{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical Methods\n", "\n", "# Lecture 1: Interpolation and curve fitting\n", "\n", "## Exercise solutions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# some imports we will make at the start of every notebook\n", "# later notebooks may add to this with specific SciPy modules\n", "\n", "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import scipy.interpolate as si" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.1: The Lagrange basis polynomials evaluated at the data locations \n", "\n", "For a given $i$, what value does $\\ell_i(x_j)$ takes for every value of $j$ (i.e. for each of the data points).\n", "\n", "What is the mathematical name for the function $\\ell_i(x)$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Actually I did this in the lecture notes!:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For all $j\\neq i$, $\\ell_j(x)$ includes the term $(x-x_i)$ in the numerator (the thing on the top), so the whole product will be zero when evaluated at $x=x_i$:\n", "\n", "$$\\ell_{j\\ne i}(x_i) = \\prod_{m\\neq j} \\frac{x_i-x_m}{x_j-x_m} = \\frac{(x_i-x_0)}{(x_j-x_0)} \\cdots \\frac{(x_i-x_i)}{(x_j-x_i)} \\cdots \\frac{(x_i-x_N)}{(x_j-x_N)} = 0.$$\n", "\n", "On the other hand a basis function $i$ evaluated at location $x_i$ returns 1:\n", "\n", "$$\\ell_i(x_i) = \\prod_{m\\neq i} \\frac{x_i-x_m}{x_i-x_m} = 1.$$\n", "\n", "and $\\ell_i(x)$ is the Lagrange basis polynomial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.2: Picewise-linear Lagrange interpolant \n", "\n", "What are the Lagrange basis polynomials when $N=1$?\n", "\n", "Evaluate by *pen and paper* the linear approximation $L_1(x)$ (i.e. the Lagrange polynomial of degree 1) which passes through the two points $(0.0,0.1),(1.0,0.9)$.\n", "\n", "Notice that this method is just a glorified approach to obtain the equation of a line you are familar with: $y=mx+c$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we have $N=1$ and $N+1=2$ data points: $\\{(x_0,y_0),(x_1,y_1)\\}$.\n", "\n", "The Lagrange basis polynomials are then\n", "\n", "$$ \\ell_0(x) = \\frac{x - x_1}{x_0-x_1}, \\;\\;\\;\\;\\;\\;\\;\\; \\ell_1(x) = \\frac{x - x_0}{x_1-x_0}, $$\n", "\n", "and the Lagrange polynomial is\n", "\n", "$$ y = L(x) = \\ell_0(x)\\,y_0 + \\ell_1(x)\\,y_1 = \\frac{x - x_1}{x_0-x_1}\\,y_0 + \\frac{x - x_0}{x_1-x_0}\\,y_1, $$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set up figure\n", "fig = plt.figure(figsize=(8, 6))\n", "ax1 = fig.add_subplot(111)\n", "ax1.margins(0.1)\n", "\n", "x0 = 0\n", "y0 = 0.1\n", "x1 = 1\n", "y1 = 0.9\n", "\n", "x = np.linspace(-0.1, 1.1, 100)\n", "\n", "y = (x-x1)/(x0-x1) * y0 + (x-x0)/(x1-x0) * y1\n", "\n", "ax1.plot(x, y, 'b')\n", "\n", "ax1.plot(x0,y0,'ro')\n", "ax1.plot(x1,y1,'ro')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# let's also plot l1 and l2\n", "\n", "# set up figure\n", "fig = plt.figure(figsize=(8, 6))\n", "ax1 = fig.add_subplot(111)\n", "\n", "x0 = 0\n", "y0 = 0.1\n", "x1 = 1\n", "y1 = 0.9\n", "\n", "x = np.linspace(0, 1, 100)\n", "\n", "l0 = (x-x1)/(x0-x1) \n", "l1 = (x-x0)/(x1-x0)\n", "\n", "ax1.plot(x, l0, 'b')\n", "ax1.plot(x,l1,'k')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Try repeating this for the case where $N=2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.3: Approximating a function \n", "\n", "Sample the function $y(x)=x^3$ at the points $x=(1,2,3)$. \n", "\n", "Write your own Python function to construct the Lagrange polynomials $L_0$ (the constant interpolant going through the $x=2$ data point only), $L_1$ (the linear interpolant going through the $x=1$ and $x=3$ points) and $L_2$ (the quadratic interpolant going through all three points). Plot the resulting polynomials along with the error compared to the original exact function.\n", "\n", "**Tip**: Using the function [fill_between](http://matplotlib.org/examples/pylab_examples/fill_between_demo.html) provides a nice way of illustrating the difference between graphs." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# this is the function we are going to approximate with low degree polynomials\n", "def func_x3(x):\n", " return x**3\n", "\n", "# as we will plot our approximation several times let's write a small function to do this\n", "def plot_approximation(f, xi, ax):\n", " # Relatively fine x points for plotting our functions\n", " x = np.linspace(0.5, 3.5, 100)\n", " # Plot the original function\n", " ax.plot(x, f(x), 'k', label = 'Original function')\n", "\n", " # construct and plot the Lagrange polynomial\n", " lp = si.lagrange(xi, f(xi))\n", " # evaluate and plot the Lagrange polynomial at the x points\n", " ax.plot(x, lp(x), 'b', label = 'Lagrange poly. interpolant')\n", "\n", " # shade the region between the two to emphasise the difference\n", " ax.fill_between(x, f(x), lp(x))\n", " \n", " # add some axis labels\n", " ax.set_xlabel('$x$', fontsize=14)\n", " ax.set_ylabel('$f(x), \\; P_N(x)$', fontsize=14)\n", "\n", " # and add on top the interpolation points\n", " ax.plot(xi, f(xi), 'ko')\n", " \n", " # and a legend\n", " ax.legend(loc='best', fontsize=13)\n", "\n", "\n", "# set up our figs for plotting - we want three subplots arranged in a 1x3 grid\n", "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(14, 4))\n", "# add some padding otherwise axes the labels can overlap with the next subplot\n", "fig.tight_layout(w_pad=4) \n", "\n", "# L0\n", "plot_approximation(func_x3, np.array([2., ]), ax1)\n", "ax1.set_title('Approximating a cubic with a constant', fontsize=16)\n", "\n", "# L1\n", "plot_approximation(func_x3, np.array([1., 3.]), ax2)\n", "ax2.set_title('Approximating a cubic with a linear', fontsize=16)\n", "\n", "# L2\n", "plot_approximation(func_x3, np.array([1., 2., 3.]), ax3)\n", "ax3.set_title('Approximating a cubic with a quadratic', fontsize=16);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.4: Squared error calculation\n", "\n", "As described in the docs ([numpy.polyfit](http://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html)), least squares fitting minimises the square of the difference between the data provided and the polynomial,\n", "\n", "$$E = \\sum_{i=0}^{N} (p(x_i) - y_i)^2,$$\n", "\n", "where $p(x_i)$ is the value of the polynomial function that has been fit to the data evaluated at point $x_i$, and $y_i$ is the $i^{th}$ data value.\n", "\n", "Write a Python function that evaluates the squared error, $E$, and use this function to evaluate the error for each of the polynomials calculated above. Tip: Try to pass the function *p* in as an argument to your error calculation function. One of the great features of Python is that it is easy to pass in functions as arguments.\n", "\n", "Why is the square of the difference used? " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# create the polynomials using code from the lecture\n", "\n", "# consider the above example data again\n", "xi=np.array([0.5,2.0,4.0,5.0,7.0,9.0])\n", "yi=np.array([0.5,0.4,0.3,0.1,0.9,0.8])\n", "\n", "# Calculate coefficients of polynomial degree 0 - ie a constant value.\n", "poly_coeffs=np.polyfit(xi, yi, 0)\n", "\n", "# Construct a polynomial function which we can use to evaluate for arbitrary x values.\n", "p0 = np.poly1d(poly_coeffs)\n", "\n", "# Fit a polynomial degree 1 - ie a straight line.\n", "poly_coeffs=np.polyfit(xi, yi, 1)\n", "p1 = np.poly1d(poly_coeffs)\n", "\n", "# Quadratic\n", "poly_coeffs=np.polyfit(xi, yi, 2)\n", "p2 = np.poly1d(poly_coeffs)\n", "\n", "# Cubic\n", "poly_coeffs=np.polyfit(xi, yi, 3)\n", "p3 = np.poly1d(poly_coeffs)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# and plot again\n", "def plot_raw_data(xi, yi, ax):\n", " \"\"\"plot x vs y on axes ax, \n", " add axes labels and turn on grid\n", " \"\"\"\n", " ax.plot(xi, yi, 'ko', label='raw data')\n", " ax.set_xlabel('$x$', fontsize=16)\n", " ax.set_ylabel('$y$', fontsize=16)\n", " ax.grid(True)\n", " \n", " \n", "# set up figure\n", "fig = plt.figure(figsize=(8, 6))\n", "ax1 = fig.add_subplot(111)\n", "ax1.margins(0.1)\n", "\n", "x = np.linspace(0.4, 9.1, 100)\n", "\n", "ax1.plot(x, p0(x), 'k', label='Constant')\n", "ax1.plot(x, p1(x), 'b', label='Linear')\n", "ax1.plot(x, p2(x), 'r', label='Quadratic')\n", "ax1.plot(x, p3(x), 'g', label='Cubic')\n", "\n", "# Overlay raw data\n", "plot_raw_data(xi, yi, ax1)\n", "\n", "ax1.legend(loc='best', fontsize = 12)\n", "ax1.set_title('Polynomial approximations of differing degree', fontsize=16);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.4600000000000001\n", "0.33298899237933954\n", "0.1994782421425496\n", "0.15730343662323767\n" ] } ], "source": [ "# we use the square of the difference to ensure each contribution\n", "# to the total error is positive, otherwise errors of different signs\n", "# could/would cancel out giving a false estimate of how good our approximation is\n", "\n", "\n", "def sqr_error(p, xi, yi):\n", " \"\"\"\"function to evaluate the sum of square of errors\"\"\"\n", " # first compute the square of the differences\n", " diff2 = (p(xi)-yi)**2\n", " # and return their sum\n", " return diff2.sum()\n", "\n", "\n", "print(sqr_error(p0, xi, yi))\n", "print(sqr_error(p1, xi, yi))\n", "print(sqr_error(p2, xi, yi))\n", "print(sqr_error(p3, xi, yi))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.5: Degree of approximation \n", "\n", "Extend the example above by fitting and plotting polynomials of increasing degree past cubic. At what *degree* does the resulting polynomial approximation equate to the Lagrange interpolant?\n", "\n", "Why does this make sense? \n", "\n", "Hint: think about the number of free parameters in a polynomial, and the amount of data you have." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of points to fit: 6\n", "poly_coeffs = \n", "[[ 0.5 0. 0. 0. 0. 0. ]\n", " [ 0.0508044 0.26714649 0. 0. 0. 0. ]\n", " [ 0.02013603 -0.13983999 0.55279339 0. 0. 0. ]\n", " [-0.00552147 0.09889271 -0.43193108 0.75909819 0. 0. ]\n", " [-0.00420655 0.07403681 -0.38492428 0.59251888 0.27906056 0. ]\n", " [-0.00301599 0.06536037 -0.49614427 1.59623195 -2.08266478 1.20030166]]\n", "square of the difference between the data and the polynomial of degree 0 = 4.60000000e-01\n", "square of the difference between the data and the polynomial of degree 1 = 3.32988992e-01\n", "square of the difference between the data and the polynomial of degree 2 = 1.99478242e-01\n", "square of the difference between the data and the polynomial of degree 3 = 1.57303437e-01\n", "square of the difference between the data and the polynomial of degree 4 = 4.69232378e-02\n", "square of the difference between the data and the polynomial of degree 5 = 7.23216068e-26\n" ] } ], "source": [ "print(\"Number of points to fit: \", np.size(xi))\n", "# in this example we have 6 pieces of information, to fit a polynomial\n", "# that exactly goes through these points we need 6 unknowns, or free \n", "# parameters, to choose in the polynomial. [Too few and we won't be able\n", "# to fit the data exaclty, and too many would just be a waste. Cf. over-\n", "# and under-determined systems.]\n", "# A 5th order polynomial has 6 free parameters (all the powers up to 5,\n", "# including 0).\n", "# So calling polyfit to fit a polynomial of degree 5 (size(x)-1) should\n", "# fit the data exactly (repeat below with size(x)-2 etc, and size(x) and \n", "# above to convince yourself of this).\n", "# Let's check the errors up to this point:\n", "\n", "xi = np.array([0.5, 2.0, 4.0, 5.0, 7.0, 9.0])\n", "yi = np.array([0.5, 0.4, 0.3, 0.1, 0.9, 0.8])\n", "\n", "# Let's set up some space to store all the polynomial coefficients\n", "# there are some redundancies here, and we have assumed we will only \n", "# consider polynomials up to degree N\n", "N = 6\n", "poly_coeffs = np.zeros((N, N))\n", "\n", "for i in range(N):\n", " poly_coeffs[i, :(i+1)] = np.polyfit(xi, yi, i)\n", "\n", "print('poly_coeffs = \\n{}'.format(poly_coeffs))\n", "\n", "# and now compute the errors\n", "for i in range(N):\n", " p = np.poly1d(poly_coeffs[i, :(i+1)])\n", " print('square of the difference between the data and the '\n", " 'polynomial of degree {0:1d} = {1:.8e}'.format(i, sqr_error(p, xi, yi)))\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.6: Extrapolation \n", "\n", "Recreate the plots in the example above for different degrees of polynomial, setting the x-range from -2.0 to 11.0. What do you notice about extrapolation when you use higher degree polynomials." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Extrapolation example - narrower interval')" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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A6DlQlf/XML7U/8oq7WcY9eIbGM/1HTen78W4QxiJ8WNYlSYfN+2o6q6d7fVjJ/ACxvNGn9ByWzAG6/g2xiAqn5ndeKs091rUatJYso9IpZRfHdMPaa0rlFLzMPpSLtRanwfWKqWigU1KqXCtddUtypPAQ0qpnRi3x69orW1b4tYSMS6Wv1VKrQI8MB5IvYHxC4qtYmCXMoaP7Q68Zi7/azD60yql3gb+Ryl1G+M5kFEYdwMSaPzC+KRS6hjGQ+zfwLjNbeskxhDI8zF+wSvUWp+2TaS1PqGU+ivwqvlrQSLGF+JXMB6ETG0glibRWhcopVZilF8fjD7d+RhfMu4F4rXWf1FKdcPoxpIB/EhrXaKUegLjovcyRjlWlcELSqkXMboa3IcxWkxbuI6xL1/FuHC9gLH/32hgmc0YleknSqlfYVTA3TCeo3kEeNS2q0cr7MXol34P5h0frXWlUuozjC9vnzXUsNFaW5RSrwH/Tyn1B4znGIZifHGw/YLwE4zy/kwpFYexn3piPLQ9WGu9yE7b1Bx1nstKqeeAHeYx9SHGudoX41zJ1Fq/3cT8/4TxTMNrGA+w2/7y2tTzUXQ+Ut9IfVNVBlLfNN0ejOeU/mTGE4hRlpm08pEUs277CbBBKfVnjO6h/TEa3ul8NdQ2Wut8pdRhjJHqtlg9s7MPeM7q/1Xpm3TctCb+Fjhp/vucUuqPGI2WVK11vHkebTXP7QMYA1oEY4zi90JTnp00t/nvGOURiPHcpbXmXotaT7dyhIi7+Y+GRyfSGA9dD8C4Rftnm2X7YHQ1+hhzNBCMXzi+xLiNWT2CB8YoM1n1xHAfcASjYjqHMZrNq8aurTUiyE8xhlvMMtfxObVH21IY3TVOY/zyeBXjVw7vOvJ71eqzH8YX2lvm32aMPqSamsNBB5jbXGjOi7cpy2CrtK4YFedFjJPxovnZ1SpNsLnc0zbxzTCnz2jCfnwQ4+JUYJbjWYy7GVXDzK4xp4fZLPcyxsV3qvnZHeOB6hxz+/4PCKmjrF41p7nY5JdRx3FStR3326bD+EJ0DqPyOgLcZ7PsJmxGOsO4C/EqxoOhpRjH5kFzmktjZdXM8+Oaud+shzZdYVseNvvxKZvpy839XoLRlWGauf2bbNIFAf8Po1tI1XG7G/hOY+XeQPw1yq85xxr1nMvmvCnmsXHLnJ+Bce5MsUoTTx2jeFnNdza3UWM15GwLzsdax4j8dcw/pL551eqz1DdS39QbcwP7+HEzlhKMLm0LbOOubx/b5Dm0nli+g9EoLMXokvY+EFhHup+b+SyxmlY1Ul5GPXk3eNzUt08bKbumHit17dtVGPVtpXU5YzQ8l5vlUILRsDuKMdS6T2NlbJX/Q2aaGiPjtfBa9GpjZdHYX9VFU3RxyngJ4U+11i83mlh0aMp4UWqC1vo7jo5FCCFsSX3TdUh9I4SMhieEEEIIIYQQdZLGkhBCCCGEEELUQbrhCSGEEEIIIUQd5M6SEEIIIYQQQtShSw8d7ufnp4ODg1u8/O3bt/Hw8LBfQA4i29FxdIVtANmOjqQzbMOXX355Q2vdx9FxdEStraegcxwD7UnK4ytSFjVJedQk5VFTfXVVl24sBQcHc+jQocYT1iM+Pp4ZM2bYLyAHke3oOLrCNoBsR0fSGbZBKXXR0TF0VK2tp6BzHAPtScrjK1IWNUl51CTlUVN9dZV0wxNCCCGEEEKIOkhjSQghhBBCCCHqII0lIYQQQgghhKhDl35mSQghmqq8vJysrCxKSkocHUqz+Pj4kJaW5ugwAHBzcyMoKAhXV1dHhyKEEELYhTSWhBACyMrKwsvLi+DgYJRSjg6nyQoLC/Hy8nJ0GGityc3NJSsri5CQEEeHI4QQQtiFdMMTQgigpKSE3r17d6qGUkeilKJ3796d7s6cEEII0RBpLAkhhEkaSq0j5SeEEKKrkcaSEEIIIYQQQtRBGktCCNFBODs7ExkZSWhoKBEREbz99ttYLBZHh1XtrbfeYujQoYwYMYJ///vfjg5HCCGEaHMywIMQQnQQ7u7upKSkAJCdnc0TTzxBfn4+r732WqvzrqysxNnZucXLnzx5kr/97W+cOHGCK1eucP/993PmzJlW5SmEEEJ0dHJnSQghOiB/f382btxIXFwcWmsqKytZuXIlUVFRhIeHs2HDBgAsFgtLly4lNDSUOXPm8OCDD7J161YAgoODef3115k2bRpbtmzh3LlzzJ49m/HjxzN9+nROnToFQE5ODvPmzSMqKoqoqCj2799fK54dO3awYMECunfvTkhICEOHDuXAgQPtVyBCCCGEA8idJSGEsPHaP05w8kqBXfMc3c+bVQ+HNmuZwYMHY7FYyM7OZseOHfj4+HDw4EFKS0uZOnUq0dHRJCQkkJGRwbFjx8jOzmbUqFEsWrSoOg83NzcSEhIAmDVrFuvXr2fYsGEkJyezdOlS9u7dy/Lly1mxYgXTpk0jMzOTmJiYWu9uunz5MpMnT67+HBQUxOXLl1tRIkIIIUTHJ40lIYTowLTWAOzatYvU1NTqu0b5+fmkp6eTlJREbGwsTk5OBAQEMHPmzBrLz58/H4CioiISExOJjY2tnldaWgrAnj17OHnyZPX0goKCWu9vqorDmox+J4QQoquTxpIQQtho7h2gtnL+/HmcnZ3x9/dHa80777xDTExMjTTbt29vMA8PDw/A6K7n6+tb/UyUNYvFQlJSEu7u7vXmExQUxKVLl6o/Z2Vl0a9fv+ZsjhBCCNHpyDNL9SgvK+VOznUqysocHYoQ4i6Uk5PDkiVLWLZsGUopYmJiWLduHeXl5QCcOXOG27dvM2XKFLZt24bFYuH69evEx8fXmZ+3tzchISFs2bIFMO4UHT16FIDo6Gji4uKq09bVoHrkkUf429/+RmlpKRcuXCA9PZ2JEyfaeauFEEI40u28WxTdzMVSWenoUDoMubNUj4tHj5C29X3Gjo0kcOgIR4cjhLgLFBcXExkZSXl5OS4uLixcuJDnn38egKeffpqMjAzGjRuH1po+ffrw0UcfMXfuXBITEwkLC2P48OFMmjQJHx+fOvPfvHkzzz77LG+++Sbl5eUsWLCAiIgI1q5dy3PPPUd4eDgVFRXcc889rF+/vsayoaGhPP7444wePRoXFxd++9vfykh4QgjRRRTm3iBxy184Eb8HrS0o5UQPX18Gj53AzO89g2u37o4O0WGksVSPXv2DALh5OUsaS0KIdlHZwC95Tk5OrF69mtWrV9eYXlhYyJo1a/D09CQ3N5eJEycyZswYADIyMmqkDQkJYefOnbXy9vPz44MPPmg0vpdeeomXXnqpCVsihBCiM6goKyNx61848vHf0drC2Aceple/IIpu5ZJ37SrH9u0m5+IF5v7Xy3j26u3ocB1CGkv18PEPACcnbl2V0Z6EEB3bnDlzyMvLo6ysjFdeeYWAgABHhySEEKKD0xYL/1z7C84e/ILR02fytce/g49/3xppRkyZzsfvrGHziyuY+18vEzB0uIOidRxpLNXD2cUFN29fbl7OcnQoQgjRoPqeUxJCCCHqorUm87M93EhLZeZTixn3wCN1phsaNZlvvfFLPvrlG3z4+os89fbv8Pbzb+doHUsGeGiAW89e3LwijSUhhBBCCNF1JG7ZzI20VCY99ni9DaUqfQaF8PhP3kJrzb5N77ZThB2HNJYa4Obbi1tXr8iIIEIIIYQQoks4vm83X2z7G71HjmHq/IVNWsbHvy+TvzGfsweTOH/kYBtH2LFIY6kB3X17YamsID/7mqNDEUIIIYQQolWKbuay74/vMiA0nEH3fr1ZLxef8PBj9OoXxN4/bKC8rLQNo+xYpLHUADffXgDSFU8IIYQQQnR6ezdtwFJRwdcXL0M5Na8Z4OziyqzvP0v+9Wsc3LG1jSLseKSx1AC3nmZjSQZ5EEK0A2dnZyIjIwkNDSUiIoK3334bi8Xi6LAAyM3NZebMmXh6erJs2TJHhyOEEKKZzh5KJj05kcnzFtAzoF+L8hgYFsHIqfdyYMfWu6bnlTSWGuDS3Y0ePr5yZ0kI0S7c3d1JSUnhxIkT7N69m48//pjXXnvNLnk39A6npnBzc+ONN95gzZo1dolHCCFE+ykrvsMnv1+H34BBTHj4G63K655vfw9LZSWpe2q/t68rksZSI3r1D+LmFXnXkhCiffn7+7Nx40bi4uLQWlNZWcnKlSuJiooiPDycDRs2AGCxWFi6dCmhoaHMmTOHBx98kK1bje4RwcHBvP7660ybNo0tW7Zw7tw5Zs+ezfjx45k+fTqnTp0CICcnh3nz5hEVFUVUVBT79++vFY+HhwfTpk3Dzc2t/Qqhg1FK/V4pla2UOl7P/BlKqXylVIr595P2jlEIIeqy/4M/U3Qzl68vXoazS+veHOTV24/B46I48eknVFZU2CnCjkves9SIXv2COJOc6OgwhBDt6V8/hmvH7JtnwBh44GfNWmTw4MFYLBays7PZsWMHPj4+HDx4kNLSUqZOnUp0dDQJCQlkZGRw7NgxsrOzGTVqFIsWLarOw83NjYSEBABmzZrF+vXrGTZsGMnJySxdupS9e/eyfPlyVqxYwbRp08jMzCQmJoa0tDS7bn4XsQmIA/7UQJrPtdZz2iccIYRoXEFONim7PmbMfdH0Gz7KLnmOuS+ac4eSuXDkEEOjJtslz45KGkuN6NVvACWFBdwpyKeHt4+jwxFC3GW01gDs2rWL1NTU6rtG+fn5pKenk5SURGxsLE5OTgQEBDBz5sway8+fPx+AoqIiEhMTiY2NrZ5XWmqMZrRnzx5OnjxZPb2goIDCwkK8vLzadNs6G631Z0qpYEfHIYQQzZH80YcoBZO/scBueYZETsCjZy+O7f23NJbudr369QeMEfGksSTEXaKZd4Dayvnz53F2dsbf3x+tNe+88w4xMTE10mzfvr3BPDw8PACju56vry8pKSm10lgsFpKSknB3d7df8HevKUqpo8AV4L+01idsEyilFgOLAfr27Ut8fHyrVlhUVNTqPLoSKY+vSFnUdDeWR2lhPif27sJvVDiHj9e8HLW2PLxChnH+yAF2/d8/6ObZdX9ck8ZSI3r1DwKMEfGCRoY6OBohxN0iJyeHJUuWsGzZMpRSxMTEsG7dOu677z5cXV05c+YM/fv3Z8qUKXz44Yc8+eST5OTkEB8fzxNPPFErP29vb0JCQtiyZQuxsbForUlNTSUiIoLo6Gji4uJYuXIlACkpKURGRrb3JncFh4FBWusipdSDwEfAMNtEWuuNwEaACRMm6BkzZrRqpfHx8bQ2j65EyuMrUhY13Y3lsfvdOJycnHh06XK8/frUmNfa8sgbOYL3DifjXXaHyTMebmWkHZcM8NAIL78+uLh2kxHxhBBtrri4uHro8Pvvv5/o6GhWrVoFwNNPP83o0aMZN24cYWFhPPPMM1RUVDB37lyCgoKqp02aNAkfn7rvgm/evJn33nuPiIgIQkND2bFjBwBr167l0KFDhIeHM3r0aNavX1/n8sHBwTz//PNs2rSJoKCgGl33BGitC7TWReb/PwZclVJ+Dg5LCHGXKsjJ5vi+PYTdF1OroWQPvgGBDAwL5/i+XegO8pqLttAh7ywppX4PzAGytdZh5rRXgf8AcsxkL5qVUZtycnKmZ2A/bkljSQjRxhoa3tvJyYnVq1ezevXqGtMLCwtZs2YNnp6e5ObmMnHiRMaMGQNARkZGjbQhISHs3Fl7qFc/Pz8++OCDRuOzzU/UpJQKAK5rrbVSaiLGD5K5Dg5LCHGXqnpWaeLcb7bZOsLui+Hjtb8k83gqg8K7Zo+EDtlYov4Rh36ttW73l3z07D+A7PNn23u1QgjRJHPmzCEvL4+ysjJeeeUVAgICHB1Sl6SU+iswA/BTSmUBqwBXAK31euCbwLNKqQqgGFigq0boEEKIdlR0M5fj+/Yw5r7oNrmrVGVY1BS69/DgVOJn0lhqTx1txKFe/YJI/2I/FeXluLi6OjocIYSo4W57YNlRtNbfamR+HMYPfUII4VBH9/wLi6Wy1S+gbYxLt24MHBNBRuphtNYopdp0fY7QIRtLDVimlPoucAj4kdb6lm0Ce44yVDVKyM38ArS2sPsfO3Dv1fm6n3eV0V+6wuGqoZAAACAASURBVHZ0hW2ArrkdPj4+FBYWOjagFqisrOxQcZeUlHSJY0MIITqrivJyUvfsZPC4KHz7tn1Pg+CI8aQnJ5KblYnfgEFtvr721pkaS+uANwBt/vsrYJFtInuOMlQ1Ssj1gUFc2PNPhvQPZPikqS3Oz1G6yugvXWE7usI2QNfcjrS0tE75XqGO9j4kNzc3xo4d6+gwhBDirnUm6XPu5Ocxdnb7jFAXHDEOgIyjh7tkY6nTjIantb6uta7UWluAd4GJ7bXuXv2M4cNzszLba5VCCCGEEEI025Gd/6BXvyAGjWmfZ4i8/frQO2ggGUcPt8v62lunaSwppQKtPj4GHG+vdbu6ueHj35fcS9JYEkIIIYQQHdPV9NNcO5dO5Ow57fr8UHDEOLLSjlNeWtJu62wvHbKxZI44lASMUEplKaW+D/xCKXVMKZUKzARWtGdMvQcM4sali+25SiHEXcbZ2bn6PUsRERG8/fbbWDrIuyt2797N+PHjGTNmDOPHj2fv3r2ODkkIIYSNIzv/QTf3HoTec1+7rjc4YhyV5eVknWy3exntpkM+s1TPiEPvtXsgVvwGDCIj5UsqK8pxdpER8YQQ9ufu7k5KSgoA2dnZPPHEE+Tn5/Paa6+1Ou/KykqcnZ1bvLyfnx//+Mc/6NevH8ePHycmJobLly+3Oi4hhBD2cTvvFqeTEoiMfpBu7j3add1Bo8Jw6dadC0e/JGTshHZdd1vrkHeWOiK/gcFYKiu5eUW+HAgh2p6/vz8bN24kLi4OrTWVlZWsXLmSqKgowsPD2bBhAwAWi4WlS5cSGhrKnDlzePDBB9m6dSsAwcHBvP7660ybNo0tW7Zw7tw5Zs+ezfjx45k+fTqnTp0CICcnh3nz5hEVFUVUVBT79++vFc/YsWPp168fAKGhoZSUlFBaWtpOpSGEEKIxx/ftxlJZQUT0Q+2+bpdu3QgaHUbG0SPtvu621iHvLHVEVaN73Lh0kT4Dgx0bjBCiTf38wM85dfOUXfMc2WskL0x8oVnLDB48GIvFQnZ2Njt27MDHx4eDBw9SWlrK1KlTiY6OJiEhgYyMDI4dO0Z2djajRo1i0aKvBgp1c3MjISEBgFmzZrF+/XqGDRtGcnIyS5cuZe/evSxfvpwVK1Ywbdo0MjMziYmJIS0trd64tm3bxtixY+nevXvLCkMIIYRdaa058ekegkaF0atff4fEEBIxjn1/fJf87Gv4+Hedl6NLY6mJevXrj5OzM7ny3JIQoh1prQHYtWsXqamp1XeN8vPzSU9PJykpidjYWJycnAgICGDmzJk1lp8/fz5gvFMqMTGR2NjY6nlVd4b27NnDyZMnq6cXFBTUOyT5iRMneOGFF9i1a5d9N1QIIUSLXTmdxq2rV5j46OMOiyE4cjz88V0yjh4m4usPOiwOe5PGUhM5u7jSM7C/DPIgxF2guXeA2sr58+dxdnbG398frTXvvPMOMTExNdJs3769wTw8PDwAo7uer69v9TNR1iwWC0lJSbi7uzeYV1ZWFo899hh/+tOfGDJkSDO3RgghRFs5Hr8bVzd3hk923PtAewb2x7uPf5drLMkzS83gN2AQNzIzHB2GEOIukJOTw5IlS1i2bBlKKWJiYli3bh3l5eUAnDlzhtu3bzNlyhS2bduGxWLh+vXrxMfH15mft7c3ISEhbNmyBTDuWB09ehSA6Oho4uLiqtPW1aDKy8vjoYce4q233mLq1M73cm4hhOiqykqKOZ2UwIgp0+jm1vCPXm1JKcWA0eFcPnWyuldEVyCNpWbwGzCI/OzrlJUUOzoUIUQXVFxcXD10+P333090dDSrVq0C4Omnn2b06NGMGzeOsLAwnnnmGSoqKpg7dy5BQUHV0yZNmoSPj0+d+W/evJn33nuPiIgIQkND2bFjBwBr167l0KFDhIeHM3r0aNavX19r2bi4OM6ePcsbb7xBZGQkkZGRZGdnt11hCCGEaJIzX+ynvKSY0Bn3OzoUAocNp7iwgIKc644OxW6kG14z9B5oDPKQm5VJ4NARDo5GCNHVVFZW1jvPycmJ1atXs3r16hrTCwsLWbNmDZ6enuTm5jJx4kTGjBkDQEZGRo20ISEh7Ny5s1befn5+fPDBBw3G9vLLL/Pyyy83cUuEEEK0lxPxe+gZ2I/+I0Y7OhQCzO/HV9NPd5lBHuTOUjNYj4gnhBAdxZw5c4iMjGT69Om88sorBAR0jQpKCCFEw25du0JW2nFC770fpZSjw8FvwCBcXLtx7dwZR4diN3JnqRl8/QNw6dadG5nSWBJCdBz1PackhBCiazv56Sco5cToe+9zdCgAOLu44D94KFfTu05jSe4sNYNycqJ30EC5sySEEEIIIRxKa03a/k8ZOCYCr15+jg6nWuDQYWRfOEdlRYWjQ7ELaSw1k9+AQfKuJSGEEEII4VDXzp4h//o1Rk6919Gh1BAwdAQV5WVdZgRpaSw1k9+AgdzOu8WdgnxHhyKEEEIIIe5SafvjcXZ1ZdjEKY4OpYbAocMBusxzS9JYaia/gcEAcndJCCGEEEI4hKWyktOJnzN4bBTde3g4OpwavPv0xd3bp8s8tySNpWaSEfGEEG3F2dm5+j1LERERvP3221gsFkeHBcCBAweq368UERHB9u3bHR2SEELctS6dOMad/DxGTutYXfDAeDlt4NDhXebOkoyG10wePXvh5uEpjSUhhN25u7uTkpICQHZ2Nk888QT5+fm89tprrc67srISZ2fnFi8fFhbGoUOHcHFx4erVq0RERPDwww/j4iLViBBCtLe0/fF0c3cnZOwER4dSp4Chwzl/5BCld+7QvUcPR4fTKnJnqZmUUvgNDCanizy0JoTomPz9/dm4cSNxcXForamsrGTlypVERUURHh7Ohg0bALBYLCxdupTQ0FDmzJnDgw8+yNatWwEIDg7m9ddfZ9q0aWzZsoVz584xe/Zsxo8fz/Tp0zl16hQAOTk5zJs3j6ioKKKioti/f3+teHr06FHdMCopKekQ7/MQQoi7UUVZGenJiQyb+DVcu3V3dDh1Chw6ArTm+vl0R4fSavKTYAv0CQ7h2N5dWCyVODm1/JdaIUTHdG31akrTTtk1z+6jRhLw4ovNWmbw4MFYLBays7PZsWMHPj4+HDx4kNLSUqZOnUp0dDQJCQlkZGRw7NgxsrOzGTVqFIsWLarOw83NjYSEBABmzZrF+vXrGTZsGMnJySxdupS9e/eyfPlyVqxYwbRp08jMzCQmJoa0tLRa8SQnJ7No0SIuXrzI+++/L3eVhBDCAS6kHKKs+E6HGwXPWsAQY5CHq+mnGRgW4eBoWkdquhbwDx5CRWkpt65eoXf/AY4ORwjRhWmtAdi1axepqanVd43y8/NJT08nKSmJ2NhYnJycCAgIYObMmTWWnz9/PgBFRUUkJiYSGxtbPa+0tBSAPXv2cPLkyerpBQUFFBYW4uXlVSOvSZMmceLECdLS0njyySd54IEHcHNzs/9GCyGEqNephE/p4ePboRshbp6e9Azsz9Wznf+5JWkstYB/8GAAsi+ck8aSEF1Qc+8AtZXz58/j7OyMv78/WmveeecdYmJiaqRpbKAFDw9jlCSLxYKvr2/1M1HWLBYLSUlJuLu7NymuUaNG4eHhwfHjx5kwoWP2lxdCiK6orKSY84cPEjrz6zi14jnU9hAwdDiZx1LQWnfqrtvyzFIL9A4aiLOLC9kZ5x0dihCii8rJyWHJkiUsW7YMpRQxMTGsW7eO8vJyAM6cOcPt27eZMmUK27Ztw2KxcP36deLj4+vMz9vbm5CQELZs2QIYd6yOHj0KQHR0NHFxcdVp62pQXbhwgQrzbewXL17k9OnTBAcH23GLhRBCNObCkUNUlJcxYso0R4fSqIAhw7idd4vbebccHUqryJ2lFnB2ccFvYDDZF845OhQhRBdSXFxMZGQk5eXluLi4sHDhQp5//nkAnn76aTIyMhg3bhxaa/r06cNHH33E3LlzSUxMJCwsjOHDhzNp0iR8fHzqzH/z5s08++yzvPnmm5SXl7NgwQIiIiJYu3Ytzz33HOHh4VRUVHDPPfewfv36GssmJCTws5/9DFdXV5ycnPjd736Hn59fm5eJEEKIr5xJSqCHjy/9R452dCiNqnrdTu6lTDx79nJwNC0njaUW8g8eTPqBpE5/a1EI0XFUVlbWO8/JyYnVq1ezevXqGtMLCwtZs2YNnp6e5ObmMnHiRMaMGQNARkZGjbQhISHs3LmzVt5+fn588MEHDca2cOFCFi5c2MQtEUIIYW/lJSWcTzlE6D2zOsUAY72DBgKQm3WRQeGRDo6m5aSx1EL+wUM4tncXhbk5ePv5OzocIcRdbM6cOeTl5VFWVsYrr7xCQECAo0MSQghhZxdSDlFRWsrwyVMdHUqT9PDxxc3LmxtZmY4OpVWksdRC/iFVgzycl8aSEMKh6ntOSQghRNdx+ov9uHv7EDQqzNGhNIlSCr+ggeRe6tyNJRngoYX6DAwBpbguzy0JIYQQQog2VF5awoXDBxkWNaXDj4JnrXfQQHKzMqtfg9EZSWOphVzd3OgV2J/sDGksCSGEEEKItpORcpjy0hKGT+74o+BZ6z1gIKV3blN0M9fRobSYNJZawT9kiAwfLoQQQggh2tSZ5P24eXkzIHSMo0Nplq9GxLvo4EhaThpLreAfMoSi3BvcKch3dChCCCGEEKILqigr49yXBxgWNblTdcGDr0bE68yDPEhjqRX8g81BHuTukhDCDpydnYmMjCQ0NJSIiAjefvttLBaLo8OqITMzE09PT9asWePoUO56+dnX2bVhLXduZDs6FCFEG7p47AjlJcUMm9Q5RsGz1sPbhx4+vuRKY+nu5B8yBEBeTiuEsAt3d3dSUlI4ceIEu3fv5uOPP+a1116zS94NvcOpOVasWMEDDzxgl7xE61gslRzbu0saS0J0cekHkujew4OBYeGODqVFenfyEfGksdQK7p5eePn1kcaSEMLu/P392bhxI3FxcWitqaysZOXKlURFRREeHs6GDRsAsFgsLF26lNDQUObMmcODDz7I1q1bAQgODub1119n2rRpbNmyhXPnzjF79mzGjx/P9OnTOXXqFAA5OTnMmzePqKgooqKi2L9/f50xffTRRwwePJjQ0ND2KQTRIG+/PqAUZYXSFVyIrspSWcm5Lw8QMnYCzi6ujg6nRXoHDeRGJx4RT96z1Er+wTLIgxBdzecfnuHGpSK75uk3wJPpjw9v1jKDBw/GYrGQnZ3Njh078PHx4eDBg5SWljJ16lSio6NJSEggIyODY8eOkZ2dzahRo1i0aFF1Hm5ubiQkJAAwa9Ys1q9fz7Bhw0hOTmbp0qXs3buX5cuXs2LFCqZNm0ZmZiYxMTGkpaXViOX27dv8/Oc/Z/fu3dIFr4NwdnHFs1dvSuW5WSG6rKy0E5QUFjBs4hRHh9JifgMGUl5STOGNHLz7dL53k0pjqZX6hgzh3JfJlN65Q/cePRwdjhCii6n6JW7Xrl2kpqZW3zXKz88nPT2dpKQkYmNjcXJyIiAggJkzZ9ZYfv78+QAUFRWRmJhIbGxs9bzS0lIA9uzZw8mTJ6unFxQUUFhYiJeXV/W0VatWsWLFCjw9PdtmQ0WL+PTpS36+NJaE6KrOHkzCxbUbwZHjHR1Ki301yMNFaSzdjQKGDgetuX4+nYFhEY4ORwhhB829A9RWzp8/j7OzM/7+/miteeedd4iJiamRZvv27Q3m4eHhARjd9Xx9fUlJSamVxmKxkJSUhLu7e735JCcns3XrVv77v/+bvLw8nJyccHNzY9myZS3YMmEvPn38ye7ED04LIeqntebswS8YFDGWbm71X587ut7Vw4dnMnhslIOjaT55ZqmVAoYaX6qupp92cCRCiK4kJyeHJUuWsGzZMpRSxMTEsG7dOsrLywE4c+YMt2/fZsqUKWzbtg2LxcL169eJj4+vMz9vb29CQkLYsmULYFTCR48eBSA6Opq4uLjqtHU1qD7//HMyMjLIyMjghz/8IS+++KI0lDoAb/8Aym8XUVlR7uhQhBB2dv38WQpzcxga1Xm74IHxjL9Hz16ddkQ8aSy1krunFz0D+3H17BlHhyKE6OSKi4urhw6///77iY6OZtWqVQA8/fTTjB49mnHjxhEWFsYzzzxDRUUFc+fOJSgoqHrapEmT8PHxqTP/zZs389577xEREUFoaCg7duwAYO3atRw6dIjw8HBGjx7N+vXr222bRev49PEHrSm8ccPRoQgh7Cz9QCLKyYkh4yc6OpRW6x00kBuddEQ86YZnBwFDR5B5LAWtNUopR4cjhOikGhre28nJidWrV7N69eoa0wsLC1mzZg2enp7k5uYyceJExowx3vCekZFRI21ISAg7d+6slbefnx8ffPBBk+N89dVXm5xWtC0f/74A5Odcxzcg0MHRCCHs6eyBJIJGheHu5e3oUFrNL2ggqXv/jbZYUE6d615N54q2gwocOpzbebcozM1xdChCiLvQnDlziIyMZPr06bzyyisEBAQ4OiTRTnz8jX2dn33dwZEIIewp9/Ilbl7J6tSj4FnrPWAgFaWl5Od0vvfCyZ0lOwgcOgKAq+ln8PbrfKN8CCE6t/qeUxJdn2ev3qAUBTnSWBKiKzl78AsAhkyY7OBI7KN3kDnIQ1Ymvn071w96cmfJDvoEh+Ds6sq1c/LckhBCiPbj5OxMN09vubMkRBdz7tAX9B081Hj5dBfQM7AfAHnXrjo4kuaTxpIdOLu44h88WEbEE0II0e66e3mTL3eWhOgyim7d5Gr6aYZMmOToUOzG3cubbu7u5F2XxpJdKKV+r5TKVkodt5rWSym1WymVbv7b05Ex2gocOoLrF85iaeABbSGEEMLeunn7UNAJnwMQQtTt/JcHADr9kOHWlFL49u1HvjSW7GYTMNtm2o+BT7TWw4BPzM8dRsCwEVSUlnLj0kVHhyKEEOIu0t3Lh9u3blJeVuroUIQQdnD20Bf4+PfFz3yZa1fh2zdA7izZi9b6M+CmzeS5wB/N//8ReLRdg2pE4BB5Oa0QonWcnZ2r37MUERHB22+/jcVicXRYgDEMubu7O5GRkURGRrJkyRJHhyRM3byN92oV3pARWYXo7MqK75B5/ChDJkzucq+j8QkIJD87G4ulc/XC6kyj4fXVWl8F0FpfVUrVOeycUmoxsBigb9++rRolqqioqMnLa61xcXPnSMKn3HJ1b/E620JztqMj6wrb0RW2Abrmdvj4+FBYWOjQeNzd3fn8888ByMnJ4fvf/z7Z2dm89NJL9S5TWVnZpLgrKytxdnZucWxFRUWEhIRUxwfUud6SkpIucWx0Jt3Nd7DkZ1+nV78gB0cjhGiNjKOHqSwvZ2hU1xgFz5pv3wAslRUU3rhR/Y64zqAzNZaaRGu9EdgIMGHCBD1jxowW5xUfH09zlr+V/CkFOdnNWqY9NHc7OqqusB1dYRuga25HWloaXl5ejg0IqmPw8vLivffeIyoqirfeeguLxcKPf/xj4uPjKS0t5bnnnuOZZ54hPz+fF154gU8//ZSQkBAsFguLFi3im9/8JsHBwSxatIhdu3axbNkyoqKieO6558jJyaFHjx68++67jBw5kpycHJYsWUJmpvF29f/93/9l6tSpNeLy9PTEycmp0TJyc3Nj7NixbVM4ok7dvIw7SzJ8uBCd39lDybh5etF/xGhHh2J3vn2NF2fnXb8qjaU2cl0pFWjeVQoEOtzTrIFDR3Ah5UtK79yhe48ejg5HCNFC+zZtJPviebvm6T9oMDOfWtysZQYPHozFYiE7O5sdO3bg4+PDwYMHKS0tZerUqURHR5OQkEBGRgbHjh0jOzubUaNGsWjRouo83NzcSEhIAGDWrFmsX7+eYcOGkZyczNKlS9m7dy/Lly9nxYoVTJs2jczMTGJiYkhLS6sVz4ULFxg7dize3t68+eabTJ8+vXWFIuzC1cMTZxcXGT5ciE6usqKCC4cPMnj8RJxa0ROgo6pqLOVfvwZjHBxMM3SmxtLfgSeBn5n/7nBsOLUFDhsBWnPt7BkGhUc6OhwhRBegtQZg165dpKamsnXrVgDy8/NJT08nKSmJ2NhYnJycCAgIYObMmTWWnz9/PmB0o0tMTCQ2NrZ6XmmpMSDAnj17OHnyZPX0goICCgsLa9xFCgwMJDMzk969e/Pll1/y6KOPcuLECby9vdtmw0WTKaXw7uNPvoyIJ0SndvnUSUpuF7V5F7zKSgt51+9QeEVz4vPLFBeW49rdGTcPF7p7uNJngBcevt3tvl7P3r1xcnbh1rUrds+7LXXIxpJS6q/ADMBPKZUFrMJoJH2olPo+kAnE1p+DYwQOG4lSTlw+fUIaS0J0Ys29A9RWzp8/j7OzM/7+/miteeedd4iJiamRZvv27Q3m4eHhAYDFYsHX15eUlJRaaSwWC0lJSbi71/+8Zffu3ene3ag8x48fz5AhQzhz5gwTJkxo7maJNuDdpy8F2dccHYYQohXOHkrCxbUbweHj7J737fxSLh7L5eKJXLLSblJWYgyykEndA5P1DPRgwMieDBnXh8ChvnYZbMLJyRmfvgHGnaVOpEM2lrTW36pn1qx2DaSZuvfoQZ/gELLSTjg6FCFEJ1f1HNGyZctQShETE8O6deu47777cHV15cyZM/Tv358pU6bw4Ycf8uSTT5KTk0N8fDxPPPFErfy8vb0JCQlhy5YtxMbGorUmNTWViIgIoqOjiYuLY+XKlQCkpKQQGRlZK55evXrh7OzM+fPnSU9PZ/Dgwe1SFqJxPn36kn7hnKPDEEK0kNaac4cOMHBMBK5ubnbLN/tiAUf3XuLsoWwslRrPnt0ZOqEv/Yb5ci4zjemzptDDqxvlZZWU3C6nuLCca+fyyTp1k5MJV0jdl0XAYB/GPzCIQWG9W91o6ozDh3fIxlJnFjQylNRP/k1lRTnOLq6ODkcI0YkUFxcTGRlJeXk5Li4uLFy4kOeffx6Ap59+moyMDMaNG4fWmj59+vDRRx8xd+5cEhMTCQsLY/jw4UyaNAkfH58689+8eTPPPvssb775JuXl5SxYsICIiAjWrl3Lc889R3h4OBUVFdxzzz2sX7++xrKfffYZP/nJT3BxccHZ2Zn169fTq1evNi8T0TTe/n0pLiygrKSYbm4da0RWIUTjbly6SEHOdSY9Zp+OU9czCkjcdpYr6Xm4dncm7N7+jJ7aj179PKobPFeLT+HVy2iYObs64ebhiq8/BA7xYWz0QCrKKklLvMrhXRf5529T6TPQi1lPjqJ3f88Wx+XbN5CstBNore02NPrpm6f59eFf84t7foF3N/t3DZfGkp0FjQrj8L/+zvXzZ+k3fJSjwxFCdCKVlfW/e8LJyYnVq1ezevXqGtMLCwtZs2YNnp6e5ObmMnHiRMaMMZ6czcjIqJE2JCSEnTt31srbz8+PDz74oMHY5s2bx7x585q4JaK9+fQx3qZRkH0dv4HBjg1GCNFs5w5+AcCQ8ZNalc+dgjKSPjrHqcSruHt3Y+o3hzJqaj+6uzf/K79LN2fGzAhi9PR+nEm+RtL2c2x56xBTHhtC+MwglFPzGzu+fQMoLymmuCCfHj6+zV7e1snckyzevZjuzt3JL8mXxlJn0H+kMdRjVtoJaSwJIdrFnDlzyMvLo6ysjFdeeYWAgABHhyTamY+/sc/zc7KlsSREJ3Tuy2QCh47Aw7dni5bXWnMq6SoJH6ZTUW5h7NcHMuHBYLq1oJFky9nZiVFf68egMD/2vZ9GwpZ0Lh6/QfT3w3DzbF4vKh+r4cNb21g6fuM4i3cvxtPVk/ei32OA94BW5VcfaSzZWQ8fX3r1C+LyqRMw95uODkcIcReQl8CKqneWyPDhQnQ+RTdzuXYunWkLvtui5UtulxO/+RTnDufQf7gvM749Et++9n+FTQ/vbjy4NJwTn18h4cN0tr99mEeWR+Lh0/SR86rftXTtaqtuKhzNOcqS3Uvw6e7DezHv0d+zf4vzaoxTm+V8F+s/KpTLp05isdTfpUYIIUTnopT6vVIqWyl1vJ75Sim1Vil1VimVqpSy/5BW9XD39sGle3cKcjrXKFNCCDj35QEAhkxofhe8K+l5fPDmAS6k3GDKY0N45Idj26ShVEUpRdg9/ZnzgwgKc0v4/9YcpuBGcZOX9/HvC0q1apCHQ9cOsXjXYnq69eQPMX9o04YSSGOpTQSNCqP0zm1uZF50dChCCCHsZxMwu4H5DwDDzL/FwLp2iAkwvsD49g3k1rXONcqUEALOHfoC376B9A4a2KzlTu6/wo5fH8HZ1Yl5L4xnXMwgnFrwHFFLBI3oySM/jKT0djnbf3WYvOt3mrScS7duePXyI6+Fw4cnXknk2T3P0tejL3+I+QOBnoEtyqc5pLHUBoJGhgLIEOJCCNGFaK0/A242kGQu8Cdt+ALwVUq1fU1u6hnYj1tXO9fLHoW425WVFJN5/ChDJkxs8uhwFosmYUs6+94/Rf+RPYn98QT8B7X/C8IDQnx49PlxVFZY+EfcUUqKypu0XEuHD//00qf84JMfMNB7IH+I+QN9Pfo2O4+WkGeW2oB3H3+8/Ppw+dQJxj3wsKPDEUII0T76A5esPmeZ02p8K1BKLca480Tfvn1b/cxZUVER8fHxFJZVcuvaFfbt3Ytyunt/C60qDyFlYasjlset82eorKig0Ll7k2KzVGguJWqKrkCv4eAVdoukA/tbtG57lUfAJE3G3nL++ovPCZ6hGh0l744F8i9lNmvdR24fYdONTfTv1p9FHos4lnyslVE3nTSW2kjQqDAuph6x6zjyQgjRWp6enhQVFdU7Py8vj7/85S8sXbq0HaPqMuq62OtaE7TeCGwEmDBhgp4xY0arVhofH8+MGTM4TgXXjiQTOXokPQP6tSrPzqyqPISUha2OWB7/OnEYNw9PHlrwbZycnRtMW1pcwT9/e5Siq/nc+63hzlng4QAAIABJREFUhN0b1Kp127M8Tg+4xp4/nERdDeTeJ0Y0+N03+VY2CaeO8bVJE+nm3vjzVdvTt7MpaROR/pHEzYrDq5uXXWJuqrv3p6c2FjQylDv5eeRdky4RQnRFmzdvJjg4GCcnJ4KDg9m8ebPd8tZaY7FY7JZfc+Tl5fG73/3OIevuArIA67Frg4B2qwR6BhoPOd+6erm9VimEaAVLZSXnjxwiZFxUow2l4sIydvz6CNfPFxD9/dBWN5TsbcSkAMbFDOLE51c4Ft/wNcg3oGr48MafW/pL2l/4SeJPmBw4mXX3r2v3hhJIY6nN9B8lzy0J0VVt3ryZxYsXc/HiRbTWXLx4kcWLF7eqwZSRkcGoUaNYunQp48aN49KlSzz77LNMmDCB0NBQVq1aBcCBAwf4xje+AcCOHTvw9/enrKyMkpISBg8eXCvfCxcuMGXKFKKionjllVeqpxcVFTFr1izGjRvHmDFj2LFjBwA//vGPOXfuHJGRkaxcubLedKJOfwe+a46KNxnI11q324gLPQONu0m3rsiPdEJ0BldOp1FSWMDQRkbBu51fyvZfHebm1ds88OwYhk1on2d1mmvy3MEEh/uxf1s6uZfr78Hga/WupfpordlwdANvHXiLWQNn8c5979DDte1G+WuINJbaSK9+QfTw8SXz+FFHhyKEsLOXXnqJO3dqjvxz584dXnrppVble/r0ab773e9y5MgRBg0axE9/+lMOHTpEamoqn376KampqYwbN44jR44A8PnnnzNq1CgOHjxIcnIykybVrnCXL1/Os88+y8GDB2u8rNbNzY3t27dz+PBh9u3bx49+9CO01vzsZz9jyJAhpKSk8Mtf/rLedHcjpdRfgSRghFIqSyn1faXUEqXUEjPJx8B54CzwLtCufRndvbxx8/CUO0tCdBJnv0zG2cWF4Ij63zJQXFTG33+TQuHNEh7+QQTBY/zaMcLmUU6K+xaOpLu7C3s2naSysu4eEj59jboor57RO7XWrDm0hriUOB4e/DBr7l1DN+dubRZ3Y+SZpTailGJgWASZx4+iLZa7+mFbIbqazMzMZk1vqkGDBjF58uTqzx9++CEbN26koqKCq1evcvLkScLDwxk6dChpaWkcOHCAZcuW8dlnn1FZWcn06dNr5bl//362bdsGwMKFC3nhhRcAozJ68cUX+eyzz3BycuLy5ctcv177hab1pbNueN0ttNbfamS+Bp5rp3BqUUrRM7C/NJaE6AS01pw79AUDQsPrfW6n5HY5f/9NCvk5xcxZFkH/4T3bOcrmc/fqxownRvKvDcf48uMMJj5cu8eDm4cnbp5e5GfX7oZXYangtaTX+OjsRzwx8glemPgCTsqx36HlG3wbCo4Yx538PHIyMxwdihDCjgYOrPtdGPVNbyoPD4/q/1+4cIE1a9bwySefkJqaykMPPURJSQnw/7N33+FRVekDx793SjIzqZPeSCUFSCcQepViA7Er6rqoiLv+1LWXtaCy7uraFRVFVIRVsSFKUZDeew8JCem9l5lMptzfH0OLEGlJJoHzeZ55Jsy55b1jxtx3zjnvgaFDh7JkyRLUajUjR45k3bp1rFu3jmHDhp32uKebaDtv3jwqKirYvn07u3btwt/f//jxz2c7oWsQ5cMFoXuoLiqktrSEqLQBp21vMVpY9O5u+9C7aQmExHb9ROmYyBRfYtL92b4kj/K8+tNu4+bjS0NVZavXTFYTj65+lB8P/8i0pGk82f9JhydKIJKlDhWakARA3t5dDo5EEIT2NGPGDHS61t8E6nQ6ZsyY0W7nqK+vx8XFBQ8PD8rKyliyZMnxtmHDhvHWW28xcOBAfHx8qKqqIiMjgz59+pxynMGDB/PVV18BtJpTVVdXh5+fH2q1mpUrV5KXZ19E283NjYaGhjNuJ3RN+sBgGqoqMJtEQisIXVn29s0ARPXtf0qb1WJjyUd7qcxvYPw98YT18e7s8C7Y0Btj0LqpWfH5QayWU4fjuXn7tEqWGlsauW/5fazIX8ET/Z7g78l/7zLVpEWy1IHcvHzwDgklb89OR4ciCEI7mjx5MrNmzSIsLAxJkggLC2PWrFlMnjy53c6RlJRESkoKffr0YcqUKQwePPh4W3p6OmVlZcd7khITE0lMTDztH5a3336b999/n379+lFXV9fqGrZt20ZaWhrz5s0jLi4OAG9vbwYPHkx8fDyPPfZYm9sJXZM+yF4Rr625AIIgdA3Z2zbjFxGFm3frOUiyTWbF5wcpzKhh1B1xRCT5OijCC6NxUTN8chzVxU3sW33q0GA3b18aqioAqDJWMWXZFHaW7eSVoa9wW+/bOjvcPyXmLHWwsIRk9ixfiqWlBZWT4yanCYLQviZPntyuyVF4eDj79u1r9dpnn3122m21Wi0mkwmAhoYGZs2a1eZxIyIi2Lhx4/F/P/nkkwD4+Pi0ev1k8+fPb/XvtrYTup6Ty4f7hkU4OBpBEE6nqbaG4qwMBl1/6ylt678/TNbWMgZOiiJ2QKADoms/4Qne9OilZ+svR4hND0Djqj7e5ubtg6mpiZzyLO5f9yAVhgreGfUOQ0NOnXvraKJnqYOFJaZgMbdQlHHA0aEIgiAIF7lj65eIeUuC0HXl7NwKskzUH0qG715RwO7lBSSMDCFl7IXNge0KJEli8PXRtBgtbPnlSKs2dx97j9n/LZxKfUs9n4z7pEsmSiCSpQ4X0jsehVJF3l4xFE8QBEHoWE4aLa5e3qIiniB0QccWM08aNY5/LV7Fb+tP9Nrn7qlk3bdZRKb4MuSG6C4zX+dCeQe70ntIEPtWF1FT2nT89XzZXn3V3eTEF5d/QZJvkqNCPCORLHUwJ42WoNg48vaIIg+C0NVdqusHtRfx/nUN+sBgqkWyJAhdSqvFzIHqxqbji5lXFjby6+z9+PZw47I7e6NQXByJ0jH9r45E7aRg/XeHAfg552deOvAaAH+PuptIj1PLi3clIlnqBGEJKZTnZmOorzvzxoIgOIRGo6Gqqkrc8J8nWZapqqpCo9E4OpRLnigfLghdT1uLmT/11NP8MnM3TholV9yXiNpZ6aAIO47O3Ym+l4eTt7eKWUvm8dTap4gJTQBJQmpocXR4ZyQKPHSCsMRk1n89l7y9u+g1eLijwxEE4TRCQkIoLCykoqLC0aGck+bm5i6ToGg0GkJCQhwdxiVPHxhMc0M9xoZ6tG7ujg5HEATaXrS8sKCA5gYzkx5NxVXv3MlRdZ4+I4JYv+wguSsbuPzKy3l5yMvMWXg3DZVd/2+uSJY6gX9kTzQuruTt2SmSJUHootRqNRER3a962KpVq0hJSXF0GEIXcqIiXrFIlgShiwgNDT3tOnWerr6MvrM3fmEX72fVYDbwxPonqPaFQXmTuCb4JpyUTq3Kh3dlYhheJ1AolIQmJJO7ewey7dSFuQRBEAShvZxcPlwQhK5hxowZaP8wCkCtcuaBu5+kZ18/B0XV8SqNlUxZNoU1hWu48qpBaFzV7Fhi72X748K0XZVIljpJVFo6TTXVlOZkOToUQRAE4SLm4eePpFCIZEkQupDJkyfz8J23oddpkSQJL1c//u+W53ju9YccHVqHya7NZvIvk8mpy+HtkW9za8ItJF/Wg/z9VVTkN+DmY0+WuvpcYTEMr5NEpKQhKRRkb9tCYM9YR4cjCIIgXKSUKhWe/gHUFItkSRC6ClmWiXCCDx7/B0bD5SjVCm54qt9FV/numI3FG3lk1SM4KZ2YM24OfXz6AJAwPISdv+azbfERfP09sLSYaMjMPDH3VpJAoUSh1aDQaJC0WiSFY/t2RLLUSbSubgTH9SZ7+2aG3Hy7o8MRBEEQLmKifLggdC3VRQXUlpag0vTFZLBw3RNpaFzUjg6rQ3x34Bs+WTaDYSY/7vWegG72LxSWfoKltAxrTQ3Bmr7kGEYhH/gYAp05cPONeBjbqIonSSg9PFB6eaHy8kLl7486JAR1SDBOoWE4x0Sj0us79HpEstSJeqYNYNUXn1BXXoqHX4CjwxEEQRAuUl7BPcjbsxOrxYJSJf7UC4KjHd66CYCGmkAumxKLT4irgyNqH5aaGpr37qX5YAbNGQcp2b2J2JJa3pABCmlmJiZnZ9QBAaj8/XHuFUdvDx35ZVYM/W6EwoVo//pXgsIj4ehwPNlixdZsRG5uxtbUhLW2FktVNdaqKoy7d1O/dClYrcdjUPr44Bzdk8CXXsYpJLjdr1H8H7QTRfVNZ9UXn5C9bTOpV0x0dDiCIAjCRco3NByrxUJtaTHeIaGODkcQLnkH1q5DUvrTZ1gscQMCHR3OeZFlmZbcXAxbt2LYtg3j7t2Y806URK/31nDIy4TblX0YPugWNBGROIWFodTrkaTWww3j5h9i/1oTALbYnniMu+rs47BYMJeW0XLkCKbDhzFlZmLKzETp7tY+F/oHIlnqRJ4BgXiHhJK9XSRLgiAIQsfxCQ0HoCI/VyRLguBgJYeLqC7Kwd1/BENvinZ0OOfEUl1N0/r1NK1bR9OGjViOrkWo9PFBm5yE53XXY4gJ5smyWew3HeGJfv9kUq9bz3jc+BHB7F1diKRQnnNFPEmlwikkGKeQYFyHDjmv6zoXIlnqZFFp6Wz96TuaGxvRuF4cXbCCIAhC1+IV3ANJoaAyPw8GOToaQbh0Wa02ln64CIDLplyFSq10cER/TpZlTFlZNP7+Ow2/r6R5716QZZSenrgMGoSuf390/fvjFBGOJEnsKt/FQysfwmQ1MXP0TAYHDz6r83gHuRIcoyd3hxv1FeUde1EXSCRLnSyqbzpbflzAkd3bxQK1giAIQodQqdXoA4OpLMh1dCiCcEnb/GMOtSV7cfH0Izypa1ZDlmUZ08GD1C9ZSv2yZZjz7UPrNImJ+Pzf/bgOHYqmd28kZetE78fDP/LixhcJcAlg9rjZRHlGndN5jxg38/KPC6mZP4+wN2cyY8YMJk+e3G7X1V5EstTJAnvGoPPwJHvrJpEsCYIgCB3GJzScsuxMR4chCJes3L2V7Pg1C9laSK+hE0+Zt+NoyooKKt57n/pFi2jJywOlEpcBA/CeMgXXkSNR+59+sVyLzcKb29/kiwNfkB6YzuvDX8fD2eOczj1v3jyefeVRDAYDAHl5eUydOhWgyyVMIlnqZJJCQWRqfzI3rcNiNqNSX5xlIwVBEATH8u0RRubGtbQYDThpdY4ORxAuKY01JlZ8dhCdazGmWis9+w10dEgAWBubqF/8C3U//IjPzp1UShK69HS87pqC25gxZyzDXWeq47HVj7GxZCO3xN3CY/0eQ60493vZZ5555niidIzBYOCZZ54RyZIAMemD2LfyV3J376BnWrqjwxEEQRAuQseKPFQW5BMUE+fYYAThEmKzySyfsx+LxYZPQDEtjXqCoh03BE+WZZp376ZmwQLqlyxFNhhw6hlFw6RrSHnwQdQBZ7ecTVZNFg/8/gClhlJeGPgC18Vcd94x5efnn9PrjuTYJXEvUaEJyWjc3Dm0YY2jQxEEQRAuUieSpVyHxiEIl5odS/MoyqxlyPXhFB3cTVRaOpKi82+5bQYDNQsWcOS668i9+RYalizF48orCP/6KyIXLcIwbtxZJ0rL85YzefFkTFYTc8bNuaBECSA09PRVOtt63ZFEz5IDKFUqYtIHcWDtSszNzag1GkeHJAiCIFxkPHz9UDtr7BXxBEHoFKU5dWz5+QjR/fxx1pZiNjUT3clD8MxFRVTPm0/tggXYGhpwjo0l4IUXcL/qKpSuLud0LKvNyrs732X2vtkk+iTy5sg38dOdfi7TuZgxYwZTp05tNRRPq9EyY8aMCz52exPJkoPEDR7OnuVLyd6+mThR6EEQBEFoZ5JCgU+PMCrzcx0diiBcEkxGC7/O3o+r3pnht8ay8rP3cNLq6BGf2CnnN+7aRdWnc2hYvhwkCbexY/C6/Xa0KSnnVVyitrmWx9c8zsaSjdwQcwNP9n8SJ6VTu8R6bF7SU089RUFBAXpXPXff8HiXm68EIllymJC4Prh6eZOxYY1IlgRBEIQO4RMaRtbWTciy3OUqcQnCxUSWZVbPP0RjjYlrH01F7SSRvX0Lkan9UKo6rpiXbLPRuGo1VbNnY9y+HYW7O953TUF/662oAwPP+7j7K/fz8KqHqTBWMH3QdK6NvrYdo7abPHkyt956K+/+5Qa8e/SnvrYfzU1mNC5dq/iZmLPkIJJCQezAoRzZuZ3mxkZHhyMIgiB0M+aSEooefhhFdXWb2/iEhtPcUE9TbU0nRiYIl57MzaVkbS2j/1URBER6UJSxn+aG+g6rgidbLNQtWsSRiRMp/NvfMJcU4//0U0Sv/B2/Rx4570RJlmUWZC7g9iW3IyPzxeVfdEiidIwkSbh5++CkbcZmlTm8razDznW+RLLkQHGDhmGzWsjassHRoQiCIAjdjGy10bDid9y+/6HNbXx6hANQWSDmLQlCR6mrMLL6q0wCe3qQOj4MgKytG1Gq1USk9G3Xc8ktLdQsWED25VdQ/NjjAAS99io9ly3D6447ULic25ykkxktRp5d/ywvbnyRfgH9+Pqqr4n3iW+v0Nvk5uOLyVCDV5ALGZtKz21nmw0qs2DPN2Czdkh83W4YniRJuUADYAUssiynOTai8+cfFY2nfyAZ61eTMGqso8MRBEEQuhGnkGC875pC5cwPMGzbhi7t1D+HPqH2G7fK/FzCE1M6O0RBuOjZrDaWz9mPJElc9tfeKBQSss1G1paNhCWm4KTRtst55JYWahcupOrDjzAXFaGJj8f/icdxHTWqXSrtHak7wiOrH+FwzWHuTbyX+5LuQ6lQtkPkZ+bq5U1VYT79JgWw8ftsassMePqfZm04WYa6AijaAcU77M8lu8FUb28PSAS/9l8modslS0eNlGW50tFBXChJkogbPIzNPyygqbYGF88/XwhMEARBEE7mfffdlP3vK0r/9S8iFixAUra+udG5e+DiqRcV8QShg2xbkkdpTj1j7uqNu7c9MSrNzqKxqpIhN91+wceXLRbqFv5E5cyZ9iQpMZGA55/DZejQdpuHuPTIUp7f8DxOSidmXjaTIcFD2uW4Z8vFU4+hrpaYND82/ZDNoc2lpE+IhMbyo4nRTntyVLwTmirsOynUEBAPCTdAcCoEpYBPdIfE112TpYtG3OARbPr+aw6sXUm/qztuTKggCIJw8VHodDRcOwnl7E+p/e479DfeeMo2PqHhYq0lQegApTl1bFucS0y6PzH9TqxXlLl5PQqlkqi+6ed9bNlmo37JEirffY+W3Fw08fHtniSZZTMvb3qZrw99TbJvMq8Nf40Al7Nbd6k9uXh6YbNaURSuJCTAzKHf99I/awJSQ4F9A0kBPrEQPdaeFAWngn88qJw7Jb7umCzJwK+SJMnAR7Iszzq5UZKkqcBUAH9/f1atWnXeJ2psbLyg/c+WS0AQmxf9QKOrvkOqFXXWdXS0i+E6LoZrAHEdXcnFcA3ChTGlpaHdvZuKN9/Cffx4lO7urdp9eoSx+9fF2GxWFJ00rEYQLnYtzRZ+m3MAV09nht0ce/x1WZbJ2rKB0IRkNK6u53xcWZZpWreO8jfexHTwIM7R0YS89y6uo0e36z1ibl0ur5e8TpG5iDv73MkDqQ+gVnRSFboWA5TuPT6UznXPAUBP0/y7iJX7sbz5Ico8LidgYJg9OQpMAudzfy/bS3dMlgbLslwsSZIf8JskSRmyLK851ng0eZoFkJaWJo8YMeK8T7Rq1SouZP+z5StZWTrzTXr6+9Cjd0K7H7+zrqOjXQzXcTFcA4jr6EouhmsQLpAkEfD00xy57noq3nuPgKefbtXsGxaBxdxCTXEx3iE9HBSkIFxc1i3Ior7SyKSHU3HWnridLs/Noa6slP4TbzjnYxr37KH8v69j2LIFdUgIQa+9ivuVV7bLnKSTLcpexEubXkJhU/D+6PcZFjKsXY/fitUMZftPzDEq3gnlB0E+WozBLRCdbyJkGGga/jLh/a9G8dx+svX3EjCoZ8fFdQ66XbIky3Lx0edySZJ+APoDa/58r64tZsBgVn42i70rlnVIsiQIgiBc3DS9e+N5803UfDkPz0mT0PTqdbwtIMo+jr80O1MkS4LQDnJ2VXBwfQmp48IIivZs1Za1eQOSQkHPfgPO+ngthYVUvPEG9YuXoPTywv+ZZ9DfdCOSU/ssAHtMk7mJf23+Fz9l/0SqXyrXqK9p30TJZoOqrNYFGEr3gtVkb9fqISgVYsYfnWeUCu6BuJaWwNp7aNSG4eztR0hcMTk7yxl0bVSXWB+uWyVLkiS5AApZlhuO/jwWeNHBYV0wtbOGXkNHsPf3Xxn513vRuro5OiRBEAShm/F76CEalv1K6fQXCZs/7/i30fqgYJy0WkqzM+kzfLSDoxSE7q2pzsTKuRn49HCl/9URrdpkWSZz83p69I5H5+5xxmNZ6+up/OBDar78EpRKvO+bhvddd6N0Pf/y323ZX7WfJ9Y8QUFDAX9L+hv3JN7DujXrzv+Asgy1+a17jIp3QUuDvV3tAkHJ0P+eE4mRPhxOk/wcK3B2bD24qBQ/Vn6ZQWVBI76hjr8n7lbJEuAP/HA0y1QB82VZXurYkNpHwqhx7Fr2CwfX/E7qFRMdHY4gCILQzSg9PPB77DFKnnqKuu+/x/P66wFQKJT4R0ZTejjTwREKQvcmyzK/f5GBucXKmCl9UKpaD4+rKsynpriQ1Msn/PlxLBZqvv6aynffw1pXh8ekSfg++ABqf/92j9km2/hs/2e8u/NdvDXezB47m7SA81h1p6HsD4nRDjBU2duUTvaCC0k32ZOioBTwjYWznCOp1mhw0mppqrUvsB2R5MOqeZC9s1wkS+dKluUcIMnRcXQEv/BIAnrGsGfFMlIun9Aluh0FQRCE7sXjmonUfvct5a/9F9fRo1Hp7d/YBkRFs/2XhVjMZlTqTprELQgXmX2ri8jfX8XQm2LwCjy19ydr8waQJKL7D2zzGI1r11H273/Tkp2NLj0d/yefaDVstj2VNpXyz3X/ZHPpZsaEjeG5Ac/hqfE8847G2hMJ0bHkqL7I3iYpwLcXxFwOwSn25Mg/HlQXNmTQxdOLphp7z5LWzYmgGE9ydlYwYGLUBR23PXSrZOlilzh6PL9+9A7FmRkEx3bMB0cQBEG4eEmSRMBzz3Fk0rWUv/46QS+/DEBAzxhsVgsVeTkE9ow9w1EEQfijmtImNnx3mB69vUgYHnzabTI3ryc4tvdp1800HTlC+X9epXHVKtRhoYS8/559QdkO+nJ8We4yXtz4ImabmRcHvcg1Pa85/blamqBkz0mJ0Q6ozjnR7hUJoQNPDKULTASn9h8m6KLXHx+GB/aheGu+yqS6pOm0iWlnEslSFxI7aCirvviYXct+FsmSIAiCcF40MTF4/eUvVH/6KR4TJuDSvz8BUTGAfbFMkSwJwrmxWm0sn3MApZOC0Xf0QlKcmnRUFRVQmZ/LyDuntt63sYmqDz+g6vMvUDg54ffYo+hvvx1FOxdvOKa+pZ5XNr/Czzk/k+CTwCtDXyHMPczeaGmB8v3Hk6K0zLWwugBkm73dPdg+hC558omFXrWnJn4dwcVDT9mRw8f/HZnsy5qvMsnZWY5XYMSf7NnxRLLUhThptCSMGsuOJYsYeutfcPfxc3RIgiAIQjfke//fafj1V0qfe56IhT/i5u2Di6fePm9pnKOjE4TuZdsvuZTnNTDunnhcPE+/EOqhDWtBkohJHwzY5zfV//wL5a++iqWiAo9Jk/B7+B+ofH07LM5NJZt4dv2zVBgq+FvSfdwTMBxVznooetfeY1S6r1VluhZNOPS90d5jFJwKbp2/IO0xLnovmnac6Fly8XQmINKD7J0VpF0hkiXhJKlXTGTHkkXsWLyQEXfc4+hwBEEQhG5IodMRMP0FCu66m8oPP8TvwQfxjxJFHgThXJXm1LF9SS6xAwLo2ff0X2LLssyhjWsJ6dUHVy9vmg9lUvbSSxi2bUMTH0/Iu++gTU7usBgNLU28tfEl/pf7C+FKF+ZafUhYPANanrJv4OQKgcmQPvVEYuQZxp7Vq7vMOn0unnrMpmZamo04abQARKX6sv7bw9RVGPHw1TosNpEsdTHuPn7EDRrGnhW/MuC6W9C4OG7FYkEQBKH7ch08GI+JE6j6+BPcL7+cwKgYcrZvwWRowlnn2DkAgtAdtDRb+G3OAVz1GobeFNPmdlUFeVQXFZA0Ygxlr/yb6i+/ROnmRsCL0/G8/vp2X1SWhtLjQ+l2FW3gmZY88lUKbqur54H6MrT+CZB0y4l5Rj7RZ12ZzlGOlw+vqcYp0D4nLDLZniwd2V1B8mWhDotNJEtdUNrV13Jw3Sr2LF9K/4nXOzocQRAEoZvye/JJGtespfTZ5/B/8lEAynIOExp/URaWFYR2tf67w9RXGpn0cArO2rZvmTM2rEWSJNSvv011eQWeN96I70MPHq9GeUEM1VCy60RVuqId0FBMsyTxrt6Tue5uBKq1zA67mv7RE8Gv9wVXpnMEF70XAE01NeiPJkvuPlr0gS7k7asSyZLQml94JKEJyexY8hOpV0wUZV4FQRCE86LS6/F/+imKH3scjy07ACg5nCmSJUE4gyN7KjmwtpiUsaEERbed9JiOHGH/j9/iVd+Eq48vAe++izYx8fxO2tIEJbtPVKUr2gE1R060e0VB+GB26YN4tnIDucYyboy5kYfTHsZF3b17i12P9SzV1bR6PSzemz0rC2hptuCkcUzaIpKlLqrf1dfy3b+eI2PdKuJHjnF0OIIgCEI35X7VVdQvWUr9zJl4DE4R85YE4QwM9S2snHsQ7xBX0q+OPO02NpOJqo8/IefzT2mMDCRxyHDCn/gnkvIsh7tZWqBs39Gk6OiaRhUZJ1WmC7GvY5R6h304XWASBpUzb+94m/9l/I9Al0A+HvsxAwIHtNNVO5bupGF4JwuL92bXb/klXxPXAAAgAElEQVQUHaohIqnjimP8GZEsdVFhiSn4hoaz9afv6D18FIouPtZUEARB6JokSSLghefJuXoC7lU1lMoiWRKEtsiyzMovM2gxWpn4UG+U6lPnGzVt3EjpC9Npycujakg/pKZaku5/qO1EyWaFyszWPUZl+8DaYm/XedvnFvW6+kQBBtfWxSQ2FG1g+sbplDSVcHPczTyY+mC37006mdbNHYVSRWNt656lwCgP1M5K8vZViWRJaE2SJAZcfwuL3niFA2tWEj/iMkeHJAiCIHRTaj8/Av75DNn/mUEBFhqrq3D18nZ0WILQ5RxYV0zunkqG3BCNd3DrIluW6mrK/v1v6n9aZF9Y9pOPWf/1HMIik9G5e9g3kmX70LmT5xiV7AZzk73dyQ2CkiF92okCDJ6h0MbitDXNNby29TUW5Swi3D2cz8Z/Rqp/ake+BQ4hSRIunvpTepaUKgU9enmRt68KWZY7bBHfPyOSpS4suv8g/COj2bBgHnGDh4u5S4IgCMJ5c7/qKgJ/XsjB2lLy16+h99WTHB2SIHQptWUG1i3IokcvPYkjQ46/Lssydd9/T/mrr2E1GPC+bxo+995LWWEedeVlpA/sBStesvcaFe8E49HeEaUzBCZCym32BV6DU8E7Gs6iOp4sy/yc8zOvbX2NhpYGpiZOZWriVJyVp1/n6WLg4ulJ0x96lsA+FC9nVwXVxU2nJLCdQSRLXZgkSQy55Q6+m/Ese5YvIfXyCY4OSRAEQeimJEmi1/MvsurBe8j6/DN6jbsSyan7Vc0ShI5gtdr4bc4BlCoFo+7ojaSw92CYco5Q+vzzGLZuRZucSODUq3FWlcAPf+XghnyUkgfRB/8FWdgr0Z08lM6vNyjP/Yvu3LpcXt78MptLNpPkm8TzA58nWh/dzlfc9bjovagrLzvl9dA+9l7wvH1VIlkSThWWkEyP3gls/uEb4keOOb5QlyAIgiCcK01QEAEhoZRlH6bi/Zn4/eMhR4ckCF3Ctl9yKc+tZ9w98bjqnZEba6h8+z9U/W8RkkoiYLgSz4ClSGuWAmDziuZQXRCRUX5opi4F/3hw0l1QDCariU/3fsrHez9Go9Twz/R/ckPsDSikdl6nqYty8dRTfOjgKa+76p3xDnElb18VqePCOj2uS+Pd78bsvUt/wVBXy47FPzk6HEEQBKGbixg6ggatMyWzP8GwbZujwxEEhys+VMH2JbnE9aynZ8ELGP6ZRs6oflTOXYhbUBNRN8joRyUjXfY83LEQnsgjf9hHGEw2ek2YAj36X3CitK5oHdcuvJaZu2dyWdhl/DTpJ26Ku+mSSZTAniwZG+qxWiyntIXFe1OaXYfJeGpbRxM9S91AUEwcUWnpbP3pOxJHj0Pn4enokARBEIRuqkcf+xowdaHBFD/+BBELf0Tp5ubgqAShk9is9hLdRyvTmfL3s3z/FNwUNgZVPULpejdqDipR6T0IeXYybhNvO6UyHcDBdatwdnEhIiXtgsIpaSzh1a2vsjx/OeHu4Xw05iMGBQ26oGN2Vy6e9oVpDXW1uHn7tGoLi/dmx9I8Cg9WE5V66n+PjnTppKvd3NBb7sTS0sLqLz91dCiCIAhCNxYQFY3aWYNx+BDMpaWUvvgSsiw7OixBaH+yDFXZsPdbWPo0yTufgldC4INB8NP9sPdb1hRPpNHmy+BeVRSu70lNhgr97bcT+dsa3CY/fNpEydzcTNaWjcSkD0Z1nvP+mi3NfLj7Qyb8OIF1Ret4MPVBvpvw3SWbKIF9zhKcutYSQECEO846FXn7qzo7LNGz1F14h/Sg34Rr7XOXRlx2/JtBQRAEQTgXSpWK4F59KC4rJvXvf6Py3fdwGTAAz+uudXRognD+ZBnqi09UpDtWuru51t6u0iDpwuyLvAalQHBfMrNdyZxzkFhVJqb3ZuIc3ZOQd95Fm5z8p6c6vH0zZlMzvYaMOI8wZX7P/53Xtr1GUWMRY8PG8mjaowS6Bp7HRV9cXDztI6ea6k6tiKdQKgiO0VOYcWpbRxPJUjeSPulGDq5bzfLZH3DHq++gVIlS4oIgCJey3Lrc89qvR+8E1s7/DO0zL6HbspXSl19Gm5yEc1TUWR/DarZReqSOysJGDHUmGmtNNDeaUSgVqJ0UqJyUuHlr8Ap0QR/ogqefFoVSDGgR2omhuvUir8U7oPFoJTVJCf69offEE2sZ+fVi59r1jBgxAoC6CgOr5m7EozGfoN0f4vvgA3jfdddZVYjMWLcKV28fQnrFn1PIh6oP8erWV9lSuoWenj2ZPXY2/QP7n+uVX7SODcNrqjl9QhQcqydnVwX1lUbcfTqv4JlIlroRtbOG0XdN44d/T2fboh9In3Sjo0MSBEEQHORA1QFu/vlmknRJRNVH0cO9x1nvGxqfBEBBxn56vvoqRyZNouihfxC+4BsUGk2b+zU3mcnYWELevipKsuuwmm0AKFQSLh7OaF3VWK0yVrMNc7OFprqW4/s6aZSE9PIitLcXYfHeuOrbPo8gtGJqsC/senJyVJt3tFECn2iIHHkiMQqIB3XbN9PN+QX88vIGbDZXUuVNRC38HufIyLMKxVBfR+7uHaReMRHpLNZLAqg0VvL+rvf5Put73JzceKr/U9wYeyMqhbgNP9mxnqXG0wzDAwiJ0wNQeKiG3iJZEtoSmdKP6P6D2PTdV8QOGoanf4CjQxIEQRAcIMIjgr8l/42Pd3/MhIUTuDXuVqYmTsXD2eOM+/pFROKsc6Fg/x56DR5O0H/+TcE9Uyn71ysEvjj9lO0rCxvYu7KQzC1lWMw2vINdiB8aTHCsJ/4RHmjd1EiSdMp+ZpOV2jID1cWNFGfVkn+gmpydFSBBSKyeXoMCiUz2ReWkbJf3RLgImJuhbH/rHqOKQ8DReXUeoRCcAmlT7MlRYBJozvw7D4DNRtVnn7H52wxqQsYyqE8dvf7vg7NOegAObVyLzWo9qyF4RouRuQfmMnvvbFqsLdwadyvTkqad1Wf0UqRUqdG6udNUe/pkSR+gQ+fuRGFGDb0HB3VaXCJZ6oZG3jmVvL27WPzef7n5hf+gUIo/MoIgCJcarUrLtKRpBFYEskO3g7kH5vLj4R+ZmjiVm+Nuxlnp3Oa+CoWSkN7xFOzfA4Dr0KF433MPVR9/jDYlBc9J1wBgqG9h4w+HydhYispJQcyAABKGh+ATcnYLQ6qdlfiGuuEb6kbsgEBkWaamxMDhHeVkbCzht08P4KxT0WdYMEmjeqBzF4vkXlKsFntlupMTo7IDYDPb21187T1FfSbZn4NSwNX3vE7VfCgTr1dfI7NGyZHkh4hO8iDlvlHnfJwDq1fgGxqOb1hE25dls7IoZxHv7nyXckM5o0NH81DqQ4R7hJ9X7JcSF089TbW1p22TJIngWD2Fh2qQZfm0X9B0BJEsdUNu3j6Muefv/PLOa2z8dj6Db7rd0SEJgiAIDuKh8mD6oOncGncrb+54k/9u+y/zD87n/pT7uSLiCpSK03+h1qN3ItnbNlNfWYG7jy++Dz6Acc8eSl94AaeYGLIr3Nm0MAdLi5XUcaGkjA1D43Jhc2UlScIryIX+QRH0uyKcoswa9q0pYseyPHavKKD34CBSx4Xhqm870RO6KZsNqnNaF2Ao3QNmg73d2QOCkmHQ/ScSI48QuMAbYltLC1UffkjlrI+xuerJGPgc7m4ujPhr0jkfq7Igj9LsLEbccfdpb9RlWWZN4Rre2vEWh2sPE+8dz6vDXqWvf98LuoZLiYveq82eJbAPxcvaWkZNiQGvIJdOiUkkS22QzWaURUWODqNNcYOHk7t7J5t++IbQ+CRRHU8QBOESF+sVy4eXfcimkk28se0Nnl73NHP2z+HBlAcZFjLslJu7Hn0SACjYv4c+w0cjqVQEv/5fDt14Oz/9ZwNVukh69NIz9KYY9AHtf1MiKSRC4rwIifOiprSJnb/ms39NEQfXF5M8JpSUsaE4acRtSrcky1Bf9IcCDLvAVGdvV2khMBFS/3JinpFXJJzDcLizYdixk5Jnn6UlOxv3CRNYoR1Nc6WS6+7uc16/W/tXr0ChVJ52CN6Osh28veNtdpTvINQtlP8O/y9jw8Z2Wu/HxcLFU091UWGb7SGxx+YtVYtkydEa16/H56WXyfn6G9yvvgqPK65AHRzs6LBaGTXlXoozD7D4vde549V30bq5OzokQRCEi5YkSeOBtwEl8Iksy//+Q/udwGvAsW/a3pNl+ZNODRIYEDiAr676il9zf+W9Xe9x/+/3k+ybzAOpD9AvoN/x7XxDw9lbVs1/Jl1PZW0doaGhPPnws2j7PkFTXQtJ8jYG3f9Ipwz11ge4MOqOXqRdEc6mH7PZtjiX/euKGTAxkl4DA5EU4oazS2uqaj2UrmgHNJXb2xQq8O8D8deeSIx840DZcbeg1sYmKt58k5r581EFBtDj41kcsUbQ8FUmg6+Pwi/s3O+XrBYLB9b8TkRKP3Qensdfz6jO4J0d77C2aC0+Wh+eSX+G62KuQ60QFYvPh30YXtvD7Nx9tLj7aCjMqCFx5NkXtbkQIllqgzYpifqbb8I/4xAVr79BxetvoE1Jwf3yy3EbPw61X+euHnw6ThotVz7wOPP/+SiL33udSY8/J+YvCYIgdABJkpTA+8AYoBDYKknST7IsH/jDpl/Lsnx/pwf4BwpJwfiI8YwOG82Ph3/kw90fMmXZFNID0rk/5X6S/ZKZ/7//8dWGbZjM9vkheXl5PPjI37lz/BM8ckUfrG/PofIdJ/z+8VCnxe3uo2Xs3fEkjq5jw7eHWTk3g4wNJQyfHIt30NnNkxI6WHO9vTLdyclRbf7RRgl8YqDnaHtSFJwK/vGg7rzKh42rV1PywnQspaXob7sNv4cepKraxrr/bMM1EJJGnd8Ndu7uHRjqaokfcRkAWTVZfLD7A37L+w13J3f+0fcf3BJ3C1pV51Vpuxi5eHphs1pobmxosxMgOFZPzs4KbDYZRSd8kSKSpTao9HqMI0YQ/sILtBQUUP/LL9QvXkLZv/5F2SuvoOvbF7dx43AbOwa1v7/D4vSP7Mnou6bx26z3+H3OR4y+6z7R5SsIgtD++gOHZVnOAZAk6StgIvDHZKlTTV+0nw0HjHxwaOOfbBWCF88jKdewrWQxt5fejou1D3seW348UTqmxWLiy/UfUXvl91wdP4y+H33ER/ky++IGdOyFnI6bjH+oGnNuHfNf3EKhv4q8ABXyGW6OamvP9H5cOi70vVDLLYSbs4kyZ9ofLZkEWgtRHK1MV670J1sdQ7bbGLLVMRxR98SocIFy7I9dZmBnu1zLmegM9Yxf/RWJGZso9wripxufotCnJ4rPd5N6yIQSmcVqE4s/3nRex++591vc1Doe215I+d4p1Cu2ocAZH+uVeDePYdl6HcvW72rnq+pYXfGz4l1aThQw7ePVNLv4nHYb32oLvQwW7nl7A406+9DN3kHuPH91nw6JSSRLZ8GpRw98pk3DZ9o0TNnZ1C9ZSsOyZZTNmEHZjBlok5JwvWw0bqMvwzmy7eooHSVx9HhqS0vY+tN36AOD6HvlNZ0egyAIwkUuGCg46d+FQPpptrtOkqRhQCbwD1mWC/64gSRJU4GpAP7+/qxateq8gyosNGG1Wqlto3rUyZT0xVdKoEm3niaXNRirq067naGmnNq6OuanXoVnRSETfv2UPJULBT6dM+TlZLVKOBIMfapVhJaBZ3ULO3wt1DvLbe5ztu/HOZFlnM1NaFoacLIYcbI0o7BZsCrVWBUqLEpnmpw9aXZyu+CCBO3pXN4LhWwlXC4kxpZ9/BEhF6DCCkAVnmQqoliuGkCmIoosRSR10tFv/i1HH0Yz0M7v/ZnIMmnZ27lmy0I05maWJI9jeeJorEoV1NSSWqFCa1KwIcCMESst5/G7obYY8azMJDNYzWHNi0iyGtemkbg2DUMh62igBWg543G6mg75rFwgRYv9s22qLqfWfPo0xWiDXjijKW+i0NP++1loq2fVqooOiUkkS+fIOSoK3/v/ju/9f8eUc4SGX3+l4ddfjw/Vc4qMxG3USFxHjECbnIyk6py3eOgtf6G2rIRVc2fj7udPdL+BnXJeQeiOZFmmubEBY3Ul+ft2Y2yox2axIMsysizjpNWi89Cj8/DAzcsH1Vms6C5c9E53B/zHO/ZFwP9kWTZJkjQN+Bw4pTaxLMuzgFkAaWlp8ogRI847qBEjYNWqVZzbMSZiMBsIfSaUqpJTE6awsFCWPXE5AJZpg8m9/gae2DyP8AULUPs7bgh67t5KVs7NYFSZmX5XRZA6Luy0Q3DO/f04lSzLlOfmkLN9CyWHD1GWcxhD3ZlvKtXOGrxDehDSO4GI5DSC43qhVDlu7kqb74XNBtXZJ4bRFe+Ekj1gMdrbNR72anRBJ+YZebsHMVCS6Ep3Fy2FRZQ+/zxN69ejTU4m8KUXSYiO5uGj7QfWFbPyywz6Xx3B/VdGnNfvxr7KfXw1/78oZJn8nmXck3g3t/e+Hb1G3+7X09na47PS3spzc5j7xE+8eHUcMemD29xu/vTNjNM78/4DyR0ek0iWLoBzZATO0+7FZ9q9mIuLafh9JQ0rllP12edUfTIbpacnLkOG4DpsKC5DhqDy8uqwWCSFgsvvf4TG6U/zy9uvMuHhp4lM7XfmHQXhImc2NVN+JIfS7Ewq8nKpLi6guqgQk6EJOPMYKoVSiXdIKP6R0QRGx9IzLb3V5N5LgcFsQKfWOToMRysETu5aCQGKT95AluWTM4+Pgf90QlznRafW8cKjr/DIE/9Hi8V0/HWls5Jb/3ErNtmGQlKg8vIi5IOZ5N1yKwX3TSN87lwULp1TgeqPwhN8uOW5dFZ/dYjNC3MoOFDNmCm9cdW333yYqsJ89q78jcNbNlBXXoYkKfAO6UFEchr+kVF4BgShc/dA6+6OSu2E2WTCbGqmuaGB6uJCKgvzqMg7wo7FP7Ft0fc4abVEpQ0g8bLxBMf2dswweVmGusLWc4yKd5+oTKfW2Rd2TfvriXlGXpFdqofsj2SLheov5lLx7rtIkoT/s/9Ef8strRaXrSxsZM3XmfTopafv5eHndnxZZmvpVj7Z+wkbizdyzd5gpAAvvpkyTywo28G07vbeSmN93Z9uFxLjycFNpdisNhTK9q2i+EciWWon6qAgvG6bjNdtk7E2NNC0fj2NK1fSuHYd9T//DJKEJj4elyGDcR08GG1SEpK6fb9tUjs5M+mpF/huxrMs/O8MrnrocaL7D2rXcwhCV2cyNFF4cD8F+/dQcGAvFXlHkG02wF5lxyu4B3GDh+MZEEh+SRlpAwehc3dHoVKjUChAkjAZmjDU1WKoq6WmpIjS7CwOb9vEvpW/svzj9+nRJ56YAUPpNXQETpruPZnXJtuobq6muLGYkqYSSptKKW4spripmJLGEoqbimkyN7Httm2XenWnrUC0JEkR2Kvd3QzcevIGkiQFyrJccvSfE4CDnRvi2WuobkZXEseUq57k522zKSwsxEvvTsjt4SzyXMTeH/cyJX4KV0ZeiSY2luC33qTgvr9R+PDD9Hj//U4bNfFHGlc14+6OJzy+hFX/y+Srl7cw+o5eRCSd30KlALLNxpFd29mx5Cfy9uxEoVQRlphM+qSbiEpLR+d+djfHIb3jj//cYjSQv28POTu2cGjjOg6uXYl3SCjJ464ifuQYVO3897+Vpkp7UlS0nYS9v8HWfGg6OjxJobZXpku47kRi5BPboZXp2lvzgQOUPPsczfv34zpiBAHPPYs6KKjVNi3NFpZ9vA9nnYrL/trnrIsAWG1WVuSvYM6+Oeyr2oe3xpsHAv5Cff0qRt94u0iUOsGxz5vhDMlSYLQne1cXUVnYeF7VDc9F9/l0dCNKNzfcx4/Hffx4ZJuN5v37aVyzhqZ166n6aBZVH3yIQqdD168fuoEDcBk4EOfo6FbfiJwvrasbNzw7g+9eeZ5Fb/6bK/7v0Xa4IkHoumSbjfLcHI7s2s6RXdspycpAttlQqlQExsTRf+L1BPSMJSAqGld9697dxlWrCI0/uzXKZFmmsiCPzE3rOLRhLcs/eZ91X31B3ysmknL51TjrHPNt+5+RZZn6lnpKm0opM5RR2lR64mEopaSxhDJDGWZb60n+LmoXAl0CCXINItkvmSDXIKw26yWdLMmybJEk6X5gGfbS4Z/KsrxfkqQXgW2yLP8EPCBJ0gTsszeqgTsdFvCfMJusLP5gD1azjX998BgfBLzAtzOepb6inNtff48V+SuYvW82z214jnd2vsOtcbdyY/qNBDz3HKXPP0/piy8RMP0FhxYTih0QiH+EB8s+2cfiD/aSNLoHA6+NQnkO3zDLssyRXdtYO/9zKvNzcdV7MeTmO0gYPe6sE6S2OGl19Ow3gJ79BjDyL1PJ2LCG3b8tYcXsmWz5cQEDrruZPsNHo7zQpLO5zr5+UfHOoz1HO6HuRGU6jS4EosecKNnt36dTK9O1J5vBQMV771P9+eco9XqC33oTt3HjTvk9lGWZ3784SF25gYn/SEHnfuZh1AazgZ+yf2LugbnkN+QT6hbKswOeZULUBFbN+pBMjZZeQ4Z31KUJJ1Gq1DjrXDDW1//pdoFR9s9oyeE6kSx1d5JCgTYhAW1CAr5//zvW+nqaNm2iacMGDBs30bh6NQBKT0978tS/P7p+afbk6TzLgDvrXLj+6Rf54T8v8ss7rxHUfwjy8OGiSp5w0bCYzRTs20329s1kb9tMY419tW//yJ70n3g9ofHJBMbEonZybrdzSpKEb2g4vqHhDLphMiVZh9j8w9es/+ZLtv38A/2vuYG0qyZ1Wvn+Yz1C+aZ8VuavpNxQTpmhzP5oKjv+s/HYHISjlJISP50fgS6BJPgmMNZlLIEugQS4BBxPkNyc3DrlGrobWZYXA4v/8NpzJ/38FPBUZ8d1Lo7dSFYWNnLl3xKPLzbbs99AVsyeSX1JCeMjxjMufBwbSzbyxf4veGfnO3y892MmRE3gxjtuoPaLb1AHBeEz7V6HXounv47rH09j/XeH2b2igPK8esbdE3/mHYGSw4dYM28OhQf24ekfyOX3P0LswKEXnrychlqjIWHUWOJHjiF/727Wfz2X32a9y9aF3zLyzqlnP2TebITSva3XMqrKOtHuGQYhfSF9qn2+UWASWzdu73JzUs5H49q1lL4wHXNREZ433IDfo4+g9Dh9Qrt7RQHZOyoYeG0UwTF/Pq+orKmMrw59xTeHvqG+pZ4EnwTe6PsGo3qMQqlQ0tzYyKGNa+k9dCRO2kt+KHKn0bq7n3GOoKteg5u3hpLsWpJGd2zxGZEsdTKluzvuY8fiPnYsAOaSEpo2bsKwdSuGLVto+O03ABRubmhTktGl9kWbmoI2IQGF9uyH+zhpdVz71Av8+tG7ZKxfzaI3rYy/7yHxYRe6vHnz5vHMM8+Qn59PaGgoM2bMYPLkybQYDeTs3MbhLRs5smsbLUYjamcN4cmpRPVNJzwpFRfPtv8wyrKM1WzDarFhtcjYrDZammTqq4wgg0IpoVAqUKokVE5KlKq2v6GWJImgmDgmPfE8ZUey2fDNl6yd/xlZm9czbtqD+ISGn/f1y7JMnamOCmMFFYYK+7OxgnJDORWGiuNJUZWxCotsse9Uan9SSSp8db746fyI0ccwLGQY/jp//F38CXAJIEAXgI/WB6VCrMd2qdq/tpjD28sZOCmK8IQTZXl7pqWzYvZMsrZsxDskFEmSGBQ0iEFBg8isyeSL/V/wfdb3fBPUwvQ0P3jrLRR6D7xuutmBVwNKtYJhN8cQEOXOyrkZfD1jK/5pbVfKMxmaWDv/c3YvX4LO3YPRU+4jYfTYTinCIEkSYYnJhCYkkbNjK2vmzeGH/0wnuv8gRt45FTfvk8okW81QfqB1AYbyg2A7+pl3DbD3FiXeBMEp9l4jXcfNi3YUS0UFZa/8m/rFi3GKjCTsy7no0tLa3L44q5YN32cTmeJLypjQ024jyzK7KnYx7+A8VuStwIaN0aGjuaP3HST5JrX6YvnA2t+xtJhIHHN5u1+b0DatuwfGhj8fhgcQ2NODwoNtL2DbXkSy5GDqwEA8r52E57WTAHtlF+P2bRi2bcewfTsVa9baN1Sp0MTGok1KRJOYiDYxCafwsD8duqd21nDF/z1KoyxxeNMa5hU+wlUPPYHvBdzICUJHmjdvHlOnTsVgMAD2RTLvvusuti36njCVDavZjNbdg5iBw+jRuy/6wBhMBjDUt5CxqQ5jfSXGphZMTRZMBjMmg4UWo4UWkxWzyXpq7TIga9Hp15hQKCXUGiXOWhUaVye0rmq0bmpc9Rpc9c64eWnw8NPiGxbJNY8/x6GNa/n90w+Z++RDDL7pNrIaTa2SvukvTWfMpDFUGauoNFZS2VxJpbGSKmMVFYYKKo2VVBjtz38cFgfg5uSGn9YPX50v6YHp+Ov88dX5UpFTwej+o/HT+eGl8RKJkNCmugoD6787TEic/pQbSVcvbwKjY8navIEB197Uqi1GH8PLQ17mob4PsSBzAe85f82UaonkF6azrmE3w29/0uFzOWL6BeAd7MrSj/aRu7KFPb6FJIwIbnUDlbV5AyvmfIihtpbU8Vcz+KbbHPIFoiRJRPXtT3hSCtsW/cCm774id/d2RoxKJsG3Hqlkp70HydJs30HjaU+MBo89Mc/IPejPT9LNyTYbtd98Q/nrbyA3N+Nz//14T70HxZ9UJm2qM7Hs4324+2gYdUevU26ejRYjGxo2MPPnmRysPoib2o3JvSZzc9zNhLiFnBqDLLNn+VICoqLxj4hq92sU2qZz96CuvOyM2wVGeZK5uYz6SiMevh33WRbJUhuyarL4vPJztm7dipfGC2+tt/1ZY3/20nrhrGy/IT7HOIUE4xQSjMfEiQBYamow7t6NcecujLt2UffjQmrm/w8Ahasrmj590MT3QdunD869euEU1jqBkiQJ/4BQVwMAACAASURBVKQ0Bo4ew89vv8qXTz5I/4nXk37tzR07wVQQzsMzzzxzPFE6ptlk4vOfl/L6tGdQa2OxmP3I3m3h8M5mYE+rbdXOSjSuajQuapx1Klw8NThplTg5q1BrlKicFChVJx6HMg8RFxcLgM0qH3+YW6yYm+0JlslgxthoxlDfQmVBA4b6FuSTki6FEpz1EiovC9q0q2jJWsVbr8zg2+17MVvs6z/k5eUx5e6/EvF7ED7pntgkkI8+3DSeeLn44OXiQ5p/Gj46H3y1vvYeIq0fvlpffHQ+ba4Kv6p0FX18OmYhPuHiYbPJrPjsIAqFZL+RPM2E97jBw1n52SzKc3PwC488pd1H68N9Sfdxd/zdLE/6haJHZhDxxo88WLyUkFFXckPsDST6JDpsyLd3kCs3PJnGV6+tYe3XmVQUNDD8lhis5mZWfPohB9euxDcsgmse/ScBPWMcEqO9Ml0BFO1AWbyD9LodxPY8yG/5Afy2ZDNH3GsZ29cNbdpd9qQoOBX0EV26Ml17a87IoPSF6Rh37UKXnk7A88+fcQ1Lq8XGsln7aGm2MOHBZJy1J25vs2uz+TbzWxYeXkiDuYFofTTPDniWqyKv+tMqn0WHDlBVmM/Yex9ot2sTzo7WzYPSw5ln3C6w54l5SyJZcoCa5hpymnPYd2gfzdbm026jU+nQa/R4abzQa/Tone0/e2o80Tvr0Wv0eDp74unsiV6jx83JDYV0bkUcVHo9biNG4HZ0zLFstdKSk4Nxzx6M+/bRvG8/NV/MpfroKuwKnQ7nuDicY2PQxNqfJaOR0PgR3Pn6TFbPnc2m778mc9N6Rk2ZRlhCx9enF4Q/stlkGmuaqa8wUldhpOxIPsWHdpKXl3fa7WuajDi5jMJV73z0ocHFwwmdhzM6Dyd0bk44K80oLSZsBoP9YTRiM9RhMxqQjUZsBiO2aiNyswlbsxHZ2EzokRw8DnlhazFha26mpbkJi9GA0mREbTJhazHhajaD2QxmC5LFhmwDi9INs5MXzRo/DDo/DGX+NLoE06wNQCXfxNJ9C44nSsevuUXG8GUZczb+cT5Q1dHHIVAqkVQq+0OtQlKrMalVFKvVSE5qFE5qJCcVCmcnJLUKhbMan8Y6yn/7DslZhdJZhcJZhUJjfyidlSg0SpQaBUqNAkkh24f3WFvsw3msZrCZj7520s/H2k7e7q9LulXFLKG1Xcvz+X/2zjtOiir720+Fzj3dkzMzQxhyjpJzUEBFAQOmNe2qqz9X3deArrom1DXsuuruYs4oCkgWUBBEJOcMAwMzTI6du6vq/aOHIcsAk9B65lOf6umuuvdWh6p76pzzPUf2lTPsljZERJ8+wb9t/yEs//QDNi+ez7Db7zljWwbJwKVtr0SZNoTdk67hwemHeEmezw37ZtEqqhVXZV7F6GajG8TbZLTINOkvYHWls3buAY7s3oGnZA6ukiJ6j7+eXuMm1kle0hlxFVSF0m04lmfkKQq/JhogsT2R3a9g/OVdWLfLzfLZC/hoo4NL+11DWvtO9TfORoDqdocFHD76CMnpJGnKCzivuKJGxvfyL/dwZF85I25vR0yKHW/Iy6KDi5i+ezobCjYgizLD04bTytuKW0feWqM2Ny9egNFipXWfAbVxeDrngNXpxFtZcdbwuuhEGyarzJG9ZbTunVRn49GvfGegZ1JPnk59mkGDBuEJeij2FlPiL6HEW0KJr4RSfynF3mJK/aWUeEso9BSyq2QXpb5SAurpqziLgojT6MRpclYbUQ6To/qx0+TEYXLgMDrCj43hx8cbWYIkYcrMxJSZSeTVVwOgBQL49+7Ft2MHvm3b8e3aRcXsOZR9/gUA8cCel1/GlJlJ1+YtaDJgBCs3rWb6s4+T2rY9fSZMoknbDsCZ80V0dM4VVVGpLPFTXuChvNBLWYGn2jgqK3Sj+HNRAvtRg/vR1HB5miibjVK3+5S2UpwOBvtmoOxxo7pc4cXtRnG7KXe7KfV6OcHdc7axCRAyiCgGyJLBL2v4ZI2gBEEZgpJAUIaQHUISIIuIsoRBMmCUJAySikkqxSyWEyXuI0kQsQkCMmYCWgJl7tMnpuaFQkj9mhOtHEBQQ6AqaIoKSnitqSqaKoAKmiqgVa1VRUDzgFYhoKoCoVD4OTUkYAwJlKzeGt7vLAiyimTQkMwakgkkM8gWAckqIlskJJuMHCEj24zIDiOi2RSe0BmtoKk1fn91GhfFuS5++XY/zTrH0bJX4hm3M9vttOrTnx0rljLghlvPKosvORxkvv8xB2++hclf5bL3yZv5SFjNC6tf4JW1rzA8YzhXtriSnok9z/lG4YUgCAI9R2dQcmgZ25d9gyg7GXHX32g/8My5LrWCtwyObDxOgGEDVByuGpQYluhuOTIsvpDSFRLagxyOUBGA7l0hrfcI5v7zJaY/+wQDJt1CtzHjfvPiTJqmUfndIvJfeIFQXh6REycS/8BfkCJrVs9u2/Ictv2YQ5cRaXjT83n65/+wIGsBrqCLdEc6D3Z7kMtbXE60OZqlS5fW6P30VJSze9UK2g8egcF8caoHXsxYHU5URcHvdmO228+4nSAKJDZ3cmTf2fObLgTdWKoBVoMVq8FKE86utqFpGt6Ql1J/KaW+Usr8ZdXrMn8Z5f5ySn2llPvLOeI+ws7SnZT7y09RrDoeAQG70V5tPDmMDhymsBEVYYggwhgRfr2zA3uPftiNo7Ab7NiK3BizjnDwh+WkKhr+PXvw/LwKKRCgjyBwKCaCfcpmvty+lTizjQOuAFPmzsfrDxcoPHjwIHfeeSfAKQaTph0LWVJVDU05caIqSAKiKFQlzQsXdLLXDbh6QlXO4HUIgBI6wevgLNsG+wVCPh9luR7K83yUFSuUlwlUuA1UeM24glY0jk2QRKUMybcDJZhFQC1EERQEDZyeIIll5SSWu1EjHPzN48F3nOFjFgTuddgo/GE2ISMEjBp+I3gN4EnQcBvBZYRyo0C5WaDSKOA1gt8AfqOAz1D12AABGYySgh0NpxbEqahEqiqRikqkqlStVSIVhShFJarq8QlR8qIBJMOxdfVjGSQjiBWkRZs4WOLnZKLs8SySH8Bu99A8MYfMlDzio90I8kltilVtVT82VLUtn7Ldhi3b6dKtB5oKakBF9QVRvAFUTwDF60N1+VDcHlSXB6XShVJRgVJWjlJair+0FHdOKWpFBaACgaolHAopRkQgx8Uhx0fTZHwIUT67BK9O40LTNJZ/sRuDSWLg9a3Oei7uOGwU25YtYedPy+g4dNRZ25djY0n/4H0O3nQzmX//nA/efYeDfcx8s+cb5mbNZe7+uSTaEhnbbCyXN7+cDGdGLR3ZqRx/rYh1OhjWqilXXzGeivLe/DTdhcmWT2b3hNrpLOAJ5xXlhusZkbMeSvYdez2qKaT1guS7woZRYkcwnXnSd5T4jGZMev5VFrz9Oss+eY/8rH2M+OO9GEy/zQl74OBB8p59Dvfy5ZhatSLl1Vexdu1S4/2P7Ctn2Re7ENI8TBEeJGvefsySmREZI7iyxZV0T+h+XvOPzYvmowSDdBk15pz31blwLMfVWvo1YwnCEuIHtxTjrQxgiaiba5RuLJ2Bp2dvY+V2L2/vOn3yd82RgNiq5dRXoqsWlSAKbhTBjYIHVXCjCJ6q5zwoIQ8ur4dyPChCESrZKIIXBQ+acHpPVjVtQdAMSO0tSEoMCeUGUos0kkpUEks8RLgFKoIhXlv4Y7WhdBSPx8N9f/w/ypcaUSQLmmBAQELQBARqfgJSBFDF8KKIAooIinRsHZIgdNw6KIcf79y4iJVfvogSPGbA3XzrbbyxZA/pvUaGG9c0RCWIpPiRQgFEJYCkBBHVIIIaQlRDCKqKoIWXk7P8NUFEEyQ0UUQVZTRRRhVlVMmAIhnDi2xClYxnjBsXNBWJEJKmIBNC1kIn/L9n9VJWzJ5GRWkxzqhoho65gm7duyBpyhn2CyGjhP8/qa2T2w5vG6puS67+P4R0tA0UZC2IhFLdtlTVthBQEIMqWgCUoIgaEFGCAmpAJBQQ8SoOXGo8lUIcLjEejxSH2xDP+pkF+ExRIDiB8IlNCvmweAuwerNxevNQ1CN4pTIqTSHcxnCOnKyGsGgeJMlD0OKlJFojqwWUmwVKzVG03S6yfXEBvtIghmgDsePj+aRPFJ8c935bVBGzJmFWJSyaAZMmY1INmDQDRs2EUzNi0EwYNTOyZsGgWZAVC1LIgioYUZBRBIkylw85IpJyQaZElgnJEoogE0KuWlf9L8jhfZBqlDuQeMVCDn86BSVw7PdkkGRaj7uDnekGYsvsVBzMZNOBTNxmgbwYiYIomaDh3C/qZWXNiMw/PuRPrlpOit82cOyEcxKSEsLqrcTmqcDuqcDuLsfuLifCXYbdXU58fjlp56DGqdN42Le+kJzdZQy8rmWN6s0kZbYmNi2DTYvm18hYApDj4kj74AOyb7qJQ7ffQfrU/zH5ksk81OMhfjj0A7P2zuLdre8ydctU2sW0Y3Sz0YzKGEWc9fwLyZ7MyeIwhWXlzNi4g9H3ZnDN2H4s+O8WvntnG6VH3PQY0/TcJtBKEPK3HQujO6pMp1X97iKSw96izteFBRiSu1yQMp3RYmXsXx5l9cyvWDHtY4pzDjHu4b8REX3qPOJiRfV6KZ46leJ33kUwGEh47FGirr++xsWOy/3lLNi6hCMfmfDILr5OeIX25jbc1O5JRmWMwm48u2F6JpRQkI3fzSWjczdiUupWklrn9FgjwnWTPBVlRCen/Oq2SS3CHsgj+8pp1rn2zinHoxtLjQQRAyKRGLQqt3PNI4rQCKHgRRW8p117fKUYLaDgRVRDiJIFj8NBkcFJwBGJ0xeNze+kzLPwtO2XuIuxlG/HFpQxKCEkJYCkBNAI4jOo+IwaXqOA1yThM8r4TAb8RiMBg4mgbCIkmxAwIauG8KLIyKqMrMgYghJmn4RBkZAVEUEDNB+a5gXVw/SZ/642lI6iBPzs+vIfTPDvAjUQXs7lDTtPBLRw+JWoYJaCmKUQVimITfZjlQJY5SA2OYBNCmKVA9jkAKIAn24JMHW2D0+VwFl5aQkLvnifq9yfM6lDze+CKIgohCfuVeYQoZBMKCQTCEj4FYFgQCKoiHiCAkpAQA2BFhAgICEERYSAhhRQkQIackBFCkDQ6MBnisZvjsJnisJnjsZnjgmv7TEoJwmZCEolmlqEwn58WhFeqYgKYyFuQzGapmCxmHG4TUQYjIiEDeL8qBBHYlwciVUoc0iImBFJRNRMiJiRsCBqFkTMRKZa6DfCgqgde17yWxCxIGlWRMwInBrSExDCy7lQ5i0j0lizUI9z4aghv2XWf/CUFGB3RjO2TRNaWMvY7YSCaBOSohFXqpBYHKJ5ToimuSEKoiRy4mXclvoLWQJQJJlKexSV9tNLr7dNdjDgNx4K9FskGFD46es9xKTaadv/1yccRxEEgY7DRvH9e/8hb98eEptn1mg/Q0I8aR9+QPYtfyD7tttp8tab2Hr3ZlTGKEZljKLQU8j8rPnM2T+Hl9a8xD/W/oPuCd0ZmTGS4enDiTL/ej2cs3EmcZjJkyczadIkrri/C0s/3cmauQcoy/cw5KY2yMbTKEeqChTtOTHHKG8LKFXXIUtU2CBqdWnYKEruCo7az5UQBIFe4yYSl9GUOa+/xGePP8RVDz9JXPqvCx00djRNw7VkCfnPv0AwNxfHmDHE//WvGBLiz7qvK+Bi6eGlLMxayKpDqxmz+R6cioXIq1zM7PE1TSJqx7DZ/fMK3GWljLz08lppT+fcOepZ8lacPbwuPj0CURZ0Y6kheHJsO5ZGFDJoUO+GHsqvo2lnDJfSQgFKC7ysWroTUyCJ/MMhSouPGRVGo0ZklEpUYgin00XSN7EcKSo6pYtIq4USYQ0lRpBMYJDC3gpjKIjRH8LsDRFdGsLsVTEFNERNQwM0BDQBVFHAaxRxmwTcJhGvUcJvEAlKIiFJQhVE/EgEVAlJFU/wWJW6S0572GVuN6oci6TZEQULgmACwYiAEQQjCAZUUUWRA4RkH4rsQ5E9qLIHRfagyR4U2QeSF03yIcg+NMGPAIiaiKhKiIqIoIqIIRFBERFCIv6giDsoIQRkhKCA4BcQ3CAop45RAzSzwPPfLak2lI7iCcKfvxc41GMAkqoiBRWkgIIcUJH9CrJfweBXMPoVDD4Voz+E0a9iql40LIHjDUSVOeXlvFZUSF4oRKJs4J6kDAYnNsdtc+C2ROC1OfBFOwkanYRkJ5oUCUIEwkm5BEHRg89Ujs9Sic9eQNDuRYnwQUQA0aFgNhmozCogTY7BWOzHVCDiOGJGdccAIBpkHBmpxGa2IKlVG5q0bo/DFolFttRr3kJNWLp0ad39xv/YG3iq+t9ty5aw4K3XuFXeyIg77z1h0+JcF1uX5bDz5yMklvhJaRVFj8sySGl19glknR6DzkXNhoUHcZX4Gf6HtoinUb87E237D+bHT99n8+L5NTaWAAyJiaR/8jHZt97GoT/+iZTXXydiyGAA4qxx3NTuJm5qdxP7y/YzL2seCw8s5JlVz/D8L8/TI7EHw9OHMyRtCLGWc/OgaKpKdvbpxWGys7OBcD2mITe3ISrJxs8z9lFR7OPSP7bHpuWdmGN0ZCMEXFUHZIPkztDzjnAoXXJXiMqoV2W6Zl16cO3TLzLjxaf54sn/x9gHHiOjY83D1BoT/v37yX/+BdwrVmDKzCTtow+x9ez5q/tUBCpYdmgZiw8uZkXOCgJqgHhLPDfkPozsjWTMPR1Jb197HjdN01g371uik1Mv2vf5t8AxY6nirNvKBomEdAdH9v56EdsL4aIzlgRBGAX8k3AU2zuapk2pk478Lqzu7Ko7SqfmbISfO1k1KnjidqeoSwWOe64m251Gker4fZTAsTCAKjyKk+xAFw75O3E40BGPGg3EYhaKSTTuJNO+j1g5i1jDfuxicficXxFeXh4Q4M7ZnDCxtxrg1eEig9J3ke+PoMRvpTxgojxooCRoAhGwVS3ngKhpGEIqNp+CMaRgCAUwKirGkHLCkmgwkBc8teZMoslIv9zVhGSRgMFEwBhBwGAnKNmqF0WzoYSsqIoNNRCLihUNGwi/IpmuBQAvaF6EqgXNh6j6ENTwWlL9iIq/ysPmRw4FERU/ghJE0BQ0VSX8ByERylynz0crK/Ni2KAhaGAMCZhCIsYQGBURSTMhClI4L0U2ErCY8TltqEYbismKIltRDFZU0YIqmvl5xxo+WTSVQChcsPBIKMjTR7LZkzmeHpnDqvuUrQKmCAmnQ8YWacQWacIRbcEZYyUqNgJHtAWDScLvceMuLaWiqICKwnzKCwsoy86lJOcwZXm5xIRCQD6qKBKdnEpi934ktmhJUouWxKal10uBx4uNdgOHUpJ7mNUzvyK1TXva9h9c/VpMsp2B17Wi1+XN2L4il03fH2LmaxtIzoyk55imNTKadHSOp6LYy/rvsmnRPZ7kzHP7/pisNlr3GcCOn5Yx4IZbMdtqHtIkx8aS/tGHZN9xJ4fvu4/kF17AOfbEvI9mkc34c5c/c0/ne9hVuouFBxay6OAinln1DM+uepYu8V0Y3GQwg9MGk+5I/9X+gj4f8998FafFQpnn1HNtWtqxelKCq4CuGduJ7HOARauaMf3x2Yx2PkOs4WA4JzCxA3S69lgto9iW4doADUx8RjOuf/YVZkx5ihlTnmLU3X+hTb9BDT2sGqO4XBS9+RYlH3+MaLGQ8Ogj4ZC7M5QvyXPnsezQMr4/9D2rj6wmpIWIt8QzsdVERmSMwPtTBBuys+k3MbNWDSWA3N07yd+/h6G33f2rdSx16hbrcTlLNSGphZONiw8RDCgYTucxvkAuKmNJEAQJeBMYDhwG1giC8K2madtrvbODK+m55l5Yc6ENCadJAK96LFYlbZ/w2ACmiJMSvU+X3H2srQqvlX2HY8g6HMmRQgsgYDYrNGkWJDXNjcuzlx6XtEGQu4PY+4yJ45MkA0z/lslPv0D24RzSmqSGxRRuuBGAk53/qqLgc7vwuSrxuVyooRBKKISiBBEQECQJURSRZAMGsxmDyYTBbMFssyNXFZbTNA3N40GpqEB1uVCOUzpT3R6eXryI+997D2/gWF6WRZZ5bNBgUtMz0IIB1EAALRBE8/rQQpUQDKEFg2FlMSUEIQVUFU3TQFEICTJB2UpQqloMtvAiWwnJ1up1SDYTkiIJSRZCsomQaEQTzv0nE2XfTqmr4NTnbdHIliFomouQ6iaoutA0N5rqBu3oRV8BvOFFLQWfAH4zgmBGkMxIshnJYGbm8o8JhE4MVwyG/Mzf+D9uuaUjRrOMbBTQNBVNUQgFgwT9PoJFXvIOeTngduFzufC5KnCXlhIKnpgHJ8kyjrgEolNSada1BwWVLvqPuJSY1LTqz1Ln7PSdeAO5u3awaOq/SWjagpjUE8NGzDYDXUem03FIKttX5LJuwUFmvraBJm2j6Xt1C2JSzj8OX+f3xaqZ+xGAPle1OK/9u4way9YfFrF29gz6XXvjOe0rRUaS9v57HL77HnL/+ldCBflE33qqXLMgCLSObk3r6Nbc1+U+9pTtYfHBxXyf/T2vrHuFV9a9QlNnUwakDGBgk4F0ju+MQTw2wa4sKWLmS89QeCCLB+76I1Pe/t8JoXhWs4nnbuoDX0wKh9VV5ADQTBC5qtkQ5h66lW8qXmXEeAcZfTtDIxYwiYiJ5ZqnX2LWy88w79+v4Pd46DzisoYe1q+iKQpl33xD4ev/RCkpIXL81cTdfz9yTMwJ2ymqwrbibazIWcHSQ0vZUbIDgCYRTbix3Y0MSxtG+9j2iILI9hW5rFy4k3b9k+k4+NRCshfK+nmzMNlstBswpNbb1qk5stGI0WKpURgehIvT7t9YhLvUT2RC7ddbuqiMJaAnsFfTtP0AgiB8AVwB1L6xlNSRbW0fol37TmdRvjr5seFEo0asWUL4ueJzBdm7Lp9dv+STtz/8ZYptYqfHmDiadowlNtVeXXRw6dKlCK0H1ajdSbfdzaTb7q7RtqIkYXU4q+8AnA+CICDYbIi207um7rz6Kmz9+jUaNTwlqBL0K8eKlgYUlKBCKKASCqgoIRVFUVGCarVS4IORk3n29Ufw+Y/d9TSbLDxw9xP0HzoOQQwrBwqigCQLiJKIICqEAm6UoJugr5Kg30XI7ybocxPwVRL0ewl43PjcLgJeFyWu059QCkqKWTfnk1OeFwQRg9mEwWTGaLFgtkVgdTiITk7BGhmFPTIKW1Q0EbFxOOMSsEdFn3CXbenSpSQ0O79J2O8ZUZIYfd9f+ejh+5j92gtMeu7V08rSygaJjoOb0LZfMluX5bB23gGmPbuatv2S6Tm2WY0S9XV+vxTnutizNp+uI9PPWFPpbMRnNKNVnwGsmzeTLqPGYIs8N++UZLfT5J2p5D78MAUv/4PgkTwSHn0EQTr9XV9BEGgZ1ZKWUS25u/Pd5LhyWHpoKcsOLePTnZ/y4fYPsRvs9ErqRZ/kPrQJNWHlG2/j93q58oH/R7MEiWb2Uia/OZ3sIjdpToHnhgpMEudCQTNI630slC6pI3FGG+NL/cx9axPzvnDRV8mn4+DURi3TbbJaGffoU8x5/UWWvPsWfreLXuMmNvSwTot79WryX5iCf8cOLF27kvCf/2Dp0L769UJPIauOrOKn3J9YmbOSUn8pAgKd4jpxf9f7GdxkME2dJwpxHNxazNLPdpHWNpr+17as9c+qoqiAPatX0m30lbpceCPA4nDW2LOU3iGGjI51J4BysRlLKcCh4/4/DPQ6fgNBEO4E7gRISEhg6dKl592Zy9qFwoLj7+RqHJPWrX80TcNbDCV7NCoOhcuemJwQ30nA2QSMdg8eDrJt/0HYf2w/l8t1Qe9DQ5OSksIHH3yAy+XCXiUhedEcjwh9R3XkQfkB3nnnHQoKCoiPj+f222+n37DOVJB14vZK1XIUiaowx3CsowiYq5bjSfhsBvn5+ad0Hx8fT+db70UjXNhNEEWEKgP+1y40LsAVgvy8QsgrPPX1i/w7dZSGOo7UgSPYM/srPpvyd9IHjfj1jWXIGKlRuA22rchlx6pcEjsLRDYLTzB/K5+FTu2xZs4BDCaJLsPSzr7xr9B34iR2r1rBqm+mMfTWP53z/qLRSMorr1CQkEjJBx8Qys8j+cUXEa1nv/ObYk9hUptJTGozCXfQzarcVSzPWc7KnJ/Ys3ol/TfFohg11M7F7Fk2kUivl0moTHo0jUJjE+I6jagSYOgSFmU4DfYoE1c91I1F721jxZd7KMv30H9iJqLUeMOvDEYTlz/wGAveeo0VX3xEwOel37U3NRojz5+VRcE/XsG1ZAlyUhLJr/wDx2WX4Qq6WHpoKb8c+YVf8n5hT+keAKJMUfRN6Uv/lP70Se5DpPn0gjuF2ZUsmLqVmBQbI+9sj1QHn9HaOTMQBEGXC28kWCPChWlrQl1//89qLAmCcK2maV/U6ShqzunejRNk0DRN+x/wP4Du3btrgwYNOu/OwonT579/baGEVPasyWfjkkMUH3ZhNEu0H5BEmz5JxDaxn/VL0liO40K5mI9j0KBBPPvss3V2DK+88soJsrkAVquVV199laEjR9Z6fxfzZ3E8DXkcy1BYO/sbhl5zPalt2p99h5FQmudm6ae7yF1TBmWRDJrUik071/wmPotzpZFdmxoNRYdd7FtfQPfLMjDbLyx3MCophQ5DRrB58QK6jb6SyIQzF7Q9E4IokvDIwxiSk8if8iIHrp9Ek7fexJCcfPadq5TpbLnrGZqzniE561m9tZgV+U0w2Nzs71zIKqfEl4TDuppHpNM9+RIsxRYmdZ1Eou3s4zWYJC79Ywd+nrmPDd9lU17oZeQd7TFZGu+9ZEmWuezPD2I0W1g98ytURWHApD80qMEUKi2l6O23Kf3sc0SjEfs9d7JnZGtmlG9hEaum/wAAIABJREFU3dyP2FmyE1VTMUkmOsd35v6u99MnuQ+toludVfinotjLnH9vwmyTGXNPJ4zm2v9sPOVlbFnyHW0HDMERe3ZlPp26x+JwUFl8quhYQ1CTb9xHVd6aP9dJbtC5cRhOqAybCuQ20FjqnKBfYfuKXDYuzsZV6icmxcagSa3I7JFQJycLnYuXo2GJjSVcUefs9Bl/PbtX/cSi//2bG196A/kMyc7HE5Vo48q/dGHHz0dY+fVepj27hrgOGtoArTrs9ndEY7o2NRrWzM3CaJboNLR2ZJR7X30d25d9z8qvPuWyPz943u1E33QTxqZNyfnLA2RNmEjqG2+cWHxU06D0wHG1jDaeoEwXkiNYVNyJ7flNaN2uGSP/dC9yXAtCmsLWoq2szV/L2vy1zN43G0/IwwfTPyDJlkTn+M50jO1Ih7gOtI5ujemkUggAgijQ56oWRCZYWfbpLr5+aR2j7+6IM67x1hYTRJFht9+NIEmsnf0NqqIw6Kbb691gUr1eCj/8gJKp76B5veztl87n/TS2au/Bz2CSTHSI7cAdHe6gV1IvOsZ1PO1ncCY8FQG+/edGlJDK5fd3xRZZ833PhfXzvyUUDNDj8vF10r7OuWNxOCnI2nf2DeuBmsy4uwFvARsEQXgDeErTNFfdDuuMrAEyBUFoCuQA1wLXN9BY6gwlqLL1xxzWLTiAtzJIcmYkgya1Jq1ddKNxtes0PiZNmqQbRxcRBrOZYbfdxTdTnmLNrOn0Hn9djfYTRIG2fZPJ6BDLD5/s5MCGIma/sZGhN7ets4lEI6UxXZsaBYWHKtm/oZAeozMw22pHkdIeHUOXS8eyZvY3dB8zjviMZuffVv/+ZEz7gkN3383Bm24i4Q9jiepsQcjdEBZg8FaVipBMVcp010FKV1y2Fnz74TSO5O6iz8RJXHLVtdXXQlmQ6Rzfmc7xnbm9w+2E1BCfLfoMKU1iQ8EG1uevZ37W/PC2okxmZCZtY9rSNqYtbaLb0CKqBRY5bBS17ZuMM9bC/P9tYfqUtVz6p/bnrCRYnwiiyNBb/4QkSayfNwtVURjyhz/W6TwhqATZV76PHQVb8cyaS4tv1uEoD7K2hcCng0W8qZ5w3lHcBLrEd6F9bHuM0vnlWPq9IWa/sRF3qZ/L7+9CTHLdCNz4PW42LJhDy159z1oAVaf+sDqceCoq0DStwee+ZzWWNE3bAvQXBOFm4EXgOkEQHtI07fM6H92pYwkJgvBnYCHhbI73NE3bVt/jqCs0VWPnqjxWz9mPq8RPSqtIel3enKTm5y+goKOj03hp2qU7rXr355cZ02jVpz/RyTVXd7I6jFx2VwdmvLuUI5vL+fyZXxh2S1syOtRdkmtjojFdmxoLa+ZkYbTIteZVOkqPK8azdeli5r/5Ktc/9woG4zka5Z6SsJcoZz2mnPU0HXCQ3CV+8qfOwJvmI2l0EmLr0ccEGOLbVivTHdmzi29feQ6fx83YvzxCy0v6/WpXsiiTZkpjUJtBTGoTvnlU4ClgS+EWNhdtZnvxdhYdXMTXe74GQBRE0iLSaBnVkhaRLWge2Zxed6Wz+eMSZr2+kYHXt6Jt3xqEDDYQgiAw6OY7EESRdXNnIkpSrXiYQmqIHFcO+8r2sb98P3tK97C7dDcHy7LoviPINT+qtC6BnHQbW+4dRkrf4UyNaU9qRO2IZIQCCvPe2kxJjpvL7ulYp/OgjQvnEvB66HnlhDrrQ+fcsTqcqEqIgNeDyXqO9WlqmRrHcmma9qEgCDOB54GPjwt/qFdjRdO0ecC8+uyzPsjLKmf5F7spOFhJfHoEQ25sQ5M20Q09LB0dnTpm8C13cmDzeha/8xYTnnjunCYagiAQ3UJgyNieLJi6lblvbqb76Ax6jG56TkVIL2Yay7WpoSnNc5O1qYgeozMwWWu3zpnFHsGl9zzANy88ybKP3mXY7b+imBpww5FNxxV6XQ+lxwnZxLRAat2f1MFdKF5+hMIPv8H3XTQpr96LuVWrE5ra8sN3LHnnLezRMVz/zD+ISz+5gEXNiLfGMzR9KEPThwJhsaQcVw67Snaxq3QXu0p2saNkB4sOLkKrSoO2pNu4LHQnP3yssXD9UuKGaKQ5m5BiTyHJloTVUPvyxOeLIAgMvPE2VFVh/bxZiJJUoxymgBLgiPsIhysPk+PK4VDlIQ5WHORgxUEOVR4iqB6rcZhoTWBETgyPzLfjOFiM0Dyd5GceovWQobV+118JqiyYupXcvWWMuLUd6e1izr7TeRL0+1g3bxZNO3cjoWnzOutH59yxHFdr6aIxlgA0TSsH7hEE4R3gI04Mf6isiwH+1vG6Aqz8Zh87Vx7B6jQy7A9tadkzocFdjjo6OvWDLTKKvhNv4Pv3/8uBjeto2qX7ObcRmWBl/P/rxrLPd7F27gEKsioYfmu7C07wv1jQr02w6fvDSLJI+4G1X3sGoGnnbnQfexVrZ39DWodOtOzVF0J+yN96LMcodz0U7gxLtQI4UiGlC3S9Kew1SuoMlrDamQDE9gHLwNHkPPRXDoyfQPxDDxJ1440EA36WvPs223/8nrT2nRhz/8NYIhy1diyCIJAakUpqRGq1AQXgDXnJKs9iX9k+DlQc4EDGdny/VNBkW0e2Ht7Bay3/SUAOl4CINEWSZEsi3hpfvcRYYog2RxNjjiHKHEWkKZIIY8RZBQxq65gG33wnqhIWjnErHlIu7c9Wz1ZK95RS6C2kwFNAoaeQfE8+ee48in3FJ7RhFI2kOdLIcGQwMHUgTZ1Nae5sRtLWfFxvv4Nvy2YMaWnEvfhXHGPGnFEG/kJQQmFD6eCW4uoc7bpky5KFeCvK6dlIJdh/zxwtS+OtKCcqsWG9uzUylgRBMABdgEuOWzKqXr4HuFYQhLs0Tfu2Lgb5W0TTNPauK2D5tN34PSG6jkyj26UZunCDjs7vkI7DRrFu7kyWf/ERGZ26nlfleNkoMeSmNiQ2c/LjtN1Mf2ktY+7pVCcF+hoL+rUpTMivse/nI7TslVB3NbhUhX6Du3N47VK+e+NFElZV4qzYCkpVKQ1rTDiErs3Y8DqlK9jPripmu+QSmn07iyOTHyf/hSnk/LCENQ4TpQV59B5/HZdcfS2iWPuT8tNhkS3V+UzVDIFty3P48QuBu/e/RPSVHorNueS6cslz55HnzmNz4WZK/aWnbVMURGwGGxGGCOxGO3aDHYtswSJbMMtmjJIRg2jAKBmRBAlREJGE8PFqaGiahopKUAkSUkME1SB+xY9f8eMNefEEPbiDbtxBN66gi0q5kp5NnKx7+11m3fcQngo/hhgDCVcnkD44nThLHAnWBFpHtybBlkCyLTlsONpTibPGVRt2mqbhWrqUoseeo2jLFgzJySQ9+wzOK65AqIEYzfmgKCrfvbuNA5uLGHBtS9r1r9v8oYDPy6oZX5LWviOprdvVaV86584xz1LN5MPrkppIh68EOgMmQAU2AbOBn4AVhEuyPAlMFwThPk3T/lN3w/1t4C73s+yzXWRtKiI+PYIr7m9DTErdJC7q6Og0fiTZQJ+JNzD/36+wa9UKWvcZcF7tCIJAu/4pRCfbmff2Zqa/tJbL/tShUSepny/6tekYpXshFFTpNKSWcpU0LRw6l7M+LLyQsx6ObEIKuhltNfOx0pVvNtm4euxtOFpeEjaMnE3OuwC7HB1N0r/+yYrnn2bD1g0YKlUuHXoZbcZf3yiiLNr1TyEqycaC/26h8FMbw265gma9407YJqgEKfYVhxdvMeX+csr8ZZT5y6gMVOIKuHAFXbiDbioCFeR78vGGvASVIAE1QEAJoGoqiqagVnnmBAQQQETEIBkwiAZkUcYkmTBLZkyyCZvBRpItCZvRht1gx2lysjVvK1+vf49AMBQeW3GQkk9KmDJgCpOu+HURIE1RqFy0mKL//Rf/9h0YUlNJ/PvTRF55JYKx7ophK4rKone3s39DIf0mZNJhUN14SI9n/dxZeCvK6XftzXXel865c9Sz5Ckva+CR1Myz5AKmEL4ArdI0zX2abR4UBCEfeAz4zV6QaoMDW4r4/qMdBHwKfa5qQaehqY26AJ6Ojk790LrvANbMms7KLz8hs2cfJPn8vcxJzZ2Mf7gbc/69mVmvb2TozW1o2fPca+Q0cvRrE+GwpZI9Gk3aRJ3/TbeK3GNGUW6VgeSt8pRIJkjqCF0mQUo3IpO7Mq7Ax8x/PMfn3x3h6m6diY28sOK3+fv3svA//6TwYBbNO3ahzc4s1H+9xaG1G0j8+98xptb9xPlsJLeIZMKjPZj/ny3M/88Wuo/OoOfoptWS/QbJQKItsUa1neqajHEZ1YbSUTweD5MnTz6jYqoaCFDx7bcUv/MugQMHMKank/T88zjHjqkzT9JRQkGFhVPDHqU+V7eodYGS0+GtrGDN7G9o0eMSkjJbnX0HnXrH4giH3noryht4JDVTwztLeflqfiR84dI5DUpQZeWMvWz+/jAxKXau/Es7opMbNmFNR0en8SCKEn2vvYlZLz/DtmWL6Th01AW154yzcvX/68aC/25h0Xvb8XtC9XK3tr7Qr01h9q4rIOSDTkNraLB4SqqEFzYcE2Bw5YVfE6SwEt3xoXTxbUE6cbKcGgfXPDWFr194ki+eepgr//pEzQorn0R5QR4/f/0F25d9jzUykssffIzMnn3QVJWyadMoePkf7B89hpg/3knMbbchmhpWGj8i2sxVD3Vl2Wfh3MDC7EqG3dK21mTaa4vs7OwaP6+UlVH6xTRKPv0EpbAIU9s2pLz+GhHDh9dJTtLJBP0K897ezOGdpQy8rmWd5dydzOpZ0wn4vPS95sZ66U/n3DGYzMgmE97Ki8BYOgc2AVfUYnu/GSqKvSz471YKsyvpODiV3lc1RzbUTwy2jo7OxUPzbj1Jatman6d/Tpv+g89dovkkzDYDY+7txMKp2/jxi90EfCG6jkxvFKFN9chv9tqkaRqblhzC6IC0tqdRT/W7qiW7qz1GpQeOvR6TCc0GHjOMEjuAoWaFWOPSm3Ld31/m6+f/xrSnH6VN34H0Hn8dUUm/nmeiaRrFh7PZMH82W5cuQhBFulw6lt7jr8NsC3vGBFEk6rrrsA8aRP5LL1H0rzconzGThEcfxT54UIN+f2WjxJCb2xCf4WDFV3v48vk1jLqzPfHptSdAcaGkpaVx8ODBU55Pij+WQ+bft4/STz+lbMZMNK8XW9++RL8wBVvfPvX2/vrcQea9tZm8/eUMvbkNrXsn1Uu/lSVFbFwwh7b9BxPbJL1e+tQ5P6yOyIsjZ6mmaJrmJRwvrnMch3eWsPCdbaghlcvu6kDTTnFn30lHR+d3iSAI9LvmRr56ZjI7lv9wwd4lANkgMeqP7fn+wx2smrkfvydE73HNfzcG02/52pS3v4LC7EqSugsIagBytx7zFuVugKJdx5TpnE0guQt0uyVsHCV3BvOF1a5xxidw/bOv8MvML9m4cC47V/5Im74DadK+E3FpGUSnNkENhXCVluAqKebQti3s+eUnSnIPI8kyHYeNoteVE7FHn14a2pCUROprr+GeOJG8Z5/j8N13Y+3Rg/i/PoSlY8cLGvuFIAgCHQalEpcWwcKpW/n65XX0n9iSdv2TG8Xv6rnnnuPOO+/E4/FUP2c0yAxqmsyW96biXLEK98qVCAYDjjFjiL7lFsytWtbrGCtLfMz+10bKC72MuL09LbqdXQyktvh5+ueoqkqfCXoR98aO1eG4OMLwdM6Po3f8Vn69l8hEG5f9qcNvWpVKR0endmjSriPxTZuzbs5MOgwecV7KeCcjSSLDbmmL0Syz4btsBAEuufL3YzD9VkmMLOWy7quJLJkBz++Do3VxrLFhT1HbKyClW9hIstfNjTqz3c7AG26l+5hxrJ41nS1LFrJ9+Q+n3VYQRJq0a0+XSy8ns2dvbJE1Ex6x9e5Ns5kzKP3yS4refIsDE68hYuRI4v58D6bMzNo8nHMisZmTiZN7sPi97Sz7bBc5u0sZNKk1JkvDTq2O5iVNnjyZ7OxsmqSk8NdBg7C6i1g8fyY9y3y0uv//iJwwATmm7moYnYmiw5XMfmMToYDK2Ps6k9qq/gRoPIX57Pj+O7qOGoszvm5lyXUuHIvDibvs9EqT9YluLNUBqqLy4xe72bY8l+Zd4hhycxtdElxHR6dGCIJA9zHjmPfGP8jauI5mXXvUTruiwIDrWqIB6xdmI8oivcY2q5W2dRoGQRRoWvgmpZYM6HJP2Ci6QGW688UWGcXgm+9g4I23UpaXR1F2FsWHDyGbTNijorFFRhObll6tcHWuCAYD0ZMm4bziSkref5/i99+ncuFCIkaMIPauP2Fu06aWj6hmWOxGxvy5E+u/O8gv32ZRcKCC4be1I7HphXntLpTrJkxgbEws+999B9P2HbBmLYbel7DCrLHGVEFa/z7ENoChdHBbMQunbsVolrnqoa71qgSsaRrZK5ZgiXDQe8L19davzvljdTgpyj41pLS+0WfwtUzAF+K7d7ZxcGsxXUemc8kVzarVcnR0dHRqQstL+vHjZx+wds6MWjOWIGyIDby2JWpIZe3cA0iySPdLM2qtfZ16JjINHj7Iph9/ZNCgQQ09GiAsVBKdnEJ0ct3UyJHsNuLu/TNRN0yi5MMPKf3kUyq/+w5b//5E33Qjtr5966TfX0MQBbqNyiClZRTfvbONGS+vp8eYpnQdmVavareaquLduJGKOXOomDcfpawMOTKSmFtvJXLCeIxpaSRXlPPl048y48W/c/VjfyeldduzN1wbY9M0NnyXzc8z9xGTYmfMPR2xR5nrpe+j7Fj+A+68XEb+6f+q8+N0GjcWhxNPRRmapjVsrmKD9fwbxFMRYM6/N1F0qJKB17ei/YC6Laimo6Pz20SSZbpeejk/fvIe+Vn7SGjavNbaFkSBQTe0RlFUfpm1H5NF/k2p5P2uEIR69yA1FuSoKOLvv5+YW2+l9NNPKfnsMw7dcSfGZs2w9OiB0qULkrN+vTuJzZxc83gPln22i1++3c/BrUUMvaUtkfF1F4KvaRq+rVup/O47KubOI5ibi2A2EzFkMM5x41gbDNJ+yJDq7a0OJxOeeI5pTz3CN1OeYsLjz5LYom7zlUIBhe8/3smeNfk07xrP0JvbYDDVr8iV3+Nh2SfvYYtPot3AofXat875Y4lwoASDBH1ejJaGS2XRC/zUEq5SHzNeWU9pnpvL7u6oG0o6OjoXRMehIzFaLKybM6PW2xZFgaE3tSGjYyw/TtvNvg0Ftd6Hjk59IDkcxN51F5lLlpD88kuIViuOadPY038AOQ88iGvFT2ih0NkbqiVMVgMjbm/P8NvaUprnYdqzq9my9DCaqtVaH1oggPvnn8l7/nn2Dh3KgQkTKX7/A4zNmpH84hQyV6wg5dVXsffvD6fJebRFRjHhieewREQw/fknyN+/t9bGdjKleW6mv7iOPWvz6XVFM0be0a7eDSWAn7/+HE9FOU36D6mVPFCd+sHqjARocEU83bNUC5QXepj1+kb87iBj7+tMcovIhh6Sjo7ORY7JaqPDkBFsWDCH/tffQkRMbK22L0oiI25vx7evb2DRu9ux/J+R5Ez93KVzcSIYjTjHjsU5diwrPvqYFgcPUj5nDhXz5iFFRRExYgSOUSOxdu9e50VWAVr2SCS5RRQ/fLyDH7/YzZ61+Qy+oTVRiedXXzFw6BDulT/j/ukn3D/9hOp2IxiN2Pr2JeLe+4gYPAgpsua/34iYWCY88Txf/v1Rpj/7OOOfeK5WPdgAO1cdYdnnu5FlkdF3dySjQ+2ew2pK/v69bJj/LR0GD8cYXz/y5Dq1w9EcR29FOZEJDVfwWTevL5DSPDcz/rGegC/EFX/pohtKOjo6tUbXS69AUzU2LZpfJ+0bjBKj7+5ERIyZeW9vpiTXXSf96OjUJ6G0JiQ+8TiZPy4j5V//xNa7N+WzZ5P9h1vZ3bsPh++9j9KvviJw+DCaVnsen5OxR5kYc28nht7chpJcN188u5o1c7NQguqv7qdpGv6sLMq+/prcxyazd9hw9g0fQd6TT+LdvBnH6NGkvvUWLVf9TJO33yJy3JXnZCgdxRmfwMS/PY/BYmH6s49TcGD/+R7qCfjcQRa/v50lH+wgPi2Cax7v2WCGUigYZP6br2J1OBkw6dYGGYPO+WNxhOuXeRpYPlz3LF0AZQUeZr62AU2DcQ/Ur6qLjo7Obx9HXDwZnbuybdli+ky8HlGs/fAVs93A2Hs78fVL65j71iYmPNIDs73u77zr6NQ1osmEY8QIHCNGoHq9uFaswP3jclzLl1O5aBEAckIC1m7dsHTujLldW0ytWiPZz8/7czoEQaB17yTS2sXw4xe7WT07i12r8ug3MZOMDrFooRCB7EP49+zBt307vq1b8W3dilIenhxKkZFYunUj+pZbsPXpg7FpRq0mujvjE5n4txf48ulH+eqZyYyf/AwJzVqcd3tZm4tY+ulOvJVBeozOoPvopogNKHK18qtPKT6czVWPPIXZrs/RLjYsEcc8Sw2JbiydJ5UlPma9vgE1pHHlA110Q0lHR6dOaD94OLNffYEDm9bTrEvtKeMdjyPWwqV/6sDMVzewYOoWxt7XGakeVbx0dOoa0WLBMXw4juHD0TSNwN69uNeswbt2HZ61a6mYNy+8oSBgSGuCKaMpxox0DOnpGBKTkBPiMSQkIEVGIsg1nzppgQChkhKEwiL6tigkLVjK2p0+5r65mThfFs23f461Iie8sSxjyszEPnwYlg4dsXbvhrFp0zrPsYlMSGTi357ny2ce46tnJnP1Y38nKbPVObXhqQjw09d72P1LPjEpNkbf3ZH4dEcdjbhm5O7ewdpvv6HDkBE07dK9Qceic35YIiIA8LldDToO3Vg6D9xlfma+toGAV+HKv+iGko6OTt3RvFtPLA4nW79fVGfGEoSVvAbd0IolH+xgxZd7GHjduU2WdHQuFgRBwJSZGS5oe/31aJpGqKAg7NnZsQP/rt0EDhzA/csvaD7fqftbrUgREYhWa9hwMsgIooQWCqGFgmjBIKrbg1pZieb3n7gv0N1sJbf1GPY5+7Cq66O0SA3SbWgS0V1bI5pM9fQunEhkYhLXPvUiXz0zma+efZyrHnmS1Dbtz7qfoqhs+eEwa+ZkEQqodL8sg+6XZSDJDXuzJej3seCt17DHxDDwxtsbdCw654/RYkUQRXyuygYdh24snSN+T5Bv/7URb0WAy/+vM3FpEQ09JB0dnd8wkmygbf/BbFgwG095WbU6UF3Q+pIkinPcbFyUTUyKXVf11PldIAgChoQEDAkJRAweXP28pqqECgsJ5ecTKiggmJ+PUl6OWlGJUlmB6vFAKIQWDKGpCoJsQJBlBFlGtNkQHRFIERFIkVHI8XHIcXHI8QnIcbG0FUX6VgZYO/8AW5flkPVZKe0PZ9N5WBr2qIYxmBxx8Ux86gWmP/M4Xz//JFc8+BgZnbuddltN08jaVMSqmfsozfOQ1i6afhMyz1vAojbRNI3FU9+kNO8IEx5/FpO14SSndS4MQRAw2+y6sXQxoQRV5r29hbJ8D2Pv7URis4at0K2jo/P7oMOQEaybO5Pty3+g+5hxddpX73HNKcl1s3zabuLSIkjIaNhQGh2dhkIQxWojqi6wRBjpP7ElnYY0YfWcLDb/cJgtyw7TuncSXYan1Wl9pjMRER3LxCdf4Ovn/8aMl/7OqHseoE3fgdWva5rGwS3FrJ6TRWF2Jc54C6Pv7kh6h5gGLRp6PBsWzGH78h/oM3ESae07NfRwdC4Qc4QDr6thw/D0oPQaoqkaiz/YTu6eMobe0obU1tENPSQdHZ3fCTGpaSRltmLrD4vqVL0LwjWYhv+hLVankYX/24rPHazT/nR0fu84Yi0Mu6Utk56+hDa9k9j58xE+/dsqZr+xkazNRai1WKOpJtgio7jmqSkkt2rDvH+9zPp5swgGFLb/lMu059Yw963N+D1Bht7chuuf7EVGx9hGYygd3rGVZR+/Q/Puvbhk3DUNPRydWsBsb3jPkm4s1ZCV3+xl77oCel/VnJY9Gk7rXUdH5/dJ+8HDKT6czZE9u+q8L7PdwKg7OuAu97Pkg+21WlBTR0fn9DjjLAya1JqbnutDjzFNKT7sYt5bm/l48kp++novhdmVdX6z5Cgmq42rHnmatPY9+OHDqfznruf4/qPtoGkMuak11z99Ca17JyE2IiEYV0kxs1+bgjM+gUvveUAvPvsbwWKPwFeph+E1eravyGXj4kN0GJxKl+FpDT0cHR2d3yGteg/ghw+nsnXpIpJbtq7z/hKaOug7vgXLp+1hw6Jsuo5Mr/M+dXR0wOY00XNMU7pdms6BTUXs+PkIm5ccYuOibCITrKR3iCG9bQxJmU5kQ+2WE1AUlYKsCrK3l7B3XQGleX2RTQECrtWktA4x7qFHMFkaXw6Q11XJ1y88SdDnY8ITz2GyNnzulE7tYLZHUHToYIOOQTeWzkLu3jKWfb6LtLbh5MXG4mrW0dH5fWGyWsns0Zs9v6xk6K13IZ2DfPH50mFQKrl7yvnl2/1k9kggItpc533q6OiEkSSR5l3jad41Hp8ryL4NBexdV8CWpYfZtPgQskEkPsNBXHoECekOYlLsRMSaMRhrZkBpmkZliY/iwy6KDrvIP1BB7u4ygn4FQYDkllF0GZ5G084D2LliIT98MJVpTz7Mlf/vCRyx8XV89DUn4PXwzQtPUpp7mHEPP0VsE/3Gzm8Jsz2iwcPwdGPpVwi4NRb8dwsRMWaG39auQQur6ejo6LS8pB87Vizl0NZNZ1Spqk0EQWDIja0pGJCsG0o6Og2I2W6gXf8U2vVPIehXyNldyqEdJeRnVbB1aQ6bQoeqt7U6jNijzZgsEuWVKksObEfVNNSQhhJS8VYGcZf7cZf7UUNVYX0CRMZbadUrkdQ2UaS0jMJsO1acusuosUQlJjP79ReemrfrAAAgAElEQVT55JH7uezPD9bLOehsBAN+Zr70DPn793L5A4+R3rFzQw9Jp5Yx2+0EvF6UUBBJbpiC6bqxdAaCfoVDyzXUoMroBzuecNLQ0dHRaQgyOnXFaLGwa9WKepuoGC2yLmijo9OIMJgkMjrEktEhFgiHzpXkuCnNc1NR5KOiyIurzE/AG8JfAYd3lyKKApIsIkoCZruBpOZObJEmHLEWYlPtRCfbMJp/fUqY0bkb1z/3CnNem8LXLzxJr3ET6TNhEqJUu6GANcXvcTP7tSkc2vH/27v3+KqrO9//r5WEZO+dG5eQRK4JggIBEpCANsiRAyepra1jkYr4o51J/QmSdBicM1OmlhGmSu05jEMVKydOZzozhxkvOIItaqNiVEYGgSkgFwWEEAKYRJBAQrJz2ev8kZASEjCQnf3de+f9fDx4kP3da6/vZ32N+fLJWuvz3cs3fvg/GZl9qyNxSM9yxbU+mLamhti+/RyJQcnSFRzff4b6avjmooygeG6AiEhUdDQ3Tr6Vwx9tZdaDBQFZiiciwS0yMoKBw+I7fe5jSUkJd9yR47dzDRg8lHlP/C3v/rqIba++RPmBvXz94SX0Tb3Bb+foiurKCl79+Qq+PHWCvIWL25U3l/DiDoJkSaVCrmDExIGM+oZp+82NiEgwuPm2adTX1lC2d7fToYhIL9QnxkXugj/lzsI/p+pYKf/0F4Vs/82/42tuDsj5Tx48wL/+5M+p+fI0s3/8N4y7Y1ZAzivOuDizVFdzzrEYlCxdRXS89iiJSHAZPmES0W4Pn279wOlQRKQXG3v7DP74qV8yfEIW7//ff+Bff/I/OXnwQI+dr7mpka3r/40Xl/8V0S438x7/Wz10the4dBmeU5QsiYiEkKg+fRg5eSqHt2+luUkPjBUR58T3T+Lu//kT7vqzH3H+dBX/tuwvePV//Q1VZaUArFu3jrS0NCIiIkhLS2PdunXXdZ6TBz/hX360mA9fXsdNt+Yw74m/pf+gIX4ciQQrd/zFZMm5inha8C4iEmJuuu129n/wLmUfaymeiDjLGMPNt91O+sTJ/Nfrr7HjN//OP//lDzkR4WLtq7+lrr4egGPHjvHQQw8B8MADD3xlv9ZaTn56gB2/fZXDO/6T+P5J3POjxxgxKbtHxyPB5Q8zS0qWRESki4ZPmNi6FG8LrrEqlSsizot2ubn1O/eRmfsNdv72Vb79/z/clihddOHCBR599NErJkvWWs6cKKds7y72f/Aunx8+iCs2jql/NIcpd99LdBA+EFd6VrTbg4mIULIkIiJdF9WnDyOzb+Xwjq1kjJ7gdDgiIm3ccfFMm/s9zs77407fP3bsGK/97Uo8ffvhSUig0eul7tw56s5XU3HkMLVnvwSg36AhzMx/mIz/NpM+Lj3nrbcyxuCKjVOyJCIi1+bGyVPZ//5maj4/4XQoIiIdDBs2jGPHjnU4npSYwJmT5Rzf/zH1NeeJ7NMHd0Ii7rh4hmZMYNi4TIaNm0BicqoDUUswcsUnUOdggQclSyIiIWj4+IlEREZSfeyI06GIiHTwxBNP8NBDD3HhwoW2Yx6Ph9XP/rJtGZ6vuRkTEYExqj4sV+aKi6P+vEqHi4jINYjxeBg8OkPJkogEpQceeICioiKGDx+OMYbhw4dTVFTUbr9SRGSkEiX5Su64eEdLh2tmSUQkRI2YOJnj+/ZwrqqShIHJTocjItLOAw880KXKdyJX44qL54vjHZd0BopmlkREQlR6awndI7/f4XAkIiIiPcMVF0/deecKPChZEhEJUf0HDSE6IZGjv9/udCgiIiI9whUXR2N9nWMPYleyJCISoowxJA4fQdnePTQ2eJ0OR0RExO/+8GBaZ/YtKVkSEQlhicNG0NTg5fi+PU6HIiIi4nduJUsiInK94gcNJSomhqPatyQiImHo4sxSXY0z5cNDJlkyxiw3xpwwxuxq/fMNp2MSEXFaRFQUw8ZlcuS/dmCtdTocERERv9IyvGvzd9barNY/rzsdjIhIMBgxMZtzVRWcOVHudChhzRjzdWPMp8aYw8aYpZ28H2OMebH1/W3GmLTARykiEl7+kCw5UxEv1JIlERG5TFrmRADK9u5yOJLwZYyJBJ4F7gTGAvcbY8Ze1uwHwJfW2pHA3wE/D2yUIiLhxx3fmiydd2YZXqg9lLbQGPM9YAfw59baLy9vYIx5CHgIICUlhZKSkus+WU1NTbc+Hyw0juARDmMAjSOY1NTU8Pv9nxAdn8B/lWym2hXvdEjhagpw2Fp7BMAY8wJwN7D/kjZ3A8tbv14PrDHGGKv1kSIi1y3a7cFERFBf68wyvKBKlowxbwOpnbz1KPAc8FPAtv79t0D+5Q2ttUVAEcDkyZPtHXfccd3xlJSU0J3PBwuNI3iEwxhA4wgmF8fg/WQ3hz/ayn+bPh0ToUUDPWAwcPyS1+XA1Cu1sdY2GWOqgQHAF5c28ucv9SA8kn5/0vX4A12L9nQ92gul6xEZHcNnn35KkwPxBlWyZK2d1ZV2xpjngd/2cDgiIiFjaMYE9r77FpXHjpKSfqPT4YQj08mxy2eMutLGr7/Ug/BI+v1J1+MPdC3a0/VoL5Sux5GNL9A/Id6ReEPm14/GmBsueXkPsNepWEREgs3QjPEAHN+72+FIwlY5MPSS10OAk1dqY4yJAhKBMwGJTkQkjLni4lTgoQv+lzHmY2PMHmAGsMTpgEREgkV8/yT6DRpCmR5O21O2A6OMMenGmGhgLvDaZW1eA77f+vW9wGbtVxIR6T53XLxjpcODahne1Vhr5zsdg4hIMBuWMYH9H7xLc1MTkVEh8+M9JLTuQSoEfgdEAv9grd1njPkbYIe19jXgV8C/GGMO0zKjNNe5iEVEwocrNo4vjh9z5Ny6m4qIhImhGRPY/dbrVBw5zKCbRjsdTthpfb7f65cd++tLvq4H5gQ6LhGRcOeKT6DuvJbhiYhIN7TtW9JSPBERCSOuuDga6+tobmoM+LmVLImIhAlPQiIDh6VRpiIPIiISRlxxrQ+mdWDfkpIlEZEwMnRcJic/PUBTQ4PToYiIiPiFuy1ZCvxSPCVLIiJhZGjGBJoaGzh16BOnQxEREfGLizNLdUqWRESkO4aMyQBjOL7/Y6dDERER8QstwxMREb9wxcYxcOhwTh7UzJKIiIQHl5bhiYiIvwy6eQynDn2Cz9fsdCgiIiLd5o5vTZbOnwv4uZUsiYiEmUE3jaGhro7Tx8ucDkVERKTbot0eTEQE9bVahiciIt006OaxAJw8eMDhSERERLrPGIMrNo46zSyJiEh3JSan4Ensy8lPlSyJiEh4cMXF4a2tDfh5lSyJiIQZYwyDbhrDCc0siYhImIjxxOK9oGRJRET8YNDNY6iu+Jzas186HYqIiEi3xcRqZklERPxk0E1jAO1bEhGR8BDjiaVeM0siIuIPKek3EhkVpectiYhIWIiJjcWrangiIuIPUdHRpIwYpSIPIiISFrRnSURE/GrQzWOoOHKIpsZGp0MRERHpFldsHM2NjTQ1NAT0vEqWRETC1KCbRtPc1ETl0cNOhyIiItItMZ5YgIDPLilZEhEJUxeLPJzQUjwREQlxMbEtyVJ9gPctKVkSEQlTsX37kZiSqn1LIiIS8i4mSw0XLgT0vEqWRETC2A0jb6biiJbhiYhIaIvxxAEEvCKekiURkTCWkn4j509X6eG0IiIS0lwXl+Fpz5KIiPhLyo2jAKhQkQcREQlhbQUeapUsiYiInySn3QjGaCmeiIiEtIt7llQNT0RE/CbG46HfDYOVLImISEiLio4hIjJKe5ZERMS/UkeMVLIkIiIhzRhDTGxswGeWogJ6NhERCbiUEaM4sKWEmi/PENevv9PhyFdobGykvLyc+vr6LrVPTEzkwAGVh7/o4vVwuVwMGTKEPn36OB2SiPiJKzaW+gDvWVKyJCIS5lJG3AhAxZHDxN0yxeFo5KuUl5cTHx9PWloaxpivbH/+/Hni4+MDEFloOH/+PHFxcZw+fZry8nLS09OdDklE/CTGE/iZJS3DExEJc8npKvIQSurr6xkwYECXEiXpnDGGAQMGdHl2TkRCQ0xsnPYsiYiIf0W73AwYPJSKI4ecDkW6SIlS9+kaioSfGE+sSoeLiIj/paTfSMXRz5wOQ0RE5Lo5UeBByZKISC+QcuMoar88Q82Z006HIiEgMjKSrKwsMjIyyMzM5KmnnsLn8zkdVpuf/exnjBw5kptvvpnf/e53TocjIgHixMySCjyIiPQCKSNGAfD5kcOM7D/A4Wgk2Lndbnbt2gVAZWUl8+bNo7q6mhUrVnS77+bmZiIjI6/78/v37+eFF15g3759nDx5klmzZnHw4MFu9SkiocEVG0dTYwNNDQ1ERUcH5JxKlkREeoHktHSMiaDiyGFGTp7qdDjSRSt+s4/9J89dtc21Jh9jByXw2Lcyutw+OTmZoqIisrOzWb58OT6fj6VLl1JSUoLX66WgoIAFCxbg8/koLCzkvffeIz09HZ/PR35+Pvfeey9paWnk5+dTXFxMYWEh2dnZFBQUUFVVhcfj4fnnn2f06NFUVVWxcOFCysrKAFi9ejU5OTnt4tm4cSNz584lJiaG9PR0Ro4cyUcffcRtt93W5TGJSGiK8cQC4L1Qq2RJRET8p0+MiwFDVORBrs+IESPw+XxUVlayceNGEhMT2b59O16vl5ycHHJzc9m5cyelpaV8/PHHVFZWMmbMGPLz89v6cLlcbNmyBYCZM2eydu1aRo0axbZt21i0aBGbN29m8eLFLFmyhGnTplFWVkZeXl6HZ0idOHGCW2+9te31kCFDOHHiRGAuhIg4Kib2D8lSbN9+ATmnkiURkV4iZcQoju7agbVWlcJCRFdmgAL1nCVrLQDFxcXs2bOH9evXA1BdXc2hQ4fYsmULc+bMISIigtTUVGbMmNHu8/fddx8ANTU1fPjhh8yZM6ftPa/XC8Dbb7/N/v37246fO3euw/guxnEpfT+L9A5tyVIA9y0pWRIR6SWS00ew7723uVB9NmC/kZPwcOTIESIjI0lOTsZayzPPPENeXl67Nps2bbpqH7Gt/8jx+Xz07du3bU/UpXw+H1u3bsXtdl+xnyFDhnD8+PG21+Xl5QwaNOhahiMiISrGEwcQ0GctqRqeiEgvMXBYGgBVx446G4iElIv7iAoLCzHGkJeXx3PPPUdjYyMABw8epLa2lmnTpvHKK6/g8/moqKigpKSk0/4SEhJIT0/n5ZdfBlpminbv3g1Abm4ua9asaWvbWUL17W9/mxdeeAGv18vRo0c5dOgQU6ZM8fOoRSQYuVp/6VIfwPLhmlkSEeklki5JltIyJzkbjAS1uro6srKyaGxsJCoqivnz5/PII48A8OCDD1JaWsqkSZOw1jJw4EA2bNjA7Nmzeeeddxg3bhw33XQTU6dOJTExsdP+161bx8MPP8zjjz9OY2Mjc+fOJTMzk6effpqCggImTJhAU1MT06dPZ+3ate0+m5GRwXe/+13Gjh1LVFQUzz77rCrhifQSbQUetAxPRET8zR2fQFz/AVSVlTodigS55ubmK74XERHBypUrWblyZYf3Vq1aRVxcHKdPn2bKlCmMHz8egNLS0nbt0tPTefPNNzt8PikpiRdffPEr43v00Ud59NFHv7KdiISXSws8BIqSJRGRXmTg8HS+0DI86SF33XUXZ8+epaGhgWXLlpGamup0SCISRqKiY4iIjAronqWgSpaMMXOA5cAYYIq1dscl7/0V8AOgGfhTa60e2S0ico0GDkvj2J5dNDc1EhnVx+lwJMxcaZ+SiIg/GGOIiY3Fe+FCwM4ZbAUe9gLfAd6/9KAxZiwwF8gAvg780hijBcoiItcoaXg6vuYmzpzUc2lERCT0uGJjA7oML6iSJWvtAWvtp528dTfwgrXWa609ChwGVPpGROQaXayIp6V4IiISimI8sb13Gd5VDAb+85LX5a3HOjDGPAQ8BJCSktKtJQE1NTVhsaRA4wge4TAG0DiCybWOwTY3YyIi2bnlfSqa9SBPEREJLdGe2PAuHW6MeRvobMfno9bajVf6WCfHOj7CG7DWFgFFAJMnT7Z33HHH9YQJtKy97s7ng4XGETzCYQygcQST6xnD8eKNuG1zyI9dRER6H5cnlpozpwN2voAvw7PWzrLWjuvkz5USJWiZSRp6yeshwMmejVREJDwNHJam8uFyVZGRkWRlZZGRkUFmZiZPPfUUPp/P6bAAOH36NDNmzCAuLo7CwkKnwxGRAIvpzXuWruI1YK4xJsYYkw6MAj5yOCYRkZA0cFgatV+e4cK5aqdDkSDldrvZtWsX+/bt46233uL1119nxYoVfun7as9w6gqXy8VPf/pTVq1a5Zd4RCS0xMTG9d6H0hpj7gGeAQYCm4wxu6y1edbafcaYl4D9QBNQYK3t3k9bEZFeKml4OgBflJUybFymw9HIVb2xFD7/+KpN3M1NEHkNt/PU8XDnk11unpycTFFREdnZ2Sxfvhyfz8fSpUspKSnB6/VSUFDAggUL8Pl8FBYW8t5775Geno7P5yM/P597772XtLQ08vPzKS4uprCwkOzsbAoKCqiqqsLj8fD8888zevRoqqqqWLhwIWVlZQCsXr2anJycdvHExsYybdo0Dh8+3PUxi0jYiPHE0tTgpamxkag+Pf8IjKBKlqy1rwKvXuG9J4AnAhuRiEj4SW5NlqqOKVmSrhkxYgQ+n4/Kyko2btxIYmIi27dvx+v1kpOTQ25uLjt37qS0tJSPP/6YyspKxowZQ35+flsfLpeLLVu2ADBz5kzWrl3LqFGj2LZtG4sWLWLz5s0sXryYJUuWMG3aNMrKysjLy+PAgQNODVtEglBMbCwADRdqiUrs2+PnC6pkSUREep4nsS+exL5Ulal8eNDrwgxQ3fnzxMfH93go1rbUVSouLmbPnj2sX78egOrqag4dOsSWLVuYM2cOERERpKamMmPGjHafv++++4CWCo4ffvghc+bMaXvP6/UC8Pbbb7N///624+fOneN8gMYnIqHB5WlJlupra/EoWRIRkZ4wcHg6VXrWknTRkSNHiIyMJDk5GWstzzzzDHl5ee3abNq06ap9xLb+Ntjn89G3b1927drVoY3P52Pr1q243W7/BS8iYSUmNg4A74XAPGspVAo8iIiIHyUNS+N0eRm+bm62l/B3cR9RYWEhxhjy8vJ47rnnaGxsBODgwYPU1tYybdo0XnnlFXw+HxUVFVd8/ldCQgLp6em8/PLLQMuM1e7duwHIzc1lzZo1bW07S6hEpHeLaZ1ZClSRB80siYj0QgOHpdHc2MiXp04wYMgwp8ORIFNXV0dWVhaNjY1ERUUxf/58HnnkEQAefPBBSktLmTRpEtZaBg4cyIYNG5g9ezbvvPMO48aN46abbmLq1KkkJiZ22v+6det4+OGHefzxx2lsbGTu3LlkZmby9NNPU1BQwIQJE2hqamL69OmsXbu2w+fT0tI4d+4cDQ0NbNiwgeLiYsaOHduj10REgsPFPUuBKh+uZElEpBdKGjocgNPlZUqWpIOrlfeOiIhg5cqVrFy5ssN7q1atIi4ujtOnTzNlyhTGjx8PQGlpabt26enpvPnmmx0+n5SUxIsvvviV8V3en4j0Hm3JkmaWRESkp/QfPASM4XT5cadDkTBy1113cfbsWRoaGli2bBmpqalOhyQiYcbladmzVF8bmD1LSpZERHqhPjEuEpKSOX1CyZL4z5X2KYmI+EtUTAwRkZEBW4anAg8iIr3UgMFDOKNkSUREQogxhhhPbMCW4SlZEhHppfoPGcaZk+X4fKqIJyIioSMmNlYzSyIi0rMGDB5Kc2Mj5yornQ5FRESky2I8cXgDtGdJyZKISC/Vf/BQAO1bEhGRkBITG0u9ZpZERKQnDbiYLJWXORxJcDPG9DfGvGWMOdT6d78rtGs2xuxq/fNaoOP0p8jISLKyssjIyCAzM5OnnnoKn8/ndFgAvPXWW9xyyy2MHz+eW265hc2bNzsdkogEmCuAe5ZUDU9EpJdyxcUR27cfZ06UOx1KsFsKvGOtfdIYs7T19Y86aVdnrc0KbGg9w+12s2vXLgAqKyuZN28e1dXVrFixott9Nzc3ExkZed2fT0pK4je/+Q2DBg1i79695OXlceLEiW7HJSKhI9oTuD1LSpZERHqx/oOHqiLeV7sbuKP1638CSug8WfK7n3/0cz4588lV21xr8jG6/2h+NKXr4ScnJ1NUVER2djbLly/H5/OxdOlSSkpK8Hq9FBQUsGDBAnw+H4WFhbz33nukp6fj8/nIz8/n3nvvJS0tjfz8fIqLiyksLCQ7O5uCggKqqqrweDw8//zzjB49mqqqKhYuXEhZWcts5+rVq8nJyWkXz8SJE9u+zsjIoL6+Hq/XS0xMTJfHJCKhLcbjpqGuLiDnUrIkItKLDRgylP3vb8ZaizHG6XCCVYq19hSAtfaUMSb5Cu1cxpgdQBPwpLV2Q2eNjDEPAQ8BpKSkdHg2UWJiIufPnwegoaGB5uarVyu01n5lm0s1NDS09X81l7YZOHAgPp+PI0eOsGnTJlwuF5s3b8br9ZKbm8vXvvY1du3axeHDh/nwww+pqqoiOzub+++/n/Pnz7d9f73xxhsAfOtb3+Lv/u7vGDlyJNu3b2fBggX89re/ZdGiRSxYsIDbbruN48ePc88997Bjx44rxrhhwwYmTJhAQ0MDDQ0NQEvyeDH2+vr6Xv3sp5qaml49/svperQXytfjZEUVjfV1vLt5MyaiZ3cVKVkSEenF+g8eSkNdHTVfnia+f5LT4TjGGPM2kNrJW49eQzfDrLUnjTEjgM3GmI+ttZ9d3shaWwQUAUyePNnecccd7d4/cOAA8fHxACybtuwrT3r+/Pm29v50eZ/WWuLi4nj//ffZs2cPv/nNbwCorq7m1KlT7Ny5k/vvv5/ExEQSExOZMWMGbreb+Ph4jDF873vfIz4+npqaGrZt28af/MmftPXt9XqJj4/nvffe49ChQ23Ha2pqOo0FYN++fSxfvpzi4uJ27196PVwuV7uZqN6mpKSEy7+/ejNdj/ZC+XrsrD3LqR0f8rVbpxLjie3RcylZEhHpxS4WeThTXt6rkyVr7awrvWeMqTDG3NA6q3QD0GmtdWvtyda/jxhjSoCJQIdkKRQdOXKEyMhIkpOTsdbyzDPPkJeX167Npk2brtpHbGzLP2h8Ph99+/Zt2xN1KZ/Px9atW3G73Vftq7y8nHvuuYd//ud/5sYbb7zG0YhIqIt2ewDwXrjQ48mSquGJiPRiA4YMA+D0CVXEu4rXgO+3fv19YOPlDYwx/YwxMa1fJwE5wP6ARdiDLu4jKiwsxBhDXl4ezz33HI2NjQAcPHiQ2tpapk2bxiuvvILP56OiouKKy3sSEhJIT0/n5ZdfBlpmrHbv3g1Abm4ua9asaWvbWUJ19uxZvvnNb/Kzn/2sw34mEekdLiZLDXUXevxcSpZERHoxT2JfYmJjVeTh6p4E/ocx5hDwP1pfY4yZbIz5+9Y2Y4AdxpjdwLu07FkK2WSprq6urXT4rFmzyM3N5bHHHgPgwQcfZOzYsUyaNIlx48axYMECmpqamD17NkOGDGk7NnXqVBITEzvtf926dfzqV78iMzOTjIwMNm5syT+ffvppduzYwYQJExg7dixr167t8Nk1a9Zw+PBhfvrTn5KVlUVWVhaVerCySK8S0zr7HIhkScvwRER6MWMM/QcP1YNpr8JaexqY2cnxHcCDrV9/CIwPcGg95moFIyIiIli5ciUrV67s8N6qVauIi4vj9OnTTJkyhfHjWy5JaWlpu3bp6em8+eabHT6flJTEiy++eNXYfvKTn/CTn/ykC6MQkXAV7WmdWbqgZElERHrYgMHD+GznNqfDkDBw1113cfbsWRoaGli2bBmpqZ3VzBAR6Z62PUsBKB+uZElEpJcbMHgIe98tpu78OdzxCU6HIyEsVMsQi0ho0Z4lEREJmP5DWiriaSmeiIiEghiPkiUREQmQAYNbKuKdKVeyJCIiwa+PywW0lA7vaUqWRER6uYSkgURFx3DmpJIlEREJfhERkfRxuWmoq+35c/X4GUREJKiZiAj6pqTy5amTTociIiLSJTFuN94LPV/gQcmSiIjQ74bBfPn5KafDkCARGRnZ9pylzMxMnnrqKXw+n9NhAfDRRx+1PV8pMzOTV1991emQRMQB0W6PnrMkIiKB0feGQXy28yN8zc1EREY6HY44zO12s2vXLgAqKyuZN28e1dXVrFixott9Nzc3E9mN77Fx48axY8cOoqKiOHXqFJmZmXzrW98iKkr/pBHpTaI9SpZERCRA+qUOwtfcxLkvquibomfjBIvPV67Ee+CTq7Zpam7mzDUkHzFjRpP64x93uX1ycjJFRUVkZ2ezfPlyfD4fS5cupaSkBK/XS0FBAQsWLMDn81FYWMh7771Heno6Pp+P/Px87r33XtLS0sjPz6e4uJjCwkKys7MpKCigqqoKj8fD888/z+jRo6mqqmLhwoWUlZUBsHr1anJyctrF42mtggVQX1+PMabLYxGR8BHt9uBVsiQiIoHQL3UQAGdPnVCyJB2MGDECn89HZWUlGzduJDExke3bt+P1esnJySE3N5edO3dSWlrKxx9/TGVlJWPGjCE/P7+tD5fLxZYtWwCYOXMma9euZdSoUWzbto1FixaxefNmFi9ezJIlS5g2bRplZWXk5eVx4MCBDvFs27aN/Px8jh07xr/8y79oVkmkF4pxe6j98kyPn0c/XUREhH6DBgNw5tRJ0rJucTgauagrM0Dnz58nPj6+x2Ox1gJQXFzMnj17WL9+PQDV1dUcOnSILVu2MGfOHCIiIkhNTWXGjBntPn/fffcBUFNTw4cffsicOXPa3vN6vQC8/fbb7N+/v+34uXPnOh3f1KlT2bdvHwcOHOD73/8+d955J67WUsIi0uJgmfQAABngSURBVDu07Fnq+QIPSpZERARPYl/6uNyc/VwV8aSjI0eOEBkZSXJyMtZannnmGfLy8tq12bRp01X7iI2NBcDn89G3b9+2PVGX8vl8bN26Fbfb3aW4xowZQ2xsLHv37mXy5MldHI2IhINoj1sPpRURkcAwxtAvdRBfKlmSy1zcR1RYWIgxhry8PJ577jkaGxsBOHjwILW1tUybNo1XXnkFn89HRUUFJSUlnfaXkJBAeno6L7/8MtAyY7V7924AcnNzWbNmTVvbzhKqo0eP0tTUBMCxY8f49NNPSUtL8+OIRSQUxLTuWbo4691TNLMkIiJAS0W8yiOHnQ5DgkBdXR1ZWVk0NjYSFRXF/PnzeeSRRwB48MEHKS0tZdKkSVhrGThwIBs2bGD27Nm88847jBs3jptuuompU6eSmJjYaf/r1q3j4Ycf5vHHH6exsZG5c+eSmZnJ008/TUFBARMmTKCpqYnp06ezdu3adp/dsmULTz75JH369CEiIoJf/vKXJCUl9fg1EZHgEu32gLU0euuJdnVtNvp6KFkSEREA+t8wiEPb/oPmpkYio/o4HY44qLm5+YrvRUREsHLlSlauXNnhvVWrVhEXF8fp06eZMmUK48ePB6C0tLRdu/T0dN58880On09KSuLFF1+8amzz589n/vz5XRiFiISzGE/L0t6GCxeULImISM/rmzoI6/NRXVlB/0FDnA5HQtBdd93F2bNnaWhoYNmyZaSmqrKiiPSM6Na9jd66C8QxoMfOo2RJREQA6HdDS/nwL0+dVLIk1+VK+5RERPwtuvWZaz1d5EEFHkREBGiZWQJUEU9ERIJetLs1WbrQs+XDlSyJiAgA7vgEXLFxfHlKyZKIiAS3GLdmlkREJICMMfS9QeXDRUQk+F2cWfIqWRIRkUDplzqIL0+dcDoMERGRq2rbs3ShtkfPE1TJkjFmjjFmnzHGZ4yZfMnxNGNMnTFmV+uftVfrR0RErk/f1EGcP/0FTQ0NTociDoqMjCQrK4uMjAwyMzN56qmn8Pl8TofVTllZGXFxcaxatcrpUETEARfLhff0zFKwVcPbC3wH+D+dvPeZtTYrwPGIiPQq/W4YBNZytuIUSUOHOx2OOMTtdrNr1y4AKisrmTdvHtXV1axYsaLbfTc3NxMZGdntfpYsWcKdd97Z7X5EJDRFRkURFR1DQ13PFngIqmTJWnsAWtbNi4hI4PW7YTAAX35+UslSEPjgpYN8cbzmqm2uNflIGhrH7d+9qcvtk5OTKSoqIjs7m+XLl+Pz+Vi6dCklJSV4vV4KCgpYsGABPp+PwsJC3nvvPdLT0/H5fOTn53PvvfeSlpZGfn4+xcXFFBYWkp2dTUFBAVVVVXg8Hp5//nlGjx5NVVUVCxcupKysDIDVq1eTk5PTIaYNGzYwYsQIYmNjuzwOEQk/0W43DRd618zS1aQbY34PnAN+Yq39oLNGxpiHgIcAUlJSuvXMh5qamrB4ZoTGETzCYQygcQQTf4+h2esFYOeWDzhR6/VbvxLaRowYgc/no7Kyko0bN5KYmMj27dvxer3k5OSQm5vLzp07KS0t5eOPP6ayspIxY8aQn5/f1ofL5WLLli0AzJw5k7Vr1zJq1Ci2bdvGokWL2Lx5M4sXL2bJkiVMmzaNsrIy8vLyOHDgQLtYamtr+fnPf85bb72lJXgivVyMxxN+y/CMMW8DnT3S+1Fr7cYrfOwUMMxae9oYcwuwwRiTYa09d3lDa20RUAQwefJke8cdd1x3rCUlJXTn88FC4wge4TAG0DiCSU+M4dP1/0x/jyvkr0046MoM0Pnz54mPj+/xWKy1ABQXF7Nnzx7Wr18PQHV1NYcOHWLLli3MmTOHiIgIUlNTmTFjRrvP33fffUBLgv/hhx8yZ86ctve8rUn622+/zf79+9uOnzt3rsP4HnvsMZYsWUJcXFzPDFREQka029PjpcMDnixZa2ddx2e8gLf1653GmM+Am4Adfg5PRKTX65eq8uHS3pEjR4iMjCQ5ORlrLc888wx5eXnt2mzatOmqfVxcMufz+ejbt2/bnqhL+Xw+tm7ditvtvmI/27ZtY/369fzlX/4lZ8+eJSIiApfLRWFh4XWMTERCWSCSpaCqhnclxpiBxpjI1q9HAKOAI85GJSISnvqmpFJdWeF0GBIkLu4jKiwsxBhDXl4ezz33HI2NjQAcPHiQ2tpapk2bxiuvvILP56OiouKKy0MTEhJIT0/n5ZdfBlpmrHbv3g1Abm4ua9asaWvbWUL1wQcfUFpaSmlpKX/2Z3/Gj3/8YyVKIr1UtNvT43uWgipZMsbcY4wpB24DNhljftf61nRgjzFmN7AeWGitPeNUnCIi4SwxJZXzp7+guanR6VDEIXV1dW2lw2fNmkVubi6PPfYYAA8++CBjx45l0qRJjBs3jgULFtDU1MTs2bMZMmRI27GpU6eSmJjYaf/r1q3jV7/6FZmZmWRkZLBxY8sq/KeffpodO3YwYcIExo4dy9q1elKIiFxZjNuNt5dVw3sVeLWT468ArwQ+IhGR3icxORWs5VxVZVt1POldmpubr/heREQEK1euZOXKlR3eW7VqFXFxcZw+fZopU6Ywfvx4AEpLS9u1S09P58033+zw+aSkJF588cUux7l8+fIutxWR8BPtCcM9SyIiEtwSk1MAqK6sULIk1+Suu+7i7NmzNDQ0sGzZMlJTO6vnJCLiHxf3LFlre+zRQ0qWRESkncTkln/gVld+7nAkEmpCvRS/iISWaLcHX3MzTY0N9ImO6ZFzBNWeJRERcV5cv/5ERkWpyIOIiAS1GLcHoEeLPChZEhGRdkxEBAnJqVRXaGZJRESCV7SnNVnqwX1LSpZERKSDxOQUzmoZnoiIBLHoizNLPVgRT8mSiIh0kJicyjktwxMRkSAW0zqz5L1Q22PnULIkIiIdJCanUF9bQ31tjdOhiAMiIyPbnrOUmZnJU089hc/nczosoKUMudvtJisri6ysLBYuXOh0SCLikIszS94eXIanangiItJB37aKeBW40uMcjkYCze12s2vXLgAqKyuZN28e1dXVrFixott9Nzc3ExkZ2a0+brzxxrb4RKT3CkSBByVLIiLSQULbs5Y+JyX9Roej6b3e/XURlceOXLVNc1MzkVFdTz6Sh49gxh8/1PX2yckUFRWRnZ3N8uXL8fl8LF26lJKSErxeLwUFBSxYsACfz0dhYSHvvfce6enp+Hw+8vPzuffee0lLSyM/P5/i4mIKCwvJzs6moKCAqqoqPB4Pzz//PKNHj6aqqoqFCxdSVlYGwOrVq8nJyelyrCLSuwSiwIOSJRER6aBvSuvMkiriCTBixAh8Ph+VlZVs3LiRxMREtm/fjtfrJScnh9zcXHbu3ElpaSkff/wxlZWVjBkzhvz8/LY+XC4XW7ZsAWDmzJmsXbuWUaNGsW3bNhYtWsTmzZtZvHgxS5YsYdq0aZSVlZGXl8eBAwc6xHP06FEmTpxIQkICjz/+OLfffnvAroWIBI9AFHhQsiQiIh3EeGJxxcXrWUsO68oM0Pnz54mPj+/xWKy1ABQXF7Nnzx7Wr18PQHV1NYcOHWLLli3MmTOHiIgIUlNTmTFjRrvP33fffQDU1NTw4YcfMmfOnLb3vF4vAG+//Tb79+9vO37u3LkO47vhhhsoKytjwIAB7Ny5kz/6oz9i3759JCQk9MzARSRoRfXpQ2RUlPYsiYhI4CUmp1Ct8uECHDlyhMjISJKTk7HW8swzz5CXl9euzaZNm67aR2xsLAA+n4++fft2uufI5/OxdetW3G73FfuJiYkhJiYGgFtuuYUbb7yRgwcPMnny5GsdloiEgWi3Rw+lFRGRwEtMTtXMkrTtIyosLMQYQ15eHs899xyNjY0AHDx4kNraWqZNm8Yrr7yCz+ejoqKCkpKSTvtLSEggPT2dl19+GWiZsdq9ezcAubm5rFmzpq1tZwlVVVUVzc3NQEsSd+jQIUaMGOHPIYtICIn2eLRnSUREAi8xOYXPdvwnPl8zERHdq14moaWuro6srCwaGxuJiopi/vz5PPLIIwA8+OCDlJaWMmnSJKy1DBw4kA0bNjB79mzeeecdxo0bx0033cTUqVNJTEzstP9169bx8MMP8/jjj9PY2MjcuXPJzMzk6aefpqCggAkTJtDU1MT06dNZu3Ztu8++//77/PVf/zVRUVFERkaydu1a+vfv3+PXRESCU7Tbo2V4IiISeInJqTQ3NVFz5gwJSQOdDkcC6OLMTWciIiJYuXIlK1eu7PDeqlWriIuL4/Tp00yZMoXx48cDLc9GulR6ejpvvvlmh88nJSXx4osvXjW22bNnM3v27C6MQkR6gxi3ZpZERMQBia3lw89VVihZki656667OHv2LA0NDSxbtozU1FSnQxKRMBftdlNz5kyP9a9kSUREOpXYWj78bOXnDBk7zuFoJBRcaZ+SiEhPiXZ7aKgr77H+VeBBREQ6lZA0EGMiVORBRESCVoynZ/csKVkSEZFORUb1IW7AAJUPFxGRoBXdw3uWlCyJiMgV9U1OpbpCyZKIiASnaLeH5sZGmlofZ+BvSpZEROSKEpJTqK7SMjwREQlO0W4PQI/NLilZEhGRK+qbnErtl2do9NY7HYpcwUsvvURaWhoRERGkpaWxbt06p0Pqkri4uKu+f/bsWX75y18GKBoRCVUxntZk6YKSJRERCbAxt9/B3L/530REqnhqMFq3bh0//OEPOXbsGNZajh07xkMPPeS3hMlai8/n80tf10rJkoh0xfAJE/nuYz8jtl+/HulfyZKIiFxRYnIqg28eQ2SUkqVg9Oijj1JXV9fu2IULF3j00Uevu8/S0lLGjBnDokWLmDRpEsePH+fhhx9m8uTJZGRk8NhjjwHw0Ucf8Z3vfAeAjRs34na7aWhooL6+nhEjRnTo9+jRo9x2221kZ2ezbNmytuM1NTXMnDmTSZMmMX78eDZu3AjA0qVL+eyzz8jKyuIv/uIvrthORHq3uH79GTp2PH1iXD3Sv+5+IiIiIaqsrOyajnfVp59+yj/+4z+2zew88cQT9O/fn+bmZmbOnMmePXuYNGkSv//97wH44IMPGDduHNu3b6epqYmpU6d26HPx4sU8/PDDfO973+PZZ59tO+5yuXj11VdJSEjgiy++4NZbb+Xb3/42Tz75JHv37mXXrl0ANDU1ddrOGNOtsYqIXI1mlkRERELUsGHDrul4Vw0fPpxbb7217fVLL73EpEmTmDhxIvv27WP//v1ERUUxcuRIDhw4wEcffcQjjzzC+++/zwcffMDtt9/eoc//+I//4P777wdg/vz5bcettfz4xz9mwoQJzJo1ixMnTlBR0bGoSFfbiYj4k5IlERGREPXEE0/gdrvbHfN4PDzxxBPd6jc2Nrbt66NHj7Jq1Sreeecd9uzZwze/+U3q61sKftx+++288cYb9OnTh1mzZrFlyxa2bNnC9OnTO+23s1mgdevWUVVVxc6dO9m1axcpKSlt/V9POxERf1KyJCIiEqIeeOABnnnmGYYPH44xhuHDh1NUVMQDDzzgt3OcO3eO2NhYEhMTqaio4I033mh7b/r06axevZrbbruNgQMHcvr0aT755BMyMjI69JOTk8MLL7wA0K4ARXV1NcnJyfTp04d3332XY8eOARAfH8/58+e/sp2ISE/SniUREZEQ9t3vfpcf/OAHPdZ/ZmYmEydOJCMjgxEjRpCTk9P23tSpU6moqGibSZowYQLJycmdziD94he/YN68efziF79g9uzZbccfeOABvvWtbzF58mSysrIYPXo0AAMGDCAnJ4dx48Zx55138qMf/ajTdiIiPUnJkoiIiLRJS0tj79697Y79+te/7rSt2+3G6/W2vS4qKrpiv+np6WzdurXt9dKlSwFISkpqd/xS//qv/9ru9ZXaiYj0FC3DExERuQpjzBxjzD5jjM8YM/kq7b5ujPnUGHPYGLM0kDGKiEjPULIkIiJydXuB7wDvX6mBMSYSeBa4ExgL3G+MGRuY8EREpKcoWRIREbkKa+0Ba+2nX9FsCnDYWnvEWtsAvADc3Y1zXu9HpZWuoYj4g/YsiYiIdN9g4Pglr8uBjk9mBYwxDwEPAaSkpFBSUtLu/bi4OMrLy0lMTOzSA1ebm5vbVY3r7Zqbmzl37hzV1dXU1tZ2uL69SU1NTa8e/+V0PdrT9egaJUsiItLrGWPeBlI7eetRa+3GrnTRybFOpzastUVAEcDkyZPtHXfc0e79xsZGysvLOXHiRBdOC/X19bhcri617Q0uXg+Xy0VmZiZ9+vRxOiTHlJSUcPn3V2+m69GerkfXKFkSEZFez1o7q5tdlANDL3k9BDh5PR316dOH9PT0LrcvKSlh4sSJ13OqsKTrISL+pD1LIiIi3bcdGGWMSTfGRANzgdccjklERLpJyZKIiMhVGGPuMcaUA7cBm4wxv2s9PsgY8zqAtbYJKAR+BxwAXrLW7nMqZhER8Q8twxMREbkKa+2rwKudHD8JfOOS168DrwcwNBER6WEmnEtrGmOqgGPd6CIJ+MJP4ThJ4wge4TAG0DiCSSiMYbi1dqDTQQQjP9ynIDS+BwJJ1+MPdC3a0/VoT9ejvU7vVWGdLHWXMWaHtfaKT2sPFRpH8AiHMYDGEUzCYQzSPfoeaE/X4w90LdrT9WhP16NrtGdJRERERESkE0qWREREREREOqFk6eqKnA7ATzSO4BEOYwCNI5iEwxike/Q90J6uxx/oWrSn69GerkcXaM+SiIiIiIhIJzSzJCIiIiIi0gklSyIiIiIiIp1QsvQVjDH/2xjziTFmjzHmVWNMX6djuhbGmK8bYz41xhw2xix1Op5rZYwZaox51xhzwBizzxiz2OmYusMYE2mM+b0x5rdOx3K9jDF9jTHrW/+/OGCMuc3pmK6VMWZJ6/fTXmPMvxljXE7H1BXGmH8wxlQaY/Zecqy/MeYtY8yh1r/7ORmjBE6o/3z3p3C7V/hLONxz/CUc7l3+FKr3QScoWfpqbwHjrLUTgIPAXzkcT5cZYyKBZ4E7gbHA/caYsc5Gdc2agD+31o4BbgUKQnAMl1oMHHA6iG76BfCmtXY0kEmIjccYMxj4U2CytXYcEAnMdTaqLvs18PXLji0F3rHWjgLeaX0tYS5Mfr77U7jdK/wlHO45/hLS9y5/CvH7YMApWfoK1tpia21T68v/BIY4Gc81mgIcttYesdY2AC8Adzsc0zWx1p6y1v5X69fnafnhNtjZqK6PMWYI8E3g752O5XoZYxKA6cCvAKy1Ddbas85GdV2iALcxJgrwACcdjqdLrLXvA2cuO3w38E+tX/8T8EcBDUqcEvI/3/0pnO4V/hIO9xx/CaN7lz+F5H3QCUqWrk0+8IbTQVyDwcDxS16XE8I3D2NMGjAR2OZsJNdtNfCXgM/pQLphBFAF/GPr0o6/N8bEOh3UtbDWngBWAWXAKaDaWlvsbFTdkmKtPQUt/2AEkh2ORwIjrH6++1MY3Cv8JRzuOf4S8vcufwrD+2CPUrIEGGPebl2zefmfuy9p8ygt0/zrnIv0mplOjoVkrXhjTBzwCvBn1tpzTsdzrYwxdwGV1tqdTsfSTVHAJOA5a+1EoJYQW/bVuqfnbiAdGATEGmP+P2ejErlmYfPz3Z9C/V7hL2F0z/GXkL93+ZPug9dGyRJgrZ1lrR3XyZ+NAMaY7wN3AQ/Y0HowVTkw9JLXQwjBaVZjTB9abn7rrLX/7nQ81ykH+LYxppSW5TL/3Rjzf50N6bqUA+XW2ou/sV1Pyw0olMwCjlprq6y1jcC/A19zOKbuqDDG3ADQ+nelw/FIYITFz3d/CpN7hb+Eyz3HX8Lh3uVP4XYf7FFKlr6CMebrwI+Ab1trLzgdzzXaDowyxqQbY6Jp2bz3msMxXRNjjKFljfEBa+1TTsdzvay1f2WtHWKtTaPlv8Nma23I/RbHWvs5cNwYc3ProZnAfgdDuh5lwK3GGE/r99dMQnuj72vA91u//j6w0cFYJHBC/ue7P4XLvcJfwuWe4y9hcu/yp3C7D/aoKKcDCAFrgBjgrZbvJ/7TWrvQ2ZC6xlrbZIwpBH5HS6WTf7DW7nM4rGuVA8wHPjbG7Go99mNr7esOxtTb/RBY1/oPtCPAnzgczzWx1m4zxqwH/ouWpbW/B4qcjaprjDH/BtwBJBljyoHHgCeBl4wxP6DlBjjHuQglUMLk57s/6V4hXyWk713+FMr3QSeY0FpVJiIiIiIiEhhahiciIiIiItIJJUsiIiIiIiKdULIkIiIiIiLSCSVLIiIiIiIinVCyJCIiIiIi0gklSyIiIiIiIp1QsiQiIiIiItIJJUsiIiIiIiKdULIkEmSMMSONMY3GmBWXHX/OGHPeGDPZqdhERER0n5LeRMmSSJCx1h4G/h5YYoxJAjDG/DWQD9xjrd3hZHwiItK76T4lvYmx1jodg4hcxhiTCnwG/BL4BCgC7rfWvuRoYCIiIug+Jb1HlNMBiEhH1trPjTGrgT+n5f/TP9UNSEREgoXuU9JbaBmeSPA6BMQAW621zzodjIiIyGV0n5Kwp2RJJAgZY/478H+ArUCOMSbT4ZBERETa6D4lvYWSJZEgY4yZBGygZfPsHUAZsNLJmERERC7SfUp6EyVLIkHEGDMSeAMoBn5orW0AVgDfMMZMdzQ4ERHp9XSfkt5G1fBEgkRrZaEPafkNXZ611tt6PBLYC3xprf2agyGKiEgvpvuU9EZKlkRERERERDqhZXgiIiIiIiKdULIkIiIiIiLSCSVLIiIiIiIinVCyJCIiIiIi0gklSyIiIiIiIp1QsiQiIiIiItIJJUsiIiIiIiKdULIkIiIiIiLSif8HUZhn/V27/g4AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# consider the above example data again\n", "xi = np.array([0.5, 2.0, 4.0, 5.0, 7.0, 9.0])\n", "yi = np.array([0.5, 0.4, 0.3, 0.1, 0.9, 0.8])\n", "\n", "# Let's set up some space to store all the polynomial coefficients\n", "# there are some redundancies here, and we have assumed we will only \n", "# consider polynomials up to degree N\n", "N = 6\n", "poly_coeffs = np.zeros((N, N))\n", "\n", "for i in range(N):\n", " poly_coeffs[i, :(i+1)] = np.polyfit(xi, yi, i)\n", "\n", "# plot over a couple of different x ranges\n", "x1 = np.linspace(-2., 11., 100)\n", "x2 = np.linspace(0., 9.5, 100)\n", "\n", "# set up figure\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 7))\n", "\n", "for i in range(N):\n", " p = np.poly1d(poly_coeffs[i, :(i+1)])\n", " ax1.plot(x1, p(x1), label='Degree %i' % i)\n", "\n", "# Overlay raw data\n", "plot_raw_data(xi, yi, ax1)\n", "# Add a legend\n", "ax1.legend(loc='best')\n", "ax1.set_title('Extrapolation example - wider interval', fontsize=16)\n", "\n", "# NB. if you set the limits of the x data to numpy.linspace(0., 9.5, 100)\n", "# and replot this will result in you zooming in on the data to better see\n", "# how each polynomial fits the data, but less clearly shows the major\n", "# problem with extrapolation.\n", "\n", "for i in range(N):\n", " p = np.poly1d(poly_coeffs[i, :(i+1)])\n", " ax2.plot(x2, p(x2), label='Degree %i' % i)\n", "\n", "# Overlay raw data\n", "plot_raw_data(xi, yi, ax2)\n", "# Add a legend\n", "ax2.legend(loc='best')\n", "ax2.set_title('Extrapolation example - narrower interval', fontsize=16)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Exercise 1.7: Submarine landslide size in the North Atlantic \n", "\n", "Open the data file [Length-Width.dat](data/Length-Width.dat) (located in the data directory) giving the lengths and widths of submarine landslides in the North Atlantic basin [from [Huhnerbach & Masson, 2004](http://www.sciencedirect.com/science/article/pii/S0025322704002774), Fig. 7]. Fit a linear best fit line using polyfit and try to recreate the image below.\n", "\n", "Hint: You will need to take the log of the data before fitting a line to it. \n", "\n", "![\"Cloud of point data for submarine landslide widths and depths in the North Atlantic, and a correspondong best (linear) curve fit.\"](images/Width-Length.png)\n", "\n", "\n", "Reference: [V. Huhnerbach, D.G. Masson, Landslides in the North Atlantic and its adjacent seas:\n", "an analysis of their morphology, setting and behaviour, Marine Geology 213 (2004) 343 – 362.](http://www.sciencedirect.com/science/article/pii/S0025322704002774)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lagrange polynomial coefficients = [1.0266104 0.37698383]\n", "R squared value calculated from Lagrange polynomial fit to the data in log-log space = 0.5653751967433511\n", "\n", "Linear regression ... slope, intercept, r_value = 1.02661040, 0.37698383, 0.75191435\n", "r_value squared = 0.56537520\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# this solution includes some statistical measures of the fit (R-squared value)\n", "# you can just ignore this.\n", "\n", "import scipy.stats as ss\n", "\n", "file = open(\"data/Length-Width.dat\", 'r')\n", "\n", "xi = []\n", "yi = []\n", "for line in file:\n", " xi.append(float(line.split()[0]))\n", " yi.append(float(line.split()[1]))\n", "xi = np.array(xi)\n", "yi = np.array(yi)\n", "\n", "# set up figure\n", "fig, ax1 = plt.subplots(1, 1, figsize=(7, 7))\n", "# plot the raw data\n", "ax1.loglog(xi, yi, 'ko')\n", "\n", "# fit a linear line to the log of the data using numpy.polyfit\n", "logxi = np.log(xi)\n", "logyi = np.log(yi)\n", "poly_coeffs = np.polyfit(logxi, logyi, 1)\n", "# Construct the corresponding polynomial function from these coefficients\n", "p1 = np.poly1d(poly_coeffs)\n", "# print the polynomial coefficients to compare with regression\n", "print('Lagrange polynomial coefficients = {}'.format(poly_coeffs))\n", "\n", "# calculate and print an R-squared value for this fit using the mathematical\n", "# definition from https://en.wikipedia.org/wiki/Coefficient_of_determination\n", "SS_res = sqr_error(p1, logxi, logyi)\n", "SS_tot = np.sum((np.mean(logyi) - logyi)**2)\n", "r2 = 1. - SS_res/SS_tot\n", "print('R squared value calculated from Lagrange polynomial fit to the data in log-log space = {}\\n'.format(r2))\n", "\n", "# only need two points to plot a linear\n", "x = np.linspace(min(xi), max(xi), 2)\n", "ax1.loglog(x, p1(x), 'b', label='$\\log(y) = $%.3f$\\,\\log(x) + $%.3f' %\n", " (poly_coeffs[0], poly_coeffs[1]))\n", "ax1.legend(loc='best', fontsize=12)\n", "\n", "# check values computed above against scipy's linear regression\n", "slope, intercept, r_value, p_value, std_err = ss.linregress(logxi, logyi)\n", "print('Linear regression ... slope, intercept, r_value = {0:.8f}, {1:.8f}, {2:.8f}'\\\n", " .format(slope, intercept, r_value))\n", "print('r_value squared = {:.8f}'.format(r_value**2))\n", "\n", "\n", "ax1.set_title('Submarine landslide dimensions', fontsize=16)\n", "ax1.set_xlabel('Length [km]', fontsize=16)\n", "ax1.set_ylabel('Width [km]', fontsize=16)\n", "\n", "ax1.text(0.76, 0.05, 'R2 = %.6f' % r2, transform=ax1.transAxes);" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "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": "3.7.7" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": false, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": false, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }