{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Scipy -- Library of scientific algorithms for Python\n", "\n", "Based on lecture at http://github.com/jrjohansson/scientific-python-lectures." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The SciPy framework builds on top of the low-level NumPy framework for multidimensional arrays, and provides a large number of higher-level scientific algorithms. Some of the topics that SciPy covers are:\n", "\n", "* Special functions ([scipy.special](http://docs.scipy.org/doc/scipy/reference/special.html))\n", "* Integration ([scipy.integrate](http://docs.scipy.org/doc/scipy/reference/integrate.html))\n", "* Optimization ([scipy.optimize](http://docs.scipy.org/doc/scipy/reference/optimize.html))\n", "* Interpolation ([scipy.interpolate](http://docs.scipy.org/doc/scipy/reference/interpolate.html))\n", "* Fourier Transforms ([scipy.fftpack](http://docs.scipy.org/doc/scipy/reference/fftpack.html))\n", "* Signal Processing ([scipy.signal](http://docs.scipy.org/doc/scipy/reference/signal.html))\n", "* Linear Algebra ([scipy.linalg](http://docs.scipy.org/doc/scipy/reference/linalg.html))\n", "* Sparse Eigenvalue Problems ([scipy.sparse](http://docs.scipy.org/doc/scipy/reference/sparse.html))\n", "* Statistics ([scipy.stats](http://docs.scipy.org/doc/scipy/reference/stats.html))\n", "* Multi-dimensional image processing ([scipy.ndimage](http://docs.scipy.org/doc/scipy/reference/ndimage.html))\n", "* File IO ([scipy.io](http://docs.scipy.org/doc/scipy/reference/io.html))\n", "\n", "Each of these submodules provides a number of functions and classes that can be used to solve problems in their respective topics.\n", "\n", "In this lecture we will look at how to use some of these subpackages.\n", "\n", "To access the SciPy package in a Python program, we start by importing everything from the `scipy` module." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "WARNING: In the new version of python many functionalities are now moved from `scipy` to `numpy`, but they are still available in `scipy` and a deprecated warning is displayed. The work-around is to first import functions from `scipy` and after that from `numpy`, to overwrite scipy functions with the same name." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from scipy import *\n", "from numpy import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we only need to use part of the SciPy framework we can selectively include only those modules we are interested in. For example, to include the linear algebra package under the name `la`, we can do:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import scipy.linalg as la" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Special functions\n", "\n", "A large number of mathematical special functions are important for many computional physics problems. SciPy provides implementations of a very extensive set of special functions. For details, see the list of functions in the reference documention at http://docs.scipy.org/doc/scipy/reference/special.html#module-scipy.special. \n", "\n", "To demonstrate the typical usage of special functions we will look in more detail at the Bessel functions:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#\n", "# The scipy.special module includes a large number of Bessel-functions\n", "# Here we will use the functions jn and yn, which are the Bessel functions \n", "# of the first and second kind and real-valued order. We also include the \n", "# function jn_zeros and yn_zeros that gives the zeroes of the functions jn\n", "# and yn.\n", "#\n", "from scipy.special import jn, yn, jn_zeros, yn_zeros" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "J_0(0.000000) = 1.000000\n", "Y_0(1.000000) = 0.088257\n" ] } ], "source": [ "n = 0 # order\n", "x = 0.0 # x-point\n", "\n", "# Bessel function of first kind\n", "print(\"J_%d(%f) = %f\" % (n, x, jn(n, x)))\n", "\n", "x = 1.0\n", "# Bessel function of second kind\n", "print(\"Y_%d(%f) = %f\" % (n, x, yn(n, x)))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from IPython.display import Image" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = linspace(0, 10, 100)\n", "\n", "\n", "for n in range(4):\n", " plt.plot(x, jn(n, x), label=('$J_%d(x)$' % n))\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integration\n", "\n", "### Numeric integration with general purpose quadrature" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numerical evaluation of a function of the type\n", "\n", "$\\displaystyle \\int_a^b f(x) dx$\n", "\n", "is called *numerical quadrature*, or simply *quadature*. SciPy provides a series of functions for different kind of quadrature, for example the `quad`, `dblquad` and `tplquad` for single, double and triple integrals, respectively.\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import quad, dblquad, tplquad" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `quad` function takes a large number of optional arguments, which can be used to fine-tune the behaviour of the function (try `help(quad)` for details).\n", "\n", "The basic usage is as follows:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Value= 0.33333333333333337 error= 3.700743415417189e-15\n" ] } ], "source": [ "x_lower, x_upper = 0.0, 1.0\n", "val, abserr = quad( lambda x: x**2, x_lower, x_upper)\n", "print('Value=', val, 'error=', abserr)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "L=10*pi\n", "x=linspace(1e-12,L)\n", "plt.plot(x,sin(x)/x)\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.440892098500626e-16\n" ] } ], "source": [ "y1=quad(lambda x: sin(x)/x, 0,L)\n", "from scipy import special\n", "y2=special.sici(L)\n", "print(y1[0]-y2[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we need to pass extra arguments to integrand function we can use the `args` keyword argument. Let's say we want to evaluate\n", "\n", "$f(x) = \\displaystyle \\int_0^x \\frac{j_n(t)+j_m(t)}{t} dt$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "f2 = lambda t,n,m: (jn(n,t)+jn(m,t))/t\n", "\n", "def f3(t,n,m):\n", " return (jn(n,t)+jn(m,t))/t\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5396292385998932" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# First specific case for x=1, n=1\n", "# integrating (j_1(t)+j_2(t))/t\n", "quad(f2, 0, 1, args=(1,2))[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now simpler: $f_n(x) = n \\displaystyle \\int_0^x \\frac{j_n(t)}{t} dt$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = linspace(1e-10,30,300)\n", "\n", "for ns in range(1,4):\n", " fs=[ns * quad(lambda t,n: jn(n, t)/t, 0, x, args=(ns,))[0] for x in xs]\n", " plt.plot(xs,fs, label='n='+str(ns))\n", "plt.legend(loc='best')" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# here we can get away withouth args since function is defined inline\n", "\n", "for ns in range(1,4):\n", " fs=[ns * quad(lambda t: jn(ns, t)/t, 0, x)[0] for x in xs]\n", " plt.plot(xs,fs, label='n='+str(ns))\n", "plt.legend(loc='best')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Higher-dimensional integration works in the same way:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we pass lambda functions for the limits for the y integration, since these in general can be functions of x.\n", "\n", "\\begin{equation}\n", "\\int_{x_a}^{x_b} \\int_{y_a(x)}^{y_b(x)} f(x,y) dy dx\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.7853981633974476 0.6960409996039545 1.4675161390126584e-08\n" ] } ], "source": [ "def integrand(x, y, z):\n", " return exp(-x**2-y**2-z**2)\n", "\n", "x_a,x_b = 0,10\n", "y_a,y_b = 0,10\n", "z_a,z_b = 0,10\n", "\n", "val1, abserr = dblquad(integrand, x_a, x_b, lambda x:y_a, lambda x:y_b, args=(0,))\n", "\n", "val2, abserr = tplquad(integrand, x_a, x_b, lambda x:y_a, lambda x:y_b, lambda x,y:z_a, lambda x,y:z_b)\n", "\n", "print(val1, val2, abserr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ordinary differential equations (ODEs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "SciPy provides two different ways to solve ODEs: An API based on the function `odeint`, and object-oriented API based on the class `ode`. Usually `odeint` is easier to get started with, but the `ode` class offers some finer level of control.\n", "\n", "Here we will use the `odeint` functions. For more information about the class `ode`, try `help(ode)`. It does pretty much the same thing as `odeint`, but in an object-oriented fashion.\n", "\n", "To use `odeint`, first import it from the `scipy.integrate` module" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from scipy import *\n", "from numpy import *\n", "from scipy.integrate import odeint, ode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A system of ODEs should be formulated in standard form, which is:\n", "\n", "$y' = f(y, t)$\n", "\n", "where we are searching for function $y(t)$ and\n", "where \n", "\n", "$y = [y_1(t), y_2(t), ..., y_n(t)]$ \n", "\n", "and $f$ is some function that gives the derivatives of the function $y_i(t)$. To solve an ODE we need to know the function $f$ and an initial condition, $y(0)$.\n", "\n", "Note that higher-order ODEs can always be written in this form by introducing new variables for the intermediate derivatives.\n", "\n", "Once we have defined the Python function `f` and array `y_0` (that is $f$ and $y(0)$ in the mathematical formulation), we can use the `odeint` function as:\n", "\n", " y_t = odeint(f, y_0, t)\n", "\n", "where `t` is and array with time-coordinates for which to solve the ODE problem. `y_t` is an array with one row for each point in time in `t`, where each column corresponds to a solution `y_i(t)` at that point in time. \n", "\n", "We will see how we can implement `f` and `y_0` in Python code in the examples below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: double pendulum\n", "\n", "Let's consider a physical example: The double compound pendulum, described in some detail here: http://en.wikipedia.org/wiki/Double_pendulum" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image(url='http://upload.wikimedia.org/wikipedia/commons/c/c9/Double-compound-pendulum-dimensioned.svg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equations of motion of the pendulum are given on the wiki page:\n", "\n", "${\\dot \\theta_1} = \\frac{6}{m\\ell^2} \\frac{ 2 p_{\\theta_1} - 3 \\cos(\\theta_1-\\theta_2) p_{\\theta_2}}{16 - 9 \\cos^2(\\theta_1-\\theta_2)}$\n", "\n", "${\\dot \\theta_2} = \\frac{6}{m\\ell^2} \\frac{ 8 p_{\\theta_2} - 3 \\cos(\\theta_1-\\theta_2) p_{\\theta_1}}{16 - 9 \\cos^2(\\theta_1-\\theta_2)}.$\n", "\n", "${\\dot p_{\\theta_1}} = -\\frac{1}{2} m \\ell^2 \\left [ {\\dot \\theta_1} {\\dot \\theta_2} \\sin (\\theta_1-\\theta_2) + 3 \\frac{g}{\\ell} \\sin \\theta_1 \\right ]$\n", "\n", "${\\dot p_{\\theta_2}} = -\\frac{1}{2} m \\ell^2 \\left [ -{\\dot \\theta_1} {\\dot \\theta_2} \\sin (\\theta_1-\\theta_2) + \\frac{g}{\\ell} \\sin \\theta_2 \\right]$\n", "\n", "To make the Python code simpler to follow, let's introduce new variable names and the vector notation: $x = [\\theta_1, \\theta_2, p_{\\theta_1}, p_{\\theta_2}]$\n", "\n", "${\\dot x_1} = \\frac{6}{m\\ell^2} \\frac{ 2 x_3 - 3 \\cos(x_1-x_2) x_4}{16 - 9 \\cos^2(x_1-x_2)}$\n", "\n", "${\\dot x_2} = \\frac{6}{m\\ell^2} \\frac{ 8 x_4 - 3 \\cos(x_1-x_2) x_3}{16 - 9 \\cos^2(x_1-x_2)}$\n", "\n", "${\\dot x_3} = -\\frac{1}{2} m \\ell^2 \\left [ {\\dot x_1} {\\dot x_2} \\sin (x_1-x_2) + 3 \\frac{g}{\\ell} \\sin x_1 \\right ]$\n", "\n", "${\\dot x_4} = -\\frac{1}{2} m \\ell^2 \\left [ -{\\dot x_1} {\\dot x_2} \\sin (x_1-x_2) + \\frac{g}{\\ell} \\sin x_2 \\right]$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function odeint in module scipy.integrate._odepack_py:\n", "\n", "odeint(func, y0, t, args=(), Dfun=None, col_deriv=0, full_output=0, ml=None, mu=None, rtol=None, atol=None, tcrit=None, h0=0.0, hmax=0.0, hmin=0.0, ixpr=0, mxstep=0, mxhnil=0, mxordn=12, mxords=5, printmessg=0, tfirst=False)\n", " Integrate a system of ordinary differential equations.\n", " \n", " .. note:: For new code, use `scipy.integrate.solve_ivp` to solve a\n", " differential equation.\n", " \n", " Solve a system of ordinary differential equations using lsoda from the\n", " FORTRAN library odepack.\n", " \n", " Solves the initial value problem for stiff or non-stiff systems\n", " of first order ode-s::\n", " \n", " dy/dt = func(y, t, ...) [or func(t, y, ...)]\n", " \n", " where y can be a vector.\n", " \n", " .. note:: By default, the required order of the first two arguments of\n", " `func` are in the opposite order of the arguments in the system\n", " definition function used by the `scipy.integrate.ode` class and\n", " the function `scipy.integrate.solve_ivp`. To use a function with\n", " the signature ``func(t, y, ...)``, the argument `tfirst` must be\n", " set to ``True``.\n", " \n", " Parameters\n", " ----------\n", " func : callable(y, t, ...) or callable(t, y, ...)\n", " Computes the derivative of y at t.\n", " If the signature is ``callable(t, y, ...)``, then the argument\n", " `tfirst` must be set ``True``.\n", " y0 : array\n", " Initial condition on y (can be a vector).\n", " t : array\n", " A sequence of time points for which to solve for y. The initial\n", " value point should be the first element of this sequence.\n", " This sequence must be monotonically increasing or monotonically\n", " decreasing; repeated values are allowed.\n", " args : tuple, optional\n", " Extra arguments to pass to function.\n", " Dfun : callable(y, t, ...) or callable(t, y, ...)\n", " Gradient (Jacobian) of `func`.\n", " If the signature is ``callable(t, y, ...)``, then the argument\n", " `tfirst` must be set ``True``.\n", " col_deriv : bool, optional\n", " True if `Dfun` defines derivatives down columns (faster),\n", " otherwise `Dfun` should define derivatives across rows.\n", " full_output : bool, optional\n", " True if to return a dictionary of optional outputs as the second output\n", " printmessg : bool, optional\n", " Whether to print the convergence message\n", " tfirst : bool, optional\n", " If True, the first two arguments of `func` (and `Dfun`, if given)\n", " must ``t, y`` instead of the default ``y, t``.\n", " \n", " .. versionadded:: 1.1.0\n", " \n", " Returns\n", " -------\n", " y : array, shape (len(t), len(y0))\n", " Array containing the value of y for each desired time in t,\n", " with the initial value `y0` in the first row.\n", " infodict : dict, only returned if full_output == True\n", " Dictionary containing additional output information\n", " \n", " ======= ============================================================\n", " key meaning\n", " ======= ============================================================\n", " 'hu' vector of step sizes successfully used for each time step\n", " 'tcur' vector with the value of t reached for each time step\n", " (will always be at least as large as the input times)\n", " 'tolsf' vector of tolerance scale factors, greater than 1.0,\n", " computed when a request for too much accuracy was detected\n", " 'tsw' value of t at the time of the last method switch\n", " (given for each time step)\n", " 'nst' cumulative number of time steps\n", " 'nfe' cumulative number of function evaluations for each time step\n", " 'nje' cumulative number of jacobian evaluations for each time step\n", " 'nqu' a vector of method orders for each successful step\n", " 'imxer' index of the component of largest magnitude in the\n", " weighted local error vector (e / ewt) on an error return, -1\n", " otherwise\n", " 'lenrw' the length of the double work array required\n", " 'leniw' the length of integer work array required\n", " 'mused' a vector of method indicators for each successful time step:\n", " 1: adams (nonstiff), 2: bdf (stiff)\n", " ======= ============================================================\n", " \n", " Other Parameters\n", " ----------------\n", " ml, mu : int, optional\n", " If either of these are not None or non-negative, then the\n", " Jacobian is assumed to be banded. These give the number of\n", " lower and upper non-zero diagonals in this banded matrix.\n", " For the banded case, `Dfun` should return a matrix whose\n", " rows contain the non-zero bands (starting with the lowest diagonal).\n", " Thus, the return matrix `jac` from `Dfun` should have shape\n", " ``(ml + mu + 1, len(y0))`` when ``ml >=0`` or ``mu >=0``.\n", " The data in `jac` must be stored such that ``jac[i - j + mu, j]``\n", " holds the derivative of the `i`th equation with respect to the `j`th\n", " state variable. If `col_deriv` is True, the transpose of this\n", " `jac` must be returned.\n", " rtol, atol : float, optional\n", " The input parameters `rtol` and `atol` determine the error\n", " control performed by the solver. The solver will control the\n", " vector, e, of estimated local errors in y, according to an\n", " inequality of the form ``max-norm of (e / ewt) <= 1``,\n", " where ewt is a vector of positive error weights computed as\n", " ``ewt = rtol * abs(y) + atol``.\n", " rtol and atol can be either vectors the same length as y or scalars.\n", " Defaults to 1.49012e-8.\n", " tcrit : ndarray, optional\n", " Vector of critical points (e.g., singularities) where integration\n", " care should be taken.\n", " h0 : float, (0: solver-determined), optional\n", " The step size to be attempted on the first step.\n", " hmax : float, (0: solver-determined), optional\n", " The maximum absolute step size allowed.\n", " hmin : float, (0: solver-determined), optional\n", " The minimum absolute step size allowed.\n", " ixpr : bool, optional\n", " Whether to generate extra printing at method switches.\n", " mxstep : int, (0: solver-determined), optional\n", " Maximum number of (internally defined) steps allowed for each\n", " integration point in t.\n", " mxhnil : int, (0: solver-determined), optional\n", " Maximum number of messages printed.\n", " mxordn : int, (0: solver-determined), optional\n", " Maximum order to be allowed for the non-stiff (Adams) method.\n", " mxords : int, (0: solver-determined), optional\n", " Maximum order to be allowed for the stiff (BDF) method.\n", " \n", " See Also\n", " --------\n", " solve_ivp : solve an initial value problem for a system of ODEs\n", " ode : a more object-oriented integrator based on VODE\n", " quad : for finding the area under a curve\n", " \n", " Examples\n", " --------\n", " The second order differential equation for the angle `theta` of a\n", " pendulum acted on by gravity with friction can be written::\n", " \n", " theta''(t) + b*theta'(t) + c*sin(theta(t)) = 0\n", " \n", " where `b` and `c` are positive constants, and a prime (') denotes a\n", " derivative. To solve this equation with `odeint`, we must first convert\n", " it to a system of first order equations. By defining the angular\n", " velocity ``omega(t) = theta'(t)``, we obtain the system::\n", " \n", " theta'(t) = omega(t)\n", " omega'(t) = -b*omega(t) - c*sin(theta(t))\n", " \n", " Let `y` be the vector [`theta`, `omega`]. We implement this system\n", " in Python as:\n", " \n", " >>> def pend(y, t, b, c):\n", " ... theta, omega = y\n", " ... dydt = [omega, -b*omega - c*np.sin(theta)]\n", " ... return dydt\n", " ...\n", " \n", " We assume the constants are `b` = 0.25 and `c` = 5.0:\n", " \n", " >>> b = 0.25\n", " >>> c = 5.0\n", " \n", " For initial conditions, we assume the pendulum is nearly vertical\n", " with `theta(0)` = `pi` - 0.1, and is initially at rest, so\n", " `omega(0)` = 0. Then the vector of initial conditions is\n", " \n", " >>> y0 = [np.pi - 0.1, 0.0]\n", " \n", " We will generate a solution at 101 evenly spaced samples in the interval\n", " 0 <= `t` <= 10. So our array of times is:\n", " \n", " >>> t = np.linspace(0, 10, 101)\n", " \n", " Call `odeint` to generate the solution. To pass the parameters\n", " `b` and `c` to `pend`, we give them to `odeint` using the `args`\n", " argument.\n", " \n", " >>> from scipy.integrate import odeint\n", " >>> sol = odeint(pend, y0, t, args=(b, c))\n", " \n", " The solution is an array with shape (101, 2). The first column\n", " is `theta(t)`, and the second is `omega(t)`. The following code\n", " plots both components.\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> plt.plot(t, sol[:, 0], 'b', label='theta(t)')\n", " >>> plt.plot(t, sol[:, 1], 'g', label='omega(t)')\n", " >>> plt.legend(loc='best')\n", " >>> plt.xlabel('t')\n", " >>> plt.grid()\n", " >>> plt.show()\n", "\n" ] } ], "source": [ "help(odeint)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def dx(x,t):\n", " \"\"\"\n", " The right-hand side of the pendulum ODE\n", " x=[x1,x2,x3,x4]\n", " \"\"\"\n", " g, L, m = 9.82, 1., 1.\n", " x1,x2,x3,x4 = x\n", " c1 = 1/(m*L**2)\n", " dx1 = 6.*c1 * (2*x3-3*cos(x1-x2)*x4)/(16.-9.*cos(x1-x2)**2)\n", " dx2 = 6.*c1 * (8*x4-3*cos(x1-x2)*x3)/(16.-9.*cos(x1-x2)**2)\n", " dx3 = -0.5/c1 * (dx1*dx2 * sin(x1-x2) + 3*g/L * sin(x1))\n", " dx4 = -0.5/c1 * (-dx1*dx2 * sin(x1-x2)+ g/L * sin(x2))\n", " return array([dx1,dx2,dx3,dx4])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# choose an initial state\n", "x0 = [pi/4, pi/2, 0, 0]\n", "\n", "# time coodinate to solve the ODE for: from 0 to 10 seconds\n", "t = linspace(0, 10, 250)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# solve the ODE problem\n", "x = odeint(dx, x0, t)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the angles as a function of time\n", "fig, axes = plt.subplots(1,2,figsize=(12,4))\n", "axes[0].plot(t, x[:, 0], label=\"theta1\")\n", "axes[0].plot(t, x[:, 1], label=\"theta2\")\n", "axes[0].legend(loc='best')\n", "axes[0].set_xlabel('time')\n", "\n", "L = 0.5\n", "x1 = L * sin(x[:, 0])\n", "y1 = -L * cos(x[:, 0])\n", "\n", "x2 = x1 + L * sin(x[:, 1])\n", "y2 = y1 - L * cos(x[:, 1])\n", " \n", "axes[1].plot(x1, y1, label=\"pendulum1\")\n", "axes[1].plot(x2, y2, label=\"pendulum2\")\n", "axes[1].set_ylim([-1, 0])\n", "axes[1].set_xlim([-1, 1])\n", "axes[1].legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "examples for subplot creation: \n", "https://towardsdatascience.com/the-many-ways-to-call-axes-in-matplotlib-2667a7b06e06" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "matplotlib examples:\n", "https://matplotlib.org/3.1.1/gallery/index.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See animation in `pendulum.py`.\n", "\n", "(To get it work within jupyter seems a bit challenging at the moment.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Damped harmonic oscillator\n", "\n", "ODE problems are important in computational physics, so we will look at one more example: the damped harmonic oscillation. This problem is well described on the wiki page: http://en.wikipedia.org/wiki/Damping\n", "\n", "The equation of motion for the damped oscillator is:\n", "\n", "$\\displaystyle \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\omega^2_0 x = 0$\n", "\n", "where $x$ is the position of the oscillator, $\\omega_0$ is the frequency, and $\\zeta$ is the damping ratio. To write this second-order ODE on standard form we introduce $p = \\frac{\\mathrm{d}x}{\\mathrm{d}t}$:\n", "\n", "$\\displaystyle \\frac{\\mathrm{d}p}{\\mathrm{d}t} = - 2\\zeta\\omega_0 p - \\omega^2_0 x$\n", "\n", "$\\displaystyle \\frac{\\mathrm{d}x}{\\mathrm{d}t} = p$\n", "\n", "In the implementation of this example we will add extra arguments to the RHS function for the ODE, rather than using global variables as we did in the previous example. As a consequence of the extra arguments to the RHS, we need to pass an keyword argument `args` to the `odeint` function:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def dy(y, t, zeta, w0):\n", " \"\"\"\n", " The right-hand side of the damped oscillator ODE\n", " \"\"\"\n", " x, p = y #y[0], y[1]\n", " \n", " dx = p\n", " dp = -2 * zeta * w0 * p - w0**2 * x\n", "\n", " return array([dx, dp])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# initial state: \n", "y0 = [1.0, 0.0]\n", "\n", "# time coodinate to solve the ODE for\n", "t = linspace(0, 10, 1000)\n", "w0 = 2*pi*1.0" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# solve the ODE problem for three different values of the damping ratio\n", "\n", "y1 = odeint(dy, y0, t, args=(0.0, w0)) # undamped\n", "y2 = odeint(dy, y0, t, args=(0.2, w0)) # under damped\n", "y3 = odeint(dy, y0, t, args=(1.0, w0)) # critial damping\n", "y4 = odeint(dy, y0, t, args=(5.0, w0)) # over damped" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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3GneV38Uugx7TWzv6X1f0gkVw1ILLx/CkfMJtal8HQPVFFwHQsfifxHfqOzRN7lXQdxGrK/MYtpHUju7+r2hkUmbMmFs6w/0SnGEGjnl7V//HRpnXuL1OdgywGNhsEkblCj2ReB/zeQZGjXkgpQzkxnlmmAvXGzUlLsOOP4jG+ydlRlZ/W7v6/x7qBYvgqIgGhzyrZUu3PG/Ld+gheKZMIRWJsOvRR/UMjbae/v0staVuw355dgwUs4FJ2fauMHX9mO5K3A4CBi3Jb+nqn5QZpbdFfxiI4BgZg8XsctgMaSbt6TVWYk8YtTJwMDWsttTY5uj+UFvmMaxi3Z8PTk9YBEdFNPrqANgclOfhSJKUVXHa//o4yYB+/Qx2BfofZ2/kVuBt3VFqSvvGbOT+PWYkCy2dYeoNVAmRD3Z0DzzB2OuyG5JMDkZw6gy6iO3ojvSrooJc/WVEstAdiVPi6Z+UyWqI8T7nwUhZnYEvQo0Gi+CoiNHlIwFoiwcIxuSS4NJvHINr5EiSnZ10/OMfusU2ENP2uRyEo8a7cgTYFYzmzBoyA+R0j7li3tEdGTBmr8uYnYF3dIcHJAvDSt2G7HbdOkDKFeQLje0G9MK19tN8LoPaMmNWrLV2DULKyt2GJGWdoVi/bTzAnKRML1gER0VUVY6kLD1kc0vPFgAku52qC/8HgJ0LHyIVM6anwYgwmvyZD7oGOVG5ncZMQ7T1DEwkq/0udhqwwmdHz8BqSLXfxU4DTrseTMGp8bsN+TkPZHwFuVS8zYCfs0wk+1cka0s97DAgwWntjjBsACJZV+YxJPntCscpG+BcpxcsgqMm/DW7K6m6d5eGl596KvZhNcSbm+l89lnNwzIi084Hg4VtVGUBBk5H1ZZ6DOlZGOzqsbrEbTqyUF1iTLIgp3v6X3ir/C52GfRzHjRmo37OA5CFKoOS3+1dA5Myo37Osq+zr4VAT1gER034a7O9cLZ0b8k+bHO7qTr/fAB23X8/qaS2lQdd4TilA+SkQSYLIYOlqYYiZUY1OA6GYQYtyU+lUtgGUMqqS1zsChjvc94ViFHl6//kKpMF48U8mBpSZdDPuXWQVKBRP+fB/FlVfmO2EdgViA5IFlwOmyGr1dq6+y8C0RMWwVETJbU0xGWi0Bxoznmq8pxzsPn9RNatp+e11zQNa6AKqgyM2GdhKPlT7ndirHRfKpUaVHWSS1SN9TkPhWq/y5BN6AYjZfLEeePF3BGMUjHAMV3jN2azv1090QHPHdUlxlRDdgWiVA1AFjxOO5GY8cjCrkC03yIQI2NnIEq1RXC+QvAPY3hmXEPPtpyn7GVlVHz7HED78Q1t3f13182g0mc8CXQo+bPS76LdYCfXYDSBb4CSWoAKgzahG6zAy6jpnsFQ5XcbMt2TSjEgKZMVHOPF3DFI+tLnchhO+QV5HMZA6p5R0R6IUjlIzEYswrRSVF819CI4zd1b+zxddf73kJxOQitXEnjnHc3C2hkY+CoMjKng7OwZ/OrAiJ6FXYEo1YNchckxG0t1CkUTuPtpLpaBbDI2XhpicFJmvpj9BvWUJZPmM/rvCkSpMBnB2TmEgiNJxuvAbKWovmpwl1KblD/ibYFtfZ521tVS8a2zANhx552amX935rHwGk0NGeoqrNKAakhbT2TQk1Slz0WHwWLeGYgMemxUlxhPDRmKlJW6HXSHjUcWBoMkGbMDsxGVg6EQT6RwOQZe6ow426k9ODjBqfA6jXe+G+LCWQ9YBEdNSBJV9goAumI9BGJ9G/tV/+AHSC4XoRUrCSxdqklYncEoFb5B/CwGrCzoDMYoHyJmoy28Q+XRjRjzzkFKxAHKPA66wsZSnfqbyN0bRmyqGE8kDRlXsTAiWRgK5V6X4UaQDDQ7K4OqEgNehAYGX1f0gEVwVIbHO4zStOO9uae5z/POurqsF0crFacjGBtUsq30GfDLM4ghE6DSb7wrmqGUsnKvkw6DnVgHM2SCMZUFM3osBivFz0CSjNXSIZ5IYhuClJV5nIYjwEOhyu803AXdUKjyGe8idKDZWXrCIjhqw1+z22jcT5oKoGbuXCSPh/AHH2pSUdURig1KFozowekIxagcIt1jNDVkKAXHiFOjhyJlYLw0RXtgcMKegZE+645QbFDVCaDU46TLQKm1zlBsyCt0o6m/yWRqyOPVqCb0wWBE9ddo5wWwCI7qsJfW0pAmOC2Bln63cQwbRuV3zwWg7c67VD8Rd4Zig5ZcV/qdhlNwOoKDkzKn3WY40117IEq1waoKhsJQ1RtGxFB+BQCf20HIQF2jO4JDG1+NpqTKqcDBYzaaR6srPPi5DmTjvJH69+Rz/q82aJWd0WARHJXhKq3J9sLZs1S8N6ovugibz0f400/p+e9/VY1pqJEHboedaNxYvSE6Q1HDtQEfCu15LGJGQz6pE4fNZqjjo30ITxnIpswOA/VJag/EhiQL5V6nobwh7cHBVVSACp+xPuddgaHTl5UGq2bMZ+SBERVrI8IiOCrDWVI9ZIoKwFFZSeX5cwDYceddmnc3NjqMmN8dCl2hOGWewU9UNkkibqCupJ2hwc3cIC9ihlp4A7EhFRyjLbz5kLJyr8NQn3M+ZKHc66TLQDG3B6NDkjLDEck8VFS5AtM4MYdjCdwO452fLYKjNrxV2RRVfybj3qi+4AJsJSVE1q6l69nntIjuSwbJUBUc8WRy0PJUMB5ZyEfBKfc56QwZ5+oxn9SJbOg2Tsyy0T+fz9k4x0Z7YGiyUOYxVsy7TKmU5UN+jRVzxxBVrnrBIjhqw1dFQ6L/cQ17wl5RQfVFFwGwY8ECklHxJ2Ql/h4jmTLzQZnHQXfEOKbMfGC0/j3BaBy/a/ArsQqvsa4e80pR+Vx0GijmjlB+pMxIi9iuIcrxwXgxd+QZs5Eqv/K5yCg1WLuGoVo16AWL4KgNb1U2RbUjtINYcvCDsur8OTiGDSO2dSsdTzwhPJxQLIHXNfD4gAw8TjsRA/ks8kGZweTxfFDmddIZMhYpG6o/i9HSPYFInJJBRmKA8Ury24PmUxa6QvGh1T2jxZyHn8WIMQ/pg7PbDKVWd+RxPOsBi+CoDV81VYkkrlSKZCrJ9sD2QTe3+XzUXPZDANruvodEd7fQcIaqRsqgzOswDFmIxBM47UMfqmUGO1HlgzKDXT3mAyN2Uc2HlBnp2OjIMw1hlO8g5FeRZLSY81FDPE4bYQPN0OoKxSjzDn0RaiR0BKNDfs56wCI4asNXhQ2oz/hwhkhTAVSccQauMWNIdHQIH8SZT+4fjEUW8um/AcbqsptIpvLqVFvmMQ6RzBdG84bkA6NVUQ3VqRaM9R2E9MI7hGleTp0YR5HMJ2ajdZTOh5QZDXJfp6+ognP33XczevRoPB4P06dP54033hhw2wsuuABJkvrc9t133+w2Cxcu7HebcDisxZ+jDN5KgGypeD4ER3I4qL3yRwDseughYttbhYXTEcqPaRupI2lnMEa5d+gvj5FSVPmcWMFYMefruTKaBycfGM0YnQ+MljoJxxJ4nIMvGfJ0dOOkTmTVyVxqSFc4v3OHkZCPD04PqE5wFi1axLx587jmmmt4//33OfzwwznhhBPYvHlzv9v//ve/p7m5OXtramqiqqqKb33rWznblZWV5WzX3NyMx+NR+89RDruTiN2/u1R8kF44vVFyzDF4p00jFQ7T9oc/CAunc4gxDRkY6eTakaeCI8vjxrh6zPcqTDY4GiPmYDSBLw9/VoXPOBVJ+ZKycoMpOPnA7bATM1ALATCe2jEUusNxSvMgC0b6s7ryPHfYbZJhjg+jqk6qE5zbb7+dCy+8kIsuuohJkyaxYMECGhsbueeee/rdvry8nPr6+uxtxYoVtLe38/3vfz9nO0mScrarr69X+08pGBFXxe5S8TwUHJD/vtqrrwKgY/FiIuvXC4llqDENGZQZiCzk7RsykuqU5xe+zGMcBSffmI1kMo7Ek4NOEs/AiGTBgvpIJgdvatobRqka7QoNbYwGY6m/+casNVQlONFolJUrVzJ79uycx2fPns3SPCdn33///XzjG99g5MiROY/39PQwcuRI9t57b0466STef//9AfcRiUTo6urKuWmJuKsir27Ge8J34IGUfOMYSCbZfvMtQr6A+XpwjFQ6mW9HYCMZo2WyMLQaUuY1jm8oX4LjddoJGcSUmW8q0EgIxxK4h0j1mBkG4QmK4Hc76DFIi4lIPJFXU1Mjqb/dBk2rqfota2trI5FIUFdXl/N4XV0dLS39z2XqjebmZp5//nkuSveGyWCfffZh4cKFPPPMMzz++ON4PB4OO+ww1q1b1+9+brrpJsrLy7O3xsbGwv+oApD0VGZTVAPNoxoIdVdfDU4ngTffFDKIsyOUX660zOMwTN+QTgWkzChptaHmfWVgpMZo+RIc2fOmQUB5wJQeC4PK+YNBycWVy2EjbJC5X/kep2UGG2yaD4x0vsvHn6UHNIloz7xtKpVfhcnChQupqKjgtNNOy3l8xowZnHfeeRxwwAEcfvjh/O1vf2PChAncdddd/e5n/vz5dHZ2Zm9NTU0F/y0FwVeVYzJWdLIYOZKq9AiH1ptvIVVk8798DbtGUnDyJmUGuqLJlyx4nHYiMWOkToyaRx8MnXmMwzAauvL0hYB87jTCENlwHlVfGRipVDzfU22512mYC7p8YaTPGYzpz1KV4NTU1GC32/uoNa2trX1UnT2RSqV44IEHmDNnDi7X4AuyzWbj4IMPHlDBcbvdlJWV5dy0hM1fTV08jgREEhF2hXcpen3N//4v9upqops2seuxvxYVS0cwT2+Iga4O8o25xOWg22QEB4xjcOwM5qc6GQn59GbZDWOM8ugOxygdojFhBqUGaSOg5HM2irIQTyTz9t8YJWbIn5SVGWxWmRGhKsFxuVxMnz6dJUuW5Dy+ZMkSZs2aNehrX3vtNdavX8+FF1445PukUilWrVpFQ0NDUfGqBUdJNS6gRpKJmtI0lb2khNofzQOg7e67ie9SRpB6I5/5SJAxvxqDLHSF87tKN1KJalfYjGqI+WKWPTj5kYUSt52eqP7HtFzZk1/MRll4lXidjNK8sjuPLsYZGOVzlrMb+W1rlJiNDNVTVFdeeSX33XcfDzzwAKtXr+ZHP/oRmzdv5pJLLgHk9NH555/f53X3338/hx56KPvtt1+f566//npefPFFPv/8c1atWsWFF17IqlWrsvs0GtylNQA0IJ/U8q2k6o3y00/HPXkSye5udvz+TqHx9QeXw0bcIBPNQ9EEviHmIxkNZvRZKCE4DpuNSFx/n0U+rfgzKPU4DaHw5Vu6DMZZxJR4nYwSc6cJSVm+rRrAWDYCo0J1gnPOOeewYMECbrjhBqZOncrrr7/Oc889l62Kam5u7tMTp7Ozk8WLFw+o3nR0dHDxxRczadIkZs+ezdatW3n99dc55JBD1P5zCoKrbBgADWm+oKSSKgPJbqf+Zz8DoOPvfye8Zo2w+IyP/DxbRkK+JmOQJWkjlKh2hvKfCFzqMUY6UImyIMes/4LQFY6ZTsFRQn6NErMSUmaUCsxOBWMajFKgEI0ncdiMZzAG0KT84NJLL+XSSy/t97mFCxf2eay8vJxgMDjg/u644w7uuOMOUeGpDindzXh4LAauwhQcAN9BB1F6/PF0v/AC23/1a0Y88rDpFv6vCqLx/E2ZPreDYDSBP09fhlpQsohl1JCaErfKUQ0OORWYr5/FKApOjFHV/ry2NQxZUGDmLvc6+XxHj8oRDY18hoNmYJjPWUFq2ygm424FhF1rGJN2fdngrQCgPiZXQBVKcADqrr4KyeMhuGIFXc88o+i1RlAJ1IbDZiNqgCnoSj5qo8zQCkbj+PNMBZZ5DaKGKFh4jaLgmNKDo9hkrD+RVDLywCifc2dQYVrNAJ+zEq+T1rAIjhbwVADQEA4AxREc5157UZNWw7bf8lsSnZ15vzYST+J2KPGyGKPqRAmMsvAqgZFGTOSrCBpFDVGy8BolrdYdNqGyoMDMbZQKTCVpYqOoIV0Kjg2P024QH5yl4Hy14SkHYHi4G4DmnsIJDkD1Bd/DNW4siV27aFWQqlNy5QjygqB31YlMsPJPwxllQVACoxgclcAoakgklsCdR1UgGKeZm5IFodTjNESHXSULr1G+g0qM/iVuBz0RA5AFBaTMKOjOs8pVD1gERwukCU59uptxe6SdUDxU8O4kl4v6X/wCgI5FfyP04Yd5va47HKNEgc/DCM2vAtE4fnf+qpMRFjGlqcAyj/6fs1LIaTX9F15QojoZg5T1hON5fw9LPA56DPA5K+mR5HfbCRiClOVv2JWPIf3VarO2arAUnK8y7E4iNi9lyRR+hxcoLk0F4D/kEMpPPRVSKZqvu45UfOgTSk8k//JUMIY3RKnqZIQBdOFYEo+CsnYjzaPKF0ZJUSmBUWJOplI47PmdeksMMiNJiepklMGmSsrEZehfsKHENyRD/5gtD44FIvYSJKDBXQVAS4+yZn/9ofbHV2MrLyfy6Wra//r4kNt3h+OUKCQLekvNSnqGgDHk8e5I/p1qwRgTxZWmAo2ihiiBGWMucRvDNxRLKPXv6Q8lVVRGQVdI2QWdEWB5cCwQc5YC0OCS01XFKjgAjupqan/0IwB2/P73xLZvH3R7peV8JW4HAZ3z0j0RZWm1UgOoTj0KVScjVJ0EonFKFKQCjaCGpFIpRdVqRjEZK4HdJpmy+tEI3SuC0bjpGoT2RJSdo10OSXejcb6d5vWARXA0QixNbBocJQBsCyhv9tcfKs7+Fp4D9icZCNBy/Q2DngxlM5gCguNx0BPRlyx0KY3Z7dA9/98TiVPizv8Lb4TPuSeiTN0zghoSUdBrCMDv0p+wFwIjkAWzQmmfML3JZCCirB+WEY5pJc02tYZFcDRC0iUP+GyweQDl86gGgmSz0fCrX4HTSc/LL9P13HMDbtsdVrbw+g1QWaA0RWUEU2aPwlRgqQF8Fj0KP2cjqCFKzY22PAcvqgm9F1ALA8PrshOO6esdisTzrwoEY5zvZA+OlaL6SiOVrqRqQL7iLGRcw0DwTJhAzQ9+AMD2X/9mwGGcisvE3Ub48ihPq+lOyiJxRR4cWcHRX2ZWkgo0gpG0O6IsZiMgHFOmOpkVkiSRMFkPrRK3g26dlVRQpjqVGiBmpdW5WsIiOBpByvTCScoHrwgPTm/UXDwX94QJJNrb2f6bG/vdRjFZMELqROHCKxMcA8Ss4HP2Ou2EdO43JFfYKT1J6auIBBSm1YwA+TtoTDl/IMQTSewK1a8St4OAASa3K0GpAdQQpTCCgqOkKlBrGDOqLyEknzyPqiFdzr09sJ1EUtxVu+Ry0fCbX4PNRtezz9L98it9tlHqsygxhIJTQIpK53SP0isaSZIUmWXVgFIiKUPfoHtMqOAo9ZSB/uNHAtEE/jwnXGdghHOHUhilJF8JStzGaARpVFgERyM4fRUADItGsEt24qk4baE2oe/hnTKFqu9fAEDLddeR6OrKeV5px8lSt5NuA5AFJcqC22HXfRaVUiIJ+htJlVarGQFKDZkgf856jh8ppKRWb9JeyPGsd8yFTLg2JSkzwAWdkWERHI3g9MsKjj3SSZ2vDhCfpgIYdtlluEaOJN7ayvZbbsl5LqygrT0YoyOpkduADwSlHhxQNpxTDSjtkWQE9ERiigmO32XXNXWiVJEE/VMngUhc8eesd/+eQtKXJR6Hrhd0hRjQSw3SJ8mosAiORnCVyg3+CHdS768H1CE4No9HTlVJEp2L/0n3yy/nPK/EwOaw23Q3CnZHlI1qMAKUenCMgJ5InFIFFXYATrtN1x4cPZGEYiKpd/8epYok6G8k7S4gfVlqBNVJacw6KzjKhyFbCs5QsAiORnCnFRzCnQwvGQ6IraTqDd9BB1H1/e8D0Pzza4nv3AnonwYpBCkDG9gGQiEnV73/N4WQMr1LxQtRFvSOuRAFR28jaaCA41nvdE8h30G9yUJBMev8OReSCtQSxo3sSwZb2oNDuJMGfwOgjoKTwbB5V8hVVbt20XztLxR3fbVQOAKRuGJTpt5qSCFX6SVup64pzEAB6p6s4OinhhRGFvQ1khaaotKzmrGn4Jh1JDhh88Vs9EpGi+BohXSZOKEOGkpkgiOq2V9/sLlcDL/1t0jpBoCdixer9l5qolBSpmdDtVRKeVM5va/ECikTL3HbdT25FkbK9I3ZjMqC3G9IeepET6WsEGO03upeQWZunT04Rq9ktAiOVvBUyD/jIRo8NYC4cQ0DvuXEiQybNw+Alt/cSGVnq6rvZxR4XQ5CMXO15C/x6NtyXWkHVZA7XesZcyHKghFi9ilVnYxg2FXozyo1gOqkmJS5nbqrTkpj9htCKTOuR9IiOFrBXUYy3RhtuEMevCliovhQqLrge/gOPphUKMRJ/76XVFzZScecHUnt5iv3NEBHUqVze/w6z/2SB4QqIzg+l74x90QSplNwCkkF6u0b6gkrTxPrHXMhRNLl0LcQpJCLDC1hERytYLMRtvkAqE/Po+qOddMd7Vb1bSW7neE33wQ+P3VN62i750+KXq9nR9JYIonDrtx9q3deuhDDsN4pqkIgkzJ9DY5KVSe9O+wGo4UZo/U8NroLSF8aoopKYcw+p51AVM+qQGOrIf3BSlFZyCJkkyeJ++JhKtwVgLpG4wyce+2F/f/9BIC2u+8msHx53q/166iGBKMJfAqvwkB/U2YhKPGYr7W93gpOKlWI6qRvb6dgNIFP4SwqvQl7wX1w9CY4CmO22fTtKF7YuBR9EShAkdQSFsHREGFHWfpOx+5Kqh71CQ5A6Ihj2TLzWEil2Hr11dnS8aGgJ1kIRRP4XMqvaPQkZZF4ApdCVQH0NwsWAr3JQiHQexhrKpVSbEAvdTvp0rXyS3nHaLfDRkTHydyFVKvpjULSanqjkGabWsIiOBoimvbeEO5kr5K9ANjSs0WT9w5GE2w+9xJc48aS2NHGtp/8lFRy6BOQnlJzIBoviODoGXNhM530vUovdHSB3spCIfC5HQRNp5Tp6ynrKaDtgays6SeHGD110h+MXnLdHwrxlGkJi+BoiLhrN8HZu3RvALZ0a0Vw4njK/Ox9xx1IHg+BN99k5/33D/k6Pb0hIROmqHoKMApC2huiU8zBWGGfs94pqoK8Ti7zkTKH3UZS57YHSqeJ642eAlQnvdFdICnTsxDEMhlbyCLpSqeoQh3sXZImOBoqOD6XHff48dT//BoAdiz4PcH33h/0dX4dr9IDkcIUHL+OvU4Knenk15FIFjpaQs90T6GNK82YVtMf5qqiBAgVqP7qiULTanoa542eCrQIjoZIZnrh6KTgZK7Sy888k7KTToJEgq1XXjmoH0dPBScYTeAr4MujZ8MuuflcYWk1vUyZhcr5eio4kXiyIK+TEearWdAGSg3oAC6HpFtH8UK6L4O+5+hCVSetYBEcLZHpZhzuyBKcrT1bNem6G+xl2JUkifrrrsM1Zgzxlha2/ujKAfvj6OlnKaTiBPQdIVBIGTDom6IKRRN4C/icfU47QZ3Kao1+5dgf9OyuXRwKT0+Z7W/WkywU0vYA9FfZjVzabhEcDWH3pglOpJvh/uFISITiIXaG86toKgZ7llzbS/zsfded2Hw+gu+8Q+vvbuv3dXoaSQPRwr48eqaoAtFEQZUQup6kCvyc5WogvXL/xXgs9PGTBKMJvCarkpFR2P/Y7bQTietXSVUIfC6HbqQdClOdZMVanyq7QKSw851WsAiOhrB7M2XiXTjtTur99YA2aapgPzlp99ixNNx8EwC7Fi6k89ln+7xOz4U3VOCCUOp26miMjuMtIPevZ1ltoZ+zniiuSkY/Q2Yh6csM9FBDkslUQYsugN9lPr+T3o0gC4HfpZ+SCsrbHmgJi+BoCGdmonikCyAnTaU2BmLaZbNnUz13LgDNP7+W8Jq1Oc/r6WcJROP4TWYyLvSKRpKkgqqCRKDQz1lPFOpX0BOFqnsAHp3UkGKODb9bXzWkEPjcdl1nlRUCn87VjEaGJgTn7rvvZvTo0Xg8HqZPn84bb7wx4Lavvvpq+mSfe/vss89ytlu8eDGTJ0/G7XYzefJknnzySbX/jKLh9FfIdyLyeIZsLxwNFBz5Kr3/E9WweVfgnzWTVCjElssuI9HZmX3O57Lr1jdksJgHg55G0lCssJih8MnpxSJYYENFPWHGniHyoM3CYvbrVN5eDJHUK+ZoPFlwWbtfx1llhX7/5ZjNRcq0guoEZ9GiRcybN49rrrmG999/n8MPP5wTTjiBzZs3D/q6NWvW0NzcnL2NHz8++9yyZcs455xzmDNnDh988AFz5szh7LPP5u2331b7zykKbn/GZJxWcDQsFR/MZyHZ7Qy/7Tacw4cT27yZLfPmkYrJOV2fjl+eYvK7eqkh/aUCjY5gJF5QHxw9Ucjk5QxcDpsulTLFxOxz2wnq8D0shkj63PpcHBUytDIDvS7oikk/6vU5mwGqE5zbb7+dCy+8kIsuuohJkyaxYMECGhsbueeeewZ9XW1tLfX19dmb3b77xLBgwQKOPfZY5s+fzz777MP8+fM55phjWLBggcp/TXFwl1TKd/ZIUWmh4IRjCTyOgU+ujspK9r77j0g+H8Fly2n59W9IpVLpKyG91BDzkQVTkrJYMQqOVHAn5GIQKKC7bgZ6XfEW0xTN79LHG9ITSVBiss+5GCIptz7QPuZIPImngEpGyBwbloLTH1QlONFolJUrVzJ79uycx2fPns3SpUsHfe20adNoaGjgmGOO4ZVXXsl5btmyZX32edxxxw24z0gkQldXV85ND3izBKcbksndBEcDBSeVYkgzmGeffdjrd7eCJNGxaBHtjzyielyDIRAprA+Onig0raYnionZ77brtPAWbjLWq3+PKWMusAkkZDw4On3OJou5u8ARLyB/B4M6HBuyDcC4BmNQmeC0tbWRSCSoq6vLebyuro6WlpZ+X9PQ0MCf//xnFi9ezD//+U8mTpzIMcccw+uvv57dpqWlRdE+b7rpJsrLy7O3xsbGIv+ywmDLVFGRgmhPNkW1PbCdaCKqS0x7ovToo6m9+moAtt98Cz2vvaZbLMEC+7PoiUJLrgEcNhtRPYykRahOel3xFreI6UPKgkWYjOWY9fmcC1ed7Lp0ui5OKdPncy5e3dMh5mhxVYFaQBOT8Z5lhqnUwKWHEydOZO7cuRx44IHMnDmTu+++m29+85v87ne/K3if8+fPp7OzM3tramoq4q8pAg4PcdIHcaSLKk8VXoeXFCm29WzTJ6Z+UPX9Cyg/60xIJtl65f+jplWfz2t3isw8CMeSg6YCB4PPbSekw4mqmFSgXn2SiloQdFJDZJNxgceGy6HLVXoxDRX1GmxajFKm1+dcDGHX0+tk9EpGVQlOTU0Ndru9j7LS2traR4EZDDNmzGDdunXZ3+vr6xXt0+12U1ZWlnPTBZJEyOaX70e6kSRJ0zRVvpAkiYZf/ALfIYeQDAQ4/e+3Edu+Xe+wFEEvNaSYvhB6+SyKSQXqVXVSzBRjubpHL2+IuZSFomM22+fs1kd1Kso3pNPxbIZu4qoSHJfLxfTp01myZEnO40uWLGHWrFl57+f999+noaEh+/vMmTP77POll15StE+9ELL55Dt7VlJpNJMqX0guF3vf+Xtco0ZR1rWLpovmktDJu1QI9FJDioFeV2KhWOGpQL2GVxaVOnHrp4aYTXUq5nOWuwKb63PWK+aecOGVX16nnZBOBnSjKziqR3fllVcyZ84cDjroIGbOnMmf//xnNm/ezCWXXALI6aOtW7fy8MMPA3KF1KhRo9h3332JRqM8+uijLF68mMWLF2f3ecUVV3DEEUdwyy23cOqpp/L000/zn//8hzfffFPtP6do7FZwciupmrp1SpsNAntFBY333ceHp54J69ax5f9+SON9f8Hmdusd2pDIqCHlvsJOGoWimF42elWdFJMK1CtFFYrGC5pTBlDituvSvLIo1Ukn31AxV+l6HRvd4TiNlb6CXquX16kY755enYTl9hJfcQ/OOeecw4IFC7jhhhuYOnUqr7/+Os899xwjR44EoLm5OacnTjQa5aqrrmL//ffn8MMP58033+TZZ5/ljDPOyG4za9YsnnjiCR588EH2339/Fi5cyKJFizj00EPV/nOKxp4EZ0TpCAA2dw/eF6gYxBOFN75y7b0XL3xvPlJJCcF332Xbj39CKmF8ZcSMvSF8Ln0WsWLg17G1fcGpQJ3UkGJ6JMneEHOZufXr3VO4siCrITrFbLJeVIGopeAAcOmll3LppZf2+9zChQtzfv/xj3/Mj3/84yH3edZZZ3HWWWeJCE9TROxpgpNOUY0sk4neps5Nqr1ncX1OIDJiLN6bf0fwR5fR/eKLbL+xhrqfX1PwjBotYMbunnLqRA8Fp/DXlrgdbOkIiQsmTxQTs0+vqpNiqtV064NTxKgGnWIOFqGG6HVOC0bj+NyFqU56wQxNTa1ZVBoj5iiV76QVnNHlowHZgxNPqnMyCBbZT8bnthOdciB73XIzAO2PPUbbH+8WFV6/SBQx5A/MqYaYMWa91JBiUKJbzEUY0HXyOgUjiYK7XHucNsIx7Ylk8VPbtW9cWUwLAb0gj3gxdswWwdEYcWeJfCc9j6rWV4vH7iGeiqtWKh4swq8AUJK+4i078UTqrrkGgLY//IGd9z8gKsQ+CBWpOumhhiSSxU3W9btMOJxQ10nGhUEvslAM5FSg9p9zPJnE5ShsmdBLDTHj8NiACdSQPREoQt3TChbB0RhJV1rBSaeobJKNEWWyD2dT1yZV3jMYLVbB2V11UjXnPIbNmwdA6623suuvfxURYh8EI4XLzKCPGlKsZOsz4cLrc+nTRbUYyOZXc6UC3Q4bER3UEDPCrN3Ei+3aXsw8q0JQ7LqiBSyCozFS7twUFcCoslGAej6cYqdF79mDo+aSH1B98cUAbL/hV3Q8+VSxIfaB3MW48C+PHh6cYiVbPRScZJGpQL/bQVDjhVdu6ln46/UqBS4GRva7GQ3ReBKX3VxLm+zPKvwc7XbYiWjc96vYdUULmOso+DLAnZ4onk5RwW6j8RddX6jylsVKtv11JB32o3lUzpkDQPM119D1/PNFxbgniimbBH2qqIomkjqUAhebCvTqoOCEY0ncRaRcXQ4bsYT2PguLo2iH4gihpIMaEi9KddIjVWyZjC30gc2TSVF1Zh8bVT4KUI/ghIo03fXXkVSSJOp+Np+Kb50lj3S46mq6nnuu2FCzKFZm1kPBKTYnrUcpcLG5f59T+74hxXrKZGi7gGm9YFooHG6nTXM1JJYoTnXSw+xvhtJ2i+BoDJs3o+DsTlFlS8VV8uAIWXj7URYkSaL+uusoP+00SCTYetXVdD7zTBGR7kagyKoCvw4KTihWLJHUvqy2WCLpsNtIJrXP/Ru9/8aeKL6yx7wwG7mTL+i0/R6mUsWpTnooOKFYcaqTFrAIjsZw+NIEJ9zXg7M9uJ1gLCj8PeWFt8jUyQDKgmS303Djb7JKzraf/JSOxf8s+L0yCBUt2WpPFuSFt9h0j9aqk/GvwvZE0IQmUjNUnOwJEcTE47QTjukxE65w+ExYzahHw81ILIm7wAo7rWDs6L6EyBKcXh6ccnc5le5KQJ2OxsV09oShTZmSzUb99ddT8Z1vQypF8zXX0L7obwW/HxS/8Pp1SPcEI/GCZzqB7A2JJ7VdDMxwFbYnxKSotDXEiOn6KmmqlkXixXmdQL9mf8VADy9csf4snw4XR2B887tFcDSG2y8Tmd4pKlC3o3EoWtzCm88XXrLZqP/FL7LG45Zf/pJdjzxa8HsW233Zq0uZuPEbX+0JucGYuQiOmDJgbdMmxQyAzMDrshOOa7eIBaOJoomk1q0PRKhOsp/FfAqO1nO/DM5tAIvgaA53SYV8JxGFWDj7+JiKMQBs6Nwg/D2LvXrM1/yaMR5Xff/7AGz/zW/YcdcfCjrpFDvIzeWwEde4UkZut24ushAoolNtBlqf6ESoIQ6bjaiGRlIRKSq/y67pIhYQMExRa7O/rDoVt6z5TdhGQI+YzWCtsgiOxvCVlO/+pVeaamz5WAA2dIgnOGL64OT35ZEkidofX03N//0fAG1//CMtN9ygeECnWdWQ4lMn2iIUK56UaX2iE1Ge6nNrO1SxWEUStK+yC8WKb+Tm76fFhJoQcd7waWwyFqE6+XSagm50WARHY/g8LsK29FC1XmmqcRXjAFjfsV74exa7IDjsNhIKLnYlSWLYZT+k7hfXgiTR8fgTbL3y/5GMRvPehxnVEDNW98gKTnGfsyRp6w0JRRNFpVxBe29Isa0aAEo09oYEIsV7nfwaL7xBAWMatE5RReJJ3I7ij2et+1FZKSoLfeBzOQhKmYniu3vhjKuUCc7mrs1EE/kTgXwgRg1RvoBVnXsue91+GziddL/4Ik0X/4BETyCv15qhS+aeKLZZlx4IFdkxGmRvSEjDbsairtK1rJQRke6RG25qqOAIaMXv03jhFVGOLx8bWqtOxap72hLJVCplpags9IXdJhHKKji7U1TDvMModZWSSCXY2LlR6HsmkynsRQyBLAZlJ5zAiHv/hM3nI7h8OV/MmUOspWXI15k2RSVADUloqIYU2zEalKUwRUCEuud1aZuiKrZjNOjgwRFwPGsdswjTvNaDTUUY0P1ubYlkJJ7EY4J0vEVwdEDIllZweqWoJElifMV4QJ00lZ7wz5rFiIcewl5dTWT1ajadfQ6hTz4Z9DUifBZaS6iilAUt1ZCQgEVMa7IggkhqnaISc2xo68ER8R30a6w6BSPFq6hap3tE9HXSPhVoDoXdIjg6IEtwwrml4mMr1DMa6w3vlP0YtWgRrnFjibe28sV5c+j+738H3D6RTOEscmCe1mqIEPOrDifXYhderStlZDO3gLSayRYErZu5CTk2NPYNifDBmdI3pHEVlYiUqxawCI4OCPeTooLdBGddxzqtQ9IErr33YtTjj+M/7DBSoRBbfngZOx94ULVW7n6Nc+kiSNmek9vVRrGzqCBdkRTT1rBbbIpKaw9OsZ25IdNR3FzpHq1VJyHHs0vbuU4iiKTXqe3xHBTgz9ICFsHRAcF+UlRANkVlRAXHJknElZRSDQB7aSmN9/6Jim+fA6kUrb/9Lc3XXquowipfaG3KFAGfxkPzQiJSJ86BR3moAWGLmJZXvEXOVgPtRwiISvdo6cERcTybMd1js2k7AV2E6qQFLIKjA3anqDpzHs8oOFu6txCKh7QOa1D43Q6CgrwhksNB/S9/Sd38n4Ik0fmPxXmbj5VAj6F5xcKvsbIQSyRxFTlPxqdxr5NwLImnyLJan9YmY1E+Cy2VhVjx6R6fxkNvRRijvU6t05dxU6ghvWGW4bEWwdEBUVuJfGePFFW1t5oqTxUpUsJUnGQyJWReiOhZJ5IkUfW979H45z9jKy8n/MGHbDzzLILvvivsPcw4NM+nsc9CxEWf9pOMU9iKrArUOmYhhl09FJwiK2VKNK5ICgkpTtB4TlnEfA1CzTI81iI4OiDhyhCcrj7PTaycCMDqXauFvFexk8QzKFFp4S05/GuM/sffce+zD4mdO/ni+//DrocfEbLyan3FK4Is+HUamlcM5Iokc8U81ABZ0RDiz9J43pAIw67bYSOiYVVgwJTtJUQ1NdWOmInocq0FLIKjA1KuUvlOuC/BmVQ9CYDVO8UQnICgXKmaZkFXYyOjHv8rZSedBPE422+8kROfuYdET09R+zWlgqOxN0TExapckWSuVKDWCo4opcxslV+SJGnaEK7YGXZ6ICjAn6U1zKI6WQRHB6Q8ZfKdPVJUIJ7giJm8rH65p83rZfitv5V9OXY7kz5dzsYzzxyyX85g0LJENZVKCSELfrdd85brxULrMnER0D6tVjzcDhthDdWQSDyBu0h/Fmjbj0pcfxZtm22aj5SZY5SORXB0gORJD9zsJ0U1uWoyAGvb1xJLxop+r0BEzNWBFpJ+xpdT8ef76SmvIfbFZr749nfY9fAjBVUIaFmiKk8xFqOUmS7d49a2OaEIeDVuISBikdfaGyLqPTVVcITNg9Mw3SOo5NrlkIjEtfkemkV1sgiODrB5Bk5R7V26NyXOEqLJqJCRDaGYmPlIsp9Fmy9PbJ8pLPnRrZQccwypWIztN97IlssuI9HRoWg/WnarFTGYENIKjoaqkwhoPX1ZBHwuh6bpHgvaIBwTozppquBEiu83BOB1andMm0V1sgiODrD7KuQ7/aSobJKNfar2AcSkqUR9ebRsfhWMxXFUVLD3H+6i7pprkJxOev7zXz4/5VR63nwr7/3IJaraXdGI+MJrme6JxIsvEQdtvU4JQVWBdptE0gzTAi0ohojjw2GzEY0X3/crH4i6CNUy7RqMWCZjCwPA4UunqKLdkOx7QGYJjoBKKlFDK7X88gQisswsSRJVc85j5BOP4xo1inhrK00XXUTz9deTDAaH3I+WTcZEdfbUcpKxiEnioHHMsUTRpctawyyTly3shpaG7mg8iavICjvQ9nsoosu1FrAIjg5west3/9KPijO5WvbhiFBwRJnBtF94d8fs3XdfRj/5TyrPOw+Ajsef4PPTTyf4/vuD7kfLk1QwKipFpZ2CIzdyKz5mp91GPKHNCi6in4zWkP1ZYk61OthwiobDLhET0AVdS3hddoIajh8RoTp5tVRwBIwe0QIWwdEBXp+fhOSUf+mvkqoqXUm1azWJfhQeJcg7dRJo69NZuTe0TEMEovE+C6/N66X+59cw4oH7cdTXywbk755H6223k4xE+t2Plt4QUUZBLStlRLTi1xoiWvFrDVFKmVlhxnYNWk9BFwEtVXZRqpPaMH6EX0J4XXYijoGb/Y0uH43P4SMUD7G+Y31R7yVf8Q5yck3E4KlL4dax8Nsx8MpN/ZY9aPnlCQ3SBtw/axZjnnma8lNPgWSSnX/5CxtPPY3AO+/02dbnEjdeYiiIaBEP2lbKmKUSojcCEVFlwNohGBMXsyRJJJLqq2XReBKHTczyoPXkdhHQelyDCHg1NM5Lkj5VfUqhCcG5++67GT16NB6Ph+nTp/PGG28MuO0///lPjj32WIYNG0ZZWRkzZ87kxRdfzNlm4cKFSJLU5xYOh9X+U4TA73IQyc6j6ktw7DY7+w/bH4BVrauKeq8hFZzXfgurHpPvJ+Pw2s3w/iN9Y9Zw3tBQzQntZWUMv+UW9rrrTuzDaohu2sTm879H87W/ING1+/P0OLXroioydaLVeUNkJYRWMYsyZGoJEeMDMtAqVSxiYnsGPqe2JfkiYMY+ST4NJ4qbxVOmOsFZtGgR8+bN45prruH999/n8MMP54QTTmDz5s39bv/6669z7LHH8txzz7Fy5UqOOuooTj75ZN7fw29RVlZGc3Nzzs3j8aj95wiBz2XfPXCznxQVwLTaaQCs2rGqqPca1GS8ayO8tUC+f+b9cPS18v0Xfw49O/rErFV/lnybE5Ydeyxjn32WirPPBqDj739nwze/SdcLL6Yb72mrhohKnWh18jBjukdcIzcAiaQGakhQULNN0M5XJpL8akUWovFk0eMwMtDScygKWraYMAtUJzi33347F154IRdddBGTJk1iwYIFNDY2cs899/S7/YIFC/jxj3/MwQcfzPjx47nxxhsZP348//rXv3K2kySJ+vr6nJtZ4HPZCdp88i/9pKgApg6bCohQcAY5Ub17HySiMPrrsN+ZcNg8qJ8CkU549y85m8ozZbQxCippTmgvK6PhhusZ+cjDuEaNIrGjja3z5tH0gx8Q2Vh8H6F8IXbh1Qai0mpaQmRazeO0EdagMZrImL1ObRpBCo3Z5dCkEWRI4PGsVbpHVC8q0O5zBvOY3VUlONFolJUrVzJ79uycx2fPns3SpUvz2kcymaS7u5uqqqqcx3t6ehg5ciR77703J510Uh+FpzcikQhdXV05Nz3hczkIkCY4Axh7pwybgoTElp4ttIXaCn6v4EBkIR6BDx6X78+4VD5i7Q742pXyY+/eB7HdKT9N1ZCY8qtH38EHM/rpp6j+30vA6STw+ht8fsqpHP7KIpKBgEqR7obINIRWCAmuhNBGDREXs1bTuUXGrJWyID5mjVQnUWk1jWKOxJO4HeaKGawUFQBtbW0kEgnq6upyHq+rq6OlpSWvfdx2220EAgHOTqchAPbZZx8WLlzIM888w+OPP47H4+Gwww5j3bp1/e7jpptuory8PHtrbGws/I8SAI/TRkDKKDj9p6hKXaWMqxwHwAetHxT8XgPK4xtehuBOKG2Acd/Y/fikU6BsL/m5dS/2fZ0GKLSJlM3tpvaKKxjzzNP4jzgcYjEOWf4sG078Jp3/flbo1dKeMOcUY5FqiF0zNUTcVbo2k9tFx6yFsiBWwdFmGKvINLFcJm6yY0MjD46a51HR0MRkvOfVf77+iMcff5zrrruORYsWUVtbm318xowZnHfeeRxwwAEcfvjh/O1vf2PChAncdddd/e5n/vz5dHZ2Zm9NTU3F/UFFQpKkXh6cgdWkbJqqCB9OLDFAt9q1afKyz0mycpOB3QFTzpLvf/T3gt+3GASjxU2qdY8eTeO997L33XfTUVFLfPt2tl11FV+cN4fQqlXiAu0FkfK4Vn1DRHtDtDi5ihoeC+mYNeh1InIR82v0OZtRwRFp9Pc5tSFlgUhc0OysjD9L/Zgj8SQek6jVqhKcmpoa7HZ7H7WmtbW1j6qzJxYtWsSFF17I3/72N77xjW8Muq3NZuPggw8eUMFxu92UlZXl3PRGKKPg9FNFlcHU2qkAvLf9PbFvnkrBuiXy/fGz+z4/5Vvyz7UvDqgwqQkRzQklSaL06KNYOPdGhs27AsnjIbRyJZu+/R22XDGP6KZNYoJNIxARd3LVMnUiotEfaDfYVKSyoFWvk8HaHiiFVj1l5KGV4giOVr4hccZobRpuhmIiCbs2x4aouXtaQFWC43K5mD59OkuWLMl5fMmSJcyaNWvA1z3++ONccMEF/PWvf+Wb3/zmkO+TSqVYtWoVDQ0NRcesFYaqogI4uO5gAD7Z+QndUYFEY8ca6NoCDg+M+lrf5+v2g8pRsgF54+vi3jdPiGwiJbk8lF10MWNffIHys84Em43uF19kw0kn03LDr4jv3CnkfeReJwLlcU2uHhP4BDWg87u1UUNEVvd4ndqlqES1tfe67IS0UJ0i4poTyoNNtfENifwOamHYDUQGb4mhBJqmL00whwo0SFFdeeWV3HfffTzwwAOsXr2aH/3oR2zevJlLLrkEkNNH559/fnb7xx9/nPPPP5/bbruNGTNm0NLSQktLC52du824119/PS+++CKff/45q1at4sILL2TVqlXZfZoB+aSoGkoaGFk2kkQqwYqWFeLefPMy+efeB4PL1/d5SYJxx8r31y3p+7wGEGVqzpTVOuvqGP7rXzP6qScp+frXIR6n/a9/ZcOxs9lx1x9y+ucUgkgsgUdQO34t0z3iTJkaXfEKT6tZht3+IFbd0ypmkQqOVseGuAsjWSkzV8pVbahOcM455xwWLFjADTfcwNSpU3n99dd57rnnGDlyJADNzc05PXHuvfde4vE4//d//0dDQ0P2dsUVV2S36ejo4OKLL2bSpEnMnj2brVu38vrrr3PIIYeo/ecIQ2iQRn+9MaNhBgDLm5eLe/Omt+WfjYcOvM34NMFZ/5+sZd5hM99MGd8eyoJnwgQa7/0TIx56CM9++5EMBmn74x9Z/41j2fHHP5LoLlwpE0fKNEr3COywq1V/FqELglubslrR5ldt+uCY8NiIiPuctUsTi/ucnXabJl2uRaqoakMTnenSSy/l0ksv7fe5hQsX5vz+6quvDrm/O+64gzvuuENAZPpht4Iz8PwnkAnOojWLxBKczel9jZgx8DajDge7Gzqb5JRW7T4yWYgmKPeaZ8LHQMqC/9BDGPW3RXS/9BJtf/wjkXXrabvrD+x66GGqLvgeVXPmYC8t1SFibbvVegSWqGpx9SjSzO1z2mnt7n+OmUiI9oZopu4J7IOjlepUXy6m2at26Z64kBl2WkIkkVQb5lmpvmTIzqIaQsE5uP5gbJKNzzs/pyWQX2l9Bv2W8wXaoD3dAG/vgwd+scsHow6T73/+CmDO7p6DxSzZbJQdfzyjn36ave64Hde4sSS7umi78y5Z0bnzLuK7dmkcsawsaDNDK4XNJlB10qSCI4G7v6rAAqAdkTRfikpoJ2ONypcDAo3RLoeNWEKbLteiPDhaQWT6Um1YBEcvuMvln4N4cADK3eXsW70vAG83v63oLSLxJJ493e4tH8o/q8aCt2LwHYw6XP75xVuAdrKtSOSzIEg2G2UnnMCYp59mr9tvwzV2LMnOTtruvpv1Rx1Nyw03ENWwtYBPI/OrSGjZZExYKtCtTbfaYtse9IZXo7lOYhUcbYzRZpzaHoiYb7ZaUGBVoNqwCI5e8KRL1cNdQ7aFzPhw3tz6pqK36Ld0ueUj+Wf9fkPvYGRawfliKaRSmjRGE91ESomyINntlJ14ImOeeZq9FtyBZ999SUUitP/1cTYcdzxbfvQjQh9/IjS+/mBOpUwb35BIaFW+nEylcAidkWQuD47bYSMaV9+7FzCRspCByLYHWmGoYchGgkVwdILNm1ZwUgmIDj5K4OuNXwfgja1vEE1E836PfnP/LR/LP+unDL2D4dPkUvLgTmhbm1Zw1F14I/EkbkHVSFDYgiDZ7ZQdfzyj/vF3RixciP/wwyGZpPv5F9h01ll8cf736HrpJVJxdT4Ln0b9WUTC7zbf9GWvRs3cRMKn0YwkWQ0RNWlemzEvIivstILIfkNawUxDei2CoxMc7hJSUvrAHiJNNaVmCsO8wwjEArzT8k7e7xGM9jPyIKvg7J9HkK7dPp0v3kr3Z1H35CpaZi5GWZAkCf+MQxnxlz8z+umnKDvlZHA4CL7zDlsvv4L13ziWtj/dS6h1B3ZBXhY5ZvORBTOqTlo1+hMJj9NGRIORGCL9WVohYEI1RG4hYK6YAxGrTNzCEPB7HCSc+RmNbZKNoxqPAuDlzS/n/R7B6B4dJ2NhaFsr36/LI0UFOWkqLa7SRcvMohZez8SJ7PXb3zJuyUtU/+AH2Csribe0sGPBAjYdcwwn/vvPhD74QEiKzYxkQavqHpEwI5HUcuit2SBSddIKcrNNcTE77eqnAwsZhqwXLIKjE7wuBzFnugx5CAUH4JgRxwDwStMrJFP5HcB9FJwdq+WUmLcKyobnF2imlLzpHbxOh+qlwKJlZr9brM/C2dBA7Y/mMe7VVxh+y8149t8fYjEmfPAGm875NhtPPY1dDz1EvL294PfQgiwkkvnNg8sXWpWJi4TboZUaYkELpFKiVSf1q6hCMXET0EGb8nYzpQItgqMT/C47UUea4Ayh4IBcLl7qLKUt1MaHOz7M6z36eHCy/pv95G7F+WCvAwEJOr6gItWh+pdHtMzsdarjWbC53ZSfeiqj/7YIx70L+WL615FcLiJr17L9pptZd8TX2XLFPHreeINUQtn7azFQMSjYKKiFyTiWSApNBUqSNJS/38JXGHYNGptG4ylhY2lAmwGyIhtXqg2L4OgEn8tOxJ7pZtwx5PZOu5MjGo8A4NnPn83rPfpM121bI/+snZx/oJ5yqJkAQE3nR6pfpYucCAwZBUdlY/S4ffj0gisZ/8br1P3iWjyTJ0MsRveLL9I092LWH/MNWu9YQGT9+rz2p8UsKtGlnnLfEJWlcROdWDMQXRVoQTtolXYVq6SqH7PIZptqwyI4OsHnchC2pz04eaSoAE4ZcwoAz218Lq9qqj4LQlt6ga0epyhW9j4IgIpdH6qu4IjukqmFZJtp1mUvL6fq3HMZ/c/FjH7yn1Sedx628nLiLS3svPdePj/pZD4/9TTa/vIXYlu3Drg/LU5SZmwwpoY0rralJRJP4hbULdrMsEkScZONedGqm7FIaDFANhwT12xTbZgjyi8hfC47IVt+JuMMDm04lDpfHV3RLl5tenXI7ftMqt25Tv5ZM15ZsHsdCIC/7QPVByqKnI8EcnNCtXud9Nf11TNpEvU/v4bxr7/GXrffRslRR4HTSWTNGnbcdjvrj/kGm879Lrv++lfibW05r7XbJJIqz5Tpt0eSwSE6rQZDtqAqGmoMJlQ7ZtH+LMikTsxFFvymNPtrE7NZzO4WwdEJPpeDgJSe5J2ngmO32TllrKziPL3h6SG3z7niTcSgfZN8v1opwZEVHPf2VYQi+ffhKQRBwQuv3OtEC8m2f9XJ5nZTduKJNN5zNxPeeJ36G67Hd8ghIEmE3nuP7Tf8inWHH8Gm757HzgcXEt2yBVBfWQjFxHcjVTtmM3VQzUB0yhXkxUXNoYpqEEmvBv17RB9/Ws3QEgkzEkk1YREcneBz2XcTnDwVHCBLcN7a+hatwdZBt5Vns6QXhF0bIRkHpz//CqoM6vYFhwdbpBN/4Atlr1WIYO+YBUCuqjCGGmKvqKDy7LMZ+fBDjHv1FWp/8hM8U6ZAKkVo5Upab7mFDd84ls9PO52ZbzxJeM0a1TwcajQYM6MaYkZSpvZVunoxq7fwqqU6aTFtXiS0IJJmgkVwdILPbaebDMEZfKJ4b4wqH8WBtQeSSCV44rMnBt02FI3v7guRSU9Vj1V+Vrc7oWEqAMN71B1VEBQ4mFArhGL9NFQcAs66Oqq/fwGj//43xr38X+p+9jNZ2bHZiHz2GbPefJKNp57GhmNn03LDDXS/8grJYFBYzMFI3HQ9Q9RQQ2ySupUyapAyv1tdVVINf5b6pEy86qRNnyTRo2nM19tJTVgERyf4XA66UspSVBmcP/l8ABatWUQwNvCil6PgtBXov8kgbTQeFf6ssNfnCTPOZil2EXMOH07V+XMY+fBDjH/rTRp+8xs2jJuG5HIR27KF9r8+zpb/vZS1M2ay+cKL2PXQQ0Q+31iUuiNaKctAzaohNVrEq93NWA1S5nWqG7Ma/iy1DbtqqE5qj/KIJ5LYBKtO8uesrgfHJPYbAMy1knyJ4HXa6UgqT1EBHNl4JI2ljTR1N/H0hqf5zj7f6Xe7nHK+rMF4QmEB7zUdgNGR1YW9Pk+occWrNkSqIY7KSirOPIOnehr581mTCbz9Nj2vv07g9TeIbdtG4K23CLz1Ftx0M87GRvwzZ+KfcSi+Qw7BUVOTf8zROFUlLiExZ+By2Igm1KsaUuPYyCy85V6n0P1moAYpU/sqXQ1/ls+pbszqqE4qk1/BBRWg/udsNlgERyfYbRJBhSbj3a+1c96k87jpnZt45NNH+NaEb+Gw9f1X5pTz7dwg/1RaIp5BWsFpjG6QRz44PYXtZwioccWrNtRRQyTw+ig9+mhKjz6aVCpF9PPP6Xn9DQJvvE7w3RXEmproaGqi429/A8A1biz+Q2fgO/QQfAcfjKOycvCYRV/xpsmCegRHPCmTFwR1/SyqkDIVm7kFIuKncqtNFtRQnXwuO+1B9YoqQqp4ndT9nNXwOqkJi+DoiJAt0+hPGcEBOG3cafzpgz/R1N3EU+uf4qwJZ/W7XfZgzFRQVY0uIFKgvBH8w3AEdsD2j7OERzQCJmzmFlBtEdtNnCRJwj12LO6xY6n+/gUkAwECb79D8O23Cbz9NpHPPiO6fgPR9Rtof+wxkCTcEyfiO/hgfNOm4p02DWdDQ3b/qnhD0ifXCp/Q3WYRjIqd2wPqT24PRuNU+ASTMrUVHBVmOvnc6pIyNVQnLdJqwkmZW11jtNkuQM21knzJkCU4kfxNxhn4nD4u3v9ibnn3Fu5edTcnjj4Rn3OAlSUWgu5m+X7FqMKClSQ5TbX2Bdi6UjWCE4kl8DjFWsMyZbUi2/z3RkiFL31Gah5IGbL5/ZQefRSlR8tDWOPt7QTfeVcmPO+8TXT9BiKffUbks89of+QRABz19fgOnIZ36jRcwXI8+9WKjVmD6h7RSpnaZCEYTTC8wlzm14BKn3NzZ0zoPntDFbKg8nw1NciC2t9BM3UxBovg6IocBSeZBJuyhf3siWfz6OpH2dqzlUdXP8rF+1/c/4YdTfJPVwn4qgoPuDfBUQmplPgmUpmGXaUedXwWaowQ8CmslHFUVlJ23GzKjpsNQHzHDgLvvEPovfcJvf8+4TVriLe00PXc83Q99zxHA7F7PHwxZT88U6bg2XdfvPvti3PECCSFx2EGXk28IWZbxNRQ99QtBQ5F41QLTgWqNRMug5AK1Zc+lRUcVfxZKhvQg9EEXqd5aIN5Iv0SIpjpZEwKoj3gKVP0epfdxQ+n/ZD5b8znvo/u44TRJ9BY2th3w45075qKkcVZ4IfLHY1TW1dinizs7oZdahGcZEq8OlTswusYNozyb36T8m9+E4BkIEDoo48JrXqf4Pvvs+vtlbjDAYIrVhBcsSL7OltJCZ7Jk/Hstx+efSfj3Td/0qO6sqBGdY/KjSDVWcTsbO8OC91nb6iSCnTZVe2CHoioQyTVJgtmrFazFBwLeSEmucDmhGRMNhorJDgAJ44+kX+u+yfvtrzL9cuu5y/H/qWvApLx31SOLC7g9MgGaed6CHWAt6K4/RWDZBK+eBNaPgLJDsOnQeMh/RI4LaZzi4Zos6DN78c/41D8Mw4F4DcPv8PtMyqJffQh4U8+IfTJJ0RWf0ayp4fgO+8QfOed3a8tKcE9YQLuiRPwTJgg358wAXtpaZ+YVScLgq8e1S8TVyd1ov4ipkIqUEUPTjCWoNIv9gJG7fNGUIXZamoPvQ3FzNWnzCI4OkKy2Uh5ypCCO+U0VbnyfdgkG9fNvI4znzmTt5vf5u9r/87ZE8/O3Sij4FSOKi5gXxU7XXtRHd0K296HsUcVt79C8cUy+Nfl0LY29/HayXDSHTBiRs7D8tWjNVOmNxIpCf+E8TBhPJx5JgCpWIzIhg2EP/6Y0CefEP7kUyKfyaQn9N57hN57L2cfjoYG3BPG45kwEfeECVTGSwnaGwGx3p4M1FgQvC47O3siQvfZG2osCGZMBaqtLMg+OBVMxqoao81l2AVLwbGgAD6XnZQrTXAUlor3xoiyEVw27TJuXXErN79zM5OrJzOhYjJOezqt0N4rRVUkmksmU71rq+zD0YPgrHocnr4UUknwlMOYIyGZgM9fhdZP4YHj4ahr4IirsmqOz+0wXct1PTqSSk4nnn32wbPPPlScJVflZUhPZO1aImvXEl67lsjadcRbWog3NxNvbibw2usAjEnvZ93wBtyjx+AaPRrX6FG4x8j3HXV1Rfmr4skkLsFTjNXuGyKnTsymOqlhfjWfUuay24jG1Zz5laChXJ20uVqwCI6FvOFz2Um4SuV20grGNfSH8yafx4rtK3il6RXmvTKPPx/zCL5MLwtRKSqgrWxf2LUEtr439MaisW4JPPW/QAqmfAu+eZtMcgBC7fDiz2HVo/DKryGwA064BSTJpAqOMWbK9CY9vZHo7CSybl2a8MikJ7BuPbbuLuLbmolva5YbEvbel8+He9QoXKNG4ty7EWfj3rgaG+X79XVIDu1PR2ovvKGY+JJrtTvsmjGtpkZ1j9r9XkImM+xCZpSOeWI2T6RfQvhcDuKuMpxQUC+c3rBJNm782o1859nvsKlrE/Neu5R9HD+Wn+wQp+B0VO4Pm4CtKzIlT0XvM4NoPInDPsD+dn0Oiy8EUjD1PDjlrtyqM28lnPZHaDgAnv8xvHOv/NhR8w1DFpTA57LT0qWekbRY2MvL8R10EL6DdrcLWLFpF6s+3sS5wyH6+edENm4k+vlGohs3Em1qIhUMEv70U8Kfftp3hw4HzoYGXI1755KfhgYc9Q04huXfpVkJvCqnAlMqGdBV74MjmCy4HTYicXONalAbZlNDQI65rtQ8qpO5jogvGXwuOzFHCV4oqBfOnihxlfCHY/7ABS9cwMau9XQ6bqG9YwGVGXWoYkTR7xGonkxKsiP1bIeubVC+V9H7zCA0UHfdVAqeuVxWufY+GE66feCS+kMvBrsD/v0jeO1mKBuOzzWbgEoLQjKZAhVqysxIyrwuO50uP74DJ+I78MCc51LRKNEtW2Sys7mJWFMT0S1NxJq2ENuyhVQsRqxJfhyW9d25w8FF/go2vTQSZ309zoZ6HPUN6Z/1OBsasFdWKr7q9rvVTgWqc2wEVUy5RuNJXHbxvajUhBqVX2ojYLKmeWD1wbGgAD6Xg6gjXSpepIKTwciykdw3+z7mPPc9dsU28N2XLuSPTgejnRXgLhny9UPB7S2lu2wCZZ2rYdt7QglOcCBD5gdPwKY3wOGFM+8Dh3vwHR30PzL5ev1WePb/UfeNx/lEKnDI6BAIx8U3JgT1y2rVwGDpHsnlwj1mDO4xY/o8l0omibe2yqSnaQuxLemfTU3EmpuJ79gB8TjlnW2EVrYRGuD9JbcbR00NjmHDcAyrwZ65n/0pP+6orkZyylehPpX7s4ieFg3gcdqIqOwpM1M7fjBfdQ+oo5SpDTWM/mrCIjg6wueyE7anSUcRJuM9MbZiLP9vyu+5/cMf0xRq5dzh9cxPlnNyqvg5Ij6XnZ3l+8oEZ+tKmHSyoKhlQ2afDqrRACz5hXz/yJ/kXwl21DWw4zNY/S/2e+tyPpr6CJDnaxVArennapbVqjXxu9DUiWSzyapMfT2+gw/u83wqHife2sqvHnyF/ze1gnhLC7HmFmItzcSbW4i1tJDYuZNUJEJs61ZiW7cO+Z72ykocw4Zhq6rmiK4ULWvHYq+qlB+vrMReWYW9shJ7ZQWOysosITICzEY+dkO9uKPx5O65e0KhrslYjbE0dptELJHcXWQiEOrM3VMP5on0Swify07YlpkoXnyKqjcqnXtz/sjbWbr1Kt4Lt3CNrZslL1/OVQdfxciywr04PpedltJ9Gc0/hHc07ncGztv3QqBVJjYz/i//nUkSnPpH2P4p7l0bOPKTa+CY5xV3ix4KwYg6VzQ+t3rKQiSexK2CnC8bScWTMsnhwNHQwLa9J1D+zb4ECCAZjRLfvp34jjbibTuI79hBvK2N+I4dJHa0Ze/Hd+6ERIJEezuJ9nYAJgLtny4fNAZbaWkvwlOFvaICW1kp9rJy7GWl2MrKsKdvttIy7OVlcp8glcikSrsFhNrqNIMaHdDVhlrpnoySWu4VT3BC0bhw07yasAiOjvC5HLu7GQtKUWUQiCSo9Vdzv38KD2z7jHuqKnl1y6u8ue1NTh17Kufvez5jyvumC/KJ+QvfJPmXre8XNGJiwJije0wxDnfCWwvk+0f+DBwK28d7yuGcR0j+5WhGdSyHN26Dr18tJNYMgjGFk5dT6a7VwZ1gc8jjM/ppmOhzqpeiCkTi+FU6sarldYomBi8Rt7lcuBobcTX208m7F1LJJIn2dpnwtO4gsWsnj734IWeNL02Tnl3E29tJtHfIv3d0QDJJsrubZHc3sc2bFcU9z2Zn7b1p4pMhQGWl2Px+7H4/tpxbyR6/+7LbST6f6RbwLwNskkQ8kcShghoSiSdUUZ0yPYfKveJVR7MZozUhOHfffTe33norzc3N7LvvvixYsIDDDz98wO1fe+01rrzySj755BOGDx/Oj3/8Yy655JKcbRYvXsy1117Lhg0bGDt2LL/5zW84/fTT1f5ThMLnttMjZQZuiiU4oWiCMq8TR3czF3d2cczBP+R34U28ufVNFq9bzOJ1i5nRMIMTR5/IMSOPocyVXxdln8vOFudIcPog2g0718GwicJizqmEWLlQJjk1E2FK/9PSh0TdvnQf81vKX7wcXr1R7nY85utC4oU8ZebOLfDxYtj4Omx5t69a562EYZNg1GEw6msw8jBVpy+rKY2rlf4SVVIr2Ww4qqtxVFfDRPm4Xdk+nEsv6F8ZSiUSJLq60oRnl0yOdu0i2dVForOLRHeXfL+rm0RX5r58Ix7HnsxViwoPXMohP98NwRcv1yB5Pdg8Xmwez+77Pi/Sno95PUheLzZv+vHMYx4PNp8PyeXSgECpKDupBDlVnKBMBYID6qhOfhUrA4Mxdc4dakH1SBctWsS8efO4++67Oeyww7j33ns54YQT+PTTTxkxom9Vz8aNGznxxBOZO3cujz76KG+99RaXXnopw4YN48x0x9Vly5Zxzjnn8Ktf/YrTTz+dJ598krPPPps333yTQw89VO0/SRh8TjtdZFJUghWcaJyGCg90yX6EscMO4J6JP2Hl9pU89MlDvNr0Ksubl7O8eTnXL7ue/Wr245D6Q5haO5WJlROp9dX2++WTv/BAw1TYvFTuhyOI4ASivZSFeBSW/0m+f9jlYCv8qsE27VyWLX+BmZ3PweKL4JI3oLReQMTpFNVAku3mt2Wj8/r/0Ofk7vDIzQoTUbmHz+al8u31W8FbiWvSKYzp3heSU4v62/uN2WRGQZAnXKt15TjYGiPZ7TjSvhwYnfc+U6kUwc4ebnjiba4/egTJ7m4SnV0ku2UylAwE0rcekoEAiezvwV7PyTeSSUilSPb0kOzpAaABCDZ/Xtwfvuff6nIhuVxckrSxbqEfW/p3ye1O/3Rhc7n7ecyFlPO4E1vmeZcbyelAcjoZs2EjXW9GsbucSA4nktMpP+eQn5ccDnA4kVzO3Mfsdt3Uq0yquEylOXZqQM0ZWpGYOkUVakF1gnP77bdz4YUXctFFFwGwYMECXnzxRe655x5uuummPtv/6U9/YsSIESxYsACASZMmsWLFCn73u99lCc6CBQs49thjmT9/PgDz58/ntddeY8GCBTz++ONq/0nC4Hc72JLyyr8IVnCyUmLXNvmBsuEATK+bzvS66TR1N/H8xud5fuPzrO9Yzwc7PuCDHR9kX1/hrmBM+RiGlwynwd9AQ0kDtd5aknEvLaFd7Kzfl7LNS3FuXQlTvyMs5jJP+pD85Eno3gYldXJTvyLgczl4pPKHzPRshu0fwz8uhPOflsvJi465nxRVTys8eyWs/tfux0YeBpNOgRGHQvX43RVt0SDs2gDbVsGmN2HDfyGwA+m9h7gK4PbbYL+zYP9vyaRSwIk+GB0iRZWIQ9cW6G6B7mbo3g6RboiHIRGR02xOr1zN5vDKE+r9w8BfQ2W8FeKRoSvdFCIUje9uXGkCSJJEyOEiVTMMz4QJBe8nlUqRCodlctOLCC14ZhWXHdZIMhQmGQ6RCoVJhkKkwqE+j2Xvh8OkQqH0Y/L9VCy2+72iUVLRKH4gHhR7PgI4Hdj6t8JeKzmd4MwlPtn7TgdzumJsfLYMyW4Hhx3JZkdy2MFmlx+z7/nThmR3ZH8O9Nz0De10bajEXuZDstvkbWzp97A70o85ej1nA8kGNkneV+Z+78fT9/favJbgSvm+ZJPkVH/vbWz2nMez9202mfDtuU368dJ4iGB7F8kKmRzmbm8rmiyaKVUqpdTSlIFoNIrP5+Pvf/97TvroiiuuYNWqVbz22mt9XnPEEUcwbdo0fv/732cfyyg0wWAQp9PJiBEj+NGPfsSPfvSj7DZ33HEHCxYs4Isvvuizz0gkQiSye95MV1cXjY2NdHZ2UlamfMClKGzY0cPrr7zI9z/9HyjbG678RNi+b33xM07et5p97hsnP3D15+Cv7nfbbT3beLv5bd5peYfVO1ezqWsTiVR+VwCeFLg95bjtbjx2Dy67C4/dg9vhxmFzYJfs2CRb/z9tu3+3STbWbe+h1OOgodwLq5+BYDvSXgdCw/4ASL2qMHLuD/CF673NK2t2cPRIN3zyT6REDPaahtRYvNq3obUHSZIYM8wvL/y7NsDGN+RFXpJkdathGnjzHDSWTMrEbucGYjvW40ztXoDwVEDNeKgZt7uDcwHY1hGiPRhj3+FlEAvLfqDet1C7PP6iGDhc4PCByyunM50+mRRlfjo8YHfK6pTNId8g7Z5N7f6ZiEMiSmcgyM7OAGOqXZCI7b4l4/Kt9/1kTH5dKkFWOUtBjoom2eQhrTYbO4MJqks8ciySbffPzDaStPt3ei1Ekg3IXM3uEXcqRSSeoLUrTGOlt5crOLn7fs7fiqzo5fye2mO/u9HcGaa+3CMf4wOuN0MvRFIyhT0GtngKezxFKpaksytCnceFLQ62hPy4LX2zJ3rdj6ewJeh1v+9z9ngKKSE/F48lcSFhT6SQkunXZu/Lv0vJFDb1ZkVaSCMlyTcApPQ3Q5JyH5PSd3ptm0iBzS6lt9+9L9LbZu5nno/W+Jj1r7eFxt7V1UV5eXle67eqCk5bWxuJRIK6urqcx+vq6mhpaen3NS0tLf1uH4/HaWtro6GhYcBtBtrnTTfdxPXXX1/EX6IO/C4H7cm0giO4iioYTVAa3SH/4vDIV9kDYHjJcE4ffzqnj5dJaCQRYX3Hepq6mtgW2Ma2nm00B5rZGdpJZ6ST5p5dJAjKYUsQFtCkMIsuoBX5yCwrge618k0AHv8CKPEAHuhZD6vXC9kvwLK2Xr/4XUDaEB3ZCpuGLlvuF2XpWLNIQPdn8k0AVvX3b3MApT4h+4cE0APxHojDgA1sFGBZa54bKhF7/EAqJIcrGg6gW4X9+oDYkFvlBwlwpm9eQNVrvj2vp7Or4+5HUinsCbAnwZEARxLsCfl+n8eSYE+kcKQft6XAlkzfUvL22Z+DPp7Cnn5t5rnM9v093vv1Uvp3e5qL2lIpbCmQ0rf+7u/5s7/7Sp6zKZQpMq8d/H8z0GP5IyCJVwKVQBO30J5X2Kkh+rH0t/2ejyvZ5/z587nyyiuzv2cUHL3hddnpSKQJTrRbvmoW5LcIRhL4I7vkX8qGK0ptuO1u9q3el32r9+33+Yseepd7z5tG1+0TCEQ6iH7rIcI1Y4kkIoTjYflnIkwimSCZSpJI9fqZ3OP39M9UKsUb63Ywoa6U2i0vQfMqUg37w6RTSPX6kvW+v/vivP/nM8dNihT//nAbJ+0/XH5s/X+h+X2wOWH/s6G0Ie/PZk+samqnMbGF6ubXIR6Sr+obZ0DjoUX/L5/9aBvfnCKnFolHYOd6eaBox2b6enrc4C5LKyOutAKThFgIIj1ybAPBUw7+2myaCf8wWS0qQIp+9sNtfHNSJcSCcg+jaGD3/d6PxcOyypJMKy/9LXySJP+P7C6i2EngwOv1yn+f3ZlWgPb4mblvc6Q//4zCIe2+n0JWS1IJSCb4oGkn+zWUYCeZ9rvE0z+Tu7dLpZWXzP3ez0P6s5JyfgZjSQKRBMNKPekYbGk1qNeint3e1uf12c8/u33m/5FifWsPjdU+3Dnm177fjUEe6ItUilAsQWt3hJFVA5Hcgd5joP3vfnxLe4gqvxOf05HX9vntH+KpFE07g4yu8Q+4TaFo7Yngdtgp9ziG4L/Kvyvrd/QwbljxzVezSKUgBe2BGKlkkhqfCyn9mJSSn5dSMiGTVcFeJCeVkv+CNEmT2L096celVIrNO4OMqPKl99d3P5n3ydz3+QtXmkVAVYJTU1OD3W7vo6y0trb2UWAyqK+v73d7h8NBdXX1oNsMtE+3243bLdYTIAI+l52diV5xRbr7LRkuBMFYAk+wWf6lTFy34QzsdgeVDQdSuX4JdDTDxOIb/jV/8SlzRlcy8tXfyAvymb+QPSsC8MGH73LZtHSlzAH/C389Gza8DG//Db7/XGFG6cBO1i79ARPalsi/1+4Lp90Nw6cKifnDj97l8gP7qe7paZUrsja+Dl8sldNiqU5k6WsQ+KqhdjJrU3uRqJ7EpKkzoW4yuEuFxJuJ+bJDDlKWp0+lZLM1pNNG9j7k6t8fbiOWSHL6tL2FxZrBlX9bxfePmkyFT2EbgiGwdH0bq1u6ufBr+ZuT88X1//qEs2eNYmS12EX9462dvPRJC5fPFlM40Bt/fGU9M8ZUMX3kwGpyIdjeFWbBf9Zx+RlThO4X4G8rmijzODl+PzFFCRkkkikueXQll5950NAbK8Qrn7WypSPEnBkjhe/7woXvcv0AFYdGhKoEx+VyMX36dJYsWZLjwVmyZAmnnnpqv6+ZOXMm//rXv3Iee+mllzjooINwpruJzpw5kyVLluR4cF566SVmzZqlwl+hHpx2G5GUE+xu2bwZ6RJGcELRBK5gmgSqQHAAeS7U+iWweZk8A6pIBKNxqj5/SiY3wybJJd1qwO6Esx+GB0+Elg/hgePhvMWw14FDvxbkBfmTf8LzP2FCYIc8m+vwK+GIHyvv1TPkW/WjTJbUymXzmdL5jLrT3SL7Z2LB3SqGtxLKGmSVKp2mfOPNjUyqL4UR4gdYup12wrGksiotSRrSlBxUsZIl04G5QlRmLg01K7/UGrgZiqk3tNKvUsxq9mbxudRp1xBUcQ6VV6WGm2aE6imqK6+8kjlz5nDQQQcxc+ZM/vznP7N58+ZsX5v58+ezdetWHn74YQAuueQS/vCHP3DllVcyd+5cli1bxv33359THXXFFVdwxBFHcMstt3Dqqafy9NNP85///Ic333xT7T9HHXjKILBDaKl4KpXC1p1bQSUcow6Tf37xlpDJ4sFIHN9Hj8i/TL9A3Zaq7lK5kuqxs+SOzAtPghNvhannDv6+bevhhZ/KxA5o9Ywiddo91O0jnlw77TaiiSRuxxAnQocb6vaVb3kgGFFvbo/PKffgEL3/UDRBfZln6A0LwGAztIqBmouYWjEHIgobVyqAOT9nO82dosxOu6Hm0Eq1yG8iWfyoH62hekH7Oeecw4IFC7jhhhuYOnUqr7/+Os899xwjR8ryWXNzM5t7dQcdPXo0zz33HK+++ipTp07lV7/6FXfeeWe2RBxg1qxZPPHEEzz44IPsv//+LFy4kEWLFpmqB04OMhUxgo3GdKbNrWoRnL0Okv0QPdth54aid1fX8yn21k9kH8n+ZwsIsDek9OTvXvBVySRn7NEQC8DTl8JDJ8OGV2R/SAbJhFzCvfgi+GNatbK74Mj53Db6PlyN4mVm2N2RVDSCMfXmyah1clVz8rLXqc7nHFKpoSLIMavRzK3fcSmCoNbxrObQSq9Kw1iDghpX9gefWp9zzHz9szQxGV966aVceuml/T63cOHCPo99/etf57333ht0n2eddRZnnVVgd1ujwZ0uWxDcCyfT5I9y8b4FAJwemeRsXgpfvCmXLxeBw7v+Ld+ZfNqgVV+FwOuyE+pvYXeXwnf/AW/eAa/dIk8t3/SG/D+pHJUu/f5cJkAZTDgejv0VDJtAz2Pvqfal96eveEWnToIR9ebJ+NwOQipMulaTLPjddgIqkIVgNEGjya7S1epyDXLM27siQ2+oEIFoAp9ax7NLnZEpaqbV1Gr0F4zGVfuc1YJ5WhJ+meFJExzB3Yz3bPInDr3UkEyaatNbxe0y3MWhgVfk+9MvKG5f/WDQ/L/NDkdcBZe9BwddKPtWIl2yP2f7RzK5cZfDtPPg4tfg3EUwTG7eptY8GcgsYuosvKopOE47gYg6Mau5IJjtiletYaxyK371FBx1VKe4qqQsqIIHJxRTO02s0kWGiZptgjVs0xhQQcFxpKLyFG4QbjL2uuyE4+krvZGHAbcW78P56O+4U2F57tSIGULjhd4n10HMrBWNcNLtcMIt0LYOOpvkqp7yveUGewOUfauVl1bNs6DyIqaWpK+aZ0GlBSEQUdEb4rTT2i1eDQmp4J/KwKcSkVRz9IgZj2evasZocw3aBIvgGAASKU+53Hcg3CFsrxXxnfIdu1suDxaIzILgcznkSiebQ06HtW+CqgJLYt97SP6pkrnYr4Qs2J1y+XTdZOFxKIFa8ngkpqbqpJ48rt7Ca6dHJdXJr6ayoJK6p6b5VY1p88FoguEV6lTYKTpvKICan7PbYSMSE98OWs30pVqwUlQ6w+O0EXelTcahDiH7jCeSVCfTrXUVNvnLBz63nWBm4XX5Ya/p8v3PXy1sh9veh+YPiOGEA74tJMY9oZY8ribUnCiulurkd8vTl0VDVcNu2p8lGqqaX1U07Kpr5lbLGK3isaGaMVqdmNX6bqtpQFcLFsHRGT6XnZgz48HpELLPYCxBPWkFR4UeOH3y0uO+If9c/5/CdrhyofzDf7hwc3EGavXgUBNqKThqwuu0E1RBDUmmwG5Ti5Q51DGSqpgK9LkcqhDJoIoLr7rGaBXVkLg6asigA2+LhBocR81yfLVgERyd4XM5CGcIjiAFJxRNMCyVJjjlahCcPRaE8cfKPz9/VW46pwSRHvjoHwC8UXaSmAD7QZ+YTQC1SlTVhFopqmJn4gwGNZUFz1A9jAqEWqXAQVUrklQiZTH1Fl611BA1U65qwYxl4hbB0Rk+l52wXSzBCUTiuSkqwehzcq0/AErqINojjw5Qgo8XQ7SHZNVYtpRNExtoL6iZ7lELfrf50mpqpXvUhFrKAqSwqaQ6qVaRpGJ1j8epjjdEzVSgWlAz5aoWLA+OBcXwux0E7OlZQKF2IfsMRhNUxdWpoALZeJfTN8Rmg3FpFWfdS/nvKJWCFQ8AENjvPHwqlS5DOmbBCk40nsRpV+8rpJYpU02YkZSppSyoCbWOjWg8qZoBXT01xHwLr5pjPNSCGauoLIKjM7xOO0FbeqKsKA9ONEFZbIf8iwoEp1/j3cQT5J+fPi1PWs4HXyyF5lXg8LBr/FmqnqTUMAuqfeWoVlmtmvA51UoFqtciXi0jqZrwOOxEVCJlZmvHr6YxWi2Eouo121QLarYQUAsWwdEZfredLkQrOHFKIhkFR3yKqt/Or+O+ITfD69oqdzbOB8v+IP884Dv02MtVNd31UZ0EQM3xAZC5ShcbcyyRxGFT72uvHllQz4OjVsm1mqTMZpNIqfeRmAphFdseyBD/QauthtgkiXhCbDrQUnAsKIbX5aBb8su/xIIQjxa9z1A4hDeqXhVVv+ZXpwcmnyzf/+jvQ++kbR2seV6+P/P/VK3egIxnQezCq2afE1BHwVH7JCVX2ImNOaXySu6020jsOadMCCwGohXMpjrJFXZqnjvEfw9lA7q5UoEWwdEZfpedjqSP7NWegDRVqqsFiZQ8ENJfU/T+9oTfPUD58pT0gMxPnoJYaPCdLL0TSMGEE6BmfHp8gIoKjgreEPVTVGqQMnVlZjUGV4ZjSTwmk/MtDATzkT5JkoQT4EgsgcepppKqxsWRlaKyoBBel51gLLl7oriANJWtu9cUcRWubAaczzLqa1A+QiZpHy4aeAc71sL7j8n3vzYPUHcAJMjekKBgb0ggGldVwfGqMEJAzTlUQLpqSOxiYMb+G8lkynSqgoX+4Vcphanm8aHOxZGVorKgENlW4N4K+QEBpeL2nhb5jgrpKUhXnfRHFmx2OPQH8v1lf4TkAF+w/14PqQRMPDE7d0rthVeNFJXaCo4aZMGM3UjNWCUTipnvc9YCNhXUELWh1jBWNaGGryxswmPaIjg6I8u0vZXyAwIUHHcgM0VcLYIzCFk4cA54KqBtLax6rO/za56Hz/4Nkg2O+WX2YbXlT5fDRjzf6q48obbJWA0EInFVU4FqwIxXjoGo+T7neCKJTWXVSY2FV22hzIxd0NUw+6dSqNbXSS1YBEdn+NwO+QvvqZAfEODB8YS2y3dUqKCCTLfaAU5SnnI44mr5/pJfQOeW3c+1fwHPXCbfn/lDqN0n+5Tahl01YEZlIRhT18ytBsyYolJzPlIGNptYNUTN0RIZmFUNEV3NqDZ8TvF9ksyYcbUIjs7ITOYWqeD4whmCo46C43LYiA1WgnjIxTB8mvy3PHoWbH0PNr0JD50MgR1QPwWO+lnOS8zY+MqM/TeCEXVn4KgBNQcT9obIai0tVCfR3hAtPme/4AaFCQ28Tj63GUmZQ5XxI2aDuS7lvoTwZap7yivkBwR4cEqjaYKjwhyqvOBwwVkPwoMnwI7V8Jejdj9XOQq+swic3pyXBCPmu0o3YxoiGI1T6jHX114LsuBKD1UUVa0VjMbxqXxseNP+vVKPU8j+1B4ACeJTVFqoe2bsKC6vK+aKWQ1YCo7OcNltRONJoSmq8mwXY3VSVHmhajRcuAQmnQw2Bzi8MPU8mPtKv8RL7b4QakCLNIRohDRJUUkkBaZOtPA6iR5squbQygxEe0M0IQtuscNYtVBR5aIKcaRME9XJhL4hNWCus/OXENkDXVSKKhGjLLFLvq9SiipvVDTCOY/KoxskadAkbjCi/hWvaAQi6p9cMz047ILMfQENUlS+9MBNUVVxoWiC6hK3kH0NBL9bboxWKWh/WvizfC47AYELrxYpKtELb1CDiwzRMWtRYSeasJsVloJjCEjiysS7m7Flmvz5xDf5Kwg225AONS2ueEGszyIUU5+UZciCKGgxT0aNRUx986td6FW6VikqkceGFj440WqIFseGWdNqIr+DsiJrPpexRXCMAlEKTle6RLy0QSYWJkEimcKh4mRuALfTTiQurlRcq6t0kQtCQINqNa8ZFwSn2NSJJiZjt2gFx4zkV4uYxafVNPmc+2vGWiDCcXU7L6sF80X8ZYUoD05Xpoux+ukptWcEiYbPKXZBCGrQNE/0yVW7K17RMZssDaFB6kT0WAxzqiHaxCzSZKyVImm2Y0MNWATHKBCl4HSmCY7KFVRuh1g1RAv4BRscUylx3piBoMYVr0/FjtFgTlLmddkJCbzi1cKf5Xc7TLfwmvHY8LnsQkuutSHsapi5zWfZtQiOUdDbg1OMMpJJUalcQeVToVOm2lBjXIPaEJ3u0WJUg+hjIxiNqzrGAzLDWAXGHFO/hYBX8MKrheokWg0JxeKqL7yiiaRW30GR542ACQdtgkVwDAGXQyLqLJN/ScYgGih4XymNUlRm7O4pfmie+qY7v+ArsaRGqpPIY0ML86tXsAdHm6Z5ZlRw1FBDzJbuUd9T5nbYiMQE+w1NNocKLIJjCHidDoIpN9jSDbuK8OEkO9KjEdQmOCbt7ilWwVHfgyRawdECotvxR2JJ3A51T1XCzdwR9RcE4enLmPoLrypqiOoGdMFm7pj6MYvus6PF56wGLIJjAMg9OJJiSsW7NUpRCZx1kkymNJlzYsbmV6IVHC0gfjihRo3RRJbja9RCQCQpC0UTqvuz1DG/qhuzw24jKXyMh7n8LGaMGSyCYwhkr9KLNRonYth61J1DlUF2SKgAyCWI6l8diIxZK5iRlJlTdRK78EbjSVwqtz3wuRxCSZkWaQg1KhnNVt1jzpjNN5YGLIJjCGSv0r1V8gOhXYXtqLsFiRQJyQH+YeIC7Afy1aOYk6vcXVf9q4PsYFMBSGrQbh3EmwW1gPhUoPpQQylTfwikeAVH7TSEaDUkFI2rbtgVDS36DYHY6d9aGKPVgEVwDAC55XoCfNXyA4G2wnaUNhgH3LWqN/kTKelrld/1CWyMpkW7dTAnWTCj6mTKmAUSdoBIXH2vk2iYUQ3RwjQPxRXj7gkrRdUP2tvbmTNnDuXl5ZSXlzNnzhw6OjoG3D4Wi/GTn/yEKVOm4Pf7GT58OOeffz7btm3L2e7II49EkqSc27e//W01/xRV4XM55B4c/jTBCRao4HTKBuOgp15QZANDZMt1raZy+wSaX7UYAAliS9u1VJ1EVspoATOm1Rx2GwmBQ0218DqJhlmH9GqhWIO4ZqxaGKPVgKoE59xzz2XVqlW88MILvPDCC6xatYo5c+YMuH0wGOS9997j2muv5b333uOf//wna9eu5ZRTTumz7dy5c2lubs7e7r33XjX/FFXRR8EJFqfgRHwNgiIbGCKNpFpdHfgF9uDQqvGV3J/FZF4nU6pO5ovZAoSj5hshoMV4CQC300Y0IaZUXIvSdjWg2hl69erVvPDCCyxfvpxDDz0UgL/85S/MnDmTNWvWMHHixD6vKS8vZ8mSJTmP3XXXXRxyyCFs3ryZESNGZB/3+XzU16uvVGgBn8tORzC2ezhmcGdhO0o3+Yv61Sc4Iq94tfryiGyMppU07nM6BHudtCA44shvNJ7EqbJZF8Buk0w3esSCDC1UJ0mSSCZT2AT0kNLq3OFNnzvcjuLfy4ypQFBRwVm2bBnl5eVZcgMwY8YMysvLWbp0ad776ezsRJIkKioqch5/7LHHqKmpYd999+Wqq66iu7t7wH1EIhG6urpybkaCz+WQG6MV68FJp6iSKpeIg9ixB1p9eUQ2RtNiWjSITVFp5XVyO2xE4uaK2YKFweBx2gkLOqbDsSQeAaRjKPjd4hpumvV7qJqC09LSQm1tbZ/Ha2traWlpyWsf4XCYn/70p5x77rmUlZVlH//ud7/L6NGjqa+v5+OPP2b+/Pl88MEHfdSfDG666Sauv/76wv4QDeDLtImvLVbBkVNUqdK9BUU2MLwCDY6ygqN+ukdkKbBWnT1dDhvxpBiZORCNa5L7F3lFrVXMIhGNJ3GobPI3N8SpIVohk5IXc57S5m8X6Tn8ypiMr7vuuj4G3z1vK1asAPo/0aVS+RnZYrEY3/72t0kmk9x99905z82dO5dvfOMb7Lfffnz729/mH//4B//5z3947733+t3X/Pnz6ezszN6ampqU/tmqIlsK7EuXiRdKcNKDNm0V6k8S9wvsKaOVgiNSWQhE1G+KJhpBE16FmVEaD5kwZi3hdYlTQ7TyRHsFtsXQCiLnfmlVNSoais/QP/zhD4esWBo1ahQffvgh27dv7/Pcjh07qKurG/T1sViMs88+m40bN/Lyyy/nqDf94cADD8TpdLJu3ToOPPDAPs+73W7cbveg+9AT2R4cvT04qZSyb288AoFWAByVjSpEmQuRX55gRJurA5HKQkiDtvaiYcaFVyt1TySCGnQxzkCSEKKGJJIpbBqxhUx5u5n+r36Xg6DAafNaQGSn65QGM+zUgOIjrKamhpqamiG3mzlzJp2dnbzzzjsccsghALz99tt0dnYya9asAV+XITfr1q3jlVdeobq6esj3+uSTT4jFYjQ0qG+uVQPZq4OMBycelgduukvy30naYByTXHjK1G3yB2KHuZnxKj0YTdBQ7tQ7DEUwY7rHjMdGQCPCDru9IcW+n5ZVMnKDwgQoOL3pDW+m0tVEEOmTNKv/XrVE8aRJkzj++OOZO3cuy5cvZ/ny5cydO5eTTjopp4Jqn3324cknnwQgHo9z1llnsWLFCh577DESiQQtLS20tLQQjUYB2LBhAzfccAMrVqxg06ZNPPfcc3zrW99i2rRpHHbYYWr9OarCn2m57vKDwyM/qLRUPO2/6XAO0yR1IlINMWMbcK1UJ5Ewo1FQKzN3BiIqqbTs+iqqA7MW088zkJuEFq8sJDTq6wQZD475FBxRJmOzQlUn3GOPPcaUKVOYPXs2s2fPZv/99+eRRx7J2WbNmjV0dnYCsGXLFp555hm2bNnC1KlTaWhoyN4ylVcul4v//ve/HHfccUycOJHLL7+c2bNn85///Ae73Vwn7ww8TptsBpOkwkvF0/6bnbZhplt4gxqeXEXBlMqCGYmkhp+z22knEi9eldSSsIvyhmj5OftcDiFqiJa+EDP2SRJpMjYrVF1VqqqqePTRRwfdpvcV06hRo4a8gmpsbOS1114TEp9RkHMV4quCri0QUEhw0grOTvsw9tGs3boY3VJOnZht4dXWG5KvOX8wyMqCNjHbJIl4IomjyB42wUiCcp82qcCMN6TYZohaEna/W4waoi3BEVPNqHlaTYAakkymAO1Up81fcYJj1TIaDf4CFZw0wWl3qO+/EQ2tUyci0hCaKgsOMcpCIJLQTFkQNassqKFvSO4oLogsaKgsiFFDtOmuC5l+VMV/zlqeN0Q1rwzFtOu87BVoMjYrLIJjNBQ6riGdotrl6Nt7yOiIxpO4NOhWC+C0i2lfrqVhV1SzPy1VJ59bjDwe0HAR87ochESRMq1SVE5Raoh2pExUF3TZzK1hispkqUC/2yHkIkNWjwUEpAMsgmM0FOrB6ZK7GO+ym0/BAW3arYO4vHQwot3CK8rgqKUHR9Skay3Jgqj5alqnqESoIVpWfvndotQQDQm7KAVHw/J4UWXi4VgStwl74IBFcAyEdNqk0HENWQVHO4LjsNmICkidaAlR/XviySQujbxOXoGkTMuTq7h0j5ZKmbn8LKKODS1TVF5B89WCGlarySZjAceGhv2zfIJG0wSjcc3UPdGwCI7RUJImKD2t+b8mGoTQLgB22bVLUfnc4kYfaAU5ZnPlpUVNQQ9oaMoUlu6JJDQrExel7oU0/Jz9gkqBtU2diFPKNPWUiUoFms7MncBvsq7tGVgExyDIVJ1Qkp6Q3pPfvC4g2+Qv5SohbPerEF3/ENXPQkv4BZkytYQoZSGRTGkymRsELmIxbRcEMURSO6VM1Hw1zVMnwkzGGqXVBBmjtVRRRY2m0fLCSDQsgmMQZA1hpekxFt19x1wMiLT/JlU6HI+GpctmJAuirsS0hN8tRtLXErL5VcwipsXkZciQBZOpIYK+g1r3wRHxHdSyvYQoIqmlD06Ur1GuvrQUHAtFIPsFyig4gVZI5vmFSvtv4iUNlGh4IIr40ic17EYK4nLpWkJUybWWEFW+DGg2dVpcV2Dt/CyiVFRNDeii0moaqiEuh42YgOpLU85WsxQcC8XCnzFl+ocBEqSS+RuNO74AIFLSqOmXR4RsG9IwBQHmVHC8TvP1szAjKRNVjh/Qsg+OIHVPWwO6qBYC5uvMrWUvKlGwFBwLRcObuXq0O9Ikh/x9OB2bAQj699b0yyNCwdH6JCUi/6/lDBwQOzRPK/gEpXu0hChTZiqVKrqDc74QVY6vZV8ncWqI+RZeLRtXioIZY87AIjgGQU4PDqU+nHZZwenxDNdWwRHQg0ProZUi8v9aq05el11IRZKWEDe7R7sxxqJSJ1pOXhY1QkDLajVRCETMt/CaUQ0JRM13bGRgERyDIEdZUFpJlU5RdXqGa6vgOItfxLSeQ+UTUN0TjGibR5eNpOZSnUSle7SEKCOplnDZxfSiiieTmlXYiUIgou2keRHQw89S7GiaoAmJZAbmOqK/xMi54s0qOHkQnHg0Wybe7qzXXMEp1hsSjCbwaXhFIyJFFYgmtCVlAshCUGMi6RekLGgJUSZjLdvaa0lajQYtvU6i0KOxguNyFD+aJhCxTMYWikTOIpZRcPIhOJ1NQAqcPtqlCu0X3iJTJ7LMrOHCK6C6R75y1LZarViyoDmRFKDuxRNJ7BpVUEG6tF3I7B4BwVgYEsmkdl6nDIpWQzRWcETM0AqY0OuUgUVwDAKfu1f5cmkmRZWHBydtMKZiRDpXqrGfpcgvT1DDBmMgJg0R1FjBEaEsaE0khXzOMW2PDZtN+gqTE/MpQVqLV26nnUiR6UAtZ36BmE7XWs6DEw2L4BgEuQqOghRV2n8jExyN/SwCUieBiLZfHhGl7XLll3YnKY/TRjhW3IlVayIpolImqOG06N0ojuGYd/Ky9syuWDVEa4ipWEtpq0oKKMkPRBKWB8dCcciZ/KpEwWnPEJyRBDXO74pomqf1wiuELGjcy0L2WRS3GGhNJEUgqDGRFAEzT17WEm5H8WqI1vzI7zZfk1ARc+y0HGoqGhbBMQhyTca9PDjJIU4COSkqbd3uQhQcjeVPIWTBlN1ItSWSMoq7UjXjiTWg0+TlYtSQeCKJTWPZyaxVdmaLWW4EWSwpS2nWTVw0LIJjEOQw7dIGkGyQjMkjGwbDrs/ln5WjNO9lIcKUqXUfHBEwY9mkGbu+ajktWhS0VlEB3E5bUWpIIJrQdMQLZPp+mVANKZIsaK06mbFzu0hYBMcgyBn0Z3fKJAego2ngF6VSsHO9fL9mvOYKjmzKLO4b22NKsmC+xlf6EMnilTKtpkWLQk8krjlZ8DqL81kEo9r3k/EWaZyPxrXv2yPCz6I1RDWvNCssgmMQ9On8Wt4o/+zcPPCLeloh0gVIUDWGcCyBx2muf6kZHfpmbF2uNfkVgWBE22o1AJskES/CHK21AR3SPYeKUFL1MJH6i1QWQjpcZIjws2gNUXO/zApzrYZfYthtEsneakhFmuAMpuBk1JuKEeBwA+Zr/GXGHgsBXap7ikNQF9WpWA+O9g3G/G5HkWRBe8LudRXXcFOPCdfFxtyjA2Evth9VNJ7E5dB2yTUjKRMJi+AYFVkFZzCCs07+WTNe/XhUQiSWwK3xl75Y6FHdU7SyoEMq0GmXihojoIcx2u8uzmehjxpSXLqnRwdSVuwA2aAOYxqK/Zz1IJLFmozNVsq/J8y1snyVoETBqTYvwQHtVSe7TSqqR0sgqr2CU6yyENQh5mKb/ekRs99d3NwvWcHReBEr0mehhzG62JjlcSnax1wMwQnoYJovttt8NKG96iQS5o38y47yEfLPwRSctgzBGat+PF8iFHslFoklNVediiULeiy8xTZV1OOK1+9y0FNEd2491JCijw0dUoHFekOCehDJItWQgMZDemGP/moFwIxVrr1hERyjonKU/LN908C9cPqkqLT339gkiUTSXDKmiDECWqtOxZao6qGGFHvFq0eZuL/IRUyP9KVMJIv8nHVYeIuJWeuBt1C8GqL1uBQo/tjQuju+aFgEx6ioHAk2B8SC0L2t7/OJmEx+AKrHpXOl2hMNEdO5tYbfXfy4Bq1RbFltJK6916n4FFUcr8Yn1xK3nZ5izK8R7XvK5LSYKAABHfwsPiExm0wN0XhWIAhKE5usCKQ3LIJjIEiSRDKjhtidu1WctnV9N965HpJxcJVA6XAicX1axJuxN4TXWbyCozV8ruKbKmqvOhWbotLBsFsk+dUtFVhEWi2gAynzmVBZ6NPKQyH0UHDcDhuRuLliFgmL4BgIfToDZ8zDGTNxb7R8LP+s2w9sNt0OxGLKEPVy6BdbKaMHRHRR1RrFGnb1GNVQrAdHj4W32PJlXap7ilUWdPCGiEm5ahtzsRc1AR0M6CJhERwDoc8XqGac/LM/BaflQ/ln/X6AXrOGiktR6ak6FZNL1wNmVMr8RaZ7Uik0n4FjxiqqErcANUSHFFUxx0Ygqn3H6KLVEBM2NTVjg9DesAiOgdBnOnfNBPnnzn4Izva0glM/BdDvy+Mrop+FnqpTsMCrdN1UJxM27Cr1OIpaxPTwlPndxfks4omU5iMERPTu0b7fUHGTufVoXFm8GmLGIb3a+7NEQtVvYnt7O3PmzKG8vJzy8nLmzJlDR0fHoK+54IILkCQp5zZjxoycbSKRCJdddhk1NTX4/X5OOeUUtmzZouJfog36KDjDJsk/Wz7OndKWSkHLR/L9ujTB0amcrxjZ1qyqkx7jMIo1kuoB2RtirphL3MWlqPSAHHORqpMO3pBimkCacoadDk0gi4UZY+4NVc/U5557LqtWreKFF17ghRdeYNWqVcyZM2fI1x1//PE0Nzdnb88991zO8/PmzePJJ5/kiSee4M0336Snp4eTTjqJRMJcJ6Y94XPvsfDW7weSXZ4o3tWrkqp9EwR2gM0JdZOBzHwkHRQcV+FltXrIzFCcWVCPjsBQXMz6eZ3MRxZ8RZIyPSal+N0OesKFx5xMpXBorDpJklTUZG09OhkXCzOqIXqMSxEJ1c7Uq1ev5oUXXmD58uUceuihAPzlL39h5syZrFmzhokTJw74WrfbTX19fb/PdXZ2cv/99/PII4/wjW98A4BHH32UxsZG/vOf/3DccceJ/2M0gs+5hxri9ELtZNj+EWx7D8r3kh/fvEz+OXyavA1pBUcXslC4giPHrAcpK1J10inmQlNU4VgSjw5ep5IiF149UOJ20FOEUqYHl3Tabblz7L4CCEQT+HQ4pouBHt2XM0ilUgWl2CyT8QBYtmwZ5eXlWXIDMGPGDMrLy1m6dOmgr3311Vepra1lwoQJzJ07l9bW1uxzK1euJBaLMXv27Oxjw4cPZ7/99htwv5FIhK6urpybEeFz91PuOXyq/HPb+7sfyxCckTOzDwV1U0MKT/foNZW7j9dJAfQy3RXTN0SvmEs8hashcrsE7eUQj9NGxGQGdNCHWOmJZFJ71alYBHXocg3Fqb96NK4UCdWOkJaWFmpra/s8XltbS0tLy4CvO+GEE3jsscd4+eWXue2223j33Xc5+uijiUQi2f26XC4qKytzXldXVzfgfm+66aasD6i8vJzGxsYi/jL1IPc62WNB2Gu6/POLNKlJpWDjG/L9EbsJjh7zkaDYdI9eMZtPdfIXUSkT1CnmYtSQYEyfY0PrXkEWCoNe/6Ziht4GdPIcFlMZqEfHaJFQTHCuu+66PibgPW8rVqwA+j9ZDCWVnXPOOXzzm99kv/324+STT+b5559n7dq1PPvss4PGNdh+58+fT2dnZ/bW1DTIfCcd0W/DrnHHyD+blkOgTTYXt28EhwdGHpbdTI/ZLFBc6kSvq4M+XicF0Et1KqYjqV4KjtthIxIrcDHQ6XguBpF4QrfBhGbkZZJkvmnVsipZ2PcwmUxh17jtARTXnVuPjtEioTjyH/7wh3z7298edJtRo0bx4Ycfsn379j7P7dixg7q6urzfr6GhgZEjR7JunVwqXV9fTzQapb29PUfFaW1tZdasWf3uw+1243a7835PvdDvIlYxAur3l/verHl+d9O/8bPBU5bdTC5B1EcNKTx1kqDK7xIc0dAwperkLLwUWC9zo3zBUdgC1hOJU2IyQ6aefoVieIJeHMPlsKWrEpX/n/WKOaNKlvuc+gRQAPxFVNnp0WxTJBR/G2tqaqipqRlyu5kzZ9LZ2ck777zDIYccAsDbb79NZ2fngESkP+zcuZOmpiYaGhoAmD59Ok6nkyVLlnD22WcD0NzczMcff8xvf/tbpX+OoTBga/tJJ8sE59WbIJz2D+13Zs4mehnYikmd6HWV7t3TzK0AeqlODruNQmea9piw1NOMCo6ebe0zaojSFFs0nsRh10f+yZS362GALxSmNc4XSHBSKX1UJ1FQTU+dNGkSxx9/PHPnzmX58uUsX76cuXPnctJJJ+VUUO2zzz48+eSTAPT09HDVVVexbNkyNm3axKuvvsrJJ59MTU0Np59+OgDl5eVceOGF/L//9//473//y/vvv895553HlClTslVVZsWAaYiD/keeOdW1FaLdcgPAfU7K2USvq/RiUidBnVQnu00qWBrXSymTUXjMehjQi0GPCWMO6GjILHQYa0jHyp5iu0brgWLUEL3g76945SsCVY/sxx57jMsvvzxb8XTKKafwhz/8IWebNWvW0NnZCYDdbuejjz7i4YcfpqOjg4aGBo466igWLVpEaWlp9jV33HEHDoeDs88+m1AoxDHHHMPChQux28UuPIlEglgsJnSfg8ElxZGSMcLhcO4T9hI44xF47WaZ6Mz+FcTi8i2zSTKOPRXv+1qVYUskcRb4vqlEDI+U0DxmgAoXBb1vLBah1OFRPWan0ynseO4Jxynz6iWpF3b1p2e6R5IkEgX4JfRUnUrS3YyVvr+epKzE7aC7ADUkGk9q3i06g2K6c+vlkyoxIZEUBVWP7KqqKh599NFBt+l9Je31ennxxReH3K/H4+Guu+7irrvuKjrGgWJqaWkZsuuyaCSTKQ6vT7Fx48Z+nm2AI34v3+0CunK3OX6kjdat+pinTxnrGCDmwTGzNkFoVwsbO7T/5p82zllQzJNLYjhDO9m4sV2FqHJRUVFBfX190ZU93ZE4e1V6BUWlDfQkC/JYjDhlHmWkUO76qo+6V+J20B2J07dudXAEdGyYV+jCG9KpFxWYtzv31o6Q3mHoAnNpwBohQ25qa2vx+XyalY4mUymaO0LsVelT/FpXe7Cg14lAoe/tag/SUO7VfKBi5r0LiXl7V5hKn0vVaplUKkUwGMz2f8r4zwqFnikqh00iGk8q/rx6InGGV3hUimpwZFInygmOjqSsQLKgZ/M52b+nPOYeHQdA+t0OukLKVf1oPKmbl8WMaTVRsAjOHkgkEllyU11drfn72wNJPB7lJ3a7M1HQ60Sg0Pe2OxN4vR5deo8UGrMtmMTn9ajeZMzrlRWX1tZWamtr0+mqwj6nHgMsvC6Hsmo5vUZiQEZZUO5Z0NM3VKiRVC8fHMjpnkJSVHqOaSj1ONhWgBoSiMQpVUiYRaHQYaxydsW8BmOwpon3QcZz4/Ppo4Z81WC2xmpJDasKMsdgbx9YsoBSqp5InFKPPgtvoZ4FPdWQQudR6dkzpNDqHl3Jb399v/JAdyROqY6EvZDj2YzkNxxL4jVxkz+wCM6AMNvCa0E5CqmkSqW0Ozb2fB+/206ogDECPWE9FRx7YWmISEK3BaHQK95ANKFb755C0z2BqH7kt9C0Wk9YX7JQSMzdZow5EjNdL6o9YREcC19J2GxSwX1l9EKhVSfBaFy3wYQFe0N0rUgyn+pUUuDkdj0X3lKPbIxWip5InBKd0j0ZM7dSyDGbTHXS8dgQBYvgfAmQTKVUK0F89dVXkSRpyIoyI7dcHzVqFAsWLMh5zCZhugnMJR4HPZHC2hboYeSGwklZj07DY6EINURP35CnsBRVd9hScJSg0AGyPZGYbjG7HTaiceUjU+S0mnk6NvcHi+B8CZBMprDpmFKzScrVEL0JkU2SCvKz6InSAsmCnijUZxGJJfA49Tk9ySkq5TEHovr17im0fFnPRaxQ31C3jp4yeWRKYUqZXjEXmlLvCeunOomCRXAMCKWLf0LndtqFqCHJlPw6vSCTMnMRnGJaruuFQq94QT8fXKFkQU5R6ddTpuA0hE6LWKHT5vVUcGQltDCjv9nSPXqauUXBIjgGgzxTRtlrMgpOf6mYqVOnct1116X3LXHfffdx+umn4/P5GD9+PM8880zO9s899xwTJkzA6/Vy1FFHsWnTppznd+7cyXe+8x323ntvfD4fU6ZM4Zl//j2HLBx55JFcdtllzJs3j8rKSurq6vjzn/9MIBDg+9//PqWlpUwYP47X/vtS9jWZVNizzz7LAQccgMfj4dBDD+Wjjz7Kef+lS5dyxBFH4PV6aWxs5PLLLycQCGSfb21t5eSTT8br9TJ69Ggee+yxfj8zmw3TqU4lHudXag6OXig0dRKNJ3E7dCI4BVar6bnwepw2wgWMl+iJxEynLOjtZynk1GUpOBaEw26TSBSghuTbluX666/n7LPP5sMPP+TEE0/ku9/9Lrt27QKgqamJM844gxNPPJFVq1Zx0UUX8dOf/jTn9eFwmOnTp/Pvf/+bjz/+mIsvvpjLL7mQ5cvfztnuoYceoqamhnfeeYfLLruM//3f/+Vb3/oWs2bN4r333uMbx87miv+dSzAYzHnd1Vdfze9+9zveffddamtrOeWUU7Jl0h999BHHHXccZ5xxBh9++CGLFi3izTff5Ic//GH29RdccAGbNm3i5Zdf5h//+Ad33313tmFebxSi4GhZIt4fCjVl6gkzzhsq1LCrJwqt/NKT4BScOtFZWSiILOhoMi4UZlSd9oRFcAwGewHekIQCD84FF1zAd77zHcaNG8eNN95IIBDgnXfeAeCee+5hzJgx3HHHHUycOJHvfve7XHDBBTmv32uvvbjqqquYOnUqY8aM4bLLLuOoY47ln4v/kbPdAQccwM9//nPGjx/P/Pnz8Xq91NTUMHfuXMaPH89PfnYN7bt28uGHH+a87pe//CXHHnssU6ZM4aGHHmL79u3ZYay33nor5557LvPmzWP8+PHMmjWLO++8k4cffphwOMzatWt5/vnnue+++5g5cybTp0/n/vvvJxTq25irEA9OIomuXqfSAjwL0XgSh02/r3mJ2246BcfnthMsIHWiZ2cJt8NekJHUjNOiu02oLHSH45TqaNgt5NjUs0eSKJg7eo1xzZMfsb1L3SGLkXgSh03CbpOoK/Pwm9OnDPkaJcrC/vvvn73v9/spLS3NKhyrV69mxowZOVdWM2fOzHl9IpHg5ptvZtGiRWzdupVIJEIkEqGkxD/g+9jtdqqrq5kyZfffMmyYPDVnT3Wl9/tVVVUxceJEVq9eDcDKlStZv359TtoplUqRTCbZuHEja9euxeFwcNBBB2Wf32effaioqOjzOdht8kBFJUimUujIFQpKQwR0vnIscTtNR3AKTauZzNJlWoRjCbw6tT0oFHorOE67jUg8oSiFqmeDUFEwd/QaIx+yUSzauiN4nDZFfR4SyRROuw2bzdbHJ7LnNHSnM3e/kiSRTMpXfvl4TG677TbuuOMOFixYwJQpU/D7/fzfZZcTjUaHfJ/ejyXTLcAz7z0YMoQrmUzygx/8gMsvv7zPNiNGjGDNmjU52w8GuwTRApQyu46X6YUsvHrLzIWkTuKJpK5KmddpJ1xAQ0W9e4Pq/f5aQs9GrHabRDyRVDSuRW62qR8p86fHjygiOF+CPjjmjv5LCFtBHpwUNpvEsGHDaG5uzj7e1dWlaGL25MmTeeqpp3IeW758ec7vb7zxBqeeeirnnXee/N7JJJ9vWM/4Cfsoi3kAcrF8+XJGjBgBQHt7O2vXrmWffeR9H3jggXzyySeMGzeu39dOmjSJeDzOihUrOOSQQwBYs2ZNvz185EZ/hX3OeqHE46A7rKwPju4Ex+UgoNBIqncKQpIkxWqM3gZ0OQa9I/hqIDOrrNyXP8GJJfQzoMPukvwqf/4z4fRWnUTA8uAYDHab7PVQgkRSViSOPvpoHnnkEd544w0+/vhjvve976WHNOaHSy65hA0bNnDllVeyZs0a/vrXv7Jw4cKcbcaNG8eSJUtYunQpq1ev5gc/+AGt27eTUlg6ORCJu+GGG/jvf//Lxx9/zAUXXEBNTQ2nnXYaAD/5yU9YtmwZ//d//8eqVatYt24dzzzzDJdddhkAEydO5Pjjj2fu3Lm8/fbbrFy5kosuuig7uLI37FIBKSqd+w2Vup2K++DonUe32STFi393WPkkb70RiiXwmCxtYgS4HHLqxEwo8TjoLrDhpl7wF+CF69GxcaUoWATHYCjEZJxRFubPn88RRxzBSSedxIknnshpp53G2LFj897PiBEjWLx4Mf/617844IAD+NOf/sSNN96Ys821117LgQceyHHHHceRRx5JfX09J59yakGl7f3h5ptv5oorrmD69Ok0NzfzzDPP4HLJVx37778/r732GuvWrePwww9n2rRpXHvttTQ0NGRf/+CDD9LY2MjXv/51zjjjDC6++GJqa2v7vI/dVoDJOIWuhkyP06Y4dWLGq7CucMx0uX+5kZu+pExuMZH/Ma23AR12p07MBDPGXOJ2Ku7ObUYD+p4w11nkK4BCUlQZb0hZWRmLFi3Kee573/te9n5/J7890zcnnXQSJ510Us5j3//+97P3q6qq+qSxovEkO7oj2d9fffXVPu+zZz+dZCpFKBrvc9X7ta99jY8//rjP6zM4+OCDeemllwZ8vr6+nn//+985j82ZM6fPdgWlApMpXHb9vvCF+A56wuZr1qVn19dC0R2OUaZzzG6HnUg8mbeSpLcBHZSnToyQCjRjb6dC0ttfBlgKjsFQUOpEZ2+I3TZwymkgJFL6llzbCvBZJHT+nAuBngMgd0PZZ9YdjhlCDVGi8HUZgJQpnfultz8LlJOFcCx/AqcWzEhwyjzKx7wYgEsWDYvgGAyFmF9TBiALitNqyZSuoxoKQTKlrwdHhrL3N8IiprS1vRE8OErHCOg5lTsDpU0VjZAKVDrYtDtikJgVfM6JZErXqi+AMo+TLpN1QRcBi+AYDIUoOHqjkC9vIpmb3z3yyCNJpVL99qwxCvaM2QwwRrpHGQHuNsDCW+pRZug2guqktKlijwGODaVT0I1Quqx0SGggGqdExxJxSHdBt1JUFvRGIbOozAq9r2qUIqmzUpaBEh+CEVJUSkdMGIGUKV0QjBCzX2HqRM9J4hkoJmWGiFnh52yAzstlXiddofxjjiWSOHT0G4qCRXAMBrMt+l8lGCGt5nXZCSmopOrRccJ1BmVKyUJE/4okUyo4StUQA5iMlU5uNwJZUNpRPGAAUqaUsBshZhGwCI6FrywkCcV+J70JqFJ5vCsc093PovTq0QgVSWZUcMo8TkX9WboNUGFXotD82q3zoE2QVSclpKzbACMPlHpwjHA8i4BFcEwOI5RNZmCkWPJBIeZovaE03RNVUDasFso8TkVkocsAPWVKlS68BjBGKyWSRlBwlB4bRlBwShWSBSP4hnwuOyEFZm5jFCcUD4vgmBx6l4hnYJNkj4qZYC+gF47eUKrgGAFlXoeiBSESS+Bx6ntqUnrFa4SKpDKPg66QQrKg8yJW7lVIFgyw8MrHhoLP2QAxKx0/oncHdFGwCI5Bka8aYpTKHiXl7clkyhCDAc2o4JizB4dT0cIL+qcClaaojKAslHnNt/CWeZ10KiFlBlCdPE4bYQXz1brDMdORha5QjDKvuWLuDxbBMSCUKAvyHCp1F4NXX30VSZL6HVqZgd2Wf3l7YogW4EceeSTz5s1TGKVyyDHnt62S9NvChQtVK3dX6lkwApQuvEaAUpNxIpnCqWC6tBqQiaS5fBalCpsTdoVjuntwlJLvrlCccq+5DLudoZjpYu4PFsExIGwK5iQZRsFRoIYYJWYlHZiNEnOZx5E3WTCKJ0rpwmsEmLFviJwKVGIyjumu4CgdxtplwoXXjGShK6R/cYIIWATHgLBL+U8Ul9UQdePJB0OpTtFoNHs/MztLbygiZQYZPCcbSfNbxILRBF4DTANWuvAaAUpNxkaA22EnGs/zxIHs33MY4OSh5FTQFYpTZjKy0GmQdI/dJhHPc2HpNKHq1B/0P7ot9IESP0tvZWHUqFEsWLAg5/mpU6dy3XXXZX+XJIn77ruP008/HZ/Px/jx43nmmWdyXvPcc88xYcIEvF4vRx11VJ9BmQBLly7liCOOwOv10tjYyM+uvpKu7p7s86NGjeLXv/41F1xwAeXl5cydO7ffmAOBAOeffz4lJSU0NDRw22239XmvRx99lIMOOojS0lLq6+s599xzaW1tzT6fSaG9+OKLTJs2Da/Xy9FHH01rayvPP/88kyZNoqysjO985zsEg8Hs604+/liuuvIKfvjDH1JRUUF1dTU///nPc64oo9EoP/7xjxk9cgTj9qrh0EMP7TNMdOHChYwYMQKfz8fpp5/Ozp07+/wNolCuwLPQFY5RboATa6kCD048kTREM0W5P4u5JkabFUqERiXDRNVGvsqT/D3UnywoSbvKpEz/mIuFRXDyQSoF0YBmN3ssSCLcI/8+xJeoEDXk+uuv5+yzz+bDDz/kxBNP5Lvf/S67du0CoKmpiTPOOIMTTzyRVatWcdFFF/HTn/405/UfffQRxx13HGeccQYffvghixYt4u1lS7n6yitytrv11lvZb7/9WLlyJddee2328WQvNeTqq6/mlVde4cknn+Sll17i1VdfZeXKlTn7iUaj/OpXv+KDDz7gqaeeYuPGjVxwwQV9/q7rrruOP/zhDyxdupSmpibOPvtsFixYwF//+leeffZZlixZwl133ZXzmkV/fRSHw8Hbb7/NnXfeyR133MF9992Xff773/8+b731Fg8+9CivLX2Xb33rWxx//PGsW7cOgLfffpv/+Z//4dJLL2XVqlUcddRR/PrXv1b0/1ACRQQnpH/pMshqSL4KjhFMpEC6MjG/BcwoqcCvBozxWStpuBkwgJkblKmSRiFlxULVT729vZ3LL788qxCccsop3HXXXYMaMAcycP32t7/l6quvBmQT6muvvZbz/DnnnMMTTzwhJvA9EQvCjcPV2Xc/qO79y8+2gcs/4LaFeEMuuOACvvOd7wBw4403ctddd/HOO+9w/PHHc8899zBmzBjuuOMOJEli4sSJfPTRR9xyyy3Z1996662ce+65WSPw+PHjufW2Ozhh9jE88Jc/4/F4ADj66KO56qqr+o3Z5bDR09PD/fffz8MPP8yxxx4LwEMPPcTee++ds/3//M//ZO+PGTOGO++8k0MOOYSenh5KSkqyz/3617/msMMOA+DCCy9k/vz5bNiwgTFjxgBw1lln8corr/CTn/wEkKXx4Xvt3edvveOOO5g7dy4bNmzg8ccfZ8uWLfgrakik4OADruKFF17gwQcf5MYbb+T3v/89xx13XJYETpgwgaVLl/LCCy8o+p/kC6UKjhGuwpx2W94GdCP0k1EKI0y4NjMcdolYIqm7SVsJytM9h3x5pIBTKf2rAkGZ2V/24OhPyoqFqkfUueeey6pVq3jhhRd44YUXWLVqFXPmzBn0Nc3NzTm3Bx54AEmSOPPMM3O2mzt3bs529957r5p/imGRLMAbsv/++2fv+/1+SktLsymf1atXM2PGjJwv5MyZM3Nev3LlShYuXEhJSUn2dvop3ySZTLJx48bsdgcddFC/759IylO5N2zYQDQazdl/VVUVEydOzNn+/fff59RTT2XkyJGUlpZy5JFHArB58+YB/666ujp8Pl+W3GQe653akpCYNv3gPn/runXrSCQSvPfee6RSKSZMmMBetVWMqKuipKSE1157jQ0bNmQ/rz0/nz1/F4kSBZOMzWgUNEI/GaUwwnDQDORZdkOTyVgiaQhPGWSa/ZnL76S0vN0IUFKgkEgaw59VLFT7Vq5evZoXXniB5cuXc+ihhwLwl7/8hZkzZ7JmzZo+i1gG9fX1Ob8//fTTHHXUUTkLFYDP5+uzrWpw+mQlRSMEI3F6onFqSz3yew+CRHJ3oz+bzdbn5BaL9T2gnc7cRU+SJJJJ2XyWz8kxmUzygx/8gMsvvzz7WDSeoD0YY+zYsdnH/P7+laeMYTef9woEAsyePZvZs2fz6KOPMmzYMDZv3sxxxx2XY1ze8++SJGnQv1N+YHDBO5lMYrfbWblyJR2hOB6XHX/6ii2jHGmdnlByJSgrOMZYePOFGRWcLgOUW2fgdzsIRBNDpkSMVNmTMc5X+V2DbicXBBiHlJnROJ9vNaMBBCchUO1buWzZMsrLy7PkBmDGjBmUl5ezdOnSAQlOb2zfvp1nn32Whx56qM9zjz32GI8++ih1dXWccMIJ/PKXv6S0tLTf/UQiESKRSPb3rq4uZX+MJA2aJhINu5QgnoiCyzvktr09OMOGDaO5uTn7XFdXV46ikg8mT57MU089lfPY8uXLc34/8MAD+eSTTxg3blz2sXgySXNHGJdr8JNUNmabxLhx43A6nSxfvpwRI0YAclpz7dq1fP3rXwfgs88+o62tjZtvvpnGxkYAVqxYoehvGggS8P6Kd3IeW758OePHj8dutzNt2jQSiQStra2M3/9gyr1OvK7cVMTkyZP7fD57/q4XOoMxxgwrGXpDA8EIvVkykNJVdkN1CjfCoM0MyjyysmAqguPJTw0xwkynDMrzrGZMpYzR1BSUj8X4MkA1DaqlpYXa2to+j9fW1tLS0pLXPh566CFKS0s544wzch7/7ne/y+OPP86rr77Ktddey+LFi/ts0xs33XQT5eXl2VtmoTQqlDTNg91X9UcffTSPPPIIb7zxBh9//DHf+973sNuVeQMuueQSNmzYwJVX/v/2zjwuynL9/5/ZF4Yd2RIEREMCVzQxS8/RpKOSS7mbcTQ7paUcS8yjuVTiUsfqK51jllsnyRaX9Pw8KVqZpiiBkClqoggqyD4wMMwwM/fvj4nBYVYQmXvG+/16zevlPM89M9fz+PDcn+e6rvu6FuHy5ctIT0/Hjh07jMYsWbIEp0+fxvz585Gbm4vff/8d/+/gQSxPWWTXbzQLHJlMhjlz5mDx4sU4duwYfvvtNyQlJYHLbbksQ0NDIRQKsWnTJly7dg0HDhzA22+/3aZjskbJrVuGY/3iiy+wadMmLFyoT5bu2bMnZsyYgVmzZuHgt/tQdKMQWVlZWL9+PQ4dOgQAWLBgAb777jts2LABV65cQVpa2n3Lv2krtY00Lam1b0k+TWLBTciDwo7+PbWNGmryFTwk9rVroEngeNpZRoCmGjgeEr5doqyxSQcRJflZbe2h5Qq0WeCsWrUKHA7H6qv5CducO12vaO2TtNu2bcOMGTMMSavNzJ07FyNHjkRMTAymTp2Kb775BkePHkVOTo7Z71m6dCnkcrnhVVxc3Maj7lzaKnCaWbp0KZ544gmMHTsWo0ePxvjx441CRvYQGhqKPXv24ODBg+jTpw82b96M1NRUozG9e/fG8ePH8fvvv+Pxxx9Hv379sGLFCvgH2BcyJASGpcDvvvsunnjiCTz99NMYOXIkhg4digEDBhjGdunSBTt27MDXX3+N6OhorFu3Du+9916bjskaEyZPg1KpxKBBgzB//ny8+uqrePHFFw37t2/fjlmzZuGtN5ci9pFeePrpp3HmzBmDSB48eDA+/fRTbNq0CX379sWRI0ewfPnyDrPPEvaExmhKFJSJeKi3QyzQNfEKIG+wPYnVNKjhJbXtuewM7G2LQdN5trdJKE1Ll+314NQ20pMH5yGxr3glLaUaOgTSRsrLy0l+fr7Vl1KpJFu3biWenp4mn/f09CTbtm2z+Ts//fQTAUByc3NtjtXpdEQgEJDdu3fbdQxyuZwAIHK53GSfUqkkFy9eJEql0q7vul9cL1d06LjOwNlsHjZsGPnri/PsGnu9XEF0Ot19tsgYS9fi/F3ZpF7VZPPzi7/OJeV1jffLvDbx5v7z5GZ1g81xG49cJudv1nSCRbbZeOQy+bXYti2fnbpOvr90pxMssk36mRvkyIVSm+P2n7tJ9p+72QkW2SbjQilJP3PD5riffy8nn5641gkW2Sa3qJp8ePSKzXGXS2vJ2kP5nWCRba6VK8jqAxdsjqtSqMiiL23Pu47C2vzdmjY/3vn5+cHPz8/muPj4eMjlcpw9exaDBg0CoK8ZIpfLMWTIEJuf37p1KwYMGIA+ffrYHHvhwgU0NTUhKCjI9gEwGK0gdnoVaVjqCbQsFbe1RJWWOjhAi2fhIS/reWU0eRa8pQLUKNU2x9U0NCHmITpsbosHJ9TH+gKGzsJDIsDVcoXNcTRdG/auoqLKZjtXUdFk871y33JwevXqhaeeegpz585FZmYmMjMzMXfuXIwdO9YowTgqKgr79u0z+mxtbS2+/vprvPDCCybfW1BQgLfeegu//PILCgsLcejQIUyaNAn9+vUz1EB5UNBRlMDWDHGyomccDtoVDnQk9tbC0eh0EPLpWOppb26IPtxDx83V202IantCVMomekJUduazyBvomcTsDffIKQq52h2iokgstCWsRovN98p9vVp27dqFBQsWYNSoUQD0hf7S0tKMxly+fBlyudxo2+7du0EIMRSjuxuhUIhjx47hww8/hEKhQEhICMaMGYOVK1e2OaGWdmx5Fmjp6dQM748WE9ZsokkA/fjjjyipUUKjI+A70aXjYWduCEWn+o9ltbbzLBSUVH0F9BNCUVWDzXE1lIkFp/Ms2CvKlE0I9+u81azWsLc6Ny19qACAb2fBTZpsvlfu61H4+Pjg888/tzrG3IT34osvGiV63k1ISIhJFWNXhMtproBpeYyOkg7XzTQnR1urD6UjtpfddibtTeh2JG2pZkwLbSmMRkso0FsqRF6x3OY4fSIpHROCvZ3bqRI4bbGZEu+evdW55comRPo7V6kGmq6Ne4UO/zXDBB6XA42NPyCtHTU6OhP7bAaVoswatIUCnVHgeDmhzd5SoV05ODqKqr7aW46fljYeACAV8tDgZCvs7MUZba51kU7iABM41MLj2n5C0LajTcP9xB6xQGNYzdlstkfgaHX2l2PoDLykQlTX2xYLNOEpFaDGjlAgTXiI7avPotURano/2XudMrHQMdhKE6BpOf69QscVzjDB7onXGQUORTbz7bWZR4/N9iQL0pTcCADebgJUN1gXOPYUAuxMPMT21Q2hCT6PS9157Cgam7SQUFI0z17klPWDa27lYQ1XSjJmAodSeFwOtERndQxtYsE+gUNPkz/AvrCaRkfAp8hmezw4VQ1q+LjRc5PylgptekMUag01VYwB+zwLNCXNPwjQ5JXkcfVd0K1BUygQALykApueVNpE2b3ABA6l2CMWaJt4+RznEwt6IWmPKKPnT8WehN3qejW8bTQv7EzEAh5UGutPjjQtXbaXxiYdxELn8irQCJfDgcaGWKANHzehTa8koSyNwEsqtPPe4Vx/h5ag567NMILfSZ6FHTt2wMvLy+Y4Dodj0oSzNW0RZWFhYfjggw/sNxRAUlISxo8f36bP2ILH5UKrtWGz1vQ8Dx8+HMnJyR1qi724i/hQqKwnZVY3NMGHktos9lLT0ERNDRx7qVGq4UWZKONwrP8dNmnp8qICes9CjRMmoVc5WV6Zl8R2qLhJq4PImepmWIGOtY0ME+wK92jJPXsWpkyZgtGjRxver1q1Cvv370dubq7RuJKSEnh7e1v9LrtzcCjKZ+Fy9KukrKHVEYgFxjbv3bsXAoFjJjYul2Ozxk11PT39keylRqmmzoPTLBYsCYKqenoKEzbTnKNlyYNXXa+GD0XePUBfVLGmQQ0/mcjsfhpFmY+b8wkcbzfnS5y/F5gHh1LsXb58L3/zTU1NkEgkZru+tyYwMBAikfmbTzPOGFazJ6ZvzmYfHx+4u7vfL7PuGX0ODl2TGGA9Z6WqXg1fCxOco7CV0F1Vr4avG102+7gJUGXlKb2SQoHjIxWiqt7yea5uUMObMsHu4yZEtRWbaVvJCABeEr2QfFBgAodSeDbczM3c/Qek0+mwfv16REZGQiQSITQ0FGvWrAEAFBYWgsPh4KuvvsLw4cMhFovx+eefG4WoduzYgdWrVyMvL8/QGX7Hjh2G37k7RHXz5k1MnToVPj4+cHNzQ1xcHM6ePQtA305j3LhxCAgIgEwmw8CBA3H06NE/bCR2darVarVYtGgRvLy84Ovri5SUFJPJ8bvvvsPQoUMNY8aOHYuCggLD/ruP+fHHH4dEIsHAgQNx5coVZGVlIS4uDjKZDM9PHo/y8nLD55pDYatXr4a/vz8eDgnAK/NfhlrdcmNoHaIKCwtDamoqZs+eDXd3d4SGhmLLli1G9p46dQp9+/aFWCxGXFwc9u/fDw6HY+It6wj0T+l0eRbEAh6UTZbzcCoUavhSNvHacunrRRllNttYkl9Vr4YPZaLM24Y3pIqynDLgD5utXBs1DfSFL72kAqvtR/Qr8OgSZfcCEzh2QAhBQ1NDp74atUoom5RtWqWxdOlSrF+/Hm+++SYuXryI9PR0BAQEGI1ZsmQJFixYgPz8fCQkJBjtmzJlCl577TU88sgjKCkpQUlJCaZMmWLyOwqFAsOGDcPt27dx4MAB5OXlISUlBTqdzrB/9OjROHr0KM6dO4eEhAQkJiaiqKgIgH1ek3/+85/Ytm0btm7dipMnT6KqqsqkZ1l9fT0WLVqErKwsHDt2DFwuFxMmTDDY0czKlSuxfPly5OTkgM/nY9q0aUhJScGHH36IEydOoKjwOlasWGH0mWPHjiE/Px8//PADPvx4O77dvx+rV6+2aXNcXBzOnTuHefPm4eWXX8alS5cAAHV1dUhMTERsbCxycnLw9ttvY8mSJTbPgyXEAh6UVpZ7UvvEa+XmWlWvok4s2OpHpRdldIkFW+e5QqGCH2Xn2UdqPWFX7ymj0GZbQpK282xDSLrSEnGA5eDYhVKjxKPpjzrkt89MPwOpwLTrb2vhU1dXhw8//BBpaWl4/vnnAQDdu3fH0KFDjcYlJydj4sSJZn9LIpFAJpOBz+cjMDDQok3p6ekoLy9HVlYWfHx8AACRkZEAgMKKevTp08eoC/w777yDffv24cCBAxg79a92HDXwwQcfYOnSpXjmmWcAAJs3b8bhw4eNxjTva2br1q3w9/fHxYsXERMTY9j++uuvG8TcwoULMW3aNBw7dszQnHXyjFn49ut0o+8SCoXYtm0bpFIp3ALC8NZbb2Hx4sV4++23wbWQ9zR69GjMmzcPgF5Ivv/++/jxxx8RFRWFXbt2gcPh4JNPPoFYLEZ0dDRu3bqFuXPn2nU+WuPjJkRlvQpdheY7QtPUH6mZZs+CpY7ilQr6QideUoFVl75elPl2okW28bZj4qWtfYC3mxCX79RZ3F9FY1jNhliopFCU+clEqLRhM22e33uBeXCcFB2BUagnPz8fKpUKI0aMsPq5uLi4e/7t3Nxc9OvXzyBuWqNQKJCSkoLo6Gh4eXlBJpPh0qVLBg+OLeRyOUpKShAfH2/YxufzTWwvKCjA9OnTERERAQ8PD4SHhwOAye/07t3b8O9mj1ZsbKxhm3+AP8rKyow+06dPH0ilLeIhPj4eCoUCxcXFFu2++3c4HA4CAwMN33v58mX07t0bYrHYMGbQoEEWv8sWtm6uWoraBzTjIxXYDEPQtvLLVv0eGj0L3lLrOTi0igXbYTW6bPa2sUy8msJQoFTIQ4OVFZg02nwvMA+OHUj4EpyZfqbTf7eosgEintjsPq1OB/5dq5EkEvNPxa1xc7v3brzWfovP4+D1xa8j48gRvPfee4iMjIREIsGzzz4LlUrVoT2dEhMTERISgk8++QTBwcHQ6XSIiYkxypUBYLTaqTk8dvc2PpdnEtayhLXwWutVVRwOx/C95jrD30uROD+Z0OqTGI34ykSorFdZ3K8j9Ikyb6kQt6otN9ysVNCXG2JLLFTSmBgttZ7PUqlQo1+I9VWcnY2bkId6K2Khsl6NYC/z929HYSs9gHlwHkA4HA6kAmmnv2QiKSzlGWtaLV3t0aMHJBIJjh07dk/HKhQKodVaL8jWu3dv5ObmoqqqymQfn8vFyRMnkJSUhAkTJiA2NhaBgYEoLCyEjsCuFVSenp4ICgpCZmamYZtGo0F2drbhfWVlJfLz87F8+XKMGDECvXr1QnV1dRuOtAVzEae8vDwolUpDo83MzEzIZDJ07dq1Xb8RFRWFX3/9FSpVywT/yy+/tOu7AMDHTYQqhXMJnC7uIpTXWRY4NNLFXYQKhWWbaerp1IyfTIRyKzbTWMjNXcy32lGcxnwWDsd6uQYak7lt4WoeHLr+MhlG8Llci9U9WxefE4vFWLJkCVJSUvDZZ5+hoKAAmZmZ2Lp1a5t+MywsDNevX0dubi4qKiqMJuRmpk2bhsDAQIwfPx4///wzrl27hj179uD06dPg8zgIj+iOvXv3Ijc3F3l5eZg+fTp0Ol2bntAXLlyIdevWYd++fbh06RLmzZuHmpoaw35vb2/4+vpiy5YtuHr1Kr7//nssWrSoTcfaDI/DQev7lFqtxpw5c3D+/G/46VgGVq5ciVdeecVi/o0tms/Biy++iPz8fBw+fBjvvfcegPaVn7cWomps0kIkoO9P21kFTpmT2ewlFUBuJaym1tBXyI3L5QAmf4Ut0BgKBGDVI02rzVyu5arRzIPD6DT4PMvVjDU6nYlYePPNN/Haa69hxYoV6NWrF6ZMmWKSW2KLZ555Bk899RT+9Kc/oUuXLvjiiy9MxgiFQhw5cgT+/v4YPXo0YmNjsW7dOvB4PPC5HLyz7l14e3tjyJAhSExMREJCAvr37w9ipwcHAF577TXMmjULSUlJiI+Ph7u7OyZMmGDYz+VysXv3bmRnZyMmJgZ///vf8e6777bpWFu+y9SmESNGoEePHhjx5z/h5TnPITExEatWrWrX9wOAh4cHDh48iNzcXPTt2xfLli0zrNy6Oy/HXnxlQlRYCPeU16ng706XaxywLnAam7TUeUIAfcNNW41NaYO22iv2Ys0b0tikhZjKRpuWy3nQWG8IAHytLG8vr1Ohi4y+e0d7YTk4FMPncqCx0EagSWtaXZfL5WLZsmVYtmyZyfiwsDCzOR9JSUlISkoyvBeJRPjmm29MxrX+bLdu3cyOU6g0CA4Jxffff2+0ff78+ahUqAyTWGFhodnjaobP5+ODDz6w2s5h5MiRuHjxokU7zR3z8OHDTbYlJSXh6UnTTb5/9erVWPTGcmh1OhO37Y8//mj03tzxtK5vM2TIEOTl5Rne79q1CwKBAKGhoSaftYWfTIRKCyGqsjoVurjT52Z2F/FR12g+DEFjPRnAulhQa3RUijJnpdmzQFseljV8/1jNaO6BokGlgZuIvim2+d5hzuayukb4e9B372gv9J19hgE+jwul2vyEoNHqwKeoAWQz1kSZRkcgEdL3dCmw5inTdtwk9tlnnyEiIgIPPfQQ8vLysGTJEkyePNnuBPG78bayfLm8rpFKgaMvHml+X4VCRV3iqy3KFXQKSaCl03Xra5deT4g+cb6qXg1/D+fxIPh7iFBWS6fH1BK+MqHFvDK1Rkft9dEemMChGFseHD5FPZ2asSYWzN1waYDL4fxRwdOUJi2BtINEWWlpKVasWIHS0lIEBQVh0qRJhkrTbcVagmN5nQpdfczXx6GVUnkjgjzpnCT4PPNioVSuRCClNvu565/SW9t3p5beJ/Qu7mKU1alMBI5CpYGUQk8IAPhbCLveywrJ+40176+rQedVwwBgPQcHgF0tDzobrpUWE+a6ctNA6zBEc3sKwHyuU3tJSUlBSkpKh3yXNcrqVOjfja4ltc1Y8iyU1jYilFJR5ifTr6QK8jT2tJXKVQig1NvQRaafeFsLnFJ5I7U2+7uLUFbXCMDTaPud2kYEUi3KGk221zZq4C6mc3rt4i7CrzdrTLbTLMraC32P0wwD9vajoglbCY7OlgBJqygDLLdrKKulN3Tia+HpsVTeSK03xFJydGktvV4nfw+R2Ym3tLYRgTQLnFrT83yHYlEW4GHe5rLaRgRQem0Ee0pwu8b02pArm+BBWfXze4UJHIqxJAacQWk7g413w+HAYpiKVlEW4CFGaa3pjYrGQm7N+LuLcMeMzaXyRgR5tD0XqTPoYmniraV34vV3F5sVZVTb7CE2uyT/Tp0T2lyrQgCleTkBniKUyk3/Bu/U0uuRbC9M4DgBrcWCRkevVwHQhyFae55oFzxCHhdqC7UhaCXQ07xY0BHjIpA00dVbils1SpPt+qdHOl36wZ4SlMhNbS6h2OsU4CFCiZlJrFRuGraihQAPS+KX3om3i8y8p4xmISni89Bk5l53p7YRAZR6ftsLEziUYy4Ph/allAIe1+QPSENpUnQzAr6pzTod6dDWEh1NgIfY7IRAscno6i3BzeoGs/to9ZSF+EhQXG0qcBpUGsgoTX4N8Zbiphmb71AdohLjjgVPGa02C/lcNJlZCKL3OjmXWNAnoNN5ntsLvbMkA4B5saDW6CDk0/tfJ+BzTP7o1Vq6bRbyuFBrWp1nrQ5CioVkoIfYxNUsb6A7jq4XOMYTLyF0C8mu3lLcMiMWaLbZUhf0xiYtJEI6lwHzuByznl6aV35Z4nYNvSvsAEAk4KKxyTh/72a1EiHedCb6txd6794MAH8InFYTr8oZxEIrUabS6CCiWCyYFZJaHQQUn+euPlIUt/KGFFc3IITS1UiAXpS1Dp3IlU3wENMrysQCnslkoA/B0qtwLHnDtJSHis3lwqkor83iKTFtjVEqb0SwJ505ZQAQ6CEx+Tu8UVmPUF967x3tgd67NwMAIORxoG7tDXFGsaDR4cv0/8DLy8sxRtlAwDd/nlsLSQ6Hg/3793eiZZYJ8hCjpNVqiKKqBoR403tj5fO4JhPY9Yp6hPnde5f7zuRWtRIPUdYpujUCHhcqTYswU1BaWfdu/D3EuHNXTgvtuXsAEOIjRVGV8YOGjphvAUMLwV5ilLTKhatt1MCTYu9ve6B3lmQA0Md4W3tDqM9nsRDuoTkxms81nXibNHSHqLhc0yahxVV0e3CauXviKiivR/cuMgdaYxupiA+FqqWq+LUKBSIotznYy3g5cGFFPSIoF5KhPlIUV7VMvPqVPXSHp7r5SHGjqt7wXqXRQkDx/RkAuvm64Xplve2BTg69d28GAPMhKoCehMymJtNGhPpYuvE2nY60uxN3Z0FgPPHSnoMDAGIB16gWDu0hKkDfCb3yrk7o18oViOhC98Qb4i1B8V1P6dfK6+m32aeVzRX1CKdc4IR4G3tDrlfUI8yXbptDfY1tdoZclp4BMvx+R2F4L1c2UVuY8F6g++7N0JfkR8vEq7OSkKlSqbBgwQL4+/tDLBZj6NChyMrK0n9Op0PXrl2xefNmo8/k5OSAw+Hg2rVrAAC5XI4XX3wR/v7+8PDwwJ///GejBpGrVq1C3759sW3bNkREREAkEpl1I3M4wLbt2xEaGgqpVIq/PT8VlZWVRmMKCgowbtw4BAQEQCaTYeDAgTh69KjRmLCwMLzzzjuYNWsWZDIZunXrhm+//Rbl5eUYN24cZDIZYmNj8csvvxg+s2PHDnh5eWH//v3o2bMnxGIxnnzySRQXFxt998GDBzFgwACIxWJEREQg7b21aFS3CLaCq1cxfPgwiMViREdHIyMjw/yJdyBhvm4ovOtJrFRO74qTZh4OdMelkjrD++tOMPH2CJDhyp0Wm53BgxPm54brFS3XRqETnOduvlIU3m1zJf3hy1AfKW5UtAicQicIuYZ4S43Eb1FlA7pRLiTbAxM4dkAIga6hwSEvQggE3Jal4iorK6hSUlKwZ88e7Ny5Ezk5OYiMjERCQgKqqqrA5XIxdepU7Nq1y+gz6enpiI+PR0REBAghGDNmDEpLS3Ho0CFkZ2ejf//+GDFiBKqqqgyfuXr1Kr766ivs2bPHpGN2Mxdyf8ELc+Zg3rx5yMrOwZChw/DOO+8YjVEoFBg9ejSOHj2Kc+fOISEhAYmJiSgqKjIa9/777+Oxxx7DuXPnMGbMGDz33HOYNWsWZs6caTjOWbNmGQmthoYGrFmzBjt37sTPP/+M2tpaTJ061bD/8OHDmDlzJhYsWICLFy/i448/xje7P8fbf9io0Wox76/TwePxkJmZic2bN2PJkiU2rpTOJ7zVJKYjoLYGTjOPBHviwm254b0zNPiLCfbEb7dabC6paUQQ5UIyKtAdl0qdS0hG+stwtazFs+AMoqylxYQeZzjPrcPbBeUK6sOX7YLcR9555x0SHx9PJBIJ8fT0tOszOp2OrFy5kgQFBRGxWEyGDRtGfvvtN6MxjY2N5JVXXiG+vr5EKpWSxMREUlxcbLddcrmcACByudxkn1KpJBcvXiRKpdKwTVtfTy4+HOWQl7a+npTVNpJapZoQQkilQkWq61UmdisUCiIQCMiuXbsM29RqNQkODiYbNmwghBCSk5NDOBwOKSws1B+XVkseeugh8tFHHxFCCDl27Bjx8PAgjY2NRt/dvXt38vHHHxNCCFm5ciURCASkrKzM6jl+ZtIUMuLJUYQQQmqValJe20imTJli8zqIjo4mmzZtMrzv1q0bmTlzpuF9SUkJAUDefPNNw7bTp08TAKSkpIQQQsj27dsJAJKZmWkYk5+fTwCQM2fOEEIIefzxx0lqaqrRb3+ybQcJCAwkhBBy4L+HCI/HM7qu/ve//xEAZN++fVaPoaMwdy225tfiGvLud5cIIYSU1TaS177K7RTb7oWaBjV5NT2HEEJIY5OGzN2Z5WCLbKPR6sjs7WcJIfp71PPbzjjYItvodDqSdJedzmAzIcTI5jk7zhK1RutAa+xj9vazRKPVEUIIWfhFjtl7NG0s+jKXVCr0dr598AL5/U6tgy2yD2vzd2vuqwdHrVZj0qRJePnll+3+zIYNG7Bx40akpaUhKysLgYGBePLJJ1FX1/IkkpycjH379mH37t04efIkFAoFxo4dC63WtC+PKyC5q2aBskkLiZmn3YKCAjQ1NeGxxx4zbBMIBBg0aBDy8/MBAP369UNUVBS++OILAMDx48dRVlaGyZMnAwCys7OhUCjg6+sLmUxmeF2/fh0FBQWG7+3WrRu6dOli1earVy6jX9wgAECDWl97Iz4+3mhMfX09UlJSEB0dDS8vL8hkMly6dMnEg9O7d2/DvwMCAgAAsbGxJtvKysoM2/h8PuLi4gzvo6Ki4OXlZTgX2dnZeOutt4yO89V5L+FOaSkaGhpw/sJFdA0JRdeuXQ3f0dp+GogKcsel0loAQE5RNfqFejnWIDvwlAhQ26gPBf52qxaPBHva+ITj4XE50BECnY6guIr+HAtAH94W8PT3DoVKAzehc+RY+P5RHVinI9DqiEljVhqJDJDh8h/esuqGJnhJhQ62yDa9gtwNXsmCcgXC/egOubaH+3rFr169GoBxd2ZrEELwwQcfYNmyZZg4cSIAYOfOnQgICEB6ejr+9re/QS6XY+vWrfjPf/6DkSNHAgA+//xzhISE4OjRo0hISOjw4+BIJHg4J7vDv9fe35YSoEKhRhd3y0X+yB/hmdbJx4QQo20zZsxAeno63njjDaSnpyMhIQF+fn4A9Hk6QUFB+PHHH02+/+7l3W5u9rgyiSGsplRrzTZ/XLx4MQ4fPoz33nsPkZGRkEgkePbZZ6FWGxcoEwhali42H4u5bTqdcTK2uUTsu8euXr3acJ01U1RZD5FIBFWTFq0jPbQkdt9N882/sUmL0wWVmDk41MEW2YeXRIDyOhUyr1ViULiPo82xi4guMvxepkBucTUGOonNfUO9kHOjGsomLQZQ2mG+NY+G++B0QSXCfN0QHezhaHPsIj7CF6cKKuAh4VPbgLU18d19cSDvNvp384ZYwKM+tN0eqJLG169fR2lpKUaNGmXYJhKJMGzYMJw6dQqA/sm7qanJaExwcDBiYmIMY1qjUqlQW1tr9GoLHA4HXKnUIS8OhwMulwMOR5/pLuJzzU60kZGREAqFOHnypGFbU1MTfvnlF/Tq1cuwbfr06Th//jyys7PxzTffYMaMGYZ9/fv3R2lpKfh8PiIjI41ezSLIXqKjo5GXnYVaZRN4XA64HA4yMzONxpw4cQJJSUmYMGECYmNjERgYiMLCwjb9jiU0Go1R4vHly5dRU1ODqKgoAPpjvXz5sslxRkc9DIVKi+49o1BUVITbt28bvuP06dMdYltHM6xnFxzIvY2CcgX1y62beSomEPvO3cTPVyswMMw5Jt6/xARib85NHDpfij9H+TvaHLsYHROEvedu4UDebSTEBDraHLsY2SsAB/NKsO/cLfwlJsjR5tjF4AhfHL9Sjv3nbjnNee4V6IHzN+X4NvcW/uQk13NboUrglJaWAmgJOTQTEBBg2FdaWgqhUAhvb2+LY1qzdu1aeHp6Gl4hISH3wfr7S4CHGNX1arOeEEDvVXn55ZexePFifPfdd7h48SLmzp2LhoYGzJkzxzAuPDwcQ4YMwZw5c6DRaDBu3DjDvpEjRyI+Ph7jx4/H4cOHUVhYiFOnTmH58uVGYsEeFixYgB+PZSB13XrIS24gLS0N3333ndGYyMhI7N27F7m5ucjLy8P06dNNvDDtRSAQ4NVXX8WZM2eQk5ODv/71rxg8eDAGDdKHzVasWIHPPvsMq1atwoULF5Cfn48vv/wS/7f+bVQ3NGFi4lN4+OGHMWvWLOTl5eHEiRNYtmxZh9jW0UyKC8Hx38vxtye6U+llMseT0YG4WqbAjEe7Ud1X7W4GdPOGRkeQ8EggtT2oWhPm54au3hL0CvLAQ170FoC8G283IYZG+kIs4CHmIfrDl4C+2vXE/g/hVo0Sw3taD9/TApfLwdzHI3DmWhXG9Q12tDn3hTbfWVatWgUOh2P11dbJsDW2wizmsDZm6dKlkMvlhlfr5cLOgFjAQ5ifm9V49Lp16/DMM8/gueeeQ//+/XH16lUcPnzYRAzOmDEDeXl5mDhxIiSSlpseh8PBoUOH8MQTT2D27Nno2bMnpk6disLCQhPRaYvBgwfj008/xa5tH2PQwAE4cuQIli9fbjTm/fffh7e3N4YMGYLExEQkJCSgf//+bfodS0ilUixZsgTTp09HfHw8JBIJdu/ebdifkJCA//73v8jIyMDAgQMxePBgbNy4EeHhYQjzc4NMLMS+ffugUqkwaNAgvPDCC1izZk2H2NbRiAU8fDS9P4b2aJuXzZHwuBxseLYPxvR2jid0QP/38ebYaEx/1DnCgM0kj+yJl4Z1d7QZbSLpsXC88ZcoR5vRJib064q1E3s7zUMGAPwpyh//N60fRHy6VzG2Fw4hbauFXVFRgYqKCqtjwsLCIBa3xCF37NiB5ORk1NTUWP3ctWvX0L17d+Tk5KBfv36G7ePGjYOXlxd27tyJ77//3rBs+e6Ju0+fPhg/frwh78catbW18PT0hFwuh4eHcYy3sbER169fR3h4uNExMJwHe6832mHXIoPBYBhjbf5uTZv9rH5+fm3Ox7CX8PBwBAYGIiMjwyBw1Go1jh8/jvXr1wMABgwYAIFAgIyMDMPqn5KSEvz222/YsGHDfbGLwWAwGAyGc3FfA8lFRUWoqqpCUVERtFqtoShcZGQkZDJ9MmRUVBTWrl2LCRMmgMPhIDk5GampqejRowd69OiB1NRUSKVSTJ8+HQDg6emJOXPm4LXXXoOvry98fHzw+uuvIzY21rCqisFgMBgMxoPNfRU4K1aswM6dOw3vm70yP/zwA4YPHw5Av7pFLm+pEJqSkgKlUol58+ahuroajz76KI4cOQJ3d3fDmPfffx98Ph+TJ0+GUqnEiBEjsGPHDvB4rhlHZLSNpKQkJCUlOdoMBoPBYDiQNufguAIsB4fhDLBrkcFgMIxpSw6Oc6zPZDAYDAaDwWgDTOBYoKPqsTAY7YVdgwwGg9F+nKNaVSciFArB5XJx+/ZtdOnSBUKh0KnqGjCcH0II1Go1ysvLweVyIRTS39eGwWAwaIMJnFZwuVyEh4ejpKTEqEw/g9HZSKVShIaGgstljlYGg8FoK0zgmEEoFCI0NBQajcZlO5Qz6IbH44HP5zPvIYPBYLQTJnAswOFwIBAIjLpWMxgMBoPBcA6Y75vBYDAYDIbLwQQOg8FgMBgMl4MJHAaDwWAwGC7HA5mD01y8uba21sGWMBgMBoPBsJfmedueJgwPpMCpq6sDAISEhDjYEgaDwWAwGG2lrq4Onp6eVsc8kL2odDodbt++DXd39w5fhltbW4uQkBAUFxfb7JPBaD/sPHcO7Dx3Duw8dx7sXHcO9+s8E0JQV1eH4OBgmzXCHkgPDpfLRdeuXe/rb3h4eLA/nk6AnefOgZ3nzoGd586DnevO4X6cZ1uem2ZYkjGDwWAwGAyXgwkcBoPBYDAYLgcTOB2MSCTCypUrIRKJHG2KS8POc+fAznPnwM5z58HOdedAw3l+IJOMGQwGg8FguDbMg8NgMBgMBsPlYAKHwWAwGAyGy8EEDoPBYDAYDJeDCRwGg8FgMBguBxM4Hci//vUvhIeHQywWY8CAAThx4oSjTXI51q5di4EDB8Ld3R3+/v4YP348Ll++7GizXJ61a9eCw+EgOTnZ0aa4HLdu3cLMmTPh6+sLqVSKvn37Ijs729FmuRQajQbLly9HeHg4JBIJIiIi8NZbb0Gn0znaNKfmp59+QmJiIoKDg8HhcLB//36j/YQQrFq1CsHBwZBIJBg+fDguXLjQafYxgdNBfPnll0hOTsayZctw7tw5PP744/jLX/6CoqIiR5vmUhw/fhzz589HZmYmMjIyoNFoMGrUKNTX1zvaNJclKysLW7ZsQe/evR1tistRXV2Nxx57DAKBAP/73/9w8eJF/POf/4SXl5ejTXMp1q9fj82bNyMtLQ35+fnYsGED3n33XWzatMnRpjk19fX16NOnD9LS0szu37BhAzZu3Ii0tDRkZWUhMDAQTz75pKEf5H2HMDqEQYMGkZdeesloW1RUFHnjjTccZNGDQVlZGQFAjh8/7mhTXJK6ujrSo0cPkpGRQYYNG0YWLlzoaJNciiVLlpChQ4c62gyXZ8yYMWT27NlG2yZOnEhmzpzpIItcDwBk3759hvc6nY4EBgaSdevWGbY1NjYST09Psnnz5k6xiXlwOgC1Wo3s7GyMGjXKaPuoUaNw6tQpB1n1YCCXywEAPj4+DrbENZk/fz7GjBmDkSNHOtoUl+TAgQOIi4vDpEmT4O/vj379+uGTTz5xtFkux9ChQ3Hs2DFcuXIFAJCXl4eTJ09i9OjRDrbMdbl+/TpKS0uN5kWRSIRhw4Z12rz4QDbb7GgqKiqg1WoREBBgtD0gIAClpaUOssr1IYRg0aJFGDp0KGJiYhxtjsuxe/du5OTkICsry9GmuCzXrl3Dv//9byxatAj/+Mc/cPbsWSxYsAAikQizZs1ytHkuw5IlSyCXyxEVFQUejwetVos1a9Zg2rRpjjbNZWme+8zNizdu3OgUG5jA6UA4HI7Re0KIyTZGx/HKK6/g119/xcmTJx1tistRXFyMhQsX4siRIxCLxY42x2XR6XSIi4tDamoqAKBfv364cOEC/v3vfzOB04F8+eWX+Pzzz5Geno5HHnkEubm5SE5ORnBwMJ5//nlHm+fSOHJeZAKnA/Dz8wOPxzPx1pSVlZmoV0bH8Oqrr+LAgQP46aef0LVrV0eb43JkZ2ejrKwMAwYMMGzTarX46aefkJaWBpVKBR6P50ALXYOgoCBER0cbbevVqxf27NnjIItck8WLF+ONN97A1KlTAQCxsbG4ceMG1q5dywTOfSIwMBCA3pMTFBRk2N6Z8yLLwekAhEIhBgwYgIyMDKPtGRkZGDJkiIOsck0IIXjllVewd+9efP/99wgPD3e0SS7JiBEjcP78eeTm5hpecXFxmDFjBnJzc5m46SAee+wxkzIHV65cQbdu3RxkkWvS0NAALtd4uuPxeGyZ+H0kPDwcgYGBRvOiWq3G8ePHO21eZB6cDmLRokV47rnnEBcXh/j4eGzZsgVFRUV46aWXHG2aSzF//nykp6fj22+/hbu7u8Fr5unpCYlE4mDrXAd3d3eTvCY3Nzf4+vqyfKcO5O9//zuGDBmC1NRUTJ48GWfPnsWWLVuwZcsWR5vmUiQmJmLNmjUIDQ3FI488gnPnzmHjxo2YPXu2o01zahQKBa5evWp4f/36deTm5sLHxwehoaFITk5GamoqevTogR49eiA1NRVSqRTTp0/vHAM7Za3WA8JHH31EunXrRoRCIenfvz9bunwfAGD2tX37dkeb5vKwZeL3h4MHD5KYmBgiEolIVFQU2bJli6NNcjlqa2vJwoULSWhoKBGLxSQiIoIsW7aMqFQqR5vm1Pzwww9m78fPP/88IUS/VHzlypUkMDCQiEQi8sQTT5Dz5893mn0cQgjpHCnFYDAYDAaD0TmwHBwGg8FgMBguBxM4DAaDwWAwXA4mcBgMBoPBYLgcTOAwGAwGg8FwOZjAYTAYDAaD4XIwgcNgMBgMBsPlYAKHwWAwGAyGy8EEDoPBYDAYDJeDCRwGg8FgMBguBxM4DAaDwWAwXA4mcBgMBoPBYLgcTOAwGAwGg8FwOf4/4HLMz6JNS5AAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, y1[:,0], label=\"undamped\", linewidth=0.5)\n", "plt.plot(t, y2[:,0], label=\"under damped\")\n", "plt.plot(t, y3[:,0], label=r\"critical damping\")\n", "plt.plot(t, y4[:,0], label=\"over damped\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fourier transform\n", "\n", "Fourier transforms are one of the universal tools in computational physics, which appear over and over again in different contexts. SciPy provides functions for accessing the classic [FFTPACK](http://www.netlib.org/fftpack/) library from NetLib, which is an efficient and well tested FFT library written in FORTRAN. The SciPy API has a few additional convenience functions, but overall the API is closely related to the original FORTRAN library.\n", "\n", "To use the `fftpack` module in a python program, include it using:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from scipy.fftpack import *\n", "from numpy.fft import fftfreq" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To demonstrate how to do a fast Fourier transform with SciPy, let's look at the FFT of the solution to the damped oscillator from the previous section:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "# calculate the fast fourier transform\n", "# y2 is the solution to the under-damped oscillator from the previous section\n", "F = fft(y2[:,0]) \n", "\n", "# calculate the frequencies for the components in F\n", "w = fftfreq(len(t), t[1]-t[0])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.0999, 0.1998, 0.2997, 0.3996, 0.4995,\n", " 0.5994, 0.6993, 0.7992, 0.8991, 0.999 , 1.0989,\n", " 1.1988, 1.2987, 1.3986, 1.4985, 1.5984, 1.6983,\n", " 1.7982, 1.8981, 1.998 , 2.0979, 2.1978, 2.2977,\n", " 2.3976, 2.4975, 2.5974, 2.6973, 2.7972, 2.8971,\n", " 2.997 , 3.0969, 3.1968, 3.2967, 3.3966, 3.4965,\n", " 3.5964, 3.6963, 3.7962, 3.8961, 3.996 , 4.0959,\n", " 4.1958, 4.2957, 4.3956, 4.4955, 4.5954, 4.6953,\n", " 4.7952, 4.8951, 4.995 , 5.0949, 5.1948, 5.2947,\n", " 5.3946, 5.4945, 5.5944, 5.6943, 5.7942, 5.8941,\n", " 5.994 , 6.0939, 6.1938, 6.2937, 6.3936, 6.4935,\n", " 6.5934, 6.6933, 6.7932, 6.8931, 6.993 , 7.0929,\n", " 7.1928, 7.2927, 7.3926, 7.4925, 7.5924, 7.6923,\n", " 7.7922, 7.8921, 7.992 , 8.0919, 8.1918, 8.2917,\n", " 8.3916, 8.4915, 8.5914, 8.6913, 8.7912, 8.8911,\n", " 8.991 , 9.0909, 9.1908, 9.2907, 9.3906, 9.4905,\n", " 9.5904, 9.6903, 9.7902, 9.8901, 9.99 , 10.0899,\n", " 10.1898, 10.2897, 10.3896, 10.4895, 10.5894, 10.6893,\n", " 10.7892, 10.8891, 10.989 , 11.0889, 11.1888, 11.2887,\n", " 11.3886, 11.4885, 11.5884, 11.6883, 11.7882, 11.8881,\n", " 11.988 , 12.0879, 12.1878, 12.2877, 12.3876, 12.4875,\n", " 12.5874, 12.6873, 12.7872, 12.8871, 12.987 , 13.0869,\n", " 13.1868, 13.2867, 13.3866, 13.4865, 13.5864, 13.6863,\n", " 13.7862, 13.8861, 13.986 , 14.0859, 14.1858, 14.2857,\n", " 14.3856, 14.4855, 14.5854, 14.6853, 14.7852, 14.8851,\n", " 14.985 , 15.0849, 15.1848, 15.2847, 15.3846, 15.4845,\n", " 15.5844, 15.6843, 15.7842, 15.8841, 15.984 , 16.0839,\n", " 16.1838, 16.2837, 16.3836, 16.4835, 16.5834, 16.6833,\n", " 16.7832, 16.8831, 16.983 , 17.0829, 17.1828, 17.2827,\n", " 17.3826, 17.4825, 17.5824, 17.6823, 17.7822, 17.8821,\n", " 17.982 , 18.0819, 18.1818, 18.2817, 18.3816, 18.4815,\n", " 18.5814, 18.6813, 18.7812, 18.8811, 18.981 , 19.0809,\n", " 19.1808, 19.2807, 19.3806, 19.4805, 19.5804, 19.6803,\n", " 19.7802, 19.8801, 19.98 , 20.0799, 20.1798, 20.2797,\n", " 20.3796, 20.4795, 20.5794, 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-3.4965,\n", " -3.3966, -3.2967, -3.1968, -3.0969, -2.997 , -2.8971,\n", " -2.7972, -2.6973, -2.5974, -2.4975, -2.3976, -2.2977,\n", " -2.1978, -2.0979, -1.998 , -1.8981, -1.7982, -1.6983,\n", " -1.5984, -1.4985, -1.3986, -1.2987, -1.1988, -1.0989,\n", " -0.999 , -0.8991, -0.7992, -0.6993, -0.5994, -0.4995,\n", " -0.3996, -0.2997, -0.1998, -0.0999])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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C6ehxnPMB+BPhA4DrRna7pDec5j/nIxSg5wPwE8IHANfF08/vsBtOs0of6WEk5Ox2IXwAfkD4AOC6RK6ttllj0oNGKLXbha22gD8QPgC4LhZPDx/Ja9lFjfTn1UG78kH6APyA8AHAdbmPVzc5x0gj53zEWXUBfIHwAcB16T0f+Q4ZS39aFUo1nNLzAfgC4QOA6zLCh3JvtU3kaDiNsewC+ALhA4Dr0sOHc8hYgfBRHaLhFPATwgcA18USo3e7ZC+7pFdC7HM+aDgF/IHwAcB1GQ2nqd8y2Q2nJqPhNLXbhZYPwBcIHwBcl175UN6ej5E/O7tdqHwAvkD4AOC6RI6ej+xll8xDxjjhFPATwgcA1+Xq+chuOLWXXQJWcnlGInwAfkH4AOC6XJWP0YeMyRkT5N4ugK8QPgC4LpZxyFjhcz4si/AB+A3hA4Dr4mm7XfKdcJpIW3YJ2OEje20GQEUifABwXTx1Wlihu9raOSNgWSMnnLLXFvAFwgcA18XT+jny7XYZqXxYTsNp9hgAlYnwAcB19nkdhXa72O0dliWn5yNGzwfgC4QPAK6z79GS0XCaKFD5COQeA6AyET4AuC6Rs+E0a0wi7ZwPGk4BXyF8AHCd3TgaDKad86Eizvmg4RTwBcIHANelb7XN3/OR45wPKh+ALxA+ALguveHUynN0uhM+JA4ZA3yG8AHAdekNp3m32qaNCRE+AF8hfABwXXrlI98ZHvG03S720gxbbQF/IHwAcF1G5SNPVSOedv+XUCD5q4ittoA/ED4AuM6pfGTcNC5zjLMdN2AplT2ofAA+QfgA4Lp4WrAIOrtdsns+7N0uGql8sNsF8AXCBwDXpS+p2IeMZW+jzdiOS+UD8BXCBwDXpYePfNto03e7BNPOAqHvA6h8hA8ArovlCB+FdrvYyy7p1wFULsIHANfZ1Yv0E05HVz5GN5zmGgeg8hA+ALgud+Ujc8zIXW2VWfkgfAAVj/ABwHUZ22jtE07znPMRSAsoEk2ngB8QPgC4bjh1d9pQMG3ZJXurbdpul1Ba+KDyAVQ+wgcA18VSJ4pVBQJ5d7vYh44FUqeg2vkjln0aGYCKQ/gA4Dp76SQUHHu3i73NNhRM/joapvIBVLxxhY/Nmzfr6quvVkNDg+bPn69bbrlFb7zxRsYYY4w6OjrU2tqq2tparVq1SgcOHHB10gDKWyye3vNReLeL3Wvq3Nk2TvgAKt24wsfOnTu1bt067d69Wzt27FAsFtOaNWs0MDDgjNmyZYsefPBBbd26VXv27FFLS4tWr16tvr4+1ycPoDzFUieIVQUDTvjIv9slVflIhY/hBMsuQKULjWfw008/nfH88ccf1/z587V3715df/31MsbooYce0n333adbb71VkvTEE0+oublZ27Zt0xe+8AX3Zg6gbDkNpwHLCRn5drvYyzJVqWWXGJUPoOJNquejp6dHkjR79mxJ0qFDh9TV1aU1a9Y4Y8LhsFauXKldu3bl/BmRSES9vb0ZDwDTW67KR6HdLlKyP0SShmk4BSrehMOHMUb33HOPrr32Wi1evFiS1NXVJUlqbm7OGNvc3Oy8lm3z5s1qampyHm1tbROdEoAyEYvnaDjNs9vFcpZdAqnrVD6ASjfh8LF+/Xq98sorevLJJ0e9Zv8ysRljRl2zbdy4UT09Pc6js7NzolMCUCac3S6BgAKB3JUPZ7eL3XCaqnzE6PkAKt64ej5sX/ziF/XjH/9Yzz33nBYuXOhcb2lpkZSsgCxYsMC53t3dPaoaYguHwwqHwxOZBoAyZZ/VEQpaCsbtykfmGGMyez6chlN6PoCKN67KhzFG69ev11NPPaVf/OIXWrRoUcbrixYtUktLi3bs2OFci0aj2rlzp1asWOHOjAGUvfSG05HdLnmOV7doOAX8ZlyVj3Xr1mnbtm3653/+ZzU0NDh9HE1NTaqtrZVlWdqwYYM2bdqk9vZ2tbe3a9OmTaqrq9Ntt93myf8AAOXHDhZVwYACgXjGtewxduXD/sqyC1D5xhU+HnnkEUnSqlWrMq4//vjj+uxnPytJuvfee3X27FndfffdOnPmjJYtW6ZnnnlGDQ0NrkwYQPmzA0QoaDm7WfLtdglknXBK5QOofOMKH8aM/UvBsix1dHSoo6NjonMCMM2NLLsExtzt4iy7UPkAfIN7uwBwndNwmrppnJT/hNPs3S40nAKVj/ABwHXDaTeWG+veLqNOOKXyAVQ8wgcA16U3nAbz7XZJPbfPAHIaTql8ABWP8AHAVcYYJ3wkl12S1/NWPrJOOI1xwilQ8QgfAFyV3rMRCqY1nOY94dRedrErHyy7AJWO8AHAVek9G6GAlbbskjnOfp691ZaGU6DyET4AuCp92SQUtJyejvwNp6mxgdzjAFQewgcAV6U3jFYVPOcj65Ax+94u7HYBKh7hA4Cr7J6NgCUFAvlPOLWf2+eAcMIp4B+EDwCuGjnjI/nrpdjdLjScAv5B+ADgquFYMjxUp8LHWLtd7MqHPT5C+AAqHuEDgKuGU+GhOpSqfIyx28WufNjjozHCB1DpCB8AXBVJhQd7GWWs49VThQ8nfEQIH0DFI3wAcFV25cNedpEyd7w4u11Sr4dDQUlUPgA/IHwAcFXUqXykwoc1Ej7Sd7xkn3DKsgvgH4QPAK6yTyitztrtImUuvWTvdiF8AP5B+ADgqmg8LmkkTITS0kcio/KR/Bp0ll3sno94KaYJYAoRPgC4KhrLrHyk93zEMno+khWOUDAzfETZagtUPMIHAFfZ4cHu+QilhY942uml9kmmwaxzPlh2ASof4QOAq5xDxuxzPgKW7J7TWI7dLnY4CVex1RbwC8IHAFdlVz6k3HesjTl3tU2Oqw6y1RbwC8IHAFeNnPMxstxiL63E0u5Ym135YLcL4B+EDwCuimbd20Ua2fGSWflIjss+54NlF6DyET4AuCrXsstI5aNAzwfhA/ANwgcAV0WzGk6lsXo+spddOOcDqHSEDwCuGi5U+YjnqHwEM7faUvkAKh/hA4Cr7MpHOEflI73hdOScj+Q4e6ttNJ6QMZl3wAVQWQgfAFyVfWM5SQoGi+j5SG21NSZzHIDKQ/gA4Cp72aSmamK7XdJ/BoDKRPgA4KqIs+wSdK4V7PnIET446wOobIQPAK4aGk7uVsmsfOTf7RJKuwGdPY7wAVQ2wgcAVxWsfBQ44VTilFPALwgfAFwVSZ3TES6y8hFMCx8jB41x1gdQyQgfAFw1NFyo8pG/50PiiHXALwgfAFyVu/KRY7dLPHO3i5S27BInfACVjPABwFWR4dGHjBWufIyMc045HSZ8AJWM8AHAVUMxe7fLyLKLfYR6PP2EU7vnI5je85H8HiofQGUjfABwVcHKR4FzPiR2uwB+QfgA4KqRcz7SKh9Zu12MMTl3u1Sz2wXwBcIHAFdFctxYLrvnI/3WLaEcW22pfACVjfABwDXGmJyHjGXvdkk/bCzXOR+ED6CyET4AuCb9fI7049WzKx/pW27Td7uEU0s1Z4dZdgEqGeEDgGsGoyOhoa465Px5pOcjGU7St9ymVz7qq4Ojfg6AykP4AOAau2JRHQpkhIpRlY94euVjZJwdWAajMc/nCmDqED4AuOZsKjTUpu10kUbO+RiOJUPHcKoCYllSICN8UPkA/IDwAcA1dmiwQ4StKnVyqd1oOpyqfNjXbfXhVOUjQvgAKhnhA4BrzqbCR22e8GGHDvu+LtVZ4cMOLQMsuwAVjfABwDWDqZ6PvMsu8UTG11Da0eqSVO/0fFD5ACoZ4QOAa87mWXapdiofydARjeVedqkLpyofESofQCUjfABwzaCz7BLKuD5q2SWRe9nFrnxwzgdQ2QgfAFxjh4a6qnw9H5nLLlVZyy52rwiVD6CyET4AuMbZajuq4TSz58NedgnlqXzQ8wFUNsIHANf0R8bYaptadhmpfNDzAfgR4QOAa/qHkqGhoaYq47odMqJx+3h1u+eD3S6AHxE+ALimPzIsSWqoyW44zb3skq/yEUsY7mwLVDDCBwDX9DmVj9y7XbKXXbLP+UhvVOX+LkDlInwAcE1/pHD4iI7a7ZL5KygUDKg6lLw2wNILULEIHwBc05uqfMwIZ/d8ZC672BWQ7HM+JKnevrkcTadAxSJ8AHBN/1Cy52NGuPCySzTPsosk1aWaTql8AJWL8AHANWP1fIw+ZCxH5SPVdErPB1C5CB8AXJO/5yNZ4YgWseziVD4iVD6ASkX4AOCKeMI453OMOucjlHvZJVflww4uvWeHPZsrgKlF+ADgCvuAMSlHz0cg97JLrp6PptpkcOkhfAAVi/ABwBV9qQPGwqGR7bK2qlDmbpdCPR8z65Lh4z3CB1CxCB8AXJGv2VRKO+cjZocP+4TT/JUPll2AykX4AOAKu9k0e8lFSlZDpJFeDzuE1FQFR41l2QWofIQPAK7Id1M5SQqHkiEjEkvIGKNILJ66nmPZpbZakvTeYNSrqQKYYoQPAK7ozXPAmCSFq5K/aoxJLrlEhpOVDzuUpGuk8gFUvHGHj+eee04333yzWltbZVmW/umf/injdWOMOjo61NraqtraWq1atUoHDhxwa74AypQdFuxlk3TpFY5ILK5IatnFDiXp7O+n4RSoXOMOHwMDA7riiiu0devWnK9v2bJFDz74oLZu3ao9e/aopaVFq1evVl9f36QnC6B8nepPLpPMnlE96rX0w8QisUThZZc6Gk6BSje6PjqGtWvXau3atTlfM8booYce0n333adbb71VkvTEE0+oublZ27Zt0xe+8IXJzRZA2TqT6tGYUz86fFiWpXAokAoeiZHKR45ll/SGU2OMLGv0jhgA05urPR+HDh1SV1eX1qxZ41wLh8NauXKldu3alfN7IpGIent7Mx4App9TA8nwMatudPiQRqockeF4Ws9H/srHcHzkxFQAlcXV8NHV1SVJam5uzrje3NzsvJZt8+bNampqch5tbW1uTglAiZxJhY85OZZdJClcNbLjxVl2ydHzUVsVdM7/oOkUqEye7HbJLpMWKp1u3LhRPT09zqOzs9OLKQHw2OliKx9jLLtYljXSdDpI+AAq0bh7PgppaWmRlKyALFiwwLne3d09qhpiC4fDCofDbk4DwBSwl11m5+j5kLKWXWL5l12kZIA52R91+kgAVBZXKx+LFi1SS0uLduzY4VyLRqPauXOnVqxY4eZbASgjxpixl13SDhqLDMczrmWb15D8B8m7fRG3pwqgDIy78tHf368333zTeX7o0CHt27dPs2fP1rnnnqsNGzZo06ZNam9vV3t7uzZt2qS6ujrddtttrk4cQPnoHYoplkjeryXvsktVjmWXHD0fEuEDqHTjDh8vvPCCbrjhBuf5PffcI0n6zGc+o+985zu69957dfbsWd199906c+aMli1bpmeeeUYNDQ3uzRpAWbGrHvXVwZz3a5HSez7GXnaZNyMVPvoJH0AlGnf4WLVqlYwxeV+3LEsdHR3q6OiYzLwATCPONts8/R7SyBLL0PDIbpfqfOGDygdQ0bi3C4BJO5mqUMyZkb95vDZVEekfGtZw3GRcy0b4ACob4QPApHX1DEmSFjTW5B1TF04GjZP9IztY6qpzF18JH0BlI3wAmLSu3mT4aGnKHz7qU0HDDhRVQWvsZRd6PoCKRPgAMGl25aNQ+KirTlY+7ECRr+ohjTScnh6IajiecGuaAMoE4QPApDnLLgXDRzJsnHTCR+5+Dym5XTcUsDLGA6gchA8Ak2YvuzQX6PmoT/V82MsuhcJHIGA5P+vYe2fdmiaAMkH4ADApxhgd70kGhEKVj9pqu+E0GT7qw4V3+i+cVStJOnqG8AFUGsIHgEnpPRvT0HCyL6Ng5SO17GJvsy1U+ZCkcwgfQMUifACYlGOpqsesuqq8p5tKo8NGfYGGU0laOKtOEuEDqESEDwCT8vapQUnSubPrCo7LXmapHaPysXBmsvLxDj0fQMUhfACYlCOnByRJ582pLziuqbYq4/nMuqo8I5NGej4GJzE7AOWI8AFgUg6nKh/nzSlc+ci+70u+u9/a7J6Pd86cLXg/KQDTD+EDwKS8faq4ysesrErHWOGjdWatQgFLkVjC2coLoDIQPgBMit3zcf4YlY/aqqDCacepzy5wB1xJqgoGdG7qZ77VPTDJWQIoJ4QPABMWjSWcQ8DOHSN8WJaVETiyl2FyuXDeDEnSW+/2T2KWAMoN4QPAhB06OaCEkWaEQ879WAqZmbbUMofwAfgW4QPAhL3e1StJuqSlQZZljTn+kuYZzp8vmj+jwMikC+cl+0gIH0BlIXwAmLCDJ/okSRc3NxQ1/rr2eZKkK8+dWfBAMtuFqYDyZjfhA6gkhY8YBIAC3uhKho9LW4oLH5e0NOjPr1005rZcmx1qTvRGdHogOmaTKoDpgfABYMJe7xpf5WPxOU1afE5T0T9/RjikRXPrdejkgA4c63EqJwCmN5ZdAExIz+Cwc9+VYisfE3F5a6Mk6dV3ej17DwClRfgAMCGvvPOepOTJpsVsm52o96XCx4FjPZ69B4DSInwAmJB9R96TJF2xcKan77O4NblM88pRwgdQKQgfACbk5aPvSZKuaJvp6ft84NyZCljSkdOD6urhmHWgEhA+AIybMUYvpSofH2grvoF0Ihprqpy+j98cPu3pewEoDcIHgHE7eKJfpwaiqqkKjGv3ykRdc/4cSdJvDp3y/L0AeI/wAWDcfvXWSUnS0vNmKxwa+7Cwybpm0WxJ0m8OUfkAKgHhA8C4/er3yQrE8gvnlOT9rj5/lqRkxeX0QLQk7wnAO4QPAOMSicX1728mw8eHLppbkvecMyPsnCWy82B3Sd4TgHcIHwDGZffvT6s/EtP8hrCWlKDfw7b68mZJ0o7XTpTsPQF4g/ABYFyeOdAlSbrxsmYFAmPfydYtdvjY+ca7GhqOl+x9AbiP8AGgaImE0c9/m6w8rEmFgVJ5/zlNamms0UA0rl+9xa4XYDojfAAo2t4jZ3SiN6L66mDJmk1tlmU51Y///cqxkr43AHcRPgAU7X/u6ZQk/dH7F6imyvstttlu+YNzJEk/3d+lvqHhkr8/AHcQPgAUpT8S07/sPy5J+sTVbVMyhyvPnakL59Xr7HBc//LK8SmZA4DJI3wAKMr/efmYBqNxLZpbr6XnzZqSOViWpU8sTQafJ1NVGADTD+EDwJgSCaNvP/97SdKnrm6TZZVul0u2W69cqOpgQC93vqc93OsFmJYIHwDG9K+vd+utdwfUEA7p08vOndK5zGsI62NXJXs/vrXzrSmdC4CJIXwAKMgYo2/825uSpNs/eJ4aa6qmeEbS56+7QJYl/fy33XrtWO9UTwfAOBE+ABT001e7tK/zPdVWBfVn154/1dORJF0wb4Zuev8CSdIDT78+xbMBMF6EDwB5RWMJbUn95f756y/Q/IaaKZ7RiP/y0UtUFbT03MF39dzBd6d6OgDGgfABIK9Hnn1Lh08Nau6MsL5w/QVTPZ0M582p139afr4k6f/+51c1GI1N7YQAFI3wASCngyf6tPXffidJuv/my1UfDk3xjEbb8JF2tTbV6O1Tg/rqz96Y6ukAKBLhA8Aog9GY1m97UcNxo49cNl//YcmCqZ5STg01Vdr8sSWSpO/sOqxdb52c4hkBKAbhA0AGY4z+649e1cET/ZrXENamW98/ped6jGXlxfP0yaVtMkZav+0lvfPe2ameEoAxED4AZPh/nz+kp156R8GApa2f/oOyajLNp+OP36fLFzTq9EBUX/juC/R/AGWO8AHA8cO9R/WVn/xWkrRx7aVadkFp71w7UbXVQX3rjqs0q65Kr77Tq//8P/ZqaDg+1dMCkAfhA4Ak6akXj+reH74iSfr8dYv0uWsXTfGMxqdtdp0e++zVqqsO6pdvntTd/9+LBBCgTBE+AJ8zxuixXx7SPf/zZcUTRp9YulAb115W1n0e+Vx57iw99pmrFQ4F9IvXu3Xbt3fr9EB0qqcFIAvhA/CxoeG4/ssPXtF/+z+vSZL+rw+drwduXaJAYPoFD9vyC+fof/zZNWqsCenFI+/pY4/s0htdfVM9LQBpCB+AT73Z3a+Pf/NX+sHeowpYyR6P/+c/XD6tg4dt2QVz9NTdK3TOzFodOjmgP976S2379REZY6Z6agAkWabM/t/Y29urpqYm9fT0qLGxcaqnA1ScWDyhx355SF/bcVDRWEKz6qq09bYr9aGL5k711Fx3qj+iv/xfL+vZN5LHr99wyTz97Z8sVtvsuimeGVB5xvP3N+ED8JFn3+jWV/7lt/pdd7+k5BkZD3zs/VrQVDvFM/NOImH07ed/r689c1DReEK1VUHdvepCfe66RaqrLr9TW4HpivABIMOew6f13//1d3r+d8kTQGfVVWnj2sv08aULp2Vj6US82d2v+360X78+dFqSNHdGWH9x40X6xNI21VQFp3h2wPRH+ACgeMLo317v1jd3vqUX3j4jSaoKWvrsivO1/oZ2NdVVTfEMS88Yox+/fExfe+agjpwelCTNnVGtOz54vv70g+dqzozwFM8QmL4IH4CPHTk1qP+1t1M/2HtUx3uGJEnVwYD+49KFuvP6C3XuHPodorGEvr/niB559i0dsz+jUEBrF7fo1isX6tqL5ipYAY23QCkRPgCfOXpmUD87cEI/e7VLvzl82rk+s65Kn7y6TZ/70CLNbyz/Y9JLbTie0E9f7dJjz/9eLx/tca7Pbwjrj69o1UcXt+jKc2cRRIAiED6ACheNJbSv8z39+5sn9fPfntCBY73Oa5YlXXvRXH1iaZvWvK9Z4RD9DGMxxuiVoz166sWj+vHLx3RmcNh5bVZdlW64dL5uvLRZyy+co9n11VM4U6B8ET6ACjMQienVd3r04pH3tOutk3rh8BmdTTs6PGBJS8+frY++r0V/uLhF58ys3N0rXovGEvrF6916+tXj+rc33lXP2eGM1y9pbtAHL5itD14wR1edN4uKEpBC+ACmsYFITG929+vAsV693PmeXj76ng6e6FMi6/+pc+qrtfzCObq+fZ5uvGw+zZIeiMUTeuHtM/rX357QzoPv6uCJ/lFjmhvDev85TXr/OTO1ZGGT3ndOo+bNCPtmFxFgI3wAZc4Yo56zw3r71KDe7O7Xwe4+/e5Evw6e6NPRM2dzfk9LY42WLGzSBy+YoxUXzdElzQ38BVdip/oj+s2h0/r1odPa/ftTOUOhlOy1aZ8/QxfNb1D7/Blqb56hC+bNUEtjDf0jqFiED2CKGWPUOxRTd++QjvcMqfPMoI6cGtSR0yOPvqFY3u+fOyOsS1sadEVbk65YOFNXtM1UM+X9sjMYjem1Y7165WiPXn2nR6+806O33u1Xvt+qVUFL58ysVdvsOrXNrtO5s+vUNqtObbNr1dJYozkzwoQTTFvj+fub4/2AcYjGEjozGNWp/qhOD0R1ejCqd/siOtE7pK6eIZ3otR+RjJ6MfOY1hHXhvHpd3Nyg9uYGXTx/hi5ubtAsmhqnhbrqkJaeP1tLz5/tXBsajuv37w7od919erO7P1nR6u7TkVODGo4bHT41qMOnBnP+vICV/G+ipbFG8xtr1Nw48ud5M8KaVV+tOfXVmlVfrfrqIJUvTFuED/hOPGHUH4mp9+yw+oZi6htKfu0dGnneOxRLhou0x5mBqPoi+asVuTTVVqmlsUZts2udf+naj4Wz6lRbzU6USlNTFdTlrY26vDXzX37xhFFX75COnBpU55lBdZ5OPo6cHtQ7753Vu30RJYx0ojeiE70RST253yClOhTQ7LrqjEAyp75ajbVVaqwJqbGmSg01ITXWJr821CSvN9RUqTrEPUUxtQgfKFvxhFE0ltDQcFyDw3GdjcY0GI1rMBrX2dTXwWhMZ4fjaddjGnBejzlj00NF/zgDRLaAJc2ur9asumrNrq/W3NS/VJsbw2purFFLY41ammo0v6GGcAFHMJBccjlnZq2Wa86o1+MJo5P9EadyNlJFG1JXb0SnByI63R/VqYGoIrGEorGEunqH1NU7NO651FQFnDAyIxxSXXVIddVB1VYHVV8dUm11UHXVQdWHQ6qtSv65LhxSXVVQdeHgyPiqoMKhgMKhoMJVAVUHAxVxV2R4j/DhM8YYDceNYomEhuNG8YRRLJ7QsP019VosbhTLvpYwyetp451xqZ+XHJ9wfjlGnEfceR5NPU8fE80xJpark89F4dDIL+CGWvtfhSE1hKvUWBvSrPrq3P+yrKniFyxcFwxYam6sKaq3ZzAaS1XjhnVqIKIzg1GdHhjW6YGIepyK3kh1z67q2cF7aDihoeGI3u2LuP6/ozoUGAkkoYDCVWl/DgUUrhr5c03qz1XBgKpDAYUClkLBgKqDya9VwYCqgpZCgeTXqtS1UNBSdeprKBBQdcgeMzIulPoasCwFA5aClqVgMPk1EJBCgYAClli6miK+Ch/PHOjSf/7u3qmeBkqkOhhw/gVnl6Dt8nNDTahg6TmWMHq3z5tfzoCXqoIBza6vznkYWiJh1BfJDCYD0ZgGIqnK4nA8b7NssaKpfzz0aXIVRnjriT+7Risvnjdl7+9Z+Hj44Yf11a9+VcePH9f73vc+PfTQQ7ruuuu8ersxGWP0Vz98ZcreH6UXjScUPZtQz9lh5x4nAADpv/7Tfj1/74en7P09CR/f//73tWHDBj388MP60Ic+pG9961tau3atXnvtNZ177rlevOWYLMvSf//0H+iOx34zwe+XrNTPsVLPJclS8gXLGWPlHC9nfPJaMGApYFkKWBr5c0CpkmDyedCyZKVeDwas5Pelnlup15N/llNWTP5spX5eqsRoyfmZdgnTLkkm33tSHy0AlC1jpISREia5zOw8jFEikVw2TqSep79uj4+l/TmRkGKJhOImWUXK/llGyX/oJoxklByv7GsmOSdjkuMTxqTmaKTUV+PMe+RnmqzXJuur//GKyf+QSfDknI9ly5bpyiuv1COPPOJcu+yyy3TLLbdo8+bNBb+Xcz4AAJh+xvP3t+v7raLRqPbu3as1a9ZkXF+zZo127do1anwkElFvb2/GAwAAVC7Xw8fJkycVj8fV3Nyccb25uVldXV2jxm/evFlNTU3Oo62tze0pAQCAMuLZSTPZ25eMMTm3NG3cuFE9PT3Oo7Oz06spAQCAMuB6w+ncuXMVDAZHVTm6u7tHVUMkKRwOKxzmbpwAAPiF65WP6upqXXXVVdqxY0fG9R07dmjFihVuvx0AAJhmPNlqe8899+iOO+7Q0qVLtXz5cj366KM6cuSI7rzzTi/eDgAATCOehI9PfvKTOnXqlP72b/9Wx48f1+LFi/WTn/xE5513nhdvBwAAphFPzvmYDM75AABg+pnScz4AAAAKIXwAAICSInwAAICSInwAAICSInwAAICS8mSr7WTYm2+4wRwAANOH/fd2MZtoyy589PX1SRI3mAMAYBrq6+tTU1NTwTFld85HIpHQsWPH1NDQkPNGdH7T29urtrY2dXZ2cu6Jh/icS4fPujT4nEuDz3mEMUZ9fX1qbW1VIFC4q6PsKh+BQEALFy6c6mmUncbGRt//h10KfM6lw2ddGnzOpcHnnDRWxcNGwykAACgpwgcAACgpwkeZC4fDuv/++xUOh6d6KhWNz7l0+KxLg8+5NPicJ6bsGk4BAEBlo/IBAABKivABAABKivABAABKivABAABKivAxDUQiEX3gAx+QZVnat29fxmtHjhzRzTffrPr6es2dO1d/8Rd/oWg0OjUTnYYOHz6sz33uc1q0aJFqa2t14YUX6v777x/1GfI5u+Phhx/WokWLVFNTo6uuukrPP//8VE9pWtu8ebOuvvpqNTQ0aP78+brlllv0xhtvZIwxxqijo0Otra2qra3VqlWrdODAgSmacWXYvHmzLMvShg0bnGt8zuND+JgG7r33XrW2to66Ho/HddNNN2lgYEC//OUvtX37dv3whz/UX/7lX07BLKen119/XYlEQt/61rd04MAB/cM//IO++c1v6stf/rIzhs/ZHd///ve1YcMG3XfffXrppZd03XXXae3atTpy5MhUT23a2rlzp9atW6fdu3drx44disViWrNmjQYGBpwxW7Zs0YMPPqitW7dqz549amlp0erVq537aGF89uzZo0cffVRLlizJuM7nPE4GZe0nP/mJufTSS82BAweMJPPSSy9lvBYIBMw777zjXHvyySdNOBw2PT09UzDbyrBlyxazaNEi5zmfszuuueYac+edd2Zcu/TSS81f//VfT9GMKk93d7eRZHbu3GmMMSaRSJiWlhbzwAMPOGOGhoZMU1OT+eY3vzlV05y2+vr6THt7u9mxY4dZuXKl+dKXvmSM4XOeCCofZezEiRP6/Oc/r+9+97uqq6sb9fqvfvUrLV68OKMq8tGPflSRSER79+4t5VQrSk9Pj2bPnu0853OevGg0qr1792rNmjUZ19esWaNdu3ZN0awqT09PjyQ5//0eOnRIXV1dGZ97OBzWypUr+dwnYN26dbrpppv0kY98JOM6n/P4ld2N5ZBkjNFnP/tZ3XnnnVq6dKkOHz48akxXV5eam5szrs2aNUvV1dXq6uoq0Uwry1tvvaWvf/3r+trXvuZc43OevJMnTyoej4/6HJubm/kMXWKM0T333KNrr71WixcvliTns831ub/99tsln+N0tn37dr344ovas2fPqNf4nMePykeJdXR0yLKsgo8XXnhBX//619Xb26uNGzcW/HmWZY26ZozJed1Piv2c0x07dkx/+Id/qI9//OP68z//84zX+Jzdkf158Rm6Z/369XrllVf05JNPjnqNz31yOjs79aUvfUnf+973VFNTk3ccn3PxqHyU2Pr16/WpT32q4Jjzzz9ff/d3f6fdu3ePul/A0qVLdfvtt+uJJ55QS0uLfv3rX2e8fubMGQ0PD49K4H5T7OdsO3bsmG644QYtX75cjz76aMY4PufJmzt3roLB4KgqR3d3N5+hC774xS/qxz/+sZ577jktXLjQud7S0iIp+S/zBQsWONf53Mdn79696u7u1lVXXeVci8fjeu6557R161ZnhxGf8zhMYb8JCnj77bfN/v37ncfPfvYzI8n84Ac/MJ2dncaYkUbIY8eOOd+3fft2GiHH6ejRo6a9vd186lOfMrFYbNTrfM7uuOaaa8xdd92Vce2yyy6j4XQSEomEWbdunWltbTUHDx7M+XpLS4v5+7//e+daJBKhEXKcent7M34f79+/3yxdutT86Z/+qdm/fz+f8wQQPqaJQ4cOjdrtEovFzOLFi82NN95oXnzxRfPzn//cLFy40Kxfv37qJjrNvPPOO+aiiy4yH/7wh83Ro0fN8ePHnYeNz9kd27dvN1VVVeaxxx4zr732mtmwYYOpr683hw8fnuqpTVt33XWXaWpqMs8++2zGf7uDg4POmAceeMA0NTWZp556yuzfv998+tOfNgsWLDC9vb1TOPPpL323izF8zuNF+JgmcoUPY5IVkptuusnU1taa2bNnm/Xr15uhoaGpmeQ09PjjjxtJOR/p+Jzd8Y1vfMOcd955prq62lx55ZXOllBMTL7/dh9//HFnTCKRMPfff79paWkx4XDYXH/99Wb//v1TN+kKkR0++JzHxzLGmClY7QEAAD7FbhcAAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBShA8AAFBS/z+6nuPrjWeDHwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(w, abs(F));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Properties of Fourier transform of a real signal:\n", "\\begin{eqnarray}\n", "&& F(\\omega) = \\int e^{i\\omega t} x(t) dt\\\\\n", "&& F^*(\\omega) = F(-\\omega)\\\\\n", "&& Re(F(\\omega)) = Re(F(-\\omega))\\\\\n", "&& Im(F(\\omega)) = -Im(F(-\\omega))\n", "\\end{eqnarray}" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-2.0, 2.0)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+mpCQEDZt2oSiKLz88ss8+eSTXHfddaSnp/Puu+9SU1PD+++/78ywhBuyNeZLd2F9jU1ksJEeseq+VNtkewUhziqvvJacslr0OhicGuHyx7ctLrBNXQtxKpfV2FgsFhYvXkx1dTWjR48mIyOD/Px8Jk+ebL+NyWRiwoQJbNiw4YzHMZvNVFRUtDoJz+fKrRTaItNRQpyfbcfLAOiXGEawyc/lj28fscmTERvRNqcnNrt37yYkJASTycS9997L0qVL6d+/P/n5+QDEx8e3un18fLz9d22ZP38+4eHh9lNqaqpT4xeuYXuTcuWKqJYksRHi/Nj3h9JgGgqat1vJLqmlvKZBkxiEe3N6YtOnTx927NjBpk2buO+++5g5cyb79u2z/16na11RryjKade19Pjjj1NeXm4/ZWdnOy124RrlNQ32Fulaj9jsPFFGg8WqSQxCeAIt62sAIoKMpEQGAjJqI9rm9MTGaDTSs2dPRowYwfz58xk8eDD/+Mc/SEhIADhtdKagoOC0UZyWTCaTfZWV7SQ8m+3NKSUykPAgf01i6B4TQnigP3UNVvbnyfSmEG2prbfYp42HuXhFVEu2kd19sjJKtMHlfWwURcFsNpOWlkZCQgLLly+3/66+vp7Vq1czZswYV4clNLRPg8Z8p9LrdQyTfaOEOKtdJ8potCrEhZrsoyZaGCCN+sRZODWxeeKJJ1i7di2ZmZns3r2bJ598klWrVnHrrbei0+mYO3cuzzzzDEuXLmXPnj3MmjWLoKAgpk+f7sywhJtpXhGlzTSUzYimnb4lsRGibVubVg2O6BZ51pIBZ7NtrWB77xCiJaeWtJ88eZIZM2aQl5dHeHg4gwYN4rvvvuOyyy4D4NFHH6W2tpbZs2dTWlrKyJEjWbZsGaGhoc4MS7gZ+4qoZG2nFW1D69sksRGiTba/DS2noaB5xOZoYRW19RaX974S7s2pic2///3vs/5ep9Mxb9485s2b58wwhBurrbdwtFDdfFKrwmGbwanhGPQ6csvryC2rJSlCu6F2IdyNoiia7OjdlrhQEzEhRoqq6jmQX8FQjRMt4V5kryihqf35FVgViAkxERdq0jSWIKMf/RPVUSNp1CdEaxlF1ZTWNGD002v+JUSn09lj2CN1NuIUktgITbXc0VvLOXsb6WcjRNtsfxODU8Ix+mn/0dG8MkrqbERr2v/vFD7N9qak5YqoloZ1lTobIdpiG8UcpvE0lI2sjBJnIomN0JRtv5f0ZG2Htm1sIzZ7cyuoMjdqHI0Q7uPnDLXjsNaFwza2lVEH8iqlqaZoRRIboZkGi5WD+epO7u4yYpMcEUi36CAarQrrjxRpHY4QbiG7pIajhdUY9DpGpUVrHQ4AqZFBhJr8qLdYOVJQpXU4wo1IYiM0czivDJOlilCTgdTIIK3DsZvYJw6AVQcLNI5ECPdg+1sY3iVSs+7gp9LrdfRLkn424nSu35pVeK/Gejj4DVSdhLoKMJc3/axo82f/hmp2B8CmgPHo9VO0jt5uUt843tmQycoDhefcu0wIX7DyYCEAE/vGahxJa4OSw/k5o4RdJ8q5cYRsiCxUktgIx1AU+PA2OPx9u+96gXkD1NeA0T1GbUamRRHgrye/oo4D+ZX0S3SPaTIhtFDXYGHDUXVadlLTaKa7GJwaAaib1wphI4mNcIyf3lSTGoMJ+kwBUxgEhDf9DGvz583/2c8/y+4njjLI2wldR2v9LAAI8DcwtkcMPx4oYOXBAklshE/bdKyYugYrieEB9E1wr67wQ5oSm/15FdQ1WAjwlw7EQhIb4Qj5e2D5H9Xzlz8NF959zrvU1DeyufAg2w09udywBXK2uE1iA+p01I8HClh5oIDZE3tqHY4Qmll5QK2vmdgnzu2mZVMiA4kKNlJSXc/+POlALFRSPCw6p74GPvkVWOqh9xVwwV3ndbe9uRVYrAqH/fuoV5zY7MQg229iH7WWYOvxUsprGjSORghtKIpir6+Z1Me96mtA7UA8OEVtFbEzu0zbYITbkMRGdM73T0DRQQhJgKtfhfP8Rmd7E6qNH6ZecWKrkwLsmJTIIHrHh2BVYM3hQq3DEUITx4qqySqpwd+gY2zPGK3DaZOtzmbXCVkZJVSS2IiO2/8lbF0E6ODaNyD4/Ptb7Gx6EwrvcSHo9FBxAirynBRox9gKJVfKsm/ho2zTUCPTogk2uWflgi2x2SEFxKKJJDaiY8pz4IsH1PNjH4Qek9p1d9uITf+uSRDXX70yZ4sDA+w8Wz+b1QcLsVoVjaMRwvVW2ZZ5u+E0lM3glAgAjhVWU14r08ZCEhvREVYLLL0HakshaShM+kO77l5SXU9WSQ0AA1PCIWWE+gs3q7MZ0S2SUJMfxdX17JIGYMLHVJsb+SmjGICL+7rXMu+WooKNdIlSW0XslukogSQ2oiPWvQSZa8E/GK7/N/gZ23V3W8+J7rHBhAf6Q7ItsXGvERt/g57xvdW6AtuQvBC+Yt2RIhosCl2jg0iLCdY6nLOSfjaiJUlsRPuc2AIrn1HPT30Bonu0+xC2aaghTUPIpFyg/szdDhb32nhStlcQvsr2f36SGy7zPpVtZdQOWRklkMRGtEddhbq0W7FA+vUw+JYOHcaW2Ni+ZRHTW23c11ADBfscE6uDTOyt1hbsPFFOYaVZ42iEcA1FUVh5wP3ra2xsjfp2ZJehKFIP5+sksRHn7+tHoOw4RHSBq14676XdLSmKYl8RZU9s9HpIblr27WYFxHFhAaQnq52H1xySZd/CNxzIryS/oo4Afz2jurvHbt5nMyApHINeR2GlmfyKOq3DERqTxEacn50fwu6PQGeA6/6lbpfQASdKaymprsffoKNfYov27LbpKDers4HmZd8rZDpK+Ahbi4MxPWI8YpuCQKOBPvHq+4k06hOS2IhzKzkGXz+snp/4e+gyssOHss2B908Mw+TX4g0z2T1XRoG6vQKoIzaNFqvG0QjhfKuapqEmufFqqFPZ+9lky8ooXyeJjTg7SwMsuQvqq6DLGBj/SKcOd1p9jY1tyXfRIagt69RjONrglAgig/yprGtkW1aZ1uEI4VTlNQ1szSoFmmvMPMGQVNlaQagksRFnt/IZyNmqTj1dtxD0nRuWti3HtDXVsguOgcg09XyOe22vYNDrmND0Bi9diIW3W3O4EItVoVdcCKlN/WE8ge3L0u6ccizSUNOnSWIjzixjjdqzBmDaPyEitVOHa7RY2Z1zSuFwS7ZRGzdLbKB5SF762QhvZ0vePWkaCqBXXChBRgNV5kaOFVZpHY7QkCQ2om3VxfDprwEFht0OA67p9CEPnayirsFKqMmP7m01/LIXELtfnc1FvWLR69TVIrlltVqHI4RTWK0Kqz1gG4W2GPQ60pOln42QxEa0xWpVt0yozFN7zEx51iGHtU1DDUoNR69vY6l4yw7EbtaLIjLYyNAukUDz/jlCeJvdOeUUV9cTYvLjgm5RWofTbkOkA7FAEhvRlo0L4Mhy8AuAGxaB0THt1O2Fw6fW19gkDASDCWpL1JVYbmZSH6mzEd7N9n97fK8Y/A2e9/Fge2/ZKSujfJrn/c8VznViC/z4Z/X8lGchId1hh7YNDw86U2LjZ4TEQc1xuBnb9grrjxRhbrRoHI0QjmerIbP1bvI0g5q2VtifV0Fdg/yN+ipJbESz2lL4+A6wNsKAa2H4LIcduqa+kcMFakHfkLYKh21sdTZu1oEYYEBSGHGhJmrqLWzOKNU6HCEcqrDSbO8KPsHD6mtsUiIDiQ420mhV2J9XoXU4QiOS2AiVosAXD0B5FkR2g2n/6NCWCWeyN7cCi1UhPsxEQnjAmW+Y4r6N+nQ6nb2gcoWsjhJexrZlyICkMOLDzvI36sZ0Ol3zTt9SQOyzJLERqs3/gv1fgt5fravp4JYJZ3LO+hobWwFx/m5ocL/VR5Nkt2/hpVYe9OxpKBt7nc0JqbPxVZLYCMjbCd8/oZ6f/NfmDSkdaMeZOg6fKqILBMep02F5uxweR2eN6xWDn17HsaJqMouqtQ5HCIdotFjtIzae1r/mVIOlA7HPk8TG15kr1boaSz30uRJG3uuUh7EtvzxrfQ2o01/2Rn3uV2cTGuBvXwYrozbCW2zPLqOirpGIIP9z/426OduIzbGiasprGrQNRmhCEhtfpijw1W+g5CiEpcDVrzq0rsamuMpMdok6rTQw5TymuNy4zgZgUl/bsm/pZyO8g61mbELvWAxt9ZjyIJHBRrpGq1tB7Mop0zYYoQlJbHzZ9vdg98egM8AN/4Yg5zTk2tU0190jNpiwAP9z38Hegdj9RmyguQZh47FiautlSanwfJ6+zPtUzf1syjSNQ2hDEhtfVbAfvvmdev7iP0CXUU57qPOur7FJGgrooDwbKvOdFVaH9YwLITkikPpGKxuOFmkdjhCdkldey4H8SnQ6uMiDdvM+G9t7zQ5p1OeTJLHxRfU18PEsaKyFHhfD2LlOfbjzrq+xMYVCXH/1vBuO2uh0uhbTUVJnIzybbYuQIakRRAUbNY7GMYakNu8ZpbjZ9izC+SSx8UXfPQaFByAkHq5dCHrn/TdQFOX8l3q3lDJc/emGBcQAF9t3+y6UN07h0WzTUBd7yTQUwICkcAx6HUVVZvLK67QOR7iYUxOb+fPnc8EFFxAaGkpcXBzXXHMNBw8ebHUbRVGYN28eSUlJBAYGMnHiRPbu3evMsHzbro9h238AHVz3FoQ4d+g5u6SW0poGjAY9fRNDz/+Obl5nM7p7DEY/PTlltRxp6qgshKcxN1pYf0SdTvX0Zd4tBfgb6Jugvt9InY3vcWpis3r1au6//342bdrE8uXLaWxsZPLkyVRXN/f/eO6553jxxRdZsGABmzdvJiEhgcsuu4zKykpnhuabio/CV3PV8xMehe4TnP6QO5qmofolhWHyM5z/He1bK2wDq/sV6AYaDYzuHg3IdJTwXJszSqmutxAbaqJ/YpjW4TiUvc5Gdvr2OU5NbL777jtmzZrFgAEDGDx4MIsWLSIrK4utW7cC6mjNyy+/zJNPPsl1111Heno67777LjU1Nbz//vvODM33NNSpdTX1VdB1HEx4zCUPa/u2NOR8lnm3FNMbjKHQUK0WOruhSbK9gvBwtqR8Yu9Y9B6+zPtUQ2RllM9yaY1NeblaoR4VpS4rzsjIID8/n8mTJ9tvYzKZmDBhAhs2bHBlaN7NaoFP74b8XRAUDde/Bfp2jJ50ws72roiy0RuaOyC7bT8bdeh+S2YpFXXSCEx4Hvs2Cl40DWVje8/ZfaIci1Xq4HyJyxIbRVF4+OGHGTduHOnp6QDk56tLeePj41vdNj4+3v67U5nNZioqKlqdxFnYmvDt/wIMRnUfqLAklzx0g8XKnlw1mW13YgNu3YEYoGt0MN1jg2m0Kqw/LMu+hWc5XlzNscJq/PQ6xvWK0Toch+sZF0KQ0UB1vYWjhVIH50tcltjMmTOHXbt28cEHH5z2O90p3W4VRTntOpv58+cTHh5uP6WmpjolXq/x419g27ug08P1/3JJXY3NoZOV1DVYCQ3wIy06uP0HcPMCYmhuaCZ1NsLT2JZ5j+gWeX6NMz2MQa9jYHLzsm/hO1yS2DzwwAN88cUXrFy5kpSUFPv1CQkJAKeNzhQUFJw2imPz+OOPU15ebj9lZ2c7L3BPt+EVWPeiev6ql6D/1S59+J1NzbEGp0R0bP7ettN34UGoc89GW82JjSz7Fp7FW3bzPhtb7yyps/EtTk1sFEVhzpw5fPrpp6xYsYK0tLRWv09LSyMhIYHly5fbr6uvr2f16tWMGTOmzWOaTCbCwsJanUQbtv8Plv1BPX/JUzB8lstDaK6vaWfhsE1ILER0BRR1dZQbuiAtkiCjgcJKM3tzZVpUeIbaegsbjxYD3llfY2ObAt8pK6N8ilMTm/vvv5/33nuP999/n9DQUPLz88nPz6e2Vt0QUafTMXfuXJ555hmWLl3Knj17mDVrFkFBQUyfPt2ZoXm3A1/DFw+o50fPgXG/0SQM25tJuxrzncq+7Ns9p6NMfgbG9VTrEz7ZekLjaIQ4P1/uysXcaCU5IpBecSFah+M0tsTmQF4ldQ3u1zZCOIdTE5vXX3+d8vJyJk6cSGJiov304Ycf2m/z6KOPMnfuXGbPns2IESPIyclh2bJlhIa2o5mbaJa5Dj6+AxQLDLkVJv+fU3bsPpea+kYOnVR7EZ33Vgptse/07Z6JDcDMMd0A+ODnLAorzdoGI8Q5WKwKr686CsDMMV3PWM/oDZLCA4gJMdFoVdiXJyOqvsLpU1FtnWbNmmW/jU6nY968eeTl5VFXV8fq1avtq6ZEO+XthPdvBosZ+lwJ0/6pSVIDsCenAqsCieEBxIUFdPxA9gLizeoKLzc0pkc0Q1IjMDda+de6Y1qHI8RZfb07j4yiaiKC/Ll1ZFetw3EqnU5n3zdK6mx8h+wV5S2KjsB/r4P6SrUB3w1vg8FPs3A6tD9UWxIGqsvUa4qhNLOzYTmFTqfjgYt7AvDexuOU1dRrHJEQbbNaFV5dcQSAX41NI9ik3XuEqwyWRn0+RxIbb1CRC/+9FmqKIGEQ3PI++AdqGpKtjXmH+te05GdSnxO49XTUxX3j6JcYRnW9hUXrM7UOR4g2/bD/JAdPVhJq8rNPoXq75gJi91xZKRxPEhtPV1OiJjXlWRDVA277FAI6uArJgTq9IqolNy8gBnXUZs4kddRm0foMKqUTsXAziqKwYKU6WjNjdFfCA72vd01bBjVt55JRVC2jqT5CEhtPZq6C/90IhQcgNBFmLHX6bt3no6jKzInSWnQ67A2yOsVeQOyeWyvYTElPoEdsMBV1jby3KUvrcIRoZe3hInadKCfAX8+d49LOfQcvERFkpFt0EAC7ZNTGJ0hi46ka6+GjGeooRkCEmtREukch4K6maagesSGEOqKjqS2xydulbubppgx6HbMnqqM2/1p7jNp6WV4q3MeCptqaW0d2JTrEpHE0rjVYGvX5FElsPFF9NXx0OxxdAf5BcOsnENdP66jsdrToOOwQEV0hKAasDZC/2zHHdJJfDEkiNSqQ4up6PvhZRm2Ee/jpWDE/Z5ZgNOj59UXdtQ7H5ewFxNKozydIYuNpKnLh7Slw6FswmOCm/0LqBVpH1YrtW9EQR9TXgLpkveWybzfmb9Bz3wR11GbhmmOYG2XURmjPVltz44gU4jvTfsFD2UZsdmSXy9YnPkASG0+SuwPeuhjyd6kjGLO+gp6Xah1VK4qiNHcc7uyKqJbcfKfvlq4fnkxCWAD5FXUs2ZqjdTjCx+3ILmPt4SIMeh33TuihdTiaGJAUhp9eR1GVmdxy953OFo4hiY2n2P8VLLoCKvMgth/cvQJSL9Q6qtNkldRQVtOA0aCnb4ID9/HykAJiULdZsA33v776CI0Wq8YRCV9mq625ZkgyqVFBGkejjQB/A30T1W72Umfj/SSxcXeKAuv/AR/eBg010OMSuPN7tykUPtWOpjeN/klhGP0c+N8raRigg7IsqCpw3HGd5JYLuxAdbCS7pJYvduZqHY7wUfvzKvhh/0l0Opg9yTdHa2ykUZ/vkMTGnTXWwxdzYPmfAAUuuBumf+QWfWrOZGdT4XCn9odqS0AYxPZVz7txoz6bQKOBO8erS2pfXXkEi1Xm9YXrvdpUWzN1YCI9Yr13s8vz0VxnU6ZpHML5JLFxVzUl8N51sP090Onhiudg6guabpNwPprra5yQfHnQdBTAjFFdCQvw42hhNd/tydc6HOFjjhZW8fXuPADub2oe6ctsX7Z255TLFw0vJ4mNOyo+Cv++DDLXgjEEbvkQRt6jdVTn1GCxsifHwUu9W/KgAmKA0AB/7hirjtosWHlEVmMIl3p91VEUBS7tF0+/RAfWu3moHrEhBBsN1NRbOFJQpXU4wokksXE3mevgX5dA8REIT4U7l0HvyVpHdV4O5ldibrQSFuBHt+hgxz+AfWuFbWD1jGXUd4ztRrDRwP68ClYccP/aIOEdsktqWLpdXZE352IZrQG1gebAFNnp2xdIYuNOtv8P/nMN1JZC8nC460eIH6B1VOfN1q58cGoEer3O8Q8Q21cdwaqvgsKDjj++E0QEGblttFro/coKGbURrvHmmqNYrArje8U4vt7NgzVviFmmaRzCuSSxcQeWBlj+FHw+W+2uO+BamPU1hMZrHVm7rD9aBDhpGgpAb2hO9AoPOOcxnOCucd0x+enZkV3GhqPFWocjvNzJijo+2nwCwL4xq1ANaXpv2nC0WL5keDFJbLR2cq869bT+ZfXyRb+D698G/0BNw2qvspp6lu87CaibQTpNZNPmfaWZznsMB4sNNXHLhV0AeGXFYY2jEd5u4Zpj1FusXNgtipHdo7UOx62M7x1LoL+BjKJqtmWVah2OcBJJbLRiaYDVz8ObEyBvJwRGwg2L4OI/gN7zXpYvduZS32ilf2IY6Y7Y0ftMomyJTYbzHsMJfn1Rd/wNOjYdK2FLZonW4QgvVVxl5v2f1D3K7pfamtOEmPyYOigRwD6qJbyP532CegPbKM3K/1OnnvpMhdk/Qfp1WkfWYR9tyQbUvWicKrKb+rPEsxKbpIhArh+m/tvY9u0RwtHeXp9BbYOFQSnhXNQrRutw3NIvR6QC8NWuXGrqGzWORjiDJDauZGmANS1GaQIi4Lq34Ob/eVw9TUv7civYk1OB0aDnmiHJzn0w+1TUcec+jhPcN7EHeh2sOljI7qZCayEcpby2gf9sUP8u5kzqiU7nhAJ+L3BBt0i6RQdRXW/hm93SX8obSWLjKif3qaM0K1qM0tz/Mwz6pbp7tQf7eKs6WnNZ/3gig43OfTDbVFTFCbUzswfpGh3M1U2J36syaiMc7D8bMqk0N9InPpRL+3nuFyVn0+l03Ng0amMbaRbeRRIbZ7M0No3SXNQ8SnPtQo8fpbGpb7TyWVO/jBucPQ0FEBwL/sGgWKHc896UZk9U9+v5bm8+h05WahyN8BbV5kb+vV6dnr3/4p7OabfgRa4bloxeBz9nlJBZVK11OMLBJLFxplNHaXpfAff/BINv8vhRGpsf95+ktKaBhLAALuoV6/wH1Ok8ts4GoFd8KFc0rRp74fuDsuRUOMS/1mZQVtNAWkwwUwcmah2O20sMD2R80/vVJ1uliNjbSGLjDJYGWPMCLJwAeTuaR2lu+QBCnbgUWgO2odzrhiVjcNW3RFti42Ero2weuLgXBr2OZftO8tbaY1qHIzzc6kOF/OPHQwA8eElP1/0dejhbEfEnW0/I3lFeRhIbR7JaYc+n8OpIWPFXsNR75SiNzcmKOlYfKgSwz1m7RJTn9bJpqX9SGH+6qj8Az357gJUHZasF0THHCquY8/42rAr8ckSK84v3vcil/eOICPInv6KOdUeKtA5HOJAkNo5ydAW8NQk+uQNKjkJQDFz7pleO0tgs2XYCqwIXdosiLcYJe0OdiX3EJtN1j+lgt4/uys0XpGJV4MEPtnO0UDblE+1TUdfAXf/ZQmVdI8O7RvLXa9JlJVQ7mPwM9kRQioi9iyQ2nZWzDd79Bfz3WnXayRgCE5+Ah3bA4Ju9bpTGRlEUPt6izk27pGi4JduSbw+ssbHR6XT85ep0RnSNpLKukbvf3UJ5bYPWYQkPYbEqPPTBdo4VVpMYHsDrtw3D5GfQOiyPY+u7tXzvScpqPGuVpTgzSWw6qugIfDRTHaXJWA0GI4y8Dx7aCRMfA1Oo1hE61dbjpWQUVRNkNLi+WLHliI0HF98a/fS8fttwksIDOFZUzYMfbJe5fnFenv/+ICsPFmLy07NwxgjiQgO0DskjDUgKp39iGPUWK5/vyNU6HOEgkti0V0UefDkXXr0Q9n0G6GDQzTBnC1zxLAT7RrdP29DtVYMSCTb5ufbBI7qATg8N1VBd6NrHdrDYUBMLbx9BgL+e1YcKee47z9ncU2jjs+05vLH6KADP3TCIgSlO3MLEB/yyadRGpqO8hyQ256u2DH6YB/8cClsXgWKB3lPg3nVw3ZsQ2VXrCF2m2tzI17vyABcXDdv4GSGsafrLg6ejbNKTw3n+hsEAvLnmGEu3y/JT0bZdJ8p4bMkuQO1kfbUUC3fa1UOSMRr07M2tYG+udAT3BpLYnEtNibp0+x+DYd1L0FgLqSPhjm9h+oeQkK51hC73ze48qustpMUEM6JrpDZB2BJJDy4gbmna4CTun6Q273tsyW52ZJdpG5BwOwUVdfz6P1sxN1q5uG8cv53cR+uQvEJksJHL+qvNUm11g8KzSWJzJgUH4MuH4MX+6tLtujKI7Qc3fwC/+h66jtE6Qs3Yi4aHp2i3CsNDd/k+m0cu68Ol/eKob7Ryz3+3UFBRp3VIwk2YGy3c895W8ivq6BEbzMs3D5F+NQ5kKyL+bEcO5kaLxtGIzpLEpiWrFQ4tU1c4vTYStr6jjtAkDFIb7N23Hvpe6bUrnc5HRlE1P2eWoNdh361aE16w5PtUer2Ol24aQq+4EE5WmPn1f7dS1yBvsr5OURSeXLqH7VllhAX48a+ZFxAW4K91WF5lfK9YEsICKKtp4Mf90lfK00liA2Cugp/fglcvgPdvVHvS6PTQb5o65XTPGrXBnl6WU37StOHlhN6xJIRruBLDC5Z8tyU0wJ9/zRxBeKA/O7LLeHLpHtl2wce9vT6TT7aeQK+DBdOHubZnlI8w6HVcP1x62ngL305syrJh2R/hpf7wzW+h+AiYwmD0HHhwO9z0njrl5MMjNC1ZrApLtqobXmpSNNySF47Y2HSNDubV6cMw6HUs2XaCf6/zruRNnL81hwp5+ut9ADxxZT8u6u3A/disFvUkALhxuPqetuZQIfnlMg3syVy8TtcNKApkbYKf3oD9X6qrm0AdARh1HwyZ7vU9aDpq7eFC8ivqiAzy55J+cdoGY6uxqcqH+howBmkbj4ON6xXDk1f24y9f7eOZb/bTKz6UCY78UBNuL6Oo2r5dwvXDUrhzXJpjDqwosOXf8MOfwdoIiYMhaWjTaRhEdQe9733n7RYTzIXdovg5s4Ql205w/6SeWockOsh3EpuSY7DrI9j1oXreJm0CjJoNvSb75B9ze9iKhq8ekqx9l9PASAgIh7pyddQmvr+28TjBHWO7sT+vgo+3nuCB97fx+ZxxMg3hIyrrGrj7P1uoqGtkSGoET1/roO0SKnLh8zlw9Mfm67I2qicbU5ia7CQPa054Irr6xMj1jSNS+DmzhI+3ZDN7Yg/ZosJDeXdiU1MCe5eqyUz2T83X+wdB+nVqQhM/QLv4PEhpdT3L950EmnfF1VxkmrqNhZcmNjqdjv+7Np2jhVVsyyrjznc38+4dF5Ia5V2jU6K1iroG7v/fNo4UVBEfZmLhjOEE+Hfyi4SiwJ4l8PXD6pcBvwC4dB50n6T+DeVsg9ztkL8LzBWQuVY92QRGqQlO9wkw+gGv/RJ45cBE5n2xl8ziGrYcL+WCblFahyQ6wPsSm0YzHF4GOxerPy1N+3/o9OrozOCboe9VYArRNk4P8/mOHOotVtKTw+ifFKZ1OKooW2LjvTUoJj8Db8wYztUL1nOssJqp/1zLczcMZkq6d26s6ut2nShjzvvbySqpad4uIayTRfo1JWpCs3epejlpqLpBb2xTH5y4vur7IoClAQoPqEmOLdk5uRdqS9RRnqM/Qlx/6HVZ52JyU8EmP6YOSuSjLSf4aHO2JDYeyqlp95o1a5g2bRpJSUnodDo+++yzVr9XFIV58+aRlJREYGAgEydOZO/evR17sOzN6lYHL/SGD2+DA1+pSU38QLjsr/CbfXD7Z+ofsCQ17fZR0zSUrcDOLXhxAXFLcaEBfHzvaIZ2iaCirpF739vKvC/2Sr8NL6IoCovWZ3D96xvIKqkhOSKQxb8exeDUiM4d+NAyeG2UmtToDDDxcbhzeXNScyqDPyQMhGG3w7SX4Z7V8EQO3L1C7bQOcPCbzsXk5mwj0l/vzqPa3KhxNKIjnJrYVFdXM3jwYBYsWNDm75977jlefPFFFixYwObNm0lISOCyyy6jsrKy/Q/23rXqVgd1ZRCaCGMehPs2wH3rYOyDEObijRq9yJ6ccvblVWA06Ll6SJLW4TTz0iXfbUmJDOKje0Zzz4TuALyzIZPrX99AZlG1xpGJziqvaeCe/27lz1/uo8GicPmAeL55cDxDu3Siq7e5Sm0w+v6NUHUSYnrDXT/AxN+ryUt7+JkgeTiMuFO9fOh7j9589lyGd42ke0wwNfUWvt6dp3U4ogOcOhV1xRVXcMUVV7T5O0VRePnll3nyySe57rrrAHj33XeJj4/n/fff55577mnfg/kFweBrYNBNkHaR9JxxoE+2qqM1lw2IJyLIqHE0LfjIiI2Nv0HP41f0Y1RaNA9/tIM9ORVc9co6nr1+IFcNcqOEU5y37VmlzHl/OzlltRgNep6c2o/bR3ftXNFq1iZYek/z38Wo++GSP4J/YOeCTbtIrU+syFFrcRIHd+54bkqn03HDiBSe++4gH2/Jdp+aQnHeNKsAy8jIID8/n8mTJ9uvM5lMTJgwgQ0bNpzxfmazmYqKilYnAB7aDte+AT0mSVLjQOZGC5/tUHvXuN0fuG3Jd9lxn+rHMalvHN88NJ4Lu0VRZW5kzvvbeWLpbulS7EGsVoW31hzjxjc2klNWS9foIJbcN4aZY7p1PKlpNMPyp+DtKWpSE54KM7+EKc90PqkB8A9Qi40BDn7X+eO5seuHpaDXwebMUo4VVmkdjmgnzRKb/Px8AOLj41tdHx8fb/9dW+bPn094eLj9lJra9GFrlGWwzvDDvgLKahpIDA9gXM8YrcNpLSwZ9P5qLVWlbw0ZJ4YH8v7dI5kzqSc6Hbz/UxbXvLqeo/Im7PZKq+u56z9bePqb/TRaFaYOSuSrB8YxMCW84wct2A8LJ8H6lwEFhtyqbgGTdpGjwlb1aaqzOfStY4/rZuLDAux9o2wj1sJzaL5m79RvJ4qinPUby+OPP055ebn9lJ0t7a+dydZe/PphKe636Z7eABFd1PM+UGdzKj+Dnt9e3of//OpCYkKMHMivZNor61i6Xd6I3dXmzBKu/OdaVhwowOin5+lr01lwy1BCO7P30/4v4a1LoGAvBMXAze/DNa+pfZ4crdfl6s/c7VDh3V8mbCPUS7adwGL13poib6RZYpOQoC5XPXV0pqCg4LRRnJZMJhNhYWGtTsI58sprWXu4EFB38nZL9job30tsbMb3iuWbB8czuns0NfUWfvPhTn738U5q6mVFh7uwWhVeXXmEmxduIq+8ju4xwXw2eyy3juxEPY3VCiufUVeBNlSrozOzN0HfqY4NvqXQeLWQGODw9857HDdwSb94ooKNnKwws6bpfVB4Bs0Sm7S0NBISEli+fLn9uvr6elavXs2YMWO0Cku08Om2HKwKXJgWRTd37Xhrq7PxkQLiM4kLC+C9u0bym0t7o9fBx1tPcPWC9Ww8WiybaGrs8MlKZi76mee/P4jFqnDt0GS+fGBc5/pBmSvVhGb139TLo2bDbUshxAXbbvRuWhDi5XU2Rr/mVaAfy8aYHsWpq6Kqqqo4cuSI/XJGRgY7duwgKiqKLl26MHfuXJ555hl69epFr169eOaZZwgKCmL69OnODEuch7oGC4s3ZwFuWDTckg8t+T4Xg17HQ5f24sK0KB5avJ3DBVXc8tYmBqdGcO9F3Zk8IMH9phO9lKIobM4s5c3VR/nxQAEAAf56/nJ1OjcOT+ncqqfio7B4utpIz2BS+80MceF7Zp8psPL/4NgqaKh1TGGym7pxeCqL1meyfN9JcspqSY7w3ufqTZya2GzZsoVJkybZLz/88MMAzJw5k3feeYdHH32U2tpaZs+eTWlpKSNHjmTZsmWEhsomlFp7+uv9ZJfUEhNi4sqBbtzl1seWfJ+P0T2i+eah8by0/BCfbD3Bzuwy7vvfNrpFB3H3Rd25flhK51v0izZZrArL953kzTVH2Z5VBqhbLF3eP4FHJvemV3wn39uO/ACf/ErdFiE0EW76H6QM73zg7RGfDmEpUHECjq1uLij2Qv2TwuwbY85dvJ0P7h6Fn0Hz0lRxDjrFw8epKyoqCA8Pp7y8XOptHOS7PXnc+942AP7zqwu5yJ13lT65F14fo26K+Vim1tG4naIqM//ZkMm7G49TXtsAQEyIkVljunHbqK7u1ZfIg9U1WFi6PYe31hzjWFPTRKOfnuuHpXD3+DS6x3ay27miwIZ/wg/zQLFCyoVw038hVKMvHV8/Apv/BcNnwbR/aBODi2QV13DlP9dSZW7kwUt68fBlvbUOyWs46/NbEhvRyonSGq78x1oq6hq5Z0J3Hr+in9YhnZ25CuYnq+cfOw6BEZqG466qzY18tCWbf63NIKesFoAgo4GbLkjlznFppETKxpodUV7TwHs/HWfR+kyKqswAhAX4MWN0V2aO6UZcaCf3eQKor4EvH4TdH6uXh86AqX9XOwJr5fAP8L/r1VGjh/d7/c7fX+zM5cEPtqPTwf/uGsmYHm7W+sJDSWJzBpLYOE6jxcpNCzex9XgpQ1Ij+Pje0fh7wrDr872gugB+vRqShmgdjVtrsFj5Znceb6w+xv48tbmlQa9j2qBEfn1RD/fZ4NTN5ZbV8va6DD74OYvqerUxYlJ4AHeO785NF6QSYnLQLH9ZtlpPk78L9H4w5Vm44C7tE4mGOniuu7oa69er1I01vdxjn+ziwy3ZxIeZ+Pahi4gKltHOznLW57f37e4tOuzlHw6z9XgpoSY/XrllqGckNaDW2VQXqHU2kticlb9Bz9VDkvnF4CTWHi5i4ZpjrDtSxGc7cvlsRy4jukYysU8sE3rHMSApDL0UGwNqMXBGUTVrDhWy5nARaw4V0tjU26RvQij3TOjOVYOSHPs3c3wDfDgDaoogKBp++R/oNs5xx+8M/wC1y/uBr+Dgtz6R2Dz1i/5sOV7C0cJqfvvxTv49c0TnisCF00hiIwDYcKSIV1epK9ieuW4gqVEeNDURlQYnfvbpXjbtpdPpuKh3LBf1jmVPTjlvrjnG17ty2XK8lC3HS3lh2SGig42M7xXDRb1jGd8rlthQDac+NFBlbmTDkSJWHypkzeFCsktqW/1+TI9o7pnQg4t6xTj2A05R1PqV734P1kZ1t+2b329uRuku+lzRnNhMekLraJwuyOjHgunDuPrV9aw4UMDb6zO5c1ya1mGJNkhiIyiuMjP3wx0oCtx8QSrTBnvYhoqyMqpT0pPDeeWWoTx+RV9WHChgzaFCNhwtpri63j6SAzAgKUxNhnrFMrxrJEY/DxnRO09Wq8K+vApWHypk9aFCth0vtY/KAPgbdFzQLYqLescyqU8cfRKcsHqzrgK+mgt7lqiXB1wHV78KRjf8otHrckCnTpOV50B4stYROV2/xDD+OLUff/x8L89+u58Lu0V1bisM4RSS2Pg4q1XhkY93UlBppmdcCE9NG6B1SO0nvWwcIikikNtGdeW2UV1psFjZdrzUPlqxJ6eCvbnq6fVVRwk2GhjdI4ZxPaPpHR9K99gQ4sNMHjU0X1JdT0ZRFUcKqth0rIS1hwspqqpvdZtu0UFMaBrZGtU9mmBH1c60JW8XfDwLSo6CzgCXzoMxD2hfT3MmIbGQcoE6WnroO7jgTq0jconbRnVl3ZEivt97kgc+2MZXD453XE2VcAh5NXzc2+szWHWwEJOfngXThxJo9MD+Jvbuw5LYOIq/Qc/I7tGM7B7No1P6UlhpZt2RQtYcKrInAD/sP8kP+0/a7xNkNJAWE0xaTDDdY0PoHhNM91j1cqf2QuqEugYLmcXVHCusJqNI/XmsqIqMomrKahpOu70tYZvQJ5YJvWLpEu2CkRJFga2L4Nvfg8Ws9oi54W3oMtL5j91Zfab4XGKj0+n42/WD2H1iLZnFNfzxsz28dNMQrcMSLciqKB+260QZ17++gQaLwv9dk85to7pqHVLHVObD3/uATg9/KACDNh+ivqLllM3W46VkFFWTVVJz1o0CY0NNpMUE0yM2mPTkcG4def7/1xRFoa7BSnV9IzVmC1XmRmrqG6mut1BjbvpZ36heb7ZQXttgT2Zyy2s52ztcckQgaTHBDEwJZ0LvWIZ1cfEUm7kSvpwLez5RL/e6HK59A4KiXBdDZ5zcB6+PVjsgP5YBRjfdesUJtmSWcNPCTVisCn+/cTDXu+t+em5MVkUJh6qsa+CBD7bTYFG4Ij2BW0e6WWFie4TEg18gNNZCWRZE99A6Iq+m1+tITw4nPbm5tqDBYiWrpIaMFiMiR5tGSQorzfbTzxklXNCt6rwTm2F/XU5pTf1Zk5NzCQvwU0eQYoPpHhNMWox6vlt0sLYjlPm74aOZLaaenoLRD4Deg2qX4vqpRc1lWeoWC87cgNPNjOgWxW8u7cULyw7xx8/3MLRLROcbMQqHkMTGBymKwpNL93C8uIbkiECevW6QR9VGnEanUwuIC/erBcSS2Licv0FPj9gQesSGAPGtfldR10CmfRqomoSw829aZ1WUVklNsNFAkMlP/Wn0I9ik/gwx+RFkNBBsUs93iQqyT4NFBRvd6/+3osDWd+Dbx5qmnpLhhkWeMfV0Kp1O3RTz5zfV1VE+lNgA3DexJ+uPFLPxWDFz3t/O0vvHYPLzwOl8LyOJjQ/6eOsJvtiZi0Gv45+3DCE8yAumbqLSmhIbqbNxN2EB/gxKiWBQSkS77/vlnHGY/PWEmPwI8DN4fl+d06aeJsO1b3rO1FNb+kxRE5tD34PV6lkjTp1k0Ot4+eYhXPGPtezLq2D+NweY9wsPXIDhZXznf6AA4EhBFU99vheAhy/rzfCuHvyG2pIs+fZKqVFBxIUGEGT08/ykJn8PLJyoJjU6A1z2F7jlQ89OagC6jgNjqNokM3e71tG4XHxYAH+/cTAA72xQdwIX2pLExofUNViY8/42ahssjO0Zzb0TvGjKRpZ8C3dlm3r61yVQfESderrjGxj7kHeMbvgZoefF6vlD32obi0Ym9Y3jrqZmfb/7ZCd55bXnuIdwJi/4qxLn65lv9nMgv5LoYCMv/XIIBk//BtySfcTmuKZhCNFK5UlYfCt8+RA01qlTT/eshS6jtI7MsXpfof48+J22cWjo0Sl9GZgcTllNAw8t3nHWVYLCuSSx8QEWq8KLyw/xn43qh/4LvxxMXDsKOD1Cy142nt3BQHgDRYHdn8BrI+Hg16D3h0v/rE49BUdrHZ3j9Zqstls4uVvduNMHGf30vHLLUIKNBn7OKGHuhzuoMjdqHZZPksTGy52sqOPWf23inz8eBuCBi3syqU+cxlE5QUQXQAf1VVBdpHU0wpdVFcCHt8GSO6G2FBIGqTtgj5vrHVNPbQmOhpQL1fOHfHfUpltMMM/dMBiDXseXO3P5xSvr2JtbrnVYPsdL/8oEwJpDhVz5j7VsOlZCkNHAyzcN4ZHJfbQOyzn8TGrtAkgBsdCGoqh7PL06Ut0cUu8HE5+Au1dAQrrW0TlfnynqTx9ObACmDkrkw1+PIjE8gGNF1Vz72gb+u+k4Ht4L16NIYuOFGi1WnvvuALe//TPF1fX0SwzjqwfGcc1QL9+kTrZWEFqpKoSPbodPfgW1JRA/EO5eCRMf851O2LY6m4w1YK7SNhaNjegWxTcPjueSvnHUN1r542d7mPPBdirqTt/GQzieJDZeJq+8llve2sRrq44CcOvILiydPcY3OmJGNnWzlREb4Up7l6q1NPu/UEdpJvxeHaVJHKR1ZK4V20ct4rfUw7GVWkejuchgI/+aOYI/TO2Hn17H17vyuOqf69h1okzr0LyeJDZeZMWBk1z5j7VsziwlxOTHgulDefragQT4+0gnTFnyLVypukjdjfvjWVBTDHED1IRm0uPqEmhfY+tCDD69OqolnU7HXeO78/G9o0mOCCSrpIbrX9/AovUZMjXlRJLYeIEGi5VnvtnPr97ZQmlNA+nJ6tTTVYOStA7NtaRJn3CVfZ+rtTR7l6rN9i56VC0QThysdWTaallnY7VoG4sbGdolkm8eHM/k/vE0WBT+/OU+7n1vK+Vt7DAvOk8SGw93orSGX765kYVrjgEwa0w3ltw3hm4xvrPLrp3U2AhnK89Ra2k+uh1qiiC2H9z9I1z8pG+O0pyqyxgwhan/NjlbtY7GrYQH+fPmjOE8Na0//gYd3+89yZX/XMv2rFKtQ/M6kth4sO/35nPlP9ayPauM0AA/3rhtGPN+McB3N2GzTUVV5kGDdP4UDmRpgPX/gAUXqKM1Oj2MfwTuWQ1JQ7WOzn34GaHnJer5g77ZhfhsdDodd4xNY8l9Y+gSFUROWS03vrGRt9YcwyoN/RxGEhsPtDO7jAc/2M49/91KRV0jg1PC+ebB8UxJT9Q6NG0FRoIpXD0vHYiFo2SshTfGwfI/QUM1pI6Ee9bAJX9S2wyI1mx1Nj6+7PtsBqVE8NWD45g6MJFGq8LT3+znlrc2seLASUlwHEB29/YQDRYr3+7J5531GWzLKrNff+e4NB6b0hejn+So6HQQ1Q3ydqrTUXF9tY5IeLLKfFj2B9j9sXo5KEbduHLwLd7baM8Rel2mjmgV7FO/YNhWK4pWwgL8WTB9KKN/iuYvX+3jp4wSfsooIS0mmJmju3LDiFRCTPIR3RHyr+bmSqrr+eDnLP678Tj5FXUA+Bt0TBuUxB1j0xiYEq5xhG4msltTYpOpdSTCU1kaYfNbsPIZMFcAOhjxK7jkj+qooDi7oCjoMhqOr1dHbUbeo3VEbkun03HbqK5M6B3LfzZmsnhzNhlF1cz7ch9/X3aIG0ekMmtMN7pEB2kdqkeRxMZNHcivYNG6TD7bkYO50QpATIiRW0d25dZRXYgL9bK9nhxFlnyLzsjaBF8/Aif3qJeTh8PUv0sdTXv1nqImNge/lcTmPKRGBfHk1P7MvbQ3S7ad4J31mRwrqubt9Rks2pDBJX3j+dXYbozuEY1O50WbFzuJJDZuxGJV+HH/SRatz2TjsWL79enJYdwxJo2rBif6bmHw+ZIl36Ijqgrhh6dgx//Uy4GRcMlTMGymTDt1RJ8rYPkfIXMd1FVAQJjWEXmEYJMft4/uxm0ju7L6cCGL1mey5lAhP+w/yQ/7T9I3IZQ7xnbj6iHJvtOfrAMksdGYoigcyK9k1cFCPvg5i6ySGgAMeh2XD4jnjrFpjOgaKVn6+ZIl36I9LI2wdRGs+CvUNW1WOOx2uGSed+7C7SoxvSCqB5QchaMrYMA1WkfkUfR6HZP6xDGpTxxHCqp4Z0MGS7bmcCC/kseW7ObZbw9w0wVduLRfHINTI/A3SPLdkk7x8PaHFRUVhIeHU15eTliYZ3wryCuvZe3hItYfUU9FVfX234UH+nPzhancProbyRGBGkbpoUoz4R+DwWCCJ/Pl27Y4s8M/wLInofCAejlhEEx9EVIv0DYub/H9k7BxgTrq9Yt/ah2NxyuvaeDDLVm8u+E4OWXN7SxCTH6M6h7F2J4xjO8VQ4/YEI/5Iuysz28ZsXGBiroGNh0tZv2RItYeKeJYYXWr3wf6GxjZPYrJ/RO4ZmgSQUZ5WTosLEXdr8diVvvZhHv5xp+i/U7uVVc7HV2hXg6MgklPqAXCehnedxhbF+bio9rG4SXCg/z59UU9+NXYNH7Yf5Ivd+Wx4UgRpTUN/LC/gB/2FwAQH2ayJzlje8QQF+Z79ZjyCeoEVeZG9uaUs/5IEeuOFLHzRDmWFr0J9Dq1j8H4XjGM7RnDsC6RslzbUQx+EJ6qTkWVZkpiI5pVnoSVT8P2/4JiBYNRLWwd/1sIjNA6Ou8TKdPCzuBn0DMlPZEp6YlYrQr78ipY1zT6/3NGCScrzHy6LYdPt+UA0Cc+lLE9YxjXK5rBKRFEh3h/7yVJbDrB3GjhaEE1h05WcvBkJYfyKzmQX9lqmNCme0xw03+uGEZ1jyY80F+DiH1EVFpTYpMB3cZqHY3QWkOtOiWy7mWor1Kv638NXDqvuSZLOJ6tkL8iFxrqwN/3Rg6cTa/XkZ4cTnpyOPdO6EFdg4Wtx0vtpQ57css52PT59PZ6NcGMCTHRJyGE3vGh9E0IpXd8KL3iQ72qZ473PBMnarRYyS6t5WB+JQfzK+2JTEZRdauRmJbiw0yMTItmXM8YxvaKkXoZV5Il3wLAalWb6/34F6g4oV6XPBwufwa6jNI2Nl8QHAPGEDWZLMuC2N5aR+T1AvwNjO2pzgQAlFbXs+FoMeuOFLHpWDGZxdUUVZkpOmJm/ZHiVvdNiQy0Jzp9mn52jw32yJW4Pp/YKIpCRW0jOWW15JbVkldeS05ZHblNl3PLajlZaT5jAhMW4EffhDB6J4TQJz6UPglh9I4PISJINsTTjCz5Fsc3wPdPQO529XJ4qjpCM+A6KSh3FZ1O/Vs8uUf9W5TExuUig41MHZTI1EHqdjs19Y0cPlmljuLYvqTnV1JQaeZEaS0nSmvttTo2saEmksIDSIoItJ+SIwJIDFfPx4QY3a5Y2WsTm9p6CyU19ZRU1VNcbaakut5+Kq6qJ6+ijrymxKW63nLO45n89PSOD20evksIpU98KPFhJrd7UX2eLPn2XcVH1X40+79ULxtDYPzDMGo2+MuoqcvZExv5W3QHQUY/BqdGMDg1otX1pdX1ajlFU6JzMF+dlaisa6Sw0kxhpZmdJ8rbPKbRT29PfBLD1UQnMthIVLCRaPtPE5HB/oSY/Fzyeek1ic29722hymqkuEpNXmobzp2stBQdbCQxIoCkcFtGastO1RcsNsSEXi8JjEeQERvfU3kSVv8Ntr0L1kZ1r6JhM9XVTiFxWkfnu2x/izIt7NYig42M6h7NqO7NvZsURaG0pqHV7EVueZ19diO3rJaCSjP1jVYyi2vILK455+MY/fREBTUlOyFGgqk/5306wmsSm3WHi9GbWu+n4W/QERVsJCrYZM8cbaeEsAB74pIYHkig0fPmEcUZ2N5Ma4ql66m3M1fChldgwwJ1522Anpepm1XG99c2NtFi9DRT0zBE++l0OvvnZXpy23sS1jdaOVnRVLpRXktuWR0l1fWUVtdT3HKWpNpMXYOV+kYr+RV19n0PreZzJ0Md4TWJzV+uHkBKXDRRIc3DX64a9hJuxhSq7sRcU6S+oSYO0joi4WiN9WrH4NXPqa8zqIXBl/4Z0sZrG5toJku+vZrRT09qVBCpUefepLO23mIvCyluSn5yCop58GXHx+UWic1rr73G888/T15eHgMGDODll19m/Pj2vTmFBfpjURT7fKDwbSMDUoioKWLHru2cLJGpCK+hWEnI/pZee14iqDobgOqQbhwe+DAnkydDjQ725mscpLAJqgphPGApzuCHPXlqQbEQqPtiJUc6Z9dyzRObDz/8kLlz5/Laa68xduxY3nzzTa644gr27dtHly5dzvs4cxfvOG0qSviul/2DuMYA36zZyEJLjNbhCAcYq9/N7/0+YKA+E4BCJZyXG6/nw6KJNK70A7ZpGp84nR+NHDTpMFjN/PG9HykgUuuQhBvx2qmoF198kTvvvJO77roLgJdffpnvv/+e119/nfnz55/3cYakRuAfGOysMIWHaajqCtUbGB5WzvAweTP1ZGkNR7it6m2G1KtLt2t0gXwWdCNfBV+LWRfAYI3jE2dXVBhHvPUklyXWcMDYXetwhBtpqDWS7YTjaroJZn19PUFBQXz88cdce+219usfeughduzYwerVq0+7j9lsxmxunmqqqKggNTWV8hcuICxQ8zxNuIuCvc3n4wZoF4fouJoiqDp5+vUh8WoNlfAM8rcozqCitpHw3272rk0wi4qKsFgsxMfHt7o+Pj6e/Py258nnz5/Pn//85zYOdgBMMn8r2tDyjVV4vqqTbSc8wv3J36JoyeyccRW3GOI4deWSoihnXM30+OOP8/DDD9sv20ZsuOl9CJWpKNGkMh8+u1c9f+sn6o7fwvMc+UHtQ5MgK9s81vqX4dgqCI6D6xZqHY1wJ5XV8Ow0hx9W03f7mJgYDAbDaaMzBQUFp43i2JhMJkymNnYn7X4ROHAoS3g4qxW+mguNdRDdUzY79FQ9JmkdgeisujI1sYnsKq+naK2iwimH1XTTFKPRyPDhw1m+fHmr65cvX86YMWM0ikp4Bb2+RQdi6aEhhGYipUmfcC3Nx+cffvhhZsyYwYgRIxg9ejQLFy4kKyuLe++9V+vQhKeL7AaFB+QNVQgt2UZLqwvVTtGmUG3jEV5P88Tmpptuori4mL/85S/k5eWRnp7ON998Q9euXbUOTXg62zdF2afGfeTvVj/YbKNpwvsFhENgJNSWQulxSEjXOiLh5TSdirKZPXs2mZmZmM1mtm7dykUXXaR1SMIbyGaY7qMiDz6/H94YD8v+oHU0wtVkawXhQpqP2AjhNFHyZqq5+mp1g8r1L0NDU5dRvT9YGsDgr2lowoUiu0HuNvmSIVxCEhvhvexTUZmgKLJPjStZrbBrMfz4V6jMVa9LuQAufwZSL9Q2NuF6UTItLFxHEhvhvSK6ADqor4SaEgiO1joi35CxFpY9CXk71csRXeDSeTDgOkkufZVMCwsXksRGeC//AAhLgoocdTpKEhvnKjoCy/8EB79WL5vCYPwjMPJe9bUQvktqbIQLSWIjvFtkt6bEJhNSRmgdjXeqKYHVf4PN/wJrI+gMMOIOmPg4BMueToLmEZuyLLA0gkE+eoTzyP8u4d0i0+D4epnbd4bGevh5Iax5DurK1et6XQ6T/wqxfbSNTbiXsCQwGMFSr37RiJR2HsJ5JLER3s32TbH4sKZheJ2jK+Gb30LxEfVyfDpM/j9pmS/apjdARFf177A0QxIb4VSS2AjvljJc/Xl0pbpSR+8WrZs8V3kOfP8E7PtMvRwcB5f8EYbcqn54CXEmkd2aEptMrSMRXk4SG+Hduo4DYyhUF0Du9uZER7SPpQE2vQ6rnoWGatDp4cJfw6Qn1M6yQpyLLPkWLiKJjfBufkboeTHs+xwOfSuJTUdkrFWnnQoPqJdTLoSpf4fEQdrGJTyLLPkWLiLj8sL79b5C/XnwO23j8DSVJ2HJ3fDuVWpSExQNV78Kv/pekhrRfrLkW7iIjNgI79drsjp1cnI3lGVDRKrWEbk3SyNsfgtWPgPmCkAHI34FF/8BgqK0jk54KhmxES4iIzbC+wVHQ+pI9fwhGbU5q6yfYOFE+O73alKTNAzuXgFXvShJjegcW2JTV672PhLCSSSxEb6h9xT1pyQ2bastVXfffnuyOrIVEAFXvQx3/QDJw7SOTngDYxCExKvnZTpKOJEkNsI39Gmqs8lYA+YqbWNxN4eWwWujYft76uWhM+CBbWr3YFnCLRzJXmeTqWkYwrtJYiN8Q0xv9U3VUg/HVmodjXuoLYPP7of3b4TKPIjuqRYGX71A9tUSziFLvoULSGIjfINO1zxqI6uj4PAP6ijNjvcAHYyeA/eugy6jtI5MeDMpIBYuIKuihO/oPQU2vQaHv/fdLsR15fD9k7D9v+rlqO5w9WvQdbS2cQnfIFNRwgUksRG+o+sYMIVDdSHkbIXUC7SOyLWO/AhfPKBuQogORt0HF/9RLeoUwhVkxEa4gA9+ZRU+y+APPS9Rzx/8RttYXKmuAr54EN67rmln5TS44xuYMl+SGuFathqb8hPQaNY2FuG1JLERvsVWZ+Mry76ProTXx8C2d9XLF94D961XR6+EcLXgWPAPBhS1WaYQTiCJjfAtPS8FnQEK9kHpca2jcR5zFXz1G/jvNVCerU4BzPoarnwOjMFaRyd8lU7XYjpKVkYJ55DERviWoKjmlT/eOmpzch+8NQm2vK1evuBuuHc9dBunbVxCgNTZCKeTxEb4HlsX4oPfahuHoykKbPsvvHUxFB2C0CS4/QuY+gKYQrSOTgiV9LIRTiaJjfA9tjqbzHVqYa03MFfB0nvhiznQWKtOud27FrpP0DoyIVqTqSjhZJLYCN8T0wuieoC1AY6u0DqazrNNPe1arNYPXfIUTP8YgmO0jkyI00kvG+FkktgI3+QNq6MURd3fyT71lAizvoLxD/tm80HhGaJaJDaKomkowjvJu5/wTbY6m8PLwGrRNpaOqK+Gz+5Td+RurIUel6hbIsgybuHuwlNBp4eGGqgq0Doa4YUksRG+qcsoCAiHmmI4sVnraNrn5D5YOAl2fqB+QFzyJ7j1E5l6Ep7BzwhhKep5qbMRTiCJjfBNBn/oNVk970mro+xTTwfVqaeZX8H4R2TqSXiWyK7qT6mzEU4g74bCd9mmozyhzqa+Gpa2nHq6GO5ZC93Gah2ZEO0nS76FE8kmmMJ39bwU9H5QeEB9g7W92bqbkmOw+Fa1W7JOD5OehHFSICw8mDTpE04k74zCdwVGQJfR6nl3HbU5ukKtpynYByEJ6tTTRb+VpEZ4NvuSbxmxEY4n747Ct9mWfbvbbt+KAhtegfeuh7oySLkAfr1Kpp6Ed7CN2MhUlHACSWyEb7PV2RzfAHXl2sZi01ALS++BZX8AxQpDb1M3sAxL1DoyIRzDNu1bXaDWjwnhQJLYCN8W3QNieoO1EY78oHU0UH4C3p4Cuz5Uuwhf8Tz8YgH4mbSOTAjHCYyEgAj1vNTZCAeTxEYI+6aYGtfZHN8ICydC3g4IjILbP4ORvwadTtu4hHAGKSAWTiKJjRC2OpvDy8DSqE0MW96Gd6dBdSHED1TradIu0iYWIVxBlnwLJ5HERoiUC9Wh8boyyP7JtY/dWA9f/UY9WRtgwLVw5/fNDcyE8FYyYiOcxKmJzdNPP82YMWMICgoiIiKizdtkZWUxbdo0goODiYmJ4cEHH6S+vt6ZYQnRmsGvuQvxIRd2Ia4qgP/8Qh2tQadujXDDIjAGuy4GIbQiS76Fkzg1samvr+fGG2/kvvvua/P3FouFqVOnUl1dzbp161i8eDFLlizhkUcecWZYQpzO1XU2OdvUepqsjWAKg+kfqlsjSD2N8BUyYiOcxKmdh//85z8D8M4777T5+2XLlrFv3z6ys7NJSkoC4O9//zuzZs3i6aefJiwszJnhCdGs5yVqF+Liw1B8VF0t5QxWK/y8EH54ChrrILoX3PIBxPRyzuMJ4a5sNTalx8FqAb1B23iE19C0xmbjxo2kp6fbkxqAyy+/HLPZzNatW9u8j9lspqKiotVJiE4LCIeuTc3vnLUpZlk2/Pdq+O4xNanpPQXu/lGSGuGbwpJB76/WllXkaB2N8CKaJjb5+fnEx8e3ui4yMhKj0Uh+fn6b95k/fz7h4eH2U2pqqitCFb7AtjrK0dsrKArseB9eHwMZa8A/CKb+HW5ZrCZUQvgivQEiuqjnZTpKOFC7E5t58+ah0+nOetqyZct5H0/XRk2BoihtXg/w+OOPU15ebj9lZ2e39ykI0baWXYhrSx1zzKpC+PA2+Ow+MFeoK7DuXQcX3CX1NELIkm/fVJoJq5+HNyc65fDtrrGZM2cON99881lv061bt/M6VkJCAj/91Hp5bWlpKQ0NDaeN5NiYTCZMJunCKpwgKg1i+6q7fR/5EQbe0LnjHfgavnxI7U2j94dJj8OYh9RVWEIIKSD2JbWlsPcztat61kb1OrPilIdq9ztsTEwMMTExDnnw0aNH8/TTT5OXl0dioroPzrJlyzCZTAwfPtwhjyFEu/SeoiY2B7/peGJTVwHfPQ473lMvx/WHa9+ExEGOi1MIbyBLvr1bY73a+HTXh+oUv8XWykUH3SdA91/As3c5/GGd+tUxKyuLkpISsrKysFgs7NixA4CePXsSEhLC5MmT6d+/PzNmzOD555+npKSE3/72t9x9992yIkpoo8+VsP5l2LsUCg9B0hBIHgZJQyFuAPgZz37/jLXw2WwozwJ0MPZBmPSk7PUkRFtkxMb7KAqc2Aw7F8PeT1tP68cNgME3wcAbISwJKioAD0ts/vSnP/Huu+/aLw8dOhSAlStXMnHiRAwGA19//TWzZ89m7NixBAYGMn36dF544QVnhiXEmaWMgNSRagfik7vV0/b/qr8zGCE+XU1ybMlOTB91aqmhDn78C2x6Vb1tRFe49g3oOka75yKEu5MaG+9RnqO+V+76EEqONV8fkqCOfg++GRIGuiQUnaIozpnkcpGKigrCw8MpLy+XUR7hGIqiLj/N3a420svdrp7qyk6/rX8QJAyCmmK1Bw7A8Fkw+f/AFOrKqIXwPOYqmJ+snn8sU93aRHiW7M2w6TXY9zkoFvU6/2DoNw0G/RK6TzxjjyJnfX5LFaMQp9LpIDxFPfWbpl6nKGodgC3Jyd2hnuorIXuTepuQePjFAug9WavIhfAsphAIjoPqAnU6ShIbz2BpUBOZTa9DTotV0F3HwbDboe9U9bXViCQ2QpwPnQ6iuqun9OvV66xWKD6iJjq1peq8cXC0tnEK4Wkiu6mJTUmGOr0r3FdNCWx9B35+Cypz1esMRvW9b+S9brNAQhIbITpKr4fY3upJCNExUWlw4mcpIHZnBQfgp9dh54fQWKteFxyn9uMacQeExGkb3ykksRFCCKEdWfLtnqxWOPqjWj9zdEXz9QmDYNRsSL/ObVd7SmIjhBBCO7Lk270oirpf3oq/QsE+9TqdXq2bGTUbuox2+67pktgIIYTQjn3Jd6amYQjg+Eb4YV7zgghTmFoMfOHdzQmoB5DERgghhHZsH5gVJ9ROtedqgikc7+RetQ+XbQNgv0AYdR+MfQgCIzQNrSMksRFCCKGdkHj1g7SxFsqzIbqH1hH5jrIsWPmM2iUYBXQGdYRmwmMQlqh1dB0miY0QQgjt6HTqqE3hfrWAWBIb56sugjUvwJZ/N+/f1P8auPiPENNT09AcQRIbIYQQ2opKUxMb2VrBucxVsPFV2PCK2lwUIG0CXPoUJHvPxtOS2AghhNCWrIxyLksjbF0Eq/8G1YXqdYmD4dJ50ONiTUNzBklshBBCaMveyyZT0zC8UsEB+Hw25GxVL0d1h4v/AP2vVZuMeiFJbIQQQmhLdvl2PEsjbHxFLQ621IMpHC75o7pJr8Ff6+icShIbIYQQ2mo5FaUobt8Azu2dOkrTazJM+weEJWkbl4tIYiOEEEJbEV0AHTRUqzUgbrb3kMdoa5RmynwYMt2nkkVJbIQQQmjLzwRhyWqTvtJMSWw6ovAgfHafz47StOSdlUNCCCE8i9TZdIylEda9BG+MV5MaUzhc/RpM/8gnkxqQERshhBDuILIrZK6VlVHtIaM0bZLERgghhPbsS75lxOac7LU088Fi9tlamjORxEYIIYT2bCujZCrq7GpL4aPbIWONernnZeooTXiytnG5EUlshBBCaC9KmvSdU/FReP+XUHwEjCFwxd9gyK0ySnMKSWyEEEJoL6q7+rMqH2rLIDBCy2jcT+Y6+PA2dcQmPBWmfwjxA7SOyi3JqighhBDaC4xsno6yFcMK1fb/wX+uUZOa5BFw14+S1JyFJDZCCCHcQ8oF6k9JbFRWK/wwT+0ibG2AAdfCrK8gNF7ryNyaJDZCCCHcQ/II9eeJzdrG4Q7qa+Dj29UeNQAX/Q6ufxv8A7WNywNIjY0QQgj3YBuxObHFt/eMqsiDD26GvB1gMMIvXoHBN2sdlceQxEYIIYR7SEhXP8hrS6DkGET30Doi18vbpSY1FTkQGAU3vw9dR2sdlUeRqSghhBDuwc8EiYPV8ye2aBuLFg5+C29PUZOamN5w94+S1HSAJDZCCCHch72A2IcSG0WBDQvgg1vUHc7TJsCdy5uXwIt2kakoIYQQ7iN5uPrTVwqIrVb45hHY8rZ6efgsuPIFMPhrGpYnk8RGCCGE+7CN2OTvhoZa714FpCjw7aNNSY0OJv8fjL7fd4umHUSmooQQQriPiC4QHAvWRrWQ1putehY2vwXo4Lq3YMwcSWocQBIbIYQQ7kOna7Hs24uno356E1Y/q56/8nkYdKO28XgRSWyEEEK4l5SmRn3eWkC86yN1Cgpg4hNw4d3axuNlJLERQgjhXuwdiL0wsTm0DD67Tz1/4T0w4VFt4/FCktgIIYRwL8nDAB2UZ0NlvtbROE7WJvjodrV+aOCNMOVZqalxAklshBBCuBdTKMT1U897y6hN/h54/5fQWAs9L4NrXge9fAQ7g/yrCiGEcD/eVGdTkgHvXQd15ZA6Cn75H+lT40SS2AghhHA/LTfE9GSVJ+G/10DVSYgbANMXgzFI66i8mtMSm8zMTO68807S0tIIDAykR48ePPXUU9TX17e6XVZWFtOmTSM4OJiYmBgefPDB024jhBDCx9gKiHO2gdWibSwdVVumjtSUZkJEV5jxKQRGah2V13Na5+EDBw5gtVp588036dmzJ3v27OHuu++murqaF154AQCLxcLUqVOJjY1l3bp1FBcXM3PmTBRF4ZVXXnFWaEIIIdxdbB8whkJ9JRTsV3f+9iT1Neou3Sf3QHAc3P4ZhCZoHZVP0CmKorjqwZ5//nlef/11jh07BsC3337LVVddRXZ2NklJSQAsXryYWbNmUVBQQFhY2DmPWVFRQXh4OOXl5ed1eyGEEB7i3WmQsQauehlG3KF1NOfP0gCLb4XD34MpHO74GhIGah2V23HW57dLa2zKy8uJioqyX964cSPp6en2pAbg8ssvx2w2s3Xr1jaPYTabqaioaHUSQgjhhTxxp2+rFT6/X01q/AJg+oeS1LiYyxKbo0eP8sorr3Dvvffar8vPzyc+Pr7V7SIjIzEajeTnt927YP78+YSHh9tPqampTo1bCCGERjyxUd/qZ2HXh6AzqKufuo7WOiKf0+7EZt68eeh0urOetmxp/Z8wNzeXKVOmcOONN3LXXXe1+p2ujeZEiqK0eT3A448/Tnl5uf2UnZ3d3qcghBDCE9iWfBceVJdKu7tjq2H1c+r5X7wCvS/XNh4f1e7i4Tlz5nDzzTef9TbdunWzn8/NzWXSpEmMHj2ahQsXtrpdQkICP/30U6vrSktLaWhoOG0kx8ZkMmEymdobthBCCE8TEqeuJio7rq6O6jFJ64jOrKoAPr0bUGDY7TD0Vq0j8lntTmxiYmKIiYk5r9vm5OQwadIkhg8fzqJFi9Cf0mVx9OjRPP300+Tl5ZGYmAjAsmXLMJlMDB8+vL2hCSGE8DYpI9TE5sQW901srFb49Ndqr5rYfjDlb1pH5NOcVmOTm5vLxIkTSU1N5YUXXqCwsJD8/PxWtTOTJ0+mf//+zJgxg+3bt/Pjjz/y29/+lrvvvltWOAkhhPCMAuL1L8GxleAXCDe+Iw34NOa0PjbLli3jyJEjHDlyhJSUlFa/s60wNxgMfP3118yePZuxY8cSGBjI9OnT7X1uhBBC+Dh7AfFmUBT32zQyaxOseFo9P/UFiOurbTzCtX1snEH62AghhBdrNMP8FLDUw4PbIaq71hE1qymBN8ZDxQkY+Eu4bqH7JV5uzCv62AghhBDt4meChEHq+RNt9zfThKLAZ7PVpCaqB1z1oiQ1bkISGyGEEO4tpcV0lLvY9Doc+hYMJrWuxhSqdUSiiSQ2Qggh3Ju7FRDnbIPlf1LPX/40JA7SNh7RiiQ2Qggh3FtyU/uPvF3QUKdtLHXl8MkdYG2Afr+AC+46932ES0liI4QQwr1FdoOgGDWZyN+tXRyKAl8+BKWZENFF7S4sdTVuRxIbIYQQ7k2na56O0rLOZusi2LsU9H5wwzsQGKFdLOKMJLERQgjh/lKapqO0Smzy98C3v1fPXzqvOR7hdiSxEUII4f60LCA2V6l1NRYz9LocRt3v+hjEeZPERgghhPtLGgbooCxL3XDSlb75HRQdgtAkuOZ10MtHpzuTV0cIIYT7CwiD2KbtCk64cNRmxwew833Q6eGGf0NwtOseW3SIJDZCCCE8g6sb9RUdga8fUc9PegK6jnHN44pOkcRGCCGEZ3BlYtNYD0vuhIZq6DYexj3s/McUDiGJjRBCCM9gKyDO3Q5Wi3Mfa8VfIW8HBEapm1vqDc59POEwktgIIYTwDLF9wRgC9VVQeMB5j3N0BWz4p3r+6gUQluS8xxIOJ4mNEEIIz6A3QNJQ9byzCoiri2Dpver5EXdC36nOeRzhNJLYCCGE8BzO7ECsKPDZbKg6qY4OXf604x9DOJ0kNkIIITyHvYDYCSM2Py+Ew9+DwQQ3vA3+gY5/DOF0ktgIIYTwHMlNiU3hAaircNxx8/fAsj+q5yf/H8QPcNyxhUtJYiOEEMJzhMZDeBdAgdxtjjlmfY26tNtiht5T4MK7HXNcoQlJbIQQQngWR09HLXtSHQEKSYCrX1V3ExceSxIbIYQQnsWRic3+r2DL2+r5a9+A4JjOH1NoShIbIYQQnqXlTt+K0vHjlOfAF3PU82MehB6TOh+b0JwkNkIIITxLwiDQ+0N1IZQd79gxrBZYeg/UlkLiELj4jw4NUWhHEhshhBCexT8AEgaq5zs6HbX+ZchcC/7B6tJuP6PDwhPaksRGCCGE57E36utAYnNiC6xoar535fMQ3cNxcQnNSWIjhBDC83R0p++6CnVpt2KBAdfBkOmOj01oyk/rAIQQQoh2syU2+bug0Qx+ptNvoyhQXw3mCjWhMVfAptegNFPthXPVS7K02wtJYiOEEMLzRKZBUDTUFMPHs9Qkxp7AlDf9rFRHZk6l08P1/4LACFdHLVxAEhshhBCeR6eDLqPhwFdw8Jtz3FYPpjAICIOACBg9B7qMdEmYwvUksRFCCOGZLn9GXartZ2xOXEzhTT/Dmn8ag2XKyYdIYiOEEMIzRXaFCb/TOgrhZmRVlBBCCCG8hiQ2QgghhPAaktgIIYQQwmtIYiOEEEIIryGJjRBCCCG8hiQ2QgghhPAaktgIIYQQwms4NbH5xS9+QZcuXQgICCAxMZEZM2aQm5vb6jZZWVlMmzaN4OBgYmJiePDBB6mvr3dmWEIIIYTwUk5NbCZNmsRHH33EwYMHWbJkCUePHuWGG26w/95isTB16lSqq6tZt24dixcvZsmSJTzyyCPODEsIIYQQXkqnKIriqgf74osvuOaaazCbzfj7+/Ptt99y1VVXkZ2dTVJSEgCLFy9m1qxZFBQUEBYWds5jVlRUEB4eTnl5+XndXgghhBDac9bnt8tqbEpKSvjf//7HmDFj8Pf3B2Djxo2kp6fbkxqAyy+/HLPZzNatW10VmhBCCCG8hNMTm8cee4zg4GCio6PJysri888/t/8uPz+f+Pj4VrePjIzEaDSSn5/f5vHMZjMVFRWtTkIIIYQQ0IHEZt68eeh0urOetmzZYr/97373O7Zv386yZcswGAzcfvvttJz90rWx46qiKG1eDzB//nzCw8Ptp9TU1PY+BSGEEEJ4qXbX2BQVFVFUVHTW23Tr1o2AgIDTrj9x4gSpqals2LCB0aNH86c//YnPP/+cnTt32m9TWlpKVFQUK1asYNKkSacdw2w2Yzab7ZfLy8vp0qUL2dnZUmMjhBBCeIiKigpSU1MpKysjPDzcYcf1a+8dYmJiiImJ6dCD2XIoW2IyevRonn76afLy8khMTARg2bJlmEwmhg8f3uYxTCYTJpPJftmWZMnIjRBCCOF5iouLHZrYOG1V1M8//8zPP//MuHHjiIyM5NixY/zpT38iLy+PvXv3YjKZsFgsDBkyhPj4eJ5//nlKSkqYNWsW11xzDa+88sp5PU5ZWRmRkZFkZWU59B/G3dkyXV8bqZLnLc/bF8jzluftC2wzLqWlpURERDjsuO0esTlfgYGBfPrppzz11FNUV1eTmJjIlClTWLx4sX3ExWAw8PXXXzN79mzGjh1LYGAg06dP54UXXjjvx9Hr1TKh8PBwn/oPYRMWFibP24fI8/Yt8rx9i68+b9vnuKM4LbEZOHAgK1asOOftunTpwldffeWsMIQQQgjhQ2SvKCGEEEJ4DY9PbEwmE0899VSrgmJfIM9bnrcvkOctz9sXyPN27PN26ZYKQgghhBDO5PEjNkIIIYQQNpLYCCGEEMJrSGIjhBBCCK8hiY0QQgghvIbHJTaZmZnceeedpKWlERgYSI8ePXjqqaeor68/6/0URWHevHkkJSURGBjIxIkT2bt3r4uidoynn36aMWPGEBQUdN5dGmfNmnXaJqWjRo1ybqAO1pHn7Q2vd2lpKTNmzLBv+DpjxgzKysrOeh9PfL1fe+010tLSCAgIYPjw4axdu/ast1+9ejXDhw8nICCA7t2788Ybb7goUsdqz/NetWpVmxsOHzhwwIURd96aNWuYNm0aSUlJ6HQ6Pvvss3Pexxte7/Y+b294vefPn88FF1xAaGgocXFxXHPNNRw8ePCc93PE6+1xic2BAwewWq28+eab7N27l5deeok33niDJ5544qz3e+6553jxxRdZsGABmzdvJiEhgcsuu4zKykoXRd559fX13Hjjjdx3333tut+UKVPIy8uzn7755hsnRegcHXne3vB6T58+nR07dvDdd9/x3XffsWPHDmbMmHHO+3nS6/3hhx8yd+5cnnzySbZv38748eO54ooryMrKavP2GRkZXHnllYwfP57t27fzxBNP8OCDD7JkyRIXR9457X3eNgcPHmz12vbq1ctFETtGdXU1gwcPZsGCBed1e295vdv7vG08+fVevXo1999/P5s2bWL58uU0NjYyefJkqqurz3gfh73eihd47rnnlLS0tDP+3mq1KgkJCcqzzz5rv66urk4JDw9X3njjDVeE6FCLFi1SwsPDz+u2M2fOVK6++mqnxuMq5/u8veH13rdvnwIomzZtsl+3ceNGBVAOHDhwxvt52ut94YUXKvfee2+r6/r27av8/ve/b/P2jz76qNK3b99W191zzz3KqFGjnBajM7T3ea9cuVIBlNLSUhdE5xqAsnTp0rPexlte75bO53l74+tdUFCgAMrq1avPeBtHvd4eN2LTlvLycqKios74+4yMDPLz85k8ebL9OpPJxIQJE9iwYYMrQtTUqlWriIuLo3fv3tx9990UFBRoHZJTecPrvXHjRsLDwxk5cqT9ulGjRhEeHn7O5+Apr3d9fT1bt25t9ToBTJ48+YzPcePGjafd/vLLL2fLli00NDQ4LVZH6sjzthk6dCiJiYlccsklrFy50plhugVveL07w5te7/LycoCzflY76vX2+MTm6NGjvPLKK9x7771nvE1+fj4A8fHxra6Pj4+3/85bXXHFFfzvf/9jxYoV/P3vf2fz5s1cfPHFmM1mrUNzGm94vfPz84mLizvt+ri4uLM+B096vYuKirBYLO16nfLz89u8fWNjI0VFRU6L1ZE68rwTExNZuHAhS5Ys4dNPP6VPnz5ccsklrFmzxhUha8YbXu+O8LbXW1EUHn74YcaNG0d6evoZb+eo19ttEpt58+a1WSzV8rRly5ZW98nNzWXKlCnceOON3HXXXed8DJ1O1+qyoiinXedqHXne7XHTTTcxdepU0tPTmTZtGt9++y2HDh3i66+/duCzaD9nP2/w/Ne7rVjP9Rzc9fU+m/a+Tm3dvq3r3V17nnefPn24++67GTZsGKNHj+a1115j6tSpvPDCC64IVVPe8nq3h7e93nPmzGHXrl188MEH57ytI15vp+3u3V5z5szh5ptvPuttunXrZj+fm5vLpEmTGD16NAsXLjzr/RISEgA1G0xMTLRfX1BQcFp26Grtfd6dlZiYSNeuXTl8+LDDjtkRznze3vB679q1i5MnT572u8LCwnY9B3d5vdsSExODwWA4bZTibK9TQkJCm7f38/MjOjraabE6Ukeed1tGjRrFe++95+jw3Io3vN6O4qmv9wMPPMAXX3zBmjVrSElJOettHfV6u01iExMTQ0xMzHndNicnh0mTJjF8+HAWLVqEXn/2gae0tDQSEhJYvnw5Q4cOBdR57tWrV/O3v/2t07F3RnuetyMUFxeTnZ3d6gNfC8583t7weo8ePZry8nJ+/vlnLrzwQgB++uknysvLGTNmzHk/nru83m0xGo0MHz6c5cuXc+2119qvX758OVdffXWb9xk9ejRffvllq+uWLVvGiBEj8Pf3d2q8jtKR592W7du3u+Xr6kje8Ho7iqe93oqi8MADD7B06VJWrVpFWlraOe/jsNe7XaXGbiAnJ0fp2bOncvHFFysnTpxQ8vLy7KeW+vTpo3z66af2y88++6wSHh6ufPrpp8ru3buVW265RUlMTFQqKipc/RQ67Pjx48r27duVP//5z0pISIiyfft2Zfv27UplZaX9Ni2fd2VlpfLII48oGzZsUDIyMpSVK1cqo0ePVpKTk736eSuKd7zeU6ZMUQYNGqRs3LhR2bhxozJw4EDlqquuanUbT3+9Fy9erPj7+yv//ve/lX379ilz585VgoODlczMTEVRFOX3v/+9MmPGDPvtjx07pgQFBSm/+c1vlH379in//ve/FX9/f+WTTz7R6il0SHuf90svvaQsXbpUOXTokLJnzx7l97//vQIoS5Ys0eopdEhlZaX97xdQXnzxRWX79u3K8ePHFUXx3te7vc/bG17v++67TwkPD1dWrVrV6nO6pqbGfhtnvd4el9gsWrRIAdo8tQQoixYtsl+2Wq3KU089pSQkJCgmk0m56KKLlN27d7s4+s6ZOXNmm8975cqV9tu0fN41NTXK5MmTldjYWMXf31/p0qWLMnPmTCUrK0ubJ9BB7X3eiuIdr3dxcbFy6623KqGhoUpoaKhy6623nrb80xte71dffVXp2rWrYjQalWHDhrVaDjpz5kxlwoQJrW6/atUqZejQoYrRaFS6deumvP766y6O2DHa87z/9re/KT169FACAgKUyMhIZdy4ccrXX3+tQdSdY1vGfOpp5syZiqJ47+vd3uftDa/3mT6nW75PO+v11jUFIIQQQgjh8dxmVZQQQgghRGdJYiOEEEIIryGJjRBCCCG8hiQ2QgghhPAaktgIIYQQwmtIYiOEEEIIryGJjRBCCCG8hiQ2QgghhPAaktgIIYQQwmtIYiOEEEIIryGJjRBCCCG8hiQ2QgghhPAa/w+07eFiJp2sigAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(w,F.real)\n", "plt.plot(w,F.imag)\n", "plt.xlim(-2,2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the signal is real, the spectrum is symmetric. We therefore only need to plot the part that corresponds to the postive frequencies. To extract that part of the `w` and `F` we can use some of the indexing tricks for NumPy arrays that we saw in Lecture 2:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "indices = where(w > 0) # select only indices for elements that corresponds to positive frequencies\n", "w_pos = w[indices]\n", "F_pos = F[indices]" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(w_pos,F_pos.real);\n", "plt.xlim(0,3);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, we now see a peak in the spectrum that is centered around 1, which is the frequency we used in the damped oscillator example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimization\n", "\n", "Optimization (finding minima or maxima of a function) is a large field in mathematics, and optimization of complicated functions or in many variables can be rather involved. Here we will only look at a few very simple cases. For a more detailed introduction to optimization with SciPy see: http://scipy-lectures.github.com/advanced/mathematical_optimization/index.html\n", "\n", "To use the optimization module in scipy first include the `optimize` module:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "from scipy import optimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding a minima\n", "\n", "Let's first look at how to find the minima of a simple function of a single variable:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return 4*x**3 + (x-2)**2 + x**4" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = linspace(-5, 3, 100)\n", "plt.plot(x, f(x));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the `fmin_bfgs` function to find the minima of a function:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: -3.506641\n", " Iterations: 5\n", " Function evaluations: 16\n", " Gradient evaluations: 8\n" ] }, { "data": { "text/plain": [ "array([-2.67298155])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_min = optimize.fmin_bfgs(f, -2)\n", "x_min " ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 2.804988\n", " Iterations: 3\n", " Function evaluations: 10\n", " Gradient evaluations: 5\n" ] }, { "data": { "text/plain": [ "array([0.46961745])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.fmin_bfgs(f, 0.5) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use the `brent` or `fminbound` functions. They have a bit different syntax and use different algorithms. " ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4696174340948085" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.brent(f, brack=(1,2))" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2.6729822917513886" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.fminbound(f, -4, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding a solution to a function, i.e., zeros\n", "\n", "To find the root for a function of the form $f(x) = 0$ we can use the `fsolve` function. \n", "\n", "It is based on Powell's hybrid method as implemented in MINPACK’s library (hybrd):\n", "https://www.extremeoptimization.com/Documentation/Mathematics/Solving-Equations/Solving-Systems-of-Non-Linear-Equations.aspx\n", "\n", "*Powell's dogleg method, also called Powell's hybrid method, attempts to minimize the sum of the squares of the function values. It does this using a combination of **Newton's** method and the **steepest descent** method. This is a so-called trust region method. This means that every step moves the current point to within a finite region. This makes the method more stable than Newton's method.*\n", "\n", "\n", "*On the other hand, the fact that the method is, in essence, a specialized minimizer means that the algorithm can get stuck in a local minimum that does not correspond to a solution of the system of equations.*\n" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/gif": 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A/rqi+XCUflWgMKqcDjkPF6aiNcqiJppG8vBdcfOiOxqjPSpH8VBmGTakjxOi2hBRLqCkEfF9hLWgUIqbRcpH7UBNJjCfVRqbTFoNZYZSXRqlV+pI6bBWTzqmZPql0XBhVKqmVsqmzwCkUAana7qc48BYSWqnMVGmqkQO5rVkfHqnNyoOazVXg0qoICkOWihbiYorcqpaNcSljxqneKoNdIphNFqpXnqp2AAHt+NgnAqpnmoNXrA8o7o5fjpL2rBWOpqqJRqptjVhsFoRFxdRQlqrfrmqvXQNGbSluqqqsroLXGUCEhqsNrqo07AH8yOmyGqrvCpO08BYovqspFqo/tAAqvRjrRfRa0yFqNx6rcrKDEz1quEaq6V6DIFqQ+fardG6Tsywro7artA6rLKwVrlKr7tqr7CwVpSqr+L5rvSUDBH1rwBrqdhaDMoErAcrrOkKDFporA3rrvy6Cgt7rBObrBWhM8p0ApuasQg7rsGwsB8Lsp2asL9AsiZLsQ+rCyq7sg6LsrzwsjBbry17CzRbs+K6sSkrNyWrs54ZqTkLtIrKs7xAVSbws0TboGyKtBi7tPt6s7GwrhILtTErsrYgr09rtQcqta5wqmdjsFx7slg7C2BrNmI7tkHrtaugrY2ltldrtLTgtvMKtztLEd+iB1v0pnYLomzLrGfD/rd9G7C/yVXgOrhFi7ezkEFpirg2K7OsoIVA5rh3GxHHQlXVSrmJa7n9ijv6qbnxQFtUu7WgS6R5CAdxQ7qliw+opQe3k7arq7GKuwqA+7axW7miwgoZZK63uxCVJbm9G7ez6weYG7zCy7l+sK4n8LnGaw8C209+gLqKpLrNWx3Pa1GuG7bV+7ggOT+Cu71rexEGYFTgu7kPsQUF8Dfly70RYV7pm7nrqzYVoa0FkLTxi7sV2DcFALv3S5gUkUEG0L/4exDK5AIhGb86ta5pc8DrK1PS602aw8Dlu1K1WwL+I8Hgu1IZFEEYvL0cRVXg2sHVW1EPnLki3Lz8tAe3/oNOJ2y8/JRBC9XCwTtPyqSjMty76nS2abNTAmy+M6Q49svDPbykBjE/wnfDt8tLNdxRQ0zEA6HDFtXE8isQe5A+QcxSUoyuAgHD0JvFvlumIDywXsyjAuG2JwCvY2yd/zA/dYfEsRtHysS3bry6aHS2jUtP0ZHGhMsPKqxImjbHpetFWmiwgAy6VbSuhyvGerzHKKo4y/uni8zI+JBBaVvImvtC68q7TBzJIYujjmyknEy285BBGOsAeRzKUUsPVKXJUYzKTEsP2Ys2J+rKsvsOpDzLtNy18pDJFprLugxFirPDuOzLrIuZg/ygxGy68XC2rIzGyUyh8uDIGWjJ/pTLOcqUr1H1zMUMDw98x72szdaiiH1zxcgMztw5g+v6vV1szqFLgn0sy7PJzu3sDlpIvVklz/OsDg+cyOWMz3KpDuPMvNTsuEKTzmbpz6WJDu8szKCJ0P98Dspkz0nl0A9dDnoQSItI0Yu5epZDzg2t0fxpDmerzqwK0iFdDn1zxlVzyiaNLuZAVdisyC0tEoIXzB040+SQMhF90zjt0uPwzt58kz3t0+KgTEoLyUMNDhJz0dV0fUmt1PzW0cw7U08N1eLwwCQNylU9guIg1ay31VwNDliNeWCtDQDT0YPnxWcrOltrAgzNCnlUNhLxbCOd1ll8qirgAi4AA3rN/tdHnQpu/QoqIMwqYAJzDQ6Wo9JkfdeFZQyB7Qon8NaHzQ1nG9OOxNI9fKr8DFDoFDUAJTVSh3qq8NipoAea47oeC9roBAd0x0F78DqsrWnjktgFx6dw4AW4ndu6vdu83du+/du/3YaaDQtyrQqoS2l5ja+qAM9+sDUkN2nNbdipkJW26QdvU64XQ9mBW9t2Cmal993gHd4oaAvD/Qpl4zjHnQpbkzusbTZ089hlozvBtF+aU9ipAKoQpAd6Njz8gzmszTpcei20zd1w6t3ifeAIvq21sNapmwrFfd9h1tzUpQo+NDyBXTaeFNmqUNxlo0QmMDfWHeF+cKrNrBeF/jbWBK6mBp7gLA7ekg0Lp5p4fL3XQHbexh3hW7MK5qU7bh3frKDh6i3dKqDYqWBA18M/LXTRm90Ky4LW/abWjW3eJdC2OC7d0+2oofrjhC3do8MKFR7i4bMHUU6RfobiKT7E5e0KNg7hyG3lI47l1GVANwTkflDczJ0KX84/YT7m3uBnZATiT87YS77myVvlq3CqPJ42VVwC4UPn9u0HJ0DkIX7kjK4KYr7kI5MNYt7U9gblS25AcW3oqoDogL3DeK0KQ47q0g3qlu5NqaDnrY7pqzAryjTV0urpMI5hW0A2rNPmh47lwsw/ulM2MRA4xd3HLadC/F3pAMXnHdNl/u9c4hkt6LGAuWLu66MO7JYON5oDUk/66H7wZI8J5rFeC61CVX99n88MB/pZcnCQ7pl+DekT1A5X1k1xZOsq0Vpt7wxYDZbz4vXO7/0+rXlFagI/8NLw58yC2dOQBzRJD24Aje6ABQzfDn0AlPEwB9SIKJUS7YaWDW1QlfJABRgPDxGQkvPAB2QyD1ggIDEGYlRl60h9DW8g8v9R8u/wg/SwBysvDy0/KZXSN/Qe6NcQ8vVgBTjvDidPDypfDz8vKXuy6Bb8Z9nABhXABlif9Vq/9Vzf9V7/9WAf9lyvAVQg9mZ/9mif9ljvAGGg9m7/9mpfh3A/93T/9VSgAW4//hNoAAR83/d+zwThgAd1EDEnBnJzlg1QIQWKv/iM3/iK7wA64PiSv/gXEAGTf/l+cvmS7wDrofmO3xue3/gOoAGhz/gaAPqlr/gJEPmpLwWV3/qKn/mtHwEXAPs6QACwLwWjD/unn/uQD/sVgPqpXxcwQQdM0ATHHwQ+cPzHTwbggAdA4Py6cHJY4JG2oPO28PS3bgskfwtNfwtOaQs1jwtLn/0uL9O00P228P22EP61MP63gP21gAWISAsDoBNJ4AMVrw104APSDwh+goOEhYM6OoaKi4yNjo+QkY0OkpWWflgJlhF5lVhUlpSVVFiVfBGWGm+VbxqbfJ5WoZak/qaolaqsrpWcnqCVA5fCw8TFxkk+fYV9dml1yoN4yn1rz4bNeH592YR8a3TQgtuCdmvc2mk+Yufaa2vhi4jG8/T1gqL2w5mvvrOjpZJOpVolqc0uSRFgSfrkT1KtgLck5ZLk5mCkhP2A5RvGp47HjyBDihxJsmRJdpKQhevTxIdLH0DKDAriRMxLIXSiKXmpZIwPbixf+hgz6IyPNUNeMlHm86UdQVOEioFXSN7Gq1gZ4csaaR+vTgtlVdoK6WEkgbgIRmrFb+EvSWQfmYWEVqJaSGx5Kez6NlIwrpFsCh1MuLDhw4iFKhGmcpDNdXzSCPkpKEiQIc7I+BAyCAkQ/jJ46iBxyS3JZzx2nAwVZMYHzTprdpLxw6f1lDqCmKhDbdMJI6uAg2+MK1yRV4R7ITEcSwvg2YiRJkYyuAlsV7GSGDS3NbASdb2xLP0tzkhw4vPo07tcfKmxoCTsBZXxkaayj6eCWj5NJ2ZQnyCUobHaIEsAoUxrSwzChw/s0eHDbH446NsgqqF0SCLkZVgMcRoKctxF1inXFyQcMjLXI3VFd9cjeSGXEVyWWOEcXdBBIh1eFkHSi1vidaiIeeoFKSRPjCWzSB1RnVEZZ4P4lFOFhECp2lPTtLaGH63JNBMSgjgIoU9XTpOOGfFg6OOZJKJZyIc6JvfIcjD+w11a/t7l+AhGPDInJ0TdUWSnI3jy1aOa/vVh6KGIJqrooow2yugw7gmSRhOjvaSkH0EkQch8Vy5hZJOU7VSYTK3VN4gQXEb4YH6G9acIcITGSkiJGmbCxx635orrrrry4UAevfIq7K2fBGssr7/2Meyyt5KS67G95uEAs9RmwIayz1LLhxsXQMtsBHPg6q2uxWo7rAPjDuusubrOMS0f2LKrwbXs4tpHG93Wmyu44tZbbrq5jifrwMd86odqQjRhhh0CXhpEfH5w6odu8NiUzU5noJHxxk+VSgiqXa7qR0tlbKwxGjm9aibBsYYxMBYEOBBBBDLTPHPNOEfAgM0859yz/gNA3yx0z0LvLLPPSEeQgNFDJ03zzkRHfXTQTiMdtNRNRxAz1kQDfXXVRXNt9ddZ/0yAzWCjfXTZOXstdtNMv/103GkDzfLdkH5qB4OE+KTlw4RodqVNKedG2ZTdSIPlUR+n6qUgYBLCzG8r4215hhVdvp3mCIXIeSMpft4InKKXXiQ0/BGCDISADyIxHnwLUgdpfqQzoSCedkxf4+QMODvEqplqCKymF29Mi8YbcmLygwTKvII1Po/JiNJX74d7fAARRBp4oKEEgERhCrHEftiExBhTaE+ZH5424Y5uTLDG+KmpLjjEGNmotkQadESlaZnWC6AjkFc9GQnQDzuy/l7opIcF7BzweZGSjEuAMBUgsKd18pmfH86QhCAg4QyqUUgfxACECbpqccLzA8gE4YQSmmoMAIKJE6hCCOI98IAElN7ynuc86eWBAgck3Q0FaAcLOYKGFCsEaoThJtTQsCqVG6IUp0jFKlrxislLBxr848FY2RCLYAyjGMdIxjJGog9CCMIY0kCGpKTwTF80oxznSMc62rF0eGBCCX2QhMKpKY53DKQgB0nIQtbjiWgCpCEXychGOvKRHVIkJCdJyUpa8pI1jCImN8nJTnpSjpL8pChHScpSli6UpkylKlfJSsCgspWwjKUsZwlAWtrylric5Stzycte+pKRu/ylPTCHScwx6iACiEimMpfJzGY685nQjKY0p0nNalrzmtjMpja3yc1uevOb4AynOMdJznKa85zoTKc6mRmBQAAAIfkEBWQAfwAsVAAVAEMCvQEAB/6Af4KDhIWDAoMOhouMjY6PkJGSk5SVlpeYmZqbnJ2en6ChoqOkpaAAEX2mq6ytrq+wsbKztLW2t40Af1S4vb6/wMHCw8TFxsfIycrLzM3Oz9DR0tPU1dbX2Nna29zd3t/g4eLj5OXm5+jp6uvs7e7v8PHy8/T19tt+9/r7/P3+/wADChxIsKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzvsnIsaNHSjo+ihxJsqTJkyhTqlzJsqXLl8+wwJxJs50AADdr6tyZTsBGnkCDCh1KVCWWBFakCFJVtKlTYXmeSp1KtarVq1izat3KtavXr2DDih1LtqzZs2jTql3Ltq3bt/5w48qdS7eu3bt48+rdy7ev37+AAwseTLiw4cOIEytezLix48eQI0ueTLmy5cuYM2vezLmz58+gQ4seTbq06dOoU6tezbq169ewY8ueTbu27du4c+vezbu379/AgwsfTry48ePIkytfzry58+fQo0ufTr269evYs2vfzr279+/gw4sfT768+fPo06tfz769+/fw48ufT7++/fv48+vfz7+///8ABijggAQWaOCBCCao4IIMNujggxBGKOGEFFZo4YUYZqjhhhx26OGHIIYo4ogklmjiiSimqOKKLLbo4oswxijjjDTWaOONOOao44489ujjj0AGKeSQRBZp5JFIJv6p5JJMNunkk1BGKeWUVFZp5ZVYZqnlllx26eWXYCaYT5hklmnmmWimqeaabLbp5ptwxinnnHTWaeedeOap55589unnn4AGKuig7JlA6KGIJqrooow26uijkEYq6aQO7UHppZhmqummnHbq6aeghtqUFaJSw0apwYShCU6oSsPHH7rI1OqsAl0giC60NpPBTbyyCpYFvFHgQAYGvcqmGyG9g9Oyf2jAJ7IPuVEmtAwRaya17JDahqDYAqTGIt+i2UayuTbTbbnKnIsuMnecuu678MYr77z01mvvvfiG0wcWVMj6hg535GvLHm5QMAAfbETAgLsC15KHAFaQ2/AtDP4QYOzEt+hAAMa47OGAAHMQ8gapHL9CxR0CyBRVGwkoUvIqc+SBhUwMVPCGuxe4/HIpFQxAMhUQD5Lzzqb0EdUgIQutM9GxDM10LHM4wEDST1dt9dVYZ6311lx37fXXYIct9thkl2322WinrfbabLft9ttwxy333HTXbffdeOet99589+3334AHLvjghBdu+OGIJ6744ow37vjjkEcu+eSUV2755ZhnrvnmnHfu+eeghy766KSXbvrpqKeu+uqst+7667DHLvvstNdu++2456777ry3qUfvwAcv/PDEF2/88cgnr/zyzDfv/PPQRy/99NRXb/312Gev/fbcd+/99/7ghy/++OSXb/75BJ2A/vrst+/++/DHL//89EtnaakXG58/8iTzhoUDVgigAAdIQAGqSm1USEAFKMDABjrwgRQggLMQ6AA2qMGCGLygBjPIhgRQjTa86A0VKrjBEnLwgh68Tf92M8ITunCDKaTECvU0pma00IQ4xGAMJxHCG41hEHiAyA1f6MIdglAtS/jGEHNoQiPOZoZAsUM/lkhEGH4wElB8BAMqkcUS1VAfI5yZGMdIRjEy4CeTkAJTJsGHPbTxjW6MIxz3Vwo35E+OeOTDGhtirbjQsR68IEACBEnIQRqykAQggAMioAhG/sGRkFyaIy0RyUc28pLCcFklN0aJSWpE4A+LDKUlR1nJSywSlJ88pSpT+UlLtIyVqIzlKrfYkCAmYSLbKskfAZTEwBwtO2QYSw+nsctl/BJKXcQIH1o5nEAAACH5BAVkAH8ALDsAEQBdAsQBAAf+gH+Cg4SFhoeIiYJ+io2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys7S1tre4ubq7vL2+v8DBwsPExcbHrVYAABXIzs/Q0dLT1NXW19jZ2tu5Utzf4OHi49Y65Ofo6err7O3u7/Dx8vP09fb3lgD4+/z9/rJSvP0bSLCgQUwaDipcyLChw4cQI7LrI7GixYsYM2rcyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbOmzZs4c+rcybOnz59AgwodSrSoUWEX9B1dyjQYAAFP9c1pSrWq1atY2V1h8IeKID5Zw4rtNGfq2LNo06pdy7at27f+cOPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069uvXr2LNr3869u/fv4MOLH0++vPnz6NOrX8++vfv38OPLn0+/vv37+PPr389/6Rs2FPWHWh4OPDUABwKeFkFUAgiAYIKj8QHVhA7qAaFoXTD4lBUXjlbAhAAMcEeHonFQgIFYkEjaFRUEqKJobZjz4mhuyDhjaDXeKFqOOoLGY4+e/QgkZ0IOqVmRRmL+FmOSRNrIJGZIPklZlFJKRmWVkF2JpWNabslYl14qBmaYiI1JpmFmnklYmmoKxmabTMFQyptw+kVnnXwtieeXTu5ZZp9+oglooGsOSqibhh4K2J2K0sVoo3I9Cilckk7qVqWWsoVppmptyilann46VqiihqVnqXyRiupVqq5aVauuNgVrrEvNSqtRtt5KVK66CsVrr0D9CqxPwg7LU7HG6oRssjgty6xNzj5LE51zXIGFi4O4AUkb0sL0JhY69MEAh4PMQUUekLghBbbdpsQmGwxQxAZYguQRAb2QvOFAuyyxOe4hDqQ4iQ4J8etuooYog24hWBBQyRsAvGEwSmP+qjsAAeQS4gAFhKhhhVd/5CEFG4gQcMHEJ405BxsCaKAtIRALJMgbUgjAhr0OZFxIBAOgbJKZLJPMsAA6C0KADhmwW4gFEftMkplU9GwIFQIITIgGA0isiA4AhOH0SGY6sO/UAFg9CBYALJwIFWV/LdKYfQwAciFUF/0H12bnMbcgXL/s9kdjhgGAWUPv/QcWbiSQEFhz8FxIBQKo/XdHY0rB1SFxy5jHG+b+oUECeVwhiBVSD+JAApODNKYDhhNSwdjKFCz4yaOXbrTdqWcEZh4CaH3IHGkLQvgfw5NOiBsDKJ07RmBekUEjVCBcu+tCL8/RlVhMFYHkiGighiL+eWhAgNBY4G79RVdiLMXwioTx/SNYVH/+Rlf2wX4nys+PvvT6E8t//8f6HwCVJcABNquABjzFFhwSrQRqpIEOZB4CIygTCFKwIha8YEQyqMGHcLCDDfkgCBciwsmVwCMlHKFBUqhCgrCwhf94IQz7IcMZ7qOGNrwHDnNYjx3ycB4+/GE8gijEdxCxiO04IolOAKoJIlF1TnwiCqMoxetRsYoPvCIWJbjFfmmxixj8Ihg3KMYxerCMZgwhGtNIwjWy8SBKfKM24ihHbNCxjta4Ix6pocc9SqOPfoQGIAPpjEES8hiGPGQxEqnIYTCykcF45CvexzBBCACSx3MjOqD+gklFSFITfqMEui4pCG51MpPuIAAnT+mJT3aClIp5QW2uQDt6/MsRT7HL82qTgQoUbB0F0lCDPNcI7rFyHhoA0SV36YhmzIURvaplLo95kVpS0x2+q8T9rkkQrxnCm9wMpzjHSc5ymvOc6EynOtfJzna6853wdMc240nPvPyynvTIHz73KZcAjYif8ZgnQNkxtoGuw5p/UIpBF8rQhj5DTg5dhwkiStGKWvSiGM2oRjfK0Y569KMgDalIR0rSkpr0pChNqUpXytKWuvSlMI2pTGdK05ra9KY4zalOd8rTnvr0p0ANqlCHStSiGvWoSE2qUpfK1KY6NXcLfKpUp0r+1apa9apYzapWt8rVrnr1q2ANq1jHStaymvWsaE2rWtfK1ra69a1wjatc50rXutr1rnjNq173yte++vWvgA2sYAdLWL7uobCITaxiF8vYxjr2sZCNrGQnS9nKWvaymM2sZjfL2c569rOgDa1oR0ta+By2rlGl6wlLy9rWuva1sI2tbGdL29ra9rYzhShud8vb3vr2t8ANrnAHos+2QnMh2TzGcY1RXJEacxinHW5fW5ceK1j3utjN7nVFdxpNRicCEaCAeMdL3vJSwAEMoC4sLscUBsisP2pgQ3znK9/60je+VIjAWO9r3/7SVwoci4h644Ev+Pr3wPTNr0TMpx3+MoCEvxDur4IlwV5IMDgtz5WJGAZR4EKgwQ6acLAkKNKEg0T4xGqYcDhCOYoBI6Kg4amDQk6MYDaouCYuFkaHqYKHTiRBIjSGcIr1S4octyK5orjwISpsGxEPIn8/NgkWpkzlKluZylK4Vyr2wAcue7nLYN4D4frw5TKHmQ/3dMQe2JDmUKzrGW7YsScckIcuL8XJgmguJ8iAhjP0uc8y5kcCCDDoQhP60IYmAAHYG4F9NfoPj4702CQNaUdbGtKFcIB+Nf0HTnuayKbbtKg7DWpJEPnTpE71pwfQ6FGjmtODoLSsL13pWs8a09AQ260pHetL71psEgGxEoihZ5gkRlkQDqaDa4cNUzQQYgqNSHYloG0JPNe0x9JFahnwugZVBAIAACH5BAVkAH8ALC8ADwBoAsMBAAf+gH+Cg4SFhoeIiYqGAouOj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys7S1tre4ubq7vL2+v8DBwsPExcbHyMnKy8zNzs/QshnR1NXW19jZ2tvc3d7f4KIAAg5+4efo6errqFcCjezx8vP09YQCAPb6+/z91AIJ/AkcSLCgwYMIEypcyLChw4cQI0qcSLGixYsYM2YCMECjx48gjVEJSbKkyZMoU6pcybKly5cwY8qcSbOmzZs4c+rcybOnz1cA5vwcSrSo0aNIkypdyrSp06ehHAAYB7WqVWLjsoa5yrUrrgrwvIodOwuf2T9vyKpdayrrWbb+cOOGkiKoj9y7ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPrFnRmt+9racz8Hg7NCRniyJfRSWInufNjY6Y8nz4Mj5I11LP/MsNEu/ddfZj0/k7e1holeMqrnzVlzPr3r+wkqQO//ioyTuzrP8VnSZpDMZSw34CaoMGEXQQm2EkfTZSh4IOb0IEehBReIoYYFWY4iXx0DKKCITHAoeGIf5TRBIkoJhIeGim2WEgaS/Dh4ox/GEeji3UkkcUJN6Y4RhQ9pogHESwEiSIYRRj+SSIfRXig5IhY7DDCkxriAAKVGWZBQweE7IFlgiHc8CWFLdjwwZgQemDDlGgqeEMIbSrYAQ0kDOJlnPZNMAGeBI6wJZ8DeiCmIHoA+l4Mf9jg5AleGArfB2s6at8NV/7RqKTqzVknpu+BMCin69FwJqjvsUmqegBweeqqrFpGgFt/CNWqcyRsGQA+s04XZq7ZjWAmr9RBOog5wCL35h8pFJucpso6p2ezyfmpKrTDCSpIDHdSq5ui2g73AQ2mOuJGt61RSq5vc057Lm6eWtLGuqWVOSq8t4lgA724xXCDk/jaxgK41/Y72w17CkybluoaDJsUnyoMmxfcOhxbFZH+SgxbD5Va7BobdGr8WhQNe6zaHTskLDJqYNx78mp9NLnyamlI+bJqRxQ882l1EGHyzaKR0QPPp/FBhAhAm4ZGEeEWDRqDdCk9Gh1EoOD0aGL8PHVodhixAiEwXM1ZGUeY4PVnfSwx0i7jjs1UGlETEgOxalvmxBNxd1YHElvXvdmPAuqdmXVF+p3ZGUkKjll4Zxtu2RpGSD0IDHAr7tgUdEtemR1E5G35ZD5vTpnQRHsu2dFJi97YEXCaDlkcRGzaUNqqowOyPBqYc0XsB71RckUI4r6NFSr7vpgXO/BrUVjCV0Nx6ftEkDw95mrkwPPRrNCxRxdQ/0y72h+Gwq/+B0mBfPfeqNmPjIhYAcDt5HsTMT9qjA+JDn/k0f4zczJfULb3Z/Msj/5gwCIE2D9r1Gpn+pCRrBARljtEgg0EQF8Bd7GrglhhFGqY4C58ZbyJsEGDzICU4wpChbSAUBvHaknkTjiLOWWBhX2ZQA9WCEO5oIAIcajhXqhwIB3qRTw+JEsXEJEGJUgwiHFpDxLvIh/6LDEu+HmiVbYgNhX5R4pwMVDvsKgUKj6iQQ15FxeNIaH0jJEsFzojWfCQhA6pUSwmeqNYysYiOXYFRke0Y1VspEeiXMoROWpOH60SnUFaxTrYMSRUztAdRT4lPONxZFPOY0ZJMkWJlmRKEzP+yRAvIOpDtYgiJxVSxVv05z+jFIiXugYJRLVCiysRYyo1AcZZHmU5lbQlUdKoy6JYx429RMcWlBHHYA5lRcYcCoy2mMyd8LGZPAkkNHtSyGnuhA/XseZOGMlMbS7Di9VggnC8iRNKkhMnmDynMvpmDTYCU50zESU8Z3LKeTqDf81AwxK6qR8Zse9JtXzQBxORjxTh0p4z4aWGZJSPrcCORIikUeISw05rmOFECP1FC5LWgodGww1EcE9VsFABdmgAE40oKDOyVxGWGuKk17DBDHBwFZeqgwHvcItKISG/vbjyG1M4Tn3oh9Kd8qWi3JDmjUoqCFxRiAzSQVPTBlT+Tyo5EEKwvFEeK9SEcarFoz40Z0ZhotCx8qIEW8DnNdx5F/v5sJhmtcUWkOqNsqEyrizRJz/xapJn8jUlSv3rLf7IjWoKFiURPewrCHuOiyoWJZB87EmKuNW9VJZ66TyMAzI4Ish9Y5OIIarw5ImYy26uqpIlSVYRo1bRMchBjLkqhQD4jTI+hgEXAOt+aKiNsiKGqYPoqd/YyhjeWg6uqQUJHZNLEjwyNyR+fW4phqmOwEo3I4a9birouo3EahcjjPxuRiIr3ouItbwVySx6ScHKb/DBieuNr064K9/62ve++LWEF+ib3/76t2glYOx/B1LKPxRqwAhOsIIXzOD+Bjv4wRCOsIQnTOEKW/jCGM6whp/H3w17+MMgDrGIR0ziEpv4xChOsYpXzOIWu/jFMI6xjGsyxBnb+MY4flKHc3yMGvP4xyr5KZCPIeQhGzkkxj2yLoqs5CY7+clQjrKUp0zlKlv5yljOspa3zOUue/nLYA6zmPXR2jGb+cxoTrOa18zmNvOszG6Os5znHBI40/nOeM6znk3S3j37+c+ADrSgB03oQhv60K7Zw44RzehGO/rRkI40OAQs6Uo7ogR2trSmN83pTnv606AOtag7gelRm1oUST71lmmr6la7+tWAXjSsZ01rU++11ngVEQBdIAhe41ogqWZwsB2RaTv+CcILXjiwL2796/oWuNmVljW0p03taluZR1ugtLW3DWhtc/vbwwo1s8EdCRN+WpaeNje5FWGFdrv73fB290QFHYEIUMDeFMi3vve9bwLUrTuN/APAcSFImKiBDQdPOMIXrvCE+7vQDWe4xBv+8Ehc8BsXxxMe7lqTiHt84hXfx7ydk59K9CEJkAACIbyqk4+7HOEhf8TI45YG+BLCB4J4pyCUQAiM/mTiQPd4zO2RcUgQ8K8vd/nQSVJ03xR8EkigSdCn7nB/zFwR07uNyhcBW0fwXClYCLvYx072sS89FhjIBRVMewgGjBs2LCeEg3ReiKcjJSAJIEDe9673vvOBnQCA/4MDnDd4wRP+8II/+h8iMD3GL77xkHdA1knh+MpD/vGPJ8DgL295zA+i8KBHfOgFMfrSE14QjrdF51d/eat0XaSR6IMd4MbxMMP+EF8XRNftPoiC+3wQ8E2kIWyu5q5P4veCqP0g3o5ypjRdcMb/A8uRHwqcO+XqK+N9LwIBACH5BAVkAH8ALDkADwBfAsMBAAf+gH+Cg4SFhoeIiYYAio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys6F9tLe4ubq7vL2+v8DBwsPExcbHyMmbe8rNzs/Q0dLT1NXW19jZ2rRUAgLb4OHi4+TWAgARtuXr7O3u76pYAIxU8Pb3+Pn6i98a+/8AAwqsBoDBwIMIEypcyLChw4fgvkGcSLGiRUJUdFzcyLHjP0YeQ4ocWU4iyZMoUzrz80eKypcwY8qcSbOmzZs4c+rcybOnz59AgwodSrSo0aNIkypdyrSp06dQdzKLSrWq1atYs2rdyrWr168oL4AES7YsLgDnzv2ZY7at21T+adGOfUu3bqgr9f7wscu376Q7b/wKHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069uvXr2LNr387dMAwT3cOLH0++vPnz6NPrU6K+vfv38OPLn88JBn33MODc38+/v///AAYo4IAEFmjgVjDoceCCDDboIGMlDKLgg9SlQOF1LF2o4YYcdhiVDYNM5SFz4I1o4okopkgTCYPYp+KLMMYo44w0qvJBjTjmqOOO2xTAY25dRPgjbyXsMOSRSCb+qaQuLmS45JNQRillJjA4OeWVWKbURpZcdnkPi16GKeaYZJZp5plopqnmmmy26eabcMYpJ0dbzInZCROC4oadXd0oiIt8BiroKngOauihiLZmR6KQjVFIk4xGKikkQk5q6aWYXqZfpn0lwemnoIYq6qikbuVpqaimqupSZqzq6quwxirrrLTWausrld6qa5Jr7EpWgu7oYIsVmFCxl69Z7Wklssz+OFezpFzREAWEhPEHsYPsCe1TzyZCwLZFJaCBP45sCe4oLpyr7rqIqJMItuwGFUa3j/hzbLw/uasXvlZlwO9NgT3CFiRuDKDvvwmZ+wobCCtSZMPVSTEwxEP++REwxRhnrGSvGnfs8ccghxxgFyKKbLJ5gJ7snMIqt+wUxy7HLPPMNNdsc5Z13qzzzjz37DNkKf8s9GpdBD300UgnrfTSTG/IXtNQR11eF1JXbTWXeV6t9dZcd00KGl6HLfbYENdB9tlop/3QsJ6RvKYaajuUwMSMGd1mHn+o9QfLcd8Dr3flnNH3PmDsx4hJxPg7kgWIKJ4ovdyJUcF/iIuXx+TcyTXJBYOgNQjD3c2BeYAahXf5dtJOAjnk2d0x+nsHC1Ky5a8PDo/rtuNzeu729GEt78AHL/zwxBdv/PGkCR478tiAHXy6DbFhRV58UIHFVsunOkc3V+xRgQP+LjGfjQMV6IA3WeSu2s31Zc2OqhsAaCu+NlQMkJcgVmhwsVXZl+oGFhGIwL7CIAUCJEArdPuD/KyjAnb06l6c6EMb8uASKwyAD8RihhW+ZTP3TQQLAqCALd4gAAcQQgN/gwrnYnUHQtBte1fp36wigAUr7G9+1SjgAAggQxz6MBEn+GE4gmgZ0BligY1AIpSWBZk+WIB9hOiDFIzoCD5YIIFCnMUFHEcIC/wuEn1IAN8w1sOEAQCLVjAhJdRwwSzSwoCG2AMAoDiJAYTPja9IY0Ho+AcqAOB8gugDFqSArTlc4IaCEIsH8YgKN2gAAFZIIAG65YYIAOANbmAAAfj+KAg/cpKRqagAvQDAwULkAQA6oFYirgAALoJSFQMQoCkLgggGnFERakDHK1lxBwDcbxBtAIAaDaEDACxSEMEc5i5RYQUAjLGXpSyELaloiFwybpmpiEA0CeE5Q1BhDgBwCd6sQM1m/hKbpQgnIhwwlznMQQ3ESgAD3oCFNzAgdYPwIzXRKYo3OBMR8lCYBQBALj+SywIpjMAB+WkKKmyzEPYbRB/odjGEFmKODDUFAz4JzAEccxAWHYQVVpjRUBCrDbJUBBauqYiQriWlYtvDIAt5yE4IkpCCMCQiLzFHYT3iDec0REjbkEKxVfKSmdxkI97AhqY61amAzJYlMan+SY5WIg8t5MQcEnCBqKaND6hUpSOo4ICymtWs+/yDHFNZ0lDYEoudSMAtVSqFutrVrhdrAxX2yte++vWvgA2sYPeKT64V86OZOGwjsCBYhb3hClaAbA0ja4XJStYKlLVsZTF72cxydrOevYJVDbSppbAzrYcg61nPitrTtvUTVPCnOP9whQjcsRBtCEMYsKBb3fLWq52U7R/OR87XVsKd8PwDA+aJBTZIAQsEKJ0l3BkGYi2Xnn+wZ2GNC4mBFpSgaxFEGJRJCe92EryCcCl3ITFRQtwQspho7yD2p15R5AGCoExfKOrLCSP2EqbILCMygScF4HqCv5qwAD6bmcL+KUaCDxnY6dliO1z8dgLBmNgiITLwrAp8ERJ7EGPf/DiAHYpiqxew8CWCSbcI/DKNlWBDG9fbCTgSwgEiAutoFWFHGm9Cjxt1L0b+KNGZ5rSmh1CkjzPBhmJG0lvPOipVlZpajC4ZE6JsBCkNcUq2KoKVrrxyHQE8S4MY4q2NyCWZxQyJXgaVEMk8hGIVEWc2U6KZYyQENA8xzTQDgKV2joQ2HdFNjIBzttcqpy8DPQkB3HadY0FuPJmb3XsWQp+MjgQ481yIgKYXvQYFaUIXmulHOBQSEf2DfAVB3xRaudSOCPIj2uBRR6h3pLBuxEnXnIiV2hpec+B1rjuHBZ/+SgKojRhqUYdtSgNrAsXOZra0p03talv72tjOtra3ze1u9yZn3g63uMdN7nKb+9zoTre6183udrv73fCOt7znTe962/ve+M53Ieym7xD1+98AD/gnoCfwQTAR4KUtuMIXzvCGO/zhEI+4xCdO8Ypb/OIYz7jGN87xjnv84w0rEchHTnI2Jzy+6OZ3yVfO8leaIGv9BnfLZ07zmtv85jjPuc53zvOe+/znVFE50IdO9KIb/ehIT7rSKSNzoh986SGj2hbAA3OAx4BKw4aBC4ROCZFHgoiEuDrUx+4yrufbPl5ouMi9XnKqkf3tcI+73JMi4SyqeO4aX3aUMMv3vvv+ve8RkO5l9FsYOiQlgBRIvOIXz3gKMIC8F6ldePCwFDaowfKYv7zmM9/UDDz6Ih8OGec3T/rMa+Dz23jz1UbPetJ7vhx6xwant9IEScDsD0+bhODAWJTW+14Npy/V7q3y+9a/Hhd194TqEwF5YyQfUcUvPRuOf4vZE2P5r7A+WJynilNBYvg6if7og0+O2NfSGc+/DPipgoX2u//98Hd/BgTviBbyYQ9314QbSDoKKQh4EA6Qf8GwB/tXCfiHf11xe4qABmfAgA5YEwYUgQkggRQ4gZOwUBOYgRVIgQTQgX8QASYEgh8YgiRYCCAoQA6Agir4Byk4Cc0naCUogjI72ILpYXiaoICSQHnM1is6aAg9mAiCkwaIsCjeZoND6AjrRwm5l2swk4SRgIOGwH24gVgw0gfL4ySBAAAAIfkEBWQAfwAsLwASAGkCwwEAB/6Af4KDhIWGh4iJioUWi46PkJGSk5SVlpeYmZqbnJ2en6ChoqOkpaaGfaeqq6ytrq+wsbKztLW2ghe3uru8vb6/wMHCw8TFxsfIycrLzM3Oz9DR0tPUsVLV2Nna29zdrjre4eLj5OXcCebp6uvs7e7v8PHy88MA9Pf4+fr7/P3+/wADChxIsKAwKQIMKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlwpMiHLlzBjypxJM2KqmjhzLrwiQIA9nUCDCvQptKjRo0iTKl3KtOlCn1D/vHFKtarVq1hJWsnKtWuvOXO8ih1LtqzZs2jTql3Ltq3bt/5w48qdS7eu3bt48+rdy7ev37+AAwseTLiw4cOIEytezLix48eQI0ueTLmy5cuYM2vezLmz58+gQ4seTbo0Kz+mU8vzg1q1a3asX8s2x7r17NveYuPeva0279/YdAMfDs038ePNjCNfjkw48+fDlEOf/ss59eu6pGPfTks79++uvIMfr0o8+fOjrKNfH0r5CUMw9LCfb0k9/fuYzOPfL4n1Hv4A1mcbIS4EaCAirG1hQiEuyHfgg4P40QWEFCIIhwoVZkiIHjBo6OEeMZTgoYZdmCDiiBW6cCKKEIa4YoEsBnjCijEaqCKNNQJYAo3/5bjfjoJg6OOPQA6pI45G0v63I5JJsldkk/R1WOSEUDr5ZJVWCkIlluct+QeMXHJn3JVhblfbhV6WCV6CJpKp5nV+7HHjjir0+CZ2XrS54xYD3nndkirAYZ+fyy1ZQgx7DErocAo+qd+iw12pKKS/PdnjpJTiBuR7hGCa6WtewmCnIJ5+mpqbnfZpqmxpJlLqqqGhasirsHom66yq1jpaq47QqitmtyKY66+dtUmJr8RKFqwiyCbr2I2XNOvsYiZmIu20h22x7CPXYksYtH90GO2w3jo2YyfdluuXtkyOq25kKoKS7rt4wXGuvOTSOxi7osyr71zxppfvv33Zu+KWnvhLcFvaDhJovwMvfJecL/6SorDEZ9l7WsQYx+VHw0HCYcrFHXtFcXgcl8yWxq+QrLJVH7d7issvOyUnIaK2QnPNSvnBsiw783zUx7YELXRQcYLZXcpHX+VHntkx3TRVfsRQiINASz31Un7oIaQgVtdi9NYwSSjzLGOTrVKc4vqSttonPc2pIFuMKrbWcOtUdXR4502Tz18H87bfH328IDGDE75R0sckrjhGEibj+OMUsa3M5JRHJDchiBaDeeYOgZhc36CDBLgzn5dekOjPpK56QE8HPvrrLLEejeu08+PF3LeTnvtEe8Bw9jLN1qZqyr7/vk2JBNrNDLLGD/hoqskrP40eAQcntW/CTV8I7v7W7wKyNr7aV3z14TODZje0eiet9+lT42JuHEePK/WkDgp+/K9UG06p9sNfhKKnP/Txbxgq2NY0XuU+9RiPWfs7oCme1DZuMDBXDRwY/CSIDGOV44KHyOAiNsjBYigwGwA0nwOdYx0SllAYJ0Rh/VTYpweiRjsufKEveEWbGQqrNTY0TgsNqENZAOlw6kihq4CoG+UMsYjK4GESI6YfIXYqVQKEojFiSL9eaZCK0iOiFlfBxS4K6w+emtQD0SjGMU6wBLJzh6LW6EVIRNCNkSgB7+KhRjymowQm2AI+7uhHXgTSeXxsYyGbYYLO6YOQi6QFohQpw0iuI1H+gKQlR/4hyEMkipK9AeUmBSfKUI6yG3zK4Ts0eUqLlZJ9r2ylKWKwxy8NMJYWxKUsYaHK1ehyl5ygJbd+mUtg9o6YxTQm6pAJS2U+j5XFYaYz0SVNM07Tc9CURjavucRq/s+brUSYuyoHzmuKbJjl/CY3gbFN7a2zF70cSDuvOc9KvpMTSqtEPAtST2Duk5/pzNwWwtaygE5xnUjkZT+TecouCLKWWRPJQukF0aUZtB0TJZZ8COqICm7sohgF6S4zqs57loekJTVpKVAqDpaW8J/kVKnAWOJS/sHUIjVN301xKtJVIZKdPR1kUKG4U8gNVYc5PahM85NUpS5Vn0116suEaf7PnERVcUX1yFX9tlXYHPVBCdXeV//R1a2VNaRPHeFZ0doxrGlzrWwlyBUgwyd3cm2swmCDIlxCoazGDa/MIIBg8kkNuCbSHW3QhACw4CG/psSwr8lnWO1aFcim5gUcIMcbNosVzr4DAFABLQAcUKUMZEADWdEAavHxk0XwIS8ebekdusKHxH42tH9YrSMoYAF7CHYuk/3pAi2LjzzY1h1R+cNrJ8HXP7gBP7qZLVdqO5DWGiID0CWuPowLj+M+ormEAO96HFsT6jJkuffRLj+460zxhGW63h0pYDPCXi41cr7UzBd6sbKHPPgTv2ndRAwmOw7yBnht6j2wHAGsYP6CGLjBvxCnNSHMlAdTeBYS7iGDL5zJBFM4tvTz3XOz4oc5vOG9td0vB+c1FRLngQ1Y6MOLw+DfBzmywCSjwDWcdoU5xFeCHpZIGGL8QgtjxQ2MfWmQJeKHMFhhVHx47++MfIjfKuUNfcBCWFKRByzodcppo4JV+rCHO/jXy3yosRvCAOZTDKAqMG7xG7DQ4j+w4cuqo/IgpOsUP9xEEH92LpvzHNAfN+XOpdOzWvagBiJPh7Aa5nCFNyzpRXA0jt+kNDwRFAlNa0i4pjSICO24ZOwQOMQLUeEkFH1PVufyeH1z9TRlzdBbCqjSqy61K3HIQiHSENekdkgAB4grAv6GUNfD4SiOIaLqYueL1jE6Z2JWOKxHQZtFpxbMqIsNQU8De5mwrrYakf3tpZ3R2Whk4/fIXe6IHpt6NzR2Fp3FvMaYx4lNzPe6262RcRM7Qv8OOL952u06ChxbJsjwYOJtcAge/Fe8k/ZK1phVipOMjg7POLvbS8Avdpzaw9bExa898E1gvNsfP/bGSz6zsU3v4/iGucxnTvOQszxqpXy5zG9Z8577/OSUcmtNNjjzH95cc9xjo7hhrvIb5u/oDuZeyscVmyB6G+oWzZ/T1U11rT8c6/xg4b7HSSosrvTqYNenK9tj67H3Ku3GSNvOuvdEUqO93VUXJc167Xa7w/4dqA8GetcF/r6V//0TdVf6rQ8vaoyH0TYWXzrjAVrFGnbc6FXKdmcwBXK13n3yaHv2rwsOeoFYe/TdLL3px41Bzhte9VBtOM/TzfW2w77DDbd6vC3/+duvwnu+ZiLkLe973A/z6QA/+OuLH2x0yn75zGdW7Y+v1q9HP5HQ+yLyry/U9pCc++APv/jHT/7ym//86E+/+tfP/sxpvv3wj7/1Oin/h4C4/vj3DKjzzw/68///ABiAAjiABFiABniACJiACriADNiADviAEBiBEjiBFEgTkFaB69B7GMgJQreBHviB83F/IDgO+zeC3NCBJpiCKriCQoOCLPiCMBiDGP7jgjJYgzZ4gzi4S8qWgzzYgz74g0AYhEI4hERYhEZoIDR4hEq4hExIHF7ACRpIgTvYhFToEApXhViYhU1xhVrYhV74hWAYhmI4hmQYgSaQhGWYhhMRaGrYhrvgB+/nhrMkh7NwOBdIh3iYhxARh3rYh374h20RhYA4cE8oJOIigoPID1xICmyogCW4CGg4CA4CB13wiIl4iZJwAoLUBSJiiZhYCf5XCXfohS4AA6N4CnGEiJ+4iqz4CqfYipZgNYsIi5UwNxXVCQsSAxJHi47whLz4i+Qwi8A4jOvQiMR4LAwhZX9haDnCjMcYCXX2jJXgjNLoDQ5QAVaQjdq4jf7cqI2RVAcEQQHOwAAVQAHmeI7omI4RYGX5kAvN4ADgwBJN8AfzKAjzWI+cUQFsoAb72I/8+I/+iAXsiA9J1n4ZoI/+mJAAyY8CmRU1hhd2sAZtoY8LqZABiQ44MWJvQQeDgAeR4ANjUB8BYZEVWZIkeZImmZIoaZEHuZIACWMDSRUqNhMhKQgeOQlAIAjgWAhJQAhO8Ac1aQZ29AdM4BUIqZL/2Ggx+Qka6RDUCBkcOZJI6ZJUOZVWSZKCQJFUCZOlEI0N4ZWQ8JBGcQaQYAeGcJOUgASSIJRN0ZJVCWMYWRNNyRU+gIyUwJZvcQERgAV82Zd++ZdYYAVLqQgawP4GxogIbKBblLAHfMCYjtmYkMmYf0AFM9kJh7kIEQCZkWCYkNAHbYBdkhAByviYpKmZL0GWh0AGhTCTaHkGaOCasGkJZQCbr4kGUekUBEAACaCbvLmbvsmbuRkBf+AAwkmcw1mcyPkHDBABxElazPkHzxmdxnmc1Gmc1pmcl3Cd1YmdkTCd0/kIA8CcwjkK2lmeyLmc5rmdg8AAQCGRYjAJfIAHlykJdiCInQCWkvaeofCThWCWeEmLqimRiYCWhFCUgyCUAmoIlcmTVCFmIrGgfJEGhKCflsCfiEChgiChi6ChNfkHOVkVW/EMEEoMeSCO0OEHlTmf1ciLqrmilgZwm6cQCAAAIfkEBWQAfwAsOwAOAF0CxwEAB/6Af4KDhIWGh4iJgw6KjY6PkJGSk5SVlpeYmZqbnJ2en6ChoqOkpZYCpqmqq6ytrq+wsbKztLW2t7i5uru8vb6/wMHCw8TFxsfIycrLzM3Oz9DR0tPU1dbX2Nna29zd3t/IFODj5OXm56YCDn7o7e7v8PCo8fT19vfUGvj7/P3+uQz+CRxIsKDBgwgTKhQ1b6HDhxAjSpxIsSKweRgsatzIEVnDjiBDirw1Z6TJkyhTqlzJsqXLlzBjypxJs6bNmzhz6tzJs6fPn/feAB1KtKjRo0iTKl1qDgsAAB+ZSp06jEFUqliz7hIAFarWr2DDih1LtqzZs2jTql3LFugdof5t48qdS7eu3bt48+rdy7ev37+AAwseTLiw4cOIEytezLix48eQI0ueTLmy5cuYM2vezLmz58+gQ4seTbq06dOoU6tezbq169ewY8ueTbu27du4c+vezbu379/AgwsfTry48ePIkytfzry58+fQo0ufTr269evYs2vfzr279+/gw4sfT768+fPo06tfz769+/fw48ufT7++/fv48+vfz7+///8ABijggAQWaOCBCCao4IIMNujggxBGKOGEFFZo4YUYZqjhhhx26OGHIIYo4ogklmjiiSimqOKKLLbo4oswxijjjDTWaOONOOao44489ujjj0AGKeSQRBZp5JFIJv6p5JJMNunkk1BGKeWUVFZp5ZVYZqnlllx26eWXYIYp5phklmnmmWimqeaabLbp5ptwxinnnHTWaeedeOap55589unnn4AGKuighBZq6KGIJqrooow26uijkEYq6aSUVmrppXexUYEDUvCBaT1YCMCVAAak8Gk8BnT1FAennnMCIaN2dUCr7wQQqwAr0OrOCl0JwEAfurrjRgQESAFssO7kUYEnbFjhhiF5lORIHnkgS4uynVygxhsDeDoIFldEQgUW1sqC7SYaSPFHH2EQgoW6kuhgRbmwzLGsJm50a8gbBBwbSR8EtEGvK+dmwkAEh3BaiQ6MDMxKwZZcQYEAFf60S8gcAKgxSB7vPvuHGsYeEgYAbDi8ir2ZtCGFAGFIO8jKcP3BBxsOJPCHFRE44DIheQAAr8mmQGxJBgQcEgEA/grChgBYUKEIH74CnYrQlRCgjyEJDHDIAA0rMkDRUpdC9SRzMH0IAVob4gDCjaAddikoY2KFANVifdUcDKQtyBvyFjJAQG+PMrYkmyIycd2DULG0UNVKUYHZgkAtTuCiDB4JAfMeMrfAf7zBhxUCD0BFy8cOQO7eAjhNeSiWP/IGADvzPEDmDBBwegWmb5yAt39gMcAeq7N+ryVWdH2IFJPzwXsfiP8hxc4Z6BC88Jg4UHIifTAQMyJY6IBF5v55OMD79J3ELcnnf7hxtSL2jl9IHgSgrXoFsZO/SeuIqMFA05DsYUXzieDDFYBnv0/gDxHUmkTSZJO555gPPO0CQHIOuBuNgQKAwrnD8IjzOk20y2MT3KBxrjIJ1SmHgr6RoGNewDlqhIFtxsnArbxiQkVw5Q8tTM4FJgcd6SmibiQ0DgaJc6s/ZCASFyhgiYZYnRsqcRtMFCJ3ovhED1Gxisy4AxZts8AtevGLYAyjGMdIxjKa8YyKqVu1uvgjK6gQjXB8DzviSEeNLHB7SLIZVeYYBosJqYHrmkr9/sAGCw4piFpxgx+FNMipEFBphlQSHqWiyDoSY5GWzKQmN/7JyU568pOgDKUot6OHUZrylKhMpSpXycpWuvKVsIylLGdJy1ra8pa4zKUud8nLXvryl8AMpjCHScxiGvOYyEymMpfJzGY685nQjKY0p8mWLVDzmtjMpja3yc1uevOb4AynOMdJznKa85zoTKc618nOdrrznfCMpzznSc962vOe+MynPvfJz376858ADahAB0rQgooIBgZNqEIXytCGOvShEI2oRCdK0Ypa9KIYzahGN8rRjnr0oyANqUhHSlLNzLGkk3pkNq25zRKg9KUwzRIbY0rTmtqUKTBwAUJvytOe+vSnQA2qUIdK1KIa9ahINclJsznTVkQyqVCNKpKsQP7Vqlr1qlU9naVEmI0IUOCrYA2rWL+aAB7qhAE/E4wdgsCWQrpVDW+NK1zh6gCt0nKucs0rXveqVzZEwK6OyGFK3JcXPKTBLn3lK17rKolJnuSKaCGDXxSbWLf+VRIgDI8YBkHYQaDBDpAA7R+UYAjJSgJYTRgEHpBCWb4SsrV9ZWwkHIuhOiBCtFiBLWwvG4nMDnYsqy0EbieRBEmcgSi6rWxyZcsTyBbFtIOYaXELg4XqWve62LVuGBwwQD40lRBuSKIl+LAH8pq3vOglr/O+m4nOOsIB5WUveN2LCPFO4rz4TS96aXLcRtAhuqkgAxrOMOAB2xYsCSBAghes4I4GMzh+xlvbHyRM4ZwJwsKQSFuFJ4ywCjcsZx0OMYdH/GFGWPjEJpYwJRwANhKLuMKAmwSK/zDjGdM4xTfOMYb/oMedQHcW8qWGYNk0XUFI9r+JGG5v6AsSQJ4kuIMosi9IOx7nBqOGLZlCI45cCS1b4seeUekx+ABDZTgZJX2AcijwEGSpOqoM3lwDKwIBACH5BAVkAH8ALDwADgBcAsYBAAf+gH+Cg4SFhoeIiYIRio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWVAKapqqusra6vsLGys7S1g262ubq7vL2+v8DBwsPExcbHyMnKy8zNzs/Q0dLT1NXW19jZ2tvc3d7f4OHAFeLl5ufo6aUAEX3q7/Dx8vP09fb3+M6oOvn9/v8AZQlIELCgwYMIEypcyLChJVQOI0qcSLGixYsYd2nIyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbOmzZs4c+rcybOnT0oA5vwcSrSo0aNI/wwQkLSpU2dMn0qdSgxAVKpYs9ayylWr169gw4qlxlUAKqFj06pdy7atqyv+buPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069unXmMeBc3869u/fv4MOLH0++vPnz6NOrX8++vfv38OPLn0+//mk99vPrJ7xnv///AAYo4IDGxEDggQgmqOCCDDbo4IMQRijhhBRWaKFKMPhx4YYcdughJhp+KOKIJJZo4okopqjiiiy26OKLMMYo44w01mjjjTgqVEKOhuHH449ABinkkNTAQOSRSI7+ckKSfIXI5JNQPrJklFRWaeWVWGap5ZZcdunll2COaGSYZJZppksxOHnmmmy26eabcMYp55yIZEjnnXjmqeeefPbp55+ABirooIQWauihiCaq6KKMNuroo5BGKumklFZq6aWYZqrpnyVssemnoIYq6qiklmrqH1uYcOqqq6VaSh94sNoQHmmQ4YQSSpQhq0G02oprE2OkgYc7u/ZDaxm3KgGssMQWi0+vTiyRxLJ2NOusPXisgeyvwVZ77bNr2CotsGh4+y224UY7bbfWnguPF39ku60STLDrbj1ZhCFuEvWmYe698ozQwRM9GEGvvQAH3EEIN+xAxBFjlNtuwun+CMywDTTY8MQVckxMMTgEEGLxDRjbMMEHL3ycTgFmReUAyRlP4AEJKaj8jsB/tGyVASSMYLM6Fk9Q8gQElIWKFz7+/E3QQ8/ss9Lh9GckCQsLHbPTfyxpINTgvLBCCFabjHUzd3B9yR1YUAGz2D3vEobZq+BBhxlHEFED20/DDY7cZkyxhBJG9OBBB6bkkYqakeACNd9+0yuGGVmkzErZpETAj96NMP43E2KgUYfHy6hRyBuNvI2I6OfyMbcY0nJ+Rh18DNIfLYZnongkDDDwB1yJzHHVqaqfwXoSS4hxBh2g54IWL31AJGrwwzMxxfHJY34N9K1Pj/wj2lkPDfb+/GpfvTmUfwu+9NQn5DwisUt6vviauNrPG4gfCj0TxBu//Uim/1F+oHyog/Dwt4QpmIEO7QOFCvIxO0P1QYBiIKD2EhgKPYxJIgwY35ceOEDiTTAjeeBdBkTxvzBxMIIePB4FO8KGSWiwECvc0gkleMAY1qKB9qjfa/bgBt4Rwg0XGCFJZujBGioKCyIhYgGNOKkSRkSJBkTgL5JGpNitjyJ9sAMaxNAED5aBDrHyXjeyuMUuFvCLYTTGBQWxIzE+wg1h+MIRjICEJBzhC2Zo4TRuVw3UQYcBVniEVf7AR3zgwAY7mMEPZlCDHdgAB88QYjgk+RymbESQ9shiGlD+uAQnHDCN0diacPJQyHhooA2PIIcgCKIOTY6BCbhyAhqz0UZC6PAaTpxKKd9RO0msT49jtEMaXhnLMqwBlCki5UFaVg5XwlIJsjwmjXZZDtJhYinXcKYSOkkGaeJImQdZniBeWAxXmtEJ3URmOai4HGp+xZzEQ6c347HG5YDzncIcwznTKZheZsWdR4EVGvQ5A2imk5zy6NSoYDXMJhRTWG7kBkP1GUt+JmQLtdxUPh1q0HlGNBsbrahHI4HQj+5iDb+yqEnDUdKVujQ98HqpTMsDzLAAtEpzoIIAsGDDU9lJIZabqVC/8ruhGrVFfECilm5HBULgMCv949IAxlL+06N2I6pW1UZVs5oNP86mnly9hqrCmg1PDWJKZM3GLdP6jIyy9a1wjatcqQTWudq1JG69q173ytfmeCGvfQ2sYPlSgpgOdhhjFQQ7D8vYxjr2sZCNrGQnS9nKWvaymM2sZjfL2UkBtrOgDa1oR0va0rpHlKZNrWpXy9rWuva1sI2tbGerqC7Q9ra4zS1CPqtbTNi2t8CtBWqDW4nhEve4rFgrcg1h3OU697nQja50p0vd6lr3utjNrna3y93ueve74A2vX54q3vKa97zoTa9610ta8rL3vfClrXvjS9/62texzb2vfvfL3/7692d1/a+ABxzXPfCWwAhOMFu7p4n+lpI2wAqOsIQnTOEKW/jCGM6whjfM4ZmUYL4dDrGIQ4XWEZv4xCiG04EprNwUu9h6Dn6xmbSzJBf8wcY2lvEwWow5HjcCxIWYnReQZosY6zhQiT2ybkssiPwq+ck/MyyUG7ukLUh5yljOspa3HKettjM81vwuKsEbZi7PwgpoTrOa16zmFKkuMBGIAAXmTOc625kCDmAld5jQBCYIYgnAAIJTMCAINqjB0Ig+tKITzehFO7rRkH70odlgBd1lNtKYlnSmN/1oSjtAPhSkg48lYYc1RIIOReG0qjXNakxT2tKS8KdznGAJPiSBEGJIBBDGwIkpoKPVwF61sIPN6kH+DPvYxGb0q+uThjocwgeCoMOt4yWIaQuiCX/gtSQ05OdB+BodyA53ssfNaEKXgtyHvgKsI9HT6KDBFUo4BKoPoU5voFvc+Ca2se/N71Vb4dOTkLUjAimJdcPHDObIt8L7/Whzk+LelTZFUyUB8EgQvDOCboSuHhHvy2Dh4yAPuchBHgYqZJDieeADkAtBhXZz4gp74IORHZEBNiCUDZcEy7tTYeqMJIAAPw860IcudIIQ/ehFJ3olBqDnRyT96Ur/A9Kn/nMCWD0BDohA1v+w9a4zYusho4TXuf71spNdEGNP+9cXUfFGlD3rn9b6H+ROdwe0XRR2n3vc9653vTNpIimATkQWR02PMj+q44LQVc8RkUZsF8LZglj841MjcJFM3CQrRLwi5t0IxHN+Ei7fycULM/qS7FwQuVaE4hHheESIwVqSR8TOtf0HaPfk8oXBvUk0ZAdNAJrwwTX1GQph7e2SIfKrCAQAACH5BAVkAH8ALDkAEABeAsIBAAf+gH+Cg4SFhoeIiX9tio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys6UVtLe4ubq7vL2+v8B/e8HExcbHyMnKy8zNzs/Q0dLT1NXW19jZ2tvc3d7f4OHBAOLl5ufo6agC6u3u7/DxggAM8vb3+Pn6+/z9/v+K2AEcSLCgQUpSpBxcyLAhQHIOI0qcGG8AxYsYM2rcyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbOmTXUC3tzcybOnz59AgwoduhMi0aNIuQkwmrSpU2hLoz6dShWZhapYsxaLCkCg1q9gw4oday4B2bNo06pdy7at27f+cOPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0CepiE69uvXr2LNr387dEgw43cOLH0++vPnz6NOrX8+eKIz28OPLn0+/vv37+PPr38+/v///AKrkQoC0eUHggQgmqOCCDDbo4IMQRijhhBSy1kUJFWao4YYcdqicC354KOKIJJZo4okopqjiiiy26OKLMMYo44w01mjjjTjmqOOOPPZ4DIg+BinkkKfBMAyRSCb+6YkeSjbp5JNQRikKkFJWaeWVWGappVrgbenll2CGKeaYZPZHZZlopqnmmmy26eabcGYyIJRsWHGIG31M4kacK/VhARY6EdIHFWpQkkcGgfIExwlZZpDBH3kS8qclfSTAyE1+vJelGwDMYYgVDmDCxgB88FkSAWYVwgcAWGQygEKmhgQqPa0SQgUAeQiKhRR2/vEGoopkAMCRMTG6pRsaAGCFp4QQwJQgbkQAwBtuMEBArYjcim2sHlXw7DwEHLKqDhQ8cgUAj3L70QARGHIHPYgwgOsjagDQrrodzQEAFYa0Ae8hOgz7iL+h4suRFdMakgcA4R7iAABs0AvAVQb+bxRBw4X0AYBFhlDxBgAKlXpFBLAWgjC/FWsEMiIPEzLHHHX+wQADc2DBhhRYEKBDxxC3NGeYH19qCBYACG0BABoIcuujzIZRMCERpJoyRlRgfMgAKEPKrCCJCmJFr4SwOnVGDGxryBsDENvIziZTPLZE/EbrCBYXPCLFHYXMEUGkb8/Sx669/tq1Jn/zyjWwnwiAhQ58KzJH1tnqlEepi4DdNy3RTlvttY28oQYboIcOeq6GZE6ttWZvkgfenEix8QBWX67LwuRCIoUDuOeee6HiAlC77A7JS7oowkOya0LII58oH28034bz0L/xvPTRPz/99dVnT/32jQOvSsD+aoMCvvFUlC9F+eYnqgYFFFRQQfvvuw///PK7X3/8+NOf//3tD+79KX14WMQeQQXdGXCADuuZXraQISroK2SCCAMFIDeINoQhDFi44AUzOLxCeGxlIiPZ//rxspglgAFvaFXNOIXASrxMDXaaWc1uljO2jTAfR0vaH26lw0FQwH+SyKHS0PWHpj3thvfow9Z8VQg2pOsSe1ji4L6GiskhsRp8sMIALAeKHoYiZkW0V7+654g9XTEXThuFFDr4CQtcgVkI46IUWggJPlgAiGd0BRts+AmP/cGKn7jAoyJ1tEJUIAyUslQeYXEFB1hBCuHjxK0GADtQcGqJEYAcqET+Rap9mMAQXYhki9hoDFQVwgHEWlXqJvGqRfpjVmUjRNdu1cHCBQ5xiBCWKOWhqTMiS1lLLISzSiet03EuEdpyZT+81QiG9e53jTjXEzUSIj6xSxHvqschiueIet2LI2SIk74oWAh/adMQ43MEwZS5D4ThURALi90gBCgxt7HzHhdrhMY45sGPQXBkJSPEyQaiBCWMcGWNaNkgShhDmtkMZzrjGR3vCY+gza1ogxDiDoloRENEzR4FpWjVIIG1QShRlibj4h/ENg0GfnISBqWoIWL5CLTtEp2fsmc4kiDTbP1BbpGgm91Yt9C9iQMNPQ3I4sjYiMc1wo+AbINKq5H+hCb8AalJhcQdSLkJ11FSntHwACHEkIasHoSrhRBrId5pVn4MoCvf+oNa2zqRLsxDKob4QAfoKhIG8rUhHriBIeDKjlD+9SCBLcReD9uQEchVsIRY7CNuylh3JDayviCq49C6or9RoVZv0EEwOSLZP6hgQHCg7CkEwFQi7cENFSCVG3CHyIZQrrKE4IMAqOBFgtz2DzwdhGObkQDV8sgBBODsPX4bXFeM1hJHJIQDApokHYA1HszNrXGBIS1EeOUQhfrtjfogra3xoXzK5UZrrSE0SDjALFYoF4+WJQA7lQoLWiSnNlpbB/FCgklV5ITUHhHXQuzhuyuawx0w+Af+B1TgDQh0wESp0b0liAG3obhASXe420FIob4ULoSFJWEgbBTYSX3ooGb/UIFzMqMOZhjEiO+RXivhjQ3fNAaMZXzhfdQNERFAMCHaK4grmDRHedDZsoBR4R4PRL+DCFQb1nsIZWEYHjV2RK6659+x1QEPIMmxJHrbIjMqJrouikCWSYHVQcSYI1kkhQWey6IIdJnNhXizSAbsiO0OYqppXvMl2nzDNlSAzPtQ8ycITQzDMkPQzOHdIZYyEDtngtEioTN5IN0ORUuC0WVIRi+hwWnm5IrSC/E0IurADD38LBsrLs6JO2JpilJMyB+RQE+TxZWlOADKhUA1QWowg1z+LkOn37CFcR5GWLg+4s5XHgQfiGyOpHHlD7hUBAWQHY8kLKFF1G4HtCFh5nJ4W0bTJsi3hL3Tb5OBDjYKdznkjYhn3WGY3Wguj9INEFGOGxoGDTWR6L2WgD+J3wU3+JUIrpUylLWaA/FztCdO8Ypb/OIYz7h1qKzxjnscw6/ux55gxfGjMGva//64yltB3ZW7fDKzfjl0riBxmbtDvHmobZYYzuegUC5XOoeWzQky4SgtMdZV+W250cTwoyx96PsIOtRrZKypW/3qWM+61rfO9a57/etgD7vYx072spu9GEY6u9rXzva2u/3tcI87X7ok97rb/e54z7ve9873vvv+/e+AD7zgB0/4whv+8IhPvOIXz/jGO/7xkI+85CdP+cpb/vKYz7zmN08Zv3L+86APvehHT/rSm/70qE+96lfP+ta7/vWwj73sZ0/72tv+9rMZNe53z/ve+/73wB8I3YNP/OIb//jIT77yl8/85jv/+dCPvvSnT/3qW//62M++9kvx0u17//vgD7/4x0/+8mPY8+ZPv/rXz/72u//98I+//OdP//pnRvf2z7/+98///vv//wD4Guj3fxAXgHRlV1vwSQDGfDGQCfgneTDgAg9ogBQYdxOIfBdYgbZnVxrYgR74gYwnaSZRcr9Qc72gadjRdMT3dCDYgpnwNTAYgzL+CIMJsErH4GI3Il+jQAERoIOg8F6SUC5iFglDeAgRcITsk4RKuITsQwCIZgxS0HM38jlUyAZVeIVWmIVYuIVa2IVc+IVeqIVq8GNgWIZhaIZl+Ado6IUJgHR492O3sIZYmAAoqA4qqDB9gQdlBRBn2Idy6IeA+IefowuCmIV0SBEpBxNNAATIUYifc4j4cIeFUGpIUQdIUAgxFRfTRAuOSDMoAWgpsYfBEYhhCIn3IImEwGnABiObOAudWIfpgIrSdk9YUIu2eIu4iIsoFA17wAe9+Iu+GIy/+FOJKAhtAIeS0ItvcQZowIzM2BYEcF2dkACoUo3UeI3W+AdmYY1s3IiN2EgA/PQMEeAA7UKODVaO6MgA44iO59iO5jhP7GiO8piO4/gH9XiPoYKPlYCDIyFwkABm0oYHJBiJWRVO8KYKmbh5obYGj/BtgsCQlQCQDzkI+tYTqygjBmkJBfgIopgUoFgmfUBlgQAAACH5BAVkAH8ALDkAEgBfAsMBAAf+gH+Cg4SFhoeIiYUWio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys7S1tre4ubq7vL2+oRS/wsPExcbHyMnKy8zNzs/Q0atU0tXW19jZ2qka297f4OHi1gnj5ufo6err7O3u7/Dx8vP09facVDr3+/z9/v8AAwocyIwKAIIIEypcOOgNw4cQI0qcSLGixYsYM2rcyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbOmzZuEBODcybOnz59Agwodyu8C0aNIsTlMyrSp06dQo0qdSrWq1atYs2rdyrWr169gw4odS7as2bNo06pdy7at27f+cOPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27N6YThmDo8U28uPHjyJMrX878lIvhzaNLn069uvXr2LNr3859rIvu4MOLH193D/nz6BP7Sc++vfv38OMPhCHfNf36p7vg38+/v///AAYo4IAEFmjggdDEYB6CkW1hAoMQRojTghJWaKFJMFB44YYcdujhhyCGKOKIJJZo4okopqjiiiy26OJYD77YFxwy1mjjjTjm2NF3g2So449A7qJCkHPxSOSRSLr+ogKNSTbp5JNQRlmMj1JWaeWVWGapZWDQbflVDF6GKeaYWm2hIZloHkllmmy26eabcMZ5kYJy1tnifVf6sZ4hek6yp50t6dknIYJSUqhNXgwpZp9/CjKooY/GtAeYYx5KaKOQYgooSZE62imkm5okaKeW/jGqp5pemipKMZI5Kqafvloqn5+G+lGtuM6KiK62ehRrraYCWwivvW6kK7HEDitssRgdC2yyqjILUq6pnroer9BKW9GzjVor66+rhoRnm8g+emihe/6qra/hBjtIpLBquuy6Ey2b7bu00qvRte16+gip8+ory6nB9uvnuQFnarC7ijCa7sICD/xtI9/+EqysrKAkDMmrERtjMcUVc6txxwTdi4nJBVf8bsgst+xyyCTbgrIlKLe88ss456xyzLN83DDLicy8lX4WWovqITYjjW7BPCPkrcNC0wo1xk0LhHC8Jw+6NMNamUDphvAqm0nYl6IyctXN+PwJxDQ/LC/bjqI9zNkHj3K12AfDLbcrdEficMbX+lt2JVHvbbbam3C8Nrzd6n3xPiUYsoXjH1JOC8A3j2254fAoHnfmN7v98+bYxABcIUZyfrGw4HquNOmqszMvtQsXbo3ppsAepr0i/9t3PxMzC225tf8+T9LSDt+7I7a3g7zAs9NuKtNSAw802gEzPrXrRx9/Pef+91p698P5uvN87IIz/yfZK5cPjX6R+w4z+j9vrPHb4NB4Pv27cu37/9HKRgzgMD/+SQJx9auf1nSnixKUwAVmopoBL2E8kDWvFw50oApi4IU9XHCC8eBeITKYQRNA0IMglIie9uCFLcBAUX8gIQlNmEKLbOEPLjCBDHdYAhjWkCIx4iEJBfG1H05EiCQ8AQSNSBEkOrBHW/ACApnIj+GAyYmRe9C4UFVBKqoDBidAYt064SwAvogPHGHhC3k4iBPQR4p+YyAXGxfHHLEhAhARFBy2oAIZLo4Tf2vfAeVoISso5FVqDGP87MZAZ+ntg16Mo6z20IXUnaKLgsTbGCP+6YmWdakVmOSe+O5WPReh8Q9Lecf+YhFKn41yaq/j5CALKIkzkQKT/gNd6EbXojkYQg3hWCUvcJkrpakPSAOohjALwaRctLJa0DzmigxWjmUs8xDmOZ0unmnMx+kyfTfyJTKumTbYLW+X/DIXLm1FTkdMSpu+aOWuFgjL9EGyTu3MRheJ171XflNf+awEPImxz3YtMJP+W6eE2iCz74UCDkU8RkF5OTrRsdOh9+hbICn6uoPWKA+pCKj3FGa/4hGSSCJVxSeL8TuFaqYPDA0URm2hgslZ86StYYMidCIQkLaNlhdxqWbCAIoEiHNbM+2FJZkh1My0gaeX4GlM65X+VFzAYYvXaKqYfJqy4CmjVcrEaWaMMpI3RMANb0irWtMajRZkg63S0oBc5yrXDHRDEHc9RgbOIVfbMACqhdCHInwKWO8BtRlYBUcfdAoVrq5DHwAQQGQnQdYQVvUZYBWELbGxB8Y+5ZTtiOxBBpLSniw2Ko5dR2H3UVqhdDYqoAXIar3R2qSctrEC6cM3aluNZr7jtVCJ7VZ4K8B53PYpqaUKcbVyXKcI1ymvcoAI+eE1sVrzqE7ZrFCWK0t6cHcdMchsd7s63fE67bD/Mm9GJajebbX3J9Z9r1qIJt/6riax98jDHGLqhzbcwb4S4cMbsDCHxaphqgAmBJ0IEgb+NrRBuwlWyICxG2GI5OEKz0UKguE04FSisg0ZRgqFw5SHO6gBmOvJQxuwgIWj6LYQWADmovLgBzegEgt9cMh6BhyUF484TXeI8Xr4cAXP/qENHq4wQGKrIQEzBcJwYsMd5pDco7DByG5yA4tb/BQZk2apSg7zZIroQzEzBMpm/od408zmNrv5zXCOSETjTGe+rLnOeM6zno3YhTvv+R4uiO+fB20VE9CX0PCAp28RzehGO/rRkB7FSiNN6Upb+tKYzrSmN83pTnv606D+iJ9DTepSm/rUqE61qp+B31W7+tWwjrWsZ03rWtv61rjOta53zete+zoeo/61sIftlBv+ErsXrT62sveB5mWvwtjOjra0p03talv72tjOtra3ze1ue/vb4A63uMeNIDCT+9zGmDS6183udrs7Jup+t7znTW94xLve+M63vtNx7337+98AD7jAB07wghv84Ai/ypwTzvCGO1wT/X64xCdO8Ud4AZDzXnjFN87xjjf80B4PuchHTvKSm/zk3zZBxFHO8kK8uOUwj3mszS3zmos72DbPuc7/Leid0+viirpPsn2uCpCn4uWWbnYjVi4I6MChC0onOqxPcMMuRC7qA4e2JWiubBfAgOunKPMfhi71skca7KhYtLQ1bvZEPGiABr942+dO944jfeI9D0eSx7mMENf+nUF7dwvWU7Rh3VCDiQSgghUWz/jGO37xV8CFA1iDhzqIJAIUwKMoGMCAVAQDEpmXRAQwT4HSm/70p3dA5w8/Cx0QgC1NYEITBMGEXeChH2xQQ+53r/ve8/73vg8+8Icv/N5Pgg17bUaRi098KmgeIobUUfKZT33iW7/62L8+8P+AhTCcWPu6d744Ag8K1rfk9oOow901YYc1RML97si+/MFP//kXfxD2r7/+84/9PxQ59/InfpLQeZvhA5WAB0pACGOQCAbICWIQFPy3fxIYgcbXfd+HfWoggOBAfo3gdy6xgIKAfpIABImQBITgBJtgBw/YDhQ4gS5of86QAP/+d4HXp4HosQRU0YI6+ILXx33eN382GArRZwsc+BV2YAgiOAlI8A872IQ8GHwxOIMB+HyiYH60YGNU0YAHdBsJYAVb9oVg+IU6QIWigAV8sAceeAh9gIZseIZu2IYawAbrpwjJFxbw9wdpiAZnoId6SAhpEAllsIeCiAZ08A8EkACHmIiIuIiK+HqM+IiNyIinEImU+Ih/UImYaAkEgImQuIkJEAGTB4p/IIqkGIqTVwkOQIaPkIqmOIqtCIoOwIquOIulSAi1eIutaAqn2BK1RwhHKAp5d2pl8Ad32AgoWAi/+Ad/eAjJOAg4yG1k8ArL6GvT+AjDWIwnKAnVGAkkJNgYaVgbdpCEllB762cHj/SN2faHaFAIS7hx2/hwhZgKgQAAACH5BAVkAH8ALDwADgBcAscBAAf+gH+Cg4SFhoeIiYIOV4qOj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmlQKnqqusra6vsLGys7S1tre4ubq7vL2+v8DBwsPExcbHyMnKy8zNzs/Q0dKvfdPW19jZ2tvc3d7f4OHi4+Tl5ufo6err7O3u7/Dx8vP09fb3+PnHDPr9/v8AAwocSLCgwYMIEypcyLChQ12p/mB4SLGiRWARL2rcyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbOmzZvgAMzBybOnz59Ag/4hAECo0aPNiiJdyjSYAwAAMjadSrVW1KtVs2rdyrXrtKsCiu70Sras2bNo06pdy7at27f+cOPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069uvXr2LNr3869u/fv4MOLH0++vPnz6NOrX8++vfv38OPLn0+/vv37+PPr38+/v///AAYo4IAEFmjggQgmqOCCDDbo4IMQRijhhBRWaOGFGGao4YYcdujhhyCGKOKIJJZo4okopqjiiiy26OKLMMYo44w01mjjjTjmqOOOPPbo449ABinkkEQWaeSRSCb+qeSSTDbp5JNQRinllFRWaeWVWGap5ZZcdunll2CGKeaYZJZp5plopqnmmmy26eabcMYp55x01mnnnXjmqeeefPbp55+ABirooIQWauihiCaq6KKMNuroo5BGKumklFZq3QmWZqrpppwWWE2n7uThhgOgFuZHF6WmiswAAu0x6KdjqSprVXnMaqtWnw5SayH83PrNHb6WA2ywxBZr7LHIJqvssraEwWw0UT2LjVJuSDuNFdZGI1U/CThLJwPYPhJtMRfsQkC5z1iQYioaOMKHIEr5E8GuzLia7R/zIijqOmFtO0lY/+SLYLXqxHvJuP0IjAym6eQ61b4D0SuvxDT+2VsVwf1Q/IcaAWv8ix7vONwUxJYpbCDGlZlccVYkp+yxTMNOJTJlKt+7TM02J4NzzsfszHMxPv88TNBCB0N00Zf0gYUVsQ7yxsyHvGExIhG8K4sXxuZBwRxWkEoIFWxE0ocObyhyNNKUMOBsHmEPooO3kjiAciFnh4JqQi/z1EetMb9lRQKHYOH1JG8Q8HLVrkxdbB4DUHHIAFhY4oAOVOctShclHNsHFU9JUTYhVwhg9R9vXCHFrlY4fggVoh9SN9qK7OFGBASwQbEDrOoaxgAZ/CFFBIMXggUAkRuC+E1YWA7U3GwlUMHjvX49wBVwH8KGAO0ar/wmilPEfIf+dwAQLiF8CBCBIW0IIIUjbwjwvPGj05RH9X0L1b1aoTctyBzmP656InkAwPm0V6DtmSUDBDhEHwAQvUFgIQHBc4MOiieINwAge3SL30vycIW2/QEL1fuD/pDihhB6hQDrOwQBEkg+Klghd3zgYAYEQK/r/Y8QrysJ1KgSPzZ4kCz8+94fLpC7P4RNB7ITABusYK82NDB038vhI0AWkp1o8CglPIsVWGg9AJSNDwNgwOdWOJY8MCABMZNCA3F4RQSZsCsVSCEiHKC6POTKjoSYwwDGxwAK0s2AkIDBz/pgOEXMIQFt1FU1KuCtMLzPdYCEXSHe4CwrjC8RasDgIf7+ZklB5KECO8RXIiWxhZ9RIQKdhEQerBBKQrwBC62UoiT3dz9VHG+WQ4skLmshy13GIodw8OUvdSnMYULCDy4opjGV6YteMnMVznzmKaIpzVJQs5qjqBnWsCmLa3ITFApD5jdnIbBajpMVAjPBOcmZh22uExZ5kAIBHsCBd8KCDwwQQL/qac9WWAEq/SpAP1thAbAAgIsDPcUGDBq8hJpiAGD5oUNN8QAGVECIE82oRjfK0Y569KMgDalIR0rSkpr0pChNqUpXytKWuvSlMI2pTGdKU6+UsqY4zalOd8rTnvr0p0ANqlCHStSiGvWoSE2qUpfK1KY69alQjapUp0r+1apa9apYzapWt8rVrnr1q2ANq1jHStaymvWszBAkWtfK1ra69a1wjatc50rXutr1rnjNq173yte++vWvgA2sYAdL2MIa1kd+OGyl1KnYxjr2sZDNTisjS9nKWvaymM2sZjfL2c569rOgDa1oR0taFCV2qJNdhUT1klphvKEN1/mcUGH7l1FmSLbIuaSeLMnb3vq2tzck0iNLQYEBfqO42YwABYq73OY697kI5SgbOPaI6VpXDdfNLnaxG114BBdP29WueLfb3W7YdpN9Gq96uTsOYmqFDMFZ73rL+xkxDGKUaLDDJuA7iWo0oTXyDW946duO77KlDq4RcICnS2CpRBgYGec1hG5pggdPJME2C1Zwg7Ph3pnwdxA7vDBysEDiEpv4xCbecCzcEGFCoIsSfDDnS87wCDqAWBVkQMMZdKxjBI8GcARIQJCHLOQiE3mFKtYEqYDH5D844HxPdjKUBxjlKk9ZypoAHr6WzOUtE8LKWAbzk9dIkAqLGBIfpkVrcZnm4bQYQEqAHRoIMQVHwNfGlajzJdpsGRkLp8KlnWUZjLqGVgQCAAAh+QQFZAB/ACwqAA4AbgLGAQAH/oB/goOEhYaHiImKihFWi4+QkZKTlJWWl5iZmpucnZ6foKGio6SlpqeKAKirrK2ur7CxsrO0tba3uLm6u7y9vr/AwcLDxMXGx8jJysvMzc7P0NHS09TV1tfY2drboBnc3+Dh4uPWVgAAFYIR5Ozt7u/w8fLz9PX29/j5+vv8/f7/AAMKHEiwoMGDCBMqXMiwocOHEPlJkRKxosWL4TRg3Mixo8ePIENWpCKypMmTKFOqXMmypcuXMGPKnEmzps2bOHPq3Mmzp8+fQIMKHUq0qNEBAowqXcpNgCqmUKNKnUrVJACnSatq3cq1q9evYMOKHUu2KgMrFP/0Kcu2rdu3/nDjyp1Lt67du3jz6t3Lt6/fv4ADCx5MuLDhw4gTK17MuLHjx5AjS55MubLly5gza97MubPnz6BDix5NurTp06hTq17NurXr17Bjy55Nu7bt27hz697Nu7fv38CDCx9OvLjx48iTK1/OvLnz59CjS59OfVQMONWza9/Ovbv37+DDix9Pvrz58+jTq1/Pvr379/Djy59Pv779++X34N/Pv7///wAGKOCABBZo4IEIJqjgggw26OCDEEYo4YQUVmjhhaT4geGGHHbo4YcghijiiCSWaOKJKKao4oostujiizBOEkOMi5VAI2N63Kjjjjz26GNAMPwo5JBEFmnkkUgm/qnkkkw26eSTJnkB5ZRUVmnllVhmqeWWXK4Yg4ZdhinmmGSWaeaZaKap5ppstunmm3DGKeecdNZp55145qnnnnz26eefkkkJ6KCEFmrooYgmquiijDbq6KOQRspKCVtIaumlmGaq6aacdsrLFiZ4KuqopJZq6qmopqrqI2msCpEYdoCzR6WhIoKdq5s0QYc8guKqSR9K4OHrQnwoMexCdDBxrEJoTLFsQmOU8SxCTrQ6rUFLxHotQX0ksRYv+m0bjB1L6ALmH7WK+0saTtwSrrrFlDEGLe/Ca8wUaNjrCR9tbMNEHfp6QpI2SQgbcD94GHuwJwRgs0YTC4PyhjVn/ogRsScTWyPGGRdvMochbEija8elUPHUMsGSrMm5gtxhSALKdPutyqJ8vEwdytJ8is3GpOGszqXMbAwZ0gJNT7WbqGC0NEsAfIkeQS4djcxSx4NHuVXDs0a7VF7gjVvyUomFICeXJUa+lKQLo1OGEOByWf9OmVW/biXBB40JXKXJwGwljImNIJY9ieAXqTEMGFg/0kIhJPTI9jVf76IRMDbs8EjkhVwgIlZXEY7XGGZs2fBYTaxhCcvZCB0Vvwtl9UfIXi1hcD71SkV3QK4bckFaXFGdiNq/sR5Pxpe8DRa5/qge1e0B8TxIGF+x+0/tUAk/HhlkTMc8eFNY+4/y/kxZD162j1Baj/NQUc+d71m343chWwDePjcPz++OGfPaz87Z+rMzcv/jSBkAw8GHJAxQHDg7YCTcAI1mVcR4RPHDx5wHvuREqyKwm1IfRocMJ5gOVAo8BANyNwgseE4YsgshN9j3kCvczXaF0dwkHPEIHbwCeejBwgsj84YTGoICiMjDKKRnEQj+QYhMuYIhoFecsFlke0wx4iAymJfJacKKgyChKaYABuAx5A5YMJwgrEBFNxAPKlSUDBb/IMZVMCELF9mhIfoARaYwMS8+LAQD/8CHHuLCgCfJwxmZksbAqEEAdNPiIN6GvlPggQjyC8ntUGcUPoRMjoah5Czi/sADFd4CCzIkBRhy4MlhIBETUPBAKUchxUVo0hM86MAqTYkJGjTuD5GcJTSyQANdXoMFNvClNTxwA2FWIwSqNOY0biBLZUrDBiNwpjR6+YcUSLMZWxhBMAWhvmsWowPF9KYzQjABcTajBBNIpjmXYYNmrlMZNIjmO5MxAmrOExkd2OY9j+GBcu7zGOn8w4z+KQy9PYCgxOAcQoURyoUO4wAOLYYqsTKAiPoiBCGwaDBuoE6N9gKaHv1FPEPai3qStBfgPCkvyKnSXQS0pbloJ0xxUYKRztQWJr2pLfKpU1v0s6e1mEBGgToLZhJ1Fja45VFhYc+luiIL+nRqK6oQ/k6ptgIKQ7UqK3jQUa2eIpZeXUUfiCDPsJoCD5Yz6ynW0Em1msIMUHCrKcRAQ7mOogljs+solMAFvYoCD4D0KygSKFhQONCLhcXEBXOZWEwgjRBdaCwmstVNyU6ChQK1bCWQ5welCWKgmpUEEUOLCScW4pWkNQS+PpvaSjBhV3+IbGslASxMzhYS77vtJOgAMd1OwgwW860kZMAx4UaiCQ0wbiQEqFxFYLa5hiAsdBPhs+kqgmjWTcRjs2sI8nG3EM/l7tW+a4j6kZcQ+DsvIfinXkG8tr2CKBh8c6te6aoXDcFtL+jg+4fS8TeF7Q1vdnHY3tGqtwzZg2/3+Bu3/gB7a74Kay9v+Qtc/m6Mv/9rL3PPW0D+2ve8DoTvBeHrwf9qS70CFmtPCSwL1HrUwOdFMH9XC98Gt1e+7aXveScM34rxlw7Fha/T+EvkIhv5yEhOspKXzOQll6CyTY6ylM16gilb+cpYXipjs4wJF3P5y16tIJgT5QJBlHnM/fCyML3Qq2OIGYC3EqwJEPs3brY3aomFMiWqXAjQNnbLqW0zmi8haL8CGhN+nu4WCs1dPTd60JCOtKRn0cZlNBIZbxaGo4Uxhz2up44gsW2jBimSU0IK1B8R9aQJYYVWu/rVsH51XpPDB9hWJwIRoICud83rXlPAAQ5YjLJy9odh/u/ixLLBQhigxwY1NPvZzo42tKct7Wo329rYnvbuXCVDans72+D+trjDTe5n/+EKbAhZudc97nZLOwO8uwWqtSJHW3sCD957hL2l0m12+9vdAP/3H5TtbDYG/OD/jja8K8O1SnQrEkDI3136jfCKJ9ziIUN3Bi/O8XYvXDU+EMS+DQExiRcisH8o2iFmNxWKd/zlGM/2wMNQcEHA/ObN1kC8UeXymPsc5wXXeCGA7vOP48LTeUH2JJDQlp4T/ekAn3nNBwH1hBv9FqSWChAeofJFRBg5VLijKLBA9rKb/exlx4ANTcGGPfAh03/YAxvWGAm4zwRtuSjDGdCw972PmRw0oyNAAgRP+MEbnvB/OLziC194QSz+8YQnAAEYsA4HVP7yf7B85tdxiQgEuxSWD7bn/zD60lseZqYnvehXr/rPMyRWX19E1ynRBzucK9+6MfV2Zn+IE/eWEEM23SGGrNa/K4LHhMD9IOCOctLo/hiqPgbfSqJ8RUhL+CQfhcRDnpromxKIzairSeyeCTyQf9U6TTD2TxEIAAAh+QQFZAB/ACwwABIAaALCAQAH/oB/goOEhYaHiImKhBWLjo+QkZKTlJWWl5iZmpucnZ6foKGio6SlpoV7p6qrrK2ur7CxsrO0tbZ/F7e6u7y9vr/AwcK/VAICgw7DysvMzc7P0NGaV9LV1tfY2drboVLc3+Dh4uPktDrl6Onq6+zrCe3w8fLz9PX29/j5+vv8/f7/AHdRORewoMGDCHsBSMiwocOHo6Qcg0ixosWLiqTMwcixo8ePIEOKHEmypMmTKFOqXMmypcuXMGPKnEmzps2bOHMWEvBGp8+fQIMKHdoxFdGjSDFOTMq0qdOnUKPeEgCAqtSrWNtZyMq1qzqqYL2KHUu2rFmZV6gI4nO2rdu3/nDjyp1Lt67du3jz6t3Lt6/fv4ADCx5MuLDhw4gTK17MuLHjx5AjS55MubLly5gza97MubPnz6BDix5NurTp06hTq17NurXr17Bjy55Nu7bt27hz697Nu7fv38CDCx9OvLjx48iTK1/OvLnz59CjS59Ovbr169iza9/Ovbv37+DDix9Pvrz58+jTq1/Pvr379/Djy59Pv779+7304N/Pv7///wAGKOCABAoTQ4EIJqjgggw26OCDEEYo4YQUVmjhhfPB4AeGHHbo4YcghijiiCSWaOKJKKao4oostujiizDGKOOMNNZoY2Iw3Kjjjjz26OOPQAYp5JBEWndCkZNt/ojkkkzCcoJ+TUYp5ZRUVmklcXBcqeWWXHbpZShZfvlXjmKW6RobVhziRh+TtGHmVX1YgEVPhPRBhRqU5JEBnQ2F+WYtFmTwB5uEyGlJHwm4+SdTbgCwUSFWJHMJGwOwtShSCRBgyB4AYJHJAN4Y1EUJl9ISKQAMeEoIFQDkUScWUlDzxxt7KpIBAEaVChQbOgBgxaODELBQIW5EAMAbbTBAgKqIsMqsP0fqWksFwxYCgKaG8AGADhQ8cgUAGkgb1AARGHIHqogw0OojagBQrrg+natWIW0AIKkhveaqSL33wouTFceaey0iDgDABrsAbOVvThFga0hVh1DxBgDe/rAVBgXzQgpAxgvbJECohhRMyBxzqJEmAwy8gcUcWDR6cCGsvlwPHNF2XMvEihqCBQA5WwCuIKyGOwgFfA4SwTs220SFw4b0QUDGfQA7KyFsCPrws0nLlOq+A+iLCB9WDJAmIVYonPVMxTqCRS6PhNHvHBEQKk/NVPYBq6y0Fq2J3bEKkjcoWOjgNSJzcJwIr4O0MfbZ1uxR7LFuKIv1IW+owcblmF/uKrHGIis5KFJncoUDVkghN+PbaMttJFI44Prrr8tMCKerD7M56uGoe3soCayrtg5SBC988Hrj3lC+pCCvNhVUSME8884XfXQC1Fdv/fXYZ6/99tXvbrww/n0ULPsiVMBu/vjIAICnJ0a1L4j7f8Av//v0x1///N8vQ8UcFP9hqSBWcMMh2hCGAhrQgN4D2sQq9oeLGS5/HiGZyf6QgJQxyw0CmJwkJHgyC7LMZRAMic+EFrRB7EEKEdBgJEYItJ8NrXghvEjUCFE0KvAhhZiY4SCKVrVV5OF/MZxHGPCEw1CATWyiQNMg+PeuxJ3uETkLYjQy1bsBoK8TbgNFnOY0CIAt7g9SuOIi+GABGEqRGX0oYhIJ4okMCEpuPmNEGA6VqDNKQ42ewALpTPeJeoUuAhmLFCYoBUQ72iOBnMhUyIyiLRVGAlSGHMmptkbDQbBqd3zDW60S/nGrwUUSI7zyVegIISxDPM5zy1KEs4YBpU86g1qLGFi2ttUtR3xLaK70CLkUcS4GpMt3i2hXE3OJEXnty16IUN4i+EXMjgDMjII4F9MIIT6Ema2ZFmmYIyBmCIn1z2IYOwTAHojNh3zMESJbYsk6qLIPGqyb7yxnRXCmNp4NgoV/KOELDXE0eVpkaY9wGtSkxkOrWcuRqjCBP69BSUe0oWuOOOIX/1C2hVIkbZFYGySyuMS4WfQhWMBlJN5ATkMgThCK+yhERrmJ0ZXuiavYgkJVGhBE0vSmOM2pTnfK056CQg9d+AOpfErUohr1qEi9yhmSytSmOvWpN2klVEWS/iu6TfWqZLkDrOgEK5hKggyzkCpWd8EHNqCMohFwgE0fkYaxykKAwQhDp0rqVhkKoF+VKGRd9+GAWu71I29QliGsAE1B0OEUYv0rMv7A0l2EkSf+Q6kVFfuLOQwAGG2w0xz2ILaV+Q9gYqRsLPKA0Ftkao5/iMBkKaqt0IrWsZe1BR9y1YfNheECEgHZa2fxxAT6EhgkZRUbd+uLOzBjDwRwLXGXixqwMve5m5moIewA3YDgtboMue4fqIvdgmj3E560UQVE6pbvasKqPArDUuKC16VOYqgpWt8n1jqWfh3WTNWqSzL6oIRI6MEFVJIuXMyLCADL6Jo4Ue4tbMAk/rBUhZuFpddgENzde7g3EXo4kJYUhjTK0rch+f2rXi2SgeG69cPsiOI2C4Hi64TXKyMuSCqMex6viqXFFeZHjMX14q7geFE0NouNc0zkIhuZJj0+Mj0urOQmO/nJUI4yUN5QtB8fpbZ/CLJ3ErtSavhBDfIdy4bCfJ22jqojLxtyVt4AV8lcQQC5aqyUydFmRZT2LFiwMpMI0OFCyEoRIc5KFOUclSuoWTGB/kMb1gsXV8lMy12585/qLBa22NQNkr5LBvpsQmeglyN5uILMsIBalGKF0sQyjIn9oqRD7Lgpry4Mow/3PgwuQsCiQIJMSHYWTE8mtofYnJbNq+eh/iRZKng69mU4HYo1zFkZfn02TD4t7Uv8eRHFZkWrq83tbnv72+AONzPIJO5yk2UEf1CBudfNbt/ogdrtjre8570g/ZBAECXwAr2/UTN17/vfQHkguQFujYUkmuAFDwvCsbGVB8964RCvicIjTvGKWzw7I9jBxTfO8Y57/OPiminImXHvkZv85ChPucpvhO6Vu/zlMI+5dDQu85rb/OY4z7nOd/6l/vIcFvf9+SvaKvRXOLfoSEcHl5PO9KY7/elyce8WoG6KqVOdFPq+uta3Pg8mc90TZvi62MdO9rKb/SlHP7vadaHhtbv97XBXB7PjTvdJ1KHuoFA23vfO9777/v3vgOfGwANP+ML/Ie2GT7zi8774xjv+8ZD/Q9sjT/nKW/7ySSc65iEx+M0nYtuKP7Tnd74H+JZd86Pne6xTb/nOs/71sI+97GdP+9rb/va4z73ud8/73vv+98APvvCHT/ziG//4yE++8uEFekroXV9LV3vWuW76Tcw0+n03sNibv/zuQ7z6iRc5J1xfd3iPHfyPwD7hue/99rv//TKPMEqyTUwVu2T1FpX/SejfEbpW2woAGIACOIAASAVz5wyr9h7RVg7lsoD7EAERQAESOIEUWIEUMEy34AAJiBh4MBcYgA2iZjkiyAYjWIIkeIImmIIHo4IsiIIuyIJYME0Q/kdqePKCNtiCLEgJOGiDMVgK+mcI/DcfNziEO1iERHiEKjgIRriESNiETIgnovYHNfiETliFVGg5PUgKP1gI+IcTTXAKRxd2QbcIoscaNDgIVpiGV+iEWTgK9vcIQfgTqHcIdycI3OVzguAEh/cIYQcRaviHa2iESgiIhBiIN/gHUSgIU1iIjEiFbSgKW7hcZ0g1hliJaviIoRCJgxCHMsFdr5AEkOBs/9CIpGiIg2iJqAiIiDg+i5iKrsiDMthHecUUaDAJY9gdVpBpqoAFvNiLvviLvXgFCTBbXfgHbkCMjtAHbWBQkrAHxOiM0PiMyJgUZfAHoogIntgJZIAGfGfAjdxYh60RW1TEZ+Q4jlT0B+WYjuZYjui4ju7IZ4LwjvJIAMCWVqmVDPaYj3ilj/fYj5rAjwDpAL+VE32ICLfoCh24D5ooEsWYHh1Yi3oYHZxYHNmYCNVIC3joGg3ZCxPJGAeZh6KAeLKhd79wQ5LBfvA3dhc5h6QQCAAAIfkEBWQAfwAsKgAOAG4CxwEAB/6Af4KDhIWGh4iJiooOV4uPkJGSk5SVlpeYmZqbnJ2en6ChoqOkpaanigKoq6ytrq+wsbKztLW2t7i5uru8vb6/wMHCk37DxsfIycrLzM3Oz9DR0tPU1bzF1tna29zd3q4Z3+Lj5OXm5RTn6uvs7e64Vu/y8/T19vf4+fr7/IMA/QADChwoTBXBgwgTKlzIsKHDhxAjSpxIsaLFixghGsSQsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bNmzhz6tzJs6fPn0CDCh1KtKjRo4L6IF3KtKnTp1CjSp1KtarVcheuat3KtavXr2DDBsRCQKzZs5DmoF3Ltq3bt/5w48qdS7eu3bt48+rdy7ev37+AAwseTLiw4cOIEytezLix48eQI0ueTLmy5cuYM2vezLmz58+gQ4seTbq06dOoU6tezbq169ewY8ueTbu27du4c+vezbu379/AgwsfTry48ePIkytfzry58+cHYeiBTr269evYs2vfzr279+/gw4sfT768+fPo06tfz769+/e29sCfT18xtvr48+vfz7//ORj+BSjggAQWaOCBCCao4IIMNujggxAGFoN8EVZo4YUYykJhhhx26OGHIIYo4ogklmjiiSimqOKKLLbo4oswxigjZSbMaBgcNuao44489kiQCz4GKSQuKgzJ14ZGJv6pZCgq4Ljkk1BGKeWUVFZp5ZVYZqllZ9NtaVYMXoZpmR/3EUImJWWK2ROZZ5rZJjFvEuRFIVsgqeYqZ6YZJ5xp3mkTm4bsiaagfs4kKKCZEIrPFjUWKgubeyIqCKSTKlppn466BKmefW4q6SGf4tNoprMQamqoiKBKakuHKqpqoJauihKqr75aiK2ynkSrq7EOgmuuJfEKKqDFqPorsCMJ6yuxnraK6TleFIlsLbW+ieinrU7LkqWSxlnmqdquFOuxlLoZrkq9/pFupW4+O86oUJZ7LJ/YzDuou+Y+Yi2+5w7TbLr/7uppKPzSW3C/yZQLScCnrmvLwQgvY+8l8/4yDHHE+ExsScUMt2vxxyB/jLG/E1ucqsOS1DvpyuqyrHLLML8ss8sjk5xnvrd2DOvNGtc8EKUK95xznv/G5OSV1+6L8rD1enuxzwJ563Gi3+J8ytJQa0P0KAqDonTOaGbtzMBcPx1J0E5XIrTYuaydstkLF7us1XyyzQzWZ3fNSaj7Ug233dz8HTesl2qCN+BR630ftknj6zbi/GyaiLOST374K0dDfkyvDR/8uOb6jMur55eDng+u1ZIu+CsmgGl6MKiPHvfqr9sDMKZAq9tw7Q7dPnXAO/POELlf6/5tp7QLL8+63VY9N+GzlKD8Mw4TH2ny07ezdPXHY19JDP4nZA8N3swv7r346pw/dOmagI9+5O/HL//89Ndfmfr2945/NHPmHwv71cic/1zxuQHqz4C62h8CCQLABS6kgQ5MCAQjeJAJsgJeFLybBTMIkA1ysB8exESXPriLPBQiDIZTICXsNEA/zOENdxAEH9rAQl+oZWMqJOHC8sAGLPRBD2oIgwm3EUIdEuMKc3CDN4poxEmEwYeBy2ETJ+EGLAhjDgk4hCMWwURC1HCKvgrDFTbUhze0QYqZ+MegwEiLN/QBC29o2RzmgIU23OINfEhKIfZABYOcjI2x4MMe8qCWMLCBD0P8gxCH4UfoAfIVVYzjH94Ax0G0oZK8GOEgdP4wrEf+L4+DAOUgemgMKQzNk7uQDw+FoRSwoVIXb3SDG5XRxVcaTmJotGU5Ghg+XWYikWNbHRxc50tNsCGXV6tlMSMRBmR2ggGdXGYtmqnBT2hyRPEQCTVp6UwTYWEAf2jkRLYZDGg+z0UoxAQAxPmHBNyQIuQ0BsoEKCNRCkKJGYkn7BwGBwCJiAACUGMl1vkHKnhEn75gAMr8OQgMYigr4axJHYehAUk+4gWFGMEf7PihdXo0oIJ45yPwaQ2I5kIDGhAGSh8RjkNYQJqmUObeCsbQFH30HxrgqKa6iYnDfTEbPz2KPSNCUorIlGr8aCVUgDkQgQ4CpH8w5UWOiv5DnjojqEYZ6jriYVFIiDOGH6HqGgGi1KcwNSBKEWlIxPo2RNDzHVgtilZBw9bBLeesdLWqvvQajbI6Za6fqasi0tU6e6iVKXHVjGCZBlNuUqtPMXBoY3exWLpNVp58tdo1L/uLyuqOs7j8X2ZBO1NYeNaTevvsXrmo1zd1gbSeqNw5Wes4q54WlVubrV2jiYo2bWEibgCrUVz4h8PmBVz3+mNvRysONkBFKc7Vi8BwqNyYFoNR3JmDTu9CtmWZr02ycyQpbvsav9alu+zybrHC68qyMdeXyJ2a5XAnRTJtViJX6OpGEVsI/cJluqccbHy99l5yRHcqrUwnXQDc3v6T0VcUfkhsRIwbFKXcQbiEYMOB5bK7ABfOu7yNbf8qcgcsKNgQbqDwTjbcF2Wp91LNe/An/EBMiwAWKebN8IJdvN7KOU3GnXirSPLg36Wc+L/uYhZ4l9y3ECcKuyYhaYEP+ocbo0V0LEvvh1UrXkzsAUiwbUXsaqtabmEPDr0MczK5bDkBM7nNmYiB9AQhLTW7F2IcY20mXDBnQUjYzhQbbelMMGfJAloah5Pzob+BNz4vmtFP8wKhHw3pSZSgz5SOIiT2AINLC6LGmbZGunDk6VAv8WCeTrOptYYvOfd5yqu2riJKHetTHwIOKqB1rbshqC4QGtO71rQhdB1sYf7/gdN/IHaxiVgmT5vgtcvm9X1SHW1Iv1bZ1c4Gm7ZwaWBnW9tk6jS2v12NCPO52+Tuhh5yfekT3Dfd0/h1CVSwB1jDmxTddkEB7+0LT8dg3/zmxbgDLo2BE/wZ6D64NQyu8GYwvOHLeDjEkyHxiR+j4hYfBsYzDoyNc/wXHv94L0Iu8l2QvOS5ODnKb6Hyldei5S6XhaJjnoyZ0/wYNr/5MHKu82DwvOe+oLG3gX4NUBO9FzQ+OuyMrnRd+OG3TQ861KN+DWhT3en2vnqDtX6LMw2d66L9g6HB/oo9TZ3sZc862EN1drSz4kxfHkRN3Y4nta8dU3+me2n1Xiq7a/4dUVbn+9v9/nfCX528dHeA4anuBwcI/lGLbzrAH6+2yEve8kpHvNs1j3ZBtZ3yBOP83UGfdtITsGAGMH1sMX900Y/+Ee9WPZxkX3faL9f2a8Z9KVzPdd4fHmVM172AhT9e1hPd978nftmUH3q4xZ75bIb+3qXfCeQz3vhAt37UtZ957Pec+92n/urFX33v6xyAwRf+5KkP/tab/+al08PYid/+47+f5vX//v1jvsH0yz7/+kd+1SeABFiABniACJiACriADNiAp2ECz+eAEtgLOTaBuucH82eBf+B/Gih2HfiBIBgKGRiCJFiCJoh0J/hI/jR3KTgRFShNeXcIEf44CF0CB10Qg7iwfy04Mqq2gz64CXUmdwI4guInZD9oCEQYCUZ4hApYIzGwhMqXhEw4hVRYhc/wgh+og2KhhexRVCZhZcKAVxMnhu/jBpzkDAYFDWDYEdnEcQRgBXAYh3I4h3FoRbqQUmaBB3VgFxEwERFAAYAYiII4iBSQABVgCgwgVTDRBH/AiILAiI54GGygBpNYiZR4iZbIYvuQiZjYiZz4iZ5IiYJgSKEIig5gh5rTUptYiqwIiq6oBoLQip7IBhGAipDghZGwhjqBB4Swh6BgB2sgCcFIELL4isZYjMh4jJOoitCgiciQjJd4ipOwXZJAhkiBB0oQCT4wBv6DcAZ/MIz6chXMaBLQqGG1SEVnOAm66BLcKAi8mAi+WAhAYAjvmASG0I6GkI2g8gdMMAh2cBDlGJDKKJChOI7OMIl/4IzCEJDSKAnUGAnWeAhtiBZ0oBUGSRLlSIu2OFKWsI6DkIYsEY+R8I+F8I6VgASRkAYDQZAD2ZIseYkXyQwIKQgK+QsMuZFgoZJ/4AORAI5c+BxWQABYMJREWZRGaWKNUFaCtJR7wJR8gIteQQaFoFUm6QllcAZogJVYWZEoQQAJ4JVg+ZViGZZe+QdkOZZoWZYVcZZsOZaCkJZwCZYEUBYOEAGOZ5d/gJd6WZdcUQaKAI7qiAdKBZiUYFUHP4kKD1k/OmkIJPkHi1kIjQl2VZkIUkmYj7AG/VgIlilDj2CP7OGRwDCRKiEGkLCZj0Cal4CP8zgaoMkLeZAOzwCSKBGZoWCYVqiAUumDXLkKgQAAACH5BAVkAH8ALDsADgBdAscBAAf+gH+Cg4SFhoeIiYRWio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys7S1tre4ubq7vL2+v8DBwsPExcbHyMnKy8zNzs/Q0dLT1NXW19jZ2tvc3d7f4OHi4+Tl5ufo6eqbVOvu7/DxxQJ/GvL3+Pn6rAD7/v8AAwocSLCgwYMIEypcyLChw4e8+v3JALGixYu7qEjEyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbOmzZs4c5qbo7Onz59AgwodSrSo0aNIkypdyrSp06dQo0qdSrWq1atYK15JkLWrV0F3voodS7as2bNo06pdy7at27f+cOPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069uvXr2LNr3869u/fv4MOLH0++vPnz6NOrX8++vfv38OPLn0+/vv37+PPr38+/v///AAYo4IAEFmjggQgmqOCCDDbo4IMQRijhhBRWaOGFGGao4YYcdujhhyCGKOKIJJZo4okopqjiiiy26OKLMMYo44w01mjjjTjmqOOOPPbo449ABinkkEQWaeSRSCb+qeSSTDbp5JNQRinllFRWaeWVWGap5ZZcdunll2CGKeaYZJZp5plopqnmmmy26eabcMYp55x01mnnnXjmqeeefPbp55+ABirooIQWauihiCaq6EMnLOroo5Bmh0WkqfARTB6UjpIHG5mS00anoFb16S9vMHAII6FqggWmgvjxhxu4UBHGHzyxmionV/BUCKy09PHHG37QMwgfVmx0ayS+HqPGILYeGwmnwOSR7B97WOosJtNeq+223Hbr7bfghisuSFeMm82sxpqr7kkACLtuMwKk++5qIxDCwQsLZhDvvu1WQ9E/BFxywby4OEBJDBDyS08Gb3xlsCSuqpYHr5j+zXEFFtkKMqojFGNiam8dG6SDQmHY4wCqgsxBRbOKuCFFxpQ8rA7MR01MTrktuZGApWzYykcE1kLyhsyWEI3OHk6FLNCyCzHQjiERTDqJFP9WMkcCuqZDs1E2W2aFAGEVgsUAVgPQMCX6tnsAb0o/1oYUAxBgRcYOUECIGlY8zYcU0BpCQAWUFMsvB+kgzVTXk93BxgAahDyHACMP8oYUAvRMgQNPQ032JA6063kBWxhuTthKbe02AEwTEgYAmQ/CgAYaBH3IBQK0rUgBnscbAcGTUCEAzF9LTYgOtTdCufCQcJA7AMjz7ogDRguiUfN/YAFA1oj4Tr0jB7QrgBT+ziM7QOuDFIvyIMQ3n0frlPctyaYsh68IGwKcXcjq5GPhxut/BB3B7oOgXfzkBwoqcOUQfWCcIPjwBpX9QQcEIJYgsPA/QjjggAQkhQPAh4gLfOxr/1KDAAD3KjZoAICCkFsGScGH+iXicazCXtYiQAUGYE1jA5DdH7ywwk5ggYSJoII9FEEFKjiAALq6wKx6+Aks8CQC2EOEDpaoCCkMrHqt68JCBhgU0kEmAVaQgv0aEQYqNgILfRMdEzXRhyh2wnQESd0a50jHqWBhY4KwnU+woEM3rugOckwKziKGhUDCaIxBsVQe/OgGM77oCu5rAyJzosc/sMGQM5qkTnT+SIhG5mgOfiTKJev4i2XBkZSoTKUqV8nKVrrylbCMJWj0IMta2vKWuMylLnfJy1768pfADKYwh0nMYhrzmMhMpjKXycxmOvOZ0IymNKdJzWpa85rYzKY2t8nNbnrzm+AMpzh1sYVxmvOc6EynOtfJzna6853wjKc850nPetrznvjMpz73yc9++vOfAA2oQAdK0IIa9KAITahCF8rQhjr0oRCNqEQnSlHAwKCiGM2oRjfK0Y569KMgDalIR0rSkpr0pChNqUpXytKWuvSlMI2pTGdKU4eqUZzlPGcJasrTnvr0p0ANqlCHStSiGvWoSE2qUpfK1KY69alQjaot8Sj+zkp2c4jIOJ9Uh2GFrnr1q2D96jT/R4GymvWsaL0cBiHhgMiZqGozuaRc1TDXutKVDVb4GDTpyle7+hWv0XMEF7Pj174atrCIPaxiE8vYvl6xsZBdrGQjS1lvUPaueaUEJ7NChqxM9rOXDS1oDduN0drVCoFtxGBbIoZhJQINdtBEZyXhqyakQ7S4Na1u6/rY3fo2t6G17G7xqtdIbDYudSjKb5cL3NGWNrTEPQseOpEEfDT3usw9bG+xy13mCpeygKXEan8y20FsrboGwoJ618ve9q43DDXkXB74UK360ve+9r0pTk7JCTKg4Qz//W9yF5IAAhT4wAZOMIIL/IdOBSv4wQxmiIMnnOBKcAXCGC4wATYcsAgYzMN/ALGIP7yU8saCvytEryA6SweNKqGHaCDEFBrB4krM2BImps4eUEiX6W6VYGVQ5xpUEQgAACH5BAVkAH8ALDwADgBcAsYBAAf+gH+Cg4SFhoeIiYIRio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWmp6ipqqusra6vsLGys5cCALS4ubq7vL2+v8DBwsPExcbHyMnKy8zNzs/Q0dLT1NXW19jZ2tvc3d7f4OHi4+Tl5uJX5+rr7O3u7/Dx8vP09fb3+PmODPr9/v8AAwocSLCgwYMIEypcyLChQ10CHkqcSLGixYsY573JyLGjx48gQ4ocSbKkyZMoU6pcybKly5cwY8qcSbMmrI02c+rcybOnz59AgwodSrSo0aNIDwGwFTGp06emKjSFSrXqKZxWs2rdyrUrKQZWvIodS7as2bNo06pdy7at27f+cOPKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069uvXr2LNr3869u/fv4MOLH0++vPnz6NOrX8++vfv3hmLAn0+/vv37+PPr38+/v///AAYooDkw+DHggQgmqOAhBi7o4IMQRijhhBRWaOGFGGao4YYcdujhhyCGKOKIJMpSQolz6YHiiiy26OKLwsAA44w0anJCjWk1iOOOPBJyY49ABinkkEQWGZQXRib+qeSSTDbpJEYyPinllFReFIOOVWap5ZZcdunll2ASWWCYZJZp5plopqnmmmy26eabcMYp55x01mmnbFHeqeeefPbp558j9gEoSGiQMWhHdChhxqEZ4dGEGIIyalEfYzCBh6QXnaHEGphatIYSZ3RakR1MiLFMCVuIakwfYjTBh6oTlaFEHbBKlEYSaNT6kB1LjKGrQ3044cSrwpjwqzJjLGHHsQyhkUQawOzB7DKJljGtQo5OEWkvWxh77TGUWvotQppyOq5Bn4Z6bkF4lLpuQaw2cem7A8lKK70C3ZqrLHuk6i2+x/DqK8AA9THFsAQDRMYS9ybcj7PQOtxPHUv+GCqxPtlue7E94c678T3lfozPp4teIq3I3bRrKsr1xOvxI9LmyXI39kKioqhzGJOOLvo6fHM+Akv8hhv5GOyExjPDs/CySctza8RNGzOVKRRbjDIWWP2xURvCUDH1KHw0oW3SWPxCgCFsDLLHLaVUynTUvvBx8h99/HzKGUmYC7c7iZa8dzsq/61IzuDEO0e3gq9jhhJhJM7OrVeo4Lg6vD5x4uTm9HEEDyNgfs4XNHTguTlX0ODBiGG9pcUOIMxoS1kv3DABi68XQkAeY01gAwk0ck2WB6Ff+PVdHexwuoUZCMK2XSuQYMPsf3ReoQaJZJ1I7V0pIAMCgyR/4VL+4A+vlnwh7CD6H6myRqxAF3TVgemz+d6cA4k43/psfMifz/BLVTXBDdKjjf4AgjuGEABpgyhgKvhRiBDY4Hy1yd8/FDiIxikkdYWgnytuBrzj4WaAliHcJt4gABBSwnkh2I0Eb5OATSzANyakTNpGZw7xJaKFNPzG8kqxhRJ0QAFMWcrOcsiNEciOiOPQXQCROAwcaqJ8EGSiK87GIBtu4n3HQ5IUgQEA6kWCCoiw3xaBYT1HZA2BKPjfEsfYjATgpAKHcGAU2fgKCmJCB3BERAcDMocYBsWOkKHiKVZggxQK5A1lE4QFjaIG2uiIC0cUxJgA0jiiXesJuxNECuj+iI3SzbEgV1hfrdZAA0MuJGtl7MkVsKQ11uDhCNBbSB7C0EhBANInidzWDFHDKs5xBwuWbI0ZiLACjgQTKFcQYWrWkAQwgkdjbNilaEj1BZHc8iduWCRojMaFy3HEj0FpnCg7szA6cFIbPTsnNqqGPh+pMxp8cMLYDMHKdyKLCUz70R+8aU9m4E1v/ZRG3wJKDUetjKDRcBlCpbE4cwrCDy5YKDOYuS9BwEGiyyDVwDDaDIO5iqPOWFjDQKqMdJJUGew0hBf4edK4yROBLSWG2xgU0Zj+4p+ImNs+tWhTWgw0Ef/6g916CguDwpSovlAoUonR0KUSg6JOHYZGoyr+DI+Ok6q8EClWgWHSRnRhq61IKVh5Ec95jnUXlXrZWXGBN6itFRc/fSsujDqJocrVE6wS111p0VRKwIGle9UEVC0B2MBeYqqGjYVVExsLrTL2FV197CrEKtlVlPWol7hoZR2RrLdhQj6bjQTEQruKapFWFXiQAaROmwoxMAECrEXF4gAa21HQIQnqqi0pAqdbUizWEJjt7STKwDDhjuJpxhUFr6yWXLy+lBRfrW1nmwsKZ9GWupqogxKshd1O0PUUhWWsa9WKiugyFm8O7e4mbptbVoA2sXY4aCveq9769qKe9pUEffPL3/76978ADrCAB0zgAhv4wAhOsIIXzOD+Bjv4wRCOsIQnTOEKW/jCGM6whjfM4Q57+MMgDrF19iviEpv4xChOsTplpuIWu/jFMI6xjGdM4xrb+MY4zrGOd8zjHvv4x0BWcQl0GmQI47fI59QnkpfM5CanKbxOjrKUPRfcKXvpoj+qaU2tPIwjg9ULPJVFlTGqWeyaIKiauByRG8xiQZTAy5td8yWULAgSYxfKXF4rnicR5jxv9UZb6LN995xTDMvZz4gOLZwZPGbzpDLRkNYKOCN9EmeewgqYzrSmN51pbc6FD+ltRx5LEQEK5MLUpig1qVEdiwqwehQRKHWpKUDrWtva1gTw4kmY8AdeC4LXvs6FZ39yAU/+Y0QNamBDspet7GYz+9nOjvay/wDtaks7AXfYUfuaIUh4WPvbzU6AMnciylBzAg9ubYS5xQHudkv73e6ON7yd7b2hyBva4p6JEyzRhyQQQr6FAMJGNdHoa8z73gdPOMLBfYFiE0Xh7853UNIw0kH4QBDrLkQT/jBwQvj7HguHeMhH7uxnEAALtPS2yKMt8bgowR4rJ7nMV95wYxeDDd1+B8lbbpVhRwIJ9pi50GN+cEYSPdk8lwkQHMFdR7zcNVSwuTqwQPWqW/3qV2fAow9RcI747RAZJ0UZzoAGspM97AIhQALUzva1u73tav8D3N9O97hLY+54X/sf6s53uO9tPe95l3vf+W4KJw4e7wQggAMiQD/G/8HxkNfgTJpOiT7YQUfppsfW6/T0SLxt44Vo2HUFUfE/dJ4ck6bIVZlDeUmAnhCZF0TXpXNNuwDcEV9//SFWO4jRI2KjF2/MoYmxerr4nNK9tZjvQxEIAAAh+QQFZAB/ACxJAA8ATgLFAQAH/oB/goOEhYaHhwCIi4yNjo+QkZKTlJWWl5iZmpucnZ6foKGio6SRAAKEAoqlrK2ur7CxsrO0tba3uIV9uby9vr/AwcLDxMXGx8jJysvMzc6Ne8/S09TV1tfYhBfZ3N3e3+Dh4uPk5ebn6IdW6ezt7u/w8fLz9PX29/j5+vvnCfz/AAMKHEiwoMGDCBMqXMiwocOHECMOWiWxosWLGDNq3Mixo8ePIEOKHEmypMmTKFOqXMmypcuXMGPKnEmzps2b1ubg3Mmzp8+fQBERoBi0qFFnV1QdXcpUmdKmUKP6UvVUqtWrrywQxcq16yudXsOKHUu2rNmzaNOqXcu2rdu3/nDjyp1Lt67du3jz6t3Lt6/fv4ADCx5MuLDhw4gTK17MuLHjx5AjS55MubLly5gza97MubPnz6BDix5NurTp06hTq17NurXr17Bjy55Nu7bt27hz697Nu7fv38CDCx9OvLjx48iTK1/OfHUMOM2jS59Ovbr169iza9/Ovbv37+DDix9Pvrz58+jTq19/VQ/79/Djy59Pvz599/bz69/Pv7///wAGKOCABBZo4IEIJqjgggw26OCDEEYo4YQUVmjhhRhmqOGGHHbo4YcghijiiCSWaOKJKKao4oostujiizDGKOOMNNZoI0r43ajjjjz26OOPL0EH5JBEFmlkgUIe/qnkkkw26eSTUEYp5ZRUVmnllVhmqeWWXHbp5ZdghinmmGSWaeaZaKap5pps2hJDm3DGKeecdNZp55145qnnnnw+REefgManhwuBFmrooYgmquiiV+qxhQmMRlrZHjGcIOmlUP2J6aacdurppy7p0cUfJYCqkBempqrqqiWWweqrsJ6naay01hrfm7ZW0oYgYeRKyh3LrPMHWL6qREaxs0QADB+b+oGMssiK4gZDOUbbyht/MCvIANZucgWxw/qyqyB9cEuIFVt1W0mvw/hTiBqD5IGKuhUpQS86a9yrbznYvlPpvgAvZWnA4RhB8DhNHEwOCQqjE42JVzTMzill/o1gY7+CACvxxholkC7H1lgA8jenlKyKA1SAu8gp40YlcooOmFyyXAXolkc9Mk/yslSlEmLAw7dpO8/MklTwkNC0MCCJAzY/VJVRFh/CtDlAY4V0PC1XojFEVz9SNSVTG8KwIWGTs0tXNx+khsp/wMtV2bZ1/docH4sCtzhfW5W2dFEzcnc4Z3Mld2QZTHsLA/NKwi5ueUcGABuRKO1IBpZQRfHIsWSN+T0k2DCIUlRsXokfiZuySeOSsGFF6NlKAbnolEj+SZKQvEEFAGHkQQHKsCNSriujWsJABhoM3vshAlA+yM6ICGtI35voIIDmxxfCdiPgGu8JFgJcX70l/mAxX4oUAkQ8iBVSpLyx98iEwYYDlDPLhwMVGM3NGxi3sTVU7FO3xxtzCJ0UCMCHdVghA+YDhxrUgDGrvK4xfmhgKaIWA9RRwgoC2MYf2CAA+0kBcQwIXDbUQD1AqQAU+1NZGwjgNtg4izx52IUO9vY9SezgFjpgwBUMN47+NcWHnzGYR/YnlRe2TTVjM4/GHqiaJGikhVhY3B9KaBQsSJBGFpyiVJDmBin+SHtGYUMLa8gMeImQM3UgoxrXyMY2uvGNcIyjHOeojzMQolp0zONqVHcIN5zREVTUYyUqYEVDuI4SecjAFX2kh4Gh5AKU+1oFvBiJPiQgkIIEJADY/maFv0WCDQMAYyaF4i5C8AEAWMjEAKQwSkl0EgAMSCUhbkfDPmBBCsJ6gyIZkYG6zQiPKGmDBgBgBZUNxRBtiAAA3tAGBhBAloi4HTRv5MiVVOBjACDAIU6pA/s14goAUF4rHzEAaBHiDrBEBAM2+Qg2AMCT4ywEOllHiDak8xA6AEAWB2FPeMbzfMs0BDq1KTUAjFEQVuAhrwAgvhHZESgRIKghLlcIKrwBAKHbmxsEMM0/oIueNqKdSgTAyoISYg5zUMM6EsCAN8iyD1KIQEdvx8R/GuKiVMQCAFqmFQ0I4nY+/ekeZFoICpTSpoeggkQPMQB69gFcGAsDvIia/oqOIpUQsWTEGwawzz8wIAFDGcADreDNq57vD24w5yKwoMFG7IKqw1LrpmyJS0HocpGWoGsud/kJjgbVEQGEBFXb4DxPpXWZzXxmI97AhsY61rE0FEQyEetMq2oiD0A82B4A0E1IUMEBoA1taGsqiM121qyGWGdmLeGx1d5SCrCNLWwbGIEIUMC2uL2tbnPL2936trfA/W1hI5XPrl6iuJDAAhWWy1zmNhB/0I2udKdL3epad7qRZVTMDrqIz4pWtKQVxHZRW9GLslJbUtABSPkZhva6t71YyO4fLAqA855LoVZSwkMFglKVerWlqQwDLikpCZTykQEAHoQbUBnP/p7+FABBdYAV/qgzCD/4r3uIqWXz+FRC9GsPOkjAAFaLiD1AdZZ8gCsp8iBKgGWAAqKQ6h9U7Ak+DgsAMC5EGyjMCEyCig+y+8RXwxreTFjgWwglZiEOOYlE4hVUeVivJ966YUxA8g9n00ohJpnXS64KCwRYLitorAl7gisCIO0kJkDZ4ki1ORgEOOofHAC0U1YZEqskL0JjltVBNJCWhNCrXfmKiF7qeYrDLOYijqljZTKzsoyQ5qGv2YhsbpOzZV0EOMWJ2nIyAp1Bxio7HeFOf7JnVnihm5TreU9DIFeTpkaPvfqCrif/YaCIGK8j1MDQ/vAYLhF1BEVnedGM/t63EB/tjxHrUl9HxOykKV1pggWx4Jk+jrw4dYROeWrh+Xb7DxmmsVH1rFQ8O/XEg6BCijvKUT332RFb7aqMVUxW1K4jrZJgqyMSAFYAiFUQc5CrTVGpA+OedNW6mLEsCatnzJaCzIeOuMTLNOuJk6LiFk/GrwXhhxNm/OMgD7nIR07ykpv85ChPucpXzvKWu/zlMI+5zGdO85rbfBIGv7nOd87znvv857KAAdCHXlqiG/3oSD9EzpPO9KY7/elQj7rUp071qlv96ljPepr20DOte/3rYA+72MdO9rKb/exoT7va1872trv97XCPu9znTve62/3ueM+73vfO9777/n10mTB41YDJclSNvOucgNQfCH9zQhnCBEsf5bL/TvnKW/7yD2K8zyeP+c57/vPniLwwSNwbW3tE9L94s4N83BHVb8n0yEA4M+T7EdlTqKEeQZ8wrMD73vv+97y/AO6Nk+NS3NZuCSi+I2As8FAcnxTPv4XyWRH9RtSWAtjPvva3vzs5qwUP7VCDGMcv/vKT//zmTz/616/+9rOf/X+4QAWKDBL32//9988//vcvfio03zj6F4D8N4AC6H7W4H0MUYDj53/NoYAOSIAQeH9tJQ3PJGMO4YBqwIAnkTCWgHEKwV3MMH8ROIIPWIKQcwWNdUTL8EAm2IIkyH8aGBRp4FQIHsgINcgOLpiDL2iA1VBKkAOCBfGAMagcQKgMIqiDSLiDFoGBQ4gWTvQOSRiFL9gNYvQMUniFBNiEIJNAvoAFXviFYBiGXxhTK+EqjeAq+QIJZ4AGa7iGIwFWcBhnchiHcfgHdDiHeAhWceEPediHcUgABOAAyiKIczaIhliIodYQ4HcIZrAJiygIfIAHgZOGlfCIhoF6yoGGjGCJjJAGiGAH6QB7oEKJheB6hUF7yYCJwGB7HeGJgzAFZ/gHlLhfjjAFy+aKnWGKEjFcI9EHeACKWpcvtJh0uFgKgQAAACH5BAVkAH8ALDsADgBdAscBAAf+gH+Cg4SFhoeIiYMOio2Oj5CRkpOUlZaXmJmam5ydnp+goaKjpKWWAqapqqusra6vsLGys7S1iACotrq7vL2+v8DBwr9+w8bHyMnKy8zNzs/Q0dLT1NW+xdbZ2tvc3d7f4OHi4+Tl5ufo6err1gIO2Ozx8vP09YOoUvb6+/z9/v8AAwocaIkBwYMIEypcyLChw4cQI0qcCFFKPooYM2r8pmGjx48gmw0ISbKkyV5zTqpcybKly5cwY8qcSbOmzZs4c+rcybOnz59Agwod2u8N0aNIkypdyrSp06frsACASrWqMwa5rGrdGkwALlxcw4qddWGs2bNo06pdy7ZtvwT+V9zKnUu3rt27ePPq3cu3r9+/gAMLHky4sOHDiBMrXsy4sePHkCNLnky5suXLmDNr3sy5s+fPoEOLHk26tOnTqFOrXs26tevXsGPLnk27tu3buHPr3s27t+/fwIMLH068uPHjyJMrX868ufPn0KNLn069uvXr2DvD0JO9u/fv4MOLH0++vPnz6NOrX8++vfv38OPLn0+/vv371ffg38+/v///AAYoYCr6DRgbDAYmqOCCDDbo4IMQRijhhBRWaOGFGDoVQ4EZdujhhyB6wmGIJJZo4okopqjiiiy26OKLMMYo44w01mjjjTjmqKNOJuy4GBw+BinkkEQWSY4LRib+qaQqKiwZ2IhORimlJCoAOeWVWGap5ZZcdunll2CGKeZa3I2pVgxmpqnmmj1tASWbcMYp55x01mnnnXhmsmGefPbp55+ABirooIQWauihiCaq6KKMNupoiWU+KumklFZq6aVewoNpTH5oumlLnXr6qUqhijpqSaWeCmqnqrIUaqsrvXoMHAgSYgKasDaTaq4mycorSb4K08Wv1ARLrEe7DlPCsdIYy2xGzvYSwwnPRhNttRIl20uk2D6jbbcTXQuuQ+L60uO4yJSLrkLfrksuq+5GpG68BM1bi5X0DtNuvgnZy+8//v7bT8AC77NvwQEdjDBABENy7sLfNFwItxD+kyNxxewonEitGIfCxxxv5CFIHm6YKsvFrd7xR0rC+JEHFmH88QYbYfShC8odp5LHFSDvgjOxLLcM880/H2vzMFiwYUvROauyBxZYGDIHH6w4+ya9V3Bocxu9uLGzzdi8LHIqxlIsMBZG/cKHH2+sjXYeVLN9xdikaJwv1cdAPbYaWLD8hh9zl8I0s24YwrUgb/C8NCF+FJgHG29gcXgosnrRNN7O8PFGG1dM7omvTTY9jR9Y0M3J4AV7bnGnV4tuT6eWu+5P41vITk3aoPihBwwP2x5N1J/44YULy/pOTcyedKFC8cZTA/wmW5jA/CBmN6/M85jEID0hoVsfDfL+l8BQwvhFTiVI0H+Y3hT2knA3/vRCipxV4VqxH8n73nsDPiTEkw9jWX7ZXyNewIECDqIFL8qAVxYIlknQTysdaUQGBHGACg7CAjDCiiGmooNGjC0rWjHZIBCEPxsxEBUaUF0iABgWEf5Bev7DEgsbCC1nuZBxmxBhCXMEwpqwCl6C8FfRTPU++G1JfeH6ITwI9jNR7TBLYUCiAOVlKiBGwoqTCJWVnqiO1hXKhjdExMVYF4Mi0uNoiSoVFq0oq2th8RGdip4ZHYFGcHhRUGosRLDU6MYwGsILy3vfrfyYP1GAUVQaa1gRSwCDOxbSFIc0hLr8pb0iVumNj1wFJiP+qQh/4e8EXUBdJiuxyTcai42YpJ4gdjgvNYyScqX0VKqWqCl1lbB6r2xFKtv4ql3t0YVcrEQCctmJVP4BXrzEhrZSGUxMPJCYlhBXG3EYRF9isQsnaCY0Y2HMajYij8d0Ygy3OQslOqKb3gwnIeRoxE6wcBxeq4rKVIYauw0CnfeEhx76Fwp6lgN3KvQTITHBzogobV38FAX6huPI38iRnObYZzvTU8c94K43fuhC7+gzRdw0TnwkWehTRAoc4VFLI1c46CHcQNKhqBQRHaVNp3C1kYFaqlP4YokrxxLT14Qqei55ZqVYB9FyiLKox3gVTf/QPaRmY18NdSozZPX+sI1KdXT4vGqzsqpVaBy1q9f4Klh54as9cGysW9VUTtHqVa6yVRn2XNUh3BpENok1iYi0aTX16iRnwaGpL/mhHvm61zBFS6MzASMm7iqjuMLElHSdK2GDFC2z0gSc+axlMjs5WR3ZywTDCuy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"text/plain": [ "" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Gradient_descent.svg/1920px-Gradient_descent.svg.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "To use fsolve, we need an initial guess: " ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "omega_c = 3.0\n", "def f(omega):\n", " # a transcendental equation: resonance frequencies of a low-Q SQUID terminated microwave resonator\n", " return tan(2*pi*omega) - omega_c/omega" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-5.0, 5.0)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = linspace(1e-6, 3, 1000)\n", "y = f(x)\n", "plt.plot(x,y)\n", "plt.ylim(-5,5)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = linspace(1e-6, 3, 1000)\n", "y = f(x)\n", "mask = where(abs(y) > 50)\n", "x[mask] = y[mask] = NaN # get rid of vertical line when the function flip sign\n", "\n", "plt.plot(x, y)\n", "plt.plot([0, 3], [0, 0], 'k')\n", "plt.ylim(-5,5);" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.23743014])" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.fsolve(f, 0.1)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.71286972])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.fsolve(f, 0.6)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.18990285])" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.fsolve(f, 1.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Change of sign can occur when there is a zero or a pole. \n", "To use bracketing technique, we need to carefully bracket the zeros (and not the poles)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-299.93708533274634, -6.0)" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(0.01),f(0.5)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-2999.993716732008,\n", " 1.6331239353195358e+16,\n", " -13.077683537175254,\n", " 3.806226047209912)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(0.001),f(0.25),f(0.3),f(0.73)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "`toms748(f, a, b, args=(), k=1, xtol=2e-12, rtol=8.881784197001252e-16,\n", " maxiter=100, full_output=False, disp=True)`\n", " \n", "Finds a zero of the function `f` on the interval `[a , b]`, where `f(a)` and\n", "`f(b)` must have opposite signs.\n", "\n", "It uses a mixture of inverse cubic interpolation and\n", "\"Newton-quadratic\" steps. [APS1995]." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.2374301406360339, 0.7128697158579146]" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[optimize.toms748(f,0.01,0.25),optimize.toms748(f, 0.3, 0.73)]" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.23743014])" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.toms748(f,-0.012,0.01)\n", "optimize.fsolve(f, 1e-16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpolation\n", "\n", "Interpolation is simple and convenient in scipy: The `interp1d` function, when given arrays describing X and Y data, returns and object that behaves like a function that can be called for an arbitrary value of x (in the range covered by X), and it returns the corresponding interpolated y value:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "from scipy.interpolate import *\n", "from numpy import random" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return sin(x)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "n = linspace(0, 9, 10) \n", "x = linspace(0, 9, 300)\n", "\n", "y_meas = f(n) + 0.05 * random.randn(len(n)) # simulate measurement with noise\n", "y_real = f(x)\n", "\n", "linear_interpolation = interp1d(n, y_meas, kind='linear')\n", "y_interp1 = linear_interpolation(x)\n", "\n", "cubic_interpolation = interp1d(n, y_meas, kind='cubic')\n", "y_interp2 = cubic_interpolation(x)\n", "\n", "cubic_smooth = UnivariateSpline(n, y_meas, s=0.5)\n", "y_interp3 = cubic_smooth(x)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10,4))\n", "ax.plot(n, y_meas, 'bs', label='noisy data')\n", "ax.plot(x, y_real, 'k', lw=2, label='true function')\n", "ax.plot(x, y_interp1, 'r', label='linear interp')\n", "ax.plot(x, y_interp2, 'g', label='cubic interp')\n", "ax.plot(x, y_interp3, 'b', label='cubic smooth')\n", "ax.legend(loc=3);" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cubic_interpolation = interp1d(n, f(n), kind='cubic')\n", "diff = cubic_interpolation(x)-f(x)\n", "\n", "cubic_smooth = UnivariateSpline(n, f(n), s=0.0, k=4)\n", "diff2 = cubic_smooth(x)-f(x)\n", "\n", "plt.plot(x, diff)\n", "plt.plot(x, diff2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`interpolate.make_interp_spline` allows boundary condition at the two ends.\n", "\n", "`bc_type2 -- tuple or None`\n", "\n", "Default is `None`, which means choosing the boundary conditions automatically. Otherwise, it must be a length-two tuple where the first element sets the boundary conditions at `x[0]` and the second element sets the boundary conditions at `x[-1]`. Each of these must be an iterable of pairs (order, value) which gives the values of derivatives of specified orders at the given edge of the interpolation interval. Alternatively, the following string aliases are recognized:`\n", "\n", "* \"clamped\": The first derivatives at the ends are zero. This is equivalent to bc_type=([(1, 0.0)], [(1, 0.0)]).\n", "* \"natural\": The second derivatives at ends are zero. This is equivalent to bc_type=([(2, 0.0)], [(2, 0.0)]).\n", "* \"not-a-knot\" (default): The first and second segments are the same polynomial. This is equivalent to having bc_type=None. In this case the spline requires that the third derivative of the spline is continuous at `x[0]` and `x[-1]`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Also `interp2d` exists with similar syntax\n", "\n", "\n", "`UnivariateSpline` is object oriented analog for spline interpolation, and offers a bit more functionality: s=Positive smoothing factor" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "from scipy import interpolate\n", "fx = interpolate.UnivariateSpline(x, sin(x),s=0)\n", "fx1=fx.derivative(1)\n", "fx2=fx.derivative(2)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,fx(x))\n", "plt.plot(x,sin(x))\n", "plt.plot(x,fx1(x))" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,fx1(x))\n", "plt.plot(x,fx2(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further reading\n", "\n", "* http://www.scipy.org - The official web page for the SciPy project.\n", "* http://docs.scipy.org/doc/scipy/reference/tutorial/index.html - A tutorial on how to get started using SciPy. \n", "* https://github.com/scipy/scipy/ - The SciPy source code. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.18" } }, "nbformat": 4, "nbformat_minor": 4 }