From af006cc563de57b7822c7a66a9f7a8cb42cb1d79 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 17 Nov 2023 07:57:40 +0000 Subject: [PATCH 1/9] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- doc/notebooks/Atom_Grid.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/notebooks/Atom_Grid.ipynb b/doc/notebooks/Atom_Grid.ipynb index 2f6631aff..f725630fa 100644 --- a/doc/notebooks/Atom_Grid.ipynb +++ b/doc/notebooks/Atom_Grid.ipynb @@ -180,7 +180,7 @@ "y_axis = radial_rho\n", "x_axis = radial_grid.points\n", "\n", - "plt.plot(x_axis, y_axis, label='He(1s¹2s¹)', color='black')\n", + "plt.plot(x_axis, y_axis, label='He(1s\u00b92s\u00b9)', color='black')\n", "plt.scatter(x_axis, y_axis, color='red', marker='o')\n", "plt.xlabel(\"r (bohr)\")\n", "plt.ylabel(r\"Radial $\\rho(r)$\")\n", From 7116c505da5c6e81838dd2ceb0bede9271054fd1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marco=20Mart=C3=ADnez=20Gonz=C3=A1lez?= Date: Thu, 7 Dec 2023 16:02:57 -0500 Subject: [PATCH 2/9] Make var names consistent --- doc/notebooks/One_dimensional_grids.ipynb | 665 +++++++++++----------- 1 file changed, 337 insertions(+), 328 deletions(-) diff --git a/doc/notebooks/One_dimensional_grids.ipynb b/doc/notebooks/One_dimensional_grids.ipynb index 2109b97ac..bada47645 100644 --- a/doc/notebooks/One_dimensional_grids.ipynb +++ b/doc/notebooks/One_dimensional_grids.ipynb @@ -1,350 +1,359 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": false - }, - "source": [ - "# One-dimensional (radial) grids\n", - "\n", - "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1,1] interval). These are used to integrate functions numerically:\n", - "\n", - "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n", - "\n", - " The following table shows some of the available quadrature rules and the corresponding grid points and weights.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "ExecuteTime": { - "end_time": "2023-06-19T16:51:32.568341203Z", - "start_time": "2023-06-19T16:51:31.905745917Z" - }, - "collapsed": true - }, - "outputs": [], - "source": [ - "from grid.onedgrid import *\n", - "\n", - "# Select and compare several grid types with 30 points in the interval [-1,1]\n", - "# -------------------------------------\n", - "npoints = 31\n", - "# Gauss-Chebyshev\n", - "gaus_cheb = GaussChebyshev(npoints)\n", - "\n", - "# Gauss-Legendre\n", - "gaus_leg = GaussLegendre(npoints)\n", - "\n", - "# Tanh-Sinh\n", - "tanh_sinh = TanhSinh(npoints)\n", - "\n", - "# Trapezoidal\n", - "trap_lob = Trapezoidal(npoints)\n", - "\n", - "# Simpson\n", - "simp_lob = Simpson(npoints)\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Different quadrature rules have the points located at different positions and thus are appropriate for different problems. A higher point density is usually required where the integrand is more rapidly varying. The following figure shows the points for different quadrature rules supported by Grid." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "# create a list of names and a list of grid objects\n", - "names = ['GaussChebyshev', 'GaussLegendre', 'TanhSinh', 'Trapezoidal', 'Simpson']\n", - "grids = [gaus_cheb, gaus_leg, tanh_sinh, trap_lob, simp_lob]\n", - "\n", - "\n", - "for i in range(len(grids)):\n", - " plt.scatter(grids[i].points, [i + 1] * len(grids[i].points), marker='o') # Switched x and y values\n", - "\n", - "# set the y-ticks to be the names\n", - "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", - "\n", - "# set the labels\n", - "plt.xlabel('Number of Points')\n", - "plt.ylabel('Quadrature Rule')\n", - "\n", - "# show the plot\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The one-dimensional grids can be used to perform integrals in the defined interval and are very accurate even for a small number of points. \n", - "\n", - "As an example, let's find the integral of the function $f(x) = \\sqrt(1-x^2)$ in the interval $[-1,1]$ using the previously defined grids. The exact value of the integral is $\\pi/2$." - ] + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# One-dimensional (radial) grids\n", + "\n", + "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1,1] interval). These are used to integrate functions numerically:\n", + "\n", + "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n", + "\n", + " The following table shows some of the available quadrature rules and the corresponding grid points and weights.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "ExecuteTime": { + "end_time": "2023-06-19T16:51:32.568341203Z", + "start_time": "2023-06-19T16:51:31.905745917Z" }, + "collapsed": true + }, + "outputs": [], + "source": [ + "from grid.onedgrid import *\n", + "\n", + "# Select and compare several grid types with 30 points in the interval [-1,1]\n", + "# -------------------------------------\n", + "npoints = 31\n", + "# Gauss-Chebyshev\n", + "gaus_cheb = GaussChebyshev(npoints)\n", + "\n", + "# Gauss-Legendre\n", + "gaus_leg = GaussLegendre(npoints)\n", + "\n", + "# Tanh-Sinh\n", + "tanh_sinh = TanhSinh(npoints)\n", + "\n", + "# Trapezoidal\n", + "trap_lob = Trapezoidal(npoints)\n", + "\n", + "# Simpson\n", + "simp_lob = Simpson(npoints)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Different quadrature rules have the points located at different positions and thus are appropriate for different problems. A higher point density is usually required where the integrand is more rapidly varying. The following figure shows the points for different quadrature rules supported by Grid." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The integral of sqrt(1-x^2) from -1 to 1 is pi/2 = 1.5707963267948966\n", - "Integral of sqrt(1-x^2) using GaussChebyshev is 1.5707963267948966\n", - "Integral of sqrt(1-x^2) using GaussLegendre is 1.5708227035118671\n", - "Integral of sqrt(1-x^2) using TanhSinh is 1.5706704474237596\n", - "Integral of sqrt(1-x^2) using Trapezoidal is 1.5606957062377849\n", - "Integral of sqrt(1-x^2) using Simpson is 1.5668324581559745\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "# define the function to integrate\n", - "function = lambda x: np.sqrt(1 - x ** 2)\n", - "\n", - "print('The integral of sqrt(1-x^2) from -1 to 1 is pi/2 =', np.pi / 2)\n", - "\n", - "error_relative = []\n", - "\n", - "for i in range(len(grids)):\n", - " # calculate the function values at the grid points\n", - " vals = function(grids[i].points)\n", - " # integrate the function using the grid\n", - " integral = grids[i].integrate(vals)\n", - " print('Integral of sqrt(1-x^2) using', names[i], 'is', integral)\n", - " error_relative.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - "\n", - "# plot the relative error as columns graph\n", - "plt.figure(figsize=(8.5, 5))\n", - "plt.title(r'Relative Error for Different Grids with ' + str(npoints) + ' Points for $\\int_{-1}^1 \\sqrt{1-x^2} dx$')\n", - "plt.bar(names, error_relative)\n", - "plt.ylabel('Relative Error %')\n", - "plt.show()\n", - "\n", - "\n" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# create a list of names and a list of grid objects\n", + "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\", \"Trapezoidal\", \"Simpson\"]\n", + "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh, trap_lob, simp_lob]\n", + "\n", + "\n", + "for i in range(len(onedgrids)):\n", + " plt.scatter(\n", + " onedgrids[i].points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", + " ) \n", + "\n", + "# set the y-ticks to be the names\n", + "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", + "\n", + "# set the labels\n", + "plt.xlabel(\"R\")\n", + "plt.ylabel(\"Quadrature Rule\")\n", + "\n", + "# show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The one-dimensional grids can be used to perform integrals in the defined interval and are very accurate even for a small number of points. \n", + "\n", + "As an example, let's find the integral of the function $f(x) = \\sqrt(1-x^2)$ in the interval $[-1,1]$ using the previously defined grids. The exact value of the integral is $\\pi/2$." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following example shows how the error in the integral converges with the number of points for the different quadrature rules. The function to test is the same as before, $f(x) = \\sqrt(1-x^2)$ and the integral is performed in the interval $[-1,1]$." - ] + "name": "stdout", + "output_type": "stream", + "text": [ + "The integral of sqrt(1-x^2) from -1 to 1 is pi/2 = 1.5707963267948966\n", + "Integral of sqrt(1-x^2) using GaussChebyshev is 1.5707963267948966\n", + "Integral of sqrt(1-x^2) using GaussLegendre is 1.5708227035118671\n", + "Integral of sqrt(1-x^2) using TanhSinh is 1.5706704474237596\n", + "Integral of sqrt(1-x^2) using Trapezoidal is 1.5606957062377849\n", + "Integral of sqrt(1-x^2) using Simpson is 1.5668324581559745\n" + ] }, { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[2.82715972e-14 1.41357986e-14 1.41357986e-14 0.00000000e+00]\n", - " [1.32550164e+00 3.25313217e-01 3.47241509e-02 1.41361473e-02]\n", - " [7.06296872e+01 5.30277668e+01 1.68869830e+01 6.11617195e+00]\n", - " [3.63380228e+01 1.30361218e+01 3.32773329e+00 2.01237879e+00]\n", - " [1.51173637e+01 5.26882153e+00 1.31839796e+00 7.94070592e-01]]\n" - ] - }, - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'Relative Error %')" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "npoints_list = [3,5,11,15]\n", - "error_relative = []\n", - "\n", - "for i in range(len(npoints_list)):\n", - " error_relative.append([])\n", - " grid_list = [GaussChebyshev(npoints_list[i]), GaussLegendre(npoints_list[i]), TanhSinh(npoints_list[i]), Trapezoidal(npoints_list[i]), Simpson(npoints_list[i])]\n", - "\n", - " for j in range(len(grid_list)):\n", - " vals = function(grid_list[j].points)\n", - " integral = grid_list[j].integrate(vals)\n", - " error_relative[-1].append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - " \n", - "error_relative = np.array(error_relative).T\n", - "print(error_relative)\n", - "for i in range(len(names)):\n", - " plt.plot(npoints_list, error_relative[i], label=names[i])\n", - "plt.legend()\n", - "plt.xlabel('Number of Points')\n", - "plt.ylabel('Relative Error %')\n", - " " + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# define the function to integrate\n", + "function = lambda x: np.sqrt(1 - x**2)\n", + "\n", + "print(\"The integral of sqrt(1-x^2) from -1 to 1 is pi/2 =\", np.pi / 2)\n", + "\n", + "relative_error = []\n", + "\n", + "for i in range(len(onedgrids)):\n", + " # calculate the function values at the grid points\n", + " vals = function(onedgrids[i].points)\n", + " # integrate the function using the grid\n", + " integral = onedgrids[i].integrate(vals)\n", + " print(\"Integral of sqrt(1-x^2) using\", names[i], \"is\", integral)\n", + " relative_error.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + "\n", + "# plot the relative error as columns graph\n", + "plt.figure(figsize=(8, 5))\n", + "plt.title(\n", + " r\"Relative Error for Different Grids with \"\n", + " + str(npoints)\n", + " + \" Points for $\\int_{-1}^1 \\sqrt{1-x^2} dx$\"\n", + ")\n", + "plt.bar(names, relative_error)\n", + "plt.ylabel(\"Relative Error %\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example shows how the error in the integral converges with the number of points for the different quadrature rules. The function to test is the same as before, $f(x) = \\sqrt(1-x^2)$ and the integral is performed in the interval $[-1,1]$." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": { - "collapsed": false - }, - "source": [ - "#### Transformation of grids integration intervals\n", - "The $[-1,1]$ interval is too small for being of real use in quantum chemistry, where the integrals are usually performed in the interval $[0,\\infty)$. To solve this issue, Grid supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. The following figure shows the location of the points for different quadrature rules after a Becke transformation:" - ] + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2.82715972e-14 1.41357986e-14 1.41357986e-14 0.00000000e+00]\n", + " [1.32550164e+00 3.25313217e-01 3.47241509e-02 1.41361473e-02]\n", + " [7.06296872e+01 5.30277668e+01 1.68869830e+01 6.11617195e+00]\n", + " [3.63380228e+01 1.30361218e+01 3.32773329e+00 2.01237879e+00]\n", + " [1.51173637e+01 5.26882153e+00 1.31839796e+00 7.94070592e-01]]\n" + ] }, { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "ExecuteTime": { - "end_time": "2023-06-19T16:51:37.054546020Z", - "start_time": "2023-06-19T16:51:37.044961659Z" - }, - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from grid.rtransform import BeckeRTransform\n", - "\n", - "# create a list of names and a list of grid objects\n", - "names = ['GaussChebyshev', 'GaussLegendre', 'TanhSinh']\n", - "grids = [gaus_cheb, gaus_leg, tanh_sinh]\n", - "\n", - "# Becke R-transform (goes from 0 to \\infty) to transform the Gauss-Chebyshev grid\n", - "radial_grid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(gaus_cheb)\n", - "\n", - "# plot the grid\n", - "plt.figure(figsize=(10, 5))\n", - "\n", - "plt.xlim(0, 2500)\n", - "for i in range(len(grids)):\n", - " radial_grid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(grids[i])\n", - " plt.scatter(radial_grid.points, [i + 1] * len(grids[i].points), marker='o') # Switched x and y values\n", - "\n", - "# set the y-ticks to be the names\n", - "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", - "\n", - "# set the labels\n", - "plt.xlabel('R')\n", - "plt.ylabel('Quadrature Rule')\n", - "\n", - "# show the plot\n", - "plt.show()" + "data": { + "text/plain": [ + "Text(0, 0.5, 'Relative Error %')" ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" }, { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is usually more rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). \n", - "\n", - "As en example, let's find the following integral:\n", - "\n", - "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n", - "\n", - "using a one dimensional grid with 20 points and an appropriate transformation. The exact value of the integral is 2." + "data": { + "image/png": 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", + "text/plain": [ + "
" ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npoints_list = [3, 5, 11, 15]\n", + "relative_error = []\n", + "\n", + "for i in range(len(npoints_list)):\n", + " relative_error.append([])\n", + " grid_list = [\n", + " GaussChebyshev(npoints_list[i]),\n", + " GaussLegendre(npoints_list[i]),\n", + " TanhSinh(npoints_list[i]),\n", + " Trapezoidal(npoints_list[i]),\n", + " Simpson(npoints_list[i]),\n", + " ]\n", + "\n", + " for j in range(len(grid_list)):\n", + " vals = function(grid_list[j].points)\n", + " integral = grid_list[j].integrate(vals)\n", + " relative_error[-1].append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + "\n", + "relative_error = np.array(relative_error).T\n", + "print(relative_error)\n", + "for i in range(len(names)):\n", + " plt.plot(npoints_list, relative_error[i], label=names[i])\n", + "plt.legend()\n", + "plt.xlabel(\"Number of Points\")\n", + "plt.ylabel(\"Relative Error %\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "#### Transformation of onedgrids integration intervals\n", + "The $[-1,1]$ interval is too small for being of real use in quantum chemistry, where the integrals are usually performed in the interval $[0,\\infty)$. To solve this issue, Grid supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. The following figure shows the location of the points for different quadrature rules after a Becke transformation:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "ExecuteTime": { + "end_time": "2023-06-19T16:51:37.054546020Z", + "start_time": "2023-06-19T16:51:37.044961659Z" }, + "collapsed": false + }, + "outputs": [ { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Integral of r^2 * exp(-r) from 0 to infinity:1.9999900526117749 should be close to 2.0\n" - ] - } - ], - "source": [ - "# set the radial grid\n", - "one_d_grid = GaussChebyshev(20)\n", - "radial_grid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(one_d_grid)\n", - "\n", - "# calculate the function values at the grid points\n", - "vals = radial_grid.points ** 2 * np.exp(-radial_grid.points)\n", - "\n", - "integral = radial_grid.integrate(vals)\n", - "\n", - "print(f'Integral of r^2 * exp(-r) from 0 to infinity:{integral} should be close to 2.0')" + "data": { + "image/png": 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+ "text/plain": [ + "
" ] + }, + "metadata": {}, + "output_type": "display_data" } - ], - "metadata": { - "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": "3.10.12" + ], + "source": [ + "from grid.rtransform import BeckeRTransform\n", + "\n", + "# create a list of names and a list of grid objects\n", + "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\"]\n", + "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh]\n", + "\n", + "# Becke R-transform (goes from 0 to \\infty) to transform the Gauss-Chebyshev grid\n", + "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(gaus_cheb)\n", + "\n", + "# plot the grid\n", + "plt.figure(figsize=(8, 5))\n", + "\n", + "plt.xlim(0, 2500)\n", + "for i in range(len(onedgrids)):\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(onedgrids[i])\n", + " plt.scatter(\n", + " rgrid.points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", + " ) # Switched x and y values\n", + "\n", + "# set the y-ticks to be the names\n", + "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", + "\n", + "# set the labels\n", + "plt.xlabel(\"R\")\n", + "plt.ylabel(\"Quadrature Rule\")\n", + "\n", + "# show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is usually more rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). \n", + "\n", + "As en example, let's find the following integral:\n", + "\n", + "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n", + "\n", + "using a one dimensional grid with 20 points and an appropriate transformation. The exact value of the integral is 2." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Integral of r^2 * exp(-r) from 0 to infinity:1.9999900526117749 should be close to 2.0\n" + ] } + ], + "source": [ + "# set the radial grid\n", + "oned = GaussChebyshev(20)\n", + "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(one_d_grid)\n", + "\n", + "# calculate the function values at the grid points\n", + "vals = rgrid.points**2 * np.exp(-rgrid.points)\n", + "\n", + "integral = rgrid.integrate(vals)\n", + "\n", + "print(f\"Integral of r^2 * exp(-r) from 0 to infinity:{integral} should be close to 2.0\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 0 + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 } From cc0d8d02ffc8a2f0c583c6d6060dac1edc542a27 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Thu, 7 Dec 2023 21:05:34 +0000 Subject: [PATCH 3/9] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- doc/notebooks/One_dimensional_grids.ipynb | 674 +++++++++++----------- 1 file changed, 337 insertions(+), 337 deletions(-) diff --git a/doc/notebooks/One_dimensional_grids.ipynb b/doc/notebooks/One_dimensional_grids.ipynb index bada47645..fde31ceeb 100644 --- a/doc/notebooks/One_dimensional_grids.ipynb +++ b/doc/notebooks/One_dimensional_grids.ipynb @@ -1,359 +1,359 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": false - }, - "source": [ - "# One-dimensional (radial) grids\n", - "\n", - "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1,1] interval). These are used to integrate functions numerically:\n", - "\n", - "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n", - "\n", - " The following table shows some of the available quadrature rules and the corresponding grid points and weights.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": { - "ExecuteTime": { - "end_time": "2023-06-19T16:51:32.568341203Z", - "start_time": "2023-06-19T16:51:31.905745917Z" + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# One-dimensional (radial) grids\n", + "\n", + "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1,1] interval). These are used to integrate functions numerically:\n", + "\n", + "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n", + "\n", + " The following table shows some of the available quadrature rules and the corresponding grid points and weights.\n" + ] }, - "collapsed": true - }, - "outputs": [], - "source": [ - "from grid.onedgrid import *\n", - "\n", - "# Select and compare several grid types with 30 points in the interval [-1,1]\n", - "# -------------------------------------\n", - "npoints = 31\n", - "# Gauss-Chebyshev\n", - "gaus_cheb = GaussChebyshev(npoints)\n", - "\n", - "# Gauss-Legendre\n", - "gaus_leg = GaussLegendre(npoints)\n", - "\n", - "# Tanh-Sinh\n", - "tanh_sinh = TanhSinh(npoints)\n", - "\n", - "# Trapezoidal\n", - "trap_lob = Trapezoidal(npoints)\n", - "\n", - "# Simpson\n", - "simp_lob = Simpson(npoints)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Different quadrature rules have the points located at different positions and thus are appropriate for different problems. A higher point density is usually required where the integrand is more rapidly varying. The following figure shows the points for different quadrature rules supported by Grid." - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [ { - "data": { - "image/png": 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", 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" + "cell_type": "code", + "execution_count": 60, + "metadata": { + "ExecuteTime": { + "end_time": "2023-06-19T16:51:32.568341203Z", + "start_time": "2023-06-19T16:51:31.905745917Z" + }, + "collapsed": true + }, + "outputs": [], + "source": [ + "from grid.onedgrid import *\n", + "\n", + "# Select and compare several grid types with 30 points in the interval [-1,1]\n", + "# -------------------------------------\n", + "npoints = 31\n", + "# Gauss-Chebyshev\n", + "gaus_cheb = GaussChebyshev(npoints)\n", + "\n", + "# Gauss-Legendre\n", + "gaus_leg = GaussLegendre(npoints)\n", + "\n", + "# Tanh-Sinh\n", + "tanh_sinh = TanhSinh(npoints)\n", + "\n", + "# Trapezoidal\n", + "trap_lob = Trapezoidal(npoints)\n", + "\n", + "# Simpson\n", + "simp_lob = Simpson(npoints)" ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "# create a list of names and a list of grid objects\n", - "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\", \"Trapezoidal\", \"Simpson\"]\n", - "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh, trap_lob, simp_lob]\n", - "\n", - "\n", - "for i in range(len(onedgrids)):\n", - " plt.scatter(\n", - " onedgrids[i].points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", - " ) \n", - "\n", - "# set the y-ticks to be the names\n", - "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", - "\n", - "# set the labels\n", - "plt.xlabel(\"R\")\n", - "plt.ylabel(\"Quadrature Rule\")\n", - "\n", - "# show the plot\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The one-dimensional grids can be used to perform integrals in the defined interval and are very accurate even for a small number of points. \n", - "\n", - "As an example, let's find the integral of the function $f(x) = \\sqrt(1-x^2)$ in the interval $[-1,1]$ using the previously defined grids. The exact value of the integral is $\\pi/2$." - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [ + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "The integral of sqrt(1-x^2) from -1 to 1 is pi/2 = 1.5707963267948966\n", - "Integral of sqrt(1-x^2) using GaussChebyshev is 1.5707963267948966\n", - "Integral of sqrt(1-x^2) using GaussLegendre is 1.5708227035118671\n", - "Integral of sqrt(1-x^2) using TanhSinh is 1.5706704474237596\n", - "Integral of sqrt(1-x^2) using Trapezoidal is 1.5606957062377849\n", - "Integral of sqrt(1-x^2) using Simpson is 1.5668324581559745\n" - ] + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Different quadrature rules have the points located at different positions and thus are appropriate for different problems. A higher point density is usually required where the integrand is more rapidly varying. The following figure shows the points for different quadrature rules supported by Grid." + ] }, { - "data": { - "image/png": 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", - "text/plain": [ - "
" + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# create a list of names and a list of grid objects\n", + "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\", \"Trapezoidal\", \"Simpson\"]\n", + "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh, trap_lob, simp_lob]\n", + "\n", + "\n", + "for i in range(len(onedgrids)):\n", + " plt.scatter(\n", + " onedgrids[i].points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", + " ) \n", + "\n", + "# set the y-ticks to be the names\n", + "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", + "\n", + "# set the labels\n", + "plt.xlabel(\"R\")\n", + "plt.ylabel(\"Quadrature Rule\")\n", + "\n", + "# show the plot\n", + "plt.show()" ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# define the function to integrate\n", - "function = lambda x: np.sqrt(1 - x**2)\n", - "\n", - "print(\"The integral of sqrt(1-x^2) from -1 to 1 is pi/2 =\", np.pi / 2)\n", - "\n", - "relative_error = []\n", - "\n", - "for i in range(len(onedgrids)):\n", - " # calculate the function values at the grid points\n", - " vals = function(onedgrids[i].points)\n", - " # integrate the function using the grid\n", - " integral = onedgrids[i].integrate(vals)\n", - " print(\"Integral of sqrt(1-x^2) using\", names[i], \"is\", integral)\n", - " relative_error.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - "\n", - "# plot the relative error as columns graph\n", - "plt.figure(figsize=(8, 5))\n", - "plt.title(\n", - " r\"Relative Error for Different Grids with \"\n", - " + str(npoints)\n", - " + \" Points for $\\int_{-1}^1 \\sqrt{1-x^2} dx$\"\n", - ")\n", - "plt.bar(names, relative_error)\n", - "plt.ylabel(\"Relative Error %\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following example shows how the error in the integral converges with the number of points for the different quadrature rules. The function to test is the same as before, $f(x) = \\sqrt(1-x^2)$ and the integral is performed in the interval $[-1,1]$." - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [ + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[2.82715972e-14 1.41357986e-14 1.41357986e-14 0.00000000e+00]\n", - " [1.32550164e+00 3.25313217e-01 3.47241509e-02 1.41361473e-02]\n", - " [7.06296872e+01 5.30277668e+01 1.68869830e+01 6.11617195e+00]\n", - " [3.63380228e+01 1.30361218e+01 3.32773329e+00 2.01237879e+00]\n", - " [1.51173637e+01 5.26882153e+00 1.31839796e+00 7.94070592e-01]]\n" - ] + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The one-dimensional grids can be used to perform integrals in the defined interval and are very accurate even for a small number of points. \n", + "\n", + "As an example, let's find the integral of the function $f(x) = \\sqrt(1-x^2)$ in the interval $[-1,1]$ using the previously defined grids. The exact value of the integral is $\\pi/2$." + ] }, { - "data": { - "text/plain": [ - "Text(0, 0.5, 'Relative Error %')" + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The integral of sqrt(1-x^2) from -1 to 1 is pi/2 = 1.5707963267948966\n", + "Integral of sqrt(1-x^2) using GaussChebyshev is 1.5707963267948966\n", + "Integral of sqrt(1-x^2) using GaussLegendre is 1.5708227035118671\n", + "Integral of sqrt(1-x^2) using TanhSinh is 1.5706704474237596\n", + "Integral of sqrt(1-x^2) using Trapezoidal is 1.5606957062377849\n", + "Integral of sqrt(1-x^2) using Simpson is 1.5668324581559745\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# define the function to integrate\n", + "function = lambda x: np.sqrt(1 - x**2)\n", + "\n", + "print(\"The integral of sqrt(1-x^2) from -1 to 1 is pi/2 =\", np.pi / 2)\n", + "\n", + "relative_error = []\n", + "\n", + "for i in range(len(onedgrids)):\n", + " # calculate the function values at the grid points\n", + " vals = function(onedgrids[i].points)\n", + " # integrate the function using the grid\n", + " integral = onedgrids[i].integrate(vals)\n", + " print(\"Integral of sqrt(1-x^2) using\", names[i], \"is\", integral)\n", + " relative_error.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + "\n", + "# plot the relative error as columns graph\n", + "plt.figure(figsize=(8, 5))\n", + "plt.title(\n", + " r\"Relative Error for Different Grids with \"\n", + " + str(npoints)\n", + " + \" Points for $\\int_{-1}^1 \\sqrt{1-x^2} dx$\"\n", + ")\n", + "plt.bar(names, relative_error)\n", + "plt.ylabel(\"Relative Error %\")\n", + "plt.show()" ] - }, - "execution_count": 63, - "metadata": {}, - "output_type": "execute_result" }, { - "data": { - "image/png": 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", - "text/plain": [ - "
" + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example shows how the error in the integral converges with the number of points for the different quadrature rules. The function to test is the same as before, $f(x) = \\sqrt(1-x^2)$ and the integral is performed in the interval $[-1,1]$." ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "npoints_list = [3, 5, 11, 15]\n", - "relative_error = []\n", - "\n", - "for i in range(len(npoints_list)):\n", - " relative_error.append([])\n", - " grid_list = [\n", - " GaussChebyshev(npoints_list[i]),\n", - " GaussLegendre(npoints_list[i]),\n", - " TanhSinh(npoints_list[i]),\n", - " Trapezoidal(npoints_list[i]),\n", - " Simpson(npoints_list[i]),\n", - " ]\n", - "\n", - " for j in range(len(grid_list)):\n", - " vals = function(grid_list[j].points)\n", - " integral = grid_list[j].integrate(vals)\n", - " relative_error[-1].append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - "\n", - "relative_error = np.array(relative_error).T\n", - "print(relative_error)\n", - "for i in range(len(names)):\n", - " plt.plot(npoints_list, relative_error[i], label=names[i])\n", - "plt.legend()\n", - "plt.xlabel(\"Number of Points\")\n", - "plt.ylabel(\"Relative Error %\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": false - }, - "source": [ - "#### Transformation of onedgrids integration intervals\n", - "The $[-1,1]$ interval is too small for being of real use in quantum chemistry, where the integrals are usually performed in the interval $[0,\\infty)$. To solve this issue, Grid supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. The following figure shows the location of the points for different quadrature rules after a Becke transformation:" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": { - "ExecuteTime": { - "end_time": "2023-06-19T16:51:37.054546020Z", - "start_time": "2023-06-19T16:51:37.044961659Z" }, - "collapsed": false - }, - "outputs": [ { - "data": { - "image/png": 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4OO9VCAAAAOCGl69gEhMT4zbNaVwAAAAAvMFhjDG2i0DJkp6eLqfTqbS0NIWGhtouBwAAAJewsb/m0QMWAQAAAMCbCCYAAAAArCOYAAAAALCOYAIAAADAuusOJmfPnvVGHQAAAABKMI+CSU5Ojp5//nlVq1ZNZcqU0cGDByVJ48aN0zvvvOPVAgEAAADc+DwKJi+88ILmz5+vqVOnuj1csWnTpnr77be9VhwAAACAksGjYLJw4UK9+eab6tu3r3x9fV3zmzVrpr1793qtOAAAAAAlg0fB5Ndff1VkZGSu+Tk5OTp//vx1FwUAAACgZPEomDRu3FjffvttrvkfffSRWrRocd1FAQAAAChZSnnyppiYGPXv31+//vqrcnJytGzZMu3bt08LFy7UihUrvF0jAAAAgBucR0dMunXrpqVLl+rLL7+Uw+HQ+PHjtWfPHi1fvlydOnXydo0AAAAAbnD5PmKSlZWlSZMm6bHHHtO6desKoiYAAAAAJUy+j5iUKlVKL7/8srKzswuiHgAAAAAlkEencnXs2FFr1671cikAAAAASiqPLn6/9957NXbsWO3cuVMtW7ZUcHCw2/IHHnjAK8UBAAAAKBkcxhiT3zf5+Fz5QIvD4eA0L1xVenq6nE6n0tLSFBoaarscAAAAXMLG/ppHR0xycnK8XQcAAACAEsyja0wAAAAAwJs8OmLy3HPPXXX5+PHjPSoGAAAAQMnk0TUmLVq0cJs+f/68EhMTVapUKdWtW1dxcXFeKxCFZ+3aterQoYNSU1NVtmzZAluP65zFMSEKDXBIVZpL1VpKEa2ls6lScCUpJFyKuEU6vEk69R+pTBWpZnvJx9e9s5xsKWn91dt4m411AsUd2w0AFCvF5hqT+Pj4XPPS09M1aNAg9ezZ87qLupqUlBRNnjxZX3zxhX755Rc5nU7Vq1dP/fr104ABAxQUFFSg67+Wwtq5v6H854cLr7h33ec7fCTzh+uZQqtKXaZIjf5717fdn0srn5HSj1y5jbfZWCdQ3LHdAADywGvXmISGhuq5557TuHHjvNVlLgcPHlSLFi20atUqvfjii4qPj9fq1av11FNPafny5Vq9enWBrRtSdnZ24d74wFyyrvRk6cMBF3Zydn9+4d9/3NG5tI232VgnUNyx3QAA8sirF7+fOHFCaWlp3uzSzdChQ1WqVClt3bpVvXv3VsOGDdW0aVP9+c9/1hdffKFu3bpJkqZPn66mTZsqODhYERERGjp0qE6dOuXqZ8KECbrpppvc+n7ttddUq1Yt1/TatWvVpk0bBQcHq2zZsrr11luVlJQkSfrhhx/UoUMHhYSEKDQ0VC1bttTWrVvz9BnOnTun0aNHq1q1agoODtYtt9yS62GVb731liIiIhQUFKSePXtq+vTpuY6+LF++XC1btlTp0qVVp04dTZw4UVlZWa7lDodDb7/9tnr27KmgoCDVq1dPn3/uvgPw5ZdfKioqSoGBgerQoYN+/vlnt+Xz589X2bJltWLFCjVq1EgBAQFKSkrK02coGP896/CrZy789VWXOwvxv/NWjrlw6oi35GQX/jqB4o7tBgCQDx6dyjVz5ky3aWOMkpOT9d5776lLly5eKexSx48fdx0pufSBjhc5HA5JF56zMnPmTNWqVUuJiYkaOnSoRo8erTlz5uRpXVlZWerRo4f++te/avHixTp37pw2b97s6r9v375q0aKF5s6dK19fXyUkJMjPzy9PfT/66KP6+eeftWTJElWtWlWffPKJunTpoh07dqhevXr6/vvv9cQTT2jKlCl64IEHtHr16lxHof7973+rX79+mjlzpm6//XYdOHBAjz/+uCQpJibG1W7ixImaOnWqXn75Zc2aNUt9+/ZVUlKSypcvr8OHD6tXr1564oknNGTIEG3dulVPP/10rnozMjI0efJkvf3226pQoYIqV658zc9wqczMTGVmZrqm09PT8/RdXZ6RTh65dpv0Xy+cz1779utY1x8krc/9F9+CXidQ3LHdAADywaNg8uqrr7pN+/j4qFKlSho4cKDGjh3rlcIu9dNPP8kYo/r167vNr1ixos6ePStJGjZsmKZMmaLo6GjX8tq1a+v555/XkCFD8hxM0tPTlZaWpq5du6pu3bqSpIYNG7qWHzp0SP/4xz/UoEEDSbrszvjlHDhwQIsXL9Yvv/yiqlWrSpJGjRqllStXat68eXrxxRc1a9Ys3XvvvRo1apQkKSoqSuvXr9eKFStc/UyaNEljxozRwIEDJUl16tTR888/r9GjR7sFk0GDBqlPnz6S5Op78+bN6tKli+bOnas6dero1VdflcPhUP369bVjxw5NmTLFrebz589rzpw5at68eZ4/w6UmT56siRMn5uk78qpT/yn8vry5TqC4Y7sBAOSDR8EkMTHR23Xk2cWjFhdt3rxZOTk56tu3r+uv8rGxsXrxxRe1e/dupaenKysrS2fPntXp06eveLTlj8qXL69Bgwapc+fO6tSpkzp27KjevXsrPDxckjRy5EgNHjxY7733njp27KgHH3zQFWCuJi4uTsYYRUVFuc3PzMxUhQoVJEn79u3LdQOBNm3auAWTbdu2acuWLZo0aZJrXnZ2ts6ePauMjAzXDQCaNWvmWh4cHKyQkBAdPXpUkrRnzx61bdvW7fts165drpr9/f3d+snLZ7jU2LFjNXLkSNd0enq6IiIiLtvWq8pUKfy+vLlOoLhjuwEA5INH15g89thjOnnyZK75p0+f1mOPPXbdRV1OZGSkHA6H9u7d6za/Tp06ioyMVGBgoCQpKSlJ9913n5o0aaKPP/5Y27Zt0+uvvy7pwl//pQtHeC69S/LFZRfNmzdPGzZsUPv27bV06VJFRUVp48aNki5co7Jr1y7df//9WrNmjRo1aqRPPvnkmp8hJydHvr6+2rZtmxISElyvPXv2aMaMGZIunBZ3afi6tNacnBxNnDjRrY8dO3Zo//79Kl26tKvdpaeXORwO18Xreb1LdGBgoFs9efkMlwoICFBoaKjby3MOKaTqhTv6yHHlNqHVLtyO1Ftqti/8dQLFHdsNACAfPAomCxYs0JkzZ3LNP3PmjBYuXHjdRV1OhQoV1KlTJ82ePVunT5++YrutW7cqKytL06ZNU9u2bRUVFaUjR9zPca5UqZJSUlLcds4TEhJy9dWiRQuNHTtW69evV5MmTfTBBx+4lkVFRempp57SqlWr1KtXL82bN++an6FFixbKzs7W0aNHFRkZ6fYKCwuTJDVo0ECbN2/O9Zn+6Oabb9a+ffty9REZGSkfn7wNaaNGjVxB66JLpz39DAXnvzs39065cJvRP867tE2Xl7z7jAQf38JfJ1Dcsd0AAPIhX8Hk4rUXxhidPHlS6enprldqaqq+/PJLVa5cuaBq1Zw5c5SVlaVWrVpp6dKl2rNnj/bt26f3339fe/fula+vr+rWrausrCzNmjVLBw8e1Hvvvac33njDrZ+77rpLx44d09SpU3XgwAG9/vrr+uqrr1zLExMTNXbsWG3YsEFJSUlatWqVfvzxRzVs2FBnzpzR8OHDtXbtWiUlJen777/Xli1b3K5BkaQdO3a4HVFISEhQVFSU+vbtqwEDBmjZsmVKTEzUli1bNGXKFH355ZeSpBEjRujLL7/U9OnTtX//fv3rX//SV1995XbUYvz48Vq4cKHryM2ePXu0dOlSPfvss3n+Lp944gkdOHBAI0eO1L59+/TBBx9o/vz513xfXj6D1zgu+XmGVpV6L7zw3INGD1z4d2j4ldt4m411AsUd2w0AIK9MPjgcDuPj43PFl6+vr3nhhRfy02W+HTlyxAwfPtzUrl3b+Pn5mTJlypg2bdqYl19+2Zw+fdoYY8z06dNNeHi4CQwMNJ07dzYLFy40kkxqaqqrn7lz55qIiAgTHBxsBgwYYCZNmmRq1qxpjDEmJSXF9OjRw4SHhxt/f39Ts2ZNM378eJOdnW0yMzPNww8/bCIiIoy/v7+pWrWqGT58uDlz5owxxpjY2FijC/fBzPUyxphz586Z8ePHm1q1ahk/Pz8TFhZmevbsabZv3+6q7c033zTVqlUzgYGBpkePHuaFF14wYWFhbt/DypUrTfv27U1gYKAJDQ01bdq0MW+++aZruSTzySefuL3H6XSaefPmuaaXL19uIiMjTUBAgLn99tvNu+++6/Y9zZs3zzidzlxjkJfPcDVpaWlGkkkbE2JMTKgxc2435rNoY+IWGbN+tjE/LDXm4P8Zcz7zwn+3f3Thv9lZuTvLzrp2G2+zsU6guGO7AYBixbW/lpZWaOt0GJPHiw0krVu3TsYY3X333fr4449Vvnx51zJ/f3/VrFnTdacmeM9f//pX7d27V99++63tUrwiPT1dTqdTaWlp13m9CQAAAAqCjf21fN2V684775R04VSniIiIPF/PgPx55ZVX1KlTJwUHB+urr77SggUL8nyrYwAAAKA48uh2wTVr1pR04eF7hw4d0rlz59yW//H2ssi/zZs3a+rUqTp58qTq1KmjmTNnavDgwbbLAgAAAAqMR8Hk2LFjevTRR90uGP+j7Ozs6yqqpPvwww9tlwAAAAAUKo/OxYqOjlZqaqo2btyowMBArVy5UgsWLFC9evX0+eefe7tGAAAAADc4j46YrFmzRp999plat24tHx8f1axZU506dVJoaKgmT56s+++/39t1AgAAALiBeXTE5PTp067nlZQvX17Hjh2TJDVt2lRxcXHeqw4AAABAieBRMKlfv7727dsnSbrpppv0r3/9S7/++qveeOMNhYeHX+PdAAAAAODOo1O5oqOjlZycLEmKiYlR586dtWjRIvn7++fp6eEAAAAA8Ef5esDilWRkZGjv3r2qUaOGKlas6I26cAPjAYsAAABFm439tXyfynX+/HnVqVNHu3fvds0LCgrSzTffTCgBAAAA4JF8BxM/Pz9lZmbK4XAURD0AAAAASiCPLn4fMWKEpkyZoqysLG/XAwAAAKAE8uji902bNumbb77RqlWr1LRpUwUHB7stX7ZsmVeKAwAAAFAyeBRMypYtqz//+c/ergUAAABACeVRMJk3b5636wAAAABQgnl0jQkAAAAAeFOej5i0aNEiz3fiiouL87ggAAAAACVPnoNJjx49XP8+e/as5syZo0aNGqldu3aSpI0bN2rXrl0aOnSo14sEAAAAcGPLczCJiYlx/Xvw4MF68skn9fzzz+dqc/jwYe9VBwAAAKBEcBhjTH7f5HQ6tXXrVtWrV89t/v79+9WqVSulpaV5rUDceNLT0+V0OpWWlqbQ0FDb5QAAAOASNvbXPLr4PTAwUN99912u+d99951Kly593UUBAAAAKFk8ul1wdHS0hgwZom3btqlt27aSLlxj8u6772r8+PFeLRAAAADAjc+jYDJmzBjVqVNHM2bM0AcffCBJatiwoebPn6/evXt7tUAAAAAANz6PrjEBrgfXmAAAABRtxeYaEwAAAADwJo9O5crOztarr76qDz/8UIcOHdK5c+fclv/+++9eKQ4AAABAyeDREZOJEydq+vTp6t27t9LS0jRy5Ej16tVLPj4+mjBhgpdLBAAAAHCj8yiYLFq0SG+99ZZGjRqlUqVKqU+fPnr77bc1fvx4bdy40ds1AgAAALjBeRRMUlJS1LRpU0lSmTJlXA9U7Nq1q7744gvvVQcAAACgRPAomFSvXl3JycmSpMjISK1atUqStGXLFgUEBHivOgAAAAAlgkfBpGfPnvrmm28kSX//+981btw41atXTwMGDNBjjz3m1QIBAAAA3Pi88hyTjRs3av369YqMjNQDDzzgjbpwA+M5JgAAAEWbjf01j24XfKm2bduqbdu23ugKAAAAQAnkUTBZuHDhVZcPGDDAo2IAAAAAlEwencpVrlw5t+nz588rIyND/v7+CgoK4gGLuCpO5QIAACjabOyveXTxe2pqqtvr1KlT2rdvn2677TYtXrzY2zUCAAAAuMF5FEwup169enrppZf097//3VtdAgAAACghvBZMJMnX11dHjhzxZpcAAAAASgCPLn7//PPP3aaNMUpOTtbs2bN16623eqUwAAAAACWHR8GkR48ebtMOh0OVKlXS3XffrWnTpnmjLgAAAAAliEfBJCcnx9t1AAAAACjBrusak99++03p6eneqgUAAABACZXvYHLixAkNGzZMFStWVJUqVVSuXDmFhYVp7NixysjIKIgaAQAAANzg8nUq1++//6527drp119/Vd++fdWwYUMZY7Rnzx7NmjVLX3/9tb777jv98MMP2rRpk5588smCqhsAAADADSRfweS5556Tv7+/Dhw4oCpVquRads8996h///5atWqVZs6c6dVCAQAAANy48hVMPv30U/3rX//KFUokKSwsTFOnTtV9992nmJgYDRw40GtFAgAAALix5esak+TkZDVu3PiKy5s0aSIfHx/FxMRcd2EAAAAASo58BZOKFSvq559/vuLyxMREVa5c+XprAgAAAFDC5CuYdOnSRf/85z917ty5XMsyMzM1btw4denSxWvFAQAAACgZHMYYk9fGv/zyi1q1aqWAgAANGzZMDRo0kCTt3r1bc+bMUWZmprZs2aIaNWoUWMEo/tLT0+V0OpWWlqbQ0FDb5QAAAOASNvbX8nXxe/Xq1bVhwwYNHTpUY8eO1cVM43A41KlTJ82ePZtQAgAAACDf8hVMJKl27dr66quvlJqaqv3790uSIiMjVb58ea8XBwAAAKBkyHcwuahcuXJq06aNN2sBAAAAUELl6+J3AAAAACgIBBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1hFMAAAAAFhHMAEAAABgHcEEAAAAgHUEEwAAAADWEUwAAAAAWEcwAQAAAGAdwQQAAACAdQQTAAAAANYRTAAAAABYRzABAAAAYB3BBAAAAIB1BBMAAAAA1pWyXcCNYtCgQTpx4oQ+/fRTj/uYP3++oqOjdeLECa/V9Uc///yzateurfj4eN10000Fso78aBLzb/kEBKlFdadqVAhW1XKlVT4oQBVDAhQWWlptapeXJG1O/F1HT55V5ZAL83x9HJftLzvH5LmtTcWlTgAAUDDYF7g868EkJSVFkydP1hdffKFffvlFTqdT9erVU79+/TRgwAAFBQXZLlHGGL311lt65513tGvXLpUqVUqRkZHq16+fHn/88SJRY3EW/0ua4n9JyzW/bJCfJOlExnnXvHBnacV0a6QuTcLd2q7cmayJy3crOe3sNdvaVFzqBAAABYN9gSuzeirXwYMH1aJFC61atUovvvii4uPjtXr1aj311FNavny5Vq9ebbM8l/79+ys6Olrdu3dXbGysEhISNG7cOH322WdatWqV7fJuWCcyzruFEklKSTurIe/HaeXOZNe8lTuTNeT9OLcN/EptbSoudQIAgILBvsDVWQ0mQ4cOValSpbR161b17t1bDRs2VNOmTfXnP/9ZX3zxhbp16yZJmj59upo2barg4GBFRERo6NChOnXqlKufCRMm5Do16bXXXlOtWrVc02vXrlWbNm0UHByssmXL6tZbb1VSUpIk6YcfflCHDh0UEhKi0NBQtWzZUlu3bpUkffjhh1q0aJEWL16s//f//p9at26tWrVqqXv37lqzZo06dOjgtt5XXnlF4eHhqlChgoYNG6bz5/+3Y33u3DmNHj1a1apVU3BwsG655RatXbs21/fy6aefKioqSqVLl1anTp10+PBhSRdOxfLx8XHVdtGsWbNUs2ZNGWOUmpqqvn37qlKlSgoMDFS9evU0b948t/YHDx5Uhw4dFBQUpObNm2vDhg1uy9evX6877rhDgYGBioiI0JNPPqnTp09LksaOHau2bdvmqrlZs2aKiYnJNd/bzH//O3H5bmXnGGXnGE1cvts1/2ptbSoudQIAgILBvsC1WQsmx48f16pVqzRs2DAFBwdfto3DceFcOx8fH82cOVM7d+7UggULtGbNGo0ePTrP68rKylKPHj105513avv27dqwYYMef/xxV/99+/ZV9erVtWXLFm3btk1jxoyRn9+F04gWLVqk+vXrq3v37petz+l0uqZjY2N14MABxcbGasGCBZo/f77mz5/vWv7oo4/q+++/15IlS7R9+3Y9+OCD6tKli/bv3+9qk5GRoUmTJmnBggX6/vvvlZ6erocffliSVKtWLXXs2DFX0Jg3b54GDRokh8OhcePGaffu3frqq6+0Z88ezZ07VxUrVnRr/89//lOjRo1SQkKCoqKi1KdPH2VlZUmSduzYoc6dO6tXr17avn27li5dqu+++07Dhw93fVebNm3SgQMHXP3t2rVLO3bsUN++fS/7/WdmZio9Pd3tdT2MpOS0s9qc+Ls2J/6e668OV2prU3GpEwAAFAz2Ba7NWjD56aefZIxR/fr13eZXrFhRZcqUUZkyZfTMM89IkqKjo9WhQwfVrl1bd999t55//nl9+OGHeV5Xenq60tLS1LVrV9WtW1cNGzbUwIEDVaNGDUnSoUOH1LFjRzVo0ED16tXTgw8+qObNm0uS9u/fn6vGKylXrpxmz56tBg0aqGvXrrr//vv1zTffSJIOHDigxYsX66OPPtLtt9+uunXratSoUbrtttvcgsb58+c1e/ZstWvXTi1bttSCBQu0fv16bd68WZI0ePBgLV68WJmZmZIuHO1JSEjQo48+6vosLVq0UKtWrVxB5uKRp4tGjRql+++/X1FRUZo4caKSkpL0008/SZJefvllPfLII4qOjla9evXUvn17zZw5UwsXLtTZs2fVpEkTNWvWTB988IGrv0WLFql169aKioq67PcyefJkOZ1O1ysiIiJP3+e1HD15VkdPXnkDv7StTcWlTgAAUDDYF7g267cLvnjU4qLNmzcrISFBjRs3du18x8bGqlOnTqpWrZpCQkI0YMAAHT9+3HV60bWUL19egwYNUufOndWtWzfNmDFDycn/O4dv5MiRGjx4sDp27KiXXnrJ7WiAMSZXjVfSuHFj+fr6uqbDw8N19OhRSVJcXJyMMYqKinIFrzJlymjdunVu6ytVqpRatWrlmm7QoIHKli2rPXv2SJJ69OihUqVK6ZNPPpEkvfvuu+rQoYPrtLUhQ4ZoyZIluummmzR69GitX78+V53NmjVzq1GSq85t27Zp/vz5bjV27txZOTk5SkxMlHThqMmiRYtc38/ixYuveLREunD6V1pamut18dS061U5pLQqh5TOc1ubikudAACgYLAvcG3WgklkZKQcDof27t3rNr9OnTqKjIxUYGCgJCkpKUn33XefmjRpoo8//ljbtm3T66+/Lkmu6zd8fHxkjPv5eH+8tkO6cLrThg0b1L59ey1dulRRUVHauHGjpAvXqOzatUv333+/1qxZo0aNGrl2/KOiolyh4Founv51kcPhUE5OjiQpJydHvr6+2rZtmxISElyvPXv2aMaMGbned6mL8/z9/dW/f3/NmzdP586d0wcffKDHHnvM1e7ee+9VUlKSoqOjdeTIEf3pT3/SqFGjrljnxX7/WOff/vY3txp/+OEH7d+/X3Xr1pUkPfLII/rxxx8VFxen9evX6/Dhw67TzS4nICBAoaGhbq/r4dCFu1e0qV1ebWqXV7iztK4UHf/Y1qbiUicAACgY7Atcm7VgUqFCBXXq1EmzZ8++6pGPrVu3KisrS9OmTVPbtm0VFRWlI0eOuLWpVKmSUlJS3MJJQkJCrr5atGihsWPHav369WrSpInb6UhRUVF66qmntGrVKvXq1ct1etXFnfDPPvssV3/GGKWl5b7N7eW0aNFC2dnZOnr0qCIjI91eYWFhrnZZWVluF7fv27dPJ06cUIMGDVzzBg8erNWrV2vOnDk6f/68evXqlev7GDRokN5//3299tprevPNN/NUoyTdfPPN2rVrV64aIyMj5e/vL0mqXr267rjjDi1atEiLFi1Sx44dVaVKlTyv43pc3JhjujWSr49Dvj4OxXRr5LbsSm1tKi51AgCAgsG+wLVZPZVrzpw5ysrKUqtWrbR06VLt2bNH+/bt0/vvv6+9e/fK19dXdevWVVZWlmbNmqWDBw/qvffe0xtvvOHWz1133aVjx45p6tSpOnDggF5//XV99dVXruWJiYkaO3asNmzYoKSkJK1atUo//vijGjZsqDNnzmj48OFau3atkpKS9P3332vLli1q2LChJKl379566KGH1KdPH02ePFlbt25VUlKSVqxYoY4dOyo2NjZPnzUqKkp9+/bVgAEDtGzZMiUmJmrLli2aMmWKvvzyS1c7Pz8/jRgxQps2bVJcXJweffRRtW3bVm3atHG1adiwodq2batnnnlGffr0cR1dkqTx48frs88+008//aRdu3ZpxYoVrs+SF88884w2bNigYcOGKSEhQfv379fnn3+uESNGuLXr27evlixZoo8++kj9+vXLc//5UTbIz/Usk4vCnKU1t9/Nbvf57tIkXHP73awwZ+lrtrWpuNQJAAAKBvsC12AsO3LkiBk+fLipXbu28fPzM2XKlDFt2rQxL7/8sjl9+rQxxpjp06eb8PBwExgYaDp37mwWLlxoJJnU1FRXP3PnzjUREREmODjYDBgwwEyaNMnUrFnTGGNMSkqK6dGjhwkPDzf+/v6mZs2aZvz48SY7O9tkZmaahx9+2ERERBh/f39TtWpVM3z4cHPmzBlX39nZ2Wbu3LmmdevWJigoyISGhpqWLVuaGTNmmIyMDGOMMQMHDjTdu3d3+2x///vfzZ133umaPnfunBk/frypVauW8fPzM2FhYaZnz55m+/btxhhj5s2bZ5xOp/n4449NnTp1jL+/v7n77rvNzz//nOt7e+edd4wks3nzZrf5zz//vGnYsKEJDAw05cuXN927dzcHDx40xhiTmJhoJJn4+HhX+9TUVCPJxMbGuuZt3rzZdOrUyZQpU8YEBwebZs2amUmTJrmtJzU11QQEBJigoCBz8uTJKw/wZaSlpRlJJiL6Q1PzmRWmx6xvzZMfxJmXvtpt3lx3wCyL+8Ws/+k3k5WdY7Kyc8z6n34zn8b/b96V5KetTcWlTgAAUDCKw77Axf21tLS0QlunwxhTcm+WXIxNmjRJS5Ys0Y4dO2yXkm/p6elyOp1KS0u77utNAAAA4H029tes35UL+XPq1Clt2bJFs2bN0pNPPmm7HAAAAMArCCbFzPDhw3XbbbfpzjvvdLsbFwAAAFCccSoXCh2ncgEAABRtnMoFAAAAoEQimAAAAACwjmACAAAAwDqCCQAAAADrCCYAAAAArCOYAAAAALCOYAIAAADAulK2C0DJc/HROenp6ZYrAQAAwOVc3E8rzEceEkxQ6I4fPy5JioiIsFwJAAAArub48eNyOp2Fsi6CCQpd+fLlJUmHDh0qtB867ElPT1dERIQOHz5caE+OhT2Md8nCeJcsjHfJkpaWpho1arj22woDwQSFzsfnwqVNTqeT/7GVIKGhoYx3CcJ4lyyMd8nCeJcsF/fbCmVdhbYmAAAAALgCggkAAAAA6wgmKHQBAQGKiYlRQECA7VJQCBjvkoXxLlkY75KF8S5ZbIy3wxTmPcAAAAAA4DI4YgIAAADAOoIJAAAAAOsIJgAAAACsI5gAAAAAsI5ggkI3Z84c1a5dW6VLl1bLli317bff2i4J+TRhwgQ5HA63V1hYmGu5MUYTJkxQ1apVFRgYqLvuuku7du1y6yMzM1MjRoxQxYoVFRwcrAceeEC//PJLYX8UXMb//d//qVu3bqpataocDoc+/fRTt+XeGt/U1FT1799fTqdTTqdT/fv314kTJwr40+FS1xrvQYMG5dre27Zt69aG8S4+Jk+erNatWyskJESVK1dWjx49tG/fPrc2bOM3jryMd1HaxgkmKFRLly5VdHS0/vnPfyo+Pl6333677r33Xh06dMh2acinxo0bKzk52fXasWOHa9nUqVM1ffp0zZ49W1u2bFFYWJg6deqkkydPutpER0frk08+0ZIlS/Tdd9/p1KlT6tq1q7Kzs218HPzB6dOn1bx5c82ePfuyy701vo888ogSEhK0cuVKrVy5UgkJCerfv3+Bfz64u9Z4S1KXLl3ctvcvv/zSbTnjXXysW7dOw4YN08aNG/X1118rKytL99xzj06fPu1qwzZ+48jLeEtFaBs3QCFq06aNeeKJJ9zmNWjQwIwZM8ZSRfBETEyMad68+WWX5eTkmLCwMPPSSy+55p09e9Y4nU7zxhtvGGOMOXHihPHz8zNLlixxtfn111+Nj4+PWblyZYHWjvyRZD755BPXtLfGd/fu3UaS2bhxo6vNhg0bjCSzd+/eAv5UuJJLx9sYYwYOHGi6d+9+xfcw3sXb0aNHjSSzbt06Ywzb+I3u0vE2pmht4xwxQaE5d+6ctm3bpnvuucdt/j333KP169dbqgqe2r9/v6pWraratWvr4Ycf1sGDByVJiYmJSklJcRvngIAA3Xnnna5x3rZtm86fP+/WpmrVqmrSpAm/hSLOW+O7YcMGOZ1O3XLLLa42bdu2ldPp5DdQBK1du1aVK1dWVFSU/vrXv+ro0aOuZYx38ZaWliZJKl++vCS28RvdpeN9UVHZxgkmKDS//fabsrOzVaVKFbf5VapUUUpKiqWq4IlbbrlFCxcu1L///W+99dZbSklJUfv27XX8+HHXWF5tnFNSUuTv769y5cpdsQ2KJm+Nb0pKiipXrpyr/8qVK/MbKGLuvfdeLVq0SGvWrNG0adO0ZcsW3X333crMzJTEeBdnxhiNHDlSt912m5o0aSKJbfxGdrnxlorWNl7Kkw8GXA+Hw+E2bYzJNQ9F27333uv6d9OmTdWuXTvVrVtXCxYscF0w58k481soPrwxvpdrz2+g6HnooYdc/27SpIlatWqlmjVr6osvvlCvXr2u+D7Gu+gbPny4tm/fru+++y7XMrbxG8+VxrsobeMcMUGhqVixonx9fXMl56NHj+b6ywyKl+DgYDVt2lT79+933Z3rauMcFhamc+fOKTU19YptUDR5a3zDwsL0n//8J1f/x44d4zdQxIWHh6tmzZrav3+/JMa7uBoxYoQ+//xzxcbGqnr16q75bOM3piuN9+XY3MYJJig0/v7+atmypb7++mu3+V9//bXat29vqSp4Q2Zmpvbs2aPw8HDVrl1bYWFhbuN87tw5rVu3zjXOLVu2lJ+fn1ub5ORk7dy5k99CEeet8W3Xrp3S0tK0efNmV5tNmzYpLS2N30ARd/z4cR0+fFjh4eGSGO/ixhij4cOHa9myZVqzZo1q167ttpxt/MZyrfG+HKvbeJ4vkwe8YMmSJcbPz8+88847Zvfu3SY6OtoEBwebn3/+2XZpyIenn37arF271hw8eNBs3LjRdO3a1YSEhLjG8aWXXjJOp9MsW7bM7Nixw/Tp08eEh4eb9PR0Vx9PPPGEqV69ulm9erWJi4szd999t2nevLnJysqy9bHwXydPnjTx8fEmPj7eSDLTp0838fHxJikpyRjjvfHt0qWLadasmdmwYYPZsGGDadq0qenatWuhf96S7mrjffLkSfP000+b9evXm8TERBMbG2vatWtnqlWrxngXU0OGDDFOp9OsXbvWJCcnu14ZGRmuNmzjN45rjXdR28YJJih0r7/+uqlZs6bx9/c3N998s9st61A8PPTQQyY8PNz4+fmZqlWrml69epldu3a5lufk5JiYmBgTFhZmAgICzB133GF27Njh1seZM2fM8OHDTfny5U1gYKDp2rWrOXToUGF/FFxGbGyskZTrNXDgQGOM98b3+PHjpm/fviYkJMSEhISYvn37mtTU1EL6lLjoauOdkZFh7rnnHlOpUiXj5+dnatSoYQYOHJhrLBnv4uNyYy3JzJs3z9WGbfzGca3xLmrbuOO/RQMAAACANVxjAgAAAMA6ggkAAAAA6wgmAAAAAKwjmAAAAACwjmACAAAAwDqCCQAAAADrCCYAAAAArCOYAAAAALCOYAIAgIcGDRokh8Mhh8OhUqVKqUaNGhoyZIhSU1NtlwYAxQ7BBACA69ClSxclJyfr559/1ttvv63ly5dr6NChtssCgGKnlO0CAAAozgICAhQWFiZJql69uh566CHNnz/fblEAUAxxxAQAAC85ePCgVq5cKT8/P9ulAECxwxETAACuw4oVK1SmTBllZ2fr7NmzkqTp06dbrgoAih+CCQAA16FDhw6aO3euMjIy9Pbbb+vHH3/UiBEjbJcFAMUOp3IBAHAdgoODFRkZqWbNmmnmzJnKzMzUxIkTbZcFAMUOwQQAAC+KiYnRK6+8oiNHjtguBQCKFYIJAABedNddd6lx48Z68cUXbZcCAMUKwQQAAC8bOXKk3nrrLR0+fNh2KQBQbDiMMcZ2EQAAAABKNo6YAAAAALCOYAIAAADAOoIJAAAAAOsIJgAAAACsI5gAAAAAsI5gAgAAAMA6ggkAAAAA6wgmAAAAAKwjmAAAAACwjmACAAAAwDqCCQAAAADrCCYAAAAArPv/z7oChnJTGNgAAAAASUVORK5CYII=", - "text/plain": [ - "
" + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[2.82715972e-14 1.41357986e-14 1.41357986e-14 0.00000000e+00]\n", + " [1.32550164e+00 3.25313217e-01 3.47241509e-02 1.41361473e-02]\n", + " [7.06296872e+01 5.30277668e+01 1.68869830e+01 6.11617195e+00]\n", + " [3.63380228e+01 1.30361218e+01 3.32773329e+00 2.01237879e+00]\n", + " [1.51173637e+01 5.26882153e+00 1.31839796e+00 7.94070592e-01]]\n" + ] + }, + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Relative Error %')" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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q3r17TZZPnDhRrVmzpmpnZ6eWLVtWff7559XIyEhVVVU1KipKBdT//vvPuP3169dVQN22bZtx2d69e9X27durjo6OqoODg1q3bl110qRJJs9z/fp11cbGRrW3t1eTkpLu/z9YffD3aH5+fyuqqu2Mbxs3bqRjx46cOHEix+AnVVWZMGECX3zxBdevX6dp06bMnz+fwMDAPO8/MTERFxcXEhISiuSUE0DE1Qj6/dmPWxm36ODTgelB09EpZnEQTAhRiqSmphIVFYWfnx+2trZaxxFFZNKkSaxatco4wNicPeh7ND+/vzX/DduhQ4dcR3FD1uCjkJAQLl68SGpqKjt27MhXkdFKzXI1mdN2DpY6SzbGbGRa2DSZJVgIIUShunnzJmFhYcydO5dhw4ZpHadIaV5mSqpmns2Y3GoyACsiVrAkfMlDHiGEEEI8uqFDh9KqVSuCgoJMPsVUGkiZKUSd/DrxXuP3AJi9fza/nflN40RCCCFKqqVLl5KWlsbq1atN5rQpDaTMFLI+tfvQt3ZfAMb/PZ5d53dpG0gIIYQoYaTMFIF3Gr3DM/7PkKlmMmL7CI5eOap1JCGEEKLEkDJTBHSKjoktJtLcszkpmSkM2TKEs4lntY4lhBBClAhSZoqIlYUVs9vOpmbZmlxLvcbATQO5knJF61hCCCFEsSdlpgg5WDmwoN0CKjlW4tzNcwzePJhbGfefqlsIIYQQDydlpoiVtyvPovaLKGtblohrEbyz7R0y9BkPf6AQQghRQLZv346iKNy4cUPrKAVCyowGfJx9mP/0fOws7fjn4j98tPsjDKpB61hCCGFW4uLiePvtt6latSq2tra4u7vTqlUrFi1aRHJystbxSlwhKM4stQ5QWgWWD2RWm1m8teUtfo/8HTc7N0Y0HqF1LCGEMAuRkZG0bNkSV1dXJk+eTJ06dcjMzOTkyZN88803eHl58b///U/rmCWWXq9HURR0uuJxzKN4pCyhWlVsxYSWEwBYEr6Eb8O/1TiREEKYh8GDB2Npacm+ffvo3r07NWvWpE6dOrz44ov8/vvvPPfccwDMmjWLOnXq4ODggLe3N4MHD+bmzZvG/YSEhFC/fn2Tfc+ZMwdfX1/j/e3bt9OkSRMcHBxwdXWlZcuWxMTEAHDo0CHatm2Lk5MTzs7ONGrUiH379uXpNaSnpzNq1CgqVqyIg4MDTZs2Zfv27SbbfPnll3h7e2Nvb88LL7zArFmzcHV1Ndlm3bp1NGrUCFtbW/z9/ZkwYQKZmZnG9Yqi8NVXX/HCCy9gb29PtWrV+O0300la//jjDwICArCzs6Nt27ZER0ebrF+6dCmurq6sX7+eWrVqYWNjQ0xMTJ5egzmQMqOx/1X5H8MbDgdg+r7pbIja8OAHCCHE41BVSL9V9Ld8XJ/u6tWrbNy4kSFDhuDg4JDrNoqiAKDT6fj88885evQoy5YtY+vWrYwaNSrPz5WZmUmXLl0ICgri8OHD/PPPP7zxxhvG/ffu3ZtKlSoRFhbG/v37ef/997GyssrTvvv168fff//NqlWrOHz4MN26dSM4OJhTp04B8PfffzNo0CDefvttDh48SPv27Zk0aZLJPv78809efvllhg0bxrFjx/jiiy9YunRpju0mTJhA9+7dOXz4MJ07d6Z3795cu3YNgNjYWLp27Urnzp05ePAg/fv35/3338+RNzk5mSlTpvDVV18RHh6Om5vbQ1+DuZDTTGbgtcDXuJxymRURK/hg1weUsS1DM89mWscSQpREGckw2avon/eDC2CdezG51+nTp1FVlerVq5ssL1++PKmpqQAMGTKEqVOnMnz4cON6Pz8/Jk6cyJtvvsmCBQvy9FyJiYkkJCTw7LPPUqVKFQBq1qxpXH/27Fnee+89atSoAUC1atXytN8zZ86wcuVKzp07h5dX1vs9cuRIQkNDWbJkCZMnT2bu3Ll06tSJkSNHAhAQEMDu3btZv369cT+TJk3i/fff59VXXwXA39+fiRMnMmrUKMaPH2/crm/fvvTq1QvAuO+9e/cSHBzMwoUL8ff3Z/bs2SiKQvXq1Tly5AhTp041yZyRkcGCBQuoV69enl+DuZAyYwYURWHUE6O4knKFP6P/ZPi24SwNXkqNsjW0jiaEEJq5c3Tkjr1792IwGOjduzdpaWkAbNu2jcmTJ3Ps2DESExPJzMwkNTWVW7du3feoTnZly5alb9++dOzYkfbt29OuXTu6d++Op6cnACNGjKB///589913tGvXjm7duhlLz4McOHAAVVUJCAgwWZ6Wlka5cuUAOHHiBC+88ILJ+iZNmpiUmf379xMWFmZyJEav15OamkpycjL29vYA1K1b17jewcEBJycn4uPjAYiIiKBZs2Ym72fz5s1zZLa2tjbZT15eg7mQMmMmdIqOya0mcy31GmFxYby5+U2+6/QdlZwqaR1NCFGSWNlnHSXR4nnzqGrVqiiKwvHjx02W+/v7A2BnZwdATEwMnTt3ZtCgQUycOJGyZcuya9cuXn/9dTIysqa80Ol0qPec4rqz7o4lS5YwbNgwQkNDWb16NR9++CGbNm2iWbNmhISE8NJLL/H777+zYcMGxo8fz6pVq3KUkHsZDAYsLCzYv39/jos+Ojo6AqCqao7Cdm9Wg8HAhAkT6Nq1a47nsLW1NX5976kvRVEwGAy57vN+7OzsTPLk5TWYCykzZsTawprP2n5G39C+nLx+kkGbB/Ftp28pa1tW62hCiJJCUfJ8ukcr5cqVo3379sybN4+33nrrvkdY9u3bR2ZmJjNnzjR+6mbNmjUm21SoUIG4uDiT4nDw4MEc+2rQoAENGjRgzJgxNG/enO+//55mzbJO9wcEBBAQEMA777xDr169WLJkyUPLTIMGDdDr9cTHx/Pkk0/muk2NGjXYu3dvjteUXcOGDTlx4gRVq1Z94PM9SK1atfjll19Mlv37778PfVxeXoO5kAHAZsbJ2omF7Rbi6eBJTGIMQ7cMJTlD+/kUhBCiKC1YsIDMzEwaN27M6tWriYiI4MSJEyxfvpzjx49jYWFBlSpVyMzMZO7cuURGRvLdd9+xaNEik/20adOGy5cvM23aNM6cOcP8+fPZsOHuBy2ioqIYM2YM//zzDzExMWzcuJGTJ09Ss2ZNUlJSGDp0KNu3bycmJoa///6bsLAwkzE1AEeOHOHgwYMmt4CAAHr37k2fPn34+eefiYqKIiwsjKlTp/LHH38A8NZbb/HHH38wa9YsTp06xRdffMGGDRtMjo6MGzeOb7/9lpCQEMLDw4mIiDAePcqrQYMGcebMGUaMGMGJEyf4/vvvWbp06UMfl5fXYDbUEi4hIUEF1ISEBK2j5MuZG2fUlitbqoFLA9U3N72ppuvTtY4khChmUlJS1GPHjqkpKSlaR3kkFy5cUIcOHar6+fmpVlZWqqOjo9qkSRN1+vTp6q1bt1RVVdVZs2apnp6eqp2dndqxY0f122+/VQH1+vXrxv0sXLhQ9fb2Vh0cHNQ+ffqokyZNUn18fFRVVdW4uDi1S5cuqqenp2ptba36+Pio48aNU/V6vZqWlqb27NlT9fb2Vq2trVUvLy916NChxvdz27ZtKpDrTVVVNT09XR03bpzq6+urWllZqR4eHuoLL7ygHj582Jht8eLFasWKFVU7Ozu1S5cu6ieffKJ6eHiYvA+hoaFqixYtVDs7O9XZ2Vlt0qSJunjxYuN6QF27dq3JY1xcXNQlS5YY769bt06tWrWqamNjoz755JPqN998Y/I+LVmyRHVxccnx/yAvr+FxPOh7ND+/vxVVzcfn5YqhxMREXFxcSEhIwNnZWes4+XIw/iADNg4gVZ9Kl6pd+LjFxznOrwohxP2kpqYSFRWFn5+fyfgKYb4GDBjA8ePH+euvv7SOUiQe9D2an9/fcprJjNV3q8/0oOnoFB2/nP6Fuf/N1TqSEEKIAjRjxgwOHTrE6dOnmTt3LsuWLTN+DFvknZQZM9fGuw3jmo0D4MsjX7Lq+CqNEwkhhCgoe/fupX379tSpU4dFixbx+eef079/f61jFTvyaaZi4MWAF7mccpn5B+czec9kytuVp51PO61jCSGEeEz3fvpKPBo5MlNMDKw7kG4B3VBRGb1zNPvi8nZtECGEEKKkkzJTTCiKwtimY3nK+ynSDekM2zqMk9dPah1LCCGE0JyUmWLEQmfB1NZTaeDWgKSMJN7c/CZxt+K0jiWEEEJoSspMMWNracvcp+ZSxaUK8cnxDNw0kIS0BK1jCSGEEJqRMlMMudi4sKj9Itzs3YhMiOStrW+RmpmqdSwhhBBCE1JmiikPBw8WtVuEk5UT/8X/x6ido8g0ZGodSwghhChyUmaKsWplqvH5U59jrbNmW+w2Ju+ZnOerowohRGmlKEqOCy/mV0hICPXr18/XY3x9fZkzZ85jPa/InZSZYq6xR2Omtp6KgsIPJ3/gi8NfaB1JCCEemaIoD7z17du3SHL89NNPNG3aFBcXF5ycnKhduzbvvvuucf3IkSPZsmVLkWQRDydlpgRo59OOD5p+AMD8g/P56eRPGicSQohHc/HiReNtzpw5ODs7myz77LPPCj3D5s2b6dmzJ//3f//H3r172b9/P5MmTSI9Pd24jaOjI+XKlSv0LCJvpMyUED1r9GRAnQEAfPzvx2w7u03jREIIkX8eHh7Gm4uLC4qiGO9bWVkxaNAgKlWqhL29PXXq1GHlypUmj2/Tpg3Dhg1j1KhRlC1bFg8PD0JCQnI8z5UrV3jhhRewt7enWrVq/Pbbb8Z169evp1WrVrz33ntUr16dgIAAunTpwty5d6+Pd+9ppr59+9KlSxdmzJiBp6cn5cqVY8iQIWRkZJg8b3JyMq+99hpOTk5UrlyZxYsXF8wbV8pJmSlB3mrwFi9UfQGDamDUzlEcjD+odSQhhJlRVZXkjOQivxXEeL7U1FQaNWrE+vXrOXr0KG+88QavvPIKe/bsMdlu2bJlODg4sGfPHqZNm8bHH3/Mpk2bTLaZMGEC3bt35/Dhw3Tu3JnevXtz7do1IKtQhYeHc/To0Xzl27ZtG2fOnGHbtm0sW7aMpUuXsnTpUpNtZs6cSePGjfnvv/8YPHgwb775JsePH8//myFMyLWZShBFURjXfBxXU6+y89xOhm4dyredvsXfxV/raEIIM5GSmULT75sW+fPueWkP9lb2j7WPihUrMnLkSOP9t956i9DQUH744QeaNr37murWrcv48eMBqFatGvPmzWPLli20b9/euE3fvn3p1asXAJMnT2bu3Lns3buX4OBg3nrrLf766y/q1KmDj48PzZo1o0OHDvTu3RsbG5v75itTpgzz5s3DwsKCGjVq8Mwzz7BlyxYGDBhg3KZz584MHjwYgNGjRzN79my2b99OjRo1Huu9Ke3kyEwJY6mzZHrr6dQpX4eEtAQGbRpEfHK81rGEEOKx6fV6Jk2aRN26dSlXrhyOjo5s3LiRs2fPmmxXt25dk/uenp7Ex8ffdxsHBwecnJyM2zg4OPD7779z+vRpPvzwQxwdHXn33Xdp0qQJycnJ981Xu3ZtLCws8vy8d06h3buNyD85MlMC2VvZM//p+fTZ0IfoxGgGbR7E0uClOFs7ax1NCKExO0s79ry05+EbFsLzPq6ZM2cye/Zs5syZQ506dXBwcGD48OEmA3MBrKysTO4rioLBYMj3NlWqVKFKlSr079+fsWPHEhAQwOrVq+nXr1+u+QrqeUX+SZkpocrYlmFhu4W8suEVTl0/xfBtw1nUbhHWFtZaRxNCaEhRlMc+3aOVv/76i+eff56XX34ZAIPBwKlTp6hZs2ahP7evry/29vbcunWr0J9L5J/mp5nOnz/Pyy+/TLly5bC3t6d+/frs37/fuF5VVUJCQvDy8sLOzo42bdoQHh6uYeLio5JTJRa2W4iDlQNhcWGM+WsMBlX+AhBCFE9Vq1Zl06ZN7N69m4iICAYOHEhcXMFfbDckJIRRo0axfft2oqKi+O+//3jttdfIyMgwGXcjzIemZeb69eu0bNkSKysrNmzYwLFjx5g5cyaurq7GbaZNm8asWbOYN28eYWFheHh40L59e5KSkrQLXozUKFuDz9p+hqXOko0xG5m6d6rMEiyEKJY++ugjGjZsSMeOHWnTpg0eHh506dKlwJ8nKCiIyMhI+vTpQ40aNejUqRNxcXFs3LiR6tWrF/jzicenqBr+Znv//ff5+++/+euvv3Jdr6oqXl5eDB8+nNGjRwOQlpaGu7s7U6dOZeDAgTkek5aWRlpamvF+YmIi3t7eJCQk4OxceseMbIjawKidowAY3nA4r9d5XeNEQojClpqaSlRUFH5+ftja2modR4gcHvQ9mpiYiIuLS55+f2t6ZOa3336jcePGdOvWDTc3Nxo0aMCXX35pXB8VFUVcXBwdOnQwLrOxsSEoKIjdu3fnus8pU6bg4uJivHl7exf66ygOOvl1YtQTWWVmzoE5/Hbmt4c8QgghhCgeNC0zkZGRLFy4kGrVqvHnn38yaNAghg0bxrfffgtgPBfq7u5u8jh3d/f7nicdM2YMCQkJxltsbGzhvohi5JVar9CvdtYo/PF/j2fX+V0aJxJCCCEen6afZjIYDDRu3JjJkycD0KBBA8LDw1m4cCF9+vQxbqcoisnjVFXNsewOGxubB05qVNoNbzSc+JR4fo/8nRHbR/BNx28ILB+odSwhhBDikWl6ZMbT05NatWqZLKtZs6ZxAiQPDw+AHEdh4uPjcxytEXmjU3RMbDGR5p7NSclMYciWIcQkxmgdSwghhHhkmpaZli1bcuLECZNlJ0+exMfHBwA/Pz88PDxMrqmRnp7Ojh07aNGiRZFmLUmsLKyY3XY2NcvW5FrqNQZuGsiVlCtaxxJCCCEeiaZl5p133uHff/9l8uTJnD59mu+//57FixczZMgQIOv00vDhw5k8eTJr167l6NGj9O3bF3t7e1566SUtoxd7DlYOLGi3gEqOlTh/8zyDNw/mVoZMBiWEEKL40bTMPPHEE6xdu5aVK1cSGBjIxIkTmTNnDr179zZuM2rUKIYPH87gwYNp3Lgx58+fZ+PGjTg5OWmYvGQob1eeL9p/QVnbskRci+Cdbe+Qoc94+AOFEEIIM6LpPDNFIT+fUy+tjl45ymt/vkZKZgrP+D/D5FaT0SmaTw4thHhMMs+MMHclYp4ZYR4Cywcyq80sLBVLfo/8ndn7Z2sdSQghhMgzKTMCgFYVW/Fxy48BWBq+lG/Dv9U4kRBClCwhISHUr1//gdv07ds3X5doiI6ORlEUDh48+FjZijspM8LouSrPMbzhcACm75vOhqgN2gYSQpQ6iqI88Na3b1+tIz6ykSNHsmXLFq1jlEiaTponzM9rga9xOeUyKyJW8MGuDyhjW4Zmns20jiWEKCUuXrxo/Hr16tWMGzfOZAoPOzs7k+0zMjKwsrIqsnyPw9HREUdHR61jlEhyZEaYUBSFUU+MoqNvRzINmQzfNpyIqxFaxxJClBIeHh7Gm4uLC4qiGO+npqbi6urKmjVraNOmDba2tixfvpyrV6/Sq1cvKlWqhL29PXXq1GHlypUm+23Tpg1Dhw5l6NChuLq6Uq5cOT788EOyfwYmPT2dUaNGUbFiRRwcHGjatCnbt2832UduR4uio6MBOHv2LM8//zyOjo44OzvTvXt3Ll26ZHz8vaeZ9Ho9I0aMMOYZNWoU934mJzQ0lFatWhm3efbZZzlz5kzBveElhJQZkYNO0TG51WSe8HiCWxm3eHPzm5xLOqd1LCFEAVBVFUNycpHfCvKDs6NHj2bYsGFERETQsWNHUlNTadSoEevXr+fo0aO88cYbvPLKK+zZs8fkccuWLcPS0pI9e/bw+eefM3v2bL766ivj+n79+vH333+zatUqDh8+TLdu3QgODubUqVMA/Pzzz1y8eNF469q1K9WrV8fd3R1VVenSpQvXrl1jx44dbNq0iTNnztCjR4/7vo6ZM2fyzTff8PXXX7Nr1y6uXbvG2rVrTba5desWI0aMICwsjC1btqDT6XjhhRcwGAwF9n6WBHKaSeTK2sKaz9p+Rt/Qvpy8fpJBmwfxbadvKWtbVutoQojHoKakcKJhoyJ/3uoH9qPY2xfIvoYPH07Xrl1Nlo0cOdL49VtvvUVoaCg//PADTZs2NS739vZm9uzZKIpC9erVOXLkCLNnz2bAgAGcOXOGlStXcu7cOby8vIz7DA0NZcmSJUyePJmyZe/+/Js9ezZbt25lz5492NnZsWnTJg4fPkxUVBTe3t4AfPfdd9SuXZuwsDCeeOKJHK9jzpw5jBkzhhdffBGARYsW8eeff5psc2fdHV9//TVubm4cO3aMwEC5rt4dcmRG3JeTtRML2y3E08GTmMQYhm4ZSnJGstaxhBClXOPGjU3u6/V6Jk2aRN26dSlXrhyOjo5s3LjReJ2/O5o1a2ZykeLmzZtz6tQp9Ho9Bw4cQFVVAgICjGNbHB0d2bFjR47TOhs2bOD9999n9erVBAQEABAREYG3t7exyADUqlULV1dXIiJynqpPSEjg4sWLNG/e3LjM0tIyx2s7c+YML730Ev7+/jg7O+Pn5weQ47WVdnJkRjyQm70bi9ovos+GPhy5coSRO0by2VOfYaUrHgPuhBCmFDs7qh/Yr8nzFhQHBweT+zNnzmT27NnMmTOHOnXq4ODgwPDhw0lPT8/zPg0GAxYWFuzfvx8LCwuTddkH7R47doyePXvy6aef0qFDB+NyVVVNitLDlufVc889h7e3N19++SVeXl4YDAYCAwPz9dpKAykz4qH8XfyZ99Q8BmwcwF/n/2LC7glMbDnxsf6BCiG0oShKgZ3uMRd//fUXzz//PC+//DKQVUxOnTpFzZo1Tbb7999/c9yvVq0aFhYWNGjQAL1eT3x8PE8++WSuz3P16lWee+45unbtyjvvvGOyrlatWpw9e5bY2Fjj0Zljx46RkJCQIweAi4sLnp6e/Pvvv7Ru3RqAzMxM9u/fT8OGDY3PFxERwRdffGHMtGvXrvy+PaWCnGYSeVLfrT4zgmZgoVjw65lfmfvfXK0jCSEEAFWrVmXTpk3s3r2biIgIBg4cSFxcXI7tYmNjGTFiBCdOnGDlypXMnTuXt99+G4CAgAB69+5Nnz59+Pnnn4mKiiIsLIypU6fyxx9/ANC1a1fs7OwICQkhLi7OeNPr9bRr1466devSu3dvDhw4wN69e+nTpw9BQUE5Th3d8fbbb/Ppp5+ydu1ajh8/zuDBg7lx44ZxfZkyZShXrhyLFy/m9OnTbN26lREjRhT8G1gCSJkReRbkHcRHzT4C4MsjX7Ly+MqHPEIIIQrfRx99RMOGDenYsSNt2rTBw8Mj11l0+/TpQ0pKCk2aNGHIkCG89dZbvPHGG8b1S5YsoU+fPrz77rtUr16d//3vf+zZs8d4pGXnzp2Eh4fj6+uLp6en8RYbG4uiKPzyyy+UKVOG1q1b065dO/z9/Vm9evV9c7/77rv06dOHvn370rx5c5ycnHjhhReM63U6HatWrWL//v0EBgbyzjvvMH369IJ740oQudCkyLdFhxYx/+B8FBRmBM2gg2+Hhz9ICFHk5EKTd7Vp04b69eszZ84craOIbORCk0IzA+sOpHtAd1RUxvw1hn1x+7SOJIQQohSTMiPyTVEUPmj6AU95P0W6IZ1hW4dx8vpJrWMJIYQopaTMiEdiobNgauupNHBrQFJGEm9ufpOLNy8+/IFCCKGB7du3yymmEkzKjHhktpa2zH1qLlVcqhCfHM+gzYNISEvQOpYQQohSRsqMeCwuNi4sar8IN3s3IhMiGbplKKmZqVrHEkIIUYpImRGPzcPBgy/afYGTtRMHLx9k1M5RZBoytY4lhBCilJAyIwpE1TJVmfvUXKx11myL3cakPZMK9Cq5QgghxP1ImREFppF7I6a2noqCwo8nf2TR4UVaRxJCCFEKSJkRBaqdTzvGNh0LwIKDC/jx5I8aJxJCCFHSSZkRBa5HjR68UTdrivCJ/05k29ltGicSQpQ0dy4fIARImRGFZGj9obxQ9QUMqoH3dr7HwfiDWkcSQhQj8fHxDBw4kMqVK2NjY4OHhwcdO3bkn3/+AeDixYt06tRJ45TCXFhqHUCUTIqiMK75OK6mXmXnuZ0M3TqUb4O/xd/VX+toQohi4MUXXyQjI4Nly5bh7+/PpUuX2LJlC9euXQPAw8ND44TCnMiRGVFoLHWWTG89nbrl65KQlsDLG15me+x2rWMJIczcjRs32LVrF1OnTqVt27b4+PjQpEkTxowZwzPPPAOYnmaKjo5GURTWrFnDk08+iZ2dHU888QQnT54kLCyMxo0b4+joSHBwMJcvXzY+T9++fenSpQsTJkzAzc0NZ2dnBg4cSHp6unGbH3/8kTp16mBnZ0e5cuVo164dt27dAsBgMPDxxx9TqVIlbGxsqF+/PqGhocbH3sn1888/07ZtW+zt7alXr57x6JIoOFJmRKGyt7Jn3tPzqFuhLknpSby19S1m7Z8l89AIoRFVVclI0xf5LT9TNTg6OuLo6Mgvv/xCWlpanh83fvx4PvzwQw4cOIClpSW9evVi1KhRfPbZZ/z111+cOXOGcePGmTxmy5YtREREsG3bNlauXMnatWuZMGECkHUqq1evXrz22mtERESwfft2unbtanwtn332GTNnzmTGjBkcPnyYjh078r///Y9Tp06ZPMfYsWMZOXIkBw8eJCAggF69epGZKT8DC5KilvDJQPJzCXFReDL0GczaP4vlEcsBaOjWkOlB03Gzd9M4mRAlV2pqKlFRUfj5+WFrawtARpqexW/vKPIsb3wWhJWNRZ63/+mnnxgwYAApKSk0bNiQoKAgevbsSd26dYGsIzNr166lS5cuREdH4+fnx1dffcXrr78OwKpVq+jVqxdbtmzhqaeeAuDTTz9l6dKlHD9+HMg6MrNu3TpiY2Oxt7cHYNGiRbz33nskJCRw8OBBGjVqRHR0ND4+PjkyVqxYkSFDhvDBBx8YlzVp0oQnnniC+fPn55rr2LFj1K5dm4iICGrUqPEI72TJktv36B35+f0tR2ZEkbCysGJ0k9HMDJqJg5UDB+IP0G1dN/Zc3KN1NCGEGXrxxRe5cOECv/32Gx07dmT79u00bNiQpUuX3vcxd4oOgLu7OwB16tQxWRYfH2/ymHr16hmLDEDz5s25efMmsbGx1KtXj6effpo6derQrVs3vvzyS65fvw5k/aK9cOECLVu2NNlfy5YtiYiIuG8uT09PgBw5xOORAcCiSHXw7UD1stUZsX0EJ6+f5I1NbzC43mAG1B2ATpFuLURhs7TW8cZnQZo8b37Z2trSvn172rdvz7hx4+jfvz/jx4+nb9++uW5vZWVl/FpRlFyXGQyGPD23oihYWFiwadMmdu/ezcaNG5k7dy5jx45lz549lCtXzuR57lBVNcey3HLlNYfIG/ntIYqcj7MPKzqvMH50e97BeQzeMpjrqde1jiZEiacoClY2FkV+u/cX/KOoVauWcfBtQTl06BApKSnG+//++y+Ojo5UqlQJyHq/WrZsyYQJE/jvv/+wtrZm7dq1ODs74+Xlxa5du0z2t3v3bmrWrFmgGcXDyZEZoQlbS1s+bvkxDd0bMunfSfx9/m+6r+/OjKAZ1KtQT+t4QggNXb16lW7duvHaa69Rt25dnJyc2LdvH9OmTeP5558v0OdKT0/n9ddf58MPPyQmJobx48czdOhQdDode/bsYcuWLXTo0AE3Nzf27NnD5cuXjWXlvffeY/z48VSpUoX69euzZMkSDh48yIoVKwo0o3g4KTNCU12qdqFWuVq8u/1dohOj6buhL+82fpfeNXsXyF9yQojix9HRkaZNmzJ79mzOnDlDRkYG3t7eDBgwwGSwbUF4+umnqVatGq1btyYtLY2ePXsSEhICgLOzMzt37mTOnDkkJibi4+PDzJkzjZP1DRs2jMTERN59913i4+OpVasWv/32G9WqVSvQjOLh5NNMwizcTL9JyD8h/Bn9JwDtfdozocUEnKydNE4mRPH1oE+KiKxPM924cUMui6Ah+TSTKFEcrR2Z3no67zd5H0udJZtiNtFzfU9OXDuhdTQhhBBmTsqMMBuKotC7Zm+WBS/D08GTs0ln6f1Hb9aeWqt1NCGEEGZM0zITEhKCoigmt+zX21BVlZCQELy8vLCzs6NNmzaEh4drmFgUhboV6rLm2TU8WfFJ0vRpjNs9jg93fUhKZsrDHyyEEHm0dOlSOcVUQmh+ZKZ27dpcvHjReDty5Ihx3bRp05g1axbz5s0jLCwMDw8P2rdvT1JSkoaJRVFwtXVl3tPzGNZgGDpFx69nfqX3H72JTojWOpoQQggzo3mZsbS0xMPDw3irUKECkHVUZs6cOYwdO5auXbsSGBjIsmXLSE5O5vvvv9c4tSgKOkXHgLoD+LL9l5SzLcep66fosb4HodGhD3+wEMKohH/OQxRjBfW9qXmZOXXqFF5eXvj5+dGzZ08iIyMBiIqKIi4ujg4dOhi3tbGxISgoiN27d993f2lpaSQmJprcRPHWxLMJPzz3A43dG5Ocmcx7O95jyp4pZOgztI4mhFm7M/NscnKyxkmEyN2d783ssyQ/Ck3nmWnatCnffvstAQEBXLp0iU8++YQWLVoQHh5OXFwccPf6Gne4u7sTExNz331OmTLFeMVTUXJUsK/Alx2+ZN5/8/j66Nd8f/x7jlw5woygGXg5emkdTwizZGFhgaurq/E6QPb29jJ/kzALqqqSnJxMfHw8rq6uWFjk/SKkuTGreWZu3bpFlSpVGDVqFM2aNaNly5ZcuHDBeGEugAEDBhAbG0toaO6nGtLS0kwuGZ+YmIi3t7fMM1OC7IjdwQe7PiAxPREXGxcmt5pM60qttY4lhFlSVZW4uDhu3LihdRQhcnB1dcXDwyPXkp2feWbMagZgBwcH6tSpw6lTp+jSpQsAcXFxJmUmPj4+x9Ga7GxsbLCxsSnsqEJDQd5BrHluDSO3j+To1aMM2TKE/nX6M6T+ECx1ZvUtLYTmFEXB09MTNzc3MjLk1KwwH1ZWVo99ROYOs/rJn5aWRkREBE8++SR+fn54eHiwadMmGjRoAGRdQ2PHjh1MnTpV46RCaxUdK7Ks0zJm7JvByuMr+erIVxy6fIhpradR3q681vGEMDsWFhYF9otDCHOj6QDgkSNHsmPHDqKiotizZw//93//R2JiIq+++iqKojB8+HAmT57M2rVrOXr0KH379sXe3p6XXnpJy9jCTFhbWPNB0w+Y3no69pb2hMWF0W1dN8LiwrSOJoQQoghpemTm3Llz9OrViytXrlChQgWaNWvGv//+i4+PDwCjRo0iJSWFwYMHc/36dZo2bcrGjRtxcpLr9Yi7gv2CqV62OiO2j+D0jdP039iftxq8xWuBr6FTNP/AnhBCiEJmVgOAC4NcaLL0SMlM4ZN/P+G3M78B0LpSaya3moyLjYvGyYQQQuSXXGhSlEp2lnZ80vITQpqHYK2zZue5nXRf152jV45qHU0IIUQhkjIjShRFUXgx4EVWPLMCbydvLty6wCsbXuH7iO9lFlQhhCihpMyIEqlG2RqsfnY17Sq3I9OQyZS9Uxi1cxS3Mm5pHU0IIUQBkzIjSiwnaydmtZnFe43fw1KxJDQ6lJ7re3Lq+imtowkhhChAUmZEiaYoCn1q92FJ8BLc7d2JTozmpd9f4tfTv2odTQghRAGRMiNKhfpu9fnhuR9o6dWSVH0qH/79IeN3jyc1M1XraEIIIR6TlBlRapSxLcOCdgsYUn8ICgo/n/qZl/94mZjE+1+4VAghhPmTMiNKFZ2iY1C9QXzR/gvK2pblxPUT9Fzfk80xm7WOJoQQ4hFJmRGlUnOv5qx5dg0N3RpyM+Mm72x/h6l7p5KhlwvxCSFEcfNYZebKlSv8/vvv/Pbbb1y8eLGgMglRJNwd3Pmq41f0q90PgOURy+n3Zz/ibsVpnEwIIUR+PHKZ+emnn6hatSoTJkxg/PjxVKlShSVLlhRkNiEKnZXOihGNR/BZ289wsnLi0OVDdFvXjb/P/611NCGEEHmU52sz3bx5E0dHR+P9unXr8uOPPxIQEADA77//zoABA7hw4ULhJH1Ecm0mkVexSbG8u/1dIq5FoKDwRt03eLPem1joLLSOJoQQpU6hXJupUaNG/Prr3bk5LC0tiY+PN96/dOkS1tbWjxBXCPPg7eTNd52/o3tAd1RUvjj8BQM3D+RqylWtowkhhHiAPB+ZiY6OZvDgwdjY2DB//nzOnDlDz5490ev1ZGZmotPpWLp0KZ07dy7szPkiR2bEo1gfuZ6P//mYlMwU3OzcmB40nYbuDbWOJYQQpUahHJnx9fXljz/+oFu3bgQFBXHo0CFOnz7Npk2b2Lx5M2fPnjW7IiPEo3rW/1lWPrMSfxd/4lPiee3P11hydIlcrFIIIcxQvgcAv/TSS+zdu5f//vuPNm3aYDAYqF+/Pra2toWRTwjNVHGtwspnVvKM/zPoVT2z9s9i2LZhJKQlaB1NCCFENnk+zQSwYcMGjh07Rr169WjXrh3bt29nyJAhdO7cmY8//hg7O7vCzPpI5DSTeFyqqvLDyR/4dO+nZBgyqOhYkZltZlK7XG2towkhRIlVKKeZRo0aRd++fQkLC2PgwIFMnDiRNm3a8N9//2FjY0P9+vXZsGHDY4cXwtwoikL36t35rvN3VHSsyPmb53nlj1dYc2KNnHYSQggzkOcjM+XLl+fPP/+kUaNGXLt2jWbNmnHy5Enj+vDwcAYOHMiuXbsKLeyjkCMzoiAlpCXw0d8fsS12GwCd/Tozvvl47K3sNU4mhBAlS6EcmbG3tycqKgqA2NjYHGNkateubXZFRoiC5mLjwmdtP+PdRu9ioVjwR9Qf9Pq9F2dunNE6mhBClFp5LjNTpkyhT58+eHl5ERQUxMSJEwszlxBmS1EU+gb25euOX+Nm50ZkQiS9fu/F+sj1WkcTQohSKV8DgK9evUpkZCTVqlXD1dW1EGMVHDnNJArT1ZSrjP5rNHsu7gGgW0A3RjcZjY2FjcbJhBCieMvP7+98lZniSMqMKGx6g55FhxfxxaEvUFGpWbYmM9vMxNvJW+toQghRbBXKmBkhRO4sdBYMqT+ERe0W4WrjSsS1CHqs68HWs1u1jiaEEKWClBkhCkiLii344bkfqFehHkkZSby97W1m7ptJhiFD62hCCFGiSZkRogB5OHiwJHgJr9R6BYCl4Uvp/2d/Lt26pHEyIYQoufJVZjIyMujXrx+RkZGFlUeIYs9KZ8WoJ0Yxu81sHK0cORB/gO7ru/PPhX+0jiaEECVSvsqMlZUVa9euLawsQpQo7XzasfrZ1VQvU51rqdcYuGkgCw8txKAatI4mhBAlSr5PM73wwgv88ssvhRBFiJKnsnNllndezovVXkRFZcHBBby5+U2upV7TOpoQQpQYlvl9QNWqVZk4cSK7d++mUaNGODg4mKwfNmxYgYUToiSwtbQlpEUIDd0bMvGfiey+sJtu67oxM2gm9d3qax1PCCGKvXzPM+Pn53f/nSmK2Y2nkXlmhDk5ef0k725/l+jEaCwVS95p9A6v1HoFRVG0jiaEEGZFJs3LRsqMMDe3Mm4RsjuE0OhQANpVbsfHLT/GydpJ42RCCGE+imzSPFVVKeFdSIgC52DlwLTW0/ig6QdY6izZfHYzPdb34Pi141pHE0KIYumRysy3335LnTp1sLOzw87Ojrp16/Ldd98VdDYhSixFUehVoxffdfoOLwcvYpNi6f17b348+aP8gSCEEPmU7zIza9Ys3nzzTTp37syaNWtYvXo1wcHBDBo0iNmzZxdGRiFKrMDygax5bg2tK7Um3ZDOhH8m8OHfH5Kckax1NCGEKDYeaQDwhAkT6NOnj8nyZcuWERISQlRUVIEGfFwyZkYUBwbVwDdHv2Huf3MxqAaqulZlZpuZ+Lv4ax1NCCE0UahjZi5evEiLFi1yLG/RogUXL17M7+6EEIBO0dG/Tn++6vAV5e3Kc/rGaXqt78WGqA1aRxNCCLOX7zJTtWpV1qxZk2P56tWrqVat2iMHmTJlCoqiMHz4cOMyVVUJCQnBy8sLOzs72rRpQ3h4+CM/hxDm7gmPJ/jhuR94wuMJkjOTGbVzFJP+nUS6Pl3raEIIYbbyPWnehAkT6NGjBzt37qRly5YoisKuXbvYsmVLriUnL8LCwli8eDF169Y1WT5t2jRmzZrF0qVLCQgI4JNPPqF9+/acOHECJyf5GKsomcrblWdx+8UsOLiAL498yaoTqzh65Sgz2sygomNFreMJIYTZyfeRmRdffJG9e/dSvnx5fvnlF37++WfKly/P3r17eeGFF/Id4ObNm/Tu3Zsvv/ySMmXKGJerqsqcOXMYO3YsXbt2JTAwkGXLlpGcnMz333+f7+cRojix1FkyrOEw5j89HxcbF45ePUr3dd3ZEbtD62hCCGF2Humq2a6urixfvpz9+/dz4MABli9fToMGDR4pwJAhQ3jmmWdo166dyfKoqCji4uLo0KGDcZmNjQ1BQUHs3r37vvtLS0sjMTHR5CZEcdW6UmvWPLuGOuXrkJieyNCtQ5mzfw6ZhkytowkhhNnQ9KrZq1at4sCBA0yZMiXHuri4OADc3d1Nlru7uxvX5WbKlCm4uLgYb97e3gWWVwgteDl6sSx4GS/VeAmAr49+zYCNA7icfFnjZEIIYR40u2p2bGwsb7/9NsuXL8fW1va+2917zRpVVR94HZsxY8aQkJBgvMXGxj52ViG0ZmVhxZimY5gRNAMHKwf2XdpHt3Xd2Htxr9bRhBBCc5pdNXv//v3Ex8fTqFEj4zK9Xs/OnTuZN28eJ06cALKO0Hh6ehq3iY+Pz3G0JjsbGxtsbGzy85KEKDY6+nakepnqjNgxglPXTzFg0wCG1B9C/zr90SmPdXUSIYQotjS7anZSUhIxMTEmy/r160eNGjUYPXo0tWvXxsvLi3feeYdRo0YBkJ6ejpubG1OnTmXgwIF5eh6ZNE+URCmZKUzeM5lfTv8CQKuKrZjSagqutq6a5hJCiIKSn9/f+Toyo6oq27Ztw83NDXt7+8cK6eTkRGBgoMkyBwcHypUrZ1w+fPhwJk+eTLVq1ahWrRqTJ0/G3t6el1566bGeW4jizs7SjoktJ9LQrSGT9kxi1/lddF/fnRlBM6hboe7DdyCEECVIvo5Lq6pKQEAA58+fL6w8JkaNGsXw4cMZPHgwjRs35vz582zcuFHmmBHitheqvcCKziuo7FSZi7cu8mroq6yIWCEXqxRClCr5Ps1Uu3Ztvv76a5o1a1ZYmQqUnGYSpcHN9JuM2z2OTTGbAOjg04EJLSbgaO2ocTIhhHg0hXptpmnTpvHee+9x9OjRRw4ohChYjtaOzAyayftN3sdSsWRjzEZ6/t6TE9dOaB1NCCEKXb6PzJQpU4bk5GQyMzOxtrbGzs7OZP21a9cKNODjkiMzorQ5dPkQI3eMJO5WHDYWNoxtOpYXquV/dm4hhNBSoQ0ABpgzZ86j5hJCFIF6Feqx5tk1jNk1hr/P/8243eP4L/4/Pmj6AbaW95/TSQghiqt8H5kpbuTIjCitDKqBr458xfyD8zGoBgLKBDCrzSx8nH20jiaEEA9VKGNm1qxZQ3p6uvF+dHQ0er3eeD85OZlp06Y9QlwhRGHQKTreqPsGi9svpqxtWU5eP0mP9T3YGL1R62hCCFGg8nxkxsLCgosXL+Lm5gaAs7MzBw8exN/fH4BLly7h5eVlUnDMgRyZEQLik+N5b8d7HIg/AEDvmr15t9G7WFlYaZxMCCFyVyhHZu7tPCX87JQQJYqbvRtfd/ya1wJfA2BFxAr6hvbl4s2LGicTQojHJxdzEaKUsNRZ8k6jd5j71FycrJ04fOUw3dZ3469zf2kdTQghHouUmceQFhmJaman1YR4mDbebVjz7BpqlatFQloCg7cM5vMDn6M3yPeyEKJ4ytdHs//8809cXFwAMBgMbNmyxTh53o0bNwo8nDm7unQp8TNn4TZ8OOVef03rOELkSyWnSnzX6TumhU1j9YnVfHnkSw5fPsynrT+lvF15reMJIUS+5HkAsE738IM4iqKUmgHAN378kYsffoRibY3fzz9hU7Vqge1biKL0R+QfhPwTQkpmChXsKjCt9TQaezTWOpYQopQrlAHABoPhoTdzKzKFyeXFF3EIao2ans6F98egZmRoHUmIR9LZvzOrnl1FVdeqXE65TP+N/fn6yNcYVIPW0YQQIk9kzMwjUhQFz48nonNxIfXoUa58+aXWkYR4ZP4u/qzovILn/J9Dr+qZc2AOw7YOIyEtQetoQgjxUFJmHoOVuxseH44F4MqChaRGRGicSIhHZ29lz6RWkxjffDzWOmt2nNtBj/U9CL8SrnU0IYR4ICkzj8n52Wdxat8eMjO5MPp9DNlmSRaiuFEUhf8L+D+Wd16Ot5M352+e55UNr7Dq+CqZW0oIYbakzDwmRVHwCBmPRZkypJ08yZV587WOJMRjq1muJqueXcVT3k+RYchg0p5JjN45mlsZt7SOJoQQOUiZKQCW5crhMSEEgKtffUXKoUPaBhKiADhbOzOn7RxGNh6JpWLJhugN9Fzfk9PXT2sdTQghTDxSmblx4wZfffUVY8aM4dq1awAcOHCA8+fPF2i44sS5Qwecn3sODAYuvD8GQ2qq1pGEeGyKovBq7Vf5Jvgb3OzdiE6M5qU/XmLdmXVaRxNCCKN8l5nDhw8TEBDA1KlTmTFjhnGyvLVr1zJmzJiCzleseHw4FssKFUiPiuLy7DlaxxGiwDRwa8APz/1Ac8/mpGSm8MGuDwjZHUKaPk3raEIIkf8yM2LECPr27cupU6ewtbU1Lu/UqRM7d+4s0HDFjYWLC56fTATg2rffkhwWpnEiIQpOWduyLGy3kMH1BqOg8NOpn3j5j5eJTYzVOpoQopTLd5kJCwtj4MCBOZZXrFiRuLi4AglVnDkGBeHyfy+CqnJhzAcYbsmASVFyWOgseLP+myxqv4gyNmU4fu04Pdb3YEvMFq2jCSFKsXyXGVtbWxITE3MsP3HiBBUqVCiQUMWd+/vvY+nlSca5c1yaPl3rOEIUuBZeLfjhuR9o4NaApIwkhm8fzvSw6WQYZCZsIUTRy3eZef755/n444/JuD19v6IonD17lvfff58XX3yxwAMWRxaOjnhNngzAjVWrubnrb40TCVHw3B3c+brj17xa61UAvj32La+FvkbcLTlCK4QoWvkuMzNmzODy5cu4ubmRkpJCUFAQVatWxcnJiUmTJhVGxmLJoVkzyvTuDcDFDz9En8vRLCGKOyudFSOfGMmctnNwsnLi4OWDdF/Xnd0XdmsdTQhRiuT5qtn32rp1KwcOHMBgMNCwYUPatWtX0NkKRGFdNTsvDMnJRL7wAhkxZ3Hp0gWvT6cU6fMLUZRiE2N5d8e7RFyLQEFhUL1BDKw7EAudhdbRhBDFUH5+f+e7zERHR+Pr6/s4+YqUlmUGIPnAAWJ6vwyqSqUF83F66qkizyBEUUnTp/Hp3k/58eSPADTzbManT35KObtyGicTQhQ3+fn9ne/TTP7+/rRq1YovvvjCOGGeuD/7hg0p+1o/AC6OG0/m9esaJxKi8NhY2DC++Xgmt5qMnaUd/178l+7ruvNf/H9aRxNClGD5LjP79u2jefPmfPLJJ3h5efH888/zww8/kJYmk2fdT4Vhw7CuWgX9lStcmjhR6zhCFLrnqjzH952/x8/Fj/iUePqF9mNZ+DK5WKUQolDku8w0bNiQ6dOnc/bsWTZs2ICbmxsDBw7Ezc2N1157rTAyFns6Gxu8pnwKFhYk/rGBxA0btI4kRKGrWqYqq55ZRSe/TuhVPTP2zWD4tuEkpstgeCFEwXrkAcDZHThwgNdff53Dhw+j1+sLIleB0XrMTHaXP/+cKwsWYuHqiv+637CUeXlEKaCqKmtOrGFq2FQyDBlUcqzEzDYzqVWultbRhBBmrFDHzNwRGxvLtGnTqF+/Pk888QQODg7MmzfvUXdXKpQfNAibmjXR37jBxfEhcshdlAqKotCjRg++6/QdFR0rcu7mOV754xV+OPmD/BsQQhSIfJeZxYsXExQUhJ+fH8uWLaN79+6cOXOGXbt28eabbxZGxhJDsbbG69NPwcqKm1u3kvDrr1pHEqLI1C5fm9XPrqaNdxvSDel8/M/HfLDrA5IzkrWOJoQo5vJ9msnb25uePXvSu3dv6tevX0ixCo45nWa648oXi7k8ezY6Jyf81/2GlYeH1pGEKDKqqrI0fCmfHfgMvaqniksVZrWZhb+rv9bRhBBmpFDnmVFVFUVRHitgUTLHMqNmZhLduzephw7j0LIl3l99WazeUyEKwr64fYzaOYrLKZexs7QjpHkInf07ax1LCGEmCrzMHD58mMDAQHQ6HYcPH37gtnXr1s1f2kJmjmUGIC0yiqgXXkBNS8MjJIQyPXtoHUmIIncl5Qrv73yfPXF7AOhRvQejnhiFtYW1xsmEEFor8DKj0+mIi4vDzc0NnU6HoigmA/fu3FcURT7NlA/Xli3j0pRPUezt8f/1F6y9vbWOJESR0xv0LDy0kC8OfwFArXK1mBk0k0pOlTROJoTQUoGXmZiYGCpXroyiKMTExDxwWx8fn/ylLWTmXGZUg4GzfV4led8+7Bs3pvK3y1B0j/wBMyGKtV3ndzHmrzHcSLuBk7UTk1pOom3ltlrHEkJopMA/mu3j42Mc0xETE0PFihXx8fExuVWsWPGhRedeCxcupG7dujg7O+Ps7Ezz5s3ZkG1COVVVCQkJwcvLCzs7O9q0aUN4eHi+nsOcKTodnlMmo9jbk7xvH9e/+07rSEJoplXFVvzw3A/UrVCXpPQkhm0bxqz9s8g0ZGodTQhh5vJ9GKBt27a5XpMpISGBtm3z91dUpUqV+PTTT9m3bx/79u3jqaee4vnnnzcWlmnTpjFr1izmzZtHWFgYHh4etG/fnqSkpPzGNlvW3t64j3oPgPhZs0mLjNI4kRDa8XDwYGnHpbxc82UAlhxdwut/vk58crzGyYQQ5izfn2bS6XRcunSJCvfMXnvy5EkaN25MYuLjTVVetmxZpk+fzmuvvYaXlxfDhw9n9OjRAKSlpeHu7s7UqVMZOHBgro9PS0szuU5UYmIi3t7eZnma6Q5VVYl9vT+3du/Gtl5dfFesQLG01DqWEJraFLOJj/7+iFsZtyhrW5aprafSzLOZ1rGEEEUkP6eZ8vwbs2vXrkDWYN++fftiY2NjXKfX6zl8+DAtWrR4xMhZ+/jhhx+4desWzZs3Jyoqiri4ODp06GDcxsbGhqCgIHbv3n3fMjNlyhQmTJjwyDm0oCgKnpM+IfK5/5F66DBXv1lC+TcGaB1LCE2192lPQJkARmwfwcnrJxm4aSCD6w1mQN0B6BQZWyaEuCvPPxFcXFxwcXFBVVWcnJyM911cXPDw8OCNN95g+fLl+Q5w5MgRHB0dsbGxYdCgQaxdu5ZatWoRFxcHgLu7u8n27u7uxnW5GTNmDAkJCcZbbGxsvjNpwcrTE/exYwG4PHcuqSdOapxICO35OPuwovMKulbrikE1MO/gPAZvGcz11OtaRxNCmJE8H5lZsmQJAL6+vowcORIHB4cCCVC9enUOHjzIjRs3+Omnn3j11VfZsWOHcf29k8k9bNI+Gxsbk6NGxYlLl+dJ2rSJm1u3cmHM+/itWoViLfNtiNLN1tKWCS0m0MCtAZP+ncTf5/+m27puzAiaQX23+lrHE0KYgXwfqx0/fnyBFRkAa2trqlatSuPGjZkyZQr16tXjs88+w+P2FP/3HoWJj4/PcbSmpFAUBc8JIVi4uJB2LIIri77QOpIQZqNL1S6seGYFvs6+XEq+RL/Qfiw/tlwuVimEeLSrZv/44490796dZs2a0bBhQ5Pb41JVlbS0NPz8/PDw8GDTpk3Gdenp6ezYseOxxuaYO8sKFfAIGQ/AlS++IOXIUY0TCWE+AsoEsPKZlXT07UimmsnUsKm8u+NdktJLzicchRD5l+8y8/nnn9OvXz/c3Nz477//aNKkCeXKlSMyMpJOnTrla18ffPABf/31F9HR0Rw5coSxY8eyfft2evfujaIoDB8+nMmTJ7N27VqOHj1K3759sbe356WXXspv7GLFuVMnnDoFg17PhTHvY8j26SwhSjtHa0emt57OmCZjsNRZsilmEz3X9+TEtRNaRxNCaCTfZWbBggUsXryYefPmYW1tzahRo9i0aRPDhg0jISEhX/u6dOkSr7zyCtWrV+fpp59mz549hIaG0r59ewBGjRrF8OHDGTx4MI0bN+b8+fNs3LgRJyen/MYudjzGjcOifHnST5/h8uefax1HCLOiKAov1XyJZcHL8HTw5GzSWXr/0Zu1p9ZqHU0IoYF8zzNjb29PREQEPj4+uLm5sWnTJurVq8epU6do1qwZV69eLaysj8ScL2fwMElbt3Ju8BBQFHxWrMC+YQOtIwlhdm6k3uCDXR/w1/m/AHi+yvOMbTYWO0s7jZMJIR5HgV/OIDsPDw9jYfHx8eHff/8FICoqSgbiFTCnp57CpUsXUNWs003JyVpHEsLsuNq6Mu/pebzd8G10io5fz/xK7z96E5Ugs2kLUVrku8w89dRTrFu3DoDXX3+dd955h/bt29OjRw9eeOGFAg9Y2rl/MAZLd3cyYs4SP2u21nGEMEs6RUf/Ov35qsNXlLMtx6nrp+i5vieh0aFaRxNCFIF8n2YyGAwYDAYsb0+3v2bNGnbt2kXVqlUZNGgQ1mY2L0pxPs10x81dfxPbvz8AlZcuwaGZTOkuxP1cTr7MqJ2j2HdpHwAv1XiJkY1HYmVhpXEyIUR+5Of3d77LTHFTEsoMwMWQEG6sWo2Vlxd+v/2KhaOj1pGEMFuZhkzmH5zPV0e+AqBO+TrMCJqBl6OXxsmEEHlV4GXm8OHDeX7yunXr5nnbolBSyozh1i0in+9CxrlzuHb7PzwnTtQ6khBmb+e5nYz5awyJ6Yk4Wzsz5ckptK7UWutYQog8KPAyo9PpUBTloQN8FUVBr9fnL20hKyllBuDW3r2cfbUvqCrei7/AsbX8UBbiYc7fPM/I7SM5ejVrAsr+dfozpP4QLHVyZXohzFmBl5mYmJg8P7mPj0+ety0KJanMAFyaMoVry77FskIF/Nf9hoWrq9aRhDB76fp0ZuybwcrjKwF4wuMJprWeRnm78honE0Lcj4yZyaaklRlDaipRL3QlPSoK5+eeo+L0aVpHEqLYCI0KZfzu8SRnJlPerjzTWk/jCY8ntI4lhMhFoc4zA/Ddd9/RsmVLvLy8jEdt5syZw6+//voouxP5oLO1xevTKaDTkbhuHYkbN2odSYhiI9gvmFXPrqKqa1WupFyh/8b+fHXkKwyqQetoQojHkO8ys3DhQkaMGEHnzp25ceOGcYyMq6src+bMKeh8Ihd29epR7vZHteNCJpB57ZrGiYQoPvxc/Pj+me/5X5X/YVANfHbgM97a+hYJafm7HIsQwnzku8zMnTuXL7/8krFjx2JhYWFc3rhxY44cOVKg4cT9lR86BJuAAPTXrhE3PkRmXxYiH+ws7fik5SdMaDEBGwsbdp7bSfd13TlyWX6GCVEc5bvMREVF0aBBzmsE2djYcOvWrQIJJR5OZ22ddbrJ0pKkTZtIXP+71pGEKFYURaFrta4s77wcbydvLty6QJ/QPnwf8b38cSBEMZPvMuPn58fBgwdzLN+wYQO1atUqiEwij2xr1aL84DcBiPvkEzIuxWucSIjip0bZGqx+djXtKrcj05DJlL1TGLVzFLcy5I8zIYqLfJeZ9957jyFDhrB69WpUVWXv3r1MmjSJDz74gPfee68wMooHKD9gALa1a2NISODiuI/kL0ohHoGTtROz2sxi1BOjsFQsCY0Opef6npy8flLraEKIPHikj2Z/+eWXfPLJJ8TGxgJQsWJFQkJCeP311ws84OMqaR/Nzk3aqVNEvfh/qOnpeE76BNcXX9Q6khDF1sH4g4zcMZJLyZewtbDlw2Yf8nzV57WOJUSpU2TzzFy5cgWDwYCbmxsA58+fp2LFio+6u0JRGsoMwNWvvyZ++gx0Dg74//YrVmb2/0GI4uR66nXG/DWGvy/8DUDXal0Z02QMtpa2GicTovQo9Hlm7ihfvjxubm7ExcXx1ltvUbVq1cfZnXgMZfv2xa5BAwy3bnFh7IeoBpk3Q4hHVca2DAvaLWBI/SEoKPx86mde/uNlYhLzPhu6EKLo5LnM3Lhxg969e1OhQgW8vLz4/PPPMRgMjBs3Dn9/f/7991+++eabwswqHkCxsMBrymQUW1uS//2X6ytXah1JiGJNp+gYVG8QX7T/grK2ZTlx/QQ91vdgU8wmraMJIe6R59NMgwcPZt26dfTo0YPQ0FAiIiLo2LEjqampjB8/nqCgoMLO+khKy2mmO64tX8GlTz5BsbPD/5e1WJvZtbKEKI4u3brEqJ2jOBB/AICXa77MiEYjsLKw0jiZECVXoZxm+v3331myZAkzZszgt99+Q1VVAgIC2Lp1q9kWmdKozEu9sG/WDDUlhQtjPkA1s6uYC1EcuTu481XHr+hXux8AyyOW0+/PfsTditM4mRAC8lFmLly4YJxHxt/fH1tbW/rfnlJfmA9Fp8Nr0ifoHBxIOXCAa0uXaR1JiBLBSmfFiMYj+Lzt5zhZO3Ho8iG6revGrvO7tI4mRKmX5zJjMBiwsrp7SNXCwgIHB4dCCSUej1XFiriPeR+Ay599Rtrp0xonEqLkaFu5LWueXUPNsjW5kXaDwZsHM++/eegNchRUCK3kecyMTqejU6dO2NjYALBu3TqeeuqpHIXm559/LviUj6G0jZm5Q1VVYgcN4taOndgGBuK7aiWKpaXWsYQoMdL0aUzbO401J9cA0NSzKVOfnEo5u3IaJxOiZCiUeWb69euXpydfsmRJnrYrKqW1zABkXIon8n//w5CQQIW3h1H+zTe1jiREifN75O9M+GcCKZkpVLCrwPSg6TRyb6R1LCGKvSKbNK84KM1lBiBh3TouvDcKLC3x+2ENtjVrah1JiBIn8kYk72x/h8iESCwUC4Y1HEa/2v1QFEXraEIUW0U2aZ4wf87PPotT+/aQmcmF98dgSE/XOpIQJY6/qz8rn1nJM/7PoFf1zN4/m2HbhpGQlqB1NCFKBSkzJZyiKHiEjMeiTBnSTpzgyvwFWkcSokSyt7JnSqspfNTsI6x0VmyP3U6P9T0IvxqudTQhSjwpM6WAZblyeEwIAeDql1+ScuiQtoGEKKEURaF79e4s77ycio4VOX/zPK/88Qqrj6+WK9oLUYikzJQSzh064Pzcc2AwZJ1uSk3VOpIQJVatcrVY89wa2nq3JcOQwSd7PuH9v94nOSNZ62hClEhSZkoRjw/HYlmhAulRUVyePUfrOEKUaM7WznzW9jPebfQuFooFf0T9Qa/fe3HmxhmtowlR4kiZKUUsXFzw/GQiANe+/ZbksDCNEwlRsimKQt/AvnzT8Rvc7NyITIik1++9WHdmndbRhChRpMyUMo5BQbj834ugqlwY8wGGW7e0jiREidfQvSFrnltDM89mpGSm8MGuD/j4n49J06dpHU2IEkHKTCnk/v77WHp5knHuHJdmzNA6jhClQjm7cixqt4hB9QahoPDDyR945Y9XiE2K1TqaEMWelJlSyMLREa/JkwG4sXIVN//+W+NEQpQOFjoLhtQfwqJ2iyhjU4aIaxH0WNeDLWe3aB1NiGJNykwp5dCsGWV69wbg4tgP0SclaZxIiNKjRcUWrHluDfUq1CMpI4nh24YzI2wGGYYMraMJUSxJmSnF3N4dgZVPZTLj4rg0eYrWcYQoVTwcPFgSvIRXar0CwLJjy3j9z9e5dOuSxsmEKH40LTNTpkzhiSeewMnJCTc3N7p06cKJEydMtlFVlZCQELy8vLCzs6NNmzaEh8uMmgVBZ2+P15QpoCgkrF1L0tZtWkcSolSx0lkx6olRzG4zG0crR/6L/4/u67vzz4V/tI4mRLGiaZnZsWMHQ4YM4d9//2XTpk1kZmbSoUMHbmX7hM20adOYNWsW8+bNIywsDA8PD9q3b0+SnBYpEPYNG1L2tawrol8cN47M69c1TiRE6dPOpx2rn11NjbI1uJZ6jYGbBrLw4EL0Br3W0YQoFszqqtmXL1/Gzc2NHTt20Lp1a1RVxcvLi+HDhzN69GgA0tLScHd3Z+rUqQwcOPCh+yztV83OC0NaGlEvvkj66TM4d+5ExVmztI4kRKmUmpnKp3s/5adTPwHQwqsFU56cQlnbshonE6LoFdurZickZF1htmzZrH+4UVFRxMXF0aFDB+M2NjY2BAUFsXv37lz3kZaWRmJioslNPJjOxgavKZ+ChQWJf2wgccMGrSMJUSrZWtoS0iKESa0mYWthy+4Lu+m2rhsH4w9qHU0Is2Y2ZUZVVUaMGEGrVq0IDAwEIC4uDgB3d3eTbd3d3Y3r7jVlyhRcXFyMN29v78INXkLY1Qmk/MA3AIib8DGZV65onEiI0ut/Vf7H9898j6+zL/HJ8fQL7cey8GVysUoh7sNsyszQoUM5fPgwK1euzLFOURST+6qq5lh2x5gxY0hISDDeYmNlQqq8Kj9oEDY1a6K/cYOL48bLD04hNFStTDVWPbuKTr6dyFQzmbFvBu9sf4ekdBkvKMS9zKLMvPXWW/z2229s27aNSpUqGZd7eHgA5DgKEx8fn+NozR02NjY4Ozub3ETeKNbWeH36KVhZcXPrVhJ+/VXrSEKUag5WDkxtPZUPmn6Apc6SLWe30GN9D45fO651NCHMiqZlRlVVhg4dys8//8zWrVvx8/MzWe/n54eHhwebNm0yLktPT2fHjh20aNGiqOOWCrbVA6gwdCgAlyZNJuM+p/OEEEVDURR61ejFd52+w8vBi9ikWHr/3psfT/4oR0+FuE3TMjNkyBCWL1/O999/j5OTE3FxccTFxZGSkgJk/SMePnw4kydPZu3atRw9epS+fftib2/PSy+9pGX0Eq3c669hW7cuhqQkLo79UH5gCmEGAssHsua5NQRVCiLdkM6EfyYwdtdYkjOStY4mhOY0/Wj2/ca9LFmyhL59+wJZR28mTJjAF198wfXr12natCnz5883DhJ+GPlo9qNJi4wk6oWuqGlpeEyYQJke3bWOJIQADKqBb45+w9z/5mJQDVR1rcrMNjPxd/HXOpoQBSo/v7/Nap6ZwiBl5tFdW7aMS1M+RbG3x//XX7CWT4YJYTbC4sIYtXMUV1KuYG9pT0iLEDr5ddI6lhAFptjOMyPMS5lXXsG+cWPU5GQufjAW1WDQOpIQ4rYnPJ7gh+d+oIlHE5Izkxm1cxSf/PsJ6fp0raMJUeSkzIj7UnQ6PKdMRrG3JzksjOvLl2sdSQiRTXm78ixuv5gBdQYAsPrEavps6MP5m+c1TiZE0ZIyIx7I2tsb91HvARA/cxZpkVEaJxJCZGehs2BYw2HMf3o+LjYuhF8Np/u67uyI3aF1NCGKjJQZ8VCuPXrg0KIFaloaF8eMQc3M1DqSEOIerSu15odnf6Bu+bokpicydOtQZu+fTaZB/r2Kkk/KjHgoRVHwnPQJOkdHUg4d4uo3S7SOJITIhaejJ0uDl9K7Zm8Avjn6Df039udy8mWNkwlRuKTMiDyx8vTEfexYAK7MnUvqiZMaJxJC5MbKwor3m7zPjKAZOFg5sP/Sfrqt68bei3u1jiZEoZEyI/LMpcvzOLZti5qRwYUx76NmZGgdSQhxHx19O7LqmVVUK1ONq6lXGbBpAPMPzuda6jWtowlR4GSeGZEvmZcvE/nsc+gTEig/ZAgV3hqqdSQhxAOkZKYwec9kfjn9CwAWigVNPJrQya8TT1V+ChcbF20DCnEfMmleNlJmCl7ihg2cf2cEWFjgu3o1doG1tY4khHiI9ZHr+e7Ydxy7esy4zFJnSQuvFgT7BtPWuy2O1o4aJhTClJSZbKTMFI5z77xD0oZQbKpVxffHH9HZ2GgdSQiRB2cTzxIaHUpodCinrp8yLrfWWfNkpScJ9g2mdaXW2FvZa5hSCCkzJqTMFI7M69eJfO5/6K9coVz/13EbOVLrSEKIfDpz40xWsYkKJTox2rjcztKOoEpBBPsG06pSK2ws5I8VUfSkzGQjZabwJG3dyrnBQ0BR8FmxAvuGDbSOJIR4BKqqcvL6STZEbSA0OtRkBmEHKwee8n6KYL9gmns2x8rCSsOkojSRMpONlJnCdeH9MST88gtWPpXxX7sWnb0cmhaiOFNVlfCr4YRGZZ2KupR8ybjO2dqZdj7t6OjbkSYeTbDUWWqYVJR0UmaykTJTuPSJiUQ+9z8yL12izMsv4/HhWK0jCSEKiEE1cOjyIUKjQtkYs5ErKVeM68ralqVd5XYE+wXT0K0hFjoLDZOKkkjKTDaFVWZUVSU+Jgl3XylIN3f9TWz//gBUXroUh2ZNNU4khChoeoOe/Zf2ExodyuaYzVxPu25cV8GuAh18OxDsG0y9CvVQFEXDpKKkkDKTTWGVmVP7LrHxq3CqPeFOy/+rioNL6R4gd3F8CDdWr8bKywu/337FwlE+4ilESZVhyCDsYhgbojew5ewWktKTjOs8HTzp6NuRYN9gapWrJcVGPDIpM9kUVpkJ+z2KsPVRqCrY2FvS/IUq1GrphaIrnf9w9TdvEdWlCxnnzuHarRueEz/WOpIQoghk6DPYfWE3odGhbD27leTMZOM6bydvgn2D6ejbkYAyAVJsRL5ImcmmMMfMxMcksn3FCS6fzfqrxMPfhTa9q1OuYuk8KnFr717OvtoXVBXvxV/g2Lq11pGEEEUoNTOVXed3ERodyo7YHaTqU43r/Fz86OTbiY5+HfF38dcwpSgupMxkU9gDgA16A0e2n2fPb5FkpOnR6RTqt69M42d8sbIufQPiLk2ZwrVl32Lp5ob/ut+wcJGp0oUojZIzktlxbgehUaHsOr+LdEO6cV1AmQCCfYMJ9g3G29lbw5TCnEmZyaaoPs2UdC2Vv1afJOpQ1mh/5/K2tO5ZHZ/AcoX2nObIkJpK1AtdSY+Kwvl/z1Fx2jStIwkhNJaUnsS22G2ERoXyz4V/yFQzjetql6ttPBXl6eipYUphbqTMZFPUH82OPHiZv1af5Ob1NACqNnKjVfdqpWqAcMqhQ0T3egkMBirO/Rzn9u21jiSEMBMJaQlsObuFDVEb2Bu3F4NqMK6rX6E+wX7BdPDpQAX7ChqmFOZAykw2Wswzk56ayd51URzeGouqgrWtBc1fqELtJyuWmgHC8bNmc3XxYizKlsV//Tosy5bVOpIQwsxcTbnK5pjNhEaHsv/SflSyfh0pKDT2aEywbzDtfNpR1lZ+fpRGUmay0XLSvMtnk9i+4jjxMVkDhN39nGnTuzrlKzkVaQ4tGNLTif6/bqSdPIlThw5U/GyOfJJBCHFf8cnxbIzeSGh0KIcuHzIut1AsaOLRhE5+nXiq8lO42Mg4vNJCykw2Ws8AbDCoHN1xjn9/jSQjVY+iU6j3tDdNnvXDyqZkDxBOPXaMqO49IDMTrxkzcHn2Ga0jCSGKgQs3L/Bn9J+ERody7Oox43JLnSUtvFoQ7BtMW++2OFqXzk+OlhZSZrLRuszccfN6GrvWnOTMf5cBcCxrQ1DP6vjWLa9ZpqJwecECrnw+F52LC/6//YaVu5vWkYQQxcjZxLNZV/aODuXU9VPG5dY6a56s9CTBvsG0rtQaeyu5LlxJI2UmG3MpM3dEH77CjlUnuHkta4BwlQYVaNU9AMcyJXOAsJqRQXTPXqSGh6NYWWFTvTq2gbWxq1MH28BAbKpUQbGUi9UJIR4u8kYkodGhbIjaQHRitHG5naUdQZWCCPYNplWlVthYlMyfp6WNlJlszK3MAGSk6dm7PopDW2JRDSpWthY0e96fwKBK6ErgAOG0yEhiBw4iIzY2xzrF1hbbmjWxrROIXWAgtoGBWPv6ouh0GiQVQhQHqqpy8vpJY7E5f/O8cZ2DlQNPeT9FsF8wzT2bY2VhpWFS8TikzGRjjmXmjivnkti+4gSXohIBcPNxok3vGlSoXPIGCKuqSsb5C6QePULq0aOkHDlKang4hps3c2yrc3DAtnbtuwWnTh2sKlaUAcRCiBxUVSX8ajihUVmnoi4lXzKuc7Z25unKTxPsF0wTjyZY6uQocHEiZSYbcy4zkDVA+Nhf5/ln7RnSU/UoCtR9ypsmz/lhbVuy/+GpBgPp0TGkhh8l5cgRUo+Gk3rsGGpqao5tLVxcsA0MNCk4lm5uUnCEEEYG1cChy4cIjQplY8xGrqRcMa4ra1uWdpXbEewXTEO3hljoSvYHMEoCKTPZmHuZueNWQhq71pzi9P54ABzL2PBkjwD865euiaPUzEzSzkRmHb05mlVw0o4fR83IyLGtRYXy2AXWMRmDI/PZCCEA9AY9+y/tJzQ6lM0xm7medt24roJdBTr4diDYN5i6FeqiU+S0tjmSMpNNcSkzd8QcvcqOlSdIupp1dMKvXnme7BGAU1lbjZNpx5CeTtrJU6QePULK0aNZBefUKdDrc2xr6eV5u+AEYlcnENvatbEoBv/fhRCFJ8OQQdjFMDZEb2DL2S0kpScZ13k4eBivE1WrXC052mtGpMxkU9zKDEBGup59v0dxcFMsBoOKlY0FTf/nT502FdFZyF8QAIaUFFKPHyf1yNHbp6mOkh4VBbl8O1v7+GSdorpTcGrWROfgoEFqIYTWMvQZ7L6wm9DoULae3UpyZrJxnbeTt/E6UQFlAqTYaEzKTDbFsczccfX8TbavOEFcZAIAFSo70aZ3ddx8itfrKCr6mzdJDT9G6tG7BSe3T1Ch02FTxR/b2nfH4NjUqIHORj7OKURpkpqZyq7zuwiNDmVH7A5S9XfH6/m5+BmP2Pi7+muYsvSSMpNNcS4zAKpB5djfF/hn7RnSkjNRFKjTphJN/+ePtV3JHiBcEPQ3bpByNNxkDE5mXFzODS0tsQmodncMTmAgNtWqoVjJxzqFKA2SM5LZcW4HoVGh7Dq/i3RDunFdQJkAY7HxdvbWMGXpImUmm+JeZu5ITkxn1w+nOBWW9bFDBxdrnuyZNUBYDoXmT+bly1ljb44cJSU867/6a9dybKdYW2NTs4bJGBxrPz8UC/kUhBAlWVJ6EttitxEaFco/F/4hU800rqtdrrbxVJSno6eGKUs+KTPZlJQyc8fZY1fZsfIkiZdTAPCtW54ne1TDuZydxsmKL1VVybx40VhwUsOPknI0HENiYo5tFXt7bGvVNCk4VpUrS6EUooRKSEtgy9ktbIjawN64vRhUg3Fd/Qr1CfYLpoNPByrYl65PnhYFKTPZlLQyA5CZrmffhmj+23gWg17F0lpHk+f8qfdUJRkgXEBUVSXj7Nm7BefoUVKOHUNNTs6xrc7ZGbvA2iZjcCw9PaXgCFHCXE25yuaYzYRGh7L/0n5Usn59Kig09mhMsG8w7XzaUdZWpogoCMWmzOzcuZPp06ezf/9+Ll68yNq1a+nSpYtxvaqqTJgwgcWLF3P9+nWaNm3K/PnzqV27dp6foySWmTuuXbjF9u+Pc/F01gDhcpUcadO7Oh5+LhonK5lUvZ70qKis2Ytvj8FJiziOmp6eY1uLcuWyxt5kLzgV5C83IUqK+OR4NkZvJDQ6lEOXDxmXWygWNPFoQie/TjxV+SlcbOTn8aMqNmVmw4YN/P333zRs2JAXX3wxR5mZOnUqkyZNYunSpQQEBPDJJ5+wc+dOTpw4gZNT3qb8L8llBrIGCEf8c5HdP50mLTkTFKjTuiJNu1TBRgYIFzo1I4O0U6eM89+kHD1C2slTkJmZY1tLDw/j4GLbwDrY1q6FZZkyGqQWQhSkCzcv8Gf0n4RGh3Ls6jHjckudJS28WhDsG0xb77Y4WjtqmLL4KTZlJjtFUUzKjKqqeHl5MXz4cEaPHg1AWloa7u7uTJ06lYEDB+a6n7S0NNLS0oz3ExMT8fb2LrFl5o7kxHR2/3SaE3uyPqlj72LNk90DqNJQBggXNUNaGmnHj5uMwUk7fSbXOXCsvL1vF5ysMTi2tWth4Sg/8IQors4mniU0Ous6UaeunzIut9ZZ82SlJwn2DaZ1pdbYW9lrmLJ4KBFlJjIykipVqnDgwAEaNGhg3O7555/H1dWVZcuW5bqfkJAQJkyYkGN5SS8zd8Qev8aO70+QEJ81QLhy7XIE9QrAubwMENaS4dYtUiMiTMbgpMfE5NxQUbD28zMtODVroLOT/39CFDeRNyKNV/aOTow2LreztCOoUhDBvsG0qtQKGwuZ4yo3JaLM7N69m5YtW3L+/Hm8vLyM273xxhvExMTw559/5rqf0npkJrvMDD37Q2M4EBqTNUDYSscTz/pRr503FjJA2GzoExJIPXbMZAxO5oWLOTe0sMCmatW7F9msHYht9QAUa+uiDy2EyDdVVTl5/WTWEZuoUM7dPGdc52DlwFPeTxHsF0xzz+ZYWcjcVneUqDJz4cIFPD3vfpZ/wIABxMbGEhoamqf9lvQxMw9yPe4W21ec4MKpGwCUq+hAm9418PCXAWnmKvPqVVLDw41XEU85egT95Ss5tlOsrLCpXv1uwQmsg00VfxRLGSclhDlTVZXwq+GERoXyZ8yfxN26O4mns7UzT1d+mmC/YJp4NMFSV7r/PZeIMvOop5nuVZrLDGT9wzn+Txy7fzpN6q0MUKB2Ky+adamCrYP8BWDuVFUlMz6e1CNHTE5R6RMScmyr2NlhW7Pm3auI1w7E2tcHRSdH44QwRwbVwOHLh9kQtYGNMRu5knL3D5eytmVpV7kdwX7BNHRriIWu9E3WWSLKzJ0BwO+88w6jRo0CID09HTc3twcOAL5XaS8zd6TczBogfPyfrL8C7JytadWtKtUau8sA4WJGVVUyzp27fWrqziDjcAy3buXYVufoiG3t2ncLTmAgVhUryv9zIcyM3qDnQPwBNkRtYHPMZq6nXTeuq2BXgQ6+HQj2DaZuhbrolNLxB0qxKTM3b97k9OnTADRo0IBZs2bRtm1bypYtS+XKlZk6dSpTpkxhyZIlVKtWjcmTJ7N9+3b5aPZjOH/iOtu/P8GNS1mTv3nXKktQrwBcKsjI+uJMNRhIj47OKji3j96kRkSgpqbm2NbC1fX2VcSzFRx3dw1SCyFyk2nIZO/FvYRGh7L57GaS0pOM6zwcPIzXiapVrlaJ/sOk2JSZ7du307Zt2xzLX331VZYuXWqcNO+LL74wmTQvMDAwz88hZSYnfYaBAxtj2L8hBn2mAQsrHY07+9KgfWUsLEtH4y8N1MxM0s6cuV1wssbgpJ44ARkZOba1rFAhq+AYx+AEYllWZjEVQmsZ+gx2X9hNaHQo22K3cSvj7hFYbydv43WiAsoElLhiU2zKTFGQMnN/Ny4ls/37E5w/kXU4s4ynA216V8erqqu2wUShMaSnk3biJKlHjxgn+ks7fRr0+hzbWnl5mRac2rWxkH9DQmgmNTOVXed3ERodyo7YHaTq7x559XPxMx6x8Xf11zBlwZEyk42UmQdTVZWTe+LY9eNpUm9m/cVeq6UnzbtWlQHCpYQhJYXUiON3C86Ro6RHReW6rbWPD7Z16tydybhWLXT2copSiKKWnJHMznM72RC1gV3nd5FuuHtZlYAyAcZi4+3srWHKxyNlJhspM3mTejOD3WtPE/F31jwndk5WtPy/agQ0kQHCpZE+KYnU8GO3ryCeVXAyzp3LuaFOh00V/6zLM9weg2NTvTo6G5kETIiicjP9Jttit7EhagP/XPiHTPXu5VRql6ttPBXl6ej5gL2YHykz2UiZyZ8Lp26wfcVxrsdlDRCuVKMMQb2q4+ouf32XdpnXr2eNuwm/O8g489KlnBtaWWFbrZrJKSqbqlVRrORInxCFLSEtgS1nt7AhagN74/ZiUA3GdfUq1KOTXyc6+HSggr35X/hWykw2UmbyT59p4L9NZ9n3RzT6DAMWljoadfKhYQcfLKxkgLC4KyM+Pqvg3J7BOPXIUfTXr+fYTrGxwbZGDZOCY+3nh2JR+ubOEKKoXE25yuaYzYRGh7L/0n5Usn7dKyg0cm9EJ79OtPNpR1lb8xzsL2UmGykzj+5GfDI7V54gNuL2AGEPe4Jeqk7FALnSs8idqqpkXrhAytFwk0HGhqSkHNvq7O2xrVXLpOBYVa4spzWFKATxyfFsjN5IaHQohy4fMi63UCxo4tGEYL9gnq78NC425jNDvJSZbKTMPB5VVTm17xK71pwiJSlrgHCNFp607FoVW0c5bSAeTjUYyDh7NqvgHDlCSvhRUo9FoCYn59hW5+yMXWBtkzE4lh4eUnCEKEAXbl7gz+g/CY0O5djVY8blljpLWni1INg3mLbebXG0dtQwpZQZE1JmCkbqrQz+/eUM4X9dAMDW0YqWL1alejP5RSPyT9XrSY+MzHaRzaOkRUSg5jIHjkW5ctmuIn674JQvr0FqIUqes4lnsy6AGR3KqeunjMutddY8WelJgn2DaV2pNfZWRT9uUspMNlJmCtbFMwlsX3GcaxeyJm6qGOBK0EvVKePhoHEyUdyp6emknT5tWnBOnsx1DhxLDw/s6ty+gnhgIHaBtbFwdS360EKUIJE3IgmNDmVD1AaiE6ONy+0s7WhdqTWdfDvRqlIrbCyK5tOKUmaykTJT8PR6A4c2xxK2PorMDAM6S4VGHX1oGOyDpZUM6BQFx5CaStrx4yanqNLPREIuP7asvL3vFpw6gdjWqo2Fo5RsIfJLVVVOXj+ZdcQmKpRzN+9Oy+Bg5UBb77YE+wbTwqsFVhaFN9xAykw2UmYKT+KVFHasPMHZ8GsAuLpnDRCuVF0GCIvCo795i7SIYyYFJyPmbM4NFQVrf3+TMTi2NWuis7Ut+tBCFFOqqhJ+NZzQqFD+jPmTuFtxxnXO1s48Xflpgv2CaeLRBEudZYE+t5SZbKTMFC5VVTm9P55da06RnJg1A2X1Zh60fLEqdk7WGqcTpYU+IYHU8PC7p6jCj5J54WLODS0ssKlWLdsYnEBsA6qhWMv3qhAPY1ANHL58mA1RG9gYs5ErKVeM6zr7dWZq66kF+nxSZrKRMlM00pIz+PfXSI7uPA8q2DhY0qJrVWq28JQBwkITmVeumBaco0fRX7mSYzvFygqbGjVMCo5NFX8Uy4L9K1OIkkRv0HMg/gAbojawOWYzo5uM5hn/Zwr0OaTMZCNlpmjFRSWwffkJrp6/CYBXtawBwmU9ZeyC0JaqqmReunT3CuK3C44hISHHtoqdHbY1a2aNwbl9FXFrHx8UnUwaKcS9Mg2ZqKpa4ONnpMxkI2Wm6On1Bg5vOcfe9ZFkphvQWSg07OhDzRae2DlZY2Ujg4SFeVBVlYxz57LG3tweg5MaHo4htzlwHB2xrV07W8Gpg1VFLznyKEQhkTKTjZQZ7SReTWHnqpPEHLlqstzSSoedkzV2TlbYOlpj72SFrZM1do5WxuV2jrf/K+VHFDHVYCA9KirryM3tU1SpERGoaWk5trUoU+Z2sbl9FfHAOli5u2mQWoiSR8pMNlJmtKWqKpH/XWbPuigSL6egzzQ8/EH3kPIjtKZmZpJ2+rRpwTl5EnKZ5M+yQgVs69yd4M82MBDLMvIJPyHyS8pMNlJmzIeqqmSk6UlJyiDlZnrWf5PSSb2ZQXJSOqn3LE9JypDyI8yWIT2dtBMnTApO2unTYMj5PWtVsWLW5H53TlHVro2Fk5MGqYUoPqTMZCNlpviS8iOKG0NyMqnHj5uMwUmPjs51W2tfX9OCU7MmOvuinzJeCHMlZSYbKTOlh0n5SUon5eadkpP1dWqO5Y9Yfqx1JuXGzvF2+bmn9NwpQ1J+Sjd9UhKp4Xc+PZVVcDLOn8+5oU6HTZUqJlcRt6lRA53MgSNKKSkz2UiZEfcj5UdoJfP69axxN9lOUWXGx+fc0MoK22rVTMbg2FSpgmIlV6wXJZ+UmWykzIiCIuVHFKaMS/GkhmcrOEeOoL9xI8d2io0NtjVqmBQca19fFAv5PhAli5SZbKTMCK1I+RGPQ1VVMs5fuH0E5/YYnKNHMdy8mWNbnb09trVrm4zBsfL2ljlwRLEmZSYbKTOiuNCy/Ng5WWObW/lxtsbKWsqPuVANBtJjYm7PYHy74Bw7hpqSkmNbnYsLdrcLzp0xOJYeHlJwRLEhZSYbKTOipLpbfm5/ouue8pNi/MSXlJ+STM3MJC0yktQjR0kNzzpFlXb8OGouc+DoHBzQ2duj2Nuhs7VDZ2eHzt4OJbev7WxR7OzQ2dnn+FpnZ3f7/t0bVlZSlESBkjKTjZQZIbJI+Sk91PR0Uk+eyjpFdafgnDoFen3hPamFhbHYZC86ip3t7RJk+rWUJfEwUmaykTIjxKOR8lOyGFJTybh4ETU1FUNKCobkFNTUlFy/NqSmoBq/TkVNSTZ+bUhJRjV+nQKZmUXzAm6XJZNCZGubdZTJzj7H1zr724XI1i7H1zq720eg7O+WL0XKktnJz+9vuca9ECJXiqJgbWuJta0lLhUevv2jlp/MdANJ11JJupaap1yW1jqT0nNnoLOtkxX2TtbYZl/uJOXnDp2tLTZ+fgW+XzU93VhsDMnJd8tSyu1ClOPr24XI+HVKVllKufO4ZNSUu/swliW9Pmvw882bFMrxpbyWpfuenrv9uHu+znqcvZSlQiZlRghRIB6p/KTqTWdxzlZ0Um5mlZ/k27M+m5Sfq6kkXZXyYw4Ua2ssrK2xKKQj32pGRq7l6FHLksk+UlPvXl+rKMrSvUeP7OxMClK+y9KdU3JSlqTMCCG0oSgK1naWWNtJ+RH3p1hZYWFlVQRl6fbptFwLkWk5uvfoUe6lKpeydOsW3LpV+GXJ9u5YowIZv1QMypKUGSFEsSDlRxQGsylLqalZ45JSbo9fSr5TiFKyxijdLkdqcrLxa0NKStGVJZ0u55GkbIXIqWMHXLt0KYxnzhMpM0KIEknKjzAHRVKWbhchNSXZ+LVpQSqAsmQwPLAs2QQEFMrryyspM0IIQeGUn3uv9G7IVPNffmwssorP7U9zZX1tne1K71bYO98tQVJ+ShdjWXJyKpT9m5SlB3z6zbZGjUJ5/rySMvOozh+A2D1g63L75prtaxewcQIzPr8ohHg8RVZ+0vQkpekLpPzY2Fuis1BQdAo6i9s3Xfb7OnS3vzYuy3FfZ7r8zte39yNKlsIuSwVFysyjitoBm0Puv17RmZabHKXH9e4yO9ec21nZSxkSogQx1/JTkBQFk3Kjs9Ddc/8hRel2mbq3bOl0t0vTnbKly1aisu8z15Kmy6W03d2HhYWCotM9cF+meXXGxyoKZj0otjSRMvOoylWDwBch5QakJmS73QB9OqgGSLmedXsUOqucBSe30mPrmvOokJ0rWNoU1CsVQmigMMpPenImBgMY9AZUg4rBoGLQ374Z1KxlehWD3pB1X59tm3vu554B1EwVA3fWF+KMw2YiezHS6ZRc7user2zlKG663MtWLo/NfhTtgflylMr75NEpZlveZAbgwpCRYlpwjIXnhmnpMSlB2bZTC+AHgKXt/U+BPbQYOYOF1eNnEEKUSKqqZhUXY7kxGEuOet+CdOe+Ab3+nqJ053HZytSDy9a95Sr38nU3Ty75st03yXN7e9P7KpTo35R5d7+jYnXaVKJxJ98Cfa4SNwPwggULmD59OhcvXqR27drMmTOHJ598UutY92dll3Vz8sj/Y1UV0m89vPCYrM++LBFQITMVbqbCzUuP+BocHlJ6HlCObJxBJ4MQhSipFCXrFAs6hax/6SX/37uxXN0pQSbFyXDfomTIXrhylLb73M+2T2NJy1au1GxHz+63Xp/L8z84n2lBVA25tzeDQQWDmuOYW2aatkfhzL7MrF69muHDh7NgwQJatmzJF198QadOnTh27BiVK1fWOl7BUxSwccy6uVTM/+MNBkhLzFmC7i1GOU6P3d4m/WbWfjJuZd2SLjza67Bxzll6LCyzxhIpOkC5/bWSy/3cluX2OCXb/fvtS3fPdvduc+8y5QHPl9vjctn3fR/3oNd87+N4SM68vr57953b+/uwfQshFF3WKZ+SX9uyqAYVg/qgI2jZypZBxc7RWtO8Zn+aqWnTpjRs2JCFCxcal9WsWZMuXbowZcqUhz6+sE4zqapKSkYJPB9syITURJS0rIKjpN5ASU2EtASU2/dJTUBJS0RJTchannLj9vpElMwUrV+BKGDqAwsdOUsQdwuSmpeyZ1L0chYqFe5fuvJQglVFl/VCHrHkqeSnPOeeT81rsb5PFtVke8j9NeRShm8vU02e+34F9T7L8739fTa/74qCet7isv2DHpPf7Qsmk1oA+7d19UBx9rrP9o+mxJxmSk9PZ//+/bz//vsmyzt06MDu3btzfUxaWhppaWnG+4mJiYWSLSVDT61xfxbKvs2PDeB2+/Zg1mTgTDLOyq17/puMJZnoUMn69aDC7f/euZ/bMkXJ+jr7Ngqmy5R7lj9wmfKgxxvI+lWcM6POuC7rqtC6bNvqlHuXZf1XyXZfd/vHhXLPNln/zZkRk8fd5715wOvN/n7d2d+jUlCzxnE9wm7kuI4QpUNGi+FYdZig2fObdZm5cuUKer0ed3d3k+Xu7u7ExcXl+pgpU6YwYYJ2b2hpl44VV3DhiuqStcCsj/uVJvkrfw8tj4qaazEDcpS/3IvdvfvEpBTmu/Tm9lqUB7/G3JeZFlqT90LJ+VrubPvw0mu4J/ftdUrW/h70/+C+pTePZf3efd4rt2VZy3NXUNvn9sMh/89ZUNnz/oOqMLPkex/5/EMlP9nz+x6WtXbMV5aCZtZl5o57Pwqmqup9Px42ZswYRowYYbyfmJiIt7d3gWeys7Lg2McdC3y/QgghRHFjZaXtaCKzLjPly5fHwsIix1GY+Pj4HEdr7rCxscHGpvDnWFEUBXtrs377hBBCiFJBp3WAB7G2tqZRo0Zs2rTJZPmmTZto0aKFRqmEEEIIYU7M/tDCiBEjeOWVV2jcuDHNmzdn8eLFnD17lkGDBmkdTQghhBBmwOzLTI8ePbh69Soff/wxFy9eJDAwkD/++AMfHx+towkhhBDCDJj9PDOPS5PLGQghhBDiseTn97dZj5kRQgghhHgYKTNCCCGEKNakzAghhBCiWJMyI4QQQohiTcqMEEIIIYo1KTNCCCGEKNakzAghhBCiWJMyI4QQQohiTcqMEEIIIYo1s7+cweO6M8FxYmKixkmEEEIIkVd3fm/n5UIFJb7MJCUlAeDt7a1xEiGEEELkV1JSEi4uLg/cpsRfm8lgMHDhwgWcnJxQFEXrOIUuMTERb29vYmNj5VpUDyHvVd7Je5U/8n7lnbxXeVfa3itVVUlKSsLLywud7sGjYkr8kRmdTkelSpW0jlHknJ2dS8U3e0GQ9yrv5L3KH3m/8k7eq7wrTe/Vw47I3CEDgIUQQghRrEmZEUIIIUSxJmWmhLGxsWH8+PHY2NhoHcXsyXuVd/Je5Y+8X3kn71XeyXt1fyV+ALAQQgghSjY5MiOEEEKIYk3KjBBCCCGKNSkzQgghhCjWpMwIIYQQoliTMlMCTZkyBUVRGD58uNZRzNb58+d5+eWXKVeuHPb29tSvX5/9+/drHcvsZGZm8uGHH+Ln54ednR3+/v58/PHHGAwGraNpbufOnTz33HN4eXmhKAq//PKLyXpVVQkJCcHLyws7OzvatGlDeHi4NmE19qD3KiMjg9GjR1OnTh0cHBzw8vKiT58+XLhwQbvAGnvY91Z2AwcORFEU5syZU2T5zJGUmRImLCyMxYsXU7duXa2jmK3r16/TsmVLrKys2LBhA8eOHWPmzJm4urpqHc3sTJ06lUWLFjFv3jwiIiKYNm0a06dPZ+7cuVpH09ytW7eoV68e8+bNy3X9tGnTmDVrFvPmzSMsLAwPDw/at29vvF5cafKg9yo5OZkDBw7w0UcfceDAAX7++WdOnjzJ//73Pw2SmoeHfW/d8csvv7Bnzx68vLyKKJkZU0WJkZSUpFarVk3dtGmTGhQUpL799ttaRzJLo0ePVlu1aqV1jGLhmWeeUV977TWTZV27dlVffvlljRKZJ0Bdu3at8b7BYFA9PDzUTz/91LgsNTVVdXFxURctWqRBQvNx73uVm71796qAGhMTUzShzNj93q9z586pFStWVI8ePar6+Pios2fPLvJs5kSOzJQgQ4YM4ZlnnqFdu3ZaRzFrv/32G40bN6Zbt264ubnRoEEDvvzyS61jmaVWrVqxZcsWTp48CcChQ4fYtWsXnTt31jiZeYuKiiIuLo4OHToYl9nY2BAUFMTu3bs1TFY8JCQkoCiKHC29D4PBwCuvvMJ7771H7dq1tY5jFkr8hSZLi1WrVnHgwAHCwsK0jmL2IiMjWbhwISNGjOCDDz5g7969DBs2DBsbG/r06aN1PLMyevRoEhISqFGjBhYWFuj1eiZNmkSvXr20jmbW4uLiAHB3dzdZ7u7uTkxMjBaRio3U1FTef/99XnrppVJzMcX8mjp1KpaWlgwbNkzrKGZDykwJEBsby9tvv83GjRuxtbXVOo7ZMxgMNG7cmMmTJwPQoEEDwsPDWbhwoZSZe6xevZrly5fz/fffU7t2bQ4ePMjw4cPx8vLi1Vdf1Tqe2VMUxeS+qqo5lom7MjIy6NmzJwaDgQULFmgdxyzt37+fzz77jAMHDsj3UjZymqkE2L9/P/Hx8TRq1AhLS0ssLS3ZsWMHn3/+OZaWluj1eq0jmhVPT09q1ar1/+3df0zU9R8H8OdxHlzeBchhHDe6uxQGN2BcDJsehlbWtZbWlrtKdxNpbVaG2XHVau3I8uSYaUXYgi1j5frp8tcSsjrScGmiLJd5iZ1p84p+0JyxyQHv7x+OT35AAf1iHw6ej+22+7w/n8/7/Xq/+fXi/Xm/QVZms9lw8uRJhSIau7xeL5555hk88MADyM/Ph9vtxsqVK7FmzRqlQxvTjEYjgH9naPp1dHQMmq2h86LRKFwuF8LhMHbt2sVZmUvYs2cPOjo6YDabpe/3P//8MzweD6xWq9LhKYYzM+PAbbfdhsOHD8vKli5dipycHDz99NNQq9UKRTY2FRcXIxQKycp+/PFHWCwWhSIau7q6uhAXJ/+dR61Wc2v2MG644QYYjUbs2rULN954IwCgu7sbX331FQKBgMLRjT39icyxY8cQDAZhMBiUDmnMcrvdg9ZFOp1OuN1uLF26VKGolMdkZhy49tprkZeXJyvT6XQwGAyDyglYuXIlHA4H/H4/XC4X9u/fj7q6OtTV1Skd2pgzf/58rF69GmazGbm5uTh06BDWrVuHsrIypUNT3NmzZ9He3i4dh8NhtLW1ISUlBWazGU888QT8fj+ysrKQlZUFv9+PyZMnY9GiRQpGrYyhxspkMmHhwoU4ePAgduzYgd7eXmlGKyUlBfHx8UqFrZjhPrcGJnsajQZGoxHZ2dn/dahjh9Lbqejq4NbsoW3fvl3k5eWJhIQEkZOTI+rq6pQOaUw6c+aMWLFihTCbzUKr1Ypp06aJ5557Tpw7d07p0BQXDAYFgEGvJUuWCCHOb8/2+XzCaDSKhIQEUVJSIg4fPqxs0AoZaqzC4fBFzwEQwWBQ6dAVMdzn1kDcmi2ESggh/tPsiYiIiGgUcQEwERERxTQmM0RERBTTmMwQERFRTGMyQ0RERDGNyQwRERHFNCYzREREFNOYzBAREVFMYzJDREREMY3JDBGNuhMnTkClUqGtrU3pUCRHjx7FzJkzodVqYbfbr0obzc3NUKlU+Pvvv69K/UR0cUxmiMah0tJSqFQqVFVVycq3bNkClUqlUFTK8vl80Ol0CIVC+OKLLy56Tf+4qVQqaDQaTJs2DRUVFfjnn39G1IbD4UAkEkFSUtKI4yotLcW999474uuJaDAmM0TjlFarRSAQQGdnp9KhjJru7u4rvvf48eOYPXs2LBbLkP+V+c4770QkEsFPP/2El156CRs2bEBFRcWI2oiPj4fRaJywCSORUpjMEI1T8+bNg9FoxJo1ay55TWVl5aBHLq+88gqsVqt03D9z4Pf7kZaWhuTkZLzwwgvo6emB1+tFSkoKMjIy8NZbbw2q/+jRo3A4HNBqtcjNzUVzc7Ps/JEjR3DXXXdBr9cjLS0Nbrcbf/zxh3R+7ty5WL58OZ588kmkpqbi9ttvv2g/+vr6sGrVKmRkZCAhIQF2ux2NjY3SeZVKhdbWVqxatQoqlQqVlZWXHJOEhAQYjUZcf/31WLRoERYvXowtW7YAAM6dO4fy8nJcd9110Gq1mD17Nr799lvp3oGPmd5++20kJyejqakJNpsNer1eSpb6x7+hoQFbt26VZoSam5vR3d2N5cuXIz09HVqtFlardciPI9FEx2SGaJxSq9Xw+/2oqanBL7/88n/V9eWXX+L06dPYvXs31q1bh8rKStx9992YMmUK9u3bh2XLlmHZsmU4deqU7D6v1wuPx4NDhw7B4XBgwYIF+PPPPwEAkUgEc+bMgd1ux4EDB9DY2IjffvsNLpdLVkdDQwMmTZqElpYWvPnmmxeN79VXX8XLL7+MtWvX4rvvvoPT6cSCBQtw7Ngxqa3c3Fx4PB5EIpERz7QAwDXXXINoNAoAeOqpp7B582Y0NDTg4MGDyMzMhNPpxF9//XXJ+7u6urB27Vq888472L17N06ePCm1X1FRAZfLJSU4kUgEDocDr732GrZt24YPP/wQoVAI7777rizBJKIBlP633UQ0+pYsWSLuueceIYQQM2fOFGVlZUIIIT755BNx4Ze9z+cTBQUFsnvXr18vLBaLrC6LxSJ6e3ulsuzsbHHzzTdLxz09PUKn04n33ntPCCFEOBwWAERVVZV0TTQaFRkZGSIQCAghhHj++efFHXfcIWv71KlTAoAIhUJCCCHmzJkj7Hb7sP01mUxi9erVsrIZM2aIRx99VDouKCgQPp9vyHouHDchhNi3b58wGAzC5XKJs2fPCo1GIzZt2iSd7+7uFiaTSVRXVwshhAgGgwKA6OzsFEIIsXHjRgFAtLe3S/fU1taKtLS0S7YphBCPP/64uPXWW0VfX9+wfSciITgzQzTOBQIBNDQ04MiRI1dcR25uLuLi/v12kZaWhvz8fOlYrVbDYDCgo6NDdt+sWbOk95MmTUJRURF++OEHAEBrayuCwSD0er30ysnJAXB+fUu/oqKiIWM7c+YMTp8+jeLiYll5cXGx1Nbl2LFjB/R6PbRaLWbNmoWSkhLU1NTg+PHjiEajsnY0Gg1uuummIduZPHkypk+fLh2np6cPGqeBSktL0dbWhuzsbJSXl+Ozzz677H4QTSSTlA6AiK6ukpISOJ1OPPvssygtLZWdi4uLgxBCVtb/SOVCGo1Gdty/22dgWV9f37Dx9C+O7evrw/z58xEIBAZdk56eLr3X6XTD1nlhvf2EEFe0EPeWW27BG2+8AY1GA5PJJPWzf53L5bZzsXEaOOYDFRYWIhwOY+fOnfj888/hcrkwb948fPzxx5fdH6KJgDMzRBNAVVUVtm/fjr1798rKp06dil9//VX2w3U0/zbMN998I73v6elBa2urNPtSWFiI77//HlarFZmZmbLXSBMYAEhMTITJZMLXX38tK9+7dy9sNttlx6zT6ZCZmQmLxSJLRDIzMxEfHy9rJxqN4sCBA1fUTr/4+Hj09vYOKk9MTMT999+P+vp6fPDBB9i8efOQa3OIJjLOzBBNAPn5+Vi8eDFqampk5XPnzsXvv/+O6upqLFy4EI2Njdi5cycSExNHpd3a2lpkZWXBZrNh/fr16OzsRFlZGQDgscceQ319PR588EF4vV6kpqaivb0d77//Purr66FWq0fcjtfrhc/nw/Tp02G327Fx40a0tbVh06ZNo9IP4HyS88gjj0g7uMxmM6qrq9HV1YWHHnroiuu1Wq1oampCKBSCwWBAUlISXn/9daSnp8NutyMuLg4fffQRjEYjkpOTR60/ROMJZ2aIJogXX3xx0OMNm82GDRs2oLa2FgUFBdi/f/9l7fQZTlVVFQKBAAoKCrBnzx5s3boVqampAACTyYSWlhb09vbC6XQiLy8PK1asQFJSkmx9zkiUl5fD4/HA4/EgPz8fjY2N2LZtG7KyskatL/39ue++++B2u1FYWIj29nY0NTVhypQpV1znww8/jOzsbBQVFWHq1KloaWmBXq9HIBBAUVERZsyYgRMnTuDTTz+97HEhmihUYriHt0RERERjGNN8IiIiimlMZoiIiCimMZkhIiKimMZkhoiIiGIakxkiIiKKaUxmiIiIKKYxmSEiIqKYxmSGiIiIYhqTGSIiIoppTGaIiIgopjGZISIiopj2PyN7BZHMvxUsAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npoints_list = [3, 5, 11, 15]\n", + "relative_error = []\n", + "\n", + "for i in range(len(npoints_list)):\n", + " relative_error.append([])\n", + " grid_list = [\n", + " GaussChebyshev(npoints_list[i]),\n", + " GaussLegendre(npoints_list[i]),\n", + " TanhSinh(npoints_list[i]),\n", + " Trapezoidal(npoints_list[i]),\n", + " Simpson(npoints_list[i]),\n", + " ]\n", + "\n", + " for j in range(len(grid_list)):\n", + " vals = function(grid_list[j].points)\n", + " integral = grid_list[j].integrate(vals)\n", + " relative_error[-1].append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + "\n", + "relative_error = np.array(relative_error).T\n", + "print(relative_error)\n", + "for i in range(len(names)):\n", + " plt.plot(npoints_list, relative_error[i], label=names[i])\n", + "plt.legend()\n", + "plt.xlabel(\"Number of Points\")\n", + "plt.ylabel(\"Relative Error %\")" ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from grid.rtransform import BeckeRTransform\n", - "\n", - "# create a list of names and a list of grid objects\n", - "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\"]\n", - "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh]\n", - "\n", - "# Becke R-transform (goes from 0 to \\infty) to transform the Gauss-Chebyshev grid\n", - "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(gaus_cheb)\n", - "\n", - "# plot the grid\n", - "plt.figure(figsize=(8, 5))\n", - "\n", - "plt.xlim(0, 2500)\n", - "for i in range(len(onedgrids)):\n", - " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(onedgrids[i])\n", - " plt.scatter(\n", - " rgrid.points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", - " ) # Switched x and y values\n", - "\n", - "# set the y-ticks to be the names\n", - "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", - "\n", - "# set the labels\n", - "plt.xlabel(\"R\")\n", - "plt.ylabel(\"Quadrature Rule\")\n", - "\n", - "# show the plot\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is usually more rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). \n", - "\n", - "As en example, let's find the following integral:\n", - "\n", - "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n", - "\n", - "using a one dimensional grid with 20 points and an appropriate transformation. The exact value of the integral is 2." - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": {}, - "outputs": [ + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Integral of r^2 * exp(-r) from 0 to infinity:1.9999900526117749 should be close to 2.0\n" - ] + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "#### Transformation of onedgrids integration intervals\n", + "The $[-1,1]$ interval is too small for being of real use in quantum chemistry, where the integrals are usually performed in the interval $[0,\\infty)$. To solve this issue, Grid supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. The following figure shows the location of the points for different quadrature rules after a Becke transformation:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "ExecuteTime": { + "end_time": "2023-06-19T16:51:37.054546020Z", + "start_time": "2023-06-19T16:51:37.044961659Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from grid.rtransform import BeckeRTransform\n", + "\n", + "# create a list of names and a list of grid objects\n", + "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\"]\n", + "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh]\n", + "\n", + "# Becke R-transform (goes from 0 to \\infty) to transform the Gauss-Chebyshev grid\n", + "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(gaus_cheb)\n", + "\n", + "# plot the grid\n", + "plt.figure(figsize=(8, 5))\n", + "\n", + "plt.xlim(0, 2500)\n", + "for i in range(len(onedgrids)):\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(onedgrids[i])\n", + " plt.scatter(\n", + " rgrid.points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", + " ) # Switched x and y values\n", + "\n", + "# set the y-ticks to be the names\n", + "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", + "\n", + "# set the labels\n", + "plt.xlabel(\"R\")\n", + "plt.ylabel(\"Quadrature Rule\")\n", + "\n", + "# show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is usually more rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). \n", + "\n", + "As en example, let's find the following integral:\n", + "\n", + "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n", + "\n", + "using a one dimensional grid with 20 points and an appropriate transformation. The exact value of the integral is 2." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Integral of r^2 * exp(-r) from 0 to infinity:1.9999900526117749 should be close to 2.0\n" + ] + } + ], + "source": [ + "# set the radial grid\n", + "oned = GaussChebyshev(20)\n", + "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(one_d_grid)\n", + "\n", + "# calculate the function values at the grid points\n", + "vals = rgrid.points**2 * np.exp(-rgrid.points)\n", + "\n", + "integral = rgrid.integrate(vals)\n", + "\n", + "print(f\"Integral of r^2 * exp(-r) from 0 to infinity:{integral} should be close to 2.0\")" + ] + } + ], + "metadata": { + "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": "3.10.12" } - ], - "source": [ - "# set the radial grid\n", - "oned = GaussChebyshev(20)\n", - "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(one_d_grid)\n", - "\n", - "# calculate the function values at the grid points\n", - "vals = rgrid.points**2 * np.exp(-rgrid.points)\n", - "\n", - "integral = rgrid.integrate(vals)\n", - "\n", - "print(f\"Integral of r^2 * exp(-r) from 0 to infinity:{integral} should be close to 2.0\")" - ] - } - ], - "metadata": { - "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": "3.10.12" - } - }, - "nbformat": 4, - "nbformat_minor": 0 + "nbformat": 4, + "nbformat_minor": 0 } From e7af8965593137ab32f168aa9f69681d616d09ef Mon Sep 17 00:00:00 2001 From: Farnaz Heidar-Zadeh Date: Wed, 3 Jan 2024 21:05:07 +0330 Subject: [PATCH 4/9] Disable zero division warning in BeckeRTransform BeckeRTransform of certain OneDGrids with points at 1.0 (like Trapezoidal) resulted in RuntimeWarning: divide by zero encountered in deriv and deriv2 methods. To avoid printing a warning message, the zero devision was disabled. --- src/grid/rtransform.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/src/grid/rtransform.py b/src/grid/rtransform.py index e3d5d4e27..7c2a2d8ea 100644 --- a/src/grid/rtransform.py +++ b/src/grid/rtransform.py @@ -269,7 +269,8 @@ def deriv(self, x: np.ndarray): np.ndarray(N,) First derivative of Becke transformation at each point. """ - deriv = 2 * self._R / ((1 - x) ** 2) + with np.errstate(divide="ignore"): + deriv = 2 * self._R / ((1 - x) ** 2) if self.trim_inf: deriv = self._convert_inf(deriv) return deriv @@ -290,7 +291,8 @@ def deriv2(self, x: np.ndarray): np.ndarray(N,) Second derivative of Becke transformation at each point. """ - return 4 * self._R / (1 - x) ** 3 + with np.errstate(divide="ignore"): + return 4 * self._R / (1 - x) ** 3 def deriv3(self, x: np.ndarray): r"""Compute the third derivative of Becke transformation. From 87f3c51d50292211fadfc12926ecba824194ced0 Mon Sep 17 00:00:00 2001 From: Farnaz Heidar-Zadeh Date: Wed, 3 Jan 2024 21:24:35 +0330 Subject: [PATCH 5/9] Add class attribute name to various OneDGrid subclasses To simply tutorials and make it easier to keep track of the name of 1-dimensional grids, name was added as a class attribute. --- src/grid/onedgrid.py | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/src/grid/onedgrid.py b/src/grid/onedgrid.py index dc1831b37..ceb33c803 100644 --- a/src/grid/onedgrid.py +++ b/src/grid/onedgrid.py @@ -46,6 +46,7 @@ class GaussLaguerre(OneDGrid): \sum_{i=1}^n \left(\frac{w_i}{x_i^\alpha e^{-x_i}}\right) g(x_i) = \sum_{i=1}^n w_i' g(x_i) """ + name = "Gauss-Laguerre" def __init__(self, npoints: int, alpha: float = 0): r"""Generate grid on :math:`[0, \infty)` based on generalized Gauss-Laguerre quadrature. @@ -91,6 +92,7 @@ class GaussLegendre(OneDGrid): roots of the nth Legendre polynomial. """ + name = "Gauss-Legendre" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1, 1]` interval based on Gauss-Legendre quadrature. @@ -137,6 +139,7 @@ class GaussChebyshev(OneDGrid): \sum_{i=1}^n w_i'g(x_i) """ + name = "Gauss-Chebyshev" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1, 1]` interval based on Gauss-Chebyshev quadrature. @@ -172,6 +175,7 @@ class UniformInteger(OneDGrid): w_i =& 1.0 """ + name = "Uniform-Integer" def __init__(self, npoints: int): r"""Generate grid on [0, npoints] interval using equally spaced uniform distribution. @@ -212,6 +216,7 @@ class GaussChebyshevType2(OneDGrid): \sum_{i=1}^n w_i' g(x_i) """ + name = "Gauss-Chebyshev-Type2" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1, 1]` interval based on Gauss-Chebyshev Type 2. @@ -253,6 +258,7 @@ class GaussChebyshevLobatto(OneDGrid): \int_{-1}^{1}g(x) dx \approx \sum_{i=1}^n \left(w_i \sqrt{1-x_i^2}\right) g(x_i) = \sum_{i=1}^n w_i' g(x_i) """ + name = "Gauss-Chebyshev-Lobatto" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1, 1]` interval based on Gauss-Chebyshev-Lobatto quadrature. @@ -294,6 +300,7 @@ class Trapezoidal(OneDGrid): w_{i\neq 1,n} =& \frac{2}{n} """ + name = "Trapezoidal-Lobatto" def __init__(self, npoints: int): r"""Generate grid on [-1, 1] interval based on Trapezoidal (Euler-Maclaurin) rule. @@ -340,6 +347,7 @@ class RectangleRuleSineEndPoints(OneDGrid): .. [#] Boyd, John P. Chebyshev and Fourier spectral methods. Courier Corporation, 2001. """ + name = "Rectangle-Rule-Sine" def __init__(self, npoints: int): r""" @@ -455,6 +463,7 @@ class TanhSinh(OneDGrid): endpoints of :math:`[-1, 1]`. """ + name = "Tanh-Sinh" def __init__(self, npoints: int, delta: float = 0.1): r"""Generate grid on :math:`[-1, 1]` interval based on Tanh-Sinh rule. @@ -507,6 +516,7 @@ class Simpson(OneDGrid): \end{cases} """ + name = "Simpson" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1,1]` interval based on Simpson rule. @@ -548,6 +558,7 @@ class MidPoint(OneDGrid): w_i =& \frac{2}{n} """ + name = "MidPoint" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1, 1]` interval based on Mid-Point rule. @@ -597,6 +608,7 @@ class ClenshawCurtis(OneDGrid): and handled separately. """ + name = "Clenshaw-Curtis" def __init__(self, npoints: int): r"""Generate grid on :math:`[-1,1]` interval based on Clenshaw-Curtis method. @@ -653,6 +665,7 @@ class FejerFirst(OneDGrid): and handled separately. """ + name = "Fejer-First" def __init__(self, npoints: int): r"""Generate 1D grid on :math:`(-1,1)` interval based on Fejer's first rule. @@ -705,6 +718,7 @@ class FejerSecond(OneDGrid): recommended to break the intervals at the discontinuities and handled separately. """ + name = "Fejer-Second" def __init__(self, npoints: int): r"""Generate grid on :math:`(-1,1)` interval based on Fejer's second rule. @@ -776,6 +790,8 @@ class TrefethenCC(OneDGrid): """ + name = "Trefethen-Polynomial-Transformation-Clenshaw-Curtis" + def __init__(self, npoints: int, d: int = 9): r"""Generate 1D grid on :math:`[-1,1]` interval based on Trefethen-Clenshaw-Curtis. @@ -820,6 +836,8 @@ class TrefethenGC2(OneDGrid): """ + name = "Trefethen-Polynomial-Transformation-Gauss-Chebyshev-Type2" + def __init__(self, npoints: int, d: int = 9): r"""Generate 1D grid on [-1,1] interval based on Trefethen-Gauss-Chebyshev. @@ -864,6 +882,8 @@ class TrefethenGeneral(OneDGrid): """ + name = "Trefethen-Polynomial" + def __init__(self, npoints: int, quadrature: OneDGrid, d=9): r"""Generate 1D grid on :math:`[-1,1]` interval based on Trefethen-General. @@ -957,6 +977,8 @@ class TrefethenStripCC(OneDGrid): """ + name = "Trefethen-Strip-Transformation-Clenshaw-Curtis" + def __init__(self, npoints: int, rho: float = 1.1): r"""Generate grid on :math:`[-1,1]` interval based on Trefethen-Clenshaw-Curtis. @@ -987,6 +1009,8 @@ class TrefethenStripGC2(OneDGrid): """ + name = "Trefethen-Strip-Transformation-Gauss-Chebyshev-Type2" + def __init__(self, npoints: int, rho: float = 1.1): r"""Generate grid on :math:`[-1,1]` interval based on Trefethen-Gauss-Chebyshev. @@ -1018,6 +1042,8 @@ class TrefethenStripGeneral(OneDGrid): """ + name = "Trefethen-Strip-General" + def __init__(self, npoints: int, quadrature, rho: float = 1.1): r"""Generate grid on :math:`[-1,1]` interval based on Trefethen-General. @@ -1055,6 +1081,7 @@ class ExpSinh(OneDGrid): - Using this quadrature requires heavy parameter-tuning in-order to work. """ + name = "Exponential-Hyperbolic-Sine" def __init__(self, npoints: int, h: float = 1.0): r"""Generate 1D grid on :math:`(0, \infty)` interval based on exp-sinh quadrature. @@ -1106,6 +1133,7 @@ class LogExpSinh(OneDGrid): - Using this quadrature requires heavy parameter-tuning in-order to work. """ + name = "Logarithm-Exponential-Hyperbolic-Sine" def __init__(self, npoints: int, h: float = 0.1): r"""Generate 1D grid on :math:`(0, \infty)` interval based on log-exp-sinh quadrature. @@ -1157,6 +1185,7 @@ class ExpExp(OneDGrid): - Using this quadrature requires heavy parameter-tuning in-order to work. """ + name = "Exponential-Exponential" def __init__(self, npoints: int, h: float = 0.1): r"""Generate 1D grid on :math:`(0, \infty)` interval based on exp-exp quadrature. @@ -1203,6 +1232,7 @@ class SingleTanh(OneDGrid): w_k = \frac{h}{\cosh^2(kh)} """ + name = "Hyperbolic-Tan" def __init__(self, npoints: int, h: float = 0.1): r"""Generate 1D grid on :math:`(-1, +1)` interval based on tanh-sinh quadrature. @@ -1249,6 +1279,7 @@ class SingleExp(OneDGrid): - Using this quadrature requires heavy parameter-tuning in-order to work. """ + name = "Single-Exponential" def __init__(self, npoints: int, h: float = 0.1): r"""Generate 1D grid on :math:`(0, \infty)` interval based on exponential quadrature. @@ -1299,6 +1330,7 @@ class SingleArcSinhExp(OneDGrid): - Using this quadrature requires heavy parameter-tuning in-order to work. """ + name = "Single-Arc-Hyperbolic-Sine-Exponential" def __init__(self, npoints: int, h: float = 0.1): r"""Generate 1D grid on :math:`(0, \infty)` interval based on tanh-sinh quadrature. From ffecfad83fd391ade24e63c7da295202b15b67e5 Mon Sep 17 00:00:00 2001 From: Farnaz Heidar-Zadeh Date: Wed, 3 Jan 2024 21:48:32 +0330 Subject: [PATCH 6/9] Improve One_dimensional_grids.ipynb notebook --- doc/notebooks/One_dimensional_grids.ipynb | 651 ++++++++++------------ 1 file changed, 307 insertions(+), 344 deletions(-) diff --git a/doc/notebooks/One_dimensional_grids.ipynb b/doc/notebooks/One_dimensional_grids.ipynb index fde31ceeb..4ddace328 100644 --- a/doc/notebooks/One_dimensional_grids.ipynb +++ b/doc/notebooks/One_dimensional_grids.ipynb @@ -1,359 +1,322 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": false - }, - "source": [ - "# One-dimensional (radial) grids\n", - "\n", - "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1,1] interval). These are used to integrate functions numerically:\n", - "\n", - "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n", - "\n", - " The following table shows some of the available quadrature rules and the corresponding grid points and weights.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": { - "ExecuteTime": { - "end_time": "2023-06-19T16:51:32.568341203Z", - "start_time": "2023-06-19T16:51:31.905745917Z" - }, - "collapsed": true - }, - "outputs": [], - "source": [ - "from grid.onedgrid import *\n", - "\n", - "# Select and compare several grid types with 30 points in the interval [-1,1]\n", - "# -------------------------------------\n", - "npoints = 31\n", - "# Gauss-Chebyshev\n", - "gaus_cheb = GaussChebyshev(npoints)\n", - "\n", - "# Gauss-Legendre\n", - "gaus_leg = GaussLegendre(npoints)\n", - "\n", - "# Tanh-Sinh\n", - "tanh_sinh = TanhSinh(npoints)\n", - "\n", - "# Trapezoidal\n", - "trap_lob = Trapezoidal(npoints)\n", - "\n", - "# Simpson\n", - "simp_lob = Simpson(npoints)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Different quadrature rules have the points located at different positions and thus are appropriate for different problems. A higher point density is usually required where the integrand is more rapidly varying. The following figure shows the points for different quadrature rules supported by Grid." - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "# create a list of names and a list of grid objects\n", - "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\", \"Trapezoidal\", \"Simpson\"]\n", - "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh, trap_lob, simp_lob]\n", - "\n", - "\n", - "for i in range(len(onedgrids)):\n", - " plt.scatter(\n", - " onedgrids[i].points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", - " ) \n", - "\n", - "# set the y-ticks to be the names\n", - "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", - "\n", - "# set the labels\n", - "plt.xlabel(\"R\")\n", - "plt.ylabel(\"Quadrature Rule\")\n", - "\n", - "# show the plot\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The one-dimensional grids can be used to perform integrals in the defined interval and are very accurate even for a small number of points. \n", - "\n", - "As an example, let's find the integral of the function $f(x) = \\sqrt(1-x^2)$ in the interval $[-1,1]$ using the previously defined grids. The exact value of the integral is $\\pi/2$." - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The integral of sqrt(1-x^2) from -1 to 1 is pi/2 = 1.5707963267948966\n", - "Integral of sqrt(1-x^2) using GaussChebyshev is 1.5707963267948966\n", - "Integral of sqrt(1-x^2) using GaussLegendre is 1.5708227035118671\n", - "Integral of sqrt(1-x^2) using TanhSinh is 1.5706704474237596\n", - "Integral of sqrt(1-x^2) using Trapezoidal is 1.5606957062377849\n", - "Integral of sqrt(1-x^2) using Simpson is 1.5668324581559745\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# define the function to integrate\n", - "function = lambda x: np.sqrt(1 - x**2)\n", - "\n", - "print(\"The integral of sqrt(1-x^2) from -1 to 1 is pi/2 =\", np.pi / 2)\n", - "\n", - "relative_error = []\n", - "\n", - "for i in range(len(onedgrids)):\n", - " # calculate the function values at the grid points\n", - " vals = function(onedgrids[i].points)\n", - " # integrate the function using the grid\n", - " integral = onedgrids[i].integrate(vals)\n", - " print(\"Integral of sqrt(1-x^2) using\", names[i], \"is\", integral)\n", - " relative_error.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - "\n", - "# plot the relative error as columns graph\n", - "plt.figure(figsize=(8, 5))\n", - "plt.title(\n", - " r\"Relative Error for Different Grids with \"\n", - " + str(npoints)\n", - " + \" Points for $\\int_{-1}^1 \\sqrt{1-x^2} dx$\"\n", - ")\n", - "plt.bar(names, relative_error)\n", - "plt.ylabel(\"Relative Error %\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following example shows how the error in the integral converges with the number of points for the different quadrature rules. The function to test is the same as before, $f(x) = \\sqrt(1-x^2)$ and the integral is performed in the interval $[-1,1]$." - ] - }, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# One-Dimensional and Radial Grids\n", + "\n", + "[OneDGrid](https://grid.qcdevs.org/pyapi/grid.basegrid.html#grid.basegrid.OneDGrid)\n", + "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1, 1] interval).\n", + "\n", + "### Example: Visualize One-Dimensional Grid Points\n", + "\n", + "Here, we showcase some of the quadrature rules available each with a unique set of points. [Click here for a full list of one-dimensional grid classes.](https://grid.qcdevs.org/pyapi/grid.onedgrid.html)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "ExecuteTime": { + "end_time": "2023-06-19T16:51:32.568341203Z", + "start_time": "2023-06-19T16:51:31.905745917Z" + } + }, + "outputs": [], + "source": [ + "from grid.onedgrid import *\n", + "\n", + "# Make several 1-dimensional grids for a given number of points\n", + "npoints = 31\n", + "\n", + "grids = [\n", + " GaussChebyshev(npoints),\n", + " GaussLegendre(npoints),\n", + " TanhSinh(npoints),\n", + " Simpson(npoints),\n", + " Trapezoidal(npoints),\n", + "]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[2.82715972e-14 1.41357986e-14 1.41357986e-14 0.00000000e+00]\n", - " [1.32550164e+00 3.25313217e-01 3.47241509e-02 1.41361473e-02]\n", - " [7.06296872e+01 5.30277668e+01 1.68869830e+01 6.11617195e+00]\n", - " [3.63380228e+01 1.30361218e+01 3.32773329e+00 2.01237879e+00]\n", - " [1.51173637e+01 5.26882153e+00 1.31839796e+00 7.94070592e-01]]\n" - ] - }, - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'Relative Error %')" - ] - }, - "execution_count": 63, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "npoints_list = [3, 5, 11, 15]\n", - "relative_error = []\n", - "\n", - "for i in range(len(npoints_list)):\n", - " relative_error.append([])\n", - " grid_list = [\n", - " GaussChebyshev(npoints_list[i]),\n", - " GaussLegendre(npoints_list[i]),\n", - " TanhSinh(npoints_list[i]),\n", - " Trapezoidal(npoints_list[i]),\n", - " Simpson(npoints_list[i]),\n", - " ]\n", - "\n", - " for j in range(len(grid_list)):\n", - " vals = function(grid_list[j].points)\n", - " integral = grid_list[j].integrate(vals)\n", - " relative_error[-1].append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - "\n", - "relative_error = np.array(relative_error).T\n", - "print(relative_error)\n", - "for i in range(len(names)):\n", - " plt.plot(npoints_list, relative_error[i], label=names[i])\n", - "plt.legend()\n", - "plt.xlabel(\"Number of Points\")\n", - "plt.ylabel(\"Relative Error %\")" + "data": { + "image/png": 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", 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" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "names = []\n", + "for i, oned in enumerate(grids):\n", + " plt.scatter(oned.points, np.repeat(i + 1, oned.size), marker=\"o\")\n", + " names.append(oned.name)\n", + "\n", + "# set the y-ticks to be the 1D grid names, and set labels\n", + "plt.title(f\"{npoints} Grid Points in One Dimension\", fontsize=16)\n", + "plt.yticks(range(1, len(grids) + 1), names)\n", + "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", + "plt.ylabel(\"Quadrature Rule\", fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example: Integration of One-Variable Function on $[-1, 1]$\n", + "\n", + "The one-dimensional grids can accurately integrate one-variable functions over an interval (defined by their domain), even with a small number of points. Here, we numerically compute the integral below and compute the relative percent error. The analytical value of this integral is $\\pi/2$.\n", + "\n", + "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": { - "collapsed": false - }, - "source": [ - "#### Transformation of onedgrids integration intervals\n", - "The $[-1,1]$ interval is too small for being of real use in quantum chemistry, where the integrals are usually performed in the interval $[0,\\infty)$. To solve this issue, Grid supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. The following figure shows the location of the points for different quadrature rules after a Becke transformation:" - ] + "name": "stdout", + "output_type": "stream", + "text": [ + "Integral of sqrt(1-x^2) from -1 to 1:\n", + " 1.57079633 from Analytical integration (which is equal to pi/2)\n", + " 1.57079633 from Gauss-Chebyshev integration\n", + " 1.57082270 from Gauss-Legendre integration\n", + " 1.57067045 from Tanh-Sinh integration\n", + " 1.56683246 from Simpson integration\n", + " 1.56069571 from Trapezoidal-Lobatto integration\n" + ] }, { - "cell_type": "code", - "execution_count": 64, - "metadata": { - "ExecuteTime": { - "end_time": "2023-06-19T16:51:37.054546020Z", - "start_time": "2023-06-19T16:51:37.044961659Z" - }, - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from grid.rtransform import BeckeRTransform\n", - "\n", - "# create a list of names and a list of grid objects\n", - "names = [\"GaussChebyshev\", \"GaussLegendre\", \"TanhSinh\"]\n", - "onedgrids = [gaus_cheb, gaus_leg, tanh_sinh]\n", - "\n", - "# Becke R-transform (goes from 0 to \\infty) to transform the Gauss-Chebyshev grid\n", - "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(gaus_cheb)\n", - "\n", - "# plot the grid\n", - "plt.figure(figsize=(8, 5))\n", - "\n", - "plt.xlim(0, 2500)\n", - "for i in range(len(onedgrids)):\n", - " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(onedgrids[i])\n", - " plt.scatter(\n", - " rgrid.points, [i + 1] * len(onedgrids[i].points), marker=\"o\"\n", - " ) # Switched x and y values\n", - "\n", - "# set the y-ticks to be the names\n", - "plt.yticks(range(1, len(names) + 1), names) # Adjusted the range for y-ticks\n", - "\n", - "# set the labels\n", - "plt.xlabel(\"R\")\n", - "plt.ylabel(\"Quadrature Rule\")\n", - "\n", - "# show the plot\n", - "plt.show()" + "data": { + "image/png": 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", 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" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# define the function to integrate\n", + "function = lambda x: np.sqrt(1 - x**2)\n", + "\n", + "print(\"Integral of sqrt(1-x^2) from -1 to 1:\")\n", + "print(f\"{np.pi / 2: .8f} from Analytical integration (which is equal to pi/2)\")\n", + "\n", + "names = []\n", + "error_relative = []\n", + "for oned in grids:\n", + " # integrate the function evaluated on the grid points\n", + " integral = oned.integrate(function(oned.points))\n", + " print(f\"{integral: .8f} from {oned.name} integration\")\n", + " error_relative.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + " names.append(oned.name)\n", + "\n", + "# plot the relative error as columns graph\n", + "plt.figure(figsize=(8.5, 5))\n", + "plt.bar(names, error_relative)\n", + "title = r\"Numerical Integration of $\\int_{-1}^1 \\sqrt{1-x^2} dx$ with \" + str(npoints) + \" Points\"\n", + "plt.title(title, fontsize=16)\n", + "plt.xlabel(\"Quadrature Rule\", fontsize=14)\n", + "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Changing the number of grid points increases the accuracy of each quadrature. Here we show how the relative integration error converges to zero when increasing the number of points.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is usually more rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). \n", - "\n", - "As en example, let's find the following integral:\n", - "\n", - "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n", - "\n", - "using a one dimensional grid with 20 points and an appropriate transformation. The exact value of the integral is 2." + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npoints = [3, 5, 11, 15, 17, 19, 21, 31]\n", + "grid_classes = [GaussChebyshev, GaussLegendre, TanhSinh, Simpson, Trapezoidal]\n", + "\n", + "for grid_class in grid_classes:\n", + " errors = []\n", + " for npoint in npoints:\n", + " # make 1-dimensional grid for the given number of points\n", + " oned = grid_class(npoint)\n", + " # compute relative percent error of integration\n", + " integral = oned.integrate(function(oned.points))\n", + " errors.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + " # plot relative percent error vs. number of grid points\n", + " plt.plot(npoints, errors, label=oned.name)\n", + "\n", + "plt.legend(frameon=False, fontsize=12)\n", + "plt.title(r\"Numerical Integration of $\\int_{-1}^1 \\sqrt{1-x^2} dx$\", fontsize=16)\n", + "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", + "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", + "plt.xticks(npoints)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Radial Grid: Transformation of 1D-Integration Intervals\n", + "\n", + "Generally, areas where the integrand changes more rapidly demand a denser concentration of points. So, the $[-1, 1]$ interval is not suitable for most applications encountered in quantum chemistry, where the integrals are usually performed on $[0,\\infty)$ domain. `grid` supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. [Click here for a full list of radial transformations.](https://grid.qcdevs.org/pyapi/grid.rtransform.html)\n", + "\n", + "### Visualize Radial Grid Points\n", + "\n", + "Here we visualize the OneDGrid points for different quadrature rules after a Becke transformation.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "ExecuteTime": { + "end_time": "2023-06-19T16:51:37.054546020Z", + "start_time": "2023-06-19T16:51:37.044961659Z" + } + }, + "outputs": [ { - "cell_type": "code", - "execution_count": 65, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Integral of r^2 * exp(-r) from 0 to infinity:1.9999900526117749 should be close to 2.0\n" - ] - } - ], - "source": [ - "# set the radial grid\n", - "oned = GaussChebyshev(20)\n", - "rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(one_d_grid)\n", - "\n", - "# calculate the function values at the grid points\n", - "vals = rgrid.points**2 * np.exp(-rgrid.points)\n", - "\n", - "integral = rgrid.integrate(vals)\n", - "\n", - "print(f\"Integral of r^2 * exp(-r) from 0 to infinity:{integral} should be close to 2.0\")" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] + }, + "metadata": {}, + "output_type": "display_data" } - ], - "metadata": { - "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": "3.10.12" + ], + "source": [ + "from grid.rtransform import BeckeRTransform\n", + "\n", + "names = []\n", + "for i, oned in enumerate(grids):\n", + " # Becke R-transform (goes from 0 to \\infty) to transform 1D-grid\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", + " # plot radial grid points for each transformed 1D-grid\n", + " plt.scatter(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", + " names.append(oned.name)\n", + "\n", + "# set the ticks, labels, and title\n", + "plt.title(\"Becke Radial Transformation of 1D-Grids\", fontsize=16)\n", + "plt.yticks(range(1, len(grids) + 1), names)\n", + "plt.xlim(0, 2500)\n", + "plt.xlabel(\"R\", fontsize=14)\n", + "plt.ylabel(\"Quadrature Rule\", fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example: Integration of One-Variable Function on $[0, \\infty]$\n", + "\n", + "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). Here, we integrate (which has the exact value of 2.0):\n", + "\n", + "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Integration of r^2 * exp(-r) from 0 to infinity:\n", + " 2.000000 Analytical integration\n", + " 2.000003 from BeckeRTransform radial grid of Gauss-Chebyshev\n", + " 1.999996 from BeckeRTransform radial grid of Gauss-Legendre\n", + " 1.999993 from BeckeRTransform radial grid of Tanh-Sinh\n", + " 1.998949 from BeckeRTransform radial grid of Simpson\n", + " 2.000006 from BeckeRTransform radial grid of Trapezoidal-Lobatto\n" + ] } + ], + "source": [ + "print(\"Integration of r^2 * exp(-r) from 0 to infinity:\")\n", + "print(f\"{2.0: .6f} Analytical integration\")\n", + "\n", + "# Make several 1-dimensional grids for a given number of points\n", + "npoints = 21\n", + "grids = [\n", + " GaussChebyshev(npoints),\n", + " GaussLegendre(npoints),\n", + " TanhSinh(npoints),\n", + " Simpson(npoints),\n", + " Trapezoidal(npoints),\n", + "]\n", + "\n", + "for oned in grids:\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", + " func_vals = rgrid.points**2 * np.exp(-rgrid.points)\n", + " integral = rgrid.integrate(func_vals)\n", + " print(f\"{integral: .6f} from BeckeRTransform radial grid of {oned.name}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 0 + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + } + }, + "nbformat": 4, + "nbformat_minor": 1 } From cb66a6ffdb877bdedf119fc33093efa85f85809f Mon Sep 17 00:00:00 2001 From: Ali-Tehrani Date: Wed, 3 Jan 2024 17:37:17 -0500 Subject: [PATCH 7/9] Update oned notebook - Add relative error for [0, infty) integration - Added log plot to one of the plots --- doc/notebooks/One_dimensional_grids.ipynb | 146 +++++++++++++++------- 1 file changed, 101 insertions(+), 45 deletions(-) diff --git a/doc/notebooks/One_dimensional_grids.ipynb b/doc/notebooks/One_dimensional_grids.ipynb index 4ddace328..3b1924682 100644 --- a/doc/notebooks/One_dimensional_grids.ipynb +++ b/doc/notebooks/One_dimensional_grids.ipynb @@ -6,8 +6,7 @@ "source": [ "# One-Dimensional and Radial Grids\n", "\n", - "[OneDGrid](https://grid.qcdevs.org/pyapi/grid.basegrid.html#grid.basegrid.OneDGrid)\n", - "Grid supports several quadrature rules for one-dimensional grids (most of them in the [-1, 1] interval).\n", + "Grid supports several quadrature rules for one-dimensional grids, most of them in the [-1, 1] interval, within the [OneDGrid](https://grid.qcdevs.org/pyapi/grid.basegrid.html#grid.basegrid.OneDGrid) module.\n", "\n", "### Example: Visualize One-Dimensional Grid Points\n", "\n", @@ -16,11 +15,11 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 1, "metadata": { "ExecuteTime": { - "end_time": "2023-06-19T16:51:32.568341203Z", - "start_time": "2023-06-19T16:51:31.905745917Z" + "end_time": "2024-01-03T22:36:20.643610321Z", + "start_time": "2024-01-03T22:36:20.291101489Z" } }, "outputs": [], @@ -41,15 +40,18 @@ }, { "cell_type": "code", - "execution_count": 21, - "metadata": {}, + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.133162129Z", + "start_time": "2024-01-03T22:36:20.645646412Z" + } + }, "outputs": [ { "data": { - "image/png": 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", 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\n" }, "metadata": {}, "output_type": "display_data" @@ -84,8 +86,13 @@ }, { "cell_type": "code", - "execution_count": 23, - "metadata": {}, + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.338777861Z", + "start_time": "2024-01-03T22:36:21.146684630Z" + } + }, "outputs": [ { "name": "stdout", @@ -102,10 +109,8 @@ }, { "data": { - "image/png": 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", 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\n" }, "metadata": {}, "output_type": "display_data" @@ -148,15 +153,18 @@ }, { "cell_type": "code", - "execution_count": 26, - "metadata": {}, + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.461375714Z", + "start_time": "2024-01-03T22:36:21.349492787Z" + } + }, "outputs": [ { "data": { - "image/png": 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", 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5mDJlCgYNGgQHBwfo6OiA4zhs2bJFMr8iFLe/4n5PvnyPv0bWzyA9PR0Aimz1EdPV1S2xwCluX/h4z8UH9JIGkTQ3N8fz58/x8ePHQvPk9bmUN4e8KGOBo6amhs6dO+Po0aPYsGEDwsPDi72LR9Hevn0rUwua+P9NaWRnZ0NXVxdxcXEwNTWVe4/LYWFhAAp6vS+OuNW9uAJH0RkrGp2iUkKqqqr46aefAAA///wz8vLyilyuuEJDrCz/+eRB/MW5efPmYptXxQ95jWMjPiCXtiv/P//8E7m5uejXrx+WLVuGhg0bQldXV/JexsbGyiUXX2T9DMQH9C9b5T4n6wGYj/dc/D68e/eu2GUSEhIAlFzUVZUcyljgAAWnqeLi4nD9+nUcPXqUt9vDd+3a9dX/L0U9SiomPpeTk4OePXvi6dOnUFNTw/v37yWjssuL+P+Rvb19kfMfPXqEt2/fwtjYuMhbzisiY0WjAkdJ9evXD05OToiKiip2HCPxQen9+/dFzv/aL3h5EzfD379/v8K26ezsDACSJtWvEfeV4unpWeT8irr2pjxK6gRS1s+gTp06AP7rI+NLr169KrH1piTlec9l7fBSvD8PHz4scv7Hjx8lBwTxsoqgLDmUtcDp2LEjBAIBQkNDER4eXq5+fpTZyJEjERYWhvbt22PTpk0ACvo7ys/Pl9s2xD9Aivthu3HjRgDFt95URMaKRgWOklJRUUFgYCAAYMGCBUU23xsbG0NfXx+ZmZl48OBBoflbtmxReM7P+fv7Ayj4NVTWi2Nl1aNHDwDAkSNH8OLFi68uL+4VVvyr+XOPHz/G0aNH5ZpPEcT7UNRpPlk/A19fXwDAoUOHimypKc9goeV5z0va15J06NABALB//36pTivFNm7ciOzsbNja2qJu3bplWndlzKGsBY6Ojg7atGmDDRs2oE6dOtDQ0OA7ktzNnj0bu3btgqurK/bv348hQ4agTp06ePz4MXbt2iW37VhaWgIArl27VmjenTt3sH79egBFFzgVlbGiUYGjxPr06QNXV1fExMTg0qVLheZzHCf5Ap08ebLUl9iOHTuwbdu2CssKAO7u7ujbty+SkpLg6+tbqNfX/Px8nDt3DgMHDkR2drZcttmkSRP4+/sjKysLnTp1QkREhNT858+fY9myZZLnLVu2BACsW7cOt2/flkx/+vQp+vTpUym+YGvVqgUACA8PLzRP1s+gXbt2cHNzQ2JiIgYMGCB1yu/IkSNYtGiRzINZluc9L2lfS9KmTRt4eHggOzsb/fv3lzpFdOrUKcybNw9AwUWUihwWRVlyKGuBAxScpkpOTq6Sd09t2bIFCxcuhJWVFY4fPw49PT2oqqpKhpmYP39+sZcglJX4dNn8+fMlF7cDwNmzZ9GpUyfk5OQAKHwjQUVmrHAKuwGdlMqX/eB86cCBAyX2gfDo0SOmo6Mj6bSvcePGzNLSkuH/e2MVv+5LxU1n7Ov964SFhRXqEErs48ePzNfXV7L+mjVrsmbNmjFXV1cmFAol0z/v++JrecRK6sm4efPmknXY2dkxd3d3Zm5uXmg/cnNz2TfffMOAgh5069evz1xcXCS91i5YsIABYEOHDi319kuTubh+cMq6r4wx9vvvv0te7+Liwry9vZm3tze7desWY0z2z+Dznoy1tLSYu7s7s7Ozk/QLI8706tWrMu1Led7zr+1rSe/Vs2fPWI0aNST90DRu3FjSiSUANnjw4GJ7Mi6OLH8DsuRgTL794Ij72wEgUy/BivT27Vumrq7OkpKSyvS6ixcvMmNjY8lD3Ou1lpaW1PQv/14ryokTJ5iamhrT0dGR6nmbsYKeiuvUqcMAsI0bN8ple1FRUZLeiNXU1JiLi4vk/6+zszNzcHBgAKSyVHTGikYFDs++VuCIRCLWsGHDEjt5unnzJuvYsSPT1dVl2trazNPTkx09epQx9vWO/opSngKHsYJecXfv3s06dOjATExMmLq6OrO0tGTNmjVj06dPL7Lr8fIUOIwxlpOTw9auXctatGjB9PX1maamJrO3t2e9e/eWvBdiqampbMKECczKyoqpq6uzGjVqsG+//Za9fftW0tGiMhc4jDG2atUq5ubmJlWwhIWFSebL8hkwxtjz589Zv379mLGxMdPU1GSurq5szZo1jDEm6QTsw4cPZdoXxmR/z0uzryW9V+/fv2dTp05ljo6OTCAQMD09Pebl5cV27txZZFGhiAJHlhyMybfA+emnnyT7VlQHkHz7vLf00hJ/D33twcfwArdu3WI6OjpMVVWVHT9+vMhldu7cyQAwGxsblpWVJZft3r17l7Vv355paWkxLS0t5uLiwubOncsSExOZQCBgampqkm3xlbEicYyV8T5UQki1k5SUBBMTExgYGFSuwfYIAGDKlClYsWIFgILTlOLb3QmpyuivnBDyVSEhIQCKvxOKKDfxNThaWloKKW5ev36NCRMmoFmzZtDU1FTo9USElBYVOIQQAAW9IG/atEnqglTGGHbt2oW5c+cCKBhagCi/1NRUPHr0CCKRCMB/vUSXtkPMsnr+/Dn2798PMzMzNGvWTCHbIKSsqMAhhAAoOA01evRoGBgYwMHBAU2bNoWpqSkGDx6MrKwsjB49mreO2EjpPXnyBAYGBnBycpL0vyMeisPOzk4h2/Ty8kJ8fDyOHj2KTp06KWQbhJQVFTiEEAAFnQROmzYNrq6uSE1Nxa1bt8AYQ9u2bbFv3z5s2LCB74ikFOrUqYOaNWsCAIKDg7Fnzx5JB47i/o7kja7pIcqILjImhJAqRjy+1+fs7e0RGRkJIyMjhW578eLFmDlzZpnHUSNE3qjsJoSQKubbb7/Fli1bJIOaDho0CFeuXFF4cUOIMqHRxAkhpAoaOXIkRo4cWebXffz4EW/evPnqcpaWltDX15clGiEVggocQgghEsePH0f//v2/ulxISAiGDRum+ECEyIgKHEIIIRL9+vVDv379+I5BSLnRNTiEEEIIqXKoBYcQQki5HThwAABw//59qedOTk5wcnLiLRepvug2cUIIIeVW3PAMgYGBCAoKqtgwhIBacAghhMgB/VYmyqZaFjgikQhv376Frq4uDQpHCCGEVBKMMXz8+BFWVlZf7UG7WhY4b9++hY2NDd8xCCGEECKD2NhY1KhRo8RlqmWBo6urC6DgDdLT0+M5DSGEEEJKIy0tDTY2NpLjeEmqZYEjPi2lp6dHBQ4hhBBSyZTm8hLqB4cQQgghVQ4VOIQQQgipcqjAIYQQQkiVQwUOIYQQQqocKnAIIYQQUuVQgUMIIYSQKocKHEIIIYRUOVTgEEIIIaTKoQKHEEIIIVUOFTiEEEIIqXKowCGEEEJIlUMFDiGEEEKqHCpw5OzZh2dISE/gOwYhhBBSrSldgWNnZweO4wo9xo0bBwBgjCEoKAhWVlYQCoXw8fHBgwcPeE5dIDgiGD1De2Lv4718RyGEkGLdvXsXI0eOhIODA4RCIYRCIRwdHTF69GhERkbyHa/cEhISMGPGDLi6ukJHRweamppwdHTEpEmT8OzZM8lyw4YNg46Ojly3bWdnBz8/P7mu82sUsR9VgdIVOBEREYiLi5M8Tp8+DQDo06cPACA4OBgrVqzAmjVrEBERAQsLC/j6+uLjx498xgYANDJrBAAIfRGKPFEez2kIIaSwjRs3okmTJrh27RomTZqEY8eO4fjx4wgICMCDBw/g4eGBFy9e8B1TZtevX4erqyu2bt2K3r1749ChQ/jnn38wdepU3Lx5E02bNuU7IqkganwH+JKpqanU88WLF8PBwQHe3t5gjGHlypWYPXs2evbsCQDYsWMHzM3NsWfPHowePZqPyBI+NXxgKDDE+8z3uPTmErxtvHnNQwghn7t06RLGjh2LLl264MCBA9DQ0JDMa9OmDcaNG4f9+/dDKBTymFJ2aWlp6N69OzQ1NXH58mXUqFFDMs/HxwejR4/GgQMHeExIKpLSteB8LicnB7t27cKIESPAcRyioqIQHx+P9u3bS5YRCATw9vbG5cuXi11PdnY20tLSpB6KoK6qDj+HgqbJw88PK2QbhJCKxxhDRk6e0jwYYzLtx8KFC6GqqoqNGzdKFTef69OnD6ysrAAAkZGR6NevH+zs7CAUCmFnZ4f+/fsjJiZG6jVBQUHgOK7QurZv3w6O4xAdHS2ZdvbsWfj4+MDY2BhCoRA1a9ZEr169kJGRIVlm/fr1aNCgAXR0dKCrq4t69eph1qxZX92/zZs3Iz4+HsHBwVLFzed69+5daNrz58/RuXNn6OjowMbGBlOmTEF2drbUMjk5OViwYAHq1asHgUAAU1NTDB8+HO/fvy9yO4cPH4abmxs0NTVRq1YtrF69WjLv06dPMDAwKPJHeXR0NFRVVbF06VIAQEZGBqZOnQp7e3toamrCyMgI7u7u2Lu38KUQ8tqPHj16wNbWFiKRqNA2mjVrhsaNGxe5z8pG6VpwPnfkyBGkpKRg2LBhAID4+HgAgLm5udRy5ubmhf7DfW7RokWYN2+ewnJ+zr+2P3Y+3Inw2HAkZibCRGhSIdslhChOZm4+nH46yXcMiYfzO0BLo2xf3/n5+QgLC4O7uzssLS1L9Zro6GjUrVsX/fr1g5GREeLi4rB+/Xp4eHjg4cOHMDEp2/dbdHQ0unTpglatWmHbtm0wMDDAmzdv8M8//yAnJwdaWlrYt28fxo4diwkTJmDZsmVQUVHB8+fP8fDhw6+u/9SpU1BVVUXXrl1LnSk3NxfdunXDyJEjMWXKFJw/fx4///wz9PX18dNPPwEARCIRunfvjgsXLmDatGnw9PRETEwMAgMD4ePjg8jISKlWr9u3byMgIABBQUGwsLDA7t27MWnSJOTk5GDq1KnQ0dHBiBEjsGnTJgQHB0NfX1/y2nXr1kFDQwMjRowAAEyePBk7d+7EggUL0KhRI6Snp+P+/ftISkpS2H6MGDEC3bt3x9mzZ9GuXTvJNh4/fozr169LFWvKTKkLnK1bt6JTp06SXxNiX/5SYIwV+etBbObMmZg8ebLkeVpaGmxsbOQb9v85GjrC1cQV9xLv4fjL4xjqPFQh2yGEkLJITExEZmYmbG1tC83Lz8+XahVSVVUFx3Ho3bu3VItHfn4+/Pz8JJcFTJw4sUwZbty4gaysLCxduhQNGjSQTB8wYIDk35cuXYKBgYHUQbRt27alWv+rV69gamoKbW3tUmfKycnBvHnzJNd5tm3bFpGRkdizZ4+kMPjzzz/xzz//4ODBg5LLIwCgQYMG8PDwwPbt2zFmzBjJ9Ldv3+LWrVuSfezUqRPevXuHn3/+GWPHjoWWlhbGjx+PVatWISQkBAEBAQCArKwsbNu2Df3794exsbHk/Wjfvj1++OEHyfq7dOmi0P3o3LkzzM3NERISIlXghISEQENDQ+rzUmpMSUVHRzMVFRV25MgRybQXL14wAOzmzZtSy3br1o0NGTKk1OtOTU1lAFhqaqrc8n7uj8d/MJftLqzb4W5MJBIpZBuEkIojEolYenau0jxk+V6Jj49nAFi/fv0KzWvQoAEDIHksXbqUMcbYx48f2bRp05iDgwNTVVWVWub777+XvD4wMJAVdTgJCQlhAFhUVBRjjLHnz58zDQ0N1rRpU7Z9+3b24sWLQq/5/fffJTmPHDnC3r9/X2iZ3NxcqYf4/ahXrx6zsLAo9XsydOhQxnEcy8zMlJo+Y8YMpqmpKXk+cOBAZmBgwHJycgpt28LCgvXt21eyrK2tLXNxcSn2vbhw4YJkWrdu3Zijo6Mk/9atWxkAduPGDckyI0aMYAKBgE2fPp2FhYWxjIyMCtmPKVOmME1NTZaSksIYYywvL49ZWlqyPn36lPymKlhZjt9Kew1OSEgIzMzMpCpVe3t7WFhYSO6sAgqq1vDwcHh6evIRs0id7DtBU1UTL1Nf4m7iXb7jEELKieM4aGmoKc2jpBbr4piYmEAoFBZ5On/Pnj2IiIhAaGio1PQBAwZgzZo1+Pbbb3Hy5Elcv34dERERMDU1RWZmZpkzODg44N9//4WZmRnGjRsHBwcHODg4YNWqVZJlBg8ejG3btiEmJga9evWCmZkZmjVrJvW9r66uLvXYsWMHAKBmzZp4//490tPTS51JS0sLmpqaUtMEAgGysrIkzxMSEpCSkgINDY1C246Pj0diYqLU6y0sLAptRzzt81NL4tvWxfu2du1aNG/eXOoal9WrV2P69Ok4cuQIWrduDSMjI/To0UPqdndF7MeIESOQlZWFffv2AQBOnjyJuLg4DB8+vIR3U7ko5SkqkUiEkJAQDB06FGpq/0XkOA4BAQFYuHAhHB0d4ejoiIULF0JLS0upmsx0NXTha+uLoy+P4vCzw2hg2uDrLyKEEAVSVVVFmzZtcOrUKcTFxUldh+Pk5AQAUhcDp6am4tixYwgMDMSMGTMk07Ozs5GcnCy1bvGBNTs7GwKBQDL9ywM/ALRq1QqtWrVCfn4+IiMj8dtvvyEgIADm5ubo168fAGD48OEYPnw40tPTcf78eQQGBsLPzw9Pnz6Fra0tIiIipNZpb28PAOjQoQNOnTqFo0ePStYlDyYmJjA2NsY///xT5HxdXV2p5+LrRYuaJj71BBTcuebi4oI1a9ZAR0cHN2/exK5du6Rep62tjXnz5mHevHlISEjAiRMnMGPGDHTt2hWPHz9W2H44OTmhadOmCAkJwejRoxESEgIrKyupm3yUXgW0KJXZyZMnGQD25MmTQvNEIhELDAxkFhYWTCAQMC8vL3bv3r0yrV/Rp6gYY+x63HXmst2FNd3VlKXnpCtsO4QQUloXL15kKioqrFu3biwnJ6fQ/KioKMkpKvH35KJFi6SWWbNmDQPAhg4dKpm2d+9eBoBdv35dalkvLy+pU1RFSUlJYQDYjz/+WOwyR44cYQDY8ePHS9y/lJQUZmFhwWxsbNjr16+LXObgwYOSfw8dOpRpa2sXWubLU267du1iANjVq1dL3D5jBaeoOI5jt2/flpru6+vLdHV1WXq69PFg06ZNTEVFhXl5eTFzc3OWnZ391W0EBAQwAJJ1KWI/GGNs/fr1ktNqAoGAzZw5s1SvU6SyHL+VsgWnffv2xd4GyXEcgoKCEBQUVLGhysjd3B02ujaI/RiLUzGn0KN2D74jEUKquRYtWmDt2rWYMGECGjdujO+++w7Ozs5QUVFBXFwcDh48CADQ09ODnp4evLy8sHTpUpiYmMDOzg7h4eHYunUrDAwMpNbbuXNnGBkZYeTIkZg/fz7U1NSwfft2xMbGSi23YcMGnD17Fl26dEHNmjUlF9UCkFzMOmrUKAiFQrRo0QKWlpaIj4/HokWLoK+vDw8PjxL3T19fH3/99Rf8/PzQqFEjjB8/Hs2bN4eGhgaePXuGXbt24c6dO1IX2JZGv379sHv3bnTu3BmTJk1C06ZNoa6ujtevXyMsLAzdu3eHv7+/ZHkrKyt069YNQUFBsLS0xK5du3D69GksWbIEWlpaUuseNGgQZs6cifPnz2POnDmFbt9v1qwZ/Pz84ObmBkNDQzx69Ag7d+5E8+bNC61L3vvRv39/TJ48Gf3790d2drbkjuZKQ/H1lvKpiBYcxhjbdGcTc9nuwob8XfoLoAkhRNFu377Nhg8fzuzt7ZlAIGCampqsdu3abMiQIezMmTOS5V6/fs169erFDA0Nma6uLuvYsSO7f/8+s7W1lWrBYYyx69evM09PT6atrc2sra1ZYGAg27Jli1QLzpUrV5i/vz+ztbVlAoGAGRsbM29vbxYaGipZz44dO1jr1q2Zubk509DQYFZWVqxv377s7t27pd6/+Ph4Nn36dObs7My0tLSYQCBgtWvXZqNHj5Zq8S9tywdjBRc2L1u2jDVo0IBpamoyHR0dVq9ePTZ69Gj27NkzyXK2trasS5cu7MCBA8zZ2ZlpaGgwOzs7tmLFimLzDhs2jKmpqRXZ6jRjxgzm7u7ODA0NmUAgYLVq1WI//PADS0xMVOh+iA0YMIABYC1atCg2f0Uqy/GbY0zGHqMqsbS0NOjr6yM1NRV6enoK205CegLaH2wPERPhaI+jsNO3U9i2CCGEVD45OTmws7NDy5Yt8eeff/IdR+mV5fittHdRVQXm2uZoYdUCAHDk+RF+wxBCCFEa79+/x8WLFzFmzBjJ4KBEvqjAUTB/x4LzmTQAJyGEELHjx4+jVatWOHHiBNatW1dphj+oTOgUlQJPUQFAbn4u2u5viw/ZH7CmzRoagJMQQgiREZ2iUiI0ACchhBBS8ajAqQD+tQtOU4kH4CSEEEKIYlGBUwHEA3DmsTwcf3mc7ziEEEJIlUcFTgURd/R36NmhYjsxJIQQQoh8UIFTQWgATkIIIaTiUIFTQcQDcALA4Wd0sTEhhBCiSFTgVCBxnzgnok4gIzeD5zSEEEJI1UUFTgUSD8CZkZeBUzGn+I5DCKmm7t69i5EjR8LBwQFCoRBCoRCOjo4YPXo0IiMj+Y4ns+joaHAch2XLlvEdRWF8fHzg4+PDd4xKgQqcCsRxnOSWcTpNRQjhw8aNG9GkSRNcu3YNkyZNwrFjx3D8+HEEBATgwYMH8PDwwIsXL/iOSUi5qfEdoLrp5tANa26vwc13NxGdGk0DcBJCKsylS5cwduxYdOnSBQcOHICGhoZkXps2bTBu3Djs378fQqGQx5SkvHJzc8FxHNTUqvchnlpwKhgNwEkI4cvChQuhqqqKjRs3ShU3n+vTpw+srKwAAJGRkejXrx/s7OwgFAphZ2eH/v37IyYmRuo1QUFB4Diu0Lq2b98OjuMQHR0tmXb27Fn4+PjA2NgYQqEQNWvWRK9evZCR8d91ievXr0eDBg2go6MDXV1d1KtXD7NmzZLDO1AgLS0NU6dOhb29PTQ0NGBtbY2AgACkp6dLLZeSkoKRI0fCyMgIOjo66NKlC16+fAmO4xAUFCS17LNnzzBgwACYmZlBIBCgfv36WLt2rdQy586dA8dx2Lt3L2bPng0rKyvo6emhXbt2ePLkidSyjDEEBwfD1tYWmpqaaNy4MU6cOFFoX8Tr3LlzJ6ZMmQJra2sIBAI8f/4cAPDvv/+ibdu20NPTg5aWFlq0aIEzZ87I4V1UftW7vOOJv6M/Lry5gNAXoRjfaDzUVOhjIESpMQYo040B6lpAEQVFSfLz8xEWFgZ3d3dYWlqW6jXR0dGoW7cu+vXrByMjI8TFxWH9+vXw8PDAw4cPYWJiUqYM0dHR6NKlC1q1aoVt27bBwMAAb968wT///IOcnBxoaWlh3759GDt2LCZMmIBly5ZBRUUFz58/x8OHD8u0reJkZGTA29sbr1+/xqxZs+Dm5oYHDx7gp59+wr179/Dvv/+C4ziIRCJ07doVkZGRCAoKQuPGjXHlyhV07Nix0DofPnwIT09P1KxZE8uXL4eFhQVOnjyJiRMnIjExEYGBgVLLz5o1Cy1atMCWLVuQlpaG6dOno2vXrnj06BFUVVUBAPPmzcO8efMwcuRI9O7dG7GxsRg1ahTy8/NRt27dQhlmzpyJ5s2bY8OGDVBRUYGZmRl27dqFIUOGoHv37tixYwfU1dWxceNGdOjQASdPnkTbtm3l8p4qKzqy8sCnhg8MBYZ4n/kel95cogE4CVF2uRnAQiu+U/xn1ltAQ7tML0lMTERmZiZsbW0LzcvPz5fqgFRVVRUcx6F3797o3bu31HJ+fn4wNzfHnj17MHHixDJluHHjBrKysrB06VI0aNBAMn3AgAGSf1+6dAkGBgZYvXq1ZJo8D8SrV6/G3bt3ce3aNbi7u0vWb21tjd69e+Off/5Bp06d8M8//+DixYtYv349vv/+ewCAr68vNDQ0MHPmTKl1Tp48Gbq6urh48aJkAEhfX19kZ2dj8eLFmDhxIgwNDSXLOzk5YdeuXZLnqqqq6Nu3LyIiIvDNN98gJSUFS5Ysgb+/P7Zs2SJZztnZGS1atCiywHFwcMD+/fslzzMyMjBp0iT4+fnh8OH/rvns3LkzGjdujFmzZuHatWvleSuVHp2i4gENwEkIUSZNmjSBurq65LF8+XIAwKdPnzB9+nTUrl0bampqUFNTg46ODtLT0/Ho0aMyb6dhw4bQ0NDAd999hx07duDly5eFlmnatClSUlLQv39//PXXX0hMLDx+X15entSjLL3DHzt2DC4uLmjYsKHUOjp06ACO43Du3DkAQHh4OACgb9++Uq/v37+/1POsrCycOXMG/v7+0NLSklpn586dkZWVhatXr0q9plu3blLP3dzcAEBy6u/KlSvIysrCwIEDpZbz9PQsskAFgF69ekk9v3z5MpKTkzF06FCpTCKRCB07dkREREShU3JVDbXg8MS/tj92PtwpGYDTRFi2pl5CSAVS1ypoNVEW6lplfomJiQmEQmGh62cAYM+ePcjIyEBcXJzUwXfAgAE4c+YM5s6dCw8PD+jp6YHjOHTu3BmZmZllzuDg4IB///0XwcHBGDduHNLT01GrVi1MnDgRkyZNAgAMHjwYeXl52Lx5M3r16gWRSAQPDw8sWLAAvr4FnaWqq6tLrTckJATDhg0rVYaEhAQ8f/680DrExAVVUlIS1NTUYGRkJDXf3Nxc6nlSUhLy8vLw22+/4bfffitxnWLGxsZSzwUCAQBI3tOkpCQAgIWFRaF1FTUNQKHTjgkJCQAg1QL3peTkZGhrl60lsDKhAocn4gE47yXew/GXxzHUeSjfkQghxeG4Mp8SUjaqqqpo06YNTp06hbi4OKkDopOTEwBIXQycmpqKY8eOITAwEDNmzJBMz87ORnJystS6NTU1JfPEB2ug8IEdAFq1aoVWrVohPz8fkZGR+O233xAQEABzc3P069cPADB8+HAMHz4c6enpOH/+PAIDA+Hn54enT5/C1tYWERERUuu0t7cv9fsgLvS2bdtW7HygoAjJy8tDcnKyVJETHx8vtbyhoSFUVVUxePBgjBs3rsh1liWfeNtFbUs8zc7OrtD0Ly/yFu/Hb7/9hm+++abI7XxZrFU1VODwyN/RH/cS7+HQs0MY4jSkyLsQCCFEXmbOnIkTJ07g+++/x4EDB4ptxQAKDpiMMamCBQC2bNmC/Px8qWniA+7du3fh4eEhmX706NFi16+qqopmzZqhXr162L17N27evCkpcMS0tbXRqVMn5OTkoEePHnjw4AFsbW0l187Iws/PDwsXLoSxsXGJhYe3tzeCg4Pxxx9/YMyYMZLp+/btk1pOS0sLrVu3xq1bt+Dm5lbs3Wll8c0330BTUxO7d++WOvV0+fJlxMTEFFngfKlFixYwMDDAw4cPMX78+HJnqoyowOFRR7uOCL4eLBmAs4Fpg6+/iBBCZNSiRQusXbsWEyZMQOPGjfHdd9/B2dkZKioqiIuLw8GDBwEAenp60NPTg5eXF5YuXQoTExPY2dkhPDwcW7duhYGBgdR6O3fuDCMjI4wcORLz58+Hmpoatm/fjtjYWKnlNmzYgLNnz6JLly6oWbMmsrKyJC0p7dq1AwCMGjUKQqEQLVq0gKWlJeLj47Fo0SLo6+tLFU8luXfvHg4cOFBouoeHBwICAnDw4EF4eXnhhx9+gJubG0QiEV69eoVTp05hypQpaNasGTp27IgWLVpgypQpSEtLQ5MmTXDlyhX8/vvvAAAVlf8uYV21ahVatmyJVq1aYcyYMbCzs8PHjx/x/PlzHD16FGfPni3dB/T/DA0NMXXqVCxYsADffvst+vTpg9jYWAQFBRV7iupLOjo6+O233zB06FAkJyejd+/eMDMzw/v373Hnzh28f/8e69evL1OuSodVQ6mpqQwAS01N5TsKm3VhFnPZ7sICLwXyHYUQUk3cvn2bDR8+nNnb2zOBQMA0NTVZ7dq12ZAhQ9iZM2cky71+/Zr16tWLGRoaMl1dXdaxY0d2//59Zmtry4YOHSq1zuvXrzNPT0+mra3NrK2tWWBgINuyZQsDwKKiohhjjF25coX5+/szW1tbJhAImLGxMfP29mahoaGS9ezYsYO1bt2amZubMw0NDWZlZcX69u3L7t69+9X9ioqKYgCKfYSEhDDGGPv06RObM2cOq1u3LtPQ0GD6+vrM1dWV/fDDDyw+Pl6yvuTkZDZ8+HBmYGDAtLS0mK+vL7t69SoDwFatWlVo2yNGjGDW1tZMXV2dmZqaMk9PT7ZgwQLJMmFhYQwA279/f5G5xfkYY0wkErFFixYxGxsbpqGhwdzc3NjRo0eZt7c38/b2/uo6xcLDw1mXLl2YkZERU1dXZ9bW1qxLly7FLq/synL85hgrw+XnVURaWhr09fWRmpoquaWPLxHxERhxcgS01LQQ1jcMWjJcPEgIIaRi7NmzBwMHDsSlS5fg6enJd5xqpyzHbzpFxTPxAJyxH2NxKuYUetTuwXckQgghAPbu3Ys3b97A1dUVKioquHr1KpYuXQovLy8qbioB6geHZzQAJyGEKCddXV3s27cP//vf/9C5c2ds3rwZw4YNK/HiaaI86BQVz6eoACAhPQHtD7aHiIlwtMdRGoCTEEIIKUJZjt/UgqMEaABOQgghRL6owFES/o4Fp6lCX4QiT5THcxpCCCGkcqMCR0l8OQAnIYQQQmRHBY6SoAE4CSGEEPmhAkeJiO+mEg/ASQghhBDZUIGjRMQDcOaxPBx/eZzvOIQQQkilRQWOkhFfbHzo2SFUwzv4CSGEELmgAkfJdLTrCE1VTckAnIQQQggpOypwlIyuhi7a27UHQD0bE0Lkh+O4Uj3OnTsnt22eO3cOHMcVObJ3WZw8eRLt27eHlZUVBAIBrKys4OPjg8WLF0stZ2dnh2HDhsm0DR8fH7i4uJQrJ1EuSlngvHnzBoMGDYKxsTG0tLTQsGFD3LhxQzKfMYagoCBYWVlBKBTCx8cHDx484DGxfInHozoRdQIZuRn8hiGEVAlXrlyRenTu3BlCobDQ9MaNG/MdVcqGDRvQsWNH6OnpYc2aNTh58iSWLFmC+vXrFyqcDh8+jLlz5/KUlCgbpRts88OHD2jRogVat26NEydOwMzMDC9evICBgYFkmeDgYKxYsQLbt29HnTp1sGDBAvj6+uLJkyfQ1dXlL7ycuJu7o6ZuTbz6+IoG4CSEyMU333wj9dzU1BQqKiqFpiubRYsWwcvLq1AxM3jwYIhEIqlpjRo1qshoRMkpXQvOkiVLYGNjg5CQEDRt2hR2dnZo27YtHBwcABS03qxcuRKzZ89Gz5494eLigh07diAjIwN79uwpcp3Z2dlIS0uTeigzjuMkRQ2dpiKEf4wxZORmKM1DUTcgrF27Fl5eXjAzM4O2tjZcXV0RHByM3NxcqeXEp3MiIiLQqlUraGlpoVatWli8eHGhogMAcnNzMXv2bFhZWUFPTw/t2rXDkydPSpUpKSkJlpaWRc5TUZE+hH15ikp8imzv3r2l3n5p94koP6VrwQkNDUWHDh3Qp08fhIeHw9raGmPHjsWoUaMAAFFRUYiPj0f79u0lrxEIBPD29sbly5cxevToQutctGgR5s2bV2H7IA/dHLphze01uPnuJqJTo2kATkJ4lJmXiWZ7mvEdQ+LagGvQUteS+3pfvHiBAQMGwN7eHhoaGrhz5w5++eUXPH78GNu2bZNaNj4+HgMHDsSUKVMQGBiIw4cPY+bMmbCyssKQIUOklp01axZatGiBLVu2IC0tDdOnT0fXrl3x6NEjqKqqlpipefPmOHjwIIKCguDv7w8XF5evvuZLpd1+WfaJKD+lK3BevnyJ9evXY/LkyZg1axauX7+OiRMnQiAQYMiQIYiPjwcAmJubS73O3NwcMTExRa5z5syZmDx5suR5WloabGxsFLcTciAegPPCmws48vwIApoE8B2JEFLFrVixQvJvkUiEVq1awdjYGMOHD8fy5cthaGgomZ+UlIS///4bTZs2BQC0a9cO586dw549ewoVA05OTti1a5fkuaqqKvr27YuIiIivniLbsGEDevTogXnz5mHevHkQCoXw9PSEv78/vvvuO6irq391v0q7/bLsE1F+SlfgiEQiuLu7Y+HChQAKzqk+ePAA69evl/oD4zhO6nWMsULTxAQCAQQCgeJCK4i/oz8uvLmA0BehGN9oPNRUlO7jIqRaEKoJcW3ANb5jSAjVhApZ761btxAYGIhLly4hOTlZat7Tp0/RrNl/rVgWFhaSQkDMzc0Nt2/fLrTebt26FVoOAGJiYvDNN9+AMYb8/HypZdTUCr7vHBwccOfOHVy8eBHnzp1DZGQkwsPDcebMGYSEhODixYvQ1NQscb++tn1Z9okoP6U7YlpaWsLJyUlqWv369XHw4EEABX+AQEFT4ufnZd+9e1eoVaey+3IATm8bb74jEVItcRynkFNCyuTVq1do1aoV6tati1WrVsHOzg6ampq4fv06xo0bh8zMTKnljY2NC61DIBAUWq6oZcU/OMXL7tixA8OHD5da5vPrjFRUVODl5QUvLy8AQHp6OkaOHIk//vgD27Ztw9ixY0vct69tX5Z9IspP6S4ybtGiRaGLv54+fQpbW1sAgL29PSwsLHD69GnJ/JycHISHh8PT07NCsyoaDcBJCKkoR44cQXp6Og4dOoRBgwahZcuWcHd3h4aGhsK33bVrV0REREg9SqKtrY2ZM2cCAO7fv6/wfKRyUroWnB9++AGenp5YuHAh+vbti+vXr2PTpk3YtGkTgIJfUgEBAVi4cCEcHR3h6OiIhQsXQktLCwMGDOA5vfz51/bHzoc7JQNwmghN+I5ECKmCxKf4Pz+dzxjD5s2bFb5tY2PjIltPACAuLq7Iu6gePXoEALCyslJoNlJ5KV2B4+HhIblyff78+bC3t8fKlSsxcOBAyTLTpk1DZmYmxo4diw8fPqBZs2Y4depUlegD50viATjvJd7D8ZfHMdR5KN+RCCFVkK+vLzQ0NNC/f39MmzYNWVlZWL9+PT58+MBrLmdnZ7Rt2xadOnWCg4MDsrKycO3aNSxfvhzm5uYYOXIkr/mI8lK6U1QA4Ofnh3v37iErKwuPHj2S3CIuxnEcgoKCEBcXh6ysLISHh1fpLrZpAE5CiKLVq1cPBw8exIcPH9CzZ09MmDABDRs2xOrVq3nNJe6H5pdffkHnzp3RrVs3/P777xgwYAAiIyOL7SOHEI5VwyNmWloa9PX1kZqaCj09Pb7jfNXHnI9o82cbZOVnYVfnXWhg2oDvSIQQQkiFK8vxWylbcIg0GoCTEEIIKRsqcCoJGoCTEEIIKT0qcCoJ8QCcGXkZOBVziu84hBBCiFKjAqeSoAE4CSGEkNKjAqcS6ebQDSqcimQATkIIIYQUTaYCp1atWhg/fry8s5CvEA/ACQBHnh/hNwwhhBCixGQqcBITE6tkp3qVQU/HngCA0BehyBPl8ZyGEEIIUU4yFTgNGzbE06dP5Z2FlIJ3DW+pATgJIYQQUphMBc706dNx9OhRhIWFyTsP+QoagJMQQgj5OpnGokpKSkL79u3h6+sLf39/eHh4wNzcXDJY2+eGDBlS7pBEGg3ASQghhJRMpqEaVFRUwHFcoXGRPi9wGGPgOA75+fnlTylnlW2ohqIMOD4A9xLvYar7VBqAkxBSateuXcPixYtx48YNJCQkwMDAALVq1YKnpyeWL18OAPDx8QEAnDt3jr+ghBShLMdvmVpwQkJCZApG5Mff0R/3Eu/h0LNDGOI0pMjWM0II+dzx48fRrVs3+Pj4IDg4GJaWloiLi0NkZCT27dsnKXDWrVvHc1JCyo8G26ykLTg0ACchpKy8vb3x5s0bPH78GGpq0r9vRSIRVFSoazSi3GiwzWqABuAkpOIwxiDKyFCah6y/S5OSkmBiYlKouAEgVdz4+PhITlMBQHR0NDiOw9KlS7FkyRLY2dlBKBTCx8cHT58+RW5uLmbMmAErKyvo6+vD398f7969k1q/nZ0d/Pz8cPjwYbi5uUFTUxO1atXC6tWrpZYTiURYsGAB6tatC6FQCAMDA7i5uWHVqlVSy128eBFt27aFrq4utLS04OnpiePHj0sts337dnAch7CwMIwZMwYmJiYwNjZGz5498fbtW5neQ1J5yHSKSiwmJga7d+/G7du3JdVUw4YNMXDgQNjZ2ckpIilOj9o9EPoiFCeiTmCaxzRoqWvxHYmQKollZuJJ4yZ8x5Coe/MGOK2y/39v3rw5tmzZgokTJ2LgwIFo3Lgx1NXVS/36tWvXws3NDWvXrkVKSgqmTJmCrl27olmzZlBXV8e2bdsQExODqVOn4ttvv0VoaKjU62/fvo2AgAAEBQXBwsICu3fvxqRJk5CTk4OpU6cCAIKDgxEUFIQ5c+bAy8sLubm5ePz4MVJSUiTrCQ8Ph6+vL9zc3LB161YIBAKsW7cOXbt2xd69e/G///1ParvffvstunTpgj179iA2NhY//vgjBg0ahLNnz5b5PSSVh8ynqNasWYOpU6ciNze30K8JdXV1BAcHY9KkSXIJKW9V4RQVUPCr0u+wH159fIWfW/wsGauKECJfoowMpStwVGQocJKSktCjRw9cvHgRQMF3tYeHB7p27Yrx48dDR0cHQOGLjKOjo2Fvb48GDRrg5s2bktaeVatWISAgAN26dcNff/0l2c4PP/yAlStXSn3H2tnZ4dWrV7h16xYaNPjvlHr79u1x7do1xMXFQUtLC127dsXr169x69atYvejefPmePnyJV68eCHJnJ+fj4YNGyIlJQWvXr0Cx3HYvn07hg8fjrFjx2Lt2rWS1y9duhTTpk1DXFwcLCwsyvw+Ev4o/CLjv//+GxMnToSZmRl++OEH+Pj4wMLCAgkJCTh37hxWrFiByZMno3bt2ujSpYtMO0G+TjwA5+pbq3H42WEqcAhREE4oRN2bN/iOIcEJhTK9ztjYGBcuXEBkZCTOnDmDyMhInDt3DjNnzsTGjRsREREBE5Piu53o3Lmz1Kms+vXrA0Ch73nx9FevXsHFxUUy3dnZWaq4AYABAwbg9OnTuHnzJlq2bImmTZvi+PHjGDt2LLp3747mzZtLHcjS09Nx7do1jBkzRlLcAICqqioGDx6M6dOn48mTJ6hXr55kXrdu3aS26ebmBqDgLAQVOFWXTAXOsmXLYGxsjJs3b8LKykoy3dbWFk2bNsXAgQPRsGFDrFixggocBevm0A1rbq+RDMBpp2/HdyRCqhyO42Q6JaSs3N3d4e7uDgDIzc3F9OnT8euvvyI4OBjBwcHFvs7IyEjquYaGRonTs7KypKYXVUyIpyUlJQEAZs6cCW1tbezatQsbNmyAqqoqvLy8sGTJEri7u+PDhw9gjMHS0rLQusTHI/G6xIyNjaWeCwQCAEBmZmax+0oqP5kuMr558yb69u0rVdx8ztraGn379sWNG8rzi6eqogE4CSHloa6ujsDAQADA/fv3Fbqt+Pj4YqeJixA1NTVMnjwZN2/eRHJyMvbu3YvY2Fh06NABGRkZMDQ0hIqKCuLi4gqtS3zhcEmtUKT6kKnAycnJgba2donLaGtrIycnR6ZQpGxoAE5CSGkUVRQAwKNHjwCg2B+t8vLgwQPcuXNHatqePXugq6uLxo0bF1rewMAAvXv3xrhx45CcnIzo6Ghoa2ujWbNmOHTokFQLjEgkwq5du1CjRg3UqVNHoftBKgeZTlHVqVMHR48excKFC4u83TAvLw/Hjh2jP7IK4l3DG0aaRpIBOL1tvPmORAhRQh06dECNGjXQtWtX1KtXDyKRCLdv38by5cuho6Oj8BtDrKys0K1bNwQFBcHS0hK7du3C6dOnsWTJEmj9/ynArl27wsXFBe7u7jA1NUVMTAxWrlwJW1tbODo6AgAWLVoEX19ftG7dGlOnToWGhgbWrVuH+/fvY+/evdTxKQEgYwvO0KFD8eTJE3To0KHQaajIyEh06tQJT548wdChNIRARVBXVYdfLRqAkxBSsjlz5sDQ0BC//vorunXrhk6dOmH16tVo164drl+/DldXV4VuX3xt5vLly9G9e3dcunQJK1aswLRp0yTLtG7dGufPn8f3338PX19fzJkzB23btkV4eLjklnZvb2+cPXsW2traGDZsGPr164fU1FSEhoYWukWcVF8y3Saen5+Pvn374vDhw+A4DkKhEObm5khISEBmZiYYY+jevTsOHjyolD1jVpXbxD/37MMz9AztCTVODaf7nKYBOAkhSsXOzg4uLi44duwY31FIJabwnoxVVVVx8OBB7NixAz4+PhAIBHj16hUEAgFat26NHTt24PDhw0pZ3FRVjoaOcDVxRR7Lw/GXx7/+AkIIIaQKk+kanFevXkFDQwODBw/G4MGD5Z2JyEg8AOfex3vRv15/aKhq8B2JEEII4YVMTSz29vaYPXu2vLOQcupi3wUmQhO8+fQGex/v5TsOIYRIREdH0+kpUqFkKnCMjIwKdexE+KelroWJjSYCADbe2YgPWR94TkQIIYTwQ6YCp1WrVrh69aq8sxA56ObQDXUN6+Jj7kdsuLOB7ziEEEIIL2QqcBYtWoT79+9j3rx5yMujjuWUiaqKKqZ6FIzK+8eTP/Ay9SXPiQghhJCKJ9Nt4iNGjMCzZ89w+fJlWFhYoEGDBjA3Ny/UuRLHcdi6davcwspLVbxN/EsTzkzAudfn4FPDB7+1/Y3vOIQQQki5leX4LVOBU9rbvzmOQ35+fllXr3DVocCJSo1Cz796Io/lYXP7zfjG8hu+IxFCCCHlUpbjt0y3iUdFRckUjFQce3179KnbB3sf78WyiGX4w+8PqKqo8h2LEEIIqRAyFTjh4eEwNzdHhw4d5J2HyNGYBmNw7MUxPPnwBKEvQuHv6M93JEIIIaRCyHSR8ciRI3Hy5El5ZyFyZqhpiNENRgMAfrv1GzJyM3hORAjhC8dxpXqcO3eO76gKNWzYMNjZ2ZVqWY7jEBQUVOZtREdHg+M4bN++/avLnjt3DhzH4cCBA2XejiLXJfbw4UMEBQUhOjq60Lw9e/Zg5cqVctuWvMlU4FhaWiInJ0feWYgC9K/XHzV0auB95nuEPAjhOw4hhCdXrlyRenTu3BlCobDQ9MaNG/MdVaHmzp2Lw4dpUOLSevjwIebNm1cpCxyZTlH16NEDJ0+eRHZ2NgQCgbwzETnSUNXAZPfJmHxuMrbf345ejr1goW3BdyxCSAX75hvpGw1MTU2hoqJSaPqXMjIyoKWlpchoFcrBwYHvCKSCyNSC8/PPP0NHRwf+/v548OCBXAMFBQUVajK1sPjvgMwYQ1BQEKysrCAUCuHj4yP3DFVNu5rt0NisMbLys/DbLbplnBBSNB8fH7i4uOD8+fPw9PSElpYWRowYAQD4448/0L59e1haWkIoFKJ+/fqYMWMG0tPTpdYxbNgw6Ojo4MGDB2jbti20tbVhamqK8ePHIyND+jQ5Ywzr1q1Dw4YNIRQKYWhoiN69e+Ply//67xKfdinq8fmpJpFIhODgYNSrVw8CgQBmZmYYMmQIXr9+XSjfl6eo0tLSMGrUKBgbG0NHRwcdO3bE06dPC70/z58/x/Dhw+Ho6AgtLS1YW1uja9euuHfvnixvd5ncv38f3bt3h6GhITQ1NdGwYUPs2LGjyGWzsrIwefJkWFhYQCgUwtvbG7du3ZJaJjIyEv369YOdnR2EQiHs7OzQv39/xMTESJbZvn07+vTpAwBo3bq15H3fvn07fHx8cPz4ccTExEh9JmLJyckYO3YsrK2toaGhgVq1amH27NnIzs5WwLtTNJlacBo1aoTs7Gzcvn0bJ0+ehKamJszMzIrsB+fFixdlXr+zszP+/fdfyXNV1f/u/gkODsaKFSuwfft21KlTBwsWLICvry+ePHkCXV1dWXanyuM4Dj96/Ij+x/sj9EUoBtQbAGcTZ75jEVJpMMaQlyPiO4aEmoZKoe9beYmLi8OgQYMwbdo0LFy4UNItyLNnz9C5c2cEBARAW1sbjx8/xpIlS3D9+nWcPXtWah25ubno3LkzRo8ejRkzZuDy5ctYsGABYmJicPToUclyo0ePxvbt2zFx4kQsWbIEycnJmD9/Pjw9PXHnzh2Ym5ujcePGuHLlitT6nz17hpEjR8LZ+b/vsTFjxmDTpk0YP348/Pz8EB0djblz5+LcuXO4efMmTExMitxfxhh69OiBy5cv46effoKHhwcuXbqETp06FVr27du3MDY2xuLFi2Fqaork5GTs2LEDzZo1w61bt1C3bl2Z3/eSPHnyBJ6enjAzM8Pq1athbGyMXbt2YdiwYUhISMC0adOklp81axYaN26MLVu2IDU1FUFBQfDx8cGtW7dQq1YtAAXXCdWtWxf9+vWDkZER4uLisH79enh4eODhw4cwMTFBly5dsHDhQsyaNQtr166VnL50cHBA06ZN8d133+HFixeFTvllZWWhdevWePHiBebNmwc3NzdcuHABixYtwu3bt3H8+HGFvE9fkqnAEYlE0NDQQM2aNaWmf9mljgxd7BSEUlOTarX5fH0rV67E7Nmz0bNnTwDAjh07YG5ujj179mD06NFFri87O1uqakxLS5MpV2XmYuICv1p+OPbyGJZGLkVIhxCFfUESUtXk5YiwaVI43zEkvlvlDXWBYrp9SE5Oxv79+9GmTRup6XPmzJH8mzGGFi1aoH79+vD29sbdu3fh5uYmmZ+Tk4MpU6Zg4sSCsfF8fX2hrq6O2bNn49KlS2jRogWuXr2KzZs3Y/ny5Zg8ebLkta1atUKdOnWwYsUKLFmyBHp6elKn0d69e4eBAweiTp062L17NwDg8ePH2LRpE8aOHYvffvuvlbpRo0Zo1qwZfv31V/zyyy9F7u/JkycRFhaGVatWSeXV0NAoNKi0l5cXvLy8JM/z8/PRpUsXODs7Y+PGjVixYkXp3uQyCgoKQk5ODsLCwmBjYwMA6Ny5M1JSUjBv3jyMHj0a+vr6kuVNTU1x+PBhyXd8y5Yt4ejoiEWLFmHz5s0AgN69e6N3795S++Ln5yc5nk6cOBGmpqZwdHQEADg5OUl9DqampjAwMIBAICh0mnPHjh24e/cu/vzzT0kLkK+vL3R0dDB9+nScPn0avr6+CninpMl0iio6OhpRUVGlesji2bNnsLKygr29Pfr16ydproyKikJ8fDzat28vWVYgEMDb2xuXL18udn2LFi2Cvr6+5CH+A6luJjWeBIGqADcSbuDsq7NffwEhpNoxNDQsVNwAwMuXLzFgwABYWFhAVVUV6urq8Pb2BgA8evSo0PIDBw6Uej5gwAAAQFhYGADg2LFj4DgOgwYNQl5enuQh7h2/qLu50tPT0aVLF2RlZeHEiRMwMDCQWuewYcOklm/atCnq16+PM2fOFLu/4tcWl/dzeXl5WLhwIZycnKChoQE1NTVoaGjg2bNnRb4HX77280dZGgDOnj2Ltm3bFjp2DRs2DBkZGYVauAYMGCD1A9bW1haenp6SfQWAT58+Yfr06ahduzbU1NSgpqYGHR0dpKenf3VfSpNXW1tbqoAS5wVQ4uchTzK14ChSs2bN8Pvvv6NOnTpISEjAggUL4OnpiQcPHiA+Ph4AYG5uLvUac3NzqfOGX5o5c6bUL4S0tLRqWeRYaFtgiNMQbL63GSturIBXDS+oq6rzHYsQpaemoYLvVnnzHUNCTUOm36alYmlpWWjap0+f0KpVK2hqamLBggWoU6cOtLS0EBsbi549eyIzM1M6n5oajI2NpaaJW+WTkpIAAAkJCWCMFfo+FxOfShHLy8tD79698fTpU5w/f17qO1y8zqKyW1lZlXh8SEpKKjHv5yZPnoy1a9di+vTp8Pb2hqGhIVRUVPDtt98Weg8+Fx0dDXt7e6lpYWFh8PHxKfY1X2Ysbt/E87+W3cLCAnfu3JE8HzBgAM6cOYO5c+fCw8MDenp64DgOnTt3LnFfSpvXwsKi0FkCMzMzqKmpFcqrKAorcNLS0pCSklLoNNbXfH7e09XVFc2bN4eDgwN27NghaQb78k1jjJV4ukUgENDdXv9vpOtIHHp2CK8+vsK+J/sw2Gkw35EIUXocxynslJCyKeq79OzZs3j79i3OnTsnabUBgJSUlCLXkZeXh6SkJKmiQfwDVTzNxMQEHMfhwoULRX4/fzntu+++w5kzZ/D333+jQYMGUvPE64yLi0ONGjWk5r19+7bY62/Ery0p7+d27dqFIUOGYOHChVLTExMTJa1JRbGyskJERITUtLJcr2NsbIy4uLhC09++fQsAhfavqOzx8fGS/UtNTcWxY8cQGBiIGTNmSJbJzs5GcnJyqXOVlPfatWuFjs3v3r1DXl5eiZ+HPJX6Z4CRkRGWLl0qNe2PP/6QXAvzpV9//bVQxSoLbW1tuLq64tmzZ5Kq9MsP7927d8X+CiDStNW1MaHRBADAhjsbkJqdynMiQoiyEx+kviw6Nm7cWOxrxNfHiO3ZswcAJK0Wfn5+YIzhzZs3cHd3L/RwdXWVvHbOnDkICQnBli1b0K5du0LbEp9S27Vrl9T0iIgIPHr0CG3bti02Z+vWrUvM+zmO4wq9B8ePH8ebN2+KXT8AaGhoFNq/stwU07ZtW0mR+bnff/8dWlpaha6B2bt3r9QpsJiYGFy+fFny3nMcB8ZYoX3ZsmVLofEjxcsU1aojEAiKnN62bVt8+vQJR44cKZRXPL8ilLoFJyUlpdCOPH78GH/99ZfcQ30uOzsbjx49QqtWrWBvbw8LCwucPn0ajRo1AlBwMVt4eDiWLFmi0BxVSY/aPbD78W48+/AMG+5swPSm0/mORAhRYp6enjA0NMT333+PwMBAqKurY/fu3VKnPD6noaGB5cuX49OnT/Dw8JDcRdWpUye0bNkSANCiRQt89913GD58OCIjI+Hl5QVtbW3ExcXh4sWLcHV1xZgxY7B//3788ssv6N27N+rUqYOrV69KtiMQCNCoUSPUrVsX3333HX777TeoqKigU6dOkruobGxs8MMPPxS7b+3bt4eXlxemTZuG9PR0uLu749KlS9i5c2ehZf38/LB9+3bUq1cPbm5uuHHjBpYuXVqo1UgWn+/X57y9vREYGIhjx46hdevW+Omnn2BkZITdu3fj+PHjCA4OlrrAGCj40e/v749Ro0YhNTUVgYGB0NTUxMyZMwEAenp68PLywtKlS2FiYgI7OzuEh4dj69athVqiXFxcAACbNm2Crq4uNDU1YW9vD2NjY7i6uuLQoUNYv349mjRpAhUVFbi7u2PIkCFYu3Ythg4diujoaLi6uuLixYtYuHAhOnfuXGSRqhCslDiOY/PmzZOaFhQUxFRUVIpcvqR5JZkyZQo7d+4ce/nyJbt69Srz8/Njurq6LDo6mjHG2OLFi5m+vj47dOgQu3fvHuvfvz+ztLRkaWlppd5GamoqA8BSU1PLnK+quPzmMnPZ7sIa7mjIolKi+I5DCKlgQ4cOZdra2lLTvL29mbOzc5HLX758mTVv3pxpaWkxU1NT9u2337KbN28yACwkJKTQeu/evct8fHyYUChkRkZGbMyYMezTp0+F1rtt2zbWrFkzpq2tzYRCIXNwcGBDhgxhkZGRjDHGAgMDGYAiH7a2tpL15OfnsyVLlrA6deowdXV1ZmJiwgYNGsRiY2ML7ffnr2OMsZSUFDZixAhmYGDAtLS0mK+vL3v8+DEDwAIDAyXLffjwgY0cOZKZmZkxLS0t1rJlS3bhwgXm7e3NvL29JctFRUUVel+KExYWVuz+AWBhYWGMMcbu3bvHunbtyvT19ZmGhgZr0KBBofWL17Vz5042ceJEZmpqygQCAWvVqpXk/RR7/fo169WrFzM0NGS6urqsY8eO7P79+8zW1pYNHTpUatmVK1cye3t7pqqqKrVfycnJrHfv3szAwIBxHMc+LymSkpLY999/zywtLZmamhqztbVlM2fOZFlZWV99T0pSluO30hU4//vf/5ilpSVTV1dnVlZWrGfPnuzBgweS+SKRiAUGBjILCwsmEAiYl5cXu3fvXpm2QQVOgbH/jmUu213YhDMT+I5CCKkiiiqcCJGXshy/le4uqn379pU4Xzz4mSwDoBFpU5pMwaU3lxAWG4brcdfR1LIp35EIIYQQuVDcvYZE6dUyqIXedQr6KVgWuQwipjw9tRJCCCHlQQVONTe24VjoqOvgUfIjHH1x9OsvIISQEmzfvh2fPn3iOwYh4BgrXXeKKioqMDExkbp/PTExEUlJSUXezy+e9+UtZ8ogLS0N+vr6SE1NhZ6eHt9xeBdyPwQrbqyAmdAMR/2PQku96owcTAghpOooy/G7TAVOWXEcRwVOJZCdn43uR7rjzac3GNtgLMY0HMN3JEIIIaSQshy/S121iESiMj+UsbghhQlUBfihSUE/ESEPQpCQnsBzIkIIIaR86BocAgBob9seDU0bIjMvE7/d+u3rLyCEEEKUGBU4BEDB6cQfPX4EAIS+CMXDpIc8JyKEEEJkRwUOkXAzdUNn+85gYFgWuQylvDyLEEIIUTpU4BApkxpPgoaKBiLiIxAWG8Z3HEIIIUQmVOAQKVY6VhjiPAQAsOLGCuTm5/KciBBCCCk7KnBIISNdRsJI0wgxaTH48+mffMchhBBCyowKHFKIjoYOxjcaDwBYd3sdUrNTeU5ECCGElI1MBc78+fNx/vz5Epe5dOkS5s+fL1Mowj//2v6obVAbaTlp2Hh3I99xCCGEkDKRqcAJCgrCuXPnSlzm4sWLmDdvniyrJ0pATUUNP7oX3Da+9/FexKTF8JyIEEIIKT2FnaLKycmRaXgHojw8rT3R0rol8kR5+PXGr3zHIYQQQkpN5gqE47hi5+Xk5ODChQswNzeXdfVESUxpMgUqnArOvDqDiPgIvuMQQgghpaJW2gVr1aol9fzXX39FSEhIoeXy8/ORmJiIrKwsjBo1qvwJCa9qG9ZGb8fe+PPpn1gWuQx7u+yFCkctc4QQQpRbmQbbZIyBMQaO4yT//vKhrq4OZ2dn/Pjjj1i+fLkis5MKMrbhWGira+Nh0kMcf3mc7ziEEELIV5W6BSc6OlrybxUVFfzwww/46aefFJGJKBljoTFGuY7CypsrsfLmSrSzbQehmpDvWIQQQkixZDrXEBUVhUmTJsk7C1Fig5wGwUrbCu8y3mHHgx18xyGEEEJKJFOBY2trC319fXlnIUpMoCrAD01+AABsu78N7zLe8ZyIEEIIKV6pT1F96f379wgJCUFERARSUlKQn59faBmO43DmzJlyBSTKo4NdB+x8tBN339/FmltrML8FdeRICCFEOclU4Ny9exdt2rTBhw8fwBgrdrmSbiUnlQ/HcZjmMQ2D/h6EI8+PYED9AahnVI/vWIQQQkghMp2imjJlCpKTkzF79mxERUUhNzcXIpGo0KOoVh1SuTUwbYCOdh3BwLAsYlmJBS4hhBDCF5kKnCtXrqBHjx6YP38+bG1toaqqKu9cRIkFNAmAhooGrsVfw/nXJY9JRgghhPBBpgJHQ0MDDg4O8s5CKglrHWsMchoEAFgWuQy5olyeExFCCCHSZCpw2rRpg8jISHlnIZXIt67fwkjTCNFp0dj/ZD/fcQghhBApMhU4S5cuxYMHD7Bs2TJ55yGVhK6GLsY1HAcAWH9nPVKzU3lORAghhPyHYzJcJTpixAhERUXh/PnzsLe3R4MGDYrsF4fjOGzdulUuQeUpLS0N+vr6SE1NhZ6eHt9xKq08UR56h/bGi9QXGOo0FFM9pvIdiRBCSBVWluO3TAWOikrpGn44jlPKO6mowJGfi28uYsy/Y6CmoobQ7qGw0bPhOxIhhJAqqizHb5n6wYmKipIpGKl6Wlq3RAurFrj09hJ+vfkrVvis4DsSIYQQIluBY2trK+8cpBKb4j4FV45ewemY07iRcANNzJvwHYkQQkg1J9NFxl9KTk5GbGysPFZFKiFHQ0f0dOwJAFgWsQwiJuI5ESGEkOpO5gInNTUVkyZNgrm5OUxNTWFvby+Zd+3aNXTu3Bk3btyQS0ii/MY1HActNS3cT7qPv6P+5jsOIYSQak6mAic5ORnNmjXDb7/9BhsbG9SvX1+qy343NzdcunQJu3fvlltQotxMhCYY5TYKALDyxkpk5mXynIgQQkh1JlOBExQUhKdPn2Lv3r2IjIxEnz59pOYLhUJ4e3vj7NmzcglJKodB9QfBUtsSCRkJ2PlwJ99xCCGEVGMyFTihoaHw8/PD//73v2KXsbW1xevXr2UOBgCLFi0Cx3EICAiQTGOMISgoCFZWVhAKhfDx8cGDBw/KtR0iH5pqmghoHAAA2HJvCxIzE/kNRAghpNqSqcCJi4uDk5NTictoamoiPT1dplAAEBERgU2bNsHNzU1qenBwMFasWIE1a9YgIiICFhYW8PX1xcePH2XeFpGfTvad4Gbihsy8TKy5tYbvOIQQQqopmQocY2Pjr9419fjxY1haWsoU6tOnTxg4cCA2b94MQ0NDyXTGGFauXInZs2ejZ8+ecHFxwY4dO5CRkYE9e/bItC0iXxzH4UePHwEAh54dwpPkJzwnIoQQUh3JVOB4eXkhNDQUb968KXL+w4cP8c8//6Bdu3YyhRo3bhy6dOlS6PVRUVGIj49H+/btJdMEAgG8vb1x+fLlYteXnZ2NtLQ0qQdRnIZmDdHetj0YGJZFLoMMnWUTQggh5SJTgTN79mzk5eWhRYsW2LNnDxITC661ePToEbZu3Yo2bdpAIBDgxx9/LPO69+3bh5s3b2LRokWF5sXHxwMAzM3Npaabm5tL5hVl0aJF0NfXlzxsbGg4AUULaBIAdRV1XI27igtvLvAdhxBCSDUjU4Hj6uqKP/74AykpKRg8eDDWrVsHxhhcXFwwatQoZGZm4s8//4Sjo2OZ1hsbG4tJkyZh165d0NTULHY5juOknjPGCk373MyZM5Gamip5UKeEimeja4NB9QcBAJZFLkOuKJfnRIQQQqoTmYZqAIBu3brh5cuX2LFjB65du4bk5GTo6emhWbNmGD58OExMTMq8zhs3buDdu3do0uS/rv7z8/Nx/vx5rFmzBk+eFFzPER8fL3V9z7t37wq16nxOIBBAIBCUOQ8pn2/dvsWR50cQlRqFg08Pol+9fnxHIoQQUk3IXOAAgJGREX744Qd5ZUHbtm1x7949qWnDhw9HvXr1MH36dNSqVQsWFhY4ffo0GjVqBADIyclBeHg4lixZIrccRD70NPQwtuFY/HLtF6y7vQ6da3WGngaN3k4IIUTxylXgyJuuri5cXFykpmlra8PY2FgyPSAgAAsXLoSjoyMcHR2xcOFCaGlpYcCAAXxEJl/Ru05v7H28Fy9TX2LL3S2Y7D6Z70iEEEKqAZmuwVmxYgVMTEzw9u3bIue/ffsWpqamWL16dbnCFWXatGkICAjA2LFj4e7ujjdv3uDUqVPQ1dWV+7ZI+ampqGGK+xQAwK5HuxD7ka5/IoQQongck+Ee3ubNm0MoFJY4FIOvry/S09NLvH2bL2lpadDX10dqair09OiUiaIxxjD69GhcibuC9rbtsdxnOd+RCCGEVEJlOX7L1ILz9OnTQqeSvuTs7Ixnz57JsnpSxXAchynuU8CBw6mYU7j97jbfkQghhFRxMhU4GRkZ0NbWLnEZTU1NfPr0SaZQpOqpa1QXPR17AgCCI4IhYiKeExFCCKnKZCpwbG1tv3rq6cqVK6hRo4ZMoUjVNL7ReAjVhLiXeA//RP3DdxxCCCFVmEwFjp+fHy5evIht27YVOX/Lli24ePEiunbtWq5wpGoxEZrgW9dvAQArb65EVl4Wz4kIIYRUVTJdZPz+/Xs0atQIcXFx8Pb2hq+vL6ytrSV3NJ0/fx5WVla4efMmTE1NFZG7XOgiY/5k5WWh65GuiE+Px6TGkyQFDyGEEPI1ZTl+y1TgAMCzZ88waNAgREREFKyI4ySDKjZt2hS7du1C7dq1ZVm1wlGBw69jL49h5oWZ0FLTwvGex2EiLHuv14QQQqqfCilwxCIjI3H9+nWkpKTAwMAATZs2hbu7e3lWqXBU4PBLxEQYeHwg7ifdR+86vRHYPJDvSIQQQioBhRc4I0aMgJubGwICAmTNyCsqcPh3M+Emhv4zFCqcCg50PQBHw7INzEoIIaT6UXg/OHv27EFCQoJM4aq63Ox8ZKXTyNlf09i8MXxtfSFiIiyPpI7/CCGEyJdMBU7t2rURFxcn7yyVXsTxKGyZch73zr3mO0ql8EPjH6CmooZLby/h4puLfMchhBBShchU4IwcORLHjx/Hmzdv5J2nUtM2EECUxxB9L4nvKJWCjZ4NBtYbCABYFrEMeaI8nhMRQgipKmQqcPz9/dGsWTN4enpi7dq1uH79OmJiYvDq1atCj+rE1tkYAPAuJg0ZaTk8p6kcvmvwHQwEBniR+gKHnh3iOw4hhJAqQqaLjFVUVCS3hXMcV/zKOQ55ecr3q1yRFxn/8ct1JMZ+Qrth9VH3G0u5rruq2vNoDxZdXwQjTSMc8z8GXQ0aGZ4QQkhhZTl+q8mygSFDhpRY2FRnti7GSIz9hOj7SVTglFKfun2w9/FeRKdFY8u9LfihyQ98RyKEEFLJyVTgbN++Xc4xqg47VxPcOBGD2IfJEOWLoKIq01nAakVdRR1T3adi/Nnx2PlwJ/rW7QtrHWu+YxFCCKnE6OgrZ2Z2etDUVkd2Rh7iX6bxHafS8KrhhWaWzZArysWqG6v4jkMIIaSSK1eBEx8fj3Xr1mHixIkYOXKkZPr79+9x/fp1ZGZmljtgZaOiwqGmsxEAIOY+3U1VWhzH4Uf3H8GBw4noE7j97jbfkQghhFRiMhc469atg729PcaPH481a9ZInbZ69+4dmjdvjl27dskjY6Vj61JwNxUVOGVT16guetTuAQBYGrkU5RxFhBBCSDUmU4Fz9OhRjB8/Hq6urggNDcWYMWOk5js7O8PNzQ1HjhyRR8ZKp6aTMTgOSHrzCR+Ts/iOU6mMbzQeQjUh7r6/i5PRJ/mOQwghpJKSqcBZunQpatasibCwMPj5+cHMzKzQMq6urnj48GG5A1ZGmjrqMLfXBwC8ekCtOGVhpmWGES4jAAC/3vgV2fnZPCcihBBSGclU4Ny+fRtdunSBtrZ2sctYW1tX6/GqxKepqFfjshvqPBRmWmZ4m/4Wux5Wz9OchBBCykemAkckEkFdXb3EZd6/fw+BQCBTqKrA1rWgwHn9OBn5uSKe01QuQjUhAhoHAAA239uMpEwqEgkhhJSNTAVO3bp1cfFi8YMj5uXlITw8HK6urjIHq+xMauhAS18DeTkivH2WwnecSqdLrS5wMnZCem461t1ex3ccQgghlYxMBc7AgQNx8+ZNLFiwoNC8/Px8TJ06FS9fvsSQIUPKHbCy4jjuv9NU9xN5TlP5qHAq+NH9RwDAgWcH8PzDc54TEUIIqUxkKnAmTJgAb29vBAYGom7dujh48CAAoG/fvnB0dMTq1avh6+sr1TdOdWTnYgKAbheXlbuFO9rWbAsRE2H5jeV8xyGEEFKJyFTgqKur4+TJk5gxYwYSExNx//59MMZw4MABJCcnY/r06QgNDa3241XVqGcIFVUOqe8ykZKQwXecSumHJj9ATUUNF99cxKU3l/iOQwghpJKQuaM/DQ0N/PLLL0hMTMTDhw9x8eJF3L17F0lJSVi0aBE0NDTkmbNS0hCqwbK2AQBqxZGVrZ4t+tfrDwBYFrkMeSLlG52eEEKI8inTYJsfPnzAmjVrEBERAQBo2rQpxo8fj3r16ikkXFVg52qMN08+IOZBEhq0teE7TqU02m00Ql+E4nnKcxx+fhh96vThOxIhhBAlV+oWnKSkJLi7uyMoKAjHjh3DsWPHEBgYCA8PDyQnJysyY6UmvtD4zdMPyMmi1gdZ6Av0MaZBQW/Za26twaecTzwnIoQQouxKXeAsXLgQUVFR8PHxwb59+7Bv3z54eXnhxYsXWLx4sSIzVmoG5lrQM9GEKI/hzZMPfMeptPrW7Qs7PTskZyVj6/2tfMchhBCi5DhWyhEN69evj/z8fDx69AiqqqoACvq7qV+/PtTV1SvVsAxpaWnQ19dHamoq9PT0FL698/ue4t6513BuZQWfgXQ6T1Zhr8IwMWwiNFQ0cNT/KKx0rPiORAghpAKV5fhd6hacmJgYdOjQQVLcAICamho6duyI6OhomcNWB5+PLk4jZMvOx8YHHhYeyBHlYNXNVXzHIYQQosRKXeBkZWXB1NS00HQTExNkZ9OAiCWxrmMANXUVfPqQjeS36XzHqbQ4jsNU96ngwOHvqL9x9/1dviMRQghRUjLfJk5KT01DFdb1DAEA0feoV+PycDJ2QjeHbgCApRFLqUWMEEJIkcp0m/jFixcRHBxcaBoALF1a9MFm2rRp5YhXddg6GyPmXhJi7iehSUc7vuNUahMaTcCpmFO4/f42TsWcQge7DnxHIoQQomRKfZGxikrZG3s4jkN+fn6ZX6doFX2RMQCkJWZi55wr4FQ4jFjaEpraJY/GTkq2/vZ6rLuzDtY61virx18QqFbfkesJIaS6KMvxu9QtOCEhIeUOVp3pmQhhaKmND3HpiH2UDEd3c74jVWpDnYfiwNMDePPpDfY82oPhLsP5jkQIIUSJlLrAGTp0qCJzSKxfvx7r16+X3Jnl7OyMn376CZ06dQIAMMYwb948bNq0CR8+fECzZs2wdu1aODs7V0i+8rBzMcaHuHTE3E+iAqectNS1MLHxRMy5NAeb7m5C99rdYaRpxHcsQgghSkLpLjKuUaMGFi9ejMjISERGRqJNmzbo3r07Hjx4AAAIDg7GihUrJENGWFhYwNfXFx8/fuQ5+deJbxd/9SAJTEQXx5ZXV4euqG9UH59yP2H97fV8xyGEEKJElK7A6dq1Kzp37ow6deqgTp06+OWXX6Cjo4OrV6+CMYaVK1di9uzZ6NmzJ1xcXLBjxw5kZGRgz549xa4zOzsbaWlpUg8+WNTWh4amKjI/5uJdjPIXZMpOhVPBjx4/AgD2P92PlykveU5ECCFEWShdgfO5/Px87Nu3D+np6WjevDmioqIQHx+P9u3bS5YRCATw9vbG5cuXi13PokWLoK+vL3nY2PAz6KWqqgpsnApOo8Tcp9vF5cHDwgOtbVojn+Vj+Y3lfMchhBCiJJSywLl37x50dHQgEAjw/fff4/Dhw3ByckJ8fDwAwNxc+voVc3NzybyizJw5E6mpqZJHbGysQvOX5PNejYl8TG4yGWqcGs6/Po/Lb4svdAkhhFQfSlng1K1bF7dv38bVq1cxZswYDB06VGqsK47jpJZnjBWa9jmBQAA9PT2pB19qOhcUOO9iPiIjLYe3HFWJnb4d+tXrBwBYFrkM+SLl65qAEEJIxVLKAkdDQwO1a9eGu7s7Fi1ahAYNGmDVqlWwsLAAgEKtNe/evSvUqqOstPUFMK2pC4BaceTp+wbfQ09DD88+PMOR50f4jkMIIYRnSlngfIkxhuzsbNjb28PCwgKnT5+WzMvJyUF4eDg8PT15TFg2dJpK/vQF+vi+wfcAgN9u/Yb0XBrzixBCqrNyFTjx8fFYt24dJk6ciG+//VYy/f3797h+/ToyMzPLvM5Zs2bhwoULiI6Oxr179zB79mycO3cOAwcOBMdxCAgIwMKFC3H48GHcv38fw4YNg5aWFgYMGFCeXalQtq4FBU7so2Tk54t4TlN19KvbDzV1ayIpKwlb723lOw4hhBAeyVzgrFu3Dvb29hg/fjzWrFkj1dPxu3fv0Lx5c+zatavM601ISMDgwYNRt25dtG3bFteuXcM///wDX19fAAVjWwUEBGDs2LFwd3fHmzdvcOrUKejq6sq6KxXOzFYPmjrqyMnMQ/yLVL7jVBnqquqY7D4ZAPD7w98Rn178heeEEEKqtlKPRfW5o0ePonv37nB3d8dPP/2EEydOYMOGDVLjTjVq1AhWVlY4fvy4XAPLAx9jUX3pdMgDPL2WgEbta8KzZ21eMlRFjDEMPzkcNxJuwK+WHxa1WsR3JEIIIXJSluO3TC04S5cuRc2aNREWFgY/Pz+YmZkVWsbV1VXqzicizc7FBABdhyNvHMdJOv879vIY7ife5zkRIYQQPshU4Ny+fRtdunSBtrZ2sctYW1sjISFB5mBVnY2TETgOSH6bjo/JWXzHqVKcjZ3RzaEbAGBpxFLI0EhJCCGkkpOpwBGJRFBXVy9xmffv30MgEMgUqjrQ1FaHhYM+AGrFUYQJjSZAU1UTN9/dxL+v/uU7DiGEkAomU4FTt25dXLx4sdj5eXl5CA8Ph6urq8zBqgPJ7eL3aNgGebPQtsAwl2EAgBWRK5CTT50qEkJIdSJTgTNw4EDcvHkTCxYsKDQvPz8fU6dOxcuXLzFkyJByB6zKxAXO68cfkJdLve/K23Dn4TAVmuL1p9fY+3gv33EIIYRUIJkKnAkTJsDb2xuBgYGoW7cuDh48CADo27cvHB0dsXr1avj6+mLkyJFyDVvVGFvrQNtAgLxcEd4+TeE7TpWjpa6FCY0mAAA23tmID1kfeE5ECCGkoshU4Kirq+PkyZOYMWMGEhMTcf/+fTDGcODAASQnJ2P69OkIDQ0tcXwoUnDHj7gVJ5quw1GIbg7dUM+oHj7mfsSGOxv4jkMIIaSCyNQPzucYY3jy5AmSk5Ohp6eH+vXrQ1VVVV75FEIZ+sERe3n7PU5suAc9E00M+rk5FYUKcC3uGr499S1UOVUc6n4ItfRr8R2JEEKIDBTeD87nOI5DvXr14OnpCRcXF6UvbpRNjXqGUFHlkJaYhZSEDL7jVEnNLJvBp4YP8lk+fo38le84hBBCKoBMBU6dOnXw888/4+XLl/LOU+1oaKrBytEAAN0urkiT3SdDjVPDudfncDXuKt9xCCGEKJhMBU5CQgICAwPh6OiIli1bYuPGjfjwgS7glJWdK/VqrGj2+vboW7cvAGBZxDLki+iuNUIIqcpkKnDevXuHvXv3onPnzoiIiMDYsWNhaWmJXr164fDhw8jNzZV3zipNfKHx22cpyMnK4zlN1TWmwRjoaujiyYcnCH0RynccQgghCiRTgSMQCPC///0PR48exdu3b7Fq1So0bNgQhw8fRu/evWFhYYExY8aU2Bkg+Y++mRB6pkKI8hleP6aWMEUx0DTAaLfRAIDVt1YjI5eueSKEkKqq3BcZGxsbY/z48bh69SqePn2KuXPnwtjYGBs3boSPj48cIlZ9HMfBTtyrMZ2mUqj+9frDRtcGiZmJCHkQwnccQgghClLuAudztWvXRps2beDt7Q11dXUa5LAMbD8rcOh9UxwNVQ1MbjIZALD9/nbEp8fznIgQQogiyKXAefDgAWbNmgU7Ozu0bt0aW7duhZ2dHYKCguSx+mrBqo4B1DRUkJ6SjaQ3n/iOU6W1rdkWjc0aIys/C7/d+o3vOIQQQhRA5gInLi4Oy5cvR6NGjeDm5obFixcjIyMDY8aMwZUrV/DkyRPMnTtXnlmrNDV1VdSoZwQAiL5Hp6kUieM4/OjxIwAg9EUoHiQ+4DkRIYQQeZOpwPH19UXNmjXx448/4vHjx+jVqxf++usvvH37FmvWrEGzZs3knbNaEJ+mekXX4Sici4kL/Gr5AQCWRi6l04KEEFLFyFTgnD17Fi1atMDmzZuRkJCAP//8E127doWampq881Ur4gIn/mUqstLpVntFm9R4EgSqAtxIuIGzr87yHYcQQogcyVTgREVF4dy5cxg5ciTvYzlVJbpGmjCy0gZjwKuH1IqjaBbaFhjqPBQAsPzGcuTmU1FJCCFVhUwFTs2aNeWdg/w/W7pdvEKNdBkJE6EJYj/GYu/jvXzHIYQQIielOqd0/vx5AEDTpk2hqakpeV4aXl5esiWrpuxcjXHr1Cu8up8MkYhBRYVGF1ckLXUtTGg0AYGXA7Hx7kZ0r90d+gJ9vmMRQggpp1IVOD4+PuA4Do8ePUKdOnUkz0sjP5/G/CkL81r60BCqISs9F++i02BRiw62itbdoTt2P9qNpx+eYsOdDZjedDrfkQghhJRTqQqcn376CRzHwcTEROo5kT9VVRXUdDLC8xvvEHM/iQqcCqCqooqp7lPx3envsO/xPvyv7v9gp2/HdyxCCCHlwLFqeH9sWloa9PX1kZqaqpQXST++EoczOx7BtKYu+s7y4DtOtTHuzDicf30erW1aY3Wb1XzHIYQQ8oWyHL9lusj41atXSEtLK3GZjx8/4tWrV7Ksvtqr6VxwofH7Vx+RnprNc5rqY0qTKVDlVBEWG4brcdf5jkMIIaQcZCpw7O3tsWrVqhKXWbduHezt7WUKVd1p6WnAzFYXAN1NVZFqGdRCnzp9ABR0/pcvouvHCCGkspKpwGGMfbXn12p45kuuqFdjfoxpOAa66rp4nPwYR18e5TsOIYQQGcl1NPHPvX79Grq6uopafZVn61pwQferR8nIzxfxnKb6MNI0wndu3wEAVt9cjYzcDJ4TEUIIkUWpx1aYP3++1PNz584VuVx+fj5ev36Nffv20ZhU5WBWUxdCXXVkfsxF3PNU1KhryHekamNA/QHY92Qf3nx6gx0PdmBMwzF8RyKEEFJGpb6LSkXlv8YejuO+egrKysoKhw8fhoeH8t0FpOx3UYn9u/0hnlyNR0PfmmjRqzbfcaqVU9GnMCV8CoRqQhztcRTm2uZ8RyKEkGqvLMfvUrfghIWFASi4tqZNmzYYNmwYhg4dWmg5VVVVGBkZoV69elJFESk7WxdjPLkaj5j7SVTgVDBfW180MmuEW+9u4bdbv2FBywV8RyKEEFIGpS5wvL29Jf8ODAxE69ataRgGBbOpbwROhcOHuHSkJWZCz0TId6Rqg+M4THWfioF/D0Toi1AMqD8ATsZOfMcihBBSSjI1sQQGBlJxUwE0tdVhUaugCY5uF694bqZu6GzfGQwMyyKX0Z2BhBBSiZS6Bac4sbGxePv2LbKzi+6Qjgqh8rFzNUHc81TE3E+Cq08NvuNUOwGNA3Dm1RlExEcgLDYMbWq24TsSIYSQUpC5wDl69Ch+/PFHPHv2rMTlaLDN8rF1McaVwy/w+skH5OXkQ01Dle9I1YqljiWGOA3B5nubseLGCrSybgV1VXW+YxFCCPkKmU5RnTt3Dv7+/vj06RPGjx8Pxhi8vLzw3XffwcnJCYwxdOnSBT/99FOZ171o0SJ4eHhAV1cXZmZm6NGjB548eSK1DGMMQUFBsLKyglAohI+PDx48eCDLrig9Iytt6BgKkJ8rwpunKXzHqZZGuo6EkaYRYtJi8OfTP/mOQwghpBRkKnAWL14MHR0d3LhxQzJkQ+vWrbF+/XrcvXsXv/zyC86cOYPu3buXed3h4eEYN24crl69itOnTyMvLw/t27dHenq6ZJng4GCsWLECa9asQUREBCwsLODr64uPHz/KsjtKjeM4Sa/GMfcSeU5TPWmra2NCowkAgHW31yE1O5XnRIQQQr5GpgInIiICPXr0gLn5f32DiEQFve1yHIeZM2eiUaNGMrXg/PPPPxg2bBicnZ3RoEEDhISE4NWrV7hx4waAgtablStXYvbs2ejZsydcXFywY8cOZGRkYM+ePbLsjtITFzjR95PoQlee+Nf2R22D2kjLScPGuxv5jkMIIeQrZCpwMjIyYG1tLXkuEAgKjS7+zTff4NKlS+VLByA1teDXspGREQAgKioK8fHxaN++vdT2vb29cfny5SLXkZ2djbS0NKlHZVKjnhFU1Dh8TMrCh3gaOoAPqiqq+NH9RwDA3sd7EZMWw3MiQgghJZGpwLGwsMD79+8lz62trQtdA5OUlFTuC4wZY5g8eTJatmwJFxcXAEB8fDwASLUeiZ+L531p0aJF0NfXlzxsbGzKlauiqQtUYV2nYKgGul2cP57Wnmhp3RJ5ojz8euNXvuMQQggpgUwFToMGDXD//n3J89atWyMsLAz79u1Deno6Tp48iT/++ANubm7lCjd+/HjcvXsXe/fuLTSP4zip54yxQtPEZs6cidTUVMkjNja2XLn4YOv8/9fhUIHDq6nuU6HKqUpuHSeEEKKcZCpwunXrhtu3byMmpqCZftasWdDR0cHAgQOhp6eHzp07Iz8/HwsWyN69/YQJExAaGoqwsDDUqPFf/y8WFhYAUKi15t27d4VadcQEAgH09PSkHpWNrWtBgRP3LAU5mXk8p6m+HAwc0LtObwDA0oilEDEa6Z0QQpSRTAXOiBEjkJGRAVtbWwCAvb09IiIi8P3336N9+/YYNWoUrl27JlMnf4wxjB8/HocOHcLZs2dhb28vNd/e3h4WFhY4ffq0ZFpOTg7Cw8Ph6ekpy+5UCgZmWtA3E0IkYoh9nMx3nGptTIMx0FHXwaPkRzj28hjfcQghhBSh3D0Zizk4OGDt2rXlXs+4ceOwZ88e/PXXX9DV1ZW01Ojr60MoFILjOAQEBGDhwoVwdHSEo6MjFi5cCC0tLQwYMKDc21dmdi4muHM2FjH3kuDQyIzvONWWsdAYo9xG4dcbv2LVzVXwtfWFUI3GCSOEEGWidMN9r1+/HqmpqfDx8YGlpaXk8ccff0iWmTZtGgICAjB27Fi4u7vjzZs3OHXqFHR1dXlMrniS/nDodnHeDaw/ENY61niX8Q47HuzgOw4hhJAvcKwUR8rz58/LvAFlHIsqLS0N+vr6SE1NrVTX4+TnirBl6gXkZeej7ywPmNas2gWdsvsn6h/8eP5HCNWEOOZ/DGZa1KpGCCGKVJbjd6lOUfn4+BR7h9LX0FhU8qOqrgKbeoaIupOImPuJVODwrINdB+x8tBN339/FmltrML/FfL4jEUII+X+lKnB++uknmQscIl+2Lsb/X+Akwb2z/ddfQBSG4zhM85iGQX8PwpHnRzCg/gDUM6rHdyxCCCEoZYETFBSk4BiktMTX4cRHpSHzUw6EOho8J6reGpg2QCe7TjgRfQLLIpZhc/vN9GOAEEKUgNJdZExKpmOoCWNrHYABrx7Q7eLKYFKTSdBQ0cC1+GsIfx3OdxxCCCEoZ4ETHx+PdevWYeLEiRg5cqRk+vv373H9+nVkZmaWOyAp7PO7qQj/rHWsMdhpMABgeeRy5IpyeU5ECCFE5gJn3bp1sLe3x/jx47FmzRps375dMu/du3do3rw5du3aJY+M5AviXo1fPUyCSES3iyuDb12/hZGmEaLTorH/yX6+4xBCSLUnU4Fz9OhRjB8/Hq6urggNDcWYMWOk5js7O8PNzQ1HjhyRR0byBQt7PQi01JCdnoeEqMo1MnpVpaOhg3ENxwEA1t1Zh9TsVJ4TEUJI9SZTgbN06VLUrFkTYWFh8PPzg5lZ4f4/XF1d8fDhw3IHJIWpqKrAxskIABBzP5HnNESsp2NPOOg7IDU7FcP+GYZXaa/4jkQIIdWWTAXO7du30aVLF2hraxe7jLW1NRISEmQORkpmR9fhKB01FTUsarUIpkJTPE95jn7H+uH8a9k7ySSEECI7mQockUgEdXX1Epd5//49BAKBTKHI19V0NgY4IDH2Ez59yOY7Dvl/9Y3r4w+/P9DQtCE+5n7E+DPjseHOBhp1nBBCKphMBU7dunVx8eLFYufn5eUhPDwcrq6uMgcjJRPqasDcrqCb6lcPqBVHmZhqmWJbh234X93/gYFh7e21CAgLwKecT3xHI4SQakOmAmfgwIG4efMmFixYUGhefn4+pk6dipcvX2LIkCHlDkiKR7eLKy91VXXM+WYO5nvOh7qKOsJiw9D/eH+8TH3JdzRCCKkWSjXY5pdyc3PRvn17nD9/HrVr14ZAIMCDBw/Qq1cvREZGIjo6Gu3bt8eJEyeUslfXyjrY5pfexaRh/6JIqAtUMXJ5K6iqUb+Nyuje+3v44dwPSMhIgLa6Nha2XIg2NdvwHYsQQiqdshy/ZToiqqur4+TJk5gxYwYSExNx//59MMZw4MABJCcnY/r06QgNDVXK4qYqMbXRhVBPA7nZ+Xj7PIXvOKQYrqau+MPvD7ibuyM9Nx2TwiZhza01dF0OIYQokEwtOJ9jjOHJkydITk6Gnp4e6tevD1VVVXnlUwhFtuBkPngAzbp1wamVapivcjuz4yEeX4lHg3Y2aNnbsUK2SWSTK8rFisgV2PWooAPMVtatsNhrMfQ0Km8rIiGEVCSFt+B8juM41KtXD56ennBxcZEUN1FRURg2bFh5V1+pJG7chOg+fZG0eXOFbdPWxQQAEHOPrsNRduoq6pjedDoWtlwIgaoAF95cQP9j/fHswzO+oxFCSJUj94s2Xr16hVGjRqFevXrYuXOnvFev1NStrACRCO/XrkPmgwcVsk0bJyNwKhxSEjKQ+j6jQrZJyqerQ1fs7LQTVtpWePXxFQb+PRAno0/yHYsQQqqUMhU4Fy9eROvWraGnpwcjIyN0794dT548AQBkZGRg8uTJqFOnDrZu3QpTU1OsXr1aIaGVlZ5fF+h27Ajk5eHt9OkQZSu+fxqBUA2WDvoAgJj7NLp4ZVHfuD72+e1DM8tmyMzLxNTwqfj1xq/IF+XzHY0QQqqEUhc4N27cQLt27RAeHo5Pnz4hJSUFR48eRevWrfH8+XM0bdoUK1euhImJCVatWoUXL15g3LhxisyudDiOg0XgT1A1MUHO8xd4v3JVhWxXPPgmDdtQuRhqGmJDuw0Y7jwcALDt/jaMPTMWKVkp/AYjhJAqoNQFTnBwMHJycrBo0SK8e/cO7969w/z58xEfH49WrVrh8ePHmDNnDp4/f44JEyZU216M1QwNYfnzfABA8vbtSL9+XeHbFPeH8+ZJCnJzqAWgMlFTUcNk98lY6rUUQjUhLr+9jH7H++Fx8mO+oxFCSKVW6gLn0qVLaNOmDaZPnw4TExOYmJhgzpw58Pb2xrt37xAcHIz58+dDU1NTkXkrBd3WrWHQpzfAGOJmzkL+J8X2YGtkqQ0dIwHy80R48+SDQrdFFKOjfUfs6rwLNXRq4M2nNxj892Acf3mc71iEEFJplbrAeffuHZo0aVJouoeHBwBg6NCh8ktVBZhNnwF1a2vkvnmDhMWLFbotjuNgR3dTVXp1DOtgn98+tLRuiaz8LMy4MAPBEcHIE+XxHY0QQiqdUhc4eXl5RY4eLp5mbGwsv1RVgKqONqwWLwI4DqkHDuLj2TCFbu/zYRvK2bUR4ZG+QB9r2qzBKNdRAICdD3fiu9PfISmTCldCCCkL6ttfgbQ8PGA0vOAC0ri5c5GXrLi7nKzrGUJVTQUfk7OQHJeusO0QxVNVUcXExhPxq8+v0FLTQkR8BPod74cHiRXT9QAhhFQFpe7JWEVFBbVr10bt2rWlpj9//hwvXrxAhw4dCq+c43D8uPJdR1CRY1GJsrMR3bs3sp89h66vL6xXr1LYEBZHf7uNVw+S0bynAxq3t1XINkjFepHyAgFhAYhOi4aGigbmNp+LHrV78B2LEEJ4UZbjd5kKnLLiOA75+cp3V09FD7aZ9fAhovr+D8jLg1XwEuh366aQ7dwNi8WFP55BqKuOJp3s4NTSCuoayj1sBvm6jzkfMevCLJx7fQ4A0K9uP0zzmAZ1VXV+gxFCSAVTSIETExMjUxhbW+VrSeBjNPHEDRvwfuUqqOjqolboX1C3tJT7NjI/5eDA4kikJWYBAIS66mjQ1gYu3jUgEFbM2FhEMURMhI13N2Ld7XUAgMZmjbHcZzlMhCY8JyOEkIqjkAKnKuGjwGF5eYgeOBBZd+5Cq/k3qLl1KzgZWsW+Ji83H4+vxOPmyRh8TCoodDSEanD1sUaDNjYQ6mrIfZuk4oTHhmPGhRn4lPsJZkIzrGi9Ag1MG/AdixBCKgQVOF/BR4EDANlRUYjy7wmWlQXzOXNgNGigwrYlyhfhWUQCbvwTgw/xBWNUqWmowLmlNRr62kDHkPorqqyiU6MREBaAF6kvoKaihlnNZqFPnT58xyKEEIWjAucr+CpwACB5924k/LwAnKYm7A8dgqCWvUK3x0QMUXcSEXkiGu9ffQQAqKhyqPeNBRp1sIWBmZZCt08UIz03HXMuzsG/r/4FAPRy7IVZzWZBQ5Va6AghVRcVOF/BZ4HDRCLEfjsK6ZcvQ9PNDXZ7doNTU/z1MYwxxD5Kxo0TMXj7LAUAwHFAbXdzNOloC2NrHYVnIPLFGMPW+1ux+uZqMDC4mbphhfcKmGub8x2NEEIUggqcr+CzwAGA3Ph4vOzaDaKPH2E6aSJMxoyp0O3HPU/BjX9iEHP/v87j7NxM0KSTLSzs9Ss0Cym/i28uYvr56UjLSYOxpjFW+KxAY/PGfMcihBC5owLnK/gucAAg9ehRvP1xGqCmBrs/9kHo7FzhGd6/+ogb/8Tgxa13wP//FdSoZ4gmHW1hXddQYf31EPmL/RiLgLAAPP3wFGqcGqY1nYZ+dfvRZ0gIqVKowPkKZShwGGN4E/ADPp48CY3aDrA/eBAqPI3A/iE+HTdPxuDptQSIRAV/Dub2emjSyQ52rsZ0kKwkMnIzEHQ5CCeiTwAAujl0w9xv5kJTjS4oJ4RUDVTgfIUyFDgAkPfhA1527Yb8xEQYDR8O8+nTeMsCAGlJmbh9OhYPL71Ffq4IAGBsrY3GHW1Ru4k5VFSo0FF2jDH8/vB3rLixAiImgpOxE1b6rISljvz7XSKEkIpGBc5XKEuBAwAfw8LwesxYgONQc8d2aDdtymseAMhIy8GdM69wL/wNcrMKeqLWNxWicQdb1G1mAVV1GsJM2V2Nu4ofw39ESnYKDAWGWOa9DE0t+f/bIoSQ8qAC5yuUqcABCgbiTNl/AOrW1rD/6whUdZTjjqas9FzcO/cad87GIjs9DwCgbSBAI9+aBcNACGgYCGX29tNbBIQF4FHyI6hyqpjcZDIGOw2mU46EkEqrLMdvpfspfv78eXTt2hVWVlbgOA5HjhyRms8YQ1BQEKysrCAUCuHj44MHDyr3KMtm02dA3doauW/eIGHxYr7jSGhqq8Ojiz2G/OKJFr1rQ1tfA+kp2bi4/xl+n30ZkSeikZ2Ry3dMUgwrHSv83ul3dHPohnyWj6WRSzHjwgxk5mXyHY0QQhRO6Qqc9PR0NGjQAGvWrClyfnBwMFasWIE1a9YgIiICFhYW8PX1xcePHys4qfyo6mjDavEigOOQeuAgPp4N4zuSFA1NNTRsVxODF3jCZ2Bd6JloIutTLq799RK/z7qMK0deICMth++YpAiaappY0GIBZjSdATVODX9H/Y3Bfw/G64+v+Y5GCCEKpdSnqDiOw+HDh9GjRw8ABa03VlZWCAgIwPTp0wEA2dnZMDc3x5IlSzB69Ogi15OdnY3s7GzJ87S0NNjY2CjNKSqxhOClSN62DarGxqh1NBRqRkZ8RyqSKF+EZ5HvcPNkDJLfpgMA1NRV4NTSCg19a0LXiO7aUUaR8ZGYEj4FyVnJ0BfoI7hVMDytPfmORQghpVapT1GVJCoqCvHx8Wjfvr1kmkAggLe3Ny5fvlzs6xYtWgR9fX3Jw8bGpiLilpnppIkQONZGflIS4gODoKy1p4qqCuo2s0C/OU3R6XtXmNnqIi9XhLthr7Fr7hWc3fkIKQkZfMckX3C3cMcffn/A1cQVqdmpGHNmDLbe26q0f2eEEFIelarAiY+PBwCYm0t3RW9ubi6ZV5SZM2ciNTVV8oiNjVVoTlmpCASwWrIEUFPDx9OnkXb0KN+RSsSpcKjV0BS9Z7ij26SGsK5jAFE+w6NLcdgTdBWnttxH4utPfMckn7HQtkBIxxD0dOwJERNh5c2VmBI+BRm5VJASQqqWSlXgiH15FwhjrMQ7QwQCAfT09KQeykrTyQmm48cBAOJ/XoDcuDieE30dx3GwqW+EHpMbo+ePTWDnagzGgGeR7/DHgus4vvYO4l+m8h2T/D+BqgBBzYMw95u5UFNRw+mY0xj490DEpMXwHY0QQuSmUhU4FhYWAFCotebd/7V353FRlX3/wD/nzJkFkH1REFkVcUXFUnKpzHDJJEuzXVvu7kpLs82sFMvcWm7tzsrHJzWfum/7keaSWrngUma5YaaICyCiIIrAsM52rt8fM3OYYQYGEmZg+L5fr3mdmeucc13XDAfmw3W2oiKbUZ22LPCZZ6BK6AuxvBxX5swBE0VXd6nRQmN9cc+0BEx++xZ0HRgCcEDuyWJsWHoUm/51DJfO3KBdIq0Ax3F4sPuDWDNqDYI9gnG+9Dwe/uFh7M/f7+quEUJIs2hTASc6OhqdOnXCzp07pTKtVot9+/bhttvc52BJThAQtngxOJUKVb8dQsl//uvqLjVZULg3Rj3TG4+mDkaP20LB8xwuZ5Viy7IMfLfkKLIzroGJFHRcrV9IP3w77lv0C+6Hcl05pu+eji9OfAGRtZ1QTQgh9rS6gFNRUYGMjAxkZGQAMB5YnJGRgby8PHAch5kzZ2LhwoX4/vvv8ddff2Hq1Knw9PTEI4884tqONzNldDRCXnsVAFD04YfQZOe4uEd/j19HT4x4ogceW5CEvneGQ5DzKMpVY8cXJ7F+wR84+0chRAN9mbpSsGcwVo9ajcndJ4OBYUXGCsxMn4kKLR0/RQhpu1rdaeJ79+7FnXfeaVM+ZcoUrF27FowxzJ8/HytXrkRJSQkGDRqEFStWoHfv3o1uo7Vdybg+TBRx6Zl/oPLgQaj69kXUf74BJwiu7tZNqVJrcWLPJfy1Nx9a020gfII9MCA5AvGDQ+k2EC72/bnv8d6h96ATdYjyicLyEcsR4xvj6m4RQggAulWDQ20l4ACArrAQ2feOh1hejuAZLyHo+edd3aVmoanS4eTeyzix5xJqKoxXQ/byVaDf3RHoNawz3QbChU5eO4mX976Mq1VX4SX3wvtD38ddEXe5uluEEEIBx5G2FHAAoGzrVlx57XVAEBD17Xp49Orl6i41G53GgNO/XMHxnXmoLDVejFHlJUfCXeHoc0c4lJ5yF/ewfSquLsar+17FkatHAADP9n0W0/pNA8/RCBshxHUo4DjQ1gIOYwyXZ76M8p9+gqJrLKI3bACvVLq6W83KoBOR9Xshjv50EeprxnslyVUy9Lk9HAl3dYGnj8LFPWx/dKIOHx/5GF9nfg0AGNZ5GBYPXwwfRev/nSGEuCcKOA60tYADAPqSEmTfOx6G69cR8OST6PjG667uUosQDSLOHyvC0R21t4GQmW4D0Z9uA+ESWy9sxfzf5kNj0CDCOwLL7lyGbv7dXN0tQkg7RAHHgbYYcACgPD0d+c+/AHAcIr5aC69bb3V1l1oMExlyT17HkR0XUZSrBgDwPIe4wZ2QOCoSfh09XdzD9iWzOBMz02fiSuUVeAgeeG/IexgVNcrV3SKEtDMUcBxoqwEHAAreeQelad9B3rkzojdvgqxDB1d3qUUxxpCfVYKjOy7iclaJsZADug4IQeKYSASFe7u2g+1ISU0JXtv/Gn4v+B0A8GTvJzGj/wzIeDognBDiHBRwHGjLAcdQUYmclBToLl+G78QHELZggau75DSF2WU4+uNF5P55XSqL7BOIxNFRCI31dWHP2g+9qMcnxz7BmlNrAABJoUlYOnwp/FR+ru0YIaRdoIDjQFsOOABQdfgwLj4xBWAM4Z99Bu8RttcNcmfX8ytw7KeLOH/kKsxbb+c4PySOjkJ4D/8G70tGmsePOT9i7sG5qNZXo3OHzlh25zLEB8S7uluEEDdHAceBth5wAODq0g9wY/VqyAIDEbN1C4SAAFd3yelKr1bh+M8XceZQIUSDcTMOifRG4pgoRPcNAsdT0GlJZ0vOYsaeGcivyIdKpkLqbam4J+YeV3eLEOLGKOA44A4BR9RokDtxIjTnzsP77rvR+ZPl7XbkoqKkBsd35uH0gSvQ64y3ffAP9ULi6Eh0GxgCXkbXbmkpZZoyzD4wG79c/gUA8HjPxzErcRYEvm1fcZsQ0jpRwHHAHQIOANScPo2cBycDej3Cli6B7/jxru6SS1WXG28DcTLd4jYQQSr0T45EfFInCHI6GLYlGEQDVmSswKqTqwAAt3S6BUuHL0WQR5CLe0YIcTcUcBxwl4ADANe/+ALXli0H7+2NmC2bIQ8NdXWXXE5Trcdf+/JxYvclVJcbbwPh6atA/7sj0HNoGBQqGl1oCbsu7sJbv7yFKn0VVDIVkqOSMSluEhKCE9rt6CIhpHlRwHHAnQIO0+uR++ijqDnxJzyTBiPiyy/B8bRLBgB0WuNtIDJ25qGipPY2EH1HGG8DofKi20A0twulF/DmgTeReSNTKovzj8OkuEm4J+YeeCvotH5CyN9HAccBdwo4AKDJyUHOhPvBamrQ8e23EfDYo67uUqti0BtvA3Hsx4soM98GQilD79s7o9/ICLoNRDNjjOHEtRNIO5uGn3J/gsZgDJceggfGRI/BxG4T0TuoN43qEEKajAKOA+4WcADgxtff4OqCBeBUKkSn/T8ou9Gl9OsSRYYLpttAFF+uAGC6DcRtoeiXHAGfQA8X99D9lGnK8EP2D0jLSsOFsgtSeXxAvDSq4yX3cmEPCSFtCQUcB9wx4DBRxKVnnkHlwd8AAPLOnaHq2ROqXj2N0x49IAQHu7iXrQNjDBdPFuPIjlxczbG4DcSgjhgwKhL+negLt7kxxnC86DjSzqbh59yfoRW1AIyjOmOjx2JS90noFdjLxb0khLR2FHAccMeAAwC6wkLkvzQDNX/+aXe+EBxsG3rCwtrtrgLGGC6fLcXRHbnIP1N7G4jY/iFIHB2J4Ag6XqQllNaUYsuFLUg7m4Zcda5U3iuwFybGTcTY6LHwlNO9xgghtijgOOCuAcfMoFajJvMMak6flh7anBxAFG2Wlfn61gaenj2h7NEDisjIdnegcmFOGY79eBE5J2pvAxHRKxADx0QitKuf6zrmxhhjOHL1CNLOpmHXxV3QicYz3rzkXrgn+h5M6j6Jro5MCLFCAccBdw849ohVVajJyrIIPZnQnD8P6HQ2y/JeXlD2iDeN8piCT2wMOMH9T68uvmy8DcS5w7W3gQjr5ofEMZHo0iOg3Y52tbQbNTew5fwWfHfuO1xUX5TK+wT1waS4SRgVNYpGdQghFHAcaY8Bxx5Rq4Xm3Dkp9GhOZ6ImKwuspsZmWU6phLJ7d6h69qgNPXHdwCuVLuh5yyu7VoVjP+fhzG8FEPXGX5HgCG8kjolETEIw3QaihTDG8EfhH0g7m4bdebuhF/UAAG+5N8bFjsOkuEno5k8H0BPSXlHAcYACTv2YXg9tTo7VSE9NZibEigrbhQUByq5dpeN5VL16QtW9O3gv9zlIt6JEg4xdeTh14DL0WtNtIDp5InF0JLre0hEyug1EiymuLsam85vw3dnvkF+RL5X3C+6HiXETMSpqFFSCyoU9JIQ4GwUcByjgNA0TReguXbIOPadOwVBaarswx0ERHW0denr0gMzX1+n9bk7VFVr8uScff6bnQ1ttGlUIVGHAKLoNREsTmYhDBYfw3dnvkJ6XDj0zff4Kb4yPHY9JcZMQ6xfr4l4SQpyBAo4DFHBuHmMM+sJCY+A5dRo1mZmoOX0a+qtX7S4vDw83HcjcQzqgWQhqe/cq0lbrcbLubSB8FOg3MgK9htNtIFra9err+P7c99hwbgMuV1yWygeEDMDEuIlIjkqGUuaeu00JIRRwHKKA03L016+bwk6mNOKju3TJ7rJCSEjtKI859ISGtokDeXVaAzJ/LcDxny9Kt4FQegnoe2cX9L2TbgPR0kQm4uCVg0jLSsO+/H0wMOPNVX2VvhgfOx7jY8cjzj8OPEe7EAlxJxRwHKCA41yGsjLjaeuZtaFHm50N2Nn0ZH5+VqM8qp49IY+IaLWnrRv0Is7+UYhjP+Wh9GoVAEAm8OgQoISXrxKevgp4+Zimvgp4Ss+VUHoJbSLMtXZFVUXYeG4jNpzbgMLKQqncR+GD/iH9MaDjAAwIGYBegb0gl1HwJKQto4DjAAUc1xOrqlBzJgs1mRanrZ87B+j1NstanbZuvl5PTOs6bV26DcSPF1Gcb+eAbDt4gYOnjzHsePoo4OmrNIUgRW048lXCw1sOng5mdsggGvDrlV/x3dnvcKjgEKr11VbzVTIV+gb3lQJPQnACnXpOSBtDAccBCjitk6jVQnP2nEXoOQ3NmSwwjcZmWavT1nv2hKpnL+Np6wrX3jiTMYaya9WoLNWgqkyLKrUWlWXG55VlGum1ptI2yNWLAzw6yGsDkK8SXnUCkfm5oKCDnQFAJ+qQdSMLR68exbGrx3Cs6BhKNaVWy8g4GXoE9EBix0Qp9Pip/FzSX0JI41DAcYACTtvB9HposrOhMe/eMh3QLFZW2i5sedq6+RHfHbxn6/sv3aATUVVeG36qyjSoNE/VWqmsqlwHJjb+V1ThIZhCkMXuMMtdZKYgpPBoX7vHGGPIKcvBkatHcKzoGI5dPYaCygKb5WJ9Y41hp+MAJIYkIrRDqAt6SwipDwUcByjgtG1MFKHLy6s9pueUcbTH4Wnr5keP+DZz2rooMtRU6GxGgaxCkdo4Nehsb8VRH5mcN+0Ksx4RMu8WM44KKeDhrQDvphc1LKgowNGio9IoT3ZZts0yYV5hVoEn2je6XQVDQlobCjgOUMBxPzanrZt2cemLiuwuX3vaek/pWj1t8bR1M8YYtNV6U+CpMyJkCkHmXWaaqsbvHuN4Dh7ecosDpk1ByOI4IfMokUzeto8TKqkpkUZ3jl09hswbmdLZWWb+Sn/0D+mPxI6JSOyYiO4B3SHwredYMELcHQUcByjgtB/SaesWoUeXn293WSEkxGKkp0ebOm29KfRag+lYIOsgJJWZRoSqy7VAE/46KD0FaReYyksOuUoGhUqAQiWDwkOAQiXYlFm+bm0HUlfpqpBxLUM6hufPa39CY7A+HsxT8ERCcIJxhKdjIvoE9aGrKxPSgijgOEABp32TTluve7f1ek9brx3lae2nrTcn0SCiulxntVvM3gHTVWqtdL+umyHIecg9TOHHFHrkKgEKjzqvLcrshShBwbdIKNUZdDhVfMq4S6voGI4XHUe5ttz6PfACegX2QkJwAiJ9IhHeIRzh3uEI7RAKOU+nqBNysyjgOEABh9QlVlaiJutsbejJbPi0dfMFCpWm0NPaTlt3JsYYNFV6qwOmNdV6aKsN0NbooasxTrU1Bmir9dBpjFNzWVOOHWoMjgPkShkEhQyCgjdNZZBLz2vLBAUPuUWZ3Gp+/WWCwINxDOdKzkm7tY5ePYpr1dfs9onneIR6hUqBJ9w7vPZ5h3D4Kn3dbqSQkJZAAceBFgs4BSeAnP1AYFfjwy8SEFx72jL5+6TT1k+fqg09DZ22Ht8dqh49oIyLg8zbB7yHCpzKwzRVgffwAK8yPTdN28NIkCMGg2gMQdWmEGQZiuyWGaCrqS2X5lXr7Q3CtRhBXht65EoZBDkPg0yPSlSgUixHFatEhViOcoMaWtTAwOuh53QQeT30vB4GXgcDp4eB10MuFxDg5YeADv4I8gpEiE8wOnYIQZhvJ3Ty6QilUgFBzkMmGB90N3vSXlHAcaDFAs4v/wJ2pda+5mSAX0Rt4AmMrZ36hAP05dbmmE9bl67TY77bur3T1huBUyqNYcccfkxT3kMFTqmqDUkqFTgPFXgpMFkHJ06ptAhQtvPaw+gAYwx6nSiNEum1IvRag+khQqe1LDO/tl5OZzFfr6udZ67PoG/e0aa/TcYgE3gIchnkcpkx+JgCkCDnwQs8ZDIOnIwDzxsfDp/LOPAyY3gyv7Z5blrW7nOZ5bJ8k+rgzX3lOApvpEEUcBxosYCT+QPw13dA8QXjQ9fAl56gAgJiLEJPVyDA9NwryDjOTtoE6bR18yjPhWyI1VVg1TUQa2rAqqshajTGaU2N3RGglsbVHT0yhyWrcGURoKRwVX+osq7PA5xC4fZBShRZnVBkDkLW4UinMcCgNwYig85ianqu14sw6BgMehFarQ7VmhrUaDTQaHXQ6/Qw6ESIBgAGHrwogyAK4NA+/iHiODQijFkHMbvBq7HhTtZAGGtMMLN53YRwV6ev7v770xwo4DjglGNwGAPKC4Hi88bHDVPoKT4P3MgBRF396yp9rYNPYKzxERALqOiYobaOGQxgGk1t+KmpgVhdA1ZTDbG6BmJNNViNORyZppbzLINTjUWZpsZqHtM1sI21BI6rDUsKBThBACeXS1PIza/lVuUO58trl4NUrrA7n5PLAUEw1iHIAJnMWC6TATIBnCAzPjeVWT6HTNbqvmAYYyiuKcYl9SVcKstHftllFJQVolB9FVfLr6G0Sg2ZKIMgyiFjcshEwfhgAjjGg2cy8Iw3PTe+5hgPHqYyUQYZZBAghwABAuSQQZAeAgTwzLiEjMnAQ2aamuuqrd/44MCJpinjAJEDzFMRAOPARAAijFNipbHhrm54alK4Mwe6OqN3jQl3jsOedbjz9DFeab05tYuA89lnn+GDDz5AQUEBevXqhWXLlmHYsGGNWtflBxkb9EBZXu1IjzkEFV8Ayi6hwXNzO3S03t1lHvUJiAYEpdPeAmn9mF4PsUZjDEdWYcoiQNkLV/WFKotRKKmsuhowGBx3pq2Q1R+ArJ4LpsAkkwGCDFyd55Dx4HhZE6Yy4/FYMhk4GQ/wjqeQ8dBDRJmuHDd0pbihLUWxtgTF2hKUaNXQMR10MEAv6qWpFnromB4iGJgpe0gPAIzjpNciAJiyCVCbVayXt34tck1YhwHgeAC8aXRKZpry4CCTyhWcEnJeCQWngpxTQM7JjWWcAgooIHByyKGAwAmmoCaH3BTUBM4Y9qTAZgprvDTlwcMY+mTm8FcnsMEU2MA4wGDxRkXjiB4TGUSRQTSYnhtYbbnFc4OBgVm8bg8GjIpE0oTYZq2zKd/fbfK0j2+//RYzZ87EZ599hiFDhmDlypUYM2YMTp8+jYiICFd3zzGZYNw9FRADdLvbep6uBijJsQg952tDUOU1oOKq8XHxV+v1OB7w7WIMPio/4x9AXjBOOfNz02vzPKtyvk6ZxXJSueU8czlfp+7GtllP/a3sP+i2jBMEyDoIQAevFm2H6XTWwam6BkyrBdPrjKNIej2YTgem14PpLJ9rwfR6QHqtqzNfB6Y3ra+1LKudx3Q6wGYdvbFegwHMYDCuX+c5xHqGD8zLabVNuQSQy/mYHlEu7kfTNS0cmwaB6g9ZFmWWIcscuuoLZlKoc7ROnXV5jjeOXPIcwPEWU3M5D870muN4gOfB88YpxwvgOAEcL5f+JnK8HBwvAJxgnG96zvMCwMnB8TJTmcy4Llf795PjZeAggOOMf38ZeFNg5SEyHgwcRHAAeIjgwCwelvMZODBmLgcYM5Uzzvj+GQeRcWAMxqlUhtoyZhyh4ytLb34TuQltcgRn0KBBGDBgAD7//HOprEePHrjvvvuwaNEih+u31AgOYwzVuhb8b7ZGDb7kArgbF8AXG6fcjfPgb1wAp23cHaxbO2YZmKyey8DsBijjlNUtswhYjOcBzn7YYjbBq3ZZZhPMLNezqEuq29hfxlkGNYvAZhXeOJvZtS8crXMTZVblnJ3Zjparfc4a3XZd9cz7O+vUW95wfUwUAVE0hhmDeWoAM4i1IUdkFuX2lqtnPfNrZlrG3JZpallm7MNNzrcpM7UPwPitIwIMYKYpRNH4TcQYGJO+lf7ecuZvNcvlRNP6DSxH2gfPJx5E5Jz5zVqnW4/gaLVaHD16FLNnz7YqT05OxsGDB+2uo9FooLE4sFOtVrdI36p1BvSc+1OL1G3NG0A/0wMAGIKgRjRXgCi+EJ7QQIABMhggA4MMBgicATxECBBN5SJkEE3LmZ5LyzSwLFf73HYZAwSI4Dnres3l0nOu/p3vHBMBg9b4qDuvBT5JQloVDm3wr3LTMYbaPfHM9JQBAFfntTkPcdavpXU5mzJmb55VfVzta6mt2rKGljcAMICDngF6cNBznPE1TK8BGJhpynEwMON8AwcYTOsYwEFEbV0G00iJAYAI4zoiZxwJEWFcTzStw2AuN71mplEtGEdSOFbnYSrjTe+VN70Pvs58e+vYrGv6PMzr2iszrsOkunRlBxBpfxNwijb3q3T9+nUYDAZ07NjRqrxjx44oLCy0u86iRYswf37zpsjWhcN1+OI688VhQ7yrO9MIDDyYRUiyE4Y483ODtKzjsGVdj8xUj1BnPZtgxpmCWd3AZ1FHbV9E+8ty1m0DMP3Jgek5GlVm/qtqPSbCbJazX5/tf8aNWdfuPK7+uqzXbbgt2zrqK2/ov3r78xoe72ncKEFjl3PU3s3U2zLru1oj+m9ngLA5tUS1vOlRe01qy7RVt33njlSJAHQcoANnnHIc9Byg5QA9x0FrKrOcXzuvtkwH23nGemrn6SyXN83Tc4AW1vMe8+/k1M+grjYXcMzqnu3AGKv3DIg333wTs2bNkl6r1Wp06dKl2fvkIZfh9Lujmr1eQgghpCE8jF/oHq7uiAUPucyl7be5gBMUFASZTGYzWlNUVGQzqmOmVCqhVLb8GUYcx8FT0eY+UkIIIcTttLkrRykUCiQmJmLnzp1W5Tt37sRtt93mol4RQgghpDVpk8MNs2bNwuOPP46BAwciKSkJ//M//4O8vDw899xzru4aIYQQQlqBNhlwJk+ejOLiYrz77rsoKChA7969sX37dkRGuvJ4bUIIIYS0Fm3yOjg3y+VXMiaEEEJIkzXl+7vNHYNDCCGEEOIIBRxCCCGEuB0KOIQQQghxOxRwCCGEEOJ2KOAQQgghxO1QwCGEEEKI26GAQwghhBC3QwGHEEIIIW6HAg4hhBBC3E6bvFXDzTJfvFmtVru4J4QQQghpLPP3dmNuwtAuA055eTkAoEuXLi7uCSGEEEKaqry8HL6+vg0u0y7vRSWKIq5cuQJvb29wHNesdavVanTp0gWXLl1yyX2uXN1+e0efv+s/A2qftkHiWi25DTLGUF5ejrCwMPB8w0fZtMsRHJ7nER4e3qJt+Pj4uPSPi6vbb+/o83f9Z0Dt0zZIXKultkFHIzdmdJAxIYQQQtwOBRxCCCGEuB0KOM1MqVRi3rx5UCqV7bL99o4+f9d/BtQ+bYPEtVrLNtguDzImhBBCiHujERxCCCGEuB0KOIQQQghxOxRwCCGEEOJ2KOAQQgghxO1QwGkGn3/+Ofr27Std1CgpKQk7duxwWvupqangOM7q0alTJ6e13x7t378f9957L8LCwsBxHDZt2mQ1f+PGjRg1ahSCgoLAcRwyMjJc0s+W5OgzmDp1qs12OXjwYKe1X7dt8+ODDz5wSvtXr17F1KlTERYWBk9PT4wePRrnzp1rlrYBYNGiRbjlllvg7e2NkJAQ3HfffcjKyrJapj1sh8R1HH33uXr7o4DTDMLDw7F48WIcOXIER44cwYgRI5CSkoJTp045rQ+9evVCQUGB9Dh58qTT2m6PKisrkZCQgE8//bTe+UOGDMHixYud3DPncfQZAMDo0aOttsvt27c7rX3LdgsKCrB69WpwHIcHHnigxdtnjOG+++5DdnY2Nm/ejOPHjyMyMhIjR45EZWVls7S/b98+TJs2DYcOHcLOnTuh1+uRnJxsVX972A6J6zj67nP59sdIi/D392f/+7//65S25s2bxxISEpzSFrEFgH3//fd25+Xk5DAA7Pjx407tk7PZ+wymTJnCUlJSXNZ+XSkpKWzEiBFOaT8rK4sBYH/99ZdUptfrWUBAAFu1alWL9KGoqIgBYPv27bOZ1162Q+J69r77XLX90QhOMzMYDFi/fj0qKyuRlJTktHbPnTuHsLAwREdH46GHHkJ2drbT2iakPnv37kVISAji4uLwj3/8A0VFRS7px9WrV7Ft2zY8/fTTTmlPo9EAAFQqlVQmk8mgUCjwyy+/tEibZWVlAICAgIAWqZ+Qhrjqu68hFHCaycmTJ9GhQwcolUo899xz+P7779GzZ0+ntD1o0CCsW7cOP/30E1atWoXCwkLcdtttKC4udkr7hNgzZswYfPPNN9izZw8++ugjHD58GCNGjJC+/J3pq6++gre3N+6//36ntBcfH4/IyEi8+eabKCkpgVarxeLFi1FYWIiCgoJmb48xhlmzZmHo0KHo3bt3s9dPSH1c+d3nSLu8m3hL6N69OzIyMlBaWooNGzZgypQp2Ldvn1N+0GPGjJGe9+nTB0lJSYiNjcVXX32FWbNmtXj7hNgzefJk6Xnv3r0xcOBAREZGYtu2bU4LGmarV6/Go48+ajWi0pLkcjk2bNiAp59+GgEBAZDJZBg5cqTV72pzmj59Ov78888WGx0ipD6u/O5zhAJOM1EoFOjatSsAYODAgTh8+DCWL1+OlStXOr0vXl5e6NOnT7OesUHIzQoNDUVkZKTTt8sDBw4gKysL3377rVPbTUxMREZGBsrKyqDVahEcHIxBgwZh4MCBzdrOiy++iC1btmD//v0IDw9v1roJcaQ1fffVRbuoWghjzCVD8YBx/39mZiZCQ0Nd0j4h9hQXF+PSpUtO3y6//PJLJCYmIiEhwantmvn6+iI4OBjnzp3DkSNHkJKS0iz1MsYwffp0bNy4EXv27EF0dHSz1EvIzXDld19dNILTDObMmYMxY8agS5cuKC8vx/r167F37178+OOPTmn/1Vdfxb333ouIiAgUFRVhwYIFUKvVmDJlilPab48qKipw/vx56XVOTg4yMjIQEBCAiIgI3LhxA3l5ebhy5QoASNcn6dSpk9tco6ihzyAgIACpqal44IEHEBoaitzcXMyZMwdBQUGYMGFCi7cfEREBAFCr1UhLS8NHH33ULG02pf20tDQEBwcjIiICJ0+exIwZM3DfffchOTm5WdqfNm0a/vOf/2Dz5s3w9vZGYWEhAGOg8vDwAIB2sR0S13H03efy7c+p52y5qaeeeopFRkYyhULBgoOD2V133cV+/vlnp7U/efJkFhoayuRyOQsLC2P3338/O3XqlNPab4/S09MZAJvHlClTGGOMrVmzxu78efPmubTfzamhz6CqqoolJyez4OBgJpfLWUREBJsyZQrLy8tzSvtmK1euZB4eHqy0tLTZ2m1s+8uXL2fh4eHS+3/77beZRqNptvbttQ2ArVmzRlqmPWyHxHUcffe5evvjGGOsxdITIYQQQogL0DE4hBBCCHE7FHAIIYQQ4nYo4BBCCCHE7VDAIYQQQojboYBDCCGEELdDAYcQQgghbocCDiGEEELcDgUcQgghhLgdCjiEOMnUqVPBcRxyc3Nd3ZVm8fXXX6Nfv37o0KEDOI5Damqqy/rCcRzuuOMOl7XfFPn5+fD09MTSpUud1mZTt73c3FxwHIepU6e2SH/27t3r1G1m3rx58Pb2xtWrV53SHmkdKOCQNsf8x5fjOIwbN87uMuY/oM8995yTe9c+HDx4EI8//jiqqqowbdo0zJs3z2HAiIqKkn5uHMdBJpMhKCgIycnJ2Lx5s3M63oC1a9eC4zisXbu2RduZM2cOOnTogGnTptmdX1BQgHfeeQeDBg1CYGAg5HI5AgICkJSUhDlz5kj382ltfv31V0yaNAmdO3eGQqGAv78/4uPj8cgjj+Crr75yad9efvllyGQyzJ0716X9IM5FN9skbdq2bduwf/9+DB8+3NVdaVe2b98OAFi3bh0GDx7c6PVkMhnefvttAIBWq8WZM2ewZcsW7Ny5Ex9++CFeeeWVv9WfzMxMeHp6/q11nens2bP4+uuvMXfuXHh5ednMX79+PZ5++mlUVVWhX79+ePDBBxEQEAC1Wo1jx45h6dKlWLJkCbZu3YqxY8c2ut1FixZh9uzZ6Ny5c3O+HcnatWvx1FNPQRAEjB07Ft26dUN1dTWys7Oxfft27N+/3+rmv7feeisyMzMRFBTUIv2py8/PD8888wyWLVuGOXPmIDIy0intEteigEParKioKOTl5eGNN97Ab7/95urutCvmuwM39Y7AgiDY7Jb4+eefMXr0aMydOxfPP//83woq8fHxTV7HFVauXAnGGB577DGbeTt27MCjjz6KwMBAbN68GSNHjrRZ5tKlS1iwYAFKS0ub1G5oaChCQ0P/brcbVFVVhZdeegne3t749ddf0bt3b6v5Op0Oe/futSrz9PR0+s/ssccew0cffYRVq1ZhwYIFTm2buIhTbulJSDPKyclhANioUaPYlClTGAC2YcMGq2XMd3r+5z//aVUeGRnJIiMj7dZ7++23s7q/EvPmzWMAWHp6Olu9ejXr3bs3U6lULCoqii1fvpwxxpgoimzZsmWse/fuTKlUsm7durF169bZ1G/u6/nz59nChQtZbGwsUyqVrGvXrmzp0qXMYDDY7de+ffvYuHHjWGBgIFMoFKxr167srbfeYpWVlXbf87x589jBgwdZcnIy8/X1tXlP9fn111/Z2LFjmb+/P1Mqlax79+5s3rx5Vu3UdwftxrQRGRnJlEql3Xnx8fEMADt8+LBUtnXrVnbHHXcwHx8fplKpWEJCAvvXv/7F9Hq9zfoA2O23325VZv68c3Jy2IoVK1h8fDxTKpUsIiKCpaamWn3e5mUbel9XrlxhL730EuvatStTqVTM39+f9e7dmz3//POsrKzM4fs3GAwsKCiI9e/f32aeTqdj0dHRDADbv3+/w7p0Op3Va/N2XVJSwl588UUWHh7OZDKZdGdxy8/Ckl6vZ4sXL5a2xdjYWLZw4UJ24cIFmzuz1+f3339nAFhKSorDZc0st1Uz8+9afY+6P1+NRsM++ugj1r9/f+bp6ck6dOjAhg4dyjZv3lxvu926dWOdO3dudD9J20YjOKRNe/fdd7F+/XrMmTMHKSkpkMlkLdLOsmXLsHfvXqSkpGDEiBHYsGEDZsyYAU9PT5w4cQJpaWkYN24cRowYgfXr1+OJJ55AdHQ0hg4dalPXzJkzcejQITz44INQqVTYuHEjXn/9dZw/fx4rV660WvaLL77ACy+8AH9/f9x7770IDg7G4cOH8f777yM9PR3p6elQKBRW6xw8eBALFy7EnXfeiWeffRZ5eXkO39+GDRvw0EMPQaFQYPLkyQgJCcGuXbswf/58/Pzzz0hPT4dSqURUVBTmzZuHTZs24cSJE5gxYwb8/Pxu6rO1Z/ny5Zg5cyYCAgLwyCOPwMvLC1u3bsXLL7+MAwcO4LvvvgPHcY2q67XXXsPevXsxbtw4JCcnY9OmTUhNTYVWq8X7778PALjvvvtQWlqKzZs3IyUlBf369bOqo6qqCkOGDEFubi6Sk5MxYcIEaLVaZGdnY+3atXj99dfh4+PTYD/+/PNPXL9+HZMmTbKZl56ejpycHAwbNgzDhg1z+J4EwfZPt0ajwYgRI1BeXo57770XCoUCHTt2bLCeZ599FqtXr0Z0dDSmTZuGmpoafPzxxzh48KDDPpgFBAQAAHJyciCKInj+7x3aWd8xXIcPH8b27dutRvY0Gg1Gjx6NvXv3on///nj66aeh0+mwbds2pKSk4N///jemT59uU1dSUhLWrVuHrKwsdO/e/W/1k7Qhrk5YhDSV5QgOY4zNmjWLAWArV66UlmnuEZyAgAB24cIFqTwvL48pFArm6+vL4uLiWFFRkTTP/B/t+PHjreoy/xfdsWNHdvnyZam8vLyc9enTx+a/91OnTjFBEFj//v1ZcXGxVV2LFi1iANiHH35o854BsC+//NLue7RHrVYzPz8/plQq2YkTJ6RyURTZI488wgCw9957z+57qTsi0JD6RnB++uknxnEc8/T0ZJWVlezChQtMEAQWEhLC8vLypOU0Go30M/q///s/qzrQwAhOdHQ0u3LlilR+7do15ufnx7y9vZlGo5HK16xZwwBIox6WtmzZwgCwl19+2WaeWq22qqc+K1asYADYqlWrbObNnz+fAWBz5851WI89kZGRDABLTk5mVVVVNvPt/bzM20tCQgKrqKiQyvPz81lQUFCjR3BEUWQDBgyQfgZr1qxhp0+ftjvSVrdtyxEce3JyclhwcDDz9/dnWVlZUvmcOXMYAJaamspEUZTK1Wo1GzhwIFMoFFa/Y2bLly9nANjq1asdvi/S9tFZVKTNe+utt+Dr64v58+ejqqqqRdp46aWXEBMTI73u0qULhg4dirKyMrz11lsIDg6W5t16662IiYnBiRMn6q0rLCxMet2hQwfp7A7Ls01WrlwJvV6PTz75RPov2ez1119HcHAw/vvf/9rU379/fzz11FONfm+bNm1CaWkpnnrqKfTt21cq5zgOixcvhiAIzXZmkV6vR2pqKlJTU/HWW2/h/vvvx9ixY8EYw4IFC+Dp6YlvvvkGer0er7zyCrp06SKtq1AosHjxYgBoUn/eeecdq+NPgoKCkJKSgvLy8iafkeTh4WFT5u3tbTOKZk9+fj4A2B1VKSwsBACr7cIsOztb+szMj6+//tpuGx988IHdPtqzbt06ALA54Llz586YMWNGo+oAjNtJWloakpKSsG/fPjz55JPo2bMnfHx8MHLkSKxduxYGg6HR9Zmp1WqMGzcOJSUlSEtLQ1xcHABAFEV8/vnn6Nq1K+bOnWs1kuft7Y25c+dCq9Vi48aNNnWaP3vzz4K4N9pFRdq8gIAAvPHGG5gzZ450lkRz69+/v02Z+Uuz7u4M87zff//dbl32dkGYyzIyMqSyQ4cOAQB+/PFH7Nq1y2YduVyOM2fO2JTfeuutdtutz/HjxwHY30XQpUsXxMbGIisrC+Xl5fD29m5S3XUZDAbMnz8fAMDzPPz9/XHXXXdh2rRpGD9+vMP+DB48GB4eHlafkyMDBgywKQsPDweARh+sO3z4cHTq1AmLFi1CRkYG7rnnHgwdOhR9+vRp9K6y4uJiAIC/v7/NPMZYvetlZ2dLn5nZqFGjbA5UVqlU6NOnT6P6AkAK4A1tj40VExODgwcPIiMjA7t27cLhw4dx8OBB7N69G7t378a6deuwY8cOKJXKRtVnMBjw8MMP49SpU/j8889x1113SfOysrJQUlKCsLAwm88FAK5duwYAdn83zP8oXL9+vUnvj7RNFHCIW5g5cyY+/fRTLF26FP/85z+bvX57x1eYj4Oob55er7dbV0hIiN0ynudRVlYmld24cQMApONEGsvRcRd1qdXqBtfr1KkTsrKyoFarbzrgKJVK1NTU3FR/QkJCcPny5Ua36evra1Nm/tk1dmTB19cXv/32G+bNm4etW7dKp8mHh4fjzTffxAsvvOCwDvPISnV1tc0883u1975GjhwpBaDc3FxER0fbrT8kJKTRYQsAysrKwPO83VO1m7oNmfXr188q8O/duxePPfYY0tPT8dlnn+Hll19uVD2vvPIKtm/fjpdeesnmWlbm34tTp07h1KlT9dZRWVlpU2b+7NvCJQXIzaNdVMQteHh4IDU1FWVlZVi4cGG9y/E8X2/wsAwXLamoqMhumSiKVl/G5uCkVqvBGKv3UVdTvuQs26nvKq/mckcH0TYXR/0pKipyWl8sRUVF4auvvsK1a9dw/PhxLFmyBIwxTJs2ze6uwrrMuzHNX9CWbrvtNgDGg43/rqb+3H19fSGKot3RjOa64u8dd9yB9957DwCwZ8+eRq2zcuVKLF++HKNGjcLHH39sM9/8s3/ggQca/L1Ys2aNzbrmz95ylzJxXxRwiNt46qmnEB8fjxUrVtR75pC/vz+KiopsQk5lZSXOnTvnjG7iwIED9ZZZ/vc7aNAgALW7qlqKefdb3WuVAMYRhQsXLiAmJuamR2+aoz9//PEHqqur7e4WvFnmM/AcjerIZDL069cPr7/+uhRstmzZ4rB+8+4je9vZiBEjEBkZiV9++QX79+9vatf/loSEBAANb4/Nwd4FDeuzZ88eTJ8+HT179sS3335r96zIHj16wMfHB0eOHIFOp2tSX8zHXDVlVx5puyjgELchk8mwcOFCaDQavPvuu3aXGThwIHQ6Hb755hupjDGGN9980+6Qdkv45JNPpAvlAUBFRYXU3yeeeEIqf+GFFyAIAl588UVcunTJpp7S0lLpeJWbkZKSAl9fX6xZs8ZqyN/8ueh0uha7J5E9jzzyCARBwMcff2z1Oel0OsyePRsAWqQ/5uMz7B2A+tdff+HixYs25eaRjsYc2Dts2DDwPI8//vjDZp4gCPj000/BcRwmTpxo95groPHHDDWGeVt79913rbb9y5cvY/ny5Y2uJycnB59++inKy8tt5lVWVkp12btkgqWzZ89i4sSJ8PX1xdatW+3uWgSMn9Xzzz+Pixcv4tVXX7Ubcv766y+7I6W///47BEGQRsyIe6NjcIhbmTBhApKSkuq9svH06dOxZs0aPPPMM9i5cyeCg4Nx4MABlJaWIiEhod4zn5rTLbfcgoSEBEyePBlKpRIbN25Ebm4u/vGPf1jdcqJ379747LPP8Pzzz6N79+4YO3YsYmNjoVarkZ2djX379mHq1Kn44osvbqo/Pj4+WLVqFR5++GEMGjQIkydPRnBwMHbv3o0jR47g1ltvxWuvvXazb7vRYmNjsWTJErzyyivo27cvHnzwQXh5eeGHH37AmTNnkJKSYvdKwDcrKSkJHh4eWLZsGdRqtbQbY/bs2di1axdeeeUVDBkyBPHx8QgMDER2dja2bNkCDw8Pu9dcqcvf3x/Dhw/HgQMHoNFobA64HTduHNatW4dnn30Wd999N/r164ekpCQEBASgpKQEFy5cwO7du8HzfLN8Qd9xxx148sknsWbNGvTp0wcTJkyARqPBt99+i8GDB+OHH35oVD1lZWV48cUX8dprr2HYsGHo1asXPDw8cPnyZfzwww+4ceMGEhMT8eKLLzZYz8yZM1FSUoIxY8ZIZ3hZioqKkoLt/PnzcezYMXzyySfYtm0bbr/9dgQHB+Py5cs4efIkTpw4gd9++83qeLeKigocOnQId999d5NGlUgb5tyz0gm5eXWvg1PX/v37pevB1L0ODmOM7d69mw0aNIgplUoWGBjIHn/8cVZYWOjwSsZ1NXQtGHt11b2ScUxMDFMoFCw2NpYtWbKk3uuG/PHHH+yhhx5iYWFhTC6Xs6CgIDZgwAA2e/ZslpmZKS3X2GuL1Gf//v1szJgxzM/PjykUChYXF8feeecdq2ukNOa916ehKxnbs3nzZnb77bczb29vplQqWZ8+fdhHH31kcxVfxhxfybiu+n6u27ZtY7fccgvz8PCwupLx6dOn2YwZM1j//v1ZYGAgUyqVLCYmhk2dOpWdPn260e/pv//9r90rb1vKz89nc+bMYYmJiczPz48JgsD8/f3ZoEGD2BtvvMHOnDljs05D13dirOErGS9atEjaFmNiYtjChQvZ+fPnG30dnJqaGrZhwwb27LPPsoSEBBYUFMRkMhnz9/dnQ4cOZR9//DGrrq62Wsfetmr+nanvUffnq9fr2cqVK9mQIUOYj4+PdJXq0aNHs88//9xmu127di0DwDZt2uTwPRH3wDHWwPmJhBBCmo1Wq0VcXBx69OiBHTt2uLo77crw4cNRWFiIzMzMFrviOWld6BgcQghxEoVCgYULF+LHH3+s9zpJpPmlp6fjwIEDWLJkCYWbdoSOwSGEECd6+OGHkZ+fTxebc6KysjJ8+OGHmDBhgqu7QpyIdlERQgghxO3QLipCCCGEuB0KOIQQQghxOxRwCCGEEOJ2KOAQQgghxO1QwCGEEEKI26GAQwghhBC3QwGHEEIIIW6HAg4hhBBC3A4FHEIIIYS4nf8PdM57ns1PMhkAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" @@ -191,7 +199,7 @@ "source": [ "## Radial Grid: Transformation of 1D-Integration Intervals\n", "\n", - "Generally, areas where the integrand changes more rapidly demand a denser concentration of points. So, the $[-1, 1]$ interval is not suitable for most applications encountered in quantum chemistry, where the integrals are usually performed on $[0,\\infty)$ domain. `grid` supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. [Click here for a full list of radial transformations.](https://grid.qcdevs.org/pyapi/grid.rtransform.html)\n", + "Generally, areas where the integrand changes more rapidly demand a denser concentration of points. So, the $[-1, 1]$ interval is not suitable for most applications encountered in quantum chemistry, where the integrals are usually performed on $[0,\\infty)$ domain. [Grid](https://github.com/theochem/grid) supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. [Click here for a full list of radial transformations.](https://grid.qcdevs.org/pyapi/grid.rtransform.html)\n", "\n", "### Visualize Radial Grid Points\n", "\n", @@ -200,20 +208,18 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 5, "metadata": { "ExecuteTime": { - "end_time": "2023-06-19T16:51:37.054546020Z", - "start_time": "2023-06-19T16:51:37.044961659Z" + "end_time": "2024-01-03T22:36:21.851432041Z", + "start_time": "2024-01-03T22:36:21.470246478Z" } }, "outputs": [ { "data": { - "image/png": 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", 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\n" }, "metadata": {}, "output_type": "display_data" @@ -222,20 +228,25 @@ "source": [ "from grid.rtransform import BeckeRTransform\n", "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5), sharey=True)\n", "names = []\n", "for i, oned in enumerate(grids):\n", " # Becke R-transform (goes from 0 to \\infty) to transform 1D-grid\n", " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " # plot radial grid points for each transformed 1D-grid\n", - " plt.scatter(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", + " # plot radial grid points for each transformed 1D-grid \n", + " ax1.scatter(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", + " # plot log plot\n", + " ax2.semilogx(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", " names.append(oned.name)\n", "\n", "# set the ticks, labels, and title\n", - "plt.title(\"Becke Radial Transformation of 1D-Grids\", fontsize=16)\n", - "plt.yticks(range(1, len(grids) + 1), names)\n", - "plt.xlim(0, 2500)\n", - "plt.xlabel(\"R\", fontsize=14)\n", - "plt.ylabel(\"Quadrature Rule\", fontsize=14)\n", + "plt.suptitle(\"Plot & Log-Plot of Becke Radial Transformation of 1D-Grids\", fontsize=17)\n", + "ax1.set_yticks(range(1, len(grids) + 1), names, fontsize=11)\n", + "ax1.set_xlim(0, 2500)\n", + "ax2.set_xlim(1e-4, 2500)\n", + "ax1.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", + "ax2.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", + "ax1.set_ylabel(\"Quadrature Rule\", fontsize=17)\n", "plt.show()" ] }, @@ -252,8 +263,13 @@ }, { "cell_type": "code", - "execution_count": 19, - "metadata": {}, + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.855941638Z", + "start_time": "2024-01-03T22:36:21.851891608Z" + } + }, "outputs": [ { "name": "stdout", @@ -285,17 +301,57 @@ "\n", "for oned in grids:\n", " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " func_vals = rgrid.points**2 * np.exp(-rgrid.points)\n", + " x = rgrid.points\n", + " func_vals = x**2 * np.exp(-x)\n", " integral = rgrid.integrate(func_vals)\n", " print(f\"{integral: .6f} from BeckeRTransform radial grid of {oned.name}\")" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:22.028092961Z", + "start_time": "2024-01-03T22:36:21.856079509Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npoints = [11, 21, 31, 41, 51, 61]\n", + "grid_classes = [GaussChebyshev, GaussLegendre, TanhSinh, Simpson, Trapezoidal]\n", + "\n", + "for grid_class in grid_classes:\n", + " errors = []\n", + " for npoint in npoints:\n", + " # make 1-dimensional grid for the given number of points\n", + " oned = grid_class(npoint)\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", + " # Calculate x^2 e^-x\n", + " x = rgrid.points\n", + " func_vals = x**2.0 * np.exp(-x)\n", + " # compute relative percent error of integration\n", + " integral = rgrid.integrate(func_vals)\n", + " errors.append(np.abs(integral - 2.0) / 2.0 * 100)\n", + " # plot relative percent error vs. number of grid points\n", + " plt.semilogy(npoints, errors, label=oned.name)\n", + "\n", + "plt.legend(frameon=False, fontsize=12)\n", + "plt.title(r\"Numerical Integration of $\\int_0^\\infty x^2 e^{-x}dx$\", fontsize=16)\n", + "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", + "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", + "plt.xticks(npoints)\n", + "plt.show()" + ] } ], "metadata": { From d698c10f556b258e589d8c95c11ba647e794b95b Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Wed, 3 Jan 2024 22:41:52 +0000 Subject: [PATCH 8/9] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- doc/notebooks/One_dimensional_grids.ipynb | 732 +++++++++++----------- 1 file changed, 366 insertions(+), 366 deletions(-) diff --git a/doc/notebooks/One_dimensional_grids.ipynb b/doc/notebooks/One_dimensional_grids.ipynb index 3b1924682..3d8b340f1 100644 --- a/doc/notebooks/One_dimensional_grids.ipynb +++ b/doc/notebooks/One_dimensional_grids.ipynb @@ -1,378 +1,378 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# One-Dimensional and Radial Grids\n", - "\n", - "Grid supports several quadrature rules for one-dimensional grids, most of them in the [-1, 1] interval, within the [OneDGrid](https://grid.qcdevs.org/pyapi/grid.basegrid.html#grid.basegrid.OneDGrid) module.\n", - "\n", - "### Example: Visualize One-Dimensional Grid Points\n", - "\n", - "Here, we showcase some of the quadrature rules available each with a unique set of points. [Click here for a full list of one-dimensional grid classes.](https://grid.qcdevs.org/pyapi/grid.onedgrid.html)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:20.643610321Z", - "start_time": "2024-01-03T22:36:20.291101489Z" - } - }, - "outputs": [], - "source": [ - "from grid.onedgrid import *\n", - "\n", - "# Make several 1-dimensional grids for a given number of points\n", - "npoints = 31\n", - "\n", - "grids = [\n", - " GaussChebyshev(npoints),\n", - " GaussLegendre(npoints),\n", - " TanhSinh(npoints),\n", - " Simpson(npoints),\n", - " Trapezoidal(npoints),\n", - "]" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:21.133162129Z", - "start_time": "2024-01-03T22:36:20.645646412Z" - } - }, - "outputs": [ + "cells": [ { - "data": { - "text/plain": "
", - "image/png": 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\n" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "names = []\n", - "for i, oned in enumerate(grids):\n", - " plt.scatter(oned.points, np.repeat(i + 1, oned.size), marker=\"o\")\n", - " names.append(oned.name)\n", - "\n", - "# set the y-ticks to be the 1D grid names, and set labels\n", - "plt.title(f\"{npoints} Grid Points in One Dimension\", fontsize=16)\n", - "plt.yticks(range(1, len(grids) + 1), names)\n", - "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", - "plt.ylabel(\"Quadrature Rule\", fontsize=14)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Example: Integration of One-Variable Function on $[-1, 1]$\n", - "\n", - "The one-dimensional grids can accurately integrate one-variable functions over an interval (defined by their domain), even with a small number of points. Here, we numerically compute the integral below and compute the relative percent error. The analytical value of this integral is $\\pi/2$.\n", - "\n", - "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:21.338777861Z", - "start_time": "2024-01-03T22:36:21.146684630Z" - } - }, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# One-Dimensional and Radial Grids\n", + "\n", + "Grid supports several quadrature rules for one-dimensional grids, most of them in the [-1, 1] interval, within the [OneDGrid](https://grid.qcdevs.org/pyapi/grid.basegrid.html#grid.basegrid.OneDGrid) module.\n", + "\n", + "### Example: Visualize One-Dimensional Grid Points\n", + "\n", + "Here, we showcase some of the quadrature rules available each with a unique set of points. [Click here for a full list of one-dimensional grid classes.](https://grid.qcdevs.org/pyapi/grid.onedgrid.html)\n" + ] + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Integral of sqrt(1-x^2) from -1 to 1:\n", - " 1.57079633 from Analytical integration (which is equal to pi/2)\n", - " 1.57079633 from Gauss-Chebyshev integration\n", - " 1.57082270 from Gauss-Legendre integration\n", - " 1.57067045 from Tanh-Sinh integration\n", - " 1.56683246 from Simpson integration\n", - " 1.56069571 from Trapezoidal-Lobatto integration\n" - ] + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:20.643610321Z", + "start_time": "2024-01-03T22:36:20.291101489Z" + } + }, + "outputs": [], + "source": [ + "from grid.onedgrid import *\n", + "\n", + "# Make several 1-dimensional grids for a given number of points\n", + "npoints = 31\n", + "\n", + "grids = [\n", + " GaussChebyshev(npoints),\n", + " GaussLegendre(npoints),\n", + " TanhSinh(npoints),\n", + " Simpson(npoints),\n", + " Trapezoidal(npoints),\n", + "]" + ] }, { - "data": { - "text/plain": "
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\n" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "\n", - "# define the function to integrate\n", - "function = lambda x: np.sqrt(1 - x**2)\n", - "\n", - "print(\"Integral of sqrt(1-x^2) from -1 to 1:\")\n", - "print(f\"{np.pi / 2: .8f} from Analytical integration (which is equal to pi/2)\")\n", - "\n", - "names = []\n", - "error_relative = []\n", - "for oned in grids:\n", - " # integrate the function evaluated on the grid points\n", - " integral = oned.integrate(function(oned.points))\n", - " print(f\"{integral: .8f} from {oned.name} integration\")\n", - " error_relative.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - " names.append(oned.name)\n", - "\n", - "# plot the relative error as columns graph\n", - "plt.figure(figsize=(8.5, 5))\n", - "plt.bar(names, error_relative)\n", - "title = r\"Numerical Integration of $\\int_{-1}^1 \\sqrt{1-x^2} dx$ with \" + str(npoints) + \" Points\"\n", - "plt.title(title, fontsize=16)\n", - "plt.xlabel(\"Quadrature Rule\", fontsize=14)\n", - "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Changing the number of grid points increases the accuracy of each quadrature. Here we show how the relative integration error converges to zero when increasing the number of points.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:21.461375714Z", - "start_time": "2024-01-03T22:36:21.349492787Z" - } - }, - "outputs": [ + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.133162129Z", + "start_time": "2024-01-03T22:36:20.645646412Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "names = []\n", + "for i, oned in enumerate(grids):\n", + " plt.scatter(oned.points, np.repeat(i + 1, oned.size), marker=\"o\")\n", + " names.append(oned.name)\n", + "\n", + "# set the y-ticks to be the 1D grid names, and set labels\n", + "plt.title(f\"{npoints} Grid Points in One Dimension\", fontsize=16)\n", + "plt.yticks(range(1, len(grids) + 1), names)\n", + "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", + "plt.ylabel(\"Quadrature Rule\", fontsize=14)\n", + "plt.show()" + ] + }, { - "data": { - "text/plain": "
", - "image/png": 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\n" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "npoints = [3, 5, 11, 15, 17, 19, 21, 31]\n", - "grid_classes = [GaussChebyshev, GaussLegendre, TanhSinh, Simpson, Trapezoidal]\n", - "\n", - "for grid_class in grid_classes:\n", - " errors = []\n", - " for npoint in npoints:\n", - " # make 1-dimensional grid for the given number of points\n", - " oned = grid_class(npoint)\n", - " # compute relative percent error of integration\n", - " integral = oned.integrate(function(oned.points))\n", - " errors.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", - " # plot relative percent error vs. number of grid points\n", - " plt.plot(npoints, errors, label=oned.name)\n", - "\n", - "plt.legend(frameon=False, fontsize=12)\n", - "plt.title(r\"Numerical Integration of $\\int_{-1}^1 \\sqrt{1-x^2} dx$\", fontsize=16)\n", - "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", - "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", - "plt.xticks(npoints)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Radial Grid: Transformation of 1D-Integration Intervals\n", - "\n", - "Generally, areas where the integrand changes more rapidly demand a denser concentration of points. So, the $[-1, 1]$ interval is not suitable for most applications encountered in quantum chemistry, where the integrals are usually performed on $[0,\\infty)$ domain. [Grid](https://github.com/theochem/grid) supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. [Click here for a full list of radial transformations.](https://grid.qcdevs.org/pyapi/grid.rtransform.html)\n", - "\n", - "### Visualize Radial Grid Points\n", - "\n", - "Here we visualize the OneDGrid points for different quadrature rules after a Becke transformation.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:21.851432041Z", - "start_time": "2024-01-03T22:36:21.470246478Z" - } - }, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example: Integration of One-Variable Function on $[-1, 1]$\n", + "\n", + "The one-dimensional grids can accurately integrate one-variable functions over an interval (defined by their domain), even with a small number of points. Here, we numerically compute the integral below and compute the relative percent error. The analytical value of this integral is $\\pi/2$.\n", + "\n", + "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n" + ] + }, { - "data": { - "text/plain": "
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zav4uJyTYQCGWU4K9YMEC60fi448/toa72rheuHDBJCYmGkmmfv36Zvv27VbZP//8Y+2QlCpVypw4ccJpLDn9cLmjX79+VlK4evVqr8eXmacJ9tGjR60dlI4dO5oDBw5YZVu2bDE1a9Y0kkzt2rWzJCj2HbNSpUqZ9evXW8OPHz9uevXqZYKCgvIswU5JSbFiq1evnkOZqx20d9991zq48swzz1jzk5aWZubNm2ftIGY8YJM5ltxas2aNlciMHTvWYUdl2bJlJioqykgyQ4cOzdLW2/XPVYJ9/Phxs3r1atOyZUsjyVSsWNGcPn06S/sJEyZYOzOffvqpQ9nnn39uihcvbiSZt956y6Hsjz/+MOHh4UaSufbaa83ff//tUL5161Yzbdo0h2HOvr+HDh0yTZo0MZLM1VdfbY4cOeLQ5pVXXrESgnnz5pm0tDSr7KeffjIVK1a0kg1P5JRgf/HFF9Z6MX/+/CzlX3/9tVmxYoW5ePGiw/CDBw+aW2+91Ugy3bp1y9JuxYoV1ninTJlitU9LSzMvvfSS8ff3tw4KepJgL1myxPz4448O/WOMMbt27TLdu3c3ksywYcOytMvPBNue/GTcWU1JSTHnz583xqQvz88++8ycPXvWoX1SUpKZOHGilbBkZk+wAwMDTUhIiMN6kpaWZh599FFr25D54E3dunWtgygZD4AZk74sZ8+e7ZAgGpP9Tr4xvtkWBQYGmieeeMJh/bLHZ/8dCAwMND169DCHDx+26ixbtsxaf/r27Wvi4uLMt99+a5UfOHDAmueBAwdmiT2367W761Febr+Dg4PNk08+6RD722+/bSWBq1atyja2zOzrTUhIiMM2ICUlxcyYMcOa7sKFC7O0dXWQLLfyKsFesmSJVT/jCQh3LF682Grr7MCXJ9zdRrj67p07d85UqVLF+h3Zs2ePVbZ582ZTsWJFax3K3Pa6664zksyNN95ojh8/7lB24sQJM2fOHPPbb795NX+XExJsoBDLLsFes2aNKVWqlJFkSpYs6ZAUuNq42n+cAwICsuxAGWPMkSNHTGRkpJFkHn/8caexeJtgv/322yY4ONhKSMLDw82KFSu8GmdmnibY9h2EokWLOj179ccff1iJ4YIFC6zhO3futHZKvvrqqyztzp49a+1A+DrBPnXqlLn77rut8sxHxl3toNnPoNx2221Op2lPJGNiYhx24H2RYHfo0MFIMu3atXNabk8SAwMDzd69ex3KfJVgu/oLCQkxY8aMyZK4GmPM3r17TVBQkPH393c4iJLRBx98YCSZ6tWrOwzv27evkWSaNWvm9tnjzN/f7du3m0qVKhlJ5rrrrsuS4Jw5c8Y6G7548WKn41y3bp2x2WymSJEi1k6YJ7FkXn/37dtn3nrrLeuMcu3atbMkGzlJS0szpUuXNjabzeGgljH/7ih36dLFads77rjD5Xcjt8nwqVOnTGBgoImMjMyyrPIzwZZk3n333VxPo1mzZkaSWbduncNwe4JtP2jhjP1qnOeff95huP1MY+YDr9nJKcH2xbbojjvucDl9++9AXFyc0+26/UCvJPP+++9nKV+6dKn1u+CJ7NZrbxNsX/TZ4MGDnba1Xx0zatSonGfyf06fPm1dnfPwww87rWM/CF2jRo0sZZdKgr1p0yarvqdX3j3//PNWW0++P864u41w9d17++23jSQTFBTkkFzbfffdd9b4M7etWrWqkWR++eUXr+bhSsE92MAlYNOmTWrRooVatGihZs2aqUyZMmrZsqX27duniIgIvfvuu249JGTp0qWSpD59+jjcU2sXGxur2267TZL02Wef+XYm/jf9QYMGKS4uTj///LOefvppnT59Wt26ddPy5cuz1H/33Xdls9nUtGlTn8eSOS4p/eEjUVFRWcqrVatmPegkY7988cUXMsboqquucvrU6ZCQEA0cONAnMd5zzz3WOlCnTh0VL17cul/y2muvtZ5Omp2tW7darwgaPXq00zr333+//P39dezYMf3www8+iV2Szpw5o5UrV2Y77SFDhqh48eK6ePGi0/XBFxISEtS8eXPrr379+oqNjdW5c+f01ltvOX0P+5IlS3ThwgU1bNjQelVVZtdee60CAwP1xx9/WPehnTt3zlq3HnjggVw9sGb9+vW6+uqrtX37dg0dOlSLFi1SaGioQ50VK1boyJEjKlmypMunZzdq1Ehly5bViRMnsty37Y7du3c73C9aqlQpDRw4UEeOHNENN9ygr7/+2uVr4k6dOqU5c+botttuU+fOndWyZUu1aNFCLVu21MmTJ2WMcXh40JkzZ6yHId53331Ox+lquDuOHDmiF154QYMGDVLHjh2teDp16iQ/Pz+dPHnS+p4UhMjISF1//fXZ1jl//rwWLlyo//znP+rSpYtatWplbR+2b98uSdkuZ1fbi6uvvlqSssx/uXLlJEnvvPOO2/ORHV9ti26//fYcpzVgwACn2/UGDRpIkooUKaIbbrghS7n9u378+HEdO3YsS7mn67W3fNVnni777Hz33Xc6ceKEgoKCXI533LhxkqTff/9dO3fudHvchUlERIT1/+TkZI/aZqyfcTwZjR8/3ul7uV29EtOdbYQz9v2XPn36qEyZMlnKmzdvrkaNGjlta98GvPfeez5/N/jliNd0AZeA5ORkh1dPhIeHq2bNmmrfvr3uu+8+a8OXE/urP+xPnnamdu3aDnV95fz587r99tuVlpam1157TWXKlNHIkSNljNH999+vnj17atGiRQ7vmrQ/NMnVBt9X3O2XJUuWOPTLli1bJEl169Z12a5evXo+iXHz5s3W/wMCAhQbG6vWrVvrlltu0YABA9x64Jc99qCgIFWpUsVpndjYWJUuXVp///23/vzzT4cH6Xlj+/bt1gN0XPVzYGCgqlevrsOHD+fZa2qcvaZLSn+Y1i233KIRI0bo5MmTeuCBB6yy//73v5KknTt3qkWLFi7HbV8Ge/bsUXx8vLZt26Zz585Jyt07j9evX682bdro7Nmzmj59usaPH++0nj2+s2fPZhufPUnYs2ePtTPtrozvwb548aJ2796tgwcPKigoSI0aNVLx4sWdtvvhhx/Up0+fHB9+k/GhUNu2bbPWlZo1azqtX7VqVQUEBHj8UKaPP/5YgwYNyvHduTk9fC0v2efNla1bt6p79+45JkKu5qFYsWIuX5tVokQJSenJY0bjxo3TbbfdpuHDh+upp55S+/bt1bRpU7Vs2VKVK1fONg5nfLUtSkxMzHFaruKzvzWgUqVK2ZZL6f2Rsc9ys157y1d9Zn/Hdmaulr07MZUtW9Z6l3RmiYmJ8vf3V2pqqv7880+nB/cLO/sD/CS5nE9XMh7cOXXqlNP25cuXd/iN2Lx5c7bbqJy2Ea7Yl5er7aqUvrzWr1+fZfiYMWP09ddf64knntBbb72ljh07qmnTpmrRokW2+05XKhJs4BLQunVrp0/i9JT9SGrJkiVd1omPj3eo6yuff/65Dh48qLJly6pTp07W8FGjRiktLU1jxoxR7969tWDBAl133XVWG0nq16+fT2PJLLf9Yv/RdXZ2xC7zU0Dt+vXr53TnbOLEierSpUuW4StXrvT66ar22O1P23UlPj5ef//9t0/XgYzjsu/IuZp25vr5oWfPnpo6dapGjhypRx99VHfddZdiY2MlpZ/BkqRDhw7p0KFDOY7rzJkzkhznwdOdMkn6559/dObMGQUHB2d7oMYeX1JSklvvgLXH54nM78E2xujDDz/UwIEDNXr0aIWFhek///mPQ5uTJ0+qV69eOnjwoFq1aqUJEyaobt26iomJUVBQkCSpVatWWrNmjcNbBTLuzGZMcjLy9/dXbGysDh486PY8/P333+rfv7/OnTunXr166d5771ViYqKio6MVGBgoKT1R2LNnT4G+5SA8PNxlWVpamvr06aNt27apVq1amjJliho3bqy4uDirTwcOHKi3337b5TxkN377diHzE+dvvfVWxcTE6Omnn9batWv12muv6bXXXpOUvrM+bdo0j9497qttUXbzklMd+wGxnMolx/7I7XrtrbzuM1fL3p2YsvvtDAgIULFixXTw4MF83677Ssanudt/vw4cOKC+ffs6rf/hhx9afZLxTPHOnTudHpC/++67dffdd1uf27dvr2+++cZlPO6s987Yt63Z/Qa7Kmvfvr1Wrlyp6dOna8WKFXrrrbesNzpUqFBBEyZM0B133JGruC5HJNjAFcSeCGZ+FVdG9qQvu6QxN+xnW5ydbR89erSMMRo7dqz69eund999V6VLl9aPP/6oJk2aWK+iyitRUVE6fvy4x/1iT56z22nImCxktH79eu3evTvLcE8SBk/ZYz906JDS0tJc7qTlxTqQcVwHDx5U6dKl823a7mrZsqWk9AT0l19+Ubt27ST9e1nf0KFD9cILL7g9vozzkJSUZL3Oyl3XXXedypUrp2nTpunaa6/VwoULrVsVMrLH17Vr1zy5tcMZm82mfv366fDhwxo2bJjuv/9+de/e3XrVmZT+PvGDBw+qTJkyWrZsmdPbWJyd4ct4UOrQoUMqVapUljqpqakenx18//33de7cOTVs2FAffPBBlkv2jTHWwYrCasOGDdq8ebNCQkL09ddfOz0AkVdn36+77jpdd911OnnypH766SetWbNGH374oTZv3qzevXtr6dKlDlcgZacgt0Xeyu167a3C2Gfu7FOkpKToyJEj+RZTXli9erWk9Pd12xPkc+fOuTygab9ySZJatGghm80mY4xWrVqV7RVvec2+bc1uPyO7slatWqlVq1Y6d+6c1q9fr++++05LlizRunXrdOedd+rixYsaOnSoz+O+FHEPNnAFqVatmiTp//7v/1zWsZdVr17dYbi37xy2JwF//fWXjDFZyseMGaPHH39cKSkpuvHGG9W/f3/5+fnpqaee8mq67shtv9gvtbNfouuM/b2Ume3atUsm/UGTDn+u3lvpC/b5vHDhgsv3Zh87dkz//POPJMd59Xb5V6pUybqkzVU/X7x40bqELfP6lx8ynrmx7xBK/942kfEMrjuqVKmikJAQSXLrzLIzU6dO1fTp03X+/Hn17dtXH374YZY69vh++uknr95jmxt33323EhMTdfbsWT344IMOZTt27JCUfouHsyTk2LFj1m0WGVWuXNlKfl29h3jLli0ez6s9npYtWzq9H/7XX3/16PLYgmCfh+rVqztNrlNSUpxe3ulLkZGRat++vaZOnarNmzdbZ65nz57t9ji82RYVtNyu15J329HC2Gf2mLI7Y/77779b9+wWpuXorqSkJM2bN0+S1K1bN+tql/Llyzv9DTfGWO+al6TixYurQ4cOkqSXXnqpQK+OsS8vV9vVnMrsQkJC1LJlS02YMEE//fST7r33XknSrFmzfBPoZYAEG7iCdO/eXZK0aNEipw8bOXbsmF5//XVJynImwr4jcfbs2VxNu23btpLSL3udO3eu0zpjx47VtGnTlJqaqr1796pPnz65unfVU/Z+efXVV53uJGzdulWffPKJJMd+6dSpk2w2m3bs2GE9wCuj8+fP6+23386jqD1XpUoV6969mTNnOq3z9NNPKzU1VbGxsQ4Pl8u4I5mbdSAsLMy6H9DVtOfNm6dDhw4pMDBQHTt29Hga3lqzZo31/4z3Zfbq1UsBAQH69ddf9fHHH7s9vuDgYGvdmjFjhkeXXmY0fvx4PfPMM7p48aL69++f5UFsHTp0UNGiRXX06FGPzrD7gp+fnyZNmiQp/aGEGRML+zrj6j7Vp556yunDcsLCwtS6dWtJ0nPPPee0ravh2ckpnieeeMLjceY3+zwcPHjQ6YHKOXPm6PDhw/kWj81ms64wsid27vBmW1TQcrteZ2ybm21oYeyzFi1aqEiRIrpw4YKef/55p3Xs36saNWo4JJ6XgvPnz2vgwIE6fvy4/P39sxxEdNfUqVPl7++vrVu36t5773X63c0PXbt2lZR+Cbuz7+sPP/yQqwN09tvXPNkGXO5IsIErSL9+/ZSYmKiUlBT17dvXOhIv/Xs/0cmTJ1WqVCndeeedDm3tCcd3332XqyOw1apVs87O3nXXXXryyScddjLS0tL0+eef6/3337eGLV682OkZO1+7++67VbJkSR0/flzXX3+9wyVS27ZtU79+/ZSamqo6deqod+/eVlmFChXUv39/Sen3PWZ8au+JEyd00003FbofHPsDvubMmaPnnnvO2hE0xuidd97Rk08+KSk9qbOffZXSH4xkv494xYoVuZr2pEmT5Ofnp2+++Ubjx4/X+fPnrbLly5dbT8a98847nV4WnJeWLFli9U3dunVVv359q6x8+fK6//77JUk333yzXn/9dV24cMGh/bFjx/TWW29pzJgxDsOnTZumsLAwfffdd+rXr1+W9WH79u165JFHcozvvvvu00svvaS0tDTdcsstmjNnjlUWERGhxx57TFL67RaPP/64Tp8+7dD+1KlTWrRokVtPXfZUv379VLNmTaWmpmrq1KnWcPtO148//qiXXnrJ2qlMSUnRM888oxkzZjisYxnZHzL32Wef6dFHH3VYT1999VW98cYbHj/kxx7Phx9+6HCg5Ny5cxo7dqzmz59v3UNbWDVr1kxBQUHat2+fJk6caJ3FN8bovffe04gRI1z2aW4lJyerT58+WrZsmcN3VkrfPr7yyiuSPH8YZW63RQXNm/Xa/jv622+/5ep2oMLWZ2FhYRo7dqwk6dFHH3X4/U5NTdXMmTOtA4IZtw2F3alTp7Rw4UI1btzYOrj+4osvWlcLeapp06bWQZGXXnpJHTt21Jo1a7IciDl//rzef/99l1dAeOv6669XpUqVdOHCBd1www0Ov0e///67Bg0aZJ2hz8x+BVXm35b9+/dbVxrm9QNpLyn58jIwALmS3Xuws5Pd+0e3bNliypYtayQZPz8/U7NmTVO3bl0TEBBgJJnY2Fjz448/Zmn3999/m7CwMOu9os2aNTOtW7c2N9xwg9txnTt3zuHdo6GhoaZevXqmfv36Jjo62kgy/v7+ZsKECWbixInW+xqXLVvm0fzb338aHBxsYmNjXf5dddVVVpu1a9eaokWLWu9hrlu3rqlZs6b1/uvy5cubbdu2ZZnWkSNHTM2aNa15qlq1qmnQoIEJCQkxYWFh5oknnjCSHKblLk/f1ZmRvV3m96gaY8y4ceOs8mLFipnGjRub+Ph4a9jAgQNNampqlnbDhw+31pvatWub1q1bm9atW3u0fF544QWrT6OiokyjRo1M+fLlrWl37Ngxy3uejfHde7ATEhJM8+bNrb/69eub2NhYa/ply5Y1W7ZsydI+NTXVDBs2zKoXFhZm6tWrZxo3bmzKly9vvQ/d2Xd12bJlJioqyuq76tWrmwYNGljvgo+Ojnaon933d86cOcbPz8/YbDbz0ksvOZQ99thjVt8GBQWZ2rVrmyZNmphKlSpZwz19H7ur92BntnDhQmv+fvvtN2v44MGDrT4rWbKkadiwoYmJibHeYWz/rs6ZMyfLOCdNmmS1jY2NNY0aNTIlS5Y0ksz999/v8h26rt41nJqaatq2bWuNs1y5cqZhw4YmIiLCSDKPPvqox+P0lDvvwc5pGlOmTHHol4YNG1r90rlzZ3PzzTc7/a7Y34Od3bJ0tu4dP37cml5gYKCpXr26tV7Zh1eqVMns27cvx3FllpttUcbtYnayW7eMca+/XW1Hc7tep6WlWe8aDw8PN40aNbK2o/v3789xusbkXZ/ldh1PTU01N954ozX+UqVKmcaNGztsVx988EGnbb19D/bw4cMdftMDAwOtfYuMw7/77juHdhn7o2bNmtbvQaNGjUzFihWt7aX9+/L555/nKr7M5s+fb60nkkxkZKSpVauWadq0qUlMTDShoaFWWYsWLcyvv/7q0N7dZZTdd2/jxo3Wu8sDAgJM3bp1TWJiorHZbKZy5cpmxIgRTttm3EerXLmyadKkialWrZrx9/e39gszbvuvdCTYQCGWFwm2Mek7TJMmTTK1a9c2YWFhJiQkxFStWtWMGjUqy05SRt99953p0qWLKVasWK532I0x5vPPPzd9+/Y1pUuXNoGBgSYyMtLUrl3b3H///WbHjh3GmPQdkf79+1s/lqtXr3Z7/Padm5z+Mic2//zzjxk5cqSpWrWqlSDXrl3bTJ482Zw4ccLl9JKTk82ECRNMxYoVTVBQkImLizPXX3+9+e2338ynn35qJJm6det63E95lWAbY8zXX39trrvuOlOiRAkTGBhoYmNjTadOncyiRYtcjvPs2bNm4sSJplq1aiYkJMSahqsdWFc2bNhgbrzxRmv5FylSxLRq1cq88cYbJiUlxWkbXyXYmf/8/f1NTEyMadGihXniiSfMyZMnsx3P2rVrzcCBA81VV11lQkJCTEREhKlSpYrp2rWrmT17ttmzZ4/Tdnv37jWjR482iYmJJiwszISFhZmKFSua66+/Pkuf5/T9fe+996wDYs8884xD2ebNm83dd99tqlat6jCddu3amSeeeMJs3brV7T7LGEtO3/OMiUO/fv2s4ampqeapp54yNWrUMEFBQSY6Oto0a9bMvPnmm8aYnJOgjz76yLRs2dJERESYiIgI07hxYzN37lxjjOud8+x2Qs+ePWsefPBBU7FiRRMYGGhiYmJMu3btzMcff5zrcXrCFwm2McbMnTvXNGjQwAQHB5uIiAhTr14989RTT5mUlBSX35XcJtgpKSnmvffeM7fffrupVauWKVasmPH39zdRUVGmcePG5rHHHnP6vXEnwTbG821RYUiwvVmv9+zZYwYNGmQSEhKshDDzNHy9/c7LBNvugw8+MB07djSxsbEmICDAlChRwvTq1cusWLHCZRtvE2z7up7TX+bxZ+yPjH9hYWGmZMmS5uqrrzZDhw41S5cudfmblFsnT540s2fPNt27dzcJCQkmNDTUBAcHmxIlSpiWLVuasWPHmg0bNjht64sE25j0+R80aJApUaKECQoKMuXLlzf33nuvOX78uMu2n3zyiRk+fLipX7++KVGihAkICDARERGmTp06ZsKECebQoUO56I3Ll82YAroRAACuAE8++aTGjh2r3r17a9GiRQUdDgAAAPIQ92ADQB65ePGida+s/aFNAAAAuHyRYAOAFy5cuKCJEyfq77//dhi+b98+3XDDDfrjjz9UtGhR3XzzzQUUIQAAAPILl4gDgBfOnTun0NBQSenvuyxXrpxOnz6tLVu2KC0tTaGhofrggw+yvPYMAAAAlx8SbADwQlpammbOnKkvv/xSW7Zs0dGjRyVJZcqUUdu2bTVq1ChVrVq1gKMEAABAfiDBBgAAAADAB7gHGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfCCgoAMACqO0tDTt27dPkZGRstlsBR0OAFxRjDE6efKkSpUqJT8/zgXY8dsEAAXDk98lEmzAiX379ikhIaGgwwCAK9qePXtUpkyZgg6j0OC3CQAKlju/SyTYgBORkZGS0r9EUVFRBRwNAFxZkpOTlZCQYG2LkY7fJgAoGJ78LpFgA07YL72LiopiJwYACgiXQTvitwkACpY7v0vc2AQAAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPFOoE22az5fg3d+7cgg7Tp2w2m2bOnJltnQ0bNshms2nVqlUejXvKlCmKiIjIsd7gwYNVs2ZNj8ad2a5du2Sz2fThhx96NR67KVOmaO3atW4PBwAAAID8FlDQAWTnhx9+cPh89dVX65577tGNN95oDatYsWJ+h5WnfvjhB5UrV66gwyh0pk6dqoiICDVr1syt4b7y6n3fKjQoXOXqxKpWy9LyC/DT2ZMXFB4VrPjKReTnZ8uT6QIAAGSUlma0f9sJnU4+7/F+iDtts6vjqizz8BIVo3VwR5Jbn8MigmRssvarnJWdSTqvsycvKjQySOFR/9bP2NbZ/3PbLrtYMu7/Scp2vl31T07D83N5I+8U6gS7adOmWYaVLVvW6XC7c+fOKSQkJC/DylPZzRsKzu7/HtXu/x51GBZeJFgtb6isivXiCigqAABwJdix6ZDWLNim0yfOW8Pc3Q9xp212dSQ5LavcKE7b1h9yGG6zScbI7c8ZZVeW37KLJTgsQLJJ50+nuKzvqn+yG+7u8vDF8kbeKtSXiOfEfsnzunXrdPXVVyskJESzZs2SJI0fP161atVSRESESpcurQEDBmj//v0O7du0aaPu3bvrrbfeUsWKFRUaGqo2bdpoy5YtDvWMMZo5c6aqVKmi4OBgXXXVVXrmmWcc6ri6hH3KlClWnTVr1qhFixYKDQ1VbGysbrnlFh08eDDLeDJfIv7II4+oZMmSioiIUO/evXXo0KEsffHUU0+pUaNGio6OVlxcnLp3766tW7d63KfucmdeJOn06dO67bbbFB0drZiYGI0aNUopKf9ukPbv369bb71VV111lUJDQ1W5cmU98MADOn8+48Y6/YjbmDFjrH5dtWqVy+FS+oGW+++/X6VLl1ZwcLBq1aql9957z6d9cPrEeX3xymbt2JR1eQAAAPjCjk2H9MUrmx0SJsm9/RB32uZUx1XZL1/tyTI8c1Ka02d3y/JbdrGcP5PikFw7q++qf7Ib7u7y8HZ5I+8V6jPY7rhw4YJuuukmjRw5UtOnT1fRokUlSYcOHdIDDzygUqVK6fDhw3rqqafUunVr/f777woI+He2f/75Z+3YsUMzZsyQJD344IPq1KmTtmzZouDgYEnSvffeq9dff10TJ05UkyZNtHbtWo0bN06hoaG6++67JWW9nH358uWaPHmyqlatKknauHGj2rdvr5YtW2rhwoU6duyYxo8fr7Zt22rjxo0uz7rPnj1bDz30kEaPHq327dtr+fLluvPOO7PU27t3r4YPH65y5copOTlZL7/8spo1a6atW7cqJibGy1525Mm8PPDAA+rYsaMWLlyon3/+WZMmTVJQUJDV30eOHFFMTIyefvppFS1aVFu3btWUKVN04MABvfnmm5LS+zbz7QE1atRwOVySbrrpJn3++ed65JFHVLNmTb3//vu66aablJqaqltuucWn/fHdwm2qUKc4l94AAPLFxfOpung+taDDQD5ISzNasyD7EyZrFmxTmWoxTi8xzqnt6ve3ir2XwsOd5eHN8nbVFjnzZJt7ySfYFy9e1GOPPaZ+/fo5DLcnZ5KUmpqqq6++WmXKlNGKFSvUsWNHq+zgwYP69ttvVbly+iUwdevWVbVq1TRv3jzdeeed2rFjh2bPnq2XX37ZSmzbt2+vU6dOaerUqbrzzjvl5+fncGn3tm3b9Oyzz+r222/XgAEDJEmPPvqo4uLi9PnnnysoKEiSVKVKFTVr1kzvv/++Bg8enGXeUlNTNX36dN1yyy168sknJUmdOnXS/v37NX/+fIe6Gc+op6amqkOHDoqLi9OHH37oNCH3hifzUrFiRc2ZM8eK/cyZM3r66ac1btw4FS1aVLVq1XI4Y9+8eXOFh4dr0KBBmj17tsLCwqy+zXx7gKvhv/76qxYvXqwXXnhBQ4cOtaa9b98+PfTQQ04T7PPnzzucNU9OTna7P04dP6/9206odNWibrcBACAnrn6b5oz7TqFB4QUVFgqZ0yfO6/WRq3PV9kzSBR9HA2+4szy8Wd7etL3Snb1w2u26l/Ql4nZdu3bNMmzZsmVq1qyZoqOjFRAQoDJlykhSlsuma9asaSXXklS5cmXVrFlTP/74oyTp66+/liT16dNHKSkp1l+7du104MAB7dmzx2F8ycnJuvbaa1WtWjW98MIL1vA1a9bouuuusxJSKf2hbeXKldOaNWucztfevXu1b98+9erVy2F43759s9T98ccf1aFDB8XGxiogIEBhYWE6depUtpeJp6amOsyTuzyZl8yx9+7dW2fOnNH//d//SUq//P7ZZ59VjRo1FBoaqsDAQN10001KSUnRX3/95XZMmeOTpBtuuMFh+IABA7R79+4sy0ySpk+frujoaOsvISHBo2meTj6fcyUAADzg7W8TACD/XfJnsMPCwhQe7ngUd/369erZs6euvfZajR8/XnFxcbLZbGratKnOnTvnUDcuLuvN/nFxcdb92keOHJExRsWKFXM6/T179lhP/U5LS9NNN92kEydO6JtvvnFIQI8fP66SJUtmaV+yZEkdO3bM6bjtMWSOsUSJEg6f//77b3Xs2FENGzbUK6+8olKlSikoKEjdunXLMr8ZVaxYUbt377Y+79y5U+XLl3dZPzfzkjl2+2f7vD377LMaPXq0xo4dq2uuuUZFixbV+vXrNWzYsGxjzym+gIAAxcbGZolPko4dO5ZlJ2XChAkaNWqU9Tk5OdmjHZnwqOBcxQoAgCuufpuGPN5CUVFRBRgZ8su+bSe0dPZ/c6zXfXgdlfrf0609bYtLjzfL21lb5Cw5OVlj5rhX95JPsO0Pusroo48+UnR0tBYuXCg/v/ST9BkTyYycPTDs0KFDatCggSQpJiZGNptN3333nUPCbGe/x1qSJk6cqOXLl+vbb79VfHy8Q72YmBinDwE7cOCAEhMTncZmH0fmGDOP54svvtCpU6e0ePFiFSlSRJKUkpLiMnG3+/TTTx0uPStVqlS29e08mZfMsds/2+ftgw8+UM+ePTV9+nSrzu+//+5WHNnFZ5//jPefHzhwwCrPLDg42Lrn3lMRRf99ZQMAAL7i6rcpMNhfgcH+BRAR8ltCjRiFFwnO8tCqjCKKBiuhRtb7at1pG14kSJIt2zrIP+4sD2+Wt6u2yJkn29zL4hLxzM6ePavAwECH5Pvdd991Wnfz5s3atm2b9Xnbtm3avHmzmjRpIklq166dJOno0aNq2LBhlr/IyEhJ0vvvv68ZM2boxRdfdPqqrRYtWmjJkiW6ePGiNeynn37S7t271bJlS6exlSlTRvHx8froo48chn/44YdZ5tdmsykwMNAatnDhwhwv+65Vq5bDvDg7gOCMJ/OSOfbFixcrLCxMtWrVsmLPPF1nyyowMNDpGW1nw1u0aCEpvQ8yWrBggcqVK+fzS+xaXF+ZDRUAAPA5Pz+b9aosV1zth7jTtuUNVXKsg/zjzvLwZnmzz5o/Lvkz2M506NBBzz77rO655x716tVLP/zwg95++22ndUuUKKGePXvq4YcfljFGDz30kEqXLq1BgwZJSn9417Bhw3TLLbdozJgxatKkiS5evKitW7dq5cqVWrJkif766y/deuutuuaaa5SYmGjdvy2lJ8llypTRxIkT1axZM3Xt2lX33nuvjh07pgkTJqhGjRrq37+/09j8/f01fvx43XvvvSpRooQ6dOigL7/8UqtXOz6coG3btpKkIUOG6K677tLvv/+umTNnWmezcyM5OTlLIi9JrVu39mheduzYoSFDhqh///76+eef9fjjj+u+++6znvbeoUMHPffcc5o9e7aqVKmid999V9u3b88y3erVq+vjjz9Wy5YtFR4erqpVqyoyMtLp8Nq1a6tPnz4aNWqUzpw5o8TERC1cuFBffPGF3nrrrVz3SWYRRYPV4nreKQgAAPJOxXpx6nxXzSzvNnZnP8TdttnVkbK+BzuiaLAqNbwy34MdEh4go+zfg+2qf7Ib7u7y8MXyRt66LBPsrl276vHHH9esWbM0Z84cNW/eXEuXLlWVKlWy1K1fv7769OmjMWPGaP/+/WrSpIlefvllh1dNPf/886patapeeeUVTZs2zUrkrr/+eknp90CfPXtWK1eu1NVXX+0w/smTJ2vKlClq0KCBvvrqK02YMEF9+/ZVWFiYunbtqpkzZ7p8RZck3XPPPTpx4oReeOEFvfjii2rfvr1eeeUVde/e3apTq1YtzZkzR1OnTlX37t1Vt25dffjhh1merO6JPXv2OG2/cuVKtWnTxu15efTRR7Vq1Sr169dP/v7+Gjp0qB599FGrfNKkSTp8+LAmTZokKf0Bbs8//7x69OjhMJ4XXnhB9957r7p06WL1dZs2bVwOf+eddzRx4kTNnDlTR44cUZUqVfTOO+/opptuylV/lKsTq1otS8svwE9nT15QeFT6ZeEcBQQAAHmtYr04VahTXPu3ndDp5PMe7Ye40zanOq7Kru5VyWF4iYrROrgjya3PYRFBMjZZ+1XOys4kndfZkxcVGhmk8Kh/62ds6+z/uW2XXSwZ9/8kZTvfrvonp+H5tbyRt2zGFJZjRfmvTZs2ioiI0NKlSws6FBQyycnJio6OVlJSEg+SAYB8xjbYOfoFAAqGJ9vfy/IebAAAAAAA8hsJNgAAAAAAPnBZ3oPtrlWrVhV0CAAAAACAywRnsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB8gwQYAAAAAwAdIsAEAAAAA8AESbAAAAAAAfIAEGwAAAAAAHyDBBgAAAADAB0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABEmwAAAAAAHyABBsAAAAAAB/wSYK9fft2DR8+XNWrV1dERIQCAgIcyt944w1NmzZNp06d8sXkAAAAAAAodAJyrpK9hQsXasiQITp37pyMMZIkm83mUOfYsWOaOnWqatSoob59+3o7SfjAu+++q+eee05btmyRMUalS5dW8+bN9dhjjykuLk6S1KZNG0VERGjp0qUFHG3B2dKgoSICAhTetq2K9r9BtoAApR49poDixRXWsIFs/v4FHSIAALgCmNRUndmwUSmHD3u8H+JO2+zquCrLPDy0Xl2d3fSLW5/9Y2MlGWu/yllZyuEjSj12TAExMfIvXtyqn7Gts//ntl12sWTc/5OU7Xy76p+chufn8kbe8SrB/r//+z/dcsstSk1N1dChQ9W3b1+NHj1aP//8s0O9fv36ady4cfr4449JsAuBGTNm6IEHHtDIkSM1bdo0GWO0efNmvfvuu9q3b5+VYL/44ovy58soGaPT33yj09984zA4oGRJlXhggqI6diygwAAAwJUgeflyHXxsulIOHLCGubsf4k7b7OpIcloW1a2rkj/73GG4/PyktDT3P2eUXVl+yyYWvyJFJElpJ064rO+qf7Ib7u7y8MXyRt6yGftp51y45ZZb9N5772nmzJkaOXKkJKlly5Zau3atUlNTHeqWLFlSJUuW1C+//OJVwPBe6dKl1alTJ7355ptZytLS0uTnx635ycnJio6O1rpKlRXh6iDD/67UKP3cs2ywAMCH7NvgpKQkRUVFFXQ4hQb9cmVKXr5c/9x7n5R5l92N/RB32kpyXSf3aQI84e7ykPfLm33W3PFk++vVGexVq1YpMjJS9913X451ExIStHv3bm8mBx85ceKE4uPjnZZlTK4zXyI+ZcoUzZw5U99++62GDh2qX3/9VdWqVdPrr7+uxMREjRw5UgsWLFBYWJhGjx7tsF4MHjxYGzZs0JNPPqkxY8Zo+/btSkxM1AsvvKCmTZta9T755BNNmzZNf/75pwICAlSpUiVNmzZNXbt2lZR+AGDGjBl67bXXtG/fPpUtW1bDhg1zmJY9zrVr12ro0KH6+eefddVVV+mpp55Sp06dfNeRxkg2mw4+Nl2R7dpx6Q0AIF+knTmjtACv7/LDJcCkpurgI486T3SNkWzSwUcfU/jVVzu9xDintgceeVQ2+2dndZA/3F0eXi5vV22Rs7QzZ9yu69XW+dChQ6pVq1aWe66d8fPzU3JysjeTg480aNBAL7/8sipUqKDu3burZMmSbre9ePGibr31Vo0cOVJxcXEaN26cevfurRYtWqhEiRJasGCBPv74Y40cOVKNGzdWs2bNrLb79+/X0KFDNWXKFBUtWlQzZsxQp06dtG3bNsXFxWnHjh3q27evBgwYoOnTpystLU3//e9/dfz4cWscY8aM0bPPPqsHHnhALVu21FdffaWRI0fq5MmTeuihhxzivPnmmzVixAg99NBDmj59uvr06aPdu3crNjY2y3ydP39e58+ftz67va4ao5QDB3Rmw0aFN2nsdj8CAJATV79N21q2cn11Fa4sRko5eFBbG+ViH8RIqYcO+T4m5I47y8PL5Z3rttCpTFdnZ8erBDsyMlIHDx50q+6uXbucJjbIfy+++KJ69eqlO+64Q5JUoUIF9ejRQyNHjlT58uWzbXvhwgU9/vjj6ty5s6T0M8o9evRQamqqnn76aUlS27Zt9cEHH+iDDz5wSLCPHTumDz74QG3btpUktWrVSgkJCXr22Wf12GOPadOmTbp48aJmz56tyMhISXI443zkyBHNmjVL999/vx5++GFJUseOHZWcnKzHH39cI0eOVEREhBXnjBkzrDPfFStWVOXKlbVs2TLdfPPNWeZr+vTpmjp1qsd9aZdy+HCu2wIA4Iy3v00AgPznVYJdq1YtrVmzRn/++aeqVavmst7KlSt1+PBh9ejRw5vJwUdq1qyp3377TV9//bWWL1+ub7/9Vs8//7zmzJmj1atXq27dui7b+vn5WQmyJFWpUkWS1L59e2uYv7+/KlasqD179ji0jY6OdmhbpEgRtW3bVj/++KMkqXbt2vL399eNN96oO++8U61atVJ0dLRV/6efftLFixd1ww03OIx3wIABevXVV7Vp0ya1bNnSijNjTJUqVVJQUJD27t3rdL4mTJigUaNGWZ+Tk5OVkJDgsh8yCyhe3O26AAC4w9VvU+U1q7kH+wpxZsMG7bnzrhzrJbz6isIaNsxVW1x6vFneztoiZ8nJyZKLW2wz8yrB7t+/v7799lvdfffd+vTTT62zjhn9888/uuuuu2Sz2ZyeOUTBCAoKUteuXa0zvF9++aW6deumadOmafHixS7bhYaGKigoyGE8UnqynHn8586dcxhW3EkSGhcXp61bt0pKT9aXLl2qxx57TL169ZKfn586d+6s2bNnq2zZstal4pkvabd/PnbsmMs4JSkwMDBLTHbBwcEKDg52Od8u2WwKKFHCemUDAAC+4uq3yS8sTH5hYQUQEfJbePPmCihZUikHDzq/t/Z/+yHhzZtnua/Wnbb+cXGySUo5dIh7rguaO8vDy+Xtqi1y5peS4n5dbyZ02223qUGDBlq9erXq1KmjBx54QIf+d+/AokWLNHLkSCUmJmr79u1q1aoVr+gqxDp16qQ6derojz/+yLNpHHZyGfWhQ4ccHrjWuXNnrV69WseOHdM777yjjRs3asiQIZKkmJgYScpyW8KB/72GwF6eb/737IESD0xgQwUAAHzO5u9vvSpLmZ95lMN+iDttS058QCUmPpBtHadl8C0Ploc3y5t91vzhVYIdEBCgzz77TM2aNdOuXbv0+OOPa/v27ZKk66+/Xs8//7ySk5PVrFkzLVq0yK2HoSHvObtv/uzZs9qzZ49HDzzzVFJSklasWJHlc5MmTbLUjYqK0vXXX6/+/ftbSX/jxo0VGBiohQsXOtRdsGCBwsPDVb9+/TyL3ZmAEiV43QEAAMhTUR07qvRzzyqgRAmH4e7sh7jTNts6zz+n0s8/l7WsZEnF3HarAjLvN2Z+1WtOn90ty2/ZxOJXpIj1LmxX9V31j8vh7i4PHyxv5D2v3/EQFxenNWvWaNGiRVq4cKH11OeIiAjVrl1b119/vQYMGEByXYjUqlVLPXr0UKdOnRQfH699+/Zp1qxZOnLkiO699948m25MTIxuu+02TZ06VUWKFNGMGTMkyXrF1iuvvKK1a9eqS5cuio+P186dO/XOO++o4/82BsWKFdOIESM0c+ZMBQcHq3nz5vrmm2/0yiuvaOrUqQoPD8+bwG02hbdtq6L9b5AtIECpR48poHhxhTVswFFAAACQ56I6dlRku3Y6s2GjUg4f9mg/xJ22OdVxVRY3apTD8NB6dXV20y9uffaPjZVkrP0qZ2Uph48o9dgxBcTEyL94cat+xrbO/p/bdtnFknH/T1K28+2qf3Ianl/LG3nLJy9RtNls6tu3L5eAXyKmTJmiTz/9VKNGjdLhw4dVrFgx1a5dW998842uueaaPJtufHy8Hn/8cY0ZM0Y7duxQYmKivvzyS5X431G22rVrW3EdPXpUJUuW1IABA6wnhkvSE088oaJFi+q1117T9OnTVbZsWT311FMaOXJknsRcdeMGHiQDAAAKnM3fP9evBHWnbXZ1XJU5G+7pZ3fL8ltOsbgzX570W27q5EVbeM9mDE80QN4bPHiwNmzYoM2bNxd0KG5JTk5WdHS0kpKSSLABIJ+xDXaOfgGAguHJ9rcQ3ewAAAAAAMCly+1LxKdNm+aTCU6aNMkn4wEAAAAAoDBx+xJxPz8/rx5UZoyRzWZTampqrscB5BcuwwOAgsM22Dn6BQAKhifbX7fPYA8cOJAngQMAAAAA4ILbCfbcuXPzMAwAAAAAAC5tPOQMAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABt+/Bdsbf39+j+jabTSkpKd5MEgAAAACAQsmrBNvNN3zluj4AAAAAAJcKrxLsnTt3uiy7cOGCtm/frpdfflnLly/Xiy++qLZt23ozOQAAAAAACi2vEuxy5cplW165cmV16dJF999/v+655x5t2LDBm8kBAAAAAFBo5ctDzh555BHZbDZNnTo1PyYHAAAAAEC+y5cEOzQ0VNWqVdOqVavyY3IAAAAAAOS7fHtN15EjR3T8+PH8mhwAAAAAAPkqXxLsb775Rrt371aZMmXyY3IAAAAAAOQ7rx5ytnr1apdlxhgdPHhQ33//vd58803ZbDZdf/313kwOAAAAAIBCy6sEu02bNrLZbDnWM8aoWbNmevDBB72ZHAAAAAAAhZZXCXbZsmVdJtg2m03h4eGqUqWKevbsqZtvvln+/v7eTA4AAAAAgELLqwR7165dPgoDAAAAAIBLW749RVySfv/99/ycHAAAAAAA+SZfEuytW7dqwIABqlOnTn5MDgAAAACAfJfrBNsYo8OHD+vs2bMu6+zYsUMDBw5UYmKiFixYoLS0tNxODgAAAACAQs3jBPvYsWO6/fbbVbRoUZUsWVIRERFKTEzUhx9+aNU5ffq0RowYoRo1aujdd99VamqqatasqYULF/o0eAAAAAAACguPHnJ27tw5tWrVSn/88YeMMdbwP/74QzfccIPee+89NWvWTO3bt9f27dtljFFiYqImT56svn37+jx4AAAAAAAKC48S7Jdfftl6UNn111+vq6++WmfOnNFnn32mtWvXauLEiSpWrJi2bdumChUqaPr06br++uvzJHAAAAAAAAoTjxLsJUuWyGaz6fnnn9ewYcOs4RMmTNCAAQO0YMEC7dy5U926ddOCBQsUFhbm84ABAAAAACiMPLoH+/fff1d0dLSGDh2apeyBBx6QJAUGBuqNN94guQYAAAAAXFE8SrBPnDihihUrymazZSmrXLmyJKlSpUqKi4vzTXQAAAAAAFwiPEqwU1JSFBoa6rQsJCREkhQTE+N9VAAAAAAAXGJy/R5sAAAAAADwL48eciZJhw4d0ltvvZXr8oEDB3o6SQAAAAAACj2byfhC6xz4+fk5vf/a7YnZbEpJScl1eyC/JCcnKzo6WklJSYqKiirocADgisI22Dn6BQAKhifbX4/PYHuQj/u0LQAAAAAAhZlHCXZaWlpexQEAAAAAwCWNh5wBAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4QIAvRnLixAm9/vrr+uabb7Rnzx6dPXtWO3bssMo/++wzHT16VP3791dQUJAvJgkAAAAAQKHidYK9evVq9evXT0eOHJExRpJks9kc6vz000969NFHVaxYMXXt2tXbSQIAAAAAUOh4dYn4rl271KNHDx0+fFjdunXTnDlzlJiYmKVe//79ZYzRkiVLvJkcAAAAAACFllcJ9uOPP66TJ09qzJgx+uSTTzRo0CAVKVIkS70aNWqoSJEi2rhxozeTAwAAAACg0PIqwV6+fLnCwsL08MMP51i3QoUK2rdvnzeTAwAAAACg0PIqwf7nn39UuXJltx5cFhQUpOPHj3szOQAAAAAACi2vEuywsDCdOHHCrbp79+51evk4AAAAAACXA68S7KpVq2rv3r3as2dPtvV+/vln/fPPP6pTp443kwMAAAAAoNDyKsHu3bu3UlNTdd999yk1NdVpnVOnTunuu++WzWZTv379vJkcAAAAAACFllcJ9rBhw3TVVVdpyZIlat68uV599VUlJydLSj9r/dxzz6l27drauHGjatasqUGDBvkkaAAAAAAACpsAbxqHhYXp888/V/fu3bVu3TqtX7/eKmvUqJEkyRijypUr6+OPP1ZgYKB30QIAAAAAUEh5dQZbkqpUqaJNmzbpiSeeUIMGDRQQECBjjPz8/FSrVi098sgj2rhxo8qXL++DcAEAAAAAKJy8OoNtvxw8KipKo0eP1ujRoyVJZ86cUVhYmPfRAQAAAABwifDqDHaRIkVUsWJFXbx40WE4yTUAAAAA4ErjVYIdERGhihUrcm81AAAAAOCK51WCfdVVV+no0aO+igUAAAAAgEuWVwl2//799ddff2njxo2+igcAAAAAgEuSVwn2/fffr6ZNm6pv37766aeffBUTAAAAAACXHK+eIn7XXXepXLlyWrdunZo1a6bq1asrMTFR4eHhTuvbbDa98cYb3kwSAAAAAIBCyWaMMblt7OfnJ5vNJndHYbPZlJqamtvJAfkmOTlZ0dHRSkpKUlRUVEGHAwBXFLbBztEvAFAwPNn+enUGe/Lkyd40BwAAAADgskGCDQAAAACAD3j1kDMAAAAAAJCOBBsAAAAAAB/w6hLx1atXe9ymVatW3kwSAAAAAIBCyasEu02bNrLZbG7Xt9lsSklJ8WaSAAAAAAAUSl4l2GXLlnWZYF+4cEGHDh1SamqqgoKCFB8f782kAAAAAAAo1LxKsHft2pVt+alTp/Taa69p4sSJuuuuuzR+/HhvJgcAAAAAQKHlVYKdk4iICI0cOVKxsbEaMmSI6tSpoy5duuTlJAEAAAAAKBD58hTxgQMHqnjx4po5c2Z+TO6KZbPZcvybO3euT6bVpk0bde/ePdft3333XTVu3FjR0dGKiopS9erVdfvtt+vQoUNeT6N8+fIaPnx4rmMDAAAAgNzI0zPYGZUrV04///xzfk3uivTDDz84fL766qt1zz336MYbb7SGVaxYMb/DymLGjBl64IEHNHLkSE2bNk3GGG3evFnvvvuu9u3bp7i4OEnSiy++KH9//wKNtel7TRUbHasmJZuodGRpxYTEKDY0VsXDissYo2Pnjql4WHHVj6svSfr50M86fOawNczfz3n8qWmpbtfNiS/HlRcKe3yXKvoVwOUut9u5/GrnSX1f182POjm1z23b3JTlV5uCKCtMyzyzvKqbm/oF1S438i3B3rlzpy5cuJBfk7siNW3aNMuwsmXLOh1ekGbNmqXBgwfrqaeesoZ16dJFY8aMUVpamjWsRo0aBRFeFicunNCXf3+ZbZ3ooGjJJiWdT7KGlQgrofGNx6t9ufYOdb/e/bVmrJuhg2cO5lg3J74cV14o7PFdquhXAJe73G7n8qudJ/V9XTc/6kjKtn1u2+amrGuFrvp85+d53qYgynLqy/xc5nm93npTv6Da5ZbNGGN8PtZM7Gcs69Wrp40bN+b15PA/NptNTz75pEaPHi1J+uyzz/Tss8/qv//9r86dO6fq1atr6tSp6ty5s9Vm7ty5GjJkiDZu3KiJEydq9erVKlWqlB566CENHDjQqtemTRtFRERo0KBBevDBB/XPP/+ocePGeu2113I8Sx4eHq777rtPjz76aLb17NNYunSpJGnKlCmaOXOm1q5dq6FDh+rnn3/WVVddpaeeekqdOnWy2pUvX17du3dXtWrV9OSTT+rEiRO65ppr9Nprr6l48eJu9V1ycrKio6NV/aXq8g/N3dEtm9KfsP90m6cdNmyjVo2Skcmxbk58Oa68UNjju1TRr7gS2LfBSUlJioqKKuhwCo0rpV9yu53Lr3ae1Pd1XUl5XifzsMztBycO1tzf5nrcNjdlrvi6TUGUSdn3pZR/y9xeJ6/W29x+fzLK73aZebL99SrBnjZtmssyY4wOHjyotWvX6v/+7/8kSa+88opuv/323E4OHsqcYM+ePVtpaWmqWrWq/Pz8tGzZMj377LNasWKF2rRpI+nfBLt69eq64447VLNmTb3yyitavHixNm/ebJ1VbtOmjbZv367SpUtr/PjxSk1N1X333aeEhIQsl6pn1qpVK/322296/PHH1b17d5UsWdJpPWcJ9vTp01W1alWNGDFCCQkJmj59ujZs2KDdu3crNjZWUnqCnZaWpurVq+uee+7RkSNHdN9996lz5856//333eo7XyTYUvqXt0RYCX3R5wtJUqdFnRyOnrmqm9MlK6lpqT4bV14o7PFdquhXXCmulETSU1dCv+S0nZPSzzx91POjLJfYXvfJdTp05lCetvOkviSf1o0LTb+F7tDZvK+THT+bn9JMWs4VkaOc+jI/l3lerbe5/f7kx/fbk/0mT7a/Xl0iPmXKFJfvwZbSk2xJ8vPz0+jRo0muC1jGB3+lpaXpmmuu0W+//aZXX33VSrAz1h06dKik9EvPP/vsMy1evNjhsu0TJ05o06ZN1lnhEydO6I477tDevXtVpkwZl3G8+OKL6tWrl+644w5JUoUKFdSjRw+NHDlS5cuXz3YeLly4oBkzZqhr166S0u8pr1y5spYtW6abb77ZqmeM0SeffKLg4GBJ0vbt2/XEE08oLS1Nfn5Zn+13/vx5nT9/3vqcnJycbRzuMjI6cOaAfj6U/vyB7HYYMtZtVLJRtuP9+dDPPhtXXijs8V2q6FfgypJXv02FWU7bOSn9t7TZ+808Hnd+tfOkvid13UmIfVUnOyTXvpNTX+bnMs+r9TYvvz/etsur/SavEuyBAwe6TLBtNpvCw8NVpUoVde/eXRUqVPBmUvCBvXv3auLEifr666+1f/9+6wBIgwYNstTt2LGj9f/IyEglJCRo7969DnXq1q3rcMm1Pfm2J9ipqanKeIGEv7+/bDabatasqd9++01ff/21li9frm+//VbPP/+85syZo9WrV6tu3bou58HPz0/t2/97GUelSpUUFBSUJbbWrVtbybU9tosXL+rQoUNOz5hPnz5dU6dOdTldbx0+c9indd0dnyfT9aXCHt+lin4Frix5/dtUGLH9ApDffL3d8SrB9tUrn5D30tLS1LNnTyUlJWnatGmqVKmSwsPDNWnSJP39999Z6hcpUsThc1BQkM6dO5djHUlWvXbt2unbb7+1yleuXGmdKQ8KClLXrl2tM9FffvmlunXrpmnTpmnx4sUu5yM0NNSajl1gYKDHsWU2YcIEjRo1yvqcnJyshIQEl3F4qniYe/d+u1vX3fF5Ml1fKuzxXaroV+DKkte/TYWRu9uvF9u9qAYl/j1BsPHgRg39Zmiet/OkviSf1wXyUl6tt7n5/uTn99vX+0359hRxFKzt27dr06ZNWrJkia699lpr+NmzZ/Nsmq+88opOnjxpfa5atarLup06dVKdOnX0xx9/5Fk82QkODnY44+0r9ns77K/xKhFWQofOHHL60IvMdbNTP66+z8aVFwp7fJcq+hW4suTVb1Nh5u52rlmpZg73TDYr1Sxf2nlSX3Lvd9/dunGhcZJNeV4nJ342PxljctUWjrLry/xc5nm53ub2+5Of329f7zdlvRnVA23bttV9993nVt2RI0eqXbt23kwOXrAn0hnP/u7evVvff/99nk2zatWqatiwofUXGRkpSTp4MOu9VWfPntWePXtcPvDsUmR/OuG4xuPk7+cvfz9/63UN9jJXdXPiy3HlhcIe36WKfgVwucvtdi6/2nlS39d1xzcZn291XJXZZNOgGoNy1TY3Za74uk1BlLnTl/m5zPNqvc3t9yej/G7nLa8S7FWrVunnn392q+4vv/yiVatWeTM5eKFatWoqU6aMxo8fr6VLl2rBggXq1KmTSpcune+x1KpVS7fddpsWLlyoNWvWaMGCBerQoYOOHDmie++9N9/j8YUiQUUUHRztMKxEWIksj/5vX669nm7ztOLC4nKsmxNfjisvFPb4LlX0K4DLXW63c/nVzpP6vq6bH3WeafOMnmnzjMv2oxqOylXb3JSVDCupIYlDVCKsRJ62KYiynPoyP5d5Xq+3GRX277cvePWaLj8/P7Vo0UKrV6/OsW6rVq30ww8/6OLFi7mdHDyU+TVd69ev17Bhw/R///d/SkhI0IMPPqgVK1Zow4YN2rx5s6R/X9N1+PBhFStWzBpXzZo11bBhQ+u++8yv0JKkDRs2qFGjRg73Wjvz4osv6tNPP9X//d//WdOpXbu2xo4dq2uuucaq5+o92KdOnXIYX0REhEaPHq0pU6ZI+vc92LNnz7bqfPjhh+rXr5927tyZ45PKJcfXdMVGx6pJySYqHVlaMSExig2NVfGw4jLG6Ni5YyoeVty6tOTnQz/r8JnD1jBXR8RS01LdrpsTX44rLxT2+C5V9CsuZ1fC66hy40rrl9xu5/KrnSf1fV03P+rk1D63bXNTll9tCqKsMC3zzPKqbm7qF1Q7u3x7D7YnCXbZsmV1+vRpHT16NLeTA/LNlbYTAwCFCdtg5+gXACgYefYe7F9//VW//PKLw7BDhw7prbfectnm7NmzWrVqlfbu3etwdhIAAAAAgMuJRwn2Rx99pGnTpjkM27Ztm4YMGZJtO2OM/Pz8HF41AQAAAADA5cSjBLt8+fJq1aqV9fnbb79VVFSU6tat67S+zWZTWFiYKlWqpJtuukmNGjXyKlgAAAAAAAorjxLsQYMGadCgQdZnPz8/1apVSytXrvR5YAAAAAAAXEo8SrAzW7lypaKjo3OuCAAAAADAZc6rBLt169a+igMAAAAAgEuaX0EHAAAAAADA5cAnCfbixYvVo0cPlSpVSsHBwfL393f6FxDg1QlzAAAAAAAKLa8z3ttuu01z586VMSbHuu7UAQAAAADgUuTVGez3339fc+bMUaVKlbR8+XI1bNhQNptNO3bs0Lp16/Tss8+qUqVKCg0N1ZtvvqmdO3f6Km4AAAAAAAoVrxLsN998UzabTe+8847at2+v4OBgSVKFChXUsGFDjRgxQr/++qtatGihYcOG6fTp0z4JGgAAAACAwsarBHvTpk2Kj49Xo0aNXNYJCQnR3LlzdfHiRT322GPeTA4AAAAAgELLqwQ7OTlZpUqVsj4HBQVJkk6ePOlQLz4+XomJiVq1apU3kwMAAAAAoNDyKsEuVqyYzpw5Y32OjY2VJP31119Z6l64cEFHjhzxZnIAAAAAABRaXiXYCQkJOnDggPW5Tp06kqRFixY51NuyZYu2bt2qmJgYbyYHAAAAAECh5VWC3bp1ax0/ftx6Oni/fv1ks9n02GOPacyYMVq6dKlee+01de7cWWlpaercubNPggYAAAAAoLDxKsHu2bOnYmJitHLlSklSlSpV9MADDygtLU1PP/20rr32Wt19993avXu34uPj9fDDD/skaAAAAAAACpsAbxo3b95chw8fdhg2bdo01apVS3PnztWOHTsUFhamNm3aaOzYsSpZsqRXwQIAAAAAUFh5lWC70q9fP/Xr1y8vRg0AAAAAQKHk1SXivXv31vXXX6/z58/7Kh4AAAAAAC5JXiXYS5cu1datWxUcHOyreAAAAAAAuCR5lWCXLFlS/v7+vooFAAAAAIBLllcJdtu2bfX7778rKSnJV/EAAAAAAHBJ8irBfvDBB+Xv76/hw4crLS3NVzEBAAAAAHDJ8eop4vv27dODDz6ohx56SP/97381cOBAJSYmKjw83GWbVq1aeTNJAAAAAAAKJa8S7DZt2shms0mSfvvtN40bNy7b+jabTSkpKd5MEgAAAACAQsmrBLts2bJWgg0AAAAAwJXMqwR7165dPgoDAAAAAIBLm1cPOQMAAAAAAOlIsAEAAAAA8AESbAAAAAAAfMDte7Cvuuoqrydms9m0Y8cOr8cDAAAAAEBh43aC7YsHmvHEcQAAAADA5crtBHvlypVOh69bt04PPvigIiIidPvttysxMVElSpTQwYMH9dtvv+mNN97QqVOn9Mgjj6hRo0Y+CxwAAAAAgMLEZowxuW38xx9/qHHjxrrmmms0f/58hYeHZ6lz5swZ9e/fXytXrtT69etVrVo1rwIG8kNycrKio6OVlJSkqKiogg4HAK4obIOdo18AoGB4sv316iFn06ZNU2pqqubNm+c0uZaksLAwzZ07VykpKZo2bZo3kwMAAAAAoNDyKsFetWqVEhMTVbRo0WzrxcTEKDEx0eVl5gAAAAAAXOq8SrBPnDihkydPulX31KlTOnHihDeTAwAAAACg0PIqwS5btqy2bdumdevWZVtv3bp12rp1q8qWLevN5AAAAAAAKLS8SrD79+8vY4yuvfZaLVq0yGmdxYsXq1evXrLZbOrfv783kwMAAAAAoNDy6iniZ8+eVYsWLbRp0ybZbDaVLl1aNWrUsF7T9ccff2jv3r0yxqhu3br67rvvFBYW5sv4gTzBk1oBoOCwDXaOfgGAguHJ9tft92A7ExoaqhUrVmjEiBF69913tXfvXu3du9ehjp+fn2666SY9//zzJNcAAAAAgMuWVwm2JEVHR2vevHl65JFHtGzZMv355586efKkIiMjVa1aNXXu3Jl7rwEAAAAAlz2vE2y7hIQE3Xnnnb4aHQAAAAAAlxSvHnIGAAAAAADSkWADAAAAAOADPkmwFy9erB49eqhUqVIKDg6Wv7+/07+AAJ9dkQ4AAAAAQKHidcZ72223ae7cuXLnbV9evBEMAAAAAIBCzasz2O+//77mzJmjSpUqafny5WrYsKFsNpt27NihdevW6dlnn1WlSpUUGhqqN998Uzt37vRV3AAAAAAAFCpeJdhvvvmmbDab3nnnHbVv317BwcGSpAoVKqhhw4YaMWKEfv31V7Vo0ULDhg3T6dOnfRI0AAAAAACFjVcJ9qZNmxQfH69GjRq5rBMSEqK5c+fq4sWLeuyxx7yZHAAAAAAAhZZXCXZycrJKlSplfQ4KCpIknTx50qFefHy8EhMTtWrVKm8mBwAAAABAoeVVgl2sWDGdOXPG+hwbGytJ+uuvv7LUvXDhgo4cOeLN5AAAAAAAKLS8SrATEhJ04MAB63OdOnUkSYsWLXKot2XLFm3dulUxMTHeTA4AAAAAgELLqwS7devWOn78uPV08H79+slms+mxxx7TmDFjtHTpUr322mvq3Lmz0tLS1LlzZ58EDQAAAABAYeNVgt2zZ0/FxMRo5cqVkqQqVarogQceUFpamp5++mlde+21uvvuu7V7927Fx8fr4Ycf9knQAAAAAAAUNgHeNG7evLkOHz7sMGzatGmqVauW5s6dqx07digsLExt2rTR2LFjVbJkSa+CBQAAAACgsPIqwXalX79+6tevX16MGgAAAACAQsmrS8QBAAAAAEA6EmwAAAAAAHzAq0vEb731Vo/q22w2vfHGG95MEgAAAACAQsmrBHvu3Lmy2Wwyxjgtt9ls1v+NMSTYAAAAAIDLllcJ9uTJk12WXbhwQdu3b9dnn32m1NRUDR8+XBEREd5MDgAAAACAQivPEmy7f/75R926ddOqVav0/fffezM5AAAAAAAKrTx/yFnp0qW1YMEC/fzzz5oxY0ZeTw4AAAAAgAKRL08Rr1q1qqpWrar58+fnx+QAAAAAAMh3+faarqCgIO3evTu/JgcAAAAAQL7KlwT7yJEj2rJli8LCwvJjcgAAAAAA5Ls8T7A3bdqkXr166cKFC2rVqlVeTw4AAAAAgALh1VPEr7rqKpdlxhgdOnRI586dkzFG4eHhmjJlijeTAwAAAACg0PIqwd61a1eOdWw2m1q3bq2nnnpKtWvX9mZyAAAAAAAUWl4l2CtXrnRZZrPZFB4erkqVKik6OtqbyQAAAAAAUOh5lWC3bt3aV3EAAAAAAHBJy7fXdAEAAAAAcDnz6gy2lP4ws19//VV79+5VcnKywsPDVbFiRVWvXl1+fuTvAAAAAIArQ64T7D179mjGjBmaP3++kpKSspTHxsbq5ptv1rhx41SiRAmvgsxvy5Yt06xZs7R+/XqdOHFCMTExaty4se6++2517dpVNputoEPM0a5du1ShQgV98MEH6tu3b0GH47UjR46oePHimjNnjgYPHpx/E55eRgoJkhIaS2UaSRHFpYg4KTJeKtcsvc7utdKpg1JEifRhfv6eTSMt1ftxoHBhmQKAbxWW7aov48jNuNxtk1O97Mo9LZN8NyyhibTnJ8/qePs5t3Fktx/oqg9z2+++Xv7erFs5KSzf1QKMJVcJ9kcffaQhQ4bo5MmTMsY4rXPkyBE999xzevvtt/Xee++pQ4cOVtnFixe1bt06NW/ePHdR56EHHnhA06dPV69evTR79mzFx8fr4MGDWrJkiXr27KlPPvlE3bp1K+gwkZ/MRenv79P/MgotKskmnT3277CoUlLnx6UaPd0b9++fSF+Mk5L35X4cKFxYpgDgW4Vlu+rLOHIzLnfb5FQvu3LJszJn+0LeDLP5SSbNszrefs5tHK72A2v2lTZ/mLUPXQ3Pqd/ty9ZXy98ZX63bheW7WsCx2IyrDNmFZcuW6dprr1VKSoqioqJ04403qm3btqpcubIiIiJ06tQpbdu2TStWrNB7772n5ORkhYSEaOXKlWrSpInOnj2rXr16qVmzZpo0aVJezVeufPbZZ+revbsmT57s9J3d69evl5+fnxo0aJD/wXnoSjyDfeHCBQUEBPjk1oTk5GRFR0craXykooI9uWLhf3WvfyvnL+/vn0gLB0rK/BX0YBwoXFimgE9Y2+CkJEVFRRV0OIXGFdkvhWW76ss4cjMud9vkVK/ZPdLaWS7KXaUE2ZXBOzn1u9KXreSb5e/NupWTwvJdzaNYPNn+epSJnDp1SoMHD1ZKSoq6d++u7du368UXX1Tfvn1Vp04dVaxYUXXq1FHfvn314osvavv27erWrZvOnTungQMH6sSJE+rSpYu++uorj2Yovzz99NOKj4/Xgw8+6LS8UaNGVnL92WefqUOHDoqLi1NUVJSaNGmiL774wqH+lClTFBERkWU8ERERDgn8999/r1atWik6OlqRkZGqVauW5s2b53Z5bhljNHPmTFWpUkXBwcG66qqr9Mwzz2Sp99FHH6lq1aoKCQlR48aNtWHDhizzIKX3SZMmTRQaGqrixYvrP//5j06fPm2Vr1q1SjabTcuXL9eNN96oyMhIlStXTk888USWab722msqX768wsLC1K5dO23fvj1LnfLly2v48OF68sknVa5cOYWGhuro0aOSpLlz56p27doKCQlR6dKlNXHiRKWkpHjZY+743xf5i/Hpl6W4kpaaflTN6UbVzXGgcGGZAoBvubVdHSedS5YunM67v3PJ0rKxvokjN+Nyt82Z4znUM9IPs7Mfj1Mk13nHjX5fNtZHy1+5X7dyWrd9+R3Jl+9r3u6PeXSJ+GuvvabDhw+rbdu2WrJkSY5nCosVK6YlS5aoQ4cO+vbbb1WjRg0dOHBAsbGx6t27t1eB+1pKSoq+//579e3bVwEBOXfLzp071aNHD40ePVp+fn5atmyZunbtqhUrVqhNmzZuTzc5OVndunVTixYtNH/+fAUHB+v333/XiRMn3Cr3xr333qvXX39dEydOVJMmTbR27VqNGzdOoaGhuvvuuyVJmzZtUr9+/dSjRw8988wz2r17t/r376+LFy86jOvDDz/UDTfcoCFDhmjq1Knav3+/xo8fr+PHj+v99993qPuf//xHt9xyiz766CMtXrxY48aNU+3atdW5c2dJ0tKlS3XnnXdq8ODB6t+/vzZs2KD+/fs7nYdFixapSpUqeu655+Tv76+wsDA9/fTTGjt2rEaOHKmnnnpKf/zxhyZOnKjU1FTNmDHD6XjOnz+v8+fPW5+Tk5Nz3a+SkZL/Sb/no0JL51V2r3W8ZCU340DhwjIF4GO+/W26BLm1Xd0nzUjIt5DyPo7cjOt/bZ4o70bVtJzroBAx0sn9Oddxa/l7sW55vW4Xlu+qlB/7Yx4l2EuXLpXNZtMzzzzj9mW4/v7+euaZZ1SvXj0dOHBAMTEx+uqrr1SzZs1cBZxXjh49qvPnzyshwXHBG2OUmvrvEQ4/Pz/5+flp+PDh1rC0tDRdc801+u233/Tqq696lGBv3bpVSUlJmj59umrVqiVJateundvlubVjxw7Nnj1bL7/8su68805JUvv27XXq1ClNnTpVd955p/z8/DR9+nRVqFBBixYtspZ5aGiohgwZYo3LGKPRo0frhhtu0Ouvv24NL1GihLp3766HHnpIiYmJ1vA+ffpYZ7/btm2rpUuX6sMPP7QS7EceeUQtW7bUnDlzJEmdOnXS6dOnNX369CzzkZKSomXLliksLEySdPLkSU2ePFljx47VY489Jknq0KGDAgICNHr0aI0ZM0axsbFZxjN9+nRNnTo11/3p1KmDuSvLTT0UPJYpAB/Lk9+mSwnbSwB5JQ+3Lx4l2H/88YfKlCljJXruqlOnjsqUKaN//vlHy5cvV926dT1qnx/st6JnfkL4okWL1K9fP+vzsGHDNHv2bO3du1cTJ07U119/rf3791vtPb0/u2LFioqKitJ//vMfjRgxQtdcc42KFy/udrmrAwA5+frrryWlJ7sZL51u166dnnzySe3Zs0flypXT+vXrdd111zmM89prr3UY19atW7V79249++yzDuNq3bq1bDabNmzY4JBgd+zY0SHeatWqae/evZKk1NRUbdy4Mctl43379nWaYLdp08ZKriVp7dq1OnXqlPr16+cQS9u2bXX27Flt3rxZrVu3zjKeCRMmaNSoUdbn5OTkLAdbPBaRzdPzsyvLTT0UPJYpAB/Lk9+mS4m728ubPvz3ic55Yfda6V03nmfjThy5GZe7bdpPkb6eknM9XJ7cXf65WbdyWrd9+R3xlrux5OH+mEf3YB87dkzx8fG5mlB8fLxsNpvq16+fq/Z5rVixYgoODrYSPbt27dpp/fr1Wr9+vTXvaWlp6tmzp7777jtNmzZNK1eu1Pr169WlSxedO3fOo+kWLVpUX331lSIjI3XLLbeoZMmSatOmjf7v//7PrfJ58+YpMDDQ+rv11lvdmu6RI0dkjFGxYsUc2tvPIu/Zs0eStH//foeE3h5TYGCgw7gkqVevXg7jioiIUFpamjUuuyJFijh8DgoKsvrt8OHDSklJUVxcnEMdV696y1zPHkv9+vUdYqlevbrDfGUWHBysqKgoh7/cs0lRpbPfgJRrlv4kQ7l6gJob40DhwjIF4GO+/W26BLm7Xa3YVgoKz7u/im19F0duxuVum6bDcqin9KdjZ1eOQsYmRZby0fL3Yt3Kad325Xckv76vebg/5tEZ7MjIyFzf+3vixIksiVVhEhAQoObNm+ubb75Ramqq/P3T35FWtGhRNWzYUFJ6IihJ27dv16ZNm7RkyRKHs7lnz551GGdISEiWe5XPnz+vM2fOOAxr3Lixli1bprNnz2rlypUaPXq0rrvuOu3YsSPH8h49emj9+vXWuIoVK+bW/MbExMhms+m7776z5iujqlWrSko/MHL48GGHsuPHjzvMV0xMjCRp9uzZatKkSZZxlSpVyq2YJKl48eIKCAjQoUOHHIYfPOj8Mo7MVxzYY1m8eLHTo/wVKlRwO5bc+V88nWdk/549P//01wQsHKisT5B0cxwoXFimAOBbhWW76ss4cjMud9sEBOVc7+rh/3uKuLNy4+T/OZXBOzn1u6Qu/3uNly+Wf27XrZzW7cLyXS0ksXh0Brt8+fLavn27Dhw44NFE9u/fr+3bt6t8+fIetctvo0aN0r59+6x7d12xJ9IZE9Pdu3fr++8d35NcpkwZXbhwwUqUpfRLs129GS00NFRdu3bVf/7zH+3cuTPL2XBn5bGxsWrYsKH1524f2+/jPnr0qEN7+19kZKSk9CenL126VGlp/z4UY8mSJQ7jqlatmsqUKaO//vrL6bg8SbD9/f1Vv359ffTRRw7DP/zwQ7faN2vWTGFhYdq7d6/TWJzdf51roTHpfxlFlXL/0f81eqbXjcp0VYgn40DhwjIFAN8qLNtVX8aRm3G52yaneh0fzqb87fQ/T8qc7Qt5M8zm53kdbz/nNg6n+4GlpWYj/ncG1Z3hOfX7/5atr5a/N+tWTgrLd7UQxOLRGex27dpp48aNevjhh/XCCy+43e7hhx+WlP6wqcKsW7duGj9+vCZNmqRffvlFN9xwg+Lj45WUlKQ1a9bowIEDioyMtBLK8ePHKzU1VadPn9bkyZNVunRph/F16dJF4eHhuuOOOzRu3Djt3btXzz33nENi/tlnn+mNN95Qr169VLZsWR04cECzZs1S8+bNFRISkmN5Tn788ccsw4oXL67WrVtr2LBhuuWWWzRmzBg1adJEFy9e1NatW7Vy5UoriZ4wYYIaNWqkPn366M4779SuXbv01FNPKSgoyLov22az6emnn9aNN96o06dPq1u3bgoPD9fu3bv12Wef6bHHHlOVKlXcXg4TJ07UtddeqyFDhlhPEX/vvffcahsdHa1p06Zp7Nix2rt3r6655hr5+fnpr7/+0scff6xFixY53LPtFluglNBYKtNIiiguRcRJkfGO96+cOph+L0e5Zp4dEavRU6rWzbtxoHBhmQKAbxWW7aov48jNuNxtk1O9nMo9LZN8NyyhibTnJ8/qePs5t3Fktx/Yfopnw3Pqd18uf2/WrZwUlu9qQcdiPLBr1y4THBxs/Pz8zBNPPOFWm8cff9zYbDYTHBxsdu7c6cnkCszSpUtNly5dTGxsrAkICDBxcXGmS5cu5t133zWpqanGGGPWrVtnGjVqZEJCQkzlypXNvHnzzKBBg0xiYqLDuL744guTmJhoQkJCTNOmTc0vv/xiwsPDzeTJk40xxvz555+mT58+JiEhwQQFBZlSpUqZwYMHm/3797tV7srOnTv/98LDrH+tW7c2xhiTlpZmZs2aZWrWrGmCgoJM0aJFTdOmTc3TTz/tMK5FixaZKlWqmODgYNOgQQOzZs0a4+/vb5599lmHesuXLzetW7c24eHhJjw83CQmJpr777/fnDhxwhhjzMqVK40ks379eod23bp1s2Kye/nll01CQoIJCQkxrVu3NmvXrjWSzJw5c6w65cqVM8OGDXM6//PnzzeNGjUyoaGhJioqytSrV8889NBD5uLFi9n2m11SUpKRZJKSktyqDwDwHbbBztEvAFAwPNn+2oxxcb2yCw8//LAmT54sm82m5s2b695779U111xj3fsqpT8MbcWKFXr++eety6YnT56sSZMmeX9EAAXu66+/VocOHbRq1SqnT+S+HCQnJys6OlpJSUlX3kNlAKCAsQ12jn4BgILhyfbXo0vEJemhhx7SoUOH9MILL+j777+3EugiRYooIiJCp06dsh6EZs/dhw4dSnJ9CRs6dKjatWun2NhY/fbbb3r44YdVr149tWyZNy9nBwAAAIBLkccJtiTNmjVLbdq00aRJk/THH39ISn+y9PHjxx3qVatWTVOnTnV4jzQuPSdOnNA999yjI0eOKDo6Wp07d9bMmTPdet82AAAAAFwpPL5EPLONGzdqzZo12rNnj06ePKnIyEglJCSoZcuWatCgga/iBPIVl+EBQMFhG+wc/QIABSNPLxHPrEGDBiTSAAAAAIArHtf4AgAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPkGADAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPkGADAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPkGADAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPkGADAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPkGADAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+AAJNgAAAAAAPkCCDQAAAACAD5BgAwAAAADgAyTYAAAAAAD4AAk2AAAAAAA+QIINAAAAAIAPkGADAAAAAOADJNgAAAAAAPgACTYAAAAAAD5Agg0AAAAAgA+QYAMAAAAA4AMk2AAAAAAA+MBln2AvW7ZMXbt2VfHixRUYGKgSJUqoR48e+uyzz2SMKejwPPL3339r6NChqlChgoKDg1W0aFF17NhRn376qTUvU6ZMUUREhE+mN3fuXNlsNh05csQn48vO4MGDVbNmzTyfDgAAAADklYCCDiAvPfDAA5o+fbp69eql2bNnKz4+XgcPHtSSJUvUs2dPffLJJ+rWrVtBh+mW9evXq1OnTipatKhGjx6tmjVr6uTJk1q+fLmuv/56ffHFF2rdunVBh3nZqTn5SwWFhKl+uaJqWC5GV1eMlZ+fTUdOnVdcZIgaV4iRv59NqWlG63Ye06GT5xyG+0pejx8A3MX2CJ66FNeZvIo5t+N1t5079bKrk5syZ8Ml5WpYg3JFtXH3cZefc9MmN+PwZh5y2jfMaRl5W56f65snLsXtgPRv3Lv2H3a7zWWbYH/22WeaPn26Jk+erClTpjiU9evXT/fdd5/8/C6NE/jnz59Xv379VLJkSa1du1ZFihSxyrp3765hw4bJZiv8K+ilKsVI63Yd17pdx/XitzscyuKjQ9SzTrw++e9+7U865zB8co8a6lwz3uvpf7F5v6Z++nuejR8A3MX2CJ66FNeZvIo5t+N1t5079bKrI8njMmf7QEXCAiVJJ85c9HiYn01Ky3CBaebPuWmTm3F4Mw/Z7RvmtM+Y0zL0ZB3K6/XNE5fidkByjDvt/Bm3210aGWYuPP3004qPj9eDDz7otLxRo0Zq0KCBpPRkvEOHDoqLi1NUVJSaNGmiL774wqG+q0uvIyIiHBL477//Xq1atVJ0dLQiIyNVq1YtzZs3z+1yZz744APt3r1bM2bMcEiu7apWraoqVao4DPv111/VokULhYWFqWbNmvryyy+ztJs7d65q166tkJAQlS5dWhMnTlRKSkqWetu3b1fbtm0VFham8uXL680337TKPvnkE9lsNm3bts2hTVJSksLCwvT8889Lkn777Td17dpVsbGxCgsLU9WqVfXEE09kmdaqVatUr149hYeHq3Hjxtq4caNDuTFGM2fOVJUqVRQcHKyrrrpKzzzzjEN7m82WpV1qaqpKlCihsWPHZpmmN/YnndMrq3c6bDAk6UDSOf3nnZ/1xeb9Xo3/i8379Z93fs6z8QOAu9gewVOX4jqTVzHndrzutnOnXnZ17n7nZ93tYZmrfaATZy46JJyeDEvLdPdm5s+5aZObcXgzD676Jad9xumf/57tMsypPOM6lNfrmycuxe2A5Dpud1yWZ7BTUlL0/fffq2/fvgoIyHkWd+7cqR49emj06NHy8/Oz7ttesWKF2rRp4/Z0k5OT1a1bN7Vo0ULz589XcHCwfv/9d504ccKtcldWrVolf39/dejQwa04Ll68qJtvvlkjRozQQw89pOnTp6tPnz7avXu3YmNjJaUfgBg7dqxGjhypp556Sn/88YcmTpyo1NRUzZgxw2F8/fv311133aVx48bp/fff12233aZSpUqpc+fO6tatm0qXLq0333xT06dPt9rMnz9faWlpuvnmmyVJPXv2VFxcnN544w1FR0dr+/bt2rt3r8N0Dhw4oBEjRmj8+PGKiorS+PHj1atXL+3YsUOBgelHCO+99169/vrrmjhxopo0aaK1a9dq3LhxCg0N1d13361WrVqpdOnSmj9/vnUARZJWrFihQ4cOacCAAW71obeMJJvSj/Z2qFEyV5fApKYZTf30dzl7UoAvxg8A7mJ7BE+5s85M+eR3Na9UrNCsM6lpRpM/+c3nMed2vO62a3pVbI71Jn/8m2STyzquXFpPK7o02fv4tTU7s10+2ZVnXIck5en65sn6n1ffqbyWXdzuuCwT7KNHj+r8+fNKSEhwGG6MUWpqqvXZz89Pfn5+Gj58uDUsLS1N11xzjX777Te9+uqrHiXYW7duVVJSkqZPn65atWpJktq1a+d2uSv//POPihcvrtDQULfiuHDhgmbMmKGuXbtKkipWrKjKlStr2bJluvnmm3Xy5ElNnjxZY8eO1WOPPSZJ6tChgwICAjR69GiNGTPGSsQlaeDAgZowYYIkqVOnTtqxY4emTZumzp07y9/fX0OGDNGbb76pRx55RP7+/pKkN998U9ddd51iYmJ05MgR/fXXX3r22WfVo0cPSdI111yTJe5jx47p22+/VWJioiQpJCREHTp00E8//aQWLVpox44dmj17tl5++WXdeeedkqT27dvr1KlTmjp1qu688075+fnphhtu0IIFC/Tkk09al87Pnz9fVatWVb169Zz22fnz53X+/Hnrc3Jyslt9nR2j9KOV63Ye09UVY3Osn9m6nceyPWrm7fgBwF1sjwpGXvw25Rd31pkDyedUa8ry/AvKS3kVc27Ha29Xd9pXOdY7ePJ8tnVQ8DKfRfek3JN1yNv1zZfr/6W4HXDHZXmJuP2J2pnvS160aJECAwOtvxEjRkiS9u7dq0GDBql06dIKCAhQYGCgli9frq1bt3o03YoVKyoqKkr/+c9/tHDhQh0+fNijcmOMUlJSrL+0tDRruCf3WPv5+al9+/bW50qVKikoKMg6Y7x27VqdOnVK/fr1c5he27ZtdfbsWW3evNlhfL169cryecOGDdbBittuu0379++3LqvfvHmz1q9fr9tuu02SFBsbq3LlymnChAmaN29eljPXdqVKlbKSa0mqUSP9nh97/a+//lqS1KdPH4e427VrpwMHDmjPnj2SpAEDBmjv3r367rvvJKUfcPjoo4904403uuyz6dOnKzo62vrLfHDGG4dOen5piSftcjt+AHAX26OCkZe/TXmNdQHAleqyPINdrFgxBQcHZ0nk2rVrp/Xr10tKv2RZSj9j3bNnTyUlJWnatGmqVKmSwsPDNWnSJP39998eTbdo0aL66quvNHnyZN1yyy1KSUlRy5YtNWvWLNWqVSvH8nnz5mnIkCHW+AYNGqS5c+eqTJky+uabb3Tu3DmFhITkGEdoaKiCgoIchgUGBurcufQfO/trt+rXr++0vT1RtYuLi8vy+eLFizpy5IhKlCih8uXLq0OHDnrjjTfUrVs3vfHGGypXrpx1dt5ms+nLL7/Ugw8+qGHDhun06dOqX7++nnnmGbVq1coab+b7y+3zkDFuY4yKFSvmMu5y5cqpYcOGqly5subPn6+WLVtq2bJlOnHiRLaXh0+YMEGjRo2yPicnJ/tsRyYuMudl5k273I4fANzF9qhg5OVvU15zd12YO6SR9STmgrZu5zENnrM+x3qexpzb8brbblznqnr8iy1ux4PL19whjSQpT9c3T9b/vPpO5TV343blskywAwIC1Lx5c33zzTdKTU21LlsuWrSoGjZsKOnf5G379u3atGmTlixZomuvvdYax9mzZx3GGRISoosXHR9icP78eZ054/hEucaNG2vZsmU6e/asVq5cqdGjR+u6667Tjh07cizv0aOHdQBAkpVIXnPNNXrjjTf01VdfWZdYeyMmJn0FXrx4sdMf6goVKjh8PnTokEqXLu3wOTAw0CHRveOOO3TjjTfqn3/+0bvvvqthw4Y5PKW9atWq+uCDD3Tx4kWtXbtWDzzwgHr06KF//vnH7fd2x8TEyGaz6bvvvstyAME+DbsBAwbopZde0vPPP6/3339fDRo0UOXKlV2OOzg4WMHBwW7F4S6bpJLRIbneYDSuEKP46BAdSDrn9B4Qb8cPAO5ie1Qw8uK3Kb+4u860rFy80Nx72bJy8TyJObfjdbfdbS2u0ls/7M62XomoYEk2HUx2XgcFz88mGeP6vvfsyjOuQ5LydH3zZP3Pq+9UXssp7pxclpeIS9KoUaO0b98+6x5jV+yJdMaEbffu3fr+++8d6pUpU0YXLlywEmUp/ZJl++XomYWGhqpr1676z3/+o507d1pnYbMrj42NVcOGDa2/8uXLS5L69u1rXWLt7P6rbdu2eXQ5e7NmzRQWFqa9e/c6TM/+l/H+a0n66KOPsnxu0KCBdeBCkq699loVLVpUN954o44ePepwJj6jwMBAtW7dWuPHj1dycrL27dvndtz2M+JHjx51GndkZKRVd8CAATp8+LA+/fRTffrpp9leHp4X7JuIyT1q5HqD4e9ns16NkXkMvhg/ALiL7RE8dSmuM3kVc27H6267oAC/HOtN6ZmoKT2zr+NpGXzD9r+/O1pWsD57Wi79uw7l9frmyfp/KW4HpOzjdsdlm2B369ZN48eP16RJk9SnTx8tXLhQa9as0dKlSzVu3DgdOHBAkZGRqlatmsqUKaPx48dr6dKlWrBggTp16uRwxlaSunTpovDwcN1xxx368ssv9cYbb2jChAkOiflnn32m3r176+2339a3336rBQsWaNasWWrevLlCQkJyLHclODhYCxcu1L59+9SgQQO9+OKLWr16tT7//HONGjVKdevW1f797j/iPjo6WtOmTdPYsWM1btw4ffHFF1q+fLlefvlldenSJctZ+bfeekvTp0/Xl19+qSFDhmjNmjV66KGHHOoEBgZq0KBBWr16tdq3b6+yZctaZb/++qs6dOig119/XStXrtSSJUv0yCOPqHz58qpYsaLbcVepUkXDhg3TLbfcokcffVRff/21li1bpueee07XXXedQ91q1aqpXr16Gj58uM6cOaMbbrjB7el4Ij46RHe1qqD4aMflVzI6RC/dXN/rd/t1rhmvl26ur5J5NH4AcBfbI3jqUlxn8irm3I7X3Xbu1Muuzss319fLHpa52gcqEhZovR/a02GZ86zMn3PTJjfj8GYeXPVLTvuME7rWyHYZ5lSecR3K6/XNE5fidkByHbdbzGVu6dKlpkuXLiY2NtYEBASYuLg406VLF/Puu++a1NRUY4wx69atM40aNTIhISGmcuXKZt68eWbQoEEmMTHRYVxffPGFSUxMNCEhIaZp06bml19+MeHh4Wby5MnGGGP+/PNP06dPH5OQkGCCgoJMqVKlzODBg83+/fvdKs/J7t27zd13323KlStnAgMDTZEiRUz79u3N/PnzTVpamjHGmMmTJ5vw8PAsbTPGaTd//nzTqFEjExoaaqKioky9evXMQw89ZC5evGiMMWbOnDlGklm7dq1p3bq1CQkJMWXLljWvvvqq0/jWrl1rJJkFCxY4DD948KC5+eabzVVXXWWCg4NNXFyc6dOnj9m6datVx1l/Hz582Egyc+bMsYalpaWZWbNmmZo1a5qgoCBTtGhR07RpU/P0009nieeJJ54wkkzr1q1d9qkrSUlJRpJJuG+hqTh+qen30vfm8c//MKu3HDLfbTtslmzaa9ZuP2JSUtP7PSU1zazdfiTLcF/J6/EDgLvyY3tk3wYnJSX5fNyXsku1Xy7F37C8ijm343W3nTv1squTmzJnw3M77PzF1Gw/56ZNbsbhzTzktG+Y0zLytjy3dX3RLr/HmR/scb+35g+3t782Y1xc4wx4aNKkSXrxxRf1zz//XLL3jNklJycrOjpaSUlJioqKKuhwAOCKwjbYOfoFAAqGJ9vfy/IhZ8hfW7Zs0ZYtWzRr1iwNGzbskk+uAQAAACA3SLDhtbvuuks//vijOnfurAkTJhR0OAAAAABQIEiw4bVVq1YVdAgAAAAAUOAu26eIAwAAAACQn0iwAQAAAADwARJsAAAAAAB8gAQbAAAAAAAfIMEGAAAAAMAHSLABAAAAAPABXtMFOGGMkSQlJycXcCQAcOWxb3vt22Kk47cJAAqGJ79LJNiAE0ePHpUkJSQkFHAkAHDlOnr0qKKjows6jEKD3yYAKFgnT57M8XeJBBtwIiYmRpL0999/s3OXSXJyshISErRnzx5FRUUVdDiFBv3iGn3jHP3iWlJSksqWLWtti5HOm9+mRo0aaf369bmqk3l4dp+d/d/+rzfrfE7xuxt7buP/5ptvvPq+5lX87v7fm/gLet0prH2fXcyXQ9/nR/yX0vfWGKOTJ0+qVKlSObYjwQac8PNLfzxBdHQ0O74uREVF0TdO0C+u0TfO0S+u2bfFSOfNb5O/v3+ObVzVyTw8u8/O/p+5fm7W+Zzidzd2b+PP7fc1r+L39P950feexH859b07MV/KfZ8f8V9q31t3D2zyywUAAHCZGzZsWK7rZB6e3Wdn/3dn2rmNLadyZ8Mvp/g9/X9usO64HpZTzJdy37s7/dzEllP5pfK9/f/27jwuymr/A/hnlMUBdWBkFyGuLJUguKOiAhmLAS65JF0DI7uW4gb6wjQHNQMrzaVsodJbSXrNBa+JW4KkCCEp7kWKCiiyCaOgw3buH/5mfjzMDMzIwDDwfb9evF5ynjPPfM93jgOH5znfUYbHqIIIIXLEYjEEAgEqKyvpylITlBvFKC/KUW4Uo7woR7lRTNfzosvx63LsgG7Hr8uxAxS/NmkrdrqCTYgChoaGEIlEMDQ01HYoHQ7lRjHKi3KUG8UoL8pRbhTT9bzocvy6HDug2/HrcuwAxa9N2oqdrmATQgghhBBCCCEaQFewCSGEEEIIIYQQDaAFNiGEEEIIIYQQogG0wCaEEEIIIYQQQjSAFtiEEEIIIYQQQogG0AKbEEIIIYQQQgjRAFpgE6LAtm3b4ODggB49emDIkCH47bfftB1Sm4mNjQWPx+N8WVlZyY4zxhAbGwsbGxvw+Xx4e3vjypUrnHNIJBJERkbCzMwMxsbGCAkJQUFBQXsPpdXS0tIQHBwMGxsb8Hg8HDhwgHNcU7l48OABZs2aBYFAAIFAgFmzZqGioqKNR/fsWspLeHi43Bzy9PTk9OmMeYmLi8OwYcPQq1cvWFhYYNKkSfjzzz85fbrqnFElN1113rSn6upq2NvbIzo6WtuhqOXhw4cYNmwYPDw84ObmhoSEBG2HpJb8/Hx4e3vjxRdfxMCBA7Fnzx5th6SWyZMnw9TUFFOnTtV2KCo5dOgQXFxc4OTkhG+++Ubb4ahN1/ItpevzvE3fZxghhGPXrl1MX1+fJSQksKtXr7KFCxcyY2Njdvv2bW2H1iZEIhEbMGAAu3fvnuyruLhYdjw+Pp716tWL7d27l126dInNmDGDWVtbM7FYLOszd+5c1rdvX3b8+HH2xx9/MB8fH+bu7s7q6uq0MaRndvjwYbZixQq2d+9eBoDt37+fc1xTuQgICGCurq4sPT2dpaenM1dXVxYUFNRew1RbS3kJCwtjAQEBnDlUVlbG6dMZ8+Lv78+2b9/OLl++zC5cuMBeeeUVZmdnxx49eiTr01XnjCq56arzpj299957bNq0aSwqKkrboailrq6OVVVVMcYYq6qqYg4ODqy0tFTLUanu7t277Pz584wxxu7fv8/69u3Lmfsd3cmTJ9nBgwfZq6++qu1QWlRbW8ucnJxYQUEBE4vFzNHRUe59pKPTpXw3puvzvC3fZ2iBTUgTw4cPZ3PnzuW0Pf/88ywmJkZLEbUtkUjE3N3dFR5raGhgVlZWLD4+Xtb25MkTJhAI2JdffskYY6yiooLp6+uzXbt2yfoUFhaybt26sSNHjrRp7G2p6UJSU7m4evUqA8AyMjJkfc6ePcsAsOvXr7fxqFpP2QJ74sSJSh/TFfLCGGPFxcUMADt16hRjjOZMY01zwxjNm7b2119/sSlTprDt27fr3AK7sbKyMmZnZ8dKSkq0Hcozc3NzY3fu3NF2GGpJSUnRiQXfmTNn2KRJk2TfL1iwgCUmJmoxomejK/luji7OcylNv8/QLeKENFJTU4Ps7Gz4+flx2v38/JCenq6lqNpebm4ubGxs4ODggNdeew03b94EAOTl5aGoqIiTD0NDQ4wbN06Wj+zsbNTW1nL62NjYwNXVtVPlTFO5OHv2LAQCAUaMGCHr4+npCYFAoNP5Sk1NhYWFBZydnTFnzhwUFxfLjnWVvFRWVgIAhEIhAJozjTXNjVRXnTctbbsAWr9VKTo6GnFxcRqKmKs94q+oqIC7uztsbW2xbNkymJmZaSj69olf6ty5c2hoaEC/fv1aGfVT7Rl7e2jteO7evYu+ffvKvre1tUVhYWF7hA5At18PTcau6XmuCk3E31bvM7TAJqSR0tJS1NfXw9LSktNuaWmJoqIiLUXVtkaMGIHvv/8eR48eRUJCAoqKijBq1CiUlZXJxtxcPoqKimBgYABTU1OlfToDTeWiqKgIFhYWcue3sLDQ2XwFBgZi586dOHnyJDZs2ICsrCz4+vpCIpEA6Bp5YYxhyZIl8PLygqurKwCaM1KKcgN07XlTVVUFd3d3fPbZZwqP7969G4sWLcKKFStw/vx5jBkzBoGBgbhz546sz5AhQ+Dq6ir3dffuXSQlJcHZ2RnOzs46GT8AmJiYICcnB3l5eUhMTMT9+/d1Kn4AKCsrwxtvvIGvv/5a52JvL60dD2NM7jE8Hq9NY25ME6+Htmgq9raY56rQRPxt9T6jp5GzENLJNH1zZoy16xt2ewoMDJT9283NDSNHjkT//v3x73//W1Zw6Fny0VlzpolcKOqvy/maMWOG7N+urq4YOnQo7O3t8csvv2DKlClKH9eZ8jJ//nxcvHgRp0+fljvW1eeMstx05XkTGBjIee9tauPGjYiIiMBbb70FANi0aROOHj2KL774QnZVOjs7W+njMzIysGvXLuzZswePHj1CbW0tevfujVWrVulE/I1ZWlpi4MCBSEtLw7Rp01ofPNonfolEgsmTJ2P58uUYNWqURuJur9jbU2vH07dvX84V64KCAs4dLW1NE6+Htmgi9raa56rQZO41/T5DV7AJacTMzAzdu3eXu/JRXFwsdxWqszI2Noabmxtyc3Nl1cSby4eVlRVqamrw4MEDpX06A03lwsrKSuFfSEtKSjpNvqytrWFvb4/c3FwAnT8vkZGROHjwIFJSUmBraytrpzmjPDeKdLV5o4wmtirFxcUhPz8ft27dwieffII5c+ZobHHdEk3Ef//+fYjFYgCAWCxGWloaXFxcNB6rIpqInzGG8PBw+Pr6YtasWW0RpkKdbZubKuMZPnw4Ll++jMLCQjx8+BCHDx+Gv7+/NsKVo8uvhyqxa2ueq0KV+NvyfYYW2IQ0YmBggCFDhuD48eOc9uPHj7f7X+a0RSKR4Nq1a7C2toaDgwOsrKw4+aipqcGpU6dk+RgyZAj09fU5fe7du4fLly93qpxpKhcjR45EZWUlfv/9d1mfzMxMVFZWdpp8lZWVIT8/H9bW1gA6b14YY5g/fz727duHkydPwsHBgXO8K8+ZlnKjSFeZNy3R9a1Kmoi/oKAAY8eOhbu7O7y8vDB//nwMHDiwLcKVo4n4z5w5g927d+PAgQPw8PCAh4cHLl261Bbhcmhq7vj7+2PatGk4fPgwbG1tkZWVpelQVaLKePT09LBhwwb4+Phg0KBBWLp0Kfr06aONcOWo+np0lHw3pkrs2prnqlAl/rZ8n6FbxAlpYsmSJZg1axaGDh2KkSNH4uuvv8adO3cwd+5cbYfWJqKjoxEcHAw7OzsUFxfjgw8+gFgsRlhYGHg8HhYtWoQPP/wQTk5OcHJywocffggjIyOEhoYCAAQCASIiIhAVFYU+ffpAKBQiOjoabm5uGD9+vJZHp55Hjx7h77//ln2fl5eHCxcuQCgUws7OTiO5eOGFFxAQEIA5c+bgq6++AgC8/fbbCAoKarcrNOpqLi9CoRCxsbF49dVXYW1tjVu3buG9996DmZkZJk+eDKDz5mXevHlITExEUlISevXqJfuhLRAIwOfzNfb/pzPm5tGjR1123qhKU1uVwsPDNRSReloT/5AhQ3DhwoU2iEp1rYnfy8sLDQ0NbRGWSlo7d44eParpkFqlpfGEhIQgJCSkvcNSWUvxd7R8N9Zc7Nqe56poLv42fZ/RSC1yQjqZzz//nNnb2zMDAwM2ePBgzkfLdDbSz+XV19dnNjY2bMqUKezKlSuy4w0NDUwkEjErKytmaGjIxo4dyy5dusQ5x+PHj9n8+fOZUChkfD6fBQUF6eRHNaSkpDAAcl9hYWGMMc3loqysjL3++uusV69erFevXuz1119nDx48aKdRqq+5vFRXVzM/Pz9mbm7O9PX1mZ2dHQsLC5Mbc2fMi6KcAGDbt2+X9emqc6al3HTledMUmnz0nUQiYd27d2f79u3j9FuwYAEbO3ZsO0fXMopfe3Q5dkV0fTy6HL8ux85Yx4ufFtiEEEIIIVrS9BdDxhgbPnw4e+eddzhtL7zwAouJiWnHyFRD8WuPLseuiK6PR5fj1+XYGet48dMt4oQQQggh7ail7SgdfasSxa89uhy7Iro+Hl2OX5djBzp4/G2+hCeEEEIIITItbUdhrGNvVaL4tUeXY1dE18ejy/HrcuyMdez4eYwp+IR2QgghhBBCCCGEqIU+posQQgghhBBCCNEAWmATQgghhBBCCCEaQAtsQgghhBBCCCFEA2iBTQghhBBCCCGEaAAtsAkhOi0zMxO+vr7o06cPeDwevL29tR1Su7l16xZ4PB7Cw8O1HYpWpKamgsfjITY2ltP+3HPP4bnnntNKTIQQQgjp2miBTUgXwePx1PrSBZWVlQgODsYff/yB0NBQiESiLrvYVEd1dTU2b94MHx8fmJubQ19fH0KhEF5eXoiPj0dJSYm2Q9Q5O3bsAI/Hw44dO7QdCiGEEEK0SE/bARBC2odIJJJrW716NQQCARYtWtT+AWlAVlYWSkpKEBcXh5iYGG2HoxNycnIwceJE3L59G/b29ggJCYGlpSXEYjEyMjKwfPlyxMXF4e7duzA2NtZ2uM/k119/1XYIhBBCCOmiaIFNSBfR9DZa4OkC28TEROExXXD37l0AgJWVlZYj0Q0FBQXw8/NDaWkpNmzYgIULF6J79+6cPufPn8f8+fNRW1urpShbr3///toOgRBCCCFdFN0iTgjhaLyv9/r165gyZQrMzMzA4/Fw69YtAMD+/fsxc+ZMODo6wsjICAKBAGPGjMHevXubPd/NmzcxdepUmJqawtjYGOPHj0dOTo7cY3JzczF79mw4ODigR48eMDMzw+DBgxEVFSXrw+PxEBYWBgCYPXu27Nb21NRUWZ8rV65gxowZsLCwgKGhIRwcHLB48WKUl5fLPad0325FRQUWLFiAfv36QU9PDzt27OCM4dq1awgKCoKJiQlMTU0xc+ZMlJaWAni6H/zll19G7969YWpqijlz5qCqqkphntPS0hAcHAwzMzMYGhrCyckJK1euRHV1tVzf+vp6rF+/Ho6OjujRowccHR0RFxeHhoYG5S+kAitWrEBxcTHee+89LFmyRG5xDQCDBg3CqVOn0Lt3b077oUOH4OPjA4FAAD6fDw8PD2zatAn19fUKn0vV/qrMt8ePHyMmJgb9+vVDjx494OrqioSEBKXjVLQHOzY2VjY//vOf/2Dw4MHg8/mwtrbGggUL8PjxY07/mpoabN26Ff7+/ujXrx8MDQ1hYWGBKVOm4Pz585y+4eHhmD17NgDuXGy61eLhw4cQiUQYMGAA+Hw+TExMEBAQgNOnTysdS1Ph4eHg8Xi4efMmPv30UwwYMACGhoa0NYIQQgjpIOgKNiFEob///huenp4YMGAAwsLCUF5eDgMDAwDA8uXLYWBgAC8vL1hbW6OkpAQHDx7E1KlTsWXLFkRGRsqd79atWxgxYgRefPFFvPnmm7hx4waSkpLg4+ODa9euwdLSEsDTq9LDhw9HVVUVXnnlFcyYMQOPHj1Cbm4utm7dig0bNgB4esv7hQsXkJSUhIkTJ8LDwwMAZAur9PR0+Pn5QSKRYOrUqXjuueeQkZGBTZs24ZdffsHZs2fRp08fTowSiQS+vr54+PAhgoODYWBgIIsLAPLy8jBq1CgMHToUb731Fs6dO4ddu3YhPz8f69evx8svv4yXX34Zb7/9NlJTU/HNN98AgNxi8Msvv8S7774LU1NTBAcHw9zcHFlZWVi3bh1SUlKQkpIiyzUAvP322/juu+/g4OCAefPm4cmTJ9i4cSPS09NVfj2rq6uxa9cu8Pl8REdHN9tXT4/7o2Hz5s1YtGgRhEIhQkNDYWxsjP/+979YvHgxfvvtN/z888+cxaS6/QHl862hoQEhISE4ceIE3NzcEBoairKyMixevBg+Pj4qj1/q888/R3JyMiZOnAhvb28cOXIEW7duRVlZGXbu3CnrV15ejkWLFmHMmDGYMGECTE1NcfPmTRw8eBDJyclIS0vDsGHDAACTJk1CRUWF3FxsrLy8HGPHjsWVK1cwZswY+Pv7o7KyUvZ/YM+ePZg0aZLK44iMjERGRgZeeeUVBAUFceYpIUT7MjMzsXz5cuTk5KC8vBzjxo3j/AG4M7t16xYcHBwQFhbWJetSpKamwsfHByKRiHOHoPT3E+kfj0knxgghXRYAZm9vz2nLy8tjABgA9v777yt83I0bN+TaHj58yNzc3JhAIGBVVVUKzxcfH895zMqVKxkAFhcXJ2vbsmULA8A2b94s9xwlJSWc77dv384AsO3bt3Pa6+vrmZOTEwPAjhw5wjm2fPlyBoBFRERw2u3t7RkA5ufnx6qrqznHGo9h06ZNsvaGhgY2YcIEBoCZmJiwAwcOyI7V1NSwgQMHMn19fVZUVCRrv3LlCtPT02ODBg1iZWVlnOeJi4tjANgnn3wia0tJSWEAmLu7O3v06JGsvaCggJmZmTEALCwsTC5XTaWmpjIAzMvLq8W+jd24cYPp6ekxCwsLdufOHVm7RCJh48aNYwDYDz/88Mz9W5pv0tc4ICCA1dXVydovXrzIDAwMGAAmEok4j7G3t5eb1yKRiAFgAoGAXb9+XdZeXV3NnJ2dGY/HY4WFhbL2J0+esIKCArl4Ll++zHr27MnGjx+vMM6mc1EqNDSUAWDfffcdp72oqIj169ePmZubs8ePHyt8bGNhYWEMALO1tWW3b99usT8hHZ30/7+qX7qgoqKCmZubM4FAwObPn89EIpHS94bOSPq+rsrPpsaqqqrYpk2bmLe3NzMzM2N6enrM1NSUjR49msXFxbHi4uK2CVjDpD+3VfnZ1NZa+tlE2gbdIk4IUcjKygorV65UeOwf//iHXFvPnj0RHh6OyspKZGVlyR13cHDA0qVLOW0REREAoLA/n8+XazMzM1Mp9jNnziA3NxeBgYHw9/fnHFuxYgX69OmDxMRE1NTUyD32448/VvjcwNNxN746z+Px8NprrwF4emv1xIkTZcf09fUxdepU1NbW4tq1a7L2r776CnV1ddiyZQuEQiHn/MuWLYO5uTl++uknWdv3338PAFi1ahWn6Fjfvn2xcOHCFnMhVVRUBACwtbVV+TEAsHPnTtTV1SEqKgr9+vWTtRsYGCA+Ph4AOFco1O0vpWy+Sce/bt06zi3tbm5umDVrllpjAYCFCxfCxcVF9j2fz8fMmTPBGEN2dras3dDQEH379pV7/IABA+Dj44O0tDSV96mXlpZi9+7deOmll2S3kktZWlpi6dKlKCkpwYkTJ1Qex9KlS2FnZ6dyf0I6KpFIJPcFAAKBQOmxjk5agDMmJgZbt25FbGwsbeNoQU5ODl588UUsWrQIeXl5CAkJwdKlSxEaGoonT55g+fLlcHR0VLrtShf8+uuvVISzi6BbxAkhCrm7u3NuU26suLgY8fHxSE5Oxu3bt+X2r0qLjzU9X7du3L/pSRd7FRUVsragoCDExMRg3rx5OH78OAICAuDl5QVnZ2eVY5fukVX0mdjGxsYYOnQojh49ir/++guurq6yYz169ICbm5vS8yoag7W1NQAovC1YeqywsFDWlpGRAQA4cuSIwgWVvr4+rl+/Lvteukd9zJgxcn0VtWlac7n09PQEn8/HhQsXnrm/lLL5lpOTAyMjIwwePFju2JgxY/Dtt9+qNpD/o+g8iuYhAFy4cAEfffQRTp8+jaKiIrkFdWlpqew1bk5WVhbq6+vx5MkThQUFc3NzAQDXr19HUFCQSuMYPny4Sv0I6eioACehApyks6Er2IQQhZTt6SwvL8ewYcPw6aefok+fPoiIiMDKlSshEolkV3AlEonc4wQCgVybdK9v48JXDg4OOHv2LIKDg5GcnIyIiAi4uLjg+eefx549e1SKXSwWNzsG6S89lZWVnHYLC4tmPwO8aeGvxmNo7ljjXwikBdbWrVuH1atXy33dvXuX8xf6yspKdOvWTeHVe3X23UrH3Hixr4qWcmlhYcHJo7r9pZT1r6yshIWFhcJjz7LvWNV5mJ6eDk9PT+zbtw8eHh6IjIzEqlWrIBKJ4O7uDkDxPFdE+pqfOXNG4WuemJgIAGpdmaE916SroQKcVICTCnBSAU5dQVewCSEKKVtofvvtt7hz5w4++OADrFixgnMsPj4eSUlJrX7ugQMHYu/evaitrUV2djaSk5OxZcsWzJgxAzY2Nhg9enSzj5f+AL5//77C49L2pj+om1tca4r0OcViMXr16tVif4FAgIaGBpSWlsLc3JxzTNn4FBk2bBgMDAxw7tw5iMVihX8QaC7e+/fvw97eXu54cXEx51zq9pdSlnuBQIDi4mKFx9QZv7rWrVsHiUSC06dPy823jIwMhb98KyMdb1RUFD755BONxNcec5WQjogKcFIBTikqwEkFODssbW8CJ4RoD5opcqasOMm//vUvBoBdvHhR7pi04FfjYhotnQ8AGzduXIuxfv/99wwAi4mJkbUpK96RlpbGALDAwEC581RVVTEzMzPG5/OZRCKRtTdXfKS5MSgrZqIsvnfeeYcBYMeOHWt2vFKzZ89mANjevXvljq1du1atQjJvvPEGA8BWrVrVbL/a2lpWX1/PGGNszZo1DABbv369XL/MzEwGgPn6+sra1O3f0vzw8fFhAFh2drbcsYiICLWLnKWkpMidR9Hr5OLiwoRCoVzfqqoqZm5uzgCwvLw8Wbt0fn7zzTdyj7l37x7j8Xhs1KhRCseoDmmRs8bPTUhn09zPJlABToVjoAKcT1EBTirA2RHQLeKEELVIr0o2vXUoMTERhw8fbvX5s7KyFF6xlF6tVFaArLHRo0ejf//+SE5OltvnHBcXh9LSUsycOVPpHvO29O6770JPTw+RkZHIz8+XO15RUcG5zeuNN94AAKxZs4ZzS19hYSE2b96s1nOvW7cO5ubmWLduHbZs2aLwNr6LFy/C29tbdqt3aGgo9PT0sHHjRs7e+traWsTExAAA5xYwdfu3RFrIbMWKFZxb+C5duoQffvhB5fOoy97eHg8ePMCVK1dkbfX19YiOjkZJSYlcf2nBuoKCArljVlZWmD59OtLT0/Hxxx+DMSbXJzMzU+EtmIQQLirAKY8KcFIBTirA2bHQLeKEELXMmjUL69evR2RkJFJSUmBvb4+LFy/ixIkTmDJlCvbt29eq8+/cuRPbtm2Dt7c3HB0d0bt3b1y9ehWHDx+GmZkZ3nzzzRbP0a1bN+zYsQP+/v6YMGECpk2bBnt7e2RmZuLkyZPo37+/7Adqe3N1dcW2bdvwzjvvwMXFBRMmTED//v0hFotx8+ZNnDp1CuHh4fjyyy8BPC0WNnv2bGzfvh1ubm6YPHkyJBIJdu/eDU9PTxw6dEjl57a1tcWxY8cwadIkLFy4EJ9++ileeuklWFpaQiwW4/fff0dWVhZ69+4NfX19AE+Lsqxfvx5RUVEYOHAgpk+fDmNjYxw6dAjXr1/HxIkT8c9//lP2HOr2b0lYWBgSExNx5MgRDBo0CIGBgSgvL8dPP/0EPz8/tcavjsjISBw7dgxeXl6YPn06evTogdTUVBQWFsLb21vu82xHjhwJPp+PTZs2QSwWy27nl/5RYdu2bfjzzz+xbNky/PDDDxg5ciQEAgHy8/ORnZ2N3Nxc3Lt3D0ZGRm0yHkI6CyrAKY8KcHJRAU4qwKlttMAmhKjF1tYWp06dwrJly3DixAnU1dVh8ODBOHbsGPLz81u9wJ45cyaePHmCM2fOICsrCxKJBLa2tpg3bx6io6NV/iu3l5cXMjIysGbNGhw7dgyVlZWwsbHBggUL8P7776t8xaEtzJkzBx4eHti4cSPS0tJw8OBBCAQC2NnZYfHixbICOVIJCQlwdnZGQkICPvvsM9ja2mLJkiWYPn262gtMDw8PXL16FQkJCdi/fz+SkpJQUVGBnj174oUXXsDatWsxd+5czhWJJUuWwNHRERs3bsSPP/6ImpoaODs7Y8OGDViwYIHcnjV1+zenW7duSEpKwurVq7Fz505s3rwZ/fv3x8aNG+Hs7NxmC+ygoCD8/PPP+PDDD/Hjjz/CyMgIvr6+2L9/P9asWSPXXygU4ueff0ZsbCy++OIL2S/20gW2UChEeno6PvvsM+zevRs7d+5EQ0MDrKys4O7urvU5SYiuaKkA5507dzB69GiMHz8eJiYm6N69u2xPtCYKcK5evRrJycmyopsuLi5Yu3Ytpk2b1mLsulKAUxW6UICz8TnV7S/VXAHOxlfCVXlMc9QpwOnr6wsA8PPzg5OTE3r27Akej4cDBw4gJyfnmQpwnjlzRmk/KsD5DLR9jzohhBBCCCFSeIb6IB999BEDwD744AO5Y9I9xJqqD1JTU8POnj3LVq1axUxMTBiPx2OnT5+WHVe273Xz5s1Ka1QwxlhAQIBcjZP2qg8yePBgBoCJxWKFz9WUtH9xcbHcMem+alX2YFdVVTEDAwPG5/NZZWWlSs/NGGOTJ09mAFhmZqbC43w+n1NHQ93+Lc0PoVDIjIyMFB7bsWNHm9UHke6tbzzfpPz9/eVqdDS3B/vgwYMMAIuKilI4DnVQfRAu2oNNCCGEEEJ02o0bNwAAISEhcsd+++03jT6Xvr4+PD09sXr1amzZsgWMMZXuphk0aBAAyG0xAZ5W0z537hz4fD5nL257GTFiBID/v1W8JdKPK1SUW3XybWRkhNdeew2PHz+WVWJXpq6uTlY7pLlc/v7773j8+DHn9nh1+7fE3d0d1dXV+OOPP+SOaXq+NXbjxg0IhUK5T7dQFot0f7iijy0bNmwYeDwezp492zbBdmG0wCaEEEIIITqNCnC2DhXgpAKcjApwagztwSaEEEIIITqNCnC2DhXgpAKcVIBTc2iBTQghhBBCdBoV4Gw9KsBJBTipAKdm8Jii+wEIIYQQQgghhBCiFtqDTQghhBBCCCGEaAAtsAkhhBBCCCGEEA2gBTYhhBBCCCGEEKIBtMAmhBBCCCGEEEI0gBbYhBBCCCGEEEKIBtACmxBCCCGEEEII0QBaYBNCCCGEEEIIIRpAC2xCCCGEEEIIIUQDaIFNCCGEEEIIIYRoAC2wCSGEEEIIIYQQDaAFNiGEEEIIIYQQogG0wCaEEEIIIYQQQjTgf0+RVHucU6hHAAAAAElFTkSuQmCC\n" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from grid.rtransform import BeckeRTransform\n", - "\n", - "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5), sharey=True)\n", - "names = []\n", - "for i, oned in enumerate(grids):\n", - " # Becke R-transform (goes from 0 to \\infty) to transform 1D-grid\n", - " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " # plot radial grid points for each transformed 1D-grid \n", - " ax1.scatter(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", - " # plot log plot\n", - " ax2.semilogx(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", - " names.append(oned.name)\n", - "\n", - "# set the ticks, labels, and title\n", - "plt.suptitle(\"Plot & Log-Plot of Becke Radial Transformation of 1D-Grids\", fontsize=17)\n", - "ax1.set_yticks(range(1, len(grids) + 1), names, fontsize=11)\n", - "ax1.set_xlim(0, 2500)\n", - "ax2.set_xlim(1e-4, 2500)\n", - "ax1.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", - "ax2.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", - "ax1.set_ylabel(\"Quadrature Rule\", fontsize=17)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Example: Integration of One-Variable Function on $[0, \\infty]$\n", - "\n", - "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). Here, we integrate (which has the exact value of 2.0):\n", - "\n", - "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:21.855941638Z", - "start_time": "2024-01-03T22:36:21.851891608Z" - } - }, - "outputs": [ + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.338777861Z", + "start_time": "2024-01-03T22:36:21.146684630Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Integral of sqrt(1-x^2) from -1 to 1:\n", + " 1.57079633 from Analytical integration (which is equal to pi/2)\n", + " 1.57079633 from Gauss-Chebyshev integration\n", + " 1.57082270 from Gauss-Legendre integration\n", + " 1.57067045 from Tanh-Sinh integration\n", + " 1.56683246 from Simpson integration\n", + " 1.56069571 from Trapezoidal-Lobatto integration\n" + ] + }, + { + "data": { + "text/plain": "
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\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# define the function to integrate\n", + "function = lambda x: np.sqrt(1 - x**2)\n", + "\n", + "print(\"Integral of sqrt(1-x^2) from -1 to 1:\")\n", + "print(f\"{np.pi / 2: .8f} from Analytical integration (which is equal to pi/2)\")\n", + "\n", + "names = []\n", + "error_relative = []\n", + "for oned in grids:\n", + " # integrate the function evaluated on the grid points\n", + " integral = oned.integrate(function(oned.points))\n", + " print(f\"{integral: .8f} from {oned.name} integration\")\n", + " error_relative.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + " names.append(oned.name)\n", + "\n", + "# plot the relative error as columns graph\n", + "plt.figure(figsize=(8.5, 5))\n", + "plt.bar(names, error_relative)\n", + "title = r\"Numerical Integration of $\\int_{-1}^1 \\sqrt{1-x^2} dx$ with \" + str(npoints) + \" Points\"\n", + "plt.title(title, fontsize=16)\n", + "plt.xlabel(\"Quadrature Rule\", fontsize=14)\n", + "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", + "plt.show()" + ] + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Integration of r^2 * exp(-r) from 0 to infinity:\n", - " 2.000000 Analytical integration\n", - " 2.000003 from BeckeRTransform radial grid of Gauss-Chebyshev\n", - " 1.999996 from BeckeRTransform radial grid of Gauss-Legendre\n", - " 1.999993 from BeckeRTransform radial grid of Tanh-Sinh\n", - " 1.998949 from BeckeRTransform radial grid of Simpson\n", - " 2.000006 from BeckeRTransform radial grid of Trapezoidal-Lobatto\n" - ] - } - ], - "source": [ - "print(\"Integration of r^2 * exp(-r) from 0 to infinity:\")\n", - "print(f\"{2.0: .6f} Analytical integration\")\n", - "\n", - "# Make several 1-dimensional grids for a given number of points\n", - "npoints = 21\n", - "grids = [\n", - " GaussChebyshev(npoints),\n", - " GaussLegendre(npoints),\n", - " TanhSinh(npoints),\n", - " Simpson(npoints),\n", - " Trapezoidal(npoints),\n", - "]\n", - "\n", - "for oned in grids:\n", - " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " x = rgrid.points\n", - " func_vals = x**2 * np.exp(-x)\n", - " integral = rgrid.integrate(func_vals)\n", - " print(f\"{integral: .6f} from BeckeRTransform radial grid of {oned.name}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "ExecuteTime": { - "end_time": "2024-01-03T22:36:22.028092961Z", - "start_time": "2024-01-03T22:36:21.856079509Z" - } - }, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Changing the number of grid points increases the accuracy of each quadrature. Here we show how the relative integration error converges to zero when increasing the number of points.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.461375714Z", + "start_time": "2024-01-03T22:36:21.349492787Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npoints = [3, 5, 11, 15, 17, 19, 21, 31]\n", + "grid_classes = [GaussChebyshev, GaussLegendre, TanhSinh, Simpson, Trapezoidal]\n", + "\n", + "for grid_class in grid_classes:\n", + " errors = []\n", + " for npoint in npoints:\n", + " # make 1-dimensional grid for the given number of points\n", + " oned = grid_class(npoint)\n", + " # compute relative percent error of integration\n", + " integral = oned.integrate(function(oned.points))\n", + " errors.append(np.abs(integral - np.pi / 2) / (np.pi / 2) * 100)\n", + " # plot relative percent error vs. number of grid points\n", + " plt.plot(npoints, errors, label=oned.name)\n", + "\n", + "plt.legend(frameon=False, fontsize=12)\n", + "plt.title(r\"Numerical Integration of $\\int_{-1}^1 \\sqrt{1-x^2} dx$\", fontsize=16)\n", + "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", + "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", + "plt.xticks(npoints)\n", + "plt.show()" + ] + }, { - "data": { - "text/plain": "
", - "image/png": 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\n" - }, - "metadata": {}, - "output_type": "display_data" + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Radial Grid: Transformation of 1D-Integration Intervals\n", + "\n", + "Generally, areas where the integrand changes more rapidly demand a denser concentration of points. So, the $[-1, 1]$ interval is not suitable for most applications encountered in quantum chemistry, where the integrals are usually performed on $[0,\\infty)$ domain. [Grid](https://github.com/theochem/grid) supports several transformations of the one-dimensional grids to other intervals. Some of these transformations have a parameter that can be used to control the density of points across different ranges of the new interval. [Click here for a full list of radial transformations.](https://grid.qcdevs.org/pyapi/grid.rtransform.html)\n", + "\n", + "### Visualize Radial Grid Points\n", + "\n", + "Here we visualize the OneDGrid points for different quadrature rules after a Becke transformation.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.851432041Z", + "start_time": "2024-01-03T22:36:21.470246478Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from grid.rtransform import BeckeRTransform\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5), sharey=True)\n", + "names = []\n", + "for i, oned in enumerate(grids):\n", + " # Becke R-transform (goes from 0 to \\infty) to transform 1D-grid\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", + " # plot radial grid points for each transformed 1D-grid \n", + " ax1.scatter(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", + " # plot log plot\n", + " ax2.semilogx(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", + " names.append(oned.name)\n", + "\n", + "# set the ticks, labels, and title\n", + "plt.suptitle(\"Plot & Log-Plot of Becke Radial Transformation of 1D-Grids\", fontsize=17)\n", + "ax1.set_yticks(range(1, len(grids) + 1), names, fontsize=11)\n", + "ax1.set_xlim(0, 2500)\n", + "ax2.set_xlim(1e-4, 2500)\n", + "ax1.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", + "ax2.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", + "ax1.set_ylabel(\"Quadrature Rule\", fontsize=17)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example: Integration of One-Variable Function on $[0, \\infty]$\n", + "\n", + "This transformation tends to concentrate the points close to the origin. Because of this, it is usually used for defining radial grids for atoms where the function to integrate is rapidly varying close to the origin (e.g. the electron density is more concentrated close to the nucleus). Here, we integrate (which has the exact value of 2.0):\n", + "\n", + "$$ \\int_0^\\infty x^2 e^{-x} dx $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:21.855941638Z", + "start_time": "2024-01-03T22:36:21.851891608Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Integration of r^2 * exp(-r) from 0 to infinity:\n", + " 2.000000 Analytical integration\n", + " 2.000003 from BeckeRTransform radial grid of Gauss-Chebyshev\n", + " 1.999996 from BeckeRTransform radial grid of Gauss-Legendre\n", + " 1.999993 from BeckeRTransform radial grid of Tanh-Sinh\n", + " 1.998949 from BeckeRTransform radial grid of Simpson\n", + " 2.000006 from BeckeRTransform radial grid of Trapezoidal-Lobatto\n" + ] + } + ], + "source": [ + "print(\"Integration of r^2 * exp(-r) from 0 to infinity:\")\n", + "print(f\"{2.0: .6f} Analytical integration\")\n", + "\n", + "# Make several 1-dimensional grids for a given number of points\n", + "npoints = 21\n", + "grids = [\n", + " GaussChebyshev(npoints),\n", + " GaussLegendre(npoints),\n", + " TanhSinh(npoints),\n", + " Simpson(npoints),\n", + " Trapezoidal(npoints),\n", + "]\n", + "\n", + "for oned in grids:\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", + " x = rgrid.points\n", + " func_vals = x**2 * np.exp(-x)\n", + " integral = rgrid.integrate(func_vals)\n", + " print(f\"{integral: .6f} from BeckeRTransform radial grid of {oned.name}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2024-01-03T22:36:22.028092961Z", + "start_time": "2024-01-03T22:36:21.856079509Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
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\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npoints = [11, 21, 31, 41, 51, 61]\n", + "grid_classes = [GaussChebyshev, GaussLegendre, TanhSinh, Simpson, Trapezoidal]\n", + "\n", + "for grid_class in grid_classes:\n", + " errors = []\n", + " for npoint in npoints:\n", + " # make 1-dimensional grid for the given number of points\n", + " oned = grid_class(npoint)\n", + " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", + " # Calculate x^2 e^-x\n", + " x = rgrid.points\n", + " func_vals = x**2.0 * np.exp(-x)\n", + " # compute relative percent error of integration\n", + " integral = rgrid.integrate(func_vals)\n", + " errors.append(np.abs(integral - 2.0) / 2.0 * 100)\n", + " # plot relative percent error vs. number of grid points\n", + " plt.semilogy(npoints, errors, label=oned.name)\n", + "\n", + "plt.legend(frameon=False, fontsize=12)\n", + "plt.title(r\"Numerical Integration of $\\int_0^\\infty x^2 e^{-x}dx$\", fontsize=16)\n", + "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", + "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", + "plt.xticks(npoints)\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" } - ], - "source": [ - "npoints = [11, 21, 31, 41, 51, 61]\n", - "grid_classes = [GaussChebyshev, GaussLegendre, TanhSinh, Simpson, Trapezoidal]\n", - "\n", - "for grid_class in grid_classes:\n", - " errors = []\n", - " for npoint in npoints:\n", - " # make 1-dimensional grid for the given number of points\n", - " oned = grid_class(npoint)\n", - " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " # Calculate x^2 e^-x\n", - " x = rgrid.points\n", - " func_vals = x**2.0 * np.exp(-x)\n", - " # compute relative percent error of integration\n", - " integral = rgrid.integrate(func_vals)\n", - " errors.append(np.abs(integral - 2.0) / 2.0 * 100)\n", - " # plot relative percent error vs. number of grid points\n", - " plt.semilogy(npoints, errors, label=oned.name)\n", - "\n", - "plt.legend(frameon=False, fontsize=12)\n", - "plt.title(r\"Numerical Integration of $\\int_0^\\infty x^2 e^{-x}dx$\", fontsize=16)\n", - "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", - "plt.ylabel(\"Relative Percent Error\", fontsize=14)\n", - "plt.xticks(npoints)\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - } - }, - "nbformat": 4, - "nbformat_minor": 1 + "nbformat": 4, + "nbformat_minor": 1 } From f13c33fbb6c9ca47d285b6f8c9095539990e4db9 Mon Sep 17 00:00:00 2001 From: Farnaz Heidar-Zadeh Date: Thu, 4 Jan 2024 22:59:45 +0330 Subject: [PATCH 9/9] Minor changes to the One_dimensional_grids.ipynb --- doc/notebooks/One_dimensional_grids.ipynb | 59 +++++++++++++++-------- 1 file changed, 39 insertions(+), 20 deletions(-) diff --git a/doc/notebooks/One_dimensional_grids.ipynb b/doc/notebooks/One_dimensional_grids.ipynb index 3d8b340f1..d26755b22 100644 --- a/doc/notebooks/One_dimensional_grids.ipynb +++ b/doc/notebooks/One_dimensional_grids.ipynb @@ -50,14 +50,17 @@ "outputs": [ { "data": { - "text/plain": "
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\n" + "image/png": 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", + "text/plain": [ + "
" + ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ + "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "names = []\n", @@ -67,7 +70,7 @@ "\n", "# set the y-ticks to be the 1D grid names, and set labels\n", "plt.title(f\"{npoints} Grid Points in One Dimension\", fontsize=16)\n", - "plt.yticks(range(1, len(grids) + 1), names)\n", + "plt.yticks(np.arange(1, len(grids) + 1), names)\n", "plt.xlabel(\"Number of Points (Grid Size)\", fontsize=14)\n", "plt.ylabel(\"Quadrature Rule\", fontsize=14)\n", "plt.show()" @@ -81,7 +84,7 @@ "\n", "The one-dimensional grids can accurately integrate one-variable functions over an interval (defined by their domain), even with a small number of points. Here, we numerically compute the integral below and compute the relative percent error. The analytical value of this integral is $\\pi/2$.\n", "\n", - "$$ \\int_{-1}^1 f(x) dx \\approx \\sum_{i=0}^{N-1} w_i f(x_i) $$\n" + "$$ \\int*{-1}^1 f(x) dx \\approx \\sum*{i=0}^{N-1} w_i f(x_i) $$\n" ] }, { @@ -109,8 +112,10 @@ }, { "data": { - "text/plain": "
", - "image/png": 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\n" + "image/png": 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LFwEgU6ZM0RqDg4ODAJA333wz3zHqcvToUaVFM1tmZqY4OjpKo0aNlOOU83wdMmSIAJCffvpJ577IT/JtrPM5p2+++Ubj2HTv3l3++ecfveYvyOT7zp070r59ewEgZcqUUb4L8nM9el7yndd9/LzjFxgYKADkzJkzundAMcI+30XcgAEDULNmTURGRmLNmjUFvr4hQ4ZolDVs2FD5/zvvvKMxvVGjRgCe3hiV05YtWwA8fZJe6dKlNeaztbVF+/btISI4cOCA1ngGDhyod+wAlP7cPXr0UPq36SMmJgazZs1C79690a5dO7z00kt46aWXsH79egD/DcdV0IYOHapR5uPjA2trayQnJyMxMTFPyzP0GGTfkNOzZ0+t40i//fbbz133846dKff5rl27AAC9evVChQoVNKaPGDECVlZWuH79OiIjIzWmG+u45DcOY8k52kFRuTGxW7duePTokdqoJ1u3bsVrr71WiFEVjNKlS2Ps2LEAgHHjxqFLly5ITk7GDz/8gC5dumjUj46O1vlwo8GDB2tdR3h4OLZt24ZKlSop63o2Bi8vLwDaRzrJa4y6+Pr6wt7eHqdOncKDBw8AAKdPn0ZycjJat26N1q1bAwD27dunzLN//34A0NnnPL+MfZ0FgIoVKyIgIABNmzZVnji6Z88erFu3DpmZmfmOOS9mzJihXE+9vb3h4eGBv/76CxYWFli6dKnyXVCQ1yNj72MPDw8AwMaNG0vEIBQc57uIMzMzwxdffIGBAwdi2rRp6NevH8zNC+6waXtgQ/bT1VxcXLSOKZs9/dnhi/755x8ATxNAXTcuZt9kcevWLa3Ts78c9BUREQHg6Z3m+vr5558xYsQIPHnyRGedpKSkPMVhKF0PzHBxccGNGzfw8OFDODs76708Q49B9g05uoYf8/T0hIODQ643a+Z27Ey9zy9dugQAqFu3rtbppUuXhoeHB65cuYJLly4pN0plM9ZxyW8cxlIUk++WLVuibNmy2Lp1K7p06YL09HREREQUyigcn332GbZu3Zrn+VasWAF/f3+96n7wwQeYN28ejhw5AuBpgjt8+PA8r1OXdevWAXj6I9jKykprnewROnTtY2PEaG5ujhYtWmDXrl04ePAgXnnlFSXRbt26tXKN2bdvHwYNGoTY2FhcvnwZbm5ueWpAyQtjX2eBpwlsr169lPdHjx7F8OHDMWPGDCQlJeHHH3/MV8x5cfnyZeUabmlpiQoVKqBVq1b4+OOP1RrTCvJ6ZOx9/MEHH+Dnn3/GtGnT8Msvv+CVV15By5Yt0bZt2zzdfFxUsOW7GOjXrx9q166NK1euYNWqVQW6Lm3DeWXfuaxrqK/s6c/+Gs0eAeXKlSs4ePCg1lf244yzh1F7Vl6H0spOBvUdpP/q1asYNmwYnjx5go8//hinTp1CSkoKsrKyICJYunQpACA9PT1PcRhK1/Zmj+uc11/8hh6DR48eAYDW1vJsuU0DdG9LYezz7GQz+8ET2mS3VmW3zuVkrOOS3ziMpSgm3+bm5ujcuTNCQkIgIti3b1+BtXw+z+3btxEZGZnnV/Z5o4/U1FTlHHJxcTH6kzj37NkD4OnTkHXJ/mulruTbWDE+27q9b98+qFQqtGzZEtWqVUOlSpXUpuWcpyAY+zqrTbNmzbB9+3ZYWVlhyZIlSiOHKaxYsUL5y0hqaiquX7+OVatWqSXeQMFej4y9jxs2bIj9+/ejY8eOuHXrFhYvXoy33noLlSpVQmBgoNLwVlww+S4GzMzMMGnSJADAtGnTkJGRobWeriQ4W16+GIwh+0t96dKlOv9kmv0KDg42yjqzvyj0fUTtb7/9hvT0dPTt2xdz585Fw4YNUbp0aWVf3rhxwyhxFRZDj0H2hTO3hzEYmhwWxj7P3g/x8fE669y5cwfA839UlIQ4imLyDTztehIbG4tjx44hJCSk0IYYXL169XPPF22v3BLdnNLS0tCzZ09cunQJ5ubmuHv3LjZu3GjUbcg+j6pWrap1ekREBG7fvg1nZ2etLYfGjDH7R9S+ffuULm7e3t5Ky2erVq1w7do13Lx50yTJt6m4u7ujYcOGyMrKMlnXxbwoKtcjfTVv3hw7d+7EvXv38Oeff2Ls2LGoVKkSdu3ahQ4dOhSrR9Mz+S4m+vbti7p16yIqKkoZ7/dZ2QnT3bt3tU6/cuVKQYWnVfafss6dO2eyddarVw8AlD+TPk/2GKUtWrTQOr0oXjCfpW3c9myGHoNatWoB+G8M4GfFxMTk2uUkN/nZ57lta26yt+fChQtapz948EBJVrLrFoSiEkdRTb5feeUVWFlZYevWrdi3b1++xjEvyoYMGYI9e/agY8eOWLJkCYCn47kbs29w9o9jXY0uixcvBqC71duYMTZt2hQ2NjY4ceIEjh07hqSkJLXkOvv/e/fuNbi/t6HXhoKW3Vimq9GsMBWV6xGQt+Nnb2+PwMBAzJo1CxcvXkT16tVx69Yt7NixowAjNC4m38VEqVKlMHnyZADA9OnTtf5J3tnZGY6Ojvj3339x/vx5jek//fRTgceZU48ePQA8bUUy5AYWQ3Tv3h3A0yeKXb169bn1s58WmP3rPqeLFy8iJCTEqPEVhOxt0NZ1x9Bj0KFDBwDA5s2btbZw6/oBqI/87PPctjU3gYGBAIANGzaoPTAq2+LFi5GamgpPT0/Url07T8sujnEU1eTb3t4e7dq1w6JFi1CrVi1YWloWdkhGN2HCBKxevRo+Pj7YsGEDBg4ciFq1auHixYtYvXq10dbj5uYG4Gnf42edOXNG6YOsLfk2doyWlpZo1qwZ0tPTMXPmTADqLdvZifbGjRsREREBFxcXnf2QdTH02lCQoqOjlcaEovgE0aJyPQIMP362trbw8fEB8LS7WHHB5LsY6dWrF3x8fHD9+nUcPHhQY7pKpVJOpqCgILUv2J9//hnLly83WawA4Ofnh969eyMxMREdOnTQeLJVZmYm9u7di/79+yM1NdUo62zcuDF69OiBJ0+eoFOnTjh+/Lja9CtXrmDu3LnK+5deegkAsHDhQpw+fVopv3TpEnr16lUsvvyrVasGQH20gGyGHoP27dujfv36SEhIQL9+/dT+nPf7779j5syZGo9T1ld+9nlu25qbdu3aoUmTJkhNTcWbb76p9mfWXbt2KY82HzduXIG2oBWVOIpq8g087XqSlJRUIkc5+emnnzBjxgy4u7tj27ZtcHBwgJmZGSZOnAgAmDp1qtFaSLO7wEydOlW5sQ4A/v77b3Tq1AlpaWkANG+qLqgYs5Pt7BtZc7Zs16lTB66urti6dStExKC+/oZeG/IjPDwckydP1hjpCwD+/PNPdOrUCRkZGejcubPOGxALU1G5HgHPP37vvfce1q9fr/G00P379ysjJPn6+hZojEZl5KELKZ+eHef7WRs3bsx1jNeIiAixt7cX4OkDc3x9fcXNzU2Ap0+cyp7vWbrKRZ4/fviePXuUQfqf9eDBA+nQoYOy/MqVK0uzZs3Ex8dHbGxslPKcY/s+L55suT3h0t/fX1lGlSpVxM/PT1xdXTW2Iz09XZo3by7A0ycrenl5ibe3t/JkrunTpysD++u7fn1i1jXOd163VeS/B1IAEG9vb2ndurW0bt1aTp06JSKGH4OcT7i0tbUVPz8/qVKlijKGa3ZMMTExedqW/Ozz521rbvvq8uXLUqlSJWVcW19fX+UBUsDTB3roesKlLoZ8BgyJQ8S443xnj98LwKCnRxak27dvi4WFhSQmJuZpvrCwMHF2dlZe2Q8UsbW1VSt/9vNqKjt27BBzc3Oxt7dXe+qiyNMHs9SqVUsAGO1hIVFRUcpTKs3NzcXb21s5f+vVqyfVq1cXAGqxFGSMu3fvVj5zXl5eGtN79eqlTP/22291LkfXOafPtcHY53P2dx/w9Imffn5+Ur9+feW6CUCaNGkid+/e1Zi3ID6vz3vCpTaGXo+eN87382LM6/Fr0KCB8ln28vKSpk2bqo1//9Zbb+m9zUUBk+8i5nnJd1ZWljRs2FBn8i0icvLkSXnllVeUp2u1aNFCQkJCROT5D9nRJj/Jt8jTByqsWbNGAgMDpVy5cmJhYSFubm7SrFkzGTt2rNbHJecn+RYRSUtLkx9++EECAgLE0dFRrK2tpWrVqvLGG28o+yJbcnKyjBo1Stzd3cXCwkIqVaokQ4cOldu3bysPOSrKybeIyIIFC6R+/fpqyfSePXuU6YYcAxGRK1euSN++fcXZ2Vmsra3Fx8dHvv/+exER5QEc9+7dy9O2iBi+z/XZ1tz21d27d+WTTz6RmjVripWVlTg4OEirVq1k1apVWr9gCiL5NiQOEeMm35MmTVK2TdvDlwpbzqfo6itnIpTbK6/HyhhOnTol9vb2YmZmJtu2bdNaZ9WqVQJAPDw85MmTJ0ZZ79mzZ6Vjx45ia2srtra24u3tLV988YUkJCSIlZWVmJubK+sq6BgfP34slpaWAkBGjBihMf37779XjtHp06d1Lie3c+551wZjn89JSUmyYMECee2116R69epib28vlpaW4ubmJp06dZIVK1YoT/V9VkF8Xg1JvkUMux4ZO/kWyf34/f333/Lhhx+Kr6+vuLi4iKWlpXh6ekpgYKBs3bpVZ5xFlUqkBIxWTkQmlZiYiHLlysHJyQn37t0r7HAojz7++GPMmzcPwNOuR9nDfxERUcHjFZeI8mzFihUAdI9YQkVbdp9vW1vbAkm8b968iVGjRqFZs2awtrYusiNREBEVBibfRKTVP//8gyVLlqjdnCciWL16Nb744gsATx8/TEVfcnIyIiIikJWVBeC/p4fq+zCqvLpy5Qo2bNiA8uXLo1mzZgWyDiKi4orJNxFplZiYiOHDh8PJyQnVq1dH06ZN4eLiggEDBuDJkycYPnx4oT0EhfQXGRkJJycn1K1bVxnPN/vR01WqVCmQdbZq1QpxcXEICQlBp06dCmQdRETFFZNvItKqbt26+Oyzz+Dj44Pk5GScOnUKIoKXX34Zv/76KxYtWlTYIZIeatWqhcqVKwMAZs+ejbVr1yoPT8oez93Y2IeciEg33nBJRFTC/fTTTxg2bJhaWdWqVXHixAmULVu2QNc9a9YsjB8/HvyqISJ6is0TREQl3NChQ/HTTz+hevXqsLe3x1tvvYXDhw8XeOJNRESazAs7ACIiKnhDhgzBkCFD8jzfgwcPcOvWrefWc3Nzg6OjoyGhERG9UJh8ExGRTtu2bcObb7753HorVqzA4MGDCz4gIqJijsk3ERHp1LdvX/Tt27ewwyAiKjHY55uIiIiIyETY8k1EREa3ceNGAMC5c+fU3tetWxd169YttLiIiAobhxokIiKj0/VI+cmTJyM4ONi0wRARFSFs+SYiIqNjuw4RkXbs801EREREZCJs+QaQlZWF27dvo3Tp0jr/VEpEREREpI2I4MGDB3B3d0epUrm3bTP5BnD79m14eHgUdhhEREREVIzduHEDlSpVyrUOk28ApUuXBvB0hzk4OBRyNERERERUnKSkpMDDw0PJKXPD5Bv/3ZXv4ODA5JuIiIiIDKJP92XecElEREREZCJMvomIiIiITITJNxERERGRiTD5JiIiIiIyESbfREREREQmwuSbiIiIiMhEmHwTEREREZkIk28iIiIiIhNh8k1EREREZCJMvomIiIiITITJNxERERGRiTD5JiIiIiIyESbfREREREQmwuSbiIiIiMhEmHwTEREREZmIeWEHQERERFScVRm3rbBDoByiZ3Up7BByxZZvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEykSCbfCxcuRNWqVWFtbY3GjRvjwIEDudZPTU3FhAkT4OnpCSsrK1SvXh3Lly83UbRERERERPoxL+wAnrV+/XqMGTMGCxcuREBAABYvXoxOnTrhwoULqFy5stZ5evfujTt37mDZsmWoUaMG4uPjkZGRYeLIiYiIiIhypxIRKewgcmrWrBl8fX3x448/KmVeXl7o3r07Zs6cqVH/zz//RN++fXHt2jWULVvWoHWmpKTA0dERycnJcHBwMDh2IiIievFUGbetsEOgHKJndTH5OvOSSxapbidpaWkIDw9Hx44d1co7duyIQ4cOaZ1n69at8PPzw+zZs1GxYkXUqlULn3zyCf79919ThExEREREpLci1e0kISEBmZmZcHV1VSt3dXVFXFyc1nmuXbuGsLAwWFtbY8uWLUhISMD777+PpKQknf2+U1NTkZqaqrxPSUkx3kYQEREREelQpFq+s6lUKrX3IqJRli0rKwsqlQpr1qxB06ZN0blzZ8ybNw8rV67U2fo9c+ZMODo6Ki8PDw+jbwMRERER0bOKVPJdrlw5mJmZabRyx8fHa7SGZ3Nzc0PFihXh6OiolHl5eUFEcPPmTa3zjB8/HsnJycrrxo0bxtsIIiIiIiIdilTybWlpicaNGyM0NFStPDQ0FC1atNA6T0BAAG7fvo2HDx8qZZcuXUKpUqVQqVIlrfNYWVnBwcFB7UVEREREVNCKVPINAEFBQfjpp5+wfPlyRERE4KOPPkJMTAxGjBgB4Gmr9cCBA5X6/fr1g7OzM95++21cuHAB+/fvx6effop33nkHNjY2hbUZREREREQaitQNlwDQp08fJCYmYurUqYiNjYW3tze2b98OT09PAEBsbCxiYmKU+vb29ggNDcWoUaPg5+cHZ2dn9O7dG9OnTy+sTSAiIiIi0qrIjfNdGDjONxERERmK43wXLRznm4iIiIiIADD5JiIiIiIyGSbfREREREQmwuSbiIiIiMhEmHwTEREREZkIk28iIiIiIhNh8k1EREREZCJMvomIiIiITITJNxERERGRiTD5JiIiIiIyESbfREREREQmwuSbiIiIiMhEmHwTEREREZkIk28iIiIiIhNh8k1EREREZCJMvomIiIiITITJNxERERGRiTD5JiIiIiIyESbfREREREQmwuSbiIiIiMhEmHwTEREREZkIk28iIiIiIhNh8k1EREREZCJMvomIiIiITITJNxERERGRiTD5JiIiIiIyESbfREREREQmwuSbiIiIiMhEmHwTEREREZkIk28iIiIiIhNh8k1EREREZCJMvomIiIiITITJNxERERGRiTD5JiIiIiIyESbfREREREQmwuSbiIiIiMhEmHwTEREREZkIk28iIiIiIhNh8k1EREREZCIGJd/VqlXDyJEjjR0LEREREVGJZlDynZCQgNKlSxs7FiIiIiKiEs2g5Lthw4a4dOmSsWMhIiIiIirRDEq+x44di5CQEOzZs8fY8RARERERlVjmhsyUmJiIjh07okOHDujRoweaNGkCV1dXqFQqjboDBw7Md5BERERERCWBSkQkrzOVKlUKKpUKz86aM/kWEahUKmRmZuY/ygKWkpICR0dHJCcnw8HBobDDISIiomKkyrhthR0C5RA9q4vJ15mXXNKglu8VK1YYFBgRERER0YvMoOR70KBBxo5DzcKFCzFnzhzExsaiXr16mD9/Plq2bKm17t69e9G2bVuN8oiICNSpU6dA4yQiIiIiyosi95Cd9evXY8yYMZgwYQJOnTqFli1bolOnToiJicl1vsjISMTGxiqvmjVrmihiIiIiIiL9GNTyne369etYs2YNTp8+rfRxadiwIfr3748qVaoYtMx58+ZhyJAhGDp0KABg/vz52LlzJ3788UfMnDlT53zly5eHk5OTQeskIiIiIjIFg1u+v//+e9SuXRtffPEFNm7ciNDQUGzatAlffPEFateujQULFuR5mWlpaQgPD0fHjh3Vyjt27IhDhw7lOm+jRo3g5uaGl19+mUMgEhEREVGRZFDyvX37dowePRpOTk6YMWMGDh8+jKioKBw5cgSzZs1CmTJlEBQUhG3b8nb3b0JCAjIzM+Hq6qpW7urqiri4OK3zuLm5YcmSJdi0aRM2b96M2rVr4+WXX8b+/ft1ric1NRUpKSlqLyIiIiKigmZQt5O5c+fC2dkZJ0+ehLu7u1Lu6emJpk2bon///mjYsCHmzZuHLl3yPtzLs+OFZw9bqE3t2rVRu3Zt5b2/vz9u3LiBuXPnolWrVlrnmTlzJqZMmZLnuIiIiIiI8sOglu+TJ0+id+/eaol3ThUrVkTv3r0RHh6ep+WWK1cOZmZmGq3c8fHxGq3huWnevDkuX76sc/r48eORnJysvG7cuJGnOImIiIiIDGFQ8p2WlgY7O7tc69jZ2SEtLS1Py7W0tETjxo0RGhqqVh4aGooWLVrovZxTp07Bzc1N53QrKys4ODiovYiIiIiICppB3U5q1aqFkJAQzJgxA+bmmovIyMjA//73P9SqVSvPyw4KCsKAAQPg5+cHf39/LFmyBDExMRgxYgSAp63Wt27dwi+//ALg6WgoVapUQb169ZCWlobVq1dj06ZN2LRpkyGbRkRERERUYAxq+R40aBAiIyMRGBio0bXkxIkT6NSpEyIjIw16GE+fPn0wf/58TJ06FQ0bNsT+/fuxfft2eHp6AgBiY2PVxvxOS0vDJ598gvr166Nly5YICwvDtm3b0LNnT0M2jYiIiIiowKhERPI6U2ZmJnr37o0tW7ZApVLBxsYGrq6uuHPnDv7991+ICLp164ZNmzahVKki9xwfDSkpKXB0dFTGKiciIiLSV5VxeRvdjQpW9Ky8D/aRX3nJJQ3KjM3MzLBp0yb8/PPPaNOmDaysrBATEwMrKyu0bdsWP//8M7Zs2VIsEm8iIiIiIlMxqM93TEwMLC0tMWDAAAwYMMDYMRERERERlUgGNU1XrVoVEyZMMHYsREREREQlmkHJd9myZVG2bFljx0JEREREVKIZlHy3bNkSR44cMXYsREREREQlmkHJ98yZM3Hu3DlMmTIFGRkZxo6JiIiIiKhEMuiGy6+++gre3t6YOnUqlixZggYNGsDV1RUqlUqtnkqlwrJly4wSKBERERFRcWdQ8r1y5Url/7GxsYiNjdVaj8k3EREREdF/DEq+o6KijB0HEREREVGJZ1DyvW/fPri6uiIwMNDY8RARERERlVgG3XA5ZMgQ7Ny509ixEBERERGVaAYl325ubkhLSzN2LEREREREJZpByXf37t0RGhqK1NRUY8dDRERERFRiGZR8T5s2Dfb29ujRowfOnz9v7JiIiIiIiEokg264bNSoEVJTU3H69Gns3LkT1tbWKF++vNZxvq9evWqUQImIiIiIijuDku+srCxYWlqicuXKauUikut7IiIiIqIXmUHJd3R0tJHDICIiIiIq+Qzq801ERERERHlXYMl3SkoKYmJiCmrxRERERETFjt7Jd9myZTFnzhy1svXr16Nnz55a63/zzTeoWrVq/qIjIiIiIipB9E6+79+/j3///Vet7OLFi/jjjz+MHhQRERERUUnEPt9ERERERCbC5JuIiIiIyESYfBMRERERmQiTbyIiIiIiE2HyTURERERkInl6wuX333+PX3/9VXmfkJAAAKhbt65G3expRERERET0VJ6S74SEBK1J9cWLF7XWV6lUhkVFRERERFQC6Z18Z2VlFWQcREREREQlHvt8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJmJQ8j116lTs378/1zoHDx7E1KlTDQqKiIiIiKgkMij5Dg4Oxt69e3OtExYWhilTphiyeCIiIiKiEqnAup2kpaWhVCn2aiEiIiIiymZwdqxSqXROS0tLw4EDB+Dq6mro4omIiIiIShxzfStWq1ZN7f0333yDFStWaNTLzMxEQkICnjx5gmHDhuU/QiIiIiKiEkLv5DsrK0tp7VapVBARiIhGPQsLC9SrVw/t2rXDF198YbxIiYiIiIiKOb2T7+joaOX/pUqVwkcffYRJkyYVRExERERERCWS3sl3TlFRUXBycjJyKEREREREJZtBybenp6ex4yAiIiIiKvEMSr4B4O7du1ixYgWOHz+O+/fvIzMzU6OOSqXC7t278xUgEREREVFJYVDyffbsWbRr1w737t3TetNlttyGIyQiIiIietEYNM73xx9/jKSkJEyYMAFRUVFIT09HVlaWxktba7g+Fi5ciKpVq8La2hqNGzfGgQMH9Jrv4MGDMDc3R8OGDQ1aLxERERFRQTIo+T58+DC6d++OqVOnwtPTE2ZmZkYLaP369RgzZgwmTJiAU6dOoWXLlujUqRNiYmJynS85ORkDBw7Eyy+/bLRYiIiIiIiMyaDk29LSEtWrVzd2LACAefPmYciQIRg6dCi8vLwwf/58eHh44Mcff8x1vuHDh6Nfv37w9/cvkLiIiIiIiPLLoOS7Xbt2OHHihLFjQVpaGsLDw9GxY0e18o4dO+LQoUM651uxYgWuXr2KyZMn67We1NRUpKSkqL2IiIiIiAqaQcn3nDlzcP78ecydO9eowSQkJCAzMxOurq5q5a6uroiLi9M6z+XLlzFu3DisWbMG5ub63T86c+ZMODo6Ki8PD498x05ERERE9DwGjXYybdo01KtXD2PHjsWiRYvQoEEDODo6atRTqVRYtmxZnpf/7CgpIqJ15JTMzEz069cPU6ZMQa1atfRe/vjx4xEUFKS8T0lJYQJORERERAXOoOR75cqVyv+vXbuGa9euaa2X1+S7XLlyMDMz02jljo+P12gNB4AHDx7gxIkTOHXqFEaOHAkAyMrKgojA3Nwcu3btQrt27TTms7KygpWVld5xEREREREZg8GPly8IlpaWaNy4MUJDQ9GjRw+lPDQ0FN26ddOo7+DggH/++UetbOHChfj777+xceNGVK1atUDiJCIiIiIyRJF7vHxQUBAGDBgAPz8/+Pv7Y8mSJYiJicGIESMAPO0ycuvWLfzyyy8oVaoUvL291eYvX748rK2tNcqJiIiIiAqbwY+XzykpKQmPHj0ySr/pPn36IDExEVOnTkVsbCy8vb2xfft2JeGPjY197pjfRERERERFkUpyez58LpKTkzFp0iT8+uuvSEhIgEqlQkZGBgDg6NGjmDJlCqZNm4bGjRsbNeCCkJKSAkdHRyQnJ8PBwaGwwyEiIqJipMq4bYUdAuUQPauLydeZl1zSoKEGk5KS0KxZM3z33Xfw8PCAl5cXcubw9evXx8GDB7FmzRpDFk9EREREVCIZlHwHBwfj0qVLWLduHU6cOIFevXqpTbexsUHr1q3x999/GyVIIiIiIqKSwKDke+vWrXj11VfRp08fnXU8PT1x8+ZNgwMjIiIiIippDEq+Y2NjUbdu3VzrWFtb49GjRwYFRURERERUEhmUfDs7O+PGjRu51rl48SLc3NwMCoqIiIiIqCQyKPlu1aoVtm7dilu3bmmdfuHCBfz5559o3759voIjIiIiIipJDEq+J0yYgIyMDAQEBGDt2rVISEgAAERERGDZsmVo164drKys8Omnnxo1WCIiIiKi4sygh+z4+Phg/fr1GDhwIAYMGAAAEBF4e3tDRFC6dGn89ttvqFmzplGDJSIiIiIqzgx+wuVrr72Ga9eu4eeff8bRo0eRlJQEBwcHNGvWDG+//TbKlStnzDiJiIiIiIq9fD1evmzZsvjoo4+MFQsRERERUYlmUJ9vIiIiIiLKO4OS73nz5qFcuXK4ffu21um3b9+Gi4sLvv3223wFR0RERERUkhiUfG/YsAH169eHu7u71unu7u5o2LAhfv3113wFR0RERERUkhiUfF+6dAne3t651qlXrx4uX75sUFBERERERCWRQcn348ePYWdnl2sda2trPHz40KCgiIiIiIhKIoOSb09PTxw6dCjXOocPH0alSpUMCoqIiIiIqCQyKPl+9dVXERYWhuXLl2ud/tNPPyEsLAxdu3bNV3BERERERCWJSkQkrzPdvXsXjRo1QmxsLFq3bo0OHTqgYsWKuHXrFnbt2oX9+/fD3d0dJ0+ehIuLS0HEbVQpKSlwdHREcnIyHBwcCjscIiIiKkaqjNtW2CFQDtGzuph8nXnJJQ16yI6Liwv27NmDt956C3v37sXevXuhUqmQncc3bdoUq1evLhaJNxERERGRqRj8hMuaNWvi6NGjOHHiBI4dO4b79+/DyckJTZs2hZ+fnzFjJCIiIiIqEQxKvt955x3Ur18fY8aMgZ+fH5NtIiIiIiI9GHTD5dq1a3Hnzh1jx0JEREREVKIZlHzXqFEDsbGxxo6FiIiIiKhEMyj5HjJkCLZt24Zbt24ZOx4iIiIiohLLoD7fPXr0wO7du9GiRQt89tlnaNKkCVxdXaFSqTTqVq5cOd9BEhERERGVBAYl39WqVVOGFhw9erTOeiqVChkZGQYHR0RERERUkhiUfA8cOFBrKzcREREREelmUPK9cuVKI4dBRERERFTyGXTDJRERERER5Z3BT7gEgLi4OGzevBkXL17Eo0ePsGzZMgDA3bt3ERUVBR8fH9jY2BglUCIiIiKi4s7g5HvhwoX4+OOPkZqaCuDpzZXZyXd8fDz8/f2xaNEiDBs2zDiREhEREREVcwZ1OwkJCcHIkSPh4+ODrVu34r333lObXq9ePdSvXx+///67MWIkIiIiIioRDGr5njNnDipXrow9e/bAzs4O4eHhGnV8fHxw4MCBfAdIRERERFRSGNTyffr0aXTp0gV2dnY661SsWBF37twxODAiIiIiopLGoOQ7KysLFhYWuda5e/curKysDAqKiIiIiKgkMij5rl27NsLCwnROz8jIwL59++Dj42NwYEREREREJY1ByXf//v1x8uRJTJ8+XWNaZmYmPvnkE1y7dg0DBw7Md4BERERERCWFQTdcjho1CiEhIZg8eTJWrVqldC/p3bs3Tpw4gejoaHTs2BFDhgwxarBERERERMWZQS3fFhYW2LlzJ8aNG4eEhAScO3cOIoKNGzciKSkJY8eOxdatW6FSqYwdLxERERFRsWXwQ3YsLS3x5ZdfYvr06YiMjERSUhIcHBzg5eUFMzMzY8ZIRERERFQi5Cn5vnfvHr7//nscP34cANC0aVOMHDkSderUKZDgiIiIiIhKEr2T78TERDRt2hTR0dEQEQDAtm3b8PPPP+Po0aMoW7ZsgQVJRERERFQS6N3ne8aMGYiKikKbNm3w66+/4tdff0WrVq1w9epVzJo1qyBjJCIiIiIqEVSS3Yz9HF5eXsjMzERERITSpzsjIwNeXl6wsLDAhQsXCjTQgpSSkgJHR0ckJyfDwcGhsMMhIiKiYqTKuG2FHQLlED2ri8nXmZdcUu+W7+vXryMwMFDtZkpzc3O88soriI6ONjhYIiIiIqIXhd7J95MnT+Di4qJRXq5cOaSmpho1KCIiIiKiksigcb4L2sKFC1G1alVYW1ujcePGOHDggM66YWFhCAgIgLOzM2xsbFCnTh188803JoyWiIiIiEg/eRpqMCwsDLNnz9YoA4A5c+ZAW/fxzz77LE8BrV+/HmPGjMHChQsREBCAxYsXo1OnTrhw4QIqV66sUd/Ozg4jR45E/fr1YWdnh7CwMAwfPhx2dnZ4991387RuIiIiIqKCpPcNl6VK5b2RXKVSITMzM0/zNGvWDL6+vvjxxx+VMi8vL3Tv3h0zZ87Uaxk9e/aEnZ0dVq1apVd93nBJREREhuINl0VLUb/hUu+W7xUrVuQ7sOdJS0tDeHg4xo0bp1besWNHHDp0SK9lnDp1CocOHcL06dN11klNTVXrp56SkmJYwEREREREeaB38j1o0KCCjAMAkJCQgMzMTLi6uqqVu7q6Ii4uLtd5K1WqhLt37yIjIwPBwcEYOnSozrozZ87ElClTjBIzEREREZG+iuQNlyqVSu29iGiUPevAgQM4ceIEFi1ahPnz52PdunU6644fPx7JycnK68aNG0aJm4iIiIgoN3m64bKglStXDmZmZhqt3PHx8Rqt4c+qWrUqAMDHxwd37txBcHAw3nzzTa11raysYGVlZZygiYiIiIj0VKRavi0tLdG4cWOEhoaqlYeGhqJFixZ6L0dEOPY4ERERERU5RarlGwCCgoIwYMAA+Pn5wd/fH0uWLEFMTAxGjBgB4GmXkVu3buGXX34BAPzwww+oXLky6tSpA+Dp0Idz587FqFGjCm0biIiIiIi0KXLJd58+fZCYmIipU6ciNjYW3t7e2L59Ozw9PQEAsbGxiImJUepnZWVh/PjxiIqKgrm5OapXr45Zs2Zh+PDhhbUJRERERERa6T3Od0nGcb6JiIjIUBznu2gp6uN8F6k+30REREREJVm+up3ExcVh8+bNuHjxIh4/foyffvoJAHD37l1ERUXBx8cHNjY2RgmUiIiIiKi4Mzj5XrhwIT7++GNlVBGVSqUk3/Hx8fD398eiRYswbNgw40RKRERERFTMGdTtJCQkBCNHjoSPjw+2bt2K9957T216vXr1UL9+ffz+++/GiJGIiIiIqEQwqOV7zpw5qFy5Mvbs2QM7OzuEh4dr1PHx8cGBAwfyHSARERERUUlhUMv36dOn0aVLF9jZ2emsU7FiRdy5c8fgwIiIiIiIShqDku+srCxYWFjkWufu3bt8hDsRERERUQ4GJd+1a9dGWFiYzukZGRnYt28ffHx8DA6MiIiIiKikMSj57t+/P06ePInp06drTMvMzMQnn3yCa9euYeDAgfkOkIiIiIiopDDohstRo0YhJCQEkydPxqpVq5TuJb1798aJEycQHR2Njh07YsiQIUYNloiIiIioODOo5dvCwgI7d+7EuHHjkJCQgHPnzkFEsHHjRiQlJWHs2LHYunUrVCqVseMlIiIiIiq2DH7IjqWlJb788ktMnz4dkZGRSEpKgoODA7y8vGBmZmbMGImIiIiISoR8PV4eePpkyzp16hgjFiIiIiKiEs2gbie1atXCtGnTcO3aNWPHQ0RERERUYhmUfN+5cweTJ09GzZo18dJLL2Hx4sW4d++esWMjIiIiIipRDEq+4+PjsW7dOnTu3BnHjx/H+++/Dzc3N7z++uvYsmUL0tPTjR0nEREREVGxZ1DybWVlhT59+iAkJAS3b9/GggUL0LBhQ2zZsgVvvPEGKlSogPfeey/XB/EQEREREb1oVCIixlrYlStXsHr1aqxduxZXrlxBqVKlkJGRYazFF5iUlBQ4OjoiOTkZDg4OhR0OERERFSNVxm0r7BAoh+hZXUy+zrzkkvke7SSnGjVqoF27drh16xauX79eLBJvIiIiIiJTMUryff78eaxZswZr167FjRs3ICKoWbMm3nrrLWMsnoiIiIioRDA4+Y6NjcXatWuxevVqnD17FiKCcuXK4b333sOAAQPQrFkzY8ZJRERUbLAbQtFRGF0QiHJjUPLdoUMH7N27F5mZmbCyssLrr7+OAQMGoFOnTjA3N2pPFiIiIiKiEsOgTPnvv/9Gy5YtMWDAAPTq1Ys3KRIRERER6cGg5DsqKgqVK1c2dixERERERCWaQeN8M/EmIiIiIso7vVq+9+/fDwBo2rQprK2tlff6aNWqlWGRERERERGVMHol323atIFKpUJERARq1aqlvNdHZmZmvgIkIiIiIiop9Eq+J02aBJVKhXLlyqm9JyIiIiIi/emVfAcHB+f6noiIiIiIns+gGy5jYmKQkpKSa50HDx4gJibGoKCIiIiIiEoig5LvqlWrYsGCBbnWWbhwIapWrWpQUEREREREJZFBybeIQESeW4eIiIiIiP5jUPKtj5s3b6J06dIFtXgiIiIiomJH7ydcTp06Ve393r17tdbLzMzEzZs38euvv6JZs2b5Co6IiIiIqCTRO/nOOcKJSqXC3r17dSbgAODu7o6vvvoqP7EREREREZUoeiffe/bsAfC0L3e7du0wePBgDBo0SKOemZkZypYtizp16qBUqQLr1UJEREREVOzonXy3bt1a+f/kyZPRtm1bPjqeiIiIiCgP9E6+c5o8ebKx4yAiIiIiKvEMSr5zunHjBm7fvo3U1FSt09k6TkRERET0lMHJd0hICD799FNcvnw513qZmZmGroKIiIiIqEQx6I7IvXv3okePHnj48CFGjhwJEUGrVq3w7rvvom7duhARdOnSBZMmTTJ2vERERERExZZByfesWbNgb2+P8PBw5THzbdu2xY8//oizZ8/iyy+/xO7du9GtWzejBktEREREVJwZlHwfP34c3bt3h6urq1KWlZUF4OkY4OPHj0ejRo3Y8k1ERERElINByffjx49RsWJF5b2VlRVSUlLU6jRv3hwHDx7MX3RERERERCWIQcl3hQoVcPfuXeV9xYoVcf78ebU6iYmJvNmSiIiIiCgHg5LvBg0a4Ny5c8r7tm3bYs+ePfj111/x6NEj7Ny5E+vXr0f9+vWNFigRERERUXFnUPL92muv4fTp07h+/ToA4PPPP4e9vT369+8PBwcHdO7cGZmZmZg+fbpBQS1cuBBVq1aFtbU1GjdujAMHDuisu3nzZnTo0AEuLi5wcHCAv78/du7cadB6iYiIiIgKkkHJ9zvvvIPHjx/D09MTAFC1alUcP34cI0aMQMeOHTFs2DAcPXrUoAfsrF+/HmPGjMGECRNw6tQptGzZEp06dUJMTIzW+vv370eHDh2wfft2hIeHo23btujatStOnTplyKYRERERERUYlYhIYQeRU7NmzeDr64sff/xRKfPy8kL37t0xc+ZMvZZRr1499OnTR+/RVlJSUuDo6Ijk5GQ4ODgYFDcREVG2KuO2FXYI9P+iZ3Up8HXweBctpjjmz8pLLmlQy3dBSUtLQ3h4ODp27KhW3rFjRxw6dEivZWRlZeHBgwcoW7aszjqpqalISUlRexERERERFTS9Hi+/f/9+g1eQl64nCQkJyMzMVBs/HABcXV0RFxen1zK+/vprPHr0CL1799ZZZ+bMmZgyZYrecRERERERGYNeyXebNm2gUqkMWoEhww0+uy4R0Wv969atQ3BwMP744w+UL19eZ73x48cjKChIeZ+SkgIPD488x0lERERElBd6Jd+TJk0yOPnOi3LlysHMzEyjlTs+Pl6jNfxZ69evx5AhQ7Bhwwa0b98+17pWVlawsrLKd7xERERERHmhV/IdHBxcwGE8ZWlpicaNGyM0NBQ9evRQykNDQ9GtWzed861btw7vvPMO1q1bhy5dTN/JnoiIiIhIH3ol36YUFBSEAQMGwM/PD/7+/liyZAliYmIwYsQIAE+7jNy6dQu//PILgKeJ98CBA7FgwQI0b95caTW3sbGBo6NjoW0HEREREdGz8pV8x8XFYfPmzbh48SIePXqEZcuWAQDu3r2LqKgo+Pj4wMbGJk/L7NOnDxITEzF16lTExsbC29sb27dvV8YUj42NVRvze/HixcjIyMAHH3yADz74QCkfNGgQVq5cmZ/NIyIiIiIyKoPH+V64cCE+/vhjpKamPl2QSqXcXHn+/HnUr18fixYtwrBhw4wXbQHhON9ERGRMHPe56OA43y+eEjnOd0hICEaOHAkfHx9s3boV7733ntr0evXqoX79+vj9998NWTwRERERUYlkULeTOXPmoHLlytizZw/s7OwQHh6uUcfHxwcHDhzId4BERERERCWFQS3fp0+fRpcuXWBnZ6ezTsWKFXHnzh2DAyMiIiIiKmkMSr6zsrJgYWGRa527d+9yLG0iIiIiohwMSr5r166NsLAwndMzMjKwb98++Pj4GBwYEREREVFJY1Dy3b9/f5w8eRLTp0/XmJaZmYlPPvkE165dw8CBA/MdIBERERFRSWHQDZejRo1CSEgIJk+ejFWrVindS3r37o0TJ04gOjoaHTt2xJAhQ4waLBERERFRcWZQy7eFhQV27tyJcePGISEhAefOnYOIYOPGjUhKSsLYsWOxdetWqFQqY8dLRERERFRsGfyES0tLS3z55ZeYPn06IiMjkZSUBAcHB3h5ecHMzMyYMRIRERERlQgGtXznpFKpUKdOHbRo0QLe3t5K4h0VFYXBgwfnd/FERERERCVGvpPvZ8XExGDYsGGoU6cOVq1aZezFExEREREVW3lKvsPCwtC2bVs4ODigbNmy6NatGyIjIwEAjx8/RlBQEGrVqoVly5bBxcUF3377bYEETURERERUHOnd5zs8PBzt27dHWlqaUhYSEoLjx49j//796N69Oy5cuAB3d3eMHTsW7777Lh+yQ0RERESUg94t37Nnz0ZaWhpmzpyJ+Ph4xMfHY+rUqYiLi0PLli1x8eJFTJw4EVeuXMGoUaOYeBMRERERPUPvlu+DBw+iXbt2GDt2rFI2ceJE7N69G/v378ecOXMQFBRUIEESEREREZUEerd8x8fHo3HjxhrlTZo0AQAMGjTIeFEREREREZVAeiffGRkZsLOz0yjPLnN2djZeVEREREREJZDRhxokIiIiIiLt8vSEy9WrV+PIkSNqZVeuXAEAdO7cWaO+SqXCtm3b8hEeEREREVHJkafk+8qVK0qy/aw///xTo0ylUhkWFRERERFRCaR38h0VFVWQcRARERERlXh6J9+enp4FGQcRERERUYnHGy6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiRTL5XrhwIapWrQpra2s0btwYBw4c0Fk3NjYW/fr1Q+3atVGqVCmMGTPGdIESEREREeVBkUu+169fjzFjxmDChAk4deoUWrZsiU6dOiEmJkZr/dTUVLi4uGDChAlo0KCBiaMlIiIiItJfkUu+582bhyFDhmDo0KHw8vLC/Pnz4eHhgR9//FFr/SpVqmDBggUYOHAgHB0dTRwtEREREZH+ilTynZaWhvDwcHTs2FGtvGPHjjh06JDR1pOamoqUlBS1FxERERFRQStSyXdCQgIyMzPh6uqqVu7q6oq4uDijrWfmzJlwdHRUXh4eHkZbNhERERGRLkUq+c6mUqnU3ouIRll+jB8/HsnJycrrxo0bRls2EREREZEu5oUdQE7lypWDmZmZRit3fHy8Rmt4flhZWcHKyspoyyMiIiIi0keRavm2tLRE48aNERoaqlYeGhqKFi1aFFJURERERETGUaRavgEgKCgIAwYMgJ+fH/z9/bFkyRLExMRgxIgRAJ52Gbl16xZ++eUXZZ7Tp08DAB4+fIi7d+/i9OnTsLS0RN26dQtjE4iIiIiItCpyyXefPn2QmJiIqVOnIjY2Ft7e3ti+fTs8PT0BPH2ozrNjfjdq1Ej5f3h4ONauXQtPT09ER0ebMnQiIiIiolwVueQbAN5//328//77WqetXLlSo0xECjgiIiIiIqL8K1J9vomIiIiISjIm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiITMS/sAIiISroq47YVdgiUQ/SsLoUdAhG9wIpky/fChQtRtWpVWFtbo3Hjxjhw4ECu9fft24fGjRvD2toa1apVw6JFi0wUKRERERGR/opc8r1+/XqMGTMGEyZMwKlTp9CyZUt06tQJMTExWutHRUWhc+fOaNmyJU6dOoXPP/8co0ePxqZNm0wcORERERFR7opc8j1v3jwMGTIEQ4cOhZeXF+bPnw8PDw/8+OOPWusvWrQIlStXxvz58+Hl5YWhQ4finXfewdy5c00cORERERFR7opUn++0tDSEh4dj3LhxauUdO3bEoUOHtM5z+PBhdOzYUa0sMDAQy5YtQ3p6OiwsLDTmSU1NRWpqqvI+OTkZAJCSkpLfTSB6Lu/JOws7BMrh3JTAAl9HVurjAl8H6c8U13oe86KDx/vFUxj5XPY6ReS5dYtU8p2QkIDMzEy4urqqlbu6uiIuLk7rPHFxcVrrZ2RkICEhAW5ubhrzzJw5E1OmTNEo9/DwyEf0RFQcOc4v7AjI1HjMXyw83i+ewjzmDx48gKOjY651ilTynU2lUqm9FxGNsufV11aebfz48QgKClLeZ2VlISkpCc7Ozrmuh7RLSUmBh4cHbty4AQcHh8IOh0yAx/zFw2P+4uExf7HweOePiODBgwdwd3d/bt0ilXyXK1cOZmZmGq3c8fHxGq3b2SpUqKC1vrm5OZydnbXOY2VlBSsrK7UyJycnwwMnAICDgwNP2BcMj/mLh8f8xcNj/mLh8Tbc81q8sxWpGy4tLS3RuHFjhIaGqpWHhoaiRYsWWufx9/fXqL9r1y74+flp7e9NRERERFRYilTyDQBBQUH46aefsHz5ckREROCjjz5CTEwMRowYAeBpl5GBAwcq9UeMGIHr168jKCgIERERWL58OZYtW4ZPPvmksDaBiIiIiEirItXtBAD69OmDxMRETJ06FbGxsfD29sb27dvh6ekJAIiNjVUb87tq1arYvn07PvroI/zwww9wd3fHt99+i9dff72wNuGFY2VlhcmTJ2t05aGSi8f8xcNj/uLhMX+x8Hibjkr0GROFiIiIiIjyrch1OyEiIiIiKqmYfBMRERERmQiTbyIiIiIiE2HyTQZp06YNxowZk69lBAcHo2HDhkaJR5u9e/dCpVLh/v37BbYOKppWrlzJsfvzSKVS4ffffzf6cgcPHozu3bsXiVheBNx3lE2f79i8np/R0dFQqVQ4ffp0vmLLzYtw/WbyXYDi4uLw4YcfokaNGrC2toarqyteeuklLFq0CI8fPy7s8HRKS0vD7Nmz0aBBA9ja2qJcuXIICAjAihUrkJ6eXtjhFUvF8bPwIlwAiwuVSpXra/DgwYUW2+LFi9GgQQPY2dnByckJjRo1wldffaVMX7BgAVauXFlo8ZU08fHxGD58OCpXrgwrKytUqFABgYGBOHz4MICnI4J16tSpkKMsPoryuZVfn3zyCXbv3m3y9RaVhq8qVapg/vz5amVF5XutyA01WFJcu3YNAQEBcHJywowZM+Dj44OMjAxcunQJy5cvh7u7O1577bXCDlNDWloaAgMDcebMGUybNg0BAQFwcHDAkSNHMHfuXDRq1KhAW6tLouL6WSjJ0tPTi9VDuGJjY5X/r1+/HpMmTUJkZKRSZmNjUxhhYdmyZQgKCsK3336L1q1bIzU1FWfPnsWFCxeUOvo+8Y308/rrryM9PR0///wzqlWrhjt37mD37t1ISkoC8PSpz6S/vJ5bxenaYW9vD3t7+8IOg7QRKhCBgYFSqVIlefjwodbpWVlZIiLy9ddfi7e3t9ja2kqlSpXkvffekwcPHij1Jk+eLA0aNFCb95tvvhFPT0/l/Z49e6RJkyZia2srjo6O0qJFC4mOjhYRkdOnT0ubNm3E3t5eSpcuLb6+vnL8+HGdcX/11VdSqlQpOXnypMa0tLQ0ZXtat24to0aNkk8//VTKlCkjrq6uMnnyZLX69+/fl2HDhomLi4uULl1a2rZtK6dPn9bYtkWLFkmlSpXExsZG3njjDbl3756IiOzbt0/Mzc0lNjZWbblBQUHSsmVLERGJjo6WV199VZycnMTW1lbq1q0r27ZtU/YLAPnrr7+kcePGYmNjI/7+/nLx4kW15W3dulV8fX3FyspKqlatKsHBwZKeni4iIn379pU+ffpo7AdnZ2dZvny5zv2YU3H9LKxYsUIcHR11Tn/e8RURmTZtmri4uIi9vb0MGTJExo4dq7ENy5cvlzp16oiVlZXUrl1bfvjhB2VaVFSUAJBNmzZJmzZtxMbGRurXry+HDh3SiNXDw0NsbGyke/fuMnfuXLXYs/fdsmXLpGrVqqJSqSQrK0uvbShqnj0uCQkJ0rdvX6lYsaLY2NiIt7e3rF27Vm0efc5XALJ06VLp3r272NjYSI0aNeSPP/7INZZu3brJ4MGDc60zaNAg6datW4HH8iK4d++eAJC9e/fqrANAtmzZIiL/nT/r16+Xl156SaytrcXPz08iIyPl2LFj0rhxY7Gzs5PAwECJj49XlpF9zIKDg5Vz491335XU1FSlzoYNG8Tb21usra2lbNmy8vLLLyvXuMzMTJkyZYpUrFhRLC0tpUGDBrJjxw5lXn3Pa1N79tzKuf9at24tVlZWsnz5cr3PuQ8++EA++OADcXR0lLJly8qECROU672ISGpqqnz66afi7u4utra20rRpU9mzZ4/aMgBovKKiokRE5Pr16/Laa6+JnZ2dlC5dWnr16iVxcXHK/M9+Z2RkZMhHH32kxPPpp5/KwIED1c7PHTt2SEBAgFKnS5cucuXKFY19curUKZ37Mfu7N/u7/FlJSUkyYMAAcXJyEhsbG3nllVfk0qVLGsdhy5YtUrNmTbGyspL27dtLTEyMUufKlSvy2muvSfny5cXOzk78/PwkNDQ0132XHVfOV/a153kxGRuT7wKQkJAgKpVKZs6c+dy633zzjfz9999y7do12b17t9SuXVvee+89ZfrzEq709HRxdHSUTz75RK5cuSIXLlyQlStXyvXr10VEpF69evLWW29JRESEXLp0SX777bdck4v69etLx44dnxt369atxcHBQYKDg+XSpUvy888/i0qlkl27donI04QyICBAunbtKsePH5dLly7Jxx9/LM7OzpKYmKhsm52dnbRr105OnTol+/btkxo1aki/fv2U9dSqVUtmz56tvE9PT5fy5csriW+XLl2kQ4cOcvbsWbl69aqEhITIvn37ROS/C0CzZs1k7969cv78eWnZsqW0aNFCWd6ff/4pDg4OsnLlSrl69ars2rVLqlSpIsHBwSIiEhISIjY2NmpJcEhIiFhbW0tycvJz91Nx/izklnzrc3xXr14t1tbWsnz5comMjJQpU6aIg4OD2jYsWbJE3NzcZNOmTXLt2jXZtGmTlC1bVlauXCki/13o69SpI//73/8kMjJS3njjDfH09FR+IB05ckTZx5GRkbJgwQJxcnLSSL6zk4yTJ0/KmTNn9NqGoujZ43Lz5k2ZM2eOnDp1Sq5evSrffvutmJmZyZEjR5Q6zztfRZ4mbZUqVZK1a9fK5cuXZfTo0WJvb5/rvhg+fLjUqVNH+YGnjbbkuyBieRGkp6eLvb29jBkzRp48eaK1jrbku06dOvLnn3/KhQsXpHnz5uLr6ytt2rSRsLAwOXnypNSoUUNGjBihLGPQoEFib28vffr0kXPnzsn//vc/cXFxkc8//1xERG7fvi3m5uYyb948iYqKkrNnz8oPP/ygXCfnzZsnDg4Osm7dOrl48aJ89tlnYmFhoSQz+pzXhUFX8l2lShXlGnXr1i29zzl7e3v58MMP5eLFi7J69WqxtbWVJUuWKHX69esnLVq0kP3798uVK1dkzpw5YmVlpeynxMREiY2NVV49e/aU2rVry+PHjyUrK0saNWokL730kpw4cUKOHDkivr6+0rp1a2X5z35nfPXVV+Lo6CgbN26UCxcuyJAhQ6R06dJq5+fGjRtl06ZNcunSJTl16pR07dpVfHx8JDMzU22f5Cf5fu2118TLy0v2798vp0+flsDAQKlRo4akpaUpx8HCwkL8/Pzk0KFDcuLECWnatKnad/fp06dl0aJFcvbsWbl06ZJMmDBBrK2tle+7xMREqVSpkkydOlXZf6mpqTJ//nxxcHBQyrI/s8+LydiYfBeAI0eOCADZvHmzWrmzs7PY2dmJnZ2dfPbZZ1rn/e2338TZ2Vl5/7yEKzExMdeWkNKlSyuJjD5sbGxk9OjRz63XunVreemll9TKmjRpImPHjhURkd27d4uDg4PGF0T16tVl8eLFIvJ028zMzOTGjRvK9B07dkipUqWU1u6vvvpKvLy8lOm///672NvbKy0sPj4+SqL8rJwt39m2bdsmAOTff/8VEZGWLVvKjBkz1OZbtWqVuLm5icjTVu5y5crJL7/8okx/8803pVevXs/bRSJSvD8LuSXf+hzfZs2ayQcffKA2PSAgQG0bPDw8NFqMpk2bJv7+/iLy34X+p59+UqafP39eAEhERISIPD0er7zyitoy+vTpo5F8W1hYqLXu6bMNRdHz/iIhItK5c2f5+OOPlffPO19FniZtEydOVN4/fPhQVCqVWovls27fvi3NmzcXAFKrVi0ZNGiQrF+/XvmiFtGefBdELC+KjRs3SpkyZcTa2lpatGgh48ePlzNnzijTtSXfOc+fdevWCQDZvXu3UjZz5kypXbu28n7QoEFStmxZefTokVL2448/ir29vWRmZkp4eLgA0Pmjy93dXb788ku1siZNmsj777+vM65nz+vCoCv5nj9//nPn1XbOeXl5qbV0jx07Vvk+u3LliqhUKrl165bacl5++WUZP368xvLnzZsnTk5OEhkZKSIiu3btEjMzM7XW4Ox9eOzYMRHR/M5wc3OTWbNmKe/T09OlUqVKaufns+Lj4wWA/PPPPyKS/+T70qVLAkAOHjyolCUkJIiNjY389ttvIvL0OABQ+zETEREhAOTo0aM611u3bl357rvvlPeenp7yzTffqNXRdv3UJyZj4w2XBUilUqm9P3bsGE6fPo169eohNTUVALBnzx506NABFStWROnSpTFw4EAkJibi0aNHeq2jbNmyGDx4MAIDA9G1a1csWLBArQ9bUFAQhg4divbt22PWrFm4evWqMi27P5i9vT1GjBgBABARjbh1qV+/vtp7Nzc3xMfHAwDCw8Px8OFDODs7q60nKipKLYbKlSujUqVKynt/f39kZWUpfe4GDx6MK1eu4MiRIwCA5cuXo3fv3rCzswMAjB49GtOnT0dAQAAmT56Ms2fP5hqnm5sbAKjFOXXqVLUYhw0bhtjYWDx+/BgWFhbo1asX1qxZAwB49OgR/vjjD/Tv31+vfZStOH4WcqPP8Y2MjETTpk3V5sv5/u7du7hx4waGDBmitozp06erxQbkfgwjIiLg7++vVv/Z9wDg6ekJFxeXPG1DcZCZmYkvv/wS9evXV7Zl165diImJUauX2/mqrY6dnR1Kly6t1KlXr56yj7Jv6HNzc8Phw4fxzz//YPTo0UhPT8egQYPwyiuvICsrS2fM+Y3lRfb666/j9u3b2Lp1KwIDA7F37174+vrmelNrzn3p6uoKAPDx8VEre3bfZt9wn83f3x8PHz7EjRs30KBBA7z88svw8fFBr169sHTpUty7dw8AkJKSgtu3byMgIEBteQEBAYiIiNAZ17PndVHi5+en9l7fc6558+Zq135/f39cvnwZmZmZOHnyJEQEtWrVUrv+7Nu3T+P6s2PHDowbNw7r169HrVq1ADy97nl4eMDDw0OpV7duXTg5OWnsZwBITk5GbGys2rXR3NxcY9uuXr2Kfv36oVq1anBwcEDVqlUBQGPbsmm7LuQmIiIC5ubmaNasmVLm7OyM2rVrq8X9bGx16tRR27ZHjx7hs88+U7bZ3t4eFy9e1BmnMWIyJt5wWQBq1KgBlUqFixcvqpVXq1YNwH83cFy/fh2dO3fGiBEjMG3aNJQtWxZhYWEYMmSIMqpIqVKlICJqy3l2xJEVK1Zg9OjR+PPPP7F+/XpMnDgRoaGhaN68OYKDg9GvXz9s27YNO3bswOTJk/Hrr7+iR48eakMFOTg4AABq1aql94ft2ZtOVCqV8oWblZUFNzc37N27V2O+3O40zr5QZf9bvnx5dO3aFStWrEC1atWwfft2tWUOHToUgYGB2LZtG3bt2oWZM2fi66+/xqhRo7TGmb3cnHFOmTIFPXv21IjF2toaANC/f3+0bt0a8fHxCA0NhbW1td6jCRTnz0Ju9D2+z/7oyBl/9jFYunSp2kUPAMzMzNTe53YMn90numT/YMvrNhR1X3/9Nb755hvMnz8fPj4+sLOzw5gxY5CWlqZWL7fzVZ8627dvVz5vz96E5u3tDW9vb3zwwQcICwtDy5YtsW/fPrRt21ZrzPmN5UVnbW2NDh06oEOHDpg0aRKGDh2KyZMn6xyZQ9v582yZvvtWpVLBzMwMoaGhOHToEHbt2oXvvvsOEyZMwNGjR+Hs7Ky2nmzaGnZyO6+LkmevHfqec7nJysqCmZkZwsPDNa53OW+SvHDhAvr27YtZs2ahY8eOSrmuhrK8NKBp07VrV3h4eGDp0qVwd3dHVlYWvL29dW5bbtcFbXRdr7XFrW07sss+/fRT7Ny5E3PnzkWNGjVgY2ODN954I0/HwJCYjIXJdwFwdnZGhw4d8P3332PUqFEaJ262EydOICMjA19//TVKlXr6R4jffvtNrY6Liwvi4uLUPgTaxtds1KgRGjVqhPHjx8Pf3x9r165F8+bNATxNqGvVqoWPPvoIb775JlasWIEePXqgRo0aGsvp168fPv/8c5w6dQqNGjVSm5aRkYHU1FSd25OTr68v4uLiYG5ujipVquisFxMTg9u3b8Pd3R0AcPjwYZQqVUr5dQ88TbD79u2LSpUqoXr16hotKh4eHhgxYgRGjBiB8ePHY+nSpWrJ9/PijIyM1LovsrVo0QIeHh5Yv349duzYgV69esHS0lKv5Rfnz0Ju9Dm+tWvXxrFjxzBgwAC17czm6uqKihUr4tq1a3n+S0JOdevWVf4yku3Z99ro+xkt6g4cOIBu3brhrbfeAvD0S/3y5cvw8vIy6no8PT31qle3bl0A0PsvNpR/devWNfrY3mfOnMG///6rJFRHjhyBvb298pdKlUqFgIAABAQEYNKkSfD09MSWLVsQFBQEd3d3hIWFoVWrVsryDh06pPGXsOJK33NO23WpZs2aMDMzQ6NGjZCZmYn4+Hi0bNlS63oSExPRtWtX9OzZEx999JHatLp16yImJgY3btxQWr8vXLiA5ORkree+o6Mj3NzccOTIEeW4ZGRkIDw8HL6+vsr6IiIisHjxYiWmsLCwXPeFvteFnHFnZGTg6NGjaNGihbLeS5cuqcWdkZGBEydOKJ+ZyMhI3L9/H3Xq1AHw9BgMHjwYPXr0AAA8fPgQ0dHRauuytLREZmbmc8v0jcmY2O2kgCxcuBAZGRnw8/PD+vXrERERgcjISKxevRoXL16EmZkZqlevjoyMDHz33Xe4du0aVq1ahUWLFqktp02bNrh79y5mz56Nq1ev4ocffsCOHTuU6VFRURg/fjwOHz6M69evY9euXcoH5t9//8XIkSOxd+9eXL9+HQcPHsTx48dz/TCNGTMGAQEBePnll/HDDz/gzJkzuHbtGn777Tc0a9YMly9f1mv727dvD39/f3Tv3h07d+5EdHQ0Dh06hIkTJ6olYNbW1hg0aBDOnDmDAwcOYPTo0ejdu7facFmBgYFwdHTE9OnT8fbbb2vEu3PnTkRFReHkyZP4+++/83SyTJo0Cb/88guCg4Nx/vx5REREKC3G2VQqFfr164dFixYhNDRUueDqq7h+FoCnf149ffq02uvChQt6Hd9Ro0Zh2bJl+Pnnn3H58mVMnz4dZ8+eVWtJCA4OxsyZM7FgwQJcunQJ//zzD1asWIF58+bpvX+zW/pnz56NS5cu4fvvv8eff/753Pn0/YwWdTVq1FBaISMiIjB8+HDExcWZZN3vvfcepk2bhoMHD+L69es4cuQIBg4cCBcXF61dfyh/EhMT0a5dO6xevRpnz55FVFQUNmzYgNmzZ6Nbt25GXVdaWhqGDBmCCxcuKH8pGzlyJEqVKoWjR49ixowZOHHiBGJiYrB582bcvXtXuZ58+umn+Oqrr7B+/XpERkZi3LhxOH36ND788EOjxlhY9D3nbty4gaCgIERGRmLdunX47rvvlH1Qq1Yt9O/fHwMHDsTmzZsRFRWF48eP46uvvsL27dsBAD179oSNjQ2Cg4MRFxenvDIzM9G+fXvUr18f/fv3x8mTJ3Hs2DEMHDgQrVu31uhKku3DDz/ErFmzsGXLFly8eBHvv/++2ljcZcqUgbOzM5YsWYIrV67g77//RlBQkMH76Z9//tH4/qhZsya6deuGYcOGISwsDGfOnMFbb72FihUrqn2GLSwsMGrUKBw9ehQnT57E22+/jebNmyvJeI0aNbB582acPn0aZ86cQb9+/TT+alKlShXs378ft27dQkJCglL28OFD7N69GwkJCXj8+LHeMRlVgfQkJxF5ejPSyJEjpWrVqmJhYSH29vbStGlTmTNnjnIjy7x588TNzU1sbGwkMDBQfvnlF40bFX788Ufx8PAQOzs7GThwoHz55ZfKTXZxcXHSvXt3cXNzE0tLS/H09JRJkyZJZmampKamSt++fcXDw0MsLS3F3d1dRo4cqdxsqMuTJ09k5syZ4uPjowwjFRAQICtXrlTuRG/durV8+OGHavN169ZNBg0apLxPSUmRUaNGibu7u1hYWIiHh4f0799fuUEk+2aQhQsXiru7u1hbW0vPnj0lKSlJI6YvvvhCzMzM5Pbt22rlI0eOlOrVq4uVlZW4uLjIgAEDJCEhQUS03/Rx6tQptaGaRJ6OeNKiRQuxsbERBwcHadq0qdod6SL/3cji6empdgONvorjZyH7ppdnX9nre97xFRGZOnWqlCtXTuzt7eWdd96R0aNHS/PmzdXWs2bNGmnYsKFYWlpKmTJlpFWrVsoNqtpu7skebi3nkFzLli1Thqvs2rWrzqEGn6XPNhQ1z94wlJiYKN26dRN7e3spX768TJw4UWP4MH3OV+S4US+bo6OjrFixQmcsGzdulM6dOyufOXd3d3n99dfl7NmzSh1tN1wWRCwvgidPnsi4cePE19dXHB0dxdbWVmrXri0TJ06Ux48fi4j2Gy5znj/arovPfqayj9mkSZPE2dlZ7O3tZejQocrNyRcuXJDAwEBxcXERKysrqVWrltqNbjmHGrSwsNA51ODzzmtT03XD5bM3F+p7zr3//vsyYsQIcXBwkDJlysi4cePUvj/S0tJk0qRJUqVKFbGwsJAKFSpIjx49lPNH2/U35/dXXocaTE9Plw8//FAcHBzEyclJgoKCNOIODQ0VLy8vsbKykvr168vevXuf+5l6lrYh/bJfIv8N6+fo6Kh832kbanDTpk1SrVo1sbS0lHbt2qnd4BsVFSVt27YVGxsb8fDwkO+//17j2nL48GGpX7++WFlZKesWERkxYoQ4OztrHWpQV0zGphLRs8MkUSEaNmwY7ty5g61btxZ2KJQPHTp0QIUKFbBq1arCDoWIdBg8eDDu37/Px9TnQ5s2bdCwYUONJywSAezzTUVccnIyjh8/jjVr1uCPP/4o7HAoDx4/foxFixYhMDAQZmZmWLduHf766y+EhoYWdmhERESFhsk3FWndunXDsWPHMHz4cHTo0KGww6E8UKlU2L59O6ZPn47U1FTUrl0bmzZtQvv27Qs7NCIiokLDbidERERERCbC0U6IiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExEVE4MHD4ZKpUJ0dHRhh/JC4v4nImNg8k1EL6w9e/agT58+8PDwgJWVFZydndGyZUt89913SEtLK+zwCsXKlSuhUqmwcuXKwg4lT4KDg6FSqdRetra28Pb2xoQJE5CSklLYIRIRAeBDdojoBZSRkYEPPvgAS5YsgZ2dHTp16oQaNWogOTkZu3btwujRo7F48WJs374dlStXLuxwKQ9ef/11eHt7AwDi4uKwY8cOzJgxA//73/9w7NgxWFlZFXKERPSiY/JNRC+c8ePHY8mSJWjSpAm2bNmCihUrKtMyMzMxdepUTJ06FZ07d8bx48dhY2NTiNFSXrzxxhvo27ev8v7Jkydo3rw5zpw5g7Vr1+Ltt98uxOiIiNjthIheMJcvX8a8efNQtmxZhISEqCXeAGBmZoYpU6agX79+OH/+PL799lu16SqVCm3atNG67CpVqqBKlSpqZZcuXcJnn30GX19fODs7w9raGrVq1cK4cePw8OFDrcs5f/48Xn31VZQuXRqOjo7o3Lkzzp07p7Vuzm4i27ZtQ8uWLVG6dGkljrS0NHz33XcIDAxUuteUL18ePXv2xKlTp9SWNXjwYCU5ffvtt9W6cOS2jdnatGmjVhf4rzvI3r178fPPP6Nx48awtbVV24cPHjzA5MmTUa9ePdjY2MDJyQmvvPIKwsLCtK4nL6ytrdG/f38AQHh4uFIeHR0NlUqFwYMHa50vt+Oszf79+9G1a1eUK1cOVlZWqFmzJiZOnIjHjx/nJ3wiKoHY8k1EL5SVK1ciKysL7777LlxdXXXW++KLL7B27VosXboUY8eONXh9mzdvxrJly9C2bVu0adMGWVlZOHLkCL766ivs27cP+/fvh4WFhVL/3LlzCAgIwMOHD9GzZ0/UrFkTx44dQ0BAABo0aKBzPRs2bMCuXbvw6quv4v3338eDBw8AAElJSRgzZgxatmyJzp07o0yZMrh27Rq2bt2KHTt2YP/+/WjSpAkAoHv37rh//z7++OMPdOvWDQ0bNjR4u581Z84c7NmzB6+99ho6dOgAc3NzJb5WrVrh/PnzaNmyJQIDA5GcnIw//vgDbdu2xYYNG9C9e/d8rVtEAEBZp7EtWrQI77//PsqUKYOuXbvCxcUFx48fx5dffok9e/Zgz549sLS0LJB1E1ExJEREL5A2bdoIAAkNDX1uXXd3dwEgsbGxShkAad26tdb6np6e4unpqVZ28+ZNSU1N1ag7ZcoUASCrV69WK2/durXW8vHjxwsAASBRUVFK+YoVKwSAqFQqrdv05MkTuXnzpkb5uXPnxN7eXtq3b69Wnr28FStW6L2Nz8ae0+TJkwWA2NnZydmzZzXm6devnwCQ5cuXq5XHxcWJh4eHuLi4yL///qt1fdrWs27dOrXyx48fi4+PjwCQDRs2KOVRUVECQAYNGqR1edqO86BBgzT2//nz58Xc3FwaNWokiYmJavVnzpwpAGTu3LnPjZ+IXhzsdkJEL5S4uDgAgIeHx3PrZte5deuWweurWLGi1lbPkSNHAgD++usvpSwmJgb79u1D/fr1la4S2T7//HM4OTnpXE/37t3Rvn17jXIrKyuNrjUAUK9ePbRt2xb79+9Henq6vptjsHfffRc+Pj5qZQkJCVi/fj1efvlljb7Yrq6u+PTTT3H37l21ffQ8GzduRHBwMIKDg/Hee++hVq1a+Oeff9CtWzf07NnTKNuS0+LFi5GRkYFvv/0WZcuWVZv22WefwcXFBevWrTP6eomo+GK3EyIiHeT/uytkZWXlaxkrVqzAypUrce7cOSQnJ6st7/bt28r/z5w5AwB46aWXNJZjb2+Phg0bYu/evVrX07RpU50xnD59GrNnz0ZYWBji4uI0ku2EhAS4ubnlZbPyTFt8x48fR2ZmJp48eYLg4GCN6ZcvXwYAXLx4Ea+++qpe69m0aRM2bdqkVtazZ09s3LhRoz+6MRw5cgQA8Oeff2r9kWBhYYGLFy8afb1EVHwx+SaiF0qFChVw8eJF3LhxA7Vr18617s2bNwFAa8uxvkaPHo3vv/8eHh4eeO211+Dm5qYMdzdlyhSkpqYqdZOTkwEA5cuX17qs3Pqo65p26NAhtGvXDgDQsWNH1KxZE/b29lCpVPj9999x5swZtRgKirb4kpKSAAAHDx7EwYMHdc776NEjvdezbt069O3bFxkZGYiMjMQnn3yCzZs3Y9KkSZg2bVreA3+O7G348ssvjb5sIiqZmHwT0QulRYsW2Lt3L3bv3q21m0a2ixcv4vbt2yhTpgwqVKiglKtUKmRkZGidJzk5GY6Ojsr7+Ph4/PDDD6hfvz4OHz4MW1tbZVpcXBymTJmiNn/2vPHx8VqXf+fOHZ3x6mrV/fLLL5GamoqwsDAEBASoTTty5IjS2q6vUqVK6XwAUfaPB33jc3BwAAB8/PHHmDt3bp7ieB5zc3PUq1cPW7ZsgY+PD7788kv06NEDvr6+AJ5uBwCtxzK37XhW9jakpKSgdOnSRoiciEo69vkmohfK4MGDUapUKSxduhR3797VWS+7JfOtt95SEjUAKFOmjNY+4NHR0bh//75a2bVr1yAiaN++vVriDQAHDhzQWEb2aCbahth7+PAhTp8+rTNeXa5evYqyZctqJN6PHz/GyZMnNeqbmZkBeDreuTZlypRBfHy8RtL66NEjpZuIvpo0aQKVSoXDhw/nab68sLa2xty5cyEiGDdunFKe3X9e27F8dgjG3DRr1gzAf91PiIieh8k3Eb1QatasiaCgICQmJqJr166IjY1Vm56VlYVp06Zh9erVcHJywpgxY9Sm+/n5ITo6Wq3vdVpaGoKCgjTW5enpCeBp14+c/bxv3ryplghmq1y5Mlq1aoWzZ89izZo1atNmzJihkdzrw9PTE/fu3cP58+eVsszMTHzyySdaf3xk3zSY3eXmWX5+fkhPT1eLT0Qwfvz4PHUPAZ52AerduzcOHTqEOXPmKH3sczp69Gi+x8ru1q0bfH19ERoaqvzocXBwQK1atRAWFoYrV64odR88eIDx48frvez3338f5ubmGDVqFG7cuKEx/f79+3lK5omo5GO3EyJ64cycORPJyclYunQpatasiS5duqB69epISUnBrl27cPnyZVhbW+PXX39FtWrV1Ob96KOPsGvXLnTp0gVvvvkmbG1tERoaCicnJ42bFt3c3PD6669j06ZN8PPzw8svv4w7d+7gf//7H9q1a4dr165pxPbDDz8gICAAAwcOxO+//46aNWvi+PHjOHbsGFq2bKm1xTw3o0aNwq5du/DSSy+hd+/esLa2xt69e3Hr1i20adNG4wZOf39/2NjYYP78+UhJSYGLiwsAKD8WRo4ciRUrVmDo0KEIDQ2Fi4sLDhw4gPv376NBgwZ57saycOFCREZG4rPPPsOqVavg7+8PR0dH3LhxA+Hh4bh8+TJiY2M1/nKQV8HBwXjttdcwadIk7NmzBwAQFBSEESNGwN/fH7169UJWVhZ27NgBPz8/vZfr7e2NhQsX4r333kPt2rXRuXNn5bN07do17Nu3D4MHD8aiRYvyFT8RlSCFOc4hEVFh2r17t/Tu3Vvc3d3F3NxcGUe7adOmcvnyZZ3zrV+/Xnx8fMTS0lIqVKggo0aNkgcPHmgdA/vBgwfy8ccfS5UqVcTKykpq1qwp06ZNk7S0NJ1jhv/zzz/SuXNnsbe3l9KlS0unTp3kn3/+0TrO9PPG5RYR2bhxo/j6+oqtra2UK1dOevfuLVevXtW6PBGRbdu2SZMmTcTGxkbZJ8/ut2bNmomVlZU4OzvLgAEDJC4uLtdxvvfs2aMzvsePH8vs2bOlcePGYmdnJzY2NlK1alXp3r27/PLLL5Kenq5z3mfX8+w43zn5+fkJANm9e7dS9t1330mNGjXEwsJCKleuLJMmTdJ5bHTtLxGRY8eOSd++fcXd3V0sLCykXLly4uvrK+PGjZOIiIjnxk9ELw6ViJa/8xERvYAuXbqE5s2bw8LCAmFhYahZs2Zhh0RERCUM+3wTEf2/WrVqYePGjbh37x46dOigs98zERGRodjyTUT0jJCQEISHh6NOnTro27dvYYdDREQlCJNvIiIiIiITYbcTIiIiIiITYfJNRERERGQiTL6JiIiIiEyEyTcRERERkYkw+SYiIiIiMhEm30REREREJsLkm4iIiIjIRJh8ExERERGZCJNvIiIiIiIT+T91GoKSeid06QAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] }, "metadata": {}, "output_type": "display_data" @@ -163,8 +168,10 @@ "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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5mDJlCgYNGgQHBwfo6OiA4zhs2bJFMr8iFLe/4n5PvnyPv0bWzyA9PR0Aimz1EdPV1S2xwCluX/h4z8UH9JIGkTQ3N8fz58/x8ePHQvPk9bmUN4e8KGOBo6amhs6dO+Po0aPYsGEDwsPDi72LR9Hevn0rUwua+P9NaWRnZ0NXVxdxcXEwNTWVe4/LYWFhAAp6vS+OuNW9uAJH0RkrGp2iUkKqqqr46aefAAA///wz8vLyilyuuEJDrCz/+eRB/MW5efPmYptXxQ95jWMjPiCXtiv/P//8E7m5uejXrx+WLVuGhg0bQldXV/JexsbGyiUXX2T9DMQH9C9b5T4n6wGYj/dc/D68e/eu2GUSEhIAlFzUVZUcyljgAAWnqeLi4nD9+nUcPXqUt9vDd+3a9dX/L0U9SiomPpeTk4OePXvi6dOnUFNTw/v37yWjssuL+P+Rvb19kfMfPXqEt2/fwtjYuMhbzisiY0WjAkdJ9evXD05OToiKiip2HCPxQen9+/dFzv/aL3h5EzfD379/v8K26ezsDACSJtWvEfeV4unpWeT8irr2pjxK6gRS1s+gTp06AP7rI+NLr169KrH1piTlec9l7fBSvD8PHz4scv7Hjx8lBwTxsoqgLDmUtcDp2LEjBAIBQkNDER4eXq5+fpTZyJEjERYWhvbt22PTpk0ACvo7ys/Pl9s2xD9Aivthu3HjRgDFt95URMaKRgWOklJRUUFgYCAAYMGCBUU23xsbG0NfXx+ZmZl48OBBoflbtmxReM7P+fv7Ayj4NVTWi2Nl1aNHDwDAkSNH8OLFi68uL+4VVvyr+XOPHz/G0aNH5ZpPEcT7UNRpPlk/A19fXwDAoUOHimypKc9goeV5z0va15J06NABALB//36pTivFNm7ciOzsbNja2qJu3bplWndlzKGsBY6Ojg7atGmDDRs2oE6dOtDQ0OA7ktzNnj0bu3btgqurK/bv348hQ4agTp06ePz4MXbt2iW37VhaWgIArl27VmjenTt3sH79egBFFzgVlbGiUYGjxPr06QNXV1fExMTg0qVLheZzHCf5Ap08ebLUl9iOHTuwbdu2CssKAO7u7ujbty+SkpLg6+tbqNfX/Px8nDt3DgMHDkR2drZcttmkSRP4+/sjKysLnTp1QkREhNT858+fY9myZZLnLVu2BACsW7cOt2/flkx/+vQp+vTpUym+YGvVqgUACA8PLzRP1s+gXbt2cHNzQ2JiIgYMGCB1yu/IkSNYtGiRzINZluc9L2lfS9KmTRt4eHggOzsb/fv3lzpFdOrUKcybNw9AwUWUihwWRVlyKGuBAxScpkpOTq6Sd09t2bIFCxcuhJWVFY4fPw49PT2oqqpKhpmYP39+sZcglJX4dNn8+fMlF7cDwNmzZ9GpUyfk5OQAKHwjQUVmrHAKuwGdlMqX/eB86cCBAyX2gfDo0SOmo6Mj6bSvcePGzNLSkuH/e2MVv+5LxU1n7Ov964SFhRXqEErs48ePzNfXV7L+mjVrsmbNmjFXV1cmFAol0z/v++JrecRK6sm4efPmknXY2dkxd3d3Zm5uXmg/cnNz2TfffMOAgh5069evz1xcXCS91i5YsIABYEOHDi319kuTubh+cMq6r4wx9vvvv0te7+Liwry9vZm3tze7desWY0z2z+Dznoy1tLSYu7s7s7Ozk/QLI8706tWrMu1Led7zr+1rSe/Vs2fPWI0aNST90DRu3FjSiSUANnjw4GJ7Mi6OLH8DsuRgTL794Ij72wEgUy/BivT27Vumrq7OkpKSyvS6ixcvMmNjY8lD3Ou1lpaW1PQv/14ryokTJ5iamhrT0dGR6nmbsYKeiuvUqcMAsI0bN8ple1FRUZLeiNXU1JiLi4vk/6+zszNzcHBgAKSyVHTGikYFDs++VuCIRCLWsGHDEjt5unnzJuvYsSPT1dVl2trazNPTkx09epQx9vWO/opSngKHsYJecXfv3s06dOjATExMmLq6OrO0tGTNmjVj06dPL7Lr8fIUOIwxlpOTw9auXctatGjB9PX1maamJrO3t2e9e/eWvBdiqampbMKECczKyoqpq6uzGjVqsG+//Za9fftW0tGiMhc4jDG2atUq5ubmJlWwhIWFSebL8hkwxtjz589Zv379mLGxMdPU1GSurq5szZo1jDEm6QTsw4cPZdoXxmR/z0uzryW9V+/fv2dTp05ljo6OTCAQMD09Pebl5cV27txZZFGhiAJHlhyMybfA+emnnyT7VlQHkHz7vLf00hJ/D33twcfwArdu3WI6OjpMVVWVHT9+vMhldu7cyQAwGxsblpWVJZft3r17l7Vv355paWkxLS0t5uLiwubOncsSExOZQCBgampqkm3xlbEicYyV8T5UQki1k5SUBBMTExgYGFSuwfYIAGDKlClYsWIFgILTlOLb3QmpyuivnBDyVSEhIQCKvxOKKDfxNThaWloKKW5ev36NCRMmoFmzZtDU1FTo9USElBYVOIQQAAW9IG/atEnqglTGGHbt2oW5c+cCKBhagCi/1NRUPHr0CCKRCMB/vUSXtkPMsnr+/Dn2798PMzMzNGvWTCHbIKSsqMAhhAAoOA01evRoGBgYwMHBAU2bNoWpqSkGDx6MrKwsjB49mreO2EjpPXnyBAYGBnBycpL0vyMeisPOzk4h2/Ty8kJ8fDyOHj2KTp06KWQbhJQVFTiEEAAFnQROmzYNrq6uSE1Nxa1bt8AYQ9u2bbFv3z5s2LCB74ikFOrUqYOaNWsCAIKDg7Fnzx5JB47i/o7kja7pIcqILjImhJAqRjy+1+fs7e0RGRkJIyMjhW578eLFmDlzZpnHUSNE3qjsJoSQKubbb7/Fli1bJIOaDho0CFeuXFF4cUOIMqHRxAkhpAoaOXIkRo4cWebXffz4EW/evPnqcpaWltDX15clGiEVggocQgghEsePH0f//v2/ulxISAiGDRum+ECEyIgKHEIIIRL9+vVDv379+I5BSLnRNTiEEEIIqXKoBYcQQki5HThwAABw//59qedOTk5wcnLiLRepvug2cUIIIeVW3PAMgYGBCAoKqtgwhIBacAghhMgB/VYmyqZaFjgikQhv376Frq4uDQpHCCGEVBKMMXz8+BFWVlZf7UG7WhY4b9++hY2NDd8xCCGEECKD2NhY1KhRo8RlqmWBo6urC6DgDdLT0+M5DSGEEEJKIy0tDTY2NpLjeEmqZYEjPi2lp6dHBQ4hhBBSyZTm8hLqB4cQQgghVQ4VOIQQQgipcqjAIYQQQkiVQwUOIYQQQqocKnAIIYQQUuVQgUMIIYSQKocKHEIIIYRUOVTgEEIIIaTKoQKHEEIIIVUOFTiEEEIIqXKowCGEEEJIlUMFDiGEEEKqHCpw5OzZh2dISE/gOwYhhBBSrSldgWNnZweO4wo9xo0bBwBgjCEoKAhWVlYQCoXw8fHBgwcPeE5dIDgiGD1De2Lv4718RyGEkGLdvXsXI0eOhIODA4RCIYRCIRwdHTF69GhERkbyHa/cEhISMGPGDLi6ukJHRweamppwdHTEpEmT8OzZM8lyw4YNg46Ojly3bWdnBz8/P7mu82sUsR9VgdIVOBEREYiLi5M8Tp8+DQDo06cPACA4OBgrVqzAmjVrEBERAQsLC/j6+uLjx498xgYANDJrBAAIfRGKPFEez2kIIaSwjRs3okmTJrh27RomTZqEY8eO4fjx4wgICMCDBw/g4eGBFy9e8B1TZtevX4erqyu2bt2K3r1749ChQ/jnn38wdepU3Lx5E02bNuU7IqkganwH+JKpqanU88WLF8PBwQHe3t5gjGHlypWYPXs2evbsCQDYsWMHzM3NsWfPHowePZqPyBI+NXxgKDDE+8z3uPTmErxtvHnNQwghn7t06RLGjh2LLl264MCBA9DQ0JDMa9OmDcaNG4f9+/dDKBTymFJ2aWlp6N69OzQ1NXH58mXUqFFDMs/HxwejR4/GgQMHeExIKpLSteB8LicnB7t27cKIESPAcRyioqIQHx+P9u3bS5YRCATw9vbG5cuXi11PdnY20tLSpB6KoK6qDj+HgqbJw88PK2QbhJCKxxhDRk6e0jwYYzLtx8KFC6GqqoqNGzdKFTef69OnD6ysrAAAkZGR6NevH+zs7CAUCmFnZ4f+/fsjJiZG6jVBQUHgOK7QurZv3w6O4xAdHS2ZdvbsWfj4+MDY2BhCoRA1a9ZEr169kJGRIVlm/fr1aNCgAXR0dKCrq4t69eph1qxZX92/zZs3Iz4+HsHBwVLFzed69+5daNrz58/RuXNn6OjowMbGBlOmTEF2drbUMjk5OViwYAHq1asHgUAAU1NTDB8+HO/fvy9yO4cPH4abmxs0NTVRq1YtrF69WjLv06dPMDAwKPJHeXR0NFRVVbF06VIAQEZGBqZOnQp7e3toamrCyMgI7u7u2Lu38KUQ8tqPHj16wNbWFiKRqNA2mjVrhsaNGxe5z8pG6VpwPnfkyBGkpKRg2LBhAID4+HgAgLm5udRy5ubmhf7DfW7RokWYN2+ewnJ+zr+2P3Y+3Inw2HAkZibCRGhSIdslhChOZm4+nH46yXcMiYfzO0BLo2xf3/n5+QgLC4O7uzssLS1L9Zro6GjUrVsX/fr1g5GREeLi4rB+/Xp4eHjg4cOHMDEp2/dbdHQ0unTpglatWmHbtm0wMDDAmzdv8M8//yAnJwdaWlrYt28fxo4diwkTJmDZsmVQUVHB8+fP8fDhw6+u/9SpU1BVVUXXrl1LnSk3NxfdunXDyJEjMWXKFJw/fx4///wz9PX18dNPPwEARCIRunfvjgsXLmDatGnw9PRETEwMAgMD4ePjg8jISKlWr9u3byMgIABBQUGwsLDA7t27MWnSJOTk5GDq1KnQ0dHBiBEjsGnTJgQHB0NfX1/y2nXr1kFDQwMjRowAAEyePBk7d+7EggUL0KhRI6Snp+P+/ftISkpS2H6MGDEC3bt3x9mzZ9GuXTvJNh4/fozr169LFWvKTKkLnK1bt6JTp06SXxNiX/5SYIwV+etBbObMmZg8ebLkeVpaGmxsbOQb9v85GjrC1cQV9xLv4fjL4xjqPFQh2yGEkLJITExEZmYmbG1tC83Lz8+XahVSVVUFx3Ho3bu3VItHfn4+/Pz8JJcFTJw4sUwZbty4gaysLCxduhQNGjSQTB8wYIDk35cuXYKBgYHUQbRt27alWv+rV69gamoKbW3tUmfKycnBvHnzJNd5tm3bFpGRkdizZ4+kMPjzzz/xzz//4ODBg5LLIwCgQYMG8PDwwPbt2zFmzBjJ9Ldv3+LWrVuSfezUqRPevXuHn3/+GWPHjoWWlhbGjx+PVatWISQkBAEBAQCArKwsbNu2Df3794exsbHk/Wjfvj1++OEHyfq7dOmi0P3o3LkzzM3NERISIlXghISEQENDQ+rzUmpMSUVHRzMVFRV25MgRybQXL14wAOzmzZtSy3br1o0NGTKk1OtOTU1lAFhqaqrc8n7uj8d/MJftLqzb4W5MJBIpZBuEkIojEolYenau0jxk+V6Jj49nAFi/fv0KzWvQoAEDIHksXbqUMcbYx48f2bRp05iDgwNTVVWVWub777+XvD4wMJAVdTgJCQlhAFhUVBRjjLHnz58zDQ0N1rRpU7Z9+3b24sWLQq/5/fffJTmPHDnC3r9/X2iZ3NxcqYf4/ahXrx6zsLAo9XsydOhQxnEcy8zMlJo+Y8YMpqmpKXk+cOBAZmBgwHJycgpt28LCgvXt21eyrK2tLXNxcSn2vbhw4YJkWrdu3Zijo6Mk/9atWxkAduPGDckyI0aMYAKBgE2fPp2FhYWxjIyMCtmPKVOmME1NTZaSksIYYywvL49ZWlqyPn36lPymKlhZjt9Kew1OSEgIzMzMpCpVe3t7WFhYSO6sAgqq1vDwcHh6evIRs0id7DtBU1UTL1Nf4m7iXb7jEELKieM4aGmoKc2jpBbr4piYmEAoFBZ5On/Pnj2IiIhAaGio1PQBAwZgzZo1+Pbbb3Hy5Elcv34dERERMDU1RWZmZpkzODg44N9//4WZmRnGjRsHBwcHODg4YNWqVZJlBg8ejG3btiEmJga9evWCmZkZmjVrJvW9r66uLvXYsWMHAKBmzZp4//490tPTS51JS0sLmpqaUtMEAgGysrIkzxMSEpCSkgINDY1C246Pj0diYqLU6y0sLAptRzzt81NL4tvWxfu2du1aNG/eXOoal9WrV2P69Ok4cuQIWrduDSMjI/To0UPqdndF7MeIESOQlZWFffv2AQBOnjyJuLg4DB8+vIR3U7ko5SkqkUiEkJAQDB06FGpq/0XkOA4BAQFYuHAhHB0d4ejoiIULF0JLS0upmsx0NXTha+uLoy+P4vCzw2hg2uDrLyKEEAVSVVVFmzZtcOrUKcTFxUldh+Pk5AQAUhcDp6am4tixYwgMDMSMGTMk07Ozs5GcnCy1bvGBNTs7GwKBQDL9ywM/ALRq1QqtWrVCfn4+IiMj8dtvvyEgIADm5ubo168fAGD48OEYPnw40tPTcf78eQQGBsLPzw9Pnz6Fra0tIiIipNZpb28PAOjQoQNOnTqFo0ePStYlDyYmJjA2NsY///xT5HxdXV2p5+LrRYuaJj71BBTcuebi4oI1a9ZAR0cHN2/exK5du6Rep62tjXnz5mHevHlISEjAiRMnMGPGDHTt2hWPHz9W2H44OTmhadOmCAkJwejRoxESEgIrKyupm3yUXgW0KJXZyZMnGQD25MmTQvNEIhELDAxkFhYWTCAQMC8vL3bv3r0yrV/Rp6gYY+x63HXmst2FNd3VlKXnpCtsO4QQUloXL15kKioqrFu3biwnJ6fQ/KioKMkpKvH35KJFi6SWWbNmDQPAhg4dKpm2d+9eBoBdv35dalkvLy+pU1RFSUlJYQDYjz/+WOwyR44cYQDY8ePHS9y/lJQUZmFhwWxsbNjr16+LXObgwYOSfw8dOpRpa2sXWubLU267du1iANjVq1dL3D5jBaeoOI5jt2/flpru6+vLdHV1WXq69PFg06ZNTEVFhXl5eTFzc3OWnZ391W0EBAQwAJJ1KWI/GGNs/fr1ktNqAoGAzZw5s1SvU6SyHL+VsgWnffv2xd4GyXEcgoKCEBQUVLGhysjd3B02ujaI/RiLUzGn0KN2D74jEUKquRYtWmDt2rWYMGECGjdujO+++w7Ozs5QUVFBXFwcDh48CADQ09ODnp4evLy8sHTpUpiYmMDOzg7h4eHYunUrDAwMpNbbuXNnGBkZYeTIkZg/fz7U1NSwfft2xMbGSi23YcMGnD17Fl26dEHNmjUlF9UCkFzMOmrUKAiFQrRo0QKWlpaIj4/HokWLoK+vDw8PjxL3T19fH3/99Rf8/PzQqFEjjB8/Hs2bN4eGhgaePXuGXbt24c6dO1IX2JZGv379sHv3bnTu3BmTJk1C06ZNoa6ujtevXyMsLAzdu3eHv7+/ZHkrKyt069YNQUFBsLS0xK5du3D69GksWbIEWlpaUuseNGgQZs6cifPnz2POnDmFbt9v1qwZ/Pz84ObmBkNDQzx69Ag7d+5E8+bNC61L3vvRv39/TJ48Gf3790d2drbkjuZKQ/H1lvKpiBYcxhjbdGcTc9nuwob8XfoLoAkhRNFu377Nhg8fzuzt7ZlAIGCampqsdu3abMiQIezMmTOS5V6/fs169erFDA0Nma6uLuvYsSO7f/8+s7W1lWrBYYyx69evM09PT6atrc2sra1ZYGAg27Jli1QLzpUrV5i/vz+ztbVlAoGAGRsbM29vbxYaGipZz44dO1jr1q2Zubk509DQYFZWVqxv377s7t27pd6/+Ph4Nn36dObs7My0tLSYQCBgtWvXZqNHj5Zq8S9tywdjBRc2L1u2jDVo0IBpamoyHR0dVq9ePTZ69Gj27NkzyXK2trasS5cu7MCBA8zZ2ZlpaGgwOzs7tmLFimLzDhs2jKmpqRXZ6jRjxgzm7u7ODA0NmUAgYLVq1WI//PADS0xMVOh+iA0YMIABYC1atCg2f0Uqy/GbY0zGHqMqsbS0NOjr6yM1NRV6enoK205CegLaH2wPERPhaI+jsNO3U9i2CCGEVD45OTmws7NDy5Yt8eeff/IdR+mV5fittHdRVQXm2uZoYdUCAHDk+RF+wxBCCFEa79+/x8WLFzFmzBjJ4KBEvqjAUTB/x4LzmTQAJyGEELHjx4+jVatWOHHiBNatW1dphj+oTOgUlQJPUQFAbn4u2u5viw/ZH7CmzRoagJMQQgiREZ2iUiI0ACchhBBS8ajAqQD+tQtOU4kH4CSEEEKIYlGBUwHEA3DmsTwcf3mc7ziEEEJIlUcFTgURd/R36NmhYjsxJIQQQoh8UIFTQWgATkIIIaTiUIFTQcQDcALA4Wd0sTEhhBCiSFTgVCBxnzgnok4gIzeD5zSEEEJI1UUFTgUSD8CZkZeBUzGn+I5DCKmm7t69i5EjR8LBwQFCoRBCoRCOjo4YPXo0IiMj+Y4ns+joaHAch2XLlvEdRWF8fHzg4+PDd4xKgQqcCsRxnOSWcTpNRQjhw8aNG9GkSRNcu3YNkyZNwrFjx3D8+HEEBATgwYMH8PDwwIsXL/iOSUi5qfEdoLrp5tANa26vwc13NxGdGk0DcBJCKsylS5cwduxYdOnSBQcOHICGhoZkXps2bTBu3Djs378fQqGQx5SkvHJzc8FxHNTUqvchnlpwKhgNwEkI4cvChQuhqqqKjRs3ShU3n+vTpw+srKwAAJGRkejXrx/s7OwgFAphZ2eH/v37IyYmRuo1QUFB4Diu0Lq2b98OjuMQHR0tmXb27Fn4+PjA2NgYQqEQNWvWRK9evZCR8d91ievXr0eDBg2go6MDXV1d1KtXD7NmzZLDO1AgLS0NU6dOhb29PTQ0NGBtbY2AgACkp6dLLZeSkoKRI0fCyMgIOjo66NKlC16+fAmO4xAUFCS17LNnzzBgwACYmZlBIBCgfv36WLt2rdQy586dA8dx2Lt3L2bPng0rKyvo6emhXbt2ePLkidSyjDEEBwfD1tYWmpqaaNy4MU6cOFFoX8Tr3LlzJ6ZMmQJra2sIBAI8f/4cAPDvv/+ibdu20NPTg5aWFlq0aIEzZ87I4V1UftW7vOOJv6M/Lry5gNAXoRjfaDzUVOhjIESpMQYo040B6lpAEQVFSfLz8xEWFgZ3d3dYWlqW6jXR0dGoW7cu+vXrByMjI8TFxWH9+vXw8PDAw4cPYWJiUqYM0dHR6NKlC1q1aoVt27bBwMAAb968wT///IOcnBxoaWlh3759GDt2LCZMmIBly5ZBRUUFz58/x8OHD8u0reJkZGTA29sbr1+/xqxZs+Dm5oYHDx7gp59+wr179/Dvv/+C4ziIRCJ07doVkZGRCAoKQuPGjXHlyhV07Nix0DofPnwIT09P1KxZE8uXL4eFhQVOnjyJiRMnIjExEYGBgVLLz5o1Cy1atMCWLVuQlpaG6dOno2vXrnj06BFUVVUBAPPmzcO8efMwcuRI9O7dG7GxsRg1ahTy8/NRt27dQhlmzpyJ5s2bY8OGDVBRUYGZmRl27dqFIUOGoHv37tixYwfU1dWxceNGdOjQASdPnkTbtm3l8p4qKzqy8sCnhg8MBYZ4n/kel95cogE4CVF2uRnAQiu+U/xn1ltAQ7tML0lMTERmZiZsbW0LzcvPz5fqgFRVVRUcx6F3797o3bu31HJ+fn4wNzfHnj17MHHixDJluHHjBrKysrB06VI0aNBAMn3AgAGSf1+6dAkGBgZYvXq1ZJo8D8SrV6/G3bt3ce3aNbi7u0vWb21tjd69e+Off/5Bp06d8M8//+DixYtYv349vv/+ewCAr68vNDQ0MHPmTKl1Tp48Gbq6urh48aJkAEhfX19kZ2dj8eLFmDhxIgwNDSXLOzk5YdeuXZLnqqqq6Nu3LyIiIvDNN98gJSUFS5Ysgb+/P7Zs2SJZztnZGS1atCiywHFwcMD+/fslzzMyMjBp0iT4+fnh8OH/rvns3LkzGjdujFmzZuHatWvleSuVHp2i4gENwEkIUSZNmjSBurq65LF8+XIAwKdPnzB9+nTUrl0bampqUFNTg46ODtLT0/Ho0aMyb6dhw4bQ0NDAd999hx07duDly5eFlmnatClSUlLQv39//PXXX0hMLDx+X15entSjLL3DHzt2DC4uLmjYsKHUOjp06ACO43Du3DkAQHh4OACgb9++Uq/v37+/1POsrCycOXMG/v7+0NLSklpn586dkZWVhatXr0q9plu3blLP3dzcAEBy6u/KlSvIysrCwIEDpZbz9PQsskAFgF69ekk9v3z5MpKTkzF06FCpTCKRCB07dkREREShU3JVDbXg8MS/tj92PtwpGYDTRFi2pl5CSAVS1ypoNVEW6lplfomJiQmEQmGh62cAYM+ePcjIyEBcXJzUwXfAgAE4c+YM5s6dCw8PD+jp6YHjOHTu3BmZmZllzuDg4IB///0XwcHBGDduHNLT01GrVi1MnDgRkyZNAgAMHjwYeXl52Lx5M3r16gWRSAQPDw8sWLAAvr4FnaWqq6tLrTckJATDhg0rVYaEhAQ8f/680DrExAVVUlIS1NTUYGRkJDXf3Nxc6nlSUhLy8vLw22+/4bfffitxnWLGxsZSzwUCAQBI3tOkpCQAgIWFRaF1FTUNQKHTjgkJCQAg1QL3peTkZGhrl60lsDKhAocn4gE47yXew/GXxzHUeSjfkQghxeG4Mp8SUjaqqqpo06YNTp06hbi4OKkDopOTEwBIXQycmpqKY8eOITAwEDNmzJBMz87ORnJystS6NTU1JfPEB2ug8IEdAFq1aoVWrVohPz8fkZGR+O233xAQEABzc3P069cPADB8+HAMHz4c6enpOH/+PAIDA+Hn54enT5/C1tYWERERUuu0t7cv9fsgLvS2bdtW7HygoAjJy8tDcnKyVJETHx8vtbyhoSFUVVUxePBgjBs3rsh1liWfeNtFbUs8zc7OrtD0Ly/yFu/Hb7/9hm+++abI7XxZrFU1VODwyN/RH/cS7+HQs0MY4jSkyLsQCCFEXmbOnIkTJ07g+++/x4EDB4ptxQAKDpiMMamCBQC2bNmC/Px8qWniA+7du3fh4eEhmX706NFi16+qqopmzZqhXr162L17N27evCkpcMS0tbXRqVMn5OTkoEePHnjw4AFsbW0l187Iws/PDwsXLoSxsXGJhYe3tzeCg4Pxxx9/YMyYMZLp+/btk1pOS0sLrVu3xq1bt+Dm5lbs3Wll8c0330BTUxO7d++WOvV0+fJlxMTEFFngfKlFixYwMDDAw4cPMX78+HJnqoyowOFRR7uOCL4eLBmAs4Fpg6+/iBBCZNSiRQusXbsWEyZMQOPGjfHdd9/B2dkZKioqiIuLw8GDBwEAenp60NPTg5eXF5YuXQoTExPY2dkhPDwcW7duhYGBgdR6O3fuDCMjI4wcORLz58+Hmpoatm/fjtjYWKnlNmzYgLNnz6JLly6oWbMmsrKyJC0p7dq1AwCMGjUKQqEQLVq0gKWlJeLj47Fo0SLo6+tLFU8luXfvHg4cOFBouoeHBwICAnDw4EF4eXnhhx9+gJubG0QiEV69eoVTp05hypQpaNasGTp27IgWLVpgypQpSEtLQ5MmTXDlyhX8/vvvAAAVlf8uYV21ahVatmyJVq1aYcyYMbCzs8PHjx/x/PlzHD16FGfPni3dB/T/DA0NMXXqVCxYsADffvst+vTpg9jYWAQFBRV7iupLOjo6+O233zB06FAkJyejd+/eMDMzw/v373Hnzh28f/8e69evL1OuSodVQ6mpqQwAS01N5TsKm3VhFnPZ7sICLwXyHYUQUk3cvn2bDR8+nNnb2zOBQMA0NTVZ7dq12ZAhQ9iZM2cky71+/Zr16tWLGRoaMl1dXdaxY0d2//59Zmtry4YOHSq1zuvXrzNPT0+mra3NrK2tWWBgINuyZQsDwKKiohhjjF25coX5+/szW1tbJhAImLGxMfP29mahoaGS9ezYsYO1bt2amZubMw0NDWZlZcX69u3L7t69+9X9ioqKYgCKfYSEhDDGGPv06RObM2cOq1u3LtPQ0GD6+vrM1dWV/fDDDyw+Pl6yvuTkZDZ8+HBmYGDAtLS0mK+vL7t69SoDwFatWlVo2yNGjGDW1tZMXV2dmZqaMk9PT7ZgwQLJMmFhYQwA279/f5G5xfkYY0wkErFFixYxGxsbpqGhwdzc3NjRo0eZt7c38/b2/uo6xcLDw1mXLl2YkZERU1dXZ9bW1qxLly7FLq/synL85hgrw+XnVURaWhr09fWRmpoquaWPLxHxERhxcgS01LQQ1jcMWjJcPEgIIaRi7NmzBwMHDsSlS5fg6enJd5xqpyzHbzpFxTPxAJyxH2NxKuYUetTuwXckQgghAPbu3Ys3b97A1dUVKioquHr1KpYuXQovLy8qbioB6geHZzQAJyGEKCddXV3s27cP//vf/9C5c2ds3rwZw4YNK/HiaaI86BQVz6eoACAhPQHtD7aHiIlwtMdRGoCTEEIIKUJZjt/UgqMEaABOQgghRL6owFES/o4Fp6lCX4QiT5THcxpCCCGkcqMCR0l8OQAnIYQQQmRHBY6SoAE4CSGEEPmhAkeJiO+mEg/ASQghhBDZUIGjRMQDcOaxPBx/eZzvOIQQQkilRQWOkhFfbHzo2SFUwzv4CSGEELmgAkfJdLTrCE1VTckAnIQQQggpOypwlIyuhi7a27UHQD0bE0Lkh+O4Uj3OnTsnt22eO3cOHMcVObJ3WZw8eRLt27eHlZUVBAIBrKys4OPjg8WLF0stZ2dnh2HDhsm0DR8fH7i4uJQrJ1EuSlngvHnzBoMGDYKxsTG0tLTQsGFD3LhxQzKfMYagoCBYWVlBKBTCx8cHDx484DGxfInHozoRdQIZuRn8hiGEVAlXrlyRenTu3BlCobDQ9MaNG/MdVcqGDRvQsWNH6OnpYc2aNTh58iSWLFmC+vXrFyqcDh8+jLlz5/KUlCgbpRts88OHD2jRogVat26NEydOwMzMDC9evICBgYFkmeDgYKxYsQLbt29HnTp1sGDBAvj6+uLJkyfQ1dXlL7ycuJu7o6ZuTbz6+IoG4CSEyMU333wj9dzU1BQqKiqFpiubRYsWwcvLq1AxM3jwYIhEIqlpjRo1qshoRMkpXQvOkiVLYGNjg5CQEDRt2hR2dnZo27YtHBwcABS03qxcuRKzZ89Gz5494eLigh07diAjIwN79uwpcp3Z2dlIS0uTeigzjuMkRQ2dpiKEf4wxZORmKM1DUTcgrF27Fl5eXjAzM4O2tjZcXV0RHByM3NxcqeXEp3MiIiLQqlUraGlpoVatWli8eHGhogMAcnNzMXv2bFhZWUFPTw/t2rXDkydPSpUpKSkJlpaWRc5TUZE+hH15ikp8imzv3r2l3n5p94koP6VrwQkNDUWHDh3Qp08fhIeHw9raGmPHjsWoUaMAAFFRUYiPj0f79u0lrxEIBPD29sbly5cxevToQutctGgR5s2bV2H7IA/dHLphze01uPnuJqJTo2kATkJ4lJmXiWZ7mvEdQ+LagGvQUteS+3pfvHiBAQMGwN7eHhoaGrhz5w5++eUXPH78GNu2bZNaNj4+HgMHDsSUKVMQGBiIw4cPY+bMmbCyssKQIUOklp01axZatGiBLVu2IC0tDdOnT0fXrl3x6NEjqKqqlpipefPmOHjwIIKCguDv7w8XF5evvuZLpd1+WfaJKD+lK3BevnyJ9evXY/LkyZg1axauX7+OiRMnQiAQYMiQIYiPjwcAmJubS73O3NwcMTExRa5z5syZmDx5suR5WloabGxsFLcTciAegPPCmws48vwIApoE8B2JEFLFrVixQvJvkUiEVq1awdjYGMOHD8fy5cthaGgomZ+UlIS///4bTZs2BQC0a9cO586dw549ewoVA05OTti1a5fkuaqqKvr27YuIiIivniLbsGEDevTogXnz5mHevHkQCoXw9PSEv78/vvvuO6irq391v0q7/bLsE1F+SlfgiEQiuLu7Y+HChQAKzqk+ePAA69evl/oD4zhO6nWMsULTxAQCAQQCgeJCK4i/oz8uvLmA0BehGN9oPNRUlO7jIqRaEKoJcW3ANb5jSAjVhApZ761btxAYGIhLly4hOTlZat7Tp0/RrNl/rVgWFhaSQkDMzc0Nt2/fLrTebt26FVoOAGJiYvDNN9+AMYb8/HypZdTUCr7vHBwccOfOHVy8eBHnzp1DZGQkwsPDcebMGYSEhODixYvQ1NQscb++tn1Z9okoP6U7YlpaWsLJyUlqWv369XHw4EEABX+AQEFT4ufnZd+9e1eoVaey+3IATm8bb74jEVItcRynkFNCyuTVq1do1aoV6tati1WrVsHOzg6ampq4fv06xo0bh8zMTKnljY2NC61DIBAUWq6oZcU/OMXL7tixA8OHD5da5vPrjFRUVODl5QUvLy8AQHp6OkaOHIk//vgD27Ztw9ixY0vct69tX5Z9IspP6S4ybtGiRaGLv54+fQpbW1sAgL29PSwsLHD69GnJ/JycHISHh8PT07NCsyoaDcBJCKkoR44cQXp6Og4dOoRBgwahZcuWcHd3h4aGhsK33bVrV0REREg9SqKtrY2ZM2cCAO7fv6/wfKRyUroWnB9++AGenp5YuHAh+vbti+vXr2PTpk3YtGkTgIJfUgEBAVi4cCEcHR3h6OiIhQsXQktLCwMGDOA5vfz51/bHzoc7JQNwmghN+I5ECKmCxKf4Pz+dzxjD5s2bFb5tY2PjIltPACAuLq7Iu6gePXoEALCyslJoNlJ5KV2B4+HhIblyff78+bC3t8fKlSsxcOBAyTLTpk1DZmYmxo4diw8fPqBZs2Y4depUlegD50viATjvJd7D8ZfHMdR5KN+RCCFVkK+vLzQ0NNC/f39MmzYNWVlZWL9+PT58+MBrLmdnZ7Rt2xadOnWCg4MDsrKycO3aNSxfvhzm5uYYOXIkr/mI8lK6U1QA4Ofnh3v37iErKwuPHj2S3CIuxnEcgoKCEBcXh6ysLISHh1fpLrZpAE5CiKLVq1cPBw8exIcPH9CzZ09MmDABDRs2xOrVq3nNJe6H5pdffkHnzp3RrVs3/P777xgwYAAiIyOL7SOHEI5VwyNmWloa9PX1kZqaCj09Pb7jfNXHnI9o82cbZOVnYVfnXWhg2oDvSIQQQkiFK8vxWylbcIg0GoCTEEIIKRsqcCoJGoCTEEIIKT0qcCoJ8QCcGXkZOBVziu84hBBCiFKjAqeSoAE4CSGEkNKjAqcS6ebQDSqcimQATkIIIYQUTaYCp1atWhg/fry8s5CvEA/ACQBHnh/hNwwhhBCixGQqcBITE6tkp3qVQU/HngCA0BehyBPl8ZyGEEIIUU4yFTgNGzbE06dP5Z2FlIJ3DW+pATgJIYQQUphMBc706dNx9OhRhIWFyTsP+QoagJMQQgj5OpnGokpKSkL79u3h6+sLf39/eHh4wNzcXDJY2+eGDBlS7pBEGg3ASQghhJRMpqEaVFRUwHFcoXGRPi9wGGPgOA75+fnlTylnlW2ohqIMOD4A9xLvYar7VBqAkxBSateuXcPixYtx48YNJCQkwMDAALVq1YKnpyeWL18OAPDx8QEAnDt3jr+ghBShLMdvmVpwQkJCZApG5Mff0R/3Eu/h0LNDGOI0pMjWM0II+dzx48fRrVs3+Pj4IDg4GJaWloiLi0NkZCT27dsnKXDWrVvHc1JCyo8G26ykLTg0ACchpKy8vb3x5s0bPH78GGpq0r9vRSIRVFSoazSi3GiwzWqABuAkpOIwxiDKyFCah6y/S5OSkmBiYlKouAEgVdz4+PhITlMBQHR0NDiOw9KlS7FkyRLY2dlBKBTCx8cHT58+RW5uLmbMmAErKyvo6+vD398f7969k1q/nZ0d/Pz8cPjwYbi5uUFTUxO1atXC6tWrpZYTiURYsGAB6tatC6FQCAMDA7i5uWHVqlVSy128eBFt27aFrq4utLS04OnpiePHj0sts337dnAch7CwMIwZMwYmJiYwNjZGz5498fbtW5neQ1J5yHSKSiwmJga7d+/G7du3JdVUw4YNMXDgQNjZ2ckpIilOj9o9EPoiFCeiTmCaxzRoqWvxHYmQKollZuJJ4yZ8x5Coe/MGOK2y/39v3rw5tmzZgokTJ2LgwIFo3Lgx1NXVS/36tWvXws3NDWvXrkVKSgqmTJmCrl27olmzZlBXV8e2bdsQExODqVOn4ttvv0VoaKjU62/fvo2AgAAEBQXBwsICu3fvxqRJk5CTk4OpU6cCAIKDgxEUFIQ5c+bAy8sLubm5ePz4MVJSUiTrCQ8Ph6+vL9zc3LB161YIBAKsW7cOXbt2xd69e/G///1ParvffvstunTpgj179iA2NhY//vgjBg0ahLNnz5b5PSSVh8ynqNasWYOpU6ciNze30K8JdXV1BAcHY9KkSXIJKW9V4RQVUPCr0u+wH159fIWfW/wsGauKECJfoowMpStwVGQocJKSktCjRw9cvHgRQMF3tYeHB7p27Yrx48dDR0cHQOGLjKOjo2Fvb48GDRrg5s2bktaeVatWISAgAN26dcNff/0l2c4PP/yAlStXSn3H2tnZ4dWrV7h16xYaNPjvlHr79u1x7do1xMXFQUtLC127dsXr169x69atYvejefPmePnyJV68eCHJnJ+fj4YNGyIlJQWvXr0Cx3HYvn07hg8fjrFjx2Lt2rWS1y9duhTTpk1DXFwcLCwsyvw+Ev4o/CLjv//+GxMnToSZmRl++OEH+Pj4wMLCAgkJCTh37hxWrFiByZMno3bt2ujSpYtMO0G+TjwA5+pbq3H42WEqcAhREE4oRN2bN/iOIcEJhTK9ztjYGBcuXEBkZCTOnDmDyMhInDt3DjNnzsTGjRsREREBE5Piu53o3Lmz1Kms+vXrA0Ch73nx9FevXsHFxUUy3dnZWaq4AYABAwbg9OnTuHnzJlq2bImmTZvi+PHjGDt2LLp3747mzZtLHcjS09Nx7do1jBkzRlLcAICqqioGDx6M6dOn48mTJ6hXr55kXrdu3aS26ebmBqDgLAQVOFWXTAXOsmXLYGxsjJs3b8LKykoy3dbWFk2bNsXAgQPRsGFDrFixggocBevm0A1rbq+RDMBpp2/HdyRCqhyO42Q6JaSs3N3d4e7uDgDIzc3F9OnT8euvvyI4OBjBwcHFvs7IyEjquYaGRonTs7KypKYXVUyIpyUlJQEAZs6cCW1tbezatQsbNmyAqqoqvLy8sGTJEri7u+PDhw9gjMHS0rLQusTHI/G6xIyNjaWeCwQCAEBmZmax+0oqP5kuMr558yb69u0rVdx8ztraGn379sWNG8rzi6eqogE4CSHloa6ujsDAQADA/fv3Fbqt+Pj4YqeJixA1NTVMnjwZN2/eRHJyMvbu3YvY2Fh06NABGRkZMDQ0hIqKCuLi4gqtS3zhcEmtUKT6kKnAycnJgba2donLaGtrIycnR6ZQpGxoAE5CSGkUVRQAwKNHjwCg2B+t8vLgwQPcuXNHatqePXugq6uLxo0bF1rewMAAvXv3xrhx45CcnIzo6Ghoa2ujWbNmOHTokFQLjEgkwq5du1CjRg3UqVNHoftBKgeZTlHVqVMHR48excKFC4u83TAvLw/Hjh2jP7IK4l3DG0aaRpIBOL1tvPmORAhRQh06dECNGjXQtWtX1KtXDyKRCLdv38by5cuho6Oj8BtDrKys0K1bNwQFBcHS0hK7du3C6dOnsWTJEmj9/ynArl27wsXFBe7u7jA1NUVMTAxWrlwJW1tbODo6AgAWLVoEX19ftG7dGlOnToWGhgbWrVuH+/fvY+/evdTxKQEgYwvO0KFD8eTJE3To0KHQaajIyEh06tQJT548wdChNIRARVBXVYdfLRqAkxBSsjlz5sDQ0BC//vorunXrhk6dOmH16tVo164drl+/DldXV4VuX3xt5vLly9G9e3dcunQJK1aswLRp0yTLtG7dGufPn8f3338PX19fzJkzB23btkV4eLjklnZvb2+cPXsW2traGDZsGPr164fU1FSEhoYWukWcVF8y3Saen5+Pvn374vDhw+A4DkKhEObm5khISEBmZiYYY+jevTsOHjyolD1jVpXbxD/37MMz9AztCTVODaf7nKYBOAkhSsXOzg4uLi44duwY31FIJabwnoxVVVVx8OBB7NixAz4+PhAIBHj16hUEAgFat26NHTt24PDhw0pZ3FRVjoaOcDVxRR7Lw/GXx7/+AkIIIaQKk+kanFevXkFDQwODBw/G4MGD5Z2JyEg8AOfex3vRv15/aKhq8B2JEEII4YVMTSz29vaYPXu2vLOQcupi3wUmQhO8+fQGex/v5TsOIYRIREdH0+kpUqFkKnCMjIwKdexE+KelroWJjSYCADbe2YgPWR94TkQIIYTwQ6YCp1WrVrh69aq8sxA56ObQDXUN6+Jj7kdsuLOB7ziEEEIIL2QqcBYtWoT79+9j3rx5yMujjuWUiaqKKqZ6FIzK+8eTP/Ay9SXPiQghhJCKJ9Nt4iNGjMCzZ89w+fJlWFhYoEGDBjA3Ny/UuRLHcdi6davcwspLVbxN/EsTzkzAudfn4FPDB7+1/Y3vOIQQQki5leX4LVOBU9rbvzmOQ35+fllXr3DVocCJSo1Cz796Io/lYXP7zfjG8hu+IxFCCCHlUpbjt0y3iUdFRckUjFQce3179KnbB3sf78WyiGX4w+8PqKqo8h2LEEIIqRAyFTjh4eEwNzdHhw4d5J2HyNGYBmNw7MUxPPnwBKEvQuHv6M93JEIIIaRCyHSR8ciRI3Hy5El5ZyFyZqhpiNENRgMAfrv1GzJyM3hORAjhC8dxpXqcO3eO76gKNWzYMNjZ2ZVqWY7jEBQUVOZtREdHg+M4bN++/avLnjt3DhzH4cCBA2XejiLXJfbw4UMEBQUhOjq60Lw9e/Zg5cqVctuWvMlU4FhaWiInJ0feWYgC9K/XHzV0auB95nuEPAjhOw4hhCdXrlyRenTu3BlCobDQ9MaNG/MdVaHmzp2Lw4dpUOLSevjwIebNm1cpCxyZTlH16NEDJ0+eRHZ2NgQCgbwzETnSUNXAZPfJmHxuMrbf345ejr1goW3BdyxCSAX75hvpGw1MTU2hoqJSaPqXMjIyoKWlpchoFcrBwYHvCKSCyNSC8/PPP0NHRwf+/v548OCBXAMFBQUVajK1sPjvgMwYQ1BQEKysrCAUCuHj4yP3DFVNu5rt0NisMbLys/DbLbplnBBSNB8fH7i4uOD8+fPw9PSElpYWRowYAQD4448/0L59e1haWkIoFKJ+/fqYMWMG0tPTpdYxbNgw6Ojo4MGDB2jbti20tbVhamqK8ePHIyND+jQ5Ywzr1q1Dw4YNIRQKYWhoiN69e+Ply//67xKfdinq8fmpJpFIhODgYNSrVw8CgQBmZmYYMmQIXr9+XSjfl6eo0tLSMGrUKBgbG0NHRwcdO3bE06dPC70/z58/x/Dhw+Ho6AgtLS1YW1uja9euuHfvnixvd5ncv38f3bt3h6GhITQ1NdGwYUPs2LGjyGWzsrIwefJkWFhYQCgUwtvbG7du3ZJaJjIyEv369YOdnR2EQiHs7OzQv39/xMTESJbZvn07+vTpAwBo3bq15H3fvn07fHx8cPz4ccTExEh9JmLJyckYO3YsrK2toaGhgVq1amH27NnIzs5WwLtTNJlacBo1aoTs7Gzcvn0bJ0+ehKamJszMzIrsB+fFixdlXr+zszP+/fdfyXNV1f/u/gkODsaKFSuwfft21KlTBwsWLICvry+ePHkCXV1dWXanyuM4Dj96/Ij+x/sj9EUoBtQbAGcTZ75jEVJpMMaQlyPiO4aEmoZKoe9beYmLi8OgQYMwbdo0LFy4UNItyLNnz9C5c2cEBARAW1sbjx8/xpIlS3D9+nWcPXtWah25ubno3LkzRo8ejRkzZuDy5ctYsGABYmJicPToUclyo0ePxvbt2zFx4kQsWbIEycnJmD9/Pjw9PXHnzh2Ym5ujcePGuHLlitT6nz17hpEjR8LZ+b/vsTFjxmDTpk0YP348/Pz8EB0djblz5+LcuXO4efMmTExMitxfxhh69OiBy5cv46effoKHhwcuXbqETp06FVr27du3MDY2xuLFi2Fqaork5GTs2LEDzZo1w61bt1C3bl2Z3/eSPHnyBJ6enjAzM8Pq1athbGyMXbt2YdiwYUhISMC0adOklp81axYaN26MLVu2IDU1FUFBQfDx8cGtW7dQq1YtAAXXCdWtWxf9+vWDkZER4uLisH79enh4eODhw4cwMTFBly5dsHDhQsyaNQtr166VnL50cHBA06ZN8d133+HFixeFTvllZWWhdevWePHiBebNmwc3NzdcuHABixYtwu3bt3H8+HGFvE9fkqnAEYlE0NDQQM2aNaWmf9mljgxd7BSEUlOTarX5fH0rV67E7Nmz0bNnTwDAjh07YG5ujj179mD06NFFri87O1uqakxLS5MpV2XmYuICv1p+OPbyGJZGLkVIhxCFfUESUtXk5YiwaVI43zEkvlvlDXWBYrp9SE5Oxv79+9GmTRup6XPmzJH8mzGGFi1aoH79+vD29sbdu3fh5uYmmZ+Tk4MpU6Zg4sSCsfF8fX2hrq6O2bNn49KlS2jRogWuXr2KzZs3Y/ny5Zg8ebLkta1atUKdOnWwYsUKLFmyBHp6elKn0d69e4eBAweiTp062L17NwDg8ePH2LRpE8aOHYvffvuvlbpRo0Zo1qwZfv31V/zyyy9F7u/JkycRFhaGVatWSeXV0NAoNKi0l5cXvLy8JM/z8/PRpUsXODs7Y+PGjVixYkXp3uQyCgoKQk5ODsLCwmBjYwMA6Ny5M1JSUjBv3jyMHj0a+vr6kuVNTU1x+PBhyXd8y5Yt4ejoiEWLFmHz5s0AgN69e6N3795S++Ln5yc5nk6cOBGmpqZwdHQEADg5OUl9DqampjAwMIBAICh0mnPHjh24e/cu/vzzT0kLkK+vL3R0dDB9+nScPn0avr6+CninpMl0iio6OhpRUVGlesji2bNnsLKygr29Pfr16ydproyKikJ8fDzat28vWVYgEMDb2xuXL18udn2LFi2Cvr6+5CH+A6luJjWeBIGqADcSbuDsq7NffwEhpNoxNDQsVNwAwMuXLzFgwABYWFhAVVUV6urq8Pb2BgA8evSo0PIDBw6Uej5gwAAAQFhYGADg2LFj4DgOgwYNQl5enuQh7h2/qLu50tPT0aVLF2RlZeHEiRMwMDCQWuewYcOklm/atCnq16+PM2fOFLu/4tcWl/dzeXl5WLhwIZycnKChoQE1NTVoaGjg2bNnRb4HX77280dZGgDOnj2Ltm3bFjp2DRs2DBkZGYVauAYMGCD1A9bW1haenp6SfQWAT58+Yfr06ahduzbU1NSgpqYGHR0dpKenf3VfSpNXW1tbqoAS5wVQ4uchTzK14ChSs2bN8Pvvv6NOnTpISEjAggUL4OnpiQcPHiA+Ph4AYG5uLvUac3NzqfOGX5o5c6bUL4S0tLRqWeRYaFtgiNMQbL63GSturIBXDS+oq6rzHYsQpaemoYLvVnnzHUNCTUOm36alYmlpWWjap0+f0KpVK2hqamLBggWoU6cOtLS0EBsbi549eyIzM1M6n5oajI2NpaaJW+WTkpIAAAkJCWCMFfo+FxOfShHLy8tD79698fTpU5w/f17qO1y8zqKyW1lZlXh8SEpKKjHv5yZPnoy1a9di+vTp8Pb2hqGhIVRUVPDtt98Weg8+Fx0dDXt7e6lpYWFh8PHxKfY1X2Ysbt/E87+W3cLCAnfu3JE8HzBgAM6cOYO5c+fCw8MDenp64DgOnTt3LnFfSpvXwsKi0FkCMzMzqKmpFcqrKAorcNLS0pCSklLoNNbXfH7e09XVFc2bN4eDgwN27NghaQb78k1jjJV4ukUgENDdXv9vpOtIHHp2CK8+vsK+J/sw2Gkw35EIUXocxynslJCyKeq79OzZs3j79i3OnTsnabUBgJSUlCLXkZeXh6SkJKmiQfwDVTzNxMQEHMfhwoULRX4/fzntu+++w5kzZ/D333+jQYMGUvPE64yLi0ONGjWk5r19+7bY62/Ery0p7+d27dqFIUOGYOHChVLTExMTJa1JRbGyskJERITUtLJcr2NsbIy4uLhC09++fQsAhfavqOzx8fGS/UtNTcWxY8cQGBiIGTNmSJbJzs5GcnJyqXOVlPfatWuFjs3v3r1DXl5eiZ+HPJX6Z4CRkRGWLl0qNe2PP/6QXAvzpV9//bVQxSoLbW1tuLq64tmzZ5Kq9MsP7927d8X+CiDStNW1MaHRBADAhjsbkJqdynMiQoiyEx+kviw6Nm7cWOxrxNfHiO3ZswcAJK0Wfn5+YIzhzZs3cHd3L/RwdXWVvHbOnDkICQnBli1b0K5du0LbEp9S27Vrl9T0iIgIPHr0CG3bti02Z+vWrUvM+zmO4wq9B8ePH8ebN2+KXT8AaGhoFNq/stwU07ZtW0mR+bnff/8dWlpaha6B2bt3r9QpsJiYGFy+fFny3nMcB8ZYoX3ZsmVLofEjxcsU1aojEAiKnN62bVt8+vQJR44cKZRXPL8ilLoFJyUlpdCOPH78GH/99ZfcQ30uOzsbjx49QqtWrWBvbw8LCwucPn0ajRo1AlBwMVt4eDiWLFmi0BxVSY/aPbD78W48+/AMG+5swPSm0/mORAhRYp6enjA0NMT333+PwMBAqKurY/fu3VKnPD6noaGB5cuX49OnT/Dw8JDcRdWpUye0bNkSANCiRQt89913GD58OCIjI+Hl5QVtbW3ExcXh4sWLcHV1xZgxY7B//3788ssv6N27N+rUqYOrV69KtiMQCNCoUSPUrVsX3333HX777TeoqKigU6dOkruobGxs8MMPPxS7b+3bt4eXlxemTZuG9PR0uLu749KlS9i5c2ehZf38/LB9+3bUq1cPbm5uuHHjBpYuXVqo1UgWn+/X57y9vREYGIhjx46hdevW+Omnn2BkZITdu3fj+PHjCA4OlrrAGCj40e/v749Ro0YhNTUVgYGB0NTUxMyZMwEAenp68PLywtKlS2FiYgI7OzuEh4dj69athVqiXFxcAACbNm2Crq4uNDU1YW9vD2NjY7i6uuLQoUNYv349mjRpAhUVFbi7u2PIkCFYu3Ythg4diujoaLi6uuLixYtYuHAhOnfuXGSRqhCslDiOY/PmzZOaFhQUxFRUVIpcvqR5JZkyZQo7d+4ce/nyJbt69Srz8/Njurq6LDo6mjHG2OLFi5m+vj47dOgQu3fvHuvfvz+ztLRkaWlppd5GamoqA8BSU1PLnK+quPzmMnPZ7sIa7mjIolKi+I5DCKlgQ4cOZdra2lLTvL29mbOzc5HLX758mTVv3pxpaWkxU1NT9u2337KbN28yACwkJKTQeu/evct8fHyYUChkRkZGbMyYMezTp0+F1rtt2zbWrFkzpq2tzYRCIXNwcGBDhgxhkZGRjDHGAgMDGYAiH7a2tpL15OfnsyVLlrA6deowdXV1ZmJiwgYNGsRiY2ML7ffnr2OMsZSUFDZixAhmYGDAtLS0mK+vL3v8+DEDwAIDAyXLffjwgY0cOZKZmZkxLS0t1rJlS3bhwgXm7e3NvL29JctFRUUVel+KExYWVuz+AWBhYWGMMcbu3bvHunbtyvT19ZmGhgZr0KBBofWL17Vz5042ceJEZmpqygQCAWvVqpXk/RR7/fo169WrFzM0NGS6urqsY8eO7P79+8zW1pYNHTpUatmVK1cye3t7pqqqKrVfycnJrHfv3szAwIBxHMc+LymSkpLY999/zywtLZmamhqztbVlM2fOZFlZWV99T0pSluO30hU4//vf/5ilpSVTV1dnVlZWrGfPnuzBgweS+SKRiAUGBjILCwsmEAiYl5cXu3fvXpm2QQVOgbH/jmUu213YhDMT+I5CCKkiiiqcCJGXshy/le4uqn379pU4Xzz4mSwDoBFpU5pMwaU3lxAWG4brcdfR1LIp35EIIYQQuVDcvYZE6dUyqIXedQr6KVgWuQwipjw9tRJCCCHlQQVONTe24VjoqOvgUfIjHH1x9OsvIISQEmzfvh2fPn3iOwYh4BgrXXeKKioqMDExkbp/PTExEUlJSUXezy+e9+UtZ8ogLS0N+vr6SE1NhZ6eHt9xeBdyPwQrbqyAmdAMR/2PQku96owcTAghpOooy/G7TAVOWXEcRwVOJZCdn43uR7rjzac3GNtgLMY0HMN3JEIIIaSQshy/S121iESiMj+UsbghhQlUBfihSUE/ESEPQpCQnsBzIkIIIaR86BocAgBob9seDU0bIjMvE7/d+u3rLyCEEEKUGBU4BEDB6cQfPX4EAIS+CMXDpIc8JyKEEEJkRwUOkXAzdUNn+85gYFgWuQylvDyLEEIIUTpU4BApkxpPgoaKBiLiIxAWG8Z3HEIIIUQmVOAQKVY6VhjiPAQAsOLGCuTm5/KciBBCCCk7KnBIISNdRsJI0wgxaTH48+mffMchhBBCyowKHFKIjoYOxjcaDwBYd3sdUrNTeU5ECCGElI1MBc78+fNx/vz5Epe5dOkS5s+fL1Mowj//2v6obVAbaTlp2Hh3I99xCCGEkDKRqcAJCgrCuXPnSlzm4sWLmDdvniyrJ0pATUUNP7oX3Da+9/FexKTF8JyIEEIIKT2FnaLKycmRaXgHojw8rT3R0rol8kR5+PXGr3zHIYQQQkpN5gqE47hi5+Xk5ODChQswNzeXdfVESUxpMgUqnArOvDqDiPgIvuMQQgghpaJW2gVr1aol9fzXX39FSEhIoeXy8/ORmJiIrKwsjBo1qvwJCa9qG9ZGb8fe+PPpn1gWuQx7u+yFCkctc4QQQpRbmQbbZIyBMQaO4yT//vKhrq4OZ2dn/Pjjj1i+fLkis5MKMrbhWGira+Nh0kMcf3mc7ziEEELIV5W6BSc6OlrybxUVFfzwww/46aefFJGJKBljoTFGuY7CypsrsfLmSrSzbQehmpDvWIQQQkixZDrXEBUVhUmTJsk7C1Fig5wGwUrbCu8y3mHHgx18xyGEEEJKJFOBY2trC319fXlnIUpMoCrAD01+AABsu78N7zLe8ZyIEEIIKV6pT1F96f379wgJCUFERARSUlKQn59faBmO43DmzJlyBSTKo4NdB+x8tBN339/FmltrML8FdeRICCFEOclU4Ny9exdt2rTBhw8fwBgrdrmSbiUnlQ/HcZjmMQ2D/h6EI8+PYED9AahnVI/vWIQQQkghMp2imjJlCpKTkzF79mxERUUhNzcXIpGo0KOoVh1SuTUwbYCOdh3BwLAsYlmJBS4hhBDCF5kKnCtXrqBHjx6YP38+bG1toaqqKu9cRIkFNAmAhooGrsVfw/nXJY9JRgghhPBBpgJHQ0MDDg4O8s5CKglrHWsMchoEAFgWuQy5olyeExFCCCHSZCpw2rRpg8jISHlnIZXIt67fwkjTCNFp0dj/ZD/fcQghhBApMhU4S5cuxYMHD7Bs2TJ55yGVhK6GLsY1HAcAWH9nPVKzU3lORAghhPyHYzJcJTpixAhERUXh/PnzsLe3R4MGDYrsF4fjOGzdulUuQeUpLS0N+vr6SE1NhZ6eHt9xKq08UR56h/bGi9QXGOo0FFM9pvIdiRBCSBVWluO3TAWOikrpGn44jlPKO6mowJGfi28uYsy/Y6CmoobQ7qGw0bPhOxIhhJAqqizHb5n6wYmKipIpGKl6Wlq3RAurFrj09hJ+vfkrVvis4DsSIYQQIluBY2trK+8cpBKb4j4FV45ewemY07iRcANNzJvwHYkQQkg1J9NFxl9KTk5GbGysPFZFKiFHQ0f0dOwJAFgWsQwiJuI5ESGEkOpO5gInNTUVkyZNgrm5OUxNTWFvby+Zd+3aNXTu3Bk3btyQS0ii/MY1HActNS3cT7qPv6P+5jsOIYSQak6mAic5ORnNmjXDb7/9BhsbG9SvX1+qy343NzdcunQJu3fvlltQotxMhCYY5TYKALDyxkpk5mXynIgQQkh1JlOBExQUhKdPn2Lv3r2IjIxEnz59pOYLhUJ4e3vj7NmzcglJKodB9QfBUtsSCRkJ2PlwJ99xCCGEVGMyFTihoaHw8/PD//73v2KXsbW1xevXr2UOBgCLFi0Cx3EICAiQTGOMISgoCFZWVhAKhfDx8cGDBw/KtR0iH5pqmghoHAAA2HJvCxIzE/kNRAghpNqSqcCJi4uDk5NTictoamoiPT1dplAAEBERgU2bNsHNzU1qenBwMFasWIE1a9YgIiICFhYW8PX1xcePH2XeFpGfTvad4Gbihsy8TKy5tYbvOIQQQqopmQocY2Pjr9419fjxY1haWsoU6tOnTxg4cCA2b94MQ0NDyXTGGFauXInZs2ejZ8+ecHFxwY4dO5CRkYE9e/bItC0iXxzH4UePHwEAh54dwpPkJzwnIoQQUh3JVOB4eXkhNDQUb968KXL+w4cP8c8//6Bdu3YyhRo3bhy6dOlS6PVRUVGIj49H+/btJdMEAgG8vb1x+fLlYteXnZ2NtLQ0qQdRnIZmDdHetj0YGJZFLoMMnWUTQggh5SJTgTN79mzk5eWhRYsW2LNnDxITC661ePToEbZu3Yo2bdpAIBDgxx9/LPO69+3bh5s3b2LRokWF5sXHxwMAzM3Npaabm5tL5hVl0aJF0NfXlzxsbGg4AUULaBIAdRV1XI27igtvLvAdhxBCSDUjU4Hj6uqKP/74AykpKRg8eDDWrVsHxhhcXFwwatQoZGZm4s8//4Sjo2OZ1hsbG4tJkyZh165d0NTULHY5juOknjPGCk373MyZM5Gamip5UKeEimeja4NB9QcBAJZFLkOuKJfnRIQQQqoTmYZqAIBu3brh5cuX2LFjB65du4bk5GTo6emhWbNmGD58OExMTMq8zhs3buDdu3do0uS/rv7z8/Nx/vx5rFmzBk+eFFzPER8fL3V9z7t37wq16nxOIBBAIBCUOQ8pn2/dvsWR50cQlRqFg08Pol+9fnxHIoQQUk3IXOAAgJGREX744Qd5ZUHbtm1x7949qWnDhw9HvXr1MH36dNSqVQsWFhY4ffo0GjVqBADIyclBeHg4lixZIrccRD70NPQwtuFY/HLtF6y7vQ6da3WGngaN3k4IIUTxylXgyJuuri5cXFykpmlra8PY2FgyPSAgAAsXLoSjoyMcHR2xcOFCaGlpYcCAAXxEJl/Ru05v7H28Fy9TX2LL3S2Y7D6Z70iEEEKqAZmuwVmxYgVMTEzw9u3bIue/ffsWpqamWL16dbnCFWXatGkICAjA2LFj4e7ujjdv3uDUqVPQ1dWV+7ZI+ampqGGK+xQAwK5HuxD7ka5/IoQQongck+Ee3ubNm0MoFJY4FIOvry/S09NLvH2bL2lpadDX10dqair09OiUiaIxxjD69GhcibuC9rbtsdxnOd+RCCGEVEJlOX7L1ILz9OnTQqeSvuTs7Ixnz57JsnpSxXAchynuU8CBw6mYU7j97jbfkQghhFRxMhU4GRkZ0NbWLnEZTU1NfPr0SaZQpOqpa1QXPR17AgCCI4IhYiKeExFCCKnKZCpwbG1tv3rq6cqVK6hRo4ZMoUjVNL7ReAjVhLiXeA//RP3DdxxCCCFVmEwFjp+fHy5evIht27YVOX/Lli24ePEiunbtWq5wpGoxEZrgW9dvAQArb65EVl4Wz4kIIYRUVTJdZPz+/Xs0atQIcXFx8Pb2hq+vL6ytrSV3NJ0/fx5WVla4efMmTE1NFZG7XOgiY/5k5WWh65GuiE+Px6TGkyQFDyGEEPI1ZTl+y1TgAMCzZ88waNAgREREFKyI4ySDKjZt2hS7du1C7dq1ZVm1wlGBw69jL49h5oWZ0FLTwvGex2EiLHuv14QQQqqfCilwxCIjI3H9+nWkpKTAwMAATZs2hbu7e3lWqXBU4PBLxEQYeHwg7ifdR+86vRHYPJDvSIQQQioBhRc4I0aMgJubGwICAmTNyCsqcPh3M+Emhv4zFCqcCg50PQBHw7INzEoIIaT6UXg/OHv27EFCQoJM4aq63Ox8ZKXTyNlf09i8MXxtfSFiIiyPpI7/CCGEyJdMBU7t2rURFxcn7yyVXsTxKGyZch73zr3mO0ql8EPjH6CmooZLby/h4puLfMchhBBShchU4IwcORLHjx/Hmzdv5J2nUtM2EECUxxB9L4nvKJWCjZ4NBtYbCABYFrEMeaI8nhMRQgipKmQqcPz9/dGsWTN4enpi7dq1uH79OmJiYvDq1atCj+rE1tkYAPAuJg0ZaTk8p6kcvmvwHQwEBniR+gKHnh3iOw4hhJAqQqaLjFVUVCS3hXMcV/zKOQ55ecr3q1yRFxn/8ct1JMZ+Qrth9VH3G0u5rruq2vNoDxZdXwQjTSMc8z8GXQ0aGZ4QQkhhZTl+q8mygSFDhpRY2FRnti7GSIz9hOj7SVTglFKfun2w9/FeRKdFY8u9LfihyQ98RyKEEFLJyVTgbN++Xc4xqg47VxPcOBGD2IfJEOWLoKIq01nAakVdRR1T3adi/Nnx2PlwJ/rW7QtrHWu+YxFCCKnE6OgrZ2Z2etDUVkd2Rh7iX6bxHafS8KrhhWaWzZArysWqG6v4jkMIIaSSK1eBEx8fj3Xr1mHixIkYOXKkZPr79+9x/fp1ZGZmljtgZaOiwqGmsxEAIOY+3U1VWhzH4Uf3H8GBw4noE7j97jbfkQghhFRiMhc469atg729PcaPH481a9ZInbZ69+4dmjdvjl27dskjY6Vj61JwNxUVOGVT16guetTuAQBYGrkU5RxFhBBCSDUmU4Fz9OhRjB8/Hq6urggNDcWYMWOk5js7O8PNzQ1HjhyRR8ZKp6aTMTgOSHrzCR+Ts/iOU6mMbzQeQjUh7r6/i5PRJ/mOQwghpJKSqcBZunQpatasibCwMPj5+cHMzKzQMq6urnj48GG5A1ZGmjrqMLfXBwC8ekCtOGVhpmWGES4jAAC/3vgV2fnZPCcihBBSGclU4Ny+fRtdunSBtrZ2sctYW1tX6/GqxKepqFfjshvqPBRmWmZ4m/4Wux5Wz9OchBBCykemAkckEkFdXb3EZd6/fw+BQCBTqKrA1rWgwHn9OBn5uSKe01QuQjUhAhoHAAA239uMpEwqEgkhhJSNTAVO3bp1cfFi8YMj5uXlITw8HK6urjIHq+xMauhAS18DeTkivH2WwnecSqdLrS5wMnZCem461t1ex3ccQgghlYxMBc7AgQNx8+ZNLFiwoNC8/Px8TJ06FS9fvsSQIUPKHbCy4jjuv9NU9xN5TlP5qHAq+NH9RwDAgWcH8PzDc54TEUIIqUxkKnAmTJgAb29vBAYGom7dujh48CAAoG/fvnB0dMTq1avh6+sr1TdOdWTnYgKAbheXlbuFO9rWbAsRE2H5jeV8xyGEEFKJyFTgqKur4+TJk5gxYwYSExNx//59MMZw4MABJCcnY/r06QgNDa3241XVqGcIFVUOqe8ykZKQwXecSumHJj9ATUUNF99cxKU3l/iOQwghpJKQuaM/DQ0N/PLLL0hMTMTDhw9x8eJF3L17F0lJSVi0aBE0NDTkmbNS0hCqwbK2AQBqxZGVrZ4t+tfrDwBYFrkMeSLlG52eEEKI8inTYJsfPnzAmjVrEBERAQBo2rQpxo8fj3r16ikkXFVg52qMN08+IOZBEhq0teE7TqU02m00Ql+E4nnKcxx+fhh96vThOxIhhBAlV+oWnKSkJLi7uyMoKAjHjh3DsWPHEBgYCA8PDyQnJysyY6UmvtD4zdMPyMmi1gdZ6Av0MaZBQW/Za26twaecTzwnIoQQouxKXeAsXLgQUVFR8PHxwb59+7Bv3z54eXnhxYsXWLx4sSIzVmoG5lrQM9GEKI/hzZMPfMeptPrW7Qs7PTskZyVj6/2tfMchhBCi5DhWyhEN69evj/z8fDx69AiqqqoACvq7qV+/PtTV1SvVsAxpaWnQ19dHamoq9PT0FL698/ue4t6513BuZQWfgXQ6T1Zhr8IwMWwiNFQ0cNT/KKx0rPiORAghpAKV5fhd6hacmJgYdOjQQVLcAICamho6duyI6OhomcNWB5+PLk4jZMvOx8YHHhYeyBHlYNXNVXzHIYQQosRKXeBkZWXB1NS00HQTExNkZ9OAiCWxrmMANXUVfPqQjeS36XzHqbQ4jsNU96ngwOHvqL9x9/1dviMRQghRUjLfJk5KT01DFdb1DAEA0feoV+PycDJ2QjeHbgCApRFLqUWMEEJIkcp0m/jFixcRHBxcaBoALF1a9MFm2rRp5YhXddg6GyPmXhJi7iehSUc7vuNUahMaTcCpmFO4/f42TsWcQge7DnxHIoQQomRKfZGxikrZG3s4jkN+fn6ZX6doFX2RMQCkJWZi55wr4FQ4jFjaEpraJY/GTkq2/vZ6rLuzDtY61virx18QqFbfkesJIaS6KMvxu9QtOCEhIeUOVp3pmQhhaKmND3HpiH2UDEd3c74jVWpDnYfiwNMDePPpDfY82oPhLsP5jkQIIUSJlLrAGTp0qCJzSKxfvx7r16+X3Jnl7OyMn376CZ06dQIAMMYwb948bNq0CR8+fECzZs2wdu1aODs7V0i+8rBzMcaHuHTE3E+iAqectNS1MLHxRMy5NAeb7m5C99rdYaRpxHcsQgghSkLpLjKuUaMGFi9ejMjISERGRqJNmzbo3r07Hjx4AAAIDg7GihUrJENGWFhYwNfXFx8/fuQ5+deJbxd/9SAJTEQXx5ZXV4euqG9UH59yP2H97fV8xyGEEKJElK7A6dq1Kzp37ow6deqgTp06+OWXX6Cjo4OrV6+CMYaVK1di9uzZ6NmzJ1xcXLBjxw5kZGRgz549xa4zOzsbaWlpUg8+WNTWh4amKjI/5uJdjPIXZMpOhVPBjx4/AgD2P92PlykveU5ECCFEWShdgfO5/Px87Nu3D+np6WjevDmioqIQHx+P9u3bS5YRCATw9vbG5cuXi13PokWLoK+vL3nY2PAz6KWqqgpsnApOo8Tcp9vF5cHDwgOtbVojn+Vj+Y3lfMchhBCiJJSywLl37x50dHQgEAjw/fff4/Dhw3ByckJ8fDwAwNxc+voVc3NzybyizJw5E6mpqZJHbGysQvOX5PNejYl8TG4yGWqcGs6/Po/Lb4svdAkhhFQfSlng1K1bF7dv38bVq1cxZswYDB06VGqsK47jpJZnjBWa9jmBQAA9PT2pB19qOhcUOO9iPiIjLYe3HFWJnb4d+tXrBwBYFrkM+SLl65qAEEJIxVLKAkdDQwO1a9eGu7s7Fi1ahAYNGmDVqlWwsLAAgEKtNe/evSvUqqOstPUFMK2pC4BaceTp+wbfQ09DD88+PMOR50f4jkMIIYRnSlngfIkxhuzsbNjb28PCwgKnT5+WzMvJyUF4eDg8PT15TFg2dJpK/vQF+vi+wfcAgN9u/Yb0XBrzixBCqrNyFTjx8fFYt24dJk6ciG+//VYy/f3797h+/ToyMzPLvM5Zs2bhwoULiI6Oxr179zB79mycO3cOAwcOBMdxCAgIwMKFC3H48GHcv38fw4YNg5aWFgYMGFCeXalQtq4FBU7so2Tk54t4TlN19KvbDzV1ayIpKwlb723lOw4hhBAeyVzgrFu3Dvb29hg/fjzWrFkj1dPxu3fv0Lx5c+zatavM601ISMDgwYNRt25dtG3bFteuXcM///wDX19fAAVjWwUEBGDs2LFwd3fHmzdvcOrUKejq6sq6KxXOzFYPmjrqyMnMQ/yLVL7jVBnqquqY7D4ZAPD7w98Rn178heeEEEKqtlKPRfW5o0ePonv37nB3d8dPP/2EEydOYMOGDVLjTjVq1AhWVlY4fvy4XAPLAx9jUX3pdMgDPL2WgEbta8KzZ21eMlRFjDEMPzkcNxJuwK+WHxa1WsR3JEIIIXJSluO3TC04S5cuRc2aNREWFgY/Pz+YmZkVWsbV1VXqzicizc7FBABdhyNvHMdJOv879vIY7ife5zkRIYQQPshU4Ny+fRtdunSBtrZ2sctYW1sjISFB5mBVnY2TETgOSH6bjo/JWXzHqVKcjZ3RzaEbAGBpxFLI0EhJCCGkkpOpwBGJRFBXVy9xmffv30MgEMgUqjrQ1FaHhYM+AGrFUYQJjSZAU1UTN9/dxL+v/uU7DiGEkAomU4FTt25dXLx4sdj5eXl5CA8Ph6urq8zBqgPJ7eL3aNgGebPQtsAwl2EAgBWRK5CTT50qEkJIdSJTgTNw4EDcvHkTCxYsKDQvPz8fU6dOxcuXLzFkyJByB6zKxAXO68cfkJdLve/K23Dn4TAVmuL1p9fY+3gv33EIIYRUIJkKnAkTJsDb2xuBgYGoW7cuDh48CADo27cvHB0dsXr1avj6+mLkyJFyDVvVGFvrQNtAgLxcEd4+TeE7TpWjpa6FCY0mAAA23tmID1kfeE5ECCGkoshU4Kirq+PkyZOYMWMGEhMTcf/+fTDGcODAASQnJ2P69OkIDQ0tcXwoUnDHj7gVJ5quw1GIbg7dUM+oHj7mfsSGOxv4jkMIIaSCyNQPzucYY3jy5AmSk5Ohp6eH+vXrQ1VVVV75FEIZ+sERe3n7PU5suAc9E00M+rk5FYUKcC3uGr499S1UOVUc6n4ItfRr8R2JEEKIDBTeD87nOI5DvXr14OnpCRcXF6UvbpRNjXqGUFHlkJaYhZSEDL7jVEnNLJvBp4YP8lk+fo38le84hBBCKoBMBU6dOnXw888/4+XLl/LOU+1oaKrBytEAAN0urkiT3SdDjVPDudfncDXuKt9xCCGEKJhMBU5CQgICAwPh6OiIli1bYuPGjfjwgS7glJWdK/VqrGj2+vboW7cvAGBZxDLki+iuNUIIqcpkKnDevXuHvXv3onPnzoiIiMDYsWNhaWmJXr164fDhw8jNzZV3zipNfKHx22cpyMnK4zlN1TWmwRjoaujiyYcnCH0RynccQgghCiRTgSMQCPC///0PR48exdu3b7Fq1So0bNgQhw8fRu/evWFhYYExY8aU2Bkg+Y++mRB6pkKI8hleP6aWMEUx0DTAaLfRAIDVt1YjI5eueSKEkKqq3BcZGxsbY/z48bh69SqePn2KuXPnwtjYGBs3boSPj48cIlZ9HMfBTtyrMZ2mUqj+9frDRtcGiZmJCHkQwnccQgghClLuAudztWvXRps2beDt7Q11dXUa5LAMbD8rcOh9UxwNVQ1MbjIZALD9/nbEp8fznIgQQogiyKXAefDgAWbNmgU7Ozu0bt0aW7duhZ2dHYKCguSx+mrBqo4B1DRUkJ6SjaQ3n/iOU6W1rdkWjc0aIys/C7/d+o3vOIQQQhRA5gInLi4Oy5cvR6NGjeDm5obFixcjIyMDY8aMwZUrV/DkyRPMnTtXnlmrNDV1VdSoZwQAiL5Hp6kUieM4/OjxIwAg9EUoHiQ+4DkRIYQQeZOpwPH19UXNmjXx448/4vHjx+jVqxf++usvvH37FmvWrEGzZs3knbNaEJ+mekXX4Sici4kL/Gr5AQCWRi6l04KEEFLFyFTgnD17Fi1atMDmzZuRkJCAP//8E127doWampq881Ur4gIn/mUqstLpVntFm9R4EgSqAtxIuIGzr87yHYcQQogcyVTgREVF4dy5cxg5ciTvYzlVJbpGmjCy0gZjwKuH1IqjaBbaFhjqPBQAsPzGcuTmU1FJCCFVhUwFTs2aNeWdg/w/W7pdvEKNdBkJE6EJYj/GYu/jvXzHIYQQIielOqd0/vx5AEDTpk2hqakpeV4aXl5esiWrpuxcjXHr1Cu8up8MkYhBRYVGF1ckLXUtTGg0AYGXA7Hx7kZ0r90d+gJ9vmMRQggpp1IVOD4+PuA4Do8ePUKdOnUkz0sjP5/G/CkL81r60BCqISs9F++i02BRiw62itbdoTt2P9qNpx+eYsOdDZjedDrfkQghhJRTqQqcn376CRzHwcTEROo5kT9VVRXUdDLC8xvvEHM/iQqcCqCqooqp7lPx3envsO/xPvyv7v9gp2/HdyxCCCHlwLFqeH9sWloa9PX1kZqaqpQXST++EoczOx7BtKYu+s7y4DtOtTHuzDicf30erW1aY3Wb1XzHIYQQ8oWyHL9lusj41atXSEtLK3GZjx8/4tWrV7Ksvtqr6VxwofH7Vx+RnprNc5rqY0qTKVDlVBEWG4brcdf5jkMIIaQcZCpw7O3tsWrVqhKXWbduHezt7WUKVd1p6WnAzFYXAN1NVZFqGdRCnzp9ABR0/pcvouvHCCGkspKpwGGMfbXn12p45kuuqFdjfoxpOAa66rp4nPwYR18e5TsOIYQQGcl1NPHPvX79Grq6uopafZVn61pwQferR8nIzxfxnKb6MNI0wndu3wEAVt9cjYzcDJ4TEUIIkUWpx1aYP3++1PNz584VuVx+fj5ev36Nffv20ZhU5WBWUxdCXXVkfsxF3PNU1KhryHekamNA/QHY92Qf3nx6gx0PdmBMwzF8RyKEEFJGpb6LSkXlv8YejuO+egrKysoKhw8fhoeH8t0FpOx3UYn9u/0hnlyNR0PfmmjRqzbfcaqVU9GnMCV8CoRqQhztcRTm2uZ8RyKEkGqvLMfvUrfghIWFASi4tqZNmzYYNmwYhg4dWmg5VVVVGBkZoV69elJFESk7WxdjPLkaj5j7SVTgVDBfW180MmuEW+9u4bdbv2FBywV8RyKEEFIGpS5wvL29Jf8ODAxE69ataRgGBbOpbwROhcOHuHSkJWZCz0TId6Rqg+M4THWfioF/D0Toi1AMqD8ATsZOfMcihBBSSjI1sQQGBlJxUwE0tdVhUaugCY5uF694bqZu6GzfGQwMyyKX0Z2BhBBSiZS6Bac4sbGxePv2LbKzi+6Qjgqh8rFzNUHc81TE3E+Cq08NvuNUOwGNA3Dm1RlExEcgLDYMbWq24TsSIYSQUpC5wDl69Ch+/PFHPHv2rMTlaLDN8rF1McaVwy/w+skH5OXkQ01Dle9I1YqljiWGOA3B5nubseLGCrSybgV1VXW+YxFCCPkKmU5RnTt3Dv7+/vj06RPGjx8Pxhi8vLzw3XffwcnJCYwxdOnSBT/99FOZ171o0SJ4eHhAV1cXZmZm6NGjB548eSK1DGMMQUFBsLKyglAohI+PDx48eCDLrig9Iytt6BgKkJ8rwpunKXzHqZZGuo6EkaYRYtJi8OfTP/mOQwghpBRkKnAWL14MHR0d3LhxQzJkQ+vWrbF+/XrcvXsXv/zyC86cOYPu3buXed3h4eEYN24crl69itOnTyMvLw/t27dHenq6ZJng4GCsWLECa9asQUREBCwsLODr64uPHz/KsjtKjeM4Sa/GMfcSeU5TPWmra2NCowkAgHW31yE1O5XnRIQQQr5GpgInIiICPXr0gLn5f32DiEQFve1yHIeZM2eiUaNGMrXg/PPPPxg2bBicnZ3RoEEDhISE4NWrV7hx4waAgtablStXYvbs2ejZsydcXFywY8cOZGRkYM+ePbLsjtITFzjR95PoQlee+Nf2R22D2kjLScPGuxv5jkMIIeQrZCpwMjIyYG1tLXkuEAgKjS7+zTff4NKlS+VLByA1teDXspGREQAgKioK8fHxaN++vdT2vb29cfny5SLXkZ2djbS0NKlHZVKjnhFU1Dh8TMrCh3gaOoAPqiqq+NH9RwDA3sd7EZMWw3MiQgghJZGpwLGwsMD79+8lz62trQtdA5OUlFTuC4wZY5g8eTJatmwJFxcXAEB8fDwASLUeiZ+L531p0aJF0NfXlzxsbGzKlauiqQtUYV2nYKgGul2cP57Wnmhp3RJ5ojz8euNXvuMQQggpgUwFToMGDXD//n3J89atWyMsLAz79u1Deno6Tp48iT/++ANubm7lCjd+/HjcvXsXe/fuLTSP4zip54yxQtPEZs6cidTUVMkjNja2XLn4YOv8/9fhUIHDq6nuU6HKqUpuHSeEEKKcZCpwunXrhtu3byMmpqCZftasWdDR0cHAgQOhp6eHzp07Iz8/HwsWyN69/YQJExAaGoqwsDDUqPFf/y8WFhYAUKi15t27d4VadcQEAgH09PSkHpWNrWtBgRP3LAU5mXk8p6m+HAwc0LtObwDA0oilEDEa6Z0QQpSRTAXOiBEjkJGRAVtbWwCAvb09IiIi8P3336N9+/YYNWoUrl27JlMnf4wxjB8/HocOHcLZs2dhb28vNd/e3h4WFhY4ffq0ZFpOTg7Cw8Ph6ekpy+5UCgZmWtA3E0IkYoh9nMx3nGptTIMx0FHXwaPkRzj28hjfcQghhBSh3D0Zizk4OGDt2rXlXs+4ceOwZ88e/PXXX9DV1ZW01Ojr60MoFILjOAQEBGDhwoVwdHSEo6MjFi5cCC0tLQwYMKDc21dmdi4muHM2FjH3kuDQyIzvONWWsdAYo9xG4dcbv2LVzVXwtfWFUI3GCSOEEGWidMN9r1+/HqmpqfDx8YGlpaXk8ccff0iWmTZtGgICAjB27Fi4u7vjzZs3OHXqFHR1dXlMrniS/nDodnHeDaw/ENY61niX8Q47HuzgOw4hhJAvcKwUR8rz58/LvAFlHIsqLS0N+vr6SE1NrVTX4+TnirBl6gXkZeej7ywPmNas2gWdsvsn6h/8eP5HCNWEOOZ/DGZa1KpGCCGKVJbjd6lOUfn4+BR7h9LX0FhU8qOqrgKbeoaIupOImPuJVODwrINdB+x8tBN339/FmltrML/FfL4jEUII+X+lKnB++uknmQscIl+2Lsb/X+Akwb2z/ddfQBSG4zhM85iGQX8PwpHnRzCg/gDUM6rHdyxCCCEoZYETFBSk4BiktMTX4cRHpSHzUw6EOho8J6reGpg2QCe7TjgRfQLLIpZhc/vN9GOAEEKUgNJdZExKpmOoCWNrHYABrx7Q7eLKYFKTSdBQ0cC1+GsIfx3OdxxCCCEoZ4ETHx+PdevWYeLEiRg5cqRk+vv373H9+nVkZmaWOyAp7PO7qQj/rHWsMdhpMABgeeRy5IpyeU5ECCFE5gJn3bp1sLe3x/jx47FmzRps375dMu/du3do3rw5du3aJY+M5AviXo1fPUyCSES3iyuDb12/hZGmEaLTorH/yX6+4xBCSLUnU4Fz9OhRjB8/Hq6urggNDcWYMWOk5js7O8PNzQ1HjhyRR0byBQt7PQi01JCdnoeEqMo1MnpVpaOhg3ENxwEA1t1Zh9TsVJ4TEUJI9SZTgbN06VLUrFkTYWFh8PPzg5lZ4f4/XF1d8fDhw3IHJIWpqKrAxskIABBzP5HnNESsp2NPOOg7IDU7FcP+GYZXaa/4jkQIIdWWTAXO7du30aVLF2hraxe7jLW1NRISEmQORkpmR9fhKB01FTUsarUIpkJTPE95jn7H+uH8a9k7ySSEECI7mQockUgEdXX1Epd5//49BAKBTKHI19V0NgY4IDH2Ez59yOY7Dvl/9Y3r4w+/P9DQtCE+5n7E+DPjseHOBhp1nBBCKphMBU7dunVx8eLFYufn5eUhPDwcrq6uMgcjJRPqasDcrqCb6lcPqBVHmZhqmWJbh234X93/gYFh7e21CAgLwKecT3xHI4SQakOmAmfgwIG4efMmFixYUGhefn4+pk6dipcvX2LIkCHlDkiKR7eLKy91VXXM+WYO5nvOh7qKOsJiw9D/eH+8TH3JdzRCCKkWSjXY5pdyc3PRvn17nD9/HrVr14ZAIMCDBw/Qq1cvREZGIjo6Gu3bt8eJEyeUslfXyjrY5pfexaRh/6JIqAtUMXJ5K6iqUb+Nyuje+3v44dwPSMhIgLa6Nha2XIg2NdvwHYsQQiqdshy/ZToiqqur4+TJk5gxYwYSExNx//59MMZw4MABJCcnY/r06QgNDVXK4qYqMbXRhVBPA7nZ+Xj7PIXvOKQYrqau+MPvD7ibuyM9Nx2TwiZhza01dF0OIYQokEwtOJ9jjOHJkydITk6Gnp4e6tevD1VVVXnlUwhFtuBkPngAzbp1wamVapivcjuz4yEeX4lHg3Y2aNnbsUK2SWSTK8rFisgV2PWooAPMVtatsNhrMfQ0Km8rIiGEVCSFt+B8juM41KtXD56ennBxcZEUN1FRURg2bFh5V1+pJG7chOg+fZG0eXOFbdPWxQQAEHOPrsNRduoq6pjedDoWtlwIgaoAF95cQP9j/fHswzO+oxFCSJUj94s2Xr16hVGjRqFevXrYuXOnvFev1NStrACRCO/XrkPmgwcVsk0bJyNwKhxSEjKQ+j6jQrZJyqerQ1fs7LQTVtpWePXxFQb+PRAno0/yHYsQQqqUMhU4Fy9eROvWraGnpwcjIyN0794dT548AQBkZGRg8uTJqFOnDrZu3QpTU1OsXr1aIaGVlZ5fF+h27Ajk5eHt9OkQZSu+fxqBUA2WDvoAgJj7NLp4ZVHfuD72+e1DM8tmyMzLxNTwqfj1xq/IF+XzHY0QQqqEUhc4N27cQLt27RAeHo5Pnz4hJSUFR48eRevWrfH8+XM0bdoUK1euhImJCVatWoUXL15g3LhxisyudDiOg0XgT1A1MUHO8xd4v3JVhWxXPPgmDdtQuRhqGmJDuw0Y7jwcALDt/jaMPTMWKVkp/AYjhJAqoNQFTnBwMHJycrBo0SK8e/cO7969w/z58xEfH49WrVrh8ePHmDNnDp4/f44JEyZU216M1QwNYfnzfABA8vbtSL9+XeHbFPeH8+ZJCnJzqAWgMlFTUcNk98lY6rUUQjUhLr+9jH7H++Fx8mO+oxFCSKVW6gLn0qVLaNOmDaZPnw4TExOYmJhgzpw58Pb2xrt37xAcHIz58+dDU1NTkXkrBd3WrWHQpzfAGOJmzkL+J8X2YGtkqQ0dIwHy80R48+SDQrdFFKOjfUfs6rwLNXRq4M2nNxj892Acf3mc71iEEFJplbrAeffuHZo0aVJouoeHBwBg6NCh8ktVBZhNnwF1a2vkvnmDhMWLFbotjuNgR3dTVXp1DOtgn98+tLRuiaz8LMy4MAPBEcHIE+XxHY0QQiqdUhc4eXl5RY4eLp5mbGwsv1RVgKqONqwWLwI4DqkHDuLj2TCFbu/zYRvK2bUR4ZG+QB9r2qzBKNdRAICdD3fiu9PfISmTCldCCCkL6ttfgbQ8PGA0vOAC0ri5c5GXrLi7nKzrGUJVTQUfk7OQHJeusO0QxVNVUcXExhPxq8+v0FLTQkR8BPod74cHiRXT9QAhhFQFpe7JWEVFBbVr10bt2rWlpj9//hwvXrxAhw4dCq+c43D8uPJdR1CRY1GJsrMR3bs3sp89h66vL6xXr1LYEBZHf7uNVw+S0bynAxq3t1XINkjFepHyAgFhAYhOi4aGigbmNp+LHrV78B2LEEJ4UZbjd5kKnLLiOA75+cp3V09FD7aZ9fAhovr+D8jLg1XwEuh366aQ7dwNi8WFP55BqKuOJp3s4NTSCuoayj1sBvm6jzkfMevCLJx7fQ4A0K9uP0zzmAZ1VXV+gxFCSAVTSIETExMjUxhbW+VrSeBjNPHEDRvwfuUqqOjqolboX1C3tJT7NjI/5eDA4kikJWYBAIS66mjQ1gYu3jUgEFbM2FhEMURMhI13N2Ld7XUAgMZmjbHcZzlMhCY8JyOEkIqjkAKnKuGjwGF5eYgeOBBZd+5Cq/k3qLl1KzgZWsW+Ji83H4+vxOPmyRh8TCoodDSEanD1sUaDNjYQ6mrIfZuk4oTHhmPGhRn4lPsJZkIzrGi9Ag1MG/AdixBCKgQVOF/BR4EDANlRUYjy7wmWlQXzOXNgNGigwrYlyhfhWUQCbvwTgw/xBWNUqWmowLmlNRr62kDHkPorqqyiU6MREBaAF6kvoKaihlnNZqFPnT58xyKEEIWjAucr+CpwACB5924k/LwAnKYm7A8dgqCWvUK3x0QMUXcSEXkiGu9ffQQAqKhyqPeNBRp1sIWBmZZCt08UIz03HXMuzsG/r/4FAPRy7IVZzWZBQ5Va6AghVRcVOF/BZ4HDRCLEfjsK6ZcvQ9PNDXZ7doNTU/z1MYwxxD5Kxo0TMXj7LAUAwHFAbXdzNOloC2NrHYVnIPLFGMPW+1ux+uZqMDC4mbphhfcKmGub8x2NEEIUggqcr+CzwAGA3Ph4vOzaDaKPH2E6aSJMxoyp0O3HPU/BjX9iEHP/v87j7NxM0KSTLSzs9Ss0Cym/i28uYvr56UjLSYOxpjFW+KxAY/PGfMcihBC5owLnK/gucAAg9ehRvP1xGqCmBrs/9kHo7FzhGd6/+ogb/8Tgxa13wP//FdSoZ4gmHW1hXddQYf31EPmL/RiLgLAAPP3wFGqcGqY1nYZ+dfvRZ0gIqVKowPkKZShwGGN4E/ADPp48CY3aDrA/eBAqPI3A/iE+HTdPxuDptQSIRAV/Dub2emjSyQ52rsZ0kKwkMnIzEHQ5CCeiTwAAujl0w9xv5kJTjS4oJ4RUDVTgfIUyFDgAkPfhA1527Yb8xEQYDR8O8+nTeMsCAGlJmbh9OhYPL71Ffq4IAGBsrY3GHW1Ru4k5VFSo0FF2jDH8/vB3rLixAiImgpOxE1b6rISljvz7XSKEkIpGBc5XKEuBAwAfw8LwesxYgONQc8d2aDdtymseAMhIy8GdM69wL/wNcrMKeqLWNxWicQdb1G1mAVV1GsJM2V2Nu4ofw39ESnYKDAWGWOa9DE0t+f/bIoSQ8qAC5yuUqcABCgbiTNl/AOrW1rD/6whUdZTjjqas9FzcO/cad87GIjs9DwCgbSBAI9+aBcNACGgYCGX29tNbBIQF4FHyI6hyqpjcZDIGOw2mU46EkEqrLMdvpfspfv78eXTt2hVWVlbgOA5HjhyRms8YQ1BQEKysrCAUCuHj44MHDyr3KMtm02dA3doauW/eIGHxYr7jSGhqq8Ojiz2G/OKJFr1rQ1tfA+kp2bi4/xl+n30ZkSeikZ2Ry3dMUgwrHSv83ul3dHPohnyWj6WRSzHjwgxk5mXyHY0QQhRO6Qqc9PR0NGjQAGvWrClyfnBwMFasWIE1a9YgIiICFhYW8PX1xcePHys4qfyo6mjDavEigOOQeuAgPp4N4zuSFA1NNTRsVxODF3jCZ2Bd6JloIutTLq799RK/z7qMK0deICMth++YpAiaappY0GIBZjSdATVODX9H/Y3Bfw/G64+v+Y5GCCEKpdSnqDiOw+HDh9GjRw8ABa03VlZWCAgIwPTp0wEA2dnZMDc3x5IlSzB69Ogi15OdnY3s7GzJ87S0NNjY2CjNKSqxhOClSN62DarGxqh1NBRqRkZ8RyqSKF+EZ5HvcPNkDJLfpgMA1NRV4NTSCg19a0LXiO7aUUaR8ZGYEj4FyVnJ0BfoI7hVMDytPfmORQghpVapT1GVJCoqCvHx8Wjfvr1kmkAggLe3Ny5fvlzs6xYtWgR9fX3Jw8bGpiLilpnppIkQONZGflIS4gODoKy1p4qqCuo2s0C/OU3R6XtXmNnqIi9XhLthr7Fr7hWc3fkIKQkZfMckX3C3cMcffn/A1cQVqdmpGHNmDLbe26q0f2eEEFIelarAiY+PBwCYm0t3RW9ubi6ZV5SZM2ciNTVV8oiNjVVoTlmpCASwWrIEUFPDx9OnkXb0KN+RSsSpcKjV0BS9Z7ij26SGsK5jAFE+w6NLcdgTdBWnttxH4utPfMckn7HQtkBIxxD0dOwJERNh5c2VmBI+BRm5VJASQqqWSlXgiH15FwhjrMQ7QwQCAfT09KQeykrTyQmm48cBAOJ/XoDcuDieE30dx3GwqW+EHpMbo+ePTWDnagzGgGeR7/DHgus4vvYO4l+m8h2T/D+BqgBBzYMw95u5UFNRw+mY0xj490DEpMXwHY0QQuSmUhU4FhYWAFCotebd/7V353FRlX3/wD/nzJkFkH1REFkVcUXFUnKpzHDJJEuzXVvu7kpLs82sFMvcWm7tzsrHJzWfum/7keaSWrngUma5YaaICyCiIIrAsM52rt8fM3OYYQYGEmZg+L5fr3mdmeucc13XDAfmw3W2oiKbUZ22LPCZZ6BK6AuxvBxX5swBE0VXd6nRQmN9cc+0BEx++xZ0HRgCcEDuyWJsWHoUm/51DJfO3KBdIq0Ax3F4sPuDWDNqDYI9gnG+9Dwe/uFh7M/f7+quEUJIs2hTASc6OhqdOnXCzp07pTKtVot9+/bhttvc52BJThAQtngxOJUKVb8dQsl//uvqLjVZULg3Rj3TG4+mDkaP20LB8xwuZ5Viy7IMfLfkKLIzroGJFHRcrV9IP3w77lv0C+6Hcl05pu+eji9OfAGRtZ1QTQgh9rS6gFNRUYGMjAxkZGQAMB5YnJGRgby8PHAch5kzZ2LhwoX4/vvv8ddff2Hq1Knw9PTEI4884tqONzNldDRCXnsVAFD04YfQZOe4uEd/j19HT4x4ogceW5CEvneGQ5DzKMpVY8cXJ7F+wR84+0chRAN9mbpSsGcwVo9ajcndJ4OBYUXGCsxMn4kKLR0/RQhpu1rdaeJ79+7FnXfeaVM+ZcoUrF27FowxzJ8/HytXrkRJSQkGDRqEFStWoHfv3o1uo7Vdybg+TBRx6Zl/oPLgQaj69kXUf74BJwiu7tZNqVJrcWLPJfy1Nx9a020gfII9MCA5AvGDQ+k2EC72/bnv8d6h96ATdYjyicLyEcsR4xvj6m4RQggAulWDQ20l4ACArrAQ2feOh1hejuAZLyHo+edd3aVmoanS4eTeyzix5xJqKoxXQ/byVaDf3RHoNawz3QbChU5eO4mX976Mq1VX4SX3wvtD38ddEXe5uluEEEIBx5G2FHAAoGzrVlx57XVAEBD17Xp49Orl6i41G53GgNO/XMHxnXmoLDVejFHlJUfCXeHoc0c4lJ5yF/ewfSquLsar+17FkatHAADP9n0W0/pNA8/RCBshxHUo4DjQ1gIOYwyXZ76M8p9+gqJrLKI3bACvVLq6W83KoBOR9Xshjv50EeprxnslyVUy9Lk9HAl3dYGnj8LFPWx/dKIOHx/5GF9nfg0AGNZ5GBYPXwwfRev/nSGEuCcKOA60tYADAPqSEmTfOx6G69cR8OST6PjG667uUosQDSLOHyvC0R21t4GQmW4D0Z9uA+ESWy9sxfzf5kNj0CDCOwLL7lyGbv7dXN0tQkg7RAHHgbYYcACgPD0d+c+/AHAcIr5aC69bb3V1l1oMExlyT17HkR0XUZSrBgDwPIe4wZ2QOCoSfh09XdzD9iWzOBMz02fiSuUVeAgeeG/IexgVNcrV3SKEtDMUcBxoqwEHAAreeQelad9B3rkzojdvgqxDB1d3qUUxxpCfVYKjOy7iclaJsZADug4IQeKYSASFe7u2g+1ISU0JXtv/Gn4v+B0A8GTvJzGj/wzIeDognBDiHBRwHGjLAcdQUYmclBToLl+G78QHELZggau75DSF2WU4+uNF5P55XSqL7BOIxNFRCI31dWHP2g+9qMcnxz7BmlNrAABJoUlYOnwp/FR+ru0YIaRdoIDjQFsOOABQdfgwLj4xBWAM4Z99Bu8RttcNcmfX8ytw7KeLOH/kKsxbb+c4PySOjkJ4D/8G70tGmsePOT9i7sG5qNZXo3OHzlh25zLEB8S7uluEEDdHAceBth5wAODq0g9wY/VqyAIDEbN1C4SAAFd3yelKr1bh+M8XceZQIUSDcTMOifRG4pgoRPcNAsdT0GlJZ0vOYsaeGcivyIdKpkLqbam4J+YeV3eLEOLGKOA44A4BR9RokDtxIjTnzsP77rvR+ZPl7XbkoqKkBsd35uH0gSvQ64y3ffAP9ULi6Eh0GxgCXkbXbmkpZZoyzD4wG79c/gUA8HjPxzErcRYEvm1fcZsQ0jpRwHHAHQIOANScPo2cBycDej3Cli6B7/jxru6SS1WXG28DcTLd4jYQQSr0T45EfFInCHI6GLYlGEQDVmSswKqTqwAAt3S6BUuHL0WQR5CLe0YIcTcUcBxwl4ADANe/+ALXli0H7+2NmC2bIQ8NdXWXXE5Trcdf+/JxYvclVJcbbwPh6atA/7sj0HNoGBQqGl1oCbsu7sJbv7yFKn0VVDIVkqOSMSluEhKCE9rt6CIhpHlRwHHAnQIO0+uR++ijqDnxJzyTBiPiyy/B8bRLBgB0WuNtIDJ25qGipPY2EH1HGG8DofKi20A0twulF/DmgTeReSNTKovzj8OkuEm4J+YeeCvotH5CyN9HAccBdwo4AKDJyUHOhPvBamrQ8e23EfDYo67uUqti0BtvA3Hsx4soM98GQilD79s7o9/ICLoNRDNjjOHEtRNIO5uGn3J/gsZgDJceggfGRI/BxG4T0TuoN43qEEKajAKOA+4WcADgxtff4OqCBeBUKkSn/T8ou9Gl9OsSRYYLpttAFF+uAGC6DcRtoeiXHAGfQA8X99D9lGnK8EP2D0jLSsOFsgtSeXxAvDSq4yX3cmEPCSFtCQUcB9wx4DBRxKVnnkHlwd8AAPLOnaHq2ROqXj2N0x49IAQHu7iXrQNjDBdPFuPIjlxczbG4DcSgjhgwKhL+negLt7kxxnC86DjSzqbh59yfoRW1AIyjOmOjx2JS90noFdjLxb0khLR2FHAccMeAAwC6wkLkvzQDNX/+aXe+EBxsG3rCwtrtrgLGGC6fLcXRHbnIP1N7G4jY/iFIHB2J4Ag6XqQllNaUYsuFLUg7m4Zcda5U3iuwFybGTcTY6LHwlNO9xgghtijgOOCuAcfMoFajJvMMak6flh7anBxAFG2Wlfn61gaenj2h7NEDisjIdnegcmFOGY79eBE5J2pvAxHRKxADx0QitKuf6zrmxhhjOHL1CNLOpmHXxV3QicYz3rzkXrgn+h5M6j6Jro5MCLFCAccBdw849ohVVajJyrIIPZnQnD8P6HQ2y/JeXlD2iDeN8piCT2wMOMH9T68uvmy8DcS5w7W3gQjr5ofEMZHo0iOg3Y52tbQbNTew5fwWfHfuO1xUX5TK+wT1waS4SRgVNYpGdQghFHAcaY8Bxx5Rq4Xm3Dkp9GhOZ6ImKwuspsZmWU6phLJ7d6h69qgNPXHdwCuVLuh5yyu7VoVjP+fhzG8FEPXGX5HgCG8kjolETEIw3QaihTDG8EfhH0g7m4bdebuhF/UAAG+5N8bFjsOkuEno5k8H0BPSXlHAcYACTv2YXg9tTo7VSE9NZibEigrbhQUByq5dpeN5VL16QtW9O3gv9zlIt6JEg4xdeTh14DL0WtNtIDp5InF0JLre0hEyug1EiymuLsam85vw3dnvkF+RL5X3C+6HiXETMSpqFFSCyoU9JIQ4GwUcByjgNA0TReguXbIOPadOwVBaarswx0ERHW0denr0gMzX1+n9bk7VFVr8uScff6bnQ1ttGlUIVGHAKLoNREsTmYhDBYfw3dnvkJ6XDj0zff4Kb4yPHY9JcZMQ6xfr4l4SQpyBAo4DFHBuHmMM+sJCY+A5dRo1mZmoOX0a+qtX7S4vDw83HcjcQzqgWQhqe/cq0lbrcbLubSB8FOg3MgK9htNtIFra9err+P7c99hwbgMuV1yWygeEDMDEuIlIjkqGUuaeu00JIRRwHKKA03L016+bwk6mNOKju3TJ7rJCSEjtKI859ISGtokDeXVaAzJ/LcDxny9Kt4FQegnoe2cX9L2TbgPR0kQm4uCVg0jLSsO+/H0wMOPNVX2VvhgfOx7jY8cjzj8OPEe7EAlxJxRwHKCA41yGsjLjaeuZtaFHm50N2Nn0ZH5+VqM8qp49IY+IaLWnrRv0Is7+UYhjP+Wh9GoVAEAm8OgQoISXrxKevgp4+Zimvgp4Ss+VUHoJbSLMtXZFVUXYeG4jNpzbgMLKQqncR+GD/iH9MaDjAAwIGYBegb0gl1HwJKQto4DjAAUc1xOrqlBzJgs1mRanrZ87B+j1NstanbZuvl5PTOs6bV26DcSPF1Gcb+eAbDt4gYOnjzHsePoo4OmrNIUgRW048lXCw1sOng5mdsggGvDrlV/x3dnvcKjgEKr11VbzVTIV+gb3lQJPQnACnXpOSBtDAccBCjitk6jVQnP2nEXoOQ3NmSwwjcZmWavT1nv2hKpnL+Np6wrX3jiTMYaya9WoLNWgqkyLKrUWlWXG55VlGum1ptI2yNWLAzw6yGsDkK8SXnUCkfm5oKCDnQFAJ+qQdSMLR68exbGrx3Cs6BhKNaVWy8g4GXoE9EBix0Qp9Pip/FzSX0JI41DAcYACTtvB9HposrOhMe/eMh3QLFZW2i5sedq6+RHfHbxn6/sv3aATUVVeG36qyjSoNE/VWqmsqlwHJjb+V1ThIZhCkMXuMMtdZKYgpPBoX7vHGGPIKcvBkatHcKzoGI5dPYaCygKb5WJ9Y41hp+MAJIYkIrRDqAt6SwipDwUcByjgtG1MFKHLy6s9pueUcbTH4Wnr5keP+DZz2rooMtRU6GxGgaxCkdo4Nehsb8VRH5mcN+0Ksx4RMu8WM44KKeDhrQDvphc1LKgowNGio9IoT3ZZts0yYV5hVoEn2je6XQVDQlobCjgOUMBxPzanrZt2cemLiuwuX3vaek/pWj1t8bR1M8YYtNV6U+CpMyJkCkHmXWaaqsbvHuN4Dh7ecosDpk1ByOI4IfMokUzeto8TKqkpkUZ3jl09hswbmdLZWWb+Sn/0D+mPxI6JSOyYiO4B3SHwredYMELcHQUcByjgtB/SaesWoUeXn293WSEkxGKkp0ebOm29KfRag+lYIOsgJJWZRoSqy7VAE/46KD0FaReYyksOuUoGhUqAQiWDwkOAQiXYlFm+bm0HUlfpqpBxLUM6hufPa39CY7A+HsxT8ERCcIJxhKdjIvoE9aGrKxPSgijgOEABp32TTluve7f1ek9brx3lae2nrTcn0SCiulxntVvM3gHTVWqtdL+umyHIecg9TOHHFHrkKgEKjzqvLcrshShBwbdIKNUZdDhVfMq4S6voGI4XHUe5ttz6PfACegX2QkJwAiJ9IhHeIRzh3uEI7RAKOU+nqBNysyjgOEABh9QlVlaiJutsbejJbPi0dfMFCpWm0NPaTlt3JsYYNFV6qwOmNdV6aKsN0NbooasxTrU1Bmir9dBpjFNzWVOOHWoMjgPkShkEhQyCgjdNZZBLz2vLBAUPuUWZ3Gp+/WWCwINxDOdKzkm7tY5ePYpr1dfs9onneIR6hUqBJ9w7vPZ5h3D4Kn3dbqSQkJZAAceBFgs4BSeAnP1AYFfjwy8SEFx72jL5+6TT1k+fqg09DZ22Ht8dqh49oIyLg8zbB7yHCpzKwzRVgffwAK8yPTdN28NIkCMGg2gMQdWmEGQZiuyWGaCrqS2X5lXr7Q3CtRhBXht65EoZBDkPg0yPSlSgUixHFatEhViOcoMaWtTAwOuh53QQeT30vB4GXgcDp4eB10MuFxDg5YeADv4I8gpEiE8wOnYIQZhvJ3Ty6QilUgFBzkMmGB90N3vSXlHAcaDFAs4v/wJ2pda+5mSAX0Rt4AmMrZ36hAP05dbmmE9bl67TY77bur3T1huBUyqNYcccfkxT3kMFTqmqDUkqFTgPFXgpMFkHJ06ptAhQtvPaw+gAYwx6nSiNEum1IvRag+khQqe1LDO/tl5OZzFfr6udZ67PoG/e0aa/TcYgE3gIchnkcpkx+JgCkCDnwQs8ZDIOnIwDzxsfDp/LOPAyY3gyv7Z5blrW7nOZ5bJ8k+rgzX3lOApvpEEUcBxosYCT+QPw13dA8QXjQ9fAl56gAgJiLEJPVyDA9NwryDjOTtoE6bR18yjPhWyI1VVg1TUQa2rAqqshajTGaU2N3RGglsbVHT0yhyWrcGURoKRwVX+osq7PA5xC4fZBShRZnVBkDkLW4UinMcCgNwYig85ianqu14sw6BgMehFarQ7VmhrUaDTQaHXQ6/Qw6ESIBgAGHrwogyAK4NA+/iHiODQijFkHMbvBq7HhTtZAGGtMMLN53YRwV6ev7v770xwo4DjglGNwGAPKC4Hi88bHDVPoKT4P3MgBRF396yp9rYNPYKzxERALqOiYobaOGQxgGk1t+KmpgVhdA1ZTDbG6BmJNNViNORyZppbzLINTjUWZpsZqHtM1sI21BI6rDUsKBThBACeXS1PIza/lVuUO58trl4NUrrA7n5PLAUEw1iHIAJnMWC6TATIBnCAzPjeVWT6HTNbqvmAYYyiuKcYl9SVcKstHftllFJQVolB9FVfLr6G0Sg2ZKIMgyiFjcshEwfhgAjjGg2cy8Iw3PTe+5hgPHqYyUQYZZBAghwABAuSQQZAeAgTwzLiEjMnAQ2aamuuqrd/44MCJpinjAJEDzFMRAOPARAAijFNipbHhrm54alK4Mwe6OqN3jQl3jsOedbjz9DFeab05tYuA89lnn+GDDz5AQUEBevXqhWXLlmHYsGGNWtflBxkb9EBZXu1IjzkEFV8Ayi6hwXNzO3S03t1lHvUJiAYEpdPeAmn9mF4PsUZjDEdWYcoiQNkLV/WFKotRKKmsuhowGBx3pq2Q1R+ArJ4LpsAkkwGCDFyd55Dx4HhZE6Yy4/FYMhk4GQ/wjqeQ8dBDRJmuHDd0pbihLUWxtgTF2hKUaNXQMR10MEAv6qWpFnromB4iGJgpe0gPAIzjpNciAJiyCVCbVayXt34tck1YhwHgeAC8aXRKZpry4CCTyhWcEnJeCQWngpxTQM7JjWWcAgooIHByyKGAwAmmoCaH3BTUBM4Y9qTAZgprvDTlwcMY+mTm8FcnsMEU2MA4wGDxRkXjiB4TGUSRQTSYnhtYbbnFc4OBgVm8bg8GjIpE0oTYZq2zKd/fbfK0j2+//RYzZ87EZ599hiFDhmDlypUYM2YMTp8+jYiICFd3zzGZYNw9FRADdLvbep6uBijJsQg952tDUOU1oOKq8XHxV+v1OB7w7WIMPio/4x9AXjBOOfNz02vzPKtyvk6ZxXJSueU8czlfp+7GtllP/a3sP+i2jBMEyDoIQAevFm2H6XTWwam6BkyrBdPrjKNIej2YTgem14PpLJ9rwfR6QHqtqzNfB6Y3ra+1LKudx3Q6wGYdvbFegwHMYDCuX+c5xHqGD8zLabVNuQSQy/mYHlEu7kfTNS0cmwaB6g9ZFmWWIcscuuoLZlKoc7ROnXV5jjeOXPIcwPEWU3M5D870muN4gOfB88YpxwvgOAEcL5f+JnK8HBwvAJxgnG96zvMCwMnB8TJTmcy4Llf795PjZeAggOOMf38ZeFNg5SEyHgwcRHAAeIjgwCwelvMZODBmLgcYM5Uzzvj+GQeRcWAMxqlUhtoyZhyh4ytLb34TuQltcgRn0KBBGDBgAD7//HOprEePHrjvvvuwaNEih+u31AgOYwzVuhb8b7ZGDb7kArgbF8AXG6fcjfPgb1wAp23cHaxbO2YZmKyey8DsBijjlNUtswhYjOcBzn7YYjbBq3ZZZhPMLNezqEuq29hfxlkGNYvAZhXeOJvZtS8crXMTZVblnJ3Zjparfc4a3XZd9cz7O+vUW95wfUwUAVE0hhmDeWoAM4i1IUdkFuX2lqtnPfNrZlrG3JZpallm7MNNzrcpM7UPwPitIwIMYKYpRNH4TcQYGJO+lf7ecuZvNcvlRNP6DSxH2gfPJx5E5Jz5zVqnW4/gaLVaHD16FLNnz7YqT05OxsGDB+2uo9FooLE4sFOtVrdI36p1BvSc+1OL1G3NG0A/0wMAGIKgRjRXgCi+EJ7QQIABMhggA4MMBgicATxECBBN5SJkEE3LmZ5LyzSwLFf73HYZAwSI4Dnres3l0nOu/p3vHBMBg9b4qDuvBT5JQloVDm3wr3LTMYbaPfHM9JQBAFfntTkPcdavpXU5mzJmb55VfVzta6mt2rKGljcAMICDngF6cNBznPE1TK8BGJhpynEwMON8AwcYTOsYwEFEbV0G00iJAYAI4zoiZxwJEWFcTzStw2AuN71mplEtGEdSOFbnYSrjTe+VN70Pvs58e+vYrGv6PMzr2iszrsOkunRlBxBpfxNwijb3q3T9+nUYDAZ07NjRqrxjx44oLCy0u86iRYswf37zpsjWhcN1+OI688VhQ7yrO9MIDDyYRUiyE4Y483ODtKzjsGVdj8xUj1BnPZtgxpmCWd3AZ1FHbV9E+8ty1m0DMP3Jgek5GlVm/qtqPSbCbJazX5/tf8aNWdfuPK7+uqzXbbgt2zrqK2/ov3r78xoe72ncKEFjl3PU3s3U2zLru1oj+m9ngLA5tUS1vOlRe01qy7RVt33njlSJAHQcoANnnHIc9Byg5QA9x0FrKrOcXzuvtkwH23nGemrn6SyXN83Tc4AW1vMe8+/k1M+grjYXcMzqnu3AGKv3DIg333wTs2bNkl6r1Wp06dKl2fvkIZfh9Lujmr1eQgghpCE8jF/oHq7uiAUPucyl7be5gBMUFASZTGYzWlNUVGQzqmOmVCqhVLb8GUYcx8FT0eY+UkIIIcTttLkrRykUCiQmJmLnzp1W5Tt37sRtt93mol4RQgghpDVpk8MNs2bNwuOPP46BAwciKSkJ//M//4O8vDw899xzru4aIYQQQlqBNhlwJk+ejOLiYrz77rsoKChA7969sX37dkRGuvJ4bUIIIYS0Fm3yOjg3y+VXMiaEEEJIkzXl+7vNHYNDCCGEEOIIBRxCCCGEuB0KOIQQQghxOxRwCCGEEOJ2KOAQQgghxO1QwCGEEEKI26GAQwghhBC3QwGHEEIIIW6HAg4hhBBC3E6bvFXDzTJfvFmtVru4J4QQQghpLPP3dmNuwtAuA055eTkAoEuXLi7uCSGEEEKaqry8HL6+vg0u0y7vRSWKIq5cuQJvb29wHNesdavVanTp0gWXLl1yyX2uXN1+e0efv+s/A2qftkHiWi25DTLGUF5ejrCwMPB8w0fZtMsRHJ7nER4e3qJt+Pj4uPSPi6vbb+/o83f9Z0Dt0zZIXKultkFHIzdmdJAxIYQQQtwOBRxCCCGEuB0KOM1MqVRi3rx5UCqV7bL99o4+f9d/BtQ+bYPEtVrLNtguDzImhBBCiHujERxCCCGEuB0KOIQQQghxOxRwCCGEEOJ2KOAQQgghxO1QwGkGn3/+Ofr27Std1CgpKQk7duxwWvupqangOM7q0alTJ6e13x7t378f9957L8LCwsBxHDZt2mQ1f+PGjRg1ahSCgoLAcRwyMjJc0s+W5OgzmDp1qs12OXjwYKe1X7dt8+ODDz5wSvtXr17F1KlTERYWBk9PT4wePRrnzp1rlrYBYNGiRbjlllvg7e2NkJAQ3HfffcjKyrJapj1sh8R1HH33uXr7o4DTDMLDw7F48WIcOXIER44cwYgRI5CSkoJTp045rQ+9evVCQUGB9Dh58qTT2m6PKisrkZCQgE8//bTe+UOGDMHixYud3DPncfQZAMDo0aOttsvt27c7rX3LdgsKCrB69WpwHIcHHnigxdtnjOG+++5DdnY2Nm/ejOPHjyMyMhIjR45EZWVls7S/b98+TJs2DYcOHcLOnTuh1+uRnJxsVX972A6J6zj67nP59sdIi/D392f/+7//65S25s2bxxISEpzSFrEFgH3//fd25+Xk5DAA7Pjx407tk7PZ+wymTJnCUlJSXNZ+XSkpKWzEiBFOaT8rK4sBYH/99ZdUptfrWUBAAFu1alWL9KGoqIgBYPv27bOZ1162Q+J69r77XLX90QhOMzMYDFi/fj0qKyuRlJTktHbPnTuHsLAwREdH46GHHkJ2drbT2iakPnv37kVISAji4uLwj3/8A0VFRS7px9WrV7Ft2zY8/fTTTmlPo9EAAFQqlVQmk8mgUCjwyy+/tEibZWVlAICAgIAWqZ+Qhrjqu68hFHCaycmTJ9GhQwcolUo899xz+P7779GzZ0+ntD1o0CCsW7cOP/30E1atWoXCwkLcdtttKC4udkr7hNgzZswYfPPNN9izZw8++ugjHD58GCNGjJC+/J3pq6++gre3N+6//36ntBcfH4/IyEi8+eabKCkpgVarxeLFi1FYWIiCgoJmb48xhlmzZmHo0KHo3bt3s9dPSH1c+d3nSLu8m3hL6N69OzIyMlBaWooNGzZgypQp2Ldvn1N+0GPGjJGe9+nTB0lJSYiNjcVXX32FWbNmtXj7hNgzefJk6Xnv3r0xcOBAREZGYtu2bU4LGmarV6/Go48+ajWi0pLkcjk2bNiAp59+GgEBAZDJZBg5cqTV72pzmj59Ov78888WGx0ipD6u/O5zhAJOM1EoFOjatSsAYODAgTh8+DCWL1+OlStXOr0vXl5e6NOnT7OesUHIzQoNDUVkZKTTt8sDBw4gKysL3377rVPbTUxMREZGBsrKyqDVahEcHIxBgwZh4MCBzdrOiy++iC1btmD//v0IDw9v1roJcaQ1fffVRbuoWghjzCVD8YBx/39mZiZCQ0Nd0j4h9hQXF+PSpUtO3y6//PJLJCYmIiEhwantmvn6+iI4OBjnzp3DkSNHkJKS0iz1MsYwffp0bNy4EXv27EF0dHSz1EvIzXDld19dNILTDObMmYMxY8agS5cuKC8vx/r167F37178+OOPTmn/1Vdfxb333ouIiAgUFRVhwYIFUKvVmDJlilPab48qKipw/vx56XVOTg4yMjIQEBCAiIgI3LhxA3l5ebhy5QoASNcn6dSpk9tco6ihzyAgIACpqal44IEHEBoaitzcXMyZMwdBQUGYMGFCi7cfEREBAFCr1UhLS8NHH33ULG02pf20tDQEBwcjIiICJ0+exIwZM3DfffchOTm5WdqfNm0a/vOf/2Dz5s3w9vZGYWEhAGOg8vDwAIB2sR0S13H03efy7c+p52y5qaeeeopFRkYyhULBgoOD2V133cV+/vlnp7U/efJkFhoayuRyOQsLC2P3338/O3XqlNPab4/S09MZAJvHlClTGGOMrVmzxu78efPmubTfzamhz6CqqoolJyez4OBgJpfLWUREBJsyZQrLy8tzSvtmK1euZB4eHqy0tLTZ2m1s+8uXL2fh4eHS+3/77beZRqNptvbttQ2ArVmzRlqmPWyHxHUcffe5evvjGGOsxdITIYQQQogL0DE4hBBCCHE7FHAIIYQQ4nYo4BBCCCHE7VDAIYQQQojboYBDCCGEELdDAYcQQgghbocCDiGEEELcDgUcQgghhLgdCjiEOMnUqVPBcRxyc3Nd3ZVm8fXXX6Nfv37o0KEDOI5Damqqy/rCcRzuuOMOl7XfFPn5+fD09MTSpUud1mZTt73c3FxwHIepU6e2SH/27t3r1G1m3rx58Pb2xtWrV53SHmkdKOCQNsf8x5fjOIwbN87uMuY/oM8995yTe9c+HDx4EI8//jiqqqowbdo0zJs3z2HAiIqKkn5uHMdBJpMhKCgIycnJ2Lx5s3M63oC1a9eC4zisXbu2RduZM2cOOnTogGnTptmdX1BQgHfeeQeDBg1CYGAg5HI5AgICkJSUhDlz5kj382ltfv31V0yaNAmdO3eGQqGAv78/4uPj8cgjj+Crr75yad9efvllyGQyzJ0716X9IM5FN9skbdq2bduwf/9+DB8+3NVdaVe2b98OAFi3bh0GDx7c6PVkMhnefvttAIBWq8WZM2ewZcsW7Ny5Ex9++CFeeeWVv9WfzMxMeHp6/q11nens2bP4+uuvMXfuXHh5ednMX79+PZ5++mlUVVWhX79+ePDBBxEQEAC1Wo1jx45h6dKlWLJkCbZu3YqxY8c2ut1FixZh9uzZ6Ny5c3O+HcnatWvx1FNPQRAEjB07Ft26dUN1dTWys7Oxfft27N+/3+rmv7feeisyMzMRFBTUIv2py8/PD8888wyWLVuGOXPmIDIy0intEteigEParKioKOTl5eGNN97Ab7/95urutCvmuwM39Y7AgiDY7Jb4+eefMXr0aMydOxfPP//83woq8fHxTV7HFVauXAnGGB577DGbeTt27MCjjz6KwMBAbN68GSNHjrRZ5tKlS1iwYAFKS0ub1G5oaChCQ0P/brcbVFVVhZdeegne3t749ddf0bt3b6v5Op0Oe/futSrz9PR0+s/ssccew0cffYRVq1ZhwYIFTm2buIhTbulJSDPKyclhANioUaPYlClTGAC2YcMGq2XMd3r+5z//aVUeGRnJIiMj7dZ7++23s7q/EvPmzWMAWHp6Olu9ejXr3bs3U6lULCoqii1fvpwxxpgoimzZsmWse/fuTKlUsm7durF169bZ1G/u6/nz59nChQtZbGwsUyqVrGvXrmzp0qXMYDDY7de+ffvYuHHjWGBgIFMoFKxr167srbfeYpWVlXbf87x589jBgwdZcnIy8/X1tXlP9fn111/Z2LFjmb+/P1Mqlax79+5s3rx5Vu3UdwftxrQRGRnJlEql3Xnx8fEMADt8+LBUtnXrVnbHHXcwHx8fplKpWEJCAvvXv/7F9Hq9zfoA2O23325VZv68c3Jy2IoVK1h8fDxTKpUsIiKCpaamWn3e5mUbel9XrlxhL730EuvatStTqVTM39+f9e7dmz3//POsrKzM4fs3GAwsKCiI9e/f32aeTqdj0dHRDADbv3+/w7p0Op3Va/N2XVJSwl588UUWHh7OZDKZdGdxy8/Ckl6vZ4sXL5a2xdjYWLZw4UJ24cIFmzuz1+f3339nAFhKSorDZc0st1Uz8+9afY+6P1+NRsM++ugj1r9/f+bp6ck6dOjAhg4dyjZv3lxvu926dWOdO3dudD9J20YjOKRNe/fdd7F+/XrMmTMHKSkpkMlkLdLOsmXLsHfvXqSkpGDEiBHYsGEDZsyYAU9PT5w4cQJpaWkYN24cRowYgfXr1+OJJ55AdHQ0hg4dalPXzJkzcejQITz44INQqVTYuHEjXn/9dZw/fx4rV660WvaLL77ACy+8AH9/f9x7770IDg7G4cOH8f777yM9PR3p6elQKBRW6xw8eBALFy7EnXfeiWeffRZ5eXkO39+GDRvw0EMPQaFQYPLkyQgJCcGuXbswf/58/Pzzz0hPT4dSqURUVBTmzZuHTZs24cSJE5gxYwb8/Pxu6rO1Z/ny5Zg5cyYCAgLwyCOPwMvLC1u3bsXLL7+MAwcO4LvvvgPHcY2q67XXXsPevXsxbtw4JCcnY9OmTUhNTYVWq8X7778PALjvvvtQWlqKzZs3IyUlBf369bOqo6qqCkOGDEFubi6Sk5MxYcIEaLVaZGdnY+3atXj99dfh4+PTYD/+/PNPXL9+HZMmTbKZl56ejpycHAwbNgzDhg1z+J4EwfZPt0ajwYgRI1BeXo57770XCoUCHTt2bLCeZ599FqtXr0Z0dDSmTZuGmpoafPzxxzh48KDDPpgFBAQAAHJyciCKInj+7x3aWd8xXIcPH8b27dutRvY0Gg1Gjx6NvXv3on///nj66aeh0+mwbds2pKSk4N///jemT59uU1dSUhLWrVuHrKwsdO/e/W/1k7Qhrk5YhDSV5QgOY4zNmjWLAWArV66UlmnuEZyAgAB24cIFqTwvL48pFArm6+vL4uLiWFFRkTTP/B/t+PHjreoy/xfdsWNHdvnyZam8vLyc9enTx+a/91OnTjFBEFj//v1ZcXGxVV2LFi1iANiHH35o854BsC+//NLue7RHrVYzPz8/plQq2YkTJ6RyURTZI488wgCw9957z+57qTsi0JD6RnB++uknxnEc8/T0ZJWVlezChQtMEAQWEhLC8vLypOU0Go30M/q///s/qzrQwAhOdHQ0u3LlilR+7do15ufnx7y9vZlGo5HK16xZwwBIox6WtmzZwgCwl19+2WaeWq22qqc+K1asYADYqlWrbObNnz+fAWBz5851WI89kZGRDABLTk5mVVVVNvPt/bzM20tCQgKrqKiQyvPz81lQUFCjR3BEUWQDBgyQfgZr1qxhp0+ftjvSVrdtyxEce3JyclhwcDDz9/dnWVlZUvmcOXMYAJaamspEUZTK1Wo1GzhwIFMoFFa/Y2bLly9nANjq1asdvi/S9tFZVKTNe+utt+Dr64v58+ejqqqqRdp46aWXEBMTI73u0qULhg4dirKyMrz11lsIDg6W5t16662IiYnBiRMn6q0rLCxMet2hQwfp7A7Ls01WrlwJvV6PTz75RPov2ez1119HcHAw/vvf/9rU379/fzz11FONfm+bNm1CaWkpnnrqKfTt21cq5zgOixcvhiAIzXZmkV6vR2pqKlJTU/HWW2/h/vvvx9ixY8EYw4IFC+Dp6YlvvvkGer0er7zyCrp06SKtq1AosHjxYgBoUn/eeecdq+NPgoKCkJKSgvLy8iafkeTh4WFT5u3tbTOKZk9+fj4A2B1VKSwsBACr7cIsOztb+szMj6+//tpuGx988IHdPtqzbt06ALA54Llz586YMWNGo+oAjNtJWloakpKSsG/fPjz55JPo2bMnfHx8MHLkSKxduxYGg6HR9Zmp1WqMGzcOJSUlSEtLQ1xcHABAFEV8/vnn6Nq1K+bOnWs1kuft7Y25c+dCq9Vi48aNNnWaP3vzz4K4N9pFRdq8gIAAvPHGG5gzZ450lkRz69+/v02Z+Uuz7u4M87zff//dbl32dkGYyzIyMqSyQ4cOAQB+/PFH7Nq1y2YduVyOM2fO2JTfeuutdtutz/HjxwHY30XQpUsXxMbGIisrC+Xl5fD29m5S3XUZDAbMnz8fAMDzPPz9/XHXXXdh2rRpGD9+vMP+DB48GB4eHlafkyMDBgywKQsPDweARh+sO3z4cHTq1AmLFi1CRkYG7rnnHgwdOhR9+vRp9K6y4uJiAIC/v7/NPMZYvetlZ2dLn5nZqFGjbA5UVqlU6NOnT6P6AkAK4A1tj40VExODgwcPIiMjA7t27cLhw4dx8OBB7N69G7t378a6deuwY8cOKJXKRtVnMBjw8MMP49SpU/j8889x1113SfOysrJQUlKCsLAwm88FAK5duwYAdn83zP8oXL9+vUnvj7RNFHCIW5g5cyY+/fRTLF26FP/85z+bvX57x1eYj4Oob55er7dbV0hIiN0ynudRVlYmld24cQMApONEGsvRcRd1qdXqBtfr1KkTsrKyoFarbzrgKJVK1NTU3FR/QkJCcPny5Ua36evra1Nm/tk1dmTB19cXv/32G+bNm4etW7dKp8mHh4fjzTffxAsvvOCwDvPISnV1tc0883u1975GjhwpBaDc3FxER0fbrT8kJKTRYQsAysrKwPO83VO1m7oNmfXr188q8O/duxePPfYY0tPT8dlnn+Hll19uVD2vvPIKtm/fjpdeesnmWlbm34tTp07h1KlT9dZRWVlpU2b+7NvCJQXIzaNdVMQteHh4IDU1FWVlZVi4cGG9y/E8X2/wsAwXLamoqMhumSiKVl/G5uCkVqvBGKv3UVdTvuQs26nvKq/mckcH0TYXR/0pKipyWl8sRUVF4auvvsK1a9dw/PhxLFmyBIwxTJs2ze6uwrrMuzHNX9CWbrvtNgDGg43/rqb+3H19fSGKot3RjOa64u8dd9yB9957DwCwZ8+eRq2zcuVKLF++HKNGjcLHH39sM9/8s3/ggQca/L1Ys2aNzbrmz95ylzJxXxRwiNt46qmnEB8fjxUrVtR75pC/vz+KiopsQk5lZSXOnTvnjG7iwIED9ZZZ/vc7aNAgALW7qlqKefdb3WuVAMYRhQsXLiAmJuamR2+aoz9//PEHqqur7e4WvFnmM/AcjerIZDL069cPr7/+uhRstmzZ4rB+8+4je9vZiBEjEBkZiV9++QX79+9vatf/loSEBAANb4/Nwd4FDeuzZ88eTJ8+HT179sS3335r96zIHj16wMfHB0eOHIFOp2tSX8zHXDVlVx5puyjgELchk8mwcOFCaDQavPvuu3aXGThwIHQ6Hb755hupjDGGN9980+6Qdkv45JNPpAvlAUBFRYXU3yeeeEIqf+GFFyAIAl588UVcunTJpp7S0lLpeJWbkZKSAl9fX6xZs8ZqyN/8ueh0uha7J5E9jzzyCARBwMcff2z1Oel0OsyePRsAWqQ/5uMz7B2A+tdff+HixYs25eaRjsYc2Dts2DDwPI8//vjDZp4gCPj000/BcRwmTpxo95groPHHDDWGeVt79913rbb9y5cvY/ny5Y2uJycnB59++inKy8tt5lVWVkp12btkgqWzZ89i4sSJ8PX1xdatW+3uWgSMn9Xzzz+Pixcv4tVXX7Ubcv766y+7I6W///47BEGQRsyIe6NjcIhbmTBhApKSkuq9svH06dOxZs0aPPPMM9i5cyeCg4Nx4MABlJaWIiEhod4zn5rTLbfcgoSEBEyePBlKpRIbN25Ebm4u/vGPf1jdcqJ379747LPP8Pzzz6N79+4YO3YsYmNjoVarkZ2djX379mHq1Kn44osvbqo/Pj4+WLVqFR5++GEMGjQIkydPRnBwMHbv3o0jR47g1ltvxWuvvXazb7vRYmNjsWTJErzyyivo27cvHnzwQXh5eeGHH37AmTNnkJKSYvdKwDcrKSkJHh4eWLZsGdRqtbQbY/bs2di1axdeeeUVDBkyBPHx8QgMDER2dja2bNkCDw8Pu9dcqcvf3x/Dhw/HgQMHoNFobA64HTduHNatW4dnn30Wd999N/r164ekpCQEBASgpKQEFy5cwO7du8HzfLN8Qd9xxx148sknsWbNGvTp0wcTJkyARqPBt99+i8GDB+OHH35oVD1lZWV48cUX8dprr2HYsGHo1asXPDw8cPnyZfzwww+4ceMGEhMT8eKLLzZYz8yZM1FSUoIxY8ZIZ3hZioqKkoLt/PnzcezYMXzyySfYtm0bbr/9dgQHB+Py5cs4efIkTpw4gd9++83qeLeKigocOnQId999d5NGlUgb5tyz0gm5eXWvg1PX/v37pevB1L0ODmOM7d69mw0aNIgplUoWGBjIHn/8cVZYWOjwSsZ1NXQtGHt11b2ScUxMDFMoFCw2NpYtWbKk3uuG/PHHH+yhhx5iYWFhTC6Xs6CgIDZgwAA2e/ZslpmZKS3X2GuL1Gf//v1szJgxzM/PjykUChYXF8feeecdq2ukNOa916ehKxnbs3nzZnb77bczb29vplQqWZ8+fdhHH31kcxVfxhxfybiu+n6u27ZtY7fccgvz8PCwupLx6dOn2YwZM1j//v1ZYGAgUyqVLCYmhk2dOpWdPn260e/pv//9r90rb1vKz89nc+bMYYmJiczPz48JgsD8/f3ZoEGD2BtvvMHOnDljs05D13dirOErGS9atEjaFmNiYtjChQvZ+fPnG30dnJqaGrZhwwb27LPPsoSEBBYUFMRkMhnz9/dnQ4cOZR9//DGrrq62Wsfetmr+nanvUffnq9fr2cqVK9mQIUOYj4+PdJXq0aNHs88//9xmu127di0DwDZt2uTwPRH3wDHWwPmJhBBCmo1Wq0VcXBx69OiBHTt2uLo77crw4cNRWFiIzMzMFrviOWld6BgcQghxEoVCgYULF+LHH3+s9zpJpPmlp6fjwIEDWLJkCYWbdoSOwSGEECd6+OGHkZ+fTxebc6KysjJ8+OGHmDBhgqu7QpyIdlERQgghxO3QLipCCCGEuB0KOIQQQghxOxRwCCGEEOJ2KOAQQgghxO1QwCGEEEKI26GAQwghhBC3QwGHEEIIIW6HAg4hhBBC3A4FHEIIIYS4nf8PdM57ns1PMhkAAAAASUVORK5CYII=\n" 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", + "text/plain": [ + "
" + ] }, "metadata": {}, "output_type": "display_data" @@ -208,7 +215,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2024-01-03T22:36:21.851432041Z", @@ -216,10 +223,20 @@ } }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/wk/kmp6fyrn3396qjpx40d2qk600000gn/T/ipykernel_75060/2869605059.py:18: UserWarning: Attempt to set non-positive xlim on a log-scaled axis will be ignored.\n", + " ax2.set_xlim(0, 2500)\n" + ] + }, { "data": { - "text/plain": "
", - "image/png": 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\n" + "image/png": 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IMsuWLfNr/i4mJNhAMZZXgj1//nzrR+LDDz+0hnvauJ47d84kJycbSaZRo0Zm69atVtlff/1l7ZCUK1fOHDt2zG0sef1weaN///5WUrh69Wq/x5edrwn24cOHrR2UK6+80uzbt88q+/33302dOnWMJFOvXr0cCYpzx6xcuXJm/fr11vCjR4+a3r17m5CQkAJLsNPS0qzYGjZs6FLmaQftrbfesg6uPPvss9b8ZGRkmHnz5lk7iFkP2GSPJb/WrFljJTIPPPCAy47KsmXLTExMjJFkhg0blqOtv+ufpwT76NGjZvXq1aZ169ZGkqlatao5efJkjvbjxo2zdmY+/vhjl7JPPvnElC5d2kgyr7/+ukvZb7/9ZiIjI40kc9VVV5k///zTpXzz5s1mypQpLsPcfX8PHDhgmjdvbiSZyy+/3Bw6dMilzcsvv2wlBPPmzTMZGRlW2ffff2+qVq1qJRu+yCvBXr58ubVevPPOOznKP//8c/Pll1+a8+fPuwzfv3+/uemmm4wk07179xztvvzyS2u8kyZNstpnZGSYF1980QQGBloHBX1JsBcvXmy+++47l/4xxpgdO3aYHj16GElm+PDhOdoVZoLtTH6y7qympaWZs2fPGmMyl+fSpUvN6dOnXdqnpKSY8ePHWwlLds4EOzg42ISFhbmsJxkZGeaxxx6ztg3ZD940aNDAOoiS9QCYMZnLctasWS4JojG57+QbY8+2KDg42Dz55JMu65czPufvQHBwsOnZs6c5ePCgVWfZsmXW+tOvXz9TpkwZ89VXX1nl+/bts+Z58ODBOWLP73rt7XpUkNvv0NBQ89RTT7nE/sYbb1hJ4KpVq3KNLTvnehMWFuayDUhLSzPTpk2zprtgwYIcbT0dJMuvgkqwFy9ebNXPegLCGx988IHV1t2BL194u43w9N07c+aMqVGjhvU7smvXLqts06ZNpmrVqtY6lL3t1VdfbSSZ6667zhw9etSl7NixY2bOnDnml19+8Wv+LiYk2EAxlluCvWbNGlOuXDkjySQkJLgkBZ42rs4f56CgoBw7UMYYc+jQIRMdHW0kmSeeeMJtLP4m2G+88YYJDQ21EpLIyEjz5Zdf+jXO7HxNsJ07CCVLlnR79uq3336zEsP58+dbw7dv327tlHz22Wc52p0+fdragbA7wT5x4oS54447rPLsR8Y97aA5z6DcfPPNbqfpTCTj4uJcduDtSLA7depkJJkOHTq4LXcmicHBwWb37t0uZXYl2J7+wsLCzOjRo3MkrsYYs3v3bhMSEmICAwNdDqJk9d577xlJpnbt2i7D+/XrZySZFi1aeH32OPv3d+vWraZatWpGkrn66qtzJDinTp2yzoZ/8MEHbse5bt0643A4TIkSJaydMF9iyb7+7tmzx7z++uvWGeV69erlSDbykpGRYcqXL28cDofLQS1j/t5R7tq1q9u2t956q8fvRn6T4RMnTpjg4GATHR2dY1kVZoItybz11lv5nkaLFi2MJLNu3TqX4c4E23nQwh3n1TgzZsxwGe4805j9wGtu8kqw7dgW3XrrrR6n7/wdKFOmjNvtuvNAryTz7rvv5ihfsmSJ9bvgi9zWa38TbDv6bOjQoW7bOq+Oue+++/Keyf938uRJ6+qcRx55xG0d50HoSy+9NEfZhZJgb9y40arv65V3M2bMsNr68v1xx9tthKfv3htvvGEkmZCQEJfk2unrr7+2xp+9bc2aNY0k89NPP/k1D/8U3IMNXAA2btyoVq1aqVWrVmrRooUqVKig1q1ba8+ePYqKitJbb73l1UNClixZIknq27evyz21TvHx8br55pslSUuXLrV3Jv5/+kOGDFGZMmX0448/avr06Tp58qS6d++uFStW5Kj/1ltvyeFw6LLLLrM9luxxSZkPH4mJiclRXqtWLetBJ1n7Zfny5TLG6JJLLnH71OmwsDANHjzYlhjvuusuax2oX7++Spcubd0vedVVV1lPJ83N5s2brVcEjRo1ym2d+++/X4GBgTpy5Ii+/fZbW2KXpFOnTmnlypW5TvvGG29U6dKldf78ebfrgx2SkpLUsmVL669Ro0aKj4/XmTNn9Prrr7t9D/vixYt17tw5NWnSxHpVVXZXXXWVgoOD9dtvv1n3oZ05c8Zatx588MF8PbBm/fr1uvzyy7V161YNGzZMCxcuVHh4uEudL7/8UocOHVJCQoLHp2c3bdpUFStW1LFjx3Lct+2NnTt3utwvWq5cOQ0ePFiHDh3SNddco88//9zja+JOnDihOXPm6Oabb1aXLl3UunVrtWrVSq1bt9bx48dljHF5eNCpU6eshyHee++9bsfpabg3Dh06pBdeeEFDhgzRlVdeacXTuXNnBQQE6Pjx49b3pChER0drwIABudY5e/asFixYoDvvvFNdu3ZVmzZtrO3D1q1bJSnX5expe3H55ZdLUo75r1SpkiTpzTff9Ho+cmPXtuiWW27Jc1rXXnut2+1648aNJUklSpTQNddck6Pc+V0/evSojhw5kqPc1/XaX3b1ma/LPjdff/21jh07ppCQEI/jHTNmjCTp119/1fbt270ed3ESFRVl/T81NdWntlnrZx1PVmPHjnX7Xm5Pr8T0ZhvhjnP/pW/fvqpQoUKO8pYtW6pp06Zu2zq3AW+//bbt7wa/GPGaLuACkJqa6vLqicjISNWpU0cdO3bUvffea2348uJ89YfzydPu1KtXz6WuXc6ePatbbrlFGRkZeuWVV1ShQgWNHDlSxhjdf//96tWrlxYuXOjyrknnQ5M8bfDt4m2/LF682KVffv/9d0lSgwYNPLZr2LChLTFu2rTJ+n9QUJDi4+PVtm1b3XDDDbr22mu9euCXM/aQkBDVqFHDbZ34+HiVL19ef/75p/73v/+5PEjPH1u3brUeoOOpn4ODg1W7dm0dPHiwwF5T4+41XVLmw7RuuOEG3X333Tp+/LgefPBBq+w///mPJGn79u1q1aqVx3E7l8GuXbuUmJioLVu26MyZM5Ly987j9evXq127djp9+rSmTp2qsWPHuq3njO/06dO5xudMEnbt2mXtTHsr63uwz58/r507d2r//v0KCQlR06ZNVbp0abftvv32W/Xt2zfPh99kfSjUli1brHWlTp06buvXrFlTQUFBPj+U6cMPP9SQIUPyfHduXg9fK0jOefNk8+bN6tGjR56JkKd5KFWqlMfXZpUtW1ZSZvKY1ZgxY3TzzTdrxIgReuaZZ9SxY0dddtllat26tapXr55rHO7YtS1KTk7Oc1qe4nO+NaBatWq5lkuZ/ZG1z/KzXvvLrj5zvmM7O0/L3puYKlasaL1LOrvk5GQFBgYqPT1d//vf/9we3C/unA/wk+RxPj3JenDnxIkTbttXrlzZ5Tdi06ZNuW6j8tpGeOJcXp62q1Lm8lq/fn2O4aNHj9bnn3+uJ598Uq+//rquvPJKXXbZZWrVqlWu+07/VCTYwAWgbdu2bp/E6SvnkdSEhASPdRITE13q2uWTTz7R/v37VbFiRXXu3Nkaft999ykjI0OjR49Wnz59NH/+fF199dVWG0nq37+/rbFkl99+cf7oujs74pT9KaBO/fv3d7tzNn78eHXt2jXH8JUrV/r9dFVn7M6n7XqSmJioP//809Z1IOu4nDtynqadvX5h6NWrlyZPnqyRI0fqscce0+233674+HhJmWewJOnAgQM6cOBAnuM6deqUJNd58HWnTJL++usvnTp1SqGhobkeqHHGl5KS4tU7YJ3x+SL7e7CNMXr//fc1ePBgjRo1ShEREbrzzjtd2hw/fly9e/fW/v371aZNG40bN04NGjRQXFycQkJCJElt2rTRmjVrXN4qkHVnNmuSk1VgYKDi4+O1f/9+r+fhzz//1MCBA3XmzBn17t1b99xzj5KTkxUbG6vg4GBJmYnCrl27ivQtB5GRkR7LMjIy1LdvX23ZskV169bVpEmT1KxZM5UpU8bq08GDB+uNN97wOA+5jd+5Xcj+xPmbbrpJcXFxmj59utauXatXXnlFr7zyiqTMnfUpU6b49O5xu7ZFuc1LXnWcB8TyKpdc+yO/67W/CrrPPC17b2LK7bczKChIpUqV0v79+wt9u26XrE9zd/5+7du3T/369XNb//3337f6JOuZ4u3bt7s9IH/HHXfojjvusD537NhRX3zxhcd4vFnv3XFuW3P7DfZU1rFjR61cuVJTp07Vl19+qddff916o0OVKlU0btw43XrrrfmK62JEgg38gzgTweyv4srKmfTlljTmh/Nsi7uz7aNGjZIxRg888ID69++vt956S+XLl9d3332n5s2bW6+iKigxMTE6evSoz/3iTJ5z22nImixktX79eu3cuTPHcF8SBl85Yz9w4IAyMjI87qQVxDqQdVz79+9X+fLlC23a3mrdurWkzAT0p59+UocOHST9fVnfsGHD9MILL3g9vqzzkJKSYr3OyltXX321KlWqpClTpuiqq67SggULrFsVsnLG161btwK5tcMdh8Oh/v376+DBgxo+fLjuv/9+9ejRw3rVmZT5PvH9+/erQoUKWrZsmdvbWNyd4ct6UOrAgQMqV65cjjrp6ek+nx189913debMGTVp0kTvvfdejkv2jTHWwYri6ocfftCmTZsUFhamzz//3O0BiII6+3711Vfr6quv1vHjx/X9999rzZo1ev/997Vp0yb16dNHS5YscbkCKTdFuS3yV37Xa38Vxz7zZp8iLS1Nhw4dKrSYCsLq1aslZb6v25kgnzlzxuMBTeeVS5LUqlUrORwOGWO0atWqXK94K2jObWtu+xm5lbVp00Zt2rTRmTNntH79en399ddavHix1q1bp9tuu03nz5/XsGHDbI/7QsQ92MA/SK1atSRJ//3vfz3WcZbVrl3bZbi/7xx2JgF//PGHjDE5ykePHq0nnnhCaWlpuu666zRw4EAFBATomWee8Wu63shvvzgvtXNeouuO872U2e3YsUMm80GTLn+e3ltpB+d8njt3zuN7s48cOaK//vpLkuu8+rv8q1WrZl3S5qmfz58/b13Cln39KwxZz9w4dwilv2+byHoG1xs1atRQWFiYJHl1ZtmdyZMna+rUqTp79qz69eun999/P0cdZ3zff/+9X++xzY877rhDycnJOn36tB566CGXsm3btknKvMXDXRJy5MgR6zaLrKpXr24lv57eQ/z777/7PK/OeFq3bu32fviff/7Zp8tji4JzHmrXru02uU5LS3N7eaedoqOj1bFjR02ePFmbNm2yzlzPmjXL63H4sy0qavldryX/tqPFsc+cMeV2xvzXX3+17tktTsvRWykpKZo3b54kqXv37tbVLpUrV3b7G26Msd41L0mlS5dWp06dJEkvvvhikV4d41xenrareZU5hYWFqXXr1ho3bpy+//573XPPPZKkmTNn2hPoRYAEG/gH6dGjhyRp4cKFbh82cuTIEf373/+WpBxnIpw7EqdPn87XtNu3by8p87LXuXPnuq3zwAMPaMqUKUpPT9fu3bvVt2/ffN276itnv/zrX/9yu5OwefNmffTRR5Jc+6Vz585yOBzatm2b9QCvrM6ePas33nijgKL2XY0aNax7955++mm3daZPn6709HTFx8e7PFwu645kftaBiIgI635AT9OeN2+eDhw4oODgYF155ZU+T8Nfa9assf6f9b7M3r17KygoSD///LM+/PBDr8cXGhpqrVvTpk3z6dLLrMaOHatnn31W58+f18CBA3M8iK1Tp04qWbKkDh8+7NMZdjsEBARowoQJkjIfSpg1sXCuM57uU33mmWfcPiwnIiJCbdu2lSQ9//zzbtt6Gp6bvOJ58sknfR5nYXPOw/79+90eqJwzZ44OHjxYaPE4HA7rCiNnYucNf7ZFRS2/63XWtvnZhhbHPmvVqpVKlCihc+fOacaMGW7rOL9Xl156qUvieSE4e/asBg8erKNHjyowMDDHQURvTZ48WYGBgdq8ebPuuecet9/dwtCtWzdJmZewu/u+fvvtt/k6QOe8fc2XbcDFjgQb+Afp37+/kpOTlZaWpn79+llH4qW/7yc6fvy4ypUrp9tuu82lrTPh+Prrr/N1BLZWrVrW2dnbb79dTz31lMtORkZGhj755BO9++671rAPPvjA7Rk7u91xxx1KSEjQ0aNHNWDAAJdLpLZs2aL+/fsrPT1d9evXV58+fayyKlWqaODAgZIy73vM+tTeY8eO6frrry92PzjOB3zNmTNHzz//vLUjaIzRm2++qaeeekpSZlLnPPsqZT4YyXkf8ZdffpmvaU+YMEEBAQH64osvNHbsWJ09e9YqW7FihfVk3Ntuu83tZcEFafHixVbfNGjQQI0aNbLKKleurPvvv1+SNGjQIP373//WuXPnXNofOXJEr7/+ukaPHu0yfMqUKYqIiNDXX3+t/v3751gftm7dqkcffTTP+O699169+OKLysjI0A033KA5c+ZYZVFRUXr88cclZd5u8cQTT+jkyZMu7U+cOKGFCxd69dRlX/Xv31916tRRenq6Jk+ebA137nR99913evHFF62dyrS0ND377LOaNm2ayzqWlfMhc0uXLtVjjz3msp7+61//0quvvurzQ36c8bz//vsuB0rOnDmjBx54QO+88451D21x1aJFC4WEhGjPnj0aP368dRbfGKO3335bd999t8c+za/U1FT17dtXy5Ytc/nOSpnbx5dfflmS7w+jzO+2qKj5s147f0d/+eWXfN0OVNz6LCIiQg888IAk6bHHHnP5/U5PT9fTTz9tHRDMum0o7k6cOKEFCxaoWbNm1sH12bNnW1cL+eqyyy6zDoq8+OKLuvLKK7VmzZocB2LOnj2rd9991+MVEP4aMGCAqlWrpnPnzumaa65x+T369ddfNWTIEOsMfXbOK6iy/7bs3bvXutKwoB9Ie0EplJeBAciX3N6DnZvc3j/6+++/m4oVKxpJJiAgwNSpU8c0aNDABAUFGUkmPj7efPfddzna/fnnnyYiIsJ6r2iLFi1M27ZtzTXXXON1XGfOnHF592h4eLhp2LChadSokYmNjTWSTGBgoBk3bpwZP3689b7GZcuW+TT/zvefhoaGmvj4eI9/l1xyidVm7dq1pmTJktZ7mBs0aGDq1Kljvf+6cuXKZsuWLTmmdejQIVOnTh1rnmrWrGkaN25swsLCTEREhHnyySeNJJdpecvXd3Vm5WyX/T2qxhgzZswYq7xUqVKmWbNmJjEx0Ro2ePBgk56enqPdiBEjrPWmXr16pm3btqZt27Y+LZ8XXnjB6tOYmBjTtGlTU7lyZWvaV155ZY73PBtj33uwk5KSTMuWLa2/Ro0amfj4eGv6FStWNL///nuO9unp6Wb48OFWvYiICNOwYUPTrFkzU7lyZet96O6+q8uWLTMxMTFW39WuXds0btzYehd8bGysS/3cvr9z5swxAQEBxuFwmBdffNGl7PHHH7f6NiQkxNSrV880b97cVKtWzRru6/vYPb0HO7sFCxZY8/fLL79Yw4cOHWr1WUJCgmnSpImJi4uz3mHs/K7OmTMnxzgnTJhgtY2PjzdNmzY1CQkJRpK5//77Pb5D19O7htPT00379u2tcVaqVMk0adLEREVFGUnmscce83mcvvLmPdh5TWPSpEku/dKkSROrX7p06WIGDRrk9rvifA92bsvS3bp39OhRa3rBwcGmdu3a1nrlHF6tWjWzZ8+ePMeVXX62RVm3i7nJbd0yxrv+9rQdze96nZGRYb1rPDIy0jRt2tTaju7duzfP6RpTcH2W33U8PT3dXHfdddb4y5UrZ5o1a+ayXX3ooYfctvX3PdgjRoxw+U0PDg629i2yDv/6669d2mXtjzp16li/B02bNjVVq1a1tpfO78snn3ySr/iye+edd6z1RJKJjo42devWNZdddplJTk424eHhVlmrVq3Mzz//7NLe22WU23dvw4YN1rvLg4KCTIMGDUxycrJxOBymevXq5u6773bbNus+WvXq1U3z5s1NrVq1TGBgoLVfmHXb/09Hgg0UYwWRYBuTucM0YcIEU69ePRMREWHCwsJMzZo1zX333ZdjJymrr7/+2nTt2tWUKlUq3zvsxhjzySefmH79+pny5cub4OBgEx0dberVq2fuv/9+s23bNmNM5o7IwIEDrR/L1atXez1+585NXn/ZE5u//vrLjBw50tSsWdNKkOvVq2cmTpxojh075nF6qampZty4caZq1aomJCTElClTxgwYMMD88ssv5uOPPzaSTIMGDXzup4JKsI0x5vPPPzdXX321KVu2rAkODjbx8fGmc+fOZuHChR7Hefr0aTN+/HhTq1YtExYWZk3D0w6sJz/88IO57rrrrOVfokQJ06ZNG/Pqq6+atLQ0t23sSrCz/wUGBpq4uDjTqlUr8+STT5rjx4/nOp61a9eawYMHm0suucSEhYWZqKgoU6NGDdOtWzcza9Yss2vXLrftdu/ebUaNGmWSk5NNRESEiYiIMFWrVjUDBgzI0ed5fX/ffvtt64DYs88+61K2adMmc8cdd5iaNWu6TKdDhw7mySefNJs3b/a6z7LGktf3PGvi0L9/f2t4enq6eeaZZ8yll15qQkJCTGxsrGnRooV57bXXjDF5J0GLFi0yrVu3NlFRUSYqKso0a9bMzJ071xjjeec8t53Q06dPm4ceeshUrVrVBAcHm7i4ONOhQwfz4Ycf5nucvrAjwTbGmLlz55rGjRub0NBQExUVZRo2bGieeeYZk5aW5vG7kt8EOy0tzbz99tvmlltuMXXr1jWlSpUygYGBJiYmxjRr1sw8/vjjbr833iTYxvi+LSoOCbY/6/WuXbvMkCFDTFJSkpUQZp+G3dvvgkywnd577z1z5ZVXmvj4eBMUFGTKli1revfubb788kuPbfxNsJ3rel5/2ceftT+y/kVERJiEhARz+eWXm2HDhpklS5Z4/E3Kr+PHj5tZs2aZHj16mKSkJBMeHm5CQ0NN2bJlTevWrc0DDzxgfvjhB7dt7Uiwjcmc/yFDhpiyZcuakJAQU7lyZXPPPfeYo0ePemz70UcfmREjRphGjRqZsmXLmqCgIBMVFWXq169vxo0bZw4cOJCP3rh4OYwpohsBAOAf4KmnntIDDzygPn36aOHChUUdDgAAAAoQ92ADQAE5f/68da+s86FNAAAAuHiRYAOAH86dO6fx48frzz//dBm+Z88eXXPNNfrtt99UsmRJDRo0qIgiBAAAQGHhEnEA8MOZM2cUHh4uKfN9l5UqVdLJkyf1+++/KyMjQ+Hh4XrvvfdyvPYMAAAAFx8SbADwQ0ZGhp5++ml9+umn+v3333X48GFJUoUKFdS+fXvdd999qlmzZhFHCQAAgMJAgg0AAAAAgA24BxsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANggqKgDAIqjjIwM7dmzR9HR0XI4HEUdDgD8oxhjdPz4cZUrV04BAZwLcOK3CQCKhi+/SyTYgBt79uxRUlJSUYcBAP9ou3btUoUKFYo6jGKD3yYAKFre/C6RYANuREdHS8r8EsXExBRxNADwz5KamqqkpCRrW4xM/DYBQNHw5XeJBBtww3npXUxMDDsxAFBEuAzaFb9NAFC0vPld4sYmAAAAAABsQIINAAAAAIANSLABAAAAALABCTYAAAAAADYgwQYAAAAAwAYk2AAAAAAA2IAEGwAAAAAAG5BgAwAAAABgAxJsAAAAAABsUKwTbIfDkeff3LlzizpMWzkcDj399NO51vnhhx/kcDi0atUqn8Y9adIkRUVF5Vlv6NChqlOnjk/jzm7Hjh1yOBx6//33/RqP06RJk7R27VqvhwMAAABAYQsq6gBy8+2337p8vvzyy3XXXXfpuuuus4ZVrVq1sMMqUN9++60qVapU1GEUO5MnT1ZUVJRatGjh1XC7/OverxQeEqlK9eNVt3V5BQQF6PTxc4qMCVVi9RIKCHAUyHQBAACcMjKM9m45ppOpZ33eB/G2rad63g4vWzVW+7el5OtzRFSIjEM6ffxcnv8/lXJWp4+fV3h0iCJjvG+Xn/97Mx+J1UtIUo4+cjfM2e/eLJPCWOYoGMU6wb7ssstyDKtYsaLb4U5nzpxRWFhYQYZVoHKbNxSdnf85rJ3/OewyLLJEqFpfU11VG5YpoqgAAMDFbtvGA1ozf4tOHjtrDfN2H8Tbtp7qVW9aRlvWH/BquMMhGaN8fy6u8oo7NCJIckhnT6blOszZ75LyXCaFscxRcIr1JeJ5cV7yvG7dOl1++eUKCwvTzJkzJUljx45V3bp1FRUVpfLly+vaa6/V3r17Xdq3a9dOPXr00Ouvv66qVasqPDxc7dq10++//+5Szxijp59+WjVq1FBoaKguueQSPfvssy51PF3CPmnSJKvOmjVr1KpVK4WHhys+Pl433HCD9u/fn2M82S8Rf/TRR5WQkKCoqCj16dNHBw4cyNEXzzzzjJo2barY2FiVKVNGPXr00ObNm33uU295My+SdPLkSd18882KjY1VXFyc7rvvPqWl/b2x2bt3r2666SZdcsklCg8PV/Xq1fXggw/q7NmsG+zMI26jR4+2+nXVqlUeh0uZB1ruv/9+lS9fXqGhoapbt67efvttW/vg5LGzWv7yJm3bmHN5AAAA+GvbxgNa/vIml2RJ8m4fxNu2udX76bNdXg/Pniz7+rm4yivus6fSXBJpT8Oc/Z7XMimMZY6CdUEn2JJ07tw5XX/99brhhhu0fPlyXXnllZKkAwcO6MEHH9TSpUv1/PPPa8eOHWrbtq1LcidJP/74o6ZOnapp06bp9ddf1969e9W5c2eXBO+ee+7RhAkTNGTIEC1dulRDhw7VmDFj9NJLL1l1vv32W5e/yZMnS5Jq1qwpSdqwYYM6duyosLAwLViwQNOnT9fnn3+u9u3b68yZMx7nb9asWXr44Yd1ww03aOHChapSpYpuu+22HPV2796tESNG6MMPP9S///1vZWRkqEWLFjpy5Ej+O9cDX+blwQcfVEZGhhYsWKDRo0dr5syZeuihh6zyQ4cOKS4uTtOnT9fy5cv1wAMPaN68ebrzzjutOs5bBe666y6rfxs1auRxuCRdf/31mj17tu677z599NFHatKkia6//nq98cYbtvfH1wu2KCPjAvmVAAAAF4SMDKM187fkWsfTPoi3bdPSMvKsh8KzZv7mAl/m7LMWvGJ9ibg3zp8/r8cff1z9+/d3Gf7aa69Z/09PT9fll1+uChUq6Msvv7SScEnav3+/vvrqK1WvnnnJRoMGDVSrVi3NmzdPt912m7Zt26ZZs2bppZdeshLbjh076sSJE5o8ebJuu+02BQQEuFzavWXLFj333HO65ZZbdO2110qSHnvsMZUpU0affPKJQkJCJEk1atRQixYt9O6772ro0KE55i09PV1Tp07VDTfcoKeeekqS1LlzZ+3du1fvvPOOS92sZ9TT09PVqVMnlSlTRu+//77bhNwfvsxL1apVNWfOHCv2U6dOafr06RozZoxKliypunXrupyxb9mypSIjIzVkyBDNmjVLERERVt9mvz3A0/Cff/5ZH3zwgV544QUNGzbMmvaePXusgxXZnT171uWgSmpqqtf9ceLoWe3dckzla5b0ug0AAHnx57cJF769W47lOBOZnad9EG/bblq1O896KDwnj53Ls46/y5x91oJ3wZ/BlqRu3brlGLZs2TK1aNFCsbGxCgoKUoUKFSQpx2XTderUsZJrSapevbrq1Kmj7777TpL0+eefS5L69u2rtLQ0669Dhw7at2+fdu3a5TK+1NRUXXXVVapVq5ZeeOEFa/iaNWt09dVXWwmplPnQtkqVKmnNmjVu52v37t3as2ePevfu7TK8X79+Oep+99136tSpk+Lj4xUUFKSIiAidOHEi18vE09PTXebJW77MS/bY+/Tpo1OnTum///2vpMzL75977jldeumlCg8PV3BwsK6//nqlpaXpjz/+8Dqm7PFJ0jXXXOMy/Nprr9XOnTtzLDNJmjp1qmJjY62/pKQkn6Z5MpUfJwCAvfz9bcKFzdt9C3f1vG2bcui0TzGhePBnmbPPWvAu+AQ7IiJCkZGRLsPWr1+vXr16qVy5cnrjjTf07bffWglz9kuYy5TJebN/mTJlrPu1Dx06JGOMSpUqpeDgYOuvS5cukuSSrGVkZOj666/XsWPHtHDhQpcE9OjRo0pISMgxrYSEBI+XcTtjyB5j2bJlXT7/+eefuvLKK5Wenq6XX35Z33zzjdavX68yZcrkevl51apVXeZpx44dHutm5cu8ZI/d+dk5b88995zuv/9+XXXVVfrwww+1bt0668BEbrHnFV9QUJDi4+NzxCfJbX+PGzdOKSkp1p+7JDw3kTGh+YoVAABP/P1twoXN230Ld/W8bRtbKtynmFA8+LPM2WcteBf8JeLOB11ltWjRIsXGxmrBggUKCMg8hrBz50637d09MOzAgQNq3LixJCkuLk4Oh0Nff/21S8Ls5LzHWpLGjx+vFStW6KuvvlJiYqJLvbi4OLcPAdu3b5+Sk5PdxuYcR/YYs49n+fLlOnHihD744AOVKFFCkpSWlpbn/dcff/yxy6Vn5cqVy7W+ky/zkj1252fnvL333nvq1auXpk6datX59ddfvYojt/ic8x8XF+cSn7M8u9DQUIWG5m+DE1Xy79cxAABgF39+m3DhS6xeQpElQnO97NfTPoi3beu0q6CfPs/5wDIUjcgSIZIcBbrM2WcteBf8GWx3Tp8+reDgYJfk+6233nJbd9OmTdqy5e8HAmzZskWbNm1S8+bNJUkdOnSQJB0+fFhNmjTJ8RcdHS1JevfddzVt2jTNnj3b7au2WrVqpcWLF+v8+fPWsO+//147d+5U69at3cZWoUIFJSYmatGiRS7D33///Rzz63A4FBwcbA1bsGBBnpd9161b12Ve3B1AcMeXecke+wcffKCIiAjVrVvXij37dN0tq+DgYLdntN0Nb9WqlaTMPshq/vz5qlSpku2X2LUaUJ13CwIAAFsFBDis1zp54mkfxNu2QUEBedZD4Wl9TY0CX+bssxa8C/4MtjudOnXSc889p7vuuku9e/fWt99+6/Hp0WXLllWvXr30yCOPyBijhx9+WOXLl9eQIUMkZT68a/jw4brhhhs0evRoNW/eXOfPn9fmzZu1cuVKLV68WH/88YduuukmXXHFFUpOTrYuR5cyk+QKFSpo/PjxatGihbp166Z77rlHR44c0bhx43TppZdq4MCBbmMLDAzU2LFjdc8996hs2bLq1KmTPv30U61evdqlXvv27SVJN954o26//Xb9+uuvevrpp62z2fmRmpqaI5GXpLZt2/o0L9u2bdONN96ogQMH6scff9QTTzyhe++9VyVLZj5coVOnTnr++ec1a9Ys1ahRQ2+99Za2bt2aY7q1a9fWhx9+qNatWysyMlI1a9ZUdHS02+H16tVT3759dd999+nUqVNKTk7WggULtHz5cr3++uv57pPsokqGqtUA3ikIAAAKRtWGZdTl9jo53mvszT6It21zq1etSc73XXsa/k99D3ZYZJCMXN957W6Ys9+lnO/Bzr5MCnqZo2BdlAl2t27d9MQTT2jmzJmaM2eOWrZsqSVLlqhGjRo56jZq1Eh9+/bV6NGjtXfvXjVv3lwvvfSSwsLCrDozZsxQzZo19fLLL2vKlClWIjdgwABJmfdAnz59WitXrtTll1/uMv6JEydq0qRJaty4sT777DONGzdO/fr1U0REhLp166ann37aZVrZ3XXXXTp27JheeOEFzZ49Wx07dtTLL7+sHj16WHXq1q2rOXPmaPLkyerRo4caNGig999/P8eT1X2xa9cut+1Xrlypdu3aeT0vjz32mFatWqX+/fsrMDBQw4YN02OPPWaVT5gwQQcPHtSECRMkZT7AbcaMGerZs6fLeF544QXdc8896tq1q9XX7dq18zj8zTff1Pjx4/X000/r0KFDqlGjht58801df/31+eqPSvXjVbd1eQUEBej08XOKjMm8xIajgAAAoCBVbVhGVeqXznxKdOpZn/ZBvG2bW73Le1fzanjZqrHavy0lX58jokJkHNLp4+fy/P+plLM6ffy8wqNDFBnjfbv8/N+b+XBecp29j9wNc/Z7XsukMJY5Co7DmAvh2FHBaNeunaKiorRkyZKiDgXFTGpqqmJjY5WSkqKYmJiiDgcA/lHYBrtHvwBA0fBl+3tR3oMNAAAAAEBhI8EGAAAAAMAGF+U92N5atWpVUYcAAAAAALhIcAYbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABiTYAAAAAADYgAQbAAAAAAAbkGADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANiDBBgAAAADABrYk2Fu3btWIESNUu3ZtRUVFKSgoyKX81Vdf1ZQpU3TixAk7JgcAAAAAQLETlHeV3C1YsEA33nijzpw5I2OMJMnhcLjUOXLkiCZPnqxLL71U/fr183eSsMFbb72l559/Xr///ruMMSpfvrxatmypxx9/XGXKlJEktWvXTlFRUVqyZEkRR1t0fm/cRFFBQYps314lB14jR1CQ0g8fUVDp0opo0liOwMCiDhEAAFzkTHq6Tv2wQWkHD/q8D+JtW0/1vB0e3rCBTm/8KV+fA+PjJRmlHz6S5//TDh5S+pEjCoqLU2Dp0l63y8//vZmPiCaNJSlHH7kb5ux3b5ZJYSxzFAy/Euz//ve/uuGGG5Senq5hw4apX79+GjVqlH788UeXev3799eYMWP04YcfkmAXA9OmTdODDz6okSNHasqUKTLGaNOmTXrrrbe0Z88eK8GePXu2AvkySsbo5Bdf6OQXX7gMDkpIUNkHxynmyiuLKDAAAHCxS12xQvsfn6q0ffusYd7ug3jb1lO9mO7dlLr0E6+GKyBAysjI/+fiKo+4A0qUkCRlHDuW6zBnv0vKc5kUxjJHwXEY52nnfLjhhhv09ttv6+mnn9bIkSMlSa1bt9batWuVnp7uUjchIUEJCQn66aef/AoY/itfvrw6d+6s1157LUdZRkaGAgK4NT81NVWxsbFaV626ojwdZPj/KzXKP/8cGywAsJFzG5ySkqKYmJiiDqfYoF/+eVJXrNBf99wrZd9d92IfxNu2HuvBXg6H5z7OskwkFfgyh+982f76lUmtWrVK0dHRuvfee/Osm5SUpD179vgzOdjk2LFjSkxMdFuWNblu166devToYX2eNGmSoqKitGHDBjVv3lzh4eFq2LChNmzYoDNnzujOO+9UXFycKlSooOeee85lvEOHDlWdOnW0bNky1alTR2FhYWrcuLG+++47l3offfSRmjRpoqioKJUoUUJNmjTRJ598YpVnZGTo8ccfV5UqVRQaGqrq1avnmJYzzp9//lmtWrVSRESE6tSpo08//TSfPebB/2+89j8+VSbbASUAAAB/mPR07X98qvukLI99EG/bZpw757ke7JVbH/9/2b7HHtf+xx4v0GXOPmvB8yvBPnDggKpVq5bjnmu3EwoIUGpqqj+Tg00aN26sl156Sf/+97+1L+ulPV44f/68brrpJt15551auHCh0tLS1KdPH918880KDw/X/PnzdfXVV2vkyJFau3atS9u9e/dq2LBhGj16tBYsWKDQ0FB17txZBw4ckCRt27ZN/fr1U3JyshYtWqT58+drwIABOnr0qDWO0aNH6+GHH9agQYP08ccfW9N65JFHcsQ5aNAgDR06VIsWLVKpUqXUt29fHT582O18nT17VqmpqS5/XjFGafv26dQPG3zoRQAA8pbv3yZcFE79sMH1EuzsctkH8bbt0bffyb0eCo8xSt+/X2n79+dax99lzj5rwfPrHuzo6Gjtz20lyGLHjh2Kj4/3Z3KwyezZs9W7d2/deuutkqQqVaqoZ8+eGjlypCpXrpxr23PnzumJJ55Qly5dJGWeUe7Zs6fS09M1ffp0SVL79u313nvv6b333lOLFi2stkeOHNF7772n9u3bS5LatGmjpKQkPffcc3r88ce1ceNGnT9/XrNmzVJ0dLQkqXPnzlb7Q4cOaebMmbr//vuthPrKK69UamqqnnjiCY0cOVJRUVFWnNOmTVO3bt0kSVWrVlX16tW1bNkyDRo0KMd8TZ06VZMnT/a5L53SDh7Md1sAANzx97cJFzZv9y3c1fO27bldu3yKCcWDP8ucfdaC59cZ7Lp162rv3r363//+l2u9lStX6uDBg2rSpIk/k4NN6tSpo19++UVLly7VPffco9jYWM2YMUP16tXL8x75gIAAK0GWpBo1akiSOnbsaA0LDAxU1apVtSvbRjs2NtalbYkSJdS+fXvrMvF69eopMDBQ1113nT7++GOlpKS4tP/+++91/vx5XXPNNS7Dr732Wp08eVIbN250iTNrTNWqVVNISIh2797tdr7GjRunlJQU6y977HkJKl3ap/oAAOTF398mXNi83bdwV8/btiFJST7FhOLBn2XOPmvB8yvBHjhwoDIyMnTHHXfo+PHjbuv89ddfuv322+VwONyeOUTRCAkJUbdu3fTcc89p48aNWr58uU6dOqUpU6bk2i48PFwhISEu45Eyk+Xs4z9z5ozLsNJuvtBlypTR3r17JWUm60uWLFFKSop69+6t0qVLq1evXvrzzz8lybpUPCEhwWUczs9HjhzxGKckBQcH54jJKTQ0VDExMS5/XnE4FJSQYL2OAQAAu+T7twkXhYgmjRWUkGA9oCqHXPZBvG1b8rprc6+HwuNwKLBsWQWVLVugy5x91oLnV4J98803q3Hjxlq9erXq16+vBx980LqfduHChRo5cqSSk5O1detWtWnThld0FWOdO3dW/fr19dtvvxXYNA66uSTlwIEDLg9c69Kli1avXq0jR47ozTff1IYNG3TjjTdKkuLi4iQpx20JzvvIneWF5v83YGUfHMe7BQEAgK0cgYHWa51yJE157IN42zYgJMRzPdgra/96WCYJ4x9U2fEP5lrH32XOPmvB8yvBDgoK0tKlS9WiRQvt2LFDTzzxhLZu3SpJGjBggGbMmKHU1FS1aNFCCxcu9OphaCh47u6bP336tHbt2pXj7LCdUlJS9OWXX+b43Lx58xx1Y2JiNGDAAA0cONBK+ps1a6bg4GAtWLDApe78+fMVGRmpRo0aFVjs7gSVLcvrDgAAQIGJufJKlX/+ucyzmll4sw/ibVuP9RISFHfzTZlnRb0YruyvefX1c3GVR9wBJUpY773ObVhQ2bIqP+N5lZ/xfK7LpDCWOQqWXw85kzIv8V2zZo0WLlyoBQsW6D//+Y+OHj2qqKgo1atXTwMGDNC1115Lcl2M1K1bVz179lTnzp2VmJioPXv2aObMmTp06JDuueeeAptuXFycbr75Zk2ePFklSpTQtGnTJMl6zdvLL7+stWvXqmvXrkpMTNT27dv15ptv6sr/3xiUKlVKd999t55++mmFhoaqZcuW+uKLL/Tyyy9r8uTJioyMLJjAHQ5Ftm+vkgOvkSMoSOmHjyiodGlFNGnMUUAAAFCgYq68UtEdOmQ+JfrgQZ/2Qbxtm1u9Mvfd59Xw8IYNdHrjT/n6HBgfL8ko/fCRPP+fdvCQ0o8cUVBcnAJLl/a6XX7+7818OC+5zt5H7oY5+z2vZVIYyxwFx+8EW5IcDof69evHJeAXiEmTJunjjz/Wfffdp4MHD6pUqVKqV6+evvjiC11xxRUFNt3ExEQ98cQTGj16tLZt26bk5GR9+umnKvv/R9nq1atnxXX48GElJCTo2muvdXkF15NPPqmSJUvqlVde0dSpU1WxYkU988wzGjlyZIHEXHPDD9zzBgAAipQjMFCRzZsVaFtP9XwZ7u/n4sqbuL0dJnm3TApjmaNgOIzhzfIoeEOHDtUPP/ygTZs2FXUoXklNTVVsbKxSUlJIsAGgkLENdo9+AYCi4cv29wK5+QEAAAAAgOLN60vE83p9k7cmTJhgy3gAAAAAAChOvL5EPCAgwK8HlRlj5HA4lJ6enu9xAIWFy/AAoOiwDXaPfgGAouHL9tfrM9iDBw/mSeAAAAAAAHjgdYI9d+7cAgwDAAAAAIALGw85AwAAAADABiTYAAAAAADYgAQbAAAAAAAbeH0PtjuBgYE+1Xc4HEpLS/NnkgAAAAAAFEt+JdhevuEr3/UBAAAAALhQ+JVgb9++3WPZuXPntHXrVr300ktasWKFZs+erfbt2/szOQAAAAAAii2/EuxKlSrlWl69enV17dpV999/v+666y798MMP/kwOAAAAAIBiq1Aecvboo4/K4XBo8uTJhTE5AAAAAAAKXaEk2OHh4apVq5ZWrVpVGJMDAAAAAKDQFdprug4dOqSjR48W1uQAAAAAAChUhZJgf/HFF9q5c6cqVKhQGJMDAAAAAKDQ+fWQs9WrV3ssM8Zo//79+uabb/Taa6/J4XBowIAB/kwOAAAAAIBiy68Eu127dnI4HHnWM8aoRYsWeuihh/yZHAAAAAAAxZZfCXbFihU9JtgOh0ORkZGqUaOGevXqpUGDBikwMNCfyQEAAAAAUGz5lWDv2LHDpjAAAAAAALiwFdpTxCXp119/LczJAQAAAABQaAolwd68ebOuvfZa1a9fvzAmBwAAAABAoct3gm2M0cGDB3X69GmPdbZt26bBgwcrOTlZ8+fPV0ZGRn4nBwAAAABAseZzgn3kyBHdcsstKlmypBISEhQVFaXk5GS9//77Vp2TJ0/q7rvv1qWXXqq33npL6enpqlOnjhYsWGBr8AAAAAAAFBc+PeTszJkzatOmjX777TcZY6zhv/32m6655hq9/fbbatGihTp27KitW7fKGKPk5GRNnDhR/fr1sz14AAAAAACKC58S7Jdeesl6UNmAAQN0+eWX69SpU1q6dKnWrl2r8ePHq1SpUtqyZYuqVKmiqVOnasCAAQUSOAAAAAAAxYlPCfbixYvlcDg0Y8YMDR8+3Bo+btw4XXvttZo/f762b9+u7t27a/78+YqIiLA9YAAAAAAAiiOf7sH+9ddfFRsbq2HDhuUoe/DBByVJwcHBevXVV0muAQAAAAD/KD4l2MeOHVPVqlXlcDhylFWvXl2SVK1aNZUpU8ae6AAAAAAAuED4lGCnpaUpPDzcbVlYWJgkKS4uzv+oAAAAAAC4wOT7PdgAAAAAAOBvPj3kTJIOHDig119/Pd/lgwcP9nWSAAAAAAAUew6T9YXWeQgICHB7/7XXE3M4lJaWlu/2QGFJTU1VbGysUlJSFBMTU9ThAMA/Cttg9+gXACgavmx/fT6D7UM+bmtbAAAAAACKM58S7IyMjIKKAwAAAACACxoPOQMAAAAAwAYk2AAAAAAA2IAEGwAAAAAAG5BgAwAAAABgAxJsAAAAAABsQIINAAAAAIANSLABAAAAALABCTYAAAAAADYgwQYAAAAAwAYk2AAAAAAA2CDIjpEcO3ZM//73v/XFF19o165dOn36tLZt22aVL126VIcPH9bAgQMVEhJixyQBAAAAAChW/E6wV69erf79++vQoUMyxkiSHA6HS53vv/9ejz32mEqVKqVu3br5O0kAAAAAAIodvy4R37Fjh3r27KmDBw+qe/fumjNnjpKTk3PUGzhwoIwxWrx4sT+TAwAAAACg2PIrwX7iiSd0/PhxjR49Wh999JGGDBmiEiVK5Kh36aWXqkSJEtqwYYM/kwMAAAAAoNjyK8FesWKFIiIi9Mgjj+RZt0qVKtqzZ48/kwMAAAAAoNjyK8H+66+/VL16da8eXBYSEqKjR4/6MzkAAAAAAIotvxLsiIgIHTt2zKu6u3fvdnv5OAAAAAAAFwO/EuyaNWtq9+7d2rVrV671fvzxR/3111+qX7++P5MDAAAAAKDY8ivB7tOnj9LT03XvvfcqPT3dbZ0TJ07ojjvukMPhUP/+/f2ZHAAAAAAAxZZfCfbw4cN1ySWXaPHixWrZsqX+9a9/KTU1VVLmWevnn39e9erV04YNG1SnTh0NGTLElqABAAAAAChugvxpHBERoU8++UQ9evTQunXrtH79equsadOmkiRjjKpXr64PP/xQwcHB/kULAAAAAEAx5dcZbEmqUaOGNm7cqCeffFKNGzdWUFCQjDEKCAhQ3bp19eijj2rDhg2qXLmyDeECAAAAAFA8+XUG23k5eExMjEaNGqVRo0ZJkk6dOqWIiAj/owMAAAAA4ALh1xnsEiVKqGrVqjp//rzLcJJrAAAAAMA/jV8JdlRUlKpWrcq91QAAAACAfzy/EuxLLrlEhw8ftisWAAAAAAAuWH4l2AMHDtQff/yhDRs22BUPAAAAAAAXJL8S7Pvvv1+XXXaZ+vXrp++//96umAAAAAAAuOD49RTx22+/XZUqVdK6devUokUL1a5dW8nJyYqMjHRb3+Fw6NVXX/VnkgAAAAAAFEsOY4zJb+OAgAA5HA55OwqHw6H09PT8Tg4oNKmpqYqNjVVKSopiYmKKOhwA+EdhG+we/QIARcOX7a9fZ7AnTpzoT3MAAAAAAC4aJNgAAAAAANjAr4ecAQAAAACATCTYAAAAAADYwK9LxFevXu1zmzZt2vgzSQAAAAAAiiW/Eux27drJ4XB4Xd/hcCgtLc2fSQIAAAAAUCz5lWBXrFjRY4J97tw5HThwQOnp6QoJCVFiYqI/kwIAAAAAoFjzK8HesWNHruUnTpzQK6+8ovHjx+v222/X2LFj/ZkcAAAAAADFll8Jdl6ioqI0cuRIxcfH68Ybb1T9+vXVtWvXgpwkAAAAAABFolCeIj548GCVLl1aTz/9dGFM7h/L4XDk+Td37lxbptWuXTv16NEj3+3feustNWvWTLGxsYqJiVHt2rV1yy236MCBA35Po3LlyhoxYkS+YwMAAACA/CjQM9hZVapUST/++GNhTe4f6dtvv3X5fPnll+uuu+7SddddZw2rWrVqYYeVw7Rp0/Tggw9q5MiRmjJliowx2rRpk9566y3t2bNHZcqUkSTNnj1bgYGBRRrrZW9fpvjYeDVPaK7y0eUVFxan+PB4lY4oLWOMjpw5otIRpdWoTCNJ0o8HftTBUwetYYEB7uNPz0j3um5e7BxXQSju8V2o6FcAFyt/tm/5aVvQbbyta2c9O+rkVl5cygqrjT9lhVFeVOtZYdbPbxs72vqq0BLs7du369y5c4U1uX+kyy67LMewihUruh1elGbOnKmhQ4fqmWeesYZ17dpVo0ePVkZGhjXs0ksvLYrwcjh27pg+/fPTXOvEhsRKDinlbIo1rGxEWY1tNlYdK3V0qfv5zs81bd007T+1P8+6ebFzXAWhuMd3oaJfAVys/Nm+5adtQbfxtq6d9eyok1u5pGJR1q1KN32y/ZMCb+NPWV59aUe5VDTrWVYFXT+/bexomx8OY4yxfazZOM9YNmzYUBs2bCjoyeH/ORwOPfXUUxo1apQkaenSpXruuef0n//8R2fOnFHt2rU1efJkdenSxWozd+5c3XjjjdqwYYPGjx+v1atXq1y5cnr44Yc1ePBgq167du0UFRWlIUOG6KGHHtJff/2lZs2a6ZVXXsnzLHlkZKTuvfdePfbYY7nWc05jyZIlkqRJkybp6aef1tq1azVs2DD9+OOPuuSSS/TMM8+oc+fOVrvKlSurR48eqlWrlp566ikdO3ZMV1xxhV555RWVLl3aq75LTU1VbGysar9YW4Hh+Tu65VDmE/ant5vusgG8b9V9MjJ51s2LneMqCMU9vgsV/Yp/Auc2OCUlRTExMUUdTrFxsfeLP9u3/LQt6Dbe1rWzniS/6wxNHqq5v8x1W559WFGVeWJ3G3/KpNz70o5yb5e53etZ9mS8IOvnt40dbbPyZfvrV4I9ZcoUj2XGGO3fv19r167Vf//7X0nSyy+/rFtuuSW/k4OPsifYs2bNUkZGhmrWrKmAgAAtW7ZMzz33nL788ku1a9dO0t8Jdu3atXXrrbeqTp06evnll/XBBx9o06ZN1lnldu3aaevWrSpfvrzGjh2r9PR03XvvvUpKSspxqXp2bdq00S+//KInnnhCPXr0UEJCgtt67hLsqVOnqmbNmrr77ruVlJSkqVOn6ocfftDOnTsVHx8vKTPBzsjIUO3atXXXXXfp0KFDuvfee9WlSxe9++67XvWdHQm2lPnlLRtRVsv7LpckdV7Y2eXomae63lwiY9e4CkJxj+9CRb/in+JiTyTz62LuF3+2b/lpW9BtJO9+85f2Xqpui7rZUq9MeBnJIb/qSFKAI0AZJsNjObyXV1/6U+7tMrd7Pcv6vfD1e1RY31UnO/ebfNn++nWJ+KRJkzy+B1vKTLIlKSAgQKNGjSK5LmJZH/yVkZGhK664Qr/88ov+9a9/WQl21rrDhg2TlHnp+dKlS/XBBx+4XLZ97Ngxbdy40TorfOzYMd16663avXu3KlSo4DGO2bNnq3fv3rr11lslSVWqVFHPnj01cuRIVa5cOdd5OHfunKZNm6Zu3bpJyrynvHr16lq2bJkGDRpk1TPG6KOPPlJoaKgkaevWrXryySeVkZGhgICcz/Y7e/aszp49a31OTU3NNQ5vGRntO7VPPx7IfP5Abj9oWes2TWia63h/PPCjbeMqCMU9vgsV/Qr8sxTUb1Nx5M/2LT9tC7qN5N1v/vzN822rt/+053Jv60giubZRXn3pT7m3y9zu9Szr98LX71FhfVedimq/ya8Ee/DgwR4TbIfDocjISNWoUUM9evRQlSpV/JkUbLB7926NHz9en3/+ufbu3WsdAGncuHGOuldeeaX1/+joaCUlJWn37t0udRo0aOByybUz+XYm2Onp6cp6gURgYKAcDofq1KmjX375RZ9//rlWrFihr776SjNmzNCcOXO0evVqNWjQwOM8BAQEqGPHvy/jqFatmkJCQnLE1rZtWyu5dsZ2/vx5HThwwO0Z86lTp2ry5Mkep+uvg6cO2lrX2/H5Ml07Fff4LlT0K/DPUtC/TcWJP9u3/LQtrDZ52ZW6y9Z6gDt2r2fOddzX70Rhf++Kar/JrwTbrlc+oeBlZGSoV69eSklJ0ZQpU1StWjVFRkZqwoQJ+vPPP3PUL1GihMvnkJAQnTlzJs86kqx6HTp00FdffWWVr1y50jpTHhISom7dullnoj/99FN1795dU6ZM0QcffOBxPsLDw63pOAUHB/scW3bjxo3TfffdZ31OTU1VUlKSxzh8VTrCu3u/va3r7fh8ma6dint8Fyr6FfhnKejfpuLEn+1bftoWVpu8JMV4tzy9rQe4Y/d65lzHff1OFPb3rqj2mwrlPdgoelu3btXGjRs1ffp03XzzzWrbtq2aNGmi06dPF9g0X375Za1fv976c3em3Klz586qX7++fvvttwKLJzehoaGKiYlx+bODQw4lRCSoUZlGalSmkcpGlLUeqpBb3bzYOa6CUNzju1DRr8A/S0H9NhVH/mzf8tO2oNt4W/eaGtfYVq9seFm/60iZ9/3mVg7v5dWX/pR7u8ztXs+yfi98/R4V1nfVjrb+8CvBbt++ve69916v6o4cOVIdOnTwZ3LwgzORznr2d+fOnfrmm28KbJo1a9ZUkyZNrL/o6GhJ0v79Oe+FOH36tHbt2uXxgWcXIueXeUyzMQoMCFRgQKD1OofsX/TsdfNi57gKQnGP70JFvwK4WPmzfctP24Ju423dkKAQ2+qNbT7W7zoOOTTk0iG5jqM4lHlidxt/yvLqS3/LJe+Wud3rWdbvha/fo8L6rtrR1h9+JdirVq3Sjz/+6FXdn376SatWrfJncvBDrVq1VKFCBY0dO1ZLlizR/Pnz1blzZ5UvX77QY6lbt65uvvlmLViwQGvWrNH8+fPVqVMnHTp0SPfcc0+hx2OHEiElFBsa6zKsbETZHI/+71ipo6a3m64yEWXyrJsXO8dVEIp7fBcq+hXAxcqf7Vt+2hZ0G2/r2lnPjjr3NbnPY/mz7Z7Vs+2eLfKyhIgE3Zh8o8pGlC3QNv6U5dWXdpR7u8wl+9dHp4Kun982drTNL79e0xUQEKBWrVpp9erVedZt06aNvv32W50/fz6/k4OPsr+ma/369Ro+fLj++9//KikpSQ899JC+/PJL/fDDD9q0aZOkv1/TdfDgQZUqVcoaV506ddSkSRPrvvvsr9CSpB9++EFNmzZ1udfandmzZ+vjjz/Wf//7X2s69erV0wMPPKArrrjCqufpPdgnTpxwGV9UVJRGjRqlSZMmSfr7PdizZs2y6rz//vvq37+/tm/fnueTyiXX13TFx8areUJzlY8ur7iwOMWHx6t0RGkZY3TkzBGVjihtXVry44EfdfDUQWuYpyNi6RnpXtfNi53jKgjFPb4LFf2Ki9nF/Doqf/xT+sWf7Vt+2hZ0G2/r2lnPjjq5lReXssJq409ZYZQX1XpWmPXz28aOtlIhvgfblwS7YsWKOnnypA4fPpzfyQGF5p+yEwMAxRHbYPfoFwAoGgX2Huyff/5ZP/30k8uwAwcO6PXXX/fY5vTp01q1apV2797tcnYSAAAAAICLiU8J9qJFizRlyhSXYVu2bNGNN96YaztjjAICAlxeNQEAAAAAwMXEpwS7cuXKatOmjfX5q6++UkxMjBo0aOC2vsPhUEREhKpVq6brr79eTZs29StYAAAAAACKK58S7CFDhmjIkCHW54CAANWtW1crV660PTAAAAAAAC4kPiXY2a1cuVKxsbF5VwQAAAAA4CLnV4Ldtm1bu+IAAAAAAOCCFlDUAQAAAAAAcDGwJcH+4IMP1LNnT5UrV06hoaEKDAx0+xcU5NcJcwAAAAAAii2/M96bb75Zc+fOlTEmz7re1AEAAAAA4ELk1xnsd999V3PmzFG1atW0YsUKNWnSRA6HQ9u2bdO6dev03HPPqVq1agoPD9drr72m7du32xU3AAAAAADFil8J9muvvSaHw6E333xTHTt2VGhoqCSpSpUqatKkie6++279/PPPatWqlYYPH66TJ0/aEjQAAAAAAMWNXwn2xo0blZiYqKZNm3qsExYWprlz5+r8+fN6/PHH/ZkcAAAAAADFll8JdmpqqsqVK2d9DgkJkSQdP37cpV5iYqKSk5O1atUqfyYHAAAAAECx5VeCXapUKZ06dcr6HB8fL0n6448/ctQ9d+6cDh065M/kAAAAAAAotvxKsJOSkrRv3z7rc/369SVJCxcudKn3+++/a/PmzYqLi/NncgAAAAAAFFt+Jdht27bV0aNHraeD9+/fXw6HQ48//rhGjx6tJUuW6JVXXlGXLl2UkZGhLl262BI0AAAAAADFjV8Jdq9evRQXF6eVK1dKkmrUqKEHH3xQGRkZmj59uq666irdcccd2rlzpxITE/XII4/YEjQAAAAAAMVNkD+NW7ZsqYMHD7oMmzJliurWrau5c+dq27ZtioiIULt27fTAAw8oISHBr2ABAAAAACiu/EqwPenfv7/69+9fEKMGAAAAAKBY8usS8T59+mjAgAE6e/asXfEAAAAAAHBB8ivBXrJkiTZv3qzQ0FC74gEAAAAA4ILkV4KdkJCgwMBAu2IBAAAAAOCC5VeC3b59e/36669KSUmxKx4AAAAAAC5IfiXYDz30kAIDAzVixAhlZGTYFRMAAAAAABccv54ivmfPHj300EN6+OGH9Z///EeDBw9WcnKyIiMjPbZp06aNP5MEAAAAAKBY8ivBbteunRwOhyTpl19+0ZgxY3Kt73A4lJaW5s8kAQAAAAAolvxKsCtWrGgl2AAAAAAA/JP5lWDv2LHDpjAAAAAAALiw+fWQMwAAAAAAkIkEGwAAAAAAG5BgAwAAAABgA6/vwb7kkkv8npjD4dC2bdv8Hg8AAAAAAMWN1wm2HQ8044njAAAAAICLldcJ9sqVK90OX7dunR566CFFRUXplltuUXJyssqWLav9+/frl19+0auvvqoTJ07o0UcfVdOmTW0LHAAAAACA4sRhjDH5bfzbb7+pWbNmuuKKK/TOO+8oMjIyR51Tp05p4MCBWrlypdavX69atWr5FTBQGFJTUxUbG6uUlBTFxMQUdTgA8I/CNtg9+gUAioYv21+/HnI2ZcoUpaena968eW6Ta0mKiIjQ3LlzlZaWpilTpvgzOQAAAAAAii2/EuxVq1YpOTlZJUuWzLVeXFyckpOTPV5mDgAAAADAhc6vBPvYsWM6fvy4V3VPnDihY8eO+TM5AAAAAACKLb8S7IoVK2rLli1at25drvXWrVunzZs3q2LFiv5MDgAAAACAYsuvBHvgwIEyxuiqq67SwoUL3db54IMP1Lt3bzkcDg0cONCfyQEAAAAAUGz59RTx06dPq1WrVtq4caMcDofKly+vSy+91HpN12+//abdu3fLGKMGDRro66+/VkREhJ3xAwWCJ7UCQNFhG+we/QIARcOX7a/X78F2Jzw8XF9++aXuvvtuvfXWW9q9e7d2797tUicgIEDXX3+9ZsyYQXINAAAAALho+ZVgS1JsbKzmzZunRx99VMuWLdP//vc/HT9+XNHR0apVq5a6dOnCvdcAAAAAgIue3wm2U1JSkm677Ta7RgcAAAAAwAXFr4ecAQAAAACATCTYAAAAAADYwJYE+4MPPlDPnj1Vrlw5hYaGKjAw0O1fUJBtV6QDAAAAAFCs+J3x3nzzzZo7d668eduXH28EAwAAAACgWPPrDPa7776rOXPmqFq1alqxYoWaNGkih8Ohbdu2ad26dXruuedUrVo1hYeH67XXXtP27dvtihsAAAAAgGLFrwT7tddek8Ph0JtvvqmOHTsqNDRUklSlShU1adJEd999t37++We1atVKw4cP18mTJ20JGgAAAACA4savBHvjxo1KTExU06ZNPdYJCwvT3Llzdf78eT3++OP+TA4AAAAAgGLLrwQ7NTVV5cqVsz6HhIRIko4fP+5SLzExUcnJyVq1apU/kwMAAAAAoNjyK8EuVaqUTp06ZX2Oj4+XJP3xxx856p47d06HDh3yZ3IAAAAAABRbfiXYSUlJ2rdvn/W5fv36kqSFCxe61Pv999+1efNmxcXF+TM5AAAAAACKLb8S7LZt2+ro0aPW08H79+8vh8Ohxx9/XKNHj9aSJUv0yiuvqEuXLsrIyFCXLl1sCRoAAAAAgOLGrwS7V69eiouL08qVKyVJNWrU0IMPPqiMjAxNnz5dV111le644w7t3LlTiYmJeuSRR2wJGgAAAACA4ibIn8YtW7bUwYMHXYZNmTJFdevW1dy5c7Vt2zZFRESoXbt2euCBB5SQkOBXsAAAAAAAFFd+Jdie9O/fX/379y+IUQMAAAAAUCz5dYk4AAAAAADIRIINAAAAAIAN/LpE/KabbvKpvsPh0KuvvurPJAEAAAAAKJb8SrDnzp0rh8MhY4zbcofDYf3fGEOCDQAAAAC4aPmVYE+cONFj2blz57R161YtXbpU6enpGjFihKKiovyZHAAAAAAAxVaBJdhOf/31l7p3765Vq1bpm2++8WdyAAAAAAAUWwX+kLPy5ctr/vz5+vHHHzVt2rSCnhwAAAAAAEWiUJ4iXrNmTdWsWVPvvPNOYUwOAAAAAIBCV2iv6QoJCdHOnTsLa3IAAAAAABSqQkmwDx06pN9//10RERGFMTkAAAAAAApdgSfYGzduVO/evXXu3Dm1adOmoCcHAAAAAECR8Osp4pdcconHMmOMDhw4oDNnzsgYo8jISE2aNMmfyQEAAAAAUGz5lWDv2LEjzzoOh0Nt27bVM888o3r16vkzOQAAAAAAii2/EuyVK1d6LHM4HIqMjFS1atUUGxvrz2QAAAAAACj2/Eqw27Zta1ccAAAAAABc0ArtNV0AAAAAAFzM/DqDLWU+zOznn3/W7t27lZqaqsjISFWtWlW1a9dWQAD5OwAAAADgnyHfCfauXbs0bdo0vfPOO0pJSclRHh8fr0GDBmnMmDEqW7asX0EWtmXLlmnmzJlav369jh07pri4ODVr1kx33HGHunXrJofDUdQh5mnHjh2qUqWK3nvvPfXr16+ow/HboUOHVLp0ac2ZM0dDhw4tvAlPrSCFhUhJzaQKTaWo0lJUGSk6UarUIrPOzrXSif1SVNnMYQGBvk0jI93/caB4YZkCgH2KyzbVzjjyMy5v2+RVL7/l7oZL+a+b1Fza9b1vdXz9nJ9xepovb4d5mv/chtux3Apj3fJGcfm+FmEs+UqwFy1apBtvvFHHjx+XMcZtnUOHDun555/XG2+8obfffludOnWyys6fP69169apZcuW+Yu6AD344IOaOnWqevfurVmzZikxMVH79+/X4sWL1atXL3300Ufq3r17UYeJwmTOS39+k/mXVXhJSQ7p9JG/h8WUk7o8IV3ay7tx//qRtHyMlLon/+NA8cIyBQD7FJdtqp1x5Gdc3rbJq15+y+v0kza97zrc036Qt3UdAZLJ8K2Or5/zM053bbwd5mn+cxve5YnM//uz3JwKct3yRnH5vhZxLA7jKUP2YNmyZbrqqquUlpammJgYXXfddWrfvr2qV6+uqKgonThxQlu2bNGXX36pt99+W6mpqQoLC9PKlSvVvHlznT59Wr1791aLFi00YcKEgpqvfFm6dKl69OihiRMnun1n9/r16xUQEKDGjRsXfnA++ieewT537pyCgoJsuTUhNTVVsbGxShkbrZhQX65Y+P+6A17P+8v760fSgsGSsn8FfRgHiheWKWALaxuckqKYmJiiDqfY+Mf1S3HZptoZR37G5W2bvOq1uEtaOzMf5Sg4Dnnuby+Xm7fL3591yxvF5ftaQLH4sv31KRM5ceKEhg4dqrS0NPXo0UNbt27V7Nmz1a9fP9WvX19Vq1ZV/fr11a9fP82ePVtbt25V9+7ddebMGQ0ePFjHjh1T165d9dlnn/k0Q4Vl+vTpSkxM1EMPPeS2vGnTplZyvXTpUnXq1EllypRRTEyMmjdvruXLl7vUnzRpkqKionKMJyoqyiWB/+abb9SmTRvFxsYqOjpadevW1bx587wuzy9jjJ5++mnVqFFDoaGhuuSSS/Tss8/mqLdo0SLVrFlTYWFhatasmX744Ycc8yBl9knz5s0VHh6u0qVL684779TJkyet8lWrVsnhcGjFihW67rrrFB0drUqVKunJJ5/MMc1XXnlFlStXVkREhDp06KCtW7fmqFO5cmWNGDFCTz31lCpVqqTw8HAdPnxYkjR37lzVq1dPYWFhKl++vMaPH6+0tDQ/e8wb//9FXj4287IUTzLSM4+qud2oejkOFC8sUwCwT3HZptoZR37G5W2btHN51DPSt7PyWY6Ck1t/e7Pc5OXyV/7XrYJatwtKMYjFpwT7lVde0cGDB9W+fXstXrxYpUqVyrV+qVKltHjxYrVr105bt27VpZdeqtWrVysuLk59+vTxK3C7paWl6ZtvvlH79u0VFJT3lfPbt29Xz5499cYbb2jhwoVq2bKlunXrplWrVvk03dTUVHXv3l0xMTF65513tHjxYt122206duyYV+X+uOeeezRhwgQNGTJES5cu1dChQzVmzBi99NJLVp2NGzeqf//+uvTSS/XBBx/oxhtv1MCBA3X+/HmXcb3//vvq1auX6tatq0WLFunJJ5/UBx98oJtvvjnHdO+8807VqFFDixYtUvfu3TVmzBiXgxNLlizRbbfdpiuuuEKLFi1S+/btNXDgQLfzsHDhQi1ZskTPP/+8Fi9erIiICE2fPl233HKLOnfurI8//lhjxozRjBkzPB44kaSzZ88qNTXV5S//jJT6V+Y9H57sXOt6yUp+xoHihWUKwGb2/jZdYIrLNtXOOPIzLm/brH8lj3pyvQw6P+UoGrkuF2+Xvx/rVkGt2wWlGMTi0z3YS5YskcPh0LPPPuv1ZbiBgYF69tln1bBhQ+3bt09xcXH67LPPVKdOnXwFXFAOHz6ss2fPKikpyWW4MUbp6X8f4QgICFBAQIBGjBhhDcvIyNAVV1yhX375Rf/617/Url07r6e7efNmpaSkaOrUqapbt64kqUOHDl6X59e2bds0a9YsvfTSS7rtttskSR07dtSJEyc0efJk3XbbbQoICNDUqVNVpUoVLVy40Frm4eHhuvHGG61xGWM0atQoXXPNNfr3v/9tDS9btqx69Oihhx9+WMnJydbwvn37Wme/27dvryVLluj9999Xly5dJEmPPvqoWrdurTlz5kiSOnfurJMnT2rq1Kk55iMtLU3Lli1TRESEJOn48eOaOHGiHnjgAT3++OOSpE6dOikoKEijRo3S6NGjFR8fn2M8U6dO1eTJk/Pdn26d2J+/svzUQ9FjmQKwWYH8Nl0oiss21c448jMub9sc3eFdPVycvF3++Vm3CmrdLijFIBafzmD/9ttvqlChgpXoeat+/fqqUKGCdXlwgwYNfGpfGJy3omd/QvjChQsVHBxs/d19992SpN27d2vIkCEqX768goKCFBwcrBUrVmjz5s0+Tbdq1aqKiYnRnXfeqQULFujgwYM+lRtjlJaWZv1lZHh39PHzzz+XlJnsZm3foUMH7du3T7t27ZKUed95jx49XA6oXHXVVS7j2rx5s3bu3KkBAwa4jKtt27ZyOBz64YcfXOpfeeWV1v8DAgJUq1Yt7d69W5KUnp6uDRs2qHfv3i5tPN1H3q5dOyu5lqS1a9fqxIkT6t+/v0ss7du31+nTp7Vp0ya34xk3bpxSUlKsP+f8+yUql6fn51aWn3ooeixTADYrkN+mC0Vx2abaGUd+xuVtm5KVvauHi5O3yz8/61ZBrdsFpRjE4lOCfeTIESUmJuZrQomJiXI4HGrUqFG+2he0UqVKKTQ01Er0nDp06KD169dr/fr11rxnZGSoV69e+vrrrzVlyhStXLlS69evV9euXXXmzBmfpluyZEl99tlnio6O1g033KCEhAS1a9dO//3vf70qnzdvnssBgJtuusmr6R46dEjGGJUqVcqlvfMssvNHfO/evSpdunSOmIODg13GJUm9e/d2GVdUVJQyMjJy7BCUKFHC5XNISIjVbwcPHlRaWprKlCnjUsfTq96y13PG0qhRI5dYateu7TJf2YWGhiomJsblL/8cUkz5v1/f4E6lFplPMpSnB6h5MQ4ULyxTADaz97fpAlNctql2xpGfcXnbpumtedRT5tOy/SlH0ch1uXi7/P1Ytwpq3S4oxSAWny4Rj46Ozve9v8eOHcuRWBUnQUFBatmypb744gulp6crMDDzHWklS5ZUkyZNJGUmgpK0detWbdy4UYsXL3Y5m3v69GmXcYaFheW4V/ns2bM6deqUy7BmzZpp2bJlOn36tFauXKlRo0bp6quv1rZt2/Is79mzp9avX2+NK6/74p3i4uLkcDj09ddfW/OVVc2aNSVlHhjJftb86NGjLvMVFxcnSZo1a5aaN2+eY1zlypXzKiZJKl26tIKCgnTgwAGX4fv3u7+MI/sVB85YPvjggxyX+0tSlSpVvI4lf/4/ni7Tcn/PXkBg5msCFgxWzidIejkOFC8sUwCwT3HZptoZR37G5W2boJC8610+4v+fRu1rOQpO1r7O53Lzdvnnd90qqHW7oBSDWHw6g125cmVt3bpV+/bt82kie/fu1datW1W5cmWf2hW2++67T3v27LHu3fXEmUhnTUx37typb75xfU9yhQoVdO7cOStRljIvzfb0ZrTw8HB169ZNd955p7Zv357jbLi78vj4eDVp0sT687aPnfdxHz582KW98y86OlpS5pPTlyxZ4nLp+eLFi13GVatWLVWoUEF//PGH23H5kmAHBgaqUaNGWrRokcvw999/36v2LVq0UEREhHbv3u02Fnf3X+dbeFzmX1Yx5bx/9P+lvTLrxmS7KsSXcaB4YZkCgH2KyzbVzjjyMy5v2+RV78pH8lleXmpx9/+fFczC7X6QD3UdAb7X8fVzfsbpro23wzzNv8fh5aQBb2T+5Xe5ebv8/Vm3vFFcvq/FIBafzmB36NBBGzZs0COPPKIXXnjB63aPPPKIpMyHTRVn3bt319ixYzVhwgT99NNPuuaaa5SYmKiUlBStWbNG+/btU3R0tJVQjh07Vunp6Tp58qQmTpyo8uXLu4yva9euioyM1K233qoxY8Zo9+7dev75510S86VLl+rVV19V7969VbFiRe3bt08zZ85Uy5YtFRYWlmd5Xr777rscw0qXLq22bdtq+PDhuuGGGzR69Gg1b95c58+f1+bNm7Vy5UoriR43bpyaNm2qvn376rbbbtOOHTv0zDPPKCQkxLov2+FwaPr06bruuut08uRJde/eXZGRkdq5c6eWLl2qxx9/XDVq1PB6OYwfP15XXXWV9cTyH374QW+//bZXbWNjYzVlyhQ98MAD2r17t6644goFBATojz/+0IcffqiFCxe63LPtFUewlNRMqtBUiiotRZWRohP/vrRk59rMByVElc0c5ssRsUt7SbW6+zcOFC8sUwCwT3HZptoZR37G5W2bvOr5U95xUs7hUv7rJjWXdn3vWx1fP+dnnJ7my9thnuY/t+GSf8utMNYtbxSX72tRx2J8sGPHDhMaGmoCAgLMk08+6VWbJ554wjgcDhMaGmq2b9/uy+SKzJIlS0zXrl1NfHy8CQoKMmXKlDFdu3Y1b731lklPTzfGGLNu3TrTtGlTExYWZqpXr27mzZtnhgwZYpKTk13GtXz5cpOcnGzCwsLMZZddZn766ScTGRlpJk6caIwx5n//+5/p27evSUpKMiEhIaZcuXJm6NChZu/evV6Ve7J9+/b/f3lezr+2bdsaY4zJyMgwM2fONHXq1DEhISGmZMmS5rLLLjPTp093GdfChQtNjRo1TGhoqGncuLFZs2aNCQwMNM8995xLvRUrVpi2bduayMhIExkZaZKTk839999vjh07ZowxZuXKlUaSWb9+vUu77t27WzE5vfTSSyYpKcmEhYWZtm3bmrVr1xpJZs6cOVadSpUqmeHDh7ud/3feecc0bdrUhIeHm5iYGNOwYUPz8MMPm/Pnz+fab04pKSlGkklJSfGqPgDAPmyD3aNfAKBo+LL9dRjj4XplDx555BFNnDhRDodDLVu21D333KMrrrjCuvdVynwY2pdffqkZM2ZYl01PnDhREyZM8P+IAIrc559/rk6dOmnVqlVq27ZtUYdTIFJTUxUbG6uUlJR/1kNlAKAYYBvsHv0CAEXDl+2vT5eIS9LDDz+sAwcO6IUXXtA333xjJdAlSpRQVFSUTpw4YT0IzZm7Dxs2jOT6AjZs2DB16NBB8fHx+uWXX/TII4+oYcOGat26dVGHBgAAAADFhs8JtiTNnDlT7dq104QJE/Tbb79Jynyy9NGjR13q1apVS5MnT1b//v39jxRF5tixY7rrrrt06NAhxcbGqkuXLnr66add3o0NAAAAAP90Pl8int2GDRu0Zs0a7dq1S8ePH1d0dLSSkpLUunVrNW7c2K44gULFZXgAUHTYBrtHvwBA0SjQS8Sza9y4MYk0AAAAAOAfj2t8AQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk2AAAAAAA2IMEGAAAAAMAGJNgAAAAAANiABBsAAAAAABuQYAMAAAAAYIOLPsFetmyZunXrptKlSys4OFhly5ZVz549tXTpUhljijo8n/z5558aNmyYqlSpotDQUJUsWVJXXnmlPv74Y2teJk2apKioKFumN3fuXDkcDh06dMiW8eVm6NChqlOnToFPBwAAAAAKSlBRB1CQHnzwQU2dOlW9e/fWrFmzlJiYqP3792vx4sXq1auXPvroI3Xv3r2ow/TK+vXr1blzZ5UsWVKjRo1SnTp1dPz4ca1YsUIDBgzQ8uXL1bZt26IO86JTZ+KnCgmLUKNKJdWkUpwurxqvgACHDp04qzLRYWpWJU6BAQ6lZxit235EB46fcRlul4IePwB4i+0RvHWhrisFFXd+x+ttO2/q5VXHU7kvwyXla1jjSiW1YedRn+rk9Tk/4/BnHrzZL8xvWX7Wo4Je53xxoW8Pduw96HWbizbBXrp0qaZOnaqJEydq0qRJLmX9+/fXvffeq4CAC+ME/tmzZ9W/f38lJCRo7dq1KlGihFXWo0cPDR8+XA5H8V9BL1RpRlq346jW7Tiq2V9tcylLjA1Tr/qJ+ug/e7U35YzL8Ik9L1WXOol+T3/5pr2a/PGvBTZ+APAW2yN460JdVwoq7vyO19t23tTLq46nck/7Oe6Gl4gIliQdO3Xe52EBDikjy8Wl3tTJ63N+xuHPPOS1XyjJ4zLIrczbZZhVQa9zvrgYtgcZZ0953e7CyDDzYfr06UpMTNRDDz3ktrxp06Zq3LixpMxkvFOnTipTpoxiYmLUvHlzLV++3KW+p0uvo6KiXBL4b775Rm3atFFsbKyio6NVt25dzZs3z+tyd9577z3t3LlT06ZNc0munWrWrKkaNWq4DPv555/VqlUrRUREqE6dOvr0009ztJs7d67q1aunsLAwlS9fXuPHj1daWlqOelu3blX79u0VERGhypUr67XXXrPKPvroIzkcDm3ZssWlTUpKiiIiIjRjxgxJ0i+//KJu3bopPj5eERERqlmzpp588skc01q1apUaNmyoyMhINWvWTBs2bHApN8bo6aefVo0aNRQaGqpLLrlEzz77rEt7h8ORo116errKli2rBx54IMc0/bE35YxeXr3dZYMhSftSzujON3/U8k17/Rr/8k17deebPxbY+AHAW2yP4K0LdV0pqLjzO15v23lTL686Uz/51W25p/0cT8OPnTrvknD6Miwj252b3tTJ63N+xuHPPOS2X3jHmz/qDg/LILcyb5dh1vWooNc5X1xs2wNvXJQJdlpamr755hu1b99eQUF5n6Tfvn27evbsqTfeeEMLFy5Uy5Yt1a1bN61atcqn6aampqp79+6KiYnRO++8o8WLF+u2227TsWPHvCr3ZNWqVQoMDFSnTp28iuP8+fMaNGiQhg4dqkWLFqlUqVLq27evDh8+bNWZPn26brnlFnXu3Fkff/yxxowZoxkzZrg9IDFw4EB16tRJixYt0hVXXKGbb77ZOgDRvXt3lS9f3iXplqR33nlHGRkZGjRokCSpV69eOnr0qF599VUtXbpUo0aN0smTJ13a7Nu3T3fffbdGjx6t+fPn69SpU+rdu7fOn/9743XPPfdowoQJGjJkiJYuXaqhQ4dqzJgxeumllyRJbdq0Ufny5fXOO++4jPvLL7/UgQMHdO2113rVh/5ybqsnf/yr0rNvub2UnmE0+eNf5a61HeMHAG+xPYK3LtR1paDizu94vW13Li0jz3qTPvpFkz7yXMdIemXNdrflsEdufetNWV7LUPp7PSrodc6X78DFuD3wxkV5ifjhw4d19uxZJSUluQw3xig9Pd36HBAQoICAAI0YMcIalpGRoSuuuEK//PKL/vWvf6ldu3ZeT3fz5s1KSUnR1KlTVbduXUlShw4dvC735K+//lLp0qUVHh7uVRznzp3TtGnT1K1bN0lS1apVVb16dS1btkyDBg3S8ePHNXHiRD3wwAN6/PHHJUmdOnVSUFCQRo0apdGjRys+Pt4a3+DBgzVu3DhJUufOnbVt2zZNmTJFXbp0UWBgoG688Ua99tprevTRRxUYGChJeu2113T11VcrLi5Ohw4d0h9//KHnnntOPXv2lCRdccUVOeI+cuSIvvrqKyUnJ0uSwsLC1KlTJ33//fdq1aqVtm3bplmzZumll17SbbfdJknq2LGjTpw4ocmTJ+u2225TQECArrnmGs2fP19PPfWUden8O++8o5o1a6phw4Zu++zs2bM6e/as9Tk1NdWrvs6NUeaRzHXbj+jyqvF51s9u3fYjuR4183f8AOAttkdFoyB+mwrahbquFFTc+R2vt+3e+HZHnvX2pZ71WO5UzPIbZOHNMsy6Hun//+9N3fysc758By7W7UFeLsoz2M4name/L3nhwoUKDg62/u6++25J0u7duzVkyBCVL19eQUFBCg4O1ooVK7R582afplu1alXFxMTozjvv1IIFC3Tw4EGfyo0xSktLs/4yMjKs4b7cYx0QEKCOHTtan6tVq6aQkBDt3r1bkrR27VqdOHFC/fv3d5le+/btdfr0aW3atMllfL17987x+YcffrAOVtx8883au3evdVZ706ZNWr9+vW6++WZJUnx8vCpVqqRx48Zp3rx5VhzZlStXzkquJenSSzPvR3HW//zzzyVJffv2dYm7Q4cO2rdvn3bt2iVJuvbaa7V79259/fXXkjIPOCxatEjXXXedxz6bOnWqYmNjrb/sB2f8ceB4/r6g3rbL7/gBwFtsj4pGQf42FZQLdV0pqLjzO15v2+084v19obj4HTh+psDXOV++Axf79sCTizLBLlWqlEJDQ3Mkch06dND69eu1fv16JSZm3lCfkZGhXr166euvv9aUKVO0cuVKrV+/Xl27dtWZM751bsmSJfXZZ58pOjpaN9xwgxISEtSuXTv997//9ap83rx5LgcAbrrpJklShQoVdPDgQa/jCQ8PV0hIiMuw4OBgq73ztVuNGjVymV7t2rUlyUpUncqUKZPj8/nz563xVK5cWZ06ddKrr74qSXr11VdVqVIl6+y8w+HQp59+qtq1a2v48OFKSkpS48aNtXr1apfxZr+/3DkPWeM2xqhUqVIucXfp0sUl7iZNmqh69erWZeLLli3TsWPHcr08fNy4cUpJSbH+sveBP8pEhxVou/yOHwC8xfaoaBTkb1NBuVDXlYKKO7/j9bZdpbgIn+LBxa1MdFiBr3O+fAcu9u2BJxflJeJBQUFq2bKlvvjiC6Wnp1uXLZcsWVJNmjSR9HfytnXrVm3cuFGLFy/WVVddZY3j9OnTLuMMCwtzuRdYyrx069Qp1yOHzZo107Jly3T69GmtXLlSo0aN0tVXX61t27blWd6zZ0+tX7/eGlepUqUkZV5O/eqrr+qzzz6zLrH2R1xc5msFPvjgA7dHw6tUqeLy+cCBAypfvrzL5+DgYCs+Sbr11lt13XXX6a+//tJbb72l4cOHuzylvWbNmnrvvfd0/vx5rV27Vg8++KB69uypv/76y+v3dsfFxcnhcOjrr7/OcQDBOQ2na6+9Vi+++KJmzJihd999V40bN1b16tU9jjs0NFShoaFexeEth6SE2L9f4+CrZlXilBgbpn0pZ9zeA+Lv+AHAW2yPikZB/DYVtAt1XSmouPM7Xm/b3XB5Zf376+251isbEyrJof2p7utImU/SNib3+4FRNLxZhtnXo4Jc53z5Dlys24O8XJRnsCXpvvvu0549e6x7jD1xJtJZE7adO3fqm2++calXoUIFnTt3zkqUpcxLlp2Xo2cXHh6ubt266c4779T27dtznH12Vx4fH68mTZpYf5UrV5Yk9evXz7rE2t39V1u2bPHpcvYWLVooIiJCu3fvdpme8y/r/deStGjRohyfGzdubB24kKSrrrpKJUuW1HXXXafDhw/rxhtvdDvt4OBgtW3bVmPHjlVqaqr27NnjddzOM+KHDx92G3d0dLRV99prr9XBgwf18ccf6+OPP8718vCC4Lygf2LPS/P9jr/AAIf12obsY7Bj/ADgLbZH8NaFuq4UVNz5Ha+37UKCAvKsN6lXsib18lzHIenW1lXclsMeDg//97Ysr2Uo/b0eFfQ658t34GLcHnjjok2wu3fvrrFjx2rChAnq27evFixYoDVr1mjJkiUaM2aM9u3bp+joaNWqVUsVKlTQ2LFjtWTJEs2fP1+dO3d2OWMrSV27dlVkZKRuvfVWffrpp3r11Vc1btw4l8R86dKl6tOnj9544w199dVXmj9/vmbOnKmWLVsqLCwsz3JPQkNDtWDBAu3Zs0eNGzfW7NmztXr1an3yySe677771KBBA+3d6/0j7mNjYzVlyhQ98MADGjNmjJYvX64VK1bopZdeUteuXXOclX/99dc1depUffrpp7rxxhu1Zs0aPfzwwy51goODNWTIEK1evVodO3ZUxYoVrbKff/5ZnTp10r///W+tXLlSixcv1qOPPqrKlSuratWqXsddo0YNDR8+XDfccIMee+wxff7551q2bJmef/55XX311S51a9WqpYYNG2rEiBE6deqUrrnmGq+n44vE2DDd3qaKEmNdl19CbJheHNTI73f7damTqBcHNVJCAY0fALzF9gjeulDXlYKKO7/j9badN/XyqjOu26Vuyz3t53gaXiIi2Ho/tK/DsudY3tTJ63N+xuHPPOS2X/jSoEZ6ycMyyK3M22WYdT0q6HXOFxfb9sAr5iK3ZMkS07VrVxMfH2+CgoJMmTJlTNeuXc1bb71l0tPTjTHGrFu3zjRt2tSEhYWZ6tWrm3nz5pkhQ4aY5ORkl3EtX77cJCcnm7CwMHPZZZeZn376yURGRpqJEycaY4z53//+Z/r27WuSkpJMSEiIKVeunBk6dKjZu3evV+V52blzp7njjjtMpUqVTHBwsClRooTp2LGjeeedd0xGRoYxxpiJEyeayMjIHG2zxun0zjvvmKZNm5rw8HATExNjGjZsaB5++GFz/vx5Y4wxc+bMMZLM2rVrTdu2bU1YWJipWLGi+de//uU2vrVr1xpJZv78+S7D9+/fbwYNGmQuueQSExoaasqUKWP69u1rNm/ebNVx198HDx40ksycOXOsYRkZGWbmzJmmTp06JiQkxJQsWdJcdtllZvr06TniefLJJ40k07ZtW4996klKSoqRZJLuXWCqjl1i+r/4jXnik9/M6t8PmK+3HDSLN+42a7ceMmnpmf2elp5h1m49lGO4XQp6/ADgrcLYHjm3wSkpKbaP+0J2ofXLhfrbVVBx53e83rbzpl5edTyV+zI8v8POnk/3uU5en/MzDn/mwZv9wvyW5Wc9Kuh1zhcX+vbg7TW/eb39dRjj4RpnwEcTJkzQ7Nmz9ddff11w94xll5qaqtjYWKWkpCgmJqaowwGAfxS2we7RLwBQNHzZ/l6UDzlD4fr999/1+++/a+bMmRo+fPgFn1wDAAAAQH6QYMNvt99+u7777jt16dJF48aNK+pwAAAAAKBIkGDDb6tWrSrqEAAAAACgyF20TxEHAAAAAKAwkWADAAAAAGADEmwAAAAAAGxAgg0AAAAAgA1IsAEAAAAAsAEJNgAAAAAANuA1XYAbxhhJUmpqahFHAgD/PM5tr3NbjEz8NgFA0fDld4kEG3Dj8OHDkqSkpKQijgQA/rkOHz6s2NjYog6j2Dh+/LgkfpsAoKgcP348z98lEmzAjbi4OEnSn3/+yc5dNqmpqUpKStKuXbsUExNT1OEUG/SLZ/SNe/SLZykpKapYsaK1LUamcuXKadeuXYqOjpbD4fC6XdOmTbV+/Xqfy90Nzz4s62d3/2/atKm++OILv9b1gorf07xkr+NP/HnF/k+K39d150KP3/mvP9t6vrvFJ35jjI4fP65y5crl2Y4EG3AjICDz8QSxsbHs+HoQExND37hBv3hG37hHv3jm3BYjU0BAgCpUqOBzu8DAwFzXMU/l7oZnH5b1s7v/Zx2W33W9oOL3NC+e6uQn/rxi/yfF7+u6c6HHn71+QcT/T/3uFlX83p5045cLAADgIjZ8+PB8lbsbnn1Y1s/u/p/XtL1RUPF7mpfc6vjKm/b/lPh9XXe8nX5+YvOmjr/xF+d1P/tn4vctvrw4DE8QAXJITU1VbGysUlJSOLOUDX3jHv3iGX3jHv3iGX1zcbnQlyfxFy3iLzoXcuxS0cXPGWzAjdDQUE2cOFGhoaFFHUqxQ9+4R794Rt+4R794Rt9cXC705Un8RYv4i86FHLtUdPFzBhsAAAAAABtwBhsAAAAAABuQYAMAAAAAYAMSbAAAAAAAbECCDQAAAACADUiwAQAAAACwAQk24Mbs2bNVpUoVhYWFqXHjxlqzZk1Rh1RgJk2aJIfD4fKXkJBglRtjNGnSJJUrV07h4eFq166dfvnlF5dxnD17VnfddZdKlSqlyMhI9erVS7t37y7sWfHb6tWr1bNnT5UrV04Oh0OLFy92KberL44ePaobbrhBsbGxio2N1Q033KBjx44V8NzlX179MnTo0Bzr0GWXXeZS52Lsl6lTp6pp06aKjo5WmTJldPXVV+v33393qfNPXWe86Zt/6nqD3B0/flz/196dRzV1bX8A/0YZDKiByKgI5QnSKgjOEypQZbA41qHSZ9FS+2wVZ11YrVFbC7Z17kxbfbVSfdbxWXGqIFWEolWc36OKAygyFaKgjPv94S/3R0iARAIhsD9rsZacc+7NPifHhJN7z07fvn3h5eUFDw8PREdH6zskrdy7dw8+Pj7o1q0bevTogd27d+s7JK2MGzcOlpaWmDBhgr5D0cihQ4fg5uYGV1dXfPvtt/oOR2uGNt5VGfpcb9DXGmKMKdm5cycZGxtTdHQ0Xbt2jebOnUvm5uZ0584dfYfWIGQyGXXv3p0ePHgg/GRnZwv1UVFR1K5dO9qzZw9dvnyZJk+eTPb29iSXy4U2M2fOpE6dOtHx48fpjz/+IF9fX/L09KTy8nJ9dOm5HT58mJYtW0Z79uwhALRv3z6lel2NRWBgILm7u1NiYiIlJiaSu7s7BQcHN1Y3tVbXuISGhlJgYKDSHMrLy1Nq0xzHJSAggLZu3UpXrlyhixcv0iuvvEKOjo70+PFjoU1LnTOajE1LnTesduXl5VRUVEREREVFReTs7Ey5ubl6jkpz9+/fpwsXLhAR0cOHD6lTp05K876pO3nyJB08eJBeffVVfYdSp7KyMnJ1daWMjAySy+Xk4uKi8hrS1BnSeFdn6HO9IV9reIHNWDX9+vWjmTNnKpW9+OKLFBERoaeIGpZMJiNPT0+1dZWVlWRnZ0dRUVFC2dOnT0kikdBXX31FREQFBQVkbGxMO3fuFNpkZmZSq1at6MiRIw0ae0OqvpDU1Vhcu3aNAFBSUpLQ5uzZswSAbty40cC9qr+aFthjxoyp8ZiWMC5ERNnZ2QSATp06RUQ8Z6qqPjZEPG9Y3fLy8sjR0ZFycnL0Hcpz8/DwoLt37+o7DK3ExcUZxILvzJkzNHbsWOH3OXPmUExMjB4jej6GMt51McS5rqDr1xq+RZyxKkpLS3H+/Hn4+/srlfv7+yMxMVFPUTW8tLQ0dOzYEc7Oznjttddw69YtAEB6ejqysrKUxsPU1BTDhg0TxuP8+fMoKytTatOxY0e4u7s3qzHT1VicPXsWEokE/fv3F9oMGDAAEonEoMcrPj4eNjY26Nq1K2bMmIHs7GyhrqWMS2FhIQBAKpUC4DlTVfWxUeB5Y3jq2jIC1H+bVUFBATw9PeHg4IAlS5bAyspKR9E3TvwK586dQ2VlJTp37lzPqJ9pzNgbQ337c//+fXTq1En43cHBAZmZmY0ROgDDfz50Gb+u57omdBF/Q73W8AKbsSpyc3NRUVEBW1tbpXJbW1tkZWXpKaqG1b9/f/zwww84evQooqOjkZWVhUGDBiEvL0/oc23jkZWVBRMTE1haWtbYpjnQ1VhkZWXBxsZG5fw2NjYGO15BQUHYsWMHTp48iXXr1iElJQV+fn4oKSkB0DLGhYiwYMECeHt7w93dHQDPGQV1YwPwvDFURUVF8PT0xGeffaa2fteuXZg3bx6WLVuGCxcuYMiQIQgKCsLdu3eFNr1794a7u7vKz/379wEAFhYWSE1NRXp6OmJiYvDw4UODih8A8vLy8MYbb+Cbb74xuNgbS337Q0Qqx4hEogaNuSpdPB/6pKv4G2Kua0IX8TfUa42RTs7CWDNT/QWaiBr1RbsxBQUFCf/28PDAwIED0aVLF/zzn/8UEg49z3g01zHTxVioa2/I4zV58mTh3+7u7ujTpw+cnJzwyy+/YPz48TUe15zGZfbs2bh06RJOnz6tUtfS50xNY8PzxjAFBQUpvW9Ut379eoSFheGtt94CAGzcuBFHjx7Fl19+icjISADP7k7QhK2tLXr06IGEhARMnDix/sGjceIvKSnBuHHjsHTpUgwaNEgncTdW7I2pvv3p1KmT0hXrjIwMpbtZGpoung990kX8DTXXNaHL8df1aw1fwWasCisrK7Ru3Vrlykd2drbKVajmytzcHB4eHkhLSxOyidc2HnZ2digtLcVff/1VY5vmQFdjYWdnp/YT0pycnGYzXvb29nByckJaWhqA5j8u4eHhOHjwIOLi4uDg4CCU85ypeWzUaWnzpjnSxTarhw8fQi6XAwDkcjkSEhLg5uam81jV0UX8RIRp06bBz88PU6dObYgw1WpuW9w06U+/fv1w5coVZGZm4tGjRzh8+DACAgL0Ea4KQ38+NIlfX3NdE5rE35CvNbzAZqwKExMT9O7dG8ePH1cqP378eKN/MqcvJSUluH79Ouzt7eHs7Aw7Ozul8SgtLcWpU6eE8ejduzeMjY2V2jx48ABXrlxpVmOmq7EYOHAgCgsL8fvvvwttkpOTUVhY2GzGKy8vD/fu3YO9vT2A5jsuRITZs2dj7969OHnyJJydnZXqW/KcqWts1Gkp86Y508U2q4yMDAwdOhSenp7w9vbG7Nmz0aNHj4YIV4Uu4j9z5gx27dqF/fv3w8vLC15eXrh8+XJDhKtEV1vcAgICMHHiRBw+fBgODg5ISUnRdaga0aQ/RkZGWLduHXx9fdGzZ08sXrwYHTp00Ee4KjR9PprKeFenSfz6muua0CT+hnyt4VvEGatmwYIFmDp1Kvr06YOBAwfim2++wd27dzFz5kx9h9YgFi1ahFGjRsHR0RHZ2dn48MMPIZfLERoaCpFIhHnz5uGjjz6Cq6srXF1d8dFHH8HMzAwhISEAAIlEgrCwMCxcuBAdOnSAVCrFokWL4OHhgeHDh+u5d9p5/Pgx/vzzT+H39PR0XLx4EVKpFI6OjjoZi5deegmBgYGYMWMGvv76awDA22+/jeDg4Ea7SqOt2sZFKpVi5cqVePXVV2Fvb4/bt2/jvffeg5WVFcaNGweg+Y7LrFmzEBMTgwMHDqBdu3bCm7ZEIoFYLNbZ/5/mODaPHz9usfOmJajPNqvevXvj4sWLDRCV5uoTv7e3NyorKxsiLI3Ud4vb0aNHdR1SvdTVn9GjR2P06NGNHZbG6oq/qY13dbXFr++5rona4m/Q1xqd5CJnrJn5/PPPycnJiUxMTKhXr15KXy3T3Ci+l9fY2Jg6duxI48ePp6tXrwr1lZWVJJPJyM7OjkxNTWno0KF0+fJlpXM8efKEZs+eTVKplMRiMQUHBxvkVzXExcURAJWf0NBQItLdWOTl5dHrr79O7dq1o3bt2tHrr79Of/31VyP1Unu1jUtxcTH5+/uTtbU1GRsbk6OjI4WGhqr0uTmOi7oxAUBbt24V2rTUOVPX2LTkedOcoNrX9pWUlFDr1q1p7969Su3mzJlDQ4cObeTo6mbI8Rty7OoYen84fv1qavHzApsxxhhjjGmt+h+1RET9+vWjd955R6nspZdeooiIiEaMTDOGHL8hx66OofeH49evphY/3yLOGGOMMcY0UtdWmqa+zcqQ4zfk2NUx9P5w/PrVpONv8CU8Y4wxxhhrFuraSkPUtLdZGXL8hhy7OobeH45fv5py/CIiNd/SzhhjjDHGGGOMMa3w13QxxhhjjDHGGGM6wAtsxhhjjDHGGGNMB3iBzRhjjDHGGGOM6QAvsBljjDHGGGOMMR3gBTZjzKAlJyfDz88PHTp0gEgkgo+Pj75DajS3b9+GSCTCtGnT9B2KXsTHx0MkEmHlypVK5S+88AJeeOEFvcTEGGOMsZaNF9iMtRAikUirH0NQWFiIUaNG4Y8//kBISAhkMlmLXWxqo7i4GJs2bYKvry+sra1hbGwMqVQKb29vREVFIScnR98hGpxt27ZBJBJh27Zt+g6FMcYYY3pkpO8AGGONQyaTqZStWrUKEokE8+bNa/yAdCAlJQU5OTmIjIxERESEvsMxCKmpqRgzZgzu3LkDJycnjB49Gra2tpDL5UhKSsLSpUsRGRmJ+/fvw9zcXN/hPpdff/1V3yEwxhhjrIXiBTZjLUT122iBZwtsCwsLtXWG4P79+wAAOzs7PUdiGDIyMuDv74/c3FysW7cOc+fORevWrZXaXLhwAbNnz0ZZWZmeoqy/Ll266DsExhhjjLVQfIs4Y0xJ1X29N27cwPjx42FlZQWRSITbt28DAPbt24cpU6bAxcUFZmZmkEgkGDJkCPbs2VPr+W7duoUJEybA0tIS5ubmGD58OFJTU1WOSUtLw/Tp0+Hs7Iw2bdrAysoKvXr1wsKFC4U2IpEIoaGhAIDp06cLt7bHx8cLba5evYrJkyfDxsYGpqamcHZ2xvz585Gfn6/ymIp9uwUFBZgzZw46d+4MIyMjbNu2TakP169fR3BwMCwsLGBpaYkpU6YgNzcXwLP94CNGjED79u1haWmJGTNmoKioSO04JyQkYNSoUbCysoKpqSlcXV2xfPlyFBcXq7StqKjA2rVr4eLigjZt2sDFxQWRkZGorKys+YlUY9myZcjOzsZ7772HBQsWqCyuAaBnz544deoU2rdvr1R+6NAh+Pr6QiKRQCwWw8vLCxs3bkRFRYXax9K0vSbz7cmTJ4iIiEDnzp3Rpk0buLu7Izo6usZ+qtuDvXLlSmF+/Otf/0KvXr0gFothb2+POXPm4MmTJ0rtS0tLsWXLFgQEBKBz584wNTWFjY0Nxo8fjwsXLii1nTZtGqZPnw5AeS5W32rx6NEjyGQydO/eHWKxGBYWFggMDMTp06dr7Et106ZNg0gkwq1bt7BhwwZ0794dpqamvDWCMcYYayL4CjZjTK0///wTAwYMQPfu3REaGor8/HyYmJgAAJYuXQoTExN4e3vD3t4eOTk5OHjwICZMmIDNmzcjPDxc5Xy3b99G//790a1bN7z55pu4efMmDhw4AF9fX1y/fh22trYAnl2V7tevH4qKivDKK69g8uTJePz4MdLS0rBlyxasW7cOwLNb3i9evIgDBw5gzJgx8PLyAgBhYZWYmAh/f3+UlJRgwoQJeOGFF5CUlISNGzfil19+wdmzZ9GhQwelGEtKSuDn54dHjx5h1KhRMDExEeICgPT0dAwaNAh9+vTBW2+9hXPnzmHnzp24d+8e1q5dixEjRmDEiBF4++23ER8fj2+//RYAVBaDX331Fd59911YWlpi1KhRsLa2RkpKCtasWYO4uDjExcUJYw0Ab7/9Nr7//ns4Oztj1qxZePr0KdavX4/ExESNn8/i4mLs3LkTYrEYixYtqrWtkZHyW8OmTZswb948SKVShISEwNzcHP/+978xf/58/Pbbb/j555+VFpPatgdqnm+VlZUYPXo0Tpw4AQ8PD4SEhCAvLw/z58+Hr6+vxv1X+PzzzxEbG4sxY8bAx8cHR44cwZYtW5CXl4cdO3YI7fLz8zFv3jwMGTIEI0eOhKWlJW7duoWDBw8iNjYWCQkJ6Nu3LwBg7NixKCgoUJmLVeXn52Po0KG4evUqhgwZgoCAABQWFgr/B3bv3o2xY8dq3I/w8HAkJSXhlVdeQXBwsNI8ZYzpX3JyMpYuXYrU1FTk5+dj2LBhSh8AN2e3b9+Gs7MzQkNDW2Reivj4ePj6+kImkyndIaj4+0Tx4TFrxogx1mIBICcnJ6Wy9PR0AkAA6P3331d73M2bN1XKHj16RB4eHiSRSKioqEjt+aKiopSOWb58OQGgyMhIoWzz5s0EgDZt2qTyGDk5OUq/b926lQDQ1q1blcorKirI1dWVANCRI0eU6pYuXUoAKCwsTKncycmJAJC/vz8VFxcr1VXtw8aNG4XyyspKGjlyJAEgCwsL2r9/v1BXWlpKPXr0IGNjY8rKyhLKr169SkZGRtSzZ0/Ky8tTepzIyEgCQJ9++qlQFhcXRwDI09OTHj9+LJRnZGSQlZUVAaDQ0FCVsaouPj6eAJC3t3edbau6efMmGRkZkY2NDd29e1coLykpoWHDhhEA2r59+3O3r2u+KZ7jwMBAKi8vF8ovXbpEJiYmBIBkMpnSMU5OTirzWiaTEQCSSCR048YNoby4uJi6du1KIpGIMjMzhfKnT59SRkaGSjxXrlyhtm3b0vDhw9XGWX0uKoSEhBAA+v7775XKs7KyqHPnzmRtbU1PnjxRe2xVoaGhBIAcHBzozp07dbZnrKlT/P/X9McQFBQUkLW1NUkkEpo9ezbJZLIaXxuaI8XruibvTVUVFRXRxo0bycfHh6ysrMjIyIgsLS1p8ODBFBkZSdnZ2Q0TsI4p3rc1eW9qaHW9N7GGwbeIM8bUsrOzw/Lly9XW/e1vf1Mpa9u2LaZNm4bCwkKkpKSo1Ds7O2Px4sVKZWFhYQCgtr1YLFYps7Ky0ij2M2fOIC0tDUFBQQgICFCqW7ZsGTp06ICYmBiUlpaqHPvJJ5+ofWzgWb+rXp0XiUR47bXXADy7tXrMmDFCnbGxMSZMmICysjJcv35dKP/6669RXl6OzZs3QyqVKp1/yZIlsLa2xk8//SSU/fDDDwCAFStWKCUd69SpE+bOnVvnWChkZWUBABwcHDQ+BgB27NiB8vJyLFy4EJ07dxbKTUxMEBUVBQBKVyi0ba9Q03xT9H/NmjVKt7R7eHhg6tSpWvUFAObOnQs3Nzfhd7FYjClTpoCIcP78eaHc1NQUnTp1Ujm+e/fu8PX1RUJCgsb71HNzc7Fr1y68/PLLwq3kCra2tli8eDFycnJw4sQJjfuxePFiODo6atyesaZKJpOp/ACARCKpsa6pUyTgjIiIwJYtW7By5UrexlGH1NRUdOvWDfPmzUN6ejpGjx6NxYsXIyQkBE+fPsXSpUvh4uJS47YrQ/Drr79yEs4Wgm8RZ4yp5enpqXSbclXZ2dmIiopCbGws7ty5o7J/VZF8rPr5WrVS/kxPsdgrKCgQyoKDgxEREYFZs2bh+PHjCAwMhLe3N7p27apx7Io9suq+E9vc3Bx9+vTB0aNH8d///hfu7u5CXZs2beDh4VHjedX1wd7eHgDU3hasqMvMzBTKkpKSAABHjhxRu6AyNjbGjRs3hN8Ve9SHDBmi0lZdma7VNpYDBgyAWCzGxYsXn7u9Qk3zLTU1FWZmZujVq5dK3ZAhQ/Ddd99p1pH/o+486uYhAFy8eBEff/wxTp8+jaysLJUFdW5urvAc1yYlJQUVFRV4+vSp2oSCaWlpAIAbN24gODhYo37069dPo3aMNXWcgJNxAk7W3PAVbMaYWjXt6czPz0ffvn2xYcMGdOjQAWFhYVi+fDlkMplwBbekpETlOIlEolKm2OtbNfGVs7Mzzp49i1GjRiE2NhZhYWFwc3PDiy++iN27d2sUu1wur7UPij96CgsLlcptbGxq/Q7w6om/qvahtrqqfxAoEqytWbMGq1atUvm5f/++0if0hYWFaNWqldqr99rsu1X0uepiXxN1jaWNjY3SOGrbXqGm9oWFhbCxsVFb9zz7jjWdh4mJiRgwYAD27t0LLy8vhIeHY8WKFZDJZPD09ASgfp6ro3jOz5w5o/Y5j4mJAQCtrszwnmvW0nACTk7AyQk4OQGnoeAr2IwxtWpaaH733Xe4e/cuPvzwQyxbtkypLioqCgcOHKj3Y/fo0QN79uxBWVkZzp8/j9jYWGzevBmTJ09Gx44dMXjw4FqPV7wBP3z4UG29orz6G3Vti2tdUTymXC5Hu3bt6mwvkUhQWVmJ3NxcWFtbK9XV1D91+vbtCxMTE5w7dw5yuVztBwK1xfvw4UM4OTmp1GdnZyudS9v2CjWNvUQiQXZ2tto6bfqvrTVr1qCkpASnT59WmW9JSUlq//iuiaK/CxcuxKeffqqT+BpjrjLWFHECTk7AqcAJODkBZ5Ol703gjDH9QS1JzmpKTvKPf/yDANClS5dU6hQJv6om06jrfABo2LBhdcb6ww8/EACKiIgQympK3pGQkEAAKCgoSOU8RUVFZGVlRWKxmEpKSoTy2pKP1NaHmpKZ1BTfO++8QwDo2LFjtfZXYfr06QSA9uzZo1L3wQcfaJVI5o033iAAtGLFilrblZWVUUVFBRERrV69mgDQ2rVrVdolJycTAPLz8xPKtG1f1/zw9fUlAHT+/HmVurCwMK2TnMXFxamcR93z5ObmRlKpVKVtUVERWVtbEwBKT08XyhXz89tvv1U55sGDByQSiWjQoEFq+6gNRZKzqo/NWHNT23sTOAGn2j5wAs5nOAEnJ+BsCvgWccaYVhRXJavfOhQTE4PDhw/X+/wpKSlqr1gqrlbWlICsqsGDB6NLly6IjY1V2eccGRmJ3NxcTJkypcY95g3p3XffhZGREcLDw3Hv3j2V+oKCAqXbvN544w0AwOrVq5Vu6cvMzMSmTZu0euw1a9bA2toaa9aswebNm9Xexnfp0iX4+PgIt3qHhITAyMgI69evV9pbX1ZWhoiICABQugVM2/Z1USQyW7ZsmdItfJcvX8b27ds1Po+2nJyc8Ndff+Hq1atCWUVFBRYtWoScnByV9oqEdRkZGSp1dnZ2mDRpEhITE/HJJ5+AiFTaJCcnq70FkzGmjBNwquIEnJyAkxNwNi18izhjTCtTp07F2rVrER4ejri4ODg5OeHSpUs4ceIExo8fj71799br/Dt27MAXX3wBHx8fuLi4oH379rh27RoOHz4MKysrvPnmm3Weo1WrVti2bRsCAgIwcuRITJw4EU5OTkhOTsbJkyfRpUsX4Q21sbm7u+OLL77AO++8Azc3N4wcORJdunSBXC7HrVu3cOrUKUybNg1fffUVgGfJwqZPn46tW7fCw8MD48aNQ0lJCXbt2oUBAwbg0KFDGj+2g4MDjh07hrFjx2Lu3LnYsGEDXn75Zdja2kIul+P3339HSkoK2rdvD2NjYwDPkrKsXbsWCxcuRI8ePTBp0iSYm5vj0KFDuHHjBsaMGYO///3vwmNo274uoaGhiImJwZEjR9CzZ08EBQUhPz8fP/30E/z9/bXqvzbCw8Nx7NgxeHt7Y9KkSWjTpg3i4+ORmZkJHx8fle+zHThwIMRiMTZu3Ai5XC7czq/4UOGLL77Af/7zHyxZsgTbt2/HwIEDIZFIcO/ePZw/fx5paWl48OABzMzMGqQ/jDUXnIBTFSfgVMYJODkBp77xApsxphUHBwecOnUKS5YswYkTJ1BeXo5evXrh2LFjuHfvXr0X2FOmTMHTp09x5swZpKSkoKSkBA4ODpg1axYWLVqk8afc3t7eSEpKwurVq3Hs2DEUFhaiY8eOmDNnDt5//32Nrzg0hBkzZsDLywvr169HQkICDh48CIlEAkdHR8yfP19IkKMQHR2Nrl27Ijo6Gp999hkcHBywYMECTJo0SesFppeXF65du4bo6Gjs27cPBw4cQEFBAdq2bYuXXnoJH3zwAWbOnKl0RWLBggVwcXHB+vXr8eOPP6K0tBRdu3bFunXrMGfOHJU9a9q2r02rVq1w4MABrFq1Cjt27MCmTZvQpUsXrF+/Hl27dm2wBXZwcDB+/vlnfPTRR/jxxx9hZmYGPz8/7Nu3D6tXr1ZpL5VK8fPPP2PlypX48ssvhT/sFQtsqVSKxMREfPbZZ9i1axd27NiByspK2NnZwdPTU+9zkjFDUVcCzrt372Lw4MEYPnw4LCws0Lp1a2FPtC4ScK5atQqxsbFC0k03Nzd88MEHmDhxYp2xG0oCTk0YQgLOqufUtr1CbQk4q14J1+SY2miTgNPPzw8A4O/vD1dXV7Rt2xYikQj79+9HamrqcyXgPHPmTI3tOAHnc9D3PeqMMcYYY4wp4Dnyg3z88ccEgD788EOVOsUeYl3lByktLaWzZ8/SihUryMLCgkQiEZ0+fVqor2nf66ZNm2rMUUFEFBgYqJLjpLHyg/Tq1YsAkFwuV/tY1SnaZ2dnq9Qp9lVrsge7qKiITExMSCwWU2FhoUaPTUQ0btw4AkDJyclq68VisVIeDW3b1zU/pFIpmZmZqa3btm1bg+UHUeytrzrfFAICAlRydNS2B/vgwYMEgBYuXKi2H9rg/CDKeA82Y4wxxhgzaDdv3gQAjB49WqXut99+0+ljGRsbY8CAAVi1ahU2b94MItLobpqePXsCgMoWE+BZNu1z585BLBYr7cVtLP379wfw/7eK10XxdYXqxlab8TYzM8Nrr72GJ0+eCJnYa1JeXi7kDqltLH///Xc8efJE6fZ4bdvXxdPTE8XFxfjjjz9U6nQ936q6efMmpFKpyrdb1BSLYn+4uq8t69u3L0QiEc6ePdswwbZgvMBmjDHGGGMGjRNw1g8n4OQEnMQJOHWG92AzxhhjjDGDxgk464cTcHICTk7AqTu8wGaMMcYYYwaNE3DWHyfg5AScnIBTN0Sk7n4AxhhjjDHGGGOMaYX3YDPGGGOMMcYYYzrAC2zGGGOMMcYYY0wHeIHNGGOMMcYYY4zpAC+wGWOMMcYYY4wxHeAFNmOMMcYYY4wxpgO8wGaMMcYYY4wxxnSAF9iMMcYYY4wxxpgO8AKbMcYYY4wxxhjTAV5gM8YYY4wxxhhjOsALbMYYY4wxxhhjTAd4gc0YY4wxxhhjjOkAL7AZY4wxxhhjjDEd+B9RAKZDHP8pkwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] }, "metadata": {}, "output_type": "display_data" @@ -233,17 +250,17 @@ "for i, oned in enumerate(grids):\n", " # Becke R-transform (goes from 0 to \\infty) to transform 1D-grid\n", " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " # plot radial grid points for each transformed 1D-grid \n", + " # plot radial grid points for each transformed 1D-grid\n", " ax1.scatter(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", - " # plot log plot\n", - " ax2.semilogx(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\")\n", + " # plot log plot of radial grid points\n", + " ax2.semilogx(rgrid.points, np.repeat(i + 1, rgrid.size), marker=\"o\", linestyle=\"\")\n", " names.append(oned.name)\n", "\n", "# set the ticks, labels, and title\n", "plt.suptitle(\"Plot & Log-Plot of Becke Radial Transformation of 1D-Grids\", fontsize=17)\n", - "ax1.set_yticks(range(1, len(grids) + 1), names, fontsize=11)\n", + "ax1.set_yticks(np.arange(1, len(grids) + 1), names, fontsize=11)\n", "ax1.set_xlim(0, 2500)\n", - "ax2.set_xlim(1e-4, 2500)\n", + "ax2.set_xlim(1.0e-4, 2500)\n", "ax1.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", "ax2.set_xlabel(\"Transformed Coordinate r\", fontsize=14)\n", "ax1.set_ylabel(\"Quadrature Rule\", fontsize=17)\n", @@ -309,7 +326,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2024-01-03T22:36:22.028092961Z", @@ -319,8 +336,10 @@ "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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\n" 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", + "text/plain": [ + "
" + ] }, "metadata": {}, "output_type": "display_data" @@ -336,7 +355,7 @@ " # make 1-dimensional grid for the given number of points\n", " oned = grid_class(npoint)\n", " rgrid = BeckeRTransform(0.0, R=1.5).transform_1d_grid(oned)\n", - " # Calculate x^2 e^-x\n", + " # calculate x^2 e^-x\n", " x = rgrid.points\n", " func_vals = x**2.0 * np.exp(-x)\n", " # compute relative percent error of integration\n",