE2SBCGsVRRkEYyzTnegyDIceWKb7YoYwS7+q4pMy8bVWmZuMZ22Z7mTPcSjaNjfisRulfS0XYnNi5HhV3UGH3BPT6XRMmDCB6667juuuu44JEya0uelVeyUkJFBQUABAZGRkg8uYph84cKDO9H379rVpvZZKch2Jg6O8bd1v0GiyMJbVHVQeQ0V5qcoRdR9JhzfhrFQDxv4OPbFM98XCR82iFGfj4+IDGPSyTKpJ2kHLD2lWwNQmluw5BoxfSI0wfm765O5VOZruxSnHcgW5pM/0JpbsOfpaVW2T45vV5ZFnudurt0r4ejLrMsxusl9Vt9Dp2UZmZibBwcHou+jkIykpyfw4MLDhTvVBQUH1li0pKSErK6tF62VkZFBWVoara8OdsCsrK+tURisqKjJO7zOZ6urqlr4Uu5biPZGAgnU4K9XE7PuVqClXqh1St1BmNb6DGDBLHi8AiobTrqMYWbYHPwqJj9nFgGGT1I6qe7C6Q+USOVseL4CDiyeJjoOJrD5FiDjHueRT9O4XoXZYqquurqZvqeXE1HvYPHm8AJ4BIZzV9KGf4TyDquPIy87Aw9tP7bBUV11dzQCrZquBIxfI4wXwCx9DIe54UUJk2WFKSktxcnRUOyxVqX1ctCqRycvLw9fXeCX94v4ljcnKykII0frI2siUNGi1WhwcHBpcxpSAFBYW1lsPaHTcG+vEpbCwsNFE5tVXX+XFF1+sN/283o9169Y18wp6hkptGKbWtul7vye1UN6yBhiWtQsAvVA4U+pKhjxeANDrBjESY9Wy+M0riTub38wa9k8YBFMK9oMCZcKJpGw9afJ4AUBxGEJk9SkA9v+0DG3YTFXj6Q6EvoZ5+lOgQLbw5mRKDnFp8ngBcNFF06/qPDrFwOZv38OxryxAIypLuMKQDAokir7EHouDY3Fqh9Ut9NJFM7lmH55KGV99+T9cAwaqHZKqysrKVN1/i88er7jiCtatW8eDDz7IW2+9RWhoaIv7v7S3n4ytefrpp3nsscfMz4uKiujXrx+XXLkEPz95pQcgP2c0hvffQ6MIIqtO0nfhwuZXsnP5mWkEHDkHQKJuIIsWX6dyRN3HuaQQ+HoFAOHV8Qxa+J7KEanvQsIhesUUABDnPJwrr7pK3YC6kfjeLvCrsa9kWE0SQxe+oXJE6kvctxY3xdhSINFjHJdf3sMLQ1iJcS6FPcZxqkJFGiMXPqdyROqL2/wZWsV4Efq8/2QWyt9osyPVSXDC2BUhVLnA2IUPqxyRunJzc1Xdf4sTmZMnTyKEqDMgZZ8+fZrtjK/X6zl//nzbI2wlT09P836rq6sbvCtjyh69vLzqrQfGATgbYp11Wq97MScnJ5yc6veFcXBwaPQuUU8TENSPBIeBDKpJIMyQSk7OefyDQtUOS1XnD60noPZxdu8pDJbHilno4BGcpzd9yGRg5Qn0VWU4u/XQgdlqZR/7jf61j0v6TJffLVYGj5lF4Xo3vJRSwksOotOAou3Z709ZnKUZon7AbHm8WBk4cSFVu7U4Knr65u3BQaeDHnYB9mKGpK3mxw6D58njxUq/8VfCCWOrG7/MnT3+vVH79be4J/GuXbv49ttv+eqrr8zTDh48SEpKSpN/+/fv75TAGxMeHm5+nJGR0eAyFy5cqLesu7s7AQEBLVovMDCw0WZlUsvl9LYMxpa2/xcVI+kmkizjO7gNmdfEgj2Poiik+Rr7xTgqepL2y+pCrmcsFf98h1/SxJI9j4ODA/FuxuZBnpRy9sQulSNSn2+m5T3oO0ZeXbfm5eVNnGM0AEGGTPLO9fAmVEIQnGtsylspHIgYI3+PrAX1jyBF6QdAeFU8FUXq3pHo6VqcyAQGBnLttdea70TMmDEDxxZ0cHJycmL69K6rjjJo0CBzjHFxDX8ZmaaPGzeuzvTx48e3aT2pbbysyuoqST27rK4w6AkrMib9xcKFgSNlRaGLaSNmmx+Xx/Xssrr6ylIGlB8DIF34EREpy3RfrCJkpvlxbg8vk1pZmEFYdSIAccoAQvqHqBxR95MbaKn6d/5gz76wVnbhFL0MxjLdx3VRBPjJQWUvdtbHOF6VVhGkHZR9zdTU5tquW7ZsqTfYpLWamhri4uLw8PBgy5YtjS7X0bRaLddccw0Amzdvrje/sLCQAwcOoNFoWLx4cZ15S5YsaXQ9gE2bNtVZTmqfgaNnUSKMhRXCig4gDD23rO65k3vxphiAY9ponJydVY6o+4mYcBnVwtiUNTC7Z19hTzu8ESeMlWKO64ahlaNL1xM4ytIHxON8zy6Taj2Q7DmfiT2u32pLeEZbBqvWpXTdOUt3dP6g5XjJCpjSxJI9l3aQZbzBqviefWGN0hxVd9/mX78777yT4uLiRufn5uYSFRVFREQEhw8fbutu2uSvf/0rjo6OfPrpp3UqkwG8++67VFZWcvvttxMSUveq1I033sigQYPYt28fu3fvrjNv9+7d7N27l8GDB3PjjTd2+mvoCRydnEhwGw2AD0WkntijckTqyTpquaJz3m2oipF0X35+/sQ7GMdy6ms4T0F6osoRqacodoP5cabHMBUj6b4iIgaTjHGA0LCKU9SU9txKd1Xxm8yPtQNnN7FkzzVk1GRyhLGvbEjRIaipUjki9Vi3kHCJnKtiJN3XgLHzqRTGviGB2XugC6vzdjdV3/1B1f23OZFZsWJFo53iAXx9fVm1ahURERF1Kni1RXZ2NhkZGXX6rjQ0zSQiIoKPPvqInJwcLr30Unbt2kVycjJvvvkmzz//PGPGjOGtt96qt56DgwOrVq3C19eXxYsX88MPP5CamsoPP/zA4sWL8fX15fvvv1dtsE97VNF/pvlx9tGee3vW7azlinGVn0xkGpNr1a/qzIGe2/zDr3bgPr1QEL2iVI6me9JoFNK8jUXetYrgzKEe2rzMqr9DqXAifLQc2LAhrk6OnHQZa3xMBTlxO1SOSCU1lfQtPARApvBmyPAJzazQMwX5+3Fca/zu7WXIouJCD+1XVV6Ac84xVUNocyLT3NgwDg4OXH311bz33nscPXq0rbsBjH1SgoKCzANSgrE/y8XTrN16663s2rWLXr16cdVVVxEVFcVHH33Ec889x86dO/Hw8GhwvaFDh3Ls2DGuuOIKHn74YQYPHszDDz/MFVdcwbFjxxg6VJ5kdqTgMZbmH549tPlHVWkh4RWxAJwhEHfvgGbW6Lk8rPpVaXpov6qK3DP0q0kD4JRmIF5ubipH1H0pEZbmH+UnNzSxpP0qO3cMH4PxbtQRZQhBvj272l9TSvvNMD/OOdozE9+SxJ04YyzTfVAZhp97/QqsklGW1YW184fWNrGk/So+tRktBlVjaNethZa0sz1x4gR6ffv6PqSmprZpvYkTJ7JmzZpWr9enTx+WLVvWpn1KrRMSEcVZJYh+4gLhFSepKCnA2d1b7bC6VMrB3xisGD8jad4TenrVzyYNGTWN/F898FGKCSk6gNBX97iyumcOrGNQ7eN0v0nyeGlC+NgFVB7Q4aTUEJC929j8o4e9YemH1hJR+zjZeRjy+nrjAkZeAqefB8DtXM+8sJZ9dD3utY/PuMpmq01xjpwPF2rHNEvaDDyhajxqyD/+K94qx9DiOzL/+c9/GDBggPkPYOzYsXWmXfzXu3dvlixZYq4GJkkXUxTFXP3DQdGTuL/nXQUrs7pSrETI9utNcXF2JM7V2K/KgzIyTva8Tv81py39HZwGz2liSalfoL+l+Yc+k8rMeJUj6nqaZMudyyIfeWLalKGDB3JShALQpyIBUZKtbkAqcE7ban5c7hutXiA2YOjIiWQKbwD6FByCmkp1A+pqQnSLQiotTmQKCgpITU01/ymKwtmzZ+tMu/gvOzubESNG8M4773Tma5BsnMMgS2fCirhNTSxpnwJyjCfj1ULLgDELmllaKu/J/aoMevrmGUeULhIuDB49o5kVJOuqS+cO9rDmH1Vl9C06CsB54Y+vb2914+nmnHRakjyMF141CHKO97DxqkqyCCo/DcBxQyhBPg03wZeMArxcOOJgvLDmTCXlST3swlpuIj5VDY+72JVanMg88sgj5kEuk5OTEUJw4MCBRgfCTEtLo6CggMOHDxMVJTujSo2LmLDQXFY3KKdnfREUpZ+mjz4dgFO6SHr5+6scUfcXONoymJ/7uZ7VIbco5RCeogiA444j8fOU/WOa4xpluTggEhsurW+vihO24VhbpvuY0xjcHHtWs7q20A+wFEMoPtGzEpnik5YywnGuY3GVdY2aVRhsGX8ou4f1qyo52T0+Hy0+TL28vMwDTQKEhIQQGhqKn59fpwQm9Rw+Pr6ccBjC0JoT9DFcIOdMHP79I9UOq0ukHfgFU2OP3N5Tm1xWMho8cDCJ9COCs4RUnkJfmo/WrWcM2Hbh8Fo8ax8XBk9TNRZbMXTUJLI2exOgFNC34KCx+YeuZ3Rgzjm6HtM19dK+0+hZvcnaJnTUbMpinHBVKvHL2NWj+lUVnvjNfLxU9J9J80OeSz7DFmBIexmNInBK61njD5Wd3GDuT6WmNlctS0lJkUmM1GHygywnZWd7UPMPJcnyxec5dL6KkdgOrUYh1bt2VGUEZw71nOZljqlbzY99h1/S+IKSmb+HMzGOluYfJad7zl1f19oO63qh4D9MjgfSEkP7B3AQYysSL30uIjNW5Yi6iBB4pRvvcJcKJ/oMm65yQLZh9JCBnKjtV9W77DQUZ6obUFepqcQ7y9jMOVuoWwmx04eDzsnJMRcHkKTGeFudlGmTe0ZZXaGvJqToAAD5woOo0fKHo6U0EZaTsrKeUla3sph+pccBSBGBDB82QuWAbEdJX8tnK6un9KsqPE/vihQAjokIRg4MVTceG6HTajjnN9n8PCemhzQXyjyBR00eAPtENKPD5DAALeHv7kSsyxjz8/L4HtLP98weHA0VAOw2qFsUokMSmZqaGjIyMjhz5ky9v9TUVNLS0jpiN5IdGzxyKnnCeFN7QMkhDNX2P6pyxsldeFAGQJzraFyc5Y38lho0fh4VtaMq987e1SNGVc4+vgkdxjLd8W7jcHWUDdhbyn+EpZ+M85ltKkbSdfKt+nckeozDzUkeLy3lMMhSDbCqh5yYFsdaLggle42Xx0srlPebaX5cePxX9QLpQmWnLMdLmtdYFSNpZyKTkJDAlVdeiYeHB3369CEsLKze34QJsmq91DxHBx2n3Y0fBnfKSTuufkm/zpZl1THQuhKX1Ly+AX4c0xqvAvnrsym/cFLliDpfvtUPZE3oTPUCsUGjhgzihCEMgODyBCjJUjmizldidWJqGCDLurdG9LCxnBPGwisB+YegqkzliDpfudWJqSZClnVvjeBh0ykRzgC4n98BBnUHiOwK1QnGwikGoaALU7e/ZpsTmbS0NCZNmsTatWvp1asXAMHBwfTv35/+/fvj6OiIEAKtVktISEiHBSzZr+pQS7WYvB5wO9/dasC1YKtKXFLL5PTuWWV1vdN3AsYy3X1lme5WcXfSEe9uGc+s4ISdN0c06PHNNPYFKhIuhI6QzVZbIzLIk32Ksemmg6hGn2rn/aqqyvDNPQTAOeFPZNQolQOyLeMjgthjMParcq/Jh8zjKkfUyYoz8SqMA+CECCUqIkzVcNqcyLzyyisEBQVx9uxZzpw5g6urK9u2bTOXXy4rK+OHH37Ay8uLTz/9tCNjluxUv3GXmR97p9t3Wd2akjxCK04BkEg/Bg0crHJEtsc92nIyryTad78qQ24KAdXnAIhhEEND+6gcke2xLqtbaOdldUX6Udz0xjLd+xjKqNBeKkdkWzQahbxASxXJ/GN23lwobRc6YSzTvUsMZ3Sor8oB2RZfN0cSrC6UlNv7eHhJlt/bnWIEI/vaaGf/jRs38vLLLxMcHNzgfEVRWLRoEW+88Qavv/56mwOUeo7+IeEkKsa7d2FVCZQX2O+oymmH1qFVjP06zvpMQKPpGeU9O9LwURPJEMayy32LDkF1hcoRdZ6MI5Y7Tmd9J6HTdnqdFrsTOmKmufmHz4Wddt38I++45Y72Od9JOOrk8dJantHz0Avj97LGzgvQFMdaErV0v0k4O2hVjMY2GawulFg307NHFXGW13feb5Lq/ana/O124cIFRoywVM1RFIXq6up6y02fPp39+/e3dTdSD6IoCul+kwDQKIKUA/bbXKjC6odDM1CWXW4LbzcnYp2N1WKcqSI/3n77VVXHWe4g6AbL46UtRob1Zj/GflWe+jxE5gmVI+o8+njLiYajPF7aZGxkGEdFBAC+ZclQeE7liDrRaeNAmDVCg0ukLNPdFoOHjOCMwXjn0yv7IFSVqhxRJzEYUJKNw0YUCxe8B6k//l2bExlvb29qamrMzz08PEhKSqq33Llz5yguLm7rbqQexjlynvlxVfzGJpa0YQYDwTnG/g5lwomB42V/h7Yq7TfD/DjHXkdVrq4gMNd4MShLeDNk1JRmVpAa4qjTcM53ovl5rr02FyrLw7/gGAAJhj4MHzpc5YBs0wB/Nw7rLH1Fak7b6V2Z3CQ8So2VZQ+JQYwdHKpuPDZqwgB/tgvjZ00raiB1p8oRdZILR3GqygdgjyGKCRG9VQ6oHYnMgAED2LDBctVnyJAh/OMf/6C01JKFFhcX8+yzzxIUFNS+KKUeY9A4S1ndPrl77LKsbnHqIXwMxi+CGIcRBPt7qxuQDQscdQmG2uYfrufs845MVfIOnISx2dx+7WjCAzyaWUNqjONgy4WSaju9UGJI3IwG4/fmbs1oooI9VY7INimKUudCSdEJ+0x8xWnL52Anoxje11u9YGyYl6sDqV6WKr3Wza/sitXxsl2MZEyIj4rBGLU5kVmwYAFPPfUU7777LgA33ngju3fvJjw8nEWLFrFo0SLCw8PZvXs3V199dYcFLNk3by8vTjoar2r0ErnkpMSoHFHHO3fgJ/Pjgj4zmlhSas6IweHEYqyY0qciEVGcoXJEHS/r8C/mxwV9ZqIosj9VWw0dOoqztc0//POO2GXzj4IYS5Pcgj4z0Mr+d23WJ2oKhcIVAJdzO8GgVzmijld+0pKg5QXPlP2p2sEpYhY1wvj+6RPss8N/dZyl5UNW72mq94+BdiQyN954I9OmTePgwYMA3HnnnVx++eVkZWXx008/8dNPP5GTk8OIESN46aWXOixgyf4V9bHUJD9vh2V1nVMtTRR6jbpCxUhsn5NOS7KXpblQ1hH7a17mUnu81AgNASMvUTka2xYV7MU+zUgAHKhGn2JnzT8MelzSjO3XS4QzQcPk+DHtMXFgb3YZhgLgUlMI6UfVDaijVZXhdM5YWvqC8KVfpLoDG9q60YNDOCwGAuBWkgp5yeoG1NFKstFlHAXglKEfgwdHqRtPrTYnMoMGDeLXX381l1ZWFIWffvqJ7777jgceeID777+f5cuXs3fvXjw8ZFMIqeX8RlxqfuyUal/tkg0lufQvNw7eeFr0ZdjQoSpHZPuUCMvJWulJO2v+kZuEX+UZwNh+fcKQASoHZNs0GoXcIKuyujF2dqEk/QguNQUA7DQMY8pg2ay7Pfr5unLCZYz5eXW8nZXtTt2B1lAFwBb9CKYOlGW622NcmC9bDVZj8CTYWfOyxE0otc1WtxpGMjncX+WAjNqcyJw5cwbRQP+FxYsX8/bbb/Pf//6XpUuX4ujo2K4ApZ4nctg40mtHVR5QdhR9eZHKEXWcc4fWosVY9jXJezJOOlnmsr0iRs+mqLb5R++sXaCvaWYN21FwfJ35cYLnJLxcHVSMxj54R8+jShg/dw7Jm+yqH17lKcsdyROu4+nr46piNPahJsxSxavipH3d8dUnWBKzQ47jiAqS/anaw9PZgXP+lhYlVXH2dbyI05bEbKcymtEh3uoFY6XNiUxYWBg5OTkdGYskAeCg05LgZazM5EgNqXZUhrks1nJiqh0ky6J2hMhgX/ZqjFfB3AzFVKXuUTmijlMWa/khVAbK6nYdYUJkKPsNkQB4VZyH7HiVI+o4FVZ3JBVZ1r1DRA8ZQqzBOL6ZR+4xKM5UOaIOIgQ1tWXdq4QWJXymHM+sAwQNGs252gux2jO7oLJE5Yg6iL4GQ+JmAAqFK7qQid3mQmybExkhBH/84x/ZtMk+OzRJ6tIMtvQFKDtuJ4mMQU9QtrE9crFwYciEec2sILWERqOQE2wZjCzz4BoVo+lAVWX0yjGWXU4XvgwdNbGZFaSWCPFz5bCzpbpQ5al1TSxtQ0qy8Mo3jo1z0hDCyOghKgdkHyYN8GOzdXOh03bSXCjnNE4lxrFx9hsiGT+ov8oB2YdJ4f5s0Y8EQGuohuStqsbTYc7tR1tZCMB2w3AmD1S/7LJJu8pTVFRUcPnllzNgwABeeeUV0tPTOyouqYeLnLyQMuEEQJ+cHXYxCndx8n68hLGZ3FGHkfSVZZc7jN/IheZRuJ1T7KOsbk3ydhyEcZDh3cpohsmyqB1CURRqIix3t+zmQknt1VKAbWIkEwf4qRiM/QjwdOa0p2Xspmp7SXytErKthpFMHdg9+jvYurGhvmwVoy0TEuyk36ZVM8Tf9aOYEtF9jpd2JTKffPIJ58+f56GHHuKbb74hJCSEyy+/nDVr1qDX21+ZQqnrBPh4c9xpJAC+ooCc07bfXCj94M/mx4V9ZqoXiB2aGD2II2IQAL0qUu2iWkzuUUvZ5bzgmbKMbgcaPmwUiYZgALxyDkNZnsoRtV+pVbPVzIDuURbVXgQMmUyOMPYfUZK3QnWFugF1gBqrwgWJXpMI9nZRMRr74e6koyR4EuXC2D9cn7DBLi7EmvrHGITCUacx3ao/VZsTmS1btuDr64ufnx+PPPIIx44dY8eOHQQHB7N06VL69evH008/TWJiYkfGK/UgRf0tnSwv7Lf95kIuqZYrpgGjZdnljuTl6kC81VXTvCM/N7G0DRACpxTj8VL1/+3dd3hUVfrA8e/MZNJ7DwQSSAiBSA2hSQlVKQqCFBUVUVy7CyisZRcpiu6C2HH5USzAqlQLRelI7x1CCz0BAiQhpM+c3x83mRATIAlJJuX9PM88zNz6Djkzc88957xHGfBtIuMdSlObEC/LXVM95nyTAlZKpmxsYrW0y8nKEd+I9nfZQRRHh/p+lu5CNqZUOFPJ03Zn3EB/Vrs5eM7sQ1BYU+vGU8VEhtRgkzkCAMPNSxBfyefDSzyH7rKWbXWfCqFBaN0KNZ6qxBWZjh07YmOT/45P69atmT59OnFxcUyYMIEZM2ZQv359OnXqdJujCHF7NaP6WJ67nlt9hy0rPnPSRWqnHwXgiAqiSUS4lSOqevQN8sZVpR+q5N0/Lh/BPUPrqrvdHE7bBkFWDqhqcbKzIc4/bzLalMrevezsFuyybwBa//X2YZJ2uTS1quPJel3eHCsqppJ3FzqxGn1Ot9W15qa0D/O1ckBVS9sQb9ZWpTTMJ/Ju9Kw1Na1Q3crgHruWFebChQt8/PHHfPDBB1y7dg2lFFu2VP5uQaL8hdcL47AuBICgzBOkXz1n5YhKLm77Ysvz4+4dKky2j6qkabPWllnbfa/thPTKm7Y79cAvlucHnNvh62pvxWiqpoCIjpZZ221PrwFTlpUjKjnT0byK2BablkTUqDjdPqoCe6OBzKCOlrTd2UdXVO603TF52RDXqkhah8h4qtLUItiDjbq8cTKqso+TuWV8zFpzU+6vIPPH5CpxRaZu3bpcvXoVAJPJxOLFi+nVqxfBwcGMHTuW2NhYQkJC+PDDDzl79mypBSyqD71ex4VbcrKf2br4DltXbJmH88Y72DTsZcVIqq7wAFe22mh3TW3IJuNY5W3FSz+Y1zXOfEsGP1F6OjSowXpzEwCtNePcNitHVEJKkX1I+37JVnqyQ7pVqG4fVUXL+rXZatZmMjfeOAdXjlo5ohIyZVvmj7mhHEgPbIOzjKcqVfZGA0F163PErGWC013cDSmXrRxVCWWkoE5q3VbjlQfXXRsQ5FWx5qcqcUXm9OnTHD58mNGjRxMYGMijjz7K8uXLsbGxYfDgwaxZs4Zjx44xevRofH2l2VKUjFOjvIv+Stucn3GDwOt5aXSbt4q2bjxVlE6n40ZQF8vra3t+ucPWFVhyHJ6JeWl0WzRuYuWAqqZ6vs7stmtpeZ11pJJOXnf5CHYpWmv1NnMDWoTXsXJAVVN0fR/W3NpdKKaSlpezWzCkXwdgvbkJrevVtHJAVVOHet5VI233yTXoTBkArDI1p209H3S6inWj5J66lkVHRzNlyhQuXbpEw4YNmTp1KhcuXGDu3LlER0eXUoiiOmvcMppLyh2A4OQdqMxU6wZUAtf2L8eINtv8Hoc2+Et2mDJTq1l3buak7XY5t6ZSZou5tZvQBn0UkUEeVoym6tLpdBjCulvSdmcerqTjqmLyystKcyQd6/tYMZiqK8THmUNOeXM5mSrrjbWYvHL+hylS0i6XkQ5hPqwxVYGK7y2/R3+YW1S48TFwjxUZBwcHhg4dyubNmzlw4ACvv/46np6epRWbEDjb23LYuQ0A9mRycc/vd9mj4kncvcTyPCu0h/UCqQba1K/JJtUIAOfsRNT5HVaOqPiS9+Zl6LsR3B0bQ6kPZRQ5ohqGsisnbbfTjVOQUPmybGYeyuu2es63E74uMp6qLOh0OkLqN+K4WWvB0F/YATcTrBxVMSmFyrkwzVIGdtm2oEmgm5WDqprq+ToT7xzBFaX9/6oTqyHzppWjKiZTtmUenBvKga3mhlWvInPo0CFmzpxJ69Yy47QoO9mheWMEkvdUsnEypix8L20AIFk5ENZKKjJlydnOhlivDpbXibsrWXnJuIFLnJYc5aLyJKzJ/XfZQdyL+0O9WGOOzFtwtJKl7U6Ow/bSXkDrhnhfw/usG08V1zHMh1VmbRC3TpnztW5UCpcPo0s8A8A2czjNwoLlRkkZ0el0tKvvx0qT9v2iy07LN2ltpXB2M6QnArDO3IT6Nb3xdrazbkyFKHEJHjt2LD4+0oQtyl79tg9bugvVvLRWu0tQSaSe+BNns5YWdbshkgaBkh2mrDlE9CZbaV9t+qO/Vq7sQidWYZOTFnW1OZLo+n5WDqhqc7E3cjEgb76qjAOVbL6qWy6kV5oj6Rwu41HLUttQb/5QeeOqOFLJKr5H88rLKnMknepLeSlLHcJ8WGGOyltQicvLSlMLoitot9V7qsg4OmqZCzIyMti6dSsLFy7k5k2t6SwlJaV0IhTVXm0/T3baaj8eriqZq4fXWjmioru0I69F4HqtrhVukFxV1L5pONvMDQBwSz8Plw5aOaKiu7EvL0HBWZ9o3ByNVoymemgQ0ZTDZm2eHrtLeyDpvJUjKjrTLRca2+3a0KimdBMqS24ORvQ1I7motC706uRaSE+yclTFcGvF1yTjqcpau1BvtqkIknPSvHPsd8jOtG5QRaWUZXxMpjKw1tyUjmEVs7zcU5tiamoqr7/+Ot7e3tx///0MHDiQS5cuAdC5c2cGDRpEQkIl60MqKqSUunldsq5sn2/FSIpBKVzPaJlKspSBGlEPWzmg6qGOtxO7nPLSdt/cW0m6l5myMJ5aBWjdEP0bd7NyQNVD1wa+rDDdetf0t9tvXJFk3EAXux7QuiEG1G8paZfLQcf6vvyeU1505qzKM9lh8kW4uBvQuiF6B4ZWyG5CVYm7oy0NAm/JXpaRBKc3WDeoorp0EJK0qVO2mhuCvStNa7lbN6bbKHFFJj09nc6dO/P5559bWmFu9cQTT7Bx40batWtHYmLivcQoBPXuf4QMpd2d9ruwslJko8q+sAevrHgAdtKQFuHB1g2oGrGJ6G15nnWwknQXit2AfbY2ied6cxOiIyQtankI9XVmv2texTf7UCUpL8d+R2/WuiGuNEXSuYF0QywPner7ssJ0a/eySpLm/ZZuTSvNkURLt7Jy0SHMp3LeKPlLtrL29bwr7HiqEkf16aefsmPHDkaMGEFMTAxpaWmWrmYAr7/+Onv37sXGxoZPP/20VIItrtOnTzNixAgaN26Mh4cH9vb2hIaG8sILLxAbG3vb/WJiYhgyZAgBAQHY29sTEhLCm2++SVJSJWpCrmLq1Qpgp01TADzM10g+sdm6ARVB/JYfLM9j/bphZ2OwYjTVy/1NG7HLXA8A95QTkHDcyhHdXea+hZbnO506EuLjbMVoqg+dTkdowyhOmgMAMJzbCilXrBzV3alDiyzPf1etJY1uObmvpitnnRuRoFwBUCdWQWWYFuBQXsv0UlMrOsl4qnLRMcybDebGpOfciOXoUjCbrBtUURxaYnm6ytS8wnYrg3uoyPz444+MGTOGKVOmUK9ePWxtbQts4+Pjw4QJE1i8uPy7dqxZs4aGDRvy5Zdf8thjj7Fhwwb27t3LyJEj+d///kfjxo3ZunVrgf3WrVtHs2bN2LlzJ9988w1Hjhzh3Xff5euvv6Z58+bExcWV+3sR2sXG9dp52cvitv5kxWiKQCkcj2t3wLKVHq8W/a0cUPXSqKYbm4xtLa8zKnqrjCkLdVS7U5eq7LBv8OBddhClqWuEP7/nDMrVYc43N0uFlHEDdVzrhnhFuaFqt8bVXsZTlQedTkd0gxr8kZuNKisVTlbwbFTJcaiz2vXOcXNNrjrUpbGMpyoXTQLdsbF3Zr05Z2Ljm5ehok8LcPkIXDkCwA5zGPF40aEqVmSOHz/OoEGD7rpds2bNOH36dElPU2IjRowgLS2N0aNH89Zbb9GoUSPCw8N56aWXmDx5MikpKfztb3/Lt09iYiIDBgxAKcWyZct44IEHqFOnDs888wz//e9/OXXqFE899VS5vxehCWzTnyyltWp4nv29QmejMl3Yi2fmRQC2qQjaNQm3ckTVi16vIyssr3tZ2r4KPk4mdgN2WVqL72pzM7o2CbZuPNVMiyAPNt5S8TUfruDdhWJWoM+ZbXuZqSWdG9SwckDVS9cGvvxurkTZy478gg7t93KZuRUd6/vKeKpyYmPQ0zHMh99NLfIWVvTvl3ytd62p7+dCgFvFnci7zDu8JSUloaxwwXn8uNaVpE2bNgXW5S7bv38/V69etSz//PPPSUhIoE+fPtStWzffPoMHD6ZGjRqsWrWKTZs2lWHk4nYahwazS6/Nk+CTHU/qmV1Wjuj24rf8z/I81q8rTnY2VoymemrZvBkHzcEAuF8/CNfPWDegO8g6kNdN6E/bdkTW9rBiNNWPjUGPf/3WXFA56dFjN0DadesGdSeHl1ieLjO1pnuEjI8pT/eHerPb0IhkpV3cqZjlkJ1h5aju4JYL099MrYmWbmXlqksDX1aZm5OZcyOWw0sq7jhfpSzlxax0LDO1qvDZ7UpckQkPD2fOnDl33e7//u//aNiwYUlPU2JNmmjNeIcPHy6wLneZTqfD3j5vFuT587VsWF26dCmwj16vp3PnzoDWrU6UP71ex6WaeZmcLm6ca8Vo7kApHKRbmdW1quPFGn3eZL2mAwvvsLUVmbJQOXd0byo7HBs+KHdLraBrhD/LcwZx681ZFfcue3oy6vhKAC4rd274RhLk5WTloKoXe6OBVqEBrMyZTFWXkQwnVlk5qttIvpivW9kpXS06yHiqchUd5kuKzpkN5sbaguQLcHaLdYO6ncuHIeEYADtUfS7jQXQF7lYG91CReeKJJ/j444955ZVXOHnypGV57jwZJ0+e5KWXXmLatGlW6Y41bdo0atasycSJE5k/fz5paWlkZmaycuVKRo4cCUDHjh1xctJ+AG7evMmhQ4cArZJWmNzlO3ZU8P6NVZh/m8GW7mVesb9UyLsa5ovSrawisLXRk1g3L+V12u4KegMidgO2mVq3sjXmZnRtXMfKAVVPHcJ8WE47y2u1v4KOwzv2O7qcbmXLTVF0u0+y21lD1wa+/GK6P29BRS0vh/O6lS01t6JVHU/cHQuOaRZlx8PJlhZBnvxiyuu+ysEF1gvoTv7Seudib0NUHU8rBnR3Je7v8vLLL7N48WK++uorpk2bhqurK2lpaXTu3Jnk5GRLyuXo6Gief/750oq3yJo2bUpMTAxTp05l2LBh3Lx5E51OhznnwrdJkybMmjXLsn1sbKxlnb+/f6HHDAjQstrcWnErTEZGBhkZec3MyclaStWsrCyysrJK/qYETUKD2KpvSnu1Cw9TAklH1uAY1tHaYeVzefM8ci8tTvh0oaWBIv/dc7eTclI6mjZqzO4ToTTXn8A58ShZF/aDbwNrh5XfvgXkDtNea2jHxFouUl6swE4PTsGRnDrrT119PJzeSNbVs+AaYO3Q8jEcXGi5A7nM1Jp36nsX6e8vZaV0tQ/15F1zBAnKFW9dMurYCrJTroGdi7VDy8dwcJGlvCw1tWZwuI+UFyuIru/FF6cjSVO2OOgyUYeWkN31fTBUoCQdSmFzcBE6tG5lK0wt6djQG8wmsu6Qac3aZaTEFRmj0cjy5csZOXIks2bNsqQmPnPmjGX9c889x5QpUzAYyj/t7PXr1xk6dCi//fYbo0aNYsCAAdjZ2bFhwwbi4+MZNWoUHh55/dBzKxsADg6FD2rKTS99tzTMkyZNYty4cQWWr127Nl+KalEyFxxa0T5VGx8Ts/Rz4k4UnMfIapSZdoe1Oy3ZSs8F23osW7bsLjsVtHLlytKOrFrKNMFSc1ua608AcPLnfxNTc4CVo8qjN2fS7eASjECKsueyS0NW/r6i2MeR8lI6/M06fjG35e/6RehQxCz6gJO+Pe6+YzkxZt/ggePaBIyXlDunbMM4tftPYovRE1HKSump4WRgaUYrnrZZiS47nQM/TeKcV7u771hOHDOu0O38NgCOmWtyXAWijzvIsmUHi3wMKS+lw5AKqdiz0hzJw4Yt6NKusfOnyVx2a2Lt0CzcUk8TfU27Ub/N3IAruOOVfoFly87fcb/UVOumH7+nEciOjo58/fXXjBs3jrVr13L2rDYLaFBQEJ06dcLX1zoDypRSPPjgg2zfvp23336b999/37KucePGLF68mAYNGjBz5kx69epV6ud/6623LN3XQKsk1apVi06dOuHl5VXq56tu9oU35ea8mTjpMmiYtpNm3eeCTcWYodh8cj12e68BsEE15YXH++FSjLSoWVlZrFy5km7dumE0VqA7NZXY2BRHsk/OwUZnJihlFyE9ZoGuYoxB0R1egs0+7UdguaklTz3Yhk7FGFgp5aV0tUrJ4In/XOLvaMkXGpoOU7/n51aOKo9+1ywMB7Q7oz+b7ufhVnXp9WD9Iu0rZaX0xTqe4uc19/O0jXax39TmBI16fmDlqPLo/5xseb7Y1J77argy5JHWd9gjj5SX0qWUYu65jfyS2JaHDdr4mFaOZzH1fMvKkeXRr3zH8vw3c2ts9DpeG9AVV4c7//1vTZplDaWSSsnPz4/BgweXxqFKxZo1a9i+fTsAo0aNKrD+kUceYcyYMfTt25ft27fTrFkzXF1dLevT0tIKPW5urdPN7c751+3s7LCzK3hhbTQa5QuhFESG1WalTSu6mzbgrFJIPLoK92Z9rR0WAPHb55HbMfFEQC86u5SsBU7KSunp3KIxm47fR0fDfhxSL0L8HqjdytphAWA6MN/yfLkhmmnhfhhLMHGqlJfS4e9hxL9uI/afrUNjfSz6+H3ok06Ddz1rh6Y5mFdeFpnaM7FRjWL/3aWslJ5ejWvwyep6nDP7UEt/BX3sevQZ18G5AmQFU8pSXsxKxxLT/Twe4S/lxYq6NvBnzqbGJClH3HSp6I8tR6+ywLYC9NQxZUHOJLsZyobfTK1pFeqJl+vdY7N2+Sjz9MvXr1+3ZPsqL7t2ad2O/Pz88PQsfJBSeHg42dnZzJgxA4A6depYEhXEx8cXuk/uZJghISGlHbIoBp1OR3K9vpbX17bOs14wt8pMxf201o0sWTkS3FaylVUE7cO8+d3Q3vI6e18FGfSfcgXdSS3T0UXliUfDTtiVoBIjSlevRjX4+dZBubdUNq3q6knLRHpHzLVJcKpHM0nTbVX1/FwI9XXhF3PONA/KlG+wtFWd3wk53YS2mhsQhxfdIwof/yvKR9cGvmRitGRHJDMFYorf9bxMnFgNN68AsMrcnCSc6dqgcqR1L/OKTGZmJuvXry/r0xRKd4fuI3q99tbPn9f6/jk5OREREQHA0aNHC90nd3lUVFRphilKoFH7R7imnAGoeWlthZjzIf3gL9ibtda8lbrWdIyobeWIBICdjQF9eG/SlXbXyHxgQcWY8+HgQvRK6ya0xNSOPs1qWTkgAfBAhB/LVVvMSvv9UPt+qBjZEffnVcAXmtrTs5E/BknTbXU9GwXw863Zy/ZWkBtr+3+wPF1kbk+QlyNhfs5WDEhE1fHEzcHIYlPejTX2fG+9gG61L6/cLjR1AKg0FZkidS27lxaVzMzMEu9bUmFhYYDWspKUlFRoV7CYmBggf4ayAQMGcPDgQVavXs3w4cPzbW82m1mzZo1lO2Fd9Wt6ssSuE30zf8WOTBK2zMW78ytWjSlp63fkzkqUULef3F2vQLo1r8eKQ1H0NWzWUh0f/Q3us26LWfbeeZYv4LV2nXk+RMbPVQReznaEhNTjz9ON6GjYjy7xDJzeAHWjrReUUrBPuzA1KR0/m9oyrUkN68UjLHo28uez1bXYb9a6IxK3F+L2QYAVB3FnZ8JBbd6sNGXLclNLnojwv+PNXVH2jAY93Rv6MX9XOKfNfgTrL8GpddpkzR5B1gss7TrELAcgQbmywdyYcH8XanlWgC5vRVCkisy6devu6STl/eHp3r07fn5+XLp0ic8++4x//vOf+davWLHC0rrSv3/excyrr77KZ599xs8//0xsbCx16uTN5/DDDz9w8eJFOnfuTPv27RHWl930CdiuTVpn2vkNdHrZeoO4k87jc1kbwHfO7EPz9hUn05GAtiFevGTsTl/zZgCyd36LjTUrMvEHsYnfB8B+cx3ui2yJjaHMG8hFEfVqFMAPJzvR0bBfW7D7O+tWZE5vhEQtI+hGcyNs3WvQXLqVVQj1/Vyo6+3Ej9c7aRUZgN3fQy8rVmRilll6KfxhbsFNHHiosVR8K4KejQKYv+s8P5k6MlqfM/fQ3rnQ6W3rBXVwEZi0RoefTfeTjU2l6oZY5MH+ixYtypeuuKiuXr1a7i0Yjo6OzJ07lz59+jB+/Hh0Oh2PPvoodnZ2rFmzhjFjxgBaxaV79+6W/Tw8PPjpp5/o1asXPXr04LPPPqNevXqsW7eO1157jeDgYL7/voI0AwqiO3Rm79YQmupP4pd6nOwLe7AJbG6VWFI2z8IZrfvJH7ZdGBYsd9crEqNBT0DjrsTunkYd/SVsTq+H66fBI9g6Ae2abXk639SRR5vKpIYVSfcIf95b0oKrygUv3Q3UkV/RpV4DRytNDLczb86z+aaO9G4SgF66lVUIOp2Ono0C+HZtW961mYODLlObHLP7BDAWPpVDmfvL90uQlyP31XS9ww6ivLQN9cLF3oaF6R0YZZyPAQV75kLHMaC3Qi8OpWDXN5aXi3K6vfVuXLHmz7qTIldk2rZtW6J0ypcuXUIpVez97lWXLl3Yt28fU6dO5fvvv+f999/HZDLh4+ND+/btGT58OD179iywX+fOndmzZw/jx4/nqaee4vr169SsWZPnn3+ef/7zn7i7u5f7exGF83a2Y5lfH5pe+RiAuLXTqfXk1+UfiCkb9nynPVU6TE2HSBN+BTSgRW1+2tGJMfqcvuN75kDnd8s/kMybmPf9iB5IVXbsduvG+MA7Z0IU5cvTyZbW9fxZeLIDz9ssRWfK1MaotH6x/INJuQJHtJbnBOXK7+Yolki3sgqlRyN/vlh7gqXm1jxq2AAZSXD4F2gyqPyDuXpS664EnDb7sckcwcuNa8hvUgVhZ2OgWwM/Fu3JZr2pCZ0NeyH5vPY3C+1S/gFd2A3xWsvzPnNdDqlg6vk6E+ZXsSZ2vZMi9WWIjY3Fx6focxvcysfHh9jY2BLte69CQkL44osviImJIS0tjczMTC5cuMDixYsLrcTkCg8PZ968ecTHx5ORkcGpU6eYMmWKVGIqoKAOQ7iptFTXXqd+gczynxzTdGwFzplato/V5ub0atei3GMQd3dfTVf2efUgW2lfe9m7vtcqoeXt4EL0mTcA+MXUhm7Nw+QiowLq3zyQH03ReQt2favdvSxve+eCWZs5e4GpI7V93GgYIHfXK5KGAa7U8Xbih+zovIW7v7VOMLfcXf+fqTMKPQ9JxbdC6dFIa+3I//3yjVViYedMy9O5Jq0i1bNR5WmNgSJWZIKCgkr8Q6vX6wkKsuIgJlGl3d+wDqsN2kzKjuomydvnlnsMiRv+a3l+MKAfNd2t1J1A3JFOp6NzVGPWmJsBYHMz3iqpL9XOvG4f/zN34dHIwHKPQdxdt4Z+XLYLYodZSx7DlSNwZnP5BmE2/+XCtBMPN6kpFd8KRqfT0bdpTXaq+pw051wEntkEl4+UbyDZGVrFF8hUBuabOhLm50x9/8pzd706aF/PGydbA2vMzUkgpzX+6FJIPFe+gaRdtySFuKlz4leTlka8VyXqVgbFSL+8YcMGy8NkMt1x24yMDMaPH5/vIURZsDHoSYp4yvI6a/O08r1revUkHnF/AnBeedOoQ7/yO7cotkea1eR/5m6W12rrtPIN4MJudBd3A3DQHIx7SCsCPSpHZpjqxt5ooHfjGnyfnVde2PpV+QZxcg1c13o0/Gm6jzPKn37NZTxVRfRIs5qAjjmmrnkLy/v75dASSNVmWV9hbsk1XOktg/wrHHujgS4N/MjChu+zcsqLMuVrHSkXe/8H2ekA/JTVjjTsCfOrXN3KoBgVmejoaKKjo+nUqRNJSUl33DYzM5PZs2cze/Zspk+fzrhx4+45UCFuJ7pTd3aY6wPglXqKrONryu3cNzd8jh6t4vSLzQN0alB5Mn1UR17OdhjDunLcrF0M6s5uhot7yy+ALV9Yns4xdWVwS5lrqCJ7NDKQ5eZWxKucRDdHl8K1cuwqveVzy9M5pm7cH+pVaVKiVje1vRyJCvbgJ1M0ySqnVX7/j3DzavkEoFS+8pJbAZduZRVTn6ba32WeqQvZucPVd30DmanlE4ApG7bljSnOrYD3alT5ykux8n1u376dU6dO4eHhwdmzZws8crm4uBAbG0tsbCwrVqwo9aCFuFUtT0d2BQy2vL62emr5nDj1GsYD/wPQxulEPiMpdCuBQS1rM8v0YN6C8rprmngWdWgJkJOr374zXSrJhGPVVfPa7gR6u/GdpVVGwfbp5XPyuP35Bm2vNEcysIVMmlqR9WseyE0c+Cl37EN2Ouyadcd9Sk3sBog/AMBec112qPpEBXtQx9upfM4viqVDmA9eTrZcwZ3fzFqXLtKuw4H55RPAkV8sKd132TTjpNJu7vVuUrm6lUExKzK1a9e2jJcJDg6mTp06+R6Fkb68ojw07fYE55U3AH6X/oQrMWV+zsxtM7A1a82yC82deLR9ozI/p7h30fV92eHajetKm+VaHVwIyXFlf+KtX6NTWrfc77O78VBkXWxtpOJbkel0Oh6NDOR/ps6kK6O2cPf3kH7nXgmlYsuXlqczTT1wtrflgUo0t0N11LNRALY2er4xPYAp9/Jq+wxt7EpZu6W1d0Z2L0DHAKn4VlhGQ14ShplZD+St2PKFNjauLCkFmz+zvPw4Vbux17SWOyE+zmV77jJQ4l/RtWvXsmbNGlavXo2dnR1z5swpzbiEKJZWIb4sc+xjeX11xYdle8KsNLK3aIP8TUrHhfCh+LrYl+05Rakw6HUMalOfeabOAOjMWbD587vsdY/SrqN2aym605WROeZuPNFKkqBUBgNaBJJicGORSUsqQuaNsm+VSToPBxcAkKicWGDqQN9mNbE3WmGeCVFkbg5GujXw47zyZaUpUluYEm8ZgF9mLh2G438AcEH5sNzcEkdbA70qWfap6kYbVwUHVF0O2+bcCE04Bkd+LtsTn94IF/cAEO9Qj03m+wDoX0kTz5S4ItOxY0c6duxIdHQ0BoOBVq1alWZcQhSLTqfDp+PzlrvsHieXaPn0y4h552wcMxMAWGGO4pEu95fZuUTpG9iiFj/oepGmbAFQO2fBjUtld8ItX6LLSbm80NSByAb1qO0lYx0qA18Xex68L4Dppt6YVE4Pgy1fQsaNsjvpnx+DWUsN/r2pG2nYMzhKxlNVBgOjtFaQr7Ifzlv458eQnVl2J13/keXprOwHMKFVYpzsijxVoLCCxoFu1PXRuv59kNI7b8WGyWXbKvPnZMvTzzO01jtbg56HKlm2slzSr0FUGT1b1ONHG+3HQ4+ZxBXvl82JMlPJXJf3RbCpxjDC/WVeh8rEzdFIu2YRlrz5uuy0fE3tpSr1miU7WqYyMM30MM+2K7wrrqiYnmoTxGkVwBJzTqtM2vWya5VJPAs5rXcpyp6Z2T1oVceThjXkO6YyaB/qTZCXI/tVCGtMTbWFSefKrlUm/iAcXgJAot7D8p0m3coqPp1OR7+cVpmN5vuIc47QVlw6CMeWl81JY/+0jL1Lc6rFj6nNAejSwBd3R9uyOWcZk+p6BZeVlXXXdNcij3f0i1zeugtXXSq2cTtJj4sBj9LtwmPaNReD0ZF0oyPrTI15qEs06enppXLsrKwsbGxsSE9Pl7872jxURqOxTMbaDbs/mMe3P8QQwyrsdVmoHTPRtX0VXEp5HMLmz9BlpgDwkykat4AQWtbxLN1ziDLVIsiDcH8XPr/Ul776jRh0SuuOGPUc2LuV7sk2TLZMgDnL9CCJuPDM/cGlew5RZvR6HY+3rM2k5Uf5NLufNnM7aK0yTR8HG7vSPeG6SZann2X0Jh07wvyciQr2KN3ziDLRPzKQj1cew6x0/Cf9YT7mkLZizfsQ9iDoS7E7qVKwZoLl5TzHJ8i+qlUD+jevnN3KQCoyFVZycjIJCQlkZJTDIMEqpKGXDafbfYwLNwEwn7+EPrEUm2jNZpQhGN39U1CAq8ELd1MisbGJpXJ4pRT+/v6cO3dOEmXkMBgMODo64uvri61t6d0xqufnQvOI+syN6cqzNsu1Vpk1E6DPl3ffuaiSzsNWLcVlhrLhy+y+jG5fR/62lYxOp+OpNsG8vfgGS8z309+wUWuV2TAZuk+4+wGK6vIR2KONN01WDszI7klNdwe6Sna7SuXRyECm/HGMfaZQNtKMduyBpLNahsR2fy+9E53dCkd/AyDJxpu56VprzFNtguU7ppIIcHOgSwM/Vh6+xKKU+xgb0Ai36wfg8iGtFa/5U3c/SFEd+x3ObQMgyzOMSee1sTF+rnZE1/cpvfOUs2JVZKZMmYKTU8FUfllZWXz22Wd4eha8y3j58uWSR1dNJScnc+HCBZydnfH29i6zO9JV1fWbNXBOOYNRp7VoKDcfdHalk4lDJcehc/ECIEk54ucRiJNt6d0PMJvNpKSk4OzsjF5fvXt+KqUwmUykpaWRlJTE6dOnCQwMxNGx9MaWvNKpHk8f6sMAw3pcdamoPXPRRQ2HGk1L5wQr/wXZaYA2D4idVy0ekgnqKqV+zWvy8coYpt4cQG/9Nux0WdqFaeRQ8Aq59xMoBSv+oU2MB0zP7k0yzrzUJkjSulcyXs529Gzkz5K9F5mYMYhldvvQY9Yqvk0fB2ffez+J2QTLR1tefpzRhwxscbG3sQwiF5XDkNZBrDx8CdDxmXEo/2SUtmLNRIh4BOxKYYLK7Az4/S3Ly+U+w8i+qH2vPN6ycn/HFOsKbPLkyYUuV0rx+eeFZ/1RSslFeDElJCTg7OxMYGCg/N+VgJ+tHfGZ3tRQWiXalH4Zg6sn6O7xg5qVhspORGejw6R0ZNj64+dauqkKzWYzmZmZ2NvbV/uKTC5nZ2c8PT05c+YMCQkJ1K5deoOeGwW60bh+CJ+eeIR/GueiI+dicugyuNf//zOb4eBCAK4qFz7N7se/Oter1D8Y1Zm90cCwdnX494pM/s/Uk1dsfta6gP3+Djz2P7jX7+qjSy19188pH/7P1AsXexsebyWD/CujoffXYcneixxVtfnNphsPZ/+uZbxbNQ76lkKr7545ELcPgASnenx/tROgJTKRQf6VS/tQb2p5OnDuWhozzwYwMqInTieXQcolLZFD94n3fpLNn8O1UwCYa7dl/IlQIBMbvY7BLSv3eKpilfbWrVsXu2vHzZs32bVrV7H2qc6ysrLIyMjA29tbKjElpNfrcHTzIfV6Eo66DAymDNSNS+hc7yEjh1KYr5+xZMe4gjs+bqVwl0QUicFgwNPTk7i4OLKzs7GxKb0f6lc712NwzAM8blhDiD4Ozm6BnTOh5fCSHzQrDX55zfJycvZAPLx86NtUWmMqsyGtg5i27iRfpfdhoGE9vrpEbVDuoUVwX/+SHzjtOix7w/Ly/awnyMCWv7UNxtXeeO+Bi3LXtJY7ret6svXUNcal9KWH8yaM2Smwdw7c1w9Cu5T84MlxsPKflpdvpz2BGT06nZaYQlQu2riqID5acRSAmfZDec2wCkyZWobEiEegZmTJT3D1pNYaCKAzsCF0NAnHUgHoHuGHn2vlnjqiWFcDixcvxte3eE2iBw8epEmTJsXapzrLHeBtNMqP171wczBy/oYvDtnntBulKfHaoFzbEnZLSrmEPqeLULoyYnL0wcFW5nQoT3Z22iDZ0q7IRAZ50PW+QP55+Bnm2X6gLVz5L+1Cw7NuyQ66egJcPQ7AXnMIP5o68XHXMGmNqeRc7Y081SaIL9eeZFzWU3xpm5PpbukoCGoHLiUcy7LiLbihTcq6wdyEFeYonGy1FiBReb3QMYStp65xFTdm2D/Niyk5LTG/vAYvbS5Zogil4NfXLJOynvTvwR+nwwDo3bgGQV4Fu/+Lim9QVC0+XX2M9Cwz0/Yrhke/gcOfH4Ayw8+vwPC1YCxBhcOUDYv/ZunirKKeY/K+vN/PIa0rf8W3yL+qTZo0KdHFtaOjI40bNy72ftWdtMbcG51Oh5eHO5dx114D5uunLXMzFEtGCupGPKD9hlzU+eLn6lBqsYqiKcvPxD96hLND14jvs7tqC7JSYcEwrWWluGKWw1btgiVDGRmV9QKNa3nycBNpjakKhrevi6u9DUvNrVlqypk/Le06LBquXTQU1955sO9/2mH0TozOfA7Q8VTb4EqbDlVoOob50CBAS5v974Q2XPdrq61IPg+/vKr9oBTXli8tk18qZz9evDrYsurlTqUwVktYhaeTLYNyUmanZZmYYXoY/HMmybx8GFaMKdmB138I53fknKQum+u8zMELyQA0qulGm7pe9xq61RW5IrNnzx48PIqfzq9u3brs2bOn2PsJca8cbW1Qzn6WSQ/1pgzU9TPF+/HIzkRdj9XGTgBXcMPT3V3urFcxQV5OPN0mmEnZj3PanHNX/eIe+PXvxSsvV47BouctL/+dPYiTqib/eqgher3cnKgK3B1teblTKADvZj1Doj7ndzF2vdaSVxznd2llLMc76U8SjxcejkZe6CgXpZWdTqezVC4UekakP4eyy5kP6PDP8OeU4h3w5Jp8XcpW13uXYze0G8zdGvrJfGaV3HPt62LI+Z2Yve086b2/ApucVphd38DOWcU74MFFsOE/2nOdHh6Zzpcb4yyrX4wOqRI3zeVqTFRpvq4OxBsCyFZaUddlJKMSzxbt4tSUibp6Al1OK84N5UC6vR9uDtLtryr6e7cwPNw9eCFrBKkqZ66H/T/A728XrbxcOwXf9YEM7W7Xb6ZWzDT1YGCLQJrXljkdqpKn2wZT092B67jyXNqrmHU5XTW2fpl34XA38Qdgbn8waSn2Vzj0ZJG5AwCvd6kn3zNVRM/7AojImcx03SV7tjX7CK2PAFq69x0zi3ags1vhhyFaVyMgvc0o3tyXN+fVa53rlWbYwgpqeTrSu7E2lvfazUzmxDpD70/yNvhtJBxYULSDHftD61KWq9t4dplD2XzyKgB1vJ14IKKU50yzEqnIiCpNr9MR4OXGefww51yL6tKuoa7HaukrbycrDZVwHF3ORUaGsiFe70cNd4cqcQdDFORsZ8Okfo04qmozKusFzCrn77z1K/j55Tt3Mzu/E2b1gBsXAThsDmJ01t/wd3XgnV4NyyF6UZ7sjQb+0SMcgJ0qnA/1z+atXDMRVrwNpqzbH+DUOvj2Ia1LGhDv3pxXr2tdhOr6OPFEFei3LjR6vc5SVgDe3O9PVvS7eRssHQnrPgLzHeY7O/IbzOkPWdr8aIT1YGp2f66namWsT9MaNAos5YlZhVVorSTa8y/WniA5/FFo80rOWqW1+G/56s431/bOgx+f0JIFADR9AtX6ZT5aftSyyd865LX+VHZSkRFVnr3RgIenF+fULZWZ9CTUlaPahYS65QfElA034lBXYtDlfAlkKhtOU4NAL1fpUnYPdDqd5REcHGztcArVIcyHx1rWZrm5FWOyb8latncuTI/WJhS7tQJ845LWnWjWg1pCCSDGHMiQzLdIxZ6PHm0sd9arqN6NA+gcriW/mX6zI7/6vpi3cuuXMKOrVmG59QI16TwsfQO+f8RSiUn3a07vq6+SlZN758N+jTHK90yV0r6eD/eHamMRzl1L45P0XtBuRN4G6z6Ab3vD2W35L1CvnYLFL2oXpZkp2rK6nTjR8XNmbz4LgK2NnjcfqF9eb0WUsXB/V/rkjKdMTM1i+vpTWvrlyKHaBsqkzQcz91FL+m2LKzHw45Ow5MW8SkzEI/DQZ6w9doXtp68BUNfbif6RgeX0jsqeJBsXlU5wcDBnzpyxvB44cCA//vhjoduuW7eOTp06FVg+duTzvDfqBbh+GnSGnH6oZshKB1Ruwz9pypYz+BPo5Vrps5SlpqbSvn17dDodf/75Jw4O5ZuwIC4ujnPnztGyZctyPW9xjX2oIYcuJjH/fDTpypb/2P4f9mTAlaMwbyA4eoN3mDYnxKXDlgkMQbs7/3zm37mGK691qUfHsMo7W7K4M51Ox8S+99Ht4/XczDTx6tn2+Ef5EHVokja/TNxerauhs782YWZaIlw5ku/GiSmkG48nPEtClrbsqTZBtKxTcGJpUfm991AEPT/7kyyT4r8bYnn41ZHUt3eD1eO1MnFmE8zqDq6B4BEMqQnad86t7uuP6aEvGD1zD5kmrcw8164OgR6lN0mwsL5R3euz9EAcWSbFjI2neKJ1bQJ6TQVHr7xxVSdWaQ/3IHCrpWU9vHYy/4Ein4Gek8lCz4e3tMa8+UD9KnWzpOq8E1Ft7Nixg7i4ONq0aQPATz/9xGeffVbotm3btiUuLo64OG2A2wcfTebPXQd54W+33G1XJq3JPisNcgb1KwVXlCuxuprU9HLFuQrM5XDo0CF2797Nrl27OHToULmf39/fHx+fin9hb280MG1IJD4udvxqbkufjHEcNYTlbZCaAGc3a2MccioxJr2Rr8z9GZzxNtdwpVtDP/7eRfqsV3U13B14/5FGltdP7GnI4R4/gu8t3QlT4rWL1MuH8ioxRifMXcbxum4Muy9py0J9nRnzYDiiaqrn58KLOQkcss2Kv/+0j/RWr8GTi/OneU8+D2c25q/E2LtBrynQfyYztsax+2wioI1zeE2+Z6qcWp6OlrTI6Vlm/rnkEEqngy7/gsHzwLVm3saJZ7TycmslxskH+v0fPPQJGGyY8Wcsxy5pLXpNarnz4H1VY2xMLqnIiErHx8cHf39/bG1tLfOJvPHGG2zdurXAtra2tvj7++Pvr31wA3y9aBZRn0SXMGLN/iQqJ7JUXktLhjJyRblyTAWSaPQlxMcFlypQiQFo2rQpAwcOZODAgTRt2tTa4VRoNd0dmPdcK7ycbIlRtelx81+8ah7FKa+OmO21gfsKHRnu9fjD43E6pk3m35n9ycaG9vW8+fyxZpKlrJro26wmT+ZcdGRmmxn0Wza7e/4C/WdCaFewyxm7oDOA330Q/TbZL+9kTHwnfjt4GQBHWwNfD2kuM7JXcS91CiXER5vn5UhcMuN/Owx1o+GlrdDnS6jTAWydtY31RghoAl3fg1f3QNRzbIu9xr9/j7Ec78N+jbA3Vu6eAqJwf+8ShrezlnRm1ZFLrDiodV0mvBe8sgN6T4XabcEmp2eFjT3UbAEPTIJXd0PjgQCcuXqTT1cfA0Cvgwl9IqrcOF/51hSV2oABAzh16hTbtm1j4MCB7N69G29v7zvu42RnQ5ifC1dv2nLppjMZ2Sb0SqFykiw7GA34ONvh4WisUh94o9F42y54oqB6fi7Mf6ENz3+/ixOXU/g1M5JfL0QCitouOm5m67kan3+A7iPNajJJLi6qnX/2bsjZa6msP3aFGxnZDJ6xk4l9WzHgif5aN9XsdDDYgt7A5eR03liwnw3HrgBgo9fx5ePNCfV1sep7EGXP3mjgyyea0/fLTaRnmZm37Sx1vJwY3qEuNBuiPZTKV15ynbicwktzd2PKGej5SqdQWlWBOUBE4dwcjbz3cENemadNX/LOkoM0re1OgJsD2DpBi2Haw2zWxsMYjPnKC2g3Vl7/YS/pOV1Xn24bTONA9/J+K2VOWmREpWZra8uCBQvw8fHh3LlzPPHEE5jvlP0lh16vo0GdQMIDXGlSy4Ne9zejro8zDQNcqefnwsiXn0ev11sGp58+fdqy75w5c/INXH/vvfc4ePAgPXr0wMXFBT8/P5555hmuXNEuVE6ePEnfvn1xd3fH3d2dgQMHWrq6FebQoUM88cQTBAQEYGtrS0BAAAMGDGD79u35ttu4cWO+OIYOHUpcXBzDhg2jRo0aGAwGy/KhQ4fm23bdunWFnnvFihX07NkTb29vS2vWgw8+yGeffcb169fzbbt7925Gjx5NZGQkXl5e2NvbExYWxsiRI0lISLjr36AyqOvjzJKX7+fJ1kHkNbDoOHsDrqbllTMPRyP/frQxHw9sIpWYasjWRs/XQyItk8tlZpsZvWA//adt5qdd59l/KYPNp64zafkRukxZb6nEGA06Ph3cjE45SQNE1Rfu78rEvnndEd9fdoQZf55C5Q7y1+nA6JDvojQm/gZDZmzj6k1tAPf9oV6M6BaGqNp6NQqgawNtXrNrNzN5ee5uMrP/cn2j14PRvkAlBuDD5UfZey4RgNqejozqXjWTQkhFRlR6gYGB/PjjjxgMBv744w/Gjx9fpP0OHz5sqRzodFpLTW5Wsk8//ZS4uDgCAwtm9nj00UeJi4tj1KhRABw7doyRI0fyr3/9i127dvHiiy/yzTff0LNnT+Li4njzzTcZM2YM27Zt47XXXmP+/Pk89NBDeT9ct1i4cCGdO3dm+/btfP311xw+fJjp06dz4MAB2rZty9y5cy3btmrViri4OD755BMAEhIS6NWrFx07dmTz5s2sXLkSX1/ffO8nd1xRYd566y169OgBwC+//EJMTAzffPMN169f5/XXX2fYsGH5tn/88ceZOXMmr776Klu3bmXv3r288847zJ8/nxYtWnD58uUi/R0qOmc7Gyb0vY/Vo6J5KTqEprXc8Xa2o4abPR3DfBjfJ4INozsxsEWtKtWCJ4rHwdbAt8Na8ljL2pZlu88mMnrBfh7+YhOPz9jGf9ef4kaGNi+Vp5Mt3z/bil4580aI6uPRyEBG3lIRmbj0CCN+3MvVlIx825nNip92nKPfV5uIT04HIKKGK189EVllUueK29PpdPzn0cbUdNe6j+0+m8jIn/ZaWuXuZObGWGZtigW0GyZfPN4M5yradbVqvitR7XTq1IkPP/yQN998kwkTJtCmTRseeOCBO+7j6+tLampqoevc3Nxwc3PDYCh4l8Pe3h5/f3+cnbW+zAsWLODMmTMEBGgXJO+99x6rVq1i06ZN9O7dm99++82ybvz48axatYotW7awZcsW2rZtaznuqVOnGDp0KACrV6+2pCgODQ0lKiqKunXr8vzzz9OhQwdq1aqF0WjE398fNzetD/7SpUv59ddf6d27N6Bld3v++edJTk62vB9bW9tC3+9PP/3Ehx9+SJMmTfj5558xGrVxQXXq1KFVq1Y0aNCgQMWrZs2afPDBB/Tr18+yLDw8nNDQUNq1a8f48eP54osvbv8HqGTqeDsxWgZjizuwtdEzqV8jujf04/1lRzhxOaXANkaDjv7NAxn9YDieToV/HkXV92rnUExmxaerjwOwZO9F/jh8ie4N/Qj1dSYxNYs1Ry9zKuGmZZ/7arry7TMtJaV7NeLhZMtXTzRnwH+3kJlt5rf9Wm+OyQMKb/1XSvH1+lN8tCIvWcR7D0dUyS5luaQiUwk99PlGrtzIuPuGFYyPix2/vtquzI7/xhtvsH37dubPn88TTzzBnj17qFWrVpmdL1fXrl0tFZVcUVFRbNq0CT8/vwLrWrZsyZYtW9i9e3e+iszUqVNJTU2lf//+1K5dO98+/v7+9O3bl//973/MmjWLsWPHFoijTp06lkpMrgkTJhTpPUycOBGAF1980VKJyeXh4cHgwYMtXeVyrV69utBjtW7dGtAqVlWpIiNEUXUK9yW6vg+7z15n66lrXExMw87GQHiAC53q++LjYmftEIWV6XQ6RnQLo66PE+8uPsiNjGxSM00s2Xux0O37NavJ+480qvTTAIjia1LLna+HNOf573aRbVb8tj+O45dSGPtQQ9qEeFl6Apy6ksLEpUdYczSvN8RrXerxRKuqPcGuVGQqoSs3MizNzCK/WbNmcejQIQ4fPsyAAQPYsGHDbVshSktISEiBZa6urrddl9uC8tcxJ3/88QcAzZo1K/Q8detqKTo3bdpU6Prw8JK1FsTFxXHgwAFAq4AVJrf72q0yMjL48ssvWbRoESdOnODmzZv5Wm0uXLhQoniEqAp0Oh2RQZ5EBsm8MOL2+jStSZsQLz5ffYLFey6QktP1MFfbEC9e7hTK/aF3TmIjqrbO4X58PSSS137YQ2qmiZhLN3h8xjZqujtQ18eJKzcyOBp/I98+b3QP4+VOoVaKuPxIRaYSqqx388ojbmdnZxYtWkTLli3Ztm0bo0aN4vPPPy/Tc3p6FrxQyb1Dcqd1JpMp3/KzZ7WZmidMmMCkSZMK7JeVlQXcvoJQ0jlacs9bnGOkpqYSHR3Njh076NmzJ9999x1BQUGWrnj16tWzxCuEEOL2fF3smdD3Pt7t3YCjcTe4lJyOg62BBgGulhS8QnRt6Meil9oy6qd9HLqYDMCFxDQuJKbl287XxY6Jfe+je0TVmi/mdqQiUwmVZfesqqB+/fp8++239OvXjy+++IJ27doxaNCgEh2rsAH5f3WnAd4lGfz97rvvMnDgQPT6wnNx/LXr172cq6S++uorduzYQUREBL/88kuhY4mEEEIUnZ2NgSa13K0dhqjAwv1d+eWVdvyy7wI/7TjPnnPXSc8yo9dp6/o2q8HglrVxrSLz3xWFVGREldS3b1/+8Y9/MGnSJJ577jmaNGlS6Ha5F+B/bR3JVZ5phIOCgoiJicHGxobQ0NDbVmRK263jca5cuVKkcUXr168HoHPnzlKJEUIIIcqJQa/jkWaBPNIsEJNZkZKRjb1Rj51N9fwtlvTLosqaOHEi3bp1IyUlhf79+xe6ze3Gq4A2duR2Wc3KQvfu3QHYtWtXoetTUlJo2bIlH3/8cameNyAggEaNtHkN/jpXTa6JEycyYMAASwvVnebqkbExQgghRNkz6HW4ORirbSUGpCIjqjC9Xs///vc/goKCOHz4cKHbuLq6UqdOHW7evMnRo0fzrZs1a1Z5hGkxYsQInJycWLp0KbGxsQXWf/LJJ+zcuZNu3bqV+rnfffddAL7++muys/MPNo2Li2Py5Mn4+vpauq+1bNkSgJUrVxbYfv78+aUenxBCCCHEX0lFRlQ6V65cIT4+nszMTNLS0oiPjy+QGjiXl5cXCxcuxN7e/rbHe+mllwAYOnQomzZt4vTp00ybNo3du3dbul3lnhMgMzOT+Ph4UlK0OSJSUlIs8ZR0HWjpk7/77jvMZjPdunXjp59+4syZM+zZs4c333yTsWPHMnnyZEvriclkIj4+nqSkJADL/0VunLdKSkrKd65r164RHx9v6VI3cOBAxowZw759++jbty9bt27l9OnT/Prrr3Tv3p2AgADef/99y/FeeeUVatWqxdGjR+nfvz9bt24lJiaGqVOnMm7cOMt28fHxXLt2zfI89++UG/vt/m5CCCGEEHelqriUlBT1wQcfqBYtWig3Nzfl4OCg6tSpox5++GH19ddfF7rP1q1bVZ8+fZS3t7eyt7dXDRs2VBMmTFDp6ekliiEpKUkBKiEh4a7bpqWlqcOHD6u0tLQSnas6CAoKUkC+R1BQ0B33mTVrlgLU7NmzC6wzm83qo48+UnXr1lVGo1EFBgaqMWPGqPT09ALnysrKUmvXri1wfkCtXbu2xOtymUwmtWXLFvXkk0+qmjVrKltbWxUYGKh69uypVq1alS/u2NjYQo9X2Mf66aefLnS72NjYfNstW7ZMPfjgg8rT01PZ29ur8PBwNWbMGHX16tUCx7xw4YIaOnSo8vPzUzY2NsrX11f169dP7d69O985OnbsqJRShZ7/bn+3W8lno6DMzEy1ZMkSlZmZae1QRAUnZUUUh5QXUVQJCQkKUElJSVY5v06pIqRlqqSOHz9Ot27d8PHx4Z133qFJkyZkZGSwbNky3n77bby9vTl//ny+febNm8dTTz1FVFQU//73v6lRowZLlizhH//4B82aNWPNmjWWGd2LKndm9YSEBLy8vO64bXp6OrGxsdSpU+eOrQiiajKbzSQnJ+Pq6lpug/0rC/lsFJSVlcWyZcvo2bPnbbPZCQFSVkTxSHkRRXX16lW8vb1JSkqyzKFXnqps1rKbN2/SvXt3fH192bBhQ74Ln/DwcNLT01mwYEG+fU6ePMmwYcPw8vJi+fLluLu7AzBq1CgyMjJ45513GDFiBP/3f/9Xnm9FCCGEEEII8RdV9pbvpEmTOH36NBMnTiz07u3bb7/N7t278y374IMPyMjI4JlnnrFUYnK9/PLL2NnZMWvWrHwTCAohhBBCCCHKX5WsyJhMJmbNmoWdnR2dO3cu8j6LFi0CoEuXLgXWu7m5ERUVhdlsLtCSI4QQQgghhChfVbIic/DgQeLi4ggODiY5OZkxY8bQsGFDPD09CQkJYejQoRw6dCjfPseOHSMxMRHQup4VJnf5jh07yjR+IYQQQgghxJ1VyTEy+/fvB7R0tJGRkTRq1Ihp06bh7e3Nhg0beOutt/jhhx+YP38+Dz30EKCNj8nl7+9f6HEDAgIKbFuYjIwMMjIyLK+Tk5MBbfBcVlbWHffNyspCKYXZbL7jpIOiasrNvZFbBkQes9mMUoqsrCwMhuo7+detcr9P7va9IoSUFVEcUl5EUVm7jFTJikzu3BRnz56lWbNmLFmyxJIBKiIiguDgYHr27MmQIUM4efIk3t7elsqGwWC4bYYOR0dHAMu8HbczadKkfHNp5Fq7dq3lGLdjY2ODv78/KSkpljk/RPVz48YNa4dQ4eTOG7Rhw4YCk3BWdytXrrR2CKKSkLIiikPKi7ib1NRUq56/SlZkbv1PfeWVVwqkse3RowdhYWEcO3aMb7/9llGjRpXq+d966y1GjhxpeZ2cnEytWrXo1KlTkdIvnzt3DmdnZ0kxWw0ppbhx4wYuLi7odDprh1OhpKen4+DgQIcOHeSzkSMrK4uVK1fSrVs3SZEq7kjKiigOKS+iqK5evWrV81fJioyDg4PlecOGDQvdJjIykmPHjrF9+3YAS+5rk8lEVlZWoR/c3AqSm5vbHc9vZ2eHnZ1dgeVGo/GuXwgmkwmdToder5d5RKqh3O5kuWVA5NHr9eh0uiJ9jqob+T8RRSVlRRSHlBdxN9YuH1XySil3LAuAp6dnodu4uLgAcP36dQBCQkIs6+Lj4wvdJy4ursC2QgghhBBCiPJXJSsyzZo1szy/dOlSodvkLvfw8AAgLCzM0tJy9OjRQvfJXR4VFVVqsQohhBBCCCGKr0pWZBo0aEBYWBgA+/btK3Sbw4cPA9C2bVtAG+Tfr18/AFavXl1g+6SkJHbs2IFer6d///5lEbYQQgghhBCiiKpkRQbgnXfeAWDatGkFMhwtW7aM48eP4+XlxdNPP21Z/vbbb2Nra8vs2bMLZCb78ssvycjIYOjQoQQFBZX9GxBCCCGEEELcVpWtyDz11FMMHz6cw4cP069fP3bs2MGZM2f4/vvvefrpp3F1dWXBggW4u7tb9gkNDWXGjBkkJCTQo0cPNm3axKlTp5gyZQpjx44lMjKSTz75xGrvSQghhBBCCKGpshUZgOnTp/PDDz9w48YNunXrRlhYGGPHjmXAgAHs3buX6OjoAvs8+eSTbNq0CR8fH/r06UPDhg2ZMWMG//znP9m4caMlSYAQQgghhBDCeqpk+uVbDRo0iEGDBhVrn9atW/Pzzz+XUURCCCGEEEKIe1WlW2SEsLbg4GB0Op3lUR2sW7cu33seOnSotUMSQgghRBUkFRlRZcTFxWFjY4PBYODChQvWDgeAHTt2WOYfKi2nT5/mvffe45tvvrntNgcOHMDf358XX3yxVM9dFG3btiUuLk7GkwkhhBCiTElFRlQZs2fPxmQyYTab73iRX558fHzw9/cv1WOePn2acePG3fE9rlixgkuXLvH999+X6rmLwtbWFn9/f8u8TEIIIYQQZUEqMqJKUEoxa9YsvL29AZg1axZKKStHZT0DBgygffv2vP3229YORQghhBCiTFT5wf6ieli3bh1nzpxh2bJldO/enVOnTrFu3To6depk7dCsIjg4mA0bNlg7DCGEEEKIMiMtMqJKmDlzJr169aJbt260bNnSsuyvNm7cWGAg+vnz53n88cfx9vbGwcGBFi1asGzZskLPExMTw7hx42jTpg1+fn7Y2dkRHBzM8OHDOX36dJHj/eabb/LF8ddkAKdPny6wLncQfW7lbP369fnWv/fee0DREgxkZWXx1Vdf0bp1a1xdXbGzs6Nu3boMHjyYH3/8kaysLMu2ZrOZZcuW8cwzzxAREYGzszPOzs60aNGCqVOnFphwVgghhBCiPEhFRlR6iYmJLFy4kOHDhwNY/l20aBFJSUn5tm3VqlW+gegJCQkMHjyYJ554gh07dvD9998TGxvLww8/zM6dOwuc6/XXX+fDDz9k8ODBrF+/nkOHDjFlyhQ2b95M8+bNOXr0aJFiHjRoEHFxcdSuXRuA7777Ll9SgFq1ahEXF8ff/vY3WrRoQVxcnGUQ/cKFCwFo06YNcXFxlscbb7wB3D3BQFpaGg888AAvv/wy7dq1Y8uWLRw4cICxY8eyYcMGBg8ezFdffWXZ/vLly/Tq1Yu9e/cyefJkDh48yKZNm+jXrx//+Mc/6Nu3L2azuUjvWwghhBCitEjXMlHpzZ07F29vbx588EEABg8ezIgRI0hJSWHevHn5MncZjcZ8A9GXLl3Kpk2baNu2LQB16tTh4sWLvP7663z99dfMmDEj37n8/Pz46KOPeO211yzLQkNDadWqFbVr1+aNN97gt99+u2vMDg4OODg48MwzzzBu3Dh+/vlnnnzySUuFwGAw4OXlxZIlS5gwYYIlYYC/vz+enp5A3qD6v/Lx8bnjuUeNGsXatWt56aWXmDx5smV5WFgYYWFhtG3bNt/4IoPBQJ06dfjtt9+oWbOmZXmTJk1QSvHuu++yaNEiHn300bu+byGEEEKI0iIVmcrovx0h5bK1oyg+Z1/42/pSP+zMmTMZOnQoBoNBO42zM4MGDWLmzJnMnDnzjimI69evb6nE5GrVqhUAe/fuLbD9t99+W+hxAgMDqVmzJitXriQzMxNbW9sixT5s2DAmTJjAL7/8wuXLly3JCgB+/fVXbt68yWOPPVakYxXFpUuXLJWzWytjudq0aUNkZCR2dnaWZT4+Ppw6darQ47Vu3RrQKoRSkRFCCCFEeZKKTGWUchluXLR2FBXC7t272bt3L4sWLcq3fPjw4cycOZNdu3axf/9+GjduXOj+oaGhBZbltnhcv369wDqz2czs2bOZN28eR44c4caNG5bWi9TUVJRSJCQkUKNGjSLFX7t2bbp3786KFSv49ttvGTVqlGXdjBkzGDRoEM7OzkU6VlGsXbuWrKwsXFxcqF+/fqHbFNalLi4ujilTprBy5UouXLhAeno6ACaTCaDCzNsjhBBCiOpDKjKVkbOvtSMomTKIe8aMGXTt2pXg4OB8y1u1akWjRo04cOAAM2fO5NNPPy10fy8vrwLLjEYjkHeRnkspRd++ffn1119p06YN//3vfwkNDbVsHx0dzYULF8jMzCzWe3juuedYsWIFM2fOtFRkzp8/z++//87mzZuLday7OXPmDHD37me3Onr0KO3bt+fatWv8/e9/p2/fvgQEBACwbds2hgwZUuz3LIQQQghxr6QiUxmVQfesyigtLY158+aRmppaaKtFRkYGAHPmzOHf//53vu5SuW6X1aswCxcu5Ndff8XHx4cVK1bg6uqab72NTck+Tg8//DC+vr7ExMTw559/0qRJE2bPnk1ERISlm5s1vfHGGyQkJPC3v/2NKVOm5Ft3/vx5K0UlhBBCiOpOspaJSmvBggUYjUYOHjzI3r17Czx27NiB0Wjk2rVrLFmy5J7Pt369VoHMTVlcWoxGI0899RSgtTDldl/Lzb5WmoKCggC4cuVKkffJfd/du3cv9XiEEEIIIUpKKjKi0poxYwaDBw8mLCyM0NDQAo+mTZvywAMPAIXPKVNcd0oxbDabiY+PL/Gxn3vuOUBr9fn555+5dOkSQ4YMKXRbvb7gxzYtLY34+Pi7pkHu1KkTRqORGzdu3DZV9MCBA5kwYYLl9Z2OKWNjhBBCCGEtUpERldLx48fZsGEDTz/99B23e/LJJwFYvXo1Z8+evadz5k60uXnz5gLz0/zyyy+WrmwlUb9+fdq3b09aWhp///vf6d+/Px4eHoVu6+7uDsDNmzcty77++msCAgIsg/Bvx8/Pz1Jp+vzzzwusX758OfPnzyc8PNyyLPd9FzZJ6Pz58+/8xoQQQgghyohUZESlYjKZiI+PZ9q0adStW5fAwEBSUlIK3TYpKYmWLVvi6OiI2Wxm2rRpXLhwgbNnz1oqIrktGWlpaYDW5Sq321XuuXK3HTx4ME2bNuXq1av06tWLdevWceLECWbPns1zzz1nGSNz6zGuXLmSr6UmPj7+ti03uRWM5ORky/PCNGjQAF9fXw4ePMj69es5cOAAs2fPtrzXws55a1eyKVOm0KlTJ7766itGjx7N4cOHOXbsGNOnT2fIkCEMHjw4XyrlCRMmYDQamT17Nu+8846lK9+LL77IihUrAMjMzCQ+Pp6UlBTL87/+H/+18ieEEEIIcU+UKHNJSUkKUAkJCXfdNi0tTR0+fFilpaWVQ2SVT2xsrALyPcaOHVvotk8//XSBbW/3mD17tlJKqaCgoALrnn76acsxExMT1WuvvaZq1aqlbGxslIeHh3rggQfUmjVr8u0bFBR02+Pd7mOXmpqq3NzcVGhoqDKZTHf8f1i/fr2KiopSdnZ2ysPDQ/Xo0UMdO3bstufMjSdXZmam+uKLL1RUVJRycnJSrq6uKjIyUn399dcqKyurwPm2bNmiHnzwQeXq6qqMRqMKDg5WL730kvrxxx8L/C3Wrl1b6Hu+9f+xJOSzUVBmZqZasmSJyszMtHYoooKTsiKKQ8qLKKqEhAQFqKSkJKucX6fULVN4izKRnJyMm5sbCQkJhab7vVV6ejqxsbHUqVMHe3v7copQVBT16tXjySef5N133y10LEx1Jp+NgrKysli2bBk9e/a0pAEXojBSVkRxSHkRRXX16lW8vb1JSkoq1URIRSVXSkJUEBs3buTMmTM89thj1g5FCCGEEKLCk4qMEFayZMkS/vjjD8vr//73v/Tt27dYk1UKIYQQQlRXMiGmEFayatUqtmzZQlBQEPv372f+/Pls2bLF2mEJIYQQQlQKUpERwkrq1avHwoULadSoEbVr12b27Nk0adKE5ORka4cmhBBCCFHhSUVGCCt5/fXXef311/Mtu9uElkIIIYQQQiNjZIQQQgghhBCVjlRkhBBCCCGEEJWOVGSEEEIIIYQQlY5UZCoomadUiPzkMyGEEEKIW0lFpoLJnc3dZDJZORIhKpbcz0TuZ0QIIYQQ1ZtcEVQwRqMRg8FAWlqatUMRokK5ceMGRqMRo9Fo7VCEEEIIUQFIRaaC0el0ODo6kpSUJK0yQuRIS0sjOTkZFxcXdDqdtcMRQgghRAUg88hUQL6+vpw+fZozZ87g6emJnZ2dXLxVE2azmczMTNLT06t9FyqlFCaTiRs3bpCcnIydnR3e3t7WDksIIYQQFYRUZCogW1tbAgMDSUhIIC4uztrhiHKklCItLQ0HBwepvOYwGo24u7vj7e2NwWCwdjhCCCGEqCCkIlNBOTo6Urt2bbKzs8nOzrZ2OKKcZGVlsWHDBjp06CBjQdAG9huNRqnUCSGEEKIAqchUcDY2NtjYyJ+pujAYDGRnZ2Nvby8VGSGEEEKIO6hWnfBHjBiBTqcjODjY2qEIIYQQQggh7kG1qchs27aNzz77rMjb9u3bFx8fHxwcHIiIiGDixIlkZGSUcZRCCCGEEEKIoqgWFZnMzEyeffZZAgMD77rtvHnzuP/++7l06RKLFi3i4MGDDBs2jHHjxtG+fXtSUlLKIWIhhBBCCCHEnVSLiswHH3zAhQsX+PDDD++43cmTJxk2bBheXl4sX76c9u3bExISwqhRoxg3bhw7duxgxIgR5RS1EEIIIYQQ4naqfEXm0KFDTJo0icmTJxMQEHDHbT/44AMyMjJ45plncHd3z7fu5Zdfxs7OjlmzZnH27NkyjFgIIYQQQghxN1W6ImM2m3n22Wdp164dzz777B23NZlMLFq0CIAuXboUWO/m5kZUVBRms5kFCxaUSbxCCCGEEEKIoqnSFZlPP/2U/fv3M3369Ltue+zYMRITEwEIDw8vdJvc5Tt27Ci1GIUQQgghhBDFV2UnKImNjeXdd99l/PjxhISE3HX7kydPWp77+/sXuk1u17Rbty1MRkZGvgxnSUlJAFy7du2ucYjqLSsri9TUVK5evSrzyIi7kvIiikrKiigOKS+iqHKvbZVSVjl/la3IDB8+nAYNGhR5cH5ycjKgTUh4uw+to6MjkFcxuZ1JkyYxbty4AsvDwsKKFIsQQgghhBCVxdWrV3Fzcyv381bJiszMmTNZv349O3fuxGAwlPv533rrLUaOHGl5nZiYSFBQEGfPnrXKH1lUHsnJydSqVYtz587h6upq7XBEBSflRRSVlBVRHFJeRFElJSVRu3ZtPD09rXL+KleRiYuL44033mD06NE0adKkyPvlflBNJhNZWVmFtsqkpqYC3LUyYmdnh52dXYHlbm5u8oUgisTV1VXKiigyKS+iqKSsiOKQ8iKKSq+3zrD7KjfY/48//iAxMZGpU6fi7Oyc79GjRw8Azp49m285kG8cTXx8fKHHjouLK7CtEEIIIYQQovxVuRaZfv36cf/99xe6btu2bQwZMoQaNWqwbt26fOvCwsJwc3MjKSmJo0ePUqtWrQL7Hz16FICoqKhSj1sIIYQQQghRdFWuIuPi4oKLi0uh686fPw+AjY0NoaGh+dYZDAb69evH7NmzWb16Nd26dcu3PikpiR07dqDX6+nfv3+xYrKzs2Ps2LGFdjcT4lZSVkRxSHkRRSVlRRSHlBdRVNYuKzplrXxpVrBu3To6depEUFAQp0+fLrD+xIkTRERE4O7uzrFjx/KNhfnggw945513GDZsGDNnzizHqIUQQgghhBB/VeXGyBTmypUrxMfHW3Jdm0wm4uPjiY+PJyUlxbJdaGgoM2bMICEhgR49erBp0yZOnTrFlClTGDt2LJGRkXzyySdWehdCCCGEEEKIXNWiRSY4OJgzZ84Uum7s2LG89957+ZZt3bqVSZMmsWnTJlJSUqhTpw6PPfYYo0ePxt7evhwiFkIIIYQQQtxJtajICCGEEEIIIaqWatG1TAghKrMRI0ag0+kIDg62dihCCCGqoM2bN1O/fn10Ol2h48grKqnIlKEVK1bQrVs3PD09cXJyonnz5nzxxReYzWZrhybK2dmzZ5kwYQL3338/Hh4eGI1G/Pz86NmzJwsWLLjjvtu2baNv3774+Pjg4OBAREQEEydOJCMjo5yiF9a0bds2PvvssyJvK2Wlerp58yaTJk0iKioKd3d3HB0dqVu3Ln369OG///1voftIeal+Tp8+zYgRI2jcuDEeHh7Y29sTGhrKCy+8QGxs7G33i4mJYciQIQQEBGBvb09ISAhvvvkmSUlJ5Ri9KAtpaWmMGjWKDh06cOzYsSLvV9Lvj7i4OF544QVq166NnZ0dtWvX5oUXXuDixYslewNKlIkPP/xQAap3795q586dKiYmRo0ePVoB6qGHHlJZWVnWDlGUk3Xr1ikbGxtlZ2en3n33XbVjxw51/PhxNX/+fFWvXj0FqMcee0yZTKYC+86dO1cZDAbVunVrtWHDBnXixAk1efJkZWNjo6KiotSNGzes8I5EecnIyFARERGqdu3aClBBQUG33VbKSvV17NgxFRQUpFq0aKEWL16sTp06pY4cOaKmTJmi7OzsVM2aNQvsI+Wl+lm9erVycHBQRqNRffDBB2r//v3qyJEj6ssvv1Surq7K2dlZbdmypcB+a9euVQ4ODqp+/fpqxYoV6tSpU2rWrFnK2dlZ1a1bV128eNEK70aUhhMnTqiwsDAVFBSk/vjjDwUoQMXGxt5xv5J+fxw6dEh5eXkpf39/tWDBAnXq1Cm1YMEC5efnp7y8vNShQ4eK/R6kIlMGNmzYoADVsGFDlZmZmW/d8OHDFaAmTpxopehEeVu8eLEC1GeffVZg3YULF5SLi4sC1PTp0/OtO3HihLKzs1O+vr7q+vXr+da9//77ClDPPfdcWYYurGzs2LHK3d1dzZs3744VGSkr1VdKSooKDg5WUVFRKi0trcD6999/XzVr1izfMikv1VPjxo0VoN55550C66ZPn64A1bhx43zLr1+/rry9vZW9vb06efJkvnVz585VgOratWuZxi3Kzs8//6xefPFFS8WjKBWZkn5/ZGVlqfDwcAWoTZs25Vu3ceNGBagGDRoU+0a/VGTKQOfOnRWgpk2bVmDd0aNHFaBcXV1VamqqFaIT5W3x4sXKYDCopKSkQtc//vjjhf4YDBs2TAFqzJgxBfZJTExUdnZ2Sq/XqzNnzpRJ3MK6Dh48qGxtbdWMGTPU2rVr71iRkbJSfb3zzjsKUL///nuR95HyUj05ODgoQP32228F1h04cMByEZuQkGBZPn78eAWoQYMGFdjHZDKpGjVqKEBt3LixTGMXZSM7Ozvf66JUZEr6/fHdd98pQLVq1arQ47Zu3VoBas6cOcV6DzJGppRduXKFdevWAdClS5cC6+vXr09gYCDJycksX768nKMT1tCrVy+uXbuGq6troesDAwMBLPMcgTbX0aJFi4DCy5GbmxtRUVGYzea7jrERlY/ZbObZZ5+lXbt2PPvss3fcVspK9WUymZg1axZ2dnZ07ty5yPtIeamemjRpAsDhw4cLrMtdptPp8k0zMX/+fKDwsqLX6y3l7scffyz1eEXZMxgMxdr+Xr4/7lSWALp27QoUvyxJRaaU7dy5E7PZjNFoJCQkpNBtwsPDAdixY0d5hiasxGg03rYSA9rAN4BGjRpZlh07dozExEQgr7z8lZSjquvTTz9l//79TJ8+/a7bSlmpvg4ePEhcXBzBwcEkJyczZswYGjZsiKenJyEhIQwdOpRDhw7l20fKS/U1bdo0atasycSJE5k/fz5paWlkZmaycuVKRo4cCUDHjh1xcnICtAQSueVHyoqAe/v+2LZtW4n2uxubYm0t7urkyZMA+Pj4oNcXXk8MCAjIt62ovrKzs1m5ciUAL7/8smX5rWXD39+/0H2lHFVNsbGxvPvuu4wfP/62N0NuJWWl+tq/fz+gZR2KjIykUaNGTJs2DW9vbzZs2MBbb73FDz/8wPz583nooYcAKS/VWdOmTYmJiWHq1KkMGzaMmzdvotPpLJlUmzRpwqxZsyzbx8bGWtZJWRFQ8u+PlJQULl++XKT94uPjSU1NxdHRsUgxSUWmlCUnJwPg4OBw221y/ziStlDMmjWL+Ph4XnzxRaKioizLc8uRwWDAaDQWuq+Uo6pp+PDhNGjQgBEjRhRpeykr1deVK1cALb17s2bNWLJkieUGWkREBMHBwfTs2ZMhQ4Zw8uRJvL29pbxUY9evX2fo0KH89ttvjBo1igEDBmBnZ8eGDRuIj49n1KhReHh4WLbPLStw+2saKSvVS0m/P4pTlnL3LWpFRrqWCWElJ06c4I033qBNmzZ8/PHH1g5HVAAzZ85k/fr1zJw5s9h9l0X1k5qaann+yiuvFOgF0KNHD8LCwkhOTubbb78t7/BEBaKU4sEHH+SXX37hH//4B//+97+JioqicePGvPLKK0RGRtKgQQOWLl1q7VCFKBapyJSy3LEQaWlpt90m98fHzc2tXGISFU9cXBzdu3cnNDSU5cuX5xtcCXnlyGQykZWVVegxpBxVLXFxcbzxxhuMHj3aMii3KKSsVF+33tls2LBhodtERkYCsH37dkDKS3W1Zs0aSxkYNWpUgfWPPPIIrq6u9O3blz179gDkG9t5u2saKSvVS0m/P4pTlv66791IRaaU5fZpv3LliqVv6V/lDu4uSv93UfVcvHiRLl264Ovry+rVqwv9wN5aNuLj4ws9jpSjquWPP/4gMTGRqVOn4uzsnO/Ro0cPQOtCdOtykLJSneX2KQfw9PQsdBsXFxdA61YEUl6qq127dgHg5+d327ISHh5OdnY2M2bMAKBOnTrodDpAyorQlPT7w9nZGV9f3yLt5+/vX+RuZSAVmVIXGRmJXq8nKyvrtoPfjh49CpBvTISoHs6cOUOHDh3w9fVl1apV+foj3yosLMxSwcktL38l5ahq6devH8ePH2f//v3s3bs33yP3wqJGjRr5loOUleqsWbNmlueXLl0qdJvc5bnfNVJeqrfciklhcrsmnj9/HgAnJyciIiIAKStCcy/fHy1btizRfncjFZlS5uvrS8eOHQFYvXp1gfUxMTGcP38eFxcXHnzwwfIOT1jR8ePHad++PSEhISxfvtxyRx207EO3lgeDwUC/fv2AwstRUlISO3bsQK/X079//7IPXpQ5FxcXQkNDC33UrFkTABsbm3zLQcpKddagQQPCwsIA2LdvX6Hb5M4P0rZtW0DKS3WVW07i4+NvOzA/JiYGyJ9VasCAAUDhZcVsNrNmzZp824mq7V6+P+5UlgBWrVqVb7siK9b0maJI1q1bpwAVERGhsrKy8q0bPny4AtT48eOtFJ2whoMHDyp/f3/Vp08flZ6eXmB97szttzp+/LiytbVVvr6+KjExMd+6999/XwFq2LBhZRq3qBhyy0dQUFCh66WsVF/ffvutAlTDhg0L/N4sXbpUAcrLy0tdv37dslzKS/Vz8+ZN5efnd9vrj+XLl1tmdf/9998ty69du6a8vLyUvb29OnXqVL595s6dqwDVuXPnMo9flI/cMhAbG3vbbUr6/ZGZmanCwsIUoDZt2pRv3aZNmxSg6tevX+B77K4xF2trUWS5f8zevXurXbt2qZiYGDVmzBgFqJ49exb7DyUqrwMHDihvb28FqCZNmqjIyMgCj9wP91999913Sq/XqzZt2qiNGzeqkydPqsmTJysbGxsVGRmpkpOTrfCORHm5fPmyiouLUwsXLlSACgwMVHFxcSouLk7duHEj37ZSVqqv3BtkDz30kNq+fbs6ffq0+u6775S3t7dydXVVa9euLbCPlJfqZ9WqVcrJyUnZ2NioCRMmqCNHjqhTp06pGTNmKC8vLwWoV199tcB+q1evVvb29qp+/frq999/V6dOnVKzZs1Szs7OKjg4WF24cMEK70aUltzfmbi4OEtFZvv27ZZlhSnp98eBAweUp6en8vf3VwsXLlSxsbFq4cKFyt/fX3l6eqoDBw4UO36pyJShZcuWqS5duig3Nzfl6OiomjZtqj799FOVnZ1t7dBEOZo6darly+Fuj8Js2bJFPfzww8rLy0vZ2dmp8PBwNW7cOJWWllbO70SUt6CgoNuWlbFjxxbYXspK9fXDDz+o6Oho5ebmpmxtbVWdOnXUiy++WOAu+q2kvFQ/J06cUC+//LIKCwtT9vb2ymg0qho1aqi+ffuqpUuX3na/I0eOqMcee0z5+flZytfIkSPztfSJyulOvzN36rhV0u+P8+fPq+HDh6vAwEBla2urAgMD1fDhw9X58+dLFL9OKaWK1xlNCCGEEEIIIaxLBvsLIYQQQgghKh2pyAghhBBCCCEqHanICCGEEEIIISodqcgIIYQQQgghKh2pyAghhBBCCCEqHanICCGEEEIIISodqcgIIYQQQgghKh2pyAghhBBCCCEqHanICCGEEEIIISodqcgIIYQQQgghKh2pyAghhBB3oNPpCjzOnz9f4uPZ29sXON7p06dLL2AhhKgmpCIjhBDitqKjowu9kL/bY+jQoZZj/O1vfyMgIIBDhw5Z742Ugu3btxMXF0dcXBw1atQo8XHOnDljOY4QQoiSk4qMEEKIOxo4cKDlwjv3MXDgwNuua9OmTb7958yZQ3x8PMuXL7dG+KXGx8cHf39//P390etL/vPp5+dnOY4QQoiSs7F2AEIIISo2BweHAhfdDg4Ot11na2ub7/W7777L8uXLefTRR8s2UCGEENWKVGSEEELcVrdu3fDx8bmnfd566y3eeuut0g5NCCFENSddy4QQQtzWO++8w/PPP1+ifb755pt842bee+89yzZz5swpsO7gwYP06NEDFxcX/Pz8eOaZZ7hy5QoAJ0+epG/fvri7u+Pu7m7p0nY7Bw4c4PHHHycgIABbW1sCAgIYMGAA27dvL9H/w93s2LGDRx99lODgYOzs7PDz86N3797Mnj2bxMTEMjmnEEJUd1KREUIIUSYGDRpEXFwco0aNKrDu0Ucfzbfu2LFjjBw5kn/961/s2rWLF198kW+++YaePXsSFxfHm2++yZgxY9i2bRuvvfYa8+fP56GHHkIpVeDYCxcupEWLFmzbto2vv/6aw4cPM336dA4cOEDbtm2ZO3duqb7P5cuX06ZNG27evMmcOXM4duwYixcvxtbWlmHDhvHJJ5+U6vmEEEJopGuZEEKIMuHg4ICDgwPOzs4F1tnb2+Pv729Zt2DBAs6cOUNAQAAA7733HqtWrWLTpk307t2b3377zbJu/PjxrFq1ii1btrBlyxbatm1rOe6pU6d46qmnAFi7di21a9cGIDQ0lKioKOrWrcvzzz9Phw4dqFWrVqm8z48++giTycT333+Pt7c3AEFBQcyfP5/77ruvVM4hhBCiIGmREUIIYXVdu3a1VFRyRUVFAVqWr7+ua9myJQC7d+/Ot3zq1KmkpqbSv39/SyUml7+/P3379iU1NZVZs2aVWuy53d/Onj2bb7nBYOCTTz6hZ8+epXYuIYQQeaQiI4QQwupCQkIKLHN1db3tOjc3NwCuX7+eb/kff/wBQIsWLQo9T926dQHYtGlTyYP9iy5dugBakoMPPvggX4XmgQcesFS6hBBClC6pyAghhLA6T0/PAst0Ot1d15lMpnzLcysRb7/9Ns7OzgUe//nPfwC4cOFCqcU+adIknn76aRITE3nnnXcICgqiadOmfPTRR5bWGiGEEKVPxsgIIYSwutyKSXHX3c77779Pnz59brveaDQW+5i34+TkxDfffMP48eOZO3cuP/30E3v37mXfvn38+9//ZsGCBXTq1KnUzieEEEIjFRkhhBBVRlBQEDExMdjY2BAaGlqu565du7ZlzpxDhw7x5ptvsnz5cp588knOnz9frrEIIUR1IF3LhBBCVBndu3cHuO18MSkpKbRs2ZKPP/641M75xhtvsHfv3nzLIiIiWLRoEU5OTly4cIHLly+X2vmEEEJopCIjhBCiyhgxYgROTk4sXryY2NjYAus/+eQTdu7cSbdu3UrtnAsWLGD+/PkFliulMJlMuLi44OHhUWrnE0IIoZGuZUIIIYrs2rVrZGZmkpaWBkBaWhrx8fE4ODhYMonlSktLIykpiZSUFEBrDYmPj8fNzQ2DwcC1a9cKrMsd2F+Sdba2ttSpU4c5c+YwePBgunTpwocffkirVq24du0a8+bN4+OPP2by5Mk0atSoVP9f/vOf/2Bvb89DDz2Eh4cHsbGxTJo0ifT0dD766KNSHZMjhBBCo1OFTYsshBBCFCI6Opr169cXWP7000/zzTff5Fv2zTff8MwzzxTYdvbs2QQHBxc6AH7t2rUAJVoXHR1teX348GE++ugjVq9ezZUrV/D19aVx48aMHDnSki65qHKTDcTGxhIcHFxg/dGjR/nxxx9ZunQpMTExpKenExAQQJMmTRgxYkS+uIp7bCGEELcnFRkhhBDiDsqysiEVGSGEKDkZIyOEEEIIIYSodGSMjBBCCFEEERERlhaUY8eOUaNGjRIdx9vbm/T09NIMTQghqiWpyAghhBB3cPz48QLL/Pz8Sny87du3Yzab8y0LDAws8fGEEKK6kjEyQgghhBBCiEpHxsgIIYQQQgghKh2pyAghhBBCCCEqHanICCGEEEIIISodqcgIIYQQQgghKh2pyAghhBBCCCEqHanICCGEEEIIISodqcgIIYQQQgghKh2pyAghhBBCCCEqHanICCGEEEIIISqd/wemUkkatmEFIQAAAABJRU5ErkJggg==", | |
| "text/plain": [ | |
| "<Figure size 900x400 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Plot the numerical solution and the exact solution.\n", | |
| "pyplot.figure(figsize=(9.0, 4.0)) # set the size of the figure\n", | |
| "pyplot.title('Elevation of the phugoid over the time') # set the title\n", | |
| "pyplot.xlabel('Time [s]') # set the x-axis label\n", | |
| "pyplot.ylabel('Elevation [m]') # set the y-axis label\n", | |
| "pyplot.xlim(t[0], t[-1]) # set the x-axis limits\n", | |
| "pyplot.ylim(40.0, 160.0) # set the y-axis limits\n", | |
| "pyplot.grid() # set a background grid to improve readability\n", | |
| "pyplot.plot(t, z, label='Numerical',\n", | |
| " color='C0', linestyle='-', linewidth=2)\n", | |
| "pyplot.plot(t, z_exact, label='Analytical',\n", | |
| " color='C1', linestyle='-', linewidth=2)\n", | |
| "pyplot.legend(); # set the legend" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "That looks like pretty good agreement, but what's happening towards the end? We'll come back to this. For now, re-run the previous steps with a different time step, say $dt=0.01$ and pay attention to the difference.\n", | |
| "\n", | |
| "Euler's method, like all numerical methods, introduces some errors. If the method is *convergent*, the approximation will get closer and closer to the exact solution as we reduce the size of the step, $\\Delta t$. The error in the numerical method should tend to zero, in fact, when $\\Delta t\\rightarrow 0$—when this happens, we call the method _consistent_. We'll define these terms more carefully in the theory components of this course. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Convergence" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "To compare the two solutions, we need to use a **norm** of the difference, like the $L_1$ norm, for example.\n", | |
| "\n", | |
| "$$\n", | |
| "E = \\Delta t \\sum_{n=0}^N \\left|z(t_n) - z_n\\right|\n", | |
| "$$\n", | |
| "\n", | |
| "The $L_1$ norm is the sum of the individual differences between the exact and the numerical solutions, at each mesh point. In other words, $E$ is the discrete representation of the integral over the interval $T$ of the (absolute) difference between the computed $z$ and $z_{\\rm exact}$:\n", | |
| "\n", | |
| "$$\n", | |
| "E = \\int \\vert z-z_\\rm{exact}\\vert dt\n", | |
| "$$\n", | |
| "\n", | |
| "We check for convergence by calculating the numerical solution using progressively smaller values of `dt`. We already have most of the code that we need. We just need to add an extra loop and an array of different $\\Delta t$ values to iterate through." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### Warning" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The cell below can take a little while to finish (the last $\\Delta t$ value alone requires 1 million iterations!). If the cell is still running, the input label will say `In [*]`. When it finishes, the `*` will be replaced by a number." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Set the list of time-step sizes.\n", | |
| "dt_values = [0.1, 0.05, 0.01, 0.005, 0.001, 0.0001]\n", | |
| "\n", | |
| "# Create an empty list that will contain the solution of each grid.\n", | |
| "z_values = []\n", | |
| "\n", | |
| "for dt in dt_values:\n", | |
| " N = int(T / dt) + 1 # number of time-steps\n", | |
| " t = numpy.linspace(0.0, T, num=N) # time grid\n", | |
| " # Set the initial conditions.\n", | |
| " u = numpy.array([z0, b0])\n", | |
| " z = numpy.empty_like(t)\n", | |
| " z[0] = z0\n", | |
| " # Temporal integration using Euler's method.\n", | |
| " for n in range(1, N):\n", | |
| " rhs = numpy.array([u[1], g * (1 - u[0] / zt)])\n", | |
| " u = u + dt * rhs\n", | |
| " z[n] = u[0] # store the elevation at time-step n+1\n", | |
| " z_values.append(z) # store the elevation over the time" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Calculate the error" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We now have numerical solutions for each $\\Delta t$ in the array `z_values`. To calculate the error corresponding to each $\\Delta t$, we can write a function! " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def l1_error(z, z_exact, dt):\n", | |
| " \"\"\"\n", | |
| " Computes and returns the error\n", | |
| " (between the numerical and exact solutions)\n", | |
| " in the L1 norm.\n", | |
| " \n", | |
| " Parameters\n", | |
| " ----------\n", | |
| " z : numpy.ndarray\n", | |
| " The numerical solution as an array of floats.\n", | |
| " z_exact : numpy.ndarray\n", | |
| " The analytical solution as an array of floats.\n", | |
| " dt : float\n", | |
| " The time-step size.\n", | |
| " \n", | |
| " Returns\n", | |
| " -------\n", | |
| " error: float\n", | |
| " L1-norm of the error with respect to the exact solution.\n", | |
| " \"\"\"\n", | |
| " error = dt * numpy.sum(numpy.abs(z - z_exact))\n", | |
| " return error" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**Note**: in the first line of the function, we perform an 'array operation': \n", | |
| "\n", | |
| "`z - z_exact`\n", | |
| "\n", | |
| "We are *not* subtracting one value from another. Instead, we are taking the difference between elements at each corresponding index in both arrays. Here is a quick example:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([3, 2, 1])" | |
| ] | |
| }, | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a = numpy.array([1, 2, 3])\n", | |
| "b = numpy.array([4, 4, 4])\n", | |
| "\n", | |
| "b - a" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now, we iterate through each $\\Delta t$ value and calculate the corresponding error.\n", | |
| "In the following code cell, we use the built-in function [`zip`](https://docs.python.org/3/library/functions.html#zip) to iterate over the two lists `z_values` and `dt_values`." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Create an empty list to store the errors on each time grid.\n", | |
| "error_values = []\n", | |
| "\n", | |
| "for z, dt in zip(z_values, dt_values):\n", | |
| " N = int(T / dt) + 1 # number of time-steps\n", | |
| " t = numpy.linspace(0.0, T, num=N) # time grid\n", | |
| " # Compute the exact solution.\n", | |
| " z_exact = (b0 * (zt / g)**0.5 * numpy.sin((g / zt)**0.5 * t) +\n", | |
| " (z0 - zt) * numpy.cos((g / zt)**0.5 * t) + zt)\n", | |
| " # Calculate the L1-norm of the error for the present time grid.\n", | |
| " error_values.append(l1_error(z, z_exact, dt))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Remember, *if* the method is convergent then the error should get smaller as $\\Delta t$ gets smaller. To visualize this, let's plot $\\Delta t$ vs. error. If you use `pyplot.plot` you won't get a very useful result. Instead, use `pyplot.loglog` to create the same plot with a log-log scale. This is what we do almost always to assess the errors of a numerical scheme graphically." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "<>:4: SyntaxWarning: invalid escape sequence '\\D'\n", | |
| "<>:4: SyntaxWarning: invalid escape sequence '\\D'\n", | |
| "/tmp/ipykernel_97725/542614714.py:4: SyntaxWarning: invalid escape sequence '\\D'\n", | |
| " pyplot.xlabel('$\\Delta t$') # set the x-axis label\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 600x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Plot the error versus the time-step size.\n", | |
| "pyplot.figure(figsize=(6.0, 6.0))\n", | |
| "pyplot.title('L1-norm error vs. time-step size') # set the title\n", | |
| "pyplot.xlabel('$\\Delta t$') # set the x-axis label\n", | |
| "pyplot.ylabel('Error') # set the y-axis label\n", | |
| "pyplot.grid()\n", | |
| "pyplot.loglog(dt_values, error_values,\n", | |
| " color='C0', linestyle='--', marker='o') # log-log plot\n", | |
| "pyplot.axis('equal'); # make axes scale equally" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "This is the kind of result we like to see! As $\\Delta t$ shrinks (towards the left), the error gets smaller and smaller, like it should." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### Challenge!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We calculated the solution for several different time-step sizes using two nested `for` loops.\n", | |
| "That worked, but whenever possible, we like to re-use code (and not just copy and paste it!).\n", | |
| "\n", | |
| "Create a function that implements Euler's method and re-write the code cell that computes the solution for different time-step sizes using your function." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "---\n", | |
| "\n", | |
| "###### The cell below loads the style of this notebook." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n", | |
| "<link href='http://fonts.googleapis.com/css?family=Arvo:400,700,400italic' rel='stylesheet' type='text/css'>\n", | |
| "<link href='http://fonts.googleapis.com/css?family=PT+Mono' rel='stylesheet' type='text/css'>\n", | |
| "<link href='http://fonts.googleapis.com/css?family=Shadows+Into+Light' rel='stylesheet' type='text/css'>\n", | |
| "<link href='http://fonts.googleapis.com/css?family=Nixie+One' rel='stylesheet' type='text/css'>\n", | |
| "<link href='https://fonts.googleapis.com/css?family=Source+Code+Pro' rel='stylesheet' type='text/css'>\n", | |
| "<style>\n", | |
| "\n", | |
| "@font-face {\n", | |
| " font-family: \"Computer Modern\";\n", | |
| " src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n", | |
| "}\n", | |
| "\n", | |
| "#notebook_panel { /* main background */\n", | |
| " background: rgb(245,245,245);\n", | |
| "}\n", | |
| "\n", | |
| "div.cell { /* set cell width */\n", | |
| " width: 750px;\n", | |
| "}\n", | |
| "\n", | |
| "div #notebook { /* centre the content */\n", | |
| " background: #fff; /* white background for content */\n", | |
| " width: 1000px;\n", | |
| " margin: auto;\n", | |
| " padding-left: 0em;\n", | |
| "}\n", | |
| "\n", | |
| "#notebook li { /* More space between bullet points */\n", | |
| " margin-top:0.8em;\n", | |
| "}\n", | |
| "\n", | |
| "/* draw border around running cells */\n", | |
| "div.cell.border-box-sizing.code_cell.running { \n", | |
| " border: 1px solid #111;\n", | |
| "}\n", | |
| "\n", | |
| "/* Put a solid color box around each cell and its output, visually linking them*/\n", | |
| "div.cell.code_cell {\n", | |
| " background-color: rgb(256,256,256); \n", | |
| " border-radius: 0px; \n", | |
| " padding: 0.5em;\n", | |
| " margin-left:1em;\n", | |
| " margin-top: 1em;\n", | |
| "}\n", | |
| "\n", | |
| "div.text_cell_render{\n", | |
| " font-family: 'Alegreya Sans' sans-serif;\n", | |
| " line-height: 140%;\n", | |
| " font-size: 125%;\n", | |
| " font-weight: 400;\n", | |
| " width:600px;\n", | |
| " margin-left:auto;\n", | |
| " margin-right:auto;\n", | |
| "}\n", | |
| "\n", | |
| "\n", | |
| "/* Formatting for header cells */\n", | |
| ".text_cell_render h1 {\n", | |
| " font-family: 'Nixie One', serif;\n", | |
| " font-style:regular;\n", | |
| " font-weight: 400; \n", | |
| " font-size: 45pt;\n", | |
| " line-height: 100%;\n", | |
| " color: rgb(0,51,102);\n", | |
| " margin-bottom: 0.5em;\n", | |
| " margin-top: 0.5em;\n", | |
| " display: block;\n", | |
| "}\n", | |
| "\n", | |
| ".text_cell_render h2 {\n", | |
| " font-family: 'Nixie One', serif;\n", | |
| " font-weight: 400;\n", | |
| " font-size: 30pt;\n", | |
| " line-height: 100%;\n", | |
| " color: rgb(0,51,102);\n", | |
| " margin-bottom: 0.1em;\n", | |
| " margin-top: 0.3em;\n", | |
| " display: block;\n", | |
| "}\t\n", | |
| "\n", | |
| ".text_cell_render h3 {\n", | |
| " font-family: 'Nixie One', serif;\n", | |
| " margin-top:16px;\n", | |
| " font-size: 22pt;\n", | |
| " font-weight: 600;\n", | |
| " margin-bottom: 3px;\n", | |
| " font-style: regular;\n", | |
| " color: rgb(102,102,0);\n", | |
| "}\n", | |
| "\n", | |
| ".text_cell_render h4 { /*Use this for captions*/\n", | |
| " font-family: 'Nixie One', serif;\n", | |
| " font-size: 14pt;\n", | |
| " text-align: center;\n", | |
| " margin-top: 0em;\n", | |
| " margin-bottom: 2em;\n", | |
| " font-style: regular;\n", | |
| "}\n", | |
| "\n", | |
| ".text_cell_render h5 { /*Use this for small titles*/\n", | |
| " font-family: 'Nixie One', sans-serif;\n", | |
| " font-weight: 400;\n", | |
| " font-size: 16pt;\n", | |
| " color: rgb(163,0,0);\n", | |
| " font-style: italic;\n", | |
| " margin-bottom: .1em;\n", | |
| " margin-top: 0.8em;\n", | |
| " display: block;\n", | |
| "}\n", | |
| "\n", | |
| ".text_cell_render h6 { /*use this for copyright note*/\n", | |
| " font-family: 'PT Mono', sans-serif;\n", | |
| " font-weight: 300;\n", | |
| " font-size: 9pt;\n", | |
| " line-height: 100%;\n", | |
| " color: grey;\n", | |
| " margin-bottom: 1px;\n", | |
| " margin-top: 1px;\n", | |
| "}\n", | |
| "\n", | |
| ".CodeMirror{\n", | |
| " font-family: \"Source Code Pro\";\n", | |
| " font-size: 90%;\n", | |
| "}\n", | |
| "\n", | |
| ".alert-box {\n", | |
| " padding:10px 10px 10px 36px;\n", | |
| " margin:5px;\n", | |
| "}\n", | |
| "\n", | |
| ".success {\n", | |
| " color:#666600;\n", | |
| " background:rgb(240,242,229);\n", | |
| "}\n", | |
| "</style>\n", | |
| "\n", | |
| "<script>\n", | |
| " MathJax.Hub.Config({\n", | |
| " TeX: {\n", | |
| " extensions: [\"AMSmath.js\"],\n", | |
| " equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n", | |
| " },\n", | |
| " tex2jax: {\n", | |
| " inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n", | |
| " displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n", | |
| " },\n", | |
| " displayAlign: 'center', // Change this to 'center' to center equations.\n", | |
| " \"HTML-CSS\": {\n", | |
| " styles: {'.MathJax_Display': {\"margin\": 4}}\n", | |
| " }\n", | |
| " });\n", | |
| " MathJax.Hub.Queue(\n", | |
| " [\"resetEquationNumbers\", MathJax.InputJax.TeX],\n", | |
| " [\"PreProcess\", MathJax.Hub],\n", | |
| " [\"Reprocess\", MathJax.Hub]\n", | |
| " );\n", | |
| "</script>\n" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.HTML object>" | |
| ] | |
| }, | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "from IPython.core.display import HTML\n", | |
| "css_file = '../../styles/numericalmoocstyle.css'\n", | |
| "HTML(open(css_file, 'r').read())" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "dolfinx-env", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.12.3" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 1 | |
| } | |
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